id	sid	tid	token	lemma	pos
ejpam-5090	1	1	european	european	PROPN
ejpam-5090	1	2	journal	journal	PROPN
ejpam-5090	1	3	of	of	ADP
ejpam-5090	1	4	pure	pure	ADJ
ejpam-5090	1	5	and	and	CCONJ
ejpam-5090	1	6	applied	apply	VERB
ejpam-5090	1	7	mathematics	mathematic	NOUN
ejpam-5090	1	8	vol	vol	NOUN
ejpam-5090	1	9	.	.	PROPN
ejpam-5090	2	1	17	17	NUM
ejpam-5090	2	2	,	,	PUNCT
ejpam-5090	2	3	no	no	INTJ
ejpam-5090	2	4	.	.	NOUN
ejpam-5090	2	5	2	2	NUM
ejpam-5090	2	6	,	,	PUNCT
ejpam-5090	2	7	2024	2024	NUM
ejpam-5090	2	8	,	,	PUNCT
ejpam-5090	2	9	1113	1113	NUM
ejpam-5090	2	10	-	-	SYM
ejpam-5090	2	11	1128	1128	NUM
ejpam-5090	2	12	issn	issn	PROPN
ejpam-5090	2	13	1307	1307	NUM
ejpam-5090	2	14	-	-	SYM
ejpam-5090	2	15	5543	5543	NUM
ejpam-5090	2	16	–	–	PUNCT
ejpam-5090	3	1	ejpam.com	ejpam.com	X
ejpam-5090	3	2	published	publish	VERB
ejpam-5090	3	3	by	by	ADP
ejpam-5090	3	4	new	new	PROPN
ejpam-5090	3	5	york	york	PROPN
ejpam-5090	3	6	business	business	PROPN
ejpam-5090	3	7	global	global	PROPN
ejpam-5090	3	8	fermatean	fermatean	PROPN
ejpam-5090	3	9	neutrosophic	neutrosophic	PROPN
ejpam-5090	3	10	ink	ink	NOUN
ejpam-5090	3	11	-	-	PUNCT
ejpam-5090	3	12	algebras	algebras	PROPN
ejpam-5090	3	13	anas	anas	PROPN
ejpam-5090	3	14	al	al	PROPN
ejpam-5090	3	15	-	-	PROPN
ejpam-5090	3	16	masarwah	masarwah	PROPN
ejpam-5090	3	17	1	1	NUM
ejpam-5090	3	18	,	,	PUNCT
ejpam-5090	3	19	m.	m.	NOUN
ejpam-5090	3	20	kaviyarasu2,∗	kaviyarasu2,∗	PROPN
ejpam-5090	3	21	,	,	PUNCT
ejpam-5090	3	22	kholood	kholood	NOUN
ejpam-5090	3	23	alnefaie3	alnefaie3	NOUN
ejpam-5090	3	24	,	,	PUNCT
ejpam-5090	3	25	m.	m.	NOUN
ejpam-5090	3	26	rajeshwari	rajeshwari	NOUN
ejpam-5090	3	27	4	4	NUM
ejpam-5090	3	28	1	1	NUM
ejpam-5090	3	29	department	department	NOUN
ejpam-5090	3	30	of	of	ADP
ejpam-5090	3	31	mathematics	mathematic	NOUN
ejpam-5090	3	32	,	,	PUNCT
ejpam-5090	3	33	faculty	faculty	NOUN
ejpam-5090	3	34	of	of	ADP
ejpam-5090	3	35	science	science	NOUN
ejpam-5090	3	36	,	,	PUNCT
ejpam-5090	3	37	ajloun	ajloun	ADJ
ejpam-5090	3	38	national	national	ADJ
ejpam-5090	3	39	university	university	PROPN
ejpam-5090	3	40	,	,	PUNCT
ejpam-5090	3	41	p.	p.	PROPN
ejpam-5090	3	42	o.	o.	PROPN
ejpam-5090	3	43	box	box	PROPN
ejpam-5090	3	44	43	43	NUM
ejpam-5090	3	45	,	,	PUNCT
ejpam-5090	3	46	ajloun	ajloun	ADJ
ejpam-5090	3	47	26810	26810	NUM
ejpam-5090	3	48	,	,	PUNCT
ejpam-5090	3	49	jordan	jordan	PROPN
ejpam-5090	3	50	2	2	NUM
ejpam-5090	3	51	department	department	NOUN
ejpam-5090	3	52	of	of	ADP
ejpam-5090	3	53	mathematics	mathematic	NOUN
ejpam-5090	3	54	,	,	PUNCT
ejpam-5090	3	55	vel	vel	PROPN
ejpam-5090	3	56	tech	tech	PROPN
ejpam-5090	3	57	rangarajan	rangarajan	PROPN
ejpam-5090	3	58	dr	dr	PROPN
ejpam-5090	3	59	sagunthala	sagunthala	PROPN
ejpam-5090	3	60	r&d	r&d	PROPN
ejpam-5090	3	61	institute	institute	PROPN
ejpam-5090	3	62	of	of	ADP
ejpam-5090	3	63	science	science	NOUN
ejpam-5090	3	64	and	and	CCONJ
ejpam-5090	3	65	technology	technology	NOUN
ejpam-5090	3	66	,	,	PUNCT
ejpam-5090	3	67	chennai	chennai	PROPN
ejpam-5090	3	68	,	,	PUNCT
ejpam-5090	3	69	tamil	tamil	PROPN
ejpam-5090	3	70	nadu	nadu	NOUN
ejpam-5090	3	71	,	,	PUNCT
ejpam-5090	3	72	india-600	india-600	ADP
ejpam-5090	3	73	062	062	NUM
ejpam-5090	3	74	3	3	NUM
ejpam-5090	3	75	department	department	NOUN
ejpam-5090	3	76	of	of	ADP
ejpam-5090	3	77	mathematics	mathematic	NOUN
ejpam-5090	3	78	,	,	PUNCT
ejpam-5090	3	79	college	college	NOUN
ejpam-5090	3	80	of	of	ADP
ejpam-5090	3	81	science	science	PROPN
ejpam-5090	3	82	,	,	PUNCT
ejpam-5090	3	83	taibah	taibah	PROPN
ejpam-5090	3	84	university	university	PROPN
ejpam-5090	3	85	,	,	PUNCT
ejpam-5090	3	86	madinah	madinah	PROPN
ejpam-5090	3	87	42353	42353	NUM
ejpam-5090	3	88	,	,	PUNCT
ejpam-5090	3	89	saudi	saudi	PROPN
ejpam-5090	3	90	arabia	arabia	PROPN
ejpam-5090	3	91	4	4	NUM
ejpam-5090	3	92	department	department	NOUN
ejpam-5090	3	93	of	of	ADP
ejpam-5090	3	94	mathematics	mathematic	NOUN
ejpam-5090	3	95	,	,	PUNCT
ejpam-5090	3	96	presidency	presidency	NOUN
ejpam-5090	3	97	university	university	NOUN
ejpam-5090	3	98	,	,	PUNCT
ejpam-5090	3	99	bangalore	bangalore	NOUN
ejpam-5090	3	100	,	,	PUNCT
ejpam-5090	3	101	560064	560064	NUM
ejpam-5090	3	102	,	,	PUNCT
ejpam-5090	3	103	india	india	PROPN
ejpam-5090	3	104	.	.	PUNCT
ejpam-5090	3	105	abstract	abstract	PROPN
ejpam-5090	3	106	.	.	PUNCT
ejpam-5090	4	1	this	this	DET
ejpam-5090	4	2	paper	paper	NOUN
ejpam-5090	4	3	introduces	introduce	VERB
ejpam-5090	4	4	the	the	DET
ejpam-5090	4	5	concept	concept	NOUN
ejpam-5090	4	6	of	of	ADP
ejpam-5090	4	7	the	the	DET
ejpam-5090	4	8	direct	direct	ADJ
ejpam-5090	4	9	product	product	NOUN
ejpam-5090	4	10	of	of	ADP
ejpam-5090	4	11	sets	set	NOUN
ejpam-5090	4	12	that	that	PRON
ejpam-5090	4	13	involve	involve	VERB
ejpam-5090	4	14	fermatean	fermatean	PROPN
ejpam-5090	4	15	neutrosophic	neutrosophic	PROPN
ejpam-5090	4	16	(	(	PUNCT
ejpam-5090	4	17	fn	fn	NOUN
ejpam-5090	4	18	)	)	PUNCT
ejpam-5090	4	19	elements	element	NOUN
ejpam-5090	4	20	in	in	ADP
ejpam-5090	4	21	structures	structure	NOUN
ejpam-5090	4	22	called	call	VERB
ejpam-5090	4	23	ink	ink	NOUN
ejpam-5090	4	24	-	-	PUNCT
ejpam-5090	4	25	algebras	algebras	NOUN
ejpam-5090	4	26	.	.	PUNCT
ejpam-5090	5	1	it	it	PRON
ejpam-5090	5	2	defines	define	VERB
ejpam-5090	5	3	terms	term	NOUN
ejpam-5090	5	4	like	like	ADP
ejpam-5090	5	5	the	the	DET
ejpam-5090	5	6	direct	direct	ADJ
ejpam-5090	5	7	product	product	NOUN
ejpam-5090	5	8	of	of	ADP
ejpam-5090	5	9	fermatean	fermatean	PROPN
ejpam-5090	5	10	neutrosophic	neutrosophic	ADJ
ejpam-5090	5	11	ink	ink	NOUN
ejpam-5090	5	12	-	-	PUNCT
ejpam-5090	5	13	ideals	ideal	NOUN
ejpam-5090	5	14	(	(	PUNCT
ejpam-5090	5	15	fnink	fnink	NOUN
ejpam-5090	5	16	-	-	PUNCT
ejpam-5090	5	17	is	be	AUX
ejpam-5090	5	18	)	)	PUNCT
ejpam-5090	5	19	in	in	ADP
ejpam-5090	5	20	ink	ink	NOUN
ejpam-5090	5	21	-	-	PUNCT
ejpam-5090	5	22	algebras	algebra	NOUN
ejpam-5090	5	23	and	and	CCONJ
ejpam-5090	5	24	fermatean	fermatean	ADJ
ejpam-5090	5	25	neutrosophic	neutrosophic	ADJ
ejpam-5090	5	26	sets	set	NOUN
ejpam-5090	5	27	(	(	PUNCT
ejpam-5090	5	28	fnss	fnss	NOUN
ejpam-5090	5	29	)	)	PUNCT
ejpam-5090	5	30	,	,	PUNCT
ejpam-5090	5	31	fnink	fnink	NOUN
ejpam-5090	5	32	-	-	PUNCT
ejpam-5090	5	33	is	be	AUX
ejpam-5090	5	34	,	,	PUNCT
ejpam-5090	5	35	and	and	CCONJ
ejpam-5090	5	36	fermatean	fermatean	PROPN
ejpam-5090	5	37	neutrosophic	neutrosophic	PROPN
ejpam-5090	5	38	closed	close	VERB
ejpam-5090	5	39	ink	ink	NOUN
ejpam-5090	5	40	-	-	PUNCT
ejpam-5090	5	41	ideals	ideal	NOUN
ejpam-5090	5	42	(	(	PUNCT
ejpam-5090	5	43	fncink	fncink	NOUN
ejpam-5090	5	44	-	-	PUNCT
ejpam-5090	5	45	is	be	AUX
ejpam-5090	5	46	)	)	PUNCT
ejpam-5090	5	47	.	.	PUNCT
ejpam-5090	6	1	the	the	DET
ejpam-5090	6	2	proof	proof	NOUN
ejpam-5090	6	3	of	of	ADP
ejpam-5090	6	4	theorems	theorem	NOUN
ejpam-5090	6	5	illustrating	illustrate	VERB
ejpam-5090	6	6	the	the	DET
ejpam-5090	6	7	relationships	relationship	NOUN
ejpam-5090	6	8	between	between	ADP
ejpam-5090	6	9	these	these	DET
ejpam-5090	6	10	ideas	idea	NOUN
ejpam-5090	6	11	is	be	AUX
ejpam-5090	6	12	included	include	VERB
ejpam-5090	6	13	in	in	ADP
ejpam-5090	6	14	the	the	DET
ejpam-5090	6	15	paper	paper	NOUN
ejpam-5090	6	16	.	.	PUNCT
ejpam-5090	7	1	it	it	PRON
ejpam-5090	7	2	also	also	ADV
ejpam-5090	7	3	defines	define	VERB
ejpam-5090	7	4	the	the	DET
ejpam-5090	7	5	ink	ink	NOUN
ejpam-5090	7	6	-	-	PUNCT
ejpam-5090	7	7	subalgebra	subalgebra	NOUN
ejpam-5090	7	8	embedded	embed	VERB
ejpam-5090	7	9	in	in	ADP
ejpam-5090	7	10	an	an	DET
ejpam-5090	7	11	ink	ink	NOUN
ejpam-5090	7	12	-	-	PUNCT
ejpam-5090	7	13	algebra	algebra	NOUN
ejpam-5090	7	14	and	and	CCONJ
ejpam-5090	7	15	gives	give	VERB
ejpam-5090	7	16	a	a	DET
ejpam-5090	7	17	theorem	theorem	NOUN
ejpam-5090	7	18	elucidating	elucidate	VERB
ejpam-5090	7	19	the	the	DET
ejpam-5090	7	20	connection	connection	NOUN
ejpam-5090	7	21	between	between	ADP
ejpam-5090	7	22	the	the	DET
ejpam-5090	7	23	direct	direct	ADJ
ejpam-5090	7	24	product	product	NOUN
ejpam-5090	7	25	of	of	ADP
ejpam-5090	7	26	fnink	fnink	NOUN
ejpam-5090	7	27	-	-	PUNCT
ejpam-5090	7	28	is	be	AUX
ejpam-5090	7	29	and	and	CCONJ
ejpam-5090	7	30	the	the	DET
ejpam-5090	7	31	images	image	NOUN
ejpam-5090	7	32	of	of	ADP
ejpam-5090	7	33	these	these	DET
ejpam-5090	7	34	subalgebras	subalgebra	NOUN
ejpam-5090	7	35	.	.	PUNCT
ejpam-5090	8	1	in	in	ADP
ejpam-5090	8	2	essence	essence	NOUN
ejpam-5090	8	3	,	,	PUNCT
ejpam-5090	8	4	the	the	DET
ejpam-5090	8	5	paper	paper	NOUN
ejpam-5090	8	6	investigates	investigate	VERB
ejpam-5090	8	7	and	and	CCONJ
ejpam-5090	8	8	establishes	establish	VERB
ejpam-5090	8	9	connections	connection	NOUN
ejpam-5090	8	10	between	between	ADP
ejpam-5090	8	11	different	different	ADJ
ejpam-5090	8	12	mathematical	mathematical	ADJ
ejpam-5090	8	13	ideas	idea	NOUN
ejpam-5090	8	14	concerning	concern	VERB
ejpam-5090	8	15	ink	ink	NOUN
ejpam-5090	8	16	-	-	PUNCT
ejpam-5090	8	17	algebras	algebra	NOUN
ejpam-5090	8	18	and	and	CCONJ
ejpam-5090	8	19	fnss	fns	NOUN
ejpam-5090	8	20	.	.	PUNCT
ejpam-5090	9	1	2020	2020	NUM
ejpam-5090	9	2	mathematics	mathematic	NOUN
ejpam-5090	9	3	subject	subject	NOUN
ejpam-5090	9	4	classifications	classification	NOUN
ejpam-5090	9	5	:	:	PUNCT
ejpam-5090	9	6	03e72	03e72	NUM
ejpam-5090	9	7	,	,	PUNCT
ejpam-5090	9	8	03g25	03g25	NUM
ejpam-5090	9	9	,	,	PUNCT
ejpam-5090	9	10	28e10	28e10	NUM
ejpam-5090	9	11	,	,	PUNCT
ejpam-5090	9	12	03b52	03b52	VERB
ejpam-5090	9	13	key	key	ADJ
ejpam-5090	9	14	words	word	NOUN
ejpam-5090	9	15	and	and	CCONJ
ejpam-5090	9	16	phrases	phrase	NOUN
ejpam-5090	9	17	:	:	PUNCT
ejpam-5090	9	18	ink	ink	NOUN
ejpam-5090	9	19	-	-	PUNCT
ejpam-5090	9	20	algebra	algebra	NOUN
ejpam-5090	9	21	,	,	PUNCT
ejpam-5090	9	22	direct	direct	ADJ
ejpam-5090	9	23	product	product	NOUN
ejpam-5090	9	24	,	,	PUNCT
ejpam-5090	9	25	fermatean	fermatean	PROPN
ejpam-5090	9	26	neutrosophic	neutrosophic	PROPN
ejpam-5090	9	27	set	set	NOUN
ejpam-5090	9	28	,	,	PUNCT
ejpam-5090	9	29	fermatean	fermatean	PROPN
ejpam-5090	9	30	neutrosophic	neutrosophic	ADJ
ejpam-5090	9	31	ink	ink	NOUN
ejpam-5090	9	32	-	-	PUNCT
ejpam-5090	9	33	ideal	ideal	NOUN
ejpam-5090	9	34	,	,	PUNCT
ejpam-5090	9	35	fermatean	fermatean	PROPN
ejpam-5090	9	36	neutrosophic	neutrosophic	PROPN
ejpam-5090	9	37	closed	close	VERB
ejpam-5090	9	38	ink	ink	NOUN
ejpam-5090	9	39	-	-	PUNCT
ejpam-5090	9	40	ideal	ideal	NOUN
ejpam-5090	9	41	1	1	NUM
ejpam-5090	9	42	.	.	PUNCT
ejpam-5090	10	1	introduction	introduction	NOUN
ejpam-5090	10	2	zadeh	zadeh	NOUN
ejpam-5090	11	1	[	[	X
ejpam-5090	11	2	1	1	NUM
ejpam-5090	11	3	]	]	X
ejpam-5090	11	4	seminal	seminal	ADJ
ejpam-5090	11	5	work	work	NOUN
ejpam-5090	11	6	on	on	ADP
ejpam-5090	11	7	fuzzy	fuzzy	ADJ
ejpam-5090	11	8	sets	set	NOUN
ejpam-5090	11	9	established	establish	VERB
ejpam-5090	11	10	the	the	DET
ejpam-5090	11	11	basis	basis	NOUN
ejpam-5090	11	12	for	for	ADP
ejpam-5090	11	13	fuzzy	fuzzy	ADJ
ejpam-5090	11	14	logic	logic	NOUN
ejpam-5090	11	15	.	.	PUNCT
ejpam-5090	12	1	fuzzy	fuzzy	ADJ
ejpam-5090	12	2	sets	set	NOUN
ejpam-5090	12	3	provide	provide	VERB
ejpam-5090	12	4	a	a	DET
ejpam-5090	12	5	more	more	ADV
ejpam-5090	12	6	flexible	flexible	ADJ
ejpam-5090	12	7	representation	representation	NOUN
ejpam-5090	12	8	of	of	ADP
ejpam-5090	12	9	uncertainty	uncertainty	NOUN
ejpam-5090	12	10	by	by	ADP
ejpam-5090	12	11	assigning	assign	VERB
ejpam-5090	12	12	degrees	degree	NOUN
ejpam-5090	12	13	of	of	ADP
ejpam-5090	12	14	membership	membership	NOUN
ejpam-5090	12	15	to	to	ADP
ejpam-5090	12	16	elements	element	NOUN
ejpam-5090	12	17	.	.	PUNCT
ejpam-5090	13	1	atanassov	atanassov	PROPN
ejpam-5090	14	1	[	[	X
ejpam-5090	14	2	2	2	NUM
ejpam-5090	14	3	]	]	PUNCT
ejpam-5090	14	4	paper	paper	NOUN
ejpam-5090	14	5	explores	explore	NOUN
ejpam-5090	14	6	intuitionistic	intuitionistic	ADJ
ejpam-5090	14	7	fuzzy	fuzzy	ADJ
ejpam-5090	14	8	sets	set	NOUN
ejpam-5090	14	9	,	,	PUNCT
ejpam-5090	14	10	which	which	PRON
ejpam-5090	14	11	include	include	VERB
ejpam-5090	14	12	degrees	degree	NOUN
ejpam-5090	14	13	of	of	ADP
ejpam-5090	14	14	membership	membership	NOUN
ejpam-5090	14	15	and	and	CCONJ
ejpam-5090	14	16	degrees	degree	NOUN
ejpam-5090	14	17	of	of	ADP
ejpam-5090	14	18	non	non	ADJ
ejpam-5090	14	19	-	-	NOUN
ejpam-5090	14	20	membership	membership	NOUN
ejpam-5090	14	21	.	.	PUNCT
ejpam-5090	15	1	this	this	PRON
ejpam-5090	15	2	gives	give	VERB
ejpam-5090	15	3	a	a	DET
ejpam-5090	15	4	more	more	ADV
ejpam-5090	15	5	complete	complete	ADJ
ejpam-5090	15	6	picture	picture	NOUN
ejpam-5090	15	7	of	of	ADP
ejpam-5090	15	8	uncertainty	uncertainty	NOUN
ejpam-5090	15	9	in	in	ADP
ejpam-5090	15	10	decision	decision	NOUN
ejpam-5090	15	11	-	-	PUNCT
ejpam-5090	15	12	making	making	NOUN
ejpam-5090	15	13	.	.	PUNCT
ejpam-5090	16	1	neutrosophic	neutrosophic	ADJ
ejpam-5090	16	2	logic	logic	NOUN
ejpam-5090	16	3	has	have	AUX
ejpam-5090	16	4	been	be	AUX
ejpam-5090	16	5	introduced	introduce	VERB
ejpam-5090	16	6	by	by	ADP
ejpam-5090	16	7	smarandache	smarandache	NOUN
ejpam-5090	16	8	which	which	PRON
ejpam-5090	16	9	involves	involve	VERB
ejpam-5090	16	10	various	various	ADJ
ejpam-5090	16	11	disciplines	discipline	NOUN
ejpam-5090	16	12	of	of	ADP
ejpam-5090	16	13	philosophy	philosophy	NOUN
ejpam-5090	16	14	and	and	CCONJ
ejpam-5090	16	15	mathematics	mathematic	NOUN
ejpam-5090	16	16	that	that	PRON
ejpam-5090	16	17	studies	study	VERB
ejpam-5090	16	18	indeterminacy	indeterminacy	NOUN
ejpam-5090	16	19	,	,	PUNCT
ejpam-5090	16	20	uncertainty	uncertainty	NOUN
ejpam-5090	16	21	,	,	PUNCT
ejpam-5090	16	22	and	and	CCONJ
ejpam-5090	16	23	contradictions	contradiction	NOUN
ejpam-5090	16	24	.	.	PUNCT
ejpam-5090	17	1	neutrosophic	neutrosophic	ADJ
ejpam-5090	17	2	logic	logic	NOUN
ejpam-5090	17	3	is	be	AUX
ejpam-5090	17	4	a	a	DET
ejpam-5090	17	5	three	three	NUM
ejpam-5090	17	6	-	-	PUNCT
ejpam-5090	17	7	valued	value	VERB
ejpam-5090	17	8	logic	logic	NOUN
ejpam-5090	17	9	system	system	NOUN
ejpam-5090	17	10	∗corresponding	∗corresponde	VERB
ejpam-5090	17	11	author	author	NOUN
ejpam-5090	17	12	.	.	PUNCT
ejpam-5090	18	1	doi	doi	NOUN
ejpam-5090	18	2	:	:	PUNCT
ejpam-5090	18	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5090	https://doi.org/10.29020/nybg.ejpam.v17i2.5090	PRON
ejpam-5090	18	4	email	email	NOUN
ejpam-5090	18	5	addresses	address	NOUN
ejpam-5090	18	6	:	:	PUNCT
ejpam-5090	18	7	anas.almasarwah@anu.edu.jo	anas.almasarwah@anu.edu.jo	PROPN
ejpam-5090	18	8	(	(	PUNCT
ejpam-5090	18	9	a.	a.	PROPN
ejpam-5090	18	10	al	al	PROPN
ejpam-5090	18	11	-	-	PROPN
ejpam-5090	18	12	masarwah	masarwah	NOUN
ejpam-5090	18	13	)	)	PUNCT
ejpam-5090	18	14	,	,	PUNCT
ejpam-5090	18	15	kavitamilm@gmail.com	kavitamilm@gmail.com	PROPN
ejpam-5090	18	16	(	(	PUNCT
ejpam-5090	18	17	m.	m.	PROPN
ejpam-5090	18	18	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	18	19	)	)	PUNCT
ejpam-5090	18	20	,	,	PUNCT
ejpam-5090	18	21	knefaie@taibahu.edu.sa	knefaie@taibahu.edu.sa	PROPN
ejpam-5090	18	22	(	(	PUNCT
ejpam-5090	18	23	k.	k.	PROPN
ejpam-5090	18	24	alnefaie	alnefaie	PROPN
ejpam-5090	18	25	)	)	PUNCT
ejpam-5090	18	26	,	,	PUNCT
ejpam-5090	19	1	rajeshwari@presidencyuniversity.in	rajeshwari@presidencyuniversity.in	PROPN
ejpam-5090	19	2	(	(	PUNCT
ejpam-5090	19	3	m.	m.	NOUN
ejpam-5090	19	4	rajeshwari	rajeshwari	PROPN
ejpam-5090	19	5	)	)	PUNCT
ejpam-5090	19	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5090	19	7	1113	1113	NUM
ejpam-5090	19	8	©	©	ADP
ejpam-5090	19	9	2024	2024	NUM
ejpam-5090	19	10	ejpam	ejpam	NOUN
ejpam-5090	19	11	all	all	DET
ejpam-5090	19	12	rights	right	NOUN
ejpam-5090	19	13	reserved	reserve	VERB
ejpam-5090	19	14	.	.	PUNCT
ejpam-5090	20	1	m.	m.	NOUN
ejpam-5090	20	2	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	20	3	et	et	PROPN
ejpam-5090	20	4	al	al	PROPN
ejpam-5090	20	5	.	.	PUNCT
ejpam-5090	20	6	/	/	SYM
ejpam-5090	20	7	eur	eur	PROPN
ejpam-5090	20	8	.	.	PUNCT
ejpam-5090	21	1	j.	j.	PROPN
ejpam-5090	21	2	pure	pure	PROPN
ejpam-5090	21	3	appl	appl	PROPN
ejpam-5090	21	4	.	.	PROPN
ejpam-5090	21	5	math	math	PROPN
ejpam-5090	21	6	,	,	PUNCT
ejpam-5090	21	7	17	17	NUM
ejpam-5090	21	8	(	(	PUNCT
ejpam-5090	21	9	2	2	NUM
ejpam-5090	21	10	)	)	PUNCT
ejpam-5090	21	11	(	(	PUNCT
ejpam-5090	21	12	2024	2024	NUM
ejpam-5090	21	13	)	)	PUNCT
ejpam-5090	21	14	,	,	PUNCT
ejpam-5090	21	15	1113	1113	NUM
ejpam-5090	21	16	-	-	SYM
ejpam-5090	21	17	1128	1128	NUM
ejpam-5090	21	18	1114	1114	NUM
ejpam-5090	21	19	that	that	PRON
ejpam-5090	21	20	includes	include	VERB
ejpam-5090	21	21	the	the	DET
ejpam-5090	21	22	truth	truth	NOUN
ejpam-5090	21	23	values	value	NOUN
ejpam-5090	21	24	”	"	PUNCT
ejpam-5090	21	25	true	true	ADJ
ejpam-5090	21	26	”	"	PUNCT
ejpam-5090	21	27	and	and	CCONJ
ejpam-5090	21	28	”	"	PUNCT
ejpam-5090	21	29	false	false	ADJ
ejpam-5090	21	30	,	,	PUNCT
ejpam-5090	21	31	”	"	PUNCT
ejpam-5090	21	32	as	as	ADV
ejpam-5090	21	33	well	well	ADV
ejpam-5090	21	34	as	as	ADP
ejpam-5090	21	35	a	a	DET
ejpam-5090	21	36	third	third	ADJ
ejpam-5090	21	37	value	value	NOUN
ejpam-5090	21	38	termed	term	VERB
ejpam-5090	21	39	indeterminate	indeterminate	NOUN
ejpam-5090	21	40	,	,	PUNCT
ejpam-5090	21	41	which	which	PRON
ejpam-5090	21	42	represents	represent	VERB
ejpam-5090	21	43	uncertain	uncertain	ADJ
ejpam-5090	21	44	or	or	CCONJ
ejpam-5090	21	45	ambiguous	ambiguous	ADJ
ejpam-5090	21	46	information	information	NOUN
ejpam-5090	21	47	.	.	PUNCT
ejpam-5090	22	1	this	this	DET
ejpam-5090	22	2	method	method	NOUN
ejpam-5090	22	3	is	be	AUX
ejpam-5090	22	4	especially	especially	ADV
ejpam-5090	22	5	beneficial	beneficial	ADJ
ejpam-5090	22	6	for	for	ADP
ejpam-5090	22	7	dealing	deal	VERB
ejpam-5090	22	8	with	with	ADP
ejpam-5090	22	9	difficulties	difficulty	NOUN
ejpam-5090	22	10	involving	involve	VERB
ejpam-5090	22	11	inadequate	inadequate	ADJ
ejpam-5090	22	12	or	or	CCONJ
ejpam-5090	22	13	inconsistent	inconsistent	ADJ
ejpam-5090	22	14	data	datum	NOUN
ejpam-5090	22	15	,	,	PUNCT
ejpam-5090	22	16	which	which	PRON
ejpam-5090	22	17	are	be	AUX
ejpam-5090	22	18	widespread	widespread	ADJ
ejpam-5090	22	19	in	in	ADP
ejpam-5090	22	20	domains	domain	NOUN
ejpam-5090	22	21	such	such	ADJ
ejpam-5090	22	22	as	as	ADP
ejpam-5090	22	23	artificial	artificial	ADJ
ejpam-5090	22	24	intelligence	intelligence	NOUN
ejpam-5090	22	25	,	,	PUNCT
ejpam-5090	22	26	decision	decision	NOUN
ejpam-5090	22	27	making	making	NOUN
ejpam-5090	22	28	,	,	PUNCT
ejpam-5090	22	29	philosophy	philosophy	NOUN
ejpam-5090	22	30	,	,	PUNCT
ejpam-5090	22	31	and	and	CCONJ
ejpam-5090	22	32	cognitive	cognitive	ADJ
ejpam-5090	22	33	science	science	NOUN
ejpam-5090	22	34	.	.	PUNCT
ejpam-5090	23	1	abdel	abdel	PROPN
ejpam-5090	23	2	-	-	PUNCT
ejpam-5090	23	3	bassset	bassset	PROPN
ejpam-5090	23	4	et	et	PROPN
ejpam-5090	23	5	al	al	PROPN
ejpam-5090	23	6	.	.	PUNCT
ejpam-5090	24	1	[	[	X
ejpam-5090	24	2	3	3	X
ejpam-5090	24	3	]	]	X
ejpam-5090	24	4	present	present	ADJ
ejpam-5090	24	5	a	a	DET
ejpam-5090	24	6	decision	decision	NOUN
ejpam-5090	24	7	-	-	PUNCT
ejpam-5090	24	8	making	make	VERB
ejpam-5090	24	9	framework	framework	NOUN
ejpam-5090	24	10	for	for	ADP
ejpam-5090	24	11	professional	professional	ADJ
ejpam-5090	24	12	selection	selection	NOUN
ejpam-5090	24	13	based	base	VERB
ejpam-5090	24	14	on	on	ADP
ejpam-5090	24	15	bipolar	bipolar	ADJ
ejpam-5090	24	16	neutrosophic	neutrosophic	ADJ
ejpam-5090	24	17	sets	set	NOUN
ejpam-5090	24	18	.	.	PUNCT
ejpam-5090	25	1	the	the	DET
ejpam-5090	25	2	approach	approach	NOUN
ejpam-5090	25	3	seeks	seek	VERB
ejpam-5090	25	4	to	to	PART
ejpam-5090	25	5	address	address	VERB
ejpam-5090	25	6	uncertainty	uncertainty	NOUN
ejpam-5090	25	7	and	and	CCONJ
ejpam-5090	25	8	imprecision	imprecision	NOUN
ejpam-5090	25	9	in	in	ADP
ejpam-5090	25	10	decision	decision	NOUN
ejpam-5090	25	11	-	-	PUNCT
ejpam-5090	25	12	making	make	VERB
ejpam-5090	25	13	processes	process	NOUN
ejpam-5090	25	14	,	,	PUNCT
ejpam-5090	25	15	his	his	PRON
ejpam-5090	25	16	work	work	NOUN
ejpam-5090	25	17	expands	expand	VERB
ejpam-5090	25	18	on	on	ADP
ejpam-5090	25	19	intuitionistic	intuitionistic	ADJ
ejpam-5090	25	20	fuzzy	fuzzy	ADJ
ejpam-5090	25	21	sets	set	NOUN
ejpam-5090	25	22	to	to	PART
ejpam-5090	25	23	include	include	VERB
ejpam-5090	25	24	neutrosophic	neutrosophic	ADJ
ejpam-5090	25	25	sets	set	NOUN
ejpam-5090	25	26	,	,	PUNCT
ejpam-5090	25	27	allowing	allow	VERB
ejpam-5090	25	28	for	for	ADP
ejpam-5090	25	29	indeterminacy	indeterminacy	NOUN
ejpam-5090	25	30	,	,	PUNCT
ejpam-5090	25	31	uncertainty	uncertainty	NOUN
ejpam-5090	25	32	,	,	PUNCT
ejpam-5090	25	33	and	and	CCONJ
ejpam-5090	25	34	contradictory	contradictory	ADJ
ejpam-5090	25	35	information	information	NOUN
ejpam-5090	25	36	[	[	X
ejpam-5090	25	37	4	4	NUM
ejpam-5090	25	38	]	]	PUNCT
ejpam-5090	25	39	.	.	PUNCT
ejpam-5090	26	1	jun	jun	PROPN
ejpam-5090	27	1	[	[	X
ejpam-5090	27	2	5	5	NUM
ejpam-5090	27	3	]	]	PUNCT
ejpam-5090	27	4	research	research	NOUN
ejpam-5090	27	5	on	on	ADP
ejpam-5090	27	6	neutrosophic	neutrosophic	ADJ
ejpam-5090	27	7	subalgebras	subalgebras	PROPN
ejpam-5090	27	8	in	in	ADP
ejpam-5090	27	9	bck	bck	PROPN
ejpam-5090	27	10	/	/	SYM
ejpam-5090	27	11	bci	bci	NOUN
ejpam-5090	27	12	-	-	PUNCT
ejpam-5090	27	13	algebras	algebras	PROPN
ejpam-5090	27	14	advances	advance	VERB
ejpam-5090	27	15	our	our	PRON
ejpam-5090	27	16	understanding	understanding	NOUN
ejpam-5090	27	17	of	of	ADP
ejpam-5090	27	18	algebraic	algebraic	ADJ
ejpam-5090	27	19	structures	structure	NOUN
ejpam-5090	27	20	with	with	ADP
ejpam-5090	27	21	neutrosophic	neutrosophic	ADJ
ejpam-5090	27	22	elements	element	NOUN
ejpam-5090	27	23	.	.	PUNCT
ejpam-5090	28	1	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	28	2	et	et	PROPN
ejpam-5090	28	3	al	al	PROPN
ejpam-5090	28	4	.	.	PUNCT
ejpam-5090	29	1	[	[	X
ejpam-5090	29	2	6	6	NUM
ejpam-5090	29	3	]	]	PUNCT
ejpam-5090	29	4	investigates	investigate	VERB
ejpam-5090	29	5	fuzzy	fuzzy	ADJ
ejpam-5090	29	6	subalgebras	subalgebra	NOUN
ejpam-5090	29	7	and	and	CCONJ
ejpam-5090	29	8	fuzzy	fuzzy	ADJ
ejpam-5090	29	9	ink	ink	NOUN
ejpam-5090	29	10	-	-	PUNCT
ejpam-5090	29	11	ideals	ideal	NOUN
ejpam-5090	29	12	in	in	ADP
ejpam-5090	29	13	ink	ink	NOUN
ejpam-5090	29	14	-	-	PUNCT
ejpam-5090	29	15	algebras	algebras	X
ejpam-5090	29	16	,	,	PUNCT
ejpam-5090	29	17	providing	provide	VERB
ejpam-5090	29	18	insights	insight	NOUN
ejpam-5090	29	19	into	into	ADP
ejpam-5090	29	20	the	the	DET
ejpam-5090	29	21	integration	integration	NOUN
ejpam-5090	29	22	of	of	ADP
ejpam-5090	29	23	fuzzy	fuzzy	ADJ
ejpam-5090	29	24	logic	logic	NOUN
ejpam-5090	29	25	in	in	ADP
ejpam-5090	29	26	algebraic	algebraic	ADJ
ejpam-5090	29	27	structures	structure	NOUN
ejpam-5090	29	28	.	.	PUNCT
ejpam-5090	30	1	additionally	additionally	ADV
ejpam-5090	30	2	,	,	PUNCT
ejpam-5090	30	3	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	30	4	and	and	CCONJ
ejpam-5090	30	5	indhira	indhira	PROPN
ejpam-5090	30	6	present	present	VERB
ejpam-5090	30	7	a	a	DET
ejpam-5090	30	8	review	review	NOUN
ejpam-5090	30	9	of	of	ADP
ejpam-5090	30	10	bci	bci	PROPN
ejpam-5090	30	11	/	/	SYM
ejpam-5090	30	12	bck	bck	NOUN
ejpam-5090	30	13	-	-	PUNCT
ejpam-5090	30	14	algebras	algebras	PROPN
ejpam-5090	30	15	and	and	CCONJ
ejpam-5090	30	16	discuss	discuss	VERB
ejpam-5090	30	17	their	their	PRON
ejpam-5090	30	18	development	development	NOUN
ejpam-5090	30	19	,	,	PUNCT
ejpam-5090	30	20	contributing	contribute	VERB
ejpam-5090	30	21	to	to	ADP
ejpam-5090	30	22	the	the	DET
ejpam-5090	30	23	understanding	understanding	NOUN
ejpam-5090	30	24	of	of	ADP
ejpam-5090	30	25	these	these	DET
ejpam-5090	30	26	specific	specific	ADJ
ejpam-5090	30	27	algebraic	algebraic	ADJ
ejpam-5090	30	28	structures	structure	NOUN
ejpam-5090	30	29	[	[	X
ejpam-5090	30	30	7	7	NUM
ejpam-5090	30	31	]	]	PUNCT
ejpam-5090	30	32	,	,	PUNCT
ejpam-5090	30	33	investigate	investigate	VERB
ejpam-5090	30	34	fuzzy	fuzzy	ADJ
ejpam-5090	30	35	p	p	NOUN
ejpam-5090	30	36	-	-	PUNCT
ejpam-5090	30	37	ideals	ideal	NOUN
ejpam-5090	30	38	in	in	ADP
ejpam-5090	30	39	ink	ink	NOUN
ejpam-5090	30	40	-	-	PUNCT
ejpam-5090	30	41	algebras	algebras	NOUN
ejpam-5090	31	1	[	[	X
ejpam-5090	31	2	8	8	NUM
ejpam-5090	31	3	]	]	PUNCT
ejpam-5090	31	4	,	,	PUNCT
ejpam-5090	31	5	adding	add	VERB
ejpam-5090	31	6	to	to	ADP
ejpam-5090	31	7	the	the	DET
ejpam-5090	31	8	understanding	understanding	NOUN
ejpam-5090	31	9	of	of	ADP
ejpam-5090	31	10	fuzzy	fuzzy	ADJ
ejpam-5090	31	11	ideals	ideal	NOUN
ejpam-5090	31	12	in	in	ADP
ejpam-5090	31	13	the	the	DET
ejpam-5090	31	14	context	context	NOUN
ejpam-5090	31	15	of	of	ADP
ejpam-5090	31	16	specific	specific	ADJ
ejpam-5090	31	17	algebraic	algebraic	ADJ
ejpam-5090	31	18	structures	structure	NOUN
ejpam-5090	31	19	.	.	PUNCT
ejpam-5090	32	1	jun	jun	PROPN
ejpam-5090	32	2	et	et	PROPN
ejpam-5090	32	3	al.[9	al.[9	PROPN
ejpam-5090	32	4	]	]	PUNCT
ejpam-5090	32	5	collaboration	collaboration	NOUN
ejpam-5090	32	6	aims	aim	VERB
ejpam-5090	32	7	to	to	PART
ejpam-5090	32	8	integrate	integrate	VERB
ejpam-5090	32	9	neutrosophic	neutrosophic	ADJ
ejpam-5090	32	10	n	n	CCONJ
ejpam-5090	32	11	-	-	PUNCT
ejpam-5090	32	12	structures	structure	NOUN
ejpam-5090	32	13	into	into	ADP
ejpam-5090	32	14	bck	bck	PROPN
ejpam-5090	32	15	/	/	SYM
ejpam-5090	32	16	bci	bci	NOUN
ejpam-5090	32	17	-	-	PUNCT
ejpam-5090	32	18	algebras	algebras	X
ejpam-5090	32	19	.	.	PUNCT
ejpam-5090	33	1	jun	jun	PROPN
ejpam-5090	33	2	et	et	PROPN
ejpam-5090	33	3	al.[10	al.[10	PROPN
ejpam-5090	33	4	]	]	PUNCT
ejpam-5090	33	5	investigate	investigate	VERB
ejpam-5090	33	6	neutrosophic	neutrosophic	ADJ
ejpam-5090	33	7	positive	positive	ADJ
ejpam-5090	33	8	implicative	implicative	ADJ
ejpam-5090	33	9	n	n	CCONJ
ejpam-5090	33	10	-	-	PUNCT
ejpam-5090	33	11	ideals	ideal	NOUN
ejpam-5090	33	12	in	in	ADP
ejpam-5090	33	13	the	the	DET
ejpam-5090	33	14	context	context	NOUN
ejpam-5090	33	15	of	of	ADP
ejpam-5090	33	16	bck	bck	PROPN
ejpam-5090	33	17	-	-	PUNCT
ejpam-5090	33	18	algebras	algebras	X
ejpam-5090	33	19	,	,	PUNCT
ejpam-5090	33	20	advancing	advance	VERB
ejpam-5090	33	21	our	our	PRON
ejpam-5090	33	22	understanding	understanding	NOUN
ejpam-5090	33	23	of	of	ADP
ejpam-5090	33	24	neutrosophic	neutrosophic	ADJ
ejpam-5090	33	25	structures	structure	NOUN
ejpam-5090	33	26	in	in	ADP
ejpam-5090	33	27	algebraic	algebraic	PROPN
ejpam-5090	33	28	systems	system	NOUN
ejpam-5090	33	29	.	.	PUNCT
ejpam-5090	34	1	ozturk	ozturk	PROPN
ejpam-5090	34	2	and	and	CCONJ
ejpam-5090	34	3	jun	jun	PROPN
ejpam-5090	35	1	[	[	X
ejpam-5090	35	2	11	11	NUM
ejpam-5090	35	3	]	]	PUNCT
ejpam-5090	35	4	investigates	investigate	VERB
ejpam-5090	35	5	neutrosophic	neutrosophic	ADJ
ejpam-5090	35	6	ideals	ideal	NOUN
ejpam-5090	35	7	in	in	ADP
ejpam-5090	35	8	bck	bck	PROPN
ejpam-5090	35	9	/	/	SYM
ejpam-5090	35	10	bci	bci	PROPN
ejpam-5090	35	11	algebras	algebras	PROPN
ejpam-5090	35	12	based	base	VERB
ejpam-5090	35	13	on	on	ADP
ejpam-5090	35	14	neutrosophic	neutrosophic	ADJ
ejpam-5090	35	15	points	point	NOUN
ejpam-5090	35	16	,	,	PUNCT
ejpam-5090	35	17	broadening	broaden	VERB
ejpam-5090	35	18	the	the	DET
ejpam-5090	35	19	application	application	NOUN
ejpam-5090	35	20	of	of	ADP
ejpam-5090	35	21	neutrosophic	neutrosophic	ADJ
ejpam-5090	35	22	concepts	concept	NOUN
ejpam-5090	35	23	to	to	ADP
ejpam-5090	35	24	algebraic	algebraic	ADJ
ejpam-5090	35	25	structures	structure	NOUN
ejpam-5090	35	26	.	.	PUNCT
ejpam-5090	36	1	songsaeng	songsaeng	PROPN
ejpam-5090	36	2	and	and	CCONJ
ejpam-5090	36	3	iampan	iampan	PROPN
ejpam-5090	36	4	[	[	X
ejpam-5090	36	5	12	12	NUM
ejpam-5090	36	6	]	]	PUNCT
ejpam-5090	36	7	introduce	introduce	VERB
ejpam-5090	36	8	neutrosophic	neutrosophic	ADJ
ejpam-5090	36	9	set	set	NOUN
ejpam-5090	36	10	theory	theory	NOUN
ejpam-5090	36	11	to	to	ADP
ejpam-5090	36	12	up	up	ADP
ejpam-5090	36	13	-	-	PUNCT
ejpam-5090	36	14	algebra	algebra	NOUN
ejpam-5090	36	15	and	and	CCONJ
ejpam-5090	36	16	demonstrate	demonstrate	VERB
ejpam-5090	36	17	its	its	PRON
ejpam-5090	36	18	utility	utility	NOUN
ejpam-5090	36	19	in	in	ADP
ejpam-5090	36	20	a	a	DET
ejpam-5090	36	21	specific	specific	ADJ
ejpam-5090	36	22	algebraic	algebraic	ADJ
ejpam-5090	36	23	context.kaviyarasu	context.kaviyarasu	NOUN
ejpam-5090	36	24	,	,	PUNCT
ejpam-5090	36	25	indhira	indhira	NOUN
ejpam-5090	36	26	and	and	CCONJ
ejpam-5090	36	27	chandrasekaran	chandrasekaran	VERB
ejpam-5090	37	1	[	[	X
ejpam-5090	37	2	[	[	X
ejpam-5090	37	3	13	13	NUM
ejpam-5090	37	4	]	]	PUNCT
ejpam-5090	37	5	,	,	PUNCT
ejpam-5090	38	1	[	[	X
ejpam-5090	38	2	14	14	NUM
ejpam-5090	38	3	]	]	PUNCT
ejpam-5090	38	4	,	,	PUNCT
ejpam-5090	38	5	[	[	X
ejpam-5090	38	6	15	15	NUM
ejpam-5090	38	7	]	]	X
ejpam-5090	38	8	]	]	PUNCT
ejpam-5090	38	9	investigate	investigate	VERB
ejpam-5090	38	10	the	the	DET
ejpam-5090	38	11	direct	direct	ADJ
ejpam-5090	38	12	product	product	NOUN
ejpam-5090	38	13	of	of	ADP
ejpam-5090	38	14	intuitionistic	intuitionistic	ADJ
ejpam-5090	38	15	fuzzy	fuzzy	ADJ
ejpam-5090	38	16	ink	ink	NOUN
ejpam-5090	38	17	-	-	PUNCT
ejpam-5090	38	18	ideals	ideal	NOUN
ejpam-5090	38	19	,	,	PUNCT
ejpam-5090	38	20	providing	provide	VERB
ejpam-5090	38	21	insights	insight	NOUN
ejpam-5090	38	22	into	into	ADP
ejpam-5090	38	23	the	the	DET
ejpam-5090	38	24	interaction	interaction	NOUN
ejpam-5090	38	25	of	of	ADP
ejpam-5090	38	26	different	different	ADJ
ejpam-5090	38	27	algebraic	algebraic	ADJ
ejpam-5090	38	28	structures	structure	NOUN
ejpam-5090	38	29	;	;	PUNCT
ejpam-5090	38	30	discuss	discuss	VERB
ejpam-5090	38	31	intuitionistic	intuitionistic	ADJ
ejpam-5090	38	32	fuzzy	fuzzy	ADJ
ejpam-5090	38	33	translation	translation	NOUN
ejpam-5090	38	34	in	in	ADP
ejpam-5090	38	35	ink	ink	NOUN
ejpam-5090	38	36	-	-	PUNCT
ejpam-5090	38	37	algebra	algebra	NOUN
ejpam-5090	38	38	,	,	PUNCT
ejpam-5090	38	39	contributing	contribute	VERB
ejpam-5090	38	40	to	to	ADP
ejpam-5090	38	41	the	the	DET
ejpam-5090	38	42	understanding	understanding	NOUN
ejpam-5090	38	43	of	of	ADP
ejpam-5090	38	44	translation	translation	NOUN
ejpam-5090	38	45	operations	operation	NOUN
ejpam-5090	38	46	in	in	ADP
ejpam-5090	38	47	algebraic	algebraic	ADJ
ejpam-5090	38	48	structures	structure	NOUN
ejpam-5090	38	49	;	;	PUNCT
ejpam-5090	38	50	and	and	CCONJ
ejpam-5090	38	51	apply	apply	VERB
ejpam-5090	38	52	neutrosophic	neutrosophic	ADJ
ejpam-5090	38	53	sets	set	NOUN
ejpam-5090	38	54	in	in	ADP
ejpam-5090	38	55	ink	ink	NOUN
ejpam-5090	38	56	-	-	PUNCT
ejpam-5090	38	57	algebra	algebra	NOUN
ejpam-5090	38	58	,	,	PUNCT
ejpam-5090	38	59	extending	extend	VERB
ejpam-5090	38	60	the	the	DET
ejpam-5090	38	61	study	study	NOUN
ejpam-5090	38	62	of	of	ADP
ejpam-5090	38	63	neutrosophic	neutrosophic	ADJ
ejpam-5090	38	64	concepts	concept	NOUN
ejpam-5090	38	65	to	to	ADP
ejpam-5090	38	66	a	a	DET
ejpam-5090	38	67	specific	specific	ADJ
ejpam-5090	38	68	algebraic	algebraic	ADJ
ejpam-5090	38	69	context	context	NOUN
ejpam-5090	38	70	.	.	PUNCT
ejpam-5090	39	1	as	as	ADP
ejpam-5090	39	2	an	an	DET
ejpam-5090	39	3	extension	extension	NOUN
ejpam-5090	39	4	of	of	ADP
ejpam-5090	39	5	partial	partial	ADJ
ejpam-5090	39	6	algebra	algebra	NOUN
ejpam-5090	39	7	,	,	PUNCT
ejpam-5090	39	8	smarandache	smarandache	NOUN
ejpam-5090	39	9	[	[	X
ejpam-5090	39	10	16	16	NUM
ejpam-5090	39	11	]	]	PUNCT
ejpam-5090	39	12	presents	present	VERB
ejpam-5090	39	13	the	the	DET
ejpam-5090	39	14	theory	theory	NOUN
ejpam-5090	39	15	of	of	ADP
ejpam-5090	39	16	neutro	neutro	PROPN
ejpam-5090	39	17	algebra	algebra	PROPN
ejpam-5090	39	18	,	,	PUNCT
ejpam-5090	39	19	which	which	PRON
ejpam-5090	39	20	advances	advance	VERB
ejpam-5090	39	21	the	the	DET
ejpam-5090	39	22	development	development	NOUN
ejpam-5090	39	23	of	of	ADP
ejpam-5090	39	24	algebraic	algebraic	ADJ
ejpam-5090	39	25	structures	structure	NOUN
ejpam-5090	39	26	in	in	ADP
ejpam-5090	39	27	addition	addition	NOUN
ejpam-5090	39	28	to	to	ADP
ejpam-5090	39	29	neutro	neutro	NOUN
ejpam-5090	39	30	and	and	CCONJ
ejpam-5090	39	31	anti	anti	ADJ
ejpam-5090	39	32	-	-	ADJ
ejpam-5090	39	33	algebraic	algebraic	ADJ
ejpam-5090	39	34	structures	structure	NOUN
ejpam-5090	39	35	,	,	PUNCT
ejpam-5090	39	36	which	which	PRON
ejpam-5090	39	37	provide	provide	VERB
ejpam-5090	39	38	additional	additional	ADJ
ejpam-5090	39	39	insights	insight	NOUN
ejpam-5090	39	40	into	into	ADP
ejpam-5090	39	41	mathematical	mathematical	ADJ
ejpam-5090	39	42	structures	structure	NOUN
ejpam-5090	39	43	.	.	PUNCT
ejpam-5090	40	1	abdel	abdel	NOUN
ejpam-5090	40	2	-	-	PUNCT
ejpam-5090	40	3	basset	basset	PROPN
ejpam-5090	40	4	et	et	PROPN
ejpam-5090	40	5	al	al	PROPN
ejpam-5090	40	6	.	.	PROPN
ejpam-5090	40	7	proposed	propose	VERB
ejpam-5090	40	8	a	a	DET
ejpam-5090	40	9	novel	novel	ADJ
ejpam-5090	40	10	plithogenic	plithogenic	ADJ
ejpam-5090	40	11	model	model	NOUN
ejpam-5090	40	12	for	for	ADP
ejpam-5090	40	13	supply	supply	NOUN
ejpam-5090	40	14	chain	chain	NOUN
ejpam-5090	40	15	problem	problem	NOUN
ejpam-5090	40	16	solving	solving	NOUN
ejpam-5090	40	17	,	,	PUNCT
ejpam-5090	40	18	which	which	PRON
ejpam-5090	40	19	incorporates	incorporate	VERB
ejpam-5090	40	20	neutrosophic	neutrosophic	ADJ
ejpam-5090	40	21	and	and	CCONJ
ejpam-5090	40	22	plithogenic	plithogenic	ADJ
ejpam-5090	40	23	sets	set	NOUN
ejpam-5090	40	24	into	into	ADP
ejpam-5090	40	25	optimization	optimization	NOUN
ejpam-5090	40	26	theory	theory	NOUN
ejpam-5090	40	27	[	[	X
ejpam-5090	40	28	17	17	NUM
ejpam-5090	40	29	]	]	PUNCT
ejpam-5090	40	30	.	.	PUNCT
ejpam-5090	41	1	making	make	VERB
ejpam-5090	41	2	contributions	contribution	NOUN
ejpam-5090	41	3	to	to	ADP
ejpam-5090	41	4	the	the	DET
ejpam-5090	41	5	fields	field	NOUN
ejpam-5090	41	6	of	of	ADP
ejpam-5090	41	7	environmental	environmental	ADJ
ejpam-5090	41	8	technology	technology	NOUN
