id	sid	tid	token	lemma	pos
cana-3816	1	1	communications	communication	NOUN
cana-3816	1	2	on	on	ADP
cana-3816	1	3	applied	apply	VERB
cana-3816	1	4	nonlinear	nonlinear	ADJ
cana-3816	1	5	analysis	analysis	NOUN
cana-3816	1	6	issn	issn	NOUN
cana-3816	1	7	:	:	PUNCT
cana-3816	1	8	1074	1074	NUM
cana-3816	1	9	-	-	PUNCT
cana-3816	1	10	133x	133x	NUM
cana-3816	1	11	vol	vol	NOUN
cana-3816	1	12	32	32	NUM
cana-3816	1	13	no	no	NOUN
cana-3816	1	14	.	.	NOUN
cana-3816	1	15	3	3	NUM
cana-3816	1	16	(	(	PUNCT
cana-3816	1	17	2025	2025	NUM
cana-3816	1	18	)	)	PUNCT
cana-3816	1	19	ternary	ternary	ADJ
cana-3816	1	20	algebraic	algebraic	ADJ
cana-3816	1	21	structure	structure	NOUN
cana-3816	1	22	convey	convey	VERB
cana-3816	1	23	to	to	ADP
cana-3816	1	24	new	new	ADJ
cana-3816	1	25	type	type	NOUN
cana-3816	1	26	of	of	ADP
cana-3816	1	27	intuitionistic	intuitionistic	ADJ
cana-3816	1	28	q1	q1	PROPN
cana-3816	1	29	anti	anti	ADJ
cana-3816	1	30	fuzzy	fuzzy	ADJ
cana-3816	1	31	ideals	ideal	NOUN
cana-3816	1	32	of	of	ADP
cana-3816	1	33	an	an	DET
cana-3816	1	34	regular	regular	ADJ
cana-3816	1	35	ordered	order	VERB
cana-3816	1	36	ternary	ternary	NOUN
cana-3816	1	37	semigroups	semigroups	PROPN
cana-3816	1	38	r.	r.	PROPN
cana-3816	1	39	balaji1	balaji1	PROPN
cana-3816	1	40	,	,	PUNCT
cana-3816	1	41	p.srikanth	p.srikanth	ADJ
cana-3816	1	42	rao2	rao2	PROPN
cana-3816	1	43	,	,	PUNCT
cana-3816	1	44	k	k	PROPN
cana-3816	1	45	rajeshwar	rajeshwar	PROPN
cana-3816	1	46	reddy3	reddy3	PROPN
cana-3816	1	47	,	,	PUNCT
cana-3816	1	48	aiyared	aiyare	VERB
cana-3816	1	49	iampan4,∗	iampan4,∗	ADJ
cana-3816	1	50	1department	1department	NUM
cana-3816	1	51	of	of	ADP
cana-3816	1	52	mathematics	mathematic	NOUN
cana-3816	1	53	,	,	PUNCT
cana-3816	1	54	saveetha	saveetha	PROPN
cana-3816	1	55	school	school	PROPN
cana-3816	1	56	of	of	ADP
cana-3816	1	57	engineering	engineering	PROPN
cana-3816	1	58	,	,	PUNCT
cana-3816	1	59	saveetha	saveetha	PROPN
cana-3816	1	60	institute	institute	PROPN
cana-3816	1	61	of	of	ADP
cana-3816	1	62	medical	medical	ADJ
cana-3816	1	63	and	and	CCONJ
cana-3816	1	64	technical	technical	ADJ
cana-3816	1	65	sciences	science	NOUN
cana-3816	1	66	,	,	PUNCT
cana-3816	1	67	chennai-602105	chennai-602105	ADJ
cana-3816	1	68	,	,	PUNCT
cana-3816	1	69	india	india	PROPN
cana-3816	1	70	.	.	PUNCT
cana-3816	2	1	2b	2b	PROPN
cana-3816	2	2	v	v	X
cana-3816	2	3	raju	raju	PROPN
cana-3816	2	4	institute	institute	PROPN
cana-3816	2	5	of	of	ADP
cana-3816	2	6	technology	technology	PROPN
cana-3816	2	7	,	,	PUNCT
cana-3816	2	8	narsapur	narsapur	NOUN
cana-3816	2	9	medak	medak	PROPN
cana-3816	2	10	dist	dist	PROPN
cana-3816	2	11	,	,	PUNCT
cana-3816	2	12	telangana	telangana	PROPN
cana-3816	2	13	state-502313	state-502313	PROPN
cana-3816	2	14	,	,	PUNCT
cana-3816	2	15	india	india	PROPN
cana-3816	2	16	.	.	PUNCT
cana-3816	3	1	3department	3department	NUM
cana-3816	3	2	of	of	ADP
cana-3816	3	3	mathematics	mathematic	NOUN
cana-3816	3	4	,	,	PUNCT
cana-3816	3	5	malla	malla	PROPN
cana-3816	3	6	reddy	reddy	PROPN
cana-3816	3	7	college	college	PROPN
cana-3816	3	8	of	of	ADP
cana-3816	3	9	engineering	engineering	NOUN
cana-3816	3	10	and	and	CCONJ
cana-3816	3	11	technology	technology	NOUN
cana-3816	3	12	,	,	PUNCT
cana-3816	3	13	maisammaguda	maisammaguda	NOUN
cana-3816	3	14	,	,	PUNCT
cana-3816	3	15	medchal	medchal	ADJ
cana-3816	3	16	malkangiri	malkangiri	NOUN
cana-3816	3	17	,	,	PUNCT
cana-3816	3	18	telangana	telangana	PROPN
cana-3816	3	19	state-500014	state-500014	VERB
cana-3816	3	20	.	.	PUNCT
cana-3816	4	1	4department	4department	NUM
cana-3816	4	2	of	of	ADP
cana-3816	4	3	mathematics	mathematic	NOUN
cana-3816	4	4	,	,	PUNCT
cana-3816	4	5	school	school	NOUN
cana-3816	4	6	of	of	ADP
cana-3816	4	7	science	science	NOUN
cana-3816	4	8	,	,	PUNCT
cana-3816	4	9	university	university	NOUN
cana-3816	4	10	of	of	ADP
cana-3816	4	11	phayao	phayao	NOUN
cana-3816	4	12	,	,	PUNCT
cana-3816	4	13	19	19	NUM
cana-3816	4	14	moo	moo	NOUN
cana-3816	4	15	2	2	NUM
cana-3816	4	16	,	,	PUNCT
cana-3816	4	17	tambon	tambon	PROPN
cana-3816	4	18	mae	mae	PROPN
cana-3816	4	19	ka	ka	PROPN
cana-3816	4	20	,	,	PUNCT
cana-3816	4	21	amphur	amphur	PROPN
cana-3816	4	22	mueang	mueang	NOUN
cana-3816	4	23	,	,	PUNCT
cana-3816	4	24	phayao	phayao	NOUN
cana-3816	4	25	56000	56000	NUM
cana-3816	4	26	,	,	PUNCT
cana-3816	4	27	thailand	thailand	PROPN
cana-3816	4	28	.	.	PUNCT
cana-3816	5	1	e	e	X
cana-3816	5	2	-	-	VERB
cana-3816	5	3	mails:1balaji	mails:1balaji	ADJ
cana-3816	5	4	2410@yahoo.co.in	2410@yahoo.co.in	NUM
cana-3816	5	5	,	,	PUNCT
cana-3816	5	6	2srikanthrao.p@bvrit.ac.in	2srikanthrao.p@bvrit.ac.in	NUM
cana-3816	5	7	,	,	PUNCT
cana-3816	5	8	3kattarajeshwarreddy@gmail.com	3kattarajeshwarreddy@gmail.com	NUM
cana-3816	5	9	,	,	PUNCT
cana-3816	5	10	4aiyared.ia@up.ac.th	4aiyared.ia@up.ac.th	NUM
cana-3816	5	11	,	,	PUNCT
cana-3816	5	12	∗corresponding	∗corresponde	VERB
cana-3816	5	13	author	author	NOUN
cana-3816	5	14	:	:	PUNCT
cana-3816	5	15	aiyared	aiyared	PROPN
cana-3816	5	16	iampan	iampan	PROPN
cana-3816	5	17	.	.	PUNCT
cana-3816	6	1	received	receive	VERB
cana-3816	6	2	:	:	PUNCT
cana-3816	6	3	04	04	NUM
cana-3816	6	4	-	-	SYM
cana-3816	6	5	11	11	NUM
cana-3816	6	6	-	-	PUNCT
cana-3816	6	7	2024	2024	NUM
cana-3816	6	8	revised	revise	VERB
cana-3816	6	9	:	:	PUNCT
cana-3816	6	10	12	12	NUM
cana-3816	6	11	-	-	SYM
cana-3816	6	12	12	12	NUM
cana-3816	6	13	-	-	PUNCT
cana-3816	6	14	2024	2024	NUM
cana-3816	6	15	accepted	accept	VERB
cana-3816	6	16	:	:	PUNCT
cana-3816	6	17	01	01	NUM
cana-3816	6	18	-	-	SYM
cana-3816	6	19	01	01	NUM
cana-3816	6	20	-	-	PUNCT
cana-3816	6	21	2025	2025	NUM
cana-3816	6	22	.	.	PUNCT
cana-3816	7	1	abstract	abstract	ADV
cana-3816	7	2	we	we	PRON
cana-3816	7	3	examine	examine	VERB
cana-3816	7	4	some	some	PRON
cana-3816	7	5	of	of	ADP
cana-3816	7	6	the	the	DET
cana-3816	7	7	properties	property	NOUN
cana-3816	7	8	of	of	ADP
cana-3816	7	9	these	these	DET
cana-3816	7	10	ordered	order	VERB
cana-3816	7	11	ternary	ternary	ADJ
cana-3816	7	12	semigroups	semigroup	NOUN
cana-3816	7	13	,	,	PUNCT
cana-3816	7	14	such	such	ADJ
cana-3816	7	15	as	as	ADP
cana-3816	7	16	intuitionistic	intuitionistic	ADJ
cana-3816	7	17	q1	q1	PROPN
cana-3816	7	18	anti	anti	PROPN
cana-3816	7	19	fuzzy	fuzzy	PROPN
cana-3816	7	20	left	leave	VERB
cana-3816	7	21	ideal	ideal	NOUN
cana-3816	7	22	,	,	PUNCT
cana-3816	7	23	q1	q1	PROPN
cana-3816	7	24	anti	anti	ADJ
cana-3816	7	25	fuzzy	fuzzy	ADJ
cana-3816	7	26	right	right	ADJ
cana-3816	7	27	ideal	ideal	NOUN
cana-3816	7	28	,	,	PUNCT
cana-3816	7	29	q1	q1	X
cana-3816	7	30	anti	anti	ADJ
cana-3816	7	31	fuzzy	fuzzy	ADJ
cana-3816	7	32	lateral	lateral	ADJ
cana-3816	7	33	ideal	ideal	NOUN
cana-3816	7	34	,	,	PUNCT
cana-3816	7	35	q1	q1	X
cana-3816	7	36	anti	anti	ADJ
cana-3816	7	37	fuzzy	fuzzy	ADJ
cana-3816	7	38	ideal	ideal	NOUN
cana-3816	7	39	and	and	CCONJ
cana-3816	7	40	q1	q1	PROPN
cana-3816	7	41	anti	anti	PROPN
cana-3816	7	42	fuzzy	fuzzy	ADJ
cana-3816	7	43	bi	bi	NOUN
cana-3816	7	44	-	-	NOUN
cana-3816	7	45	ideal	ideal	ADJ
cana-3816	7	46	.	.	PUNCT
cana-3816	8	1	we	we	PRON
cana-3816	8	2	introduce	introduce	VERB
cana-3816	8	3	the	the	DET
cana-3816	8	4	idea	idea	NOUN
cana-3816	8	5	of	of	ADP
cana-3816	8	6	tss	tss	NOUN
cana-3816	8	7	.	.	PUNCT
cana-3816	9	1	the	the	DET
cana-3816	9	2	q1	q1	PROPN
cana-3816	9	3	anti	anti	X
cana-3816	9	4	anti	anti	X
cana-3816	9	5	fuzzy	fuzzy	ADJ
cana-3816	9	6	ideal	ideal	NOUN
cana-3816	9	7	is	be	AUX
cana-3816	9	8	extended	extend	VERB
cana-3816	9	9	in	in	ADP
cana-3816	9	10	a	a	DET
cana-3816	9	11	new	new	ADJ
cana-3816	9	12	way	way	NOUN
cana-3816	9	13	over	over	ADP
cana-3816	9	14	ternary	ternary	ADJ
cana-3816	9	15	semigroups	semigroup	NOUN
cana-3816	9	16	b.	b.	PROPN
cana-3816	9	17	keywords	keyword	NOUN
cana-3816	9	18	:	:	PUNCT
cana-3816	9	19	ternary	ternary	ADJ
cana-3816	9	20	semigroups	semigroup	NOUN
cana-3816	9	21	,	,	PUNCT
cana-3816	9	22	anti	anti	X
cana-3816	9	23	fuzzy	fuzzy	ADJ
cana-3816	9	24	ideals	ideal	NOUN
cana-3816	9	25	,	,	PUNCT
cana-3816	9	26	anti	anti	X
cana-3816	9	27	fuzzy	fuzzy	ADJ
cana-3816	9	28	bi	bi	NOUN
cana-3816	9	29	-	-	NOUN
cana-3816	9	30	ideals	ideal	NOUN
cana-3816	9	31	,	,	PUNCT
cana-3816	9	32	q1	q1	X
cana-3816	9	33	anti	anti	X
cana-3816	9	34	fuzzy	fuzzy	ADJ
cana-3816	9	35	bi	bi	NOUN
cana-3816	9	36	-	-	NOUN
cana-3816	9	37	ideals	ideal	NOUN
cana-3816	9	38	.	.	PUNCT
cana-3816	10	1	1	1	NUM
cana-3816	10	2	introduction	introduction	NOUN
cana-3816	10	3	the	the	DET
cana-3816	10	4	ternary	ternary	ADJ
cana-3816	10	5	algebraic	algebraic	ADJ
cana-3816	10	6	systems	system	NOUN
cana-3816	10	7	known	know	VERB
cana-3816	10	8	as	as	ADP
cana-3816	10	9	triplex	triplex	ADJ
cana-3816	10	10	structures	structure	NOUN
cana-3816	10	11	were	be	AUX
cana-3816	10	12	initially	initially	ADV
cana-3816	10	13	conceived	conceive	VERB
cana-3816	10	14	in	in	ADP
cana-3816	10	15	1932	1932	NUM
cana-3816	10	16	by	by	ADP
cana-3816	10	17	d.	d.	PROPN
cana-3816	10	18	h.	h.	PROPN
cana-3816	10	19	lehmer.1	lehmer.1	PROPN
cana-3816	10	20	vandiver	vandiver	VERB
cana-3816	10	21	came	come	VERB
cana-3816	10	22	up	up	ADP
cana-3816	10	23	with	with	ADP
cana-3816	10	24	the	the	DET
cana-3816	10	25	idea	idea	NOUN
cana-3816	10	26	of	of	ADP
cana-3816	10	27	the	the	DET
cana-3816	10	28	semiring	semiring	NOUN
cana-3816	10	29	in	in	ADP
cana-3816	10	30	1934	1934	NUM
cana-3816	10	31	.	.	PUNCT
cana-3816	11	1	in	in	ADP
cana-3816	11	2	1962	1962	NUM
cana-3816	11	3	hestenes2	hestenes2	PROPN
cana-3816	11	4	used	use	VERB
cana-3816	11	5	linear	linear	PROPN
cana-3816	11	6	transformation	transformation	NOUN
cana-3816	11	7	and	and	CCONJ
cana-3816	11	8	matrices	matrix	NOUN
cana-3816	11	9	as	as	ADP
cana-3816	11	10	examples	example	NOUN
cana-3816	11	11	to	to	PART
cana-3816	11	12	establish	establish	VERB
cana-3816	11	13	the	the	DET
cana-3816	11	14	concept	concept	NOUN
cana-3816	11	15	of	of	ADP
cana-3816	11	16	ternary	ternary	ADJ
cana-3816	11	17	algebra	algebra	NOUN
cana-3816	11	18	.	.	PUNCT
cana-3816	12	1	in	in	ADP
cana-3816	12	2	1971	1971	NUM
cana-3816	12	3	,	,	PUNCT
cana-3816	12	4	after	after	ADP
cana-3816	12	5	describing	describe	VERB
cana-3816	12	6	those	those	DET
cana-3816	12	7	additive	additive	ADJ
cana-3816	12	8	subgroups	subgroup	NOUN
cana-3816	12	9	of	of	ADP
cana-3816	12	10	rings	ring	NOUN
cana-3816	12	11	that	that	PRON
cana-3816	12	12	are	be	AUX
cana-3816	12	13	closed	close	VERB
cana-3816	12	14	under	under	ADP
cana-3816	12	15	the	the	DET
cana-3816	12	16	triple	triple	ADJ
cana-3816	12	17	ring	ring	NOUN
cana-3816	12	18	product	product	NOUN
cana-3816	12	19	,	,	PUNCT
cana-3816	12	20	lister	lister	PROPN
cana-3816	12	21	talked	talk	VERB
cana-3816	12	22	about	about	ADP
cana-3816	12	23	this	this	DET
cana-3816	12	24	algebraic	algebraic	ADJ
cana-3816	12	25	system	system	NOUN
cana-3816	12	26	as	as	ADP
cana-3816	12	27	a	a	DET
cana-3816	12	28	ternary	ternary	ADJ
cana-3816	12	29	ring	ring	NOUN
cana-3816	12	30	.	.	PUNCT
cana-3816	13	1	the	the	DET
cana-3816	13	2	fuzzy	fuzzy	ADJ
cana-3816	13	3	set	set	NOUN
cana-3816	13	4	(	(	PUNCT
cana-3816	13	5	fs	fs	NOUN
cana-3816	13	6	)	)	PUNCT
cana-3816	13	7	theory	theory	NOUN
cana-3816	13	8	,	,	PUNCT
cana-3816	13	9	which	which	PRON
cana-3816	13	10	was	be	AUX
cana-3816	13	11	created	create	VERB
cana-3816	13	12	by	by	ADP
cana-3816	13	13	zadeh,3	zadeh,3	PROPN
cana-3816	13	14	works	work	VERB
cana-3816	13	15	best	well	ADV
cana-3816	13	16	when	when	SCONJ
cana-3816	13	17	it	it	PRON
cana-3816	13	18	comes	come	VERB
cana-3816	13	19	to	to	ADP
cana-3816	13	20	handling	handle	VERB
cana-3816	13	21	ambiguity	ambiguity	NOUN
cana-3816	13	22	and	and	CCONJ
cana-3816	13	23	uncertainty	uncertainty	NOUN
cana-3816	13	24	.	.	PUNCT
cana-3816	14	1	an	an	DET
cana-3816	14	2	element	element	NOUN
cana-3816	14	3	with	with	ADP
cana-3816	14	4	a	a	DET
cana-3816	14	5	single	single	ADJ
cana-3816	14	6	value	value	NOUN
cana-3816	14	7	inside	inside	ADP
cana-3816	14	8	the	the	DET
cana-3816	14	9	interval	interval	NOUN
cana-3816	14	10	is	be	AUX
cana-3816	14	11	called	call	VERB
cana-3816	14	12	a	a	DET
cana-3816	14	13	member	member	NOUN
cana-3816	14	14	of	of	ADP
cana-3816	14	15	an	an	DET
cana-3816	14	16	fs	fs	PROPN
cana-3816	14	17	.	.	PUNCT
cana-3816	15	1	the	the	DET
cana-3816	15	2	nmg	nmg	NOUN
cana-3816	15	3	might	might	AUX
cana-3816	15	4	not	not	PART
cana-3816	15	5	always	always	ADV
cana-3816	15	6	be	be	AUX
cana-3816	15	7	equal	equal	ADJ
cana-3816	15	8	to	to	ADP
cana-3816	15	9	one	one	NUM
cana-3816	15	10	minus	minus	ADP
cana-3816	15	11	the	the	DET
cana-3816	15	12	mg	mg	NOUN
cana-3816	15	13	in	in	ADP
cana-3816	15	14	practice	practice	NOUN
cana-3816	15	15	,	,	PUNCT
cana-3816	15	16	though	though	ADV
cana-3816	15	17	,	,	PUNCT
cana-3816	15	18	because	because	SCONJ
cana-3816	15	19	of	of	ADP
cana-3816	15	20	potential	potential	ADJ
cana-3816	15	21	pushback	pushback	NOUN
cana-3816	15	22	.	.	PUNCT
cana-3816	16	1	a	a	DET
cana-3816	16	2	growing	grow	VERB
cana-3816	16	3	number	number	NOUN
cana-3816	16	4	of	of	ADP
cana-3816	16	5	hybrid	hybrid	ADJ
cana-3816	16	6	fuzzy	fuzzy	ADJ
cana-3816	16	7	models	model	NOUN
cana-3816	16	8	are	be	AUX
cana-3816	16	9	being	be	AUX
cana-3816	16	10	created	create	VERB
cana-3816	16	11	as	as	ADP
cana-3816	16	12	fs	fs	ADP
cana-3816	16	13	theory	theory	NOUN
cana-3816	16	14	develops	develop	VERB
cana-3816	16	15	quickly	quickly	ADV
cana-3816	16	16	.	.	PUNCT
cana-3816	17	1	as	as	ADP
cana-3816	17	2	a	a	DET
cana-3816	17	3	result	result	NOUN
cana-3816	17	4	of	of	ADP
cana-3816	17	5	the	the	DET
cana-3816	17	6	uncertainties	uncertainty	NOUN
cana-3816	17	7	,	,	PUNCT
cana-3816	17	8	several	several	ADJ
cana-3816	17	9	theories	theory	NOUN
cana-3816	17	10	of	of	ADP
cana-3816	17	11	uncertainty	uncertainty	NOUN
cana-3816	17	12	have	have	AUX
cana-3816	17	13	been	be	AUX
cana-3816	17	14	created	create	VERB
cana-3816	17	15	,	,	PUNCT
cana-3816	17	16	such	such	ADJ
cana-3816	17	17	as	as	ADP
cana-3816	17	18	pythagorean	pythagorean	PROPN
cana-3816	17	19	fs	fs	PROPN
cana-3816	17	20	(	(	PUNCT
cana-3816	17	21	pfs),5	pfs),5	PROPN
cana-3816	17	22	intuitionistic	intuitionistic	PROPN
cana-3816	17	23	fs	fs	X
cana-3816	17	24	(	(	PUNCT
cana-3816	17	25	ifs),4	ifs),4	PROPN
cana-3816	17	26	and	and	CCONJ
cana-3816	17	27	fs.3	fs.3	PROPN
cana-3816	17	28	an	an	DET
cana-3816	17	29	fs	fs	NOUN
cana-3816	17	30	is	be	AUX
cana-3816	17	31	composed	compose	VERB
cana-3816	17	32	of	of	ADP
cana-3816	17	33	mg	mg	PROPN
cana-3816	17	34	sets	set	NOUN
cana-3816	17	35	,	,	PUNCT
cana-3816	17	36	or	or	CCONJ
cana-3816	17	37	sets	set	NOUN
cana-3816	17	38	with	with	ADP
cana-3816	17	39	grades	grade	NOUN
cana-3816	17	40	ranging	range	VERB
cana-3816	17	41	from	from	ADP
cana-3816	17	42	0	0	NUM
cana-3816	17	43	to	to	ADP
cana-3816	17	44	1	1	NUM
cana-3816	17	45	.	.	PUNCT
cana-3816	18	1	although	although	SCONJ
cana-3816	18	2	atanassov4	atanassov4	PROPN
cana-3816	18	3	asserts	assert	VERB
cana-3816	18	4	that	that	SCONJ
cana-3816	18	5	non	non	ADJ
cana-3816	18	6	-	-	ADJ
cana-3816	18	7	membership	membership	ADJ
cana-3816	18	8	grades	grade	NOUN
cana-3816	18	9	(	(	PUNCT
cana-3816	18	10	nmg	nmg	NOUN
cana-3816	18	11	)	)	PUNCT
cana-3816	18	12	can	can	AUX
cana-3816	18	13	only	only	ADV
cana-3816	18	14	be	be	AUX
cana-3816	18	15	worth	worth	ADJ
cana-3816	18	16	1	1	NUM
cana-3816	18	17	,	,	PUNCT
cana-3816	18	18	ifs	ifs	PROPN
cana-3816	18	19	is	be	AUX
cana-3816	18	20	classified	classify	VERB
cana-3816	18	21	as	as	ADP
cana-3816	18	22	mg	mg	PROPN
cana-3816	18	23	.	.	PUNCT
cana-3816	19	1	there	there	PRON
cana-3816	19	2	are	be	VERB
cana-3816	19	3	times	time	NOUN
cana-3816	19	4	when	when	SCONJ
cana-3816	19	5	the	the	DET
cana-3816	19	6	sum	sum	NOUN
cana-3816	19	7	of	of	ADP
cana-3816	19	8	mgs	mgs	NOUN
cana-3816	19	9	and	and	CCONJ
cana-3816	19	10	nmgs	nmgs	VERB
cana-3816	19	11	throughout	throughout	ADP
cana-3816	19	12	a	a	DET
cana-3816	19	13	decision	decision	NOUN
cana-3816	19	14	-	-	PUNCT
cana-3816	19	15	making	make	VERB
cana-3816	19	16	process	process	NOUN
cana-3816	19	17	can	can	AUX
cana-3816	19	18	approach	approach	VERB
cana-3816	19	19	1	1	NUM
cana-3816	19	20	.	.	PUNCT
cana-3816	20	1	the	the	DET
cana-3816	20	2	generalized	generalized	ADJ
cana-3816	20	3	mg	mg	PROPN
cana-3816	20	4	and	and	CCONJ
cana-3816	20	5	nmg	nmg	PROPN
cana-3816	20	6	logic	logic	NOUN
cana-3816	20	7	,	,	PUNCT
cana-3816	20	8	which	which	PRON
cana-3816	20	9	is	be	AUX
cana-3816	20	10	based	base	VERB
cana-3816	20	11	on	on	ADP
cana-3816	20	12	the	the	DET
cana-3816	20	13	square	square	NOUN
cana-3816	20	14	of	of	ADP
cana-3816	20	15	the	the	DET
cana-3816	20	16	mgs	mgs	NOUN
cana-3816	20	17	and	and	CCONJ
cana-3816	20	18	nmgs	nmgs	NOUN
cana-3816	20	19	and	and	CCONJ
cana-3816	20	20	has	have	VERB
cana-3816	20	21	a	a	DET
cana-3816	20	22	value	value	NOUN
cana-3816	20	23	of	of	ADP
cana-3816	20	24	no	no	DET
cana-3816	20	25	more	more	ADJ
cana-3816	20	26	than	than	ADP
cana-3816	20	27	1	1	NUM
cana-3816	20	28	,	,	PUNCT
cana-3816	20	29	was	be	AUX
cana-3816	20	30	developed	develop	VERB
cana-3816	20	31	by	by	ADP
cana-3816	20	32	yager5	yager5	NOUN
cana-3816	20	33	using	use	VERB
cana-3816	20	34	pfs	pfs	PROPN
cana-3816	20	35	logic	logic	NOUN
cana-3816	20	36	.	.	PUNCT
cana-3816	21	1	since	since	SCONJ
cana-3816	21	2	the	the	DET
cana-3816	21	3	neutral	neutral	ADJ
cana-3816	21	4	state	state	NOUN
cana-3816	21	5	is	be	AUX
cana-3816	21	6	neither	neither	CCONJ
cana-3816	21	7	positive	positive	ADJ
cana-3816	21	8	nor	nor	CCONJ
cana-3816	21	9	negative	negative	ADJ
cana-3816	21	10	,	,	PUNCT
cana-3816	21	11	it	it	PRON
cana-3816	21	12	can	can	AUX
cana-3816	21	13	not	not	PART
cana-3816	21	14	be	be	AUX
cana-3816	21	15	described	describe	VERB
cana-3816	21	16	by	by	ADP
cana-3816	21	17	these	these	DET
cana-3816	21	18	theories	theory	NOUN
cana-3816	21	19	.	.	PUNCT
cana-3816	22	1	palanikumar	palanikumar	PROPN
cana-3816	22	2	and	and	CCONJ
cana-3816	22	3	colleagues	colleague	NOUN
cana-3816	22	4	have	have	AUX
cana-3816	22	5	introduced	introduce	VERB
cana-3816	22	6	an	an	DET
cana-3816	22	7	intuitionistic	intuitionistic	ADJ
cana-3816	22	8	fuzzy	fuzzy	ADJ
cana-3816	22	9	normal	normal	ADJ
cana-3816	22	10	subbisemiring	subbisemiring	NOUN
cana-3816	22	11	of	of	ADP
cana-3816	22	12	bisemiring.6	bisemiring.6	PROPN
cana-3816	22	13	the	the	DET
cana-3816	22	14	idea	idea	NOUN
cana-3816	22	15	of	of	ADP
cana-3816	22	16	bisemiring	bisemiring	NOUN
cana-3816	22	17	was	be	AUX
cana-3816	22	18	created	create	VERB
cana-3816	22	19	by	by	ADP
cana-3816	22	20	palanikumar	palanikumar	PROPN
cana-3816	22	21	et	et	PROPN
cana-3816	22	22	al.7	al.7	PROPN
cana-3816	22	23	employing	employ	VERB
cana-3816	22	24	bipolar	bipolar	ADV
cana-3816	22	25	-	-	PUNCT
cana-3816	22	26	valued	value	VERB
cana-3816	22	27	neutrosophic	neutrosophic	ADJ
cana-3816	22	28	normal	normal	ADJ
cana-3816	22	29	sets	set	NOUN
cana-3816	22	30	.	.	PUNCT
cana-3816	23	1	bi	bi	ADJ
cana-3816	23	2	-	-	NOUN
cana-3816	23	3	ideals	ideal	NOUN
cana-3816	23	4	on	on	ADP
cana-3816	23	5	ordered	order	VERB
cana-3816	23	6	semigroups	semigroup	NOUN
cana-3816	23	7	were	be	AUX
cana-3816	23	8	examined	examine	VERB
cana-3816	23	9	by	by	ADP
cana-3816	23	10	hila	hila	PROPN
cana-3816	23	11	and	and	CCONJ
cana-3816	23	12	associates.8	associates.8	PROPN
cana-3816	23	13	dutta	dutta	PROPN
cana-3816	23	14	t.k	t.k	PROPN
cana-3816	23	15	.	.	PROPN
cana-3816	23	16	and	and	CCONJ
cana-3816	23	17	associates	associate	NOUN
cana-3816	23	18	presented	present	VERB
cana-3816	23	19	novel	novel	ADJ
cana-3816	23	20	concepts	concept	NOUN
cana-3816	23	21	based	base	VERB
cana-3816	23	22	on	on	ADP
cana-3816	23	23	ternary	ternary	ADJ
cana-3816	23	24	semiring	semire	VERB
cana-3816	23	25	prime	prime	ADJ
cana-3816	23	26	ideals	ideal	NOUN
cana-3816	23	27	and	and	CCONJ
cana-3816	23	28	prime	prime	ADJ
cana-3816	23	29	radicals.9	radicals.9	ADJ
cana-3816	23	30	several	several	ADJ
cana-3816	23	31	prime	prime	ADJ
cana-3816	23	32	and	and	CCONJ
cana-3816	23	33	semiprime	semiprime	NOUN
cana-3816	23	34	bi	bi	NOUN
cana-3816	23	35	-	-	NOUN
cana-3816	23	36	ideals	ideal	NOUN
cana-3816	23	37	of	of	ADP
cana-3816	23	38	the	the	DET
cana-3816	23	39	rings	ring	NOUN
cana-3816	23	40	were	be	AUX
cana-3816	23	41	discussed	discuss	VERB
cana-3816	23	42	by	by	ADP
cana-3816	23	43	palanikumar	palanikumar	PROPN
cana-3816	23	44	and	and	CCONJ
cana-3816	23	45	associates11	associates11	NOUN
cana-3816	23	46	and	and	CCONJ
cana-3816	23	47	others	other	NOUN
cana-3816	23	48	.	.	PUNCT
cana-3816	24	1	the	the	DET
cana-3816	24	2	several	several	ADJ
cana-3816	24	3	ideals	ideal	NOUN
cana-3816	24	4	of	of	ADP
cana-3816	24	5	semigroups	semigroup	NOUN
cana-3816	24	6	,	,	PUNCT
cana-3816	24	7	semirings	semiring	NOUN
cana-3816	24	8	,	,	PUNCT
cana-3816	24	9	and	and	CCONJ
cana-3816	24	10	ternary	ternary	ADJ
cana-3816	24	11	semirings	semiring	NOUN
cana-3816	24	12	were	be	AUX
cana-3816	24	13	examined	examine	VERB
cana-3816	24	14	by	by	ADP
cana-3816	24	15	palanikumar	palanikumar	PROPN
cana-3816	24	16	et	et	PROPN
cana-3816	24	17	al.12	al.12	NOUN
cana-3816	24	18	,	,	PUNCT
cana-3816	24	19	22–25	22–25	NUM
cana-3816	24	20	https://internationalpubls.com	https://internationalpubls.com	SYM
cana-3816	24	21	761	761	NUM
cana-3816	24	22	communications	communication	NOUN
cana-3816	24	23	on	on	ADP
cana-3816	24	24	applied	apply	VERB
cana-3816	24	25	nonlinear	nonlinear	ADJ
cana-3816	24	26	analysis	analysis	NOUN
cana-3816	24	27	issn	issn	NOUN
cana-3816	24	28	:	:	PUNCT
cana-3816	24	29	1074	1074	NUM
cana-3816	24	30	-	-	PUNCT
cana-3816	24	31	133x	133x	NUM
cana-3816	24	32	vol	vol	NOUN
cana-3816	24	33	32	32	NUM
cana-3816	24	34	no	no	NOUN
cana-3816	24	35	.	.	NOUN
cana-3816	24	36	3	3	NUM
cana-3816	24	37	(	(	PUNCT
cana-3816	24	38	2025	2025	NUM
cana-3816	24	39	)	)	PUNCT
cana-3816	24	40	2	2	NUM
cana-3816	24	41	(	(	PUNCT
cana-3816	24	42	∝1,∝2	∝1,∝2	PROPN
cana-3816	24	43	)	)	PUNCT
cana-3816	24	44	intuitionistic	intuitionistic	PROPN
cana-3816	24	45	q1	q1	PROPN
cana-3816	24	46	anti	anti	ADJ
cana-3816	24	47	fuzzy	fuzzy	ADJ
cana-3816	24	48	ideals	ideal	NOUN
cana-3816	24	49	here	here	ADV
cana-3816	24	50	b	b	PROPN
cana-3816	24	51	denotes	denote	VERB
cana-3816	24	52	the	the	DET
cana-3816	24	53	ordered	order	VERB
cana-3816	24	54	ternary	ternary	ADJ
cana-3816	24	55	semigroup	semigroup	NOUN
cana-3816	24	56	and	and	CCONJ
cana-3816	24	57	(	(	PUNCT
cana-3816	24	58	∝1,∝2	∝1,∝2	PROPN
cana-3816	24	59	)	)	PUNCT
cana-3816	24	60	∈	∈	PROPN
cana-3816	25	1	[	[	X
cana-3816	25	2	0	0	NUM
cana-3816	25	3	,	,	PUNCT
cana-3816	25	4	1	1	NUM
cana-3816	25	5	]	]	PUNCT
cana-3816	25	6	be	be	AUX
cana-3816	25	7	such	such	ADJ
cana-3816	25	8	that	that	SCONJ
cana-3816	25	9	0	0	NUM
cana-3816	25	10	6∝1<∝26	6∝1<∝26	NUM
cana-3816	25	11	1	1	NUM
cana-3816	25	12	both	both	PRON
cana-3816	25	13	(	(	PUNCT
cana-3816	25	14	∝1,∝2	∝1,∝2	PROPN
cana-3816	25	15	)	)	PUNCT
cana-3816	25	16	are	be	AUX
cana-3816	25	17	arbitrary	arbitrary	ADJ
cana-3816	25	18	fixed	fix	VERB
cana-3816	25	19	.	.	PUNCT
cana-3816	26	1	definition	definition	NOUN
cana-3816	26	2	2.1	2.1	NUM
cana-3816	26	3	.	.	PUNCT
cana-3816	27	1	a	a	DET
cana-3816	27	2	ifs	ifs	PROPN
cana-3816	27	3	a	a	X
cana-3816	27	4	=	=	X
cana-3816	28	1	[	[	X
cana-3816	28	2	ta,>a	ta,>a	NOUN
cana-3816	28	3	]	]	PUNCT
cana-3816	28	4	of	of	ADP
cana-3816	28	5	b	b	NOUN
cana-3816	28	6	and	and	CCONJ
cana-3816	28	7	q1	q1	PROPN
cana-3816	28	8	is	be	AUX
cana-3816	28	9	a	a	DET
cana-3816	28	10	any	any	DET
cana-3816	28	11	non	non	ADJ
cana-3816	28	12	-	-	ADJ
cana-3816	28	13	empty	empty	ADJ
cana-3816	28	14	set	set	NOUN
cana-3816	28	15	of	of	ADP
cana-3816	28	16	a	a	DET
cana-3816	28	17	,	,	PUNCT
cana-3816	28	18	the	the	DET
cana-3816	28	19	pair	pair	NOUN
cana-3816	28	20	(	(	PUNCT
cana-3816	28	21	a	a	DET
cana-3816	28	22	,	,	PUNCT
cana-3816	28	23	q1	q1	NOUN
cana-3816	28	24	)	)	PUNCT
cana-3816	28	25	q1ifs	q1if	VERB
cana-3816	28	26	is	be	AUX
cana-3816	28	27	called	call	VERB
cana-3816	28	28	a	a	DET
cana-3816	28	29	(	(	PUNCT
cana-3816	28	30	∝1,∝2	∝1,∝2	NOUN
cana-3816	28	31	)	)	PUNCT
cana-3816	28	32	iq1tfss	iq1tfss	NOUN
cana-3816	28	33	of	of	ADP
cana-3816	28	34	b	b	NOUN
cana-3816	28	35	if	if	SCONJ
cana-3816	28	36	1	1	NUM
cana-3816	28	37	.	.	PUNCT
cana-3816	29	1	if	if	SCONJ
cana-3816	29	2	]	]	X
cana-3816	29	3	6	6	NUM
cana-3816	29	4	ø	ø	NOUN
cana-3816	29	5	,	,	PUNCT
cana-3816	29	6	then	then	ADV
cana-3816	29	7	t	t	PROPN
cana-3816	29	8	(	(	PUNCT
cana-3816	29	9	]	]	SYM
cana-3816	29	10	)	)	PUNCT
cana-3816	29	11	6	6	NUM
cana-3816	29	12	t	t	NOUN
cana-3816	29	13	(	(	PUNCT
cana-3816	29	14	ø	ø	NOUN
cana-3816	29	15	)	)	PUNCT
cana-3816	29	16	and	and	CCONJ
cana-3816	29	17	>	>	X
cana-3816	29	18	(	(	PUNCT
cana-3816	29	19	]	]	X
cana-3816	29	20	)	)	PUNCT
cana-3816	29	21	>	>	X
cana-3816	29	22	>	>	X
cana-3816	29	23	(	(	PUNCT
cana-3816	29	24	ø	ø	NOUN
cana-3816	29	25	)	)	PUNCT
cana-3816	29	26	,	,	PUNCT
cana-3816	29	27	2	2	X
cana-3816	29	28	.	.	NUM
cana-3816	29	29	min{t	min{t	NOUN
cana-3816	29	30	(	(	PUNCT
cana-3816	29	31	]	]	X
cana-3816	29	32	∂ø	∂ø	PROPN
cana-3816	29	33	,	,	PUNCT
cana-3816	29	34	ι),∝1	ι),∝1	PROPN
cana-3816	29	35	}	}	PUNCT
cana-3816	29	36	6	6	NUM
cana-3816	29	37	max{t	max{t	NOUN
cana-3816	29	38	(	(	PUNCT
cana-3816	29	39	]	]	X
cana-3816	29	40	,	,	PUNCT
cana-3816	29	41	ι),t	ι),t	PUNCT
cana-3816	29	42	(	(	PUNCT
cana-3816	29	43	∂	∂	NUM
cana-3816	29	44	,	,	PUNCT
cana-3816	29	45	ι),t	ι),t	X
cana-3816	29	46	(	(	PUNCT
cana-3816	29	47	ø	ø	NOUN
cana-3816	29	48	,	,	PUNCT
cana-3816	29	49	ι),∝2	ι),∝2	NOUN
cana-3816	29	50	}	}	PUNCT
cana-3816	29	51	3	3	NUM
cana-3816	29	52	.	.	X
cana-3816	29	53	max{>(]∂ø	max{>(]∂ø	NUM
cana-3816	29	54	,	,	PUNCT
cana-3816	29	55	ι),∝1	ι),∝1	PROPN
cana-3816	29	56	}	}	PUNCT
cana-3816	29	57	>	>	X
cana-3816	29	58	min	min	PROPN
cana-3816	29	59	{	{	PUNCT
cana-3816	29	60	>	>	X
cana-3816	29	61	(	(	PUNCT
cana-3816	29	62	]	]	X
cana-3816	29	63	,	,	PUNCT
cana-3816	29	64	ι),>(∂	ι),>(∂	PROPN
cana-3816	29	65	,	,	PUNCT
cana-3816	29	66	ι),>(ø	ι),>(ø	NOUN
cana-3816	29	67	,	,	PUNCT
cana-3816	29	68	ι),∝2	ι),∝2	NOUN
cana-3816	29	69	}	}	PUNCT
cana-3816	29	70	for	for	ADP
cana-3816	29	71	all	all	PRON
cana-3816	29	72	]	]	X
cana-3816	29	73	,	,	PUNCT
cana-3816	29	74	∂	∂	NUM
cana-3816	29	75	,	,	PUNCT
cana-3816	29	76	ø	ø	PROPN
cana-3816	29	77	∈	∈	PROPN
cana-3816	29	78	b	b	PROPN
cana-3816	29	79	and	and	CCONJ
cana-3816	29	80	q	q	PROPN
cana-3816	29	81	∈	∈	PROPN
cana-3816	29	82	q1	q1	PROPN
cana-3816	29	83	.	.	PUNCT
cana-3816	29	84	example	example	NOUN
cana-3816	29	85	2.2	2.2	NUM
cana-3816	29	86	.	.	PUNCT
cana-3816	30	1	let	let	VERB
cana-3816	30	2	b	b	NOUN
cana-3816	30	3	=	=	PRON
cana-3816	30	4	{	{	PUNCT
cana-3816	30	5	øl	øl	PROPN
cana-3816	30	6	,	,	PUNCT
cana-3816	30	7	øm	øm	ADP
cana-3816	30	8	,	,	PUNCT
cana-3816	30	9	øn	øn	INTJ
cana-3816	30	10	,	,	PUNCT
cana-3816	30	11	øo	øo	ADP
cana-3816	30	12	}	}	PUNCT
cana-3816	30	13	with	with	ADP
cana-3816	30	14	the	the	DET
cana-3816	30	15	cayley	cayley	ADJ
cana-3816	30	16	table	table	NOUN
cana-3816	30	17	:	:	PUNCT
cana-3816	30	18	·	·	PUNCT
cana-3816	31	1	øl	øl	VERB
cana-3816	31	2	øm	øm	INTJ
cana-3816	31	3	øn	øn	ADP
cana-3816	31	4	øo	øo	ADP
cana-3816	31	5	øl	øl	PROPN
cana-3816	31	6	t	t	PROPN
cana-3816	31	7	t	t	PROPN
cana-3816	31	8	t	t	PROPN
cana-3816	31	9	t	t	PROPN
cana-3816	31	10	øm	øm	INTJ
cana-3816	31	11	t	t	NOUN
cana-3816	31	12	o	o	X
cana-3816	31	13	p	p	X
cana-3816	31	14	c	c	X
cana-3816	31	15	øn	øn	NOUN
cana-3816	31	16	t	t	PROPN
cana-3816	31	17	p	p	PROPN
cana-3816	32	1	p	p	X
cana-3816	32	2	p	p	X
cana-3816	32	3	øo	øo	ADP
cana-3816	32	4	t	t	PROPN
cana-3816	33	1	p	p	X
cana-3816	33	2	p	p	X
cana-3816	33	3	p	p	X
cana-3816	33	4	·	·	PUNCT
cana-3816	33	5	øl	øl	PROPN
cana-3816	33	6	øm	øm	INTJ
cana-3816	33	7	øn	øn	INTJ
cana-3816	33	8	øo	øo	ADP
cana-3816	33	9	t	t	PROPN
cana-3816	33	10	øl	øl	PROPN
cana-3816	33	11	øl	øl	PROPN
cana-3816	33	12	øl	øl	PROPN
cana-3816	33	13	øl	øl	PROPN
cana-3816	33	14	o	o	NOUN
cana-3816	33	15	øl	øl	ADJ
cana-3816	33	16	øm	øm	INTJ
cana-3816	33	17	øn	øn	INTJ
cana-3816	33	18	øo	øo	ADP
cana-3816	33	19	p	p	PROPN
cana-3816	33	20	øl	øl	PROPN
cana-3816	33	21	øn	øn	NOUN
cana-3816	33	22	øn	øn	NOUN
cana-3816	33	23	øn	øn	X
cana-3816	33	24	c	c	NOUN
cana-3816	33	25	øl	øl	PROPN
cana-3816	33	26	øn	øn	NOUN
cana-3816	33	27	øn	øn	NOUN
cana-3816	33	28	øn	øn	ADP
cana-3816	33	29	6	6	NUM
cana-3816	33	30	:	:	PUNCT
cana-3816	33	31	=	=	SYM
cana-3816	33	32	{	{	PUNCT
cana-3816	33	33	(	(	PUNCT
cana-3816	33	34	øl	øl	PROPN
cana-3816	33	35	,	,	PUNCT
cana-3816	33	36	øl	øl	PROPN
cana-3816	33	37	)	)	PUNCT
cana-3816	33	38	,	,	PUNCT
cana-3816	33	39	(	(	PUNCT
cana-3816	33	40	øl	øl	PROPN
cana-3816	33	41	,	,	PUNCT
cana-3816	33	42	øm	øm	ADJ
cana-3816	33	43	)	)	PUNCT
cana-3816	33	44	,	,	PUNCT
cana-3816	33	45	(	(	PUNCT
cana-3816	33	46	øl	øl	PROPN
cana-3816	33	47	,	,	PUNCT
cana-3816	33	48	øn	øn	NOUN
cana-3816	33	49	)	)	PUNCT
cana-3816	33	50	,	,	PUNCT
cana-3816	33	51	(	(	PUNCT
cana-3816	33	52	øl	øl	PROPN
cana-3816	33	53	,	,	PUNCT
cana-3816	33	54	øo	øo	PROPN
cana-3816	33	55	)	)	PUNCT
cana-3816	33	56	,	,	PUNCT
cana-3816	33	57	(	(	PUNCT
cana-3816	33	58	øm	øm	X
cana-3816	33	59	,	,	PUNCT
cana-3816	33	60	øm	øm	ADJ
cana-3816	33	61	)	)	PUNCT
cana-3816	33	62	,	,	PUNCT
cana-3816	33	63	(	(	PUNCT
cana-3816	33	64	øm	øm	ADP
cana-3816	33	65	,	,	PUNCT
cana-3816	33	66	øn	øn	NOUN
cana-3816	33	67	)	)	PUNCT
cana-3816	33	68	,	,	PUNCT
cana-3816	33	69	(	(	PUNCT
cana-3816	33	70	øm	øm	X
cana-3816	33	71	,	,	PUNCT
cana-3816	33	72	øo	øo	NOUN
cana-3816	33	73	)	)	PUNCT
cana-3816	33	74	,	,	PUNCT
cana-3816	33	75	(	(	PUNCT
cana-3816	33	76	øn	øn	NOUN
cana-3816	33	77	,	,	PUNCT
cana-3816	33	78	øn	øn	PROPN
cana-3816	33	79	)	)	PUNCT
cana-3816	33	80	,	,	PUNCT
cana-3816	33	81	(	(	PUNCT
cana-3816	33	82	øo	øo	X
cana-3816	33	83	,	,	PUNCT
cana-3816	33	84	øn	øn	NOUN
cana-3816	33	85	)	)	PUNCT
cana-3816	33	86	,	,	PUNCT
cana-3816	33	87	(	(	PUNCT
cana-3816	33	88	øo	øo	X
cana-3816	33	89	,	,	PUNCT
cana-3816	33	90	øo	øo	NOUN
cana-3816	33	91	)	)	PUNCT
cana-3816	33	92	}	}	PUNCT
cana-3816	33	93	.	.	PUNCT
cana-3816	34	1	define	define	VERB
cana-3816	34	2	a	a	DET
cana-3816	34	3	=	=	X
cana-3816	34	4	[	[	X
cana-3816	34	5	ta,>a	ta,>a	NOUN
cana-3816	34	6	]	]	PUNCT
cana-3816	34	7	:	:	PUNCT
cana-3816	34	8	b×b×b→	b×b×b→	VERB
cana-3816	34	9	[	[	X
cana-3816	34	10	0	0	NUM
cana-3816	34	11	,	,	PUNCT
cana-3816	34	12	1	1	NUM
cana-3816	34	13	]	]	PUNCT
cana-3816	34	14	.	.	PUNCT
cana-3816	35	1	t	t	PROPN
cana-3816	35	2	(	(	PUNCT
cana-3816	35	3	ø	ø	PROPN
cana-3816	35	4	,	,	PUNCT
cana-3816	35	5	ι	ι	PROPN
cana-3816	35	6	)	)	PUNCT
cana-3816	35	7	=	=	PUNCT
cana-3816	36	1			PROPN
cana-3816	36	2	0.26	0.26	NUM
cana-3816	36	3	if	if	SCONJ
cana-3816	36	4	ø	ø	NOUN
cana-3816	36	5	=	=	SYM
cana-3816	36	6	øl	øl	PROPN
cana-3816	36	7	0.33	0.33	NUM
cana-3816	36	8	if	if	SCONJ
cana-3816	36	9	ø	ø	PROPN
cana-3816	36	10	=	=	SYM
cana-3816	36	11	øm	øm	ADP
cana-3816	36	12	0.43	0.43	NUM
cana-3816	36	13	if	if	SCONJ
cana-3816	36	14	ø	ø	PROPN
cana-3816	36	15	=	=	PUNCT
cana-3816	36	16	øn	øn	ADP
cana-3816	36	17	0.38	0.38	NUM
cana-3816	36	18	if	if	SCONJ
cana-3816	36	19	ø	ø	PROPN
cana-3816	36	20	=	=	VERB
cana-3816	36	21	øo	øo	PART
cana-3816	36	22	>	>	X
cana-3816	36	23	(	(	PUNCT
cana-3816	36	24	ø	ø	PROPN
cana-3816	36	25	,	,	PUNCT
cana-3816	36	26	ι	ι	PROPN
cana-3816	36	27	)	)	PUNCT
cana-3816	36	28	=	=	PUNCT
cana-3816	37	1			NUM
cana-3816	37	2	0.58	0.58	NUM
cana-3816	37	3	if	if	SCONJ
cana-3816	37	4	ø	ø	PROPN
cana-3816	37	5	=	=	SYM
cana-3816	37	6	øl	øl	PROPN
cana-3816	37	7	0.38	0.38	NUM
cana-3816	37	8	if	if	SCONJ
cana-3816	37	9	ø	ø	PROPN
cana-3816	37	10	=	=	SYM
cana-3816	37	11	øm	øm	ADP
cana-3816	37	12	0.08	0.08	NUM
cana-3816	37	13	if	if	SCONJ
cana-3816	37	14	ø	ø	PROPN
cana-3816	37	15	=	=	PUNCT
cana-3816	37	16	øn	øn	ADP
cana-3816	37	17	0.18	0.18	NUM
cana-3816	37	18	if	if	SCONJ
cana-3816	37	19	ø	ø	PROPN
cana-3816	37	20	=	=	VERB
cana-3816	37	21	øo	øo	NOUN
cana-3816	37	22	then	then	ADV
cana-3816	37	23	a	a	PRON
cana-3816	37	24	is	be	AUX
cana-3816	37	25	a	a	DET
cana-3816	37	26	(	(	PUNCT
cana-3816	37	27	0.48	0.48	NUM
cana-3816	37	28	,	,	PUNCT
cana-3816	37	29	0.63	0.63	NUM
cana-3816	37	30	)	)	PUNCT
cana-3816	37	31	iq1tfss	iq1tfss	NOUN
cana-3816	37	32	of	of	ADP
cana-3816	37	33	b.	b.	PROPN
cana-3816	37	34	definition	definition	NOUN
cana-3816	37	35	2.3	2.3	NUM
cana-3816	37	36	.	.	PUNCT
cana-3816	38	1	a	a	DET
cana-3816	38	2	intuitionistic	intuitionistic	ADJ
cana-3816	38	3	q1	q1	PROPN
cana-3816	38	4	subset	subset	VERB
cana-3816	38	5	a	a	PRON
cana-3816	38	6	of	of	ADP
cana-3816	38	7	b	b	NOUN
cana-3816	38	8	is	be	AUX
cana-3816	38	9	called	call	VERB
cana-3816	38	10	a	a	DET
cana-3816	38	11	(	(	PUNCT
cana-3816	38	12	∝1,∝2)-iq1afbi	∝1,∝2)-iq1afbi	X
cana-3816	38	13	of	of	ADP
cana-3816	38	14	b	b	NOUN
cana-3816	38	15	if	if	SCONJ
cana-3816	38	16	1	1	NUM
cana-3816	38	17	.	.	PUNCT
cana-3816	39	1	if	if	SCONJ
cana-3816	39	2	]	]	X
cana-3816	39	3	6	6	NUM
cana-3816	39	4	ø	ø	NOUN
cana-3816	39	5	,	,	PUNCT
cana-3816	39	6	then	then	ADV
cana-3816	39	7	t	t	PROPN
cana-3816	39	8	(	(	PUNCT
cana-3816	39	9	]	]	SYM
cana-3816	39	10	)	)	PUNCT
cana-3816	39	11	6	6	NUM
cana-3816	39	12	t	t	NOUN
cana-3816	39	13	(	(	PUNCT
cana-3816	39	14	ø	ø	NOUN
cana-3816	39	15	)	)	PUNCT
cana-3816	39	16	and	and	CCONJ
cana-3816	39	17	>	>	X
cana-3816	39	18	(	(	PUNCT
cana-3816	39	19	]	]	X
cana-3816	39	20	)	)	PUNCT
cana-3816	39	21	>	>	X
cana-3816	40	1	>	>	X
cana-3816	40	2	(	(	PUNCT
