id	sid	tid	token	lemma	pos
ejpam-6392	1	1	european	european	PROPN
ejpam-6392	1	2	journal	journal	PROPN
ejpam-6392	1	3	of	of	ADP
ejpam-6392	1	4	pure	pure	ADJ
ejpam-6392	1	5	and	and	CCONJ
ejpam-6392	1	6	applied	applied	ADJ
ejpam-6392	1	7	mathematics	mathematic	NOUN
ejpam-6392	1	8	2025	2025	NUM
ejpam-6392	1	9	,	,	PUNCT
ejpam-6392	1	10	vol	vol	NOUN
ejpam-6392	1	11	.	.	PROPN
ejpam-6392	1	12	18	18	NUM
ejpam-6392	1	13	,	,	PUNCT
ejpam-6392	1	14	issue	issue	NOUN
ejpam-6392	1	15	4	4	NUM
ejpam-6392	1	16	,	,	PUNCT
ejpam-6392	1	17	article	article	NOUN
ejpam-6392	1	18	number	number	NOUN
ejpam-6392	1	19	6392	6392	NUM
ejpam-6392	1	20	issn	issn	VERB
ejpam-6392	1	21	1307	1307	NUM
ejpam-6392	1	22	-	-	SYM
ejpam-6392	1	23	5543	5543	NUM
ejpam-6392	1	24	–	–	PUNCT
ejpam-6392	1	25	ejpam.com	ejpam.com	X
ejpam-6392	1	26	published	publish	VERB
ejpam-6392	1	27	by	by	ADP
ejpam-6392	1	28	new	new	PROPN
ejpam-6392	1	29	york	york	PROPN
ejpam-6392	1	30	business	business	PROPN
ejpam-6392	1	31	global	global	PROPN
ejpam-6392	1	32	neutrosophic	neutrosophic	PROPN
ejpam-6392	1	33	bi	bi	NOUN
ejpam-6392	1	34	-	-	NOUN
ejpam-6392	1	35	ideals	ideal	NOUN
ejpam-6392	1	36	in	in	ADP
ejpam-6392	1	37	ink	ink	NOUN
ejpam-6392	1	38	-	-	PUNCT
ejpam-6392	1	39	algebras	algebras	NOUN
ejpam-6392	1	40	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6392	1	41	remala1	remala1	PROPN
ejpam-6392	1	42	,	,	PUNCT
ejpam-6392	1	43	eswarlal	eswarlal	PROPN
ejpam-6392	1	44	tamma1,∗	tamma1,∗	NOUN
ejpam-6392	1	45	,	,	PUNCT
ejpam-6392	1	46	yella	yella	ADJ
ejpam-6392	1	47	bhargavi1	bhargavi1	NOUN
ejpam-6392	1	48	1	1	NUM
ejpam-6392	1	49	department	department	NOUN
ejpam-6392	1	50	of	of	ADP
ejpam-6392	1	51	engineering	engineering	NOUN
ejpam-6392	1	52	mathematics	mathematic	NOUN
ejpam-6392	1	53	,	,	PUNCT
ejpam-6392	1	54	college	college	NOUN
ejpam-6392	1	55	of	of	ADP
ejpam-6392	1	56	engineering	engineering	PROPN
ejpam-6392	1	57	,	,	PUNCT
ejpam-6392	1	58	koneru	koneru	PROPN
ejpam-6392	1	59	lakshmaiah	lakshmaiah	PROPN
ejpam-6392	1	60	education	education	PROPN
ejpam-6392	1	61	foundation	foundation	PROPN
ejpam-6392	1	62	,	,	PUNCT
ejpam-6392	1	63	vaddeswaram	vaddeswaram	PROPN
ejpam-6392	1	64	,	,	PUNCT
ejpam-6392	1	65	andhra	andhra	PROPN
ejpam-6392	1	66	pradesh	pradesh	PROPN
ejpam-6392	1	67	,	,	PUNCT
ejpam-6392	1	68	india	india	PROPN
ejpam-6392	1	69	abstract	abstract	PROPN
ejpam-6392	1	70	.	.	PUNCT
ejpam-6392	2	1	the	the	DET
ejpam-6392	2	2	main	main	ADJ
ejpam-6392	2	3	aim	aim	NOUN
ejpam-6392	2	4	of	of	ADP
ejpam-6392	2	5	this	this	DET
ejpam-6392	2	6	research	research	NOUN
ejpam-6392	2	7	article	article	NOUN
ejpam-6392	2	8	is	be	AUX
ejpam-6392	2	9	to	to	PART
ejpam-6392	2	10	identify	identify	VERB
ejpam-6392	2	11	the	the	DET
ejpam-6392	2	12	bi	bi	NOUN
ejpam-6392	2	13	-	-	NOUN
ejpam-6392	2	14	ideals	ideal	NOUN
ejpam-6392	2	15	in	in	ADP
ejpam-6392	2	16	ink	ink	NOUN
ejpam-6392	2	17	-	-	PUNCT
ejpam-6392	2	18	algebra	algebra	NOUN
ejpam-6392	2	19	.	.	PUNCT
ejpam-6392	3	1	this	this	DET
ejpam-6392	3	2	paper	paper	NOUN
ejpam-6392	3	3	introduces	introduce	VERB
ejpam-6392	3	4	the	the	DET
ejpam-6392	3	5	notion	notion	NOUN
ejpam-6392	3	6	of	of	ADP
ejpam-6392	3	7	neutrosophic	neutrosophic	ADJ
ejpam-6392	3	8	bi	bi	NOUN
ejpam-6392	3	9	-	-	NOUN
ejpam-6392	3	10	ideals	ideal	NOUN
ejpam-6392	3	11	in	in	ADP
ejpam-6392	3	12	ink	ink	NOUN
ejpam-6392	3	13	-	-	PUNCT
ejpam-6392	3	14	algebra	algebra	NOUN
ejpam-6392	3	15	and	and	CCONJ
ejpam-6392	3	16	discusses	discuss	VERB
ejpam-6392	3	17	basic	basic	ADJ
ejpam-6392	3	18	operations	operation	NOUN
ejpam-6392	3	19	such	such	ADJ
ejpam-6392	3	20	as	as	ADP
ejpam-6392	3	21	order	order	NOUN
ejpam-6392	3	22	-	-	PUNCT
ejpam-6392	3	23	reversing	reverse	VERB
ejpam-6392	3	24	and	and	CCONJ
ejpam-6392	3	25	order	order	NOUN
ejpam-6392	3	26	-	-	PUNCT
ejpam-6392	3	27	preserving	preserve	VERB
ejpam-6392	3	28	properties	property	NOUN
ejpam-6392	3	29	.	.	PUNCT
ejpam-6392	4	1	it	it	PRON
ejpam-6392	4	2	is	be	AUX
ejpam-6392	4	3	shown	show	VERB
ejpam-6392	4	4	that	that	SCONJ
ejpam-6392	4	5	the	the	DET
ejpam-6392	4	6	intersection	intersection	NOUN
ejpam-6392	4	7	and	and	CCONJ
ejpam-6392	4	8	union	union	NOUN
ejpam-6392	4	9	(	(	PUNCT
ejpam-6392	4	10	with	with	ADP
ejpam-6392	4	11	containment	containment	NOUN
ejpam-6392	4	12	)	)	PUNCT
ejpam-6392	4	13	of	of	ADP
ejpam-6392	4	14	two	two	NUM
ejpam-6392	4	15	neutrosophic	neutrosophic	ADJ
ejpam-6392	4	16	bi	bi	NOUN
ejpam-6392	4	17	-	-	NOUN
ejpam-6392	4	18	ideals	ideal	NOUN
ejpam-6392	4	19	result	result	VERB
ejpam-6392	4	20	in	in	ADP
ejpam-6392	4	21	another	another	DET
ejpam-6392	4	22	neutrosophic	neutrosophic	ADJ
ejpam-6392	4	23	bi	bi	NOUN
ejpam-6392	4	24	-	-	NOUN
ejpam-6392	4	25	ideal	ideal	ADJ
ejpam-6392	4	26	.	.	PUNCT
ejpam-6392	5	1	further	far	ADV
ejpam-6392	5	2	,	,	PUNCT
ejpam-6392	5	3	the	the	DET
ejpam-6392	5	4	paper	paper	NOUN
ejpam-6392	5	5	explores	explore	VERB
ejpam-6392	5	6	homomorphisms	homomorphisms	PROPN
ejpam-6392	5	7	and	and	CCONJ
ejpam-6392	5	8	epimorphisms	epimorphism	NOUN
ejpam-6392	5	9	between	between	ADP
ejpam-6392	5	10	neutrosophic	neutrosophic	ADJ
ejpam-6392	5	11	bi	bi	NOUN
ejpam-6392	5	12	-	-	NOUN
ejpam-6392	5	13	ideals	ideal	NOUN
ejpam-6392	5	14	in	in	ADP
ejpam-6392	5	15	inkalgebras	inkalgebra	NOUN
ejpam-6392	5	16	.	.	PUNCT
ejpam-6392	6	1	it	it	PRON
ejpam-6392	6	2	is	be	AUX
ejpam-6392	6	3	demonstrated	demonstrate	VERB
ejpam-6392	6	4	that	that	SCONJ
ejpam-6392	6	5	the	the	DET
ejpam-6392	6	6	direct	direct	ADJ
ejpam-6392	6	7	product	product	NOUN
ejpam-6392	6	8	of	of	ADP
ejpam-6392	6	9	two	two	NUM
ejpam-6392	6	10	neutrosophic	neutrosophic	ADJ
ejpam-6392	6	11	sets	set	NOUN
ejpam-6392	6	12	in	in	ADP
ejpam-6392	6	13	an	an	DET
ejpam-6392	6	14	ink	ink	NOUN
ejpam-6392	6	15	-	-	PUNCT
ejpam-6392	6	16	subalgebra	subalgebra	NOUN
ejpam-6392	6	17	remains	remain	VERB
ejpam-6392	6	18	within	within	ADP
ejpam-6392	6	19	the	the	DET
ejpam-6392	6	20	same	same	ADJ
ejpam-6392	6	21	structure	structure	NOUN
ejpam-6392	6	22	.	.	PUNCT
ejpam-6392	7	1	observations	observation	NOUN
ejpam-6392	7	2	regarding	regard	VERB
ejpam-6392	7	3	the	the	DET
ejpam-6392	7	4	direct	direct	ADJ
ejpam-6392	7	5	product	product	NOUN
ejpam-6392	7	6	of	of	ADP
ejpam-6392	7	7	neutrosophic	neutrosophic	ADJ
ejpam-6392	7	8	biideals	biideal	NOUN
ejpam-6392	7	9	in	in	ADP
ejpam-6392	7	10	ink	ink	NOUN
ejpam-6392	7	11	-	-	PUNCT
ejpam-6392	7	12	algebras	algebra	NOUN
ejpam-6392	7	13	are	be	AUX
ejpam-6392	7	14	provided	provide	VERB
ejpam-6392	7	15	.	.	PUNCT
ejpam-6392	8	1	finally	finally	ADV
ejpam-6392	8	2	,	,	PUNCT
ejpam-6392	8	3	an	an	DET
ejpam-6392	8	4	application	application	NOUN
ejpam-6392	8	5	related	relate	VERB
ejpam-6392	8	6	to	to	ADP
ejpam-6392	8	7	neutrosophic	neutrosophic	ADJ
ejpam-6392	8	8	bi	bi	NOUN
ejpam-6392	8	9	-	-	NOUN
ejpam-6392	8	10	ideals	ideal	NOUN
ejpam-6392	8	11	is	be	AUX
ejpam-6392	8	12	discussed	discuss	VERB
ejpam-6392	8	13	.	.	PUNCT
ejpam-6392	9	1	2020	2020	NUM
ejpam-6392	9	2	mathematics	mathematic	NOUN
ejpam-6392	9	3	subject	subject	NOUN
ejpam-6392	9	4	classifications	classification	NOUN
ejpam-6392	9	5	:	:	PUNCT
ejpam-6392	9	6	03e72	03e72	NUM
ejpam-6392	9	7	,	,	PUNCT
ejpam-6392	9	8	08a72	08a72	NUM
ejpam-6392	9	9	,	,	PUNCT
ejpam-6392	9	10	06f25	06f25	X
ejpam-6392	9	11	key	key	ADJ
ejpam-6392	9	12	words	word	NOUN
ejpam-6392	9	13	and	and	CCONJ
ejpam-6392	9	14	phrases	phrase	NOUN
ejpam-6392	9	15	:	:	PUNCT
ejpam-6392	9	16	ink	ink	NOUN
ejpam-6392	9	17	-	-	PUNCT
ejpam-6392	9	18	algebra	algebra	NOUN
ejpam-6392	9	19	,	,	PUNCT
ejpam-6392	9	20	neutrosophic	neutrosophic	ADJ
ejpam-6392	9	21	set	set	NOUN
ejpam-6392	9	22	,	,	PUNCT
ejpam-6392	9	23	neutrosophic	neutrosophic	ADJ
ejpam-6392	9	24	ink	ink	NOUN
ejpam-6392	9	25	-	-	PUNCT
ejpam-6392	9	26	algebra	algebra	NOUN
ejpam-6392	9	27	,	,	PUNCT
ejpam-6392	9	28	neutrosophic	neutrosophic	ADJ
ejpam-6392	9	29	bi	bi	NOUN
ejpam-6392	9	30	-	-	NOUN
ejpam-6392	9	31	ideal	ideal	ADJ
ejpam-6392	9	32	,	,	PUNCT
ejpam-6392	9	33	homomorphism	homomorphism	NOUN
ejpam-6392	9	34	of	of	ADP
ejpam-6392	9	35	neutrosophic	neutrosophic	ADJ
ejpam-6392	9	36	bi	bi	NOUN
ejpam-6392	9	37	-	-	NOUN
ejpam-6392	9	38	ideal	ideal	ADJ
ejpam-6392	9	39	,	,	PUNCT
ejpam-6392	9	40	direct	direct	ADJ
ejpam-6392	9	41	product	product	NOUN
ejpam-6392	9	42	of	of	ADP
ejpam-6392	9	43	neutrosophic	neutrosophic	ADJ
ejpam-6392	9	44	bi	bi	NOUN
ejpam-6392	9	45	-	-	ADJ
ejpam-6392	9	46	ideal	ideal	ADJ
ejpam-6392	9	47	1	1	NUM
ejpam-6392	9	48	.	.	PUNCT
ejpam-6392	9	49	introduction	introduction	NOUN
ejpam-6392	9	50	iseki	iseki	PROPN
ejpam-6392	9	51	and	and	CCONJ
ejpam-6392	9	52	tanaka	tanaka	PROPN
ejpam-6392	10	1	[	[	X
ejpam-6392	10	2	1	1	NUM
ejpam-6392	10	3	,	,	PUNCT
ejpam-6392	10	4	2	2	NUM
ejpam-6392	10	5	]	]	PUNCT
ejpam-6392	10	6	have	have	AUX
ejpam-6392	10	7	worked	work	VERB
ejpam-6392	10	8	on	on	ADP
ejpam-6392	10	9	the	the	DET
ejpam-6392	10	10	concept	concept	NOUN
ejpam-6392	10	11	of	of	ADP
ejpam-6392	10	12	bck	bck	PROPN
ejpam-6392	10	13	and	and	CCONJ
ejpam-6392	10	14	bci	bci	PROPN
ejpam-6392	10	15	algebras	algebra	NOUN
ejpam-6392	10	16	to	to	PART
ejpam-6392	10	17	pick	pick	VERB
ejpam-6392	10	18	-	-	PUNCT
ejpam-6392	10	19	up	up	ADP
ejpam-6392	10	20	their	their	PRON
ejpam-6392	10	21	characteristics	characteristic	NOUN
ejpam-6392	10	22	and	and	CCONJ
ejpam-6392	10	23	applications	application	NOUN
ejpam-6392	10	24	.	.	PUNCT
ejpam-6392	11	1	there	there	PRON
ejpam-6392	11	2	exists	exist	VERB
ejpam-6392	11	3	an	an	DET
ejpam-6392	11	4	immense	immense	ADJ
ejpam-6392	11	5	area	area	NOUN
ejpam-6392	11	6	of	of	ADP
ejpam-6392	11	7	empirical	empirical	ADJ
ejpam-6392	11	8	applications	application	NOUN
ejpam-6392	11	9	in	in	ADP
ejpam-6392	11	10	fuzzy	fuzzy	ADJ
ejpam-6392	11	11	sets	set	NOUN
ejpam-6392	11	12	,	,	PUNCT
ejpam-6392	11	13	intuitionistic	intuitionistic	ADJ
ejpam-6392	11	14	fuzzy	fuzzy	ADJ
ejpam-6392	11	15	sets	set	NOUN
ejpam-6392	11	16	and	and	CCONJ
ejpam-6392	11	17	neutrosophic	neutrosophic	ADJ
ejpam-6392	11	18	sets	set	NOUN
ejpam-6392	11	19	.	.	PUNCT
ejpam-6392	12	1	the	the	DET
ejpam-6392	12	2	literature	literature	NOUN
ejpam-6392	12	3	works	work	VERB
ejpam-6392	12	4	of	of	ADP
ejpam-6392	12	5	fuzzy	fuzzy	ADJ
ejpam-6392	12	6	sub	sub	NOUN
ejpam-6392	12	7	algebras	algebra	NOUN
ejpam-6392	12	8	and	and	CCONJ
ejpam-6392	12	9	fuzzy	fuzzy	ADJ
ejpam-6392	12	10	k	k	NOUN
ejpam-6392	12	11	-	-	NOUN
ejpam-6392	12	12	ideals	ideal	NOUN
ejpam-6392	12	13	in	in	ADP
ejpam-6392	12	14	ink	ink	NOUN
ejpam-6392	12	15	-	-	PUNCT
ejpam-6392	12	16	algebras	algebra	NOUN
ejpam-6392	12	17	,	,	PUNCT
ejpam-6392	12	18	fuzzy	fuzzy	ADJ
ejpam-6392	12	19	p	p	NOUN
ejpam-6392	12	20	-	-	PUNCT
ejpam-6392	12	21	ideal	ideal	NOUN
ejpam-6392	12	22	in	in	ADP
ejpam-6392	12	23	ink	ink	NOUN
ejpam-6392	12	24	-	-	PUNCT
ejpam-6392	12	25	algebra	algebra	NOUN
ejpam-6392	12	26	,	,	PUNCT
ejpam-6392	12	27	fuzzy	fuzzy	ADJ
ejpam-6392	12	28	translation	translation	NOUN
ejpam-6392	12	29	of	of	ADP
ejpam-6392	12	30	ink	ink	NOUN
ejpam-6392	12	31	-	-	PUNCT
ejpam-6392	12	32	ideal	ideal	NOUN
ejpam-6392	12	33	of	of	ADP
ejpam-6392	12	34	ink	ink	NOUN
ejpam-6392	12	35	-	-	PUNCT
ejpam-6392	12	36	algebras	algebras	PROPN
ejpam-6392	12	37	also	also	ADV
ejpam-6392	12	38	they	they	PRON
ejpam-6392	12	39	proposed	propose	VERB
ejpam-6392	12	40	on	on	ADP
ejpam-6392	12	41	intuitionistic	intuitionistic	ADJ
ejpam-6392	12	42	fuzzy	fuzzy	ADJ
ejpam-6392	12	43	ink	ink	NOUN
ejpam-6392	12	44	-	-	PUNCT
ejpam-6392	12	45	ideals	ideal	NOUN
ejpam-6392	12	46	of	of	ADP
ejpam-6392	12	47	ink	ink	NOUN
ejpam-6392	12	48	-	-	PUNCT
ejpam-6392	12	49	algebras	algebra	NOUN
ejpam-6392	12	50	,	,	PUNCT
ejpam-6392	12	51	direct	direct	ADJ
ejpam-6392	12	52	product	product	NOUN
ejpam-6392	12	53	of	of	ADP
ejpam-6392	12	54	intuitionistic	intuitionistic	ADJ
ejpam-6392	12	55	fuzzy	fuzzy	ADJ
ejpam-6392	12	56	k	k	NOUN
ejpam-6392	12	57	-	-	NOUN
ejpam-6392	12	58	ideals	ideal	NOUN
ejpam-6392	12	59	of	of	ADP
ejpam-6392	12	60	ink	ink	NOUN
ejpam-6392	12	61	-	-	PUNCT
ejpam-6392	12	62	algebras	algebras	PROPN
ejpam-6392	12	63	,	,	PUNCT
ejpam-6392	12	64	intuitionistic	intuitionistic	ADJ
ejpam-6392	12	65	fuzzy	fuzzy	ADJ
ejpam-6392	12	66	translation	translation	NOUN
ejpam-6392	12	67	on	on	ADP
ejpam-6392	12	68	ink	ink	NOUN
ejpam-6392	12	69	-	-	PUNCT
ejpam-6392	12	70	algebra	algebra	NOUN
ejpam-6392	12	71	and	and	CCONJ
ejpam-6392	12	72	also	also	ADV
ejpam-6392	12	73	they	they	PRON
ejpam-6392	12	74	have	have	AUX
ejpam-6392	12	75	discussed	discuss	VERB
ejpam-6392	12	76	neutosophic	neutosophic	ADJ
ejpam-6392	12	77	set	set	NOUN
ejpam-6392	12	78	in	in	ADP
ejpam-6392	12	79	ink	ink	NOUN
ejpam-6392	12	80	-	-	PUNCT
ejpam-6392	12	81	algebra	algebra	NOUN
ejpam-6392	12	82	,	,	PUNCT
ejpam-6392	12	83	neutrosophic	neutrosophic	ADJ
ejpam-6392	12	84	h	h	NOUN
ejpam-6392	12	85	-	-	PUNCT
ejpam-6392	12	86	ideal	ideal	NOUN
ejpam-6392	12	87	in	in	ADP
ejpam-6392	12	88	ink	ink	NOUN
ejpam-6392	12	89	-	-	PUNCT
ejpam-6392	12	90	algebra	algebra	NOUN
ejpam-6392	12	91	have	have	AUX
ejpam-6392	12	92	discussed	discuss	VERB
ejpam-6392	12	93	by	by	ADP
ejpam-6392	12	94	kaviyarasu	kaviyarasu	PROPN
ejpam-6392	12	95	and	and	CCONJ
ejpam-6392	12	96	indhira	indhira	PROPN
ejpam-6392	12	97	,	,	PUNCT
ejpam-6392	13	1	[	[	X
ejpam-6392	13	2	3–7	3–7	NOUN
ejpam-6392	13	3	]	]	PUNCT
ejpam-6392	13	4	and	and	CCONJ
ejpam-6392	13	5	homomorphism	homomorphism	NOUN
ejpam-6392	13	6	and	and	CCONJ
ejpam-6392	13	7	anti	anti	NOUN
ejpam-6392	13	8	-	-	NOUN
ejpam-6392	13	9	homomorphism	homomorphism	NOUN
ejpam-6392	13	10	of	of	ADP
ejpam-6392	13	11	neutrosophic	neutrosophic	ADJ
ejpam-6392	13	12	ink	ink	NOUN
ejpam-6392	13	13	-	-	PUNCT
ejpam-6392	13	14	algebras	algebra	NOUN
ejpam-6392	13	15	have	have	AUX
ejpam-6392	13	16	done	do	VERB
ejpam-6392	13	17	by	by	ADP
ejpam-6392	13	18	mounikalakshmi	mounikalakshmi	NOUN
ejpam-6392	13	19	,	,	PUNCT
ejpam-6392	13	20	eswarlal	eswarlal	PROPN
ejpam-6392	13	21	,	,	PUNCT
ejpam-6392	13	22	venkata	venkata	PROPN
ejpam-6392	13	23	kalyani	kalyani	PROPN
ejpam-6392	13	24	and	and	CCONJ
ejpam-6392	13	25	aiyred	aiyre	VERB
ejpam-6392	13	26	iampan	iampan	NOUN
ejpam-6392	14	1	[	[	X
ejpam-6392	14	2	8	8	NUM
ejpam-6392	14	3	]	]	PUNCT
ejpam-6392	14	4	.	.	PUNCT
ejpam-6392	15	1	recently	recently	ADV
ejpam-6392	15	2	,	,	PUNCT
ejpam-6392	15	3	kaviyarasu	kaviyarasu	NOUN
ejpam-6392	15	4	and	and	CCONJ
ejpam-6392	15	5	rajeshwari	rajeshwari	NOUN
ejpam-6392	15	6	[	[	X
ejpam-6392	15	7	9	9	NUM
ejpam-6392	15	8	]	]	PUNCT
ejpam-6392	15	9	discussed	discuss	VERB
ejpam-6392	15	10	translation	translation	NOUN
ejpam-6392	15	11	of	of	ADP
ejpam-6392	15	12	neutrosophic	neutrosophic	ADJ
ejpam-6392	15	13	ink	ink	NOUN
ejpam-6392	15	14	-	-	PUNCT
ejpam-6392	15	15	algebras	algebra	NOUN
ejpam-6392	15	16	and	and	CCONJ
ejpam-6392	15	17	mounikalakshmi	mounikalakshmi	NOUN
ejpam-6392	15	18	,	,	PUNCT
ejpam-6392	15	19	eswarlal	eswarlal	NOUN
ejpam-6392	16	1	[	[	X
ejpam-6392	16	2	10	10	NUM
ejpam-6392	16	3	,	,	PUNCT
ejpam-6392	16	4	11	11	NUM
ejpam-6392	16	5	]	]	PUNCT
ejpam-6392	16	6	worked	work	VERB
ejpam-6392	16	7	on	on	ADP
ejpam-6392	16	8	bipolar	bipolar	ADJ
ejpam-6392	16	9	fuzzy	fuzzy	ADJ
ejpam-6392	16	10	ink	ink	NOUN
ejpam-6392	16	11	subalgebras	subalgebra	NOUN
ejpam-6392	16	12	of	of	ADP
ejpam-6392	16	13	ink	ink	NOUN
ejpam-6392	16	14	∗corresponding	∗corresponde	VERB
ejpam-6392	16	15	author	author	NOUN
ejpam-6392	16	16	.	.	PUNCT
ejpam-6392	17	1	doi	doi	NOUN
ejpam-6392	17	2	:	:	PUNCT
ejpam-6392	17	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6392	https://doi.org/10.29020/nybg.ejpam.v18i4.6392	NOUN
ejpam-6392	17	4	email	email	NOUN
ejpam-6392	17	5	addresses	address	NOUN
ejpam-6392	17	6	:	:	PUNCT
ejpam-6392	17	7	mouninaidu0521@gmail.com	mouninaidu0521@gmail.com	X
ejpam-6392	18	1	(	(	PUNCT
ejpam-6392	18	2	m.	m.	NOUN
ejpam-6392	18	3	remala	remala	NOUN
ejpam-6392	18	4	)	)	PUNCT
ejpam-6392	18	5	,	,	PUNCT
ejpam-6392	18	6	eswarlal@kluniversity.in	eswarlal@kluniversity.in	PROPN
ejpam-6392	18	7	(	(	PUNCT
ejpam-6392	18	8	e.	e.	PROPN
ejpam-6392	18	9	tamma	tamma	PROPN
ejpam-6392	18	10	)	)	PUNCT
ejpam-6392	18	11	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6392	19	1	1	1	NUM
ejpam-6392	19	2	copyright	copyright	NOUN
ejpam-6392	19	3	:	:	PUNCT
ejpam-6392	19	4	©	©	PROPN
ejpam-6392	19	5	2025	2025	NUM
ejpam-6392	19	6	the	the	DET
ejpam-6392	19	7	author(s	author(s	NOUN
ejpam-6392	19	8	)	)	PUNCT
ejpam-6392	19	9	.	.	PUNCT
ejpam-6392	20	1	(	(	PUNCT
ejpam-6392	20	2	cc	cc	NOUN
ejpam-6392	20	3	by	by	ADP
ejpam-6392	20	4	-	-	PUNCT
ejpam-6392	20	5	nc	nc	PROPN
ejpam-6392	20	6	4.0	4.0	NUM
ejpam-6392	20	7	)	)	PUNCT
ejpam-6392	20	8	m.	m.	NOUN
ejpam-6392	20	9	remala	remala	NOUN
ejpam-6392	20	10	,	,	PUNCT
ejpam-6392	20	11	e.	e.	PROPN
ejpam-6392	20	12	tamma	tamma	PROPN
ejpam-6392	20	13	,	,	PUNCT
ejpam-6392	20	14	y.	y.	PROPN
ejpam-6392	20	15	bhargavi	bhargavi	PROPN
ejpam-6392	20	16	/	/	SYM
ejpam-6392	20	17	eur	eur	PROPN
ejpam-6392	20	18	.	.	PUNCT
ejpam-6392	21	1	j.	j.	PROPN
ejpam-6392	21	2	pure	pure	PROPN
ejpam-6392	21	3	appl	appl	PROPN
ejpam-6392	21	4	.	.	PROPN
ejpam-6392	21	5	math	math	PROPN
ejpam-6392	21	6	,	,	PUNCT
ejpam-6392	21	7	18	18	NUM
ejpam-6392	21	8	(	(	PUNCT
ejpam-6392	21	9	4	4	NUM
ejpam-6392	21	10	)	)	PUNCT
ejpam-6392	21	11	(	(	PUNCT
ejpam-6392	21	12	2025	2025	NUM
ejpam-6392	21	13	)	)	PUNCT
ejpam-6392	21	14	,	,	PUNCT
ejpam-6392	21	15	6392	6392	NUM
ejpam-6392	21	16	2	2	NUM
ejpam-6392	21	17	of	of	ADP
ejpam-6392	21	18	20	20	NUM
ejpam-6392	21	19	algebras	algebra	NOUN
ejpam-6392	21	20	and	and	CCONJ
ejpam-6392	21	21	implicative	implicative	ADJ
ejpam-6392	21	22	ideals	ideal	NOUN
ejpam-6392	21	23	and	and	CCONJ
ejpam-6392	21	24	positive	positive	ADJ
ejpam-6392	21	25	implicative	implicative	ADJ
ejpam-6392	21	26	ink	ink	NOUN
ejpam-6392	21	27	-	-	PUNCT
ejpam-6392	21	28	ideals	ideal	NOUN
ejpam-6392	21	29	in	in	ADP
ejpam-6392	21	30	neutrosophic	neutrosophic	ADJ
ejpam-6392	21	31	inkalgebra	inkalgebra	NOUN
ejpam-6392	21	32	.	.	PUNCT
ejpam-6392	22	1	moreover	moreover	ADV
ejpam-6392	22	2	,	,	PUNCT
ejpam-6392	22	3	the	the	DET
ejpam-6392	22	4	work	work	NOUN
ejpam-6392	22	5	of	of	ADP
ejpam-6392	22	6	ink	ink	NOUN
ejpam-6392	22	7	-	-	PUNCT
ejpam-6392	22	8	algebra	algebra	NOUN
ejpam-6392	22	9	has	have	AUX
ejpam-6392	22	10	been	be	AUX
ejpam-6392	22	11	explored	explore	VERB
ejpam-6392	22	12	in	in	ADP
ejpam-6392	22	13	different	different	ADJ
ejpam-6392	22	14	aspects	aspect	NOUN
ejpam-6392	22	15	of	of	ADP
ejpam-6392	22	16	fuzzy	fuzzy	ADJ
ejpam-6392	22	17	sets	set	NOUN
ejpam-6392	22	18	,	,	PUNCT
ejpam-6392	22	19	bipolar	bipolar	ADJ
ejpam-6392	22	20	fuzzy	fuzzy	ADJ
ejpam-6392	22	21	sets	set	NOUN
ejpam-6392	22	22	,	,	PUNCT
ejpam-6392	22	23	intuitionistic	intuitionistic	ADJ
ejpam-6392	22	24	fuzzy	fuzzy	ADJ
ejpam-6392	22	25	sets	set	NOUN
ejpam-6392	22	26	and	and	CCONJ
ejpam-6392	22	27	also	also	ADV
ejpam-6392	22	28	in	in	ADP
ejpam-6392	22	29	neutrosophic	neutrosophic	ADJ
ejpam-6392	22	30	sets	set	NOUN
ejpam-6392	22	31	.	.	PUNCT
ejpam-6392	23	1	zadeh	zadeh	PROPN
ejpam-6392	23	2	,	,	PUNCT
ejpam-6392	23	3	traversed	traverse	VERB
ejpam-6392	23	4	the	the	DET
ejpam-6392	23	5	notion	notion	NOUN
ejpam-6392	23	6	of	of	ADP
ejpam-6392	23	7	fuzzy	fuzzy	ADJ
ejpam-6392	23	8	sets	set	NOUN
ejpam-6392	23	9	in	in	ADP
ejpam-6392	23	10	1965	1965	NUM
ejpam-6392	23	11	,	,	PUNCT
ejpam-6392	23	12	which	which	PRON
ejpam-6392	23	13	is	be	AUX
ejpam-6392	23	14	an	an	DET
ejpam-6392	23	15	extension	extension	NOUN
ejpam-6392	23	16	of	of	ADP
ejpam-6392	23	17	classical	classical	ADJ
ejpam-6392	23	18	set	set	NOUN
ejpam-6392	23	19	theory	theory	NOUN
ejpam-6392	23	20	that	that	SCONJ
ejpam-6392	23	21	deals	deal	VERB
ejpam-6392	23	22	with	with	ADP
ejpam-6392	23	23	vagueness	vagueness	NOUN
ejpam-6392	23	24	and	and	CCONJ
ejpam-6392	23	25	uncertainty	uncertainty	NOUN
ejpam-6392	23	26	in	in	ADP
ejpam-6392	23	27	the	the	DET
ejpam-6392	23	28	given	give	VERB
ejpam-6392	23	29	data	datum	NOUN
ejpam-6392	23	30	.	.	PUNCT
ejpam-6392	24	1	classical	classical	ADJ
ejpam-6392	24	2	set	set	NOUN
ejpam-6392	24	3	theory	theory	NOUN
ejpam-6392	24	4	asserts	assert	VERB
ejpam-6392	24	5	that	that	SCONJ
ejpam-6392	24	6	an	an	DET
ejpam-6392	24	7	element	element	NOUN
ejpam-6392	24	8	is	be	AUX
ejpam-6392	24	9	either	either	CCONJ
ejpam-6392	24	10	a	a	DET
ejpam-6392	24	11	member	member	NOUN
ejpam-6392	24	12	of	of	ADP
ejpam-6392	24	13	a	a	DET
ejpam-6392	24	14	set	set	NOUN
ejpam-6392	24	15	or	or	CCONJ
ejpam-6392	24	16	not	not	PART
ejpam-6392	24	17	.	.	PUNCT
ejpam-6392	25	1	fuzzy	fuzzy	ADJ
ejpam-6392	25	2	set	set	VERB
ejpam-6392	25	3	theory	theory	NOUN
ejpam-6392	25	4	discourses	discourse	VERB
ejpam-6392	25	5	this	this	PRON
ejpam-6392	25	6	by	by	ADP
ejpam-6392	25	7	introducing	introduce	VERB
ejpam-6392	25	8	membership	membership	NOUN
ejpam-6392	25	9	values	value	NOUN
ejpam-6392	25	10	scaling	scale	VERB
ejpam-6392	25	11	from	from	ADP
ejpam-6392	25	12	0	0	NUM
ejpam-6392	25	13	to	to	ADP
ejpam-6392	25	14	1	1	NUM
ejpam-6392	25	15	,	,	PUNCT
ejpam-6392	25	16	which	which	PRON
ejpam-6392	25	17	have	have	AUX
ejpam-6392	25	18	been	be	AUX
ejpam-6392	25	19	used	use	VERB
ejpam-6392	25	20	to	to	PART
ejpam-6392	25	21	represent	represent	VERB
ejpam-6392	25	22	the	the	DET
ejpam-6392	25	23	degree	degree	NOUN
ejpam-6392	25	24	to	to	PART
ejpam-6392	25	25	which	which	PRON
ejpam-6392	25	26	an	an	DET
ejpam-6392	25	27	element	element	NOUN
ejpam-6392	25	28	is	be	AUX
ejpam-6392	25	29	affiliated	affiliate	VERB
ejpam-6392	25	30	with	with	ADP
ejpam-6392	25	31	a	a	DET
ejpam-6392	25	32	set	set	NOUN
ejpam-6392	25	33	.	.	PUNCT
ejpam-6392	26	1	fuzzy	fuzzy	ADJ
ejpam-6392	26	2	set	set	PROPN
ejpam-6392	26	3	theory	theory	NOUN
ejpam-6392	26	4	has	have	VERB
ejpam-6392	26	5	innumerable	innumerable	ADJ
ejpam-6392	26	6	implementations	implementation	NOUN
ejpam-6392	26	7	in	in	ADP
ejpam-6392	26	8	diverse	diverse	ADJ
ejpam-6392	26	9	fields	field	NOUN
ejpam-6392	26	10	,	,	PUNCT
ejpam-6392	26	11	comprises	comprise	NOUN
ejpam-6392	26	12	of	of	ADP
ejpam-6392	26	13	artificial	artificial	ADJ
ejpam-6392	26	14	intelligence	intelligence	NOUN
ejpam-6392	26	15	,	,	PUNCT
ejpam-6392	26	16	decisionmaking	decisionmake	VERB
ejpam-6392	26	17	and	and	CCONJ
ejpam-6392	26	18	control	control	NOUN
ejpam-6392	26	19	systems	system	NOUN
ejpam-6392	26	20	that	that	PRON
ejpam-6392	26	21	allow	allow	VERB
ejpam-6392	26	22	the	the	DET
ejpam-6392	26	23	both	both	DET
ejpam-6392	26	24	modeling	modeling	NOUN
ejpam-6392	26	25	and	and	CCONJ
ejpam-6392	26	26	handling	handling	NOUN
ejpam-6392	26	27	of	of	ADP
ejpam-6392	26	28	vague	vague	ADJ
ejpam-6392	26	29	and	and	CCONJ
ejpam-6392	26	30	imprecise	imprecise	ADJ
ejpam-6392	26	31	information	information	NOUN
ejpam-6392	26	32	.	.	PUNCT
ejpam-6392	27	1	moreover	moreover	ADV
ejpam-6392	27	2	,	,	PUNCT
ejpam-6392	27	3	kuroki	kuroki	PROPN
ejpam-6392	27	4	[	[	X
ejpam-6392	27	5	12	12	NUM
ejpam-6392	27	6	,	,	PUNCT
ejpam-6392	27	7	13	13	NUM
ejpam-6392	27	8	]	]	PUNCT
ejpam-6392	27	9	discussed	discuss	VERB
ejpam-6392	27	10	his	his	PRON
ejpam-6392	27	11	work	work	NOUN
ejpam-6392	27	12	on	on	ADP
ejpam-6392	27	13	fuzzy	fuzzy	ADJ
ejpam-6392	27	14	bi	bi	NOUN
ejpam-6392	27	15	-	-	NOUN
ejpam-6392	27	16	ideals	ideal	NOUN
ejpam-6392	27	17	in	in	ADP
ejpam-6392	27	18	semigroups	semigroup	NOUN
ejpam-6392	27	19	and	and	CCONJ
ejpam-6392	27	20	fuzzy	fuzzy	ADJ
ejpam-6392	27	21	generalized	generalized	ADJ
ejpam-6392	27	22	bi	bi	NOUN
ejpam-6392	27	23	-	-	NOUN
ejpam-6392	27	24	ideals	ideal	NOUN
ejpam-6392	27	25	in	in	ADP
ejpam-6392	27	26	semigroups	semigroup	NOUN
ejpam-6392	27	27	.	.	PUNCT
ejpam-6392	28	1	yiarayong	yiarayong	PROPN
ejpam-6392	29	1	[	[	X
ejpam-6392	29	2	14	14	NUM
ejpam-6392	29	3	]	]	PUNCT
ejpam-6392	29	4	have	have	AUX
ejpam-6392	29	5	done	do	VERB
ejpam-6392	29	6	results	result	NOUN
ejpam-6392	29	7	on	on	ADP
ejpam-6392	29	8	fuzzy	fuzzy	ADJ
ejpam-6392	29	9	bi	bi	ADJ
ejpam-6392	29	10	-	-	ADJ
ejpam-6392	29	11	ideal	ideal	ADJ
ejpam-6392	29	12	theory	theory	NOUN
ejpam-6392	29	13	applied	apply	VERB
ejpam-6392	29	14	on	on	ADP
ejpam-6392	29	15	semi	semi	NOUN
ejpam-6392	29	16	-	-	NOUN
ejpam-6392	29	17	groups	group	NOUN
ejpam-6392	29	18	.	.	PUNCT
ejpam-6392	30	1	eventually	eventually	ADV
ejpam-6392	30	2	,	,	PUNCT
ejpam-6392	30	3	atanassov	atanassov	PROPN
ejpam-6392	30	4	proposed	propose	VERB
ejpam-6392	30	5	the	the	DET
ejpam-6392	30	6	generalization	generalization	NOUN
ejpam-6392	30	7	of	of	ADP
ejpam-6392	30	8	fuzzy	fuzzy	ADJ
ejpam-6392	30	9	set	set	NOUN
ejpam-6392	30	10	,	,	PUNCT
ejpam-6392	30	11	which	which	PRON
ejpam-6392	30	12	is	be	AUX
ejpam-6392	30	13	intuitionistic	intuitionistic	ADJ
ejpam-6392	30	14	fuzzy	fuzzy	ADJ
ejpam-6392	30	15	set(ifs	set(if	NOUN
ejpam-6392	30	16	)	)	PUNCT
ejpam-6392	30	17	in	in	ADP
ejpam-6392	30	18	the	the	DET
ejpam-6392	30	19	year	year	NOUN
ejpam-6392	30	20	1980	1980	NUM
ejpam-6392	30	21	,	,	PUNCT
ejpam-6392	30	22	which	which	PRON
ejpam-6392	30	23	gives	give	VERB
ejpam-6392	30	24	information	information	NOUN
ejpam-6392	30	25	about	about	ADP
ejpam-6392	30	26	a	a	DET
ejpam-6392	30	27	fresh	fresh	ADJ
ejpam-6392	30	28	parameter	parameter	NOUN
ejpam-6392	30	29	known	know	VERB
ejpam-6392	30	30	as	as	ADP
ejpam-6392	30	31	“	"	PUNCT
ejpam-6392	30	32	non	non	ADJ
ejpam-6392	30	33	-	-	ADJ
ejpam-6392	30	34	membership	membership	ADJ
ejpam-6392	30	35	degree	degree	NOUN
ejpam-6392	30	36	,	,	PUNCT
ejpam-6392	30	37	”	"	PUNCT
ejpam-6392	30	38	where	where	SCONJ
ejpam-6392	30	39	fuzzy	fuzzy	ADJ
ejpam-6392	30	40	tells	tell	VERB
ejpam-6392	30	41	us	we	PRON
ejpam-6392	30	42	about	about	ADP
ejpam-6392	30	43	the	the	DET
ejpam-6392	30	44	membership	membership	NOUN
ejpam-6392	30	45	degree	degree	NOUN
ejpam-6392	30	46	but	but	CCONJ
ejpam-6392	30	47	in	in	ADP
ejpam-6392	30	48	ifs	ifs	PROPN
ejpam-6392	30	49	gives	give	VERB
ejpam-6392	30	50	information	information	NOUN
ejpam-6392	30	51	about	about	ADP
ejpam-6392	30	52	uncertainty	uncertainty	NOUN
ejpam-6392	30	53	and	and	CCONJ
ejpam-6392	30	54	vagueness	vagueness	NOUN
ejpam-6392	30	55	regarding	regard	VERB
ejpam-6392	30	56	membership	membership	NOUN
ejpam-6392	30	57	degrees	degree	NOUN
ejpam-6392	30	58	and	and	CCONJ
ejpam-6392	30	59	non	non	ADJ
ejpam-6392	30	60	-	-	ADJ
ejpam-6392	30	61	membership	membership	ADJ
ejpam-6392	30	62	degrees	degree	NOUN
ejpam-6392	30	63	.	.	PUNCT
ejpam-6392	31	1	intuitionistic	intuitionistic	ADJ
ejpam-6392	31	2	fuzzy	fuzzy	ADJ
ejpam-6392	31	3	sets	set	NOUN
ejpam-6392	31	4	have	have	VERB
ejpam-6392	31	5	applications	application	NOUN
ejpam-6392	31	6	in	in	ADP
ejpam-6392	31	7	decision	decision	NOUN
ejpam-6392	31	8	-	-	PUNCT
ejpam-6392	31	9	making	making	NOUN
ejpam-6392	31	10	where	where	SCONJ
ejpam-6392	31	11	uncertainty	uncertainty	NOUN
ejpam-6392	31	12	plays	play	VERB
ejpam-6392	31	13	a	a	DET
ejpam-6392	31	14	significant	significant	ADJ
ejpam-6392	31	15	role	role	NOUN
ejpam-6392	31	16	.	.	PUNCT
ejpam-6392	32	1	various	various	ADJ
ejpam-6392	32	2	approaches	approach	NOUN
ejpam-6392	32	3	of	of	ADP
ejpam-6392	32	4	ifs	ifs	PROPN
ejpam-6392	32	5	include	include	VERB
ejpam-6392	32	6	expert	expert	NOUN
ejpam-6392	32	7	systems	system	NOUN
ejpam-6392	32	8	,	,	PUNCT
ejpam-6392	32	9	risk	risk	NOUN
ejpam-6392	32	10	assessment	assessment	NOUN
ejpam-6392	32	11	and	and	CCONJ
ejpam-6392	32	12	medical	medical	ADJ
ejpam-6392	32	13	diagnosis	diagnosis	NOUN
ejpam-6392	32	14	,	,	PUNCT
ejpam-6392	32	15	where	where	SCONJ
ejpam-6392	32	16	precise	precise	ADJ
ejpam-6392	32	17	decisions	decision	NOUN
ejpam-6392	32	18	are	be	AUX
ejpam-6392	32	19	difficult	difficult	ADJ
ejpam-6392	32	20	to	to	PART
ejpam-6392	32	21	maintain	maintain	VERB
ejpam-6392	32	22	on	on	ADP
ejpam-6392	32	23	vague	vague	ADJ
ejpam-6392	32	24	or	or	CCONJ
ejpam-6392	32	25	uncertain	uncertain	ADJ
ejpam-6392	32	26	data	datum	NOUN
ejpam-6392	32	27	or	or	CCONJ
ejpam-6392	32	28	information	information	NOUN
ejpam-6392	32	29	.	.	PUNCT
ejpam-6392	33	1	young	young	ADJ
ejpam-6392	33	2	bae	bae	PROPN
ejpam-6392	33	3	jun	jun	PROPN
ejpam-6392	33	4	and	and	CCONJ
ejpam-6392	33	5	kyung	kyung	PROPN
ejpam-6392	33	6	ho	ho	PROPN
ejpam-6392	33	7	kim	kim	PROPN
ejpam-6392	34	1	[	[	X
ejpam-6392	34	2	15	15	NUM
ejpam-6392	34	3	]	]	PUNCT
ejpam-6392	34	4	have	have	AUX
ejpam-6392	34	5	done	do	VERB
ejpam-6392	34	6	work	work	NOUN
ejpam-6392	34	7	on	on	ADP
ejpam-6392	34	8	intuitionistic	intuitionistic	ADJ
ejpam-6392	34	9	fuzzy	fuzzy	ADJ
ejpam-6392	34	10	ideals	ideal	NOUN
ejpam-6392	34	11	of	of	ADP
ejpam-6392	34	12	bck	bck	NOUN
ejpam-6392	34	13	-	-	PUNCT
ejpam-6392	34	14	algebra	algebra	NOUN
ejpam-6392	34	15	.	.	PUNCT
ejpam-6392	35	1	few	few	ADJ
ejpam-6392	35	2	authors	author	NOUN
ejpam-6392	35	3	,	,	PUNCT
ejpam-6392	35	4	kim	kim	PROPN
ejpam-6392	35	5	and	and	CCONJ
ejpam-6392	35	6	lee	lee	PROPN
ejpam-6392	36	1	[	[	X
ejpam-6392	36	2	16	16	NUM
ejpam-6392	36	3	,	,	PUNCT
ejpam-6392	36	4	17	17	NUM
ejpam-6392	36	5	]	]	PUNCT
ejpam-6392	36	6	have	have	AUX
ejpam-6392	36	7	discussed	discuss	VERB
ejpam-6392	36	8	results	result	NOUN
ejpam-6392	36	9	of	of	ADP
ejpam-6392	36	10	on	on	ADP
ejpam-6392	36	11	intuitionistic	intuitionistic	ADJ
ejpam-6392	36	12	fuzzy	fuzzy	ADJ
ejpam-6392	36	13	bi	bi	NOUN
ejpam-6392	36	14	-	-	NOUN
ejpam-6392	36	15	ideals	ideal	NOUN
ejpam-6392	36	16	of	of	ADP
ejpam-6392	36	17	semi	semi	NOUN
ejpam-6392	36	18	-	-	NOUN
ejpam-6392	36	19	groups	group	NOUN
ejpam-6392	36	20	,	,	PUNCT
ejpam-6392	36	21	interval	interval	NOUN
ejpam-6392	36	22	valued	value	VERB
ejpam-6392	36	23	intuitionistic	intuitionistic	ADJ
ejpam-6392	36	24	fuzzy	fuzzy	ADJ
ejpam-6392	36	25	bi	bi	NOUN
ejpam-6392	36	26	-	-	NOUN
ejpam-6392	36	27	ideals	ideal	NOUN
ejpam-6392	36	28	of	of	ADP
ejpam-6392	36	29	semigroups	semigroup	NOUN
ejpam-6392	36	30	.	.	PUNCT
ejpam-6392	37	1	also	also	ADV
ejpam-6392	37	2	,	,	PUNCT
ejpam-6392	37	3	bhargavi	bhargavi	VERB
ejpam-6392	37	4	[	[	X
ejpam-6392	37	5	18	18	NUM
ejpam-6392	37	6	,	,	PUNCT
ejpam-6392	37	7	19	19	NUM
ejpam-6392	37	8	]	]	PUNCT
ejpam-6392	37	9	and	and	CCONJ
ejpam-6392	37	10	raagamayi	raagamayi	X
ejpam-6392	38	1	[	[	X
ejpam-6392	38	2	20	20	NUM
ejpam-6392	38	3	]	]	PUNCT
ejpam-6392	38	4	have	have	AUX
ejpam-6392	38	5	discussed	discuss	VERB
ejpam-6392	38	6	the	the	DET
ejpam-6392	38	7	results	result	NOUN
ejpam-6392	38	8	on	on	ADP
ejpam-6392	38	9	vague	vague	ADJ
ejpam-6392	38	10	bi	bi	NOUN
ejpam-6392	38	11	-	-	NOUN
ejpam-6392	38	12	ideals	ideal	NOUN
ejpam-6392	38	13	.	.	PUNCT
ejpam-6392	39	1	sindhu	sindhu	NOUN
ejpam-6392	39	2	and	and	CCONJ
ejpam-6392	39	3	himaya	himaya	PROPN
ejpam-6392	39	4	jaleela	jaleela	PROPN
ejpam-6392	39	5	begun	begin	VERB
ejpam-6392	39	6	[	[	PUNCT
ejpam-6392	39	7	21	21	NUM
ejpam-6392	39	8	]	]	PUNCT
ejpam-6392	39	9	have	have	AUX
ejpam-6392	39	10	worked	work	VERB
ejpam-6392	39	11	on	on	ADP
ejpam-6392	39	12	intuitionistic	intuitionistic	ADJ
ejpam-6392	39	13	fuzzy	fuzzy	ADJ
ejpam-6392	39	14	bi	bi	NOUN
ejpam-6392	39	15	-	-	NOUN
ejpam-6392	39	16	ideals	ideal	NOUN
ejpam-6392	39	17	of	of	ADP
ejpam-6392	39	18	bck	bck	NOUN
ejpam-6392	39	19	-	-	PUNCT
ejpam-6392	39	20	algebras	algebras	PROPN
ejpam-6392	39	21	.	.	PUNCT
ejpam-6392	40	1	sequentially	sequentially	ADV
ejpam-6392	40	2	,	,	PUNCT
ejpam-6392	40	3	vinnela	vinnela	PROPN
ejpam-6392	40	4	and	and	CCONJ
ejpam-6392	40	5	raagamayi	raagamayi	NOUN
ejpam-6392	41	1	[	[	X
ejpam-6392	41	2	22	22	NUM
ejpam-6392	41	3	]	]	PUNCT
ejpam-6392	41	4	have	have	AUX
ejpam-6392	41	5	worked	work	VERB
ejpam-6392	41	6	on	on	ADP
ejpam-6392	41	7	bipolar	bipolar	ADJ
ejpam-6392	41	8	fuzzy	fuzzy	ADJ
ejpam-6392	41	9	bi	bi	NOUN
ejpam-6392	41	10	-	-	NOUN
ejpam-6392	41	11	ideals	ideal	NOUN
ejpam-6392	41	12	of	of	ADP
ejpam-6392	41	13	gamma	gamma	NOUN
ejpam-6392	41	14	near	near	ADP
ejpam-6392	41	15	ring	ring	PROPN
ejpam-6392	41	16	.	.	PUNCT
ejpam-6392	42	1	sub	sub	ADJ
ejpam-6392	42	2	-	-	ADJ
ejpam-6392	42	3	sequentially	sequentially	ADV
ejpam-6392	42	4	few	few	ADJ
ejpam-6392	42	5	more	more	ADJ
ejpam-6392	42	6	authors	author	NOUN
ejpam-6392	42	7	have	have	AUX
ejpam-6392	42	8	completed	complete	VERB
ejpam-6392	42	9	work	work	NOUN
ejpam-6392	42	10	on	on	ADP
ejpam-6392	42	11	bi	bi	NOUN
ejpam-6392	42	12	-	-	NOUN
ejpam-6392	42	13	ideals	ideal	NOUN
ejpam-6392	42	14	[	[	X
ejpam-6392	42	15	7	7	NUM
ejpam-6392	42	16	,	,	PUNCT
ejpam-6392	42	17	23–25	23–25	NUM
ejpam-6392	42	18	]	]	PUNCT
ejpam-6392	42	19	like	like	ADP
ejpam-6392	42	20	bi	bi	NOUN
ejpam-6392	42	21	-	-	NOUN
ejpam-6392	42	22	ideals	ideal	NOUN
ejpam-6392	42	23	in	in	ADP
ejpam-6392	42	24	semi	semi	NOUN
ejpam-6392	42	25	-	-	NOUN
ejpam-6392	42	26	groups	group	NOUN
ejpam-6392	42	27	,	,	PUNCT
ejpam-6392	42	28	fuzzy	fuzzy	ADJ
ejpam-6392	42	29	bi	bi	NOUN
ejpam-6392	42	30	-	-	NOUN
ejpam-6392	42	31	ideals	ideal	NOUN
ejpam-6392	42	32	and	and	CCONJ
ejpam-6392	42	33	generalized	generalize	VERB
ejpam-6392	42	34	fuzzy	fuzzy	ADJ
ejpam-6392	42	35	bi	bi	NOUN
ejpam-6392	42	36	-	-	NOUN
ejpam-6392	42	37	ideals	ideal	NOUN
ejpam-6392	42	38	in	in	ADP
ejpam-6392	42	39	semigroups	semigroup	NOUN
ejpam-6392	42	40	also	also	ADV
ejpam-6392	42	41	[	[	X
ejpam-6392	42	42	14	14	NUM
ejpam-6392	42	43	,	,	PUNCT
ejpam-6392	42	44	26	26	NUM
ejpam-6392	42	45	,	,	PUNCT
ejpam-6392	42	46	27	27	NUM
ejpam-6392	42	47	]	]	PUNCT
ejpam-6392	42	48	.	.	PUNCT
ejpam-6392	43	1	later	later	ADV
ejpam-6392	43	2	,	,	PUNCT
ejpam-6392	43	3	the	the	DET
ejpam-6392	43	4	neutrosophic	neutrosophic	ADJ
ejpam-6392	43	5	sets	set	NOUN
ejpam-6392	43	6	were	be	AUX
ejpam-6392	43	7	introduced	introduce	VERB
ejpam-6392	43	8	by	by	ADP
ejpam-6392	43	9	smarandache	smarandache	NOUN
ejpam-6392	43	10	in	in	ADP
ejpam-6392	43	11	1990	1990	NUM
ejpam-6392	43	12	,	,	PUNCT
ejpam-6392	43	13	which	which	PRON
ejpam-6392	43	14	is	be	AUX
ejpam-6392	43	15	the	the	DET
ejpam-6392	43	16	generalization	generalization	NOUN
ejpam-6392	43	17	of	of	ADP
ejpam-6392	43	18	classical	classical	ADJ
ejpam-6392	43	19	sets	set	NOUN
ejpam-6392	43	20	,	,	PUNCT
ejpam-6392	43	21	fuzzy	fuzzy	ADJ
ejpam-6392	43	22	sets	set	NOUN
ejpam-6392	43	23	and	and	CCONJ
ejpam-6392	43	24	intuitionistic	intuitionistic	ADJ
ejpam-6392	43	25	fuzzy	fuzzy	ADJ
ejpam-6392	43	26	sets	set	NOUN
ejpam-6392	43	27	by	by	ADP
ejpam-6392	43	28	involving	involve	VERB
ejpam-6392	43	29	a	a	DET
ejpam-6392	43	30	new	new	ADJ
ejpam-6392	43	31	parameter	parameter	NOUN
ejpam-6392	43	32	called	call	VERB
ejpam-6392	43	33	“	"	PUNCT
ejpam-6392	43	34	indeterminancy	indeterminancy	NOUN
ejpam-6392	43	35	.	.	PUNCT
ejpam-6392	43	36	”	"	PUNCT
ejpam-6392	44	1	neutrosophic	neutrosophic	ADJ
ejpam-6392	44	2	sets	set	NOUN
ejpam-6392	44	3	are	be	AUX
ejpam-6392	44	4	particularly	particularly	ADV
ejpam-6392	44	5	useful	useful	ADJ
ejpam-6392	44	6	in	in	ADP
ejpam-6392	44	7	situations	situation	NOUN
ejpam-6392	44	8	where	where	SCONJ
ejpam-6392	44	9	uncertainty	uncertainty	NOUN
ejpam-6392	44	10	exist	exist	VERB
ejpam-6392	44	11	also	also	ADV
ejpam-6392	44	12	holds	hold	VERB
ejpam-6392	44	13	the	the	DET
ejpam-6392	44	14	basic	basic	ADJ
ejpam-6392	44	15	components	component	NOUN
ejpam-6392	44	16	of	of	ADP
ejpam-6392	44	17	truth	truth	NOUN
ejpam-6392	44	18	,	,	PUNCT
ejpam-6392	44	19	falsehood	falsehood	NOUN
ejpam-6392	44	20	and	and	CCONJ
ejpam-6392	44	21	indeterminacy	indeterminacy	NOUN
ejpam-6392	44	22	are	be	AUX
ejpam-6392	44	23	simultaneously	simultaneously	ADV
ejpam-6392	44	24	considered	consider	VERB
ejpam-6392	44	25	.	.	PUNCT
ejpam-6392	45	1	neutrosophic	neutrosophic	ADJ
ejpam-6392	45	2	sets	set	NOUN
ejpam-6392	45	3	have	have	VERB
ejpam-6392	45	4	plenty	plenty	NOUN
ejpam-6392	45	5	of	of	ADP
ejpam-6392	45	6	approaches	approach	NOUN
ejpam-6392	45	7	in	in	ADP
ejpam-6392	45	8	many	many	ADJ
ejpam-6392	45	9	fields	field	NOUN
ejpam-6392	45	10	like	like	ADP
ejpam-6392	45	11	decision	decision	NOUN
ejpam-6392	45	12	making	making	NOUN
ejpam-6392	45	13	,	,	PUNCT
ejpam-6392	45	14	expert	expert	NOUN
ejpam-6392	45	15	systems	system	NOUN
ejpam-6392	45	16	,	,	PUNCT
ejpam-6392	45	17	image	image	NOUN
ejpam-6392	45	18	processing	processing	NOUN
ejpam-6392	45	19	and	and	CCONJ
ejpam-6392	45	20	fuzzy	fuzzy	ADJ
ejpam-6392	45	21	logic	logic	NOUN
ejpam-6392	45	22	thus	thus	ADV
ejpam-6392	45	23	enables	enable	VERB
ejpam-6392	45	24	us	we	PRON
ejpam-6392	45	25	to	to	PART
ejpam-6392	45	26	do	do	VERB
ejpam-6392	45	27	effective	effective	ADJ
ejpam-6392	45	28	modeling	modeling	NOUN
ejpam-6392	45	29	and	and	CCONJ
ejpam-6392	45	30	analysis	analysis	NOUN
ejpam-6392	45	31	in	in	ADP
ejpam-6392	45	32	situations	situation	NOUN
ejpam-6392	45	33	where	where	SCONJ
ejpam-6392	45	34	classical	classical	ADJ
ejpam-6392	45	35	set	set	NOUN
ejpam-6392	45	36	theory	theory	NOUN
ejpam-6392	45	37	falls	fall	VERB
ejpam-6392	45	38	short	short	ADJ
ejpam-6392	45	39	.	.	PUNCT
ejpam-6392	46	1	some	some	DET
ejpam-6392	46	2	authors	author	NOUN
ejpam-6392	46	3	de	de	ADP
ejpam-6392	46	4	gruyter	gruyter	NOUN
ejpam-6392	46	5	[	[	X
ejpam-6392	46	6	28	28	NUM
ejpam-6392	46	7	]	]	PUNCT
ejpam-6392	46	8	have	have	AUX
ejpam-6392	46	9	discussed	discuss	VERB
ejpam-6392	46	10	few	few	ADJ
ejpam-6392	46	11	results	result	NOUN
ejpam-6392	46	12	on	on	ADP
ejpam-6392	46	13	mbj	mbj	PROPN
ejpam-6392	46	14	-	-	PUNCT
ejpam-6392	46	15	neutrosophic	neutrosophic	ADJ
ejpam-6392	46	16	ideals	ideal	NOUN
ejpam-6392	46	17	of	of	ADP
ejpam-6392	46	18	bck	bck	PROPN
ejpam-6392	46	19	/	/	SYM
ejpam-6392	46	20	bci	bci	NOUN
ejpam-6392	46	21	-	-	PUNCT
ejpam-6392	46	22	algebras	algebras	X
ejpam-6392	46	23	.	.	PUNCT
ejpam-6392	47	1	muhuuddin	muhuuddin	NOUN
ejpam-6392	47	2	and	and	CCONJ
ejpam-6392	47	3	young	young	ADJ
ejpam-6392	47	4	bae	bae	PROPN
ejpam-6392	47	5	jun	jun	PROPN
ejpam-6392	48	1	[	[	X
ejpam-6392	48	2	29	29	NUM
ejpam-6392	48	3	]	]	PUNCT
ejpam-6392	48	4	have	have	AUX
ejpam-6392	48	5	done	do	VERB
ejpam-6392	48	6	further	further	ADJ
ejpam-6392	48	7	results	result	NOUN
ejpam-6392	48	8	of	of	ADP
ejpam-6392	48	9	neutrosophic	neutrosophic	ADJ
ejpam-6392	48	10	subalgebras	subalgebra	NOUN
ejpam-6392	48	11	in	in	ADP
ejpam-6392	48	12	bck	bck	PROPN
ejpam-6392	48	13	/	/	SYM
ejpam-6392	48	14	bci	bci	NOUN
ejpam-6392	48	15	-	-	PUNCT
ejpam-6392	48	16	algebras	algebras	PROPN
ejpam-6392	48	17	based	base	VERB
ejpam-6392	48	18	on	on	ADP
ejpam-6392	48	19	neutrosophic	neutrosophic	ADJ
ejpam-6392	48	20	points	point	NOUN
ejpam-6392	48	21	.	.	PUNCT
ejpam-6392	49	1	now	now	ADV
ejpam-6392	49	2	in	in	ADP
ejpam-6392	49	3	this	this	DET
ejpam-6392	49	4	article	article	NOUN
ejpam-6392	49	5	we	we	PRON
ejpam-6392	49	6	look	look	VERB
ejpam-6392	49	7	over	over	ADP
ejpam-6392	49	8	the	the	DET
ejpam-6392	49	9	concept	concept	NOUN
ejpam-6392	49	10	of	of	ADP
ejpam-6392	49	11	bi	bi	NOUN
ejpam-6392	49	12	-	-	NOUN
ejpam-6392	49	13	ideals	ideal	NOUN
ejpam-6392	49	14	in	in	ADP
ejpam-6392	49	15	ink	ink	NOUN
ejpam-6392	49	16	-	-	PUNCT
ejpam-6392	49	17	algebra	algebra	NOUN
ejpam-6392	49	18	in	in	ADP
ejpam-6392	49	19	terms	term	NOUN
ejpam-6392	49	20	of	of	ADP
ejpam-6392	49	21	neutrosophic	neutrosophic	ADJ
ejpam-6392	49	22	sets	set	NOUN
ejpam-6392	49	23	.	.	PUNCT
ejpam-6392	50	1	m.	m.	NOUN
ejpam-6392	50	2	remala	remala	NOUN
ejpam-6392	50	3	,	,	PUNCT
ejpam-6392	50	4	e.	e.	PROPN
ejpam-6392	50	5	tamma	tamma	PROPN
ejpam-6392	50	6	,	,	PUNCT
ejpam-6392	50	7	y.	y.	PROPN
ejpam-6392	50	8	bhargavi	bhargavi	PROPN
ejpam-6392	50	9	/	/	SYM
ejpam-6392	50	10	eur	eur	PROPN
ejpam-6392	50	11	.	.	PUNCT
ejpam-6392	51	1	j.	j.	PROPN
ejpam-6392	51	2	pure	pure	PROPN
ejpam-6392	51	3	appl	appl	PROPN
ejpam-6392	51	4	.	.	PROPN
ejpam-6392	51	5	math	math	PROPN
ejpam-6392	51	6	,	,	PUNCT
ejpam-6392	51	7	18	18	NUM
ejpam-6392	51	8	(	(	PUNCT
ejpam-6392	51	9	4	4	NUM
ejpam-6392	51	10	)	)	PUNCT
ejpam-6392	51	11	(	(	PUNCT
ejpam-6392	51	12	2025	2025	NUM
ejpam-6392	51	13	)	)	PUNCT
ejpam-6392	51	14	,	,	PUNCT
ejpam-6392	51	15	6392	6392	NUM
ejpam-6392	51	16	3	3	NUM
ejpam-6392	51	17	of	of	ADP
ejpam-6392	51	18	20	20	NUM
ejpam-6392	51	19	2	2	NUM
ejpam-6392	51	20	.	.	PUNCT
ejpam-6392	51	21	preliminaries	preliminary	NOUN
ejpam-6392	51	22	in	in	ADP
ejpam-6392	51	23	this	this	DET
ejpam-6392	51	24	segment	segment	NOUN
ejpam-6392	52	1	,	,	PUNCT
ejpam-6392	52	2	we	we	PRON
ejpam-6392	52	3	have	have	AUX
ejpam-6392	52	4	used	use	VERB
ejpam-6392	52	5	the	the	DET
ejpam-6392	52	6	some	some	PRON
ejpam-6392	52	7	of	of	ADP
ejpam-6392	52	8	the	the	DET
ejpam-6392	52	9	definitions	definition	NOUN
ejpam-6392	52	10	which	which	PRON
ejpam-6392	52	11	are	be	AUX
ejpam-6392	52	12	being	be	AUX
ejpam-6392	52	13	utilized	utilize	VERB
ejpam-6392	52	14	for	for	ADP
ejpam-6392	52	15	this	this	DET
ejpam-6392	52	16	work	work	NOUN
ejpam-6392	52	17	.	.	PUNCT
ejpam-6392	53	1	definition	definition	NOUN
ejpam-6392	53	2	2.1	2.1	NUM
ejpam-6392	53	3	.	.	PUNCT
ejpam-6392	54	1	[	[	X
ejpam-6392	54	2	30	30	NUM
ejpam-6392	54	3	]	]	X
ejpam-6392	54	4	an	an	DET
ejpam-6392	54	5	ink	ink	NOUN
ejpam-6392	54	6	-	-	PUNCT
ejpam-6392	54	7	algebra	algebra	NOUN
ejpam-6392	54	8	(	(	PUNCT
ejpam-6392	54	9	¨̈u	¨̈u	NOUN
ejpam-6392	54	10	,	,	PUNCT
ejpam-6392	54	11	•	•	NUM
ejpam-6392	54	12	,	,	PUNCT
ejpam-6392	54	13	0	0	NUM
ejpam-6392	54	14	)	)	PUNCT
ejpam-6392	54	15	is	be	AUX
ejpam-6392	54	16	said	say	VERB
ejpam-6392	54	17	to	to	PART
ejpam-6392	54	18	be	be	AUX
ejpam-6392	54	19	an	an	DET
ejpam-6392	54	20	ink	ink	NOUN
ejpam-6392	54	21	-	-	PUNCT
ejpam-6392	54	22	algebra	algebra	NOUN
ejpam-6392	54	23	if	if	SCONJ
ejpam-6392	54	24	it	it	PRON
ejpam-6392	54	25	satisfies	satisfy	VERB
ejpam-6392	54	26	the	the	DET
ejpam-6392	54	27	following	follow	VERB
ejpam-6392	54	28	conditions	condition	NOUN
ejpam-6392	54	29	for	for	ADP
ejpam-6392	54	30	any	any	DET
ejpam-6392	54	31	e	e	NOUN
ejpam-6392	54	32	,	,	PUNCT
ejpam-6392	54	33	3	3	NUM
ejpam-6392	54	34	,	,	PUNCT
ejpam-6392	54	35	ä	ä	PROPN
ejpam-6392	54	36	∈	∈	PROPN
ejpam-6392	54	37	¨̈u	¨̈u	NOUN
ejpam-6392	54	38	:	:	PUNCT
ejpam-6392	54	39	•	•	ADP
ejpam-6392	54	40	ink-1	ink-1	ADP
ejpam-6392	54	41	:	:	PUNCT
ejpam-6392	54	42	(	(	PUNCT
ejpam-6392	54	43	(	(	PUNCT
ejpam-6392	54	44	e	e	NOUN
ejpam-6392	54	45	•	•	NOUN
ejpam-6392	54	46	3	3	NUM
ejpam-6392	54	47	)	)	PUNCT
ejpam-6392	54	48	•	•	NOUN
ejpam-6392	54	49	(	(	PUNCT
ejpam-6392	54	50	e	e	NOUN
ejpam-6392	54	51	•	•	NUM
ejpam-6392	54	52	ä	ä	NOUN
ejpam-6392	54	53	)	)	PUNCT
ejpam-6392	54	54	)	)	PUNCT
ejpam-6392	55	1	•	•	X
ejpam-6392	56	1	(	(	PUNCT
ejpam-6392	56	2	ä	ä	NOUN
ejpam-6392	56	3	•	•	NUM
ejpam-6392	56	4	3	3	NUM
ejpam-6392	56	5	)	)	PUNCT
ejpam-6392	56	6	=	=	SYM
ejpam-6392	56	7	0	0	NUM
ejpam-6392	56	8	.	.	NOUN
ejpam-6392	56	9	•	•	NUM
ejpam-6392	56	10	ink-2	ink-2	PRON
ejpam-6392	56	11	:	:	PUNCT
ejpam-6392	56	12	(	(	PUNCT
ejpam-6392	56	13	(	(	PUNCT
ejpam-6392	56	14	e	e	NOUN
ejpam-6392	56	15	•	•	NUM
ejpam-6392	56	16	ä	ä	NOUN
ejpam-6392	56	17	)	)	PUNCT
ejpam-6392	56	18	•	•	NOUN
ejpam-6392	56	19	(	(	PUNCT
ejpam-6392	56	20	3	3	NUM
ejpam-6392	56	21	•	•	NUM
ejpam-6392	56	22	ä	ä	NOUN
ejpam-6392	56	23	)	)	PUNCT
ejpam-6392	56	24	)	)	PUNCT
ejpam-6392	56	25	•	•	X
ejpam-6392	56	26	(	(	PUNCT
ejpam-6392	56	27	e	e	NOUN
ejpam-6392	56	28	•	•	NOUN
ejpam-6392	56	29	3	3	NUM
ejpam-6392	56	30	)	)	PUNCT
ejpam-6392	56	31	=	=	SYM
ejpam-6392	57	1	0	0	NUM
ejpam-6392	57	2	.	.	NOUN
ejpam-6392	57	3	•	•	NUM
ejpam-6392	57	4	ink-3	ink-3	PART
ejpam-6392	57	5	:	:	PUNCT
ejpam-6392	57	6	e	e	NOUN
ejpam-6392	57	7	•	•	NOUN
ejpam-6392	57	8	0	0	X
ejpam-6392	58	1	=	=	SYM
ejpam-6392	58	2	e.	e.	PROPN
ejpam-6392	58	3	•	•	PUNCT
ejpam-6392	58	4	ink-4	ink-4	ADV
ejpam-6392	58	5	:	:	PUNCT
ejpam-6392	58	6	e	e	X
ejpam-6392	58	7	•	•	NOUN
ejpam-6392	58	8	3	3	NUM
ejpam-6392	58	9	=	=	SYM
ejpam-6392	58	10	0	0	NUM
ejpam-6392	58	11	and	and	CCONJ
ejpam-6392	58	12	3	3	NUM
ejpam-6392	58	13	•	•	NUM