ejpam-5090	41	9	and	and	CCONJ
ejpam-5090	41	10	innovation	innovation	NOUN
ejpam-5090	41	11	,	,	PUNCT
ejpam-5090	41	12	mohamed	mohamed	PROPN
ejpam-5090	41	13	and	and	CCONJ
ejpam-5090	41	14	abdel	abdel	PROPN
ejpam-5090	42	1	[	[	X
ejpam-5090	42	2	[	[	X
ejpam-5090	42	3	18	18	NUM
ejpam-5090	42	4	]	]	PUNCT
ejpam-5090	42	5	,	,	PUNCT
ejpam-5090	42	6	[	[	X
ejpam-5090	42	7	19	19	NUM
ejpam-5090	42	8	]	]	PUNCT
ejpam-5090	42	9	,	,	PUNCT
ejpam-5090	42	10	[	[	X
ejpam-5090	42	11	20	20	NUM
ejpam-5090	42	12	]	]	PUNCT
ejpam-5090	42	13	]	]	X
ejpam-5090	42	14	introduce	introduce	VERB
ejpam-5090	42	15	an	an	DET
ejpam-5090	42	16	integrated	integrate	VERB
ejpam-5090	42	17	plithogenic	plithogenic	ADJ
ejpam-5090	42	18	mcdm	mcdm	ADJ
ejpam-5090	42	19	approach	approach	NOUN
ejpam-5090	42	20	for	for	ADP
ejpam-5090	42	21	assessing	assess	VERB
ejpam-5090	42	22	the	the	DET
ejpam-5090	42	23	financial	financial	ADJ
ejpam-5090	42	24	performance	performance	NOUN
ejpam-5090	42	25	of	of	ADP
ejpam-5090	42	26	manufacturing	manufacturing	NOUN
ejpam-5090	42	27	industries	industry	NOUN
ejpam-5090	42	28	,	,	PUNCT
ejpam-5090	42	29	utilizing	utilize	VERB
ejpam-5090	42	30	a	a	DET
ejpam-5090	42	31	combination	combination	NOUN
ejpam-5090	42	32	of	of	ADP
ejpam-5090	42	33	mathematical	mathematical	ADJ
ejpam-5090	42	34	decision	decision	NOUN
ejpam-5090	42	35	-	-	PUNCT
ejpam-5090	42	36	making	make	VERB
ejpam-5090	42	37	methods	method	NOUN
ejpam-5090	42	38	,	,	PUNCT
ejpam-5090	42	39	as	as	ADV
ejpam-5090	42	40	well	well	ADV
ejpam-5090	42	41	as	as	ADP
ejpam-5090	42	42	a	a	DET
ejpam-5090	42	43	novel	novel	ADJ
ejpam-5090	42	44	framework	framework	NOUN
ejpam-5090	42	45	for	for	ADP
ejpam-5090	42	46	assessing	assess	VERB
ejpam-5090	42	47	the	the	DET
ejpam-5090	42	48	innovation	innovation	NOUN
ejpam-5090	42	49	value	value	NOUN
ejpam-5090	42	50	proposition	proposition	NOUN
ejpam-5090	42	51	for	for	ADP
ejpam-5090	42	52	smart	smart	ADJ
ejpam-5090	42	53	productservice	productservice	NOUN
ejpam-5090	42	54	systems	system	NOUN
ejpam-5090	42	55	.	.	PUNCT
ejpam-5090	43	1	neutrosophic	neutrosophic	ADJ
ejpam-5090	43	2	vague	vague	ADJ
ejpam-5090	43	3	binary	binary	ADJ
ejpam-5090	43	4	bck	bck	PROPN
ejpam-5090	43	5	/	/	SYM
ejpam-5090	43	6	bci	bci	NOUN
ejpam-5090	43	7	-	-	NOUN
ejpam-5090	43	8	algebra	algebra	NOUN
ejpam-5090	43	9	,	,	PUNCT
ejpam-5090	43	10	which	which	PRON
ejpam-5090	43	11	explores	explore	VERB
ejpam-5090	43	12	the	the	DET
ejpam-5090	43	13	use	use	NOUN
ejpam-5090	43	14	of	of	ADP
ejpam-5090	43	15	vague	vague	ADJ
ejpam-5090	43	16	and	and	CCONJ
ejpam-5090	43	17	neutrosophic	neutrosophic	ADJ
ejpam-5090	43	18	notions	notion	NOUN
ejpam-5090	43	19	in	in	ADP
ejpam-5090	43	20	a	a	DET
ejpam-5090	43	21	binary	binary	ADJ
ejpam-5090	43	22	algebraic	algebraic	ADJ
ejpam-5090	43	23	framework	framework	NOUN
ejpam-5090	43	24	,	,	PUNCT
ejpam-5090	43	25	is	be	AUX
ejpam-5090	43	26	covered	cover	VERB
ejpam-5090	43	27	by	by	ADP
ejpam-5090	43	28	remya	remya	NOUN
ejpam-5090	43	29	and	and	CCONJ
ejpam-5090	43	30	francina	francina	PROPN
ejpam-5090	43	31	shalini	shalini	PROPN
ejpam-5090	43	32	[	[	X
ejpam-5090	43	33	21	21	NUM
ejpam-5090	43	34	]	]	PUNCT
ejpam-5090	43	35	.	.	PUNCT
ejpam-5090	44	1	muralikrishna	muralikrishna	NOUN
ejpam-5090	44	2	and	and	CCONJ
ejpam-5090	44	3	manokaran	manokaran	NOUN
ejpam-5090	44	4	[	[	X
ejpam-5090	44	5	22	22	NUM
ejpam-5090	44	6	]	]	PUNCT
ejpam-5090	44	7	introduce	introduce	VERB
ejpam-5090	44	8	mbjneutrosophic	mbjneutrosophic	ADJ
ejpam-5090	44	9	b	b	NOUN
ejpam-5090	44	10	-	-	PUNCT
ejpam-5090	44	11	ideals	ideal	NOUN
ejpam-5090	44	12	in	in	ADP
ejpam-5090	44	13	b	b	NOUN
ejpam-5090	44	14	-	-	PUNCT
ejpam-5090	44	15	algebras	algebra	NOUN
ejpam-5090	44	16	,	,	PUNCT
ejpam-5090	44	17	which	which	PRON
ejpam-5090	44	18	adds	add	VERB
ejpam-5090	44	19	to	to	ADP
ejpam-5090	44	20	the	the	DET
ejpam-5090	44	21	understanding	understanding	NOUN
ejpam-5090	44	22	of	of	ADP
ejpam-5090	44	23	neutrosophic	neutrosophic	ADJ
ejpam-5090	44	24	ideals	ideal	NOUN
ejpam-5090	44	25	in	in	ADP
ejpam-5090	44	26	specific	specific	ADJ
ejpam-5090	44	27	algebraic	algebraic	ADJ
ejpam-5090	44	28	structures	structure	NOUN
ejpam-5090	44	29	.	.	PUNCT
ejpam-5090	45	1	for	for	ADP
ejpam-5090	45	2	more	more	ADJ
ejpam-5090	45	3	results	result	NOUN
ejpam-5090	45	4	on	on	ADP
ejpam-5090	45	5	algebraic	algebraic	ADJ
ejpam-5090	45	6	structures	structure	NOUN
ejpam-5090	45	7	with	with	ADP
ejpam-5090	45	8	uncertainty	uncertainty	NOUN
ejpam-5090	45	9	(	(	PUNCT
ejpam-5090	45	10	see	see	VERB
ejpam-5090	45	11	works	work	NOUN
ejpam-5090	45	12	m.	m.	PROPN
ejpam-5090	45	13	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	45	14	et	et	PROPN
ejpam-5090	45	15	al	al	PROPN
ejpam-5090	45	16	.	.	PUNCT
ejpam-5090	45	17	/	/	SYM
ejpam-5090	45	18	eur	eur	PROPN
ejpam-5090	45	19	.	.	PUNCT
ejpam-5090	46	1	j.	j.	PROPN
ejpam-5090	46	2	pure	pure	PROPN
ejpam-5090	46	3	appl	appl	PROPN
ejpam-5090	46	4	.	.	PROPN
ejpam-5090	46	5	math	math	PROPN
ejpam-5090	46	6	,	,	PUNCT
ejpam-5090	46	7	17	17	NUM
ejpam-5090	46	8	(	(	PUNCT
ejpam-5090	46	9	2	2	NUM
ejpam-5090	46	10	)	)	PUNCT
ejpam-5090	46	11	(	(	PUNCT
ejpam-5090	46	12	2024	2024	NUM
ejpam-5090	46	13	)	)	PUNCT
ejpam-5090	46	14	,	,	PUNCT
ejpam-5090	46	15	1113	1113	NUM
ejpam-5090	46	16	-	-	SYM
ejpam-5090	46	17	1128	1128	NUM
ejpam-5090	46	18	1115	1115	NUM
ejpam-5090	46	19	by	by	ADP
ejpam-5090	46	20	the	the	DET
ejpam-5090	46	21	authors	author	NOUN
ejpam-5090	46	22	of	of	ADP
ejpam-5090	46	23	[	[	X
ejpam-5090	46	24	23–27	23–27	NUM
ejpam-5090	46	25	]	]	X
ejpam-5090	46	26	.	.	PUNCT
ejpam-5090	47	1	this	this	DET
ejpam-5090	47	2	paper	paper	NOUN
ejpam-5090	47	3	presents	present	VERB
ejpam-5090	47	4	a	a	DET
ejpam-5090	47	5	new	new	ADJ
ejpam-5090	47	6	concept	concept	NOUN
ejpam-5090	47	7	based	base	VERB
ejpam-5090	47	8	on	on	ADP
ejpam-5090	47	9	two	two	NUM
ejpam-5090	47	10	distinct	distinct	ADJ
ejpam-5090	47	11	sets	set	NOUN
ejpam-5090	47	12	,	,	PUNCT
ejpam-5090	47	13	called	call	VERB
ejpam-5090	47	14	fnss	fns	NOUN
ejpam-5090	47	15	,	,	PUNCT
ejpam-5090	47	16	and	and	CCONJ
ejpam-5090	47	17	investigates	investigate	VERB
ejpam-5090	47	18	their	their	PRON
ejpam-5090	47	19	direct	direct	ADJ
ejpam-5090	47	20	product	product	NOUN
ejpam-5090	47	21	in	in	ADP
ejpam-5090	47	22	the	the	DET
ejpam-5090	47	23	framework	framework	NOUN
ejpam-5090	47	24	of	of	ADP
ejpam-5090	47	25	ink	ink	NOUN
ejpam-5090	47	26	-	-	PUNCT
ejpam-5090	47	27	algebra	algebra	NOUN
ejpam-5090	47	28	.	.	PUNCT
ejpam-5090	48	1	specifically	specifically	ADV
ejpam-5090	48	2	,	,	PUNCT
ejpam-5090	48	3	it	it	PRON
ejpam-5090	48	4	looks	look	VERB
ejpam-5090	48	5	at	at	ADP
ejpam-5090	48	6	the	the	DET
ejpam-5090	48	7	relation	relation	NOUN
ejpam-5090	48	8	between	between	ADP
ejpam-5090	48	9	fnink	fnink	NOUN
ejpam-5090	48	10	-	-	PUNCT
ejpam-5090	48	11	ss	ss	NOUN
ejpam-5090	48	12	and	and	CCONJ
ejpam-5090	48	13	fnink	fnink	NOUN
ejpam-5090	48	14	-	-	PUNCT
ejpam-5090	48	15	is	be	AUX
ejpam-5090	48	16	,	,	PUNCT
ejpam-5090	48	17	as	as	ADV
ejpam-5090	48	18	well	well	ADV
ejpam-5090	48	19	as	as	ADP
ejpam-5090	48	20	the	the	DET
ejpam-5090	48	21	conditions	condition	NOUN
ejpam-5090	48	22	that	that	PRON
ejpam-5090	48	23	hold	hold	VERB
ejpam-5090	48	24	for	for	ADP
ejpam-5090	48	25	this	this	DET
ejpam-5090	48	26	relation	relation	NOUN
ejpam-5090	48	27	.	.	PUNCT
ejpam-5090	49	1	1.1	1.1	NUM
ejpam-5090	49	2	.	.	PUNCT
ejpam-5090	49	3	motivation	motivation	NOUN
ejpam-5090	49	4	•	•	ADP
ejpam-5090	49	5	it	it	PRON
ejpam-5090	49	6	aims	aim	VERB
ejpam-5090	49	7	to	to	PART
ejpam-5090	49	8	provide	provide	VERB
ejpam-5090	49	9	a	a	DET
ejpam-5090	49	10	new	new	ADJ
ejpam-5090	49	11	perspective	perspective	NOUN
ejpam-5090	49	12	on	on	ADP
ejpam-5090	49	13	fn	fn	NOUN
ejpam-5090	49	14	elements	element	NOUN
ejpam-5090	49	15	in	in	ADP
ejpam-5090	49	16	mathematical	mathematical	ADJ
ejpam-5090	49	17	structures	structure	NOUN
ejpam-5090	49	18	.	.	PUNCT
ejpam-5090	50	1	•	•	NOUN
ejpam-5090	50	2	ensures	ensure	VERB
ejpam-5090	50	3	a	a	DET
ejpam-5090	50	4	systematic	systematic	ADJ
ejpam-5090	50	5	and	and	CCONJ
ejpam-5090	50	6	coherent	coherent	ADJ
ejpam-5090	50	7	discussion	discussion	NOUN
ejpam-5090	50	8	of	of	ADP
ejpam-5090	50	9	these	these	DET
ejpam-5090	50	10	mathematical	mathematical	ADJ
ejpam-5090	50	11	concepts	concept	NOUN
ejpam-5090	50	12	.	.	PUNCT
ejpam-5090	51	1	•	•	NUM
ejpam-5090	51	2	validating	validate	VERB
ejpam-5090	51	3	the	the	DET
ejpam-5090	51	4	proposed	propose	VERB
ejpam-5090	51	5	connections	connection	NOUN
ejpam-5090	51	6	rigorously	rigorously	ADV
ejpam-5090	51	7	through	through	ADP
ejpam-5090	51	8	theorems	theorem	NOUN
ejpam-5090	51	9	adds	add	VERB
ejpam-5090	51	10	credibility	credibility	NOUN
ejpam-5090	51	11	and	and	CCONJ
ejpam-5090	51	12	reliability	reliability	NOUN
ejpam-5090	51	13	.	.	PUNCT
ejpam-5090	52	1	•	•	NUM
ejpam-5090	52	2	exploration	exploration	NOUN
ejpam-5090	52	3	of	of	ADP
ejpam-5090	52	4	substructures	substructure	NOUN
ejpam-5090	52	5	contributes	contribute	VERB
ejpam-5090	52	6	to	to	ADP
ejpam-5090	52	7	a	a	DET
ejpam-5090	52	8	more	more	ADV
ejpam-5090	52	9	comprehensive	comprehensive	ADJ
ejpam-5090	52	10	understanding	understanding	NOUN
ejpam-5090	52	11	of	of	ADP
ejpam-5090	52	12	the	the	DET
ejpam-5090	52	13	intricate	intricate	ADJ
ejpam-5090	52	14	relationships	relationship	NOUN
ejpam-5090	52	15	within	within	ADP
ejpam-5090	52	16	the	the	DET
ejpam-5090	52	17	algebraic	algebraic	ADJ
ejpam-5090	52	18	framework	framework	NOUN
ejpam-5090	52	19	.	.	PUNCT
ejpam-5090	53	1	1.2	1.2	NUM
ejpam-5090	53	2	.	.	PUNCT
ejpam-5090	53	3	novelty	novelty	NOUN
ejpam-5090	53	4	•	•	ADP
ejpam-5090	53	5	the	the	DET
ejpam-5090	53	6	paper	paper	NOUN
ejpam-5090	53	7	aims	aim	VERB
ejpam-5090	53	8	to	to	PART
ejpam-5090	53	9	present	present	VERB
ejpam-5090	53	10	a	a	DET
ejpam-5090	53	11	novel	novel	ADJ
ejpam-5090	53	12	mathematical	mathematical	ADJ
ejpam-5090	53	13	framework	framework	NOUN
ejpam-5090	53	14	by	by	ADP
ejpam-5090	53	15	introducing	introduce	VERB
ejpam-5090	53	16	the	the	DET
ejpam-5090	53	17	concept	concept	NOUN
ejpam-5090	53	18	of	of	ADP
ejpam-5090	53	19	the	the	DET
ejpam-5090	53	20	direct	direct	ADJ
ejpam-5090	53	21	product	product	NOUN
ejpam-5090	53	22	,	,	PUNCT
ejpam-5090	53	23	which	which	PRON
ejpam-5090	53	24	involves	involve	VERB
ejpam-5090	53	25	sets	set	NOUN
ejpam-5090	53	26	with	with	ADP
ejpam-5090	53	27	fn	fn	NOUN
ejpam-5090	53	28	elements	element	NOUN
ejpam-5090	53	29	within	within	ADP
ejpam-5090	53	30	the	the	DET
ejpam-5090	53	31	domain	domain	NOUN
ejpam-5090	53	32	of	of	ADP
ejpam-5090	53	33	ink	ink	NOUN
ejpam-5090	53	34	-	-	PUNCT
ejpam-5090	53	35	algebras	algebras	PROPN
ejpam-5090	53	36	.	.	PUNCT
ejpam-5090	54	1	•	•	NUM
ejpam-5090	54	2	the	the	DET
ejpam-5090	54	3	goal	goal	NOUN
ejpam-5090	54	4	is	be	AUX
ejpam-5090	54	5	to	to	PART
ejpam-5090	54	6	create	create	VERB
ejpam-5090	54	7	a	a	DET
ejpam-5090	54	8	precise	precise	ADJ
ejpam-5090	54	9	mathematical	mathematical	ADJ
ejpam-5090	54	10	language	language	NOUN
ejpam-5090	54	11	by	by	ADP
ejpam-5090	54	12	defining	define	VERB
ejpam-5090	54	13	terms	term	NOUN
ejpam-5090	54	14	like	like	ADP
ejpam-5090	54	15	direct	direct	ADJ
ejpam-5090	54	16	product	product	NOUN
ejpam-5090	54	17	of	of	ADP
ejpam-5090	54	18	fnink	fnink	NOUN
ejpam-5090	54	19	-	-	PUNCT
ejpam-5090	54	20	is	be	AUX
ejpam-5090	54	21	,	,	PUNCT
ejpam-5090	54	22	fn	fn	NOUN
ejpam-5090	54	23	-	-	PUNCT
ejpam-5090	54	24	ss	ss	NOUN
ejpam-5090	54	25	and	and	CCONJ
ejpam-5090	54	26	fncink	fncink	NOUN
ejpam-5090	54	27	-	-	PUNCT
ejpam-5090	54	28	is	be	AUX
ejpam-5090	54	29	,	,	PUNCT
ejpam-5090	54	30	which	which	PRON
ejpam-5090	54	31	will	will	AUX
ejpam-5090	54	32	improve	improve	VERB
ejpam-5090	54	33	discourse	discourse	NOUN
ejpam-5090	54	34	clarity	clarity	NOUN
ejpam-5090	54	35	.	.	PUNCT
ejpam-5090	55	1	•	•	NOUN
ejpam-5090	55	2	the	the	DET
ejpam-5090	55	3	study	study	NOUN
ejpam-5090	55	4	illuminates	illuminate	VERB
ejpam-5090	55	5	complex	complex	ADJ
ejpam-5090	55	6	mathematical	mathematical	ADJ
ejpam-5090	55	7	relationships	relationship	NOUN
ejpam-5090	55	8	through	through	ADP
ejpam-5090	55	9	rigorous	rigorous	ADJ
ejpam-5090	55	10	theorem	theorem	NOUN
ejpam-5090	55	11	proofs	proof	NOUN
ejpam-5090	55	12	,	,	PUNCT
ejpam-5090	55	13	delving	delve	VERB
ejpam-5090	55	14	into	into	ADP
ejpam-5090	55	15	interconnected	interconnected	ADJ
ejpam-5090	55	16	ideas	idea	NOUN
ejpam-5090	55	17	in	in	ADP
ejpam-5090	55	18	ink	ink	NOUN
ejpam-5090	55	19	-	-	PUNCT
ejpam-5090	55	20	algebras	algebras	PROPN
ejpam-5090	55	21	and	and	CCONJ
ejpam-5090	55	22	fn	fn	NOUN
ejpam-5090	55	23	-	-	PUNCT
ejpam-5090	55	24	ss	ss	NOUN
ejpam-5090	55	25	.	.	PROPN
ejpam-5090	55	26	1.3	1.3	NUM
ejpam-5090	55	27	.	.	PUNCT
ejpam-5090	56	1	structure	structure	NOUN
ejpam-5090	56	2	of	of	ADP
ejpam-5090	56	3	the	the	DET
ejpam-5090	56	4	paper	paper	NOUN
ejpam-5090	56	5	the	the	DET
ejpam-5090	56	6	paper	paper	NOUN
ejpam-5090	56	7	begins	begin	VERB
ejpam-5090	56	8	with	with	ADP
ejpam-5090	56	9	an	an	DET
ejpam-5090	56	10	introductory	introductory	ADJ
ejpam-5090	56	11	exploration	exploration	NOUN
ejpam-5090	56	12	of	of	ADP
ejpam-5090	56	13	the	the	DET
ejpam-5090	56	14	novel	novel	ADJ
ejpam-5090	56	15	concept	concept	NOUN
ejpam-5090	56	16	of	of	ADP
ejpam-5090	56	17	the	the	DET
ejpam-5090	56	18	direct	direct	ADJ
ejpam-5090	56	19	product	product	NOUN
ejpam-5090	56	20	within	within	ADP
ejpam-5090	56	21	structures	structure	NOUN
ejpam-5090	56	22	known	know	VERB
ejpam-5090	56	23	as	as	ADP
ejpam-5090	56	24	ink	ink	NOUN
ejpam-5090	56	25	-	-	PUNCT
ejpam-5090	56	26	algebras	algebra	NOUN
ejpam-5090	56	27	,	,	PUNCT
ejpam-5090	56	28	which	which	PRON
ejpam-5090	56	29	include	include	VERB
ejpam-5090	56	30	sets	set	NOUN
ejpam-5090	56	31	enriched	enrich	VERB
ejpam-5090	56	32	with	with	ADP
ejpam-5090	56	33	fn	fn	NOUN
ejpam-5090	56	34	elements	element	NOUN
ejpam-5090	56	35	.	.	PUNCT
ejpam-5090	57	1	it	it	PRON
ejpam-5090	57	2	then	then	ADV
ejpam-5090	57	3	defines	define	VERB
ejpam-5090	57	4	key	key	ADJ
ejpam-5090	57	5	terms	term	NOUN
ejpam-5090	57	6	like	like	ADP
ejpam-5090	57	7	the	the	DET
ejpam-5090	57	8	direct	direct	ADJ
ejpam-5090	57	9	product	product	NOUN
ejpam-5090	57	10	of	of	ADP
ejpam-5090	57	11	fninks	fnink	NOUN
ejpam-5090	57	12	,	,	PUNCT
ejpam-5090	57	13	fn	fn	NOUN
ejpam-5090	57	14	-	-	PUNCT
ejpam-5090	57	15	ss	ss	NOUN
ejpam-5090	57	16	and	and	CCONJ
ejpam-5090	57	17	fncink	fncink	NOUN
ejpam-5090	57	18	-	-	PUNCT
ejpam-5090	57	19	is	be	AUX
ejpam-5090	57	20	.	.	PUNCT
ejpam-5090	58	1	the	the	DET
ejpam-5090	58	2	narrative	narrative	NOUN
ejpam-5090	58	3	then	then	ADV
ejpam-5090	58	4	proceeds	proceed	VERB
ejpam-5090	58	5	to	to	PART
ejpam-5090	58	6	provide	provide	VERB
ejpam-5090	58	7	a	a	DET
ejpam-5090	58	8	comprehensive	comprehensive	ADJ
ejpam-5090	58	9	exposition	exposition	NOUN
ejpam-5090	58	10	,	,	PUNCT
ejpam-5090	58	11	including	include	VERB
ejpam-5090	58	12	proofs	proof	NOUN
ejpam-5090	58	13	of	of	ADP
ejpam-5090	58	14	theorems	theorem	NOUN
ejpam-5090	58	15	that	that	PRON
ejpam-5090	58	16	intricately	intricately	ADV
ejpam-5090	58	17	illustrate	illustrate	VERB
ejpam-5090	58	18	the	the	DET
ejpam-5090	58	19	relationships	relationship	NOUN
ejpam-5090	58	20	between	between	ADP
ejpam-5090	58	21	these	these	DET
ejpam-5090	58	22	defined	define	VERB
ejpam-5090	58	23	concepts	concept	NOUN
ejpam-5090	58	24	.	.	PUNCT
ejpam-5090	59	1	furthermore	furthermore	ADV
ejpam-5090	59	2	,	,	PUNCT
ejpam-5090	59	3	it	it	PRON
ejpam-5090	59	4	broadens	broaden	VERB
ejpam-5090	59	5	its	its	PRON
ejpam-5090	59	6	scope	scope	NOUN
ejpam-5090	59	7	to	to	PART
ejpam-5090	59	8	define	define	VERB
ejpam-5090	59	9	an	an	DET
ejpam-5090	59	10	ink	ink	NOUN
ejpam-5090	59	11	-	-	PUNCT
ejpam-5090	59	12	subalgebra	subalgebra	NOUN
ejpam-5090	59	13	embedded	embed	VERB
ejpam-5090	59	14	within	within	ADP
ejpam-5090	59	15	an	an	DET
ejpam-5090	59	16	ink	ink	NOUN
ejpam-5090	59	17	-	-	PUNCT
ejpam-5090	59	18	algebra	algebra	NOUN
ejpam-5090	59	19	,	,	PUNCT
ejpam-5090	59	20	as	as	ADV
ejpam-5090	59	21	well	well	ADV
ejpam-5090	59	22	as	as	ADP
ejpam-5090	59	23	a	a	DET
ejpam-5090	59	24	theorem	theorem	NOUN
ejpam-5090	59	25	that	that	PRON
ejpam-5090	59	26	explains	explain	VERB
ejpam-5090	59	27	the	the	DET
ejpam-5090	59	28	relationship	relationship	NOUN
ejpam-5090	59	29	between	between	ADP
ejpam-5090	59	30	the	the	DET
ejpam-5090	59	31	direct	direct	ADJ
ejpam-5090	59	32	product	product	NOUN
ejpam-5090	59	33	of	of	ADP
ejpam-5090	59	34	fninks	fnink	NOUN
ejpam-5090	59	35	and	and	CCONJ
ejpam-5090	59	36	the	the	DET
ejpam-5090	59	37	images	image	NOUN
ejpam-5090	59	38	of	of	ADP
ejpam-5090	59	39	these	these	DET
ejpam-5090	59	40	sub	sub	NOUN
ejpam-5090	59	41	algebras	algebras	X
ejpam-5090	59	42	.	.	PUNCT
ejpam-5090	60	1	in	in	ADP
ejpam-5090	60	2	essence	essence	NOUN
ejpam-5090	60	3	,	,	PUNCT
ejpam-5090	60	4	the	the	DET
ejpam-5090	60	5	paper	paper	NOUN
ejpam-5090	60	6	culminates	culminate	VERB
ejpam-5090	60	7	in	in	ADP
ejpam-5090	60	8	a	a	DET
ejpam-5090	60	9	thorough	thorough	ADJ
ejpam-5090	60	10	investigation	investigation	NOUN
ejpam-5090	60	11	,	,	PUNCT
ejpam-5090	60	12	establishing	establish	VERB
ejpam-5090	60	13	connections	connection	NOUN
ejpam-5090	60	14	and	and	CCONJ
ejpam-5090	60	15	interrelations	interrelation	NOUN
ejpam-5090	60	16	between	between	ADP
ejpam-5090	60	17	diverse	diverse	ADJ
ejpam-5090	60	18	mathematical	mathematical	ADJ
ejpam-5090	60	19	ideas	idea	NOUN
ejpam-5090	60	20	concerning	concern	VERB
ejpam-5090	60	21	both	both	PRON
ejpam-5090	60	22	ink	ink	NOUN
ejpam-5090	60	23	-	-	PUNCT
ejpam-5090	60	24	algebras	algebras	PROPN
ejpam-5090	60	25	.	.	PUNCT
ejpam-5090	61	1	m.	m.	PROPN
ejpam-5090	61	2	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	61	3	et	et	PROPN
ejpam-5090	61	4	al	al	PROPN
ejpam-5090	61	5	.	.	PUNCT
ejpam-5090	61	6	/	/	SYM
ejpam-5090	61	7	eur	eur	PROPN
ejpam-5090	61	8	.	.	PUNCT
ejpam-5090	62	1	j.	j.	PROPN
ejpam-5090	62	2	pure	pure	PROPN
ejpam-5090	62	3	appl	appl	PROPN
ejpam-5090	62	4	.	.	PROPN
ejpam-5090	62	5	math	math	PROPN
ejpam-5090	62	6	,	,	PUNCT
ejpam-5090	62	7	17	17	NUM
ejpam-5090	62	8	(	(	PUNCT
ejpam-5090	62	9	2	2	NUM
ejpam-5090	62	10	)	)	PUNCT
ejpam-5090	62	11	(	(	PUNCT
ejpam-5090	62	12	2024	2024	NUM
ejpam-5090	62	13	)	)	PUNCT
ejpam-5090	62	14	,	,	PUNCT
ejpam-5090	62	15	1113	1113	NUM
ejpam-5090	62	16	-	-	SYM
ejpam-5090	62	17	1128	1128	NUM
ejpam-5090	62	18	1116	1116	NUM
ejpam-5090	62	19	2	2	NUM
ejpam-5090	62	20	.	.	PUNCT
ejpam-5090	62	21	basic	basic	ADJ
ejpam-5090	62	22	definitions	definition	NOUN
ejpam-5090	62	23	in	in	ADP
ejpam-5090	62	24	the	the	DET
ejpam-5090	62	25	beginning	beginning	NOUN
ejpam-5090	62	26	the	the	DET
ejpam-5090	62	27	research	research	NOUN
ejpam-5090	62	28	,	,	PUNCT
ejpam-5090	62	29	the	the	DET
ejpam-5090	62	30	definition	definition	NOUN
ejpam-5090	62	31	and	and	CCONJ
ejpam-5090	62	32	beneficial	beneficial	ADJ
ejpam-5090	62	33	properties	property	NOUN
ejpam-5090	62	34	of	of	ADP
ejpam-5090	62	35	ink	ink	NOUN
ejpam-5090	62	36	-	-	PUNCT
ejpam-5090	62	37	algebras	algebras	PROPN
ejpam-5090	62	38	will	will	AUX
ejpam-5090	62	39	be	be	AUX
ejpam-5090	62	40	explained	explain	VERB
ejpam-5090	62	41	.	.	PUNCT
ejpam-5090	63	1	definition	definition	NOUN
ejpam-5090	63	2	1	1	NUM
ejpam-5090	63	3	(	(	PUNCT
ejpam-5090	63	4	[	[	X
ejpam-5090	63	5	15	15	NUM
ejpam-5090	63	6	]	]	NUM
ejpam-5090	63	7	)	)	PUNCT
ejpam-5090	63	8	.	.	PUNCT
ejpam-5090	64	1	an	an	DET
ejpam-5090	64	2	ink	ink	NOUN
ejpam-5090	64	3	-	-	PUNCT
ejpam-5090	64	4	algebra	algebra	NOUN
ejpam-5090	64	5	is	be	AUX
ejpam-5090	64	6	a	a	DET
ejpam-5090	64	7	mathematical	mathematical	ADJ
ejpam-5090	64	8	structure	structure	NOUN
ejpam-5090	64	9	with	with	ADP
ejpam-5090	64	10	specific	specific	ADJ
ejpam-5090	64	11	rules	rule	NOUN
ejpam-5090	64	12	;	;	PUNCT
ejpam-5090	64	13	it	it	PRON
ejpam-5090	64	14	is	be	AUX
ejpam-5090	64	15	represented	represent	VERB
ejpam-5090	64	16	by	by	ADP
ejpam-5090	64	17	the	the	DET
ejpam-5090	64	18	notation	notation	NOUN
ejpam-5090	64	19	(	(	PUNCT
ejpam-5090	64	20	χ	χ	NOUN
ejpam-5090	64	21	,	,	PUNCT
ejpam-5090	64	22	·	·	PUNCT
ejpam-5090	64	23	,	,	PUNCT
ejpam-5090	64	24	0	0	NUM
ejpam-5090	64	25	)	)	PUNCT
ejpam-5090	64	26	.	.	PUNCT
ejpam-5090	65	1	for	for	ADP
ejpam-5090	65	2	any	any	DET
ejpam-5090	65	3	elements	element	NOUN
ejpam-5090	65	4	ϑ	ϑ	X
ejpam-5090	65	5	,	,	PUNCT
ejpam-5090	65	6	η	η	PROPN
ejpam-5090	65	7	,	,	PUNCT
ejpam-5090	65	8	z	z	PROPN
ejpam-5090	65	9	∈	∈	PROPN
ejpam-5090	65	10	χ	χ	X
ejpam-5090	65	11	(	(	PUNCT
ejpam-5090	65	12	1	1	NUM
ejpam-5090	65	13	)	)	PUNCT
ejpam-5090	65	14	(	(	PUNCT
ejpam-5090	65	15	(	(	PUNCT
ejpam-5090	65	16	ϑ	ϑ	X
ejpam-5090	65	17	·	·	PUNCT
ejpam-5090	65	18	η	η	NOUN
ejpam-5090	65	19	)	)	PUNCT
ejpam-5090	65	20	·	·	PUNCT
ejpam-5090	65	21	(	(	PUNCT
ejpam-5090	65	22	ϑ	ϑ	X
ejpam-5090	65	23	·	·	PUNCT
ejpam-5090	65	24	z	z	NOUN
ejpam-5090	65	25	)	)	PUNCT
ejpam-5090	65	26	)	)	PUNCT
ejpam-5090	65	27	·	·	PUNCT
ejpam-5090	65	28	(	(	PUNCT
ejpam-5090	65	29	z	z	X
ejpam-5090	65	30	·	·	PUNCT
ejpam-5090	65	31	η	η	NOUN
ejpam-5090	65	32	)	)	PUNCT
ejpam-5090	65	33	=	=	SYM
ejpam-5090	65	34	0	0	NUM
ejpam-5090	65	35	,	,	PUNCT
ejpam-5090	65	36	(	(	PUNCT
ejpam-5090	65	37	2	2	NUM
ejpam-5090	65	38	)	)	PUNCT
ejpam-5090	65	39	(	(	PUNCT
ejpam-5090	65	40	(	(	PUNCT
ejpam-5090	65	41	ϑ	ϑ	X
ejpam-5090	65	42	·	·	PUNCT
ejpam-5090	65	43	z	z	X
ejpam-5090	65	44	)	)	PUNCT
ejpam-5090	65	45	·	·	PUNCT
ejpam-5090	65	46	(	(	PUNCT
ejpam-5090	65	47	η	η	X
ejpam-5090	65	48	·	·	PUNCT
ejpam-5090	65	49	z	z	NOUN
ejpam-5090	65	50	)	)	PUNCT
ejpam-5090	65	51	)	)	PUNCT
ejpam-5090	65	52	·	·	PUNCT
ejpam-5090	65	53	(	(	PUNCT
ejpam-5090	65	54	ϑ	ϑ	X
ejpam-5090	65	55	·	·	PUNCT
ejpam-5090	65	56	η	η	NOUN
ejpam-5090	65	57	)	)	PUNCT
ejpam-5090	65	58	=	=	SYM
ejpam-5090	65	59	0	0	NUM
ejpam-5090	65	60	,	,	PUNCT
ejpam-5090	65	61	(	(	PUNCT
ejpam-5090	65	62	3	3	X
ejpam-5090	65	63	)	)	PUNCT
ejpam-5090	65	64	(	(	PUNCT
ejpam-5090	65	65	ϑ	ϑ	X
ejpam-5090	65	66	·	·	PUNCT
ejpam-5090	65	67	0	0	NUM
ejpam-5090	65	68	)	)	PUNCT
ejpam-5090	65	69	=	=	SYM
ejpam-5090	65	70	0	0	NUM
ejpam-5090	65	71	,	,	PUNCT
ejpam-5090	65	72	(	(	PUNCT
ejpam-5090	65	73	4	4	NUM
ejpam-5090	65	74	)	)	PUNCT
ejpam-5090	65	75	(	(	PUNCT
ejpam-5090	65	76	ϑ	ϑ	X
ejpam-5090	65	77	·	·	PUNCT
ejpam-5090	65	78	η	η	NOUN
ejpam-5090	65	79	)	)	PUNCT
ejpam-5090	65	80	=	=	SYM
ejpam-5090	65	81	0	0	NUM
ejpam-5090	65	82	and	and	CCONJ
ejpam-5090	65	83	η	η	PROPN
ejpam-5090	65	84	·	·	PUNCT
ejpam-5090	65	85	ϑ	ϑ	X
ejpam-5090	65	86	=	=	SYM
ejpam-5090	65	87	0	0	NUM
ejpam-5090	65	88	imply	imply	PROPN
ejpam-5090	65	89	η	η	NOUN
ejpam-5090	65	90	=	=	PRON
ejpam-5090	65	91	ϑ.	ϑ.	VERB
ejpam-5090	65	92	the	the	DET
ejpam-5090	65	93	operation	operation	NOUN
ejpam-5090	65	94	·	·	PUNCT
ejpam-5090	65	95	denotes	denote	VERB
ejpam-5090	65	96	a	a	DET
ejpam-5090	65	97	binary	binary	ADJ
ejpam-5090	65	98	operation	operation	NOUN
ejpam-5090	65	99	and	and	CCONJ
ejpam-5090	65	100	0	0	NUM
ejpam-5090	65	101	is	be	AUX
ejpam-5090	65	102	a	a	DET
ejpam-5090	65	103	constant	constant	ADJ
ejpam-5090	65	104	belonging	belonging	NOUN
ejpam-5090	65	105	to	to	ADP
ejpam-5090	65	106	the	the	DET
ejpam-5090	65	107	set	set	NOUN
ejpam-5090	65	108	χ	χ	NOUN
ejpam-5090	65	109	.	.	PUNCT
ejpam-5090	66	1	definition	definition	NOUN
ejpam-5090	66	2	2	2	NUM
ejpam-5090	66	3	(	(	PUNCT
ejpam-5090	66	4	[	[	X
ejpam-5090	66	5	6	6	NUM
ejpam-5090	66	6	]	]	NUM
ejpam-5090	66	7	)	)	PUNCT
ejpam-5090	66	8	.	.	PUNCT
ejpam-5090	67	1	a	a	DET
ejpam-5090	67	2	non	non	ADJ
ejpam-5090	67	3	-	-	ADJ
ejpam-5090	67	4	empty	empty	ADJ
ejpam-5090	67	5	subset	subset	NOUN
ejpam-5090	67	6	s	s	NOUN
ejpam-5090	67	7	of	of	ADP
ejpam-5090	67	8	a	a	PRON
ejpam-5090	67	9	ink	ink	NOUN
ejpam-5090	67	10	-	-	PUNCT
ejpam-5090	67	11	algebra	algebra	NOUN
ejpam-5090	67	12	(	(	PUNCT
ejpam-5090	67	13	χ	χ	NOUN
ejpam-5090	67	14	,	,	PUNCT
ejpam-5090	67	15	·	·	PUNCT
ejpam-5090	67	16	,	,	PUNCT
ejpam-5090	67	17	0	0	NUM
ejpam-5090	67	18	)	)	PUNCT
ejpam-5090	67	19	is	be	AUX
ejpam-5090	67	20	considered	consider	VERB
ejpam-5090	67	21	as	as	ADP
ejpam-5090	67	22	an	an	DET
ejpam-5090	67	23	ink	ink	NOUN
ejpam-5090	67	24	-	-	PUNCT
ejpam-5090	67	25	subalgebra	subalgebra	NOUN
ejpam-5090	67	26	of	of	ADP
ejpam-5090	67	27	χ	χ	NOUN
ejpam-5090	67	28	,	,	PUNCT
ejpam-5090	67	29	if	if	SCONJ
ejpam-5090	67	30	for	for	ADP
ejpam-5090	67	31	every	every	DET
ejpam-5090	67	32	elements	element	NOUN
ejpam-5090	67	33	ϑ	ϑ	X
ejpam-5090	67	34	and	and	CCONJ
ejpam-5090	67	35	η	η	PROPN
ejpam-5090	67	36	∈	∈	PROPN
ejpam-5090	67	37	χ	χ	NOUN
ejpam-5090	67	38	,	,	PUNCT
ejpam-5090	67	39	the	the	DET
ejpam-5090	67	40	result	result	NOUN
ejpam-5090	67	41	of	of	ADP
ejpam-5090	67	42	the	the	DET
ejpam-5090	67	43	operation	operation	NOUN
ejpam-5090	67	44	(	(	PUNCT
ejpam-5090	67	45	ϑ	ϑ	X
ejpam-5090	67	46	·	·	PUNCT
ejpam-5090	67	47	η	η	X
ejpam-5090	67	48	)	)	PUNCT
ejpam-5090	67	49	is	be	AUX
ejpam-5090	67	50	also	also	ADV
ejpam-5090	67	51	an	an	DET
ejpam-5090	67	52	element	element	NOUN
ejpam-5090	67	53	of	of	ADP
ejpam-5090	67	54	s.	s.	PROPN
ejpam-5090	67	55	definition	definition	NOUN
ejpam-5090	67	56	3	3	NUM
ejpam-5090	67	57	(	(	PUNCT
ejpam-5090	67	58	[	[	X
ejpam-5090	67	59	6	6	NUM
ejpam-5090	67	60	]	]	PUNCT
ejpam-5090	67	61	)	)	PUNCT
ejpam-5090	67	62	.	.	PUNCT
ejpam-5090	68	1	let	let	VERB
ejpam-5090	68	2	(	(	PUNCT
ejpam-5090	68	3	χ	χ	X
ejpam-5090	68	4	,	,	PUNCT
ejpam-5090	68	5	·	·	PUNCT
ejpam-5090	68	6	,	,	PUNCT
ejpam-5090	68	7	0	0	NUM
ejpam-5090	68	8	)	)	PUNCT
ejpam-5090	68	9	be	be	AUX
ejpam-5090	68	10	an	an	DET
ejpam-5090	68	11	ink	ink	NOUN
ejpam-5090	68	12	-	-	PUNCT
ejpam-5090	68	13	algebra	algebra	NOUN
ejpam-5090	68	14	.	.	PUNCT
ejpam-5090	69	1	an	an	DET
ejpam-5090	69	2	ideal	ideal	NOUN
ejpam-5090	69	3	of	of	ADP
ejpam-5090	69	4	χ	χ	PROPN
ejpam-5090	69	5	is	be	AUX
ejpam-5090	69	6	defined	define	VERB
ejpam-5090	69	7	as	as	ADP
ejpam-5090	69	8	a	a	DET
ejpam-5090	69	9	nonempty	nonempty	NOUN
ejpam-5090	69	10	subset	subset	VERB
ejpam-5090	69	11	ℑ	ℑ	NOUN
ejpam-5090	69	12	of	of	ADP
ejpam-5090	69	13	χ	χ	PRON
ejpam-5090	69	14	such	such	ADJ
ejpam-5090	69	15	that	that	SCONJ
ejpam-5090	69	16	it	it	PRON
ejpam-5090	69	17	satisfies	satisfy	VERB
ejpam-5090	69	18	the	the	DET
ejpam-5090	69	19	following	follow	VERB
ejpam-5090	69	20	conditions	condition	NOUN
ejpam-5090	69	21	,	,	PUNCT
ejpam-5090	69	22	∀ϑ	∀ϑ	NUM
ejpam-5090	69	23	,	,	PUNCT
ejpam-5090	69	24	η	η	PROPN
ejpam-5090	69	25	∈	∈	PROPN
ejpam-5090	69	26	χ	χ	X
ejpam-5090	69	27	(	(	PUNCT
ejpam-5090	69	28	1	1	NUM
ejpam-5090	69	29	)	)	PUNCT
ejpam-5090	69	30	0	0	NUM
ejpam-5090	69	31	∈	∈	PROPN
ejpam-5090	69	32	ℑ	ℑ	PROPN
ejpam-5090	69	33	,	,	PUNCT
ejpam-5090	69	34	(	(	PUNCT
ejpam-5090	69	35	2	2	NUM
ejpam-5090	69	36	)	)	PUNCT
ejpam-5090	69	37	(	(	PUNCT
ejpam-5090	69	38	ϑ	ϑ	X
ejpam-5090	69	39	·	·	PUNCT
ejpam-5090	69	40	η	η	PROPN
ejpam-5090	69	41	)	)	PUNCT
ejpam-5090	69	42	∈	∈	PROPN
ejpam-5090	69	43	ℑ	ℑ	PROPN
ejpam-5090	69	44	and	and	CCONJ
ejpam-5090	69	45	η	η	PROPN
ejpam-5090	69	46	∈	∈	PROPN
ejpam-5090	69	47	ℑ	ℑ	PROPN
ejpam-5090	69	48	imply	imply	VERB
ejpam-5090	69	49	ϑ	ϑ	X
ejpam-5090	69	50	∈	∈	ADJ
ejpam-5090	69	51	ℑ.	ℑ.	NOUN
ejpam-5090	69	52	definition	definition	NOUN
ejpam-5090	69	53	4	4	NUM
ejpam-5090	69	54	(	(	PUNCT
ejpam-5090	69	55	[	[	X
ejpam-5090	69	56	6	6	NUM
ejpam-5090	69	57	]	]	PUNCT
ejpam-5090	69	58	)	)	PUNCT
ejpam-5090	69	59	.	.	PUNCT
ejpam-5090	70	1	let	let	VERB
ejpam-5090	70	2	an	an	DET
ejpam-5090	70	3	ink	ink	NOUN
ejpam-5090	70	4	-	-	PUNCT
ejpam-5090	70	5	algebra	algebra	NOUN
ejpam-5090	70	6	χ	χ	PART
ejpam-5090	70	7	have	have	VERB
ejpam-5090	70	8	a	a	DET
ejpam-5090	70	9	non	non	ADJ
ejpam-5090	70	10	-	-	ADJ
ejpam-5090	70	11	empty	empty	ADJ
ejpam-5090	70	12	subset	subset	ADJ
ejpam-5090	70	13	ℑ.	ℑ.	NOUN
ejpam-5090	70	14	if	if	SCONJ
ejpam-5090	70	15	all	all	PRON
ejpam-5090	70	16	of	of	ADP
ejpam-5090	70	17	the	the	DET
ejpam-5090	70	18	following	follow	VERB
ejpam-5090	70	19	hold	hold	NOUN
ejpam-5090	70	20	for	for	ADP
ejpam-5090	70	21	every	every	DET
ejpam-5090	70	22	ϑ	ϑ	PROPN
ejpam-5090	70	23	,	,	PUNCT
ejpam-5090	70	24	η	η	PROPN
ejpam-5090	70	25	,	,	PUNCT
ejpam-5090	70	26	z	z	PROPN
ejpam-5090	70	27	∈	∈	PROPN
ejpam-5090	70	28	χ	χ	NOUN
ejpam-5090	70	29	,	,	PUNCT
ejpam-5090	70	30	then	then	ADV
ejpam-5090	70	31	ℑ	ℑ	PROPN
ejpam-5090	70	32	is	be	AUX
ejpam-5090	70	33	called	call	VERB
ejpam-5090	70	34	an	an	DET
ejpam-5090	70	35	ink	ink	NOUN
ejpam-5090	70	36	-	-	PUNCT
ejpam-5090	70	37	ideal	ideal	NOUN
ejpam-5090	70	38	of	of	ADP
ejpam-5090	70	39	χ	χ	NOUN
ejpam-5090	70	40	.	.	PUNCT
ejpam-5090	71	1	(	(	PUNCT
ejpam-5090	71	2	1	1	NUM
ejpam-5090	71	3	)	)	PUNCT
ejpam-5090	71	4	0	0	NUM
ejpam-5090	71	5	∈	∈	PROPN
ejpam-5090	71	6	ℑ	ℑ	PROPN
ejpam-5090	71	7	,	,	PUNCT
ejpam-5090	71	8	(	(	PUNCT
ejpam-5090	71	9	2	2	NUM
ejpam-5090	71	10	)	)	PUNCT
ejpam-5090	71	11	(	(	PUNCT
ejpam-5090	71	12	z	z	NOUN
ejpam-5090	71	13	·	·	PUNCT
ejpam-5090	71	14	ϑ	ϑ	X
ejpam-5090	71	15	)	)	PUNCT
ejpam-5090	71	16	·	·	PUNCT
ejpam-5090	71	17	(	(	PUNCT
ejpam-5090	71	18	z	z	X
ejpam-5090	71	19	·	·	PUNCT
ejpam-5090	71	20	η	η	PROPN
ejpam-5090	71	21	)	)	PUNCT
ejpam-5090	71	22	∈	∈	PROPN
ejpam-5090	71	23	ℑ	ℑ	PROPN
ejpam-5090	71	24	and	and	CCONJ
ejpam-5090	71	25	z	z	NOUN
ejpam-5090	71	26	∈	∈	PROPN
ejpam-5090	71	27	ℑ	ℑ	PROPN
ejpam-5090	71	28	imply	imply	VERB
ejpam-5090	71	29	ϑ	ϑ	X
ejpam-5090	71	30	∈	∈	ADJ
ejpam-5090	71	31	ℑ.	ℑ.	NOUN
ejpam-5090	71	32	definition	definition	NOUN
ejpam-5090	71	33	5	5	NUM
ejpam-5090	71	34	(	(	PUNCT
ejpam-5090	71	35	[	[	X
ejpam-5090	71	36	22	22	NUM
ejpam-5090	71	37	]	]	PUNCT
ejpam-5090	71	38	)	)	PUNCT
ejpam-5090	71	39	.	.	PUNCT
ejpam-5090	72	1	the	the	DET
ejpam-5090	72	2	structure	structure	NOUN
ejpam-5090	72	3	of	of	ADP
ejpam-5090	72	4	a	a	DET
ejpam-5090	72	5	fns	fns	PROPN
ejpam-5090	72	6	m	m	VERB
ejpam-5090	72	7	defined	define	VERB
ejpam-5090	72	8	on	on	ADP
ejpam-5090	72	9	a	a	DET
ejpam-5090	72	10	nonempty	nonempty	NOUN
ejpam-5090	72	11	set	set	VERB
ejpam-5090	72	12	χ	χ	NOUN
ejpam-5090	72	13	can	can	AUX
ejpam-5090	72	14	be	be	AUX
ejpam-5090	72	15	expressed	express	VERB
ejpam-5090	72	16	as	as	ADP
ejpam-5090	72	17	:	:	PUNCT
ejpam-5090	72	18	m	m	PROPN
ejpam-5090	72	19	=	=	SYM
ejpam-5090	72	20	{	{	PUNCT
ejpam-5090	72	21	〈	〈	PROPN
ejpam-5090	72	22	ϑ	ϑ	X
ejpam-5090	72	23	,	,	PUNCT
ejpam-5090	72	24	ρtm(ϑ	ρtm(ϑ	PROPN
ejpam-5090	72	25	)	)	PUNCT
ejpam-5090	72	26	,	,	PUNCT
ejpam-5090	72	27	ρim(ϑ	ρim(ϑ	PROPN
ejpam-5090	72	28	)	)	PUNCT
ejpam-5090	72	29	,	,	PUNCT
ejpam-5090	72	30	ρfm(ϑ	ρfm(ϑ	PROPN
ejpam-5090	72	31	)	)	PUNCT
ejpam-5090	72	32	〉	〉	NOUN
ejpam-5090	72	33	|ϑ	|ϑ	X
ejpam-5090	72	34	∈	∈	PROPN
ejpam-5090	72	35	χ	χ	X
ejpam-5090	72	36	}	}	PUNCT
ejpam-5090	72	37	,	,	PUNCT
ejpam-5090	72	38	where	where	SCONJ
ejpam-5090	72	39	ρt	ρt	ADV
ejpam-5090	72	40	:	:	PUNCT
ejpam-5090	72	41	χ	χ	X
ejpam-5090	72	42	→	→	SYM
ejpam-5090	72	43	[	[	X
ejpam-5090	72	44	0	0	NUM
ejpam-5090	72	45	,	,	PUNCT
ejpam-5090	72	46	1	1	NUM
ejpam-5090	72	47	]	]	PUNCT
ejpam-5090	72	48	is	be	AUX
ejpam-5090	72	49	a	a	DET
ejpam-5090	72	50	membership	membership	NOUN
ejpam-5090	72	51	function	function	NOUN
ejpam-5090	72	52	ρi	ρi	NOUN
ejpam-5090	72	53	:	:	PUNCT
ejpam-5090	72	54	χ	χ	X
ejpam-5090	72	55	→	→	PUNCT
ejpam-5090	72	56	[	[	X
ejpam-5090	72	57	0	0	NUM
ejpam-5090	72	58	,	,	PUNCT
ejpam-5090	72	59	1	1	NUM
ejpam-5090	72	60	]	]	PUNCT
ejpam-5090	72	61	is	be	AUX
ejpam-5090	72	62	a	a	DET
ejpam-5090	72	63	indeterminate	indeterminate	ADJ
ejpam-5090	72	64	membership	membership	NOUN
ejpam-5090	72	65	function	function	NOUN
ejpam-5090	72	66	and	and	CCONJ
ejpam-5090	72	67	ρf	ρf	X
ejpam-5090	72	68	:	:	PUNCT
ejpam-5090	72	69	χ	χ	X
ejpam-5090	72	70	→	→	SYM
ejpam-5090	72	71	[	[	X
ejpam-5090	72	72	0	0	NUM
ejpam-5090	72	73	,	,	PUNCT
ejpam-5090	72	74	1	1	NUM
ejpam-5090	72	75	]	]	PUNCT
ejpam-5090	72	76	is	be	AUX
ejpam-5090	72	77	a	a	DET
ejpam-5090	72	78	non	non	ADJ
ejpam-5090	72	79	-	-	ADJ
ejpam-5090	72	80	membership	membership	ADJ
ejpam-5090	72	81	function	function	NOUN
ejpam-5090	72	82	and	and	CCONJ
ejpam-5090	72	83	these	these	DET
ejpam-5090	72	84	three	three	NUM
ejpam-5090	72	85	functions	function	NOUN
ejpam-5090	72	86	are	be	AUX
ejpam-5090	72	87	satisfying	satisfy	VERB
ejpam-5090	72	88	the	the	DET
ejpam-5090	72	89	inequalities	inequality	NOUN
ejpam-5090	72	90	;	;	PUNCT
ejpam-5090	72	91	0	0	NUM
ejpam-5090	72	92	≤	≤	NUM
ejpam-5090	72	93	(	(	PUNCT
ejpam-5090	72	94	ρtm(ϑ))3+(ρfm(ϑ))3	ρtm(ϑ))3+(ρfm(ϑ))3	PROPN
ejpam-5090	72	95	≤	≤	NOUN
ejpam-5090	72	96	1	1	NUM
ejpam-5090	72	97	,	,	PUNCT
ejpam-5090	72	98	0	0	NUM
ejpam-5090	72	99	≤	≤	NUM
ejpam-5090	72	100	(	(	PUNCT
ejpam-5090	72	101	ρim(ϑ))3	ρim(ϑ))3	NOUN
ejpam-5090	72	102	≤	≤	NOUN
ejpam-5090	72	103	1	1	NUM
ejpam-5090	72	104	and	and	CCONJ
ejpam-5090	72	105	0	0	NUM
ejpam-5090	72	106	≤	≤	NOUN
ejpam-5090	72	107	(	(	PUNCT
ejpam-5090	72	108	ρtm(ϑ))3+(ρim(ϑ))3+(ρfm(ϑ))3	ρtm(ϑ))3+(ρim(ϑ))3+(ρfm(ϑ))3	ADV
ejpam-5090	72	109	≤	≤	ADJ
ejpam-5090	72	110	2	2	NUM
ejpam-5090	72	111	.	.	PUNCT
ejpam-5090	73	1	here	here	ADV
ejpam-5090	73	2	,	,	PUNCT
ejpam-5090	73	3	ρtm(ϑ	ρtm(ϑ	PROPN
ejpam-5090	73	4	)	)	PUNCT
ejpam-5090	73	5	and	and	CCONJ
ejpam-5090	73	6	ρfm(ϑ	ρfm(ϑ	PROPN
ejpam-5090	73	7	)	)	PUNCT
ejpam-5090	73	8	are	be	AUX
ejpam-5090	73	9	dependent	dependent	ADJ
ejpam-5090	73	10	components	component	NOUN
ejpam-5090	73	11	and	and	CCONJ
ejpam-5090	73	12	ρim(ϑ	ρim(ϑ	PROPN
ejpam-5090	73	13	)	)	PUNCT
