id	sid	tid	token	lemma	pos
cana-5350	1	1	communications	communication	NOUN
cana-5350	1	2	on	on	ADP
cana-5350	1	3	applied	apply	VERB
cana-5350	1	4	nonlinear	nonlinear	ADJ
cana-5350	1	5	analysis	analysis	NOUN
cana-5350	1	6	issn	issn	NOUN
cana-5350	1	7	:	:	PUNCT
cana-5350	1	8	1074	1074	NUM
cana-5350	1	9	-	-	PUNCT
cana-5350	1	10	133x	133x	NUM
cana-5350	1	11	vol	vol	VERB
cana-5350	1	12	32	32	NUM
cana-5350	1	13	no	no	NOUN
cana-5350	1	14	.	.	PUNCT
cana-5350	2	1	10s	10	NOUN
cana-5350	2	2	(	(	PUNCT
cana-5350	2	3	2025	2025	NUM
cana-5350	2	4	)	)	PUNCT
cana-5350	2	5	1795	1795	NUM
cana-5350	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5350	2	7	exploring	explore	VERB
cana-5350	2	8	quadruple	quadruple	ADJ
cana-5350	2	9	fixed	fix	VERB
cana-5350	2	10	points	point	NOUN
cana-5350	2	11	in	in	ADP
cana-5350	2	12	fuzzy	fuzzy	ADJ
cana-5350	2	13	metric	metric	ADJ
cana-5350	2	14	spaces	space	NOUN
cana-5350	2	15	for	for	ADP
cana-5350	2	16	occasionally	occasionally	ADV
cana-5350	2	17	weakly	weakly	ADJ
cana-5350	2	18	compatible	compatible	ADJ
cana-5350	2	19	mappings	mapping	NOUN
cana-5350	2	20	1sandhya	1sandhya	NUM
cana-5350	2	21	shukla	shukla	NOUN
cana-5350	2	22	,	,	PUNCT
cana-5350	2	23	2priyanka	2priyanka	NUM
cana-5350	2	24	nigam	nigam	PROPN
cana-5350	2	25	*	*	PROPN
cana-5350	2	26	1university	1university	NUM
cana-5350	2	27	institute	institute	PROPN
cana-5350	2	28	of	of	ADP
cana-5350	2	29	technology	technology	PROPN
cana-5350	2	30	,	,	PUNCT
cana-5350	2	31	rgpv	rgpv	ADV
cana-5350	2	32	bhopal	bhopal	PROPN
cana-5350	2	33	,	,	PUNCT
cana-5350	2	34	462033	462033	NUM
cana-5350	2	35	,	,	PUNCT
cana-5350	2	36	madhya	madhya	PROPN
cana-5350	2	37	pradesh	pradesh	PROPN
cana-5350	2	38	,	,	PUNCT
cana-5350	2	39	india	india	PROPN
cana-5350	2	40	2presidency	2presidency	PROPN
cana-5350	2	41	university	university	PROPN
cana-5350	2	42	,	,	PUNCT
cana-5350	2	43	bengaluru	bengaluru	PROPN
cana-5350	2	44	,	,	PUNCT
cana-5350	2	45	560089	560089	NUM
cana-5350	2	46	,	,	PUNCT
cana-5350	2	47	karnataka	karnataka	PROPN
cana-5350	2	48	,	,	PUNCT
cana-5350	2	49	india	india	PROPN
cana-5350	2	50	.	.	PUNCT
cana-5350	3	1	article	article	PROPN
cana-5350	3	2	history	history	NOUN
cana-5350	3	3	:	:	PUNCT
cana-5350	3	4	received	receive	VERB
cana-5350	3	5	:	:	PUNCT
cana-5350	3	6	12	12	NUM
cana-5350	3	7	-	-	SYM
cana-5350	3	8	01	01	NUM
cana-5350	3	9	-	-	PUNCT
cana-5350	3	10	2025	2025	NUM
cana-5350	3	11	revised	revise	VERB
cana-5350	3	12	:	:	PUNCT
cana-5350	3	13	15	15	NUM
cana-5350	3	14	-	-	NUM
cana-5350	3	15	02	02	NUM
cana-5350	3	16	-	-	PUNCT
cana-5350	3	17	2025	2025	NUM
cana-5350	3	18	accepted	accept	VERB
cana-5350	3	19	:	:	PUNCT
cana-5350	3	20	01	01	NUM
cana-5350	3	21	-	-	SYM
cana-5350	3	22	03	03	NUM
cana-5350	3	23	-	-	PUNCT
cana-5350	3	24	2025	2025	NUM
cana-5350	3	25	abstract	abstract	NOUN
cana-5350	3	26	:	:	PUNCT
cana-5350	3	27	in	in	ADP
cana-5350	3	28	this	this	DET
cana-5350	3	29	research	research	NOUN
cana-5350	3	30	paper	paper	NOUN
cana-5350	3	31	we	we	PRON
cana-5350	3	32	prove	prove	VERB
cana-5350	3	33	some	some	DET
cana-5350	3	34	quadruple	quadruple	NOUN
cana-5350	3	35	fixed	fix	VERB
cana-5350	3	36	point	point	NOUN
cana-5350	3	37	theorems	theorem	NOUN
cana-5350	3	38	for	for	ADP
cana-5350	3	39	occasionally	occasionally	ADV
cana-5350	3	40	weakly	weakly	ADJ
cana-5350	3	41	compatible	compatible	ADJ
cana-5350	3	42	mappings	mapping	NOUN
cana-5350	3	43	in	in	ADP
cana-5350	3	44	fuzzy	fuzzy	ADJ
cana-5350	3	45	metric	metric	ADJ
cana-5350	3	46	space	space	NOUN
cana-5350	3	47	.	.	PUNCT
cana-5350	4	1	keywords	keyword	NOUN
cana-5350	4	2	:	:	PUNCT
cana-5350	4	3	occasionally	occasionally	ADV
cana-5350	4	4	weakly	weakly	ADJ
cana-5350	4	5	compatible	compatible	ADJ
cana-5350	4	6	mappings	mapping	NOUN
cana-5350	4	7	,	,	PUNCT
cana-5350	4	8	quadruple	quadruple	NOUN
cana-5350	4	9	fixed	fix	VERB
cana-5350	4	10	point	point	NOUN
cana-5350	4	11	,	,	PUNCT
cana-5350	4	12	fuzzy	fuzzy	ADJ
cana-5350	4	13	metric	metric	ADJ
cana-5350	4	14	space	space	NOUN
cana-5350	4	15	.	.	PUNCT
cana-5350	5	1	2000	2000	NUM
cana-5350	5	2	mathematics	mathematic	NOUN
cana-5350	5	3	subject	subject	ADJ
cana-5350	5	4	classification	classification	NOUN
cana-5350	5	5	:	:	PUNCT
cana-5350	5	6	47h10	47h10	NUM
cana-5350	5	7	;	;	PUNCT
cana-5350	5	8	54h25	54h25	NUM
cana-5350	5	9	.	.	X
cana-5350	6	1	1	1	X
cana-5350	6	2	.	.	X
cana-5350	6	3	introduction	introduction	NOUN
cana-5350	6	4	1	1	NUM
cana-5350	6	5	introduction	introduction	NOUN
cana-5350	6	6	zadeh	zadeh	NOUN
cana-5350	7	1	[	[	X
cana-5350	7	2	14	14	NUM
cana-5350	7	3	]	]	PUNCT
cana-5350	7	4	introduced	introduce	VERB
cana-5350	7	5	the	the	DET
cana-5350	7	6	concept	concept	NOUN
cana-5350	7	7	of	of	ADP
cana-5350	7	8	fuzzy	fuzzy	ADJ
cana-5350	7	9	sets	set	NOUN
cana-5350	7	10	,	,	PUNCT
cana-5350	7	11	while	while	SCONJ
cana-5350	7	12	kramosil	kramosil	NOUN
cana-5350	7	13	and	and	CCONJ
cana-5350	7	14	michalek	michalek	VERB
cana-5350	7	15	[	[	X
cana-5350	7	16	11	11	NUM
cana-5350	7	17	]	]	PUNCT
cana-5350	7	18	developed	develop	VERB
cana-5350	7	19	the	the	DET
cana-5350	7	20	idea	idea	NOUN
cana-5350	7	21	of	of	ADP
cana-5350	7	22	fuzzy	fuzzy	ADJ
cana-5350	7	23	metric	metric	ADJ
cana-5350	7	24	spaces	space	NOUN
cana-5350	7	25	.	.	PUNCT
cana-5350	8	1	later	later	ADV
cana-5350	8	2	,	,	PUNCT
cana-5350	8	3	george	george	PROPN
cana-5350	8	4	and	and	CCONJ
cana-5350	8	5	veermani	veermani	NOUN
cana-5350	9	1	[	[	X
cana-5350	9	2	5	5	NUM
cana-5350	9	3	]	]	PUNCT
cana-5350	9	4	refined	refine	VERB
cana-5350	9	5	this	this	DET
cana-5350	9	6	concept	concept	NOUN
cana-5350	9	7	by	by	ADP
cana-5350	9	8	proposing	propose	VERB
cana-5350	9	9	a	a	DET
cana-5350	9	10	new	new	ADJ
cana-5350	9	11	framework	framework	NOUN
cana-5350	9	12	for	for	ADP
cana-5350	9	13	fuzzy	fuzzy	ADJ
cana-5350	9	14	metric	metric	ADJ
cana-5350	9	15	spaces	space	NOUN
cana-5350	9	16	using	use	VERB
cana-5350	9	17	continuous	continuous	ADJ
cana-5350	9	18	t	t	NOUN
cana-5350	9	19	-	-	PUNCT
cana-5350	9	20	norms	norm	NOUN
cana-5350	9	21	.	.	PUNCT
cana-5350	10	1	numerous	numerous	ADJ
cana-5350	10	2	researchers	researcher	NOUN
cana-5350	10	3	have	have	AUX
cana-5350	10	4	since	since	SCONJ
cana-5350	10	5	established	establish	VERB
cana-5350	10	6	common	common	ADJ
cana-5350	10	7	fixed	fix	VERB
cana-5350	10	8	point	point	NOUN
cana-5350	10	9	theorems	theorem	NOUN
cana-5350	10	10	for	for	ADP
cana-5350	10	11	mappings	mapping	NOUN
cana-5350	10	12	under	under	ADP
cana-5350	10	13	various	various	ADJ
cana-5350	10	14	commutativity	commutativity	NOUN
cana-5350	10	15	conditions	condition	NOUN
cana-5350	10	16	.	.	PUNCT
cana-5350	11	1	the	the	DET
cana-5350	11	2	study	study	NOUN
cana-5350	11	3	of	of	ADP
cana-5350	11	4	fixed	fix	VERB
cana-5350	11	5	point	point	NOUN
cana-5350	11	6	theorems	theorem	NOUN
cana-5350	11	7	involving	involve	VERB
cana-5350	11	8	four	four	NUM
cana-5350	11	9	self	self	NOUN
cana-5350	11	10	-	-	PUNCT
cana-5350	11	11	maps	map	NOUN
cana-5350	11	12	initially	initially	ADV
cana-5350	11	13	relied	rely	VERB
cana-5350	11	14	on	on	ADP
cana-5350	11	15	the	the	DET
cana-5350	11	16	assumption	assumption	NOUN
cana-5350	11	17	of	of	ADP
cana-5350	11	18	commutativity	commutativity	NOUN
cana-5350	11	19	.	.	PUNCT
cana-5350	12	1	sessa	sessa	PROPN
cana-5350	12	2	[	[	X
cana-5350	12	3	13	13	NUM
cana-5350	12	4	]	]	PUNCT
cana-5350	12	5	relaxed	relax	VERB
cana-5350	12	6	this	this	DET
cana-5350	12	7	assumption	assumption	NOUN
cana-5350	12	8	by	by	ADP
cana-5350	12	9	introducing	introduce	VERB
cana-5350	12	10	the	the	DET
cana-5350	12	11	notion	notion	NOUN
cana-5350	12	12	of	of	ADP
cana-5350	12	13	pairwise	pairwise	NOUN
cana-5350	12	14	weakly	weakly	ADJ
cana-5350	12	15	commuting	commuting	NOUN
cana-5350	12	16	maps	map	NOUN
cana-5350	12	17	.	.	PUNCT
cana-5350	13	1	jungck	jungck	PROPN
cana-5350	13	2	extended	extend	VERB
cana-5350	13	3	this	this	PRON
cana-5350	13	4	further	far	ADV
cana-5350	13	5	to	to	ADP
cana-5350	13	6	pairwise	pairwise	VERB
cana-5350	13	7	compatible	compatible	ADJ
cana-5350	14	1	[	[	X
cana-5350	14	2	6	6	NUM
cana-5350	14	3	]	]	PUNCT
cana-5350	14	4	and	and	CCONJ
cana-5350	14	5	pairwise	pairwise	NOUN
cana-5350	14	6	weakly	weakly	ADV
cana-5350	14	7	compatible	compatible	ADJ
cana-5350	14	8	mappings	mapping	NOUN
cana-5350	15	1	[	[	X
cana-5350	15	2	7	7	NUM
cana-5350	15	3	]	]	X
cana-5350	15	4	.	.	PUNCT
cana-5350	16	1	subsequently	subsequently	ADV
cana-5350	16	2	,	,	PUNCT
cana-5350	16	3	jungck	jungck	PROPN
cana-5350	16	4	and	and	CCONJ
cana-5350	16	5	rhoades	rhoade	NOUN
cana-5350	17	1	[	[	X
cana-5350	17	2	8	8	NUM
cana-5350	17	3	]	]	PUNCT
cana-5350	17	4	introduced	introduce	VERB
cana-5350	17	5	the	the	DET
cana-5350	17	6	concept	concept	NOUN
cana-5350	17	7	of	of	ADP
cana-5350	17	8	occasionally	occasionally	ADV
cana-5350	17	9	weakly	weakly	ADV
cana-5350	17	10	compatible	compatible	ADJ
cana-5350	17	11	(	(	PUNCT
cana-5350	17	12	owc	owc	NOUN
cana-5350	17	13	)	)	PUNCT
cana-5350	17	14	mappings	mapping	NOUN
cana-5350	17	15	.	.	PUNCT
cana-5350	18	1	the	the	DET
cana-5350	18	2	research	research	NOUN
cana-5350	18	3	in	in	ADP
cana-5350	18	4	works	work	NOUN
cana-5350	18	5	[	[	X
cana-5350	18	6	1	1	NUM
cana-5350	18	7	]	]	PUNCT
cana-5350	18	8	,	,	PUNCT
cana-5350	18	9	[	[	X
cana-5350	18	10	3	3	NUM
cana-5350	18	11	]	]	PUNCT
cana-5350	18	12	,	,	PUNCT
cana-5350	18	13	[	[	X
cana-5350	18	14	9	9	NUM
cana-5350	18	15	]	]	PUNCT
cana-5350	18	16	,	,	PUNCT
cana-5350	18	17	and	and	CCONJ
cana-5350	18	18	[	[	X
cana-5350	18	19	10	10	NUM
cana-5350	18	20	]	]	PUNCT
cana-5350	18	21	on	on	ADP
cana-5350	18	22	quadruple	quadruple	ADJ
cana-5350	18	23	fixed	fix	VERB
cana-5350	18	24	points	point	NOUN
cana-5350	18	25	is	be	AUX
cana-5350	18	26	truly	truly	ADV
cana-5350	18	27	noteworthy	noteworthy	ADJ
cana-5350	18	28	.	.	PUNCT
cana-5350	19	1	in	in	ADP
cana-5350	19	2	this	this	DET
cana-5350	19	3	paper	paper	NOUN
cana-5350	19	4	we	we	PRON
cana-5350	19	5	introduce	introduce	VERB
cana-5350	19	6	some	some	DET
cana-5350	19	7	quadruple	quadruple	NOUN
cana-5350	19	8	fixed	fix	VERB
cana-5350	19	9	point	point	NOUN
cana-5350	19	10	theorems	theorem	NOUN
cana-5350	19	11	for	for	ADP
cana-5350	19	12	occasionally	occasionally	ADV
cana-5350	19	13	weakly	weakly	ADJ
cana-5350	19	14	compatible	compatible	ADJ
cana-5350	19	15	mappings	mapping	NOUN
cana-5350	19	16	in	in	ADP
cana-5350	19	17	fuzzy	fuzzy	ADJ
cana-5350	19	18	metric	metric	ADJ
cana-5350	19	19	space	space	NOUN
cana-5350	19	20	.	.	PUNCT
cana-5350	20	1	2	2	NUM
cana-5350	20	2	preliminary	preliminary	ADJ
cana-5350	20	3	notes	note	NOUN
cana-5350	20	4	definition	definition	NOUN
cana-5350	20	5	2.1	2.1	NUM
cana-5350	20	6	a	a	DET
cana-5350	20	7	fuzzy	fuzzy	ADJ
cana-5350	20	8	set	set	NOUN
cana-5350	20	9	a	a	PRON
cana-5350	20	10	in	in	NOUN
cana-5350	20	11	x	x	SYM
cana-5350	20	12	is	be	AUX
cana-5350	20	13	a	a	DET
cana-5350	20	14	function	function	NOUN
cana-5350	20	15	with	with	ADP
cana-5350	20	16	domain	domain	NOUN
cana-5350	20	17	x	x	PUNCT
cana-5350	20	18	and	and	CCONJ
cana-5350	20	19	values	value	NOUN
cana-5350	20	20	in	in	ADP
cana-5350	20	21	[	[	X
cana-5350	20	22	0,1	0,1	NUM
cana-5350	20	23	]	]	PUNCT
cana-5350	20	24	.	.	PUNCT
cana-5350	21	1	definition	definition	NOUN
cana-5350	21	2	2.2	2.2	NUM
cana-5350	21	3	a	a	DET
cana-5350	21	4	binary	binary	ADJ
cana-5350	21	5	operation	operation	NOUN
cana-5350	22	1	∗∶	∗∶	PROPN
cana-5350	23	1	[	[	X
cana-5350	23	2	0,1]	0,1]	X
cana-5350	24	1	[	[	X
cana-5350	24	2	0,1]→	0,1]→	NOUN
cana-5350	24	3	[	[	X
cana-5350	24	4	0,1	0,1	NUM
cana-5350	24	5	]	]	PUNCT
cana-5350	24	6	is	be	AUX
cana-5350	24	7	a	a	DET
cana-5350	24	8	continuous	continuous	ADJ
cana-5350	24	9	t	t	NOUN
cana-5350	24	10	-	-	PUNCT
cana-5350	24	11	norm	norm	NOUN
cana-5350	24	12	if	if	SCONJ
cana-5350	24	13	∗	∗	NOUN
cana-5350	24	14	is	be	AUX
cana-5350	24	15	satisfying	satisfy	VERB
cana-5350	24	16	conditions	condition	NOUN
cana-5350	24	17	:	:	PUNCT