ejpam-6392	58	14	e	e	NOUN
ejpam-6392	58	15	=	=	SYM
ejpam-6392	58	16	0	0	NUM
ejpam-6392	58	17	imply	imply	NOUN
ejpam-6392	58	18	e	e	PROPN
ejpam-6392	58	19	=	=	SYM
ejpam-6392	58	20	3	3	X
ejpam-6392	58	21	.	.	X
ejpam-6392	58	22	note	note	NOUN
ejpam-6392	58	23	.	.	PUNCT
ejpam-6392	59	1	in	in	ADP
ejpam-6392	59	2	¨̈u	¨̈u	NOUN
ejpam-6392	59	3	we	we	PRON
ejpam-6392	59	4	can	can	AUX
ejpam-6392	59	5	interpret	interpret	VERB
ejpam-6392	59	6	≤	≤	NUM
ejpam-6392	59	7	by	by	ADP
ejpam-6392	59	8	e	e	NOUN
ejpam-6392	59	9	≤	≤	ADV
ejpam-6392	59	10	3	3	NUM
ejpam-6392	59	11	if	if	SCONJ
ejpam-6392	59	12	and	and	CCONJ
ejpam-6392	59	13	only	only	ADV
ejpam-6392	59	14	if	if	SCONJ
ejpam-6392	59	15	e	e	NOUN
ejpam-6392	59	16	•	•	NOUN
ejpam-6392	59	17	3	3	NUM
ejpam-6392	59	18	=	=	SYM
ejpam-6392	59	19	0	0	PROPN
ejpam-6392	59	20	.	.	PUNCT
ejpam-6392	60	1	definition	definition	NOUN
ejpam-6392	60	2	2.2	2.2	NUM
ejpam-6392	60	3	.	.	PUNCT
ejpam-6392	61	1	[	[	X
ejpam-6392	61	2	30	30	NUM
ejpam-6392	61	3	]	]	PUNCT
ejpam-6392	61	4	let	let	VERB
ejpam-6392	61	5	y	y	PRON
ejpam-6392	61	6	be	be	AUX
ejpam-6392	61	7	a	a	DET
ejpam-6392	61	8	non	non	ADJ
ejpam-6392	61	9	-	-	ADJ
ejpam-6392	61	10	empty	empty	ADJ
ejpam-6392	61	11	subset	subset	NOUN
ejpam-6392	61	12	of	of	ADP
ejpam-6392	61	13	a	a	DET
ejpam-6392	61	14	ink	ink	NOUN
ejpam-6392	61	15	-	-	PUNCT
ejpam-6392	61	16	algebra	algebra	NOUN
ejpam-6392	61	17	¨̈u	¨̈u	NOUN
ejpam-6392	61	18	,	,	PUNCT
ejpam-6392	61	19	then	then	ADV
ejpam-6392	61	20	y	y	PROPN
ejpam-6392	61	21	is	be	AUX
ejpam-6392	61	22	said	say	VERB
ejpam-6392	61	23	to	to	PART
ejpam-6392	61	24	be	be	AUX
ejpam-6392	61	25	an	an	DET
ejpam-6392	61	26	ink	ink	NOUN
ejpam-6392	61	27	-	-	PUNCT
ejpam-6392	61	28	sub	sub	NOUN
ejpam-6392	61	29	-	-	NOUN
ejpam-6392	61	30	algebra	algebra	NOUN
ejpam-6392	61	31	of	of	ADP
ejpam-6392	61	32	¨̈u	¨̈u	NOUN
ejpam-6392	61	33	,	,	PUNCT
ejpam-6392	61	34	if	if	SCONJ
ejpam-6392	61	35	e•	e•	VERB
ejpam-6392	61	36	3∈	3∈	PROPN
ejpam-6392	61	37	y	y	PROPN
ejpam-6392	61	38	where	where	SCONJ
ejpam-6392	61	39	e	e	X
ejpam-6392	61	40	,	,	PUNCT
ejpam-6392	61	41	3	3	NUM
ejpam-6392	61	42	∈	∈	NOUN
ejpam-6392	61	43	¨̈u	¨̈u	NOUN
ejpam-6392	61	44	.	.	PUNCT
ejpam-6392	62	1	definition	definition	NOUN
ejpam-6392	62	2	2.3	2.3	NUM
ejpam-6392	62	3	.	.	PUNCT
ejpam-6392	63	1	[	[	X
ejpam-6392	63	2	3	3	X
ejpam-6392	63	3	]	]	PUNCT
ejpam-6392	63	4	a	a	DET
ejpam-6392	63	5	fuzzy	fuzzy	ADJ
ejpam-6392	63	6	set	set	VERB
ejpam-6392	63	7	g	g	NOUN
ejpam-6392	63	8	in	in	ADP
ejpam-6392	63	9	a	a	DET
ejpam-6392	63	10	ink	ink	NOUN
ejpam-6392	63	11	-	-	PUNCT
ejpam-6392	63	12	algebra	algebra	NOUN
ejpam-6392	63	13	¨̈u	¨̈u	NOUN
ejpam-6392	63	14	is	be	AUX
ejpam-6392	63	15	known	know	VERB
ejpam-6392	63	16	as	as	ADP
ejpam-6392	63	17	fink	fink	NOUN
ejpam-6392	63	18	-	-	PUNCT
ejpam-6392	63	19	subalgebra	subalgebra	NOUN
ejpam-6392	63	20	of	of	ADP
ejpam-6392	63	21	¨̈u	¨̈u	NOUN
ejpam-6392	63	22	if	if	SCONJ
ejpam-6392	63	23	g(e•	g(e•	PROPN
ejpam-6392	63	24	3	3	NUM
ejpam-6392	63	25	)	)	PUNCT
ejpam-6392	63	26	≥	≥	NOUN
ejpam-6392	63	27	min{g(e	min{g(e	PROPN
ejpam-6392	63	28	)	)	PUNCT
ejpam-6392	63	29	,	,	PUNCT
ejpam-6392	63	30	g(3	g(3	PROPN
ejpam-6392	63	31	)	)	PUNCT
ejpam-6392	63	32	}	}	PUNCT
ejpam-6392	63	33	∀	∀	PUNCT
ejpam-6392	64	1	e	e	NOUN
ejpam-6392	64	2	,	,	PUNCT
ejpam-6392	64	3	3∈	3∈	PROPN
ejpam-6392	64	4	¨̈u	¨̈u	NOUN
ejpam-6392	64	5	.	.	PUNCT
ejpam-6392	65	1	definition	definition	NOUN
ejpam-6392	65	2	2.4	2.4	NUM
ejpam-6392	65	3	.	.	PUNCT
ejpam-6392	66	1	[	[	X
ejpam-6392	66	2	3	3	X
ejpam-6392	66	3	]	]	PUNCT
ejpam-6392	66	4	let	let	VERB
ejpam-6392	66	5	fuzzy	fuzzy	ADJ
ejpam-6392	66	6	set	set	VERB
ejpam-6392	66	7	g	g	NOUN
ejpam-6392	66	8	in	in	ADP
ejpam-6392	66	9	ink	ink	NOUN
ejpam-6392	66	10	-	-	PUNCT
ejpam-6392	66	11	algebra	algebra	NOUN
ejpam-6392	66	12	¨̈u	¨̈u	NOUN
ejpam-6392	66	13	is	be	AUX
ejpam-6392	66	14	known	know	VERB
ejpam-6392	66	15	as	as	ADP
ejpam-6392	66	16	fuzzy	fuzzy	ADJ
ejpam-6392	66	17	-	-	PUNCT
ejpam-6392	66	18	ideal	ideal	ADJ
ejpam-6392	66	19	,	,	PUNCT
ejpam-6392	66	20	if	if	SCONJ
ejpam-6392	66	21	it	it	PRON
ejpam-6392	66	22	satisfies	satisfy	VERB
ejpam-6392	66	23	:	:	PUNCT
ejpam-6392	66	24	fid-1	fid-1	NUM
ejpam-6392	66	25	:	:	PUNCT
ejpam-6392	66	26	g(0	g(0	NOUN
ejpam-6392	66	27	)	)	PUNCT
ejpam-6392	66	28	≥	≥	NOUN
ejpam-6392	66	29	g(e	g(e	PROPN
ejpam-6392	66	30	)	)	PUNCT
ejpam-6392	66	31	fid-2	fid-2	ADP
ejpam-6392	66	32	:	:	PUNCT
ejpam-6392	66	33	g(e	g(e	PROPN
ejpam-6392	66	34	)	)	PUNCT
ejpam-6392	66	35	≥	≥	NOUN
ejpam-6392	66	36	min{g(e•	min{g(e•	PROPN
ejpam-6392	66	37	3	3	NUM
ejpam-6392	66	38	)	)	PUNCT
ejpam-6392	66	39	,	,	PUNCT
ejpam-6392	66	40	g(3	g(3	PROPN
ejpam-6392	66	41	)	)	PUNCT
ejpam-6392	66	42	}	}	PUNCT
ejpam-6392	66	43	∈	∈	PROPN
ejpam-6392	66	44	¨̈u	¨̈u	NOUN
ejpam-6392	66	45	.	.	PUNCT
ejpam-6392	67	1	definition	definition	NOUN
ejpam-6392	67	2	2.5	2.5	NUM
ejpam-6392	67	3	.	.	PUNCT
ejpam-6392	68	1	[	[	X
ejpam-6392	68	2	3	3	X
ejpam-6392	68	3	]	]	PUNCT
ejpam-6392	68	4	let	let	VERB
ejpam-6392	68	5	f	f	PRON
ejpam-6392	68	6	be	be	AUX
ejpam-6392	68	7	a	a	DET
ejpam-6392	68	8	non	non	ADJ
ejpam-6392	68	9	-	-	ADJ
ejpam-6392	68	10	empty	empty	ADJ
ejpam-6392	68	11	subset	subset	NOUN
ejpam-6392	68	12	of	of	ADP
ejpam-6392	68	13	a	a	DET
ejpam-6392	68	14	ink	ink	NOUN
ejpam-6392	68	15	-	-	PUNCT
ejpam-6392	68	16	algebra	algebra	NOUN
ejpam-6392	68	17	¨̈u	¨̈u	NOUN
ejpam-6392	68	18	.	.	PUNCT
ejpam-6392	69	1	then	then	ADV
ejpam-6392	69	2	f	f	PROPN
ejpam-6392	69	3	is	be	AUX
ejpam-6392	69	4	defined	define	VERB
ejpam-6392	69	5	as	as	ADP
ejpam-6392	69	6	ink	ink	NOUN
ejpam-6392	69	7	-	-	PUNCT
ejpam-6392	69	8	ideal	ideal	NOUN
ejpam-6392	69	9	of	of	ADP
ejpam-6392	69	10	¨̈u	¨̈u	NOUN
ejpam-6392	69	11	if	if	SCONJ
ejpam-6392	69	12	(	(	PUNCT
ejpam-6392	69	13	i	i	NOUN
ejpam-6392	69	14	)	)	PUNCT
ejpam-6392	69	15	0	0	PUNCT
ejpam-6392	70	1	∈	∈	PROPN
ejpam-6392	70	2	f	f	X
ejpam-6392	70	3	,	,	PUNCT
ejpam-6392	70	4	(	(	PUNCT
ejpam-6392	70	5	ii	ii	NOUN
ejpam-6392	70	6	)	)	PUNCT
ejpam-6392	70	7	(	(	PUNCT
ejpam-6392	70	8	(	(	PUNCT
ejpam-6392	70	9	ä	ä	NOUN
ejpam-6392	70	10	•	•	NUM
ejpam-6392	70	11	e	e	NOUN
ejpam-6392	70	12	)	)	PUNCT
ejpam-6392	70	13	•	•	NOUN
ejpam-6392	70	14	(	(	PUNCT
ejpam-6392	70	15	ä	ä	NOUN
ejpam-6392	70	16	•	•	NUM
ejpam-6392	70	17	3	3	NUM
ejpam-6392	70	18	)	)	PUNCT
ejpam-6392	70	19	)	)	PUNCT
ejpam-6392	71	1	∈	∈	PROPN
ejpam-6392	71	2	f	f	PROPN
ejpam-6392	71	3	and	and	CCONJ
ejpam-6392	71	4	3	3	NUM
ejpam-6392	71	5	∈	∈	NOUN
ejpam-6392	71	6	f	f	X
ejpam-6392	71	7	imply	imply	VERB
ejpam-6392	71	8	e	e	PROPN
ejpam-6392	71	9	∈	∈	PROPN
ejpam-6392	71	10	f	f	PROPN
ejpam-6392	71	11	for	for	ADP
ejpam-6392	71	12	all	all	DET
ejpam-6392	71	13	e	e	NOUN
ejpam-6392	71	14	,	,	PUNCT
ejpam-6392	71	15	3,ä	3,ä	PROPN
ejpam-6392	71	16	∈	∈	PROPN
ejpam-6392	71	17	¨̈u	¨̈u	NOUN
ejpam-6392	71	18	.	.	PUNCT
ejpam-6392	72	1	definition	definition	NOUN
ejpam-6392	72	2	2.6	2.6	NUM
ejpam-6392	72	3	.	.	PUNCT
ejpam-6392	73	1	[	[	X
ejpam-6392	73	2	6	6	NUM
ejpam-6392	73	3	]	]	PUNCT
ejpam-6392	73	4	a	a	DET
ejpam-6392	73	5	neutrosophic	neutrosophic	ADJ
ejpam-6392	73	6	set	set	VERB
ejpam-6392	73	7	g=(gt	g=(gt	NOUN
ejpam-6392	73	8	,	,	PUNCT
ejpam-6392	73	9	gi	gi	INTJ
ejpam-6392	73	10	,	,	PUNCT
ejpam-6392	73	11	gf	gf	NOUN
ejpam-6392	73	12	)	)	PUNCT
ejpam-6392	73	13	in	in	ADP
ejpam-6392	73	14	x	x	PROPN
ejpam-6392	73	15	is	be	AUX
ejpam-6392	73	16	called	call	VERB
ejpam-6392	73	17	a	a	DET
ejpam-6392	73	18	neutrosophic	neutrosophic	ADJ
ejpam-6392	73	19	ink	ink	NOUN
ejpam-6392	73	20	sub	sub	NOUN
ejpam-6392	73	21	-	-	NOUN
ejpam-6392	73	22	algebra	algebra	NOUN
ejpam-6392	73	23	of	of	ADP
ejpam-6392	73	24	¨̈u	¨̈u	NOUN
ejpam-6392	73	25	if	if	SCONJ
ejpam-6392	73	26	it	it	PRON
ejpam-6392	73	27	satisfies	satisfy	VERB
ejpam-6392	73	28	the	the	DET
ejpam-6392	73	29	following	follow	VERB
ejpam-6392	73	30	condition	condition	NOUN
ejpam-6392	73	31	,	,	PUNCT
ejpam-6392	73	32	for	for	ADP
ejpam-6392	73	33	all	all	DET
ejpam-6392	73	34	e	e	NOUN
ejpam-6392	73	35	,	,	PUNCT
ejpam-6392	73	36	3	3	NUM
ejpam-6392	73	37	,	,	PUNCT
ejpam-6392	73	38	ä∈	ä∈	NOUN
ejpam-6392	73	39	¨̈u	¨̈u	NOUN
ejpam-6392	73	40	.	.	PUNCT
ejpam-6392	74	1	(	(	PUNCT
ejpam-6392	74	2	i	i	NOUN
ejpam-6392	74	3	)	)	PUNCT
ejpam-6392	74	4	gt	gt	PROPN
ejpam-6392	74	5	(	(	PUNCT
ejpam-6392	74	6	e•	e•	NOUN
ejpam-6392	74	7	3	3	NUM
ejpam-6392	74	8	)	)	PUNCT
ejpam-6392	74	9	≥	≥	NOUN
ejpam-6392	74	10	min	min	PROPN
ejpam-6392	74	11	{	{	PUNCT
ejpam-6392	74	12	gt	gt	PROPN
ejpam-6392	74	13	(	(	PUNCT
ejpam-6392	74	14	e	e	NOUN
ejpam-6392	74	15	)	)	PUNCT
ejpam-6392	74	16	,	,	PUNCT
ejpam-6392	74	17	gt	gt	PROPN
ejpam-6392	74	18	(	(	PUNCT
ejpam-6392	74	19	3	3	NUM
ejpam-6392	74	20	)	)	PUNCT
ejpam-6392	74	21	}	}	PUNCT
ejpam-6392	74	22	(	(	PUNCT
ejpam-6392	74	23	ii	ii	NOUN
ejpam-6392	74	24	)	)	PUNCT
ejpam-6392	74	25	gf	gf	NOUN
ejpam-6392	74	26	(	(	PUNCT
ejpam-6392	74	27	e•	e•	NOUN
ejpam-6392	74	28	3	3	NUM
ejpam-6392	74	29	)	)	PUNCT
ejpam-6392	74	30	≤	≤	NUM
ejpam-6392	74	31	max	max	PROPN
ejpam-6392	74	32	{	{	PUNCT
ejpam-6392	74	33	gf	gf	X
ejpam-6392	74	34	(	(	PUNCT
ejpam-6392	74	35	e	e	NOUN
ejpam-6392	74	36	)	)	PUNCT
ejpam-6392	74	37	,	,	PUNCT
ejpam-6392	74	38	gf	gf	X
ejpam-6392	74	39	(	(	PUNCT
ejpam-6392	74	40	3	3	NUM
ejpam-6392	74	41	)	)	PUNCT
ejpam-6392	74	42	}	}	PUNCT
ejpam-6392	74	43	(	(	PUNCT
ejpam-6392	74	44	iii	iii	X
ejpam-6392	74	45	)	)	PUNCT
ejpam-6392	74	46	gf	gf	NOUN
ejpam-6392	74	47	(	(	PUNCT
ejpam-6392	74	48	e•	e•	NOUN
ejpam-6392	74	49	3	3	NUM
ejpam-6392	74	50	)	)	PUNCT
ejpam-6392	74	51	≤	≤	NUM
ejpam-6392	74	52	max	max	PROPN
ejpam-6392	74	53	{	{	PUNCT
ejpam-6392	74	54	gf	gf	X
ejpam-6392	74	55	(	(	PUNCT
ejpam-6392	74	56	e	e	NOUN
ejpam-6392	74	57	)	)	PUNCT
ejpam-6392	74	58	,	,	PUNCT
ejpam-6392	74	59	gf	gf	X
ejpam-6392	74	60	(	(	PUNCT
ejpam-6392	74	61	3	3	NUM
ejpam-6392	74	62	)	)	PUNCT
ejpam-6392	74	63	}	}	PUNCT
ejpam-6392	74	64	example	example	NOUN
ejpam-6392	74	65	2.1	2.1	NUM
ejpam-6392	74	66	.	.	PUNCT
ejpam-6392	75	1	consider	consider	VERB
ejpam-6392	75	2	the	the	DET
ejpam-6392	75	3	ink	ink	NOUN
ejpam-6392	75	4	-	-	PUNCT
ejpam-6392	75	5	algebra	algebra	NOUN
ejpam-6392	75	6	¨̈u	¨̈u	NOUN
ejpam-6392	75	7	=	=	SYM
ejpam-6392	75	8	{	{	PUNCT
ejpam-6392	75	9	0	0	NUM
ejpam-6392	75	10	,	,	PUNCT
ejpam-6392	75	11	a	a	DET
ejpam-6392	75	12	,	,	PUNCT
ejpam-6392	75	13	b	b	NOUN
ejpam-6392	75	14	}	}	PUNCT
ejpam-6392	75	15	with	with	ADP
ejpam-6392	75	16	the	the	DET
ejpam-6392	75	17	following	follow	VERB
ejpam-6392	75	18	cayley	cayley	ADJ
ejpam-6392	75	19	table	table	NOUN
ejpam-6392	75	20	.	.	PUNCT
ejpam-6392	76	1	•	•	NUM
ejpam-6392	76	2	0	0	NUM
ejpam-6392	76	3	a	a	DET
ejpam-6392	76	4	b	b	NOUN
ejpam-6392	76	5	0	0	NUM
ejpam-6392	76	6	0	0	NUM
ejpam-6392	76	7	b	b	PROPN
ejpam-6392	76	8	a	a	DET
ejpam-6392	76	9	a	a	DET
ejpam-6392	76	10	a	a	DET
ejpam-6392	76	11	0	0	NUM
ejpam-6392	76	12	b	b	PROPN
ejpam-6392	76	13	b	b	PROPN
ejpam-6392	76	14	b	b	PROPN
ejpam-6392	76	15	a	a	DET
ejpam-6392	76	16	0	0	NUM
ejpam-6392	76	17	m.	m.	NOUN
ejpam-6392	76	18	remala	remala	NOUN
ejpam-6392	76	19	,	,	PUNCT
ejpam-6392	76	20	e.	e.	PROPN
ejpam-6392	76	21	tamma	tamma	PROPN
ejpam-6392	76	22	,	,	PUNCT
ejpam-6392	76	23	y.	y.	PROPN
ejpam-6392	76	24	bhargavi	bhargavi	PROPN
ejpam-6392	76	25	/	/	SYM
ejpam-6392	76	26	eur	eur	PROPN
ejpam-6392	76	27	.	.	PUNCT
ejpam-6392	77	1	j.	j.	PROPN
ejpam-6392	77	2	pure	pure	PROPN
ejpam-6392	77	3	appl	appl	PROPN
ejpam-6392	77	4	.	.	PROPN
ejpam-6392	77	5	math	math	PROPN
ejpam-6392	77	6	,	,	PUNCT
ejpam-6392	77	7	18	18	NUM
ejpam-6392	77	8	(	(	PUNCT
ejpam-6392	77	9	4	4	NUM
ejpam-6392	77	10	)	)	PUNCT
ejpam-6392	77	11	(	(	PUNCT
ejpam-6392	77	12	2025	2025	NUM
ejpam-6392	77	13	)	)	PUNCT
ejpam-6392	77	14	,	,	PUNCT
ejpam-6392	77	15	6392	6392	NUM
ejpam-6392	77	16	4	4	NUM
ejpam-6392	77	17	of	of	ADP
ejpam-6392	77	18	20	20	NUM
ejpam-6392	77	19	a	a	DET
ejpam-6392	77	20	neutrosophic	neutrosophic	ADJ
ejpam-6392	77	21	set	set	NOUN
ejpam-6392	77	22	g	g	PROPN
ejpam-6392	77	23	=	=	SYM
ejpam-6392	77	24	(	(	PUNCT
ejpam-6392	77	25	gt	gt	INTJ
ejpam-6392	77	26	,	,	PUNCT
ejpam-6392	77	27	gi	gi	INTJ
ejpam-6392	77	28	,	,	PUNCT
ejpam-6392	77	29	gf	gf	PROPN
ejpam-6392	77	30	)	)	PUNCT
ejpam-6392	77	31	on	on	ADP
ejpam-6392	77	32	¨̈u	¨̈u	NOUN
ejpam-6392	77	33	is	be	AUX
ejpam-6392	77	34	defined	define	VERB
ejpam-6392	77	35	by	by	ADP
ejpam-6392	77	36	0	0	NUM
ejpam-6392	77	37	a	a	DET
ejpam-6392	77	38	b	b	X
ejpam-6392	78	1	gt	gt	INTJ
ejpam-6392	78	2	0.2	0.2	NUM
ejpam-6392	78	3	0.5	0.5	NUM
ejpam-6392	78	4	0.6	0.6	NUM
ejpam-6392	78	5	gi	gi	NOUN
ejpam-6392	78	6	0.9	0.9	NUM
ejpam-6392	78	7	0.8	0.8	NUM
ejpam-6392	78	8	0.8	0.8	NUM
ejpam-6392	78	9	gf	gf	NOUN
ejpam-6392	78	10	0.8	0.8	NUM
ejpam-6392	78	11	0.5	0.5	NUM
ejpam-6392	78	12	0.4	0.4	NUM
ejpam-6392	78	13	then	then	ADV
ejpam-6392	78	14	g=(gt	g=(gt	NOUN
ejpam-6392	78	15	,	,	PUNCT
ejpam-6392	78	16	gi	gi	INTJ
ejpam-6392	78	17	,	,	PUNCT
ejpam-6392	78	18	gf	gf	AUX
ejpam-6392	78	19	)	)	PUNCT
ejpam-6392	78	20	be	be	AUX
ejpam-6392	78	21	a	a	DET
ejpam-6392	78	22	neutrosophic	neutrosophic	ADJ
ejpam-6392	78	23	sub	sub	NOUN
ejpam-6392	78	24	-	-	NOUN
ejpam-6392	78	25	algebra	algebra	NOUN
ejpam-6392	78	26	.	.	PUNCT
ejpam-6392	79	1	let	let	VERB
ejpam-6392	79	2	us	we	PRON
ejpam-6392	79	3	take	take	VERB
ejpam-6392	79	4	(	(	PUNCT
ejpam-6392	79	5	randomly	randomly	ADV
ejpam-6392	79	6	)	)	PUNCT
ejpam-6392	79	7	for	for	ADP
ejpam-6392	79	8	truthmembership	truthmembership	NOUN
ejpam-6392	79	9	degree	degree	NOUN
ejpam-6392	79	10	e=	e=	X
ejpam-6392	79	11	a	a	DET
ejpam-6392	79	12	&	&	CCONJ
ejpam-6392	79	13	3=	3=	NUM
ejpam-6392	79	14	b.	b.	NOUN
ejpam-6392	80	1	so	so	ADV
ejpam-6392	80	2	,	,	PUNCT
ejpam-6392	80	3	gt	gt	PROPN
ejpam-6392	80	4	(	(	PUNCT
ejpam-6392	80	5	a	a	DET
ejpam-6392	80	6	•	•	NUM
ejpam-6392	80	7	b	b	NOUN
ejpam-6392	80	8	)	)	PUNCT
ejpam-6392	80	9	≥	≥	PROPN
ejpam-6392	80	10	min	min	PROPN
ejpam-6392	80	11	{	{	PUNCT
ejpam-6392	80	12	gt	gt	PROPN
ejpam-6392	80	13	(	(	PUNCT
ejpam-6392	80	14	a	a	NOUN
ejpam-6392	80	15	)	)	PUNCT
ejpam-6392	80	16	,	,	PUNCT
ejpam-6392	80	17	gt	gt	PROPN
ejpam-6392	80	18	(	(	PUNCT
ejpam-6392	80	19	b	b	NOUN
ejpam-6392	80	20	)	)	PUNCT
ejpam-6392	80	21	}	}	PUNCT
ejpam-6392	80	22	gt	gt	PROPN
ejpam-6392	80	23	(	(	PUNCT
ejpam-6392	80	24	b	b	NOUN
ejpam-6392	80	25	)	)	PUNCT
ejpam-6392	80	26	≥	≥	PROPN
ejpam-6392	80	27	min	min	PROPN
ejpam-6392	80	28	{	{	PUNCT
ejpam-6392	80	29	gt	gt	PROPN
ejpam-6392	80	30	(	(	PUNCT
ejpam-6392	80	31	a	a	NOUN
ejpam-6392	80	32	)	)	PUNCT
ejpam-6392	80	33	,	,	PUNCT
ejpam-6392	80	34	gt	gt	PROPN
ejpam-6392	80	35	(	(	PUNCT
ejpam-6392	80	36	b	b	NOUN
ejpam-6392	80	37	)	)	PUNCT
ejpam-6392	80	38	}	}	PUNCT
ejpam-6392	80	39	=	=	SYM
ejpam-6392	80	40	0.6	0.6	NUM
ejpam-6392	80	41	>	>	SYM
ejpam-6392	80	42	0.5	0.5	NUM
ejpam-6392	80	43	also	also	ADV
ejpam-6392	80	44	,	,	PUNCT
ejpam-6392	80	45	gi(a	gi(a	VERB
ejpam-6392	80	46	•	•	NUM
ejpam-6392	80	47	b	b	X
ejpam-6392	80	48	)	)	PUNCT
ejpam-6392	80	49	≤	≤	NOUN
ejpam-6392	81	1	max	max	PROPN
ejpam-6392	81	2	{	{	PUNCT
ejpam-6392	81	3	gi	gi	INTJ
ejpam-6392	81	4	(	(	PUNCT
ejpam-6392	81	5	a	a	NOUN
ejpam-6392	81	6	)	)	PUNCT
ejpam-6392	81	7	,	,	PUNCT
ejpam-6392	81	8	gi	gi	INTJ
ejpam-6392	81	9	(	(	PUNCT
ejpam-6392	81	10	b	b	NOUN
ejpam-6392	81	11	)	)	PUNCT
ejpam-6392	81	12	}	}	PUNCT
ejpam-6392	81	13	gi(b	gi(b	PROPN
ejpam-6392	81	14	)	)	PUNCT
ejpam-6392	81	15	≤	≤	NUM
ejpam-6392	82	1	max	max	PROPN
ejpam-6392	82	2	{	{	PUNCT
ejpam-6392	82	3	gi	gi	INTJ
ejpam-6392	82	4	(	(	PUNCT
ejpam-6392	82	5	a	a	NOUN
ejpam-6392	82	6	)	)	PUNCT
ejpam-6392	82	7	,	,	PUNCT
ejpam-6392	82	8	gi	gi	INTJ
ejpam-6392	82	9	(	(	PUNCT
ejpam-6392	82	10	b	b	NOUN
ejpam-6392	82	11	)	)	PUNCT
ejpam-6392	82	12	}	}	PUNCT
ejpam-6392	82	13	=	=	SYM
ejpam-6392	82	14	0.8	0.8	NUM
ejpam-6392	82	15	=	=	SYM
ejpam-6392	82	16	0.8	0.8	NUM
ejpam-6392	82	17	similarly	similarly	ADV
ejpam-6392	82	18	,	,	PUNCT
ejpam-6392	82	19	gf	gf	X
ejpam-6392	82	20	(	(	PUNCT
ejpam-6392	82	21	a	a	DET
ejpam-6392	82	22	•	•	NUM
ejpam-6392	82	23	b	b	NOUN
ejpam-6392	82	24	)	)	PUNCT
ejpam-6392	82	25	≤	≤	NUM
ejpam-6392	82	26	max	max	PROPN
ejpam-6392	82	27	{	{	PUNCT
ejpam-6392	82	28	gf	gf	X
ejpam-6392	82	29	(	(	PUNCT
ejpam-6392	82	30	a	a	NOUN
ejpam-6392	82	31	)	)	PUNCT
ejpam-6392	82	32	,	,	PUNCT
ejpam-6392	82	33	gf	gf	X
ejpam-6392	82	34	(	(	PUNCT
ejpam-6392	82	35	b	b	NOUN
ejpam-6392	82	36	)	)	PUNCT
ejpam-6392	82	37	}	}	PUNCT
ejpam-6392	82	38	gf	gf	X
ejpam-6392	82	39	(	(	PUNCT
ejpam-6392	82	40	b	b	NOUN
ejpam-6392	82	41	)	)	PUNCT
ejpam-6392	82	42	≤	≤	NUM
ejpam-6392	82	43	max	max	PROPN
ejpam-6392	82	44	{	{	PUNCT
ejpam-6392	82	45	gf	gf	X
ejpam-6392	82	46	(	(	PUNCT
ejpam-6392	82	47	a	a	NOUN
ejpam-6392	82	48	)	)	PUNCT
ejpam-6392	82	49	,	,	PUNCT
ejpam-6392	82	50	gf	gf	X
ejpam-6392	82	51	(	(	PUNCT
ejpam-6392	82	52	b	b	NOUN
ejpam-6392	82	53	)	)	PUNCT
ejpam-6392	82	54	}	}	PUNCT
ejpam-6392	82	55	=	=	PUNCT
ejpam-6392	82	56	0.4	0.4	NUM
ejpam-6392	82	57	<	<	SYM
ejpam-6392	82	58	0.5	0.5	NUM
ejpam-6392	82	59	likely	likely	ADJ
ejpam-6392	82	60	,	,	PUNCT
ejpam-6392	82	61	for	for	ADP
ejpam-6392	82	62	all	all	DET
ejpam-6392	82	63	outcomes	outcome	NOUN
ejpam-6392	82	64	the	the	DET
ejpam-6392	82	65	above	above	ADJ
ejpam-6392	82	66	condition	condition	NOUN
ejpam-6392	82	67	satisfied	satisfied	ADJ
ejpam-6392	82	68	.	.	PUNCT
ejpam-6392	83	1	definition	definition	NOUN
ejpam-6392	83	2	2.7	2.7	NUM
ejpam-6392	83	3	.	.	PUNCT
ejpam-6392	84	1	[	[	X
ejpam-6392	84	2	6	6	NUM
ejpam-6392	84	3	]	]	PUNCT
ejpam-6392	84	4	a	a	DET
ejpam-6392	84	5	neutrosophic	neutrosophic	ADJ
ejpam-6392	84	6	set	set	NOUN
ejpam-6392	84	7	g	g	PROPN
ejpam-6392	84	8	=	=	SYM
ejpam-6392	84	9	(	(	PUNCT
ejpam-6392	84	10	gt	gt	INTJ
ejpam-6392	84	11	,	,	PUNCT
ejpam-6392	84	12	gi	gi	INTJ
ejpam-6392	84	13	,	,	PUNCT
ejpam-6392	84	14	gf	gf	NOUN
ejpam-6392	84	15	)	)	PUNCT
ejpam-6392	84	16	in	in	ADP
ejpam-6392	84	17	¨̈u	¨̈u	NOUN
ejpam-6392	84	18	is	be	AUX
ejpam-6392	84	19	termed	term	VERB
ejpam-6392	84	20	as	as	ADP
ejpam-6392	84	21	neutrosophic	neutrosophic	ADJ
ejpam-6392	84	22	ideal	ideal	NOUN
ejpam-6392	84	23	of	of	ADP
ejpam-6392	84	24	¨̈u	¨̈u	NOUN
ejpam-6392	84	25	if	if	SCONJ
ejpam-6392	84	26	it	it	PRON
ejpam-6392	84	27	satisfies	satisfy	VERB
ejpam-6392	84	28	the	the	DET
ejpam-6392	84	29	following	follow	VERB
ejpam-6392	84	30	condition	condition	NOUN
ejpam-6392	84	31	,	,	PUNCT
ejpam-6392	84	32	for	for	ADP
ejpam-6392	84	33	all	all	DET
ejpam-6392	84	34	e	e	NOUN
ejpam-6392	84	35	,	,	PUNCT
ejpam-6392	84	36	3	3	NUM
ejpam-6392	84	37	∈	∈	NOUN
ejpam-6392	84	38	¨̈u	¨̈u	NOUN
ejpam-6392	84	39	:	:	PUNCT
ejpam-6392	84	40	(	(	PUNCT
ejpam-6392	84	41	i	i	NOUN
ejpam-6392	84	42	)	)	PUNCT
ejpam-6392	84	43	gt	gt	PROPN
ejpam-6392	84	44	(	(	PUNCT
ejpam-6392	84	45	0	0	NUM
ejpam-6392	84	46	)	)	PUNCT
ejpam-6392	84	47	≥	≥	NOUN
ejpam-6392	84	48	gt	gt	INTJ
ejpam-6392	84	49	(	(	PUNCT
ejpam-6392	84	50	e	e	NOUN
ejpam-6392	84	51	)	)	PUNCT
ejpam-6392	84	52	,	,	PUNCT
ejpam-6392	84	53	gi(0	gi(0	PROPN
ejpam-6392	84	54	)	)	PUNCT
ejpam-6392	84	55	≤	≤	NUM
ejpam-6392	84	56	gi(e	gi(e	NOUN
ejpam-6392	84	57	)	)	PUNCT
ejpam-6392	84	58	,	,	PUNCT
ejpam-6392	84	59	gf	gf	X
ejpam-6392	84	60	(	(	PUNCT
ejpam-6392	84	61	0	0	NUM
ejpam-6392	84	62	)	)	PUNCT
ejpam-6392	84	63	≤	≤	NOUN
ejpam-6392	84	64	gf	gf	X
ejpam-6392	84	65	(	(	PUNCT
ejpam-6392	84	66	e	e	NOUN
ejpam-6392	84	67	)	)	PUNCT
ejpam-6392	84	68	.	.	PUNCT
ejpam-6392	85	1	(	(	PUNCT
ejpam-6392	85	2	ii	ii	X
ejpam-6392	85	3	)	)	PUNCT
ejpam-6392	85	4	gt	gt	PROPN
ejpam-6392	85	5	(	(	PUNCT
ejpam-6392	85	6	e	e	NOUN
ejpam-6392	85	7	)	)	PUNCT
ejpam-6392	85	8	≥	≥	PROPN
ejpam-6392	85	9	min	min	PROPN
ejpam-6392	85	10	{	{	PUNCT
ejpam-6392	85	11	gt	gt	PROPN
ejpam-6392	85	12	(	(	PUNCT
ejpam-6392	85	13	e	e	NOUN
ejpam-6392	85	14	•	•	NOUN
ejpam-6392	85	15	3	3	NUM
ejpam-6392	85	16	)	)	PUNCT
ejpam-6392	85	17	,	,	PUNCT
ejpam-6392	85	18	gt	gt	PROPN
ejpam-6392	85	19	(	(	PUNCT
ejpam-6392	85	20	3	3	NUM
ejpam-6392	85	21	)	)	PUNCT
ejpam-6392	85	22	}	}	PUNCT
ejpam-6392	85	23	.	.	PUNCT
ejpam-6392	86	1	(	(	PUNCT
ejpam-6392	86	2	iii	iii	NOUN
ejpam-6392	86	3	)	)	PUNCT
ejpam-6392	86	4	gi(e	gi(e	NOUN
ejpam-6392	86	5	)	)	PUNCT
ejpam-6392	87	1	≤	≤	NUM
ejpam-6392	87	2	max	max	PROPN
ejpam-6392	87	3	{	{	PUNCT
ejpam-6392	87	4	gi(e	gi(e	NOUN
ejpam-6392	87	5	•	•	ADP
ejpam-6392	87	6	3	3	NUM
ejpam-6392	87	7	)	)	PUNCT
ejpam-6392	87	8	,	,	PUNCT
ejpam-6392	87	9	gi(3	gi(3	PROPN
ejpam-6392	87	10	)	)	PUNCT
ejpam-6392	87	11	}	}	PUNCT
ejpam-6392	87	12	.	.	PUNCT
ejpam-6392	88	1	(	(	PUNCT
ejpam-6392	88	2	iv	iv	X
ejpam-6392	88	3	)	)	PUNCT
ejpam-6392	88	4	gf	gf	X
ejpam-6392	88	5	(	(	PUNCT
ejpam-6392	88	6	e	e	NOUN
ejpam-6392	88	7	)	)	PUNCT
ejpam-6392	88	8	≤	≤	NUM
ejpam-6392	88	9	max	max	PROPN
ejpam-6392	88	10	{	{	PUNCT
ejpam-6392	88	11	gf	gf	X
ejpam-6392	88	12	(	(	PUNCT
ejpam-6392	88	13	e	e	NOUN
ejpam-6392	88	14	•	•	NOUN
ejpam-6392	88	15	3	3	NUM
ejpam-6392	88	16	)	)	PUNCT
ejpam-6392	88	17	,	,	PUNCT
ejpam-6392	88	18	gf	gf	X
ejpam-6392	88	19	(	(	PUNCT
ejpam-6392	88	20	3	3	NUM
ejpam-6392	88	21	)	)	PUNCT
ejpam-6392	88	22	}	}	PUNCT
ejpam-6392	88	23	.	.	PUNCT
ejpam-6392	89	1	definition	definition	NOUN
ejpam-6392	89	2	2.8	2.8	NUM
ejpam-6392	89	3	.	.	PUNCT
ejpam-6392	90	1	[	[	X
ejpam-6392	90	2	6	6	NUM
ejpam-6392	90	3	]	]	PUNCT
ejpam-6392	90	4	a	a	DET
ejpam-6392	90	5	neutrosophic	neutrosophic	ADJ
ejpam-6392	90	6	set	set	NOUN
ejpam-6392	90	7	g	g	PROPN
ejpam-6392	90	8	=	=	SYM
ejpam-6392	90	9	(	(	PUNCT
ejpam-6392	90	10	gt	gt	INTJ
ejpam-6392	90	11	,	,	PUNCT
ejpam-6392	90	12	gi	gi	INTJ
ejpam-6392	90	13	,	,	PUNCT
ejpam-6392	90	14	gf	gf	NOUN
ejpam-6392	90	15	)	)	PUNCT
ejpam-6392	90	16	in	in	ADP
ejpam-6392	90	17	x	x	PROPN
ejpam-6392	90	18	is	be	AUX
ejpam-6392	90	19	termed	term	VERB
ejpam-6392	90	20	as	as	ADP
ejpam-6392	90	21	neutrosophic	neutrosophic	ADJ
ejpam-6392	90	22	ink	ink	NOUN
ejpam-6392	90	23	-	-	PUNCT
ejpam-6392	90	24	ideal	ideal	NOUN
ejpam-6392	90	25	of	of	ADP
ejpam-6392	90	26	¨̈u	¨̈u	NOUN
ejpam-6392	90	27	if	if	SCONJ
ejpam-6392	90	28	it	it	PRON
ejpam-6392	90	29	satisfies	satisfy	VERB
ejpam-6392	90	30	the	the	DET
ejpam-6392	90	31	following	follow	VERB
ejpam-6392	90	32	condition	condition	NOUN
ejpam-6392	90	33	,	,	PUNCT
ejpam-6392	90	34	for	for	ADP
ejpam-6392	90	35	all	all	DET
ejpam-6392	90	36	e	e	NOUN
ejpam-6392	90	37	,	,	PUNCT
ejpam-6392	90	38	3,ä	3,ä	PROPN
ejpam-6392	90	39	∈	∈	PROPN
ejpam-6392	90	40	¨̈u	¨̈u	NOUN
ejpam-6392	90	41	:	:	PUNCT
ejpam-6392	90	42	(	(	PUNCT
ejpam-6392	90	43	i	i	NOUN
ejpam-6392	90	44	)	)	PUNCT
ejpam-6392	90	45	gt	gt	PROPN
ejpam-6392	91	1	(	(	PUNCT
ejpam-6392	91	2	0	0	NUM
ejpam-6392	91	3	)	)	PUNCT
ejpam-6392	91	4	≥	≥	NOUN
ejpam-6392	92	1	gt	gt	INTJ
ejpam-6392	92	2	(	(	PUNCT
ejpam-6392	92	3	e	e	NOUN
ejpam-6392	92	4	)	)	PUNCT
ejpam-6392	92	5	,	,	PUNCT
ejpam-6392	92	6	gi(0	gi(0	PROPN
ejpam-6392	92	7	)	)	PUNCT
ejpam-6392	92	8	≤	≤	NUM
ejpam-6392	92	9	gi(e	gi(e	NOUN
ejpam-6392	92	10	)	)	PUNCT
ejpam-6392	92	11	,	,	PUNCT
ejpam-6392	92	12	gf	gf	X
ejpam-6392	92	13	(	(	PUNCT
ejpam-6392	92	14	0	0	NUM
ejpam-6392	92	15	)	)	PUNCT
ejpam-6392	92	16	≤	≤	NOUN
ejpam-6392	92	17	gf	gf	X
ejpam-6392	92	18	(	(	PUNCT
ejpam-6392	92	19	e	e	NOUN
ejpam-6392	92	20	)	)	PUNCT
ejpam-6392	92	21	.	.	PUNCT
ejpam-6392	93	1	(	(	PUNCT
ejpam-6392	93	2	ii	ii	X
ejpam-6392	93	3	)	)	PUNCT
ejpam-6392	93	4	gt	gt	PROPN
ejpam-6392	93	5	(	(	PUNCT
ejpam-6392	93	6	e	e	NOUN
ejpam-6392	93	7	)	)	PUNCT
ejpam-6392	93	8	≥	≥	PROPN
ejpam-6392	93	9	min	min	PROPN
ejpam-6392	93	10	{	{	PUNCT
ejpam-6392	93	11	gt	gt	PROPN
ejpam-6392	93	12	(	(	PUNCT
ejpam-6392	93	13	(	(	PUNCT
ejpam-6392	93	14	ä	ä	NOUN
ejpam-6392	93	15	•	•	NUM
ejpam-6392	93	16	e	e	NOUN
ejpam-6392	93	17	)	)	PUNCT
ejpam-6392	93	18	•	•	NOUN
ejpam-6392	93	19	(	(	PUNCT
ejpam-6392	93	20	ä	ä	NOUN
ejpam-6392	93	21	•	•	NUM
ejpam-6392	93	22	3	3	NUM
ejpam-6392	93	23	)	)	PUNCT
ejpam-6392	93	24	)	)	PUNCT
ejpam-6392	93	25	,	,	PUNCT
ejpam-6392	93	26	gt	gt	PROPN
ejpam-6392	93	27	(	(	PUNCT
ejpam-6392	93	28	3	3	NUM
ejpam-6392	93	29	)	)	PUNCT
ejpam-6392	93	30	}	}	PUNCT
ejpam-6392	93	31	.	.	PUNCT
ejpam-6392	94	1	(	(	PUNCT
ejpam-6392	94	2	iii	iii	NOUN
ejpam-6392	94	3	)	)	PUNCT
ejpam-6392	94	4	gi(e	gi(e	NOUN
ejpam-6392	94	5	)	)	PUNCT
ejpam-6392	94	6	≤	≤	NUM
ejpam-6392	94	7	max	max	PROPN
ejpam-6392	94	8	{	{	PUNCT
ejpam-6392	94	9	gi((ä	gi((ä	PROPN
ejpam-6392	94	10	•	•	NUM
ejpam-6392	94	11	e	e	NOUN
ejpam-6392	94	12	)	)	PUNCT
ejpam-6392	94	13	•	•	NOUN
ejpam-6392	94	14	(	(	PUNCT
ejpam-6392	94	15	ä	ä	NOUN
ejpam-6392	94	16	•	•	NUM
ejpam-6392	94	17	3	3	NUM
ejpam-6392	94	18	)	)	PUNCT
ejpam-6392	94	19	)	)	PUNCT
ejpam-6392	94	20	,	,	PUNCT
ejpam-6392	94	21	gi(3	gi(3	PROPN
ejpam-6392	94	22	)	)	PUNCT
ejpam-6392	94	23	}	}	PUNCT
ejpam-6392	94	24	.	.	PUNCT
ejpam-6392	95	1	(	(	PUNCT
ejpam-6392	95	2	iv	iv	X
ejpam-6392	95	3	)	)	PUNCT
ejpam-6392	95	4	gf	gf	X
ejpam-6392	95	5	(	(	PUNCT
ejpam-6392	95	6	e	e	NOUN
ejpam-6392	95	7	)	)	PUNCT
ejpam-6392	95	8	≤	≤	NUM
ejpam-6392	95	9	max	max	PROPN
ejpam-6392	95	10	{	{	PUNCT
ejpam-6392	95	11	gf	gf	X
ejpam-6392	95	12	(	(	PUNCT
ejpam-6392	95	13	(	(	PUNCT
ejpam-6392	95	14	ä	ä	NOUN
ejpam-6392	95	15	•	•	NUM
ejpam-6392	95	16	e	e	NOUN
ejpam-6392	95	17	)	)	PUNCT
ejpam-6392	95	18	•	•	NOUN
ejpam-6392	95	19	(	(	PUNCT
ejpam-6392	95	20	ä	ä	NOUN
ejpam-6392	95	21	•	•	NUM
ejpam-6392	95	22	3	3	NUM
ejpam-6392	95	23	)	)	PUNCT
ejpam-6392	95	24	)	)	PUNCT
ejpam-6392	95	25	,	,	PUNCT
ejpam-6392	95	26	gf	gf	X
ejpam-6392	95	27	(	(	PUNCT
ejpam-6392	95	28	3	3	NUM
ejpam-6392	95	29	)	)	PUNCT
ejpam-6392	95	30	}	}	PUNCT
ejpam-6392	95	31	.	.	PUNCT
ejpam-6392	96	1	definition	definition	NOUN
ejpam-6392	96	2	2.9	2.9	NUM
ejpam-6392	96	3	.	.	PUNCT
ejpam-6392	97	1	[	[	X
ejpam-6392	97	2	6	6	NUM
ejpam-6392	97	3	]	]	PUNCT
ejpam-6392	97	4	let	let	VERB
ejpam-6392	97	5	g=(gt	g=(gt	NOUN
ejpam-6392	97	6	,	,	PUNCT
ejpam-6392	97	7	gi	gi	INTJ
ejpam-6392	97	8	,	,	PUNCT
ejpam-6392	97	9	gf	gf	PROPN
ejpam-6392	97	10	)	)	PUNCT
ejpam-6392	97	11	and	and	CCONJ
ejpam-6392	97	12	h=(ht	h=(ht	NOUN
ejpam-6392	97	13	,	,	PUNCT
ejpam-6392	97	14	hi	hi	INTJ
ejpam-6392	97	15	,	,	PUNCT
ejpam-6392	97	16	hf	hf	INTJ
ejpam-6392	97	17	)	)	PUNCT
ejpam-6392	97	18	be	be	AUX
ejpam-6392	97	19	two	two	NUM
ejpam-6392	97	20	neutrosophic	neutrosophic	ADJ
ejpam-6392	97	21	sets	set	NOUN
ejpam-6392	97	22	in	in	ADP
ejpam-6392	97	23	¨̈u	¨̈u	NOUN
ejpam-6392	97	24	,	,	PUNCT
ejpam-6392	97	25	then	then	ADV
ejpam-6392	97	26	the	the	DET
ejpam-6392	97	27	union	union	NOUN
ejpam-6392	97	28	and	and	CCONJ
ejpam-6392	97	29	intersection	intersection	NOUN
ejpam-6392	97	30	are	be	AUX
ejpam-6392	97	31	defined	define	VERB
ejpam-6392	97	32	by	by	ADP
ejpam-6392	97	33	(	(	PUNCT
ejpam-6392	97	34	i	i	NOUN
ejpam-6392	97	35	)	)	PUNCT
ejpam-6392	97	36	g	g	PROPN
ejpam-6392	97	37	∪	∪	ADJ
ejpam-6392	97	38	h	h	NOUN
ejpam-6392	97	39	(	(	PUNCT
ejpam-6392	97	40	e	e	NOUN
ejpam-6392	97	41	)	)	PUNCT
ejpam-6392	97	42	=	=	SYM
ejpam-6392	97	43	{	{	PUNCT
ejpam-6392	97	44	<	<	X
ejpam-6392	97	45	e	e	PROPN
ejpam-6392	97	46	,	,	PUNCT
ejpam-6392	97	47	max{tg(e	max{tg(e	PROPN
ejpam-6392	97	48	)	)	PUNCT
ejpam-6392	97	49	,	,	PUNCT
ejpam-6392	97	50	th(e	th(e	NUM
ejpam-6392	97	51	)	)	PUNCT
ejpam-6392	97	52	}	}	PUNCT
ejpam-6392	97	53	,	,	PUNCT
ejpam-6392	97	54	min	min	PROPN
ejpam-6392	97	55	{	{	PUNCT
ejpam-6392	97	56	i	i	PRON
ejpam-6392	97	57	g(e	g(e	PROPN
ejpam-6392	97	58	)	)	PUNCT
ejpam-6392	97	59	,	,	PUNCT
ejpam-6392	97	60	ih(e	ih(e	NOUN
ejpam-6392	97	61	)	)	PUNCT
ejpam-6392	97	62	}	}	PUNCT
ejpam-6392	97	63	,	,	PUNCT
ejpam-6392	97	64	min	min	PROPN
ejpam-6392	97	65	{	{	PUNCT
ejpam-6392	97	66	f	f	PROPN
ejpam-6392	97	67	g(e	g(e	PROPN
ejpam-6392	97	68	)	)	PUNCT
ejpam-6392	97	69	,	,	PUNCT
ejpam-6392	97	70	fh(e	fh(e	NUM
ejpam-6392	97	71	)	)	PUNCT
ejpam-6392	97	72	}	}	PUNCT
ejpam-6392	97	73	}	}	PUNCT
ejpam-6392	97	74	(	(	PUNCT
ejpam-6392	97	75	ii	ii	NOUN
ejpam-6392	97	76	)	)	PUNCT
ejpam-6392	97	77	g	g	PROPN
ejpam-6392	97	78	∩	∩	ADJ
ejpam-6392	97	79	h	h	NOUN
ejpam-6392	97	80	(	(	PUNCT
ejpam-6392	97	81	e	e	NOUN
ejpam-6392	97	82	)	)	PUNCT
ejpam-6392	97	83	=	=	SYM
ejpam-6392	97	84	{	{	PUNCT
ejpam-6392	97	85	<	<	X
ejpam-6392	97	86	e	e	NOUN
ejpam-6392	97	87	,	,	PUNCT
ejpam-6392	97	88	min{tg(e	min{tg(e	PROPN
ejpam-6392	97	89	)	)	PUNCT
ejpam-6392	97	90	,	,	PUNCT
ejpam-6392	97	91	th(e	th(e	NUM
ejpam-6392	97	92	)	)	PUNCT
ejpam-6392	97	93	}	}	PUNCT
ejpam-6392	97	94	,	,	PUNCT
ejpam-6392	97	95	max	max	PROPN
ejpam-6392	97	96	{	{	PUNCT
ejpam-6392	97	97	i	i	PROPN
ejpam-6392	97	98	g(e	g(e	PROPN
ejpam-6392	97	99	)	)	PUNCT
ejpam-6392	97	100	,	,	PUNCT
ejpam-6392	97	101	ih(e	ih(e	NOUN
ejpam-6392	97	102	)	)	PUNCT
ejpam-6392	97	103	}	}	PUNCT
ejpam-6392	97	104	,	,	PUNCT
ejpam-6392	97	105	max	max	PROPN
ejpam-6392	97	106	{	{	PUNCT
ejpam-6392	97	107	f	f	PROPN
ejpam-6392	97	108	g(e	g(e	PROPN
ejpam-6392	97	109	)	)	PUNCT
ejpam-6392	97	110	,	,	PUNCT
ejpam-6392	97	111	fh(e	fh(e	NUM
ejpam-6392	97	112	)	)	PUNCT
ejpam-6392	97	113	}	}	PUNCT
ejpam-6392	97	114	}	}	PUNCT
ejpam-6392	97	115	.	.	PUNCT
ejpam-6392	98	1	definition	definition	NOUN
ejpam-6392	98	2	2.10	2.10	NUM
ejpam-6392	98	3	.	.	PUNCT
ejpam-6392	99	1	[	[	X
ejpam-6392	99	2	8	8	X
ejpam-6392	99	3	]	]	PUNCT
ejpam-6392	99	4	a	a	DET
ejpam-6392	99	5	mapping	mapping	NOUN
ejpam-6392	99	6	¢	¢	NOUN
ejpam-6392	99	7	:	:	PUNCT
ejpam-6392	99	8	¨̈u	¨̈u	PROPN
ejpam-6392	99	9	→	→	SYM
ejpam-6392	99	10	˘̈̈	˘̈̈	PROPN
ejpam-6392	99	11	u	u	PROPN
ejpam-6392	99	12	of	of	ADP
ejpam-6392	99	13	ink	ink	NOUN
ejpam-6392	99	14	-	-	PUNCT
ejpam-6392	99	15	algebras	algebras	PROPN
ejpam-6392	99	16	is	be	AUX
ejpam-6392	99	17	known	know	VERB
ejpam-6392	99	18	as	as	ADP
ejpam-6392	99	19	homomorphism	homomorphism	NOUN
ejpam-6392	99	20	if	if	SCONJ
ejpam-6392	99	21	¢(e•	¢(e•	PROPN
ejpam-6392	99	22	3	3	NUM
ejpam-6392	99	23	)	)	PUNCT
ejpam-6392	99	24	=	=	PUNCT
ejpam-6392	99	25	¢(e	¢(e	NOUN
ejpam-6392	99	26	)	)	PUNCT
ejpam-6392	99	27	•	•	ADV
ejpam-6392	99	28	¢(3	¢(3	NOUN
ejpam-6392	99	29	)	)	PUNCT
ejpam-6392	99	30	for	for	ADP
ejpam-6392	99	31	all	all	DET
ejpam-6392	99	32	e	e	NOUN
ejpam-6392	99	33	,	,	PUNCT
ejpam-6392	99	34	3∈	3∈	PROPN
ejpam-6392	99	35	¨̈u	¨̈u	NOUN
ejpam-6392	99	36	.	.	PUNCT
ejpam-6392	100	1	if	if	SCONJ
ejpam-6392	100	2	¢	¢	NUM
ejpam-6392	100	3	:	:	PUNCT
ejpam-6392	100	4	¨̈u	¨̈u	PROPN
ejpam-6392	100	5	→	→	SYM
ejpam-6392	100	6	˘̈̈	˘̈̈	PROPN
ejpam-6392	100	7	u	u	PROPN
ejpam-6392	100	8	is	be	AUX
ejpam-6392	100	9	a	a	DET
ejpam-6392	100	10	homomorphism	homomorphism	NOUN
ejpam-6392	100	11	then	then	ADV
ejpam-6392	100	12	¢(0)=0	¢(0)=0	PROPN
ejpam-6392	100	13	.	.	PUNCT
ejpam-6392	100	14	m.	m.	NOUN
ejpam-6392	100	15	remala	remala	NOUN
ejpam-6392	100	16	,	,	PUNCT
ejpam-6392	100	17	e.	e.	PROPN
ejpam-6392	100	18	tamma	tamma	PROPN
ejpam-6392	100	19	,	,	PUNCT
ejpam-6392	100	20	y.	y.	PROPN
ejpam-6392	100	21	bhargavi	bhargavi	PROPN
ejpam-6392	100	22	/	/	SYM
ejpam-6392	100	23	eur	eur	PROPN
ejpam-6392	100	24	.	.	PUNCT
ejpam-6392	101	1	j.	j.	PROPN
ejpam-6392	101	2	pure	pure	PROPN
ejpam-6392	101	3	appl	appl	PROPN
ejpam-6392	101	4	.	.	PROPN
ejpam-6392	101	5	math	math	PROPN
ejpam-6392	101	6	,	,	PUNCT
ejpam-6392	101	7	18	18	NUM
ejpam-6392	101	8	(	(	PUNCT
ejpam-6392	101	9	4	4	NUM
ejpam-6392	101	10	)	)	PUNCT
ejpam-6392	101	11	(	(	PUNCT
ejpam-6392	101	12	2025	2025	NUM
ejpam-6392	101	13	)	)	PUNCT
ejpam-6392	101	14	,	,	PUNCT
ejpam-6392	101	15	6392	6392	NUM
ejpam-6392	101	16	5	5	NUM
ejpam-6392	101	17	of	of	ADP
ejpam-6392	101	18	20	20	NUM
ejpam-6392	101	19	3	3	NUM
ejpam-6392	101	20	.	.	PUNCT
ejpam-6392	101	21	intersection	intersection	NOUN
ejpam-6392	101	22	and	and	CCONJ
ejpam-6392	101	23	union	union	NOUN
ejpam-6392	101	24	on	on	ADP
ejpam-6392	101	25	neutrosophic	neutrosophic	ADJ
ejpam-6392	101	26	bi	bi	NOUN
ejpam-6392	101	27	-	-	ADJ
ejpam-6392	101	28	ideals	ideal	NOUN
ejpam-6392	101	29	definition	definition	NOUN
ejpam-6392	101	30	3.1	3.1	NUM
ejpam-6392	101	31	.	.	PUNCT
ejpam-6392	102	1	an	an	DET
ejpam-6392	102	2	ink	ink	NOUN
ejpam-6392	102	3	-	-	PUNCT
ejpam-6392	102	4	algebra	algebra	NOUN
ejpam-6392	102	5	¨̈u	¨̈u	NOUN
ejpam-6392	102	6	is	be	AUX
ejpam-6392	102	7	said	say	VERB
ejpam-6392	102	8	to	to	PART
ejpam-6392	102	9	be	be	AUX
ejpam-6392	102	10	associative	associative	ADJ
ejpam-6392	102	11	ink	ink	NOUN
ejpam-6392	102	12	algebra	algebra	NOUN
ejpam-6392	102	13	if	if	SCONJ
ejpam-6392	102	14	it	it	PRON
ejpam-6392	102	15	satisfies	satisfy	VERB
ejpam-6392	102	16	(	(	PUNCT
ejpam-6392	102	17	e•	e•	NOUN
ejpam-6392	102	18	3)•ä=	3)•ä=	NUM
ejpam-6392	102	19	e•	e•	NOUN
ejpam-6392	102	20	(	(	PUNCT
ejpam-6392	102	21	3•ä	3•ä	NOUN
ejpam-6392	102	22	)	)	PUNCT
ejpam-6392	102	23	definition	definition	NOUN
ejpam-6392	102	24	3.2	3.2	NUM
ejpam-6392	102	25	.	.	PUNCT
ejpam-6392	103	1	let	let	VERB
ejpam-6392	103	2	f	f	PRON
ejpam-6392	103	3	be	be	AUX
ejpam-6392	103	4	a	a	DET
ejpam-6392	103	5	non	non	ADJ
ejpam-6392	103	6	-	-	ADJ
ejpam-6392	103	7	empty	empty	ADJ
ejpam-6392	103	8	subset	subset	NOUN
ejpam-6392	103	9	of	of	ADP
ejpam-6392	103	10	a	a	DET
ejpam-6392	103	11	ink	ink	NOUN
ejpam-6392	103	12	algebra	algebra	NOUN
ejpam-6392	103	13	¨̈u	¨̈u	VERB
ejpam-6392	103	14	.	.	PUNCT
ejpam-6392	104	1	then	then	ADV
ejpam-6392	104	2	f	f	PROPN
ejpam-6392	104	3	is	be	AUX
ejpam-6392	104	4	defined	define	VERB
ejpam-6392	104	5	as	as	ADP
ejpam-6392	104	6	bi	bi	NOUN
ejpam-6392	104	7	-	-	NOUN
ejpam-6392	104	8	ideal	ideal	NOUN
ejpam-6392	104	9	of	of	ADP
ejpam-6392	104	10	ink	ink	NOUN
ejpam-6392	104	11	-	-	PUNCT
ejpam-6392	104	12	algebra	algebra	NOUN
ejpam-6392	104	13	¨̈u	¨̈u	VERB
ejpam-6392	104	14	if	if	SCONJ
ejpam-6392	104	15	(	(	PUNCT
ejpam-6392	104	16	i	i	NOUN
ejpam-6392	104	17	)	)	PUNCT
ejpam-6392	104	18	0	0	PUNCT
ejpam-6392	105	1	∈	∈	PROPN
ejpam-6392	105	2	f	f	X
ejpam-6392	105	3	,	,	PUNCT
ejpam-6392	105	4	(	(	PUNCT
ejpam-6392	105	5	ii	ii	NOUN
ejpam-6392	105	6	)	)	PUNCT
ejpam-6392	105	7	e•	e•	NOUN
ejpam-6392	105	8	3•	3•	NUM
ejpam-6392	105	9	ä∈	ä∈	NOUN
ejpam-6392	105	10	f	f	PROPN
ejpam-6392	105	11	and	and	CCONJ
ejpam-6392	105	12	ä∈	ä∈	PROPN
ejpam-6392	106	1	f	f	X
ejpam-6392	106	2	imply	imply	VERB
ejpam-6392	106	3	that	that	DET
ejpam-6392	106	4	e•	e•	VERB
ejpam-6392	106	5	3∈	3∈	PROPN
ejpam-6392	106	6	f	f	PROPN
ejpam-6392	106	7	for	for	ADP
ejpam-6392	106	8	all	all	DET
ejpam-6392	106	9	e	e	NOUN
ejpam-6392	106	10	,	,	PUNCT
ejpam-6392	106	11	3	3	NUM
ejpam-6392	106	12	,	,	PUNCT
ejpam-6392	106	13	ä∈	ä∈	NOUN
ejpam-6392	106	14	¨̈u	¨̈u	NOUN
ejpam-6392	106	15	.	.	PUNCT
ejpam-6392	107	1	definition	definition	NOUN
ejpam-6392	107	2	3.3	3.3	NUM
ejpam-6392	107	3	.	.	PUNCT
ejpam-6392	108	1	a	a	DET
ejpam-6392	108	2	neutrosophic	neutrosophic	ADJ
ejpam-6392	108	3	set	set	VERB
ejpam-6392	108	4	g=(gt	g=(gt	NOUN
ejpam-6392	108	5	,	,	PUNCT
ejpam-6392	108	6	gi	gi	INTJ
ejpam-6392	108	7	,	,	PUNCT
ejpam-6392	108	8	gf	gf	PROPN
ejpam-6392	108	9	)	)	PUNCT
ejpam-6392	108	10	is	be	AUX
ejpam-6392	108	11	called	call	VERB
ejpam-6392	108	12	a	a	DET
ejpam-6392	108	13	neutrosophic	neutrosophic	ADJ
ejpam-6392	108	14	bi	bi	NOUN
ejpam-6392	108	15	-	-	NOUN
ejpam-6392	108	16	ideal	ideal	NOUN
ejpam-6392	108	17	of	of	ADP
ejpam-6392	108	18	ink	ink	NOUN
ejpam-6392	108	19	-	-	PUNCT
ejpam-6392	108	20	algebra	algebra	NOUN
ejpam-6392	108	21	¨̈u	¨̈u	NOUN
ejpam-6392	108	22	if	if	SCONJ
ejpam-6392	108	23	it	it	PRON
ejpam-6392	108	24	satisfies	satisfy	VERB
ejpam-6392	108	25	(	(	PUNCT
ejpam-6392	108	26	i	i	NOUN
ejpam-6392	108	27	)	)	PUNCT
ejpam-6392	108	28	gt	gt	PROPN
ejpam-6392	108	29	(	(	PUNCT
ejpam-6392	108	30	0	0	NUM
ejpam-6392	108	31	)	)	PUNCT
ejpam-6392	108	32	≥	≥	NOUN
ejpam-6392	108	33	gt	gt	INTJ
ejpam-6392	108	34	(	(	PUNCT
ejpam-6392	108	35	e	e	NOUN
ejpam-6392	108	36	)	)	PUNCT
ejpam-6392	108	37	,	,	PUNCT
ejpam-6392	108	38	gi(0	gi(0	PROPN
ejpam-6392	108	39	)	)	PUNCT
ejpam-6392	108	40	≤	≤	NUM
ejpam-6392	108	41	gi(e	gi(e	NOUN
ejpam-6392	108	42	)	)	PUNCT
ejpam-6392	108	43	,	,	PUNCT
ejpam-6392	108	44	gf	gf	X
ejpam-6392	108	45	(	(	PUNCT
ejpam-6392	108	46	0	0	NUM
ejpam-6392	108	47	)	)	PUNCT
ejpam-6392	108	48	≤	≤	NOUN
ejpam-6392	108	49	gf	gf	X
ejpam-6392	108	50	(	(	PUNCT
ejpam-6392	108	51	e	e	NOUN
ejpam-6392	108	52	)	)	PUNCT
ejpam-6392	108	53	(	(	PUNCT
ejpam-6392	108	54	ii	ii	NOUN
ejpam-6392	108	55	)	)	PUNCT
ejpam-6392	108	56	gt	gt	PROPN
ejpam-6392	108	57	(	(	PUNCT
ejpam-6392	108	58	e•	e•	NOUN
ejpam-6392	108	59	3	3	NUM
ejpam-6392	108	60	)	)	PUNCT
ejpam-6392	108	61	≥	≥	NOUN
ejpam-6392	108	62	min	min	PROPN
ejpam-6392	108	63	{	{	PUNCT
ejpam-6392	108	64	gt	gt	PROPN
ejpam-6392	108	65	(	(	PUNCT
ejpam-6392	108	66	e•	e•	PROPN
ejpam-6392	108	67	3•	3•	NUM
ejpam-6392	108	68	ä	ä	NOUN
ejpam-6392	108	69	)	)	PUNCT
ejpam-6392	108	70	,	,	PUNCT
ejpam-6392	108	71	gt	gt	PROPN
ejpam-6392	108	72	(	(	PUNCT
ejpam-6392	108	73	ä	ä	NOUN
ejpam-6392	108	74	)	)	PUNCT
ejpam-6392	108	75	}	}	PUNCT
ejpam-6392	108	76	.	.	PUNCT
ejpam-6392	109	1	(	(	PUNCT
ejpam-6392	109	2	iii	iii	X
ejpam-6392	109	3	)	)	PUNCT
ejpam-6392	109	4	gi(e•	gi(e•	PROPN
ejpam-6392	109	5	3	3	X
ejpam-6392	109	6	)	)	PUNCT
ejpam-6392	109	7	≤	≤	NUM
ejpam-6392	109	8	max	max	PROPN
ejpam-6392	109	9	{	{	PUNCT
ejpam-6392	109	10	gi(e•	gi(e•	PROPN
ejpam-6392	109	11	3•	3•	NUM
ejpam-6392	109	12	ä	ä	NOUN
ejpam-6392	109	13	)	)	PUNCT
ejpam-6392	109	14	,	,	PUNCT
ejpam-6392	109	15	gi(ä	gi(ä	NOUN
ejpam-6392	109	16	)	)	PUNCT
ejpam-6392	109	17	}	}	PUNCT
ejpam-6392	109	18	.	.	PUNCT
ejpam-6392	110	1	(	(	PUNCT
ejpam-6392	110	2	iv	iv	X
ejpam-6392	110	3	)	)	PUNCT
ejpam-6392	110	4	gf	gf	NOUN
ejpam-6392	110	5	(	(	PUNCT
ejpam-6392	110	6	e•	e•	NOUN
ejpam-6392	110	7	3	3	NUM
ejpam-6392	110	8	)	)	PUNCT
ejpam-6392	110	9	≤	≤	NUM
ejpam-6392	110	10	max	max	PROPN
ejpam-6392	110	11	{	{	PUNCT
ejpam-6392	110	12	gf	gf	PROPN
ejpam-6392	110	13	(	(	PUNCT
ejpam-6392	110	14	e•	e•	VERB
ejpam-6392	110	15	3•	3•	NUM
ejpam-6392	110	16	ä	ä	NOUN
ejpam-6392	110	17	)	)	PUNCT
ejpam-6392	110	18	,	,	PUNCT
ejpam-6392	110	19	gf	gf	X
ejpam-6392	110	20	(	(	PUNCT
ejpam-6392	110	21	ä	ä	NOUN
ejpam-6392	110	22	)	)	PUNCT
ejpam-6392	110	23	}	}	PUNCT
ejpam-6392	110	24	for	for	ADP
ejpam-6392	110	25	all	all	DET
ejpam-6392	110	26	e	e	NOUN
ejpam-6392	110	27	,	,	PUNCT
ejpam-6392	110	28	3	3	NUM
ejpam-6392	110	29	,	,	PUNCT
ejpam-6392	110	30	ä∈	ä∈	NOUN
ejpam-6392	110	31	¨̈u	¨̈u	PROPN
ejpam-6392	110	32	.	.	PUNCT
ejpam-6392	111	1	example	example	NOUN
ejpam-6392	111	2	3.1	3.1	NUM
ejpam-6392	111	3	.	.	PUNCT
ejpam-6392	111	4	consider	consider	VERB
ejpam-6392	111	5	ink	ink	NOUN
ejpam-6392	111	6	-	-	PUNCT
ejpam-6392	111	7	algebra	algebra	NOUN
ejpam-6392	111	8	¨̈u={0	¨̈u={0	PROPN
ejpam-6392	111	9	,	,	PUNCT
ejpam-6392	111	10	2	2	NUM
ejpam-6392	111	11	,	,	PUNCT
ejpam-6392	111	12	4	4	NUM
ejpam-6392	111	13	,	,	PUNCT
ejpam-6392	111	14	6	6	NUM
ejpam-6392	111	15	}	}	PUNCT
ejpam-6392	111	16	with	with	ADP
ejpam-6392	111	17	cayley	cayley	ADJ
ejpam-6392	111	18	table	table	NOUN
ejpam-6392	111	19	•	•	NOUN
ejpam-6392	111	20	0	0	NUM
ejpam-6392	111	21	2	2	NUM
ejpam-6392	111	22	4	4	NUM
ejpam-6392	111	23	6	6	NUM
ejpam-6392	111	24	0	0	NUM
ejpam-6392	111	25	0	0	NUM
ejpam-6392	111	26	0	0	NUM
ejpam-6392	111	27	0	0	NUM
ejpam-6392	111	28	0	0	NUM
ejpam-6392	111	29	2	2	NUM
ejpam-6392	111	30	2	2	NUM
ejpam-6392	111	31	0	0	NUM
ejpam-6392	111	32	0	0	NUM
ejpam-6392	111	33	2	2	NUM
ejpam-6392	111	34	4	4	NUM
ejpam-6392	111	35	4	4	NUM
ejpam-6392	111	36	2	2	NUM
ejpam-6392	111	37	0	0	NUM
ejpam-6392	111	38	4	4	NUM
ejpam-6392	111	39	6	6	NUM
ejpam-6392	111	40	6	6	NUM
ejpam-6392	111	41	6	6	NUM
ejpam-6392	111	42	6	6	NUM
ejpam-6392	111	43	0	0	NUM
ejpam-6392	111	44	•	•	NUM
ejpam-6392	111	45	0	0	NUM
ejpam-6392	111	46	2	2	NUM
ejpam-6392	111	47	4	4	NUM
ejpam-6392	111	48	6	6	NUM
ejpam-6392	111	49	gt	gt	PROPN
ejpam-6392	111	50	0.8	0.8	NUM
ejpam-6392	111	51	0.7	0.7	NUM
ejpam-6392	111	52	0.6	0.6	NUM
ejpam-6392	111	53	0.5	0.5	NUM
ejpam-6392	111	54	gi	gi	NOUN
ejpam-6392	111	55	0.7	0.7	NUM
ejpam-6392	111	56	0.8	0.8	NUM
ejpam-6392	111	57	0.8	0.8	NUM
ejpam-6392	111	58	0.9	0.9	NUM
ejpam-6392	111	59	gf	gf	NOUN
ejpam-6392	111	60	0.4	0.4	NUM
ejpam-6392	111	61	0.5	0.5	NUM
ejpam-6392	111	62	0.5	0.5	NUM
ejpam-6392	111	63	0.8	0.8	NUM
ejpam-6392	111	64	let	let	VERB
ejpam-6392	111	65	us	we	PRON
ejpam-6392	111	66	take	take	VERB
ejpam-6392	111	67	(	(	PUNCT
ejpam-6392	111	68	randomly	randomly	ADV
ejpam-6392	111	69	)	)	PUNCT
ejpam-6392	111	70	e=	e=	X
ejpam-6392	111	71	0	0	NUM
ejpam-6392	111	72	,	,	PUNCT
ejpam-6392	111	73	3=	3=	NUM
ejpam-6392	111	74	4	4	NUM
ejpam-6392	111	75	,	,	PUNCT
ejpam-6392	111	76	ä=	ä=	ADV
ejpam-6392	111	77	6	6	NUM
ejpam-6392	111	78	.	.	PUNCT
ejpam-6392	112	1	so	so	ADV
ejpam-6392	112	2	,	,	PUNCT
ejpam-6392	112	3	gt	gt	PROPN
ejpam-6392	112	4	(	(	PUNCT
ejpam-6392	112	5	0	0	NUM
ejpam-6392	112	6	•	•	NUM
ejpam-6392	112	7	4	4	NUM
ejpam-6392	112	8	)	)	PUNCT
ejpam-6392	112	9	≥	≥	NOUN
ejpam-6392	112	10	min	min	PROPN
ejpam-6392	112	11	{	{	PUNCT
ejpam-6392	112	12	gt	gt	PROPN
ejpam-6392	112	13	(	(	PUNCT
ejpam-6392	112	14	0	0	NUM
ejpam-6392	112	15	•	•	NUM
ejpam-6392	112	16	4	4	NUM
ejpam-6392	112	17	•	•	NOUN
ejpam-6392	112	18	6	6	NUM
ejpam-6392	112	19	)	)	PUNCT
ejpam-6392	112	20	,	,	PUNCT
ejpam-6392	112	21	gt	gt	PROPN
ejpam-6392	112	22	(	(	PUNCT
ejpam-6392	112	23	6	6	NUM
ejpam-6392	112	24	)	)	PUNCT
ejpam-6392	112	25	}	}	PUNCT
ejpam-6392	112	26	gt	gt	PROPN
ejpam-6392	112	27	(	(	PUNCT
ejpam-6392	112	28	0	0	NUM
ejpam-6392	112	29	)	)	PUNCT
ejpam-6392	112	30	≥	≥	PROPN
ejpam-6392	112	31	min	min	PROPN
ejpam-6392	112	32	{	{	PUNCT
ejpam-6392	112	33	gt	gt	PROPN
ejpam-6392	112	34	(	(	PUNCT
ejpam-6392	112	35	0	0	NUM
ejpam-6392	112	36	)	)	PUNCT
ejpam-6392	112	37	,	,	PUNCT
ejpam-6392	112	38	gt	gt	PROPN
ejpam-6392	112	39	(	(	PUNCT
ejpam-6392	112	40	6	6	NUM
ejpam-6392	112	41	)	)	PUNCT
ejpam-6392	112	42	}	}	PUNCT
ejpam-6392	112	43	=	=	PUNCT
ejpam-6392	112	44	0.8	0.8	NUM
ejpam-6392	112	45	>	>	SYM
ejpam-6392	112	46	0.5	0.5	NUM
ejpam-6392	112	47	also	also	ADV
ejpam-6392	112	48	,	,	PUNCT
ejpam-6392	112	49	gi(0	gi(0	PROPN
ejpam-6392	112	50	•	•	ADJ
ejpam-6392	112	51	4	4	NUM
ejpam-6392	112	52	)	)	PUNCT
ejpam-6392	112	53	≤	≤	NUM
ejpam-6392	112	54	max	max	PROPN
ejpam-6392	112	55	{	{	PUNCT
ejpam-6392	112	56	gi(0	gi(0	PROPN
ejpam-6392	112	57	•	•	ADV
ejpam-6392	112	58	4	4	NUM
ejpam-6392	112	59	•	•	NOUN
ejpam-6392	112	60	6	6	NUM
ejpam-6392	112	61	)	)	PUNCT
ejpam-6392	112	62	,	,	PUNCT
ejpam-6392	112	63	gi(6	gi(6	NOUN
ejpam-6392	112	64	)	)	PUNCT
ejpam-6392	112	65	}	}	PUNCT
ejpam-6392	112	66	gi(0	gi(0	NOUN
ejpam-6392	112	67	)	)	PUNCT
ejpam-6392	112	68	≤	≤	NUM
ejpam-6392	112	69	max	max	PROPN
ejpam-6392	112	70	{	{	PUNCT
ejpam-6392	112	71	gi(0	gi(0	PROPN
ejpam-6392	112	72	)	)	PUNCT
ejpam-6392	112	73	,	,	PUNCT
ejpam-6392	112	74	gi(6	gi(6	NOUN
ejpam-6392	112	75	)	)	PUNCT
ejpam-6392	112	76	}	}	PUNCT
ejpam-6392	112	77	=	=	PUNCT
ejpam-6392	112	78	0.7	0.7	NUM
ejpam-6392	112	79	<	<	X
ejpam-6392	112	80	0.9	0.9	NUM
ejpam-6392	112	81	similarly	similarly	ADV
ejpam-6392	112	82	,	,	PUNCT
ejpam-6392	112	83	gf	gf	X
ejpam-6392	112	84	(	(	PUNCT
ejpam-6392	112	85	0	0	NUM
ejpam-6392	112	86	•	•	NUM
ejpam-6392	112	87	4	4	NUM
ejpam-6392	112	88	)	)	PUNCT
ejpam-6392	112	89	≤	≤	NUM
ejpam-6392	112	90	max	max	PROPN
ejpam-6392	112	91	{	{	PUNCT
ejpam-6392	112	92	gf	gf	X
ejpam-6392	112	93	(	(	PUNCT
ejpam-6392	112	94	0	0	NUM
ejpam-6392	112	95	•	•	NUM
ejpam-6392	112	96	4	4	NUM
ejpam-6392	112	97	•	•	NOUN
ejpam-6392	112	98	6	6	NUM
ejpam-6392	112	99	)	)	PUNCT
ejpam-6392	112	100	,	,	PUNCT
ejpam-6392	112	101	gf	gf	X
ejpam-6392	112	102	(	(	PUNCT
ejpam-6392	112	103	6	6	NUM
ejpam-6392	112	104	)	)	PUNCT
ejpam-6392	112	105	}	}	PUNCT
ejpam-6392	112	106	gf	gf	X
ejpam-6392	112	107	(	(	PUNCT
ejpam-6392	112	108	0	0	NUM
ejpam-6392	112	109	)	)	PUNCT
ejpam-6392	112	110	≤	≤	NUM