ejpam-5090	73	14	is	be	AUX
ejpam-5090	73	15	an	an	DET
ejpam-5090	73	16	independent	independent	ADJ
ejpam-5090	73	17	component	component	NOUN
ejpam-5090	73	18	.	.	PUNCT
ejpam-5090	74	1	throughout	throughout	ADP
ejpam-5090	74	2	the	the	DET
ejpam-5090	74	3	current	current	ADJ
ejpam-5090	74	4	research	research	NOUN
ejpam-5090	74	5	article	article	NOUN
ejpam-5090	74	6	,	,	PUNCT
ejpam-5090	74	7	we	we	PRON
ejpam-5090	74	8	shall	shall	AUX
ejpam-5090	74	9	use	use	VERB
ejpam-5090	74	10	m	m	ADJ
ejpam-5090	74	11	=	=	SYM
ejpam-5090	74	12	〈	〈	PROPN
ejpam-5090	74	13	ρtm	ρtm	NOUN
ejpam-5090	74	14	,	,	PUNCT
ejpam-5090	74	15	ρim	ρim	NOUN
ejpam-5090	74	16	,	,	PUNCT
ejpam-5090	74	17	ρfm	ρfm	ADP
ejpam-5090	74	18	〉	〉	NOUN
ejpam-5090	74	19	for	for	ADP
ejpam-5090	74	20	the	the	DET
ejpam-5090	74	21	fns	fns	PROPN
ejpam-5090	74	22	m	m	PROPN
ejpam-5090	74	23	=	=	PUNCT
ejpam-5090	74	24	{	{	PUNCT
ejpam-5090	74	25	〈	〈	PROPN
ejpam-5090	74	26	ϑ	ϑ	X
ejpam-5090	74	27	,	,	PUNCT
ejpam-5090	74	28	ρtm(ϑ	ρtm(ϑ	PROPN
ejpam-5090	74	29	)	)	PUNCT
ejpam-5090	74	30	,	,	PUNCT
ejpam-5090	74	31	ρim(ϑ	ρim(ϑ	PROPN
ejpam-5090	74	32	)	)	PUNCT
ejpam-5090	74	33	,	,	PUNCT
ejpam-5090	74	34	ρfm(ϑ	ρfm(ϑ	PROPN
ejpam-5090	74	35	)	)	PUNCT
ejpam-5090	74	36	〉	〉	NOUN
ejpam-5090	74	37	|ϑ	|ϑ	X
ejpam-5090	74	38	∈	∈	PROPN
ejpam-5090	74	39	χ	χ	X
ejpam-5090	74	40	}	}	PUNCT
ejpam-5090	74	41	.	.	PUNCT
ejpam-5090	75	1	definition	definition	NOUN
ejpam-5090	75	2	6	6	NUM
ejpam-5090	75	3	(	(	PUNCT
ejpam-5090	75	4	[	[	X
ejpam-5090	75	5	22	22	NUM
ejpam-5090	75	6	]	]	PUNCT
ejpam-5090	75	7	)	)	PUNCT
ejpam-5090	75	8	.	.	PUNCT
ejpam-5090	76	1	if	if	SCONJ
ejpam-5090	76	2	m	m	ADV
ejpam-5090	76	3	=	=	SYM
ejpam-5090	76	4	{	{	PUNCT
ejpam-5090	76	5	〈	〈	PROPN
ejpam-5090	76	6	ρtm(ϑ	ρtm(ϑ	NOUN
ejpam-5090	76	7	)	)	PUNCT
ejpam-5090	76	8	,	,	PUNCT
ejpam-5090	76	9	ρim(ϑ	ρim(ϑ	PROPN
ejpam-5090	76	10	)	)	PUNCT
ejpam-5090	76	11	,	,	PUNCT
ejpam-5090	76	12	ρfm(ϑ	ρfm(ϑ	PROPN
ejpam-5090	76	13	)	)	PUNCT
ejpam-5090	76	14	〉	〉	NOUN
ejpam-5090	76	15	}	}	PUNCT
ejpam-5090	76	16	and	and	CCONJ
ejpam-5090	76	17	n	n	NOUN
ejpam-5090	76	18	=	=	PUNCT
ejpam-5090	76	19	{	{	PUNCT
ejpam-5090	76	20	〈	〈	PROPN
ejpam-5090	76	21	ρtn(ϑ	ρtn(ϑ	PROPN
ejpam-5090	76	22	)	)	PUNCT
ejpam-5090	76	23	,	,	PUNCT
ejpam-5090	76	24	ρ	ρ	PROPN
ejpam-5090	76	25	i	i	PROPN
ejpam-5090	76	26	n(ϑ	n(ϑ	PROPN
ejpam-5090	76	27	)	)	PUNCT
ejpam-5090	76	28	,	,	PUNCT
ejpam-5090	76	29	ρ	ρ	PROPN
ejpam-5090	76	30	f	f	PROPN
ejpam-5090	76	31	n(ϑ	n(ϑ	X
ejpam-5090	76	32	)	)	PUNCT
ejpam-5090	76	33	〉	〉	NOUN
ejpam-5090	76	34	}	}	PUNCT
ejpam-5090	76	35	be	be	VERB
ejpam-5090	76	36	two	two	NUM
ejpam-5090	76	37	fnss	fns	NOUN
ejpam-5090	76	38	,	,	PUNCT
ejpam-5090	76	39	then	then	ADV
ejpam-5090	76	40	∀ϑ	∀ϑ	VERB
ejpam-5090	76	41	∈	∈	PROPN
ejpam-5090	76	42	χ	χ	DET
ejpam-5090	76	43	m.	m.	NOUN
ejpam-5090	76	44	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	76	45	et	et	PROPN
ejpam-5090	76	46	al	al	PROPN
ejpam-5090	76	47	.	.	PUNCT
ejpam-5090	76	48	/	/	SYM
ejpam-5090	76	49	eur	eur	PROPN
ejpam-5090	76	50	.	.	PUNCT
ejpam-5090	77	1	j.	j.	PROPN
ejpam-5090	77	2	pure	pure	PROPN
ejpam-5090	77	3	appl	appl	PROPN
ejpam-5090	77	4	.	.	PROPN
ejpam-5090	77	5	math	math	PROPN
ejpam-5090	77	6	,	,	PUNCT
ejpam-5090	77	7	17	17	NUM
ejpam-5090	77	8	(	(	PUNCT
ejpam-5090	77	9	2	2	NUM
ejpam-5090	77	10	)	)	PUNCT
ejpam-5090	77	11	(	(	PUNCT
ejpam-5090	77	12	2024	2024	NUM
ejpam-5090	77	13	)	)	PUNCT
ejpam-5090	77	14	,	,	PUNCT
ejpam-5090	77	15	1113	1113	NUM
ejpam-5090	77	16	-	-	SYM
ejpam-5090	77	17	1128	1128	NUM
ejpam-5090	77	18	1117	1117	NUM
ejpam-5090	77	19	(	(	PUNCT
ejpam-5090	77	20	i	i	NOUN
ejpam-5090	77	21	)	)	PUNCT
ejpam-5090	77	22	m	m	VERB
ejpam-5090	77	23	=	=	SYM
ejpam-5090	77	24	{	{	PUNCT
ejpam-5090	77	25	〈	〈	PROPN
ejpam-5090	77	26	1−	1−	NUM
ejpam-5090	77	27	ρtm(ϑ	ρtm(ϑ	NOUN
ejpam-5090	77	28	)	)	PUNCT
ejpam-5090	77	29	,	,	PUNCT
ejpam-5090	77	30	1−	1−	NUM
ejpam-5090	77	31	ρim(ϑ	ρim(ϑ	PROPN
ejpam-5090	77	32	)	)	PUNCT
ejpam-5090	77	33	,	,	PUNCT
ejpam-5090	77	34	1−	1−	NUM
ejpam-5090	77	35	ρfm(ϑ	ρfm(ϑ	PROPN
ejpam-5090	77	36	)	)	PUNCT
ejpam-5090	77	37	〉	〉	NOUN
ejpam-5090	77	38	}	}	PUNCT
ejpam-5090	77	39	(	(	PUNCT
ejpam-5090	77	40	ii	ii	NOUN
ejpam-5090	77	41	)	)	PUNCT
ejpam-5090	77	42	m	m	PROPN
ejpam-5090	77	43	∩n	∩n	NOUN
ejpam-5090	77	44	=	=	PRON
ejpam-5090	77	45	{	{	PUNCT
ejpam-5090	77	46	〈	〈	PROPN
ejpam-5090	77	47	min{ρtm(ϑ	min{ρtm(ϑ	PROPN
ejpam-5090	77	48	)	)	PUNCT
ejpam-5090	77	49	,	,	PUNCT
ejpam-5090	77	50	ρtn(ϑ)},max{ρim(ϑ	ρtn(ϑ)},max{ρim(ϑ	PROPN
ejpam-5090	77	51	)	)	PUNCT
ejpam-5090	77	52	,	,	PUNCT
ejpam-5090	77	53	ρin(ϑ)},max{ρfm(ϑ	ρin(ϑ)},max{ρfm(ϑ	PROPN
ejpam-5090	77	54	)	)	PUNCT
ejpam-5090	77	55	,	,	PUNCT
ejpam-5090	77	56	ρfn(ϑ	ρfn(ϑ	NOUN
ejpam-5090	77	57	)	)	PUNCT
ejpam-5090	77	58	}	}	PUNCT
ejpam-5090	77	59	〉	〉	NOUN
ejpam-5090	77	60	}	}	PUNCT
ejpam-5090	77	61	.	.	PUNCT
ejpam-5090	78	1	definition	definition	NOUN
ejpam-5090	78	2	7	7	NUM
ejpam-5090	78	3	.	.	PUNCT
ejpam-5090	79	1	a	a	DET
ejpam-5090	79	2	fns	fns	PROPN
ejpam-5090	79	3	m	m	PROPN
ejpam-5090	79	4	of	of	ADP
ejpam-5090	79	5	χ	χ	PROPN
ejpam-5090	79	6	obtains	obtain	VERB
ejpam-5090	79	7	the	the	DET
ejpam-5090	79	8	title	title	NOUN
ejpam-5090	79	9	of	of	ADP
ejpam-5090	79	10	fnink	fnink	NOUN
ejpam-5090	79	11	-	-	PUNCT
ejpam-5090	79	12	ss	ss	NOUN
ejpam-5090	79	13	by	by	ADP
ejpam-5090	79	14	satisfying	satisfy	VERB
ejpam-5090	79	15	the	the	DET
ejpam-5090	79	16	requirements	requirement	NOUN
ejpam-5090	79	17	,	,	PUNCT
ejpam-5090	79	18	∀	∀	X
ejpam-5090	79	19	ϑ	ϑ	X
ejpam-5090	79	20	,	,	PUNCT
ejpam-5090	79	21	η	η	PROPN
ejpam-5090	79	22	∈	∈	PROPN
ejpam-5090	79	23	χ	χ	X
ejpam-5090	79	24	(	(	PUNCT
ejpam-5090	79	25	1	1	NUM
ejpam-5090	79	26	)	)	PUNCT
ejpam-5090	79	27	ρt(ϑ	ρt(ϑ	NUM
ejpam-5090	79	28	·	·	PUNCT
ejpam-5090	79	29	η	η	PROPN
ejpam-5090	79	30	)	)	PUNCT
ejpam-5090	79	31	≤	≤	NUM
ejpam-5090	79	32	min	min	NOUN
ejpam-5090	79	33	{	{	PUNCT
ejpam-5090	79	34	ρt(ϑ	ρt(ϑ	PROPN
ejpam-5090	79	35	)	)	PUNCT
ejpam-5090	79	36	,	,	PUNCT
ejpam-5090	79	37	ρt(η	ρt(η	ADV
ejpam-5090	79	38	)	)	PUNCT
ejpam-5090	79	39	}	}	PUNCT
ejpam-5090	79	40	,	,	PUNCT
ejpam-5090	79	41	(	(	PUNCT
ejpam-5090	79	42	2	2	X
ejpam-5090	79	43	)	)	PUNCT
ejpam-5090	79	44	ρi(ϑ	ρi(ϑ	NOUN
ejpam-5090	79	45	·	·	PUNCT
ejpam-5090	79	46	η	η	PROPN
ejpam-5090	79	47	)	)	PUNCT
ejpam-5090	79	48	≥	≥	PROPN
ejpam-5090	79	49	max	max	PROPN
ejpam-5090	79	50	{	{	PUNCT
ejpam-5090	79	51	ρi(ϑ	ρi(ϑ	NUM
ejpam-5090	79	52	)	)	PUNCT
ejpam-5090	79	53	,	,	PUNCT
ejpam-5090	79	54	ρi(η	ρi(η	NUM
ejpam-5090	79	55	)	)	PUNCT
ejpam-5090	79	56	}	}	PUNCT
ejpam-5090	79	57	,	,	PUNCT
ejpam-5090	79	58	(	(	PUNCT
ejpam-5090	79	59	3	3	X
ejpam-5090	79	60	)	)	PUNCT
ejpam-5090	79	61	ρf(ϑ	ρf(ϑ	PUNCT
ejpam-5090	79	62	·	·	PUNCT
ejpam-5090	79	63	η	η	X
ejpam-5090	79	64	)	)	PUNCT
ejpam-5090	79	65	≥	≥	PROPN
ejpam-5090	79	66	max	max	PROPN
ejpam-5090	79	67	{	{	PUNCT
ejpam-5090	79	68	ρf(ϑ	ρf(ϑ	NUM
ejpam-5090	79	69	)	)	PUNCT
ejpam-5090	79	70	,	,	PUNCT
ejpam-5090	79	71	ρf(η	ρf(η	NOUN
ejpam-5090	79	72	)	)	PUNCT
ejpam-5090	79	73	}	}	PUNCT
ejpam-5090	79	74	.	.	PUNCT
ejpam-5090	80	1	definition	definition	NOUN
ejpam-5090	80	2	8	8	NUM
ejpam-5090	80	3	.	.	PUNCT
ejpam-5090	81	1	a	a	DET
ejpam-5090	81	2	fns	fns	PROPN
ejpam-5090	81	3	m	m	PROPN
ejpam-5090	81	4	of	of	ADP
ejpam-5090	81	5	χ	χ	PROPN
ejpam-5090	81	6	is	be	AUX
ejpam-5090	81	7	considered	consider	VERB
ejpam-5090	81	8	as	as	ADP
ejpam-5090	81	9	a	a	DET
ejpam-5090	81	10	fn	fn	NOUN
ejpam-5090	81	11	-	-	PUNCT
ejpam-5090	81	12	i	i	PRON
ejpam-5090	81	13	if	if	SCONJ
ejpam-5090	81	14	it	it	PRON
ejpam-5090	81	15	meets	meet	VERB
ejpam-5090	81	16	the	the	DET
ejpam-5090	81	17	described	describe	VERB
ejpam-5090	81	18	conditions	condition	NOUN
ejpam-5090	81	19	,	,	PUNCT
ejpam-5090	81	20	∀	∀	X
ejpam-5090	81	21	ϑ	ϑ	X
ejpam-5090	81	22	,	,	PUNCT
ejpam-5090	82	1	η	η	PROPN
ejpam-5090	82	2	∈	∈	PROPN
ejpam-5090	82	3	χ	χ	X
ejpam-5090	82	4	(	(	PUNCT
ejpam-5090	82	5	1	1	X
ejpam-5090	82	6	)	)	PUNCT
ejpam-5090	82	7	ρt(0	ρt(0	NOUN
ejpam-5090	82	8	)	)	PUNCT
ejpam-5090	82	9	≤	≤	NOUN
ejpam-5090	82	10	ρt(ϑ	ρt(ϑ	NUM
ejpam-5090	82	11	)	)	PUNCT
ejpam-5090	82	12	,	,	PUNCT
ejpam-5090	82	13	ρi(0	ρi(0	PROPN
ejpam-5090	82	14	)	)	PUNCT
ejpam-5090	82	15	≥	≥	NOUN
ejpam-5090	82	16	ρi(ϑ	ρi(ϑ	NUM
ejpam-5090	82	17	)	)	PUNCT
ejpam-5090	82	18	,	,	PUNCT
ejpam-5090	82	19	ρf(0	ρf(0	PROPN
ejpam-5090	82	20	)	)	PUNCT
ejpam-5090	82	21	≥	≥	NOUN
ejpam-5090	82	22	ρf(ϑ	ρf(ϑ	NUM
ejpam-5090	82	23	)	)	PUNCT
ejpam-5090	82	24	,	,	PUNCT
ejpam-5090	82	25	(	(	PUNCT
ejpam-5090	82	26	2	2	NUM
ejpam-5090	82	27	)	)	PUNCT
ejpam-5090	82	28	ρt(ϑ	ρt(ϑ	NUM
ejpam-5090	82	29	)	)	PUNCT
ejpam-5090	82	30	≤	≤	NUM
ejpam-5090	82	31	min	min	NOUN
ejpam-5090	82	32	{	{	PUNCT
ejpam-5090	82	33	ρt(ϑ	ρt(ϑ	NUM
ejpam-5090	82	34	·	·	PUNCT
ejpam-5090	82	35	η	η	NOUN
ejpam-5090	82	36	)	)	PUNCT
ejpam-5090	82	37	,	,	PUNCT
ejpam-5090	82	38	ρt(η	ρt(η	ADV
ejpam-5090	82	39	)	)	PUNCT
ejpam-5090	82	40	}	}	PUNCT
ejpam-5090	82	41	,	,	PUNCT
ejpam-5090	82	42	(	(	PUNCT
ejpam-5090	82	43	3	3	X
ejpam-5090	82	44	)	)	PUNCT
ejpam-5090	82	45	ρi(ϑ	ρi(ϑ	NUM
ejpam-5090	82	46	)	)	PUNCT
ejpam-5090	82	47	≥	≥	PROPN
ejpam-5090	82	48	max	max	PROPN
ejpam-5090	82	49	{	{	PUNCT
ejpam-5090	82	50	ρi(ϑ	ρi(ϑ	NUM
ejpam-5090	82	51	·	·	PUNCT
ejpam-5090	82	52	η	η	NOUN
ejpam-5090	82	53	)	)	PUNCT
ejpam-5090	82	54	,	,	PUNCT
ejpam-5090	82	55	ρi(η	ρi(η	NUM
ejpam-5090	82	56	)	)	PUNCT
ejpam-5090	82	57	}	}	PUNCT
ejpam-5090	82	58	,	,	PUNCT
ejpam-5090	82	59	(	(	PUNCT
ejpam-5090	82	60	4	4	NUM
ejpam-5090	82	61	)	)	PUNCT
ejpam-5090	82	62	ρf(ϑ	ρf(ϑ	X
ejpam-5090	82	63	)	)	PUNCT
ejpam-5090	82	64	≥	≥	PROPN
ejpam-5090	82	65	max	max	PROPN
ejpam-5090	82	66	{	{	PUNCT
ejpam-5090	82	67	ρf(ϑ	ρf(ϑ	NUM
ejpam-5090	82	68	·	·	PUNCT
ejpam-5090	82	69	η	η	NOUN
ejpam-5090	82	70	)	)	PUNCT
ejpam-5090	82	71	,	,	PUNCT
ejpam-5090	82	72	ρf(η	ρf(η	NOUN
ejpam-5090	82	73	)	)	PUNCT
ejpam-5090	82	74	}	}	PUNCT
ejpam-5090	82	75	.	.	PUNCT
ejpam-5090	83	1	example	example	NOUN
ejpam-5090	84	1	1	1	NUM
ejpam-5090	84	2	.	.	PUNCT
ejpam-5090	85	1	if	if	SCONJ
ejpam-5090	85	2	χ	χ	ADJ
ejpam-5090	85	3	=	=	PRON
ejpam-5090	85	4	{	{	PUNCT
ejpam-5090	85	5	0	0	NUM
ejpam-5090	85	6	,	,	PUNCT
ejpam-5090	85	7	x	x	NOUN
ejpam-5090	85	8	,	,	PUNCT
ejpam-5090	85	9	y	y	PROPN
ejpam-5090	85	10	,	,	PUNCT
ejpam-5090	85	11	z	z	NOUN
ejpam-5090	85	12	}	}	PUNCT
ejpam-5090	85	13	is	be	AUX
ejpam-5090	85	14	a	a	DET
ejpam-5090	85	15	set	set	NOUN
ejpam-5090	85	16	with	with	ADP
ejpam-5090	85	17	a	a	DET
ejpam-5090	85	18	binary	binary	ADJ
ejpam-5090	85	19	operation	operation	NOUN
ejpam-5090	85	20	·	·	PUNCT
ejpam-5090	85	21	given	give	VERB
ejpam-5090	85	22	by	by	ADP
ejpam-5090	85	23	the	the	DET
ejpam-5090	85	24	following	follow	VERB
ejpam-5090	85	25	table	table	NOUN
ejpam-5090	85	26	:	:	PUNCT
ejpam-5090	85	27	table	table	NOUN
ejpam-5090	85	28	1	1	NUM
ejpam-5090	85	29	:	:	PUNCT
ejpam-5090	85	30	the	the	DET
ejpam-5090	85	31	operation	operation	NOUN
ejpam-5090	85	32	·	·	PUNCT
ejpam-5090	85	33	·	·	PUNCT
ejpam-5090	85	34	0	0	PUNCT
ejpam-5090	86	1	x	x	SYM
ejpam-5090	86	2	y	y	PROPN
ejpam-5090	86	3	z	z	NOUN
ejpam-5090	86	4	0	0	NUM
ejpam-5090	86	5	0	0	NUM
ejpam-5090	86	6	x	x	SYM
ejpam-5090	86	7	y	y	NOUN
ejpam-5090	86	8	z	z	NOUN
ejpam-5090	86	9	x	x	PUNCT
ejpam-5090	86	10	x	x	SYM
ejpam-5090	86	11	0	0	PUNCT
ejpam-5090	86	12	z	z	VERB
ejpam-5090	86	13	y	y	PROPN
ejpam-5090	86	14	y	y	PROPN
ejpam-5090	86	15	y	y	PROPN
ejpam-5090	86	16	z	z	NOUN
ejpam-5090	86	17	0	0	PUNCT
ejpam-5090	87	1	x	x	SYM
ejpam-5090	88	1	z	z	NOUN
ejpam-5090	88	2	z	z	NOUN
ejpam-5090	88	3	y	y	PROPN
ejpam-5090	88	4	x	x	SYM
ejpam-5090	88	5	0	0	PUNCT
ejpam-5090	88	6	thus	thus	ADV
ejpam-5090	88	7	,	,	PUNCT
ejpam-5090	88	8	(	(	PUNCT
ejpam-5090	88	9	χ	χ	X
ejpam-5090	88	10	.	.	PUNCT
ejpam-5090	88	11	·	·	PUNCT
ejpam-5090	88	12	,	,	PUNCT
ejpam-5090	88	13	0	0	NUM
ejpam-5090	88	14	)	)	PUNCT
ejpam-5090	88	15	is	be	AUX
ejpam-5090	88	16	an	an	DET
ejpam-5090	88	17	ink	ink	NOUN
ejpam-5090	88	18	-	-	PUNCT
ejpam-5090	88	19	algebra	algebra	NOUN
ejpam-5090	88	20	.	.	PUNCT
ejpam-5090	89	1	consider	consider	VERB
ejpam-5090	89	2	a	a	DET
ejpam-5090	89	3	fns	fns	PROPN
ejpam-5090	89	4	m	m	VERB
ejpam-5090	89	5	in	in	ADP
ejpam-5090	89	6	χ	χ	NOUN
ejpam-5090	89	7	,	,	PUNCT
ejpam-5090	89	8	where	where	SCONJ
ejpam-5090	89	9	ρtm(0	ρtm(0	NOUN
ejpam-5090	89	10	)	)	PUNCT
ejpam-5090	89	11	=	=	SYM
ejpam-5090	89	12	0.8	0.8	NUM
ejpam-5090	89	13	,	,	PUNCT
ejpam-5090	89	14	ρtm(x	ρtm(x	X
ejpam-5090	89	15	)	)	PUNCT
ejpam-5090	89	16	=	=	SYM
ejpam-5090	89	17	0.4	0.4	NUM
ejpam-5090	89	18	,	,	PUNCT
ejpam-5090	89	19	ρtm(y	ρtm(y	NOUN
ejpam-5090	89	20	)	)	PUNCT
ejpam-5090	89	21	=	=	SYM
ejpam-5090	89	22	ρtm(z	ρtm(z	PROPN
ejpam-5090	89	23	)	)	PUNCT
ejpam-5090	89	24	=	=	NOUN
ejpam-5090	89	25	0.2	0.2	NUM
ejpam-5090	89	26	,	,	PUNCT
ejpam-5090	89	27	ρim(0	ρim(0	NOUN
ejpam-5090	89	28	)	)	PUNCT
ejpam-5090	89	29	=	=	SYM
ejpam-5090	90	1	0.7	0.7	NUM
ejpam-5090	90	2	,	,	PUNCT
ejpam-5090	90	3	ρim(x	ρim(x	NUM
ejpam-5090	90	4	)	)	PUNCT
ejpam-5090	90	5	=	=	SYM
ejpam-5090	90	6	0.5	0.5	NUM
ejpam-5090	90	7	,	,	PUNCT
ejpam-5090	90	8	ρim(y	ρim(y	NOUN
ejpam-5090	90	9	)	)	PUNCT
ejpam-5090	90	10	=	=	SYM
ejpam-5090	91	1	ρim(z	ρim(z	X
ejpam-5090	91	2	)	)	PUNCT
ejpam-5090	91	3	=	=	SYM
ejpam-5090	91	4	0.3	0.3	NUM
ejpam-5090	91	5	and	and	CCONJ
ejpam-5090	91	6	ρfm(0	ρfm(0	NOUN
ejpam-5090	91	7	)	)	PUNCT
ejpam-5090	92	1	=	=	SYM
ejpam-5090	92	2	0.1	0.1	NUM
ejpam-5090	92	3	,	,	PUNCT
ejpam-5090	92	4	ρfm(x	ρfm(x	PROPN
ejpam-5090	92	5	)	)	PUNCT
ejpam-5090	92	6	=	=	SYM
ejpam-5090	92	7	ρfm(y	ρfm(y	X
ejpam-5090	92	8	)	)	PUNCT
ejpam-5090	92	9	=	=	SYM
ejpam-5090	92	10	0.4	0.4	NUM
ejpam-5090	92	11	,	,	PUNCT
ejpam-5090	92	12	ρfm(z	ρfm(z	PROPN
ejpam-5090	92	13	)	)	PUNCT
ejpam-5090	92	14	=	=	SYM
ejpam-5090	92	15	0.3	0.3	NUM
ejpam-5090	92	16	.	.	PUNCT
ejpam-5090	93	1	then	then	ADV
ejpam-5090	93	2	,	,	PUNCT
ejpam-5090	93	3	m	m	PROPN
ejpam-5090	93	4	is	be	AUX
ejpam-5090	93	5	a	a	DET
ejpam-5090	93	6	fn	fn	NOUN
ejpam-5090	93	7	-	-	PUNCT
ejpam-5090	93	8	i	i	PRON
ejpam-5090	93	9	of	of	ADP
ejpam-5090	93	10	χ	χ	NOUN
ejpam-5090	93	11	,	,	PUNCT
ejpam-5090	93	12	which	which	PRON
ejpam-5090	93	13	is	be	AUX
ejpam-5090	93	14	easily	easily	ADV
ejpam-5090	93	15	verified	verify	VERB
ejpam-5090	93	16	.	.	PUNCT
ejpam-5090	94	1	definition	definition	NOUN
ejpam-5090	94	2	9	9	NUM
ejpam-5090	94	3	.	.	PUNCT
ejpam-5090	95	1	a	a	DET
ejpam-5090	95	2	fns	fns	PROPN
ejpam-5090	95	3	m	m	PROPN
ejpam-5090	95	4	of	of	ADP
ejpam-5090	95	5	χ	χ	PROPN
ejpam-5090	95	6	is	be	AUX
ejpam-5090	95	7	considered	consider	VERB
ejpam-5090	95	8	as	as	ADP
ejpam-5090	95	9	a	a	DET
ejpam-5090	95	10	fnink	fnink	NOUN
ejpam-5090	95	11	-	-	PUNCT
ejpam-5090	95	12	i	i	PRON
ejpam-5090	95	13	of	of	ADP
ejpam-5090	95	14	χ	χ	NOUN
ejpam-5090	95	15	if	if	SCONJ
ejpam-5090	95	16	it	it	PRON
ejpam-5090	95	17	meets	meet	VERB
ejpam-5090	95	18	the	the	DET
ejpam-5090	95	19	described	describe	VERB
ejpam-5090	95	20	conditions	condition	NOUN
ejpam-5090	95	21	,	,	PUNCT
ejpam-5090	95	22	∀	∀	X
ejpam-5090	95	23	ϑ	ϑ	X
ejpam-5090	95	24	,	,	PUNCT
ejpam-5090	95	25	η	η	PROPN
ejpam-5090	95	26	,	,	PUNCT
ejpam-5090	96	1	z	z	PROPN
ejpam-5090	96	2	∈	∈	PROPN
ejpam-5090	96	3	χ	χ	X
ejpam-5090	96	4	(	(	PUNCT
ejpam-5090	96	5	1	1	NUM
ejpam-5090	96	6	)	)	PUNCT
ejpam-5090	96	7	ρt(0	ρt(0	NOUN
ejpam-5090	96	8	)	)	PUNCT
ejpam-5090	96	9	≤	≤	NOUN
ejpam-5090	96	10	ρt(ϑ	ρt(ϑ	NUM
ejpam-5090	96	11	)	)	PUNCT
ejpam-5090	96	12	,	,	PUNCT
ejpam-5090	96	13	ρi(0	ρi(0	PROPN
ejpam-5090	96	14	)	)	PUNCT
ejpam-5090	96	15	≥	≥	NOUN
ejpam-5090	96	16	ρi(ϑ	ρi(ϑ	NUM
ejpam-5090	96	17	)	)	PUNCT
ejpam-5090	96	18	,	,	PUNCT
ejpam-5090	96	19	ρf(0	ρf(0	PROPN
ejpam-5090	96	20	)	)	PUNCT
ejpam-5090	96	21	≥	≥	NOUN
ejpam-5090	96	22	ρf(ϑ	ρf(ϑ	NUM
ejpam-5090	96	23	)	)	PUNCT
ejpam-5090	96	24	,	,	PUNCT
ejpam-5090	96	25	(	(	PUNCT
ejpam-5090	96	26	2	2	NUM
ejpam-5090	96	27	)	)	PUNCT
ejpam-5090	96	28	ρt(ϑ	ρt(ϑ	NUM
ejpam-5090	96	29	)	)	PUNCT
ejpam-5090	96	30	≤	≤	NUM
ejpam-5090	96	31	min	min	NOUN
ejpam-5090	96	32	{	{	PUNCT
ejpam-5090	96	33	ρt((z	ρt((z	X
ejpam-5090	96	34	·	·	PUNCT
ejpam-5090	96	35	ϑ	ϑ	X
ejpam-5090	96	36	)	)	PUNCT
ejpam-5090	96	37	·	·	PUNCT
ejpam-5090	96	38	(	(	PUNCT
ejpam-5090	96	39	z	z	X
ejpam-5090	96	40	·	·	PUNCT
ejpam-5090	96	41	η	η	NOUN
ejpam-5090	96	42	)	)	PUNCT
ejpam-5090	96	43	)	)	PUNCT
ejpam-5090	96	44	,	,	PUNCT
ejpam-5090	96	45	ρt(η	ρt(η	ADV
ejpam-5090	96	46	)	)	PUNCT
ejpam-5090	96	47	}	}	PUNCT
ejpam-5090	96	48	,	,	PUNCT
ejpam-5090	96	49	(	(	PUNCT
ejpam-5090	96	50	3	3	X
ejpam-5090	96	51	)	)	PUNCT
ejpam-5090	96	52	ρi(ϑ	ρi(ϑ	NUM
ejpam-5090	96	53	)	)	PUNCT
ejpam-5090	96	54	≥	≥	PROPN
ejpam-5090	97	1	max	max	PROPN
ejpam-5090	97	2	{	{	PUNCT
ejpam-5090	97	3	ρi((z	ρi((z	PROPN
ejpam-5090	97	4	·	·	PUNCT
ejpam-5090	97	5	ϑ	ϑ	X
ejpam-5090	97	6	)	)	PUNCT
ejpam-5090	97	7	·	·	PUNCT
ejpam-5090	97	8	(	(	PUNCT
ejpam-5090	97	9	z	z	X
ejpam-5090	97	10	·	·	PUNCT
ejpam-5090	97	11	η	η	NOUN
ejpam-5090	97	12	)	)	PUNCT
ejpam-5090	97	13	)	)	PUNCT
ejpam-5090	97	14	,	,	PUNCT
ejpam-5090	97	15	ρi(η	ρi(η	NUM
ejpam-5090	97	16	)	)	PUNCT
ejpam-5090	97	17	}	}	PUNCT
ejpam-5090	97	18	,	,	PUNCT
ejpam-5090	97	19	(	(	PUNCT
ejpam-5090	97	20	4	4	NUM
ejpam-5090	97	21	)	)	PUNCT
ejpam-5090	97	22	ρf(ϑ	ρf(ϑ	X
ejpam-5090	97	23	)	)	PUNCT
ejpam-5090	97	24	≥	≥	PROPN
ejpam-5090	97	25	max	max	PROPN
ejpam-5090	97	26	{	{	PUNCT
ejpam-5090	97	27	ρf((z	ρf((z	PROPN
ejpam-5090	97	28	·	·	PUNCT
ejpam-5090	97	29	ϑ	ϑ	X
ejpam-5090	97	30	)	)	PUNCT
ejpam-5090	97	31	·	·	PUNCT
ejpam-5090	97	32	(	(	PUNCT
ejpam-5090	97	33	z	z	X
ejpam-5090	97	34	·	·	PUNCT
ejpam-5090	97	35	η	η	NOUN
ejpam-5090	97	36	)	)	PUNCT
ejpam-5090	97	37	)	)	PUNCT
ejpam-5090	97	38	,	,	PUNCT
ejpam-5090	97	39	ρf(η	ρf(η	NOUN
ejpam-5090	97	40	)	)	PUNCT
ejpam-5090	97	41	}	}	PUNCT
ejpam-5090	97	42	.	.	PUNCT
ejpam-5090	98	1	m.	m.	NOUN
ejpam-5090	98	2	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	98	3	et	et	PROPN
ejpam-5090	98	4	al	al	PROPN
ejpam-5090	98	5	.	.	PUNCT
ejpam-5090	98	6	/	/	SYM
ejpam-5090	98	7	eur	eur	PROPN
ejpam-5090	98	8	.	.	PUNCT
ejpam-5090	99	1	j.	j.	PROPN
ejpam-5090	99	2	pure	pure	PROPN
ejpam-5090	99	3	appl	appl	PROPN
ejpam-5090	99	4	.	.	PROPN
ejpam-5090	99	5	math	math	PROPN
ejpam-5090	99	6	,	,	PUNCT
ejpam-5090	99	7	17	17	NUM
ejpam-5090	99	8	(	(	PUNCT
ejpam-5090	99	9	2	2	NUM
ejpam-5090	99	10	)	)	PUNCT
ejpam-5090	99	11	(	(	PUNCT
ejpam-5090	99	12	2024	2024	NUM
ejpam-5090	99	13	)	)	PUNCT
ejpam-5090	99	14	,	,	PUNCT
ejpam-5090	99	15	1113	1113	NUM
ejpam-5090	99	16	-	-	SYM
ejpam-5090	99	17	1128	1128	NUM
ejpam-5090	99	18	1118	1118	NUM
ejpam-5090	99	19	3	3	NUM
ejpam-5090	99	20	.	.	PUNCT
ejpam-5090	99	21	formation	formation	NOUN
ejpam-5090	99	22	of	of	ADP
ejpam-5090	99	23	direct	direct	ADJ
ejpam-5090	99	24	product	product	NOUN
ejpam-5090	99	25	:	:	PUNCT
ejpam-5090	99	26	fnink	fnink	NOUN
ejpam-5090	99	27	-	-	PUNCT
ejpam-5090	99	28	ss	ss	NOUN
ejpam-5090	99	29	and	and	CCONJ
ejpam-5090	99	30	fnink	fnink	NOUN
ejpam-5090	99	31	-	-	PUNCT
ejpam-5090	99	32	is	be	AUX
ejpam-5090	99	33	definition	definition	NOUN
ejpam-5090	99	34	10	10	NUM
ejpam-5090	99	35	.	.	PUNCT
ejpam-5090	100	1	ink	ink	NOUN
ejpam-5090	100	2	-	-	PUNCT
ejpam-5090	100	3	algebras	algebras	NOUN
ejpam-5090	100	4	χ1	χ1	NOUN
ejpam-5090	100	5	and	and	CCONJ
ejpam-5090	100	6	χ2	χ2	PROPN
ejpam-5090	100	7	contain	contain	VERB
ejpam-5090	100	8	two	two	NUM
ejpam-5090	100	9	fnss	fns	NOUN
ejpam-5090	100	10	,	,	PUNCT
ejpam-5090	100	11	m	m	PRON
ejpam-5090	100	12	and	and	CCONJ
ejpam-5090	100	13	n.	n.	VERB
ejpam-5090	100	14	the	the	DET
ejpam-5090	100	15	structure	structure	NOUN
ejpam-5090	100	16	m×n	m×n	PROPN
ejpam-5090	100	17	=	=	SYM
ejpam-5090	100	18	〈	〈	PROPN
ejpam-5090	100	19	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	100	20	)	)	PUNCT
ejpam-5090	100	21	,	,	PUNCT
ejpam-5090	100	22	ρ	ρ	PROPN
ejpam-5090	100	23	i	i	PROPN
ejpam-5090	100	24	(	(	PUNCT
ejpam-5090	100	25	m×n	m×n	PROPN
ejpam-5090	100	26	)	)	PUNCT
ejpam-5090	100	27	,	,	PUNCT
ejpam-5090	100	28	ρ	ρ	PROPN
ejpam-5090	100	29	f	f	X
ejpam-5090	100	30	(	(	PUNCT
ejpam-5090	100	31	m×n	m×n	NOUN
ejpam-5090	100	32	)	)	PUNCT
ejpam-5090	100	33	〉	〉	NOUN
ejpam-5090	100	34	is	be	AUX
ejpam-5090	100	35	defined	define	VERB
ejpam-5090	100	36	as	as	ADP
ejpam-5090	100	37	the	the	DET
ejpam-5090	100	38	direct	direct	ADJ
ejpam-5090	100	39	product	product	NOUN
ejpam-5090	100	40	of	of	ADP
ejpam-5090	100	41	fnss	fns	NOUN
ejpam-5090	100	42	m	m	PROPN
ejpam-5090	100	43	and	and	CCONJ
ejpam-5090	100	44	n	n	CCONJ
ejpam-5090	100	45	,	,	PUNCT
ejpam-5090	100	46	specified	specify	VERB
ejpam-5090	100	47	by	by	ADP
ejpam-5090	100	48	,	,	PUNCT
ejpam-5090	100	49	∀(ϑ	∀(ϑ	PROPN
ejpam-5090	100	50	,	,	PUNCT
ejpam-5090	100	51	η	η	NOUN
ejpam-5090	100	52	)	)	PUNCT
ejpam-5090	100	53	∈	∈	PROPN
ejpam-5090	100	54	χ1	χ1	NOUN
ejpam-5090	100	55	×	×	NOUN
ejpam-5090	100	56	χ2	χ2	PROPN
ejpam-5090	100	57	(	(	PUNCT
ejpam-5090	100	58	1	1	X
ejpam-5090	100	59	)	)	PUNCT
ejpam-5090	100	60	ρt(m×n)(ϑ	ρt(m×n)(ϑ	PROPN
ejpam-5090	100	61	,	,	PUNCT
ejpam-5090	100	62	η	η	NOUN
ejpam-5090	100	63	)	)	PUNCT
ejpam-5090	101	1	=	=	SYM
ejpam-5090	101	2	min	min	NOUN
ejpam-5090	101	3	{	{	PUNCT
ejpam-5090	101	4	ρtm(ϑ	ρtm(ϑ	NOUN
ejpam-5090	101	5	)	)	PUNCT
ejpam-5090	101	6	,	,	PUNCT
ejpam-5090	101	7	ρtn(η	ρtn(η	PROPN
ejpam-5090	101	8	)	)	PUNCT
ejpam-5090	101	9	}	}	PUNCT
ejpam-5090	101	10	,	,	PUNCT
ejpam-5090	101	11	(	(	PUNCT
ejpam-5090	101	12	2	2	X
ejpam-5090	101	13	)	)	PUNCT
ejpam-5090	101	14	ρi(m×n)(ϑ	ρi(m×n)(ϑ	PROPN
ejpam-5090	101	15	,	,	PUNCT
ejpam-5090	101	16	η	η	NOUN
ejpam-5090	101	17	)	)	PUNCT
ejpam-5090	101	18	=	=	SYM
ejpam-5090	101	19	max	max	PROPN
ejpam-5090	101	20	{	{	PUNCT
ejpam-5090	101	21	ρim(ϑ	ρim(ϑ	PROPN
ejpam-5090	101	22	)	)	PUNCT
ejpam-5090	101	23	,	,	PUNCT
ejpam-5090	101	24	ρin(η	ρin(η	PROPN
ejpam-5090	101	25	)	)	PUNCT
ejpam-5090	101	26	}	}	PUNCT
ejpam-5090	101	27	,	,	PUNCT
ejpam-5090	101	28	(	(	PUNCT
ejpam-5090	101	29	3	3	X
ejpam-5090	101	30	)	)	PUNCT
ejpam-5090	101	31	ρf(m×n)(ϑ	ρf(m×n)(ϑ	PROPN
ejpam-5090	101	32	,	,	PUNCT
ejpam-5090	101	33	η	η	NOUN
ejpam-5090	101	34	)	)	PUNCT
ejpam-5090	101	35	=	=	SYM
ejpam-5090	101	36	max	max	PROPN
ejpam-5090	101	37	{	{	PUNCT
ejpam-5090	101	38	ρfm(ϑ	ρfm(ϑ	PROPN
ejpam-5090	101	39	)	)	PUNCT
ejpam-5090	101	40	,	,	PUNCT
ejpam-5090	101	41	ρfn(η	ρfn(η	NUM
ejpam-5090	101	42	)	)	PUNCT
ejpam-5090	101	43	}	}	PUNCT
ejpam-5090	101	44	.	.	PUNCT
ejpam-5090	102	1	definition	definition	NOUN
ejpam-5090	102	2	11	11	NUM
ejpam-5090	102	3	.	.	PUNCT
ejpam-5090	103	1	the	the	DET
ejpam-5090	103	2	direct	direct	ADJ
ejpam-5090	103	3	product	product	NOUN
ejpam-5090	103	4	of	of	ADP
ejpam-5090	103	5	fnink	fnink	NOUN
ejpam-5090	103	6	-	-	PUNCT
ejpam-5090	103	7	ss	ss	NOUN
ejpam-5090	103	8	of	of	ADP
ejpam-5090	103	9	χ1	χ1	NOUN
ejpam-5090	103	10	×	×	PROPN
ejpam-5090	103	11	χ2	χ2	PROPN
ejpam-5090	103	12	is	be	AUX
ejpam-5090	103	13	a	a	DET
ejpam-5090	103	14	fnss	fns	NOUN
ejpam-5090	103	15	m×n	m×n	PROPN
ejpam-5090	103	16	=	=	SYM
ejpam-5090	103	17	〈	〈	PROPN
ejpam-5090	103	18	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	103	19	)	)	PUNCT
ejpam-5090	103	20	,	,	PUNCT
ejpam-5090	103	21	ρ	ρ	PROPN
ejpam-5090	103	22	i	i	PROPN
ejpam-5090	103	23	(	(	PUNCT
ejpam-5090	103	24	m×n	m×n	PROPN
ejpam-5090	103	25	)	)	PUNCT
ejpam-5090	103	26	,	,	PUNCT
ejpam-5090	103	27	ρ	ρ	PROPN
ejpam-5090	103	28	f	f	X
ejpam-5090	103	29	(	(	PUNCT
ejpam-5090	103	30	m×n	m×n	NOUN
ejpam-5090	103	31	)	)	PUNCT
ejpam-5090	103	32	〉	〉	NOUN
ejpam-5090	103	33	of	of	ADP
ejpam-5090	103	34	χ1	χ1	NOUN
ejpam-5090	103	35	and	and	CCONJ
ejpam-5090	103	36	χ2	χ2	PROPN
ejpam-5090	103	37	if	if	SCONJ
ejpam-5090	103	38	,	,	PUNCT
ejpam-5090	103	39	∀(ϑ1	∀(ϑ1	ADJ
ejpam-5090	103	40	,	,	PUNCT
ejpam-5090	103	41	η1	η1	NOUN
ejpam-5090	103	42	)	)	PUNCT
ejpam-5090	103	43	,	,	PUNCT
ejpam-5090	103	44	(	(	PUNCT
ejpam-5090	103	45	ϑ2	ϑ2	NOUN
ejpam-5090	103	46	,	,	PUNCT
ejpam-5090	103	47	η2	η2	ADJ
ejpam-5090	103	48	)	)	PUNCT
ejpam-5090	103	49	∈	∈	PROPN
ejpam-5090	103	50	χ1	χ1	NOUN
ejpam-5090	103	51	×	×	NOUN
ejpam-5090	103	52	χ2	χ2	PROPN
ejpam-5090	103	53	(	(	PUNCT
ejpam-5090	103	54	1	1	NUM
ejpam-5090	103	55	)	)	PUNCT
ejpam-5090	103	56	ρt(m×n)((ϑ1	ρt(m×n)((ϑ1	NUM
ejpam-5090	103	57	,	,	PUNCT
ejpam-5090	103	58	η1	η1	NOUN
ejpam-5090	103	59	)	)	PUNCT
ejpam-5090	103	60	·	·	PUNCT
ejpam-5090	103	61	(	(	PUNCT
ejpam-5090	103	62	ϑ2	ϑ2	NOUN
ejpam-5090	103	63	,	,	PUNCT
ejpam-5090	103	64	η2	η2	NOUN
ejpam-5090	103	65	)	)	PUNCT
ejpam-5090	103	66	)	)	PUNCT
ejpam-5090	103	67	≤	≤	NUM
ejpam-5090	103	68	min	min	NOUN
ejpam-5090	103	69	{	{	PUNCT
ejpam-5090	103	70	ρt(m×n)(ϑ1	ρt(m×n)(ϑ1	ADJ
ejpam-5090	103	71	,	,	PUNCT
ejpam-5090	103	72	η1	η1	NOUN
ejpam-5090	103	73	)	)	PUNCT
ejpam-5090	103	74	,	,	PUNCT
ejpam-5090	103	75	ρ	ρ	PROPN
ejpam-5090	103	76	t	t	PROPN
ejpam-5090	103	77	(	(	PUNCT
ejpam-5090	103	78	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	103	79	,	,	PUNCT
ejpam-5090	103	80	η2	η2	PROPN
ejpam-5090	103	81	)	)	PUNCT
ejpam-5090	103	82	}	}	PUNCT
ejpam-5090	103	83	,	,	PUNCT
ejpam-5090	103	84	(	(	PUNCT
ejpam-5090	103	85	2	2	X
ejpam-5090	103	86	)	)	PUNCT
ejpam-5090	103	87	ρi(m×n)((ϑ1	ρi(m×n)((ϑ1	ADJ
ejpam-5090	103	88	,	,	PUNCT
ejpam-5090	103	89	η1	η1	NOUN
ejpam-5090	103	90	)	)	PUNCT
ejpam-5090	103	91	·	·	PUNCT
ejpam-5090	103	92	(	(	PUNCT
ejpam-5090	103	93	ϑ2	ϑ2	NOUN
ejpam-5090	103	94	,	,	PUNCT
ejpam-5090	103	95	η2	η2	NOUN
ejpam-5090	103	96	)	)	PUNCT
ejpam-5090	103	97	)	)	PUNCT
ejpam-5090	103	98	≥	≥	PROPN
ejpam-5090	103	99	max	max	PROPN
ejpam-5090	103	100	{	{	PUNCT
ejpam-5090	103	101	ρi(m×n)(ϑ1	ρi(m×n)(ϑ1	PROPN
ejpam-5090	103	102	,	,	PUNCT
ejpam-5090	103	103	η1	η1	NOUN
ejpam-5090	103	104	)	)	PUNCT
ejpam-5090	103	105	,	,	PUNCT
ejpam-5090	103	106	ρ	ρ	PROPN
ejpam-5090	103	107	i	i	PROPN
ejpam-5090	103	108	(	(	PUNCT
ejpam-5090	103	109	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	103	110	,	,	PUNCT
ejpam-5090	103	111	η2	η2	PROPN
ejpam-5090	103	112	)	)	PUNCT
ejpam-5090	103	113	}	}	PUNCT
ejpam-5090	103	114	,	,	PUNCT
ejpam-5090	103	115	(	(	PUNCT
ejpam-5090	103	116	3	3	X
ejpam-5090	103	117	)	)	PUNCT
ejpam-5090	103	118	ρf(m×n)((ϑ1	ρf(m×n)((ϑ1	ADJ
ejpam-5090	103	119	,	,	PUNCT
ejpam-5090	103	120	η1	η1	NOUN
ejpam-5090	103	121	)	)	PUNCT
ejpam-5090	103	122	·	·	PUNCT
ejpam-5090	103	123	(	(	PUNCT
ejpam-5090	103	124	ϑ2	ϑ2	NOUN
ejpam-5090	103	125	,	,	PUNCT
ejpam-5090	103	126	η2	η2	NOUN
ejpam-5090	103	127	)	)	PUNCT
ejpam-5090	103	128	)	)	PUNCT
ejpam-5090	103	129	≥	≥	PROPN
ejpam-5090	103	130	max	max	PROPN
ejpam-5090	103	131	{	{	PUNCT
ejpam-5090	103	132	ρf(m×n)(ϑ1	ρf(m×n)(ϑ1	NOUN
ejpam-5090	103	133	,	,	PUNCT
ejpam-5090	103	134	η1	η1	NOUN
ejpam-5090	103	135	)	)	PUNCT
ejpam-5090	103	136	,	,	PUNCT
ejpam-5090	103	137	ρ	ρ	PROPN
ejpam-5090	103	138	f	f	PROPN
ejpam-5090	103	139	(	(	PUNCT
ejpam-5090	103	140	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	103	141	,	,	PUNCT
ejpam-5090	103	142	η2	η2	PROPN
ejpam-5090	103	143	)	)	PUNCT
ejpam-5090	103	144	}	}	PUNCT
ejpam-5090	103	145	.	.	PUNCT
ejpam-5090	104	1	definition	definition	NOUN
ejpam-5090	104	2	12	12	NUM
ejpam-5090	104	3	.	.	PUNCT
ejpam-5090	105	1	the	the	DET
ejpam-5090	105	2	direct	direct	ADJ
ejpam-5090	105	3	product	product	NOUN
ejpam-5090	105	4	of	of	ADP
ejpam-5090	105	5	fnink	fnink	NOUN
ejpam-5090	105	6	-	-	PUNCT
ejpam-5090	105	7	i	i	PRON
ejpam-5090	105	8	of	of	ADP
ejpam-5090	105	9	χ1	χ1	NOUN
ejpam-5090	105	10	×	×	PROPN
ejpam-5090	105	11	χ2	χ2	PROPN
ejpam-5090	105	12	is	be	AUX
ejpam-5090	105	13	a	a	DET
ejpam-5090	105	14	fnss	fns	NOUN
ejpam-5090	105	15	m×n	m×n	PROPN
ejpam-5090	105	16	=	=	SYM
ejpam-5090	105	17	〈	〈	PROPN
ejpam-5090	105	18	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	105	19	)	)	PUNCT
ejpam-5090	105	20	,	,	PUNCT
ejpam-5090	105	21	ρ	ρ	PROPN
ejpam-5090	105	22	i	i	PROPN
ejpam-5090	105	23	(	(	PUNCT
ejpam-5090	105	24	m×n	m×n	PROPN
ejpam-5090	105	25	)	)	PUNCT
ejpam-5090	105	26	,	,	PUNCT
ejpam-5090	105	27	ρ	ρ	PROPN
ejpam-5090	105	28	f	f	X
ejpam-5090	105	29	(	(	PUNCT
ejpam-5090	105	30	m×n	m×n	NOUN
ejpam-5090	105	31	)	)	PUNCT
ejpam-5090	105	32	〉	〉	NOUN
ejpam-5090	105	33	of	of	ADP
ejpam-5090	105	34	χ1	χ1	NOUN
ejpam-5090	105	35	and	and	CCONJ
ejpam-5090	105	36	χ2	χ2	PROPN
ejpam-5090	105	37	if	if	SCONJ
ejpam-5090	105	38	,	,	PUNCT
ejpam-5090	105	39	∀(ϑ1	∀(ϑ1	NOUN
ejpam-5090	105	40	,	,	PUNCT
ejpam-5090	105	41	η1	η1	NOUN
ejpam-5090	105	42	)	)	PUNCT
ejpam-5090	105	43	,	,	PUNCT
ejpam-5090	105	44	(	(	PUNCT
ejpam-5090	105	45	ϑ2	ϑ2	NOUN
ejpam-5090	105	46	,	,	PUNCT
ejpam-5090	105	47	η2	η2	NOUN
ejpam-5090	105	48	)	)	PUNCT
ejpam-5090	105	49	,	,	PUNCT
ejpam-5090	105	50	(	(	PUNCT
ejpam-5090	105	51	ϑ3	ϑ3	PROPN
ejpam-5090	105	52	,	,	PUNCT
ejpam-5090	105	53	η3	η3	PROPN
ejpam-5090	105	54	)	)	PUNCT
ejpam-5090	105	55	∈	∈	PROPN
ejpam-5090	105	56	χ1	χ1	NOUN
ejpam-5090	105	57	×	×	NOUN
ejpam-5090	105	58	χ2	χ2	PROPN
ejpam-5090	105	59	(	(	PUNCT
ejpam-5090	105	60	1	1	NUM
ejpam-5090	105	61	)	)	PUNCT
ejpam-5090	105	62	ρt(m×n)(0	ρt(m×n)(0	PROPN
ejpam-5090	105	63	,	,	PUNCT
ejpam-5090	105	64	0	0	NUM
ejpam-5090	105	65	)	)	PUNCT
ejpam-5090	105	66	≤	≤	NUM
ejpam-5090	105	67	ρt(m×n)(ϑ	ρt(m×n)(ϑ	PROPN
ejpam-5090	105	68	,	,	PUNCT
ejpam-5090	105	69	η	η	NOUN
ejpam-5090	105	70	)	)	PUNCT
ejpam-5090	105	71	,	,	PUNCT
ejpam-5090	105	72	ρ	ρ	PROPN
ejpam-5090	106	1	i	i	PROPN
ejpam-5090	106	2	(	(	PUNCT
ejpam-5090	106	3	m×n)(0	m×n)(0	ADJ
ejpam-5090	106	4	,	,	PUNCT
ejpam-5090	106	5	0	0	NUM
ejpam-5090	106	6	)	)	PUNCT
ejpam-5090	106	7	≥	≥	NOUN
ejpam-5090	106	8	ρi(m×n)(ϑ	ρi(m×n)(ϑ	PROPN
ejpam-5090	106	9	,	,	PUNCT
ejpam-5090	106	10	η	η	PROPN
ejpam-5090	106	11	)	)	PUNCT
ejpam-5090	106	12	,	,	PUNCT
ejpam-5090	106	13	ρ	ρ	PROPN
ejpam-5090	106	14	f	f	PROPN
ejpam-5090	106	15	(	(	PUNCT
ejpam-5090	106	16	m×n)(0	m×n)(0	PROPN
ejpam-5090	106	17	,	,	PUNCT
ejpam-5090	106	18	0	0	NUM
ejpam-5090	106	19	)	)	PUNCT
ejpam-5090	106	20	≥	≥	NOUN
ejpam-5090	106	21	ρfm×n(ϑ	ρfm×n(ϑ	PROPN
ejpam-5090	106	22	,	,	PUNCT
ejpam-5090	106	23	η	η	NOUN
ejpam-5090	106	24	)	)	PUNCT
ejpam-5090	106	25	,	,	PUNCT
ejpam-5090	106	26	(	(	PUNCT
ejpam-5090	106	27	2	2	X
ejpam-5090	106	28	)	)	PUNCT
ejpam-5090	106	29	ρt(m×n)(((ϑ1	ρt(m×n)(((ϑ1	PROPN
ejpam-5090	106	30	,	,	PUNCT
ejpam-5090	106	31	η1	η1	NOUN
ejpam-5090	106	32	)	)	PUNCT
ejpam-5090	106	33	≤	≤	NUM
ejpam-5090	106	34	min	min	NOUN
ejpam-5090	106	35	{	{	PUNCT
ejpam-5090	106	36	ρtm×n(((ϑ3	ρtm×n(((ϑ3	PROPN
ejpam-5090	106	37	,	,	PUNCT
ejpam-5090	106	38	η3	η3	NOUN
ejpam-5090	106	39	)	)	PUNCT
ejpam-5090	106	40	·	·	PUNCT
ejpam-5090	106	41	(	(	PUNCT
ejpam-5090	106	42	ϑ1	ϑ1	NOUN
ejpam-5090	106	43	,	,	PUNCT
ejpam-5090	106	44	η1	η1	NOUN
ejpam-5090	106	45	)	)	PUNCT
ejpam-5090	106	46	)	)	PUNCT
ejpam-5090	106	47	·	·	PUNCT
ejpam-5090	107	1	(	(	PUNCT
ejpam-5090	107	2	(	(	PUNCT
ejpam-5090	107	3	ϑ3	ϑ3	NOUN
ejpam-5090	107	4	,	,	PUNCT
ejpam-5090	107	5	η3	η3	PROPN
ejpam-5090	107	6	)	)	PUNCT
ejpam-5090	107	7	·	·	PUNCT
ejpam-5090	107	8	(	(	PUNCT
ejpam-5090	107	9	ϑ2	ϑ2	NOUN
ejpam-5090	107	10	,	,	PUNCT
ejpam-5090	107	11	η2	η2	NOUN
ejpam-5090	107	12	)	)	PUNCT
ejpam-5090	107	13	)	)	PUNCT
ejpam-5090	107	14	)	)	PUNCT
ejpam-5090	107	15	,	,	PUNCT
ejpam-5090	107	16	ρ	ρ	PROPN
ejpam-5090	107	17	t	t	PROPN
ejpam-5090	107	18	(	(	PUNCT
ejpam-5090	107	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	107	20	,	,	PUNCT
ejpam-5090	107	21	η2	η2	PROPN
ejpam-5090	107	22	)	)	PUNCT
ejpam-5090	107	23	}	}	PUNCT
ejpam-5090	107	24	,	,	PUNCT
ejpam-5090	107	25	(	(	PUNCT
ejpam-5090	107	26	3	3	X
ejpam-5090	107	27	)	)	PUNCT
ejpam-5090	107	28	ρi(m×n)(ϑ1	ρi(m×n)(ϑ1	NOUN
ejpam-5090	107	29	,	,	PUNCT
ejpam-5090	107	30	η1	η1	NOUN
ejpam-5090	107	31	)	)	PUNCT
ejpam-5090	107	32	≥	≥	PROPN
ejpam-5090	107	33	max	max	PROPN
ejpam-5090	107	34	{	{	PUNCT
ejpam-5090	107	35	ρi(m×n)(((ϑ3	ρi(m×n)(((ϑ3	PROPN
ejpam-5090	107	36	,	,	PUNCT
ejpam-5090	107	37	η3	η3	PROPN
ejpam-5090	107	38	)	)	PUNCT
ejpam-5090	107	39	·	·	PUNCT
ejpam-5090	107	40	(	(	PUNCT
ejpam-5090	107	41	ϑ1	ϑ1	NOUN
ejpam-5090	107	42	,	,	PUNCT
ejpam-5090	107	43	η1	η1	NOUN
ejpam-5090	107	44	)	)	PUNCT
ejpam-5090	107	45	)	)	PUNCT
ejpam-5090	107	46	·	·	PUNCT
ejpam-5090	108	1	(	(	PUNCT
ejpam-5090	108	2	(	(	PUNCT
ejpam-5090	108	3	ϑ3	ϑ3	NOUN
ejpam-5090	108	4	,	,	PUNCT
ejpam-5090	108	5	η3	η3	PROPN
ejpam-5090	108	6	)	)	PUNCT
ejpam-5090	108	7	·	·	PUNCT
ejpam-5090	108	8	(	(	PUNCT
ejpam-5090	108	9	ϑ2	ϑ2	NOUN
ejpam-5090	108	10	,	,	PUNCT
ejpam-5090	108	11	η2	η2	NOUN
ejpam-5090	108	12	)	)	PUNCT
ejpam-5090	108	13	)	)	PUNCT
ejpam-5090	108	14	)	)	PUNCT
ejpam-5090	108	15	,	,	PUNCT
ejpam-5090	108	16	ρ	ρ	PROPN
ejpam-5090	108	17	i	i	PROPN
ejpam-5090	108	18	(	(	PUNCT
ejpam-5090	108	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	108	20	,	,	PUNCT
ejpam-5090	108	21	η2	η2	PROPN
ejpam-5090	108	22	)	)	PUNCT
ejpam-5090	108	23	}	}	PUNCT
ejpam-5090	108	24	,	,	PUNCT
ejpam-5090	108	25	(	(	PUNCT
ejpam-5090	108	26	4	4	X
ejpam-5090	108	27	)	)	PUNCT
ejpam-5090	108	28	ρf(m×n)(ϑ1	ρf(m×n)(ϑ1	NOUN
ejpam-5090	108	29	,	,	PUNCT
ejpam-5090	108	30	η1	η1	NOUN
ejpam-5090	108	31	)	)	PUNCT
ejpam-5090	108	32	≥	≥	PROPN
ejpam-5090	108	33	max	max	PROPN
ejpam-5090	108	34	{	{	PUNCT
ejpam-5090	108	35	ρf(m×n)(((ϑ3	ρf(m×n)(((ϑ3	PROPN
ejpam-5090	108	36	,	,	PUNCT
ejpam-5090	108	37	η3	η3	NOUN
ejpam-5090	108	38	)	)	PUNCT
ejpam-5090	108	39	·	·	PUNCT
ejpam-5090	108	40	(	(	PUNCT
ejpam-5090	108	41	ϑ1	ϑ1	NOUN
ejpam-5090	108	42	,	,	PUNCT
ejpam-5090	108	43	η1	η1	NOUN
ejpam-5090	108	44	)	)	PUNCT
ejpam-5090	108	45	)	)	PUNCT
ejpam-5090	108	46	·	·	PUNCT
ejpam-5090	109	1	(	(	PUNCT
ejpam-5090	109	2	(	(	PUNCT
ejpam-5090	109	3	ϑ3	ϑ3	NOUN