cana-3816	40	3	ø	ø	NOUN
cana-3816	40	4	)	)	PUNCT
cana-3816	40	5	,	,	PUNCT
cana-3816	40	6	2	2	X
cana-3816	40	7	.	.	NUM
cana-3816	40	8	min{t	min{t	NOUN
cana-3816	40	9	(	(	PUNCT
cana-3816	40	10	]	]	X
cana-3816	40	11	∂1ø	∂1ø	X
cana-3816	40	12	,	,	PUNCT
cana-3816	40	13	ι),∝1	ι),∝1	PROPN
cana-3816	40	14	}	}	PUNCT
cana-3816	40	15	6	6	NUM
cana-3816	40	16	max{t	max{t	NOUN
cana-3816	40	17	(	(	PUNCT
cana-3816	40	18	]	]	X
cana-3816	40	19	,	,	PUNCT
cana-3816	40	20	ι),t	ι),t	PUNCT
cana-3816	40	21	(	(	PUNCT
cana-3816	40	22	ø	ø	NOUN
cana-3816	40	23	,	,	PUNCT
cana-3816	40	24	ι),∝2	ι),∝2	NOUN
cana-3816	40	25	}	}	PUNCT
cana-3816	40	26	,	,	PUNCT
cana-3816	40	27	max{>(]∂1ø	max{>(]∂1ø	VERB
cana-3816	40	28	,	,	PUNCT
cana-3816	40	29	ι),∝1	ι),∝1	PROPN
cana-3816	40	30	}	}	PUNCT
cana-3816	40	31	>	>	X
cana-3816	40	32	min	min	PROPN
cana-3816	40	33	{	{	PUNCT
cana-3816	40	34	>	>	X
cana-3816	40	35	(	(	PUNCT
cana-3816	40	36	]	]	X
cana-3816	40	37	,	,	PUNCT
cana-3816	40	38	ι),>(ø	ι),>(ø	NOUN
cana-3816	40	39	,	,	PUNCT
cana-3816	40	40	ι),∝2	ι),∝2	NOUN
cana-3816	40	41	}	}	PUNCT
cana-3816	40	42	,	,	PUNCT
cana-3816	40	43	3	3	X
cana-3816	40	44	.	.	NUM
cana-3816	40	45	min{t	min{t	PROPN
cana-3816	40	46	(	(	PUNCT
cana-3816	40	47	]	]	X
cana-3816	40	48	∂1ø∂2ε	∂1ø∂2ε	NOUN
cana-3816	40	49	,	,	PUNCT
cana-3816	40	50	ι),∝1	ι),∝1	PROPN
cana-3816	40	51	}	}	PUNCT
cana-3816	40	52	6	6	NUM
cana-3816	40	53	max{t	max{t	NOUN
cana-3816	40	54	(	(	PUNCT
cana-3816	40	55	]	]	X
cana-3816	40	56	,	,	PUNCT
cana-3816	40	57	ι),t	ι),t	PUNCT
cana-3816	40	58	(	(	PUNCT
cana-3816	40	59	ε	ε	PROPN
cana-3816	40	60	,	,	PUNCT
cana-3816	40	61	ι),∝2	ι),∝2	NOUN
cana-3816	40	62	}	}	PUNCT
cana-3816	40	63	,	,	PUNCT
cana-3816	40	64	max{>(]∂1ø∂2ε	max{>(]∂1ø∂2ε	PROPN
cana-3816	40	65	,	,	PUNCT
cana-3816	40	66	ι),∝1	ι),∝1	PROPN
cana-3816	40	67	}	}	PUNCT
cana-3816	40	68	>	>	X
cana-3816	40	69	min	min	PROPN
cana-3816	40	70	{	{	PUNCT
cana-3816	40	71	>	>	X
cana-3816	40	72	(	(	PUNCT
cana-3816	40	73	]	]	X
cana-3816	40	74	,	,	PUNCT
cana-3816	40	75	ι),>(ε	ι),>(ε	X
cana-3816	40	76	,	,	PUNCT
cana-3816	40	77	ι),∝2	ι),∝2	NOUN
cana-3816	40	78	}	}	PUNCT
cana-3816	40	79	,	,	PUNCT
cana-3816	40	80	for	for	ADP
cana-3816	40	81	]	]	PUNCT
cana-3816	40	82	,	,	PUNCT
cana-3816	40	83	ø	ø	PROPN
cana-3816	40	84	,	,	PUNCT
cana-3816	40	85	ε	ε	PROPN
cana-3816	40	86	,	,	PUNCT
cana-3816	40	87	∂1	∂1	ADJ
cana-3816	40	88	,	,	PUNCT
cana-3816	40	89	∂2	∂2	PROPN
cana-3816	40	90	∈	∈	PROPN
cana-3816	40	91	b	b	PROPN
cana-3816	40	92	and	and	CCONJ
cana-3816	40	93	q	q	PROPN
cana-3816	40	94	∈	∈	PROPN
cana-3816	40	95	q1	q1	PROPN
cana-3816	40	96	.	.	PUNCT
cana-3816	40	97	example	example	NOUN
cana-3816	40	98	2.4	2.4	NUM
cana-3816	40	99	.	.	PUNCT
cana-3816	41	1	let	let	VERB
cana-3816	41	2	b	b	NOUN
cana-3816	41	3	=	=	PRON
cana-3816	41	4	{	{	PUNCT
cana-3816	41	5	øl	øl	PROPN
cana-3816	41	6	,	,	PUNCT
cana-3816	41	7	øm	øm	ADP
cana-3816	41	8	,	,	PUNCT
cana-3816	41	9	øn	øn	INTJ
cana-3816	41	10	,	,	PUNCT
cana-3816	41	11	øo	øo	ADP
cana-3816	41	12	}	}	PUNCT
cana-3816	41	13	with	with	ADP
cana-3816	41	14	cayley	cayley	ADJ
cana-3816	41	15	table	table	NOUN
cana-3816	41	16	:	:	PUNCT
cana-3816	41	17	·	·	PUNCT
cana-3816	42	1	øl	øl	VERB
cana-3816	42	2	øm	øm	INTJ
cana-3816	42	3	øn	øn	ADP
cana-3816	42	4	øo	øo	ADP
cana-3816	42	5	øl	øl	PROPN
cana-3816	42	6	t	t	PROPN
cana-3816	42	7	t	t	PROPN
cana-3816	42	8	t	t	PROPN
cana-3816	42	9	t	t	PROPN
cana-3816	42	10	øm	øm	INTJ
cana-3816	42	11	t	t	NOUN
cana-3816	42	12	o	o	X
cana-3816	42	13	p	p	X
cana-3816	42	14	c	c	X
cana-3816	42	15	øn	øn	NOUN
cana-3816	42	16	t	t	PROPN
cana-3816	42	17	p	p	PROPN
cana-3816	43	1	p	p	X
cana-3816	43	2	p	p	X
cana-3816	43	3	øo	øo	ADP
cana-3816	43	4	t	t	PROPN
cana-3816	44	1	p	p	X
cana-3816	44	2	p	p	X
cana-3816	44	3	p	p	X
cana-3816	44	4	·	·	PUNCT
cana-3816	44	5	øl	øl	PROPN
cana-3816	44	6	øm	øm	INTJ
cana-3816	44	7	øn	øn	INTJ
cana-3816	44	8	øo	øo	ADP
cana-3816	44	9	t	t	PROPN
cana-3816	44	10	øl	øl	PROPN
cana-3816	44	11	øl	øl	PROPN
cana-3816	44	12	øl	øl	PROPN
cana-3816	44	13	øl	øl	PROPN
cana-3816	44	14	o	o	NOUN
cana-3816	44	15	øl	øl	ADJ
cana-3816	44	16	øm	øm	INTJ
cana-3816	44	17	øn	øn	INTJ
cana-3816	44	18	øo	øo	ADP
cana-3816	44	19	p	p	PROPN
cana-3816	44	20	øl	øl	PROPN
cana-3816	44	21	øn	øn	NOUN
cana-3816	44	22	øn	øn	NOUN
cana-3816	44	23	øn	øn	X
cana-3816	44	24	c	c	NOUN
cana-3816	44	25	øl	øl	PROPN
cana-3816	44	26	øn	øn	NOUN
cana-3816	44	27	øn	øn	ADP
cana-3816	44	28	øn	øn	PROPN
cana-3816	44	29	·	·	PUNCT
cana-3816	44	30	øl	øl	PROPN
cana-3816	44	31	øm	øm	INTJ
cana-3816	44	32	øn	øn	INTJ
cana-3816	44	33	øo	øo	ADP
cana-3816	44	34	t	t	PROPN
cana-3816	44	35	t	t	PROPN
cana-3816	44	36	t	t	PROPN
cana-3816	44	37	t	t	PROPN
cana-3816	45	1	t	t	X
cana-3816	45	2	o	o	X
cana-3816	46	1	t	t	NOUN
cana-3816	47	1	o	o	X
cana-3816	47	2	p	p	X
cana-3816	48	1	d	d	X
cana-3816	48	2	p	p	PROPN
cana-3816	48	3	t	t	PROPN
cana-3816	48	4	p	p	NOUN
cana-3816	48	5	p	p	X
cana-3816	48	6	p	p	X
cana-3816	48	7	c	c	NOUN
cana-3816	48	8	t	t	NOUN
cana-3816	48	9	o	o	NOUN
cana-3816	48	10	p	p	X
cana-3816	48	11	c	c	X
cana-3816	48	12	·	·	PUNCT
cana-3816	48	13	øl	øl	PROPN
cana-3816	48	14	øm	øm	INTJ
cana-3816	48	15	øn	øn	INTJ
cana-3816	48	16	øo	øo	ADP
cana-3816	48	17	t	t	PROPN
cana-3816	48	18	øl	øl	PROPN
cana-3816	48	19	øl	øl	PROPN
cana-3816	48	20	øl	øl	PROPN
cana-3816	48	21	øl	øl	PROPN
cana-3816	48	22	o	o	NOUN
cana-3816	48	23	øl	øl	ADJ
cana-3816	48	24	øm	øm	INTJ
cana-3816	48	25	øn	øn	INTJ
cana-3816	48	26	øo	øo	ADP
cana-3816	48	27	p	p	PROPN
cana-3816	48	28	øl	øl	PROPN
cana-3816	48	29	øn	øn	NOUN
cana-3816	48	30	øn	øn	NOUN
cana-3816	48	31	øn	øn	ADP
cana-3816	48	32	c	c	PROPN
cana-3816	48	33	øl	øl	PROPN
cana-3816	48	34	øm	øm	INTJ
cana-3816	48	35	øn	øn	ADP
cana-3816	48	36	øo	øo	ADP
cana-3816	48	37	https://internationalpubls.com	https://internationalpubls.com	X
cana-3816	48	38	762	762	NUM
cana-3816	48	39	communications	communication	NOUN
cana-3816	48	40	on	on	ADP
cana-3816	48	41	applied	apply	VERB
cana-3816	48	42	nonlinear	nonlinear	ADJ
cana-3816	48	43	analysis	analysis	NOUN
cana-3816	48	44	issn	issn	NOUN
cana-3816	48	45	:	:	PUNCT
cana-3816	48	46	1074	1074	NUM
cana-3816	48	47	-	-	PUNCT
cana-3816	48	48	133x	133x	NUM
cana-3816	48	49	vol	vol	NOUN
cana-3816	48	50	32	32	NUM
cana-3816	48	51	no	no	NOUN
cana-3816	48	52	.	.	NOUN
cana-3816	48	53	3	3	NUM
cana-3816	48	54	(	(	PUNCT
cana-3816	48	55	2025	2025	NUM
cana-3816	48	56	)	)	PUNCT
cana-3816	48	57	6	6	NUM
cana-3816	48	58	:	:	PUNCT
cana-3816	48	59	=	=	SYM
cana-3816	48	60	{	{	PUNCT
cana-3816	48	61	(	(	PUNCT
cana-3816	48	62	øl	øl	PROPN
cana-3816	48	63	,	,	PUNCT
cana-3816	48	64	øl	øl	PROPN
cana-3816	48	65	)	)	PUNCT
cana-3816	48	66	,	,	PUNCT
cana-3816	48	67	(	(	PUNCT
cana-3816	48	68	øl	øl	PROPN
cana-3816	48	69	,	,	PUNCT
cana-3816	48	70	øm	øm	ADJ
cana-3816	48	71	)	)	PUNCT
cana-3816	48	72	,	,	PUNCT
cana-3816	48	73	(	(	PUNCT
cana-3816	48	74	øl	øl	PROPN
cana-3816	48	75	,	,	PUNCT
cana-3816	48	76	øn	øn	NOUN
cana-3816	48	77	)	)	PUNCT
cana-3816	48	78	,	,	PUNCT
cana-3816	48	79	(	(	PUNCT
cana-3816	48	80	øl	øl	PROPN
cana-3816	48	81	,	,	PUNCT
cana-3816	48	82	øo	øo	PROPN
cana-3816	48	83	)	)	PUNCT
cana-3816	48	84	,	,	PUNCT
cana-3816	48	85	(	(	PUNCT
cana-3816	48	86	øm	øm	X
cana-3816	48	87	,	,	PUNCT
cana-3816	48	88	øm	øm	ADJ
cana-3816	48	89	)	)	PUNCT
cana-3816	48	90	,	,	PUNCT
cana-3816	48	91	(	(	PUNCT
cana-3816	48	92	øm	øm	ADP
cana-3816	48	93	,	,	PUNCT
cana-3816	48	94	øn	øn	NOUN
cana-3816	48	95	)	)	PUNCT
cana-3816	48	96	,	,	PUNCT
cana-3816	48	97	(	(	PUNCT
cana-3816	48	98	øm	øm	X
cana-3816	48	99	,	,	PUNCT
cana-3816	48	100	øo	øo	NOUN
cana-3816	48	101	)	)	PUNCT
cana-3816	48	102	,	,	PUNCT
cana-3816	48	103	(	(	PUNCT
cana-3816	48	104	øn	øn	NOUN
cana-3816	48	105	,	,	PUNCT
cana-3816	48	106	øn	øn	PROPN
cana-3816	48	107	)	)	PUNCT
cana-3816	48	108	,	,	PUNCT
cana-3816	48	109	(	(	PUNCT
cana-3816	48	110	øo	øo	X
cana-3816	48	111	,	,	PUNCT
cana-3816	48	112	øn	øn	NOUN
cana-3816	48	113	)	)	PUNCT
cana-3816	48	114	,	,	PUNCT
cana-3816	48	115	(	(	PUNCT
cana-3816	48	116	øo	øo	X
cana-3816	48	117	,	,	PUNCT
cana-3816	48	118	øo	øo	NOUN
cana-3816	48	119	)	)	PUNCT
cana-3816	48	120	}	}	PUNCT
cana-3816	48	121	.	.	PUNCT
cana-3816	49	1	define	define	VERB
cana-3816	49	2	i	i	PRON
cana-3816	49	3	=	=	PUNCT
cana-3816	50	1	[	[	X
cana-3816	50	2	t	t	PROPN
cana-3816	50	3	,	,	PUNCT
cana-3816	50	4	>	>	X
cana-3816	50	5	]	]	X
cana-3816	50	6	:	:	PUNCT
cana-3816	50	7	b×b×b→	b×b×b→	VERB
cana-3816	50	8	[	[	X
cana-3816	50	9	0	0	NUM
cana-3816	50	10	,	,	PUNCT
cana-3816	50	11	1	1	NUM
cana-3816	50	12	]	]	X
cana-3816	50	13	t	t	PROPN
cana-3816	50	14	(	(	PUNCT
cana-3816	50	15	ø	ø	PROPN
cana-3816	50	16	,	,	PUNCT
cana-3816	50	17	ι	ι	PROPN
cana-3816	50	18	)	)	PUNCT
cana-3816	50	19	=	=	PUNCT
cana-3816	51	1			PROPN
cana-3816	51	2	0.32	0.32	NUM
cana-3816	51	3	if	if	SCONJ
cana-3816	51	4	ø	ø	PROPN
cana-3816	51	5	=	=	SYM
cana-3816	51	6	øl	øl	PROPN
cana-3816	51	7	0.37	0.37	NUM
cana-3816	51	8	if	if	SCONJ
cana-3816	51	9	ø	ø	PROPN
cana-3816	51	10	=	=	SYM
cana-3816	51	11	øm	øm	ADP
cana-3816	51	12	0.47	0.47	NUM
cana-3816	51	13	if	if	SCONJ
cana-3816	51	14	ø	ø	PROPN
cana-3816	51	15	=	=	SYM
cana-3816	51	16	øn	øn	ADP
cana-3816	51	17	0.42	0.42	NUM
cana-3816	51	18	if	if	SCONJ
cana-3816	51	19	ø	ø	PROPN
cana-3816	51	20	=	=	VERB
cana-3816	51	21	øo	øo	PART
cana-3816	51	22	>	>	X
cana-3816	51	23	(	(	PUNCT
cana-3816	51	24	ø	ø	PROPN
cana-3816	51	25	,	,	PUNCT
cana-3816	51	26	ι	ι	PROPN
cana-3816	51	27	)	)	PUNCT
cana-3816	51	28	=	=	PUNCT
cana-3816	52	1			PROPN
cana-3816	52	2	0.49	0.49	NUM
cana-3816	52	3	if	if	SCONJ
cana-3816	52	4	ø	ø	PROPN
cana-3816	52	5	=	=	SYM
cana-3816	52	6	øl	øl	PROPN
cana-3816	52	7	0.30	0.30	NUM
cana-3816	52	8	if	if	SCONJ
cana-3816	52	9	ø	ø	PROPN
cana-3816	52	10	=	=	SYM
cana-3816	52	11	øm	øm	ADP
cana-3816	52	12	0.02	0.02	NUM
cana-3816	52	13	if	if	SCONJ
cana-3816	52	14	ø	ø	PROPN
cana-3816	52	15	=	=	SYM
cana-3816	52	16	øn	øn	ADP
cana-3816	52	17	0.11	0.11	NUM
cana-3816	52	18	if	if	SCONJ
cana-3816	52	19	ø	ø	PROPN
cana-3816	52	20	=	=	PRON
cana-3816	52	21	øo	øo	NOUN
cana-3816	52	22	then	then	ADV
cana-3816	52	23	i	i	PRON
cana-3816	52	24	is	be	AUX
cana-3816	52	25	a	a	DET
cana-3816	52	26	(	(	PUNCT
cana-3816	52	27	0.35	0.35	NUM
cana-3816	52	28	,	,	PUNCT
cana-3816	52	29	0.50	0.50	NUM
cana-3816	52	30	)	)	PUNCT
cana-3816	52	31	iq1afbi	iq1afbi	PROPN
cana-3816	52	32	of	of	ADP
cana-3816	52	33	b.	b.	PROPN
cana-3816	52	34	theorem	theorem	VERB
cana-3816	52	35	2.5	2.5	NUM
cana-3816	52	36	.	.	PUNCT
cana-3816	53	1	a	a	DET
cana-3816	53	2	non	non	ADJ
cana-3816	53	3	-	-	ADJ
cana-3816	53	4	empty	empty	ADJ
cana-3816	53	5	subset	subset	NOUN
cana-3816	53	6	i∝1	i∝1	X
cana-3816	53	7	is	be	AUX
cana-3816	53	8	a	a	DET
cana-3816	53	9	t∝1	t∝1	NOUN
cana-3816	53	10	is	be	AUX
cana-3816	53	11	a	a	PRON
cana-3816	53	12	(	(	PUNCT
cana-3816	53	13	∝1,∝2)-iq1tfss	∝1,∝2)-iq1tfss	X
cana-3816	53	14	(	(	PUNCT
cana-3816	53	15	iq1afli	iq1afli	PROPN
cana-3816	53	16	,	,	PUNCT
cana-3816	53	17	iq1aflati	iq1aflati	PROPN
cana-3816	53	18	,	,	PUNCT
cana-3816	53	19	iq1afri	iq1afri	PROPN
cana-3816	53	20	,	,	PUNCT
cana-3816	53	21	iq1afbi	iq1afbi	PROPN
cana-3816	53	22	)	)	PUNCT
cana-3816	53	23	of	of	ADP
cana-3816	53	24	b.	b.	PROPN
cana-3816	53	25	then	then	ADV
cana-3816	53	26	the	the	DET
cana-3816	53	27	lower	low	ADJ
cana-3816	53	28	level	level	NOUN
cana-3816	53	29	set	set	VERB
cana-3816	53	30	t∝1	t∝1	NUM
cana-3816	53	31	is	be	AUX
cana-3816	53	32	an	an	DET
cana-3816	53	33	tss	tss	NOUN
cana-3816	53	34	(	(	PUNCT
cana-3816	53	35	tli	tli	PROPN
cana-3816	53	36	,	,	PUNCT
cana-3816	53	37	tlati	tlati	PROPN
cana-3816	53	38	,	,	PUNCT
cana-3816	53	39	tri	tri	NOUN
cana-3816	53	40	,	,	PUNCT
cana-3816	53	41	tbi	tbi	NOUN
cana-3816	53	42	)	)	PUNCT
cana-3816	53	43	of	of	ADP
cana-3816	53	44	b	b	NOUN
cana-3816	53	45	,	,	PUNCT
cana-3816	53	46	where	where	SCONJ
cana-3816	53	47	t∝1=	t∝1=	NOUN
cana-3816	53	48	{	{	PUNCT
cana-3816	53	49	]	]	X
cana-3816	53	50	∈	∈	PROPN
cana-3816	53	51	b|	b|	PROPN
cana-3816	53	52	t	t	PROPN
cana-3816	53	53	(	(	PUNCT
cana-3816	53	54	]	]	X
cana-3816	53	55	,	,	PUNCT
cana-3816	53	56	ι	ι	PROPN
cana-3816	53	57	)	)	PUNCT
cana-3816	53	58	≺∝1	≺∝1	PROPN
cana-3816	53	59	}	}	PUNCT
cana-3816	53	60	and	and	CCONJ
cana-3816	53	61	>	>	X
cana-3816	53	62	∝1	∝1	X
cana-3816	53	63	=	=	PUNCT
cana-3816	53	64	{	{	PUNCT
cana-3816	53	65	]	]	X
cana-3816	53	66	∈	∈	PROPN
cana-3816	53	67	b|	b|	PROPN
cana-3816	53	68	>	>	X
cana-3816	53	69	(	(	PUNCT
cana-3816	53	70	]	]	X
cana-3816	53	71	,	,	PUNCT
cana-3816	53	72	ι	ι	PROPN
cana-3816	53	73	)	)	PUNCT
cana-3816	53	74	�	�	NOUN
cana-3816	53	75	∝1	∝1	NOUN
cana-3816	53	76	}	}	PUNCT
cana-3816	53	77	.	.	PUNCT
cana-3816	54	1	proof	proof	NOUN
cana-3816	54	2	.	.	PUNCT
cana-3816	55	1	suppose	suppose	VERB
cana-3816	55	2	that	that	SCONJ
cana-3816	55	3	i∝1	i∝1	PROPN
cana-3816	55	4	is	be	AUX
cana-3816	55	5	a	a	DET
cana-3816	55	6	(	(	PUNCT
cana-3816	55	7	∝1,∝2)-iq1tfss	∝1,∝2)-iq1tfss	ADJ
cana-3816	55	8	of	of	ADP
cana-3816	55	9	b.	b.	NOUN
cana-3816	55	10	let	let	VERB
cana-3816	55	11	]	]	X
cana-3816	55	12	,	,	PUNCT
cana-3816	55	13	∂	∂	NUM
cana-3816	55	14	,	,	PUNCT
cana-3816	55	15	ø	ø	PROPN
cana-3816	55	16	∈	∈	PROPN
cana-3816	55	17	b	b	NOUN
cana-3816	55	18	such	such	ADJ
cana-3816	55	19	that	that	PRON
cana-3816	55	20	]	]	X
cana-3816	55	21	,	,	PUNCT
cana-3816	55	22	∂	∂	NUM
cana-3816	55	23	,	,	PUNCT
cana-3816	55	24	ø	ø	PROPN
cana-3816	55	25	∈t∝1	∈t∝1	PROPN
cana-3816	55	26	.	.	PUNCT
cana-3816	56	1	then	then	ADV
cana-3816	56	2	t	t	PROPN
cana-3816	56	3	(	(	PUNCT
cana-3816	56	4	]	]	X
cana-3816	56	5	,	,	PUNCT
cana-3816	56	6	ι	ι	PROPN
cana-3816	56	7	)	)	PUNCT
cana-3816	56	8	≺∝1,t	≺∝1,t	PROPN
cana-3816	56	9	(	(	PUNCT
cana-3816	56	10	∂	∂	NUM
cana-3816	56	11	,	,	PUNCT
cana-3816	56	12	ι	ι	PROPN
cana-3816	56	13	)	)	PUNCT
cana-3816	56	14	≺∝1,t	≺∝1,t	NOUN
cana-3816	56	15	(	(	PUNCT
cana-3816	56	16	ø	ø	PROPN
cana-3816	56	17	,	,	PUNCT
cana-3816	56	18	ι	ι	PROPN
cana-3816	56	19	)	)	PUNCT
cana-3816	57	1	≺∝1	≺∝1	PROPN
cana-3816	57	2	.	.	PUNCT
cana-3816	58	1	therefore	therefore	ADV
cana-3816	58	2	min{t	min{t	PROPN
cana-3816	58	3	(	(	PUNCT
cana-3816	58	4	]	]	X
cana-3816	58	5	∂ø	∂ø	PROPN
cana-3816	58	6	,	,	PUNCT
cana-3816	58	7	ι),∝1	ι),∝1	PROPN
cana-3816	58	8	}	}	PUNCT
cana-3816	58	9	6	6	NUM
cana-3816	58	10	max{t	max{t	NOUN
cana-3816	58	11	(	(	PUNCT
cana-3816	58	12	]	]	X
cana-3816	58	13	,	,	PUNCT
cana-3816	58	14	ι),t	ι),t	PUNCT
cana-3816	58	15	(	(	PUNCT
cana-3816	58	16	∂	∂	NUM
cana-3816	58	17	,	,	PUNCT
cana-3816	58	18	ι),t	ι),t	X
cana-3816	58	19	(	(	PUNCT
cana-3816	58	20	ø	ø	NOUN
cana-3816	58	21	,	,	PUNCT
cana-3816	58	22	ι),∝2	ι),∝2	NOUN
cana-3816	58	23	}	}	PUNCT
cana-3816	58	24	≺	≺	NOUN
cana-3816	58	25	max{∝1,∝1,∝1,∝2	max{∝1,∝1,∝1,∝2	NOUN
cana-3816	58	26	}	}	PUNCT
cana-3816	58	27	=	=	NOUN
cana-3816	58	28	∝2	∝2	NOUN
cana-3816	58	29	.	.	PUNCT
cana-3816	59	1	hence	hence	ADV
cana-3816	59	2	t	t	PROPN
cana-3816	59	3	(	(	PUNCT
cana-3816	59	4	]	]	X
cana-3816	59	5	∂ø	∂ø	PROPN
cana-3816	59	6	,	,	PUNCT
cana-3816	59	7	ι	ι	PROPN
cana-3816	59	8	)	)	PUNCT
cana-3816	60	1	≺∝1	≺∝1	PROPN
cana-3816	60	2	.	.	PUNCT
cana-3816	61	1	it	it	PRON
cana-3816	61	2	shows	show	VERB
cana-3816	61	3	that	that	SCONJ
cana-3816	61	4	]	]	X
cana-3816	61	5	∂ø	∂ø	PROPN
cana-3816	61	6	∈t∝1	∈t∝1	VERB
cana-3816	61	7	.	.	PUNCT
cana-3816	62	1	therefore	therefore	ADV
cana-3816	62	2	t∝1	t∝1	PROPN
cana-3816	62	3	is	be	AUX
cana-3816	62	4	a	a	DET
cana-3816	62	5	tss	tss	NOUN
cana-3816	62	6	of	of	ADP
cana-3816	62	7	b.	b.	PROPN
cana-3816	62	8	let	let	VERB
cana-3816	62	9	]	]	X
cana-3816	62	10	,	,	PUNCT
cana-3816	62	11	∂	∂	NUM
cana-3816	62	12	,	,	PUNCT
cana-3816	62	13	ø	ø	PROPN
cana-3816	62	14	∈	∈	PROPN
cana-3816	62	15	b	b	NOUN
cana-3816	62	16	such	such	ADJ
cana-3816	62	17	that	that	PRON
cana-3816	62	18	]	]	X
cana-3816	62	19	,	,	PUNCT
cana-3816	62	20	∂	∂	NUM
cana-3816	62	21	,	,	PUNCT
cana-3816	62	22	ø	ø	PROPN
cana-3816	62	23	∈	∈	PROPN
cana-3816	62	24	>	>	X
cana-3816	62	25	∝1	∝1	PROPN
cana-3816	62	26	.	.	PUNCT
cana-3816	63	1	then	then	ADV
cana-3816	63	2	>	>	X
cana-3816	63	3	(	(	PUNCT
cana-3816	63	4	]	]	X
cana-3816	63	5	,	,	PUNCT
cana-3816	63	6	ι	ι	PROPN
cana-3816	63	7	)	)	PUNCT
cana-3816	63	8	�	�	PROPN
cana-3816	63	9	∝1,>(∂	∝1,>(∂	NOUN
cana-3816	63	10	,	,	PUNCT
cana-3816	63	11	ι	ι	PROPN
cana-3816	63	12	)	)	PUNCT
cana-3816	63	13	�	�	PROPN
cana-3816	63	14	∝1	∝1	NOUN
cana-3816	63	15	>	>	X
cana-3816	63	16	(	(	PUNCT
cana-3816	63	17	ø	ø	PROPN
cana-3816	63	18	,	,	PUNCT
cana-3816	63	19	ι	ι	PROPN
cana-3816	63	20	)	)	PUNCT
cana-3816	63	21	�	�	PROPN
cana-3816	63	22	∝1	∝1	NOUN
cana-3816	63	23	.	.	PUNCT
cana-3816	64	1	therefore	therefore	ADV
cana-3816	64	2	max{>(]∂ø	max{>(]∂ø	ADJ
cana-3816	64	3	,	,	PUNCT
cana-3816	64	4	ι),∝1	ι),∝1	PROPN
cana-3816	64	5	}	}	PUNCT
cana-3816	64	6	>	>	X
cana-3816	64	7	min	min	PROPN
cana-3816	64	8	{	{	PUNCT
cana-3816	64	9	>	>	X
cana-3816	64	10	(	(	PUNCT
cana-3816	64	11	]	]	X
cana-3816	64	12	,	,	PUNCT
cana-3816	64	13	ι),>(∂	ι),>(∂	PROPN
cana-3816	64	14	,	,	PUNCT
cana-3816	64	15	ι),>(ø	ι),>(ø	NOUN
cana-3816	64	16	,	,	PUNCT
cana-3816	64	17	ι),∝2	ι),∝2	NOUN
cana-3816	64	18	}	}	PUNCT
cana-3816	64	19	�	�	PROPN
cana-3816	64	20	min{∝1,∝1,∝1,∝2	min{∝1,∝1,∝1,∝2	NOUN
cana-3816	64	21	}	}	PUNCT
cana-3816	64	22	=	=	NOUN
cana-3816	64	23	∝1	∝1	NOUN
cana-3816	64	24	.	.	PUNCT
cana-3816	65	1	hence	hence	ADV
cana-3816	65	2	>	>	X
cana-3816	65	3	(	(	PUNCT
cana-3816	65	4	]	]	X
cana-3816	65	5	∂ø	∂ø	PROPN
cana-3816	65	6	,	,	PUNCT
cana-3816	65	7	ι	ι	PROPN
cana-3816	65	8	)	)	PUNCT
cana-3816	65	9	�	�	PROPN
cana-3816	65	10	∝1	∝1	NOUN
cana-3816	65	11	.	.	PUNCT
cana-3816	66	1	it	it	PRON
cana-3816	66	2	shows	show	VERB
cana-3816	66	3	that	that	SCONJ
cana-3816	66	4	]	]	X
cana-3816	66	5	∂ø	∂ø	PROPN
cana-3816	66	6	∈	∈	PROPN
cana-3816	66	7	>	>	X
cana-3816	66	8	∝1	∝1	PROPN
cana-3816	66	9	.	.	PUNCT
cana-3816	67	1	therefore	therefore	ADV
cana-3816	67	2	>	>	X
cana-3816	67	3	∝1	∝1	PROPN
cana-3816	67	4	is	be	AUX
cana-3816	67	5	a	a	DET
cana-3816	67	6	tss	tss	NOUN
cana-3816	67	7	of	of	ADP
cana-3816	67	8	b.	b.	PROPN
cana-3816	67	9	therefore	therefore	ADV
cana-3816	67	10	i∝1	i∝1	PROPN
cana-3816	67	11	is	be	AUX
cana-3816	67	12	a	a	DET
cana-3816	67	13	tss	tss	NOUN
cana-3816	67	14	of	of	ADP
cana-3816	67	15	b.	b.	PROPN
cana-3816	67	16	theorem	theorem	VERB
cana-3816	67	17	2.6	2.6	NUM
cana-3816	67	18	.	.	PUNCT
cana-3816	68	1	a	a	DET
cana-3816	68	2	non	non	ADJ
cana-3816	68	3	-	-	ADJ
cana-3816	68	4	empty	empty	ADJ
cana-3816	68	5	subset	subset	NOUN
cana-3816	68	6	`	`	PUNCT
cana-3816	68	7	of	of	ADP
cana-3816	68	8	b	b	PROPN
cana-3816	68	9	is	be	AUX
cana-3816	68	10	a	a	DET
cana-3816	68	11	ss	ss	NOUN
cana-3816	69	1	[	[	X
cana-3816	69	2	tli	tli	X
cana-3816	69	3	,	,	PUNCT
cana-3816	69	4	tlati	tlati	PROPN
cana-3816	69	5	,	,	PUNCT
cana-3816	69	6	tri	tri	NOUN
cana-3816	69	7	,	,	PUNCT
cana-3816	69	8	tbi	tbi	NOUN
cana-3816	69	9	]	]	PUNCT
cana-3816	69	10	of	of	ADP
cana-3816	69	11	b	b	NOUN
cana-3816	69	12	if	if	SCONJ
cana-3816	69	13	and	and	CCONJ
cana-3816	69	14	only	only	ADV
cana-3816	69	15	if	if	SCONJ
cana-3816	69	16	the	the	DET
cana-3816	69	17	iq1fs	iq1fs	NOUN
cana-3816	70	1	i	i	PRON
cana-3816	70	2	=	=	PUNCT
cana-3816	71	1	[	[	X
cana-3816	71	2	t	t	PROPN
cana-3816	71	3	,	,	PUNCT
cana-3816	71	4	>	>	X
cana-3816	71	5	]	]	PUNCT
cana-3816	71	6	of	of	ADP
cana-3816	71	7	b	b	PROPN
cana-3816	71	8	is	be	AUX
cana-3816	71	9	defined	define	VERB
cana-3816	71	10	as	as	ADP
cana-3816	71	11	t	t	PROPN
cana-3816	71	12	(	(	PUNCT
cana-3816	71	13	]	]	X
cana-3816	71	14	,	,	PUNCT
cana-3816	71	15	ι	ι	PROPN
cana-3816	71	16	)	)	PUNCT
cana-3816	71	17	=	=	SYM
cana-3816	72	1	{	{	PUNCT
cana-3816	72	2	6∝2	6∝2	NUM
cana-3816	72	3	for	for	ADP
cana-3816	72	4	all	all	PRON
cana-3816	72	5	]	]	X
cana-3816	72	6	∈	∈	PROPN
cana-3816	72	7	(	(	PUNCT
cana-3816	72	8	`	`	PUNCT
cana-3816	72	9	]	]	PUNCT
cana-3816	72	10	∝1	∝1	NOUN
cana-3816	72	11	for	for	ADP
cana-3816	72	12	all	all	PRON
cana-3816	72	13	]	]	PUNCT
cana-3816	72	14	/∈	/∈	PUNCT
cana-3816	73	1	(	(	PUNCT
cana-3816	73	2	`	`	PUNCT
cana-3816	73	3	]	]	PUNCT
cana-3816	73	4	>	>	PUNCT
cana-3816	73	5	(	(	PUNCT
cana-3816	73	6	]	]	X
cana-3816	73	7	,	,	PUNCT
cana-3816	73	8	ι	ι	PROPN
cana-3816	73	9	)	)	PUNCT
cana-3816	73	10	=	=	SYM
cana-3816	73	11	{	{	PUNCT
cana-3816	73	12	>	>	X
cana-3816	73	13	∝2	∝2	NOUN
cana-3816	73	14	for	for	ADP
cana-3816	73	15	all	all	PRON
cana-3816	73	16	]	]	X
cana-3816	73	17	∈	∈	PROPN
cana-3816	73	18	(	(	PUNCT
cana-3816	73	19	`	`	PUNCT
cana-3816	73	20	]	]	PUNCT
cana-3816	73	21	∝1	∝1	NOUN
cana-3816	73	22	for	for	ADP
cana-3816	73	23	all	all	PRON
cana-3816	73	24	]	]	PUNCT
cana-3816	73	25	/∈	/∈	PUNCT
cana-3816	74	1	(	(	PUNCT
cana-3816	74	2	`	`	PUNCT
cana-3816	74	3	]	]	X
cana-3816	74	4	is	be	AUX
cana-3816	74	5	a	a	DET
cana-3816	74	6	(	(	PUNCT
cana-3816	74	7	∝1,∝2)iq1tfss[iq1afli	∝1,∝2)iq1tfss[iq1afli	NOUN
cana-3816	74	8	,	,	PUNCT
cana-3816	74	9	iq1aflati	iq1aflati	PROPN
cana-3816	74	10	,	,	PUNCT
cana-3816	74	11	iq1afri	iq1afri	PROPN
cana-3816	74	12	,	,	PUNCT
cana-3816	74	13	iq1afbi	iq1afbi	PROPN
cana-3816	74	14	]	]	PUNCT
cana-3816	74	15	of	of	ADP
cana-3816	74	16	b.	b.	PROPN
cana-3816	74	17	proof	proof	NOUN
cana-3816	74	18	.	.	PUNCT
cana-3816	75	1	suppose	suppose	VERB
cana-3816	75	2	that	that	SCONJ
cana-3816	75	3	`	`	PUNCT
cana-3816	75	4	is	be	AUX
cana-3816	75	5	an	an	DET
cana-3816	75	6	tss	tss	NOUN
cana-3816	75	7	of	of	ADP
cana-3816	75	8	b.	b.	PROPN
cana-3816	75	9	let	let	VERB
cana-3816	75	10	]	]	X
cana-3816	75	11	,	,	PUNCT
cana-3816	75	12	∂	∂	NUM
cana-3816	75	13	,	,	PUNCT
cana-3816	75	14	ø	ø	PROPN
cana-3816	75	15	∈	∈	PROPN
cana-3816	75	16	b	b	NOUN
cana-3816	75	17	be	be	AUX
cana-3816	75	18	such	such	ADJ
cana-3816	75	19	that	that	SCONJ
cana-3816	75	20	]	]	X
cana-3816	75	21	,	,	PUNCT
cana-3816	75	22	∂	∂	NUM
cana-3816	75	23	,	,	PUNCT
cana-3816	75	24	ø	ø	PROPN
cana-3816	75	25	∈	∈	PROPN
cana-3816	75	26	(	(	PUNCT
cana-3816	75	27	`	`	PUNCT
cana-3816	75	28	]	]	PUNCT
cana-3816	75	29	then	then	ADV
cana-3816	75	30	]	]	X
cana-3816	75	31	∂ø	∂ø	PROPN
cana-3816	75	32	∈	∈	PROPN
cana-3816	75	33	(	(	PUNCT
cana-3816	75	34	`	`	PUNCT
cana-3816	75	35	]	]	X
cana-3816	75	36	.	.	PUNCT
cana-3816	76	1	hence	hence	ADV
cana-3816	76	2	t	t	PROPN
cana-3816	76	3	(	(	PUNCT
cana-3816	76	4	]	]	X
cana-3816	76	5	∂ø	∂ø	PROPN
cana-3816	76	6	,	,	PUNCT
cana-3816	76	7	ι	ι	PROPN
cana-3816	76	8	)	)	PUNCT
cana-3816	76	9	6∝2	6∝2	NUM
cana-3816	76	10	and	and	CCONJ
cana-3816	76	11	>	>	X
cana-3816	76	12	(	(	PUNCT
cana-3816	76	13	]	]	X
cana-3816	76	14	∂ø	∂ø	PROPN
cana-3816	76	15	,	,	PUNCT
cana-3816	76	16	ι	ι	PROPN
cana-3816	76	17	)	)	PUNCT
cana-3816	76	18	>	>	PUNCT
cana-3816	76	19	∝2	∝2	NOUN
cana-3816	76	20	.	.	PUNCT
cana-3816	77	1	thus	thus	ADV
cana-3816	77	2	,	,	PUNCT
cana-3816	77	3	min{t	min{t	PROPN
cana-3816	77	4	(	(	PUNCT
cana-3816	77	5	]	]	X
cana-3816	77	6	∂ø	∂ø	PROPN
cana-3816	77	7	,	,	PUNCT
cana-3816	77	8	ι),∝1	ι),∝1	NOUN
cana-3816	77	9	}	}	PUNCT
cana-3816	77	10	6∝2=	6∝2=	NUM
cana-3816	77	11	max{t	max{t	NOUN
cana-3816	77	12	(	(	PUNCT
cana-3816	77	13	]	]	PUNCT
cana-3816	77	14	,	,	PUNCT
cana-3816	77	15	ι),t	ι),t	PUNCT
cana-3816	77	16	(	(	PUNCT
cana-3816	77	17	∂	∂	NUM
cana-3816	77	18	,	,	PUNCT
cana-3816	77	19	ι),t	ι),t	X
cana-3816	77	20	(	(	PUNCT
cana-3816	77	21	ø	ø	NOUN
cana-3816	77	22	,	,	PUNCT
cana-3816	77	23	ι),∝2	ι),∝2	NOUN
cana-3816	77	24	}	}	PUNCT
cana-3816	77	25	and	and	CCONJ
cana-3816	77	26	max{>(]∂ø	max{>(]∂ø	NUM
cana-3816	77	27	,	,	PUNCT
cana-3816	77	28	ι),∝1	ι),∝1	PROPN
cana-3816	77	29	}	}	PUNCT
cana-3816	77	30	>	>	PUNCT
cana-3816	77	31	∝2=	∝2=	PROPN
cana-3816	77	32	min	min	X
cana-3816	77	33	{	{	PUNCT
cana-3816	77	34	>	>	X
cana-3816	77	35	(	(	PUNCT
cana-3816	77	36	]	]	X
cana-3816	77	37	,	,	PUNCT
cana-3816	77	38	ι),>(∂	ι),>(∂	PROPN
cana-3816	77	39	,	,	PUNCT
cana-3816	77	40	ι),>(ø	ι),>(ø	NOUN
cana-3816	77	41	,	,	PUNCT
cana-3816	77	42	ι),∝2	ι),∝2	NOUN
cana-3816	77	43	}	}	PUNCT
cana-3816	77	44	.	.	PUNCT
cana-3816	78	1	if	if	SCONJ
cana-3816	78	2	]	]	X
cana-3816	78	3	/∈	/∈	PUNCT
cana-3816	79	1	(	(	PUNCT
cana-3816	79	2	`	`	PUNCT
cana-3816	79	3	]	]	X
cana-3816	79	4	or	or	CCONJ
cana-3816	79	5	∂	∂	NUM
cana-3816	79	6	/∈	/∈	PUNCT
cana-3816	79	7	(	(	PUNCT
cana-3816	79	8	`	`	PUNCT
cana-3816	79	9	]	]	PUNCT
cana-3816	79	10	or	or	CCONJ
cana-3816	79	11	ø	ø	NOUN
cana-3816	79	12	/∈	/∈	PUNCT
cana-3816	80	1	(	(	PUNCT
cana-3816	80	2	`	`	PUNCT
cana-3816	80	3	]	]	X
cana-3816	80	4	,	,	PUNCT
cana-3816	80	5	then	then	ADV
cana-3816	80	6	max{t	max{t	NOUN
cana-3816	80	7	(	(	PUNCT
cana-3816	80	8	]	]	X
cana-3816	80	9	,	,	PUNCT
cana-3816	80	10	ι),t	ι),t	PUNCT
cana-3816	80	11	(	(	PUNCT
cana-3816	80	12	∂	∂	NUM
cana-3816	80	13	,	,	PUNCT
cana-3816	80	14	ι),t	ι),t	X
cana-3816	80	15	(	(	PUNCT
cana-3816	80	16	ø	ø	NOUN
cana-3816	80	17	,	,	PUNCT
cana-3816	80	18	ι),∝2	ι),∝2	NOUN
cana-3816	80	19	}	}	PUNCT
cana-3816	80	20	=	=	NOUN
cana-3816	80	21	∝1	∝1	NOUN
cana-3816	80	22	and	and	CCONJ
cana-3816	80	23	min	min	NOUN
cana-3816	80	24	{	{	PUNCT
cana-3816	80	25	>	>	X
cana-3816	80	26	(	(	PUNCT
cana-3816	80	27	]	]	X
cana-3816	80	28	,	,	PUNCT
cana-3816	80	29	ι),>(∂	ι),>(∂	PROPN
cana-3816	80	30	,	,	PUNCT
cana-3816	80	31	ι),>(ø	ι),>(ø	NOUN
cana-3816	80	32	,	,	PUNCT
cana-3816	80	33	ι),∝2	ι),∝2	NOUN
cana-3816	80	34	}	}	PUNCT
cana-3816	80	35	=	=	SYM
cana-3816	80	36	∝2	∝2	NOUN
cana-3816	80	37	.	.	PUNCT
cana-3816	81	1	that	that	PRON
cana-3816	81	2	is	be	AUX
cana-3816	81	3	min{t	min{t	PROPN
cana-3816	81	4	(	(	PUNCT
cana-3816	81	5	]	]	X
cana-3816	81	6	∂ø	∂ø	PROPN
cana-3816	81	7	,	,	PUNCT
cana-3816	81	8	ι),∝1	ι),∝1	PROPN
cana-3816	81	9	}	}	PUNCT
cana-3816	81	10	6	6	NUM
cana-3816	81	11	max{t	max{t	NOUN
cana-3816	81	12	(	(	PUNCT
cana-3816	81	13	]	]	X
cana-3816	81	14	,	,	PUNCT
cana-3816	81	15	ι),t	ι),t	PUNCT
cana-3816	81	16	(	(	PUNCT
cana-3816	81	17	∂	∂	NUM
cana-3816	81	18	,	,	PUNCT
cana-3816	81	19	ι),t	ι),t	X
cana-3816	81	20	(	(	PUNCT
cana-3816	81	21	ø	ø	NOUN
cana-3816	81	22	,	,	PUNCT
cana-3816	81	23	ι),∝2	ι),∝2	NOUN
cana-3816	81	24	}	}	PUNCT
cana-3816	81	25	and	and	CCONJ
cana-3816	81	26	max{>(]∂ø	max{>(]∂ø	NUM
cana-3816	81	27	,	,	PUNCT
cana-3816	81	28	ι),∝1	ι),∝1	PROPN
cana-3816	81	29	}	}	PUNCT
cana-3816	81	30	>	>	X
cana-3816	81	31	min	min	PROPN
cana-3816	81	32	{	{	PUNCT
cana-3816	81	33	>	>	X
cana-3816	81	34	(	(	PUNCT
cana-3816	81	35	]	]	X
cana-3816	81	36	,	,	PUNCT
cana-3816	81	37	ι),>(∂	ι),>(∂	PROPN
cana-3816	81	38	,	,	PUNCT
cana-3816	81	39	ι),>(ø	ι),>(ø	NOUN
cana-3816	81	40	,	,	PUNCT
cana-3816	81	41	ι),∝2	ι),∝2	NOUN
cana-3816	81	42	}	}	PUNCT
cana-3816	81	43	.	.	PUNCT
cana-3816	82	1	therefore	therefore	ADV
cana-3816	82	2	i	i	PRON
cana-3816	82	3	is	be	AUX
cana-3816	82	4	a	a	DET
cana-3816	82	5	(	(	PUNCT
cana-3816	82	6	∝1,∝2	∝1,∝2	NOUN
cana-3816	82	7	)	)	PUNCT
cana-3816	82	8	iq1tfss	iq1tfss	NOUN
cana-3816	82	9	of	of	ADP
cana-3816	82	10	b.	b.	NOUN
cana-3816	82	11	conversely	conversely	ADV
cana-3816	82	12	assume	assume	VERB
cana-3816	82	13	that	that	SCONJ
cana-3816	83	1	i	i	PRON
cana-3816	83	2	=	=	PUNCT
cana-3816	84	1	[	[	X
cana-3816	84	2	t	t	PROPN
cana-3816	84	3	,	,	PUNCT
cana-3816	84	4	>	>	X
cana-3816	84	5	]	]	X
cana-3816	84	6	is	be	AUX
cana-3816	84	7	a	a	DET
cana-3816	84	8	(	(	PUNCT
cana-3816	84	9	∝1,∝2)-iq1tfss	∝1,∝2)-iq1tfss	NOUN
cana-3816	84	10	of	of	ADP
cana-3816	84	11	b.	b.	NOUN
cana-3816	84	12	let	let	VERB
cana-3816	84	13	]	]	PUNCT
cana-3816	84	14	∂ø	∂ø	PROPN
cana-3816	84	15	∈	∈	PROPN
cana-3816	84	16	(	(	PUNCT
cana-3816	84	17	`	`	PUNCT
cana-3816	84	18	]	]	PUNCT
cana-3816	84	19	.	.	PUNCT
cana-3816	85	1	then	then	ADV
cana-3816	85	2	t	t	PROPN
cana-3816	85	3	(	(	PUNCT
cana-3816	85	4	]	]	X
cana-3816	85	5	,	,	PUNCT
cana-3816	85	6	ι	ι	PROPN
cana-3816	85	7	)	)	PUNCT
cana-3816	85	8	6∝2,t	6∝2,t	NOUN
cana-3816	85	9	(	(	PUNCT
cana-3816	85	10	∂	∂	NUM
cana-3816	85	11	,	,	PUNCT
cana-3816	85	12	ι	ι	PROPN
cana-3816	85	13	)	)	PUNCT
cana-3816	85	14	6∝2,t	6∝2,t	NOUN
cana-3816	85	15	(	(	PUNCT
cana-3816	85	16	ø	ø	PROPN
cana-3816	85	17	,	,	PUNCT
cana-3816	85	18	ι	ι	PROPN
cana-3816	85	19	)	)	PUNCT
cana-3816	85	20	6∝2	6∝2	NUM
cana-3816	85	21	and	and	CCONJ
cana-3816	85	22	>	>	X
cana-3816	85	23	(	(	PUNCT
cana-3816	85	24	]	]	X
cana-3816	85	25	,	,	PUNCT
cana-3816	85	26	ι	ι	PROPN
cana-3816	85	27	)	)	PUNCT
cana-3816	85	28	>	>	PUNCT
cana-3816	85	29	∝2,>(∂	∝2,>(∂	X
cana-3816	85	30	,	,	PUNCT
cana-3816	85	31	ι	ι	PROPN
cana-3816	85	32	)	)	PUNCT
cana-3816	85	33	>	>	X
cana-3816	85	34	∝2,>(ø	∝2,>(ø	PROPN
cana-3816	85	35	,	,	PUNCT
cana-3816	85	36	ι	ι	PROPN
cana-3816	85	37	)	)	PUNCT
cana-3816	85	38	>	>	PUNCT
cana-3816	85	39	∝2	∝2	NOUN
cana-3816	85	40	.	.	PUNCT
cana-3816	86	1	now	now	ADV
cana-3816	86	2	i	i	PRON
cana-3816	86	3	=	=	PUNCT
cana-3816	87	1	[	[	X
cana-3816	87	2	t	t	PROPN
cana-3816	87	3	,	,	PUNCT
cana-3816	87	4	>	>	X
cana-3816	87	5	]	]	X
cana-3816	87	6	is	be	AUX
cana-3816	87	7	a	a	DET
cana-3816	87	8	(	(	PUNCT
cana-3816	87	9	∝1,∝2)iq1tfss	∝1,∝2)iq1tfss	PROPN
cana-3816	87	10	of	of	ADP
cana-3816	87	11	b.	b.	PROPN
cana-3816	87	12	therefore	therefore	ADV
cana-3816	87	13	min{t	min{t	PROPN
cana-3816	87	14	(	(	PUNCT
cana-3816	87	15	]	]	X
cana-3816	87	16	∂ø	∂ø	PROPN
cana-3816	87	17	,	,	PUNCT
cana-3816	87	18	ι),∝1	ι),∝1	PROPN
cana-3816	87	19	}	}	PUNCT
cana-3816	87	20	6	6	NUM
cana-3816	87	21	max{t	max{t	NOUN
cana-3816	87	22	(	(	PUNCT
cana-3816	87	23	]	]	X
cana-3816	87	24	,	,	PUNCT
cana-3816	87	25	ι),t	ι),t	PUNCT
cana-3816	87	26	(	(	PUNCT
cana-3816	87	27	∂	∂	NUM
cana-3816	87	28	,	,	PUNCT
cana-3816	87	29	ι),t	ι),t	X
cana-3816	87	30	(	(	PUNCT
cana-3816	87	31	ø	ø	NOUN
cana-3816	87	32	,	,	PUNCT
cana-3816	87	33	ι),∝2	ι),∝2	NOUN
cana-3816	87	34	}	}	PUNCT
cana-3816	87	35	6	6	NUM
cana-3816	87	36	max{∝2,∝2,∝2	max{∝2,∝2,∝2	PROPN
cana-3816	87	37	,	,	PUNCT
cana-3816	87	38	∝2	∝2	PROPN
cana-3816	87	39	}	}	PUNCT
cana-3816	87	40	=	=	NOUN
cana-3816	87	41	∝2	∝2	PROPN
cana-3816	87	42	and	and	CCONJ
cana-3816	87	43	max{>(]∂ø	max{>(]∂ø	NUM
cana-3816	87	44	,	,	PUNCT
cana-3816	87	45	ι),∝1	ι),∝1	PROPN
cana-3816	87	46	}	}	PUNCT
cana-3816	87	47	>	>	X
cana-3816	87	48	min	min	PROPN
cana-3816	87	49	{	{	PUNCT
cana-3816	87	50	>	>	X
cana-3816	87	51	(	(	PUNCT
cana-3816	87	52	]	]	X
cana-3816	87	53	,	,	PUNCT
cana-3816	87	54	ι),>(∂	ι),>(∂	PROPN
cana-3816	87	55	,	,	PUNCT
cana-3816	87	56	ι),>(ø	ι),>(ø	NOUN
cana-3816	87	57	,	,	PUNCT
cana-3816	87	58	ι),∝2	ι),∝2	NOUN
cana-3816	87	59	}	}	PUNCT
cana-3816	87	60	>	>	X
cana-3816	87	61	min{∝2,∝2,∝2,∝2	min{∝2,∝2,∝2,∝2	NOUN
cana-3816	87	62	}	}	PUNCT
cana-3816	87	63	=	=	PROPN
cana-3816	87	64	∝2	∝2	PROPN
cana-3816	87	65	.	.	PUNCT
cana-3816	88	1	it	it	PRON
cana-3816	88	2	follows	follow	VERB
cana-3816	88	3	that	that	SCONJ
cana-3816	88	4	]	]	PUNCT
cana-3816	88	5	∂ø	∂ø	PROPN
cana-3816	88	6	∈	∈	PROPN
cana-3816	88	7	(	(	PUNCT
cana-3816	88	8	`	`	PUNCT
cana-3816	88	9	]	]	PUNCT
cana-3816	88	10	.	.	PUNCT
cana-3816	89	1	therefore	therefore	ADV
cana-3816	89	2	`	`	PUNCT
cana-3816	89	3	is	be	AUX
cana-3816	89	4	a	a	DET
cana-3816	89	5	tss	tss	NOUN
cana-3816	89	6	of	of	ADP
cana-3816	89	7	b.	b.	PROPN
cana-3816	89	8	theorem	theorem	PROPN
cana-3816	89	9	2.7	2.7	NUM
cana-3816	89	10	.	.	PUNCT
cana-3816	90	1	a	a	DET
cana-3816	90	2	subset	subset	NOUN
cana-3816	90	3	i	i	PRON
cana-3816	90	4	=	=	PUNCT
cana-3816	91	1	[	[	X
cana-3816	91	2	t	t	PROPN
cana-3816	91	3	,	,	PUNCT
cana-3816	91	4	>	>	X
cana-3816	91	5	]	]	X
cana-3816	91	6	is	be	AUX
cana-3816	91	7	a	a	DET
cana-3816	91	8	(	(	PUNCT
cana-3816	91	9	∝1,∝2)−iq1tfss[iq1afli	∝1,∝2)−iq1tfss[iq1afli	NOUN
cana-3816	91	10	,	,	PUNCT
cana-3816	91	11	iq1aflati	iq1aflati	PROPN
cana-3816	91	12	,	,	PUNCT
cana-3816	91	13	iq1afri	iq1afri	PROPN
cana-3816	91	14	,	,	PUNCT
cana-3816	91	15	iq1afbi	iq1afbi	PROPN
cana-3816	91	16	]	]	PUNCT
cana-3816	91	17	of	of	ADP
cana-3816	91	18	b	b	NOUN
cana-3816	91	19	if	if	SCONJ
cana-3816	91	20	and	and	CCONJ
cana-3816	91	21	only	only	ADV
cana-3816	91	22	if	if	SCONJ
cana-3816	91	23	each	each	DET
cana-3816	91	24	non	non	ADJ
cana-3816	91	25	-	-	ADJ
cana-3816	91	26	empty	empty	ADJ
cana-3816	91	27	level	level	NOUN
cana-3816	91	28	subset	subset	VERB
cana-3816	91	29	it	it	PRON
cana-3816	91	30	is	be	AUX
cana-3816	91	31	a	a	DET
cana-3816	91	32	tss	tss	NOUN
cana-3816	91	33	[	[	PUNCT
cana-3816	91	34	tli	tli	PROPN
cana-3816	91	35	,	,	PUNCT
cana-3816	91	36	tlati	tlati	PROPN
cana-3816	91	37	,	,	PUNCT
cana-3816	91	38	tri	tri	NOUN
cana-3816	91	39	,	,	PUNCT
cana-3816	91	40	tbi	tbi	NOUN
cana-3816	91	41	]	]	PUNCT
cana-3816	91	42	of	of	ADP
cana-3816	91	43	b	b	NOUN
cana-3816	91	44	for	for	ADP
cana-3816	91	45	all	all	DET
cana-3816	91	46	t	t	NOUN
cana-3816	91	47	∈	∈	PROPN
cana-3816	91	48	(	(	PUNCT
cana-3816	91	49	∝1,∝2	∝1,∝2	PROPN
cana-3816	91	50	]	]	PUNCT
cana-3816	91	51	.	.	PUNCT
cana-3816	92	1	proof	proof	NOUN
cana-3816	92	2	.	.	PUNCT
cana-3816	93	1	assume	assume	VERB
cana-3816	93	2	that	that	SCONJ
cana-3816	93	3	it	it	PRON
cana-3816	93	4	is	be	AUX
cana-3816	93	5	a	a	DET
cana-3816	93	6	tss	tss	NOUN
cana-3816	93	7	of	of	ADP
cana-3816	93	8	b	b	PROPN
cana-3816	93	9	for	for	ADP
cana-3816	93	10	each	each	DET
cana-3816	93	11	t	t	NOUN
cana-3816	93	12	∈	∈	PROPN
cana-3816	94	1	[	[	X
cana-3816	94	2	0	0	NUM
cana-3816	94	3	,	,	PUNCT
cana-3816	94	4	1	1	NUM
cana-3816	94	5	]	]	PUNCT
cana-3816	94	6	.	.	PUNCT
cana-3816	95	1	let	let	VERB
cana-3816	95	2	t	t	NOUN
cana-3816	95	3	=	=	PUNCT
cana-3816	95	4	max{t	max{t	NOUN
cana-3816	95	5	(	(	PUNCT
cana-3816	95	6	]	]	X