ejpam-6392	112	111	max	max	PROPN
ejpam-6392	112	112	{	{	PUNCT
ejpam-6392	112	113	gf	gf	X
ejpam-6392	112	114	(	(	PUNCT
ejpam-6392	112	115	0	0	NUM
ejpam-6392	112	116	)	)	PUNCT
ejpam-6392	112	117	,	,	PUNCT
ejpam-6392	112	118	gf	gf	X
ejpam-6392	112	119	(	(	PUNCT
ejpam-6392	112	120	6	6	NUM
ejpam-6392	112	121	)	)	PUNCT
ejpam-6392	112	122	}	}	PUNCT
ejpam-6392	112	123	=	=	PUNCT
ejpam-6392	112	124	0.4	0.4	NUM
ejpam-6392	112	125	<	<	X
ejpam-6392	112	126	0.8	0.8	NUM
ejpam-6392	112	127	likely	likely	ADV
ejpam-6392	112	128	,	,	PUNCT
ejpam-6392	112	129	for	for	SCONJ
ejpam-6392	112	130	all	all	DET
ejpam-6392	112	131	outcomes	outcome	NOUN
ejpam-6392	112	132	neytrosophic	neytrosophic	ADJ
ejpam-6392	112	133	bi	bi	ADJ
ejpam-6392	112	134	-	-	ADJ
ejpam-6392	112	135	ideal	ideal	ADJ
ejpam-6392	112	136	condition	condition	NOUN
ejpam-6392	112	137	satisfied	satisfied	ADJ
ejpam-6392	112	138	.	.	PUNCT
ejpam-6392	113	1	then	then	ADV
ejpam-6392	113	2	g=(gt	g=(gt	VERB
ejpam-6392	113	3	,	,	PUNCT
ejpam-6392	113	4	gi	gi	INTJ
ejpam-6392	113	5	,	,	PUNCT
ejpam-6392	113	6	gf	gf	PROPN
ejpam-6392	113	7	)	)	PUNCT
ejpam-6392	113	8	be	be	AUX
ejpam-6392	113	9	neutrosophic	neutrosophic	ADJ
ejpam-6392	113	10	bi	bi	NOUN
ejpam-6392	113	11	-	-	NOUN
ejpam-6392	113	12	ideal	ideal	NOUN
ejpam-6392	113	13	of	of	ADP
ejpam-6392	113	14	ink	ink	NOUN
ejpam-6392	113	15	-	-	PUNCT
ejpam-6392	113	16	algebra	algebra	NOUN
ejpam-6392	113	17	of	of	ADP
ejpam-6392	113	18	¨̈u	¨̈u	NOUN
ejpam-6392	113	19	.	.	PUNCT
ejpam-6392	114	1	lemma	lemma	PROPN
ejpam-6392	114	2	3.1	3.1	NUM
ejpam-6392	114	3	.	.	PUNCT
ejpam-6392	115	1	let	let	VERB
ejpam-6392	115	2	neutrosophic	neutrosophic	ADJ
ejpam-6392	115	3	set	set	VERB
ejpam-6392	115	4	g=(gt	g=(gt	NOUN
ejpam-6392	115	5	,	,	PUNCT
ejpam-6392	115	6	gi	gi	INTJ
ejpam-6392	115	7	,	,	PUNCT
ejpam-6392	115	8	gf	gf	PROPN
ejpam-6392	115	9	)	)	PUNCT
ejpam-6392	115	10	in	in	ADP
ejpam-6392	115	11	ink	ink	NOUN
ejpam-6392	115	12	-	-	PUNCT
ejpam-6392	115	13	algebra	algebra	NOUN
ejpam-6392	115	14	¨̈u	¨̈u	NOUN
ejpam-6392	115	15	is	be	AUX
ejpam-6392	115	16	an	an	DET
ejpam-6392	115	17	neutrosophic	neutrosophic	ADJ
ejpam-6392	115	18	bi	bi	NOUN
ejpam-6392	115	19	-	-	NOUN
ejpam-6392	115	20	ideal	ideal	NOUN
ejpam-6392	115	21	of	of	ADP
ejpam-6392	115	22	¨̈u	¨̈u	NOUN
ejpam-6392	115	23	.	.	PUNCT
ejpam-6392	116	1	if	if	SCONJ
ejpam-6392	116	2	the	the	DET
ejpam-6392	116	3	inequality	inequality	NOUN
ejpam-6392	116	4	e•	e•	VERB
ejpam-6392	116	5	3≤	3≤	NUM
ejpam-6392	116	6	äholds	ähold	NOUN
ejpam-6392	116	7	in	in	ADP
ejpam-6392	116	8	¨̈u	¨̈u	NOUN
ejpam-6392	116	9	,	,	PUNCT
ejpam-6392	116	10	then	then	ADV
ejpam-6392	116	11	m.	m.	NOUN
ejpam-6392	116	12	remala	remala	NOUN
ejpam-6392	116	13	,	,	PUNCT
ejpam-6392	116	14	e.	e.	PROPN
ejpam-6392	116	15	tamma	tamma	PROPN
ejpam-6392	116	16	,	,	PUNCT
ejpam-6392	116	17	y.	y.	PROPN
ejpam-6392	116	18	bhargavi	bhargavi	PROPN
ejpam-6392	116	19	/	/	SYM
ejpam-6392	116	20	eur	eur	PROPN
ejpam-6392	116	21	.	.	PUNCT
ejpam-6392	117	1	j.	j.	PROPN
ejpam-6392	117	2	pure	pure	PROPN
ejpam-6392	117	3	appl	appl	PROPN
ejpam-6392	117	4	.	.	PROPN
ejpam-6392	117	5	math	math	PROPN
ejpam-6392	117	6	,	,	PUNCT
ejpam-6392	117	7	18	18	NUM
ejpam-6392	117	8	(	(	PUNCT
ejpam-6392	117	9	4	4	NUM
ejpam-6392	117	10	)	)	PUNCT
ejpam-6392	117	11	(	(	PUNCT
ejpam-6392	117	12	2025	2025	NUM
ejpam-6392	117	13	)	)	PUNCT
ejpam-6392	117	14	,	,	PUNCT
ejpam-6392	117	15	6392	6392	NUM
ejpam-6392	117	16	6	6	NUM
ejpam-6392	117	17	of	of	ADP
ejpam-6392	117	18	20	20	NUM
ejpam-6392	117	19	(	(	PUNCT
ejpam-6392	117	20	i	i	NOUN
ejpam-6392	117	21	)	)	PUNCT
ejpam-6392	117	22	gt	gt	PROPN
ejpam-6392	117	23	(	(	PUNCT
ejpam-6392	117	24	e•	e•	NOUN
ejpam-6392	117	25	3	3	NUM
ejpam-6392	117	26	)	)	PUNCT
ejpam-6392	117	27	≥	≥	NOUN
ejpam-6392	117	28	min	min	PROPN
ejpam-6392	117	29	{	{	PUNCT
ejpam-6392	117	30	gt	gt	PROPN
ejpam-6392	117	31	(	(	PUNCT
ejpam-6392	117	32	e	e	NOUN
ejpam-6392	117	33	)	)	PUNCT
ejpam-6392	117	34	,	,	PUNCT
ejpam-6392	117	35	gt	gt	PROPN
ejpam-6392	117	36	(	(	PUNCT
ejpam-6392	117	37	ä	ä	NOUN
ejpam-6392	117	38	)	)	PUNCT
ejpam-6392	117	39	}	}	PUNCT
ejpam-6392	117	40	.	.	PUNCT
ejpam-6392	118	1	(	(	PUNCT
ejpam-6392	118	2	ii	ii	NOUN
ejpam-6392	118	3	)	)	PUNCT
ejpam-6392	118	4	gi(e•	gi(e•	PROPN
ejpam-6392	118	5	3	3	X
ejpam-6392	118	6	)	)	PUNCT
ejpam-6392	118	7	≤	≤	NUM
ejpam-6392	118	8	max	max	PROPN
ejpam-6392	118	9	{	{	PUNCT
ejpam-6392	118	10	gi	gi	X
ejpam-6392	118	11	(	(	PUNCT
ejpam-6392	118	12	e	e	NOUN
ejpam-6392	118	13	)	)	PUNCT
ejpam-6392	118	14	,	,	PUNCT
ejpam-6392	118	15	gi	gi	INTJ
ejpam-6392	118	16	(	(	PUNCT
ejpam-6392	118	17	ä	ä	NOUN
ejpam-6392	118	18	)	)	PUNCT
ejpam-6392	118	19	}	}	PUNCT
ejpam-6392	118	20	.	.	PUNCT
ejpam-6392	119	1	(	(	PUNCT
ejpam-6392	119	2	iii	iii	X
ejpam-6392	119	3	)	)	PUNCT
ejpam-6392	119	4	gf	gf	NOUN
ejpam-6392	119	5	(	(	PUNCT
ejpam-6392	119	6	e•	e•	NOUN
ejpam-6392	119	7	3	3	NUM
ejpam-6392	119	8	)	)	PUNCT
ejpam-6392	119	9	≤	≤	NUM
ejpam-6392	119	10	max	max	PROPN
ejpam-6392	119	11	{	{	PUNCT
ejpam-6392	119	12	gf	gf	X
ejpam-6392	119	13	(	(	PUNCT
ejpam-6392	119	14	e	e	NOUN
ejpam-6392	119	15	)	)	PUNCT
ejpam-6392	119	16	,	,	PUNCT
ejpam-6392	119	17	gf	gf	X
ejpam-6392	119	18	(	(	PUNCT
ejpam-6392	119	19	ä	ä	NOUN
ejpam-6392	119	20	)	)	PUNCT
ejpam-6392	119	21	}	}	PUNCT
ejpam-6392	119	22	.	.	PUNCT
ejpam-6392	120	1	proof	proof	NOUN
ejpam-6392	120	2	.	.	PUNCT
ejpam-6392	121	1	let	let	VERB
ejpam-6392	121	2	e	e	NOUN
ejpam-6392	121	3	,	,	PUNCT
ejpam-6392	121	4	3	3	NUM
ejpam-6392	121	5	,	,	PUNCT
ejpam-6392	121	6	ä∈	ä∈	NOUN
ejpam-6392	121	7	¨̈u	¨̈u	NOUN
ejpam-6392	121	8	be	be	VERB
ejpam-6392	121	9	such	such	ADJ
ejpam-6392	121	10	that	that	DET
ejpam-6392	121	11	e•	e•	PROPN
ejpam-6392	121	12	3≤	3≤	NUM
ejpam-6392	121	13	ä.	ä.	NOUN
ejpam-6392	121	14	by	by	ADP
ejpam-6392	121	15	the	the	DET
ejpam-6392	121	16	definition	definition	NOUN
ejpam-6392	121	17	of	of	ADP
ejpam-6392	121	18	partial	partial	ADJ
ejpam-6392	121	19	order	order	NOUN
ejpam-6392	121	20	in	in	ADP
ejpam-6392	121	21	ink	ink	NOUN
ejpam-6392	121	22	algebra	algebra	NOUN
ejpam-6392	121	23	.	.	PUNCT
ejpam-6392	122	1	we	we	PRON
ejpam-6392	122	2	have	have	VERB
ejpam-6392	122	3	e•	e•	NOUN
ejpam-6392	122	4	3≤	3≤	NUM
ejpam-6392	122	5	ä=⇒	ä=⇒	PROPN
ejpam-6392	122	6	(	(	PUNCT
ejpam-6392	122	7	e•	e•	NOUN
ejpam-6392	122	8	3	3	NUM
ejpam-6392	122	9	)	)	PUNCT
ejpam-6392	122	10	•	•	NOUN
ejpam-6392	123	1	ä=0	ä=0	NOUN
ejpam-6392	123	2	=	=	NOUN
ejpam-6392	123	3	⇒	⇒	NOUN
ejpam-6392	123	4	e•	e•	NOUN
ejpam-6392	123	5	3•	3•	NUM
ejpam-6392	123	6	ä=0	ä=0	PROPN
ejpam-6392	123	7	.	.	PUNCT
ejpam-6392	124	1	since	since	SCONJ
ejpam-6392	124	2	g=(gt	g=(gt	NOUN
ejpam-6392	124	3	,	,	PUNCT
ejpam-6392	124	4	gi	gi	INTJ
ejpam-6392	124	5	,	,	PUNCT
ejpam-6392	124	6	gf	gf	PROPN
ejpam-6392	124	7	)	)	PUNCT
ejpam-6392	124	8	is	be	AUX
ejpam-6392	124	9	an	an	DET
ejpam-6392	124	10	neutrosophic	neutrosophic	ADJ
ejpam-6392	124	11	bi	bi	NOUN
ejpam-6392	124	12	-	-	NOUN
ejpam-6392	124	13	ideal	ideal	NOUN
ejpam-6392	124	14	of	of	ADP
ejpam-6392	124	15	ink	ink	NOUN
ejpam-6392	124	16	algebra	algebra	NOUN
ejpam-6392	124	17	¨̈u	¨̈u	VERB
ejpam-6392	124	18	,	,	PUNCT
ejpam-6392	124	19	by	by	ADP
ejpam-6392	124	20	def	def	PROPN
ejpam-6392	124	21	3.3.1	3.3.1	NUM
ejpam-6392	124	22	it	it	PRON
ejpam-6392	124	23	satisfies	satisfy	VERB
ejpam-6392	124	24	the	the	DET
ejpam-6392	124	25	following	follow	VERB
ejpam-6392	124	26	conditions	condition	NOUN
ejpam-6392	124	27	for	for	ADP
ejpam-6392	124	28	all	all	DET
ejpam-6392	124	29	e	e	NOUN
ejpam-6392	124	30	,	,	PUNCT
ejpam-6392	124	31	3	3	NUM
ejpam-6392	124	32	,	,	PUNCT
ejpam-6392	124	33	ä∈	ä∈	NOUN
ejpam-6392	124	34	¨̈u	¨̈u	NOUN
ejpam-6392	124	35	now	now	ADV
ejpam-6392	124	36	gt	gt	INTJ
ejpam-6392	125	1	(	(	PUNCT
ejpam-6392	125	2	e	e	NOUN
ejpam-6392	125	3	•	•	NOUN
ejpam-6392	125	4	3	3	NUM
ejpam-6392	125	5	)	)	PUNCT
ejpam-6392	125	6	≥	≥	NOUN
ejpam-6392	125	7	min{gt	min{gt	X
ejpam-6392	125	8	(	(	PUNCT
ejpam-6392	125	9	e	e	NOUN
ejpam-6392	125	10	•	•	NOUN
ejpam-6392	125	11	3	3	NUM
ejpam-6392	125	12	•	•	NUM
ejpam-6392	125	13	ä	ä	PROPN
ejpam-6392	125	14	)	)	PUNCT
ejpam-6392	125	15	,	,	PUNCT
ejpam-6392	125	16	gt	gt	PROPN
ejpam-6392	125	17	(	(	PUNCT
ejpam-6392	125	18	ä	ä	NOUN
ejpam-6392	125	19	)	)	PUNCT
ejpam-6392	125	20	}	}	PUNCT
ejpam-6392	125	21	(	(	PUNCT
ejpam-6392	125	22	3.1	3.1	NUM
ejpam-6392	125	23	)	)	PUNCT
ejpam-6392	125	24	since	since	SCONJ
ejpam-6392	125	25	gt	gt	PROPN
ejpam-6392	125	26	(	(	PUNCT
ejpam-6392	125	27	e	e	NOUN
ejpam-6392	125	28	•	•	NOUN
ejpam-6392	125	29	3	3	NUM
ejpam-6392	125	30	)	)	PUNCT
ejpam-6392	125	31	≥	≥	NOUN
ejpam-6392	125	32	min{gt	min{gt	X
ejpam-6392	125	33	(	(	PUNCT
ejpam-6392	125	34	0	0	NUM
ejpam-6392	125	35	)	)	PUNCT
ejpam-6392	125	36	,	,	PUNCT
ejpam-6392	125	37	gt	gt	PROPN
ejpam-6392	125	38	(	(	PUNCT
ejpam-6392	125	39	ä	ä	NOUN
ejpam-6392	125	40	)	)	PUNCT
ejpam-6392	125	41	}	}	PUNCT
ejpam-6392	125	42	(	(	PUNCT
ejpam-6392	125	43	3.2	3.2	NUM
ejpam-6392	125	44	)	)	PUNCT
ejpam-6392	125	45	now	now	ADV
ejpam-6392	125	46	,	,	PUNCT
ejpam-6392	125	47	using	use	VERB
ejpam-6392	125	48	the	the	DET
ejpam-6392	125	49	property	property	NOUN
ejpam-6392	125	50	of	of	ADP
ejpam-6392	125	51	neutrosophic	neutrosophic	ADJ
ejpam-6392	125	52	bi	bi	NOUN
ejpam-6392	125	53	-	-	NOUN
ejpam-6392	125	54	ideal	ideal	NOUN
ejpam-6392	125	55	that	that	SCONJ
ejpam-6392	125	56	gt	gt	PROPN
ejpam-6392	125	57	(	(	PUNCT
ejpam-6392	125	58	0	0	NUM
ejpam-6392	125	59	)	)	PUNCT
ejpam-6392	125	60	≥	≥	NOUN
ejpam-6392	125	61	gt	gt	INTJ
ejpam-6392	125	62	(	(	PUNCT
ejpam-6392	125	63	e	e	NOUN
ejpam-6392	125	64	)	)	PUNCT
ejpam-6392	125	65	,	,	PUNCT
ejpam-6392	125	66	we	we	PRON
ejpam-6392	125	67	obtain	obtain	VERB
ejpam-6392	125	68	min{gt	min{gt	NOUN
ejpam-6392	125	69	(	(	PUNCT
ejpam-6392	125	70	0	0	NUM
ejpam-6392	125	71	)	)	PUNCT
ejpam-6392	125	72	,	,	PUNCT
ejpam-6392	125	73	gt	gt	PROPN
ejpam-6392	125	74	(	(	PUNCT
ejpam-6392	125	75	ä	ä	NOUN
ejpam-6392	125	76	)	)	PUNCT
ejpam-6392	125	77	}	}	PUNCT
ejpam-6392	125	78	≥	≥	NOUN
ejpam-6392	125	79	min{gt	min{gt	X
ejpam-6392	125	80	(	(	PUNCT
ejpam-6392	125	81	e	e	NOUN
ejpam-6392	125	82	)	)	PUNCT
ejpam-6392	125	83	,	,	PUNCT
ejpam-6392	125	84	gt	gt	PROPN
ejpam-6392	125	85	(	(	PUNCT
ejpam-6392	125	86	ä	ä	NOUN
ejpam-6392	125	87	)	)	PUNCT
ejpam-6392	125	88	}	}	PUNCT
ejpam-6392	125	89	(	(	PUNCT
ejpam-6392	125	90	3.3	3.3	NUM
ejpam-6392	125	91	)	)	PUNCT
ejpam-6392	125	92	substitute	substitute	NOUN
ejpam-6392	125	93	(	(	PUNCT
ejpam-6392	125	94	3.3	3.3	NUM
ejpam-6392	125	95	)	)	PUNCT
ejpam-6392	125	96	into	into	ADP
ejpam-6392	125	97	(	(	PUNCT
ejpam-6392	125	98	3.2	3.2	NUM
ejpam-6392	125	99	)	)	PUNCT
ejpam-6392	125	100	then	then	ADV
ejpam-6392	125	101	we	we	PRON
ejpam-6392	125	102	get	get	VERB
ejpam-6392	125	103	,	,	PUNCT
ejpam-6392	125	104	gt	gt	PROPN
ejpam-6392	125	105	(	(	PUNCT
ejpam-6392	125	106	e•	e•	NOUN
ejpam-6392	125	107	3	3	NUM
ejpam-6392	125	108	)	)	PUNCT
ejpam-6392	125	109	≥	≥	NOUN
ejpam-6392	125	110	min	min	PROPN
ejpam-6392	125	111	{	{	PUNCT
ejpam-6392	125	112	gt	gt	PROPN
ejpam-6392	125	113	(	(	PUNCT
ejpam-6392	125	114	e	e	NOUN
ejpam-6392	125	115	)	)	PUNCT
ejpam-6392	125	116	,	,	PUNCT
ejpam-6392	125	117	gt	gt	PROPN
ejpam-6392	125	118	(	(	PUNCT
ejpam-6392	125	119	ä	ä	NOUN
ejpam-6392	125	120	)	)	PUNCT
ejpam-6392	125	121	}	}	PUNCT
ejpam-6392	125	122	.	.	PUNCT
ejpam-6392	126	1	therefore	therefore	ADV
ejpam-6392	126	2	gi(e	gi(e	VERB
ejpam-6392	126	3	•	•	ADV
ejpam-6392	126	4	3	3	NUM
ejpam-6392	126	5	)	)	PUNCT
ejpam-6392	126	6	≤	≤	NUM
ejpam-6392	126	7	max{gi(e	max{gi(e	NOUN
ejpam-6392	126	8	•	•	NOUN
ejpam-6392	126	9	3	3	NUM
ejpam-6392	126	10	•	•	NUM
ejpam-6392	126	11	ä	ä	NOUN
ejpam-6392	126	12	)	)	PUNCT
ejpam-6392	126	13	,	,	PUNCT
ejpam-6392	126	14	gi(ä	gi(ä	NOUN
ejpam-6392	126	15	)	)	PUNCT
ejpam-6392	126	16	}	}	PUNCT
ejpam-6392	126	17	(	(	PUNCT
ejpam-6392	126	18	3.4	3.4	NUM
ejpam-6392	126	19	)	)	PUNCT
ejpam-6392	126	20	since	since	SCONJ
ejpam-6392	126	21	e•	e•	NOUN
ejpam-6392	126	22	3•	3•	NUM
ejpam-6392	126	23	ä=0	ä=0	PROPN
ejpam-6392	126	24	,	,	PUNCT
ejpam-6392	126	25	it	it	PRON
ejpam-6392	126	26	follows	follow	VERB
ejpam-6392	126	27	(	(	PUNCT
ejpam-6392	126	28	3.1	3.1	NUM
ejpam-6392	126	29	)	)	PUNCT
ejpam-6392	126	30	gi(e	gi(e	NOUN
ejpam-6392	126	31	•	•	ADP
ejpam-6392	126	32	3	3	NUM
ejpam-6392	126	33	)	)	PUNCT
ejpam-6392	126	34	≤	≤	NUM
ejpam-6392	126	35	max{gi(0	max{gi(0	PROPN
ejpam-6392	126	36	)	)	PUNCT
ejpam-6392	126	37	,	,	PUNCT
ejpam-6392	126	38	gi(ä	gi(ä	ADV
ejpam-6392	126	39	)	)	PUNCT
ejpam-6392	126	40	}	}	PUNCT
ejpam-6392	126	41	(	(	PUNCT
ejpam-6392	126	42	3.5	3.5	NUM
ejpam-6392	126	43	)	)	PUNCT
ejpam-6392	126	44	now	now	ADV
ejpam-6392	126	45	,	,	PUNCT
ejpam-6392	126	46	using	use	VERB
ejpam-6392	126	47	the	the	DET
ejpam-6392	126	48	property	property	NOUN
ejpam-6392	126	49	of	of	ADP
ejpam-6392	126	50	neutrosophic	neutrosophic	ADJ
ejpam-6392	126	51	bi	bi	NOUN
ejpam-6392	126	52	-	-	NOUN
ejpam-6392	126	53	ideal	ideal	NOUN
ejpam-6392	126	54	that	that	PRON
ejpam-6392	126	55	gi	gi	INTJ
ejpam-6392	126	56	(	(	PUNCT
ejpam-6392	126	57	0	0	NUM
ejpam-6392	126	58	)	)	PUNCT
ejpam-6392	126	59	≤	≤	NUM
ejpam-6392	126	60	gi(e	gi(e	NOUN
ejpam-6392	126	61	)	)	PUNCT
ejpam-6392	126	62	,	,	PUNCT
ejpam-6392	126	63	we	we	PRON
ejpam-6392	126	64	obtain	obtain	VERB
ejpam-6392	126	65	max{gi(0	max{gi(0	PROPN
ejpam-6392	126	66	)	)	PUNCT
ejpam-6392	126	67	,	,	PUNCT
ejpam-6392	126	68	gi(ä	gi(ä	NOUN
ejpam-6392	126	69	)	)	PUNCT
ejpam-6392	126	70	}	}	PUNCT
ejpam-6392	126	71	≤	≤	NUM
ejpam-6392	126	72	max{gi(e	max{gi(e	NOUN
ejpam-6392	126	73	)	)	PUNCT
ejpam-6392	126	74	,	,	PUNCT
ejpam-6392	126	75	gi(ä	gi(ä	NOUN
ejpam-6392	126	76	)	)	PUNCT
ejpam-6392	126	77	}	}	PUNCT
ejpam-6392	126	78	(	(	PUNCT
ejpam-6392	126	79	3.6	3.6	NUM
ejpam-6392	126	80	)	)	PUNCT
ejpam-6392	126	81	substitute	substitute	NOUN
ejpam-6392	126	82	(	(	PUNCT
ejpam-6392	126	83	3.6	3.6	NUM
ejpam-6392	126	84	)	)	PUNCT
ejpam-6392	126	85	into	into	ADP
ejpam-6392	126	86	(	(	PUNCT
ejpam-6392	126	87	3.5	3.5	NUM
ejpam-6392	126	88	)	)	PUNCT
ejpam-6392	126	89	then	then	ADV
ejpam-6392	126	90	we	we	PRON
ejpam-6392	126	91	get	get	VERB
ejpam-6392	126	92	,	,	PUNCT
ejpam-6392	126	93	gi(e•	gi(e•	X
ejpam-6392	126	94	3	3	X
ejpam-6392	126	95	)	)	PUNCT
ejpam-6392	126	96	≤	≤	NUM
ejpam-6392	126	97	max	max	PROPN
ejpam-6392	126	98	{	{	PUNCT
ejpam-6392	126	99	gi(e	gi(e	NOUN
ejpam-6392	126	100	)	)	PUNCT
ejpam-6392	126	101	,	,	PUNCT
ejpam-6392	126	102	gt	gt	PROPN
ejpam-6392	126	103	(	(	PUNCT
ejpam-6392	126	104	ä	ä	NOUN
ejpam-6392	126	105	)	)	PUNCT
ejpam-6392	126	106	}	}	PUNCT
ejpam-6392	126	107	.	.	PUNCT
ejpam-6392	127	1	also	also	ADV
ejpam-6392	127	2	(	(	PUNCT
ejpam-6392	127	3	iii	iii	X
ejpam-6392	127	4	)	)	PUNCT
ejpam-6392	127	5	gf	gf	NOUN
ejpam-6392	127	6	(	(	PUNCT
ejpam-6392	127	7	e	e	NOUN
ejpam-6392	127	8	•	•	NOUN
ejpam-6392	127	9	3	3	NUM
ejpam-6392	127	10	)	)	PUNCT
ejpam-6392	127	11	≤	≤	NOUN
ejpam-6392	127	12	max{gf	max{gf	PUNCT
ejpam-6392	127	13	(	(	PUNCT
ejpam-6392	127	14	e	e	NOUN
ejpam-6392	127	15	•	•	NOUN
ejpam-6392	127	16	3	3	NUM
ejpam-6392	127	17	•	•	NUM
ejpam-6392	127	18	ä	ä	PROPN
ejpam-6392	127	19	)	)	PUNCT
ejpam-6392	127	20	,	,	PUNCT
ejpam-6392	127	21	gf	gf	X
ejpam-6392	127	22	(	(	PUNCT
ejpam-6392	127	23	ä	ä	NOUN
ejpam-6392	127	24	)	)	PUNCT
ejpam-6392	127	25	}	}	PUNCT
ejpam-6392	127	26	(	(	PUNCT
ejpam-6392	127	27	3.7	3.7	NUM
ejpam-6392	127	28	)	)	PUNCT
ejpam-6392	127	29	since	since	SCONJ
ejpam-6392	127	30	e•	e•	NOUN
ejpam-6392	127	31	3•	3•	NUM
ejpam-6392	127	32	ä=0	ä=0	PROPN
ejpam-6392	127	33	,	,	PUNCT
ejpam-6392	127	34	it	it	PRON
ejpam-6392	127	35	follows	follow	VERB
ejpam-6392	127	36	(	(	PUNCT
ejpam-6392	127	37	3.1	3.1	NUM
ejpam-6392	127	38	)	)	PUNCT
ejpam-6392	127	39	gf	gf	NOUN
ejpam-6392	127	40	(	(	PUNCT
ejpam-6392	127	41	e	e	NOUN
ejpam-6392	127	42	•	•	NOUN
ejpam-6392	127	43	3	3	NUM
ejpam-6392	127	44	)	)	PUNCT
ejpam-6392	127	45	≤	≤	NOUN
ejpam-6392	127	46	max{gf	max{gf	PUNCT
ejpam-6392	127	47	(	(	PUNCT
ejpam-6392	127	48	0	0	NUM
ejpam-6392	127	49	)	)	PUNCT
ejpam-6392	127	50	,	,	PUNCT
ejpam-6392	127	51	gf	gf	X
ejpam-6392	127	52	(	(	PUNCT
ejpam-6392	127	53	ä	ä	NOUN
ejpam-6392	127	54	)	)	PUNCT
ejpam-6392	127	55	}	}	PUNCT
ejpam-6392	127	56	(	(	PUNCT
ejpam-6392	127	57	3.8	3.8	NUM
ejpam-6392	127	58	)	)	PUNCT
ejpam-6392	127	59	now	now	ADV
ejpam-6392	127	60	,	,	PUNCT
ejpam-6392	127	61	using	use	VERB
ejpam-6392	127	62	the	the	DET
ejpam-6392	127	63	property	property	NOUN
ejpam-6392	127	64	of	of	ADP
ejpam-6392	127	65	neutrosophic	neutrosophic	ADJ
ejpam-6392	127	66	bi	bi	NOUN
ejpam-6392	127	67	-	-	NOUN
ejpam-6392	127	68	ideal	ideal	NOUN
ejpam-6392	127	69	that	that	SCONJ
ejpam-6392	127	70	gf	gf	NOUN
ejpam-6392	127	71	(	(	PUNCT
ejpam-6392	127	72	0	0	NUM
ejpam-6392	127	73	)	)	PUNCT
ejpam-6392	127	74	≤	≤	NOUN
ejpam-6392	127	75	gf	gf	X
ejpam-6392	127	76	(	(	PUNCT
ejpam-6392	127	77	e	e	NOUN
ejpam-6392	127	78	)	)	PUNCT
ejpam-6392	127	79	,	,	PUNCT
ejpam-6392	127	80	we	we	PRON
ejpam-6392	127	81	obtain	obtain	VERB
ejpam-6392	127	82	max{gf	max{gf	NOUN
ejpam-6392	127	83	(	(	PUNCT
ejpam-6392	127	84	0	0	NUM
ejpam-6392	127	85	)	)	PUNCT
ejpam-6392	127	86	,	,	PUNCT
ejpam-6392	127	87	gf	gf	X
ejpam-6392	127	88	(	(	PUNCT
ejpam-6392	127	89	ä	ä	NOUN
ejpam-6392	127	90	)	)	PUNCT
ejpam-6392	127	91	}	}	PUNCT
ejpam-6392	127	92	≤	≤	NUM
ejpam-6392	127	93	max{gf	max{gf	PUNCT
ejpam-6392	127	94	(	(	PUNCT
ejpam-6392	127	95	e	e	NOUN
ejpam-6392	127	96	)	)	PUNCT
ejpam-6392	127	97	,	,	PUNCT
ejpam-6392	127	98	gf	gf	X
ejpam-6392	127	99	(	(	PUNCT
ejpam-6392	127	100	ä	ä	NOUN
ejpam-6392	127	101	)	)	PUNCT
ejpam-6392	127	102	}	}	PUNCT
ejpam-6392	127	103	(	(	PUNCT
ejpam-6392	127	104	3.9	3.9	NUM
ejpam-6392	127	105	)	)	PUNCT
ejpam-6392	127	106	substitute	substitute	NOUN
ejpam-6392	127	107	(	(	PUNCT
ejpam-6392	127	108	3.9	3.9	NUM
ejpam-6392	127	109	)	)	PUNCT
ejpam-6392	127	110	into	into	ADP
ejpam-6392	127	111	(	(	PUNCT
ejpam-6392	127	112	3.8	3.8	NUM
ejpam-6392	127	113	)	)	PUNCT
ejpam-6392	127	114	then	then	ADV
ejpam-6392	127	115	we	we	PRON
ejpam-6392	127	116	get	get	VERB
ejpam-6392	127	117	,	,	PUNCT
ejpam-6392	127	118	gf	gf	X
ejpam-6392	127	119	(	(	PUNCT
ejpam-6392	127	120	e•	e•	NOUN
ejpam-6392	127	121	3	3	NUM
ejpam-6392	127	122	)	)	PUNCT
ejpam-6392	127	123	≤	≤	NUM
ejpam-6392	127	124	max	max	PROPN
ejpam-6392	127	125	{	{	PUNCT
ejpam-6392	127	126	gf	gf	X
ejpam-6392	127	127	(	(	PUNCT
ejpam-6392	127	128	e	e	NOUN
ejpam-6392	127	129	)	)	PUNCT
ejpam-6392	127	130	,	,	PUNCT
ejpam-6392	127	131	gf	gf	X
ejpam-6392	127	132	(	(	PUNCT
ejpam-6392	127	133	ä	ä	NOUN
ejpam-6392	127	134	)	)	PUNCT
ejpam-6392	127	135	}	}	PUNCT
ejpam-6392	127	136	hence	hence	ADV
ejpam-6392	127	137	proved	prove	VERB
ejpam-6392	127	138	.	.	PUNCT
ejpam-6392	128	1	lemma	lemma	PROPN
ejpam-6392	128	2	3.2	3.2	NUM
ejpam-6392	128	3	.	.	PUNCT
ejpam-6392	129	1	let	let	VERB
ejpam-6392	129	2	ns	ns	NUM
ejpam-6392	129	3	g=(gt	g=(gt	NOUN
ejpam-6392	129	4	,	,	PUNCT
ejpam-6392	129	5	gi	gi	INTJ
ejpam-6392	129	6	,	,	PUNCT
ejpam-6392	129	7	gf	gf	AUX
ejpam-6392	129	8	)	)	PUNCT
ejpam-6392	129	9	be	be	AUX
ejpam-6392	129	10	a	a	DET
ejpam-6392	129	11	neutrosophic	neutrosophic	ADJ
ejpam-6392	129	12	bi	bi	NOUN
ejpam-6392	129	13	-	-	NOUN
ejpam-6392	129	14	ideal	ideal	NOUN
ejpam-6392	129	15	of	of	ADP
ejpam-6392	129	16	¨̈u	¨̈u	NOUN
ejpam-6392	129	17	.	.	PUNCT
ejpam-6392	130	1	if	if	SCONJ
ejpam-6392	130	2	the	the	DET
ejpam-6392	130	3	inequality	inequality	NOUN
ejpam-6392	130	4	e•	e•	VERB
ejpam-6392	130	5	3≤	3≤	NUM
ejpam-6392	130	6	ä	ä	NOUN
ejpam-6392	130	7	holds	hold	VERB
ejpam-6392	130	8	in	in	ADP
ejpam-6392	130	9	¨̈u	¨̈u	NOUN
ejpam-6392	130	10	then	then	ADV
ejpam-6392	130	11	gt	gt	INTJ
ejpam-6392	130	12	(	(	PUNCT
ejpam-6392	130	13	e•	e•	NOUN
ejpam-6392	130	14	3	3	NUM
ejpam-6392	130	15	)	)	PUNCT
ejpam-6392	130	16	≥	≥	NOUN
ejpam-6392	130	17	gt	gt	INTJ
ejpam-6392	130	18	(	(	PUNCT
ejpam-6392	130	19	ä	ä	PROPN
ejpam-6392	130	20	)	)	PUNCT
ejpam-6392	130	21	,	,	PUNCT
ejpam-6392	130	22	gi(e•	gi(e•	X
ejpam-6392	130	23	3	3	X
ejpam-6392	130	24	)	)	PUNCT
ejpam-6392	130	25	≤	≤	NOUN
ejpam-6392	130	26	gi(ä	gi(ä	NOUN
ejpam-6392	130	27	)	)	PUNCT
ejpam-6392	130	28	and	and	CCONJ
ejpam-6392	130	29	gf	gf	PROPN
ejpam-6392	130	30	(	(	PUNCT
ejpam-6392	130	31	e•	e•	NOUN
ejpam-6392	130	32	3	3	NUM
ejpam-6392	130	33	)	)	PUNCT
ejpam-6392	130	34	≤	≤	NOUN
ejpam-6392	130	35	gf	gf	X
ejpam-6392	130	36	(	(	PUNCT
ejpam-6392	130	37	ä	ä	PROPN
ejpam-6392	130	38	)	)	PUNCT
ejpam-6392	130	39	that	that	PRON
ejpam-6392	130	40	gt	gt	PROPN
ejpam-6392	130	41	is	be	AUX
ejpam-6392	130	42	order	order	NOUN
ejpam-6392	130	43	reversing	reverse	VERB
ejpam-6392	130	44	and	and	CCONJ
ejpam-6392	130	45	gi	gi	INTJ
ejpam-6392	130	46	,	,	PUNCT
ejpam-6392	130	47	gf	gf	PROPN
ejpam-6392	130	48	are	be	AUX
ejpam-6392	130	49	order	order	NOUN
ejpam-6392	130	50	preserving	preserve	VERB
ejpam-6392	130	51	.	.	PUNCT
ejpam-6392	131	1	proof	proof	NOUN
ejpam-6392	131	2	.	.	PUNCT
ejpam-6392	132	1	by	by	ADP
ejpam-6392	132	2	using	use	VERB
ejpam-6392	132	3	ink	ink	NOUN
ejpam-6392	132	4	ordering	ordering	NOUN
ejpam-6392	132	5	,	,	PUNCT
ejpam-6392	132	6	e	e	X
ejpam-6392	132	7	≤	≤	NUM
ejpam-6392	132	8	3	3	NUM
ejpam-6392	132	9	⇔	⇔	X
ejpam-6392	132	10	e	e	X
ejpam-6392	132	11	•	•	ADP
ejpam-6392	132	12	3	3	NUM
ejpam-6392	132	13	=	=	SYM
ejpam-6392	132	14	0	0	NUM
ejpam-6392	132	15	.	.	PUNCT
ejpam-6392	133	1	so	so	ADV
ejpam-6392	133	2	the	the	DET
ejpam-6392	133	3	condition	condition	NOUN
ejpam-6392	133	4	e	e	NOUN
ejpam-6392	133	5	•	•	NOUN
ejpam-6392	133	6	3	3	NUM
ejpam-6392	133	7	≤	≤	NOUN
ejpam-6392	133	8	ä	ä	NOUN
ejpam-6392	133	9	implies	imply	VERB
ejpam-6392	133	10	(	(	PUNCT
ejpam-6392	133	11	e•3)•ä	e•3)•ä	NOUN
ejpam-6392	133	12	=	=	SYM
ejpam-6392	133	13	0	0	NUM
ejpam-6392	134	1	⇒	⇒	NOUN
ejpam-6392	135	1	e•3•ä	e•3•ä	PROPN
ejpam-6392	136	1	=	=	PUNCT
ejpam-6392	137	1	0	0	X
ejpam-6392	137	2	.	.	PUNCT
ejpam-6392	138	1	let	let	VERB
ejpam-6392	138	2	g	g	PROPN
ejpam-6392	138	3	=	=	SYM
ejpam-6392	138	4	(	(	PUNCT
ejpam-6392	138	5	gt	gt	INTJ
ejpam-6392	138	6	,	,	PUNCT
ejpam-6392	138	7	gi	gi	INTJ
ejpam-6392	138	8	,	,	PUNCT
ejpam-6392	138	9	gf	gf	AUX
ejpam-6392	138	10	)	)	PUNCT
ejpam-6392	138	11	be	be	AUX
ejpam-6392	138	12	a	a	DET
ejpam-6392	138	13	neutrosophic	neutrosophic	ADJ
ejpam-6392	138	14	bi	bi	NOUN
ejpam-6392	138	15	-	-	NOUN
ejpam-6392	138	16	ideal	ideal	NOUN
ejpam-6392	138	17	of	of	ADP
ejpam-6392	138	18	ink	ink	NOUN
ejpam-6392	138	19	-	-	PUNCT
ejpam-6392	138	20	algebra	algebra	NOUN
ejpam-6392	138	21	¨̈u	¨̈u	VERB
ejpam-6392	138	22	for	for	ADP
ejpam-6392	138	23	all	all	DET
ejpam-6392	138	24	e	e	NOUN
ejpam-6392	138	25	,	,	PUNCT
ejpam-6392	138	26	3,ä	3,ä	PROPN
ejpam-6392	138	27	∈	∈	PROPN
ejpam-6392	138	28	¨̈u	¨̈u	NOUN
ejpam-6392	138	29	.	.	PUNCT
ejpam-6392	139	1	m.	m.	NOUN
ejpam-6392	139	2	remala	remala	NOUN
ejpam-6392	139	3	,	,	PUNCT
ejpam-6392	139	4	e.	e.	PROPN
ejpam-6392	139	5	tamma	tamma	PROPN
ejpam-6392	139	6	,	,	PUNCT
ejpam-6392	139	7	y.	y.	PROPN
ejpam-6392	139	8	bhargavi	bhargavi	PROPN
ejpam-6392	139	9	/	/	SYM
ejpam-6392	139	10	eur	eur	PROPN
ejpam-6392	139	11	.	.	PUNCT
ejpam-6392	140	1	j.	j.	PROPN
ejpam-6392	140	2	pure	pure	PROPN
ejpam-6392	140	3	appl	appl	PROPN
ejpam-6392	140	4	.	.	PROPN
ejpam-6392	140	5	math	math	PROPN
ejpam-6392	140	6	,	,	PUNCT
ejpam-6392	140	7	18	18	NUM
ejpam-6392	140	8	(	(	PUNCT
ejpam-6392	140	9	4	4	NUM
ejpam-6392	140	10	)	)	PUNCT
ejpam-6392	140	11	(	(	PUNCT
ejpam-6392	140	12	2025	2025	NUM
ejpam-6392	140	13	)	)	PUNCT
ejpam-6392	140	14	,	,	PUNCT
ejpam-6392	140	15	6392	6392	NUM
ejpam-6392	140	16	7	7	NUM
ejpam-6392	140	17	of	of	ADP
ejpam-6392	140	18	20	20	NUM
ejpam-6392	140	19	(	(	PUNCT
ejpam-6392	140	20	i	i	NOUN
ejpam-6392	140	21	)	)	PUNCT
ejpam-6392	140	22	gt	gt	PROPN
ejpam-6392	141	1	(	(	PUNCT
ejpam-6392	141	2	e	e	NOUN
ejpam-6392	141	3	•	•	NOUN
ejpam-6392	141	4	3	3	NUM
ejpam-6392	141	5	)	)	PUNCT
ejpam-6392	141	6	≥	≥	NOUN
ejpam-6392	141	7	min{gt	min{gt	X
ejpam-6392	141	8	(	(	PUNCT
ejpam-6392	141	9	e	e	NOUN
ejpam-6392	141	10	•	•	NOUN
ejpam-6392	141	11	3	3	NUM
ejpam-6392	141	12	•ä	•ä	NOUN
ejpam-6392	141	13	)	)	PUNCT
ejpam-6392	141	14	,	,	PUNCT
ejpam-6392	141	15	gt	gt	PROPN
ejpam-6392	141	16	(	(	PUNCT
ejpam-6392	141	17	ä	ä	NOUN
ejpam-6392	141	18	)	)	PUNCT
ejpam-6392	141	19	}	}	PUNCT
ejpam-6392	141	20	.	.	PUNCT
ejpam-6392	142	1	since	since	SCONJ
ejpam-6392	142	2	gt	gt	PROPN
ejpam-6392	142	3	(	(	PUNCT
ejpam-6392	142	4	e	e	NOUN
ejpam-6392	142	5	•	•	NUM
ejpam-6392	142	6	3	3	NUM
ejpam-6392	142	7	•ä	•ä	NOUN
ejpam-6392	142	8	)	)	PUNCT
ejpam-6392	142	9	=	=	SYM
ejpam-6392	142	10	gt	gt	PROPN
ejpam-6392	142	11	(	(	PUNCT
ejpam-6392	142	12	0	0	NUM
ejpam-6392	142	13	)	)	PUNCT
ejpam-6392	142	14	and	and	CCONJ
ejpam-6392	142	15	gt	gt	INTJ
ejpam-6392	142	16	(	(	PUNCT
ejpam-6392	142	17	0	0	NUM
ejpam-6392	142	18	)	)	PUNCT
ejpam-6392	142	19	≥	≥	NOUN
ejpam-6392	142	20	gt	gt	INTJ
ejpam-6392	142	21	(	(	PUNCT
ejpam-6392	142	22	ä	ä	NOUN
ejpam-6392	142	23	)	)	PUNCT
ejpam-6392	142	24	(	(	PUNCT
ejpam-6392	142	25	from	from	ADP
ejpam-6392	142	26	the	the	DET
ejpam-6392	142	27	definition	definition	NOUN
ejpam-6392	142	28	)	)	PUNCT
ejpam-6392	142	29	,	,	PUNCT
ejpam-6392	142	30	we	we	PRON
ejpam-6392	142	31	get	get	VERB
ejpam-6392	142	32	gt	gt	INTJ
ejpam-6392	142	33	(	(	PUNCT
ejpam-6392	142	34	e	e	NOUN
ejpam-6392	142	35	•	•	NOUN
ejpam-6392	142	36	3	3	NUM
ejpam-6392	142	37	)	)	PUNCT
ejpam-6392	142	38	≥	≥	NOUN
ejpam-6392	142	39	min{gt	min{gt	X
ejpam-6392	142	40	(	(	PUNCT
ejpam-6392	142	41	0	0	NUM
ejpam-6392	142	42	)	)	PUNCT
ejpam-6392	142	43	,	,	PUNCT
ejpam-6392	142	44	gt	gt	PROPN
ejpam-6392	142	45	(	(	PUNCT
ejpam-6392	142	46	ä	ä	NOUN
ejpam-6392	142	47	)	)	PUNCT
ejpam-6392	142	48	}	}	PUNCT
ejpam-6392	142	49	=	=	SYM
ejpam-6392	142	50	gt	gt	INTJ
ejpam-6392	142	51	(	(	PUNCT
ejpam-6392	142	52	ä	ä	NOUN
ejpam-6392	142	53	)	)	PUNCT
ejpam-6392	142	54	.	.	PUNCT
ejpam-6392	143	1	(	(	PUNCT
ejpam-6392	143	2	ii	ii	NOUN
ejpam-6392	143	3	)	)	PUNCT
ejpam-6392	143	4	gi(e	gi(e	NOUN
ejpam-6392	143	5	•	•	ADP
ejpam-6392	143	6	3	3	X
ejpam-6392	143	7	)	)	PUNCT
ejpam-6392	143	8	≤	≤	NUM
ejpam-6392	143	9	max{gi(e	max{gi(e	NOUN
ejpam-6392	143	10	•	•	NOUN
ejpam-6392	143	11	3	3	NUM
ejpam-6392	143	12	•	•	NUM
ejpam-6392	143	13	ä	ä	NOUN
ejpam-6392	143	14	)	)	PUNCT
ejpam-6392	143	15	,	,	PUNCT
ejpam-6392	143	16	gi(ä	gi(ä	NOUN
ejpam-6392	143	17	)	)	PUNCT
ejpam-6392	143	18	}	}	PUNCT
ejpam-6392	143	19	.	.	PUNCT
ejpam-6392	144	1	since	since	SCONJ
ejpam-6392	144	2	gi(e	gi(e	NOUN
ejpam-6392	144	3	•	•	ADV
ejpam-6392	144	4	3	3	NUM
ejpam-6392	144	5	•	•	NUM
ejpam-6392	144	6	ä	ä	PROPN
ejpam-6392	144	7	)	)	PUNCT
ejpam-6392	144	8	=	=	SYM
ejpam-6392	144	9	gi(0	gi(0	PROPN
ejpam-6392	144	10	)	)	PUNCT
ejpam-6392	144	11	and	and	CCONJ
ejpam-6392	144	12	gi(0	gi(0	PROPN
ejpam-6392	144	13	)	)	PUNCT
ejpam-6392	144	14	≤	≤	NOUN
ejpam-6392	144	15	gi(ä	gi(ä	NOUN
ejpam-6392	144	16	)	)	PUNCT
ejpam-6392	144	17	(	(	PUNCT
ejpam-6392	144	18	from	from	ADP
ejpam-6392	144	19	the	the	DET
ejpam-6392	144	20	definition	definition	NOUN
ejpam-6392	144	21	)	)	PUNCT
ejpam-6392	144	22	,	,	PUNCT
ejpam-6392	144	23	we	we	PRON
ejpam-6392	144	24	obtain	obtain	VERB
ejpam-6392	144	25	gi(e	gi(e	NOUN
ejpam-6392	144	26	•	•	ADP
ejpam-6392	144	27	3	3	NUM
ejpam-6392	144	28	)	)	PUNCT
ejpam-6392	144	29	≤	≤	NUM
ejpam-6392	144	30	max{gi(0	max{gi(0	PROPN
ejpam-6392	144	31	)	)	PUNCT
ejpam-6392	144	32	,	,	PUNCT
ejpam-6392	144	33	gi(ä	gi(ä	ADV
ejpam-6392	144	34	)	)	PUNCT
ejpam-6392	144	35	}	}	PUNCT
ejpam-6392	144	36	=	=	SYM
ejpam-6392	144	37	gi(ä	gi(ä	PRON
ejpam-6392	144	38	)	)	PUNCT
ejpam-6392	144	39	.	.	PUNCT
ejpam-6392	145	1	(	(	PUNCT
ejpam-6392	145	2	iii	iii	X
ejpam-6392	145	3	)	)	PUNCT
ejpam-6392	145	4	gf	gf	NOUN
ejpam-6392	145	5	(	(	PUNCT
ejpam-6392	145	6	e•3	e•3	NOUN
ejpam-6392	145	7	)	)	PUNCT
ejpam-6392	145	8	≤	≤	NOUN
ejpam-6392	145	9	max{gf	max{gf	PUNCT
ejpam-6392	145	10	(	(	PUNCT
ejpam-6392	145	11	e•3•ä	e•3•ä	PROPN
ejpam-6392	145	12	)	)	PUNCT
ejpam-6392	145	13	,	,	PUNCT
ejpam-6392	145	14	gf	gf	X
ejpam-6392	145	15	(	(	PUNCT
ejpam-6392	145	16	ä	ä	NOUN
ejpam-6392	145	17	)	)	PUNCT
ejpam-6392	145	18	}	}	PUNCT
ejpam-6392	145	19	.	.	PUNCT
ejpam-6392	146	1	since	since	SCONJ
ejpam-6392	146	2	gf	gf	PROPN
ejpam-6392	146	3	(	(	PUNCT
ejpam-6392	146	4	e•3•ä	e•3•ä	PROPN
ejpam-6392	146	5	)	)	PUNCT
ejpam-6392	146	6	=	=	SYM
ejpam-6392	146	7	gf	gf	X
ejpam-6392	146	8	(	(	PUNCT
ejpam-6392	146	9	0	0	NUM
ejpam-6392	146	10	)	)	PUNCT
ejpam-6392	146	11	and	and	CCONJ
ejpam-6392	146	12	gf	gf	X
ejpam-6392	146	13	(	(	PUNCT
ejpam-6392	146	14	0	0	NUM
ejpam-6392	146	15	)	)	PUNCT
ejpam-6392	146	16	≤	≤	NOUN
ejpam-6392	146	17	gf	gf	X
ejpam-6392	146	18	(	(	PUNCT
ejpam-6392	146	19	ä	ä	NOUN
ejpam-6392	146	20	)	)	PUNCT
ejpam-6392	146	21	(	(	PUNCT
ejpam-6392	146	22	from	from	ADP
ejpam-6392	146	23	the	the	DET
ejpam-6392	146	24	definition	definition	NOUN
ejpam-6392	146	25	)	)	PUNCT
ejpam-6392	146	26	,	,	PUNCT
ejpam-6392	146	27	we	we	PRON
ejpam-6392	146	28	get	get	VERB
ejpam-6392	146	29	gf	gf	NOUN
ejpam-6392	146	30	(	(	PUNCT
ejpam-6392	146	31	e	e	NOUN
ejpam-6392	146	32	•	•	NOUN
ejpam-6392	146	33	3	3	NUM
ejpam-6392	146	34	)	)	PUNCT
ejpam-6392	146	35	≤	≤	NOUN
ejpam-6392	146	36	max{gf	max{gf	PUNCT
ejpam-6392	146	37	(	(	PUNCT
ejpam-6392	146	38	0	0	NUM
ejpam-6392	146	39	)	)	PUNCT
ejpam-6392	146	40	,	,	PUNCT
ejpam-6392	146	41	gf	gf	X
ejpam-6392	146	42	(	(	PUNCT
ejpam-6392	146	43	ä	ä	NOUN
ejpam-6392	146	44	)	)	PUNCT
ejpam-6392	146	45	}	}	PUNCT
ejpam-6392	147	1	=	=	SYM
ejpam-6392	147	2	gf	gf	X
ejpam-6392	147	3	(	(	PUNCT
ejpam-6392	147	4	ä	ä	NOUN
ejpam-6392	147	5	)	)	PUNCT
ejpam-6392	147	6	.	.	PUNCT
ejpam-6392	148	1	hence	hence	ADV
ejpam-6392	148	2	proved	prove	VERB
ejpam-6392	148	3	.	.	PUNCT
ejpam-6392	149	1	theorem	theorem	VERB
ejpam-6392	149	2	3.1	3.1	NUM
ejpam-6392	149	3	.	.	PUNCT
ejpam-6392	150	1	every	every	DET
ejpam-6392	150	2	neutrosophic	neutrosophic	ADJ
ejpam-6392	150	3	bi	bi	NOUN
ejpam-6392	150	4	-	-	NOUN
ejpam-6392	150	5	ideal	ideal	NOUN
ejpam-6392	150	6	of	of	ADP
ejpam-6392	150	7	¨̈u	¨̈u	NOUN
ejpam-6392	150	8	is	be	AUX
ejpam-6392	150	9	an	an	DET
ejpam-6392	150	10	neutrosophic	neutrosophic	ADJ
ejpam-6392	150	11	sub	sub	NOUN
ejpam-6392	150	12	-	-	NOUN
ejpam-6392	150	13	algebra	algebra	NOUN
ejpam-6392	150	14	of	of	ADP
ejpam-6392	150	15	¨̈u	¨̈u	NOUN
ejpam-6392	150	16	.	.	PUNCT
ejpam-6392	151	1	proof	proof	NOUN
ejpam-6392	151	2	.	.	PUNCT
ejpam-6392	152	1	let	let	VERB
ejpam-6392	152	2	neutrosophic	neutrosophic	ADJ
ejpam-6392	152	3	set	set	VERB
ejpam-6392	152	4	g=(gt	g=(gt	NOUN
ejpam-6392	152	5	,	,	PUNCT
ejpam-6392	152	6	gi	gi	INTJ
ejpam-6392	152	7	,	,	PUNCT
ejpam-6392	152	8	gf	gf	AUX
ejpam-6392	152	9	)	)	PUNCT
ejpam-6392	152	10	be	be	AUX
ejpam-6392	152	11	a	a	DET
ejpam-6392	152	12	neutrosophic	neutrosophic	ADJ
ejpam-6392	152	13	bi	bi	NOUN
ejpam-6392	152	14	-	-	NOUN
ejpam-6392	152	15	ideal	ideal	NOUN
ejpam-6392	152	16	of	of	ADP
ejpam-6392	152	17	¨̈u	¨̈u	NOUN
ejpam-6392	152	18	.	.	PUNCT
ejpam-6392	153	1	since	since	SCONJ
ejpam-6392	153	2	e	e	PROPN
ejpam-6392	153	3	•	•	ADP
ejpam-6392	153	4	3	3	NUM
ejpam-6392	153	5	≤	≤	NOUN
ejpam-6392	153	6	e	e	NOUN
ejpam-6392	153	7	for	for	ADP
ejpam-6392	153	8	all	all	DET
ejpam-6392	153	9	e	e	NOUN
ejpam-6392	153	10	,	,	PUNCT
ejpam-6392	153	11	3,ä	3,ä	PROPN
ejpam-6392	153	12	∈	∈	PROPN
ejpam-6392	153	13	¨̈u	¨̈u	NOUN
ejpam-6392	153	14	.	.	PUNCT
ejpam-6392	154	1	consider	consider	VERB
ejpam-6392	154	2	e	e	NOUN
ejpam-6392	154	3	•	•	ADP
ejpam-6392	154	4	3	3	NUM
ejpam-6392	154	5	•	•	NUM
ejpam-6392	154	6	3	3	NUM
ejpam-6392	154	7	≤	≤	NOUN
ejpam-6392	154	8	e	e	NOUN
ejpam-6392	154	9	for	for	ADP
ejpam-6392	154	10	all	all	DET
ejpam-6392	154	11	e	e	NOUN
ejpam-6392	154	12	,	,	PUNCT
ejpam-6392	154	13	3,ä	3,ä	PROPN
ejpam-6392	154	14	∈	∈	PROPN
ejpam-6392	154	15	¨̈u	¨̈u	NOUN
ejpam-6392	154	16	,	,	PUNCT
ejpam-6392	154	17	(	(	PUNCT
ejpam-6392	154	18	e	e	NOUN
ejpam-6392	154	19	•	•	X
ejpam-6392	154	20	(	(	PUNCT
ejpam-6392	154	21	3	3	NUM
ejpam-6392	154	22	•	•	NUM
ejpam-6392	154	23	3	3	NUM
ejpam-6392	154	24	)	)	PUNCT
ejpam-6392	154	25	•	•	NUM
ejpam-6392	154	26	e	e	X
ejpam-6392	154	27	)	)	PUNCT
ejpam-6392	155	1	=	=	SYM
ejpam-6392	155	2	0⇒(e	0⇒(e	NUM
ejpam-6392	155	3	•	•	NOUN
ejpam-6392	155	4	0	0	NUM
ejpam-6392	155	5	•	•	NUM
ejpam-6392	155	6	e	e	NOUN
ejpam-6392	155	7	)	)	PUNCT
ejpam-6392	155	8	=	=	SYM
ejpam-6392	155	9	(	(	PUNCT
ejpam-6392	155	10	(	(	PUNCT
ejpam-6392	155	11	e	e	NOUN
ejpam-6392	155	12	•	•	NOUN
ejpam-6392	155	13	0	0	NUM
ejpam-6392	155	14	)	)	PUNCT
ejpam-6392	155	15	•	•	NUM
ejpam-6392	155	16	e	e	X
ejpam-6392	155	17	)	)	PUNCT
ejpam-6392	155	18	=	=	SYM
ejpam-6392	155	19	0	0	X
ejpam-6392	155	20	.	.	PUNCT
ejpam-6392	156	1	it	it	PRON
ejpam-6392	156	2	follows	follow	VERB
ejpam-6392	156	3	that	that	SCONJ
ejpam-6392	156	4	,	,	PUNCT
ejpam-6392	156	5	gt	gt	PROPN
ejpam-6392	156	6	(	(	PUNCT
ejpam-6392	156	7	e	e	NOUN
ejpam-6392	156	8	•	•	NOUN
ejpam-6392	156	9	3	3	NUM
ejpam-6392	156	10	•	•	NUM
ejpam-6392	156	11	3	3	NUM
ejpam-6392	156	12	)	)	PUNCT
ejpam-6392	156	13	≥	≥	NOUN
ejpam-6392	156	14	gt	gt	INTJ
ejpam-6392	156	15	(	(	PUNCT
ejpam-6392	156	16	e	e	NOUN
ejpam-6392	156	17	)	)	PUNCT
ejpam-6392	156	18	,	,	PUNCT
ejpam-6392	156	19	gi(e	gi(e	NOUN
ejpam-6392	156	20	•	•	ADV
ejpam-6392	156	21	3	3	NUM
ejpam-6392	156	22	•	•	NUM
ejpam-6392	156	23	3	3	NUM
ejpam-6392	156	24	)	)	PUNCT
ejpam-6392	156	25	≤	≤	NUM
ejpam-6392	156	26	gi(e	gi(e	NOUN
ejpam-6392	156	27	)	)	PUNCT
ejpam-6392	156	28	and	and	CCONJ
ejpam-6392	156	29	gf	gf	X
ejpam-6392	156	30	(	(	PUNCT
ejpam-6392	156	31	e	e	NOUN
ejpam-6392	156	32	•	•	NOUN
ejpam-6392	156	33	3	3	NUM
ejpam-6392	156	34	•	•	NUM
ejpam-6392	156	35	3	3	NUM
ejpam-6392	156	36	)	)	PUNCT
ejpam-6392	156	37	≤	≤	NOUN
ejpam-6392	156	38	gf	gf	X
ejpam-6392	156	39	(	(	PUNCT
ejpam-6392	156	40	e	e	NOUN
ejpam-6392	156	41	)	)	PUNCT
ejpam-6392	156	42	.	.	PUNCT
ejpam-6392	157	1	by	by	ADP
ejpam-6392	157	2	considering	consider	VERB
ejpam-6392	157	3	the	the	DET
ejpam-6392	157	4	bi	bi	ADJ
ejpam-6392	157	5	-	-	ADJ
ejpam-6392	157	6	ideal	ideal	ADJ
ejpam-6392	157	7	conditions	condition	NOUN
ejpam-6392	157	8	,	,	PUNCT
ejpam-6392	157	9	and	and	CCONJ
ejpam-6392	157	10	substitute	substitute	NOUN
ejpam-6392	157	11	ä	ä	PROPN
ejpam-6392	157	12	=	=	NOUN
ejpam-6392	157	13	3	3	NUM
ejpam-6392	157	14	for	for	ADP
ejpam-6392	157	15	all	all	DET
ejpam-6392	157	16	e	e	NOUN
ejpam-6392	157	17	,	,	PUNCT
ejpam-6392	157	18	3,ä	3,ä	PROPN
ejpam-6392	157	19	∈	∈	PROPN
ejpam-6392	157	20	¨̈u	¨̈u	NOUN
ejpam-6392	157	21	.	.	PUNCT
ejpam-6392	158	1	(	(	PUNCT
ejpam-6392	158	2	i	i	NOUN
ejpam-6392	158	3	)	)	PUNCT
ejpam-6392	158	4	gt	gt	PROPN
ejpam-6392	159	1	(	(	PUNCT
ejpam-6392	159	2	e	e	NOUN
ejpam-6392	159	3	•	•	NOUN
ejpam-6392	159	4	3	3	NUM
ejpam-6392	159	5	)	)	PUNCT
ejpam-6392	159	6	≥	≥	NOUN
ejpam-6392	159	7	min	min	PROPN
ejpam-6392	159	8	{	{	PUNCT
ejpam-6392	159	9	gt	gt	INTJ
ejpam-6392	159	10	(	(	PUNCT
ejpam-6392	159	11	e	e	NOUN
ejpam-6392	159	12	•	•	NUM
ejpam-6392	159	13	3	3	NUM
ejpam-6392	159	14	•	•	NUM
ejpam-6392	159	15	ä	ä	PROPN
ejpam-6392	159	16	)	)	PUNCT
ejpam-6392	159	17	,	,	PUNCT
ejpam-6392	159	18	gt	gt	PROPN
ejpam-6392	159	19	(	(	PUNCT
ejpam-6392	159	20	ä	ä	NOUN
ejpam-6392	159	21	)	)	PUNCT
ejpam-6392	159	22	}	}	PUNCT
ejpam-6392	159	23	=	=	SYM
ejpam-6392	159	24	min{gt	min{gt	NOUN
ejpam-6392	159	25	(	(	PUNCT
ejpam-6392	159	26	e	e	NOUN
ejpam-6392	159	27	•	•	NOUN
ejpam-6392	159	28	3	3	NUM
ejpam-6392	159	29	•	•	NUM
ejpam-6392	159	30	3	3	NUM
ejpam-6392	159	31	)	)	PUNCT
ejpam-6392	159	32	,	,	PUNCT
ejpam-6392	159	33	gt	gt	PROPN
ejpam-6392	159	34	(	(	PUNCT
ejpam-6392	159	35	3	3	NUM
ejpam-6392	159	36	)	)	PUNCT
ejpam-6392	159	37	}	}	PUNCT
ejpam-6392	159	38	(	(	PUNCT
ejpam-6392	159	39	ii	ii	NOUN
ejpam-6392	159	40	)	)	PUNCT
ejpam-6392	159	41	gi(e	gi(e	NOUN
ejpam-6392	159	42	•	•	ADP
ejpam-6392	159	43	3	3	X
ejpam-6392	159	44	)	)	PUNCT
ejpam-6392	159	45	≤	≤	NUM
ejpam-6392	159	46	max	max	PROPN
ejpam-6392	159	47	{	{	PUNCT
ejpam-6392	159	48	gi(e	gi(e	NOUN
ejpam-6392	159	49	•	•	ADV
ejpam-6392	159	50	3	3	NUM
ejpam-6392	159	51	•	•	NUM
ejpam-6392	159	52	ä	ä	NOUN
ejpam-6392	159	53	)	)	PUNCT
ejpam-6392	159	54	,	,	PUNCT
ejpam-6392	159	55	gi(ä	gi(ä	NOUN
ejpam-6392	159	56	)	)	PUNCT
ejpam-6392	159	57	}	}	PUNCT
ejpam-6392	160	1	=	=	SYM
ejpam-6392	160	2	max{gi(e	max{gi(e	NUM
ejpam-6392	160	3	•	•	NOUN
ejpam-6392	160	4	3	3	NUM
ejpam-6392	160	5	•	•	NUM
ejpam-6392	160	6	3	3	NUM
ejpam-6392	160	7	)	)	PUNCT
ejpam-6392	160	8	,	,	PUNCT
ejpam-6392	160	9	gi(3	gi(3	PROPN
ejpam-6392	160	10	)	)	PUNCT
ejpam-6392	160	11	}	}	PUNCT
ejpam-6392	160	12	(	(	PUNCT
ejpam-6392	160	13	iii	iii	X
ejpam-6392	160	14	)	)	PUNCT
ejpam-6392	160	15	therefore	therefore	ADV
ejpam-6392	160	16	,	,	PUNCT
ejpam-6392	160	17	gf	gf	X
ejpam-6392	160	18	(	(	PUNCT
ejpam-6392	160	19	e	e	NOUN
ejpam-6392	160	20	•	•	NOUN
ejpam-6392	160	21	3	3	NUM
ejpam-6392	160	22	)	)	PUNCT
ejpam-6392	160	23	≤	≤	NUM
ejpam-6392	160	24	max	max	PROPN
ejpam-6392	160	25	{	{	PUNCT
ejpam-6392	160	26	gf	gf	PROPN
ejpam-6392	160	27	(	(	PUNCT
ejpam-6392	160	28	e	e	NOUN
ejpam-6392	160	29	•	•	NOUN
ejpam-6392	160	30	3	3	NUM
ejpam-6392	160	31	•	•	NUM
ejpam-6392	160	32	ä	ä	PROPN
ejpam-6392	160	33	)	)	PUNCT
ejpam-6392	160	34	,	,	PUNCT
ejpam-6392	160	35	gf	gf	X
ejpam-6392	160	36	(	(	PUNCT
ejpam-6392	160	37	ä	ä	NOUN
ejpam-6392	160	38	)	)	PUNCT
ejpam-6392	160	39	}	}	PUNCT
ejpam-6392	160	40	=	=	SYM
ejpam-6392	160	41	max{gf	max{gf	X
ejpam-6392	160	42	(	(	PUNCT
ejpam-6392	160	43	e	e	NOUN
ejpam-6392	160	44	•	•	NOUN
ejpam-6392	160	45	3	3	NUM
ejpam-6392	160	46	•	•	NUM
ejpam-6392	160	47	3	3	NUM
ejpam-6392	160	48	)	)	PUNCT
ejpam-6392	160	49	,	,	PUNCT
ejpam-6392	160	50	gf	gf	X
ejpam-6392	160	51	(	(	PUNCT
ejpam-6392	160	52	3	3	NUM
ejpam-6392	160	53	)	)	PUNCT
ejpam-6392	160	54	}	}	PUNCT
ejpam-6392	160	55	.	.	PUNCT
ejpam-6392	161	1	theorem	theorem	ADJ
ejpam-6392	161	2	3.2	3.2	NUM
ejpam-6392	161	3	.	.	PUNCT
ejpam-6392	162	1	let	let	VERB
ejpam-6392	162	2	g=(gt	g=(gt	NOUN
ejpam-6392	162	3	,	,	PUNCT
ejpam-6392	162	4	gi	gi	INTJ
ejpam-6392	162	5	,	,	PUNCT
ejpam-6392	162	6	gf	gf	PROPN
ejpam-6392	162	7	)	)	PUNCT
ejpam-6392	162	8	and	and	CCONJ
ejpam-6392	162	9	h=(ht	h=(ht	NOUN
ejpam-6392	162	10	,	,	PUNCT
ejpam-6392	162	11	hi	hi	INTJ
ejpam-6392	162	12	,	,	PUNCT
ejpam-6392	162	13	hf	hf	INTJ
ejpam-6392	162	14	)	)	PUNCT
ejpam-6392	162	15	be	be	AUX
ejpam-6392	162	16	two	two	NUM
ejpam-6392	162	17	neutrosophic	neutrosophic	ADJ
ejpam-6392	162	18	bi	bi	NOUN
ejpam-6392	162	19	-	-	NOUN
ejpam-6392	162	20	ideals	ideal	NOUN
ejpam-6392	162	21	of	of	ADP
ejpam-6392	162	22	ink	ink	NOUN
ejpam-6392	162	23	-	-	PUNCT
ejpam-6392	162	24	algebra	algebra	NOUN
ejpam-6392	162	25	¨̈u	¨̈u	NOUN
ejpam-6392	162	26	.	.	PUNCT
ejpam-6392	163	1	then	then	ADV
ejpam-6392	163	2	g	g	PROPN
ejpam-6392	163	3	∩	∩	ADJ
ejpam-6392	163	4	h	h	NOUN
ejpam-6392	163	5	=	=	SYM
ejpam-6392	163	6	(	(	PUNCT
ejpam-6392	163	7	tg∩h(e	tg∩h(e	PROPN
ejpam-6392	163	8	)	)	PUNCT
ejpam-6392	163	9	,	,	PUNCT
ejpam-6392	163	10	ig∩h(e	ig∩h(e	PROPN
ejpam-6392	163	11	)	)	PUNCT
ejpam-6392	163	12	,	,	PUNCT
ejpam-6392	163	13	fg∩h(e	fg∩h(e	PROPN
ejpam-6392	163	14	)	)	PUNCT
ejpam-6392	163	15	)	)	PUNCT
ejpam-6392	163	16	is	be	AUX
ejpam-6392	163	17	a	a	DET
ejpam-6392	163	18	neutrosophic	neutrosophic	ADJ
ejpam-6392	163	19	bi	bi	NOUN
ejpam-6392	163	20	-	-	NOUN
ejpam-6392	163	21	ideal	ideal	NOUN
ejpam-6392	163	22	of	of	ADP
ejpam-6392	163	23	ink	ink	NOUN
ejpam-6392	163	24	sub	sub	NOUN
ejpam-6392	163	25	-	-	NOUN
ejpam-6392	163	26	algebra	algebra	NOUN
ejpam-6392	163	27	of	of	ADP
ejpam-6392	163	28	¨̈u	¨̈u	NOUN
ejpam-6392	163	29	.	.	PUNCT
ejpam-6392	164	1	proof	proof	NOUN
ejpam-6392	164	2	.	.	PUNCT
ejpam-6392	165	1	let	let	VERB
ejpam-6392	165	2	g	g	NOUN
ejpam-6392	165	3	and	and	CCONJ
ejpam-6392	165	4	h	h	NOUN
ejpam-6392	165	5	be	be	VERB
ejpam-6392	165	6	two	two	NUM
ejpam-6392	165	7	neutrosophic	neutrosophic	ADJ
ejpam-6392	165	8	bi	bi	ADJ
ejpam-6392	165	9	ideals	ideal	NOUN
ejpam-6392	165	10	of	of	ADP
ejpam-6392	165	11	ink	ink	NOUN
ejpam-6392	165	12	-	-	PUNCT
ejpam-6392	165	13	algebra	algebra	NOUN
ejpam-6392	165	14	¨̈u	¨̈u	NOUN
ejpam-6392	165	15	.	.	PUNCT
ejpam-6392	166	1	(	(	PUNCT
ejpam-6392	166	2	i	i	NOUN
ejpam-6392	166	3	)	)	PUNCT
ejpam-6392	166	4	truth	truth	NOUN
ejpam-6392	166	5	membership	membership	NOUN
ejpam-6392	166	6	tg∩h(e•	tg∩h(e•	PROPN
ejpam-6392	166	7	3	3	NUM
ejpam-6392	166	8	)	)	PUNCT
ejpam-6392	166	9	=	=	PRON
ejpam-6392	166	10	min{gt	min{gt	NOUN
ejpam-6392	166	11	(	(	PUNCT
ejpam-6392	166	12	e•	e•	NOUN
ejpam-6392	166	13	3	3	NUM
ejpam-6392	166	14	)	)	PUNCT
ejpam-6392	166	15	,	,	PUNCT
ejpam-6392	166	16	ht	ht	PROPN
ejpam-6392	166	17	(	(	PUNCT
ejpam-6392	166	18	e•	e•	NOUN
ejpam-6392	166	19	3	3	NUM
ejpam-6392	166	20	)	)	PUNCT
ejpam-6392	166	21	}	}	PUNCT
ejpam-6392	166	22	≥	≥	PROPN
ejpam-6392	166	23	min	min	NOUN
ejpam-6392	166	24	{	{	PUNCT
ejpam-6392	166	25	min{gt	min{gt	ADV
ejpam-6392	166	26	(	(	PUNCT
ejpam-6392	166	27	e•	e•	NOUN
ejpam-6392	166	28	3•	3•	NUM
ejpam-6392	166	29	ä	ä	NOUN
ejpam-6392	166	30	)	)	PUNCT
ejpam-6392	166	31	,	,	PUNCT
ejpam-6392	166	32	gt	gt	PROPN
ejpam-6392	166	33	(	(	PUNCT
ejpam-6392	166	34	ä	ä	PROPN
ejpam-6392	166	35	)	)	PUNCT
ejpam-6392	166	36	}	}	PUNCT
ejpam-6392	166	37	,	,	PUNCT
ejpam-6392	166	38	min{ht	min{ht	VERB
ejpam-6392	166	39	(	(	PUNCT
ejpam-6392	166	40	e•	e•	VERB
ejpam-6392	166	41	3•	3•	NUM
ejpam-6392	166	42	ä	ä	NOUN
ejpam-6392	166	43	)	)	PUNCT
ejpam-6392	166	44	,	,	PUNCT
ejpam-6392	166	45	ht	ht	PROPN
ejpam-6392	166	46	(	(	PUNCT
ejpam-6392	166	47	ä	ä	NOUN
ejpam-6392	166	48	)	)	PUNCT
ejpam-6392	166	49	}	}	PUNCT
ejpam-6392	166	50	=	=	SYM
ejpam-6392	166	51	min{min	min{min	X
ejpam-6392	166	52	{	{	PUNCT
ejpam-6392	166	53	gt	gt	PROPN
ejpam-6392	166	54	(	(	PUNCT
ejpam-6392	166	55	e•	e•	PROPN
ejpam-6392	166	56	3•	3•	NUM
ejpam-6392	166	57	ä	ä	NOUN
ejpam-6392	166	58	)	)	PUNCT
ejpam-6392	166	59	,	,	PUNCT
ejpam-6392	166	60	ht	ht	PROPN
ejpam-6392	166	61	(	(	PUNCT
ejpam-6392	166	62	e•	e•	PROPN
ejpam-6392	166	63	3•	3•	NUM
ejpam-6392	166	64	ä	ä	NOUN
ejpam-6392	166	65	)	)	PUNCT
ejpam-6392	166	66	}	}	PUNCT
ejpam-6392	166	67	,	,	PUNCT
ejpam-6392	166	68	min{gt	min{gt	PRON
ejpam-6392	166	69	(	(	PUNCT
ejpam-6392	166	70	ä	ä	X
ejpam-6392	166	71	)	)	PUNCT
ejpam-6392	166	72	,	,	PUNCT
ejpam-6392	166	73	ht	ht	PROPN
ejpam-6392	166	74	(	(	PUNCT
ejpam-6392	166	75	ä	ä	NOUN
ejpam-6392	166	76	)	)	PUNCT
ejpam-6392	166	77	}	}	PUNCT
ejpam-6392	166	78	≥	≥	PROPN
ejpam-6392	166	79	min{tg∩h	min{tg∩h	NOUN
ejpam-6392	166	80	(	(	PUNCT
ejpam-6392	166	81	e•	e•	NOUN
ejpam-6392	166	82	3•	3•	NUM
ejpam-6392	166	83	ä	ä	NOUN
ejpam-6392	166	84	)	)	PUNCT
ejpam-6392	166	85	,	,	PUNCT
ejpam-6392	166	86	tg∩h	tg∩h	PROPN
ejpam-6392	166	87	(	(	PUNCT
ejpam-6392	166	88	ä	ä	NOUN
ejpam-6392	166	89	)	)	PUNCT
ejpam-6392	166	90	}	}	PUNCT
ejpam-6392	166	91	(	(	PUNCT
ejpam-6392	166	92	ii	ii	NOUN
ejpam-6392	166	93	)	)	PUNCT
ejpam-6392	166	94	indeterminacy	indeterminacy	NOUN
ejpam-6392	166	95	membership	membership	NOUN
ejpam-6392	166	96	ig∩h(e•	ig∩h(e•	PROPN
ejpam-6392	166	97	3	3	NUM
ejpam-6392	166	98	)	)	PUNCT
ejpam-6392	166	99	=	=	SYM
ejpam-6392	166	100	max{gi(e•	max{gi(e•	X
ejpam-6392	166	101	3	3	NUM
ejpam-6392	166	102	)	)	PUNCT
ejpam-6392	166	103	,	,	PUNCT
ejpam-6392	166	104	hi(e•	hi(e•	PROPN
ejpam-6392	166	105	3	3	NUM
ejpam-6392	166	106	)	)	PUNCT
ejpam-6392	166	107	}	}	PUNCT
ejpam-6392	166	108	≤	≤	NUM
ejpam-6392	166	109	max	max	PROPN
ejpam-6392	166	110	{	{	PUNCT
ejpam-6392	166	111	max{gi(e•	max{gi(e•	PROPN
ejpam-6392	166	112	3•	3•	NUM
ejpam-6392	166	113	ä	ä	NOUN
ejpam-6392	166	114	)	)	PUNCT
ejpam-6392	166	115	,	,	PUNCT