ejpam-5090	109	4	,	,	PUNCT
ejpam-5090	109	5	η3	η3	PROPN
ejpam-5090	109	6	)	)	PUNCT
ejpam-5090	109	7	·	·	PUNCT
ejpam-5090	109	8	(	(	PUNCT
ejpam-5090	109	9	ϑ2	ϑ2	NOUN
ejpam-5090	109	10	,	,	PUNCT
ejpam-5090	109	11	η2	η2	NOUN
ejpam-5090	109	12	)	)	PUNCT
ejpam-5090	109	13	)	)	PUNCT
ejpam-5090	109	14	)	)	PUNCT
ejpam-5090	109	15	,	,	PUNCT
ejpam-5090	109	16	ρ	ρ	PROPN
ejpam-5090	109	17	f	f	PROPN
ejpam-5090	109	18	(	(	PUNCT
ejpam-5090	109	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	109	20	,	,	PUNCT
ejpam-5090	109	21	η2	η2	PROPN
ejpam-5090	109	22	)	)	PUNCT
ejpam-5090	109	23	}	}	PUNCT
ejpam-5090	109	24	.	.	PUNCT
ejpam-5090	110	1	definition	definition	NOUN
ejpam-5090	110	2	13	13	NUM
ejpam-5090	110	3	.	.	PUNCT
ejpam-5090	111	1	the	the	DET
ejpam-5090	111	2	direct	direct	ADJ
ejpam-5090	111	3	product	product	NOUN
ejpam-5090	111	4	of	of	ADP
ejpam-5090	111	5	fncink	fncink	NOUN
ejpam-5090	111	6	-	-	PUNCT
ejpam-5090	111	7	i	i	PROPN
ejpam-5090	111	8	of	of	ADP
ejpam-5090	111	9	χ1	χ1	NOUN
ejpam-5090	111	10	×	×	PROPN
ejpam-5090	111	11	χ2	χ2	PROPN
ejpam-5090	111	12	is	be	AUX
ejpam-5090	111	13	a	a	DET
ejpam-5090	111	14	fnss	fns	NOUN
ejpam-5090	111	15	m×n	m×n	PROPN
ejpam-5090	111	16	=	=	SYM
ejpam-5090	111	17	〈	〈	PROPN
ejpam-5090	111	18	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	111	19	)	)	PUNCT
ejpam-5090	111	20	,	,	PUNCT
ejpam-5090	111	21	ρ	ρ	PROPN
ejpam-5090	111	22	i	i	PROPN
ejpam-5090	111	23	(	(	PUNCT
ejpam-5090	111	24	m×n	m×n	PROPN
ejpam-5090	111	25	)	)	PUNCT
ejpam-5090	111	26	,	,	PUNCT
ejpam-5090	111	27	ρ	ρ	PROPN
ejpam-5090	111	28	f	f	X
ejpam-5090	111	29	(	(	PUNCT
ejpam-5090	111	30	m×n	m×n	NOUN
ejpam-5090	111	31	)	)	PUNCT
ejpam-5090	111	32	〉	〉	NOUN
ejpam-5090	111	33	of	of	ADP
ejpam-5090	111	34	χ1	χ1	NOUN
ejpam-5090	111	35	and	and	CCONJ
ejpam-5090	111	36	χ2	χ2	PROPN
ejpam-5090	111	37	if	if	SCONJ
ejpam-5090	111	38	it	it	PRON
ejpam-5090	111	39	meets	meet	VERB
ejpam-5090	111	40	(	(	PUNCT
ejpam-5090	111	41	(	(	PUNCT
ejpam-5090	111	42	2	2	NUM
ejpam-5090	111	43	)	)	PUNCT
ejpam-5090	111	44	,	,	PUNCT
ejpam-5090	111	45	(	(	PUNCT
ejpam-5090	111	46	3	3	X
ejpam-5090	111	47	)	)	PUNCT
ejpam-5090	111	48	and	and	CCONJ
ejpam-5090	111	49	(	(	PUNCT
ejpam-5090	111	50	4	4	X
ejpam-5090	111	51	)	)	PUNCT
ejpam-5090	111	52	of	of	ADP
ejpam-5090	111	53	definition	definition	NOUN
ejpam-5090	111	54	12	12	NUM
ejpam-5090	111	55	)	)	PUNCT
ejpam-5090	111	56	and	and	CCONJ
ejpam-5090	111	57	the	the	DET
ejpam-5090	111	58	following	follow	VERB
ejpam-5090	111	59	inequalities	inequality	NOUN
ejpam-5090	111	60	,	,	PUNCT
ejpam-5090	111	61	∀(ϑ	∀(ϑ	PROPN
ejpam-5090	111	62	,	,	PUNCT
ejpam-5090	111	63	η	η	NOUN
ejpam-5090	111	64	)	)	PUNCT
ejpam-5090	111	65	∈	∈	PROPN
ejpam-5090	111	66	χ1	χ1	NOUN
ejpam-5090	111	67	×	×	PROPN
ejpam-5090	111	68	χ2	χ2	PROPN
ejpam-5090	111	69	m.	m.	NOUN
ejpam-5090	111	70	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	111	71	et	et	PROPN
ejpam-5090	111	72	al	al	PROPN
ejpam-5090	111	73	.	.	PUNCT
ejpam-5090	111	74	/	/	SYM
ejpam-5090	111	75	eur	eur	PROPN
ejpam-5090	111	76	.	.	PUNCT
ejpam-5090	112	1	j.	j.	PROPN
ejpam-5090	112	2	pure	pure	PROPN
ejpam-5090	112	3	appl	appl	PROPN
ejpam-5090	112	4	.	.	PROPN
ejpam-5090	112	5	math	math	PROPN
ejpam-5090	112	6	,	,	PUNCT
ejpam-5090	112	7	17	17	NUM
ejpam-5090	112	8	(	(	PUNCT
ejpam-5090	112	9	2	2	NUM
ejpam-5090	112	10	)	)	PUNCT
ejpam-5090	112	11	(	(	PUNCT
ejpam-5090	112	12	2024	2024	NUM
ejpam-5090	112	13	)	)	PUNCT
ejpam-5090	112	14	,	,	PUNCT
ejpam-5090	112	15	1113	1113	NUM
ejpam-5090	112	16	-	-	SYM
ejpam-5090	112	17	1128	1128	NUM
ejpam-5090	112	18	1119	1119	NUM
ejpam-5090	112	19	(	(	PUNCT
ejpam-5090	112	20	1	1	NUM
ejpam-5090	112	21	)	)	PUNCT
ejpam-5090	112	22	ρt(m×n)((0	ρt(m×n)((0	NOUN
ejpam-5090	112	23	,	,	PUNCT
ejpam-5090	112	24	0	0	NUM
ejpam-5090	112	25	)	)	PUNCT
ejpam-5090	112	26	·	·	PUNCT
ejpam-5090	112	27	(	(	PUNCT
ejpam-5090	112	28	ϑ	ϑ	X
ejpam-5090	112	29	,	,	PUNCT
ejpam-5090	112	30	η	η	NOUN
ejpam-5090	112	31	)	)	PUNCT
ejpam-5090	112	32	)	)	PUNCT
ejpam-5090	112	33	≤	≤	NUM
ejpam-5090	113	1	ρt(m×n)(ϑ	ρt(m×n)(ϑ	PROPN
ejpam-5090	113	2	,	,	PUNCT
ejpam-5090	113	3	η	η	NOUN
ejpam-5090	113	4	)	)	PUNCT
ejpam-5090	113	5	,	,	PUNCT
ejpam-5090	113	6	(	(	PUNCT
ejpam-5090	113	7	2	2	X
ejpam-5090	113	8	)	)	PUNCT
ejpam-5090	113	9	ρi(m×n)((0	ρi(m×n)((0	NOUN
ejpam-5090	113	10	,	,	PUNCT
ejpam-5090	113	11	0	0	NUM
ejpam-5090	113	12	)	)	PUNCT
ejpam-5090	113	13	·	·	PUNCT
ejpam-5090	113	14	(	(	PUNCT
ejpam-5090	113	15	ϑ	ϑ	X
ejpam-5090	113	16	,	,	PUNCT
ejpam-5090	113	17	η	η	NOUN
ejpam-5090	113	18	)	)	PUNCT
ejpam-5090	113	19	)	)	PUNCT
ejpam-5090	113	20	≥	≥	NOUN
ejpam-5090	114	1	ρi(m×n)(ϑ	ρi(m×n)(ϑ	PROPN
ejpam-5090	114	2	,	,	PUNCT
ejpam-5090	114	3	η	η	NOUN
ejpam-5090	114	4	)	)	PUNCT
ejpam-5090	114	5	,	,	PUNCT
ejpam-5090	114	6	(	(	PUNCT
ejpam-5090	114	7	3	3	X
ejpam-5090	114	8	)	)	PUNCT
ejpam-5090	114	9	ρf(m×n)((0	ρf(m×n)((0	NOUN
ejpam-5090	114	10	,	,	PUNCT
ejpam-5090	114	11	0	0	NUM
ejpam-5090	114	12	)	)	PUNCT
ejpam-5090	114	13	·	·	PUNCT
ejpam-5090	114	14	(	(	PUNCT
ejpam-5090	114	15	ϑ	ϑ	X
ejpam-5090	114	16	,	,	PUNCT
ejpam-5090	114	17	η	η	NOUN
ejpam-5090	114	18	)	)	PUNCT
ejpam-5090	114	19	)	)	PUNCT
ejpam-5090	114	20	≥	≥	NOUN
ejpam-5090	115	1	ρf(m×n)(ϑ	ρf(m×n)(ϑ	NOUN
ejpam-5090	115	2	,	,	PUNCT
ejpam-5090	115	3	η	η	NOUN
ejpam-5090	115	4	)	)	PUNCT
ejpam-5090	115	5	.	.	PUNCT
ejpam-5090	116	1	theorem	theorem	NOUN
ejpam-5090	116	2	1	1	NUM
ejpam-5090	116	3	.	.	PUNCT
ejpam-5090	117	1	let	let	VERB
ejpam-5090	117	2	m	m	PROPN
ejpam-5090	117	3	=	=	VERB
ejpam-5090	117	4	〈	〈	PROPN
ejpam-5090	117	5	ρtm	ρtm	NOUN
ejpam-5090	117	6	,	,	PUNCT
ejpam-5090	117	7	ρim	ρim	NOUN
ejpam-5090	117	8	,	,	PUNCT
ejpam-5090	117	9	ρfm	ρfm	ADP
ejpam-5090	117	10	〉	〉	NOUN
ejpam-5090	117	11	and	and	CCONJ
ejpam-5090	117	12	n	n	NOUN
ejpam-5090	117	13	=	=	PUNCT
ejpam-5090	117	14	〈	〈	PROPN
ejpam-5090	117	15	ρtn	ρtn	NOUN
ejpam-5090	117	16	,	,	PUNCT
ejpam-5090	117	17	ρ	ρ	PROPN
ejpam-5090	117	18	i	i	PROPN
ejpam-5090	117	19	n	n	CCONJ
ejpam-5090	117	20	,	,	PUNCT
ejpam-5090	117	21	ρ	ρ	PROPN
ejpam-5090	117	22	f	f	PROPN
ejpam-5090	117	23	n	n	PRON
ejpam-5090	117	24	〉	〉	NOUN
ejpam-5090	117	25	be	be	VERB
ejpam-5090	117	26	two	two	NUM
ejpam-5090	117	27	fnink	fnink	NOUN
ejpam-5090	117	28	-	-	PUNCT
ejpam-5090	117	29	ss	ss	NOUN
ejpam-5090	117	30	of	of	ADP
ejpam-5090	117	31	χ1	χ1	NOUN
ejpam-5090	117	32	and	and	CCONJ
ejpam-5090	117	33	χ2	χ2	PROPN
ejpam-5090	117	34	,	,	PUNCT
ejpam-5090	117	35	respectively	respectively	ADV
ejpam-5090	117	36	.	.	PUNCT
ejpam-5090	118	1	then	then	ADV
ejpam-5090	118	2	,	,	PUNCT
ejpam-5090	118	3	the	the	DET
ejpam-5090	118	4	direct	direct	ADJ
ejpam-5090	118	5	product	product	NOUN
ejpam-5090	118	6	m×n	m×n	PROPN
ejpam-5090	118	7	,	,	PUNCT
ejpam-5090	118	8	defined	define	VERB
ejpam-5090	118	9	by	by	ADP
ejpam-5090	118	10	m×n	m×n	PROPN
ejpam-5090	118	11	=	=	SYM
ejpam-5090	118	12	〈	〈	PROPN
ejpam-5090	118	13	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	118	14	)	)	PUNCT
ejpam-5090	118	15	,	,	PUNCT
ejpam-5090	118	16	ρ	ρ	PROPN
ejpam-5090	118	17	i	i	PROPN
ejpam-5090	118	18	(	(	PUNCT
ejpam-5090	118	19	m×n	m×n	PROPN
ejpam-5090	118	20	)	)	PUNCT
ejpam-5090	118	21	,	,	PUNCT
ejpam-5090	118	22	ρ	ρ	PROPN
ejpam-5090	118	23	f	f	X
ejpam-5090	118	24	(	(	PUNCT
ejpam-5090	118	25	m×n	m×n	NOUN
ejpam-5090	118	26	)	)	PUNCT
ejpam-5090	118	27	〉	〉	NOUN
ejpam-5090	118	28	,	,	PUNCT
ejpam-5090	118	29	is	be	AUX
ejpam-5090	118	30	a	a	DET
ejpam-5090	118	31	fnink	fnink	NOUN
ejpam-5090	118	32	-	-	PUNCT
ejpam-5090	118	33	s	s	NOUN
ejpam-5090	118	34	of	of	ADP
ejpam-5090	118	35	χ1	χ1	NOUN
ejpam-5090	118	36	×	×	PROPN
ejpam-5090	118	37	χ2	χ2	PROPN
ejpam-5090	118	38	.	.	PUNCT
ejpam-5090	119	1	proof	proof	NOUN
ejpam-5090	119	2	.	.	PUNCT
ejpam-5090	120	1	assume	assume	VERB
ejpam-5090	120	2	that	that	SCONJ
ejpam-5090	120	3	m	m	PROPN
ejpam-5090	120	4	and	and	CCONJ
ejpam-5090	120	5	n	n	PRON
ejpam-5090	120	6	are	be	AUX
ejpam-5090	120	7	two	two	NUM
ejpam-5090	120	8	fnink	fnink	NOUN
ejpam-5090	120	9	-	-	PUNCT
ejpam-5090	120	10	ss	ss	NOUN
ejpam-5090	120	11	.	.	PUNCT
ejpam-5090	121	1	let	let	VERB
ejpam-5090	121	2	(	(	PUNCT
ejpam-5090	121	3	ϑ1	ϑ1	NOUN
ejpam-5090	121	4	,	,	PUNCT
ejpam-5090	121	5	η1	η1	NOUN
ejpam-5090	121	6	)	)	PUNCT
ejpam-5090	121	7	,	,	PUNCT
ejpam-5090	121	8	(	(	PUNCT
ejpam-5090	121	9	ϑ2	ϑ2	NOUN
ejpam-5090	121	10	,	,	PUNCT
ejpam-5090	121	11	η2	η2	ADJ
ejpam-5090	121	12	)	)	PUNCT
ejpam-5090	121	13	∈	∈	PROPN
ejpam-5090	121	14	χ1	χ1	NOUN
ejpam-5090	121	15	×	×	NOUN
ejpam-5090	121	16	χ2	χ2	PROPN
ejpam-5090	121	17	.	.	PUNCT
ejpam-5090	122	1	then	then	ADV
ejpam-5090	122	2	,	,	PUNCT
ejpam-5090	122	3	ρt(m×n)((ϑ1	ρt(m×n)((ϑ1	NUM
ejpam-5090	122	4	,	,	PUNCT
ejpam-5090	122	5	η1	η1	NOUN
ejpam-5090	122	6	)	)	PUNCT
ejpam-5090	122	7	·	·	PUNCT
ejpam-5090	122	8	(	(	PUNCT
ejpam-5090	122	9	ϑ2	ϑ2	NOUN
ejpam-5090	122	10	,	,	PUNCT
ejpam-5090	122	11	η2	η2	NOUN
ejpam-5090	122	12	)	)	PUNCT
ejpam-5090	122	13	)	)	PUNCT
ejpam-5090	123	1	=	=	PRON
ejpam-5090	123	2	{	{	PUNCT
ejpam-5090	123	3	ρtm×n(ϑ1	ρtm×n(ϑ1	NUM
ejpam-5090	123	4	·	·	PUNCT
ejpam-5090	123	5	ϑ2	ϑ2	NOUN
ejpam-5090	123	6	)	)	PUNCT
ejpam-5090	123	7	,	,	PUNCT
ejpam-5090	123	8	(	(	PUNCT
ejpam-5090	123	9	η1	η1	NOUN
ejpam-5090	123	10	·	·	SYM
ejpam-5090	123	11	η2	η2	X
ejpam-5090	123	12	)	)	PUNCT
ejpam-5090	123	13	}	}	PUNCT
ejpam-5090	123	14	=	=	SYM
ejpam-5090	123	15	min	min	NOUN
ejpam-5090	123	16	{	{	PUNCT
ejpam-5090	123	17	ρtm(ϑ1	ρtm(ϑ1	PROPN
ejpam-5090	123	18	·	·	SYM
ejpam-5090	123	19	ϑ2	ϑ2	PROPN
ejpam-5090	123	20	)	)	PUNCT
ejpam-5090	123	21	,	,	PUNCT
ejpam-5090	123	22	ρ	ρ	PROPN
ejpam-5090	123	23	t	t	PROPN
ejpam-5090	123	24	n(η1	n(η1	X
ejpam-5090	123	25	·	·	PUNCT
ejpam-5090	123	26	η2	η2	X
ejpam-5090	123	27	)	)	PUNCT
ejpam-5090	123	28	}	}	PUNCT
ejpam-5090	123	29	≤	≤	NUM
ejpam-5090	123	30	min	min	NOUN
ejpam-5090	123	31	{	{	PUNCT
ejpam-5090	123	32	min	min	PROPN
ejpam-5090	123	33	{	{	PUNCT
ejpam-5090	123	34	ρtm(ϑ1	ρtm(ϑ1	PROPN
ejpam-5090	123	35	)	)	PUNCT
ejpam-5090	123	36	,	,	PUNCT
ejpam-5090	123	37	ρ	ρ	PROPN
ejpam-5090	123	38	t	t	PROPN
ejpam-5090	123	39	m(ϑ2	m(ϑ2	NOUN
ejpam-5090	123	40	)	)	PUNCT
ejpam-5090	123	41	}	}	PUNCT
ejpam-5090	123	42	,	,	PUNCT
ejpam-5090	123	43	min	min	PROPN
ejpam-5090	123	44	{	{	PUNCT
ejpam-5090	123	45	ρtn(η1	ρtn(η1	ADV
ejpam-5090	123	46	)	)	PUNCT
ejpam-5090	123	47	,	,	PUNCT
ejpam-5090	123	48	ρ	ρ	PROPN
ejpam-5090	123	49	t	t	PROPN
ejpam-5090	123	50	m(η2	m(η2	PROPN
ejpam-5090	123	51	)	)	PUNCT
ejpam-5090	123	52	}	}	PUNCT
ejpam-5090	123	53	}	}	PUNCT
ejpam-5090	123	54	=	=	SYM
ejpam-5090	123	55	min	min	PROPN
ejpam-5090	123	56	{	{	PUNCT
ejpam-5090	123	57	min	min	PROPN
ejpam-5090	123	58	{	{	PUNCT
ejpam-5090	123	59	ρtm(ϑ1	ρtm(ϑ1	PROPN
ejpam-5090	123	60	)	)	PUNCT
ejpam-5090	123	61	,	,	PUNCT
ejpam-5090	123	62	ρ	ρ	PROPN
ejpam-5090	123	63	t	t	PROPN
ejpam-5090	123	64	n(η1	n(η1	NOUN
ejpam-5090	123	65	)	)	PUNCT
ejpam-5090	123	66	}	}	PUNCT
ejpam-5090	123	67	,	,	PUNCT
ejpam-5090	123	68	min	min	NOUN
ejpam-5090	123	69	{	{	PUNCT
ejpam-5090	123	70	ρtm(ϑ2	ρtm(ϑ2	NOUN
ejpam-5090	123	71	)	)	PUNCT
ejpam-5090	123	72	,	,	PUNCT
ejpam-5090	123	73	ρ	ρ	PROPN
ejpam-5090	123	74	t	t	PROPN
ejpam-5090	123	75	n(η2	n(η2	NOUN
ejpam-5090	123	76	)	)	PUNCT
ejpam-5090	123	77	}	}	PUNCT
ejpam-5090	123	78	}	}	PUNCT
ejpam-5090	123	79	=	=	SYM
ejpam-5090	123	80	min	min	NOUN
ejpam-5090	123	81	{	{	PUNCT
ejpam-5090	123	82	ρt(m×n)(ϑ1	ρt(m×n)(ϑ1	ADJ
ejpam-5090	123	83	,	,	PUNCT
ejpam-5090	123	84	η1	η1	NOUN
ejpam-5090	123	85	)	)	PUNCT
ejpam-5090	123	86	,	,	PUNCT
ejpam-5090	123	87	ρ	ρ	PROPN
ejpam-5090	123	88	t	t	PROPN
ejpam-5090	123	89	(	(	PUNCT
ejpam-5090	123	90	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	123	91	,	,	PUNCT
ejpam-5090	123	92	η2	η2	PROPN
ejpam-5090	123	93	)	)	PUNCT
ejpam-5090	123	94	}	}	PUNCT
ejpam-5090	123	95	,	,	PUNCT
ejpam-5090	123	96	ρi(m×n)((ϑ1	ρi(m×n)((ϑ1	ADJ
ejpam-5090	123	97	,	,	PUNCT
ejpam-5090	123	98	η1	η1	NOUN
ejpam-5090	123	99	)	)	PUNCT
ejpam-5090	123	100	·	·	PUNCT
ejpam-5090	123	101	(	(	PUNCT
ejpam-5090	123	102	ϑ2	ϑ2	NOUN
ejpam-5090	123	103	,	,	PUNCT
ejpam-5090	123	104	η2	η2	NOUN
ejpam-5090	123	105	)	)	PUNCT
ejpam-5090	123	106	)	)	PUNCT
ejpam-5090	124	1	=	=	PRON
ejpam-5090	124	2	{	{	PUNCT
ejpam-5090	124	3	ρim×n(ϑ1	ρim×n(ϑ1	NUM
ejpam-5090	124	4	·	·	PUNCT
ejpam-5090	124	5	ϑ2	ϑ2	NOUN
ejpam-5090	124	6	)	)	PUNCT
ejpam-5090	124	7	,	,	PUNCT
ejpam-5090	124	8	(	(	PUNCT
ejpam-5090	124	9	η1	η1	NOUN
ejpam-5090	124	10	·	·	SYM
ejpam-5090	124	11	η2	η2	X
ejpam-5090	124	12	)	)	PUNCT
ejpam-5090	124	13	}	}	PUNCT
ejpam-5090	124	14	=	=	SYM
ejpam-5090	124	15	max	max	PROPN
ejpam-5090	124	16	{	{	PUNCT
ejpam-5090	124	17	ρim(ϑ1	ρim(ϑ1	PROPN
ejpam-5090	124	18	·	·	PUNCT
ejpam-5090	124	19	ϑ2	ϑ2	PROPN
ejpam-5090	124	20	)	)	PUNCT
ejpam-5090	124	21	,	,	PUNCT
ejpam-5090	124	22	ρ	ρ	PROPN
ejpam-5090	124	23	i	i	PROPN
ejpam-5090	124	24	n(η1	n(η1	AUX
ejpam-5090	124	25	·	·	PUNCT
ejpam-5090	124	26	η2	η2	X
ejpam-5090	124	27	)	)	PUNCT
ejpam-5090	124	28	}	}	PUNCT
ejpam-5090	124	29	≥	≥	PROPN
ejpam-5090	124	30	max	max	PROPN
ejpam-5090	124	31	{	{	PUNCT
ejpam-5090	124	32	max	max	PROPN
ejpam-5090	124	33	{	{	PUNCT
ejpam-5090	124	34	ρim(ϑ1	ρim(ϑ1	NOUN
ejpam-5090	124	35	)	)	PUNCT
ejpam-5090	124	36	,	,	PUNCT
ejpam-5090	124	37	ρ	ρ	PROPN
ejpam-5090	124	38	i	i	PRON
ejpam-5090	124	39	m(ϑ2	m(ϑ2	ADV
ejpam-5090	124	40	)	)	PUNCT
ejpam-5090	124	41	}	}	PUNCT
ejpam-5090	124	42	,	,	PUNCT
ejpam-5090	124	43	max	max	PROPN
ejpam-5090	124	44	{	{	PUNCT
ejpam-5090	124	45	ρin(η1	ρin(η1	PROPN
ejpam-5090	124	46	)	)	PUNCT
ejpam-5090	124	47	,	,	PUNCT
ejpam-5090	124	48	ρ	ρ	PROPN
ejpam-5090	124	49	i	i	PROPN
ejpam-5090	124	50	m(η2	m(η2	PROPN
ejpam-5090	124	51	)	)	PUNCT
ejpam-5090	124	52	}	}	PUNCT
ejpam-5090	124	53	}	}	PUNCT
ejpam-5090	124	54	=	=	SYM
ejpam-5090	124	55	max	max	PROPN
ejpam-5090	124	56	{	{	PUNCT
ejpam-5090	124	57	max	max	PROPN
ejpam-5090	124	58	{	{	PUNCT
ejpam-5090	124	59	ρim(ϑ1	ρim(ϑ1	NOUN
ejpam-5090	124	60	)	)	PUNCT
ejpam-5090	124	61	,	,	PUNCT
ejpam-5090	124	62	ρ	ρ	PROPN
ejpam-5090	124	63	i	i	NOUN
ejpam-5090	124	64	n(η1	n(η1	ADV
ejpam-5090	124	65	)	)	PUNCT
ejpam-5090	124	66	}	}	PUNCT
ejpam-5090	124	67	,	,	PUNCT
ejpam-5090	124	68	max	max	PROPN
ejpam-5090	124	69	{	{	PUNCT
ejpam-5090	124	70	ρim(ϑ2	ρim(ϑ2	PROPN
ejpam-5090	124	71	)	)	PUNCT
ejpam-5090	124	72	,	,	PUNCT
ejpam-5090	124	73	ρ	ρ	PROPN
ejpam-5090	124	74	i	i	PROPN
ejpam-5090	124	75	n(η2	n(η2	NOUN
ejpam-5090	124	76	)	)	PUNCT
ejpam-5090	124	77	}	}	PUNCT
ejpam-5090	124	78	}	}	PUNCT
ejpam-5090	124	79	=	=	SYM
ejpam-5090	124	80	max	max	PROPN
ejpam-5090	124	81	{	{	PUNCT
ejpam-5090	124	82	ρi(m×n)(ϑ1	ρi(m×n)(ϑ1	PROPN
ejpam-5090	124	83	,	,	PUNCT
ejpam-5090	124	84	η1	η1	NOUN
ejpam-5090	124	85	)	)	PUNCT
ejpam-5090	124	86	,	,	PUNCT
ejpam-5090	124	87	ρ	ρ	PROPN
ejpam-5090	124	88	i	i	PROPN
ejpam-5090	124	89	(	(	PUNCT
ejpam-5090	124	90	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	124	91	,	,	PUNCT
ejpam-5090	124	92	η2	η2	PROPN
ejpam-5090	124	93	)	)	PUNCT
ejpam-5090	124	94	}	}	PUNCT
ejpam-5090	124	95	,	,	PUNCT
ejpam-5090	124	96	and	and	CCONJ
ejpam-5090	124	97	ρf(m×n)((ϑ1η1	ρf(m×n)((ϑ1η1	X
ejpam-5090	124	98	)	)	PUNCT
ejpam-5090	124	99	·	·	PUNCT
ejpam-5090	124	100	(	(	PUNCT
ejpam-5090	124	101	ϑ2	ϑ2	NOUN
ejpam-5090	124	102	,	,	PUNCT
ejpam-5090	124	103	η2	η2	NOUN
ejpam-5090	124	104	)	)	PUNCT
ejpam-5090	124	105	)	)	PUNCT
ejpam-5090	125	1	=	=	PRON
ejpam-5090	125	2	{	{	PUNCT
ejpam-5090	125	3	ρfm×n(ϑ1	ρfm×n(ϑ1	NOUN
ejpam-5090	125	4	·	·	PUNCT
ejpam-5090	125	5	ϑ2	ϑ2	NOUN
ejpam-5090	125	6	)	)	PUNCT
ejpam-5090	125	7	,	,	PUNCT
ejpam-5090	125	8	(	(	PUNCT
ejpam-5090	125	9	η1	η1	NOUN
ejpam-5090	125	10	·	·	SYM
ejpam-5090	125	11	η2	η2	X
ejpam-5090	125	12	)	)	PUNCT
ejpam-5090	125	13	}	}	PUNCT
ejpam-5090	125	14	=	=	SYM
ejpam-5090	125	15	max	max	X
ejpam-5090	125	16	{	{	PUNCT
ejpam-5090	125	17	ρfm(ϑ1	ρfm(ϑ1	PROPN
ejpam-5090	125	18	·	·	PUNCT
ejpam-5090	125	19	ϑ2	ϑ2	PROPN
ejpam-5090	125	20	)	)	PUNCT
ejpam-5090	125	21	,	,	PUNCT
ejpam-5090	125	22	ρ	ρ	PROPN
ejpam-5090	125	23	f	f	PROPN
ejpam-5090	125	24	n(η1	n(η1	X
ejpam-5090	125	25	·	·	PUNCT
ejpam-5090	125	26	η2	η2	X
ejpam-5090	125	27	)	)	PUNCT
ejpam-5090	125	28	}	}	PUNCT
ejpam-5090	125	29	≥	≥	PROPN
ejpam-5090	125	30	max	max	PROPN
ejpam-5090	125	31	{	{	PUNCT
ejpam-5090	125	32	max	max	PROPN
ejpam-5090	125	33	{	{	PUNCT
ejpam-5090	125	34	ρfm(ϑ1	ρfm(ϑ1	PROPN
ejpam-5090	125	35	)	)	PUNCT
ejpam-5090	125	36	,	,	PUNCT
ejpam-5090	125	37	ρ	ρ	PROPN
ejpam-5090	125	38	f	f	X
ejpam-5090	125	39	m(ϑ2	m(ϑ2	ADV
ejpam-5090	125	40	)	)	PUNCT
ejpam-5090	125	41	}	}	PUNCT
ejpam-5090	125	42	,	,	PUNCT
ejpam-5090	125	43	max	max	PROPN
ejpam-5090	125	44	{	{	PUNCT
ejpam-5090	125	45	ρfn(η1	ρfn(η1	PROPN
ejpam-5090	125	46	)	)	PUNCT
ejpam-5090	125	47	,	,	PUNCT
ejpam-5090	125	48	ρ	ρ	PROPN
ejpam-5090	125	49	f	f	PROPN
ejpam-5090	125	50	m(η2	m(η2	PROPN
ejpam-5090	125	51	)	)	PUNCT
ejpam-5090	125	52	}	}	PUNCT
ejpam-5090	125	53	}	}	PUNCT
ejpam-5090	125	54	=	=	SYM
ejpam-5090	125	55	max	max	PROPN
ejpam-5090	125	56	{	{	PUNCT
ejpam-5090	125	57	max	max	PROPN
ejpam-5090	125	58	{	{	PUNCT
ejpam-5090	125	59	ρfm(ϑ1	ρfm(ϑ1	PROPN
ejpam-5090	125	60	)	)	PUNCT
ejpam-5090	125	61	,	,	PUNCT
ejpam-5090	125	62	ρ	ρ	PROPN
ejpam-5090	125	63	f	f	PROPN
ejpam-5090	125	64	n(η1	n(η1	PROPN
ejpam-5090	125	65	)	)	PUNCT
ejpam-5090	125	66	}	}	PUNCT
ejpam-5090	125	67	,	,	PUNCT
ejpam-5090	125	68	max	max	PROPN
ejpam-5090	125	69	{	{	PUNCT
ejpam-5090	125	70	ρfm(ϑ2	ρfm(ϑ2	PROPN
ejpam-5090	125	71	)	)	PUNCT
ejpam-5090	125	72	,	,	PUNCT
ejpam-5090	125	73	ρ	ρ	PROPN
ejpam-5090	125	74	f	f	PROPN
ejpam-5090	125	75	n(η2	n(η2	PROPN
ejpam-5090	125	76	)	)	PUNCT
ejpam-5090	125	77	}	}	PUNCT
ejpam-5090	125	78	}	}	PUNCT
ejpam-5090	125	79	m.	m.	NOUN
ejpam-5090	125	80	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	125	81	et	et	PROPN
ejpam-5090	125	82	al	al	PROPN
ejpam-5090	125	83	.	.	PUNCT
ejpam-5090	125	84	/	/	SYM
ejpam-5090	125	85	eur	eur	PROPN
ejpam-5090	125	86	.	.	PUNCT
ejpam-5090	126	1	j.	j.	PROPN
ejpam-5090	126	2	pure	pure	PROPN
ejpam-5090	126	3	appl	appl	PROPN
ejpam-5090	126	4	.	.	PROPN
ejpam-5090	126	5	math	math	PROPN
ejpam-5090	126	6	,	,	PUNCT
ejpam-5090	126	7	17	17	NUM
ejpam-5090	126	8	(	(	PUNCT
ejpam-5090	126	9	2	2	NUM
ejpam-5090	126	10	)	)	PUNCT
ejpam-5090	126	11	(	(	PUNCT
ejpam-5090	126	12	2024	2024	NUM
ejpam-5090	126	13	)	)	PUNCT
ejpam-5090	126	14	,	,	PUNCT
ejpam-5090	126	15	1113	1113	NUM
ejpam-5090	126	16	-	-	SYM
ejpam-5090	126	17	1128	1128	NUM
ejpam-5090	126	18	1120	1120	NUM
ejpam-5090	126	19	=	=	SYM
ejpam-5090	126	20	max	max	PROPN
ejpam-5090	126	21	{	{	PUNCT
ejpam-5090	126	22	ρf(m×n)(ϑ1	ρf(m×n)(ϑ1	NOUN
ejpam-5090	126	23	,	,	PUNCT
ejpam-5090	126	24	η1	η1	NOUN
ejpam-5090	126	25	)	)	PUNCT
ejpam-5090	126	26	,	,	PUNCT
ejpam-5090	126	27	ρ	ρ	PROPN
ejpam-5090	126	28	f	f	PROPN
ejpam-5090	126	29	(	(	PUNCT
ejpam-5090	126	30	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	126	31	,	,	PUNCT
ejpam-5090	126	32	η2	η2	PROPN
ejpam-5090	126	33	)	)	PUNCT
ejpam-5090	126	34	}	}	PUNCT
ejpam-5090	126	35	.	.	PUNCT
ejpam-5090	127	1	hence	hence	ADV
ejpam-5090	127	2	,	,	PUNCT
ejpam-5090	127	3	m×n	m×n	PROPN
ejpam-5090	127	4	=	=	SYM
ejpam-5090	127	5	〈	〈	PROPN
ejpam-5090	127	6	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	127	7	)	)	PUNCT
ejpam-5090	127	8	,	,	PUNCT
ejpam-5090	127	9	ρ	ρ	PROPN
ejpam-5090	127	10	i	i	PROPN
ejpam-5090	127	11	(	(	PUNCT
ejpam-5090	127	12	m×n	m×n	PROPN
ejpam-5090	127	13	)	)	PUNCT
ejpam-5090	127	14	,	,	PUNCT
ejpam-5090	127	15	ρ	ρ	PROPN
ejpam-5090	127	16	f	f	X
ejpam-5090	127	17	(	(	PUNCT
ejpam-5090	127	18	m×n	m×n	NOUN
ejpam-5090	127	19	)	)	PUNCT
ejpam-5090	127	20	〉	〉	NOUN
ejpam-5090	127	21	is	be	AUX
ejpam-5090	127	22	a	a	DET
ejpam-5090	127	23	fnink	fnink	NOUN
ejpam-5090	127	24	-	-	PUNCT
ejpam-5090	127	25	s	s	NOUN
ejpam-5090	127	26	of	of	ADP
ejpam-5090	127	27	χ1	χ1	PROPN
ejpam-5090	127	28	×	×	PROPN
ejpam-5090	127	29	χ2	χ2	PROPN
ejpam-5090	127	30	.	.	PUNCT
ejpam-5090	128	1	theorem	theorem	NOUN
ejpam-5090	128	2	2	2	NUM
ejpam-5090	128	3	.	.	PUNCT
ejpam-5090	129	1	let	let	VERB
ejpam-5090	129	2	m	m	PROPN
ejpam-5090	129	3	=	=	VERB
ejpam-5090	129	4	〈	〈	PROPN
ejpam-5090	129	5	ρtm	ρtm	NOUN
ejpam-5090	129	6	,	,	PUNCT
ejpam-5090	129	7	ρim	ρim	NOUN
ejpam-5090	129	8	,	,	PUNCT
ejpam-5090	129	9	ρfm	ρfm	ADP
ejpam-5090	129	10	〉	〉	NOUN
ejpam-5090	129	11	and	and	CCONJ
ejpam-5090	129	12	n	n	NOUN
ejpam-5090	129	13	=	=	PUNCT
ejpam-5090	129	14	〈	〈	PROPN
ejpam-5090	129	15	ρtn	ρtn	NOUN
ejpam-5090	129	16	,	,	PUNCT
ejpam-5090	129	17	ρ	ρ	PROPN
ejpam-5090	129	18	i	i	PROPN
ejpam-5090	129	19	n	n	CCONJ
ejpam-5090	129	20	,	,	PUNCT
ejpam-5090	129	21	ρ	ρ	PROPN
ejpam-5090	129	22	f	f	PROPN
ejpam-5090	129	23	n	n	PRON
ejpam-5090	129	24	〉	〉	NOUN
ejpam-5090	129	25	be	be	VERB
ejpam-5090	129	26	two	two	NUM
ejpam-5090	129	27	fnink	fnink	NOUN
ejpam-5090	129	28	-	-	PUNCT
ejpam-5090	129	29	is	is	NOUN
ejpam-5090	129	30	of	of	ADP
ejpam-5090	129	31	χ1	χ1	NOUN
ejpam-5090	129	32	and	and	CCONJ
ejpam-5090	129	33	χ2	χ2	PROPN
ejpam-5090	129	34	,	,	PUNCT
ejpam-5090	129	35	respectively	respectively	ADV
ejpam-5090	129	36	.	.	PUNCT
ejpam-5090	130	1	then	then	ADV
ejpam-5090	130	2	,	,	PUNCT
ejpam-5090	130	3	the	the	DET
ejpam-5090	130	4	direct	direct	ADJ
ejpam-5090	130	5	product	product	NOUN
ejpam-5090	130	6	m×n	m×n	PROPN
ejpam-5090	130	7	,	,	PUNCT
ejpam-5090	130	8	defined	define	VERB
ejpam-5090	130	9	by	by	ADP
ejpam-5090	130	10	m×n	m×n	PROPN
ejpam-5090	130	11	=	=	SYM
ejpam-5090	130	12	〈	〈	PROPN
ejpam-5090	130	13	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	130	14	)	)	PUNCT
ejpam-5090	130	15	,	,	PUNCT
ejpam-5090	130	16	ρ	ρ	PROPN
ejpam-5090	130	17	i	i	PROPN
ejpam-5090	130	18	(	(	PUNCT
ejpam-5090	130	19	m×n	m×n	PROPN
ejpam-5090	130	20	)	)	PUNCT
ejpam-5090	130	21	,	,	PUNCT
ejpam-5090	130	22	ρ	ρ	PROPN
ejpam-5090	130	23	f	f	X
ejpam-5090	130	24	(	(	PUNCT
ejpam-5090	130	25	m×n	m×n	NOUN
ejpam-5090	130	26	)	)	PUNCT
ejpam-5090	130	27	〉	〉	NOUN
ejpam-5090	130	28	,	,	PUNCT
ejpam-5090	130	29	is	be	AUX
ejpam-5090	130	30	a	a	DET
ejpam-5090	130	31	fnink	fnink	NOUN
ejpam-5090	130	32	-	-	PUNCT
ejpam-5090	130	33	i	i	PRON
ejpam-5090	130	34	of	of	ADP
ejpam-5090	130	35	χ1	χ1	PROPN
ejpam-5090	130	36	×	×	PROPN
ejpam-5090	130	37	χ2	χ2	PROPN
ejpam-5090	130	38	.	.	PUNCT
ejpam-5090	131	1	proof	proof	NOUN
ejpam-5090	131	2	.	.	PUNCT
ejpam-5090	132	1	for	for	ADP
ejpam-5090	132	2	any	any	DET
ejpam-5090	132	3	(	(	PUNCT
ejpam-5090	132	4	ϑ	ϑ	X
ejpam-5090	132	5	,	,	PUNCT
ejpam-5090	132	6	η	η	NOUN
ejpam-5090	132	7	)	)	PUNCT
ejpam-5090	132	8	∈	∈	PROPN
ejpam-5090	132	9	χ1	χ1	NOUN
ejpam-5090	132	10	×	×	NOUN
ejpam-5090	132	11	χ2	χ2	PROPN
ejpam-5090	132	12	.	.	PUNCT
ejpam-5090	133	1	we	we	PRON
ejpam-5090	133	2	have	have	VERB
ejpam-5090	133	3	ρt(m×n)(0	ρt(m×n)(0	PROPN
ejpam-5090	133	4	,	,	PUNCT
ejpam-5090	133	5	0	0	NUM
ejpam-5090	133	6	)	)	PUNCT
ejpam-5090	133	7	=	=	SYM
ejpam-5090	133	8	min	min	NOUN
ejpam-5090	133	9	{	{	PUNCT
ejpam-5090	133	10	ρtm(0	ρtm(0	NOUN
ejpam-5090	133	11	)	)	PUNCT
ejpam-5090	133	12	,	,	PUNCT
ejpam-5090	133	13	ρtn(0	ρtn(0	NOUN
ejpam-5090	133	14	)	)	PUNCT
ejpam-5090	133	15	}	}	PUNCT
ejpam-5090	133	16	≤	≤	NUM
ejpam-5090	133	17	min	min	NOUN
ejpam-5090	133	18	{	{	PUNCT
ejpam-5090	133	19	ρtm(ϑ	ρtm(ϑ	NOUN
ejpam-5090	133	20	)	)	PUNCT
ejpam-5090	133	21	,	,	PUNCT
ejpam-5090	133	22	ρtn(η	ρtn(η	PROPN
ejpam-5090	133	23	)	)	PUNCT
ejpam-5090	133	24	}	}	PUNCT
ejpam-5090	133	25	=	=	PUNCT
ejpam-5090	134	1	ρi(m×n)(ϑ	ρi(m×n)(ϑ	PROPN
ejpam-5090	134	2	,	,	PUNCT
ejpam-5090	134	3	η	η	NOUN
ejpam-5090	134	4	)	)	PUNCT
ejpam-5090	134	5	,	,	PUNCT
ejpam-5090	134	6	ρim×n(0	ρim×n(0	PROPN
ejpam-5090	134	7	,	,	PUNCT
ejpam-5090	134	8	0	0	NUM
ejpam-5090	134	9	)	)	PUNCT
ejpam-5090	134	10	=	=	SYM
ejpam-5090	134	11	max	max	PROPN
ejpam-5090	134	12	{	{	PUNCT
ejpam-5090	134	13	ρim(0	ρim(0	NOUN
ejpam-5090	134	14	)	)	PUNCT
ejpam-5090	134	15	,	,	PUNCT
ejpam-5090	134	16	ρin(0	ρin(0	PROPN
ejpam-5090	134	17	)	)	PUNCT
ejpam-5090	134	18	}	}	PUNCT
ejpam-5090	134	19	≥	≥	PROPN
ejpam-5090	134	20	max	max	PROPN
ejpam-5090	134	21	{	{	PUNCT
ejpam-5090	134	22	ρim(ϑ	ρim(ϑ	PROPN
ejpam-5090	134	23	)	)	PUNCT
ejpam-5090	134	24	,	,	PUNCT
ejpam-5090	134	25	ρin(η	ρin(η	ADV
ejpam-5090	134	26	)	)	PUNCT
ejpam-5090	134	27	}	}	PUNCT
ejpam-5090	134	28	=	=	SYM
ejpam-5090	134	29	ρim×n(ϑ	ρim×n(ϑ	PROPN
ejpam-5090	134	30	,	,	PUNCT
ejpam-5090	134	31	η	η	NOUN
ejpam-5090	134	32	)	)	PUNCT
ejpam-5090	134	33	and	and	CCONJ
ejpam-5090	134	34	ρfm×n(0	ρfm×n(0	NUM
ejpam-5090	134	35	,	,	PUNCT
ejpam-5090	134	36	0	0	NUM
ejpam-5090	134	37	)	)	PUNCT
ejpam-5090	134	38	=	=	SYM
ejpam-5090	134	39	max	max	PROPN
ejpam-5090	134	40	{	{	PUNCT
ejpam-5090	134	41	ρfm(0	ρfm(0	NOUN
ejpam-5090	134	42	)	)	PUNCT
ejpam-5090	134	43	,	,	PUNCT
ejpam-5090	134	44	ρfn(0	ρfn(0	NOUN
ejpam-5090	134	45	)	)	PUNCT
ejpam-5090	134	46	}	}	PUNCT
ejpam-5090	134	47	≥	≥	PROPN
ejpam-5090	134	48	max	max	PROPN
ejpam-5090	134	49	{	{	PUNCT
ejpam-5090	134	50	ρfm(ϑ	ρfm(ϑ	PROPN
ejpam-5090	134	51	)	)	PUNCT
ejpam-5090	134	52	,	,	PUNCT
ejpam-5090	134	53	ρfn(η	ρfn(η	NUM
ejpam-5090	134	54	)	)	PUNCT
ejpam-5090	134	55	}	}	PUNCT
ejpam-5090	134	56	=	=	SYM
ejpam-5090	134	57	ρfm×n(ϑ	ρfm×n(ϑ	PROPN
ejpam-5090	134	58	,	,	PUNCT
ejpam-5090	134	59	η	η	NOUN
ejpam-5090	134	60	)	)	PUNCT
ejpam-5090	134	61	.	.	PUNCT
ejpam-5090	135	1	also	also	ADV
ejpam-5090	135	2	,	,	PUNCT
ejpam-5090	135	3	for	for	ADP
ejpam-5090	135	4	any	any	DET
ejpam-5090	135	5	(	(	PUNCT
ejpam-5090	135	6	ϑ1	ϑ1	NOUN
ejpam-5090	135	7	,	,	PUNCT
ejpam-5090	135	8	η1	η1	NOUN
ejpam-5090	135	9	)	)	PUNCT
ejpam-5090	135	10	,	,	PUNCT
ejpam-5090	135	11	(	(	PUNCT
ejpam-5090	135	12	ϑ2	ϑ2	NOUN
ejpam-5090	135	13	,	,	PUNCT
ejpam-5090	135	14	η2	η2	NOUN
ejpam-5090	135	15	)	)	PUNCT
ejpam-5090	135	16	,	,	PUNCT
ejpam-5090	135	17	(	(	PUNCT
ejpam-5090	135	18	ϑ3	ϑ3	PROPN
ejpam-5090	135	19	,	,	PUNCT
ejpam-5090	135	20	η3	η3	PROPN
ejpam-5090	135	21	)	)	PUNCT
ejpam-5090	135	22	∈	∈	PROPN
ejpam-5090	135	23	χ1	χ1	NOUN
ejpam-5090	135	24	×	×	NOUN
ejpam-5090	135	25	χ2	χ2	PROPN
ejpam-5090	135	26	.	.	PUNCT
ejpam-5090	136	1	we	we	PRON
ejpam-5090	136	2	have	have	VERB
ejpam-5090	136	3	ρtm×n(ϑ1	ρtm×n(ϑ1	NUM
ejpam-5090	136	4	,	,	PUNCT
ejpam-5090	136	5	η1	η1	NOUN
ejpam-5090	136	6	)	)	PUNCT
ejpam-5090	136	7	=	=	SYM
ejpam-5090	136	8	min	min	NOUN
ejpam-5090	136	9	{	{	PUNCT
ejpam-5090	136	10	ρtm(ϑ1	ρtm(ϑ1	PROPN
ejpam-5090	136	11	)	)	PUNCT
ejpam-5090	136	12	,	,	PUNCT
ejpam-5090	136	13	ρ	ρ	PROPN
ejpam-5090	136	14	t	t	PROPN
ejpam-5090	136	15	n(η1	n(η1	NOUN
ejpam-5090	136	16	)	)	PUNCT
ejpam-5090	136	17	}	}	PUNCT
ejpam-5090	136	18	≤	≤	NUM
ejpam-5090	136	19	min	min	NOUN
ejpam-5090	136	20	{	{	PUNCT
ejpam-5090	136	21	min	min	NOUN
ejpam-5090	136	22	{	{	PUNCT
ejpam-5090	136	23	ρtm((ϑ3	ρtm((ϑ3	NOUN
ejpam-5090	136	24	·	·	PUNCT
ejpam-5090	136	25	ϑ1	ϑ1	NOUN
ejpam-5090	136	26	)	)	PUNCT
ejpam-5090	136	27	·	·	PUNCT
ejpam-5090	137	1	(	(	PUNCT
ejpam-5090	137	2	ϑ3	ϑ3	NOUN
ejpam-5090	137	3	·	·	SYM
ejpam-5090	137	4	ϑ2	ϑ2	PROPN
ejpam-5090	137	5	)	)	PUNCT
ejpam-5090	137	6	)	)	PUNCT
ejpam-5090	137	7	,	,	PUNCT
ejpam-5090	137	8	ρ	ρ	PROPN
ejpam-5090	137	9	t	t	PROPN
ejpam-5090	137	10	m(ϑ2	m(ϑ2	NOUN
ejpam-5090	137	11	)	)	PUNCT
ejpam-5090	137	12	}	}	PUNCT
ejpam-5090	137	13	,	,	PUNCT
ejpam-5090	137	14	min	min	NOUN
ejpam-5090	137	15	{	{	PUNCT
ejpam-5090	137	16	ρtn((η3	ρtn((η3	PROPN
ejpam-5090	137	17	·	·	PUNCT
ejpam-5090	137	18	η1	η1	NOUN
ejpam-5090	137	19	)	)	PUNCT
ejpam-5090	137	20	·	·	PUNCT
ejpam-5090	137	21	(	(	PUNCT
ejpam-5090	137	22	η3	η3	NOUN
ejpam-5090	137	23	·	·	PUNCT
ejpam-5090	137	24	η2	η2	PROPN
ejpam-5090	137	25	)	)	PUNCT
ejpam-5090	137	26	)	)	PUNCT
ejpam-5090	137	27	,	,	PUNCT
ejpam-5090	137	28	ρtn(η2	ρtn(η2	PROPN
ejpam-5090	137	29	)	)	PUNCT
ejpam-5090	137	30	}	}	PUNCT
ejpam-5090	137	31	}	}	PUNCT
ejpam-5090	137	32	=	=	SYM
ejpam-5090	137	33	min	min	PROPN
ejpam-5090	137	34	{	{	PUNCT
ejpam-5090	137	35	min	min	NOUN
ejpam-5090	137	36	{	{	PUNCT
ejpam-5090	137	37	ρtm((ϑ3	ρtm((ϑ3	NOUN
ejpam-5090	137	38	·	·	PUNCT
ejpam-5090	137	39	ϑ1	ϑ1	NOUN
ejpam-5090	137	40	)	)	PUNCT
ejpam-5090	137	41	·	·	PUNCT
ejpam-5090	137	42	(	(	PUNCT
ejpam-5090	137	43	ϑ3	ϑ3	NOUN
ejpam-5090	137	44	·	·	SYM
ejpam-5090	137	45	ϑ2	ϑ2	PROPN
ejpam-5090	137	46	)	)	PUNCT
ejpam-5090	137	47	)	)	PUNCT
ejpam-5090	137	48	,	,	PUNCT
ejpam-5090	137	49	ρ	ρ	PROPN
ejpam-5090	137	50	t	t	PROPN
ejpam-5090	137	51	n((η3	n((η3	NOUN
ejpam-5090	137	52	·	·	PUNCT
ejpam-5090	137	53	η1	η1	NOUN
ejpam-5090	137	54	)	)	PUNCT
ejpam-5090	137	55	·	·	PUNCT
ejpam-5090	137	56	(	(	PUNCT
ejpam-5090	137	57	η3	η3	NOUN
ejpam-5090	137	58	·	·	PUNCT
ejpam-5090	137	59	η2	η2	NUM
ejpam-5090	137	60	)	)	PUNCT
ejpam-5090	137	61	)	)	PUNCT
ejpam-5090	137	62	}	}	PUNCT
ejpam-5090	137	63	,	,	PUNCT
ejpam-5090	137	64	min	min	NOUN
ejpam-5090	137	65	{	{	PUNCT
ejpam-5090	137	66	ρtm(ϑ2	ρtm(ϑ2	NOUN
ejpam-5090	137	67	)	)	PUNCT
ejpam-5090	137	68	,	,	PUNCT
ejpam-5090	137	69	ρ	ρ	PROPN
ejpam-5090	137	70	t	t	PROPN
ejpam-5090	137	71	n(η2	n(η2	NOUN
ejpam-5090	137	72	)	)	PUNCT
ejpam-5090	137	73	}	}	PUNCT
ejpam-5090	137	74	}	}	PUNCT
ejpam-5090	137	75	=	=	SYM
ejpam-5090	137	76	min	min	NOUN
ejpam-5090	137	77	{	{	PUNCT
ejpam-5090	137	78	ρtm×n(((ϑ3	ρtm×n(((ϑ3	PROPN
ejpam-5090	137	79	,	,	PUNCT
ejpam-5090	137	80	η3	η3	NOUN
ejpam-5090	137	81	)	)	PUNCT
ejpam-5090	137	82	·	·	PUNCT
ejpam-5090	138	1	(	(	PUNCT
ejpam-5090	138	2	ϑ1	ϑ1	NOUN
ejpam-5090	138	3	,	,	PUNCT
ejpam-5090	138	4	η1	η1	NOUN
ejpam-5090	138	5	)	)	PUNCT
ejpam-5090	138	6	)	)	PUNCT
ejpam-5090	138	7	,	,	PUNCT
ejpam-5090	138	8	(	(	PUNCT
ejpam-5090	138	9	(	(	PUNCT
ejpam-5090	138	10	ϑ3	ϑ3	PROPN
ejpam-5090	138	11	,	,	PUNCT
ejpam-5090	138	12	η3	η3	PROPN
ejpam-5090	138	13	)	)	PUNCT
ejpam-5090	138	14	·	·	PUNCT
ejpam-5090	138	15	(	(	PUNCT
ejpam-5090	138	16	ϑ2	ϑ2	NOUN
ejpam-5090	138	17	,	,	PUNCT
ejpam-5090	138	18	η2	η2	NOUN
ejpam-5090	138	19	)	)	PUNCT
ejpam-5090	138	20	)	)	PUNCT
ejpam-5090	138	21	)	)	PUNCT
ejpam-5090	138	22	,	,	PUNCT
ejpam-5090	138	23	ρ	ρ	PROPN
ejpam-5090	138	24	t	t	PROPN
ejpam-5090	138	25	m×n(ϑ2	m×n(ϑ2	NOUN
ejpam-5090	138	26	,	,	PUNCT
ejpam-5090	138	27	η2	η2	PROPN
ejpam-5090	138	28	)	)	PUNCT
ejpam-5090	138	29	}	}	PUNCT
ejpam-5090	138	30	,	,	PUNCT
ejpam-5090	138	31	ρim×n(ϑ1	ρim×n(ϑ1	NOUN
ejpam-5090	138	32	,	,	PUNCT
ejpam-5090	138	33	η1	η1	NOUN
ejpam-5090	138	34	)	)	PUNCT
ejpam-5090	138	35	=	=	SYM
ejpam-5090	138	36	max	max	PROPN
ejpam-5090	138	37	{	{	PUNCT
ejpam-5090	138	38	ρim(ϑ1	ρim(ϑ1	NOUN
ejpam-5090	138	39	)	)	PUNCT
ejpam-5090	138	40	,	,	PUNCT
ejpam-5090	138	41	ρ	ρ	PROPN
ejpam-5090	138	42	i	i	NOUN
ejpam-5090	138	43	n(η1	n(η1	ADV
ejpam-5090	138	44	)	)	PUNCT
ejpam-5090	138	45	}	}	PUNCT
ejpam-5090	138	46	m.	m.	NOUN
ejpam-5090	138	47	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	138	48	et	et	PROPN
ejpam-5090	138	49	al	al	PROPN
ejpam-5090	138	50	.	.	PUNCT
ejpam-5090	138	51	/	/	SYM
ejpam-5090	138	52	eur	eur	PROPN
ejpam-5090	138	53	.	.	PUNCT
ejpam-5090	139	1	j.	j.	PROPN
ejpam-5090	139	2	pure	pure	PROPN
ejpam-5090	139	3	appl	appl	PROPN
ejpam-5090	139	4	.	.	PROPN
ejpam-5090	139	5	math	math	PROPN
ejpam-5090	139	6	,	,	PUNCT
ejpam-5090	139	7	17	17	NUM
ejpam-5090	139	8	(	(	PUNCT
ejpam-5090	139	9	2	2	NUM
ejpam-5090	139	10	)	)	PUNCT
ejpam-5090	139	11	(	(	PUNCT
ejpam-5090	139	12	2024	2024	NUM
ejpam-5090	139	13	)	)	PUNCT
ejpam-5090	139	14	,	,	PUNCT
ejpam-5090	139	15	1113	1113	NUM
ejpam-5090	139	16	-	-	SYM
ejpam-5090	139	17	1128	1128	NUM
ejpam-5090	139	18	1121	1121	NUM
ejpam-5090	139	19	≥	≥	NOUN
ejpam-5090	139	20	max	max	PROPN
ejpam-5090	139	21	{	{	PUNCT
ejpam-5090	139	22	max	max	PROPN
ejpam-5090	139	23	{	{	PUNCT
ejpam-5090	139	24	ρim((ϑ3	ρim((ϑ3	PROPN
ejpam-5090	139	25	·	·	SYM
ejpam-5090	139	26	ϑ1	ϑ1	PROPN
ejpam-5090	139	27	)	)	PUNCT
ejpam-5090	139	28	·	·	PUNCT
ejpam-5090	140	1	(	(	PUNCT
ejpam-5090	140	2	ϑ3	ϑ3	NOUN
ejpam-5090	140	3	·	·	SYM
ejpam-5090	140	4	ϑ2	ϑ2	PROPN
ejpam-5090	140	5	)	)	PUNCT
ejpam-5090	140	6	)	)	PUNCT
ejpam-5090	140	7	,	,	PUNCT
ejpam-5090	141	1	ρ	ρ	PROPN
ejpam-5090	141	2	i	i	PRON
ejpam-5090	141	3	m(ϑ2	m(ϑ2	ADV
ejpam-5090	141	4	)	)	PUNCT
ejpam-5090	141	5	}	}	PUNCT
ejpam-5090	141	6	,	,	PUNCT
ejpam-5090	141	7	max	max	PROPN
ejpam-5090	141	8	{	{	PUNCT
ejpam-5090	141	9	ρin((η3	ρin((η3	PROPN
ejpam-5090	141	10	·	·	PUNCT
ejpam-5090	141	11	η1	η1	PROPN
ejpam-5090	141	12	)	)	PUNCT
ejpam-5090	141	13	·	·	PUNCT
ejpam-5090	141	14	(	(	PUNCT
ejpam-5090	141	15	η3	η3	NOUN
ejpam-5090	141	16	·	·	PUNCT
ejpam-5090	141	17	η2	η2	NUM
ejpam-5090	141	18	)	)	PUNCT
ejpam-5090	141	19	)	)	PUNCT
ejpam-5090	141	20	,	,	PUNCT
ejpam-5090	141	21	ρin(η2	ρin(η2	NOUN
ejpam-5090	141	22	)	)	PUNCT
ejpam-5090	141	23	}	}	PUNCT
ejpam-5090	141	24	}	}	PUNCT
ejpam-5090	141	25	=	=	SYM
ejpam-5090	141	26	max	max	PROPN
ejpam-5090	141	27	{	{	PUNCT
ejpam-5090	141	28	max	max	PROPN
ejpam-5090	141	29	{	{	PUNCT
ejpam-5090	141	30	ρim((ϑ3	ρim((ϑ3	PROPN
ejpam-5090	141	31	·	·	SYM
ejpam-5090	141	32	ϑ1	ϑ1	PROPN
ejpam-5090	141	33	)	)	PUNCT
ejpam-5090	141	34	·	·	PUNCT
ejpam-5090	142	1	(	(	PUNCT
ejpam-5090	142	2	ϑ3	ϑ3	NOUN
ejpam-5090	142	3	·	·	SYM
ejpam-5090	142	4	ϑ2	ϑ2	PROPN
ejpam-5090	142	5	)	)	PUNCT
ejpam-5090	142	6	)	)	PUNCT
ejpam-5090	142	7	,	,	PUNCT
ejpam-5090	143	1	ρ	ρ	PROPN
ejpam-5090	143	2	i	i	PRON
ejpam-5090	143	3	n((η3	n((η3	VERB
ejpam-5090	143	4	·	·	PUNCT
ejpam-5090	143	5	η1	η1	NOUN
ejpam-5090	143	6	)	)	PUNCT
ejpam-5090	143	7	·	·	PUNCT
ejpam-5090	143	8	(	(	PUNCT
ejpam-5090	143	9	η3	η3	NOUN
ejpam-5090	143	10	·	·	PUNCT
ejpam-5090	143	11	η2	η2	NUM
ejpam-5090	143	12	)	)	PUNCT
ejpam-5090	143	13	)	)	PUNCT
ejpam-5090	143	14	}	}	PUNCT
