id	sid	tid	token	lemma	pos
cana-3320	1	1	communications	communication	NOUN
cana-3320	1	2	on	on	ADP
cana-3320	1	3	applied	apply	VERB
cana-3320	1	4	nonlinear	nonlinear	ADJ
cana-3320	1	5	analysis	analysis	NOUN
cana-3320	1	6	issn	issn	NOUN
cana-3320	1	7	:	:	PUNCT
cana-3320	1	8	1074	1074	NUM
cana-3320	1	9	-	-	PUNCT
cana-3320	1	10	133x	133x	NUM
cana-3320	1	11	vol	vol	NOUN
cana-3320	1	12	32	32	NUM
cana-3320	1	13	no	no	NOUN
cana-3320	1	14	.	.	PUNCT
cana-3320	2	1	6s	6s	NUM
cana-3320	2	2	(	(	PUNCT
cana-3320	2	3	2025	2025	NUM
cana-3320	2	4	)	)	PUNCT
cana-3320	2	5	generalization	generalization	NOUN
cana-3320	2	6	of	of	ADP
cana-3320	2	7	intuitionistic	intuitionistic	ADJ
cana-3320	2	8	fuzzy	fuzzy	ADJ
cana-3320	2	9	ideals	ideal	NOUN
cana-3320	2	10	via	via	ADP
cana-3320	2	11	(	(	PUNCT
cana-3320	2	12	∂̃	∂̃	PROPN
cana-3320	2	13	,	,	PUNCT
cana-3320	2	14	℘̃	℘̃	NOUN
cana-3320	2	15	)	)	PUNCT
cana-3320	2	16	intuitionistic	intuitionistic	ADJ
cana-3320	2	17	q	q	NOUN
cana-3320	2	18	interval	interval	NOUN
cana-3320	2	19	-	-	PUNCT
cana-3320	2	20	valued	value	VERB
cana-3320	2	21	fuzzy	fuzzy	ADJ
cana-3320	2	22	ideals	ideal	NOUN
cana-3320	2	23	using	use	VERB
cana-3320	2	24	regular	regular	ADJ
cana-3320	2	25	ordered	order	VERB
cana-3320	2	26	ternary	ternary	ADJ
cana-3320	2	27	semigroups	semigroup	NOUN
cana-3320	2	28	ayman	ayman	PROPN
cana-3320	2	29	hazaymeh1	hazaymeh1	PROPN
cana-3320	2	30	,	,	PUNCT
cana-3320	2	31	abdallah	abdallah	PROPN
cana-3320	2	32	al	al	PROPN
cana-3320	2	33	-	-	PUNCT
cana-3320	2	34	husban2,3	husban2,3	PROPN
cana-3320	2	35	,	,	PUNCT
cana-3320	2	36	m.palanikumar4	m.palanikumar4	PROPN
cana-3320	2	37	1department	1department	NUM
cana-3320	2	38	of	of	ADP
cana-3320	2	39	mathematics	mathematic	NOUN
cana-3320	2	40	,	,	PUNCT
cana-3320	2	41	faculty	faculty	NOUN
cana-3320	2	42	of	of	ADP
cana-3320	2	43	science	science	NOUN
cana-3320	2	44	,	,	PUNCT
cana-3320	2	45	jadara	jadara	PROPN
cana-3320	2	46	university	university	PROPN
cana-3320	2	47	,	,	PUNCT
cana-3320	2	48	p.o	p.o	PROPN
cana-3320	2	49	.	.	PROPN
cana-3320	2	50	box	box	PROPN
cana-3320	2	51	733	733	NUM
cana-3320	2	52	,	,	PUNCT
cana-3320	2	53	irbid	irbid	ADJ
cana-3320	2	54	21110	21110	NUM
cana-3320	2	55	,	,	PUNCT
cana-3320	2	56	jordan	jordan	PROPN
cana-3320	2	57	.	.	PUNCT
cana-3320	3	1	2department	2department	NUM
cana-3320	3	2	of	of	ADP
cana-3320	3	3	mathematics	mathematic	NOUN
cana-3320	3	4	,	,	PUNCT
cana-3320	3	5	faculty	faculty	NOUN
cana-3320	3	6	of	of	ADP
cana-3320	3	7	science	science	NOUN
cana-3320	3	8	and	and	CCONJ
cana-3320	3	9	technology	technology	NOUN
cana-3320	3	10	,	,	PUNCT
cana-3320	3	11	irbid	irbid	VERB
cana-3320	3	12	national	national	ADJ
cana-3320	3	13	university	university	PROPN
cana-3320	3	14	,	,	PUNCT
cana-3320	3	15	p.o	p.o	PROPN
cana-3320	3	16	.	.	PROPN
cana-3320	3	17	box	box	PROPN
cana-3320	3	18	:	:	PUNCT
cana-3320	3	19	2600	2600	NUM
cana-3320	3	20	irbid	irbid	PROPN
cana-3320	3	21	,	,	PUNCT
cana-3320	3	22	jordan	jordan	PROPN
cana-3320	3	23	.	.	PUNCT
cana-3320	4	1	3jadara	3jadara	NUM
cana-3320	4	2	research	research	NOUN
cana-3320	4	3	center	center	NOUN
cana-3320	4	4	,	,	PUNCT
cana-3320	4	5	jadara	jadara	PROPN
cana-3320	4	6	university	university	PROPN
cana-3320	4	7	,	,	PUNCT
cana-3320	4	8	irbid	irbid	VERB
cana-3320	4	9	21110	21110	NUM
cana-3320	4	10	,	,	PUNCT
cana-3320	4	11	jordan	jordan	PROPN
cana-3320	4	12	.	.	PUNCT
cana-3320	5	1	4department	4department	NUM
cana-3320	5	2	of	of	ADP
cana-3320	5	3	mathematics	mathematic	NOUN
cana-3320	5	4	,	,	PUNCT
cana-3320	5	5	saveetha	saveetha	PROPN
cana-3320	5	6	school	school	PROPN
cana-3320	5	7	of	of	ADP
cana-3320	5	8	engineering	engineering	PROPN
cana-3320	5	9	,	,	PUNCT
cana-3320	5	10	saveetha	saveetha	PROPN
cana-3320	5	11	institute	institute	PROPN
cana-3320	5	12	of	of	ADP
cana-3320	5	13	medical	medical	ADJ
cana-3320	5	14	and	and	CCONJ
cana-3320	5	15	technical	technical	ADJ
cana-3320	5	16	sciences	science	NOUN
cana-3320	5	17	,	,	PUNCT
cana-3320	5	18	chennai-602105	chennai-602105	ADJ
cana-3320	5	19	,	,	PUNCT
cana-3320	5	20	india	india	PROPN
cana-3320	5	21	.	.	PUNCT
cana-3320	6	1	e	e	X
cana-3320	6	2	-	-	ADJ
cana-3320	6	3	mails:1aymanha@	mails:1aymanha@	ADJ
cana-3320	6	4	jadara.edu.jo	jadara.edu.jo	PROPN
cana-3320	6	5	,	,	PUNCT
cana-3320	6	6	3dralhosban@inu.edu.jo	3dralhosban@inu.edu.jo	NUM
cana-3320	6	7	,	,	PUNCT
cana-3320	6	8	4palanimaths86@gmail.com	4palanimaths86@gmail.com	NUM
cana-3320	6	9	,	,	PUNCT
cana-3320	6	10	∗corresponding	∗corresponde	VERB
cana-3320	6	11	author	author	NOUN
cana-3320	6	12	:	:	PUNCT
cana-3320	6	13	m.palanikumar	m.palanikumar	X
cana-3320	6	14	.	.	PROPN
cana-3320	6	15	received	receive	VERB
cana-3320	6	16	:	:	PUNCT
cana-3320	6	17	25	25	NUM
cana-3320	6	18	-	-	SYM
cana-3320	6	19	10	10	NUM
cana-3320	6	20	-	-	PUNCT
cana-3320	6	21	2024	2024	NUM
cana-3320	6	22	;	;	PUNCT
cana-3320	6	23	revised	revise	VERB
cana-3320	6	24	:	:	PUNCT
cana-3320	6	25	02	02	NUM
cana-3320	6	26	-	-	SYM
cana-3320	6	27	12	12	NUM
cana-3320	6	28	-	-	PUNCT
cana-3320	6	29	2024	2024	NUM
cana-3320	6	30	;	;	PUNCT
cana-3320	6	31	accepted	accept	VERB
cana-3320	6	32	:	:	PUNCT
cana-3320	6	33	 	 	SPACE
cana-3320	6	34	18	18	NUM
cana-3320	6	35	-	-	SYM
cana-3320	6	36	12	12	NUM
cana-3320	6	37	-	-	PUNCT
cana-3320	6	38	2024	2024	NUM
cana-3320	6	39	abstract	abstract	NOUN
cana-3320	6	40	this	this	DET
cana-3320	6	41	paper	paper	NOUN
cana-3320	6	42	introduces	introduce	VERB
cana-3320	6	43	the	the	DET
cana-3320	6	44	notion	notion	NOUN
cana-3320	6	45	of	of	ADP
cana-3320	6	46	∂̃	∂̃	PROPN
cana-3320	6	47	,	,	PUNCT
cana-3320	6	48	℘̃	℘̃	PROPN
cana-3320	6	49	intuitionistic	intuitionistic	ADJ
cana-3320	6	50	q	q	NOUN
cana-3320	6	51	interval	interval	NOUN
cana-3320	6	52	-	-	PUNCT
cana-3320	6	53	valued	value	VERB
cana-3320	6	54	fuzzy	fuzzy	ADJ
cana-3320	6	55	subsemigroup	subsemigroup	NOUN
cana-3320	6	56	(	(	PUNCT
cana-3320	6	57	iqvfss	iqvfss	NOUN
cana-3320	6	58	)	)	PUNCT
cana-3320	6	59	,	,	PUNCT
cana-3320	6	60	fuzzy	fuzzy	ADJ
cana-3320	6	61	left	leave	VERB
cana-3320	6	62	ideal	ideal	NOUN
cana-3320	6	63	(	(	PUNCT
cana-3320	6	64	iqvfli	iqvfli	PROPN
cana-3320	6	65	)	)	PUNCT
cana-3320	6	66	,	,	PUNCT
cana-3320	6	67	fuzzy	fuzzy	ADJ
cana-3320	6	68	right	right	ADJ
cana-3320	6	69	ideal	ideal	NOUN
cana-3320	6	70	(	(	PUNCT
cana-3320	6	71	iqvfri	iqvfri	ADJ
cana-3320	6	72	)	)	PUNCT
cana-3320	6	73	,	,	PUNCT
cana-3320	6	74	fuzzy	fuzzy	ADJ
cana-3320	6	75	lateral	lateral	ADJ
cana-3320	6	76	ideal	ideal	NOUN
cana-3320	6	77	(	(	PUNCT
cana-3320	6	78	iqvflati	iqvflati	PROPN
cana-3320	6	79	)	)	PUNCT
cana-3320	6	80	,	,	PUNCT
cana-3320	6	81	fuzzy	fuzzy	ADJ
cana-3320	6	82	ideal	ideal	NOUN
cana-3320	6	83	(	(	PUNCT
cana-3320	6	84	iqvfi	iqvfi	PROPN
cana-3320	6	85	)	)	PUNCT
cana-3320	6	86	,	,	PUNCT
cana-3320	6	87	and	and	CCONJ
cana-3320	6	88	fuzzy	fuzzy	ADJ
cana-3320	6	89	bi	bi	ADJ
cana-3320	6	90	-	-	ADJ
cana-3320	6	91	ideal	ideal	ADJ
cana-3320	6	92	(	(	PUNCT
cana-3320	6	93	iqvfbi	iqvfbi	PROPN
cana-3320	6	94	)	)	PUNCT
cana-3320	6	95	of	of	ADP
cana-3320	6	96	an	an	DET
cana-3320	6	97	ordered	order	VERB
cana-3320	6	98	semigroups	semigroup	NOUN
cana-3320	6	99	.	.	PUNCT
cana-3320	7	1	let	let	VERB
cana-3320	7	2	∂̃	∂̃	NOUN
cana-3320	7	3	,	,	PUNCT
cana-3320	7	4	℘̃-iqvfi	℘̃-iqvfi	NUM
cana-3320	7	5	is	be	AUX
cana-3320	7	6	a	a	DET
cana-3320	7	7	new	new	ADJ
cana-3320	7	8	extension	extension	NOUN
cana-3320	7	9	of	of	ADP
cana-3320	7	10	iqvfi	iqvfi	NOUN
cana-3320	7	11	over	over	ADP
cana-3320	7	12	ternary	ternary	ADJ
cana-3320	7	13	semigroups	semigroup	NOUN
cana-3320	7	14	z	z	X
cana-3320	7	15	.	.	PUNCT
cana-3320	8	1	the	the	DET
cana-3320	8	2	subset	subset	NOUN
cana-3320	8	3	~	~	PUNCT
cana-3320	8	4	=	=	PUNCT
cana-3320	9	1	[	[	X
cana-3320	9	2	<	<	X
cana-3320	9	3	=]	=]	NOUN
cana-3320	9	4	represents	represent	VERB
cana-3320	9	5	a	a	DET
cana-3320	9	6	(	(	PUNCT
cana-3320	9	7	∂̃	∂̃	NOUN
cana-3320	9	8	,	,	PUNCT
cana-3320	9	9	℘̃	℘̃	PROPN
cana-3320	9	10	)	)	PUNCT
cana-3320	9	11	−	−	PROPN
cana-3320	10	1	iqv	iqv	INTJ
cana-3320	10	2	f	f	NOUN
cana-3320	11	1	ss[iqv	ss[iqv	PROPN
cana-3320	11	2	f	f	PROPN
cana-3320	11	3	li	li	PROPN
cana-3320	11	4	,	,	PUNCT
cana-3320	11	5	iqv	iqv	PROPN
cana-3320	11	6	fri	fri	NOUN
cana-3320	11	7	,	,	PUNCT
cana-3320	11	8	iqv	iqv	INTJ
cana-3320	11	9	f	f	PROPN
cana-3320	12	1	lat	lat	INTJ
cana-3320	13	1	i	i	PRON
cana-3320	13	2	,	,	PUNCT
cana-3320	13	3	iqv	iqv	PROPN
cana-3320	13	4	fbi	fbi	PROPN
cana-3320	13	5	]	]	PUNCT
cana-3320	13	6	of	of	ADP
cana-3320	13	7	z	z	NOUN
cana-3320	13	8	if	if	SCONJ
cana-3320	13	9	and	and	CCONJ
cana-3320	13	10	only	only	ADV
cana-3320	13	11	if	if	SCONJ
cana-3320	13	12	every	every	DET
cana-3320	13	13	level	level	NOUN
cana-3320	13	14	subset	subset	VERB
cana-3320	13	15	~t	~t	PUNCT
cana-3320	13	16	is	be	AUX
cana-3320	13	17	an	an	DET
cana-3320	13	18	ss	ss	NOUN
cana-3320	13	19	[	[	X
cana-3320	13	20	li	li	PROPN
cana-3320	13	21	,	,	PUNCT
cana-3320	13	22	ri	ri	PROPN
cana-3320	13	23	,	,	PUNCT
cana-3320	13	24	laiqv	laiqv	PROPN
cana-3320	13	25	f	f	PROPN
cana-3320	13	26	,	,	PUNCT
cana-3320	13	27	t	t	PROPN
cana-3320	13	28	bi	bi	PROPN
cana-3320	13	29	]	]	X
cana-3320	13	30	of	of	ADP
cana-3320	13	31	z	z	NOUN
cana-3320	13	32	for	for	ADP
cana-3320	13	33	every	every	DET
cana-3320	13	34	t	t	NOUN
cana-3320	13	35	∈	∈	PROPN
cana-3320	13	36	(	(	PUNCT
cana-3320	13	37	∂̃	∂̃	NOUN
cana-3320	13	38	,	,	PUNCT
cana-3320	13	39	℘̃	℘̃	PROPN
cana-3320	13	40	]	]	PUNCT
cana-3320	13	41	.	.	PUNCT
cana-3320	14	1	a	a	DET
cana-3320	14	2	few	few	ADJ
cana-3320	14	3	examples	example	NOUN
cana-3320	14	4	can	can	AUX
cana-3320	14	5	be	be	AUX
cana-3320	14	6	presented	present	VERB
cana-3320	14	7	to	to	PART
cana-3320	14	8	demonstrate	demonstrate	VERB
cana-3320	14	9	our	our	PRON
cana-3320	14	10	results	result	NOUN
cana-3320	14	11	.	.	PUNCT
cana-3320	15	1	keywords	keyword	NOUN
cana-3320	15	2	:	:	PUNCT
cana-3320	15	3	iqvfss	iqvfss	ADJ
cana-3320	15	4	,	,	PUNCT
cana-3320	15	5	iqvfli	iqvfli	PROPN
cana-3320	15	6	,	,	PUNCT
cana-3320	15	7	iqvfri	iqvfri	ADJ
cana-3320	15	8	,	,	PUNCT
cana-3320	15	9	iqvflati	iqvflati	PROPN
cana-3320	15	10	,	,	PUNCT
cana-3320	15	11	iqvfbi	iqvfbi	PROPN
cana-3320	15	12	.	.	PUNCT
cana-3320	16	1	1	1	NUM
cana-3320	16	2	introduction	introduction	NOUN
cana-3320	16	3	d.	d.	PROPN
cana-3320	16	4	h.	h.	PROPN
cana-3320	16	5	lehmer	lehmer	PROPN
cana-3320	16	6	initially	initially	ADV
cana-3320	16	7	introduced	introduce	VERB
cana-3320	16	8	triplexes	triplexe	NOUN
cana-3320	16	9	,	,	PUNCT
cana-3320	16	10	which	which	PRON
cana-3320	16	11	are	be	AUX
cana-3320	16	12	ternary	ternary	ADJ
cana-3320	16	13	algebraic	algebraic	ADJ
cana-3320	16	14	systems	system	NOUN
cana-3320	16	15	,	,	PUNCT
cana-3320	16	16	in	in	ADP
cana-3320	16	17	1932.1	1932.1	NUM
cana-3320	16	18	triplexes	triplexe	NOUN
cana-3320	16	19	,	,	PUNCT
cana-3320	16	20	ternary	ternary	ADJ
cana-3320	16	21	algebraic	algebraic	ADJ
cana-3320	16	22	systems	system	NOUN
cana-3320	16	23	that	that	PRON
cana-3320	16	24	prove	prove	VERB
cana-3320	16	25	to	to	PART
cana-3320	16	26	be	be	AUX
cana-3320	16	27	commutative	commutative	ADJ
cana-3320	16	28	ternary	ternary	ADJ
cana-3320	16	29	groups	group	NOUN
cana-3320	16	30	,	,	PUNCT
cana-3320	16	31	are	be	AUX
cana-3320	16	32	the	the	DET
cana-3320	16	33	subject	subject	NOUN
cana-3320	16	34	of	of	ADP
cana-3320	16	35	his	his	PRON
cana-3320	16	36	investigation	investigation	NOUN
cana-3320	16	37	.	.	PUNCT
cana-3320	17	1	the	the	DET
cana-3320	17	2	concept	concept	NOUN
cana-3320	17	3	of	of	ADP
cana-3320	17	4	a	a	DET
cana-3320	17	5	semiring	semiring	NOUN
cana-3320	17	6	was	be	AUX
cana-3320	17	7	initially	initially	ADV
cana-3320	17	8	put	put	VERB
cana-3320	17	9	out	out	ADP
cana-3320	17	10	by	by	ADP
cana-3320	17	11	vandiver	vandiver	NOUN
cana-3320	17	12	in	in	ADP
cana-3320	17	13	1934	1934	NUM
cana-3320	17	14	.	.	PUNCT
cana-3320	18	1	in	in	ADP
cana-3320	18	2	1962	1962	NUM
cana-3320	18	3	,	,	PUNCT
cana-3320	18	4	hestenes2	hestenes2	PROPN
cana-3320	18	5	used	use	VERB
cana-3320	18	6	the	the	DET
cana-3320	18	7	idea	idea	NOUN
cana-3320	18	8	of	of	ADP
cana-3320	18	9	ternary	ternary	ADJ
cana-3320	18	10	algebra	algebra	NOUN
cana-3320	18	11	to	to	ADP
cana-3320	18	12	matrices	matrix	NOUN
cana-3320	18	13	and	and	CCONJ
cana-3320	18	14	linear	linear	ADJ
cana-3320	18	15	transformation	transformation	NOUN
cana-3320	18	16	.	.	PUNCT
cana-3320	19	1	the	the	DET
cana-3320	19	2	fuzzy	fuzzy	ADJ
cana-3320	19	3	set	set	NOUN
cana-3320	19	4	(	(	PUNCT
cana-3320	19	5	fs	fs	NOUN
cana-3320	19	6	)	)	PUNCT
cana-3320	19	7	theory	theory	NOUN
cana-3320	19	8	,	,	PUNCT
cana-3320	19	9	first	first	ADV
cana-3320	19	10	presented	present	VERB
cana-3320	19	11	by	by	ADP
cana-3320	19	12	zadeh,3	zadeh,3	NOUN
cana-3320	19	13	is	be	AUX
cana-3320	19	14	the	the	DET
cana-3320	19	15	most	most	ADV
cana-3320	19	16	effective	effective	ADJ
cana-3320	19	17	approach	approach	NOUN
cana-3320	19	18	to	to	ADP
cana-3320	19	19	dealing	deal	VERB
cana-3320	19	20	with	with	ADP
cana-3320	19	21	ambiguity	ambiguity	NOUN
cana-3320	19	22	and	and	CCONJ
cana-3320	19	23	uncertainty	uncertainty	NOUN
cana-3320	19	24	.	.	PUNCT
cana-3320	20	1	if	if	SCONJ
cana-3320	20	2	an	an	DET
cana-3320	20	3	element	element	NOUN
cana-3320	20	4	in	in	ADP
cana-3320	20	5	an	an	DET
cana-3320	20	6	fs	fs	NOUN
cana-3320	20	7	has	have	VERB
cana-3320	20	8	a	a	DET
cana-3320	20	9	single	single	ADJ
cana-3320	20	10	value	value	NOUN
cana-3320	20	11	inside	inside	ADP
cana-3320	20	12	the	the	DET
cana-3320	20	13	interval	interval	NOUN
cana-3320	20	14	,	,	PUNCT
cana-3320	20	15	it	it	PRON
cana-3320	20	16	is	be	AUX
cana-3320	20	17	regarded	regard	VERB
cana-3320	20	18	as	as	ADP
cana-3320	20	19	a	a	DET
cana-3320	20	20	member	member	NOUN
cana-3320	20	21	degree	degree	NOUN
cana-3320	20	22	(	(	PUNCT
cana-3320	20	23	md	md	PROPN
cana-3320	20	24	)	)	PUNCT
cana-3320	20	25	.	.	PUNCT
cana-3320	21	1	however	however	ADV
cana-3320	21	2	,	,	PUNCT
cana-3320	21	3	the	the	DET
cana-3320	21	4	degree	degree	NOUN
cana-3320	21	5	of	of	ADP
cana-3320	21	6	non	non	ADJ
cana-3320	21	7	-	-	ADJ
cana-3320	21	8	membership	membership	ADJ
cana-3320	21	9	degree	degree	NOUN
cana-3320	21	10	(	(	PUNCT
cana-3320	21	11	nmd	nmd	PROPN
cana-3320	21	12	)	)	PUNCT
cana-3320	21	13	could	could	AUX
cana-3320	21	14	not	not	PART
cana-3320	21	15	always	always	ADV
cana-3320	21	16	be	be	AUX
cana-3320	21	17	equal	equal	ADJ
cana-3320	21	18	to	to	ADP
cana-3320	21	19	one	one	NUM
cana-3320	21	20	minus	minus	ADP
cana-3320	21	21	the	the	DET
cana-3320	21	22	md	md	PROPN
cana-3320	21	23	,	,	PUNCT
cana-3320	21	24	uncertain	uncertain	ADJ
cana-3320	21	25	theories	theory	NOUN
cana-3320	21	26	,	,	PUNCT
cana-3320	21	27	such	such	ADJ
cana-3320	21	28	as	as	ADP
cana-3320	21	29	fs,3	fs,3	PROPN
cana-3320	21	30	intuitionistic	intuitionistic	ADJ
cana-3320	21	31	fs	fs	X
cana-3320	21	32	(	(	PUNCT
cana-3320	21	33	ifs),4	ifs),4	PROPN
cana-3320	21	34	pythagorean	pythagorean	PROPN
cana-3320	21	35	fs	fs	PROPN
cana-3320	21	36	(	(	PUNCT
cana-3320	21	37	pfs),5	pfs),5	PROPN
cana-3320	21	38	and	and	CCONJ
cana-3320	21	39	spherical	spherical	ADJ
cana-3320	21	40	fs	fs	X
cana-3320	21	41	(	(	PUNCT
cana-3320	21	42	sfs).6	sfs).6	X
cana-3320	21	43	an	an	DET
cana-3320	21	44	fs	fs	NOUN
cana-3320	21	45	is	be	AUX
cana-3320	21	46	made	make	VERB
cana-3320	21	47	up	up	ADP
cana-3320	21	48	of	of	ADP
cana-3320	21	49	sets	set	NOUN
cana-3320	21	50	of	of	ADP
cana-3320	21	51	various	various	ADJ
cana-3320	21	52	grades	grade	NOUN
cana-3320	21	53	,	,	PUNCT
cana-3320	21	54	such	such	ADJ
cana-3320	21	55	as	as	ADP
cana-3320	21	56	mg	mg	PROPN
cana-3320	21	57	,	,	PUNCT
cana-3320	21	58	which	which	PRON
cana-3320	21	59	range	range	VERB
cana-3320	21	60	from	from	ADP
cana-3320	21	61	0	0	NUM
cana-3320	21	62	to	to	ADP
cana-3320	21	63	1	1	NUM
cana-3320	21	64	.	.	PUNCT
cana-3320	22	1	mg	mg	PROPN
cana-3320	22	2	is	be	AUX
cana-3320	22	3	the	the	DET
cana-3320	22	4	classification	classification	NOUN
cana-3320	22	5	for	for	ADP
cana-3320	22	6	ifs	ifs	PROPN
cana-3320	22	7	regardless	regardless	ADV
cana-3320	22	8	of	of	ADP
cana-3320	22	9	the	the	DET
cana-3320	22	10	assertion	assertion	NOUN
cana-3320	22	11	made	make	VERB
cana-3320	22	12	by	by	ADP
cana-3320	22	13	atanassov4	atanassov4	PROPN
cana-3320	22	14	that	that	DET
cana-3320	22	15	nmg	nmg	NOUN
cana-3320	22	16	can	can	AUX
cana-3320	22	17	only	only	ADV
cana-3320	22	18	be	be	AUX
cana-3320	22	19	worth	worth	ADJ
cana-3320	22	20	1	1	NUM
cana-3320	22	21	.	.	PUNCT
cana-3320	22	22	using	use	VERB
cana-3320	22	23	pfs	pfs	ADJ
cana-3320	22	24	logic	logic	NOUN
cana-3320	22	25	,	,	PUNCT
cana-3320	22	26	yager5	yager5	PROPN
cana-3320	22	27	built	build	VERB
cana-3320	22	28	the	the	DET
cana-3320	22	29	generalized	generalized	ADJ
cana-3320	22	30	mg	mg	PROPN
cana-3320	22	31	and	and	CCONJ
cana-3320	22	32	nmg	nmg	PROPN
cana-3320	22	33	,	,	PUNCT
cana-3320	22	34	which	which	PRON
cana-3320	22	35	has	have	VERB
cana-3320	22	36	a	a	DET
cana-3320	22	37	maximum	maximum	ADJ
cana-3320	22	38	value	value	NOUN
cana-3320	22	39	of	of	ADP
cana-3320	22	40	1	1	NUM
cana-3320	22	41	and	and	CCONJ
cana-3320	22	42	is	be	AUX
cana-3320	22	43	based	base	VERB
cana-3320	22	44	on	on	ADP
cana-3320	22	45	the	the	DET
cana-3320	22	46	square	square	NOUN
cana-3320	22	47	of	of	ADP
cana-3320	22	48	the	the	DET
cana-3320	22	49	mgs	mgs	NOUN
cana-3320	22	50	and	and	CCONJ
cana-3320	22	51	nmgs	nmgs	NOUN
cana-3320	22	52	.	.	PUNCT
cana-3320	23	1	the	the	DET
cana-3320	23	2	neutral	neutral	ADJ
cana-3320	23	3	condition	condition	NOUN
cana-3320	23	4	,	,	PUNCT
cana-3320	23	5	which	which	PRON
cana-3320	23	6	is	be	AUX
cana-3320	23	7	neither	neither	CCONJ
cana-3320	23	8	positive	positive	ADJ
cana-3320	23	9	nor	nor	CCONJ
cana-3320	23	10	negative	negative	ADJ
cana-3320	23	11	,	,	PUNCT
cana-3320	23	12	can	can	AUX
cana-3320	23	13	not	not	PART
cana-3320	23	14	be	be	AUX
cana-3320	23	15	adequately	adequately	ADV
cana-3320	23	16	described	describe	VERB
cana-3320	23	17	by	by	ADP
cana-3320	23	18	these	these	DET
cana-3320	23	19	concepts	concept	NOUN
cana-3320	23	20	.	.	PUNCT
cana-3320	24	1	the	the	DET
cana-3320	24	2	practical	practical	ADJ
cana-3320	24	3	applications	application	NOUN
cana-3320	24	4	of	of	ADP
cana-3320	24	5	fs	fs	ADP
cana-3320	24	6	extensions	extension	NOUN
cana-3320	24	7	were	be	AUX
cana-3320	24	8	discussed	discuss	VERB
cana-3320	24	9	by	by	ADP
cana-3320	24	10	al	al	PROPN
cana-3320	24	11	-	-	PUNCT
cana-3320	24	12	husband	husband	NOUN
cana-3320	24	13	et	et	NOUN
cana-3320	24	14	al.7-.10	al.7-.10	NOUN
cana-3320	24	15	he	he	PRON
cana-3320	24	16	investigated	investigate	VERB
cana-3320	24	17	their	their	PRON
cana-3320	24	18	characteristics	characteristic	NOUN
cana-3320	24	19	in	in	ADP
cana-3320	24	20	a	a	DET
cana-3320	24	21	manner	manner	NOUN
cana-3320	24	22	similar	similar	ADJ
cana-3320	24	23	to	to	ADP
cana-3320	24	24	that	that	PRON
cana-3320	24	25	of	of	ADP
cana-3320	24	26	set	set	NOUN
cana-3320	24	27	theory	theory	NOUN
cana-3320	24	28	.	.	PUNCT
cana-3320	25	1	rosenfeld11	rosenfeld11	NOUN
cana-3320	25	2	created	create	VERB
cana-3320	25	3	fuzzy	fuzzy	ADJ
cana-3320	25	4	subgroups	subgroup	NOUN
cana-3320	25	5	and	and	CCONJ
cana-3320	25	6	listed	list	VERB
cana-3320	25	7	some	some	PRON
cana-3320	25	8	of	of	ADP
cana-3320	25	9	their	their	PRON
cana-3320	25	10	characteristics	characteristic	NOUN
cana-3320	25	11	in	in	ADP
cana-3320	25	12	1971	1971	NUM
cana-3320	25	13	.	.	PUNCT
cana-3320	26	1	fuzzy	fuzzy	ADJ
cana-3320	26	2	semigroups	semigroup	NOUN
cana-3320	26	3	were	be	AUX
cana-3320	26	4	first	first	ADV
cana-3320	26	5	presented	present	VERB
cana-3320	26	6	by	by	ADP
cana-3320	26	7	kuroki12	kuroki12	PROPN
cana-3320	26	8	as	as	ADP
cana-3320	26	9	an	an	DET
cana-3320	26	10	expansion	expansion	NOUN
cana-3320	26	11	of	of	ADP
cana-3320	26	12	classical	classical	ADJ
cana-3320	26	13	semigroups	semigroup	NOUN
cana-3320	26	14	.	.	PUNCT
cana-3320	27	1	some	some	DET
cana-3320	27	2	fuzzy	fuzzy	ADJ
cana-3320	27	3	semigroup	semigroup	NOUN
cana-3320	27	4	characterisation	characterisation	NOUN
cana-3320	27	5	was	be	AUX
cana-3320	27	6	developed	develop	VERB
cana-3320	27	7	by	by	ADP
cana-3320	27	8	mordeson.13	mordeson.13	PROPN
cana-3320	27	9	sen	sen	PROPN
cana-3320	27	10	et	et	PROPN
cana-3320	27	11	al	al	PROPN
cana-3320	27	12	.	.	PROPN
cana-3320	27	13	supplied	supply	VERB
cana-3320	27	14	the	the	DET
cana-3320	27	15	i	i	PROPN
cana-3320	27	16	-	-	PUNCT
cana-3320	27	17	semigroups	semigroup	NOUN
cana-3320	27	18	’	'	PUNCT
cana-3320	27	19	characteristics.14	characteristics.14	NOUN
cana-3320	27	20	,	,	PUNCT
cana-3320	27	21	15	15	NUM
cana-3320	27	22	kehayopula	kehayopula	NOUN
cana-3320	27	23	looked	look	VERB
cana-3320	27	24	at	at	ADP
cana-3320	27	25	the	the	DET
cana-3320	27	26	ordered	ordered	ADJ
cana-3320	27	27	i	i	PROPN
cana-3320	27	28	-	-	PUNCT
cana-3320	27	29	semigroup.16	semigroup.16	PROPN
cana-3320	27	30	somsak	somsak	PROPN
cana-3320	27	31	lekkoksung	lekkoksung	PROPN
cana-3320	27	32	used	use	VERB
cana-3320	27	33	ordered	order	VERB
cana-3320	27	34	semigroups	semigroup	NOUN
cana-3320	27	35	to	to	PART
cana-3320	27	36	investigate	investigate	VERB
cana-3320	27	37	q	q	ADJ
cana-3320	27	38	-	-	PUNCT
cana-3320	27	39	fuzzy	fuzzy	ADJ
cana-3320	27	40	ideals.1718	ideals.1718	PROPN
cana-3320	27	41	kehayopula	kehayopula	NOUN
cana-3320	27	42	et	et	PROPN
cana-3320	27	43	al	al	PROPN
cana-3320	27	44	.	.	PROPN
cana-3320	27	45	started	start	VERB
cana-3320	27	46	the	the	DET
cana-3320	27	47	research	research	NOUN
cana-3320	27	48	on	on	ADP
cana-3320	27	49	fuzzy	fuzzy	ADJ
cana-3320	27	50	ordered	order	VERB
cana-3320	27	51	semigroups	semigroup	NOUN
cana-3320	27	52	.	.	PUNCT
cana-3320	28	1	initial	initial	ADJ
cana-3320	28	2	proposals	proposal	NOUN
cana-3320	28	3	for	for	ADP
cana-3320	28	4	the	the	DET
cana-3320	28	5	(	(	PUNCT
cana-3320	28	6	∂̃	∂̃	PROPN
cana-3320	28	7	,	,	PUNCT
cana-3320	28	8	℘̃	℘̃	NOUN
cana-3320	28	9	)	)	PUNCT
cana-3320	28	10	fuzzy	fuzzy	ADJ
cana-3320	28	11	bi	bi	NOUN
cana-3320	28	12	-	-	NOUN
cana-3320	28	13	ideal	ideal	ADJ
cana-3320	28	14	and	and	CCONJ
cana-3320	28	15	fss	fss	PROPN
cana-3320	28	16	were	be	AUX
cana-3320	28	17	made	make	VERB
cana-3320	28	18	by	by	ADP
cana-3320	28	19	muhammad	muhammad	PROPN
cana-3320	28	20	khan	khan	PROPN
cana-3320	28	21	et	et	PROPN
cana-3320	28	22	al.19	al.19	PROPN
cana-3320	28	23	numerous	numerous	ADJ
cana-3320	28	24	scholars	scholar	NOUN
cana-3320	28	25	have	have	AUX
cana-3320	28	26	recently	recently	ADV
cana-3320	28	27	examined	examine	VERB
cana-3320	28	28	the	the	DET
cana-3320	28	29	idea	idea	NOUN
cana-3320	28	30	of	of	ADP
cana-3320	28	31	ifs	ifs	PROPN
cana-3320	28	32	,	,	PUNCT
cana-3320	28	33	nss	ns	NOUN
cana-3320	28	34	,	,	PUNCT
cana-3320	28	35	and	and	CCONJ
cana-3320	28	36	its	its	PRON
cana-3320	28	37	characterisation20-.24	characterisation20-.24	NOUN
cana-3320	28	38	an	an	DET
cana-3320	28	39	ifs	ifs	PROPN
cana-3320	28	40	with	with	ADP
cana-3320	28	41	normal	normal	ADJ
cana-3320	28	42	subbisemiring	subbisemiring	NOUN
cana-3320	28	43	was	be	AUX
cana-3320	28	44	introduced	introduce	VERB
cana-3320	28	45	by	by	ADP
cana-3320	28	46	palanikumar	palanikumar	PROPN
cana-3320	28	47	et	et	PROPN
cana-3320	29	1	al.25	al.25	ADV
cana-3320	29	2	hila	hila	PROPN
cana-3320	29	3	et	et	PROPN
cana-3320	29	4	al.26	al.26	PROPN
cana-3320	29	5	explored	explore	VERB
cana-3320	29	6	bi	bi	NOUN
cana-3320	29	7	-	-	NOUN
cana-3320	29	8	ideals	ideal	NOUN
cana-3320	29	9	on	on	ADP
cana-3320	29	10	ordered	order	VERB
cana-3320	29	11	semigroups	semigroup	NOUN
cana-3320	29	12	.	.	PUNCT
cana-3320	30	1	dutta	dutta	PROPN
cana-3320	30	2	t.k	t.k	PROPN
cana-3320	30	3	.	.	PROPN
cana-3320	30	4	et	et	PROPN
cana-3320	30	5	al	al	PROPN
cana-3320	30	6	.	.	PROPN
cana-3320	30	7	introduced	introduce	VERB
cana-3320	30	8	novel	novel	ADJ
cana-3320	30	9	concepts	concept	NOUN
cana-3320	30	10	using	use	VERB
cana-3320	30	11	prime	prime	ADJ
cana-3320	30	12	ideals	ideal	NOUN
cana-3320	30	13	of	of	ADP
cana-3320	30	14	ternary	ternary	ADJ
cana-3320	30	15	semirings.27	semirings.27	NOUN
cana-3320	30	16	a	a	DET
cana-3320	30	17	number	number	NOUN
cana-3320	30	18	of	of	ADP
cana-3320	30	19	prime	prime	ADJ
cana-3320	30	20	biideals	biideal	NOUN
cana-3320	30	21	of	of	ADP
cana-3320	30	22	the	the	DET
cana-3320	30	23	rings	ring	NOUN
cana-3320	30	24	have	have	AUX
cana-3320	30	25	been	be	AUX
cana-3320	30	26	studied	study	VERB
cana-3320	30	27	by	by	ADP
cana-3320	30	28	palanikumar	palanikumar	PROPN
cana-3320	30	29	et	et	PROPN
cana-3320	30	30	al.28	al.28	PROPN
cana-3320	30	31	,	,	PUNCT
cana-3320	30	32	29	29	NUM
cana-3320	30	33	the	the	DET
cana-3320	30	34	several	several	ADJ
cana-3320	30	35	ideals	ideal	NOUN
cana-3320	30	36	of	of	ADP
cana-3320	30	37	different	different	ADJ
cana-3320	30	38	algebraic	algebraic	NOUN
cana-3320	30	39	https://internationalpubls.com	https://internationalpubls.com	X
cana-3320	30	40	579	579	NUM
cana-3320	30	41	communications	communication	NOUN
cana-3320	30	42	on	on	ADP
cana-3320	30	43	applied	apply	VERB
cana-3320	30	44	nonlinear	nonlinear	ADJ
cana-3320	30	45	analysis	analysis	NOUN
cana-3320	30	46	issn	issn	NOUN
cana-3320	30	47	:	:	PUNCT
cana-3320	30	48	1074	1074	NUM
cana-3320	30	49	-	-	PUNCT
cana-3320	30	50	133x	133x	NUM
cana-3320	30	51	vol	vol	NOUN
cana-3320	30	52	32	32	NUM
cana-3320	30	53	no	no	NOUN
cana-3320	30	54	.	.	PUNCT
cana-3320	31	1	6s	6s	NUM
cana-3320	31	2	(	(	PUNCT
cana-3320	31	3	2025	2025	NUM
cana-3320	31	4	)	)	PUNCT
cana-3320	31	5	approach	approach	NOUN
cana-3320	31	6	were	be	AUX
cana-3320	31	7	examined	examine	VERB
cana-3320	31	8	by	by	ADP
cana-3320	31	9	palanikumar	palanikumar	PROPN
cana-3320	31	10	et	et	NOUN
cana-3320	31	11	al.30–34	al.30–34	VERB
cana-3320	31	12	the	the	DET
cana-3320	31	13	notion	notion	NOUN
cana-3320	31	14	of	of	ADP
cana-3320	31	15	various	various	ADJ
cana-3320	31	16	operators	operator	NOUN
cana-3320	31	17	,	,	PUNCT
cana-3320	31	18	including	include	VERB
cana-3320	31	19	averaging	averaging	NOUN
cana-3320	31	20	,	,	PUNCT
cana-3320	31	21	geometric	geometric	ADJ
cana-3320	31	22	,	,	PUNCT
cana-3320	31	23	and	and	CCONJ
cana-3320	31	24	its	its	PRON
cana-3320	31	25	generalized	generalized	ADJ
cana-3320	31	26	forms	form	NOUN
cana-3320	31	27	,	,	PUNCT
cana-3320	31	28	was	be	AUX
cana-3320	31	29	explored	explore	VERB
cana-3320	31	30	by	by	ADP
cana-3320	31	31	new	new	ADJ
cana-3320	31	32	researchers	researcher	NOUN
cana-3320	31	33	hatamleh	hatamleh	ADJ
cana-3320	31	34	et	et	NOUN
cana-3320	31	35	al.35-,41	al.35-,41	VERB
cana-3320	31	36	bataihah,42	bataihah,42	NOUN
cana-3320	31	37	and	and	CCONJ
cana-3320	31	38	hazaymeh.43	hazaymeh.43	PRON
cana-3320	31	39	we	we	PRON
cana-3320	31	40	study	study	VERB
cana-3320	31	41	ordered	order	VERB
cana-3320	31	42	ternary	ternary	ADJ
cana-3320	31	43	semigroups	semigroup	NOUN
cana-3320	31	44	based	base	VERB
cana-3320	31	45	on	on	ADP
cana-3320	31	46	(	(	PUNCT
cana-3320	31	47	∂̃	∂̃	PROPN
cana-3320	31	48	,	,	PUNCT
cana-3320	31	49	℘̃	℘̃	NOUN
cana-3320	31	50	)	)	PUNCT
cana-3320	31	51	ternary	ternary	ADJ
cana-3320	31	52	ifs	ifs	PROPN
cana-3320	31	53	and	and	CCONJ
cana-3320	31	54	provide	provide	VERB
cana-3320	31	55	examples	example	NOUN
cana-3320	31	56	to	to	PART
cana-3320	31	57	show	show	VERB
cana-3320	31	58	their	their	PRON
cana-3320	31	59	properties	property	NOUN
cana-3320	31	60	.	.	PUNCT
cana-3320	32	1	2	2	NUM
cana-3320	32	2	basic	basic	ADJ
cana-3320	32	3	concepts	concept	NOUN
cana-3320	32	4	definition	definition	NOUN
cana-3320	32	5	2	2	NUM
cana-3320	32	6	.1	.1	NUM
cana-3320	32	7	.	.	PUNCT
cana-3320	33	1	let	let	VERB
cana-3320	33	2	i	i	PRON
cana-3320	33	3	and	and	CCONJ
cana-3320	33	4	i	i	PRON
cana-3320	33	5	1	1	NUM
cana-3320	33	6	be	be	VERB
cana-3320	33	7	subsets	subset	NOUN
cana-3320	33	8	of	of	ADP
cana-3320	33	9	z	z	NOUN
cana-3320	33	10	.	.	PUNCT
cana-3320	34	1	then	then	ADV
cana-3320	34	2	1	1	X
cana-3320	34	3	.	.	PUNCT
cana-3320	35	1	(	(	PUNCT
cana-3320	35	2	i	i	PRON
cana-3320	35	3	]	]	X
cana-3320	35	4	=	=	X
cana-3320	35	5	{	{	PUNCT
cana-3320	35	6	t	t	NOUN
cana-3320	35	7	∈	∈	PROPN
cana-3320	35	8	z	z	NOUN
cana-3320	36	1	|	|	NOUN
cana-3320	36	2	t	t	PROPN
cana-3320	36	3	6	6	NUM
cana-3320	36	4	h	h	NOUN
cana-3320	36	5	for	for	ADP
cana-3320	36	6	someh	someh	NOUN
cana-3320	36	7	∈	∈	PROPN
cana-3320	37	1	i	i	X
cana-3320	37	2	}	}	PUNCT
cana-3320	37	3	,	,	PUNCT
cana-3320	37	4	2	2	X
cana-3320	37	5	.	.	PUNCT
cana-3320	37	6	ii1	ii1	NOUN
cana-3320	37	7	=	=	SYM
cana-3320	37	8	{	{	PUNCT
cana-3320	37	9	ab	ab	NOUN
cana-3320	37	10	:	:	PUNCT
cana-3320	37	11	a	a	DET
cana-3320	37	12	∈	∈	PROPN
cana-3320	38	1	i	i	NOUN
cana-3320	38	2	,	,	PUNCT
cana-3320	38	3	b	b	PROPN
cana-3320	38	4	∈	∈	PROPN
cana-3320	38	5	i1	i1	PROPN
cana-3320	38	6	}	}	PUNCT
cana-3320	38	7	,	,	PUNCT
cana-3320	38	8	3	3	X
cana-3320	38	9	.	.	X
cana-3320	38	10	ia	ia	PROPN
cana-3320	38	11	=	=	SYM
cana-3320	38	12	{	{	PUNCT
cana-3320	38	13	(	(	PUNCT
cana-3320	38	14	b	b	NOUN
cana-3320	38	15	,	,	PUNCT
cana-3320	38	16	c	c	NOUN
cana-3320	38	17	)	)	PUNCT
cana-3320	38	18	∈	∈	PROPN
cana-3320	38	19	z	z	NOUN
cana-3320	38	20	×z	×z	ADV
cana-3320	38	21	|	|	ADV
cana-3320	38	22	a	a	DET
cana-3320	38	23	6	6	NUM
cana-3320	38	24	bc	bc	PROPN
cana-3320	38	25	}	}	PUNCT
cana-3320	38	26	.	.	PUNCT
cana-3320	39	1	definition	definition	NOUN
cana-3320	39	2	2.2	2.2	NUM
cana-3320	39	3	.	.	PUNCT
cana-3320	40	1	a	a	DET
cana-3320	40	2	fuzzy	fuzzy	ADJ
cana-3320	40	3	subset	subset	VERB
cana-3320	40	4	ð2	ð2	PROPN
cana-3320	40	5	of	of	ADP
cana-3320	40	6	an	an	DET
cana-3320	40	7	ordered	order	VERB
cana-3320	40	8	semigroup	semigroup	PROPN
cana-3320	40	9	z	z	PROPN
cana-3320	40	10	is	be	AUX
cana-3320	40	11	called	call	VERB
cana-3320	40	12	a	a	DET
cana-3320	40	13	fri(fli	fri(fli	NOUN
cana-3320	40	14	)	)	PUNCT
cana-3320	40	15	of	of	ADP
cana-3320	40	16	z	z	NOUN
cana-3320	40	17	if	if	SCONJ
cana-3320	40	18	1	1	NUM
cana-3320	40	19	.	.	PUNCT
cana-3320	41	1	a	a	DET
cana-3320	41	2	6	6	NUM
cana-3320	41	3	b⇒	b⇒	PROPN
cana-3320	41	4	ð2(a	ð2(a	NUM
cana-3320	41	5	)	)	PUNCT
cana-3320	41	6	>	>	X
cana-3320	42	1	ð2(b	ð2(b	X
cana-3320	42	2	)	)	PUNCT
cana-3320	42	3	for	for	ADP
cana-3320	42	4	all	all	DET
cana-3320	42	5	a	a	DET
cana-3320	42	6	,	,	PUNCT
cana-3320	42	7	b	b	X
cana-3320	42	8	∈	∈	PROPN
cana-3320	42	9	z	z	NOUN
cana-3320	42	10	,	,	PUNCT
cana-3320	42	11	2	2	X
cana-3320	42	12	.	.	PUNCT
cana-3320	42	13	ð2(ab	ð2(ab	NUM
cana-3320	42	14	)	)	PUNCT
cana-3320	42	15	>	>	X
cana-3320	42	16	ð2(a	ð2(a	NUM
cana-3320	42	17	)	)	PUNCT
cana-3320	42	18	(	(	PUNCT
cana-3320	42	19	resp	resp	NOUN
cana-3320	42	20	.	.	PUNCT
cana-3320	43	1	ð2(ab	ð2(ab	X
cana-3320	43	2	)	)	PUNCT
cana-3320	43	3	>	>	X
cana-3320	44	1	ð2(b	ð2(b	NOUN
cana-3320	44	2	)	)	PUNCT
cana-3320	44	3	)	)	PUNCT
cana-3320	45	1	for	for	ADP
cana-3320	45	2	all	all	DET
cana-3320	45	3	a	a	DET
cana-3320	45	4	,	,	PUNCT
cana-3320	45	5	b	b	X
cana-3320	45	6	∈	∈	PROPN
cana-3320	45	7	z	z	NOUN
cana-3320	45	8	,	,	PUNCT
cana-3320	45	9	definition	definition	NOUN
cana-3320	45	10	2.3	2.3	NUM
cana-3320	45	11	.	.	PUNCT
cana-3320	46	1	if	if	SCONJ
cana-3320	46	2	(	(	PUNCT
cana-3320	46	3	z	z	NOUN
cana-3320	46	4	,	,	PUNCT
cana-3320	46	5	+	+	X
cana-3320	46	6	)	)	PUNCT
cana-3320	46	7	is	be	AUX
cana-3320	46	8	a	a	DET
cana-3320	46	9	commutative	commutative	ADJ
cana-3320	46	10	semigroup	semigroup	NOUN
cana-3320	46	11	and	and	CCONJ
cana-3320	46	12	ternary	ternary	ADJ
cana-3320	46	13	multiplication	multiplication	NOUN
cana-3320	46	14	meets	meet	VERB
cana-3320	46	15	the	the	DET
cana-3320	46	16	following	following	ADJ
cana-3320	46	17	conditions	condition	NOUN
cana-3320	46	18	,	,	PUNCT
cana-3320	46	19	then	then	ADV
cana-3320	46	20	1	1	X
cana-3320	46	21	.	.	PUNCT
cana-3320	47	1	(	(	PUNCT
cana-3320	47	2	fgh)ij	fgh)ij	NOUN
cana-3320	47	3	=	=	PUNCT
cana-3320	47	4	f(ghi)j	f(ghi)j	NOUN
cana-3320	47	5	=	=	SYM
cana-3320	47	6	fg(hij	fg(hij	NOUN
cana-3320	47	7	)	)	PUNCT
cana-3320	47	8	,	,	PUNCT
cana-3320	47	9	2	2	X
cana-3320	47	10	.	.	PUNCT
cana-3320	48	1	(	(	PUNCT
cana-3320	48	2	f	f	X
cana-3320	48	3	+	+	CCONJ
cana-3320	48	4	g)hi	g)hi	PROPN
cana-3320	48	5	=	=	SYM
cana-3320	48	6	fhi+	fhi+	PROPN
cana-3320	48	7	ghi	ghi	PROPN
cana-3320	48	8	,	,	PUNCT
cana-3320	48	9	3	3	X
cana-3320	48	10	.	.	X
cana-3320	48	11	f(g	f(g	PROPN
cana-3320	48	12	+	+	CCONJ
cana-3320	48	13	h)i	h)i	ADJ
cana-3320	48	14	=	=	SYM
cana-3320	48	15	fgi+	fgi+	NOUN
cana-3320	48	16	fhi	fhi	NOUN
cana-3320	48	17	,	,	PUNCT
cana-3320	48	18	4	4	NUM
cana-3320	48	19	.	.	PUNCT
cana-3320	49	1	fg(h+	fg(h+	PROPN
cana-3320	49	2	i	i	NOUN
cana-3320	49	3	)	)	PUNCT
cana-3320	50	1	=	=	PUNCT
cana-3320	50	2	fgh+	fgh+	PROPN
cana-3320	50	3	fgi	fgi	NOUN
cana-3320	50	4	for	for	ADP
cana-3320	50	5	all	all	DET
cana-3320	50	6	f	f	PROPN
cana-3320	50	7	,	,	PUNCT
cana-3320	50	8	g	g	PROPN
cana-3320	50	9	,	,	PUNCT
cana-3320	50	10	h	h	NOUN
cana-3320	50	11	,	,	PUNCT
cana-3320	50	12	i	i	PRON
cana-3320	50	13	,	,	PUNCT
cana-3320	50	14	j	j	PROPN
cana-3320	50	15	∈	∈	PROPN
cana-3320	50	16	z	z	NOUN
cana-3320	50	17	definition	definition	NOUN
cana-3320	50	18	2.4	2.4	NUM
cana-3320	50	19	.	.	PUNCT
cana-3320	51	1	the	the	DET
cana-3320	51	2	subset	subset	NOUN
cana-3320	51	3	k	k	PROPN
cana-3320	51	4	of	of	ADP
cana-3320	51	5	z	z	PROPN
cana-3320	51	6	is	be	AUX
cana-3320	51	7	called	call	VERB
cana-3320	51	8	a	a	DET
cana-3320	51	9	1	1	NUM
cana-3320	51	10	.	.	PUNCT
cana-3320	51	11	ss	ss	NOUN
cana-3320	52	1	if	if	SCONJ
cana-3320	52	2	υ1υ2υ3	υ1υ2υ3	PROPN
cana-3320	52	3	∈	∈	PROPN
cana-3320	52	4	k	k	PROPN
cana-3320	52	5	for	for	ADP
cana-3320	52	6	all	all	DET
cana-3320	52	7	υ1	υ1	PROPN
cana-3320	52	8	,	,	PUNCT
cana-3320	52	9	υ2	υ2	NOUN
cana-3320	52	10	,	,	PUNCT
cana-3320	52	11	υ3	υ3	PROPN
cana-3320	52	12	∈	∈	PROPN
cana-3320	52	13	k.	k.	NOUN
cana-3320	53	1	2	2	X
cana-3320	53	2	.	.	PUNCT
cana-3320	54	1	right	right	ADJ
cana-3320	54	2	(	(	PUNCT
cana-3320	54	3	lateral	lateral	ADJ
cana-3320	54	4	,	,	PUNCT
cana-3320	54	5	left	left	ADJ
cana-3320	54	6	)	)	PUNCT
cana-3320	54	7	ideal	ideal	NOUN
cana-3320	55	1	if	if	SCONJ
cana-3320	55	2	is1s2	is1s2	PROPN
cana-3320	55	3	∈	∈	NOUN
cana-3320	55	4	k(s1is2	k(s1is2	NOUN
cana-3320	55	5	∈	∈	PROPN
cana-3320	55	6	k	k	NOUN
cana-3320	55	7	,	,	PUNCT
cana-3320	55	8	s1s2i	s1s2i	PUNCT
cana-3320	55	9	∈	∈	PROPN
cana-3320	55	10	k	k	NOUN
cana-3320	55	11	)	)	PUNCT
cana-3320	55	12	for	for	ADP
cana-3320	55	13	all	all	DET
cana-3320	55	14	s1	s1	NOUN
cana-3320	55	15	,	,	PUNCT
cana-3320	55	16	s2	s2	NOUN
cana-3320	55	17	∈	∈	PROPN
cana-3320	55	18	z	z	NOUN
cana-3320	56	1	and	and	CCONJ
cana-3320	56	2	i	i	PROPN
cana-3320	56	3	∈	∈	PROPN
cana-3320	56	4	k.	k.	NOUN
cana-3320	56	5	corollary	corollary	PROPN
cana-3320	56	6	2.5	2.5	NUM