ejpam-6392	166	116	gi(ä	gi(ä	NOUN
ejpam-6392	166	117	)	)	PUNCT
ejpam-6392	166	118	}	}	PUNCT
ejpam-6392	166	119	,	,	PUNCT
ejpam-6392	166	120	max{hi(e•	max{hi(e•	PROPN
ejpam-6392	166	121	3•	3•	NUM
ejpam-6392	166	122	ä	ä	NOUN
ejpam-6392	166	123	)	)	PUNCT
ejpam-6392	166	124	,	,	PUNCT
ejpam-6392	166	125	hi(ä	hi(ä	ADV
ejpam-6392	166	126	)	)	PUNCT
ejpam-6392	166	127	}	}	PUNCT
ejpam-6392	166	128	=	=	SYM
ejpam-6392	166	129	max{max	max{max	X
ejpam-6392	166	130	{	{	PUNCT
ejpam-6392	166	131	gi(e•	gi(e•	PROPN
ejpam-6392	166	132	3•	3•	NUM
ejpam-6392	166	133	ä	ä	NOUN
ejpam-6392	166	134	)	)	PUNCT
ejpam-6392	166	135	,	,	PUNCT
ejpam-6392	166	136	hi(e•	hi(e•	PROPN
ejpam-6392	166	137	3•	3•	NUM
ejpam-6392	166	138	ä	ä	NOUN
ejpam-6392	166	139	)	)	PUNCT
ejpam-6392	166	140	}	}	PUNCT
ejpam-6392	166	141	,	,	PUNCT
ejpam-6392	166	142	max{gi(ä	max{gi(ä	ADV
ejpam-6392	166	143	)	)	PUNCT
ejpam-6392	166	144	,	,	PUNCT
ejpam-6392	166	145	hi(ä	hi(ä	ADV
ejpam-6392	166	146	)	)	PUNCT
ejpam-6392	166	147	}	}	PUNCT
ejpam-6392	166	148	≤	≤	NUM
ejpam-6392	166	149	max{ig∩h	max{ig∩h	NOUN
ejpam-6392	166	150	(	(	PUNCT
ejpam-6392	166	151	e•	e•	NOUN
ejpam-6392	166	152	3•	3•	NUM
ejpam-6392	166	153	ä	ä	NOUN
ejpam-6392	166	154	)	)	PUNCT
ejpam-6392	166	155	,	,	PUNCT
ejpam-6392	166	156	ig∩h	ig∩h	X
ejpam-6392	166	157	(	(	PUNCT
ejpam-6392	166	158	ä	ä	NOUN
ejpam-6392	166	159	)	)	PUNCT
ejpam-6392	166	160	}	}	PUNCT
ejpam-6392	166	161	m.	m.	NOUN
ejpam-6392	166	162	remala	remala	NOUN
ejpam-6392	166	163	,	,	PUNCT
ejpam-6392	166	164	e.	e.	PROPN
ejpam-6392	166	165	tamma	tamma	PROPN
ejpam-6392	166	166	,	,	PUNCT
ejpam-6392	166	167	y.	y.	PROPN
ejpam-6392	166	168	bhargavi	bhargavi	PROPN
ejpam-6392	166	169	/	/	SYM
ejpam-6392	166	170	eur	eur	PROPN
ejpam-6392	166	171	.	.	PUNCT
ejpam-6392	167	1	j.	j.	PROPN
ejpam-6392	167	2	pure	pure	PROPN
ejpam-6392	167	3	appl	appl	PROPN
ejpam-6392	167	4	.	.	PROPN
ejpam-6392	167	5	math	math	PROPN
ejpam-6392	167	6	,	,	PUNCT
ejpam-6392	167	7	18	18	NUM
ejpam-6392	167	8	(	(	PUNCT
ejpam-6392	167	9	4	4	NUM
ejpam-6392	167	10	)	)	PUNCT
ejpam-6392	167	11	(	(	PUNCT
ejpam-6392	167	12	2025	2025	NUM
ejpam-6392	167	13	)	)	PUNCT
ejpam-6392	167	14	,	,	PUNCT
ejpam-6392	167	15	6392	6392	NUM
ejpam-6392	167	16	8	8	NUM
ejpam-6392	167	17	of	of	ADP
ejpam-6392	167	18	20	20	NUM
ejpam-6392	167	19	(	(	PUNCT
ejpam-6392	167	20	iii	iii	NOUN
ejpam-6392	167	21	)	)	PUNCT
ejpam-6392	167	22	(	(	PUNCT
ejpam-6392	167	23	falsehood	falsehood	NOUN
ejpam-6392	167	24	membership	membership	NOUN
ejpam-6392	167	25	)	)	PUNCT
ejpam-6392	167	26	fg∩h(e•	fg∩h(e•	ADP
ejpam-6392	167	27	3	3	NUM
ejpam-6392	167	28	)	)	PUNCT
ejpam-6392	167	29	=	=	PRON
ejpam-6392	167	30	max{gf	max{gf	X
ejpam-6392	167	31	(	(	PUNCT
ejpam-6392	167	32	e•	e•	NOUN
ejpam-6392	167	33	3	3	NUM
ejpam-6392	167	34	)	)	PUNCT
ejpam-6392	167	35	,	,	PUNCT
ejpam-6392	167	36	hf	hf	INTJ
ejpam-6392	167	37	(	(	PUNCT
ejpam-6392	167	38	e•	e•	NOUN
ejpam-6392	167	39	3	3	NUM
ejpam-6392	167	40	)	)	PUNCT
ejpam-6392	167	41	}	}	PUNCT
ejpam-6392	167	42	≤	≤	NUM
ejpam-6392	167	43	max	max	PROPN
ejpam-6392	167	44	{	{	PUNCT
ejpam-6392	167	45	max{gf	max{gf	X
ejpam-6392	167	46	(	(	PUNCT
ejpam-6392	167	47	e•	e•	NOUN
ejpam-6392	167	48	3•	3•	NUM
ejpam-6392	167	49	ä	ä	NOUN
ejpam-6392	167	50	)	)	PUNCT
ejpam-6392	167	51	,	,	PUNCT
ejpam-6392	167	52	gf	gf	X
ejpam-6392	167	53	(	(	PUNCT
ejpam-6392	167	54	ä	ä	NOUN
ejpam-6392	167	55	)	)	PUNCT
ejpam-6392	167	56	}	}	PUNCT
ejpam-6392	167	57	,	,	PUNCT
ejpam-6392	167	58	max{hf	max{hf	NOUN
ejpam-6392	167	59	(	(	PUNCT
ejpam-6392	167	60	e•	e•	VERB
ejpam-6392	167	61	3•	3•	NUM
ejpam-6392	167	62	ä	ä	NOUN
ejpam-6392	167	63	)	)	PUNCT
ejpam-6392	167	64	,	,	PUNCT
ejpam-6392	167	65	hf	hf	X
ejpam-6392	167	66	(	(	PUNCT
ejpam-6392	167	67	ä	ä	NOUN
ejpam-6392	167	68	)	)	PUNCT
ejpam-6392	167	69	}	}	PUNCT
ejpam-6392	167	70	=	=	SYM
ejpam-6392	167	71	max{max	max{max	NOUN
ejpam-6392	167	72	{	{	PUNCT
ejpam-6392	167	73	gf	gf	X
ejpam-6392	167	74	(	(	PUNCT
ejpam-6392	167	75	e•	e•	VERB
ejpam-6392	167	76	3•	3•	NUM
ejpam-6392	167	77	ä	ä	NOUN
ejpam-6392	167	78	)	)	PUNCT
ejpam-6392	167	79	,	,	PUNCT
ejpam-6392	167	80	hf	hf	INTJ
ejpam-6392	167	81	(	(	PUNCT
ejpam-6392	167	82	e•	e•	NOUN
ejpam-6392	167	83	3•	3•	NUM
ejpam-6392	167	84	ä	ä	NOUN
ejpam-6392	167	85	)	)	PUNCT
ejpam-6392	167	86	}	}	PUNCT
ejpam-6392	167	87	,	,	PUNCT
ejpam-6392	167	88	max{gf	max{gf	X
ejpam-6392	167	89	(	(	PUNCT
ejpam-6392	167	90	ä	ä	PROPN
ejpam-6392	167	91	)	)	PUNCT
ejpam-6392	167	92	,	,	PUNCT
ejpam-6392	167	93	hf	hf	X
ejpam-6392	167	94	(	(	PUNCT
ejpam-6392	167	95	ä	ä	NOUN
ejpam-6392	167	96	)	)	PUNCT
ejpam-6392	167	97	}	}	PUNCT
ejpam-6392	167	98	≤	≤	NUM
ejpam-6392	167	99	max{fg∩h	max{fg∩h	PROPN
ejpam-6392	167	100	(	(	PUNCT
ejpam-6392	167	101	e•	e•	PROPN
ejpam-6392	167	102	3•	3•	NUM
ejpam-6392	167	103	ä	ä	NOUN
ejpam-6392	167	104	)	)	PUNCT
ejpam-6392	167	105	,	,	PUNCT
ejpam-6392	167	106	fg∩h	fg∩h	PROPN
ejpam-6392	167	107	(	(	PUNCT
ejpam-6392	167	108	ä	ä	NOUN
ejpam-6392	167	109	)	)	PUNCT
ejpam-6392	167	110	}	}	PUNCT
ejpam-6392	167	111	remark	remark	VERB
ejpam-6392	167	112	3.1	3.1	NUM
ejpam-6392	167	113	.	.	PUNCT
ejpam-6392	168	1	the	the	DET
ejpam-6392	168	2	union	union	NOUN
ejpam-6392	168	3	of	of	ADP
ejpam-6392	168	4	neutrosophic	neutrosophic	ADJ
ejpam-6392	168	5	bi	bi	NOUN
ejpam-6392	168	6	-	-	NOUN
ejpam-6392	168	7	ideal	ideal	NOUN
ejpam-6392	168	8	of	of	ADP
ejpam-6392	168	9	ink	ink	NOUN
ejpam-6392	168	10	-	-	PUNCT
ejpam-6392	168	11	sub	sub	NOUN
ejpam-6392	168	12	algebra	algebra	NOUN
ejpam-6392	168	13	of	of	ADP
ejpam-6392	168	14	ink	ink	NOUN
ejpam-6392	168	15	-	-	PUNCT
ejpam-6392	168	16	algebra	algebra	NOUN
ejpam-6392	168	17	¨̈u	¨̈u	NOUN
ejpam-6392	168	18	need	need	NOUN
ejpam-6392	168	19	not	not	PART
ejpam-6392	168	20	be	be	AUX
ejpam-6392	168	21	a	a	DET
ejpam-6392	168	22	union	union	NOUN
ejpam-6392	168	23	of	of	ADP
ejpam-6392	168	24	neutrosophic	neutrosophic	ADJ
ejpam-6392	168	25	bi	bi	PROPN
ejpam-6392	168	26	ideal	ideal	NOUN
ejpam-6392	168	27	.	.	PUNCT
ejpam-6392	169	1	example	example	NOUN
ejpam-6392	169	2	3.2	3.2	NUM
ejpam-6392	169	3	.	.	PUNCT
ejpam-6392	170	1	consider	consider	VERB
ejpam-6392	170	2	ink	ink	NOUN
ejpam-6392	170	3	sub	sub	NOUN
ejpam-6392	170	4	algebra	algebra	NOUN
ejpam-6392	170	5	¨̈u	¨̈u	VERB
ejpam-6392	170	6	=	=	SYM
ejpam-6392	170	7	{	{	PUNCT
ejpam-6392	170	8	0	0	NUM
ejpam-6392	170	9	,	,	PUNCT
ejpam-6392	170	10	2	2	NUM
ejpam-6392	170	11	,	,	PUNCT
ejpam-6392	170	12	4	4	NUM
ejpam-6392	170	13	,	,	PUNCT
ejpam-6392	170	14	6	6	NUM
ejpam-6392	170	15	}	}	PUNCT
ejpam-6392	170	16	with	with	ADP
ejpam-6392	170	17	the	the	DET
ejpam-6392	170	18	following	follow	VERB
ejpam-6392	170	19	cayley	cayley	ADJ
ejpam-6392	170	20	table	table	NOUN
ejpam-6392	170	21	.	.	PUNCT
ejpam-6392	171	1	•	•	NUM
ejpam-6392	171	2	0	0	NUM
ejpam-6392	171	3	2	2	NUM
ejpam-6392	171	4	4	4	NUM
ejpam-6392	171	5	6	6	NUM
ejpam-6392	171	6	0	0	NUM
ejpam-6392	171	7	0	0	NUM
ejpam-6392	171	8	0	0	NUM
ejpam-6392	171	9	0	0	NUM
ejpam-6392	171	10	0	0	NUM
ejpam-6392	171	11	2	2	NUM
ejpam-6392	171	12	2	2	NUM
ejpam-6392	171	13	0	0	NUM
ejpam-6392	171	14	0	0	NUM
ejpam-6392	171	15	2	2	NUM
ejpam-6392	171	16	4	4	NUM
ejpam-6392	171	17	4	4	NUM
ejpam-6392	171	18	2	2	NUM
ejpam-6392	171	19	0	0	NUM
ejpam-6392	171	20	4	4	NUM
ejpam-6392	171	21	6	6	NUM
ejpam-6392	171	22	6	6	NUM
ejpam-6392	171	23	6	6	NUM
ejpam-6392	171	24	6	6	NUM
ejpam-6392	171	25	0	0	NUM
ejpam-6392	171	26	define	define	VERB
ejpam-6392	171	27	neutrosophic	neutrosophic	ADJ
ejpam-6392	171	28	bi	bi	NOUN
ejpam-6392	171	29	-	-	NOUN
ejpam-6392	171	30	ideal	ideal	ADJ
ejpam-6392	171	31	g	g	NOUN
ejpam-6392	171	32	=	=	SYM
ejpam-6392	171	33	(	(	PUNCT
ejpam-6392	171	34	gt	gt	INTJ
ejpam-6392	171	35	,	,	PUNCT
ejpam-6392	171	36	gi	gi	INTJ
ejpam-6392	171	37	,	,	PUNCT
ejpam-6392	171	38	gf	gf	PROPN
ejpam-6392	171	39	)	)	PUNCT
ejpam-6392	171	40	by	by	ADP
ejpam-6392	171	41	the	the	DET
ejpam-6392	171	42	component	component	NOUN
ejpam-6392	171	43	memberships	membership	VERB
ejpam-6392	171	44	below	below	ADV
ejpam-6392	171	45	.	.	PUNCT
ejpam-6392	172	1	•	•	NUM
ejpam-6392	172	2	0	0	NUM
ejpam-6392	172	3	2	2	NUM
ejpam-6392	172	4	4	4	NUM
ejpam-6392	172	5	6	6	NUM
ejpam-6392	172	6	gt	gt	PROPN
ejpam-6392	172	7	0.4	0.4	NUM
ejpam-6392	172	8	0.6	0.6	NUM
ejpam-6392	172	9	0.3	0.3	NUM
ejpam-6392	172	10	0.5	0.5	NUM
ejpam-6392	172	11	gi	gi	NOUN
ejpam-6392	172	12	0.3	0.3	NUM
ejpam-6392	172	13	0.8	0.8	NUM
ejpam-6392	172	14	0.5	0.5	NUM
ejpam-6392	172	15	0.6	0.6	NUM
ejpam-6392	172	16	gf	gf	NOUN
ejpam-6392	172	17	0.4	0.4	NUM
ejpam-6392	172	18	0.6	0.6	NUM
ejpam-6392	172	19	0.4	0.4	NUM
ejpam-6392	172	20	0.3	0.3	NUM
ejpam-6392	172	21	define	define	VERB
ejpam-6392	172	22	neutrosophic	neutrosophic	ADJ
ejpam-6392	172	23	bi	bi	ADJ
ejpam-6392	172	24	-	-	ADJ
ejpam-6392	172	25	ideal	ideal	ADJ
ejpam-6392	172	26	h	h	NOUN
ejpam-6392	172	27	=	=	PUNCT
ejpam-6392	172	28	(	(	PUNCT
ejpam-6392	172	29	ht	ht	INTJ
ejpam-6392	172	30	,	,	PUNCT
ejpam-6392	172	31	hi	hi	INTJ
ejpam-6392	172	32	,	,	PUNCT
ejpam-6392	172	33	hf	hf	PROPN
ejpam-6392	172	34	)	)	PUNCT
ejpam-6392	172	35	by	by	ADP
ejpam-6392	172	36	the	the	DET
ejpam-6392	172	37	component	component	NOUN
ejpam-6392	172	38	memberships	membership	VERB
ejpam-6392	172	39	below	below	ADV
ejpam-6392	172	40	.	.	PUNCT
ejpam-6392	173	1	•	•	NUM
ejpam-6392	173	2	0	0	NUM
ejpam-6392	173	3	2	2	NUM
ejpam-6392	173	4	4	4	NUM
ejpam-6392	173	5	6	6	NUM
ejpam-6392	173	6	ht	ht	PROPN
ejpam-6392	173	7	0.6	0.6	NUM
ejpam-6392	173	8	0.4	0.4	NUM
ejpam-6392	173	9	0.4	0.4	NUM
ejpam-6392	173	10	0.4	0.4	NUM
ejpam-6392	173	11	hi	hi	NOUN
ejpam-6392	173	12	0.7	0.7	NUM
ejpam-6392	173	13	0.8	0.8	NUM
ejpam-6392	173	14	0.5	0.5	NUM
ejpam-6392	173	15	0.4	0.4	NUM
ejpam-6392	173	16	hf	hf	NOUN
ejpam-6392	173	17	0.8	0.8	NUM
ejpam-6392	173	18	0.2	0.2	NUM
ejpam-6392	173	19	0.4	0.4	NUM
ejpam-6392	173	20	0.5	0.5	NUM
ejpam-6392	173	21	clearly	clearly	ADV
ejpam-6392	173	22	,	,	PUNCT
ejpam-6392	173	23	g	g	PROPN
ejpam-6392	173	24	and	and	CCONJ
ejpam-6392	173	25	h	h	NOUN
ejpam-6392	173	26	are	be	AUX
ejpam-6392	173	27	two	two	NUM
ejpam-6392	173	28	neutrosophic	neutrosophic	ADJ
ejpam-6392	173	29	bi	bi	NOUN
ejpam-6392	173	30	-	-	NOUN
ejpam-6392	173	31	ideals	ideal	NOUN
ejpam-6392	173	32	of	of	ADP
ejpam-6392	173	33	ink	ink	NOUN
ejpam-6392	173	34	sub	sub	NOUN
ejpam-6392	173	35	-	-	NOUN
ejpam-6392	173	36	algebras	algebras	X
ejpam-6392	173	37	.	.	PUNCT
ejpam-6392	174	1	here	here	ADV
ejpam-6392	174	2	tg∪h(2	tg∪h(2	PROPN
ejpam-6392	174	3	•	•	NOUN
ejpam-6392	174	4	4	4	NUM
ejpam-6392	174	5	)	)	PUNCT
ejpam-6392	174	6	=	=	SYM
ejpam-6392	174	7	0.4	0.4	NUM
ejpam-6392	175	1	but	but	CCONJ
ejpam-6392	175	2	it	it	PRON
ejpam-6392	175	3	is	be	AUX
ejpam-6392	175	4	not	not	PART
ejpam-6392	175	5	greater	great	ADJ
ejpam-6392	175	6	than	than	ADP
ejpam-6392	175	7	or	or	CCONJ
ejpam-6392	175	8	equal	equal	ADJ
ejpam-6392	175	9	to	to	ADP
ejpam-6392	175	10	i.e.	i.e.	X
ejpam-6392	175	11	,	,	PUNCT
ejpam-6392	175	12	0.5=	0.5=	PROPN
ejpam-6392	175	13	min	min	PROPN
ejpam-6392	175	14	{	{	PUNCT
ejpam-6392	175	15	tg∪h(2	tg∪h(2	PROPN
ejpam-6392	175	16	•	•	ADV
ejpam-6392	175	17	4	4	NUM
ejpam-6392	175	18	•	•	NUM
ejpam-6392	175	19	6	6	NUM
ejpam-6392	175	20	)	)	PUNCT
ejpam-6392	175	21	,	,	PUNCT
ejpam-6392	175	22	tg∪h(6	tg∪h(6	NOUN
ejpam-6392	175	23	)	)	PUNCT
ejpam-6392	175	24	}	}	PUNCT
ejpam-6392	175	25	.	.	PUNCT
ejpam-6392	176	1	similarly	similarly	ADV
ejpam-6392	176	2	,	,	PUNCT
ejpam-6392	176	3	for	for	ADP
ejpam-6392	176	4	ig∪h(2	ig∪h(2	PROPN
ejpam-6392	176	5	•	•	NUM
ejpam-6392	176	6	4	4	NUM
ejpam-6392	176	7	)	)	PUNCT
ejpam-6392	176	8	=	=	SYM
ejpam-6392	176	9	0.7	0.7	NUM
ejpam-6392	176	10	but	but	CCONJ
ejpam-6392	176	11	it	it	PRON
ejpam-6392	176	12	is	be	AUX
ejpam-6392	176	13	not	not	PART
ejpam-6392	176	14	less	less	ADJ
ejpam-6392	176	15	than	than	ADP
ejpam-6392	176	16	or	or	CCONJ
ejpam-6392	176	17	equal	equal	ADJ
ejpam-6392	176	18	to	to	ADP
ejpam-6392	176	19	i.e.	i.e.	X
ejpam-6392	176	20	,	,	PUNCT
ejpam-6392	176	21	0.4=	0.4=	PROPN
ejpam-6392	176	22	max	max	PROPN
ejpam-6392	176	23	{	{	PUNCT
ejpam-6392	176	24	ig∪h(2	ig∪h(2	PROPN
ejpam-6392	176	25	•	•	NUM
ejpam-6392	176	26	4	4	NUM
ejpam-6392	176	27	•	•	NUM
ejpam-6392	176	28	6	6	NUM
ejpam-6392	176	29	)	)	PUNCT
ejpam-6392	176	30	,	,	PUNCT
ejpam-6392	176	31	tg∪h(6	tg∪h(6	NOUN
ejpam-6392	176	32	)	)	PUNCT
ejpam-6392	176	33	}	}	PUNCT
ejpam-6392	176	34	.	.	PUNCT
ejpam-6392	177	1	also	also	ADV
ejpam-6392	177	2	for	for	ADP
ejpam-6392	177	3	,	,	PUNCT
ejpam-6392	177	4	ig∪h(2	ig∪h(2	PROPN
ejpam-6392	177	5	•	•	ADP
ejpam-6392	177	6	4	4	NUM
ejpam-6392	177	7	)	)	PUNCT
ejpam-6392	177	8	=	=	SYM
ejpam-6392	177	9	0.8	0.8	NUM
ejpam-6392	178	1	but	but	CCONJ
ejpam-6392	178	2	it	it	PRON
ejpam-6392	178	3	is	be	AUX
ejpam-6392	178	4	not	not	PART
ejpam-6392	178	5	less	less	ADJ
ejpam-6392	178	6	than	than	ADP
ejpam-6392	178	7	or	or	CCONJ
ejpam-6392	178	8	equal	equal	ADJ
ejpam-6392	178	9	to	to	ADP
ejpam-6392	178	10	i.e.	i.e.	X
ejpam-6392	178	11	,	,	PUNCT
ejpam-6392	178	12	0.4=	0.4=	PROPN
ejpam-6392	178	13	max	max	PROPN
ejpam-6392	178	14	{	{	PUNCT
ejpam-6392	178	15	ig∪h(2	ig∪h(2	PROPN
ejpam-6392	178	16	•	•	NUM
ejpam-6392	178	17	4	4	NUM
ejpam-6392	178	18	•	•	NUM
ejpam-6392	178	19	6	6	NUM
ejpam-6392	178	20	)	)	PUNCT
ejpam-6392	178	21	,	,	PUNCT
ejpam-6392	178	22	tg∪h(6	tg∪h(6	NOUN
ejpam-6392	178	23	)	)	PUNCT
ejpam-6392	178	24	}	}	PUNCT
ejpam-6392	178	25	.	.	PUNCT
ejpam-6392	179	1	therefore	therefore	ADV
ejpam-6392	179	2	,	,	PUNCT
ejpam-6392	179	3	g	g	PROPN
ejpam-6392	179	4	∪	∪	NOUN
ejpam-6392	179	5	h	h	NOUN
ejpam-6392	179	6	=	=	PUNCT
ejpam-6392	179	7	(	(	PUNCT
ejpam-6392	179	8	tg∪h	tg∪h	ADJ
ejpam-6392	179	9	,	,	PUNCT
ejpam-6392	179	10	ig∪h	ig∪h	NOUN
ejpam-6392	179	11	,	,	PUNCT
ejpam-6392	179	12	fg∪h	fg∪h	NOUN
ejpam-6392	179	13	)	)	PUNCT
ejpam-6392	179	14	is	be	AUX
ejpam-6392	179	15	not	not	PART
ejpam-6392	179	16	a	a	DET
ejpam-6392	179	17	neutrosophic	neutrosophic	ADJ
ejpam-6392	179	18	bi	bi	NOUN
ejpam-6392	179	19	-	-	NOUN
ejpam-6392	179	20	ideal	ideal	NOUN
ejpam-6392	179	21	of	of	ADP
ejpam-6392	179	22	ink	ink	NOUN
ejpam-6392	179	23	sub	sub	NOUN
ejpam-6392	179	24	-	-	NOUN
ejpam-6392	179	25	algebra	algebra	NOUN
ejpam-6392	179	26	.	.	PUNCT
ejpam-6392	180	1	thus	thus	ADV
ejpam-6392	180	2	,	,	PUNCT
ejpam-6392	180	3	union	union	NOUN
ejpam-6392	180	4	of	of	ADP
ejpam-6392	180	5	neutrosophic	neutrosophic	ADJ
ejpam-6392	180	6	bi	bi	NOUN
ejpam-6392	180	7	-	-	NOUN
ejpam-6392	180	8	ideal	ideal	NOUN
ejpam-6392	180	9	of	of	ADP
ejpam-6392	180	10	ink	ink	NOUN
ejpam-6392	180	11	-	-	PUNCT
ejpam-6392	180	12	sub	sub	NOUN
ejpam-6392	180	13	algebras	algebra	NOUN
ejpam-6392	180	14	is	be	AUX
ejpam-6392	180	15	not	not	PART
ejpam-6392	180	16	a	a	DET
ejpam-6392	180	17	neutrosophic	neutrosophic	ADJ
ejpam-6392	180	18	bi	bi	NOUN
ejpam-6392	180	19	-	-	NOUN
ejpam-6392	180	20	ideal	ideal	ADJ
ejpam-6392	180	21	.	.	PUNCT
ejpam-6392	181	1	in	in	ADP
ejpam-6392	181	2	particular	particular	ADJ
ejpam-6392	181	3	,	,	PUNCT
ejpam-6392	181	4	that	that	PRON
ejpam-6392	181	5	follows	follow	VERB
ejpam-6392	181	6	theorem	theorem	VERB
ejpam-6392	181	7	3.3	3.3	NUM
ejpam-6392	181	8	.	.	PUNCT
ejpam-6392	182	1	let	let	VERB
ejpam-6392	182	2	g	g	NOUN
ejpam-6392	182	3	=	=	SYM
ejpam-6392	182	4	(	(	PUNCT
ejpam-6392	182	5	gt	gt	INTJ
ejpam-6392	182	6	,	,	PUNCT
ejpam-6392	182	7	gi	gi	INTJ
ejpam-6392	182	8	,	,	PUNCT
ejpam-6392	182	9	gf	gf	PROPN
ejpam-6392	182	10	)	)	PUNCT
ejpam-6392	182	11	and	and	CCONJ
ejpam-6392	182	12	h	h	NOUN
ejpam-6392	182	13	=	=	SYM
ejpam-6392	182	14	(	(	PUNCT
ejpam-6392	182	15	ht	ht	INTJ
ejpam-6392	182	16	,	,	PUNCT
ejpam-6392	182	17	hi	hi	INTJ
ejpam-6392	182	18	,	,	PUNCT
ejpam-6392	182	19	hf	hf	INTJ
ejpam-6392	182	20	)	)	PUNCT
ejpam-6392	182	21	be	be	AUX
ejpam-6392	182	22	two	two	NUM
ejpam-6392	182	23	neutrosophic	neutrosophic	ADJ
ejpam-6392	182	24	bi	bi	NOUN
ejpam-6392	182	25	-	-	NOUN
ejpam-6392	182	26	ideals	ideal	NOUN
ejpam-6392	182	27	of	of	ADP
ejpam-6392	182	28	ink	ink	NOUN
ejpam-6392	182	29	sub	sub	NOUN
ejpam-6392	182	30	algebras	algebra	NOUN
ejpam-6392	182	31	of	of	ADP
ejpam-6392	182	32	ink	ink	NOUN
ejpam-6392	182	33	algebra	algebra	NOUN
ejpam-6392	182	34	¨̈u	¨̈u	VERB
ejpam-6392	182	35	,	,	PUNCT
ejpam-6392	182	36	then	then	ADV
ejpam-6392	182	37	g∪h	g∪h	NOUN
ejpam-6392	182	38	is	be	AUX
ejpam-6392	182	39	a	a	DET
ejpam-6392	182	40	neutrosophic	neutrosophic	ADJ
ejpam-6392	182	41	bi	bi	NOUN
ejpam-6392	182	42	-	-	NOUN
ejpam-6392	182	43	ideal	ideal	NOUN
ejpam-6392	182	44	of	of	ADP
ejpam-6392	182	45	ink	ink	NOUN
ejpam-6392	182	46	sub	sub	NOUN
ejpam-6392	182	47	-	-	NOUN
ejpam-6392	182	48	algebra	algebra	NOUN
ejpam-6392	182	49	only	only	ADV
ejpam-6392	182	50	if	if	SCONJ
ejpam-6392	182	51	g	g	PROPN
ejpam-6392	182	52	⊆	⊆	NUM
ejpam-6392	182	53	h	h	NOUN
ejpam-6392	182	54	or	or	CCONJ
ejpam-6392	182	55	h	h	NOUN
ejpam-6392	182	56	⊆	⊆	NUM
ejpam-6392	182	57	g.	g.	NOUN
ejpam-6392	182	58	proof	proof	NOUN
ejpam-6392	182	59	.	.	PUNCT
ejpam-6392	183	1	suppose	suppose	VERB
ejpam-6392	183	2	g	g	PROPN
ejpam-6392	183	3	⊆	⊆	NUM
ejpam-6392	183	4	h.	h.	NOUN
ejpam-6392	183	5	let	let	VERB
ejpam-6392	183	6	e	e	NOUN
ejpam-6392	183	7	,	,	PUNCT
ejpam-6392	183	8	3	3	NUM
ejpam-6392	183	9	∈	∈	PROPN
ejpam-6392	183	10	¨̈u	¨̈u	NOUN
ejpam-6392	183	11	.	.	PUNCT
ejpam-6392	183	12	m.	m.	NOUN
ejpam-6392	183	13	remala	remala	NOUN
ejpam-6392	183	14	,	,	PUNCT
ejpam-6392	183	15	e.	e.	PROPN
ejpam-6392	183	16	tamma	tamma	PROPN
ejpam-6392	183	17	,	,	PUNCT
ejpam-6392	183	18	y.	y.	PROPN
ejpam-6392	183	19	bhargavi	bhargavi	PROPN
ejpam-6392	183	20	/	/	SYM
ejpam-6392	183	21	eur	eur	PROPN
ejpam-6392	183	22	.	.	PUNCT
ejpam-6392	184	1	j.	j.	PROPN
ejpam-6392	184	2	pure	pure	PROPN
ejpam-6392	184	3	appl	appl	PROPN
ejpam-6392	184	4	.	.	PROPN
ejpam-6392	184	5	math	math	PROPN
ejpam-6392	184	6	,	,	PUNCT
ejpam-6392	184	7	18	18	NUM
ejpam-6392	184	8	(	(	PUNCT
ejpam-6392	184	9	4	4	NUM
ejpam-6392	184	10	)	)	PUNCT
ejpam-6392	184	11	(	(	PUNCT
ejpam-6392	184	12	2025	2025	NUM
ejpam-6392	184	13	)	)	PUNCT
ejpam-6392	184	14	,	,	PUNCT
ejpam-6392	184	15	6392	6392	NUM
ejpam-6392	184	16	9	9	NUM
ejpam-6392	184	17	of	of	ADP
ejpam-6392	184	18	20	20	NUM
ejpam-6392	184	19	(	(	PUNCT
ejpam-6392	184	20	i	i	NOUN
ejpam-6392	184	21	)	)	PUNCT
ejpam-6392	184	22	truth	truth	NOUN
ejpam-6392	184	23	membership	membership	NOUN
ejpam-6392	184	24	tg∪h(e	tg∪h(e	PROPN
ejpam-6392	184	25	•	•	NOUN
ejpam-6392	184	26	3	3	NUM
ejpam-6392	184	27	)	)	PUNCT
ejpam-6392	184	28	=	=	SYM
ejpam-6392	184	29	max	max	PROPN
ejpam-6392	184	30	{	{	PUNCT
ejpam-6392	184	31	gt	gt	PROPN
ejpam-6392	184	32	(	(	PUNCT
ejpam-6392	184	33	e	e	NOUN
ejpam-6392	184	34	•	•	NOUN
ejpam-6392	184	35	3	3	NUM
ejpam-6392	184	36	)	)	PUNCT
ejpam-6392	184	37	,	,	PUNCT
ejpam-6392	184	38	ht	ht	PROPN
ejpam-6392	184	39	(	(	PUNCT
ejpam-6392	184	40	e	e	NOUN
ejpam-6392	184	41	•	•	NOUN
ejpam-6392	184	42	3	3	NUM
ejpam-6392	184	43	)	)	PUNCT
ejpam-6392	184	44	}	}	PUNCT
ejpam-6392	185	1	=	=	SYM
ejpam-6392	185	2	ht	ht	X
ejpam-6392	185	3	(	(	PUNCT
ejpam-6392	185	4	e	e	NOUN
ejpam-6392	185	5	•	•	NOUN
ejpam-6392	185	6	3	3	NUM
ejpam-6392	185	7	)	)	PUNCT
ejpam-6392	185	8	≥	≥	NOUN
ejpam-6392	185	9	min{ht	min{ht	VERB
ejpam-6392	185	10	(	(	PUNCT
ejpam-6392	185	11	e	e	NOUN
ejpam-6392	185	12	•	•	NOUN
ejpam-6392	185	13	3	3	NUM
ejpam-6392	185	14	•	•	NUM
ejpam-6392	185	15	ä	ä	PROPN
ejpam-6392	185	16	)	)	PUNCT
ejpam-6392	185	17	,	,	PUNCT
ejpam-6392	185	18	ht	ht	PROPN
ejpam-6392	185	19	(	(	PUNCT
ejpam-6392	185	20	ä	ä	NOUN
ejpam-6392	185	21	)	)	PUNCT
ejpam-6392	185	22	}	}	PUNCT
ejpam-6392	185	23	≥	≥	NOUN
ejpam-6392	185	24	min	min	NOUN
ejpam-6392	185	25	{	{	PUNCT
ejpam-6392	185	26	max{gt	max{gt	X
ejpam-6392	185	27	(	(	PUNCT
ejpam-6392	185	28	e	e	NOUN
ejpam-6392	185	29	•	•	NOUN
ejpam-6392	185	30	3	3	NUM
ejpam-6392	185	31	•	•	NUM
ejpam-6392	185	32	ä	ä	PROPN
ejpam-6392	185	33	)	)	PUNCT
ejpam-6392	185	34	,	,	PUNCT
ejpam-6392	185	35	ht	ht	PROPN
ejpam-6392	185	36	(	(	PUNCT
ejpam-6392	185	37	e	e	NOUN
ejpam-6392	185	38	•	•	NUM
ejpam-6392	185	39	3	3	NUM
ejpam-6392	185	40	•	•	NUM
ejpam-6392	185	41	ä	ä	PROPN
ejpam-6392	185	42	)	)	PUNCT
ejpam-6392	185	43	}	}	PUNCT
ejpam-6392	185	44	•	•	ADP
ejpam-6392	185	45	max{gt	max{gt	X
ejpam-6392	185	46	(	(	PUNCT
ejpam-6392	185	47	ä	ä	NOUN
ejpam-6392	185	48	)	)	PUNCT
ejpam-6392	185	49	,	,	PUNCT
ejpam-6392	185	50	ht	ht	PROPN
ejpam-6392	185	51	(	(	PUNCT
ejpam-6392	185	52	ä	ä	NOUN
ejpam-6392	185	53	)	)	PUNCT
ejpam-6392	185	54	}	}	PUNCT
ejpam-6392	185	55	}	}	PUNCT
ejpam-6392	185	56	=	=	PUNCT
ejpam-6392	185	57	max{tg∪h(e	max{tg∪h(e	PROPN
ejpam-6392	185	58	•	•	NUM
ejpam-6392	185	59	3	3	NUM
ejpam-6392	185	60	•	•	NUM
ejpam-6392	185	61	ä	ä	NOUN
ejpam-6392	185	62	)	)	PUNCT
ejpam-6392	185	63	,	,	PUNCT
ejpam-6392	185	64	tg∪h(ä	tg∪h(ä	NOUN
ejpam-6392	185	65	)	)	PUNCT
ejpam-6392	185	66	}	}	PUNCT
ejpam-6392	185	67	.	.	PUNCT
ejpam-6392	186	1	(	(	PUNCT
ejpam-6392	186	2	ii	ii	NOUN
ejpam-6392	186	3	)	)	PUNCT
ejpam-6392	186	4	indeterminacy	indeterminacy	NOUN
ejpam-6392	186	5	membership	membership	NOUN
ejpam-6392	186	6	ig∪h(e	ig∪h(e	NOUN
ejpam-6392	186	7	•	•	NOUN
ejpam-6392	186	8	3	3	NUM
ejpam-6392	186	9	)	)	PUNCT
ejpam-6392	186	10	=	=	SYM
ejpam-6392	186	11	min	min	NOUN
ejpam-6392	186	12	{	{	PUNCT
ejpam-6392	186	13	gi(e	gi(e	NOUN
ejpam-6392	186	14	•	•	ADP
ejpam-6392	186	15	3	3	NUM
ejpam-6392	186	16	)	)	PUNCT
ejpam-6392	186	17	,	,	PUNCT
ejpam-6392	186	18	hi(e	hi(e	X
ejpam-6392	186	19	•	•	NOUN
ejpam-6392	186	20	3	3	NUM
ejpam-6392	186	21	)	)	PUNCT
ejpam-6392	186	22	}	}	PUNCT
ejpam-6392	187	1	=	=	PUNCT
ejpam-6392	187	2	hi(e	hi(e	NOUN
ejpam-6392	187	3	•	•	ADP
ejpam-6392	187	4	3	3	NUM
ejpam-6392	187	5	)	)	PUNCT
ejpam-6392	187	6	≤	≤	NUM
ejpam-6392	187	7	max{hi(e	max{hi(e	NOUN
ejpam-6392	187	8	•	•	ADP
ejpam-6392	187	9	3	3	NUM
ejpam-6392	187	10	•	•	NUM
ejpam-6392	187	11	ä	ä	NOUN
ejpam-6392	187	12	)	)	PUNCT
ejpam-6392	187	13	,	,	PUNCT
ejpam-6392	187	14	hi(ä	hi(ä	ADV
ejpam-6392	187	15	)	)	PUNCT
ejpam-6392	187	16	}	}	PUNCT
ejpam-6392	187	17	≤	≤	NUM
ejpam-6392	187	18	max	max	PROPN
ejpam-6392	187	19	{	{	PUNCT
ejpam-6392	187	20	min{gi(e	min{gi(e	NOUN
ejpam-6392	187	21	•	•	NUM
ejpam-6392	187	22	3	3	NUM
ejpam-6392	187	23	•	•	NUM
ejpam-6392	187	24	ä	ä	PROPN
ejpam-6392	187	25	)	)	PUNCT
ejpam-6392	187	26	,	,	PUNCT
ejpam-6392	187	27	hi(e	hi(e	X
ejpam-6392	187	28	•	•	NOUN
ejpam-6392	187	29	3	3	NUM
ejpam-6392	187	30	•	•	NUM
ejpam-6392	187	31	ä	ä	PROPN
ejpam-6392	187	32	)	)	PUNCT
ejpam-6392	187	33	}	}	PUNCT
ejpam-6392	187	34	•	•	NUM
ejpam-6392	187	35	min{gi(ä	min{gi(ä	NOUN
ejpam-6392	187	36	)	)	PUNCT
ejpam-6392	187	37	,	,	PUNCT
ejpam-6392	187	38	hi(ä	hi(ä	ADV
ejpam-6392	187	39	)	)	PUNCT
ejpam-6392	187	40	}	}	PUNCT
ejpam-6392	187	41	}	}	PUNCT
ejpam-6392	187	42	=	=	SYM
ejpam-6392	187	43	min	min	NOUN
ejpam-6392	187	44	{	{	PUNCT
ejpam-6392	187	45	ig∪h(e	ig∪h(e	NOUN
ejpam-6392	187	46	•	•	NOUN
ejpam-6392	187	47	3	3	NUM
ejpam-6392	187	48	•	•	NUM
ejpam-6392	187	49	ä	ä	PROPN
ejpam-6392	187	50	)	)	PUNCT
ejpam-6392	187	51	,	,	PUNCT
ejpam-6392	187	52	ig∪h(ä	ig∪h(ä	NOUN
ejpam-6392	187	53	)	)	PUNCT
ejpam-6392	187	54	}	}	PUNCT
ejpam-6392	187	55	.	.	PUNCT
ejpam-6392	188	1	(	(	PUNCT
ejpam-6392	188	2	iii	iii	X
ejpam-6392	188	3	)	)	PUNCT
ejpam-6392	188	4	falsehood	falsehood	NOUN
ejpam-6392	188	5	membership	membership	NOUN
ejpam-6392	188	6	fg∪h(e	fg∪h(e	NOUN
ejpam-6392	188	7	•	•	NOUN
ejpam-6392	188	8	3	3	NUM
ejpam-6392	188	9	)	)	PUNCT
ejpam-6392	188	10	=	=	SYM
ejpam-6392	188	11	min	min	X
ejpam-6392	188	12	{	{	PUNCT
ejpam-6392	188	13	gf	gf	X
ejpam-6392	188	14	(	(	PUNCT
ejpam-6392	188	15	e	e	NOUN
ejpam-6392	188	16	•	•	NOUN
ejpam-6392	188	17	3	3	NUM
ejpam-6392	188	18	)	)	PUNCT
ejpam-6392	188	19	,	,	PUNCT
ejpam-6392	188	20	hf	hf	X
ejpam-6392	188	21	(	(	PUNCT
ejpam-6392	188	22	e	e	NOUN
ejpam-6392	188	23	•	•	NOUN
ejpam-6392	188	24	3	3	NUM
ejpam-6392	188	25	)	)	PUNCT
ejpam-6392	188	26	}	}	PUNCT
ejpam-6392	189	1	=	=	SYM
ejpam-6392	189	2	hf	hf	X
ejpam-6392	189	3	(	(	PUNCT
ejpam-6392	189	4	e	e	NOUN
ejpam-6392	189	5	•	•	NUM
ejpam-6392	189	6	3	3	NUM
ejpam-6392	189	7	)	)	PUNCT
ejpam-6392	189	8	≤	≤	NOUN
ejpam-6392	189	9	max{hf	max{hf	NOUN
ejpam-6392	189	10	(	(	PUNCT
ejpam-6392	189	11	e	e	NOUN
ejpam-6392	189	12	•	•	NOUN
ejpam-6392	189	13	3	3	NUM
ejpam-6392	189	14	•	•	NUM
ejpam-6392	189	15	ä	ä	PROPN
ejpam-6392	189	16	)	)	PUNCT
ejpam-6392	189	17	,	,	PUNCT
ejpam-6392	189	18	hf	hf	X
ejpam-6392	189	19	(	(	PUNCT
ejpam-6392	189	20	ä	ä	NOUN
ejpam-6392	189	21	)	)	PUNCT
ejpam-6392	189	22	}	}	PUNCT
ejpam-6392	189	23	≤	≤	NUM
ejpam-6392	189	24	max	max	PROPN
ejpam-6392	189	25	{	{	PUNCT
ejpam-6392	189	26	min{gf	min{gf	PROPN
ejpam-6392	189	27	(	(	PUNCT
ejpam-6392	189	28	e	e	NOUN
ejpam-6392	189	29	•	•	NOUN
ejpam-6392	189	30	3	3	NUM
ejpam-6392	189	31	•	•	NUM
ejpam-6392	189	32	ä	ä	PROPN
ejpam-6392	189	33	)	)	PUNCT
ejpam-6392	189	34	,	,	PUNCT
ejpam-6392	189	35	hf	hf	X
ejpam-6392	189	36	(	(	PUNCT
ejpam-6392	189	37	e	e	NOUN
ejpam-6392	189	38	•	•	NOUN
ejpam-6392	189	39	3	3	NUM
ejpam-6392	189	40	•	•	NUM
ejpam-6392	189	41	ä	ä	PROPN
ejpam-6392	189	42	)	)	PUNCT
ejpam-6392	189	43	}	}	PUNCT
ejpam-6392	189	44	•	•	NUM
ejpam-6392	189	45	min{gf	min{gf	X
ejpam-6392	189	46	(	(	PUNCT
ejpam-6392	189	47	ä	ä	PROPN
ejpam-6392	189	48	)	)	PUNCT
ejpam-6392	189	49	,	,	PUNCT
ejpam-6392	189	50	hf	hf	X
ejpam-6392	189	51	(	(	PUNCT
ejpam-6392	189	52	ä	ä	NOUN
ejpam-6392	189	53	)	)	PUNCT
ejpam-6392	189	54	}	}	PUNCT
ejpam-6392	189	55	}	}	PUNCT
ejpam-6392	189	56	=	=	PUNCT
ejpam-6392	190	1	min{fg∪h(e	min{fg∪h(e	ADJ
ejpam-6392	190	2	•	•	NUM
ejpam-6392	190	3	3	3	NUM
ejpam-6392	190	4	•	•	NUM
ejpam-6392	190	5	ä	ä	PROPN
ejpam-6392	190	6	)	)	PUNCT
ejpam-6392	190	7	,	,	PUNCT
ejpam-6392	190	8	fg∪h(ä	fg∪h(ä	NOUN
ejpam-6392	190	9	)	)	PUNCT
ejpam-6392	190	10	}	}	PUNCT
ejpam-6392	190	11	.	.	PUNCT
ejpam-6392	191	1	this	this	PRON
ejpam-6392	191	2	completes	complete	VERB
ejpam-6392	191	3	the	the	DET
ejpam-6392	191	4	verification	verification	NOUN
ejpam-6392	191	5	under	under	ADP
ejpam-6392	191	6	the	the	DET
ejpam-6392	191	7	assumption	assumption	NOUN
ejpam-6392	191	8	g	g	PROPN
ejpam-6392	191	9	⊆	⊆	NUM
ejpam-6392	191	10	h.	h.	PROPN
ejpam-6392	191	11	4	4	NUM
ejpam-6392	191	12	.	.	PUNCT
ejpam-6392	192	1	homomorphism	homomorphism	NOUN
ejpam-6392	192	2	of	of	ADP
ejpam-6392	192	3	neutrosophic	neutrosophic	ADJ
ejpam-6392	192	4	bi	bi	NOUN
ejpam-6392	192	5	-	-	NOUN
ejpam-6392	192	6	ideal	ideal	NOUN
ejpam-6392	192	7	of	of	ADP
ejpam-6392	192	8	ink	ink	NOUN
ejpam-6392	192	9	sub	sub	ADJ
ejpam-6392	192	10	-	-	ADJ
ejpam-6392	192	11	algebra	algebra	ADJ
ejpam-6392	192	12	definition	definition	NOUN
ejpam-6392	192	13	4.1	4.1	NUM
ejpam-6392	192	14	.	.	PUNCT
ejpam-6392	193	1	let	let	VERB
ejpam-6392	193	2	¢	¢	NOUN
ejpam-6392	193	3	:	:	PUNCT
ejpam-6392	193	4	¨̈u	¨̈u	PROPN
ejpam-6392	193	5	→	→	SYM
ejpam-6392	193	6	˘̈̈	˘̈̈	PROPN
ejpam-6392	193	7	u	u	PROPN
ejpam-6392	193	8	be	be	AUX
ejpam-6392	193	9	a	a	DET
ejpam-6392	193	10	homomorphism	homomorphism	NOUN
ejpam-6392	193	11	of	of	ADP
ejpam-6392	193	12	ink	ink	NOUN
ejpam-6392	193	13	-	-	PUNCT
ejpam-6392	193	14	algebra	algebra	NOUN
ejpam-6392	193	15	and	and	CCONJ
ejpam-6392	193	16	g	g	NOUN
ejpam-6392	193	17	=	=	PUNCT
ejpam-6392	193	18	(	(	PUNCT
ejpam-6392	193	19	gt	gt	INTJ
ejpam-6392	193	20	,	,	PUNCT
ejpam-6392	193	21	gi	gi	INTJ
ejpam-6392	193	22	,	,	PUNCT
ejpam-6392	193	23	gf	gf	AUX
ejpam-6392	193	24	)	)	PUNCT
ejpam-6392	193	25	be	be	AUX
ejpam-6392	193	26	a	a	DET
ejpam-6392	193	27	neutrosophic	neutrosophic	ADJ
ejpam-6392	193	28	set	set	NOUN
ejpam-6392	193	29	in	in	ADP
ejpam-6392	193	30	x̆	x̆	PROPN
ejpam-6392	193	31	,	,	PUNCT
ejpam-6392	193	32	then	then	ADV
ejpam-6392	193	33	the	the	DET
ejpam-6392	193	34	neutrosophic	neutrosophic	ADJ
ejpam-6392	193	35	set	set	VERB
ejpam-6392	193	36	g[¢	g[¢	PROPN
ejpam-6392	193	37	]	]	X
ejpam-6392	194	1	=	=	X
ejpam-6392	195	1	(	(	PUNCT
ejpam-6392	195	2	gt	gt	PROPN
ejpam-6392	196	1	[	[	X
ejpam-6392	196	2	¢	¢	X
ejpam-6392	196	3	]	]	X
ejpam-6392	196	4	,	,	PUNCT
ejpam-6392	196	5	gi	gi	X
ejpam-6392	197	1	[	[	X
ejpam-6392	197	2	¢	¢	X
ejpam-6392	197	3	]	]	X
ejpam-6392	197	4	,	,	PUNCT
ejpam-6392	197	5	gf	gf	PROPN
ejpam-6392	198	1	[	[	X
ejpam-6392	198	2	¢	¢	X
ejpam-6392	198	3	]	]	X
ejpam-6392	198	4	)	)	PUNCT
ejpam-6392	198	5	in	in	ADP
ejpam-6392	198	6	¨̈u	¨̈u	NOUN
ejpam-6392	198	7	is	be	AUX
ejpam-6392	198	8	defined	define	VERB
ejpam-6392	198	9	by	by	ADP
ejpam-6392	198	10	neutrosophic	neutrosophic	ADJ
ejpam-6392	198	11	set	set	NOUN
ejpam-6392	198	12	such	such	ADJ
ejpam-6392	198	13	that	that	PRON
ejpam-6392	198	14	for	for	SCONJ
ejpam-6392	198	15	every	every	DET
ejpam-6392	198	16	e	e	PROPN
ejpam-6392	198	17	∈	∈	PROPN
ejpam-6392	198	18	¨̈u	¨̈u	NOUN
ejpam-6392	198	19	is	be	AUX
ejpam-6392	198	20	called	call	VERB
ejpam-6392	198	21	pre	pre	ADJ
ejpam-6392	198	22	-	-	NOUN
ejpam-6392	198	23	image	image	NOUN
ejpam-6392	198	24	of	of	ADP
ejpam-6392	198	25	g	g	NOUN
ejpam-6392	198	26	under	under	ADP
ejpam-6392	198	27	¢.	¢.	PROPN
ejpam-6392	198	28	gt	gt	PROPN
ejpam-6392	199	1	[	[	X
ejpam-6392	199	2	¢	¢	X
ejpam-6392	199	3	]	]	X
ejpam-6392	199	4	:	:	PUNCT
ejpam-6392	199	5	¨̈u	¨̈u	NOUN
ejpam-6392	199	6	→	→	SYM
ejpam-6392	199	7	[	[	X
ejpam-6392	199	8	0	0	NUM
ejpam-6392	199	9	,	,	PUNCT
ejpam-6392	199	10	1	1	NUM
ejpam-6392	199	11	]	]	PUNCT
ejpam-6392	199	12	,	,	PUNCT
ejpam-6392	199	13	gt	gt	PROPN
ejpam-6392	200	1	[	[	X
ejpam-6392	200	2	¢](e	¢](e	X
ejpam-6392	200	3	)	)	PUNCT
ejpam-6392	200	4	=	=	SYM
ejpam-6392	200	5	gt	gt	PROPN
ejpam-6392	200	6	(	(	PUNCT
ejpam-6392	200	7	¢(e	¢(e	PROPN
ejpam-6392	200	8	)	)	PUNCT
ejpam-6392	200	9	)	)	PUNCT
ejpam-6392	200	10	.	.	PUNCT
ejpam-6392	201	1	gi	gi	VERB
ejpam-6392	202	1	[	[	X
ejpam-6392	202	2	¢	¢	X
ejpam-6392	202	3	]	]	X
ejpam-6392	202	4	:	:	PUNCT
ejpam-6392	202	5	¨̈u	¨̈u	NOUN
ejpam-6392	202	6	→	→	SYM
ejpam-6392	203	1	[	[	X
ejpam-6392	203	2	0	0	NUM
ejpam-6392	203	3	,	,	PUNCT
ejpam-6392	203	4	1	1	NUM
ejpam-6392	203	5	]	]	PUNCT
ejpam-6392	203	6	,	,	PUNCT
ejpam-6392	203	7	gi	gi	X
ejpam-6392	203	8	[	[	X
ejpam-6392	203	9	¢](e	¢](e	X
ejpam-6392	203	10	)	)	PUNCT
ejpam-6392	203	11	=	=	PUNCT
ejpam-6392	203	12	gi(¢(e	gi(¢(e	PROPN
ejpam-6392	203	13	)	)	PUNCT
ejpam-6392	203	14	)	)	PUNCT
ejpam-6392	203	15	.	.	PUNCT
ejpam-6392	204	1	gf	gf	NOUN
ejpam-6392	205	1	[	[	X
ejpam-6392	205	2	¢	¢	X
ejpam-6392	205	3	]	]	X
ejpam-6392	205	4	:	:	PUNCT
ejpam-6392	205	5	¨̈u	¨̈u	NOUN
ejpam-6392	205	6	→	→	SYM
ejpam-6392	205	7	[	[	X
ejpam-6392	205	8	0	0	NUM
ejpam-6392	205	9	,	,	PUNCT
ejpam-6392	205	10	1	1	NUM
ejpam-6392	205	11	]	]	PUNCT
ejpam-6392	205	12	,	,	PUNCT
ejpam-6392	205	13	gf	gf	PROPN
ejpam-6392	205	14	[	[	X
ejpam-6392	205	15	¢](e	¢](e	X
ejpam-6392	205	16	)	)	PUNCT
ejpam-6392	205	17	=	=	SYM
ejpam-6392	206	1	gf	gf	X
ejpam-6392	206	2	(	(	PUNCT
ejpam-6392	206	3	¢(e	¢(e	NOUN
ejpam-6392	206	4	)	)	PUNCT
ejpam-6392	206	5	)	)	PUNCT
ejpam-6392	206	6	.	.	PUNCT
ejpam-6392	207	1	proof	proof	NOUN
ejpam-6392	207	2	.	.	PUNCT
ejpam-6392	208	1	let	let	VERB
ejpam-6392	208	2	¢	¢	NOUN
ejpam-6392	208	3	:	:	PUNCT
ejpam-6392	208	4	¨̈u	¨̈u	PROPN
ejpam-6392	208	5	→	→	SYM
ejpam-6392	208	6	˘̈̈	˘̈̈	PROPN
ejpam-6392	208	7	u	u	PROPN
ejpam-6392	208	8	be	be	AUX
ejpam-6392	208	9	a	a	DET
ejpam-6392	208	10	homomorphism	homomorphism	NOUN
ejpam-6392	208	11	of	of	ADP
ejpam-6392	208	12	ink	ink	NOUN
ejpam-6392	208	13	-	-	PUNCT
ejpam-6392	208	14	algebra	algebra	NOUN
ejpam-6392	208	15	.	.	PUNCT
ejpam-6392	209	1	if	if	SCONJ
ejpam-6392	209	2	g	g	PROPN
ejpam-6392	209	3	=	=	SYM
ejpam-6392	209	4	(	(	PUNCT
ejpam-6392	209	5	gt	gt	INTJ
ejpam-6392	209	6	,	,	PUNCT
ejpam-6392	209	7	gi	gi	INTJ
ejpam-6392	209	8	,	,	PUNCT
ejpam-6392	209	9	gf	gf	AUX
ejpam-6392	209	10	)	)	PUNCT
ejpam-6392	209	11	be	be	AUX
ejpam-6392	209	12	a	a	DET
ejpam-6392	209	13	neutrosophic	neutrosophic	ADJ
ejpam-6392	209	14	bi	bi	NOUN
ejpam-6392	209	15	-	-	NOUN
ejpam-6392	209	16	ideal	ideal	NOUN
ejpam-6392	209	17	in	in	ADP
ejpam-6392	209	18	ink	ink	NOUN
ejpam-6392	209	19	-	-	PUNCT
ejpam-6392	209	20	algebra	algebra	NOUN
ejpam-6392	209	21	y	y	PROPN
ejpam-6392	209	22	,	,	PUNCT
ejpam-6392	209	23	and	and	CCONJ
ejpam-6392	209	24	g[¢	g[¢	PROPN
ejpam-6392	209	25	]	]	X
ejpam-6392	210	1	=	=	PUNCT
ejpam-6392	210	2	(	(	PUNCT
ejpam-6392	210	3	gt	gt	PROPN
ejpam-6392	211	1	[	[	X
ejpam-6392	211	2	¢	¢	X
ejpam-6392	211	3	]	]	X
ejpam-6392	211	4	,	,	PUNCT
ejpam-6392	211	5	gi	gi	X
ejpam-6392	212	1	[	[	X
ejpam-6392	212	2	¢	¢	X
ejpam-6392	212	3	]	]	X
ejpam-6392	212	4	,	,	PUNCT
ejpam-6392	212	5	gf	gf	PROPN
ejpam-6392	213	1	[	[	X
ejpam-6392	213	2	¢	¢	X
ejpam-6392	213	3	]	]	PUNCT
ejpam-6392	213	4	)	)	PUNCT
ejpam-6392	213	5	be	be	AUX
ejpam-6392	213	6	the	the	DET
ejpam-6392	213	7	pre	pre	NOUN
ejpam-6392	213	8	-	-	NOUN
ejpam-6392	213	9	image	image	NOUN
ejpam-6392	213	10	of	of	ADP
ejpam-6392	213	11	g	g	NOUN
ejpam-6392	213	12	under	under	ADP
ejpam-6392	213	13	¢	¢	PROPN
ejpam-6392	213	14	is	be	AUX
ejpam-6392	213	15	defined	define	VERB
ejpam-6392	213	16	by	by	ADP
ejpam-6392	213	17	we	we	PRON
ejpam-6392	213	18	first	first	ADV
ejpam-6392	213	19	have	have	VERB
ejpam-6392	213	20	that	that	DET
ejpam-6392	213	21	gt	gt	PROPN
ejpam-6392	214	1	[	[	X
ejpam-6392	214	2	¢](e	¢](e	VERB
ejpam-6392	214	3	•	•	NOUN
ejpam-6392	214	4	3	3	NUM
ejpam-6392	214	5	)	)	PUNCT
ejpam-6392	214	6	=	=	SYM
ejpam-6392	214	7	gt	gt	INTJ
ejpam-6392	214	8	(	(	PUNCT
ejpam-6392	214	9	¢(e	¢(e	NOUN
ejpam-6392	214	10	•	•	NOUN
ejpam-6392	214	11	3	3	NUM
ejpam-6392	214	12	)	)	PUNCT
ejpam-6392	214	13	)	)	PUNCT
ejpam-6392	215	1	≥	≥	PROPN
ejpam-6392	216	1	gt	gt	INTJ
ejpam-6392	216	2	(	(	PUNCT
ejpam-6392	216	3	0	0	NUM
ejpam-6392	216	4	)	)	PUNCT
ejpam-6392	216	5	=	=	SYM
ejpam-6392	216	6	gt	gt	PROPN
ejpam-6392	216	7	(	(	PUNCT
ejpam-6392	216	8	¢(0	¢(0	PROPN
ejpam-6392	216	9	)	)	PUNCT
ejpam-6392	216	10	)	)	PUNCT
ejpam-6392	216	11	,	,	PUNCT
ejpam-6392	216	12	gi	gi	X
ejpam-6392	216	13	[	[	X
ejpam-6392	216	14	¢](e	¢](e	VERB
ejpam-6392	216	15	•	•	NOUN
ejpam-6392	216	16	3	3	NUM
ejpam-6392	216	17	)	)	PUNCT
ejpam-6392	216	18	=	=	PUNCT
ejpam-6392	217	1	gi(¢(e	gi(¢(e	INTJ
ejpam-6392	217	2	•	•	NOUN
ejpam-6392	217	3	3	3	NUM
ejpam-6392	217	4	)	)	PUNCT
ejpam-6392	217	5	)	)	PUNCT
ejpam-6392	218	1	≤	≤	NOUN
ejpam-6392	219	1	gi(0	gi(0	NOUN
ejpam-6392	219	2	)	)	PUNCT
ejpam-6392	219	3	=	=	SYM
ejpam-6392	219	4	gi(¢(0	gi(¢(0	NOUN
ejpam-6392	219	5	)	)	PUNCT
ejpam-6392	219	6	)	)	PUNCT
ejpam-6392	219	7	,	,	PUNCT
ejpam-6392	219	8	gf	gf	X
ejpam-6392	220	1	[	[	X
ejpam-6392	220	2	¢](e	¢](e	VERB
ejpam-6392	220	3	•	•	NOUN
ejpam-6392	220	4	3	3	NUM
ejpam-6392	220	5	)	)	PUNCT
ejpam-6392	220	6	=	=	SYM
ejpam-6392	220	7	gf	gf	X
ejpam-6392	220	8	(	(	PUNCT
ejpam-6392	220	9	¢(e	¢(e	NOUN
ejpam-6392	220	10	•	•	NOUN
ejpam-6392	220	11	3	3	NUM
ejpam-6392	220	12	)	)	PUNCT
ejpam-6392	220	13	)	)	PUNCT
ejpam-6392	220	14	≤	≤	NUM
ejpam-6392	221	1	gf	gf	X
ejpam-6392	221	2	(	(	PUNCT
ejpam-6392	221	3	0	0	NUM
ejpam-6392	221	4	)	)	PUNCT
ejpam-6392	221	5	=	=	SYM
ejpam-6392	221	6	gf	gf	X
ejpam-6392	221	7	(	(	PUNCT
ejpam-6392	221	8	¢(0	¢(0	PROPN
ejpam-6392	221	9	)	)	PUNCT
ejpam-6392	221	10	)	)	PUNCT
ejpam-6392	221	11	for	for	ADP
ejpam-6392	221	12	all	all	DET
ejpam-6392	221	13	e	e	PROPN
ejpam-6392	221	14	∈	∈	PROPN
ejpam-6392	221	15	¨̈u	¨̈u	NOUN
ejpam-6392	221	16	.	.	PUNCT
ejpam-6392	221	17	m.	m.	NOUN
ejpam-6392	221	18	remala	remala	NOUN
ejpam-6392	221	19	,	,	PUNCT
ejpam-6392	221	20	e.	e.	PROPN
ejpam-6392	221	21	tamma	tamma	PROPN
ejpam-6392	221	22	,	,	PUNCT
ejpam-6392	221	23	y.	y.	PROPN
ejpam-6392	221	24	bhargavi	bhargavi	PROPN
ejpam-6392	221	25	/	/	SYM
ejpam-6392	221	26	eur	eur	PROPN
ejpam-6392	221	27	.	.	PUNCT
ejpam-6392	222	1	j.	j.	PROPN
ejpam-6392	222	2	pure	pure	PROPN
ejpam-6392	222	3	appl	appl	PROPN
ejpam-6392	222	4	.	.	PROPN
ejpam-6392	222	5	math	math	PROPN
ejpam-6392	222	6	,	,	PUNCT
ejpam-6392	222	7	18	18	NUM
ejpam-6392	222	8	(	(	PUNCT
ejpam-6392	222	9	4	4	NUM
ejpam-6392	222	10	)	)	PUNCT
ejpam-6392	222	11	(	(	PUNCT
ejpam-6392	222	12	2025	2025	NUM
ejpam-6392	222	13	)	)	PUNCT
ejpam-6392	222	14	,	,	PUNCT
ejpam-6392	222	15	6392	6392	NUM
ejpam-6392	222	16	10	10	NUM
ejpam-6392	222	17	of	of	ADP
ejpam-6392	222	18	20	20	NUM
ejpam-6392	222	19	consider	consider	VERB
ejpam-6392	222	20	gt	gt	PROPN
ejpam-6392	223	1	[	[	X
ejpam-6392	223	2	¢](e	¢](e	VERB
ejpam-6392	223	3	•	•	NOUN
ejpam-6392	223	4	3	3	NUM
ejpam-6392	223	5	)	)	PUNCT
ejpam-6392	223	6	=	=	SYM
ejpam-6392	223	7	gt	gt	INTJ
ejpam-6392	223	8	(	(	PUNCT
ejpam-6392	223	9	¢(e	¢(e	NOUN
ejpam-6392	223	10	•	•	NOUN
ejpam-6392	223	11	3	3	NUM
ejpam-6392	223	12	)	)	PUNCT
ejpam-6392	223	13	)	)	PUNCT
ejpam-6392	223	14	≥	≥	PROPN
ejpam-6392	223	15	min	min	PROPN
ejpam-6392	223	16	{	{	PUNCT
ejpam-6392	223	17	gt	gt	PROPN
ejpam-6392	224	1	[	[	X
ejpam-6392	224	2	¢](e	¢](e	VERB
ejpam-6392	224	3	•	•	NOUN
ejpam-6392	224	4	3	3	NUM
ejpam-6392	224	5	•	•	NUM
ejpam-6392	224	6	ä	ä	PROPN
ejpam-6392	224	7	)	)	PUNCT
ejpam-6392	224	8	,	,	PUNCT
ejpam-6392	224	9	gt	gt	PROPN
ejpam-6392	225	1	[	[	X
ejpam-6392	225	2	¢](ä	¢](ä	NOUN
ejpam-6392	225	3	)	)	PUNCT
ejpam-6392	225	4	}	}	PUNCT
ejpam-6392	225	5	≥	≥	PROPN
ejpam-6392	225	6	min	min	PROPN
ejpam-6392	225	7	{	{	PUNCT
ejpam-6392	225	8	gt	gt	PROPN
ejpam-6392	225	9	(	(	PUNCT
ejpam-6392	225	10	¢(e	¢(e	NOUN
ejpam-6392	225	11	•	•	NOUN
ejpam-6392	225	12	3	3	NUM
ejpam-6392	225	13	•	•	NOUN
ejpam-6392	225	14	ä	ä	PROPN
ejpam-6392	225	15	)	)	PUNCT
ejpam-6392	225	16	)	)	PUNCT
ejpam-6392	225	17	,	,	PUNCT
ejpam-6392	225	18	gt	gt	PROPN
ejpam-6392	225	19	(	(	PUNCT
ejpam-6392	225	20	¢(ä	¢(ä	PROPN
ejpam-6392	225	21	)	)	PUNCT
ejpam-6392	225	22	)	)	PUNCT
ejpam-6392	225	23	}	}	PUNCT
ejpam-6392	225	24	≥	≥	PROPN
ejpam-6392	225	25	min	min	PROPN
ejpam-6392	225	26	{	{	PUNCT
ejpam-6392	225	27	gt	gt	PROPN
ejpam-6392	225	28	(	(	PUNCT
ejpam-6392	225	29	¢((e	¢((e	X
ejpam-6392	225	30	•	•	NOUN
ejpam-6392	225	31	3	3	NUM
ejpam-6392	225	32	)	)	PUNCT
ejpam-6392	225	33	•	•	NUM
ejpam-6392	225	34	ä	ä	PROPN
ejpam-6392	225	35	)	)	PUNCT
ejpam-6392	225	36	)	)	PUNCT
ejpam-6392	225	37	,	,	PUNCT
ejpam-6392	225	38	gt	gt	PROPN
ejpam-6392	225	39	(	(	PUNCT
ejpam-6392	225	40	¢(ä	¢(ä	PROPN
ejpam-6392	225	41	)	)	PUNCT
ejpam-6392	225	42	)	)	PUNCT
ejpam-6392	225	43	}	}	PUNCT
ejpam-6392	225	44	≥	≥	PROPN
ejpam-6392	225	45	min	min	PROPN
ejpam-6392	225	46	{	{	PUNCT
ejpam-6392	225	47	gt	gt	PROPN
ejpam-6392	225	48	(	(	PUNCT
ejpam-6392	225	49	(	(	PUNCT
ejpam-6392	225	50	¢(e	¢(e	NOUN
ejpam-6392	225	51	)	)	PUNCT
ejpam-6392	225	52	•	•	ADV
ejpam-6392	225	53	¢(3	¢(3	NOUN
ejpam-6392	225	54	)	)	PUNCT
ejpam-6392	225	55	)	)	PUNCT
ejpam-6392	226	1	•	•	X
ejpam-6392	226	2	(	(	PUNCT
ejpam-6392	226	3	¢(ä	¢(ä	NOUN
ejpam-6392	226	4	)	)	PUNCT
ejpam-6392	226	5	)	)	PUNCT
ejpam-6392	226	6	)	)	PUNCT
ejpam-6392	226	7	,	,	PUNCT
ejpam-6392	226	8	gt	gt	PROPN
ejpam-6392	226	9	(	(	PUNCT
ejpam-6392	226	10	¢(ä	¢(ä	PROPN
ejpam-6392	226	11	)	)	PUNCT
ejpam-6392	226	12	)	)	PUNCT
ejpam-6392	226	13	}	}	PUNCT
ejpam-6392	226	14	≥	≥	PROPN
ejpam-6392	226	15	min	min	PROPN
ejpam-6392	226	16	{	{	PUNCT
ejpam-6392	226	17	gt	gt	PROPN
ejpam-6392	226	18	(	(	PUNCT
ejpam-6392	226	19	¢(e	¢(e	PROPN
ejpam-6392	226	20	)	)	PUNCT
ejpam-6392	226	21	•	•	NOUN
ejpam-6392	226	22	(	(	PUNCT
ejpam-6392	226	23	¢(3	¢(3	NOUN
ejpam-6392	226	24	)	)	PUNCT
ejpam-6392	226	25	)	)	PUNCT
ejpam-6392	226	26	)	)	PUNCT
ejpam-6392	226	27	,	,	PUNCT
ejpam-6392	226	28	gt	gt	PROPN
ejpam-6392	226	29	(	(	PUNCT
ejpam-6392	226	30	¢(ä	¢(ä	PROPN
ejpam-6392	226	31	)	)	PUNCT
ejpam-6392	226	32	)	)	PUNCT
ejpam-6392	226	33	,	,	PUNCT
ejpam-6392	226	34	gt	gt	PROPN
ejpam-6392	226	35	(	(	PUNCT
ejpam-6392	226	36	¢(ä	¢(ä	PROPN
ejpam-6392	226	37	)	)	PUNCT
ejpam-6392	226	38	)	)	PUNCT
ejpam-6392	226	39	}	}	PUNCT
ejpam-6392	226	40	≥	≥	PROPN
ejpam-6392	226	41	min	min	PROPN
ejpam-6392	226	42	{	{	PUNCT
ejpam-6392	226	43	gt	gt	PROPN
ejpam-6392	226	44	(	(	PUNCT
ejpam-6392	226	45	¢(e	¢(e	NOUN
ejpam-6392	226	46	•	•	NOUN
ejpam-6392	226	47	3	3	NUM
ejpam-6392	226	48	)	)	PUNCT
ejpam-6392	226	49	)	)	PUNCT
ejpam-6392	226	50	}	}	PUNCT
ejpam-6392	226	51	.	.	PUNCT
ejpam-6392	227	1	also	also	ADV
ejpam-6392	227	2	for	for	ADP
ejpam-6392	227	3	,	,	PUNCT
ejpam-6392	227	4	gi	gi	X
ejpam-6392	228	1	[	[	X
ejpam-6392	228	2	¢](e	¢](e	VERB
ejpam-6392	228	3	•	•	NOUN
ejpam-6392	228	4	3	3	NUM
ejpam-6392	228	5	)	)	PUNCT
ejpam-6392	228	6	=	=	PUNCT
ejpam-6392	229	1	gi(¢(e	gi(¢(e	INTJ
ejpam-6392	229	2	•	•	NOUN
ejpam-6392	229	3	3	3	NUM
ejpam-6392	229	4	)	)	PUNCT
ejpam-6392	229	5	)	)	PUNCT
ejpam-6392	230	1	≤	≤	NUM
ejpam-6392	230	2	max	max	PROPN
ejpam-6392	230	3	{	{	PUNCT
ejpam-6392	230	4	gi	gi	X
ejpam-6392	230	5	[	[	X
ejpam-6392	230	6	¢](e	¢](e	VERB
ejpam-6392	230	7	•	•	NOUN
ejpam-6392	230	8	3	3	NUM
ejpam-6392	230	9	•	•	NOUN
ejpam-6392	230	10	ä	ä	PROPN
ejpam-6392	230	11	)	)	PUNCT
ejpam-6392	230	12	,	,	PUNCT
ejpam-6392	230	13	gi	gi	X
ejpam-6392	230	14	[	[	X
ejpam-6392	230	15	¢](ä	¢](ä	NOUN
ejpam-6392	230	16	)	)	PUNCT
ejpam-6392	230	17	}	}	PUNCT
ejpam-6392	230	18	≤	≤	NUM
ejpam-6392	230	19	max	max	PROPN
ejpam-6392	230	20	{	{	PUNCT
ejpam-6392	231	1	gi(¢(e	gi(¢(e	PROPN
ejpam-6392	231	2	•	•	NUM
ejpam-6392	231	3	3	3	NUM
ejpam-6392	231	4	•	•	NOUN
ejpam-6392	231	5	ä	ä	PROPN
ejpam-6392	231	6	)	)	PUNCT
ejpam-6392	231	7	)	)	PUNCT
ejpam-6392	231	8	,	,	PUNCT
ejpam-6392	231	9	gi(¢(ä	gi(¢(ä	PROPN
ejpam-6392	231	10	)	)	PUNCT
ejpam-6392	231	11	)	)	PUNCT
ejpam-6392	232	1	}	}	PUNCT
ejpam-6392	232	2	≤	≤	NUM
ejpam-6392	232	3	max	max	PROPN
ejpam-6392	232	4	{	{	PUNCT
ejpam-6392	232	5	gi(¢((e	gi(¢((e	PROPN
ejpam-6392	232	6	•	•	NOUN
ejpam-6392	232	7	3	3	NUM
ejpam-6392	232	8	)	)	PUNCT
ejpam-6392	232	9	•	•	NUM
ejpam-6392	232	10	ä	ä	PROPN
ejpam-6392	232	11	)	)	PUNCT
ejpam-6392	232	12	)	)	PUNCT
ejpam-6392	232	13	)	)	PUNCT
ejpam-6392	232	14	,	,	PUNCT
ejpam-6392	232	15	gi(¢(ä	gi(¢(ä	PROPN
ejpam-6392	232	16	)	)	PUNCT
ejpam-6392	232	17	)	)	PUNCT
ejpam-6392	232	18	}	}	PUNCT
ejpam-6392	232	19	≤	≤	NUM
ejpam-6392	232	20	max	max	PROPN
ejpam-6392	232	21	{	{	PUNCT
ejpam-6392	232	22	gi((¢(e	gi((¢(e	PROPN
ejpam-6392	232	23	)	)	PUNCT
ejpam-6392	232	24	•	•	ADV
ejpam-6392	232	25	¢(3	¢(3	NOUN
ejpam-6392	232	26	)	)	PUNCT
ejpam-6392	232	27	)	)	PUNCT
ejpam-6392	232	28	•	•	X
ejpam-6392	232	29	(	(	PUNCT
ejpam-6392	232	30	¢(ä	¢(ä	NOUN
ejpam-6392	232	31	)	)	PUNCT
ejpam-6392	232	32	)	)	PUNCT
ejpam-6392	232	33	)	)	PUNCT
ejpam-6392	232	34	,	,	PUNCT
ejpam-6392	232	35	gi(¢(ä	gi(¢(ä	PROPN
ejpam-6392	232	36	)	)	PUNCT
ejpam-6392	232	37	)	)	PUNCT
ejpam-6392	232	38	}	}	PUNCT
ejpam-6392	232	39	≤	≤	NUM
ejpam-6392	232	40	max	max	PROPN
ejpam-6392	232	41	{	{	PUNCT
ejpam-6392	232	42	gi(¢(e	gi(¢(e	PROPN
ejpam-6392	232	43	)	)	PUNCT
ejpam-6392	232	44	•	•	ADV
ejpam-6392	232	45	¢(3	¢(3	NOUN
ejpam-6392	232	46	)	)	PUNCT
ejpam-6392	232	47	)	)	PUNCT
ejpam-6392	232	48	,	,	PUNCT
ejpam-6392	232	49	gi(¢(ä	gi(¢(ä	PROPN
ejpam-6392	232	50	)	)	PUNCT
ejpam-6392	232	51	)	)	PUNCT
ejpam-6392	232	52	,	,	PUNCT
ejpam-6392	232	53	gi(¢(ä	gi(¢(ä	PROPN
ejpam-6392	232	54	)	)	PUNCT
ejpam-6392	232	55	)	)	PUNCT
ejpam-6392	232	56	}	}	PUNCT
ejpam-6392	232	57	≤	≤	NUM
ejpam-6392	232	58	max	max	PROPN
ejpam-6392	232	59	{	{	PUNCT
ejpam-6392	232	60	gi(¢(e	gi(¢(e	PROPN
ejpam-6392	232	61	•	•	NOUN
ejpam-6392	232	62	3	3	NUM
ejpam-6392	232	63	)	)	PUNCT
ejpam-6392	232	64	)	)	PUNCT
ejpam-6392	232	65	}	}	PUNCT
ejpam-6392	232	66	.	.	PUNCT
ejpam-6392	233	1	similarly	similarly	ADV
ejpam-6392	233	2	,	,	PUNCT
ejpam-6392	233	3	gf	gf	X
ejpam-6392	233	4	[	[	X
ejpam-6392	233	5	¢](e	¢](e	VERB
ejpam-6392	233	6	•	•	NOUN
ejpam-6392	233	7	3	3	NUM
ejpam-6392	233	8	)	)	PUNCT
ejpam-6392	233	9	=	=	SYM
ejpam-6392	233	10	gf	gf	X
ejpam-6392	233	11	(	(	PUNCT
ejpam-6392	233	12	¢(e	¢(e	NOUN
ejpam-6392	233	13	•	•	NOUN