cana-3816	95	7	a	a	X
cana-3816	95	8	,	,	PUNCT
cana-3816	95	9	ι),t	ι),t	PUNCT
cana-3816	95	10	(	(	PUNCT
cana-3816	95	11	]	]	X
cana-3816	95	12	b	b	X
cana-3816	95	13	,	,	PUNCT
cana-3816	95	14	ι),t	ι),t	PUNCT
cana-3816	95	15	(	(	PUNCT
cana-3816	95	16	]	]	X
cana-3816	95	17	c	c	X
cana-3816	95	18	,	,	PUNCT
cana-3816	95	19	ι	ι	PROPN
cana-3816	95	20	)	)	PUNCT
cana-3816	95	21	}	}	PUNCT
cana-3816	95	22	.	.	PUNCT
cana-3816	96	1	then	then	ADV
cana-3816	96	2	]	]	X
cana-3816	96	3	a	a	X
cana-3816	96	4	,	,	PUNCT
cana-3816	96	5	]	]	X
cana-3816	96	6	b	b	X
cana-3816	96	7	,	,	PUNCT
cana-3816	96	8	]	]	X
cana-3816	96	9	c	c	X
cana-3816	96	10	∈tt	∈tt	NOUN
cana-3816	96	11	for	for	ADP
cana-3816	96	12	each	each	DET
cana-3816	96	13	]	]	X
cana-3816	96	14	a	a	X
cana-3816	96	15	,	,	PUNCT
cana-3816	96	16	]	]	X
cana-3816	96	17	b	b	X
cana-3816	96	18	,	,	PUNCT
cana-3816	96	19	]	]	X
cana-3816	96	20	c	c	X
cana-3816	96	21	∈	∈	PROPN
cana-3816	96	22	b.	b.	PROPN
cana-3816	96	23	thus	thus	ADV
cana-3816	96	24	min{t	min{t	X
cana-3816	96	25	(	(	PUNCT
cana-3816	96	26	]	]	X
cana-3816	96	27	∂ø	∂ø	PROPN
cana-3816	96	28	,	,	PUNCT
cana-3816	96	29	ι),∝1	ι),∝1	PROPN
cana-3816	96	30	}	}	PUNCT
cana-3816	96	31	6	6	NUM
cana-3816	96	32	t	t	NOUN
cana-3816	96	33	=	=	PUNCT
cana-3816	96	34	max{t	max{t	NOUN
cana-3816	96	35	(	(	PUNCT
cana-3816	96	36	]	]	X
cana-3816	96	37	a	a	X
cana-3816	96	38	,	,	PUNCT
cana-3816	96	39	ι),t	ι),t	PUNCT
cana-3816	96	40	(	(	PUNCT
cana-3816	96	41	]	]	X
cana-3816	96	42	b	b	X
cana-3816	96	43	,	,	PUNCT
cana-3816	96	44	ι),t	ι),t	PUNCT
cana-3816	96	45	(	(	PUNCT
cana-3816	96	46	]	]	X
cana-3816	96	47	c	c	X
cana-3816	96	48	,	,	PUNCT
cana-3816	96	49	ι),∝2	ι),∝2	NOUN
cana-3816	96	50	}	}	PUNCT
cana-3816	96	51	.	.	PUNCT
cana-3816	97	1	let	let	VERB
cana-3816	97	2	t	t	NOUN
cana-3816	97	3	=	=	SYM
cana-3816	97	4	min{>(]a	min{>(]a	PROPN
cana-3816	97	5	,	,	PUNCT
cana-3816	97	6	ι),>(]b	ι),>(]b	PROPN
cana-3816	97	7	,	,	PUNCT
cana-3816	97	8	ι),>(]c	ι),>(]c	NOUN
cana-3816	97	9	,	,	PUNCT
cana-3816	97	10	ι	ι	NOUN
cana-3816	97	11	)	)	PUNCT
cana-3816	97	12	}	}	PUNCT
cana-3816	97	13	.	.	PUNCT
cana-3816	98	1	then	then	ADV
cana-3816	98	2	]	]	X
cana-3816	98	3	a	a	X
cana-3816	98	4	,	,	PUNCT
cana-3816	98	5	]	]	X
cana-3816	98	6	b	b	X
cana-3816	98	7	,	,	PUNCT
cana-3816	98	8	]	]	X
cana-3816	98	9	c	c	X
cana-3816	98	10	∈	∈	PROPN
cana-3816	98	11	>	>	X
cana-3816	98	12	t	t	PROPN
cana-3816	98	13	for	for	ADP
cana-3816	98	14	each	each	PRON
cana-3816	98	15	]	]	X
cana-3816	98	16	a	a	X
cana-3816	98	17	,	,	PUNCT
cana-3816	98	18	]	]	X
cana-3816	98	19	b	b	X
cana-3816	98	20	,	,	PUNCT
cana-3816	98	21	]	]	X
cana-3816	98	22	c	c	X
cana-3816	98	23	∈	∈	PROPN
cana-3816	98	24	b.	b.	PROPN
cana-3816	98	25	thus	thus	ADV
cana-3816	98	26	max{>(]∂ø	max{>(]∂ø	NUM
cana-3816	98	27	,	,	PUNCT
cana-3816	98	28	ι),∝1	ι),∝1	PROPN
cana-3816	98	29	}	}	PUNCT
cana-3816	98	30	>	>	PUNCT
cana-3816	98	31	t	t	PROPN
cana-3816	98	32	=	=	SYM
cana-3816	98	33	min{>(]a	min{>(]a	PROPN
cana-3816	98	34	,	,	PUNCT
cana-3816	98	35	ι),>(]b	ι),>(]b	PROPN
cana-3816	98	36	,	,	PUNCT
cana-3816	98	37	ι),>(]c	ι),>(]c	NOUN
cana-3816	98	38	,	,	PUNCT
cana-3816	98	39	ι),∝2	ι),∝2	NOUN
cana-3816	98	40	}	}	PUNCT
cana-3816	98	41	.	.	PUNCT
cana-3816	99	1	this	this	PRON
cana-3816	99	2	shows	show	VERB
cana-3816	99	3	that	that	SCONJ
cana-3816	99	4	it	it	PRON
cana-3816	99	5	is	be	AUX
cana-3816	99	6	iq1tfss	iq1tfss	ADV
cana-3816	99	7	of	of	ADP
cana-3816	99	8	b.	b.	NOUN
cana-3816	99	9	conversely	conversely	ADV
cana-3816	99	10	,	,	PUNCT
cana-3816	99	11	assume	assume	VERB
cana-3816	99	12	that	that	SCONJ
cana-3816	99	13	it	it	PRON
cana-3816	99	14	is	be	AUX
cana-3816	99	15	a	a	DET
cana-3816	99	16	iq1tfss	iq1tfss	NOUN
cana-3816	99	17	of	of	ADP
cana-3816	99	18	b.	b.	PROPN
cana-3816	99	19	for	for	ADP
cana-3816	99	20	each	each	DET
cana-3816	99	21	t	t	NOUN
cana-3816	99	22	∈	∈	PROPN
cana-3816	100	1	[	[	X
cana-3816	100	2	0	0	NUM
cana-3816	100	3	,	,	PUNCT
cana-3816	100	4	1	1	NUM
cana-3816	100	5	]	]	PUNCT
cana-3816	100	6	and	and	CCONJ
cana-3816	100	7	]	]	X
cana-3816	100	8	a	a	X
cana-3816	100	9	,	,	PUNCT
cana-3816	100	10	]	]	X
cana-3816	100	11	b	b	X
cana-3816	100	12	,	,	PUNCT
cana-3816	100	13	]	]	X
cana-3816	100	14	c	c	X
cana-3816	100	15	∈tt	∈tt	NOUN
cana-3816	100	16	.	.	PUNCT
cana-3816	101	1	we	we	PRON
cana-3816	101	2	have	have	VERB
cana-3816	101	3	t	t	PROPN
cana-3816	101	4	(	(	PUNCT
cana-3816	101	5	]	]	X
cana-3816	101	6	a	a	X
cana-3816	101	7	,	,	PUNCT
cana-3816	101	8	ι	ι	PROPN
cana-3816	101	9	)	)	PUNCT
cana-3816	101	10	6	6	NUM
cana-3816	101	11	t	t	PROPN
cana-3816	101	12	,	,	PUNCT
cana-3816	101	13	t	t	PROPN
cana-3816	101	14	(	(	PUNCT
cana-3816	101	15	]	]	X
cana-3816	101	16	b	b	X
cana-3816	101	17	,	,	PUNCT
cana-3816	101	18	ι	ι	PROPN
cana-3816	101	19	)	)	PUNCT
cana-3816	101	20	6	6	NUM
cana-3816	101	21	t	t	PROPN
cana-3816	101	22	,	,	PUNCT
cana-3816	101	23	t	t	PROPN
cana-3816	101	24	(	(	PUNCT
cana-3816	101	25	]	]	X
cana-3816	101	26	c	c	X
cana-3816	101	27	,	,	PUNCT
cana-3816	101	28	ι	ι	PROPN
cana-3816	101	29	)	)	PUNCT
cana-3816	101	30	6	6	NUM
cana-3816	101	31	t.	t.	NOUN
cana-3816	101	32	since	since	SCONJ
cana-3816	101	33	t	t	PROPN
cana-3816	101	34	is	be	AUX
cana-3816	101	35	a	a	DET
cana-3816	101	36	tss	tss	NOUN
cana-3816	101	37	of	of	ADP
cana-3816	101	38	b	b	PROPN
cana-3816	101	39	,	,	PUNCT
cana-3816	101	40	min{t	min{t	PROPN
cana-3816	101	41	(	(	PUNCT
cana-3816	101	42	]	]	SYM
cana-3816	101	43	a]b]c	a]b]c	ADJ
cana-3816	101	44	,	,	PUNCT
cana-3816	101	45	ι),∝1	ι),∝1	PROPN
cana-3816	101	46	}	}	PUNCT
cana-3816	101	47	6	6	NUM
cana-3816	101	48	max{t	max{t	NOUN
cana-3816	101	49	(	(	PUNCT
cana-3816	101	50	]	]	X
cana-3816	101	51	a	a	X
cana-3816	101	52	,	,	PUNCT
cana-3816	101	53	ι),t	ι),t	PUNCT
cana-3816	101	54	(	(	PUNCT
cana-3816	101	55	]	]	X
cana-3816	101	56	b	b	X
cana-3816	101	57	,	,	PUNCT
cana-3816	101	58	ι),t	ι),t	PUNCT
cana-3816	101	59	(	(	PUNCT
cana-3816	101	60	]	]	X
cana-3816	101	61	c	c	X
cana-3816	101	62	,	,	PUNCT
cana-3816	101	63	ι),∝2	ι),∝2	NOUN
cana-3816	101	64	}	}	PUNCT
cana-3816	101	65	6	6	NUM
cana-3816	101	66	t.	t.	NOUN
cana-3816	101	67	this	this	PRON
cana-3816	101	68	implies	imply	VERB
cana-3816	101	69	that	that	SCONJ
cana-3816	101	70	]	]	X
cana-3816	101	71	a]b]c	a]b]c	NOUN
cana-3816	101	72	∈tt	∈tt	ADJ
cana-3816	101	73	.	.	PUNCT
cana-3816	102	1	we	we	PRON
cana-3816	102	2	have	have	VERB
cana-3816	102	3	>	>	X
cana-3816	102	4	(	(	PUNCT
cana-3816	102	5	]	]	X
cana-3816	102	6	a	a	X
cana-3816	102	7	,	,	PUNCT
cana-3816	102	8	ι	ι	PROPN
cana-3816	102	9	)	)	PUNCT
cana-3816	102	10	>	>	X
cana-3816	103	1	t,>(]b	t,>(]b	PROPN
cana-3816	103	2	,	,	PUNCT
cana-3816	103	3	ι	ι	PROPN
cana-3816	103	4	)	)	PUNCT
cana-3816	103	5	>	>	X
cana-3816	104	1	t,>(]c	t,>(]c	PROPN
cana-3816	104	2	,	,	PUNCT
cana-3816	104	3	ι	ι	PROPN
cana-3816	104	4	)	)	PUNCT
cana-3816	104	5	>	>	PUNCT
cana-3816	105	1	t.	t.	PROPN
cana-3816	105	2	since	since	SCONJ
cana-3816	105	3	>	>	X
cana-3816	105	4	is	be	AUX
cana-3816	105	5	a	a	DET
cana-3816	105	6	tss	tss	NOUN
cana-3816	105	7	of	of	ADP
cana-3816	105	8	b	b	PROPN
cana-3816	105	9	,	,	PUNCT
cana-3816	105	10	max{>(]a]b]c	max{>(]a]b]c	PROPN
cana-3816	105	11	,	,	PUNCT
cana-3816	105	12	ι),∝1	ι),∝1	PROPN
cana-3816	105	13	}	}	PUNCT
cana-3816	105	14	>	>	X
cana-3816	105	15	min{>(]a	min{>(]a	PROPN
cana-3816	105	16	,	,	PUNCT
cana-3816	105	17	ι),>(]b	ι),>(]b	PROPN
cana-3816	105	18	,	,	PUNCT
cana-3816	105	19	ι),>(]c	ι),>(]c	NOUN
cana-3816	105	20	,	,	PUNCT
cana-3816	105	21	ι),∝2	ι),∝2	NOUN
cana-3816	105	22	}	}	PUNCT
cana-3816	105	23	>	>	PUNCT
cana-3816	106	1	t.	t.	NOUN
cana-3816	106	2	this	this	PRON
cana-3816	106	3	implies	imply	VERB
cana-3816	106	4	that	that	SCONJ
cana-3816	106	5	]	]	X
cana-3816	106	6	a]b]c	a]b]c	X
cana-3816	107	1	∈	∈	PROPN
cana-3816	107	2	>	>	PUNCT
cana-3816	107	3	t.	t.	PROPN
cana-3816	107	4	therefore	therefore	ADV
cana-3816	107	5	it	it	PRON
cana-3816	107	6	is	be	AUX
cana-3816	107	7	a	a	DET
cana-3816	107	8	tss	tss	NOUN
cana-3816	107	9	of	of	ADP
cana-3816	107	10	b	b	PROPN
cana-3816	107	11	for	for	ADP
cana-3816	107	12	each	each	DET
cana-3816	107	13	t	t	NOUN
cana-3816	107	14	∈	∈	PROPN
cana-3816	107	15	(	(	PUNCT
cana-3816	107	16	∝1,∝2	∝1,∝2	PROPN
cana-3816	107	17	]	]	PUNCT
cana-3816	107	18	.	.	PUNCT
cana-3816	108	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3816	108	2	763	763	NUM
cana-3816	108	3	communications	communication	NOUN
cana-3816	108	4	on	on	ADP
cana-3816	108	5	applied	apply	VERB
cana-3816	108	6	nonlinear	nonlinear	ADJ
cana-3816	108	7	analysis	analysis	NOUN
cana-3816	108	8	issn	issn	NOUN
cana-3816	108	9	:	:	PUNCT
cana-3816	108	10	1074	1074	NUM
cana-3816	108	11	-	-	PUNCT
cana-3816	108	12	133x	133x	NUM
cana-3816	108	13	vol	vol	NOUN
cana-3816	108	14	32	32	NUM
cana-3816	108	15	no	no	NOUN
cana-3816	108	16	.	.	NOUN
cana-3816	108	17	3	3	NUM
cana-3816	108	18	(	(	PUNCT
cana-3816	108	19	2025	2025	NUM
cana-3816	108	20	)	)	PUNCT
cana-3816	108	21	example	example	NOUN
cana-3816	109	1	2.8	2.8	NUM
cana-3816	109	2	.	.	PUNCT
cana-3816	110	1	every	every	DET
cana-3816	110	2	iq1tfss	iq1tfss	NOUN
cana-3816	110	3	i	i	PRON
cana-3816	110	4	of	of	ADP
cana-3816	110	5	b	b	PROPN
cana-3816	110	6	is	be	AUX
cana-3816	110	7	a	a	DET
cana-3816	110	8	(	(	PUNCT
cana-3816	110	9	∝1,∝2)-iq1tfss	∝1,∝2)-iq1tfss	NOUN
cana-3816	110	10	of	of	ADP
cana-3816	110	11	b	b	NOUN
cana-3816	110	12	,	,	PUNCT
cana-3816	110	13	but	but	CCONJ
cana-3816	110	14	converse	converse	NOUN
cana-3816	110	15	is	be	AUX
cana-3816	110	16	not	not	PART
cana-3816	110	17	true	true	ADJ
cana-3816	110	18	.	.	PUNCT
cana-3816	111	1	for	for	ADP
cana-3816	111	2	the	the	DET
cana-3816	111	3	example	example	NOUN
cana-3816	111	4	2.2	2.2	NUM
cana-3816	111	5	,	,	PUNCT
cana-3816	111	6	we	we	PRON
cana-3816	111	7	define	define	VERB
cana-3816	111	8	subset	subset	ADJ
cana-3816	111	9	i	i	PRON
cana-3816	111	10	by	by	ADP
cana-3816	111	11	t	t	PROPN
cana-3816	111	12	(	(	PUNCT
cana-3816	111	13	ø	ø	PROPN
cana-3816	111	14	,	,	PUNCT
cana-3816	111	15	ι	ι	PROPN
cana-3816	111	16	)	)	PUNCT
cana-3816	111	17	=	=	PUNCT
cana-3816	112	1			PROPN
cana-3816	112	2	0.19	0.19	NUM
cana-3816	112	3	if	if	SCONJ
cana-3816	112	4	ø	ø	PROPN
cana-3816	112	5	=	=	SYM
cana-3816	112	6	øl	øl	PROPN
cana-3816	112	7	0.24	0.24	NUM
cana-3816	112	8	if	if	SCONJ
cana-3816	112	9	ø	ø	NOUN
cana-3816	112	10	=	=	SYM
cana-3816	112	11	øm	øm	ADP
cana-3816	112	12	0.34	0.34	NUM
cana-3816	112	13	if	if	SCONJ
cana-3816	112	14	ø	ø	PROPN
cana-3816	112	15	=	=	PUNCT
cana-3816	112	16	øn	øn	ADP
cana-3816	112	17	0.29	0.29	NUM
cana-3816	112	18	if	if	SCONJ
cana-3816	112	19	ø	ø	PROPN
cana-3816	112	20	=	=	VERB
cana-3816	112	21	øo	øo	PART
cana-3816	112	22	>	>	X
cana-3816	112	23	(	(	PUNCT
cana-3816	112	24	ø	ø	PROPN
cana-3816	112	25	,	,	PUNCT
cana-3816	112	26	ι	ι	PROPN
cana-3816	112	27	)	)	PUNCT
cana-3816	112	28	=	=	PUNCT
cana-3816	113	1			PROPN
cana-3816	113	2	0.34	0.34	NUM
cana-3816	113	3	if	if	SCONJ
cana-3816	113	4	ø	ø	PROPN
cana-3816	113	5	=	=	SYM
cana-3816	113	6	øl	øl	PROPN
cana-3816	113	7	0.27	0.27	NUM
cana-3816	113	8	if	if	SCONJ
cana-3816	113	9	ø	ø	PROPN
cana-3816	113	10	=	=	PUNCT
cana-3816	113	11	øm	øm	ADP
cana-3816	113	12	0.17	0.17	NUM
cana-3816	113	13	if	if	SCONJ
cana-3816	113	14	ø	ø	PROPN
cana-3816	113	15	=	=	PUNCT
cana-3816	113	16	øn	øn	ADP
cana-3816	113	17	0.22	0.22	NUM
cana-3816	113	18	if	if	SCONJ
cana-3816	113	19	ø	ø	PROPN
cana-3816	114	1	=	=	PRON
cana-3816	114	2	øo	øo	NOUN
cana-3816	114	3	then	then	ADV
cana-3816	114	4	i	i	PRON
cana-3816	114	5	is	be	AUX
cana-3816	114	6	a	a	DET
cana-3816	114	7	(	(	PUNCT
cana-3816	114	8	0.25	0.25	NUM
cana-3816	114	9	,	,	PUNCT
cana-3816	114	10	0.39)-iq1tfss	0.39)-iq1tfss	NUM
cana-3816	114	11	of	of	ADP
cana-3816	114	12	b	b	NOUN
cana-3816	114	13	,	,	PUNCT
cana-3816	114	14	but	but	CCONJ
cana-3816	114	15	not	not	PART
cana-3816	114	16	a	a	DET
cana-3816	114	17	iq1tfss	iq1tfss	NOUN
cana-3816	114	18	.	.	PUNCT
cana-3816	115	1	since	since	SCONJ
cana-3816	115	2	t	t	PROPN
cana-3816	115	3	(	(	PUNCT
cana-3816	115	4	øo∂øo	øo∂øo	PROPN
cana-3816	115	5	,	,	PUNCT
cana-3816	115	6	ι	ι	X
cana-3816	115	7	)	)	PUNCT
cana-3816	115	8	=	=	SYM
cana-3816	115	9	0.34	0.34	NUM
cana-3816	115	10	66	66	NUM
cana-3816	115	11	max{t	max{t	NOUN
cana-3816	115	12	(	(	PUNCT
cana-3816	115	13	øo	øo	NOUN
cana-3816	115	14	,	,	PUNCT
cana-3816	115	15	q),t	q),t	ADP
cana-3816	115	16	(	(	PUNCT
cana-3816	115	17	øo	øo	PROPN
cana-3816	115	18	,	,	PUNCT
cana-3816	115	19	q	q	NOUN
cana-3816	115	20	)	)	PUNCT
cana-3816	115	21	}	}	PUNCT
cana-3816	115	22	=	=	SYM
cana-3816	115	23	0.29	0.29	NUM
cana-3816	115	24	and	and	CCONJ
cana-3816	115	25	>	>	X
cana-3816	115	26	(	(	PUNCT
cana-3816	115	27	øo∂øo	øo∂øo	NUM
cana-3816	115	28	,	,	PUNCT
cana-3816	115	29	ι	ι	X
cana-3816	115	30	)	)	PUNCT
cana-3816	115	31	=	=	PUNCT
cana-3816	116	1	0.17	0.17	NUM
cana-3816	116	2	6	6	NUM
cana-3816	116	3	>	>	X
cana-3816	116	4	min{>(øo	min{>(øo	PROPN
cana-3816	116	5	,	,	PUNCT
cana-3816	116	6	q),>(øo	q),>(øo	X
cana-3816	116	7	,	,	PUNCT
cana-3816	116	8	q	q	NOUN
cana-3816	116	9	)	)	PUNCT
cana-3816	116	10	}	}	PUNCT
cana-3816	116	11	=	=	SYM
cana-3816	116	12	0.22	0.22	NUM
cana-3816	116	13	.	.	PUNCT
cana-3816	116	14	example	example	NOUN
cana-3816	116	15	2.9	2.9	NUM
cana-3816	116	16	.	.	PUNCT
cana-3816	117	1	every	every	DET
cana-3816	117	2	iq1afbi	iq1afbi	PUNCT
cana-3816	117	3	i	i	PRON
cana-3816	117	4	=	=	PUNCT
cana-3816	118	1	[	[	X
cana-3816	118	2	t	t	PROPN
cana-3816	118	3	,	,	PUNCT
cana-3816	118	4	>	>	X
cana-3816	118	5	]	]	PUNCT
cana-3816	118	6	of	of	ADP
cana-3816	118	7	b	b	PROPN
cana-3816	118	8	is	be	AUX
cana-3816	118	9	a	a	DET
cana-3816	118	10	(	(	PUNCT
cana-3816	118	11	∝1,∝2)-iq1afbi	∝1,∝2)-iq1afbi	X
cana-3816	118	12	of	of	ADP
cana-3816	118	13	b	b	NOUN
cana-3816	118	14	,	,	PUNCT
cana-3816	118	15	but	but	CCONJ
cana-3816	118	16	converse	converse	NOUN
cana-3816	118	17	need	need	AUX
cana-3816	118	18	not	not	PART
cana-3816	118	19	be	be	AUX
cana-3816	118	20	true	true	ADJ
cana-3816	118	21	.	.	PUNCT
cana-3816	119	1	for	for	ADP
cana-3816	119	2	the	the	DET
cana-3816	119	3	example	example	NOUN
cana-3816	119	4	2.4	2.4	NUM
cana-3816	119	5	,	,	PUNCT
cana-3816	119	6	we	we	PRON
cana-3816	119	7	define	define	VERB
cana-3816	119	8	subset	subset	ADJ
cana-3816	119	9	i	i	PRON
cana-3816	119	10	by	by	ADP
cana-3816	119	11	,	,	PUNCT
cana-3816	119	12	t	t	PROPN
cana-3816	119	13	(	(	PUNCT
cana-3816	119	14	ø	ø	PROPN
cana-3816	119	15	,	,	PUNCT
cana-3816	119	16	ι	ι	PROPN
cana-3816	119	17	)	)	PUNCT
cana-3816	119	18	=	=	PUNCT
cana-3816	120	1			PROPN
cana-3816	120	2	0.08	0.08	NUM
cana-3816	120	3	if	if	SCONJ
cana-3816	120	4	ø	ø	NOUN
cana-3816	120	5	=	=	SYM
cana-3816	120	6	øl	øl	PROPN
cana-3816	120	7	0.23	0.23	NUM
cana-3816	120	8	if	if	SCONJ
cana-3816	120	9	ø	ø	PROPN
cana-3816	120	10	=	=	SYM
cana-3816	120	11	øm	øm	ADP
cana-3816	120	12	0.33	0.33	NUM
cana-3816	120	13	if	if	SCONJ
cana-3816	120	14	ø	ø	PROPN
cana-3816	120	15	=	=	PUNCT
cana-3816	120	16	øn	øn	ADP
cana-3816	120	17	0.28	0.28	NUM
cana-3816	120	18	if	if	SCONJ
cana-3816	120	19	ø	ø	PROPN
cana-3816	120	20	=	=	VERB
cana-3816	120	21	øo	øo	PART
cana-3816	120	22	>	>	X
cana-3816	120	23	(	(	PUNCT
cana-3816	120	24	ø	ø	PROPN
cana-3816	120	25	,	,	PUNCT
cana-3816	120	26	ι	ι	PROPN
cana-3816	120	27	)	)	PUNCT
cana-3816	120	28	=	=	PUNCT
cana-3816	121	1			PROPN
cana-3816	121	2	0.42	0.42	NUM
cana-3816	121	3	if	if	SCONJ
cana-3816	121	4	ø	ø	PROPN
cana-3816	121	5	=	=	SYM
cana-3816	121	6	øl	øl	PROPN
cana-3816	121	7	0.23	0.23	NUM
cana-3816	121	8	if	if	SCONJ
cana-3816	121	9	ø	ø	PROPN
cana-3816	121	10	=	=	SYM
cana-3816	121	11	øm	øm	ADP
cana-3816	121	12	0.01	0.01	NUM
cana-3816	121	13	if	if	SCONJ
cana-3816	121	14	ø	ø	PROPN
cana-3816	121	15	=	=	PUNCT
cana-3816	121	16	øn	øn	ADP
cana-3816	121	17	0.04	0.04	NUM
cana-3816	121	18	if	if	SCONJ
cana-3816	121	19	ø	ø	PROPN
cana-3816	121	20	=	=	PRON
cana-3816	121	21	øo	øo	NOUN
cana-3816	121	22	then	then	ADV
cana-3816	121	23	i	i	PRON
cana-3816	121	24	is	be	AUX
cana-3816	121	25	a	a	DET
cana-3816	121	26	(	(	PUNCT
cana-3816	121	27	0.18	0.18	NUM
cana-3816	121	28	,	,	PUNCT
cana-3816	121	29	0.43)iq1afbi	0.43)iq1afbi	PROPN
cana-3816	121	30	,	,	PUNCT
cana-3816	121	31	but	but	CCONJ
cana-3816	121	32	not	not	PART
cana-3816	121	33	a	a	DET
cana-3816	121	34	iq1afbi	iq1afbi	PROPN
cana-3816	121	35	.	.	PUNCT
cana-3816	122	1	since	since	SCONJ
cana-3816	122	2	t	t	PROPN
cana-3816	122	3	(	(	PUNCT
cana-3816	122	4	øo∂1øo∂2øo	øo∂1øo∂2øo	NOUN
cana-3816	122	5	,	,	PUNCT
cana-3816	122	6	ι	ι	X
cana-3816	122	7	)	)	PUNCT
cana-3816	122	8	=	=	NOUN
cana-3816	122	9	t	t	X
cana-3816	122	10	(	(	PUNCT
cana-3816	122	11	øn	øn	INTJ
cana-3816	122	12	,	,	PUNCT
cana-3816	122	13	ι	ι	PROPN
cana-3816	122	14	)	)	PUNCT
cana-3816	122	15	=	=	SYM
cana-3816	122	16	0.33	0.33	NUM
cana-3816	122	17	66	66	NUM
cana-3816	122	18	max{t	max{t	NOUN
cana-3816	122	19	(	(	PUNCT
cana-3816	122	20	øo	øo	PROPN
cana-3816	122	21	,	,	PUNCT
cana-3816	122	22	ι),t	ι),t	X
cana-3816	122	23	(	(	PUNCT
cana-3816	122	24	øo	øo	NOUN
cana-3816	122	25	,	,	PUNCT
cana-3816	122	26	ι	ι	PROPN
cana-3816	122	27	)	)	PUNCT
cana-3816	122	28	}	}	PUNCT
cana-3816	122	29	=	=	SYM
cana-3816	122	30	0.28	0.28	NUM
cana-3816	122	31	and	and	CCONJ
cana-3816	122	32	>	>	PUNCT
cana-3816	122	33	(	(	PUNCT
cana-3816	122	34	øo∂1øo∂2øo	øo∂1øo∂2øo	X
cana-3816	122	35	,	,	PUNCT
cana-3816	122	36	ι	ι	PROPN
cana-3816	122	37	)	)	PUNCT
cana-3816	122	38	=	=	PUNCT
cana-3816	123	1	>	>	PUNCT
cana-3816	123	2	(	(	PUNCT
cana-3816	123	3	øn	øn	NOUN
cana-3816	123	4	,	,	PUNCT
cana-3816	123	5	ι	ι	PROPN
cana-3816	123	6	)	)	PUNCT
cana-3816	123	7	=	=	SYM
cana-3816	123	8	0.01	0.01	NUM
cana-3816	123	9	6	6	NUM
cana-3816	123	10	>	>	SYM
cana-3816	123	11	min{t	min{t	PROPN
cana-3816	123	12	(	(	PUNCT
cana-3816	123	13	øo	øo	PROPN
cana-3816	123	14	,	,	PUNCT
cana-3816	123	15	ι),t	ι),t	X
cana-3816	123	16	(	(	PUNCT
cana-3816	123	17	øo	øo	NOUN
cana-3816	123	18	,	,	PUNCT
cana-3816	123	19	ι	ι	PROPN
cana-3816	123	20	)	)	PUNCT
cana-3816	123	21	}	}	PUNCT
cana-3816	123	22	=	=	NOUN
cana-3816	123	23	0.04	0.04	NUM
cana-3816	123	24	.	.	PUNCT
cana-3816	124	1	definition	definition	NOUN
cana-3816	124	2	2.10	2.10	NUM
cana-3816	124	3	.	.	PUNCT
cana-3816	125	1	if	if	SCONJ
cana-3816	125	2			NOUN
cana-3816	125	3	`	`	PUNCT
cana-3816	125	4	is	be	AUX
cana-3816	125	5	the	the	DET
cana-3816	125	6	characteristic	characteristic	ADJ
cana-3816	125	7	function	function	NOUN
cana-3816	125	8	of	of	ADP
cana-3816	125	9	`	`	PUNCT
cana-3816	125	10	,	,	PUNCT
cana-3816	125	11	then	then	ADV
cana-3816	125	12	(	(	PUNCT
cana-3816	125	13	`)∝2	`)∝2	PROPN
cana-3816	125	14	∝1	∝1	NOUN
cana-3816	125	15	is	be	AUX
cana-3816	125	16	defined	define	VERB
cana-3816	125	17	as	as	ADP
cana-3816	125	18	(	(	PUNCT
cana-3816	125	19	t	t	PROPN
cana-3816	125	20	`	`	PUNCT
cana-3816	125	21	)	)	PUNCT
cana-3816	125	22	∝2	∝2	NOUN
cana-3816	125	23	∝1	∝1	NOUN
cana-3816	125	24	(	(	PUNCT
cana-3816	125	25	]	]	X
cana-3816	125	26	,	,	PUNCT
cana-3816	125	27	ι	ι	PROPN
cana-3816	125	28	)	)	PUNCT
cana-3816	125	29	=	=	PRON
cana-3816	125	30	{	{	PUNCT
cana-3816	125	31	∝2	∝2	NOUN
cana-3816	125	32	if	if	SCONJ
cana-3816	125	33	]	]	X
cana-3816	125	34	∈	∈	PROPN
cana-3816	125	35	(	(	PUNCT
cana-3816	125	36	`	`	PUNCT
cana-3816	125	37	]	]	X
cana-3816	125	38	∝1	∝1	X
cana-3816	126	1	if	if	SCONJ
cana-3816	126	2	]	]	X
cana-3816	126	3	/∈	/∈	PUNCT
cana-3816	127	1	(	(	PUNCT
cana-3816	127	2	`	`	PUNCT
cana-3816	127	3	]	]	X
cana-3816	127	4	(	(	PUNCT
cana-3816	127	5	f	f	PROPN
cana-3816	127	6	`	`	PUNCT
cana-3816	127	7	)	)	PUNCT
cana-3816	127	8	∝2	∝2	NOUN
cana-3816	127	9	∝1	∝1	NOUN
cana-3816	127	10	(	(	PUNCT
cana-3816	127	11	]	]	X
cana-3816	127	12	,	,	PUNCT
cana-3816	127	13	ι	ι	PROPN
cana-3816	127	14	)	)	PUNCT
cana-3816	127	15	=	=	SYM
cana-3816	127	16	{	{	PUNCT
cana-3816	127	17	∝1	∝1	ADJ
cana-3816	127	18	if	if	SCONJ
cana-3816	127	19	]	]	X
cana-3816	127	20	∈	∈	PROPN
cana-3816	127	21	(	(	PUNCT
cana-3816	127	22	`	`	PUNCT
cana-3816	127	23	]	]	X
cana-3816	127	24	∝2	∝2	NOUN
cana-3816	127	25	if	if	SCONJ
cana-3816	127	26	]	]	PUNCT
cana-3816	127	27	/∈	/∈	PUNCT
cana-3816	127	28	(	(	PUNCT
cana-3816	127	29	`	`	PUNCT
cana-3816	127	30	]	]	PUNCT
cana-3816	127	31	theorem	theorem	VERB
cana-3816	127	32	2.11	2.11	NUM
cana-3816	127	33	.	.	PUNCT
cana-3816	128	1	a	a	DET
cana-3816	128	2	non	non	X
cana-3816	128	3	empty	empty	ADJ
cana-3816	128	4	subset	subset	NOUN
cana-3816	128	5	`	`	PUNCT
cana-3816	128	6	of	of	ADP
cana-3816	128	7	b	b	PROPN
cana-3816	128	8	is	be	AUX
cana-3816	128	9	a	a	DET
cana-3816	128	10	tss	tss	NOUN
cana-3816	128	11	[	[	PUNCT
cana-3816	128	12	tli	tli	NOUN
cana-3816	128	13	,	,	PUNCT
cana-3816	128	14	tlati	tlati	PROPN
cana-3816	128	15	,	,	PUNCT
cana-3816	128	16	tri	tri	NOUN
cana-3816	128	17	,	,	PUNCT
cana-3816	128	18	tbi	tbi	NOUN
cana-3816	128	19	]	]	PUNCT
cana-3816	128	20	of	of	ADP
cana-3816	128	21	b	b	NOUN
cana-3816	128	22	if	if	SCONJ
cana-3816	128	23	and	and	CCONJ
cana-3816	128	24	only	only	ADV
cana-3816	128	25	if	if	SCONJ
cana-3816	128	26	subset	subset	VERB
cana-3816	128	27			NOUN
cana-3816	128	28	(	(	PUNCT
cana-3816	128	29	`	`	PUNCT
cana-3816	128	30	]	]	X
cana-3816	128	31	is	be	AUX
cana-3816	128	32	a	a	DET
cana-3816	128	33	(	(	PUNCT
cana-3816	128	34	∝1,∝2)-iq1tfss[iq1afli	∝1,∝2)-iq1tfss[iq1afli	NUM
cana-3816	128	35	,	,	PUNCT
cana-3816	128	36	iq1aflati	iq1aflati	NOUN
cana-3816	128	37	,	,	PUNCT
cana-3816	128	38	iq1afri	iq1afri	PROPN
cana-3816	128	39	,	,	PUNCT
cana-3816	128	40	iq1afbi	iq1afbi	PROPN
cana-3816	128	41	]	]	PUNCT
cana-3816	128	42	of	of	ADP
cana-3816	128	43	b.	b.	PROPN
cana-3816	128	44	proof	proof	NOUN
cana-3816	128	45	.	.	PUNCT
cana-3816	129	1	assume	assume	VERB
cana-3816	129	2	that	that	SCONJ
cana-3816	129	3	`	`	PUNCT
cana-3816	129	4	is	be	AUX
cana-3816	129	5	a	a	DET
cana-3816	129	6	tss	tss	NOUN
cana-3816	129	7	of	of	ADP
cana-3816	129	8	b.	b.	PROPN
cana-3816	130	1	then	then	ADV
cana-3816	130	2			PROPN
cana-3816	130	3	(	(	PUNCT
cana-3816	130	4	`	`	PUNCT
cana-3816	130	5	]	]	X
cana-3816	130	6	is	be	AUX
cana-3816	130	7	a	a	DET
cana-3816	130	8	iq1tfss	iq1tfss	NOUN
cana-3816	130	9	of	of	ADP
cana-3816	130	10	b	b	NOUN
cana-3816	130	11	and	and	CCONJ
cana-3816	130	12	hence	hence	ADV
cana-3816	130	13			PROPN
cana-3816	130	14	(	(	PUNCT
cana-3816	130	15	`	`	PUNCT
cana-3816	130	16	]	]	X
cana-3816	130	17	is	be	AUX
cana-3816	130	18	an	an	DET
cana-3816	130	19	(	(	PUNCT
cana-3816	130	20	∝1,∝2)-iq1tfss	∝1,∝2)-iq1tfss	NOUN
cana-3816	130	21	of	of	ADP
cana-3816	130	22	b.	b.	NOUN
cana-3816	130	23	conversely	conversely	ADV
cana-3816	130	24	,	,	PUNCT
cana-3816	130	25	let	let	VERB
cana-3816	130	26			PRON
cana-3816	130	27	(	(	PUNCT
cana-3816	130	28	`	`	PUNCT
cana-3816	130	29	]	]	X
cana-3816	130	30	is	be	AUX
cana-3816	130	31	an	an	DET
cana-3816	130	32	(	(	PUNCT
cana-3816	130	33	∝1,∝2)-iq1tfss	∝1,∝2)-iq1tfss	NOUN
cana-3816	130	34	of	of	ADP
cana-3816	130	35	b.	b.	NOUN
cana-3816	130	36	let	let	VERB
cana-3816	130	37	]	]	X
cana-3816	130	38	,	,	PUNCT
cana-3816	130	39	∂	∂	NUM
cana-3816	130	40	,	,	PUNCT
cana-3816	130	41	ø	ø	PROPN
cana-3816	130	42	∈	∈	PROPN
cana-3816	130	43	b	b	NOUN
cana-3816	130	44	be	be	AUX
cana-3816	130	45	such	such	ADJ
cana-3816	130	46	that	that	SCONJ
cana-3816	130	47	]	]	X
cana-3816	130	48	,	,	PUNCT
cana-3816	130	49	∂	∂	NUM
cana-3816	130	50	,	,	PUNCT
cana-3816	130	51	ø	ø	PROPN
cana-3816	130	52	∈	∈	PROPN
cana-3816	130	53	(	(	PUNCT
cana-3816	130	54	`	`	PUNCT
cana-3816	130	55	]	]	X
cana-3816	130	56	.	.	PUNCT
cana-3816	131	1	then	then	ADV
cana-3816	131	2	t	t	PROPN
cana-3816	131	3	(	(	PUNCT
cana-3816	131	4	`	`	PUNCT
cana-3816	131	5	]	]	X
cana-3816	131	6	(	(	PUNCT
cana-3816	131	7	]	]	X
cana-3816	131	8	,	,	PUNCT
cana-3816	131	9	ι	ι	PROPN
cana-3816	131	10	)	)	PUNCT
cana-3816	131	11	=	=	NOUN
cana-3816	131	12	∝2	∝2	PROPN
cana-3816	131	13	,	,	PUNCT
cana-3816	131	14			PROPN
cana-3816	131	15	t	t	PROPN
cana-3816	131	16	(	(	PUNCT
cana-3816	131	17	`	`	PUNCT
cana-3816	131	18	]	]	X
cana-3816	131	19	(	(	PUNCT
cana-3816	131	20	∂	∂	NUM
cana-3816	131	21	,	,	PUNCT
cana-3816	131	22	ι	ι	NOUN
cana-3816	131	23	)	)	PUNCT
cana-3816	132	1	=	=	NOUN
cana-3816	132	2	∝2	∝2	PROPN
cana-3816	132	3	,	,	PUNCT
cana-3816	132	4			PROPN
cana-3816	132	5	t	t	PROPN
cana-3816	132	6	(	(	PUNCT
cana-3816	132	7	`	`	PUNCT
cana-3816	132	8	]	]	X
cana-3816	132	9	(	(	PUNCT
cana-3816	132	10	ø	ø	INTJ
cana-3816	132	11	,	,	PUNCT
cana-3816	132	12	ι	ι	PROPN
cana-3816	132	13	)	)	PUNCT
cana-3816	132	14	=	=	NOUN
cana-3816	132	15	∝2	∝2	NOUN
cana-3816	132	16	.	.	PUNCT
cana-3816	133	1	since	since	SCONJ
cana-3816	133	2	t	t	PROPN
cana-3816	133	3	(	(	PUNCT
cana-3816	133	4	`	`	PUNCT
cana-3816	133	5	]	]	X
cana-3816	133	6	is	be	AUX
cana-3816	133	7	a	a	DET
cana-3816	133	8	(	(	PUNCT
cana-3816	133	9	∝1,∝2)iq1tfss	∝1,∝2)iq1tfss	NOUN
cana-3816	133	10	.	.	PUNCT
cana-3816	134	1	consider	consider	VERB
cana-3816	134	2	min{t	min{t	NOUN
cana-3816	134	3	(	(	PUNCT
cana-3816	134	4	`	`	PUNCT
cana-3816	134	5	]	]	X
cana-3816	134	6	(	(	PUNCT
cana-3816	134	7	]	]	X
cana-3816	134	8	∂ø	∂ø	PROPN
cana-3816	134	9	,	,	PUNCT
cana-3816	134	10	ι),∝1	ι),∝1	PROPN
cana-3816	134	11	}	}	PUNCT
cana-3816	134	12	6	6	NUM
cana-3816	134	13	max{t	max{t	NOUN
cana-3816	134	14	(	(	PUNCT
cana-3816	134	15	`	`	PUNCT
cana-3816	134	16	]	]	X
cana-3816	134	17	(	(	PUNCT
cana-3816	134	18	]	]	X
cana-3816	134	19	,	,	PUNCT
cana-3816	134	20	ι	ι	PROPN
cana-3816	134	21	)	)	PUNCT
cana-3816	134	22	,	,	PUNCT
cana-3816	134	23	t	t	PROPN
cana-3816	134	24	(	(	PUNCT
cana-3816	134	25	`	`	PUNCT
cana-3816	134	26	]	]	X
cana-3816	134	27	(	(	PUNCT
cana-3816	134	28	∂	∂	NUM
cana-3816	134	29	,	,	PUNCT
cana-3816	134	30	ι	ι	PROPN
cana-3816	134	31	)	)	PUNCT
cana-3816	134	32	,	,	PUNCT
cana-3816	134	33	t	t	PROPN
cana-3816	134	34	(	(	PUNCT
cana-3816	134	35	`	`	PUNCT
cana-3816	134	36	]	]	X
cana-3816	134	37	(	(	PUNCT
cana-3816	134	38	ø	ø	NOUN
cana-3816	134	39	,	,	PUNCT
cana-3816	134	40	ι),∝2	ι),∝2	NOUN
cana-3816	134	41	}	}	PUNCT
cana-3816	134	42	=	=	PUNCT
cana-3816	134	43	max{∝2,∝2,∝2,∝2	max{∝2,∝2,∝2,∝2	NOUN
cana-3816	134	44	}	}	PUNCT
cana-3816	134	45	=	=	NOUN
cana-3816	134	46	∝2	∝2	NOUN
cana-3816	134	47	as	as	ADP
cana-3816	134	48	∝1≺∝2	∝1≺∝2	PROPN
cana-3816	134	49	,	,	PUNCT
cana-3816	134	50	this	this	PRON
cana-3816	134	51	implies	imply	VERB
cana-3816	134	52	that	that	SCONJ
cana-3816	134	53	t	t	PROPN
cana-3816	134	54	(	(	PUNCT
cana-3816	134	55	`	`	PUNCT
cana-3816	134	56	]	]	X
cana-3816	134	57	(	(	PUNCT
cana-3816	134	58	]	]	X
cana-3816	134	59	∂ø	∂ø	PROPN
cana-3816	134	60	,	,	PUNCT
cana-3816	134	61	ι	ι	PROPN
cana-3816	134	62	)	)	PUNCT
cana-3816	134	63	6∝2	6∝2	NOUN
cana-3816	134	64	.	.	PUNCT
cana-3816	135	1	thus	thus	ADV
cana-3816	135	2	]	]	X
cana-3816	135	3	∂ø	∂ø	PROPN
cana-3816	135	4	∈	∈	PROPN
cana-3816	135	5	(	(	PUNCT
cana-3816	135	6	`	`	PUNCT
cana-3816	135	7	]	]	X
cana-3816	135	8	.	.	PUNCT
cana-3816	136	1	thus	thus	ADV
cana-3816	136	2	]	]	X
cana-3816	136	3	∂ø	∂ø	PROPN
cana-3816	136	4	∈	∈	PROPN
cana-3816	136	5	(	(	PUNCT
cana-3816	136	6	`	`	PUNCT
cana-3816	136	7	]	]	PUNCT
cana-3816	136	8	.	.	PUNCT
cana-3816	137	1	let	let	VERB
cana-3816	137	2	]	]	X
cana-3816	137	3	,	,	PUNCT
cana-3816	137	4	∂	∂	NUM
cana-3816	137	5	,	,	PUNCT
cana-3816	137	6	ø	ø	PROPN
cana-3816	137	7	∈	∈	PROPN
cana-3816	137	8	b	b	NOUN
cana-3816	137	9	be	be	AUX
cana-3816	137	10	such	such	ADJ
cana-3816	137	11	that	that	SCONJ
cana-3816	137	12	]	]	X
cana-3816	137	13	,	,	PUNCT
cana-3816	137	14	∂	∂	NUM
cana-3816	137	15	,	,	PUNCT
cana-3816	137	16	ø	ø	PROPN
cana-3816	137	17	∈	∈	PROPN
cana-3816	137	18	(	(	PUNCT
cana-3816	137	19	`	`	PUNCT
cana-3816	137	20	]	]	PUNCT
cana-3816	137	21	.	.	PUNCT
cana-3816	138	1	then	then	ADV
cana-3816	138	2	f	f	PROPN
cana-3816	138	3	(	(	PUNCT
cana-3816	138	4	`	`	PUNCT
cana-3816	138	5	]	]	PUNCT
cana-3816	138	6	(	(	PUNCT
cana-3816	138	7	]	]	X
cana-3816	138	8	,	,	PUNCT
cana-3816	138	9	ι	ι	X
cana-3816	138	10	)	)	PUNCT
cana-3816	138	11	=	=	NOUN
cana-3816	138	12	∝1	∝1	NOUN
cana-3816	138	13	,	,	PUNCT
cana-3816	138	14			PROPN
cana-3816	138	15	f	f	X
cana-3816	138	16	(	(	PUNCT
cana-3816	138	17	`	`	PUNCT
cana-3816	138	18	]	]	X
cana-3816	138	19	(	(	PUNCT
cana-3816	138	20	∂	∂	NUM
cana-3816	138	21	,	,	PUNCT
cana-3816	138	22	ι	ι	X
cana-3816	138	23	)	)	PUNCT
cana-3816	138	24	=	=	NOUN
cana-3816	138	25	∝1	∝1	NOUN
cana-3816	138	26	,	,	PUNCT
cana-3816	138	27			PROPN
cana-3816	138	28	f	f	X
cana-3816	138	29	(	(	PUNCT
cana-3816	138	30	`	`	PUNCT
cana-3816	138	31	]	]	X
cana-3816	138	32	(	(	PUNCT
cana-3816	138	33	ø	ø	INTJ
cana-3816	138	34	,	,	PUNCT
cana-3816	138	35	ι	ι	PROPN
cana-3816	138	36	)	)	PUNCT
cana-3816	138	37	=	=	NOUN
cana-3816	138	38	∝1	∝1	NOUN
cana-3816	138	39	.	.	PUNCT
cana-3816	139	1	since	since	SCONJ
cana-3816	139	2	f	f	PROPN
cana-3816	139	3	(	(	PUNCT
cana-3816	139	4	`	`	PUNCT
cana-3816	139	5	]	]	X
cana-3816	139	6	is	be	AUX
cana-3816	139	7	a	a	DET
cana-3816	139	8	(	(	PUNCT
cana-3816	139	9	∝1,∝2)iq1tfss	∝1,∝2)iq1tfss	NOUN
cana-3816	139	10	.	.	PUNCT
cana-3816	140	1	consider	consider	VERB
cana-3816	140	2	max{f	max{f	NOUN
cana-3816	140	3	(	(	PUNCT
cana-3816	140	4	`	`	PUNCT
cana-3816	140	5	]	]	X
cana-3816	140	6	(	(	PUNCT
cana-3816	140	7	]	]	X
cana-3816	140	8	∂ø	∂ø	PROPN
cana-3816	140	9	,	,	PUNCT
cana-3816	140	10	ι),∝1	ι),∝1	PROPN
cana-3816	140	11	}	}	PUNCT
cana-3816	140	12	>	>	PUNCT
cana-3816	140	13	min{f	min{f	PROPN
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cana-3816	140	18	]	]	X
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cana-3816	140	35	`	`	PUNCT
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cana-3816	140	41	}	}	PUNCT
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cana-3816	140	44	}	}	PUNCT
cana-3816	140	45	=	=	NOUN
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cana-3816	140	48	∝1≺∝2	∝1≺∝2	PROPN
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cana-3816	140	55	`	`	PUNCT
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cana-3816	140	58	]	]	X
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cana-3816	142	6	`	`	PUNCT
cana-3816	142	7	]	]	X
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cana-3816	143	2	`	`	PUNCT
cana-3816	143	3	is	be	AUX
cana-3816	143	4	a	a	DET
cana-3816	143	5	tss	tss	NOUN
cana-3816	143	6	of	of	ADP
cana-3816	143	7	b.	b.	PROPN
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cana-3816	143	9	764	764	NUM
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cana-3816	143	11	on	on	ADP
cana-3816	143	12	applied	apply	VERB
cana-3816	143	13	nonlinear	nonlinear	ADJ
cana-3816	143	14	analysis	analysis	NOUN
cana-3816	143	15	issn	issn	NOUN
cana-3816	143	16	:	:	PUNCT
cana-3816	143	17	1074	1074	NUM
cana-3816	143	18	-	-	PUNCT
cana-3816	143	19	133x	133x	NUM
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cana-3816	143	21	32	32	NUM
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cana-3816	143	23	.	.	NOUN
cana-3816	143	24	3	3	NUM
cana-3816	143	25	(	(	PUNCT
cana-3816	143	26	2025	2025	NUM
cana-3816	143	27	)	)	PUNCT
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cana-3816	143	29	]	]	X
cana-3816	143	30	,	,	PUNCT
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cana-3816	143	32	,	,	PUNCT
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cana-3816	144	6	that	that	SCONJ
cana-3816	144	7	]	]	X
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cana-3816	144	9	∂	∂	NUM
cana-3816	144	10	,	,	PUNCT
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cana-3816	144	12	/∈	/∈	PUNCT
cana-3816	144	13	(	(	PUNCT
cana-3816	144	14	`	`	PUNCT
cana-3816	144	15	]	]	X
cana-3816	144	16	.	.	PUNCT
cana-3816	145	1	then	then	ADV
cana-3816	145	2	t	t	PROPN
cana-3816	145	3	(	(	PUNCT
cana-3816	145	4	`	`	PUNCT
cana-3816	145	5	]	]	X
cana-3816	145	6	(	(	PUNCT
cana-3816	145	7	]	]	X
cana-3816	145	8	,	,	PUNCT
cana-3816	145	9	ι	ι	X
cana-3816	145	10	)	)	PUNCT
cana-3816	145	11	=	=	NOUN
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cana-3816	145	13	,	,	PUNCT
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cana-3816	145	15	t	t	PROPN
cana-3816	145	16	(	(	PUNCT
cana-3816	145	17	`	`	PUNCT
cana-3816	145	18	]	]	X
cana-3816	145	19	(	(	PUNCT
cana-3816	145	20	∂	∂	NUM
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cana-3816	145	23	)	)	PUNCT
cana-3816	145	24	=	=	NOUN
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cana-3816	145	28	t	t	PROPN
cana-3816	145	29	(	(	PUNCT
cana-3816	145	30	`	`	PUNCT
cana-3816	145	31	]	]	X
cana-3816	145	32	(	(	PUNCT
cana-3816	145	33	ø	ø	INTJ
cana-3816	145	34	,	,	PUNCT
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cana-3816	145	36	)	)	PUNCT
cana-3816	145	37	=	=	NOUN
cana-3816	145	38	∝1	∝1	NOUN
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cana-3816	146	2	t	t	PROPN
cana-3816	146	3	(	(	PUNCT
cana-3816	146	4	`	`	PUNCT
cana-3816	146	5	]	]	X
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cana-3816	146	7	a	a	DET
cana-3816	146	8	(	(	PUNCT
cana-3816	146	9	∝1,∝2)iq1tfss	∝1,∝2)iq1tfss	NOUN
cana-3816	146	10	.	.	PUNCT
cana-3816	146	11	min{t	min{t	PROPN
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cana-3816	147	2	`	`	PUNCT
cana-3816	147	3	]	]	X
cana-3816	147	4	(	(	PUNCT
cana-3816	147	5	]	]	X
cana-3816	147	6	∂ø	∂ø	PROPN
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cana-3816	147	9	}	}	PUNCT
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cana-3816	147	13	`	`	PUNCT
cana-3816	147	14	]	]	X
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cana-3816	147	16	]	]	X