cana-3320	56	7	.	.	PUNCT
cana-3320	57	1	if	if	SCONJ
cana-3320	57	2	z	z	NOUN
cana-3320	57	3	is	be	AUX
cana-3320	57	4	regular	regular	ADJ
cana-3320	57	5	if	if	SCONJ
cana-3320	57	6	and	and	CCONJ
cana-3320	57	7	only	only	ADV
cana-3320	57	8	if	if	SCONJ
cana-3320	57	9	ri	ri	PROPN
cana-3320	57	10	i	i	PROPN
cana-3320	57	11	,	,	PUNCT
cana-3320	57	12	latif	latif	PROPN
cana-3320	57	13	i1	i1	PROPN
cana-3320	57	14	and	and	CCONJ
cana-3320	57	15	li	li	PROPN
cana-3320	57	16	i2	i2	PROPN
cana-3320	57	17	of	of	ADP
cana-3320	57	18	z	z	PROPN
cana-3320	57	19	,	,	PUNCT
cana-3320	57	20	then	then	ADV
cana-3320	57	21	(	(	PUNCT
cana-3320	57	22	ifi1fi2	ifi1fi2	NOUN
cana-3320	57	23	]	]	PUNCT
cana-3320	57	24	=	=	PUNCT
cana-3320	57	25	(	(	PUNCT
cana-3320	57	26	i∗i1∗i2	i∗i1∗i2	VERB
cana-3320	57	27	]	]	X
cana-3320	57	28	.	.	NOUN
cana-3320	58	1	3	3	NUM
cana-3320	58	2	(	(	PUNCT
cana-3320	58	3	∂̃	∂̃	PROPN
cana-3320	58	4	,	,	PUNCT
cana-3320	58	5	℘̃	℘̃	NOUN
cana-3320	58	6	)	)	PUNCT
cana-3320	58	7	ternary	ternary	ADJ
cana-3320	58	8	intuitionistic	intuitionistic	ADJ
cana-3320	58	9	q	q	NOUN
cana-3320	58	10	interval	interval	NOUN
cana-3320	58	11	-	-	PUNCT
cana-3320	58	12	valued	value	VERB
cana-3320	58	13	fuzzy	fuzzy	ADJ
cana-3320	58	14	ideals	ideal	NOUN
cana-3320	58	15	here	here	ADV
cana-3320	58	16	,	,	PUNCT
cana-3320	58	17	z	z	PROPN
cana-3320	58	18	represents	represent	VERB
cana-3320	58	19	an	an	DET
cana-3320	58	20	ordered	order	VERB
cana-3320	58	21	ternary	ternary	ADJ
cana-3320	58	22	semigroup	semigroup	NOUN
cana-3320	58	23	.	.	PUNCT
cana-3320	59	1	assuming	assume	VERB
cana-3320	59	2	(	(	PUNCT
cana-3320	59	3	∂̃	∂̃	PROPN
cana-3320	59	4	,	,	PUNCT
cana-3320	59	5	℘̃	℘̃	NOUN
cana-3320	59	6	)	)	PUNCT
cana-3320	59	7	∈	∈	PROPN
cana-3320	60	1	[	[	X
cana-3320	60	2	0	0	NUM
cana-3320	60	3	,	,	PUNCT
cana-3320	60	4	1	1	NUM
cana-3320	60	5	]	]	PUNCT
cana-3320	60	6	and	and	CCONJ
cana-3320	60	7	0	0	NUM
cana-3320	60	8	6	6	NUM
cana-3320	60	9	∂̃	∂̃	PROPN
cana-3320	60	10	≺	≺	NOUN
cana-3320	60	11	℘̃	℘̃	NOUN
cana-3320	60	12	6	6	NUM
cana-3320	60	13	1	1	NUM
cana-3320	60	14	,	,	PUNCT
cana-3320	60	15	both	both	PRON
cana-3320	60	16	(	(	PUNCT
cana-3320	60	17	∂̃	∂̃	PROPN
cana-3320	60	18	,	,	PUNCT
cana-3320	60	19	℘̃	℘̃	PROPN
cana-3320	60	20	)	)	PUNCT
cana-3320	60	21	are	be	AUX
cana-3320	60	22	arbitrary	arbitrary	ADJ
cana-3320	60	23	fixed	fix	VERB
cana-3320	60	24	points	point	NOUN
cana-3320	60	25	.	.	PUNCT
cana-3320	61	1	definition	definition	NOUN
cana-3320	61	2	3.1	3.1	NUM
cana-3320	61	3	.	.	PUNCT
cana-3320	62	1	an	an	DET
cana-3320	62	2	ivfs	ivfs	NOUN
cana-3320	62	3	n	n	NOUN
cana-3320	62	4	and	and	CCONJ
cana-3320	62	5	q	q	ADJ
cana-3320	62	6	be	be	AUX
cana-3320	62	7	any	any	DET
cana-3320	62	8	set	set	NOUN
cana-3320	62	9	,	,	PUNCT
cana-3320	62	10	then	then	ADV
cana-3320	62	11	the	the	DET
cana-3320	62	12	pair	pair	NOUN
cana-3320	62	13	n	n	DET
cana-3320	62	14	×q	×q	ADV
cana-3320	62	15	is	be	AUX
cana-3320	62	16	called	call	VERB
cana-3320	62	17	an	an	DET
cana-3320	62	18	iqvfs	iqvfs	NOUN
cana-3320	62	19	.	.	PUNCT
cana-3320	63	1	let	let	VERB
cana-3320	63	2	n	n	NOUN
cana-3320	63	3	=	=	PUNCT
cana-3320	64	1	[	[	X
cana-3320	64	2	<	<	X
cana-3320	64	3	̃n	̃n	NOUN
cana-3320	64	4	,	,	PUNCT
cana-3320	64	5	=	=	NOUN
cana-3320	64	6	̃n	̃n	NOUN
cana-3320	64	7	]	]	PUNCT
cana-3320	64	8	of	of	ADP
cana-3320	64	9	z	z	PROPN
cana-3320	64	10	is	be	AUX
cana-3320	64	11	called	call	VERB
cana-3320	64	12	a	a	DET
cana-3320	64	13	(	(	PUNCT
cana-3320	64	14	∂̃	∂̃	PROPN
cana-3320	64	15	,	,	PUNCT
cana-3320	64	16	℘̃	℘̃	PROPN
cana-3320	64	17	)	)	PUNCT
cana-3320	64	18	iqvfss	iqvfss	NOUN
cana-3320	64	19	of	of	ADP
cana-3320	64	20	z	z	NOUN
cana-3320	64	21	if	if	SCONJ
cana-3320	64	22	1	1	NUM
cana-3320	64	23	.	.	X
cana-3320	64	24	ð1	ð1	NOUN
cana-3320	64	25	6	6	NUM
cana-3320	64	26	ð3	ð3	PROPN
cana-3320	64	27	⇒	⇒	VERB
cana-3320	64	28	<	<	X
cana-3320	64	29	̃(ð1	̃(ð1	PROPN
cana-3320	64	30	)	)	PUNCT
cana-3320	64	31	>	>	X
cana-3320	64	32	<	<	X
cana-3320	64	33	̃(ð3	̃(ð3	PROPN
cana-3320	64	34	)	)	PUNCT
cana-3320	64	35	,	,	PUNCT
cana-3320	64	36	2	2	X
cana-3320	64	37	.	.	PUNCT
cana-3320	64	38	max{<̃(ð1ð2ð3	max{<̃(ð1ð2ð3	PROPN
cana-3320	64	39	,	,	PUNCT
cana-3320	64	40	ǎ	ǎ	PROPN
cana-3320	64	41	)	)	PUNCT
cana-3320	64	42	,	,	PUNCT
cana-3320	64	43	∂̃	∂̃	PROPN
cana-3320	64	44	}	}	PUNCT
cana-3320	64	45	>	>	X
cana-3320	64	46	min{<̃(ð1	min{<̃(ð1	PROPN
cana-3320	64	47	,	,	PUNCT
cana-3320	64	48	ǎ	ǎ	PROPN
cana-3320	64	49	)	)	PUNCT
cana-3320	64	50	,	,	PUNCT
cana-3320	64	51	<	<	X
cana-3320	64	52	̃(ð2	̃(ð2	PROPN
cana-3320	64	53	,	,	PUNCT
cana-3320	64	54	ǎ	ǎ	PROPN
cana-3320	64	55	)	)	PUNCT
cana-3320	64	56	,	,	PUNCT
cana-3320	64	57	<	<	X
cana-3320	64	58	̃(ð3	̃(ð3	PROPN
cana-3320	64	59	,	,	PUNCT
cana-3320	64	60	ǎ	ǎ	PROPN
cana-3320	64	61	)	)	PUNCT
cana-3320	64	62	,	,	PUNCT
cana-3320	64	63	℘̃	℘̃	PROPN
cana-3320	64	64	}	}	PUNCT
cana-3320	64	65	,	,	PUNCT
cana-3320	64	66	3	3	X
cana-3320	64	67	.	.	X
cana-3320	65	1	min{=̃(ð1ð2ð3	min{=̃(ð1ð2ð3	PROPN
cana-3320	65	2	,	,	PUNCT
cana-3320	65	3	ǎ	ǎ	NOUN
cana-3320	65	4	)	)	PUNCT
cana-3320	65	5	,	,	PUNCT
cana-3320	65	6	∂̃	∂̃	NOUN
cana-3320	65	7	}	}	PUNCT
cana-3320	65	8	6	6	NUM
cana-3320	65	9	max{=̃(ð1	max{=̃(ð1	NOUN
cana-3320	65	10	,	,	PUNCT
cana-3320	65	11	ǎ	ǎ	PROPN
cana-3320	65	12	)	)	PUNCT
cana-3320	65	13	,	,	PUNCT
cana-3320	65	14	=	=	PROPN
cana-3320	65	15	̃(ð2	̃(ð2	PROPN
cana-3320	65	16	,	,	PUNCT
cana-3320	65	17	ǎ	ǎ	PROPN
cana-3320	65	18	)	)	PUNCT
cana-3320	65	19	,	,	PUNCT
cana-3320	65	20	=	=	PROPN
cana-3320	65	21	̃(ð3	̃(ð3	PROPN
cana-3320	65	22	,	,	PUNCT
cana-3320	65	23	ǎ	ǎ	PROPN
cana-3320	65	24	)	)	PUNCT
cana-3320	65	25	,	,	PUNCT
cana-3320	65	26	℘̃	℘̃	NOUN
cana-3320	65	27	}	}	PUNCT
cana-3320	65	28	for	for	ADP
cana-3320	65	29	all	all	PRON
cana-3320	65	30	ð1,ð2,ð3	ð1,ð2,ð3	SYM
cana-3320	66	1	∈	∈	PROPN
cana-3320	66	2	z	z	PROPN
cana-3320	66	3	and	and	CCONJ
cana-3320	66	4	ǎ	ǎ	PROPN
cana-3320	66	5	∈	∈	PROPN
cana-3320	66	6	q.	q.	PROPN
cana-3320	66	7	example	example	NOUN
cana-3320	66	8	3.2	3.2	NUM
cana-3320	66	9	.	.	PUNCT
cana-3320	67	1	let	let	VERB
cana-3320	67	2	z	z	NOUN
cana-3320	67	3	=	=	PRON
cana-3320	67	4	{	{	PUNCT
cana-3320	67	5	a	a	PRON
cana-3320	67	6	,	,	PUNCT
cana-3320	67	7	b	b	NOUN
cana-3320	67	8	,	,	PUNCT
cana-3320	67	9	c	c	NOUN
cana-3320	67	10	,	,	PUNCT
cana-3320	67	11	d	d	NOUN
cana-3320	67	12	}	}	PUNCT
cana-3320	67	13	with	with	ADP
cana-3320	67	14	the	the	DET
cana-3320	67	15	following	follow	VERB
cana-3320	67	16	cayley	cayley	ADJ
cana-3320	67	17	table	table	NOUN
cana-3320	67	18	:	:	PUNCT
cana-3320	67	19	https://internationalpubls.com	https://internationalpubls.com	X
cana-3320	67	20	580	580	NUM
cana-3320	67	21	communications	communication	NOUN
cana-3320	67	22	on	on	ADP
cana-3320	67	23	applied	apply	VERB
cana-3320	67	24	nonlinear	nonlinear	ADJ
cana-3320	67	25	analysis	analysis	NOUN
cana-3320	67	26	issn	issn	NOUN
cana-3320	67	27	:	:	PUNCT
cana-3320	67	28	1074	1074	NUM
cana-3320	67	29	-	-	PUNCT
cana-3320	67	30	133x	133x	NUM
cana-3320	67	31	vol	vol	NOUN
cana-3320	67	32	32	32	NUM
cana-3320	67	33	no	no	NOUN
cana-3320	67	34	.	.	PUNCT
cana-3320	68	1	6s	6s	NUM
cana-3320	68	2	(	(	PUNCT
cana-3320	68	3	2025	2025	NUM
cana-3320	68	4	)	)	PUNCT
cana-3320	68	5	∗	∗	NOUN
cana-3320	68	6	a	a	DET
cana-3320	68	7	b	b	NOUN
cana-3320	68	8	c	c	NOUN
cana-3320	69	1	d	d	NOUN
cana-3320	69	2	a	a	DET
cana-3320	69	3	l	l	NOUN
cana-3320	69	4	l	l	NOUN
cana-3320	69	5	l	l	NOUN
cana-3320	69	6	l	l	NOUN
cana-3320	69	7	b	b	X
cana-3320	69	8	l	l	X
cana-3320	69	9	m	m	VERB
cana-3320	69	10	n	n	ADV
cana-3320	69	11	o	o	X
cana-3320	69	12	c	c	NOUN
cana-3320	69	13	l	l	NOUN
cana-3320	69	14	n	n	CCONJ
cana-3320	69	15	n	n	CCONJ
cana-3320	69	16	n	n	NOUN
cana-3320	69	17	d	d	PROPN
cana-3320	69	18	l	l	NOUN
cana-3320	69	19	n	n	CCONJ
cana-3320	69	20	n	n	CCONJ
cana-3320	69	21	n	n	PROPN
cana-3320	69	22	∗	∗	NOUN
cana-3320	69	23	a	a	DET
cana-3320	69	24	b	b	NOUN
cana-3320	69	25	c	c	NOUN
cana-3320	69	26	d	d	NOUN
cana-3320	69	27	l	l	NOUN
cana-3320	69	28	a	a	PRON
cana-3320	69	29	a	a	DET
cana-3320	69	30	a	a	DET
cana-3320	69	31	a	a	DET
cana-3320	69	32	m	m	NOUN
cana-3320	69	33	a	a	DET
cana-3320	69	34	b	b	NOUN
cana-3320	69	35	c	c	NOUN
cana-3320	69	36	d	d	PROPN
cana-3320	69	37	n	n	PROPN
cana-3320	69	38	a	a	DET
cana-3320	69	39	c	c	NOUN
cana-3320	70	1	c	c	NOUN
cana-3320	70	2	c	c	NOUN
cana-3320	70	3	o	o	NOUN
cana-3320	70	4	a	a	PRON
cana-3320	70	5	c	c	NOUN
cana-3320	70	6	c	c	NOUN
cana-3320	70	7	c	c	NOUN
cana-3320	70	8	6	6	NUM
cana-3320	70	9	:	:	PUNCT
cana-3320	70	10	=	=	SYM
cana-3320	70	11	{	{	PUNCT
cana-3320	70	12	(	(	PUNCT
cana-3320	70	13	a	a	PRON
cana-3320	70	14	,	,	PUNCT
cana-3320	70	15	a	a	NOUN
cana-3320	70	16	)	)	PUNCT
cana-3320	70	17	,	,	PUNCT
cana-3320	70	18	(	(	PUNCT
cana-3320	70	19	a	a	DET
cana-3320	70	20	,	,	PUNCT
cana-3320	70	21	b	b	NOUN
cana-3320	70	22	)	)	PUNCT
cana-3320	70	23	,	,	PUNCT
cana-3320	70	24	(	(	PUNCT
cana-3320	70	25	a	a	PRON
cana-3320	70	26	,	,	PUNCT
cana-3320	70	27	c	c	NOUN
cana-3320	70	28	)	)	PUNCT
cana-3320	70	29	,	,	PUNCT
cana-3320	70	30	(	(	PUNCT
cana-3320	70	31	a	a	DET
cana-3320	70	32	,	,	PUNCT
cana-3320	70	33	d	d	NOUN
cana-3320	70	34	)	)	PUNCT
cana-3320	70	35	,	,	PUNCT
cana-3320	70	36	(	(	PUNCT
cana-3320	70	37	b	b	X
cana-3320	70	38	,	,	PUNCT
cana-3320	70	39	b	b	NOUN
cana-3320	70	40	)	)	PUNCT
cana-3320	70	41	,	,	PUNCT
cana-3320	70	42	(	(	PUNCT
cana-3320	70	43	b	b	X
cana-3320	70	44	,	,	PUNCT
cana-3320	70	45	c	c	NOUN
cana-3320	70	46	)	)	PUNCT
cana-3320	70	47	,	,	PUNCT
cana-3320	70	48	(	(	PUNCT
cana-3320	70	49	b	b	X
cana-3320	70	50	,	,	PUNCT
cana-3320	70	51	d	d	NOUN
cana-3320	70	52	)	)	PUNCT
cana-3320	70	53	,	,	PUNCT
cana-3320	70	54	(	(	PUNCT
cana-3320	70	55	c	c	X
cana-3320	70	56	,	,	PUNCT
cana-3320	70	57	c	c	NOUN
cana-3320	70	58	)	)	PUNCT
cana-3320	70	59	,	,	PUNCT
cana-3320	70	60	(	(	PUNCT
cana-3320	70	61	d	d	X
cana-3320	70	62	,	,	PUNCT
cana-3320	70	63	c	c	NOUN
cana-3320	70	64	)	)	PUNCT
cana-3320	70	65	,	,	PUNCT
cana-3320	70	66	(	(	PUNCT
cana-3320	70	67	d	d	X
cana-3320	70	68	,	,	PUNCT
cana-3320	70	69	d	d	NOUN
cana-3320	70	70	)	)	PUNCT
cana-3320	70	71	}	}	PUNCT
cana-3320	70	72	.	.	PUNCT
cana-3320	71	1	define	define	VERB
cana-3320	71	2	the	the	DET
cana-3320	71	3	mapping	mapping	NOUN
cana-3320	71	4	n	n	NOUN
cana-3320	71	5	=	=	PUNCT
cana-3320	72	1	[	[	X
cana-3320	72	2	<	<	X
cana-3320	72	3	̃n	̃n	NOUN
cana-3320	72	4	,	,	PUNCT
cana-3320	72	5	=	=	NOUN
cana-3320	72	6	̃n	̃n	NOUN
cana-3320	72	7	]	]	PUNCT
cana-3320	72	8	:	:	PUNCT
cana-3320	72	9	z	z	NOUN
cana-3320	72	10	×z	×z	ADV
cana-3320	72	11	×z	×z	ADV
cana-3320	72	12	→	→	SYM
cana-3320	72	13	[	[	X
cana-3320	72	14	0	0	NUM
cana-3320	72	15	,	,	PUNCT
cana-3320	72	16	1	1	NUM
cana-3320	72	17	]	]	PUNCT
cana-3320	72	18	.	.	PUNCT
cana-3320	73	1	<	<	X
cana-3320	73	2	̃(κ	̃(κ	NOUN
cana-3320	73	3	,	,	PUNCT
cana-3320	73	4	ǎ	ǎ	PROPN
cana-3320	73	5	)	)	PUNCT
cana-3320	73	6	=	=	PUNCT
cana-3320	74	1			PROPN
cana-3320	75	1	[	[	X
cana-3320	75	2	0.6	0.6	NUM
cana-3320	75	3	,	,	PUNCT
cana-3320	75	4	0.65	0.65	NUM
cana-3320	75	5	]	]	PUNCT
cana-3320	75	6	if	if	SCONJ
cana-3320	75	7	κ	κ	X
cana-3320	75	8	=	=	PUNCT
cana-3320	75	9	a	a	PRON
cana-3320	76	1	[	[	X
cana-3320	76	2	0.4	0.4	NUM
cana-3320	76	3	,	,	PUNCT
cana-3320	76	4	0.45	0.45	NUM
cana-3320	76	5	]	]	PUNCT
cana-3320	76	6	if	if	SCONJ
cana-3320	76	7	κ	κ	X
cana-3320	76	8	=	=	SYM
cana-3320	76	9	b	b	PROPN
cana-3320	77	1	[	[	X
cana-3320	77	2	0.1	0.1	NUM
cana-3320	77	3	,	,	PUNCT
cana-3320	77	4	0.15	0.15	NUM
cana-3320	77	5	]	]	PUNCT
cana-3320	77	6	if	if	SCONJ
cana-3320	77	7	κ	κ	X
cana-3320	77	8	=	=	SYM
cana-3320	77	9	c	c	PROPN
cana-3320	78	1	[	[	X
cana-3320	78	2	0.2	0.2	NUM
cana-3320	78	3	,	,	PUNCT
cana-3320	78	4	0.25	0.25	NUM
cana-3320	78	5	]	]	PUNCT
cana-3320	78	6	if	if	SCONJ
cana-3320	78	7	κ	κ	X
cana-3320	78	8	=	=	SYM
cana-3320	78	9	d	d	NOUN
cana-3320	78	10	=	=	NOUN
cana-3320	78	11	̃(κ	̃(κ	NOUN
cana-3320	78	12	,	,	PUNCT
cana-3320	78	13	ǎ	ǎ	PROPN
cana-3320	78	14	)	)	PUNCT
cana-3320	78	15	=	=	PUNCT
cana-3320	79	1			PROPN
cana-3320	80	1	[	[	X
cana-3320	80	2	0.3	0.3	NUM
cana-3320	80	3	,	,	PUNCT
cana-3320	80	4	0.35	0.35	NUM
cana-3320	80	5	]	]	PUNCT
cana-3320	80	6	if	if	SCONJ
cana-3320	80	7	κ	κ	X
cana-3320	80	8	=	=	PUNCT
cana-3320	80	9	a	a	PRON
cana-3320	81	1	[	[	X
cana-3320	81	2	0.35	0.35	NUM
cana-3320	81	3	,	,	PUNCT
cana-3320	81	4	0.4	0.4	NUM
cana-3320	81	5	]	]	PUNCT
cana-3320	81	6	if	if	SCONJ
cana-3320	81	7	κ	κ	X
cana-3320	81	8	=	=	SYM
cana-3320	81	9	b	b	PROPN
cana-3320	82	1	[	[	X
cana-3320	82	2	0.45	0.45	NUM
cana-3320	82	3	,	,	PUNCT
cana-3320	82	4	0.5	0.5	NUM
cana-3320	82	5	]	]	PUNCT
cana-3320	82	6	if	if	SCONJ
cana-3320	82	7	κ	κ	X
cana-3320	82	8	=	=	PUNCT
cana-3320	82	9	c	c	PROPN
cana-3320	83	1	[	[	X
cana-3320	83	2	0.4	0.4	NUM
cana-3320	83	3	,	,	PUNCT
cana-3320	83	4	0.45	0.45	NUM
cana-3320	83	5	]	]	PUNCT
cana-3320	83	6	if	if	SCONJ
cana-3320	83	7	κ	κ	X
cana-3320	84	1	=	=	SYM
cana-3320	84	2	d	d	PROPN
cana-3320	84	3	then	then	ADV
cana-3320	84	4	n	n	PRON
cana-3320	84	5	is	be	AUX
cana-3320	84	6	a	a	DET
cana-3320	84	7	(	(	PUNCT
cana-3320	84	8	[	[	X
cana-3320	84	9	0.5	0.5	NUM
cana-3320	84	10	,	,	PUNCT
cana-3320	84	11	0.55	0.55	NUM
cana-3320	84	12	]	]	PUNCT
cana-3320	84	13	,	,	PUNCT
cana-3320	84	14	[	[	X
cana-3320	84	15	0.65	0.65	NUM
cana-3320	84	16	,	,	PUNCT
cana-3320	84	17	0.7	0.7	NUM
cana-3320	84	18	]	]	PUNCT
cana-3320	84	19	)	)	PUNCT
cana-3320	84	20	iqv	iqv	INTJ
cana-3320	84	21	fss	fss	ADV
cana-3320	84	22	of	of	ADP
cana-3320	84	23	z	z	PROPN
cana-3320	84	24	.	.	PUNCT
cana-3320	85	1	definition	definition	NOUN
cana-3320	85	2	3.3	3.3	NUM
cana-3320	85	3	.	.	PUNCT
cana-3320	86	1	a	a	DET
cana-3320	86	2	iqvfs	iqvfs	NOUN
cana-3320	86	3	n	n	PRON
cana-3320	86	4	of	of	ADP
cana-3320	86	5	z	z	PROPN
cana-3320	86	6	is	be	AUX
cana-3320	86	7	called	call	VERB
cana-3320	86	8	a	a	DET
cana-3320	86	9	(	(	PUNCT
cana-3320	86	10	∂̃	∂̃	PROPN
cana-3320	86	11	,	,	PUNCT
cana-3320	86	12	℘̃)-iqvfbi	℘̃)-iqvfbi	NOUN
cana-3320	86	13	of	of	ADP
cana-3320	86	14	z	z	NOUN
cana-3320	86	15	if	if	SCONJ
cana-3320	86	16	1	1	NUM
cana-3320	86	17	.	.	PUNCT
cana-3320	87	1	if	if	SCONJ
cana-3320	87	2	ð1	ð1	PROPN
cana-3320	87	3	6	6	NUM
cana-3320	87	4	ð3	ð3	PROPN
cana-3320	87	5	,	,	PUNCT
cana-3320	87	6	then	then	ADV
cana-3320	87	7	<	<	X
cana-3320	87	8	̃(ð1	̃(ð1	PROPN
cana-3320	87	9	)	)	PUNCT
cana-3320	87	10	>	>	X
cana-3320	88	1	<	<	X
cana-3320	88	2	̃(ð3	̃(ð3	PROPN
cana-3320	88	3	)	)	PUNCT
cana-3320	88	4	and	and	CCONJ
cana-3320	88	5	=	=	PUNCT
cana-3320	88	6	̃(ð1	̃(ð1	PROPN
cana-3320	88	7	)	)	PUNCT
cana-3320	88	8	6	6	NUM
cana-3320	88	9	=	=	SYM
cana-3320	88	10	̃(ð3	̃(ð3	PROPN
cana-3320	88	11	)	)	PUNCT
cana-3320	88	12	,	,	PUNCT
cana-3320	88	13	2	2	X
cana-3320	88	14	.	.	PUNCT
cana-3320	88	15	max{<̃(ð1ð2ð3	max{<̃(ð1ð2ð3	PROPN
cana-3320	88	16	,	,	PUNCT
cana-3320	88	17	ǎ	ǎ	PROPN
cana-3320	88	18	)	)	PUNCT
cana-3320	88	19	,	,	PUNCT
cana-3320	88	20	∂̃	∂̃	PROPN
cana-3320	88	21	}	}	PUNCT
cana-3320	88	22	>	>	X
cana-3320	88	23	min{<̃(ð1	min{<̃(ð1	PROPN
cana-3320	88	24	,	,	PUNCT
cana-3320	88	25	ǎ	ǎ	PROPN
cana-3320	88	26	)	)	PUNCT
cana-3320	88	27	,	,	PUNCT
cana-3320	89	1	<	<	X
cana-3320	89	2	̃(ð3	̃(ð3	PROPN
cana-3320	89	3	,	,	PUNCT
cana-3320	89	4	ǎ	ǎ	PROPN
cana-3320	89	5	)	)	PUNCT
cana-3320	89	6	,	,	PUNCT
cana-3320	89	7	℘̃	℘̃	PROPN
cana-3320	89	8	}	}	PUNCT
cana-3320	89	9	,	,	PUNCT
cana-3320	89	10	min{=̃(ð1ð2ð3	min{=̃(ð1ð2ð3	PROPN
cana-3320	89	11	,	,	PUNCT
cana-3320	89	12	ǎ	ǎ	NOUN
cana-3320	89	13	)	)	PUNCT
cana-3320	89	14	,	,	PUNCT
cana-3320	89	15	∂̃	∂̃	NOUN
cana-3320	89	16	}	}	PUNCT
cana-3320	89	17	6	6	NUM
cana-3320	89	18	max{=̃(ð1	max{=̃(ð1	NOUN
cana-3320	89	19	,	,	PUNCT
cana-3320	89	20	ǎ	ǎ	PROPN
cana-3320	89	21	)	)	PUNCT
cana-3320	89	22	,	,	PUNCT
cana-3320	89	23	=	=	PROPN
cana-3320	89	24	̃(ð3	̃(ð3	PROPN
cana-3320	89	25	,	,	PUNCT
cana-3320	89	26	ǎ	ǎ	PROPN
cana-3320	89	27	)	)	PUNCT
cana-3320	89	28	,	,	PUNCT
cana-3320	89	29	℘̃	℘̃	PROPN
cana-3320	89	30	}	}	PUNCT
cana-3320	89	31	,	,	PUNCT
cana-3320	89	32	3	3	X
cana-3320	89	33	.	.	PUNCT
cana-3320	89	34	max{<̃(ð1ð2ð3ð4ð5	max{<̃(ð1ð2ð3ð4ð5	PROPN
cana-3320	89	35	,	,	PUNCT
cana-3320	89	36	ǎ	ǎ	PROPN
cana-3320	89	37	)	)	PUNCT
cana-3320	89	38	,	,	PUNCT
cana-3320	89	39	∂̃	∂̃	PROPN
cana-3320	89	40	}	}	PUNCT
cana-3320	89	41	>	>	X
cana-3320	89	42	min{<̃(ð1	min{<̃(ð1	PROPN
cana-3320	89	43	,	,	PUNCT
cana-3320	89	44	ǎ	ǎ	PROPN
cana-3320	89	45	)	)	PUNCT
cana-3320	89	46	,	,	PUNCT
cana-3320	90	1	<	<	PROPN
cana-3320	90	2	̃(ð5	̃(ð5	PROPN
cana-3320	90	3	,	,	PUNCT
cana-3320	90	4	ǎ	ǎ	PROPN
cana-3320	90	5	)	)	PUNCT
cana-3320	90	6	,	,	PUNCT
cana-3320	90	7	℘̃	℘̃	PROPN
cana-3320	90	8	}	}	PUNCT
cana-3320	90	9	,	,	PUNCT
cana-3320	90	10	min{=̃(ð1ð2ð3ð4ð5	min{=̃(ð1ð2ð3ð4ð5	PROPN
cana-3320	90	11	,	,	PUNCT
cana-3320	90	12	ǎ	ǎ	PROPN
cana-3320	90	13	)	)	PUNCT
cana-3320	90	14	,	,	PUNCT
cana-3320	90	15	∂̃	∂̃	NOUN
cana-3320	90	16	}	}	PUNCT
cana-3320	90	17	6	6	NUM
cana-3320	90	18	max{=̃(ð1	max{=̃(ð1	NOUN
cana-3320	90	19	,	,	PUNCT
cana-3320	90	20	ǎ	ǎ	PROPN
cana-3320	90	21	)	)	PUNCT
cana-3320	90	22	,	,	PUNCT
cana-3320	90	23	=	=	PROPN
cana-3320	90	24	̃(ð5	̃(ð5	PROPN
cana-3320	90	25	,	,	PUNCT
cana-3320	90	26	ǎ	ǎ	PROPN
cana-3320	90	27	)	)	PUNCT
cana-3320	90	28	,	,	PUNCT
cana-3320	90	29	℘̃	℘̃	PROPN
cana-3320	90	30	}	}	PUNCT
cana-3320	90	31	,	,	PUNCT
cana-3320	90	32	for	for	ADP
cana-3320	90	33	ð1,ð2,ð3,ð4,ð5,∈	ð1,ð2,ð3,ð4,ð5,∈	PROPN
cana-3320	90	34	z	z	NOUN
cana-3320	90	35	.	.	PUNCT
cana-3320	91	1	4	4	NUM
cana-3320	91	2	level	level	NOUN
cana-3320	91	3	set	set	VERB
cana-3320	91	4	concepts	concept	NOUN
cana-3320	91	5	theorem	theorem	VERB
cana-3320	91	6	4.1	4.1	NUM
cana-3320	91	7	.	.	PUNCT
cana-3320	92	1	a	a	DET
cana-3320	92	2	subset	subset	NOUN
cana-3320	92	3	~∂̃	~∂̃	PRON
cana-3320	92	4	is	be	AUX
cana-3320	92	5	a	a	DET
cana-3320	92	6	<	<	X
cana-3320	92	7	̃∂	̃∂	NOUN
cana-3320	92	8	is	be	AUX
cana-3320	92	9	a	a	DET
cana-3320	92	10	(	(	PUNCT
cana-3320	92	11	∂̃	∂̃	NOUN
cana-3320	92	12	,	,	PUNCT
cana-3320	92	13	℘̃)-iqvfss	℘̃)-iqvfss	PROPN
cana-3320	92	14	(	(	PUNCT
cana-3320	92	15	iqvfli	iqvfli	PROPN
cana-3320	92	16	,	,	PUNCT
cana-3320	92	17	iqvflati	iqvflati	PROPN
cana-3320	92	18	,	,	PUNCT
cana-3320	92	19	iqvfri	iqvfri	PROPN
cana-3320	92	20	,	,	PUNCT
cana-3320	92	21	iqvfbi	iqvfbi	PROPN
cana-3320	92	22	)	)	PUNCT
cana-3320	92	23	of	of	ADP
cana-3320	92	24	z	z	PROPN
cana-3320	92	25	.	.	PUNCT
cana-3320	93	1	then	then	ADV
cana-3320	93	2	the	the	DET
cana-3320	93	3	lower	low	ADJ
cana-3320	93	4	level	level	NOUN
cana-3320	93	5	set	set	VERB
cana-3320	93	6	<	<	PRON
cana-3320	93	7	̃∂	̃∂	PROPN
cana-3320	93	8	is	be	AUX
cana-3320	93	9	an	an	DET
cana-3320	93	10	ss	ss	NOUN
cana-3320	93	11	(	(	PUNCT
cana-3320	93	12	li	li	PROPN
cana-3320	93	13	,	,	PUNCT
cana-3320	93	14	latif	latif	PROPN
cana-3320	93	15	,	,	PUNCT
cana-3320	93	16	ri	ri	PROPN
cana-3320	93	17	,	,	PUNCT
cana-3320	93	18	tbi	tbi	PROPN
cana-3320	93	19	)	)	PUNCT
cana-3320	93	20	of	of	ADP
cana-3320	93	21	z	z	NOUN
cana-3320	93	22	,	,	PUNCT
cana-3320	93	23	where	where	SCONJ
cana-3320	93	24	<	<	X
cana-3320	93	25	̃∂	̃∂	X
cana-3320	93	26	=	=	SYM
cana-3320	93	27	{	{	PUNCT
cana-3320	93	28	ð1	ð1	NOUN
cana-3320	93	29	∈	∈	PROPN
cana-3320	93	30	z	z	PROPN
cana-3320	93	31	|<̃(ð1	|<̃(ð1	NOUN
cana-3320	93	32	,	,	PUNCT
cana-3320	93	33	ǎ	ǎ	PROPN
cana-3320	93	34	)	)	PUNCT
cana-3320	93	35	�	�	PROPN
cana-3320	93	36	∂̃	∂̃	PROPN
cana-3320	93	37	}	}	PUNCT
cana-3320	93	38	and	and	CCONJ
cana-3320	93	39	=	=	NOUN
cana-3320	93	40	̃∂	̃∂	NOUN
cana-3320	93	41	=	=	SYM
cana-3320	93	42	{	{	PUNCT
cana-3320	93	43	ð1	ð1	NOUN
cana-3320	93	44	∈	∈	PROPN
cana-3320	93	45	z	z	PROPN
cana-3320	93	46	|<̃(ð1	|<̃(ð1	NOUN
cana-3320	93	47	,	,	PUNCT
cana-3320	93	48	ǎ	ǎ	PROPN
cana-3320	93	49	)	)	PUNCT
cana-3320	93	50	≺	≺	NOUN
cana-3320	93	51	∂̃	∂̃	PROPN
cana-3320	93	52	}	}	PUNCT
cana-3320	93	53	.	.	PUNCT
cana-3320	94	1	proof	proof	NOUN
cana-3320	94	2	.	.	PUNCT
cana-3320	95	1	suppose	suppose	VERB
cana-3320	95	2	that	that	SCONJ
cana-3320	95	3	~∂̃	~∂̃	PUNCT
cana-3320	95	4	is	be	AUX
cana-3320	95	5	a	a	DET
cana-3320	95	6	(	(	PUNCT
cana-3320	95	7	∂̃	∂̃	NOUN
cana-3320	95	8	,	,	PUNCT
cana-3320	95	9	℘̃)-iqvfss	℘̃)-iqvfss	NOUN
cana-3320	95	10	of	of	ADP
cana-3320	95	11	z	z	PROPN
cana-3320	95	12	.	.	PUNCT
cana-3320	96	1	let	let	VERB
cana-3320	96	2	ð1,ð2,ð3	ð1,ð2,ð3	PUNCT
cana-3320	97	1	∈	∈	PROPN
cana-3320	97	2	z	z	NOUN
cana-3320	98	1	such	such	ADJ
cana-3320	98	2	that	that	SCONJ
cana-3320	98	3	ð1,ð2,ð3	ð1,ð2,ð3	PUNCT
cana-3320	99	1	∈	∈	PROPN
cana-3320	99	2	<	<	X
cana-3320	99	3	̃∂	̃∂	NOUN
cana-3320	99	4	.	.	PUNCT
cana-3320	100	1	then	then	ADV
cana-3320	100	2	<	<	X
cana-3320	100	3	̃(ð1	̃(ð1	PROPN
cana-3320	100	4	,	,	PUNCT
cana-3320	100	5	ǎ	ǎ	PROPN
cana-3320	100	6	)	)	PUNCT
cana-3320	100	7	�	�	PROPN
cana-3320	100	8	∂̃	∂̃	PROPN
cana-3320	100	9	,	,	PUNCT
cana-3320	100	10	<	<	X
cana-3320	100	11	̃(ð2	̃(ð2	PROPN
cana-3320	100	12	,	,	PUNCT
cana-3320	100	13	ǎ	ǎ	PROPN
cana-3320	100	14	)	)	PUNCT
cana-3320	100	15	�	�	PROPN
cana-3320	100	16	∂̃	∂̃	PROPN
cana-3320	100	17	,	,	PUNCT
cana-3320	100	18	<	<	PROPN
cana-3320	100	19	̃(ð3	̃(ð3	PROPN
cana-3320	100	20	,	,	PUNCT
cana-3320	100	21	ǎ	ǎ	PROPN
cana-3320	100	22	)	)	PUNCT
cana-3320	100	23	�	�	PROPN
cana-3320	101	1	∂̃.	∂̃.	PROPN
cana-3320	101	2	therefore	therefore	ADV
cana-3320	101	3	max{<̃(ð1ð2ð3	max{<̃(ð1ð2ð3	PROPN
cana-3320	101	4	,	,	PUNCT
cana-3320	101	5	ǎ	ǎ	PROPN
cana-3320	101	6	)	)	PUNCT
cana-3320	101	7	,	,	PUNCT
cana-3320	101	8	∂̃	∂̃	PROPN
cana-3320	101	9	}	}	PUNCT
cana-3320	101	10	>	>	X
cana-3320	101	11	min{<̃(ð1	min{<̃(ð1	PROPN
cana-3320	101	12	,	,	PUNCT
cana-3320	101	13	ǎ	ǎ	PROPN
cana-3320	101	14	)	)	PUNCT
cana-3320	101	15	,	,	PUNCT
cana-3320	101	16	<	<	X
cana-3320	101	17	̃(ð2	̃(ð2	PROPN
cana-3320	101	18	,	,	PUNCT
cana-3320	101	19	ǎ	ǎ	PROPN
cana-3320	101	20	)	)	PUNCT
cana-3320	101	21	,	,	PUNCT
cana-3320	101	22	<	<	X
cana-3320	101	23	̃(ð3	̃(ð3	PROPN
cana-3320	101	24	,	,	PUNCT
cana-3320	101	25	ǎ	ǎ	PROPN
cana-3320	101	26	)	)	PUNCT
cana-3320	101	27	,	,	PUNCT
cana-3320	101	28	℘̃	℘̃	NOUN
cana-3320	101	29	}	}	PUNCT
cana-3320	101	30	�	�	PROPN
cana-3320	101	31	min{∂̃	min{∂̃	ADV
cana-3320	101	32	,	,	PUNCT
cana-3320	101	33	∂̃	∂̃	PROPN
cana-3320	101	34	,	,	PUNCT
cana-3320	101	35	∂̃	∂̃	PROPN
cana-3320	101	36	,	,	PUNCT
cana-3320	101	37	℘̃	℘̃	NOUN
cana-3320	101	38	}	}	PUNCT
cana-3320	101	39	=	=	PUNCT
cana-3320	102	1	∂̃.	∂̃.	NOUN
cana-3320	102	2	hence	hence	ADV
cana-3320	102	3	<	<	X
cana-3320	102	4	̃(ð1ð2ð3	̃(ð1ð2ð3	PROPN
cana-3320	102	5	,	,	PUNCT
cana-3320	102	6	ǎ	ǎ	PROPN
cana-3320	102	7	)	)	PUNCT
cana-3320	102	8	�	�	PROPN
cana-3320	103	1	∂̃.	∂̃.	NOUN
cana-3320	103	2	it	it	PRON
cana-3320	103	3	shows	show	VERB
cana-3320	103	4	that	that	SCONJ
cana-3320	103	5	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	103	6	∈	∈	PROPN
cana-3320	103	7	<	<	X
cana-3320	103	8	̃∂	̃∂	NOUN
cana-3320	103	9	.	.	PUNCT
cana-3320	104	1	therefore	therefore	ADV
cana-3320	104	2	<	<	X
cana-3320	104	3	̃∂	̃∂	PROPN
cana-3320	104	4	is	be	AUX
cana-3320	104	5	a	a	DET
cana-3320	104	6	ss	ss	NOUN
cana-3320	104	7	of	of	ADP
cana-3320	104	8	z	z	PROPN
cana-3320	104	9	.	.	PUNCT
cana-3320	105	1	let	let	VERB
cana-3320	105	2	ð1,ð2,ð3	ð1,ð2,ð3	PUNCT
cana-3320	106	1	∈	∈	PROPN
cana-3320	106	2	z	z	NOUN
cana-3320	106	3	such	such	ADJ
cana-3320	106	4	that	that	SCONJ
cana-3320	106	5	ð1,ð2,ð3	ð1,ð2,ð3	PUNCT
cana-3320	106	6	∈	∈	PROPN
cana-3320	106	7	=	=	NOUN
cana-3320	106	8	̃∂	̃∂	NOUN
cana-3320	106	9	.	.	PUNCT
cana-3320	107	1	then	then	ADV
cana-3320	107	2	=	=	PROPN
cana-3320	107	3	̃(ð1	̃(ð1	PROPN
cana-3320	107	4	,	,	PUNCT
cana-3320	107	5	ǎ	ǎ	NOUN
cana-3320	107	6	)	)	PUNCT
cana-3320	107	7	≺	≺	NOUN
cana-3320	107	8	∂̃	∂̃	NOUN
cana-3320	107	9	,	,	PUNCT
cana-3320	107	10	=	=	PROPN
cana-3320	107	11	̃(ð2	̃(ð2	PROPN
cana-3320	107	12	,	,	PUNCT
cana-3320	107	13	ǎ	ǎ	NOUN
cana-3320	107	14	)	)	PUNCT
cana-3320	107	15	≺	≺	NOUN
cana-3320	107	16	∂̃=̃(ð3	∂̃=̃(ð3	NUM
cana-3320	107	17	,	,	PUNCT
cana-3320	107	18	ǎ	ǎ	NOUN
cana-3320	107	19	)	)	PUNCT
cana-3320	107	20	≺	≺	NOUN
cana-3320	108	1	∂̃.	∂̃.	VERB
cana-3320	108	2	therefore	therefore	ADV
cana-3320	108	3	min{=̃(ð1ð2ð3	min{=̃(ð1ð2ð3	PROPN
cana-3320	108	4	,	,	PUNCT
cana-3320	108	5	ǎ	ǎ	NOUN
cana-3320	108	6	)	)	PUNCT
cana-3320	108	7	,	,	PUNCT
cana-3320	108	8	∂̃	∂̃	NOUN
cana-3320	108	9	}	}	PUNCT
cana-3320	108	10	6	6	NUM
cana-3320	108	11	max{=̃(ð1	max{=̃(ð1	NOUN
cana-3320	108	12	,	,	PUNCT
cana-3320	108	13	ǎ	ǎ	PROPN
cana-3320	108	14	)	)	PUNCT
cana-3320	108	15	,	,	PUNCT
cana-3320	108	16	=	=	PROPN
cana-3320	108	17	̃(ð2	̃(ð2	PROPN
cana-3320	108	18	,	,	PUNCT
cana-3320	108	19	ǎ	ǎ	PROPN
cana-3320	108	20	)	)	PUNCT
cana-3320	108	21	,	,	PUNCT
cana-3320	108	22	=	=	PROPN
cana-3320	108	23	̃(ð3	̃(ð3	PROPN
cana-3320	108	24	,	,	PUNCT
cana-3320	108	25	ǎ	ǎ	PROPN
cana-3320	108	26	)	)	PUNCT
cana-3320	108	27	,	,	PUNCT
cana-3320	108	28	℘̃	℘̃	NOUN
cana-3320	108	29	}	}	PUNCT
cana-3320	108	30	≺	≺	NOUN
cana-3320	108	31	max{∂̃	max{∂̃	NOUN
cana-3320	108	32	,	,	PUNCT
cana-3320	108	33	∂̃	∂̃	NOUN
cana-3320	108	34	,	,	PUNCT
cana-3320	108	35	∂̃	∂̃	PROPN
cana-3320	108	36	,	,	PUNCT
cana-3320	108	37	℘̃	℘̃	NOUN
cana-3320	108	38	}	}	PUNCT
cana-3320	108	39	=	=	PUNCT
cana-3320	108	40	℘̃.	℘̃.	ADP
cana-3320	108	41	hence	hence	ADV
cana-3320	108	42	=	=	SYM
cana-3320	108	43	̃(ð1ð2ð3	̃(ð1ð2ð3	ADJ
cana-3320	108	44	,	,	PUNCT
cana-3320	108	45	ǎ	ǎ	NOUN
cana-3320	108	46	)	)	PUNCT
cana-3320	108	47	≺	≺	NOUN
cana-3320	109	1	∂̃.	∂̃.	NOUN
cana-3320	109	2	it	it	PRON
cana-3320	109	3	shows	show	VERB
cana-3320	109	4	that	that	SCONJ
cana-3320	109	5	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	109	6	∈	∈	NOUN
cana-3320	109	7	=	=	VERB
cana-3320	109	8	̃∂	̃∂	NOUN
cana-3320	109	9	.	.	PUNCT
cana-3320	110	1	therefore	therefore	ADV
cana-3320	110	2	=	=	PRON
cana-3320	110	3	̃∂	̃∂	NOUN
cana-3320	110	4	is	be	AUX
cana-3320	110	5	a	a	DET
cana-3320	110	6	ss	ss	NOUN
cana-3320	110	7	of	of	ADP
cana-3320	110	8	z	z	PROPN
cana-3320	110	9	.	.	PUNCT
cana-3320	111	1	therefore	therefore	ADV
cana-3320	111	2	~∂̃	~∂̃	PUNCT
cana-3320	111	3	is	be	AUX
cana-3320	111	4	a	a	DET
cana-3320	111	5	ss	ss	NOUN
cana-3320	111	6	of	of	ADP
cana-3320	111	7	z	z	PROPN
cana-3320	111	8	.	.	PUNCT
cana-3320	112	1	theorem	theorem	VERB
cana-3320	112	2	4.2	4.2	NUM
cana-3320	112	3	.	.	PUNCT
cana-3320	113	1	a	a	DET
cana-3320	113	2	subset	subset	NOUN
cana-3320	113	3	i	i	PRON
cana-3320	113	4	of	of	ADP
cana-3320	113	5	z	z	PROPN
cana-3320	113	6	is	be	AUX
cana-3320	113	7	a	a	DET
cana-3320	113	8	ss	ss	NOUN
cana-3320	114	1	[	[	X
cana-3320	114	2	li	li	PROPN
cana-3320	114	3	,	,	PUNCT
cana-3320	114	4	latif	latif	PROPN
cana-3320	114	5	,	,	PUNCT
cana-3320	114	6	ri	ri	PROPN
cana-3320	114	7	,	,	PUNCT
cana-3320	114	8	tbi	tbi	PROPN
cana-3320	114	9	]	]	PUNCT
cana-3320	114	10	of	of	ADP
cana-3320	114	11	z	z	NOUN
cana-3320	114	12	if	if	SCONJ
cana-3320	114	13	and	and	CCONJ
cana-3320	114	14	only	only	ADV
cana-3320	114	15	if	if	SCONJ
cana-3320	114	16	the	the	DET
cana-3320	114	17	iqvfs	iqvfs	NOUN
cana-3320	114	18	~	~	PUNCT
cana-3320	114	19	=	=	PUNCT
cana-3320	115	1	[	[	X
cana-3320	115	2	<	<	X
cana-3320	115	3	̃	̃	PROPN
cana-3320	115	4	,	,	PUNCT
cana-3320	115	5	=	=	SYM
cana-3320	115	6	̃	̃	NOUN
cana-3320	115	7	]	]	PUNCT
cana-3320	115	8	of	of	ADP
cana-3320	115	9	z	z	PROPN
cana-3320	115	10	is	be	AUX
cana-3320	115	11	defined	define	VERB
cana-3320	115	12	as	as	ADP
cana-3320	115	13	<	<	PROPN
cana-3320	115	14	̃(ð1	̃(ð1	PROPN
cana-3320	115	15	,	,	PUNCT
cana-3320	115	16	ǎ	ǎ	PROPN
cana-3320	115	17	)	)	PUNCT
cana-3320	115	18	=	=	PRON
cana-3320	115	19	{	{	PUNCT
cana-3320	115	20	>	>	X
cana-3320	115	21	℘̃	℘̃	NOUN
cana-3320	115	22	for	for	ADP
cana-3320	115	23	all	all	DET
cana-3320	115	24	ð1	ð1	NOUN
cana-3320	115	25	∈	∈	PROPN
cana-3320	115	26	(	(	PUNCT
cana-3320	115	27	i	i	X
cana-3320	115	28	]	]	PUNCT
cana-3320	115	29	∂̃	∂̃	NOUN
cana-3320	115	30	for	for	ADP
cana-3320	115	31	all	all	DET
cana-3320	115	32	ð1	ð1	NOUN
cana-3320	115	33	/∈	/∈	PUNCT
cana-3320	116	1	(	(	PUNCT
cana-3320	116	2	i	i	NOUN
cana-3320	116	3	]	]	X
cana-3320	116	4	=	=	SYM
cana-3320	116	5	̃(ð1	̃(ð1	PROPN
cana-3320	116	6	,	,	PUNCT
cana-3320	116	7	ǎ	ǎ	PROPN
cana-3320	116	8	)	)	PUNCT
cana-3320	116	9	=	=	PRON
cana-3320	116	10	{	{	PUNCT
cana-3320	116	11	6	6	NUM
cana-3320	116	12	℘̃	℘̃	NOUN
cana-3320	116	13	for	for	ADP
cana-3320	116	14	all	all	DET
cana-3320	116	15	ð1	ð1	NOUN
cana-3320	116	16	∈	∈	PROPN
cana-3320	116	17	(	(	PUNCT
cana-3320	116	18	i	i	X
cana-3320	116	19	]	]	PUNCT
cana-3320	116	20	∂̃	∂̃	NOUN
cana-3320	116	21	for	for	ADP
cana-3320	116	22	all	all	DET
cana-3320	116	23	ð1	ð1	NOUN
cana-3320	116	24	/∈	/∈	PUNCT
cana-3320	117	1	(	(	PUNCT
cana-3320	117	2	i	i	NOUN
cana-3320	117	3	]	]	X
cana-3320	117	4	is	be	AUX
cana-3320	117	5	a	a	DET
cana-3320	117	6	(	(	PUNCT
cana-3320	117	7	∂̃	∂̃	NOUN
cana-3320	117	8	,	,	PUNCT
cana-3320	117	9	℘̃)iqv	℘̃)iqv	ADJ
cana-3320	117	10	fss[iqv	fss[iqv	PROPN
cana-3320	117	11	fli	fli	NOUN
cana-3320	117	12	,	,	PUNCT
cana-3320	117	13	iqv	iqv	ADJ
cana-3320	117	14	flati	flati	NOUN
cana-3320	117	15	,	,	PUNCT
cana-3320	117	16	iqv	iqv	NOUN
cana-3320	117	17	fri	fri	NOUN
cana-3320	117	18	,	,	PUNCT
cana-3320	117	19	iqv	iqv	PROPN
cana-3320	117	20	fbi	fbi	PROPN
cana-3320	117	21	]	]	PUNCT
cana-3320	117	22	of	of	ADP
cana-3320	117	23	z	z	PROPN
cana-3320	117	24	.	.	PUNCT
cana-3320	118	1	proof	proof	NOUN
cana-3320	118	2	.	.	PUNCT
cana-3320	119	1	suppose	suppose	VERB
cana-3320	119	2	that	that	SCONJ
cana-3320	119	3	i	i	PRON
cana-3320	119	4	is	be	AUX
cana-3320	119	5	an	an	DET
cana-3320	119	6	ss	ss	NOUN
cana-3320	119	7	of	of	ADP
cana-3320	119	8	z	z	PROPN
cana-3320	119	9	.	.	PUNCT
cana-3320	120	1	let	let	VERB
cana-3320	120	2	ð1,ð2,ð3	ð1,ð2,ð3	PRON
cana-3320	121	1	∈	∈	PROPN
cana-3320	121	2	z	z	NOUN
cana-3320	121	3	be	be	AUX
cana-3320	121	4	such	such	ADJ
cana-3320	121	5	that	that	SCONJ
cana-3320	121	6	ð1,ð2,ð3	ð1,ð2,ð3	SYM
cana-3320	122	1	∈	∈	PROPN
cana-3320	122	2	(	(	PUNCT
cana-3320	122	3	i	i	NOUN
cana-3320	122	4	]	]	PUNCT
cana-3320	122	5	then	then	ADV
cana-3320	122	6	ð1ð2ð3	ð1ð2ð3	ADP
cana-3320	122	7	∈	∈	PROPN
cana-3320	122	8	(	(	PUNCT
cana-3320	122	9	i	i	NOUN
cana-3320	122	10	]	]	X
cana-3320	122	11	.	.	PUNCT
cana-3320	123	1	hence	hence	ADV
cana-3320	123	2	<	<	X
cana-3320	123	3	̃(ð1ð2ð3	̃(ð1ð2ð3	PROPN
cana-3320	123	4	,	,	PUNCT
cana-3320	123	5	ǎ	ǎ	PROPN
cana-3320	123	6	)	)	PUNCT
cana-3320	123	7	>	>	X
cana-3320	123	8	℘̃	℘̃	PROPN
cana-3320	123	9	and	and	CCONJ
cana-3320	123	10	=	=	NOUN
cana-3320	123	11	̃(ð1ð2ð3	̃(ð1ð2ð3	ADJ
cana-3320	123	12	,	,	PUNCT
cana-3320	123	13	ǎ	ǎ	PROPN
cana-3320	123	14	)	)	PUNCT
cana-3320	123	15	6	6	NUM
cana-3320	123	16	℘̃.	℘̃.	ADP
cana-3320	123	17	thus	thus	ADV
cana-3320	123	18	max{<̃(ð1ð2ð3	max{<̃(ð1ð2ð3	PROPN
cana-3320	123	19	,	,	PUNCT
cana-3320	123	20	ǎ	ǎ	PROPN
cana-3320	123	21	)	)	PUNCT
cana-3320	123	22	,	,	PUNCT
cana-3320	123	23	∂̃	∂̃	PROPN
cana-3320	123	24	}	}	PUNCT
cana-3320	123	25	>	>	PUNCT
cana-3320	123	26	℘̃	℘̃	PROPN
cana-3320	123	27	=	=	SYM
cana-3320	123	28	min{<̃(ð1	min{<̃(ð1	PROPN
cana-3320	123	29	,	,	PUNCT
cana-3320	123	30	ǎ	ǎ	PROPN
cana-3320	123	31	)	)	PUNCT
cana-3320	123	32	,	,	PUNCT
cana-3320	123	33	<	<	X
cana-3320	123	34	̃(ð2	̃(ð2	PROPN
cana-3320	123	35	,	,	PUNCT
cana-3320	123	36	ǎ	ǎ	PROPN
cana-3320	123	37	)	)	PUNCT
cana-3320	123	38	,	,	PUNCT
cana-3320	124	1	<	<	X
cana-3320	124	2	̃(ð3	̃(ð3	PROPN
cana-3320	124	3	,	,	PUNCT
cana-3320	124	4	ǎ	ǎ	PROPN
cana-3320	124	5	)	)	PUNCT
cana-3320	124	6	,	,	PUNCT
cana-3320	124	7	℘̃	℘̃	NOUN
cana-3320	124	8	}	}	PUNCT
cana-3320	124	9	and	and	CCONJ
cana-3320	124	10	min{=̃(ð1ð2ð3	min{=̃(ð1ð2ð3	PROPN
cana-3320	124	11	,	,	PUNCT
cana-3320	124	12	ǎ	ǎ	NOUN
cana-3320	124	13	)	)	PUNCT
cana-3320	124	14	,	,	PUNCT
cana-3320	124	15	∂̃	∂̃	NOUN
cana-3320	124	16	}	}	PUNCT
cana-3320	124	17	6	6	NUM
cana-3320	124	18	℘̃	℘̃	NOUN
cana-3320	124	19	=	=	SYM
cana-3320	124	20	max{=̃(ð1	max{=̃(ð1	PROPN
cana-3320	124	21	,	,	PUNCT
cana-3320	124	22	ǎ	ǎ	PROPN
cana-3320	124	23	)	)	PUNCT
cana-3320	124	24	,	,	PUNCT
cana-3320	124	25	=	=	PROPN
cana-3320	124	26	̃(ð2	̃(ð2	PROPN
cana-3320	124	27	,	,	PUNCT
cana-3320	124	28	ǎ	ǎ	PROPN
cana-3320	124	29	)	)	PUNCT
cana-3320	124	30	,	,	PUNCT
cana-3320	124	31	=	=	PROPN
cana-3320	124	32	̃(ð3	̃(ð3	PROPN
cana-3320	124	33	,	,	PUNCT
cana-3320	124	34	ǎ	ǎ	PROPN
cana-3320	124	35	)	)	PUNCT
cana-3320	124	36	,	,	PUNCT
cana-3320	124	37	℘̃	℘̃	PROPN
cana-3320	124	38	}	}	PUNCT
cana-3320	124	39	.	.	PUNCT
cana-3320	125	1	if	if	SCONJ
cana-3320	125	2	ð1	ð1	NOUN
cana-3320	125	3	/∈	/∈	PUNCT
cana-3320	126	1	(	(	PUNCT
cana-3320	126	2	i	i	NOUN
cana-3320	126	3	]	]	PUNCT
cana-3320	126	4	or	or	CCONJ
cana-3320	126	5	ð2	ð2	PROPN
cana-3320	126	6	/∈	/∈	PUNCT
cana-3320	127	1	(	(	PUNCT
cana-3320	127	2	i	i	NOUN
cana-3320	127	3	]	]	X
cana-3320	127	4	or	or	CCONJ
cana-3320	127	5	ð3	ð3	PROPN
cana-3320	127	6	/∈	/∈	PUNCT
cana-3320	128	1	(	(	PUNCT
cana-3320	128	2	i	i	PRON
cana-3320	128	3	]	]	X
cana-3320	128	4	,	,	PUNCT
cana-3320	128	5	then	then	ADV
cana-3320	128	6	min{<̃(ð1	min{<̃(ð1	PROPN
cana-3320	128	7	,	,	PUNCT
cana-3320	128	8	ǎ	ǎ	PROPN
cana-3320	128	9	)	)	PUNCT
cana-3320	128	10	,	,	PUNCT
cana-3320	128	11	<	<	X
cana-3320	128	12	̃(ð2	̃(ð2	PROPN
cana-3320	128	13	,	,	PUNCT
cana-3320	128	14	ǎ	ǎ	PROPN
cana-3320	128	15	)	)	PUNCT
cana-3320	128	16	,	,	PUNCT
cana-3320	128	17	<	<	X
cana-3320	128	18	̃(ð3	̃(ð3	PROPN
cana-3320	128	19	,	,	PUNCT
cana-3320	128	20	ǎ	ǎ	PROPN
cana-3320	128	21	)	)	PUNCT
cana-3320	128	22	,	,	PUNCT
cana-3320	128	23	℘̃	℘̃	NOUN
cana-3320	128	24	}	}	PUNCT
cana-3320	128	25	=	=	SYM
cana-3320	128	26	∂̃	∂̃	NOUN
cana-3320	128	27	and	and	CCONJ
cana-3320	128	28	max{=̃(ð1	max{=̃(ð1	PROPN
cana-3320	128	29	,	,	PUNCT
cana-3320	128	30	ǎ	ǎ	PROPN
cana-3320	128	31	)	)	PUNCT
cana-3320	128	32	,	,	PUNCT
cana-3320	129	1	=	=	PROPN
cana-3320	129	2	̃(ð2	̃(ð2	PROPN
cana-3320	129	3	,	,	PUNCT
cana-3320	129	4	ǎ	ǎ	PROPN
cana-3320	129	5	)	)	PUNCT
cana-3320	129	6	,	,	PUNCT
cana-3320	129	7	=	=	PROPN
cana-3320	129	8	̃(ð3	̃(ð3	PROPN
cana-3320	129	9	,	,	PUNCT
cana-3320	129	10	ǎ	ǎ	PROPN
cana-3320	129	11	)	)	PUNCT
cana-3320	129	12	,	,	PUNCT
cana-3320	129	13	℘̃	℘̃	NOUN
cana-3320	129	14	}	}	PUNCT
cana-3320	129	15	=	=	PUNCT
cana-3320	129	16	℘̃.	℘̃.	ADP
cana-3320	129	17	https://internationalpubls.com	https://internationalpubls.com	X
cana-3320	129	18	581	581	NUM
cana-3320	129	19	˜	˜	PROPN
cana-3320	130	1	˜	˜	PROPN
cana-3320	130	2	˜	˜	PROPN
cana-3320	131	1	˜	˜	PROPN
cana-3320	132	1	˜	˜	PROPN
cana-3320	133	1	˜	˜	PROPN
cana-3320	134	1	˜	˜	PROPN
cana-3320	135	1	˜	˜	PROPN
cana-3320	135	2	˜	˜	PROPN
cana-3320	135	3	,	,	PUNCT
cana-3320	136	1	˜	˜	PROPN
cana-3320	136	2	˜	˜	PROPN
cana-3320	137	1	˜	˜	PROPN
cana-3320	138	1	˜	˜	PROPN
cana-3320	139	1	˜	˜	PROPN
cana-3320	140	1	˜	˜	PROPN