ejpam-5090	143	15	,	,	PUNCT
ejpam-5090	143	16	min	min	NOUN
ejpam-5090	143	17	{	{	PUNCT
ejpam-5090	143	18	ρim(ϑ2	ρim(ϑ2	PROPN
ejpam-5090	143	19	)	)	PUNCT
ejpam-5090	143	20	,	,	PUNCT
ejpam-5090	143	21	ρ	ρ	PROPN
ejpam-5090	143	22	i	i	PROPN
ejpam-5090	143	23	n(η2	n(η2	NOUN
ejpam-5090	143	24	)	)	PUNCT
ejpam-5090	143	25	}	}	PUNCT
ejpam-5090	143	26	}	}	PUNCT
ejpam-5090	143	27	=	=	SYM
ejpam-5090	143	28	max	max	X
ejpam-5090	143	29	{	{	PUNCT
ejpam-5090	143	30	ρim×n(((ϑ3	ρim×n(((ϑ3	PROPN
ejpam-5090	143	31	,	,	PUNCT
ejpam-5090	143	32	η3	η3	NOUN
ejpam-5090	143	33	)	)	PUNCT
ejpam-5090	143	34	·	·	PUNCT
ejpam-5090	143	35	(	(	PUNCT
ejpam-5090	143	36	ϑ1	ϑ1	NOUN
ejpam-5090	143	37	,	,	PUNCT
ejpam-5090	143	38	η1	η1	NOUN
ejpam-5090	143	39	)	)	PUNCT
ejpam-5090	143	40	)	)	PUNCT
ejpam-5090	143	41	,	,	PUNCT
ejpam-5090	143	42	(	(	PUNCT
ejpam-5090	143	43	(	(	PUNCT
ejpam-5090	143	44	ϑ3	ϑ3	PROPN
ejpam-5090	143	45	,	,	PUNCT
ejpam-5090	143	46	η3	η3	PROPN
ejpam-5090	143	47	)	)	PUNCT
ejpam-5090	143	48	·	·	PUNCT
ejpam-5090	143	49	(	(	PUNCT
ejpam-5090	143	50	ϑ2	ϑ2	NOUN
ejpam-5090	143	51	,	,	PUNCT
ejpam-5090	143	52	η2	η2	NOUN
ejpam-5090	143	53	)	)	PUNCT
ejpam-5090	143	54	)	)	PUNCT
ejpam-5090	143	55	)	)	PUNCT
ejpam-5090	143	56	,	,	PUNCT
ejpam-5090	143	57	ρ	ρ	PROPN
ejpam-5090	143	58	i	i	PRON
ejpam-5090	143	59	m×n(ϑ2	m×n(ϑ2	NOUN
ejpam-5090	143	60	,	,	PUNCT
ejpam-5090	143	61	η2	η2	PROPN
ejpam-5090	143	62	)	)	PUNCT
ejpam-5090	143	63	}	}	PUNCT
ejpam-5090	143	64	and	and	CCONJ
ejpam-5090	143	65	ρfm×n(ϑ1	ρfm×n(ϑ1	NUM
ejpam-5090	143	66	,	,	PUNCT
ejpam-5090	143	67	η1	η1	NOUN
ejpam-5090	143	68	)	)	PUNCT
ejpam-5090	143	69	=	=	SYM
ejpam-5090	143	70	max	max	PROPN
ejpam-5090	143	71	{	{	PUNCT
ejpam-5090	143	72	ρfm(ϑ1	ρfm(ϑ1	PROPN
ejpam-5090	143	73	)	)	PUNCT
ejpam-5090	143	74	,	,	PUNCT
ejpam-5090	143	75	ρ	ρ	PROPN
ejpam-5090	143	76	f	f	PROPN
ejpam-5090	143	77	n(η1	n(η1	PROPN
ejpam-5090	143	78	)	)	PUNCT
ejpam-5090	143	79	}	}	PUNCT
ejpam-5090	143	80	≥	≥	PROPN
ejpam-5090	143	81	max	max	PROPN
ejpam-5090	143	82	{	{	PUNCT
ejpam-5090	143	83	max	max	PROPN
ejpam-5090	143	84	{	{	PUNCT
ejpam-5090	143	85	ρfm((ϑ3	ρfm((ϑ3	PROPN
ejpam-5090	143	86	·	·	SYM
ejpam-5090	143	87	ϑ1	ϑ1	NOUN
ejpam-5090	143	88	)	)	PUNCT
ejpam-5090	143	89	·	·	PUNCT
ejpam-5090	144	1	(	(	PUNCT
ejpam-5090	144	2	ϑ3	ϑ3	NOUN
ejpam-5090	144	3	·	·	SYM
ejpam-5090	144	4	ϑ2	ϑ2	PROPN
ejpam-5090	144	5	)	)	PUNCT
ejpam-5090	144	6	)	)	PUNCT
ejpam-5090	144	7	,	,	PUNCT
ejpam-5090	145	1	ρ	ρ	PROPN
ejpam-5090	145	2	f	f	X
ejpam-5090	145	3	m(ϑ2	m(ϑ2	ADV
ejpam-5090	145	4	)	)	PUNCT
ejpam-5090	145	5	}	}	PUNCT
ejpam-5090	145	6	,	,	PUNCT
ejpam-5090	145	7	max	max	PROPN
ejpam-5090	145	8	{	{	PUNCT
ejpam-5090	145	9	ρfn((η3	ρfn((η3	PROPN
ejpam-5090	145	10	·	·	SYM
ejpam-5090	145	11	η1	η1	NOUN
ejpam-5090	145	12	)	)	PUNCT
ejpam-5090	145	13	·	·	PUNCT
ejpam-5090	145	14	(	(	PUNCT
ejpam-5090	145	15	η3	η3	NOUN
ejpam-5090	145	16	·	·	PUNCT
ejpam-5090	145	17	η2	η2	PROPN
ejpam-5090	145	18	)	)	PUNCT
ejpam-5090	145	19	)	)	PUNCT
ejpam-5090	145	20	,	,	PUNCT
ejpam-5090	145	21	ρ	ρ	PROPN
ejpam-5090	145	22	f	f	PROPN
ejpam-5090	145	23	n(η2	n(η2	PROPN
ejpam-5090	145	24	)	)	PUNCT
ejpam-5090	145	25	}	}	PUNCT
ejpam-5090	145	26	}	}	PUNCT
ejpam-5090	145	27	=	=	SYM
ejpam-5090	145	28	max	max	PROPN
ejpam-5090	145	29	{	{	PUNCT
ejpam-5090	145	30	max	max	PROPN
ejpam-5090	145	31	{	{	PUNCT
ejpam-5090	145	32	ρfm((ϑ3	ρfm((ϑ3	PROPN
ejpam-5090	145	33	·	·	SYM
ejpam-5090	145	34	ϑ1	ϑ1	NOUN
ejpam-5090	145	35	)	)	PUNCT
ejpam-5090	145	36	·	·	PUNCT
ejpam-5090	146	1	(	(	PUNCT
ejpam-5090	146	2	ϑ3	ϑ3	NOUN
ejpam-5090	146	3	·	·	SYM
ejpam-5090	146	4	ϑ2	ϑ2	PROPN
ejpam-5090	146	5	)	)	PUNCT
ejpam-5090	146	6	)	)	PUNCT
ejpam-5090	146	7	,	,	PUNCT
ejpam-5090	146	8	ρ	ρ	PROPN
ejpam-5090	146	9	f	f	PROPN
ejpam-5090	146	10	n((η3	n((η3	PROPN
ejpam-5090	146	11	·	·	PUNCT
ejpam-5090	146	12	η1	η1	NOUN
ejpam-5090	146	13	)	)	PUNCT
ejpam-5090	146	14	·	·	PUNCT
ejpam-5090	146	15	(	(	PUNCT
ejpam-5090	146	16	η3	η3	NOUN
ejpam-5090	146	17	·	·	PUNCT
ejpam-5090	146	18	η2	η2	NUM
ejpam-5090	146	19	)	)	PUNCT
ejpam-5090	146	20	)	)	PUNCT
ejpam-5090	146	21	}	}	PUNCT
ejpam-5090	146	22	,	,	PUNCT
ejpam-5090	146	23	min	min	NOUN
ejpam-5090	146	24	{	{	PUNCT
ejpam-5090	146	25	ρfm(ϑ2	ρfm(ϑ2	NOUN
ejpam-5090	146	26	)	)	PUNCT
ejpam-5090	146	27	,	,	PUNCT
ejpam-5090	146	28	ρ	ρ	PROPN
ejpam-5090	146	29	f	f	PROPN
ejpam-5090	146	30	n(η2	n(η2	PROPN
ejpam-5090	146	31	)	)	PUNCT
ejpam-5090	146	32	}	}	PUNCT
ejpam-5090	146	33	}	}	PUNCT
ejpam-5090	146	34	=	=	SYM
ejpam-5090	146	35	max	max	X
ejpam-5090	146	36	{	{	PUNCT
ejpam-5090	146	37	ρfm×n(((ϑ3	ρfm×n(((ϑ3	PROPN
ejpam-5090	146	38	,	,	PUNCT
ejpam-5090	146	39	η3	η3	PROPN
ejpam-5090	146	40	)	)	PUNCT
ejpam-5090	146	41	·	·	PUNCT
ejpam-5090	146	42	(	(	PUNCT
ejpam-5090	146	43	ϑ1	ϑ1	NOUN
ejpam-5090	146	44	,	,	PUNCT
ejpam-5090	146	45	η1	η1	NOUN
ejpam-5090	146	46	)	)	PUNCT
ejpam-5090	146	47	)	)	PUNCT
ejpam-5090	146	48	,	,	PUNCT
ejpam-5090	146	49	(	(	PUNCT
ejpam-5090	146	50	(	(	PUNCT
ejpam-5090	146	51	ϑ3	ϑ3	PROPN
ejpam-5090	146	52	,	,	PUNCT
ejpam-5090	146	53	η3	η3	PROPN
ejpam-5090	146	54	)	)	PUNCT
ejpam-5090	146	55	·	·	PUNCT
ejpam-5090	146	56	(	(	PUNCT
ejpam-5090	146	57	ϑ2	ϑ2	NOUN
ejpam-5090	146	58	,	,	PUNCT
ejpam-5090	146	59	η2	η2	NOUN
ejpam-5090	146	60	)	)	PUNCT
ejpam-5090	146	61	)	)	PUNCT
ejpam-5090	146	62	)	)	PUNCT
ejpam-5090	146	63	,	,	PUNCT
ejpam-5090	146	64	ρ	ρ	PROPN
ejpam-5090	146	65	f	f	PROPN
ejpam-5090	146	66	m×n(ϑ2	m×n(ϑ2	PROPN
ejpam-5090	146	67	,	,	PUNCT
ejpam-5090	146	68	η2	η2	PROPN
ejpam-5090	146	69	)	)	PUNCT
ejpam-5090	146	70	}	}	PUNCT
ejpam-5090	146	71	hence	hence	ADV
ejpam-5090	146	72	,	,	PUNCT
ejpam-5090	146	73	m×n	m×n	PROPN
ejpam-5090	146	74	=	=	SYM
ejpam-5090	146	75	〈	〈	PROPN
ejpam-5090	146	76	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	146	77	)	)	PUNCT
ejpam-5090	146	78	,	,	PUNCT
ejpam-5090	146	79	ρ	ρ	PROPN
ejpam-5090	146	80	i	i	PROPN
ejpam-5090	146	81	(	(	PUNCT
ejpam-5090	146	82	m×n	m×n	PROPN
ejpam-5090	146	83	)	)	PUNCT
ejpam-5090	146	84	,	,	PUNCT
ejpam-5090	146	85	ρ	ρ	PROPN
ejpam-5090	146	86	f	f	X
ejpam-5090	146	87	(	(	PUNCT
ejpam-5090	146	88	m×n	m×n	NOUN
ejpam-5090	146	89	)	)	PUNCT
ejpam-5090	146	90	〉	〉	NOUN
ejpam-5090	146	91	is	be	AUX
ejpam-5090	146	92	a	a	DET
ejpam-5090	146	93	fnink	fnink	NOUN
ejpam-5090	146	94	-	-	PUNCT
ejpam-5090	146	95	i	i	PRON
ejpam-5090	146	96	of	of	ADP
ejpam-5090	146	97	χ1	χ1	PROPN
ejpam-5090	146	98	×	×	PROPN
ejpam-5090	146	99	χ2	χ2	PROPN
ejpam-5090	146	100	.	.	PUNCT
ejpam-5090	147	1	theorem	theorem	VERB
ejpam-5090	147	2	3	3	X
ejpam-5090	147	3	.	.	PUNCT
ejpam-5090	148	1	let	let	VERB
ejpam-5090	148	2	m	m	PROPN
ejpam-5090	148	3	=	=	VERB
ejpam-5090	148	4	〈	〈	PROPN
ejpam-5090	148	5	ρtm	ρtm	NOUN
ejpam-5090	148	6	,	,	PUNCT
ejpam-5090	148	7	ρim	ρim	NOUN
ejpam-5090	148	8	,	,	PUNCT
ejpam-5090	148	9	ρfm	ρfm	ADP
ejpam-5090	148	10	〉	〉	NOUN
ejpam-5090	148	11	and	and	CCONJ
ejpam-5090	148	12	n	n	NOUN
ejpam-5090	148	13	=	=	PUNCT
ejpam-5090	148	14	〈	〈	PROPN
ejpam-5090	148	15	ρtn	ρtn	NOUN
ejpam-5090	148	16	,	,	PUNCT
ejpam-5090	148	17	ρ	ρ	PROPN
ejpam-5090	148	18	i	i	PROPN
ejpam-5090	148	19	n	n	CCONJ
ejpam-5090	148	20	,	,	PUNCT
ejpam-5090	148	21	ρ	ρ	PROPN
ejpam-5090	148	22	f	f	PROPN
ejpam-5090	148	23	n	n	PRON
ejpam-5090	148	24	〉	〉	NOUN
ejpam-5090	148	25	be	be	VERB
ejpam-5090	148	26	two	two	NUM
ejpam-5090	148	27	fncink	fncink	NOUN
ejpam-5090	148	28	-	-	PUNCT
ejpam-5090	148	29	is	is	NOUN
ejpam-5090	148	30	of	of	ADP
ejpam-5090	148	31	χ1	χ1	NOUN
ejpam-5090	148	32	and	and	CCONJ
ejpam-5090	148	33	χ2	χ2	PROPN
ejpam-5090	148	34	,	,	PUNCT
ejpam-5090	148	35	respectively	respectively	ADV
ejpam-5090	148	36	.	.	PUNCT
ejpam-5090	149	1	then	then	ADV
ejpam-5090	149	2	,	,	PUNCT
ejpam-5090	149	3	the	the	DET
ejpam-5090	149	4	direct	direct	ADJ
ejpam-5090	149	5	product	product	NOUN
ejpam-5090	149	6	m×n	m×n	PROPN
ejpam-5090	149	7	,	,	PUNCT
ejpam-5090	149	8	defined	define	VERB
ejpam-5090	149	9	by	by	ADP
ejpam-5090	149	10	m×n	m×n	PROPN
ejpam-5090	149	11	=	=	SYM
ejpam-5090	149	12	〈	〈	PROPN
ejpam-5090	149	13	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	149	14	)	)	PUNCT
ejpam-5090	149	15	,	,	PUNCT
ejpam-5090	149	16	ρ	ρ	PROPN
ejpam-5090	149	17	i	i	PROPN
ejpam-5090	149	18	(	(	PUNCT
ejpam-5090	149	19	m×n	m×n	PROPN
ejpam-5090	149	20	)	)	PUNCT
ejpam-5090	149	21	,	,	PUNCT
ejpam-5090	149	22	ρ	ρ	PROPN
ejpam-5090	149	23	f	f	X
ejpam-5090	149	24	(	(	PUNCT
ejpam-5090	149	25	m×n	m×n	NOUN
ejpam-5090	149	26	)	)	PUNCT
ejpam-5090	149	27	〉	〉	NOUN
ejpam-5090	149	28	,	,	PUNCT
ejpam-5090	149	29	is	be	AUX
ejpam-5090	149	30	a	a	DET
ejpam-5090	149	31	fncink	fncink	ADJ
ejpam-5090	149	32	-	-	PUNCT
ejpam-5090	149	33	i	i	NOUN
ejpam-5090	149	34	of	of	ADP
ejpam-5090	149	35	χ1	χ1	PROPN
ejpam-5090	149	36	×	×	PROPN
ejpam-5090	149	37	χ2	χ2	PROPN
ejpam-5090	149	38	.	.	PUNCT
ejpam-5090	150	1	proof	proof	NOUN
ejpam-5090	150	2	.	.	PUNCT
ejpam-5090	151	1	by	by	ADP
ejpam-5090	151	2	applying	apply	VERB
ejpam-5090	151	3	theorem	theorem	NOUN
ejpam-5090	151	4	2	2	NUM
ejpam-5090	151	5	,	,	PUNCT
ejpam-5090	151	6	the	the	DET
ejpam-5090	151	7	fns	fns	PROPN
ejpam-5090	151	8	m	m	PROPN
ejpam-5090	151	9	×	×	PROPN
ejpam-5090	151	10	n	n	CCONJ
ejpam-5090	151	11	=	=	PUNCT
ejpam-5090	151	12	〈	〈	PROPN
ejpam-5090	151	13	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	151	14	)	)	PUNCT
ejpam-5090	151	15	,	,	PUNCT
ejpam-5090	151	16	ρ	ρ	PROPN
ejpam-5090	151	17	i	i	PROPN
ejpam-5090	151	18	(	(	PUNCT
ejpam-5090	151	19	m×n	m×n	PROPN
ejpam-5090	151	20	)	)	PUNCT
ejpam-5090	151	21	,	,	PUNCT
ejpam-5090	151	22	ρ	ρ	PROPN
ejpam-5090	151	23	f	f	X
ejpam-5090	151	24	(	(	PUNCT
ejpam-5090	151	25	m×n	m×n	NOUN
ejpam-5090	151	26	)	)	PUNCT
ejpam-5090	151	27	〉	〉	NOUN
ejpam-5090	151	28	is	be	AUX
ejpam-5090	151	29	a	a	DET
ejpam-5090	151	30	fnink	fnink	NOUN
ejpam-5090	151	31	-	-	PUNCT
ejpam-5090	151	32	i	i	PRON
ejpam-5090	151	33	of	of	ADP
ejpam-5090	151	34	χ1	χ1	PROPN
ejpam-5090	151	35	×	×	PROPN
ejpam-5090	151	36	χ2	χ2	PROPN
ejpam-5090	151	37	.	.	PUNCT
ejpam-5090	152	1	now	now	ADV
ejpam-5090	152	2	,	,	PUNCT
ejpam-5090	152	3	∀(ϑ	∀(ϑ	PROPN
ejpam-5090	152	4	,	,	PUNCT
ejpam-5090	152	5	η	η	NOUN
ejpam-5090	152	6	)	)	PUNCT
ejpam-5090	152	7	∈	∈	PROPN
ejpam-5090	152	8	χ1	χ1	NOUN
ejpam-5090	152	9	×	×	NOUN
ejpam-5090	152	10	χ2	χ2	PROPN
ejpam-5090	152	11	,	,	PUNCT
ejpam-5090	152	12	we	we	PRON
ejpam-5090	152	13	have	have	AUX
ejpam-5090	152	14	ρtm×n((0	ρtm×n((0	PROPN
ejpam-5090	152	15	,	,	PUNCT
ejpam-5090	152	16	0	0	NUM
ejpam-5090	152	17	)	)	PUNCT
ejpam-5090	152	18	·	·	PUNCT
ejpam-5090	152	19	(	(	PUNCT
ejpam-5090	152	20	ϑ	ϑ	X
ejpam-5090	152	21	,	,	PUNCT
ejpam-5090	152	22	η	η	NOUN
ejpam-5090	152	23	)	)	PUNCT
ejpam-5090	152	24	)	)	PUNCT
ejpam-5090	152	25	≤	≤	PUNCT
ejpam-5090	153	1	ρtm×n((0	ρtm×n((0	NUM
ejpam-5090	153	2	·	·	PUNCT
ejpam-5090	153	3	ϑ	ϑ	X
ejpam-5090	153	4	)	)	PUNCT
ejpam-5090	153	5	,	,	PUNCT
ejpam-5090	153	6	(	(	PUNCT
ejpam-5090	153	7	0	0	NUM
ejpam-5090	153	8	·	·	SYM
ejpam-5090	153	9	η	η	NOUN
ejpam-5090	153	10	)	)	PUNCT
ejpam-5090	153	11	)	)	PUNCT
ejpam-5090	154	1	=	=	SYM
ejpam-5090	154	2	min	min	NOUN
ejpam-5090	154	3	{	{	PUNCT
ejpam-5090	154	4	ρtm(0	ρtm(0	NOUN
ejpam-5090	154	5	·	·	PUNCT
ejpam-5090	154	6	ϑ	ϑ	X
ejpam-5090	154	7	)	)	PUNCT
ejpam-5090	154	8	,	,	PUNCT
ejpam-5090	154	9	ρtn(0	ρtn(0	X
ejpam-5090	154	10	·	·	PUNCT
ejpam-5090	154	11	η	η	NOUN
ejpam-5090	154	12	)	)	PUNCT
ejpam-5090	154	13	}	}	PUNCT
ejpam-5090	154	14	≤	≤	NUM
ejpam-5090	154	15	min	min	NOUN
ejpam-5090	154	16	{	{	PUNCT
ejpam-5090	154	17	ρtm(ϑ	ρtm(ϑ	NOUN
ejpam-5090	154	18	)	)	PUNCT
ejpam-5090	154	19	,	,	PUNCT
ejpam-5090	154	20	ρtn(η	ρtn(η	PROPN
ejpam-5090	154	21	)	)	PUNCT
ejpam-5090	154	22	}	}	PUNCT
ejpam-5090	154	23	=	=	SYM
ejpam-5090	154	24	ρtm×n(ϑ	ρtm×n(ϑ	NOUN
ejpam-5090	154	25	,	,	PUNCT
ejpam-5090	154	26	η	η	NOUN
ejpam-5090	154	27	)	)	PUNCT
ejpam-5090	154	28	,	,	PUNCT
ejpam-5090	154	29	ρim×n((0	ρim×n((0	PROPN
ejpam-5090	154	30	,	,	PUNCT
ejpam-5090	154	31	0	0	NUM
ejpam-5090	154	32	)	)	PUNCT
ejpam-5090	154	33	·	·	PUNCT
ejpam-5090	154	34	(	(	PUNCT
ejpam-5090	154	35	ϑ	ϑ	X
ejpam-5090	154	36	,	,	PUNCT
ejpam-5090	154	37	η	η	NOUN
ejpam-5090	154	38	)	)	PUNCT
ejpam-5090	154	39	)	)	PUNCT
ejpam-5090	154	40	≥	≥	X
ejpam-5090	155	1	ρim×n((0	ρim×n((0	X
ejpam-5090	155	2	·	·	PUNCT
ejpam-5090	155	3	ϑ	ϑ	X
ejpam-5090	155	4	)	)	PUNCT
ejpam-5090	155	5	,	,	PUNCT
ejpam-5090	155	6	(	(	PUNCT
ejpam-5090	155	7	0	0	NUM
ejpam-5090	155	8	·	·	SYM
ejpam-5090	155	9	η	η	NOUN
ejpam-5090	155	10	)	)	PUNCT
ejpam-5090	155	11	)	)	PUNCT
ejpam-5090	156	1	=	=	SYM
ejpam-5090	156	2	max	max	PROPN
ejpam-5090	156	3	{	{	PUNCT
ejpam-5090	156	4	ρim(0	ρim(0	NOUN
ejpam-5090	156	5	·	·	PUNCT
ejpam-5090	156	6	ϑ	ϑ	X
ejpam-5090	156	7	)	)	PUNCT
ejpam-5090	156	8	,	,	PUNCT
ejpam-5090	156	9	ρin(0	ρin(0	NOUN
ejpam-5090	156	10	·	·	PUNCT
ejpam-5090	156	11	η	η	PROPN
ejpam-5090	156	12	)	)	PUNCT
ejpam-5090	156	13	}	}	PUNCT
ejpam-5090	156	14	≥	≥	PROPN
ejpam-5090	156	15	max	max	PROPN
ejpam-5090	156	16	{	{	PUNCT
ejpam-5090	156	17	ρim(ϑ	ρim(ϑ	PROPN
ejpam-5090	156	18	)	)	PUNCT
ejpam-5090	156	19	,	,	PUNCT
ejpam-5090	156	20	ρin(η	ρin(η	ADV
ejpam-5090	156	21	)	)	PUNCT
ejpam-5090	156	22	}	}	PUNCT
ejpam-5090	156	23	=	=	SYM
ejpam-5090	156	24	ρim×n(ϑ	ρim×n(ϑ	PROPN
ejpam-5090	156	25	,	,	PUNCT
ejpam-5090	156	26	η	η	NOUN
ejpam-5090	156	27	)	)	PUNCT
ejpam-5090	156	28	and	and	CCONJ
ejpam-5090	156	29	ρfm×n((0	ρfm×n((0	PROPN
ejpam-5090	156	30	,	,	PUNCT
ejpam-5090	156	31	0	0	NUM
ejpam-5090	156	32	)	)	PUNCT
ejpam-5090	156	33	·	·	PUNCT
ejpam-5090	156	34	(	(	PUNCT
ejpam-5090	156	35	ϑ	ϑ	X
ejpam-5090	156	36	,	,	PUNCT
ejpam-5090	156	37	η	η	NOUN
ejpam-5090	156	38	)	)	PUNCT
ejpam-5090	156	39	)	)	PUNCT
ejpam-5090	156	40	≥	≥	NOUN
ejpam-5090	157	1	ρfm×n((0	ρfm×n((0	PROPN
ejpam-5090	157	2	·	·	PUNCT
ejpam-5090	157	3	ϑ	ϑ	X
ejpam-5090	157	4	)	)	PUNCT
ejpam-5090	157	5	,	,	PUNCT
ejpam-5090	157	6	(	(	PUNCT
ejpam-5090	157	7	0	0	NUM
ejpam-5090	157	8	·	·	SYM
ejpam-5090	157	9	η	η	NOUN
ejpam-5090	157	10	)	)	PUNCT
ejpam-5090	157	11	)	)	PUNCT
ejpam-5090	157	12	m.	m.	NOUN
ejpam-5090	157	13	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	157	14	et	et	PROPN
ejpam-5090	157	15	al	al	PROPN
ejpam-5090	157	16	.	.	PUNCT
ejpam-5090	157	17	/	/	SYM
ejpam-5090	157	18	eur	eur	PROPN
ejpam-5090	157	19	.	.	PUNCT
ejpam-5090	158	1	j.	j.	PROPN
ejpam-5090	158	2	pure	pure	PROPN
ejpam-5090	158	3	appl	appl	PROPN
ejpam-5090	158	4	.	.	PROPN
ejpam-5090	158	5	math	math	PROPN
ejpam-5090	158	6	,	,	PUNCT
ejpam-5090	158	7	17	17	NUM
ejpam-5090	158	8	(	(	PUNCT
ejpam-5090	158	9	2	2	NUM
ejpam-5090	158	10	)	)	PUNCT
ejpam-5090	158	11	(	(	PUNCT
ejpam-5090	158	12	2024	2024	NUM
ejpam-5090	158	13	)	)	PUNCT
ejpam-5090	158	14	,	,	PUNCT
ejpam-5090	158	15	1113	1113	NUM
ejpam-5090	158	16	-	-	SYM
ejpam-5090	158	17	1128	1128	NUM
ejpam-5090	158	18	1122	1122	NUM
ejpam-5090	158	19	=	=	SYM
ejpam-5090	158	20	max	max	PROPN
ejpam-5090	158	21	{	{	PUNCT
ejpam-5090	158	22	ρfm(0	ρfm(0	NOUN
ejpam-5090	158	23	·	·	PUNCT
ejpam-5090	158	24	ϑ	ϑ	X
ejpam-5090	158	25	)	)	PUNCT
ejpam-5090	158	26	,	,	PUNCT
ejpam-5090	158	27	ρfn(0	ρfn(0	X
ejpam-5090	158	28	·	·	PUNCT
ejpam-5090	158	29	η	η	NOUN
ejpam-5090	158	30	)	)	PUNCT
ejpam-5090	158	31	}	}	PUNCT
ejpam-5090	158	32	≥	≥	PROPN
ejpam-5090	158	33	max	max	PROPN
ejpam-5090	158	34	{	{	PUNCT
ejpam-5090	158	35	ρfm(ϑ	ρfm(ϑ	PROPN
ejpam-5090	158	36	)	)	PUNCT
ejpam-5090	158	37	,	,	PUNCT
ejpam-5090	158	38	ρfn(η	ρfn(η	NUM
ejpam-5090	158	39	)	)	PUNCT
ejpam-5090	158	40	}	}	PUNCT
ejpam-5090	158	41	=	=	SYM
ejpam-5090	158	42	ρfm×n(ϑ	ρfm×n(ϑ	PROPN
ejpam-5090	158	43	,	,	PUNCT
ejpam-5090	158	44	η	η	NOUN
ejpam-5090	158	45	)	)	PUNCT
ejpam-5090	158	46	.	.	PUNCT
ejpam-5090	159	1	hence	hence	ADV
ejpam-5090	159	2	,	,	PUNCT
ejpam-5090	159	3	m×n	m×n	PROPN
ejpam-5090	159	4	=	=	SYM
ejpam-5090	159	5	〈	〈	PROPN
ejpam-5090	159	6	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	159	7	)	)	PUNCT
ejpam-5090	159	8	,	,	PUNCT
ejpam-5090	159	9	ρ	ρ	PROPN
ejpam-5090	159	10	i	i	PROPN
ejpam-5090	159	11	(	(	PUNCT
ejpam-5090	159	12	m×n	m×n	PROPN
ejpam-5090	159	13	)	)	PUNCT
ejpam-5090	159	14	,	,	PUNCT
ejpam-5090	159	15	ρ	ρ	PROPN
ejpam-5090	159	16	f	f	X
ejpam-5090	159	17	(	(	PUNCT
ejpam-5090	159	18	m×n	m×n	NOUN
ejpam-5090	159	19	)	)	PUNCT
ejpam-5090	159	20	〉	〉	NOUN
ejpam-5090	159	21	is	be	AUX
ejpam-5090	159	22	a	a	DET
ejpam-5090	159	23	fncink	fncink	ADJ
ejpam-5090	159	24	-	-	PUNCT
ejpam-5090	159	25	i	i	NOUN
ejpam-5090	159	26	of	of	ADP
ejpam-5090	159	27	χ1	χ1	PROPN
ejpam-5090	159	28	×	×	PROPN
ejpam-5090	159	29	χ2	χ2	PROPN
ejpam-5090	159	30	.	.	PUNCT
ejpam-5090	160	1	theorem	theorem	VERB
ejpam-5090	160	2	4	4	NUM
ejpam-5090	160	3	.	.	PUNCT
ejpam-5090	161	1	let	let	VERB
ejpam-5090	161	2	m	m	PROPN
ejpam-5090	161	3	=	=	VERB
ejpam-5090	161	4	〈	〈	PROPN
ejpam-5090	161	5	ρtm	ρtm	NOUN
ejpam-5090	161	6	,	,	PUNCT
ejpam-5090	161	7	ρim	ρim	NOUN
ejpam-5090	161	8	,	,	PUNCT
ejpam-5090	161	9	ρfm	ρfm	ADP
ejpam-5090	161	10	〉	〉	NOUN
ejpam-5090	161	11	and	and	CCONJ
ejpam-5090	161	12	n	n	NOUN
ejpam-5090	161	13	=	=	PUNCT
ejpam-5090	161	14	〈	〈	PROPN
ejpam-5090	161	15	ρtn	ρtn	NOUN
ejpam-5090	161	16	,	,	PUNCT
ejpam-5090	161	17	ρ	ρ	PROPN
ejpam-5090	161	18	i	i	PROPN
ejpam-5090	161	19	n	n	CCONJ
ejpam-5090	161	20	,	,	PUNCT
ejpam-5090	161	21	ρ	ρ	PROPN
ejpam-5090	161	22	f	f	PROPN
ejpam-5090	161	23	n	n	PRON
ejpam-5090	161	24	〉	〉	NOUN
ejpam-5090	161	25	be	be	VERB
ejpam-5090	161	26	two	two	NUM
ejpam-5090	161	27	fnink	fnink	NOUN
ejpam-5090	161	28	-	-	PUNCT
ejpam-5090	161	29	is	is	NOUN
ejpam-5090	161	30	of	of	ADP
ejpam-5090	161	31	χ1	χ1	NOUN
ejpam-5090	161	32	and	and	CCONJ
ejpam-5090	161	33	χ2	χ2	PROPN
ejpam-5090	161	34	,	,	PUNCT
ejpam-5090	161	35	respectively	respectively	ADV
ejpam-5090	161	36	.	.	PUNCT
ejpam-5090	162	1	then	then	ADV
ejpam-5090	162	2	,	,	PUNCT
ejpam-5090	162	3	m	m	VERB
ejpam-5090	162	4	×	×	NOUN
ejpam-5090	162	5	n	n	CCONJ
ejpam-5090	162	6	=	=	PUNCT
ejpam-5090	162	7	〈	〈	PROPN
ejpam-5090	162	8	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	162	9	)	)	PUNCT
ejpam-5090	162	10	,	,	PUNCT
ejpam-5090	162	11	ρ	ρ	PROPN
ejpam-5090	162	12	i	i	PROPN
ejpam-5090	162	13	(	(	PUNCT
ejpam-5090	162	14	m×n	m×n	PROPN
ejpam-5090	162	15	)	)	PUNCT
ejpam-5090	162	16	,	,	PUNCT
ejpam-5090	162	17	ρ	ρ	PROPN
ejpam-5090	162	18	t	t	PROPN
ejpam-5090	162	19	(	(	PUNCT
ejpam-5090	162	20	m×n	m×n	NOUN
ejpam-5090	162	21	)	)	PUNCT
ejpam-5090	162	22	〉	〉	NOUN
ejpam-5090	162	23	is	be	AUX
ejpam-5090	162	24	a	a	DET
ejpam-5090	162	25	fnink	fnink	NOUN
ejpam-5090	162	26	-	-	PUNCT
ejpam-5090	162	27	i	i	PRON
ejpam-5090	162	28	of	of	ADP
ejpam-5090	162	29	χ1	χ1	PROPN
ejpam-5090	162	30	×	×	PROPN
ejpam-5090	162	31	χ2	χ2	PROPN
ejpam-5090	162	32	,	,	PUNCT
ejpam-5090	162	33	where	where	SCONJ
ejpam-5090	162	34	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	162	35	)	)	PUNCT
ejpam-5090	162	36	=	=	SYM
ejpam-5090	162	37	1−	1−	NUM
ejpam-5090	162	38	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	162	39	)	)	PUNCT
ejpam-5090	162	40	.	.	PUNCT
ejpam-5090	163	1	proof	proof	NOUN
ejpam-5090	163	2	.	.	PUNCT
ejpam-5090	164	1	according	accord	VERB
ejpam-5090	164	2	to	to	ADP
ejpam-5090	164	3	theorem	theorem	ADJ
ejpam-5090	164	4	2	2	NUM
ejpam-5090	164	5	.	.	PUNCT
ejpam-5090	164	6	m×n	m×n	PROPN
ejpam-5090	164	7	=	=	SYM
ejpam-5090	164	8	〈	〈	PROPN
ejpam-5090	164	9	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	164	10	)	)	PUNCT
ejpam-5090	164	11	,	,	PUNCT
ejpam-5090	164	12	ρ	ρ	PROPN
ejpam-5090	164	13	i	i	PROPN
ejpam-5090	164	14	(	(	PUNCT
ejpam-5090	164	15	m×n	m×n	PROPN
ejpam-5090	164	16	)	)	PUNCT
ejpam-5090	164	17	,	,	PUNCT
ejpam-5090	164	18	ρ	ρ	PROPN
ejpam-5090	164	19	f	f	X
ejpam-5090	164	20	(	(	PUNCT
ejpam-5090	164	21	m×n	m×n	NOUN
ejpam-5090	164	22	)	)	PUNCT
ejpam-5090	164	23	〉	〉	NOUN
ejpam-5090	164	24	is	be	AUX
ejpam-5090	164	25	a	a	DET
ejpam-5090	164	26	fnink	fnink	NOUN
ejpam-5090	164	27	-	-	PUNCT
ejpam-5090	164	28	i	i	PRON
ejpam-5090	164	29	of	of	ADP
ejpam-5090	164	30	χ1	χ1	PROPN
ejpam-5090	164	31	×	×	PROPN
ejpam-5090	164	32	χ2	χ2	PROPN
ejpam-5090	164	33	.	.	PUNCT
ejpam-5090	165	1	then	then	ADV
ejpam-5090	165	2	,	,	PUNCT
ejpam-5090	165	3	ρt(m×n)(0	ρt(m×n)(0	PROPN
ejpam-5090	165	4	,	,	PUNCT
ejpam-5090	165	5	0	0	NUM
ejpam-5090	165	6	)	)	PUNCT
ejpam-5090	165	7	≤	≤	NUM
ejpam-5090	165	8	ρt(m×n)(ϑ	ρt(m×n)(ϑ	PROPN
ejpam-5090	165	9	,	,	PUNCT
ejpam-5090	165	10	η	η	NOUN
ejpam-5090	165	11	)	)	PUNCT
ejpam-5090	165	12	1−	1−	NUM
ejpam-5090	165	13	ρtm×n(0	ρtm×n(0	NUM
ejpam-5090	165	14	,	,	PUNCT
ejpam-5090	165	15	0	0	NUM
ejpam-5090	165	16	)	)	PUNCT
ejpam-5090	165	17	≥	≥	NOUN
ejpam-5090	165	18	1−	1−	NUM
ejpam-5090	166	1	ρt(m)×n)(ϑ	ρt(m)×n)(ϑ	VERB
ejpam-5090	166	2	,	,	PUNCT
ejpam-5090	166	3	η	η	NOUN
ejpam-5090	166	4	)	)	PUNCT
ejpam-5090	166	5	ρtm×n(0	ρtm×n(0	PROPN
ejpam-5090	166	6	,	,	PUNCT
ejpam-5090	166	7	0	0	NUM
ejpam-5090	166	8	)	)	PUNCT
ejpam-5090	166	9	≥	≥	NOUN
ejpam-5090	166	10	ρt(m×n)(ϑ	ρt(m×n)(ϑ	PROPN
ejpam-5090	166	11	,	,	PUNCT
ejpam-5090	166	12	η	η	NOUN
ejpam-5090	166	13	)	)	PUNCT
ejpam-5090	166	14	.	.	PUNCT
ejpam-5090	167	1	now	now	ADV
ejpam-5090	167	2	,	,	PUNCT
ejpam-5090	167	3	for	for	ADP
ejpam-5090	167	4	any	any	DET
ejpam-5090	167	5	(	(	PUNCT
ejpam-5090	167	6	ϑ1	ϑ1	NOUN
ejpam-5090	167	7	,	,	PUNCT
ejpam-5090	167	8	η1	η1	NOUN
ejpam-5090	167	9	)	)	PUNCT
ejpam-5090	167	10	,	,	PUNCT
ejpam-5090	167	11	(	(	PUNCT
ejpam-5090	167	12	ϑ2	ϑ2	NOUN
ejpam-5090	167	13	,	,	PUNCT
ejpam-5090	167	14	η2	η2	NOUN
ejpam-5090	167	15	)	)	PUNCT
ejpam-5090	167	16	,	,	PUNCT
ejpam-5090	167	17	(	(	PUNCT
ejpam-5090	167	18	ϑ3	ϑ3	PROPN
ejpam-5090	167	19	,	,	PUNCT
ejpam-5090	167	20	η3	η3	PROPN
ejpam-5090	167	21	)	)	PUNCT
ejpam-5090	167	22	∈	∈	PROPN
ejpam-5090	167	23	χ1	χ1	NOUN
ejpam-5090	167	24	×	×	NOUN
ejpam-5090	167	25	χ2	χ2	PROPN
ejpam-5090	167	26	.	.	PUNCT
ejpam-5090	168	1	we	we	PRON
ejpam-5090	168	2	have	have	VERB
ejpam-5090	168	3	ρt(m×n)(ϑ1	ρt(m×n)(ϑ1	NOUN
ejpam-5090	168	4	,	,	PUNCT
ejpam-5090	168	5	η1	η1	NOUN
ejpam-5090	168	6	)	)	PUNCT
ejpam-5090	168	7	≤	≤	NUM
ejpam-5090	168	8	min	min	NOUN
ejpam-5090	168	9	{	{	PUNCT
ejpam-5090	168	10	ρtm×n(((ϑ3	ρtm×n(((ϑ3	PROPN
ejpam-5090	168	11	,	,	PUNCT
ejpam-5090	168	12	η3	η3	NOUN
ejpam-5090	168	13	)	)	PUNCT
ejpam-5090	168	14	·	·	PUNCT
ejpam-5090	169	1	(	(	PUNCT
ejpam-5090	169	2	ϑ1	ϑ1	NOUN
ejpam-5090	169	3	,	,	PUNCT
ejpam-5090	169	4	η1	η1	NOUN
ejpam-5090	169	5	)	)	PUNCT
ejpam-5090	169	6	)	)	PUNCT
ejpam-5090	169	7	·	·	PUNCT
ejpam-5090	170	1	(	(	PUNCT
ejpam-5090	170	2	(	(	PUNCT
ejpam-5090	170	3	ϑ3	ϑ3	NOUN
ejpam-5090	170	4	,	,	PUNCT
ejpam-5090	170	5	η3	η3	PROPN
ejpam-5090	170	6	)	)	PUNCT
ejpam-5090	170	7	·	·	PUNCT
ejpam-5090	170	8	(	(	PUNCT
ejpam-5090	170	9	ϑ2	ϑ2	NOUN
ejpam-5090	170	10	,	,	PUNCT
ejpam-5090	170	11	η2	η2	NOUN
ejpam-5090	170	12	)	)	PUNCT
ejpam-5090	170	13	)	)	PUNCT
ejpam-5090	170	14	)	)	PUNCT
ejpam-5090	170	15	,	,	PUNCT
ejpam-5090	170	16	ρ	ρ	PROPN
ejpam-5090	170	17	t	t	PROPN
ejpam-5090	170	18	(	(	PUNCT
ejpam-5090	170	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	170	20	,	,	PUNCT
ejpam-5090	170	21	η2	η2	PROPN
ejpam-5090	170	22	)	)	PUNCT
ejpam-5090	170	23	}	}	PUNCT
ejpam-5090	170	24	1−	1−	NUM
ejpam-5090	170	25	ρt(m×n)(ϑ1	ρt(m×n)(ϑ1	ADJ
ejpam-5090	170	26	,	,	PUNCT
ejpam-5090	170	27	η1	η1	NOUN
ejpam-5090	170	28	)	)	PUNCT
ejpam-5090	170	29	≥	≥	NOUN
ejpam-5090	170	30	1−min	1−min	PROPN
ejpam-5090	170	31	{	{	PUNCT
ejpam-5090	170	32	ρt(m×n)(((ϑ3	ρt(m×n)(((ϑ3	PROPN
ejpam-5090	170	33	,	,	PUNCT
ejpam-5090	170	34	η3	η3	PROPN
ejpam-5090	170	35	)	)	PUNCT
ejpam-5090	170	36	·	·	PUNCT
ejpam-5090	170	37	(	(	PUNCT
ejpam-5090	170	38	ϑ1	ϑ1	NOUN
ejpam-5090	170	39	,	,	PUNCT
ejpam-5090	170	40	η1	η1	NOUN
ejpam-5090	170	41	)	)	PUNCT
ejpam-5090	170	42	)	)	PUNCT
ejpam-5090	170	43	·	·	PUNCT
ejpam-5090	171	1	(	(	PUNCT
ejpam-5090	171	2	(	(	PUNCT
ejpam-5090	171	3	ϑ3	ϑ3	NOUN
ejpam-5090	171	4	,	,	PUNCT
ejpam-5090	171	5	η3	η3	PROPN
ejpam-5090	171	6	)	)	PUNCT
ejpam-5090	171	7	·	·	PUNCT
ejpam-5090	171	8	(	(	PUNCT
ejpam-5090	171	9	ϑ2	ϑ2	NOUN
ejpam-5090	171	10	,	,	PUNCT
ejpam-5090	171	11	η2	η2	NOUN
ejpam-5090	171	12	)	)	PUNCT
ejpam-5090	171	13	)	)	PUNCT
ejpam-5090	171	14	)	)	PUNCT
ejpam-5090	171	15	,	,	PUNCT
ejpam-5090	171	16	ρ	ρ	PROPN
ejpam-5090	171	17	t	t	PROPN
ejpam-5090	171	18	(	(	PUNCT
ejpam-5090	171	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	171	20	,	,	PUNCT
ejpam-5090	171	21	η2	η2	PROPN
ejpam-5090	171	22	)	)	PUNCT
ejpam-5090	171	23	}	}	PUNCT
ejpam-5090	171	24	ρt(m×n)(ϑ1	ρt(m×n)(ϑ1	VERB
ejpam-5090	171	25	,	,	PUNCT
ejpam-5090	171	26	η1	η1	NOUN
ejpam-5090	171	27	)	)	PUNCT
ejpam-5090	171	28	≥	≥	NOUN
ejpam-5090	171	29	max	max	PROPN
ejpam-5090	171	30	{	{	PUNCT
ejpam-5090	171	31	1−	1−	NUM
ejpam-5090	171	32	ρt(m×n)(((ϑ3	ρt(m×n)(((ϑ3	PROPN
ejpam-5090	171	33	,	,	PUNCT
ejpam-5090	171	34	η3	η3	PROPN
ejpam-5090	171	35	)	)	PUNCT
ejpam-5090	171	36	·	·	PUNCT
ejpam-5090	171	37	(	(	PUNCT
ejpam-5090	171	38	ϑ1	ϑ1	NOUN
ejpam-5090	171	39	,	,	PUNCT
ejpam-5090	171	40	η1	η1	NOUN
ejpam-5090	171	41	)	)	PUNCT
ejpam-5090	171	42	)	)	PUNCT
ejpam-5090	171	43	·	·	PUNCT
ejpam-5090	172	1	(	(	PUNCT
ejpam-5090	172	2	(	(	PUNCT
ejpam-5090	172	3	ϑ3	ϑ3	NOUN
ejpam-5090	172	4	,	,	PUNCT
ejpam-5090	172	5	η3	η3	PROPN
ejpam-5090	172	6	)	)	PUNCT
ejpam-5090	172	7	·	·	PUNCT
ejpam-5090	172	8	(	(	PUNCT
ejpam-5090	172	9	ϑ2	ϑ2	NOUN
ejpam-5090	172	10	,	,	PUNCT
ejpam-5090	172	11	η2	η2	NOUN
ejpam-5090	172	12	)	)	PUNCT
ejpam-5090	172	13	)	)	PUNCT
ejpam-5090	172	14	)	)	PUNCT
ejpam-5090	172	15	,	,	PUNCT
ejpam-5090	172	16	1−	1−	NUM
ejpam-5090	172	17	ρt(m×n)(ϑ2	ρt(m×n)(ϑ2	NOUN
ejpam-5090	172	18	,	,	PUNCT
ejpam-5090	172	19	η2	η2	PROPN
ejpam-5090	172	20	)	)	PUNCT
ejpam-5090	172	21	}	}	PUNCT
ejpam-5090	172	22	ρt(m×n)(ϑ1	ρt(m×n)(ϑ1	VERB
ejpam-5090	172	23	,	,	PUNCT
ejpam-5090	172	24	η1	η1	NOUN
ejpam-5090	172	25	)	)	PUNCT
ejpam-5090	172	26	≥	≥	PROPN
ejpam-5090	172	27	max	max	PROPN
ejpam-5090	172	28	{	{	PUNCT
ejpam-5090	172	29	ρt(m×n)(((ϑ3	ρt(m×n)(((ϑ3	PROPN
ejpam-5090	172	30	,	,	PUNCT
ejpam-5090	172	31	η3	η3	PROPN
ejpam-5090	172	32	)	)	PUNCT
ejpam-5090	172	33	·	·	PUNCT
ejpam-5090	172	34	(	(	PUNCT
ejpam-5090	172	35	ϑ1	ϑ1	NOUN
ejpam-5090	172	36	,	,	PUNCT
ejpam-5090	172	37	η1	η1	NOUN
ejpam-5090	172	38	)	)	PUNCT
ejpam-5090	172	39	)	)	PUNCT
ejpam-5090	172	40	·	·	PUNCT
ejpam-5090	173	1	(	(	PUNCT
ejpam-5090	173	2	(	(	PUNCT
ejpam-5090	173	3	ϑ3	ϑ3	NOUN
ejpam-5090	173	4	,	,	PUNCT
ejpam-5090	173	5	η3	η3	PROPN
ejpam-5090	173	6	)	)	PUNCT
ejpam-5090	173	7	·	·	PUNCT
ejpam-5090	173	8	(	(	PUNCT
ejpam-5090	173	9	ϑ2	ϑ2	NOUN
ejpam-5090	173	10	,	,	PUNCT
ejpam-5090	173	11	η2	η2	NOUN
ejpam-5090	173	12	)	)	PUNCT
ejpam-5090	173	13	)	)	PUNCT
ejpam-5090	173	14	)	)	PUNCT
ejpam-5090	173	15	,	,	PUNCT
ejpam-5090	173	16	ρ	ρ	PROPN
ejpam-5090	173	17	t	t	PROPN
ejpam-5090	173	18	(	(	PUNCT
ejpam-5090	173	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	173	20	,	,	PUNCT
ejpam-5090	173	21	η2	η2	PROPN
ejpam-5090	173	22	)	)	PUNCT
ejpam-5090	173	23	}	}	PUNCT
ejpam-5090	173	24	.	.	PUNCT
ejpam-5090	174	1	hence	hence	ADV
ejpam-5090	174	2	,	,	PUNCT
ejpam-5090	174	3	m×n	m×n	PROPN
ejpam-5090	174	4	=	=	SYM
ejpam-5090	174	5	〈	〈	PROPN
ejpam-5090	174	6	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	174	7	)	)	PUNCT
ejpam-5090	174	8	,	,	PUNCT
ejpam-5090	174	9	ρ	ρ	PROPN
ejpam-5090	174	10	i	i	PROPN
ejpam-5090	174	11	(	(	PUNCT
ejpam-5090	174	12	m×n	m×n	PROPN
ejpam-5090	174	13	)	)	PUNCT
ejpam-5090	174	14	,	,	PUNCT
ejpam-5090	174	15	ρ	ρ	PROPN
ejpam-5090	174	16	t	t	PROPN
ejpam-5090	174	17	(	(	PUNCT
ejpam-5090	174	18	m×n	m×n	NOUN
ejpam-5090	174	19	)	)	PUNCT
ejpam-5090	174	20	〉	〉	NOUN
ejpam-5090	174	21	is	be	AUX
ejpam-5090	174	22	a	a	DET
ejpam-5090	174	23	fnink	fnink	NOUN
ejpam-5090	174	24	-	-	PUNCT
ejpam-5090	174	25	i	i	PRON
ejpam-5090	174	26	of	of	ADP
ejpam-5090	174	27	χ1	χ1	PROPN
ejpam-5090	174	28	×	×	PROPN
ejpam-5090	174	29	χ2	χ2	PROPN
ejpam-5090	174	30	.	.	PUNCT
ejpam-5090	175	1	theorem	theorem	VERB
ejpam-5090	175	2	5	5	NUM
ejpam-5090	175	3	.	.	PUNCT
ejpam-5090	176	1	let	let	VERB
ejpam-5090	176	2	m	m	PROPN
ejpam-5090	176	3	=	=	VERB
ejpam-5090	176	4	〈	〈	PROPN
ejpam-5090	176	5	ρtm	ρtm	NOUN
ejpam-5090	176	6	,	,	PUNCT
ejpam-5090	176	7	ρim	ρim	NOUN
ejpam-5090	176	8	,	,	PUNCT
ejpam-5090	176	9	ρfm	ρfm	ADP
ejpam-5090	176	10	〉	〉	NOUN
ejpam-5090	176	11	and	and	CCONJ
ejpam-5090	176	12	n	n	NOUN
ejpam-5090	176	13	=	=	PUNCT
ejpam-5090	176	14	〈	〈	PROPN
ejpam-5090	176	15	ρtn	ρtn	NOUN
ejpam-5090	176	16	,	,	PUNCT
ejpam-5090	176	17	ρ	ρ	PROPN
ejpam-5090	176	18	i	i	PROPN
ejpam-5090	176	19	n	n	CCONJ
ejpam-5090	176	20	,	,	PUNCT
ejpam-5090	176	21	ρ	ρ	PROPN
ejpam-5090	176	22	f	f	PROPN
ejpam-5090	176	23	n	n	PRON
ejpam-5090	176	24	〉	〉	NOUN
ejpam-5090	176	25	be	be	VERB
ejpam-5090	176	26	two	two	NUM
ejpam-5090	176	27	fnink	fnink	NOUN
ejpam-5090	176	28	-	-	PUNCT
ejpam-5090	176	29	is	is	NOUN
ejpam-5090	176	30	of	of	ADP
ejpam-5090	176	31	χ1	χ1	NOUN
ejpam-5090	176	32	and	and	CCONJ
ejpam-5090	176	33	χ2	χ2	PROPN
ejpam-5090	176	34	,	,	PUNCT
ejpam-5090	176	35	respectively	respectively	ADV
ejpam-5090	176	36	.	.	PUNCT
ejpam-5090	177	1	then	then	ADV
ejpam-5090	177	2	,	,	PUNCT
ejpam-5090	177	3	m	m	VERB
ejpam-5090	177	4	×	×	NOUN
ejpam-5090	177	5	n	n	CCONJ
ejpam-5090	177	6	=	=	PUNCT
ejpam-5090	177	7	〈	〈	PROPN
ejpam-5090	177	8	ρf(m×n	ρf(m×n	NUM
ejpam-5090	177	9	)	)	PUNCT
ejpam-5090	177	10	,	,	PUNCT
ejpam-5090	177	11	ρ	ρ	PROPN
ejpam-5090	177	12	i	i	PROPN
ejpam-5090	177	13	(	(	PUNCT
ejpam-5090	177	14	m×n	m×n	PROPN
ejpam-5090	177	15	)	)	PUNCT
ejpam-5090	177	16	,	,	PUNCT
ejpam-5090	177	17	ρ	ρ	PROPN
ejpam-5090	177	18	f	f	X
ejpam-5090	177	19	(	(	PUNCT
ejpam-5090	177	20	m×n	m×n	NOUN
ejpam-5090	177	21	)	)	PUNCT
ejpam-5090	177	22	〉	〉	NOUN
ejpam-5090	177	23	is	be	AUX
ejpam-5090	177	24	a	a	DET
ejpam-5090	177	25	fnink	fnink	NOUN
ejpam-5090	177	26	-	-	PUNCT
ejpam-5090	177	27	i	i	PRON
ejpam-5090	177	28	of	of	ADP
ejpam-5090	177	29	χ1	χ1	PROPN
ejpam-5090	177	30	×	×	PROPN
ejpam-5090	177	31	χ2	χ2	PROPN
ejpam-5090	177	32	,	,	PUNCT
ejpam-5090	177	33	where	where	SCONJ
ejpam-5090	177	34	ρf(m×n	ρf(m×n	NUM
ejpam-5090	177	35	)	)	PUNCT
ejpam-5090	177	36	=	=	SYM
ejpam-5090	177	37	1−	1−	NUM
ejpam-5090	177	38	ρf(m×n	ρf(m×n	NUM
ejpam-5090	177	39	)	)	PUNCT
ejpam-5090	177	40	.	.	PUNCT
ejpam-5090	178	1	proof	proof	NOUN
ejpam-5090	178	2	.	.	PUNCT
ejpam-5090	179	1	according	accord	VERB
ejpam-5090	179	2	to	to	ADP
ejpam-5090	179	3	theorem	theorem	ADJ
ejpam-5090	179	4	2	2	NUM
ejpam-5090	179	5	.	.	PUNCT
ejpam-5090	179	6	m×n	m×n	PROPN
ejpam-5090	179	7	=	=	SYM
ejpam-5090	179	8	〈	〈	PROPN
ejpam-5090	179	9	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	179	10	)	)	PUNCT
ejpam-5090	179	11	,	,	PUNCT
ejpam-5090	179	12	ρ	ρ	PROPN
ejpam-5090	179	13	i	i	PROPN
ejpam-5090	179	14	(	(	PUNCT
ejpam-5090	179	15	m×n	m×n	PROPN
ejpam-5090	179	16	)	)	PUNCT
ejpam-5090	179	17	,	,	PUNCT
ejpam-5090	179	18	ρ	ρ	PROPN
ejpam-5090	179	19	f	f	X
ejpam-5090	179	20	(	(	PUNCT
ejpam-5090	179	21	m×n	m×n	NOUN
ejpam-5090	179	22	)	)	PUNCT
ejpam-5090	179	23	〉	〉	NOUN
ejpam-5090	179	24	is	be	AUX
ejpam-5090	179	25	a	a	DET
ejpam-5090	179	26	fnink	fnink	NOUN
ejpam-5090	179	27	-	-	PUNCT
ejpam-5090	179	28	i	i	PRON
ejpam-5090	179	29	of	of	ADP
ejpam-5090	179	30	χ1	χ1	PROPN
ejpam-5090	179	31	×	×	PROPN
ejpam-5090	179	32	χ2	χ2	PROPN
ejpam-5090	179	33	.	.	PUNCT
ejpam-5090	180	1	then	then	ADV
ejpam-5090	180	2	,	,	PUNCT
ejpam-5090	180	3	ρf(m×n)(0	ρf(m×n)(0	PROPN
ejpam-5090	180	4	,	,	PUNCT
ejpam-5090	180	5	0	0	NUM
ejpam-5090	180	6	)	)	PUNCT
ejpam-5090	180	7	≥	≥	NOUN
ejpam-5090	180	8	ρf(m×n)(ϑ	ρf(m×n)(ϑ	NOUN
ejpam-5090	180	9	,	,	PUNCT
ejpam-5090	180	10	η	η	NOUN
ejpam-5090	180	11	)	)	PUNCT
ejpam-5090	180	12	1−	1−	NUM
ejpam-5090	180	13	ρfm×n(0	ρfm×n(0	NUM
ejpam-5090	180	14	,	,	PUNCT
ejpam-5090	180	15	0	0	NUM
ejpam-5090	180	16	)	)	PUNCT
ejpam-5090	180	17	≤	≤	NOUN
ejpam-5090	180	18	1−	1−	NUM
ejpam-5090	180	19	ρf(m)×n)(ϑ	ρf(m)×n)(ϑ	VERB
ejpam-5090	180	20	,	,	PUNCT
ejpam-5090	180	21	η	η	NOUN
ejpam-5090	180	22	)	)	PUNCT
ejpam-5090	180	23	m.	m.	NOUN
ejpam-5090	180	24	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	180	25	et	et	PROPN
ejpam-5090	180	26	al	al	PROPN
ejpam-5090	180	27	.	.	PUNCT
ejpam-5090	180	28	/	/	SYM
ejpam-5090	180	29	eur	eur	PROPN
ejpam-5090	180	30	.	.	PUNCT
ejpam-5090	181	1	j.	j.	PROPN
ejpam-5090	181	2	pure	pure	PROPN
ejpam-5090	181	3	appl	appl	PROPN
ejpam-5090	181	4	.	.	PROPN
ejpam-5090	181	5	math	math	PROPN
ejpam-5090	181	6	,	,	PUNCT
ejpam-5090	181	7	17	17	NUM
ejpam-5090	181	8	(	(	PUNCT
ejpam-5090	181	9	2	2	NUM
ejpam-5090	181	10	)	)	PUNCT
ejpam-5090	181	11	(	(	PUNCT
ejpam-5090	181	12	2024	2024	NUM
ejpam-5090	181	13	)	)	PUNCT
ejpam-5090	181	14	,	,	PUNCT
ejpam-5090	181	15	1113	1113	NUM
ejpam-5090	181	16	-	-	SYM
ejpam-5090	181	17	1128	1128	NUM
ejpam-5090	181	18	1123	1123	NUM
ejpam-5090	181	19	ρfm×n(0	ρfm×n(0	NUM
ejpam-5090	181	20	,	,	PUNCT
ejpam-5090	181	21	0	0	NUM
ejpam-5090	181	22	)	)	PUNCT
ejpam-5090	181	23	≤	≤	NOUN
ejpam-5090	182	1	ρf(m×n)(ϑ	ρf(m×n)(ϑ	VERB
ejpam-5090	182	2	,	,	PUNCT
ejpam-5090	182	3	η	η	NOUN
ejpam-5090	182	4	)	)	PUNCT
ejpam-5090	182	5	.	.	PUNCT
ejpam-5090	183	1	now	now	ADV
ejpam-5090	183	2	,	,	PUNCT
ejpam-5090	183	3	for	for	ADP
ejpam-5090	183	4	any	any	DET
ejpam-5090	183	5	(	(	PUNCT
ejpam-5090	183	6	ϑ1	ϑ1	NOUN
ejpam-5090	183	7	,	,	PUNCT
ejpam-5090	183	8	η1	η1	NOUN
ejpam-5090	183	9	)	)	PUNCT
ejpam-5090	183	10	,	,	PUNCT
ejpam-5090	183	11	(	(	PUNCT
ejpam-5090	183	12	ϑ2	ϑ2	NOUN
ejpam-5090	183	13	,	,	PUNCT
ejpam-5090	183	14	η2	η2	NOUN
ejpam-5090	183	15	)	)	PUNCT
ejpam-5090	183	16	,	,	PUNCT
ejpam-5090	183	17	(	(	PUNCT
ejpam-5090	183	18	ϑ3	ϑ3	PROPN