cana-5350	24	18	(	(	PUNCT
cana-5350	24	19	i	i	NOUN
cana-5350	24	20	)	)	PUNCT
cana-5350	24	21	∗	∗	NOUN
cana-5350	24	22	is	be	AUX
cana-5350	24	23	an	an	DET
cana-5350	24	24	commutative	commutative	ADJ
cana-5350	24	25	and	and	CCONJ
cana-5350	24	26	associative	associative	ADJ
cana-5350	24	27	;	;	PUNCT
cana-5350	24	28	(	(	PUNCT
cana-5350	24	29	ii	ii	NOUN
cana-5350	24	30	)	)	PUNCT
cana-5350	24	31	∗	∗	NOUN
cana-5350	24	32	is	be	AUX
cana-5350	24	33	continuous	continuous	ADJ
cana-5350	24	34	;	;	PUNCT
cana-5350	24	35	(	(	PUNCT
cana-5350	24	36	iii	iii	X
cana-5350	24	37	)	)	PUNCT
cana-5350	24	38	𝑎	𝑎	NOUN
cana-5350	24	39	∗	∗	NOUN
cana-5350	24	40	1	1	NUM
cana-5350	24	41	=	=	SYM
cana-5350	24	42	𝑎	𝑎	NOUN
cana-5350	24	43	for	for	ADP
cana-5350	24	44	all	all	DET
cana-5350	24	45	a	a	PROPN
cana-5350	24	46	[	[	X
cana-5350	24	47	0,1	0,1	NUM
cana-5350	24	48	]	]	PUNCT
cana-5350	24	49	;	;	PUNCT
cana-5350	24	50	communications	communication	NOUN
cana-5350	24	51	on	on	ADP
cana-5350	24	52	applied	apply	VERB
cana-5350	24	53	nonlinear	nonlinear	ADJ
cana-5350	24	54	analysis	analysis	NOUN
cana-5350	24	55	issn	issn	NOUN
cana-5350	24	56	:	:	PUNCT
cana-5350	24	57	1074	1074	NUM
cana-5350	24	58	-	-	PUNCT
cana-5350	24	59	133x	133x	NUM
cana-5350	24	60	vol	vol	VERB
cana-5350	24	61	32	32	NUM
cana-5350	24	62	no	no	NOUN
cana-5350	24	63	.	.	PUNCT
cana-5350	25	1	10s	10	NOUN
cana-5350	25	2	(	(	PUNCT
cana-5350	25	3	2025	2025	NUM
cana-5350	25	4	)	)	PUNCT
cana-5350	25	5	1796	1796	NUM
cana-5350	25	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5350	25	7	(	(	PUNCT
cana-5350	25	8	iv	iv	X
cana-5350	25	9	)	)	PUNCT
cana-5350	26	1	𝑎	𝑎	PRON
cana-5350	26	2	∗	∗	NOUN
cana-5350	26	3	𝑏𝑐	𝑏𝑐	NOUN
cana-5350	26	4	∗	∗	NOUN
cana-5350	26	5	𝑑	𝑑	NOUN
cana-5350	26	6	whenever	whenever	SCONJ
cana-5350	26	7	ca	can	AUX
cana-5350	26	8			NOUN
cana-5350	26	9	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5350	26	10	db	db	PROPN
cana-5350	26	11			PROPN
cana-5350	26	12	and	and	CCONJ
cana-5350	26	13	𝑎	𝑎	NOUN
cana-5350	26	14	,	,	PUNCT
cana-5350	26	15	𝑏	𝑏	NOUN
cana-5350	26	16	,	,	PUNCT
cana-5350	26	17	𝑐	𝑐	NOUN
cana-5350	26	18	,	,	PUNCT
cana-5350	26	19	𝑑[0,1	𝑑[0,1	NOUN
cana-5350	26	20	]	]	PUNCT
cana-5350	26	21	.	.	PUNCT
cana-5350	27	1	definitions	definition	VERB
cana-5350	27	2	2.3	2.3	NUM
cana-5350	27	3	a	a	DET
cana-5350	27	4	3	3	NUM
cana-5350	27	5	-	-	PUNCT
cana-5350	27	6	tuple	tuple	NOUN
cana-5350	27	7	(	(	PUNCT
cana-5350	27	8	𝑋	𝑋	PROPN
cana-5350	27	9	,	,	PUNCT
cana-5350	27	10	𝑀,∗	𝑀,∗	PROPN
cana-5350	27	11	)	)	PUNCT
cana-5350	27	12	is	be	AUX
cana-5350	27	13	said	say	VERB
cana-5350	27	14	to	to	PART
cana-5350	27	15	be	be	AUX
cana-5350	27	16	a	a	DET
cana-5350	27	17	fuzzy	fuzzy	ADJ
cana-5350	27	18	metric	metric	ADJ
cana-5350	27	19	space	space	NOUN
cana-5350	27	20	if	if	SCONJ
cana-5350	27	21	x	x	PRON
cana-5350	27	22	is	be	AUX
cana-5350	27	23	an	an	DET
cana-5350	27	24	arbitrary	arbitrary	ADJ
cana-5350	27	25	set	set	NOUN
cana-5350	27	26	,	,	PUNCT
cana-5350	27	27	∗	∗	NOUN
cana-5350	27	28	is	be	AUX
cana-5350	27	29	a	a	DET
cana-5350	27	30	continuous	continuous	ADJ
cana-5350	27	31	𝑡	𝑡	NOUN
cana-5350	27	32	−	−	NOUN
cana-5350	27	33	𝑛𝑜𝑟𝑚	𝑛𝑜𝑟𝑚	NOUN
cana-5350	27	34	and	and	CCONJ
cana-5350	27	35	m	m	NOUN
cana-5350	27	36	is	be	AUX
cana-5350	27	37	a	a	DET
cana-5350	27	38	fuzzy	fuzzy	ADJ
cana-5350	27	39	set	set	NOUN
cana-5350	27	40	on	on	ADP
cana-5350	27	41	(	(	PUNCT
cana-5350	27	42	)	)	PUNCT
cana-5350	27	43			X
cana-5350	27	44	,	,	PUNCT
cana-5350	27	45	02x	02x	NOUN
cana-5350	27	46	satisfying	satisfy	VERB
cana-5350	27	47	the	the	DET
cana-5350	27	48	following	following	ADJ
cana-5350	27	49	conditions	condition	NOUN
cana-5350	27	50	,	,	PUNCT
cana-5350	27	51	for	for	ADP
cana-5350	27	52	all	all	DET
cana-5350	27	53	𝑥	𝑥	PROPN
cana-5350	27	54	,	,	PUNCT
cana-5350	27	55	𝑦	𝑦	NOUN
cana-5350	27	56	,	,	PUNCT
cana-5350	27	57	𝑧	𝑧	PRON
cana-5350	27	58			PROPN
cana-5350	27	59	𝑋	𝑋	PROPN
cana-5350	27	60	,	,	PUNCT
cana-5350	27	61	𝑠	𝑠	PROPN
cana-5350	27	62	,	,	PUNCT
cana-5350	27	63	𝑡	𝑡	X
cana-5350	27	64	>	>	X
cana-5350	27	65	0	0	NUM
cana-5350	27	66	,	,	PUNCT
cana-5350	27	67	(	(	PUNCT
cana-5350	27	68	𝑖	𝑖	X
cana-5350	27	69	)	)	PUNCT
cana-5350	27	70	0	0	NUM
cana-5350	27	71	)	)	PUNCT
cana-5350	27	72	,	,	PUNCT
cana-5350	27	73	,	,	PUNCT
cana-5350	27	74	(	(	PUNCT
cana-5350	27	75	tyxm	tyxm	ADV
cana-5350	27	76	;	;	PUNCT
cana-5350	27	77	(	(	PUNCT
cana-5350	27	78	𝑖𝑖	𝑖𝑖	NOUN
cana-5350	27	79	)	)	PUNCT
cana-5350	27	80	1	1	NUM
cana-5350	27	81	)	)	PUNCT
cana-5350	27	82	,	,	PUNCT
cana-5350	27	83	,	,	PUNCT
cana-5350	27	84	(	(	PUNCT
cana-5350	27	85	=	=	NOUN
cana-5350	27	86	tyxm	tyxm	NOUN
cana-5350	27	87	𝑖𝑓	𝑖𝑓	ADP
cana-5350	27	88	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-5350	27	89	𝑜𝑛𝑙𝑦	𝑜𝑛𝑙𝑦	ADV
cana-5350	27	90	𝑖𝑓	𝑖𝑓	ADP
cana-5350	27	91	yx	yx	PROPN
cana-5350	27	92	=	=	PUNCT
cana-5350	27	93	;	;	PUNCT
cana-5350	27	94	(	(	PUNCT
cana-5350	27	95	𝑖𝑖𝑖	𝑖𝑖𝑖	NOUN
cana-5350	27	96	)	)	PUNCT
cana-5350	27	97	)	)	PUNCT
cana-5350	27	98	,	,	PUNCT
cana-5350	27	99	,	,	PUNCT
cana-5350	27	100	(	(	PUNCT
cana-5350	27	101	tyxm	tyxm	NOUN
cana-5350	27	102	=	=	PUNCT
cana-5350	27	103	)	)	PUNCT
cana-5350	27	104	,	,	PUNCT
cana-5350	27	105	,	,	PUNCT
cana-5350	27	106	(	(	PUNCT
cana-5350	27	107	txym	txym	INTJ
cana-5350	27	108	;	;	PUNCT
cana-5350	27	109	(	(	PUNCT
cana-5350	27	110	𝑖𝑣	𝑖𝑣	X
cana-5350	27	111	)	)	PUNCT
cana-5350	27	112	)	)	PUNCT
cana-5350	27	113	,	,	PUNCT
cana-5350	27	114	,	,	PUNCT
cana-5350	27	115	(	(	PUNCT
cana-5350	27	116	tyxm	tyxm	NOUN
cana-5350	27	117	∗	∗	NOUN
cana-5350	27	118	)	)	PUNCT
cana-5350	27	119	,	,	PUNCT
cana-5350	27	120	,	,	PUNCT
cana-5350	27	121	(	(	PUNCT
cana-5350	27	122	szym	szym	NOUN
cana-5350	27	123	)	)	PUNCT
cana-5350	27	124	,	,	PUNCT
cana-5350	27	125	,	,	PUNCT
cana-5350	27	126	(	(	PUNCT
cana-5350	27	127	stzxm	stzxm	ADJ
cana-5350	27	128	+	+	ADJ
cana-5350	27	129			NOUN
cana-5350	27	130	;	;	PUNCT
cana-5350	27	131	(	(	PUNCT
cana-5350	27	132	𝑣	𝑣	X
cana-5350	27	133	)	)	PUNCT
cana-5350	27	134	]	]	X
cana-5350	27	135	1,0(),0	1,0(),0	NUM
cana-5350	27	136	(:	(:	NOUN
cana-5350	27	137	)	)	PUNCT
cana-5350	27	138	,	,	PUNCT
cana-5350	27	139	,	,	PUNCT
cana-5350	27	140	(	(	PUNCT
cana-5350	27	141	→yxm	→yxm	NOUN
cana-5350	27	142	is	be	AUX
cana-5350	27	143	continuous	continuous	ADJ
cana-5350	27	144	.	.	PUNCT
cana-5350	28	1	then	then	ADV
cana-5350	28	2	m	m	PROPN
cana-5350	28	3	is	be	AUX
cana-5350	28	4	called	call	VERB
cana-5350	28	5	a	a	DET
cana-5350	28	6	𝑓𝑢𝑧𝑧𝑦	𝑓𝑢𝑧𝑧𝑦	NOUN
cana-5350	28	7	𝑚𝑒𝑡𝑟𝑖𝑐	𝑚𝑒𝑡𝑟𝑖𝑐	NOUN
cana-5350	28	8	on	on	ADP
cana-5350	28	9	x.	x.	PROPN
cana-5350	28	10	then	then	ADV
cana-5350	28	11	)	)	PUNCT
cana-5350	28	12	,	,	PUNCT
cana-5350	28	13	,	,	PUNCT
cana-5350	28	14	(	(	PUNCT
cana-5350	28	15	tyxm	tyxm	NOUN
cana-5350	28	16	denotes	denote	VERB
cana-5350	28	17	the	the	DET
cana-5350	28	18	degree	degree	NOUN
cana-5350	28	19	of	of	ADP
cana-5350	28	20	nearness	nearness	NOUN
cana-5350	28	21	between	between	ADP
cana-5350	28	22	x	x	PROPN
cana-5350	28	23	and	and	CCONJ
cana-5350	28	24	y	y	PROPN
cana-5350	28	25	with	with	ADP
cana-5350	28	26	respect	respect	NOUN
cana-5350	28	27	to	to	ADP
cana-5350	28	28	t.	t.	PROPN
cana-5350	28	29	example	example	NOUN
cana-5350	28	30	2.4	2.4	NUM
cana-5350	28	31	let	let	NOUN
cana-5350	28	32	)	)	PUNCT
cana-5350	28	33	,	,	PUNCT
cana-5350	28	34	(	(	PUNCT
cana-5350	28	35	dx	dx	PROPN
cana-5350	28	36	be	be	AUX
cana-5350	28	37	a	a	DET
cana-5350	28	38	metric	metric	ADJ
cana-5350	28	39	space	space	NOUN
cana-5350	28	40	.	.	PUNCT
cana-5350	29	1	denote	denote	VERB
cana-5350	29	2	𝑎	𝑎	NOUN
cana-5350	29	3	∗	∗	NOUN
cana-5350	29	4	𝑏	𝑏	NOUN
cana-5350	29	5	=	=	SYM
cana-5350	29	6	𝑎𝑏	𝑎𝑏	PROPN
cana-5350	29	7	for	for	ADP
cana-5350	29	8	all	all	DET
cana-5350	29	9			ADJ
cana-5350	29	10	1,0	1,0	PRON
cana-5350	29	11	,	,	PUNCT
cana-5350	29	12	ba	ba	VERB
cana-5350	29	13	and	and	CCONJ
cana-5350	29	14	let	let	VERB
cana-5350	29	15	dm	dm	PRON
cana-5350	29	16	be	be	AUX
cana-5350	29	17	fuzzy	fuzzy	ADJ
cana-5350	29	18	sets	set	NOUN
cana-5350	29	19	on	on	ADP
cana-5350	29	20	(	(	PUNCT
cana-5350	29	21	)	)	PUNCT
cana-5350	29	22			X
cana-5350	29	23	,	,	PUNCT
cana-5350	29	24	02x	02x	NOUN
cana-5350	29	25	defined	define	VERB
cana-5350	29	26	as	as	ADP
cana-5350	29	27	follows	follow	VERB
cana-5350	29	28	:	:	PUNCT
cana-5350	29	29	)	)	PUNCT
cana-5350	29	30	,	,	PUNCT
cana-5350	29	31	(	(	PUNCT
cana-5350	29	32	yxdt	yxdt	PROPN
cana-5350	29	33	t	t	PROPN
cana-5350	29	34	m	m	PROPN
cana-5350	29	35	d	d	NOUN
cana-5350	29	36	+	+	CCONJ
cana-5350	30	1	=	=	NOUN
cana-5350	30	2	.	.	PUNCT
cana-5350	31	1	then	then	ADV
cana-5350	31	2	(	(	PUNCT
cana-5350	31	3	𝑋	𝑋	PROPN
cana-5350	31	4	,	,	PUNCT
cana-5350	31	5	𝑀𝑑,∗	𝑀𝑑,∗	PROPN
cana-5350	31	6	)	)	PUNCT
cana-5350	31	7	is	be	AUX
cana-5350	31	8	a	a	DET
cana-5350	31	9	fuzzy	fuzzy	ADJ
cana-5350	31	10	metric	metric	ADJ
cana-5350	31	11	space	space	NOUN
cana-5350	31	12	.	.	PUNCT
cana-5350	32	1	lemma	lemma	PROPN
cana-5350	32	2	2.5	2.5	NUM
cana-5350	32	3	let	let	VERB
cana-5350	32	4	(	(	PUNCT
cana-5350	32	5	x	x	NOUN
cana-5350	32	6	,	,	PUNCT
cana-5350	32	7	m	m	PROPN
cana-5350	32	8	,	,	PUNCT
cana-5350	32	9	*	*	PUNCT
cana-5350	32	10	)	)	PUNCT
cana-5350	32	11	be	be	AUX
cana-5350	32	12	a	a	DET
cana-5350	32	13	fuzzy	fuzzy	ADJ
cana-5350	32	14	metric	metric	ADJ
cana-5350	32	15	space	space	NOUN
cana-5350	32	16	.	.	PUNCT
cana-5350	33	1	if	if	SCONJ
cana-5350	33	2	there	there	PRON
cana-5350	33	3	exists	exist	VERB
cana-5350	33	4	)	)	PUNCT
cana-5350	33	5	1,0(q	1,0(q	NUM
cana-5350	33	6	such	such	ADJ
cana-5350	33	7	that	that	SCONJ
cana-5350	33	8	m(x	m(x	PROPN
cana-5350	33	9	,	,	PUNCT
cana-5350	33	10	y	y	PROPN
cana-5350	33	11	,	,	PUNCT
cana-5350	33	12	qt	qt	NOUN
cana-5350	33	13	)	)	PUNCT
cana-5350	33	14			PROPN
cana-5350	33	15	m(x	m(x	PROPN
cana-5350	33	16	,	,	PUNCT
cana-5350	33	17	y	y	PROPN
cana-5350	33	18	,	,	PUNCT
cana-5350	33	19	t	t	PROPN
cana-5350	33	20	)	)	PUNCT
cana-5350	33	21	for	for	ADP
cana-5350	33	22	all	all	DET
cana-5350	33	23	x	x	NOUN
cana-5350	33	24	,	,	PUNCT
cana-5350	33	25	y	y	PROPN
cana-5350	33	26			NOUN
cana-5350	33	27	x	x	PUNCT
cana-5350	33	28	and	and	CCONJ
cana-5350	33	29	t>0	t>0	NOUN
cana-5350	33	30	,	,	PUNCT
cana-5350	33	31	then	then	ADV
cana-5350	33	32	x	x	X
cana-5350	33	33	=	=	PUNCT
cana-5350	33	34	y.	y.	NOUN
cana-5350	33	35	definition	definition	NOUN
cana-5350	33	36	2.6	2.6	NUM
cana-5350	33	37	let	let	VERB
cana-5350	33	38	x	x	PRON
cana-5350	33	39	be	be	AUX
cana-5350	33	40	a	a	DET
cana-5350	33	41	non	non	ADJ
cana-5350	33	42	-	-	ADJ
cana-5350	33	43	empty	empty	ADJ
cana-5350	33	44	set	set	NOUN
cana-5350	33	45	.	.	PUNCT
cana-5350	34	1	an	an	DET
cana-5350	34	2	element	element	NOUN
cana-5350	34	3	(	(	PUNCT
cana-5350	34	4	𝑥	𝑥	PROPN
cana-5350	34	5	,	,	PUNCT
cana-5350	34	6	𝑦	𝑦	NOUN
cana-5350	34	7	,	,	PUNCT
cana-5350	34	8	𝑧	𝑧	NOUN
cana-5350	34	9	,	,	PUNCT
cana-5350	34	10	𝑡	𝑡	NOUN
cana-5350	34	11	)	)	PUNCT
cana-5350	34	12	∈	∈	PROPN
cana-5350	34	13	𝑋	𝑋	NOUN
cana-5350	34	14	×	×	NOUN
cana-5350	34	15	𝑋	𝑋	NOUN
cana-5350	34	16	×	×	NOUN
cana-5350	34	17	𝑋	𝑋	NOUN
cana-5350	34	18	×	×	NOUN
cana-5350	34	19	𝑋	𝑋	PROPN
cana-5350	34	20	is	be	AUX
cana-5350	34	21	called	call	VERB
cana-5350	34	22	a	a	DET
cana-5350	34	23	quadruple	quadruple	NOUN
cana-5350	34	24	fixed	fix	VERB
cana-5350	34	25	point	point	NOUN
cana-5350	34	26	of	of	ADP
cana-5350	34	27	a	a	PRON
cana-5350	34	28	given	give	VERB
cana-5350	34	29	mapping	mapping	NOUN
cana-5350	34	30	𝑓	𝑓	X
cana-5350	34	31	:	:	PUNCT
cana-5350	34	32	𝑋	𝑋	PROPN
cana-5350	34	33	×	×	NOUN
cana-5350	34	34	𝑋	𝑋	PROPN
cana-5350	34	35	×	×	NOUN
cana-5350	34	36	𝑋	𝑋	NOUN
cana-5350	34	37	×	×	NOUN
cana-5350	34	38	𝑋	𝑋	PROPN
cana-5350	34	39	→	→	PUNCT
cana-5350	34	40	𝑋	𝑋	PROPN
cana-5350	34	41	if	if	SCONJ
cana-5350	34	42	𝑥	𝑥	PRON
cana-5350	34	43	=	=	SYM
cana-5350	34	44	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5350	34	45	,	,	PUNCT
cana-5350	34	46	𝑦	𝑦	NOUN
cana-5350	34	47	,	,	PUNCT