cana-3320	141	1	˜	˜	PROPN
cana-3320	141	2	˜	˜	PROPN
cana-3320	141	3	,	,	PUNCT
cana-3320	142	1	˜	˜	PROPN
cana-3320	142	2	˜	˜	PROPN
cana-3320	143	1	˜	˜	PROPN
cana-3320	144	1	˜	˜	PROPN
cana-3320	145	1	˜	˜	PROPN
cana-3320	146	1	˜	˜	PROPN
cana-3320	147	1	˜	˜	PROPN
cana-3320	148	1	˜	˜	PROPN
cana-3320	149	1	˜	˜	PROPN
cana-3320	149	2	˜	˜	PROPN
cana-3320	149	3	,	,	PUNCT
cana-3320	150	1	˜	˜	PROPN
cana-3320	150	2	˜	˜	PROPN
cana-3320	151	1	˜	˜	PROPN
cana-3320	152	1	˜	˜	PROPN
cana-3320	153	1	˜	˜	PROPN
cana-3320	154	1	˜	˜	PROPN
cana-3320	155	1	˜	˜	PROPN
cana-3320	156	1	˜	˜	PROPN
cana-3320	157	1	˜	˜	PROPN
cana-3320	158	1	˜	˜	PROPN
cana-3320	159	1	˜	˜	PROPN
cana-3320	160	1	˜	˜	PROPN
cana-3320	161	1	˜	˜	PROPN
cana-3320	162	1	˜	˜	PROPN
cana-3320	163	1	˜	˜	PROPN
cana-3320	164	1	˜	˜	PROPN
cana-3320	165	1	˜	˜	PROPN
cana-3320	166	1	˜	˜	PROPN
cana-3320	167	1	˜	˜	PROPN
cana-3320	168	1	˜	˜	PROPN
cana-3320	169	1	˜	˜	PROPN
cana-3320	170	1	˜	˜	PROPN
cana-3320	171	1	˜	˜	PROPN
cana-3320	172	1	˜	˜	PROPN
cana-3320	173	1	˜	˜	PROPN
cana-3320	174	1	˜	˜	PROPN
cana-3320	175	1	˜	˜	PROPN
cana-3320	176	1	˜	˜	PROPN
cana-3320	177	1	˜	˜	PROPN
cana-3320	178	1	˜	˜	PROPN
cana-3320	179	1	˜	˜	PROPN
cana-3320	180	1	˜	˜	PROPN
cana-3320	181	1	˜	˜	PROPN
cana-3320	182	1	˜	˜	PROPN
cana-3320	183	1	˜	˜	PROPN
cana-3320	183	2	˜	˜	PROPN
cana-3320	183	3	communications	communication	NOUN
cana-3320	183	4	on	on	ADP
cana-3320	183	5	applied	apply	VERB
cana-3320	183	6	nonlinear	nonlinear	ADJ
cana-3320	183	7	analysis	analysis	NOUN
cana-3320	183	8	issn	issn	NOUN
cana-3320	183	9	:	:	PUNCT
cana-3320	183	10	1074	1074	NUM
cana-3320	183	11	-	-	PUNCT
cana-3320	183	12	133x	133x	NUM
cana-3320	183	13	vol	vol	NOUN
cana-3320	183	14	32	32	NUM
cana-3320	183	15	no	no	NOUN
cana-3320	183	16	.	.	PUNCT
cana-3320	184	1	6s	6s	NUM
cana-3320	184	2	(	(	PUNCT
cana-3320	184	3	2025	2025	NUM
cana-3320	184	4	)	)	PUNCT
cana-3320	184	5	that	that	PRON
cana-3320	184	6	is	be	AUX
cana-3320	184	7	max{<(ð1ð2ð3	max{<(ð1ð2ð3	NOUN
cana-3320	184	8	,	,	PUNCT
cana-3320	184	9	̌a	̌a	NOUN
cana-3320	184	10	)	)	PUNCT
cana-3320	184	11	,	,	PUNCT
cana-3320	184	12	∂̃	∂̃	NOUN
cana-3320	184	13	}	}	PUNCT
cana-3320	184	14	>	>	X
cana-3320	184	15	min{<(ð1	min{<(ð1	NOUN
cana-3320	184	16	,	,	PUNCT
cana-3320	184	17	̌a	̌a	PROPN
cana-3320	184	18	)	)	PUNCT
cana-3320	184	19	,	,	PUNCT
cana-3320	184	20	<	<	X
cana-3320	184	21	(	(	PUNCT
cana-3320	184	22	ð2	ð2	NOUN
cana-3320	184	23	,	,	PUNCT
cana-3320	184	24	̌a	̌a	NOUN
cana-3320	184	25	)	)	PUNCT
cana-3320	184	26	,	,	PUNCT
cana-3320	184	27	<	<	X
cana-3320	184	28	(	(	PUNCT
cana-3320	184	29	ð3	ð3	NOUN
cana-3320	184	30	,	,	PUNCT
cana-3320	184	31	̌a	̌a	NOUN
cana-3320	184	32	)	)	PUNCT
cana-3320	184	33	,	,	PUNCT
cana-3320	184	34	℘̃	℘̃	NOUN
cana-3320	184	35	}	}	PUNCT
cana-3320	184	36	and	and	CCONJ
cana-3320	184	37	min{=(ð1ð2ð3	min{=(ð1ð2ð3	NOUN
cana-3320	184	38	,	,	PUNCT
cana-3320	184	39	̌a	̌a	NOUN
cana-3320	184	40	)	)	PUNCT
cana-3320	184	41	,	,	PUNCT
cana-3320	184	42	∂̃	∂̃	NOUN
cana-3320	184	43	}	}	PUNCT
cana-3320	184	44	6	6	NUM
cana-3320	184	45	max{=(ð1	max{=(ð1	NOUN
cana-3320	184	46	,	,	PUNCT
cana-3320	184	47	̌a	̌a	NOUN
cana-3320	184	48	)	)	PUNCT
cana-3320	184	49	,	,	PUNCT
cana-3320	184	50	=(	=(	PROPN
cana-3320	184	51	ð2	ð2	PROPN
cana-3320	184	52	,	,	PUNCT
cana-3320	184	53	̌a	̌a	NOUN
cana-3320	184	54	)	)	PUNCT
cana-3320	184	55	,	,	PUNCT
cana-3320	184	56	=(	=(	PROPN
cana-3320	184	57	ð3	ð3	PROPN
cana-3320	184	58	,	,	PUNCT
cana-3320	184	59	̌a	̌a	NOUN
cana-3320	184	60	)	)	PUNCT
cana-3320	184	61	,	,	PUNCT
cana-3320	184	62	℘̃	℘̃	PROPN
cana-3320	184	63	}	}	PUNCT
cana-3320	184	64	.	.	PUNCT
cana-3320	185	1	therefore	therefore	ADV
cana-3320	185	2	~	~	PUNCT
cana-3320	185	3	is	be	AUX
cana-3320	185	4	a	a	DET
cana-3320	185	5	(	(	PUNCT
cana-3320	185	6	∂̃	∂̃	PROPN
cana-3320	185	7	,	,	PUNCT
cana-3320	185	8	℘̃	℘̃	PROPN
cana-3320	185	9	)	)	PUNCT
cana-3320	185	10	iqvfss	iqvfss	NOUN
cana-3320	185	11	of	of	ADP
cana-3320	185	12	z	z	PROPN
cana-3320	185	13	.	.	PUNCT
cana-3320	186	1	conversely	conversely	ADV
cana-3320	186	2	assume	assume	VERB
cana-3320	186	3	that	that	SCONJ
cana-3320	186	4	~	~	PUNCT
cana-3320	186	5	=	=	PUNCT
cana-3320	187	1	[	[	X
cana-3320	187	2	<	<	X
cana-3320	187	3	=]	=]	NOUN
cana-3320	187	4	is	be	AUX
cana-3320	187	5	a	a	DET
cana-3320	187	6	(	(	PUNCT
cana-3320	187	7	∂̃	∂̃	NOUN
cana-3320	187	8	,	,	PUNCT
cana-3320	187	9	℘̃)-iqvfss	℘̃)-iqvfss	NOUN
cana-3320	187	10	of	of	ADP
cana-3320	187	11	z	z	PROPN
cana-3320	187	12	.	.	PUNCT
cana-3320	188	1	let	let	VERB
cana-3320	188	2	ð1ð2ð3	ð1ð2ð3	ADP
cana-3320	188	3	∈	∈	PROPN
cana-3320	188	4	(	(	PUNCT
cana-3320	188	5	i	i	NOUN
cana-3320	188	6	]	]	X
cana-3320	188	7	.	.	PUNCT
cana-3320	189	1	then	then	ADV
cana-3320	189	2	<	<	X
cana-3320	189	3	(	(	PUNCT
cana-3320	189	4	ð1	ð1	NOUN
cana-3320	189	5	,	,	PUNCT
cana-3320	189	6	̌a	̌a	PROPN
cana-3320	189	7	)	)	PUNCT
cana-3320	189	8	>	>	X
cana-3320	190	1	℘̃	℘̃	PROPN
cana-3320	190	2	,	,	PUNCT
cana-3320	190	3	<	<	X
cana-3320	190	4	(	(	PUNCT
cana-3320	190	5	ð2	ð2	NOUN
cana-3320	190	6	,	,	PUNCT
cana-3320	190	7	̌a	̌a	PROPN
cana-3320	190	8	)	)	PUNCT
cana-3320	190	9	>	>	X
cana-3320	190	10	℘̃	℘̃	PROPN
cana-3320	190	11	,	,	PUNCT
cana-3320	190	12	<	<	X
cana-3320	190	13	(	(	PUNCT
cana-3320	190	14	ð3	ð3	NOUN
cana-3320	190	15	,	,	PUNCT
cana-3320	190	16	̌a	̌a	PROPN
cana-3320	190	17	)	)	PUNCT
cana-3320	190	18	>	>	X
cana-3320	190	19	℘̃	℘̃	PROPN
cana-3320	190	20	and	and	CCONJ
cana-3320	190	21	=(	=(	NOUN
cana-3320	190	22	ð1	ð1	NOUN
cana-3320	190	23	,	,	PUNCT
cana-3320	190	24	̌a	̌a	NOUN
cana-3320	190	25	)	)	PUNCT
cana-3320	190	26	6	6	NUM
cana-3320	190	27	℘̃	℘̃	NOUN
cana-3320	190	28	,	,	PUNCT
cana-3320	190	29	=(	=(	PROPN
cana-3320	190	30	ð2	ð2	PROPN
cana-3320	190	31	,	,	PUNCT
cana-3320	190	32	̌a	̌a	NOUN
cana-3320	190	33	)	)	PUNCT
cana-3320	190	34	6	6	NUM
cana-3320	190	35	℘̃	℘̃	NOUN
cana-3320	190	36	,	,	PUNCT
cana-3320	190	37	=(	=(	PROPN
cana-3320	190	38	ð3	ð3	PROPN
cana-3320	190	39	,	,	PUNCT
cana-3320	190	40	̌a	̌a	NOUN
cana-3320	190	41	)	)	PUNCT
cana-3320	190	42	6	6	NUM
cana-3320	190	43	℘̃.	℘̃.	ADP
cana-3320	190	44	now	now	ADV
cana-3320	190	45	~	~	PUNCT
cana-3320	190	46	=	=	PUNCT
cana-3320	191	1	[	[	X
cana-3320	191	2	<	<	X
cana-3320	191	3	=]	=]	NOUN
cana-3320	191	4	is	be	AUX
cana-3320	191	5	a	a	DET
cana-3320	191	6	(	(	PUNCT
cana-3320	191	7	∂̃	∂̃	NOUN
cana-3320	191	8	,	,	PUNCT
cana-3320	191	9	℘̃)-iqvfss	℘̃)-iqvfss	NOUN
cana-3320	191	10	of	of	ADP
cana-3320	191	11	z	z	PROPN
cana-3320	191	12	.	.	PUNCT
cana-3320	192	1	therefore	therefore	ADV
cana-3320	192	2	max{<(ð1ð2ð3	max{<(ð1ð2ð3	NOUN
cana-3320	192	3	,	,	PUNCT
cana-3320	192	4	̌a	̌a	NOUN
cana-3320	192	5	)	)	PUNCT
cana-3320	192	6	,	,	PUNCT
cana-3320	192	7	∂̃	∂̃	NOUN
cana-3320	192	8	}	}	PUNCT
cana-3320	192	9	>	>	X
cana-3320	192	10	min{<(ð1	min{<(ð1	NOUN
cana-3320	192	11	,	,	PUNCT
cana-3320	192	12	̌a	̌a	PROPN
cana-3320	192	13	)	)	PUNCT
cana-3320	192	14	,	,	PUNCT
cana-3320	192	15	<	<	X
cana-3320	192	16	(	(	PUNCT
cana-3320	192	17	ð2	ð2	NOUN
cana-3320	192	18	,	,	PUNCT
cana-3320	192	19	̌a	̌a	NOUN
cana-3320	192	20	)	)	PUNCT
cana-3320	192	21	,	,	PUNCT
cana-3320	192	22	<	<	X
cana-3320	192	23	(	(	PUNCT
cana-3320	192	24	ð3	ð3	NOUN
cana-3320	192	25	,	,	PUNCT
cana-3320	192	26	̌a	̌a	NOUN
cana-3320	192	27	)	)	PUNCT
cana-3320	192	28	,	,	PUNCT
cana-3320	192	29	℘̃	℘̃	PROPN
cana-3320	192	30	}	}	PUNCT
cana-3320	192	31	>	>	X
cana-3320	192	32	min	min	PROPN
cana-3320	192	33	{	{	PUNCT
cana-3320	192	34	̃℘	̃℘	PROPN
cana-3320	192	35	,	,	PUNCT
cana-3320	192	36	℘̃	℘̃	PROPN
cana-3320	192	37	,	,	PUNCT
cana-3320	192	38	℘̃	℘̃	PROPN
cana-3320	192	39	,	,	PUNCT
cana-3320	192	40	℘̃	℘̃	NOUN
cana-3320	192	41	}	}	PUNCT
cana-3320	192	42	=	=	SYM
cana-3320	192	43	℘̃	℘̃	NOUN
cana-3320	192	44	and	and	CCONJ
cana-3320	192	45	min{=(ð1ð2ð3	min{=(ð1ð2ð3	NOUN
cana-3320	192	46	,	,	PUNCT
cana-3320	192	47	̌a	̌a	NOUN
cana-3320	192	48	)	)	PUNCT
cana-3320	192	49	,	,	PUNCT
cana-3320	192	50	∂̃	∂̃	NOUN
cana-3320	192	51	}	}	PUNCT
cana-3320	192	52	6	6	NUM
cana-3320	192	53	max{=(ð1	max{=(ð1	NOUN
cana-3320	192	54	,	,	PUNCT
cana-3320	192	55	̌a	̌a	NOUN
cana-3320	192	56	)	)	PUNCT
cana-3320	192	57	,	,	PUNCT
cana-3320	192	58	=(	=(	PROPN
cana-3320	192	59	ð2	ð2	PROPN
cana-3320	192	60	,	,	PUNCT
cana-3320	192	61	̌a	̌a	NOUN
cana-3320	192	62	)	)	PUNCT
cana-3320	192	63	,	,	PUNCT
cana-3320	192	64	=(	=(	PROPN
cana-3320	192	65	ð3	ð3	PROPN
cana-3320	192	66	,	,	PUNCT
cana-3320	192	67	̌a	̌a	NOUN
cana-3320	192	68	)	)	PUNCT
cana-3320	192	69	,	,	PUNCT
cana-3320	192	70	℘̃	℘̃	NOUN
cana-3320	192	71	}	}	PUNCT
cana-3320	192	72	6	6	NUM
cana-3320	192	73	max	max	PROPN
cana-3320	192	74	{	{	PUNCT
cana-3320	192	75	̃℘	̃℘	PROPN
cana-3320	192	76	,	,	PUNCT
cana-3320	192	77	℘̃	℘̃	PROPN
cana-3320	192	78	,	,	PUNCT
cana-3320	192	79	℘̃	℘̃	PROPN
cana-3320	192	80	,	,	PUNCT
cana-3320	192	81	℘̃	℘̃	NOUN
cana-3320	192	82	}	}	PUNCT
cana-3320	192	83	=	=	PUNCT
cana-3320	192	84	℘̃.	℘̃.	ADP
cana-3320	192	85	it	it	PRON
cana-3320	192	86	follows	follow	VERB
cana-3320	192	87	that	that	SCONJ
cana-3320	192	88	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	192	89	∈	∈	PROPN
cana-3320	192	90	(	(	PUNCT
cana-3320	192	91	i	i	NOUN
cana-3320	192	92	]	]	PUNCT
cana-3320	192	93	.	.	PUNCT
cana-3320	193	1	therefore	therefore	ADV
cana-3320	193	2	i	i	PRON
cana-3320	193	3	is	be	AUX
cana-3320	193	4	a	a	DET
cana-3320	193	5	ss	ss	NOUN
cana-3320	193	6	of	of	ADP
cana-3320	193	7	z	z	PROPN
cana-3320	193	8	.	.	PUNCT
cana-3320	194	1	theorem	theorem	VERB
cana-3320	194	2	4.3	4.3	NUM
cana-3320	194	3	.	.	PUNCT
cana-3320	195	1	a	a	DET
cana-3320	195	2	subset	subset	NOUN
cana-3320	195	3	~	~	PUNCT
cana-3320	195	4	=	=	PUNCT
cana-3320	196	1	[	[	X
cana-3320	196	2	<	<	X
cana-3320	196	3	=]	=]	NOUN
cana-3320	196	4	is	be	AUX
cana-3320	196	5	a	a	DET
cana-3320	196	6	(	(	PUNCT
cana-3320	196	7	∂̃	∂̃	PROPN
cana-3320	196	8	,	,	PUNCT
cana-3320	196	9	℘̃	℘̃	PROPN
cana-3320	196	10	)	)	PUNCT
cana-3320	196	11	−	−	NOUN
cana-3320	197	1	iqv	iqv	INTJ
cana-3320	197	2	f	f	NOUN
cana-3320	198	1	ss[iqv	ss[iqv	PROPN
cana-3320	198	2	f	f	PROPN
cana-3320	198	3	li	li	PROPN
cana-3320	198	4	,	,	PUNCT
cana-3320	198	5	iqv	iqv	INTJ
cana-3320	199	1	f	f	PROPN
cana-3320	199	2	lat	lat	INTJ
cana-3320	200	1	i	i	PRON
cana-3320	200	2	,	,	PUNCT
cana-3320	200	3	iqv	iqv	PROPN
cana-3320	200	4	fri	fri	PROPN
cana-3320	200	5	,	,	PUNCT
cana-3320	200	6	iqv	iqv	PROPN
cana-3320	200	7	fbi	fbi	PROPN
cana-3320	200	8	]	]	PUNCT
cana-3320	200	9	of	of	ADP
cana-3320	200	10	z	z	NOUN
cana-3320	200	11	if	if	SCONJ
cana-3320	200	12	and	and	CCONJ
cana-3320	200	13	only	only	ADV
cana-3320	200	14	if	if	SCONJ
cana-3320	200	15	each	each	DET
cana-3320	200	16	level	level	NOUN
cana-3320	200	17	subset	subset	VERB
cana-3320	200	18	~t	~t	PUNCT
cana-3320	200	19	is	be	AUX
cana-3320	200	20	a	a	DET
cana-3320	200	21	ss	ss	NOUN
cana-3320	201	1	[	[	X
cana-3320	201	2	li	li	PROPN
cana-3320	201	3	,	,	PUNCT
cana-3320	201	4	laiqvf	laiqvf	PROPN
cana-3320	201	5	,	,	PUNCT
cana-3320	201	6	ri	ri	PROPN
cana-3320	201	7	,	,	PUNCT
cana-3320	201	8	tbi	tbi	PROPN
cana-3320	201	9	]	]	PUNCT
cana-3320	201	10	of	of	ADP
cana-3320	201	11	z	z	NOUN
cana-3320	201	12	for	for	ADP
cana-3320	201	13	all	all	DET
cana-3320	201	14	t	t	NOUN
cana-3320	201	15	∈	∈	PROPN
cana-3320	201	16	(	(	PUNCT
cana-3320	201	17	∂̃	∂̃	PROPN
cana-3320	201	18	,	,	PUNCT
cana-3320	201	19	℘̃	℘̃	PROPN
cana-3320	201	20	]	]	PUNCT
cana-3320	201	21	.	.	PUNCT
cana-3320	202	1	proof	proof	NOUN
cana-3320	202	2	.	.	PUNCT
cana-3320	203	1	assume	assume	VERB
cana-3320	203	2	that	that	SCONJ
cana-3320	203	3	~t	~t	PUNCT
cana-3320	203	4	is	be	AUX
cana-3320	203	5	a	a	DET
cana-3320	203	6	ss	ss	NOUN
cana-3320	203	7	of	of	ADP
cana-3320	203	8	z	z	NOUN
cana-3320	203	9	for	for	ADP
cana-3320	203	10	each	each	DET
cana-3320	203	11	t	t	NOUN
cana-3320	203	12	∈	∈	PROPN
cana-3320	204	1	[	[	X
cana-3320	204	2	0	0	NUM
cana-3320	204	3	,	,	PUNCT
cana-3320	204	4	1	1	NUM
cana-3320	204	5	]	]	PUNCT
cana-3320	204	6	.	.	PUNCT
cana-3320	205	1	let	let	VERB
cana-3320	205	2	t	t	NOUN
cana-3320	205	3	=	=	SYM
cana-3320	205	4	min{<(ð1	min{<(ð1	NOUN
cana-3320	205	5	,	,	PUNCT
cana-3320	205	6	̌a	̌a	NOUN
cana-3320	205	7	)	)	PUNCT
cana-3320	205	8	,	,	PUNCT
cana-3320	205	9	<	<	X
cana-3320	205	10	(	(	PUNCT
cana-3320	205	11	ð2	ð2	NOUN
cana-3320	205	12	,	,	PUNCT
cana-3320	205	13	̌a	̌a	NOUN
cana-3320	205	14	)	)	PUNCT
cana-3320	205	15	,	,	PUNCT
cana-3320	205	16	<	<	X
cana-3320	205	17	(	(	PUNCT
cana-3320	205	18	ð3	ð3	NOUN
cana-3320	205	19	,	,	PUNCT
cana-3320	205	20	̌a	̌a	NOUN
cana-3320	205	21	)	)	PUNCT
cana-3320	205	22	}	}	PUNCT
cana-3320	205	23	.	.	PUNCT
cana-3320	206	1	then	then	ADV
cana-3320	206	2	ð1	ð1	NOUN
cana-3320	206	3	,	,	PUNCT
cana-3320	206	4	ð2	ð2	PROPN
cana-3320	206	5	,	,	PUNCT
cana-3320	206	6	ð3	ð3	PROPN
cana-3320	206	7	∈	∈	PROPN
cana-3320	207	1	<	<	X
cana-3320	207	2	t	t	X
cana-3320	207	3	for	for	ADP
cana-3320	207	4	each	each	DET
cana-3320	207	5	ð1	ð1	NOUN
cana-3320	207	6	,	,	PUNCT
cana-3320	207	7	ð2	ð2	PROPN
cana-3320	207	8	,	,	PUNCT
cana-3320	207	9	ð3	ð3	PROPN
cana-3320	207	10	∈	∈	PROPN
cana-3320	207	11	z	z	X
cana-3320	207	12	.	.	PUNCT
cana-3320	208	1	thus	thus	ADV
cana-3320	208	2	max{<(ð1ð2ð3	max{<(ð1ð2ð3	NOUN
cana-3320	208	3	,	,	PUNCT
cana-3320	208	4	̌a	̌a	NOUN
cana-3320	208	5	)	)	PUNCT
cana-3320	208	6	,	,	PUNCT
cana-3320	208	7	∂̃	∂̃	PROPN
cana-3320	208	8	}	}	PUNCT
cana-3320	208	9	>	>	PUNCT
cana-3320	208	10	t	t	PROPN
cana-3320	208	11	=	=	SYM
cana-3320	208	12	min{<(ð1	min{<(ð1	NOUN
cana-3320	208	13	,	,	PUNCT
cana-3320	208	14	̌a	̌a	NOUN
cana-3320	208	15	)	)	PUNCT
cana-3320	208	16	,	,	PUNCT
cana-3320	208	17	<	<	X
cana-3320	208	18	(	(	PUNCT
cana-3320	208	19	ð2	ð2	NOUN
cana-3320	208	20	,	,	PUNCT
cana-3320	208	21	̌a	̌a	NOUN
cana-3320	208	22	)	)	PUNCT
cana-3320	208	23	,	,	PUNCT
cana-3320	208	24	<	<	X
cana-3320	208	25	(	(	PUNCT
cana-3320	208	26	ð3	ð3	NOUN
cana-3320	208	27	,	,	PUNCT
cana-3320	208	28	̌a	̌a	NOUN
cana-3320	208	29	)	)	PUNCT
cana-3320	208	30	,	,	PUNCT
cana-3320	208	31	℘̃	℘̃	NOUN
cana-3320	208	32	}	}	PUNCT
cana-3320	208	33	.	.	PUNCT
cana-3320	209	1	let	let	VERB
cana-3320	209	2	t	t	NOUN
cana-3320	209	3	=	=	SYM
cana-3320	209	4	max{=(ð1	max{=(ð1	PROPN
cana-3320	209	5	,	,	PUNCT
cana-3320	209	6	̌a	̌a	NOUN
cana-3320	209	7	)	)	PUNCT
cana-3320	209	8	,	,	PUNCT
cana-3320	209	9	=(	=(	PROPN
cana-3320	209	10	ð2	ð2	PROPN
cana-3320	209	11	,	,	PUNCT
cana-3320	209	12	̌a	̌a	NOUN
cana-3320	209	13	)	)	PUNCT
cana-3320	209	14	,	,	PUNCT
cana-3320	209	15	=(	=(	PROPN
cana-3320	209	16	ð3	ð3	PROPN
cana-3320	209	17	,	,	PUNCT
cana-3320	209	18	̌a	̌a	NOUN
cana-3320	209	19	)	)	PUNCT
cana-3320	209	20	}	}	PUNCT
cana-3320	209	21	.	.	PUNCT
cana-3320	210	1	then	then	ADV
cana-3320	210	2	ð1	ð1	NOUN
cana-3320	210	3	,	,	PUNCT
cana-3320	210	4	ð2	ð2	PROPN
cana-3320	210	5	,	,	PUNCT
cana-3320	210	6	ð3	ð3	PROPN
cana-3320	210	7	∈	∈	PROPN
cana-3320	211	1	=	=	NOUN
cana-3320	211	2	t	t	PROPN
cana-3320	211	3	for	for	ADP
cana-3320	211	4	each	each	DET
cana-3320	211	5	ð1	ð1	NOUN
cana-3320	211	6	,	,	PUNCT
cana-3320	211	7	ð2	ð2	PROPN
cana-3320	211	8	,	,	PUNCT
cana-3320	211	9	ð3	ð3	PROPN
cana-3320	211	10	∈	∈	PROPN
cana-3320	211	11	z	z	X
cana-3320	211	12	.	.	PUNCT
cana-3320	212	1	thus	thus	ADV
cana-3320	212	2	min{=(ð1ð2ð3	min{=(ð1ð2ð3	NOUN
cana-3320	212	3	,	,	PUNCT
cana-3320	212	4	̌a	̌a	NOUN
cana-3320	212	5	)	)	PUNCT
cana-3320	212	6	,	,	PUNCT
cana-3320	212	7	∂̃	∂̃	NOUN
cana-3320	212	8	}	}	PUNCT
cana-3320	212	9	6	6	NUM
cana-3320	212	10	t	t	NOUN
cana-3320	212	11	=	=	SYM
cana-3320	212	12	max{=(ð1	max{=(ð1	PROPN
cana-3320	212	13	,	,	PUNCT
cana-3320	212	14	̌a	̌a	NOUN
cana-3320	212	15	)	)	PUNCT
cana-3320	212	16	,	,	PUNCT
cana-3320	212	17	=(	=(	PROPN
cana-3320	212	18	ð2	ð2	PROPN
cana-3320	212	19	,	,	PUNCT
cana-3320	212	20	̌a	̌a	NOUN
cana-3320	212	21	)	)	PUNCT
cana-3320	212	22	,	,	PUNCT
cana-3320	212	23	=(	=(	PROPN
cana-3320	212	24	ð3	ð3	PROPN
cana-3320	212	25	,	,	PUNCT
cana-3320	212	26	̌a	̌a	NOUN
cana-3320	212	27	)	)	PUNCT
cana-3320	212	28	,	,	PUNCT
cana-3320	212	29	℘̃	℘̃	PROPN
cana-3320	212	30	}	}	PUNCT
cana-3320	212	31	.	.	PUNCT
cana-3320	213	1	this	this	PRON
cana-3320	213	2	shows	show	VERB
cana-3320	213	3	that	that	SCONJ
cana-3320	213	4	~t	~t	PUNCT
cana-3320	213	5	is	be	AUX
cana-3320	213	6	iqvfss	iqvfss	ADJ
cana-3320	213	7	of	of	ADP
cana-3320	213	8	z	z	NOUN
cana-3320	213	9	.	.	PUNCT
cana-3320	214	1	conversely	conversely	ADV
cana-3320	214	2	,	,	PUNCT
cana-3320	214	3	assume	assume	VERB
cana-3320	214	4	that	that	SCONJ
cana-3320	214	5	~t	~t	PUNCT
cana-3320	214	6	is	be	AUX
cana-3320	214	7	a	a	DET
cana-3320	214	8	iqvfss	iqvfss	NOUN
cana-3320	214	9	of	of	ADP
cana-3320	214	10	z	z	PROPN
cana-3320	214	11	.	.	PUNCT
cana-3320	215	1	for	for	ADP
cana-3320	215	2	each	each	DET
cana-3320	215	3	t	t	NOUN
cana-3320	215	4	∈	∈	PROPN
cana-3320	216	1	[	[	X
cana-3320	216	2	0	0	NUM
cana-3320	216	3	,	,	PUNCT
cana-3320	216	4	1	1	NUM
cana-3320	216	5	]	]	PUNCT
cana-3320	216	6	and	and	CCONJ
cana-3320	216	7	ð1	ð1	NOUN
cana-3320	216	8	,	,	PUNCT
cana-3320	216	9	ð2	ð2	PROPN
cana-3320	216	10	,	,	PUNCT
cana-3320	216	11	ð3	ð3	PROPN
cana-3320	216	12	∈	∈	PROPN
cana-3320	216	13	<	<	AUX
cana-3320	216	14	t.	t.	X
cana-3320	216	15	we	we	PRON
cana-3320	216	16	have	have	VERB
cana-3320	216	17	<	<	X
cana-3320	216	18	(	(	PUNCT
cana-3320	216	19	ð1	ð1	NOUN
cana-3320	216	20	,	,	PUNCT
cana-3320	216	21	̌a	̌a	PROPN
cana-3320	216	22	)	)	PUNCT
cana-3320	216	23	>	>	X
cana-3320	217	1	t	t	PROPN
cana-3320	217	2	,	,	PUNCT
cana-3320	217	3	<	<	X
cana-3320	217	4	(	(	PUNCT
cana-3320	217	5	ð2	ð2	NOUN
cana-3320	217	6	,	,	PUNCT
cana-3320	217	7	̌a	̌a	PROPN
cana-3320	217	8	)	)	PUNCT
cana-3320	217	9	>	>	X
cana-3320	218	1	t	t	PROPN
cana-3320	218	2	,	,	PUNCT
cana-3320	218	3	<	<	X
cana-3320	218	4	(	(	PUNCT
cana-3320	218	5	ð3	ð3	NOUN
cana-3320	218	6	,	,	PUNCT
cana-3320	218	7	̌a	̌a	NOUN
cana-3320	218	8	)	)	PUNCT
cana-3320	218	9	>	>	X
cana-3320	219	1	t.	t.	PROPN
cana-3320	219	2	since	since	SCONJ
cana-3320	219	3	<	<	X
cana-3320	219	4	is	be	AUX
cana-3320	219	5	a	a	DET
cana-3320	219	6	ss	ss	NOUN
cana-3320	219	7	of	of	ADP
cana-3320	219	8	z	z	NOUN
cana-3320	219	9	,	,	PUNCT
cana-3320	219	10	max{<(ð1ð2ð3	max{<(ð1ð2ð3	NOUN
cana-3320	219	11	,	,	PUNCT
cana-3320	219	12	̌a	̌a	NOUN
cana-3320	219	13	)	)	PUNCT
cana-3320	219	14	,	,	PUNCT
cana-3320	219	15	∂̃	∂̃	NOUN
cana-3320	219	16	}	}	PUNCT
cana-3320	219	17	>	>	X
cana-3320	219	18	min{<(ð1	min{<(ð1	NOUN
cana-3320	219	19	,	,	PUNCT
cana-3320	219	20	̌a	̌a	PROPN
cana-3320	219	21	)	)	PUNCT
cana-3320	219	22	,	,	PUNCT
cana-3320	219	23	<	<	X
cana-3320	219	24	(	(	PUNCT
cana-3320	219	25	ð2	ð2	NOUN
cana-3320	219	26	,	,	PUNCT
cana-3320	219	27	̌a	̌a	NOUN
cana-3320	219	28	)	)	PUNCT
cana-3320	219	29	,	,	PUNCT
cana-3320	219	30	<	<	X
cana-3320	219	31	(	(	PUNCT
cana-3320	219	32	ð3	ð3	NOUN
cana-3320	219	33	,	,	PUNCT
cana-3320	219	34	̌a	̌a	NOUN
cana-3320	219	35	)	)	PUNCT
cana-3320	219	36	,	,	PUNCT
cana-3320	219	37	℘̃	℘̃	NOUN
cana-3320	219	38	}	}	PUNCT
cana-3320	219	39	>	>	PUNCT
cana-3320	219	40	t.	t.	NOUN
cana-3320	220	1	this	this	PRON
cana-3320	220	2	implies	imply	VERB
cana-3320	220	3	that	that	SCONJ
cana-3320	220	4	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	220	5	∈	∈	PROPN
cana-3320	220	6	<	<	X
cana-3320	220	7	t.	t.	X
cana-3320	220	8	we	we	PRON
cana-3320	220	9	have	have	VERB
cana-3320	220	10	=(	=(	NOUN
cana-3320	220	11	ð1	ð1	NOUN
cana-3320	220	12	,	,	PUNCT
cana-3320	220	13	̌a	̌a	NOUN
cana-3320	220	14	)	)	PUNCT
cana-3320	220	15	6	6	NUM
cana-3320	220	16	t	t	PROPN
cana-3320	220	17	,	,	PUNCT
cana-3320	220	18	=(	=(	PROPN
cana-3320	220	19	ð2	ð2	PROPN
cana-3320	220	20	,	,	PUNCT
cana-3320	220	21	̌a	̌a	PROPN
cana-3320	220	22	)	)	PUNCT
cana-3320	220	23	6	6	NUM
cana-3320	220	24	t	t	PROPN
cana-3320	220	25	,	,	PUNCT
cana-3320	220	26	=(	=(	PROPN
cana-3320	220	27	ð3	ð3	PROPN
cana-3320	220	28	,	,	PUNCT
cana-3320	220	29	̌a	̌a	NOUN
cana-3320	220	30	)	)	PUNCT
cana-3320	220	31	6	6	NUM
cana-3320	220	32	t.	t.	NOUN
cana-3320	220	33	since	since	SCONJ
cana-3320	220	34	=	=	PRON
cana-3320	220	35	is	be	AUX
cana-3320	220	36	a	a	DET
cana-3320	220	37	ss	ss	NOUN
cana-3320	220	38	of	of	ADP
cana-3320	220	39	z	z	NOUN
cana-3320	220	40	,	,	PUNCT
cana-3320	220	41	min{=(ð1ð2ð3	min{=(ð1ð2ð3	NOUN
cana-3320	220	42	,	,	PUNCT
cana-3320	220	43	̌a	̌a	NOUN
cana-3320	220	44	)	)	PUNCT
cana-3320	220	45	,	,	PUNCT
cana-3320	220	46	∂̃	∂̃	NOUN
cana-3320	220	47	}	}	PUNCT
cana-3320	220	48	6	6	NUM
cana-3320	220	49	max{=(ð1	max{=(ð1	NOUN
cana-3320	220	50	,	,	PUNCT
cana-3320	220	51	̌a	̌a	NOUN
cana-3320	220	52	)	)	PUNCT
cana-3320	220	53	,	,	PUNCT
cana-3320	220	54	=(	=(	PROPN
cana-3320	220	55	ð2	ð2	PROPN
cana-3320	220	56	,	,	PUNCT
cana-3320	220	57	̌a	̌a	NOUN
cana-3320	220	58	)	)	PUNCT
cana-3320	220	59	,	,	PUNCT
cana-3320	220	60	=(	=(	PROPN
cana-3320	220	61	ð3	ð3	PROPN
cana-3320	220	62	,	,	PUNCT
cana-3320	220	63	̌a	̌a	NOUN
cana-3320	220	64	)	)	PUNCT
cana-3320	220	65	,	,	PUNCT
cana-3320	220	66	℘̃	℘̃	NOUN
cana-3320	220	67	}	}	PUNCT
cana-3320	220	68	6	6	NUM
cana-3320	220	69	t.	t.	NOUN
cana-3320	220	70	this	this	PRON
cana-3320	220	71	implies	imply	VERB
cana-3320	220	72	that	that	SCONJ
cana-3320	220	73	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	220	74	∈	∈	PROPN
cana-3320	220	75	=	=	SYM
cana-3320	220	76	t.	t.	NOUN
cana-3320	220	77	therefore	therefore	ADV
cana-3320	220	78	~t	~t	PUNCT
cana-3320	220	79	is	be	AUX
cana-3320	220	80	a	a	DET
cana-3320	220	81	ss	ss	NOUN
cana-3320	220	82	of	of	ADP
cana-3320	220	83	z	z	NOUN
cana-3320	220	84	for	for	ADP
cana-3320	220	85	each	each	DET
cana-3320	220	86	t	t	NOUN
cana-3320	220	87	∈	∈	PROPN
cana-3320	220	88	(	(	PUNCT
cana-3320	220	89	∂̃	∂̃	PROPN
cana-3320	220	90	,	,	PUNCT
cana-3320	220	91	℘̃	℘̃	PROPN
cana-3320	220	92	]	]	PUNCT
cana-3320	220	93	.	.	PUNCT
cana-3320	221	1	example	example	NOUN
cana-3320	221	2	4.4	4.4	NUM
cana-3320	221	3	.	.	PUNCT
cana-3320	222	1	every	every	DET
cana-3320	222	2	iqvfss	iqvfss	NOUN
cana-3320	222	3	~	~	PUNCT
cana-3320	222	4	of	of	ADP
cana-3320	222	5	z	z	PROPN
cana-3320	222	6	is	be	AUX
cana-3320	222	7	a	a	DET
cana-3320	222	8	(	(	PUNCT
cana-3320	222	9	∂̃	∂̃	NOUN
cana-3320	222	10	,	,	PUNCT
cana-3320	222	11	℘̃)-iqvfss	℘̃)-iqvfss	NOUN
cana-3320	222	12	of	of	ADP
cana-3320	222	13	z	z	NOUN
cana-3320	222	14	,	,	PUNCT
cana-3320	222	15	but	but	CCONJ
cana-3320	222	16	reverse	reverse	VERB
cana-3320	222	17	need	need	AUX
cana-3320	222	18	not	not	PART
cana-3320	222	19	be	be	AUX
cana-3320	222	20	true	true	ADJ
cana-3320	222	21	.	.	PUNCT
cana-3320	223	1	<	<	X
cana-3320	223	2	̃(κ	̃(κ	NOUN
cana-3320	223	3	,	,	PUNCT
cana-3320	223	4	ǎ	ǎ	PROPN
cana-3320	223	5	)	)	PUNCT
cana-3320	223	6	=	=	PUNCT
cana-3320	224	1			PROPN
cana-3320	225	1	[	[	X
cana-3320	225	2	0.42	0.42	NUM
cana-3320	225	3	,	,	PUNCT
cana-3320	225	4	0.47	0.47	NUM
cana-3320	225	5	]	]	X
cana-3320	225	6	if	if	SCONJ
cana-3320	225	7	κ	κ	X
cana-3320	225	8	=	=	PUNCT
cana-3320	225	9	a	a	PRON
cana-3320	226	1	[	[	X
cana-3320	226	2	0.35	0.35	NUM
cana-3320	226	3	,	,	PUNCT
cana-3320	226	4	0.40	0.40	NUM
cana-3320	226	5	]	]	PUNCT
cana-3320	226	6	if	if	SCONJ
cana-3320	226	7	κ	κ	X
cana-3320	226	8	=	=	SYM
cana-3320	226	9	b	b	PROPN
cana-3320	227	1	[	[	X
cana-3320	227	2	0.25	0.25	NUM
cana-3320	227	3	,	,	PUNCT
cana-3320	227	4	0.30	0.30	NUM
cana-3320	227	5	]	]	PUNCT
cana-3320	227	6	if	if	SCONJ
cana-3320	227	7	κ	κ	X
cana-3320	227	8	=	=	SYM
cana-3320	227	9	c	c	PROPN
cana-3320	228	1	[	[	X
cana-3320	228	2	0.30	0.30	NUM
cana-3320	228	3	,	,	PUNCT
cana-3320	228	4	0.35	0.35	NUM
cana-3320	228	5	]	]	PUNCT
cana-3320	228	6	if	if	SCONJ
cana-3320	228	7	κ	κ	X
cana-3320	228	8	=	=	SYM
cana-3320	228	9	d	d	NOUN
cana-3320	228	10	=	=	NOUN
cana-3320	228	11	̃(κ	̃(κ	NOUN
cana-3320	228	12	,	,	PUNCT
cana-3320	228	13	ǎ	ǎ	PROPN
cana-3320	228	14	)	)	PUNCT
cana-3320	228	15	=	=	PUNCT
cana-3320	229	1			PROPN
cana-3320	230	1	[	[	X
cana-3320	230	2	0.27	0.27	NUM
cana-3320	230	3	,	,	PUNCT
cana-3320	230	4	0.32	0.32	NUM
cana-3320	230	5	]	]	PUNCT
cana-3320	230	6	if	if	SCONJ
cana-3320	230	7	κ	κ	X
cana-3320	230	8	=	=	PUNCT
cana-3320	230	9	a	a	PRON
cana-3320	231	1	[	[	X
cana-3320	231	2	0.32	0.32	NUM
cana-3320	231	3	,	,	PUNCT
cana-3320	231	4	0.37	0.37	NUM
cana-3320	231	5	]	]	PUNCT
cana-3320	231	6	if	if	SCONJ
cana-3320	231	7	κ	κ	X
cana-3320	231	8	=	=	SYM
cana-3320	231	9	b	b	PROPN
cana-3320	232	1	[	[	X
cana-3320	232	2	0.42	0.42	NUM
cana-3320	232	3	,	,	PUNCT
cana-3320	232	4	0.47	0.47	NUM
cana-3320	232	5	]	]	X
cana-3320	232	6	if	if	SCONJ
cana-3320	232	7	κ	κ	X
cana-3320	232	8	=	=	SYM
cana-3320	232	9	c	c	PROPN
cana-3320	233	1	[	[	X
cana-3320	233	2	0.37	0.37	NUM
cana-3320	233	3	,	,	PUNCT
cana-3320	233	4	0.42	0.42	NUM
cana-3320	233	5	]	]	PUNCT
cana-3320	233	6	if	if	SCONJ
cana-3320	233	7	κ	κ	X
cana-3320	234	1	=	=	SYM
cana-3320	234	2	d	d	NOUN
cana-3320	234	3	here	here	ADV
cana-3320	234	4	,	,	PUNCT
cana-3320	234	5	~	~	PUNCT
cana-3320	234	6	is	be	AUX
cana-3320	234	7	a	a	DET
cana-3320	234	8	(	(	PUNCT
cana-3320	234	9	[	[	X
cana-3320	234	10	0.33	0.33	NUM
cana-3320	234	11	,	,	PUNCT
cana-3320	234	12	0.38	0.38	NUM
cana-3320	234	13	]	]	PUNCT
cana-3320	234	14	,	,	PUNCT
cana-3320	234	15	[	[	X
cana-3320	234	16	0.47	0.47	NUM
cana-3320	234	17	,	,	PUNCT
cana-3320	234	18	0.52])-iqvfss	0.52])-iqvfss	NOUN
cana-3320	234	19	of	of	ADP
cana-3320	234	20	z	z	NOUN
cana-3320	234	21	,	,	PUNCT
cana-3320	234	22	but	but	CCONJ
cana-3320	234	23	not	not	PART
cana-3320	234	24	a	a	DET
cana-3320	234	25	iqvfss	iqvfss	NOUN
cana-3320	234	26	.	.	PUNCT
cana-3320	235	1	since	since	SCONJ
cana-3320	235	2	<	<	X
cana-3320	235	3	̃(dbd	̃(dbd	PROPN
cana-3320	235	4	)	)	PUNCT
cana-3320	235	5	=	=	NOUN
cana-3320	235	6	0.25	0.25	NUM
cana-3320	235	7	6	6	NUM
cana-3320	235	8	>	>	X
cana-3320	235	9	min{<̃(d	min{<̃(d	ADJ
cana-3320	235	10	,	,	PUNCT
cana-3320	235	11	q	q	NOUN
cana-3320	235	12	)	)	PUNCT
cana-3320	235	13	,	,	PUNCT
cana-3320	235	14	<	<	X
cana-3320	235	15	̃(d	̃(d	ADJ
cana-3320	235	16	,	,	PUNCT
cana-3320	235	17	q	q	NOUN
cana-3320	235	18	)	)	PUNCT
cana-3320	235	19	}	}	PUNCT
cana-3320	235	20	=	=	SYM
cana-3320	235	21	0.30	0.30	NUM
cana-3320	235	22	and	and	CCONJ
cana-3320	235	23	=	=	NUM
cana-3320	235	24	̃(dbd	̃(dbd	NOUN
cana-3320	235	25	)	)	PUNCT
cana-3320	235	26	=	=	SYM
cana-3320	235	27	0.42	0.42	NUM
cana-3320	235	28	66	66	NUM
cana-3320	235	29	max{=̃(d	max{=̃(d	NOUN
cana-3320	235	30	,	,	PUNCT
cana-3320	235	31	q	q	NOUN
cana-3320	235	32	)	)	PUNCT
cana-3320	235	33	,	,	PUNCT
cana-3320	235	34	=	=	NOUN
cana-3320	235	35	̃(d	̃(d	ADJ
cana-3320	235	36	,	,	PUNCT
cana-3320	235	37	q	q	NOUN
cana-3320	235	38	)	)	PUNCT
cana-3320	235	39	}	}	PUNCT
cana-3320	235	40	=	=	SYM
cana-3320	235	41	0.37	0.37	NUM
cana-3320	235	42	.	.	PUNCT
cana-3320	235	43	definition	definition	NOUN
cana-3320	235	44	4.5	4.5	NUM
cana-3320	235	45	.	.	PUNCT
cana-3320	236	1	if	if	SCONJ
cana-3320	236	2	ii	ii	PROPN
cana-3320	236	3	is	be	AUX
cana-3320	236	4	the	the	DET
cana-3320	236	5	characteristic	characteristic	ADJ
cana-3320	236	6	function	function	NOUN
cana-3320	236	7	is	be	AUX
cana-3320	236	8	defined	define	VERB
cana-3320	236	9	as	as	ADP
cana-3320	236	10	(	(	PUNCT
cana-3320	236	11	i	i	X
cana-3320	236	12	>	>	X
cana-3320	236	13	i	i	PROPN
cana-3320	236	14	)	)	PUNCT
cana-3320	236	15	℘̃	℘̃	PROPN
cana-3320	236	16	∂̃	∂̃	PROPN
cana-3320	236	17	(	(	PUNCT
cana-3320	236	18	ð1	ð1	PROPN
cana-3320	236	19	,	,	PUNCT
cana-3320	236	20	ǎ	ǎ	PROPN
cana-3320	236	21	)	)	PUNCT
cana-3320	236	22	=	=	SYM
cana-3320	236	23	{	{	PUNCT
cana-3320	236	24	℘̃	℘̃	PROPN
cana-3320	236	25	if	if	SCONJ
cana-3320	236	26	ð1	ð1	NOUN
cana-3320	236	27	∈	∈	PROPN
cana-3320	236	28	(	(	PUNCT
cana-3320	236	29	i	i	NOUN
cana-3320	236	30	]	]	PUNCT
cana-3320	236	31	∂̃	∂̃	PROPN
cana-3320	236	32	if	if	SCONJ
cana-3320	236	33	ð1	ð1	NOUN
cana-3320	236	34	/∈	/∈	PUNCT
cana-3320	237	1	(	(	PUNCT
cana-3320	237	2	i	i	NOUN
cana-3320	237	3	]	]	X
cana-3320	237	4	(	(	PUNCT
cana-3320	237	5	iz	iz	INTJ
cana-3320	237	6	i	i	NOUN
cana-3320	237	7	)	)	PUNCT
cana-3320	237	8	℘̃	℘̃	PROPN
cana-3320	237	9	∂̃	∂̃	PROPN
cana-3320	237	10	(	(	PUNCT
cana-3320	237	11	ð1	ð1	PROPN
cana-3320	237	12	,	,	PUNCT
cana-3320	237	13	ǎ	ǎ	PROPN
cana-3320	237	14	)	)	PUNCT
cana-3320	237	15	=	=	PRON
cana-3320	237	16	{	{	PUNCT
cana-3320	237	17	∂̃	∂̃	NOUN
cana-3320	237	18	if	if	SCONJ
cana-3320	237	19	ð1	ð1	NOUN
cana-3320	237	20	∈	∈	PROPN
cana-3320	237	21	(	(	PUNCT
cana-3320	237	22	i	i	NOUN
cana-3320	237	23	]	]	X
cana-3320	237	24	℘̃	℘̃	PROPN
cana-3320	237	25	if	if	SCONJ
cana-3320	237	26	ð1	ð1	NOUN
cana-3320	237	27	/∈	/∈	PUNCT
cana-3320	238	1	(	(	PUNCT
cana-3320	238	2	i	i	NOUN
cana-3320	238	3	]	]	PUNCT
cana-3320	238	4	theorem	theorem	VERB
cana-3320	238	5	4.6	4.6	NUM
cana-3320	238	6	.	.	PUNCT
cana-3320	239	1	a	a	DET
cana-3320	239	2	non	non	X
cana-3320	239	3	empty	empty	ADJ
cana-3320	239	4	subset	subset	NOUN
cana-3320	239	5	i	i	PRON
cana-3320	239	6	of	of	ADP
cana-3320	239	7	z	z	PROPN
cana-3320	239	8	is	be	AUX
cana-3320	239	9	a	a	DET
cana-3320	239	10	ss	ss	NOUN
cana-3320	240	1	[	[	X
cana-3320	240	2	li	li	PROPN
cana-3320	240	3	,	,	PUNCT
cana-3320	240	4	laiqv	laiqv	PROPN
cana-3320	240	5	f	f	PROPN
cana-3320	240	6	,	,	PUNCT
cana-3320	240	7	ri	ri	PROPN
cana-3320	240	8	,	,	PUNCT
cana-3320	240	9	tbi	tbi	PROPN
cana-3320	240	10	]	]	PUNCT
cana-3320	240	11	of	of	ADP
cana-3320	240	12	z	z	NOUN
cana-3320	240	13	if	if	SCONJ
cana-3320	240	14	and	and	CCONJ
cana-3320	240	15	only	only	ADV
cana-3320	240	16	if	if	SCONJ
cana-3320	240	17	subset	subset	VERB
cana-3320	240	18	i	i	PRON
cana-3320	240	19	(	(	PUNCT
cana-3320	240	20	i	i	NOUN
cana-3320	240	21	]	]	X
cana-3320	240	22	is	be	AUX
cana-3320	240	23	a	a	DET
cana-3320	240	24	(	(	PUNCT
cana-3320	240	25	∂̃	∂̃	PROPN
cana-3320	240	26	,	,	PUNCT
cana-3320	240	27	℘̃)-iqv	℘̃)-iqv	PROPN
cana-3320	240	28	fss[iqv	fss[iqv	PROPN
cana-3320	240	29	fli	fli	NOUN
cana-3320	240	30	,	,	PUNCT
cana-3320	240	31	iqv	iqv	ADJ
cana-3320	240	32	flati	flati	NOUN
cana-3320	240	33	,	,	PUNCT
cana-3320	240	34	iqv	iqv	NOUN
cana-3320	240	35	fri	fri	NOUN
cana-3320	240	36	,	,	PUNCT
cana-3320	240	37	iqv	iqv	PROPN
cana-3320	240	38	fbi	fbi	PROPN
cana-3320	240	39	]	]	PUNCT
cana-3320	240	40	of	of	ADP
cana-3320	240	41	z	z	PROPN
cana-3320	240	42	.	.	PUNCT
cana-3320	241	1	proof	proof	NOUN
cana-3320	241	2	.	.	PUNCT
cana-3320	242	1	assume	assume	VERB
cana-3320	242	2	that	that	SCONJ
cana-3320	242	3	i	i	PRON
cana-3320	242	4	is	be	AUX
cana-3320	242	5	a	a	DET
cana-3320	242	6	ss	ss	NOUN
cana-3320	242	7	of	of	ADP
cana-3320	242	8	z	z	PROPN
cana-3320	242	9	.	.	PUNCT
cana-3320	243	1	then	then	ADV
cana-3320	243	2	i	i	PRON
cana-3320	243	3	(	(	PUNCT
cana-3320	243	4	i	i	NOUN
cana-3320	243	5	]	]	X
cana-3320	243	6	is	be	AUX
cana-3320	243	7	a	a	DET
cana-3320	243	8	iqvfss	iqvfss	NOUN
cana-3320	243	9	of	of	ADP
cana-3320	243	10	z	z	NOUN
cana-3320	243	11	and	and	CCONJ
cana-3320	243	12	hence	hence	ADV
cana-3320	243	13	i	i	PRON
cana-3320	243	14	(	(	PUNCT
cana-3320	243	15	i	i	NOUN
cana-3320	243	16	]	]	X
cana-3320	243	17	is	be	AUX
cana-3320	243	18	an	an	DET
cana-3320	243	19	(	(	PUNCT
cana-3320	243	20	∂̃	∂̃	NOUN
cana-3320	243	21	,	,	PUNCT
cana-3320	243	22	℘̃)-iqvfss	℘̃)-iqvfss	NOUN
cana-3320	243	23	of	of	ADP
cana-3320	243	24	z	z	PROPN
cana-3320	243	25	.	.	PUNCT
cana-3320	244	1	conversely	conversely	ADV
cana-3320	244	2	,	,	PUNCT
cana-3320	244	3	let	let	VERB
cana-3320	244	4	i	i	PRON
cana-3320	244	5	(	(	PUNCT
cana-3320	244	6	i	i	NOUN
cana-3320	244	7	]	]	X
cana-3320	244	8	is	be	AUX
cana-3320	244	9	an	an	DET
cana-3320	244	10	(	(	PUNCT
cana-3320	244	11	∂̃	∂̃	NOUN
cana-3320	244	12	,	,	PUNCT
cana-3320	244	13	℘̃)-iqvfss	℘̃)-iqvfss	NOUN
cana-3320	244	14	of	of	ADP
cana-3320	244	15	z	z	PROPN
cana-3320	244	16	.	.	PUNCT
cana-3320	245	1	let	let	VERB
cana-3320	245	2	ð1,ð2,ð3	ð1,ð2,ð3	PRON
cana-3320	246	1	∈	∈	PROPN
cana-3320	246	2	z	z	NOUN
cana-3320	246	3	be	be	AUX
cana-3320	246	4	such	such	ADJ
cana-3320	246	5	that	that	SCONJ
cana-3320	246	6	ð1,ð2,ð3	ð1,ð2,ð3	SYM
cana-3320	247	1	∈	∈	PROPN
cana-3320	247	2	(	(	PUNCT
cana-3320	247	3	i	i	NOUN
cana-3320	247	4	]	]	X
cana-3320	247	5	.	.	PUNCT
cana-3320	248	1	then	then	ADV
cana-3320	248	2	i	i	PRON
cana-3320	248	3	>	>	X
cana-3320	248	4	(	(	PUNCT
cana-3320	248	5	i	i	NOUN
cana-3320	248	6	]	]	X
cana-3320	248	7	(	(	PUNCT
cana-3320	248	8	ð1	ð1	NOUN
cana-3320	248	9	,	,	PUNCT
cana-3320	248	10	ǎ	ǎ	PROPN
cana-3320	248	11	)	)	PUNCT
cana-3320	248	12	=	=	SYM
cana-3320	248	13	℘̃,i	℘̃,i	NOUN
cana-3320	248	14	>	>	X
cana-3320	248	15	(	(	PUNCT
cana-3320	248	16	i	i	NOUN
cana-3320	248	17	]	]	X
cana-3320	248	18	(	(	PUNCT
cana-3320	248	19	ð2	ð2	PROPN
cana-3320	248	20	,	,	PUNCT
cana-3320	248	21	ǎ	ǎ	PROPN
cana-3320	248	22	)	)	PUNCT
cana-3320	248	23	=	=	SYM
cana-3320	248	24	℘̃,i	℘̃,i	NOUN
cana-3320	248	25	>	>	X
cana-3320	248	26	(	(	PUNCT
cana-3320	248	27	i	i	NOUN
cana-3320	248	28	]	]	X
cana-3320	248	29	(	(	PUNCT
cana-3320	248	30	ð3	ð3	PROPN
cana-3320	248	31	,	,	PUNCT
cana-3320	248	32	ǎ	ǎ	PROPN
cana-3320	248	33	)	)	PUNCT
cana-3320	248	34	=	=	PUNCT
cana-3320	249	1	℘̃.	℘̃.	ADP
cana-3320	249	2	since	since	SCONJ
cana-3320	249	3	i	i	PRON
cana-3320	249	4	>	>	X
cana-3320	249	5	(	(	PUNCT
cana-3320	249	6	i	i	NOUN
cana-3320	249	7	]	]	X
cana-3320	249	8	is	be	AUX
cana-3320	249	9	a	a	DET
cana-3320	249	10	(	(	PUNCT
cana-3320	249	11	∂̃	∂̃	PROPN
cana-3320	249	12	,	,	PUNCT
cana-3320	249	13	℘̃)iqvfss	℘̃)iqvfss	PRON
cana-3320	249	14	.	.	PUNCT
cana-3320	250	1	consider	consider	VERB
cana-3320	250	2	max{i	max{i	ADJ
cana-3320	250	3	>	>	X
cana-3320	250	4	(	(	PUNCT
cana-3320	250	5	i	i	NOUN
cana-3320	250	6	]	]	X
cana-3320	250	7	(	(	PUNCT
cana-3320	250	8	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	250	9	,	,	PUNCT
cana-3320	250	10	ǎ	ǎ	NOUN
cana-3320	250	11	)	)	PUNCT
cana-3320	250	12	,	,	PUNCT
cana-3320	250	13	∂̃	∂̃	PROPN
cana-3320	250	14	}	}	PUNCT
cana-3320	250	15	>	>	X
cana-3320	250	16	min{i	min{i	PROPN
cana-3320	250	17	>	>	X
cana-3320	250	18	(	(	PUNCT
cana-3320	250	19	i	i	NOUN
cana-3320	250	20	]	]	X
cana-3320	250	21	(	(	PUNCT
cana-3320	250	22	ð1	ð1	NOUN
cana-3320	250	23	,	,	PUNCT
cana-3320	250	24	ǎ),i	ǎ),i	PROPN
cana-3320	250	25	>	>	X
cana-3320	250	26	(	(	PUNCT
cana-3320	250	27	i	i	NOUN
cana-3320	250	28	]	]	X
cana-3320	250	29	(	(	PUNCT
cana-3320	250	30	ð2	ð2	PROPN
cana-3320	250	31	,	,	PUNCT
cana-3320	250	32	ǎ),i	ǎ),i	PROPN
cana-3320	250	33	>	>	X
cana-3320	250	34	(	(	PUNCT
cana-3320	250	35	i	i	NOUN
cana-3320	250	36	]	]	X
cana-3320	250	37	(	(	PUNCT
cana-3320	250	38	ð3	ð3	PROPN
cana-3320	250	39	,	,	PUNCT
cana-3320	250	40	ǎ	ǎ	PROPN
cana-3320	250	41	)	)	PUNCT
cana-3320	250	42	,	,	PUNCT
cana-3320	250	43	℘̃	℘̃	NOUN
cana-3320	250	44	}	}	PUNCT
cana-3320	250	45	=	=	SYM
cana-3320	250	46	min{℘̃	min{℘̃	PROPN
cana-3320	250	47	,	,	PUNCT