ejpam-5090	183	19	,	,	PUNCT
ejpam-5090	183	20	η3	η3	PROPN
ejpam-5090	183	21	)	)	PUNCT
ejpam-5090	183	22	∈	∈	PROPN
ejpam-5090	183	23	χ1	χ1	NOUN
ejpam-5090	183	24	×	×	NOUN
ejpam-5090	183	25	χ2	χ2	PROPN
ejpam-5090	183	26	.	.	PUNCT
ejpam-5090	184	1	we	we	PRON
ejpam-5090	184	2	have	have	AUX
ejpam-5090	184	3	ρf(m×n)(ϑ1	ρf(m×n)(ϑ1	VERB
ejpam-5090	184	4	,	,	PUNCT
ejpam-5090	184	5	η1	η1	NOUN
ejpam-5090	184	6	)	)	PUNCT
ejpam-5090	184	7	≥	≥	NOUN
ejpam-5090	184	8	max	max	PROPN
ejpam-5090	184	9	{	{	PUNCT
ejpam-5090	184	10	ρfm×n(((ϑ3	ρfm×n(((ϑ3	PROPN
ejpam-5090	184	11	,	,	PUNCT
ejpam-5090	184	12	η3	η3	PROPN
ejpam-5090	184	13	)	)	PUNCT
ejpam-5090	184	14	·	·	PUNCT
ejpam-5090	185	1	(	(	PUNCT
ejpam-5090	185	2	ϑ1	ϑ1	NOUN
ejpam-5090	185	3	,	,	PUNCT
ejpam-5090	185	4	η1	η1	NOUN
ejpam-5090	185	5	)	)	PUNCT
ejpam-5090	185	6	)	)	PUNCT
ejpam-5090	185	7	·	·	PUNCT
ejpam-5090	186	1	(	(	PUNCT
ejpam-5090	186	2	(	(	PUNCT
ejpam-5090	186	3	ϑ3	ϑ3	NOUN
ejpam-5090	186	4	,	,	PUNCT
ejpam-5090	186	5	η3	η3	PROPN
ejpam-5090	186	6	)	)	PUNCT
ejpam-5090	186	7	·	·	PUNCT
ejpam-5090	186	8	(	(	PUNCT
ejpam-5090	186	9	ϑ2	ϑ2	NOUN
ejpam-5090	186	10	,	,	PUNCT
ejpam-5090	186	11	η2	η2	NOUN
ejpam-5090	186	12	)	)	PUNCT
ejpam-5090	186	13	)	)	PUNCT
ejpam-5090	186	14	)	)	PUNCT
ejpam-5090	186	15	,	,	PUNCT
ejpam-5090	186	16	ρ	ρ	PROPN
ejpam-5090	186	17	f	f	PROPN
ejpam-5090	186	18	(	(	PUNCT
ejpam-5090	186	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	186	20	,	,	PUNCT
ejpam-5090	186	21	η2	η2	PROPN
ejpam-5090	186	22	)	)	PUNCT
ejpam-5090	186	23	}	}	PUNCT
ejpam-5090	186	24	1−	1−	NUM
ejpam-5090	186	25	ρf(m×n)(ϑ1	ρf(m×n)(ϑ1	NOUN
ejpam-5090	186	26	,	,	PUNCT
ejpam-5090	186	27	η1	η1	NOUN
ejpam-5090	186	28	)	)	PUNCT
ejpam-5090	186	29	≤	≤	NUM
ejpam-5090	186	30	1−max	1−max	NUM
ejpam-5090	186	31	{	{	PUNCT
ejpam-5090	186	32	ρf(m×n)(((ϑ3	ρf(m×n)(((ϑ3	PROPN
ejpam-5090	186	33	,	,	PUNCT
ejpam-5090	186	34	η3	η3	NOUN
ejpam-5090	186	35	)	)	PUNCT
ejpam-5090	186	36	·	·	PUNCT
ejpam-5090	186	37	(	(	PUNCT
ejpam-5090	186	38	ϑ1	ϑ1	NOUN
ejpam-5090	186	39	,	,	PUNCT
ejpam-5090	186	40	η1	η1	NOUN
ejpam-5090	186	41	)	)	PUNCT
ejpam-5090	186	42	)	)	PUNCT
ejpam-5090	186	43	·	·	PUNCT
ejpam-5090	187	1	(	(	PUNCT
ejpam-5090	187	2	(	(	PUNCT
ejpam-5090	187	3	ϑ3	ϑ3	NOUN
ejpam-5090	187	4	,	,	PUNCT
ejpam-5090	187	5	η3	η3	PROPN
ejpam-5090	187	6	)	)	PUNCT
ejpam-5090	187	7	·	·	PUNCT
ejpam-5090	187	8	(	(	PUNCT
ejpam-5090	187	9	ϑ2	ϑ2	NOUN
ejpam-5090	187	10	,	,	PUNCT
ejpam-5090	187	11	η2	η2	NOUN
ejpam-5090	187	12	)	)	PUNCT
ejpam-5090	187	13	)	)	PUNCT
ejpam-5090	187	14	)	)	PUNCT
ejpam-5090	187	15	,	,	PUNCT
ejpam-5090	187	16	ρ	ρ	PROPN
ejpam-5090	187	17	f	f	PROPN
ejpam-5090	187	18	(	(	PUNCT
ejpam-5090	187	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	187	20	,	,	PUNCT
ejpam-5090	187	21	η2	η2	PROPN
ejpam-5090	187	22	)	)	PUNCT
ejpam-5090	187	23	}	}	PUNCT
ejpam-5090	187	24	ρf(m×n)(ϑ1	ρf(m×n)(ϑ1	VERB
ejpam-5090	187	25	,	,	PUNCT
ejpam-5090	187	26	η1	η1	NOUN
ejpam-5090	187	27	)	)	PUNCT
ejpam-5090	187	28	≤	≤	NUM
ejpam-5090	187	29	min	min	NOUN
ejpam-5090	187	30	{	{	PUNCT
ejpam-5090	187	31	1−	1−	NUM
ejpam-5090	187	32	ρf(m×n)(((ϑ3	ρf(m×n)(((ϑ3	PROPN
ejpam-5090	187	33	,	,	PUNCT
ejpam-5090	187	34	η3	η3	NOUN
ejpam-5090	187	35	)	)	PUNCT
ejpam-5090	187	36	·	·	PUNCT
ejpam-5090	187	37	(	(	PUNCT
ejpam-5090	187	38	ϑ1	ϑ1	NOUN
ejpam-5090	187	39	,	,	PUNCT
ejpam-5090	187	40	η1	η1	NOUN
ejpam-5090	187	41	)	)	PUNCT
ejpam-5090	187	42	)	)	PUNCT
ejpam-5090	187	43	·	·	PUNCT
ejpam-5090	188	1	(	(	PUNCT
ejpam-5090	188	2	(	(	PUNCT
ejpam-5090	188	3	ϑ3	ϑ3	NOUN
ejpam-5090	188	4	,	,	PUNCT
ejpam-5090	188	5	η3	η3	PROPN
ejpam-5090	188	6	)	)	PUNCT
ejpam-5090	188	7	·	·	PUNCT
ejpam-5090	188	8	(	(	PUNCT
ejpam-5090	188	9	ϑ2	ϑ2	NOUN
ejpam-5090	188	10	,	,	PUNCT
ejpam-5090	188	11	η2	η2	NOUN
ejpam-5090	188	12	)	)	PUNCT
ejpam-5090	188	13	)	)	PUNCT
ejpam-5090	188	14	)	)	PUNCT
ejpam-5090	188	15	,	,	PUNCT
ejpam-5090	188	16	1−	1−	NUM
ejpam-5090	188	17	ρf(m×n)(ϑ2	ρf(m×n)(ϑ2	NOUN
ejpam-5090	188	18	,	,	PUNCT
ejpam-5090	188	19	η2	η2	PROPN
ejpam-5090	188	20	)	)	PUNCT
ejpam-5090	188	21	}	}	PUNCT
ejpam-5090	188	22	ρf(m×n)(ϑ1	ρf(m×n)(ϑ1	VERB
ejpam-5090	188	23	,	,	PUNCT
ejpam-5090	188	24	η1	η1	NOUN
ejpam-5090	188	25	)	)	PUNCT
ejpam-5090	188	26	≤	≤	NUM
ejpam-5090	188	27	min	min	NOUN
ejpam-5090	188	28	{	{	PUNCT
ejpam-5090	188	29	ρf(m×n)(((ϑ3	ρf(m×n)(((ϑ3	PROPN
ejpam-5090	188	30	,	,	PUNCT
ejpam-5090	188	31	η3	η3	NOUN
ejpam-5090	188	32	)	)	PUNCT
ejpam-5090	188	33	·	·	PUNCT
ejpam-5090	189	1	(	(	PUNCT
ejpam-5090	189	2	ϑ1	ϑ1	NOUN
ejpam-5090	189	3	,	,	PUNCT
ejpam-5090	189	4	η1	η1	NOUN
ejpam-5090	189	5	)	)	PUNCT
ejpam-5090	189	6	)	)	PUNCT
ejpam-5090	189	7	·	·	PUNCT
ejpam-5090	190	1	(	(	PUNCT
ejpam-5090	190	2	(	(	PUNCT
ejpam-5090	190	3	ϑ3	ϑ3	NOUN
ejpam-5090	190	4	,	,	PUNCT
ejpam-5090	190	5	η3	η3	PROPN
ejpam-5090	190	6	)	)	PUNCT
ejpam-5090	190	7	·	·	PUNCT
ejpam-5090	190	8	(	(	PUNCT
ejpam-5090	190	9	ϑ2	ϑ2	NOUN
ejpam-5090	190	10	,	,	PUNCT
ejpam-5090	190	11	η2	η2	NOUN
ejpam-5090	190	12	)	)	PUNCT
ejpam-5090	190	13	)	)	PUNCT
ejpam-5090	190	14	)	)	PUNCT
ejpam-5090	190	15	,	,	PUNCT
ejpam-5090	190	16	ρ	ρ	PROPN
ejpam-5090	190	17	f	f	PROPN
ejpam-5090	190	18	(	(	PUNCT
ejpam-5090	190	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	190	20	,	,	PUNCT
ejpam-5090	190	21	η2	η2	PROPN
ejpam-5090	190	22	)	)	PUNCT
ejpam-5090	190	23	}	}	PUNCT
ejpam-5090	190	24	.	.	PUNCT
ejpam-5090	191	1	hence	hence	ADV
ejpam-5090	191	2	,	,	PUNCT
ejpam-5090	191	3	m×n	m×n	PROPN
ejpam-5090	191	4	=	=	SYM
ejpam-5090	191	5	〈	〈	PROPN
ejpam-5090	191	6	ρf(m×n	ρf(m×n	PROPN
ejpam-5090	191	7	)	)	PUNCT
ejpam-5090	191	8	,	,	PUNCT
ejpam-5090	191	9	ρ	ρ	PROPN
ejpam-5090	191	10	i	i	PROPN
ejpam-5090	191	11	(	(	PUNCT
ejpam-5090	191	12	m×n	m×n	PROPN
ejpam-5090	191	13	)	)	PUNCT
ejpam-5090	191	14	,	,	PUNCT
ejpam-5090	191	15	ρ	ρ	PROPN
ejpam-5090	191	16	f	f	X
ejpam-5090	191	17	(	(	PUNCT
ejpam-5090	191	18	m×n	m×n	NOUN
ejpam-5090	191	19	)	)	PUNCT
ejpam-5090	191	20	〉	〉	NOUN
ejpam-5090	191	21	is	be	AUX
ejpam-5090	191	22	a	a	DET
ejpam-5090	191	23	fnink	fnink	NOUN
ejpam-5090	191	24	-	-	PUNCT
ejpam-5090	191	25	i	i	PRON
ejpam-5090	191	26	of	of	ADP
ejpam-5090	191	27	χ1	χ1	PROPN
ejpam-5090	191	28	×	×	PROPN
ejpam-5090	191	29	χ2	χ2	PROPN
ejpam-5090	191	30	.	.	PUNCT
ejpam-5090	192	1	theorem	theorem	VERB
ejpam-5090	192	2	6	6	NUM
ejpam-5090	192	3	.	.	PUNCT
ejpam-5090	193	1	let	let	VERB
ejpam-5090	193	2	m	m	PROPN
ejpam-5090	193	3	=	=	VERB
ejpam-5090	193	4	〈	〈	PROPN
ejpam-5090	193	5	ρtm	ρtm	NOUN
ejpam-5090	193	6	,	,	PUNCT
ejpam-5090	193	7	ρim	ρim	NOUN
ejpam-5090	193	8	,	,	PUNCT
ejpam-5090	193	9	ρfm	ρfm	ADP
ejpam-5090	193	10	〉	〉	NOUN
ejpam-5090	193	11	and	and	CCONJ
ejpam-5090	193	12	n	n	NOUN
ejpam-5090	193	13	=	=	PUNCT
ejpam-5090	193	14	〈	〈	PROPN
ejpam-5090	193	15	ρtn	ρtn	NOUN
ejpam-5090	193	16	,	,	PUNCT
ejpam-5090	193	17	ρ	ρ	PROPN
ejpam-5090	193	18	i	i	PROPN
ejpam-5090	193	19	n	n	CCONJ
ejpam-5090	193	20	,	,	PUNCT
ejpam-5090	193	21	ρ	ρ	PROPN
ejpam-5090	193	22	f	f	PROPN
ejpam-5090	193	23	n	n	PRON
ejpam-5090	193	24	〉	〉	NOUN
ejpam-5090	193	25	be	be	VERB
ejpam-5090	193	26	two	two	NUM
ejpam-5090	193	27	fnink	fnink	NOUN
ejpam-5090	193	28	-	-	PUNCT
ejpam-5090	193	29	is	is	NOUN
ejpam-5090	193	30	of	of	ADP
ejpam-5090	193	31	χ1	χ1	NOUN
ejpam-5090	193	32	and	and	CCONJ
ejpam-5090	193	33	χ2	χ2	PROPN
ejpam-5090	193	34	,	,	PUNCT
ejpam-5090	193	35	respectively	respectively	ADV
ejpam-5090	193	36	.	.	PUNCT
ejpam-5090	194	1	then	then	ADV
ejpam-5090	194	2	,	,	PUNCT
ejpam-5090	194	3	m	m	VERB
ejpam-5090	194	4	×	×	NOUN
ejpam-5090	194	5	n	n	CCONJ
ejpam-5090	194	6	=	=	PUNCT
ejpam-5090	194	7	〈	〈	PROPN
ejpam-5090	194	8	ρf(m×n	ρf(m×n	NUM
ejpam-5090	194	9	)	)	PUNCT
ejpam-5090	194	10	,	,	PUNCT
ejpam-5090	194	11	ρ	ρ	PROPN
ejpam-5090	194	12	i	i	PROPN
ejpam-5090	194	13	(	(	PUNCT
ejpam-5090	194	14	m×n	m×n	PROPN
ejpam-5090	194	15	)	)	PUNCT
ejpam-5090	194	16	,	,	PUNCT
ejpam-5090	194	17	ρ	ρ	PROPN
ejpam-5090	194	18	t	t	PROPN
ejpam-5090	194	19	(	(	PUNCT
ejpam-5090	194	20	m×n	m×n	NOUN
ejpam-5090	194	21	)	)	PUNCT
ejpam-5090	194	22	〉	〉	NOUN
ejpam-5090	194	23	is	be	AUX
ejpam-5090	194	24	a	a	DET
ejpam-5090	194	25	fnink	fnink	NOUN
ejpam-5090	194	26	-	-	PUNCT
ejpam-5090	194	27	i	i	PRON
ejpam-5090	194	28	of	of	ADP
ejpam-5090	194	29	χ1	χ1	PROPN
ejpam-5090	194	30	×	×	PROPN
ejpam-5090	194	31	χ2	χ2	PROPN
ejpam-5090	194	32	,	,	PUNCT
ejpam-5090	194	33	where	where	SCONJ
ejpam-5090	194	34	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	194	35	)	)	PUNCT
ejpam-5090	194	36	=	=	SYM
ejpam-5090	194	37	1−	1−	NUM
ejpam-5090	194	38	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	194	39	)	)	PUNCT
ejpam-5090	194	40	and	and	CCONJ
ejpam-5090	194	41	ρf(m×n	ρf(m×n	NUM
ejpam-5090	194	42	)	)	PUNCT
ejpam-5090	194	43	=	=	SYM
ejpam-5090	194	44	1−	1−	NUM
ejpam-5090	194	45	ρf(m×n	ρf(m×n	NUM
ejpam-5090	194	46	)	)	PUNCT
ejpam-5090	194	47	.	.	PUNCT
ejpam-5090	195	1	proof	proof	NOUN
ejpam-5090	195	2	.	.	PUNCT
ejpam-5090	196	1	the	the	DET
ejpam-5090	196	2	proof	proof	NOUN
ejpam-5090	196	3	is	be	AUX
ejpam-5090	196	4	produced	produce	VERB
ejpam-5090	196	5	by	by	ADP
ejpam-5090	196	6	using	use	VERB
ejpam-5090	196	7	theorem	theorem	ADJ
ejpam-5090	196	8	4	4	NUM
ejpam-5090	196	9	and	and	CCONJ
ejpam-5090	196	10	theorem	theorem	VERB
ejpam-5090	196	11	5	5	NUM
ejpam-5090	196	12	together	together	ADV
ejpam-5090	196	13	.	.	PUNCT
ejpam-5090	197	1	theorem	theorem	VERB
ejpam-5090	197	2	7	7	NUM
ejpam-5090	197	3	.	.	PUNCT
ejpam-5090	198	1	let	let	VERB
ejpam-5090	198	2	m	m	PRON
ejpam-5090	198	3	×n	×n	PROPN
ejpam-5090	198	4	=	=	PUNCT
ejpam-5090	198	5	〈	〈	NOUN
ejpam-5090	198	6	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	198	7	)	)	PUNCT
ejpam-5090	198	8	,	,	PUNCT
ejpam-5090	198	9	ρ	ρ	PROPN
ejpam-5090	198	10	i	i	PROPN
ejpam-5090	198	11	(	(	PUNCT
ejpam-5090	198	12	m×n	m×n	PROPN
ejpam-5090	198	13	)	)	PUNCT
ejpam-5090	198	14	,	,	PUNCT
ejpam-5090	198	15	ρ	ρ	PROPN
ejpam-5090	198	16	f	f	X
ejpam-5090	198	17	(	(	PUNCT
ejpam-5090	198	18	m×n	m×n	NOUN
ejpam-5090	198	19	)	)	PUNCT
ejpam-5090	198	20	〉	〉	NOUN
ejpam-5090	198	21	be	be	VERB
ejpam-5090	198	22	a	a	DET
ejpam-5090	198	23	fnink	fnink	NOUN
ejpam-5090	198	24	-	-	PUNCT
ejpam-5090	198	25	i	i	PRON
ejpam-5090	198	26	of	of	ADP
ejpam-5090	198	27	χ1	χ1	PROPN
ejpam-5090	198	28	×	×	PROPN
ejpam-5090	198	29	χ2	χ2	PROPN
ejpam-5090	198	30	.	.	PUNCT
ejpam-5090	199	1	then	then	ADV
ejpam-5090	199	2	,	,	PUNCT
ejpam-5090	199	3	(	(	PUNCT
ejpam-5090	199	4	m×n)s	m×n)s	NOUN
ejpam-5090	199	5	=	=	PUNCT
ejpam-5090	199	6	〈	〈	PROPN
ejpam-5090	199	7	ρt(m×n)s	ρt(m×n)s	PROPN
ejpam-5090	199	8	,	,	PUNCT
ejpam-5090	199	9	ρ	ρ	PROPN
ejpam-5090	199	10	i	i	PROPN
ejpam-5090	199	11	(	(	PUNCT
ejpam-5090	199	12	m×n)s	m×n)s	PROPN
ejpam-5090	199	13	,	,	PUNCT
ejpam-5090	199	14	ρ	ρ	PROPN
ejpam-5090	199	15	f	f	PROPN
ejpam-5090	199	16	(	(	PUNCT
ejpam-5090	199	17	m×n)s	m×n)s	NOUN
ejpam-5090	199	18	〉	〉	NOUN
ejpam-5090	199	19	is	be	AUX
ejpam-5090	199	20	a	a	DET
ejpam-5090	199	21	fnink	fnink	NOUN
ejpam-5090	199	22	-	-	PUNCT
ejpam-5090	199	23	i	i	PRON
ejpam-5090	199	24	of	of	ADP
ejpam-5090	199	25	χ1	χ1	PROPN
ejpam-5090	199	26	×	×	PROPN
ejpam-5090	199	27	χ2	χ2	PROPN
ejpam-5090	199	28	.	.	PUNCT
ejpam-5090	200	1	proof	proof	NOUN
ejpam-5090	200	2	.	.	PUNCT
ejpam-5090	201	1	for	for	ADP
ejpam-5090	201	2	any	any	DET
ejpam-5090	201	3	(	(	PUNCT
ejpam-5090	201	4	ϑ	ϑ	X
ejpam-5090	201	5	,	,	PUNCT
ejpam-5090	201	6	η	η	NOUN
ejpam-5090	201	7	)	)	PUNCT
ejpam-5090	201	8	∈	∈	PROPN
ejpam-5090	201	9	χ1	χ1	NOUN
ejpam-5090	201	10	×	×	NOUN
ejpam-5090	201	11	χ2	χ2	PROPN
ejpam-5090	201	12	.	.	PUNCT
ejpam-5090	202	1	then	then	ADV
ejpam-5090	202	2	,	,	PUNCT
ejpam-5090	202	3	ρt(m×n)(0	ρt(m×n)(0	PROPN
ejpam-5090	202	4	,	,	PUNCT
ejpam-5090	202	5	0	0	NUM
ejpam-5090	202	6	)	)	PUNCT
ejpam-5090	202	7	≤	≤	NUM
ejpam-5090	202	8	ρt(m×n)(ϑ	ρt(m×n)(ϑ	PROPN
ejpam-5090	202	9	,	,	PUNCT
ejpam-5090	202	10	η	η	NOUN
ejpam-5090	202	11	)	)	PUNCT
ejpam-5090	202	12	{	{	PUNCT
ejpam-5090	202	13	ρt(m×n)(0	ρt(m×n)(0	PROPN
ejpam-5090	202	14	,	,	PUNCT
ejpam-5090	202	15	0	0	NUM
ejpam-5090	202	16	)	)	PUNCT
ejpam-5090	202	17	}	}	PUNCT
ejpam-5090	202	18	s	s	PART
ejpam-5090	202	19	≤	≤	NOUN
ejpam-5090	202	20	{	{	PUNCT
ejpam-5090	202	21	ρt(m×n)(ϑ	ρt(m×n)(ϑ	PROPN
ejpam-5090	202	22	,	,	PUNCT
ejpam-5090	202	23	η	η	NOUN
ejpam-5090	202	24	)	)	PUNCT
ejpam-5090	202	25	}	}	PUNCT
ejpam-5090	202	26	s	s	PART
ejpam-5090	202	27	{	{	PUNCT
ejpam-5090	202	28	ρt(m×n)(0	ρt(m×n)(0	PROPN
ejpam-5090	202	29	,	,	PUNCT
ejpam-5090	202	30	0	0	NUM
ejpam-5090	202	31	)	)	PUNCT
ejpam-5090	202	32	s	s	PART
ejpam-5090	202	33	}	}	PUNCT
ejpam-5090	202	34	≤	≤	NOUN
ejpam-5090	202	35	{	{	PUNCT
ejpam-5090	202	36	ρt(m×n)(ϑ	ρt(m×n)(ϑ	PROPN
ejpam-5090	202	37	,	,	PUNCT
ejpam-5090	202	38	η	η	NOUN
ejpam-5090	202	39	)	)	PUNCT
ejpam-5090	202	40	s	s	PART
ejpam-5090	202	41	}	}	PUNCT
ejpam-5090	202	42	{	{	PUNCT
ejpam-5090	202	43	ρt(m×n)s(0	ρt(m×n)s(0	PROPN
ejpam-5090	202	44	,	,	PUNCT
ejpam-5090	202	45	0	0	NUM
ejpam-5090	202	46	)	)	PUNCT
ejpam-5090	202	47	}	}	PUNCT
ejpam-5090	202	48	≤	≤	NOUN
ejpam-5090	202	49	{	{	PUNCT
ejpam-5090	202	50	ρt(m×n)s(ϑ	ρt(m×n)s(ϑ	PROPN
ejpam-5090	202	51	,	,	PUNCT
ejpam-5090	202	52	η	η	NOUN
ejpam-5090	202	53	)	)	PUNCT
ejpam-5090	202	54	}	}	PUNCT
ejpam-5090	202	55	,	,	PUNCT
ejpam-5090	202	56	ρi(m×n)(0	ρi(m×n)(0	PROPN
ejpam-5090	202	57	,	,	PUNCT
ejpam-5090	202	58	0	0	NUM
ejpam-5090	202	59	)	)	PUNCT
ejpam-5090	202	60	≥	≥	NOUN
ejpam-5090	202	61	ρi(m×n)(ϑ	ρi(m×n)(ϑ	PROPN
ejpam-5090	202	62	,	,	PUNCT
ejpam-5090	202	63	η	η	NOUN
ejpam-5090	202	64	)	)	PUNCT
ejpam-5090	202	65	{	{	PUNCT
ejpam-5090	202	66	ρi(m×n)(0	ρi(m×n)(0	PROPN
ejpam-5090	202	67	,	,	PUNCT
ejpam-5090	202	68	0	0	NUM
ejpam-5090	202	69	)	)	PUNCT
ejpam-5090	202	70	}	}	PUNCT
ejpam-5090	202	71	s	s	PART
ejpam-5090	202	72	≥	≥	NOUN
ejpam-5090	202	73	{	{	PUNCT
ejpam-5090	202	74	ρi(m×n)(ϑ	ρi(m×n)(ϑ	PROPN
ejpam-5090	202	75	,	,	PUNCT
ejpam-5090	202	76	η	η	NOUN
ejpam-5090	202	77	)	)	PUNCT
ejpam-5090	202	78	}	}	PUNCT
ejpam-5090	202	79	s	s	PART
ejpam-5090	202	80	{	{	PUNCT
ejpam-5090	202	81	ρi(m×n)(0	ρi(m×n)(0	NOUN
ejpam-5090	202	82	,	,	PUNCT
ejpam-5090	202	83	0	0	NUM
ejpam-5090	202	84	)	)	PUNCT
ejpam-5090	202	85	s	s	PART
ejpam-5090	202	86	}	}	PUNCT
ejpam-5090	202	87	≥	≥	X
ejpam-5090	202	88	{	{	PUNCT
ejpam-5090	202	89	ρi(m×n)(ϑ	ρi(m×n)(ϑ	PROPN
ejpam-5090	202	90	,	,	PUNCT
ejpam-5090	202	91	η	η	PROPN
ejpam-5090	202	92	)	)	PUNCT
ejpam-5090	202	93	s	s	PART
ejpam-5090	202	94	}	}	PUNCT
ejpam-5090	202	95	{	{	PUNCT
ejpam-5090	202	96	ρi(m×n)s(0	ρi(m×n)s(0	PROPN
ejpam-5090	202	97	,	,	PUNCT
ejpam-5090	202	98	0	0	NUM
ejpam-5090	202	99	)	)	PUNCT
ejpam-5090	202	100	}	}	PUNCT
ejpam-5090	202	101	≥	≥	X
ejpam-5090	202	102	{	{	PUNCT
ejpam-5090	202	103	ρi(m×n)s(ϑ	ρi(m×n)s(ϑ	PROPN
ejpam-5090	202	104	,	,	PUNCT
ejpam-5090	202	105	η	η	NOUN
ejpam-5090	202	106	)	)	PUNCT
ejpam-5090	202	107	}	}	PUNCT
ejpam-5090	202	108	and	and	CCONJ
ejpam-5090	202	109	ρf(m×n)(0	ρf(m×n)(0	NUM
ejpam-5090	202	110	,	,	PUNCT
ejpam-5090	202	111	0	0	NUM
ejpam-5090	202	112	)	)	PUNCT
ejpam-5090	202	113	≥	≥	NOUN
ejpam-5090	202	114	ρf(m×n)(ϑ	ρf(m×n)(ϑ	NOUN
ejpam-5090	202	115	,	,	PUNCT
ejpam-5090	202	116	η	η	NOUN
ejpam-5090	202	117	)	)	PUNCT
ejpam-5090	202	118	m.	m.	NOUN
ejpam-5090	202	119	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	202	120	et	et	PROPN
ejpam-5090	202	121	al	al	PROPN
ejpam-5090	202	122	.	.	PUNCT
ejpam-5090	202	123	/	/	SYM
ejpam-5090	202	124	eur	eur	PROPN
ejpam-5090	202	125	.	.	PUNCT
ejpam-5090	203	1	j.	j.	PROPN
ejpam-5090	203	2	pure	pure	PROPN
ejpam-5090	203	3	appl	appl	PROPN
ejpam-5090	203	4	.	.	PROPN
ejpam-5090	203	5	math	math	PROPN
ejpam-5090	203	6	,	,	PUNCT
ejpam-5090	203	7	17	17	NUM
ejpam-5090	203	8	(	(	PUNCT
ejpam-5090	203	9	2	2	NUM
ejpam-5090	203	10	)	)	PUNCT
ejpam-5090	203	11	(	(	PUNCT
ejpam-5090	203	12	2024	2024	NUM
ejpam-5090	203	13	)	)	PUNCT
ejpam-5090	203	14	,	,	PUNCT
ejpam-5090	203	15	1113	1113	NUM
ejpam-5090	203	16	-	-	SYM
ejpam-5090	203	17	1128	1128	NUM
ejpam-5090	203	18	1124	1124	NUM
ejpam-5090	203	19	{	{	PUNCT
ejpam-5090	203	20	ρf(m×n)(0	ρf(m×n)(0	PROPN
ejpam-5090	203	21	,	,	PUNCT
ejpam-5090	203	22	0	0	NUM
ejpam-5090	203	23	)	)	PUNCT
ejpam-5090	203	24	}	}	PUNCT
ejpam-5090	203	25	s	s	PART
ejpam-5090	203	26	≥	≥	NOUN
ejpam-5090	203	27	{	{	PUNCT
ejpam-5090	203	28	ρf(m×n)(ϑ	ρf(m×n)(ϑ	PROPN
ejpam-5090	203	29	,	,	PUNCT
ejpam-5090	203	30	η	η	NOUN
ejpam-5090	203	31	)	)	PUNCT
ejpam-5090	203	32	}	}	PUNCT
ejpam-5090	203	33	s	s	PART
ejpam-5090	203	34	{	{	PUNCT
ejpam-5090	203	35	ρf(m×n)(0	ρf(m×n)(0	PROPN
ejpam-5090	203	36	,	,	PUNCT
ejpam-5090	203	37	0	0	NUM
ejpam-5090	203	38	)	)	PUNCT
ejpam-5090	203	39	s	s	PART
ejpam-5090	203	40	}	}	PUNCT
ejpam-5090	203	41	≥	≥	X
ejpam-5090	203	42	{	{	PUNCT
ejpam-5090	203	43	ρf(m×n)(ϑ	ρf(m×n)(ϑ	PROPN
ejpam-5090	203	44	,	,	PUNCT
ejpam-5090	203	45	η	η	NOUN
ejpam-5090	203	46	)	)	PUNCT
ejpam-5090	203	47	s	s	AUX
ejpam-5090	203	48	}	}	PUNCT
ejpam-5090	203	49	{	{	PUNCT
ejpam-5090	203	50	ρf(m×n)s(0	ρf(m×n)s(0	ADP
ejpam-5090	203	51	,	,	PUNCT
ejpam-5090	203	52	0	0	NUM
ejpam-5090	203	53	)	)	PUNCT
ejpam-5090	203	54	}	}	PUNCT
ejpam-5090	203	55	≥	≥	X
ejpam-5090	203	56	{	{	PUNCT
ejpam-5090	203	57	ρf(m×n)s(ϑ	ρf(m×n)s(ϑ	X
ejpam-5090	203	58	,	,	PUNCT
ejpam-5090	203	59	η	η	NOUN
ejpam-5090	203	60	)	)	PUNCT
ejpam-5090	203	61	}	}	PUNCT
ejpam-5090	203	62	.	.	PUNCT
ejpam-5090	204	1	if	if	SCONJ
ejpam-5090	204	2	(	(	PUNCT
ejpam-5090	204	3	ϑ1	ϑ1	NOUN
ejpam-5090	204	4	,	,	PUNCT
ejpam-5090	204	5	η1	η1	NOUN
ejpam-5090	204	6	)	)	PUNCT
ejpam-5090	204	7	,	,	PUNCT
ejpam-5090	204	8	(	(	PUNCT
ejpam-5090	204	9	ϑ2	ϑ2	NOUN
ejpam-5090	204	10	,	,	PUNCT
ejpam-5090	204	11	η2	η2	PROPN
ejpam-5090	204	12	)	)	PUNCT
ejpam-5090	204	13	and	and	CCONJ
ejpam-5090	204	14	(	(	PUNCT
ejpam-5090	204	15	ϑ3	ϑ3	PROPN
ejpam-5090	204	16	,	,	PUNCT
ejpam-5090	204	17	η3	η3	PROPN
ejpam-5090	204	18	)	)	PUNCT
ejpam-5090	204	19	∈	∈	PROPN
ejpam-5090	204	20	χ1	χ1	NOUN
ejpam-5090	204	21	×	×	NOUN
ejpam-5090	204	22	χ2	χ2	PROPN
ejpam-5090	204	23	,	,	PUNCT
ejpam-5090	204	24	then	then	ADV
ejpam-5090	204	25	{	{	PUNCT
ejpam-5090	204	26	ρt(m×n)(ϑ1	ρt(m×n)(ϑ1	ADJ
ejpam-5090	204	27	,	,	PUNCT
ejpam-5090	204	28	η1	η1	NOUN
ejpam-5090	204	29	)	)	PUNCT
ejpam-5090	204	30	}	}	PUNCT
ejpam-5090	204	31	s	s	PART
ejpam-5090	204	32	≤	≤	NUM
ejpam-5090	204	33	min	min	NOUN
ejpam-5090	204	34	{	{	PUNCT
ejpam-5090	204	35	ρt(m×n)(((ϑ3	ρt(m×n)(((ϑ3	PROPN
ejpam-5090	204	36	,	,	PUNCT
ejpam-5090	204	37	η3	η3	PROPN
ejpam-5090	204	38	)	)	PUNCT
ejpam-5090	204	39	·	·	PUNCT
ejpam-5090	205	1	(	(	PUNCT
ejpam-5090	205	2	ϑ1	ϑ1	NOUN
ejpam-5090	205	3	,	,	PUNCT
ejpam-5090	205	4	η1	η1	NOUN
ejpam-5090	205	5	)	)	PUNCT
ejpam-5090	205	6	)	)	PUNCT
ejpam-5090	205	7	·	·	PUNCT
ejpam-5090	206	1	(	(	PUNCT
ejpam-5090	206	2	(	(	PUNCT
ejpam-5090	206	3	ϑ3	ϑ3	NOUN
ejpam-5090	206	4	,	,	PUNCT
ejpam-5090	206	5	η3	η3	PROPN
ejpam-5090	206	6	)	)	PUNCT
ejpam-5090	206	7	·	·	PUNCT
ejpam-5090	206	8	(	(	PUNCT
ejpam-5090	206	9	ϑ2	ϑ2	NOUN
ejpam-5090	206	10	,	,	PUNCT
ejpam-5090	206	11	η2	η2	NOUN
ejpam-5090	206	12	)	)	PUNCT
ejpam-5090	206	13	)	)	PUNCT
ejpam-5090	206	14	)	)	PUNCT
ejpam-5090	206	15	,	,	PUNCT
ejpam-5090	206	16	ρ	ρ	PROPN
ejpam-5090	206	17	t	t	PROPN
ejpam-5090	206	18	(	(	PUNCT
ejpam-5090	206	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	206	20	,	,	PUNCT
ejpam-5090	206	21	η2	η2	PROPN
ejpam-5090	206	22	)	)	PUNCT
ejpam-5090	206	23	}	}	PUNCT
ejpam-5090	206	24	s	s	PART
ejpam-5090	206	25	{	{	PUNCT
ejpam-5090	206	26	ρt(m×n)(ϑ1	ρt(m×n)(ϑ1	ADJ
ejpam-5090	206	27	,	,	PUNCT
ejpam-5090	206	28	η1	η1	NOUN
ejpam-5090	206	29	)	)	PUNCT
ejpam-5090	206	30	s	s	PART
ejpam-5090	206	31	}	}	PUNCT
ejpam-5090	206	32	≤	≤	NUM
ejpam-5090	206	33	min	min	NOUN
ejpam-5090	206	34	{	{	PUNCT
ejpam-5090	206	35	ρt(m×n)(((ϑ3	ρt(m×n)(((ϑ3	PROPN
ejpam-5090	206	36	,	,	PUNCT
ejpam-5090	206	37	η3	η3	PROPN
ejpam-5090	206	38	)	)	PUNCT
ejpam-5090	206	39	·	·	PUNCT
ejpam-5090	206	40	(	(	PUNCT
ejpam-5090	206	41	ϑ1	ϑ1	NOUN
ejpam-5090	206	42	,	,	PUNCT
ejpam-5090	206	43	η1	η1	NOUN
ejpam-5090	206	44	)	)	PUNCT
ejpam-5090	206	45	)	)	PUNCT
ejpam-5090	206	46	·	·	PUNCT
ejpam-5090	207	1	(	(	PUNCT
ejpam-5090	207	2	(	(	PUNCT
ejpam-5090	207	3	ϑ3	ϑ3	NOUN
ejpam-5090	207	4	,	,	PUNCT
ejpam-5090	207	5	η3	η3	PROPN
ejpam-5090	207	6	)	)	PUNCT
ejpam-5090	207	7	·	·	PUNCT
ejpam-5090	207	8	(	(	PUNCT
ejpam-5090	207	9	ϑ2	ϑ2	NOUN
ejpam-5090	207	10	,	,	PUNCT
ejpam-5090	207	11	η2	η2	NOUN
ejpam-5090	207	12	)	)	PUNCT
ejpam-5090	207	13	)	)	PUNCT
ejpam-5090	207	14	)	)	PUNCT
ejpam-5090	208	1	s	s	X
ejpam-5090	208	2	,	,	PUNCT
ejpam-5090	208	3	ρt(m×n)(ϑ2	ρt(m×n)(ϑ2	NOUN
ejpam-5090	208	4	,	,	PUNCT
ejpam-5090	208	5	η2	η2	PROPN
ejpam-5090	208	6	)	)	PUNCT
ejpam-5090	208	7	s	s	PART
ejpam-5090	208	8	}	}	PUNCT
ejpam-5090	208	9	{	{	PUNCT
ejpam-5090	208	10	ρt(m×n)s(ϑ1	ρt(m×n)s(ϑ1	NOUN
ejpam-5090	208	11	,	,	PUNCT
ejpam-5090	208	12	η1	η1	NOUN
ejpam-5090	208	13	)	)	PUNCT
ejpam-5090	208	14	}	}	PUNCT
ejpam-5090	208	15	≤	≤	NUM
ejpam-5090	208	16	min	min	NOUN
ejpam-5090	208	17	{	{	PUNCT
ejpam-5090	208	18	ρt(m×n)s(((ϑ3	ρt(m×n)s(((ϑ3	PROPN
ejpam-5090	208	19	,	,	PUNCT
ejpam-5090	208	20	η3	η3	PROPN
ejpam-5090	208	21	)	)	PUNCT
ejpam-5090	208	22	·	·	PUNCT
ejpam-5090	209	1	(	(	PUNCT
ejpam-5090	209	2	ϑ1	ϑ1	NOUN
ejpam-5090	209	3	,	,	PUNCT
ejpam-5090	209	4	η1	η1	NOUN
ejpam-5090	209	5	)	)	PUNCT
ejpam-5090	209	6	)	)	PUNCT
ejpam-5090	209	7	·	·	PUNCT
ejpam-5090	210	1	(	(	PUNCT
ejpam-5090	210	2	(	(	PUNCT
ejpam-5090	210	3	ϑ3	ϑ3	NOUN
ejpam-5090	210	4	,	,	PUNCT
ejpam-5090	210	5	η3	η3	PROPN
ejpam-5090	210	6	)	)	PUNCT
ejpam-5090	210	7	·	·	PUNCT
ejpam-5090	210	8	(	(	PUNCT
ejpam-5090	210	9	ϑ2	ϑ2	NOUN
ejpam-5090	210	10	,	,	PUNCT
ejpam-5090	210	11	η2	η2	NOUN
ejpam-5090	210	12	)	)	PUNCT
ejpam-5090	210	13	)	)	PUNCT
ejpam-5090	210	14	)	)	PUNCT
ejpam-5090	210	15	,	,	PUNCT
ejpam-5090	210	16	ρ	ρ	PROPN
ejpam-5090	210	17	t	t	PROPN
ejpam-5090	210	18	(	(	PUNCT
ejpam-5090	210	19	m×n)s(ϑ2	m×n)s(ϑ2	PROPN
ejpam-5090	210	20	,	,	PUNCT
ejpam-5090	210	21	η2	η2	PROPN
ejpam-5090	210	22	)	)	PUNCT
ejpam-5090	210	23	}	}	PUNCT
ejpam-5090	210	24	,	,	PUNCT
ejpam-5090	210	25	{	{	PUNCT
ejpam-5090	210	26	ρi(m×n)(ϑ1	ρi(m×n)(ϑ1	NOUN
ejpam-5090	210	27	,	,	PUNCT
ejpam-5090	210	28	η1	η1	NOUN
ejpam-5090	210	29	)	)	PUNCT
ejpam-5090	210	30	}	}	PUNCT
ejpam-5090	210	31	s	s	PART
ejpam-5090	210	32	≥	≥	NOUN
ejpam-5090	210	33	max	max	PROPN
ejpam-5090	210	34	{	{	PUNCT
ejpam-5090	210	35	ρi(m×n)(((ϑ3	ρi(m×n)(((ϑ3	PROPN
ejpam-5090	210	36	,	,	PUNCT
ejpam-5090	210	37	η3	η3	PROPN
ejpam-5090	210	38	)	)	PUNCT
ejpam-5090	210	39	·	·	PUNCT
ejpam-5090	210	40	(	(	PUNCT
ejpam-5090	210	41	ϑ1	ϑ1	NOUN
ejpam-5090	210	42	,	,	PUNCT
ejpam-5090	210	43	η1	η1	NOUN
ejpam-5090	210	44	)	)	PUNCT
ejpam-5090	210	45	)	)	PUNCT
ejpam-5090	210	46	·	·	PUNCT
ejpam-5090	211	1	(	(	PUNCT
ejpam-5090	211	2	(	(	PUNCT
ejpam-5090	211	3	ϑ3	ϑ3	NOUN
ejpam-5090	211	4	,	,	PUNCT
ejpam-5090	211	5	η3	η3	PROPN
ejpam-5090	211	6	)	)	PUNCT
ejpam-5090	211	7	·	·	PUNCT
ejpam-5090	211	8	(	(	PUNCT
ejpam-5090	211	9	ϑ2	ϑ2	NOUN
ejpam-5090	211	10	,	,	PUNCT
ejpam-5090	211	11	η2	η2	NOUN
ejpam-5090	211	12	)	)	PUNCT
ejpam-5090	211	13	)	)	PUNCT
ejpam-5090	211	14	)	)	PUNCT
ejpam-5090	211	15	,	,	PUNCT
ejpam-5090	211	16	ρ	ρ	PROPN
ejpam-5090	211	17	i	i	PROPN
ejpam-5090	211	18	(	(	PUNCT
ejpam-5090	211	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	211	20	,	,	PUNCT
ejpam-5090	211	21	η2	η2	PROPN
ejpam-5090	211	22	)	)	PUNCT
ejpam-5090	211	23	}	}	PUNCT
ejpam-5090	211	24	s	s	PART
ejpam-5090	211	25	{	{	PUNCT
ejpam-5090	211	26	ρi(m×n)(ϑ1	ρi(m×n)(ϑ1	PROPN
ejpam-5090	211	27	,	,	PUNCT
ejpam-5090	211	28	η1	η1	NOUN
ejpam-5090	211	29	)	)	PUNCT
ejpam-5090	211	30	s	s	PART
ejpam-5090	211	31	}	}	PUNCT
ejpam-5090	211	32	≥	≥	PROPN
ejpam-5090	211	33	max	max	PROPN
ejpam-5090	211	34	{	{	PUNCT
ejpam-5090	211	35	ρi(m×n)(((ϑ3	ρi(m×n)(((ϑ3	PROPN
ejpam-5090	211	36	,	,	PUNCT
ejpam-5090	211	37	η3	η3	PROPN
ejpam-5090	211	38	)	)	PUNCT
ejpam-5090	211	39	·	·	PUNCT
ejpam-5090	211	40	(	(	PUNCT
ejpam-5090	211	41	ϑ1	ϑ1	NOUN
ejpam-5090	211	42	,	,	PUNCT
ejpam-5090	211	43	η1	η1	NOUN
ejpam-5090	211	44	)	)	PUNCT
ejpam-5090	211	45	)	)	PUNCT
ejpam-5090	211	46	·	·	PUNCT
ejpam-5090	212	1	(	(	PUNCT
ejpam-5090	212	2	(	(	PUNCT
ejpam-5090	212	3	ϑ3	ϑ3	NOUN
ejpam-5090	212	4	,	,	PUNCT
ejpam-5090	212	5	η3	η3	PROPN
ejpam-5090	212	6	)	)	PUNCT
ejpam-5090	212	7	·	·	PUNCT
ejpam-5090	212	8	(	(	PUNCT
ejpam-5090	212	9	ϑ2	ϑ2	NOUN
ejpam-5090	212	10	,	,	PUNCT
ejpam-5090	212	11	η2	η2	NOUN
ejpam-5090	212	12	)	)	PUNCT
ejpam-5090	212	13	)	)	PUNCT
ejpam-5090	212	14	)	)	PUNCT
ejpam-5090	213	1	s	s	X
ejpam-5090	213	2	,	,	PUNCT
ejpam-5090	213	3	ρi(m×n)(ϑ2	ρi(m×n)(ϑ2	ADJ
ejpam-5090	213	4	,	,	PUNCT
ejpam-5090	213	5	η2	η2	X
ejpam-5090	213	6	)	)	PUNCT
ejpam-5090	213	7	s	s	PART
ejpam-5090	213	8	}	}	PUNCT
ejpam-5090	213	9	{	{	PUNCT
ejpam-5090	213	10	ρi(m×n)s(ϑ1	ρi(m×n)s(ϑ1	NOUN
ejpam-5090	213	11	,	,	PUNCT
ejpam-5090	213	12	η1	η1	NOUN
ejpam-5090	213	13	)	)	PUNCT
ejpam-5090	213	14	}	}	PUNCT
ejpam-5090	213	15	≥	≥	PROPN
ejpam-5090	213	16	max	max	PROPN
ejpam-5090	213	17	{	{	PUNCT
ejpam-5090	213	18	ρi(m×n)s(((ϑ3	ρi(m×n)s(((ϑ3	PROPN
ejpam-5090	213	19	,	,	PUNCT
ejpam-5090	213	20	η3	η3	PROPN
ejpam-5090	213	21	)	)	PUNCT
ejpam-5090	213	22	·	·	PUNCT
ejpam-5090	214	1	(	(	PUNCT
ejpam-5090	214	2	ϑ1	ϑ1	NOUN
ejpam-5090	214	3	,	,	PUNCT
ejpam-5090	214	4	η1	η1	NOUN
ejpam-5090	214	5	)	)	PUNCT
ejpam-5090	214	6	)	)	PUNCT
ejpam-5090	214	7	·	·	PUNCT
ejpam-5090	215	1	(	(	PUNCT
ejpam-5090	215	2	(	(	PUNCT
ejpam-5090	215	3	ϑ3	ϑ3	NOUN
ejpam-5090	215	4	,	,	PUNCT
ejpam-5090	215	5	η3	η3	PROPN
ejpam-5090	215	6	)	)	PUNCT
ejpam-5090	215	7	·	·	PUNCT
ejpam-5090	215	8	(	(	PUNCT
ejpam-5090	215	9	ϑ2	ϑ2	NOUN
ejpam-5090	215	10	,	,	PUNCT
ejpam-5090	215	11	η2	η2	NOUN
ejpam-5090	215	12	)	)	PUNCT
ejpam-5090	215	13	)	)	PUNCT
ejpam-5090	215	14	)	)	PUNCT
ejpam-5090	215	15	,	,	PUNCT
ejpam-5090	215	16	ρ	ρ	PROPN
ejpam-5090	215	17	i	i	PROPN
ejpam-5090	215	18	(	(	PUNCT
ejpam-5090	215	19	m×n)s(ϑ2	m×n)s(ϑ2	NOUN
ejpam-5090	215	20	,	,	PUNCT
ejpam-5090	215	21	η2	η2	PROPN
ejpam-5090	215	22	)	)	PUNCT
ejpam-5090	215	23	}	}	PUNCT
ejpam-5090	215	24	and	and	CCONJ
ejpam-5090	215	25	{	{	PUNCT
ejpam-5090	215	26	ρf(m×n)(ϑ1	ρf(m×n)(ϑ1	NOUN
ejpam-5090	215	27	,	,	PUNCT
ejpam-5090	215	28	η1	η1	NOUN
ejpam-5090	215	29	)	)	PUNCT
ejpam-5090	215	30	}	}	PUNCT
ejpam-5090	215	31	s	s	PART
ejpam-5090	215	32	≥	≥	NOUN
ejpam-5090	215	33	max	max	PROPN
ejpam-5090	215	34	{	{	PUNCT
ejpam-5090	215	35	ρf(m×n)(((ϑ3	ρf(m×n)(((ϑ3	PROPN
ejpam-5090	215	36	,	,	PUNCT
ejpam-5090	215	37	η3	η3	NOUN
ejpam-5090	215	38	)	)	PUNCT
ejpam-5090	215	39	·	·	PUNCT
ejpam-5090	215	40	(	(	PUNCT
ejpam-5090	215	41	ϑ1	ϑ1	NOUN
ejpam-5090	215	42	,	,	PUNCT
ejpam-5090	215	43	η1	η1	NOUN
ejpam-5090	215	44	)	)	PUNCT
ejpam-5090	215	45	)	)	PUNCT
ejpam-5090	215	46	·	·	PUNCT
ejpam-5090	216	1	(	(	PUNCT
ejpam-5090	216	2	(	(	PUNCT
ejpam-5090	216	3	ϑ3	ϑ3	NOUN
ejpam-5090	216	4	,	,	PUNCT
ejpam-5090	216	5	η3	η3	PROPN
ejpam-5090	216	6	)	)	PUNCT
ejpam-5090	216	7	·	·	PUNCT
ejpam-5090	216	8	(	(	PUNCT
ejpam-5090	216	9	ϑ2	ϑ2	NOUN
ejpam-5090	216	10	,	,	PUNCT
ejpam-5090	216	11	η2	η2	NOUN
ejpam-5090	216	12	)	)	PUNCT
ejpam-5090	216	13	)	)	PUNCT
ejpam-5090	216	14	)	)	PUNCT
ejpam-5090	216	15	,	,	PUNCT
ejpam-5090	216	16	ρ	ρ	PROPN
ejpam-5090	216	17	f	f	PROPN
ejpam-5090	216	18	(	(	PUNCT
ejpam-5090	216	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	216	20	,	,	PUNCT
ejpam-5090	216	21	η2	η2	PROPN
ejpam-5090	216	22	)	)	PUNCT
ejpam-5090	216	23	}	}	PUNCT
ejpam-5090	216	24	s	s	PART
ejpam-5090	216	25	{	{	PUNCT
ejpam-5090	216	26	ρf(m×n)(ϑ1	ρf(m×n)(ϑ1	NOUN
ejpam-5090	216	27	,	,	PUNCT
ejpam-5090	216	28	η1	η1	NOUN
ejpam-5090	216	29	)	)	PUNCT
ejpam-5090	216	30	s	s	PART
ejpam-5090	216	31	}	}	PUNCT
ejpam-5090	216	32	≥	≥	PROPN
ejpam-5090	216	33	max	max	PROPN
ejpam-5090	216	34	{	{	PUNCT
ejpam-5090	216	35	ρf(m×n)(((ϑ3	ρf(m×n)(((ϑ3	PROPN
ejpam-5090	216	36	,	,	PUNCT
ejpam-5090	216	37	η3	η3	NOUN
ejpam-5090	216	38	)	)	PUNCT
ejpam-5090	216	39	·	·	PUNCT
ejpam-5090	216	40	(	(	PUNCT
ejpam-5090	216	41	ϑ1	ϑ1	NOUN
ejpam-5090	216	42	,	,	PUNCT
ejpam-5090	216	43	η1	η1	NOUN
ejpam-5090	216	44	)	)	PUNCT
ejpam-5090	216	45	)	)	PUNCT
ejpam-5090	216	46	·	·	PUNCT
ejpam-5090	217	1	(	(	PUNCT
ejpam-5090	217	2	(	(	PUNCT
ejpam-5090	217	3	ϑ3	ϑ3	NOUN
ejpam-5090	217	4	,	,	PUNCT
ejpam-5090	217	5	η3	η3	PROPN
ejpam-5090	217	6	)	)	PUNCT
ejpam-5090	217	7	·	·	PUNCT
ejpam-5090	217	8	(	(	PUNCT
ejpam-5090	217	9	ϑ2	ϑ2	NOUN
ejpam-5090	217	10	,	,	PUNCT
ejpam-5090	217	11	η2	η2	NOUN
ejpam-5090	217	12	)	)	PUNCT
ejpam-5090	217	13	)	)	PUNCT
ejpam-5090	217	14	)	)	PUNCT
ejpam-5090	218	1	s	s	X
ejpam-5090	218	2	,	,	PUNCT
ejpam-5090	218	3	ρf(m×n)(ϑ2	ρf(m×n)(ϑ2	NOUN
ejpam-5090	218	4	,	,	PUNCT
ejpam-5090	218	5	η2	η2	X
ejpam-5090	218	6	)	)	PUNCT
ejpam-5090	218	7	s	s	PART
ejpam-5090	218	8	}	}	PUNCT
ejpam-5090	218	9	{	{	PUNCT
ejpam-5090	218	10	ρf(m×n)s(ϑ1	ρf(m×n)s(ϑ1	NOUN
ejpam-5090	218	11	,	,	PUNCT
ejpam-5090	218	12	η1	η1	NOUN
ejpam-5090	218	13	)	)	PUNCT
ejpam-5090	218	14	}	}	PUNCT
ejpam-5090	218	15	≥	≥	PROPN
ejpam-5090	218	16	max	max	PROPN
ejpam-5090	218	17	{	{	PUNCT
ejpam-5090	218	18	ρf(m×n)s(((ϑ3	ρf(m×n)s(((ϑ3	PROPN
ejpam-5090	218	19	,	,	PUNCT
ejpam-5090	218	20	η3	η3	PROPN
ejpam-5090	218	21	)	)	PUNCT
ejpam-5090	218	22	·	·	PUNCT
ejpam-5090	218	23	(	(	PUNCT
ejpam-5090	218	24	ϑ1	ϑ1	NOUN
ejpam-5090	218	25	,	,	PUNCT
ejpam-5090	218	26	η1	η1	NOUN
ejpam-5090	218	27	)	)	PUNCT
ejpam-5090	218	28	)	)	PUNCT
ejpam-5090	218	29	·	·	PUNCT
ejpam-5090	218	30	(	(	PUNCT
ejpam-5090	218	31	(	(	PUNCT
ejpam-5090	218	32	ϑ3	ϑ3	NOUN
ejpam-5090	218	33	,	,	PUNCT
ejpam-5090	218	34	η3	η3	PROPN
ejpam-5090	218	35	)	)	PUNCT
ejpam-5090	218	36	·	·	PUNCT
ejpam-5090	218	37	(	(	PUNCT
ejpam-5090	218	38	ϑ2	ϑ2	NOUN
ejpam-5090	218	39	,	,	PUNCT
ejpam-5090	218	40	η2	η2	NOUN
ejpam-5090	218	41	)	)	PUNCT
ejpam-5090	218	42	)	)	PUNCT
ejpam-5090	218	43	)	)	PUNCT
ejpam-5090	218	44	,	,	PUNCT
ejpam-5090	218	45	ρ	ρ	PROPN
ejpam-5090	218	46	f	f	PROPN
ejpam-5090	218	47	(	(	PUNCT
ejpam-5090	218	48	m×n)s(ϑ2	m×n)s(ϑ2	NOUN
ejpam-5090	218	49	,	,	PUNCT
ejpam-5090	218	50	η2	η2	PROPN
ejpam-5090	218	51	)	)	PUNCT
ejpam-5090	218	52	}	}	PUNCT
ejpam-5090	218	53	.	.	PUNCT
ejpam-5090	219	1	hence	hence	ADV
ejpam-5090	219	2	,	,	PUNCT
ejpam-5090	219	3	(	(	PUNCT
ejpam-5090	219	4	m×n)s	m×n)s	NOUN
ejpam-5090	219	5	=	=	PUNCT
ejpam-5090	219	6	〈	〈	PROPN
ejpam-5090	219	7	ρt(m×n)s	ρt(m×n)s	PROPN
ejpam-5090	219	8	,	,	PUNCT
ejpam-5090	219	9	ρ	ρ	PROPN
ejpam-5090	219	10	i	i	PROPN
ejpam-5090	219	11	(	(	PUNCT
ejpam-5090	219	12	m×n)s	m×n)s	PROPN
ejpam-5090	219	13	,	,	PUNCT
ejpam-5090	219	14	ρ	ρ	PROPN
ejpam-5090	219	15	f	f	PROPN
ejpam-5090	219	16	(	(	PUNCT
ejpam-5090	219	17	m×n)s	m×n)s	NOUN
ejpam-5090	219	18	〉	〉	NOUN
ejpam-5090	219	19	is	be	AUX
ejpam-5090	219	20	a	a	DET
ejpam-5090	219	21	fnink	fnink	NOUN
ejpam-5090	219	22	-	-	PUNCT
ejpam-5090	219	23	i	i	PRON
ejpam-5090	219	24	of	of	ADP
ejpam-5090	219	25	χ1	χ1	PROPN
ejpam-5090	219	26	×	×	PROPN
ejpam-5090	219	27	χ2	χ2	PROPN
ejpam-5090	219	28	.	.	PUNCT
ejpam-5090	220	1	theorem	theorem	VERB
ejpam-5090	220	2	8	8	NUM
ejpam-5090	220	3	.	.	PUNCT
ejpam-5090	221	1	let	let	VERB
ejpam-5090	221	2	m×n	m×n	PROPN
ejpam-5090	221	3	=	=	SYM
ejpam-5090	221	4	〈	〈	PROPN
ejpam-5090	221	5	ρt(m×n	ρt(m×n	NOUN
ejpam-5090	221	6	)	)	PUNCT
ejpam-5090	221	7	,	,	PUNCT
ejpam-5090	222	1	ρ	ρ	PROPN
ejpam-5090	222	2	i	i	PROPN
ejpam-5090	222	3	(	(	PUNCT
ejpam-5090	222	4	m×n	m×n	PROPN
ejpam-5090	222	5	)	)	PUNCT
ejpam-5090	222	6	,	,	PUNCT
ejpam-5090	222	7	ρ	ρ	PROPN
ejpam-5090	222	8	f	f	X
ejpam-5090	222	9	(	(	PUNCT
ejpam-5090	222	10	m×n	m×n	NOUN
ejpam-5090	222	11	)	)	PUNCT
ejpam-5090	222	12	〉	〉	NOUN
ejpam-5090	222	13	and	and	CCONJ
ejpam-5090	222	14	d×	d×	NOUN
ejpam-5090	222	15	e	e	NOUN
ejpam-5090	222	16	=	=	PUNCT
ejpam-5090	222	17	〈	〈	PROPN
ejpam-5090	222	18	ρt(d×e	ρt(d×e	NOUN
ejpam-5090	222	19	)	)	PUNCT
ejpam-5090	222	20	,	,	PUNCT
ejpam-5090	222	21	ρ	ρ	PROPN
ejpam-5090	222	22	i	i	PROPN
ejpam-5090	222	23	(	(	PUNCT
ejpam-5090	222	24	d×e	d×e	PROPN
ejpam-5090	222	25	)	)	PUNCT
ejpam-5090	222	26	,	,	PUNCT
ejpam-5090	222	27	ρ	ρ	PROPN
ejpam-5090	222	28	f	f	X
ejpam-5090	222	29	(	(	PUNCT
ejpam-5090	222	30	d×e	d×e	PROPN
ejpam-5090	222	31	)	)	PUNCT
ejpam-5090	222	32	〉	〉	NOUN
ejpam-5090	222	33	be	be	VERB
ejpam-5090	222	34	two	two	NUM
ejpam-5090	222	35	fnink	fnink	NOUN
ejpam-5090	222	36	-	-	PUNCT
ejpam-5090	222	37	is	is	NOUN
ejpam-5090	222	38	of	of	ADP
ejpam-5090	222	39	χ1	χ1	NOUN
ejpam-5090	222	40	×	×	NOUN
ejpam-5090	222	41	χ2	χ2	PROPN
ejpam-5090	222	42	.	.	PUNCT
ejpam-5090	223	1	then	then	ADV
ejpam-5090	223	2	,	,	PUNCT
ejpam-5090	223	3	(	(	PUNCT
ejpam-5090	223	4	m×n	m×n	NOUN
ejpam-5090	223	5	)	)	PUNCT
ejpam-5090	223	6	∩	∩	NOUN
ejpam-5090	223	7	(	(	PUNCT
ejpam-5090	223	8	d×	d×	NOUN
ejpam-5090	223	9	e	e	NOUN
ejpam-5090	223	10	)	)	PUNCT
ejpam-5090	223	11	=	=	SYM
ejpam-5090	223	12	〈	〈	PROPN
ejpam-5090	223	13	ρt(m×n)∩(d×e	ρt(m×n)∩(d×e	NOUN
ejpam-5090	223	14	)	)	PUNCT
ejpam-5090	223	15	,	,	PUNCT
ejpam-5090	223	16	ρ	ρ	PROPN
ejpam-5090	223	17	i	i	PROPN
ejpam-5090	223	18	(	(	PUNCT
ejpam-5090	223	19	m×n)∩(d×e	m×n)∩(d×e	PROPN
ejpam-5090	223	20	)	)	PUNCT
ejpam-5090	223	21	,	,	PUNCT
ejpam-5090	223	22	ρ	ρ	PROPN
ejpam-5090	223	23	f	f	X
ejpam-5090	223	24	(	(	PUNCT
ejpam-5090	223	25	m×n)∩(d×e	m×n)∩(d×e	NOUN
ejpam-5090	223	26	)	)	PUNCT
ejpam-5090	223	27	〉	〉	NOUN
ejpam-5090	223	28	is	be	AUX
ejpam-5090	223	29	a	a	DET
ejpam-5090	223	30	fnink	fnink	NOUN
ejpam-5090	223	31	-	-	PUNCT
ejpam-5090	223	32	i	i	PRON
ejpam-5090	223	33	of	of	ADP
ejpam-5090	223	34	χ1	χ1	PROPN