cana-5350	34	48	𝑧	𝑧	NOUN
cana-5350	34	49	,	,	PUNCT
cana-5350	34	50	𝑡	𝑡	NOUN
cana-5350	34	51	)	)	PUNCT
cana-5350	34	52	,	,	PUNCT
cana-5350	34	53	𝑦	𝑦	NOUN
cana-5350	34	54	=	=	PUNCT
cana-5350	34	55	𝑓(𝑦	𝑓(𝑦	PROPN
cana-5350	34	56	,	,	PUNCT
cana-5350	34	57	𝑧	𝑧	PRON
cana-5350	34	58	,	,	PUNCT
cana-5350	34	59	𝑡	𝑡	PROPN
cana-5350	34	60	,	,	PUNCT
cana-5350	34	61	𝑥	𝑥	NOUN
cana-5350	34	62	)	)	PUNCT
cana-5350	34	63	,	,	PUNCT
cana-5350	34	64	𝑧	𝑧	X
cana-5350	34	65	=	=	SYM
cana-5350	34	66	𝑓(𝑧	𝑓(𝑧	PROPN
cana-5350	34	67	,	,	PUNCT
cana-5350	34	68	𝑡	𝑡	NOUN
cana-5350	34	69	,	,	PUNCT
cana-5350	34	70	𝑥	𝑥	NOUN
cana-5350	34	71	,	,	PUNCT
cana-5350	34	72	𝑦	𝑦	NOUN
cana-5350	34	73	)	)	PUNCT
cana-5350	34	74	,	,	PUNCT
cana-5350	34	75	𝑡	𝑡	PROPN
cana-5350	34	76	=	=	PUNCT
cana-5350	34	77	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5350	34	78	,	,	PUNCT
cana-5350	34	79	𝑥	𝑥	PRON
cana-5350	34	80	,	,	PUNCT
cana-5350	34	81	𝑦	𝑦	NOUN
cana-5350	34	82	,	,	PUNCT
cana-5350	34	83	𝑧	𝑧	NOUN
cana-5350	34	84	)	)	PUNCT
cana-5350	34	85	.	.	PUNCT
cana-5350	35	1	definition	definition	NOUN
cana-5350	35	2	2.7	2.7	NUM
cana-5350	35	3	an	an	DET
cana-5350	35	4	element	element	NOUN
cana-5350	35	5	(	(	PUNCT
cana-5350	35	6	𝑥	𝑥	PROPN
cana-5350	35	7	,	,	PUNCT
cana-5350	35	8	𝑦	𝑦	NOUN
cana-5350	35	9	,	,	PUNCT
cana-5350	35	10	𝑧	𝑧	NOUN
cana-5350	35	11	,	,	PUNCT
cana-5350	35	12	𝑡	𝑡	NOUN
cana-5350	35	13	)	)	PUNCT
cana-5350	35	14	∈	∈	PROPN
cana-5350	35	15	𝑋	𝑋	NOUN
cana-5350	35	16	×	×	NOUN
cana-5350	35	17	𝑋	𝑋	NOUN
cana-5350	35	18	×	×	NOUN
cana-5350	35	19	𝑋	𝑋	NOUN
cana-5350	35	20	×	×	NOUN
cana-5350	35	21	𝑋	𝑋	PROPN
cana-5350	35	22	is	be	AUX
cana-5350	35	23	called	call	VERB
cana-5350	35	24	a	a	DET
cana-5350	35	25	quadruple	quadruple	NOUN
cana-5350	35	26	coincidence	coincidence	NOUN
cana-5350	35	27	point	point	NOUN
cana-5350	35	28	of	of	ADP
cana-5350	35	29	a	a	DET
cana-5350	35	30	mapping	mapping	NOUN
cana-5350	35	31	𝑓	𝑓	X
cana-5350	35	32	:	:	PUNCT
cana-5350	35	33	𝑋	𝑋	PROPN
cana-5350	35	34	×	×	NOUN
cana-5350	35	35	𝑋	𝑋	PROPN
cana-5350	35	36	×	×	NOUN
cana-5350	35	37	𝑋	𝑋	NOUN
cana-5350	35	38	×	×	NOUN
cana-5350	35	39	𝑋	𝑋	PROPN
cana-5350	35	40	→	→	SYM
cana-5350	35	41	𝑋	𝑋	PROPN
cana-5350	35	42	and	and	CCONJ
cana-5350	35	43	𝑔	𝑔	NOUN
cana-5350	35	44	:	:	PUNCT
cana-5350	35	45	𝑋	𝑋	PROPN
cana-5350	35	46	→	→	SYM
cana-5350	35	47	𝑋	𝑋	PROPN
cana-5350	35	48	if	if	SCONJ
cana-5350	35	49	𝑔𝑥	𝑔𝑥	PROPN
cana-5350	35	50	=	=	PUNCT
cana-5350	35	51	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5350	35	52	,	,	PUNCT
cana-5350	35	53	𝑦	𝑦	NOUN
cana-5350	35	54	,	,	PUNCT
cana-5350	35	55	𝑧	𝑧	NOUN
cana-5350	35	56	,	,	PUNCT
cana-5350	35	57	𝑡	𝑡	NOUN
cana-5350	35	58	)	)	PUNCT
cana-5350	35	59	,	,	PUNCT
cana-5350	35	60	𝑔𝑦	𝑔𝑦	ADV
cana-5350	35	61	=	=	PUNCT
cana-5350	35	62	𝑓(𝑦	𝑓(𝑦	PROPN
cana-5350	35	63	,	,	PUNCT
cana-5350	35	64	𝑧	𝑧	PRON
cana-5350	35	65	,	,	PUNCT
cana-5350	35	66	𝑡	𝑡	PROPN
cana-5350	35	67	,	,	PUNCT
cana-5350	35	68	𝑥	𝑥	NOUN
cana-5350	35	69	)	)	PUNCT
cana-5350	35	70	,	,	PUNCT
cana-5350	35	71	𝑔𝑧	𝑔𝑧	ADP
cana-5350	35	72	=	=	SYM
cana-5350	35	73	𝑓(𝑧	𝑓(𝑧	PROPN
cana-5350	35	74	,	,	PUNCT
cana-5350	35	75	𝑡	𝑡	NOUN
cana-5350	35	76	,	,	PUNCT
cana-5350	35	77	𝑥	𝑥	NOUN
cana-5350	35	78	,	,	PUNCT
cana-5350	35	79	𝑦	𝑦	NOUN
cana-5350	35	80	)	)	PUNCT
cana-5350	35	81	,	,	PUNCT
cana-5350	35	82	𝑔𝑡	𝑔𝑡	ADP
cana-5350	35	83	=	=	SYM
cana-5350	35	84	𝑓(𝑡	𝑓(𝑡	NOUN
cana-5350	35	85	,	,	PUNCT
cana-5350	35	86	𝑥	𝑥	PRON
cana-5350	35	87	,	,	PUNCT
cana-5350	35	88	𝑦	𝑦	NOUN
cana-5350	35	89	,	,	PUNCT
cana-5350	35	90	𝑧	𝑧	NOUN
cana-5350	35	91	)	)	PUNCT
cana-5350	35	92	in	in	ADP
cana-5350	35	93	this	this	DET
cana-5350	35	94	case	case	NOUN
cana-5350	35	95	(	(	PUNCT
cana-5350	35	96	𝑔𝑥	𝑔𝑥	INTJ
cana-5350	35	97	,	,	PUNCT
cana-5350	35	98	𝑔𝑦	𝑔𝑦	PROPN
cana-5350	35	99	,	,	PUNCT
cana-5350	35	100	𝑔𝑧	𝑔𝑧	PROPN
cana-5350	35	101	,	,	PUNCT
cana-5350	35	102	𝑔𝑡	𝑔𝑡	NOUN
cana-5350	35	103	)	)	PUNCT
cana-5350	35	104	is	be	AUX
cana-5350	35	105	called	call	VERB
cana-5350	35	106	a	a	DET
cana-5350	35	107	quadruple	quadruple	NOUN
cana-5350	35	108	point	point	NOUN
cana-5350	35	109	of	of	ADP
cana-5350	35	110	coincidence	coincidence	NOUN
cana-5350	35	111	.	.	PUNCT
cana-5350	36	1	definition	definition	NOUN
cana-5350	36	2	2.8	2.8	NUM
cana-5350	36	3	the	the	DET
cana-5350	36	4	mappings	mapping	NOUN
cana-5350	36	5	𝑓	𝑓	X
cana-5350	36	6	:	:	PUNCT
cana-5350	36	7	𝑋	𝑋	NOUN
cana-5350	36	8	×	×	NOUN
cana-5350	36	9	𝑋	𝑋	PROPN
cana-5350	36	10	×	×	NOUN
cana-5350	36	11	𝑋	𝑋	NOUN
cana-5350	36	12	×	×	NOUN
cana-5350	36	13	𝑋	𝑋	PROPN
cana-5350	36	14	→	→	SYM
cana-5350	36	15	𝑋	𝑋	PROPN
cana-5350	36	16	and	and	CCONJ
cana-5350	36	17	𝑔	𝑔	NOUN
cana-5350	36	18	:	:	PUNCT
cana-5350	36	19	𝑋	𝑋	PROPN
cana-5350	36	20	→	→	SYM
cana-5350	36	21	𝑋	𝑋	PROPN
cana-5350	36	22	of	of	ADP
cana-5350	36	23	a	a	DET
cana-5350	36	24	set	set	NOUN
cana-5350	36	25	x	x	SYM
cana-5350	36	26	are	be	AUX
cana-5350	36	27	occasionally	occasionally	ADV
cana-5350	36	28	weakly	weakly	ADV
cana-5350	36	29	compatible	compatible	ADJ
cana-5350	36	30	(	(	PUNCT
cana-5350	36	31	𝑜𝑤𝑐	𝑜𝑤𝑐	PROPN
cana-5350	36	32	)	)	PUNCT
cana-5350	36	33	iff	iff	NOUN
cana-5350	36	34	there	there	PRON
cana-5350	36	35	is	be	VERB
cana-5350	36	36	a	a	DET
cana-5350	36	37	point	point	NOUN
cana-5350	36	38	(	(	PUNCT
cana-5350	36	39	𝑥	𝑥	NOUN
cana-5350	36	40	,	,	PUNCT
cana-5350	36	41	𝑦	𝑦	NOUN
cana-5350	36	42	,	,	PUNCT
cana-5350	36	43	𝑧	𝑧	NOUN
cana-5350	36	44	,	,	PUNCT
cana-5350	36	45	𝑡	𝑡	NOUN
cana-5350	36	46	)	)	PUNCT
cana-5350	36	47	∈	∈	PROPN
cana-5350	36	48	𝑋	𝑋	NOUN
cana-5350	36	49	×	×	NOUN
cana-5350	36	50	𝑋	𝑋	NOUN
cana-5350	36	51	×	×	NOUN
cana-5350	36	52	𝑋	𝑋	NOUN
cana-5350	36	53	×	×	NOUN
cana-5350	36	54	𝑋	𝑋	NOUN
cana-5350	36	55	which	which	PRON
cana-5350	36	56	is	be	AUX
cana-5350	36	57	a	a	DET
cana-5350	36	58	coincidence	coincidence	NOUN
cana-5350	36	59	point	point	NOUN
cana-5350	36	60	of	of	ADP
cana-5350	36	61	f	f	PROPN
cana-5350	36	62	and	and	CCONJ
cana-5350	36	63	g	g	PROPN
cana-5350	36	64	at	at	ADP
cana-5350	36	65	which	which	PRON
cana-5350	36	66	f	f	PROPN
cana-5350	36	67	and	and	CCONJ
cana-5350	36	68	g	g	PROPN
cana-5350	36	69	commute	commute	NOUN
cana-5350	36	70	i.e.	i.e.	X
cana-5350	36	71	(	(	PUNCT
cana-5350	36	72	𝑓	𝑓	PROPN
cana-5350	36	73	,	,	PUNCT
cana-5350	36	74	𝑔	𝑔	NOUN
cana-5350	36	75	)	)	PUNCT
cana-5350	36	76	are	be	AUX
cana-5350	36	77	occasionally	occasionally	ADV
cana-5350	36	78	weakly	weakly	ADJ
cana-5350	36	79	compatible	compatible	ADJ
cana-5350	36	80	maps	map	NOUN
cana-5350	36	81	iff	iff	VERB
cana-5350	36	82	𝑓(𝑥	𝑓(𝑥	NOUN
cana-5350	36	83	,	,	PUNCT
cana-5350	36	84	𝑦	𝑦	NOUN
cana-5350	36	85	,	,	PUNCT
cana-5350	36	86	𝑧	𝑧	NOUN
cana-5350	36	87	,	,	PUNCT
cana-5350	36	88	𝑡	𝑡	NOUN
cana-5350	36	89	)	)	PUNCT
cana-5350	36	90	=	=	SYM
cana-5350	36	91	𝑔(𝑥	𝑔(𝑥	PROPN
cana-5350	36	92	)	)	PUNCT
cana-5350	36	93	,	,	PUNCT
cana-5350	36	94	𝑓(𝑦	𝑓(𝑦	PROPN
cana-5350	36	95	,	,	PUNCT
cana-5350	36	96	𝑧	𝑧	PRON
cana-5350	36	97	,	,	PUNCT
cana-5350	36	98	𝑡	𝑡	NOUN
cana-5350	36	99	,	,	PUNCT
cana-5350	36	100	𝑥	𝑥	NOUN
cana-5350	36	101	)	)	PUNCT
cana-5350	36	102	=	=	SYM
cana-5350	36	103	𝑔(𝑦	𝑔(𝑦	PROPN
cana-5350	36	104	)	)	PUNCT
cana-5350	36	105	,	,	PUNCT
cana-5350	36	106	𝑓(𝑧	𝑓(𝑧	PROPN
cana-5350	36	107	,	,	PUNCT
cana-5350	36	108	𝑡	𝑡	NOUN
cana-5350	36	109	,	,	PUNCT
cana-5350	36	110	𝑥	𝑥	NOUN
cana-5350	36	111	,	,	PUNCT
cana-5350	36	112	𝑦	𝑦	NOUN
cana-5350	36	113	)	)	PUNCT
cana-5350	36	114	=	=	SYM
cana-5350	36	115	𝑔(𝑧	𝑔(𝑧	PROPN
cana-5350	36	116	)	)	PUNCT
cana-5350	36	117	,	,	PUNCT
cana-5350	36	118	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5350	36	119	,	,	PUNCT
cana-5350	36	120	𝑥	𝑥	PRON
cana-5350	36	121	,	,	PUNCT
cana-5350	36	122	𝑦	𝑦	NOUN
cana-5350	36	123	,	,	PUNCT
cana-5350	36	124	𝑧	𝑧	NOUN
cana-5350	36	125	)	)	PUNCT
cana-5350	36	126	=	=	SYM
cana-5350	36	127	𝑔(𝑡	𝑔(𝑡	PROPN
cana-5350	36	128	)	)	PUNCT
cana-5350	36	129	implies	imply	VERB
cana-5350	36	130	𝑔𝑓(𝑥	𝑔𝑓(𝑥	NOUN
cana-5350	36	131	,	,	PUNCT
cana-5350	36	132	𝑦	𝑦	NOUN
cana-5350	36	133	,	,	PUNCT
cana-5350	36	134	𝑧	𝑧	NOUN
cana-5350	36	135	,	,	PUNCT
cana-5350	36	136	𝑡	𝑡	NOUN
cana-5350	36	137	)	)	PUNCT
cana-5350	36	138	=	=	SYM
cana-5350	36	139	𝑓(𝑔𝑥	𝑓(𝑔𝑥	PROPN
cana-5350	36	140	,	,	PUNCT
cana-5350	36	141	𝑔𝑦	𝑔𝑦	PROPN
cana-5350	36	142	,	,	PUNCT
cana-5350	36	143	𝑔𝑧	𝑔𝑧	PROPN
cana-5350	36	144	,	,	PUNCT
cana-5350	36	145	𝑔𝑡	𝑔𝑡	NOUN
cana-5350	36	146	)	)	PUNCT
cana-5350	36	147	,	,	PUNCT
cana-5350	36	148	𝑔𝑓(𝑦	𝑔𝑓(𝑦	X
cana-5350	36	149	,	,	PUNCT
cana-5350	36	150	𝑧	𝑧	PROPN
cana-5350	36	151	,	,	PUNCT
cana-5350	36	152	𝑡	𝑡	PROPN
cana-5350	36	153	,	,	PUNCT
cana-5350	36	154	𝑥	𝑥	NOUN
cana-5350	36	155	)	)	PUNCT
cana-5350	36	156	=	=	SYM
cana-5350	36	157	𝑓(𝑔𝑦	𝑓(𝑔𝑦	ADJ
cana-5350	36	158	,	,	PUNCT
cana-5350	36	159	𝑔𝑧	𝑔𝑧	PROPN
cana-5350	36	160	,	,	PUNCT
cana-5350	36	161	𝑔𝑡	𝑔𝑡	ADP
cana-5350	36	162	,	,	PUNCT
cana-5350	36	163	𝑔𝑥	𝑔𝑥	PROPN
cana-5350	36	164	)	)	PUNCT
cana-5350	36	165	,	,	PUNCT
cana-5350	36	166	𝑔𝑓(𝑧	𝑔𝑓(𝑧	NUM
cana-5350	36	167	,	,	PUNCT
cana-5350	36	168	𝑡	𝑡	PROPN
cana-5350	36	169	,	,	PUNCT
cana-5350	36	170	𝑥	𝑥	NOUN
cana-5350	36	171	,	,	PUNCT
cana-5350	36	172	𝑦	𝑦	NOUN
cana-5350	36	173	)	)	PUNCT
cana-5350	36	174	=	=	SYM
cana-5350	37	1	𝑓(𝑔𝑧	𝑓(𝑔𝑧	PROPN
cana-5350	37	2	,	,	PUNCT
cana-5350	37	3	𝑔𝑡	𝑔𝑡	ADP
cana-5350	37	4	,	,	PUNCT
cana-5350	37	5	𝑔𝑥	𝑔𝑥	PROPN
cana-5350	37	6	,	,	PUNCT
cana-5350	37	7	𝑔𝑦	𝑔𝑦	NOUN
cana-5350	37	8	)	)	PUNCT
cana-5350	37	9	,	,	PUNCT
cana-5350	37	10	𝑔𝑓(𝑡	𝑔𝑓(𝑡	NUM
cana-5350	37	11	,	,	PUNCT
cana-5350	37	12	𝑥	𝑥	X
cana-5350	37	13	,	,	PUNCT
cana-5350	37	14	𝑦	𝑦	NOUN
cana-5350	37	15	,	,	PUNCT
cana-5350	37	16	𝑧	𝑧	NOUN
cana-5350	37	17	)	)	PUNCT
cana-5350	37	18	=	=	SYM
cana-5350	37	19	𝑓(𝑔𝑡	𝑓(𝑔𝑡	PROPN
cana-5350	37	20	,	,	PUNCT
cana-5350	37	21	𝑔𝑥	𝑔𝑥	PROPN
cana-5350	37	22	,	,	PUNCT
cana-5350	37	23	𝑔𝑦	𝑔𝑦	PROPN
cana-5350	37	24	,	,	PUNCT
cana-5350	37	25	𝑔𝑧	𝑔𝑧	PROPN
cana-5350	37	26	)	)	PUNCT
cana-5350	37	27	for	for	ADP
cana-5350	37	28	(	(	PUNCT
cana-5350	37	29	𝑥	𝑥	PROPN
cana-5350	37	30	,	,	PUNCT
cana-5350	37	31	𝑦	𝑦	NOUN
cana-5350	37	32	,	,	PUNCT
cana-5350	37	33	𝑧	𝑧	NOUN
cana-5350	37	34	,	,	PUNCT
cana-5350	37	35	𝑡	𝑡	NOUN
cana-5350	37	36	)	)	PUNCT
cana-5350	37	37	∈	∈	PROPN
cana-5350	37	38	𝑋	𝑋	NOUN
cana-5350	37	39	×	×	NOUN
cana-5350	37	40	𝑋	𝑋	NOUN
cana-5350	37	41	×	×	NOUN
cana-5350	37	42	𝑋	𝑋	PROPN
cana-5350	37	43	×	×	PROPN
cana-5350	37	44	𝑋.	𝑋.	PROPN
cana-5350	37	45	example	example	NOUN
cana-5350	37	46	2.10.1	2.10.1	NUM
cana-5350	37	47	let	let	VERB
cana-5350	37	48	(	(	PUNCT
cana-5350	37	49	x	x	NOUN
cana-5350	37	50	,	,	PUNCT
cana-5350	37	51	ℱ,∗	ℱ,∗	NUM
cana-5350	37	52	)	)	PUNCT
cana-5350	37	53	be	be	AUX
cana-5350	37	54	a	a	DET
cana-5350	37	55	fuzzy	fuzzy	ADJ
cana-5350	37	56	metric	metric	ADJ
cana-5350	37	57	space	space	NOUN
cana-5350	37	58	,	,	PUNCT
cana-5350	37	59	where	where	SCONJ
cana-5350	37	60	x	x	X
cana-5350	37	61	=	=	PUNCT
cana-5350	38	1	[	[	X
cana-5350	38	2	0,1	0,1	NUM
cana-5350	38	3	]	]	PUNCT
cana-5350	38	4	with	with	ADP
cana-5350	38	5	𝑎	𝑎	NOUN
cana-5350	38	6	∗	∗	NOUN
cana-5350	38	7	𝑏	𝑏	NOUN
cana-5350	38	8	=	=	SYM
cana-5350	38	9	min{𝑎	min{𝑎	PROPN
cana-5350	38	10	,	,	PUNCT
cana-5350	38	11	𝑏	𝑏	NOUN
cana-5350	38	12	}	}	PUNCT
cana-5350	38	13	and	and	CCONJ
cana-5350	38	14	communications	communication	NOUN
cana-5350	38	15	on	on	ADP
cana-5350	38	16	applied	apply	VERB
cana-5350	38	17	nonlinear	nonlinear	ADJ
cana-5350	38	18	analysis	analysis	NOUN
cana-5350	38	19	issn	issn	NOUN
cana-5350	38	20	:	:	PUNCT
cana-5350	38	21	1074	1074	NUM
cana-5350	38	22	-	-	PUNCT
cana-5350	38	23	133x	133x	NUM
cana-5350	38	24	vol	vol	VERB
cana-5350	38	25	32	32	NUM
cana-5350	38	26	no	no	NOUN
cana-5350	38	27	.	.	PUNCT
cana-5350	39	1	10s	10	NOUN
cana-5350	39	2	(	(	PUNCT
cana-5350	39	3	2025	2025	NUM
cana-5350	39	4	)	)	PUNCT
cana-5350	39	5	1797	1797	NUM
cana-5350	39	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5350	39	7	m(x	m(x	PROPN
cana-5350	39	8	,	,	PUNCT
cana-5350	39	9	y	y	PROPN
cana-5350	39	10	,	,	PUNCT
cana-5350	39	11	t	t	PROPN
cana-5350	39	12	)	)	PUNCT