ejpam-6392	233	14	3	3	NUM
ejpam-6392	233	15	)	)	PUNCT
ejpam-6392	233	16	)	)	PUNCT
ejpam-6392	234	1	≤	≤	NUM
ejpam-6392	234	2	max	max	PROPN
ejpam-6392	234	3	{	{	PUNCT
ejpam-6392	234	4	gf	gf	NOUN
ejpam-6392	235	1	[	[	X
ejpam-6392	235	2	¢](e	¢](e	VERB
ejpam-6392	235	3	•	•	NOUN
ejpam-6392	235	4	3	3	NUM
ejpam-6392	235	5	•	•	NOUN
ejpam-6392	235	6	ä	ä	PROPN
ejpam-6392	235	7	)	)	PUNCT
ejpam-6392	235	8	,	,	PUNCT
ejpam-6392	235	9	gf	gf	X
ejpam-6392	236	1	[	[	X
ejpam-6392	236	2	¢](ä	¢](ä	NOUN
ejpam-6392	236	3	)	)	PUNCT
ejpam-6392	236	4	}	}	PUNCT
ejpam-6392	236	5	≤	≤	NUM
ejpam-6392	236	6	max	max	PROPN
ejpam-6392	236	7	{	{	PUNCT
ejpam-6392	236	8	gf	gf	X
ejpam-6392	236	9	(	(	PUNCT
ejpam-6392	236	10	¢(e	¢(e	NOUN
ejpam-6392	236	11	•	•	NOUN
ejpam-6392	236	12	3	3	NUM
ejpam-6392	236	13	•	•	NOUN
ejpam-6392	236	14	ä	ä	PROPN
ejpam-6392	236	15	)	)	PUNCT
ejpam-6392	236	16	)	)	PUNCT
ejpam-6392	236	17	,	,	PUNCT
ejpam-6392	236	18	gf	gf	X
ejpam-6392	236	19	(	(	PUNCT
ejpam-6392	236	20	¢(ä	¢(ä	PROPN
ejpam-6392	236	21	)	)	PUNCT
ejpam-6392	236	22	)	)	PUNCT
ejpam-6392	236	23	}	}	PUNCT
ejpam-6392	236	24	≤	≤	NUM
ejpam-6392	236	25	max	max	PROPN
ejpam-6392	236	26	{	{	PUNCT
ejpam-6392	236	27	gf	gf	X
ejpam-6392	236	28	(	(	PUNCT
ejpam-6392	236	29	¢((e	¢((e	X
ejpam-6392	236	30	•	•	NOUN
ejpam-6392	236	31	3	3	NUM
ejpam-6392	236	32	)	)	PUNCT
ejpam-6392	236	33	•	•	NUM
ejpam-6392	236	34	ä	ä	PROPN
ejpam-6392	236	35	)	)	PUNCT
ejpam-6392	236	36	)	)	PUNCT
ejpam-6392	236	37	)	)	PUNCT
ejpam-6392	236	38	,	,	PUNCT
ejpam-6392	236	39	gf	gf	X
ejpam-6392	236	40	(	(	PUNCT
ejpam-6392	236	41	¢(ä	¢(ä	PROPN
ejpam-6392	236	42	)	)	PUNCT
ejpam-6392	236	43	)	)	PUNCT
ejpam-6392	236	44	}	}	PUNCT
ejpam-6392	236	45	≤	≤	NUM
ejpam-6392	236	46	max	max	PROPN
ejpam-6392	236	47	{	{	PUNCT
ejpam-6392	236	48	gf	gf	X
ejpam-6392	236	49	(	(	PUNCT
ejpam-6392	236	50	(	(	PUNCT
ejpam-6392	236	51	¢(e	¢(e	NOUN
ejpam-6392	236	52	)	)	PUNCT
ejpam-6392	236	53	•	•	ADV
ejpam-6392	236	54	¢(3	¢(3	NOUN
ejpam-6392	236	55	)	)	PUNCT
ejpam-6392	236	56	)	)	PUNCT
ejpam-6392	237	1	•	•	X
ejpam-6392	237	2	(	(	PUNCT
ejpam-6392	237	3	¢(ä	¢(ä	NOUN
ejpam-6392	237	4	)	)	PUNCT
ejpam-6392	237	5	)	)	PUNCT
ejpam-6392	237	6	)	)	PUNCT
ejpam-6392	237	7	,	,	PUNCT
ejpam-6392	237	8	gf	gf	X
ejpam-6392	237	9	(	(	PUNCT
ejpam-6392	237	10	¢(ä	¢(ä	PROPN
ejpam-6392	237	11	)	)	PUNCT
ejpam-6392	237	12	)	)	PUNCT
ejpam-6392	237	13	}	}	PUNCT
ejpam-6392	237	14	≤	≤	NUM
ejpam-6392	237	15	max	max	PROPN
ejpam-6392	237	16	{	{	PUNCT
ejpam-6392	237	17	gf	gf	X
ejpam-6392	237	18	(	(	PUNCT
ejpam-6392	237	19	¢(e	¢(e	NOUN
ejpam-6392	237	20	)	)	PUNCT
ejpam-6392	237	21	•	•	ADV
ejpam-6392	237	22	¢(3	¢(3	NOUN
ejpam-6392	237	23	)	)	PUNCT
ejpam-6392	237	24	)	)	PUNCT
ejpam-6392	237	25	,	,	PUNCT
ejpam-6392	237	26	gf	gf	X
ejpam-6392	237	27	(	(	PUNCT
ejpam-6392	237	28	¢(ä	¢(ä	PROPN
ejpam-6392	237	29	)	)	PUNCT
ejpam-6392	237	30	)	)	PUNCT
ejpam-6392	237	31	,	,	PUNCT
ejpam-6392	237	32	gf	gf	X
ejpam-6392	237	33	(	(	PUNCT
ejpam-6392	237	34	¢(ä	¢(ä	PROPN
ejpam-6392	237	35	)	)	PUNCT
ejpam-6392	237	36	)	)	PUNCT
ejpam-6392	237	37	}	}	PUNCT
ejpam-6392	237	38	≤	≤	NUM
ejpam-6392	237	39	max	max	PROPN
ejpam-6392	237	40	{	{	PUNCT
ejpam-6392	237	41	gf	gf	X
ejpam-6392	237	42	(	(	PUNCT
ejpam-6392	237	43	¢(e	¢(e	NOUN
ejpam-6392	237	44	•	•	NOUN
ejpam-6392	237	45	3	3	NUM
ejpam-6392	237	46	)	)	PUNCT
ejpam-6392	237	47	)	)	PUNCT
ejpam-6392	237	48	}	}	PUNCT
ejpam-6392	237	49	.	.	PUNCT
ejpam-6392	238	1	theorem	theorem	VERB
ejpam-6392	238	2	4.1	4.1	NUM
ejpam-6392	238	3	.	.	PUNCT
ejpam-6392	239	1	let	let	VERB
ejpam-6392	239	2	¢	¢	NOUN
ejpam-6392	239	3	:	:	PUNCT
ejpam-6392	239	4	¨̈u	¨̈u	PROPN
ejpam-6392	239	5	→	→	SYM
ejpam-6392	239	6	˘̈̈	˘̈̈	PROPN
ejpam-6392	239	7	u	u	NOUN
ejpam-6392	239	8	be	be	VERB
ejpam-6392	239	9	an	an	DET
ejpam-6392	239	10	epimorphism	epimorphism	NOUN
ejpam-6392	239	11	of	of	ADP
ejpam-6392	239	12	ink	ink	NOUN
ejpam-6392	239	13	-	-	PUNCT
ejpam-6392	239	14	algebra	algebra	NOUN
ejpam-6392	239	15	.	.	PUNCT
ejpam-6392	240	1	if	if	SCONJ
ejpam-6392	240	2	g[¢	g[¢	PROPN
ejpam-6392	240	3	]	]	X
ejpam-6392	240	4	=	=	PUNCT
ejpam-6392	240	5	(	(	PUNCT
ejpam-6392	240	6	gt	gt	PROPN
ejpam-6392	241	1	[	[	X
ejpam-6392	241	2	¢	¢	X
ejpam-6392	241	3	]	]	X
ejpam-6392	241	4	,	,	PUNCT
ejpam-6392	241	5	gi	gi	X
ejpam-6392	242	1	[	[	X
ejpam-6392	242	2	¢	¢	X
ejpam-6392	242	3	]	]	X
ejpam-6392	242	4	,	,	PUNCT
ejpam-6392	242	5	gf	gf	PROPN
ejpam-6392	243	1	[	[	X
ejpam-6392	243	2	¢	¢	X
ejpam-6392	243	3	]	]	X
ejpam-6392	243	4	)	)	PUNCT
ejpam-6392	243	5	is	be	AUX
ejpam-6392	243	6	an	an	DET
ejpam-6392	243	7	neutrosophic	neutrosophic	ADJ
ejpam-6392	243	8	bi	bi	NOUN
ejpam-6392	243	9	-	-	NOUN
ejpam-6392	243	10	ideal	ideal	NOUN
ejpam-6392	243	11	of	of	ADP
ejpam-6392	243	12	ink	ink	NOUN
ejpam-6392	243	13	sub	sub	NOUN
ejpam-6392	243	14	-	-	NOUN
ejpam-6392	243	15	algebra	algebra	NOUN
ejpam-6392	243	16	of	of	ADP
ejpam-6392	243	17	ink	ink	NOUN
ejpam-6392	243	18	-	-	PUNCT
ejpam-6392	243	19	algebra	algebra	NOUN
ejpam-6392	243	20	¨̈u	¨̈u	NOUN
ejpam-6392	243	21	,	,	PUNCT
ejpam-6392	243	22	then	then	ADV
ejpam-6392	243	23	g	g	PROPN
ejpam-6392	243	24	=	=	PUNCT
ejpam-6392	243	25	(	(	PUNCT
ejpam-6392	243	26	gt	gt	INTJ
ejpam-6392	243	27	,	,	PUNCT
ejpam-6392	243	28	gi	gi	INTJ
ejpam-6392	243	29	,	,	PUNCT
ejpam-6392	243	30	gf	gf	PROPN
ejpam-6392	243	31	)	)	PUNCT
ejpam-6392	243	32	is	be	AUX
ejpam-6392	243	33	an	an	DET
ejpam-6392	243	34	neutrosophic	neutrosophic	ADJ
ejpam-6392	243	35	bi	bi	NOUN
ejpam-6392	243	36	-	-	NOUN
ejpam-6392	243	37	ideal	ideal	NOUN
ejpam-6392	243	38	of	of	ADP
ejpam-6392	243	39	ink	ink	NOUN
ejpam-6392	243	40	sub	sub	NOUN
ejpam-6392	243	41	-	-	NOUN
ejpam-6392	243	42	algebra	algebra	NOUN
ejpam-6392	243	43	of	of	ADP
ejpam-6392	243	44	ink	ink	NOUN
ejpam-6392	243	45	-	-	PUNCT
ejpam-6392	243	46	algebra	algebra	NOUN
ejpam-6392	243	47	¨̈u	¨̈u	NOUN
ejpam-6392	243	48	.	.	PUNCT
ejpam-6392	244	1	proof	proof	NOUN
ejpam-6392	244	2	.	.	PUNCT
ejpam-6392	245	1	let	let	VERB
ejpam-6392	245	2	e	e	NOUN
ejpam-6392	245	3	,	,	PUNCT
ejpam-6392	245	4	3	3	NUM
ejpam-6392	245	5	∈	∈	NOUN
ejpam-6392	245	6	¨̈u	¨̈u	NOUN
ejpam-6392	245	7	,	,	PUNCT
ejpam-6392	245	8	there	there	PRON
ejpam-6392	245	9	exist	exist	VERB
ejpam-6392	245	10	e	e	NOUN
ejpam-6392	245	11	,	,	PUNCT
ejpam-6392	245	12	3	3	NUM
ejpam-6392	245	13	∈	∈	NOUN
ejpam-6392	245	14	x	x	PUNCT
ejpam-6392	245	15	such	such	ADJ
ejpam-6392	245	16	that	that	DET
ejpam-6392	245	17	¢(e	¢(e	NOUN
ejpam-6392	245	18	•	•	NOUN
ejpam-6392	245	19	3	3	NUM
ejpam-6392	245	20	)	)	PUNCT
ejpam-6392	245	21	=	=	SYM
ejpam-6392	246	1	e	e	NOUN
ejpam-6392	246	2	•	•	ADP
ejpam-6392	246	3	3	3	NUM
ejpam-6392	246	4	.	.	PUNCT
ejpam-6392	247	1	then	then	ADV
ejpam-6392	247	2	gt	gt	INTJ
ejpam-6392	247	3	(	(	PUNCT
ejpam-6392	247	4	e	e	NOUN
ejpam-6392	247	5	•	•	NOUN
ejpam-6392	247	6	3	3	NUM
ejpam-6392	247	7	)	)	PUNCT
ejpam-6392	247	8	=	=	SYM
ejpam-6392	247	9	gt	gt	PROPN
ejpam-6392	247	10	(	(	PUNCT
ejpam-6392	247	11	¢)(e	¢)(e	NUM
ejpam-6392	247	12	•	•	NOUN
ejpam-6392	247	13	3	3	NUM
ejpam-6392	247	14	)	)	PUNCT
ejpam-6392	247	15	,	,	PUNCT
ejpam-6392	247	16	gt	gt	PROPN
ejpam-6392	248	1	[	[	X
ejpam-6392	248	2	¢](e	¢](e	VERB
ejpam-6392	248	3	•	•	NOUN
ejpam-6392	248	4	3	3	NUM
ejpam-6392	248	5	)	)	PUNCT
ejpam-6392	248	6	≥	≥	NOUN
ejpam-6392	249	1	gt	gt	NOUN
ejpam-6392	250	1	=	=	SYM
ejpam-6392	250	2	gt	gt	PROPN
ejpam-6392	250	3	(	(	PUNCT
ejpam-6392	250	4	¢(0	¢(0	PROPN
ejpam-6392	250	5	)	)	PUNCT
ejpam-6392	250	6	)	)	PUNCT
ejpam-6392	251	1	=	=	PUNCT
ejpam-6392	251	2	gt	gt	PROPN
ejpam-6392	251	3	(	(	PUNCT
ejpam-6392	251	4	0	0	NUM
ejpam-6392	251	5	)	)	PUNCT
ejpam-6392	251	6	,	,	PUNCT
ejpam-6392	251	7	gi(e	gi(e	NOUN
ejpam-6392	251	8	•	•	ADP
ejpam-6392	251	9	3	3	X
ejpam-6392	251	10	)	)	PUNCT
ejpam-6392	251	11	=	=	SYM
ejpam-6392	252	1	gi(¢)(e	gi(¢)(e	NOUN
ejpam-6392	252	2	•	•	NOUN
ejpam-6392	252	3	3	3	NUM
ejpam-6392	252	4	)	)	PUNCT
ejpam-6392	252	5	,	,	PUNCT
ejpam-6392	252	6	gi	gi	X
ejpam-6392	253	1	[	[	X
ejpam-6392	253	2	¢](e	¢](e	VERB
ejpam-6392	253	3	•	•	NOUN
ejpam-6392	253	4	3	3	NUM
ejpam-6392	253	5	)	)	PUNCT
ejpam-6392	253	6	≤	≤	NOUN
ejpam-6392	253	7	gi	gi	NOUN
ejpam-6392	253	8	=	=	SYM
ejpam-6392	253	9	gi(¢(0	gi(¢(0	NOUN
ejpam-6392	253	10	)	)	PUNCT
ejpam-6392	253	11	)	)	PUNCT
ejpam-6392	254	1	=	=	SYM
ejpam-6392	254	2	gi(0	gi(0	PROPN
ejpam-6392	254	3	)	)	PUNCT
ejpam-6392	254	4	,	,	PUNCT
ejpam-6392	254	5	gf	gf	X
ejpam-6392	254	6	(	(	PUNCT
ejpam-6392	254	7	e	e	NOUN
ejpam-6392	254	8	•	•	NOUN
ejpam-6392	254	9	3	3	NUM
ejpam-6392	254	10	)	)	PUNCT
ejpam-6392	254	11	=	=	SYM
ejpam-6392	254	12	gf	gf	X
ejpam-6392	254	13	(	(	PUNCT
ejpam-6392	254	14	¢)(e	¢)(e	NUM
ejpam-6392	254	15	•	•	NOUN
ejpam-6392	254	16	3	3	NUM
ejpam-6392	254	17	)	)	PUNCT
ejpam-6392	254	18	,	,	PUNCT
ejpam-6392	254	19	gf	gf	X
ejpam-6392	255	1	[	[	X
ejpam-6392	255	2	¢](e	¢](e	VERB
ejpam-6392	255	3	•	•	NOUN
ejpam-6392	255	4	3	3	NUM
ejpam-6392	255	5	)	)	PUNCT
ejpam-6392	255	6	≤	≤	NOUN
ejpam-6392	255	7	gf	gf	NOUN
ejpam-6392	255	8	=	=	PUNCT
ejpam-6392	255	9	gf	gf	X
ejpam-6392	255	10	(	(	PUNCT
ejpam-6392	255	11	¢(0	¢(0	PROPN
ejpam-6392	255	12	)	)	PUNCT
ejpam-6392	255	13	)	)	PUNCT
ejpam-6392	256	1	=	=	SYM
ejpam-6392	256	2	gf	gf	X
ejpam-6392	256	3	(	(	PUNCT
ejpam-6392	256	4	0	0	NUM
ejpam-6392	256	5	)	)	PUNCT
ejpam-6392	256	6	.	.	PUNCT
ejpam-6392	257	1	consider	consider	VERB
ejpam-6392	257	2	gt	gt	PROPN
ejpam-6392	257	3	(	(	PUNCT
ejpam-6392	257	4	e	e	NOUN
ejpam-6392	257	5	•	•	NOUN
ejpam-6392	257	6	3	3	NUM
ejpam-6392	257	7	)	)	PUNCT
ejpam-6392	257	8	=	=	SYM
ejpam-6392	257	9	gt	gt	PROPN
ejpam-6392	257	10	(	(	PUNCT
ejpam-6392	257	11	¢)(e	¢)(e	NUM
ejpam-6392	257	12	•	•	NOUN
ejpam-6392	257	13	3	3	NUM
ejpam-6392	257	14	)	)	PUNCT
ejpam-6392	257	15	=	=	SYM
ejpam-6392	258	1	gt	gt	PROPN
ejpam-6392	259	1	[	[	X
ejpam-6392	259	2	¢](e	¢](e	VERB
ejpam-6392	259	3	•	•	NOUN
ejpam-6392	259	4	3	3	NUM
ejpam-6392	259	5	)	)	PUNCT
ejpam-6392	259	6	≥	≥	NOUN
ejpam-6392	259	7	min	min	PROPN
ejpam-6392	259	8	{	{	PUNCT
ejpam-6392	259	9	gt	gt	X
ejpam-6392	259	10	(	(	PUNCT
ejpam-6392	259	11	[	[	X
ejpam-6392	259	12	¢](e	¢](e	VERB
ejpam-6392	259	13	•	•	NOUN
ejpam-6392	259	14	3	3	NUM
ejpam-6392	259	15	)	)	PUNCT
ejpam-6392	259	16	•	•	NUM
ejpam-6392	259	17	[	[	X
ejpam-6392	259	18	¢](ä	¢](ä	NOUN
ejpam-6392	259	19	)	)	PUNCT
ejpam-6392	259	20	)	)	PUNCT
ejpam-6392	259	21	,	,	PUNCT
ejpam-6392	259	22	gt	gt	PROPN
ejpam-6392	260	1	[	[	X
ejpam-6392	260	2	¢](ä	¢](ä	NOUN
ejpam-6392	260	3	)	)	PUNCT
ejpam-6392	260	4	}	}	PUNCT
ejpam-6392	260	5	≥	≥	PROPN
ejpam-6392	260	6	min	min	PROPN
ejpam-6392	260	7	{	{	PUNCT
ejpam-6392	260	8	gt	gt	X
ejpam-6392	260	9	(	(	PUNCT
ejpam-6392	261	1	[	[	X
ejpam-6392	261	2	¢](e	¢](e	VERB
ejpam-6392	261	3	•	•	NOUN
ejpam-6392	261	4	3	3	NUM
ejpam-6392	261	5	•	•	NOUN
ejpam-6392	261	6	ä	ä	PROPN
ejpam-6392	261	7	)	)	PUNCT
ejpam-6392	261	8	)	)	PUNCT
ejpam-6392	261	9	,	,	PUNCT
ejpam-6392	261	10	gt	gt	PROPN
ejpam-6392	262	1	[	[	X
ejpam-6392	262	2	¢](ä	¢](ä	NOUN
ejpam-6392	262	3	)	)	PUNCT
ejpam-6392	262	4	}	}	PUNCT
ejpam-6392	262	5	≥	≥	PROPN
ejpam-6392	262	6	min	min	PROPN
ejpam-6392	262	7	{	{	PUNCT
ejpam-6392	262	8	gt	gt	PROPN
ejpam-6392	262	9	(	(	PUNCT
ejpam-6392	262	10	(	(	PUNCT
ejpam-6392	262	11	¢(e	¢(e	NOUN
ejpam-6392	262	12	•	•	NOUN
ejpam-6392	262	13	3	3	NUM
ejpam-6392	262	14	•	•	NOUN
ejpam-6392	262	15	ä	ä	PROPN
ejpam-6392	262	16	)	)	PUNCT
ejpam-6392	262	17	)	)	PUNCT
ejpam-6392	262	18	,	,	PUNCT
ejpam-6392	262	19	gt	gt	PROPN
ejpam-6392	262	20	(	(	PUNCT
ejpam-6392	262	21	¢(ä	¢(ä	PROPN
ejpam-6392	262	22	)	)	PUNCT
ejpam-6392	262	23	)	)	PUNCT
ejpam-6392	262	24	}	}	PUNCT
ejpam-6392	262	25	≥	≥	PROPN
ejpam-6392	262	26	min	min	PROPN
ejpam-6392	262	27	{	{	PUNCT
ejpam-6392	262	28	gt	gt	PROPN
ejpam-6392	262	29	(	(	PUNCT
ejpam-6392	262	30	e	e	NOUN
ejpam-6392	262	31	•	•	NUM
ejpam-6392	262	32	3	3	NUM
ejpam-6392	262	33	•	•	NUM
ejpam-6392	262	34	ä	ä	PROPN
ejpam-6392	262	35	)	)	PUNCT
ejpam-6392	262	36	,	,	PUNCT
ejpam-6392	262	37	gt	gt	PROPN
ejpam-6392	262	38	(	(	PUNCT
ejpam-6392	262	39	ä	ä	NOUN
ejpam-6392	262	40	)	)	PUNCT
ejpam-6392	262	41	}	}	PUNCT
ejpam-6392	262	42	.	.	PUNCT
ejpam-6392	263	1	m.	m.	NOUN
ejpam-6392	263	2	remala	remala	NOUN
ejpam-6392	263	3	,	,	PUNCT
ejpam-6392	263	4	e.	e.	PROPN
ejpam-6392	263	5	tamma	tamma	PROPN
ejpam-6392	263	6	,	,	PUNCT
ejpam-6392	263	7	y.	y.	PROPN
ejpam-6392	263	8	bhargavi	bhargavi	PROPN
ejpam-6392	263	9	/	/	SYM
ejpam-6392	263	10	eur	eur	PROPN
ejpam-6392	263	11	.	.	PUNCT
ejpam-6392	264	1	j.	j.	PROPN
ejpam-6392	264	2	pure	pure	PROPN
ejpam-6392	264	3	appl	appl	PROPN
ejpam-6392	264	4	.	.	PROPN
ejpam-6392	264	5	math	math	PROPN
ejpam-6392	264	6	,	,	PUNCT
ejpam-6392	264	7	18	18	NUM
ejpam-6392	264	8	(	(	PUNCT
ejpam-6392	264	9	4	4	NUM
ejpam-6392	264	10	)	)	PUNCT
ejpam-6392	264	11	(	(	PUNCT
ejpam-6392	264	12	2025	2025	NUM
ejpam-6392	264	13	)	)	PUNCT
ejpam-6392	264	14	,	,	PUNCT
ejpam-6392	264	15	6392	6392	NUM
ejpam-6392	264	16	11	11	NUM
ejpam-6392	264	17	of	of	ADP
ejpam-6392	264	18	20	20	NUM
ejpam-6392	264	19	also	also	ADV
ejpam-6392	264	20	for	for	ADP
ejpam-6392	264	21	gi(e	gi(e	NOUN
ejpam-6392	264	22	•	•	ADP
ejpam-6392	264	23	3	3	NUM
ejpam-6392	264	24	)	)	PUNCT
ejpam-6392	264	25	=	=	SYM
ejpam-6392	264	26	gi(¢)(e	gi(¢)(e	NOUN
ejpam-6392	264	27	•	•	NOUN
ejpam-6392	264	28	3	3	NUM
ejpam-6392	264	29	)	)	PUNCT
ejpam-6392	265	1	=	=	VERB
ejpam-6392	265	2	gi	gi	NOUN
ejpam-6392	266	1	[	[	PUNCT
ejpam-6392	266	2	¢](e	¢](e	VERB
ejpam-6392	266	3	•	•	NOUN
ejpam-6392	266	4	3	3	NUM
ejpam-6392	266	5	)	)	PUNCT
ejpam-6392	266	6	≤	≤	NUM
ejpam-6392	266	7	max	max	PROPN
ejpam-6392	266	8	{	{	PUNCT
ejpam-6392	266	9	gi([¢](e	gi([¢](e	VERB
ejpam-6392	266	10	•	•	NOUN
ejpam-6392	266	11	3	3	NUM
ejpam-6392	266	12	)	)	PUNCT
ejpam-6392	266	13	•	•	NUM
ejpam-6392	267	1	[	[	X
ejpam-6392	267	2	¢](ä	¢](ä	NOUN
ejpam-6392	267	3	)	)	PUNCT
ejpam-6392	267	4	)	)	PUNCT
ejpam-6392	267	5	,	,	PUNCT
ejpam-6392	268	1	gi	gi	X
ejpam-6392	268	2	[	[	X
ejpam-6392	268	3	¢](ä	¢](ä	NOUN
ejpam-6392	268	4	)	)	PUNCT
ejpam-6392	268	5	}	}	PUNCT
ejpam-6392	268	6	≤	≤	NUM
ejpam-6392	268	7	max	max	PROPN
ejpam-6392	268	8	{	{	PUNCT
ejpam-6392	268	9	gi([¢](e	gi([¢](e	VERB
ejpam-6392	268	10	•	•	NOUN
ejpam-6392	268	11	3	3	NUM
ejpam-6392	268	12	•	•	NOUN
ejpam-6392	268	13	ä	ä	PROPN
ejpam-6392	268	14	)	)	PUNCT
ejpam-6392	268	15	)	)	PUNCT
ejpam-6392	268	16	,	,	PUNCT
ejpam-6392	268	17	gi	gi	X
ejpam-6392	269	1	[	[	X
ejpam-6392	269	2	¢](ä	¢](ä	NOUN
ejpam-6392	269	3	)	)	PUNCT
ejpam-6392	269	4	}	}	PUNCT
ejpam-6392	269	5	≤	≤	NUM
ejpam-6392	269	6	max	max	PROPN
ejpam-6392	269	7	{	{	PUNCT
ejpam-6392	269	8	gi((¢(e	gi((¢(e	NUM
ejpam-6392	269	9	•	•	NUM
ejpam-6392	269	10	3	3	NUM
ejpam-6392	269	11	•	•	NUM
ejpam-6392	269	12	ä	ä	PROPN
ejpam-6392	269	13	)	)	PUNCT
ejpam-6392	269	14	)	)	PUNCT
ejpam-6392	269	15	,	,	PUNCT
ejpam-6392	269	16	gi(¢(ä	gi(¢(ä	PROPN
ejpam-6392	269	17	)	)	PUNCT
ejpam-6392	269	18	)	)	PUNCT
ejpam-6392	269	19	}	}	PUNCT
ejpam-6392	270	1	≤	≤	NUM
ejpam-6392	270	2	max	max	PROPN
ejpam-6392	270	3	{	{	PUNCT
ejpam-6392	270	4	gi(e	gi(e	NOUN
ejpam-6392	270	5	•	•	ADP
ejpam-6392	270	6	3	3	NUM
ejpam-6392	270	7	•	•	NUM
ejpam-6392	270	8	ä	ä	NOUN
ejpam-6392	270	9	)	)	PUNCT
ejpam-6392	270	10	,	,	PUNCT
ejpam-6392	270	11	gi(ä	gi(ä	ADV
ejpam-6392	270	12	)	)	PUNCT
ejpam-6392	270	13	}	}	PUNCT
ejpam-6392	270	14	.	.	PUNCT
ejpam-6392	271	1	similarly	similarly	ADV
ejpam-6392	271	2	,	,	PUNCT
ejpam-6392	271	3	gf	gf	X
ejpam-6392	271	4	(	(	PUNCT
ejpam-6392	271	5	e	e	NOUN
ejpam-6392	271	6	•	•	NOUN
ejpam-6392	271	7	3	3	NUM
ejpam-6392	271	8	)	)	PUNCT
ejpam-6392	271	9	=	=	SYM
ejpam-6392	271	10	gf	gf	X
ejpam-6392	271	11	(	(	PUNCT
ejpam-6392	271	12	¢)(e	¢)(e	NUM
ejpam-6392	271	13	•	•	NOUN
ejpam-6392	271	14	3	3	NUM
ejpam-6392	271	15	)	)	PUNCT
ejpam-6392	271	16	=	=	PUNCT
ejpam-6392	271	17	gf	gf	X
ejpam-6392	272	1	[	[	X
ejpam-6392	272	2	¢](e	¢](e	VERB
ejpam-6392	272	3	•	•	NOUN
ejpam-6392	272	4	3	3	NUM
ejpam-6392	272	5	)	)	PUNCT
ejpam-6392	272	6	≤	≤	NUM
ejpam-6392	272	7	max	max	PROPN
ejpam-6392	272	8	{	{	PUNCT
ejpam-6392	272	9	gi([¢](e	gi([¢](e	VERB
ejpam-6392	272	10	•	•	NOUN
ejpam-6392	272	11	3	3	NUM
ejpam-6392	272	12	)	)	PUNCT
ejpam-6392	272	13	•	•	NUM
ejpam-6392	273	1	[	[	X
ejpam-6392	273	2	¢](ä	¢](ä	NOUN
ejpam-6392	273	3	)	)	PUNCT
ejpam-6392	273	4	)	)	PUNCT
ejpam-6392	273	5	,	,	PUNCT
ejpam-6392	273	6	gf	gf	X
ejpam-6392	274	1	[	[	X
ejpam-6392	274	2	¢](ä	¢](ä	NOUN
ejpam-6392	274	3	)	)	PUNCT
ejpam-6392	274	4	}	}	PUNCT
ejpam-6392	274	5	≤	≤	NUM
ejpam-6392	274	6	max	max	PROPN
ejpam-6392	274	7	{	{	PUNCT
ejpam-6392	274	8	gf	gf	X
ejpam-6392	274	9	(	(	PUNCT
ejpam-6392	274	10	[	[	X
ejpam-6392	274	11	¢](e	¢](e	VERB
ejpam-6392	274	12	•	•	NOUN
ejpam-6392	274	13	3	3	NUM
ejpam-6392	274	14	•	•	NOUN
ejpam-6392	274	15	ä	ä	PROPN
ejpam-6392	274	16	)	)	PUNCT
ejpam-6392	274	17	)	)	PUNCT
ejpam-6392	274	18	,	,	PUNCT
ejpam-6392	275	1	gf	gf	X
ejpam-6392	276	1	[	[	X
ejpam-6392	276	2	¢](ä	¢](ä	NOUN
ejpam-6392	276	3	)	)	PUNCT
ejpam-6392	276	4	}	}	PUNCT
ejpam-6392	276	5	≤	≤	NUM
ejpam-6392	276	6	max	max	PROPN
ejpam-6392	276	7	{	{	PUNCT
ejpam-6392	276	8	gf	gf	X
ejpam-6392	276	9	(	(	PUNCT
ejpam-6392	276	10	(	(	PUNCT
ejpam-6392	276	11	¢(e	¢(e	NOUN
ejpam-6392	276	12	•	•	NOUN
ejpam-6392	276	13	3	3	NUM
ejpam-6392	276	14	•	•	NOUN
ejpam-6392	276	15	ä	ä	PROPN
ejpam-6392	276	16	)	)	PUNCT
ejpam-6392	276	17	)	)	PUNCT
ejpam-6392	276	18	,	,	PUNCT
ejpam-6392	276	19	gf	gf	X
ejpam-6392	276	20	(	(	PUNCT
ejpam-6392	276	21	¢(ä	¢(ä	PROPN
ejpam-6392	276	22	)	)	PUNCT
ejpam-6392	276	23	)	)	PUNCT
ejpam-6392	276	24	}	}	PUNCT
ejpam-6392	276	25	≤	≤	NUM
ejpam-6392	276	26	max	max	PROPN
ejpam-6392	276	27	{	{	PUNCT
ejpam-6392	276	28	gf	gf	X
ejpam-6392	276	29	(	(	PUNCT
ejpam-6392	276	30	e	e	NOUN
ejpam-6392	276	31	•	•	NOUN
ejpam-6392	276	32	3	3	NUM
ejpam-6392	276	33	•	•	NUM
ejpam-6392	276	34	ä	ä	PROPN
ejpam-6392	276	35	)	)	PUNCT
ejpam-6392	276	36	,	,	PUNCT
ejpam-6392	276	37	gf	gf	X
ejpam-6392	276	38	(	(	PUNCT
ejpam-6392	276	39	ä	ä	NOUN
ejpam-6392	276	40	)	)	PUNCT
ejpam-6392	276	41	}	}	PUNCT
ejpam-6392	276	42	.	.	PUNCT
ejpam-6392	277	1	5	5	X
ejpam-6392	277	2	.	.	X
ejpam-6392	277	3	direct	direct	ADJ
ejpam-6392	277	4	product	product	NOUN
ejpam-6392	277	5	of	of	ADP
ejpam-6392	277	6	neutrosophic	neutrosophic	ADJ
ejpam-6392	277	7	bi	bi	NOUN
ejpam-6392	277	8	-	-	NOUN
ejpam-6392	277	9	ideal	ideal	NOUN
ejpam-6392	277	10	of	of	ADP
ejpam-6392	277	11	ink	ink	NOUN
ejpam-6392	277	12	sub	sub	ADJ
ejpam-6392	277	13	-	-	ADJ
ejpam-6392	277	14	algebra	algebra	ADJ
ejpam-6392	277	15	definition	definition	NOUN
ejpam-6392	277	16	5.1	5.1	NUM
ejpam-6392	277	17	.	.	PUNCT
ejpam-6392	278	1	let	let	VERB
ejpam-6392	278	2	g=(gt	g=(gt	NOUN
ejpam-6392	278	3	,	,	PUNCT
ejpam-6392	278	4	gi	gi	INTJ
ejpam-6392	278	5	,	,	PUNCT
ejpam-6392	278	6	gf	gf	PROPN
ejpam-6392	278	7	)	)	PUNCT
ejpam-6392	278	8	and	and	CCONJ
ejpam-6392	278	9	h=(ht	h=(ht	NOUN
ejpam-6392	278	10	,	,	PUNCT
ejpam-6392	278	11	hi	hi	INTJ
ejpam-6392	278	12	,	,	PUNCT
ejpam-6392	278	13	hf	hf	INTJ
ejpam-6392	278	14	)	)	PUNCT
ejpam-6392	278	15	be	be	AUX
ejpam-6392	278	16	two	two	NUM
ejpam-6392	278	17	neutrosophic	neutrosophic	ADJ
ejpam-6392	278	18	sets	set	NOUN
ejpam-6392	278	19	of	of	ADP
ejpam-6392	278	20	ink	ink	NOUN
ejpam-6392	278	21	algebras	algebras	PROPN
ejpam-6392	278	22	¨̈u1	¨̈u1	PROPN
ejpam-6392	278	23	and	and	CCONJ
ejpam-6392	278	24	¨̈u2	¨̈u2	NOUN
ejpam-6392	278	25	respectively	respectively	ADV
ejpam-6392	278	26	.	.	PUNCT
ejpam-6392	279	1	then	then	ADV
ejpam-6392	279	2	the	the	DET
ejpam-6392	279	3	direct	direct	ADJ
ejpam-6392	279	4	product	product	NOUN
ejpam-6392	279	5	of	of	ADP
ejpam-6392	279	6	neutrosophic	neutrosophic	ADJ
ejpam-6392	279	7	set	set	NOUN
ejpam-6392	279	8	g	g	PROPN
ejpam-6392	279	9	and	and	CCONJ
ejpam-6392	279	10	h	h	NOUN
ejpam-6392	279	11	is	be	AUX
ejpam-6392	279	12	given	give	VERB
ejpam-6392	279	13	by	by	ADP
ejpam-6392	279	14	g	g	PROPN
ejpam-6392	279	15	×	×	PROPN
ejpam-6392	279	16	h=	h=	X
ejpam-6392	279	17	(	(	PUNCT
ejpam-6392	279	18	gt	gt	INTJ
ejpam-6392	279	19	(	(	PUNCT
ejpam-6392	279	20	g×h	g×h	PROPN
ejpam-6392	279	21	)	)	PUNCT
ejpam-6392	279	22	,	,	PUNCT
ejpam-6392	279	23	gi	gi	INTJ
ejpam-6392	279	24	(	(	PUNCT
ejpam-6392	279	25	g×h	g×h	NOUN
ejpam-6392	279	26	)	)	PUNCT
ejpam-6392	279	27	,	,	PUNCT
ejpam-6392	279	28	gf	gf	X
ejpam-6392	279	29	(	(	PUNCT
ejpam-6392	279	30	g×h	g×h	PROPN
ejpam-6392	279	31	)	)	PUNCT
ejpam-6392	279	32	)	)	PUNCT
ejpam-6392	279	33	with	with	ADP
ejpam-6392	279	34	(	(	PUNCT
ejpam-6392	279	35	i	i	NOUN
ejpam-6392	279	36	)	)	PUNCT
ejpam-6392	279	37	gt	gt	PROPN
ejpam-6392	279	38	(	(	PUNCT
ejpam-6392	279	39	g×h	g×h	PROPN
ejpam-6392	279	40	)	)	PUNCT
ejpam-6392	279	41	(	(	PUNCT
ejpam-6392	279	42	e1,31	e1,31	PROPN
ejpam-6392	279	43	)	)	PUNCT
ejpam-6392	280	1	=	=	SYM
ejpam-6392	280	2	min	min	PROPN
ejpam-6392	280	3	{	{	PUNCT
ejpam-6392	280	4	gt	gt	INTJ
ejpam-6392	280	5	(	(	PUNCT
ejpam-6392	280	6	g)(e1	g)(e1	PROPN
ejpam-6392	280	7	)	)	PUNCT
ejpam-6392	280	8	,	,	PUNCT
ejpam-6392	280	9	gt	gt	PROPN
ejpam-6392	280	10	(	(	PUNCT
ejpam-6392	280	11	h	h	NOUN
ejpam-6392	280	12	)	)	PUNCT
ejpam-6392	280	13	(	(	PUNCT
ejpam-6392	280	14	31	31	NUM
ejpam-6392	280	15	)	)	PUNCT
ejpam-6392	280	16	}	}	PUNCT
ejpam-6392	280	17	(	(	PUNCT
ejpam-6392	280	18	ii	ii	NOUN
ejpam-6392	280	19	)	)	PUNCT
ejpam-6392	280	20	gi	gi	NOUN
ejpam-6392	280	21	(	(	PUNCT
ejpam-6392	280	22	g×h	g×h	PROPN
ejpam-6392	280	23	)	)	PUNCT
ejpam-6392	280	24	(	(	PUNCT
ejpam-6392	280	25	e1,31	e1,31	PROPN
ejpam-6392	280	26	)	)	PUNCT
ejpam-6392	281	1	=	=	SYM
ejpam-6392	281	2	max	max	PROPN
ejpam-6392	281	3	{	{	PUNCT
ejpam-6392	281	4	gi	gi	INTJ
ejpam-6392	281	5	(	(	PUNCT
ejpam-6392	281	6	g)(e1	g)(e1	PROPN
ejpam-6392	281	7	)	)	PUNCT
ejpam-6392	281	8	,	,	PUNCT
ejpam-6392	281	9	gi	gi	INTJ
ejpam-6392	281	10	(	(	PUNCT
ejpam-6392	281	11	h	h	NOUN
ejpam-6392	281	12	)	)	PUNCT
ejpam-6392	281	13	(	(	PUNCT
ejpam-6392	281	14	31	31	NUM
ejpam-6392	281	15	)	)	PUNCT
ejpam-6392	281	16	}	}	PUNCT
ejpam-6392	281	17	(	(	PUNCT
ejpam-6392	281	18	iii	iii	X
ejpam-6392	281	19	)	)	PUNCT
ejpam-6392	281	20	gf	gf	NOUN
ejpam-6392	281	21	(	(	PUNCT
ejpam-6392	281	22	g×h	g×h	PROPN
ejpam-6392	281	23	)	)	PUNCT
ejpam-6392	281	24	(	(	PUNCT
ejpam-6392	281	25	e1,31	e1,31	PROPN
ejpam-6392	281	26	)	)	PUNCT
ejpam-6392	281	27	=	=	SYM
ejpam-6392	281	28	max	max	PROPN
ejpam-6392	281	29	{	{	PUNCT
ejpam-6392	281	30	gf	gf	PROPN
ejpam-6392	281	31	(	(	PUNCT
ejpam-6392	281	32	g)(e1	g)(e1	PROPN
ejpam-6392	281	33	)	)	PUNCT
ejpam-6392	281	34	,	,	PUNCT
ejpam-6392	281	35	gf	gf	X
ejpam-6392	281	36	(	(	PUNCT
ejpam-6392	281	37	h)(31	h)(31	NOUN
ejpam-6392	281	38	)	)	PUNCT
ejpam-6392	281	39	}	}	PUNCT
ejpam-6392	281	40	for	for	ADP
ejpam-6392	281	41	all	all	DET
ejpam-6392	281	42	e1,31	e1,31	PROPN
ejpam-6392	281	43	∈	∈	PROPN
ejpam-6392	281	44	¨̈u1	¨̈u1	X
ejpam-6392	281	45	×	×	NOUN
ejpam-6392	281	46	¨̈u2	¨̈u2	X
ejpam-6392	281	47	.	.	PUNCT
ejpam-6392	282	1	definition	definition	NOUN
ejpam-6392	282	2	5.2	5.2	NUM
ejpam-6392	282	3	.	.	PUNCT
ejpam-6392	283	1	let	let	VERB
ejpam-6392	283	2	g	g	PROPN
ejpam-6392	283	3	×	×	PROPN
ejpam-6392	283	4	h=	h=	X
ejpam-6392	283	5	(	(	PUNCT
ejpam-6392	283	6	gt	gt	INTJ
ejpam-6392	283	7	(	(	PUNCT
ejpam-6392	283	8	g×h	g×h	PROPN
ejpam-6392	283	9	)	)	PUNCT
ejpam-6392	283	10	,	,	PUNCT
ejpam-6392	283	11	gi	gi	INTJ
ejpam-6392	283	12	(	(	PUNCT
ejpam-6392	283	13	g×h	g×h	NOUN
ejpam-6392	283	14	)	)	PUNCT
ejpam-6392	283	15	,	,	PUNCT
ejpam-6392	283	16	gf	gf	X
ejpam-6392	283	17	(	(	PUNCT
ejpam-6392	283	18	g×h	g×h	PROPN
ejpam-6392	283	19	)	)	PUNCT
ejpam-6392	283	20	)	)	PUNCT
ejpam-6392	283	21	be	be	AUX
ejpam-6392	283	22	neutrosophic	neutrosophic	ADJ
ejpam-6392	283	23	set	set	VERB
ejpam-6392	283	24	in	in	ADP
ejpam-6392	283	25	inkalgebra	inkalgebra	NOUN
ejpam-6392	283	26	¨̈u1	¨̈u1	PROPN
ejpam-6392	283	27	and	and	CCONJ
ejpam-6392	283	28	¨̈u2	¨̈u2	NOUN
ejpam-6392	283	29	respectively	respectively	ADV
ejpam-6392	283	30	.	.	PUNCT
ejpam-6392	284	1	then	then	ADV
ejpam-6392	284	2	the	the	DET
ejpam-6392	284	3	direct	direct	ADJ
ejpam-6392	284	4	product	product	NOUN
ejpam-6392	284	5	of	of	ADP
ejpam-6392	284	6	neutrosophic	neutrosophic	ADJ
ejpam-6392	284	7	ink	ink	NOUN
ejpam-6392	284	8	algebra	algebra	NOUN
ejpam-6392	284	9	of	of	ADP
ejpam-6392	284	10	¨̈u1	¨̈u1	PROPN
ejpam-6392	284	11	×	×	NOUN
ejpam-6392	284	12	¨̈u2	¨̈u2	X
ejpam-6392	284	13	.	.	PUNCT
ejpam-6392	285	1	(	(	PUNCT
ejpam-6392	285	2	i	i	NOUN
ejpam-6392	285	3	)	)	PUNCT
ejpam-6392	285	4	gt	gt	PROPN
ejpam-6392	285	5	(	(	PUNCT
ejpam-6392	285	6	g×h	g×h	PROPN
ejpam-6392	285	7	)	)	PUNCT
ejpam-6392	285	8	(	(	PUNCT
ejpam-6392	285	9	e1	e1	NOUN
ejpam-6392	285	10	,	,	PUNCT
ejpam-6392	285	11	31)•	31)•	NUM
ejpam-6392	285	12	(	(	PUNCT
ejpam-6392	285	13	e2	e2	PROPN
ejpam-6392	285	14	,	,	PUNCT
ejpam-6392	285	15	32	32	NUM
ejpam-6392	285	16	)	)	PUNCT
ejpam-6392	285	17	)	)	PUNCT
ejpam-6392	285	18	≥	≥	PROPN
ejpam-6392	285	19	min	min	PROPN
ejpam-6392	285	20	{	{	PUNCT
ejpam-6392	285	21	gt	gt	PROPN
ejpam-6392	285	22	(	(	PUNCT
ejpam-6392	285	23	g×h	g×h	PROPN
ejpam-6392	285	24	)	)	PUNCT
ejpam-6392	285	25	(	(	PUNCT
ejpam-6392	285	26	e1	e1	NOUN
ejpam-6392	285	27	,	,	PUNCT
ejpam-6392	285	28	31	31	NUM
ejpam-6392	285	29	)	)	PUNCT
ejpam-6392	285	30	,	,	PUNCT
ejpam-6392	285	31	gt	gt	PROPN
ejpam-6392	285	32	(	(	PUNCT
ejpam-6392	285	33	g×h	g×h	PROPN
ejpam-6392	285	34	)	)	PUNCT
ejpam-6392	285	35	(	(	PUNCT
ejpam-6392	285	36	e2	e2	PROPN
ejpam-6392	285	37	,	,	PUNCT
ejpam-6392	285	38	32	32	NUM
ejpam-6392	285	39	)	)	PUNCT
ejpam-6392	285	40	}	}	PUNCT
ejpam-6392	285	41	(	(	PUNCT
ejpam-6392	285	42	ii	ii	NOUN
ejpam-6392	285	43	)	)	PUNCT
ejpam-6392	285	44	gi	gi	NOUN
ejpam-6392	285	45	(	(	PUNCT
ejpam-6392	285	46	g×h	g×h	PROPN
ejpam-6392	285	47	)	)	PUNCT
ejpam-6392	285	48	(	(	PUNCT
ejpam-6392	285	49	e1	e1	NOUN
ejpam-6392	285	50	,	,	PUNCT
ejpam-6392	285	51	31)•	31)•	NUM
ejpam-6392	285	52	(	(	PUNCT
ejpam-6392	285	53	e2	e2	PROPN
ejpam-6392	285	54	,	,	PUNCT
ejpam-6392	285	55	32	32	NUM
ejpam-6392	285	56	)	)	PUNCT
ejpam-6392	285	57	)	)	PUNCT
ejpam-6392	286	1	≤	≤	NUM
ejpam-6392	286	2	max	max	PROPN
ejpam-6392	286	3	{	{	PUNCT
ejpam-6392	286	4	gi	gi	X
ejpam-6392	286	5	(	(	PUNCT
ejpam-6392	286	6	g×h	g×h	PROPN
ejpam-6392	286	7	)	)	PUNCT
ejpam-6392	286	8	(	(	PUNCT
ejpam-6392	286	9	e1	e1	NOUN
ejpam-6392	286	10	,	,	PUNCT
ejpam-6392	286	11	31	31	NUM
ejpam-6392	286	12	)	)	PUNCT
ejpam-6392	286	13	,	,	PUNCT
ejpam-6392	286	14	gi	gi	INTJ
ejpam-6392	286	15	(	(	PUNCT
ejpam-6392	286	16	g×h	g×h	PROPN
ejpam-6392	286	17	)	)	PUNCT
ejpam-6392	286	18	(	(	PUNCT
ejpam-6392	286	19	e2	e2	PROPN
ejpam-6392	286	20	,	,	PUNCT
ejpam-6392	286	21	32	32	NUM
ejpam-6392	286	22	)	)	PUNCT
ejpam-6392	286	23	}	}	PUNCT
ejpam-6392	286	24	(	(	PUNCT
ejpam-6392	286	25	iii	iii	X
ejpam-6392	286	26	)	)	PUNCT
ejpam-6392	286	27	gf	gf	NOUN
ejpam-6392	286	28	(	(	PUNCT
ejpam-6392	286	29	g×h	g×h	PROPN
ejpam-6392	286	30	)	)	PUNCT
ejpam-6392	286	31	(	(	PUNCT
ejpam-6392	286	32	e1	e1	NOUN
ejpam-6392	286	33	,	,	PUNCT
ejpam-6392	286	34	31)•	31)•	NUM
ejpam-6392	286	35	(	(	PUNCT
ejpam-6392	286	36	e2	e2	PROPN
ejpam-6392	286	37	,	,	PUNCT
ejpam-6392	286	38	32	32	NUM
ejpam-6392	286	39	)	)	PUNCT
ejpam-6392	286	40	)	)	PUNCT
ejpam-6392	286	41	≤	≤	NUM
ejpam-6392	286	42	max	max	PROPN
ejpam-6392	286	43	{	{	PUNCT
ejpam-6392	286	44	gf	gf	X
ejpam-6392	286	45	(	(	PUNCT
ejpam-6392	286	46	g×h	g×h	PROPN
ejpam-6392	286	47	)	)	PUNCT
ejpam-6392	286	48	(	(	PUNCT
ejpam-6392	286	49	e1	e1	NOUN
ejpam-6392	286	50	,	,	PUNCT
ejpam-6392	286	51	31	31	NUM
ejpam-6392	286	52	)	)	PUNCT
ejpam-6392	286	53	,	,	PUNCT
ejpam-6392	286	54	gf	gf	X
ejpam-6392	286	55	(	(	PUNCT
ejpam-6392	286	56	g×h	g×h	PROPN
ejpam-6392	286	57	)	)	PUNCT
ejpam-6392	286	58	(	(	PUNCT
ejpam-6392	286	59	e2	e2	PROPN
ejpam-6392	286	60	,	,	PUNCT
ejpam-6392	286	61	32	32	NUM
ejpam-6392	286	62	)	)	PUNCT
ejpam-6392	286	63	}	}	PUNCT
ejpam-6392	286	64	for	for	ADP
ejpam-6392	286	65	all	all	DET
ejpam-6392	286	66	(	(	PUNCT
ejpam-6392	286	67	e1	e1	PROPN
ejpam-6392	286	68	,	,	PUNCT
ejpam-6392	286	69	e2	e2	PROPN
ejpam-6392	286	70	,	,	PUNCT
ejpam-6392	286	71	e3	e3	NOUN
ejpam-6392	286	72	)	)	PUNCT
ejpam-6392	286	73	and	and	CCONJ
ejpam-6392	286	74	(	(	PUNCT
ejpam-6392	286	75	31	31	NUM
ejpam-6392	286	76	,	,	PUNCT
ejpam-6392	286	77	32	32	NUM
ejpam-6392	286	78	,	,	PUNCT
ejpam-6392	286	79	33	33	NUM
ejpam-6392	286	80	)	)	PUNCT
ejpam-6392	286	81	∈	∈	PROPN
ejpam-6392	286	82	¨̈u1	¨̈u1	X
ejpam-6392	286	83	×	×	NOUN
ejpam-6392	286	84	¨̈u2	¨̈u2	X
ejpam-6392	286	85	.	.	PUNCT
ejpam-6392	287	1	¨̈u2	¨̈u2	X
ejpam-6392	287	2	.	.	PUNCT
ejpam-6392	288	1	theorem	theorem	VERB
ejpam-6392	288	2	5.1	5.1	NUM
ejpam-6392	288	3	.	.	PUNCT
ejpam-6392	289	1	let	let	VERB
ejpam-6392	289	2	g=(gt	g=(gt	NOUN
ejpam-6392	289	3	,	,	PUNCT
ejpam-6392	289	4	gi	gi	INTJ
ejpam-6392	289	5	,	,	PUNCT
ejpam-6392	289	6	gf	gf	PROPN
ejpam-6392	289	7	)	)	PUNCT
ejpam-6392	289	8	and	and	CCONJ
ejpam-6392	289	9	h=(ht	h=(ht	NOUN
ejpam-6392	289	10	,	,	PUNCT
ejpam-6392	289	11	hi	hi	INTJ
ejpam-6392	289	12	,	,	PUNCT
ejpam-6392	289	13	hf	hf	INTJ
ejpam-6392	289	14	)	)	PUNCT
ejpam-6392	289	15	be	be	AUX
ejpam-6392	289	16	two	two	NUM
ejpam-6392	289	17	neutrosophic	neutrosophic	ADJ
ejpam-6392	289	18	ink	ink	NOUN
ejpam-6392	289	19	algebras	algebras	PROPN
ejpam-6392	289	20	¨̈u1	¨̈u1	PROPN
ejpam-6392	289	21	and	and	CCONJ
ejpam-6392	289	22	¨̈u2	¨̈u2	NOUN
ejpam-6392	289	23	respectively	respectively	ADV
ejpam-6392	289	24	.	.	PUNCT
ejpam-6392	290	1	then	then	ADV
ejpam-6392	290	2	g	g	PROPN
ejpam-6392	290	3	×	×	PROPN
ejpam-6392	290	4	h	h	NOUN
ejpam-6392	290	5	=	=	PUNCT
ejpam-6392	290	6	(	(	PUNCT
ejpam-6392	290	7	gt	gt	INTJ
ejpam-6392	290	8	(	(	PUNCT
ejpam-6392	290	9	g×h	g×h	PROPN
ejpam-6392	290	10	)	)	PUNCT
ejpam-6392	290	11	,	,	PUNCT
ejpam-6392	290	12	gi	gi	INTJ
ejpam-6392	290	13	(	(	PUNCT
ejpam-6392	290	14	g×h	g×h	NOUN
ejpam-6392	290	15	)	)	PUNCT
ejpam-6392	290	16	,	,	PUNCT
ejpam-6392	290	17	gf	gf	X
ejpam-6392	290	18	(	(	PUNCT
ejpam-6392	290	19	g×h	g×h	PROPN
ejpam-6392	290	20	)	)	PUNCT
ejpam-6392	290	21	)	)	PUNCT
ejpam-6392	290	22	is	be	AUX
ejpam-6392	290	23	also	also	ADV
ejpam-6392	290	24	neutrosphic	neutrosphic	ADJ
ejpam-6392	290	25	sub	sub	NOUN
ejpam-6392	290	26	algebra	algebra	NOUN
ejpam-6392	290	27	of	of	ADP
ejpam-6392	290	28	ink	ink	NOUN
ejpam-6392	290	29	-	-	PUNCT
ejpam-6392	290	30	algebra	algebra	NOUN
ejpam-6392	290	31	of	of	ADP
ejpam-6392	290	32	¨̈u1	¨̈u1	PROPN
ejpam-6392	290	33	×	×	NOUN
ejpam-6392	290	34	¨̈u2	¨̈u2	NOUN
ejpam-6392	290	35	.	.	PUNCT
ejpam-6392	291	1	m.	m.	NOUN
ejpam-6392	291	2	remala	remala	NOUN
ejpam-6392	291	3	,	,	PUNCT
ejpam-6392	291	4	e.	e.	PROPN
ejpam-6392	291	5	tamma	tamma	PROPN
ejpam-6392	291	6	,	,	PUNCT
ejpam-6392	291	7	y.	y.	PROPN
ejpam-6392	291	8	bhargavi	bhargavi	PROPN
ejpam-6392	291	9	/	/	SYM
ejpam-6392	291	10	eur	eur	PROPN
ejpam-6392	291	11	.	.	PUNCT
ejpam-6392	292	1	j.	j.	PROPN
ejpam-6392	292	2	pure	pure	PROPN
ejpam-6392	292	3	appl	appl	PROPN
ejpam-6392	292	4	.	.	PROPN
ejpam-6392	292	5	math	math	PROPN
ejpam-6392	292	6	,	,	PUNCT
ejpam-6392	292	7	18	18	NUM
ejpam-6392	292	8	(	(	PUNCT
ejpam-6392	292	9	4	4	NUM
ejpam-6392	292	10	)	)	PUNCT
ejpam-6392	292	11	(	(	PUNCT
ejpam-6392	292	12	2025	2025	NUM
ejpam-6392	292	13	)	)	PUNCT
ejpam-6392	292	14	,	,	PUNCT
ejpam-6392	292	15	6392	6392	NUM
ejpam-6392	292	16	12	12	NUM
ejpam-6392	292	17	of	of	ADP
ejpam-6392	292	18	20	20	NUM
ejpam-6392	292	19	proof	proof	NOUN
ejpam-6392	292	20	.	.	PUNCT
ejpam-6392	293	1	for	for	ADP
ejpam-6392	293	2	any	any	DET
ejpam-6392	293	3	(	(	PUNCT
ejpam-6392	293	4	e1	e1	NOUN
ejpam-6392	293	5	,	,	PUNCT
ejpam-6392	293	6	31	31	NUM
ejpam-6392	293	7	)	)	PUNCT
ejpam-6392	293	8	,	,	PUNCT
ejpam-6392	293	9	(	(	PUNCT
ejpam-6392	293	10	e2	e2	PROPN
ejpam-6392	293	11	,	,	PUNCT
ejpam-6392	293	12	32	32	NUM
ejpam-6392	293	13	)	)	PUNCT
ejpam-6392	293	14	∈	∈	PROPN
ejpam-6392	293	15	¨̈u1	¨̈u1	X
ejpam-6392	293	16	×	×	NOUN
ejpam-6392	293	17	¨̈u2	¨̈u2	X
ejpam-6392	293	18	.	.	PUNCT
ejpam-6392	294	1	now	now	ADV
ejpam-6392	294	2	,	,	PUNCT
ejpam-6392	294	3	gt	gt	PROPN
ejpam-6392	294	4	(	(	PUNCT
ejpam-6392	294	5	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	294	6	,	,	PUNCT
ejpam-6392	294	7	31	31	NUM
ejpam-6392	294	8	)	)	PUNCT
ejpam-6392	294	9	•	•	NOUN
ejpam-6392	294	10	(	(	PUNCT
ejpam-6392	294	11	e2	e2	PROPN
ejpam-6392	294	12	,	,	PUNCT
ejpam-6392	294	13	32	32	NUM
ejpam-6392	294	14	)	)	PUNCT
ejpam-6392	294	15	=	=	SYM
ejpam-6392	294	16	gt	gt	INTJ
ejpam-6392	294	17	(	(	PUNCT
ejpam-6392	294	18	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	294	19	•	•	NUM
ejpam-6392	294	20	e2	e2	PROPN
ejpam-6392	294	21	)	)	PUNCT
ejpam-6392	294	22	,	,	PUNCT
ejpam-6392	294	23	(	(	PUNCT
ejpam-6392	294	24	31	31	NUM
ejpam-6392	294	25	•	•	NUM
ejpam-6392	294	26	32	32	NUM
ejpam-6392	294	27	)	)	PUNCT
ejpam-6392	294	28	=	=	SYM
ejpam-6392	294	29	min	min	PROPN
ejpam-6392	294	30	{	{	PUNCT
ejpam-6392	294	31	gt	gt	PROPN
ejpam-6392	294	32	(	(	PUNCT
ejpam-6392	294	33	g)(e1	g)(e1	PROPN
ejpam-6392	294	34	•	•	NUM
ejpam-6392	294	35	e2	e2	PROPN
ejpam-6392	294	36	)	)	PUNCT
ejpam-6392	294	37	,	,	PUNCT
ejpam-6392	294	38	gt	gt	PROPN
ejpam-6392	294	39	(	(	PUNCT
ejpam-6392	294	40	h)(31	h)(31	NOUN
ejpam-6392	294	41	•	•	NOUN
ejpam-6392	294	42	32	32	NUM
ejpam-6392	294	43	)	)	PUNCT
ejpam-6392	294	44	}	}	PUNCT
ejpam-6392	294	45	=	=	SYM
ejpam-6392	294	46	min	min	X
ejpam-6392	294	47	{	{	PUNCT
ejpam-6392	294	48	gt	gt	PROPN
ejpam-6392	294	49	(	(	PUNCT
ejpam-6392	294	50	g)(e1	g)(e1	PROPN
ejpam-6392	294	51	•	•	NUM
ejpam-6392	294	52	e2	e2	PROPN
ejpam-6392	294	53	)	)	PUNCT
ejpam-6392	294	54	,	,	PUNCT
ejpam-6392	294	55	gt	gt	PROPN
ejpam-6392	294	56	(	(	PUNCT
ejpam-6392	294	57	h)(31	h)(31	NOUN
ejpam-6392	294	58	•	•	NOUN
ejpam-6392	294	59	32	32	NUM
ejpam-6392	294	60	)	)	PUNCT
ejpam-6392	294	61	}	}	PUNCT
ejpam-6392	294	62	≥	≥	VERB
ejpam-6392	294	63	min{min{gt	min{min{gt	ADJ
ejpam-6392	294	64	(	(	PUNCT
ejpam-6392	294	65	g)(e1	g)(e1	NOUN
ejpam-6392	294	66	)	)	PUNCT
ejpam-6392	294	67	,	,	PUNCT
ejpam-6392	294	68	gt	gt	PROPN
ejpam-6392	294	69	(	(	PUNCT
ejpam-6392	294	70	g)(e2	g)(e2	PROPN
ejpam-6392	294	71	)	)	PUNCT
ejpam-6392	294	72	}	}	PUNCT
ejpam-6392	294	73	,	,	PUNCT
ejpam-6392	294	74	min{gt	min{gt	PRON
ejpam-6392	294	75	(	(	PUNCT
ejpam-6392	294	76	h)(31	h)(31	NOUN
ejpam-6392	294	77	)	)	PUNCT
ejpam-6392	294	78	,	,	PUNCT
ejpam-6392	294	79	gt	gt	PROPN
ejpam-6392	294	80	(	(	PUNCT
ejpam-6392	294	81	h)(32	h)(32	NOUN
ejpam-6392	294	82	)	)	PUNCT
ejpam-6392	294	83	}	}	PUNCT
ejpam-6392	294	84	}	}	PUNCT
ejpam-6392	294	85	≥	≥	PROPN
ejpam-6392	294	86	min	min	PROPN
ejpam-6392	294	87	{	{	PUNCT
ejpam-6392	294	88	gt	gt	PROPN
ejpam-6392	294	89	(	(	PUNCT
ejpam-6392	294	90	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	294	91	,	,	PUNCT
ejpam-6392	294	92	e2	e2	PROPN
ejpam-6392	294	93	)	)	PUNCT
ejpam-6392	294	94	,	,	PUNCT
ejpam-6392	294	95	gt	gt	PROPN
ejpam-6392	294	96	(	(	PUNCT
ejpam-6392	294	97	g×h)(31	g×h)(31	PROPN
ejpam-6392	294	98	,	,	PUNCT
ejpam-6392	294	99	32	32	NUM
ejpam-6392	294	100	)	)	PUNCT
ejpam-6392	294	101	}	}	PUNCT
ejpam-6392	294	102	.	.	PUNCT
ejpam-6392	295	1	then	then	ADV
ejpam-6392	295	2	,	,	PUNCT
ejpam-6392	295	3	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	295	4	,	,	PUNCT
ejpam-6392	295	5	31	31	NUM
ejpam-6392	295	6	)	)	PUNCT
ejpam-6392	295	7	•	•	NOUN
ejpam-6392	295	8	(	(	PUNCT
ejpam-6392	295	9	e2	e2	PROPN
ejpam-6392	295	10	,	,	PUNCT
ejpam-6392	295	11	32	32	NUM
ejpam-6392	295	12	)	)	PUNCT
ejpam-6392	295	13	=	=	NOUN
ejpam-6392	295	14	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	295	15	•	•	NUM
ejpam-6392	295	16	e2	e2	PROPN
ejpam-6392	295	17	)	)	PUNCT
ejpam-6392	295	18	,	,	PUNCT
ejpam-6392	295	19	(	(	PUNCT
ejpam-6392	295	20	31	31	NUM
ejpam-6392	295	21	•	•	NUM
ejpam-6392	295	22	32	32	NUM
ejpam-6392	295	23	)	)	PUNCT
ejpam-6392	295	24	=	=	SYM
ejpam-6392	295	25	max	max	X
ejpam-6392	295	26	{	{	PUNCT
ejpam-6392	295	27	gi(g)(e1	gi(g)(e1	PROPN
ejpam-6392	295	28	•	•	NUM
ejpam-6392	295	29	e2	e2	PROPN
ejpam-6392	295	30	)	)	PUNCT
ejpam-6392	295	31	,	,	PUNCT
ejpam-6392	295	32	gi(h)(31	gi(h)(31	VERB
ejpam-6392	295	33	•	•	NOUN
ejpam-6392	295	34	32	32	NUM
ejpam-6392	295	35	)	)	PUNCT
ejpam-6392	295	36	}	}	PUNCT
ejpam-6392	295	37	=	=	SYM
ejpam-6392	295	38	max	max	X
ejpam-6392	295	39	{	{	PUNCT
ejpam-6392	295	40	gi(g)(e1	gi(g)(e1	PROPN
ejpam-6392	295	41	•	•	NUM
ejpam-6392	295	42	e2	e2	PROPN
ejpam-6392	295	43	)	)	PUNCT
ejpam-6392	295	44	,	,	PUNCT
ejpam-6392	295	45	gi(h)(31	gi(h)(31	VERB
ejpam-6392	295	46	•	•	NOUN
ejpam-6392	295	47	32	32	NUM
ejpam-6392	295	48	)	)	PUNCT
ejpam-6392	295	49	}	}	PUNCT
ejpam-6392	295	50	≤	≤	NUM
ejpam-6392	295	51	max{max{gi(g)(e1	max{max{gi(g)(e1	NOUN
ejpam-6392	295	52	)	)	PUNCT
ejpam-6392	295	53	,	,	PUNCT
ejpam-6392	295	54	gi(g)(e2	gi(g)(e2	PROPN
ejpam-6392	295	55	)	)	PUNCT
ejpam-6392	295	56	}	}	PUNCT
ejpam-6392	295	57	,	,	PUNCT
ejpam-6392	295	58	max{gi(h)(31	max{gi(h)(31	PROPN
ejpam-6392	295	59	)	)	PUNCT
ejpam-6392	295	60	,	,	PUNCT
ejpam-6392	295	61	gi(h)(32	gi(h)(32	NOUN
ejpam-6392	295	62	)	)	PUNCT
ejpam-6392	295	63	}	}	PUNCT
ejpam-6392	296	1	}	}	PUNCT
ejpam-6392	296	2	≤	≤	NUM
ejpam-6392	296	3	max	max	PROPN
ejpam-6392	296	4	{	{	PUNCT
ejpam-6392	296	5	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	296	6	,	,	PUNCT
ejpam-6392	296	7	e2	e2	PROPN
ejpam-6392	296	8	)	)	PUNCT
ejpam-6392	296	9	,	,	PUNCT
ejpam-6392	296	10	gi(g×h)(31	gi(g×h)(31	PROPN
ejpam-6392	296	11	,	,	PUNCT
ejpam-6392	296	12	32	32	NUM
ejpam-6392	296	13	)	)	PUNCT
ejpam-6392	296	14	}	}	PUNCT
ejpam-6392	296	15	.	.	PUNCT
ejpam-6392	297	1	also	also	ADV
ejpam-6392	297	2	,	,	PUNCT
ejpam-6392	297	3	gf	gf	PROPN
ejpam-6392	297	4	(	(	PUNCT
ejpam-6392	297	5	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	297	6	,	,	PUNCT
ejpam-6392	297	7	31	31	NUM
ejpam-6392	297	8	)	)	PUNCT
ejpam-6392	297	9	•	•	NOUN
ejpam-6392	297	10	(	(	PUNCT
ejpam-6392	297	11	e2	e2	PROPN
ejpam-6392	297	12	,	,	PUNCT
ejpam-6392	297	13	32	32	NUM
ejpam-6392	297	14	)	)	PUNCT
ejpam-6392	297	15	=	=	SYM
ejpam-6392	298	1	gf	gf	X
ejpam-6392	298	2	(	(	PUNCT
ejpam-6392	298	3	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	298	4	•	•	NUM
ejpam-6392	298	5	e2	e2	PROPN
ejpam-6392	298	6	)	)	PUNCT
ejpam-6392	298	7	,	,	PUNCT
ejpam-6392	298	8	(	(	PUNCT
ejpam-6392	298	9	31	31	NUM
ejpam-6392	298	10	•	•	NUM
ejpam-6392	298	11	32	32	NUM
ejpam-6392	298	12	)	)	PUNCT
ejpam-6392	298	13	=	=	SYM
ejpam-6392	298	14	max	max	PROPN
ejpam-6392	298	15	{	{	PUNCT
ejpam-6392	298	16	gf	gf	X
ejpam-6392	298	17	(	(	PUNCT
ejpam-6392	298	18	g)(e1	g)(e1	PROPN
ejpam-6392	298	19	•	•	NUM
ejpam-6392	298	20	e2	e2	PROPN
ejpam-6392	298	21	)	)	PUNCT
ejpam-6392	298	22	,	,	PUNCT
ejpam-6392	298	23	gf	gf	X
ejpam-6392	298	24	(	(	PUNCT
ejpam-6392	298	25	h)(31	h)(31	X
ejpam-6392	298	26	•	•	NOUN
ejpam-6392	298	27	32	32	NUM
ejpam-6392	298	28	)	)	PUNCT
ejpam-6392	298	29	}	}	PUNCT
ejpam-6392	298	30	=	=	SYM
ejpam-6392	298	31	max	max	X
ejpam-6392	298	32	{	{	PUNCT
ejpam-6392	298	33	gf	gf	X
ejpam-6392	298	34	(	(	PUNCT
ejpam-6392	298	35	g)(e1	g)(e1	PROPN
ejpam-6392	298	36	•	•	NUM
ejpam-6392	298	37	e2	e2	PROPN
ejpam-6392	298	38	)	)	PUNCT
ejpam-6392	298	39	,	,	PUNCT
ejpam-6392	298	40	gf	gf	X
ejpam-6392	298	41	(	(	PUNCT
ejpam-6392	298	42	h)(31	h)(31	X
ejpam-6392	298	43	•	•	NOUN
ejpam-6392	298	44	32	32	NUM
ejpam-6392	298	45	)	)	PUNCT
ejpam-6392	298	46	}	}	PUNCT
ejpam-6392	298	47	≤	≤	ADV
ejpam-6392	298	48	max{max{gf	max{max{gf	NOUN
ejpam-6392	298	49	(	(	PUNCT
ejpam-6392	298	50	g)(e1	g)(e1	PROPN
ejpam-6392	298	51	)	)	PUNCT
ejpam-6392	298	52	,	,	PUNCT
ejpam-6392	298	53	gf	gf	X
ejpam-6392	298	54	(	(	PUNCT
ejpam-6392	298	55	h)(e2	h)(e2	PROPN
ejpam-6392	298	56	)	)	PUNCT
ejpam-6392	298	57	}	}	PUNCT
ejpam-6392	298	58	,	,	PUNCT
ejpam-6392	298	59	max{gf	max{gf	X
ejpam-6392	298	60	(	(	PUNCT
ejpam-6392	298	61	g)(31	g)(31	PROPN
ejpam-6392	298	62	)	)	PUNCT
ejpam-6392	298	63	,	,	PUNCT
ejpam-6392	298	64	gf	gf	X
ejpam-6392	298	65	(	(	PUNCT
ejpam-6392	298	66	h)(32	h)(32	NOUN
ejpam-6392	298	67	)	)	PUNCT
ejpam-6392	298	68	}	}	PUNCT
ejpam-6392	298	69	}	}	PUNCT
ejpam-6392	298	70	≤	≤	NUM
ejpam-6392	298	71	max	max	PROPN
ejpam-6392	298	72	{	{	PUNCT
ejpam-6392	298	73	gf	gf	PROPN
ejpam-6392	298	74	(	(	PUNCT
ejpam-6392	298	75	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	298	76	,	,	PUNCT
ejpam-6392	298	77	e2	e2	PROPN
ejpam-6392	298	78	)	)	PUNCT
ejpam-6392	298	79	,	,	PUNCT
ejpam-6392	298	80	gf	gf	PROPN
ejpam-6392	298	81	(	(	PUNCT
ejpam-6392	298	82	g×h)(31	g×h)(31	PROPN
ejpam-6392	298	83	,	,	PUNCT
ejpam-6392	298	84	32	32	NUM
ejpam-6392	298	85	)	)	PUNCT
ejpam-6392	298	86	}	}	PUNCT
ejpam-6392	298	87	.	.	PUNCT
ejpam-6392	299	1	theorem	theorem	VERB
ejpam-6392	299	2	5.2	5.2	NUM
ejpam-6392	299	3	.	.	PUNCT
ejpam-6392	300	1	let	let	VERB
ejpam-6392	300	2	g	g	PROPN
ejpam-6392	300	3	=	=	SYM
ejpam-6392	300	4	(	(	PUNCT
ejpam-6392	300	5	gt	gt	INTJ
ejpam-6392	300	6	,	,	PUNCT
ejpam-6392	300	7	gi	gi	INTJ
ejpam-6392	300	8	,	,	PUNCT
ejpam-6392	300	9	gf	gf	PROPN
ejpam-6392	300	10	)	)	PUNCT
ejpam-6392	300	11	and	and	CCONJ
ejpam-6392	300	12	h	h	NOUN
ejpam-6392	300	13	=	=	SYM
ejpam-6392	300	14	(	(	PUNCT
ejpam-6392	300	15	ht	ht	INTJ
ejpam-6392	300	16	,	,	PUNCT
ejpam-6392	300	17	hi	hi	INTJ
ejpam-6392	300	18	,	,	PUNCT
ejpam-6392	300	19	hf	hf	INTJ
ejpam-6392	300	20	)	)	PUNCT
ejpam-6392	300	21	be	be	AUX
ejpam-6392	300	22	two	two	NUM
ejpam-6392	300	23	neutrosophic	neutrosophic	ADJ
ejpam-6392	300	24	ink	ink	NOUN
ejpam-6392	300	25	algebras	algebras	PROPN
ejpam-6392	300	26	¨̈u1	¨̈u1	PROPN
ejpam-6392	300	27	and	and	CCONJ
ejpam-6392	300	28	¨̈u2	¨̈u2	NOUN
ejpam-6392	300	29	respectively	respectively	ADV
ejpam-6392	300	30	.	.	PUNCT
ejpam-6392	301	1	then	then	ADV
ejpam-6392	301	2	(	(	PUNCT
ejpam-6392	301	3	i	i	NOUN
ejpam-6392	301	4	)	)	PUNCT
ejpam-6392	301	5	gt	gt	PROPN
ejpam-6392	301	6	(	(	PUNCT
ejpam-6392	301	7	g×h)(0	g×h)(0	PROPN
ejpam-6392	301	8	,	,	PUNCT
ejpam-6392	301	9	0	0	NUM
ejpam-6392	301	10	)	)	PUNCT
ejpam-6392	301	11	=	=	SYM
ejpam-6392	301	12	gt	gt	PROPN
ejpam-6392	301	13	(	(	PUNCT
ejpam-6392	301	14	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	301	15	,	,	PUNCT
ejpam-6392	301	16	31	31	NUM
ejpam-6392	301	17	)	)	PUNCT
ejpam-6392	301	18	,	,	PUNCT
ejpam-6392	301	19	(	(	PUNCT
ejpam-6392	301	20	ii	ii	NOUN
ejpam-6392	301	21	)	)	PUNCT
ejpam-6392	301	22	gi(g×h)(0	gi(g×h)(0	PROPN
ejpam-6392	301	23	,	,	PUNCT
ejpam-6392	301	24	0	0	NUM
ejpam-6392	301	25	)	)	PUNCT
ejpam-6392	301	26	=	=	SYM
ejpam-6392	301	27	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	301	28	,	,	PUNCT
ejpam-6392	301	29	31	31	NUM
ejpam-6392	301	30	)	)	PUNCT
ejpam-6392	301	31	,	,	PUNCT
ejpam-6392	301	32	(	(	PUNCT
ejpam-6392	301	33	iii	iii	NOUN
ejpam-6392	301	34	)	)	PUNCT
ejpam-6392	301	35	gi(g×h)(0	gi(g×h)(0	PROPN
ejpam-6392	301	36	,	,	PUNCT
ejpam-6392	301	37	0	0	NUM
ejpam-6392	301	38	)	)	PUNCT
ejpam-6392	301	39	=	=	SYM
ejpam-6392	301	40	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	301	41	,	,	PUNCT
ejpam-6392	301	42	31	31	NUM
ejpam-6392	301	43	)	)	PUNCT
ejpam-6392	301	44	for	for	ADP
ejpam-6392	301	45	all	all	DET
ejpam-6392	301	46	(	(	PUNCT
ejpam-6392	301	47	e1	e1	PROPN
ejpam-6392	301	48	,	,	PUNCT
ejpam-6392	301	49	31	31	NUM
ejpam-6392	301	50	)	)	PUNCT
ejpam-6392	301	51	∈	∈	PROPN
ejpam-6392	301	52	¨̈u1	¨̈u1	X
ejpam-6392	301	53	×	×	NOUN
ejpam-6392	301	54	¨̈u2	¨̈u2	NOUN
ejpam-6392	301	55	.	.	PUNCT
ejpam-6392	302	1	proof	proof	NOUN
ejpam-6392	302	2	.	.	PUNCT
ejpam-6392	303	1	by	by	ADP
ejpam-6392	303	2	definition	definition	NOUN
ejpam-6392	303	3	,	,	PUNCT
ejpam-6392	303	4	gt	gt	PROPN
ejpam-6392	303	5	(	(	PUNCT
ejpam-6392	303	6	g×h)(0	g×h)(0	PROPN
ejpam-6392	303	7	,	,	PUNCT
ejpam-6392	303	8	0	0	NUM