ejpam-5090	223	35	×	×	PROPN
ejpam-5090	223	36	χ2	χ2	PROPN
ejpam-5090	223	37	.	.	PUNCT
ejpam-5090	224	1	proof	proof	NOUN
ejpam-5090	224	2	.	.	PUNCT
ejpam-5090	225	1	since	since	SCONJ
ejpam-5090	225	2	m×n	m×n	PROPN
ejpam-5090	225	3	and	and	CCONJ
ejpam-5090	225	4	d×e	d×e	PROPN
ejpam-5090	225	5	are	be	AUX
ejpam-5090	225	6	two	two	NUM
ejpam-5090	225	7	fnink	fnink	NOUN
ejpam-5090	225	8	-	-	PUNCT
ejpam-5090	225	9	is	is	NOUN
ejpam-5090	225	10	of	of	ADP
ejpam-5090	225	11	χ1×χ2	χ1×χ2	PROPN
ejpam-5090	225	12	.	.	PUNCT
ejpam-5090	226	1	then	then	ADV
ejpam-5090	226	2	,	,	PUNCT
ejpam-5090	226	3	∀(ϑ	∀(ϑ	PROPN
ejpam-5090	226	4	,	,	PUNCT
ejpam-5090	226	5	η	η	NOUN
ejpam-5090	226	6	)	)	PUNCT
ejpam-5090	226	7	∈	∈	PROPN
ejpam-5090	226	8	χ1×χ2	χ1×χ2	PROPN
ejpam-5090	226	9	,	,	PUNCT
ejpam-5090	226	10	we	we	PRON
ejpam-5090	226	11	have	have	VERB
ejpam-5090	226	12	ρt(m×n)∩(d×e)(0	ρt(m×n)∩(d×e)(0	NUM
ejpam-5090	226	13	,	,	PUNCT
ejpam-5090	226	14	0	0	NUM
ejpam-5090	226	15	)	)	PUNCT
ejpam-5090	226	16	=	=	SYM
ejpam-5090	226	17	min	min	PROPN
ejpam-5090	226	18	{	{	PUNCT
ejpam-5090	226	19	ρt(m×n)(0	ρt(m×n)(0	PROPN
ejpam-5090	226	20	,	,	PUNCT
ejpam-5090	226	21	0	0	NUM
ejpam-5090	226	22	)	)	PUNCT
ejpam-5090	226	23	,	,	PUNCT
ejpam-5090	226	24	ρ	ρ	PROPN
ejpam-5090	226	25	t	t	PROPN
ejpam-5090	226	26	(	(	PUNCT
ejpam-5090	226	27	d×e)(0	d×e)(0	PROPN
ejpam-5090	226	28	,	,	PUNCT
ejpam-5090	226	29	0	0	NUM
ejpam-5090	226	30	)	)	PUNCT
ejpam-5090	226	31	}	}	PUNCT
ejpam-5090	226	32	m.	m.	NOUN
ejpam-5090	226	33	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	226	34	et	et	PROPN
ejpam-5090	226	35	al	al	PROPN
ejpam-5090	226	36	.	.	PUNCT
ejpam-5090	226	37	/	/	SYM
ejpam-5090	226	38	eur	eur	PROPN
ejpam-5090	226	39	.	.	PUNCT
ejpam-5090	227	1	j.	j.	PROPN
ejpam-5090	227	2	pure	pure	PROPN
ejpam-5090	227	3	appl	appl	PROPN
ejpam-5090	227	4	.	.	PROPN
ejpam-5090	227	5	math	math	PROPN
ejpam-5090	227	6	,	,	PUNCT
ejpam-5090	227	7	17	17	NUM
ejpam-5090	227	8	(	(	PUNCT
ejpam-5090	227	9	2	2	NUM
ejpam-5090	227	10	)	)	PUNCT
ejpam-5090	227	11	(	(	PUNCT
ejpam-5090	227	12	2024	2024	NUM
ejpam-5090	227	13	)	)	PUNCT
ejpam-5090	227	14	,	,	PUNCT
ejpam-5090	227	15	1113	1113	NUM
ejpam-5090	227	16	-	-	SYM
ejpam-5090	227	17	1128	1128	NUM
ejpam-5090	227	18	1125	1125	NUM
ejpam-5090	227	19	≤	≤	NOUN
ejpam-5090	227	20	min	min	NOUN
ejpam-5090	227	21	{	{	PUNCT
ejpam-5090	227	22	ρt(m×n)(ϑ	ρt(m×n)(ϑ	PROPN
ejpam-5090	227	23	,	,	PUNCT
ejpam-5090	227	24	η	η	NOUN
ejpam-5090	227	25	)	)	PUNCT
ejpam-5090	227	26	,	,	PUNCT
ejpam-5090	227	27	ρ	ρ	PROPN
ejpam-5090	227	28	t	t	PROPN
ejpam-5090	227	29	(	(	PUNCT
ejpam-5090	227	30	d×e)(ϑ	d×e)(ϑ	PROPN
ejpam-5090	227	31	,	,	PUNCT
ejpam-5090	227	32	η	η	NOUN
ejpam-5090	227	33	)	)	PUNCT
ejpam-5090	227	34	}	}	PUNCT
ejpam-5090	227	35	=	=	SYM
ejpam-5090	227	36	ρt(m×n)∩(d×e)(ϑ	ρt(m×n)∩(d×e)(ϑ	PROPN
ejpam-5090	227	37	,	,	PUNCT
ejpam-5090	227	38	η	η	NOUN
ejpam-5090	227	39	)	)	PUNCT
ejpam-5090	227	40	,	,	PUNCT
ejpam-5090	227	41	ρi(m×n)∩(d×e)(0	ρi(m×n)∩(d×e)(0	PROPN
ejpam-5090	227	42	,	,	PUNCT
ejpam-5090	227	43	0	0	NUM
ejpam-5090	227	44	)	)	PUNCT
ejpam-5090	227	45	=	=	SYM
ejpam-5090	227	46	max	max	X
ejpam-5090	227	47	{	{	PUNCT
ejpam-5090	227	48	ρi(m×n)(0	ρi(m×n)(0	PROPN
ejpam-5090	227	49	,	,	PUNCT
ejpam-5090	227	50	0	0	NUM
ejpam-5090	227	51	)	)	PUNCT
ejpam-5090	227	52	,	,	PUNCT
ejpam-5090	227	53	ρ	ρ	PROPN
ejpam-5090	227	54	i	i	PROPN
ejpam-5090	227	55	(	(	PUNCT
ejpam-5090	227	56	d×e)(0	d×e)(0	PROPN
ejpam-5090	227	57	,	,	PUNCT
ejpam-5090	227	58	0	0	NUM
ejpam-5090	227	59	)	)	PUNCT
ejpam-5090	227	60	}	}	PUNCT
ejpam-5090	227	61	≥	≥	PROPN
ejpam-5090	227	62	max	max	PROPN
ejpam-5090	227	63	{	{	PUNCT
ejpam-5090	227	64	ρi(m×n)(ϑ	ρi(m×n)(ϑ	PROPN
ejpam-5090	227	65	,	,	PUNCT
ejpam-5090	227	66	η	η	PROPN
ejpam-5090	227	67	)	)	PUNCT
ejpam-5090	227	68	,	,	PUNCT
ejpam-5090	227	69	ρ	ρ	PROPN
ejpam-5090	227	70	i	i	PROPN
ejpam-5090	227	71	(	(	PUNCT
ejpam-5090	227	72	d×e)(ϑ	d×e)(ϑ	PROPN
ejpam-5090	227	73	,	,	PUNCT
ejpam-5090	227	74	η	η	NOUN
ejpam-5090	227	75	)	)	PUNCT
ejpam-5090	227	76	}	}	PUNCT
ejpam-5090	227	77	=	=	PUNCT
ejpam-5090	227	78	ρi(m×n)∩(d×e)(ϑ	ρi(m×n)∩(d×e)(ϑ	PROPN
ejpam-5090	227	79	,	,	PUNCT
ejpam-5090	227	80	η	η	NOUN
ejpam-5090	227	81	)	)	PUNCT
ejpam-5090	227	82	and	and	CCONJ
ejpam-5090	227	83	ρf(m×n)∩(d×e)(0	ρf(m×n)∩(d×e)(0	PROPN
ejpam-5090	227	84	,	,	PUNCT
ejpam-5090	227	85	0	0	NUM
ejpam-5090	227	86	)	)	PUNCT
ejpam-5090	228	1	=	=	SYM
ejpam-5090	228	2	max	max	PROPN
ejpam-5090	228	3	{	{	PUNCT
ejpam-5090	228	4	ρf(m×n)(0	ρf(m×n)(0	PROPN
ejpam-5090	228	5	,	,	PUNCT
ejpam-5090	228	6	0	0	NUM
ejpam-5090	228	7	)	)	PUNCT
ejpam-5090	228	8	,	,	PUNCT
ejpam-5090	228	9	ρ	ρ	PROPN
ejpam-5090	228	10	i	i	PROPN
ejpam-5090	228	11	(	(	PUNCT
ejpam-5090	228	12	d×e)(0	d×e)(0	PROPN
ejpam-5090	228	13	,	,	PUNCT
ejpam-5090	228	14	0	0	NUM
ejpam-5090	228	15	)	)	PUNCT
ejpam-5090	228	16	}	}	PUNCT
ejpam-5090	228	17	≥	≥	PROPN
ejpam-5090	228	18	max	max	PROPN
ejpam-5090	228	19	{	{	PUNCT
ejpam-5090	228	20	ρf(m×n)(ϑ	ρf(m×n)(ϑ	PROPN
ejpam-5090	228	21	,	,	PUNCT
ejpam-5090	228	22	η	η	NOUN
ejpam-5090	228	23	)	)	PUNCT
ejpam-5090	228	24	,	,	PUNCT
ejpam-5090	228	25	ρ	ρ	PROPN
ejpam-5090	228	26	i	i	PROPN
ejpam-5090	228	27	(	(	PUNCT
ejpam-5090	228	28	d×e)(ϑ	d×e)(ϑ	PROPN
ejpam-5090	228	29	,	,	PUNCT
ejpam-5090	228	30	η	η	NOUN
ejpam-5090	228	31	)	)	PUNCT
ejpam-5090	228	32	}	}	PUNCT
ejpam-5090	228	33	=	=	SYM
ejpam-5090	228	34	ρf(m×n)∩(d×e)(ϑ	ρf(m×n)∩(d×e)(ϑ	PROPN
ejpam-5090	228	35	,	,	PUNCT
ejpam-5090	228	36	η	η	NOUN
ejpam-5090	228	37	)	)	PUNCT
ejpam-5090	228	38	.	.	PUNCT
ejpam-5090	229	1	now	now	ADV
ejpam-5090	229	2	,	,	PUNCT
ejpam-5090	229	3	for	for	ADP
ejpam-5090	229	4	any	any	DET
ejpam-5090	229	5	(	(	PUNCT
ejpam-5090	229	6	ϑ1	ϑ1	NOUN
ejpam-5090	229	7	,	,	PUNCT
ejpam-5090	229	8	η1	η1	NOUN
ejpam-5090	229	9	)	)	PUNCT
ejpam-5090	229	10	,	,	PUNCT
ejpam-5090	229	11	(	(	PUNCT
ejpam-5090	229	12	ϑ2	ϑ2	NOUN
ejpam-5090	229	13	,	,	PUNCT
ejpam-5090	229	14	η2	η2	PROPN
ejpam-5090	229	15	)	)	PUNCT
ejpam-5090	229	16	and	and	CCONJ
ejpam-5090	229	17	(	(	PUNCT
ejpam-5090	229	18	ϑ3	ϑ3	PROPN
ejpam-5090	229	19	,	,	PUNCT
ejpam-5090	229	20	η3	η3	PROPN
ejpam-5090	229	21	)	)	PUNCT
ejpam-5090	229	22	∈	∈	PROPN
ejpam-5090	229	23	χ1	χ1	NOUN
ejpam-5090	229	24	×	×	NOUN
ejpam-5090	229	25	χ2	χ2	PROPN
ejpam-5090	229	26	,	,	PUNCT
ejpam-5090	229	27	we	we	PRON
ejpam-5090	229	28	have	have	VERB
ejpam-5090	229	29	ρt(m×n)∩(d×e)(ϑ1	ρt(m×n)∩(d×e)(ϑ1	NOUN
ejpam-5090	229	30	,	,	PUNCT
ejpam-5090	229	31	η1	η1	NOUN
ejpam-5090	229	32	)	)	PUNCT
ejpam-5090	230	1	=	=	SYM
ejpam-5090	230	2	min	min	NOUN
ejpam-5090	230	3	{	{	PUNCT
ejpam-5090	230	4	ρt(m×n)(ϑ1	ρt(m×n)(ϑ1	ADJ
ejpam-5090	230	5	,	,	PUNCT
ejpam-5090	230	6	η1	η1	NOUN
ejpam-5090	230	7	)	)	PUNCT
ejpam-5090	230	8	,	,	PUNCT
ejpam-5090	230	9	ρ	ρ	PROPN
ejpam-5090	230	10	t	t	PROPN
ejpam-5090	230	11	(	(	PUNCT
ejpam-5090	230	12	d×e)(ϑ1	d×e)(ϑ1	ADJ
ejpam-5090	230	13	,	,	PUNCT
ejpam-5090	230	14	η1	η1	NOUN
ejpam-5090	230	15	)	)	PUNCT
ejpam-5090	230	16	}	}	PUNCT
ejpam-5090	230	17	≤	≤	NUM
ejpam-5090	230	18	min	min	NOUN
ejpam-5090	230	19	{	{	PUNCT
ejpam-5090	230	20	min	min	PROPN
ejpam-5090	230	21	{	{	PUNCT
ejpam-5090	230	22	ρt(m×n)(((ϑ3	ρt(m×n)(((ϑ3	PROPN
ejpam-5090	230	23	,	,	PUNCT
ejpam-5090	230	24	η3	η3	PROPN
ejpam-5090	230	25	)	)	PUNCT
ejpam-5090	230	26	·	·	PUNCT
ejpam-5090	230	27	(	(	PUNCT
ejpam-5090	230	28	ϑ1	ϑ1	NOUN
ejpam-5090	230	29	,	,	PUNCT
ejpam-5090	230	30	η1	η1	NOUN
ejpam-5090	230	31	)	)	PUNCT
ejpam-5090	230	32	)	)	PUNCT
ejpam-5090	230	33	·	·	PUNCT
ejpam-5090	231	1	(	(	PUNCT
ejpam-5090	231	2	(	(	PUNCT
ejpam-5090	231	3	ϑ3	ϑ3	NOUN
ejpam-5090	231	4	,	,	PUNCT
ejpam-5090	231	5	η3	η3	PROPN
ejpam-5090	231	6	)	)	PUNCT
ejpam-5090	231	7	·	·	PUNCT
ejpam-5090	231	8	(	(	PUNCT
ejpam-5090	231	9	ϑ2	ϑ2	NOUN
ejpam-5090	231	10	,	,	PUNCT
ejpam-5090	231	11	η2	η2	NOUN
ejpam-5090	231	12	)	)	PUNCT
ejpam-5090	231	13	)	)	PUNCT
ejpam-5090	231	14	)	)	PUNCT
ejpam-5090	231	15	,	,	PUNCT
ejpam-5090	231	16	ρ	ρ	PROPN
ejpam-5090	231	17	t	t	PROPN
ejpam-5090	231	18	(	(	PUNCT
ejpam-5090	231	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	231	20	,	,	PUNCT
ejpam-5090	231	21	η2	η2	PROPN
ejpam-5090	231	22	)	)	PUNCT
ejpam-5090	231	23	}	}	PUNCT
ejpam-5090	231	24	,	,	PUNCT
ejpam-5090	231	25	min	min	PROPN
ejpam-5090	231	26	{	{	PUNCT
ejpam-5090	231	27	ρt(d×e)(((ϑ3	ρt(d×e)(((ϑ3	PROPN
ejpam-5090	231	28	,	,	PUNCT
ejpam-5090	231	29	η3	η3	NOUN
ejpam-5090	231	30	)	)	PUNCT
ejpam-5090	231	31	·	·	PUNCT
ejpam-5090	231	32	(	(	PUNCT
ejpam-5090	231	33	ϑ1	ϑ1	NOUN
ejpam-5090	231	34	,	,	PUNCT
ejpam-5090	231	35	η1	η1	NOUN
ejpam-5090	231	36	)	)	PUNCT
ejpam-5090	231	37	)	)	PUNCT
ejpam-5090	231	38	·	·	PUNCT
ejpam-5090	232	1	(	(	PUNCT
ejpam-5090	232	2	(	(	PUNCT
ejpam-5090	232	3	ϑ3	ϑ3	NOUN
ejpam-5090	232	4	,	,	PUNCT
ejpam-5090	232	5	η3	η3	PROPN
ejpam-5090	232	6	)	)	PUNCT
ejpam-5090	232	7	·	·	PUNCT
ejpam-5090	232	8	(	(	PUNCT
ejpam-5090	232	9	ϑ2	ϑ2	NOUN
ejpam-5090	232	10	,	,	PUNCT
ejpam-5090	232	11	η2	η2	NOUN
ejpam-5090	232	12	)	)	PUNCT
ejpam-5090	232	13	)	)	PUNCT
ejpam-5090	232	14	)	)	PUNCT
ejpam-5090	232	15	,	,	PUNCT
ejpam-5090	232	16	ρ	ρ	PROPN
ejpam-5090	232	17	t	t	PROPN
ejpam-5090	232	18	(	(	PUNCT
ejpam-5090	232	19	d×e)(ϑ2	d×e)(ϑ2	NOUN
ejpam-5090	232	20	,	,	PUNCT
ejpam-5090	232	21	η2	η2	PROPN
ejpam-5090	232	22	)	)	PUNCT
ejpam-5090	232	23	}	}	PUNCT
ejpam-5090	232	24	}	}	PUNCT
ejpam-5090	232	25	=	=	SYM
ejpam-5090	232	26	min	min	PROPN
ejpam-5090	232	27	{	{	PUNCT
ejpam-5090	232	28	min	min	PROPN
ejpam-5090	232	29	{	{	PUNCT
ejpam-5090	232	30	ρt(m×n)(((ϑ3	ρt(m×n)(((ϑ3	PROPN
ejpam-5090	232	31	,	,	PUNCT
ejpam-5090	232	32	η3	η3	PROPN
ejpam-5090	232	33	)	)	PUNCT
ejpam-5090	232	34	·	·	PUNCT
ejpam-5090	232	35	(	(	PUNCT
ejpam-5090	232	36	ϑ1	ϑ1	NOUN
ejpam-5090	232	37	,	,	PUNCT
ejpam-5090	232	38	η1	η1	NOUN
ejpam-5090	232	39	)	)	PUNCT
ejpam-5090	232	40	)	)	PUNCT
ejpam-5090	232	41	·	·	PUNCT
ejpam-5090	233	1	(	(	PUNCT
ejpam-5090	233	2	(	(	PUNCT
ejpam-5090	233	3	ϑ3	ϑ3	NOUN
ejpam-5090	233	4	,	,	PUNCT
ejpam-5090	233	5	η3	η3	PROPN
ejpam-5090	233	6	)	)	PUNCT
ejpam-5090	233	7	·	·	PUNCT
ejpam-5090	233	8	(	(	PUNCT
ejpam-5090	233	9	ϑ2	ϑ2	NOUN
ejpam-5090	233	10	,	,	PUNCT
ejpam-5090	233	11	η2	η2	NOUN
ejpam-5090	233	12	)	)	PUNCT
ejpam-5090	233	13	)	)	PUNCT
ejpam-5090	233	14	)	)	PUNCT
ejpam-5090	233	15	,	,	PUNCT
ejpam-5090	233	16	ρt(d×e)(((ϑ3	ρt(d×e)(((ϑ3	PROPN
ejpam-5090	233	17	,	,	PUNCT
ejpam-5090	233	18	η3	η3	NOUN
ejpam-5090	233	19	)	)	PUNCT
ejpam-5090	233	20	·	·	PUNCT
ejpam-5090	233	21	(	(	PUNCT
ejpam-5090	233	22	ϑ1	ϑ1	NOUN
ejpam-5090	233	23	,	,	PUNCT
ejpam-5090	233	24	η1	η1	NOUN
ejpam-5090	233	25	)	)	PUNCT
ejpam-5090	233	26	)	)	PUNCT
ejpam-5090	233	27	·	·	PUNCT
ejpam-5090	234	1	(	(	PUNCT
ejpam-5090	234	2	(	(	PUNCT
ejpam-5090	234	3	ϑ3	ϑ3	NOUN
ejpam-5090	234	4	,	,	PUNCT
ejpam-5090	234	5	η3	η3	PROPN
ejpam-5090	234	6	)	)	PUNCT
ejpam-5090	234	7	·	·	PUNCT
ejpam-5090	234	8	(	(	PUNCT
ejpam-5090	234	9	ϑ2	ϑ2	NOUN
ejpam-5090	234	10	,	,	PUNCT
ejpam-5090	234	11	η2	η2	NOUN
ejpam-5090	234	12	)	)	PUNCT
ejpam-5090	234	13	)	)	PUNCT
ejpam-5090	234	14	)	)	PUNCT
ejpam-5090	234	15	}	}	PUNCT
ejpam-5090	234	16	,	,	PUNCT
ejpam-5090	234	17	min	min	PROPN
ejpam-5090	234	18	{	{	PUNCT
ejpam-5090	234	19	ρt(m×n)(ϑ2	ρt(m×n)(ϑ2	NOUN
ejpam-5090	234	20	,	,	PUNCT
ejpam-5090	234	21	η2	η2	PROPN
ejpam-5090	234	22	)	)	PUNCT
ejpam-5090	234	23	,	,	PUNCT
ejpam-5090	234	24	ρ	ρ	PROPN
ejpam-5090	234	25	t	t	PROPN
ejpam-5090	234	26	(	(	PUNCT
ejpam-5090	234	27	d×e)(ϑ2	d×e)(ϑ2	NOUN
ejpam-5090	234	28	,	,	PUNCT
ejpam-5090	234	29	η2	η2	PROPN
ejpam-5090	234	30	)	)	PUNCT
ejpam-5090	234	31	}	}	PUNCT
ejpam-5090	234	32	}	}	PUNCT
ejpam-5090	234	33	=	=	SYM
ejpam-5090	234	34	min	min	NOUN
ejpam-5090	234	35	{	{	PUNCT
ejpam-5090	234	36	ρt(m×n)∩(d×e)(((ϑ3	ρt(m×n)∩(d×e)(((ϑ3	NOUN
ejpam-5090	234	37	,	,	PUNCT
ejpam-5090	234	38	η3	η3	NOUN
ejpam-5090	234	39	)	)	PUNCT
ejpam-5090	234	40	·	·	PUNCT
ejpam-5090	234	41	(	(	PUNCT
ejpam-5090	234	42	ϑ1	ϑ1	NOUN
ejpam-5090	234	43	,	,	PUNCT
ejpam-5090	234	44	η1	η1	NOUN
ejpam-5090	234	45	)	)	PUNCT
ejpam-5090	234	46	)	)	PUNCT
ejpam-5090	234	47	·	·	PUNCT
ejpam-5090	235	1	(	(	PUNCT
ejpam-5090	235	2	(	(	PUNCT
ejpam-5090	235	3	ϑ3	ϑ3	NOUN
ejpam-5090	235	4	,	,	PUNCT
ejpam-5090	235	5	η3	η3	PROPN
ejpam-5090	235	6	)	)	PUNCT
ejpam-5090	235	7	·	·	PUNCT
ejpam-5090	235	8	(	(	PUNCT
ejpam-5090	235	9	ϑ2	ϑ2	NOUN
ejpam-5090	235	10	,	,	PUNCT
ejpam-5090	235	11	η2	η2	NOUN
ejpam-5090	235	12	)	)	PUNCT
ejpam-5090	235	13	)	)	PUNCT
ejpam-5090	235	14	)	)	PUNCT
ejpam-5090	235	15	,	,	PUNCT
ejpam-5090	235	16	ρ	ρ	PROPN
ejpam-5090	235	17	t	t	PROPN
ejpam-5090	235	18	(	(	PUNCT
ejpam-5090	235	19	m×n)∩(d×e)(ϑ2	m×n)∩(d×e)(ϑ2	NOUN
ejpam-5090	235	20	,	,	PUNCT
ejpam-5090	235	21	η2	η2	PROPN
ejpam-5090	235	22	)	)	PUNCT
ejpam-5090	235	23	}	}	PUNCT
ejpam-5090	235	24	,	,	PUNCT
ejpam-5090	235	25	ρi(m×n)∩(d×e)(ϑ1	ρi(m×n)∩(d×e)(ϑ1	ADJ
ejpam-5090	235	26	,	,	PUNCT
ejpam-5090	235	27	η1	η1	NOUN
ejpam-5090	235	28	)	)	PUNCT
ejpam-5090	235	29	=	=	SYM
ejpam-5090	235	30	max	max	PROPN
ejpam-5090	235	31	{	{	PUNCT
ejpam-5090	235	32	ρi(m×n)(ϑ1	ρi(m×n)(ϑ1	PROPN
ejpam-5090	235	33	,	,	PUNCT
ejpam-5090	235	34	η1	η1	NOUN
ejpam-5090	235	35	)	)	PUNCT
ejpam-5090	235	36	,	,	PUNCT
ejpam-5090	235	37	ρ	ρ	PROPN
ejpam-5090	235	38	i	i	PRON
ejpam-5090	235	39	(	(	PUNCT
ejpam-5090	235	40	d×e)(ϑ1	d×e)(ϑ1	ADJ
ejpam-5090	235	41	,	,	PUNCT
ejpam-5090	235	42	η1	η1	NOUN
ejpam-5090	235	43	)	)	PUNCT
ejpam-5090	235	44	}	}	PUNCT
ejpam-5090	235	45	≥	≥	PROPN
ejpam-5090	235	46	max	max	PROPN
ejpam-5090	235	47	{	{	PUNCT
ejpam-5090	235	48	max	max	PROPN
ejpam-5090	235	49	{	{	PUNCT
ejpam-5090	235	50	ρi(m×n)(((ϑ3	ρi(m×n)(((ϑ3	PROPN
ejpam-5090	235	51	,	,	PUNCT
ejpam-5090	235	52	η3	η3	PROPN
ejpam-5090	235	53	)	)	PUNCT
ejpam-5090	235	54	·	·	PUNCT
ejpam-5090	235	55	(	(	PUNCT
ejpam-5090	235	56	ϑ1	ϑ1	NOUN
ejpam-5090	235	57	,	,	PUNCT
ejpam-5090	235	58	η1	η1	NOUN
ejpam-5090	235	59	)	)	PUNCT
ejpam-5090	235	60	)	)	PUNCT
ejpam-5090	235	61	·	·	PUNCT
ejpam-5090	236	1	(	(	PUNCT
ejpam-5090	236	2	(	(	PUNCT
ejpam-5090	236	3	ϑ3	ϑ3	NOUN
ejpam-5090	236	4	,	,	PUNCT
ejpam-5090	236	5	η3	η3	PROPN
ejpam-5090	236	6	)	)	PUNCT
ejpam-5090	236	7	·	·	PUNCT
ejpam-5090	236	8	(	(	PUNCT
ejpam-5090	236	9	ϑ2	ϑ2	NOUN
ejpam-5090	236	10	,	,	PUNCT
ejpam-5090	236	11	η2	η2	NOUN
ejpam-5090	236	12	)	)	PUNCT
ejpam-5090	236	13	)	)	PUNCT
ejpam-5090	236	14	)	)	PUNCT
ejpam-5090	236	15	,	,	PUNCT
ejpam-5090	236	16	ρ	ρ	PROPN
ejpam-5090	236	17	i	i	PROPN
ejpam-5090	236	18	(	(	PUNCT
ejpam-5090	236	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	236	20	,	,	PUNCT
ejpam-5090	236	21	η2	η2	PROPN
ejpam-5090	236	22	)	)	PUNCT
ejpam-5090	236	23	}	}	PUNCT
ejpam-5090	236	24	,	,	PUNCT
ejpam-5090	236	25	max	max	PROPN
ejpam-5090	236	26	{	{	PUNCT
ejpam-5090	236	27	ρi(d×e)(((ϑ3	ρi(d×e)(((ϑ3	PROPN
ejpam-5090	236	28	,	,	PUNCT
ejpam-5090	236	29	η3	η3	PROPN
ejpam-5090	236	30	)	)	PUNCT
ejpam-5090	236	31	·	·	PUNCT
ejpam-5090	236	32	(	(	PUNCT
ejpam-5090	236	33	ϑ1	ϑ1	NOUN
ejpam-5090	236	34	,	,	PUNCT
ejpam-5090	236	35	η1	η1	NOUN
ejpam-5090	236	36	)	)	PUNCT
ejpam-5090	236	37	)	)	PUNCT
ejpam-5090	236	38	·	·	PUNCT
ejpam-5090	237	1	(	(	PUNCT
ejpam-5090	237	2	(	(	PUNCT
ejpam-5090	237	3	ϑ3	ϑ3	NOUN
ejpam-5090	237	4	,	,	PUNCT
ejpam-5090	237	5	η3	η3	PROPN
ejpam-5090	237	6	)	)	PUNCT
ejpam-5090	237	7	·	·	PUNCT
ejpam-5090	237	8	(	(	PUNCT
ejpam-5090	237	9	ϑ2	ϑ2	NOUN
ejpam-5090	237	10	,	,	PUNCT
ejpam-5090	237	11	η2	η2	NOUN
ejpam-5090	237	12	)	)	PUNCT
ejpam-5090	237	13	)	)	PUNCT
ejpam-5090	237	14	)	)	PUNCT
ejpam-5090	237	15	,	,	PUNCT
ejpam-5090	237	16	ρ	ρ	PROPN
ejpam-5090	237	17	i	i	PROPN
ejpam-5090	237	18	(	(	PUNCT
ejpam-5090	237	19	d×e)(ϑ2	d×e)(ϑ2	NOUN
ejpam-5090	237	20	,	,	PUNCT
ejpam-5090	237	21	η2	η2	PROPN
ejpam-5090	237	22	)	)	PUNCT
ejpam-5090	237	23	}	}	PUNCT
ejpam-5090	237	24	}	}	PUNCT
ejpam-5090	237	25	=	=	SYM
ejpam-5090	237	26	max	max	PROPN
ejpam-5090	237	27	{	{	PUNCT
ejpam-5090	237	28	max	max	PROPN
ejpam-5090	237	29	{	{	PUNCT
ejpam-5090	237	30	ρi(m×n)(((ϑ3	ρi(m×n)(((ϑ3	PROPN
ejpam-5090	237	31	,	,	PUNCT
ejpam-5090	237	32	η3	η3	PROPN
ejpam-5090	237	33	)	)	PUNCT
ejpam-5090	237	34	·	·	PUNCT
ejpam-5090	237	35	(	(	PUNCT
ejpam-5090	237	36	ϑ1	ϑ1	NOUN
ejpam-5090	237	37	,	,	PUNCT
ejpam-5090	237	38	η1	η1	NOUN
ejpam-5090	237	39	)	)	PUNCT
ejpam-5090	237	40	)	)	PUNCT
ejpam-5090	237	41	·	·	PUNCT
ejpam-5090	238	1	(	(	PUNCT
ejpam-5090	238	2	(	(	PUNCT
ejpam-5090	238	3	ϑ3	ϑ3	NOUN
ejpam-5090	238	4	,	,	PUNCT
ejpam-5090	238	5	η3	η3	PROPN
ejpam-5090	238	6	)	)	PUNCT
ejpam-5090	238	7	·	·	PUNCT
ejpam-5090	238	8	(	(	PUNCT
ejpam-5090	238	9	ϑ2	ϑ2	NOUN
ejpam-5090	238	10	,	,	PUNCT
ejpam-5090	238	11	η2	η2	NOUN
ejpam-5090	238	12	)	)	PUNCT
ejpam-5090	238	13	)	)	PUNCT
ejpam-5090	238	14	)	)	PUNCT
ejpam-5090	238	15	,	,	PUNCT
ejpam-5090	238	16	m.	m.	NOUN
ejpam-5090	238	17	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	238	18	et	et	PROPN
ejpam-5090	238	19	al	al	PROPN
ejpam-5090	238	20	.	.	PUNCT
ejpam-5090	238	21	/	/	SYM
ejpam-5090	238	22	eur	eur	PROPN
ejpam-5090	238	23	.	.	PUNCT
ejpam-5090	239	1	j.	j.	PROPN
ejpam-5090	239	2	pure	pure	PROPN
ejpam-5090	239	3	appl	appl	PROPN
ejpam-5090	239	4	.	.	PROPN
ejpam-5090	239	5	math	math	PROPN
ejpam-5090	239	6	,	,	PUNCT
ejpam-5090	239	7	17	17	NUM
ejpam-5090	239	8	(	(	PUNCT
ejpam-5090	239	9	2	2	NUM
ejpam-5090	239	10	)	)	PUNCT
ejpam-5090	239	11	(	(	PUNCT
ejpam-5090	239	12	2024	2024	NUM
ejpam-5090	239	13	)	)	PUNCT
ejpam-5090	239	14	,	,	PUNCT
ejpam-5090	239	15	1113	1113	NUM
ejpam-5090	239	16	-	-	SYM
ejpam-5090	239	17	1128	1128	NUM
ejpam-5090	239	18	1126	1126	NUM
ejpam-5090	239	19	ρi(d×e)(((ϑ3	ρi(d×e)(((ϑ3	NOUN
ejpam-5090	239	20	,	,	PUNCT
ejpam-5090	239	21	η3	η3	PROPN
ejpam-5090	239	22	)	)	PUNCT
ejpam-5090	239	23	·	·	PUNCT
ejpam-5090	240	1	(	(	PUNCT
ejpam-5090	240	2	ϑ1	ϑ1	NOUN
ejpam-5090	240	3	,	,	PUNCT
ejpam-5090	240	4	η1	η1	NOUN
ejpam-5090	240	5	)	)	PUNCT
ejpam-5090	240	6	)	)	PUNCT
ejpam-5090	240	7	·	·	PUNCT
ejpam-5090	241	1	(	(	PUNCT
ejpam-5090	241	2	(	(	PUNCT
ejpam-5090	241	3	ϑ3	ϑ3	NOUN
ejpam-5090	241	4	,	,	PUNCT
ejpam-5090	241	5	η3	η3	PROPN
ejpam-5090	241	6	)	)	PUNCT
ejpam-5090	241	7	·	·	PUNCT
ejpam-5090	241	8	(	(	PUNCT
ejpam-5090	241	9	ϑ2	ϑ2	NOUN
ejpam-5090	241	10	,	,	PUNCT
ejpam-5090	241	11	η2	η2	NOUN
ejpam-5090	241	12	)	)	PUNCT
ejpam-5090	241	13	)	)	PUNCT
ejpam-5090	241	14	)	)	PUNCT
ejpam-5090	241	15	}	}	PUNCT
ejpam-5090	241	16	,	,	PUNCT
ejpam-5090	241	17	max	max	PROPN
ejpam-5090	241	18	{	{	PUNCT
ejpam-5090	241	19	ρt(m×n)(ϑ2	ρt(m×n)(ϑ2	NOUN
ejpam-5090	241	20	,	,	PUNCT
ejpam-5090	241	21	η2	η2	PROPN
ejpam-5090	241	22	)	)	PUNCT
ejpam-5090	241	23	,	,	PUNCT
ejpam-5090	241	24	ρ	ρ	PROPN
ejpam-5090	241	25	i	i	PROPN
ejpam-5090	241	26	(	(	PUNCT
ejpam-5090	241	27	d×e)(ϑ2	d×e)(ϑ2	NOUN
ejpam-5090	241	28	,	,	PUNCT
ejpam-5090	241	29	η2	η2	PROPN
ejpam-5090	241	30	)	)	PUNCT
ejpam-5090	241	31	}	}	PUNCT
ejpam-5090	241	32	}	}	PUNCT
ejpam-5090	241	33	=	=	SYM
ejpam-5090	241	34	max	max	X
ejpam-5090	241	35	{	{	PUNCT
ejpam-5090	241	36	ρi(m×n)∩(d×e)(((ϑ3	ρi(m×n)∩(d×e)(((ϑ3	PROPN
ejpam-5090	241	37	,	,	PUNCT
ejpam-5090	241	38	η3	η3	PROPN
ejpam-5090	241	39	)	)	PUNCT
ejpam-5090	241	40	·	·	PUNCT
ejpam-5090	241	41	(	(	PUNCT
ejpam-5090	241	42	ϑ1	ϑ1	NOUN
ejpam-5090	241	43	,	,	PUNCT
ejpam-5090	241	44	η1	η1	NOUN
ejpam-5090	241	45	)	)	PUNCT
ejpam-5090	241	46	)	)	PUNCT
ejpam-5090	241	47	·	·	PUNCT
ejpam-5090	242	1	(	(	PUNCT
ejpam-5090	242	2	(	(	PUNCT
ejpam-5090	242	3	ϑ3	ϑ3	NOUN
ejpam-5090	242	4	,	,	PUNCT
ejpam-5090	242	5	η3	η3	PROPN
ejpam-5090	242	6	)	)	PUNCT
ejpam-5090	242	7	·	·	PUNCT
ejpam-5090	242	8	(	(	PUNCT
ejpam-5090	242	9	ϑ2	ϑ2	NOUN
ejpam-5090	242	10	,	,	PUNCT
ejpam-5090	242	11	η2	η2	NOUN
ejpam-5090	242	12	)	)	PUNCT
ejpam-5090	242	13	)	)	PUNCT
ejpam-5090	242	14	)	)	PUNCT
ejpam-5090	242	15	,	,	PUNCT
ejpam-5090	242	16	ρ	ρ	PROPN
ejpam-5090	242	17	i	i	PROPN
ejpam-5090	242	18	(	(	PUNCT
ejpam-5090	242	19	m×n)∩(d×e)(ϑ2	m×n)∩(d×e)(ϑ2	NOUN
ejpam-5090	242	20	,	,	PUNCT
ejpam-5090	242	21	η2	η2	PROPN
ejpam-5090	242	22	)	)	PUNCT
ejpam-5090	242	23	}	}	PUNCT
ejpam-5090	242	24	,	,	PUNCT
ejpam-5090	242	25	and	and	CCONJ
ejpam-5090	242	26	ρf(m×n)∩(d×e)(ϑ1	ρf(m×n)∩(d×e)(ϑ1	ADJ
ejpam-5090	242	27	,	,	PUNCT
ejpam-5090	242	28	η1	η1	NOUN
ejpam-5090	242	29	)	)	PUNCT
ejpam-5090	242	30	=	=	SYM
ejpam-5090	242	31	max	max	PROPN
ejpam-5090	242	32	{	{	PUNCT
ejpam-5090	242	33	ρf(m×n)(ϑ1	ρf(m×n)(ϑ1	NOUN
ejpam-5090	242	34	,	,	PUNCT
ejpam-5090	242	35	η1	η1	NOUN
ejpam-5090	242	36	)	)	PUNCT
ejpam-5090	242	37	,	,	PUNCT
ejpam-5090	242	38	ρ	ρ	PROPN
ejpam-5090	242	39	f	f	PROPN
ejpam-5090	242	40	(	(	PUNCT
ejpam-5090	242	41	d×e)(ϑ1	d×e)(ϑ1	ADJ
ejpam-5090	242	42	,	,	PUNCT
ejpam-5090	242	43	η1	η1	NOUN
ejpam-5090	242	44	)	)	PUNCT
ejpam-5090	242	45	}	}	PUNCT
ejpam-5090	242	46	≥	≥	PROPN
ejpam-5090	242	47	max	max	PROPN
ejpam-5090	242	48	{	{	PUNCT
ejpam-5090	242	49	max	max	PROPN
ejpam-5090	242	50	{	{	PUNCT
ejpam-5090	242	51	ρf(m×n)(((ϑ3	ρf(m×n)(((ϑ3	PROPN
ejpam-5090	242	52	,	,	PUNCT
ejpam-5090	242	53	η3	η3	NOUN
ejpam-5090	242	54	)	)	PUNCT
ejpam-5090	242	55	·	·	PUNCT
ejpam-5090	242	56	(	(	PUNCT
ejpam-5090	242	57	ϑ1	ϑ1	NOUN
ejpam-5090	242	58	,	,	PUNCT
ejpam-5090	242	59	η1	η1	NOUN
ejpam-5090	242	60	)	)	PUNCT
ejpam-5090	242	61	)	)	PUNCT
ejpam-5090	242	62	·	·	PUNCT
ejpam-5090	243	1	(	(	PUNCT
ejpam-5090	243	2	(	(	PUNCT
ejpam-5090	243	3	ϑ3	ϑ3	NOUN
ejpam-5090	243	4	,	,	PUNCT
ejpam-5090	243	5	η3	η3	PROPN
ejpam-5090	243	6	)	)	PUNCT
ejpam-5090	243	7	·	·	PUNCT
ejpam-5090	243	8	(	(	PUNCT
ejpam-5090	243	9	ϑ2	ϑ2	NOUN
ejpam-5090	243	10	,	,	PUNCT
ejpam-5090	243	11	η2	η2	NOUN
ejpam-5090	243	12	)	)	PUNCT
ejpam-5090	243	13	)	)	PUNCT
ejpam-5090	243	14	)	)	PUNCT
ejpam-5090	243	15	,	,	PUNCT
ejpam-5090	243	16	ρ	ρ	PROPN
ejpam-5090	243	17	f	f	PROPN
ejpam-5090	243	18	(	(	PUNCT
ejpam-5090	243	19	m×n)(ϑ2	m×n)(ϑ2	NOUN
ejpam-5090	243	20	,	,	PUNCT
ejpam-5090	243	21	η2	η2	PROPN
ejpam-5090	243	22	)	)	PUNCT
ejpam-5090	243	23	}	}	PUNCT
ejpam-5090	243	24	,	,	PUNCT
ejpam-5090	243	25	max	max	PROPN
ejpam-5090	243	26	{	{	PUNCT
ejpam-5090	243	27	ρf(d×e)(((ϑ3	ρf(d×e)(((ϑ3	PROPN
ejpam-5090	243	28	,	,	PUNCT
ejpam-5090	243	29	η3	η3	PROPN
ejpam-5090	243	30	)	)	PUNCT
ejpam-5090	243	31	·	·	PUNCT
ejpam-5090	243	32	(	(	PUNCT
ejpam-5090	243	33	ϑ1	ϑ1	NOUN
ejpam-5090	243	34	,	,	PUNCT
ejpam-5090	243	35	η1	η1	NOUN
ejpam-5090	243	36	)	)	PUNCT
ejpam-5090	243	37	)	)	PUNCT
ejpam-5090	243	38	·	·	PUNCT
ejpam-5090	244	1	(	(	PUNCT
ejpam-5090	244	2	(	(	PUNCT
ejpam-5090	244	3	ϑ3	ϑ3	NOUN
ejpam-5090	244	4	,	,	PUNCT
ejpam-5090	244	5	η3	η3	PROPN
ejpam-5090	244	6	)	)	PUNCT
ejpam-5090	244	7	·	·	PUNCT
ejpam-5090	244	8	(	(	PUNCT
ejpam-5090	244	9	ϑ2	ϑ2	NOUN
ejpam-5090	244	10	,	,	PUNCT
ejpam-5090	244	11	η2	η2	NOUN
ejpam-5090	244	12	)	)	PUNCT
ejpam-5090	244	13	)	)	PUNCT
ejpam-5090	244	14	)	)	PUNCT
ejpam-5090	244	15	,	,	PUNCT
ejpam-5090	244	16	ρ	ρ	PROPN
ejpam-5090	244	17	f	f	PROPN
ejpam-5090	244	18	(	(	PUNCT
ejpam-5090	244	19	d×e)(ϑ2	d×e)(ϑ2	NOUN
ejpam-5090	244	20	,	,	PUNCT
ejpam-5090	244	21	η2	η2	PROPN
ejpam-5090	244	22	)	)	PUNCT
ejpam-5090	244	23	}	}	PUNCT
ejpam-5090	244	24	}	}	PUNCT
ejpam-5090	244	25	=	=	SYM
ejpam-5090	244	26	max	max	PROPN
ejpam-5090	244	27	{	{	PUNCT
ejpam-5090	244	28	max	max	PROPN
ejpam-5090	244	29	{	{	PUNCT
ejpam-5090	244	30	ρf(m×n)(((ϑ3	ρf(m×n)(((ϑ3	PROPN
ejpam-5090	244	31	,	,	PUNCT
ejpam-5090	244	32	η3	η3	NOUN
ejpam-5090	244	33	)	)	PUNCT
ejpam-5090	244	34	·	·	PUNCT
ejpam-5090	244	35	(	(	PUNCT
ejpam-5090	244	36	ϑ1	ϑ1	NOUN
ejpam-5090	244	37	,	,	PUNCT
ejpam-5090	244	38	η1	η1	NOUN
ejpam-5090	244	39	)	)	PUNCT
ejpam-5090	244	40	)	)	PUNCT
ejpam-5090	244	41	·	·	PUNCT
ejpam-5090	245	1	(	(	PUNCT
ejpam-5090	245	2	(	(	PUNCT
ejpam-5090	245	3	ϑ3	ϑ3	NOUN
ejpam-5090	245	4	,	,	PUNCT
ejpam-5090	245	5	η3	η3	PROPN
ejpam-5090	245	6	)	)	PUNCT
ejpam-5090	245	7	·	·	PUNCT
ejpam-5090	245	8	(	(	PUNCT
ejpam-5090	245	9	ϑ2	ϑ2	NOUN
ejpam-5090	245	10	,	,	PUNCT
ejpam-5090	245	11	η2	η2	NOUN
ejpam-5090	245	12	)	)	PUNCT
ejpam-5090	245	13	)	)	PUNCT
ejpam-5090	245	14	)	)	PUNCT
ejpam-5090	245	15	,	,	PUNCT
ejpam-5090	245	16	ρf(d×e)(((ϑ3	ρf(d×e)(((ϑ3	PROPN
ejpam-5090	245	17	,	,	PUNCT
ejpam-5090	245	18	η3	η3	PROPN
ejpam-5090	245	19	)	)	PUNCT
ejpam-5090	245	20	·	·	PUNCT
ejpam-5090	245	21	(	(	PUNCT
ejpam-5090	245	22	ϑ1	ϑ1	NOUN
ejpam-5090	245	23	,	,	PUNCT
ejpam-5090	245	24	η1	η1	NOUN
ejpam-5090	245	25	)	)	PUNCT
ejpam-5090	245	26	)	)	PUNCT
ejpam-5090	245	27	·	·	PUNCT
ejpam-5090	246	1	(	(	PUNCT
ejpam-5090	246	2	(	(	PUNCT
ejpam-5090	246	3	ϑ3	ϑ3	NOUN
ejpam-5090	246	4	,	,	PUNCT
ejpam-5090	246	5	η3	η3	PROPN
ejpam-5090	246	6	)	)	PUNCT
ejpam-5090	246	7	·	·	PUNCT
ejpam-5090	246	8	(	(	PUNCT
ejpam-5090	246	9	ϑ2	ϑ2	NOUN
ejpam-5090	246	10	,	,	PUNCT
ejpam-5090	246	11	η2	η2	NOUN
ejpam-5090	246	12	)	)	PUNCT
ejpam-5090	246	13	)	)	PUNCT
ejpam-5090	246	14	)	)	PUNCT
ejpam-5090	246	15	}	}	PUNCT
ejpam-5090	246	16	,	,	PUNCT
ejpam-5090	246	17	max	max	PROPN
ejpam-5090	246	18	{	{	PUNCT
ejpam-5090	246	19	ρt(m×n)(ϑ2	ρt(m×n)(ϑ2	NOUN
ejpam-5090	246	20	,	,	PUNCT
ejpam-5090	246	21	η2	η2	PROPN
ejpam-5090	246	22	)	)	PUNCT
ejpam-5090	246	23	,	,	PUNCT
ejpam-5090	246	24	ρ	ρ	PROPN
ejpam-5090	246	25	f	f	PROPN
ejpam-5090	246	26	(	(	PUNCT
ejpam-5090	246	27	d×e)(ϑ2	d×e)(ϑ2	NOUN
ejpam-5090	246	28	,	,	PUNCT
ejpam-5090	246	29	η2	η2	PROPN
ejpam-5090	246	30	)	)	PUNCT
ejpam-5090	246	31	}	}	PUNCT
ejpam-5090	246	32	}	}	PUNCT
ejpam-5090	246	33	=	=	SYM
ejpam-5090	246	34	max	max	X
ejpam-5090	246	35	{	{	PUNCT
ejpam-5090	246	36	ρf(m×n)∩(d×e)(((ϑ3	ρf(m×n)∩(d×e)(((ϑ3	PROPN
ejpam-5090	246	37	,	,	PUNCT
ejpam-5090	246	38	η3	η3	NOUN
ejpam-5090	246	39	)	)	PUNCT
ejpam-5090	246	40	·	·	PUNCT
ejpam-5090	246	41	(	(	PUNCT
ejpam-5090	246	42	ϑ1	ϑ1	NOUN
ejpam-5090	246	43	,	,	PUNCT
ejpam-5090	246	44	η1	η1	NOUN
ejpam-5090	246	45	)	)	PUNCT
ejpam-5090	246	46	)	)	PUNCT
ejpam-5090	246	47	·	·	PUNCT
ejpam-5090	246	48	(	(	PUNCT
ejpam-5090	246	49	(	(	PUNCT
ejpam-5090	246	50	ϑ3	ϑ3	NOUN
ejpam-5090	246	51	,	,	PUNCT
ejpam-5090	246	52	η3	η3	PROPN
ejpam-5090	246	53	)	)	PUNCT
ejpam-5090	246	54	·	·	PUNCT
ejpam-5090	246	55	(	(	PUNCT
ejpam-5090	246	56	ϑ2	ϑ2	NOUN
ejpam-5090	246	57	,	,	PUNCT
ejpam-5090	246	58	η2	η2	NOUN
ejpam-5090	246	59	)	)	PUNCT
ejpam-5090	246	60	)	)	PUNCT
ejpam-5090	246	61	)	)	PUNCT
ejpam-5090	246	62	,	,	PUNCT
ejpam-5090	246	63	ρ	ρ	PROPN
ejpam-5090	246	64	f	f	PROPN
ejpam-5090	246	65	(	(	PUNCT
ejpam-5090	246	66	m×n)∩(d×e)(ϑ2	m×n)∩(d×e)(ϑ2	NOUN
ejpam-5090	246	67	,	,	PUNCT
ejpam-5090	246	68	η2	η2	PROPN
ejpam-5090	246	69	)	)	PUNCT
ejpam-5090	246	70	}	}	PUNCT
ejpam-5090	246	71	.	.	PUNCT
ejpam-5090	247	1	hence	hence	ADV
ejpam-5090	247	2	,	,	PUNCT
ejpam-5090	247	3	(	(	PUNCT
ejpam-5090	247	4	m×n)∩	m×n)∩	NOUN
ejpam-5090	247	5	(	(	PUNCT
ejpam-5090	247	6	d×e	d×e	PROPN
ejpam-5090	247	7	)	)	PUNCT
ejpam-5090	247	8	=	=	SYM
ejpam-5090	247	9	〈	〈	PROPN
ejpam-5090	247	10	ρt(m×n)∩(d×e	ρt(m×n)∩(d×e	NOUN
ejpam-5090	247	11	)	)	PUNCT
ejpam-5090	247	12	,	,	PUNCT
ejpam-5090	247	13	ρ	ρ	PROPN
ejpam-5090	247	14	i	i	PROPN
ejpam-5090	247	15	(	(	PUNCT
ejpam-5090	247	16	m×n)∩(d×e	m×n)∩(d×e	PROPN
ejpam-5090	247	17	)	)	PUNCT
ejpam-5090	247	18	,	,	PUNCT
ejpam-5090	247	19	ρ	ρ	PROPN
ejpam-5090	247	20	f	f	X
ejpam-5090	247	21	(	(	PUNCT
ejpam-5090	247	22	m×n)∩(d×e	m×n)∩(d×e	NOUN
ejpam-5090	247	23	)	)	PUNCT
ejpam-5090	247	24	〉	〉	NOUN
ejpam-5090	247	25	is	be	AUX
ejpam-5090	247	26	a	a	DET
ejpam-5090	247	27	fnink	fnink	NOUN
ejpam-5090	247	28	-	-	PUNCT
ejpam-5090	247	29	i	i	PRON
ejpam-5090	247	30	of	of	ADP
ejpam-5090	247	31	χ1	χ1	PROPN
ejpam-5090	247	32	×	×	PROPN
ejpam-5090	247	33	χ2	χ2	PROPN
ejpam-5090	247	34	.	.	PUNCT
ejpam-5090	248	1	4	4	NUM
ejpam-5090	248	2	.	.	X
ejpam-5090	248	3	comparison	comparison	NOUN
ejpam-5090	248	4	analysis	analysis	NOUN
ejpam-5090	248	5	a	a	DET
ejpam-5090	248	6	common	common	ADJ
ejpam-5090	248	7	ground	ground	NOUN
ejpam-5090	248	8	between	between	ADP
ejpam-5090	248	9	fnink	fnink	NOUN
ejpam-5090	248	10	-	-	PUNCT
ejpam-5090	248	11	algebras	algebras	PROPN
ejpam-5090	248	12	and	and	CCONJ
ejpam-5090	248	13	neutrosophic	neutrosophic	ADJ
ejpam-5090	248	14	ink	ink	NOUN
ejpam-5090	248	15	-	-	PUNCT
ejpam-5090	248	16	algebras	algebras	PROPN
ejpam-5090	248	17	is	be	AUX
ejpam-5090	248	18	inkalgebra	inkalgebra	NOUN
ejpam-5090	248	19	,	,	PUNCT
ejpam-5090	248	20	which	which	PRON
ejpam-5090	248	21	emphasizes	emphasize	VERB
ejpam-5090	248	22	the	the	DET
ejpam-5090	248	23	integration	integration	NOUN
ejpam-5090	248	24	of	of	ADP
ejpam-5090	248	25	non	non	ADJ
ejpam-5090	248	26	-	-	ADJ
ejpam-5090	248	27	membership	membership	ADJ
ejpam-5090	248	28	,	,	PUNCT
ejpam-5090	248	29	indeterminacy	indeterminacy	NOUN
ejpam-5090	248	30	,	,	PUNCT
ejpam-5090	248	31	and	and	CCONJ
ejpam-5090	248	32	uncertainty	uncertainty	NOUN
ejpam-5090	248	33	in	in	ADP
ejpam-5090	248	34	algebraic	algebraic	ADJ
ejpam-5090	248	35	structures	structure	NOUN
ejpam-5090	248	36	.	.	PUNCT
ejpam-5090	249	1	both	both	DET
ejpam-5090	249	2	approaches	approach	NOUN
ejpam-5090	249	3	are	be	AUX
ejpam-5090	249	4	intended	intend	VERB
ejpam-5090	249	5	for	for	ADP
ejpam-5090	249	6	complex	complex	ADJ
ejpam-5090	249	7	system	system	NOUN
ejpam-5090	249	8	modelling	modelling	NOUN
ejpam-5090	249	9	and	and	CCONJ
ejpam-5090	249	10	analysis	analysis	NOUN
ejpam-5090	249	11	,	,	PUNCT
ejpam-5090	249	12	where	where	SCONJ
ejpam-5090	249	13	a	a	DET
ejpam-5090	249	14	high	high	ADJ
ejpam-5090	249	15	prevalence	prevalence	NOUN
ejpam-5090	249	16	of	of	ADP
ejpam-5090	249	17	imprecise	imprecise	ADJ
ejpam-5090	249	18	and	and	CCONJ
ejpam-5090	249	19	incomplete	incomplete	ADJ
ejpam-5090	249	20	information	information	NOUN
ejpam-5090	249	21	exists	exist	VERB
ejpam-5090	249	22	.	.	PUNCT
ejpam-5090	250	1	although	although	SCONJ
ejpam-5090	250	2	both	both	DET
ejpam-5090	250	3	approaches	approach	NOUN
ejpam-5090	250	4	provide	provide	VERB
ejpam-5090	250	5	useful	useful	ADJ
ejpam-5090	250	6	tools	tool	NOUN
ejpam-5090	250	7	for	for	ADP
ejpam-5090	250	8	managing	manage	VERB
ejpam-5090	250	9	uncertainties	uncertainty	NOUN
ejpam-5090	250	10	in	in	ADP
ejpam-5090	250	11	algebraic	algebraic	ADJ
ejpam-5090	250	12	structures	structure	NOUN
ejpam-5090	250	13	,	,	PUNCT
ejpam-5090	250	14	fnink	fnink	NOUN
ejpam-5090	250	15	-	-	PUNCT
ejpam-5090	250	16	algebras	algebras	PROPN
ejpam-5090	250	17	are	be	AUX
ejpam-5090	250	18	a	a	DET
ejpam-5090	250	19	better	well	ADJ
ejpam-5090	250	20	method	method	NOUN
ejpam-5090	250	21	because	because	SCONJ
ejpam-5090	250	22	of	of	ADP
ejpam-5090	250	23	their	their	PRON
ejpam-5090	250	24	improved	improved	ADJ
ejpam-5090	250	25	specificity	specificity	NOUN
ejpam-5090	250	26	and	and	CCONJ
ejpam-5090	250	27	precision	precision	NOUN
ejpam-5090	250	28	.	.	PUNCT
ejpam-5090	251	1	fnink	fnink	NOUN
ejpam-5090	251	2	-	-	PUNCT
ejpam-5090	251	3	algebras	algebras	PROPN
ejpam-5090	251	4	are	be	AUX
ejpam-5090	251	5	a	a	DET
ejpam-5090	251	6	more	more	ADV
ejpam-5090	251	7	sophisticated	sophisticated	ADJ
ejpam-5090	251	8	and	and	CCONJ
ejpam-5090	251	9	elegant	elegant	ADJ
ejpam-5090	251	10	mathematical	mathematical	ADJ
ejpam-5090	251	11	framework	framework	NOUN
ejpam-5090	251	12	because	because	SCONJ
ejpam-5090	251	13	the	the	DET
ejpam-5090	251	14	incorporation	incorporation	NOUN
ejpam-5090	251	15	of	of	ADP
ejpam-5090	251	16	fermatean	fermatean	NOUN
ejpam-5090	251	17	features	feature	NOUN
ejpam-5090	251	18	enables	enable	VERB
ejpam-5090	251	19	a	a	DET
ejpam-5090	251	20	more	more	ADV
ejpam-5090	251	21	detailed	detailed	ADJ
ejpam-5090	251	22	representation	representation	NOUN
ejpam-5090	251	23	of	of	ADP
ejpam-5090	251	24	indeterminacies	indeterminacy	NOUN
ejpam-5090	251	25	and	and	CCONJ
ejpam-5090	251	26	non	non	NOUN
ejpam-5090	251	27	-	-	NOUN
ejpam-5090	251	28	memberships	membership	NOUN
ejpam-5090	251	29	.	.	PUNCT
ejpam-5090	252	1	specialized	specialized	ADJ
ejpam-5090	252	2	conditions	condition	NOUN
ejpam-5090	252	3	for	for	ADP
ejpam-5090	252	4	fncink	fncink	NOUN
ejpam-5090	252	5	-	-	PUNCT
ejpam-5090	252	6	is	be	AUX
ejpam-5090	252	7	and	and	CCONJ
ejpam-5090	252	8	direct	direct	ADJ
ejpam-5090	252	9	products	product	NOUN
ejpam-5090	252	10	add	add	VERB
ejpam-5090	252	11	to	to	ADP
ejpam-5090	252	12	the	the	DET
ejpam-5090	252	13	robustness	robustness	NOUN
ejpam-5090	252	14	and	and	CCONJ
ejpam-5090	252	15	generalizability	generalizability	NOUN
ejpam-5090	252	16	of	of	ADP
ejpam-5090	252	17	the	the	DET
ejpam-5090	252	18	method	method	NOUN
ejpam-5090	252	19	in	in	ADP
ejpam-5090	252	20	different	different	ADJ
ejpam-5090	252	21	fields	field	NOUN
ejpam-5090	252	22	.	.	PUNCT
ejpam-5090	253	1	as	as	ADP
ejpam-5090	253	2	a	a	DET
ejpam-5090	253	3	result	result	NOUN
ejpam-5090	253	4	,	,	PUNCT
ejpam-5090	253	5	fnink	fnink	NOUN
ejpam-5090	253	6	-	-	PUNCT
ejpam-5090	253	7	algebras	algebras	PROPN
ejpam-5090	253	8	become	become	VERB
ejpam-5090	253	9	the	the	DET
ejpam-5090	253	10	method	method	NOUN
ejpam-5090	253	11	of	of	ADP
ejpam-5090	253	12	choice	choice	NOUN
ejpam-5090	253	13	for	for	ADP
ejpam-5090	253	14	accurately	accurately	ADV
ejpam-5090	253	15	and	and	CCONJ
ejpam-5090	253	16	completely	completely	ADV
ejpam-5090	253	17	representing	represent	VERB
ejpam-5090	253	18	uncertainties	uncertainty	NOUN
ejpam-5090	253	19	in	in	ADP
ejpam-5090	253	20	complex	complex	ADJ
ejpam-5090	253	21	systems	system	NOUN
ejpam-5090	253	22	.	.	PUNCT
ejpam-5090	254	1	references	reference	NOUN
ejpam-5090	254	2	1127	1127	NUM
ejpam-5090	254	3	5	5	NUM
ejpam-5090	254	4	.	.	PUNCT
ejpam-5090	254	5	conclusion	conclusion	VERB
ejpam-5090	254	6	the	the	DET
ejpam-5090	254	7	notion	notion	NOUN
ejpam-5090	254	8	of	of	ADP