cana-5350	39	13	=	=	PRON
cana-5350	39	14	{	{	PUNCT
cana-5350	39	15	t	t	NOUN
cana-5350	39	16	t	t	PROPN
cana-5350	39	17	+	+	CCONJ
cana-5350	39	18	|x	|x	NOUN
cana-5350	39	19	−	−	VERB
cana-5350	39	20	y|	y|	NOUN
cana-5350	39	21	,	,	PUNCT
cana-5350	39	22	if	if	SCONJ
cana-5350	39	23	t	t	PROPN
cana-5350	39	24	>	>	X
cana-5350	39	25	0	0	NUM
cana-5350	39	26	;	;	PUNCT
cana-5350	39	27	0	0	NUM
cana-5350	39	28	,	,	PUNCT
cana-5350	39	29	if	if	SCONJ
cana-5350	39	30	t	t	NOUN
cana-5350	39	31	=	=	SYM
cana-5350	39	32	0	0	X
cana-5350	39	33	.	.	PUNCT
cana-5350	40	1	let	let	VERB
cana-5350	40	2	f	f	X
cana-5350	40	3	:	:	PUNCT
cana-5350	40	4	x	x	SYM
cana-5350	40	5	×	×	NOUN
cana-5350	40	6	x	x	SYM
cana-5350	40	7	×	×	NOUN
cana-5350	40	8	x	x	INTJ
cana-5350	40	9	→	→	SYM
cana-5350	40	10	x	x	X
cana-5350	40	11	&	&	CCONJ
cana-5350	40	12	𝑔	𝑔	PROPN
cana-5350	40	13	:	:	PUNCT
cana-5350	40	14	x	x	SYM
cana-5350	40	15	→	→	PUNCT
cana-5350	40	16	x	x	AUX
cana-5350	40	17	be	be	AUX
cana-5350	40	18	defined	define	VERB
cana-5350	40	19	by	by	ADP
cana-5350	40	20	f(x	f(x	PROPN
cana-5350	40	21	,	,	PUNCT
cana-5350	40	22	y	y	PROPN
cana-5350	40	23	,	,	PUNCT
cana-5350	40	24	z	z	PROPN
cana-5350	40	25	,	,	PUNCT
cana-5350	40	26	w	w	PROPN
cana-5350	40	27	)	)	PUNCT
cana-5350	40	28	=	=	SYM
cana-5350	41	1	2x	2x	NOUN
cana-5350	41	2	+	+	CCONJ
cana-5350	41	3	2y	2y	PROPN
cana-5350	42	1	+	+	CCONJ
cana-5350	42	2	2z	2z	NOUN
cana-5350	42	3	+	+	CCONJ
cana-5350	42	4	w	w	PROPN
cana-5350	42	5	2	2	NUM
cana-5350	42	6	g(x	g(x	NOUN
cana-5350	42	7	)	)	PUNCT
cana-5350	43	1	=	=	PRON
cana-5350	43	2	{	{	PUNCT
cana-5350	43	3	x	x	X
cana-5350	43	4	,	,	PUNCT
cana-5350	43	5	if	if	SCONJ
cana-5350	43	6	0	0	NUM
cana-5350	43	7	≤	≤	NUM
cana-5350	43	8	x	x	X
cana-5350	43	9	<	<	X
cana-5350	43	10	1	1	NUM
cana-5350	43	11	;	;	PUNCT
cana-5350	43	12	7	7	NUM
cana-5350	43	13	2	2	NUM
cana-5350	43	14	,	,	PUNCT
cana-5350	43	15	if	if	SCONJ
cana-5350	43	16	x	x	PRON
cana-5350	43	17	≥	≥	NOUN
cana-5350	43	18	1	1	NUM
cana-5350	43	19	.	.	PUNCT
cana-5350	44	1	here	here	ADV
cana-5350	44	2	,	,	PUNCT
cana-5350	44	3	(	(	PUNCT
cana-5350	44	4	0,0,0,0	0,0,0,0	NOUN
cana-5350	44	5	)	)	PUNCT
cana-5350	44	6	and	and	CCONJ
cana-5350	44	7	(	(	PUNCT
cana-5350	44	8	1,1,1,1	1,1,1,1	NUM
cana-5350	44	9	)	)	PUNCT
cana-5350	44	10	are	be	AUX
cana-5350	44	11	two	two	NUM
cana-5350	44	12	coincidence	coincidence	NOUN
cana-5350	44	13	points	point	NOUN
cana-5350	44	14	of	of	ADP
cana-5350	44	15	f	f	PROPN
cana-5350	44	16	and	and	CCONJ
cana-5350	44	17	g.	g.	PROPN
cana-5350	44	18	that	that	PRON
cana-5350	44	19	is	be	AUX
cana-5350	44	20	f(0,0,0,0	f(0,0,0,0	NOUN
cana-5350	44	21	)	)	PUNCT
cana-5350	44	22	=	=	SYM
cana-5350	44	23	0	0	PUNCT
cana-5350	45	1	=	=	SYM
cana-5350	45	2	g(0	g(0	PROPN
cana-5350	45	3	)	)	PUNCT
cana-5350	45	4	,	,	PUNCT
cana-5350	45	5	f(1,1,1,1	f(1,1,1,1	X
cana-5350	45	6	)	)	PUNCT
cana-5350	45	7	=	=	SYM
cana-5350	45	8	1	1	NUM
cana-5350	45	9	=	=	SYM
cana-5350	45	10	g(1	g(1	NOUN
cana-5350	45	11	)	)	PUNCT
cana-5350	45	12	but	but	CCONJ
cana-5350	45	13	gf(0,0,0,0	gf(0,0,0,0	NOUN
cana-5350	45	14	)	)	PUNCT
cana-5350	45	15	=	=	SYM
cana-5350	45	16	0	0	NUM
cana-5350	45	17	=	=	SYM
cana-5350	45	18	f(g0	f(g0	NOUN
cana-5350	45	19	,	,	PUNCT
cana-5350	45	20	g0	g0	PROPN
cana-5350	45	21	,	,	PUNCT
cana-5350	45	22	g0	g0	PROPN
cana-5350	45	23	,	,	PUNCT
cana-5350	45	24	g0	g0	NOUN
cana-5350	45	25	)	)	PUNCT
cana-5350	45	26	,	,	PUNCT
cana-5350	45	27	gf(1,1,1,1	gf(1,1,1,1	NOUN
cana-5350	45	28	)	)	PUNCT
cana-5350	45	29	≠	≠	PROPN
cana-5350	45	30	f(g1	f(g1	NOUN
cana-5350	45	31	,	,	PUNCT
cana-5350	45	32	g1	g1	NOUN
cana-5350	45	33	,	,	PUNCT
cana-5350	45	34	g1	g1	NOUN
cana-5350	45	35	,	,	PUNCT
cana-5350	45	36	g1	g1	NOUN
cana-5350	45	37	)	)	PUNCT
cana-5350	45	38	.	.	PUNCT
cana-5350	46	1	thus	thus	ADV
cana-5350	46	2	f	f	PROPN
cana-5350	46	3	and	and	CCONJ
cana-5350	46	4	g	g	PROPN
cana-5350	46	5	are	be	AUX
cana-5350	46	6	owc	owc	NOUN
cana-5350	46	7	but	but	CCONJ
cana-5350	46	8	not	not	PART
cana-5350	46	9	weakly	weakly	ADV
cana-5350	46	10	compatible	compatible	ADJ
cana-5350	46	11	.	.	PUNCT
cana-5350	47	1	coincidence	coincidence	NOUN
cana-5350	47	2	points	point	NOUN
cana-5350	47	3	verification	verification	NOUN
cana-5350	47	4	:	:	PUNCT
cana-5350	47	5	𝑓(0,0,0,0	𝑓(0,0,0,0	NOUN
cana-5350	47	6	)	)	PUNCT
cana-5350	47	7	=	=	SYM
cana-5350	47	8	0.0	0.0	NUM
cana-5350	47	9	,	,	PUNCT
cana-5350	47	10	𝑔(0	𝑔(0	PROPN
cana-5350	47	11	)	)	PUNCT
cana-5350	47	12	=	=	SYM
cana-5350	47	13	0	0	NUM
cana-5350	47	14	,	,	PUNCT
cana-5350	47	15	𝑔𝑓(0,0,0,0	𝑔𝑓(0,0,0,0	NOUN
cana-5350	47	16	)	)	PUNCT
cana-5350	47	17	=	=	SYM
cana-5350	47	18	0.0	0.0	NUM
cana-5350	47	19	,	,	PUNCT
cana-5350	47	20	𝑓(𝑔0	𝑓(𝑔0	NOUN
cana-5350	47	21	,	,	PUNCT
cana-5350	47	22	𝑔0	𝑔0	NOUN
cana-5350	47	23	,	,	PUNCT
cana-5350	47	24	𝑔0	𝑔0	NOUN
cana-5350	47	25	,	,	PUNCT
cana-5350	47	26	𝑔0	𝑔0	PROPN
cana-5350	47	27	)	)	PUNCT
cana-5350	47	28	=	=	SYM
cana-5350	47	29	0.0	0.0	NUM
cana-5350	47	30	𝑓(1,1,1,1	𝑓(1,1,1,1	NOUN
cana-5350	47	31	)	)	PUNCT
cana-5350	47	32	=	=	SYM
cana-5350	47	33	3.5	3.5	NUM
cana-5350	47	34	,	,	PUNCT
cana-5350	47	35	𝑔(1	𝑔(1	NOUN
cana-5350	47	36	)	)	PUNCT
cana-5350	47	37	=	=	SYM
cana-5350	47	38	3.5	3.5	NUM
cana-5350	47	39	,	,	PUNCT
cana-5350	47	40	𝑔𝑓(1,1,1,1	𝑔𝑓(1,1,1,1	NOUN
cana-5350	47	41	)	)	PUNCT
cana-5350	47	42	=	=	SYM
cana-5350	47	43	3.5	3.5	NUM
cana-5350	47	44	,	,	PUNCT
cana-5350	47	45	𝑓(𝑔1	𝑓(𝑔1	NOUN
cana-5350	47	46	,	,	PUNCT
cana-5350	47	47	𝑔1	𝑔1	PROPN
cana-5350	47	48	,	,	PUNCT
cana-5350	47	49	𝑔1	𝑔1	PROPN
cana-5350	47	50	,	,	PUNCT
cana-5350	47	51	𝑔1	𝑔1	PROPN
cana-5350	47	52	)	)	PUNCT
cana-5350	47	53	=	=	PUNCT
cana-5350	48	1	12.25	12.25	NUM
cana-5350	48	2	f	f	NOUN
cana-5350	48	3	and	and	CCONJ
cana-5350	48	4	g	g	PROPN
cana-5350	48	5	are	be	AUX
cana-5350	48	6	occasionally	occasionally	ADV
cana-5350	48	7	weakly	weakly	ADV
cana-5350	48	8	compatible	compatible	ADJ
cana-5350	48	9	(	(	PUNCT
cana-5350	48	10	owc	owc	NOUN
cana-5350	48	11	)	)	PUNCT
cana-5350	48	12	but	but	CCONJ
cana-5350	48	13	not	not	PART
cana-5350	48	14	weakly	weakly	ADV
cana-5350	48	15	compatible	compatible	ADJ
cana-5350	48	16	.	.	PUNCT
cana-5350	49	1	3	3	NUM
cana-5350	49	2	main	main	ADJ
cana-5350	49	3	results	result	NOUN
cana-5350	49	4	theorem	theorem	VERB
cana-5350	49	5	:	:	PUNCT
cana-5350	49	6	3.1	3.1	NUM
cana-5350	49	7	let	let	NOUN
cana-5350	49	8	(	(	PUNCT
cana-5350	49	9	𝑋	𝑋	PROPN
cana-5350	49	10	,	,	PUNCT
cana-5350	49	11	𝑀	𝑀	PROPN
cana-5350	49	12	,	,	PUNCT
cana-5350	49	13			PROPN
cana-5350	49	14	)	)	PUNCT
cana-5350	49	15	be	be	AUX
cana-5350	49	16	a	a	DET
cana-5350	49	17	fuzzy	fuzzy	ADJ
cana-5350	49	18	metric	metric	ADJ
cana-5350	49	19	space	space	NOUN
cana-5350	49	20	with	with	ADP
cana-5350	49	21	𝑡	𝑡	PROPN
cana-5350	49	22	∗	∗	NOUN
cana-5350	49	23	𝑡	𝑡	X
cana-5350	49	24	=	=	PUNCT
cana-5350	49	25	𝑡	𝑡	PROPN
cana-5350	49	26	for	for	ADP
cana-5350	49	27	all	all	DET
cana-5350	49	28	𝑡	𝑡	ADP
cana-5350	49	29	∈	∈	PROPN
cana-5350	50	1	[	[	X
cana-5350	50	2	0,1	0,1	NUM
cana-5350	50	3	]	]	PUNCT
cana-5350	50	4	.	.	PUNCT
cana-5350	51	1	let	let	VERB
cana-5350	51	2	𝐴	𝐴	PROPN
cana-5350	51	3	,	,	PUNCT
cana-5350	51	4	𝐵	𝐵	PROPN
cana-5350	51	5	:	:	PUNCT
cana-5350	51	6	𝑋	𝑋	NOUN
cana-5350	51	7	×	×	NOUN
cana-5350	51	8	𝑋	𝑋	PROPN
cana-5350	51	9	×	×	NOUN
cana-5350	51	10	𝑋	𝑋	NOUN
cana-5350	51	11	×	×	NOUN
cana-5350	51	12	𝑋	𝑋	PROPN
cana-5350	51	13	→	→	SYM
cana-5350	51	14	𝑋	𝑋	PROPN
cana-5350	51	15	and	and	CCONJ
cana-5350	51	16	𝑆	𝑆	PROPN
cana-5350	51	17	,	,	PUNCT
cana-5350	51	18	𝑇	𝑇	PROPN
cana-5350	51	19	:	:	PUNCT
cana-5350	51	20	𝑋	𝑋	PROPN
cana-5350	51	21	→	→	SYM
cana-5350	51	22	𝑋	𝑋	PROPN
cana-5350	51	23	be	be	VERB
cana-5350	51	24	four	four	NUM
cana-5350	51	25	self	self	NOUN
cana-5350	51	26	-	-	PUNCT
cana-5350	51	27	mappings	mapping	NOUN
cana-5350	51	28	satisfying	satisfy	VERB
cana-5350	51	29	the	the	DET
cana-5350	51	30	following	follow	VERB
cana-5350	51	31	conditions	condition	NOUN
cana-5350	51	32	:	:	PUNCT
cana-5350	51	33	communications	communication	NOUN
cana-5350	51	34	on	on	ADP
cana-5350	51	35	applied	apply	VERB
cana-5350	51	36	nonlinear	nonlinear	ADJ
cana-5350	51	37	analysis	analysis	NOUN
cana-5350	51	38	issn	issn	NOUN
cana-5350	51	39	:	:	PUNCT
cana-5350	51	40	1074	1074	NUM
cana-5350	51	41	-	-	PUNCT
cana-5350	51	42	133x	133x	NUM
cana-5350	51	43	vol	vol	VERB
cana-5350	51	44	32	32	NUM
cana-5350	51	45	no	no	NOUN
cana-5350	51	46	.	.	PUNCT
cana-5350	52	1	10s	10	NOUN
cana-5350	52	2	(	(	PUNCT
cana-5350	52	3	2025	2025	NUM
cana-5350	52	4	)	)	PUNCT
cana-5350	52	5	1798	1798	NUM
cana-5350	52	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5350	52	7	(	(	PUNCT
cana-5350	52	8	i	i	NOUN
cana-5350	52	9	)	)	PUNCT
cana-5350	52	10	𝑀(𝐴(𝑥	𝑀(𝐴(𝑥	NOUN
cana-5350	52	11	,	,	PUNCT
cana-5350	52	12	𝑦	𝑦	NOUN
cana-5350	52	13	,	,	PUNCT
cana-5350	52	14	𝑧	𝑧	NOUN
cana-5350	52	15	,	,	PUNCT
cana-5350	52	16	𝑝	𝑝	NOUN
cana-5350	52	17	)	)	PUNCT
cana-5350	52	18	,	,	PUNCT
cana-5350	52	19	𝐵(𝑢	𝐵(𝑢	PROPN
cana-5350	52	20	,	,	PUNCT
cana-5350	52	21	𝑣	𝑣	NOUN
cana-5350	52	22	,	,	PUNCT
cana-5350	52	23	𝑤	𝑤	ADP
cana-5350	52	24	,	,	PUNCT
cana-5350	52	25	𝑟	𝑟	NOUN
cana-5350	52	26	)	)	PUNCT
cana-5350	52	27	,	,	PUNCT
cana-5350	52	28	𝑞𝑡	𝑞𝑡	PRON
cana-5350	52	29	)	)	PUNCT
cana-5350	52	30	≥	≥	PROPN
cana-5350	52	31	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5350	52	32	{	{	PUNCT
cana-5350	52	33	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	52	34	,	,	PUNCT
cana-5350	52	35	𝑇𝑢	𝑇𝑢	PROPN
cana-5350	52	36	,	,	PUNCT
cana-5350	52	37	𝑡	𝑡	NOUN
cana-5350	52	38	)	)	PUNCT
cana-5350	52	39	,	,	PUNCT
cana-5350	52	40	𝑀(𝐴(𝑥	𝑀(𝐴(𝑥	NOUN
cana-5350	52	41	,	,	PUNCT
cana-5350	52	42	𝑦	𝑦	NOUN
cana-5350	52	43	,	,	PUNCT
cana-5350	52	44	𝑧	𝑧	NOUN
cana-5350	52	45	,	,	PUNCT
cana-5350	52	46	𝑝	𝑝	NOUN
cana-5350	52	47	)	)	PUNCT
cana-5350	52	48	,	,	PUNCT
cana-5350	52	49	𝑆𝑥	𝑆𝑥	PROPN
cana-5350	52	50	,	,	PUNCT
cana-5350	52	51	𝑡	𝑡	PROPN
cana-5350	52	52	)	)	PUNCT
cana-5350	52	53	,	,	PUNCT
cana-5350	52	54	𝑀(𝐵(𝑢	𝑀(𝐵(𝑢	X
cana-5350	52	55	,	,	PUNCT
cana-5350	52	56	𝑣	𝑣	NOUN
cana-5350	52	57	,	,	PUNCT
cana-5350	52	58	𝑤	𝑤	ADP
cana-5350	52	59	,	,	PUNCT
cana-5350	52	60	𝑟	𝑟	NOUN
cana-5350	52	61	)	)	PUNCT
cana-5350	52	62	,	,	PUNCT
cana-5350	53	1	𝑇𝑢	𝑇𝑢	PROPN
cana-5350	53	2	,	,	PUNCT
cana-5350	53	3	𝑡	𝑡	PROPN
cana-5350	53	4	)	)	PUNCT
cana-5350	53	5	,	,	PUNCT
cana-5350	53	6	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	53	7	,	,	PUNCT
cana-5350	53	8	𝐵(𝑢	𝐵(𝑢	PROPN
cana-5350	53	9	,	,	PUNCT
cana-5350	53	10	𝑣	𝑣	NOUN
cana-5350	53	11	,	,	PUNCT
cana-5350	53	12	𝑤	𝑤	ADP
cana-5350	53	13	,	,	PUNCT
cana-5350	53	14	𝑟	𝑟	NOUN
cana-5350	53	15	)	)	PUNCT
cana-5350	53	16	,	,	PUNCT
cana-5350	53	17	𝑡	𝑡	PROPN
cana-5350	53	18	)	)	PUNCT
cana-5350	53	19	,	,	PUNCT
cana-5350	53	20	𝑀(𝐴(𝑥	𝑀(𝐴(𝑥	NOUN
cana-5350	53	21	,	,	PUNCT
cana-5350	53	22	𝑦	𝑦	NOUN
cana-5350	53	23	,	,	PUNCT
cana-5350	53	24	𝑧	𝑧	NOUN
cana-5350	53	25	,	,	PUNCT
cana-5350	53	26	𝑝	𝑝	NOUN
cana-5350	53	27	)	)	PUNCT
cana-5350	53	28	,	,	PUNCT
cana-5350	53	29	𝑇𝑢	𝑇𝑢	PROPN
cana-5350	53	30	,	,	PUNCT
cana-5350	53	31	𝑡	𝑡	NOUN
cana-5350	53	32	)	)	PUNCT
cana-5350	53	33	}	}	PUNCT
cana-5350	53	34	for	for	ADP
cana-5350	53	35	all	all	DET
cana-5350	53	36	𝑥	𝑥	PROPN
cana-5350	53	37	,	,	PUNCT
cana-5350	53	38	𝑦	𝑦	NOUN
cana-5350	53	39	,	,	PUNCT
cana-5350	53	40	𝑧	𝑧	PROPN
cana-5350	53	41	,	,	PUNCT
cana-5350	53	42	𝑝	𝑝	NOUN
cana-5350	53	43	,	,	PUNCT
cana-5350	53	44	𝑢	𝑢	PROPN
cana-5350	53	45	,	,	PUNCT
cana-5350	53	46	𝑣	𝑣	NOUN
cana-5350	53	47	,	,	PUNCT
cana-5350	53	48	𝑤	𝑤	ADP
cana-5350	53	49	,	,	PUNCT
cana-5350	53	50	𝑟	𝑟	X
cana-5350	53	51	∈	∈	PROPN
cana-5350	53	52	𝑋	𝑋	PROPN
cana-5350	53	53	(	(	PUNCT
cana-5350	53	54	ii	ii	PROPN
cana-5350	53	55	)	)	PUNCT
cana-5350	53	56	𝑦	𝑦	NOUN
cana-5350	53	57	=	=	SYM
cana-5350	53	58	𝐵(𝑥	𝐵(𝑥	PROPN
cana-5350	53	59	,	,	PUNCT
cana-5350	53	60	𝑦	𝑦	NOUN
cana-5350	53	61	,	,	PUNCT
cana-5350	53	62	𝑧	𝑧	NOUN
cana-5350	53	63	,	,	PUNCT
cana-5350	53	64	𝑝	𝑝	NOUN
cana-5350	53	65	)	)	PUNCT