cana-3320	250	48	℘̃	℘̃	PROPN
cana-3320	250	49	,	,	PUNCT
cana-3320	250	50	℘̃	℘̃	PROPN
cana-3320	250	51	,	,	PUNCT
cana-3320	250	52	℘̃	℘̃	NOUN
cana-3320	250	53	}	}	PUNCT
cana-3320	250	54	=	=	SYM
cana-3320	250	55	℘̃	℘̃	PROPN
cana-3320	250	56	https://internationalpubls.com	https://internationalpubls.com	X
cana-3320	250	57	582	582	NUM
cana-3320	250	58	communications	communication	NOUN
cana-3320	250	59	on	on	ADP
cana-3320	250	60	applied	apply	VERB
cana-3320	250	61	nonlinear	nonlinear	ADJ
cana-3320	250	62	analysis	analysis	NOUN
cana-3320	250	63	issn	issn	NOUN
cana-3320	250	64	:	:	PUNCT
cana-3320	250	65	1074	1074	NUM
cana-3320	250	66	-	-	PUNCT
cana-3320	250	67	133x	133x	NUM
cana-3320	250	68	vol	vol	NOUN
cana-3320	250	69	32	32	NUM
cana-3320	250	70	no	no	NOUN
cana-3320	250	71	.	.	PUNCT
cana-3320	251	1	6s	6s	NUM
cana-3320	251	2	(	(	PUNCT
cana-3320	251	3	2025	2025	NUM
cana-3320	251	4	)	)	PUNCT
cana-3320	251	5	as	as	ADP
cana-3320	251	6	∂̃	∂̃	NOUN
cana-3320	251	7	≺	≺	NOUN
cana-3320	251	8	℘̃	℘̃	PROPN
cana-3320	251	9	,	,	PUNCT
cana-3320	251	10	this	this	PRON
cana-3320	251	11	implies	imply	VERB
cana-3320	251	12	that	that	SCONJ
cana-3320	251	13	i	i	PRON
cana-3320	251	14	>	>	X
cana-3320	251	15	(	(	PUNCT
cana-3320	251	16	i	i	NOUN
cana-3320	251	17	]	]	X
cana-3320	251	18	(	(	PUNCT
cana-3320	251	19	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	251	20	,	,	PUNCT
cana-3320	251	21	ǎ	ǎ	PROPN
cana-3320	251	22	)	)	PUNCT
cana-3320	251	23	>	>	X
cana-3320	251	24	℘̃.	℘̃.	ADP
cana-3320	251	25	thus	thus	ADV
cana-3320	251	26	ð1ð2ð3	ð1ð2ð3	ADP
cana-3320	251	27	∈	∈	PROPN
cana-3320	251	28	(	(	PUNCT
cana-3320	251	29	i	i	NOUN
cana-3320	251	30	]	]	X
cana-3320	251	31	.	.	PUNCT
cana-3320	252	1	thus	thus	ADV
cana-3320	252	2	ð1ð2ð3	ð1ð2ð3	ADP
cana-3320	252	3	∈	∈	PROPN
cana-3320	252	4	(	(	PUNCT
cana-3320	252	5	i	i	NOUN
cana-3320	252	6	]	]	PUNCT
cana-3320	252	7	.	.	PUNCT
cana-3320	253	1	let	let	VERB
cana-3320	253	2	ð1,ð2,ð3	ð1,ð2,ð3	PRON
cana-3320	254	1	∈	∈	PROPN
cana-3320	254	2	z	z	NOUN
cana-3320	254	3	be	be	AUX
cana-3320	254	4	such	such	ADJ
cana-3320	254	5	that	that	SCONJ
cana-3320	254	6	ð1,ð2,ð3	ð1,ð2,ð3	SYM
cana-3320	255	1	∈	∈	PROPN
cana-3320	255	2	(	(	PUNCT
cana-3320	255	3	i	i	NOUN
cana-3320	255	4	]	]	PUNCT
cana-3320	255	5	.	.	PUNCT
cana-3320	256	1	then	then	ADV
cana-3320	256	2	iz	iz	INTJ
cana-3320	256	3	(	(	PUNCT
cana-3320	256	4	i	i	NOUN
cana-3320	256	5	]	]	X
cana-3320	256	6	(	(	PUNCT
cana-3320	256	7	ð1	ð1	NOUN
cana-3320	256	8	,	,	PUNCT
cana-3320	256	9	ǎ	ǎ	PROPN
cana-3320	256	10	)	)	PUNCT
cana-3320	256	11	=	=	SYM
cana-3320	256	12	∂̃,iz	∂̃,iz	ADJ
cana-3320	256	13	(	(	PUNCT
cana-3320	256	14	i	i	NOUN
cana-3320	256	15	]	]	X
cana-3320	256	16	(	(	PUNCT
cana-3320	256	17	ð2	ð2	PROPN
cana-3320	256	18	,	,	PUNCT
cana-3320	256	19	ǎ	ǎ	PROPN
cana-3320	256	20	)	)	PUNCT
cana-3320	256	21	=	=	SYM
cana-3320	256	22	∂̃,iz	∂̃,iz	ADJ
cana-3320	256	23	(	(	PUNCT
cana-3320	256	24	i	i	NOUN
cana-3320	256	25	]	]	X
cana-3320	256	26	(	(	PUNCT
cana-3320	256	27	ð3	ð3	PROPN
cana-3320	256	28	,	,	PUNCT
cana-3320	256	29	ǎ	ǎ	PROPN
cana-3320	256	30	)	)	PUNCT
cana-3320	256	31	=	=	PUNCT
cana-3320	257	1	∂̃.	∂̃.	NOUN
cana-3320	257	2	since	since	SCONJ
cana-3320	257	3	iz	iz	INTJ
cana-3320	257	4	(	(	PUNCT
cana-3320	257	5	i	i	NOUN
cana-3320	257	6	]	]	X
cana-3320	257	7	is	be	AUX
cana-3320	257	8	a	a	DET
cana-3320	257	9	(	(	PUNCT
cana-3320	257	10	∂̃	∂̃	PROPN
cana-3320	257	11	,	,	PUNCT
cana-3320	257	12	℘̃)iqvfss	℘̃)iqvfss	PRON
cana-3320	257	13	.	.	PUNCT
cana-3320	258	1	consider	consider	VERB
cana-3320	258	2	min{iz	min{iz	ADV
cana-3320	259	1	(	(	PUNCT
cana-3320	259	2	i	i	PRON
cana-3320	259	3	]	]	X
cana-3320	259	4	(	(	PUNCT
cana-3320	259	5	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	259	6	,	,	PUNCT
cana-3320	259	7	ǎ	ǎ	NOUN
cana-3320	259	8	)	)	PUNCT
cana-3320	259	9	,	,	PUNCT
cana-3320	259	10	∂̃	∂̃	NOUN
cana-3320	259	11	}	}	PUNCT
cana-3320	259	12	6	6	NUM
cana-3320	259	13	max{iz	max{iz	NOUN
cana-3320	259	14	(	(	PUNCT
cana-3320	259	15	i	i	PRON
cana-3320	259	16	]	]	X
cana-3320	259	17	(	(	PUNCT
cana-3320	259	18	ð1	ð1	NOUN
cana-3320	259	19	,	,	PUNCT
cana-3320	259	20	ǎ),iz	ǎ),iz	PROPN
cana-3320	259	21	(	(	PUNCT
cana-3320	259	22	i	i	NOUN
cana-3320	259	23	]	]	X
cana-3320	259	24	(	(	PUNCT
cana-3320	259	25	ð2	ð2	PROPN
cana-3320	259	26	,	,	PUNCT
cana-3320	259	27	ǎ),iz	ǎ),iz	PROPN
cana-3320	259	28	(	(	PUNCT
cana-3320	259	29	i	i	NOUN
cana-3320	259	30	]	]	X
cana-3320	259	31	(	(	PUNCT
cana-3320	259	32	ð3	ð3	PROPN
cana-3320	259	33	,	,	PUNCT
cana-3320	259	34	ǎ	ǎ	PROPN
cana-3320	259	35	)	)	PUNCT
cana-3320	259	36	,	,	PUNCT
cana-3320	259	37	℘̃	℘̃	NOUN
cana-3320	259	38	}	}	PUNCT
cana-3320	259	39	=	=	SYM
cana-3320	259	40	max{∂̃	max{∂̃	NOUN
cana-3320	259	41	,	,	PUNCT
cana-3320	259	42	∂̃	∂̃	NOUN
cana-3320	259	43	,	,	PUNCT
cana-3320	259	44	∂̃	∂̃	PROPN
cana-3320	259	45	,	,	PUNCT
cana-3320	259	46	℘̃	℘̃	NOUN
cana-3320	259	47	}	}	PUNCT
cana-3320	259	48	=	=	SYM
cana-3320	259	49	℘̃	℘̃	NOUN
cana-3320	259	50	as	as	ADP
cana-3320	259	51	∂̃	∂̃	PROPN
cana-3320	259	52	≺	≺	NOUN
cana-3320	259	53	℘̃	℘̃	PROPN
cana-3320	259	54	,	,	PUNCT
cana-3320	259	55	this	this	PRON
cana-3320	259	56	implies	imply	VERB
cana-3320	259	57	that	that	SCONJ
cana-3320	259	58	iz	iz	INTJ
cana-3320	259	59	(	(	PUNCT
cana-3320	259	60	i	i	NOUN
cana-3320	259	61	]	]	X
cana-3320	259	62	(	(	PUNCT
cana-3320	259	63	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	259	64	,	,	PUNCT
cana-3320	259	65	ǎ	ǎ	PROPN
cana-3320	259	66	)	)	PUNCT
cana-3320	259	67	6	6	NUM
cana-3320	259	68	∂̃.	∂̃.	NOUN
cana-3320	259	69	thus	thus	ADV
cana-3320	259	70	ð1ð2ð3	ð1ð2ð3	ADP
cana-3320	259	71	∈	∈	PROPN
cana-3320	259	72	(	(	PUNCT
cana-3320	259	73	i	i	NOUN
cana-3320	259	74	]	]	X
cana-3320	259	75	.	.	PUNCT
cana-3320	260	1	thus	thus	ADV
cana-3320	260	2	ð1ð2ð3	ð1ð2ð3	ADP
cana-3320	260	3	∈	∈	PROPN
cana-3320	260	4	(	(	PUNCT
cana-3320	260	5	i	i	NOUN
cana-3320	260	6	]	]	X
cana-3320	260	7	.	.	PUNCT
cana-3320	261	1	therefore	therefore	ADV
cana-3320	261	2	i	i	PRON
cana-3320	261	3	is	be	AUX
cana-3320	261	4	a	a	DET
cana-3320	261	5	ss	ss	NOUN
cana-3320	261	6	of	of	ADP
cana-3320	261	7	z	z	PROPN
cana-3320	261	8	.	.	PUNCT
cana-3320	262	1	let	let	VERB
cana-3320	262	2	ð1,ð2,ð3	ð1,ð2,ð3	PRON
cana-3320	263	1	∈	∈	PROPN
cana-3320	263	2	z	z	NOUN
cana-3320	263	3	be	be	AUX
cana-3320	263	4	such	such	ADJ
cana-3320	263	5	that	that	PRON
cana-3320	263	6	ð1,ð2,ð3	ð1,ð2,ð3	PUNCT
cana-3320	263	7	/∈	/∈	PUNCT
cana-3320	264	1	(	(	PUNCT
cana-3320	264	2	i	i	PRON
cana-3320	264	3	]	]	X
cana-3320	264	4	.	.	PUNCT
cana-3320	265	1	then	then	ADV
cana-3320	265	2	i	i	PRON
cana-3320	265	3	>	>	X
cana-3320	265	4	(	(	PUNCT
cana-3320	265	5	i	i	NOUN
cana-3320	265	6	]	]	X
cana-3320	265	7	(	(	PUNCT
cana-3320	265	8	ð1	ð1	NOUN
cana-3320	265	9	,	,	PUNCT
cana-3320	265	10	ǎ	ǎ	PROPN
cana-3320	265	11	)	)	PUNCT
cana-3320	265	12	=	=	SYM
cana-3320	265	13	∂̃,i	∂̃,i	PROPN
cana-3320	265	14	>	>	X
cana-3320	265	15	(	(	PUNCT
cana-3320	265	16	i	i	NOUN
cana-3320	265	17	]	]	X
cana-3320	265	18	(	(	PUNCT
cana-3320	265	19	ð2	ð2	PROPN
cana-3320	265	20	,	,	PUNCT
cana-3320	265	21	ǎ	ǎ	PROPN
cana-3320	265	22	)	)	PUNCT
cana-3320	265	23	=	=	SYM
cana-3320	266	1	∂̃,i	∂̃,i	PROPN
cana-3320	266	2	>	>	X
cana-3320	266	3	(	(	PUNCT
cana-3320	266	4	i	i	NOUN
cana-3320	266	5	]	]	X
cana-3320	266	6	(	(	PUNCT
cana-3320	266	7	ð3	ð3	PROPN
cana-3320	266	8	,	,	PUNCT
cana-3320	266	9	ǎ	ǎ	PROPN
cana-3320	266	10	)	)	PUNCT
cana-3320	267	1	=	=	PUNCT
cana-3320	267	2	∂̃.	∂̃.	NOUN
cana-3320	267	3	since	since	SCONJ
cana-3320	267	4	i	i	PRON
cana-3320	267	5	>	>	X
cana-3320	267	6	(	(	PUNCT
cana-3320	267	7	i	i	NOUN
cana-3320	267	8	]	]	X
cana-3320	267	9	is	be	AUX
cana-3320	267	10	a	a	DET
cana-3320	267	11	(	(	PUNCT
cana-3320	267	12	∂̃	∂̃	PROPN
cana-3320	267	13	,	,	PUNCT
cana-3320	267	14	℘̃)iqvfss	℘̃)iqvfss	NUM
cana-3320	267	15	.	.	PUNCT
cana-3320	268	1	max{i	max{i	X
cana-3320	268	2	>	>	X
cana-3320	268	3	(	(	PUNCT
cana-3320	268	4	i	i	NOUN
cana-3320	268	5	]	]	X
cana-3320	268	6	(	(	PUNCT
cana-3320	268	7	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	268	8	,	,	PUNCT
cana-3320	268	9	ǎ	ǎ	NOUN
cana-3320	268	10	)	)	PUNCT
cana-3320	268	11	,	,	PUNCT
cana-3320	268	12	∂̃	∂̃	PROPN
cana-3320	268	13	}	}	PUNCT
cana-3320	268	14	>	>	X
cana-3320	268	15	min{i	min{i	PROPN
cana-3320	268	16	>	>	X
cana-3320	268	17	(	(	PUNCT
cana-3320	268	18	i	i	NOUN
cana-3320	268	19	]	]	X
cana-3320	268	20	(	(	PUNCT
cana-3320	268	21	ð1	ð1	NOUN
cana-3320	268	22	,	,	PUNCT
cana-3320	268	23	ǎ),i	ǎ),i	PROPN
cana-3320	268	24	>	>	X
cana-3320	268	25	(	(	PUNCT
cana-3320	268	26	i	i	NOUN
cana-3320	268	27	]	]	X
cana-3320	268	28	(	(	PUNCT
cana-3320	268	29	ð2	ð2	PROPN
cana-3320	268	30	,	,	PUNCT
cana-3320	268	31	ǎ),i	ǎ),i	PROPN
cana-3320	268	32	>	>	X
cana-3320	268	33	(	(	PUNCT
cana-3320	268	34	i	i	NOUN
cana-3320	268	35	]	]	X
cana-3320	268	36	(	(	PUNCT
cana-3320	268	37	ð3	ð3	PROPN
cana-3320	268	38	,	,	PUNCT
cana-3320	268	39	ǎ	ǎ	PROPN
cana-3320	268	40	)	)	PUNCT
cana-3320	268	41	,	,	PUNCT
cana-3320	268	42	℘̃	℘̃	NOUN
cana-3320	268	43	}	}	PUNCT
cana-3320	268	44	=	=	PUNCT
cana-3320	268	45	min{∂̃	min{∂̃	X
cana-3320	268	46	,	,	PUNCT
cana-3320	268	47	∂̃	∂̃	PROPN
cana-3320	268	48	,	,	PUNCT
cana-3320	268	49	∂̃	∂̃	PROPN
cana-3320	268	50	,	,	PUNCT
cana-3320	268	51	℘̃	℘̃	NOUN
cana-3320	268	52	}	}	PUNCT
cana-3320	268	53	=	=	PUNCT
cana-3320	269	1	∂̃	∂̃	NOUN
cana-3320	269	2	as	as	ADP
cana-3320	269	3	∂̃	∂̃	PROPN
cana-3320	269	4	≺	≺	NOUN
cana-3320	269	5	℘̃	℘̃	PROPN
cana-3320	269	6	,	,	PUNCT
cana-3320	269	7	this	this	PRON
cana-3320	269	8	implies	imply	VERB
cana-3320	269	9	that	that	SCONJ
cana-3320	269	10	i	i	PRON
cana-3320	269	11	>	>	X
cana-3320	269	12	(	(	PUNCT
cana-3320	269	13	i	i	NOUN
cana-3320	269	14	]	]	X
cana-3320	269	15	(	(	PUNCT
cana-3320	269	16	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	269	17	,	,	PUNCT
cana-3320	269	18	ǎ	ǎ	PROPN
cana-3320	269	19	)	)	PUNCT
cana-3320	269	20	>	>	PUNCT
cana-3320	270	1	∂̃.	∂̃.	PROPN
cana-3320	270	2	thus	thus	ADV
cana-3320	270	3	ð1ð2ð3	ð1ð2ð3	ADP
cana-3320	270	4	6∈	6∈	PROPN
cana-3320	270	5	(	(	PUNCT
cana-3320	270	6	i	i	PRON
cana-3320	270	7	]	]	PUNCT
cana-3320	270	8	.	.	PUNCT
cana-3320	271	1	let	let	VERB
cana-3320	271	2	ð1,ð2,ð3	ð1,ð2,ð3	PRON
cana-3320	272	1	∈	∈	PROPN
cana-3320	272	2	z	z	NOUN
cana-3320	272	3	be	be	AUX
cana-3320	272	4	such	such	ADJ
cana-3320	272	5	that	that	PRON
cana-3320	272	6	ð1,ð2,ð3	ð1,ð2,ð3	PUNCT
cana-3320	272	7	/∈	/∈	PUNCT
cana-3320	273	1	(	(	PUNCT
cana-3320	273	2	i	i	PRON
cana-3320	273	3	]	]	X
cana-3320	273	4	.	.	PUNCT
cana-3320	274	1	then	then	ADV
cana-3320	274	2	iz	iz	INTJ
cana-3320	274	3	(	(	PUNCT
cana-3320	274	4	i	i	NOUN
cana-3320	274	5	]	]	X
cana-3320	274	6	(	(	PUNCT
cana-3320	274	7	ð1	ð1	NOUN
cana-3320	274	8	,	,	PUNCT
cana-3320	274	9	ǎ	ǎ	PROPN
cana-3320	274	10	)	)	PUNCT
cana-3320	274	11	=	=	SYM
cana-3320	275	1	℘̃,iz	℘̃,iz	PROPN
cana-3320	275	2	(	(	PUNCT
cana-3320	275	3	i	i	NOUN
cana-3320	275	4	]	]	X
cana-3320	275	5	(	(	PUNCT
cana-3320	275	6	ð2	ð2	PROPN
cana-3320	275	7	,	,	PUNCT
cana-3320	275	8	ǎ	ǎ	PROPN
cana-3320	275	9	)	)	PUNCT
cana-3320	275	10	=	=	SYM
cana-3320	276	1	℘̃,iz	℘̃,iz	PROPN
cana-3320	276	2	(	(	PUNCT
cana-3320	276	3	i	i	NOUN
cana-3320	276	4	]	]	X
cana-3320	276	5	(	(	PUNCT
cana-3320	276	6	ð3	ð3	PROPN
cana-3320	276	7	,	,	PUNCT
cana-3320	276	8	ǎ	ǎ	PROPN
cana-3320	276	9	)	)	PUNCT
cana-3320	276	10	=	=	PUNCT
cana-3320	277	1	℘̃.	℘̃.	ADV
cana-3320	277	2	since	since	SCONJ
cana-3320	277	3	iz	iz	INTJ
cana-3320	277	4	(	(	PUNCT
cana-3320	277	5	i	i	NOUN
cana-3320	277	6	]	]	X
cana-3320	277	7	is	be	AUX
cana-3320	277	8	a	a	DET
cana-3320	277	9	(	(	PUNCT
cana-3320	277	10	∂̃	∂̃	PROPN
cana-3320	277	11	,	,	PUNCT
cana-3320	277	12	℘̃)iqvfss	℘̃)iqvfss	NUM
cana-3320	277	13	.	.	PUNCT
cana-3320	278	1	min{iz	min{iz	PUNCT
cana-3320	279	1	(	(	PUNCT
cana-3320	279	2	i	i	PRON
cana-3320	279	3	]	]	X
cana-3320	279	4	(	(	PUNCT
cana-3320	279	5	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	279	6	,	,	PUNCT
cana-3320	279	7	ǎ	ǎ	NOUN
cana-3320	279	8	)	)	PUNCT
cana-3320	279	9	,	,	PUNCT
cana-3320	279	10	∂̃	∂̃	NOUN
cana-3320	279	11	}	}	PUNCT
cana-3320	279	12	6	6	NUM
cana-3320	279	13	max{iz	max{iz	NOUN
cana-3320	279	14	(	(	PUNCT
cana-3320	279	15	i	i	PRON
cana-3320	279	16	]	]	X
cana-3320	279	17	(	(	PUNCT
cana-3320	279	18	ð1	ð1	NOUN
cana-3320	279	19	,	,	PUNCT
cana-3320	279	20	ǎ),iz	ǎ),iz	PROPN
cana-3320	279	21	(	(	PUNCT
cana-3320	279	22	i	i	NOUN
cana-3320	279	23	]	]	X
cana-3320	279	24	(	(	PUNCT
cana-3320	279	25	ð2	ð2	PROPN
cana-3320	279	26	,	,	PUNCT
cana-3320	279	27	ǎ),iz	ǎ),iz	PROPN
cana-3320	279	28	(	(	PUNCT
cana-3320	279	29	i	i	NOUN
cana-3320	279	30	]	]	X
cana-3320	279	31	(	(	PUNCT
cana-3320	279	32	ð3	ð3	PROPN
cana-3320	279	33	,	,	PUNCT
cana-3320	279	34	ǎ	ǎ	PROPN
cana-3320	279	35	)	)	PUNCT
cana-3320	279	36	,	,	PUNCT
cana-3320	279	37	℘̃	℘̃	NOUN
cana-3320	279	38	}	}	PUNCT
cana-3320	279	39	=	=	SYM
cana-3320	279	40	max{℘̃	max{℘̃	NOUN
cana-3320	279	41	,	,	PUNCT
cana-3320	279	42	℘̃	℘̃	PROPN
cana-3320	279	43	,	,	PUNCT
cana-3320	279	44	℘̃	℘̃	PROPN
cana-3320	279	45	,	,	PUNCT
cana-3320	279	46	℘̃	℘̃	NOUN
cana-3320	279	47	}	}	PUNCT
cana-3320	279	48	=	=	SYM
cana-3320	279	49	℘̃	℘̃	NOUN
cana-3320	279	50	as	as	ADP
cana-3320	279	51	∂̃	∂̃	PROPN
cana-3320	279	52	≺	≺	NOUN
cana-3320	279	53	℘̃	℘̃	PROPN
cana-3320	279	54	,	,	PUNCT
cana-3320	279	55	this	this	PRON
cana-3320	279	56	implies	imply	VERB
cana-3320	279	57	that	that	SCONJ
cana-3320	279	58	iz	iz	INTJ
cana-3320	279	59	(	(	PUNCT
cana-3320	279	60	i	i	NOUN
cana-3320	279	61	]	]	X
cana-3320	279	62	(	(	PUNCT
cana-3320	279	63	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	279	64	,	,	PUNCT
cana-3320	279	65	ǎ	ǎ	PROPN
cana-3320	279	66	)	)	PUNCT
cana-3320	279	67	6	6	NUM
cana-3320	279	68	℘̃.	℘̃.	ADP
cana-3320	279	69	thus	thus	ADV
cana-3320	279	70	ð1ð2ð3	ð1ð2ð3	ADP
cana-3320	279	71	6∈	6∈	PROPN
cana-3320	279	72	(	(	PUNCT
cana-3320	279	73	i	i	PRON
cana-3320	279	74	]	]	X
cana-3320	279	75	.	.	PUNCT
cana-3320	280	1	therefore	therefore	ADV
cana-3320	280	2	i	i	PRON
cana-3320	280	3	is	be	AUX
cana-3320	280	4	a	a	DET
cana-3320	280	5	ss	ss	NOUN
cana-3320	280	6	of	of	ADP
cana-3320	280	7	z	z	PROPN
cana-3320	280	8	.	.	PUNCT
cana-3320	281	1	definition	definition	NOUN
cana-3320	281	2	4.7	4.7	NUM
cana-3320	281	3	.	.	PUNCT
cana-3320	282	1	for	for	ADP
cana-3320	282	2	three	three	NUM
cana-3320	282	3	iqvfss	iqvfss	NOUN
cana-3320	282	4	~	~	PROPN
cana-3320	282	5	,	,	PUNCT
cana-3320	282	6	ð2	ð2	PROPN
cana-3320	282	7	and	and	CCONJ
cana-3320	282	8	κ	κ	PROPN
cana-3320	282	9	of	of	ADP
cana-3320	282	10	z	z	NOUN
cana-3320	282	11	,	,	PUNCT
cana-3320	282	12	their	their	PRON
cana-3320	282	13	product	product	NOUN
cana-3320	282	14	~	~	PUNCT
cana-3320	282	15	∗	∗	NOUN
cana-3320	282	16	ð2	ð2	PROPN
cana-3320	282	17	∗	∗	NOUN
cana-3320	282	18	κ	κ	PROPN
cana-3320	282	19	is	be	AUX
cana-3320	282	20	defined	define	VERB
cana-3320	282	21	as	as	ADP
cana-3320	282	22	(	(	PUNCT
cana-3320	282	23	~	~	NOUN
cana-3320	282	24	>	>	X
cana-3320	282	25	∗	∗	X
cana-3320	282	26	ð>2	ð>2	PROPN
cana-3320	282	27	∗	∗	PROPN
cana-3320	282	28	κ>)(ð	κ>)(ð	PROPN
cana-3320	282	29	,	,	PUNCT
cana-3320	282	30	ǎ	ǎ	PROPN
cana-3320	282	31	)	)	PUNCT
cana-3320	282	32	=	=	PUNCT
cana-3320	283	1			PUNCT
cana-3320	283	2	sup	sup	NOUN
cana-3320	283	3	(	(	PUNCT
cana-3320	283	4	r	r	NOUN
cana-3320	283	5	,	,	PUNCT
cana-3320	283	6	s	s	PART
cana-3320	283	7	,	,	PUNCT
cana-3320	283	8	t)∈ið	t)∈ið	PROPN
cana-3320	283	9	{	{	PUNCT
cana-3320	283	10	~>(r)oð>2	~>(r)oð>2	X
cana-3320	283	11	(	(	PUNCT
cana-3320	283	12	s)oκ>(t	s)oκ>(t	NOUN
cana-3320	283	13	)	)	PUNCT
cana-3320	283	14	}	}	PUNCT
cana-3320	283	15	if	if	SCONJ
cana-3320	283	16	ið	ið	NOUN
cana-3320	283	17	6=	6=	ADP
cana-3320	283	18	0	0	NUM
cana-3320	284	1	[	[	X
cana-3320	284	2	0	0	NUM
cana-3320	284	3	,	,	PUNCT
cana-3320	284	4	0	0	NUM
cana-3320	284	5	]	]	PUNCT
cana-3320	284	6	otherwise	otherwise	ADV
cana-3320	284	7	(	(	PUNCT
cana-3320	284	8	~z	~z	NUM
cana-3320	284	9	∗	∗	NOUN
cana-3320	284	10	ðz2	ðz2	NOUN
cana-3320	284	11	∗	∗	NOUN
cana-3320	284	12	κz)(ð	κz)(ð	PROPN
cana-3320	284	13	,	,	PUNCT
cana-3320	284	14	ǎ	ǎ	PROPN
cana-3320	284	15	)	)	PUNCT
cana-3320	284	16	=	=	SYM
cana-3320	284	17			PROPN
cana-3320	284	18	inf	inf	NOUN
cana-3320	284	19	(	(	PUNCT
cana-3320	284	20	r	r	NOUN
cana-3320	284	21	,	,	PUNCT
cana-3320	284	22	s	s	X
cana-3320	284	23	,	,	PUNCT
cana-3320	284	24	t)∈ið	t)∈ið	PROPN
cana-3320	284	25	{	{	PUNCT
cana-3320	284	26	~z(r	~z(r	NOUN
cana-3320	284	27	)	)	PUNCT
cana-3320	285	1	m	m	VERB
cana-3320	285	2	ðz2	ðz2	NOUN
cana-3320	285	3	(	(	PUNCT
cana-3320	285	4	s	s	NOUN
cana-3320	285	5	)	)	PUNCT
cana-3320	285	6	m	m	NOUN
cana-3320	285	7	κz(t	κz(t	NOUN
cana-3320	285	8	)	)	PUNCT
cana-3320	285	9	}	}	PUNCT
cana-3320	285	10	if	if	SCONJ
cana-3320	285	11	ið	ið	NOUN
cana-3320	285	12	6=	6=	ADP
cana-3320	285	13	0	0	NUM
cana-3320	286	1	[	[	X
cana-3320	286	2	1	1	NUM
cana-3320	286	3	,	,	PUNCT
cana-3320	286	4	1	1	NUM
cana-3320	286	5	]	]	PUNCT
cana-3320	286	6	otherwise	otherwise	ADV
cana-3320	286	7	definition	definition	NOUN
cana-3320	286	8	4.8	4.8	NUM
cana-3320	286	9	.	.	PUNCT
cana-3320	287	1	let	let	VERB
cana-3320	287	2	~	~	PUNCT
cana-3320	287	3	be	be	AUX
cana-3320	287	4	subset	subset	VERB
cana-3320	287	5	of	of	ADP
cana-3320	287	6	z	z	NOUN
cana-3320	287	7	,	,	PUNCT
cana-3320	287	8	we	we	PRON
cana-3320	287	9	define	define	VERB
cana-3320	287	10	the	the	DET
cana-3320	287	11	subset	subset	NOUN
cana-3320	287	12	(	(	PUNCT
cana-3320	287	13	<	<	X
cana-3320	287	14	̃)℘∂	̃)℘∂	X
cana-3320	287	15	(	(	PUNCT
cana-3320	287	16	ð	ð	PROPN
cana-3320	287	17	,	,	PUNCT
cana-3320	287	18	ǎ	ǎ	PROPN
cana-3320	287	19	)	)	PUNCT
cana-3320	287	20	=	=	SYM
cana-3320	288	1	{	{	PUNCT
cana-3320	288	2	<	<	X
cana-3320	288	3	̃(ð	̃(ð	ADJ
cana-3320	288	4	,	,	PUNCT
cana-3320	288	5	ǎ)o℘̃	ǎ)o℘̃	NOUN
cana-3320	288	6	}	}	PUNCT
cana-3320	288	7	m	m	VERB
cana-3320	288	8	∂̃	∂̃	NOUN
cana-3320	288	9	,	,	PUNCT
cana-3320	288	10	(=	(=	ADV
cana-3320	288	11	̃)℘∂	̃)℘∂	X
cana-3320	288	12	(	(	PUNCT
cana-3320	288	13	ð	ð	PROPN
cana-3320	288	14	,	,	PUNCT
cana-3320	288	15	ǎ	ǎ	PROPN
cana-3320	288	16	)	)	PUNCT
cana-3320	288	17	=	=	PRON
cana-3320	289	1	{	{	PUNCT
cana-3320	289	2	=	=	SYM
cana-3320	289	3	̃(ð	̃(ð	ADJ
cana-3320	289	4	,	,	PUNCT
cana-3320	289	5	ǎ	ǎ	PROPN
cana-3320	289	6	)	)	PUNCT
cana-3320	289	7	m	m	VERB
cana-3320	289	8	℘̃}o∂̃	℘̃}o∂̃	NOUN
cana-3320	289	9	,	,	PUNCT
cana-3320	289	10	for	for	ADP
cana-3320	289	11	all	all	DET
cana-3320	289	12	ð	ð	PROPN
cana-3320	289	13	∈	∈	PROPN
cana-3320	289	14	z	z	NOUN
cana-3320	289	15	.	.	PUNCT
cana-3320	290	1	lemma	lemma	PROPN
cana-3320	290	2	4.9	4.9	NUM
cana-3320	290	3	.	.	PUNCT
cana-3320	291	1	let	let	VERB
cana-3320	291	2	i	i	PRON
cana-3320	291	3	,	,	PUNCT
cana-3320	291	4	i1	i1	PROPN
cana-3320	291	5	and	and	CCONJ
cana-3320	291	6	i2	i2	PROPN
cana-3320	291	7	be	be	VERB
cana-3320	291	8	subsets	subset	NOUN
cana-3320	291	9	of	of	ADP
cana-3320	291	10	z	z	NOUN
cana-3320	291	11	.	.	PUNCT
cana-3320	292	1	then	then	ADV
cana-3320	292	2	1	1	X
cana-3320	292	3	.	.	PUNCT
cana-3320	293	1	(	(	PUNCT
cana-3320	293	2	i	i	PRON
cana-3320	293	3	(	(	PUNCT
cana-3320	293	4	i	i	NOUN
cana-3320	293	5	]	]	X
cana-3320	293	6	oi	oi	PROPN
cana-3320	293	7	(	(	PUNCT
cana-3320	293	8	i1	i1	PROPN
cana-3320	293	9	]	]	PUNCT
cana-3320	293	10	oi	oi	PROPN
cana-3320	293	11	(	(	PUNCT
cana-3320	293	12	i2	i2	PROPN
cana-3320	293	13	]	]	PUNCT
cana-3320	293	14	)	)	PUNCT
cana-3320	293	15	℘̃	℘̃	PROPN
cana-3320	293	16	∂̃	∂̃	NOUN
cana-3320	293	17	=	=	SYM
cana-3320	293	18	(	(	PUNCT
cana-3320	293	19	i(ifi1fi2	i(ifi1fi2	PROPN
cana-3320	293	20	]	]	X
cana-3320	293	21	)	)	PUNCT
cana-3320	293	22	℘̃	℘̃	PROPN
cana-3320	293	23	∂̃	∂̃	NOUN
cana-3320	293	24	,	,	PUNCT
cana-3320	293	25	2	2	X
cana-3320	293	26	.	.	PUNCT
cana-3320	293	27	(	(	PUNCT
cana-3320	293	28	i	i	PRON
cana-3320	293	29	(	(	PUNCT
cana-3320	293	30	i	i	NOUN
cana-3320	293	31	]	]	X
cana-3320	293	32	m	m	VERB
cana-3320	293	33	i	i	INTJ
cana-3320	293	34	(	(	PUNCT
cana-3320	293	35	i1	i1	PROPN
cana-3320	293	36	]	]	PUNCT
cana-3320	293	37	m	m	VERB
cana-3320	293	38	i	i	PRON
cana-3320	293	39	(	(	PUNCT
cana-3320	293	40	i2	i2	PROPN
cana-3320	293	41	]	]	PUNCT
cana-3320	293	42	)	)	PUNCT
cana-3320	293	43	℘̃	℘̃	PROPN
cana-3320	293	44	∂̃	∂̃	NOUN
cana-3320	293	45	=	=	SYM
cana-3320	293	46	(	(	PUNCT
cana-3320	293	47	i(igi1gi2	i(igi1gi2	PROPN
cana-3320	293	48	]	]	PUNCT
cana-3320	293	49	)	)	PUNCT
cana-3320	293	50	℘̃	℘̃	PROPN
cana-3320	293	51	∂̃	∂̃	NOUN
cana-3320	293	52	,	,	PUNCT
cana-3320	293	53	3	3	X
cana-3320	293	54	.	.	PUNCT
cana-3320	293	55	(	(	PUNCT
cana-3320	293	56	i	i	PRON
cana-3320	293	57	(	(	PUNCT
cana-3320	293	58	i	i	NOUN
cana-3320	293	59	]	]	PUNCT
cana-3320	293	60	∗i(i1]∗i(i2	∗i(i1]∗i(i2	NUM
cana-3320	293	61	]	]	PUNCT
cana-3320	293	62	)	)	PUNCT
cana-3320	293	63	℘̃	℘̃	PROPN
cana-3320	293	64	∂̃	∂̃	NOUN
cana-3320	293	65	=	=	SYM
cana-3320	293	66	(	(	PUNCT
cana-3320	293	67	i(ii1i2	i(ii1i2	PROPN
cana-3320	293	68	]	]	PUNCT
cana-3320	293	69	)	)	PUNCT
cana-3320	293	70	℘̃	℘̃	PROPN
cana-3320	293	71	∂̃	∂̃	NOUN
cana-3320	293	72	.	.	PUNCT
cana-3320	294	1	proof	proof	NOUN
cana-3320	294	2	.	.	PUNCT
cana-3320	295	1	(	(	PUNCT
cana-3320	295	2	3	3	X
cana-3320	295	3	)	)	PUNCT
cana-3320	295	4	let	let	VERB
cana-3320	295	5	ð1	ð1	NOUN
cana-3320	295	6	∈	∈	PROPN
cana-3320	295	7	z	z	NOUN
cana-3320	295	8	.	.	PUNCT
cana-3320	296	1	if	if	SCONJ
cana-3320	296	2	ð1	ð1	PROPN
cana-3320	296	3	∈	∈	PROPN
cana-3320	296	4	(	(	PUNCT
cana-3320	296	5	ii1i2	ii1i2	PROPN
cana-3320	296	6	]	]	X
cana-3320	296	7	,	,	PUNCT
cana-3320	296	8	then	then	ADV
cana-3320	296	9	(	(	PUNCT
cana-3320	296	10	i(ii1i2])(ð1	i(ii1i2])(ð1	PROPN
cana-3320	296	11	,	,	PUNCT
cana-3320	296	12	ǎ	ǎ	PROPN
cana-3320	296	13	)	)	PUNCT
cana-3320	296	14	=	=	PUNCT
cana-3320	297	1	℘̃.	℘̃.	ADP
cana-3320	297	2	since	since	SCONJ
cana-3320	297	3	ð1	ð1	NOUN
cana-3320	297	4	6	6	NUM
cana-3320	297	5	abc	abc	PROPN
cana-3320	297	6	,	,	PUNCT
cana-3320	297	7	a	a	DET
cana-3320	297	8	∈	∈	PROPN
cana-3320	297	9	(	(	PUNCT
cana-3320	297	10	i],b	i],b	NOUN
cana-3320	297	11	∈	∈	PROPN
cana-3320	297	12	(	(	PUNCT
cana-3320	297	13	i1	i1	PROPN
cana-3320	297	14	]	]	PUNCT
cana-3320	297	15	and	and	CCONJ
cana-3320	297	16	c	c	PROPN
cana-3320	297	17	∈	∈	PROPN
cana-3320	297	18	(	(	PUNCT
cana-3320	297	19	i2	i2	PROPN
cana-3320	297	20	]	]	PUNCT
cana-3320	297	21	.	.	PUNCT
cana-3320	298	1	we	we	PRON
cana-3320	298	2	have	have	VERB
cana-3320	298	3	(	(	PUNCT
cana-3320	298	4	a	a	PRON
cana-3320	298	5	,	,	PUNCT
cana-3320	298	6	b	b	NOUN
cana-3320	298	7	,	,	PUNCT
cana-3320	298	8	c	c	NOUN
cana-3320	298	9	)	)	PUNCT
cana-3320	298	10	∈	∈	NOUN
cana-3320	298	11	ið1	ið1	NOUN
cana-3320	298	12	and	and	CCONJ
cana-3320	298	13	ið1	ið1	VERB
cana-3320	298	14	6=	6=	NUM
cana-3320	298	15	0	0	NUM
cana-3320	298	16	.	.	PUNCT
cana-3320	299	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3320	299	2	583	583	NUM
cana-3320	299	3	communications	communication	NOUN
cana-3320	299	4	on	on	ADP
cana-3320	299	5	applied	apply	VERB
cana-3320	299	6	nonlinear	nonlinear	ADJ
cana-3320	299	7	analysis	analysis	NOUN
cana-3320	299	8	issn	issn	NOUN
cana-3320	299	9	:	:	PUNCT
cana-3320	299	10	1074	1074	NUM
cana-3320	299	11	-	-	PUNCT
cana-3320	299	12	133x	133x	NUM
cana-3320	299	13	vol	vol	NOUN
cana-3320	299	14	32	32	NUM
cana-3320	299	15	no	no	NOUN
cana-3320	299	16	.	.	PUNCT
cana-3320	300	1	6s	6s	NUM
cana-3320	300	2	(	(	PUNCT
cana-3320	300	3	2025	2025	NUM
cana-3320	300	4	)	)	PUNCT
cana-3320	300	5	(	(	PUNCT
cana-3320	300	6	i	i	PRON
cana-3320	300	7	>	>	X
cana-3320	300	8	(	(	PUNCT
cana-3320	300	9	i	i	X
cana-3320	300	10	]	]	PUNCT
cana-3320	300	11	∗i	∗i	PROPN
cana-3320	300	12	>	>	X
cana-3320	300	13	(	(	PUNCT
cana-3320	300	14	i1	i1	PROPN
cana-3320	300	15	]	]	PUNCT
cana-3320	300	16	∗i	∗i	PROPN
cana-3320	300	17	>	>	X
cana-3320	300	18	(	(	PUNCT
cana-3320	300	19	i2	i2	PROPN
cana-3320	300	20	]	]	PUNCT
cana-3320	300	21	)	)	PUNCT
cana-3320	300	22	(	(	PUNCT
cana-3320	300	23	ð1	ð1	NOUN
cana-3320	300	24	,	,	PUNCT
cana-3320	300	25	ǎ	ǎ	PROPN
cana-3320	300	26	)	)	PUNCT
cana-3320	300	27	=	=	SYM
cana-3320	300	28	sup	sup	NOUN
cana-3320	300	29	ð1	ð1	NOUN
cana-3320	300	30	=	=	SYM
cana-3320	300	31	xyz	xyz	PROPN
cana-3320	300	32	min{i	min{i	PROPN
cana-3320	300	33	>	>	X
cana-3320	300	34	(	(	PUNCT
cana-3320	300	35	i	i	NOUN
cana-3320	300	36	]	]	X
cana-3320	300	37	(	(	PUNCT
cana-3320	300	38	x	x	X
cana-3320	300	39	,	,	PUNCT
cana-3320	300	40	ǎ),i	ǎ),i	PROPN
cana-3320	300	41	>	>	X
cana-3320	300	42	(	(	PUNCT
cana-3320	300	43	i1	i1	PROPN
cana-3320	300	44	]	]	PUNCT
cana-3320	300	45	(	(	PUNCT
cana-3320	300	46	y	y	PROPN
cana-3320	300	47	,	,	PUNCT
cana-3320	300	48	ǎ),i	ǎ),i	PROPN
cana-3320	300	49	>	>	X
cana-3320	300	50	(	(	PUNCT
cana-3320	300	51	i2	i2	PROPN
cana-3320	300	52	]	]	PUNCT
cana-3320	300	53	(	(	PUNCT
cana-3320	300	54	z	z	PROPN
cana-3320	300	55	,	,	PUNCT
cana-3320	300	56	ǎ	ǎ	PROPN
cana-3320	300	57	)	)	PUNCT
cana-3320	300	58	}	}	PUNCT
cana-3320	300	59	>	>	X
cana-3320	300	60	min{i	min{i	PROPN
cana-3320	300	61	>	>	X
cana-3320	300	62	(	(	PUNCT
cana-3320	300	63	i	i	X
cana-3320	300	64	]	]	X
cana-3320	300	65	(	(	PUNCT
cana-3320	300	66	a	a	PRON
cana-3320	300	67	,	,	PUNCT
cana-3320	300	68	ǎ),i	ǎ),i	PROPN
cana-3320	300	69	>	>	X
cana-3320	300	70	(	(	PUNCT
cana-3320	300	71	i1	i1	PROPN
cana-3320	300	72	]	]	PUNCT
cana-3320	300	73	(	(	PUNCT
cana-3320	300	74	b	b	NOUN
cana-3320	300	75	,	,	PUNCT
cana-3320	300	76	ǎ),i	ǎ),i	PROPN
cana-3320	300	77	>	>	X
cana-3320	300	78	(	(	PUNCT
cana-3320	300	79	i2	i2	PROPN
cana-3320	300	80	]	]	PUNCT
cana-3320	300	81	(	(	PUNCT
cana-3320	300	82	c	c	X
cana-3320	300	83	,	,	PUNCT
cana-3320	300	84	ǎ	ǎ	PROPN
cana-3320	300	85	)	)	PUNCT
cana-3320	300	86	}	}	PUNCT
cana-3320	300	87	=	=	SYM
cana-3320	300	88	℘̃	℘̃	NOUN
cana-3320	300	89	(	(	PUNCT
cana-3320	300	90	iz	iz	INTJ
cana-3320	300	91	(	(	PUNCT
cana-3320	300	92	i	i	NOUN
cana-3320	300	93	]	]	PUNCT
cana-3320	300	94	∗iz	∗iz	PUNCT
cana-3320	300	95	(	(	PUNCT
cana-3320	300	96	i1	i1	PROPN
cana-3320	300	97	]	]	PUNCT
cana-3320	300	98	)	)	PUNCT
cana-3320	300	99	(	(	PUNCT
cana-3320	300	100	ð1	ð1	NOUN
cana-3320	300	101	,	,	PUNCT
cana-3320	300	102	ǎ	ǎ	PROPN
cana-3320	300	103	)	)	PUNCT
cana-3320	300	104	∗iz	∗iz	PUNCT
cana-3320	300	105	(	(	PUNCT
cana-3320	300	106	i2	i2	PROPN
cana-3320	300	107	]	]	PUNCT
cana-3320	300	108	)	)	PUNCT
cana-3320	300	109	(	(	PUNCT
cana-3320	300	110	ð1	ð1	NOUN
cana-3320	300	111	,	,	PUNCT
cana-3320	300	112	ǎ	ǎ	PROPN
cana-3320	300	113	)	)	PUNCT
cana-3320	300	114	=	=	SYM
cana-3320	300	115	inf	inf	PROPN
cana-3320	300	116	ð1	ð1	NOUN
cana-3320	300	117	=	=	NOUN
cana-3320	300	118	xyz	xyz	NOUN
cana-3320	300	119	max{iz	max{iz	PUNCT
cana-3320	300	120	(	(	PUNCT
cana-3320	300	121	i	i	PRON
cana-3320	300	122	]	]	X
cana-3320	300	123	(	(	PUNCT
cana-3320	300	124	x	x	X
cana-3320	300	125	,	,	PUNCT
cana-3320	300	126	ǎ),iz	ǎ),iz	PROPN
cana-3320	300	127	(	(	PUNCT
cana-3320	300	128	i1	i1	PROPN
cana-3320	300	129	]	]	PUNCT
cana-3320	300	130	(	(	PUNCT
cana-3320	300	131	y	y	PROPN
cana-3320	300	132	,	,	PUNCT
cana-3320	300	133	ǎ),iz	ǎ),iz	PROPN
cana-3320	300	134	(	(	PUNCT
cana-3320	300	135	i2	i2	PROPN
cana-3320	300	136	]	]	PUNCT
cana-3320	300	137	(	(	PUNCT
cana-3320	300	138	z	z	PROPN
cana-3320	300	139	,	,	PUNCT
cana-3320	300	140	ǎ	ǎ	PROPN
cana-3320	300	141	)	)	PUNCT
cana-3320	300	142	}	}	PUNCT
cana-3320	300	143	6	6	NUM
cana-3320	300	144	max{iz	max{iz	NOUN
cana-3320	300	145	(	(	PUNCT
cana-3320	300	146	i	i	PRON
cana-3320	300	147	]	]	X
cana-3320	300	148	(	(	PUNCT
cana-3320	300	149	a	a	DET
cana-3320	300	150	,	,	PUNCT
cana-3320	300	151	ǎ),iz	ǎ),iz	PROPN
cana-3320	300	152	(	(	PUNCT
cana-3320	300	153	i1	i1	PROPN
cana-3320	300	154	]	]	PUNCT
cana-3320	300	155	(	(	PUNCT
cana-3320	300	156	b	b	NOUN
cana-3320	300	157	,	,	PUNCT
cana-3320	300	158	ǎ),iz	ǎ),iz	PROPN
cana-3320	300	159	(	(	PUNCT
cana-3320	300	160	i2	i2	PROPN
cana-3320	300	161	]	]	PUNCT
cana-3320	300	162	(	(	PUNCT
cana-3320	300	163	c	c	X
cana-3320	300	164	,	,	PUNCT
cana-3320	300	165	ǎ	ǎ	PROPN
cana-3320	300	166	)	)	PUNCT
cana-3320	300	167	}	}	PUNCT
cana-3320	300	168	=	=	PUNCT
cana-3320	301	1	∂̃	∂̃	NOUN
cana-3320	301	2	therefore	therefore	ADV
cana-3320	301	3	(	(	PUNCT
cana-3320	301	4	i	i	PRON
cana-3320	301	5	(	(	PUNCT
cana-3320	301	6	i	i	NOUN
cana-3320	301	7	]	]	X
cana-3320	301	8	∗i	∗i	PROPN
cana-3320	301	9	(	(	PUNCT
cana-3320	301	10	i1	i1	PROPN
cana-3320	301	11	]	]	PUNCT
cana-3320	302	1	∗i	∗i	PROPN
cana-3320	302	2	(	(	PUNCT
cana-3320	302	3	i2	i2	PROPN
cana-3320	302	4	]	]	PUNCT
cana-3320	302	5	)	)	PUNCT
cana-3320	302	6	(	(	PUNCT
cana-3320	302	7	ð1	ð1	NOUN
cana-3320	302	8	,	,	PUNCT
cana-3320	302	9	ǎ	ǎ	PROPN
cana-3320	302	10	)	)	PUNCT
cana-3320	302	11	=	=	SYM
cana-3320	302	12	(	(	PUNCT
cana-3320	302	13	i(ii1i2])(ð1	i(ii1i2])(ð1	PROPN
cana-3320	302	14	,	,	PUNCT
cana-3320	302	15	ǎ	ǎ	PROPN
cana-3320	302	16	)	)	PUNCT
cana-3320	302	17	.	.	PUNCT
cana-3320	303	1	if	if	SCONJ
cana-3320	303	2	ð1	ð1	NOUN
cana-3320	303	3	/∈	/∈	PUNCT
cana-3320	304	1	(	(	PUNCT
cana-3320	304	2	ii1i2	ii1i2	NOUN
cana-3320	304	3	]	]	X
cana-3320	304	4	then	then	ADV
cana-3320	304	5	(	(	PUNCT
cana-3320	304	6	i>(ii1i2	i>(ii1i2	X
cana-3320	304	7	]	]	X
cana-3320	304	8	)	)	PUNCT
cana-3320	304	9	(	(	PUNCT
cana-3320	304	10	ð1	ð1	NOUN
cana-3320	304	11	,	,	PUNCT
cana-3320	304	12	ǎ	ǎ	PROPN
cana-3320	304	13	)	)	PUNCT
cana-3320	304	14	=	=	SYM
cana-3320	305	1	∂̃	∂̃	NOUN
cana-3320	305	2	and	and	CCONJ
cana-3320	305	3	(	(	PUNCT
cana-3320	305	4	iz	iz	INTJ
cana-3320	305	5	(	(	PUNCT
cana-3320	305	6	ii1i2	ii1i2	PROPN
cana-3320	305	7	]	]	X
cana-3320	305	8	)	)	PUNCT
cana-3320	305	9	(	(	PUNCT
cana-3320	305	10	ð1	ð1	NOUN
cana-3320	305	11	,	,	PUNCT
cana-3320	305	12	ǎ	ǎ	PROPN
cana-3320	305	13	)	)	PUNCT
cana-3320	305	14	=	=	PUNCT
cana-3320	306	1	℘̃.	℘̃.	ADP
cana-3320	306	2	since	since	SCONJ
cana-3320	306	3	ð1	ð1	NOUN
cana-3320	306	4	6	6	NUM
cana-3320	306	5	abc	abc	PROPN
cana-3320	306	6	,	,	PUNCT
cana-3320	306	7	a	a	PRON
cana-3320	306	8	/∈	/∈	PUNCT
cana-3320	306	9	(	(	PUNCT
cana-3320	306	10	i	i	PRON
cana-3320	306	11	]	]	X
cana-3320	306	12	,	,	PUNCT
cana-3320	306	13	b	b	X
cana-3320	306	14	/∈	/∈	PUNCT
cana-3320	306	15	(	(	PUNCT
cana-3320	306	16	i1	i1	PROPN
cana-3320	306	17	]	]	PUNCT
cana-3320	306	18	and	and	CCONJ
cana-3320	306	19	c	c	PROPN
cana-3320	306	20	/∈	/∈	PUNCT
cana-3320	306	21	(	(	PUNCT
cana-3320	306	22	i2	i2	PROPN
cana-3320	306	23	]	]	PUNCT
cana-3320	306	24	.	.	PUNCT
cana-3320	307	1	we	we	PRON
cana-3320	307	2	have	have	VERB
cana-3320	307	3	(	(	PUNCT
cana-3320	307	4	i	i	PRON
cana-3320	307	5	>	>	X
cana-3320	307	6	(	(	PUNCT
cana-3320	307	7	i	i	X
cana-3320	307	8	]	]	PUNCT
cana-3320	307	9	∗i	∗i	PROPN
cana-3320	307	10	>	>	X
cana-3320	307	11	(	(	PUNCT
cana-3320	307	12	i1	i1	PROPN
cana-3320	307	13	]	]	PUNCT
cana-3320	307	14	∗i	∗i	PROPN
cana-3320	307	15	>	>	X
cana-3320	307	16	(	(	PUNCT
cana-3320	307	17	i2	i2	PROPN
cana-3320	307	18	]	]	PUNCT
cana-3320	307	19	)	)	PUNCT
cana-3320	307	20	(	(	PUNCT
cana-3320	307	21	ð1	ð1	NOUN
cana-3320	307	22	,	,	PUNCT
cana-3320	307	23	ǎ	ǎ	PROPN
cana-3320	307	24	)	)	PUNCT
cana-3320	307	25	=	=	SYM
cana-3320	307	26	sup	sup	NOUN
cana-3320	307	27	ð1	ð1	NOUN
cana-3320	307	28	=	=	SYM
cana-3320	307	29	xyz	xyz	PROPN
cana-3320	307	30	min{i	min{i	PROPN
cana-3320	307	31	>	>	X
cana-3320	307	32	(	(	PUNCT
cana-3320	307	33	i	i	NOUN
cana-3320	307	34	]	]	X
cana-3320	307	35	(	(	PUNCT
cana-3320	307	36	x	x	X
cana-3320	307	37	,	,	PUNCT
cana-3320	307	38	ǎ),i	ǎ),i	PROPN
cana-3320	307	39	>	>	X
cana-3320	307	40	(	(	PUNCT
cana-3320	307	41	i1	i1	PROPN
cana-3320	307	42	]	]	PUNCT
cana-3320	307	43	(	(	PUNCT
cana-3320	307	44	y	y	PROPN
cana-3320	307	45	,	,	PUNCT
cana-3320	307	46	ǎ),i	ǎ),i	PROPN
cana-3320	307	47	>	>	X
cana-3320	307	48	(	(	PUNCT
cana-3320	307	49	i2	i2	PROPN
cana-3320	307	50	]	]	PUNCT
cana-3320	307	51	(	(	PUNCT
cana-3320	307	52	z	z	PROPN
cana-3320	307	53	,	,	PUNCT
cana-3320	307	54	ǎ	ǎ	PROPN
cana-3320	307	55	)	)	PUNCT
cana-3320	307	56	}	}	PUNCT
cana-3320	307	57	>	>	X
cana-3320	307	58	min{i	min{i	PROPN
cana-3320	307	59	>	>	X
cana-3320	307	60	(	(	PUNCT
cana-3320	307	61	i	i	X
cana-3320	307	62	]	]	X
cana-3320	307	63	(	(	PUNCT
cana-3320	307	64	a	a	PRON
cana-3320	307	65	,	,	PUNCT
cana-3320	307	66	ǎ),i	ǎ),i	PROPN
cana-3320	307	67	>	>	X
cana-3320	307	68	(	(	PUNCT
cana-3320	307	69	i1	i1	PROPN
cana-3320	307	70	]	]	PUNCT
cana-3320	307	71	(	(	PUNCT
cana-3320	307	72	b	b	NOUN
cana-3320	307	73	,	,	PUNCT
cana-3320	307	74	ǎ),i	ǎ),i	PROPN
cana-3320	307	75	>	>	X
cana-3320	307	76	(	(	PUNCT
cana-3320	307	77	i2	i2	PROPN
cana-3320	307	78	]	]	PUNCT
cana-3320	307	79	(	(	PUNCT
cana-3320	307	80	c	c	X
cana-3320	307	81	,	,	PUNCT
cana-3320	307	82	ǎ	ǎ	PROPN
cana-3320	307	83	)	)	PUNCT
cana-3320	307	84	}	}	PUNCT
cana-3320	308	1	=	=	SYM
cana-3320	308	2	∂̃	∂̃	NOUN
cana-3320	308	3	(	(	PUNCT
cana-3320	308	4	iz	iz	INTJ
cana-3320	308	5	(	(	PUNCT
cana-3320	308	6	i	i	NOUN
cana-3320	308	7	]	]	PUNCT
cana-3320	308	8	∗iz	∗iz	PUNCT
cana-3320	308	9	(	(	PUNCT
cana-3320	308	10	i1	i1	PROPN
cana-3320	308	11	]	]	PUNCT
cana-3320	308	12	∗iz	∗iz	PUNCT
cana-3320	308	13	(	(	PUNCT
cana-3320	308	14	i2	i2	PROPN
cana-3320	308	15	]	]	PUNCT
cana-3320	308	16	)	)	PUNCT
cana-3320	308	17	(	(	PUNCT
cana-3320	308	18	ð1	ð1	NOUN
cana-3320	308	19	,	,	PUNCT
cana-3320	308	20	ǎ	ǎ	PROPN
cana-3320	308	21	)	)	PUNCT
cana-3320	308	22	=	=	SYM
cana-3320	308	23	inf	inf	PROPN
cana-3320	308	24	ð1	ð1	NOUN
cana-3320	308	25	=	=	NOUN
cana-3320	308	26	xyz	xyz	NOUN
cana-3320	308	27	max{iz	max{iz	PUNCT
cana-3320	308	28	(	(	PUNCT
cana-3320	308	29	i	i	PRON
cana-3320	308	30	]	]	X
cana-3320	308	31	(	(	PUNCT
cana-3320	308	32	x	x	X
cana-3320	308	33	,	,	PUNCT
cana-3320	308	34	ǎ),iz	ǎ),iz	PROPN
cana-3320	308	35	(	(	PUNCT
cana-3320	308	36	i1	i1	PROPN
cana-3320	308	37	]	]	PUNCT
cana-3320	308	38	(	(	PUNCT
cana-3320	308	39	y	y	PROPN
cana-3320	308	40	,	,	PUNCT
cana-3320	308	41	ǎ),iz	ǎ),iz	PROPN
cana-3320	308	42	(	(	PUNCT
cana-3320	308	43	i2	i2	PROPN
cana-3320	308	44	]	]	PUNCT
cana-3320	308	45	(	(	PUNCT
cana-3320	308	46	z	z	PROPN
cana-3320	308	47	,	,	PUNCT
cana-3320	308	48	ǎ	ǎ	PROPN
cana-3320	308	49	)	)	PUNCT
cana-3320	308	50	}	}	PUNCT
cana-3320	308	51	6	6	NUM
cana-3320	308	52	max{iz	max{iz	NOUN
cana-3320	308	53	(	(	PUNCT
cana-3320	308	54	i	i	PRON
cana-3320	308	55	]	]	X
cana-3320	308	56	(	(	PUNCT
cana-3320	308	57	a	a	DET
cana-3320	308	58	,	,	PUNCT
cana-3320	308	59	ǎ),iz	ǎ),iz	PROPN
cana-3320	308	60	(	(	PUNCT
cana-3320	308	61	i1	i1	PROPN
cana-3320	308	62	]	]	PUNCT
cana-3320	308	63	(	(	PUNCT
cana-3320	308	64	b	b	NOUN
cana-3320	308	65	,	,	PUNCT
cana-3320	308	66	ǎ),iz	ǎ),iz	PROPN
cana-3320	308	67	(	(	PUNCT
cana-3320	308	68	i2	i2	PROPN
cana-3320	308	69	]	]	PUNCT