ejpam-6392	303	9	)	)	PUNCT
ejpam-6392	303	10	=	=	SYM
ejpam-6392	303	11	gt	gt	PROPN
ejpam-6392	303	12	(	(	PUNCT
ejpam-6392	303	13	g×h	g×h	PROPN
ejpam-6392	303	14	)	)	PUNCT
ejpam-6392	303	15	(	(	PUNCT
ejpam-6392	303	16	(	(	PUNCT
ejpam-6392	303	17	e1	e1	NOUN
ejpam-6392	303	18	,	,	PUNCT
ejpam-6392	303	19	31	31	NUM
ejpam-6392	303	20	)	)	PUNCT
ejpam-6392	303	21	•	•	NOUN
ejpam-6392	303	22	(	(	PUNCT
ejpam-6392	303	23	e1	e1	NOUN
ejpam-6392	303	24	,	,	PUNCT
ejpam-6392	303	25	31	31	NUM
ejpam-6392	303	26	)	)	PUNCT
ejpam-6392	303	27	)	)	PUNCT
ejpam-6392	304	1	=	=	SYM
ejpam-6392	304	2	min	min	PROPN
ejpam-6392	304	3	{	{	PUNCT
ejpam-6392	304	4	gt	gt	PROPN
ejpam-6392	304	5	(	(	PUNCT
ejpam-6392	304	6	g×h	g×h	PROPN
ejpam-6392	304	7	)	)	PUNCT
ejpam-6392	304	8	(	(	PUNCT
ejpam-6392	304	9	(	(	PUNCT
ejpam-6392	304	10	e1	e1	NOUN
ejpam-6392	304	11	,	,	PUNCT
ejpam-6392	304	12	31	31	NUM
ejpam-6392	304	13	)	)	PUNCT
ejpam-6392	304	14	•	•	NOUN
ejpam-6392	304	15	(	(	PUNCT
ejpam-6392	304	16	e1	e1	NOUN
ejpam-6392	304	17	,	,	PUNCT
ejpam-6392	304	18	31	31	NUM
ejpam-6392	304	19	)	)	PUNCT
ejpam-6392	304	20	)	)	PUNCT
ejpam-6392	304	21	,	,	PUNCT
ejpam-6392	304	22	gt	gt	PROPN
ejpam-6392	304	23	(	(	PUNCT
ejpam-6392	304	24	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	304	25	,	,	PUNCT
ejpam-6392	304	26	31	31	NUM
ejpam-6392	304	27	)	)	PUNCT
ejpam-6392	304	28	}	}	PUNCT
ejpam-6392	304	29	≥	≥	PROPN
ejpam-6392	304	30	gt	gt	INTJ
ejpam-6392	304	31	(	(	PUNCT
ejpam-6392	304	32	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	304	33	,	,	PUNCT
ejpam-6392	304	34	31	31	NUM
ejpam-6392	304	35	)	)	PUNCT
ejpam-6392	304	36	.	.	PUNCT
ejpam-6392	305	1	gi(g×h)(0	gi(g×h)(0	PROPN
ejpam-6392	305	2	,	,	PUNCT
ejpam-6392	305	3	0	0	NUM
ejpam-6392	305	4	)	)	PUNCT
ejpam-6392	305	5	=	=	SYM
ejpam-6392	305	6	gi(g×h	gi(g×h	NUM
ejpam-6392	305	7	)	)	PUNCT
ejpam-6392	305	8	(	(	PUNCT
ejpam-6392	305	9	(	(	PUNCT
ejpam-6392	305	10	e1	e1	NOUN
ejpam-6392	305	11	,	,	PUNCT
ejpam-6392	305	12	31	31	NUM
ejpam-6392	305	13	)	)	PUNCT
ejpam-6392	305	14	•	•	NOUN
ejpam-6392	305	15	(	(	PUNCT
ejpam-6392	305	16	e1	e1	NOUN
ejpam-6392	305	17	,	,	PUNCT
ejpam-6392	305	18	31	31	NUM
ejpam-6392	305	19	)	)	PUNCT
ejpam-6392	305	20	)	)	PUNCT
ejpam-6392	306	1	=	=	SYM
ejpam-6392	306	2	max	max	PROPN
ejpam-6392	306	3	{	{	PUNCT
ejpam-6392	306	4	gi(g×h	gi(g×h	NOUN
ejpam-6392	306	5	)	)	PUNCT
ejpam-6392	306	6	(	(	PUNCT
ejpam-6392	306	7	(	(	PUNCT
ejpam-6392	306	8	e1	e1	NOUN
ejpam-6392	306	9	,	,	PUNCT
ejpam-6392	306	10	31	31	NUM
ejpam-6392	306	11	)	)	PUNCT
ejpam-6392	306	12	•	•	NOUN
ejpam-6392	306	13	(	(	PUNCT
ejpam-6392	306	14	e1	e1	NOUN
ejpam-6392	306	15	,	,	PUNCT
ejpam-6392	306	16	31	31	NUM
ejpam-6392	306	17	)	)	PUNCT
ejpam-6392	306	18	)	)	PUNCT
ejpam-6392	306	19	,	,	PUNCT
ejpam-6392	306	20	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	306	21	,	,	PUNCT
ejpam-6392	306	22	31	31	NUM
ejpam-6392	306	23	)	)	PUNCT
ejpam-6392	306	24	}	}	PUNCT
ejpam-6392	306	25	≤	≤	NUM
ejpam-6392	306	26	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	306	27	,	,	PUNCT
ejpam-6392	306	28	31	31	NUM
ejpam-6392	306	29	)	)	PUNCT
ejpam-6392	306	30	.	.	PUNCT
ejpam-6392	307	1	m.	m.	NOUN
ejpam-6392	307	2	remala	remala	NOUN
ejpam-6392	307	3	,	,	PUNCT
ejpam-6392	307	4	e.	e.	PROPN
ejpam-6392	307	5	tamma	tamma	PROPN
ejpam-6392	307	6	,	,	PUNCT
ejpam-6392	307	7	y.	y.	PROPN
ejpam-6392	307	8	bhargavi	bhargavi	PROPN
ejpam-6392	307	9	/	/	SYM
ejpam-6392	307	10	eur	eur	PROPN
ejpam-6392	307	11	.	.	PUNCT
ejpam-6392	308	1	j.	j.	PROPN
ejpam-6392	308	2	pure	pure	PROPN
ejpam-6392	308	3	appl	appl	PROPN
ejpam-6392	308	4	.	.	PROPN
ejpam-6392	308	5	math	math	PROPN
ejpam-6392	308	6	,	,	PUNCT
ejpam-6392	308	7	18	18	NUM
ejpam-6392	308	8	(	(	PUNCT
ejpam-6392	308	9	4	4	NUM
ejpam-6392	308	10	)	)	PUNCT
ejpam-6392	308	11	(	(	PUNCT
ejpam-6392	308	12	2025	2025	NUM
ejpam-6392	308	13	)	)	PUNCT
ejpam-6392	308	14	,	,	PUNCT
ejpam-6392	308	15	6392	6392	NUM
ejpam-6392	308	16	13	13	NUM
ejpam-6392	308	17	of	of	ADP
ejpam-6392	308	18	20	20	NUM
ejpam-6392	308	19	gf	gf	X
ejpam-6392	308	20	(	(	PUNCT
ejpam-6392	308	21	g×h)(0	g×h)(0	PROPN
ejpam-6392	308	22	,	,	PUNCT
ejpam-6392	308	23	0	0	NUM
ejpam-6392	308	24	)	)	PUNCT
ejpam-6392	308	25	=	=	SYM
ejpam-6392	308	26	gf	gf	X
ejpam-6392	308	27	(	(	PUNCT
ejpam-6392	308	28	g×h	g×h	PROPN
ejpam-6392	308	29	)	)	PUNCT
ejpam-6392	308	30	(	(	PUNCT
ejpam-6392	308	31	(	(	PUNCT
ejpam-6392	308	32	e1	e1	NOUN
ejpam-6392	308	33	,	,	PUNCT
ejpam-6392	308	34	31	31	NUM
ejpam-6392	308	35	)	)	PUNCT
ejpam-6392	308	36	•	•	NOUN
ejpam-6392	308	37	(	(	PUNCT
ejpam-6392	308	38	e1	e1	NOUN
ejpam-6392	308	39	,	,	PUNCT
ejpam-6392	308	40	31	31	NUM
ejpam-6392	308	41	)	)	PUNCT
ejpam-6392	308	42	)	)	PUNCT
ejpam-6392	309	1	=	=	SYM
ejpam-6392	309	2	max	max	PROPN
ejpam-6392	309	3	{	{	PUNCT
ejpam-6392	309	4	gf	gf	X
ejpam-6392	309	5	(	(	PUNCT
ejpam-6392	309	6	g×h	g×h	PROPN
ejpam-6392	309	7	)	)	PUNCT
ejpam-6392	309	8	(	(	PUNCT
ejpam-6392	309	9	(	(	PUNCT
ejpam-6392	309	10	e1	e1	NOUN
ejpam-6392	309	11	,	,	PUNCT
ejpam-6392	309	12	31	31	NUM
ejpam-6392	309	13	)	)	PUNCT
ejpam-6392	309	14	•	•	NOUN
ejpam-6392	309	15	(	(	PUNCT
ejpam-6392	309	16	e1	e1	NOUN
ejpam-6392	309	17	,	,	PUNCT
ejpam-6392	309	18	31	31	NUM
ejpam-6392	309	19	)	)	PUNCT
ejpam-6392	309	20	)	)	PUNCT
ejpam-6392	309	21	,	,	PUNCT
ejpam-6392	309	22	gf	gf	X
ejpam-6392	309	23	(	(	PUNCT
ejpam-6392	309	24	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	309	25	,	,	PUNCT
ejpam-6392	309	26	31	31	NUM
ejpam-6392	309	27	)	)	PUNCT
ejpam-6392	309	28	}	}	PUNCT
ejpam-6392	309	29	≤	≤	NUM
ejpam-6392	309	30	gf	gf	X
ejpam-6392	309	31	(	(	PUNCT
ejpam-6392	309	32	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	309	33	,	,	PUNCT
ejpam-6392	309	34	31	31	NUM
ejpam-6392	309	35	)	)	PUNCT
ejpam-6392	309	36	.	.	PUNCT
ejpam-6392	310	1	definition	definition	NOUN
ejpam-6392	310	2	5.3	5.3	NUM
ejpam-6392	310	3	.	.	PUNCT
ejpam-6392	311	1	let	let	VERB
ejpam-6392	311	2	g×h	g×h	VERB
ejpam-6392	311	3	=	=	SYM
ejpam-6392	311	4	(	(	PUNCT
ejpam-6392	311	5	gt	gt	INTJ
ejpam-6392	311	6	(	(	PUNCT
ejpam-6392	311	7	g×h	g×h	PROPN
ejpam-6392	311	8	)	)	PUNCT
ejpam-6392	311	9	,	,	PUNCT
ejpam-6392	311	10	gi(g×h	gi(g×h	NUM
ejpam-6392	311	11	)	)	PUNCT
ejpam-6392	311	12	,	,	PUNCT
ejpam-6392	311	13	gf	gf	X
ejpam-6392	311	14	(	(	PUNCT
ejpam-6392	311	15	g×h	g×h	PROPN
ejpam-6392	311	16	)	)	PUNCT
ejpam-6392	311	17	)	)	PUNCT
ejpam-6392	311	18	of	of	ADP
ejpam-6392	311	19	¨̈u1	¨̈u1	PROPN
ejpam-6392	311	20	and	and	CCONJ
ejpam-6392	311	21	¨̈u2	¨̈u2	NOUN
ejpam-6392	311	22	be	be	AUX
ejpam-6392	311	23	the	the	DET
ejpam-6392	311	24	direct	direct	ADJ
ejpam-6392	311	25	product	product	NOUN
ejpam-6392	311	26	of	of	ADP
ejpam-6392	311	27	neutrosophic	neutrosophic	ADJ
ejpam-6392	311	28	bi	bi	NOUN
ejpam-6392	311	29	-	-	NOUN
ejpam-6392	311	30	ideals	ideal	NOUN
ejpam-6392	311	31	of	of	ADP
ejpam-6392	311	32	¨̈u1	¨̈u1	NUM
ejpam-6392	311	33	×	×	NOUN
ejpam-6392	311	34	¨̈u2	¨̈u2	NOUN
ejpam-6392	311	35	if	if	SCONJ
ejpam-6392	311	36	(	(	PUNCT
ejpam-6392	311	37	i	i	NOUN
ejpam-6392	311	38	)	)	PUNCT
ejpam-6392	311	39	gt	gt	PROPN
ejpam-6392	311	40	(	(	PUNCT
ejpam-6392	311	41	g×h)(0	g×h)(0	PROPN
ejpam-6392	311	42	,	,	PUNCT
ejpam-6392	311	43	0	0	NUM
ejpam-6392	311	44	)	)	PUNCT
ejpam-6392	311	45	≥	≥	NOUN
ejpam-6392	311	46	gt	gt	INTJ
ejpam-6392	311	47	(	(	PUNCT
ejpam-6392	311	48	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	311	49	,	,	PUNCT
ejpam-6392	311	50	31	31	NUM
ejpam-6392	311	51	)	)	PUNCT
ejpam-6392	311	52	,	,	PUNCT
ejpam-6392	311	53	(	(	PUNCT
ejpam-6392	311	54	ii	ii	NOUN
ejpam-6392	311	55	)	)	PUNCT
ejpam-6392	311	56	gi(g×h)(0	gi(g×h)(0	PROPN
ejpam-6392	311	57	,	,	PUNCT
ejpam-6392	311	58	0	0	NUM
ejpam-6392	311	59	)	)	PUNCT
ejpam-6392	311	60	≤	≤	NUM
ejpam-6392	311	61	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	311	62	,	,	PUNCT
ejpam-6392	311	63	31	31	NUM
ejpam-6392	311	64	)	)	PUNCT
ejpam-6392	311	65	,	,	PUNCT
ejpam-6392	311	66	(	(	PUNCT
ejpam-6392	311	67	iii	iii	X
ejpam-6392	311	68	)	)	PUNCT
ejpam-6392	311	69	gf	gf	NOUN
ejpam-6392	311	70	(	(	PUNCT
ejpam-6392	311	71	g×h)(0	g×h)(0	PROPN
ejpam-6392	311	72	,	,	PUNCT
ejpam-6392	311	73	0	0	NUM
ejpam-6392	311	74	)	)	PUNCT
ejpam-6392	311	75	≤	≤	NOUN
ejpam-6392	311	76	gf	gf	X
ejpam-6392	311	77	(	(	PUNCT
ejpam-6392	311	78	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	311	79	,	,	PUNCT
ejpam-6392	311	80	31	31	NUM
ejpam-6392	311	81	)	)	PUNCT
ejpam-6392	311	82	,	,	PUNCT
ejpam-6392	311	83	(	(	PUNCT
ejpam-6392	311	84	iv	iv	X
ejpam-6392	311	85	)	)	PUNCT
ejpam-6392	311	86	gt	gt	PROPN
ejpam-6392	311	87	(	(	PUNCT
ejpam-6392	311	88	g×h	g×h	PROPN
ejpam-6392	311	89	)	)	PUNCT
ejpam-6392	311	90	(	(	PUNCT
ejpam-6392	311	91	(	(	PUNCT
ejpam-6392	311	92	e1	e1	NOUN
ejpam-6392	311	93	,	,	PUNCT
ejpam-6392	311	94	31)•(e2	31)•(e2	PROPN
ejpam-6392	311	95	,	,	PUNCT
ejpam-6392	311	96	32	32	NUM
ejpam-6392	311	97	)	)	PUNCT
ejpam-6392	311	98	)	)	PUNCT
ejpam-6392	312	1	≥	≥	PROPN
ejpam-6392	312	2	min	min	PROPN
ejpam-6392	312	3	{	{	PUNCT
ejpam-6392	312	4	gt	gt	PROPN
ejpam-6392	312	5	(	(	PUNCT
ejpam-6392	312	6	g×h	g×h	PROPN
ejpam-6392	312	7	)	)	PUNCT
ejpam-6392	312	8	(	(	PUNCT
ejpam-6392	312	9	(	(	PUNCT
ejpam-6392	312	10	e1	e1	NOUN
ejpam-6392	312	11	,	,	PUNCT
ejpam-6392	312	12	31)•(e2	31)•(e2	NUM
ejpam-6392	312	13	,	,	PUNCT
ejpam-6392	312	14	32)•(e3	32)•(e3	NUM
ejpam-6392	312	15	,	,	PUNCT
ejpam-6392	312	16	33	33	NUM
ejpam-6392	312	17	)	)	PUNCT
ejpam-6392	312	18	)	)	PUNCT
ejpam-6392	312	19	,	,	PUNCT
ejpam-6392	312	20	gt	gt	PROPN
ejpam-6392	312	21	(	(	PUNCT
ejpam-6392	312	22	g×h)(e3	g×h)(e3	NOUN
ejpam-6392	312	23	,	,	PUNCT
ejpam-6392	312	24	33	33	NUM
ejpam-6392	312	25	)	)	PUNCT
ejpam-6392	312	26	}	}	PUNCT
ejpam-6392	312	27	,	,	PUNCT
ejpam-6392	312	28	(	(	PUNCT
ejpam-6392	312	29	v	v	NOUN
ejpam-6392	312	30	)	)	PUNCT
ejpam-6392	312	31	gi(g×h	gi(g×h	NUM
ejpam-6392	312	32	)	)	PUNCT
ejpam-6392	312	33	(	(	PUNCT
ejpam-6392	312	34	(	(	PUNCT
ejpam-6392	312	35	e1	e1	NOUN
ejpam-6392	312	36	,	,	PUNCT
ejpam-6392	312	37	31)•(e2	31)•(e2	PROPN
ejpam-6392	312	38	,	,	PUNCT
ejpam-6392	312	39	32	32	NUM
ejpam-6392	312	40	)	)	PUNCT
ejpam-6392	312	41	)	)	PUNCT
ejpam-6392	313	1	≤	≤	NUM
ejpam-6392	313	2	max	max	PROPN
ejpam-6392	313	3	{	{	PUNCT
ejpam-6392	313	4	gi(g×h	gi(g×h	PROPN
ejpam-6392	313	5	)	)	PUNCT
ejpam-6392	313	6	(	(	PUNCT
ejpam-6392	313	7	(	(	PUNCT
ejpam-6392	313	8	e1	e1	NOUN
ejpam-6392	313	9	,	,	PUNCT
ejpam-6392	313	10	31)•(e2	31)•(e2	NUM
ejpam-6392	313	11	,	,	PUNCT
ejpam-6392	313	12	32)•(e3	32)•(e3	NUM
ejpam-6392	313	13	,	,	PUNCT
ejpam-6392	313	14	33	33	NUM
ejpam-6392	313	15	)	)	PUNCT
ejpam-6392	313	16	)	)	PUNCT
ejpam-6392	313	17	,	,	PUNCT
ejpam-6392	313	18	gi(g×h)(e3	gi(g×h)(e3	ADJ
ejpam-6392	313	19	,	,	PUNCT
ejpam-6392	313	20	33	33	NUM
ejpam-6392	313	21	)	)	PUNCT
ejpam-6392	313	22	}	}	PUNCT
ejpam-6392	313	23	,	,	PUNCT
ejpam-6392	313	24	(	(	PUNCT
ejpam-6392	313	25	vi	vi	NOUN
ejpam-6392	313	26	)	)	PUNCT
ejpam-6392	313	27	gf	gf	X
ejpam-6392	313	28	(	(	PUNCT
ejpam-6392	313	29	g×h	g×h	PROPN
ejpam-6392	313	30	)	)	PUNCT
ejpam-6392	313	31	(	(	PUNCT
ejpam-6392	313	32	(	(	PUNCT
ejpam-6392	313	33	e1	e1	NOUN
ejpam-6392	313	34	,	,	PUNCT
ejpam-6392	313	35	31)•(e2	31)•(e2	PROPN
ejpam-6392	313	36	,	,	PUNCT
ejpam-6392	313	37	32	32	NUM
ejpam-6392	313	38	)	)	PUNCT
ejpam-6392	313	39	)	)	PUNCT
ejpam-6392	313	40	≤	≤	NUM
ejpam-6392	313	41	max	max	PROPN
ejpam-6392	313	42	{	{	PUNCT
ejpam-6392	313	43	gf	gf	X
ejpam-6392	313	44	(	(	PUNCT
ejpam-6392	313	45	g×h	g×h	PROPN
ejpam-6392	313	46	)	)	PUNCT
ejpam-6392	313	47	(	(	PUNCT
ejpam-6392	313	48	(	(	PUNCT
ejpam-6392	313	49	e1	e1	NOUN
ejpam-6392	313	50	,	,	PUNCT
ejpam-6392	313	51	31)•(e2	31)•(e2	NUM
ejpam-6392	313	52	,	,	PUNCT
ejpam-6392	313	53	32)•(e3	32)•(e3	NUM
ejpam-6392	313	54	,	,	PUNCT
ejpam-6392	313	55	33	33	NUM
ejpam-6392	313	56	)	)	PUNCT
ejpam-6392	313	57	)	)	PUNCT
ejpam-6392	313	58	,	,	PUNCT
ejpam-6392	313	59	gf	gf	X
ejpam-6392	313	60	(	(	PUNCT
ejpam-6392	313	61	g×h)(e3	g×h)(e3	NOUN
ejpam-6392	313	62	,	,	PUNCT
ejpam-6392	313	63	33	33	NUM
ejpam-6392	313	64	)	)	PUNCT
ejpam-6392	313	65	}	}	PUNCT
ejpam-6392	313	66	.	.	PUNCT
ejpam-6392	314	1	theorem	theorem	VERB
ejpam-6392	314	2	5.3	5.3	NUM
ejpam-6392	314	3	.	.	PUNCT
ejpam-6392	315	1	let	let	VERB
ejpam-6392	315	2	g	g	NOUN
ejpam-6392	315	3	=	=	SYM
ejpam-6392	315	4	(	(	PUNCT
ejpam-6392	315	5	gt	gt	INTJ
ejpam-6392	315	6	,	,	PUNCT
ejpam-6392	315	7	gi	gi	INTJ
ejpam-6392	315	8	,	,	PUNCT
ejpam-6392	315	9	gf	gf	PROPN
ejpam-6392	315	10	)	)	PUNCT
ejpam-6392	315	11	and	and	CCONJ
ejpam-6392	315	12	h	h	NOUN
ejpam-6392	315	13	=	=	SYM
ejpam-6392	316	1	(	(	PUNCT
ejpam-6392	316	2	ht	ht	INTJ
ejpam-6392	316	3	,	,	PUNCT
ejpam-6392	316	4	hi	hi	INTJ
ejpam-6392	316	5	,	,	PUNCT
ejpam-6392	316	6	hf	hf	INTJ
ejpam-6392	316	7	)	)	PUNCT
ejpam-6392	316	8	be	be	AUX
ejpam-6392	316	9	two	two	NUM
ejpam-6392	316	10	neutrosophic	neutrosophic	ADJ
ejpam-6392	316	11	bi	bi	NOUN
ejpam-6392	316	12	-	-	NOUN
ejpam-6392	316	13	ideals	ideal	NOUN
ejpam-6392	316	14	of	of	ADP
ejpam-6392	316	15	ink	ink	NOUN
ejpam-6392	316	16	algebras	algebras	PROPN
ejpam-6392	316	17	¨̈u1	¨̈u1	PROPN
ejpam-6392	316	18	and	and	CCONJ
ejpam-6392	316	19	¨̈u2	¨̈u2	NOUN
ejpam-6392	316	20	respectively	respectively	ADV
ejpam-6392	316	21	.	.	PUNCT
ejpam-6392	317	1	then	then	ADV
ejpam-6392	317	2	the	the	DET
ejpam-6392	317	3	direct	direct	ADJ
ejpam-6392	317	4	product	product	NOUN
ejpam-6392	317	5	of	of	ADP
ejpam-6392	317	6	neutrosophic	neutrosophic	ADJ
ejpam-6392	317	7	bi	bi	NOUN
ejpam-6392	317	8	-	-	NOUN
ejpam-6392	317	9	ideals	ideal	NOUN
ejpam-6392	317	10	of	of	ADP
ejpam-6392	317	11	ink	ink	NOUN
ejpam-6392	317	12	-	-	PUNCT
ejpam-6392	317	13	algebra	algebra	NOUN
ejpam-6392	317	14	g	g	NOUN
ejpam-6392	317	15	and	and	CCONJ
ejpam-6392	317	16	h	h	NOUN
ejpam-6392	317	17	is	be	AUX
ejpam-6392	317	18	given	give	VERB
ejpam-6392	317	19	by	by	ADP
ejpam-6392	317	20	g	g	PROPN
ejpam-6392	317	21	×	×	PROPN
ejpam-6392	317	22	h	h	NOUN
ejpam-6392	317	23	=	=	PUNCT
ejpam-6392	317	24	(	(	PUNCT
ejpam-6392	317	25	gt	gt	INTJ
ejpam-6392	317	26	(	(	PUNCT
ejpam-6392	317	27	g×h	g×h	PROPN
ejpam-6392	317	28	)	)	PUNCT
ejpam-6392	317	29	,	,	PUNCT
ejpam-6392	317	30	gi(g×h	gi(g×h	NUM
ejpam-6392	317	31	)	)	PUNCT
ejpam-6392	317	32	,	,	PUNCT
ejpam-6392	317	33	gf	gf	X
ejpam-6392	317	34	(	(	PUNCT
ejpam-6392	317	35	g×h	g×h	PROPN
ejpam-6392	317	36	)	)	PUNCT
ejpam-6392	317	37	)	)	PUNCT
ejpam-6392	317	38	.	.	PUNCT
ejpam-6392	318	1	proof	proof	NOUN
ejpam-6392	318	2	.	.	PUNCT
ejpam-6392	319	1	for	for	ADP
ejpam-6392	319	2	any	any	DET
ejpam-6392	319	3	(	(	PUNCT
ejpam-6392	319	4	e1	e1	PROPN
ejpam-6392	319	5	,	,	PUNCT
ejpam-6392	319	6	e2	e2	PROPN
ejpam-6392	319	7	,	,	PUNCT
ejpam-6392	319	8	e3	e3	NOUN
ejpam-6392	319	9	)	)	PUNCT
ejpam-6392	319	10	and	and	CCONJ
ejpam-6392	319	11	(	(	PUNCT
ejpam-6392	319	12	31	31	NUM
ejpam-6392	319	13	,	,	PUNCT
ejpam-6392	319	14	32	32	NUM
ejpam-6392	319	15	,	,	PUNCT
ejpam-6392	319	16	33	33	NUM
ejpam-6392	319	17	)	)	PUNCT
ejpam-6392	319	18	∈	∈	PROPN
ejpam-6392	319	19	g	g	PROPN
ejpam-6392	319	20	×	×	PROPN
ejpam-6392	319	21	h.	h.	PROPN
ejpam-6392	319	22	then	then	ADV
ejpam-6392	319	23	gt	gt	PROPN
ejpam-6392	319	24	(	(	PUNCT
ejpam-6392	319	25	g×h)(0	g×h)(0	PROPN
ejpam-6392	319	26	,	,	PUNCT
ejpam-6392	319	27	0	0	NUM
ejpam-6392	319	28	)	)	PUNCT
ejpam-6392	319	29	=	=	SYM
ejpam-6392	319	30	min	min	PROPN
ejpam-6392	319	31	{	{	PUNCT
ejpam-6392	319	32	gt	gt	PROPN
ejpam-6392	319	33	(	(	PUNCT
ejpam-6392	319	34	g)(0	g)(0	X
ejpam-6392	319	35	)	)	PUNCT
ejpam-6392	319	36	,	,	PUNCT
ejpam-6392	319	37	gt	gt	PROPN
ejpam-6392	319	38	(	(	PUNCT
ejpam-6392	319	39	h)(0	h)(0	PROPN
ejpam-6392	319	40	)	)	PUNCT
ejpam-6392	319	41	}	}	PUNCT
ejpam-6392	319	42	≥	≥	X
ejpam-6392	319	43	{	{	PUNCT
ejpam-6392	319	44	gt	gt	INTJ
ejpam-6392	319	45	(	(	PUNCT
ejpam-6392	319	46	g)(e1	g)(e1	PROPN
ejpam-6392	319	47	)	)	PUNCT
ejpam-6392	319	48	,	,	PUNCT
ejpam-6392	319	49	gt	gt	PROPN
ejpam-6392	319	50	(	(	PUNCT
ejpam-6392	319	51	h)(31	h)(31	X
ejpam-6392	319	52	)	)	PUNCT
ejpam-6392	319	53	}	}	PUNCT
ejpam-6392	319	54	≥	≥	PROPN
ejpam-6392	319	55	gt	gt	INTJ
ejpam-6392	319	56	(	(	PUNCT
ejpam-6392	319	57	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	319	58	,	,	PUNCT
ejpam-6392	319	59	31	31	NUM
ejpam-6392	319	60	)	)	PUNCT
ejpam-6392	319	61	.	.	PUNCT
ejpam-6392	320	1	now	now	ADV
ejpam-6392	320	2	gi(g×h)(0	gi(g×h)(0	VERB
ejpam-6392	320	3	,	,	PUNCT
ejpam-6392	320	4	0	0	NUM
ejpam-6392	320	5	)	)	PUNCT
ejpam-6392	320	6	=	=	SYM
ejpam-6392	320	7	max	max	PROPN
ejpam-6392	320	8	{	{	PUNCT
ejpam-6392	320	9	gt	gt	PROPN
ejpam-6392	320	10	(	(	PUNCT
ejpam-6392	320	11	g)(0	g)(0	X
ejpam-6392	320	12	)	)	PUNCT
ejpam-6392	320	13	,	,	PUNCT
ejpam-6392	320	14	gi(h)(0	gi(h)(0	PROPN
ejpam-6392	320	15	)	)	PUNCT
ejpam-6392	320	16	}	}	PUNCT
ejpam-6392	320	17	≤	≤	NOUN
ejpam-6392	320	18	{	{	PUNCT
ejpam-6392	320	19	gi(g)(e1	gi(g)(e1	NOUN
ejpam-6392	320	20	)	)	PUNCT
ejpam-6392	320	21	,	,	PUNCT
ejpam-6392	320	22	gi(h)(31	gi(h)(31	NOUN
ejpam-6392	320	23	)	)	PUNCT
ejpam-6392	320	24	}	}	PUNCT
ejpam-6392	320	25	≤	≤	NUM
ejpam-6392	320	26	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	320	27	,	,	PUNCT
ejpam-6392	320	28	31	31	NUM
ejpam-6392	320	29	)	)	PUNCT
ejpam-6392	320	30	.	.	PUNCT
ejpam-6392	321	1	also	also	ADV
ejpam-6392	321	2	gi(g×h)(0	gi(g×h)(0	PROPN
ejpam-6392	321	3	,	,	PUNCT
ejpam-6392	321	4	0	0	NUM
ejpam-6392	321	5	)	)	PUNCT
ejpam-6392	321	6	=	=	SYM
ejpam-6392	321	7	max	max	PROPN
ejpam-6392	321	8	{	{	PUNCT
ejpam-6392	321	9	gt	gt	PROPN
ejpam-6392	321	10	(	(	PUNCT
ejpam-6392	321	11	g)(0	g)(0	X
ejpam-6392	321	12	)	)	PUNCT
ejpam-6392	321	13	,	,	PUNCT
ejpam-6392	321	14	gi(h)(0	gi(h)(0	PROPN
ejpam-6392	321	15	)	)	PUNCT
ejpam-6392	321	16	}	}	PUNCT
ejpam-6392	321	17	≤	≤	NOUN
ejpam-6392	321	18	{	{	PUNCT
ejpam-6392	321	19	gi(g)(e1	gi(g)(e1	NOUN
ejpam-6392	321	20	)	)	PUNCT
ejpam-6392	321	21	,	,	PUNCT
ejpam-6392	321	22	gi(h)(31	gi(h)(31	NOUN
ejpam-6392	321	23	)	)	PUNCT
ejpam-6392	321	24	}	}	PUNCT
ejpam-6392	321	25	≤	≤	NUM
ejpam-6392	321	26	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	321	27	,	,	PUNCT
ejpam-6392	321	28	31	31	NUM
ejpam-6392	321	29	)	)	PUNCT
ejpam-6392	321	30	.	.	PUNCT
ejpam-6392	322	1	now	now	ADV
ejpam-6392	322	2	gt	gt	INTJ
ejpam-6392	322	3	(	(	PUNCT
ejpam-6392	322	4	g×h	g×h	PROPN
ejpam-6392	322	5	)	)	PUNCT
ejpam-6392	322	6	(	(	PUNCT
ejpam-6392	322	7	(	(	PUNCT
ejpam-6392	322	8	e1	e1	NOUN
ejpam-6392	322	9	,	,	PUNCT
ejpam-6392	322	10	31	31	NUM
ejpam-6392	322	11	)	)	PUNCT
ejpam-6392	322	12	•	•	NOUN
ejpam-6392	322	13	(	(	PUNCT
ejpam-6392	322	14	e2	e2	PROPN
ejpam-6392	322	15	,	,	PUNCT
ejpam-6392	322	16	32	32	NUM
ejpam-6392	322	17	)	)	PUNCT
ejpam-6392	322	18	)	)	PUNCT
ejpam-6392	323	1	=	=	SYM
ejpam-6392	323	2	gt	gt	PROPN
ejpam-6392	323	3	(	(	PUNCT
ejpam-6392	323	4	g×h	g×h	PROPN
ejpam-6392	323	5	)	)	PUNCT
ejpam-6392	323	6	(	(	PUNCT
ejpam-6392	323	7	e1	e1	VERB
ejpam-6392	323	8	•	•	NOUN
ejpam-6392	323	9	31	31	NUM
ejpam-6392	323	10	,	,	PUNCT
ejpam-6392	323	11	e2	e2	VERB
ejpam-6392	323	12	•	•	NUM
ejpam-6392	323	13	32	32	NUM
ejpam-6392	323	14	)	)	PUNCT
ejpam-6392	323	15	=	=	SYM
ejpam-6392	323	16	min	min	PROPN
ejpam-6392	323	17	{	{	PUNCT
ejpam-6392	323	18	gt	gt	PROPN
ejpam-6392	323	19	(	(	PUNCT
ejpam-6392	323	20	g	g	NOUN
ejpam-6392	323	21	)	)	PUNCT
ejpam-6392	323	22	(	(	PUNCT
ejpam-6392	323	23	e1	e1	VERB
ejpam-6392	323	24	•	•	NOUN
ejpam-6392	323	25	31	31	NUM
ejpam-6392	323	26	,	,	PUNCT
ejpam-6392	323	27	e2	e2	VERB
ejpam-6392	323	28	•	•	NUM
ejpam-6392	323	29	32	32	NUM
ejpam-6392	323	30	)	)	PUNCT
ejpam-6392	323	31	}	}	PUNCT
ejpam-6392	323	32	=	=	PUNCT
ejpam-6392	323	33	min{min{gt	min{min{gt	ADJ
ejpam-6392	323	34	(	(	PUNCT
ejpam-6392	323	35	g)(e1	g)(e1	ADJ
ejpam-6392	323	36	•	•	NUM
ejpam-6392	323	37	e2	e2	PROPN
ejpam-6392	323	38	•	•	NUM
ejpam-6392	323	39	e3	e3	NOUN
ejpam-6392	323	40	)	)	PUNCT
ejpam-6392	323	41	,	,	PUNCT
ejpam-6392	323	42	gt	gt	PROPN
ejpam-6392	323	43	(	(	PUNCT
ejpam-6392	323	44	g)(e3	g)(e3	PROPN
ejpam-6392	323	45	)	)	PUNCT
ejpam-6392	323	46	}	}	PUNCT
ejpam-6392	323	47	,	,	PUNCT
ejpam-6392	323	48	min{gt	min{gt	PRON
ejpam-6392	323	49	(	(	PUNCT
ejpam-6392	323	50	h)(31	h)(31	NOUN
ejpam-6392	323	51	•	•	NOUN
ejpam-6392	323	52	32	32	NUM
ejpam-6392	323	53	•	•	NUM
ejpam-6392	323	54	33	33	NUM
ejpam-6392	323	55	)	)	PUNCT
ejpam-6392	323	56	,	,	PUNCT
ejpam-6392	323	57	gt	gt	PROPN
ejpam-6392	323	58	(	(	PUNCT
ejpam-6392	323	59	h)(33	h)(33	PROPN
ejpam-6392	323	60	)	)	PUNCT
ejpam-6392	323	61	}	}	PUNCT
ejpam-6392	323	62	}	}	PUNCT
ejpam-6392	323	63	≥	≥	PROPN
ejpam-6392	323	64	min	min	PROPN
ejpam-6392	323	65	{	{	PUNCT
ejpam-6392	323	66	gt	gt	PROPN
ejpam-6392	323	67	(	(	PUNCT
ejpam-6392	323	68	g×h	g×h	PROPN
ejpam-6392	323	69	)	)	PUNCT
ejpam-6392	323	70	(	(	PUNCT
ejpam-6392	323	71	(	(	PUNCT
ejpam-6392	323	72	e1	e1	NOUN
ejpam-6392	323	73	,	,	PUNCT
ejpam-6392	323	74	31	31	NUM
ejpam-6392	323	75	)	)	PUNCT
ejpam-6392	323	76	•	•	NOUN
ejpam-6392	323	77	(	(	PUNCT
ejpam-6392	323	78	e2	e2	PROPN
ejpam-6392	323	79	,	,	PUNCT
ejpam-6392	323	80	32	32	NUM
ejpam-6392	323	81	)	)	PUNCT
ejpam-6392	323	82	•	•	NOUN
ejpam-6392	323	83	(	(	PUNCT
ejpam-6392	323	84	e3	e3	NOUN
ejpam-6392	323	85	,	,	PUNCT
ejpam-6392	323	86	33	33	NUM
ejpam-6392	323	87	)	)	PUNCT
ejpam-6392	323	88	)	)	PUNCT
ejpam-6392	323	89	,	,	PUNCT
ejpam-6392	323	90	gt	gt	PROPN
ejpam-6392	323	91	(	(	PUNCT
ejpam-6392	323	92	g×h)(e3	g×h)(e3	NOUN
ejpam-6392	323	93	,	,	PUNCT
ejpam-6392	323	94	33	33	NUM
ejpam-6392	323	95	)	)	PUNCT
ejpam-6392	323	96	}	}	PUNCT
ejpam-6392	323	97	.	.	PUNCT
ejpam-6392	324	1	m.	m.	NOUN
ejpam-6392	324	2	remala	remala	NOUN
ejpam-6392	324	3	,	,	PUNCT
ejpam-6392	324	4	e.	e.	PROPN
ejpam-6392	324	5	tamma	tamma	PROPN
ejpam-6392	324	6	,	,	PUNCT
ejpam-6392	324	7	y.	y.	PROPN
ejpam-6392	324	8	bhargavi	bhargavi	PROPN
ejpam-6392	324	9	/	/	SYM
ejpam-6392	324	10	eur	eur	PROPN
ejpam-6392	324	11	.	.	PUNCT
ejpam-6392	325	1	j.	j.	PROPN
ejpam-6392	325	2	pure	pure	PROPN
ejpam-6392	325	3	appl	appl	PROPN
ejpam-6392	325	4	.	.	PROPN
ejpam-6392	325	5	math	math	PROPN
ejpam-6392	325	6	,	,	PUNCT
ejpam-6392	325	7	18	18	NUM
ejpam-6392	325	8	(	(	PUNCT
ejpam-6392	325	9	4	4	NUM
ejpam-6392	325	10	)	)	PUNCT
ejpam-6392	325	11	(	(	PUNCT
ejpam-6392	325	12	2025	2025	NUM
ejpam-6392	325	13	)	)	PUNCT
ejpam-6392	325	14	,	,	PUNCT
ejpam-6392	325	15	6392	6392	NUM
ejpam-6392	325	16	14	14	NUM
ejpam-6392	325	17	of	of	ADP
ejpam-6392	325	18	20	20	NUM
ejpam-6392	325	19	then	then	ADV
ejpam-6392	325	20	,	,	PUNCT
ejpam-6392	325	21	gi(g×h	gi(g×h	NUM
ejpam-6392	325	22	)	)	PUNCT
ejpam-6392	325	23	(	(	PUNCT
ejpam-6392	325	24	(	(	PUNCT
ejpam-6392	325	25	e1	e1	NOUN
ejpam-6392	325	26	,	,	PUNCT
ejpam-6392	325	27	31	31	NUM
ejpam-6392	325	28	)	)	PUNCT
ejpam-6392	325	29	•	•	NOUN
ejpam-6392	325	30	(	(	PUNCT
ejpam-6392	325	31	e2	e2	PROPN
ejpam-6392	325	32	,	,	PUNCT
ejpam-6392	325	33	32	32	NUM
ejpam-6392	325	34	)	)	PUNCT
ejpam-6392	325	35	)	)	PUNCT
ejpam-6392	326	1	=	=	PUNCT
ejpam-6392	326	2	gi(g×h	gi(g×h	X
ejpam-6392	326	3	)	)	PUNCT
ejpam-6392	326	4	(	(	PUNCT
ejpam-6392	326	5	e1	e1	VERB
ejpam-6392	326	6	•	•	NOUN
ejpam-6392	326	7	31	31	NUM
ejpam-6392	326	8	,	,	PUNCT
ejpam-6392	326	9	e2	e2	VERB
ejpam-6392	326	10	•	•	NUM
ejpam-6392	326	11	32	32	NUM
ejpam-6392	326	12	)	)	PUNCT
ejpam-6392	326	13	=	=	SYM
ejpam-6392	326	14	max	max	X
ejpam-6392	326	15	{	{	PUNCT
ejpam-6392	326	16	gi(g	gi(g	NOUN
ejpam-6392	326	17	)	)	PUNCT
ejpam-6392	326	18	(	(	PUNCT
ejpam-6392	326	19	e1	e1	VERB
ejpam-6392	326	20	•	•	NOUN
ejpam-6392	326	21	31	31	NUM
ejpam-6392	326	22	,	,	PUNCT
ejpam-6392	326	23	e2	e2	VERB
ejpam-6392	326	24	•	•	NUM
ejpam-6392	326	25	32	32	NUM
ejpam-6392	326	26	)	)	PUNCT
ejpam-6392	326	27	}	}	PUNCT
ejpam-6392	326	28	=	=	PUNCT
ejpam-6392	326	29	max{max{gi(g)(e1	max{max{gi(g)(e1	NOUN
ejpam-6392	326	30	•	•	PROPN
ejpam-6392	326	31	e2	e2	PROPN
ejpam-6392	326	32	•	•	NUM
ejpam-6392	326	33	e3	e3	NOUN
ejpam-6392	326	34	)	)	PUNCT
ejpam-6392	326	35	,	,	PUNCT
ejpam-6392	326	36	gi(g)(e3	gi(g)(e3	PROPN
ejpam-6392	326	37	)	)	PUNCT
ejpam-6392	326	38	}	}	PUNCT
ejpam-6392	326	39	,	,	PUNCT
ejpam-6392	326	40	max{gi(h)(31	max{gi(h)(31	ADP
ejpam-6392	326	41	•	•	NOUN
ejpam-6392	326	42	32	32	NUM
ejpam-6392	326	43	•	•	NUM
ejpam-6392	326	44	33	33	NUM
ejpam-6392	326	45	)	)	PUNCT
ejpam-6392	326	46	,	,	PUNCT
ejpam-6392	326	47	gi(h)(33	gi(h)(33	PUNCT
ejpam-6392	326	48	)	)	PUNCT
ejpam-6392	326	49	}	}	PUNCT
ejpam-6392	326	50	}	}	PUNCT
ejpam-6392	326	51	≤	≤	NUM
ejpam-6392	326	52	max	max	PROPN
ejpam-6392	326	53	{	{	PUNCT
ejpam-6392	326	54	gi(g×h	gi(g×h	NOUN
ejpam-6392	326	55	)	)	PUNCT
ejpam-6392	326	56	(	(	PUNCT
ejpam-6392	326	57	(	(	PUNCT
ejpam-6392	326	58	e1	e1	NOUN
ejpam-6392	326	59	,	,	PUNCT
ejpam-6392	326	60	31	31	NUM
ejpam-6392	326	61	)	)	PUNCT
ejpam-6392	326	62	•	•	NOUN
ejpam-6392	326	63	(	(	PUNCT
ejpam-6392	326	64	e2	e2	PROPN
ejpam-6392	326	65	,	,	PUNCT
ejpam-6392	326	66	32	32	NUM
ejpam-6392	326	67	)	)	PUNCT
ejpam-6392	326	68	•	•	NOUN
ejpam-6392	326	69	(	(	PUNCT
ejpam-6392	326	70	e3	e3	NOUN
ejpam-6392	326	71	,	,	PUNCT
ejpam-6392	326	72	33	33	NUM
ejpam-6392	326	73	)	)	PUNCT
ejpam-6392	326	74	)	)	PUNCT
ejpam-6392	326	75	,	,	PUNCT
ejpam-6392	326	76	gi(g×h)(e3	gi(g×h)(e3	ADJ
ejpam-6392	326	77	,	,	PUNCT
ejpam-6392	326	78	33	33	NUM
ejpam-6392	326	79	)	)	PUNCT
ejpam-6392	326	80	}	}	PUNCT
ejpam-6392	326	81	.	.	PUNCT
ejpam-6392	327	1	also	also	ADV
ejpam-6392	327	2	,	,	PUNCT
ejpam-6392	327	3	gf	gf	X
ejpam-6392	327	4	(	(	PUNCT
ejpam-6392	327	5	g×h	g×h	PROPN
ejpam-6392	327	6	)	)	PUNCT
ejpam-6392	327	7	(	(	PUNCT
ejpam-6392	327	8	(	(	PUNCT
ejpam-6392	327	9	e1	e1	NOUN
ejpam-6392	327	10	,	,	PUNCT
ejpam-6392	327	11	31	31	NUM
ejpam-6392	327	12	)	)	PUNCT
ejpam-6392	327	13	•	•	NOUN
ejpam-6392	327	14	(	(	PUNCT
ejpam-6392	327	15	e2	e2	PROPN
ejpam-6392	327	16	,	,	PUNCT
ejpam-6392	327	17	32	32	NUM
ejpam-6392	327	18	)	)	PUNCT
ejpam-6392	327	19	)	)	PUNCT
ejpam-6392	328	1	=	=	SYM
ejpam-6392	328	2	gf	gf	X
ejpam-6392	328	3	(	(	PUNCT
ejpam-6392	328	4	g×h	g×h	PROPN
ejpam-6392	328	5	)	)	PUNCT
ejpam-6392	328	6	(	(	PUNCT
ejpam-6392	328	7	e1	e1	VERB
ejpam-6392	328	8	•	•	NOUN
ejpam-6392	328	9	31	31	NUM
ejpam-6392	328	10	,	,	PUNCT
ejpam-6392	328	11	e2	e2	VERB
ejpam-6392	328	12	•	•	NUM
ejpam-6392	328	13	32	32	NUM
ejpam-6392	328	14	)	)	PUNCT
ejpam-6392	328	15	=	=	SYM
ejpam-6392	328	16	max	max	PROPN
ejpam-6392	328	17	{	{	PUNCT
ejpam-6392	328	18	gf	gf	NOUN
ejpam-6392	328	19	(	(	PUNCT
ejpam-6392	328	20	g	g	NOUN
ejpam-6392	328	21	)	)	PUNCT
ejpam-6392	328	22	(	(	PUNCT
ejpam-6392	328	23	e1	e1	VERB
ejpam-6392	328	24	•	•	NOUN
ejpam-6392	328	25	31	31	NUM
ejpam-6392	328	26	,	,	PUNCT
ejpam-6392	328	27	e2	e2	VERB
ejpam-6392	328	28	•	•	NUM
ejpam-6392	328	29	32	32	NUM
ejpam-6392	328	30	)	)	PUNCT
ejpam-6392	328	31	}	}	PUNCT
ejpam-6392	328	32	=	=	SYM
ejpam-6392	328	33	max{max{gf	max{max{gf	NOUN
ejpam-6392	328	34	(	(	PUNCT
ejpam-6392	328	35	g)(e1	g)(e1	PROPN
ejpam-6392	328	36	•	•	NUM
ejpam-6392	328	37	e2	e2	PROPN
ejpam-6392	328	38	•	•	NUM
ejpam-6392	328	39	e3	e3	NOUN
ejpam-6392	328	40	)	)	PUNCT
ejpam-6392	328	41	,	,	PUNCT
ejpam-6392	328	42	gf	gf	X
ejpam-6392	328	43	(	(	PUNCT
ejpam-6392	328	44	g)(e3	g)(e3	PROPN
ejpam-6392	328	45	)	)	PUNCT
ejpam-6392	328	46	}	}	PUNCT
ejpam-6392	328	47	,	,	PUNCT
ejpam-6392	328	48	max{gf	max{gf	X
ejpam-6392	328	49	(	(	PUNCT
ejpam-6392	328	50	h)(31	h)(31	NOUN
ejpam-6392	328	51	•	•	NOUN
ejpam-6392	328	52	32	32	NUM
ejpam-6392	328	53	•	•	NUM
ejpam-6392	328	54	33	33	NUM
ejpam-6392	328	55	)	)	PUNCT
ejpam-6392	328	56	,	,	PUNCT
ejpam-6392	328	57	gf	gf	X
ejpam-6392	328	58	(	(	PUNCT
ejpam-6392	328	59	h)(33	h)(33	PROPN
ejpam-6392	328	60	)	)	PUNCT
ejpam-6392	328	61	}	}	PUNCT
ejpam-6392	328	62	}	}	PUNCT
ejpam-6392	328	63	≤	≤	NUM
ejpam-6392	328	64	max	max	PROPN
ejpam-6392	328	65	{	{	PUNCT
ejpam-6392	328	66	gf	gf	X
ejpam-6392	328	67	(	(	PUNCT
ejpam-6392	328	68	g×h	g×h	PROPN
ejpam-6392	328	69	)	)	PUNCT
ejpam-6392	328	70	(	(	PUNCT
ejpam-6392	328	71	(	(	PUNCT
ejpam-6392	328	72	e1	e1	NOUN
ejpam-6392	328	73	,	,	PUNCT
ejpam-6392	328	74	31	31	NUM
ejpam-6392	328	75	)	)	PUNCT
ejpam-6392	328	76	•	•	NOUN
ejpam-6392	328	77	(	(	PUNCT
ejpam-6392	328	78	e2	e2	PROPN
ejpam-6392	328	79	,	,	PUNCT
ejpam-6392	328	80	32	32	NUM
ejpam-6392	328	81	)	)	PUNCT
ejpam-6392	328	82	•	•	NOUN
ejpam-6392	328	83	(	(	PUNCT
ejpam-6392	328	84	e3	e3	NOUN
ejpam-6392	328	85	,	,	PUNCT
ejpam-6392	328	86	33	33	NUM
ejpam-6392	328	87	)	)	PUNCT
ejpam-6392	328	88	)	)	PUNCT
ejpam-6392	328	89	,	,	PUNCT
ejpam-6392	328	90	gf	gf	X
ejpam-6392	328	91	(	(	PUNCT
ejpam-6392	328	92	g×h)(e3	g×h)(e3	NOUN
ejpam-6392	328	93	,	,	PUNCT
ejpam-6392	328	94	33	33	NUM
ejpam-6392	328	95	)	)	PUNCT
ejpam-6392	328	96	}	}	PUNCT
ejpam-6392	328	97	.	.	PUNCT
ejpam-6392	329	1	theorem	theorem	VERB
ejpam-6392	329	2	5.4	5.4	NUM
ejpam-6392	329	3	.	.	PUNCT
ejpam-6392	330	1	let	let	VERB
ejpam-6392	330	2	g	g	PRON
ejpam-6392	330	3	×	×	PROPN
ejpam-6392	330	4	h	h	NOUN
ejpam-6392	330	5	=	=	PUNCT
ejpam-6392	330	6	(	(	PUNCT
ejpam-6392	330	7	gt	gt	INTJ
ejpam-6392	330	8	(	(	PUNCT
ejpam-6392	330	9	g×h	g×h	PROPN
ejpam-6392	330	10	)	)	PUNCT
ejpam-6392	330	11	,	,	PUNCT
ejpam-6392	330	12	gi	gi	INTJ
ejpam-6392	330	13	(	(	PUNCT
ejpam-6392	330	14	g×h	g×h	NOUN
ejpam-6392	330	15	)	)	PUNCT
ejpam-6392	330	16	,	,	PUNCT
ejpam-6392	330	17	gf	gf	X
ejpam-6392	330	18	(	(	PUNCT
ejpam-6392	330	19	g×h	g×h	PROPN
ejpam-6392	330	20	)	)	PUNCT
ejpam-6392	330	21	)	)	PUNCT
ejpam-6392	331	1	and	and	CCONJ
ejpam-6392	331	2	i	i	PRON
ejpam-6392	331	3	×	×	VERB
ejpam-6392	331	4	j	j	PROPN
ejpam-6392	331	5	=	=	PRON
ejpam-6392	331	6	(	(	PUNCT
ejpam-6392	331	7	g	g	PROPN
ejpam-6392	331	8	t	t	PROPN
ejpam-6392	331	9	(	(	PUNCT
ejpam-6392	331	10	i×j	i×j	ADJ
ejpam-6392	331	11	)	)	PUNCT
ejpam-6392	331	12	,	,	PUNCT
ejpam-6392	331	13	gi	gi	INTJ
ejpam-6392	331	14	(	(	PUNCT
ejpam-6392	331	15	i×j	i×j	ADJ
ejpam-6392	331	16	)	)	PUNCT
ejpam-6392	331	17	,	,	PUNCT
ejpam-6392	331	18	gf	gf	X
ejpam-6392	331	19	(	(	PUNCT
ejpam-6392	331	20	i×j	i×j	ADJ
ejpam-6392	331	21	)	)	PUNCT
ejpam-6392	331	22	)	)	PUNCT
ejpam-6392	331	23	is	be	AUX
ejpam-6392	331	24	a	a	DET
ejpam-6392	331	25	neutrosophic	neutrosophic	ADJ
ejpam-6392	331	26	bi	bi	NOUN
ejpam-6392	331	27	-	-	NOUN
ejpam-6392	331	28	ideal	ideal	NOUN
ejpam-6392	331	29	of	of	ADP
ejpam-6392	331	30	ink	ink	NOUN
ejpam-6392	331	31	-	-	PUNCT
ejpam-6392	331	32	algebra	algebra	NOUN
ejpam-6392	331	33	¨̈u1	¨̈u1	NOUN
ejpam-6392	331	34	and	and	CCONJ
ejpam-6392	331	35	¨̈u2	¨̈u2	NOUN
ejpam-6392	331	36	.	.	PUNCT
ejpam-6392	332	1	then	then	ADV
ejpam-6392	332	2	(	(	PUNCT
ejpam-6392	332	3	g	g	PROPN
ejpam-6392	332	4	×	×	PROPN
ejpam-6392	332	5	h	h	NOUN
ejpam-6392	332	6	)	)	PUNCT
ejpam-6392	332	7	∩	∩	NOUN
ejpam-6392	332	8	(	(	PUNCT
ejpam-6392	332	9	i	i	PRON
ejpam-6392	332	10	×	×	PROPN
ejpam-6392	332	11	j	j	PROPN
ejpam-6392	332	12	)	)	PUNCT
ejpam-6392	332	13	=	=	PRON
ejpam-6392	332	14	(	(	PUNCT
ejpam-6392	332	15	gt	gt	INTJ
ejpam-6392	332	16	(	(	PUNCT
ejpam-6392	332	17	g×h	g×h	NOUN
ejpam-6392	332	18	)	)	PUNCT
ejpam-6392	332	19	∩	∩	NOUN
ejpam-6392	332	20	(	(	PUNCT
ejpam-6392	332	21	i×j	i×j	ADJ
ejpam-6392	332	22	)	)	PUNCT
ejpam-6392	332	23	,	,	PUNCT
ejpam-6392	332	24	gi	gi	INTJ
ejpam-6392	332	25	(	(	PUNCT
ejpam-6392	332	26	g×h	g×h	NOUN
ejpam-6392	332	27	)	)	PUNCT
ejpam-6392	332	28	∩	∩	NOUN
ejpam-6392	332	29	(	(	PUNCT
ejpam-6392	332	30	i×j	i×j	ADJ
ejpam-6392	332	31	)	)	PUNCT
ejpam-6392	332	32	,	,	PUNCT
ejpam-6392	332	33	gf	gf	X
ejpam-6392	332	34	(	(	PUNCT
ejpam-6392	332	35	g×h	g×h	NOUN
ejpam-6392	332	36	)	)	PUNCT
ejpam-6392	332	37	∩	∩	NOUN
ejpam-6392	332	38	(	(	PUNCT
ejpam-6392	332	39	i×j	i×j	ADJ
ejpam-6392	332	40	)	)	PUNCT
ejpam-6392	332	41	)	)	PUNCT
ejpam-6392	332	42	proof	proof	NOUN
ejpam-6392	332	43	.	.	PUNCT
ejpam-6392	333	1	for	for	ADP
ejpam-6392	333	2	any	any	DET
ejpam-6392	333	3	(	(	PUNCT
ejpam-6392	333	4	e1	e1	PROPN
ejpam-6392	333	5	,	,	PUNCT
ejpam-6392	333	6	e2	e2	PROPN
ejpam-6392	333	7	,	,	PUNCT
ejpam-6392	333	8	e3	e3	NOUN
ejpam-6392	333	9	)	)	PUNCT
ejpam-6392	333	10	and	and	CCONJ
ejpam-6392	333	11	(	(	PUNCT
ejpam-6392	333	12	31	31	NUM
ejpam-6392	333	13	,	,	PUNCT
ejpam-6392	333	14	32	32	NUM
ejpam-6392	333	15	,	,	PUNCT
ejpam-6392	333	16	33	33	NUM
ejpam-6392	333	17	)	)	PUNCT
ejpam-6392	333	18	∈	∈	PROPN
ejpam-6392	333	19	¨̈u1	¨̈u1	X
ejpam-6392	333	20	×	×	NOUN
ejpam-6392	333	21	¨̈u2	¨̈u2	X
ejpam-6392	333	22	.	.	PUNCT
ejpam-6392	333	23	consider	consider	VERB
ejpam-6392	333	24	gt	gt	PROPN
ejpam-6392	333	25	(	(	PUNCT
ejpam-6392	333	26	g×h)(0	g×h)(0	PROPN
ejpam-6392	333	27	,	,	PUNCT
ejpam-6392	333	28	0	0	NUM
ejpam-6392	333	29	)	)	PUNCT
ejpam-6392	333	30	≥	≥	PROPN
ejpam-6392	333	31	min	min	PROPN
ejpam-6392	333	32	{	{	PUNCT
ejpam-6392	333	33	gt	gt	PROPN
ejpam-6392	333	34	(	(	PUNCT
ejpam-6392	333	35	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	333	36	,	,	PUNCT
ejpam-6392	333	37	31	31	NUM
ejpam-6392	333	38	)	)	PUNCT
ejpam-6392	333	39	}	}	PUNCT
ejpam-6392	333	40	and	and	CCONJ
ejpam-6392	333	41	gt	gt	INTJ
ejpam-6392	333	42	(	(	PUNCT
ejpam-6392	333	43	i×j)(0	i×j)(0	PROPN
ejpam-6392	333	44	,	,	PUNCT
ejpam-6392	333	45	0	0	NUM
ejpam-6392	333	46	)	)	PUNCT
ejpam-6392	333	47	≥	≥	PROPN
ejpam-6392	333	48	min	min	PROPN
ejpam-6392	333	49	{	{	PUNCT
ejpam-6392	333	50	gt	gt	PROPN
ejpam-6392	333	51	(	(	PUNCT
ejpam-6392	333	52	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	333	53	,	,	PUNCT
ejpam-6392	333	54	31	31	NUM
ejpam-6392	333	55	)	)	PUNCT
ejpam-6392	333	56	}	}	PUNCT
ejpam-6392	333	57	.	.	PUNCT
ejpam-6392	334	1	{	{	PUNCT
ejpam-6392	334	2	gt	gt	INTJ
ejpam-6392	334	3	(	(	PUNCT
ejpam-6392	334	4	g×h)(0	g×h)(0	PROPN
ejpam-6392	334	5	,	,	PUNCT
ejpam-6392	334	6	0	0	NUM
ejpam-6392	334	7	)	)	PUNCT
ejpam-6392	334	8	,	,	PUNCT
ejpam-6392	334	9	gt	gt	PROPN
ejpam-6392	334	10	(	(	PUNCT
ejpam-6392	334	11	i×j)(0	i×j)(0	PROPN
ejpam-6392	334	12	,	,	PUNCT
ejpam-6392	334	13	0	0	NUM
ejpam-6392	334	14	)	)	PUNCT
ejpam-6392	334	15	}	}	PUNCT
ejpam-6392	334	16	≥	≥	X
ejpam-6392	334	17	{	{	PUNCT
ejpam-6392	334	18	gt	gt	PROPN
ejpam-6392	334	19	(	(	PUNCT
ejpam-6392	334	20	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	334	21	,	,	PUNCT
ejpam-6392	334	22	31	31	NUM
ejpam-6392	334	23	)	)	PUNCT
ejpam-6392	334	24	,	,	PUNCT
ejpam-6392	334	25	gt	gt	PROPN
ejpam-6392	334	26	(	(	PUNCT
ejpam-6392	334	27	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	334	28	,	,	PUNCT
ejpam-6392	334	29	31	31	NUM
ejpam-6392	334	30	)	)	PUNCT
ejpam-6392	334	31	}	}	PUNCT
ejpam-6392	334	32	,	,	PUNCT
ejpam-6392	334	33	min	min	PROPN
ejpam-6392	334	34	{	{	PUNCT
ejpam-6392	334	35	gt	gt	PROPN
ejpam-6392	334	36	(	(	PUNCT
ejpam-6392	334	37	g×h)(0	g×h)(0	PROPN
ejpam-6392	334	38	,	,	PUNCT
ejpam-6392	334	39	0	0	NUM
ejpam-6392	334	40	)	)	PUNCT
ejpam-6392	334	41	,	,	PUNCT
ejpam-6392	334	42	gt	gt	PROPN
ejpam-6392	334	43	(	(	PUNCT
ejpam-6392	334	44	i×j)(0	i×j)(0	PROPN
ejpam-6392	334	45	,	,	PUNCT
ejpam-6392	334	46	0	0	NUM
ejpam-6392	334	47	)	)	PUNCT
ejpam-6392	334	48	}	}	PUNCT
ejpam-6392	334	49	≥	≥	PROPN
ejpam-6392	334	50	min	min	PROPN
ejpam-6392	334	51	{	{	PUNCT
ejpam-6392	334	52	gt	gt	PROPN
ejpam-6392	334	53	(	(	PUNCT
ejpam-6392	334	54	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	334	55	,	,	PUNCT
ejpam-6392	334	56	31	31	NUM
ejpam-6392	334	57	)	)	PUNCT
ejpam-6392	334	58	,	,	PUNCT
ejpam-6392	334	59	gt	gt	PROPN
ejpam-6392	334	60	(	(	PUNCT
ejpam-6392	334	61	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	334	62	,	,	PUNCT
ejpam-6392	334	63	31	31	NUM
ejpam-6392	334	64	)	)	PUNCT
ejpam-6392	334	65	}	}	PUNCT
ejpam-6392	334	66	.	.	PUNCT
ejpam-6392	335	1	g	g	PROPN
ejpam-6392	335	2	t	t	PROPN
ejpam-6392	335	3	(	(	PUNCT
ejpam-6392	335	4	(	(	PUNCT
ejpam-6392	335	5	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	335	6	)	)	PUNCT
ejpam-6392	335	7	)	)	PUNCT
ejpam-6392	335	8	(	(	PUNCT
ejpam-6392	335	9	0	0	NUM
ejpam-6392	335	10	,	,	PUNCT
ejpam-6392	335	11	0	0	NUM
ejpam-6392	335	12	)	)	PUNCT
ejpam-6392	335	13	≥	≥	NOUN
ejpam-6392	335	14	g	g	PROPN
ejpam-6392	335	15	t	t	PROPN
ejpam-6392	335	16	(	(	PUNCT
ejpam-6392	335	17	(	(	PUNCT
ejpam-6392	335	18	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	335	19	)	)	PUNCT
ejpam-6392	335	20	)	)	PUNCT
ejpam-6392	336	1	(	(	PUNCT
ejpam-6392	336	2	e1	e1	NOUN
ejpam-6392	336	3	,	,	PUNCT
ejpam-6392	336	4	31	31	NUM
ejpam-6392	336	5	)	)	PUNCT
ejpam-6392	336	6	.	.	PUNCT
ejpam-6392	337	1	gi(g×h)(0	gi(g×h)(0	PROPN
ejpam-6392	337	2	,	,	PUNCT
ejpam-6392	337	3	0	0	NUM
ejpam-6392	337	4	)	)	PUNCT
ejpam-6392	337	5	≤	≤	NUM
ejpam-6392	337	6	max	max	PROPN
ejpam-6392	337	7	{	{	PUNCT
ejpam-6392	337	8	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	337	9	,	,	PUNCT
ejpam-6392	337	10	31	31	NUM
ejpam-6392	337	11	)	)	PUNCT
ejpam-6392	337	12	}	}	PUNCT
ejpam-6392	337	13	,	,	PUNCT
ejpam-6392	337	14	gi(i×j)(0	gi(i×j)(0	PROPN
ejpam-6392	337	15	,	,	PUNCT
ejpam-6392	337	16	0	0	NUM
ejpam-6392	337	17	)	)	PUNCT
ejpam-6392	337	18	≤	≤	NUM
ejpam-6392	338	1	max	max	PROPN
ejpam-6392	338	2	{	{	PUNCT
ejpam-6392	338	3	gi(i×j)(e1	gi(i×j)(e1	NOUN
ejpam-6392	338	4	,	,	PUNCT
ejpam-6392	338	5	31	31	NUM
ejpam-6392	338	6	)	)	PUNCT
ejpam-6392	338	7	}	}	PUNCT
ejpam-6392	338	8	,	,	PUNCT
ejpam-6392	338	9	{	{	PUNCT
ejpam-6392	338	10	gi(g×h)(0	gi(g×h)(0	NOUN
ejpam-6392	338	11	,	,	PUNCT
ejpam-6392	338	12	0	0	NUM
ejpam-6392	338	13	)	)	PUNCT
ejpam-6392	338	14	,	,	PUNCT
ejpam-6392	338	15	gi(i×j)(0	gi(i×j)(0	PROPN
ejpam-6392	338	16	,	,	PUNCT
ejpam-6392	338	17	0	0	NUM
ejpam-6392	338	18	)	)	PUNCT
ejpam-6392	338	19	}	}	PUNCT
ejpam-6392	338	20	≤	≤	PROPN
ejpam-6392	338	21	{	{	PUNCT
ejpam-6392	338	22	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	338	23	,	,	PUNCT
ejpam-6392	338	24	31	31	NUM
ejpam-6392	338	25	)	)	PUNCT
ejpam-6392	338	26	,	,	PUNCT
ejpam-6392	338	27	gi(i×j)(e1	gi(i×j)(e1	NOUN
ejpam-6392	338	28	,	,	PUNCT
ejpam-6392	338	29	31	31	NUM
ejpam-6392	338	30	)	)	PUNCT
ejpam-6392	338	31	}	}	PUNCT
ejpam-6392	338	32	,	,	PUNCT
ejpam-6392	338	33	max	max	PROPN
ejpam-6392	338	34	{	{	PUNCT
ejpam-6392	338	35	gi(g×h)(0	gi(g×h)(0	PROPN
ejpam-6392	338	36	,	,	PUNCT
ejpam-6392	338	37	0	0	NUM
ejpam-6392	338	38	)	)	PUNCT
ejpam-6392	338	39	,	,	PUNCT
ejpam-6392	338	40	gi(i×j)(0	gi(i×j)(0	PROPN
ejpam-6392	338	41	,	,	PUNCT
ejpam-6392	338	42	0	0	NUM
ejpam-6392	338	43	)	)	PUNCT
ejpam-6392	338	44	}	}	PUNCT
ejpam-6392	338	45	≤	≤	NUM
ejpam-6392	338	46	max	max	PROPN
ejpam-6392	338	47	{	{	PUNCT
ejpam-6392	338	48	gi(i×j)(e1	gi(i×j)(e1	NOUN
ejpam-6392	338	49	,	,	PUNCT
ejpam-6392	338	50	31	31	NUM
ejpam-6392	338	51	)	)	PUNCT
ejpam-6392	338	52	,	,	PUNCT
ejpam-6392	338	53	gi(i×j)(e1	gi(i×j)(e1	NOUN
ejpam-6392	338	54	,	,	PUNCT
ejpam-6392	338	55	31	31	NUM
ejpam-6392	338	56	)	)	PUNCT
ejpam-6392	338	57	}	}	PUNCT
ejpam-6392	338	58	.	.	PUNCT
ejpam-6392	339	1	g	g	PROPN
ejpam-6392	339	2	f	f	PROPN
ejpam-6392	339	3	(	(	PUNCT
ejpam-6392	339	4	(	(	PUNCT
ejpam-6392	339	5	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	339	6	)	)	PUNCT
ejpam-6392	339	7	)	)	PUNCT
ejpam-6392	339	8	(	(	PUNCT
ejpam-6392	339	9	0	0	NUM
ejpam-6392	339	10	,	,	PUNCT
ejpam-6392	339	11	0	0	NUM
ejpam-6392	339	12	)	)	PUNCT
ejpam-6392	339	13	≤	≤	NOUN
ejpam-6392	339	14	g	g	X
ejpam-6392	339	15	f	f	PROPN
ejpam-6392	339	16	(	(	PUNCT
ejpam-6392	339	17	(	(	PUNCT
ejpam-6392	339	18	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	339	19	)	)	PUNCT
ejpam-6392	339	20	)	)	PUNCT
ejpam-6392	339	21	(	(	PUNCT
ejpam-6392	339	22	e1	e1	NOUN
ejpam-6392	339	23	,	,	PUNCT
ejpam-6392	339	24	31	31	NUM
ejpam-6392	339	25	)	)	PUNCT
ejpam-6392	339	26	.	.	PUNCT
ejpam-6392	340	1	gf	gf	PROPN
ejpam-6392	340	2	(	(	PUNCT
ejpam-6392	340	3	g×h)(0	g×h)(0	PROPN
ejpam-6392	340	4	,	,	PUNCT
ejpam-6392	340	5	0	0	NUM
ejpam-6392	340	6	)	)	PUNCT
ejpam-6392	340	7	≤	≤	NUM
ejpam-6392	340	8	max	max	PROPN
ejpam-6392	340	9	{	{	PUNCT
ejpam-6392	340	10	gf	gf	PROPN
ejpam-6392	340	11	(	(	PUNCT
ejpam-6392	340	12	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	340	13	,	,	PUNCT
ejpam-6392	340	14	31	31	NUM
ejpam-6392	340	15	)	)	PUNCT
ejpam-6392	340	16	}	}	PUNCT
ejpam-6392	340	17	,	,	PUNCT
ejpam-6392	340	18	gf	gf	X
ejpam-6392	340	19	(	(	PUNCT
ejpam-6392	340	20	i×j)(0	i×j)(0	PROPN
ejpam-6392	340	21	,	,	PUNCT
ejpam-6392	340	22	0	0	NUM
ejpam-6392	340	23	)	)	PUNCT
ejpam-6392	340	24	≤	≤	NUM
ejpam-6392	340	25	max	max	PROPN
ejpam-6392	340	26	{	{	PUNCT
ejpam-6392	340	27	gf	gf	X
ejpam-6392	340	28	(	(	PUNCT
ejpam-6392	340	29	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	340	30	,	,	PUNCT
ejpam-6392	340	31	31	31	NUM
ejpam-6392	340	32	)	)	PUNCT
ejpam-6392	340	33	}	}	PUNCT
ejpam-6392	340	34	,	,	PUNCT
ejpam-6392	340	35	{	{	PUNCT
ejpam-6392	340	36	gf	gf	X
ejpam-6392	340	37	(	(	PUNCT
ejpam-6392	340	38	g×h)(0	g×h)(0	PROPN
ejpam-6392	340	39	,	,	PUNCT
ejpam-6392	340	40	0	0	NUM
ejpam-6392	340	41	)	)	PUNCT
ejpam-6392	340	42	,	,	PUNCT
ejpam-6392	340	43	gf	gf	X
ejpam-6392	340	44	(	(	PUNCT
ejpam-6392	340	45	i×j)(0	i×j)(0	PROPN
ejpam-6392	340	46	,	,	PUNCT
ejpam-6392	340	47	0	0	NUM
ejpam-6392	340	48	)	)	PUNCT
ejpam-6392	340	49	}	}	PUNCT
ejpam-6392	340	50	≤	≤	NOUN
ejpam-6392	340	51	{	{	PUNCT
ejpam-6392	340	52	gf	gf	X
ejpam-6392	340	53	(	(	PUNCT
ejpam-6392	340	54	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	340	55	,	,	PUNCT
ejpam-6392	340	56	31	31	NUM
ejpam-6392	340	57	)	)	PUNCT
ejpam-6392	340	58	,	,	PUNCT
ejpam-6392	340	59	gf	gf	X
ejpam-6392	340	60	(	(	PUNCT
ejpam-6392	340	61	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	340	62	,	,	PUNCT
ejpam-6392	340	63	31	31	NUM
ejpam-6392	340	64	)	)	PUNCT
ejpam-6392	340	65	}	}	PUNCT
ejpam-6392	340	66	,	,	PUNCT
ejpam-6392	340	67	max	max	PROPN
ejpam-6392	340	68	{	{	PUNCT
ejpam-6392	340	69	gf	gf	X
ejpam-6392	340	70	(	(	PUNCT
ejpam-6392	340	71	g×h)(0	g×h)(0	PROPN
ejpam-6392	340	72	,	,	PUNCT
ejpam-6392	340	73	0	0	NUM
ejpam-6392	340	74	)	)	PUNCT
ejpam-6392	340	75	,	,	PUNCT
ejpam-6392	340	76	gf	gf	X
ejpam-6392	340	77	(	(	PUNCT
ejpam-6392	340	78	i×j)(0	i×j)(0	PROPN
ejpam-6392	340	79	,	,	PUNCT
ejpam-6392	340	80	0	0	NUM
ejpam-6392	340	81	)	)	PUNCT
ejpam-6392	340	82	}	}	PUNCT
ejpam-6392	340	83	≤	≤	NUM
ejpam-6392	340	84	max	max	PROPN
ejpam-6392	340	85	{	{	PUNCT
ejpam-6392	340	86	gf	gf	X
ejpam-6392	340	87	(	(	PUNCT
ejpam-6392	340	88	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	340	89	,	,	PUNCT
ejpam-6392	340	90	31	31	NUM
ejpam-6392	340	91	)	)	PUNCT
ejpam-6392	340	92	,	,	PUNCT
ejpam-6392	340	93	gf	gf	X
ejpam-6392	340	94	(	(	PUNCT
ejpam-6392	340	95	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	340	96	,	,	PUNCT
ejpam-6392	340	97	31	31	NUM
ejpam-6392	340	98	)	)	PUNCT
ejpam-6392	340	99	}	}	PUNCT
ejpam-6392	340	100	.	.	PUNCT
ejpam-6392	341	1	m.	m.	NOUN
ejpam-6392	341	2	remala	remala	NOUN
ejpam-6392	341	3	,	,	PUNCT
ejpam-6392	341	4	e.	e.	PROPN
ejpam-6392	341	5	tamma	tamma	PROPN
ejpam-6392	341	6	,	,	PUNCT
ejpam-6392	341	7	y.	y.	PROPN
ejpam-6392	341	8	bhargavi	bhargavi	PROPN
ejpam-6392	341	9	/	/	SYM
ejpam-6392	341	10	eur	eur	PROPN
ejpam-6392	341	11	.	.	PUNCT
ejpam-6392	342	1	j.	j.	PROPN
ejpam-6392	342	2	pure	pure	PROPN
ejpam-6392	342	3	appl	appl	PROPN
ejpam-6392	342	4	.	.	PROPN
ejpam-6392	342	5	math	math	PROPN
ejpam-6392	342	6	,	,	PUNCT
ejpam-6392	342	7	18	18	NUM
ejpam-6392	342	8	(	(	PUNCT
ejpam-6392	342	9	4	4	NUM
ejpam-6392	342	10	)	)	PUNCT
ejpam-6392	342	11	(	(	PUNCT
ejpam-6392	342	12	2025	2025	NUM
ejpam-6392	342	13	)	)	PUNCT
ejpam-6392	342	14	,	,	PUNCT
ejpam-6392	342	15	6392	6392	NUM
ejpam-6392	342	16	15	15	NUM
ejpam-6392	342	17	of	of	ADP
ejpam-6392	342	18	20	20	NUM
ejpam-6392	342	19	g	g	NOUN
ejpam-6392	342	20	f	f	PROPN
ejpam-6392	342	21	(	(	PUNCT
ejpam-6392	342	22	(	(	PUNCT
ejpam-6392	342	23	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	342	24	)	)	PUNCT