cana-5350	53	66	moreover	moreover	ADV
cana-5350	53	67	if	if	SCONJ
cana-5350	53	68	the	the	DET
cana-5350	53	69	pairs	pair	NOUN
cana-5350	53	70	(	(	PUNCT
cana-5350	53	71	𝐴	𝐴	PROPN
cana-5350	53	72	,	,	PUNCT
cana-5350	53	73	𝑆	𝑆	PROPN
cana-5350	53	74	)	)	PUNCT
cana-5350	53	75	and	and	CCONJ
cana-5350	53	76	(	(	PUNCT
cana-5350	53	77	𝐵	𝐵	PROPN
cana-5350	53	78	,	,	PUNCT
cana-5350	53	79	𝑇	𝑇	PROPN
cana-5350	53	80	)	)	PUNCT
cana-5350	53	81	are	be	AUX
cana-5350	53	82	owc	owc	NUM
cana-5350	53	83	,	,	PUNCT
cana-5350	53	84	then	then	ADV
cana-5350	53	85	there	there	PRON
cana-5350	53	86	exists	exist	VERB
cana-5350	53	87	a	a	DET
cana-5350	53	88	unique	unique	ADJ
cana-5350	53	89	point	point	NOUN
cana-5350	53	90	𝑥	𝑥	NOUN
cana-5350	53	91	in	in	ADP
cana-5350	53	92	𝑋	𝑋	NOUN
cana-5350	54	1	such	such	ADJ
cana-5350	54	2	that	that	SCONJ
cana-5350	54	3	𝐴(𝑥	𝐴(𝑥	NOUN
cana-5350	54	4	,	,	PUNCT
cana-5350	54	5	𝑥	𝑥	PRON
cana-5350	54	6	,	,	PUNCT
cana-5350	54	7	𝑥	𝑥	NOUN
cana-5350	54	8	,	,	PUNCT
cana-5350	54	9	𝑥	𝑥	NOUN
cana-5350	54	10	)	)	PUNCT
cana-5350	54	11	=	=	SYM
cana-5350	54	12	𝑇(𝑥	𝑇(𝑥	X
cana-5350	54	13	)	)	PUNCT
cana-5350	54	14	=	=	SYM
cana-5350	54	15	𝐵(𝑥	𝐵(𝑥	PROPN
cana-5350	54	16	,	,	PUNCT
cana-5350	54	17	𝑥	𝑥	PROPN
cana-5350	54	18	,	,	PUNCT
cana-5350	54	19	𝑥	𝑥	NOUN
cana-5350	54	20	,	,	PUNCT
cana-5350	54	21	𝑥	𝑥	NOUN
cana-5350	54	22	)	)	PUNCT
cana-5350	54	23	=	=	SYM
cana-5350	54	24	𝑆(𝑥	𝑆(𝑥	X
cana-5350	54	25	)	)	PUNCT
cana-5350	54	26	=	=	NOUN
cana-5350	55	1	𝑥.	𝑥.	ADJ
cana-5350	55	2	proof	proof	NOUN
cana-5350	55	3	:	:	PUNCT
cana-5350	55	4	since	since	SCONJ
cana-5350	55	5	the	the	DET
cana-5350	55	6	pairs	pair	NOUN
cana-5350	55	7	(	(	PUNCT
cana-5350	55	8	a	a	DET
cana-5350	55	9	,	,	PUNCT
cana-5350	55	10	s	s	PART
cana-5350	55	11	)	)	PUNCT
cana-5350	55	12	and	and	CCONJ
cana-5350	55	13	(	(	PUNCT
cana-5350	55	14	b	b	NOUN
cana-5350	55	15	,	,	PUNCT
cana-5350	55	16	t	t	PROPN
cana-5350	55	17	)	)	PUNCT
cana-5350	55	18	are	be	AUX
cana-5350	55	19	owc	owc	NUM
cana-5350	55	20	so	so	SCONJ
cana-5350	55	21	there	there	PRON
cana-5350	55	22	are	be	VERB
cana-5350	55	23	points	point	NOUN
cana-5350	55	24	𝑎	𝑎	NOUN
cana-5350	55	25	,	,	PUNCT
cana-5350	55	26	𝑏	𝑏	NOUN
cana-5350	55	27	,	,	PUNCT
cana-5350	55	28	𝑐	𝑐	PROPN
cana-5350	55	29	,	,	PUNCT
cana-5350	55	30	𝑑	𝑑	NOUN
cana-5350	55	31	,	,	PUNCT
cana-5350	55	32	𝑎′	𝑎′	PROPN
cana-5350	55	33	,	,	PUNCT
cana-5350	55	34	𝑏′	𝑏′	PROPN
cana-5350	55	35	,	,	PUNCT
cana-5350	55	36	𝑐′	𝑐′	NUM
cana-5350	55	37	,	,	PUNCT
cana-5350	55	38	𝑑′	𝑑′	VERB
cana-5350	55	39	in	in	ADP
cana-5350	55	40	x	x	PROPN
cana-5350	55	41	such	such	ADJ
cana-5350	55	42	that	that	SCONJ
cana-5350	55	43	𝐴(𝑎	𝐴(𝑎	PROPN
cana-5350	55	44	,	,	PUNCT
cana-5350	55	45	𝑏	𝑏	NOUN
cana-5350	55	46	,	,	PUNCT
cana-5350	55	47	𝑐	𝑐	NOUN
cana-5350	55	48	,	,	PUNCT
cana-5350	55	49	𝑑	𝑑	NOUN
cana-5350	55	50	)	)	PUNCT
cana-5350	56	1	=	=	SYM
cana-5350	56	2	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	56	3	,	,	PUNCT
cana-5350	56	4	𝐴(𝑏	𝐴(𝑏	PROPN
cana-5350	56	5	,	,	PUNCT
cana-5350	56	6	𝑐	𝑐	PROPN
cana-5350	56	7	,	,	PUNCT
cana-5350	56	8	𝑑	𝑑	NOUN
cana-5350	56	9	,	,	PUNCT
cana-5350	56	10	𝑎	𝑎	NOUN
cana-5350	56	11	)	)	PUNCT
cana-5350	56	12	=	=	SYM
cana-5350	57	1	𝑆𝑏	𝑆𝑏	PROPN
cana-5350	57	2	,	,	PUNCT
cana-5350	57	3	𝐴(𝑐	𝐴(𝑐	PROPN
cana-5350	57	4	,	,	PUNCT
cana-5350	57	5	𝑑	𝑑	NOUN
cana-5350	57	6	,	,	PUNCT
cana-5350	57	7	𝑎	𝑎	NOUN
cana-5350	57	8	,	,	PUNCT
cana-5350	57	9	𝑏	𝑏	NOUN
cana-5350	57	10	)	)	PUNCT
cana-5350	57	11	=	=	SYM
cana-5350	58	1	𝑆𝑐	𝑆𝑐	PROPN
cana-5350	58	2	,	,	PUNCT
cana-5350	58	3	𝐴(𝑑	𝐴(𝑑	NOUN
cana-5350	58	4	,	,	PUNCT
cana-5350	58	5	𝑎	𝑎	X
cana-5350	58	6	,	,	PUNCT
cana-5350	58	7	𝑏	𝑏	NOUN
cana-5350	58	8	,	,	PUNCT
cana-5350	58	9	𝑐	𝑐	NOUN
cana-5350	58	10	)	)	PUNCT
cana-5350	58	11	=	=	SYM
cana-5350	59	1	𝑆𝑑	𝑆𝑑	PROPN
cana-5350	59	2	and	and	CCONJ
cana-5350	59	3	𝐵(𝑎′	𝐵(𝑎′	PROPN
cana-5350	59	4	,	,	PUNCT
cana-5350	59	5	𝑏′	𝑏′	PROPN
cana-5350	59	6	,	,	PUNCT
cana-5350	59	7	𝑐′	𝑐′	NUM
cana-5350	59	8	,	,	PUNCT
cana-5350	59	9	𝑑′	𝑑′	NOUN
cana-5350	59	10	)	)	PUNCT
cana-5350	60	1	=	=	SYM
cana-5350	60	2	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	60	3	,	,	PUNCT
cana-5350	60	4	𝐵(𝑏′	𝐵(𝑏′	NOUN
cana-5350	60	5	,	,	PUNCT
cana-5350	60	6	𝑐′	𝑐′	NUM
cana-5350	60	7	,	,	PUNCT
cana-5350	60	8	𝑑′	𝑑′	NOUN
cana-5350	60	9	,	,	PUNCT
cana-5350	60	10	𝑎′	𝑎′	NUM
cana-5350	60	11	)	)	PUNCT
cana-5350	60	12	=	=	SYM
cana-5350	60	13	𝑇𝑏′	𝑇𝑏′	PROPN
cana-5350	60	14	,	,	PUNCT
cana-5350	60	15	𝐵(𝑐′	𝐵(𝑐′	PROPN
cana-5350	60	16	,	,	PUNCT
cana-5350	60	17	𝑑′	𝑑′	NOUN
cana-5350	60	18	,	,	PUNCT
cana-5350	60	19	𝑎′	𝑎′	NUM
cana-5350	60	20	,	,	PUNCT
cana-5350	60	21	𝑏′	𝑏′	NUM
cana-5350	60	22	)	)	PUNCT
cana-5350	60	23	=	=	PUNCT
cana-5350	61	1	𝑇𝑐′	𝑇𝑐′	ADJ
cana-5350	61	2	,	,	PUNCT
cana-5350	61	3	𝐵(𝑑′	𝐵(𝑑′	PROPN
cana-5350	61	4	,	,	PUNCT
cana-5350	61	5	𝑎′	𝑎′	NUM
cana-5350	61	6	,	,	PUNCT
cana-5350	61	7	𝑏′	𝑏′	PROPN
cana-5350	61	8	,	,	PUNCT
cana-5350	61	9	𝑐′	𝑐′	NUM
cana-5350	61	10	)	)	PUNCT
cana-5350	62	1	=	=	SYM
cana-5350	62	2	𝑇𝑑′	𝑇𝑑′	NOUN
cana-5350	62	3	𝑆𝑥	𝑆𝑥	PROPN
cana-5350	62	4	=	=	PUNCT
cana-5350	62	5	𝑆𝐴(𝑎	𝑆𝐴(𝑎	NOUN
cana-5350	62	6	,	,	PUNCT
cana-5350	62	7	𝑏	𝑏	NOUN
cana-5350	62	8	,	,	PUNCT
cana-5350	62	9	𝑐	𝑐	NOUN
cana-5350	62	10	,	,	PUNCT
cana-5350	62	11	𝑑	𝑑	NOUN
cana-5350	62	12	)	)	PUNCT
cana-5350	62	13	=	=	SYM
cana-5350	62	14	𝐴(𝑆𝑎	𝐴(𝑆𝑎	NOUN
cana-5350	62	15	,	,	PUNCT
cana-5350	62	16	𝑆𝑏	𝑆𝑏	PROPN
cana-5350	62	17	,	,	PUNCT
cana-5350	62	18	𝑆𝑐	𝑆𝑐	PROPN
cana-5350	62	19	,	,	PUNCT
cana-5350	62	20	𝑆𝑑	𝑆𝑑	NOUN
cana-5350	62	21	)	)	PUNCT
cana-5350	62	22	=	=	PUNCT
cana-5350	62	23	𝐴(𝑥	𝐴(𝑥	NOUN
cana-5350	62	24	,	,	PUNCT
cana-5350	62	25	𝑦	𝑦	NOUN
cana-5350	62	26	,	,	PUNCT
cana-5350	62	27	𝑧	𝑧	NOUN
cana-5350	62	28	,	,	PUNCT
cana-5350	62	29	𝑝	𝑝	NOUN
cana-5350	62	30	)	)	PUNCT
cana-5350	62	31	𝑆𝑦	𝑆𝑦	PROPN
cana-5350	62	32	=	=	SYM
cana-5350	62	33	𝑆𝐴(𝑏	𝑆𝐴(𝑏	PROPN
cana-5350	62	34	,	,	PUNCT
cana-5350	62	35	𝑐	𝑐	NOUN
cana-5350	62	36	,	,	PUNCT
cana-5350	62	37	𝑑	𝑑	NOUN
cana-5350	62	38	,	,	PUNCT
cana-5350	62	39	𝑎	𝑎	NOUN
cana-5350	62	40	)	)	PUNCT
cana-5350	62	41	=	=	SYM
cana-5350	62	42	𝐴(𝑆𝑏	𝐴(𝑆𝑏	NOUN
cana-5350	62	43	,	,	PUNCT
cana-5350	62	44	𝑆𝑐	𝑆𝑐	PROPN
cana-5350	62	45	,	,	PUNCT
cana-5350	62	46	𝑆𝑑	𝑆𝑑	PROPN
cana-5350	62	47	,	,	PUNCT
cana-5350	62	48	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	62	49	)	)	PUNCT
cana-5350	62	50	=	=	SYM
cana-5350	62	51	𝐴(𝑦	𝐴(𝑦	X
cana-5350	62	52	,	,	PUNCT
cana-5350	62	53	𝑧	𝑧	PROPN
cana-5350	62	54	,	,	PUNCT
cana-5350	62	55	𝑝	𝑝	NOUN
cana-5350	62	56	,	,	PUNCT
cana-5350	62	57	𝑥	𝑥	NOUN
cana-5350	62	58	)	)	PUNCT
cana-5350	62	59	𝑆𝑧	𝑆𝑧	NOUN
cana-5350	62	60	=	=	PUNCT
cana-5350	62	61	𝑆𝐴(𝑐	𝑆𝐴(𝑐	PROPN
cana-5350	62	62	,	,	PUNCT
cana-5350	62	63	𝑑	𝑑	NOUN
cana-5350	62	64	,	,	PUNCT
cana-5350	62	65	𝑎	𝑎	NOUN
cana-5350	62	66	,	,	PUNCT
cana-5350	62	67	𝑏	𝑏	NOUN
cana-5350	62	68	)	)	PUNCT
cana-5350	62	69	=	=	SYM
cana-5350	62	70	𝐴(𝑆𝑐	𝐴(𝑆𝑐	PROPN
cana-5350	62	71	,	,	PUNCT
cana-5350	62	72	𝑆𝑑	𝑆𝑑	NOUN
cana-5350	62	73	,	,	PUNCT
cana-5350	62	74	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	62	75	,	,	PUNCT
cana-5350	62	76	𝑆𝑏	𝑆𝑏	PROPN
cana-5350	62	77	)	)	PUNCT
cana-5350	62	78	=	=	SYM
cana-5350	62	79	𝐴(𝑧	𝐴(𝑧	X
cana-5350	62	80	,	,	PUNCT
cana-5350	62	81	𝑝	𝑝	NOUN
cana-5350	62	82	,	,	PUNCT
cana-5350	62	83	𝑥	𝑥	PROPN
cana-5350	62	84	,	,	PUNCT
cana-5350	62	85	𝑦	𝑦	NOUN
cana-5350	62	86	)	)	PUNCT
cana-5350	62	87	𝑆𝑝	𝑆𝑝	NOUN
cana-5350	62	88	=	=	SYM
cana-5350	62	89	𝑆𝐴(𝑑	𝑆𝐴(𝑑	PROPN
cana-5350	62	90	,	,	PUNCT
cana-5350	62	91	𝑎	𝑎	NOUN
cana-5350	62	92	,	,	PUNCT
cana-5350	62	93	𝑏	𝑏	NOUN
cana-5350	62	94	,	,	PUNCT
cana-5350	62	95	𝑐	𝑐	NOUN
cana-5350	62	96	)	)	PUNCT
cana-5350	62	97	=	=	SYM
cana-5350	62	98	𝐴(𝑆𝑑	𝐴(𝑆𝑑	NUM
cana-5350	62	99	,	,	PUNCT
cana-5350	62	100	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	62	101	,	,	PUNCT
cana-5350	62	102	𝑆𝑏	𝑆𝑏	PROPN
cana-5350	62	103	,	,	PUNCT
cana-5350	62	104	𝑆𝑐	𝑆𝑐	PROPN
cana-5350	62	105	)	)	PUNCT
cana-5350	62	106	=	=	SYM
cana-5350	62	107	𝐴(𝑝	𝐴(𝑝	PROPN
cana-5350	62	108	,	,	PUNCT
cana-5350	62	109	𝑥	𝑥	PROPN
cana-5350	62	110	,	,	PUNCT
cana-5350	62	111	𝑦	𝑦	NOUN
cana-5350	62	112	,	,	PUNCT
cana-5350	62	113	𝑧	𝑧	PART
cana-5350	62	114	)	)	PUNCT
cana-5350	62	115	we	we	PRON
cana-5350	62	116	claim	claim	VERB
cana-5350	62	117	that	that	SCONJ
cana-5350	62	118	𝑆𝑎	𝑆𝑎	NOUN
cana-5350	62	119	=	=	NOUN
cana-5350	62	120	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	62	121	.	.	PUNCT
cana-5350	63	1	if	if	SCONJ
cana-5350	63	2	not	not	PART
cana-5350	63	3	,	,	PUNCT
cana-5350	63	4	by	by	ADP
cana-5350	63	5	inequality	inequality	NOUN
cana-5350	63	6	(	(	PUNCT
cana-5350	63	7	𝑖	𝑖	X
cana-5350	63	8	)	)	PUNCT
cana-5350	63	9	we	we	PRON
cana-5350	63	10	get	get	VERB
cana-5350	63	11	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	63	12	,	,	PUNCT
cana-5350	63	13	𝑏	𝑏	NOUN
cana-5350	63	14	,	,	PUNCT
cana-5350	63	15	𝑐	𝑐	PROPN
cana-5350	63	16	,	,	PUNCT
cana-5350	63	17	𝑑	𝑑	NOUN
cana-5350	63	18	)	)	PUNCT
cana-5350	63	19	,	,	PUNCT
cana-5350	63	20	𝐵(𝑎′	𝐵(𝑎′	PROPN
cana-5350	63	21	,	,	PUNCT
cana-5350	63	22	𝑏′	𝑏′	PROPN
cana-5350	63	23	,	,	PUNCT
cana-5350	63	24	𝑐′	𝑐′	NUM
cana-5350	63	25	,	,	PUNCT
cana-5350	63	26	𝑑′	𝑑′	NUM
cana-5350	63	27	)	)	PUNCT
cana-5350	63	28	,	,	PUNCT
cana-5350	63	29	𝑞𝑡	𝑞𝑡	PRON
cana-5350	63	30	)	)	PUNCT
cana-5350	63	31	≥	≥	PROPN
cana-5350	63	32	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5350	63	33	{	{	PUNCT
cana-5350	63	34	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	63	35	,	,	PUNCT
cana-5350	63	36	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	37	,	,	PUNCT
cana-5350	63	38	𝑡	𝑡	PROPN
cana-5350	63	39	)	)	PUNCT
cana-5350	63	40	,	,	PUNCT
cana-5350	63	41	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	63	42	,	,	PUNCT
cana-5350	63	43	𝑏	𝑏	NOUN
cana-5350	63	44	,	,	PUNCT
cana-5350	63	45	𝑐	𝑐	PROPN
cana-5350	63	46	,	,	PUNCT
cana-5350	63	47	𝑑	𝑑	NOUN
cana-5350	63	48	)	)	PUNCT
cana-5350	63	49	,	,	PUNCT
cana-5350	63	50	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	63	51	,	,	PUNCT
cana-5350	63	52	𝑡	𝑡	NOUN
cana-5350	63	53	)	)	PUNCT
cana-5350	63	54	,	,	PUNCT
cana-5350	63	55	𝑀(𝐵(𝑎′	𝑀(𝐵(𝑎′	PROPN
cana-5350	63	56	,	,	PUNCT
cana-5350	63	57	𝑏′	𝑏′	PROPN
cana-5350	63	58	,	,	PUNCT
cana-5350	63	59	𝑐′	𝑐′	NUM
cana-5350	63	60	,	,	PUNCT
cana-5350	63	61	𝑑′	𝑑′	NUM
cana-5350	63	62	)	)	PUNCT
cana-5350	63	63	,	,	PUNCT
cana-5350	63	64	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	65	,	,	PUNCT
cana-5350	63	66	𝑡	𝑡	PROPN
cana-5350	63	67	)	)	PUNCT
cana-5350	63	68	,	,	PUNCT
cana-5350	63	69	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	63	70	,	,	PUNCT
cana-5350	63	71	𝐵(𝑎′	𝐵(𝑎′	PROPN
cana-5350	63	72	,	,	PUNCT
cana-5350	63	73	𝑏′	𝑏′	PROPN
cana-5350	63	74	,	,	PUNCT
cana-5350	63	75	𝑐′	𝑐′	NUM
cana-5350	63	76	,	,	PUNCT
cana-5350	63	77	𝑑′	𝑑′	NOUN
cana-5350	63	78	)	)	PUNCT
cana-5350	63	79	,	,	PUNCT
cana-5350	63	80	𝑡	𝑡	PROPN
cana-5350	63	81	)	)	PUNCT
cana-5350	63	82	,	,	PUNCT
cana-5350	63	83	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	63	84	,	,	PUNCT
cana-5350	63	85	𝑏	𝑏	NOUN
cana-5350	63	86	,	,	PUNCT
cana-5350	63	87	𝑐	𝑐	PROPN
cana-5350	63	88	,	,	PUNCT
cana-5350	63	89	𝑑	𝑑	NOUN
cana-5350	63	90	)	)	PUNCT
cana-5350	63	91	,	,	PUNCT
cana-5350	63	92	𝑇𝑎′	𝑇𝑎′	PROPN
cana-5350	63	93	,	,	PUNCT
cana-5350	63	94	𝑡	𝑡	NOUN
cana-5350	63	95	)	)	PUNCT
cana-5350	63	96	}	}	PUNCT
cana-5350	63	97	or	or	CCONJ
cana-5350	63	98	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	63	99	,	,	PUNCT
cana-5350	63	100	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	101	,	,	PUNCT
cana-5350	63	102	𝑞𝑡	𝑞𝑡	PROPN
cana-5350	63	103	)	)	PUNCT
cana-5350	63	104	≥	≥	NOUN
cana-5350	63	105	𝑚𝑖𝑛{𝑀(𝑆𝑎	𝑚𝑖𝑛{𝑀(𝑆𝑎	NUM
cana-5350	63	106	,	,	PUNCT
cana-5350	63	107	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	108	,	,	PUNCT
cana-5350	63	109	𝑡	𝑡	PROPN
cana-5350	63	110	)	)	PUNCT
cana-5350	63	111	,	,	PUNCT
cana-5350	63	112	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	63	113	,	,	PUNCT
cana-5350	63	114	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	63	115	,	,	PUNCT