cana-3320	308	70	(	(	PUNCT
cana-3320	308	71	c	c	X
cana-3320	308	72	,	,	PUNCT
cana-3320	308	73	ǎ	ǎ	PROPN
cana-3320	308	74	)	)	PUNCT
cana-3320	308	75	}	}	PUNCT
cana-3320	308	76	=	=	SYM
cana-3320	308	77	℘̃	℘̃	NOUN
cana-3320	308	78	hence	hence	ADV
cana-3320	308	79	(	(	PUNCT
cana-3320	308	80	i	i	PRON
cana-3320	308	81	(	(	PUNCT
cana-3320	308	82	i	i	NOUN
cana-3320	308	83	]	]	X
cana-3320	308	84	∗i	∗i	PROPN
cana-3320	308	85	(	(	PUNCT
cana-3320	308	86	i1	i1	PROPN
cana-3320	308	87	]	]	PUNCT
cana-3320	309	1	∗i	∗i	PROPN
cana-3320	309	2	(	(	PUNCT
cana-3320	309	3	i2	i2	PROPN
cana-3320	309	4	]	]	PUNCT
cana-3320	309	5	)	)	PUNCT
cana-3320	309	6	(	(	PUNCT
cana-3320	309	7	ð1	ð1	NOUN
cana-3320	309	8	,	,	PUNCT
cana-3320	309	9	ǎ	ǎ	PROPN
cana-3320	309	10	)	)	PUNCT
cana-3320	309	11	=	=	SYM
cana-3320	309	12	(	(	PUNCT
cana-3320	309	13	i(ii1i2])(ð1	i(ii1i2])(ð1	PROPN
cana-3320	309	14	,	,	PUNCT
cana-3320	309	15	ǎ	ǎ	PROPN
cana-3320	309	16	)	)	PUNCT
cana-3320	309	17	.	.	PUNCT
cana-3320	310	1	theorem	theorem	VERB
cana-3320	310	2	4.10	4.10	NUM
cana-3320	310	3	.	.	PUNCT
cana-3320	311	1	let	let	VERB
cana-3320	311	2	{	{	PUNCT
cana-3320	311	3	ii|i	ii|i	NOUN
cana-3320	311	4	∈	∈	NOUN
cana-3320	312	1	i	i	PRON
cana-3320	312	2	}	}	PUNCT
cana-3320	312	3	be	be	VERB
cana-3320	312	4	a	a	DET
cana-3320	312	5	family	family	NOUN
cana-3320	312	6	of	of	ADP
cana-3320	312	7	subsets	subset	NOUN
cana-3320	312	8	of	of	ADP
cana-3320	312	9	z	z	PROPN
cana-3320	312	10	and	and	CCONJ
cana-3320	312	11	i	i	PROPN
cana-3320	312	12	,	,	PUNCT
cana-3320	312	13	i2	i2	PROPN
cana-3320	312	14	⊆	⊆	NUM
cana-3320	312	15	z	z	NOUN
cana-3320	312	16	.	.	PUNCT
cana-3320	313	1	then	then	ADV
cana-3320	313	2	(	(	PUNCT
cana-3320	313	3	1	1	X
cana-3320	313	4	)	)	PUNCT
cana-3320	313	5	(	(	PUNCT
cana-3320	313	6	i	i	PRON
cana-3320	313	7	]	]	PUNCT
cana-3320	313	8	⊆	⊆	NUM
cana-3320	313	9	(	(	PUNCT
cana-3320	313	10	i2	i2	PROPN
cana-3320	313	11	]	]	PUNCT
cana-3320	313	12	if	if	SCONJ
cana-3320	313	13	and	and	CCONJ
cana-3320	313	14	only	only	ADV
cana-3320	313	15	if	if	SCONJ
cana-3320	313	16	(	(	PUNCT
cana-3320	313	17	i(i	i(i	NOUN
cana-3320	313	18	]	]	SYM
cana-3320	313	19	)	)	PUNCT
cana-3320	313	20	℘̃	℘̃	PROPN
cana-3320	313	21	∂̃	∂̃	NOUN
cana-3320	313	22	6	6	NUM
cana-3320	313	23	(	(	PUNCT
cana-3320	313	24	i(i2	i(i2	NOUN
cana-3320	313	25	]	]	SYM
cana-3320	313	26	)	)	PUNCT
cana-3320	313	27	℘̃	℘̃	PROPN
cana-3320	313	28	∂̃	∂̃	NOUN
cana-3320	313	29	(	(	PUNCT
cana-3320	313	30	2	2	NUM
cana-3320	313	31	)	)	PUNCT
cana-3320	313	32	(	(	PUNCT
cana-3320	313	33	fi∈ii(ii	fi∈ii(ii	ADJ
cana-3320	313	34	]	]	SYM
cana-3320	313	35	)	)	PUNCT
cana-3320	313	36	℘̃	℘̃	PROPN
cana-3320	313	37	∂̃	∂̃	NOUN
cana-3320	313	38	=	=	SYM
cana-3320	313	39	(	(	PUNCT
cana-3320	313	40	ifi∈i(ii	ifi∈i(ii	X
cana-3320	313	41	]	]	SYM
cana-3320	313	42	)	)	PUNCT
cana-3320	313	43	℘̃	℘̃	PROPN
cana-3320	313	44	∂̃	∂̃	NOUN
cana-3320	313	45	(	(	PUNCT
cana-3320	313	46	3	3	NUM
cana-3320	313	47	)	)	PUNCT
cana-3320	313	48	(	(	PUNCT
cana-3320	313	49	gi∈ii(ii	gi∈ii(ii	PROPN
cana-3320	313	50	]	]	PUNCT
cana-3320	313	51	)	)	PUNCT
cana-3320	313	52	℘̃	℘̃	PROPN
cana-3320	313	53	∂̃	∂̃	NOUN
cana-3320	313	54	=	=	SYM
cana-3320	313	55	(	(	PUNCT
cana-3320	313	56	igi∈i(ii	igi∈i(ii	PROPN
cana-3320	313	57	]	]	X
cana-3320	313	58	)	)	PUNCT
cana-3320	313	59	℘̃	℘̃	PROPN
cana-3320	313	60	∂̃	∂̃	NOUN
cana-3320	313	61	.	.	PUNCT
cana-3320	314	1	5	5	NUM
cana-3320	314	2	regular	regular	ADJ
cana-3320	314	3	ordered	order	VERB
cana-3320	314	4	ternary	ternary	ADJ
cana-3320	314	5	semigroups	semigroup	NOUN
cana-3320	314	6	theorem	theorem	VERB
cana-3320	314	7	5.1	5.1	NUM
cana-3320	314	8	.	.	PUNCT
cana-3320	315	1	if	if	SCONJ
cana-3320	315	2	i	i	PRON
cana-3320	315	3	is	be	AUX
cana-3320	315	4	a	a	DET
cana-3320	315	5	(	(	PUNCT
cana-3320	315	6	∂̃	∂̃	NOUN
cana-3320	315	7	,	,	PUNCT
cana-3320	315	8	℘̃)-iqvfli[iqvfss	℘̃)-iqvfli[iqvfss	PROPN
cana-3320	315	9	,	,	PUNCT
cana-3320	315	10	iqvflati	iqvflati	NOUN
cana-3320	315	11	,	,	PUNCT
cana-3320	315	12	iqvfri	iqvfri	PROPN
cana-3320	315	13	]	]	PUNCT
cana-3320	315	14	of	of	ADP
cana-3320	315	15	z	z	NOUN
cana-3320	315	16	,	,	PUNCT
cana-3320	315	17	then	then	ADV
cana-3320	315	18	(	(	PUNCT
cana-3320	315	19	i)℘̃	i)℘̃	PROPN
cana-3320	315	20	∂̃	∂̃	NOUN
cana-3320	315	21	is	be	AUX
cana-3320	315	22	a	a	DET
cana-3320	315	23	iqvfli[iqvfss	iqvfli[iqvfss	PROPN
cana-3320	315	24	,	,	PUNCT
cana-3320	315	25	iqvflati	iqvflati	NOUN
cana-3320	315	26	,	,	PUNCT
cana-3320	315	27	iqvfri	iqvfri	PROPN
cana-3320	315	28	]	]	PUNCT
cana-3320	315	29	of	of	ADP
cana-3320	315	30	z	z	PROPN
cana-3320	315	31	.	.	PUNCT
cana-3320	316	1	theorem	theorem	VERB
cana-3320	316	2	5.2	5.2	NUM
cana-3320	316	3	.	.	PUNCT
cana-3320	317	1	let	let	VERB
cana-3320	317	2	i	i	PRON
cana-3320	317	3	be	be	AUX
cana-3320	317	4	an	an	DET
cana-3320	317	5	(	(	PUNCT
cana-3320	317	6	∂̃	∂̃	PROPN
cana-3320	317	7	,	,	PUNCT
cana-3320	317	8	℘̃)iqvfri	℘̃)iqvfri	NUM
cana-3320	317	9	,	,	PUNCT
cana-3320	317	10	i1	i1	PROPN
cana-3320	317	11	be	be	AUX
cana-3320	317	12	an	an	DET
cana-3320	317	13	(	(	PUNCT
cana-3320	317	14	∂̃	∂̃	NOUN
cana-3320	317	15	,	,	PUNCT
cana-3320	317	16	℘̃)iqvflati	℘̃)iqvflati	PUNCT
cana-3320	317	17	and	and	CCONJ
cana-3320	317	18	i2	i2	PROPN
cana-3320	317	19	be	be	VERB
cana-3320	317	20	an	an	DET
cana-3320	317	21	(	(	PUNCT
cana-3320	317	22	∂̃	∂̃	PROPN
cana-3320	317	23	,	,	PUNCT
cana-3320	317	24	℘̃)iqvfli	℘̃)iqvfli	NUM
cana-3320	317	25	of	of	ADP
cana-3320	317	26	z	z	PROPN
cana-3320	317	27	.	.	PUNCT
cana-3320	318	1	then	then	ADV
cana-3320	318	2	(	(	PUNCT
cana-3320	318	3	(	(	PUNCT
cana-3320	318	4	i	i	PRON
cana-3320	318	5	∗	∗	PROPN
cana-3320	318	6	i1	i1	PROPN
cana-3320	318	7	∗	∗	PROPN
cana-3320	318	8	i2])℘̃	i2])℘̃	PROPN
cana-3320	318	9	∂̃	∂̃	NOUN
cana-3320	318	10	⊆	⊆	NUM
cana-3320	318	11	(	(	PUNCT
cana-3320	318	12	if	if	SCONJ
cana-3320	318	13	i1	i1	PROPN
cana-3320	318	14	f	f	PROPN
cana-3320	319	1	i2]℘̃	i2]℘̃	PRON
cana-3320	319	2	∂̃	∂̃	PROPN
cana-3320	319	3	.	.	PUNCT
cana-3320	320	1	proof	proof	NOUN
cana-3320	320	2	.	.	PUNCT
cana-3320	321	1	let	let	VERB
cana-3320	321	2	i	i	PRON
cana-3320	321	3	=	=	PUNCT
cana-3320	322	1	[	[	X
cana-3320	322	2	<	<	X
cana-3320	322	3	̃i	̃i	NOUN
cana-3320	322	4	,	,	PUNCT
cana-3320	322	5	=	=	NOUN
cana-3320	322	6	̃i	̃i	NOUN
cana-3320	322	7	]	]	X
cana-3320	322	8	be	be	VERB
cana-3320	322	9	an	an	DET
cana-3320	322	10	(	(	PUNCT
cana-3320	322	11	∂̃	∂̃	PROPN
cana-3320	322	12	,	,	PUNCT
cana-3320	322	13	℘̃)iqvfri	℘̃)iqvfri	NUM
cana-3320	322	14	,	,	PUNCT
cana-3320	322	15	i1	i1	PROPN
cana-3320	322	16	=	=	PUNCT
cana-3320	323	1	[	[	X
cana-3320	323	2	<	<	X
cana-3320	323	3	̃i1	̃i1	INTJ
cana-3320	323	4	,	,	PUNCT
cana-3320	323	5	=	=	SYM
cana-3320	323	6	̃i1	̃i1	PROPN
cana-3320	323	7	]	]	PUNCT
cana-3320	323	8	be	be	AUX
cana-3320	323	9	an	an	DET
cana-3320	323	10	(	(	PUNCT
cana-3320	323	11	∂̃	∂̃	NOUN
cana-3320	323	12	,	,	PUNCT
cana-3320	323	13	℘̃)iqvflati	℘̃)iqvflati	PUNCT
cana-3320	323	14	and	and	CCONJ
cana-3320	323	15	i2	i2	PROPN
cana-3320	323	16	=	=	PUNCT
cana-3320	324	1	[	[	X
cana-3320	324	2	<	<	X
cana-3320	324	3	̃i2	̃i2	X
cana-3320	324	4	,	,	PUNCT
cana-3320	324	5	=	=	SYM
cana-3320	324	6	̃i2	̃i2	NOUN
cana-3320	324	7	]	]	PUNCT
cana-3320	324	8	be	be	AUX
cana-3320	324	9	an	an	DET
cana-3320	324	10	(	(	PUNCT
cana-3320	324	11	∂̃	∂̃	PROPN
cana-3320	324	12	,	,	PUNCT
cana-3320	324	13	℘̃)iqvfli	℘̃)iqvfli	NUM
cana-3320	324	14	of	of	ADP
cana-3320	324	15	z	z	PROPN
cana-3320	324	16	.	.	PUNCT
cana-3320	325	1	let	let	VERB
cana-3320	325	2	(	(	PUNCT
cana-3320	325	3	ð1,ð2,ð3	ð1,ð2,ð3	PROPN
cana-3320	325	4	,	,	PUNCT
cana-3320	325	5	ǎ	ǎ	PROPN
cana-3320	325	6	)	)	PUNCT
cana-3320	325	7	∈	∈	PROPN
cana-3320	326	1	i	i	PRON
cana-3320	326	2	}	}	PUNCT
cana-3320	326	3	.	.	PUNCT
cana-3320	327	1	if	if	SCONJ
cana-3320	327	2	i	i	PRON
cana-3320	327	3	}	}	PUNCT
cana-3320	327	4	6=	6=	ADP
cana-3320	327	5	∅	∅	NOUN
cana-3320	327	6	,	,	PUNCT
cana-3320	327	7	then	then	ADV
cana-3320	327	8	}	}	PUNCT
cana-3320	327	9	6	6	NUM
cana-3320	327	10	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	327	11	.	.	PUNCT
cana-3320	328	1	thus	thus	ADV
cana-3320	328	2	<	<	X
cana-3320	328	3	̃i	̃i	NOUN
cana-3320	328	4	(	(	PUNCT
cana-3320	328	5	}	}	PUNCT
cana-3320	328	6	,	,	PUNCT
cana-3320	328	7	ǎ	ǎ	PROPN
cana-3320	328	8	)	)	PUNCT
cana-3320	328	9	>	>	X
cana-3320	328	10	<	<	X
cana-3320	328	11	̃i(ð1ð2ð3	̃i(ð1ð2ð3	X
cana-3320	328	12	)	)	PUNCT
cana-3320	328	13	>	>	X
cana-3320	328	14	<	<	X
cana-3320	328	15	̃i(ð1	̃i(ð1	NOUN
cana-3320	328	16	,	,	PUNCT
cana-3320	328	17	ǎ	ǎ	PROPN
cana-3320	328	18	)	)	PUNCT
cana-3320	328	19	and	and	CCONJ
cana-3320	328	20	=	=	NOUN
cana-3320	328	21	̃i	̃i	NOUN
cana-3320	328	22	(	(	PUNCT
cana-3320	328	23	}	}	PUNCT
cana-3320	328	24	,	,	PUNCT
cana-3320	328	25	ǎ	ǎ	PROPN
cana-3320	328	26	)	)	PUNCT
cana-3320	328	27	6	6	NUM
cana-3320	328	28	=	=	SYM
cana-3320	328	29	̃i(ð1ð2ð3	̃i(ð1ð2ð3	NOUN
cana-3320	328	30	)	)	PUNCT
cana-3320	328	31	6	6	NUM
cana-3320	328	32	=	=	NUM
cana-3320	328	33	̃i(ð1	̃i(ð1	NOUN
cana-3320	328	34	,	,	PUNCT
cana-3320	328	35	ǎ	ǎ	NOUN
cana-3320	328	36	)	)	PUNCT
cana-3320	328	37	.	.	PUNCT
cana-3320	329	1	similarly	similarly	ADV
cana-3320	329	2	<	<	X
cana-3320	329	3	̃i1	̃i1	PROPN
cana-3320	329	4	(	(	PUNCT
cana-3320	329	5	}	}	PUNCT
cana-3320	329	6	,	,	PUNCT
cana-3320	329	7	ǎ	ǎ	PROPN
cana-3320	329	8	)	)	PUNCT
cana-3320	329	9	>	>	X
cana-3320	330	1	<	<	X
cana-3320	330	2	̃i1	̃i1	INTJ
cana-3320	330	3	(	(	PUNCT
cana-3320	330	4	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	330	5	)	)	PUNCT
cana-3320	330	6	>	>	X
cana-3320	331	1	<	<	X
cana-3320	331	2	̃i1	̃i1	PROPN
cana-3320	331	3	(	(	PUNCT
cana-3320	331	4	ð2	ð2	PROPN
cana-3320	331	5	,	,	PUNCT
cana-3320	331	6	ǎ	ǎ	PROPN
cana-3320	331	7	)	)	PUNCT
cana-3320	331	8	and	and	CCONJ
cana-3320	331	9	=	=	NUM
cana-3320	331	10	̃i1	̃i1	PROPN
cana-3320	331	11	(	(	PUNCT
cana-3320	331	12	}	}	PUNCT
cana-3320	331	13	,	,	PUNCT
cana-3320	331	14	ǎ	ǎ	PROPN
cana-3320	331	15	)	)	PUNCT
cana-3320	331	16	6	6	NUM
cana-3320	331	17	=	=	X
cana-3320	331	18	̃i1	̃i1	PROPN
cana-3320	331	19	(	(	PUNCT
cana-3320	331	20	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	331	21	)	)	PUNCT
cana-3320	331	22	6	6	NUM
cana-3320	331	23	=	=	X
cana-3320	331	24	̃i1	̃i1	PROPN
cana-3320	331	25	(	(	PUNCT
cana-3320	331	26	ð2	ð2	PROPN
cana-3320	331	27	,	,	PUNCT
cana-3320	331	28	ǎ	ǎ	PROPN
cana-3320	331	29	)	)	PUNCT
cana-3320	331	30	.	.	PUNCT
cana-3320	332	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3320	332	2	584	584	NUM
cana-3320	332	3	<	<	X
cana-3320	332	4	̃	̃	PROPN
cana-3320	332	5	<	<	X
cana-3320	332	6	̃	̃	NOUN
cana-3320	332	7	<	<	X
cana-3320	332	8	̃	̃	NOUN
cana-3320	332	9	=	=	SYM
cana-3320	332	10	̃	̃	NOUN
cana-3320	332	11	=	=	SYM
cana-3320	332	12	̃	̃	NOUN
cana-3320	332	13	=	=	SYM
cana-3320	332	14	̃	̃	NOUN
cana-3320	332	15	communications	communication	NOUN
cana-3320	332	16	on	on	ADP
cana-3320	332	17	applied	apply	VERB
cana-3320	332	18	nonlinear	nonlinear	ADJ
cana-3320	332	19	analysis	analysis	NOUN
cana-3320	332	20	issn	issn	NOUN
cana-3320	332	21	:	:	PUNCT
cana-3320	332	22	1074	1074	NUM
cana-3320	332	23	-	-	PUNCT
cana-3320	332	24	133x	133x	NUM
cana-3320	332	25	vol	vol	NOUN
cana-3320	332	26	32	32	NUM
cana-3320	333	1	no	no	NOUN
cana-3320	333	2	.	.	PUNCT
cana-3320	334	1	6s	6s	NUM
cana-3320	334	2	(	(	PUNCT
cana-3320	334	3	2025	2025	NUM
cana-3320	334	4	)	)	PUNCT
cana-3320	334	5	similarly	similarly	ADV
cana-3320	334	6	,	,	PUNCT
cana-3320	334	7	i2	i2	PROPN
cana-3320	334	8	(	(	PUNCT
cana-3320	334	9	}	}	PUNCT
cana-3320	334	10	,	,	PUNCT
cana-3320	334	11	̌a	̌a	PROPN
cana-3320	334	12	)	)	PUNCT
cana-3320	334	13	>	>	X
cana-3320	335	1	i2	i2	PROPN
cana-3320	335	2	(	(	PUNCT
cana-3320	335	3	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	335	4	)	)	PUNCT
cana-3320	335	5	>	>	X
cana-3320	335	6	i2	i2	PROPN
cana-3320	335	7	(	(	PUNCT
cana-3320	335	8	ð3	ð3	PROPN
cana-3320	335	9	,	,	PUNCT
cana-3320	335	10	̌a	̌a	NOUN
cana-3320	335	11	)	)	PUNCT
cana-3320	335	12	and	and	CCONJ
cana-3320	335	13	i2	i2	PROPN
cana-3320	335	14	(	(	PUNCT
cana-3320	335	15	}	}	PUNCT
cana-3320	335	16	,	,	PUNCT
cana-3320	335	17	̌a	̌a	PROPN
cana-3320	335	18	)	)	PUNCT
cana-3320	335	19	6	6	NUM
cana-3320	335	20	i2	i2	PROPN
cana-3320	335	21	(	(	PUNCT
cana-3320	335	22	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	335	23	)	)	PUNCT
cana-3320	335	24	6	6	NUM
cana-3320	335	25	i2	i2	PROPN
cana-3320	335	26	(	(	PUNCT
cana-3320	335	27	ð3	ð3	PROPN
cana-3320	335	28	,	,	PUNCT
cana-3320	335	29	̌a	̌a	PROPN
cana-3320	335	30	)	)	PUNCT
cana-3320	335	31	.	.	PUNCT
cana-3320	336	1	we	we	PRON
cana-3320	336	2	have	have	VERB
cana-3320	336	3	(	(	PUNCT
cana-3320	336	4	<	<	X
cana-3320	336	5	̃(i∗i1∗i2	̃(i∗i1∗i2	X
cana-3320	336	6	]	]	SYM
cana-3320	336	7	)	)	PUNCT
cana-3320	336	8	℘̃	℘̃	PROPN
cana-3320	336	9	∂̃	∂̃	NOUN
cana-3320	336	10	(	(	PUNCT
cana-3320	336	11	}	}	PUNCT
cana-3320	336	12	,	,	PUNCT
cana-3320	336	13	ǎ	ǎ	PROPN
cana-3320	336	14	)	)	PUNCT
cana-3320	336	15	=	=	SYM
cana-3320	336	16	(	(	PUNCT
cana-3320	336	17	<	<	X
cana-3320	336	18	̃(i∗i1∗i2	̃(i∗i1∗i2	X
cana-3320	336	19	]	]	PUNCT
cana-3320	336	20	(	(	PUNCT
cana-3320	336	21	}	}	PUNCT
cana-3320	336	22	,	,	PUNCT
cana-3320	336	23	ǎ)o℘̃	ǎ)o℘̃	NOUN
cana-3320	336	24	)	)	PUNCT
cana-3320	336	25	m	m	VERB
cana-3320	336	26	∂̃	∂̃	NOUN
cana-3320	336	27	=	=	PUNCT
cana-3320	337	1	[	[	PUNCT
cana-3320	337	2	[	[	PUNCT
cana-3320	337	3	sup	sup	NOUN
cana-3320	337	4	}	}	PUNCT
cana-3320	337	5	6ð1ð2ð3	6ð1ð2ð3	NUM
cana-3320	337	6	{	{	PUNCT
cana-3320	337	7	<	<	X
cana-3320	337	8	̃i(ð1	̃i(ð1	NOUN
cana-3320	337	9	,	,	PUNCT
cana-3320	337	10	ǎ)o<̃i1(ð2	ǎ)o<̃i1(ð2	PROPN
cana-3320	337	11	,	,	PUNCT
cana-3320	337	12	ǎ)o<̃i2(ð3	ǎ)o<̃i2(ð3	PROPN
cana-3320	337	13	,	,	PUNCT
cana-3320	337	14	ǎ)}o℘̃	ǎ)}o℘̃	NOUN
cana-3320	337	15	]	]	PUNCT
cana-3320	337	16	]	]	PUNCT
cana-3320	338	1	m	m	VERB
cana-3320	338	2	∂̃	∂̃	NOUN
cana-3320	338	3	=	=	PUNCT
cana-3320	338	4	[	[	PUNCT
cana-3320	338	5	sup	sup	NOUN
cana-3320	338	6	}	}	PUNCT
cana-3320	338	7	6ð1ð2ð3	6ð1ð2ð3	NUM
cana-3320	338	8	{	{	PUNCT
cana-3320	338	9	<	<	X
cana-3320	338	10	̃i(ð1	̃i(ð1	NOUN
cana-3320	338	11	,	,	PUNCT
cana-3320	338	12	ǎ)o<̃i1(ð2	ǎ)o<̃i1(ð2	PROPN
cana-3320	338	13	,	,	PUNCT
cana-3320	338	14	ǎ)o<̃i2(ð3	ǎ)o<̃i2(ð3	PROPN
cana-3320	338	15	,	,	PUNCT
cana-3320	338	16	ǎ)}o℘̃o℘̃o℘̃o℘̃	ǎ)}o℘̃o℘̃o℘̃o℘̃	NOUN
cana-3320	338	17	]	]	PUNCT
cana-3320	338	18	m	m	VERB
cana-3320	338	19	∂̃	∂̃	NOUN
cana-3320	338	20	=	=	PUNCT
cana-3320	338	21	[	[	PUNCT
cana-3320	338	22	sup	sup	NOUN
cana-3320	338	23	}	}	PUNCT
cana-3320	338	24	6ð1ð2ð3	6ð1ð2ð3	NUM
cana-3320	338	25	{	{	PUNCT
cana-3320	338	26	(	(	PUNCT
cana-3320	338	27	<	<	X
cana-3320	338	28	̃i(ð1	̃i(ð1	NOUN
cana-3320	338	29	,	,	PUNCT
cana-3320	338	30	ǎ)o℘̃)o(<̃i1(ð2	ǎ)o℘̃)o(<̃i1(ð2	PROPN
cana-3320	338	31	,	,	PUNCT
cana-3320	338	32	ǎ)o℘̃)o(<̃i2(ð3	ǎ)o℘̃)o(<̃i2(ð3	PROPN
cana-3320	338	33	,	,	PUNCT
cana-3320	338	34	ǎ)o℘̃)}o℘̃	ǎ)o℘̃)}o℘̃	NOUN
cana-3320	338	35	]	]	PUNCT
cana-3320	338	36	m	m	VERB
cana-3320	338	37	∂̃	∂̃	NUM
cana-3320	338	38	6	6	NUM
cana-3320	338	39	(	(	PUNCT
cana-3320	338	40	{	{	PUNCT
cana-3320	338	41	(	(	PUNCT
cana-3320	338	42	<	<	X
cana-3320	338	43	̃i	̃i	NOUN
cana-3320	338	44	(	(	PUNCT
cana-3320	338	45	}	}	PUNCT
cana-3320	338	46	,	,	PUNCT
cana-3320	338	47	ǎ	ǎ	PROPN
cana-3320	338	48	)	)	PUNCT
cana-3320	338	49	m	m	AUX
cana-3320	338	50	∂̃)o(<̃i1	∂̃)o(<̃i1	VERB
cana-3320	338	51	(	(	PUNCT
cana-3320	338	52	}	}	PUNCT
cana-3320	338	53	,	,	PUNCT
cana-3320	338	54	ǎ	ǎ	PROPN
cana-3320	338	55	)	)	PUNCT
cana-3320	338	56	m	m	VERB
cana-3320	338	57	∂̃)o(<̃i2	∂̃)o(<̃i2	ADJ
cana-3320	338	58	(	(	PUNCT
cana-3320	338	59	}	}	PUNCT
cana-3320	338	60	,	,	PUNCT
cana-3320	338	61	ǎ	ǎ	PROPN
cana-3320	338	62	)	)	PUNCT
cana-3320	338	63	m	m	PROPN
cana-3320	338	64	∂̃)}o℘̃	∂̃)}o℘̃	NOUN
cana-3320	338	65	)	)	PUNCT
cana-3320	338	66	m	m	VERB
cana-3320	338	67	∂̃	∂̃	NOUN
cana-3320	338	68	=	=	PUNCT
cana-3320	338	69	{	{	PUNCT
cana-3320	338	70	(	(	PUNCT
cana-3320	338	71	(	(	PUNCT
cana-3320	338	72	<	<	X
cana-3320	338	73	̃i	̃i	NOUN
cana-3320	338	74	(	(	PUNCT
cana-3320	338	75	}	}	PUNCT
cana-3320	338	76	,	,	PUNCT
cana-3320	338	77	ǎ)o<̃i1	ǎ)o<̃i1	PROPN
cana-3320	338	78	(	(	PUNCT
cana-3320	338	79	}	}	PUNCT
cana-3320	338	80	,	,	PUNCT
cana-3320	338	81	ǎ)o<̃i2	ǎ)o<̃i2	PROPN
cana-3320	338	82	(	(	PUNCT
cana-3320	338	83	}	}	PUNCT
cana-3320	338	84	,	,	PUNCT
cana-3320	338	85	ǎ	ǎ	PROPN
cana-3320	338	86	)	)	PUNCT
cana-3320	338	87	)	)	PUNCT
cana-3320	339	1	m	m	PROPN
cana-3320	339	2	∂̃)o℘̃	∂̃)o℘̃	PROPN
cana-3320	339	3	}	}	PUNCT
cana-3320	339	4	m	m	VERB
cana-3320	339	5	∂̃	∂̃	NOUN
cana-3320	339	6	=	=	PUNCT
cana-3320	339	7	{	{	PUNCT
cana-3320	339	8	(	(	PUNCT
cana-3320	339	9	(	(	PUNCT
cana-3320	339	10	<	<	X
cana-3320	339	11	̃io<̃i1	̃io<̃i1	NOUN
cana-3320	339	12	o<̃i2	o<̃i2	NOUN
cana-3320	339	13	)	)	PUNCT
cana-3320	339	14	(	(	PUNCT
cana-3320	339	15	}	}	PUNCT
cana-3320	339	16	,	,	PUNCT
cana-3320	339	17	ǎ)o℘̃	ǎ)o℘̃	NOUN
cana-3320	339	18	}	}	PUNCT
cana-3320	339	19	m	m	VERB
cana-3320	339	20	∂̃	∂̃	NOUN
cana-3320	339	21	=	=	SYM
cana-3320	339	22	(	(	PUNCT
cana-3320	339	23	<	<	X
cana-3320	339	24	̃ifi1fi2	̃ifi1fi2	NOUN
cana-3320	339	25	)	)	PUNCT
cana-3320	339	26	℘̃	℘̃	PROPN
cana-3320	339	27	∂̃	∂̃	NOUN
cana-3320	339	28	(	(	PUNCT
cana-3320	339	29	}	}	PUNCT
cana-3320	339	30	,	,	PUNCT
cana-3320	339	31	ǎ	ǎ	PROPN
cana-3320	339	32	)	)	PUNCT
cana-3320	339	33	(=	(=	X
cana-3320	339	34	̃(i∗i1∗i2	̃(i∗i1∗i2	NOUN
cana-3320	339	35	]	]	PUNCT
cana-3320	339	36	)	)	PUNCT
cana-3320	339	37	℘̃	℘̃	PROPN
cana-3320	339	38	∂̃	∂̃	NOUN
cana-3320	339	39	(	(	PUNCT
cana-3320	339	40	}	}	PUNCT
cana-3320	339	41	,	,	PUNCT
cana-3320	339	42	ǎ	ǎ	PROPN
cana-3320	339	43	)	)	PUNCT
cana-3320	339	44	=	=	SYM
cana-3320	339	45	(	(	PUNCT
cana-3320	339	46	=	=	NOUN
cana-3320	339	47	̃(i∗i1∗i2	̃(i∗i1∗i2	NOUN
cana-3320	339	48	]	]	PUNCT
cana-3320	339	49	(	(	PUNCT
cana-3320	339	50	}	}	PUNCT
cana-3320	339	51	,	,	PUNCT
cana-3320	339	52	ǎ	ǎ	PROPN
cana-3320	339	53	)	)	PUNCT
cana-3320	339	54	m	m	VERB
cana-3320	339	55	℘̃)o∂̃	℘̃)o∂̃	NOUN
cana-3320	339	56	=	=	PUNCT
cana-3320	340	1	[	[	PUNCT
cana-3320	340	2	[	[	PUNCT
cana-3320	340	3	inf	inf	NOUN
cana-3320	340	4	}	}	PUNCT
cana-3320	340	5	6ð1ð2ð3	6ð1ð2ð3	NUM
cana-3320	340	6	{	{	PUNCT
cana-3320	340	7	=	=	NOUN
cana-3320	340	8	̃i(ð1	̃i(ð1	NOUN
cana-3320	340	9	,	,	PUNCT
cana-3320	340	10	ǎ	ǎ	NOUN
cana-3320	340	11	)	)	PUNCT
cana-3320	340	12	m	m	PROPN
cana-3320	341	1	=	=	VERB
cana-3320	341	2	̃i1	̃i1	PROPN
cana-3320	341	3	(	(	PUNCT
cana-3320	341	4	ð2	ð2	PROPN
cana-3320	341	5	,	,	PUNCT
cana-3320	341	6	ǎ	ǎ	PROPN
cana-3320	341	7	)	)	PUNCT
cana-3320	341	8	m	m	VERB
cana-3320	342	1	=	=	ADJ
cana-3320	342	2	̃i2	̃i2	X
cana-3320	342	3	(	(	PUNCT
cana-3320	342	4	ð3	ð3	PROPN
cana-3320	342	5	,	,	PUNCT
cana-3320	342	6	ǎ	ǎ	PROPN
cana-3320	342	7	)	)	PUNCT
cana-3320	342	8	}	}	PUNCT
cana-3320	342	9	m	m	VERB
cana-3320	342	10	℘̃	℘̃	NOUN
cana-3320	342	11	]	]	X
cana-3320	342	12	]	]	PUNCT
cana-3320	342	13	o∂̃	o∂̃	NOUN
cana-3320	342	14	=	=	SYM
cana-3320	342	15	[	[	PUNCT
cana-3320	342	16	inf	inf	NOUN
cana-3320	342	17	}	}	PUNCT
cana-3320	342	18	6ð1ð2ð3	6ð1ð2ð3	NUM
cana-3320	342	19	{	{	PUNCT
cana-3320	342	20	=	=	NOUN
cana-3320	342	21	̃i(ð1	̃i(ð1	NOUN
cana-3320	342	22	,	,	PUNCT
cana-3320	342	23	ǎ	ǎ	NOUN
cana-3320	342	24	)	)	PUNCT
cana-3320	342	25	m	m	PROPN
cana-3320	343	1	=	=	VERB
cana-3320	343	2	̃i1	̃i1	PROPN
cana-3320	343	3	(	(	PUNCT
cana-3320	343	4	ð2	ð2	PROPN
cana-3320	343	5	,	,	PUNCT
cana-3320	343	6	ǎ	ǎ	PROPN
cana-3320	343	7	)	)	PUNCT
cana-3320	343	8	m	m	VERB
cana-3320	344	1	=	=	ADJ
cana-3320	344	2	̃i2	̃i2	X
cana-3320	344	3	(	(	PUNCT
cana-3320	344	4	ð3	ð3	PROPN
cana-3320	344	5	,	,	PUNCT
cana-3320	344	6	ǎ	ǎ	PROPN
cana-3320	344	7	)	)	PUNCT
cana-3320	344	8	}	}	PUNCT
cana-3320	344	9	m	m	VERB
cana-3320	344	10	℘̃	℘̃	PROPN
cana-3320	344	11	m	m	NOUN
cana-3320	344	12	℘̃	℘̃	NOUN
cana-3320	344	13	m	m	NOUN
cana-3320	344	14	℘̃	℘̃	NOUN
cana-3320	344	15	m	m	NOUN
cana-3320	344	16	℘̃	℘̃	NOUN
cana-3320	344	17	]	]	PUNCT
cana-3320	344	18	o∂̃	o∂̃	NOUN
cana-3320	344	19	=	=	SYM
cana-3320	344	20	[	[	PUNCT
cana-3320	344	21	inf	inf	NOUN
cana-3320	344	22	}	}	PUNCT
cana-3320	344	23	6ð1ð2ð3	6ð1ð2ð3	NUM
cana-3320	344	24	{	{	PUNCT
cana-3320	344	25	(=	(=	ADP
cana-3320	344	26	̃i(ð1	̃i(ð1	NOUN
cana-3320	344	27	,	,	PUNCT
cana-3320	344	28	ǎ	ǎ	PROPN
cana-3320	344	29	)	)	PUNCT
cana-3320	344	30	m	m	PROPN
cana-3320	344	31	℘̃	℘̃	NOUN
cana-3320	344	32	)	)	PUNCT
cana-3320	344	33	m	m	VERB
cana-3320	344	34	(=	(=	ADJ
cana-3320	344	35	̃i1	̃i1	PROPN
cana-3320	344	36	(	(	PUNCT
cana-3320	344	37	ð2	ð2	PROPN
cana-3320	344	38	,	,	PUNCT
cana-3320	344	39	ǎ	ǎ	PROPN
cana-3320	344	40	)	)	PUNCT
cana-3320	344	41	m	m	PROPN
cana-3320	344	42	℘̃	℘̃	NOUN
cana-3320	344	43	)	)	PUNCT
cana-3320	344	44	m	m	VERB
cana-3320	344	45	(=	(=	X
cana-3320	345	1	̃i2	̃i2	PROPN
cana-3320	345	2	(	(	PUNCT
cana-3320	345	3	ð3	ð3	PROPN
cana-3320	345	4	,	,	PUNCT
cana-3320	345	5	ǎ	ǎ	PROPN
cana-3320	345	6	)	)	PUNCT
cana-3320	345	7	m	m	VERB
cana-3320	345	8	℘̃	℘̃	NOUN
cana-3320	345	9	)	)	PUNCT
cana-3320	345	10	}	}	PUNCT
cana-3320	345	11	m	m	VERB
cana-3320	345	12	℘̃	℘̃	NOUN
cana-3320	345	13	]	]	PUNCT
cana-3320	345	14	o∂̃	o∂̃	NOUN
cana-3320	345	15	>	>	X
cana-3320	345	16	(	(	PUNCT
cana-3320	345	17	{	{	PUNCT
cana-3320	345	18	(=	(=	NOUN
cana-3320	345	19	̃i	̃i	NOUN
cana-3320	345	20	(	(	PUNCT
cana-3320	345	21	}	}	PUNCT
cana-3320	345	22	,	,	PUNCT
cana-3320	345	23	ǎ)o∂̃	ǎ)o∂̃	PROPN
cana-3320	345	24	)	)	PUNCT
cana-3320	345	25	m	m	VERB
cana-3320	345	26	(=	(=	VERB
cana-3320	346	1	̃i1	̃i1	DET
cana-3320	346	2	(	(	PUNCT
cana-3320	346	3	}	}	PUNCT
cana-3320	346	4	,	,	PUNCT
cana-3320	346	5	ǎ)o∂̃	ǎ)o∂̃	PROPN
cana-3320	346	6	)	)	PUNCT
cana-3320	346	7	m	m	VERB
cana-3320	346	8	(=	(=	X
cana-3320	346	9	̃i2	̃i2	NOUN
cana-3320	346	10	(	(	PUNCT
cana-3320	346	11	}	}	PUNCT
cana-3320	346	12	,	,	PUNCT
cana-3320	346	13	ǎ)o∂̃	ǎ)o∂̃	PROPN
cana-3320	346	14	)	)	PUNCT
cana-3320	346	15	}	}	PUNCT
cana-3320	346	16	m	m	VERB
cana-3320	346	17	℘̃)o∂̃	℘̃)o∂̃	NOUN
cana-3320	346	18	=	=	SYM
cana-3320	346	19	{	{	PUNCT
cana-3320	346	20	(	(	PUNCT
cana-3320	346	21	(=	(=	NOUN
cana-3320	346	22	̃i	̃i	NOUN
cana-3320	346	23	(	(	PUNCT
cana-3320	346	24	}	}	PUNCT
cana-3320	346	25	,	,	PUNCT
cana-3320	346	26	ǎ	ǎ	PROPN
cana-3320	346	27	)	)	PUNCT
cana-3320	346	28	m	m	PROPN
cana-3320	347	1	=	=	SYM
cana-3320	347	2	̃i1	̃i1	PROPN
cana-3320	347	3	(	(	PUNCT
cana-3320	347	4	}	}	PUNCT
cana-3320	347	5	,	,	PUNCT
cana-3320	347	6	ǎ	ǎ	PROPN
cana-3320	347	7	)	)	PUNCT
cana-3320	347	8	m	m	VERB
cana-3320	348	1	=	=	ADJ
cana-3320	348	2	̃i2	̃i2	X
cana-3320	348	3	(	(	PUNCT
cana-3320	348	4	}	}	PUNCT
cana-3320	348	5	,	,	PUNCT
cana-3320	348	6	ǎ))o∂̃	ǎ))o∂̃	NOUN
cana-3320	348	7	)	)	PUNCT
cana-3320	348	8	m	m	NOUN
cana-3320	348	9	℘̃}o∂̃	℘̃}o∂̃	NOUN
cana-3320	348	10	=	=	SYM
cana-3320	348	11	{	{	PUNCT
cana-3320	348	12	(	(	PUNCT
cana-3320	348	13	(=	(=	NOUN
cana-3320	348	14	̃i	̃i	PROPN
cana-3320	348	15	m	m	NOUN
cana-3320	348	16	=	=	NOUN
cana-3320	348	17	̃i1	̃i1	NOUN
cana-3320	348	18	m	m	VERB
cana-3320	348	19	=	=	ADJ
cana-3320	348	20	̃i2	̃i2	NOUN
cana-3320	348	21	)	)	PUNCT
cana-3320	348	22	(	(	PUNCT
cana-3320	348	23	}	}	PUNCT
cana-3320	348	24	,	,	PUNCT
cana-3320	348	25	ǎ	ǎ	PROPN
cana-3320	348	26	)	)	PUNCT
cana-3320	348	27	m	m	VERB
cana-3320	348	28	℘̃}o∂̃	℘̃}o∂̃	NOUN
cana-3320	348	29	=	=	SYM
cana-3320	348	30	(	(	PUNCT
cana-3320	348	31	=	=	NOUN
cana-3320	348	32	̃igi1gi2	̃igi1gi2	NOUN
cana-3320	348	33	)	)	PUNCT
cana-3320	348	34	℘̃	℘̃	PROPN
cana-3320	348	35	∂̃	∂̃	NOUN
cana-3320	348	36	(	(	PUNCT
cana-3320	348	37	}	}	PUNCT
cana-3320	348	38	,	,	PUNCT
cana-3320	348	39	ǎ	ǎ	PROPN
cana-3320	348	40	)	)	PUNCT
cana-3320	348	41	let	let	VERB
cana-3320	348	42	ð1,ð2,ð3	ð1,ð2,ð3	PUNCT
cana-3320	348	43	/∈	/∈	PUNCT
cana-3320	349	1	i	i	PRON
cana-3320	349	2	}	}	PUNCT
cana-3320	349	3	.	.	PUNCT
cana-3320	350	1	if	if	SCONJ
cana-3320	350	2	i	i	PRON
cana-3320	350	3	}	}	PUNCT
cana-3320	350	4	=	=	SYM
cana-3320	350	5	∅	∅	NOUN
cana-3320	350	6	,	,	PUNCT
cana-3320	350	7	then	then	ADV
cana-3320	350	8	(	(	PUNCT
cana-3320	350	9	<	<	X
cana-3320	350	10	̃i	̃i	X
cana-3320	350	11	∗	∗	PROPN
cana-3320	350	12	i1	i1	PROPN
cana-3320	350	13	∗	∗	VERB
cana-3320	350	14	<	<	X
cana-3320	350	15	̃i2	̃i2	NOUN
cana-3320	350	16	)	)	PUNCT
cana-3320	350	17	(	(	PUNCT
cana-3320	350	18	}	}	PUNCT
cana-3320	350	19	,	,	PUNCT
cana-3320	350	20	ǎ	ǎ	PROPN
cana-3320	350	21	)	)	PUNCT
cana-3320	350	22	=	=	SYM
cana-3320	350	23	0	0	NUM
cana-3320	350	24	and	and	CCONJ
cana-3320	350	25	(=	(=	NOUN
cana-3320	350	26	̃i	̃i	PROPN
cana-3320	350	27	∗	∗	PROPN
cana-3320	350	28	i1	i1	PROPN
cana-3320	350	29	∗	∗	VERB
cana-3320	350	30	=	=	SYM
cana-3320	350	31	̃i2	̃i2	NOUN
cana-3320	350	32	)	)	PUNCT
cana-3320	350	33	(	(	PUNCT
cana-3320	350	34	}	}	PUNCT
cana-3320	350	35	,	,	PUNCT
cana-3320	350	36	ǎ	ǎ	PROPN
cana-3320	350	37	)	)	PUNCT
cana-3320	350	38	=	=	PUNCT
cana-3320	351	1	1	1	NUM
cana-3320	351	2	such	such	ADJ
cana-3320	351	3	that	that	SCONJ
cana-3320	351	4	}	}	NUM
cana-3320	351	5	6	6	NUM
cana-3320	351	6	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	351	7	.	.	PUNCT
cana-3320	352	1	(	(	PUNCT
cana-3320	352	2	<	<	X
cana-3320	352	3	̃(i∗i1∗i2	̃(i∗i1∗i2	X
cana-3320	352	4	]	]	SYM
cana-3320	352	5	)	)	PUNCT
cana-3320	352	6	℘̃	℘̃	PROPN
cana-3320	352	7	∂̃	∂̃	NOUN
cana-3320	352	8	(	(	PUNCT
cana-3320	352	9	}	}	PUNCT
cana-3320	352	10	,	,	PUNCT
cana-3320	352	11	ǎ	ǎ	PROPN
cana-3320	352	12	)	)	PUNCT
cana-3320	352	13	=	=	SYM
cana-3320	352	14	(	(	PUNCT
cana-3320	352	15	<	<	X
cana-3320	352	16	̃(i∗i1∗i2	̃(i∗i1∗i2	X
cana-3320	352	17	]	]	PUNCT
cana-3320	352	18	(	(	PUNCT
cana-3320	352	19	}	}	PUNCT
cana-3320	352	20	,	,	PUNCT
cana-3320	352	21	ǎ)o℘̃	ǎ)o℘̃	NOUN
cana-3320	352	22	)	)	PUNCT
cana-3320	352	23	m	m	VERB
cana-3320	352	24	∂̃	∂̃	NOUN
cana-3320	352	25	=	=	SYM
cana-3320	352	26	0	0	NUM
cana-3320	352	27	m	m	VERB
cana-3320	352	28	∂̃	∂̃	NOUN
cana-3320	352	29	6	6	NUM
cana-3320	352	30	(	(	PUNCT
cana-3320	352	31	<	<	X
cana-3320	352	32	̃ifi1fi2	̃ifi1fi2	PROPN
cana-3320	352	33	(	(	PUNCT
cana-3320	352	34	}	}	PUNCT
cana-3320	352	35	,	,	PUNCT
cana-3320	352	36	ǎ)o℘̃	ǎ)o℘̃	NOUN
cana-3320	352	37	)	)	PUNCT
cana-3320	352	38	m	m	VERB
cana-3320	352	39	∂̃	∂̃	NOUN
cana-3320	352	40	=	=	SYM
cana-3320	352	41	(	(	PUNCT
cana-3320	352	42	<	<	X
cana-3320	352	43	̃ifi1fi2	̃ifi1fi2	X
cana-3320	352	44	(	(	PUNCT
cana-3320	352	45	}	}	PUNCT
cana-3320	352	46	,	,	PUNCT
cana-3320	352	47	ǎ)o℘̃	ǎ)o℘̃	NOUN
cana-3320	352	48	)	)	PUNCT
cana-3320	352	49	(=	(=	X
cana-3320	352	50	̃(i∗i1∗i2	̃(i∗i1∗i2	NOUN
cana-3320	352	51	]	]	PUNCT
cana-3320	352	52	)	)	PUNCT
cana-3320	352	53	℘̃	℘̃	PROPN
cana-3320	352	54	∂̃	∂̃	NOUN
cana-3320	352	55	(	(	PUNCT
cana-3320	352	56	}	}	PUNCT
cana-3320	352	57	,	,	PUNCT
cana-3320	352	58	ǎ	ǎ	PROPN
cana-3320	352	59	)	)	PUNCT
cana-3320	352	60	=	=	SYM
cana-3320	353	1	(	(	PUNCT
cana-3320	353	2	=	=	NOUN
cana-3320	353	3	̃(i∗i1∗i2	̃(i∗i1∗i2	NOUN
cana-3320	353	4	]	]	PUNCT
cana-3320	353	5	(	(	PUNCT
cana-3320	353	6	}	}	PUNCT
cana-3320	353	7	,	,	PUNCT
cana-3320	353	8	ǎ	ǎ	PROPN
cana-3320	353	9	)	)	PUNCT
cana-3320	353	10	m	m	VERB
cana-3320	353	11	℘̃)o∂̃	℘̃)o∂̃	NOUN
cana-3320	353	12	=	=	SYM
cana-3320	353	13	1o∂̃	1o∂̃	NUM
cana-3320	353	14	=	=	SYM
cana-3320	353	15	∂̃	∂̃	NOUN
cana-3320	353	16	>	>	X
cana-3320	353	17	(=	(=	X
cana-3320	353	18	̃igi1gi2	̃igi1gi2	PROPN
cana-3320	353	19	(	(	PUNCT
cana-3320	353	20	}	}	PUNCT
cana-3320	353	21	,	,	PUNCT
cana-3320	353	22	ǎ	ǎ	PROPN
cana-3320	353	23	)	)	PUNCT
cana-3320	353	24	m	m	VERB
cana-3320	353	25	℘̃)o∂̃	℘̃)o∂̃	NOUN
cana-3320	353	26	=	=	SYM
cana-3320	353	27	(	(	PUNCT
cana-3320	353	28	=	=	NOUN
cana-3320	353	29	̃igi1gi2	̃igi1gi2	NOUN
cana-3320	353	30	(	(	PUNCT
cana-3320	353	31	}	}	PUNCT
cana-3320	353	32	,	,	PUNCT
cana-3320	353	33	ǎ	ǎ	PROPN
cana-3320	353	34	)	)	PUNCT
cana-3320	353	35	m	m	VERB
cana-3320	353	36	℘̃	℘̃	NOUN
cana-3320	353	37	)	)	PUNCT
cana-3320	353	38	therefore	therefore	ADV
cana-3320	353	39	(	(	PUNCT
cana-3320	353	40	(	(	PUNCT
cana-3320	353	41	i	i	NOUN
cana-3320	353	42	∗	∗	NOUN
cana-3320	353	43	i1∗i2])℘̃	i1∗i2])℘̃	NOUN
cana-3320	353	44	∂̃	∂̃	NOUN
cana-3320	353	45	⊆	⊆	NUM
cana-3320	353	46	(	(	PUNCT
cana-3320	353	47	(	(	PUNCT
cana-3320	353	48	if	if	SCONJ
cana-3320	353	49	i1	i1	PROPN
cana-3320	353	50	f	f	PROPN
cana-3320	353	51	i2])℘̃	i2])℘̃	VERB
cana-3320	353	52	∂̃	∂̃	PROPN
cana-3320	353	53	.	.	PUNCT
cana-3320	354	1	theorem	theorem	VERB
cana-3320	354	2	5.3	5.3	NUM
cana-3320	354	3	.	.	PUNCT
cana-3320	355	1	let	let	VERB
cana-3320	355	2	z	z	NOUN
cana-3320	355	3	is	be	AUX
cana-3320	355	4	regular	regular	ADJ
cana-3320	355	5	,	,	PUNCT
cana-3320	355	6	i	i	PRON
cana-3320	355	7	be	be	VERB
cana-3320	355	8	an	an	DET
cana-3320	355	9	(	(	PUNCT
cana-3320	355	10	∂̃	∂̃	PROPN
cana-3320	355	11	,	,	PUNCT
cana-3320	355	12	℘̃)iqvfri	℘̃)iqvfri	NUM
cana-3320	355	13	,	,	PUNCT
cana-3320	355	14	i1	i1	PROPN
cana-3320	355	15	be	be	AUX
cana-3320	355	16	an	an	DET
cana-3320	355	17	(	(	PUNCT
cana-3320	355	18	∂̃	∂̃	PROPN
cana-3320	355	19	,	,	PUNCT
cana-3320	355	20	℘̃	℘̃	PROPN
cana-3320	355	21	)	)	PUNCT
cana-3320	355	22	iqvflati	iqvflati	NOUN
cana-3320	355	23	and	and	CCONJ
cana-3320	355	24	i2	i2	PROPN
cana-3320	355	25	be	be	VERB
cana-3320	355	26	an	an	DET
cana-3320	355	27	(	(	PUNCT
cana-3320	355	28	∂̃	∂̃	PROPN
cana-3320	355	29	,	,	PUNCT
cana-3320	355	30	℘̃)iqvfli	℘̃)iqvfli	NUM
cana-3320	355	31	of	of	ADP
cana-3320	355	32	z	z	NOUN
cana-3320	356	1	if	if	SCONJ
cana-3320	357	1	and	and	CCONJ
cana-3320	357	2	only	only	ADV
cana-3320	357	3	if	if	SCONJ
cana-3320	357	4	(	(	PUNCT
cana-3320	357	5	(	(	PUNCT
cana-3320	357	6	i	i	PRON
cana-3320	357	7	∗	∗	PROPN
cana-3320	357	8	i1	i1	PROPN
cana-3320	357	9	∗	∗	PROPN
cana-3320	357	10	i2])℘̃	i2])℘̃	PROPN
cana-3320	357	11	∂̃	∂̃	PROPN
cana-3320	357	12	=	=	SYM
cana-3320	357	13	(	(	PUNCT
cana-3320	357	14	(	(	PUNCT
cana-3320	357	15	if	if	SCONJ
cana-3320	357	16	i1	i1	PROPN
cana-3320	357	17	f	f	PROPN
cana-3320	357	18	i2])℘̃	i2])℘̃	VERB
cana-3320	357	19	∂̃	∂̃	NOUN
cana-3320	357	20	.	.	PUNCT
cana-3320	358	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3320	358	2	585	585	NUM
cana-3320	358	3	communications	communication	NOUN
cana-3320	358	4	on	on	ADP
cana-3320	358	5	applied	apply	VERB
cana-3320	358	6	nonlinear	nonlinear	ADJ
cana-3320	358	7	analysis	analysis	NOUN
cana-3320	358	8	issn	issn	NOUN
cana-3320	358	9	:	:	PUNCT
cana-3320	358	10	1074	1074	NUM
cana-3320	358	11	-	-	PUNCT
cana-3320	358	12	133x	133x	NUM
cana-3320	358	13	vol	vol	NOUN
cana-3320	358	14	32	32	NUM
cana-3320	358	15	no	no	NOUN
cana-3320	358	16	.	.	PUNCT
cana-3320	359	1	6s	6s	NUM
cana-3320	359	2	(	(	PUNCT
cana-3320	359	3	2025	2025	NUM
cana-3320	359	4	)	)	PUNCT
cana-3320	359	5	proof	proof	NOUN
cana-3320	359	6	.	.	PUNCT
cana-3320	360	1	let	let	VERB
cana-3320	360	2	z	z	PRON
cana-3320	360	3	regular	regular	ADJ
cana-3320	361	1	and	and	CCONJ
cana-3320	361	2	i	i	PRON
cana-3320	361	3	be	be	VERB
cana-3320	361	4	an	an	DET
cana-3320	361	5	(	(	PUNCT
cana-3320	361	6	∂̃	∂̃	PROPN
cana-3320	361	7	,	,	PUNCT
cana-3320	361	8	℘̃)iqvfri	℘̃)iqvfri	NUM
cana-3320	361	9	,	,	PUNCT
cana-3320	361	10	i1	i1	PROPN
cana-3320	361	11	be	be	AUX
cana-3320	361	12	an	an	DET
cana-3320	361	13	(	(	PUNCT
cana-3320	361	14	∂̃	∂̃	NOUN
cana-3320	361	15	,	,	PUNCT
cana-3320	361	16	℘̃)iqvflati	℘̃)iqvflati	PUNCT
cana-3320	361	17	and	and	CCONJ
cana-3320	361	18	i2	i2	PROPN
cana-3320	361	19	be	be	VERB
cana-3320	361	20	an	an	DET
cana-3320	361	21	(	(	PUNCT
cana-3320	361	22	∂̃	∂̃	PROPN
cana-3320	361	23	,	,	PUNCT
cana-3320	361	24	℘̃)iqvfli	℘̃)iqvfli	NUM
cana-3320	361	25	of	of	ADP
cana-3320	361	26	z	z	PROPN
cana-3320	361	27	.	.	PUNCT
cana-3320	362	1	let	let	VERB
cana-3320	362	2	(	(	PUNCT
cana-3320	362	3	ð1,ð3	ð1,ð3	PROPN
cana-3320	362	4	)	)	PUNCT
cana-3320	362	5	∈	∈	PROPN
cana-3320	363	1	i	i	PRON
cana-3320	363	2	}	}	PUNCT
cana-3320	363	3	.	.	PUNCT
cana-3320	364	1	if	if	SCONJ
cana-3320	364	2	i	i	PRON
cana-3320	364	3	}	}	PUNCT
cana-3320	364	4	6=	6=	ADP
cana-3320	364	5	∅	∅	NOUN
cana-3320	364	6	,	,	PUNCT
cana-3320	364	7	then	then	ADV
cana-3320	364	8	}	}	PUNCT
cana-3320	364	9	6	6	NUM
cana-3320	364	10	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	364	11	.	.	PUNCT
cana-3320	365	1	thus	thus	ADV
cana-3320	365	2	,	,	PUNCT
cana-3320	365	3	<	<	X
cana-3320	365	4	̃i	̃i	NOUN
cana-3320	365	5	(	(	PUNCT
cana-3320	365	6	}	}	PUNCT
cana-3320	365	7	,	,	PUNCT
cana-3320	365	8	ǎ	ǎ	PROPN
cana-3320	365	9	)	)	PUNCT
cana-3320	365	10	>	>	X
cana-3320	365	11	<	<	X
cana-3320	365	12	̃i(ð1ð2ð3	̃i(ð1ð2ð3	X
cana-3320	365	13	)	)	PUNCT
cana-3320	365	14	>	>	X
cana-3320	366	1	<	<	X
cana-3320	366	2	̃i(ð1	̃i(ð1	NOUN
cana-3320	366	3	,	,	PUNCT
cana-3320	366	4	ǎ	ǎ	PROPN
cana-3320	366	5	)	)	PUNCT
cana-3320	366	6	and	and	CCONJ
cana-3320	366	7	=	=	NOUN
cana-3320	366	8	̃i	̃i	NOUN
cana-3320	366	9	(	(	PUNCT
cana-3320	366	10	}	}	PUNCT
cana-3320	366	11	,	,	PUNCT
cana-3320	366	12	ǎ	ǎ	PROPN
cana-3320	366	13	)	)	PUNCT
cana-3320	366	14	6	6	NUM
cana-3320	366	15	=	=	SYM
cana-3320	366	16	̃i(ð1ð2ð3	̃i(ð1ð2ð3	NOUN
cana-3320	366	17	)	)	PUNCT
cana-3320	366	18	6	6	NUM
cana-3320	366	19	=	=	NUM
cana-3320	366	20	̃i(ð1	̃i(ð1	NOUN
cana-3320	366	21	,	,	PUNCT
cana-3320	366	22	ǎ	ǎ	NOUN
cana-3320	366	23	)	)	PUNCT
cana-3320	366	24	.	.	PUNCT
cana-3320	367	1	similarly	similarly	ADV
cana-3320	367	2	<	<	X
cana-3320	367	3	̃i1	̃i1	PROPN
cana-3320	367	4	(	(	PUNCT
cana-3320	367	5	}	}	PUNCT
cana-3320	367	6	,	,	PUNCT
cana-3320	367	7	ǎ	ǎ	PROPN
cana-3320	367	8	)	)	PUNCT
cana-3320	367	9	>	>	X
cana-3320	368	1	<	<	X
cana-3320	368	2	̃i1(ð1ð2ð3	̃i1(ð1ð2ð3	X
cana-3320	368	3	)	)	PUNCT
cana-3320	368	4	>	>	X
cana-3320	369	1	<	<	X
cana-3320	369	2	̃i1(ð2	̃i1(ð2	PROPN
cana-3320	369	3	,	,	PUNCT
cana-3320	369	4	ǎ	ǎ	NOUN
cana-3320	369	5	)	)	PUNCT
cana-3320	369	6	and	and	CCONJ
cana-3320	369	7	=	=	PRON
cana-3320	369	8	̃i1	̃i1	PROPN
cana-3320	369	9	(	(	PUNCT
cana-3320	369	10	}	}	PUNCT
cana-3320	369	11	,	,	PUNCT
cana-3320	369	12	ǎ	ǎ	PROPN
cana-3320	369	13	)	)	PUNCT
cana-3320	369	14	6	6	NUM
cana-3320	369	15	=	=	SYM
cana-3320	369	16	̃i1(ð1ð2ð3	̃i1(ð1ð2ð3	NOUN
cana-3320	369	17	)	)	PUNCT
cana-3320	369	18	6	6	NUM
cana-3320	369	19	=	=	SYM
cana-3320	369	20	̃i1(ð2	̃i1(ð2	PROPN
cana-3320	369	21	,	,	PUNCT
cana-3320	369	22	ǎ	ǎ	PROPN
cana-3320	369	23	)	)	PUNCT
cana-3320	369	24	.	.	PUNCT
cana-3320	370	1	similarly	similarly	ADV
cana-3320	370	2	,	,	PUNCT
cana-3320	370	3	<	<	X
cana-3320	370	4	̃i2	̃i2	X
cana-3320	370	5	(	(	PUNCT
cana-3320	370	6	}	}	PUNCT
cana-3320	370	7	,	,	PUNCT
cana-3320	370	8	ǎ	ǎ	PROPN
cana-3320	370	9	)	)	PUNCT
cana-3320	370	10	>	>	X
cana-3320	371	1	<	<	X
cana-3320	371	2	̃i2	̃i2	X
cana-3320	371	3	(	(	PUNCT
cana-3320	371	4	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	371	5	)	)	PUNCT
cana-3320	371	6	>	>	X