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cana-3816	147	22	(	(	PUNCT
cana-3816	147	23	`	`	PUNCT
cana-3816	147	24	]	]	X
cana-3816	147	25	(	(	PUNCT
cana-3816	147	26	∂	∂	NUM
cana-3816	147	27	,	,	PUNCT
cana-3816	147	28	ι	ι	PROPN
cana-3816	147	29	)	)	PUNCT
cana-3816	147	30	,	,	PUNCT
cana-3816	147	31	t	t	PROPN
cana-3816	147	32	(	(	PUNCT
cana-3816	147	33	`	`	PUNCT
cana-3816	147	34	]	]	X
cana-3816	147	35	(	(	PUNCT
cana-3816	147	36	ø	ø	NOUN
cana-3816	147	37	,	,	PUNCT
cana-3816	147	38	ι),∝2	ι),∝2	NOUN
cana-3816	147	39	}	}	PUNCT
cana-3816	147	40	=	=	SYM
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cana-3816	147	42	}	}	PUNCT
cana-3816	147	43	=	=	NOUN
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cana-3816	147	47	,	,	PUNCT
cana-3816	147	48	this	this	PRON
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cana-3816	147	50	that	that	SCONJ
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cana-3816	147	52	(	(	PUNCT
cana-3816	147	53	`	`	PUNCT
cana-3816	147	54	]	]	X
cana-3816	147	55	(	(	PUNCT
cana-3816	147	56	]	]	X
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cana-3816	147	58	,	,	PUNCT
cana-3816	147	59	ι	ι	PROPN
cana-3816	147	60	)	)	PUNCT
cana-3816	147	61	6∝1	6∝1	NOUN
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cana-3816	148	3	∂ø	∂ø	PROPN
cana-3816	148	4	6∈	6∈	NOUN
cana-3816	148	5	(	(	PUNCT
cana-3816	148	6	`	`	PUNCT
cana-3816	148	7	]	]	PUNCT
cana-3816	148	8	.	.	PUNCT
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cana-3816	149	2	]	]	X
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cana-3816	149	5	,	,	PUNCT
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cana-3816	149	7	∈	∈	PROPN
cana-3816	149	8	b	b	NOUN
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cana-3816	149	11	that	that	SCONJ
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cana-3816	149	13	,	,	PUNCT
cana-3816	149	14	∂	∂	NUM
cana-3816	149	15	,	,	PUNCT
cana-3816	149	16	ø	ø	NOUN
cana-3816	149	17	/∈	/∈	PUNCT
cana-3816	150	1	(	(	PUNCT
cana-3816	150	2	`	`	PUNCT
cana-3816	150	3	]	]	X
cana-3816	150	4	.	.	PUNCT
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cana-3816	151	2	f	f	PROPN
cana-3816	151	3	(	(	PUNCT
cana-3816	151	4	`	`	PUNCT
cana-3816	151	5	]	]	PUNCT
cana-3816	151	6	(	(	PUNCT
cana-3816	151	7	]	]	X
cana-3816	151	8	,	,	PUNCT
cana-3816	151	9	ι	ι	PROPN
cana-3816	151	10	)	)	PUNCT
cana-3816	151	11	=	=	NOUN
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cana-3816	151	13	,	,	PUNCT
cana-3816	151	14			PROPN
cana-3816	151	15	f	f	X
cana-3816	151	16	(	(	PUNCT
cana-3816	151	17	`	`	PUNCT
cana-3816	151	18	]	]	X
cana-3816	151	19	(	(	PUNCT
cana-3816	151	20	∂	∂	NUM
cana-3816	151	21	,	,	PUNCT
cana-3816	151	22	ι	ι	NOUN
cana-3816	151	23	)	)	PUNCT
cana-3816	151	24	=	=	NOUN
cana-3816	151	25	∝2	∝2	PROPN
cana-3816	151	26	,	,	PUNCT
cana-3816	151	27			PROPN
cana-3816	151	28	f	f	X
cana-3816	151	29	(	(	PUNCT
cana-3816	151	30	`	`	PUNCT
cana-3816	151	31	]	]	X
cana-3816	151	32	(	(	PUNCT
cana-3816	151	33	ø	ø	INTJ
cana-3816	151	34	,	,	PUNCT
cana-3816	151	35	ι	ι	PROPN
cana-3816	151	36	)	)	PUNCT
cana-3816	151	37	=	=	NOUN
cana-3816	151	38	∝2	∝2	NOUN
cana-3816	151	39	.	.	PUNCT
cana-3816	152	1	since	since	SCONJ
cana-3816	152	2	f	f	PROPN
cana-3816	152	3	(	(	PUNCT
cana-3816	152	4	`	`	PUNCT
cana-3816	152	5	]	]	X
cana-3816	152	6	is	be	AUX
cana-3816	152	7	a	a	DET
cana-3816	152	8	(	(	PUNCT
cana-3816	152	9	∝1,∝2)iq1tfss	∝1,∝2)iq1tfss	NOUN
cana-3816	152	10	.	.	PUNCT
cana-3816	153	1	max{f	max{f	PROPN
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cana-3816	153	3	`	`	PUNCT
cana-3816	153	4	]	]	X
cana-3816	153	5	(	(	PUNCT
cana-3816	153	6	]	]	X
cana-3816	153	7	∂ø	∂ø	PROPN
cana-3816	153	8	,	,	PUNCT
cana-3816	153	9	ι),∝1	ι),∝1	PROPN
cana-3816	153	10	}	}	PUNCT
cana-3816	153	11	>	>	PUNCT
cana-3816	153	12	min{f	min{f	PROPN
cana-3816	153	13	(	(	PUNCT
cana-3816	153	14	`	`	PUNCT
cana-3816	153	15	]	]	PUNCT
cana-3816	153	16	(	(	PUNCT
cana-3816	153	17	]	]	X
cana-3816	153	18	,	,	PUNCT
cana-3816	153	19	ι	ι	PROPN
cana-3816	153	20	)	)	PUNCT
cana-3816	153	21	,	,	PUNCT
cana-3816	153	22	f	f	PROPN
cana-3816	153	23	(	(	PUNCT
cana-3816	153	24	`	`	PUNCT
cana-3816	153	25	]	]	X
cana-3816	153	26	(	(	PUNCT
cana-3816	153	27	∂	∂	NUM
cana-3816	153	28	,	,	PUNCT
cana-3816	153	29	ι	ι	PROPN
cana-3816	153	30	)	)	PUNCT
cana-3816	153	31	,	,	PUNCT
cana-3816	153	32	f	f	PROPN
cana-3816	153	33	(	(	PUNCT
cana-3816	153	34	`	`	PUNCT
cana-3816	153	35	]	]	X
cana-3816	153	36	(	(	PUNCT
cana-3816	153	37	ø	ø	NOUN
cana-3816	153	38	,	,	PUNCT
cana-3816	153	39	ι),∝2	ι),∝2	NOUN
cana-3816	153	40	}	}	PUNCT
cana-3816	153	41	=	=	SYM
cana-3816	153	42	min{∝2,∝2,∝2,∝2	min{∝2,∝2,∝2,∝2	NOUN
cana-3816	153	43	}	}	PUNCT
cana-3816	153	44	=	=	NOUN
cana-3816	153	45	∝2	∝2	NOUN
cana-3816	153	46	as	as	ADP
cana-3816	153	47	∝1≺∝2	∝1≺∝2	PROPN
cana-3816	153	48	,	,	PUNCT
cana-3816	153	49	this	this	PRON
cana-3816	153	50	implies	imply	VERB
cana-3816	153	51	that	that	SCONJ
cana-3816	154	1	f	f	PROPN
cana-3816	154	2	(	(	PUNCT
cana-3816	154	3	`	`	PUNCT
cana-3816	154	4	]	]	X
cana-3816	154	5	(	(	PUNCT
cana-3816	154	6	]	]	X
cana-3816	154	7	∂ø	∂ø	PROPN
cana-3816	154	8	,	,	PUNCT
cana-3816	154	9	ι	ι	PROPN
cana-3816	154	10	)	)	PUNCT
cana-3816	154	11	>	>	PUNCT
cana-3816	154	12	∝2	∝2	NOUN
cana-3816	154	13	.	.	PUNCT
cana-3816	155	1	thus	thus	ADV
cana-3816	155	2	]	]	X
cana-3816	155	3	∂ø	∂ø	PROPN
cana-3816	155	4	6∈	6∈	NOUN
cana-3816	155	5	(	(	PUNCT
cana-3816	155	6	`	`	PUNCT
cana-3816	155	7	]	]	X
cana-3816	155	8	.	.	PUNCT
cana-3816	156	1	therefore	therefore	ADV
cana-3816	156	2	`	`	PUNCT
cana-3816	156	3	is	be	AUX
cana-3816	156	4	a	a	DET
cana-3816	156	5	tss	tss	NOUN
cana-3816	156	6	of	of	ADP
cana-3816	156	7	b.	b.	PROPN
cana-3816	156	8	definition	definition	NOUN
cana-3816	156	9	2.12	2.12	NUM
cana-3816	156	10	.	.	PUNCT
cana-3816	157	1	for	for	ADP
cana-3816	157	2	three	three	NUM
cana-3816	157	3	iq1afss	iq1afss	NOUN
cana-3816	157	4	i	i	NOUN
cana-3816	157	5	,	,	PUNCT
cana-3816	157	6	∂	∂	NUM
cana-3816	157	7	and	and	CCONJ
cana-3816	157	8	ð	ð	PROPN
cana-3816	157	9	of	of	ADP
cana-3816	157	10	b.	b.	PROPN
cana-3816	157	11	their	their	PRON
cana-3816	157	12	product	product	NOUN
cana-3816	157	13	i	i	PRON
cana-3816	157	14	·	·	PUNCT
cana-3816	157	15	∂	∂	NUM
cana-3816	157	16	·	·	PUNCT
cana-3816	157	17	ð	ð	PROPN
cana-3816	157	18	is	be	AUX
cana-3816	157	19	defined	define	VERB
cana-3816	157	20	as	as	ADP
cana-3816	157	21	(	(	PUNCT
cana-3816	157	22	it	it	PRON
cana-3816	157	23	·	·	PUNCT
cana-3816	158	1	∂t	∂t	PROPN
cana-3816	158	2	·	·	PUNCT
cana-3816	158	3	ðt	ðt	X
cana-3816	158	4	)	)	PUNCT
cana-3816	158	5	(	(	PUNCT
cana-3816	158	6	]	]	X
cana-3816	158	7	,	,	PUNCT
cana-3816	158	8	ι	ι	PROPN
cana-3816	158	9	)	)	PUNCT
cana-3816	158	10	=	=	SYM
cana-3816	158	11			PROPN
cana-3816	158	12	inf	inf	NOUN
cana-3816	158	13	(	(	PUNCT
cana-3816	158	14	r	r	NOUN
cana-3816	158	15	,	,	PUNCT
cana-3816	158	16	s	s	NOUN
cana-3816	158	17	,	,	PUNCT
cana-3816	158	18	t)∈	t)∈	PUNCT
cana-3816	158	19	`	`	PUNCT
cana-3816	158	20	]	]	X
cana-3816	158	21	{	{	PUNCT
cana-3816	158	22	it(r	it(r	PROPN
cana-3816	158	23	,	,	PUNCT
cana-3816	158	24	ι)5	ι)5	PROPN
cana-3816	158	25	∂t(s	∂t(s	PROPN
cana-3816	158	26	,	,	PUNCT
cana-3816	158	27	ι)5	ι)5	PROPN
cana-3816	158	28	ðt(t	ðt(t	PROPN
cana-3816	158	29	,	,	PUNCT
cana-3816	158	30	ι	ι	PROPN
cana-3816	158	31	)	)	PUNCT
cana-3816	158	32	}	}	PUNCT
cana-3816	158	33	if	if	SCONJ
cana-3816	158	34	`	`	PUNCT
cana-3816	158	35	]	]	PUNCT
cana-3816	158	36	6=	6=	ADP
cana-3816	158	37	0	0	NUM
cana-3816	158	38	1	1	NUM
cana-3816	158	39	otherwise	otherwise	ADV
cana-3816	158	40	(	(	PUNCT
cana-3816	158	41	if	if	SCONJ
cana-3816	158	42	·	·	PUNCT
cana-3816	158	43	∂f	∂f	NUM
cana-3816	158	44	·	·	PUNCT
cana-3816	158	45	ðf	ðf	X
cana-3816	158	46	)	)	PUNCT
cana-3816	158	47	(	(	PUNCT
cana-3816	158	48	]	]	X
cana-3816	158	49	,	,	PUNCT
cana-3816	158	50	ι	ι	PROPN
cana-3816	158	51	)	)	PUNCT
cana-3816	158	52	=	=	PUNCT
cana-3816	159	1			PROPN
cana-3816	159	2	sup	sup	NOUN
cana-3816	159	3	(	(	PUNCT
cana-3816	159	4	r	r	NOUN
cana-3816	159	5	,	,	PUNCT
cana-3816	159	6	s	s	NOUN
cana-3816	159	7	,	,	PUNCT
cana-3816	159	8	t)∈	t)∈	PUNCT
cana-3816	159	9	`	`	PUNCT
cana-3816	159	10	]	]	PUNCT
cana-3816	159	11	{	{	PUNCT
cana-3816	159	12	if(r	if(r	NOUN
cana-3816	159	13	,	,	PUNCT
cana-3816	159	14	ι)4	ι)4	PROPN
cana-3816	159	15	∂f(s	∂f(s	PROPN
cana-3816	159	16	,	,	PUNCT
cana-3816	159	17	ι)4	ι)4	PROPN
cana-3816	159	18	ðf(t	ðf(t	NUM
cana-3816	159	19	,	,	PUNCT
cana-3816	159	20	ι	ι	PROPN
cana-3816	159	21	)	)	PUNCT
cana-3816	159	22	}	}	PUNCT
cana-3816	159	23	if	if	SCONJ
cana-3816	159	24	`	`	PUNCT
cana-3816	159	25	]	]	PUNCT
cana-3816	159	26	6=	6=	ADP
cana-3816	159	27	0	0	NUM
cana-3816	159	28	0	0	NUM
cana-3816	159	29	otherwise	otherwise	ADV
cana-3816	159	30	definition	definition	NOUN
cana-3816	159	31	2.13	2.13	NUM
cana-3816	159	32	.	.	PUNCT
cana-3816	160	1	let	let	VERB
cana-3816	160	2	i	i	PRON
cana-3816	160	3	be	be	AUX
cana-3816	160	4	subset	subset	VERB
cana-3816	160	5	of	of	ADP
cana-3816	160	6	b	b	NOUN
cana-3816	160	7	,	,	PUNCT
cana-3816	160	8	we	we	PRON
cana-3816	160	9	define	define	VERB
cana-3816	160	10	the	the	DET
cana-3816	160	11	subset	subset	NOUN
cana-3816	160	12	(	(	PUNCT
cana-3816	160	13	t)∝2	t)∝2	PROPN
cana-3816	160	14	∝1	∝1	X
cana-3816	160	15	(	(	PUNCT
cana-3816	160	16	]	]	X
cana-3816	160	17	,	,	PUNCT
cana-3816	160	18	ι	ι	PROPN
cana-3816	160	19	)	)	PUNCT
cana-3816	160	20	=	=	SYM
cana-3816	160	21	{	{	PUNCT
cana-3816	160	22	t	t	PROPN
cana-3816	160	23	(	(	PUNCT
cana-3816	160	24	]	]	X
cana-3816	160	25	,	,	PUNCT
cana-3816	160	26	ι)5	ι)5	PROPN
cana-3816	160	27	∝2}4	∝2}4	NOUN
cana-3816	160	28	∝1	∝1	PROPN
cana-3816	160	29	and	and	CCONJ
cana-3816	160	30	(	(	PUNCT
cana-3816	160	31	>	>	ADJ
cana-3816	160	32	)	)	PUNCT
cana-3816	160	33	∝2	∝2	NOUN
cana-3816	160	34	∝1	∝1	NOUN
cana-3816	160	35	(	(	PUNCT
cana-3816	160	36	]	]	X
cana-3816	160	37	,	,	PUNCT
cana-3816	160	38	ι	ι	PROPN
cana-3816	160	39	)	)	PUNCT
cana-3816	160	40	=	=	SYM
cana-3816	160	41	{	{	PUNCT
cana-3816	160	42	>	>	X
cana-3816	160	43	(	(	PUNCT
cana-3816	160	44	]	]	X
cana-3816	160	45	,	,	PUNCT
cana-3816	160	46	ι)4	ι)4	PROPN
cana-3816	160	47	∝2}5	∝2}5	PROPN
cana-3816	160	48	∝1	∝1	PROPN
cana-3816	160	49	,	,	PUNCT
cana-3816	160	50	for	for	ADP
cana-3816	160	51	all	all	PRON
cana-3816	160	52	]	]	X
cana-3816	160	53	∈	∈	PROPN
cana-3816	160	54	b.	b.	PROPN
cana-3816	160	55	lemma	lemma	PROPN
cana-3816	160	56	2.14	2.14	NUM
cana-3816	160	57	.	.	PUNCT
cana-3816	161	1	let	let	VERB
cana-3816	161	2	`	`	PUNCT
cana-3816	161	3	,	,	PUNCT
cana-3816	161	4	`	`	PUNCT
cana-3816	161	5	1	1	NUM
cana-3816	161	6	and	and	CCONJ
cana-3816	161	7	`	`	PUNCT
cana-3816	161	8	2	2	NUM
cana-3816	161	9	be	be	AUX
cana-3816	161	10	non	non	ADJ
cana-3816	161	11	-	-	ADJ
cana-3816	161	12	empty	empty	ADJ
cana-3816	161	13	subsets	subset	NOUN
cana-3816	161	14	of	of	ADP
cana-3816	161	15	b.	b.	PROPN
cana-3816	161	16	then	then	ADV
cana-3816	162	1	1	1	X
cana-3816	162	2	.	.	PUNCT
cana-3816	163	1	(	(	PUNCT
cana-3816	163	2			NOUN
cana-3816	163	3	(	(	PUNCT
cana-3816	163	4	`	`	PUNCT
cana-3816	163	5	]	]	X
cana-3816	163	6	5	5	NUM
cana-3816	163	7			NOUN
cana-3816	163	8	(	(	PUNCT
cana-3816	163	9	`	`	PUNCT
cana-3816	163	10	1	1	X
cana-3816	163	11	]	]	SYM
cana-3816	163	12	5	5	NUM
cana-3816	163	13			NOUN
cana-3816	163	14	(	(	PUNCT
cana-3816	163	15	`	`	PUNCT
cana-3816	163	16	2	2	NUM
cana-3816	163	17	]	]	PUNCT
cana-3816	163	18	)	)	PUNCT
cana-3816	163	19	∝2	∝2	NOUN
cana-3816	163	20	∝1	∝1	NOUN
cana-3816	163	21	=	=	SYM
cana-3816	163	22	(	(	PUNCT
cana-3816	163	23	(`∪`1∪`2	(`∪`1∪`2	NOUN
cana-3816	163	24	]	]	SYM
cana-3816	163	25	)	)	PUNCT
cana-3816	163	26	∝2	∝2	NOUN
cana-3816	163	27	∝1	∝1	NOUN
cana-3816	163	28	,	,	PUNCT
cana-3816	163	29	2	2	X
cana-3816	163	30	.	.	PUNCT
cana-3816	163	31	(	(	PUNCT
cana-3816	163	32			NOUN
cana-3816	163	33	(	(	PUNCT
cana-3816	163	34	`	`	PUNCT
cana-3816	163	35	]	]	X
cana-3816	163	36	4	4	NUM
cana-3816	163	37			NOUN
cana-3816	163	38	(	(	PUNCT
cana-3816	163	39	`	`	PUNCT
cana-3816	163	40	1	1	X
cana-3816	163	41	]	]	SYM
cana-3816	163	42	4	4	NUM
cana-3816	163	43			NOUN
cana-3816	163	44	(	(	PUNCT
cana-3816	163	45	`	`	PUNCT
cana-3816	163	46	2	2	NUM
cana-3816	163	47	]	]	PUNCT
cana-3816	163	48	)	)	PUNCT
cana-3816	163	49	∝2	∝2	NOUN
cana-3816	163	50	∝1	∝1	NOUN
cana-3816	163	51	=	=	SYM
cana-3816	163	52	(	(	PUNCT
cana-3816	163	53	(`∩`1∩`2	(`∩`1∩`2	NOUN
cana-3816	163	54	]	]	PUNCT
cana-3816	163	55	)	)	PUNCT
cana-3816	163	56	∝2	∝2	NOUN
cana-3816	163	57	∝1	∝1	NOUN
cana-3816	163	58	,	,	PUNCT
cana-3816	163	59	3	3	X
cana-3816	163	60	.	.	PUNCT
cana-3816	163	61	(	(	PUNCT
cana-3816	163	62			NOUN
cana-3816	163	63	(	(	PUNCT
cana-3816	163	64	`	`	PUNCT
cana-3816	163	65	]	]	X
cana-3816	163	66	·	·	PUNCT
cana-3816	163	67	(`1]·(`2	(`1]·(`2	NOUN
cana-3816	163	68	]	]	PUNCT
cana-3816	163	69	)	)	PUNCT
cana-3816	163	70	∝2	∝2	NOUN
cana-3816	163	71	∝1	∝1	NOUN
cana-3816	163	72	=	=	SYM
cana-3816	163	73	(	(	PUNCT
cana-3816	163	74	(``1`2	(``1`2	X
cana-3816	163	75	]	]	SYM
cana-3816	163	76	)	)	PUNCT
cana-3816	163	77	∝2	∝2	NOUN
cana-3816	163	78	∝1	∝1	NOUN
cana-3816	163	79	.	.	PUNCT
cana-3816	164	1	proof	proof	NOUN
cana-3816	164	2	.	.	PUNCT
cana-3816	165	1	(	(	PUNCT
cana-3816	165	2	iii	iii	X
cana-3816	165	3	)	)	PUNCT
cana-3816	165	4	let	let	VERB
cana-3816	165	5	]	]	X
cana-3816	165	6	∈	∈	PROPN
cana-3816	165	7	b.	b.	PROPN
cana-3816	166	1	if	if	SCONJ
cana-3816	166	2	]	]	X
cana-3816	166	3	∈	∈	PROPN
cana-3816	166	4	(	(	PUNCT
cana-3816	166	5	`	`	PUNCT
cana-3816	166	6	`	`	PUNCT
cana-3816	166	7	1`2	1`2	NUM
cana-3816	166	8	]	]	X
cana-3816	166	9	,	,	PUNCT
cana-3816	166	10	then	then	ADV
cana-3816	166	11	(	(	PUNCT
cana-3816	166	12	(``1`2	(``1`2	X
cana-3816	166	13	]	]	X
cana-3816	166	14	)	)	PUNCT
cana-3816	166	15	(	(	PUNCT
cana-3816	166	16	]	]	X
cana-3816	166	17	,	,	PUNCT
cana-3816	166	18	ι	ι	PROPN
cana-3816	166	19	)	)	PUNCT
cana-3816	166	20	=	=	NOUN
cana-3816	166	21	∝2	∝2	NOUN
cana-3816	166	22	.	.	PUNCT
cana-3816	167	1	since	since	SCONJ
cana-3816	167	2	]	]	X
cana-3816	167	3	6	6	NUM
cana-3816	167	4	τ1τ2τ3	τ1τ2τ3	NOUN
cana-3816	167	5	for	for	ADP
cana-3816	167	6	some	some	DET
cana-3816	167	7	τ1	τ1	NOUN
cana-3816	167	8	∈	∈	PROPN
cana-3816	167	9	(	(	PUNCT
cana-3816	167	10	`	`	PUNCT
cana-3816	167	11	]	]	X
cana-3816	167	12	,	,	PUNCT
cana-3816	167	13	τ2	τ2	PROPN
cana-3816	167	14	∈	∈	PROPN
cana-3816	167	15	(	(	PUNCT
cana-3816	167	16	`	`	PUNCT
cana-3816	167	17	1	1	X
cana-3816	167	18	]	]	PUNCT
cana-3816	167	19	and	and	CCONJ
cana-3816	167	20	τ3	τ3	PROPN
cana-3816	167	21	∈	∈	PROPN
cana-3816	167	22	(	(	PUNCT
cana-3816	167	23	`	`	PUNCT
cana-3816	167	24	2	2	NUM
cana-3816	167	25	]	]	PUNCT
cana-3816	167	26	.	.	PUNCT
cana-3816	168	1	we	we	PRON
cana-3816	168	2	have	have	VERB
cana-3816	168	3	(	(	PUNCT
cana-3816	168	4	τ1	τ1	NOUN
cana-3816	168	5	,	,	PUNCT
cana-3816	168	6	τ2	τ2	ADJ
cana-3816	168	7	,	,	PUNCT
cana-3816	168	8	τ3	τ3	NOUN
cana-3816	168	9	)	)	PUNCT
cana-3816	168	10	∈	∈	NOUN
cana-3816	169	1	`	`	PUNCT
cana-3816	169	2	]	]	PUNCT
cana-3816	169	3	and	and	CCONJ
cana-3816	169	4	`	`	PUNCT
cana-3816	169	5	]	]	PUNCT
cana-3816	169	6	6=	6=	ADP
cana-3816	169	7	0	0	NUM
cana-3816	169	8	.	.	PUNCT
cana-3816	170	1	(	(	PUNCT
cana-3816	170	2	t	t	PROPN
cana-3816	170	3	(	(	PUNCT
cana-3816	170	4	`	`	PUNCT
cana-3816	170	5	]	]	X
cana-3816	170	6	·	·	PUNCT
cana-3816	170	7	t	t	X
cana-3816	170	8	(	(	PUNCT
cana-3816	170	9	`	`	PUNCT
cana-3816	170	10	1	1	NUM
cana-3816	170	11	]	]	PUNCT
cana-3816	170	12	·	·	PUNCT
cana-3816	171	1	t	t	X
cana-3816	171	2	(	(	PUNCT
cana-3816	171	3	`	`	PUNCT
cana-3816	171	4	2	2	NUM
cana-3816	171	5	]	]	PUNCT
cana-3816	171	6	)	)	PUNCT
cana-3816	171	7	(	(	PUNCT
cana-3816	171	8	]	]	X
cana-3816	171	9	,	,	PUNCT
cana-3816	171	10	ι	ι	PROPN
cana-3816	171	11	)	)	PUNCT
cana-3816	171	12	=	=	SYM
cana-3816	171	13	inf	inf	PROPN
cana-3816	171	14	]=	]=	NOUN
cana-3816	171	15	β1β2β3	β1β2β3	PROPN
cana-3816	171	16	max{t	max{t	NOUN
cana-3816	171	17	(	(	PUNCT
cana-3816	171	18	`	`	PUNCT
cana-3816	171	19	]	]	X
cana-3816	171	20	(	(	PUNCT
cana-3816	171	21	β1	β1	PROPN
cana-3816	171	22	,	,	PUNCT
cana-3816	171	23	ι	ι	PROPN
cana-3816	171	24	)	)	PUNCT
cana-3816	171	25	,	,	PUNCT
cana-3816	171	26			PROPN
cana-3816	171	27	t	t	PROPN
cana-3816	171	28	(	(	PUNCT
cana-3816	171	29	`	`	PUNCT
cana-3816	171	30	1	1	X
cana-3816	171	31	]	]	PUNCT
cana-3816	171	32	(	(	PUNCT
cana-3816	171	33	β2	β2	VERB
cana-3816	171	34	,	,	PUNCT
cana-3816	171	35	ι	ι	PROPN
cana-3816	171	36	)	)	PUNCT
cana-3816	171	37	,	,	PUNCT
cana-3816	171	38			PROPN
cana-3816	171	39	t	t	PROPN
cana-3816	171	40	(	(	PUNCT
cana-3816	171	41	`	`	PUNCT
cana-3816	171	42	2	2	X
cana-3816	171	43	]	]	PUNCT
cana-3816	171	44	(	(	PUNCT
cana-3816	171	45	β3	β3	ADJ
cana-3816	171	46	,	,	PUNCT
cana-3816	171	47	ι	ι	PROPN
cana-3816	171	48	)	)	PUNCT
cana-3816	171	49	}	}	PUNCT
cana-3816	171	50	6	6	NUM
cana-3816	171	51	max{t	max{t	NOUN
cana-3816	171	52	(	(	PUNCT
cana-3816	171	53	`	`	PUNCT
cana-3816	171	54	]	]	X
cana-3816	171	55	(	(	PUNCT
cana-3816	171	56	τ1	τ1	NOUN
cana-3816	171	57	,	,	PUNCT
cana-3816	171	58	ι	ι	PROPN
cana-3816	171	59	)	)	PUNCT
cana-3816	171	60	,	,	PUNCT
cana-3816	171	61			PROPN
cana-3816	171	62	t	t	PROPN
cana-3816	171	63	(	(	PUNCT
cana-3816	171	64	`	`	PUNCT
cana-3816	171	65	1	1	X
cana-3816	171	66	]	]	PUNCT
cana-3816	171	67	(	(	PUNCT
cana-3816	171	68	τ2	τ2	PROPN
cana-3816	171	69	,	,	PUNCT
cana-3816	171	70	ι	ι	PROPN
cana-3816	171	71	)	)	PUNCT
cana-3816	171	72	,	,	PUNCT
cana-3816	171	73			PROPN
cana-3816	171	74	t	t	PROPN
cana-3816	171	75	(	(	PUNCT
cana-3816	171	76	`	`	PUNCT
cana-3816	171	77	2	2	X
cana-3816	171	78	]	]	PUNCT
cana-3816	171	79	(	(	PUNCT
cana-3816	171	80	τ3	τ3	PROPN
cana-3816	171	81	,	,	PUNCT
cana-3816	171	82	ι	ι	PROPN
cana-3816	171	83	)	)	PUNCT
cana-3816	171	84	}	}	PUNCT
cana-3816	172	1	=	=	NOUN
cana-3816	172	2	∝2	∝2	PROPN
cana-3816	172	3	(	(	PUNCT
cana-3816	172	4	f	f	PROPN
cana-3816	172	5	(	(	PUNCT
cana-3816	172	6	`	`	PUNCT
cana-3816	172	7	]	]	PUNCT
cana-3816	172	8	·	·	PUNCT
cana-3816	173	1	f	f	PRON
cana-3816	173	2	(	(	PUNCT
cana-3816	173	3	`	`	PUNCT
cana-3816	173	4	1	1	NUM
cana-3816	173	5	]	]	PUNCT
cana-3816	173	6	·	·	PUNCT
cana-3816	174	1	f	f	PROPN
cana-3816	174	2	(	(	PUNCT
cana-3816	174	3	`	`	PUNCT
cana-3816	174	4	2	2	NUM
cana-3816	174	5	]	]	PUNCT
cana-3816	174	6	)	)	PUNCT
cana-3816	174	7	(	(	PUNCT
cana-3816	174	8	]	]	X
cana-3816	174	9	,	,	PUNCT
cana-3816	174	10	ι	ι	PROPN
cana-3816	174	11	)	)	PUNCT
cana-3816	174	12	=	=	SYM
cana-3816	174	13	sup	sup	NOUN
cana-3816	174	14	]=	]=	NOUN
cana-3816	174	15	β1β2β3	β1β2β3	PROPN
cana-3816	174	16	min{f	min{f	NOUN
cana-3816	174	17	(	(	PUNCT
cana-3816	174	18	`	`	PUNCT
cana-3816	174	19	]	]	X
cana-3816	174	20	(	(	PUNCT
cana-3816	174	21	β1	β1	PROPN
cana-3816	174	22	,	,	PUNCT
cana-3816	174	23	ι	ι	PROPN
cana-3816	174	24	)	)	PUNCT
cana-3816	174	25	,	,	PUNCT
cana-3816	174	26			PROPN
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cana-3816	174	28	(	(	PUNCT
cana-3816	174	29	`	`	PUNCT
cana-3816	174	30	1	1	X
cana-3816	174	31	]	]	PUNCT
cana-3816	174	32	(	(	PUNCT
cana-3816	174	33	β2	β2	VERB
cana-3816	174	34	,	,	PUNCT
cana-3816	174	35	ι	ι	PROPN
cana-3816	174	36	)	)	PUNCT
cana-3816	174	37	,	,	PUNCT
cana-3816	174	38			PROPN
cana-3816	174	39	f	f	X
cana-3816	174	40	(	(	PUNCT
cana-3816	174	41	`	`	PUNCT
cana-3816	174	42	2	2	X
cana-3816	174	43	]	]	PUNCT
cana-3816	174	44	(	(	PUNCT
cana-3816	174	45	β3	β3	ADJ
cana-3816	174	46	,	,	PUNCT
cana-3816	174	47	ι	ι	NOUN
cana-3816	174	48	)	)	PUNCT
cana-3816	174	49	}	}	PUNCT
cana-3816	174	50	>	>	X
cana-3816	174	51	min{f	min{f	PROPN
cana-3816	174	52	(	(	PUNCT
cana-3816	174	53	`	`	PUNCT
cana-3816	174	54	]	]	X
cana-3816	174	55	(	(	PUNCT
cana-3816	174	56	τ1	τ1	NOUN
cana-3816	174	57	,	,	PUNCT
cana-3816	174	58	ι	ι	PROPN
cana-3816	174	59	)	)	PUNCT
cana-3816	174	60	,	,	PUNCT
cana-3816	174	61			PROPN
cana-3816	174	62	f	f	X
cana-3816	174	63	(	(	PUNCT
cana-3816	174	64	`	`	PUNCT
cana-3816	174	65	1	1	X
cana-3816	174	66	]	]	PUNCT
cana-3816	174	67	(	(	PUNCT
cana-3816	174	68	τ2	τ2	PROPN
cana-3816	174	69	,	,	PUNCT
cana-3816	174	70	ι	ι	PROPN
cana-3816	174	71	)	)	PUNCT
cana-3816	174	72	,	,	PUNCT
cana-3816	174	73			PROPN
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cana-3816	174	75	(	(	PUNCT
cana-3816	174	76	`	`	PUNCT
cana-3816	174	77	2	2	X
cana-3816	174	78	]	]	PUNCT
cana-3816	174	79	(	(	PUNCT
cana-3816	174	80	τ3	τ3	PROPN
cana-3816	174	81	,	,	PUNCT
cana-3816	174	82	ι	ι	PROPN
cana-3816	174	83	)	)	PUNCT
cana-3816	174	84	}	}	PUNCT
cana-3816	174	85	=	=	NOUN
cana-3816	174	86	∝1	∝1	NOUN
cana-3816	174	87	https://internationalpubls.com	https://internationalpubls.com	X
cana-3816	174	88	765	765	NUM
cana-3816	174	89	communications	communication	NOUN
cana-3816	174	90	on	on	ADP
cana-3816	174	91	applied	apply	VERB
cana-3816	174	92	nonlinear	nonlinear	ADJ
cana-3816	174	93	analysis	analysis	NOUN
cana-3816	174	94	issn	issn	NOUN
cana-3816	174	95	:	:	PUNCT
cana-3816	174	96	1074	1074	NUM
cana-3816	174	97	-	-	PUNCT
cana-3816	174	98	133x	133x	NUM
cana-3816	174	99	vol	vol	NOUN
cana-3816	174	100	32	32	NUM
cana-3816	174	101	no	no	NOUN
cana-3816	174	102	.	.	NOUN
cana-3816	174	103	3	3	NUM
cana-3816	174	104	(	(	PUNCT
cana-3816	174	105	2025	2025	NUM
cana-3816	174	106	)	)	PUNCT
cana-3816	174	107	therefore	therefore	ADV
cana-3816	174	108	(	(	PUNCT
cana-3816	174	109			NOUN
cana-3816	174	110	(	(	PUNCT
cana-3816	174	111	`	`	PUNCT
cana-3816	174	112	]	]	X
cana-3816	174	113	·	·	PUNCT
cana-3816	174	114			NOUN
cana-3816	174	115	(	(	PUNCT
cana-3816	174	116	`	`	PUNCT
cana-3816	174	117	1	1	NUM
cana-3816	174	118	]	]	PUNCT
cana-3816	174	119	·	·	PUNCT
cana-3816	174	120			NOUN
cana-3816	174	121	(	(	PUNCT
cana-3816	174	122	`	`	PUNCT
cana-3816	174	123	2	2	NUM
cana-3816	174	124	]	]	PUNCT
cana-3816	174	125	)	)	PUNCT
cana-3816	174	126	(	(	PUNCT
cana-3816	174	127	]	]	X
cana-3816	174	128	,	,	PUNCT
cana-3816	174	129	ι	ι	PROPN
cana-3816	174	130	)	)	PUNCT
cana-3816	174	131	=	=	SYM
cana-3816	174	132	(	(	PUNCT
cana-3816	174	133	(``1`2	(``1`2	X
cana-3816	174	134	]	]	X
cana-3816	174	135	)	)	PUNCT
cana-3816	174	136	(	(	PUNCT
cana-3816	174	137	]	]	X
cana-3816	174	138	,	,	PUNCT
cana-3816	174	139	ι	ι	PROPN
cana-3816	174	140	)	)	PUNCT
cana-3816	174	141	.	.	PUNCT
cana-3816	175	1	if	if	SCONJ
cana-3816	175	2	]	]	X
cana-3816	175	3	/∈	/∈	PUNCT
cana-3816	176	1	(	(	PUNCT
cana-3816	176	2	`	`	PUNCT
cana-3816	176	3	`	`	PUNCT
cana-3816	176	4	1`2	1`2	NUM
cana-3816	176	5	]	]	X
cana-3816	176	6	then	then	ADV
cana-3816	176	7	(	(	PUNCT
cana-3816	176	8	t(``1`2	t(``1`2	PROPN
cana-3816	176	9	]	]	PUNCT
cana-3816	176	10	)	)	PUNCT
cana-3816	176	11	(	(	PUNCT
cana-3816	176	12	]	]	X
cana-3816	176	13	,	,	PUNCT
cana-3816	176	14	ι	ι	X
cana-3816	176	15	)	)	PUNCT
cana-3816	176	16	=	=	NOUN
cana-3816	176	17	∝1	∝1	NOUN
cana-3816	176	18	and	and	CCONJ
cana-3816	176	19	(	(	PUNCT
cana-3816	176	20	f(``1`2	f(``1`2	PROPN
cana-3816	176	21	]	]	X
cana-3816	176	22	)	)	PUNCT
cana-3816	176	23	(	(	PUNCT
cana-3816	176	24	]	]	X
cana-3816	176	25	,	,	PUNCT
cana-3816	176	26	ι	ι	PROPN
cana-3816	176	27	)	)	PUNCT
cana-3816	176	28	=	=	NOUN
cana-3816	176	29	∝2	∝2	NOUN
cana-3816	176	30	.	.	PUNCT
cana-3816	177	1	since	since	SCONJ
cana-3816	177	2	]	]	X
cana-3816	177	3	6	6	NUM
cana-3816	177	4	τ1τ2τ3	τ1τ2τ3	NOUN
cana-3816	177	5	for	for	ADP
cana-3816	177	6	some	some	DET
cana-3816	177	7	τ1	τ1	NOUN
cana-3816	177	8	/∈	/∈	PUNCT
cana-3816	178	1	(	(	PUNCT
cana-3816	178	2	`	`	PUNCT
cana-3816	178	3	]	]	X
cana-3816	178	4	,	,	PUNCT
cana-3816	178	5	τ2	τ2	NOUN
cana-3816	178	6	/∈	/∈	PUNCT
cana-3816	178	7	(	(	PUNCT
cana-3816	178	8	`	`	PUNCT
cana-3816	178	9	1	1	X
cana-3816	178	10	]	]	PUNCT
cana-3816	178	11	and	and	CCONJ
cana-3816	178	12	τ3	τ3	NOUN
cana-3816	178	13	/∈	/∈	PUNCT
cana-3816	179	1	(	(	PUNCT
cana-3816	179	2	`	`	PUNCT
cana-3816	179	3	2	2	NUM
cana-3816	179	4	]	]	PUNCT
cana-3816	179	5	.	.	PUNCT
cana-3816	180	1	we	we	PRON
cana-3816	180	2	have	have	VERB
cana-3816	180	3	(	(	PUNCT
cana-3816	180	4	t	t	X
cana-3816	180	5	(	(	PUNCT
cana-3816	180	6	`	`	PUNCT
cana-3816	180	7	]	]	X
cana-3816	180	8	·	·	PUNCT
cana-3816	181	1	t	t	X
cana-3816	181	2	(	(	PUNCT
cana-3816	181	3	`	`	PUNCT
cana-3816	181	4	1	1	NUM
cana-3816	181	5	]	]	PUNCT
cana-3816	181	6	·	·	PUNCT
cana-3816	182	1	t	t	X
cana-3816	182	2	(	(	PUNCT
cana-3816	182	3	`	`	PUNCT
cana-3816	182	4	2	2	NUM
cana-3816	182	5	]	]	PUNCT
cana-3816	182	6	)	)	PUNCT
cana-3816	182	7	(	(	PUNCT
cana-3816	182	8	]	]	X
cana-3816	182	9	,	,	PUNCT
cana-3816	182	10	ι	ι	PROPN
cana-3816	182	11	)	)	PUNCT
cana-3816	182	12	=	=	SYM
cana-3816	182	13	inf	inf	PROPN
cana-3816	182	14	]=	]=	NOUN
cana-3816	182	15	β1β2β3	β1β2β3	PROPN
cana-3816	182	16	max{t	max{t	NOUN
cana-3816	182	17	(	(	PUNCT
cana-3816	182	18	`	`	PUNCT
cana-3816	182	19	]	]	X
cana-3816	182	20	(	(	PUNCT
cana-3816	182	21	β1	β1	PROPN
cana-3816	182	22	,	,	PUNCT
cana-3816	182	23	ι	ι	PROPN
cana-3816	182	24	)	)	PUNCT
cana-3816	182	25	,	,	PUNCT
cana-3816	182	26			PROPN
cana-3816	182	27	t	t	PROPN
cana-3816	182	28	(	(	PUNCT
cana-3816	182	29	`	`	PUNCT
cana-3816	182	30	1	1	X
cana-3816	182	31	]	]	PUNCT
cana-3816	182	32	(	(	PUNCT
cana-3816	182	33	β2	β2	VERB
cana-3816	182	34	,	,	PUNCT
cana-3816	182	35	ι	ι	PROPN
cana-3816	182	36	)	)	PUNCT
cana-3816	182	37	,	,	PUNCT
cana-3816	182	38			PROPN
cana-3816	182	39	t	t	PROPN
cana-3816	182	40	(	(	PUNCT
cana-3816	182	41	`	`	PUNCT
cana-3816	182	42	2	2	X
cana-3816	182	43	]	]	PUNCT
cana-3816	182	44	(	(	PUNCT
cana-3816	182	45	β3	β3	ADJ
cana-3816	182	46	,	,	PUNCT
cana-3816	182	47	ι	ι	PROPN
cana-3816	182	48	)	)	PUNCT
cana-3816	182	49	}	}	PUNCT
cana-3816	182	50	6	6	NUM
cana-3816	182	51	max{t	max{t	NOUN
cana-3816	182	52	(	(	PUNCT
cana-3816	182	53	`	`	PUNCT
cana-3816	182	54	]	]	X
cana-3816	182	55	(	(	PUNCT
cana-3816	182	56	τ1	τ1	NOUN
cana-3816	182	57	,	,	PUNCT
cana-3816	182	58	ι	ι	PROPN
cana-3816	182	59	)	)	PUNCT
cana-3816	182	60	,	,	PUNCT
cana-3816	182	61			PROPN
cana-3816	182	62	t	t	PROPN
cana-3816	182	63	(	(	PUNCT
cana-3816	182	64	`	`	PUNCT
cana-3816	182	65	1	1	X
cana-3816	182	66	]	]	PUNCT
cana-3816	182	67	(	(	PUNCT
cana-3816	182	68	τ2	τ2	PROPN
cana-3816	182	69	,	,	PUNCT
cana-3816	182	70	ι	ι	PROPN
cana-3816	182	71	)	)	PUNCT
cana-3816	182	72	,	,	PUNCT
cana-3816	182	73			PROPN
cana-3816	182	74	t	t	PROPN
cana-3816	182	75	(	(	PUNCT
cana-3816	182	76	`	`	PUNCT
cana-3816	182	77	2	2	X
cana-3816	182	78	]	]	PUNCT
cana-3816	182	79	(	(	PUNCT
cana-3816	182	80	τ3	τ3	PROPN
cana-3816	182	81	,	,	PUNCT
cana-3816	182	82	ι	ι	PROPN
cana-3816	182	83	)	)	PUNCT
cana-3816	182	84	}	}	PUNCT
cana-3816	183	1	=	=	NOUN
cana-3816	183	2	∝1	∝1	X
cana-3816	183	3	(	(	PUNCT
cana-3816	183	4	f	f	PROPN
cana-3816	183	5	(	(	PUNCT
cana-3816	183	6	`	`	PUNCT
cana-3816	183	7	]	]	PUNCT
cana-3816	183	8	·	·	PUNCT
cana-3816	183	9	f	f	PRON
cana-3816	183	10	(	(	PUNCT
cana-3816	183	11	`	`	PUNCT
cana-3816	183	12	1	1	NUM
cana-3816	183	13	]	]	PUNCT
cana-3816	183	14	·	·	PUNCT
cana-3816	184	1	f	f	PROPN
cana-3816	184	2	(	(	PUNCT
cana-3816	184	3	`	`	PUNCT
cana-3816	184	4	2	2	NUM
cana-3816	184	5	]	]	PUNCT
cana-3816	184	6	)	)	PUNCT
cana-3816	184	7	(	(	PUNCT
cana-3816	184	8	]	]	X
cana-3816	184	9	,	,	PUNCT
cana-3816	184	10	ι	ι	PROPN
cana-3816	184	11	)	)	PUNCT
cana-3816	184	12	=	=	SYM
cana-3816	184	13	sup	sup	NOUN
cana-3816	184	14	]=	]=	NOUN
cana-3816	184	15	β1β2β3	β1β2β3	PROPN
cana-3816	184	16	min{f	min{f	NOUN
cana-3816	184	17	(	(	PUNCT
cana-3816	184	18	`	`	PUNCT
cana-3816	184	19	]	]	X
cana-3816	184	20	(	(	PUNCT
cana-3816	184	21	β1	β1	PROPN
cana-3816	184	22	,	,	PUNCT
cana-3816	184	23	ι	ι	PROPN
cana-3816	184	24	)	)	PUNCT
cana-3816	184	25	,	,	PUNCT
cana-3816	184	26			PROPN
cana-3816	184	27	f	f	X
cana-3816	184	28	(	(	PUNCT
cana-3816	184	29	`	`	PUNCT
cana-3816	184	30	1	1	X
cana-3816	184	31	]	]	PUNCT
cana-3816	184	32	(	(	PUNCT
cana-3816	184	33	β2	β2	VERB
cana-3816	184	34	,	,	PUNCT
cana-3816	184	35	ι	ι	PROPN
cana-3816	184	36	)	)	PUNCT
cana-3816	184	37	,	,	PUNCT
cana-3816	184	38			PROPN
cana-3816	184	39	f	f	X
cana-3816	184	40	(	(	PUNCT
cana-3816	184	41	`	`	PUNCT
cana-3816	184	42	2	2	X
cana-3816	184	43	]	]	PUNCT
cana-3816	184	44	(	(	PUNCT
cana-3816	184	45	β3	β3	ADJ
cana-3816	184	46	,	,	PUNCT
cana-3816	184	47	ι	ι	NOUN
cana-3816	184	48	)	)	PUNCT
cana-3816	184	49	}	}	PUNCT
cana-3816	184	50	>	>	X
cana-3816	184	51	min{f	min{f	PROPN
cana-3816	184	52	(	(	PUNCT
cana-3816	184	53	`	`	PUNCT
cana-3816	184	54	]	]	X
cana-3816	184	55	(	(	PUNCT
cana-3816	184	56	τ1	τ1	NOUN
cana-3816	184	57	,	,	PUNCT
cana-3816	184	58	ι	ι	PROPN
cana-3816	184	59	)	)	PUNCT
cana-3816	184	60	,	,	PUNCT
cana-3816	184	61			PROPN
cana-3816	184	62	f	f	X
cana-3816	184	63	(	(	PUNCT
cana-3816	184	64	`	`	PUNCT
cana-3816	184	65	1	1	X
cana-3816	184	66	]	]	PUNCT
cana-3816	184	67	(	(	PUNCT
cana-3816	184	68	τ2	τ2	PROPN
cana-3816	184	69	,	,	PUNCT
cana-3816	184	70	ι	ι	PROPN
cana-3816	184	71	)	)	PUNCT
cana-3816	184	72	,	,	PUNCT
cana-3816	184	73			PROPN
cana-3816	184	74	f	f	X
cana-3816	184	75	(	(	PUNCT
cana-3816	184	76	`	`	PUNCT
cana-3816	184	77	2	2	X
cana-3816	184	78	]	]	PUNCT
cana-3816	184	79	(	(	PUNCT
cana-3816	184	80	τ3	τ3	PROPN
cana-3816	184	81	,	,	PUNCT
cana-3816	184	82	ι	ι	PROPN
cana-3816	184	83	)	)	PUNCT
cana-3816	184	84	}	}	PUNCT
cana-3816	185	1	=	=	NOUN
cana-3816	185	2	∝2	∝2	NOUN
cana-3816	185	3	hence	hence	ADV
cana-3816	185	4	(	(	PUNCT
cana-3816	185	5			NOUN
cana-3816	185	6	(	(	PUNCT
cana-3816	185	7	`	`	PUNCT
cana-3816	185	8	]	]	X
cana-3816	185	9	·	·	PUNCT
cana-3816	185	10			NOUN
cana-3816	185	11	(	(	PUNCT
cana-3816	185	12	`	`	PUNCT
cana-3816	185	13	1	1	NUM
cana-3816	185	14	]	]	PUNCT
cana-3816	185	15	·	·	PUNCT
cana-3816	185	16			NOUN
cana-3816	185	17	(	(	PUNCT
cana-3816	185	18	`	`	PUNCT
cana-3816	185	19	2	2	NUM
cana-3816	185	20	]	]	PUNCT
cana-3816	185	21	)	)	PUNCT
cana-3816	185	22	(	(	PUNCT
cana-3816	185	23	]	]	X
cana-3816	185	24	,	,	PUNCT
cana-3816	185	25	ι	ι	PROPN
cana-3816	185	26	)	)	PUNCT
cana-3816	185	27	=	=	SYM
cana-3816	185	28	(	(	PUNCT
cana-3816	185	29	(``1`2	(``1`2	X
cana-3816	185	30	]	]	X
cana-3816	185	31	)	)	PUNCT
cana-3816	185	32	(	(	PUNCT
cana-3816	185	33	]	]	X
cana-3816	185	34	,	,	PUNCT
cana-3816	185	35	ι	ι	PROPN
cana-3816	185	36	)	)	PUNCT
cana-3816	185	37	.	.	PUNCT
cana-3816	186	1	theorem	theorem	VERB
cana-3816	186	2	2.15	2.15	NUM
cana-3816	186	3	.	.	PUNCT
cana-3816	187	1	for	for	ADP
cana-3816	187	2	`	`	PUNCT
cana-3816	187	3	,	,	PUNCT
cana-3816	187	4	`	`	PUNCT
cana-3816	187	5	2	2	NUM
cana-3816	187	6	⊆	⊆	NUM
cana-3816	187	7	b	b	NOUN
cana-3816	187	8	and	and	CCONJ
cana-3816	187	9	{	{	PUNCT
cana-3816	187	10	`	`	PUNCT
cana-3816	187	11	j	j	PROPN
cana-3816	187	12	|j	|j	PROPN
cana-3816	187	13	∈	∈	PROPN
cana-3816	187	14	j	j	X
cana-3816	187	15	}	}	PUNCT
cana-3816	187	16	be	be	VERB
cana-3816	187	17	a	a	DET
cana-3816	187	18	family	family	NOUN
cana-3816	187	19	of	of	ADP
cana-3816	187	20	subsets	subset	NOUN
cana-3816	187	21	of	of	ADP
cana-3816	187	22	b.	b.	PROPN
cana-3816	188	1	then	then	ADV
cana-3816	188	2	(	(	PUNCT
cana-3816	188	3	i	i	NOUN
cana-3816	188	4	)	)	PUNCT
cana-3816	188	5	(	(	PUNCT
cana-3816	188	6	`	`	PUNCT
cana-3816	188	7	]	]	X
cana-3816	188	8	⊆	⊆	X
cana-3816	188	9	(	(	PUNCT
cana-3816	188	10	`	`	PUNCT
cana-3816	188	11	1	1	X
cana-3816	188	12	]	]	PUNCT
cana-3816	188	13	if	if	SCONJ
cana-3816	188	14	and	and	CCONJ
cana-3816	188	15	only	only	ADV
cana-3816	188	16	if	if	SCONJ
cana-3816	188	17	(	(	PUNCT
cana-3816	188	18			NOUN
cana-3816	188	19	(	(	PUNCT
cana-3816	188	20	`	`	PUNCT
cana-3816	188	21	]	]	SYM
cana-3816	188	22	)	)	PUNCT
cana-3816	188	23	∝2	∝2	NOUN
cana-3816	188	24	∝1	∝1	NOUN
cana-3816	188	25	6	6	NUM
cana-3816	188	26	(	(	PUNCT
cana-3816	188	27	(`1	(`1	PROPN
cana-3816	188	28	]	]	NOUN
cana-3816	188	29	)	)	PUNCT
cana-3816	188	30	∝2	∝2	NOUN
cana-3816	188	31	∝1	∝1	NOUN
cana-3816	188	32	.	.	PUNCT
cana-3816	188	33	(	(	PUNCT
cana-3816	188	34	ii	ii	NOUN
cana-3816	188	35	)	)	PUNCT
cana-3816	188	36	(	(	PUNCT
cana-3816	188	37	∩j∈j	∩j∈j	NOUN
cana-3816	188	38	(`j	(`j	PROPN
cana-3816	188	39	]	]	SYM
cana-3816	188	40	)	)	PUNCT
cana-3816	188	41	∝2	∝2	NOUN
cana-3816	188	42	∝1	∝1	NOUN
cana-3816	188	43	=	=	PUNCT
cana-3816	188	44	(	(	PUNCT
cana-3816	188	45	∩j∈j	∩j∈j	NUM
cana-3816	188	46	(	(	PUNCT
cana-3816	188	47	`	`	PUNCT
cana-3816	188	48	j	j	PROPN
cana-3816	188	49	]	]	PUNCT
cana-3816	188	50	)	)	PUNCT
cana-3816	188	51	∝2	∝2	NOUN
cana-3816	188	52	∝1	∝1	NOUN
cana-3816	188	53	.	.	PUNCT
cana-3816	189	1	(	(	PUNCT
cana-3816	189	2	iii	iii	X
cana-3816	189	3	)	)	PUNCT
cana-3816	189	4	(	(	PUNCT
cana-3816	189	5	∪j∈j	∪j∈j	X
cana-3816	189	6	(`j	(`j	NOUN
cana-3816	189	7	]	]	SYM
cana-3816	189	8	)	)	PUNCT
cana-3816	189	9	∝2	∝2	NOUN
cana-3816	189	10	∝1	∝1	NOUN
cana-3816	189	11	=	=	SYM
cana-3816	189	12	(	(	PUNCT
cana-3816	189	13	∪j∈j	∪j∈j	X
cana-3816	189	14	(	(	PUNCT
cana-3816	189	15	`	`	PUNCT
cana-3816	189	16	j	j	PROPN
cana-3816	189	17	]	]	PUNCT
cana-3816	189	18	)	)	PUNCT
cana-3816	189	19	∝2	∝2	NOUN
cana-3816	189	20	∝1	∝1	NOUN
cana-3816	189	21	.	.	PUNCT
cana-3816	190	1	theorem	theorem	VERB
cana-3816	190	2	2.16	2.16	NUM
cana-3816	190	3	.	.	PUNCT
cana-3816	191	1	let	let	AUX
cana-3816	191	2	`	`	PUNCT
cana-3816	191	3	be	be	AUX
cana-3816	191	4	an	an	DET
cana-3816	191	5	(	(	PUNCT
cana-3816	191	6	∝1,∝2)iq1afri	∝1,∝2)iq1afri	PROPN
cana-3816	191	7	,	,	PUNCT
cana-3816	191	8	`	`	PUNCT
cana-3816	191	9	1	1	NUM
cana-3816	191	10	be	be	AUX