cana-5350	63	116	𝑡	𝑡	NOUN
cana-5350	63	117	)	)	PUNCT
cana-5350	63	118	,	,	PUNCT
cana-5350	63	119	𝑀(𝑇𝑎′	𝑀(𝑇𝑎′	PROPN
cana-5350	63	120	,	,	PUNCT
cana-5350	63	121	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	122	,	,	PUNCT
cana-5350	63	123	𝑡	𝑡	PROPN
cana-5350	63	124	)	)	PUNCT
cana-5350	63	125	,	,	PUNCT
cana-5350	63	126	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	63	127	,	,	PUNCT
cana-5350	63	128	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	129	,	,	PUNCT
cana-5350	63	130	𝑡)𝑀(𝑆𝑎	𝑡)𝑀(𝑆𝑎	NOUN
cana-5350	63	131	,	,	PUNCT
cana-5350	63	132	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	133	,	,	PUNCT
cana-5350	63	134	𝑡	𝑡	NOUN
cana-5350	63	135	)	)	PUNCT
cana-5350	63	136	}	}	PUNCT
cana-5350	63	137	=	=	SYM
cana-5350	63	138	𝑚𝑖𝑛{𝑀(𝑆𝑎	𝑚𝑖𝑛{𝑀(𝑆𝑎	NUM
cana-5350	63	139	,	,	PUNCT
cana-5350	63	140	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	141	,	,	PUNCT
cana-5350	63	142	𝑡	𝑡	PROPN
cana-5350	63	143	)	)	PUNCT
cana-5350	63	144	,	,	PUNCT
cana-5350	63	145	1,1	1,1	NUM
cana-5350	63	146	,	,	PUNCT
cana-5350	63	147	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	63	148	,	,	PUNCT
cana-5350	63	149	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	150	,	,	PUNCT
cana-5350	63	151	𝑡	𝑡	PROPN
cana-5350	63	152	)	)	PUNCT
cana-5350	63	153	,	,	PUNCT
cana-5350	63	154	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	63	155	,	,	PUNCT
cana-5350	63	156	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	157	,	,	PUNCT
cana-5350	63	158	𝑡	𝑡	NOUN
cana-5350	63	159	)	)	PUNCT
cana-5350	63	160	}	}	PUNCT
cana-5350	63	161	=	=	PUNCT
cana-5350	63	162	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	63	163	,	,	PUNCT
cana-5350	63	164	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	165	,	,	PUNCT
cana-5350	63	166	𝑡	𝑡	NOUN
cana-5350	63	167	)	)	PUNCT
cana-5350	63	168	⇒	⇒	VERB
cana-5350	63	169	𝑆𝑎	𝑆𝑎	NOUN
cana-5350	63	170	=	=	SYM
cana-5350	63	171	𝑇𝑎′	𝑇𝑎′	PROPN
cana-5350	63	172	therefore	therefore	ADV
cana-5350	63	173	𝐴(𝑎	𝐴(𝑎	PROPN
cana-5350	63	174	,	,	PUNCT
cana-5350	63	175	𝑏	𝑏	PROPN
cana-5350	63	176	,	,	PUNCT
cana-5350	63	177	𝑐	𝑐	NOUN
cana-5350	63	178	,	,	PUNCT
cana-5350	63	179	𝑑	𝑑	NOUN
cana-5350	63	180	)	)	PUNCT
cana-5350	63	181	=	=	SYM
cana-5350	63	182	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	63	183	=	=	PUNCT
cana-5350	63	184	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	63	185	=	=	PUNCT
cana-5350	63	186	𝐵(𝑎′	𝐵(𝑎′	PROPN
cana-5350	63	187	,	,	PUNCT
cana-5350	63	188	𝑏′	𝑏′	PROPN
cana-5350	63	189	,	,	PUNCT
cana-5350	63	190	𝑐′	𝑐′	NUM
cana-5350	63	191	,	,	PUNCT
cana-5350	63	192	𝑑′	𝑑′	NUM
cana-5350	63	193	)	)	PUNCT
cana-5350	63	194	similarly	similarly	ADV
cana-5350	63	195	𝐴(𝑏	𝐴(𝑏	PROPN
cana-5350	63	196	,	,	PUNCT
cana-5350	63	197	𝑐	𝑐	PROPN
cana-5350	63	198	,	,	PUNCT
cana-5350	63	199	𝑑	𝑑	NOUN
cana-5350	63	200	,	,	PUNCT
cana-5350	63	201	𝑎	𝑎	NOUN
cana-5350	63	202	)	)	PUNCT
cana-5350	63	203	=	=	SYM
cana-5350	63	204	𝑇𝑏′	𝑇𝑏′	NOUN
cana-5350	64	1	=	=	PUNCT
cana-5350	64	2	𝑆𝑏	𝑆𝑏	INTJ
cana-5350	64	3	=	=	NOUN
cana-5350	64	4	𝐵(𝑏′	𝐵(𝑏′	PROPN
cana-5350	64	5	,	,	PUNCT
cana-5350	64	6	𝑐′	𝑐′	NUM
cana-5350	64	7	,	,	PUNCT
cana-5350	64	8	𝑑′	𝑑′	NOUN
cana-5350	64	9	,	,	PUNCT
cana-5350	64	10	𝑎′	𝑎′	NUM
cana-5350	64	11	)	)	PUNCT
cana-5350	64	12	𝐴(𝑐	𝐴(𝑐	PROPN
cana-5350	64	13	,	,	PUNCT
cana-5350	64	14	𝑑	𝑑	NOUN
cana-5350	64	15	,	,	PUNCT
cana-5350	64	16	𝑎	𝑎	NOUN
cana-5350	64	17	,	,	PUNCT
cana-5350	64	18	𝑏	𝑏	NOUN
cana-5350	64	19	)	)	PUNCT
cana-5350	64	20	=	=	SYM
cana-5350	64	21	𝑇𝑐′	𝑇𝑐′	NOUN
cana-5350	64	22	=	=	PUNCT
cana-5350	64	23	𝑆𝑐	𝑆𝑐	PROPN
cana-5350	64	24	=	=	SYM
cana-5350	64	25	𝐵(𝑐′	𝐵(𝑐′	PROPN
cana-5350	64	26	,	,	PUNCT
cana-5350	64	27	𝑑′	𝑑′	NOUN
cana-5350	64	28	,	,	PUNCT
cana-5350	64	29	𝑎′	𝑎′	NUM
cana-5350	64	30	,	,	PUNCT
cana-5350	64	31	𝑏′	𝑏′	NUM
cana-5350	64	32	)	)	PUNCT
cana-5350	64	33	𝐴(𝑑	𝐴(𝑑	NOUN
cana-5350	64	34	,	,	PUNCT
cana-5350	64	35	𝑎	𝑎	X
cana-5350	64	36	,	,	PUNCT
cana-5350	64	37	𝑏	𝑏	NOUN
cana-5350	64	38	,	,	PUNCT
cana-5350	64	39	𝑐	𝑐	NOUN
cana-5350	64	40	)	)	PUNCT
cana-5350	64	41	=	=	SYM
cana-5350	64	42	𝑇𝑑′	𝑇𝑑′	NOUN
cana-5350	65	1	=	=	PUNCT
cana-5350	65	2	𝑆𝑑	𝑆𝑑	NOUN
cana-5350	65	3	=	=	SYM
cana-5350	65	4	𝐵(𝑑′	𝐵(𝑑′	PROPN
cana-5350	65	5	,	,	PUNCT
cana-5350	65	6	𝑎′	𝑎′	NUM
cana-5350	65	7	,	,	PUNCT
cana-5350	65	8	𝑏′	𝑏′	PROPN
cana-5350	65	9	,	,	PUNCT
cana-5350	65	10	𝑐′	𝑐′	NUM
cana-5350	65	11	)	)	PUNCT
cana-5350	65	12	thus	thus	ADV
cana-5350	65	13	the	the	DET
cana-5350	65	14	pairs	pair	NOUN
cana-5350	65	15	(	(	PUNCT
cana-5350	65	16	𝐴	𝐴	PROPN
cana-5350	65	17	,	,	PUNCT
cana-5350	65	18	𝑆	𝑆	PROPN
cana-5350	65	19	)	)	PUNCT
cana-5350	65	20	and	and	CCONJ
cana-5350	65	21	(	(	PUNCT
cana-5350	65	22	𝐵	𝐵	PROPN
cana-5350	65	23	,	,	PUNCT
cana-5350	65	24	𝑇	𝑇	PROPN
cana-5350	65	25	)	)	PUNCT
cana-5350	65	26	have	have	VERB
cana-5350	65	27	common	common	ADJ
cana-5350	65	28	coincidence	coincidence	NOUN
cana-5350	65	29	points	point	NOUN
cana-5350	65	30	.	.	PUNCT
cana-5350	66	1	let	let	VERB
cana-5350	66	2	𝐴(𝑎	𝐴(𝑎	PRON
cana-5350	66	3	,	,	PUNCT
cana-5350	66	4	𝑏	𝑏	NOUN
cana-5350	66	5	,	,	PUNCT
cana-5350	66	6	𝑐	𝑐	NOUN
cana-5350	66	7	,	,	PUNCT
cana-5350	66	8	𝑑	𝑑	NOUN
cana-5350	66	9	)	)	PUNCT
cana-5350	66	10	=	=	SYM
cana-5350	66	11	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	66	12	=	=	PUNCT
cana-5350	66	13	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	66	14	=	=	SYM
cana-5350	66	15	𝐵(𝑎′	𝐵(𝑎′	PROPN
cana-5350	66	16	,	,	PUNCT
cana-5350	66	17	𝑏′	𝑏′	PROPN
cana-5350	66	18	,	,	PUNCT
cana-5350	66	19	𝑐′	𝑐′	NUM
cana-5350	66	20	,	,	PUNCT
cana-5350	66	21	𝑑′	𝑑′	NOUN
cana-5350	66	22	)	)	PUNCT
cana-5350	67	1	=	=	SYM
cana-5350	67	2	𝑥	𝑥	PROPN
cana-5350	67	3	and	and	CCONJ
cana-5350	67	4	𝐴(𝑏	𝐴(𝑏	PROPN
cana-5350	67	5	,	,	PUNCT
cana-5350	67	6	𝑐	𝑐	PROPN
cana-5350	67	7	,	,	PUNCT
cana-5350	67	8	𝑑	𝑑	NOUN
cana-5350	67	9	,	,	PUNCT
cana-5350	67	10	𝑎	𝑎	NOUN
cana-5350	67	11	)	)	PUNCT
cana-5350	67	12	=	=	SYM
cana-5350	68	1	𝑇𝑏′	𝑇𝑏′	NOUN
cana-5350	69	1	=	=	PUNCT
cana-5350	69	2	𝑆𝑏	𝑆𝑏	INTJ
cana-5350	69	3	=	=	NOUN
cana-5350	69	4	𝐵(𝑏′	𝐵(𝑏′	PROPN
cana-5350	69	5	,	,	PUNCT
cana-5350	69	6	𝑐′	𝑐′	NUM
cana-5350	69	7	,	,	PUNCT
cana-5350	69	8	𝑑′	𝑑′	NOUN
cana-5350	69	9	,	,	PUNCT
cana-5350	69	10	𝑎′	𝑎′	NUM
cana-5350	69	11	)	)	PUNCT
cana-5350	70	1	=	=	SYM
cana-5350	70	2	𝑦	𝑦	PROPN
cana-5350	70	3	𝐴(𝑐	𝐴(𝑐	PROPN
cana-5350	70	4	,	,	PUNCT
cana-5350	70	5	𝑑	𝑑	NOUN
cana-5350	70	6	,	,	PUNCT
cana-5350	70	7	𝑎	𝑎	NOUN
cana-5350	70	8	,	,	PUNCT
cana-5350	70	9	𝑏	𝑏	NOUN
cana-5350	70	10	)	)	PUNCT
cana-5350	70	11	=	=	SYM
cana-5350	70	12	𝑇𝑐′	𝑇𝑐′	NOUN
cana-5350	70	13	=	=	PUNCT
cana-5350	70	14	𝑆𝑐	𝑆𝑐	PROPN
cana-5350	70	15	=	=	SYM
cana-5350	70	16	𝐵(𝑐′	𝐵(𝑐′	PROPN
cana-5350	70	17	,	,	PUNCT
cana-5350	70	18	𝑑′	𝑑′	NOUN
cana-5350	70	19	,	,	PUNCT
cana-5350	70	20	𝑎′	𝑎′	NUM
cana-5350	70	21	,	,	PUNCT
cana-5350	70	22	𝑏′	𝑏′	NUM
cana-5350	70	23	)	)	PUNCT
cana-5350	71	1	=	=	PRON
cana-5350	72	1	𝑧	𝑧	PRON
cana-5350	72	2	𝐴(𝑑	𝐴(𝑑	X
cana-5350	72	3	,	,	PUNCT
cana-5350	72	4	𝑎	𝑎	NOUN
cana-5350	72	5	,	,	PUNCT
cana-5350	72	6	𝑏	𝑏	NOUN
cana-5350	72	7	,	,	PUNCT
cana-5350	72	8	𝑐	𝑐	NOUN
cana-5350	72	9	)	)	PUNCT
cana-5350	72	10	=	=	SYM
cana-5350	72	11	𝑇𝑑′	𝑇𝑑′	NOUN
cana-5350	72	12	=	=	PUNCT
cana-5350	72	13	𝑆𝑑	𝑆𝑑	NOUN
cana-5350	72	14	=	=	SYM
cana-5350	72	15	𝐵(𝑑′	𝐵(𝑑′	PROPN
cana-5350	72	16	,	,	PUNCT
cana-5350	72	17	𝑎′	𝑎′	NUM
cana-5350	72	18	,	,	PUNCT
cana-5350	72	19	𝑏′	𝑏′	PROPN
cana-5350	72	20	,	,	PUNCT
cana-5350	72	21	𝑐′	𝑐′	NUM
cana-5350	72	22	)	)	PUNCT
cana-5350	73	1	=	=	SYM
cana-5350	73	2	𝑝	𝑝	PROPN
cana-5350	73	3	since	since	SCONJ
cana-5350	73	4	(	(	PUNCT
cana-5350	73	5	𝐴	𝐴	PROPN
cana-5350	73	6	,	,	PUNCT
cana-5350	73	7	𝑆	𝑆	PROPN
cana-5350	73	8	)	)	PUNCT
cana-5350	73	9	and	and	CCONJ
cana-5350	73	10	(	(	PUNCT
cana-5350	73	11	𝐵	𝐵	PROPN
cana-5350	73	12	,	,	PUNCT
cana-5350	73	13	𝑇	𝑇	PROPN
cana-5350	73	14	)	)	PUNCT
cana-5350	73	15	are	be	AUX
cana-5350	73	16	owc	owc	NUM
cana-5350	73	17	communications	communication	NOUN
cana-5350	73	18	on	on	ADP
cana-5350	73	19	applied	apply	VERB
cana-5350	73	20	nonlinear	nonlinear	ADJ
cana-5350	73	21	analysis	analysis	NOUN
cana-5350	73	22	issn	issn	NOUN
cana-5350	73	23	:	:	PUNCT
cana-5350	73	24	1074	1074	NUM
cana-5350	73	25	-	-	PUNCT
cana-5350	73	26	133x	133x	NUM
cana-5350	73	27	vol	vol	VERB
cana-5350	73	28	32	32	NUM
cana-5350	73	29	no	no	NOUN
cana-5350	73	30	.	.	PUNCT
cana-5350	74	1	10s	10	NOUN
cana-5350	74	2	(	(	PUNCT
cana-5350	74	3	2025	2025	NUM
cana-5350	74	4	)	)	PUNCT
cana-5350	74	5	1799	1799	NUM
cana-5350	74	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5350	75	1	𝑆𝑥	𝑆𝑥	PROPN
cana-5350	75	2	=	=	PUNCT
cana-5350	75	3	𝑆𝐴(𝑎	𝑆𝐴(𝑎	NOUN
cana-5350	75	4	,	,	PUNCT
cana-5350	75	5	𝑏	𝑏	NOUN
cana-5350	75	6	,	,	PUNCT
cana-5350	75	7	𝑐	𝑐	NOUN
cana-5350	75	8	,	,	PUNCT
cana-5350	75	9	𝑑	𝑑	NOUN
cana-5350	75	10	)	)	PUNCT
cana-5350	75	11	=	=	SYM
cana-5350	75	12	𝐴(𝑆𝑎	𝐴(𝑆𝑎	NOUN
cana-5350	75	13	,	,	PUNCT
cana-5350	75	14	𝑆𝑏	𝑆𝑏	PROPN
cana-5350	75	15	,	,	PUNCT
cana-5350	75	16	𝑆𝑐	𝑆𝑐	PROPN
cana-5350	75	17	,	,	PUNCT
cana-5350	75	18	𝑆𝑑	𝑆𝑑	NOUN
cana-5350	75	19	)	)	PUNCT
cana-5350	75	20	=	=	PUNCT
cana-5350	75	21	𝐴(𝑥	𝐴(𝑥	NOUN
cana-5350	75	22	,	,	PUNCT
cana-5350	75	23	𝑦	𝑦	NOUN
cana-5350	75	24	,	,	PUNCT
cana-5350	75	25	𝑧	𝑧	NOUN
cana-5350	75	26	,	,	PUNCT
cana-5350	75	27	𝑝	𝑝	NOUN
cana-5350	75	28	)	)	PUNCT
cana-5350	75	29	𝑆𝑦	𝑆𝑦	PROPN
cana-5350	75	30	=	=	SYM
cana-5350	75	31	𝑆𝐴(𝑏	𝑆𝐴(𝑏	PROPN
cana-5350	75	32	,	,	PUNCT
cana-5350	75	33	𝑐	𝑐	NOUN
cana-5350	75	34	,	,	PUNCT
cana-5350	75	35	𝑑	𝑑	NOUN
cana-5350	75	36	,	,	PUNCT
cana-5350	75	37	𝑎	𝑎	NOUN
cana-5350	75	38	)	)	PUNCT
cana-5350	75	39	=	=	SYM
cana-5350	75	40	𝐴(𝑆𝑏	𝐴(𝑆𝑏	NOUN
cana-5350	75	41	,	,	PUNCT
cana-5350	75	42	𝑆𝑐	𝑆𝑐	PROPN
cana-5350	75	43	,	,	PUNCT
cana-5350	75	44	𝑆𝑑	𝑆𝑑	PROPN
cana-5350	75	45	,	,	PUNCT
cana-5350	75	46	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	75	47	)	)	PUNCT
cana-5350	75	48	=	=	SYM
cana-5350	75	49	𝐴(𝑦	𝐴(𝑦	X
cana-5350	75	50	,	,	PUNCT
cana-5350	75	51	𝑧	𝑧	PROPN
cana-5350	75	52	,	,	PUNCT
cana-5350	75	53	𝑝	𝑝	NOUN
cana-5350	75	54	,	,	PUNCT
cana-5350	75	55	𝑥	𝑥	NOUN
cana-5350	75	56	)	)	PUNCT
cana-5350	75	57	𝑆𝑧	𝑆𝑧	NOUN
cana-5350	75	58	=	=	PUNCT
cana-5350	75	59	𝑆𝐴(𝑐	𝑆𝐴(𝑐	PROPN
cana-5350	75	60	,	,	PUNCT
cana-5350	75	61	𝑑	𝑑	NOUN
cana-5350	75	62	,	,	PUNCT
cana-5350	75	63	𝑎	𝑎	NOUN
cana-5350	75	64	,	,	PUNCT
cana-5350	75	65	𝑏	𝑏	NOUN
cana-5350	75	66	)	)	PUNCT
cana-5350	75	67	=	=	SYM
cana-5350	75	68	𝐴(𝑆𝑐	𝐴(𝑆𝑐	PROPN
cana-5350	75	69	,	,	PUNCT
cana-5350	75	70	𝑆𝑑	𝑆𝑑	NOUN
cana-5350	75	71	,	,	PUNCT
cana-5350	75	72	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	75	73	,	,	PUNCT
cana-5350	75	74	𝑆𝑏	𝑆𝑏	PROPN
cana-5350	75	75	)	)	PUNCT
cana-5350	75	76	=	=	SYM
cana-5350	75	77	𝐴(𝑧	𝐴(𝑧	X
cana-5350	75	78	,	,	PUNCT
cana-5350	75	79	𝑝	𝑝	NOUN
cana-5350	75	80	,	,	PUNCT
cana-5350	75	81	𝑥	𝑥	PROPN
cana-5350	75	82	,	,	PUNCT
cana-5350	75	83	𝑦	𝑦	NOUN
cana-5350	75	84	)	)	PUNCT
cana-5350	75	85	𝑆𝑝	𝑆𝑝	NOUN
cana-5350	75	86	=	=	SYM
cana-5350	75	87	𝑆𝐴(𝑑	𝑆𝐴(𝑑	PROPN
cana-5350	75	88	,	,	PUNCT
cana-5350	75	89	𝑎	𝑎	NOUN
cana-5350	75	90	,	,	PUNCT
cana-5350	75	91	𝑏	𝑏	NOUN
cana-5350	75	92	,	,	PUNCT
cana-5350	75	93	𝑐	𝑐	NOUN
cana-5350	75	94	)	)	PUNCT
cana-5350	75	95	=	=	SYM
cana-5350	75	96	𝐴(𝑆𝑑	𝐴(𝑆𝑑	NUM
cana-5350	75	97	,	,	PUNCT
cana-5350	75	98	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	75	99	,	,	PUNCT
cana-5350	75	100	𝑆𝑏	𝑆𝑏	PROPN
cana-5350	75	101	,	,	PUNCT
cana-5350	75	102	𝑆𝑐	𝑆𝑐	PROPN
cana-5350	75	103	)	)	PUNCT
cana-5350	75	104	=	=	SYM
cana-5350	75	105	𝐴(𝑝	𝐴(𝑝	PROPN
cana-5350	75	106	,	,	PUNCT
cana-5350	75	107	𝑥	𝑥	PROPN
cana-5350	75	108	,	,	PUNCT
cana-5350	75	109	𝑦	𝑦	NOUN
cana-5350	75	110	,	,	PUNCT
cana-5350	75	111	𝑧	𝑧	PART
cana-5350	75	112	)	)	PUNCT
cana-5350	75	113	also	also	ADV
cana-5350	75	114	𝑇𝑥	𝑇𝑥	PROPN
cana-5350	75	115	=	=	SYM
cana-5350	75	116	𝑇𝐵(𝑎′	𝑇𝐵(𝑎′	PROPN
cana-5350	75	117	,	,	PUNCT
cana-5350	75	118	𝑏′	𝑏′	PROPN
cana-5350	75	119	,	,	PUNCT
cana-5350	75	120	𝑐′	𝑐′	NUM
cana-5350	75	121	,	,	PUNCT
cana-5350	75	122	𝑑′	𝑑′	NUM