cana-3320	372	1	<	<	X
cana-3320	372	2	̃i2	̃i2	X
cana-3320	372	3	(	(	PUNCT
cana-3320	372	4	ð3	ð3	PROPN
cana-3320	372	5	,	,	PUNCT
cana-3320	372	6	ǎ	ǎ	PROPN
cana-3320	372	7	)	)	PUNCT
cana-3320	372	8	and	and	CCONJ
cana-3320	372	9	=	=	PRON
cana-3320	372	10	̃i2	̃i2	NOUN
cana-3320	372	11	(	(	PUNCT
cana-3320	372	12	}	}	PUNCT
cana-3320	372	13	,	,	PUNCT
cana-3320	372	14	ǎ	ǎ	PROPN
cana-3320	372	15	)	)	PUNCT
cana-3320	372	16	6	6	NUM
cana-3320	372	17	=	=	X
cana-3320	372	18	̃i2	̃i2	X
cana-3320	372	19	(	(	PUNCT
cana-3320	372	20	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	372	21	)	)	PUNCT
cana-3320	372	22	6	6	NUM
cana-3320	372	23	=	=	X
cana-3320	372	24	̃i2	̃i2	X
cana-3320	372	25	(	(	PUNCT
cana-3320	372	26	ð3	ð3	PROPN
cana-3320	372	27	,	,	PUNCT
cana-3320	372	28	ǎ	ǎ	PROPN
cana-3320	372	29	)	)	PUNCT
cana-3320	372	30	.	.	PUNCT
cana-3320	373	1	for	for	ADP
cana-3320	373	2	}	}	PUNCT
cana-3320	373	3	∈	∈	PROPN
cana-3320	373	4	z	z	NOUN
cana-3320	373	5	,	,	PUNCT
cana-3320	373	6	there	there	PRON
cana-3320	373	7	exists	exist	VERB
cana-3320	373	8	x	x	X
cana-3320	373	9	∈	∈	PROPN
cana-3320	373	10	z	z	NOUN
cana-3320	373	11	such	such	ADJ
cana-3320	373	12	that	that	SCONJ
cana-3320	373	13	}	}	NUM
cana-3320	373	14	6	6	NUM
cana-3320	373	15	}	}	PUNCT
cana-3320	373	16	z1}z2}z3	z1}z2}z3	PROPN
cana-3320	373	17	}	}	PUNCT
cana-3320	373	18	.	.	PUNCT
cana-3320	374	1	then	then	ADV
cana-3320	374	2	}	}	PUNCT
cana-3320	374	3	,	,	PUNCT
cana-3320	374	4	(	(	PUNCT
cana-3320	374	5	z1}z2}z3	z1}z2}z3	PROPN
cana-3320	374	6	)	)	PUNCT
cana-3320	374	7	,	,	PUNCT
cana-3320	374	8	}	}	PUNCT
cana-3320	374	9	∈	∈	PROPN
cana-3320	374	10	i	i	X
cana-3320	374	11	}	}	PUNCT
cana-3320	374	12	.	.	PUNCT
cana-3320	375	1	we	we	PRON
cana-3320	375	2	have	have	VERB
cana-3320	375	3	(	(	PUNCT
cana-3320	375	4	<	<	X
cana-3320	375	5	̃(i∗i1∗i2	̃(i∗i1∗i2	X
cana-3320	375	6	]	]	SYM
cana-3320	375	7	)	)	PUNCT
cana-3320	375	8	℘̃	℘̃	PROPN
cana-3320	375	9	∂̃	∂̃	NOUN
cana-3320	375	10	(	(	PUNCT
cana-3320	375	11	}	}	PUNCT
cana-3320	375	12	,	,	PUNCT
cana-3320	375	13	ǎ	ǎ	PROPN
cana-3320	375	14	)	)	PUNCT
cana-3320	375	15	=	=	SYM
cana-3320	375	16	(	(	PUNCT
cana-3320	375	17	<	<	X
cana-3320	375	18	̃(i∗i1∗i2	̃(i∗i1∗i2	X
cana-3320	375	19	]	]	PUNCT
cana-3320	375	20	(	(	PUNCT
cana-3320	375	21	}	}	PUNCT
cana-3320	375	22	,	,	PUNCT
cana-3320	375	23	ǎ)o℘̃	ǎ)o℘̃	NOUN
cana-3320	375	24	)	)	PUNCT
cana-3320	375	25	m	m	VERB
cana-3320	375	26	∂̃	∂̃	NOUN
cana-3320	375	27	=	=	PUNCT
cana-3320	376	1	[	[	PUNCT
cana-3320	376	2	[	[	PUNCT
cana-3320	376	3	sup	sup	NOUN
cana-3320	376	4	}	}	PUNCT
cana-3320	376	5	6}z1}z2}z3	6}z1}z2}z3	NUM
cana-3320	376	6	}	}	PUNCT
cana-3320	376	7	{	{	PUNCT
cana-3320	376	8	<	<	X
cana-3320	376	9	̃i(ð1	̃i(ð1	NOUN
cana-3320	376	10	,	,	PUNCT
cana-3320	376	11	ǎ)o<̃i1(ð2	ǎ)o<̃i1(ð2	PROPN
cana-3320	376	12	,	,	PUNCT
cana-3320	376	13	ǎ)o<̃i2(ð3	ǎ)o<̃i2(ð3	PROPN
cana-3320	376	14	,	,	PUNCT
cana-3320	376	15	ǎ)}o℘̃	ǎ)}o℘̃	NOUN
cana-3320	376	16	]	]	PUNCT
cana-3320	376	17	]	]	PUNCT
cana-3320	376	18	m	m	VERB
cana-3320	376	19	∂̃	∂̃	NOUN
cana-3320	376	20	=	=	PUNCT
cana-3320	376	21	[	[	PUNCT
cana-3320	376	22	sup	sup	NOUN
cana-3320	376	23	}	}	PUNCT
cana-3320	376	24	6}z1}z2}z3	6}z1}z2}z3	NUM
cana-3320	376	25	}	}	PUNCT
cana-3320	376	26	{	{	PUNCT
cana-3320	376	27	<	<	X
cana-3320	376	28	̃i(ð1	̃i(ð1	NOUN
cana-3320	376	29	,	,	PUNCT
cana-3320	376	30	ǎ)o<̃i1(ð2	ǎ)o<̃i1(ð2	PROPN
cana-3320	376	31	,	,	PUNCT
cana-3320	376	32	ǎ)o<̃i2(ð3	ǎ)o<̃i2(ð3	PROPN
cana-3320	376	33	,	,	PUNCT
cana-3320	376	34	ǎ)}o℘̃o℘̃o℘̃o℘̃	ǎ)}o℘̃o℘̃o℘̃o℘̃	NOUN
cana-3320	376	35	]	]	PUNCT
cana-3320	376	36	m	m	VERB
cana-3320	376	37	∂̃	∂̃	NOUN
cana-3320	376	38	=	=	PUNCT
cana-3320	376	39	[	[	PUNCT
cana-3320	376	40	sup	sup	NOUN
cana-3320	376	41	}	}	PUNCT
cana-3320	376	42	6}z1}z2}z3	6}z1}z2}z3	NUM
cana-3320	376	43	}	}	PUNCT
cana-3320	376	44	{	{	PUNCT
cana-3320	376	45	(	(	PUNCT
cana-3320	376	46	<	<	X
cana-3320	376	47	̃i(ð1	̃i(ð1	NOUN
cana-3320	376	48	,	,	PUNCT
cana-3320	376	49	ǎ)o℘̃)o(<̃i1	ǎ)o℘̃)o(<̃i1	NOUN
cana-3320	376	50	(	(	PUNCT
cana-3320	376	51	ð2	ð2	PROPN
cana-3320	376	52	,	,	PUNCT
cana-3320	376	53	ǎ)o℘̃)o(<̃i2	ǎ)o℘̃)o(<̃i2	NOUN
cana-3320	376	54	(	(	PUNCT
cana-3320	376	55	ð3	ð3	PROPN
cana-3320	376	56	,	,	PUNCT
cana-3320	376	57	ǎ)o℘̃)}o℘̃	ǎ)o℘̃)}o℘̃	PROPN
cana-3320	376	58	]	]	PUNCT
cana-3320	376	59	m	m	VERB
cana-3320	376	60	∂̃	∂̃	NOUN
cana-3320	376	61	>	>	X
cana-3320	376	62	(	(	PUNCT
cana-3320	376	63	{	{	PUNCT
cana-3320	376	64	(	(	PUNCT
cana-3320	376	65	<	<	X
cana-3320	376	66	̃i	̃i	NOUN
cana-3320	376	67	(	(	PUNCT
cana-3320	376	68	}	}	PUNCT
cana-3320	376	69	,	,	PUNCT
cana-3320	376	70	ǎ	ǎ	PROPN
cana-3320	376	71	)	)	PUNCT
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cana-3320	376	78	}	}	PUNCT
cana-3320	376	79	,	,	PUNCT
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cana-3320	376	83	∂̃)}o℘̃	∂̃)}o℘̃	NOUN
cana-3320	376	84	)	)	PUNCT
cana-3320	376	85	m	m	VERB
cana-3320	376	86	∂̃	∂̃	NOUN
cana-3320	376	87	>	>	X
cana-3320	376	88	(	(	PUNCT
cana-3320	376	89	{	{	PUNCT
cana-3320	376	90	(	(	PUNCT
cana-3320	376	91	<	<	X
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cana-3320	376	94	}	}	PUNCT
cana-3320	376	95	,	,	PUNCT
cana-3320	376	96	ǎ	ǎ	PROPN
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cana-3320	376	98	m	m	AUX
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cana-3320	376	100	(	(	PUNCT
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cana-3320	376	102	,	,	PUNCT
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cana-3320	376	107	(	(	PUNCT
cana-3320	376	108	}	}	PUNCT
cana-3320	376	109	,	,	PUNCT
cana-3320	376	110	ǎ	ǎ	PROPN
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cana-3320	376	112	m	m	PROPN
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cana-3320	376	114	)	)	PUNCT
cana-3320	376	115	m	m	VERB
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cana-3320	376	119	(	(	PUNCT
cana-3320	376	120	(	(	PUNCT
cana-3320	376	121	<	<	X
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cana-3320	376	123	(	(	PUNCT
cana-3320	376	124	}	}	PUNCT
cana-3320	376	125	,	,	PUNCT
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cana-3320	376	127	(	(	PUNCT
cana-3320	376	128	}	}	PUNCT
cana-3320	376	129	,	,	PUNCT
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cana-3320	376	131	(	(	PUNCT
cana-3320	376	132	}	}	PUNCT
cana-3320	376	133	,	,	PUNCT
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cana-3320	376	136	)	)	PUNCT
cana-3320	377	1	m	m	PROPN
cana-3320	377	2	∂̃)o℘̃	∂̃)o℘̃	PROPN
cana-3320	377	3	}	}	PUNCT
cana-3320	377	4	m	m	VERB
cana-3320	377	5	∂̃	∂̃	NOUN
cana-3320	377	6	=	=	PUNCT
cana-3320	377	7	{	{	PUNCT
cana-3320	377	8	(	(	PUNCT
cana-3320	377	9	(	(	PUNCT
cana-3320	377	10	<	<	X
cana-3320	377	11	̃io<̃i1o<̃i2	̃io<̃i1o<̃i2	X
cana-3320	377	12	)	)	PUNCT
cana-3320	377	13	(	(	PUNCT
cana-3320	377	14	}	}	PUNCT
cana-3320	377	15	,	,	PUNCT
cana-3320	377	16	ǎ)o℘̃	ǎ)o℘̃	NOUN
cana-3320	377	17	}	}	PUNCT
cana-3320	377	18	m	m	VERB
cana-3320	377	19	∂̃	∂̃	NOUN
cana-3320	377	20	=	=	SYM
cana-3320	377	21	(	(	PUNCT
cana-3320	377	22	<	<	X
cana-3320	377	23	̃ifi1fi2)℘̃	̃ifi1fi2)℘̃	ADJ
cana-3320	377	24	∂̃	∂̃	NOUN
cana-3320	377	25	(	(	PUNCT
cana-3320	377	26	}	}	PUNCT
cana-3320	377	27	,	,	PUNCT
cana-3320	377	28	ǎ	ǎ	PROPN
cana-3320	377	29	)	)	PUNCT
cana-3320	377	30	(=	(=	X
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cana-3320	377	32	]	]	PUNCT
cana-3320	377	33	)	)	PUNCT
cana-3320	377	34	℘̃	℘̃	PROPN
cana-3320	377	35	∂̃	∂̃	NOUN
cana-3320	377	36	(	(	PUNCT
cana-3320	377	37	}	}	PUNCT
cana-3320	377	38	,	,	PUNCT
cana-3320	377	39	ǎ	ǎ	PROPN
cana-3320	377	40	)	)	PUNCT
cana-3320	377	41	=	=	SYM
cana-3320	377	42	(	(	PUNCT
cana-3320	377	43	=	=	NOUN
cana-3320	377	44	̃(i∗i1∗i2	̃(i∗i1∗i2	NOUN
cana-3320	377	45	]	]	PUNCT
cana-3320	377	46	(	(	PUNCT
cana-3320	377	47	}	}	PUNCT
cana-3320	377	48	,	,	PUNCT
cana-3320	377	49	ǎ	ǎ	PROPN
cana-3320	377	50	)	)	PUNCT
cana-3320	377	51	m	m	VERB
cana-3320	377	52	℘̃)o∂̃	℘̃)o∂̃	NOUN
cana-3320	377	53	=	=	PUNCT
cana-3320	377	54	[	[	PUNCT
cana-3320	377	55	[	[	PUNCT
cana-3320	377	56	inf	inf	NOUN
cana-3320	377	57	}	}	PUNCT
cana-3320	377	58	6}z1}z2}z3	6}z1}z2}z3	NUM
cana-3320	377	59	}	}	PUNCT
cana-3320	377	60	{	{	PUNCT
cana-3320	377	61	=	=	ADJ
cana-3320	377	62	̃i(ð1	̃i(ð1	NOUN
cana-3320	377	63	,	,	PUNCT
cana-3320	377	64	ǎ	ǎ	NOUN
cana-3320	377	65	)	)	PUNCT
cana-3320	377	66	m	m	PROPN
cana-3320	378	1	=	=	VERB
cana-3320	378	2	̃i1	̃i1	PROPN
cana-3320	378	3	(	(	PUNCT
cana-3320	378	4	ð2	ð2	PROPN
cana-3320	378	5	,	,	PUNCT
cana-3320	378	6	ǎ	ǎ	PROPN
cana-3320	378	7	)	)	PUNCT
cana-3320	378	8	m	m	VERB
cana-3320	379	1	=	=	ADJ
cana-3320	379	2	̃i2	̃i2	X
cana-3320	379	3	(	(	PUNCT
cana-3320	379	4	ð3	ð3	PROPN
cana-3320	379	5	,	,	PUNCT
cana-3320	379	6	ǎ	ǎ	PROPN
cana-3320	379	7	)	)	PUNCT
cana-3320	379	8	}	}	PUNCT
cana-3320	379	9	m	m	VERB
cana-3320	379	10	℘̃	℘̃	NOUN
cana-3320	379	11	]	]	X
cana-3320	379	12	]	]	PUNCT
cana-3320	379	13	o∂̃	o∂̃	NOUN
cana-3320	379	14	=	=	SYM
cana-3320	379	15	[	[	PUNCT
cana-3320	379	16	inf	inf	NOUN
cana-3320	379	17	}	}	PUNCT
cana-3320	379	18	6}z1}z2}z3	6}z1}z2}z3	NUM
cana-3320	379	19	}	}	PUNCT
cana-3320	379	20	{	{	PUNCT
cana-3320	379	21	=	=	ADJ
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cana-3320	379	23	,	,	PUNCT
cana-3320	379	24	ǎ	ǎ	NOUN
cana-3320	379	25	)	)	PUNCT
cana-3320	379	26	m	m	PROPN
cana-3320	379	27	=	=	SYM
cana-3320	379	28	̃i1(ð2	̃i1(ð2	PROPN
cana-3320	379	29	,	,	PUNCT
cana-3320	379	30	ǎ	ǎ	PROPN
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cana-3320	379	32	m	m	PROPN
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cana-3320	379	35	,	,	PUNCT
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cana-3320	379	38	}	}	PUNCT
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cana-3320	379	41	m	m	NOUN
cana-3320	379	42	℘̃	℘̃	NOUN
cana-3320	379	43	m	m	NOUN
cana-3320	379	44	℘̃	℘̃	NOUN
cana-3320	379	45	m	m	NOUN
cana-3320	379	46	℘̃	℘̃	NOUN
cana-3320	379	47	]	]	PUNCT
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cana-3320	379	49	=	=	SYM
cana-3320	379	50	[	[	PUNCT
cana-3320	379	51	inf	inf	NOUN
cana-3320	379	52	}	}	PUNCT
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cana-3320	379	58	,	,	PUNCT
cana-3320	379	59	ǎ	ǎ	PROPN
cana-3320	379	60	)	)	PUNCT
cana-3320	379	61	m	m	PROPN
cana-3320	379	62	℘̃	℘̃	NOUN
cana-3320	379	63	)	)	PUNCT
cana-3320	379	64	m	m	VERB
cana-3320	379	65	(=	(=	PROPN
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cana-3320	379	67	,	,	PUNCT
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cana-3320	379	69	)	)	PUNCT
cana-3320	379	70	m	m	PROPN
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cana-3320	379	72	)	)	PUNCT
cana-3320	379	73	m	m	VERB
cana-3320	379	74	(=	(=	NOUN
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cana-3320	379	76	,	,	PUNCT
cana-3320	379	77	ǎ	ǎ	PROPN
cana-3320	379	78	)	)	PUNCT
cana-3320	379	79	m	m	PROPN
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cana-3320	379	81	)	)	PUNCT
cana-3320	379	82	}	}	PUNCT
cana-3320	380	1	m	m	VERB
cana-3320	380	2	℘̃	℘̃	NOUN
cana-3320	380	3	]	]	PUNCT
cana-3320	380	4	o∂̃	o∂̃	NOUN
cana-3320	380	5	6	6	NUM
cana-3320	380	6	(	(	PUNCT
cana-3320	380	7	{	{	PUNCT
cana-3320	380	8	(=	(=	NOUN
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cana-3320	380	10	(	(	PUNCT
cana-3320	380	11	}	}	PUNCT
cana-3320	380	12	,	,	PUNCT
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cana-3320	380	14	)	)	PUNCT
cana-3320	380	15	m	m	VERB
cana-3320	380	16	(=	(=	VERB
cana-3320	381	1	̃i1	̃i1	X
cana-3320	381	2	(	(	PUNCT
cana-3320	381	3	z1}z2}z3)o∂̃	z1}z2}z3)o∂̃	NOUN
cana-3320	381	4	)	)	PUNCT
cana-3320	381	5	m	m	VERB
cana-3320	381	6	(=	(=	X
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cana-3320	381	8	(	(	PUNCT
cana-3320	381	9	}	}	PUNCT
cana-3320	381	10	,	,	PUNCT
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cana-3320	381	12	)	)	PUNCT
cana-3320	381	13	}	}	PUNCT
cana-3320	381	14	m	m	VERB
cana-3320	381	15	℘̃)o∂̃	℘̃)o∂̃	NOUN
cana-3320	381	16	6	6	NUM
cana-3320	381	17	(	(	PUNCT
cana-3320	381	18	{	{	PUNCT
cana-3320	381	19	(=	(=	NOUN
cana-3320	381	20	̃i	̃i	NOUN
cana-3320	381	21	(	(	PUNCT
cana-3320	381	22	}	}	PUNCT
cana-3320	381	23	,	,	PUNCT
cana-3320	381	24	ǎ)o∂̃	ǎ)o∂̃	PROPN
cana-3320	381	25	)	)	PUNCT
cana-3320	381	26	m	m	VERB
cana-3320	381	27	(=	(=	VERB
cana-3320	381	28	̃i1	̃i1	PRON
cana-3320	381	29	(	(	PUNCT
cana-3320	381	30	}	}	PUNCT
cana-3320	381	31	,	,	PUNCT
cana-3320	381	32	ǎ)o∂̃	ǎ)o∂̃	PROPN
cana-3320	381	33	)	)	PUNCT
cana-3320	381	34	m	m	VERB
cana-3320	381	35	(=	(=	X
cana-3320	381	36	̃i2	̃i2	NOUN
cana-3320	381	37	(	(	PUNCT
cana-3320	381	38	}	}	PUNCT
cana-3320	381	39	,	,	PUNCT
cana-3320	381	40	ǎ)o∂̃	ǎ)o∂̃	PROPN
cana-3320	381	41	)	)	PUNCT
cana-3320	381	42	}	}	PUNCT
cana-3320	381	43	m	m	VERB
cana-3320	381	44	℘̃)o∂̃	℘̃)o∂̃	NOUN
cana-3320	381	45	=	=	SYM
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cana-3320	381	47	(	(	PUNCT
cana-3320	381	48	(=	(=	NOUN
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cana-3320	381	50	(	(	PUNCT
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cana-3320	381	52	,	,	PUNCT
cana-3320	381	53	ǎ	ǎ	PROPN
cana-3320	381	54	)	)	PUNCT
cana-3320	381	55	m	m	PROPN
cana-3320	382	1	=	=	SYM
cana-3320	382	2	̃i1	̃i1	PROPN
cana-3320	382	3	(	(	PUNCT
cana-3320	382	4	}	}	PUNCT
cana-3320	382	5	,	,	PUNCT
cana-3320	382	6	ǎ	ǎ	PROPN
cana-3320	382	7	)	)	PUNCT
cana-3320	382	8	m	m	VERB
cana-3320	383	1	=	=	ADJ
cana-3320	383	2	̃i2	̃i2	X
cana-3320	383	3	(	(	PUNCT
cana-3320	383	4	}	}	PUNCT
cana-3320	383	5	,	,	PUNCT
cana-3320	383	6	ǎ))o∂̃	ǎ))o∂̃	NOUN
cana-3320	383	7	)	)	PUNCT
cana-3320	383	8	m	m	NOUN
cana-3320	383	9	℘̃}o∂̃	℘̃}o∂̃	NOUN
cana-3320	383	10	=	=	SYM
cana-3320	383	11	{	{	PUNCT
cana-3320	383	12	(	(	PUNCT
cana-3320	383	13	(=	(=	NOUN
cana-3320	383	14	̃i	̃i	PROPN
cana-3320	383	15	m	m	NOUN
cana-3320	383	16	=	=	NOUN
cana-3320	383	17	̃i1	̃i1	NOUN
cana-3320	383	18	m	m	VERB
cana-3320	383	19	=	=	ADJ
cana-3320	383	20	̃i2	̃i2	NOUN
cana-3320	383	21	)	)	PUNCT
cana-3320	383	22	(	(	PUNCT
cana-3320	383	23	}	}	PUNCT
cana-3320	383	24	,	,	PUNCT
cana-3320	383	25	ǎ	ǎ	PROPN
cana-3320	383	26	)	)	PUNCT
cana-3320	383	27	m	m	VERB
cana-3320	383	28	℘̃}o∂̃	℘̃}o∂̃	NOUN
cana-3320	383	29	=	=	SYM
cana-3320	383	30	(	(	PUNCT
cana-3320	383	31	=	=	NOUN
cana-3320	383	32	̃igi1gi2	̃igi1gi2	NOUN
cana-3320	383	33	)	)	PUNCT
cana-3320	383	34	℘̃	℘̃	PROPN
cana-3320	383	35	∂̃	∂̃	NOUN
cana-3320	383	36	(	(	PUNCT
cana-3320	383	37	}	}	PUNCT
cana-3320	383	38	,	,	PUNCT
cana-3320	383	39	ǎ	ǎ	NOUN
cana-3320	383	40	)	)	PUNCT
cana-3320	383	41	thus	thus	ADV
cana-3320	383	42	,	,	PUNCT
cana-3320	383	43	(	(	PUNCT
cana-3320	383	44	(	(	PUNCT
cana-3320	383	45	i	i	PRON
cana-3320	383	46	∗	∗	PROPN
cana-3320	383	47	i1	i1	PROPN
cana-3320	383	48	∗	∗	PROPN
cana-3320	383	49	i2])℘̃	i2])℘̃	PROPN
cana-3320	383	50	∂̃	∂̃	PROPN
cana-3320	383	51	⊇	⊇	NOUN
cana-3320	383	52	(	(	PUNCT
cana-3320	383	53	(	(	PUNCT
cana-3320	383	54	if	if	SCONJ
cana-3320	383	55	i1	i1	PROPN
cana-3320	383	56	f	f	PROPN
cana-3320	383	57	i2])℘̃	i2])℘̃	VERB
cana-3320	383	58	∂̃	∂̃	PROPN
cana-3320	383	59	and	and	CCONJ
cana-3320	383	60	by	by	ADP
cana-3320	383	61	theorem	theorem	NOUN
cana-3320	383	62	5.2	5.2	NUM
cana-3320	383	63	.	.	PUNCT
cana-3320	384	1	hence	hence	ADV
cana-3320	384	2	,	,	PUNCT
cana-3320	384	3	(	(	PUNCT
cana-3320	384	4	(	(	PUNCT
cana-3320	384	5	i	i	PRON
cana-3320	384	6	∗	∗	PROPN
cana-3320	384	7	i1	i1	PROPN
cana-3320	384	8	∗	∗	PROPN
cana-3320	384	9	i2])℘̃	i2])℘̃	PROPN
cana-3320	384	10	∂̃	∂̃	PROPN
cana-3320	384	11	=	=	SYM
cana-3320	384	12	(	(	PUNCT
cana-3320	384	13	(	(	PUNCT
cana-3320	384	14	if	if	SCONJ
cana-3320	384	15	i1	i1	PROPN
cana-3320	384	16	f	f	PROPN
cana-3320	384	17	i2])℘̃	i2])℘̃	VERB
cana-3320	384	18	∂̃	∂̃	PROPN
cana-3320	384	19	.	.	PUNCT
cana-3320	385	1	conversely	conversely	ADV
cana-3320	385	2	assume	assume	VERB
cana-3320	385	3	that	that	SCONJ
cana-3320	385	4	(	(	PUNCT
cana-3320	385	5	(	(	PUNCT
cana-3320	385	6	i	i	PRON
cana-3320	385	7	∗	∗	PROPN
cana-3320	385	8	i1	i1	PROPN
cana-3320	385	9	∗	∗	PROPN
cana-3320	385	10	i2])℘̃	i2])℘̃	PROPN
cana-3320	385	11	∂̃	∂̃	PROPN
cana-3320	385	12	=	=	SYM
cana-3320	385	13	(	(	PUNCT
cana-3320	385	14	(	(	PUNCT
cana-3320	386	1	i	i	NOUN
cana-3320	386	2	f	f	PROPN
cana-3320	386	3	i1	i1	PROPN
cana-3320	386	4	f	f	PROPN
cana-3320	386	5	i2])℘̃	i2])℘̃	PROPN
cana-3320	386	6	∂̃	∂̃	PROPN
cana-3320	386	7	.	.	PUNCT
cana-3320	387	1	let	let	VERB
cana-3320	387	2	i	i	PRON
cana-3320	387	3	=	=	PUNCT
cana-3320	387	4	(	(	PUNCT
cana-3320	387	5	<	<	X
cana-3320	387	6	̃i	̃i	NOUN
cana-3320	387	7	,	,	PUNCT
cana-3320	387	8	=	=	NOUN
cana-3320	387	9	̃i	̃i	NOUN
cana-3320	387	10	)	)	PUNCT
cana-3320	387	11	be	be	VERB
cana-3320	387	12	an	an	DET
cana-3320	387	13	(	(	PUNCT
cana-3320	387	14	∂̃	∂̃	PROPN
cana-3320	387	15	,	,	PUNCT
cana-3320	387	16	℘̃)iqvfri	℘̃)iqvfri	NUM
cana-3320	387	17	,	,	PUNCT
cana-3320	387	18	i1	i1	PROPN
cana-3320	387	19	=	=	PUNCT
cana-3320	387	20	(	(	PUNCT
cana-3320	387	21	<	<	X
cana-3320	387	22	̃i1	̃i1	INTJ
cana-3320	387	23	,	,	PUNCT
cana-3320	387	24	=	=	PRON
cana-3320	387	25	̃i1	̃i1	NOUN
cana-3320	387	26	)	)	PUNCT
cana-3320	387	27	be	be	VERB
cana-3320	387	28	an	an	DET
cana-3320	387	29	(	(	PUNCT
cana-3320	387	30	∂̃	∂̃	NOUN
cana-3320	387	31	,	,	PUNCT
cana-3320	387	32	℘̃)iqvflati	℘̃)iqvflati	PUNCT
cana-3320	387	33	and	and	CCONJ
cana-3320	387	34	i2	i2	PROPN
cana-3320	387	35	=	=	SYM
cana-3320	387	36	(	(	PUNCT
cana-3320	387	37	<	<	X
cana-3320	387	38	̃i2	̃i2	NOUN
cana-3320	387	39	,	,	PUNCT
cana-3320	387	40	=	=	PRON
cana-3320	387	41	̃i2	̃i2	NOUN
cana-3320	387	42	)	)	PUNCT
cana-3320	387	43	be	be	AUX
cana-3320	387	44	an	an	DET
cana-3320	387	45	(	(	PUNCT
cana-3320	387	46	∂̃	∂̃	PROPN
cana-3320	387	47	,	,	PUNCT
cana-3320	387	48	℘̃)iqvfli	℘̃)iqvfli	NUM
cana-3320	387	49	of	of	ADP
cana-3320	387	50	z	z	PROPN
cana-3320	387	51	.	.	PUNCT
cana-3320	388	1	then	then	ADV
cana-3320	388	2	by	by	ADP
cana-3320	388	3	theorem	theorem	NOUN
cana-3320	388	4	4.6	4.6	NUM
cana-3320	388	5	,	,	PUNCT
cana-3320	388	6	ii	ii	PROPN
cana-3320	388	7	is	be	AUX
cana-3320	388	8	a	a	DET
cana-3320	388	9	(	(	PUNCT
cana-3320	388	10	∂̃	∂̃	PROPN
cana-3320	388	11	,	,	PUNCT
cana-3320	388	12	℘̃)iqvfri	℘̃)iqvfri	NUM
cana-3320	388	13	,	,	PUNCT
cana-3320	388	14	ii1	ii1	NOUN
cana-3320	388	15	is	be	AUX
cana-3320	388	16	a	a	DET
cana-3320	388	17	(	(	PUNCT
cana-3320	388	18	∂̃	∂̃	NOUN
cana-3320	388	19	,	,	PUNCT
cana-3320	388	20	℘̃)iqvflati	℘̃)iqvflati	PUNCT
cana-3320	388	21	and	and	CCONJ
cana-3320	388	22	ii2	ii2	PROPN
cana-3320	388	23	be	be	AUX
cana-3320	388	24	a	a	DET
cana-3320	388	25	(	(	PUNCT
cana-3320	388	26	∂̃	∂̃	PROPN
cana-3320	388	27	,	,	PUNCT
cana-3320	388	28	℘̃)iqvfli	℘̃)iqvfli	NUM
cana-3320	388	29	of	of	ADP
cana-3320	388	30	z	z	PROPN
cana-3320	388	31	.	.	PUNCT
cana-3320	389	1	by	by	ADP
cana-3320	389	2	lemma	lemma	PROPN
cana-3320	389	3	4.9	4.9	NUM
cana-3320	389	4	and	and	CCONJ
cana-3320	389	5	theorem	theorem	VERB
cana-3320	389	6	4.10	4.10	NUM
cana-3320	389	7	,	,	PUNCT
cana-3320	389	8	(	(	PUNCT
cana-3320	389	9	i(ifi1fi2	i(ifi1fi2	NOUN
cana-3320	389	10	]	]	X
cana-3320	389	11	)	)	PUNCT
cana-3320	389	12	℘̃	℘̃	NOUN
cana-3320	389	13	∂̃	∂̃	NOUN
cana-3320	389	14	=	=	SYM
cana-3320	389	15	(	(	PUNCT
cana-3320	389	16	ii	ii	PROPN
cana-3320	389	17	fii1	fii1	PROPN
cana-3320	389	18	fii2	fii2	PROPN
cana-3320	389	19	)	)	PUNCT
cana-3320	389	20	℘̃	℘̃	PROPN
cana-3320	389	21	∂̃	∂̃	NOUN
cana-3320	389	22	=	=	SYM
cana-3320	389	23	(	(	PUNCT
cana-3320	389	24	ii	ii	PROPN
cana-3320	389	25	∗ii1	∗ii1	PROPN
cana-3320	389	26	∗ii2	∗ii2	NOUN
cana-3320	389	27	)	)	PUNCT
cana-3320	389	28	℘̃	℘̃	PROPN
cana-3320	389	29	∂̃	∂̃	NOUN
cana-3320	389	30	=	=	SYM
cana-3320	389	31	(	(	PUNCT
cana-3320	389	32	i(i∗i1∗i2	i(i∗i1∗i2	X
cana-3320	389	33	]	]	SYM
cana-3320	389	34	)	)	PUNCT
cana-3320	389	35	℘̃	℘̃	PROPN
cana-3320	389	36	∂̃	∂̃	NOUN
cana-3320	389	37	.	.	PUNCT
cana-3320	390	1	this	this	PRON
cana-3320	390	2	implies	imply	VERB
cana-3320	390	3	(	(	PUNCT
cana-3320	390	4	if	if	SCONJ
cana-3320	390	5	i1	i1	PROPN
cana-3320	390	6	f	f	PROPN
cana-3320	391	1	i2]℘̃	i2]℘̃	PRON
cana-3320	391	2	∂̃	∂̃	PROPN
cana-3320	391	3	=	=	SYM
cana-3320	391	4	(	(	PUNCT
cana-3320	391	5	(	(	PUNCT
cana-3320	391	6	i	i	PRON
cana-3320	391	7	∗	∗	PROPN
cana-3320	391	8	i1	i1	PROPN
cana-3320	391	9	∗	∗	PROPN
cana-3320	391	10	i2])℘̃	i2])℘̃	PROPN
cana-3320	391	11	∂̃	∂̃	NOUN
cana-3320	391	12	.	.	PUNCT
cana-3320	392	1	hence	hence	ADV
cana-3320	392	2	by	by	ADP
cana-3320	392	3	corollary	corollary	ADJ
cana-3320	392	4	2.5	2.5	NUM
cana-3320	392	5	,	,	PUNCT
cana-3320	392	6	z	z	PROPN
cana-3320	392	7	is	be	AUX
cana-3320	392	8	regular	regular	ADJ
cana-3320	392	9	.	.	PUNCT
cana-3320	393	1	theorem	theorem	VERB
cana-3320	393	2	5.4	5.4	NUM
cana-3320	393	3	.	.	PUNCT
cana-3320	394	1	let	let	VERB
cana-3320	394	2	z	z	NOUN
cana-3320	394	3	is	be	AUX
cana-3320	394	4	regular	regular	ADJ
cana-3320	394	5	,	,	PUNCT
cana-3320	394	6	i	i	PRON
cana-3320	394	7	be	be	VERB
cana-3320	394	8	an	an	DET
cana-3320	394	9	(	(	PUNCT
cana-3320	394	10	∂̃	∂̃	PROPN
cana-3320	394	11	,	,	PUNCT
cana-3320	394	12	℘̃)iqvfbi	℘̃)iqvfbi	PROPN
cana-3320	394	13	,	,	PUNCT
cana-3320	394	14	i1	i1	PROPN
cana-3320	394	15	be	be	AUX
cana-3320	394	16	an	an	DET
cana-3320	394	17	(	(	PUNCT
cana-3320	394	18	∂̃	∂̃	NOUN
cana-3320	394	19	,	,	PUNCT
cana-3320	394	20	℘̃)iqvflati	℘̃)iqvflati	PUNCT
cana-3320	394	21	and	and	CCONJ
cana-3320	394	22	i2	i2	PROPN
cana-3320	394	23	be	be	VERB
cana-3320	394	24	an	an	DET
cana-3320	394	25	(	(	PUNCT
cana-3320	394	26	∂̃	∂̃	PROPN
cana-3320	394	27	,	,	PUNCT
cana-3320	394	28	℘̃)iqvfli	℘̃)iqvfli	NUM
cana-3320	394	29	of	of	ADP
cana-3320	394	30	z	z	NOUN
cana-3320	394	31	if	if	SCONJ
cana-3320	394	32	and	and	CCONJ
cana-3320	394	33	only	only	ADV
cana-3320	394	34	if	if	SCONJ
cana-3320	394	35	(	(	PUNCT
cana-3320	394	36	(	(	PUNCT
cana-3320	394	37	i	i	PRON
cana-3320	394	38	∗	∗	PROPN
cana-3320	394	39	i1	i1	PROPN
cana-3320	394	40	∗	∗	PROPN
cana-3320	394	41	i2])℘̃	i2])℘̃	PROPN
cana-3320	394	42	∂̃	∂̃	PROPN
cana-3320	394	43	=	=	SYM
cana-3320	394	44	(	(	PUNCT
cana-3320	394	45	(	(	PUNCT
cana-3320	394	46	if	if	SCONJ
cana-3320	394	47	i1	i1	PROPN
cana-3320	394	48	f	f	PROPN
cana-3320	394	49	i2])℘̃	i2])℘̃	VERB
cana-3320	394	50	∂̃	∂̃	NOUN
cana-3320	394	51	.	.	PUNCT
cana-3320	395	1	proof	proof	NOUN
cana-3320	395	2	.	.	PUNCT
cana-3320	396	1	let	let	VERB
cana-3320	396	2	z	z	NOUN
cana-3320	396	3	be	be	AUX
cana-3320	396	4	regular	regular	ADJ
cana-3320	396	5	semigroup	semigroup	NOUN
cana-3320	397	1	and	and	CCONJ
cana-3320	397	2	i	i	PRON
cana-3320	397	3	be	be	VERB
cana-3320	397	4	an	an	DET
cana-3320	397	5	(	(	PUNCT
cana-3320	397	6	∂̃	∂̃	NOUN
cana-3320	397	7	,	,	PUNCT
cana-3320	397	8	℘̃)iqvfbi	℘̃)iqvfbi	NUM
cana-3320	397	9	and	and	CCONJ
cana-3320	397	10	i2	i2	PROPN
cana-3320	397	11	be	be	VERB
cana-3320	397	12	an	an	DET
cana-3320	397	13	(	(	PUNCT
cana-3320	397	14	∂̃	∂̃	PROPN
cana-3320	397	15	,	,	PUNCT
cana-3320	397	16	℘̃)iqvfli	℘̃)iqvfli	NUM
cana-3320	397	17	of	of	ADP
cana-3320	397	18	z	z	PROPN
cana-3320	397	19	.	.	PUNCT
cana-3320	398	1	let	let	VERB
cana-3320	398	2	(	(	PUNCT
cana-3320	398	3	ð1,ð3	ð1,ð3	PROPN
cana-3320	398	4	)	)	PUNCT
cana-3320	398	5	∈	∈	PROPN
cana-3320	399	1	i	i	PRON
cana-3320	399	2	}	}	PUNCT
cana-3320	399	3	.	.	PUNCT
cana-3320	400	1	if	if	SCONJ
cana-3320	400	2	i	i	PRON
cana-3320	400	3	}	}	PUNCT
cana-3320	400	4	6=	6=	ADP
cana-3320	400	5	∅	∅	NOUN
cana-3320	400	6	,	,	PUNCT
cana-3320	400	7	then	then	ADV
cana-3320	400	8	}	}	PUNCT
cana-3320	400	9	6	6	NUM
cana-3320	400	10	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	400	11	.	.	PUNCT
cana-3320	401	1	thus	thus	ADV
cana-3320	401	2	<	<	X
cana-3320	401	3	̃i	̃i	NOUN
cana-3320	401	4	(	(	PUNCT
cana-3320	401	5	}	}	PUNCT
cana-3320	401	6	,	,	PUNCT
cana-3320	401	7	ǎ	ǎ	PROPN
cana-3320	401	8	)	)	PUNCT
cana-3320	401	9	>	>	X
cana-3320	401	10	<	<	X
cana-3320	401	11	̃i(ð1ð2ð3	̃i(ð1ð2ð3	X
cana-3320	401	12	)	)	PUNCT
cana-3320	401	13	>	>	X
cana-3320	401	14	<	<	X
cana-3320	401	15	̃i(ð1	̃i(ð1	NOUN
cana-3320	401	16	,	,	PUNCT
cana-3320	401	17	ǎ	ǎ	PROPN
cana-3320	401	18	)	)	PUNCT
cana-3320	401	19	and	and	CCONJ
cana-3320	401	20	=	=	NOUN
cana-3320	401	21	̃i	̃i	NOUN
cana-3320	401	22	(	(	PUNCT
cana-3320	401	23	}	}	PUNCT
cana-3320	401	24	,	,	PUNCT
cana-3320	401	25	ǎ	ǎ	PROPN
cana-3320	401	26	)	)	PUNCT
cana-3320	401	27	6	6	NUM
cana-3320	401	28	=	=	SYM
cana-3320	401	29	̃i(ð1ð2ð3	̃i(ð1ð2ð3	NOUN
cana-3320	401	30	)	)	PUNCT
cana-3320	401	31	6	6	NUM
cana-3320	401	32	=	=	NUM
cana-3320	401	33	̃i(ð1	̃i(ð1	NOUN
cana-3320	401	34	,	,	PUNCT
cana-3320	401	35	ǎ	ǎ	NOUN
cana-3320	401	36	)	)	PUNCT
cana-3320	401	37	.	.	PUNCT
cana-3320	402	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3320	403	1	586	586	NUM
cana-3320	403	2	<	<	X
cana-3320	403	3	̃	̃	PROPN
cana-3320	403	4	<	<	X
cana-3320	403	5	̃	̃	NOUN
cana-3320	403	6	<	<	X
cana-3320	403	7	̃	̃	NOUN
cana-3320	403	8	=	=	SYM
cana-3320	403	9	̃	̃	NOUN
cana-3320	403	10	=	=	SYM
cana-3320	403	11	̃	̃	NOUN
cana-3320	403	12	=	=	SYM
cana-3320	403	13	̃	̃	PROPN
cana-3320	403	14	<	<	X
cana-3320	403	15	̃	̃	NOUN
cana-3320	403	16	<	<	X
cana-3320	403	17	̃	̃	NOUN
cana-3320	403	18	<	<	X
cana-3320	403	19	̃	̃	NOUN
cana-3320	403	20	=	=	SYM
cana-3320	403	21	̃	̃	NOUN
cana-3320	403	22	=	=	SYM
cana-3320	403	23	̃	̃	NOUN
cana-3320	403	24	=	=	SYM
cana-3320	403	25	̃	̃	NOUN
cana-3320	403	26	communications	communication	NOUN
cana-3320	403	27	on	on	ADP
cana-3320	403	28	applied	apply	VERB
cana-3320	403	29	nonlinear	nonlinear	ADJ
cana-3320	403	30	analysis	analysis	NOUN
cana-3320	403	31	issn	issn	NOUN
cana-3320	403	32	:	:	PUNCT
cana-3320	403	33	1074	1074	NUM
cana-3320	403	34	-	-	PUNCT
cana-3320	403	35	133x	133x	NUM
cana-3320	403	36	vol	vol	NOUN
cana-3320	403	37	32	32	NUM
cana-3320	403	38	no	no	NOUN
cana-3320	403	39	.	.	PUNCT
cana-3320	404	1	6s	6s	NUM
cana-3320	404	2	(	(	PUNCT
cana-3320	404	3	2025	2025	NUM
cana-3320	404	4	)	)	PUNCT
cana-3320	404	5	similarly	similarly	ADV
cana-3320	404	6	i1	i1	PROPN
cana-3320	404	7	(	(	PUNCT
cana-3320	404	8	}	}	PUNCT
cana-3320	404	9	,	,	PUNCT
cana-3320	404	10	̌a	̌a	PROPN
cana-3320	404	11	)	)	PUNCT
cana-3320	404	12	>	>	X
cana-3320	404	13	i1	i1	PROPN
cana-3320	404	14	(	(	PUNCT
cana-3320	404	15	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	404	16	)	)	PUNCT
cana-3320	404	17	>	>	X
cana-3320	404	18	i1	i1	PROPN
cana-3320	404	19	(	(	PUNCT
cana-3320	404	20	ð2	ð2	PROPN
cana-3320	404	21	,	,	PUNCT
cana-3320	404	22	̌a	̌a	NOUN
cana-3320	404	23	)	)	PUNCT
cana-3320	404	24	and	and	CCONJ
cana-3320	404	25	i1	i1	PROPN
cana-3320	404	26	(	(	PUNCT
cana-3320	404	27	}	}	PUNCT
cana-3320	404	28	,	,	PUNCT
cana-3320	404	29	̌a	̌a	PROPN
cana-3320	404	30	)	)	PUNCT
cana-3320	404	31	6	6	NUM
cana-3320	404	32	i1	i1	PROPN
cana-3320	404	33	(	(	PUNCT
cana-3320	404	34	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	404	35	)	)	PUNCT
cana-3320	404	36	6	6	NUM
cana-3320	404	37	i1	i1	NOUN
cana-3320	404	38	(	(	PUNCT
cana-3320	404	39	ð2	ð2	PROPN
cana-3320	404	40	,	,	PUNCT
cana-3320	404	41	̌a	̌a	NOUN
cana-3320	404	42	)	)	PUNCT
cana-3320	404	43	.	.	PUNCT
cana-3320	405	1	similarly	similarly	ADV
cana-3320	405	2	,	,	PUNCT
cana-3320	405	3	i2	i2	PROPN
cana-3320	405	4	(	(	PUNCT
cana-3320	405	5	}	}	PUNCT
cana-3320	405	6	,	,	PUNCT
cana-3320	405	7	̌a	̌a	PROPN
cana-3320	405	8	)	)	PUNCT
cana-3320	405	9	>	>	X
cana-3320	405	10	i2	i2	PROPN
cana-3320	405	11	(	(	PUNCT
cana-3320	405	12	ð1ð2ð3	ð1ð2ð3	PROPN
cana-3320	405	13	)	)	PUNCT
cana-3320	405	14	>	>	X
cana-3320	405	15	i2	i2	PROPN
cana-3320	405	16	(	(	PUNCT
cana-3320	405	17	ð3	ð3	PROPN
cana-3320	405	18	,	,	PUNCT
cana-3320	405	19	̌a	̌a	NOUN
cana-3320	405	20	)	)	PUNCT
cana-3320	405	21	and	and	CCONJ
cana-3320	405	22	i2	i2	PROPN
cana-3320	405	23	(	(	PUNCT
cana-3320	405	24	}	}	PUNCT
cana-3320	405	25	,	,	PUNCT
cana-3320	405	26	̌a	̌a	PROPN
cana-3320	405	27	)	)	PUNCT
cana-3320	405	28	6	6	NUM
cana-3320	405	29	i2	i2	PROPN
cana-3320	405	30	(	(	PUNCT
cana-3320	405	31	ð1ð2ð3	ð1ð2ð3	NOUN
cana-3320	405	32	)	)	PUNCT
cana-3320	405	33	6	6	NUM
cana-3320	405	34	i2	i2	PROPN
cana-3320	405	35	(	(	PUNCT
cana-3320	405	36	ð3	ð3	PROPN
cana-3320	405	37	,	,	PUNCT
cana-3320	405	38	̌a	̌a	PROPN
cana-3320	405	39	)	)	PUNCT
cana-3320	405	40	.	.	PUNCT
cana-3320	406	1	for	for	ADP
cana-3320	406	2	}	}	PUNCT
cana-3320	406	3	∈	∈	PROPN
cana-3320	406	4	z	z	NOUN
cana-3320	406	5	,	,	PUNCT
cana-3320	406	6	there	there	PRON
cana-3320	406	7	exists	exist	VERB
cana-3320	406	8	x	x	X
cana-3320	406	9	∈	∈	PROPN
cana-3320	406	10	z	z	NOUN
cana-3320	406	11	such	such	ADJ
cana-3320	406	12	that	that	SCONJ
cana-3320	406	13	}	}	NUM
cana-3320	406	14	6	6	NUM
cana-3320	406	15	}	}	PUNCT
cana-3320	406	16	z1}z2}z3}z4}z5	z1}z2}z3}z4}z5	NUM
cana-3320	406	17	}	}	PUNCT
cana-3320	406	18	.	.	PUNCT
cana-3320	407	1	then	then	ADV
cana-3320	407	2	}	}	PUNCT
cana-3320	407	3	6	6	NUM
cana-3320	407	4	(	(	PUNCT
cana-3320	407	5	}	}	PUNCT
cana-3320	407	6	z1}z2	z1}z2	PROPN
cana-3320	407	7	}	}	PUNCT
cana-3320	407	8	,	,	PUNCT
cana-3320	407	9	̌a	̌a	PROPN
cana-3320	407	10	)	)	PUNCT
cana-3320	407	11	,	,	PUNCT
cana-3320	407	12	(	(	PUNCT
cana-3320	407	13	z3}z4}z5	z3}z4}z5	PROPN
cana-3320	407	14	)	)	PUNCT
cana-3320	407	15	,	,	PUNCT
cana-3320	407	16	}	}	PUNCT
cana-3320	407	17	∈	∈	PROPN
cana-3320	407	18	i	i	X
cana-3320	407	19	}	}	PUNCT
cana-3320	407	20	.	.	PUNCT
cana-3320	408	1	we	we	PRON
cana-3320	408	2	have	have	VERB
cana-3320	408	3	(	(	PUNCT
cana-3320	408	4	<	<	X
cana-3320	408	5	̃(i∗i1∗i2	̃(i∗i1∗i2	X
cana-3320	408	6	]	]	SYM
cana-3320	408	7	)	)	PUNCT
cana-3320	408	8	℘̃	℘̃	PROPN
cana-3320	408	9	∂̃	∂̃	NOUN
cana-3320	408	10	(	(	PUNCT
cana-3320	408	11	}	}	PUNCT
cana-3320	408	12	,	,	PUNCT
cana-3320	408	13	ǎ	ǎ	PROPN
cana-3320	408	14	)	)	PUNCT
cana-3320	408	15	=	=	SYM
cana-3320	408	16	(	(	PUNCT
cana-3320	408	17	<	<	X
cana-3320	408	18	̃(i∗i1∗i2	̃(i∗i1∗i2	X
cana-3320	408	19	]	]	PUNCT
cana-3320	408	20	(	(	PUNCT
cana-3320	408	21	}	}	PUNCT
cana-3320	408	22	,	,	PUNCT
cana-3320	408	23	ǎ)o℘̃	ǎ)o℘̃	NOUN
cana-3320	408	24	)	)	PUNCT
cana-3320	408	25	m	m	VERB
cana-3320	408	26	∂̃	∂̃	NOUN
cana-3320	408	27	=	=	PUNCT
cana-3320	409	1	[	[	PUNCT
cana-3320	409	2	[	[	PUNCT
cana-3320	409	3	sup	sup	NOUN
cana-3320	409	4	}	}	PUNCT
cana-3320	409	5	6}z1}z2}z3}z4}z5	6}z1}z2}z3}z4}z5	NUM
cana-3320	409	6	}	}	PUNCT
cana-3320	409	7	{	{	PUNCT
cana-3320	409	8	<	<	X
cana-3320	409	9	̃i(ð1	̃i(ð1	NOUN
cana-3320	409	10	,	,	PUNCT
cana-3320	409	11	ǎ)o<̃i1(ð2	ǎ)o<̃i1(ð2	PROPN
cana-3320	409	12	,	,	PUNCT
cana-3320	409	13	ǎ)o<̃i2	ǎ)o<̃i2	PROPN
cana-3320	409	14	(	(	PUNCT
cana-3320	409	15	ð3	ð3	PROPN
cana-3320	409	16	,	,	PUNCT
cana-3320	409	17	ǎ)}o℘̃	ǎ)}o℘̃	NOUN
cana-3320	409	18	]	]	PUNCT
cana-3320	409	19	]	]	PUNCT
cana-3320	409	20	m	m	VERB
cana-3320	409	21	∂̃	∂̃	NOUN
cana-3320	409	22	=	=	PUNCT
cana-3320	409	23	[	[	PUNCT
cana-3320	409	24	sup	sup	NOUN
cana-3320	409	25	}	}	PUNCT
cana-3320	409	26	6}z1}z2}z3}z4}z5	6}z1}z2}z3}z4}z5	NUM
cana-3320	409	27	}	}	PUNCT
cana-3320	409	28	{	{	PUNCT
cana-3320	409	29	<	<	NOUN
cana-3320	409	30	̃i(ð1	̃i(ð1	NOUN
cana-3320	409	31	,	,	PUNCT
cana-3320	409	32	ǎ)o<̃i1	ǎ)o<̃i1	PROPN
cana-3320	409	33	(	(	PUNCT
cana-3320	409	34	ð2	ð2	PROPN
cana-3320	409	35	,	,	PUNCT
cana-3320	409	36	ǎ)o<̃i2	ǎ)o<̃i2	PROPN
cana-3320	409	37	(	(	PUNCT
cana-3320	409	38	ð3	ð3	PROPN
cana-3320	409	39	,	,	PUNCT
cana-3320	409	40	ǎ)}o℘̃o℘̃o℘̃o℘̃	ǎ)}o℘̃o℘̃o℘̃o℘̃	NOUN
cana-3320	409	41	]	]	PUNCT
cana-3320	409	42	m	m	VERB
cana-3320	409	43	∂̃	∂̃	NOUN
cana-3320	409	44	=	=	PUNCT
cana-3320	409	45	[	[	PUNCT
cana-3320	409	46	sup	sup	NOUN
cana-3320	409	47	}	}	PUNCT
cana-3320	409	48	6}z1}z2}z3}z4}z5	6}z1}z2}z3}z4}z5	NUM
cana-3320	409	49	}	}	PUNCT
cana-3320	409	50	{	{	PUNCT
cana-3320	409	51	(	(	PUNCT
cana-3320	409	52	<	<	X
cana-3320	409	53	̃i(ð1	̃i(ð1	NOUN
cana-3320	409	54	,	,	PUNCT
cana-3320	409	55	ǎ)o℘̃)o(<̃i1	ǎ)o℘̃)o(<̃i1	NOUN
cana-3320	409	56	(	(	PUNCT
cana-3320	409	57	ð2	ð2	PROPN
cana-3320	409	58	,	,	PUNCT
cana-3320	409	59	ǎ)o℘̃)o(<̃i2	ǎ)o℘̃)o(<̃i2	NOUN
cana-3320	409	60	(	(	PUNCT
cana-3320	409	61	ð3	ð3	PROPN
cana-3320	409	62	,	,	PUNCT
cana-3320	409	63	ǎ)o℘̃)}o℘̃	ǎ)o℘̃)}o℘̃	PROPN
cana-3320	409	64	]	]	PUNCT
cana-3320	409	65	m	m	VERB
cana-3320	409	66	∂̃	∂̃	NOUN
cana-3320	409	67	>	>	X
cana-3320	409	68	(	(	PUNCT
cana-3320	409	69	{	{	PUNCT
cana-3320	409	70	(	(	PUNCT
cana-3320	409	71	<	<	X
cana-3320	409	72	̃i(}z1}z2	̃i(}z1}z2	NOUN
cana-3320	409	73	}	}	PUNCT
cana-3320	409	74	,	,	PUNCT
cana-3320	409	75	ǎ	ǎ	PROPN
cana-3320	409	76	)	)	PUNCT
cana-3320	409	77	m	m	PROPN
cana-3320	409	78	∂̃)o(<̃i1(z3}z4}z5	∂̃)o(<̃i1(z3}z4}z5	PROPN
cana-3320	409	79	)	)	PUNCT
cana-3320	409	80	m	m	VERB
cana-3320	409	81	∂̃)o(<̃i2	∂̃)o(<̃i2	ADJ
cana-3320	409	82	(	(	PUNCT
cana-3320	409	83	}	}	PUNCT
cana-3320	409	84	,	,	PUNCT
cana-3320	409	85	ǎ	ǎ	PROPN
cana-3320	409	86	)	)	PUNCT
cana-3320	409	87	m	m	PROPN
cana-3320	409	88	∂̃)}o℘̃	∂̃)}o℘̃	NOUN
cana-3320	409	89	)	)	PUNCT
cana-3320	409	90	m	m	VERB
cana-3320	410	1	∂̃	∂̃	NOUN
cana-3320	410	2	>	>	X
cana-3320	410	3	(	(	PUNCT
cana-3320	410	4	{	{	PUNCT
cana-3320	410	5	(	(	PUNCT
cana-3320	410	6	<	<	X
cana-3320	410	7	̃i	̃i	NOUN
cana-3320	410	8	(	(	PUNCT
cana-3320	410	9	}	}	PUNCT
cana-3320	410	10	,	,	PUNCT
cana-3320	410	11	ǎ	ǎ	PROPN
cana-3320	410	12	)	)	PUNCT
cana-3320	410	13	m	m	AUX
cana-3320	410	14	∂̃)o(<̃i1	∂̃)o(<̃i1	VERB
cana-3320	410	15	(	(	PUNCT
cana-3320	410	16	}	}	PUNCT
cana-3320	410	17	,	,	PUNCT
cana-3320	410	18	ǎ	ǎ	PROPN
cana-3320	410	19	)	)	PUNCT
cana-3320	410	20	m	m	VERB
cana-3320	410	21	∂̃)o(<̃i2	∂̃)o(<̃i2	ADJ
cana-3320	410	22	(	(	PUNCT
cana-3320	410	23	}	}	PUNCT
cana-3320	410	24	,	,	PUNCT
cana-3320	410	25	ǎ	ǎ	PROPN
cana-3320	410	26	)	)	PUNCT
cana-3320	410	27	m	m	PROPN
cana-3320	410	28	∂̃)}o℘̃	∂̃)}o℘̃	NOUN
cana-3320	410	29	)	)	PUNCT
cana-3320	410	30	m	m	VERB
cana-3320	410	31	∂̃	∂̃	NOUN
cana-3320	410	32	=	=	PUNCT
cana-3320	410	33	{	{	PUNCT
cana-3320	410	34	(	(	PUNCT
cana-3320	410	35	(	(	PUNCT
cana-3320	410	36	<	<	X
cana-3320	410	37	̃i	̃i	NOUN
cana-3320	410	38	(	(	PUNCT
cana-3320	410	39	}	}	PUNCT
cana-3320	410	40	,	,	PUNCT
cana-3320	410	41	ǎ)o<̃i1	ǎ)o<̃i1	PROPN
cana-3320	410	42	(	(	PUNCT
cana-3320	410	43	}	}	PUNCT
cana-3320	410	44	,	,	PUNCT
cana-3320	410	45	ǎ)o<̃i2	ǎ)o<̃i2	PROPN
cana-3320	410	46	(	(	PUNCT
cana-3320	410	47	}	}	PUNCT
cana-3320	410	48	,	,	PUNCT
cana-3320	410	49	ǎ	ǎ	PROPN
cana-3320	410	50	)	)	PUNCT
cana-3320	410	51	)	)	PUNCT
cana-3320	411	1	m	m	PROPN
cana-3320	411	2	∂̃)o℘̃	∂̃)o℘̃	PROPN
cana-3320	411	3	}	}	PUNCT
cana-3320	411	4	m	m	VERB
cana-3320	411	5	∂̃	∂̃	NOUN
cana-3320	411	6	=	=	PUNCT
cana-3320	411	7	{	{	PUNCT
cana-3320	411	8	(	(	PUNCT
cana-3320	411	9	(	(	PUNCT
cana-3320	411	10	<	<	X
cana-3320	411	11	̃io<̃i1o<̃i2	̃io<̃i1o<̃i2	X
cana-3320	411	12	)	)	PUNCT