cana-3816	191	11	an	an	DET
cana-3816	191	12	(	(	PUNCT
cana-3816	191	13	∝1,∝2)iq1aflati	∝1,∝2)iq1aflati	NOUN
cana-3816	191	14	and	and	CCONJ
cana-3816	191	15	`	`	PUNCT
cana-3816	191	16	2	2	NUM
cana-3816	191	17	be	be	AUX
cana-3816	191	18	an	an	DET
cana-3816	191	19	(	(	PUNCT
cana-3816	191	20	∝1,∝2)iq1afli	∝1,∝2)iq1afli	NOUN
cana-3816	191	21	of	of	ADP
cana-3816	191	22	b	b	PROPN
cana-3816	191	23	then	then	ADV
cana-3816	191	24	(	(	PUNCT
cana-3816	191	25	(	(	PUNCT
cana-3816	191	26	`	`	PUNCT
cana-3816	191	27	·	·	PUNCT
cana-3816	191	28	`	`	PUNCT
cana-3816	191	29	1	1	X
cana-3816	191	30	·	·	PUNCT
cana-3816	191	31	`	`	PUNCT
cana-3816	191	32	2])∝2	2])∝2	NUM
cana-3816	191	33	∝1	∝1	NOUN
cana-3816	191	34	⊆	⊆	NUM
cana-3816	191	35	(	(	PUNCT
cana-3816	191	36	`	`	PUNCT
cana-3816	191	37	∩	∩	ADJ
cana-3816	191	38	`	`	PUNCT
cana-3816	191	39	1	1	NUM
cana-3816	191	40	∩	∩	NOUN
cana-3816	191	41	`	`	PUNCT
cana-3816	191	42	2]∝2	2]∝2	NUM
cana-3816	191	43	∝1	∝1	NOUN
cana-3816	191	44	.	.	PUNCT
cana-3816	192	1	proof	proof	NOUN
cana-3816	192	2	.	.	PUNCT
cana-3816	193	1	let	let	VERB
cana-3816	193	2	`	`	PUNCT
cana-3816	193	3	=	=	PUNCT
cana-3816	194	1	[	[	X
cana-3816	194	2	t	t	X
cana-3816	194	3	`	`	PUNCT
cana-3816	194	4	,	,	PUNCT
cana-3816	194	5	>	>	X
cana-3816	194	6	`	`	PUNCT
cana-3816	194	7	]	]	PUNCT
cana-3816	194	8	be	be	AUX
cana-3816	194	9	an	an	DET
cana-3816	194	10	(	(	PUNCT
cana-3816	194	11	∝1,∝2)iq1afri	∝1,∝2)iq1afri	PROPN
cana-3816	194	12	,	,	PUNCT
cana-3816	194	13	`	`	PUNCT
cana-3816	194	14	1	1	NUM
cana-3816	194	15	=	=	SYM
cana-3816	195	1	[	[	X
cana-3816	195	2	t`1	t`1	INTJ
cana-3816	195	3	,	,	PUNCT
cana-3816	195	4	>	>	X
cana-3816	195	5	`	`	PUNCT
cana-3816	195	6	1	1	NUM
cana-3816	195	7	]	]	PUNCT
cana-3816	195	8	be	be	AUX
cana-3816	195	9	an	an	DET
cana-3816	195	10	(	(	PUNCT
cana-3816	195	11	∝1,∝2)iq1aflati	∝1,∝2)iq1aflati	NOUN
cana-3816	195	12	and	and	CCONJ
cana-3816	195	13	`	`	PUNCT
cana-3816	195	14	2	2	NUM
cana-3816	195	15	=	=	SYM
cana-3816	196	1	[	[	X
cana-3816	196	2	t`2	t`2	INTJ
cana-3816	196	3	,	,	PUNCT
cana-3816	196	4	>	>	X
cana-3816	196	5	`	`	PUNCT
cana-3816	196	6	2	2	NUM
cana-3816	196	7	]	]	PUNCT
cana-3816	196	8	be	be	AUX
cana-3816	196	9	an	an	DET
cana-3816	196	10	(	(	PUNCT
cana-3816	196	11	∝1,∝2)iq1afli	∝1,∝2)iq1afli	NOUN
cana-3816	196	12	of	of	ADP
cana-3816	196	13	b.	b.	PROPN
cana-3816	196	14	let	let	VERB
cana-3816	196	15	(	(	PUNCT
cana-3816	196	16	]	]	X
cana-3816	196	17	,	,	PUNCT
cana-3816	196	18	∂	∂	NUM
cana-3816	196	19	,	,	PUNCT
cana-3816	196	20	ø	ø	NOUN
cana-3816	196	21	)	)	PUNCT
cana-3816	196	22	∈	∈	PROPN
cana-3816	196	23	xε	xε	NOUN
cana-3816	196	24	.	.	PUNCT
cana-3816	197	1	if	if	SCONJ
cana-3816	197	2	xε	xε	PROPN
cana-3816	197	3	6=	6=	ADP
cana-3816	197	4	∅	∅	NOUN
cana-3816	197	5	,	,	PUNCT
cana-3816	197	6	then	then	ADV
cana-3816	197	7	ε	ε	PROPN
cana-3816	197	8	6	6	NUM
cana-3816	197	9	]	]	X
cana-3816	197	10	∂ø	∂ø	PROPN
cana-3816	197	11	.	.	PUNCT
cana-3816	198	1	thus	thus	ADV
cana-3816	198	2	t	t	X
cana-3816	198	3	`	`	PUNCT
cana-3816	198	4	(	(	PUNCT
cana-3816	198	5	ε	ε	PROPN
cana-3816	198	6	,	,	PUNCT
cana-3816	198	7	ι	ι	PROPN
cana-3816	198	8	)	)	PUNCT
cana-3816	198	9	6	6	NUM
cana-3816	198	10	t	t	PROPN
cana-3816	198	11	`	`	PUNCT
cana-3816	198	12	(	(	PUNCT
cana-3816	198	13	]	]	X
cana-3816	198	14	∂ø	∂ø	PROPN
cana-3816	198	15	,	,	PUNCT
cana-3816	198	16	ι	ι	PROPN
cana-3816	198	17	)	)	PUNCT
cana-3816	198	18	6	6	NUM
cana-3816	198	19	t	t	PROPN
cana-3816	198	20	`	`	PUNCT
cana-3816	198	21	(	(	PUNCT
cana-3816	198	22	]	]	X
cana-3816	198	23	,	,	PUNCT
cana-3816	198	24	ι	ι	PROPN
cana-3816	198	25	)	)	PUNCT
cana-3816	198	26	and	and	CCONJ
cana-3816	198	27	>	>	PUNCT
cana-3816	198	28	`	`	PUNCT
cana-3816	198	29	(	(	PUNCT
cana-3816	198	30	ε	ε	PROPN
cana-3816	198	31	,	,	PUNCT
cana-3816	198	32	ι	ι	PROPN
cana-3816	198	33	)	)	PUNCT
cana-3816	198	34	>	>	PUNCT
cana-3816	198	35	>	>	PUNCT
cana-3816	198	36	`	`	PUNCT
cana-3816	198	37	(	(	PUNCT
cana-3816	198	38	]	]	X
cana-3816	198	39	∂ø	∂ø	PROPN
cana-3816	198	40	,	,	PUNCT
cana-3816	198	41	ι	ι	PROPN
cana-3816	198	42	)	)	PUNCT
cana-3816	198	43	>	>	PUNCT
cana-3816	198	44	>	>	PUNCT
cana-3816	198	45	`	`	PUNCT
cana-3816	198	46	(	(	PUNCT
cana-3816	198	47	]	]	X
cana-3816	198	48	,	,	PUNCT
cana-3816	198	49	ι	ι	PROPN
cana-3816	198	50	)	)	PUNCT
cana-3816	198	51	.	.	PUNCT
cana-3816	199	1	similarly	similarly	ADV
cana-3816	199	2	t`1	t`1	ADV
cana-3816	199	3	(	(	PUNCT
cana-3816	199	4	ε	ε	PROPN
cana-3816	199	5	,	,	PUNCT
cana-3816	199	6	ι	ι	PROPN
cana-3816	199	7	)	)	PUNCT
cana-3816	199	8	6t`1	6t`1	NOUN
cana-3816	199	9	(	(	PUNCT
cana-3816	199	10	]	]	X
cana-3816	199	11	∂ø	∂ø	PROPN
cana-3816	199	12	,	,	PUNCT
cana-3816	199	13	ι	ι	PROPN
cana-3816	199	14	)	)	PUNCT
cana-3816	199	15	6t`1	6t`1	NOUN
cana-3816	199	16	(	(	PUNCT
cana-3816	199	17	∂	∂	NUM
cana-3816	199	18	,	,	PUNCT
cana-3816	199	19	ι	ι	PROPN
cana-3816	199	20	)	)	PUNCT
cana-3816	199	21	and	and	CCONJ
cana-3816	199	22	>	>	X
cana-3816	199	23	`	`	PUNCT
cana-3816	199	24	1(ε	1(ε	NUM
cana-3816	199	25	,	,	PUNCT
cana-3816	199	26	ι	ι	PROPN
cana-3816	199	27	)	)	PUNCT
cana-3816	199	28	>	>	PUNCT
cana-3816	200	1	>	>	PUNCT
cana-3816	200	2	`	`	PUNCT
cana-3816	200	3	1(]∂ø	1(]∂ø	PROPN
cana-3816	200	4	,	,	PUNCT
cana-3816	200	5	ι	ι	PROPN
cana-3816	200	6	)	)	PUNCT
cana-3816	200	7	>	>	PUNCT
cana-3816	200	8	>	>	PUNCT
cana-3816	200	9	`	`	PUNCT
cana-3816	200	10	1(∂	1(∂	NUM
cana-3816	200	11	,	,	PUNCT
cana-3816	200	12	ι	ι	PROPN
cana-3816	200	13	)	)	PUNCT
cana-3816	200	14	.	.	PUNCT
cana-3816	201	1	similarly	similarly	ADV
cana-3816	201	2	,	,	PUNCT
cana-3816	201	3	t`2	t`2	PROPN
cana-3816	201	4	(	(	PUNCT
cana-3816	201	5	ε	ε	PROPN
cana-3816	201	6	,	,	PUNCT
cana-3816	201	7	ι	ι	NOUN
cana-3816	201	8	)	)	PUNCT
cana-3816	201	9	6t`2	6t`2	NOUN
cana-3816	201	10	(	(	PUNCT
cana-3816	201	11	]	]	X
cana-3816	201	12	∂ø	∂ø	PROPN
cana-3816	201	13	,	,	PUNCT
cana-3816	201	14	ι	ι	PROPN
cana-3816	201	15	)	)	PUNCT
cana-3816	201	16	6t`2	6t`2	NOUN
cana-3816	201	17	(	(	PUNCT
cana-3816	201	18	ø	ø	PROPN
cana-3816	201	19	,	,	PUNCT
cana-3816	201	20	ι	ι	PROPN
cana-3816	201	21	)	)	PUNCT
cana-3816	201	22	and	and	CCONJ
cana-3816	201	23	>	>	PUNCT
cana-3816	201	24	`	`	PUNCT
cana-3816	201	25	2	2	NUM
cana-3816	201	26	(	(	PUNCT
cana-3816	201	27	ε	ε	PROPN
cana-3816	201	28	,	,	PUNCT
cana-3816	201	29	ι	ι	PROPN
cana-3816	201	30	)	)	PUNCT
cana-3816	201	31	>	>	PUNCT
cana-3816	201	32	>	>	PUNCT
cana-3816	201	33	`	`	PUNCT
cana-3816	201	34	2	2	NUM
cana-3816	201	35	(	(	PUNCT
cana-3816	201	36	]	]	X
cana-3816	201	37	∂ø	∂ø	PROPN
cana-3816	201	38	,	,	PUNCT
cana-3816	201	39	ι	ι	PROPN
cana-3816	201	40	)	)	PUNCT
cana-3816	201	41	>	>	PUNCT
cana-3816	202	1	>	>	PUNCT
cana-3816	202	2	`	`	PUNCT
cana-3816	202	3	2	2	NUM
cana-3816	202	4	(	(	PUNCT
cana-3816	202	5	ø	ø	PROPN
cana-3816	202	6	,	,	PUNCT
cana-3816	202	7	ι	ι	PROPN
cana-3816	202	8	)	)	PUNCT
cana-3816	202	9	.	.	PUNCT
cana-3816	203	1	we	we	PRON
cana-3816	203	2	have	have	VERB
cana-3816	203	3	(	(	PUNCT
cana-3816	203	4	t(`·`1·`2	t(`·`1·`2	NOUN
cana-3816	203	5	]	]	X
cana-3816	203	6	)	)	PUNCT
cana-3816	203	7	∝2	∝2	NOUN
cana-3816	203	8	∝1	∝1	NOUN
cana-3816	203	9	(	(	PUNCT
cana-3816	203	10	ε	ε	PROPN
cana-3816	203	11	,	,	PUNCT
cana-3816	203	12	ι	ι	PROPN
cana-3816	203	13	)	)	PUNCT
cana-3816	203	14	=	=	SYM
cana-3816	204	1	(	(	PUNCT
cana-3816	204	2	t(`·`1·`2	t(`·`1·`2	NOUN
cana-3816	204	3	]	]	X
cana-3816	204	4	(	(	PUNCT
cana-3816	204	5	ε	ε	PROPN
cana-3816	204	6	,	,	PUNCT
cana-3816	204	7	ι)5	ι)5	PROPN
cana-3816	204	8	∝2)4	∝2)4	PROPN
cana-3816	204	9	∝1	∝1	X
cana-3816	205	1	=	=	PUNCT
cana-3816	205	2	[	[	PUNCT
cana-3816	205	3	[	[	PUNCT
cana-3816	205	4	inf	inf	NOUN
cana-3816	205	5	ε6]∂ø	ε6]∂ø	PROPN
cana-3816	205	6	{	{	PUNCT
cana-3816	205	7	t	t	PROPN
cana-3816	205	8	`	`	PUNCT
cana-3816	205	9	(	(	PUNCT
cana-3816	205	10	]	]	X
cana-3816	205	11	,	,	PUNCT
cana-3816	205	12	ι)5	ι)5	PROPN
cana-3816	205	13	t`1	t`1	NOUN
cana-3816	205	14	(	(	PUNCT
cana-3816	205	15	∂	∂	NUM
cana-3816	205	16	,	,	PUNCT
cana-3816	205	17	ι)5	ι)5	PROPN
cana-3816	205	18	t`2	t`2	NOUN
cana-3816	205	19	(	(	PUNCT
cana-3816	205	20	ø	ø	PROPN
cana-3816	205	21	,	,	PUNCT
cana-3816	205	22	ι)}5	ι)}5	PROPN
cana-3816	205	23	∝2	∝2	PROPN
cana-3816	205	24	]	]	X
cana-3816	205	25	]	]	PUNCT
cana-3816	205	26	4	4	NUM
cana-3816	205	27	∝1	∝1	NOUN
cana-3816	205	28	=	=	PUNCT
cana-3816	205	29	[	[	PUNCT
cana-3816	205	30	inf	inf	NOUN
cana-3816	205	31	ε6]∂ø	ε6]∂ø	PROPN
cana-3816	205	32	{	{	PUNCT
cana-3816	205	33	t	t	PROPN
cana-3816	205	34	`	`	PUNCT
cana-3816	205	35	(	(	PUNCT
cana-3816	205	36	]	]	X
cana-3816	205	37	,	,	PUNCT
cana-3816	205	38	ι)5	ι)5	PROPN
cana-3816	205	39	t`1	t`1	NOUN
cana-3816	205	40	(	(	PUNCT
cana-3816	205	41	∂	∂	NUM
cana-3816	205	42	,	,	PUNCT
cana-3816	205	43	ι)5	ι)5	PROPN
cana-3816	205	44	t`2	t`2	NOUN
cana-3816	205	45	(	(	PUNCT
cana-3816	205	46	ø	ø	PROPN
cana-3816	205	47	,	,	PUNCT
cana-3816	205	48	ι)}5	ι)}5	PROPN
cana-3816	205	49	∝2	∝2	PROPN
cana-3816	205	50	5	5	NUM
cana-3816	205	51	∝2	∝2	PROPN
cana-3816	205	52	5	5	NUM
cana-3816	205	53	∝2	∝2	PROPN
cana-3816	205	54	5	5	NUM
cana-3816	205	55	∝2	∝2	NOUN
cana-3816	205	56	]	]	PUNCT
cana-3816	205	57	4	4	NUM
cana-3816	205	58	∝1	∝1	NOUN
cana-3816	205	59	=	=	PUNCT
cana-3816	205	60	[	[	PUNCT
cana-3816	205	61	inf	inf	NOUN
cana-3816	205	62	ε6]∂ø	ε6]∂ø	X
cana-3816	205	63	{	{	PUNCT
cana-3816	205	64	(	(	PUNCT
cana-3816	205	65	t	t	NOUN
cana-3816	205	66	`	`	PUNCT
cana-3816	205	67	(	(	PUNCT
cana-3816	205	68	]	]	X
cana-3816	205	69	,	,	PUNCT
cana-3816	205	70	ι)5	ι)5	PROPN
cana-3816	205	71	∝2)5	∝2)5	PROPN
cana-3816	205	72	(	(	PUNCT
cana-3816	205	73	t`1	t`1	X
cana-3816	205	74	(	(	PUNCT
cana-3816	205	75	∂	∂	NUM
cana-3816	205	76	,	,	PUNCT
cana-3816	205	77	ι)5	ι)5	PROPN
cana-3816	205	78	∝2)5	∝2)5	PROPN
cana-3816	205	79	(	(	PUNCT
cana-3816	205	80	t`2	t`2	X
cana-3816	205	81	(	(	PUNCT
cana-3816	205	82	ø	ø	PROPN
cana-3816	205	83	,	,	PUNCT
cana-3816	205	84	ι)5	ι)5	PROPN
cana-3816	205	85	∝2)}5	∝2)}5	ADJ
cana-3816	205	86	∝2	∝2	NOUN
cana-3816	205	87	]	]	PUNCT
cana-3816	205	88	4	4	NUM
cana-3816	205	89	∝1	∝1	NOUN
cana-3816	205	90	>	>	X
cana-3816	205	91	(	(	PUNCT
cana-3816	205	92	{	{	PUNCT
cana-3816	205	93	(	(	PUNCT
cana-3816	205	94	t	t	NOUN
cana-3816	205	95	`	`	PUNCT
cana-3816	205	96	(	(	PUNCT
cana-3816	205	97	ε	ε	PROPN
cana-3816	205	98	,	,	PUNCT
cana-3816	205	99	ι)4	ι)4	X
cana-3816	205	100	∝1)5	∝1)5	PROPN
cana-3816	205	101	(	(	PUNCT
cana-3816	205	102	t`1	t`1	X
cana-3816	205	103	(	(	PUNCT
cana-3816	205	104	ε	ε	PROPN
cana-3816	205	105	,	,	PUNCT
cana-3816	205	106	ι)4	ι)4	X
cana-3816	205	107	∝1)5	∝1)5	PROPN
cana-3816	205	108	(	(	PUNCT
cana-3816	205	109	t`2	t`2	X
cana-3816	205	110	(	(	PUNCT
cana-3816	205	111	ε	ε	PROPN
cana-3816	205	112	,	,	PUNCT
cana-3816	205	113	ι)4	ι)4	PROPN
cana-3816	205	114	∝1)}5	∝1)}5	PROPN
cana-3816	205	115	∝2)4	∝2)4	PROPN
cana-3816	205	116	∝1	∝1	ADJ
cana-3816	205	117	=	=	PRON
cana-3816	205	118	{	{	PUNCT
cana-3816	205	119	(	(	PUNCT
cana-3816	205	120	(	(	PUNCT
cana-3816	205	121	t	t	NOUN
cana-3816	205	122	`	`	PUNCT
cana-3816	205	123	(	(	PUNCT
cana-3816	205	124	ε	ε	PROPN
cana-3816	205	125	,	,	PUNCT
cana-3816	205	126	ι)5	ι)5	PROPN
cana-3816	205	127	t`1	t`1	NOUN
cana-3816	205	128	(	(	PUNCT
cana-3816	205	129	ε	ε	PROPN
cana-3816	205	130	,	,	PUNCT
cana-3816	205	131	ι)5	ι)5	PROPN
cana-3816	205	132	t`2	t`2	NOUN
cana-3816	205	133	(	(	PUNCT
cana-3816	205	134	ε	ε	PROPN
cana-3816	205	135	,	,	PUNCT
cana-3816	205	136	ι))4	ι))4	NUM
cana-3816	205	137	∝1)5	∝1)5	NOUN
cana-3816	205	138	∝2}4	∝2}4	NOUN
cana-3816	205	139	∝1	∝1	NUM
cana-3816	206	1	=	=	PRON
cana-3816	206	2	{	{	PUNCT
cana-3816	206	3	(	(	PUNCT
cana-3816	206	4	(	(	PUNCT
cana-3816	206	5	t	t	NOUN
cana-3816	206	6	`	`	NUM
cana-3816	206	7	5	5	NUM
cana-3816	206	8	t`1	t`1	NOUN
cana-3816	206	9	5	5	NUM
cana-3816	206	10	t`2)(ε	t`2)(ε	NOUN
cana-3816	206	11	,	,	PUNCT
cana-3816	206	12	ι)5	ι)5	X
cana-3816	206	13	∝2}4	∝2}4	NOUN
cana-3816	206	14	∝1	∝1	NUM
cana-3816	206	15	=	=	PUNCT
cana-3816	206	16	(	(	PUNCT
cana-3816	206	17	t`∩`1∩`2	t`∩`1∩`2	NOUN
cana-3816	206	18	)	)	PUNCT
cana-3816	206	19	∝2	∝2	NOUN
cana-3816	206	20	∝1	∝1	NOUN
cana-3816	206	21	(	(	PUNCT
cana-3816	206	22	ε	ε	PROPN
cana-3816	206	23	,	,	PUNCT
cana-3816	206	24	ι	ι	PROPN
cana-3816	206	25	)	)	PUNCT
cana-3816	206	26	https://internationalpubls.com	https://internationalpubls.com	X
cana-3816	206	27	766	766	NUM
cana-3816	206	28	communications	communication	NOUN
cana-3816	206	29	on	on	ADP
cana-3816	206	30	applied	apply	VERB
cana-3816	206	31	nonlinear	nonlinear	ADJ
cana-3816	206	32	analysis	analysis	NOUN
cana-3816	206	33	issn	issn	NOUN
cana-3816	206	34	:	:	PUNCT
cana-3816	206	35	1074	1074	NUM
cana-3816	206	36	-	-	PUNCT
cana-3816	206	37	133x	133x	NUM
cana-3816	206	38	vol	vol	NOUN
cana-3816	206	39	32	32	NUM
cana-3816	206	40	no	no	NOUN
cana-3816	206	41	.	.	NOUN
cana-3816	206	42	3	3	NUM
cana-3816	206	43	(	(	PUNCT
cana-3816	206	44	2025	2025	NUM
cana-3816	206	45	)	)	PUNCT
cana-3816	206	46	(	(	PUNCT
cana-3816	206	47	>	>	X
cana-3816	206	48	(	(	PUNCT
cana-3816	206	49	`	`	PUNCT
cana-3816	206	50	·	·	PUNCT
cana-3816	206	51	`	`	PUNCT
cana-3816	206	52	1·`2	1·`2	NUM
cana-3816	206	53	]	]	SYM
cana-3816	206	54	)	)	PUNCT
cana-3816	206	55	∝2	∝2	NOUN
cana-3816	206	56	∝1	∝1	NOUN
cana-3816	206	57	(	(	PUNCT
cana-3816	206	58	ε	ε	PROPN
cana-3816	206	59	,	,	PUNCT
cana-3816	206	60	ι	ι	PROPN
cana-3816	206	61	)	)	PUNCT
cana-3816	206	62	=	=	SYM
cana-3816	206	63	(	(	PUNCT
cana-3816	206	64	>	>	X
cana-3816	206	65	(	(	PUNCT
cana-3816	206	66	`	`	PUNCT
cana-3816	206	67	·	·	PUNCT
cana-3816	206	68	`	`	PUNCT
cana-3816	206	69	1·`2](ε	1·`2](ε	NUM
cana-3816	206	70	,	,	PUNCT
cana-3816	206	71	ι)4	ι)4	PROPN
cana-3816	206	72	∝2)5	∝2)5	PROPN
cana-3816	206	73	∝1	∝1	X
cana-3816	207	1	=	=	PUNCT
cana-3816	207	2	[	[	PUNCT
cana-3816	207	3	[	[	PUNCT
cana-3816	207	4	sup	sup	NOUN
cana-3816	207	5	ε6]∂ø	ε6]∂ø	PROPN
cana-3816	207	6	{	{	PUNCT
cana-3816	207	7	>	>	X
cana-3816	207	8	`	`	PUNCT
cana-3816	207	9	(	(	PUNCT
cana-3816	207	10	]	]	X
cana-3816	207	11	,	,	PUNCT
cana-3816	207	12	ι)4>`1	ι)4>`1	NOUN
cana-3816	207	13	(	(	PUNCT
cana-3816	207	14	∂	∂	NUM
cana-3816	207	15	,	,	PUNCT
cana-3816	207	16	ι)4>`2	ι)4>`2	X
cana-3816	207	17	(	(	PUNCT
cana-3816	207	18	ø	ø	X
cana-3816	207	19	,	,	PUNCT
cana-3816	207	20	ι)}4	ι)}4	PROPN
cana-3816	207	21	∝2	∝2	PROPN
cana-3816	207	22	]	]	X
cana-3816	207	23	]	]	PUNCT
cana-3816	207	24	5	5	NUM
cana-3816	207	25	∝1	∝1	NOUN
cana-3816	207	26	=	=	PUNCT
cana-3816	207	27	[	[	PUNCT
cana-3816	207	28	sup	sup	NOUN
cana-3816	207	29	ε6]∂ø	ε6]∂ø	PROPN
cana-3816	207	30	{	{	PUNCT
cana-3816	207	31	>	>	X
cana-3816	207	32	`	`	PUNCT
cana-3816	207	33	(	(	PUNCT
cana-3816	207	34	]	]	X
cana-3816	207	35	,	,	PUNCT
cana-3816	207	36	ι)4>`1	ι)4>`1	NOUN
cana-3816	207	37	(	(	PUNCT
cana-3816	207	38	∂	∂	NUM
cana-3816	207	39	,	,	PUNCT
cana-3816	207	40	ι)4>`2	ι)4>`2	X
cana-3816	207	41	(	(	PUNCT
cana-3816	207	42	ø	ø	X
cana-3816	207	43	,	,	PUNCT
cana-3816	207	44	ι)}4	ι)}4	PROPN
cana-3816	207	45	∝2	∝2	PROPN
cana-3816	207	46	4	4	NUM
cana-3816	207	47	∝2	∝2	NOUN
cana-3816	207	48	4	4	NUM
cana-3816	207	49	∝2	∝2	NOUN
cana-3816	207	50	4	4	NUM
cana-3816	207	51	∝2	∝2	NOUN
cana-3816	207	52	]	]	PUNCT
cana-3816	207	53	5	5	NUM
cana-3816	207	54	∝1	∝1	NOUN
cana-3816	207	55	=	=	PUNCT
cana-3816	207	56	[	[	PUNCT
cana-3816	207	57	sup	sup	NOUN
cana-3816	207	58	ε6]∂ø	ε6]∂ø	PROPN
cana-3816	207	59	{	{	PUNCT
cana-3816	207	60	(	(	PUNCT
cana-3816	207	61	>	>	X
cana-3816	207	62	`	`	PUNCT
cana-3816	207	63	(	(	PUNCT
cana-3816	207	64	]	]	X
cana-3816	207	65	,	,	PUNCT
cana-3816	207	66	ι)4	ι)4	PROPN
cana-3816	207	67	∝2)4	∝2)4	PROPN
cana-3816	207	68	(	(	PUNCT
cana-3816	207	69	>	>	X
cana-3816	207	70	`	`	PUNCT
cana-3816	207	71	1	1	NUM
cana-3816	207	72	(	(	PUNCT
cana-3816	207	73	∂	∂	NUM
cana-3816	207	74	,	,	PUNCT
cana-3816	207	75	ι)4	ι)4	PROPN
cana-3816	207	76	∝2)4	∝2)4	PROPN
cana-3816	207	77	(	(	PUNCT
cana-3816	207	78	>	>	X
cana-3816	207	79	`	`	PUNCT
cana-3816	207	80	2	2	NUM
cana-3816	207	81	(	(	PUNCT
cana-3816	207	82	ø	ø	PROPN
cana-3816	207	83	,	,	PUNCT
cana-3816	207	84	ι)4	ι)4	PROPN
cana-3816	207	85	∝2)}4	∝2)}4	NUM
cana-3816	207	86	∝2	∝2	NOUN
cana-3816	207	87	]	]	PUNCT
cana-3816	207	88	5	5	NUM
cana-3816	207	89	∝1	∝1	NUM
cana-3816	207	90	6	6	NUM
cana-3816	207	91	(	(	PUNCT
cana-3816	207	92	{	{	PUNCT
cana-3816	207	93	(	(	PUNCT
cana-3816	207	94	>	>	X
cana-3816	207	95	`	`	PUNCT
cana-3816	207	96	(	(	PUNCT
cana-3816	207	97	ε	ε	PROPN
cana-3816	207	98	,	,	PUNCT
cana-3816	207	99	ι)5	ι)5	PROPN
cana-3816	207	100	∝1)4	∝1)4	PROPN
cana-3816	207	101	(	(	PUNCT
cana-3816	207	102	>	>	X
cana-3816	207	103	`	`	PUNCT
cana-3816	207	104	1	1	NUM
cana-3816	207	105	(	(	PUNCT
cana-3816	207	106	ε	ε	PROPN
cana-3816	207	107	,	,	PUNCT
cana-3816	207	108	ι)5	ι)5	PROPN
cana-3816	207	109	∝1)4	∝1)4	PROPN
cana-3816	207	110	(	(	PUNCT
cana-3816	207	111	>	>	X
cana-3816	207	112	`	`	PUNCT
cana-3816	207	113	2	2	NUM
cana-3816	207	114	(	(	PUNCT
cana-3816	207	115	ε	ε	PROPN
cana-3816	207	116	,	,	PUNCT
cana-3816	207	117	ι)5	ι)5	NOUN
cana-3816	207	118	∝1)}4	∝1)}4	PROPN
cana-3816	207	119	∝2)5	∝2)5	PROPN
cana-3816	207	120	∝1	∝1	X
cana-3816	207	121	=	=	PRON
cana-3816	207	122	{	{	PUNCT
cana-3816	207	123	(	(	PUNCT
cana-3816	207	124	(	(	PUNCT
cana-3816	207	125	>	>	X
cana-3816	207	126	`	`	PUNCT
cana-3816	207	127	(	(	PUNCT
cana-3816	207	128	ε	ε	PROPN
cana-3816	207	129	,	,	PUNCT
cana-3816	207	130	ι)4>`1	ι)4>`1	X
cana-3816	207	131	(	(	PUNCT
cana-3816	207	132	ε	ε	PROPN
cana-3816	207	133	,	,	PUNCT
cana-3816	207	134	ι)4>`2	ι)4>`2	X
cana-3816	207	135	(	(	PUNCT
cana-3816	207	136	ε	ε	PROPN
cana-3816	207	137	,	,	PUNCT
cana-3816	207	138	ι))5	ι))5	ADP
cana-3816	207	139	∝1)4	∝1)4	PROPN
cana-3816	207	140	∝2}5	∝2}5	PROPN
cana-3816	207	141	∝1	∝1	NOUN
cana-3816	207	142	=	=	PUNCT
cana-3816	207	143	{	{	PUNCT
cana-3816	207	144	(	(	PUNCT
cana-3816	207	145	(	(	PUNCT
cana-3816	207	146	>	>	X
cana-3816	207	147	`	`	PUNCT
cana-3816	207	148	4>`1	4>`1	NUM
cana-3816	207	149	4>`2	4>`2	NUM
cana-3816	207	150	)	)	PUNCT
cana-3816	207	151	(	(	PUNCT
cana-3816	207	152	ε	ε	PROPN
cana-3816	207	153	,	,	PUNCT
cana-3816	207	154	ι)4	ι)4	PROPN
cana-3816	207	155	∝2}5	∝2}5	PROPN
cana-3816	207	156	∝1	∝1	NUM
cana-3816	207	157	=	=	PUNCT
cana-3816	207	158	(	(	PUNCT
cana-3816	207	159	>	>	X
cana-3816	207	160	`	`	PUNCT
cana-3816	207	161	∪`1∪`2	∪`1∪`2	NUM
cana-3816	207	162	)	)	PUNCT
cana-3816	207	163	∝2	∝2	NOUN
cana-3816	207	164	∝1	∝1	NOUN
cana-3816	207	165	(	(	PUNCT
cana-3816	207	166	ε	ε	PROPN
cana-3816	207	167	,	,	PUNCT
cana-3816	207	168	ι	ι	PRON
cana-3816	207	169	)	)	PUNCT
cana-3816	207	170	let	let	VERB
cana-3816	207	171	]	]	X
cana-3816	207	172	,	,	PUNCT
cana-3816	207	173	∂	∂	NUM
cana-3816	207	174	,	,	PUNCT
cana-3816	207	175	ø	ø	PROPN
cana-3816	207	176	/∈	/∈	PUNCT
cana-3816	207	177	xε	xε	PROPN
cana-3816	207	178	.	.	PUNCT
cana-3816	208	1	if	if	SCONJ
cana-3816	208	2	xε	xε	NUM
cana-3816	208	3	=	=	NOUN
cana-3816	208	4	∅	∅	NOUN
cana-3816	208	5	,	,	PUNCT
cana-3816	208	6	then	then	ADV
cana-3816	208	7	(	(	PUNCT
cana-3816	208	8	t	t	NOUN
cana-3816	208	9	`	`	PUNCT
cana-3816	208	10	·	·	PUNCT
cana-3816	208	11	`	`	PUNCT
cana-3816	208	12	1	1	NUM
cana-3816	208	13	·	·	SYM
cana-3816	208	14	t`2	t`2	NOUN
cana-3816	208	15	)	)	PUNCT
cana-3816	208	16	(	(	PUNCT
cana-3816	208	17	ε	ε	PROPN
cana-3816	208	18	,	,	PUNCT
cana-3816	208	19	ι	ι	PROPN
cana-3816	208	20	)	)	PUNCT
cana-3816	208	21	=	=	SYM
cana-3816	208	22	1	1	NUM
cana-3816	208	23	and	and	CCONJ
cana-3816	208	24	(	(	PUNCT
cana-3816	208	25	>	>	X
cana-3816	208	26	`	`	PUNCT
cana-3816	208	27	·	·	PUNCT
cana-3816	208	28	`	`	PUNCT
cana-3816	208	29	1	1	X
cana-3816	208	30	·	·	PUNCT
cana-3816	208	31	>	>	PUNCT
cana-3816	208	32	`	`	PUNCT
cana-3816	208	33	2	2	NUM
cana-3816	208	34	)	)	PUNCT
cana-3816	208	35	(	(	PUNCT
cana-3816	208	36	ε	ε	PROPN
cana-3816	208	37	,	,	PUNCT
cana-3816	208	38	ι	ι	PROPN
cana-3816	208	39	)	)	PUNCT
cana-3816	208	40	=	=	SYM
cana-3816	208	41	0	0	NUM
cana-3816	208	42	such	such	ADJ
cana-3816	208	43	that	that	SCONJ
cana-3816	208	44	ε	ε	PROPN
cana-3816	208	45	6	6	NUM
cana-3816	208	46	]	]	X
cana-3816	208	47	∂ø	∂ø	PROPN
cana-3816	208	48	.	.	PUNCT
cana-3816	209	1	(	(	PUNCT
cana-3816	209	2	t(`·`1·`2	t(`·`1·`2	NOUN
cana-3816	209	3	]	]	X
cana-3816	209	4	)	)	PUNCT
cana-3816	209	5	∝2	∝2	NOUN
cana-3816	209	6	∝1	∝1	NOUN
cana-3816	209	7	(	(	PUNCT
cana-3816	209	8	ε	ε	PROPN
cana-3816	209	9	,	,	PUNCT
cana-3816	209	10	ι	ι	PROPN
cana-3816	209	11	)	)	PUNCT
cana-3816	209	12	=	=	SYM
cana-3816	210	1	(	(	PUNCT
cana-3816	210	2	t(`·`1·`2	t(`·`1·`2	NOUN
cana-3816	210	3	]	]	X
cana-3816	210	4	(	(	PUNCT
cana-3816	210	5	ε	ε	PROPN
cana-3816	210	6	,	,	PUNCT
cana-3816	210	7	ι)5	ι)5	PROPN
cana-3816	210	8	∝2)4	∝2)4	PROPN
cana-3816	210	9	∝1	∝1	ADJ
cana-3816	210	10	=	=	PUNCT
cana-3816	210	11	14	14	NUM
cana-3816	210	12	∝1	∝1	NOUN
cana-3816	210	13	>	>	X
cana-3816	210	14	(	(	PUNCT
cana-3816	210	15	t`∩`1∩`2	t`∩`1∩`2	X
cana-3816	210	16	(	(	PUNCT
cana-3816	210	17	ε	ε	PROPN
cana-3816	210	18	,	,	PUNCT
cana-3816	210	19	ι)5	ι)5	PROPN
cana-3816	210	20	∝2)4	∝2)4	PROPN
cana-3816	210	21	∝1	∝1	ADJ
cana-3816	210	22	=	=	PUNCT
cana-3816	210	23	(	(	PUNCT
cana-3816	210	24	t`∩`1∩`2	t`∩`1∩`2	X
cana-3816	210	25	(	(	PUNCT
cana-3816	210	26	ε	ε	PROPN
cana-3816	210	27	,	,	PUNCT
cana-3816	210	28	ι)5	ι)5	PROPN
cana-3816	210	29	∝2	∝2	PROPN
cana-3816	210	30	)	)	PUNCT
cana-3816	210	31	(	(	PUNCT
cana-3816	210	32	>	>	X
cana-3816	210	33	(	(	PUNCT
cana-3816	210	34	`	`	PUNCT
cana-3816	210	35	·	·	PUNCT
cana-3816	210	36	`	`	PUNCT
cana-3816	210	37	1·`2	1·`2	NUM
cana-3816	210	38	]	]	SYM
cana-3816	210	39	)	)	PUNCT
cana-3816	210	40	∝2	∝2	NOUN
cana-3816	210	41	∝1	∝1	NOUN
cana-3816	210	42	(	(	PUNCT
cana-3816	210	43	ε	ε	PROPN
cana-3816	210	44	,	,	PUNCT
cana-3816	210	45	ι	ι	PROPN
cana-3816	210	46	)	)	PUNCT
cana-3816	210	47	=	=	SYM
cana-3816	210	48	(	(	PUNCT
cana-3816	210	49	>	>	X
cana-3816	210	50	(	(	PUNCT
cana-3816	210	51	`	`	PUNCT
cana-3816	210	52	·	·	PUNCT
cana-3816	210	53	`	`	PUNCT
cana-3816	210	54	1·`2](ε	1·`2](ε	NUM
cana-3816	210	55	,	,	PUNCT
cana-3816	210	56	ι)4	ι)4	PROPN
cana-3816	210	57	∝2)5	∝2)5	PROPN
cana-3816	210	58	∝1	∝1	AUX
cana-3816	210	59	=	=	PUNCT
cana-3816	211	1	05	05	NUM
cana-3816	211	2	∝1	∝1	X
cana-3816	212	1	=	=	SYM
cana-3816	212	2	∝1	∝1	NOUN
cana-3816	212	3	6	6	NUM
cana-3816	212	4	(	(	PUNCT
cana-3816	212	5	>	>	PUNCT
cana-3816	212	6	`	`	PUNCT
cana-3816	212	7	∪`1∪`2(ε	∪`1∪`2(ε	PROPN
cana-3816	212	8	,	,	PUNCT
cana-3816	212	9	ι)4	ι)4	PROPN
cana-3816	212	10	∝2)5	∝2)5	PROPN
cana-3816	212	11	∝1	∝1	NOUN
cana-3816	212	12	=	=	PUNCT
cana-3816	212	13	(	(	PUNCT
cana-3816	212	14	>	>	X
cana-3816	212	15	`	`	PUNCT
cana-3816	212	16	∪`1∪`2(ε	∪`1∪`2(ε	PROPN
cana-3816	212	17	,	,	PUNCT
cana-3816	212	18	ι)4	ι)4	PROPN
cana-3816	212	19	∝2	∝2	PROPN
cana-3816	212	20	)	)	PUNCT
cana-3816	212	21	therefore	therefore	ADV
cana-3816	212	22	(	(	PUNCT
cana-3816	212	23	(	(	PUNCT
cana-3816	212	24	`	`	PUNCT
cana-3816	212	25	·	·	PUNCT
cana-3816	212	26	`	`	PUNCT
cana-3816	212	27	1·`2])∝2	1·`2])∝2	NUM
cana-3816	212	28	∝1	∝1	X
cana-3816	212	29	⊆	⊆	NUM
cana-3816	212	30	(	(	PUNCT
cana-3816	212	31	(	(	PUNCT
cana-3816	212	32	`	`	PUNCT
cana-3816	212	33	∩	∩	ADJ
cana-3816	212	34	`	`	PUNCT
cana-3816	212	35	1	1	NUM
cana-3816	212	36	∩	∩	NOUN
cana-3816	212	37	`	`	PUNCT
cana-3816	212	38	2])∝2	2])∝2	NUM
cana-3816	212	39	∝1	∝1	NUM
cana-3816	212	40	.	.	PUNCT
cana-3816	213	1	theorem	theorem	VERB
cana-3816	213	2	2.17	2.17	NUM
cana-3816	213	3	.	.	PUNCT
cana-3816	214	1	an	an	DET
cana-3816	214	2	ordered	order	VERB
cana-3816	214	3	-semigroup	-semigroup	NOUN
cana-3816	214	4	b	b	NOUN
cana-3816	214	5	is	be	AUX
cana-3816	214	6	regular	regular	ADJ
cana-3816	214	7	,	,	PUNCT
cana-3816	214	8	`	`	PUNCT
cana-3816	214	9	be	be	AUX
cana-3816	214	10	an	an	DET
cana-3816	214	11	(	(	PUNCT
cana-3816	214	12	∝1,∝2)iq1afri	∝1,∝2)iq1afri	PROPN
cana-3816	214	13	,	,	PUNCT
cana-3816	214	14	`	`	PUNCT
cana-3816	214	15	1	1	NUM
cana-3816	214	16	be	be	AUX
cana-3816	214	17	an	an	DET
cana-3816	214	18	(	(	PUNCT
cana-3816	214	19	∝1,∝2)iq1aflati	∝1,∝2)iq1aflati	NOUN
cana-3816	214	20	and	and	CCONJ
cana-3816	214	21	`	`	PUNCT
cana-3816	214	22	2	2	NUM
cana-3816	214	23	be	be	AUX
cana-3816	214	24	an	an	DET
cana-3816	214	25	(	(	PUNCT
cana-3816	214	26	∝1,∝2)iq1afli	∝1,∝2)iq1afli	NOUN
cana-3816	214	27	of	of	ADP
cana-3816	214	28	b	b	PROPN
cana-3816	215	1	if	if	SCONJ
cana-3816	215	2	and	and	CCONJ
cana-3816	215	3	only	only	ADV
cana-3816	215	4	if	if	SCONJ
cana-3816	215	5	(	(	PUNCT
cana-3816	215	6	(	(	PUNCT
cana-3816	215	7	`	`	PUNCT
cana-3816	215	8	·	·	PUNCT
cana-3816	215	9	`	`	PUNCT
cana-3816	215	10	1	1	X
cana-3816	215	11	·	·	PUNCT
cana-3816	215	12	`	`	PUNCT
cana-3816	215	13	2])∝2	2])∝2	NUM
cana-3816	215	14	∝1	∝1	X
cana-3816	215	15	=	=	PUNCT
cana-3816	215	16	(	(	PUNCT
cana-3816	215	17	(	(	PUNCT
cana-3816	215	18	`	`	PUNCT
cana-3816	215	19	∩	∩	ADJ
cana-3816	215	20	`	`	PUNCT
cana-3816	215	21	1	1	NUM
cana-3816	215	22	∩	∩	NOUN
cana-3816	215	23	`	`	PUNCT
cana-3816	215	24	2])∝2	2])∝2	NUM
cana-3816	215	25	∝1	∝1	NUM
cana-3816	215	26	.	.	PUNCT
cana-3816	216	1	proof	proof	NOUN
cana-3816	216	2	.	.	PUNCT
cana-3816	217	1	let	let	VERB
cana-3816	217	2	b	b	X
cana-3816	217	3	be	be	AUX
cana-3816	217	4	an	an	DET
cana-3816	217	5	ordered	order	VERB
cana-3816	217	6	-regular	-regular	ADJ
cana-3816	217	7	ternary	ternary	ADJ
cana-3816	217	8	semigroup	semigroup	NOUN
cana-3816	217	9	and	and	CCONJ
cana-3816	217	10	`	`	PUNCT
cana-3816	217	11	be	be	AUX
cana-3816	217	12	an	an	DET
cana-3816	217	13	(	(	PUNCT
cana-3816	217	14	∝1,∝2)iq1afri	∝1,∝2)iq1afri	PROPN
cana-3816	217	15	,	,	PUNCT
cana-3816	217	16	`	`	PUNCT
cana-3816	217	17	1	1	NUM
cana-3816	217	18	be	be	AUX
cana-3816	217	19	an	an	DET
cana-3816	217	20	(	(	PUNCT
cana-3816	217	21	∝1,∝2	∝1,∝2	PROPN
cana-3816	217	22	)	)	PUNCT
cana-3816	217	23	iq1aflati	iq1aflati	PUNCT
cana-3816	218	1	and	and	CCONJ
cana-3816	218	2	`	`	PUNCT
cana-3816	218	3	2	2	NUM
cana-3816	218	4	be	be	AUX
cana-3816	218	5	an	an	DET
cana-3816	218	6	(	(	PUNCT
cana-3816	218	7	∝1,∝2)iq1afli	∝1,∝2)iq1afli	NOUN
cana-3816	218	8	of	of	ADP
cana-3816	218	9	b.	b.	PROPN
cana-3816	218	10	let	let	VERB
cana-3816	218	11	(	(	PUNCT
cana-3816	218	12	]	]	X
cana-3816	218	13	,	,	PUNCT
cana-3816	218	14	ø	ø	X
cana-3816	218	15	)	)	PUNCT
cana-3816	218	16	∈	∈	PROPN
cana-3816	218	17	xε	xε	NOUN
cana-3816	218	18	.	.	PUNCT
cana-3816	219	1	if	if	SCONJ
cana-3816	219	2	xε	xε	PROPN
cana-3816	219	3	6=	6=	ADP
cana-3816	219	4	∅	∅	NOUN
cana-3816	219	5	,	,	PUNCT
cana-3816	219	6	then	then	ADV
cana-3816	219	7	ε	ε	PROPN
cana-3816	219	8	6	6	NUM
cana-3816	219	9	]	]	X
cana-3816	219	10	∂ø	∂ø	PROPN
cana-3816	219	11	.	.	PUNCT
cana-3816	220	1	thus	thus	ADV
cana-3816	220	2	t	t	X
cana-3816	220	3	`	`	PUNCT
cana-3816	220	4	(	(	PUNCT
cana-3816	220	5	ε	ε	PROPN
cana-3816	220	6	,	,	PUNCT
cana-3816	220	7	ι	ι	PROPN
cana-3816	220	8	)	)	PUNCT
cana-3816	220	9	6	6	NUM
cana-3816	220	10	t	t	PROPN
cana-3816	220	11	`	`	PUNCT
cana-3816	220	12	(	(	PUNCT
cana-3816	220	13	]	]	X
cana-3816	220	14	∂ø	∂ø	PROPN
cana-3816	220	15	,	,	PUNCT
cana-3816	220	16	ι	ι	PROPN
cana-3816	220	17	)	)	PUNCT
cana-3816	220	18	6	6	NUM
cana-3816	220	19	t	t	PROPN
cana-3816	220	20	`	`	PUNCT
cana-3816	220	21	(	(	PUNCT
cana-3816	220	22	]	]	X
cana-3816	220	23	,	,	PUNCT
cana-3816	220	24	ι	ι	PROPN
cana-3816	220	25	)	)	PUNCT
cana-3816	220	26	and	and	CCONJ
cana-3816	220	27	>	>	PUNCT
cana-3816	220	28	`	`	PUNCT
cana-3816	220	29	(	(	PUNCT
cana-3816	220	30	ε	ε	PROPN
cana-3816	220	31	,	,	PUNCT
cana-3816	220	32	ι	ι	PROPN
cana-3816	220	33	)	)	PUNCT
cana-3816	220	34	>	>	PUNCT
cana-3816	220	35	>	>	PUNCT
cana-3816	220	36	`	`	PUNCT
cana-3816	220	37	(	(	PUNCT
cana-3816	220	38	]	]	X
cana-3816	220	39	∂ø	∂ø	PROPN
cana-3816	220	40	,	,	PUNCT
cana-3816	220	41	ι	ι	PROPN
cana-3816	220	42	)	)	PUNCT
cana-3816	220	43	>	>	PUNCT
cana-3816	220	44	>	>	PUNCT
cana-3816	220	45	`	`	PUNCT
cana-3816	220	46	(	(	PUNCT
cana-3816	220	47	]	]	X
cana-3816	220	48	,	,	PUNCT
cana-3816	220	49	ι	ι	PROPN
cana-3816	220	50	)	)	PUNCT
cana-3816	220	51	.	.	PUNCT
cana-3816	221	1	similarly	similarly	ADV
cana-3816	221	2	t`1	t`1	ADV
cana-3816	221	3	(	(	PUNCT
cana-3816	221	4	ε	ε	PROPN
cana-3816	221	5	,	,	PUNCT
cana-3816	221	6	ι	ι	PROPN
cana-3816	221	7	)	)	PUNCT
cana-3816	221	8	6t`1	6t`1	NOUN
cana-3816	221	9	(	(	PUNCT
cana-3816	221	10	]	]	X
cana-3816	221	11	∂ø	∂ø	PROPN
cana-3816	221	12	,	,	PUNCT
cana-3816	221	13	ι	ι	PROPN
cana-3816	221	14	)	)	PUNCT
cana-3816	221	15	6t`1	6t`1	NOUN
cana-3816	221	16	(	(	PUNCT
cana-3816	221	17	∂	∂	NUM
cana-3816	221	18	,	,	PUNCT
cana-3816	221	19	ι	ι	PROPN
cana-3816	221	20	)	)	PUNCT
cana-3816	221	21	and	and	CCONJ
cana-3816	221	22	>	>	PUNCT
cana-3816	221	23	`	`	PUNCT
cana-3816	221	24	1	1	NUM
cana-3816	221	25	(	(	PUNCT
cana-3816	221	26	ε	ε	PROPN
cana-3816	221	27	,	,	PUNCT
cana-3816	221	28	ι	ι	PROPN
cana-3816	221	29	)	)	PUNCT
cana-3816	221	30	>	>	PUNCT
cana-3816	222	1	>	>	PUNCT
cana-3816	222	2	`	`	PUNCT
cana-3816	222	3	1	1	NUM
cana-3816	222	4	(	(	PUNCT
cana-3816	222	5	]	]	X
cana-3816	222	6	∂ø	∂ø	PROPN
cana-3816	222	7	,	,	PUNCT
cana-3816	222	8	ι	ι	PROPN
cana-3816	222	9	)	)	PUNCT
cana-3816	222	10	>	>	PUNCT
cana-3816	223	1	>	>	PUNCT
cana-3816	223	2	`	`	PUNCT
cana-3816	223	3	1	1	NUM
cana-3816	223	4	(	(	PUNCT
cana-3816	223	5	∂	∂	NUM
cana-3816	223	6	,	,	PUNCT
cana-3816	223	7	ι	ι	PROPN
cana-3816	223	8	)	)	PUNCT
cana-3816	223	9	.	.	PUNCT
cana-3816	224	1	similarly	similarly	ADV
cana-3816	224	2	,	,	PUNCT
cana-3816	224	3	t`2	t`2	PROPN
cana-3816	224	4	(	(	PUNCT
cana-3816	224	5	ε	ε	PROPN
cana-3816	224	6	,	,	PUNCT
cana-3816	224	7	ι	ι	NOUN
cana-3816	224	8	)	)	PUNCT
cana-3816	224	9	6t`2	6t`2	NOUN
cana-3816	224	10	(	(	PUNCT
cana-3816	224	11	]	]	X
cana-3816	224	12	∂ø	∂ø	PROPN
cana-3816	224	13	,	,	PUNCT
cana-3816	224	14	ι	ι	PROPN
cana-3816	224	15	)	)	PUNCT
cana-3816	224	16	6t`2	6t`2	NOUN
cana-3816	224	17	(	(	PUNCT
cana-3816	224	18	ø	ø	PROPN
cana-3816	224	19	,	,	PUNCT
cana-3816	224	20	ι	ι	PROPN
cana-3816	224	21	)	)	PUNCT
cana-3816	224	22	and	and	CCONJ
cana-3816	224	23	>	>	PUNCT
cana-3816	224	24	`	`	PUNCT
cana-3816	224	25	2	2	NUM
cana-3816	224	26	(	(	PUNCT
cana-3816	224	27	ε	ε	PROPN
cana-3816	224	28	,	,	PUNCT
cana-3816	224	29	ι	ι	PROPN
cana-3816	224	30	)	)	PUNCT
cana-3816	224	31	>	>	PUNCT
cana-3816	224	32	>	>	PUNCT
cana-3816	224	33	`	`	PUNCT
cana-3816	224	34	2	2	NUM
cana-3816	224	35	(	(	PUNCT
cana-3816	224	36	]	]	X
cana-3816	224	37	∂ø	∂ø	PROPN
cana-3816	224	38	,	,	PUNCT
cana-3816	224	39	ι	ι	PROPN
cana-3816	224	40	)	)	PUNCT
cana-3816	224	41	>	>	PUNCT
cana-3816	225	1	>	>	PUNCT
cana-3816	225	2	`	`	PUNCT
cana-3816	225	3	2	2	NUM
cana-3816	225	4	(	(	PUNCT
cana-3816	225	5	ø	ø	PROPN
cana-3816	225	6	,	,	PUNCT
cana-3816	225	7	ι	ι	PROPN
cana-3816	225	8	)	)	PUNCT
cana-3816	225	9	.	.	PUNCT
cana-3816	226	1	for	for	ADP
cana-3816	226	2	ε	ε	PROPN
cana-3816	226	3	∈	∈	PROPN
cana-3816	226	4	b	b	PROPN
cana-3816	226	5	,	,	PUNCT
cana-3816	226	6	there	there	PRON
cana-3816	226	7	exists	exist	VERB
cana-3816	226	8	x	x	X
cana-3816	226	9	∈	∈	PROPN
cana-3816	226	10	b	b	NOUN
cana-3816	226	11	such	such	ADJ
cana-3816	226	12	that	that	DET
cana-3816	226	13	ε	ε	PROPN
cana-3816	226	14	6	6	NUM
cana-3816	226	15	εζ1εζ2εζ3ε	εζ1εζ2εζ3ε	NOUN
cana-3816	226	16	.	.	PUNCT
cana-3816	227	1	then	then	ADV
cana-3816	227	2	ε	ε	PROPN
cana-3816	227	3	,	,	PUNCT
cana-3816	227	4	(	(	PUNCT
cana-3816	227	5	ζ1εζ2εζ3	ζ1εζ2εζ3	NOUN
cana-3816	227	6	)	)	PUNCT
cana-3816	227	7	,	,	PUNCT
cana-3816	227	8	ε	ε	PROPN
cana-3816	227	9	∈	∈	PROPN
cana-3816	227	10	xε	xε	NOUN
cana-3816	227	11	.	.	PUNCT
cana-3816	228	1	we	we	PRON
cana-3816	228	2	have	have	VERB
cana-3816	228	3	(	(	PUNCT
cana-3816	228	4	t(`·`1·`2	t(`·`1·`2	NOUN
cana-3816	228	5	]	]	X
cana-3816	228	6	)	)	PUNCT
cana-3816	228	7	∝2	∝2	NOUN
cana-3816	228	8	∝1	∝1	NOUN
cana-3816	228	9	(	(	PUNCT
cana-3816	228	10	ε	ε	PROPN
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cana-3816	228	14	=	=	SYM
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cana-3816	229	6	,	,	PUNCT
cana-3816	229	7	ι)5	ι)5	PROPN
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cana-3816	229	9	∝1	∝1	X
cana-3816	230	1	=	=	PUNCT
cana-3816	230	2	[	[	PUNCT
cana-3816	230	3	[	[	PUNCT
cana-3816	230	4	inf	inf	ADJ
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cana-3816	230	6	{	{	PUNCT
cana-3816	230	7	t	t	PROPN
cana-3816	230	8	`	`	PUNCT
cana-3816	230	9	(	(	PUNCT
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cana-3816	230	11	,	,	PUNCT
cana-3816	230	12	ι)5	ι)5	PROPN
cana-3816	230	13	t`1	t`1	NOUN
cana-3816	230	14	(	(	PUNCT
cana-3816	230	15	∂	∂	NUM
cana-3816	230	16	,	,	PUNCT
cana-3816	230	17	ι)5	ι)5	PROPN
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cana-3816	230	19	(	(	PUNCT
cana-3816	230	20	ø	ø	PROPN
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cana-3816	230	22	ι)}5	ι)}5	PROPN
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cana-3816	230	26	4	4	NUM
cana-3816	230	27	∝1	∝1	NOUN
cana-3816	230	28	=	=	PUNCT
cana-3816	230	29	[	[	PUNCT
cana-3816	230	30	inf	inf	ADJ
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cana-3816	230	32	{	{	PUNCT
cana-3816	230	33	t	t	PROPN
cana-3816	230	34	`	`	PUNCT
cana-3816	230	35	(	(	PUNCT
cana-3816	230	36	]	]	X
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cana-3816	230	38	ι)5	ι)5	PROPN
cana-3816	230	39	t`1	t`1	NOUN
cana-3816	230	40	(	(	PUNCT
cana-3816	230	41	∂	∂	NUM
cana-3816	230	42	,	,	PUNCT