ejpam-5090	254	9	the	the	DET
ejpam-5090	254	10	direct	direct	ADJ
ejpam-5090	254	11	product	product	NOUN
ejpam-5090	254	12	of	of	ADP
ejpam-5090	254	13	fnss	fns	NOUN
ejpam-5090	254	14	is	be	AUX
ejpam-5090	254	15	used	use	VERB
ejpam-5090	254	16	in	in	ADP
ejpam-5090	254	17	this	this	DET
ejpam-5090	254	18	paper	paper	NOUN
ejpam-5090	254	19	to	to	PART
ejpam-5090	254	20	discuss	discuss	VERB
ejpam-5090	254	21	an	an	DET
ejpam-5090	254	22	ink	ink	NOUN
ejpam-5090	254	23	-	-	PUNCT
ejpam-5090	254	24	ideal	ideal	NOUN
ejpam-5090	254	25	inside	inside	ADP
ejpam-5090	254	26	an	an	DET
ejpam-5090	254	27	ink	ink	NOUN
ejpam-5090	254	28	-	-	PUNCT
ejpam-5090	254	29	algebra	algebra	NOUN
ejpam-5090	254	30	.	.	PUNCT
ejpam-5090	255	1	we	we	PRON
ejpam-5090	255	2	present	present	VERB
ejpam-5090	255	3	the	the	DET
ejpam-5090	255	4	direct	direct	ADJ
ejpam-5090	255	5	product	product	NOUN
ejpam-5090	255	6	for	for	ADP
ejpam-5090	255	7	fncink	fncink	NOUN
ejpam-5090	255	8	-	-	PUNCT
ejpam-5090	255	9	is	is	NOUN
ejpam-5090	255	10	and	and	CCONJ
ejpam-5090	255	11	fermatean	fermatean	PROPN
ejpam-5090	255	12	neutrosophic	neutrosophic	ADJ
ejpam-5090	255	13	ink	ink	NOUN
ejpam-5090	255	14	-	-	PUNCT
ejpam-5090	255	15	algebras	algebras	PROPN
ejpam-5090	255	16	,	,	PUNCT
ejpam-5090	255	17	examining	examine	VERB
ejpam-5090	255	18	a	a	DET
ejpam-5090	255	19	number	number	NOUN
ejpam-5090	255	20	of	of	ADP
ejpam-5090	255	21	properties	property	NOUN
ejpam-5090	255	22	.	.	PUNCT
ejpam-5090	256	1	the	the	DET
ejpam-5090	256	2	direct	direct	ADJ
ejpam-5090	256	3	product	product	NOUN
ejpam-5090	256	4	of	of	ADP
ejpam-5090	256	5	fnss	fns	NOUN
ejpam-5090	256	6	is	be	AUX
ejpam-5090	256	7	shown	show	VERB
ejpam-5090	256	8	to	to	PART
ejpam-5090	256	9	satisfy	satisfy	VERB
ejpam-5090	256	10	certain	certain	ADJ
ejpam-5090	256	11	requirements	requirement	NOUN
ejpam-5090	256	12	in	in	ADP
ejpam-5090	256	13	order	order	NOUN
ejpam-5090	256	14	to	to	PART
ejpam-5090	256	15	be	be	AUX
ejpam-5090	256	16	considered	consider	VERB
ejpam-5090	256	17	a	a	DET
ejpam-5090	256	18	direct	direct	ADJ
ejpam-5090	256	19	product	product	NOUN
ejpam-5090	256	20	of	of	ADP
ejpam-5090	256	21	fnink	fnink	NOUN
ejpam-5090	256	22	-	-	PUNCT
ejpam-5090	256	23	is	be	AUX
ejpam-5090	256	24	inside	inside	ADP
ejpam-5090	256	25	an	an	DET
ejpam-5090	256	26	ink	ink	NOUN
ejpam-5090	256	27	-	-	PUNCT
ejpam-5090	256	28	algebra	algebra	NOUN
ejpam-5090	256	29	.	.	PUNCT
ejpam-5090	257	1	references	reference	NOUN
ejpam-5090	257	2	[	[	X
ejpam-5090	257	3	1	1	NUM
ejpam-5090	257	4	]	]	PUNCT
ejpam-5090	257	5	l.	l.	PROPN
ejpam-5090	257	6	a.	a.	PROPN
ejpam-5090	257	7	zadeh	zadeh	PROPN
ejpam-5090	257	8	,	,	PUNCT
ejpam-5090	257	9	fuzzy	fuzzy	ADJ
ejpam-5090	257	10	sets	set	NOUN
ejpam-5090	257	11	,	,	PUNCT
ejpam-5090	257	12	inf	inf	PROPN
ejpam-5090	257	13	.	.	PUNCT
ejpam-5090	257	14	control	control	PROPN
ejpam-5090	257	15	8	8	NUM
ejpam-5090	257	16	:	:	SYM
ejpam-5090	257	17	338	338	NUM
ejpam-5090	257	18	-	-	SYM
ejpam-5090	257	19	353	353	NUM
ejpam-5090	257	20	,	,	PUNCT
ejpam-5090	257	21	1965	1965	NUM
ejpam-5090	257	22	.	.	PUNCT
ejpam-5090	258	1	[	[	X
ejpam-5090	258	2	2	2	X
ejpam-5090	258	3	]	]	PUNCT
ejpam-5090	258	4	k.	k.	PROPN
ejpam-5090	258	5	atanassov	atanassov	PROPN
ejpam-5090	258	6	,	,	PUNCT
ejpam-5090	258	7	intuitionistic	intuitionistic	ADJ
ejpam-5090	258	8	fuzzy	fuzzy	ADJ
ejpam-5090	258	9	sets	set	NOUN
ejpam-5090	258	10	,	,	PUNCT
ejpam-5090	258	11	fuzzy	fuzzy	ADJ
ejpam-5090	258	12	sets	set	NOUN
ejpam-5090	258	13	syst	syst	PROPN
ejpam-5090	258	14	.	.	PUNCT
ejpam-5090	258	15	,	,	PUNCT
ejpam-5090	258	16	20(1	20(1	NUM
ejpam-5090	258	17	):	):	PUNCT
ejpam-5090	258	18	87	87	NUM
ejpam-5090	258	19	-	-	SYM
ejpam-5090	258	20	96	96	NUM
ejpam-5090	258	21	,	,	PUNCT
ejpam-5090	258	22	1986	1986	NUM
ejpam-5090	258	23	.	.	PUNCT
ejpam-5090	259	1	[	[	X
ejpam-5090	259	2	3	3	X
ejpam-5090	259	3	]	]	PUNCT
ejpam-5090	259	4	m.	m.	NOUN
ejpam-5090	259	5	abdel	abdel	PROPN
ejpam-5090	259	6	basset	basset	PROPN
ejpam-5090	259	7	,	,	PUNCT
ejpam-5090	259	8	a.	a.	PROPN
ejpam-5090	259	9	gamal	gamal	PROPN
ejpam-5090	259	10	,	,	PUNCT
ejpam-5090	259	11	l.	l.	PROPN
ejpam-5090	259	12	h.	h.	PROPN
ejpam-5090	259	13	son	son	PROPN
ejpam-5090	259	14	,	,	PUNCT
ejpam-5090	259	15	f.	f.	PROPN
ejpam-5090	259	16	smarandache	smarandache	PROPN
ejpam-5090	259	17	,	,	PUNCT
ejpam-5090	259	18	a	a	DET
ejpam-5090	259	19	bipolar	bipolar	ADJ
ejpam-5090	259	20	neutrosophic	neutrosophic	ADJ
ejpam-5090	259	21	multi	multi	ADJ
ejpam-5090	259	22	criteria	criterion	NOUN
ejpam-5090	259	23	decision	decision	NOUN
ejpam-5090	259	24	making	make	VERB
ejpam-5090	259	25	framework	framework	NOUN
ejpam-5090	259	26	for	for	ADP
ejpam-5090	259	27	professional	professional	ADJ
ejpam-5090	259	28	selection	selection	NOUN
ejpam-5090	259	29	,	,	PUNCT
ejpam-5090	259	30	appl	appl	PROPN
ejpam-5090	259	31	.	.	PUNCT
ejpam-5090	260	1	sci	sci	PROPN
ejpam-5090	260	2	.	.	PROPN
ejpam-5090	260	3	,	,	PUNCT
ejpam-5090	260	4	10(4	10(4	NUM
ejpam-5090	260	5	):	):	PUNCT
ejpam-5090	260	6	1202	1202	NUM
ejpam-5090	260	7	,	,	PUNCT
ejpam-5090	260	8	2000	2000	NUM
ejpam-5090	260	9	.	.	PUNCT
ejpam-5090	261	1	[	[	X
ejpam-5090	261	2	4	4	X
ejpam-5090	261	3	]	]	X
ejpam-5090	261	4	f.	f.	PROPN
ejpam-5090	261	5	smarandache	smarandache	PROPN
ejpam-5090	261	6	,	,	PUNCT
ejpam-5090	261	7	neutrosophic	neutrosophic	ADJ
ejpam-5090	261	8	set	set	NOUN
ejpam-5090	261	9	-	-	PUNCT
ejpam-5090	261	10	a	a	DET
ejpam-5090	261	11	generalization	generalization	NOUN
ejpam-5090	261	12	of	of	ADP
ejpam-5090	261	13	the	the	DET
ejpam-5090	261	14	intuitionistic	intuitionistic	ADJ
ejpam-5090	261	15	fuzzy	fuzzy	ADJ
ejpam-5090	261	16	set	set	NOUN
ejpam-5090	261	17	,	,	PUNCT
ejpam-5090	261	18	journal	journal	NOUN
ejpam-5090	261	19	of	of	ADP
ejpam-5090	261	20	pure	pure	ADJ
ejpam-5090	261	21	applied	applied	ADJ
ejpam-5090	261	22	mathematics	mathematic	NOUN
ejpam-5090	261	23	,	,	PUNCT
ejpam-5090	261	24	24(3	24(3	NUM
ejpam-5090	261	25	):	):	PUNCT
ejpam-5090	261	26	287	287	NUM
ejpam-5090	261	27	-	-	SYM
ejpam-5090	261	28	297	297	NUM
ejpam-5090	261	29	.	.	PUNCT
ejpam-5090	261	30	2005	2005	NUM
ejpam-5090	261	31	.	.	PUNCT
ejpam-5090	262	1	[	[	X
ejpam-5090	262	2	5	5	X
ejpam-5090	262	3	]	]	X
ejpam-5090	262	4	y.	y.	PROPN
ejpam-5090	262	5	b.	b.	PROPN
ejpam-5090	262	6	jun	jun	PROPN
ejpam-5090	262	7	,	,	PUNCT
ejpam-5090	262	8	neutrosophic	neutrosophic	ADJ
ejpam-5090	262	9	subalgebras	subalgebra	NOUN
ejpam-5090	262	10	of	of	ADP
ejpam-5090	262	11	several	several	ADJ
ejpam-5090	262	12	types	type	NOUN
ejpam-5090	262	13	in	in	ADP
ejpam-5090	262	14	bck	bck	PROPN
ejpam-5090	262	15	/	/	SYM
ejpam-5090	262	16	bci	bci	NOUN
ejpam-5090	262	17	-	-	PUNCT
ejpam-5090	262	18	algebras	algebra	NOUN
ejpam-5090	262	19	,	,	PUNCT
ejpam-5090	262	20	ann	ann	PROPN
ejpam-5090	262	21	.	.	PROPN
ejpam-5090	262	22	fuzzy	fuzzy	ADJ
ejpam-5090	262	23	math	math	NOUN
ejpam-5090	262	24	.	.	PUNCT
ejpam-5090	263	1	inform	inform	NOUN
ejpam-5090	263	2	.	.	PUNCT
ejpam-5090	264	1	117(11	117(11	NUM
ejpam-5090	264	2	):	):	PUNCT
ejpam-5090	264	3	377	377	NUM
ejpam-5090	264	4	-	-	SYM
ejpam-5090	264	5	383	383	NUM
ejpam-5090	264	6	,	,	PUNCT
ejpam-5090	264	7	2017	2017	NUM
ejpam-5090	264	8	.	.	PUNCT
ejpam-5090	265	1	[	[	X
ejpam-5090	265	2	6	6	NUM
ejpam-5090	265	3	]	]	PUNCT
ejpam-5090	265	4	m.	m.	NOUN
ejpam-5090	265	5	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	265	6	,	,	PUNCT
ejpam-5090	265	7	k.	k.	PROPN
ejpam-5090	265	8	indhira	indhira	PROPN
ejpam-5090	265	9	,	,	PUNCT
ejpam-5090	265	10	v.	v.	ADP
ejpam-5090	265	11	m.	m.	NOUN
ejpam-5090	265	12	chandrasekaran	chandrasekaran	VERB
ejpam-5090	265	13	,	,	PUNCT
ejpam-5090	265	14	fuzzy	fuzzy	ADJ
ejpam-5090	265	15	subalgebras	subalgebra	NOUN
ejpam-5090	265	16	and	and	CCONJ
ejpam-5090	265	17	fuzzy	fuzzy	ADJ
ejpam-5090	265	18	ink	ink	NOUN
ejpam-5090	265	19	-	-	PUNCT
ejpam-5090	265	20	ideals	ideal	NOUN
ejpam-5090	265	21	in	in	ADP
ejpam-5090	265	22	ink	ink	NOUN
ejpam-5090	265	23	-	-	PUNCT
ejpam-5090	265	24	algebras	algebras	PROPN
ejpam-5090	265	25	,	,	PUNCT
ejpam-5090	265	26	int	int	PROPN
ejpam-5090	265	27	.	.	PUNCT
ejpam-5090	266	1	j.	j.	PROPN
ejpam-5090	266	2	pure	pure	PROPN
ejpam-5090	266	3	appl	appl	PROPN
ejpam-5090	266	4	.	.	PUNCT
ejpam-5090	266	5	math	math	PROPN
ejpam-5090	266	6	.	.	PUNCT
ejpam-5090	266	7	,	,	PUNCT
ejpam-5090	266	8	113(6	113(6	NUM
ejpam-5090	266	9	):	):	PUNCT
ejpam-5090	266	10	47	47	NUM
ejpam-5090	266	11	-	-	SYM
ejpam-5090	266	12	55	55	NUM
ejpam-5090	266	13	,	,	PUNCT
ejpam-5090	266	14	2017	2017	NUM
ejpam-5090	266	15	.	.	PUNCT
ejpam-5090	267	1	[	[	X
ejpam-5090	267	2	7	7	X
ejpam-5090	267	3	]	]	X
ejpam-5090	267	4	m.	m.	NOUN
ejpam-5090	267	5	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	267	6	,	,	PUNCT
ejpam-5090	267	7	k.	k.	PROPN
ejpam-5090	267	8	indhira	indhira	PROPN
ejpam-5090	267	9	,	,	PUNCT
ejpam-5090	267	10	review	review	NOUN
ejpam-5090	267	11	on	on	ADP
ejpam-5090	267	12	bci	bci	PROPN
ejpam-5090	267	13	/	/	SYM
ejpam-5090	267	14	bck	bck	PROPN
ejpam-5090	267	15	-	-	PUNCT
ejpam-5090	267	16	algebras	algebra	NOUN
ejpam-5090	267	17	and	and	CCONJ
ejpam-5090	267	18	development	development	NOUN
ejpam-5090	267	19	,	,	PUNCT
ejpam-5090	267	20	int	int	NOUN
ejpam-5090	267	21	.	.	PUNCT
ejpam-5090	268	1	j.	j.	PROPN
ejpam-5090	268	2	pure	pure	PROPN
ejpam-5090	268	3	appl	appl	PROPN
ejpam-5090	268	4	.	.	PUNCT
ejpam-5090	268	5	math	math	PROPN
ejpam-5090	268	6	.	.	PUNCT
ejpam-5090	268	7	,	,	PUNCT
ejpam-5090	268	8	117(11	117(11	NUM
ejpam-5090	268	9	):	):	PUNCT
ejpam-5090	268	10	377	377	NUM
ejpam-5090	268	11	-	-	SYM
ejpam-5090	268	12	383	383	NUM
ejpam-5090	268	13	,	,	PUNCT
ejpam-5090	268	14	2017	2017	NUM
ejpam-5090	268	15	.	.	PUNCT
ejpam-5090	269	1	[	[	X
ejpam-5090	269	2	8	8	NUM
ejpam-5090	269	3	]	]	X
ejpam-5090	269	4	m.	m.	NOUN
ejpam-5090	269	5	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	269	6	,	,	PUNCT
ejpam-5090	269	7	k.	k.	PROPN
ejpam-5090	269	8	indhira	indhira	PROPN
ejpam-5090	269	9	,	,	PUNCT
ejpam-5090	269	10	v.	v.	ADP
ejpam-5090	269	11	m.	m.	NOUN
ejpam-5090	269	12	chandrasekaran	chandrasekaran	VERB
ejpam-5090	269	13	,	,	PUNCT
ejpam-5090	269	14	fuzzy	fuzzy	ADJ
ejpam-5090	269	15	p	p	NOUN
ejpam-5090	269	16	-	-	PUNCT
ejpam-5090	269	17	ideal	ideal	NOUN
ejpam-5090	269	18	in	in	ADP
ejpam-5090	269	19	ink	ink	NOUN
ejpam-5090	269	20	-	-	PUNCT
ejpam-5090	269	21	algebra	algebra	NOUN
ejpam-5090	269	22	,	,	PUNCT
ejpam-5090	269	23	journal	journal	NOUN
ejpam-5090	269	24	of	of	ADP
ejpam-5090	269	25	xi’an	xi’an	PROPN
ejpam-5090	269	26	university	university	PROPN
ejpam-5090	269	27	of	of	ADP
ejpam-5090	269	28	architecture	architecture	NOUN
ejpam-5090	269	29	&	&	CCONJ
ejpam-5090	269	30	technology	technology	NOUN
ejpam-5090	269	31	,	,	PUNCT
ejpam-5090	269	32	12(3	12(3	NUM
ejpam-5090	269	33	):	):	PUNCT
ejpam-5090	269	34	47464752	47464752	NUM
ejpam-5090	269	35	,	,	PUNCT
ejpam-5090	269	36	2018	2018	NUM
ejpam-5090	269	37	.	.	PUNCT
ejpam-5090	270	1	[	[	X
ejpam-5090	270	2	9	9	NUM
ejpam-5090	270	3	]	]	X
ejpam-5090	270	4	y.	y.	PROPN
ejpam-5090	270	5	b.	b.	PROPN
ejpam-5090	270	6	jun	jun	PROPN
ejpam-5090	270	7	.	.	PROPN
ejpam-5090	270	8	,	,	PUNCT
ejpam-5090	270	9	f.	f.	PROPN
ejpam-5090	270	10	smarandache	smarandache	PROPN
ejpam-5090	270	11	,	,	PUNCT
ejpam-5090	270	12	h.	h.	PROPN
ejpam-5090	270	13	bordbar	bordbar	PROPN
ejpam-5090	270	14	,	,	PUNCT
ejpam-5090	270	15	neutrosophic	neutrosophic	ADJ
ejpam-5090	270	16	n	n	CCONJ
ejpam-5090	270	17	-	-	PUNCT
ejpam-5090	270	18	structures	structure	NOUN
ejpam-5090	270	19	applied	apply	VERB
ejpam-5090	270	20	to	to	PART
ejpam-5090	270	21	bck	bck	VERB
ejpam-5090	270	22	/	/	SYM
ejpam-5090	270	23	bci	bci	NOUN
ejpam-5090	270	24	-	-	PUNCT
ejpam-5090	270	25	algebras	algebra	NOUN
ejpam-5090	270	26	,	,	PUNCT
ejpam-5090	270	27	information	information	NOUN
ejpam-5090	270	28	8(4	8(4	NOUN
ejpam-5090	270	29	):	):	PUNCT
ejpam-5090	270	30	128	128	NUM
ejpam-5090	270	31	,	,	PUNCT
ejpam-5090	270	32	2017	2017	NUM
ejpam-5090	270	33	.	.	PUNCT
ejpam-5090	271	1	[	[	X
ejpam-5090	271	2	10	10	NUM
ejpam-5090	271	3	]	]	X
ejpam-5090	271	4	y.	y.	PROPN
ejpam-5090	271	5	b.	b.	PROPN
ejpam-5090	271	6	jun	jun	PROPN
ejpam-5090	271	7	.	.	PROPN
ejpam-5090	271	8	,	,	PUNCT
ejpam-5090	271	9	f.	f.	PROPN
ejpam-5090	271	10	smarandache	smarandache	PROPN
ejpam-5090	271	11	,	,	PUNCT
ejpam-5090	271	12	s.	s.	PROPN
ejpam-5090	271	13	z.	z.	PROPN
ejpam-5090	271	14	song	song	PROPN
ejpam-5090	271	15	,	,	PUNCT
ejpam-5090	271	16	m.	m.	PROPN
ejpam-5090	271	17	khan	khan	PROPN
ejpam-5090	271	18	,	,	PUNCT
ejpam-5090	271	19	neutrosophic	neutrosophic	ADJ
ejpam-5090	271	20	positive	positive	ADJ
ejpam-5090	271	21	implicative	implicative	ADJ
ejpam-5090	271	22	n	n	CCONJ
ejpam-5090	271	23	-	-	PUNCT
ejpam-5090	271	24	ideals	ideal	NOUN
ejpam-5090	271	25	in	in	ADP
ejpam-5090	271	26	bck	bck	NOUN
ejpam-5090	271	27	-	-	PUNCT
ejpam-5090	271	28	algebras	algebra	NOUN
ejpam-5090	271	29	,	,	PUNCT
ejpam-5090	271	30	axioms	axiom	NOUN
ejpam-5090	271	31	,	,	PUNCT
ejpam-5090	271	32	7(1	7(1	NUM
ejpam-5090	271	33	):	):	PUNCT
ejpam-5090	271	34	2018	2018	NUM
ejpam-5090	271	35	.	.	PUNCT
ejpam-5090	272	1	[	[	X
ejpam-5090	272	2	11	11	NUM
ejpam-5090	272	3	]	]	PUNCT
ejpam-5090	272	4	m.	m.	NOUN
ejpam-5090	272	5	a.	a.	PROPN
ejpam-5090	272	6	ozturk	ozturk	PROPN
ejpam-5090	272	7	,	,	PUNCT
ejpam-5090	272	8	y.	y.	PROPN
ejpam-5090	272	9	b.	b.	PROPN
ejpam-5090	272	10	jun	jun	PROPN
ejpam-5090	272	11	,	,	PUNCT
ejpam-5090	272	12	neutrosophic	neutrosophic	ADJ
ejpam-5090	272	13	ideals	ideal	NOUN
ejpam-5090	272	14	in	in	ADP
ejpam-5090	272	15	bck	bck	PROPN
ejpam-5090	272	16	/	/	SYM
ejpam-5090	272	17	bci	bci	NOUN
ejpam-5090	272	18	-	-	PUNCT
ejpam-5090	272	19	algebras	algebras	PROPN
ejpam-5090	272	20	based	base	VERB
ejpam-5090	272	21	on	on	ADP
ejpam-5090	272	22	neutrosophic	neutrosophic	ADJ
ejpam-5090	272	23	points	point	NOUN
ejpam-5090	272	24	,	,	PUNCT
ejpam-5090	272	25	journal	journal	NOUN
ejpam-5090	272	26	of	of	ADP
ejpam-5090	272	27	the	the	DET
ejpam-5090	272	28	international	international	ADJ
ejpam-5090	272	29	mathematical	mathematical	ADJ
ejpam-5090	272	30	virtual	virtual	PROPN
ejpam-5090	272	31	institute	institute	NOUN
ejpam-5090	272	32	,	,	PUNCT
ejpam-5090	272	33	8	8	NUM
ejpam-5090	272	34	:	:	SYM
ejpam-5090	272	35	1	1	NUM
ejpam-5090	272	36	-	-	SYM
ejpam-5090	272	37	17	17	NUM
ejpam-5090	272	38	,	,	PUNCT
ejpam-5090	272	39	2018	2018	NUM
ejpam-5090	272	40	.	.	PUNCT
ejpam-5090	273	1	[	[	X
ejpam-5090	273	2	12	12	NUM
ejpam-5090	273	3	]	]	PUNCT
ejpam-5090	273	4	m.	m.	NOUN
ejpam-5090	273	5	songsaeng	songsaeng	PROPN
ejpam-5090	273	6	,	,	PUNCT
ejpam-5090	273	7	a.	a.	NOUN
ejpam-5090	273	8	iampan	iampan	PROPN
ejpam-5090	273	9	,	,	PUNCT
ejpam-5090	273	10	neutrosophic	neutrosophic	ADJ
ejpam-5090	273	11	set	set	NOUN
ejpam-5090	273	12	theory	theory	NOUN
ejpam-5090	273	13	applied	apply	VERB
ejpam-5090	273	14	to	to	ADP
ejpam-5090	273	15	up	up	ADP
ejpam-5090	273	16	-	-	PUNCT
ejpam-5090	273	17	algebra	algebra	NOUN
ejpam-5090	273	18	,	,	PUNCT
ejpam-5090	273	19	eur	eur	PROPN
ejpam-5090	273	20	.	.	PUNCT
ejpam-5090	274	1	j.	j.	PROPN
ejpam-5090	274	2	pure	pure	PROPN
ejpam-5090	274	3	appl	appl	PROPN
ejpam-5090	274	4	.	.	PUNCT
ejpam-5090	274	5	math	math	PROPN
ejpam-5090	274	6	.	.	PUNCT
ejpam-5090	274	7	,	,	PUNCT
ejpam-5090	274	8	12(4	12(4	NUM
ejpam-5090	274	9	):	):	PUNCT
ejpam-5090	274	10	13821409	13821409	NUM
ejpam-5090	274	11	,	,	PUNCT
ejpam-5090	274	12	2019	2019	NUM
ejpam-5090	274	13	.	.	PUNCT
ejpam-5090	275	1	[	[	X
ejpam-5090	275	2	13	13	NUM
ejpam-5090	275	3	]	]	PUNCT
ejpam-5090	275	4	m.	m.	NOUN
ejpam-5090	275	5	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	275	6	,	,	PUNCT
ejpam-5090	275	7	k.	k.	PROPN
ejpam-5090	275	8	indhira	indhira	PROPN
ejpam-5090	275	9	,	,	PUNCT
ejpam-5090	275	10	v.	v.	ADP
ejpam-5090	275	11	m.	m.	NOUN
ejpam-5090	275	12	chandrasekaran	chandrasekaran	VERB
ejpam-5090	275	13	,	,	PUNCT
ejpam-5090	275	14	direct	direct	ADJ
ejpam-5090	275	15	product	product	NOUN
ejpam-5090	275	16	of	of	ADP
ejpam-5090	275	17	intuitionistic	intuitionistic	ADJ
ejpam-5090	275	18	fuzzy	fuzzy	ADJ
ejpam-5090	275	19	ink	ink	NOUN
ejpam-5090	275	20	-	-	PUNCT
ejpam-5090	275	21	ideals	ideal	NOUN
ejpam-5090	275	22	of	of	ADP
ejpam-5090	275	23	ink	ink	NOUN
ejpam-5090	275	24	-	-	PUNCT
ejpam-5090	275	25	algebras	algebra	NOUN
ejpam-5090	275	26	,	,	PUNCT
ejpam-5090	275	27	material	material	NOUN
ejpam-5090	275	28	today	today	NOUN
ejpam-5090	275	29	:	:	PUNCT
ejpam-5090	275	30	proceedings	proceeding	NOUN
ejpam-5090	275	31	,	,	PUNCT
ejpam-5090	275	32	16(2	16(2	NUM
ejpam-5090	275	33	):	):	PUNCT
ejpam-5090	275	34	449	449	NUM
ejpam-5090	275	35	-	-	NUM
ejpam-5090	275	36	455	455	NUM
ejpam-5090	275	37	,	,	PUNCT
ejpam-5090	275	38	2019	2019	NUM
ejpam-5090	275	39	.	.	PUNCT
ejpam-5090	276	1	references	reference	NOUN
ejpam-5090	276	2	1128	1128	NUM
ejpam-5090	276	3	[	[	X
ejpam-5090	276	4	14	14	NUM
ejpam-5090	276	5	]	]	PUNCT
ejpam-5090	276	6	m.	m.	NOUN
ejpam-5090	276	7	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	276	8	,	,	PUNCT
ejpam-5090	276	9	k.	k.	PROPN
ejpam-5090	276	10	indhira	indhira	PROPN
ejpam-5090	276	11	.	.	PUNCT
ejpam-5090	276	12	,	,	PUNCT
ejpam-5090	276	13	v.	v.	ADP
ejpam-5090	276	14	m.	m.	NOUN
ejpam-5090	276	15	chandrasekaran	chandrasekaran	VERB
ejpam-5090	276	16	,	,	PUNCT
ejpam-5090	276	17	intuitionistic	intuitionistic	ADJ
ejpam-5090	276	18	fuzzy	fuzzy	ADJ
ejpam-5090	276	19	translation	translation	NOUN
ejpam-5090	276	20	on	on	ADP
ejpam-5090	276	21	ink	ink	NOUN
ejpam-5090	276	22	-	-	PUNCT
ejpam-5090	276	23	algebra	algebra	NOUN
ejpam-5090	276	24	,	,	PUNCT
ejpam-5090	276	25	adv	adv	PROPN
ejpam-5090	276	26	.	.	PUNCT
ejpam-5090	276	27	math	math	PROPN
ejpam-5090	276	28	.	.	PUNCT
ejpam-5090	276	29	,	,	PUNCT
ejpam-5090	277	1	sci	sci	PROPN
ejpam-5090	277	2	.	.	PUNCT
ejpam-5090	277	3	j.	j.	PROPN
ejpam-5090	277	4	,	,	PUNCT
ejpam-5090	277	5	9(1	9(1	NUM
ejpam-5090	277	6	):	):	PUNCT
ejpam-5090	277	7	295	295	NUM
ejpam-5090	277	8	-	-	SYM
ejpam-5090	277	9	303	303	NUM
ejpam-5090	277	10	,	,	PUNCT
ejpam-5090	277	11	2020	2020	NUM
ejpam-5090	277	12	.	.	PUNCT
ejpam-5090	278	1	[	[	X
ejpam-5090	278	2	15	15	NUM
ejpam-5090	278	3	]	]	X
ejpam-5090	278	4	m.	m.	NOUN
ejpam-5090	278	5	kaviyarasu	kaviyarasu	PROPN
ejpam-5090	278	6	,	,	PUNCT
ejpam-5090	278	7	k.	k.	PROPN
ejpam-5090	278	8	indhira	indhira	PROPN
ejpam-5090	278	9	.	.	PUNCT
ejpam-5090	278	10	,	,	PUNCT
ejpam-5090	278	11	v.	v.	ADP
ejpam-5090	278	12	m.	m.	NOUN
ejpam-5090	278	13	chandrasekaran	chandrasekaran	VERB
ejpam-5090	278	14	,	,	PUNCT
ejpam-5090	278	15	neutrosophic	neutrosophic	PROPN
ejpam-5090	278	16	set	set	VERB
ejpam-5090	278	17	in	in	ADP
ejpam-5090	278	18	ink	ink	NOUN
ejpam-5090	278	19	-	-	PUNCT
ejpam-5090	278	20	algebra	algebra	NOUN
ejpam-5090	278	21	,	,	PUNCT
ejpam-5090	278	22	adv	adv	PROPN
ejpam-5090	278	23	.	.	PUNCT
ejpam-5090	278	24	math	math	PROPN
ejpam-5090	278	25	.	.	PUNCT
ejpam-5090	278	26	,	,	PUNCT
ejpam-5090	279	1	sci	sci	PROPN
ejpam-5090	279	2	.	.	PUNCT
ejpam-5090	279	3	j.	j.	PROPN
ejpam-5090	279	4	,	,	PUNCT
ejpam-5090	279	5	9(7	9(7	NUM
ejpam-5090	279	6	):	):	PUNCT
ejpam-5090	279	7	4345	4345	NUM
ejpam-5090	279	8	-	-	SYM
ejpam-5090	279	9	4352	4352	NUM
ejpam-5090	279	10	,	,	PUNCT
ejpam-5090	279	11	2020	2020	NUM
ejpam-5090	279	12	.	.	PUNCT
ejpam-5090	280	1	[	[	X
ejpam-5090	280	2	16	16	NUM
ejpam-5090	280	3	]	]	X
ejpam-5090	280	4	f.	f.	PROPN
ejpam-5090	280	5	smarandache	smarandache	PROPN
ejpam-5090	280	6	,	,	PUNCT
ejpam-5090	280	7	neutro	neutro	PROPN
ejpam-5090	280	8	algebra	algebra	PROPN
ejpam-5090	280	9	is	be	AUX
ejpam-5090	280	10	a	a	DET
ejpam-5090	280	11	generalization	generalization	NOUN
ejpam-5090	280	12	of	of	ADP
ejpam-5090	280	13	partial	partial	ADJ
ejpam-5090	280	14	algebra	algebra	NOUN
ejpam-5090	280	15	,	,	PUNCT
ejpam-5090	280	16	int	int	NOUN
ejpam-5090	280	17	.	.	PUNCT
ejpam-5090	281	1	j.	j.	PROPN
ejpam-5090	281	2	neutrosophic	neutrosophic	PROPN
ejpam-5090	281	3	sci	sci	PROPN
ejpam-5090	281	4	.	.	PROPN
ejpam-5090	281	5	,	,	PUNCT
ejpam-5090	281	6	2(1	2(1	NUM
ejpam-5090	281	7	):	):	PUNCT
ejpam-5090	281	8	8	8	NUM
ejpam-5090	281	9	-	-	SYM
ejpam-5090	281	10	17	17	NUM
ejpam-5090	281	11	,	,	PUNCT
ejpam-5090	281	12	2020	2020	NUM
ejpam-5090	281	13	.	.	PUNCT
ejpam-5090	282	1	[	[	X
ejpam-5090	282	2	17	17	NUM
ejpam-5090	282	3	]	]	X
ejpam-5090	282	4	f.	f.	PROPN
ejpam-5090	282	5	smarandache	smarandache	PROPN
ejpam-5090	282	6	,	,	PUNCT
ejpam-5090	282	7	introduction	introduction	NOUN
ejpam-5090	282	8	to	to	PART
ejpam-5090	282	9	neutro	neutro	VERB
ejpam-5090	282	10	algebraic	algebraic	ADJ
ejpam-5090	282	11	structures	structure	NOUN
ejpam-5090	282	12	and	and	CCONJ
ejpam-5090	282	13	anti	anti	ADJ
ejpam-5090	282	14	algebraic	algebraic	ADJ
ejpam-5090	282	15	structures	structure	NOUN
ejpam-5090	282	16	(	(	PUNCT
ejpam-5090	282	17	revisited	revisit	VERB
ejpam-5090	282	18	)	)	PUNCT
ejpam-5090	282	19	,	,	PUNCT
ejpam-5090	282	20	fuzzy	fuzzy	ADJ
ejpam-5090	282	21	sets	set	VERB
ejpam-5090	282	22	syst	syst	PROPN
ejpam-5090	282	23	.	.	PUNCT
ejpam-5090	282	24	,	,	PUNCT
ejpam-5090	282	25	31	31	NUM
ejpam-5090	282	26	:	:	SYM
ejpam-5090	282	27	1	1	NUM
ejpam-5090	282	28	-	-	SYM
ejpam-5090	282	29	16	16	NUM
ejpam-5090	282	30	,	,	PUNCT
ejpam-5090	282	31	2020	2020	NUM
ejpam-5090	282	32	.	.	PUNCT
ejpam-5090	283	1	[	[	X
ejpam-5090	283	2	18	18	NUM
ejpam-5090	283	3	]	]	PUNCT
ejpam-5090	283	4	m.	m.	NOUN
ejpam-5090	283	5	abdel	abdel	PROPN
ejpam-5090	283	6	-	-	PUNCT
ejpam-5090	283	7	basset	basset	PROPN
ejpam-5090	283	8	,	,	PUNCT
ejpam-5090	283	9	r.	r.	PROPN
ejpam-5090	283	10	mohamed	mohamed	PROPN
ejpam-5090	283	11	,	,	PUNCT
ejpam-5090	283	12	a.	a.	PROPN
ejpam-5090	283	13	h.	h.	PROPN
ejpam-5090	283	14	zaied	zaie	VERB
ejpam-5090	283	15	,	,	PUNCT
ejpam-5090	283	16	a.	a.	PROPN
ejpam-5090	283	17	gamal	gamal	PROPN
ejpam-5090	283	18	,	,	PUNCT
ejpam-5090	283	19	f.	f.	PROPN
ejpam-5090	283	20	smarandache	smarandache	PROPN
ejpam-5090	283	21	,	,	PUNCT
ejpam-5090	283	22	solving	solve	VERB
ejpam-5090	283	23	the	the	DET
ejpam-5090	283	24	supply	supply	NOUN
ejpam-5090	283	25	chain	chain	NOUN
ejpam-5090	283	26	problem	problem	NOUN
ejpam-5090	283	27	using	use	VERB
ejpam-5090	283	28	the	the	DET
ejpam-5090	283	29	best	well	ADV
ejpam-5090	283	30	-	-	PUNCT
ejpam-5090	283	31	worst	bad	ADJ
ejpam-5090	283	32	method	method	NOUN
ejpam-5090	283	33	based	base	VERB
ejpam-5090	283	34	on	on	ADP
ejpam-5090	283	35	a	a	DET
ejpam-5090	283	36	novel	novel	ADJ
ejpam-5090	283	37	plithogenic	plithogenic	ADJ
ejpam-5090	283	38	model	model	NOUN
ejpam-5090	283	39	,	,	PUNCT
ejpam-5090	283	40	optimization	optimization	NOUN
ejpam-5090	283	41	theory	theory	NOUN
ejpam-5090	283	42	based	base	VERB
ejpam-5090	283	43	on	on	ADP
ejpam-5090	283	44	neutrosophic	neutrosophic	ADJ
ejpam-5090	283	45	and	and	CCONJ
ejpam-5090	283	46	plithogenic	plithogenic	ADJ
ejpam-5090	283	47	sets	set	NOUN
ejpam-5090	283	48	,	,	PUNCT
ejpam-5090	283	49	1	1	NUM
ejpam-5090	283	50	-	-	SYM
ejpam-5090	283	51	19	19	NUM
ejpam-5090	283	52	,	,	PUNCT
ejpam-5090	283	53	2020	2020	NUM
ejpam-5090	283	54	.	.	PUNCT
ejpam-5090	284	1	[	[	X
ejpam-5090	284	2	19	19	NUM
ejpam-5090	284	3	]	]	PUNCT
ejpam-5090	284	4	m.	m.	NOUN
ejpam-5090	284	5	abdel	abdel	PROPN
ejpam-5090	284	6	basset	basset	PROPN
ejpam-5090	284	7	,	,	PUNCT
ejpam-5090	284	8	w.	w.	PROPN
ejpam-5090	284	9	ding	ding	PROPN
ejpam-5090	284	10	,	,	PUNCT
ejpam-5090	284	11	r.	r.	PROPN
ejpam-5090	284	12	mohamed	mohamed	PROPN
ejpam-5090	284	13	,	,	PUNCT
ejpam-5090	284	14	n.	n.	PROPN
ejpam-5090	284	15	metawa	metawa	PROPN
ejpam-5090	284	16	,	,	PUNCT
ejpam-5090	284	17	an	an	DET
ejpam-5090	284	18	integrated	integrate	VERB
ejpam-5090	284	19	plithogenic	plithogenic	ADJ
ejpam-5090	284	20	mcdm	mcdm	ADJ
ejpam-5090	284	21	approach	approach	NOUN
ejpam-5090	284	22	for	for	ADP
ejpam-5090	284	23	financial	financial	ADJ
ejpam-5090	284	24	performance	performance	NOUN
ejpam-5090	284	25	evaluation	evaluation	NOUN
ejpam-5090	284	26	of	of	ADP
ejpam-5090	284	27	manufacturing	manufacturing	NOUN
ejpam-5090	284	28	industries	industry	NOUN
ejpam-5090	284	29	,	,	PUNCT
ejpam-5090	284	30	risk	risk	NOUN
ejpam-5090	284	31	manag	manag	NOUN
ejpam-5090	284	32	.	.	PUNCT
ejpam-5090	284	33	,	,	PUNCT
ejpam-5090	284	34	1	1	NUM
ejpam-5090	284	35	-	-	SYM
ejpam-5090	284	36	27	27	NUM
ejpam-5090	284	37	.	.	PUNCT
ejpam-5090	284	38	2020	2020	NUM
ejpam-5090	284	39	.	.	PUNCT
ejpam-5090	285	1	[	[	X
ejpam-5090	285	2	20	20	NUM
ejpam-5090	285	3	]	]	PUNCT
ejpam-5090	285	4	m.	m.	NOUN
ejpam-5090	285	5	abdel	abdel	PROPN
ejpam-5090	285	6	basset	basset	PROPN
ejpam-5090	285	7	,	,	PUNCT
ejpam-5090	285	8	mohamed	mohamed	PROPN
ejpam-5090	285	9	.	.	PROPN
ejpam-5090	285	10	,	,	PUNCT
ejpam-5090	285	11	m.	m.	NOUN
ejpam-5090	285	12	elhoseny	elhoseny	PROPN
ejpam-5090	285	13	,	,	PUNCT
ejpam-5090	285	14	a	a	DET
ejpam-5090	285	15	novel	novel	ADJ
ejpam-5090	285	16	framework	framework	NOUN
ejpam-5090	285	17	to	to	PART
ejpam-5090	285	18	evaluate	evaluate	VERB
ejpam-5090	285	19	innovation	innovation	NOUN
ejpam-5090	285	20	value	value	NOUN
ejpam-5090	285	21	proposition	proposition	NOUN
ejpam-5090	285	22	for	for	ADP
ejpam-5090	285	23	smart	smart	ADJ
ejpam-5090	285	24	product	product	NOUN
ejpam-5090	285	25	-	-	PUNCT
ejpam-5090	285	26	service	service	NOUN
ejpam-5090	285	27	systemsl	systemsl	NOUN
ejpam-5090	285	28	,	,	PUNCT
ejpam-5090	285	29	environ	environ	PROPN
ejpam-5090	285	30	.	.	PUNCT
ejpam-5090	285	31	technol	technol	PROPN
ejpam-5090	285	32	.	.	PUNCT
ejpam-5090	285	33	innov	innov	PROPN
ejpam-5090	285	34	.	.	PROPN
ejpam-5090	285	35	,	,	PUNCT
ejpam-5090	285	36	101036	101036	NUM
ejpam-5090	285	37	,	,	PUNCT
ejpam-5090	285	38	2020	2020	NUM
ejpam-5090	285	39	.	.	PUNCT
ejpam-5090	286	1	[	[	X
ejpam-5090	286	2	21	21	NUM
ejpam-5090	286	3	]	]	X
ejpam-5090	286	4	p.	p.	PROPN
ejpam-5090	286	5	b.	b.	PROPN
ejpam-5090	286	6	remya	remya	PROPN
ejpam-5090	286	7	,	,	PUNCT
ejpam-5090	286	8	a.	a.	PROPN
ejpam-5090	286	9	francina	francina	PROPN
ejpam-5090	286	10	shalini	shalini	PROPN
ejpam-5090	286	11	,	,	PUNCT
ejpam-5090	286	12	neutrosophic	neutrosophic	ADJ
ejpam-5090	286	13	vague	vague	ADJ
ejpam-5090	286	14	binary	binary	ADJ
ejpam-5090	286	15	bck	bck	PROPN
ejpam-5090	286	16	/	/	SYM
ejpam-5090	286	17	bci	bci	NOUN
ejpam-5090	286	18	-	-	NOUN
ejpam-5090	286	19	algebra	algebra	NOUN
ejpam-5090	286	20	,	,	PUNCT
ejpam-5090	286	21	fuzzy	fuzzy	ADJ
ejpam-5090	286	22	sets	set	NOUN
ejpam-5090	286	23	syst	syst	PROPN
ejpam-5090	286	24	.	.	PUNCT
ejpam-5090	286	25	,	,	PUNCT
ejpam-5090	286	26	35	35	NUM
ejpam-5090	286	27	:	:	SYM
ejpam-5090	286	28	45	45	NUM
ejpam-5090	286	29	-	-	SYM
ejpam-5090	286	30	67	67	NUM
ejpam-5090	286	31	,	,	PUNCT
ejpam-5090	286	32	2020	2020	NUM
ejpam-5090	286	33	.	.	PUNCT
ejpam-5090	287	1	[	[	X
ejpam-5090	287	2	22	22	NUM
ejpam-5090	287	3	]	]	PUNCT
ejpam-5090	287	4	p.	p.	NOUN
ejpam-5090	287	5	muralikrishna	muralikrishna	NOUN
ejpam-5090	287	6	,	,	PUNCT
ejpam-5090	287	7	s.	s.	PROPN
ejpam-5090	287	8	manokaran	manokaran	PROPN
ejpam-5090	287	9	,	,	PUNCT
ejpam-5090	287	10	mbj	mbj	PROPN
ejpam-5090	287	11	-	-	PUNCT
ejpam-5090	287	12	neutrosophic	neutrosophic	ADJ
ejpam-5090	287	13	b	b	NOUN
ejpam-5090	287	14	-	-	PUNCT
ejpam-5090	287	15	ideal	ideal	NOUN
ejpam-5090	287	16	of	of	ADP
ejpam-5090	287	17	b	b	NOUN
ejpam-5090	287	18	-	-	PUNCT
ejpam-5090	287	19	algebra	algebra	NOUN
ejpam-5090	287	20	,	,	PUNCT
ejpam-5090	287	21	fuzzy	fuzzy	ADJ
ejpam-5090	287	22	sets	set	NOUN
ejpam-5090	287	23	syst	syst	PROPN
ejpam-5090	287	24	.	.	PUNCT
ejpam-5090	288	1	,	,	PUNCT
ejpam-5090	288	2	35	35	NUM
ejpam-5090	288	3	:	:	SYM
ejpam-5090	288	4	99	99	NUM
ejpam-5090	288	5	-	-	SYM
ejpam-5090	288	6	118	118	NUM
ejpam-5090	288	7	,	,	PUNCT
ejpam-5090	288	8	2020	2020	NUM
ejpam-5090	288	9	.	.	PUNCT
ejpam-5090	289	1	[	[	X
ejpam-5090	289	2	23	23	NUM
ejpam-5090	289	3	]	]	PUNCT
ejpam-5090	289	4	a.	a.	PROPN
ejpam-5090	289	5	al	al	PROPN
ejpam-5090	289	6	-	-	PUNCT
ejpam-5090	289	7	masarwah	masarwah	PROPN
ejpam-5090	289	8	,	,	PUNCT
ejpam-5090	289	9	m.	m.	NOUN
ejpam-5090	289	10	alqahtani	alqahtani	PROPN
ejpam-5090	289	11	,	,	PUNCT
ejpam-5090	289	12	operational	operational	ADJ
ejpam-5090	289	13	algebraic	algebraic	ADJ
ejpam-5090	289	14	properties	property	NOUN
ejpam-5090	289	15	and	and	CCONJ
ejpam-5090	289	16	subsemigroups	subsemigroup	NOUN
ejpam-5090	289	17	of	of	ADP
ejpam-5090	289	18	semigroups	semigroup	NOUN
ejpam-5090	289	19	in	in	ADP
ejpam-5090	289	20	view	view	NOUN
ejpam-5090	289	21	of	of	ADP
ejpam-5090	289	22	n	n	ADV
ejpam-5090	289	23	-	-	PUNCT
ejpam-5090	289	24	folded	fold	VERB
ejpam-5090	289	25	-structures	-structure	NOUN
ejpam-5090	289	26	,	,	PUNCT
ejpam-5090	289	27	aims	aim	VERB
ejpam-5090	289	28	math	math	NOUN
ejpam-5090	289	29	.	.	PUNCT
ejpam-5090	289	30	,	,	PUNCT
ejpam-5090	289	31	8(9	8(9	NUM
ejpam-5090	289	32	):	):	PUNCT
ejpam-5090	289	33	22081	22081	NUM
ejpam-5090	289	34	-	-	SYM
ejpam-5090	289	35	22096	22096	NUM
ejpam-5090	289	36	,	,	PUNCT
ejpam-5090	289	37	2023	2023	NUM
ejpam-5090	289	38	.	.	PUNCT
ejpam-5090	290	1	[	[	X
ejpam-5090	290	2	24	24	NUM
ejpam-5090	290	3	]	]	PUNCT
ejpam-5090	290	4	a.	a.	NOUN
ejpam-5090	290	5	fallatah	fallatah	PROPN
ejpam-5090	290	6	,	,	PUNCT
ejpam-5090	290	7	m.	m.	NOUN
ejpam-5090	290	8	massa’deh	massa’deh	PROPN
ejpam-5090	290	9	,	,	PUNCT
ejpam-5090	290	10	a.	a.	PROPN
ejpam-5090	290	11	alkouri	alkouri	PROPN
ejpam-5090	290	12	,	,	PUNCT
ejpam-5090	290	13	normal	normal	ADJ
ejpam-5090	290	14	and	and	CCONJ
ejpam-5090	290	15	cosets	coset	NOUN
ejpam-5090	290	16	of	of	ADP
ejpam-5090	290	17	(	(	PUNCT
ejpam-5090	290	18	γ	γ	X
ejpam-5090	290	19	,	,	PUNCT
ejpam-5090	290	20	δ)-fuzzy	δ)-fuzzy	ADJ
ejpam-5090	290	21	hxsubgroups	hxsubgroup	NOUN
ejpam-5090	290	22	.	.	PUNCT
ejpam-5090	291	1	j.	j.	PROPN
ejpam-5090	291	2	appl	appl	PROPN
ejpam-5090	291	3	.	.	PROPN
ejpam-5090	291	4	math	math	PROPN
ejpam-5090	291	5	.	.	PUNCT
ejpam-5090	292	1	inform	inform	NOUN
ejpam-5090	292	2	.	.	PUNCT
ejpam-5090	293	1	40	40	NUM
ejpam-5090	293	2	:	:	PUNCT
ejpam-5090	293	3	719–727	719–727	NUM
ejpam-5090	293	4	,	,	PUNCT
ejpam-5090	293	5	2022	2022	NUM
ejpam-5090	293	6	.	.	PUNCT
ejpam-5090	294	1	[	[	X
ejpam-5090	294	2	25	25	NUM
ejpam-5090	294	3	]	]	PUNCT
ejpam-5090	294	4	a.	a.	PROPN
ejpam-5090	294	5	al	al	PROPN
ejpam-5090	294	6	-	-	PUNCT
ejpam-5090	294	7	masarwah	masarwah	PROPN
ejpam-5090	294	8	,	,	PUNCT
ejpam-5090	294	9	a.g	a.g	PROPN
ejpam-5090	294	10	.	.	PROPN
ejpam-5090	294	11	ahmad	ahmad	PROPN
ejpam-5090	294	12	,	,	PUNCT
ejpam-5090	294	13	m	m	NOUN
ejpam-5090	294	14	-	-	ADJ
ejpam-5090	294	15	polar	polar	ADJ
ejpam-5090	294	16	fuzzy	fuzzy	ADJ
ejpam-5090	294	17	ideals	ideal	NOUN
ejpam-5090	294	18	of	of	ADP
ejpam-5090	294	19	bck	bck	PROPN
ejpam-5090	294	20	/	/	SYM
ejpam-5090	294	21	bci	bci	NOUN
ejpam-5090	294	22	-	-	PUNCT
ejpam-5090	294	23	algebras	algebra	NOUN
ejpam-5090	294	24	,	,	PUNCT
ejpam-5090	294	25	j.	j.	PROPN
ejpam-5090	294	26	king	king	PROPN
ejpam-5090	294	27	saud	saud	PROPN
ejpam-5090	294	28	univ	univ	PROPN
ejpam-5090	294	29	.	.	PUNCT
ejpam-5090	295	1	sci	sci	PROPN
ejpam-5090	295	2	.	.	PROPN
ejpam-5090	296	1	31	31	NUM
ejpam-5090	296	2	:	:	PUNCT
ejpam-5090	296	3	1220–1226	1220–1226	NUM
ejpam-5090	296	4	,	,	PUNCT
ejpam-5090	296	5	2019	2019	NUM
ejpam-5090	296	6	.	.	PUNCT
ejpam-5090	297	1	[	[	X
ejpam-5090	297	2	26	26	NUM
ejpam-5090	297	3	]	]	X
ejpam-5090	297	4	e.a	e.a	PROPN
ejpam-5090	297	5	.	.	PROPN
ejpam-5090	297	6	abuhijleh	abuhijleh	PROPN
ejpam-5090	297	7	,	,	PUNCT
ejpam-5090	297	8	m.	m.	NOUN
ejpam-5090	297	9	massa’deh	massa’deh	PROPN
ejpam-5090	297	10	,	,	PUNCT
ejpam-5090	297	11	a.	a.	NOUN
ejpam-5090	297	12	sheimat	sheimat	NOUN
ejpam-5090	297	13	,	,	PUNCT
ejpam-5090	297	14	a.	a.	PROPN
ejpam-5090	297	15	alkouri	alkouri	PROPN
ejpam-5090	297	16	,	,	PUNCT
ejpam-5090	297	17	complex	complex	ADJ
ejpam-5090	297	18	fuzzy	fuzzy	ADJ
ejpam-5090	297	19	groups	group	NOUN
ejpam-5090	297	20	based	base	VERB
ejpam-5090	297	21	on	on	ADP
ejpam-5090	297	22	rosenfeld	rosenfeld	PROPN
ejpam-5090	297	23	’s	’s	PART
ejpam-5090	297	24	approach	approach	NOUN
ejpam-5090	297	25	,	,	PUNCT
ejpam-5090	297	26	wseas	wseas	PROPN
ejpam-5090	297	27	trans	trans	PROPN
ejpam-5090	297	28	.	.	PROPN
ejpam-5090	298	1	math	math	NOUN
ejpam-5090	298	2	.	.	PUNCT
ejpam-5090	299	1	20	20	NUM
ejpam-5090	299	2	:	:	PUNCT
ejpam-5090	299	3	368–377	368–377	NUM
ejpam-5090	299	4	,	,	PUNCT
ejpam-5090	299	5	2021	2021	NUM
ejpam-5090	299	6	.	.	PUNCT
ejpam-5090	300	1	[	[	X
ejpam-5090	300	2	27	27	NUM
ejpam-5090	300	3	]	]	PUNCT
ejpam-5090	300	4	a.	a.	PROPN
ejpam-5090	300	5	al	al	PROPN
ejpam-5090	300	6	-	-	PUNCT
ejpam-5090	300	7	masarwah	masarwah	PROPN
ejpam-5090	300	8	,	,	PUNCT
ejpam-5090	300	9	a.g	a.g	PROPN
ejpam-5090	300	10	.	.	PROPN
ejpam-5090	300	11	ahmad	ahmad	PROPN
ejpam-5090	300	12	,	,	PUNCT
ejpam-5090	300	13	m	m	NOUN
ejpam-5090	300	14	-	-	ADJ
ejpam-5090	300	15	polar	polar	ADJ
ejpam-5090	300	16	(	(	PUNCT
ejpam-5090	300	17	α	α	NOUN
ejpam-5090	300	18	,	,	PUNCT
ejpam-5090	300	19	β)-fuzzy	β)-fuzzy	PUNCT
ejpam-5090	300	20	ideals	ideal	NOUN
ejpam-5090	300	21	in	in	ADP
ejpam-5090	300	22	bck	bck	PROPN
ejpam-5090	300	23	/	/	SYM
ejpam-5090	300	24	bci	bci	NOUN
ejpam-5090	300	25	-	-	PUNCT
ejpam-5090	300	26	algebras	algebra	NOUN
ejpam-5090	300	27	.	.	PUNCT
ejpam-5090	301	1	symmetry	symmetry	NOUN
ejpam-5090	301	2	11	11	NUM
ejpam-5090	301	3	:	:	SYM
ejpam-5090	301	4	44	44	NUM
ejpam-5090	301	5	,	,	PUNCT
ejpam-5090	301	6	2019	2019	NUM
ejpam-5090	301	7	.	.	PUNCT