cana-3320	411	13	(	(	PUNCT
cana-3320	411	14	}	}	PUNCT
cana-3320	411	15	,	,	PUNCT
cana-3320	411	16	ǎ)o℘̃	ǎ)o℘̃	NOUN
cana-3320	411	17	}	}	PUNCT
cana-3320	411	18	m	m	VERB
cana-3320	411	19	∂̃	∂̃	NOUN
cana-3320	411	20	=	=	SYM
cana-3320	411	21	(	(	PUNCT
cana-3320	411	22	<	<	X
cana-3320	411	23	̃ifi1fi2)℘̃	̃ifi1fi2)℘̃	ADJ
cana-3320	411	24	∂̃	∂̃	NOUN
cana-3320	411	25	(	(	PUNCT
cana-3320	411	26	}	}	PUNCT
cana-3320	411	27	,	,	PUNCT
cana-3320	411	28	ǎ	ǎ	PROPN
cana-3320	411	29	)	)	PUNCT
cana-3320	411	30	(=	(=	X
cana-3320	411	31	̃(i∗i1∗i2	̃(i∗i1∗i2	NOUN
cana-3320	411	32	]	]	PUNCT
cana-3320	411	33	)	)	PUNCT
cana-3320	411	34	℘̃	℘̃	PROPN
cana-3320	411	35	∂̃	∂̃	NOUN
cana-3320	411	36	(	(	PUNCT
cana-3320	411	37	}	}	PUNCT
cana-3320	411	38	,	,	PUNCT
cana-3320	411	39	ǎ	ǎ	PROPN
cana-3320	411	40	)	)	PUNCT
cana-3320	411	41	=	=	SYM
cana-3320	411	42	(	(	PUNCT
cana-3320	411	43	=	=	NOUN
cana-3320	411	44	̃(i∗i1∗i2	̃(i∗i1∗i2	NOUN
cana-3320	411	45	]	]	PUNCT
cana-3320	411	46	(	(	PUNCT
cana-3320	411	47	}	}	PUNCT
cana-3320	411	48	,	,	PUNCT
cana-3320	411	49	ǎ	ǎ	PROPN
cana-3320	411	50	)	)	PUNCT
cana-3320	411	51	m	m	VERB
cana-3320	411	52	℘̃)o∂̃	℘̃)o∂̃	NOUN
cana-3320	411	53	=	=	PUNCT
cana-3320	411	54	[	[	PUNCT
cana-3320	411	55	[	[	PUNCT
cana-3320	411	56	inf	inf	NOUN
cana-3320	411	57	}	}	PUNCT
cana-3320	411	58	6}z1}z2}z3}z4}z5	6}z1}z2}z3}z4}z5	NUM
cana-3320	411	59	}	}	PUNCT
cana-3320	411	60	{	{	PUNCT
cana-3320	411	61	=	=	NOUN
cana-3320	411	62	̃i(ð1	̃i(ð1	NOUN
cana-3320	411	63	,	,	PUNCT
cana-3320	411	64	ǎ	ǎ	NOUN
cana-3320	411	65	)	)	PUNCT
cana-3320	411	66	m	m	PROPN
cana-3320	412	1	=	=	VERB
cana-3320	412	2	̃i1	̃i1	PROPN
cana-3320	412	3	(	(	PUNCT
cana-3320	412	4	ð2	ð2	PROPN
cana-3320	412	5	,	,	PUNCT
cana-3320	412	6	ǎ	ǎ	PROPN
cana-3320	412	7	)	)	PUNCT
cana-3320	412	8	m	m	VERB
cana-3320	413	1	=	=	ADJ
cana-3320	413	2	̃i2	̃i2	X
cana-3320	413	3	(	(	PUNCT
cana-3320	413	4	ð3	ð3	PROPN
cana-3320	413	5	,	,	PUNCT
cana-3320	413	6	ǎ	ǎ	PROPN
cana-3320	413	7	)	)	PUNCT
cana-3320	413	8	}	}	PUNCT
cana-3320	413	9	m	m	VERB
cana-3320	413	10	℘̃	℘̃	NOUN
cana-3320	413	11	]	]	X
cana-3320	413	12	]	]	PUNCT
cana-3320	413	13	o∂̃	o∂̃	NOUN
cana-3320	413	14	=	=	SYM
cana-3320	413	15	[	[	PUNCT
cana-3320	413	16	inf	inf	NOUN
cana-3320	413	17	}	}	PUNCT
cana-3320	413	18	6}z1}z2}z3}z4}z5	6}z1}z2}z3}z4}z5	NUM
cana-3320	413	19	}	}	PUNCT
cana-3320	413	20	{	{	PUNCT
cana-3320	413	21	=	=	NOUN
cana-3320	413	22	̃i(ð1	̃i(ð1	NOUN
cana-3320	413	23	,	,	PUNCT
cana-3320	413	24	ǎ	ǎ	NOUN
cana-3320	413	25	)	)	PUNCT
cana-3320	413	26	m	m	PROPN
cana-3320	414	1	=	=	VERB
cana-3320	414	2	̃i1	̃i1	PROPN
cana-3320	414	3	(	(	PUNCT
cana-3320	414	4	ð2	ð2	PROPN
cana-3320	414	5	,	,	PUNCT
cana-3320	414	6	ǎ	ǎ	PROPN
cana-3320	414	7	)	)	PUNCT
cana-3320	414	8	m	m	VERB
cana-3320	415	1	=	=	ADJ
cana-3320	415	2	̃i2	̃i2	X
cana-3320	415	3	(	(	PUNCT
cana-3320	415	4	ð3	ð3	PROPN
cana-3320	415	5	,	,	PUNCT
cana-3320	415	6	ǎ	ǎ	PROPN
cana-3320	415	7	)	)	PUNCT
cana-3320	415	8	}	}	PUNCT
cana-3320	415	9	m	m	VERB
cana-3320	415	10	℘̃	℘̃	PROPN
cana-3320	415	11	m	m	NOUN
cana-3320	415	12	℘̃	℘̃	NOUN
cana-3320	415	13	m	m	NOUN
cana-3320	415	14	℘̃	℘̃	NOUN
cana-3320	415	15	m	m	NOUN
cana-3320	415	16	℘̃	℘̃	NOUN
cana-3320	415	17	]	]	PUNCT
cana-3320	415	18	o∂̃	o∂̃	NOUN
cana-3320	415	19	=	=	SYM
cana-3320	415	20	[	[	PUNCT
cana-3320	415	21	inf	inf	NOUN
cana-3320	415	22	}	}	PUNCT
cana-3320	415	23	6}z1}z2}z3}z4}z5	6}z1}z2}z3}z4}z5	NUM
cana-3320	415	24	}	}	PUNCT
cana-3320	415	25	{	{	PUNCT
cana-3320	415	26	(=	(=	ADV
cana-3320	415	27	̃i(ð1	̃i(ð1	NOUN
cana-3320	415	28	,	,	PUNCT
cana-3320	415	29	ǎ	ǎ	PROPN
cana-3320	415	30	)	)	PUNCT
cana-3320	415	31	m	m	PROPN
cana-3320	415	32	℘̃	℘̃	NOUN
cana-3320	415	33	)	)	PUNCT
cana-3320	415	34	m	m	VERB
cana-3320	415	35	(=	(=	PROPN
cana-3320	415	36	̃i1(ð2	̃i1(ð2	PROPN
cana-3320	415	37	,	,	PUNCT
cana-3320	415	38	ǎ	ǎ	NOUN
cana-3320	415	39	)	)	PUNCT
cana-3320	415	40	m	m	PROPN
cana-3320	415	41	℘̃	℘̃	NOUN
cana-3320	415	42	)	)	PUNCT
cana-3320	415	43	m	m	VERB
cana-3320	415	44	(=	(=	NOUN
cana-3320	415	45	̃i2(ð3	̃i2(ð3	PROPN
cana-3320	415	46	,	,	PUNCT
cana-3320	415	47	ǎ	ǎ	PROPN
cana-3320	415	48	)	)	PUNCT
cana-3320	415	49	m	m	PROPN
cana-3320	415	50	℘̃	℘̃	NOUN
cana-3320	415	51	)	)	PUNCT
cana-3320	415	52	}	}	PUNCT
cana-3320	416	1	m	m	VERB
cana-3320	416	2	℘̃	℘̃	NOUN
cana-3320	416	3	]	]	PUNCT
cana-3320	416	4	o∂̃	o∂̃	NOUN
cana-3320	416	5	6	6	NUM
cana-3320	416	6	(	(	PUNCT
cana-3320	416	7	{	{	PUNCT
cana-3320	416	8	(=	(=	X
cana-3320	416	9	̃i(}z1}z2	̃i(}z1}z2	PROPN
cana-3320	416	10	}	}	PUNCT
cana-3320	416	11	,	,	PUNCT
cana-3320	416	12	ǎ)o∂̃	ǎ)o∂̃	PROPN
cana-3320	416	13	)	)	PUNCT
cana-3320	416	14	m	m	VERB
cana-3320	416	15	(=	(=	VERB
cana-3320	417	1	̃i1	̃i1	X
cana-3320	417	2	(	(	PUNCT
cana-3320	417	3	z3}z4}z5)o∂̃	z3}z4}z5)o∂̃	NOUN
cana-3320	417	4	)	)	PUNCT
cana-3320	417	5	m	m	VERB
cana-3320	417	6	(=	(=	X
cana-3320	417	7	̃i2	̃i2	NOUN
cana-3320	417	8	(	(	PUNCT
cana-3320	417	9	}	}	PUNCT
cana-3320	417	10	,	,	PUNCT
cana-3320	417	11	ǎ)o∂̃	ǎ)o∂̃	PROPN
cana-3320	417	12	)	)	PUNCT
cana-3320	417	13	}	}	PUNCT
cana-3320	417	14	m	m	VERB
cana-3320	417	15	℘̃)o∂̃	℘̃)o∂̃	NOUN
cana-3320	417	16	6	6	NUM
cana-3320	417	17	(	(	PUNCT
cana-3320	417	18	{	{	PUNCT
cana-3320	417	19	(=	(=	NOUN
cana-3320	417	20	̃i	̃i	NOUN
cana-3320	417	21	(	(	PUNCT
cana-3320	417	22	}	}	PUNCT
cana-3320	417	23	,	,	PUNCT
cana-3320	417	24	ǎ)o∂̃	ǎ)o∂̃	PROPN
cana-3320	417	25	)	)	PUNCT
cana-3320	417	26	m	m	VERB
cana-3320	417	27	(=	(=	VERB
cana-3320	418	1	̃i1	̃i1	DET
cana-3320	418	2	(	(	PUNCT
cana-3320	418	3	}	}	PUNCT
cana-3320	418	4	,	,	PUNCT
cana-3320	418	5	ǎ)o∂̃	ǎ)o∂̃	PROPN
cana-3320	418	6	)	)	PUNCT
cana-3320	418	7	m	m	VERB
cana-3320	418	8	(=	(=	X
cana-3320	418	9	̃i2	̃i2	NOUN
cana-3320	418	10	(	(	PUNCT
cana-3320	418	11	}	}	PUNCT
cana-3320	418	12	,	,	PUNCT
cana-3320	418	13	ǎ)o∂̃	ǎ)o∂̃	PROPN
cana-3320	418	14	)	)	PUNCT
cana-3320	418	15	}	}	PUNCT
cana-3320	418	16	m	m	VERB
cana-3320	418	17	℘̃)o∂̃	℘̃)o∂̃	NOUN
cana-3320	418	18	=	=	SYM
cana-3320	418	19	{	{	PUNCT
cana-3320	418	20	(	(	PUNCT
cana-3320	418	21	(=	(=	NOUN
cana-3320	418	22	̃i	̃i	NOUN
cana-3320	418	23	(	(	PUNCT
cana-3320	418	24	}	}	PUNCT
cana-3320	418	25	,	,	PUNCT
cana-3320	418	26	ǎ	ǎ	PROPN
cana-3320	418	27	)	)	PUNCT
cana-3320	418	28	m	m	PROPN
cana-3320	419	1	=	=	SYM
cana-3320	419	2	̃i1	̃i1	PROPN
cana-3320	419	3	(	(	PUNCT
cana-3320	419	4	}	}	PUNCT
cana-3320	419	5	,	,	PUNCT
cana-3320	419	6	ǎ	ǎ	PROPN
cana-3320	419	7	)	)	PUNCT
cana-3320	419	8	m	m	VERB
cana-3320	420	1	=	=	ADJ
cana-3320	420	2	̃i2	̃i2	X
cana-3320	420	3	(	(	PUNCT
cana-3320	420	4	}	}	PUNCT
cana-3320	420	5	,	,	PUNCT
cana-3320	420	6	ǎ))o∂̃	ǎ))o∂̃	NOUN
cana-3320	420	7	)	)	PUNCT
cana-3320	420	8	m	m	NOUN
cana-3320	420	9	℘̃}o∂̃	℘̃}o∂̃	NOUN
cana-3320	420	10	=	=	SYM
cana-3320	420	11	{	{	PUNCT
cana-3320	420	12	(	(	PUNCT
cana-3320	420	13	(=	(=	NOUN
cana-3320	420	14	̃i	̃i	PROPN
cana-3320	420	15	m	m	NOUN
cana-3320	420	16	=	=	NOUN
cana-3320	420	17	̃i1	̃i1	NOUN
cana-3320	420	18	m	m	VERB
cana-3320	420	19	=	=	ADJ
cana-3320	420	20	̃i2	̃i2	NOUN
cana-3320	420	21	)	)	PUNCT
cana-3320	420	22	(	(	PUNCT
cana-3320	420	23	}	}	PUNCT
cana-3320	420	24	,	,	PUNCT
cana-3320	420	25	ǎ	ǎ	PROPN
cana-3320	420	26	)	)	PUNCT
cana-3320	420	27	m	m	VERB
cana-3320	420	28	℘̃}o∂̃	℘̃}o∂̃	NOUN
cana-3320	420	29	=	=	SYM
cana-3320	420	30	(	(	PUNCT
cana-3320	420	31	=	=	NOUN
cana-3320	420	32	̃igi1gi2	̃igi1gi2	NOUN
cana-3320	420	33	)	)	PUNCT
cana-3320	420	34	℘̃	℘̃	PROPN
cana-3320	420	35	∂̃	∂̃	NOUN
cana-3320	420	36	(	(	PUNCT
cana-3320	420	37	}	}	PUNCT
cana-3320	420	38	,	,	PUNCT
cana-3320	420	39	ǎ	ǎ	PROPN
cana-3320	420	40	)	)	PUNCT
cana-3320	420	41	thus	thus	ADV
cana-3320	420	42	(	(	PUNCT
cana-3320	420	43	(	(	PUNCT
cana-3320	420	44	i∗i1∗i2])℘̃	i∗i1∗i2])℘̃	PROPN
cana-3320	420	45	∂̃	∂̃	PROPN
cana-3320	420	46	⊇	⊇	NOUN
cana-3320	420	47	(	(	PUNCT
cana-3320	420	48	(	(	PUNCT
cana-3320	420	49	ifi1fi2])℘̃	ifi1fi2])℘̃	VERB
cana-3320	420	50	∂̃	∂̃	NOUN
cana-3320	420	51	and	and	CCONJ
cana-3320	420	52	by	by	ADP
cana-3320	420	53	theorem	theorem	ADJ
cana-3320	420	54	5.2	5.2	NUM
cana-3320	420	55	and	and	CCONJ
cana-3320	420	56	hence	hence	ADV
cana-3320	420	57	(	(	PUNCT
cana-3320	420	58	(	(	PUNCT
cana-3320	420	59	i∗i1∗i2])℘̃	i∗i1∗i2])℘̃	PROPN
cana-3320	420	60	∂̃	∂̃	NOUN
cana-3320	420	61	=	=	SYM
cana-3320	420	62	(	(	PUNCT
cana-3320	420	63	(	(	PUNCT
cana-3320	420	64	ifi1fi2])℘̃	ifi1fi2])℘̃	VERB
cana-3320	420	65	∂̃	∂̃	NOUN
cana-3320	420	66	.	.	PUNCT
cana-3320	421	1	conversely	conversely	ADV
cana-3320	421	2	assume	assume	VERB
cana-3320	421	3	that	that	SCONJ
cana-3320	421	4	(	(	PUNCT
cana-3320	421	5	(	(	PUNCT
cana-3320	421	6	i	i	PRON
cana-3320	421	7	∗	∗	PROPN
cana-3320	421	8	i1	i1	PROPN
cana-3320	421	9	∗	∗	PROPN
cana-3320	421	10	i2])℘̃	i2])℘̃	PROPN
cana-3320	421	11	∂̃	∂̃	PROPN
cana-3320	421	12	=	=	SYM
cana-3320	421	13	(	(	PUNCT
cana-3320	421	14	(	(	PUNCT
cana-3320	422	1	i	i	NOUN
cana-3320	422	2	f	f	PROPN
cana-3320	422	3	i1	i1	PROPN
cana-3320	422	4	f	f	PROPN
cana-3320	422	5	i2])℘̃	i2])℘̃	PROPN
cana-3320	422	6	∂̃	∂̃	PROPN
cana-3320	422	7	.	.	PUNCT
cana-3320	423	1	let	let	VERB
cana-3320	423	2	i	i	PRON
cana-3320	423	3	=	=	PUNCT
cana-3320	423	4	(	(	PUNCT
cana-3320	423	5	<	<	X
cana-3320	423	6	̃i	̃i	NOUN
cana-3320	423	7	,	,	PUNCT
cana-3320	423	8	=	=	NOUN
cana-3320	423	9	̃i	̃i	NOUN
cana-3320	423	10	)	)	PUNCT
cana-3320	423	11	be	be	VERB
cana-3320	423	12	an	an	DET
cana-3320	423	13	(	(	PUNCT
cana-3320	423	14	∂̃	∂̃	PROPN
cana-3320	423	15	,	,	PUNCT
cana-3320	423	16	℘̃)iqvfbi	℘̃)iqvfbi	PROPN
cana-3320	423	17	,	,	PUNCT
cana-3320	423	18	i1	i1	PROPN
cana-3320	423	19	=	=	PUNCT
cana-3320	423	20	(	(	PUNCT
cana-3320	423	21	<	<	X
cana-3320	423	22	̃i1	̃i1	ADJ
cana-3320	423	23	,	,	PUNCT
cana-3320	423	24	ξi1	ξi1	INTJ
cana-3320	423	25	,	,	PUNCT
cana-3320	423	26	=	=	NOUN
cana-3320	423	27	̃i1	̃i1	NOUN
cana-3320	423	28	)	)	PUNCT
cana-3320	423	29	be	be	AUX
cana-3320	423	30	an	an	DET
cana-3320	423	31	(	(	PUNCT
cana-3320	423	32	∂̃	∂̃	NOUN
cana-3320	423	33	,	,	PUNCT
cana-3320	423	34	℘̃)iqvflati	℘̃)iqvflati	PUNCT
cana-3320	423	35	and	and	CCONJ
cana-3320	423	36	i2	i2	PROPN
cana-3320	423	37	=	=	SYM
cana-3320	423	38	(	(	PUNCT
cana-3320	423	39	<	<	X
cana-3320	423	40	̃i2	̃i2	NOUN
cana-3320	423	41	,	,	PUNCT
cana-3320	423	42	=	=	PRON
cana-3320	423	43	̃i2	̃i2	NOUN
cana-3320	423	44	)	)	PUNCT
cana-3320	423	45	be	be	AUX
cana-3320	423	46	an	an	DET
cana-3320	423	47	(	(	PUNCT
cana-3320	423	48	∂̃	∂̃	PROPN
cana-3320	423	49	,	,	PUNCT
cana-3320	423	50	℘̃)iqvfli	℘̃)iqvfli	NUM
cana-3320	423	51	of	of	ADP
cana-3320	423	52	z	z	PROPN
cana-3320	423	53	.	.	PUNCT
cana-3320	424	1	then	then	ADV
cana-3320	424	2	by	by	ADP
cana-3320	424	3	theorem	theorem	NOUN
cana-3320	424	4	4.6	4.6	NUM
cana-3320	424	5	,	,	PUNCT
cana-3320	424	6	ii	ii	PROPN
cana-3320	424	7	is	be	AUX
cana-3320	424	8	a	a	DET
cana-3320	424	9	(	(	PUNCT
cana-3320	424	10	∂̃	∂̃	PROPN
cana-3320	424	11	,	,	PUNCT
cana-3320	424	12	℘̃)iqvfbi	℘̃)iqvfbi	PROPN
cana-3320	424	13	,	,	PUNCT
cana-3320	424	14	ii1	ii1	NOUN
cana-3320	424	15	is	be	AUX
cana-3320	424	16	a	a	DET
cana-3320	424	17	(	(	PUNCT
cana-3320	424	18	∂̃	∂̃	NOUN
cana-3320	424	19	,	,	PUNCT
cana-3320	424	20	℘̃)iqvflati	℘̃)iqvflati	PUNCT
cana-3320	424	21	and	and	CCONJ
cana-3320	424	22	ii2	ii2	PROPN
cana-3320	424	23	be	be	AUX
cana-3320	424	24	a	a	DET
cana-3320	424	25	(	(	PUNCT
cana-3320	424	26	∂̃	∂̃	PROPN
cana-3320	424	27	,	,	PUNCT
cana-3320	424	28	℘̃)iqvfli	℘̃)iqvfli	NUM
cana-3320	424	29	of	of	ADP
cana-3320	424	30	z	z	PROPN
cana-3320	424	31	.	.	PUNCT
cana-3320	425	1	by	by	ADP
cana-3320	425	2	lemma	lemma	PROPN
cana-3320	425	3	4.9	4.9	NUM
cana-3320	425	4	and	and	CCONJ
cana-3320	425	5	theorem	theorem	VERB
cana-3320	425	6	4.10	4.10	NUM
cana-3320	425	7	,	,	PUNCT
cana-3320	425	8	(	(	PUNCT
cana-3320	425	9	i(ifi1fi2	i(ifi1fi2	NOUN
cana-3320	425	10	]	]	X
cana-3320	425	11	)	)	PUNCT
cana-3320	425	12	℘̃	℘̃	NOUN
cana-3320	425	13	∂̃	∂̃	NOUN
cana-3320	425	14	=	=	SYM
cana-3320	425	15	(	(	PUNCT
cana-3320	425	16	ii	ii	PROPN
cana-3320	425	17	fii1	fii1	PROPN
cana-3320	425	18	fii2)℘̃	fii2)℘̃	VERB
cana-3320	425	19	∂̃	∂̃	PROPN
cana-3320	425	20	=	=	SYM
cana-3320	425	21	(	(	PUNCT
cana-3320	425	22	ii	ii	NOUN
cana-3320	425	23	∗ii1	∗ii1	NOUN
cana-3320	425	24	∗ii2)℘̃	∗ii2)℘̃	PRON
cana-3320	425	25	∂̃	∂̃	NOUN
cana-3320	425	26	=	=	SYM
cana-3320	425	27	(	(	PUNCT
cana-3320	425	28	i(i∗i1∗i2	i(i∗i1∗i2	X
cana-3320	425	29	]	]	SYM
cana-3320	425	30	)	)	PUNCT
cana-3320	425	31	℘̃	℘̃	PROPN
cana-3320	425	32	∂̃	∂̃	NOUN
cana-3320	425	33	.	.	PUNCT
cana-3320	426	1	this	this	PRON
cana-3320	426	2	implies	imply	VERB
cana-3320	426	3	(	(	PUNCT
cana-3320	426	4	if	if	SCONJ
cana-3320	426	5	i1	i1	PROPN
cana-3320	426	6	f	f	PROPN
cana-3320	427	1	i2]℘̃	i2]℘̃	PRON
cana-3320	427	2	∂̃	∂̃	PROPN
cana-3320	427	3	=	=	SYM
cana-3320	427	4	(	(	PUNCT
cana-3320	427	5	(	(	PUNCT
cana-3320	427	6	i	i	PRON
cana-3320	427	7	∗	∗	PROPN
cana-3320	427	8	i1	i1	PROPN
cana-3320	427	9	∗	∗	PROPN
cana-3320	427	10	i2])℘̃	i2])℘̃	PROPN
cana-3320	427	11	∂̃	∂̃	NOUN
cana-3320	427	12	.	.	PUNCT
cana-3320	428	1	hence	hence	ADV
cana-3320	428	2	by	by	ADP
cana-3320	428	3	corollary	corollary	ADJ
cana-3320	428	4	2.5	2.5	NUM
cana-3320	428	5	,	,	PUNCT
cana-3320	428	6	z	z	PROPN
cana-3320	428	7	is	be	AUX
cana-3320	428	8	regular	regular	ADJ
cana-3320	428	9	.	.	PUNCT
cana-3320	429	1	references	reference	NOUN
cana-3320	429	2	[	[	X
cana-3320	429	3	1	1	NUM
cana-3320	429	4	]	]	X
cana-3320	429	5	lehmer	lehmer	PROPN
cana-3320	429	6	d.	d.	PROPN
cana-3320	429	7	h.	h.	PROPN
cana-3320	429	8	,	,	PUNCT
cana-3320	429	9	a	a	DET
cana-3320	429	10	ternary	ternary	ADJ
cana-3320	429	11	analogue	analogue	NOUN
cana-3320	429	12	of	of	ADP
cana-3320	429	13	abelian	abelian	ADJ
cana-3320	429	14	groups	group	NOUN
cana-3320	429	15	.	.	PUNCT
cana-3320	430	1	american	american	ADJ
cana-3320	430	2	journal	journal	PROPN
cana-3320	430	3	of	of	ADP
cana-3320	430	4	mathematics	mathematic	NOUN
cana-3320	430	5	,	,	PUNCT
cana-3320	430	6	(	(	PUNCT
cana-3320	430	7	1932	1932	NUM
cana-3320	430	8	)	)	PUNCT
cana-3320	430	9	,	,	PUNCT
cana-3320	430	10	329	329	NUM
cana-3320	430	11	-	-	SYM
cana-3320	430	12	338	338	NUM
cana-3320	430	13	.	.	PUNCT
cana-3320	431	1	[	[	X
cana-3320	431	2	2	2	NUM
cana-3320	431	3	]	]	PUNCT
cana-3320	431	4	hestenes	hestene	NOUN
cana-3320	431	5	m.r	m.r	PROPN
cana-3320	431	6	.	.	PROPN
cana-3320	432	1	a	a	DET
cana-3320	432	2	ternary	ternary	ADJ
cana-3320	432	3	algebra	algebra	NOUN
cana-3320	432	4	with	with	ADP
cana-3320	432	5	applications	application	NOUN
cana-3320	432	6	to	to	ADP
cana-3320	432	7	matrices	matrix	NOUN
cana-3320	432	8	and	and	CCONJ
cana-3320	432	9	linear	linear	ADJ
cana-3320	432	10	transformations	transformation	NOUN
cana-3320	432	11	.	.	PUNCT
cana-3320	433	1	arch	arch	NOUN
cana-3320	433	2	.	.	PUNCT
cana-3320	434	1	ration	ration	NOUN
cana-3320	434	2	.	.	PUNCT
cana-3320	435	1	mech	mech	PROPN
cana-3320	435	2	.	.	PUNCT
cana-3320	436	1	anal	anal	PROPN
cana-3320	436	2	.	.	PUNCT
cana-3320	437	1	11(1962	11(1962	NUM
cana-3320	437	2	)	)	PUNCT
cana-3320	438	1	,	,	PUNCT
cana-3320	438	2	138	138	NUM
cana-3320	438	3	-194	-194	PROPN
cana-3320	438	4	.	.	PUNCT
cana-3320	439	1	[	[	X
cana-3320	439	2	3	3	X
cana-3320	439	3	]	]	X
cana-3320	439	4	l.	l.	PROPN
cana-3320	439	5	a.	a.	PROPN
cana-3320	439	6	zadeh	zadeh	PROPN
cana-3320	439	7	,	,	PUNCT
cana-3320	439	8	fuzzy	fuzzy	ADJ
cana-3320	439	9	sets	set	NOUN
cana-3320	439	10	,	,	PUNCT
cana-3320	439	11	information	information	NOUN
cana-3320	439	12	and	and	CCONJ
cana-3320	439	13	control	control	NOUN
cana-3320	439	14	,	,	PUNCT
cana-3320	439	15	8	8	NUM
cana-3320	439	16	,	,	PUNCT
cana-3320	439	17	(	(	PUNCT
cana-3320	439	18	1965	1965	NUM
cana-3320	439	19	)	)	PUNCT
cana-3320	439	20	,	,	PUNCT
cana-3320	439	21	338	338	NUM
cana-3320	439	22	-	-	SYM
cana-3320	439	23	353	353	NUM
cana-3320	439	24	.	.	PUNCT
cana-3320	440	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3320	440	2	587	587	NUM
cana-3320	440	3	communications	communication	NOUN
cana-3320	440	4	on	on	ADP
cana-3320	440	5	applied	apply	VERB
cana-3320	440	6	nonlinear	nonlinear	ADJ
cana-3320	440	7	analysis	analysis	NOUN
cana-3320	440	8	issn	issn	NOUN
cana-3320	440	9	:	:	PUNCT
cana-3320	440	10	1074	1074	NUM
cana-3320	440	11	-	-	PUNCT
cana-3320	440	12	133x	133x	NUM
cana-3320	440	13	vol	vol	NOUN
cana-3320	440	14	32	32	NUM
cana-3320	440	15	no	no	NOUN
cana-3320	440	16	.	.	PUNCT
cana-3320	441	1	6s	6s	NUM
cana-3320	441	2	(	(	PUNCT
cana-3320	441	3	2025	2025	NUM
cana-3320	441	4	)	)	PUNCT
cana-3320	442	1	[	[	X
cana-3320	442	2	4	4	X
cana-3320	442	3	]	]	PUNCT
cana-3320	442	4	k.	k.	PROPN
cana-3320	442	5	atanassov	atanassov	PROPN
cana-3320	442	6	,	,	PUNCT
cana-3320	442	7	intuitionistic	intuitionistic	ADJ
cana-3320	442	8	fuzzy	fuzzy	ADJ
cana-3320	442	9	sets	set	NOUN
cana-3320	442	10	,	,	PUNCT
cana-3320	442	11	fuzzy	fuzzy	ADJ
cana-3320	442	12	sets	set	NOUN
cana-3320	442	13	and	and	CCONJ
cana-3320	442	14	systems	system	NOUN
cana-3320	442	15	,	,	PUNCT
cana-3320	442	16	20(1	20(1	NUM
cana-3320	442	17	)	)	PUNCT
cana-3320	442	18	,	,	PUNCT
cana-3320	442	19	(	(	PUNCT
cana-3320	442	20	1986	1986	NUM
cana-3320	442	21	)	)	PUNCT
cana-3320	442	22	87	87	NUM
cana-3320	442	23	-	-	SYM
cana-3320	442	24	96	96	NUM
cana-3320	442	25	.	.	PUNCT
cana-3320	443	1	[	[	X
cana-3320	443	2	5	5	NUM
cana-3320	443	3	]	]	PUNCT
cana-3320	443	4	r.	r.	PROPN
cana-3320	443	5	r.	r.	PROPN
cana-3320	443	6	yager	yager	PROPN
cana-3320	443	7	,	,	PUNCT
cana-3320	443	8	pythagorean	pythagorean	PROPN
cana-3320	443	9	membership	membership	NOUN
cana-3320	443	10	grades	grade	NOUN
cana-3320	443	11	in	in	ADP
cana-3320	443	12	multi	multi	ADJ
cana-3320	443	13	criteria	criterion	NOUN
cana-3320	443	14	decision	decision	NOUN
cana-3320	443	15	-	-	PUNCT
cana-3320	443	16	making	making	NOUN
cana-3320	443	17	,	,	PUNCT
cana-3320	443	18	ieee	ieee	NOUN
cana-3320	443	19	trans	tran	NOUN
cana-3320	443	20	.	.	PUNCT
cana-3320	444	1	fuzzy	fuzzy	ADJ
cana-3320	444	2	systems	system	NOUN
cana-3320	444	3	,	,	PUNCT
cana-3320	444	4	22	22	NUM
cana-3320	444	5	,	,	PUNCT
cana-3320	444	6	(	(	PUNCT
cana-3320	444	7	2014	2014	NUM
cana-3320	444	8	)	)	PUNCT
cana-3320	444	9	,	,	PUNCT
cana-3320	444	10	958	958	NUM
cana-3320	444	11	-	-	SYM
cana-3320	444	12	965	965	NUM
cana-3320	444	13	.	.	PUNCT
cana-3320	445	1	[	[	X
cana-3320	445	2	6	6	NUM
cana-3320	445	3	]	]	PUNCT
cana-3320	445	4	s.	s.	PROPN
cana-3320	445	5	ashraf	ashraf	PROPN
cana-3320	445	6	,	,	PUNCT
cana-3320	445	7	s.	s.	PROPN
cana-3320	445	8	abdullah	abdullah	PROPN
cana-3320	445	9	,	,	PUNCT
cana-3320	445	10	t.	t.	PROPN
cana-3320	445	11	mahmood	mahmood	PROPN
cana-3320	445	12	,	,	PUNCT
cana-3320	445	13	f.	f.	PROPN
cana-3320	445	14	ghani	ghani	PROPN
cana-3320	445	15	and	and	CCONJ
cana-3320	445	16	t.	t.	PROPN
cana-3320	445	17	mahmood	mahmood	PROPN
cana-3320	445	18	,	,	PUNCT
cana-3320	445	19	spherical	spherical	ADJ
cana-3320	445	20	fuzzy	fuzzy	ADJ
cana-3320	445	21	sets	set	NOUN
cana-3320	445	22	and	and	CCONJ
cana-3320	445	23	their	their	PRON
cana-3320	445	24	applications	application	NOUN
cana-3320	445	25	in	in	ADP
cana-3320	445	26	multi	multi	ADJ
cana-3320	445	27	-	-	ADJ
cana-3320	445	28	attribute	attribute	NOUN
cana-3320	445	29	decision	decision	NOUN
cana-3320	445	30	making	make	VERB
cana-3320	445	31	problems	problem	NOUN
cana-3320	445	32	,	,	PUNCT
cana-3320	445	33	journal	journal	NOUN
cana-3320	445	34	of	of	ADP
cana-3320	445	35	intelligent	intelligent	ADJ
cana-3320	445	36	and	and	CCONJ
cana-3320	445	37	fuzzy	fuzzy	ADJ
cana-3320	445	38	systems	system	NOUN
cana-3320	445	39	,	,	PUNCT
cana-3320	445	40	36	36	NUM
cana-3320	445	41	,	,	PUNCT
cana-3320	445	42	(	(	PUNCT
cana-3320	445	43	2019	2019	NUM
cana-3320	445	44	)	)	PUNCT
cana-3320	445	45	,	,	PUNCT
cana-3320	445	46	2829	2829	NUM
cana-3320	445	47	-	-	SYM
cana-3320	445	48	284	284	NUM
cana-3320	445	49	.	.	PUNCT
cana-3320	446	1	[	[	X
cana-3320	446	2	7	7	X
cana-3320	446	3	]	]	X
cana-3320	446	4	abdallah	abdallah	PROPN
cana-3320	446	5	shihadeh	shihadeh	PROPN
cana-3320	446	6	,	,	PUNCT
cana-3320	446	7	khaled	khaled	PROPN
cana-3320	446	8	ahmad	ahmad	PROPN
cana-3320	446	9	mohammad	mohammad	PROPN
cana-3320	446	10	matarneh	matarneh	PROPN
cana-3320	446	11	,	,	PUNCT
cana-3320	446	12	raed	raed	PROPN
cana-3320	446	13	hatamleh	hatamleh	PROPN
cana-3320	446	14	,	,	PUNCT
cana-3320	446	15	randa	randa	PROPN
cana-3320	446	16	bashir	bashir	PROPN
cana-3320	446	17	yousef	yousef	PROPN
cana-3320	447	1	hijazeen	hijazeen	PROPN
cana-3320	447	2	,	,	PUNCT
cana-3320	447	3	mowafaq	mowafaq	PROPN
cana-3320	447	4	omar	omar	PROPN
cana-3320	447	5	al	al	PROPN
cana-3320	447	6	-	-	PUNCT
cana-3320	447	7	qadri	qadri	PROPN
cana-3320	447	8	,	,	PUNCT
cana-3320	447	9	abdallah	abdallah	PROPN
cana-3320	447	10	al	al	PROPN
cana-3320	447	11	-	-	PUNCT
cana-3320	447	12	husban	husban	PROPN
cana-3320	447	13	,	,	PUNCT
cana-3320	447	14	an	an	DET
cana-3320	447	15	example	example	NOUN
cana-3320	447	16	of	of	ADP
cana-3320	447	17	two	two	NUM
cana-3320	447	18	-	-	PUNCT
cana-3320	447	19	fold	fold	ADJ
cana-3320	447	20	fuzzy	fuzzy	ADJ
cana-3320	447	21	algebras	algebra	NOUN
cana-3320	447	22	based	base	VERB
cana-3320	447	23	on	on	ADP
cana-3320	447	24	neutrosophic	neutrosophic	ADJ
cana-3320	447	25	real	real	ADJ
cana-3320	447	26	numbers	number	NOUN
cana-3320	447	27	,	,	PUNCT
cana-3320	447	28	neutrosophic	neutrosophic	ADJ
cana-3320	447	29	sets	set	NOUN
cana-3320	447	30	and	and	CCONJ
cana-3320	447	31	systems	system	NOUN
cana-3320	447	32	,	,	PUNCT
cana-3320	447	33	67	67	NUM
cana-3320	447	34	,	,	PUNCT
cana-3320	447	35	(	(	PUNCT
cana-3320	447	36	2024	2024	NUM
cana-3320	447	37	)	)	PUNCT
cana-3320	447	38	,	,	PUNCT
cana-3320	447	39	169	169	NUM
cana-3320	447	40	-	-	SYM
cana-3320	447	41	178	178	NUM
cana-3320	447	42	.	.	PUNCT
cana-3320	448	1	[	[	X
cana-3320	448	2	8	8	NUM
cana-3320	448	3	]	]	PUNCT
cana-3320	448	4	.	.	PUNCT
cana-3320	449	1	abdallah	abdallah	PROPN
cana-3320	449	2	al	al	PROPN
cana-3320	449	3	-	-	PROPN
cana-3320	449	4	husban	husban	PROPN
cana-3320	449	5	&	&	CCONJ
cana-3320	449	6	abdul	abdul	PROPN
cana-3320	449	7	razak	razak	PROPN
cana-3320	449	8	salleh	salleh	PROPN
cana-3320	449	9	2015	2015	NUM
cana-3320	449	10	.	.	PUNCT
cana-3320	450	1	complex	complex	ADJ
cana-3320	450	2	fuzzy	fuzzy	ADJ
cana-3320	450	3	hyperring	hyperring	NOUN
cana-3320	450	4	based	base	VERB
cana-3320	450	5	on	on	ADP
cana-3320	450	6	complex	complex	ADJ
cana-3320	450	7	fuzzy	fuzzy	ADJ
cana-3320	450	8	spaces	space	NOUN
cana-3320	450	9	.	.	PUNCT
cana-3320	451	1	proceedings	proceeding	NOUN
cana-3320	451	2	of	of	ADP
cana-3320	451	3	2nd	2nd	ADJ
cana-3320	451	4	innovation	innovation	NOUN
cana-3320	451	5	and	and	CCONJ
cana-3320	451	6	analytics	analytic	NOUN
cana-3320	451	7	conference	conference	NOUN
cana-3320	451	8	&	&	CCONJ
cana-3320	451	9	exhibition	exhibition	PROPN
cana-3320	451	10	(	(	PUNCT
cana-3320	451	11	iace	iace	NOUN
cana-3320	451	12	)	)	PUNCT
cana-3320	451	13	,	,	PUNCT
cana-3320	451	14	1691	1691	NUM
cana-3320	451	15	,	,	PUNCT
cana-3320	451	16	aip	aip	PROPN
cana-3320	451	17	publishing	publish	VERB
cana-3320	451	18	2015	2015	NUM
cana-3320	451	19	,	,	PUNCT
cana-3320	451	20	040009	040009	NUM
cana-3320	451	21	-	-	SYM
cana-3320	451	22	040017	040017	NUM
cana-3320	451	23	.	.	PUNCT
cana-3320	452	1	[	[	X
cana-3320	452	2	9	9	NUM
cana-3320	452	3	]	]	X
cana-3320	452	4	al	al	PROPN
cana-3320	452	5	-	-	PUNCT
cana-3320	452	6	husban	husban	PROPN
cana-3320	452	7	,	,	PUNCT
cana-3320	452	8	a.	a.	PROPN
cana-3320	452	9	,	,	PUNCT
cana-3320	452	10	&	&	CCONJ
cana-3320	452	11	salleh	salleh	PROPN
cana-3320	452	12	,	,	PUNCT
cana-3320	452	13	a.	a.	PROPN
cana-3320	452	14	r.	r.	PROPN
cana-3320	452	15	complex	complex	PROPN
cana-3320	452	16	fuzzy	fuzzy	ADJ
cana-3320	452	17	hypergroups	hypergroup	NOUN
cana-3320	452	18	based	base	VERB
cana-3320	452	19	on	on	ADP
cana-3320	452	20	complex	complex	ADJ
cana-3320	452	21	fuzzy	fuzzy	ADJ
cana-3320	452	22	spaces	space	NOUN
cana-3320	452	23	.	.	PUNCT
cana-3320	453	1	international	international	ADJ
cana-3320	453	2	journal	journal	NOUN
cana-3320	453	3	of	of	ADP
cana-3320	453	4	pure	pure	ADJ
cana-3320	453	5	and	and	CCONJ
cana-3320	453	6	applied	applied	ADJ
cana-3320	453	7	mathematics	mathematic	NOUN
cana-3320	453	8	,	,	PUNCT
cana-3320	453	9	107(4	107(4	NUM
cana-3320	453	10	)	)	PUNCT
cana-3320	453	11	,	,	PUNCT
cana-3320	453	12	(	(	PUNCT
cana-3320	453	13	2016	2016	NUM
cana-3320	453	14	)	)	PUNCT
cana-3320	453	15	,	,	PUNCT
cana-3320	453	16	949	949	NUM
cana-3320	453	17	-	-	SYM
cana-3320	453	18	958	958	NUM
cana-3320	453	19	.	.	PUNCT
cana-3320	454	1	[	[	X
cana-3320	454	2	10	10	NUM
cana-3320	454	3	]	]	X
cana-3320	454	4	al	al	PROPN
cana-3320	454	5	-	-	PUNCT
cana-3320	454	6	husban	husban	PROPN
cana-3320	454	7	,	,	PUNCT
cana-3320	454	8	a.	a.	PROPN
cana-3320	454	9	,	,	PUNCT
cana-3320	454	10	amourah	amourah	PROPN
cana-3320	454	11	,	,	PUNCT
cana-3320	454	12	a.	a.	PROPN
cana-3320	454	13	,	,	PUNCT
cana-3320	454	14	&	&	CCONJ
cana-3320	454	15	jaber	jaber	PROPN
cana-3320	454	16	,	,	PUNCT
cana-3320	454	17	j.	j.	PROPN
cana-3320	454	18	j.	j.	PROPN
cana-3320	454	19	bipolar	bipolar	PROPN
cana-3320	454	20	complex	complex	ADJ
cana-3320	454	21	fuzzy	fuzzy	ADJ
cana-3320	454	22	sets	set	NOUN
cana-3320	454	23	and	and	CCONJ
cana-3320	454	24	their	their	PRON
cana-3320	454	25	properties	property	NOUN
cana-3320	454	26	.	.	PUNCT
cana-3320	455	1	italian	italian	ADJ
cana-3320	455	2	journal	journal	NOUN
cana-3320	455	3	of	of	ADP
cana-3320	455	4	pure	pure	ADJ
cana-3320	455	5	and	and	CCONJ
cana-3320	455	6	applied	applied	ADJ
cana-3320	455	7	mathematics	mathematic	NOUN
cana-3320	455	8	,	,	PUNCT
cana-3320	455	9	43	43	NUM
cana-3320	455	10	,	,	PUNCT
cana-3320	455	11	2020	2020	NUM
cana-3320	455	12	,	,	PUNCT
cana-3320	455	13	754	754	NUM
cana-3320	455	14	-	-	SYM
cana-3320	455	15	761	761	NUM
cana-3320	455	16	.	.	PUNCT
cana-3320	456	1	[	[	X
cana-3320	456	2	11	11	NUM
cana-3320	456	3	]	]	PUNCT
cana-3320	456	4	rosenfeld	rosenfeld	PROPN
cana-3320	456	5	,	,	PUNCT
cana-3320	456	6	fuzzu	fuzzu	NOUN
cana-3320	456	7	groups	group	NOUN
cana-3320	456	8	,	,	PUNCT
cana-3320	456	9	j.math	j.math	NOUN
cana-3320	456	10	.	.	PUNCT
cana-3320	457	1	anal	anal	PROPN
cana-3320	457	2	.	.	PUNCT
cana-3320	458	1	appl.35	appl.35	PROPN
cana-3320	458	2	(	(	PUNCT
cana-3320	458	3	1971	1971	NUM
cana-3320	458	4	)	)	PUNCT
cana-3320	458	5	512	512	NUM
cana-3320	458	6	-	-	SYM
cana-3320	458	7	517	517	NUM
cana-3320	458	8	.	.	PUNCT
cana-3320	459	1	[	[	X
cana-3320	459	2	12	12	NUM
cana-3320	459	3	]	]	X
cana-3320	459	4	n.	n.	PROPN
cana-3320	459	5	kuroki	kuroki	PROPN
cana-3320	459	6	,	,	PUNCT
cana-3320	459	7	on	on	ADP
cana-3320	459	8	fuzzy	fuzzy	ADJ
cana-3320	459	9	semigroups	semigroup	NOUN
cana-3320	459	10	,	,	PUNCT
cana-3320	459	11	inform	inform	NOUN
cana-3320	459	12	.	.	PUNCT
cana-3320	460	1	sci	sci	PROPN
cana-3320	460	2	.	.	PROPN
cana-3320	461	1	53	53	NUM
cana-3320	461	2	(	(	PUNCT
cana-3320	461	3	1991	1991	NUM
cana-3320	461	4	)	)	PUNCT
cana-3320	461	5	,	,	PUNCT
cana-3320	461	6	203	203	NUM
cana-3320	461	7	-	-	SYM
cana-3320	461	8	236	236	NUM
cana-3320	461	9	.	.	PUNCT
cana-3320	462	1	[	[	X
cana-3320	462	2	13	13	NUM
cana-3320	462	3	]	]	PUNCT
cana-3320	462	4	j.	j.	PROPN
cana-3320	462	5	n.	n.	PROPN
cana-3320	462	6	mordeson	mordeson	PROPN
cana-3320	462	7	,	,	PUNCT
cana-3320	462	8	d.	d.	PROPN
cana-3320	462	9	s.	s.	PROPN
cana-3320	462	10	malik	malik	PROPN
cana-3320	462	11	,	,	PUNCT
cana-3320	462	12	n.	n.	PROPN
cana-3320	462	13	kuroki	kuroki	PROPN
cana-3320	462	14	,	,	PUNCT
cana-3320	462	15	fuzzy	fuzzy	ADJ
cana-3320	462	16	semigroups	semigroup	NOUN
cana-3320	462	17	,	,	PUNCT
cana-3320	462	18	springer	springer	NOUN
cana-3320	462	19	-	-	PUNCT
cana-3320	462	20	verlag	verlag	PROPN
cana-3320	462	21	berlin	berlin	PROPN
cana-3320	462	22	heidelberg	heidelberg	PROPN
cana-3320	462	23	gmbh	gmbh	PROPN
cana-3320	462	24	,	,	PUNCT
cana-3320	462	25	2003	2003	NUM
cana-3320	462	26	.	.	PUNCT
cana-3320	463	1	[	[	X
cana-3320	463	2	14	14	NUM
cana-3320	463	3	]	]	PUNCT
cana-3320	463	4	m.	m.	PROPN
cana-3320	463	5	k.	k.	PROPN
cana-3320	463	6	sen	sen	PROPN
cana-3320	463	7	,	,	PUNCT
cana-3320	463	8	on	on	ADP
cana-3320	463	9	i	i	PROPN
cana-3320	463	10	-	-	PUNCT
cana-3320	463	11	semigroups	semigroup	NOUN
cana-3320	463	12	,	,	PUNCT
cana-3320	463	13	proceedings	proceeding	NOUN
cana-3320	463	14	of	of	ADP
cana-3320	463	15	international	international	ADJ
cana-3320	463	16	conference	conference	NOUN
cana-3320	463	17	on	on	ADP
cana-3320	463	18	algebra	algebra	PROPN
cana-3320	463	19	and	and	CCONJ
cana-3320	463	20	its	its	PRON
cana-3320	463	21	application	application	NOUN
cana-3320	463	22	decker	decker	NOUN
cana-3320	463	23	publication	publication	NOUN
cana-3320	463	24	,	,	PUNCT
cana-3320	463	25	new	new	ADJ
cana-3320	463	26	yark	yark	NOUN
cana-3320	463	27	,	,	PUNCT
cana-3320	463	28	(	(	PUNCT
cana-3320	463	29	1981	1981	NUM
cana-3320	463	30	)	)	PUNCT
cana-3320	463	31	,	,	PUNCT
cana-3320	463	32	301	301	NUM
cana-3320	463	33	.	.	PUNCT
cana-3320	464	1	[	[	X
cana-3320	464	2	15	15	NUM
cana-3320	464	3	]	]	X
cana-3320	464	4	m.	m.	NOUN
cana-3320	464	5	k.	k.	PROPN
cana-3320	464	6	sen	sen	PROPN
cana-3320	464	7	and	and	CCONJ
cana-3320	464	8	n.	n.	PROPN
cana-3320	464	9	k	k	PROPN
cana-3320	464	10	saha	saha	PROPN
cana-3320	464	11	,	,	PUNCT
cana-3320	464	12	on	on	ADP
cana-3320	464	13	i	i	PROPN
cana-3320	464	14	-	-	PUNCT
cana-3320	464	15	semigroup	semigroup	PROPN
cana-3320	464	16	,	,	PUNCT
cana-3320	464	17	i	i	PRON
cana-3320	464	18	,	,	PUNCT
cana-3320	464	19	bull.calcutta	bull.calcutta	NUM
cana-3320	464	20	math	math	NOUN
cana-3320	464	21	.	.	PUNCT
cana-3320	465	1	soc	soc	PROPN
cana-3320	465	2	.	.	PUNCT
cana-3320	466	1	,(1986	,(1986	PROPN
cana-3320	466	2	)	)	PUNCT
cana-3320	467	1	,	,	PUNCT
cana-3320	468	1	78	78	NUM
cana-3320	468	2	180	180	NUM
cana-3320	468	3	-	-	SYM
cana-3320	468	4	186	186	NUM
cana-3320	468	5	.	.	PUNCT
cana-3320	469	1	[	[	X
cana-3320	469	2	16	16	NUM
cana-3320	469	3	]	]	PUNCT
cana-3320	469	4	n.kehayopula	n.kehayopula	NOUN
cana-3320	469	5	,	,	PUNCT
cana-3320	469	6	on	on	ADP
cana-3320	469	7	ordered	order	VERB
cana-3320	469	8	i	i	PROPN
cana-3320	469	9	-	-	PUNCT
cana-3320	469	10	semigroups	semigroup	NOUN
cana-3320	469	11	,	,	PUNCT
cana-3320	469	12	scientiae	scientiae	NOUN
cana-3320	469	13	mathematicae	mathematicae	VERB
cana-3320	469	14	japonicae	japonicae	PROPN
cana-3320	469	15	online	online	PROPN
cana-3320	469	16	,	,	PUNCT
cana-3320	469	17	e-2010	e-2010	PROPN
cana-3320	469	18	,	,	PUNCT
cana-3320	469	19	37	37	NUM
cana-3320	469	20	-	-	SYM
cana-3320	469	21	43	43	NUM
cana-3320	469	22	.	.	PUNCT
cana-3320	470	1	[	[	X
cana-3320	470	2	17	17	NUM
cana-3320	470	3	]	]	X
cana-3320	470	4	somsak	somsak	ADJ
cana-3320	470	5	lekkoksung	lekkoksung	PROPN
cana-3320	470	6	,	,	PUNCT
cana-3320	470	7	on	on	ADP
cana-3320	470	8	q	q	ADJ
cana-3320	470	9	-	-	PUNCT
cana-3320	470	10	fuzzy	fuzzy	ADJ
cana-3320	470	11	ideals	ideal	NOUN
cana-3320	470	12	in	in	ADP
cana-3320	470	13	ordered	order	VERB
cana-3320	470	14	semigroups	semigroup	NOUN
cana-3320	470	15	,	,	PUNCT
cana-3320	470	16	international	international	ADJ
cana-3320	470	17	journal	journal	NOUN
cana-3320	470	18	of	of	ADP
cana-3320	470	19	pure	pure	ADJ
cana-3320	470	20	and	and	CCONJ
cana-3320	470	21	applied	apply	VERB
cana-3320	470	22	mathematics,92(3	mathematics,92(3	PROPN
cana-3320	470	23	)	)	PUNCT
cana-3320	470	24	(	(	PUNCT
cana-3320	470	25	2014	2014	NUM
cana-3320	470	26	)	)	PUNCT
cana-3320	470	27	,	,	PUNCT
cana-3320	470	28	369–379	369–379	NUM
cana-3320	470	29	.	.	PUNCT
cana-3320	471	1	[	[	X
cana-3320	471	2	18	18	NUM
cana-3320	471	3	]	]	PUNCT
cana-3320	471	4	n.kehayopula	n.kehayopula	NOUN
cana-3320	471	5	and	and	CCONJ
cana-3320	471	6	tsingelis	tsingeli	NOUN
cana-3320	471	7	,	,	PUNCT
cana-3320	471	8	fuzzy	fuzzy	ADJ
cana-3320	471	9	sets	set	NOUN
cana-3320	471	10	in	in	ADP
cana-3320	471	11	ordered	order	VERB
cana-3320	471	12	groupoids	groupoid	NOUN
cana-3320	471	13	,	,	PUNCT
cana-3320	471	14	semigroup	semigroup	PROPN
cana-3320	471	15	forum	forum	PROPN
cana-3320	471	16	,	,	PUNCT
cana-3320	471	17	65	65	NUM
cana-3320	471	18	,	,	PUNCT
cana-3320	471	19	(	(	PUNCT
cana-3320	471	20	2005	2005	NUM
cana-3320	471	21	)	)	PUNCT
cana-3320	471	22	128	128	NUM
cana-3320	471	23	-	-	SYM
cana-3320	471	24	132	132	NUM
cana-3320	471	25	.	.	PUNCT
cana-3320	472	1	[	[	X
cana-3320	472	2	19	19	NUM
cana-3320	472	3	]	]	X
cana-3320	472	4	f.	f.	PROPN
cana-3320	472	5	m.	m.	PROPN
cana-3320	472	6	khan	khan	PROPN
cana-3320	472	7	,	,	PUNCT
cana-3320	472	8	n.	n.	PROPN
cana-3320	472	9	h.	h.	PROPN
cana-3320	472	10	sarmin	sarmin	PROPN
cana-3320	472	11	and	and	CCONJ
cana-3320	472	12	a.	a.	PROPN
cana-3320	472	13	khan	khan	PROPN
cana-3320	472	14	.	.	PUNCT
cana-3320	473	1	some	some	DET
cana-3320	473	2	new	new	ADJ
cana-3320	473	3	characterization	characterization	NOUN
cana-3320	473	4	of	of	ADP
cana-3320	473	5	ordered	order	VERB
cana-3320	473	6	semigroups	semigroup	NOUN
cana-3320	473	7	in	in	ADP
cana-3320	473	8	terms	term	NOUN
cana-3320	473	9	of	of	ADP
cana-3320	473	10	(	(	PUNCT
cana-3320	473	11	κ	κ	NOUN
cana-3320	473	12	,	,	PUNCT
cana-3320	473	13	θ)-fuzzy	θ)-fuzzy	PUNCT
cana-3320	473	14	bi	bi	NOUN
cana-3320	473	15	-	-	NOUN
cana-3320	473	16	ideals	ideal	NOUN
cana-3320	473	17	,	,	PUNCT
cana-3320	473	18	international	international	ADJ
cana-3320	473	19	journal	journal	NOUN
cana-3320	473	20	of	of	ADP
cana-3320	473	21	algebra	algebra	PROPN
cana-3320	473	22	and	and	CCONJ
cana-3320	473	23	statistics	statistic	NOUN
cana-3320	473	24	,	,	PUNCT
cana-3320	473	25	1(1)(2012	1(1)(2012	NUM
cana-3320	473	26	)	)	PUNCT
cana-3320	473	27	,	,	PUNCT
cana-3320	473	28	22–32	22–32	NUM
cana-3320	473	29	.	.	PUNCT
cana-3320	474	1	[	[	X
cana-3320	474	2	20	20	NUM
cana-3320	474	3	]	]	PUNCT
cana-3320	474	4	shihadeh	shihadeh	NOUN
cana-3320	474	5	,	,	PUNCT
cana-3320	474	6	a.	a.	NOUN
cana-3320	474	7	,	,	PUNCT
cana-3320	474	8	matarneh	matarneh	PROPN
cana-3320	474	9	,	,	PUNCT
cana-3320	474	10	k.	k.	PROPN
cana-3320	474	11	a.	a.	PROPN
cana-3320	474	12	m.	m.	PROPN
cana-3320	474	13	,	,	PUNCT
cana-3320	474	14	hatamleh	hatamleh	PROPN
cana-3320	474	15	,	,	PUNCT
cana-3320	474	16	r.	r.	PROPN
cana-3320	474	17	,	,	PUNCT
cana-3320	474	18	al	al	PROPN
cana-3320	474	19	-	-	PUNCT
cana-3320	474	20	qadri	qadri	PROPN
cana-3320	474	21	,	,	PUNCT
cana-3320	474	22	m.	m.	NOUN
cana-3320	474	23	o.	o.	PROPN
cana-3320	474	24	,	,	PUNCT
cana-3320	474	25	&	&	CCONJ
cana-3320	474	26	al	al	PROPN
cana-3320	474	27	-	-	PUNCT
cana-3320	474	28	husban	husban	PROPN
cana-3320	474	29	,	,	PUNCT
cana-3320	474	30	a.	a.	NOUN
cana-3320	474	31	(	(	PUNCT
cana-3320	474	32	2024	2024	NUM
cana-3320	474	33	)	)	PUNCT
cana-3320	474	34	.	.	PUNCT