cana-3816	230	43	ι)5	ι)5	PROPN
cana-3816	230	44	t`2	t`2	NOUN
cana-3816	230	45	(	(	PUNCT
cana-3816	230	46	ø	ø	PROPN
cana-3816	230	47	,	,	PUNCT
cana-3816	230	48	ι)}5	ι)}5	PROPN
cana-3816	230	49	∝2	∝2	PROPN
cana-3816	230	50	5	5	NUM
cana-3816	230	51	∝2	∝2	PROPN
cana-3816	230	52	5	5	NUM
cana-3816	230	53	∝2	∝2	PROPN
cana-3816	230	54	5	5	NUM
cana-3816	230	55	∝2	∝2	NOUN
cana-3816	230	56	]	]	PUNCT
cana-3816	230	57	4	4	NUM
cana-3816	230	58	∝1	∝1	NOUN
cana-3816	230	59	=	=	PUNCT
cana-3816	230	60	[	[	PUNCT
cana-3816	230	61	inf	inf	NOUN
cana-3816	230	62	ε6εζ1εζ2εζ3ε	ε6εζ1εζ2εζ3ε	NOUN
cana-3816	230	63	{	{	PUNCT
cana-3816	230	64	(	(	PUNCT
cana-3816	230	65	t	t	NOUN
cana-3816	230	66	`	`	PUNCT
cana-3816	230	67	(	(	PUNCT
cana-3816	230	68	]	]	X
cana-3816	230	69	,	,	PUNCT
cana-3816	230	70	ι)5	ι)5	PROPN
cana-3816	230	71	∝2)5	∝2)5	PROPN
cana-3816	230	72	(	(	PUNCT
cana-3816	230	73	t`1	t`1	X
cana-3816	230	74	(	(	PUNCT
cana-3816	230	75	∂	∂	NUM
cana-3816	230	76	,	,	PUNCT
cana-3816	230	77	ι)5	ι)5	PROPN
cana-3816	230	78	∝2)5	∝2)5	PROPN
cana-3816	230	79	(	(	PUNCT
cana-3816	230	80	t`2	t`2	X
cana-3816	230	81	(	(	PUNCT
cana-3816	230	82	ø	ø	PROPN
cana-3816	230	83	,	,	PUNCT
cana-3816	230	84	ι)5	ι)5	PROPN
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cana-3816	230	86	∝2	∝2	NOUN
cana-3816	230	87	]	]	PUNCT
cana-3816	230	88	4	4	NUM
cana-3816	230	89	∝1	∝1	NUM
cana-3816	230	90	6	6	NUM
cana-3816	230	91	(	(	PUNCT
cana-3816	230	92	{	{	PUNCT
cana-3816	230	93	(	(	PUNCT
cana-3816	230	94	t	t	NOUN
cana-3816	230	95	`	`	PUNCT
cana-3816	230	96	(	(	PUNCT
cana-3816	230	97	ε	ε	PROPN
cana-3816	230	98	,	,	PUNCT
cana-3816	230	99	ι)4	ι)4	X
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cana-3816	230	101	(	(	PUNCT
cana-3816	230	102	t`1	t`1	X
cana-3816	230	103	(	(	PUNCT
cana-3816	230	104	ζ1εζ2εζ3)4	ζ1εζ2εζ3)4	PROPN
cana-3816	230	105	∝1)5	∝1)5	PRON
cana-3816	230	106	(	(	PUNCT
cana-3816	230	107	t`2	t`2	X
cana-3816	230	108	(	(	PUNCT
cana-3816	230	109	ε	ε	PROPN
cana-3816	230	110	,	,	PUNCT
cana-3816	230	111	ι)4	ι)4	PROPN
cana-3816	230	112	∝1)}5	∝1)}5	PROPN
cana-3816	230	113	∝2)4	∝2)4	PROPN
cana-3816	230	114	∝1	∝1	NUM
cana-3816	230	115	6	6	NUM
cana-3816	230	116	(	(	PUNCT
cana-3816	230	117	{	{	PUNCT
cana-3816	230	118	(	(	PUNCT
cana-3816	230	119	t	t	NOUN
cana-3816	230	120	`	`	PUNCT
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cana-3816	230	122	ε	ε	PROPN
cana-3816	230	123	,	,	PUNCT
cana-3816	230	124	ι)4	ι)4	X
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cana-3816	230	126	(	(	PUNCT
cana-3816	230	127	t`1	t`1	X
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cana-3816	230	129	ε	ε	PROPN
cana-3816	230	130	,	,	PUNCT
cana-3816	230	131	ι)4	ι)4	X
cana-3816	230	132	∝1)5	∝1)5	PROPN
cana-3816	230	133	(	(	PUNCT
cana-3816	230	134	t`2	t`2	X
cana-3816	230	135	(	(	PUNCT
cana-3816	230	136	ε	ε	PROPN
cana-3816	230	137	,	,	PUNCT
cana-3816	230	138	ι)4	ι)4	PROPN
cana-3816	230	139	∝1)}5	∝1)}5	PROPN
cana-3816	230	140	∝2)4	∝2)4	PROPN
cana-3816	230	141	∝1	∝1	ADJ
cana-3816	230	142	=	=	PRON
cana-3816	230	143	{	{	PUNCT
cana-3816	230	144	(	(	PUNCT
cana-3816	230	145	(	(	PUNCT
cana-3816	230	146	t	t	NOUN
cana-3816	230	147	`	`	PUNCT
cana-3816	230	148	(	(	PUNCT
cana-3816	230	149	ε	ε	PROPN
cana-3816	230	150	,	,	PUNCT
cana-3816	230	151	ι)5	ι)5	PROPN
cana-3816	230	152	t`1	t`1	NOUN
cana-3816	230	153	(	(	PUNCT
cana-3816	230	154	ε	ε	PROPN
cana-3816	230	155	,	,	PUNCT
cana-3816	230	156	ι)5	ι)5	PROPN
cana-3816	230	157	t`2	t`2	NOUN
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cana-3816	230	159	ε	ε	PROPN
cana-3816	230	160	,	,	PUNCT
cana-3816	230	161	ι))4	ι))4	NUM
cana-3816	230	162	∝1)5	∝1)5	NOUN
cana-3816	230	163	∝2}4	∝2}4	NOUN
cana-3816	230	164	∝1	∝1	NUM
cana-3816	231	1	=	=	PRON
cana-3816	231	2	{	{	PUNCT
cana-3816	231	3	(	(	PUNCT
cana-3816	231	4	(	(	PUNCT
cana-3816	231	5	t	t	NOUN
cana-3816	231	6	`	`	NUM
cana-3816	231	7	5	5	NUM
cana-3816	231	8	t`1	t`1	NUM
cana-3816	231	9	5	5	NUM
cana-3816	231	10	t`2	t`2	NOUN
cana-3816	231	11	)	)	PUNCT
cana-3816	231	12	(	(	PUNCT
cana-3816	231	13	ε	ε	PROPN
cana-3816	231	14	,	,	PUNCT
cana-3816	231	15	ι)5	ι)5	X
cana-3816	231	16	∝2}4	∝2}4	NOUN
cana-3816	231	17	∝1	∝1	NUM
cana-3816	232	1	=	=	PUNCT
cana-3816	232	2	(	(	PUNCT
cana-3816	232	3	t`∩`1∩`2)∝2	t`∩`1∩`2)∝2	NOUN
cana-3816	232	4	∝1	∝1	X
cana-3816	232	5	(	(	PUNCT
cana-3816	232	6	ε	ε	PROPN
cana-3816	232	7	,	,	PUNCT
cana-3816	232	8	ι	ι	PROPN
cana-3816	232	9	)	)	PUNCT
cana-3816	232	10	https://internationalpubls.com	https://internationalpubls.com	X
cana-3816	232	11	767	767	NUM
cana-3816	232	12	communications	communication	NOUN
cana-3816	232	13	on	on	ADP
cana-3816	232	14	applied	apply	VERB
cana-3816	232	15	nonlinear	nonlinear	ADJ
cana-3816	232	16	analysis	analysis	NOUN
cana-3816	232	17	issn	issn	NOUN
cana-3816	232	18	:	:	PUNCT
cana-3816	232	19	1074	1074	NUM
cana-3816	232	20	-	-	PUNCT
cana-3816	232	21	133x	133x	NUM
cana-3816	232	22	vol	vol	NOUN
cana-3816	232	23	32	32	NUM
cana-3816	232	24	no	no	NOUN
cana-3816	232	25	.	.	NOUN
cana-3816	232	26	3	3	NUM
cana-3816	232	27	(	(	PUNCT
cana-3816	232	28	2025	2025	NUM
cana-3816	232	29	)	)	PUNCT
cana-3816	232	30	(	(	PUNCT
cana-3816	232	31	>	>	X
cana-3816	232	32	(	(	PUNCT
cana-3816	232	33	`	`	PUNCT
cana-3816	232	34	·	·	PUNCT
cana-3816	232	35	`	`	PUNCT
cana-3816	232	36	1·`2	1·`2	NUM
cana-3816	232	37	]	]	SYM
cana-3816	232	38	)	)	PUNCT
cana-3816	232	39	∝2	∝2	NOUN
cana-3816	232	40	∝1	∝1	NOUN
cana-3816	232	41	(	(	PUNCT
cana-3816	232	42	ε	ε	PROPN
cana-3816	232	43	,	,	PUNCT
cana-3816	232	44	ι	ι	PROPN
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cana-3816	232	46	=	=	SYM
cana-3816	232	47	(	(	PUNCT
cana-3816	232	48	>	>	X
cana-3816	232	49	(	(	PUNCT
cana-3816	232	50	`	`	PUNCT
cana-3816	232	51	·	·	PUNCT
cana-3816	232	52	`	`	PUNCT
cana-3816	232	53	1·`2](ε	1·`2](ε	NUM
cana-3816	232	54	,	,	PUNCT
cana-3816	232	55	ι)4	ι)4	PROPN
cana-3816	232	56	∝2)5	∝2)5	PROPN
cana-3816	232	57	∝1	∝1	X
cana-3816	233	1	=	=	PUNCT
cana-3816	233	2	[	[	PUNCT
cana-3816	233	3	[	[	PUNCT
cana-3816	233	4	sup	sup	NOUN
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cana-3816	233	6	{	{	PUNCT
cana-3816	233	7	>	>	X
cana-3816	233	8	`	`	PUNCT
cana-3816	233	9	(	(	PUNCT
cana-3816	233	10	]	]	X
cana-3816	233	11	,	,	PUNCT
cana-3816	233	12	ι)4>`1	ι)4>`1	NOUN
cana-3816	233	13	(	(	PUNCT
cana-3816	233	14	∂	∂	NUM
cana-3816	233	15	,	,	PUNCT
cana-3816	233	16	ι)4>`2	ι)4>`2	X
cana-3816	233	17	(	(	PUNCT
cana-3816	233	18	ø	ø	X
cana-3816	233	19	,	,	PUNCT
cana-3816	233	20	ι)}4	ι)}4	PROPN
cana-3816	233	21	∝2	∝2	PROPN
cana-3816	233	22	]	]	X
cana-3816	233	23	]	]	PUNCT
cana-3816	233	24	5	5	NUM
cana-3816	233	25	∝1	∝1	NOUN
cana-3816	233	26	=	=	PUNCT
cana-3816	233	27	[	[	PUNCT
cana-3816	233	28	sup	sup	NOUN
cana-3816	233	29	ε6εζ1εζ2εζ3ε	ε6εζ1εζ2εζ3ε	NOUN
cana-3816	233	30	{	{	PUNCT
cana-3816	233	31	>	>	X
cana-3816	233	32	`	`	PUNCT
cana-3816	233	33	(	(	PUNCT
cana-3816	233	34	]	]	X
cana-3816	233	35	,	,	PUNCT
cana-3816	233	36	ι)4>`1	ι)4>`1	NOUN
cana-3816	233	37	(	(	PUNCT
cana-3816	233	38	∂	∂	NUM
cana-3816	233	39	,	,	PUNCT
cana-3816	233	40	ι)4>`2	ι)4>`2	X
cana-3816	233	41	(	(	PUNCT
cana-3816	233	42	ø	ø	X
cana-3816	233	43	,	,	PUNCT
cana-3816	233	44	ι)}4	ι)}4	PROPN
cana-3816	233	45	∝2	∝2	PROPN
cana-3816	233	46	4	4	NUM
cana-3816	233	47	∝2	∝2	NOUN
cana-3816	233	48	4	4	NUM
cana-3816	233	49	∝2	∝2	NOUN
cana-3816	233	50	4	4	NUM
cana-3816	233	51	∝2	∝2	NOUN
cana-3816	233	52	]	]	PUNCT
cana-3816	233	53	5	5	NUM
cana-3816	233	54	∝1	∝1	NOUN
cana-3816	233	55	=	=	PUNCT
cana-3816	233	56	[	[	PUNCT
cana-3816	233	57	sup	sup	NUM
cana-3816	233	58	ε6εζ1εζ2εζ3ε	ε6εζ1εζ2εζ3ε	NOUN
cana-3816	233	59	{	{	PUNCT
cana-3816	233	60	(	(	PUNCT
cana-3816	233	61	>	>	X
cana-3816	233	62	`	`	PUNCT
cana-3816	233	63	(	(	PUNCT
cana-3816	233	64	]	]	X
cana-3816	233	65	,	,	PUNCT
cana-3816	233	66	ι)4	ι)4	PROPN
cana-3816	233	67	∝2)4	∝2)4	PROPN
cana-3816	233	68	(	(	PUNCT
cana-3816	233	69	>	>	X
cana-3816	233	70	`	`	PUNCT
cana-3816	233	71	1	1	NUM
cana-3816	233	72	(	(	PUNCT
cana-3816	233	73	∂	∂	NUM
cana-3816	233	74	,	,	PUNCT
cana-3816	233	75	ι)4	ι)4	PROPN
cana-3816	233	76	∝2)4	∝2)4	PROPN
cana-3816	233	77	(	(	PUNCT
cana-3816	233	78	>	>	X
cana-3816	233	79	`	`	PUNCT
cana-3816	233	80	2	2	NUM
cana-3816	233	81	(	(	PUNCT
cana-3816	233	82	ø	ø	PROPN
cana-3816	233	83	,	,	PUNCT
cana-3816	233	84	ι)4	ι)4	PROPN
cana-3816	233	85	∝2)}4	∝2)}4	NUM
cana-3816	233	86	∝2	∝2	NOUN
cana-3816	233	87	]	]	PUNCT
cana-3816	233	88	5	5	NUM
cana-3816	233	89	∝1	∝1	NOUN
cana-3816	233	90	>	>	X
cana-3816	233	91	(	(	PUNCT
cana-3816	233	92	{	{	PUNCT
cana-3816	233	93	(	(	PUNCT
cana-3816	233	94	>	>	X
cana-3816	233	95	`	`	PUNCT
cana-3816	233	96	(	(	PUNCT
cana-3816	233	97	ε	ε	PROPN
cana-3816	233	98	,	,	PUNCT
cana-3816	233	99	ι)5	ι)5	PROPN
cana-3816	233	100	∝1)4	∝1)4	PROPN
cana-3816	233	101	(	(	PUNCT
cana-3816	233	102	>	>	X
cana-3816	233	103	`	`	PUNCT
cana-3816	233	104	1	1	NUM
cana-3816	233	105	(	(	PUNCT
cana-3816	233	106	ζ1εζ2εζ3)5	ζ1εζ2εζ3)5	ADJ
cana-3816	233	107	∝1)4	∝1)4	PROPN
cana-3816	233	108	(	(	PUNCT
cana-3816	233	109	>	>	X
cana-3816	233	110	`	`	PUNCT
cana-3816	233	111	2	2	NUM
cana-3816	233	112	(	(	PUNCT
cana-3816	233	113	ε	ε	PROPN
cana-3816	233	114	,	,	PUNCT
cana-3816	233	115	ι)5	ι)5	NOUN
cana-3816	233	116	∝1)}4	∝1)}4	PROPN
cana-3816	233	117	∝2)5	∝2)5	PROPN
cana-3816	233	118	∝1	∝1	PROPN
cana-3816	233	119	>	>	X
cana-3816	233	120	(	(	PUNCT
cana-3816	233	121	{	{	PUNCT
cana-3816	233	122	(	(	PUNCT
cana-3816	233	123	>	>	X
cana-3816	233	124	`	`	PUNCT
cana-3816	233	125	(	(	PUNCT
cana-3816	233	126	ε	ε	PROPN
cana-3816	233	127	,	,	PUNCT
cana-3816	233	128	ι)5	ι)5	PROPN
cana-3816	233	129	∝1)4	∝1)4	PROPN
cana-3816	233	130	(	(	PUNCT
cana-3816	233	131	>	>	X
cana-3816	233	132	`	`	PUNCT
cana-3816	233	133	1	1	NUM
cana-3816	233	134	(	(	PUNCT
cana-3816	233	135	ε	ε	PROPN
cana-3816	233	136	,	,	PUNCT
cana-3816	233	137	ι)5	ι)5	PROPN
cana-3816	233	138	∝1)4	∝1)4	PROPN
cana-3816	233	139	(	(	PUNCT
cana-3816	233	140	>	>	X
cana-3816	233	141	`	`	PUNCT
cana-3816	233	142	2	2	NUM
cana-3816	233	143	(	(	PUNCT
cana-3816	233	144	ε	ε	PROPN
cana-3816	233	145	,	,	PUNCT
cana-3816	233	146	ι)5	ι)5	NOUN
cana-3816	233	147	∝1)}4	∝1)}4	PROPN
cana-3816	233	148	∝2)5	∝2)5	PROPN
cana-3816	233	149	∝1	∝1	X
cana-3816	233	150	=	=	PRON
cana-3816	233	151	{	{	PUNCT
cana-3816	233	152	(	(	PUNCT
cana-3816	233	153	(	(	PUNCT
cana-3816	233	154	>	>	X
cana-3816	233	155	`	`	PUNCT
cana-3816	233	156	(	(	PUNCT
cana-3816	233	157	ε	ε	PROPN
cana-3816	233	158	,	,	PUNCT
cana-3816	233	159	ι)4>`1	ι)4>`1	X
cana-3816	233	160	(	(	PUNCT
cana-3816	233	161	ε	ε	PROPN
cana-3816	233	162	,	,	PUNCT
cana-3816	233	163	ι)4>`2	ι)4>`2	X
cana-3816	233	164	(	(	PUNCT
cana-3816	233	165	ε	ε	PROPN
cana-3816	233	166	,	,	PUNCT
cana-3816	233	167	ι))5	ι))5	ADP
cana-3816	233	168	∝1)4	∝1)4	PROPN
cana-3816	233	169	∝2}5	∝2}5	PROPN
cana-3816	233	170	∝1	∝1	NOUN
cana-3816	234	1	=	=	PUNCT
cana-3816	234	2	{	{	PUNCT
cana-3816	234	3	(	(	PUNCT
cana-3816	234	4	(	(	PUNCT
cana-3816	234	5	>	>	X
cana-3816	234	6	`	`	PUNCT
cana-3816	234	7	4>`1	4>`1	NUM
cana-3816	234	8	4>`2	4>`2	NUM
cana-3816	234	9	)	)	PUNCT
cana-3816	234	10	(	(	PUNCT
cana-3816	234	11	ε	ε	PROPN
cana-3816	234	12	,	,	PUNCT
cana-3816	234	13	ι)4	ι)4	PROPN
cana-3816	234	14	∝2}5	∝2}5	PROPN
cana-3816	234	15	∝1	∝1	NUM
cana-3816	234	16	=	=	PUNCT
cana-3816	234	17	(	(	PUNCT
cana-3816	234	18	>	>	X
cana-3816	234	19	`	`	PUNCT
cana-3816	234	20	∪`1∪`2)∝2	∪`1∪`2)∝2	X
cana-3816	234	21	∝1	∝1	X
cana-3816	234	22	(	(	PUNCT
cana-3816	234	23	ε	ε	PROPN
cana-3816	234	24	,	,	PUNCT
cana-3816	234	25	ι	ι	PROPN
cana-3816	234	26	)	)	PUNCT
cana-3816	234	27	thus	thus	ADV
cana-3816	234	28	(	(	PUNCT
cana-3816	234	29	(	(	PUNCT
cana-3816	234	30	`	`	PUNCT
cana-3816	234	31	·	·	PUNCT
cana-3816	234	32	`	`	PUNCT
cana-3816	234	33	1	1	X
cana-3816	234	34	·	·	PUNCT
cana-3816	234	35	`	`	PUNCT
cana-3816	234	36	2])∝2	2])∝2	NUM
cana-3816	234	37	∝1	∝1	NOUN
cana-3816	234	38	⊇	⊇	X
cana-3816	234	39	(	(	PUNCT
cana-3816	234	40	(	(	PUNCT
cana-3816	234	41	`	`	PUNCT
cana-3816	234	42	∩	∩	ADJ
cana-3816	234	43	`	`	PUNCT
cana-3816	234	44	1	1	NUM
cana-3816	234	45	∩	∩	NOUN
cana-3816	234	46	`	`	PUNCT
cana-3816	234	47	2])∝2	2])∝2	NUM
cana-3816	234	48	∝1	∝1	NOUN
cana-3816	234	49	and	and	CCONJ
cana-3816	234	50	by	by	ADP
cana-3816	234	51	theorem	theorem	NOUN
cana-3816	234	52	2.16	2.16	NUM
cana-3816	234	53	.	.	PUNCT
cana-3816	235	1	hence	hence	ADV
cana-3816	235	2	(	(	PUNCT
cana-3816	235	3	(	(	PUNCT
cana-3816	235	4	`	`	PUNCT
cana-3816	235	5	·	·	PUNCT
cana-3816	235	6	`	`	PUNCT
cana-3816	235	7	1	1	X
cana-3816	235	8	·	·	PUNCT
cana-3816	235	9	`	`	PUNCT
cana-3816	235	10	2])∝2	2])∝2	NUM
cana-3816	235	11	∝1	∝1	X
cana-3816	235	12	=	=	PUNCT
cana-3816	235	13	(	(	PUNCT
cana-3816	235	14	(	(	PUNCT
cana-3816	235	15	`	`	PUNCT
cana-3816	235	16	∩	∩	ADJ
cana-3816	235	17	`	`	PUNCT
cana-3816	235	18	1	1	NUM
cana-3816	235	19	∩	∩	NOUN
cana-3816	235	20	`	`	PUNCT
cana-3816	235	21	2])∝2	2])∝2	NUM
cana-3816	235	22	∝1	∝1	NUM
cana-3816	235	23	.	.	PUNCT
cana-3816	236	1	conversely	conversely	ADV
cana-3816	236	2	assume	assume	VERB
cana-3816	236	3	that	that	SCONJ
cana-3816	236	4	(	(	PUNCT
cana-3816	236	5	(	(	PUNCT
cana-3816	236	6	`	`	PUNCT
cana-3816	236	7	·	·	PUNCT
cana-3816	236	8	`	`	PUNCT
cana-3816	236	9	1	1	X
cana-3816	236	10	·	·	PUNCT
cana-3816	236	11	`	`	PUNCT
cana-3816	236	12	2])∝2	2])∝2	NUM
cana-3816	236	13	∝1	∝1	X
cana-3816	236	14	=	=	PUNCT
cana-3816	236	15	(	(	PUNCT
cana-3816	236	16	(	(	PUNCT
cana-3816	236	17	`	`	PUNCT
cana-3816	236	18	∩	∩	ADJ
cana-3816	236	19	`	`	PUNCT
cana-3816	236	20	1	1	NUM
cana-3816	236	21	∩	∩	NOUN
cana-3816	236	22	`	`	PUNCT
cana-3816	236	23	2])∝2	2])∝2	NUM
cana-3816	236	24	∝1	∝1	NUM
cana-3816	236	25	.	.	PUNCT
cana-3816	237	1	let	let	VERB
cana-3816	237	2	`	`	PUNCT
cana-3816	237	3	=	=	SYM
cana-3816	237	4	(	(	PUNCT
cana-3816	237	5	t	t	NOUN
cana-3816	237	6	`	`	PUNCT
cana-3816	237	7	,	,	PUNCT
cana-3816	237	8	>	>	PUNCT
cana-3816	237	9	`	`	PUNCT
cana-3816	237	10	)	)	PUNCT
cana-3816	237	11	be	be	AUX
cana-3816	237	12	an	an	DET
cana-3816	237	13	(	(	PUNCT
cana-3816	237	14	∝1,∝2)iq1afri	∝1,∝2)iq1afri	PROPN
cana-3816	237	15	,	,	PUNCT
cana-3816	237	16	`	`	PUNCT
cana-3816	237	17	1	1	NUM
cana-3816	237	18	=	=	SYM
cana-3816	237	19	(	(	PUNCT
cana-3816	237	20	t`1	t`1	INTJ
cana-3816	237	21	,	,	PUNCT
cana-3816	237	22	>	>	X
cana-3816	237	23	`	`	PUNCT
cana-3816	237	24	1	1	X
cana-3816	237	25	)	)	PUNCT
cana-3816	237	26	be	be	AUX
cana-3816	237	27	an	an	DET
cana-3816	237	28	(	(	PUNCT
cana-3816	237	29	∝1,∝2)iq1aflati	∝1,∝2)iq1aflati	NOUN
cana-3816	237	30	and	and	CCONJ
cana-3816	237	31	`	`	PUNCT
cana-3816	237	32	2	2	NUM
cana-3816	237	33	=	=	SYM
cana-3816	237	34	(	(	PUNCT
cana-3816	237	35	t`2	t`2	INTJ
cana-3816	237	36	,	,	PUNCT
cana-3816	237	37	ξ`2	ξ`2	NUM
cana-3816	237	38	,	,	PUNCT
cana-3816	237	39	>	>	X
cana-3816	237	40	`	`	PUNCT
cana-3816	237	41	2	2	X
cana-3816	237	42	)	)	PUNCT
cana-3816	237	43	be	be	AUX
cana-3816	237	44	an	an	DET
cana-3816	237	45	(	(	PUNCT
cana-3816	237	46	∝1,∝2)iq1afli	∝1,∝2)iq1afli	NOUN
cana-3816	237	47	of	of	ADP
cana-3816	237	48	b.	b.	PROPN
cana-3816	237	49	then	then	ADV
cana-3816	237	50	by	by	ADP
cana-3816	237	51	theorem	theorem	NOUN
cana-3816	237	52	2.11	2.11	NUM
cana-3816	237	53	,	,	PUNCT
cana-3816	237	54			PROPN
cana-3816	237	55	`	`	PUNCT
cana-3816	237	56	is	be	AUX
cana-3816	237	57	a	a	DET
cana-3816	237	58	(	(	PUNCT
cana-3816	237	59	∝1,∝2)iq1afri	∝1,∝2)iq1afri	NUM
cana-3816	237	60	,	,	PUNCT
cana-3816	237	61	`1	`1	PROPN
cana-3816	237	62	is	be	AUX
cana-3816	237	63	a	a	DET
cana-3816	237	64	(	(	PUNCT
cana-3816	237	65	∝1,∝2)iq1aflati	∝1,∝2)iq1aflati	NOUN
cana-3816	237	66	and	and	CCONJ
cana-3816	237	67	`2	`2	NOUN
cana-3816	237	68	be	be	VERB
cana-3816	237	69	a	a	DET
cana-3816	237	70	(	(	PUNCT
cana-3816	237	71	∝1,∝2)iq1afli	∝1,∝2)iq1afli	NOUN
cana-3816	237	72	of	of	ADP
cana-3816	237	73	b.	b.	PROPN
cana-3816	237	74	by	by	ADP
cana-3816	237	75	lemma	lemma	PROPN
cana-3816	237	76	2.14	2.14	NUM
cana-3816	237	77	and	and	CCONJ
cana-3816	237	78	theorem	theorem	VERB
cana-3816	237	79	2.15	2.15	NUM
cana-3816	237	80	,	,	PUNCT
cana-3816	237	81	(	(	PUNCT
cana-3816	237	82	(`∩`1∩`2	(`∩`1∩`2	NOUN
cana-3816	237	83	]	]	PUNCT
cana-3816	237	84	)	)	PUNCT
cana-3816	237	85	∝2	∝2	NOUN
cana-3816	237	86	∝1	∝1	NOUN
cana-3816	237	87	=	=	SYM
cana-3816	237	88	(	(	PUNCT
cana-3816	237	89	`∩`1	`∩`1	X
cana-3816	237	90	∩`2	∩`2	SYM
cana-3816	237	91	)	)	PUNCT
cana-3816	237	92	∝2	∝2	NOUN
cana-3816	237	93	∝1	∝1	NOUN
cana-3816	237	94	=	=	SYM
cana-3816	237	95	(	(	PUNCT
cana-3816	237	96			PROPN
cana-3816	237	97	`	`	PUNCT
cana-3816	237	98	·	·	PUNCT
cana-3816	237	99	`1	`1	NOUN
cana-3816	237	100	·	·	SYM
cana-3816	237	101	`2	`2	NOUN
cana-3816	237	102	)	)	PUNCT
cana-3816	237	103	∝2	∝2	NOUN
cana-3816	237	104	∝1	∝1	NOUN
cana-3816	237	105	=	=	SYM
cana-3816	237	106	(	(	PUNCT
cana-3816	237	107	(`·`1·`2	(`·`1·`2	PROPN
cana-3816	237	108	]	]	NOUN
cana-3816	237	109	)	)	PUNCT
cana-3816	237	110	∝2	∝2	NOUN
cana-3816	237	111	∝1	∝1	NOUN
cana-3816	237	112	.	.	PUNCT
cana-3816	238	1	this	this	PRON
cana-3816	238	2	implies	imply	VERB
cana-3816	238	3	(	(	PUNCT
cana-3816	238	4	`	`	PUNCT
cana-3816	238	5	∩	∩	ADJ
cana-3816	238	6	`	`	PUNCT
cana-3816	238	7	1	1	NUM
cana-3816	238	8	∩	∩	NOUN
cana-3816	238	9	`	`	PUNCT
cana-3816	238	10	2]∝2	2]∝2	NUM
cana-3816	238	11	∝1	∝1	NUM
cana-3816	238	12	=	=	PUNCT
cana-3816	238	13	(	(	PUNCT
cana-3816	238	14	(	(	PUNCT
cana-3816	238	15	`	`	PUNCT
cana-3816	238	16	·	·	PUNCT
cana-3816	238	17	`	`	PUNCT
cana-3816	238	18	1	1	X
cana-3816	238	19	·	·	PUNCT
cana-3816	238	20	`	`	PUNCT
cana-3816	238	21	2])∝2	2])∝2	NUM
cana-3816	238	22	∝1	∝1	NOUN
cana-3816	238	23	.	.	PUNCT
cana-3816	239	1	hence	hence	ADV
cana-3816	239	2	by	by	ADP
cana-3816	239	3	corollary	corollary	ADJ
cana-3816	239	4	?	?	PUNCT
cana-3816	239	5	?	?	PUNCT
cana-3816	239	6	,	,	PUNCT
cana-3816	239	7	b	b	PROPN
cana-3816	239	8	is	be	AUX
cana-3816	239	9	regular	regular	ADJ
cana-3816	239	10	.	.	PUNCT
cana-3816	240	1	theorem	theorem	VERB
cana-3816	240	2	2.18	2.18	NUM
cana-3816	240	3	.	.	PUNCT
cana-3816	241	1	an	an	DET
cana-3816	241	2	tss	tss	PROPN
cana-3816	241	3	b	b	PROPN
cana-3816	241	4	is	be	AUX
cana-3816	241	5	regular	regular	ADJ
cana-3816	241	6	,	,	PUNCT
cana-3816	241	7	`	`	PUNCT
cana-3816	241	8	be	be	AUX
cana-3816	241	9	an	an	DET
cana-3816	241	10	(	(	PUNCT
cana-3816	241	11	∝1,∝2)iq1afbi	∝1,∝2)iq1afbi	PROPN
cana-3816	241	12	,	,	PUNCT
cana-3816	241	13	`	`	PUNCT
cana-3816	241	14	1	1	NUM
cana-3816	241	15	be	be	AUX
cana-3816	241	16	an	an	DET
cana-3816	241	17	(	(	PUNCT
cana-3816	241	18	∝1,∝2)iq1aflati	∝1,∝2)iq1aflati	NOUN
cana-3816	241	19	and	and	CCONJ
cana-3816	241	20	`	`	PUNCT
cana-3816	241	21	2	2	NUM
cana-3816	241	22	be	be	AUX
cana-3816	241	23	an	an	DET
cana-3816	241	24	(	(	PUNCT
cana-3816	241	25	∝1,∝2)iq1afli	∝1,∝2)iq1afli	NOUN
cana-3816	241	26	of	of	ADP
cana-3816	241	27	b	b	PROPN
cana-3816	242	1	if	if	SCONJ
cana-3816	242	2	and	and	CCONJ
cana-3816	242	3	only	only	ADV
cana-3816	242	4	if	if	SCONJ
cana-3816	242	5	(	(	PUNCT
cana-3816	242	6	(	(	PUNCT
cana-3816	242	7	`	`	PUNCT
cana-3816	242	8	·	·	PUNCT
cana-3816	242	9	`	`	PUNCT
cana-3816	242	10	1	1	X
cana-3816	242	11	·	·	PUNCT
cana-3816	242	12	`	`	PUNCT
cana-3816	242	13	2])∝2	2])∝2	NUM
cana-3816	242	14	∝1	∝1	X
cana-3816	242	15	=	=	PUNCT
cana-3816	242	16	(	(	PUNCT
cana-3816	242	17	(	(	PUNCT
cana-3816	242	18	`	`	PUNCT
cana-3816	242	19	∩	∩	ADJ
cana-3816	242	20	`	`	PUNCT
cana-3816	242	21	1	1	NUM
cana-3816	242	22	∩	∩	NOUN
cana-3816	242	23	`	`	PUNCT
cana-3816	242	24	2])∝2	2])∝2	NUM
cana-3816	242	25	∝1	∝1	NUM
cana-3816	242	26	.	.	PUNCT
cana-3816	243	1	proof	proof	NOUN
cana-3816	243	2	.	.	PUNCT
cana-3816	244	1	let	let	VERB
cana-3816	244	2	b	b	X
cana-3816	244	3	be	be	AUX
cana-3816	244	4	an	an	DET
cana-3816	244	5	tss	tss	NOUN
cana-3816	244	6	and	and	CCONJ
cana-3816	244	7	`	`	PUNCT
cana-3816	244	8	be	be	AUX
cana-3816	244	9	an	an	DET
cana-3816	244	10	(	(	PUNCT
cana-3816	244	11	∝1,∝2)iq1afbi	∝1,∝2)iq1afbi	PROPN
cana-3816	244	12	and	and	CCONJ
cana-3816	244	13	`	`	PUNCT
cana-3816	244	14	2	2	NUM
cana-3816	244	15	be	be	AUX
cana-3816	244	16	an	an	DET
cana-3816	244	17	(	(	PUNCT
cana-3816	244	18	∝1,∝2)iq1afli	∝1,∝2)iq1afli	NOUN
cana-3816	244	19	of	of	ADP
cana-3816	244	20	b.	b.	PROPN
cana-3816	244	21	let	let	VERB
cana-3816	244	22	(	(	PUNCT
cana-3816	244	23	]	]	X
cana-3816	244	24	,	,	PUNCT
cana-3816	244	25	ø	ø	X
cana-3816	244	26	)	)	PUNCT
cana-3816	244	27	∈	∈	PROPN
cana-3816	245	1	xε	xε	NOUN
cana-3816	245	2	.	.	PUNCT
cana-3816	246	1	if	if	SCONJ
cana-3816	246	2	xε	xε	PROPN
cana-3816	246	3	6=	6=	ADP
cana-3816	246	4	∅	∅	NOUN
cana-3816	246	5	,	,	PUNCT
cana-3816	246	6	then	then	ADV
cana-3816	246	7	ε	ε	PROPN
cana-3816	246	8	6	6	NUM
cana-3816	246	9	]	]	X
cana-3816	246	10	∂ø	∂ø	PROPN
cana-3816	246	11	.	.	PUNCT
cana-3816	247	1	thus	thus	ADV
cana-3816	247	2	t	t	X
cana-3816	247	3	`	`	PUNCT
cana-3816	247	4	(	(	PUNCT
cana-3816	247	5	ε	ε	PROPN
cana-3816	247	6	,	,	PUNCT
cana-3816	247	7	ι	ι	PROPN
cana-3816	247	8	)	)	PUNCT
cana-3816	247	9	6	6	NUM
cana-3816	247	10	t	t	PROPN
cana-3816	247	11	`	`	PUNCT
cana-3816	247	12	(	(	PUNCT
cana-3816	247	13	]	]	X
cana-3816	247	14	∂ø	∂ø	PROPN
cana-3816	247	15	,	,	PUNCT
cana-3816	247	16	ι	ι	PROPN
cana-3816	247	17	)	)	PUNCT
cana-3816	247	18	6	6	NUM
cana-3816	247	19	t	t	PROPN
cana-3816	247	20	`	`	PUNCT
cana-3816	247	21	(	(	PUNCT
cana-3816	247	22	]	]	X
cana-3816	247	23	,	,	PUNCT
cana-3816	247	24	ι	ι	PROPN
cana-3816	247	25	)	)	PUNCT
cana-3816	247	26	and	and	CCONJ
cana-3816	247	27	>	>	PUNCT
cana-3816	247	28	`	`	PUNCT
cana-3816	247	29	(	(	PUNCT
cana-3816	247	30	ε	ε	PROPN
cana-3816	247	31	,	,	PUNCT
cana-3816	247	32	ι	ι	PROPN
cana-3816	247	33	)	)	PUNCT
cana-3816	247	34	>	>	PUNCT
cana-3816	247	35	>	>	PUNCT
cana-3816	247	36	`	`	PUNCT
cana-3816	247	37	(	(	PUNCT
cana-3816	247	38	]	]	X
cana-3816	247	39	∂ø	∂ø	PROPN
cana-3816	247	40	,	,	PUNCT
cana-3816	247	41	ι	ι	PROPN
cana-3816	247	42	)	)	PUNCT
cana-3816	247	43	>	>	PUNCT
cana-3816	247	44	>	>	PUNCT
cana-3816	247	45	`	`	PUNCT
cana-3816	247	46	(	(	PUNCT
cana-3816	247	47	]	]	X
cana-3816	247	48	,	,	PUNCT
cana-3816	247	49	ι	ι	PROPN
cana-3816	247	50	)	)	PUNCT
cana-3816	247	51	.	.	PUNCT
cana-3816	248	1	similarly	similarly	ADV
cana-3816	248	2	t`1	t`1	ADV
cana-3816	248	3	(	(	PUNCT
cana-3816	248	4	ε	ε	PROPN
cana-3816	248	5	,	,	PUNCT
cana-3816	248	6	ι	ι	PROPN
cana-3816	248	7	)	)	PUNCT
cana-3816	248	8	6t`1	6t`1	NOUN
cana-3816	248	9	(	(	PUNCT
cana-3816	248	10	]	]	X
cana-3816	248	11	∂ø	∂ø	PROPN
cana-3816	248	12	,	,	PUNCT
cana-3816	248	13	ι	ι	PROPN
cana-3816	248	14	)	)	PUNCT
cana-3816	248	15	6t`1	6t`1	NOUN
cana-3816	248	16	(	(	PUNCT
cana-3816	248	17	∂	∂	NUM
cana-3816	248	18	,	,	PUNCT
cana-3816	248	19	ι	ι	PROPN
cana-3816	248	20	)	)	PUNCT
cana-3816	248	21	and	and	CCONJ
cana-3816	248	22	>	>	X
cana-3816	248	23	`	`	PUNCT
cana-3816	248	24	1(ε	1(ε	NUM
cana-3816	248	25	,	,	PUNCT
cana-3816	248	26	ι	ι	PROPN
cana-3816	248	27	)	)	PUNCT
cana-3816	248	28	>	>	PUNCT
cana-3816	249	1	>	>	PUNCT
cana-3816	249	2	`	`	PUNCT
cana-3816	249	3	1(]∂ø	1(]∂ø	PROPN
cana-3816	249	4	,	,	PUNCT
cana-3816	249	5	ι	ι	PROPN
cana-3816	249	6	)	)	PUNCT
cana-3816	249	7	>	>	PUNCT
cana-3816	249	8	>	>	PUNCT
cana-3816	249	9	`	`	PUNCT
cana-3816	249	10	1(∂	1(∂	NUM
cana-3816	249	11	,	,	PUNCT
cana-3816	249	12	ι	ι	PROPN
cana-3816	249	13	)	)	PUNCT
cana-3816	249	14	.	.	PUNCT
cana-3816	250	1	similarly	similarly	ADV
cana-3816	250	2	,	,	PUNCT
cana-3816	250	3	t`2	t`2	PROPN
cana-3816	250	4	(	(	PUNCT
cana-3816	250	5	ε	ε	PROPN
cana-3816	250	6	,	,	PUNCT
cana-3816	250	7	ι	ι	NOUN
cana-3816	250	8	)	)	PUNCT
cana-3816	250	9	6t`2	6t`2	NOUN
cana-3816	250	10	(	(	PUNCT
cana-3816	250	11	]	]	X
cana-3816	250	12	∂ø	∂ø	PROPN
cana-3816	250	13	,	,	PUNCT
cana-3816	250	14	ι	ι	PROPN
cana-3816	250	15	)	)	PUNCT
cana-3816	250	16	6t`2	6t`2	NOUN
cana-3816	250	17	(	(	PUNCT
cana-3816	250	18	ø	ø	PROPN
cana-3816	250	19	,	,	PUNCT
cana-3816	250	20	ι	ι	PROPN
cana-3816	250	21	)	)	PUNCT
cana-3816	250	22	and	and	CCONJ
cana-3816	250	23	>	>	PUNCT
cana-3816	250	24	`	`	PUNCT
cana-3816	250	25	2	2	NUM
cana-3816	250	26	(	(	PUNCT
cana-3816	250	27	ε	ε	PROPN
cana-3816	250	28	,	,	PUNCT
cana-3816	250	29	ι	ι	PROPN
cana-3816	250	30	)	)	PUNCT
cana-3816	250	31	>	>	PUNCT
cana-3816	250	32	>	>	PUNCT
cana-3816	250	33	`	`	PUNCT
cana-3816	250	34	2	2	NUM
cana-3816	250	35	(	(	PUNCT
cana-3816	250	36	]	]	X
cana-3816	250	37	∂ø	∂ø	PROPN
cana-3816	250	38	,	,	PUNCT
cana-3816	250	39	ι	ι	PROPN
cana-3816	250	40	)	)	PUNCT
cana-3816	250	41	>	>	PUNCT
cana-3816	251	1	>	>	PUNCT
cana-3816	251	2	`	`	PUNCT
cana-3816	251	3	2	2	NUM
cana-3816	251	4	(	(	PUNCT
cana-3816	251	5	ø	ø	PROPN
cana-3816	251	6	,	,	PUNCT
cana-3816	251	7	ι	ι	PROPN
cana-3816	251	8	)	)	PUNCT
cana-3816	251	9	.	.	PUNCT
cana-3816	252	1	for	for	ADP
cana-3816	252	2	ε	ε	PROPN
cana-3816	252	3	∈	∈	PROPN
cana-3816	252	4	b	b	PROPN
cana-3816	252	5	,	,	PUNCT
cana-3816	252	6	there	there	PRON
cana-3816	252	7	exists	exist	VERB
cana-3816	252	8	x	x	X
cana-3816	252	9	∈	∈	PROPN
cana-3816	252	10	b	b	NOUN
cana-3816	252	11	such	such	ADJ
cana-3816	252	12	that	that	PRON
cana-3816	252	13	ε	ε	PROPN
cana-3816	252	14	6	6	NUM
cana-3816	252	15	εζ1εζ2εζ3εζ4εζ5ε	εζ1εζ2εζ3εζ4εζ5ε	NOUN
cana-3816	252	16	.	.	PUNCT
cana-3816	253	1	then	then	ADV
cana-3816	253	2	ε	ε	PROPN
cana-3816	253	3	6	6	NUM
cana-3816	253	4	(	(	PUNCT
cana-3816	253	5	εζ1εζ2ε	εζ1εζ2ε	NOUN
cana-3816	253	6	)	)	PUNCT
cana-3816	253	7	,	,	PUNCT
cana-3816	253	8	(	(	PUNCT
cana-3816	253	9	ζ3εζ4εζ5	ζ3εζ4εζ5	NOUN
cana-3816	253	10	)	)	PUNCT
cana-3816	253	11	,	,	PUNCT
cana-3816	253	12	ε	ε	PROPN
cana-3816	253	13	∈	∈	PROPN
cana-3816	253	14	xε	xε	NOUN
cana-3816	253	15	.	.	PUNCT
cana-3816	254	1	we	we	PRON
cana-3816	254	2	have	have	VERB
cana-3816	254	3	(	(	PUNCT
cana-3816	254	4	t(`·`1·`2	t(`·`1·`2	NOUN
cana-3816	254	5	]	]	X
cana-3816	254	6	)	)	PUNCT
cana-3816	254	7	∝2	∝2	NOUN
cana-3816	254	8	∝1	∝1	NOUN
cana-3816	254	9	(	(	PUNCT
cana-3816	254	10	ε	ε	PROPN
cana-3816	254	11	,	,	PUNCT
cana-3816	254	12	ι	ι	PROPN
cana-3816	254	13	)	)	PUNCT
cana-3816	254	14	=	=	SYM
cana-3816	255	1	(	(	PUNCT
cana-3816	255	2	t(`·`1·`2	t(`·`1·`2	NOUN
cana-3816	255	3	]	]	X
cana-3816	255	4	(	(	PUNCT
cana-3816	255	5	ε	ε	PROPN
cana-3816	255	6	,	,	PUNCT
cana-3816	255	7	ι)5	ι)5	PROPN
cana-3816	255	8	∝2)4	∝2)4	PROPN
cana-3816	255	9	∝1	∝1	X
cana-3816	256	1	=	=	PUNCT
cana-3816	256	2	[	[	PUNCT
cana-3816	256	3	[	[	PUNCT
cana-3816	256	4	inf	inf	NOUN
cana-3816	256	5	ε6εζ1εζ2εζ3εζ4εζ5ε	ε6εζ1εζ2εζ3εζ4εζ5ε	PROPN
cana-3816	256	6	{	{	PUNCT
cana-3816	256	7	t	t	PROPN
cana-3816	256	8	`	`	PUNCT
cana-3816	256	9	(	(	PUNCT
cana-3816	256	10	]	]	X
cana-3816	256	11	,	,	PUNCT
cana-3816	256	12	ι)5	ι)5	PROPN
cana-3816	256	13	t`1	t`1	NOUN
cana-3816	256	14	(	(	PUNCT
cana-3816	256	15	∂	∂	NUM
cana-3816	256	16	,	,	PUNCT
cana-3816	256	17	ι)5	ι)5	PROPN
cana-3816	256	18	t`2	t`2	NOUN
cana-3816	256	19	(	(	PUNCT
cana-3816	256	20	ø	ø	PROPN
cana-3816	256	21	,	,	PUNCT
cana-3816	256	22	ι)}5	ι)}5	PROPN
cana-3816	256	23	∝2	∝2	PROPN
cana-3816	256	24	]	]	X
cana-3816	256	25	]	]	PUNCT
cana-3816	256	26	4	4	NUM
cana-3816	256	27	∝1	∝1	NOUN
cana-3816	256	28	=	=	PUNCT
cana-3816	256	29	[	[	PUNCT
cana-3816	256	30	inf	inf	NOUN
cana-3816	256	31	ε6εζ1εζ2εζ3εζ4εζ5ε	ε6εζ1εζ2εζ3εζ4εζ5ε	PROPN
cana-3816	256	32	{	{	PUNCT
cana-3816	256	33	t	t	PROPN
cana-3816	256	34	`	`	PUNCT
cana-3816	256	35	(	(	PUNCT
cana-3816	256	36	]	]	X
cana-3816	256	37	,	,	PUNCT
cana-3816	256	38	ι)5	ι)5	PROPN
cana-3816	256	39	t`1	t`1	NOUN
cana-3816	256	40	(	(	PUNCT
cana-3816	256	41	∂	∂	NUM
cana-3816	256	42	,	,	PUNCT
cana-3816	256	43	ι)5	ι)5	PROPN
cana-3816	256	44	t`2	t`2	NOUN
cana-3816	256	45	(	(	PUNCT
cana-3816	256	46	ø	ø	PROPN
cana-3816	256	47	,	,	PUNCT
cana-3816	256	48	ι)}5	ι)}5	PROPN
cana-3816	256	49	∝2	∝2	PROPN
cana-3816	256	50	5	5	NUM
cana-3816	256	51	∝2	∝2	PROPN
cana-3816	256	52	5	5	NUM
cana-3816	256	53	∝2	∝2	PROPN
cana-3816	256	54	5	5	NUM
cana-3816	256	55	∝2	∝2	NOUN
cana-3816	256	56	]	]	PUNCT
cana-3816	256	57	4	4	NUM
cana-3816	256	58	∝1	∝1	NOUN
cana-3816	256	59	=	=	PUNCT
cana-3816	256	60	[	[	PUNCT
cana-3816	256	61	inf	inf	NOUN
cana-3816	256	62	ε6εζ1εζ2εζ3εζ4εζ5ε	ε6εζ1εζ2εζ3εζ4εζ5ε	PROPN
cana-3816	256	63	{	{	PUNCT
cana-3816	256	64	(	(	PUNCT
cana-3816	256	65	t	t	NOUN
cana-3816	256	66	`	`	PUNCT
cana-3816	256	67	(	(	PUNCT
cana-3816	256	68	]	]	X
cana-3816	256	69	,	,	PUNCT
cana-3816	256	70	ι)5	ι)5	PROPN
cana-3816	256	71	∝2)5	∝2)5	PROPN
cana-3816	256	72	(	(	PUNCT
cana-3816	256	73	t`1	t`1	X
cana-3816	256	74	(	(	PUNCT
cana-3816	256	75	∂	∂	NUM
cana-3816	256	76	,	,	PUNCT
cana-3816	256	77	ι)5	ι)5	PROPN
cana-3816	256	78	∝2)5	∝2)5	PROPN
cana-3816	256	79	(	(	PUNCT
cana-3816	256	80	t`2	t`2	X
cana-3816	256	81	(	(	PUNCT
cana-3816	256	82	ø	ø	PROPN
cana-3816	256	83	,	,	PUNCT
cana-3816	256	84	ι)5	ι)5	PROPN
cana-3816	256	85	∝2)}5	∝2)}5	ADJ
cana-3816	256	86	∝2	∝2	NOUN
cana-3816	256	87	]	]	PUNCT
cana-3816	256	88	4	4	NUM
cana-3816	256	89	∝1	∝1	NUM
cana-3816	256	90	6	6	NUM
cana-3816	256	91	(	(	PUNCT
cana-3816	256	92	{	{	PUNCT
cana-3816	256	93	(	(	PUNCT
cana-3816	256	94	t	t	NOUN
cana-3816	256	95	`	`	PUNCT
cana-3816	256	96	(	(	PUNCT
cana-3816	256	97	εζ1εζ2ε	εζ1εζ2ε	PROPN
cana-3816	256	98	,	,	PUNCT
cana-3816	256	99	ι)4	ι)4	X
cana-3816	256	100	∝1)5	∝1)5	PROPN
cana-3816	256	101	(	(	PUNCT
cana-3816	256	102	t`1	t`1	X
cana-3816	256	103	(	(	PUNCT
cana-3816	256	104	ζ3εζ4εζ5)4	ζ3εζ4εζ5)4	X
cana-3816	256	105	∝1)5	∝1)5	PRON
cana-3816	256	106	(	(	PUNCT
cana-3816	256	107	t`2	t`2	X
cana-3816	256	108	(	(	PUNCT
cana-3816	256	109	ε	ε	PROPN
cana-3816	256	110	,	,	PUNCT
cana-3816	256	111	ι)4	ι)4	PROPN
cana-3816	256	112	∝1)}5	∝1)}5	PROPN
cana-3816	256	113	∝2)4	∝2)4	PROPN
cana-3816	256	114	∝1	∝1	NUM
cana-3816	256	115	6	6	NUM
cana-3816	256	116	(	(	PUNCT
cana-3816	256	117	{	{	PUNCT
cana-3816	256	118	(	(	PUNCT
cana-3816	256	119	t	t	NOUN
cana-3816	256	120	`	`	PUNCT
cana-3816	256	121	(	(	PUNCT
cana-3816	256	122	ε	ε	PROPN
cana-3816	256	123	,	,	PUNCT
cana-3816	256	124	ι)4	ι)4	X
cana-3816	256	125	∝1)5	∝1)5	PROPN
cana-3816	256	126	(	(	PUNCT
cana-3816	256	127	t`1	t`1	X
cana-3816	256	128	(	(	PUNCT
cana-3816	256	129	ε	ε	PROPN
cana-3816	256	130	,	,	PUNCT
cana-3816	256	131	ι)4	ι)4	X
cana-3816	256	132	∝1)5	∝1)5	PROPN
cana-3816	256	133	(	(	PUNCT
cana-3816	256	134	t`2	t`2	X
cana-3816	256	135	(	(	PUNCT
cana-3816	256	136	ε	ε	PROPN
cana-3816	256	137	,	,	PUNCT
cana-3816	256	138	ι)4	ι)4	PROPN
cana-3816	256	139	∝1)}5	∝1)}5	PROPN
cana-3816	256	140	∝2)4	∝2)4	PROPN
cana-3816	256	141	∝1	∝1	ADJ
cana-3816	256	142	=	=	PRON
cana-3816	256	143	{	{	PUNCT
cana-3816	256	144	(	(	PUNCT
cana-3816	256	145	(	(	PUNCT
cana-3816	256	146	t	t	NOUN
cana-3816	256	147	`	`	PUNCT
cana-3816	256	148	(	(	PUNCT
cana-3816	256	149	ε	ε	PROPN
cana-3816	256	150	,	,	PUNCT
cana-3816	256	151	ι)5	ι)5	PROPN
cana-3816	256	152	t`1	t`1	NOUN
cana-3816	256	153	(	(	PUNCT
cana-3816	256	154	ε	ε	PROPN
cana-3816	256	155	,	,	PUNCT
cana-3816	256	156	ι)5	ι)5	PROPN
cana-3816	256	157	t`2	t`2	NOUN
cana-3816	256	158	(	(	PUNCT
cana-3816	256	159	ε	ε	PROPN
cana-3816	256	160	,	,	PUNCT
cana-3816	256	161	ι))4	ι))4	NUM
cana-3816	256	162	∝1)5	∝1)5	NOUN
cana-3816	256	163	∝2}4	∝2}4	NOUN
cana-3816	256	164	∝1	∝1	NUM
cana-3816	257	1	=	=	PRON
cana-3816	257	2	{	{	PUNCT
cana-3816	257	3	(	(	PUNCT
cana-3816	257	4	(	(	PUNCT
cana-3816	257	5	t	t	NOUN
cana-3816	257	6	`	`	NUM
cana-3816	257	7	5	5	NUM
cana-3816	257	8	t`1	t`1	NUM
cana-3816	257	9	5	5	NUM
cana-3816	257	10	t`2	t`2	NOUN
cana-3816	257	11	)	)	PUNCT
cana-3816	257	12	(	(	PUNCT
cana-3816	257	13	ε	ε	PROPN
cana-3816	257	14	,	,	PUNCT
cana-3816	257	15	ι)5	ι)5	X
cana-3816	257	16	∝2}4	∝2}4	NOUN
cana-3816	257	17	∝1	∝1	NUM
cana-3816	258	1	=	=	PUNCT
cana-3816	258	2	(	(	PUNCT
cana-3816	258	3	t`∩`1∩`2)∝2	t`∩`1∩`2)∝2	NOUN
cana-3816	258	4	∝1	∝1	X
cana-3816	258	5	(	(	PUNCT
cana-3816	258	6	ε	ε	PROPN
cana-3816	258	7	,	,	PUNCT
cana-3816	258	8	ι	ι	PROPN
cana-3816	258	9	)	)	PUNCT
cana-3816	258	10	https://internationalpubls.com	https://internationalpubls.com	X
cana-3816	258	11	768	768	NUM
cana-3816	258	12	communications	communication	NOUN
cana-3816	258	13	on	on	ADP
cana-3816	258	14	applied	apply	VERB
cana-3816	258	15	nonlinear	nonlinear	ADJ
cana-3816	258	16	analysis	analysis	NOUN
cana-3816	258	17	issn	issn	NOUN
cana-3816	258	18	:	:	PUNCT
cana-3816	258	19	1074	1074	NUM
cana-3816	258	20	-	-	PUNCT
cana-3816	258	21	133x	133x	NUM
cana-3816	258	22	vol	vol	NOUN
cana-3816	258	23	32	32	NUM
cana-3816	258	24	no	no	NOUN
cana-3816	258	25	.	.	NOUN
cana-3816	258	26	3	3	NUM
cana-3816	258	27	(	(	PUNCT
cana-3816	258	28	2025	2025	NUM
cana-3816	258	29	)	)	PUNCT
cana-3816	258	30	(	(	PUNCT
cana-3816	258	31	>	>	X
cana-3816	258	32	(	(	PUNCT
cana-3816	258	33	`	`	PUNCT
cana-3816	258	34	·	·	PUNCT
cana-3816	258	35	`	`	PUNCT
cana-3816	258	36	1·`2	1·`2	NUM
cana-3816	258	37	]	]	SYM
cana-3816	258	38	)	)	PUNCT
cana-3816	258	39	∝2	∝2	NOUN
cana-3816	258	40	∝1	∝1	NOUN
cana-3816	258	41	(	(	PUNCT
cana-3816	258	42	ε	ε	PROPN
cana-3816	258	43	,	,	PUNCT
cana-3816	258	44	ι	ι	PROPN
cana-3816	258	45	)	)	PUNCT
cana-3816	258	46	=	=	SYM
cana-3816	258	47	(	(	PUNCT
cana-3816	258	48	>	>	X
cana-3816	258	49	(	(	PUNCT
cana-3816	258	50	`	`	PUNCT
cana-3816	258	51	·	·	PUNCT
cana-3816	258	52	`	`	PUNCT
cana-3816	258	53	1·`2](ε	1·`2](ε	NUM
cana-3816	258	54	,	,	PUNCT
cana-3816	258	55	ι)4	ι)4	PROPN
cana-3816	258	56	∝2)5	∝2)5	PROPN
cana-3816	258	57	∝1	∝1	X
cana-3816	259	1	=	=	PUNCT