ejpam-6392	342	25	)	)	PUNCT
ejpam-6392	342	26	(	(	PUNCT
ejpam-6392	342	27	0	0	NUM
ejpam-6392	342	28	,	,	PUNCT
ejpam-6392	342	29	0	0	NUM
ejpam-6392	342	30	)	)	PUNCT
ejpam-6392	342	31	≤	≤	NOUN
ejpam-6392	343	1	g	g	X
ejpam-6392	343	2	f	f	PROPN
ejpam-6392	343	3	(	(	PUNCT
ejpam-6392	343	4	(	(	PUNCT
ejpam-6392	343	5	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	343	6	)	)	PUNCT
ejpam-6392	343	7	)	)	PUNCT
ejpam-6392	343	8	(	(	PUNCT
ejpam-6392	343	9	e1	e1	NOUN
ejpam-6392	343	10	,	,	PUNCT
ejpam-6392	343	11	31	31	NUM
ejpam-6392	343	12	)	)	PUNCT
ejpam-6392	343	13	.	.	PUNCT
ejpam-6392	344	1	now	now	ADV
ejpam-6392	344	2	(	(	PUNCT
ejpam-6392	344	3	e1	e1	NOUN
ejpam-6392	344	4	,	,	PUNCT
ejpam-6392	344	5	31,ä1	31,ä1	PROPN
ejpam-6392	344	6	)	)	PUNCT
ejpam-6392	344	7	,	,	PUNCT
ejpam-6392	344	8	(	(	PUNCT
ejpam-6392	344	9	e2	e2	PROPN
ejpam-6392	344	10	,	,	PUNCT
ejpam-6392	344	11	32,ä2	32,ä2	NUM
ejpam-6392	344	12	)	)	PUNCT
ejpam-6392	344	13	∈	∈	PROPN
ejpam-6392	344	14	x1	x1	VERB
ejpam-6392	344	15	×x2	×x2	PROPN
ejpam-6392	344	16	.	.	PUNCT
ejpam-6392	345	1	consider	consider	VERB
ejpam-6392	345	2	gt	gt	PROPN
ejpam-6392	345	3	(	(	PUNCT
ejpam-6392	345	4	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	345	5	,	,	PUNCT
ejpam-6392	345	6	31	31	NUM
ejpam-6392	345	7	)	)	PUNCT
ejpam-6392	345	8	=	=	SYM
ejpam-6392	345	9	min	min	PROPN
ejpam-6392	345	10	{	{	PUNCT
ejpam-6392	345	11	gt	gt	PROPN
ejpam-6392	345	12	(	(	PUNCT
ejpam-6392	345	13	g×h	g×h	PROPN
ejpam-6392	345	14	)	)	PUNCT
ejpam-6392	345	15	(	(	PUNCT
ejpam-6392	345	16	(	(	PUNCT
ejpam-6392	345	17	e1	e1	NOUN
ejpam-6392	345	18	,	,	PUNCT
ejpam-6392	345	19	31	31	NUM
ejpam-6392	345	20	)	)	PUNCT
ejpam-6392	345	21	•	•	NOUN
ejpam-6392	345	22	(	(	PUNCT
ejpam-6392	345	23	e2	e2	PROPN
ejpam-6392	345	24	,	,	PUNCT
ejpam-6392	345	25	32	32	NUM
ejpam-6392	345	26	)	)	PUNCT
ejpam-6392	345	27	•	•	NOUN
ejpam-6392	345	28	(	(	PUNCT
ejpam-6392	345	29	e3	e3	NOUN
ejpam-6392	345	30	,	,	PUNCT
ejpam-6392	345	31	33	33	NUM
ejpam-6392	345	32	)	)	PUNCT
ejpam-6392	345	33	)	)	PUNCT
ejpam-6392	345	34	,	,	PUNCT
ejpam-6392	345	35	gt	gt	PROPN
ejpam-6392	345	36	(	(	PUNCT
ejpam-6392	345	37	g×h)(e3	g×h)(e3	NOUN
ejpam-6392	345	38	,	,	PUNCT
ejpam-6392	345	39	33	33	NUM
ejpam-6392	345	40	)	)	PUNCT
ejpam-6392	345	41	}	}	PUNCT
ejpam-6392	345	42	,	,	PUNCT
ejpam-6392	345	43	gt	gt	PROPN
ejpam-6392	345	44	(	(	PUNCT
ejpam-6392	345	45	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	345	46	,	,	PUNCT
ejpam-6392	345	47	31	31	NUM
ejpam-6392	345	48	)	)	PUNCT
ejpam-6392	345	49	=	=	SYM
ejpam-6392	345	50	min	min	PROPN
ejpam-6392	345	51	{	{	PUNCT
ejpam-6392	345	52	gt	gt	INTJ
ejpam-6392	345	53	(	(	PUNCT
ejpam-6392	345	54	i×j	i×j	ADV
ejpam-6392	345	55	)	)	PUNCT
ejpam-6392	345	56	(	(	PUNCT
ejpam-6392	345	57	(	(	PUNCT
ejpam-6392	345	58	e1	e1	NOUN
ejpam-6392	345	59	,	,	PUNCT
ejpam-6392	345	60	31	31	NUM
ejpam-6392	345	61	)	)	PUNCT
ejpam-6392	345	62	•	•	NOUN
ejpam-6392	345	63	(	(	PUNCT
ejpam-6392	345	64	e2	e2	PROPN
ejpam-6392	345	65	,	,	PUNCT
ejpam-6392	345	66	32	32	NUM
ejpam-6392	345	67	)	)	PUNCT
ejpam-6392	345	68	•	•	NOUN
ejpam-6392	345	69	(	(	PUNCT
ejpam-6392	345	70	e3	e3	NOUN
ejpam-6392	345	71	,	,	PUNCT
ejpam-6392	345	72	33	33	NUM
ejpam-6392	345	73	)	)	PUNCT
ejpam-6392	345	74	)	)	PUNCT
ejpam-6392	345	75	,	,	PUNCT
ejpam-6392	345	76	gt	gt	PROPN
ejpam-6392	345	77	(	(	PUNCT
ejpam-6392	345	78	i×j)(e3	i×j)(e3	PROPN
ejpam-6392	345	79	,	,	PUNCT
ejpam-6392	345	80	33	33	NUM
ejpam-6392	345	81	)	)	PUNCT
ejpam-6392	345	82	}	}	PUNCT
ejpam-6392	345	83	.	.	PUNCT
ejpam-6392	346	1	gt	gt	INTJ
ejpam-6392	346	2	(	(	PUNCT
ejpam-6392	346	3	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	346	4	,	,	PUNCT
ejpam-6392	346	5	31	31	NUM
ejpam-6392	346	6	)	)	PUNCT
ejpam-6392	346	7	,	,	PUNCT
ejpam-6392	346	8	gt	gt	PROPN
ejpam-6392	346	9	(	(	PUNCT
ejpam-6392	346	10	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	346	11	,	,	PUNCT
ejpam-6392	346	12	31	31	NUM
ejpam-6392	346	13	)	)	PUNCT
ejpam-6392	346	14	≥	≥	PROPN
ejpam-6392	346	15	min	min	PROPN
ejpam-6392	346	16	{	{	PUNCT
ejpam-6392	346	17	min	min	PROPN
ejpam-6392	346	18	{	{	PUNCT
ejpam-6392	346	19	gt	gt	PROPN
ejpam-6392	346	20	(	(	PUNCT
ejpam-6392	346	21	g×h)((e1	g×h)((e1	PROPN
ejpam-6392	346	22	,	,	PUNCT
ejpam-6392	346	23	31	31	NUM
ejpam-6392	346	24	)	)	PUNCT
ejpam-6392	346	25	•	•	NOUN
ejpam-6392	346	26	(	(	PUNCT
ejpam-6392	346	27	e2	e2	PROPN
ejpam-6392	346	28	,	,	PUNCT
ejpam-6392	346	29	32	32	NUM
ejpam-6392	346	30	)	)	PUNCT
ejpam-6392	346	31	•	•	NOUN
ejpam-6392	346	32	(	(	PUNCT
ejpam-6392	346	33	e3	e3	NOUN
ejpam-6392	346	34	,	,	PUNCT
ejpam-6392	346	35	33	33	NUM
ejpam-6392	346	36	)	)	PUNCT
ejpam-6392	346	37	)	)	PUNCT
ejpam-6392	346	38	,	,	PUNCT
ejpam-6392	346	39	gt	gt	PROPN
ejpam-6392	346	40	(	(	PUNCT
ejpam-6392	346	41	g×h)(e3	g×h)(e3	NOUN
ejpam-6392	346	42	,	,	PUNCT
ejpam-6392	346	43	33	33	NUM
ejpam-6392	346	44	)	)	PUNCT
ejpam-6392	346	45	}	}	PUNCT
ejpam-6392	346	46	,	,	PUNCT
ejpam-6392	346	47	min	min	PROPN
ejpam-6392	346	48	{	{	PUNCT
ejpam-6392	346	49	gt	gt	PROPN
ejpam-6392	346	50	(	(	PUNCT
ejpam-6392	346	51	i×j)((e1	i×j)((e1	PROPN
ejpam-6392	346	52	,	,	PUNCT
ejpam-6392	346	53	31	31	NUM
ejpam-6392	346	54	)	)	PUNCT
ejpam-6392	346	55	•	•	NOUN
ejpam-6392	346	56	(	(	PUNCT
ejpam-6392	346	57	e2	e2	PROPN
ejpam-6392	346	58	,	,	PUNCT
ejpam-6392	346	59	32	32	NUM
ejpam-6392	346	60	)	)	PUNCT
ejpam-6392	346	61	•	•	NOUN
ejpam-6392	346	62	(	(	PUNCT
ejpam-6392	346	63	e3	e3	NOUN
ejpam-6392	346	64	,	,	PUNCT
ejpam-6392	346	65	33	33	NUM
ejpam-6392	346	66	)	)	PUNCT
ejpam-6392	346	67	)	)	PUNCT
ejpam-6392	346	68	,	,	PUNCT
ejpam-6392	346	69	gt	gt	PROPN
ejpam-6392	346	70	(	(	PUNCT
ejpam-6392	346	71	i×j)(e3	i×j)(e3	PROPN
ejpam-6392	346	72	,	,	PUNCT
ejpam-6392	346	73	33	33	NUM
ejpam-6392	346	74	)	)	PUNCT
ejpam-6392	346	75	}	}	PUNCT
ejpam-6392	346	76	}	}	PUNCT
ejpam-6392	346	77	≥	≥	PROPN
ejpam-6392	346	78	min	min	PROPN
ejpam-6392	346	79	{	{	PUNCT
ejpam-6392	346	80	min	min	PROPN
ejpam-6392	346	81	{	{	PUNCT
ejpam-6392	346	82	gt	gt	PROPN
ejpam-6392	346	83	(	(	PUNCT
ejpam-6392	346	84	g×h)((e1	g×h)((e1	PROPN
ejpam-6392	346	85	,	,	PUNCT
ejpam-6392	346	86	31	31	NUM
ejpam-6392	346	87	)	)	PUNCT
ejpam-6392	346	88	•	•	NOUN
ejpam-6392	346	89	(	(	PUNCT
ejpam-6392	346	90	e2	e2	PROPN
ejpam-6392	346	91	,	,	PUNCT
ejpam-6392	346	92	32	32	NUM
ejpam-6392	346	93	)	)	PUNCT
ejpam-6392	346	94	•	•	NOUN
ejpam-6392	346	95	(	(	PUNCT
ejpam-6392	346	96	e3	e3	NOUN
ejpam-6392	346	97	,	,	PUNCT
ejpam-6392	346	98	33	33	NUM
ejpam-6392	346	99	)	)	PUNCT
ejpam-6392	346	100	)	)	PUNCT
ejpam-6392	346	101	,	,	PUNCT
ejpam-6392	346	102	gt	gt	PROPN
ejpam-6392	346	103	(	(	PUNCT
ejpam-6392	346	104	i×j)((e1	i×j)((e1	PROPN
ejpam-6392	346	105	,	,	PUNCT
ejpam-6392	346	106	31	31	NUM
ejpam-6392	346	107	)	)	PUNCT
ejpam-6392	346	108	•	•	NOUN
ejpam-6392	346	109	(	(	PUNCT
ejpam-6392	346	110	e2	e2	PROPN
ejpam-6392	346	111	,	,	PUNCT
ejpam-6392	346	112	32	32	NUM
ejpam-6392	346	113	)	)	PUNCT
ejpam-6392	346	114	•	•	NOUN
ejpam-6392	346	115	(	(	PUNCT
ejpam-6392	346	116	e3	e3	NOUN
ejpam-6392	346	117	,	,	PUNCT
ejpam-6392	346	118	33	33	NUM
ejpam-6392	346	119	)	)	PUNCT
ejpam-6392	346	120	)	)	PUNCT
ejpam-6392	346	121	}	}	PUNCT
ejpam-6392	346	122	,	,	PUNCT
ejpam-6392	346	123	min	min	PROPN
ejpam-6392	346	124	{	{	PUNCT
ejpam-6392	346	125	gt	gt	PROPN
ejpam-6392	346	126	(	(	PUNCT
ejpam-6392	346	127	g×h)(e3	g×h)(e3	NOUN
ejpam-6392	346	128	,	,	PUNCT
ejpam-6392	346	129	33	33	NUM
ejpam-6392	346	130	)	)	PUNCT
ejpam-6392	346	131	,	,	PUNCT
ejpam-6392	346	132	gt	gt	PROPN
ejpam-6392	346	133	(	(	PUNCT
ejpam-6392	346	134	i×j)(e3	i×j)(e3	PROPN
ejpam-6392	346	135	,	,	PUNCT
ejpam-6392	346	136	33	33	NUM
ejpam-6392	346	137	)	)	PUNCT
ejpam-6392	346	138	}	}	PUNCT
ejpam-6392	346	139	}	}	PUNCT
ejpam-6392	346	140	.	.	PUNCT
ejpam-6392	347	1	g	g	PROPN
ejpam-6392	347	2	t	t	PROPN
ejpam-6392	347	3	(	(	PUNCT
ejpam-6392	347	4	(	(	PUNCT
ejpam-6392	347	5	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	347	6	)	)	PUNCT
ejpam-6392	347	7	)	)	PUNCT
ejpam-6392	348	1	(	(	PUNCT
ejpam-6392	348	2	e1	e1	NOUN
ejpam-6392	348	3	,	,	PUNCT
ejpam-6392	348	4	31	31	NUM
ejpam-6392	348	5	)	)	PUNCT
ejpam-6392	348	6	≥	≥	NOUN
ejpam-6392	348	7	{	{	PUNCT
ejpam-6392	348	8	g	g	PROPN
ejpam-6392	348	9	t	t	PROPN
ejpam-6392	348	10	(	(	PUNCT
ejpam-6392	348	11	(	(	PUNCT
ejpam-6392	348	12	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	348	13	)	)	PUNCT
ejpam-6392	348	14	)	)	PUNCT
ejpam-6392	349	1	(	(	PUNCT
ejpam-6392	349	2	(	(	PUNCT
ejpam-6392	349	3	e1	e1	NOUN
ejpam-6392	349	4	,	,	PUNCT
ejpam-6392	349	5	31)•(e2	31)•(e2	NUM
ejpam-6392	349	6	,	,	PUNCT
ejpam-6392	349	7	32)•(e3	32)•(e3	NUM
ejpam-6392	349	8	,	,	PUNCT
ejpam-6392	349	9	33	33	NUM
ejpam-6392	349	10	)	)	PUNCT
ejpam-6392	349	11	)	)	PUNCT
ejpam-6392	349	12	,	,	PUNCT
ejpam-6392	349	13	g	g	PROPN
ejpam-6392	349	14	t	t	PROPN
ejpam-6392	349	15	(	(	PUNCT
ejpam-6392	349	16	(	(	PUNCT
ejpam-6392	349	17	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	349	18	)	)	PUNCT
ejpam-6392	349	19	)	)	PUNCT
ejpam-6392	349	20	(	(	PUNCT
ejpam-6392	349	21	e3	e3	NOUN
ejpam-6392	349	22	,	,	PUNCT
ejpam-6392	349	23	33	33	NUM
ejpam-6392	349	24	)	)	PUNCT
ejpam-6392	349	25	}	}	PUNCT
ejpam-6392	349	26	.	.	PUNCT
ejpam-6392	350	1	also	also	ADV
ejpam-6392	350	2	for	for	ADP
ejpam-6392	350	3	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	350	4	,	,	PUNCT
ejpam-6392	350	5	31	31	NUM
ejpam-6392	350	6	)	)	PUNCT
ejpam-6392	351	1	=	=	SYM
ejpam-6392	351	2	max	max	PROPN
ejpam-6392	351	3	{	{	PUNCT
ejpam-6392	351	4	gi(g×h	gi(g×h	NOUN
ejpam-6392	351	5	)	)	PUNCT
ejpam-6392	351	6	(	(	PUNCT
ejpam-6392	351	7	(	(	PUNCT
ejpam-6392	351	8	e1	e1	NOUN
ejpam-6392	351	9	,	,	PUNCT
ejpam-6392	351	10	31	31	NUM
ejpam-6392	351	11	)	)	PUNCT
ejpam-6392	351	12	•	•	NOUN
ejpam-6392	351	13	(	(	PUNCT
ejpam-6392	351	14	e2	e2	PROPN
ejpam-6392	351	15	,	,	PUNCT
ejpam-6392	351	16	32	32	NUM
ejpam-6392	351	17	)	)	PUNCT
ejpam-6392	351	18	•	•	NOUN
ejpam-6392	351	19	(	(	PUNCT
ejpam-6392	351	20	e3	e3	NOUN
ejpam-6392	351	21	,	,	PUNCT
ejpam-6392	351	22	33	33	NUM
ejpam-6392	351	23	)	)	PUNCT
ejpam-6392	351	24	)	)	PUNCT
ejpam-6392	351	25	,	,	PUNCT
ejpam-6392	351	26	gi(g×h)(e3	gi(g×h)(e3	ADJ
ejpam-6392	351	27	,	,	PUNCT
ejpam-6392	351	28	33	33	NUM
ejpam-6392	351	29	)	)	PUNCT
ejpam-6392	351	30	}	}	PUNCT
ejpam-6392	351	31	,	,	PUNCT
ejpam-6392	351	32	gi(i×j)(e1	gi(i×j)(e1	NOUN
ejpam-6392	351	33	,	,	PUNCT
ejpam-6392	351	34	31	31	NUM
ejpam-6392	351	35	)	)	PUNCT
ejpam-6392	351	36	=	=	SYM
ejpam-6392	351	37	max	max	PROPN
ejpam-6392	351	38	{	{	PUNCT
ejpam-6392	351	39	gi(i×j	gi(i×j	PROPN
ejpam-6392	351	40	)	)	PUNCT
ejpam-6392	351	41	(	(	PUNCT
ejpam-6392	351	42	(	(	PUNCT
ejpam-6392	351	43	e1	e1	NOUN
ejpam-6392	351	44	,	,	PUNCT
ejpam-6392	351	45	31	31	NUM
ejpam-6392	351	46	)	)	PUNCT
ejpam-6392	351	47	•	•	NOUN
ejpam-6392	351	48	(	(	PUNCT
ejpam-6392	351	49	e2	e2	PROPN
ejpam-6392	351	50	,	,	PUNCT
ejpam-6392	351	51	32	32	NUM
ejpam-6392	351	52	)	)	PUNCT
ejpam-6392	351	53	•	•	NOUN
ejpam-6392	351	54	(	(	PUNCT
ejpam-6392	351	55	e3	e3	NOUN
ejpam-6392	351	56	,	,	PUNCT
ejpam-6392	351	57	33	33	NUM
ejpam-6392	351	58	)	)	PUNCT
ejpam-6392	351	59	)	)	PUNCT
ejpam-6392	351	60	,	,	PUNCT
ejpam-6392	351	61	gi(i×j)(e3	gi(i×j)(e3	PROPN
ejpam-6392	351	62	,	,	PUNCT
ejpam-6392	351	63	33	33	NUM
ejpam-6392	351	64	)	)	PUNCT
ejpam-6392	351	65	}	}	PUNCT
ejpam-6392	351	66	,	,	PUNCT
ejpam-6392	351	67	gi(g×h)(e1	gi(g×h)(e1	NOUN
ejpam-6392	351	68	,	,	PUNCT
ejpam-6392	351	69	31	31	NUM
ejpam-6392	351	70	)	)	PUNCT
ejpam-6392	351	71	,	,	PUNCT
ejpam-6392	351	72	gi(i×j)(e1	gi(i×j)(e1	NOUN
ejpam-6392	351	73	,	,	PUNCT
ejpam-6392	351	74	31	31	NUM
ejpam-6392	351	75	)	)	PUNCT
ejpam-6392	351	76	≤	≤	NUM
ejpam-6392	351	77	max	max	PROPN
ejpam-6392	351	78	{	{	PUNCT
ejpam-6392	351	79	max	max	PROPN
ejpam-6392	351	80	{	{	PUNCT
ejpam-6392	351	81	gi(g×h)((e1	gi(g×h)((e1	PROPN
ejpam-6392	351	82	,	,	PUNCT
ejpam-6392	351	83	31	31	NUM
ejpam-6392	351	84	)	)	PUNCT
ejpam-6392	351	85	•	•	NOUN
ejpam-6392	351	86	(	(	PUNCT
ejpam-6392	351	87	e2	e2	PROPN
ejpam-6392	351	88	,	,	PUNCT
ejpam-6392	351	89	32	32	NUM
ejpam-6392	351	90	)	)	PUNCT
ejpam-6392	351	91	•	•	NOUN
ejpam-6392	351	92	(	(	PUNCT
ejpam-6392	351	93	e3	e3	NOUN
ejpam-6392	351	94	,	,	PUNCT
ejpam-6392	351	95	33	33	NUM
ejpam-6392	351	96	)	)	PUNCT
ejpam-6392	351	97	)	)	PUNCT
ejpam-6392	351	98	,	,	PUNCT
ejpam-6392	351	99	gi(g×h)(e3	gi(g×h)(e3	ADJ
ejpam-6392	351	100	,	,	PUNCT
ejpam-6392	351	101	33	33	NUM
ejpam-6392	351	102	)	)	PUNCT
ejpam-6392	351	103	}	}	PUNCT
ejpam-6392	351	104	,	,	PUNCT
ejpam-6392	351	105	max	max	PROPN
ejpam-6392	351	106	{	{	PUNCT
ejpam-6392	351	107	gi(i×j)((e1	gi(i×j)((e1	NOUN
ejpam-6392	351	108	,	,	PUNCT
ejpam-6392	351	109	31	31	NUM
ejpam-6392	351	110	)	)	PUNCT
ejpam-6392	351	111	•	•	NOUN
ejpam-6392	351	112	(	(	PUNCT
ejpam-6392	351	113	e2	e2	PROPN
ejpam-6392	351	114	,	,	PUNCT
ejpam-6392	351	115	32	32	NUM
ejpam-6392	351	116	)	)	PUNCT
ejpam-6392	351	117	•	•	NOUN
ejpam-6392	351	118	(	(	PUNCT
ejpam-6392	351	119	e3	e3	NOUN
ejpam-6392	351	120	,	,	PUNCT
ejpam-6392	351	121	33	33	NUM
ejpam-6392	351	122	)	)	PUNCT
ejpam-6392	351	123	)	)	PUNCT
ejpam-6392	351	124	,	,	PUNCT
ejpam-6392	351	125	gi(i×j)(e3	gi(i×j)(e3	PROPN
ejpam-6392	351	126	,	,	PUNCT
ejpam-6392	351	127	33	33	NUM
ejpam-6392	351	128	)	)	PUNCT
ejpam-6392	351	129	}	}	PUNCT
ejpam-6392	351	130	}	}	PUNCT
ejpam-6392	351	131	≤	≤	NUM
ejpam-6392	351	132	max	max	PROPN
ejpam-6392	351	133	{	{	PUNCT
ejpam-6392	351	134	max	max	PROPN
ejpam-6392	351	135	{	{	PUNCT
ejpam-6392	351	136	gi(g×h)((e1	gi(g×h)((e1	PROPN
ejpam-6392	351	137	,	,	PUNCT
ejpam-6392	351	138	31	31	NUM
ejpam-6392	351	139	)	)	PUNCT
ejpam-6392	351	140	•	•	NOUN
ejpam-6392	351	141	(	(	PUNCT
ejpam-6392	351	142	e2	e2	PROPN
ejpam-6392	351	143	,	,	PUNCT
ejpam-6392	351	144	32	32	NUM
ejpam-6392	351	145	)	)	PUNCT
ejpam-6392	351	146	•	•	NOUN
ejpam-6392	351	147	(	(	PUNCT
ejpam-6392	351	148	e3	e3	NOUN
ejpam-6392	351	149	,	,	PUNCT
ejpam-6392	351	150	33	33	NUM
ejpam-6392	351	151	)	)	PUNCT
ejpam-6392	351	152	)	)	PUNCT
ejpam-6392	351	153	,	,	PUNCT
ejpam-6392	351	154	gi(i×j)((e1	gi(i×j)((e1	NOUN
ejpam-6392	351	155	,	,	PUNCT
ejpam-6392	351	156	31	31	NUM
ejpam-6392	351	157	)	)	PUNCT
ejpam-6392	351	158	•	•	NOUN
ejpam-6392	351	159	(	(	PUNCT
ejpam-6392	351	160	e2	e2	PROPN
ejpam-6392	351	161	,	,	PUNCT
ejpam-6392	351	162	32	32	NUM
ejpam-6392	351	163	)	)	PUNCT
ejpam-6392	351	164	•	•	NOUN
ejpam-6392	351	165	(	(	PUNCT
ejpam-6392	351	166	e3	e3	NOUN
ejpam-6392	351	167	,	,	PUNCT
ejpam-6392	351	168	33	33	NUM
ejpam-6392	351	169	)	)	PUNCT
ejpam-6392	351	170	)	)	PUNCT
ejpam-6392	351	171	}	}	PUNCT
ejpam-6392	351	172	,	,	PUNCT
ejpam-6392	351	173	max	max	PROPN
ejpam-6392	351	174	{	{	PUNCT
ejpam-6392	351	175	gi(g×h)(e3	gi(g×h)(e3	PROPN
ejpam-6392	351	176	,	,	PUNCT
ejpam-6392	351	177	33	33	NUM
ejpam-6392	351	178	)	)	PUNCT
ejpam-6392	351	179	,	,	PUNCT
ejpam-6392	351	180	gi(i×j)(e3	gi(i×j)(e3	PROPN
ejpam-6392	351	181	,	,	PUNCT
ejpam-6392	351	182	33	33	NUM
ejpam-6392	351	183	)	)	PUNCT
ejpam-6392	351	184	}	}	PUNCT
ejpam-6392	351	185	}	}	PUNCT
ejpam-6392	351	186	.	.	PUNCT
ejpam-6392	352	1	g	g	NOUN
ejpam-6392	352	2	i	i	PRON
ejpam-6392	352	3	(	(	PUNCT
ejpam-6392	352	4	(	(	PUNCT
ejpam-6392	352	5	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	352	6	)	)	PUNCT
ejpam-6392	352	7	)	)	PUNCT
ejpam-6392	352	8	(	(	PUNCT
ejpam-6392	352	9	e1	e1	NOUN
ejpam-6392	352	10	,	,	PUNCT
ejpam-6392	352	11	31	31	NUM
ejpam-6392	352	12	)	)	PUNCT
ejpam-6392	352	13	≤	≤	NOUN
ejpam-6392	352	14	{	{	PUNCT
ejpam-6392	352	15	g	g	NOUN
ejpam-6392	352	16	i	i	PRON
ejpam-6392	352	17	(	(	PUNCT
ejpam-6392	352	18	(	(	PUNCT
ejpam-6392	352	19	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	352	20	)	)	PUNCT
ejpam-6392	352	21	)	)	PUNCT
ejpam-6392	352	22	(	(	PUNCT
ejpam-6392	352	23	(	(	PUNCT
ejpam-6392	352	24	e1	e1	NOUN
ejpam-6392	352	25	,	,	PUNCT
ejpam-6392	352	26	31)•(e2	31)•(e2	NUM
ejpam-6392	352	27	,	,	PUNCT
ejpam-6392	352	28	32)•(e3	32)•(e3	NUM
ejpam-6392	352	29	,	,	PUNCT
ejpam-6392	352	30	33	33	NUM
ejpam-6392	352	31	)	)	PUNCT
ejpam-6392	352	32	)	)	PUNCT
ejpam-6392	352	33	,	,	PUNCT
ejpam-6392	353	1	g	g	PROPN
ejpam-6392	353	2	i	i	PRON
ejpam-6392	353	3	(	(	PUNCT
ejpam-6392	353	4	(	(	PUNCT
ejpam-6392	353	5	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	353	6	)	)	PUNCT
ejpam-6392	353	7	)	)	PUNCT
ejpam-6392	353	8	(	(	PUNCT
ejpam-6392	353	9	e3	e3	NOUN
ejpam-6392	353	10	,	,	PUNCT
ejpam-6392	353	11	33	33	NUM
ejpam-6392	353	12	)	)	PUNCT
ejpam-6392	353	13	}	}	PUNCT
ejpam-6392	353	14	.	.	PUNCT
ejpam-6392	354	1	similarly	similarly	ADV
ejpam-6392	354	2	for	for	ADP
ejpam-6392	354	3	gf	gf	PROPN
ejpam-6392	354	4	(	(	PUNCT
ejpam-6392	354	5	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	354	6	,	,	PUNCT
ejpam-6392	354	7	31	31	NUM
ejpam-6392	354	8	)	)	PUNCT
ejpam-6392	354	9	=	=	SYM
ejpam-6392	354	10	max	max	PROPN
ejpam-6392	354	11	{	{	PUNCT
ejpam-6392	354	12	gf	gf	X
ejpam-6392	354	13	(	(	PUNCT
ejpam-6392	354	14	g×h	g×h	PROPN
ejpam-6392	354	15	)	)	PUNCT
ejpam-6392	354	16	(	(	PUNCT
ejpam-6392	354	17	(	(	PUNCT
ejpam-6392	354	18	e1	e1	NOUN
ejpam-6392	354	19	,	,	PUNCT
ejpam-6392	354	20	31	31	NUM
ejpam-6392	354	21	)	)	PUNCT
ejpam-6392	354	22	•	•	NOUN
ejpam-6392	354	23	(	(	PUNCT
ejpam-6392	354	24	e2	e2	PROPN
ejpam-6392	354	25	,	,	PUNCT
ejpam-6392	354	26	32	32	NUM
ejpam-6392	354	27	)	)	PUNCT
ejpam-6392	354	28	•	•	NOUN
ejpam-6392	354	29	(	(	PUNCT
ejpam-6392	354	30	e3	e3	NOUN
ejpam-6392	354	31	,	,	PUNCT
ejpam-6392	354	32	33	33	NUM
ejpam-6392	354	33	)	)	PUNCT
ejpam-6392	354	34	)	)	PUNCT
ejpam-6392	354	35	,	,	PUNCT
ejpam-6392	354	36	gf	gf	X
ejpam-6392	354	37	(	(	PUNCT
ejpam-6392	354	38	g×h)(e3	g×h)(e3	NOUN
ejpam-6392	354	39	,	,	PUNCT
ejpam-6392	354	40	33	33	NUM
ejpam-6392	354	41	)	)	PUNCT
ejpam-6392	354	42	}	}	PUNCT
ejpam-6392	354	43	,	,	PUNCT
ejpam-6392	354	44	gf	gf	X
ejpam-6392	354	45	(	(	PUNCT
ejpam-6392	354	46	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	354	47	,	,	PUNCT
ejpam-6392	354	48	31	31	NUM
ejpam-6392	354	49	)	)	PUNCT
ejpam-6392	354	50	=	=	SYM
ejpam-6392	354	51	max	max	PROPN
ejpam-6392	354	52	{	{	PUNCT
ejpam-6392	354	53	gf	gf	X
ejpam-6392	354	54	(	(	PUNCT
ejpam-6392	354	55	i×j	i×j	ADV
ejpam-6392	354	56	)	)	PUNCT
ejpam-6392	354	57	(	(	PUNCT
ejpam-6392	354	58	(	(	PUNCT
ejpam-6392	354	59	e1	e1	NOUN
ejpam-6392	354	60	,	,	PUNCT
ejpam-6392	354	61	31	31	NUM
ejpam-6392	354	62	)	)	PUNCT
ejpam-6392	354	63	•	•	NOUN
ejpam-6392	354	64	(	(	PUNCT
ejpam-6392	354	65	e2	e2	PROPN
ejpam-6392	354	66	,	,	PUNCT
ejpam-6392	354	67	32	32	NUM
ejpam-6392	354	68	)	)	PUNCT
ejpam-6392	354	69	•	•	NOUN
ejpam-6392	354	70	(	(	PUNCT
ejpam-6392	354	71	e3	e3	NOUN
ejpam-6392	354	72	,	,	PUNCT
ejpam-6392	354	73	33	33	NUM
ejpam-6392	354	74	)	)	PUNCT
ejpam-6392	354	75	)	)	PUNCT
ejpam-6392	354	76	,	,	PUNCT
ejpam-6392	354	77	gf	gf	PROPN
ejpam-6392	354	78	(	(	PUNCT
ejpam-6392	354	79	i×j)(e3	i×j)(e3	PROPN
ejpam-6392	354	80	,	,	PUNCT
ejpam-6392	354	81	33	33	NUM
ejpam-6392	354	82	)	)	PUNCT
ejpam-6392	354	83	}	}	PUNCT
ejpam-6392	354	84	,	,	PUNCT
ejpam-6392	354	85	m.	m.	NOUN
ejpam-6392	354	86	remala	remala	NOUN
ejpam-6392	354	87	,	,	PUNCT
ejpam-6392	354	88	e.	e.	PROPN
ejpam-6392	354	89	tamma	tamma	PROPN
ejpam-6392	354	90	,	,	PUNCT
ejpam-6392	354	91	y.	y.	PROPN
ejpam-6392	354	92	bhargavi	bhargavi	PROPN
ejpam-6392	354	93	/	/	SYM
ejpam-6392	354	94	eur	eur	PROPN
ejpam-6392	354	95	.	.	PUNCT
ejpam-6392	355	1	j.	j.	PROPN
ejpam-6392	355	2	pure	pure	PROPN
ejpam-6392	355	3	appl	appl	PROPN
ejpam-6392	355	4	.	.	PROPN
ejpam-6392	355	5	math	math	PROPN
ejpam-6392	355	6	,	,	PUNCT
ejpam-6392	355	7	18	18	NUM
ejpam-6392	355	8	(	(	PUNCT
ejpam-6392	355	9	4	4	NUM
ejpam-6392	355	10	)	)	PUNCT
ejpam-6392	355	11	(	(	PUNCT
ejpam-6392	355	12	2025	2025	NUM
ejpam-6392	355	13	)	)	PUNCT
ejpam-6392	355	14	,	,	PUNCT
ejpam-6392	355	15	6392	6392	NUM
ejpam-6392	355	16	16	16	NUM
ejpam-6392	355	17	of	of	ADP
ejpam-6392	355	18	20	20	NUM
ejpam-6392	355	19	gf	gf	NOUN
ejpam-6392	355	20	(	(	PUNCT
ejpam-6392	355	21	g×h)(e1	g×h)(e1	PROPN
ejpam-6392	355	22	,	,	PUNCT
ejpam-6392	355	23	31	31	NUM
ejpam-6392	355	24	)	)	PUNCT
ejpam-6392	355	25	,	,	PUNCT
ejpam-6392	355	26	gf	gf	X
ejpam-6392	355	27	(	(	PUNCT
ejpam-6392	355	28	i×j)(e1	i×j)(e1	NOUN
ejpam-6392	355	29	,	,	PUNCT
ejpam-6392	355	30	31	31	NUM
ejpam-6392	355	31	)	)	PUNCT
ejpam-6392	355	32	≤	≤	NUM
ejpam-6392	355	33	max	max	PROPN
ejpam-6392	355	34	{	{	PUNCT
ejpam-6392	355	35	max	max	PROPN
ejpam-6392	355	36	{	{	PUNCT
ejpam-6392	355	37	gf	gf	PROPN
ejpam-6392	355	38	(	(	PUNCT
ejpam-6392	355	39	g×h)((e1	g×h)((e1	PROPN
ejpam-6392	355	40	,	,	PUNCT
ejpam-6392	355	41	31	31	NUM
ejpam-6392	355	42	)	)	PUNCT
ejpam-6392	355	43	•	•	NOUN
ejpam-6392	355	44	(	(	PUNCT
ejpam-6392	355	45	e2	e2	PROPN
ejpam-6392	355	46	,	,	PUNCT
ejpam-6392	355	47	32	32	NUM
ejpam-6392	355	48	)	)	PUNCT
ejpam-6392	355	49	•	•	NOUN
ejpam-6392	355	50	(	(	PUNCT
ejpam-6392	355	51	e3	e3	NOUN
ejpam-6392	355	52	,	,	PUNCT
ejpam-6392	355	53	33	33	NUM
ejpam-6392	355	54	)	)	PUNCT
ejpam-6392	355	55	)	)	PUNCT
ejpam-6392	355	56	,	,	PUNCT
ejpam-6392	355	57	gf	gf	X
ejpam-6392	355	58	(	(	PUNCT
ejpam-6392	355	59	g×h)(e3	g×h)(e3	NOUN
ejpam-6392	355	60	,	,	PUNCT
ejpam-6392	355	61	33	33	NUM
ejpam-6392	355	62	)	)	PUNCT
ejpam-6392	355	63	}	}	PUNCT
ejpam-6392	355	64	,	,	PUNCT
ejpam-6392	355	65	max	max	PROPN
ejpam-6392	355	66	{	{	PUNCT
ejpam-6392	355	67	gf	gf	X
ejpam-6392	355	68	(	(	PUNCT
ejpam-6392	355	69	i×j)((e1	i×j)((e1	PROPN
ejpam-6392	355	70	,	,	PUNCT
ejpam-6392	355	71	31	31	NUM
ejpam-6392	355	72	)	)	PUNCT
ejpam-6392	355	73	•	•	NOUN
ejpam-6392	355	74	(	(	PUNCT
ejpam-6392	355	75	e2	e2	PROPN
ejpam-6392	355	76	,	,	PUNCT
ejpam-6392	355	77	32	32	NUM
ejpam-6392	355	78	)	)	PUNCT
ejpam-6392	355	79	•	•	NOUN
ejpam-6392	355	80	(	(	PUNCT
ejpam-6392	355	81	e3	e3	NOUN
ejpam-6392	355	82	,	,	PUNCT
ejpam-6392	355	83	33	33	NUM
ejpam-6392	355	84	)	)	PUNCT
ejpam-6392	355	85	)	)	PUNCT
ejpam-6392	355	86	,	,	PUNCT
ejpam-6392	355	87	gf	gf	PROPN
ejpam-6392	355	88	(	(	PUNCT
ejpam-6392	355	89	i×j)(e3	i×j)(e3	PROPN
ejpam-6392	355	90	,	,	PUNCT
ejpam-6392	355	91	33	33	NUM
ejpam-6392	355	92	)	)	PUNCT
ejpam-6392	355	93	}	}	PUNCT
ejpam-6392	355	94	}	}	PUNCT
ejpam-6392	355	95	≤	≤	NUM
ejpam-6392	355	96	max	max	PROPN
ejpam-6392	355	97	{	{	PUNCT
ejpam-6392	355	98	max	max	PROPN
ejpam-6392	355	99	{	{	PUNCT
ejpam-6392	355	100	gf	gf	PROPN
ejpam-6392	355	101	(	(	PUNCT
ejpam-6392	355	102	g×h)((e1	g×h)((e1	PROPN
ejpam-6392	355	103	,	,	PUNCT
ejpam-6392	355	104	31	31	NUM
ejpam-6392	355	105	)	)	PUNCT
ejpam-6392	355	106	•	•	NOUN
ejpam-6392	355	107	(	(	PUNCT
ejpam-6392	355	108	e2	e2	PROPN
ejpam-6392	355	109	,	,	PUNCT
ejpam-6392	355	110	32	32	NUM
ejpam-6392	355	111	)	)	PUNCT
ejpam-6392	355	112	•	•	NOUN
ejpam-6392	355	113	(	(	PUNCT
ejpam-6392	355	114	e3	e3	NOUN
ejpam-6392	355	115	,	,	PUNCT
ejpam-6392	355	116	33	33	NUM
ejpam-6392	355	117	)	)	PUNCT
ejpam-6392	355	118	)	)	PUNCT
ejpam-6392	355	119	,	,	PUNCT
ejpam-6392	355	120	gf	gf	X
ejpam-6392	355	121	(	(	PUNCT
ejpam-6392	355	122	i×j)((e1	i×j)((e1	PROPN
ejpam-6392	355	123	,	,	PUNCT
ejpam-6392	355	124	31	31	NUM
ejpam-6392	355	125	)	)	PUNCT
ejpam-6392	355	126	•	•	NOUN
ejpam-6392	355	127	(	(	PUNCT
ejpam-6392	355	128	e2	e2	PROPN
ejpam-6392	355	129	,	,	PUNCT
ejpam-6392	355	130	32	32	NUM
ejpam-6392	355	131	)	)	PUNCT
ejpam-6392	355	132	•	•	NOUN
ejpam-6392	355	133	(	(	PUNCT
ejpam-6392	355	134	e3	e3	NOUN
ejpam-6392	355	135	,	,	PUNCT
ejpam-6392	355	136	33	33	NUM
ejpam-6392	355	137	)	)	PUNCT
ejpam-6392	355	138	)	)	PUNCT
ejpam-6392	356	1	}	}	PUNCT
ejpam-6392	356	2	,	,	PUNCT
ejpam-6392	356	3	max	max	PROPN
ejpam-6392	356	4	{	{	PUNCT
ejpam-6392	356	5	gf	gf	PROPN
ejpam-6392	356	6	(	(	PUNCT
ejpam-6392	356	7	g×h)(e3	g×h)(e3	NOUN
ejpam-6392	356	8	,	,	PUNCT
ejpam-6392	356	9	33	33	NUM
ejpam-6392	356	10	)	)	PUNCT
ejpam-6392	356	11	,	,	PUNCT
ejpam-6392	356	12	gf	gf	PROPN
ejpam-6392	356	13	(	(	PUNCT
ejpam-6392	356	14	i×j)(e3	i×j)(e3	PROPN
ejpam-6392	356	15	,	,	PUNCT
ejpam-6392	356	16	33	33	NUM
ejpam-6392	356	17	)	)	PUNCT
ejpam-6392	356	18	}	}	PUNCT
ejpam-6392	356	19	}	}	PUNCT
ejpam-6392	356	20	.	.	PUNCT
ejpam-6392	357	1	g	g	PROPN
ejpam-6392	357	2	f	f	PROPN
ejpam-6392	357	3	(	(	PUNCT
ejpam-6392	357	4	(	(	PUNCT
ejpam-6392	357	5	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	357	6	)	)	PUNCT
ejpam-6392	357	7	)	)	PUNCT
ejpam-6392	357	8	(	(	PUNCT
ejpam-6392	357	9	e1	e1	NOUN
ejpam-6392	357	10	,	,	PUNCT
ejpam-6392	357	11	31	31	NUM
ejpam-6392	357	12	)	)	PUNCT
ejpam-6392	357	13	≤	≤	NOUN
ejpam-6392	357	14	{	{	PUNCT
ejpam-6392	357	15	g	g	PROPN
ejpam-6392	357	16	f	f	X
ejpam-6392	357	17	(	(	PUNCT
ejpam-6392	357	18	(	(	PUNCT
ejpam-6392	357	19	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	357	20	)	)	PUNCT
ejpam-6392	357	21	)	)	PUNCT
ejpam-6392	357	22	(	(	PUNCT
ejpam-6392	357	23	(	(	PUNCT
ejpam-6392	357	24	e1	e1	NOUN
ejpam-6392	357	25	,	,	PUNCT
ejpam-6392	357	26	31)•(e2	31)•(e2	NUM
ejpam-6392	357	27	,	,	PUNCT
ejpam-6392	357	28	32)•(e3	32)•(e3	NUM
ejpam-6392	357	29	,	,	PUNCT
ejpam-6392	357	30	33	33	NUM
ejpam-6392	357	31	)	)	PUNCT
ejpam-6392	357	32	)	)	PUNCT
ejpam-6392	357	33	,	,	PUNCT
ejpam-6392	357	34	g	g	PROPN
ejpam-6392	357	35	f	f	PROPN
ejpam-6392	357	36	(	(	PUNCT
ejpam-6392	357	37	(	(	PUNCT
ejpam-6392	357	38	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	357	39	)	)	PUNCT
ejpam-6392	357	40	)	)	PUNCT
ejpam-6392	357	41	(	(	PUNCT
ejpam-6392	357	42	e3	e3	NOUN
ejpam-6392	357	43	,	,	PUNCT
ejpam-6392	357	44	33	33	NUM
ejpam-6392	357	45	)	)	PUNCT
ejpam-6392	357	46	}	}	PUNCT
ejpam-6392	357	47	.	.	PUNCT
ejpam-6392	358	1	this	this	PRON
ejpam-6392	358	2	completes	complete	VERB
ejpam-6392	358	3	the	the	DET
ejpam-6392	358	4	required	required	ADJ
ejpam-6392	358	5	formulation	formulation	NOUN
ejpam-6392	358	6	for	for	ADP
ejpam-6392	358	7	(	(	PUNCT
ejpam-6392	358	8	g×h)∩(i×j	g×h)∩(i×j	NOUN
ejpam-6392	358	9	)	)	PUNCT
ejpam-6392	358	10	=	=	SYM
ejpam-6392	359	1	(	(	PUNCT
ejpam-6392	359	2	gt	gt	INTJ
ejpam-6392	359	3	(	(	PUNCT
ejpam-6392	359	4	g×h)∩gt	g×h)∩gt	X
ejpam-6392	359	5	(	(	PUNCT
ejpam-6392	359	6	i×j	i×j	ADJ
ejpam-6392	359	7	)	)	PUNCT
ejpam-6392	359	8	,	,	PUNCT
ejpam-6392	359	9	gi(g×h)∩	gi(g×h)∩	PROPN
ejpam-6392	359	10	gi(i×j	gi(i×j	PROPN
ejpam-6392	359	11	)	)	PUNCT
ejpam-6392	359	12	,	,	PUNCT
ejpam-6392	359	13	gf	gf	X
ejpam-6392	359	14	(	(	PUNCT
ejpam-6392	359	15	g×h	g×h	NOUN
ejpam-6392	359	16	)	)	PUNCT
ejpam-6392	359	17	∩	∩	NOUN
ejpam-6392	359	18	gf	gf	X
ejpam-6392	359	19	(	(	PUNCT
ejpam-6392	359	20	i×j	i×j	ADJ
ejpam-6392	359	21	)	)	PUNCT
ejpam-6392	359	22	)	)	PUNCT
ejpam-6392	359	23	.	.	PUNCT
ejpam-6392	360	1	6	6	X
ejpam-6392	360	2	.	.	X
ejpam-6392	360	3	application	application	NOUN
ejpam-6392	360	4	of	of	ADP
ejpam-6392	360	5	bi	bi	NOUN
ejpam-6392	360	6	-	-	NOUN
ejpam-6392	360	7	ideal	ideal	NOUN
ejpam-6392	360	8	in	in	ADP
ejpam-6392	360	9	ink	ink	NOUN
ejpam-6392	360	10	-	-	PUNCT
ejpam-6392	360	11	algebra	algebra	NOUN
ejpam-6392	360	12	flowchart	flowchart	NOUN
ejpam-6392	360	13	for	for	ADP
ejpam-6392	360	14	neutrosophic	neutrosophic	ADJ
ejpam-6392	360	15	bi	bi	NOUN
ejpam-6392	360	16	-	-	NOUN
ejpam-6392	360	17	ideal	ideal	NOUN
ejpam-6392	360	18	in	in	ADP
ejpam-6392	360	19	ink	ink	NOUN
ejpam-6392	360	20	-	-	PUNCT
ejpam-6392	360	21	algebra	algebra	NOUN
ejpam-6392	360	22	figure	figure	NOUN
ejpam-6392	360	23	1	1	NUM
ejpam-6392	360	24	:	:	PUNCT
ejpam-6392	360	25	flowchart	flowchart	NOUN
ejpam-6392	360	26	for	for	ADP
ejpam-6392	360	27	neutrosophic	neutrosophic	ADJ
ejpam-6392	360	28	bi	bi	NOUN
ejpam-6392	360	29	-	-	NOUN
ejpam-6392	360	30	ideal	ideal	NOUN
ejpam-6392	360	31	in	in	ADP
ejpam-6392	360	32	ink	ink	NOUN
ejpam-6392	360	33	-	-	PUNCT
ejpam-6392	360	34	algebra	algebra	NOUN
ejpam-6392	360	35	7	7	NUM
ejpam-6392	360	36	.	.	NOUN
ejpam-6392	360	37	selection	selection	NOUN
ejpam-6392	360	38	of	of	ADP
ejpam-6392	360	39	research	research	NOUN
ejpam-6392	360	40	guide	guide	NOUN
ejpam-6392	360	41	/	/	SYM
ejpam-6392	360	42	supervisor	supervisor	NOUN
ejpam-6392	360	43	by	by	ADP
ejpam-6392	360	44	using	use	VERB
ejpam-6392	360	45	neutrosophic	neutrosophic	ADJ
ejpam-6392	360	46	bi	bi	NOUN
ejpam-6392	360	47	-	-	NOUN
ejpam-6392	360	48	ideals	ideal	NOUN
ejpam-6392	360	49	in	in	ADP
ejpam-6392	360	50	ink	ink	NOUN
ejpam-6392	360	51	-	-	PUNCT
ejpam-6392	360	52	algebra	algebra	NOUN
ejpam-6392	360	53	in	in	ADP
ejpam-6392	360	54	academic	academic	ADJ
ejpam-6392	360	55	research	research	NOUN
ejpam-6392	360	56	,	,	PUNCT
ejpam-6392	360	57	selecting	select	VERB
ejpam-6392	360	58	the	the	DET
ejpam-6392	360	59	right	right	ADJ
ejpam-6392	360	60	guide	guide	NOUN
ejpam-6392	360	61	is	be	AUX
ejpam-6392	360	62	necessary	necessary	ADJ
ejpam-6392	360	63	a	a	DET
ejpam-6392	360	64	critical	critical	ADJ
ejpam-6392	360	65	decision	decision	NOUN
ejpam-6392	360	66	that	that	PRON
ejpam-6392	360	67	can	can	AUX
ejpam-6392	360	68	be	be	AUX
ejpam-6392	360	69	effect	effect	NOUN
ejpam-6392	360	70	and	and	CCONJ
ejpam-6392	360	71	shape	shape	NOUN
ejpam-6392	360	72	scholars	scholar	NOUN
ejpam-6392	360	73	entire	entire	ADJ
ejpam-6392	360	74	research	research	NOUN
ejpam-6392	360	75	experience	experience	NOUN
ejpam-6392	360	76	.	.	PUNCT
ejpam-6392	361	1	the	the	DET
ejpam-6392	361	2	choice	choice	NOUN
ejpam-6392	361	3	or	or	CCONJ
ejpam-6392	361	4	consideration	consideration	NOUN
ejpam-6392	361	5	m.	m.	NOUN
ejpam-6392	361	6	remala	remala	NOUN
ejpam-6392	361	7	,	,	PUNCT
ejpam-6392	361	8	e.	e.	PROPN
ejpam-6392	361	9	tamma	tamma	PROPN
ejpam-6392	361	10	,	,	PUNCT
ejpam-6392	361	11	y.	y.	PROPN
ejpam-6392	361	12	bhargavi	bhargavi	PROPN
ejpam-6392	361	13	/	/	SYM
ejpam-6392	361	14	eur	eur	PROPN
ejpam-6392	361	15	.	.	PUNCT
ejpam-6392	362	1	j.	j.	PROPN
ejpam-6392	362	2	pure	pure	PROPN
ejpam-6392	362	3	appl	appl	PROPN
ejpam-6392	362	4	.	.	PROPN
ejpam-6392	362	5	math	math	PROPN
ejpam-6392	362	6	,	,	PUNCT
ejpam-6392	362	7	18	18	NUM
ejpam-6392	362	8	(	(	PUNCT
ejpam-6392	362	9	4	4	NUM
ejpam-6392	362	10	)	)	PUNCT
ejpam-6392	362	11	(	(	PUNCT
ejpam-6392	362	12	2025	2025	NUM
ejpam-6392	362	13	)	)	PUNCT
ejpam-6392	362	14	,	,	PUNCT
ejpam-6392	362	15	6392	6392	NUM
ejpam-6392	362	16	17	17	NUM
ejpam-6392	362	17	of	of	ADP
ejpam-6392	362	18	20	20	NUM
ejpam-6392	362	19	of	of	ADP
ejpam-6392	362	20	selection	selection	NOUN
ejpam-6392	362	21	of	of	ADP
ejpam-6392	362	22	guide	guide	NOUN
ejpam-6392	362	23	depends	depend	VERB
ejpam-6392	362	24	on	on	ADP
ejpam-6392	362	25	multiple	multiple	ADJ
ejpam-6392	362	26	parameters	parameter	NOUN
ejpam-6392	362	27	.	.	PUNCT
ejpam-6392	363	1	to	to	PART
ejpam-6392	363	2	model	model	VERB
ejpam-6392	363	3	this	this	DET
ejpam-6392	363	4	selection	selection	NOUN
ejpam-6392	363	5	process	process	NOUN
ejpam-6392	363	6	logically	logically	ADV
ejpam-6392	363	7	,	,	PUNCT
ejpam-6392	363	8	we	we	PRON
ejpam-6392	363	9	apply	apply	VERB
ejpam-6392	363	10	the	the	DET
ejpam-6392	363	11	concept	concept	NOUN
ejpam-6392	363	12	of	of	ADP
ejpam-6392	363	13	neutrosophic	neutrosophic	ADJ
ejpam-6392	363	14	bi	bi	NOUN
ejpam-6392	363	15	-	-	NOUN
ejpam-6392	363	16	ideal	ideal	NOUN
ejpam-6392	363	17	in	in	ADP
ejpam-6392	363	18	ink	ink	NOUN
ejpam-6392	363	19	-	-	PUNCT
ejpam-6392	363	20	algebra	algebra	NOUN
ejpam-6392	363	21	,	,	PUNCT
ejpam-6392	363	22	which	which	PRON
ejpam-6392	363	23	allows	allow	VERB
ejpam-6392	363	24	us	we	PRON
ejpam-6392	363	25	to	to	PART
ejpam-6392	363	26	evaluate	evaluate	VERB
ejpam-6392	363	27	whether	whether	SCONJ
ejpam-6392	363	28	removing	remove	VERB
ejpam-6392	363	29	a	a	DET
ejpam-6392	363	30	less	less	ADV
ejpam-6392	363	31	important	important	ADJ
ejpam-6392	363	32	factor	factor	NOUN
ejpam-6392	363	33	still	still	ADV
ejpam-6392	363	34	results	result	VERB
ejpam-6392	363	35	in	in	ADP
ejpam-6392	363	36	a	a	DET
ejpam-6392	363	37	valid	valid	ADJ
ejpam-6392	363	38	and	and	CCONJ
ejpam-6392	363	39	trustworthy	trustworthy	ADJ
ejpam-6392	363	40	decision	decision	NOUN
ejpam-6392	363	41	.	.	PUNCT
ejpam-6392	364	1	we	we	PRON
ejpam-6392	364	2	define	define	VERB
ejpam-6392	364	3	a	a	DET
ejpam-6392	364	4	set	set	NOUN
ejpam-6392	364	5	of	of	ADP
ejpam-6392	364	6	elements	element	NOUN
ejpam-6392	364	7	in	in	ADP
ejpam-6392	364	8	our	our	PRON
ejpam-6392	364	9	ink	ink	NOUN
ejpam-6392	364	10	-	-	PUNCT
ejpam-6392	364	11	algebra	algebra	NOUN
ejpam-6392	364	12	¨̈u={0	¨̈u={0	PROPN
ejpam-6392	364	13	,	,	PUNCT
ejpam-6392	364	14	a	a	PRON
ejpam-6392	364	15	,	,	PUNCT
ejpam-6392	364	16	g	g	PROPN
ejpam-6392	364	17	,	,	PUNCT
ejpam-6392	364	18	c	c	NOUN
ejpam-6392	364	19	}	}	PUNCT
ejpam-6392	364	20	where	where	SCONJ
ejpam-6392	364	21	each	each	PRON
ejpam-6392	364	22	and	and	CCONJ
ejpam-6392	364	23	every	every	DET
ejpam-6392	364	24	parameter	parameter	NOUN
ejpam-6392	364	25	represents	represent	VERB
ejpam-6392	364	26	guide	guide	NOUN
ejpam-6392	364	27	’s	’s	PART
ejpam-6392	364	28	selection	selection	NOUN
ejpam-6392	364	29	.	.	PUNCT
ejpam-6392	365	1	here	here	ADV
ejpam-6392	365	2	,	,	PUNCT
ejpam-6392	365	3	a=	a=	VERB
ejpam-6392	365	4	alignment	alignment	NOUN
ejpam-6392	365	5	/	/	SYM
ejpam-6392	365	6	p	p	NOUN
ejpam-6392	365	7	=	=	NOUN
ejpam-6392	365	8	proposal	proposal	NOUN
ejpam-6392	365	9	idea	idea	NOUN
ejpam-6392	365	10	,	,	PUNCT
ejpam-6392	365	11	g	g	NOUN
ejpam-6392	365	12	=	=	SYM
ejpam-6392	365	13	guide	guide	NOUN
ejpam-6392	365	14	’s	’s	ADV
ejpam-6392	365	15	academic	academic	ADJ
ejpam-6392	365	16	and	and	CCONJ
ejpam-6392	365	17	research	research	NOUN
ejpam-6392	365	18	experience	experience	NOUN
ejpam-6392	365	19	,	,	PUNCT
ejpam-6392	365	20	c	c	NOUN
ejpam-6392	365	21	=	=	NOUN
ejpam-6392	365	22	availability	availability	NOUN
ejpam-6392	365	23	of	of	ADP
ejpam-6392	365	24	communication	communication	NOUN
ejpam-6392	365	25	with	with	ADP
ejpam-6392	365	26	guide	guide	NOUN
ejpam-6392	365	27	.	.	PUNCT
ejpam-6392	366	1	the	the	DET
ejpam-6392	366	2	element	element	NOUN
ejpam-6392	366	3	“	"	PUNCT
ejpam-6392	366	4	0	0	NUM
ejpam-6392	366	5	”	"	PUNCT
ejpam-6392	366	6	represents	represent	VERB
ejpam-6392	366	7	an	an	DET
ejpam-6392	366	8	ideal	ideal	ADJ
ejpam-6392	366	9	guide	guide	NOUN
ejpam-6392	366	10	selection	selection	NOUN
ejpam-6392	366	11	.	.	PUNCT
ejpam-6392	367	1	in	in	ADP
ejpam-6392	367	2	this	this	DET
ejpam-6392	367	3	context	context	NOUN
ejpam-6392	367	4	,	,	PUNCT
ejpam-6392	367	5	the	the	DET
ejpam-6392	367	6	term	term	NOUN
ejpam-6392	367	7	e1	e1	NOUN
ejpam-6392	367	8	•31	•31	NOUN
ejpam-6392	367	9	interpreted	interpret	VERB
ejpam-6392	367	10	as	as	SCONJ
ejpam-6392	367	11	the	the	DET
ejpam-6392	367	12	how	how	SCONJ
ejpam-6392	367	13	much	much	ADJ
ejpam-6392	367	14	mismatch	mismatch	NOUN
ejpam-6392	367	15	is	be	AUX
ejpam-6392	367	16	still	still	ADV
ejpam-6392	367	17	there	there	ADV
ejpam-6392	367	18	when	when	SCONJ
ejpam-6392	367	19	choosing	choose	VERB
ejpam-6392	367	20	a	a	DET
ejpam-6392	367	21	guide	guide	NOUN
ejpam-6392	367	22	based	base	VERB
ejpam-6392	367	23	on	on	ADP
ejpam-6392	367	24	those	those	DET
ejpam-6392	367	25	two	two	NUM
ejpam-6392	367	26	factors	factor	NOUN
ejpam-6392	367	27	in	in	ADP
ejpam-6392	367	28	that	that	DET
ejpam-6392	367	29	order	order	NOUN
ejpam-6392	367	30	.	.	PUNCT
ejpam-6392	368	1	this	this	PRON
ejpam-6392	368	2	is	be	AUX
ejpam-6392	368	3	taken	take	VERB
ejpam-6392	368	4	for	for	ADP
ejpam-6392	368	5	a	a	DET
ejpam-6392	368	6	better	well	ADJ
ejpam-6392	368	7	experience	experience	NOUN
ejpam-6392	368	8	,	,	PUNCT
ejpam-6392	368	9	a	a	DET
ejpam-6392	368	10	mismatch	mismatch	NOUN
ejpam-6392	368	11	in	in	ADP
ejpam-6392	368	12	any	any	PRON
ejpam-6392	368	13	of	of	ADP
ejpam-6392	368	14	them	they	PRON
ejpam-6392	368	15	may	may	AUX
ejpam-6392	368	16	not	not	PART
ejpam-6392	368	17	invalidate	invalidate	VERB
ejpam-6392	368	18	the	the	DET
ejpam-6392	368	19	overall	overall	ADJ
ejpam-6392	368	20	decision	decision	NOUN
ejpam-6392	368	21	if	if	SCONJ
ejpam-6392	368	22	the	the	DET
ejpam-6392	368	23	core	core	NOUN
ejpam-6392	368	24	match	match	NOUN
ejpam-6392	368	25	is	be	AUX
ejpam-6392	368	26	strong	strong	ADJ
ejpam-6392	368	27	.	.	PUNCT
ejpam-6392	369	1	to	to	PART
ejpam-6392	369	2	evaluate	evaluate	VERB
ejpam-6392	369	3	this	this	DET
ejpam-6392	369	4	system	system	NOUN
ejpam-6392	369	5	,	,	PUNCT
ejpam-6392	369	6	we	we	PRON
ejpam-6392	369	7	construct	construct	VERB
ejpam-6392	369	8	a	a	DET
ejpam-6392	369	9	cayley	cayley	ADJ
ejpam-6392	369	10	table	table	NOUN
ejpam-6392	369	11	of	of	ADP
ejpam-6392	369	12	ink	ink	NOUN
ejpam-6392	369	13	-	-	PUNCT
ejpam-6392	369	14	algebra	algebra	NOUN
ejpam-6392	369	15	such	such	ADJ
ejpam-6392	369	16	as	as	ADP
ejpam-6392	369	17	associativity	associativity	NOUN
ejpam-6392	369	18	–	–	PUNCT
ejpam-6392	369	19	like	like	ADP
ejpam-6392	369	20	behaviour	behaviour	NOUN
ejpam-6392	369	21	,	,	PUNCT
ejpam-6392	369	22	and	and	CCONJ
ejpam-6392	369	23	conditions	condition	NOUN
ejpam-6392	369	24	of	of	ADP
ejpam-6392	369	25	ink	ink	NOUN
ejpam-6392	369	26	-	-	PUNCT
ejpam-6392	369	27	algebras	algebras	PROPN
ejpam-6392	369	28	also	also	ADV
ejpam-6392	369	29	we	we	PRON
ejpam-6392	369	30	have	have	VERB
ejpam-6392	369	31	to	to	PART
ejpam-6392	369	32	define	define	VERB
ejpam-6392	369	33	membership	membership	NOUN
ejpam-6392	369	34	values	value	NOUN
ejpam-6392	369	35	for	for	ADP
ejpam-6392	369	36	each	each	DET
ejpam-6392	369	37	parameter	parameter	NOUN
ejpam-6392	369	38	.	.	PUNCT
ejpam-6392	370	1	table	table	NOUN
ejpam-6392	370	2	:	:	PUNCT
ejpam-6392	370	3	1	1	NUM
ejpam-6392	370	4	cayley	cayley	ADJ
ejpam-6392	370	5	table	table	NOUN
ejpam-6392	370	6	on	on	ADP
ejpam-6392	370	7	¨̈u	¨̈u	NOUN
ejpam-6392	370	8	•	•	NOUN
ejpam-6392	370	9	0	0	NUM
ejpam-6392	370	10	a	a	DET
ejpam-6392	370	11	g	g	NOUN
ejpam-6392	370	12	c	c	NOUN
ejpam-6392	370	13	0	0	NUM
ejpam-6392	370	14	0	0	NUM
ejpam-6392	371	1	a	a	DET
ejpam-6392	371	2	g	g	NOUN
ejpam-6392	371	3	c	c	PROPN
ejpam-6392	371	4	a	a	DET
ejpam-6392	371	5	a	a	DET
ejpam-6392	371	6	0	0	NUM
ejpam-6392	371	7	c	c	NOUN
ejpam-6392	371	8	g	g	NOUN
ejpam-6392	371	9	g	g	PROPN
ejpam-6392	371	10	g	g	PROPN
ejpam-6392	371	11	c	c	NOUN
ejpam-6392	371	12	0	0	PUNCT
ejpam-6392	372	1	a	a	DET
ejpam-6392	372	2	c	c	NOUN
ejpam-6392	372	3	c	c	NOUN
ejpam-6392	372	4	g	g	NOUN
ejpam-6392	372	5	a	a	DET
ejpam-6392	372	6	0	0	NUM
ejpam-6392	372	7	table	table	NOUN
ejpam-6392	372	8	:	:	PUNCT
ejpam-6392	372	9	2	2	NUM
ejpam-6392	372	10	neutrosophic	neutrosophic	ADJ
ejpam-6392	372	11	membership	membership	NOUN
ejpam-6392	372	12	degrees	degree	VERB
ejpam-6392	372	13	•	•	ADP
ejpam-6392	372	14	0	0	NUM
ejpam-6392	373	1	a	a	DET
ejpam-6392	373	2	g	g	PROPN
ejpam-6392	373	3	c	c	PROPN
ejpam-6392	373	4	gt	gt	PROPN
ejpam-6392	373	5	1.0	1.0	NUM
ejpam-6392	373	6	0.9	0.9	NUM
ejpam-6392	373	7	0.9	0.9	NUM
ejpam-6392	373	8	0.6	0.6	NUM
ejpam-6392	373	9	gi	gi	NOUN
ejpam-6392	373	10	0.0	0.0	NUM
ejpam-6392	373	11	0.2	0.2	NUM
ejpam-6392	373	12	0.5	0.5	NUM
ejpam-6392	373	13	0.2	0.2	NUM
ejpam-6392	373	14	gf	gf	NOUN
ejpam-6392	373	15	0.0	0.0	NUM
ejpam-6392	373	16	0.3	0.3	NUM
ejpam-6392	373	17	0.1	0.1	NUM
ejpam-6392	373	18	0.4	0.4	NUM
ejpam-6392	373	19	{	{	PUNCT
ejpam-6392	373	20	if	if	SCONJ
ejpam-6392	373	21	e1	e1	NOUN
ejpam-6392	373	22	•	•	NOUN
ejpam-6392	373	23	31	31	NUM
ejpam-6392	373	24	•	•	NOUN
ejpam-6392	373	25	ä1	ä1	NOUN
ejpam-6392	373	26	=	=	PUNCT
ejpam-6392	373	27	e1	e1	VERB
ejpam-6392	373	28	•	•	NOUN
ejpam-6392	373	29	31	31	NUM
ejpam-6392	373	30	,	,	PUNCT
ejpam-6392	373	31	and	and	CCONJ
ejpam-6392	373	32	one	one	NUM
ejpam-6392	373	33	factor	factor	NOUN
ejpam-6392	373	34	(	(	PUNCT
ejpam-6392	373	35	eg	eg	NOUN
ejpam-6392	373	36	=	=	SYM
ejpam-6392	373	37	ä1	ä1	NOUN
ejpam-6392	373	38	)	)	PUNCT
ejpam-6392	373	39	is	be	AUX
ejpam-6392	373	40	trusted	trust	VERB
ejpam-6392	373	41	,	,	PUNCT
ejpam-6392	373	42	then	then	ADV
ejpam-6392	373	43	does	do	AUX
ejpam-6392	373	44	the	the	DET
ejpam-6392	373	45	core	core	NOUN
ejpam-6392	373	46	result	result	NOUN
ejpam-6392	373	47	e1	e1	NOUN
ejpam-6392	373	48	•	•	NUM
ejpam-6392	373	49	31	31	NUM
ejpam-6392	373	50	hold	hold	VERB
ejpam-6392	373	51	up	up	ADP
ejpam-6392	373	52	on	on	ADP
ejpam-6392	373	53	its	its	PRON
ejpam-6392	373	54	own	own	ADJ
ejpam-6392	373	55	.	.	PUNCT
ejpam-6392	373	56	}	}	PUNCT
ejpam-6392	374	1	if	if	SCONJ
ejpam-6392	374	2	the	the	DET
ejpam-6392	374	3	researcher	researcher	NOUN
ejpam-6392	374	4	consider	consider	VERB
ejpam-6392	374	5	the	the	DET
ejpam-6392	374	6	criteria	criterion	NOUN
ejpam-6392	374	7	like	like	ADP
ejpam-6392	374	8	guide	guide	VERB
ejpam-6392	374	9	academic	academic	PROPN
ejpam-6392	374	10	&	&	CCONJ
ejpam-6392	374	11	research	research	PROPN
ejpam-6392	374	12	experience	experience	NOUN
ejpam-6392	374	13	,	,	PUNCT
ejpam-6392	374	14	followed	follow	VERB
ejpam-6392	374	15	by	by	ADP
ejpam-6392	374	16	alignment	alignment	NOUN
ejpam-6392	374	17	/	/	SYM
ejpam-6392	374	18	proposal	proposal	NOUN
ejpam-6392	374	19	idea	idea	NOUN
ejpam-6392	374	20	and	and	CCONJ
ejpam-6392	374	21	then	then	ADV
ejpam-6392	374	22	communication	communication	NOUN
ejpam-6392	374	23	of	of	ADP
ejpam-6392	374	24	avialbility	avialbility	NOUN
ejpam-6392	374	25	of	of	ADP
ejpam-6392	374	26	guide	guide	NOUN
ejpam-6392	374	27	.	.	PUNCT
ejpam-6392	375	1	let	let	VERB
ejpam-6392	375	2	’s	’s	PRON
ejpam-6392	375	3	break	break	VERB
ejpam-6392	375	4	down	down	ADP
ejpam-6392	375	5	(	(	PUNCT
ejpam-6392	375	6	i	i	NOUN
ejpam-6392	375	7	)	)	PUNCT
ejpam-6392	375	8	gt	gt	PROPN
ejpam-6392	375	9	(	(	PUNCT
ejpam-6392	375	10	0	0	NUM
ejpam-6392	375	11	)	)	PUNCT
ejpam-6392	375	12	≥	≥	NOUN
ejpam-6392	376	1	gt	gt	INTJ
ejpam-6392	376	2	(	(	PUNCT
ejpam-6392	376	3	g	g	NOUN
ejpam-6392	376	4	)	)	PUNCT
ejpam-6392	376	5	⇒	⇒	VERB
ejpam-6392	376	6	1.0	1.0	NUM
ejpam-6392	376	7	>	>	SYM
ejpam-6392	376	8	0.9	0.9	NUM
ejpam-6392	376	9	,	,	PUNCT
ejpam-6392	376	10	(	(	PUNCT
ejpam-6392	376	11	ii	ii	NOUN
ejpam-6392	376	12	)	)	PUNCT
ejpam-6392	376	13	gi(0	gi(0	PROPN
ejpam-6392	376	14	)	)	PUNCT
ejpam-6392	376	15	≤	≤	NUM
ejpam-6392	376	16	gi(g	gi(g	NOUN
ejpam-6392	376	17	)	)	PUNCT
ejpam-6392	376	18	⇒	⇒	VERB
ejpam-6392	376	19	0.0	0.0	NUM
ejpam-6392	376	20	<	<	X
ejpam-6392	376	21	0.5	0.5	NUM
ejpam-6392	376	22	,	,	PUNCT
ejpam-6392	376	23	(	(	PUNCT
ejpam-6392	376	24	iii	iii	NOUN
ejpam-6392	376	25	)	)	PUNCT
ejpam-6392	376	26	gf	gf	NOUN
ejpam-6392	376	27	(	(	PUNCT
ejpam-6392	376	28	0	0	NUM
ejpam-6392	376	29	)	)	PUNCT
ejpam-6392	376	30	≤	≤	NOUN
ejpam-6392	376	31	gf	gf	X
ejpam-6392	376	32	(	(	PUNCT
ejpam-6392	376	33	g	g	NOUN
ejpam-6392	376	34	)	)	PUNCT
ejpam-6392	376	35	⇒	⇒	NOUN
ejpam-6392	376	36	0.0	0.0	NUM
ejpam-6392	376	37	<	<	X
ejpam-6392	376	38	0.1	0.1	NUM
ejpam-6392	376	39	.	.	PUNCT
ejpam-6392	377	1	m.	m.	NOUN
ejpam-6392	377	2	remala	remala	NOUN
ejpam-6392	377	3	,	,	PUNCT
ejpam-6392	377	4	e.	e.	PROPN
ejpam-6392	377	5	tamma	tamma	PROPN
ejpam-6392	377	6	,	,	PUNCT
ejpam-6392	377	7	y.	y.	PROPN
ejpam-6392	377	8	bhargavi	bhargavi	PROPN
ejpam-6392	377	9	/	/	SYM
ejpam-6392	377	10	eur	eur	PROPN
ejpam-6392	377	11	.	.	PUNCT
ejpam-6392	378	1	j.	j.	PROPN
ejpam-6392	378	2	pure	pure	PROPN
ejpam-6392	378	3	appl	appl	PROPN
ejpam-6392	378	4	.	.	PROPN
ejpam-6392	378	5	math	math	PROPN
ejpam-6392	378	6	,	,	PUNCT
ejpam-6392	378	7	18	18	NUM
ejpam-6392	378	8	(	(	PUNCT
ejpam-6392	378	9	4	4	NUM
ejpam-6392	378	10	)	)	PUNCT
ejpam-6392	378	11	(	(	PUNCT
ejpam-6392	378	12	2025	2025	NUM
ejpam-6392	378	13	)	)	PUNCT
ejpam-6392	378	14	,	,	PUNCT
ejpam-6392	378	15	6392	6392	NUM
ejpam-6392	378	16	18	18	NUM
ejpam-6392	378	17	of	of	ADP
ejpam-6392	378	18	20	20	NUM
ejpam-6392	378	19	(	(	PUNCT
ejpam-6392	378	20	iv	iv	X
ejpam-6392	378	21	)	)	PUNCT
ejpam-6392	378	22	gt	gt	PROPN