cana-3320	475	1	on	on	ADP
cana-3320	475	2	the	the	DET
cana-3320	475	3	two	two	NUM
cana-3320	475	4	-	-	ADJ
cana-3320	475	5	fold	fold	ADJ
cana-3320	475	6	fuzzy	fuzzy	ADJ
cana-3320	475	7	n	n	CCONJ
cana-3320	475	8	-	-	PUNCT
cana-3320	475	9	refined	refine	VERB
cana-3320	475	10	neutrosophic	neutrosophic	ADJ
cana-3320	475	11	rings	ring	NOUN
cana-3320	475	12	for	for	ADP
cana-3320	475	13	2=	2=	NUM
cana-3320	475	14	3	3	NUM
cana-3320	475	15	.	.	NUM
cana-3320	475	16	neutrosophic	neutrosophic	ADJ
cana-3320	475	17	sets	set	NOUN
cana-3320	475	18	and	and	CCONJ
cana-3320	475	19	systems	system	NOUN
cana-3320	475	20	,	,	PUNCT
cana-3320	475	21	68	68	NUM
cana-3320	475	22	,	,	PUNCT
cana-3320	475	23	8	8	NUM
cana-3320	475	24	-	-	SYM
cana-3320	475	25	25	25	NUM
cana-3320	475	26	.	.	PUNCT
cana-3320	476	1	[	[	X
cana-3320	476	2	21	21	NUM
cana-3320	476	3	]	]	X
cana-3320	476	4	abdallah	abdallah	PROPN
cana-3320	476	5	shihadeh	shihadeh	PROPN
cana-3320	476	6	,	,	PUNCT
cana-3320	476	7	khaled	khaled	PROPN
cana-3320	476	8	ahmad	ahmad	PROPN
cana-3320	476	9	mohammad	mohammad	PROPN
cana-3320	476	10	matarneh	matarneh	PROPN
cana-3320	476	11	,	,	PUNCT
cana-3320	476	12	raed	raed	PROPN
cana-3320	476	13	hatamleh	hatamleh	PROPN
cana-3320	476	14	,	,	PUNCT
cana-3320	476	15	randa	randa	PROPN
cana-3320	476	16	bashir	bashir	PROPN
cana-3320	476	17	yousef	yousef	PROPN
cana-3320	477	1	hijazeen	hijazeen	PROPN
cana-3320	477	2	,	,	PUNCT
cana-3320	477	3	mowafaq	mowafaq	PROPN
cana-3320	477	4	omar	omar	PROPN
cana-3320	477	5	al	al	PROPN
cana-3320	477	6	-	-	PUNCT
cana-3320	477	7	qadri	qadri	PROPN
cana-3320	477	8	,	,	PUNCT
cana-3320	477	9	abdallah	abdallah	PROPN
cana-3320	477	10	al	al	PROPN
cana-3320	477	11	-	-	PUNCT
cana-3320	477	12	husban.(2024	husban.(2024	NOUN
cana-3320	477	13	)	)	PUNCT
cana-3320	477	14	.	.	PUNCT
cana-3320	478	1	an	an	DET
cana-3320	478	2	example	example	NOUN
cana-3320	478	3	of	of	ADP
cana-3320	478	4	two	two	NUM
cana-3320	478	5	-	-	PUNCT
cana-3320	478	6	fold	fold	ADJ
cana-3320	478	7	fuzzy	fuzzy	ADJ
cana-3320	478	8	algebras	algebra	NOUN
cana-3320	478	9	based	base	VERB
cana-3320	478	10	on	on	ADP
cana-3320	478	11	neutrosophic	neutrosophic	ADJ
cana-3320	478	12	real	real	ADJ
cana-3320	478	13	numbers	number	NOUN
cana-3320	478	14	,	,	PUNCT
cana-3320	478	15	neutrosophic	neutrosophic	ADJ
cana-3320	478	16	sets	set	NOUN
cana-3320	478	17	and	and	CCONJ
cana-3320	478	18	systems	system	NOUN
cana-3320	478	19	,	,	PUNCT
cana-3320	478	20	67	67	NUM
cana-3320	478	21	,	,	PUNCT
cana-3320	478	22	169	169	NUM
cana-3320	478	23	-	-	SYM
cana-3320	478	24	178	178	NUM
cana-3320	478	25	.	.	PUNCT
cana-3320	479	1	[	[	X
cana-3320	479	2	22	22	NUM
cana-3320	479	3	]	]	PUNCT
cana-3320	479	4	raed	raed	PROPN
cana-3320	479	5	hatamleh	hatamleh	PROPN
cana-3320	479	6	,	,	PUNCT
cana-3320	479	7	abdallah	abdallah	PROPN
cana-3320	479	8	al	al	PROPN
cana-3320	479	9	-	-	PUNCT
cana-3320	479	10	husban	husban	PROPN
cana-3320	479	11	,	,	PUNCT
cana-3320	479	12	n.	n.	NOUN
cana-3320	479	13	sundarakannan	sundarakannan	NOUN
cana-3320	479	14	,	,	PUNCT
cana-3320	479	15	m.	m.	NOUN
cana-3320	479	16	s.	s.	PROPN
cana-3320	479	17	malchijah	malchijah	PROPN
cana-3320	479	18	raj	raj	PROPN
cana-3320	479	19	.	.	PUNCT
cana-3320	480	1	(	(	PUNCT
cana-3320	480	2	2025	2025	NUM
cana-3320	480	3	)	)	PUNCT
cana-3320	480	4	.	.	PUNCT
cana-3320	481	1	complex	complex	ADJ
cana-3320	481	2	cubic	cubic	ADJ
cana-3320	481	3	intuitionistic	intuitionistic	ADJ
cana-3320	481	4	fuzzy	fuzzy	ADJ
cana-3320	481	5	set	set	NOUN
cana-3320	481	6	applied	apply	VERB
cana-3320	481	7	to	to	ADP
cana-3320	481	8	subbisemirings	subbisemiring	NOUN
cana-3320	481	9	of	of	ADP
cana-3320	481	10	bisemirings	bisemiring	NOUN
cana-3320	481	11	using	use	VERB
cana-3320	481	12	homomorphism	homomorphism	NOUN
cana-3320	481	13	,	,	PUNCT
cana-3320	481	14	communications	communication	NOUN
cana-3320	481	15	on	on	ADP
cana-3320	481	16	applied	apply	VERB
cana-3320	481	17	non	non	ADJ
cana-3320	481	18	-	-	ADJ
cana-3320	481	19	linear	linear	ADJ
cana-3320	481	20	analysis	analysis	NOUN
cana-3320	481	21	,	,	PUNCT
cana-3320	481	22	32	32	NUM
cana-3320	481	23	(	(	PUNCT
cana-3320	481	24	3	3	NUM
cana-3320	481	25	)	)	PUNCT
cana-3320	481	26	,	,	PUNCT
cana-3320	481	27	418	418	NUM
cana-3320	481	28	-	-	SYM
cana-3320	481	29	435	435	NUM
cana-3320	481	30	.	.	PUNCT
cana-3320	482	1	[	[	X
cana-3320	482	2	23	23	NUM
cana-3320	482	3	]	]	SYM
cana-3320	482	4	abubaker	abubaker	X
cana-3320	482	5	,	,	PUNCT
cana-3320	482	6	ahmad	ahmad	PROPN
cana-3320	482	7	a	a	DET
cana-3320	482	8	,	,	PUNCT
cana-3320	482	9	hatamleh	hatamleh	ADJ
cana-3320	482	10	,	,	PUNCT
cana-3320	482	11	raed	raed	PROPN
cana-3320	482	12	,	,	PUNCT
cana-3320	482	13	matarneh	matarneh	PROPN
cana-3320	482	14	,	,	PUNCT
cana-3320	482	15	khaled	khaled	PROPN
cana-3320	482	16	,	,	PUNCT
cana-3320	482	17	al	al	PROPN
cana-3320	482	18	-	-	PUNCT
cana-3320	482	19	husban	husban	ADJ
cana-3320	482	20	,	,	PUNCT
cana-3320	482	21	abdallah.(2024	abdallah.(2024	NOUN
cana-3320	482	22	)	)	PUNCT
cana-3320	482	23	.	.	PUNCT
cana-3320	483	1	on	on	ADP
cana-3320	483	2	the	the	DET
cana-3320	483	3	numerica	numerica	PROPN
cana-3320	483	4	solutions	solution	NOUN
cana-3320	483	5	for	for	ADP
cana-3320	483	6	some	some	DET
cana-3320	483	7	neutrosophic	neutrosophic	ADJ
cana-3320	483	8	singular	singular	ADJ
cana-3320	483	9	boundary	boundary	ADJ
cana-3320	483	10	value	value	NOUN
cana-3320	483	11	problems	problem	NOUN
cana-3320	483	12	by	by	ADP
cana-3320	483	13	using	use	VERB
cana-3320	483	14	(	(	PUNCT
cana-3320	483	15	lpm	lpm	NOUN
cana-3320	483	16	)	)	PUNCT
cana-3320	483	17	polynomials	polynomial	NOUN
cana-3320	483	18	,	,	PUNCT
cana-3320	483	19	international	international	ADJ
cana-3320	483	20	journal	journal	NOUN
cana-3320	483	21	of	of	ADP
cana-3320	483	22	neutrosophic	neutrosophic	ADJ
cana-3320	483	23	science	science	NOUN
cana-3320	483	24	,	,	PUNCT
cana-3320	483	25	25(2	25(2	NUM
cana-3320	483	26	)	)	PUNCT
cana-3320	483	27	,	,	PUNCT
cana-3320	483	28	197	197	NUM
cana-3320	483	29	-	-	SYM
cana-3320	483	30	205	205	NUM
cana-3320	483	31	.	.	PUNCT
cana-3320	484	1	[	[	X
cana-3320	484	2	24	24	NUM
cana-3320	484	3	]	]	SYM
cana-3320	484	4	a.	a.	NOUN
cana-3320	484	5	,	,	PUNCT
cana-3320	484	6	ahmad	ahmad	PROPN
cana-3320	484	7	.	.	PROPN
cana-3320	484	8	,	,	PUNCT
cana-3320	484	9	hatamleh	hatamleh	ADJ
cana-3320	484	10	,	,	PUNCT
cana-3320	484	11	raed	raed	PROPN
cana-3320	484	12	.	.	PROPN
cana-3320	484	13	,	,	PUNCT
cana-3320	484	14	matarneh	matarneh	PROPN
cana-3320	484	15	,	,	PUNCT
cana-3320	484	16	khaled	khaled	PROPN
cana-3320	484	17	.	.	PUNCT
cana-3320	484	18	,	,	PUNCT
cana-3320	484	19	al	al	PROPN
cana-3320	484	20	-	-	PUNCT
cana-3320	484	21	husban	husban	PROPN
cana-3320	484	22	,	,	PUNCT
cana-3320	484	23	abdallah	abdallah	PROPN
cana-3320	484	24	.	.	PUNCT
cana-3320	485	1	on	on	ADP
cana-3320	485	2	the	the	DET
cana-3320	485	3	irreversible	irreversible	ADJ
cana-3320	485	4	kthreshold	kthreshold	ADJ
cana-3320	485	5	conversion	conversion	NOUN
cana-3320	485	6	number	number	NOUN
cana-3320	485	7	for	for	ADP
cana-3320	485	8	some	some	DET
cana-3320	485	9	graph	graph	NOUN
cana-3320	485	10	products	product	NOUN
cana-3320	485	11	and	and	CCONJ
cana-3320	485	12	neutrosophic	neutrosophic	ADJ
cana-3320	485	13	graphs	graph	NOUN
cana-3320	485	14	.	.	PUNCT
cana-3320	486	1	(	(	PUNCT
cana-3320	486	2	2025	2025	NUM
cana-3320	486	3	)	)	PUNCT
cana-3320	486	4	.	.	PUNCT
cana-3320	487	1	international	international	ADJ
cana-3320	487	2	journal	journal	PROPN
cana-3320	487	3	of	of	ADP
cana-3320	487	4	neutrosophic	neutrosophic	ADJ
cana-3320	487	5	science	science	NOUN
cana-3320	487	6	,	,	PUNCT
cana-3320	487	7	25(2	25(2	NUM
cana-3320	487	8	)	)	PUNCT
cana-3320	487	9	,	,	PUNCT
cana-3320	487	10	183	183	NUM
cana-3320	487	11	-	-	SYM
cana-3320	487	12	196	196	NUM
cana-3320	487	13	[	[	X
cana-3320	487	14	25	25	NUM
cana-3320	487	15	]	]	X
cana-3320	487	16	palanikumar	palanikumar	PROPN
cana-3320	487	17	m	m	PROPN
cana-3320	487	18	,	,	PUNCT
cana-3320	487	19	arulmozhi	arulmozhi	PROPN
cana-3320	487	20	k	k	X
cana-3320	487	21	,	,	PUNCT
cana-3320	487	22	on	on	ADP
cana-3320	487	23	intuitionistic	intuitionistic	ADJ
cana-3320	487	24	fuzzy	fuzzy	ADJ
cana-3320	487	25	normal	normal	ADJ
cana-3320	487	26	subbisemirings	subbisemiring	NOUN
cana-3320	487	27	of	of	ADP
cana-3320	487	28	bisemirings	bisemiring	NOUN
cana-3320	487	29	,	,	PUNCT
cana-3320	487	30	nonlinear	nonlinear	ADJ
cana-3320	487	31	studies	study	NOUN
cana-3320	487	32	,	,	PUNCT
cana-3320	487	33	28(3	28(3	NUM
cana-3320	487	34	)	)	PUNCT
cana-3320	487	35	,	,	PUNCT
cana-3320	487	36	2021	2021	NUM
cana-3320	487	37	,	,	PUNCT
cana-3320	487	38	717	717	NUM
cana-3320	487	39	-	-	SYM
cana-3320	487	40	721	721	NUM
cana-3320	487	41	.	.	PUNCT
cana-3320	488	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3320	488	2	588	588	NUM
cana-3320	488	3	communications	communication	NOUN
cana-3320	488	4	on	on	ADP
cana-3320	488	5	applied	apply	VERB
cana-3320	488	6	nonlinear	nonlinear	ADJ
cana-3320	488	7	analysis	analysis	NOUN
cana-3320	488	8	issn	issn	NOUN
cana-3320	488	9	:	:	PUNCT
cana-3320	488	10	1074	1074	NUM
cana-3320	488	11	-	-	PUNCT
cana-3320	488	12	133x	133x	NUM
cana-3320	488	13	vol	vol	NOUN
cana-3320	488	14	32	32	NUM
cana-3320	488	15	no	no	NOUN
cana-3320	488	16	.	.	PUNCT
cana-3320	489	1	6s	6s	NUM
cana-3320	489	2	(	(	PUNCT
cana-3320	489	3	2025	2025	NUM
cana-3320	489	4	)	)	PUNCT
cana-3320	490	1	[	[	X
cana-3320	490	2	26	26	NUM
cana-3320	490	3	]	]	PUNCT
cana-3320	490	4	k.	k.	PROPN
cana-3320	490	5	hila	hila	PROPN
cana-3320	490	6	and	and	CCONJ
cana-3320	490	7	e.	e.	PROPN
cana-3320	490	8	pisha	pisha	PROPN
cana-3320	490	9	.	.	PUNCT
cana-3320	491	1	on	on	ADP
cana-3320	491	2	bi	bi	NOUN
cana-3320	491	3	-	-	NOUN
cana-3320	491	4	ideals	ideal	NOUN
cana-3320	491	5	on	on	ADP
cana-3320	491	6	ordered	order	VERB
cana-3320	491	7	i	i	PROPN
cana-3320	491	8	-	-	PUNCT
cana-3320	491	9	semigroups	semigroup	NOUN
cana-3320	491	10	.	.	PUNCT
cana-3320	492	1	hacettepe	hacettepe	PROPN
cana-3320	492	2	journal	journal	PROPN
cana-3320	492	3	of	of	ADP
cana-3320	492	4	mathematics	mathematic	NOUN
cana-3320	492	5	and	and	CCONJ
cana-3320	492	6	statistics	statistic	NOUN
cana-3320	492	7	,	,	PUNCT
cana-3320	492	8	40(6	40(6	NOUN
cana-3320	492	9	)	)	PUNCT
cana-3320	492	10	,	,	PUNCT
cana-3320	492	11	(	(	PUNCT
cana-3320	492	12	2011	2011	NUM
cana-3320	492	13	)	)	PUNCT
cana-3320	492	14	,	,	PUNCT
cana-3320	492	15	793	793	NUM
cana-3320	492	16	-	-	SYM
cana-3320	492	17	804	804	NUM
cana-3320	492	18	.	.	PUNCT
cana-3320	493	1	[	[	X
cana-3320	493	2	27	27	NUM
cana-3320	493	3	]	]	X
cana-3320	493	4	dutta	dutta	PROPN
cana-3320	493	5	t.k	t.k	PROPN
cana-3320	493	6	and	and	CCONJ
cana-3320	493	7	kar	kar	PROPN
cana-3320	493	8	s	s	PROPN
cana-3320	493	9	,	,	PUNCT
cana-3320	493	10	on	on	ADP
cana-3320	493	11	prime	prime	ADJ
cana-3320	493	12	ideals	ideal	NOUN
cana-3320	493	13	and	and	CCONJ
cana-3320	493	14	prime	prime	ADJ
cana-3320	493	15	radical	radical	ADJ
cana-3320	493	16	of	of	ADP
cana-3320	493	17	ternary	ternary	ADJ
cana-3320	493	18	semirings	semiring	NOUN
cana-3320	493	19	,	,	PUNCT
cana-3320	493	20	bull.cal	bull.cal	PROPN
cana-3320	493	21	.	.	PUNCT
cana-3320	493	22	math	math	PROPN
cana-3320	493	23	.	.	PUNCT
cana-3320	494	1	soc	soc	PROPN
cana-3320	494	2	.	.	PUNCT
cana-3320	494	3	,	,	PUNCT
cana-3320	494	4	97(5	97(5	PROPN
cana-3320	494	5	)	)	PUNCT
cana-3320	494	6	,	,	PUNCT
cana-3320	494	7	2005	2005	NUM
cana-3320	494	8	,	,	PUNCT
cana-3320	494	9	445	445	NUM
cana-3320	494	10	-	-	SYM
cana-3320	494	11	454	454	NUM
cana-3320	494	12	.	.	PUNCT
cana-3320	495	1	[	[	X
cana-3320	495	2	28	28	NUM
cana-3320	495	3	]	]	X
cana-3320	495	4	palanikumar	palanikumar	PROPN
cana-3320	495	5	,	,	PUNCT
cana-3320	495	6	m.	m.	NOUN
cana-3320	495	7	;	;	PUNCT
cana-3320	495	8	jana	jana	PROPN
cana-3320	495	9	,	,	PUNCT
cana-3320	495	10	c.	c.	PROPN
cana-3320	495	11	;	;	PUNCT
cana-3320	495	12	shanqiti	shanqiti	ADV
cana-3320	495	13	,	,	PUNCT
cana-3320	495	14	o.a	o.a	PROPN
cana-3320	495	15	.	.	PROPN
cana-3320	495	16	;	;	PUNCT
cana-3320	495	17	pal	pal	NOUN
cana-3320	495	18	.	.	PUNCT
cana-3320	496	1	m.	m.	NOUN
cana-3320	496	2	a	a	DET
cana-3320	496	3	novel	novel	ADJ
cana-3320	496	4	method	method	NOUN
cana-3320	496	5	for	for	ADP
cana-3320	496	6	generating	generate	VERB
cana-3320	496	7	the	the	DET
cana-3320	496	8	m	m	NOUN
cana-3320	496	9	-	-	PUNCT
cana-3320	496	10	tri	tri	NOUN
cana-3320	496	11	-	-	NOUN
cana-3320	496	12	basis	basis	NOUN
cana-3320	496	13	of	of	ADP
cana-3320	496	14	an	an	DET
cana-3320	496	15	ordered	order	VERB
cana-3320	496	16	gamma	gamma	PROPN
cana-3320	496	17	semigroup	semigroup	PROPN
cana-3320	496	18	.	.	PUNCT
cana-3320	497	1	mathematics	mathematic	NOUN
cana-3320	497	2	2023	2023	NUM
cana-3320	497	3	,	,	PUNCT
cana-3320	497	4	11	11	NUM
cana-3320	497	5	,	,	PUNCT
cana-3320	497	6	893	893	NUM
cana-3320	497	7	[	[	SYM
cana-3320	497	8	29	29	NUM
cana-3320	497	9	]	]	PUNCT
cana-3320	497	10	mohanraj	mohanraj	NOUN
cana-3320	497	11	,	,	PUNCT
cana-3320	497	12	g	g	NOUN
cana-3320	497	13	;	;	PUNCT
cana-3320	497	14	palanikumar	palanikumar	NOUN
cana-3320	497	15	,	,	PUNCT
cana-3320	497	16	m.	m.	NOUN
cana-3320	497	17	on	on	ADP
cana-3320	497	18	various	various	ADJ
cana-3320	497	19	prime	prime	ADJ
cana-3320	497	20	and	and	CCONJ
cana-3320	497	21	semiprime	semiprime	NOUN
cana-3320	497	22	bi	bi	NOUN
cana-3320	497	23	-	-	NOUN
cana-3320	497	24	ideals	ideal	NOUN
cana-3320	497	25	of	of	ADP
cana-3320	497	26	rings	ring	NOUN
cana-3320	497	27	.	.	PUNCT
cana-3320	498	1	nonlinear	nonlinear	ADJ
cana-3320	498	2	studies	study	NOUN
cana-3320	498	3	.	.	PUNCT
cana-3320	499	1	2021	2021	NUM
cana-3320	499	2	,	,	PUNCT
cana-3320	499	3	27(3	27(3	NUM
cana-3320	499	4	)	)	PUNCT
cana-3320	499	5	,	,	PUNCT
cana-3320	499	6	811	811	NUM
cana-3320	499	7	-	-	SYM
cana-3320	499	8	815	815	NUM
cana-3320	499	9	.	.	PUNCT
cana-3320	500	1	[	[	X
cana-3320	500	2	30	30	NUM
cana-3320	500	3	]	]	X
cana-3320	500	4	palanikumar	palanikumar	PROPN
cana-3320	500	5	,	,	PUNCT
cana-3320	500	6	m	m	PROPN
cana-3320	500	7	;	;	PUNCT
cana-3320	500	8	arulmozhi	arulmozhi	ADJ
cana-3320	500	9	,	,	PUNCT
cana-3320	500	10	k.	k.	PROPN
cana-3320	500	11	jana.c	jana.c	PROPN
cana-3320	500	12	and	and	CCONJ
cana-3320	500	13	pal.m	pal.m	PROPN
cana-3320	500	14	&	&	CCONJ
cana-3320	500	15	shum.k.p	shum.k.p	NOUN
cana-3320	500	16	.	.	PUNCT
cana-3320	501	1	new	new	ADJ
cana-3320	501	2	approach	approach	NOUN
cana-3320	501	3	towards	towards	ADP
cana-3320	501	4	different	different	ADJ
cana-3320	501	5	bi	bi	NOUN
cana-3320	501	6	-	-	NOUN
cana-3320	501	7	base	base	NOUN
cana-3320	501	8	of	of	ADP
cana-3320	501	9	ordered	order	VERB
cana-3320	501	10	b	b	X
cana-3320	501	11	-	-	PUNCT
cana-3320	501	12	semiring.asian	semiring.asian	ADJ
cana-3320	501	13	-	-	PUNCT
cana-3320	501	14	european	european	ADJ
cana-3320	501	15	journal	journal	NOUN
cana-3320	501	16	of	of	ADP
cana-3320	501	17	mathematics	mathematic	NOUN
cana-3320	501	18	.	.	PUNCT
cana-3320	502	1	2023	2023	NUM
cana-3320	502	2	,	,	PUNCT
cana-3320	502	3	16(2	16(2	NUM
cana-3320	502	4	)	)	PUNCT
cana-3320	502	5	,	,	PUNCT
cana-3320	502	6	1	1	NUM
cana-3320	502	7	-	-	SYM
cana-3320	502	8	26	26	NUM
cana-3320	502	9	.	.	PUNCT
cana-3320	503	1	[	[	X
cana-3320	503	2	31	31	NUM
cana-3320	503	3	]	]	X
cana-3320	503	4	palanikumar	palanikumar	PROPN
cana-3320	503	5	,	,	PUNCT
cana-3320	503	6	m	m	PROPN
cana-3320	503	7	;	;	PUNCT
cana-3320	503	8	iampan	iampan	PROPN
cana-3320	503	9	,	,	PUNCT
cana-3320	503	10	a	a	DET
cana-3320	503	11	;	;	PUNCT
cana-3320	503	12	manavalan	manavalan	ADJ
cana-3320	503	13	,	,	PUNCT
cana-3320	503	14	l.j	l.j	PROPN
cana-3320	503	15	.	.	PROPN
cana-3320	503	16	m	m	PROPN
cana-3320	503	17	-	-	PUNCT
cana-3320	503	18	bi	bi	ADJ
cana-3320	503	19	-	-	ADJ
cana-3320	503	20	base	base	ADJ
cana-3320	503	21	generator	generator	NOUN
cana-3320	503	22	of	of	ADP
cana-3320	503	23	ordered	order	VERB
cana-3320	503	24	i	i	PROPN
cana-3320	503	25	-	-	PUNCT
cana-3320	503	26	semigroups	semigroup	NOUN
cana-3320	503	27	.	.	PUNCT
cana-3320	504	1	icic	icic	PROPN
cana-3320	504	2	express	express	VERB
cana-3320	504	3	letters	letter	NOUN
cana-3320	504	4	part	part	NOUN
cana-3320	504	5	b	b	NOUN
cana-3320	504	6	:	:	PUNCT
cana-3320	504	7	applications	application	NOUN
cana-3320	504	8	.	.	PUNCT
cana-3320	505	1	2022	2022	NUM
cana-3320	505	2	,	,	PUNCT
cana-3320	505	3	13(8	13(8	NUM
cana-3320	505	4	)	)	PUNCT
cana-3320	505	5	,	,	PUNCT
cana-3320	505	6	795	795	NUM
cana-3320	505	7	-	-	SYM
cana-3320	505	8	802	802	NUM
cana-3320	505	9	.	.	PUNCT
cana-3320	506	1	[	[	X
cana-3320	506	2	32	32	NUM
cana-3320	506	3	]	]	PUNCT
cana-3320	506	4	mohanraj	mohanraj	NOUN
cana-3320	506	5	,	,	PUNCT
cana-3320	506	6	g	g	NOUN
cana-3320	506	7	;	;	PUNCT
cana-3320	506	8	palanikumar	palanikumar	NOUN
cana-3320	506	9	,	,	PUNCT
cana-3320	506	10	m.	m.	NOUN
cana-3320	506	11	characterization	characterization	NOUN
cana-3320	506	12	of	of	ADP
cana-3320	506	13	various	various	ADJ
cana-3320	506	14	k	k	NOUN
cana-3320	506	15	-	-	NOUN
cana-3320	506	16	regular	regular	ADJ
cana-3320	506	17	in	in	ADP
cana-3320	506	18	b	b	NOUN
cana-3320	506	19	-	-	PUNCT
cana-3320	506	20	semirings	semiring	NOUN
cana-3320	506	21	,	,	PUNCT
cana-3320	506	22	aip	aip	PROPN
cana-3320	506	23	conference	conference	NOUN
cana-3320	506	24	proceedings	proceeding	NOUN
cana-3320	506	25	,	,	PUNCT
cana-3320	506	26	2019	2019	NUM
cana-3320	506	27	,	,	PUNCT
cana-3320	506	28	2112	2112	NUM
cana-3320	506	29	(	(	PUNCT
cana-3320	506	30	1	1	NUM
cana-3320	506	31	)	)	PUNCT
cana-3320	506	32	,	,	PUNCT
cana-3320	506	33	020021	020021	NUM
cana-3320	506	34	.	.	PUNCT
cana-3320	507	1	[	[	X
cana-3320	507	2	33	33	NUM
cana-3320	507	3	]	]	X
cana-3320	507	4	palanikumar	palanikumar	PROPN
cana-3320	507	5	,	,	PUNCT
cana-3320	507	6	m	m	PROPN
cana-3320	507	7	;	;	PUNCT
cana-3320	507	8	shanqiti	shanqiti	ADV
cana-3320	507	9	,	,	PUNCT
cana-3320	507	10	o.	o.	PROPN
cana-3320	507	11	al	al	PROPN
cana-3320	507	12	;	;	PUNCT
cana-3320	507	13	jana	jana	PROPN
cana-3320	507	14	,	,	PUNCT
cana-3320	507	15	c	c	X
cana-3320	507	16	;	;	PUNCT
cana-3320	507	17	pal	pal	ADJ
cana-3320	507	18	,	,	PUNCT
cana-3320	507	19	m.	m.	NOUN
cana-3320	507	20	novelty	novelty	NOUN
cana-3320	507	21	for	for	ADP
cana-3320	507	22	different	different	ADJ
cana-3320	507	23	prime	prime	ADJ
cana-3320	507	24	partial	partial	ADJ
cana-3320	507	25	bi	bi	NOUN
cana-3320	507	26	-	-	NOUN
cana-3320	507	27	ideals	ideal	NOUN
cana-3320	507	28	in	in	ADP
cana-3320	507	29	noncommutative	noncommutative	ADJ
cana-3320	507	30	partial	partial	ADJ
cana-3320	507	31	rings	ring	NOUN
cana-3320	507	32	and	and	CCONJ
cana-3320	507	33	its	its	PRON
cana-3320	507	34	extension	extension	NOUN
cana-3320	507	35	mathematics	mathematic	NOUN
cana-3320	507	36	,	,	PUNCT
cana-3320	507	37	2023	2023	NUM
cana-3320	507	38	,	,	PUNCT
cana-3320	507	39	11(6	11(6	NUM
cana-3320	507	40	)	)	PUNCT
cana-3320	507	41	,	,	PUNCT
cana-3320	507	42	1309	1309	NUM
cana-3320	507	43	.	.	PUNCT
cana-3320	508	1	[	[	X
cana-3320	508	2	34	34	NUM
cana-3320	508	3	]	]	X
cana-3320	508	4	palanikumar	palanikumar	PROPN
cana-3320	508	5	,	,	PUNCT
cana-3320	508	6	m	m	PROPN
cana-3320	508	7	;	;	PUNCT
cana-3320	508	8	mohanraj	mohanraj	NOUN
cana-3320	508	9	,	,	PUNCT
cana-3320	508	10	g	g	NOUN
cana-3320	508	11	;	;	PUNCT
cana-3320	508	12	iampan	iampan	NOUN
cana-3320	508	13	,	,	PUNCT
cana-3320	508	14	a.	a.	NOUN
cana-3320	508	15	characterization	characterization	NOUN
cana-3320	508	16	of	of	ADP
cana-3320	508	17	different	different	ADJ
cana-3320	508	18	prime	prime	ADJ
cana-3320	508	19	bi	bi	NOUN
cana-3320	508	20	-	-	NOUN
cana-3320	508	21	ideals	ideal	NOUN
cana-3320	508	22	and	and	CCONJ
cana-3320	508	23	its	its	PRON
cana-3320	508	24	generalization	generalization	NOUN
cana-3320	508	25	of	of	ADP
cana-3320	508	26	semirings	semiring	NOUN
cana-3320	508	27	,	,	PUNCT
cana-3320	508	28	international	international	ADJ
cana-3320	508	29	journal	journal	NOUN
cana-3320	508	30	of	of	ADP
cana-3320	508	31	analysis	analysis	NOUN
cana-3320	508	32	and	and	CCONJ
cana-3320	508	33	applications	application	NOUN
cana-3320	508	34	,	,	PUNCT
cana-3320	508	35	2024	2024	NUM
cana-3320	508	36	,	,	PUNCT
cana-3320	508	37	22	22	NUM
cana-3320	508	38	,	,	PUNCT
cana-3320	508	39	112	112	NUM
cana-3320	508	40	-	-	SYM
cana-3320	508	41	112	112	NUM
cana-3320	508	42	.	.	PUNCT
cana-3320	509	1	[	[	X
cana-3320	509	2	35	35	NUM
cana-3320	509	3	]	]	PUNCT
cana-3320	509	4	rajalakshmi	rajalakshmi	NOUN
cana-3320	509	5	,	,	PUNCT
cana-3320	509	6	raed	raed	PROPN
cana-3320	509	7	hatamleh	hatamleh	PROPN
cana-3320	509	8	,	,	PUNCT
cana-3320	509	9	abdallah	abdallah	PROPN
cana-3320	509	10	al	al	PROPN
cana-3320	509	11	-	-	PUNCT
cana-3320	509	12	husban	husban	PROPN
cana-3320	509	13	,	,	PUNCT
cana-3320	509	14	k.	k.	PROPN
cana-3320	509	15	lenin	lenin	PROPN
cana-3320	509	16	muthu	muthu	PROPN
cana-3320	509	17	kumaran	kumaran	PROPN
cana-3320	509	18	,	,	PUNCT
cana-3320	509	19	m.	m.	PROPN
cana-3320	509	20	s.	s.	PROPN
cana-3320	509	21	malchijah	malchijah	PROPN
cana-3320	509	22	raj	raj	PROPN
cana-3320	509	23	.	.	PUNCT
cana-3320	510	1	(	(	PUNCT
cana-3320	510	2	2025	2025	NUM
cana-3320	510	3	)	)	PUNCT
cana-3320	510	4	.	.	PUNCT
cana-3320	511	1	various	various	ADJ
cana-3320	511	2	(	(	PUNCT
cana-3320	511	3	δ1	δ1	NOUN
cana-3320	511	4	,	,	PUNCT
cana-3320	511	5	δ2	δ2	ADJ
cana-3320	511	6	)	)	PUNCT
cana-3320	511	7	neutrosophic	neutrosophic	ADJ
cana-3320	511	8	ideals	ideal	NOUN
cana-3320	511	9	of	of	ADP
cana-3320	511	10	an	an	DET
cana-3320	511	11	ordered	order	VERB
cana-3320	511	12	ternary	ternary	ADJ
cana-3320	511	13	semigroups	semigroup	NOUN
cana-3320	511	14	,	,	PUNCT
cana-3320	511	15	communications	communication	NOUN
cana-3320	511	16	on	on	ADP
cana-3320	511	17	applied	apply	VERB
cana-3320	511	18	non	non	ADJ
cana-3320	511	19	-	-	ADJ
cana-3320	511	20	linear	linear	ADJ
cana-3320	511	21	analysis	analysis	NOUN
cana-3320	511	22	,	,	PUNCT
cana-3320	511	23	32	32	NUM
cana-3320	511	24	(	(	PUNCT
cana-3320	511	25	3	3	NUM
cana-3320	511	26	)	)	PUNCT
cana-3320	511	27	,	,	PUNCT
cana-3320	511	28	400	400	NUM
cana-3320	511	29	-	-	SYM
cana-3320	511	30	417	417	NUM
cana-3320	511	31	.	.	PUNCT
cana-3320	512	1	[	[	X
cana-3320	512	2	36	36	NUM
cana-3320	512	3	]	]	X
cana-3320	512	4	raed	raed	PROPN
cana-3320	512	5	hatamleh	hatamleh	PROPN
cana-3320	512	6	,	,	PUNCT
cana-3320	512	7	abdallah	abdallah	PROPN
cana-3320	512	8	al	al	PROPN
cana-3320	512	9	-	-	PUNCT
cana-3320	512	10	husban	husban	PROPN
cana-3320	512	11	,	,	PUNCT
cana-3320	512	12	k.	k.	PROPN
cana-3320	512	13	sundareswari	sundareswari	PROPN
cana-3320	512	14	,	,	PUNCT
cana-3320	512	15	g.balaj	g.balaj	NOUN
cana-3320	512	16	,	,	PUNCT
cana-3320	512	17	m.palanikumar	m.palanikumar	X
cana-3320	512	18	(	(	PUNCT
cana-3320	512	19	2025	2025	NUM
cana-3320	512	20	)	)	PUNCT
cana-3320	512	21	.	.	PUNCT
cana-3320	513	1	complex	complex	ADJ
cana-3320	513	2	tangent	tangent	NOUN
cana-3320	513	3	trigonometric	trigonometric	ADJ
cana-3320	513	4	approach	approach	NOUN
cana-3320	513	5	applied	apply	VERB
cana-3320	513	6	to	to	ADP
cana-3320	513	7	(	(	PUNCT
cana-3320	513	8	λ	λ	INTJ
cana-3320	513	9	,	,	PUNCT
cana-3320	513	10	µ)-rung	µ)-rung	VERB
cana-3320	513	11	fuzzy	fuzzy	ADJ
cana-3320	513	12	set	set	NOUN
cana-3320	513	13	using	use	VERB
cana-3320	513	14	weighted	weight	VERB
cana-3320	513	15	averaging	averaging	NOUN
cana-3320	513	16	,	,	PUNCT
cana-3320	513	17	geometric	geometric	ADJ
cana-3320	513	18	operators	operator	NOUN
cana-3320	513	19	and	and	CCONJ
cana-3320	513	20	its	its	PRON
cana-3320	513	21	extension	extension	NOUN
cana-3320	513	22	,	,	PUNCT
cana-3320	513	23	communications	communication	NOUN
cana-3320	513	24	on	on	ADP
cana-3320	513	25	applied	apply	VERB
cana-3320	513	26	non	non	ADJ
cana-3320	513	27	-	-	ADJ
cana-3320	513	28	linear	linear	ADJ
cana-3320	513	29	analysis	analysis	NOUN
cana-3320	513	30	,	,	PUNCT
cana-3320	513	31	32	32	NUM
cana-3320	513	32	(	(	PUNCT
cana-3320	513	33	5	5	NUM
cana-3320	513	34	)	)	PUNCT
cana-3320	513	35	,	,	PUNCT
cana-3320	513	36	133	133	NUM
cana-3320	513	37	-	-	SYM
cana-3320	513	38	144	144	NUM
cana-3320	513	39	.	.	PUNCT
cana-3320	514	1	[	[	X
cana-3320	514	2	37	37	NUM
cana-3320	514	3	]	]	PUNCT
cana-3320	514	4	raed	raed	PROPN
cana-3320	514	5	hatamleh	hatamleh	PROPN
cana-3320	514	6	,	,	PUNCT
cana-3320	514	7	abdallah	abdallah	PROPN
cana-3320	514	8	al	al	PROPN
cana-3320	514	9	-	-	PUNCT
cana-3320	514	10	husban	husban	PROPN
cana-3320	514	11	,	,	PUNCT
cana-3320	514	12	m.palanikumar	m.palanikumar	PROPN
cana-3320	514	13	,	,	PUNCT
cana-3320	514	14	k.	k.	PROPN
cana-3320	514	15	sundareswari	sundareswari	PROPN
cana-3320	514	16	(	(	PUNCT
cana-3320	514	17	2025	2025	NUM
cana-3320	514	18	)	)	PUNCT
cana-3320	514	19	.	.	PUNCT
cana-3320	515	1	different	different	ADJ
cana-3320	515	2	weighted	weight	VERB
cana-3320	515	3	operators	operator	NOUN
cana-3320	515	4	such	such	ADJ
cana-3320	515	5	as	as	ADP
cana-3320	515	6	generalized	generalized	ADJ
cana-3320	515	7	averaging	averaging	NOUN
cana-3320	515	8	and	and	CCONJ
cana-3320	515	9	generalized	generalized	ADJ
cana-3320	515	10	geometric	geometric	NOUN
cana-3320	515	11	based	base	VERB
cana-3320	515	12	on	on	ADP
cana-3320	515	13	trigonometric	trigonometric	ADJ
cana-3320	515	14	q	q	ADJ
cana-3320	515	15	-	-	PUNCT
cana-3320	515	16	rung	rung	ADJ
cana-3320	515	17	interval	interval	NOUN
cana-3320	515	18	-	-	PUNCT
cana-3320	515	19	valued	value	VERB
cana-3320	515	20	approach	approach	NOUN
cana-3320	515	21	,	,	PUNCT
cana-3320	515	22	communications	communication	NOUN
cana-3320	515	23	on	on	ADP
cana-3320	515	24	applied	apply	VERB
cana-3320	515	25	non	non	ADJ
cana-3320	515	26	-	-	ADJ
cana-3320	515	27	linear	linear	ADJ
cana-3320	515	28	analysis	analysis	NOUN
cana-3320	515	29	,	,	PUNCT
cana-3320	515	30	32	32	NUM
cana-3320	515	31	(	(	PUNCT
cana-3320	515	32	5	5	NUM
cana-3320	515	33	)	)	PUNCT
cana-3320	515	34	,	,	PUNCT
cana-3320	515	35	91	91	NUM
cana-3320	515	36	-	-	SYM
cana-3320	515	37	101	101	NUM
cana-3320	515	38	.	.	PUNCT
cana-3320	516	1	[	[	X
cana-3320	516	2	38	38	NUM
cana-3320	516	3	]	]	X
cana-3320	516	4	hatamleh	hatamleh	PROPN
cana-3320	516	5	,	,	PUNCT
cana-3320	516	6	r.	r.	PROPN
cana-3320	516	7	,	,	PUNCT
cana-3320	516	8	zolotarev	zolotarev	PROPN
cana-3320	516	9	,	,	PUNCT
cana-3320	516	10	v.	v.	ADP
cana-3320	516	11	a.	a.	PROPN
cana-3320	516	12	(	(	PUNCT
cana-3320	516	13	2016	2016	NUM
cana-3320	516	14	)	)	PUNCT
cana-3320	516	15	.	.	PUNCT
cana-3320	517	1	triangular	triangular	NOUN
cana-3320	517	2	models	model	NOUN
cana-3320	517	3	of	of	ADP
cana-3320	517	4	commutative	commutative	ADJ
cana-3320	517	5	systems	system	NOUN
cana-3320	517	6	of	of	ADP
cana-3320	517	7	linear	linear	PROPN
cana-3320	517	8	operators	operator	NOUN
cana-3320	517	9	close	close	ADJ
cana-3320	517	10	to	to	ADP
cana-3320	517	11	unitary	unitary	ADJ
cana-3320	517	12	operators	operator	NOUN
cana-3320	517	13	.	.	PUNCT
cana-3320	518	1	ukrainian	ukrainian	ADJ
cana-3320	518	2	mathematical	mathematical	ADJ
cana-3320	518	3	journal	journal	NOUN
cana-3320	518	4	,	,	PUNCT
cana-3320	518	5	68(5	68(5	NUM
cana-3320	518	6	)	)	PUNCT
cana-3320	518	7	,	,	PUNCT
cana-3320	518	8	791	791	NUM
cana-3320	518	9	-	-	SYM
cana-3320	518	10	811	811	NUM
cana-3320	518	11	.	.	PUNCT
cana-3320	519	1	[	[	X
cana-3320	519	2	39	39	NUM
cana-3320	519	3	]	]	X
cana-3320	519	4	hatamleh	hatamleh	PROPN
cana-3320	519	5	,	,	PUNCT
cana-3320	519	6	r.	r.	PROPN
cana-3320	519	7	(	(	PUNCT
cana-3320	519	8	2003	2003	NUM
cana-3320	519	9	)	)	PUNCT
cana-3320	519	10	.	.	PUNCT
cana-3320	520	1	on	on	ADP
cana-3320	520	2	the	the	DET
cana-3320	520	3	form	form	NOUN
cana-3320	520	4	of	of	ADP
cana-3320	520	5	correlation	correlation	NOUN
cana-3320	520	6	function	function	NOUN
cana-3320	520	7	for	for	ADP
cana-3320	520	8	a	a	DET
cana-3320	520	9	class	class	NOUN
cana-3320	520	10	of	of	ADP
cana-3320	520	11	non	non	ADJ
cana-3320	520	12	stationary	stationary	ADJ
cana-3320	520	13	field	field	NOUN
cana-3320	520	14	with	with	ADP
cana-3320	520	15	a	a	DET
cana-3320	520	16	zero	zero	NUM
cana-3320	520	17	spectrum	spectrum	NOUN
cana-3320	520	18	.	.	PUNCT
cana-3320	521	1	rocky	rocky	ADJ
cana-3320	521	2	mountain	mountain	PROPN
cana-3320	521	3	journal	journal	NOUN
cana-3320	521	4	of	of	ADP
cana-3320	521	5	mathematics	mathematics	PROPN
cana-3320	521	6	,	,	PUNCT
cana-3320	521	7	33(1	33(1	NUM
cana-3320	521	8	)	)	PUNCT
cana-3320	521	9	,	,	PUNCT
cana-3320	521	10	1	1	NUM
cana-3320	521	11	-	-	SYM
cana-3320	521	12	13	13	NUM
cana-3320	521	13	.	.	PUNCT
cana-3320	522	1	[	[	X
cana-3320	522	2	40	40	NUM
cana-3320	522	3	]	]	X
cana-3320	522	4	hatamleh	hatamleh	PROPN
cana-3320	522	5	,	,	PUNCT
cana-3320	522	6	r.	r.	PROPN
cana-3320	522	7	,	,	PUNCT
cana-3320	522	8	zolotarev	zolotarev	PROPN
cana-3320	522	9	,	,	PUNCT
cana-3320	522	10	v.	v.	ADP
cana-3320	522	11	a.	a.	NOUN
cana-3320	522	12	(	(	PUNCT
cana-3320	522	13	2014	2014	NUM
cana-3320	522	14	)	)	PUNCT
cana-3320	522	15	.	.	PUNCT
cana-3320	523	1	on	on	ADP
cana-3320	523	2	two	two	NUM
cana-3320	523	3	-	-	PUNCT
cana-3320	523	4	dimensional	dimensional	ADJ
cana-3320	523	5	model	model	NOUN
cana-3320	523	6	representations	representation	NOUN
cana-3320	523	7	of	of	ADP
cana-3320	523	8	one	one	NUM
cana-3320	523	9	class	class	NOUN
cana-3320	523	10	of	of	ADP
cana-3320	523	11	commuting	commute	VERB
cana-3320	523	12	operators	operator	NOUN
cana-3320	523	13	,	,	PUNCT
cana-3320	523	14	ukrainian	ukrainian	ADJ
cana-3320	523	15	mathematical	mathematical	ADJ
cana-3320	523	16	journal	journal	NOUN
cana-3320	523	17	,	,	PUNCT
cana-3320	523	18	66(1	66(1	NOUN
cana-3320	523	19	)	)	PUNCT
cana-3320	523	20	,	,	PUNCT
cana-3320	523	21	122	122	NUM
cana-3320	523	22	-	-	SYM
cana-3320	523	23	144	144	NUM
cana-3320	523	24	.	.	PUNCT
cana-3320	524	1	[	[	X
cana-3320	524	2	41	41	NUM
cana-3320	524	3	]	]	X
cana-3320	524	4	hatamleh	hatamleh	PROPN
cana-3320	524	5	,	,	PUNCT
cana-3320	524	6	r.	r.	PROPN
cana-3320	524	7	,	,	PUNCT
cana-3320	524	8	zolotarev	zolotarev	PROPN
cana-3320	524	9	,	,	PUNCT
cana-3320	524	10	v.	v.	ADP
cana-3320	524	11	a.	a.	NOUN
cana-3320	524	12	(	(	PUNCT
cana-3320	524	13	2015	2015	NUM
cana-3320	524	14	)	)	PUNCT
cana-3320	524	15	.	.	PUNCT
cana-3320	525	1	on	on	ADP
cana-3320	525	2	model	model	NOUN
cana-3320	525	3	representations	representation	NOUN
cana-3320	525	4	of	of	ADP
cana-3320	525	5	non	non	ADJ
cana-3320	525	6	-	-	ADJ
cana-3320	525	7	self	self	ADJ
cana-3320	525	8	adjoint	adjoint	NOUN
cana-3320	525	9	operators	operator	NOUN
cana-3320	525	10	with	with	ADP
cana-3320	525	11	infinitely	infinitely	ADV
cana-3320	525	12	dimensional	dimensional	ADJ
cana-3320	525	13	imaginary	imaginary	ADJ
cana-3320	525	14	component	component	NOUN
cana-3320	525	15	.	.	PUNCT
cana-3320	526	1	journal	journal	PROPN
cana-3320	526	2	of	of	ADP
cana-3320	526	3	mathematical	mathematical	ADJ
cana-3320	526	4	physics	physics	NOUN
cana-3320	526	5	,	,	PUNCT
cana-3320	526	6	analysis	analysis	NOUN
cana-3320	526	7	,	,	PUNCT
cana-3320	526	8	geometry	geometry	NOUN
cana-3320	526	9	,	,	PUNCT
cana-3320	526	10	11(2	11(2	NOUN
cana-3320	526	11	)	)	PUNCT
cana-3320	526	12	,	,	PUNCT
cana-3320	526	13	174	174	NUM
cana-3320	526	14	-	-	SYM
cana-3320	526	15	186	186	NUM
cana-3320	526	16	.	.	PUNCT
cana-3320	527	1	[	[	X
cana-3320	527	2	42	42	NUM
cana-3320	527	3	]	]	X
cana-3320	527	4	bataihah	bataihah	PROPN
cana-3320	527	5	,	,	PUNCT
cana-3320	527	6	a	a	PRON
cana-3320	527	7	and	and	CCONJ
cana-3320	527	8	hazaymeh	hazaymeh	NOUN
cana-3320	527	9	,	,	PUNCT
cana-3320	527	10	a.	a.	NOUN
cana-3320	527	11	(	(	PUNCT
cana-3320	527	12	2025	2025	NUM
cana-3320	527	13	)	)	PUNCT
cana-3320	527	14	.	.	PUNCT
cana-3320	528	1	neutrosophic	neutrosophic	ADJ
cana-3320	528	2	fuzzy	fuzzy	ADJ
cana-3320	528	3	metric	metric	ADJ
cana-3320	528	4	spaces	space	NOUN
cana-3320	528	5	and	and	CCONJ
cana-3320	528	6	fixed	fix	VERB
cana-3320	528	7	points	point	NOUN
cana-3320	528	8	results	result	NOUN
cana-3320	528	9	with	with	ADP
cana-3320	528	10	integral	integral	ADJ
cana-3320	528	11	contraction	contraction	NOUN
cana-3320	528	12	type	type	NOUN
cana-3320	528	13	.	.	PUNCT
cana-3320	529	1	international	international	ADJ
cana-3320	529	2	journal	journal	PROPN
cana-3320	529	3	of	of	ADP
cana-3320	529	4	neutrosophic	neutrosophic	ADJ
cana-3320	529	5	science	science	NOUN
cana-3320	529	6	,	,	PUNCT
cana-3320	529	7	25(3	25(3	NUM
cana-3320	529	8	)	)	PUNCT
cana-3320	529	9	,	,	PUNCT
cana-3320	529	10	561	561	NUM
cana-3320	529	11	-	-	SYM
cana-3320	529	12	572	572	NUM
cana-3320	529	13	.	.	PUNCT
cana-3320	530	1	[	[	X
cana-3320	530	2	43	43	NUM
cana-3320	530	3	]	]	X
cana-3320	530	4	hazaymeh	hazaymeh	NOUN
cana-3320	530	5	,	,	PUNCT
cana-3320	530	6	ayman	ayman	PROPN
cana-3320	530	7	a	a	NOUN
cana-3320	530	8	,	,	PUNCT
cana-3320	530	9	and	and	CCONJ
cana-3320	530	10	anwar	anwar	PROPN
cana-3320	530	11	bataihah	bataihah	PROPN
cana-3320	530	12	.	.	PUNCT
cana-3320	531	1	2025	2025	NUM
cana-3320	531	2	,	,	PUNCT
cana-3320	531	3	neutrosophic	neutrosophic	ADJ
cana-3320	531	4	fuzzy	fuzzy	ADJ
cana-3320	531	5	metric	metric	ADJ
cana-3320	531	6	spaces	space	NOUN
cana-3320	531	7	and	and	CCONJ
cana-3320	531	8	fixed	fix	VERB
cana-3320	531	9	points	point	NOUN
cana-3320	531	10	for	for	ADP
cana-3320	531	11	contractions	contraction	NOUN
cana-3320	531	12	of	of	ADP
cana-3320	531	13	nonlinear	nonlinear	ADJ
cana-3320	531	14	type	type	NOUN
cana-3320	531	15	,	,	PUNCT
cana-3320	531	16	neutrosophic	neutrosophic	ADJ
cana-3320	531	17	sets	set	NOUN
cana-3320	531	18	and	and	CCONJ
cana-3320	531	19	systems	system	NOUN
cana-3320	531	20	77	77	NUM
cana-3320	531	21	:	:	PUNCT
cana-3320	531	22	96	96	NUM
cana-3320	531	23	-	-	SYM
cana-3320	531	24	112	112	NUM
cana-3320	531	25	.	.	PUNCT
cana-3320	532	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3320	532	2	589	589	NUM
cana-3320	532	3	1	1	NUM
cana-3320	532	4	introduction	introduction	NOUN
cana-3320	532	5	2	2	NUM
cana-3320	532	6	basic	basic	ADJ
cana-3320	532	7	concepts	concept	NOUN
cana-3320	532	8	3	3	NUM
cana-3320	532	9	(	(	PUNCT
cana-3320	532	10	,	,	PUNCT
cana-3320	532	11	)	)	PUNCT
cana-3320	532	12	ternary	ternary	ADJ
cana-3320	532	13	intuitionistic	intuitionistic	ADJ
cana-3320	532	14	q	q	NOUN
cana-3320	532	15	interval	interval	NOUN
cana-3320	532	16	-	-	PUNCT
cana-3320	532	17	valued	value	VERB
cana-3320	532	18	fuzzy	fuzzy	ADJ
cana-3320	532	19	ideals	ideal	NOUN
cana-3320	532	20	4	4	NUM
cana-3320	532	21	level	level	NOUN
cana-3320	532	22	set	set	VERB
cana-3320	532	23	concepts	concept	NOUN
cana-3320	532	24	5	5	NUM
cana-3320	532	25	regular	regular	ADJ
cana-3320	532	26	ordered	order	VERB
cana-3320	532	27	ternary	ternary	ADJ
cana-3320	532	28	semigroups	semigroup	NOUN