cana-3816	259	2	[	[	PUNCT
cana-3816	259	3	[	[	PUNCT
cana-3816	259	4	sup	sup	NOUN
cana-3816	259	5	ε6εζ1εζ2εζ3εζ4εζ5ε	ε6εζ1εζ2εζ3εζ4εζ5ε	NOUN
cana-3816	259	6	{	{	PUNCT
cana-3816	259	7	>	>	X
cana-3816	259	8	`	`	PUNCT
cana-3816	259	9	(	(	PUNCT
cana-3816	259	10	]	]	X
cana-3816	259	11	,	,	PUNCT
cana-3816	259	12	ι)4>`1	ι)4>`1	NOUN
cana-3816	259	13	(	(	PUNCT
cana-3816	259	14	∂	∂	NUM
cana-3816	259	15	,	,	PUNCT
cana-3816	259	16	ι)4>`2	ι)4>`2	X
cana-3816	259	17	(	(	PUNCT
cana-3816	259	18	ø	ø	X
cana-3816	259	19	,	,	PUNCT
cana-3816	259	20	ι)}4	ι)}4	PROPN
cana-3816	259	21	∝2	∝2	PROPN
cana-3816	259	22	]	]	X
cana-3816	259	23	]	]	PUNCT
cana-3816	259	24	5	5	NUM
cana-3816	259	25	∝1	∝1	NOUN
cana-3816	259	26	=	=	PUNCT
cana-3816	259	27	[	[	PUNCT
cana-3816	259	28	sup	sup	NOUN
cana-3816	259	29	ε6εζ1εζ2εζ3εζ4εζ5ε	ε6εζ1εζ2εζ3εζ4εζ5ε	NOUN
cana-3816	259	30	{	{	PUNCT
cana-3816	259	31	>	>	X
cana-3816	259	32	`	`	PUNCT
cana-3816	259	33	(	(	PUNCT
cana-3816	259	34	]	]	X
cana-3816	259	35	,	,	PUNCT
cana-3816	259	36	ι)4>`1	ι)4>`1	NOUN
cana-3816	259	37	(	(	PUNCT
cana-3816	259	38	∂	∂	NUM
cana-3816	259	39	,	,	PUNCT
cana-3816	259	40	ι)4>`2	ι)4>`2	X
cana-3816	259	41	(	(	PUNCT
cana-3816	259	42	ø	ø	X
cana-3816	259	43	,	,	PUNCT
cana-3816	259	44	ι)}4	ι)}4	PROPN
cana-3816	259	45	∝2	∝2	PROPN
cana-3816	259	46	4	4	NUM
cana-3816	259	47	∝2	∝2	NOUN
cana-3816	259	48	4	4	NUM
cana-3816	259	49	∝2	∝2	NOUN
cana-3816	259	50	4	4	NUM
cana-3816	259	51	∝2	∝2	NOUN
cana-3816	259	52	]	]	PUNCT
cana-3816	259	53	5	5	NUM
cana-3816	259	54	∝1	∝1	NOUN
cana-3816	259	55	=	=	PUNCT
cana-3816	259	56	[	[	PUNCT
cana-3816	259	57	sup	sup	NOUN
cana-3816	259	58	ε6εζ1εζ2εζ3εζ4εζ5ε	ε6εζ1εζ2εζ3εζ4εζ5ε	NUM
cana-3816	259	59	{	{	PUNCT
cana-3816	259	60	(	(	PUNCT
cana-3816	259	61	>	>	X
cana-3816	259	62	`	`	PUNCT
cana-3816	259	63	(	(	PUNCT
cana-3816	259	64	]	]	X
cana-3816	259	65	,	,	PUNCT
cana-3816	259	66	ι)4	ι)4	PROPN
cana-3816	259	67	∝2)4	∝2)4	PROPN
cana-3816	259	68	(	(	PUNCT
cana-3816	259	69	>	>	X
cana-3816	259	70	`	`	PUNCT
cana-3816	259	71	1	1	NUM
cana-3816	259	72	(	(	PUNCT
cana-3816	259	73	∂	∂	NUM
cana-3816	259	74	,	,	PUNCT
cana-3816	259	75	ι)4	ι)4	PROPN
cana-3816	259	76	∝2)4	∝2)4	PROPN
cana-3816	259	77	(	(	PUNCT
cana-3816	259	78	>	>	X
cana-3816	259	79	`	`	PUNCT
cana-3816	259	80	2	2	NUM
cana-3816	259	81	(	(	PUNCT
cana-3816	259	82	ø	ø	PROPN
cana-3816	259	83	,	,	PUNCT
cana-3816	259	84	ι)4	ι)4	PROPN
cana-3816	259	85	∝2)}4	∝2)}4	NUM
cana-3816	259	86	∝2	∝2	NOUN
cana-3816	259	87	]	]	PUNCT
cana-3816	259	88	5	5	NUM
cana-3816	259	89	∝1	∝1	NOUN
cana-3816	259	90	>	>	X
cana-3816	259	91	(	(	PUNCT
cana-3816	259	92	{	{	PUNCT
cana-3816	259	93	(	(	PUNCT
cana-3816	259	94	>	>	X
cana-3816	259	95	`	`	PUNCT
cana-3816	259	96	(	(	PUNCT
cana-3816	259	97	εζ1εζ2ε	εζ1εζ2ε	PROPN
cana-3816	259	98	,	,	PUNCT
cana-3816	259	99	ι)5	ι)5	PROPN
cana-3816	259	100	∝1)4	∝1)4	PROPN
cana-3816	259	101	(	(	PUNCT
cana-3816	259	102	>	>	X
cana-3816	259	103	`	`	PUNCT
cana-3816	259	104	1	1	NUM
cana-3816	259	105	(	(	PUNCT
cana-3816	259	106	ζ3εζ4εζ5)5	ζ3εζ4εζ5)5	NOUN
cana-3816	259	107	∝1)4	∝1)4	PROPN
cana-3816	259	108	(	(	PUNCT
cana-3816	259	109	>	>	X
cana-3816	259	110	`	`	PUNCT
cana-3816	259	111	2	2	NUM
cana-3816	259	112	(	(	PUNCT
cana-3816	259	113	ε	ε	PROPN
cana-3816	259	114	,	,	PUNCT
cana-3816	259	115	ι)5	ι)5	NOUN
cana-3816	259	116	∝1)}4	∝1)}4	PROPN
cana-3816	259	117	∝2)5	∝2)5	PROPN
cana-3816	259	118	∝1	∝1	PROPN
cana-3816	259	119	>	>	X
cana-3816	259	120	(	(	PUNCT
cana-3816	259	121	{	{	PUNCT
cana-3816	259	122	(	(	PUNCT
cana-3816	259	123	>	>	X
cana-3816	259	124	`	`	PUNCT
cana-3816	259	125	(	(	PUNCT
cana-3816	259	126	ε	ε	PROPN
cana-3816	259	127	,	,	PUNCT
cana-3816	259	128	ι)5	ι)5	PROPN
cana-3816	259	129	∝1)4	∝1)4	PROPN
cana-3816	259	130	(	(	PUNCT
cana-3816	259	131	>	>	X
cana-3816	259	132	`	`	PUNCT
cana-3816	259	133	1	1	NUM
cana-3816	259	134	(	(	PUNCT
cana-3816	259	135	ε	ε	PROPN
cana-3816	259	136	,	,	PUNCT
cana-3816	259	137	ι)5	ι)5	PROPN
cana-3816	259	138	∝1)4	∝1)4	PROPN
cana-3816	259	139	(	(	PUNCT
cana-3816	259	140	>	>	X
cana-3816	259	141	`	`	PUNCT
cana-3816	259	142	2	2	NUM
cana-3816	259	143	(	(	PUNCT
cana-3816	259	144	ε	ε	PROPN
cana-3816	259	145	,	,	PUNCT
cana-3816	259	146	ι)5	ι)5	NOUN
cana-3816	259	147	∝1)}4	∝1)}4	PROPN
cana-3816	259	148	∝2)5	∝2)5	PROPN
cana-3816	259	149	∝1	∝1	X
cana-3816	259	150	=	=	PRON
cana-3816	259	151	{	{	PUNCT
cana-3816	259	152	(	(	PUNCT
cana-3816	259	153	(	(	PUNCT
cana-3816	259	154	>	>	X
cana-3816	259	155	`	`	PUNCT
cana-3816	259	156	(	(	PUNCT
cana-3816	259	157	ε	ε	PROPN
cana-3816	259	158	,	,	PUNCT
cana-3816	259	159	ι)4>`1	ι)4>`1	X
cana-3816	259	160	(	(	PUNCT
cana-3816	259	161	ε	ε	PROPN
cana-3816	259	162	,	,	PUNCT
cana-3816	259	163	ι)4>`2	ι)4>`2	X
cana-3816	259	164	(	(	PUNCT
cana-3816	259	165	ε	ε	PROPN
cana-3816	259	166	,	,	PUNCT
cana-3816	259	167	ι))5	ι))5	ADP
cana-3816	259	168	∝1)4	∝1)4	PROPN
cana-3816	259	169	∝2}5	∝2}5	PROPN
cana-3816	259	170	∝1	∝1	NOUN
cana-3816	259	171	=	=	PUNCT
cana-3816	259	172	{	{	PUNCT
cana-3816	259	173	(	(	PUNCT
cana-3816	259	174	(	(	PUNCT
cana-3816	259	175	>	>	X
cana-3816	259	176	`	`	PUNCT
cana-3816	259	177	4>`1	4>`1	NUM
cana-3816	259	178	4>`2	4>`2	NUM
cana-3816	259	179	)	)	PUNCT
cana-3816	259	180	(	(	PUNCT
cana-3816	259	181	ε	ε	PROPN
cana-3816	259	182	,	,	PUNCT
cana-3816	259	183	ι)4	ι)4	PROPN
cana-3816	259	184	∝2}5	∝2}5	PROPN
cana-3816	259	185	∝1	∝1	NUM
cana-3816	259	186	=	=	PUNCT
cana-3816	259	187	(	(	PUNCT
cana-3816	259	188	>	>	X
cana-3816	259	189	`	`	PUNCT
cana-3816	259	190	∪`1∪`2)∝2	∪`1∪`2)∝2	X
cana-3816	259	191	∝1	∝1	X
cana-3816	259	192	(	(	PUNCT
cana-3816	259	193	ε	ε	PROPN
cana-3816	259	194	,	,	PUNCT
cana-3816	259	195	ι	ι	PROPN
cana-3816	259	196	)	)	PUNCT
cana-3816	259	197	thus	thus	ADV
cana-3816	259	198	,	,	PUNCT
cana-3816	259	199	(	(	PUNCT
cana-3816	259	200	(	(	PUNCT
cana-3816	259	201	`	`	PUNCT
cana-3816	259	202	·	·	PUNCT
cana-3816	259	203	`	`	PUNCT
cana-3816	259	204	1	1	NUM
cana-3816	259	205	·	·	PUNCT
cana-3816	259	206	`	`	PUNCT
cana-3816	259	207	2])∝2	2])∝2	NUM
cana-3816	259	208	∝1	∝1	PROPN
cana-3816	259	209	⊇	⊇	X
cana-3816	259	210	(	(	PUNCT
cana-3816	259	211	(	(	PUNCT
cana-3816	259	212	`	`	PUNCT
cana-3816	259	213	∩`1∩`2])∝2	∩`1∩`2])∝2	X
cana-3816	259	214	∝1	∝1	NOUN
cana-3816	259	215	and	and	CCONJ
cana-3816	259	216	by	by	ADP
cana-3816	259	217	theorem	theorem	NOUN
cana-3816	259	218	2.16	2.16	NUM
cana-3816	259	219	and	and	CCONJ
cana-3816	259	220	hence	hence	ADV
cana-3816	259	221	(	(	PUNCT
cana-3816	259	222	(	(	PUNCT
cana-3816	259	223	`	`	PUNCT
cana-3816	259	224	·	·	PUNCT
cana-3816	259	225	`	`	PUNCT
cana-3816	259	226	1	1	NUM
cana-3816	259	227	·	·	PUNCT
cana-3816	259	228	`	`	PUNCT
cana-3816	259	229	2])∝2	2])∝2	NUM
cana-3816	259	230	∝1	∝1	X
cana-3816	259	231	=	=	PUNCT
cana-3816	259	232	(	(	PUNCT
cana-3816	259	233	(	(	PUNCT
cana-3816	259	234	`	`	PUNCT
cana-3816	259	235	∩`1∩`2])∝2	∩`1∩`2])∝2	X
cana-3816	259	236	∝1	∝1	NOUN
cana-3816	259	237	.	.	PUNCT
cana-3816	260	1	conversely	conversely	ADV
cana-3816	260	2	assume	assume	VERB
cana-3816	260	3	that	that	SCONJ
cana-3816	260	4	(	(	PUNCT
cana-3816	260	5	(	(	PUNCT
cana-3816	260	6	`	`	PUNCT
cana-3816	260	7	·	·	PUNCT
cana-3816	260	8	`	`	PUNCT
cana-3816	260	9	1	1	X
cana-3816	260	10	·	·	PUNCT
cana-3816	260	11	`	`	PUNCT
cana-3816	260	12	2])∝2	2])∝2	NUM
cana-3816	260	13	∝1	∝1	X
cana-3816	260	14	=	=	PUNCT
cana-3816	260	15	(	(	PUNCT
cana-3816	260	16	(	(	PUNCT
cana-3816	260	17	`	`	PUNCT
cana-3816	260	18	∩	∩	ADJ
cana-3816	260	19	`	`	PUNCT
cana-3816	260	20	1	1	NUM
cana-3816	260	21	∩	∩	NOUN
cana-3816	260	22	`	`	PUNCT
cana-3816	260	23	2])∝2	2])∝2	NUM
cana-3816	260	24	∝1	∝1	NUM
cana-3816	260	25	.	.	PUNCT
cana-3816	261	1	let	let	VERB
cana-3816	261	2	`	`	PUNCT
cana-3816	261	3	=	=	SYM
cana-3816	261	4	(	(	PUNCT
cana-3816	261	5	t	t	NOUN
cana-3816	261	6	`	`	PUNCT
cana-3816	261	7	,	,	PUNCT
cana-3816	261	8	>	>	PUNCT
cana-3816	261	9	`	`	PUNCT
cana-3816	261	10	)	)	PUNCT
cana-3816	261	11	be	be	AUX
cana-3816	261	12	an	an	DET
cana-3816	261	13	(	(	PUNCT
cana-3816	261	14	∝1,∝2)iq1afbi	∝1,∝2)iq1afbi	PROPN
cana-3816	261	15	,	,	PUNCT
cana-3816	261	16	`	`	PUNCT
cana-3816	261	17	1	1	NUM
cana-3816	261	18	=	=	SYM
cana-3816	261	19	(	(	PUNCT
cana-3816	261	20	t`1	t`1	INTJ
cana-3816	261	21	,	,	PUNCT
cana-3816	261	22	ξ`1	ξ`1	PROPN
cana-3816	261	23	,	,	PUNCT
cana-3816	261	24	>	>	X
cana-3816	261	25	`	`	PUNCT
cana-3816	261	26	1	1	X
cana-3816	261	27	)	)	PUNCT
cana-3816	261	28	be	be	AUX
cana-3816	261	29	an	an	DET
cana-3816	261	30	(	(	PUNCT
cana-3816	261	31	∝1,∝2)iq1aflati	∝1,∝2)iq1aflati	NOUN
cana-3816	261	32	and	and	CCONJ
cana-3816	261	33	`	`	PUNCT
cana-3816	261	34	2	2	NUM
cana-3816	261	35	=	=	SYM
cana-3816	261	36	(	(	PUNCT
cana-3816	261	37	t`2	t`2	INTJ
cana-3816	261	38	,	,	PUNCT
cana-3816	261	39	>	>	X
cana-3816	261	40	`	`	PUNCT
cana-3816	261	41	2	2	X
cana-3816	261	42	)	)	PUNCT
cana-3816	261	43	be	be	AUX
cana-3816	261	44	an	an	DET
cana-3816	261	45	(	(	PUNCT
cana-3816	261	46	∝1,∝2)iq1afli	∝1,∝2)iq1afli	NOUN
cana-3816	261	47	of	of	ADP
cana-3816	261	48	b.	b.	PROPN
cana-3816	261	49	then	then	ADV
cana-3816	261	50	by	by	ADP
cana-3816	261	51	theorem	theorem	NOUN
cana-3816	261	52	2.11	2.11	NUM
cana-3816	261	53	,	,	PUNCT
cana-3816	261	54			PROPN
cana-3816	261	55	`	`	PUNCT
cana-3816	261	56	is	be	AUX
cana-3816	261	57	a	a	DET
cana-3816	261	58	(	(	PUNCT
cana-3816	261	59	∝1,∝2)iq1afbi	∝1,∝2)iq1afbi	PROPN
cana-3816	261	60	,	,	PUNCT
cana-3816	261	61	`1	`1	PROPN
cana-3816	261	62	is	be	AUX
cana-3816	261	63	a	a	DET
cana-3816	261	64	(	(	PUNCT
cana-3816	261	65	∝1,∝2)iq1aflati	∝1,∝2)iq1aflati	NOUN
cana-3816	261	66	and	and	CCONJ
cana-3816	261	67	`2	`2	NOUN
cana-3816	261	68	be	be	VERB
cana-3816	261	69	a	a	DET
cana-3816	261	70	(	(	PUNCT
cana-3816	261	71	∝1,∝2)iq1afli	∝1,∝2)iq1afli	NOUN
cana-3816	261	72	of	of	ADP
cana-3816	261	73	b.	b.	PROPN
cana-3816	261	74	by	by	ADP
cana-3816	261	75	lemma	lemma	PROPN
cana-3816	261	76	2.14	2.14	NUM
cana-3816	261	77	and	and	CCONJ
cana-3816	261	78	theorem	theorem	VERB
cana-3816	261	79	2.15	2.15	NUM
cana-3816	261	80	,	,	PUNCT
cana-3816	261	81	(	(	PUNCT
cana-3816	261	82	(`∩`1∩`2	(`∩`1∩`2	NOUN
cana-3816	261	83	]	]	PUNCT
cana-3816	261	84	)	)	PUNCT
cana-3816	261	85	∝2	∝2	NOUN
cana-3816	261	86	∝1	∝1	NOUN
cana-3816	261	87	=	=	SYM
cana-3816	261	88	(	(	PUNCT
cana-3816	261	89	`∩`1	`∩`1	X
cana-3816	261	90	∩`2	∩`2	SYM
cana-3816	261	91	)	)	PUNCT
cana-3816	261	92	∝2	∝2	NOUN
cana-3816	261	93	∝1	∝1	NOUN
cana-3816	261	94	=	=	SYM
cana-3816	261	95	(	(	PUNCT
cana-3816	261	96			PROPN
cana-3816	261	97	`	`	PUNCT
cana-3816	261	98	·	·	PUNCT
cana-3816	261	99	`1	`1	NOUN
cana-3816	261	100	·	·	SYM
cana-3816	261	101	`2	`2	NOUN
cana-3816	261	102	)	)	PUNCT
cana-3816	261	103	∝2	∝2	NOUN
cana-3816	261	104	∝1	∝1	NOUN
cana-3816	261	105	=	=	SYM
cana-3816	261	106	(	(	PUNCT
cana-3816	261	107	(`·`1·`2	(`·`1·`2	PROPN
cana-3816	261	108	]	]	NOUN
cana-3816	261	109	)	)	PUNCT
cana-3816	261	110	∝2	∝2	NOUN
cana-3816	261	111	∝1	∝1	NOUN
cana-3816	261	112	.	.	PUNCT
cana-3816	262	1	this	this	PRON
cana-3816	262	2	implies	imply	VERB
cana-3816	262	3	(	(	PUNCT
cana-3816	262	4	`	`	PUNCT
cana-3816	262	5	∩	∩	ADJ
cana-3816	262	6	`	`	PUNCT
cana-3816	262	7	1	1	NUM
cana-3816	262	8	∩	∩	NOUN
cana-3816	262	9	`	`	PUNCT
cana-3816	262	10	2]∝2	2]∝2	NUM
cana-3816	262	11	∝1	∝1	NUM
cana-3816	262	12	=	=	PUNCT
cana-3816	262	13	(	(	PUNCT
cana-3816	262	14	(	(	PUNCT
cana-3816	262	15	`	`	PUNCT
cana-3816	262	16	·	·	PUNCT
cana-3816	262	17	`	`	PUNCT
cana-3816	262	18	1	1	X
cana-3816	262	19	·	·	PUNCT
cana-3816	262	20	`	`	PUNCT
cana-3816	262	21	2])∝2	2])∝2	NUM
cana-3816	262	22	∝1	∝1	NOUN
cana-3816	262	23	.	.	PUNCT
cana-3816	263	1	hence	hence	ADV
cana-3816	263	2	by	by	ADP
cana-3816	263	3	corollary	corollary	ADJ
cana-3816	263	4	?	?	PUNCT
cana-3816	263	5	?	?	PUNCT
cana-3816	263	6	,	,	PUNCT
cana-3816	263	7	b	b	PROPN
cana-3816	263	8	is	be	AUX
cana-3816	263	9	regular	regular	ADJ
cana-3816	263	10	.	.	PUNCT
cana-3816	264	1	acknowledgment	acknowledgment	NOUN
cana-3816	264	2	.	.	PUNCT
cana-3816	265	1	this	this	DET
cana-3816	265	2	research	research	NOUN
cana-3816	265	3	was	be	AUX
cana-3816	265	4	supported	support	VERB
cana-3816	265	5	by	by	ADP
cana-3816	265	6	university	university	NOUN
cana-3816	265	7	of	of	ADP
cana-3816	265	8	phayao	phayao	NOUN
cana-3816	265	9	and	and	CCONJ
cana-3816	265	10	thailand	thailand	PROPN
cana-3816	265	11	science	science	PROPN
cana-3816	265	12	research	research	PROPN
cana-3816	265	13	and	and	CCONJ
cana-3816	265	14	innovation	innovation	NOUN
cana-3816	265	15	fund	fund	NOUN
cana-3816	265	16	(	(	PUNCT
cana-3816	265	17	fundamental	fundamental	ADJ
cana-3816	265	18	fund	fund	NOUN
cana-3816	265	19	2025	2025	NUM
cana-3816	265	20	,	,	PUNCT
cana-3816	265	21	grant	grant	VERB
cana-3816	265	22	no	no	NOUN
cana-3816	265	23	.	.	PROPN
cana-3816	266	1	5027/2567	5027/2567	NUM
cana-3816	266	2	)	)	PUNCT
cana-3816	266	3	.	.	PUNCT
cana-3816	267	1	conflicts	conflict	NOUN
cana-3816	267	2	of	of	ADP
cana-3816	267	3	interest	interest	NOUN
cana-3816	267	4	the	the	DET
cana-3816	267	5	author(s	author(s	NOUN
cana-3816	267	6	)	)	PUNCT
cana-3816	267	7	declare	declare	VERB
cana-3816	267	8	that	that	SCONJ
cana-3816	267	9	there	there	PRON
cana-3816	267	10	are	be	VERB
cana-3816	267	11	no	no	DET
cana-3816	267	12	conflicts	conflict	NOUN
cana-3816	267	13	of	of	ADP
cana-3816	267	14	interest	interest	NOUN
cana-3816	267	15	regarding	regard	VERB
cana-3816	267	16	the	the	DET
cana-3816	267	17	publication	publication	NOUN
cana-3816	267	18	of	of	ADP
cana-3816	267	19	this	this	DET
cana-3816	267	20	paper	paper	NOUN
cana-3816	267	21	.	.	PUNCT
cana-3816	268	1	references	reference	NOUN
cana-3816	268	2	[	[	X
cana-3816	268	3	1	1	NUM
cana-3816	268	4	]	]	X
cana-3816	268	5	lehmer	lehmer	PROPN
cana-3816	268	6	d.	d.	PROPN
cana-3816	268	7	h.	h.	PROPN
cana-3816	268	8	,	,	PUNCT
cana-3816	268	9	a	a	DET
cana-3816	268	10	ternary	ternary	ADJ
cana-3816	268	11	analogue	analogue	NOUN
cana-3816	268	12	of	of	ADP
cana-3816	268	13	abelian	abelian	ADJ
cana-3816	268	14	groups	group	NOUN
cana-3816	268	15	.	.	PUNCT
cana-3816	269	1	american	american	ADJ
cana-3816	269	2	journal	journal	PROPN
cana-3816	269	3	of	of	ADP
cana-3816	269	4	mathematics	mathematic	NOUN
cana-3816	269	5	,	,	PUNCT
cana-3816	269	6	(	(	PUNCT
cana-3816	269	7	1932	1932	NUM
cana-3816	269	8	)	)	PUNCT
cana-3816	269	9	,	,	PUNCT
cana-3816	269	10	329	329	NUM
cana-3816	269	11	-	-	SYM
cana-3816	269	12	338	338	NUM
cana-3816	269	13	.	.	PUNCT
cana-3816	270	1	[	[	X
cana-3816	270	2	2	2	NUM
cana-3816	270	3	]	]	PUNCT
cana-3816	270	4	hestenes	hestene	NOUN
cana-3816	270	5	m.r	m.r	PROPN
cana-3816	270	6	.	.	PROPN
cana-3816	271	1	a	a	DET
cana-3816	271	2	ternary	ternary	ADJ
cana-3816	271	3	algebra	algebra	NOUN
cana-3816	271	4	with	with	ADP
cana-3816	271	5	applications	application	NOUN
cana-3816	271	6	to	to	ADP
cana-3816	271	7	matrices	matrix	NOUN
cana-3816	271	8	and	and	CCONJ
cana-3816	271	9	linear	linear	ADJ
cana-3816	271	10	transformations	transformation	NOUN
cana-3816	271	11	.	.	PUNCT
cana-3816	272	1	arch	arch	NOUN
cana-3816	272	2	.	.	PUNCT
cana-3816	273	1	ration	ration	NOUN
cana-3816	273	2	.	.	PUNCT
cana-3816	274	1	mech	mech	PROPN
cana-3816	274	2	.	.	PUNCT
cana-3816	275	1	anal	anal	PROPN
cana-3816	275	2	.	.	PUNCT
cana-3816	276	1	11(1962	11(1962	NUM
cana-3816	276	2	)	)	PUNCT
cana-3816	277	1	,	,	PUNCT
cana-3816	277	2	138	138	NUM
cana-3816	277	3	-194	-194	PROPN
cana-3816	277	4	.	.	PUNCT
cana-3816	278	1	[	[	X
cana-3816	278	2	3	3	X
cana-3816	278	3	]	]	X
cana-3816	278	4	l.	l.	PROPN
cana-3816	278	5	a.	a.	PROPN
cana-3816	278	6	zadeh	zadeh	PROPN
cana-3816	278	7	,	,	PUNCT
cana-3816	278	8	fuzzy	fuzzy	ADJ
cana-3816	278	9	sets	set	NOUN
cana-3816	278	10	,	,	PUNCT
cana-3816	278	11	information	information	NOUN
cana-3816	278	12	and	and	CCONJ
cana-3816	278	13	control	control	NOUN
cana-3816	278	14	,	,	PUNCT
cana-3816	278	15	8	8	NUM
cana-3816	278	16	,	,	PUNCT
cana-3816	278	17	(	(	PUNCT
cana-3816	278	18	1965	1965	NUM
cana-3816	278	19	)	)	PUNCT
cana-3816	278	20	,	,	PUNCT
cana-3816	278	21	338	338	NUM
cana-3816	278	22	-	-	SYM
cana-3816	278	23	353	353	NUM
cana-3816	278	24	.	.	PUNCT
cana-3816	279	1	[	[	X
cana-3816	279	2	4	4	X
cana-3816	279	3	]	]	PUNCT
cana-3816	279	4	k.	k.	PROPN
cana-3816	279	5	atanassov	atanassov	PROPN
cana-3816	279	6	,	,	PUNCT
cana-3816	279	7	intuitionistic	intuitionistic	ADJ
cana-3816	279	8	fuzzy	fuzzy	ADJ
cana-3816	279	9	sets	set	NOUN
cana-3816	279	10	,	,	PUNCT
cana-3816	279	11	fuzzy	fuzzy	ADJ
cana-3816	279	12	sets	set	NOUN
cana-3816	279	13	and	and	CCONJ
cana-3816	279	14	systems	system	NOUN
cana-3816	279	15	,	,	PUNCT
cana-3816	279	16	20(1	20(1	NUM
cana-3816	279	17	)	)	PUNCT
cana-3816	279	18	,	,	PUNCT
cana-3816	279	19	(	(	PUNCT
cana-3816	279	20	1986	1986	NUM
cana-3816	279	21	)	)	PUNCT
cana-3816	279	22	87	87	NUM
cana-3816	279	23	-	-	SYM
cana-3816	279	24	96	96	NUM
cana-3816	279	25	.	.	PUNCT
cana-3816	280	1	[	[	X
cana-3816	280	2	5	5	NUM
cana-3816	280	3	]	]	PUNCT
cana-3816	280	4	r.	r.	PROPN
cana-3816	280	5	r.	r.	PROPN
cana-3816	280	6	yager	yager	PROPN
cana-3816	280	7	,	,	PUNCT
cana-3816	280	8	pythagorean	pythagorean	PROPN
cana-3816	280	9	membership	membership	NOUN
cana-3816	280	10	grades	grade	NOUN
cana-3816	280	11	in	in	ADP
cana-3816	280	12	multi	multi	ADJ
cana-3816	280	13	criteria	criterion	NOUN
cana-3816	280	14	decision	decision	NOUN
cana-3816	280	15	-	-	PUNCT
cana-3816	280	16	making	making	NOUN
cana-3816	280	17	,	,	PUNCT
cana-3816	280	18	ieee	ieee	PROPN
cana-3816	280	19	.	.	PUNCT
cana-3816	281	1	trans	trans	PROPN
cana-3816	281	2	.	.	PUNCT
cana-3816	281	3	fuzzy	fuzzy	ADJ
cana-3816	281	4	systems	system	NOUN
cana-3816	281	5	,	,	PUNCT
cana-3816	281	6	22	22	NUM
cana-3816	281	7	,	,	PUNCT
cana-3816	281	8	(	(	PUNCT
cana-3816	281	9	2014	2014	NUM
cana-3816	281	10	)	)	PUNCT
cana-3816	281	11	,	,	PUNCT
cana-3816	281	12	958	958	NUM
cana-3816	281	13	-	-	SYM
cana-3816	281	14	965	965	NUM
cana-3816	281	15	.	.	PUNCT
cana-3816	282	1	[	[	X
cana-3816	282	2	6	6	NUM
cana-3816	282	3	]	]	X
cana-3816	282	4	palanikumar	palanikumar	PROPN
cana-3816	282	5	m	m	PROPN
cana-3816	282	6	,	,	PUNCT
cana-3816	282	7	arulmozhi	arulmozhi	PROPN
cana-3816	282	8	k	k	X
cana-3816	282	9	,	,	PUNCT
cana-3816	282	10	on	on	ADP
cana-3816	282	11	intuitionistic	intuitionistic	ADJ
cana-3816	282	12	fuzzy	fuzzy	ADJ
cana-3816	282	13	normal	normal	ADJ
cana-3816	282	14	subbisemirings	subbisemiring	NOUN
cana-3816	282	15	of	of	ADP
cana-3816	282	16	bisemirings	bisemiring	NOUN
cana-3816	282	17	,	,	PUNCT
cana-3816	282	18	nonlinear	nonlinear	ADJ
cana-3816	282	19	studies	study	NOUN
cana-3816	282	20	,	,	PUNCT
cana-3816	282	21	28(3	28(3	NUM
cana-3816	282	22	)	)	PUNCT
cana-3816	282	23	,	,	PUNCT
cana-3816	282	24	2021	2021	NUM
cana-3816	282	25	,	,	PUNCT
cana-3816	282	26	717	717	NUM
cana-3816	282	27	-	-	SYM
cana-3816	282	28	721	721	NUM
cana-3816	282	29	.	.	PUNCT
cana-3816	283	1	[	[	X
cana-3816	283	2	7	7	NUM
cana-3816	283	3	]	]	X
cana-3816	283	4	palanikumar	palanikumar	PROPN
cana-3816	283	5	m	m	PROPN
cana-3816	283	6	,	,	PUNCT
cana-3816	283	7	selvi	selvi	PROPN
cana-3816	283	8	g	g	PROPN
cana-3816	283	9	,	,	PUNCT
cana-3816	283	10	ganeshsree	ganeshsree	PROPN
cana-3816	283	11	selvachandran	selvachandran	VERB
cana-3816	283	12	and	and	CCONJ
cana-3816	283	13	tan	tan	PROPN
cana-3816	283	14	s.l	s.l	PROPN
cana-3816	283	15	,	,	PUNCT
cana-3816	283	16	new	new	ADJ
cana-3816	283	17	approach	approach	NOUN
cana-3816	283	18	to	to	ADP
cana-3816	283	19	bisemiring	bisemiring	NOUN
cana-3816	283	20	theory	theory	NOUN
cana-3816	283	21	via	via	ADP
cana-3816	283	22	the	the	DET
cana-3816	283	23	bipolar	bipolar	ADV
cana-3816	283	24	-	-	PUNCT
cana-3816	283	25	valued	value	VERB
cana-3816	283	26	neutrosophic	neutrosophic	ADJ
cana-3816	283	27	normal	normal	ADJ
cana-3816	283	28	sets	set	NOUN
cana-3816	283	29	,	,	PUNCT
cana-3816	283	30	neutrosophic	neutrosophic	ADJ
cana-3816	283	31	sets	set	NOUN
cana-3816	283	32	and	and	CCONJ
cana-3816	283	33	systems	system	NOUN
cana-3816	283	34	,	,	PUNCT
cana-3816	283	35	55	55	NUM
cana-3816	283	36	,	,	PUNCT
cana-3816	283	37	427	427	NUM
cana-3816	283	38	-	-	SYM
cana-3816	283	39	450	450	NUM
cana-3816	283	40	,	,	PUNCT
cana-3816	283	41	2023	2023	NUM
cana-3816	283	42	.	.	PUNCT
cana-3816	284	1	[	[	X
cana-3816	284	2	8	8	NUM
cana-3816	284	3	]	]	PUNCT
cana-3816	284	4	k.	k.	PROPN
cana-3816	284	5	hila	hila	PROPN
cana-3816	284	6	and	and	CCONJ
cana-3816	284	7	e.	e.	PROPN
cana-3816	284	8	pisha	pisha	PROPN
cana-3816	284	9	.	.	PUNCT
cana-3816	285	1	on	on	ADP
cana-3816	285	2	bi	bi	NOUN
cana-3816	285	3	-	-	NOUN
cana-3816	285	4	ideals	ideal	NOUN
cana-3816	285	5	on	on	ADP
cana-3816	285	6	ordered	order	VERB
cana-3816	285	7	γ	γ	NOUN
cana-3816	285	8	-	-	PUNCT
cana-3816	285	9	semigroups	semigroup	NOUN
cana-3816	285	10	.	.	PUNCT
cana-3816	286	1	hacettepe	hacettepe	PROPN
cana-3816	286	2	journal	journal	PROPN
cana-3816	286	3	of	of	ADP
cana-3816	286	4	mathematics	mathematic	NOUN
cana-3816	286	5	and	and	CCONJ
cana-3816	286	6	statistics	statistic	NOUN
cana-3816	286	7	,	,	PUNCT
cana-3816	286	8	40(6	40(6	NOUN
cana-3816	286	9	)	)	PUNCT
cana-3816	286	10	,	,	PUNCT
cana-3816	286	11	(	(	PUNCT
cana-3816	286	12	2011	2011	NUM
cana-3816	286	13	)	)	PUNCT
cana-3816	286	14	,	,	PUNCT
cana-3816	286	15	793	793	NUM
cana-3816	286	16	-	-	SYM
cana-3816	286	17	804	804	NUM
cana-3816	286	18	.	.	PUNCT
cana-3816	287	1	[	[	X
cana-3816	287	2	9	9	NUM
cana-3816	287	3	]	]	X
cana-3816	287	4	dutta	dutta	PROPN
cana-3816	287	5	t.k	t.k	PROPN
cana-3816	287	6	and	and	CCONJ
cana-3816	287	7	kar	kar	PROPN
cana-3816	287	8	s	s	PROPN
cana-3816	287	9	,	,	PUNCT
cana-3816	287	10	on	on	ADP
cana-3816	287	11	prime	prime	ADJ
cana-3816	287	12	ideals	ideal	NOUN
cana-3816	287	13	and	and	CCONJ
cana-3816	287	14	prime	prime	ADJ
cana-3816	287	15	radical	radical	ADJ
cana-3816	287	16	of	of	ADP
cana-3816	287	17	ternary	ternary	ADJ
cana-3816	287	18	semirings	semiring	NOUN
cana-3816	287	19	,	,	PUNCT
cana-3816	287	20	bull.cal	bull.cal	PROPN
cana-3816	287	21	.	.	PUNCT
cana-3816	287	22	math	math	PROPN
cana-3816	287	23	.	.	PUNCT
cana-3816	288	1	soc	soc	PROPN
cana-3816	288	2	.	.	PUNCT
cana-3816	288	3	,	,	PUNCT
cana-3816	288	4	97(5	97(5	PROPN
cana-3816	288	5	)	)	PUNCT
cana-3816	288	6	,	,	PUNCT
cana-3816	288	7	2005	2005	NUM
cana-3816	288	8	,	,	PUNCT
cana-3816	288	9	445	445	NUM
cana-3816	288	10	-	-	SYM
cana-3816	288	11	454	454	NUM
cana-3816	288	12	.	.	PUNCT
cana-3816	289	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3816	289	2	769	769	NUM
cana-3816	289	3	communications	communication	NOUN
cana-3816	289	4	on	on	ADP
cana-3816	289	5	applied	apply	VERB
cana-3816	289	6	nonlinear	nonlinear	ADJ
cana-3816	289	7	analysis	analysis	NOUN
cana-3816	289	8	issn	issn	NOUN
cana-3816	289	9	:	:	PUNCT
cana-3816	289	10	1074	1074	NUM
cana-3816	289	11	-	-	PUNCT
cana-3816	289	12	133x	133x	NUM
cana-3816	289	13	vol	vol	NOUN
cana-3816	289	14	32	32	NUM
cana-3816	289	15	no	no	NOUN
cana-3816	289	16	.	.	NOUN
cana-3816	289	17	3	3	NUM
cana-3816	289	18	(	(	PUNCT
cana-3816	289	19	2025	2025	NUM
cana-3816	289	20	)	)	PUNCT
cana-3816	290	1	[	[	X
cana-3816	290	2	10	10	NUM
cana-3816	290	3	]	]	X
cana-3816	290	4	palanikumar	palanikumar	PROPN
cana-3816	290	5	,	,	PUNCT
cana-3816	290	6	m.	m.	NOUN
cana-3816	290	7	;	;	PUNCT
cana-3816	290	8	jana	jana	PROPN
cana-3816	290	9	,	,	PUNCT
cana-3816	290	10	c.	c.	PROPN
cana-3816	290	11	;	;	PUNCT
cana-3816	290	12	shanqiti	shanqiti	ADV
cana-3816	290	13	,	,	PUNCT
cana-3816	290	14	o.a	o.a	PROPN
cana-3816	290	15	.	.	PROPN
cana-3816	290	16	;	;	PUNCT
cana-3816	290	17	pal	pal	NOUN
cana-3816	290	18	.	.	PUNCT
cana-3816	290	19	m.	m.	NOUN
cana-3816	290	20	a	a	DET
cana-3816	290	21	novel	novel	ADJ
cana-3816	290	22	method	method	NOUN
cana-3816	290	23	for	for	ADP
cana-3816	290	24	generating	generate	VERB
cana-3816	290	25	the	the	DET
cana-3816	290	26	m	m	NOUN
cana-3816	290	27	-	-	PUNCT
cana-3816	290	28	tri	tri	NOUN
cana-3816	290	29	-	-	NOUN
cana-3816	290	30	basis	basis	NOUN
cana-3816	290	31	of	of	ADP
cana-3816	290	32	an	an	DET
cana-3816	290	33	ordered	order	VERB
cana-3816	290	34	gamma	gamma	PROPN
cana-3816	290	35	semigroup	semigroup	PROPN
cana-3816	290	36	.	.	PUNCT
cana-3816	291	1	mathematics	mathematic	NOUN
cana-3816	291	2	2023	2023	NUM
cana-3816	291	3	,	,	PUNCT
cana-3816	291	4	11	11	NUM
cana-3816	291	5	,	,	PUNCT
cana-3816	291	6	893	893	NUM
cana-3816	291	7	[	[	SYM
cana-3816	291	8	11	11	NUM
cana-3816	291	9	]	]	PUNCT
cana-3816	291	10	mohanraj	mohanraj	NOUN
cana-3816	291	11	,	,	PUNCT
cana-3816	291	12	g	g	NOUN
cana-3816	291	13	;	;	PUNCT
cana-3816	291	14	palanikumar	palanikumar	NOUN
cana-3816	291	15	,	,	PUNCT
cana-3816	291	16	m.	m.	NOUN
cana-3816	291	17	on	on	ADP
cana-3816	291	18	various	various	ADJ
cana-3816	291	19	prime	prime	ADJ
cana-3816	291	20	and	and	CCONJ
cana-3816	291	21	semiprime	semiprime	NOUN
cana-3816	291	22	bi	bi	NOUN
cana-3816	291	23	-	-	NOUN
cana-3816	291	24	ideals	ideal	NOUN
cana-3816	291	25	of	of	ADP
cana-3816	291	26	rings	ring	NOUN
cana-3816	291	27	.	.	PUNCT
cana-3816	292	1	nonlinear	nonlinear	ADJ
cana-3816	292	2	studies	study	NOUN
cana-3816	292	3	.	.	PUNCT
cana-3816	293	1	2021	2021	NUM
cana-3816	293	2	,	,	PUNCT
cana-3816	293	3	27(3	27(3	NUM
cana-3816	293	4	)	)	PUNCT
cana-3816	293	5	,	,	PUNCT
cana-3816	293	6	811	811	NUM
cana-3816	293	7	-	-	SYM
cana-3816	293	8	815	815	NUM
cana-3816	293	9	.	.	PUNCT
cana-3816	294	1	[	[	X
cana-3816	294	2	12	12	NUM
cana-3816	294	3	]	]	X
cana-3816	294	4	palanikumar	palanikumar	PROPN
cana-3816	294	5	,	,	PUNCT
cana-3816	294	6	m	m	PROPN
cana-3816	294	7	;	;	PUNCT
cana-3816	294	8	arulmozhi	arulmozhi	ADJ
cana-3816	294	9	,	,	PUNCT
cana-3816	294	10	k.	k.	PROPN
cana-3816	294	11	jana.c	jana.c	PROPN
cana-3816	294	12	and	and	CCONJ
cana-3816	294	13	pal.m	pal.m	PROPN
cana-3816	294	14	&	&	CCONJ
cana-3816	294	15	shum.k.p	shum.k.p	NOUN
cana-3816	294	16	.	.	PUNCT
cana-3816	295	1	new	new	ADJ
cana-3816	295	2	approach	approach	NOUN
cana-3816	295	3	towards	towards	ADP
cana-3816	295	4	different	different	ADJ
cana-3816	295	5	bi	bi	NOUN
cana-3816	295	6	-	-	NOUN
cana-3816	295	7	base	base	NOUN
cana-3816	295	8	of	of	ADP
cana-3816	295	9	ordered	order	VERB
cana-3816	295	10	b	b	X
cana-3816	295	11	-	-	PUNCT
cana-3816	295	12	semiring.asian	semiring.asian	ADJ
cana-3816	295	13	-	-	PUNCT
cana-3816	295	14	european	european	ADJ
cana-3816	295	15	journal	journal	NOUN
cana-3816	295	16	of	of	ADP
cana-3816	295	17	mathematics	mathematic	NOUN
cana-3816	295	18	.	.	PUNCT
cana-3816	296	1	2023	2023	NUM
cana-3816	296	2	,	,	PUNCT
cana-3816	296	3	16(2	16(2	NUM
cana-3816	296	4	)	)	PUNCT
cana-3816	296	5	,	,	PUNCT
cana-3816	296	6	1	1	NUM
cana-3816	296	7	-	-	SYM
cana-3816	296	8	26	26	NUM
cana-3816	296	9	.	.	PUNCT
cana-3816	297	1	[	[	X
cana-3816	297	2	13	13	NUM
cana-3816	297	3	]	]	PUNCT
cana-3816	297	4	shihadeh	shihadeh	NOUN
cana-3816	297	5	,	,	PUNCT
cana-3816	297	6	a.	a.	NOUN
cana-3816	297	7	,	,	PUNCT
cana-3816	297	8	matarneh	matarneh	PROPN
cana-3816	297	9	,	,	PUNCT
cana-3816	297	10	k.	k.	PROPN
cana-3816	297	11	a.	a.	PROPN
cana-3816	297	12	m.	m.	PROPN
cana-3816	297	13	,	,	PUNCT
cana-3816	297	14	hatamleh	hatamleh	PROPN
cana-3816	297	15	,	,	PUNCT
cana-3816	297	16	r.	r.	PROPN
cana-3816	297	17	,	,	PUNCT
cana-3816	297	18	al	al	PROPN
cana-3816	297	19	-	-	PUNCT
cana-3816	297	20	qadri	qadri	PROPN
cana-3816	297	21	,	,	PUNCT
cana-3816	297	22	m.	m.	NOUN
cana-3816	297	23	o.	o.	PROPN
cana-3816	297	24	,	,	PUNCT
cana-3816	297	25	&	&	CCONJ
cana-3816	297	26	al	al	PROPN
cana-3816	297	27	-	-	PUNCT
cana-3816	297	28	husban	husban	PROPN
cana-3816	297	29	,	,	PUNCT
cana-3816	297	30	a	a	PRON
cana-3816	297	31	,	,	PUNCT
cana-3816	297	32	on	on	ADP
cana-3816	297	33	the	the	DET
cana-3816	297	34	two	two	NUM
cana-3816	297	35	-	-	ADJ
cana-3816	297	36	fold	fold	ADJ
cana-3816	297	37	fuzzy	fuzzy	ADJ
cana-3816	297	38	n	n	CCONJ
cana-3816	297	39	-	-	PUNCT
cana-3816	297	40	refined	refine	VERB
cana-3816	297	41	neutrosophic	neutrosophic	ADJ
cana-3816	297	42	rings	ring	NOUN
cana-3816	297	43	for	for	ADP
cana-3816	297	44	2	2	NUM
cana-3816	297	45	≤	≤	NUM
cana-3816	297	46	3	3	NUM
cana-3816	297	47	.	.	NUM
cana-3816	297	48	neutrosophic	neutrosophic	ADJ
cana-3816	297	49	sets	set	NOUN
cana-3816	297	50	and	and	CCONJ
cana-3816	297	51	systems	system	NOUN
cana-3816	297	52	,	,	PUNCT
cana-3816	297	53	68	68	NUM
cana-3816	297	54	,	,	PUNCT
cana-3816	297	55	(	(	PUNCT
cana-3816	297	56	2024	2024	NUM
cana-3816	297	57	)	)	PUNCT
cana-3816	297	58	,	,	PUNCT
cana-3816	297	59	8	8	NUM
cana-3816	297	60	-	-	SYM
cana-3816	297	61	25	25	NUM
cana-3816	297	62	.	.	PUNCT
cana-3816	298	1	[	[	X
cana-3816	298	2	14	14	NUM
cana-3816	298	3	]	]	X
cana-3816	298	4	abdallah	abdallah	PROPN
cana-3816	298	5	shihadeh	shihadeh	PROPN
cana-3816	298	6	,	,	PUNCT
cana-3816	298	7	khaled	khaled	PROPN
cana-3816	298	8	ahmad	ahmad	PROPN
cana-3816	298	9	mohammad	mohammad	PROPN
cana-3816	298	10	matarneh	matarneh	PROPN
cana-3816	298	11	,	,	PUNCT
cana-3816	298	12	raed	raed	PROPN
cana-3816	298	13	hatamleh	hatamleh	PROPN
cana-3816	298	14	,	,	PUNCT
cana-3816	298	15	randa	randa	PROPN
cana-3816	298	16	bashir	bashir	PROPN
cana-3816	298	17	yousef	yousef	PROPN
cana-3816	299	1	hijazeen	hijazeen	PROPN
cana-3816	299	2	,	,	PUNCT
cana-3816	299	3	mowafaq	mowafaq	PROPN
cana-3816	299	4	omar	omar	PROPN
cana-3816	299	5	al	al	PROPN
cana-3816	299	6	-	-	PUNCT
cana-3816	299	7	qadri	qadri	PROPN
cana-3816	299	8	,	,	PUNCT
cana-3816	299	9	abdallah	abdallah	PROPN
cana-3816	299	10	al	al	PROPN
cana-3816	299	11	-	-	PUNCT
cana-3816	299	12	husban	husban	PROPN
cana-3816	299	13	,	,	PUNCT
cana-3816	299	14	an	an	DET
cana-3816	299	15	example	example	NOUN
cana-3816	299	16	of	of	ADP
cana-3816	299	17	two	two	NUM
cana-3816	299	18	-	-	PUNCT
cana-3816	299	19	fold	fold	ADJ
cana-3816	299	20	fuzzy	fuzzy	ADJ
cana-3816	299	21	algebras	algebra	NOUN
cana-3816	299	22	based	base	VERB
cana-3816	299	23	on	on	ADP
cana-3816	299	24	neutrosophic	neutrosophic	ADJ
cana-3816	299	25	real	real	ADJ
cana-3816	299	26	numbers	number	NOUN
cana-3816	299	27	,	,	PUNCT
cana-3816	299	28	neutrosophic	neutrosophic	ADJ
cana-3816	299	29	sets	set	NOUN
cana-3816	299	30	and	and	CCONJ
cana-3816	299	31	systems	system	NOUN
cana-3816	299	32	,	,	PUNCT
cana-3816	299	33	67	67	NUM
cana-3816	299	34	,	,	PUNCT
cana-3816	299	35	(	(	PUNCT
cana-3816	299	36	2024	2024	NUM
cana-3816	299	37	)	)	PUNCT
cana-3816	299	38	,	,	PUNCT
cana-3816	299	39	169	169	NUM
cana-3816	299	40	-	-	SYM
cana-3816	299	41	178	178	NUM
cana-3816	299	42	.	.	PUNCT
cana-3816	300	1	[	[	X
cana-3816	300	2	15	15	NUM
cana-3816	300	3	]	]	NOUN
cana-3816	300	4	a.	a.	NOUN
cana-3816	300	5	rajalakshmi	rajalakshmi	NOUN
cana-3816	300	6	,	,	PUNCT
cana-3816	300	7	raed	raed	PROPN
cana-3816	300	8	hatamleh	hatamleh	PROPN
cana-3816	300	9	,	,	PUNCT
cana-3816	300	10	abdallah	abdallah	PROPN
cana-3816	300	11	al	al	PROPN
cana-3816	300	12	-	-	PUNCT
cana-3816	300	13	husban	husban	PROPN
cana-3816	300	14	,	,	PUNCT
cana-3816	300	15	k.	k.	PROPN
cana-3816	300	16	lenin	lenin	PROPN
cana-3816	300	17	muthu	muthu	PROPN
cana-3816	300	18	kumaran	kumaran	PROPN
cana-3816	300	19	,	,	PUNCT
cana-3816	300	20	m.	m.	PROPN
cana-3816	300	21	s.	s.	PROPN
cana-3816	300	22	malchijah	malchijah	PROPN
cana-3816	300	23	raj	raj	PROPN
cana-3816	300	24	,	,	PUNCT
cana-3816	300	25	various	various	ADJ
cana-3816	300	26	(	(	PUNCT
cana-3816	300	27	ζ1	ζ1	NOUN
cana-3816	300	28	,	,	PUNCT
cana-3816	300	29	ζ2	ζ2	NOUN
cana-3816	300	30	)	)	PUNCT
cana-3816	300	31	neutrosophic	neutrosophic	ADJ
cana-3816	300	32	ideals	ideal	NOUN
cana-3816	300	33	of	of	ADP
cana-3816	300	34	an	an	DET
cana-3816	300	35	ordered	order	VERB
cana-3816	300	36	ternary	ternary	ADJ
cana-3816	300	37	semigroups	semigroup	NOUN
cana-3816	300	38	.	.	PUNCT
cana-3816	301	1	communications	communication	NOUN
cana-3816	301	2	on	on	ADP
cana-3816	301	3	applied	apply	VERB
cana-3816	301	4	nonlinear	nonlinear	ADJ
cana-3816	301	5	analysis	analysis	NOUN
cana-3816	301	6	,	,	PUNCT
cana-3816	301	7	32	32	NUM
cana-3816	301	8	(	(	PUNCT
cana-3816	301	9	3	3	NUM
cana-3816	301	10	)	)	PUNCT
cana-3816	301	11	,	,	PUNCT
cana-3816	301	12	(	(	PUNCT
cana-3816	301	13	2025	2025	NUM
cana-3816	301	14	)	)	PUNCT
cana-3816	301	15	,	,	PUNCT
cana-3816	301	16	400	400	NUM
cana-3816	301	17	-	-	SYM
cana-3816	301	18	417	417	NUM
cana-3816	301	19	.	.	PUNCT
cana-3816	302	1	[	[	X
cana-3816	302	2	16	16	NUM
cana-3816	302	3	]	]	X
cana-3816	302	4	raed	raed	PROPN
cana-3816	302	5	hatamleh	hatamleh	PROPN
cana-3816	302	6	,	,	PUNCT
cana-3816	302	7	abdallah	abdallah	PROPN
cana-3816	302	8	al	al	PROPN
cana-3816	302	9	-	-	PUNCT
cana-3816	302	10	husban	husban	PROPN
cana-3816	302	11	,	,	PUNCT
cana-3816	302	12	n.	n.	NOUN
cana-3816	302	13	sundarakannan	sundarakannan	NOUN
cana-3816	302	14	,	,	PUNCT
cana-3816	302	15	m.	m.	NOUN
cana-3816	302	16	s.	s.	PROPN
cana-3816	302	17	malchijah	malchijah	PROPN
cana-3816	302	18	raj	raj	PROPN
cana-3816	302	19	,	,	PUNCT
cana-3816	302	20	complex	complex	ADJ
cana-3816	302	21	cubic	cubic	ADJ
cana-3816	302	22	intuitionistic	intuitionistic	ADJ
cana-3816	302	23	fuzzy	fuzzy	ADJ
cana-3816	302	24	set	set	NOUN
cana-3816	302	25	applied	apply	VERB
cana-3816	302	26	to	to	ADP
cana-3816	302	27	subbisemirings	subbisemiring	NOUN
cana-3816	302	28	of	of	ADP
cana-3816	302	29	bisemirings	bisemiring	NOUN
cana-3816	302	30	using	use	VERB
cana-3816	302	31	homomorphism	homomorphism	PROPN
cana-3816	302	32	.	.	PUNCT