cana-5350	75	123	)	)	PUNCT
cana-5350	75	124	=	=	SYM
cana-5350	75	125	𝐵(𝑇𝑎′	𝐵(𝑇𝑎′	NOUN
cana-5350	75	126	,	,	PUNCT
cana-5350	75	127	𝑇𝑏′	𝑇𝑏′	INTJ
cana-5350	75	128	,	,	PUNCT
cana-5350	75	129	𝑇𝑐′	𝑇𝑐′	ADJ
cana-5350	75	130	,	,	PUNCT
cana-5350	75	131	𝑇𝑑′	𝑇𝑑′	ADV
cana-5350	75	132	)	)	PUNCT
cana-5350	75	133	=	=	SYM
cana-5350	75	134	𝐵(𝑥	𝐵(𝑥	PROPN
cana-5350	75	135	,	,	PUNCT
cana-5350	75	136	𝑦	𝑦	NOUN
cana-5350	75	137	,	,	PUNCT
cana-5350	75	138	𝑧	𝑧	NOUN
cana-5350	75	139	,	,	PUNCT
cana-5350	75	140	𝑝	𝑝	NOUN
cana-5350	75	141	)	)	PUNCT
cana-5350	75	142	and	and	CCONJ
cana-5350	75	143	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	75	144	=	=	SYM
cana-5350	75	145	𝑇𝐵(𝑏′	𝑇𝐵(𝑏′	PROPN
cana-5350	75	146	,	,	PUNCT
cana-5350	75	147	𝑐′	𝑐′	NUM
cana-5350	75	148	,	,	PUNCT
cana-5350	75	149	𝑑′	𝑑′	NOUN
cana-5350	75	150	,	,	PUNCT
cana-5350	75	151	𝑎′	𝑎′	NUM
cana-5350	75	152	)	)	PUNCT
cana-5350	75	153	=	=	SYM
cana-5350	75	154	𝐵(𝑇𝑏′	𝐵(𝑇𝑏′	NOUN
cana-5350	75	155	,	,	PUNCT
cana-5350	75	156	𝑇𝑐′	𝑇𝑐′	ADJ
cana-5350	75	157	,	,	PUNCT
cana-5350	75	158	𝑇𝑑′	𝑇𝑑′	ADV
cana-5350	75	159	,	,	PUNCT
cana-5350	75	160	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	75	161	)	)	PUNCT
cana-5350	75	162	=	=	PUNCT
cana-5350	76	1	𝐵(𝑦	𝐵(𝑦	NOUN
cana-5350	76	2	,	,	PUNCT
cana-5350	76	3	𝑧	𝑧	PROPN
cana-5350	76	4	,	,	PUNCT
cana-5350	76	5	𝑝	𝑝	NOUN
cana-5350	76	6	,	,	PUNCT
cana-5350	76	7	𝑥	𝑥	NOUN
cana-5350	76	8	)	)	PUNCT
cana-5350	76	9	𝑇𝑧	𝑇𝑧	PROPN
cana-5350	76	10	=	=	SYM
cana-5350	76	11	𝑇𝐵(𝑐′	𝑇𝐵(𝑐′	PROPN
cana-5350	76	12	,	,	PUNCT
cana-5350	76	13	𝑑′	𝑑′	NOUN
cana-5350	76	14	,	,	PUNCT
cana-5350	76	15	𝑎′	𝑎′	NUM
cana-5350	76	16	,	,	PUNCT
cana-5350	76	17	𝑏′	𝑏′	NUM
cana-5350	76	18	)	)	PUNCT
cana-5350	76	19	=	=	PUNCT
cana-5350	77	1	𝐵(𝑇𝑐′	𝐵(𝑇𝑐′	PROPN
cana-5350	77	2	,	,	PUNCT
cana-5350	77	3	𝑇𝑑′	𝑇𝑑′	ADV
cana-5350	77	4	,	,	PUNCT
cana-5350	77	5	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	77	6	,	,	PUNCT
cana-5350	77	7	𝑇𝑏′	𝑇𝑏′	NOUN
cana-5350	77	8	)	)	PUNCT
cana-5350	77	9	=	=	SYM
cana-5350	77	10	𝐵(𝑧	𝐵(𝑧	NUM
cana-5350	77	11	,	,	PUNCT
cana-5350	77	12	𝑝	𝑝	NOUN
cana-5350	77	13	,	,	PUNCT
cana-5350	77	14	𝑥	𝑥	PROPN
cana-5350	77	15	,	,	PUNCT
cana-5350	77	16	𝑦	𝑦	NOUN
cana-5350	77	17	)	)	PUNCT
cana-5350	78	1	𝑇𝑝	𝑇𝑝	PROPN
cana-5350	78	2	=	=	SYM
cana-5350	78	3	𝑇𝐵(𝑑′	𝑇𝐵(𝑑′	NOUN
cana-5350	78	4	,	,	PUNCT
cana-5350	78	5	𝑎′	𝑎′	NUM
cana-5350	78	6	,	,	PUNCT
cana-5350	78	7	𝑏′	𝑏′	PROPN
cana-5350	78	8	,	,	PUNCT
cana-5350	78	9	𝑐′	𝑐′	NUM
cana-5350	78	10	)	)	PUNCT
cana-5350	79	1	=	=	SYM
cana-5350	79	2	𝐵(𝑇𝑑′	𝐵(𝑇𝑑′	NOUN
cana-5350	79	3	,	,	PUNCT
cana-5350	79	4	𝑇𝑎′	𝑇𝑎′	NOUN
cana-5350	79	5	,	,	PUNCT
cana-5350	79	6	𝑇𝑏′	𝑇𝑏′	INTJ
cana-5350	79	7	,	,	PUNCT
cana-5350	79	8	𝑇𝑐′	𝑇𝑐′	ADJ
cana-5350	79	9	)	)	PUNCT
cana-5350	79	10	=	=	SYM
cana-5350	79	11	𝐵(𝑝	𝐵(𝑝	NOUN
cana-5350	79	12	,	,	PUNCT
cana-5350	79	13	𝑥	𝑥	NOUN
cana-5350	79	14	,	,	PUNCT
cana-5350	79	15	𝑦	𝑦	NOUN
cana-5350	79	16	,	,	PUNCT
cana-5350	79	17	𝑧	𝑧	NOUN
cana-5350	79	18	)	)	PUNCT
cana-5350	79	19	next	next	ADV
cana-5350	79	20	we	we	PRON
cana-5350	79	21	show	show	VERB
cana-5350	79	22	that	that	SCONJ
cana-5350	79	23	𝑥	𝑥	PROPN
cana-5350	79	24	=	=	SYM
cana-5350	79	25	𝑦	𝑦	NOUN
cana-5350	79	26	,	,	PUNCT
cana-5350	79	27	for	for	ADP
cana-5350	79	28	this	this	DET
cana-5350	79	29	putting	put	VERB
cana-5350	79	30	𝑥	𝑥	X
cana-5350	79	31	=	=	SYM
cana-5350	79	32	𝑎	𝑎	NOUN
cana-5350	79	33	,	,	PUNCT
cana-5350	79	34	𝑦	𝑦	NOUN
cana-5350	79	35	=	=	SYM
cana-5350	79	36	𝑏	𝑏	PROPN
cana-5350	79	37	,	,	PUNCT
cana-5350	79	38	𝑧	𝑧	PROPN
cana-5350	79	39	=	=	ADJ
cana-5350	79	40	𝑐	𝑐	PROPN
cana-5350	79	41	,	,	PUNCT
cana-5350	79	42	𝑝	𝑝	NOUN
cana-5350	79	43	=	=	SYM
cana-5350	79	44	𝑑	𝑑	NOUN
cana-5350	79	45	,	,	PUNCT
cana-5350	79	46	𝑢	𝑢	X
cana-5350	79	47	=	=	SYM
cana-5350	79	48	𝑏′	𝑏′	PROPN
cana-5350	79	49	,	,	PUNCT
cana-5350	79	50	𝑣	𝑣	X
cana-5350	79	51	=	=	SYM
cana-5350	79	52	𝑐′	𝑐′	NUM
cana-5350	79	53	,	,	PUNCT
cana-5350	79	54	𝑤	𝑤	X
cana-5350	79	55	=	=	SYM
cana-5350	79	56	𝑑′	𝑑′	NOUN
cana-5350	79	57	,	,	PUNCT
cana-5350	79	58	𝑟	𝑟	X
cana-5350	79	59	=	=	SYM
cana-5350	79	60	𝑎′	𝑎′	PUNCT
cana-5350	79	61	in	in	ADP
cana-5350	79	62	(	(	PUNCT
cana-5350	79	63	i	i	NOUN
cana-5350	79	64	)	)	PUNCT
cana-5350	79	65	,	,	PUNCT
cana-5350	79	66	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	79	67	,	,	PUNCT
cana-5350	79	68	𝑦	𝑦	NOUN
cana-5350	79	69	,	,	PUNCT
cana-5350	79	70	𝑞𝑡	𝑞𝑡	PRON
cana-5350	79	71	)	)	PUNCT
cana-5350	79	72	=	=	SYM
cana-5350	79	73	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	79	74	,	,	PUNCT
cana-5350	79	75	𝑏	𝑏	NOUN
cana-5350	79	76	,	,	PUNCT
cana-5350	79	77	𝑐	𝑐	PROPN
cana-5350	79	78	,	,	PUNCT
cana-5350	79	79	𝑑	𝑑	NOUN
cana-5350	79	80	)	)	PUNCT
cana-5350	79	81	,	,	PUNCT
cana-5350	79	82	𝐵(𝑏′	𝐵(𝑏′	NOUN
cana-5350	79	83	,	,	PUNCT
cana-5350	79	84	𝑐′	𝑐′	NUM
cana-5350	79	85	,	,	PUNCT
cana-5350	79	86	𝑑′	𝑑′	NOUN
cana-5350	79	87	,	,	PUNCT
cana-5350	79	88	𝑎′	𝑎′	NUM
cana-5350	79	89	)	)	PUNCT
cana-5350	79	90	,	,	PUNCT
cana-5350	79	91	𝑞𝑡	𝑞𝑡	PRON
cana-5350	79	92	)	)	PUNCT
cana-5350	79	93	≥	≥	PROPN
cana-5350	79	94	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5350	79	95	{	{	PUNCT
cana-5350	79	96	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	79	97	,	,	PUNCT
cana-5350	79	98	𝑇𝑏′	𝑇𝑏′	NOUN
cana-5350	79	99	,	,	PUNCT
cana-5350	79	100	𝑡	𝑡	NOUN
cana-5350	79	101	)	)	PUNCT
cana-5350	79	102	,	,	PUNCT
cana-5350	79	103	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	79	104	,	,	PUNCT
cana-5350	79	105	𝑏	𝑏	NOUN
cana-5350	79	106	,	,	PUNCT
cana-5350	79	107	𝑐	𝑐	PROPN
cana-5350	79	108	,	,	PUNCT
cana-5350	79	109	𝑑	𝑑	NOUN
cana-5350	79	110	)	)	PUNCT
cana-5350	79	111	,	,	PUNCT
cana-5350	79	112	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	79	113	,	,	PUNCT
cana-5350	79	114	𝑡	𝑡	NOUN
cana-5350	79	115	)	)	PUNCT
cana-5350	79	116	,	,	PUNCT
cana-5350	79	117	𝑀(𝐵(𝑏′	𝑀(𝐵(𝑏′	PROPN
cana-5350	79	118	,	,	PUNCT
cana-5350	79	119	𝑐′	𝑐′	NUM
cana-5350	79	120	,	,	PUNCT
cana-5350	79	121	𝑑′	𝑑′	NOUN
cana-5350	79	122	,	,	PUNCT
cana-5350	79	123	𝑎′	𝑎′	NUM
cana-5350	79	124	)	)	PUNCT
cana-5350	79	125	,	,	PUNCT
cana-5350	79	126	𝑇𝑏′	𝑇𝑏′	NOUN
cana-5350	79	127	,	,	PUNCT
cana-5350	79	128	𝑡	𝑡	PROPN
cana-5350	79	129	)	)	PUNCT
cana-5350	79	130	,	,	PUNCT
cana-5350	79	131	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	79	132	,	,	PUNCT
cana-5350	79	133	𝐵(𝑏′	𝐵(𝑏′	NOUN
cana-5350	79	134	,	,	PUNCT
cana-5350	79	135	𝑐′	𝑐′	NUM
cana-5350	79	136	,	,	PUNCT
cana-5350	79	137	𝑑′	𝑑′	NOUN
cana-5350	79	138	,	,	PUNCT
cana-5350	79	139	𝑎′	𝑎′	NUM
cana-5350	79	140	)	)	PUNCT
cana-5350	79	141	,	,	PUNCT
cana-5350	79	142	𝑡	𝑡	PROPN
cana-5350	79	143	)	)	PUNCT
cana-5350	79	144	,	,	PUNCT
cana-5350	79	145	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	79	146	,	,	PUNCT
cana-5350	79	147	𝑏	𝑏	NOUN
cana-5350	79	148	,	,	PUNCT
cana-5350	79	149	𝑐	𝑐	PROPN
cana-5350	79	150	,	,	PUNCT
cana-5350	79	151	𝑑	𝑑	NOUN
cana-5350	79	152	)	)	PUNCT
cana-5350	79	153	,	,	PUNCT
cana-5350	79	154	𝑇𝑏′	𝑇𝑏′	NOUN
cana-5350	79	155	,	,	PUNCT
cana-5350	79	156	𝑡	𝑡	NOUN
cana-5350	79	157	)	)	PUNCT
cana-5350	79	158	}	}	PUNCT
cana-5350	79	159	=	=	SYM
cana-5350	79	160	𝑚𝑖𝑛{𝑀(𝑥	𝑚𝑖𝑛{𝑀(𝑥	PROPN
cana-5350	79	161	,	,	PUNCT
cana-5350	79	162	𝑦	𝑦	NOUN
cana-5350	79	163	,	,	PUNCT
cana-5350	79	164	𝑡	𝑡	NOUN
cana-5350	79	165	)	)	PUNCT
cana-5350	79	166	,	,	PUNCT
cana-5350	79	167	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	79	168	,	,	PUNCT
cana-5350	79	169	𝑥	𝑥	PROPN
cana-5350	79	170	,	,	PUNCT
cana-5350	79	171	𝑡	𝑡	NOUN
cana-5350	79	172	)	)	PUNCT
cana-5350	79	173	,	,	PUNCT
cana-5350	79	174	𝑀(𝑦	𝑀(𝑦	PROPN
cana-5350	79	175	,	,	PUNCT
cana-5350	79	176	𝑦	𝑦	NOUN
cana-5350	79	177	,	,	PUNCT
cana-5350	79	178	𝑡	𝑡	NOUN
cana-5350	79	179	)	)	PUNCT
cana-5350	79	180	,	,	PUNCT
cana-5350	79	181	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	79	182	,	,	PUNCT
cana-5350	79	183	𝑦	𝑦	NOUN
cana-5350	79	184	,	,	PUNCT
cana-5350	79	185	𝑡	𝑡	NOUN
cana-5350	79	186	)	)	PUNCT
cana-5350	79	187	,	,	PUNCT
cana-5350	79	188	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	79	189	,	,	PUNCT
cana-5350	79	190	𝑦	𝑦	NOUN
cana-5350	79	191	,	,	PUNCT
cana-5350	79	192	𝑡	𝑡	NOUN
cana-5350	79	193	)	)	PUNCT
cana-5350	79	194	}	}	PUNCT
cana-5350	79	195	=	=	SYM
cana-5350	79	196	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	79	197	,	,	PUNCT
cana-5350	79	198	𝑦	𝑦	NOUN
cana-5350	79	199	,	,	PUNCT
cana-5350	79	200	𝑡	𝑡	PROPN
cana-5350	79	201	)	)	PUNCT
cana-5350	79	202	⟹	⟹	PUNCT
cana-5350	79	203	𝑥	𝑥	NOUN
cana-5350	80	1	=	=	SYM
cana-5350	80	2	𝑦	𝑦	NOUN
cana-5350	80	3	next	next	ADV
cana-5350	80	4	we	we	PRON
cana-5350	80	5	show	show	VERB
cana-5350	80	6	that	that	SCONJ
cana-5350	80	7	𝑥	𝑥	PROPN
cana-5350	80	8	=	=	PUNCT
cana-5350	80	9	𝑧	𝑧	ADJ
cana-5350	80	10	,	,	PUNCT
cana-5350	80	11	for	for	ADP
cana-5350	80	12	this	this	DET
cana-5350	80	13	putting	put	VERB
cana-5350	80	14	𝑥	𝑥	X
cana-5350	80	15	=	=	SYM
cana-5350	80	16	𝑎	𝑎	NOUN
cana-5350	80	17	,	,	PUNCT
cana-5350	80	18	𝑦	𝑦	NOUN
cana-5350	80	19	=	=	SYM
cana-5350	80	20	𝑏	𝑏	PROPN
cana-5350	80	21	,	,	PUNCT
cana-5350	80	22	𝑧	𝑧	PROPN
cana-5350	80	23	=	=	ADJ
cana-5350	80	24	𝑐	𝑐	PROPN
cana-5350	80	25	,	,	PUNCT
cana-5350	80	26	𝑝	𝑝	NOUN
cana-5350	80	27	=	=	SYM
cana-5350	80	28	𝑑	𝑑	NOUN
cana-5350	80	29	,	,	PUNCT
cana-5350	80	30	𝑢	𝑢	X
cana-5350	80	31	=	=	X
cana-5350	80	32	𝑐′	𝑐′	NOUN
cana-5350	80	33	,	,	PUNCT
cana-5350	80	34	𝑣	𝑣	X
cana-5350	80	35	=	=	SYM
cana-5350	80	36	𝑑′	𝑑′	X
cana-5350	80	37	,	,	PUNCT
cana-5350	80	38	𝑤	𝑤	ADP
cana-5350	80	39	=	=	SYM
cana-5350	80	40	𝑎′	𝑎′	NOUN
cana-5350	80	41	,	,	PUNCT
cana-5350	80	42	𝑟	𝑟	X
cana-5350	80	43	=	=	SYM
cana-5350	80	44	𝑏′	𝑏′	PROPN
cana-5350	80	45	in	in	ADP
cana-5350	80	46	(	(	PUNCT
cana-5350	80	47	i	i	NOUN
cana-5350	80	48	)	)	PUNCT
cana-5350	80	49	,	,	PUNCT
cana-5350	80	50	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	80	51	,	,	PUNCT
cana-5350	80	52	𝑧	𝑧	PROPN
cana-5350	80	53	,	,	PUNCT
cana-5350	80	54	𝑞𝑡	𝑞𝑡	PRON
cana-5350	80	55	)	)	PUNCT
cana-5350	80	56	=	=	SYM
cana-5350	80	57	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	80	58	,	,	PUNCT
cana-5350	80	59	𝑏	𝑏	NOUN
cana-5350	80	60	,	,	PUNCT
cana-5350	80	61	𝑐	𝑐	PROPN
cana-5350	80	62	,	,	PUNCT
cana-5350	80	63	𝑑	𝑑	NOUN
cana-5350	80	64	)	)	PUNCT
cana-5350	80	65	,	,	PUNCT
cana-5350	80	66	𝐵(𝑐′	𝐵(𝑐′	PROPN
cana-5350	80	67	,	,	PUNCT
cana-5350	80	68	𝑑′	𝑑′	NOUN
cana-5350	80	69	,	,	PUNCT
cana-5350	80	70	𝑎′	𝑎′	NUM
cana-5350	80	71	,	,	PUNCT
cana-5350	80	72	𝑏′	𝑏′	NUM
cana-5350	80	73	)	)	PUNCT
cana-5350	80	74	,	,	PUNCT
cana-5350	80	75	𝑞𝑡	𝑞𝑡	PRON
cana-5350	80	76	)	)	PUNCT
cana-5350	80	77	≥	≥	PROPN
cana-5350	80	78	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5350	80	79	{	{	PUNCT
cana-5350	80	80	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	80	81	,	,	PUNCT
cana-5350	80	82	𝑇𝑐′	𝑇𝑐′	ADJ
cana-5350	80	83	,	,	PUNCT
cana-5350	80	84	𝑡	𝑡	NOUN
cana-5350	80	85	)	)	PUNCT
cana-5350	80	86	,	,	PUNCT
cana-5350	80	87	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	80	88	,	,	PUNCT
cana-5350	80	89	𝑏	𝑏	NOUN
cana-5350	80	90	,	,	PUNCT
cana-5350	80	91	𝑐	𝑐	PROPN
cana-5350	80	92	,	,	PUNCT
cana-5350	80	93	𝑑	𝑑	NOUN
cana-5350	80	94	)	)	PUNCT
cana-5350	80	95	,	,	PUNCT
cana-5350	80	96	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	80	97	,	,	PUNCT
cana-5350	80	98	𝑡	𝑡	NOUN
cana-5350	80	99	)	)	PUNCT
cana-5350	80	100	,	,	PUNCT
cana-5350	80	101	𝑀(𝐵(𝑐′	𝑀(𝐵(𝑐′	VERB
cana-5350	80	102	,	,	PUNCT
cana-5350	80	103	𝑑′	𝑑′	NOUN
cana-5350	80	104	,	,	PUNCT
cana-5350	80	105	𝑎′	𝑎′	NUM
cana-5350	80	106	,	,	PUNCT
cana-5350	80	107	𝑏′	𝑏′	NUM
cana-5350	80	108	)	)	PUNCT
cana-5350	80	109	,	,	PUNCT
cana-5350	80	110	𝑇𝑐′	𝑇𝑐′	NOUN
cana-5350	80	111	,	,	PUNCT
cana-5350	80	112	𝑡	𝑡	PROPN
cana-5350	80	113	)	)	PUNCT
cana-5350	80	114	,	,	PUNCT
cana-5350	80	115	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	80	116	,	,	PUNCT
cana-5350	80	117	𝐵(𝑐′	𝐵(𝑐′	PROPN
cana-5350	80	118	,	,	PUNCT
cana-5350	80	119	𝑑′	𝑑′	NOUN
cana-5350	80	120	,	,	PUNCT
cana-5350	80	121	𝑎′	𝑎′	NUM
cana-5350	80	122	,	,	PUNCT
cana-5350	80	123	𝑏′	𝑏′	NUM