ejpam-6392	378	23	(	(	PUNCT
ejpam-6392	378	24	g	g	PROPN
ejpam-6392	378	25	•a	•a	PROPN
ejpam-6392	378	26	)	)	PUNCT
ejpam-6392	378	27	≥	≥	NOUN
ejpam-6392	378	28	min{gt	min{gt	X
ejpam-6392	378	29	(	(	PUNCT
ejpam-6392	378	30	g	g	PROPN
ejpam-6392	378	31	•a	•a	ADJ
ejpam-6392	378	32	•	•	ADP
ejpam-6392	378	33	c	c	NOUN
ejpam-6392	378	34	)	)	PUNCT
ejpam-6392	378	35	,	,	PUNCT
ejpam-6392	378	36	gt	gt	PROPN
ejpam-6392	378	37	(	(	PUNCT
ejpam-6392	378	38	c	c	NOUN
ejpam-6392	378	39	)	)	PUNCT
ejpam-6392	378	40	}	}	PUNCT
ejpam-6392	378	41	,	,	PUNCT
ejpam-6392	378	42	gt	gt	PROPN
ejpam-6392	378	43	(	(	PUNCT
ejpam-6392	378	44	g	g	NOUN
ejpam-6392	378	45	)	)	PUNCT
ejpam-6392	378	46	≥	≥	NOUN
ejpam-6392	378	47	min{gt	min{gt	X
ejpam-6392	378	48	(	(	PUNCT
ejpam-6392	378	49	g	g	NOUN
ejpam-6392	378	50	)	)	PUNCT
ejpam-6392	378	51	,	,	PUNCT
ejpam-6392	378	52	gt	gt	PROPN
ejpam-6392	378	53	(	(	PUNCT
ejpam-6392	378	54	c	c	NOUN
ejpam-6392	378	55	)	)	PUNCT
ejpam-6392	378	56	}	}	PUNCT
ejpam-6392	379	1	0.9	0.9	NUM
ejpam-6392	379	2	≥	≥	NOUN
ejpam-6392	379	3	min{0.9	min{0.9	PROPN
ejpam-6392	379	4	,	,	PUNCT
ejpam-6392	379	5	0.8	0.8	NUM
ejpam-6392	379	6	}	}	PUNCT
ejpam-6392	379	7	0.9	0.9	NUM
ejpam-6392	379	8	>	>	PUNCT
ejpam-6392	379	9	0.8	0.8	NUM
ejpam-6392	379	10	.	.	PUNCT
ejpam-6392	380	1	(	(	PUNCT
ejpam-6392	380	2	v	v	NOUN
ejpam-6392	380	3	)	)	PUNCT
ejpam-6392	380	4	gi(g	gi(g	NOUN
ejpam-6392	380	5	•a	•a	ADJ
ejpam-6392	380	6	)	)	PUNCT
ejpam-6392	380	7	≤	≤	NOUN
ejpam-6392	380	8	max{gi(g	max{gi(g	NOUN
ejpam-6392	380	9	•a	•a	ADJ
ejpam-6392	380	10	•	•	ADJ
ejpam-6392	380	11	c	c	NOUN
ejpam-6392	380	12	)	)	PUNCT
ejpam-6392	380	13	,	,	PUNCT
ejpam-6392	380	14	gi(c	gi(c	NOUN
ejpam-6392	380	15	)	)	PUNCT
ejpam-6392	380	16	}	}	PUNCT
ejpam-6392	380	17	,	,	PUNCT
ejpam-6392	380	18	gi(g	gi(g	NOUN
ejpam-6392	380	19	)	)	PUNCT
ejpam-6392	380	20	≤	≤	NUM
ejpam-6392	380	21	max{gi(g	max{gi(g	NOUN
ejpam-6392	380	22	)	)	PUNCT
ejpam-6392	380	23	,	,	PUNCT
ejpam-6392	380	24	gt	gt	PROPN
ejpam-6392	380	25	(	(	PUNCT
ejpam-6392	380	26	c	c	NOUN
ejpam-6392	380	27	)	)	PUNCT
ejpam-6392	380	28	}	}	PUNCT
ejpam-6392	380	29	0.5	0.5	NUM
ejpam-6392	380	30	≤	≤	NUM
ejpam-6392	380	31	max{0.5	max{0.5	PROPN
ejpam-6392	380	32	,	,	PUNCT
ejpam-6392	380	33	0.1	0.1	NUM
ejpam-6392	380	34	}	}	SYM
ejpam-6392	380	35	0.5	0.5	NUM
ejpam-6392	380	36	=	=	SYM
ejpam-6392	380	37	0.5	0.5	NUM
ejpam-6392	380	38	.	.	PUNCT
ejpam-6392	381	1	(	(	PUNCT
ejpam-6392	381	2	vi	vi	NOUN
ejpam-6392	381	3	)	)	PUNCT
ejpam-6392	381	4	gf	gf	NOUN
ejpam-6392	381	5	(	(	PUNCT
ejpam-6392	381	6	g	g	PROPN
ejpam-6392	381	7	•a	•a	PROPN
ejpam-6392	381	8	)	)	PUNCT
ejpam-6392	381	9	≤	≤	NOUN
ejpam-6392	381	10	max{gf	max{gf	PUNCT
ejpam-6392	381	11	(	(	PUNCT
ejpam-6392	381	12	g	g	PROPN
ejpam-6392	381	13	•a	•a	ADJ
ejpam-6392	381	14	•	•	ADP
ejpam-6392	381	15	c	c	NOUN
ejpam-6392	381	16	)	)	PUNCT
ejpam-6392	381	17	,	,	PUNCT
ejpam-6392	381	18	gf	gf	X
ejpam-6392	381	19	(	(	PUNCT
ejpam-6392	381	20	c	c	NOUN
ejpam-6392	381	21	)	)	PUNCT
ejpam-6392	381	22	}	}	PUNCT
ejpam-6392	381	23	,	,	PUNCT
ejpam-6392	381	24	gf	gf	X
ejpam-6392	381	25	(	(	PUNCT
ejpam-6392	381	26	g	g	NOUN
ejpam-6392	381	27	)	)	PUNCT
ejpam-6392	381	28	≤	≤	NOUN
ejpam-6392	381	29	max{gf	max{gf	PUNCT
ejpam-6392	381	30	(	(	PUNCT
ejpam-6392	381	31	g	g	NOUN
ejpam-6392	381	32	)	)	PUNCT
ejpam-6392	381	33	,	,	PUNCT
ejpam-6392	381	34	gf	gf	X
ejpam-6392	381	35	(	(	PUNCT
ejpam-6392	381	36	c	c	NOUN
ejpam-6392	381	37	)	)	PUNCT
ejpam-6392	381	38	}	}	PUNCT
ejpam-6392	381	39	0.1	0.1	NUM
ejpam-6392	381	40	≤	≤	NUM
ejpam-6392	381	41	max{0.1	max{0.1	PROPN
ejpam-6392	381	42	,	,	PUNCT
ejpam-6392	381	43	0.2	0.2	NUM
ejpam-6392	381	44	}	}	SYM
ejpam-6392	381	45	0.1	0.1	NUM
ejpam-6392	381	46	<	<	X
ejpam-6392	381	47	0.2	0.2	NUM
ejpam-6392	381	48	.	.	PUNCT
ejpam-6392	382	1	based	base	VERB
ejpam-6392	382	2	on	on	ADP
ejpam-6392	382	3	the	the	DET
ejpam-6392	382	4	result	result	NOUN
ejpam-6392	382	5	as	as	ADV
ejpam-6392	382	6	long	long	ADV
ejpam-6392	382	7	as	as	ADP
ejpam-6392	382	8	starting	start	VERB
ejpam-6392	382	9	with	with	ADP
ejpam-6392	382	10	guide	guide	NOUN
ejpam-6392	382	11	is	be	AUX
ejpam-6392	382	12	experienced	experience	VERB
ejpam-6392	382	13	.	.	PUNCT
ejpam-6392	383	1	then	then	ADV
ejpam-6392	383	2	,	,	PUNCT
ejpam-6392	383	3	it	it	PRON
ejpam-6392	383	4	is	be	AUX
ejpam-6392	383	5	sufficient	sufficient	ADJ
ejpam-6392	383	6	to	to	PART
ejpam-6392	383	7	make	make	VERB
ejpam-6392	383	8	reliable	reliable	ADJ
ejpam-6392	383	9	descion	descion	NOUN
ejpam-6392	383	10	.	.	PUNCT
ejpam-6392	384	1	this	this	PRON
ejpam-6392	384	2	allows	allow	VERB
ejpam-6392	384	3	us	we	PRON
ejpam-6392	384	4	to	to	PART
ejpam-6392	384	5	ignore	ignore	VERB
ejpam-6392	384	6	whether	whether	SCONJ
ejpam-6392	384	7	alignment(a	alignment(a	NOUN
ejpam-6392	384	8	)	)	PUNCT
ejpam-6392	384	9	is	be	AUX
ejpam-6392	384	10	perfect	perfect	ADJ
ejpam-6392	384	11	or	or	CCONJ
ejpam-6392	384	12	communcation(c	communcation(c	NOUN
ejpam-6392	384	13	)	)	PUNCT
ejpam-6392	384	14	is	be	AUX
ejpam-6392	384	15	ideal	ideal	ADJ
ejpam-6392	384	16	.	.	PUNCT
ejpam-6392	385	1	8	8	X
ejpam-6392	385	2	.	.	X
ejpam-6392	385	3	conclusion	conclusion	NOUN
ejpam-6392	385	4	our	our	PRON
ejpam-6392	385	5	article	article	NOUN
ejpam-6392	385	6	investigates	investigate	VERB
ejpam-6392	385	7	into	into	ADP
ejpam-6392	385	8	the	the	DET
ejpam-6392	385	9	thought	thought	NOUN
ejpam-6392	385	10	of	of	ADP
ejpam-6392	385	11	neutrosophic	neutrosophic	ADJ
ejpam-6392	385	12	bi	bi	NOUN
ejpam-6392	385	13	-	-	NOUN
ejpam-6392	385	14	ideals	ideal	NOUN
ejpam-6392	385	15	within	within	ADP
ejpam-6392	385	16	the	the	DET
ejpam-6392	385	17	framework	framework	NOUN
ejpam-6392	385	18	of	of	ADP
ejpam-6392	385	19	ink	ink	NOUN
ejpam-6392	385	20	-	-	PUNCT
ejpam-6392	385	21	algebras	algebras	PROPN
ejpam-6392	385	22	.	.	PUNCT
ejpam-6392	386	1	we	we	PRON
ejpam-6392	386	2	begin	begin	VERB
ejpam-6392	386	3	by	by	ADP
ejpam-6392	386	4	starting	start	VERB
ejpam-6392	386	5	neutrosophic	neutrosophic	ADJ
ejpam-6392	386	6	bi	bi	NOUN
ejpam-6392	386	7	-	-	NOUN
ejpam-6392	386	8	ideals	ideal	NOUN
ejpam-6392	386	9	of	of	ADP
ejpam-6392	386	10	ink	ink	NOUN
ejpam-6392	386	11	-	-	PUNCT
ejpam-6392	386	12	algebras	algebras	PROPN
ejpam-6392	386	13	.	.	PUNCT
ejpam-6392	387	1	we	we	PRON
ejpam-6392	387	2	then	then	ADV
ejpam-6392	387	3	explore	explore	VERB
ejpam-6392	387	4	their	their	PRON
ejpam-6392	387	5	properties	property	NOUN
ejpam-6392	387	6	,	,	PUNCT
ejpam-6392	387	7	including	include	VERB
ejpam-6392	387	8	how	how	SCONJ
ejpam-6392	387	9	intersection	intersection	NOUN
ejpam-6392	387	10	of	of	ADP
ejpam-6392	387	11	neutrosophic	neutrosophic	ADJ
ejpam-6392	387	12	bi	bi	NOUN
ejpam-6392	387	13	-	-	NOUN
ejpam-6392	387	14	ideals	ideal	NOUN
ejpam-6392	387	15	works	work	VERB
ejpam-6392	387	16	,	,	PUNCT
ejpam-6392	387	17	and	and	CCONJ
ejpam-6392	387	18	how	how	SCONJ
ejpam-6392	387	19	containment	containment	NOUN
ejpam-6392	387	20	relationships	relationship	NOUN
ejpam-6392	387	21	define	define	VERB
ejpam-6392	387	22	them	they	PRON
ejpam-6392	387	23	union	union	NOUN
ejpam-6392	387	24	of	of	ADP
ejpam-6392	387	25	neutrosophic	neutrosophic	ADJ
ejpam-6392	387	26	bi	bi	NOUN
ejpam-6392	387	27	-	-	NOUN
ejpam-6392	387	28	ideals	ideal	NOUN
ejpam-6392	387	29	by	by	ADP
ejpam-6392	387	30	one	one	NUM
ejpam-6392	387	31	containing	contain	VERB
ejpam-6392	387	32	the	the	DET
ejpam-6392	387	33	other	other	ADJ
ejpam-6392	387	34	.	.	PUNCT
ejpam-6392	387	35	,	,	PUNCT
ejpam-6392	387	36	also	also	ADV
ejpam-6392	387	37	,	,	PUNCT
ejpam-6392	387	38	we	we	PRON
ejpam-6392	387	39	investigate	investigate	VERB
ejpam-6392	387	40	homomorphisms	homomorphism	NOUN
ejpam-6392	387	41	and	and	CCONJ
ejpam-6392	387	42	epimorphisms	epimorphism	NOUN
ejpam-6392	387	43	of	of	ADP
ejpam-6392	387	44	neutrosophic	neutrosophic	ADJ
ejpam-6392	387	45	bi	bi	NOUN
ejpam-6392	387	46	-	-	NOUN
ejpam-6392	387	47	ideals	ideal	NOUN
ejpam-6392	387	48	.	.	PUNCT
ejpam-6392	388	1	subsequently	subsequently	ADV
ejpam-6392	388	2	,	,	PUNCT
ejpam-6392	388	3	we	we	PRON
ejpam-6392	388	4	discuss	discuss	VERB
ejpam-6392	388	5	the	the	DET
ejpam-6392	388	6	direct	direct	ADJ
ejpam-6392	388	7	product	product	NOUN
ejpam-6392	388	8	of	of	ADP
ejpam-6392	388	9	neutrosophic	neutrosophic	ADJ
ejpam-6392	388	10	sets	set	NOUN
ejpam-6392	388	11	and	and	CCONJ
ejpam-6392	388	12	demonstrate	demonstrate	VERB
ejpam-6392	388	13	that	that	SCONJ
ejpam-6392	388	14	the	the	DET
ejpam-6392	388	15	intersection	intersection	NOUN
ejpam-6392	388	16	of	of	ADP
ejpam-6392	388	17	direct	direct	ADJ
ejpam-6392	388	18	products	product	NOUN
ejpam-6392	388	19	of	of	ADP
ejpam-6392	388	20	neutrosophic	neutrosophic	ADJ
ejpam-6392	388	21	bi	bi	NOUN
ejpam-6392	388	22	-	-	NOUN
ejpam-6392	388	23	ideals	ideal	NOUN
ejpam-6392	388	24	remains	remain	VERB
ejpam-6392	388	25	a	a	DET
ejpam-6392	388	26	neutrosophic	neutrosophic	ADJ
ejpam-6392	388	27	bi	bi	NOUN
ejpam-6392	388	28	-	-	NOUN
ejpam-6392	388	29	ideal	ideal	ADJ
ejpam-6392	388	30	.	.	PUNCT
ejpam-6392	389	1	finally	finally	ADV
ejpam-6392	389	2	,	,	PUNCT
ejpam-6392	389	3	we	we	PRON
ejpam-6392	389	4	look	look	VERB
ejpam-6392	389	5	over	over	ADP
ejpam-6392	389	6	the	the	DET
ejpam-6392	389	7	application	application	NOUN
ejpam-6392	389	8	of	of	ADP
ejpam-6392	389	9	bi	bi	NOUN
ejpam-6392	389	10	-	-	NOUN
ejpam-6392	389	11	ideal	ideal	NOUN
ejpam-6392	389	12	in	in	ADP
ejpam-6392	389	13	ink	ink	NOUN
ejpam-6392	389	14	-	-	PUNCT
ejpam-6392	389	15	algebra	algebra	NOUN
ejpam-6392	389	16	by	by	ADP
ejpam-6392	389	17	considering	consider	VERB
ejpam-6392	389	18	parameters	parameter	NOUN
ejpam-6392	389	19	of	of	ADP
ejpam-6392	389	20	selecting	select	VERB
ejpam-6392	389	21	guide	guide	NOUN
ejpam-6392	389	22	by	by	ADP
ejpam-6392	389	23	a	a	DET
ejpam-6392	389	24	research	research	NOUN
ejpam-6392	389	25	scholar	scholar	NOUN
ejpam-6392	389	26	by	by	ADP
ejpam-6392	389	27	using	use	VERB
ejpam-6392	389	28	neutrosophic	neutrosophic	ADJ
ejpam-6392	389	29	bi	bi	NOUN
ejpam-6392	389	30	-	-	NOUN
ejpam-6392	389	31	ideals	ideal	NOUN
ejpam-6392	389	32	in	in	ADP
ejpam-6392	389	33	ink	ink	NOUN
ejpam-6392	389	34	-	-	PUNCT
ejpam-6392	389	35	algebra	algebra	NOUN
ejpam-6392	389	36	.	.	PUNCT
ejpam-6392	390	1	references	reference	NOUN
ejpam-6392	390	2	[	[	X
ejpam-6392	390	3	1	1	NUM
ejpam-6392	390	4	]	]	PUNCT
ejpam-6392	390	5	k.	k.	PROPN
ejpam-6392	390	6	iseki	iseki	PROPN
ejpam-6392	390	7	.	.	PUNCT
ejpam-6392	391	1	on	on	ADP
ejpam-6392	391	2	bci	bci	PROPN
ejpam-6392	391	3	-	-	PUNCT
ejpam-6392	391	4	algebras	algebra	NOUN
ejpam-6392	391	5	.	.	PUNCT
ejpam-6392	391	6	math	math	PROPN
ejpam-6392	391	7	.	.	PUNCT
ejpam-6392	391	8	semin	semin	PROPN
ejpam-6392	391	9	.	.	PUNCT
ejpam-6392	392	1	notes	notes	PROPN
ejpam-6392	392	2	,	,	PUNCT
ejpam-6392	392	3	kobe	kobe	PROPN
ejpam-6392	392	4	univ	univ	PROPN
ejpam-6392	392	5	.	.	PROPN
ejpam-6392	392	6	,	,	PUNCT
ejpam-6392	392	7	8:125–130	8:125–130	NOUN
ejpam-6392	392	8	,	,	PUNCT
ejpam-6392	392	9	1980	1980	NUM
ejpam-6392	392	10	.	.	PUNCT
ejpam-6392	393	1	[	[	X
ejpam-6392	393	2	2	2	NUM
ejpam-6392	393	3	]	]	PUNCT
ejpam-6392	393	4	k.	k.	PROPN
ejpam-6392	393	5	iseki	iseki	PROPN
ejpam-6392	393	6	and	and	CCONJ
ejpam-6392	393	7	s.	s.	PROPN
ejpam-6392	393	8	tanaka	tanaka	PROPN
ejpam-6392	393	9	.	.	PUNCT
ejpam-6392	394	1	an	an	DET
ejpam-6392	394	2	introduction	introduction	NOUN
ejpam-6392	394	3	to	to	ADP
ejpam-6392	394	4	the	the	DET
ejpam-6392	394	5	theory	theory	NOUN
ejpam-6392	394	6	of	of	ADP
ejpam-6392	394	7	bck	bck	PROPN
ejpam-6392	394	8	-	-	PUNCT
ejpam-6392	394	9	algebras	algebras	PROPN
ejpam-6392	394	10	.	.	PUNCT
ejpam-6392	395	1	math	math	PROPN
ejpam-6392	395	2	.	.	PUNCT
ejpam-6392	396	1	japan	japan	PROPN
ejpam-6392	396	2	,	,	PUNCT
ejpam-6392	396	3	23:1–26	23:1–26	NUM
ejpam-6392	396	4	,	,	PUNCT
ejpam-6392	396	5	1978	1978	NUM
ejpam-6392	396	6	.	.	PUNCT
ejpam-6392	397	1	[	[	X
ejpam-6392	397	2	3	3	X
ejpam-6392	397	3	]	]	X
ejpam-6392	397	4	m.	m.	NOUN
ejpam-6392	397	5	kaviyarasu	kaviyarasu	PROPN
ejpam-6392	397	6	,	,	PUNCT
ejpam-6392	397	7	k.	k.	PROPN
ejpam-6392	397	8	indhira	indhira	PROPN
ejpam-6392	397	9	,	,	PUNCT
ejpam-6392	397	10	and	and	CCONJ
ejpam-6392	397	11	v.	v.	ADP
ejpam-6392	397	12	m.	m.	NOUN
ejpam-6392	397	13	chandrasekaran	chandrasekaran	VERB
ejpam-6392	397	14	.	.	PUNCT
ejpam-6392	398	1	fuzzy	fuzzy	ADJ
ejpam-6392	398	2	sub	sub	NOUN
ejpam-6392	398	3	-	-	ADJ
ejpam-6392	398	4	algebras	algebras	ADJ
ejpam-6392	398	5	and	and	CCONJ
ejpam-6392	398	6	fuzzy	fuzzy	ADJ
ejpam-6392	398	7	k	k	NOUN
ejpam-6392	398	8	-	-	NOUN
ejpam-6392	398	9	ideals	ideal	NOUN
ejpam-6392	398	10	in	in	ADP
ejpam-6392	398	11	ink	ink	NOUN
ejpam-6392	398	12	-	-	PUNCT
ejpam-6392	398	13	algebras	algebras	PROPN
ejpam-6392	398	14	.	.	PUNCT
ejpam-6392	399	1	international	international	ADJ
ejpam-6392	399	2	journal	journal	PROPN
ejpam-6392	399	3	of	of	ADP
ejpam-6392	399	4	pure	pure	ADJ
ejpam-6392	399	5	and	and	CCONJ
ejpam-6392	399	6	applied	applied	ADJ
ejpam-6392	399	7	mathematics	mathematic	NOUN
ejpam-6392	399	8	,	,	PUNCT
ejpam-6392	399	9	113(6):47–55	113(6):47–55	NUM
ejpam-6392	399	10	,	,	PUNCT
ejpam-6392	399	11	2017	2017	NUM
ejpam-6392	399	12	.	.	PUNCT
ejpam-6392	400	1	[	[	X
ejpam-6392	400	2	4	4	NUM
ejpam-6392	400	3	]	]	X
ejpam-6392	400	4	m.	m.	NOUN
ejpam-6392	400	5	kaviyarasu	kaviyarasu	PROPN
ejpam-6392	400	6	,	,	PUNCT
ejpam-6392	400	7	k.	k.	PROPN
ejpam-6392	400	8	indhira	indhira	PROPN
ejpam-6392	400	9	,	,	PUNCT
ejpam-6392	400	10	v.	v.	ADP
ejpam-6392	400	11	m.	m.	NOUN
ejpam-6392	400	12	chandrasekaran	chandrasekaran	VERB
ejpam-6392	400	13	,	,	PUNCT
ejpam-6392	400	14	and	and	CCONJ
ejpam-6392	400	15	k.	k.	PROPN
ejpam-6392	400	16	jacob	jacob	PROPN
ejpam-6392	400	17	.	.	PROPN
ejpam-6392	401	1	interval	interval	NOUN
ejpam-6392	401	2	valued	value	VERB
ejpam-6392	401	3	fuzzy	fuzzy	ADJ
ejpam-6392	401	4	subalgebra	subalgebra	NOUN
ejpam-6392	401	5	and	and	CCONJ
ejpam-6392	401	6	fuzzy	fuzzy	ADJ
ejpam-6392	401	7	ink	ink	NOUN
ejpam-6392	401	8	-	-	PUNCT
ejpam-6392	401	9	ideal	ideal	NOUN
ejpam-6392	401	10	in	in	ADP
ejpam-6392	401	11	ink	ink	NOUN
ejpam-6392	401	12	-	-	PUNCT
ejpam-6392	401	13	algebra	algebra	NOUN
ejpam-6392	401	14	.	.	PUNCT
ejpam-6392	402	1	in	in	ADP
ejpam-6392	402	2	advances	advance	NOUN
ejpam-6392	402	3	in	in	ADP
ejpam-6392	402	4	algebra	algebra	NOUN
ejpam-6392	402	5	and	and	CCONJ
ejpam-6392	402	6	analysis	analysis	NOUN
ejpam-6392	402	7	,	,	PUNCT
ejpam-6392	402	8	pages	page	NOUN
ejpam-6392	402	9	19–25	19–25	NUM
ejpam-6392	402	10	.	.	PUNCT
ejpam-6392	402	11	2018	2018	NUM
ejpam-6392	402	12	.	.	PUNCT
ejpam-6392	402	13	m.	m.	NOUN
ejpam-6392	402	14	remala	remala	NOUN
ejpam-6392	402	15	,	,	PUNCT
ejpam-6392	402	16	e.	e.	PROPN
ejpam-6392	402	17	tamma	tamma	PROPN
ejpam-6392	402	18	,	,	PUNCT
ejpam-6392	402	19	y.	y.	PROPN
ejpam-6392	402	20	bhargavi	bhargavi	PROPN
ejpam-6392	402	21	/	/	SYM
ejpam-6392	402	22	eur	eur	PROPN
ejpam-6392	402	23	.	.	PUNCT
ejpam-6392	403	1	j.	j.	PROPN
ejpam-6392	403	2	pure	pure	PROPN
ejpam-6392	403	3	appl	appl	PROPN
ejpam-6392	403	4	.	.	PROPN
ejpam-6392	403	5	math	math	PROPN
ejpam-6392	403	6	,	,	PUNCT
ejpam-6392	403	7	18	18	NUM
ejpam-6392	403	8	(	(	PUNCT
ejpam-6392	403	9	4	4	NUM
ejpam-6392	403	10	)	)	PUNCT
ejpam-6392	403	11	(	(	PUNCT
ejpam-6392	403	12	2025	2025	NUM
ejpam-6392	403	13	)	)	PUNCT
ejpam-6392	403	14	,	,	PUNCT
ejpam-6392	403	15	6392	6392	NUM
ejpam-6392	403	16	19	19	NUM
ejpam-6392	403	17	of	of	ADP
ejpam-6392	403	18	20	20	NUM
ejpam-6392	403	19	[	[	SYM
ejpam-6392	403	20	5	5	NUM
ejpam-6392	403	21	]	]	PUNCT
ejpam-6392	403	22	m.	m.	NOUN
ejpam-6392	403	23	kaviyarasu	kaviyarasu	PROPN
ejpam-6392	403	24	and	and	CCONJ
ejpam-6392	403	25	k.	k.	PROPN
ejpam-6392	403	26	indhira	indhira	PROPN
ejpam-6392	403	27	.	.	PUNCT
ejpam-6392	404	1	on	on	ADP
ejpam-6392	404	2	intuitionistic	intuitionistic	ADJ
ejpam-6392	404	3	fuzzy	fuzzy	ADJ
ejpam-6392	404	4	ink	ink	NOUN
ejpam-6392	404	5	-	-	PUNCT
ejpam-6392	404	6	ideals	ideal	NOUN
ejpam-6392	404	7	of	of	ADP
ejpam-6392	404	8	ink	ink	NOUN
ejpam-6392	404	9	-	-	PUNCT
ejpam-6392	404	10	algebras	algebras	NOUN
ejpam-6392	404	11	.	.	PUNCT
ejpam-6392	405	1	in	in	ADP
ejpam-6392	405	2	iop	iop	PROPN
ejpam-6392	405	3	conference	conference	NOUN
ejpam-6392	405	4	series	series	NOUN
ejpam-6392	405	5	:	:	PUNCT
ejpam-6392	405	6	materials	material	NOUN
ejpam-6392	405	7	science	science	NOUN
ejpam-6392	405	8	and	and	CCONJ
ejpam-6392	405	9	engineering	engineering	NOUN
ejpam-6392	405	10	,	,	PUNCT
ejpam-6392	405	11	volume	volume	NOUN
ejpam-6392	405	12	263	263	NUM
ejpam-6392	405	13	,	,	PUNCT
ejpam-6392	405	14	page	page	NOUN
ejpam-6392	405	15	042142	042142	NUM
ejpam-6392	405	16	,	,	PUNCT
ejpam-6392	405	17	2017	2017	NUM
ejpam-6392	405	18	.	.	PUNCT
ejpam-6392	406	1	[	[	X
ejpam-6392	406	2	6	6	NUM
ejpam-6392	406	3	]	]	PUNCT
ejpam-6392	406	4	m.	m.	NOUN
ejpam-6392	406	5	kaviyarasu	kaviyarasu	PROPN
ejpam-6392	406	6	,	,	PUNCT
ejpam-6392	406	7	k.	k.	PROPN
ejpam-6392	406	8	indhira	indhira	PROPN
ejpam-6392	406	9	,	,	PUNCT
ejpam-6392	406	10	and	and	CCONJ
ejpam-6392	406	11	v.	v.	ADP
ejpam-6392	406	12	m.	m.	NOUN
ejpam-6392	406	13	chandrasekaran	chandrasekaran	VERB
ejpam-6392	406	14	.	.	PUNCT
ejpam-6392	407	1	direct	direct	ADJ
ejpam-6392	407	2	product	product	NOUN
ejpam-6392	407	3	of	of	ADP
ejpam-6392	407	4	neutrosophic	neutrosophic	ADJ
ejpam-6392	407	5	ink	ink	NOUN
ejpam-6392	407	6	-	-	PUNCT
ejpam-6392	407	7	algebras	algebras	PROPN
ejpam-6392	407	8	.	.	PUNCT
ejpam-6392	407	9	neutrosophic	neutrosophic	ADJ
ejpam-6392	407	10	sets	set	NOUN
ejpam-6392	407	11	and	and	CCONJ
ejpam-6392	407	12	systems	system	NOUN
ejpam-6392	407	13	,	,	PUNCT
ejpam-6392	407	14	38:228–234	38:228–234	NUM
ejpam-6392	407	15	,	,	PUNCT
ejpam-6392	407	16	2020	2020	NUM
ejpam-6392	407	17	.	.	PUNCT
ejpam-6392	408	1	[	[	X
ejpam-6392	408	2	7	7	X
ejpam-6392	408	3	]	]	X
ejpam-6392	408	4	mohammad	mohammad	PROPN
ejpam-6392	408	5	munir	munir	PROPN
ejpam-6392	408	6	.	.	PUNCT
ejpam-6392	409	1	on	on	ADP
ejpam-6392	409	2	m	m	ADJ
ejpam-6392	409	3	-	-	ADJ
ejpam-6392	409	4	bi	bi	ADJ
ejpam-6392	409	5	ideals	ideal	NOUN
ejpam-6392	409	6	in	in	ADP
ejpam-6392	409	7	semigroups	semigroup	NOUN
ejpam-6392	409	8	.	.	PUNCT
ejpam-6392	410	1	bulletin	bulletin	NOUN
ejpam-6392	410	2	of	of	ADP
ejpam-6392	410	3	the	the	DET
ejpam-6392	410	4	international	international	ADJ
ejpam-6392	410	5	mathematical	mathematical	ADJ
ejpam-6392	410	6	virtual	virtual	PROPN
ejpam-6392	410	7	institute	institute	PROPN
ejpam-6392	410	8	,	,	PUNCT
ejpam-6392	410	9	8(3):461–467	8(3):461–467	NUM
ejpam-6392	410	10	,	,	PUNCT
ejpam-6392	410	11	2018	2018	NUM
ejpam-6392	410	12	.	.	PUNCT
ejpam-6392	411	1	[	[	X
ejpam-6392	411	2	8	8	NUM
ejpam-6392	411	3	]	]	X
ejpam-6392	411	4	remala	remala	NOUN
ejpam-6392	411	5	mounikalakshmi	mounikalakshmi	NOUN
ejpam-6392	411	6	,	,	PUNCT
ejpam-6392	411	7	t.	t.	PROPN
ejpam-6392	411	8	eswarlal	eswarlal	PROPN
ejpam-6392	411	9	,	,	PUNCT
ejpam-6392	411	10	venkata	venkata	PROPN
ejpam-6392	411	11	kalyani	kalyani	PROPN
ejpam-6392	411	12	u	u	PROPN
ejpam-6392	411	13	,	,	PUNCT
ejpam-6392	411	14	and	and	CCONJ
ejpam-6392	411	15	aiyared	aiyare	VERB
ejpam-6392	411	16	iampan	iampan	PROPN
ejpam-6392	411	17	.	.	PUNCT
ejpam-6392	412	1	homomorphisms	homomorphism	NOUN
ejpam-6392	412	2	and	and	CCONJ
ejpam-6392	412	3	anti	anti	ADJ
ejpam-6392	412	4	-	-	ADJ
ejpam-6392	412	5	homomorphisms	homomorphism	NOUN
ejpam-6392	412	6	of	of	ADP
ejpam-6392	412	7	neutrosophic	neutrosophic	ADJ
ejpam-6392	412	8	ink	ink	NOUN
ejpam-6392	412	9	-	-	PUNCT
ejpam-6392	412	10	algebras	algebras	PROPN
ejpam-6392	412	11	.	.	PUNCT
ejpam-6392	413	1	international	international	ADJ
ejpam-6392	413	2	journal	journal	PROPN
ejpam-6392	413	3	of	of	ADP
ejpam-6392	413	4	neutrosophic	neutrosophic	ADJ
ejpam-6392	413	5	science	science	NOUN
ejpam-6392	413	6	,	,	PUNCT
ejpam-6392	413	7	23(1):335–340	23(1):335–340	PROPN
ejpam-6392	413	8	,	,	PUNCT
ejpam-6392	413	9	2024	2024	NUM
ejpam-6392	413	10	.	.	PUNCT
ejpam-6392	414	1	[	[	X
ejpam-6392	414	2	9	9	NUM
ejpam-6392	414	3	]	]	PUNCT
ejpam-6392	414	4	w.	w.	PROPN
ejpam-6392	414	5	f.	f.	PROPN
ejpam-6392	414	6	al	al	PROPN
ejpam-6392	414	7	-	-	PUNCT
ejpam-6392	414	8	omeri	omeri	ADJ
ejpam-6392	414	9	,	,	PUNCT
ejpam-6392	414	10	m.	m.	NOUN
ejpam-6392	414	11	kaviyarasu	kaviyarasu	PROPN
ejpam-6392	414	12	,	,	PUNCT
ejpam-6392	414	13	and	and	CCONJ
ejpam-6392	414	14	m.	m.	NOUN
ejpam-6392	414	15	rajeshwari	rajeshwari	PROPN
ejpam-6392	414	16	.	.	PUNCT
ejpam-6392	415	1	translation	translation	NOUN
ejpam-6392	415	2	of	of	ADP
ejpam-6392	415	3	neutrosophic	neutrosophic	ADJ
ejpam-6392	415	4	ink	ink	NOUN
ejpam-6392	415	5	-	-	PUNCT
ejpam-6392	415	6	algebras	algebras	PROPN
ejpam-6392	415	7	.	.	PUNCT
ejpam-6392	415	8	neutrosophic	neutrosophic	ADJ
ejpam-6392	415	9	sets	set	NOUN
ejpam-6392	415	10	and	and	CCONJ
ejpam-6392	415	11	systems	system	NOUN
ejpam-6392	415	12	,	,	PUNCT
ejpam-6392	415	13	66:119–135	66:119–135	PROPN
ejpam-6392	415	14	,	,	PUNCT
ejpam-6392	415	15	2024	2024	NUM
ejpam-6392	415	16	.	.	PUNCT
ejpam-6392	416	1	[	[	X
ejpam-6392	416	2	10	10	NUM
ejpam-6392	416	3	]	]	X
ejpam-6392	416	4	r.	r.	PROPN
ejpam-6392	416	5	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6392	416	6	,	,	PUNCT
ejpam-6392	416	7	e.	e.	PROPN
ejpam-6392	416	8	tamma	tamma	PROPN
ejpam-6392	416	9	,	,	PUNCT
ejpam-6392	416	10	and	and	CCONJ
ejpam-6392	416	11	c.	c.	PROPN
ejpam-6392	416	12	jana	jana	PROPN
ejpam-6392	416	13	.	.	PUNCT
ejpam-6392	417	1	bipolar	bipolar	ADJ
ejpam-6392	417	2	fuzzy	fuzzy	ADJ
ejpam-6392	417	3	ink	ink	NOUN
ejpam-6392	417	4	-	-	PUNCT
ejpam-6392	417	5	subalgebras	subalgebras	NOUN
ejpam-6392	417	6	of	of	ADP
ejpam-6392	417	7	ink	ink	NOUN
ejpam-6392	417	8	-	-	PUNCT
ejpam-6392	417	9	algebras	algebras	PROPN
ejpam-6392	417	10	.	.	PUNCT
ejpam-6392	418	1	aims	aim	VERB
ejpam-6392	418	2	mathematics	mathematic	NOUN
ejpam-6392	418	3	,	,	PUNCT
ejpam-6392	418	4	9(10):27593–27606	9(10):27593–27606	NUM
ejpam-6392	418	5	,	,	PUNCT
ejpam-6392	418	6	2024	2024	NUM
ejpam-6392	418	7	.	.	PUNCT
ejpam-6392	419	1	[	[	X
ejpam-6392	419	2	11	11	NUM
ejpam-6392	419	3	]	]	PUNCT
ejpam-6392	419	4	r.	r.	PROPN
ejpam-6392	419	5	mounikalakshmi	mounikalakshmi	PROPN
ejpam-6392	419	6	,	,	PUNCT
ejpam-6392	419	7	e.	e.	PROPN
ejpam-6392	419	8	tamma	tamma	PROPN
ejpam-6392	419	9	,	,	PUNCT
ejpam-6392	419	10	venkata	venkata	PROPN
ejpam-6392	419	11	kalyani	kalyani	PROPN
ejpam-6392	419	12	u	u	PROPN
ejpam-6392	419	13	,	,	PUNCT
ejpam-6392	419	14	aiyared	aiyared	ADJ
ejpam-6392	419	15	iampan	iampan	NOUN
ejpam-6392	419	16	,	,	PUNCT
ejpam-6392	419	17	and	and	CCONJ
ejpam-6392	419	18	t.	t.	PROPN
ejpam-6392	419	19	srinivasa	srinivasa	PROPN
ejpam-6392	419	20	rao	rao	PROPN
ejpam-6392	419	21	.	.	PROPN
ejpam-6392	419	22	implicative	implicative	ADJ
ejpam-6392	419	23	and	and	CCONJ
ejpam-6392	419	24	positive	positive	ADJ
ejpam-6392	419	25	implicative	implicative	ADJ
ejpam-6392	419	26	ink	ink	NOUN
ejpam-6392	419	27	-	-	PUNCT
ejpam-6392	419	28	ideals	ideal	NOUN
ejpam-6392	419	29	of	of	ADP
ejpam-6392	419	30	neutrosophic	neutrosophic	ADJ
ejpam-6392	419	31	inkalgebras	inkalgebras	PROPN
ejpam-6392	419	32	.	.	PUNCT
ejpam-6392	420	1	european	european	PROPN
ejpam-6392	420	2	journal	journal	PROPN
ejpam-6392	420	3	of	of	ADP
ejpam-6392	420	4	pure	pure	ADJ
ejpam-6392	420	5	and	and	CCONJ
ejpam-6392	420	6	applied	applied	ADJ
ejpam-6392	420	7	mathematics	mathematic	NOUN
ejpam-6392	420	8	,	,	PUNCT
ejpam-6392	420	9	18(3):6226	18(3):6226	NUM
ejpam-6392	420	10	,	,	PUNCT
ejpam-6392	420	11	2025	2025	NUM
ejpam-6392	420	12	.	.	PUNCT
ejpam-6392	421	1	[	[	X
ejpam-6392	421	2	12	12	NUM
ejpam-6392	421	3	]	]	X
ejpam-6392	421	4	nobuaki	nobuaki	ADJ
ejpam-6392	421	5	kuroki	kuroki	PROPN
ejpam-6392	421	6	.	.	PUNCT
ejpam-6392	422	1	fuzzy	fuzzy	ADJ
ejpam-6392	422	2	generalized	generalize	VERB
ejpam-6392	422	3	bi	bi	NOUN
ejpam-6392	422	4	-	-	NOUN
ejpam-6392	422	5	ideals	ideal	NOUN
ejpam-6392	422	6	in	in	ADP
ejpam-6392	422	7	semigroups	semigroup	NOUN
ejpam-6392	422	8	.	.	PUNCT
ejpam-6392	423	1	information	information	NOUN
ejpam-6392	423	2	sciences	sciences	PROPN
ejpam-6392	423	3	,	,	PUNCT
ejpam-6392	423	4	66(3):461–467	66(3):461–467	PROPN
ejpam-6392	423	5	,	,	PUNCT
ejpam-6392	423	6	2018	2018	NUM
ejpam-6392	423	7	.	.	PUNCT
ejpam-6392	424	1	[	[	X
ejpam-6392	424	2	13	13	NUM
ejpam-6392	424	3	]	]	X
ejpam-6392	424	4	nobuaki	nobuaki	ADJ
ejpam-6392	424	5	kuroki	kuroki	PROPN
ejpam-6392	424	6	.	.	PUNCT
ejpam-6392	425	1	on	on	ADP
ejpam-6392	425	2	fuzzy	fuzzy	ADJ
ejpam-6392	425	3	ideals	ideal	NOUN
ejpam-6392	425	4	and	and	CCONJ
ejpam-6392	425	5	fuzzy	fuzzy	ADJ
ejpam-6392	425	6	bi	bi	NOUN
ejpam-6392	425	7	-	-	NOUN
ejpam-6392	425	8	ideals	ideal	NOUN
ejpam-6392	425	9	in	in	ADP
ejpam-6392	425	10	semigroups	semigroup	NOUN
ejpam-6392	425	11	.	.	PUNCT
ejpam-6392	426	1	fuzzy	fuzzy	ADJ
ejpam-6392	426	2	sets	set	NOUN
ejpam-6392	426	3	and	and	CCONJ
ejpam-6392	426	4	systems	system	NOUN
ejpam-6392	426	5	,	,	PUNCT
ejpam-6392	426	6	5(2):203–211	5(2):203–211	NUM
ejpam-6392	426	7	,	,	PUNCT
ejpam-6392	426	8	1981	1981	NUM
ejpam-6392	426	9	.	.	PUNCT
ejpam-6392	427	1	[	[	X
ejpam-6392	427	2	14	14	NUM
ejpam-6392	427	3	]	]	X
ejpam-6392	427	4	pairote	pairote	ADJ
ejpam-6392	427	5	yiarayong	yiarayong	NOUN
ejpam-6392	427	6	.	.	PUNCT
ejpam-6392	428	1	a	a	DET
ejpam-6392	428	2	new	new	ADJ
ejpam-6392	428	3	approach	approach	NOUN
ejpam-6392	428	4	of	of	ADP
ejpam-6392	428	5	fuzzy	fuzzy	ADJ
ejpam-6392	428	6	bi	bi	ADJ
ejpam-6392	428	7	-	-	ADJ
ejpam-6392	428	8	ideal	ideal	ADJ
ejpam-6392	428	9	theory	theory	NOUN
ejpam-6392	428	10	applied	apply	VERB
ejpam-6392	428	11	on	on	ADP
ejpam-6392	428	12	semigroups	semigroup	NOUN
ejpam-6392	428	13	.	.	PUNCT
ejpam-6392	429	1	soft	soft	ADJ
ejpam-6392	429	2	computing	computing	NOUN
ejpam-6392	429	3	,	,	PUNCT
ejpam-6392	429	4	26(9):4227–4236	26(9):4227–4236	NUM
ejpam-6392	429	5	,	,	PUNCT
ejpam-6392	429	6	2022	2022	NUM
ejpam-6392	429	7	.	.	PUNCT
ejpam-6392	430	1	[	[	X
ejpam-6392	430	2	15	15	NUM
ejpam-6392	430	3	]	]	X
ejpam-6392	430	4	young	young	ADJ
ejpam-6392	430	5	bae	bae	PROPN
ejpam-6392	430	6	jun	jun	PROPN
ejpam-6392	430	7	and	and	CCONJ
ejpam-6392	430	8	kyung	kyung	PROPN
ejpam-6392	430	9	ho	ho	PROPN
ejpam-6392	430	10	kim	kim	PROPN
ejpam-6392	430	11	.	.	PUNCT
ejpam-6392	431	1	intuitionistic	intuitionistic	ADJ
ejpam-6392	431	2	fuzzy	fuzzy	ADJ
ejpam-6392	431	3	ideals	ideal	NOUN
ejpam-6392	431	4	of	of	ADP
ejpam-6392	431	5	bck	bck	NOUN
ejpam-6392	431	6	-	-	PUNCT
ejpam-6392	431	7	algebras	algebras	PROPN
ejpam-6392	431	8	.	.	PUNCT
ejpam-6392	432	1	international	international	ADJ
ejpam-6392	432	2	journal	journal	PROPN
ejpam-6392	432	3	of	of	ADP
ejpam-6392	432	4	mathematics	mathematics	PROPN
ejpam-6392	432	5	and	and	CCONJ
ejpam-6392	432	6	mathematical	mathematical	ADJ
ejpam-6392	432	7	sciences	science	NOUN
ejpam-6392	432	8	,	,	PUNCT
ejpam-6392	432	9	24(12):839–849	24(12):839–849	NUM
ejpam-6392	432	10	,	,	PUNCT
ejpam-6392	432	11	2000	2000	NUM
ejpam-6392	432	12	.	.	PUNCT
ejpam-6392	433	1	[	[	X
ejpam-6392	433	2	16	16	NUM
ejpam-6392	433	3	]	]	X
ejpam-6392	433	4	kung	kung	PROPN
ejpam-6392	433	5	ho	ho	PROPN
ejpam-6392	433	6	kim	kim	PROPN
ejpam-6392	433	7	.	.	PUNCT
ejpam-6392	433	8	interval	interval	NOUN
ejpam-6392	433	9	valued	value	VERB
ejpam-6392	433	10	intuitionistic	intuitionistic	ADJ
ejpam-6392	433	11	(	(	PUNCT
ejpam-6392	433	12	s	s	NOUN
ejpam-6392	433	13	*	*	NOUN
ejpam-6392	433	14	,	,	PUNCT
ejpam-6392	433	15	t*)-fuzzy	t*)-fuzzy	ADJ
ejpam-6392	433	16	bi	bi	NOUN
ejpam-6392	433	17	-	-	NOUN
ejpam-6392	433	18	ideals	ideal	NOUN
ejpam-6392	433	19	of	of	ADP
ejpam-6392	433	20	semigroups	semigroup	NOUN
ejpam-6392	433	21	.	.	PUNCT
ejpam-6392	434	1	scientiae	scientiae	PROPN
ejpam-6392	434	2	mathematicae	mathematicae	PROPN
ejpam-6392	434	3	japonicae	japonicae	PROPN
ejpam-6392	434	4	,	,	PUNCT
ejpam-6392	434	5	71(2):171–177	71(2):171–177	PROPN
ejpam-6392	434	6	,	,	PUNCT
ejpam-6392	434	7	2010	2010	NUM
ejpam-6392	434	8	.	.	PUNCT
ejpam-6392	435	1	[	[	X
ejpam-6392	435	2	17	17	NUM
ejpam-6392	435	3	]	]	X
ejpam-6392	435	4	kyung	kyung	PROPN
ejpam-6392	435	5	ho	ho	PROPN
ejpam-6392	435	6	kim	kim	PROPN
ejpam-6392	435	7	and	and	CCONJ
ejpam-6392	435	8	jong	jong	PROPN
ejpam-6392	435	9	geol	geol	PROPN
ejpam-6392	435	10	lee	lee	PROPN
ejpam-6392	435	11	.	.	PUNCT
ejpam-6392	436	1	on	on	ADP
ejpam-6392	436	2	intuitionistic	intuitionistic	ADJ
ejpam-6392	436	3	fuzzy	fuzzy	ADJ
ejpam-6392	436	4	bi	bi	NOUN
ejpam-6392	436	5	-	-	NOUN
ejpam-6392	436	6	ideals	ideal	NOUN
ejpam-6392	436	7	of	of	ADP
ejpam-6392	436	8	semigroups	semigroup	NOUN
ejpam-6392	436	9	.	.	PUNCT
ejpam-6392	437	1	turkish	turkish	ADJ
ejpam-6392	437	2	journal	journal	NOUN
ejpam-6392	437	3	of	of	ADP
ejpam-6392	437	4	mathematics	mathematic	NOUN
ejpam-6392	437	5	,	,	PUNCT
ejpam-6392	437	6	29(2):201–210	29(2):201–210	PROPN
ejpam-6392	437	7	,	,	PUNCT
ejpam-6392	437	8	2005	2005	NUM
ejpam-6392	437	9	.	.	PUNCT
ejpam-6392	438	1	[	[	X
ejpam-6392	438	2	18	18	NUM
ejpam-6392	438	3	]	]	X
ejpam-6392	438	4	v.	v.	CCONJ
ejpam-6392	438	5	chinnadurai	chinnadurai	PROPN
ejpam-6392	438	6	and	and	CCONJ
ejpam-6392	438	7	k.	k.	PROPN
ejpam-6392	438	8	bharathivelan	bharathivelan	PROPN
ejpam-6392	438	9	.	.	PUNCT
ejpam-6392	439	1	cubic	cubic	ADJ
ejpam-6392	439	2	weak	weak	ADJ
ejpam-6392	439	3	bi	bi	NOUN
ejpam-6392	439	4	-	-	NOUN
ejpam-6392	439	5	ideals	ideal	NOUN
ejpam-6392	439	6	of	of	ADP
ejpam-6392	439	7	near	near	ADJ
ejpam-6392	439	8	rings	ring	NOUN
ejpam-6392	439	9	.	.	PUNCT
ejpam-6392	440	1	palestine	palestine	PROPN
ejpam-6392	440	2	journal	journal	PROPN
ejpam-6392	440	3	of	of	ADP
ejpam-6392	440	4	mathematics	mathematic	NOUN
ejpam-6392	440	5	,	,	PUNCT
ejpam-6392	440	6	6(2):174–185	6(2):174–185	NUM
ejpam-6392	440	7	,	,	PUNCT
ejpam-6392	440	8	2017	2017	NUM
ejpam-6392	440	9	.	.	PUNCT
ejpam-6392	441	1	[	[	X
ejpam-6392	441	2	19	19	NUM
ejpam-6392	441	3	]	]	X
ejpam-6392	441	4	anas	anas	PROPN
ejpam-6392	441	5	al	al	PROPN
ejpam-6392	441	6	-	-	PROPN
ejpam-6392	441	7	masarwah	masarwah	PROPN
ejpam-6392	441	8	.	.	PUNCT
ejpam-6392	442	1	structures	structure	NOUN
ejpam-6392	442	2	on	on	ADP
ejpam-6392	442	3	doubt	doubt	NOUN
ejpam-6392	442	4	neutrosophic	neutrosophic	ADJ
ejpam-6392	442	5	ideals	ideal	NOUN
ejpam-6392	442	6	of	of	ADP
ejpam-6392	442	7	bck	bck	PROPN
ejpam-6392	442	8	/	/	SYM
ejpam-6392	442	9	bci	bci	NOUN
ejpam-6392	442	10	-	-	PUNCT
ejpam-6392	442	11	algebras	algebra	NOUN
ejpam-6392	442	12	under	under	ADP
ejpam-6392	442	13	(	(	PUNCT
ejpam-6392	442	14	s	s	NOUN
ejpam-6392	442	15	,	,	PUNCT
ejpam-6392	442	16	t)-norms	t)-norm	NOUN
ejpam-6392	442	17	.	.	PUNCT
ejpam-6392	443	1	neutrosophic	neutrosophic	ADJ
ejpam-6392	443	2	sets	set	NOUN
ejpam-6392	443	3	and	and	CCONJ
ejpam-6392	443	4	systems	system	NOUN
ejpam-6392	443	5	,	,	PUNCT
ejpam-6392	443	6	33:275–289	33:275–289	NUM
ejpam-6392	443	7	,	,	PUNCT
ejpam-6392	443	8	2020	2020	NUM
ejpam-6392	443	9	.	.	PUNCT
ejpam-6392	444	1	[	[	X
ejpam-6392	444	2	20	20	NUM
ejpam-6392	444	3	]	]	X
ejpam-6392	444	4	y.	y.	PROPN
ejpam-6392	444	5	bhargavi	bhargavi	PROPN
ejpam-6392	444	6	,	,	PUNCT
ejpam-6392	444	7	s.	s.	PROPN
ejpam-6392	444	8	ragamayi	ragamayi	PROPN
ejpam-6392	444	9	,	,	PUNCT
ejpam-6392	444	10	j.	j.	PROPN
ejpam-6392	444	11	madhusudhana	madhusudhana	PROPN
ejpam-6392	444	12	rao	rao	PROPN
ejpam-6392	444	13	,	,	PUNCT
ejpam-6392	444	14	and	and	CCONJ
ejpam-6392	444	15	t.	t.	PROPN
ejpam-6392	444	16	eswarlal	eswarlal	PROPN
ejpam-6392	444	17	.	.	PUNCT
ejpam-6392	445	1	vague	vague	ADJ
ejpam-6392	445	2	bi	bi	NOUN
ejpam-6392	445	3	-	-	NOUN
ejpam-6392	445	4	ideals	ideal	NOUN
ejpam-6392	445	5	of	of	ADP
ejpam-6392	445	6	a	a	DET
ejpam-6392	445	7	gamma	gamma	NOUN
ejpam-6392	445	8	near	near	ADP
ejpam-6392	445	9	ring	ring	NOUN
ejpam-6392	445	10	.	.	PUNCT
ejpam-6392	446	1	journal	journal	PROPN
ejpam-6392	446	2	/	/	SYM
ejpam-6392	446	3	proceedings	proceeding	NOUN
ejpam-6392	446	4	,	,	PUNCT
ejpam-6392	446	5	21(3):116–126	21(3):116–126	NOUN
ejpam-6392	446	6	,	,	PUNCT
ejpam-6392	446	7	2017	2017	NUM
ejpam-6392	446	8	.	.	PUNCT
ejpam-6392	447	1	[	[	X
ejpam-6392	447	2	21	21	NUM
ejpam-6392	447	3	]	]	X
ejpam-6392	447	4	e.	e.	PROPN
ejpam-6392	447	5	velammal	velammal	PROPN
ejpam-6392	447	6	sindhu	sindhu	PROPN
ejpam-6392	447	7	and	and	CCONJ
ejpam-6392	447	8	m.	m.	PROPN
ejpam-6392	447	9	himaya	himaya	PROPN
ejpam-6392	447	10	jaleela	jaleela	PROPN
ejpam-6392	447	11	begum	begum	PROPN
ejpam-6392	447	12	.	.	PUNCT
ejpam-6392	448	1	intuitionistic	intuitionistic	ADJ
ejpam-6392	448	2	fuzzy	fuzzy	ADJ
ejpam-6392	448	3	bi	bi	NOUN
ejpam-6392	448	4	-	-	NOUN
ejpam-6392	448	5	ideals	ideal	NOUN
ejpam-6392	448	6	of	of	ADP
ejpam-6392	448	7	bck	bck	NOUN
ejpam-6392	448	8	-	-	PUNCT
ejpam-6392	448	9	algebras	algebras	PROPN
ejpam-6392	448	10	.	.	PUNCT
ejpam-6392	449	1	american	american	PROPN
ejpam-6392	449	2	international	international	PROPN
ejpam-6392	449	3	journal	journal	PROPN
ejpam-6392	449	4	of	of	ADP
ejpam-6392	449	5	research	research	NOUN
ejpam-6392	449	6	in	in	ADP
ejpam-6392	449	7	science	science	NOUN
ejpam-6392	449	8	,	,	PUNCT
ejpam-6392	449	9	technology	technology	NOUN
ejpam-6392	449	10	,	,	PUNCT
ejpam-6392	449	11	engineering	engineering	NOUN
ejpam-6392	449	12	&	&	CCONJ
ejpam-6392	449	13	mathematics	mathematic	NOUN
ejpam-6392	449	14	,	,	PUNCT
ejpam-6392	449	15	26(1):19–23	26(1):19–23	NUM
ejpam-6392	449	16	,	,	PUNCT
ejpam-6392	449	17	2019	2019	NUM
ejpam-6392	449	18	.	.	PUNCT
ejpam-6392	450	1	[	[	X
ejpam-6392	450	2	22	22	NUM
ejpam-6392	450	3	]	]	PUNCT
ejpam-6392	450	4	v.	v.	PROPN
ejpam-6392	450	5	p.	p.	PROPN
ejpam-6392	450	6	korada	korada	PROPN
ejpam-6392	450	7	,	,	PUNCT
ejpam-6392	450	8	s.	s.	PROPN
ejpam-6392	450	9	ragamayi	ragamayi	PROPN
ejpam-6392	450	10	,	,	PUNCT
ejpam-6392	450	11	and	and	CCONJ
ejpam-6392	450	12	g.	g.	PROPN
ejpam-6392	450	13	jayalalitha	jayalalitha	PROPN
ejpam-6392	450	14	.	.	PUNCT
ejpam-6392	451	1	some	some	DET
ejpam-6392	451	2	results	result	NOUN
ejpam-6392	451	3	on	on	ADP
ejpam-6392	451	4	bipolar	bipolar	ADJ
ejpam-6392	451	5	fuzzy	fuzzy	ADJ
ejpam-6392	451	6	bi	bi	NOUN
ejpam-6392	451	7	-	-	NOUN
ejpam-6392	451	8	ideals	ideal	NOUN
ejpam-6392	451	9	of	of	ADP
ejpam-6392	451	10	gamma	gamma	NOUN
ejpam-6392	451	11	-	-	PUNCT
ejpam-6392	451	12	near	near	NOUN
ejpam-6392	451	13	rings	ring	NOUN
ejpam-6392	451	14	.	.	PUNCT
ejpam-6392	452	1	in	in	ADP
ejpam-6392	452	2	aip	aip	PROPN
ejpam-6392	452	3	conference	conference	NOUN
ejpam-6392	452	4	proceedings	proceeding	NOUN
ejpam-6392	452	5	,	,	PUNCT
ejpam-6392	452	6	volume	volume	NOUN
ejpam-6392	452	7	2707	2707	NUM
ejpam-6392	452	8	,	,	PUNCT
ejpam-6392	452	9	page	page	NOUN
ejpam-6392	452	10	020014	020014	NUM
ejpam-6392	452	11	,	,	PUNCT
ejpam-6392	452	12	2023	2023	NUM
ejpam-6392	452	13	.	.	PUNCT
ejpam-6392	453	1	[	[	X
ejpam-6392	453	2	23	23	NUM
ejpam-6392	453	3	]	]	X
ejpam-6392	453	4	niovi	niovi	NOUN
ejpam-6392	453	5	kehayopulu	kehayopulu	VERB
ejpam-6392	453	6	and	and	CCONJ
ejpam-6392	453	7	michael	michael	PROPN
ejpam-6392	453	8	tsingelis	tsingelis	PROPN
ejpam-6392	453	9	.	.	PUNCT
ejpam-6392	454	1	fuzzy	fuzzy	ADJ
ejpam-6392	454	2	bi	bi	NOUN
ejpam-6392	454	3	-	-	NOUN
ejpam-6392	454	4	ideals	ideal	NOUN
ejpam-6392	454	5	in	in	ADP
ejpam-6392	454	6	ordered	order	VERB
ejpam-6392	454	7	semigroups	semigroup	NOUN
ejpam-6392	454	8	.	.	PUNCT
ejpam-6392	455	1	m.	m.	NOUN
ejpam-6392	455	2	remala	remala	NOUN
ejpam-6392	455	3	,	,	PUNCT
ejpam-6392	455	4	e.	e.	PROPN
ejpam-6392	455	5	tamma	tamma	PROPN
ejpam-6392	455	6	,	,	PUNCT
ejpam-6392	455	7	y.	y.	PROPN
ejpam-6392	455	8	bhargavi	bhargavi	PROPN
ejpam-6392	455	9	/	/	SYM
ejpam-6392	455	10	eur	eur	PROPN
ejpam-6392	455	11	.	.	PUNCT
ejpam-6392	456	1	j.	j.	PROPN
ejpam-6392	456	2	pure	pure	PROPN
ejpam-6392	456	3	appl	appl	PROPN
ejpam-6392	456	4	.	.	PROPN
ejpam-6392	456	5	math	math	PROPN
ejpam-6392	456	6	,	,	PUNCT
ejpam-6392	456	7	18	18	NUM
ejpam-6392	456	8	(	(	PUNCT
ejpam-6392	456	9	4	4	NUM
ejpam-6392	456	10	)	)	PUNCT
ejpam-6392	456	11	(	(	PUNCT
ejpam-6392	456	12	2025	2025	NUM
ejpam-6392	456	13	)	)	PUNCT
ejpam-6392	456	14	,	,	PUNCT
ejpam-6392	456	15	6392	6392	NUM
ejpam-6392	456	16	20	20	NUM
ejpam-6392	456	17	of	of	ADP
ejpam-6392	456	18	20	20	NUM
ejpam-6392	456	19	information	information	NOUN
ejpam-6392	456	20	sciences	science	NOUN
ejpam-6392	456	21	,	,	PUNCT
ejpam-6392	456	22	171(1–3):13–28	171(1–3):13–28	PROPN
ejpam-6392	456	23	,	,	PUNCT
ejpam-6392	456	24	2005	2005	NUM
ejpam-6392	456	25	.	.	PUNCT
ejpam-6392	457	1	[	[	X
ejpam-6392	457	2	24	24	NUM
ejpam-6392	457	3	]	]	PUNCT
ejpam-6392	457	4	osman	osman	PROPN
ejpam-6392	457	5	kazanci	kazanci	PROPN
ejpam-6392	457	6	and	and	CCONJ
ejpam-6392	457	7	sultan	sultan	PROPN
ejpam-6392	457	8	yamak	yamak	PROPN
ejpam-6392	457	9	.	.	PUNCT
ejpam-6392	458	1	generalized	generalize	VERB
ejpam-6392	458	2	fuzzy	fuzzy	ADJ
ejpam-6392	458	3	bi	bi	NOUN
ejpam-6392	458	4	-	-	NOUN
ejpam-6392	458	5	ideals	ideal	NOUN
ejpam-6392	458	6	of	of	ADP
ejpam-6392	458	7	semigroups	semigroup	NOUN
ejpam-6392	458	8	.	.	PUNCT
ejpam-6392	459	1	soft	soft	ADJ
ejpam-6392	459	2	computing	computing	NOUN
ejpam-6392	459	3	,	,	PUNCT
ejpam-6392	459	4	12(11):1119–1124	12(11):1119–1124	NUM
ejpam-6392	459	5	,	,	PUNCT
ejpam-6392	459	6	2008	2008	NUM
ejpam-6392	459	7	.	.	PUNCT
ejpam-6392	460	1	[	[	X
ejpam-6392	460	2	25	25	NUM
ejpam-6392	460	3	]	]	PUNCT
ejpam-6392	460	4	aiyared	aiyare	VERB
ejpam-6392	460	5	iampan	iampan	PROPN
ejpam-6392	460	6	.	.	PUNCT
ejpam-6392	461	1	note	note	NOUN
ejpam-6392	461	2	on	on	ADP
ejpam-6392	461	3	bi	bi	NOUN
ejpam-6392	461	4	-	-	NOUN
ejpam-6392	461	5	ideals	ideal	NOUN
ejpam-6392	461	6	in	in	ADP
ejpam-6392	461	7	γ	γ	NOUN
ejpam-6392	461	8	-	-	PUNCT
ejpam-6392	461	9	semigroups	semigroup	NOUN
ejpam-6392	461	10	.	.	PUNCT
ejpam-6392	462	1	international	international	ADJ
ejpam-6392	462	2	journal	journal	NOUN
ejpam-6392	462	3	of	of	ADP
ejpam-6392	462	4	algebra	algebra	PROPN
ejpam-6392	462	5	,	,	PUNCT
ejpam-6392	462	6	3(4):181–188	3(4):181–188	NUM
ejpam-6392	462	7	,	,	PUNCT
ejpam-6392	462	8	2009	2009	NUM
ejpam-6392	462	9	.	.	PUNCT
ejpam-6392	463	1	[	[	X
ejpam-6392	463	2	26	26	NUM
ejpam-6392	463	3	]	]	PUNCT
ejpam-6392	463	4	p.	p.	PROPN
ejpam-6392	463	5	ayesha	ayesha	PROPN
ejpam-6392	463	6	parveen	parveen	PROPN
ejpam-6392	463	7	and	and	CCONJ
ejpam-6392	463	8	m.	m.	PROPN
ejpam-6392	463	9	himaya	himaya	PROPN
ejpam-6392	463	10	jaleela	jaleela	PROPN
ejpam-6392	463	11	begum	begum	PROPN
ejpam-6392	463	12	.	.	PUNCT
ejpam-6392	464	1	neutrosophic	neutrosophic	ADJ
ejpam-6392	464	2	doubt	doubt	VERB
ejpam-6392	464	3	fuzzy	fuzzy	ADJ
ejpam-6392	464	4	bi	bi	NOUN
ejpam-6392	464	5	-	-	NOUN
ejpam-6392	464	6	ideal	ideal	NOUN
ejpam-6392	464	7	of	of	ADP
ejpam-6392	464	8	bs	b	NOUN
ejpam-6392	464	9	-	-	PUNCT
ejpam-6392	464	10	algebras	algebras	PROPN
ejpam-6392	464	11	.	.	PUNCT
ejpam-6392	464	12	neutrosophic	neutrosophic	ADJ
ejpam-6392	464	13	sets	set	NOUN
ejpam-6392	464	14	and	and	CCONJ
ejpam-6392	464	15	systems	system	NOUN
ejpam-6392	464	16	,	,	PUNCT
ejpam-6392	464	17	65:101–109	65:101–109	NUM
ejpam-6392	464	18	,	,	PUNCT
ejpam-6392	464	19	2024	2024	NUM
ejpam-6392	464	20	.	.	PUNCT
ejpam-6392	465	1	[	[	X
ejpam-6392	465	2	27	27	NUM
ejpam-6392	465	3	]	]	X
ejpam-6392	465	4	p.	p.	PROPN
ejpam-6392	465	5	narasimha	narasimha	PROPN
ejpam-6392	465	6	swamy	swamy	PROPN
ejpam-6392	465	7	,	,	PUNCT
ejpam-6392	465	8	b.	b.	PROPN
ejpam-6392	465	9	jyothi	jyothi	PROPN
ejpam-6392	465	10	,	,	PUNCT
ejpam-6392	465	11	rakshita	rakshita	PROPN
ejpam-6392	465	12	deshmukh	deshmukh	PROPN
ejpam-6392	465	13	,	,	PUNCT
ejpam-6392	465	14	and	and	CCONJ
ejpam-6392	465	15	t.	t.	PROPN
ejpam-6392	465	16	srinivas	srinivas	PROPN
ejpam-6392	465	17	.	.	PUNCT
ejpam-6392	466	1	quasi	quasi	ADJ
ejpam-6392	466	2	-	-	NOUN
ejpam-6392	466	3	ideals	ideal	NOUN
ejpam-6392	466	4	and	and	CCONJ
ejpam-6392	466	5	bi	bi	NOUN
ejpam-6392	466	6	-	-	NOUN
ejpam-6392	466	7	ideals	ideal	NOUN
ejpam-6392	466	8	of	of	ADP
ejpam-6392	466	9	a	a	DET
ejpam-6392	466	10	near	near	NOUN
ejpam-6392	466	11	-	-	PUNCT
ejpam-6392	466	12	algebra	algebra	NOUN
ejpam-6392	466	13	.	.	PUNCT
ejpam-6392	467	1	international	international	ADJ
ejpam-6392	467	2	journal	journal	PROPN
ejpam-6392	467	3	of	of	ADP
ejpam-6392	467	4	engineering	engineering	NOUN
ejpam-6392	467	5	,	,	PUNCT
ejpam-6392	467	6	science	science	NOUN
ejpam-6392	467	7	and	and	CCONJ
ejpam-6392	467	8	mathematics	mathematic	NOUN
ejpam-6392	467	9	,	,	PUNCT
ejpam-6392	467	10	7(3):380–386	7(3):380–386	NUM
ejpam-6392	467	11	,	,	PUNCT
ejpam-6392	467	12	2018	2018	NUM
ejpam-6392	467	13	.	.	PUNCT
ejpam-6392	468	1	[	[	X
ejpam-6392	468	2	28	28	NUM
ejpam-6392	468	3	]	]	X
ejpam-6392	468	4	de	de	X
ejpam-6392	468	5	gruyter	gruyter	NOUN
ejpam-6392	468	6	.	.	PUNCT
ejpam-6392	469	1	mbj	mbj	PROPN
ejpam-6392	469	2	-	-	PUNCT
ejpam-6392	469	3	neutrosophic	neutrosophic	ADJ
ejpam-6392	469	4	ideals	ideal	NOUN
ejpam-6392	469	5	of	of	ADP
ejpam-6392	469	6	bck	bck	PROPN
ejpam-6392	469	7	/	/	SYM
ejpam-6392	469	8	bci	bci	NOUN
ejpam-6392	469	9	-	-	PUNCT
ejpam-6392	469	10	algebras	algebras	X
ejpam-6392	469	11	.	.	PUNCT
ejpam-6392	470	1	open	open	ADJ
ejpam-6392	470	2	mathematics	mathematic	NOUN
ejpam-6392	470	3	,	,	PUNCT
ejpam-6392	470	4	17(5):588–601	17(5):588–601	PROPN
ejpam-6392	470	5	,	,	PUNCT
ejpam-6392	470	6	2019	2019	NUM
ejpam-6392	470	7	.	.	PUNCT
ejpam-6392	471	1	[	[	X
ejpam-6392	471	2	29	29	NUM
ejpam-6392	471	3	]	]	X
ejpam-6392	471	4	g.	g.	PROPN
ejpam-6392	471	5	muhiuddin	muhiuddin	PROPN
ejpam-6392	471	6	and	and	CCONJ
ejpam-6392	471	7	young	young	ADJ
ejpam-6392	471	8	bae	bae	PROPN
ejpam-6392	471	9	jun	jun	PROPN
ejpam-6392	471	10	.	.	PROPN
ejpam-6392	471	11	further	further	ADJ
ejpam-6392	471	12	results	result	NOUN
ejpam-6392	471	13	of	of	ADP
ejpam-6392	471	14	neutrosophic	neutrosophic	ADJ
ejpam-6392	471	15	subalgebras	subalgebra	NOUN
ejpam-6392	471	16	in	in	ADP
ejpam-6392	471	17	bck	bck	PROPN
ejpam-6392	471	18	/	/	SYM
ejpam-6392	471	19	bci	bci	NOUN
ejpam-6392	471	20	-	-	PUNCT
ejpam-6392	471	21	algebras	algebras	PROPN
ejpam-6392	471	22	based	base	VERB
ejpam-6392	471	23	on	on	ADP
ejpam-6392	471	24	neutrosophic	neutrosophic	ADJ
ejpam-6392	471	25	points	point	NOUN
ejpam-6392	471	26	.	.	PUNCT
ejpam-6392	472	1	turkic	turkic	PROPN
ejpam-6392	472	2	world	world	PROPN
ejpam-6392	472	3	mathematic	mathematic	PROPN
ejpam-6392	472	4	society	society	PROPN
ejpam-6392	472	5	journal	journal	PROPN
ejpam-6392	472	6	of	of	ADP
ejpam-6392	472	7	applied	apply	VERB
ejpam-6392	472	8	and	and	CCONJ
ejpam-6392	472	9	engineering	engineering	NOUN
ejpam-6392	472	10	mathematics	mathematic	NOUN
ejpam-6392	472	11	,	,	PUNCT
ejpam-6392	472	12	10:232–240	10:232–240	NUM
ejpam-6392	472	13	,	,	PUNCT
ejpam-6392	472	14	2020	2020	NUM
ejpam-6392	472	15	.	.	PUNCT
ejpam-6392	473	1	[	[	X
ejpam-6392	473	2	30	30	NUM
ejpam-6392	473	3	]	]	X
ejpam-6392	473	4	m.	m.	NOUN
ejpam-6392	473	5	kaviyarasu	kaviyarasu	PROPN
ejpam-6392	473	6	and	and	CCONJ
ejpam-6392	473	7	k.	k.	PROPN
ejpam-6392	473	8	indhira	indhira	PROPN
ejpam-6392	473	9	.	.	PUNCT
ejpam-6392	474	1	derivation	derivation	NOUN
ejpam-6392	474	2	in	in	ADP
ejpam-6392	474	3	ink	ink	NOUN
ejpam-6392	474	4	–	–	PUNCT
ejpam-6392	474	5	algebras	algebras	X
ejpam-6392	474	6	.	.	PUNCT
ejpam-6392	475	1	in	in	ADP
ejpam-6392	475	2	aip	aip	PROPN
ejpam-6392	475	3	conference	conference	NOUN
ejpam-6392	475	4	proceedings	proceeding	NOUN
ejpam-6392	475	5	,	,	PUNCT
ejpam-6392	475	6	volume	volume	NOUN
ejpam-6392	475	7	1952	1952	NUM
ejpam-6392	475	8	,	,	PUNCT
ejpam-6392	475	9	page	page	NOUN
ejpam-6392	475	10	020049	020049	NUM
ejpam-6392	475	11	,	,	PUNCT
ejpam-6392	475	12	2018	2018	NUM
ejpam-6392	475	13	.	.	PUNCT