cana-3816	303	1	communications	communication	NOUN
cana-3816	303	2	on	on	ADP
cana-3816	303	3	applied	apply	VERB
cana-3816	303	4	non	non	ADJ
cana-3816	303	5	-	-	ADJ
cana-3816	303	6	linear	linear	ADJ
cana-3816	303	7	analysis	analysis	NOUN
cana-3816	303	8	,	,	PUNCT
cana-3816	303	9	32	32	NUM
cana-3816	303	10	(	(	PUNCT
cana-3816	303	11	3	3	NUM
cana-3816	303	12	)	)	PUNCT
cana-3816	303	13	,	,	PUNCT
cana-3816	303	14	(	(	PUNCT
cana-3816	303	15	2025	2025	NUM
cana-3816	303	16	)	)	PUNCT
cana-3816	303	17	,	,	PUNCT
cana-3816	303	18	418	418	NUM
cana-3816	303	19	-	-	SYM
cana-3816	303	20	435	435	NUM
cana-3816	303	21	.	.	PUNCT
cana-3816	304	1	[	[	X
cana-3816	304	2	17	17	NUM
cana-3816	304	3	]	]	SYM
cana-3816	304	4	abubaker	abubaker	X
cana-3816	304	5	,	,	PUNCT
cana-3816	304	6	ahmad	ahmad	PROPN
cana-3816	304	7	a	a	DET
cana-3816	304	8	,	,	PUNCT
cana-3816	304	9	hatamleh	hatamleh	ADJ
cana-3816	304	10	,	,	PUNCT
cana-3816	304	11	raed	raed	PROPN
cana-3816	304	12	,	,	PUNCT
cana-3816	304	13	matarneh	matarneh	PROPN
cana-3816	304	14	,	,	PUNCT
cana-3816	304	15	khaled	khaled	PROPN
cana-3816	304	16	,	,	PUNCT
cana-3816	304	17	al	al	PROPN
cana-3816	304	18	-	-	PUNCT
cana-3816	304	19	husban	husban	PROPN
cana-3816	304	20	,	,	PUNCT
cana-3816	304	21	abdallah	abdallah	PROPN
cana-3816	304	22	,	,	PUNCT
cana-3816	304	23	on	on	ADP
cana-3816	304	24	the	the	DET
cana-3816	304	25	numerica	numerica	PROPN
cana-3816	304	26	solutions	solution	NOUN
cana-3816	304	27	for	for	ADP
cana-3816	304	28	some	some	DET
cana-3816	304	29	neutrosophic	neutrosophic	ADJ
cana-3816	304	30	singular	singular	ADJ
cana-3816	304	31	boundary	boundary	ADJ
cana-3816	304	32	value	value	NOUN
cana-3816	304	33	problems	problem	NOUN
cana-3816	304	34	by	by	ADP
cana-3816	304	35	using	use	VERB
cana-3816	304	36	(	(	PUNCT
cana-3816	304	37	lpm	lpm	NOUN
cana-3816	304	38	)	)	PUNCT
cana-3816	304	39	polynomials	polynomial	NOUN
cana-3816	304	40	,	,	PUNCT
cana-3816	304	41	international	international	ADJ
cana-3816	304	42	journal	journal	NOUN
cana-3816	304	43	of	of	ADP
cana-3816	304	44	neutrosophic	neutrosophic	ADJ
cana-3816	304	45	science	science	NOUN
cana-3816	304	46	,	,	PUNCT
cana-3816	304	47	25(2	25(2	NUM
cana-3816	304	48	)	)	PUNCT
cana-3816	304	49	,	,	PUNCT
cana-3816	304	50	(	(	PUNCT
cana-3816	304	51	2024	2024	NUM
cana-3816	304	52	)	)	PUNCT
cana-3816	304	53	,	,	PUNCT
cana-3816	304	54	197	197	NUM
cana-3816	304	55	-	-	SYM
cana-3816	304	56	205	205	NUM
cana-3816	304	57	.	.	PUNCT
cana-3816	305	1	[	[	X
cana-3816	305	2	18	18	NUM
cana-3816	305	3	]	]	SYM
cana-3816	305	4	a.	a.	NOUN
cana-3816	305	5	,	,	PUNCT
cana-3816	305	6	ahmad	ahmad	PROPN
cana-3816	305	7	.	.	PROPN
cana-3816	305	8	,	,	PUNCT
cana-3816	305	9	hatamleh	hatamleh	ADJ
cana-3816	305	10	,	,	PUNCT
cana-3816	305	11	raed	raed	PROPN
cana-3816	305	12	.	.	PROPN
cana-3816	305	13	,	,	PUNCT
cana-3816	305	14	matarneh	matarneh	PROPN
cana-3816	305	15	,	,	PUNCT
cana-3816	305	16	khaled	khaled	PROPN
cana-3816	305	17	.	.	PUNCT
cana-3816	305	18	,	,	PUNCT
cana-3816	305	19	al	al	PROPN
cana-3816	305	20	-	-	PUNCT
cana-3816	305	21	husban	husban	PROPN
cana-3816	305	22	,	,	PUNCT
cana-3816	305	23	abdallah	abdallah	PROPN
cana-3816	305	24	.	.	PUNCT
cana-3816	306	1	on	on	ADP
cana-3816	306	2	the	the	DET
cana-3816	306	3	irreversible	irreversible	ADJ
cana-3816	306	4	kthreshold	kthreshold	ADJ
cana-3816	306	5	conversion	conversion	NOUN
cana-3816	306	6	number	number	NOUN
cana-3816	306	7	for	for	ADP
cana-3816	306	8	some	some	DET
cana-3816	306	9	graph	graph	NOUN
cana-3816	306	10	products	product	NOUN
cana-3816	306	11	and	and	CCONJ
cana-3816	306	12	neutrosophic	neutrosophic	ADJ
cana-3816	306	13	graphs	graph	NOUN
cana-3816	306	14	,	,	PUNCT
cana-3816	306	15	international	international	ADJ
cana-3816	306	16	journal	journal	NOUN
cana-3816	306	17	of	of	ADP
cana-3816	306	18	neutrosophic	neutrosophic	ADJ
cana-3816	306	19	science	science	NOUN
cana-3816	306	20	,	,	PUNCT
cana-3816	306	21	25(2	25(2	NUM
cana-3816	306	22	)	)	PUNCT
cana-3816	306	23	,	,	PUNCT
cana-3816	306	24	(	(	PUNCT
cana-3816	306	25	2025	2025	NUM
cana-3816	306	26	)	)	PUNCT
cana-3816	306	27	,	,	PUNCT
cana-3816	306	28	183	183	NUM
cana-3816	306	29	-	-	SYM
cana-3816	306	30	196	196	NUM
cana-3816	306	31	.	.	PUNCT
cana-3816	307	1	[	[	X
cana-3816	307	2	19	19	NUM
cana-3816	307	3	]	]	PUNCT
cana-3816	307	4	raed	raed	PROPN
cana-3816	307	5	hatamleh	hatamleh	PROPN
cana-3816	307	6	,	,	PUNCT
cana-3816	307	7	abdallah	abdallah	PROPN
cana-3816	307	8	al	al	PROPN
cana-3816	307	9	-	-	PUNCT
cana-3816	307	10	husban	husban	PROPN
cana-3816	307	11	,	,	PUNCT
cana-3816	307	12	k.	k.	PROPN
cana-3816	307	13	sundareswari	sundareswari	PROPN
cana-3816	307	14	,	,	PUNCT
cana-3816	307	15	g.balaj	g.balaj	NOUN
cana-3816	307	16	,	,	PUNCT
cana-3816	307	17	m.palanikumar	m.palanikumar	ADJ
cana-3816	307	18	,	,	PUNCT
cana-3816	307	19	complex	complex	ADJ
cana-3816	307	20	tangent	tangent	NOUN
cana-3816	307	21	trigonometric	trigonometric	ADJ
cana-3816	307	22	approach	approach	NOUN
cana-3816	307	23	applied	apply	VERB
cana-3816	307	24	to	to	ADP
cana-3816	307	25	(	(	PUNCT
cana-3816	307	26	α	α	X
cana-3816	307	27	,	,	PUNCT
cana-3816	307	28	β)-rung	β)-rung	PUNCT
cana-3816	307	29	fuzzy	fuzzy	ADJ
cana-3816	307	30	set	set	NOUN
cana-3816	307	31	using	use	VERB
cana-3816	307	32	weighted	weight	VERB
cana-3816	307	33	averaging	averaging	NOUN
cana-3816	307	34	,	,	PUNCT
cana-3816	307	35	geometric	geometric	ADJ
cana-3816	307	36	operators	operator	NOUN
cana-3816	307	37	and	and	CCONJ
cana-3816	307	38	its	its	PRON
cana-3816	307	39	extension	extension	NOUN
cana-3816	307	40	.	.	PUNCT
cana-3816	308	1	communications	communication	NOUN
cana-3816	308	2	on	on	ADP
cana-3816	308	3	applied	apply	VERB
cana-3816	308	4	nonlinear	nonlinear	ADJ
cana-3816	308	5	analysis	analysis	NOUN
cana-3816	308	6	,	,	PUNCT
cana-3816	308	7	32	32	NUM
cana-3816	308	8	(	(	PUNCT
cana-3816	308	9	5	5	NUM
cana-3816	308	10	)	)	PUNCT
cana-3816	308	11	,	,	PUNCT
cana-3816	308	12	(	(	PUNCT
cana-3816	308	13	2025	2025	NUM
cana-3816	308	14	)	)	PUNCT
cana-3816	308	15	,	,	PUNCT
cana-3816	308	16	133	133	NUM
cana-3816	308	17	-	-	SYM
cana-3816	308	18	144	144	NUM
cana-3816	308	19	.	.	PUNCT
cana-3816	309	1	[	[	X
cana-3816	309	2	20	20	NUM
cana-3816	309	3	]	]	PUNCT
cana-3816	309	4	raed	raed	PROPN
cana-3816	309	5	hatamleh	hatamleh	PROPN
cana-3816	309	6	,	,	PUNCT
cana-3816	309	7	abdallah	abdallah	PROPN
cana-3816	309	8	al	al	PROPN
cana-3816	309	9	-	-	PUNCT
cana-3816	309	10	husban	husban	PROPN
cana-3816	309	11	,	,	PUNCT
cana-3816	309	12	m.	m.	NOUN
cana-3816	309	13	palanikumar	palanikumar	PROPN
cana-3816	309	14	,	,	PUNCT
cana-3816	309	15	k.	k.	PROPN
cana-3816	309	16	sundareswari	sundareswari	PROPN
cana-3816	309	17	,	,	PUNCT
cana-3816	309	18	different	different	ADJ
cana-3816	309	19	weighted	weight	VERB
cana-3816	309	20	operators	operator	NOUN
cana-3816	309	21	such	such	ADJ
cana-3816	309	22	as	as	ADP
cana-3816	309	23	generalized	generalized	ADJ
cana-3816	309	24	averaging	averaging	NOUN
cana-3816	309	25	and	and	CCONJ
cana-3816	309	26	generalized	generalized	ADJ
cana-3816	309	27	geometric	geometric	NOUN
cana-3816	309	28	based	base	VERB
cana-3816	309	29	on	on	ADP
cana-3816	309	30	trigonometric	trigonometric	ADJ
cana-3816	309	31	q	q	ADJ
cana-3816	309	32	-	-	PUNCT
cana-3816	309	33	rung	rung	ADJ
cana-3816	309	34	intervalvalued	intervalvalue	VERB
cana-3816	309	35	approach	approach	NOUN
cana-3816	309	36	,	,	PUNCT
cana-3816	309	37	communications	communication	NOUN
cana-3816	309	38	on	on	ADP
cana-3816	309	39	applied	apply	VERB
cana-3816	309	40	nonlinear	nonlinear	ADJ
cana-3816	309	41	analysis	analysis	NOUN
cana-3816	309	42	,	,	PUNCT
cana-3816	309	43	32	32	NUM
cana-3816	309	44	(	(	PUNCT
cana-3816	309	45	5	5	NUM
cana-3816	309	46	)	)	PUNCT
cana-3816	309	47	,	,	PUNCT
cana-3816	309	48	(	(	PUNCT
cana-3816	309	49	2025	2025	NUM
cana-3816	309	50	)	)	PUNCT
cana-3816	309	51	,	,	PUNCT
cana-3816	309	52	91	91	NUM
cana-3816	309	53	-	-	SYM
cana-3816	309	54	101	101	NUM
cana-3816	309	55	.	.	PUNCT
cana-3816	310	1	[	[	X
cana-3816	310	2	21	21	NUM
cana-3816	310	3	]	]	X
cana-3816	310	4	abdallah	abdallah	PROPN
cana-3816	310	5	shihadeh	shihadeh	PROPN
cana-3816	310	6	,	,	PUNCT
cana-3816	310	7	raed	raed	PROPN
cana-3816	310	8	hatamleh	hatamleh	PROPN
cana-3816	310	9	,	,	PUNCT
cana-3816	310	10	m.palanikumar	m.palanikumar	PROPN
cana-3816	310	11	,	,	PUNCT
cana-3816	310	12	abdallah	abdallah	PROPN
cana-3816	310	13	al	al	PROPN
cana-3816	310	14	-	-	PUNCT
cana-3816	310	15	husban	husban	PROPN
cana-3816	310	16	,	,	PUNCT
cana-3816	310	17	new	new	ADJ
cana-3816	310	18	algebraic	algebraic	ADJ
cana-3816	310	19	structures	structure	NOUN
cana-3816	310	20	towards	towards	ADP
cana-3816	310	21	different	different	ADJ
cana-3816	310	22	(	(	PUNCT
cana-3816	310	23	[	[	X
cana-3816	310	24	,	,	PUNCT
cana-3816	310	25	`	`	PUNCT
cana-3816	310	26	)	)	PUNCT
cana-3816	310	27	intuitionistic	intuitionistic	ADJ
cana-3816	310	28	fuzzy	fuzzy	ADJ
cana-3816	310	29	ideals	ideal	NOUN
cana-3816	310	30	and	and	CCONJ
cana-3816	310	31	it	it	PRON
cana-3816	310	32	characterization	characterization	NOUN
cana-3816	310	33	of	of	ADP
cana-3816	310	34	an	an	DET
cana-3816	310	35	ordered	order	VERB
cana-3816	310	36	ternary	ternary	ADJ
cana-3816	310	37	semigroups	semigroup	NOUN
cana-3816	310	38	.	.	PUNCT
cana-3816	311	1	communications	communication	NOUN
cana-3816	311	2	on	on	ADP
cana-3816	311	3	applied	apply	VERB
cana-3816	311	4	nonlinear	nonlinear	ADJ
cana-3816	311	5	analysis	analysis	NOUN
cana-3816	311	6	,	,	PUNCT
cana-3816	311	7	32	32	NUM
cana-3816	311	8	(	(	PUNCT
cana-3816	311	9	6	6	NUM
cana-3816	311	10	)	)	PUNCT
cana-3816	311	11	,	,	PUNCT
cana-3816	311	12	(	(	PUNCT
cana-3816	311	13	2025	2025	NUM
cana-3816	311	14	)	)	PUNCT
cana-3816	311	15	,	,	PUNCT
cana-3816	311	16	568	568	NUM
cana-3816	311	17	-	-	SYM
cana-3816	311	18	578	578	NUM
cana-3816	311	19	.	.	PUNCT
cana-3816	312	1	[	[	X
cana-3816	312	2	22	22	NUM
cana-3816	312	3	]	]	X
cana-3816	312	4	palanikumar	palanikumar	PROPN
cana-3816	312	5	,	,	PUNCT
cana-3816	312	6	m	m	PROPN
cana-3816	312	7	;	;	PUNCT
cana-3816	312	8	iampan	iampan	PROPN
cana-3816	312	9	,	,	PUNCT
cana-3816	312	10	a	a	DET
cana-3816	312	11	;	;	PUNCT
cana-3816	312	12	manavalan	manavalan	ADJ
cana-3816	312	13	,	,	PUNCT
cana-3816	312	14	l.j	l.j	PROPN
cana-3816	312	15	.	.	PROPN
cana-3816	312	16	m	m	PROPN
cana-3816	312	17	-	-	PUNCT
cana-3816	312	18	bi	bi	ADJ
cana-3816	312	19	-	-	ADJ
cana-3816	312	20	base	base	ADJ
cana-3816	312	21	generator	generator	NOUN
cana-3816	312	22	of	of	ADP
cana-3816	312	23	ordered	order	VERB
cana-3816	312	24	γ	γ	NOUN
cana-3816	312	25	-	-	PUNCT
cana-3816	312	26	semigroups	semigroup	NOUN
cana-3816	312	27	.	.	PUNCT
cana-3816	313	1	icic	icic	PROPN
cana-3816	313	2	express	express	VERB
cana-3816	313	3	letters	letter	NOUN
cana-3816	313	4	part	part	NOUN
cana-3816	313	5	b	b	NOUN
cana-3816	313	6	:	:	PUNCT
cana-3816	313	7	applications	application	NOUN
cana-3816	313	8	.	.	PUNCT
cana-3816	314	1	2022	2022	NUM
cana-3816	314	2	,	,	PUNCT
cana-3816	314	3	13(8	13(8	NUM
cana-3816	314	4	)	)	PUNCT
cana-3816	314	5	,	,	PUNCT
cana-3816	314	6	795	795	NUM
cana-3816	314	7	-	-	SYM
cana-3816	314	8	802	802	NUM
cana-3816	314	9	.	.	PUNCT
cana-3816	315	1	[	[	X
cana-3816	315	2	23	23	NUM
cana-3816	315	3	]	]	PUNCT
cana-3816	315	4	mohanraj	mohanraj	NOUN
cana-3816	315	5	,	,	PUNCT
cana-3816	315	6	g	g	NOUN
cana-3816	315	7	;	;	PUNCT
cana-3816	315	8	palanikumar	palanikumar	NOUN
cana-3816	315	9	,	,	PUNCT
cana-3816	315	10	m.	m.	NOUN
cana-3816	315	11	characterization	characterization	NOUN
cana-3816	315	12	of	of	ADP
cana-3816	315	13	various	various	ADJ
cana-3816	315	14	k	k	NOUN
cana-3816	315	15	-	-	NOUN
cana-3816	315	16	regular	regular	ADJ
cana-3816	315	17	in	in	ADP
cana-3816	315	18	b	b	NOUN
cana-3816	315	19	-	-	PUNCT
cana-3816	315	20	semirings	semiring	NOUN
cana-3816	315	21	,	,	PUNCT
cana-3816	315	22	aip	aip	PROPN
cana-3816	315	23	conference	conference	NOUN
cana-3816	315	24	proceedings	proceeding	NOUN
cana-3816	315	25	,	,	PUNCT
cana-3816	315	26	2019	2019	NUM
cana-3816	315	27	,	,	PUNCT
cana-3816	315	28	2112	2112	NUM
cana-3816	315	29	(	(	PUNCT
cana-3816	315	30	1	1	NUM
cana-3816	315	31	)	)	PUNCT
cana-3816	315	32	,	,	PUNCT
cana-3816	315	33	020021	020021	NUM
cana-3816	315	34	.	.	PUNCT
cana-3816	316	1	[	[	X
cana-3816	316	2	24	24	NUM
cana-3816	316	3	]	]	X
cana-3816	316	4	palanikumar	palanikumar	PROPN
cana-3816	316	5	,	,	PUNCT
cana-3816	316	6	m	m	PROPN
cana-3816	316	7	;	;	PUNCT
cana-3816	316	8	shanqiti	shanqiti	ADV
cana-3816	316	9	,	,	PUNCT
cana-3816	316	10	o.	o.	PROPN
cana-3816	316	11	al	al	PROPN
cana-3816	316	12	;	;	PUNCT
cana-3816	316	13	jana	jana	PROPN
cana-3816	316	14	,	,	PUNCT
cana-3816	316	15	c	c	X
cana-3816	316	16	;	;	PUNCT
cana-3816	316	17	pal	pal	ADJ
cana-3816	316	18	,	,	PUNCT
cana-3816	316	19	m.	m.	NOUN
cana-3816	316	20	novelty	novelty	NOUN
cana-3816	316	21	for	for	ADP
cana-3816	316	22	different	different	ADJ
cana-3816	316	23	prime	prime	ADJ
cana-3816	316	24	partial	partial	ADJ
cana-3816	316	25	bi	bi	NOUN
cana-3816	316	26	-	-	NOUN
cana-3816	316	27	ideals	ideal	NOUN
cana-3816	316	28	in	in	ADP
cana-3816	316	29	noncommutative	noncommutative	ADJ
cana-3816	316	30	partial	partial	ADJ
cana-3816	316	31	rings	ring	NOUN
cana-3816	316	32	and	and	CCONJ
cana-3816	316	33	its	its	PRON
cana-3816	316	34	extension	extension	NOUN
cana-3816	316	35	mathematics	mathematic	NOUN
cana-3816	316	36	,	,	PUNCT
cana-3816	316	37	2023	2023	NUM
cana-3816	316	38	,	,	PUNCT
cana-3816	316	39	11(6	11(6	NUM
cana-3816	316	40	)	)	PUNCT
cana-3816	316	41	,	,	PUNCT
cana-3816	316	42	1309	1309	NUM
cana-3816	316	43	.	.	PUNCT
cana-3816	317	1	[	[	X
cana-3816	317	2	25	25	NUM
cana-3816	317	3	]	]	X
cana-3816	317	4	palanikumar	palanikumar	PROPN
cana-3816	317	5	,	,	PUNCT
cana-3816	317	6	m	m	PROPN
cana-3816	317	7	;	;	PUNCT
cana-3816	317	8	mohanraj	mohanraj	NOUN
cana-3816	317	9	,	,	PUNCT
cana-3816	317	10	g	g	NOUN
cana-3816	317	11	;	;	PUNCT
cana-3816	317	12	iampan	iampan	NOUN
cana-3816	317	13	,	,	PUNCT
cana-3816	317	14	a.	a.	NOUN
cana-3816	317	15	characterization	characterization	NOUN
cana-3816	317	16	of	of	ADP
cana-3816	317	17	different	different	ADJ
cana-3816	317	18	prime	prime	ADJ
cana-3816	317	19	bi	bi	NOUN
cana-3816	317	20	-	-	NOUN
cana-3816	317	21	ideals	ideal	NOUN
cana-3816	317	22	and	and	CCONJ
cana-3816	317	23	its	its	PRON
cana-3816	317	24	generalization	generalization	NOUN
cana-3816	317	25	of	of	ADP
cana-3816	317	26	semirings	semiring	NOUN
cana-3816	317	27	,	,	PUNCT
cana-3816	317	28	international	international	ADJ
cana-3816	317	29	journal	journal	NOUN
cana-3816	317	30	of	of	ADP
cana-3816	317	31	analysis	analysis	NOUN
cana-3816	317	32	and	and	CCONJ
cana-3816	317	33	applications	application	NOUN
cana-3816	317	34	,	,	PUNCT
cana-3816	317	35	2024	2024	NUM
cana-3816	317	36	,	,	PUNCT
cana-3816	317	37	22	22	NUM
cana-3816	317	38	,	,	PUNCT
cana-3816	317	39	112–112	112–112	NUM
cana-3816	317	40	.	.	PUNCT
cana-3816	318	1	[	[	X
cana-3816	318	2	26	26	NUM
cana-3816	318	3	]	]	X
cana-3816	318	4	hatamleh	hatamleh	PROPN
cana-3816	318	5	,	,	PUNCT
cana-3816	318	6	r.	r.	PROPN
cana-3816	318	7	,	,	PUNCT
cana-3816	318	8	zolotarev	zolotarev	PROPN
cana-3816	318	9	,	,	PUNCT
cana-3816	318	10	v.	v.	ADP
cana-3816	318	11	a.	a.	NOUN
cana-3816	318	12	(	(	PUNCT
cana-3816	318	13	2015	2015	NUM
cana-3816	318	14	)	)	PUNCT
cana-3816	318	15	.	.	PUNCT
cana-3816	319	1	on	on	ADP
cana-3816	319	2	model	model	NOUN
cana-3816	319	3	representations	representation	NOUN
cana-3816	319	4	of	of	ADP
cana-3816	319	5	non	non	ADJ
cana-3816	319	6	-	-	ADJ
cana-3816	319	7	selfadjoint	selfadjoint	ADJ
cana-3816	319	8	operators	operator	NOUN
cana-3816	319	9	with	with	ADP
cana-3816	319	10	infinitely	infinitely	ADV
cana-3816	319	11	dimensional	dimensional	ADJ
cana-3816	319	12	imaginary	imaginary	ADJ
cana-3816	319	13	component	component	NOUN
cana-3816	319	14	,	,	PUNCT
cana-3816	319	15	journal	journal	NOUN
cana-3816	319	16	of	of	ADP
cana-3816	319	17	mathematical	mathematical	ADJ
cana-3816	319	18	physics	physics	NOUN
cana-3816	319	19	,	,	PUNCT
cana-3816	319	20	analysis	analysis	NOUN
cana-3816	319	21	,	,	PUNCT
cana-3816	319	22	geometry	geometry	NOUN
cana-3816	319	23	,	,	PUNCT
cana-3816	319	24	11(2	11(2	NOUN
cana-3816	319	25	)	)	PUNCT
cana-3816	319	26	,	,	PUNCT
cana-3816	319	27	174	174	NUM
cana-3816	319	28	-	-	SYM
cana-3816	319	29	186	186	NUM
cana-3816	319	30	.	.	PUNCT
cana-3816	320	1	[	[	X
cana-3816	320	2	27	27	NUM
cana-3816	320	3	]	]	X
cana-3816	320	4	hatamleh	hatamleh	PROPN
cana-3816	320	5	,	,	PUNCT
cana-3816	320	6	r.	r.	PROPN
cana-3816	320	7	,	,	PUNCT
cana-3816	320	8	zolotarev	zolotarev	PROPN
cana-3816	320	9	,	,	PUNCT
cana-3816	320	10	v.	v.	ADP
cana-3816	320	11	a.	a.	PROPN
cana-3816	320	12	(	(	PUNCT
cana-3816	320	13	2016	2016	NUM
cana-3816	320	14	)	)	PUNCT
cana-3816	320	15	.	.	PUNCT
cana-3816	321	1	triangular	triangular	NOUN
cana-3816	321	2	models	model	NOUN
cana-3816	321	3	of	of	ADP
cana-3816	321	4	commutative	commutative	ADJ
cana-3816	321	5	systems	system	NOUN
cana-3816	321	6	of	of	ADP
cana-3816	321	7	linear	linear	PROPN
cana-3816	321	8	operators	operator	NOUN
cana-3816	321	9	close	close	ADJ
cana-3816	321	10	to	to	ADP
cana-3816	321	11	unitary	unitary	ADJ
cana-3816	321	12	operators	operator	NOUN
cana-3816	321	13	,	,	PUNCT
cana-3816	321	14	ukrainian	ukrainian	ADJ
cana-3816	321	15	mathematical	mathematical	ADJ
cana-3816	321	16	journal	journal	NOUN
cana-3816	321	17	,	,	PUNCT
cana-3816	321	18	68(5),791	68(5),791	NUM
cana-3816	321	19	-	-	PUNCT
cana-3816	321	20	811	811	NUM
cana-3816	321	21	.	.	PUNCT
cana-3816	322	1	[	[	X
cana-3816	322	2	28	28	NUM
cana-3816	322	3	]	]	X
cana-3816	322	4	hatamleh	hatamleh	PROPN
cana-3816	322	5	,	,	PUNCT
cana-3816	322	6	r.	r.	PROPN
cana-3816	322	7	,	,	PUNCT
cana-3816	322	8	zolotarev	zolotarev	PROPN
cana-3816	322	9	,	,	PUNCT
cana-3816	322	10	v.	v.	ADP
cana-3816	322	11	a.	a.	NOUN
cana-3816	322	12	(	(	PUNCT
cana-3816	322	13	2014	2014	NUM
cana-3816	322	14	)	)	PUNCT
cana-3816	322	15	.	.	PUNCT
cana-3816	323	1	on	on	ADP
cana-3816	323	2	two	two	NUM
cana-3816	323	3	-	-	PUNCT
cana-3816	323	4	dimensional	dimensional	ADJ
cana-3816	323	5	model	model	NOUN
cana-3816	323	6	representations	representation	NOUN
cana-3816	323	7	of	of	ADP
cana-3816	323	8	one	one	NUM
cana-3816	323	9	class	class	NOUN
cana-3816	323	10	of	of	ADP
cana-3816	323	11	commuting	commute	VERB
cana-3816	323	12	operators	operator	NOUN
cana-3816	323	13	,	,	PUNCT
cana-3816	323	14	ukrainian	ukrainian	ADJ
cana-3816	323	15	mathematical	mathematical	ADJ
cana-3816	323	16	journal	journal	NOUN
cana-3816	323	17	,	,	PUNCT
cana-3816	323	18	66(1	66(1	NOUN
cana-3816	323	19	)	)	PUNCT
cana-3816	323	20	,	,	PUNCT
cana-3816	323	21	122	122	NUM
cana-3816	323	22	-	-	SYM
cana-3816	323	23	144	144	NUM
cana-3816	323	24	.	.	PUNCT
cana-3816	324	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3816	324	2	770	770	NUM
cana-3816	324	3	communications	communication	NOUN
cana-3816	324	4	on	on	ADP
cana-3816	324	5	applied	apply	VERB
cana-3816	324	6	nonlinear	nonlinear	ADJ
cana-3816	324	7	analysis	analysis	NOUN
cana-3816	324	8	issn	issn	NOUN
cana-3816	324	9	:	:	PUNCT
cana-3816	324	10	1074	1074	NUM
cana-3816	324	11	-	-	PUNCT
cana-3816	324	12	133x	133x	NUM
cana-3816	324	13	vol	vol	NOUN
cana-3816	324	14	32	32	NUM
cana-3816	324	15	no	no	NOUN
cana-3816	324	16	.	.	NOUN
cana-3816	324	17	3	3	NUM
cana-3816	324	18	(	(	PUNCT
cana-3816	324	19	2025	2025	NUM
cana-3816	324	20	)	)	PUNCT
cana-3816	325	1	[	[	X
cana-3816	325	2	29	29	NUM
cana-3816	325	3	]	]	SYM
cana-3816	325	4	r.hatamleh	r.hatamleh	NOUN
cana-3816	325	5	,	,	PUNCT
cana-3816	325	6	v.a	v.a	PROPN
cana-3816	325	7	.	.	PROPN
cana-3816	325	8	zolotarev.(2017).on	zolotarev.(2017).on	NUM
cana-3816	325	9	the	the	DET
cana-3816	325	10	abstract	abstract	ADJ
cana-3816	325	11	inverse	inverse	NOUN
cana-3816	325	12	scattering	scattering	NOUN
cana-3816	325	13	problem	problem	NOUN
cana-3816	325	14	for	for	ADP
cana-3816	325	15	traces	trace	NOUN
cana-3816	325	16	class	class	NOUN
cana-3816	325	17	pertubations	pertubation	NOUN
cana-3816	325	18	.	.	PUNCT
cana-3816	326	1	journal	journal	PROPN
cana-3816	326	2	of	of	ADP
cana-3816	326	3	mathematical	mathematical	ADJ
cana-3816	326	4	physics	physics	NOUN
cana-3816	326	5	,	,	PUNCT
cana-3816	326	6	analysis	analysis	NOUN
cana-3816	326	7	,	,	PUNCT
cana-3816	326	8	geometry	geometry	NOUN
cana-3816	326	9	,	,	PUNCT
cana-3816	326	10	13(1	13(1	NUM
cana-3816	326	11	)	)	PUNCT
cana-3816	326	12	,	,	PUNCT
cana-3816	326	13	(	(	PUNCT
cana-3816	326	14	2017	2017	NUM
cana-3816	326	15	)	)	PUNCT
cana-3816	326	16	,	,	PUNCT
cana-3816	326	17	1	1	NUM
cana-3816	326	18	-	-	SYM
cana-3816	326	19	32	32	NUM
cana-3816	326	20	.	.	PUNCT
cana-3816	327	1	[	[	X
cana-3816	327	2	30	30	NUM
cana-3816	327	3	]	]	X
cana-3816	327	4	raed	raed	NOUN
cana-3816	327	5	hatamleh	hatamleh	PROPN
cana-3816	327	6	,	,	PUNCT
cana-3816	327	7	on	on	ADP
cana-3816	327	8	a	a	DET
cana-3816	327	9	novel	novel	ADJ
cana-3816	327	10	topological	topological	ADJ
cana-3816	327	11	space	space	NOUN
cana-3816	327	12	based	base	VERB
cana-3816	327	13	on	on	ADP
cana-3816	327	14	partially	partially	ADV
cana-3816	327	15	ordered	order	VERB
cana-3816	327	16	ring	ring	NOUN
cana-3816	327	17	of	of	ADP
cana-3816	327	18	weak	weak	ADJ
cana-3816	327	19	fuzzy	fuzzy	ADJ
cana-3816	327	20	complex	complex	ADJ
cana-3816	327	21	numbers	number	NOUN
cana-3816	327	22	and	and	CCONJ
cana-3816	327	23	its	its	PRON
cana-3816	327	24	relation	relation	NOUN
cana-3816	327	25	with	with	ADP
cana-3816	327	26	the	the	DET
cana-3816	327	27	partially	partially	ADV
cana-3816	327	28	ordered	order	VERB
cana-3816	327	29	neutrosophic	neutrosophic	ADJ
cana-3816	327	30	ring	ring	NOUN
cana-3816	327	31	of	of	ADP
cana-3816	327	32	real	real	ADJ
cana-3816	327	33	numbers	number	NOUN
cana-3816	327	34	,	,	PUNCT
cana-3816	327	35	neutrosophic	neutrosophic	ADJ
cana-3816	327	36	sets	set	NOUN
cana-3816	327	37	and	and	CCONJ
cana-3816	327	38	systems	system	NOUN
cana-3816	327	39	,	,	PUNCT
cana-3816	327	40	78	78	NUM
cana-3816	327	41	,	,	PUNCT
cana-3816	327	42	(	(	PUNCT
cana-3816	327	43	2025	2025	NUM
cana-3816	327	44	)	)	PUNCT
cana-3816	327	45	,	,	PUNCT
cana-3816	327	46	578	578	NUM
cana-3816	327	47	-	-	SYM
cana-3816	327	48	590	590	NUM
cana-3816	327	49	.	.	PUNCT
cana-3816	328	1	[	[	X
cana-3816	328	2	31	31	NUM
cana-3816	328	3	]	]	PUNCT
cana-3816	328	4	abdallah	abdallah	PROPN
cana-3816	328	5	al	al	PROPN
cana-3816	328	6	-	-	PROPN
cana-3816	328	7	husban	husban	PROPN
cana-3816	328	8	&	&	CCONJ
cana-3816	328	9	abdul	abdul	PROPN
cana-3816	328	10	razak	razak	PROPN
cana-3816	328	11	salleh	salleh	PROPN
cana-3816	328	12	,	,	PUNCT
cana-3816	328	13	complex	complex	ADJ
cana-3816	328	14	fuzzy	fuzzy	ADJ
cana-3816	328	15	ring	ring	NOUN
cana-3816	328	16	.	.	PUNCT
cana-3816	329	1	proceedings	proceeding	NOUN
cana-3816	329	2	of	of	ADP
cana-3816	329	3	2nd	2nd	ADJ
cana-3816	329	4	international	international	ADJ
cana-3816	329	5	conference	conference	NOUN
cana-3816	329	6	on	on	ADP
cana-3816	329	7	computing	computing	NOUN
cana-3816	329	8	,	,	PUNCT
cana-3816	329	9	mathematics	mathematic	NOUN
cana-3816	329	10	and	and	CCONJ
cana-3816	329	11	statistics	statistic	NOUN
cana-3816	329	12	,	,	PUNCT
cana-3816	329	13	ieee	ieee	NOUN
cana-3816	329	14	,	,	PUNCT
cana-3816	329	15	2015	2015	NUM
cana-3816	329	16	,	,	PUNCT
cana-3816	329	17	241	241	NUM
cana-3816	329	18	-	-	SYM
cana-3816	329	19	245	245	NUM
cana-3816	329	20	.	.	PUNCT
cana-3816	330	1	[	[	X
cana-3816	330	2	32	32	NUM
cana-3816	330	3	]	]	PUNCT
cana-3816	330	4	abdallah	abdallah	PROPN
cana-3816	330	5	al	al	PROPN
cana-3816	330	6	-	-	PROPN
cana-3816	330	7	husban	husban	PROPN
cana-3816	330	8	&	&	CCONJ
cana-3816	330	9	abdul	abdul	PROPN
cana-3816	330	10	razak	razak	PROPN
cana-3816	330	11	salleh	salleh	PROPN
cana-3816	330	12	,	,	PUNCT
cana-3816	330	13	complex	complex	ADJ
cana-3816	330	14	fuzzy	fuzzy	ADJ
cana-3816	330	15	hyperring	hyperring	NOUN
cana-3816	330	16	based	base	VERB
cana-3816	330	17	on	on	ADP
cana-3816	330	18	complex	complex	ADJ
cana-3816	330	19	fuzzy	fuzzy	ADJ
cana-3816	330	20	spaces	space	NOUN
cana-3816	330	21	.	.	PUNCT
cana-3816	331	1	proceedings	proceeding	NOUN
cana-3816	331	2	of	of	ADP
cana-3816	331	3	2nd	2nd	ADJ
cana-3816	331	4	innovation	innovation	NOUN
cana-3816	331	5	and	and	CCONJ
cana-3816	331	6	analytics	analytic	NOUN
cana-3816	331	7	conference	conference	NOUN
cana-3816	331	8	&	&	CCONJ
cana-3816	331	9	exhibition	exhibition	PROPN
cana-3816	331	10	(	(	PUNCT
cana-3816	331	11	iace	iace	NOUN
cana-3816	331	12	)	)	PUNCT
cana-3816	331	13	.	.	PUNCT
cana-3816	332	1	vol	vol	NOUN
cana-3816	332	2	.	.	PROPN
cana-3816	332	3	1691	1691	NUM
cana-3816	332	4	.	.	PUNCT
cana-3816	333	1	aip	aip	PROPN
cana-3816	333	2	publishing	publish	VERB
cana-3816	333	3	2015	2015	NUM
cana-3816	333	4	,	,	PUNCT
cana-3816	333	5	040009	040009	NUM
cana-3816	333	6	-	-	SYM
cana-3816	333	7	040017	040017	NUM
cana-3816	333	8	.	.	PUNCT
cana-3816	334	1	[	[	X
cana-3816	334	2	33	33	NUM
cana-3816	334	3	]	]	X
cana-3816	334	4	al	al	PROPN
cana-3816	334	5	-	-	PUNCT
cana-3816	334	6	husban	husban	PROPN
cana-3816	334	7	,	,	PUNCT
cana-3816	334	8	a.	a.	PROPN
cana-3816	334	9	,	,	PUNCT
cana-3816	334	10	&	&	CCONJ
cana-3816	334	11	salleh	salleh	PROPN
cana-3816	334	12	,	,	PUNCT
cana-3816	334	13	a.	a.	PROPN
cana-3816	334	14	r.	r.	PROPN
cana-3816	334	15	complex	complex	PROPN
cana-3816	334	16	fuzzy	fuzzy	ADJ
cana-3816	334	17	hyper	hyper	ADJ
cana-3816	334	18	groups	group	NOUN
cana-3816	334	19	based	base	VERB
cana-3816	334	20	on	on	ADP
cana-3816	334	21	complex	complex	ADJ
cana-3816	334	22	fuzzy	fuzzy	ADJ
cana-3816	334	23	spaces	space	NOUN
cana-3816	334	24	.	.	PUNCT
cana-3816	335	1	international	international	ADJ
cana-3816	335	2	journal	journal	NOUN
cana-3816	335	3	of	of	ADP
cana-3816	335	4	pure	pure	ADJ
cana-3816	335	5	and	and	CCONJ
cana-3816	335	6	applied	applied	ADJ
cana-3816	335	7	mathematics	mathematic	NOUN
cana-3816	335	8	,	,	PUNCT
cana-3816	335	9	107(4	107(4	NUM
cana-3816	335	10	)	)	PUNCT
cana-3816	335	11	,	,	PUNCT
cana-3816	335	12	(	(	PUNCT
cana-3816	335	13	2016	2016	NUM
cana-3816	335	14	)	)	PUNCT
cana-3816	335	15	,	,	PUNCT
cana-3816	335	16	949	949	NUM
cana-3816	335	17	-	-	SYM
cana-3816	335	18	958	958	NUM
cana-3816	335	19	.	.	PUNCT
cana-3816	336	1	[	[	X
cana-3816	336	2	34	34	NUM
cana-3816	336	3	]	]	PUNCT
cana-3816	336	4	alsarahead	alsarahead	NOUN
cana-3816	336	5	,	,	PUNCT
cana-3816	336	6	m.	m.	NOUN
cana-3816	336	7	o.	o.	PROPN
cana-3816	336	8	,	,	PUNCT
cana-3816	336	9	&	&	CCONJ
cana-3816	336	10	al	al	PROPN
cana-3816	336	11	-	-	PUNCT
cana-3816	336	12	husban	husban	PROPN
cana-3816	336	13	,	,	PUNCT
cana-3816	336	14	a	a	DET
cana-3816	336	15	,	,	PUNCT
cana-3816	336	16	complex	complex	ADJ
cana-3816	336	17	multi	multi	ADJ
cana-3816	336	18	-	-	ADJ
cana-3816	336	19	fuzzy	fuzzy	ADJ
cana-3816	336	20	subgroups	subgroup	NOUN
cana-3816	336	21	.	.	PUNCT
cana-3816	337	1	journal	journal	NOUN
cana-3816	337	2	of	of	ADP
cana-3816	337	3	discrete	discrete	ADJ
cana-3816	337	4	mathematical	mathematical	ADJ
cana-3816	337	5	sciences	science	NOUN
cana-3816	337	6	and	and	CCONJ
cana-3816	337	7	cryptography	cryptography	NOUN
cana-3816	337	8	,	,	PUNCT
cana-3816	337	9	25(8	25(8	NUM
cana-3816	337	10	)	)	PUNCT
cana-3816	337	11	,	,	PUNCT
cana-3816	337	12	(	(	PUNCT
cana-3816	337	13	2022	2022	NUM
cana-3816	337	14	)	)	PUNCT
cana-3816	337	15	,	,	PUNCT
cana-3816	337	16	2707	2707	NUM
cana-3816	337	17	-	-	SYM
cana-3816	337	18	2716	2716	NUM
cana-3816	337	19	.	.	PUNCT
cana-3816	338	1	[	[	X
cana-3816	338	2	35	35	NUM
cana-3816	338	3	]	]	X
cana-3816	338	4	al	al	PROPN
cana-3816	338	5	-	-	PUNCT
cana-3816	338	6	husban	husban	PROPN
cana-3816	338	7	,	,	PUNCT
cana-3816	338	8	a	a	PRON
cana-3816	338	9	,	,	PUNCT
cana-3816	338	10	multi	multi	ADJ
cana-3816	338	11	-	-	ADJ
cana-3816	338	12	fuzzy	fuzzy	ADJ
cana-3816	338	13	hyper	hyper	ADJ
cana-3816	338	14	groups	group	NOUN
cana-3816	338	15	.	.	PUNCT
cana-3816	339	1	italian	italian	ADJ
cana-3816	339	2	journal	journal	NOUN
cana-3816	339	3	of	of	ADP
cana-3816	339	4	pure	pure	ADJ
cana-3816	339	5	and	and	CCONJ
cana-3816	339	6	applied	applied	ADJ
cana-3816	339	7	mathematics	mathematic	NOUN
cana-3816	339	8	,	,	PUNCT
cana-3816	339	9	46	46	NUM
cana-3816	339	10	,	,	PUNCT
cana-3816	339	11	(	(	PUNCT
cana-3816	339	12	2021	2021	NUM
cana-3816	339	13	)	)	PUNCT
cana-3816	339	14	,	,	PUNCT
cana-3816	339	15	382	382	NUM
cana-3816	339	16	-	-	SYM
cana-3816	339	17	390	390	NUM
cana-3816	339	18	.	.	PUNCT
cana-3816	340	1	[	[	X
cana-3816	340	2	36	36	NUM
cana-3816	340	3	]	]	X
cana-3816	340	4	al	al	PROPN
cana-3816	340	5	-	-	PUNCT
cana-3816	340	6	husban	husban	PROPN
cana-3816	340	7	,	,	PUNCT
cana-3816	340	8	a	a	DET
cana-3816	340	9	,	,	PUNCT
cana-3816	340	10	fuzzy	fuzzy	ADJ
cana-3816	340	11	soft	soft	ADJ
cana-3816	340	12	groups	group	NOUN
cana-3816	340	13	based	base	VERB
cana-3816	340	14	on	on	ADP
cana-3816	340	15	fuzzy	fuzzy	ADJ
cana-3816	340	16	space	space	NOUN
cana-3816	340	17	,	,	PUNCT
cana-3816	340	18	wseas	wseas	VERB
cana-3816	340	19	transactions	transaction	NOUN
cana-3816	340	20	on	on	ADP
cana-3816	340	21	mathematics	mathematic	NOUN
cana-3816	340	22	.	.	PUNCT
cana-3816	341	1	21	21	NUM
cana-3816	341	2	,	,	PUNCT
cana-3816	341	3	(	(	PUNCT
cana-3816	341	4	2021	2021	NUM
cana-3816	341	5	)	)	PUNCT
cana-3816	341	6	,	,	PUNCT
cana-3816	341	7	53	53	NUM
cana-3816	341	8	-	-	SYM
cana-3816	341	9	57	57	NUM
cana-3816	341	10	.	.	PUNCT
cana-3816	342	1	[	[	X
cana-3816	342	2	37	37	NUM
cana-3816	342	3	]	]	X
cana-3816	342	4	al	al	PROPN
cana-3816	342	5	-	-	PUNCT
cana-3816	342	6	husban	husban	PROPN
cana-3816	342	7	,	,	PUNCT
cana-3816	342	8	.	.	PUNCT
cana-3816	343	1	abdallah	abdallah	PROPN
cana-3816	343	2	,	,	PUNCT
cana-3816	343	3	al	al	PROPN
cana-3816	343	4	-	-	PUNCT
cana-3816	343	5	sharoa	sharoa	NOUN
cana-3816	343	6	,	,	PUNCT
cana-3816	343	7	doaa	doaa	PROPN
cana-3816	343	8	.	.	PROPN
cana-3816	343	9	,	,	PUNCT
cana-3816	344	1	al	al	PROPN
cana-3816	344	2	-	-	PUNCT
cana-3816	344	3	kaseasbeh	kaseasbeh	PROPN
cana-3816	344	4	,	,	PUNCT
cana-3816	344	5	mohammad	mohammad	PROPN
cana-3816	344	6	.	.	PROPN
cana-3816	344	7	,	,	PUNCT
cana-3816	344	8	&	&	CCONJ
cana-3816	344	9	mahmood	mahmood	PROPN
cana-3816	344	10	,	,	PUNCT
cana-3816	344	11	r.m.s	r.m.	NOUN
cana-3816	344	12	,	,	PUNCT
cana-3816	344	13	structures	structure	NOUN
cana-3816	344	14	of	of	ADP
cana-3816	344	15	fibers	fiber	NOUN
cana-3816	344	16	of	of	ADP
cana-3816	344	17	groups	group	NOUN
cana-3816	344	18	actions	action	NOUN
cana-3816	344	19	on	on	ADP
cana-3816	344	20	graphs	graph	NOUN
cana-3816	344	21	.	.	PUNCT
cana-3816	345	1	wseas	wseas	VERB
cana-3816	345	2	transactions	transaction	NOUN
cana-3816	345	3	on	on	ADP
cana-3816	345	4	mathematics	mathematic	NOUN
cana-3816	345	5	,	,	PUNCT
cana-3816	345	6	7	7	NUM
cana-3816	345	7	,	,	PUNCT
cana-3816	345	8	(	(	PUNCT
cana-3816	345	9	2022	2022	NUM
cana-3816	345	10	)	)	PUNCT
cana-3816	345	11	,	,	PUNCT
cana-3816	345	12	650	650	NUM
cana-3816	345	13	-	-	SYM
cana-3816	345	14	658	658	NUM
cana-3816	345	15	.	.	PUNCT
cana-3816	346	1	[	[	X
cana-3816	346	2	38	38	NUM
cana-3816	346	3	]	]	PUNCT
cana-3816	346	4	hatamleh	hatamleh	PROPN
cana-3816	346	5	,	,	PUNCT
cana-3816	346	6	r.	r.	PROPN
cana-3816	346	7	,	,	PUNCT
cana-3816	346	8	heilat	heilat	PROPN
cana-3816	346	9	,	,	PUNCT
cana-3816	346	10	a.	a.	PROPN
cana-3816	346	11	s.	s.	PROPN
cana-3816	346	12	,	,	PUNCT
cana-3816	346	13	palanikumar	palanikumar	PROPN
cana-3816	346	14	,	,	PUNCT
cana-3816	346	15	m.	m.	NOUN
cana-3816	346	16	,	,	PUNCT
cana-3816	346	17	&	&	CCONJ
cana-3816	346	18	al	al	PROPN
cana-3816	346	19	-	-	PUNCT
cana-3816	346	20	husban	husban	PROPN
cana-3816	346	21	,	,	PUNCT
cana-3816	346	22	a.	a.	NOUN
cana-3816	346	23	different	different	ADJ
cana-3816	346	24	operators	operator	NOUN
cana-3816	346	25	via	via	ADP
cana-3816	346	26	weighted	weighted	ADJ
cana-3816	346	27	averaging	averaging	NOUN
cana-3816	346	28	and	and	CCONJ
cana-3816	346	29	geometric	geometric	ADJ
cana-3816	346	30	approach	approach	NOUN
cana-3816	346	31	using	use	VERB
cana-3816	346	32	trigonometric	trigonometric	ADJ
cana-3816	346	33	neutrosophic	neutrosophic	ADJ
cana-3816	346	34	interval	interval	NOUN
cana-3816	346	35	-	-	PUNCT
cana-3816	346	36	valued	value	VERB
cana-3816	346	37	set	set	NOUN
cana-3816	346	38	and	and	CCONJ
cana-3816	346	39	its	its	PRON
cana-3816	346	40	extension	extension	NOUN
cana-3816	346	41	,	,	PUNCT
cana-3816	346	42	neutrosophic	neutrosophic	ADJ
cana-3816	346	43	sets	set	NOUN
cana-3816	346	44	and	and	CCONJ
cana-3816	346	45	systems	system	NOUN
cana-3816	346	46	,	,	PUNCT
cana-3816	346	47	80	80	NUM
cana-3816	346	48	,	,	PUNCT
cana-3816	346	49	2025	2025	NUM
cana-3816	346	50	,	,	PUNCT
cana-3816	346	51	194	194	NUM
cana-3816	346	52	-	-	SYM
cana-3816	346	53	213	213	NUM
cana-3816	346	54	.	.	PUNCT
cana-3816	347	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3816	347	2	771	771	NUM
cana-3816	347	3	1	1	NUM
cana-3816	347	4	introduction	introduction	NOUN
cana-3816	347	5	2	2	NUM
cana-3816	347	6	(	(	PUNCT
cana-3816	347	7	1	1	NUM
cana-3816	347	8	,	,	PUNCT
cana-3816	347	9	2	2	X
cana-3816	347	10	)	)	PUNCT
cana-3816	347	11	intuitionistic	intuitionistic	ADJ
cana-3816	347	12	q1	q1	PROPN
cana-3816	347	13	anti	anti	X
cana-3816	347	14	fuzzy	fuzzy	ADJ
cana-3816	347	15	ideals	ideal	NOUN