cana-5350	80	124	)	)	PUNCT
cana-5350	80	125	,	,	PUNCT
cana-5350	80	126	𝑡	𝑡	PROPN
cana-5350	80	127	)	)	PUNCT
cana-5350	80	128	,	,	PUNCT
cana-5350	80	129	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	80	130	,	,	PUNCT
cana-5350	80	131	𝑏	𝑏	NOUN
cana-5350	80	132	,	,	PUNCT
cana-5350	80	133	𝑐	𝑐	PROPN
cana-5350	80	134	,	,	PUNCT
cana-5350	80	135	𝑑	𝑑	NOUN
cana-5350	80	136	)	)	PUNCT
cana-5350	80	137	,	,	PUNCT
cana-5350	80	138	𝑇𝑐′	𝑇𝑐′	ADJ
cana-5350	80	139	,	,	PUNCT
cana-5350	80	140	𝑡	𝑡	NOUN
cana-5350	80	141	)	)	PUNCT
cana-5350	80	142	}	}	PUNCT
cana-5350	80	143	=	=	SYM
cana-5350	80	144	𝑚𝑖𝑛{𝑀(𝑥	𝑚𝑖𝑛{𝑀(𝑥	PROPN
cana-5350	80	145	,	,	PUNCT
cana-5350	80	146	𝑧	𝑧	NOUN
cana-5350	80	147	,	,	PUNCT
cana-5350	80	148	𝑡	𝑡	NOUN
cana-5350	80	149	)	)	PUNCT
cana-5350	80	150	,	,	PUNCT
cana-5350	80	151	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	80	152	,	,	PUNCT
cana-5350	80	153	𝑥	𝑥	PROPN
cana-5350	80	154	,	,	PUNCT
cana-5350	80	155	𝑡	𝑡	NOUN
cana-5350	80	156	)	)	PUNCT
cana-5350	80	157	,	,	PUNCT
cana-5350	80	158	𝑀(𝑧	𝑀(𝑧	PROPN
cana-5350	80	159	,	,	PUNCT
cana-5350	80	160	𝑧	𝑧	NOUN
cana-5350	80	161	,	,	PUNCT
cana-5350	80	162	𝑡	𝑡	NOUN
cana-5350	80	163	)	)	PUNCT
cana-5350	80	164	,	,	PUNCT
cana-5350	80	165	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	80	166	,	,	PUNCT
cana-5350	80	167	𝑧	𝑧	PROPN
cana-5350	80	168	,	,	PUNCT
cana-5350	80	169	𝑡	𝑡	NOUN
cana-5350	80	170	)	)	PUNCT
cana-5350	80	171	,	,	PUNCT
cana-5350	80	172	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	80	173	,	,	PUNCT
cana-5350	80	174	𝑧	𝑧	PROPN
cana-5350	80	175	,	,	PUNCT
cana-5350	80	176	𝑡	𝑡	NOUN
cana-5350	80	177	)	)	PUNCT
cana-5350	80	178	}	}	PUNCT
cana-5350	80	179	=	=	SYM
cana-5350	80	180	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	80	181	,	,	PUNCT
cana-5350	80	182	𝑧	𝑧	NOUN
cana-5350	80	183	,	,	PUNCT
cana-5350	80	184	𝑡	𝑡	PROPN
cana-5350	80	185	)	)	PUNCT
cana-5350	80	186	⟹	⟹	PUNCT
cana-5350	81	1	𝑥	𝑥	NOUN
cana-5350	81	2	=	=	X
cana-5350	81	3	𝑧	𝑧	VERB
cana-5350	81	4	next	next	ADV
cana-5350	81	5	we	we	PRON
cana-5350	81	6	show	show	VERB
cana-5350	81	7	that	that	SCONJ
cana-5350	81	8	𝑥	𝑥	PROPN
cana-5350	81	9	=	=	SYM
cana-5350	81	10	𝑝	𝑝	NOUN
cana-5350	81	11	,	,	PUNCT
cana-5350	81	12	for	for	ADP
cana-5350	81	13	this	this	DET
cana-5350	81	14	putting	put	VERB
cana-5350	81	15	𝑥	𝑥	X
cana-5350	81	16	=	=	SYM
cana-5350	81	17	𝑎	𝑎	NOUN
cana-5350	81	18	,	,	PUNCT
cana-5350	81	19	𝑦	𝑦	NOUN
cana-5350	81	20	=	=	SYM
cana-5350	81	21	𝑏	𝑏	PROPN
cana-5350	81	22	,	,	PUNCT
cana-5350	81	23	𝑧	𝑧	PROPN
cana-5350	81	24	=	=	ADJ
cana-5350	81	25	𝑐	𝑐	PROPN
cana-5350	81	26	,	,	PUNCT
cana-5350	81	27	𝑝	𝑝	NOUN
cana-5350	81	28	=	=	SYM
cana-5350	81	29	𝑑	𝑑	NOUN
cana-5350	81	30	,	,	PUNCT
cana-5350	81	31	𝑢	𝑢	PRON
cana-5350	81	32	=	=	NOUN
cana-5350	81	33	𝑑′	𝑑′	NOUN
cana-5350	81	34	,	,	PUNCT
cana-5350	81	35	𝑣	𝑣	X
cana-5350	81	36	=	=	SYM
cana-5350	81	37	𝑐′	𝑐′	NUM
cana-5350	81	38	,	,	PUNCT
cana-5350	81	39	𝑤	𝑤	X
cana-5350	81	40	=	=	SYM
cana-5350	81	41	𝑎′	𝑎′	NOUN
cana-5350	81	42	,	,	PUNCT
cana-5350	81	43	𝑟	𝑟	X
cana-5350	81	44	=	=	SYM
cana-5350	81	45	𝑏′	𝑏′	PROPN
cana-5350	81	46	in	in	ADP
cana-5350	81	47	(	(	PUNCT
cana-5350	81	48	i	i	NOUN
cana-5350	81	49	)	)	PUNCT
cana-5350	81	50	,	,	PUNCT
cana-5350	81	51	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	81	52	,	,	PUNCT
cana-5350	81	53	𝑧	𝑧	PROPN
cana-5350	81	54	,	,	PUNCT
cana-5350	81	55	𝑞𝑡	𝑞𝑡	PRON
cana-5350	81	56	)	)	PUNCT
cana-5350	81	57	=	=	SYM
cana-5350	81	58	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	81	59	,	,	PUNCT
cana-5350	81	60	𝑏	𝑏	NOUN
cana-5350	81	61	,	,	PUNCT
cana-5350	81	62	𝑐	𝑐	PROPN
cana-5350	81	63	,	,	PUNCT
cana-5350	81	64	𝑑	𝑑	NOUN
cana-5350	81	65	)	)	PUNCT
cana-5350	81	66	,	,	PUNCT
cana-5350	81	67	𝐵(𝑑′	𝐵(𝑑′	PROPN
cana-5350	81	68	,	,	PUNCT
cana-5350	81	69	𝑐′	𝑐′	NUM
cana-5350	81	70	,	,	PUNCT
cana-5350	81	71	𝑎′	𝑎′	NUM
cana-5350	81	72	,	,	PUNCT
cana-5350	81	73	𝑏′	𝑏′	NUM
cana-5350	81	74	)	)	PUNCT
cana-5350	81	75	,	,	PUNCT
cana-5350	81	76	𝑞𝑡	𝑞𝑡	PRON
cana-5350	81	77	)	)	PUNCT
cana-5350	81	78	≥	≥	PROPN
cana-5350	81	79	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5350	81	80	{	{	PUNCT
cana-5350	81	81	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	81	82	,	,	PUNCT
cana-5350	81	83	𝑇𝑑′	𝑇𝑑′	ADV
cana-5350	81	84	,	,	PUNCT
cana-5350	81	85	𝑡	𝑡	NOUN
cana-5350	81	86	)	)	PUNCT
cana-5350	81	87	,	,	PUNCT
cana-5350	81	88	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	81	89	,	,	PUNCT
cana-5350	81	90	𝑏	𝑏	NOUN
cana-5350	81	91	,	,	PUNCT
cana-5350	81	92	𝑐	𝑐	PROPN
cana-5350	81	93	,	,	PUNCT
cana-5350	81	94	𝑑	𝑑	NOUN
cana-5350	81	95	)	)	PUNCT
cana-5350	81	96	,	,	PUNCT
cana-5350	81	97	𝑆𝑎	𝑆𝑎	PROPN
cana-5350	81	98	,	,	PUNCT
cana-5350	81	99	𝑡	𝑡	NOUN
cana-5350	81	100	)	)	PUNCT
cana-5350	81	101	,	,	PUNCT
cana-5350	81	102	𝑀(𝐵(𝑑′	𝑀(𝐵(𝑑′	NOUN
cana-5350	81	103	,	,	PUNCT
cana-5350	81	104	𝑐′	𝑐′	NUM
cana-5350	81	105	,	,	PUNCT
cana-5350	81	106	𝑎′	𝑎′	NUM
cana-5350	81	107	,	,	PUNCT
cana-5350	81	108	𝑏′	𝑏′	NUM
cana-5350	81	109	)	)	PUNCT
cana-5350	81	110	,	,	PUNCT
cana-5350	81	111	𝑇𝑑′	𝑇𝑑′	PROPN
cana-5350	81	112	,	,	PUNCT
cana-5350	81	113	𝑡	𝑡	NOUN
cana-5350	81	114	)	)	PUNCT
cana-5350	81	115	,	,	PUNCT
cana-5350	81	116	𝑀(𝑆𝑎	𝑀(𝑆𝑎	NUM
cana-5350	81	117	,	,	PUNCT
cana-5350	81	118	𝐵(𝑑′	𝐵(𝑑′	PROPN
cana-5350	81	119	,	,	PUNCT
cana-5350	81	120	𝑐′	𝑐′	NUM
cana-5350	81	121	,	,	PUNCT
cana-5350	81	122	𝑎′	𝑎′	NUM
cana-5350	81	123	,	,	PUNCT
cana-5350	81	124	𝑏′	𝑏′	NUM
cana-5350	81	125	)	)	PUNCT
cana-5350	81	126	,	,	PUNCT
cana-5350	81	127	𝑡	𝑡	PROPN
cana-5350	81	128	)	)	PUNCT
cana-5350	81	129	,	,	PUNCT
cana-5350	81	130	𝑀(𝐴(𝑎	𝑀(𝐴(𝑎	NOUN
cana-5350	81	131	,	,	PUNCT
cana-5350	81	132	𝑏	𝑏	NOUN
cana-5350	81	133	,	,	PUNCT
cana-5350	81	134	𝑐	𝑐	PROPN
cana-5350	81	135	,	,	PUNCT
cana-5350	81	136	𝑑	𝑑	NOUN
cana-5350	81	137	)	)	PUNCT
cana-5350	81	138	,	,	PUNCT
cana-5350	81	139	𝑇𝑑′	𝑇𝑑′	ADV
cana-5350	81	140	,	,	PUNCT
cana-5350	81	141	𝑡	𝑡	NOUN
cana-5350	81	142	)	)	PUNCT
cana-5350	81	143	}	}	PUNCT
cana-5350	81	144	=	=	SYM
cana-5350	81	145	𝑚𝑖𝑛{𝑀(𝑥	𝑚𝑖𝑛{𝑀(𝑥	PROPN
cana-5350	81	146	,	,	PUNCT
cana-5350	81	147	𝑝	𝑝	NOUN
cana-5350	81	148	,	,	PUNCT
cana-5350	81	149	𝑡	𝑡	NOUN
cana-5350	81	150	)	)	PUNCT
cana-5350	81	151	,	,	PUNCT
cana-5350	81	152	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	81	153	,	,	PUNCT
cana-5350	81	154	𝑥	𝑥	PROPN
cana-5350	81	155	,	,	PUNCT
cana-5350	81	156	𝑡	𝑡	NOUN
cana-5350	81	157	)	)	PUNCT
cana-5350	81	158	,	,	PUNCT
cana-5350	81	159	𝑀(𝑝	𝑀(𝑝	ADJ
cana-5350	81	160	,	,	PUNCT
cana-5350	81	161	𝑝	𝑝	NOUN
cana-5350	81	162	,	,	PUNCT
cana-5350	81	163	𝑡	𝑡	NOUN
cana-5350	81	164	)	)	PUNCT
cana-5350	81	165	,	,	PUNCT
cana-5350	81	166	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	81	167	,	,	PUNCT
cana-5350	81	168	𝑝	𝑝	NOUN
cana-5350	81	169	,	,	PUNCT
cana-5350	81	170	𝑡	𝑡	NOUN
cana-5350	81	171	)	)	PUNCT
cana-5350	81	172	,	,	PUNCT
cana-5350	81	173	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	81	174	,	,	PUNCT
cana-5350	81	175	𝑝	𝑝	NOUN
cana-5350	81	176	,	,	PUNCT
cana-5350	81	177	𝑡	𝑡	NOUN
cana-5350	81	178	)	)	PUNCT
cana-5350	81	179	}	}	PUNCT
cana-5350	81	180	communications	communication	NOUN
cana-5350	81	181	on	on	ADP
cana-5350	81	182	applied	apply	VERB
cana-5350	81	183	nonlinear	nonlinear	ADJ
cana-5350	81	184	analysis	analysis	NOUN
cana-5350	81	185	issn	issn	NOUN
cana-5350	81	186	:	:	PUNCT
cana-5350	81	187	1074	1074	NUM
cana-5350	81	188	-	-	PUNCT
cana-5350	81	189	133x	133x	NUM
cana-5350	81	190	vol	vol	VERB
cana-5350	81	191	32	32	NUM
cana-5350	81	192	no	no	NOUN
cana-5350	81	193	.	.	PUNCT
cana-5350	82	1	10s	10	NOUN
cana-5350	82	2	(	(	PUNCT
cana-5350	82	3	2025	2025	NUM
cana-5350	82	4	)	)	PUNCT
cana-5350	82	5	1800	1800	NUM
cana-5350	82	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5350	82	7	=	=	SYM
cana-5350	82	8	𝑀(𝑥	𝑀(𝑥	NOUN
cana-5350	82	9	,	,	PUNCT
cana-5350	82	10	𝑝	𝑝	NOUN
cana-5350	82	11	,	,	PUNCT
cana-5350	82	12	𝑡	𝑡	PROPN
cana-5350	82	13	)	)	PUNCT
cana-5350	82	14	⟹	⟹	PUNCT
cana-5350	83	1	𝑥	𝑥	X
cana-5350	83	2	=	=	SYM
cana-5350	83	3	𝑝	𝑝	PROPN
cana-5350	83	4	⇒	⇒	NOUN
cana-5350	83	5	𝑥	𝑥	X
cana-5350	84	1	=	=	SYM
cana-5350	84	2	𝑦	𝑦	SYM
cana-5350	84	3	=	=	SYM
cana-5350	84	4	𝑧	𝑧	X
cana-5350	84	5	=	=	SYM
cana-5350	84	6	𝑝	𝑝	PROPN
cana-5350	84	7	now	now	ADV
cana-5350	84	8	we	we	PRON
cana-5350	84	9	prove	prove	VERB
cana-5350	84	10	that	that	SCONJ
cana-5350	84	11	𝑆𝑥	𝑆𝑥	PROPN
cana-5350	84	12	=	=	PUNCT
cana-5350	84	13	𝑇𝑥	𝑇𝑥	NOUN
cana-5350	84	14	putting	put	VERB
cana-5350	84	15	𝑢	𝑢	PRON
cana-5350	84	16	=	=	SYM
cana-5350	84	17	𝑦	𝑦	PROPN
cana-5350	84	18	,	,	PUNCT
cana-5350	84	19	𝑣	𝑣	X
cana-5350	84	20	=	=	X
cana-5350	84	21	𝑧	𝑧	PROPN
cana-5350	84	22	,	,	PUNCT
cana-5350	84	23	𝑤	𝑤	X
cana-5350	84	24	=	=	SYM
cana-5350	84	25	𝑡	𝑡	PROPN
cana-5350	84	26	,	,	PUNCT
cana-5350	84	27	𝑟	𝑟	NOUN
cana-5350	84	28	=	=	SYM
cana-5350	84	29	𝑥	𝑥	PROPN
cana-5350	84	30	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	84	31	,	,	PUNCT
cana-5350	84	32	𝑇𝑥	𝑇𝑥	PROPN
cana-5350	84	33	,	,	PUNCT
cana-5350	84	34	𝑞𝑡	𝑞𝑡	PRON
cana-5350	84	35	)	)	PUNCT
cana-5350	84	36	=	=	SYM
cana-5350	84	37	𝑀(𝐴(𝑥	𝑀(𝐴(𝑥	NOUN
cana-5350	84	38	,	,	PUNCT
cana-5350	84	39	𝑦	𝑦	NOUN
cana-5350	84	40	,	,	PUNCT
cana-5350	84	41	𝑧	𝑧	NOUN
cana-5350	84	42	,	,	PUNCT
cana-5350	84	43	𝑝	𝑝	NOUN
cana-5350	84	44	)	)	PUNCT
cana-5350	84	45	,	,	PUNCT
cana-5350	84	46	𝐵(𝑦	𝐵(𝑦	ADV
cana-5350	84	47	,	,	PUNCT
cana-5350	84	48	𝑧	𝑧	PRON
cana-5350	84	49	,	,	PUNCT
cana-5350	84	50	𝑡	𝑡	PROPN
cana-5350	84	51	,	,	PUNCT
cana-5350	84	52	𝑥	𝑥	NOUN
cana-5350	84	53	)	)	PUNCT
cana-5350	84	54	,	,	PUNCT
cana-5350	84	55	𝑞𝑡	𝑞𝑡	PRON
cana-5350	84	56	)	)	PUNCT
cana-5350	84	57	≥	≥	PROPN
cana-5350	84	58	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5350	84	59	{	{	PUNCT
cana-5350	84	60	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	84	61	,	,	PUNCT
cana-5350	84	62	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	84	63	,	,	PUNCT
cana-5350	84	64	𝑡	𝑡	NOUN
cana-5350	84	65	)	)	PUNCT
cana-5350	84	66	,	,	PUNCT
cana-5350	84	67	𝑀(𝐴(𝑥	𝑀(𝐴(𝑥	NOUN
cana-5350	84	68	,	,	PUNCT
cana-5350	84	69	𝑦	𝑦	NOUN
cana-5350	84	70	,	,	PUNCT
cana-5350	84	71	𝑧	𝑧	NOUN
cana-5350	84	72	,	,	PUNCT
cana-5350	84	73	𝑝	𝑝	NOUN
cana-5350	84	74	)	)	PUNCT
cana-5350	84	75	,	,	PUNCT
cana-5350	84	76	𝑆𝑥	𝑆𝑥	PROPN
cana-5350	84	77	,	,	PUNCT
cana-5350	84	78	𝑡	𝑡	PROPN
cana-5350	84	79	)	)	PUNCT
cana-5350	84	80	,	,	PUNCT
cana-5350	84	81	𝑀(𝐵(𝑦	𝑀(𝐵(𝑦	ADV
cana-5350	84	82	,	,	PUNCT
cana-5350	84	83	𝑧	𝑧	PROPN
cana-5350	84	84	,	,	PUNCT
cana-5350	84	85	𝑡	𝑡	PROPN
cana-5350	84	86	,	,	PUNCT
cana-5350	84	87	𝑥	𝑥	NOUN
cana-5350	84	88	)	)	PUNCT
cana-5350	84	89	,	,	PUNCT
cana-5350	84	90	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	84	91	,	,	PUNCT
cana-5350	84	92	𝑡	𝑡	NOUN
cana-5350	84	93	)	)	PUNCT
cana-5350	84	94	,	,	PUNCT
cana-5350	84	95	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADV
cana-5350	84	96	,	,	PUNCT
cana-5350	84	97	𝐵(𝑦	𝐵(𝑦	NOUN
cana-5350	84	98	,	,	PUNCT
cana-5350	84	99	𝑧	𝑧	PRON
cana-5350	84	100	,	,	PUNCT
cana-5350	84	101	𝑡	𝑡	PROPN
cana-5350	84	102	,	,	PUNCT
cana-5350	84	103	𝑥	𝑥	NOUN
cana-5350	84	104	)	)	PUNCT
cana-5350	84	105	,	,	PUNCT
cana-5350	84	106	𝑡	𝑡	PROPN
cana-5350	84	107	)	)	PUNCT
cana-5350	84	108	,	,	PUNCT
cana-5350	84	109	𝑀(𝐴(𝑥	𝑀(𝐴(𝑥	NOUN
cana-5350	84	110	,	,	PUNCT
cana-5350	84	111	𝑦	𝑦	NOUN
cana-5350	84	112	,	,	PUNCT
cana-5350	84	113	𝑧	𝑧	NOUN
cana-5350	84	114	,	,	PUNCT
cana-5350	84	115	𝑝	𝑝	NOUN
cana-5350	84	116	)	)	PUNCT
cana-5350	84	117	,	,	PUNCT
cana-5350	84	118	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	84	119	,	,	PUNCT
cana-5350	84	120	𝑡	𝑡	NOUN
cana-5350	84	121	)	)	PUNCT
cana-5350	84	122	}	}	PUNCT
cana-5350	84	123	=	=	PUNCT
cana-5350	84	124	𝑚𝑖𝑛{𝑀(𝑆𝑥	𝑚𝑖𝑛{𝑀(𝑆𝑥	ADJ
cana-5350	84	125	,	,	PUNCT
cana-5350	84	126	𝑇𝑦	𝑇𝑦	NOUN
cana-5350	84	127	,	,	PUNCT
cana-5350	84	128	𝑡	𝑡	NOUN
cana-5350	84	129	)	)	PUNCT
cana-5350	84	130	,	,	PUNCT
cana-5350	84	131	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	84	132	,	,	PUNCT
cana-5350	84	133	𝑆𝑥	𝑆𝑥	PROPN
cana-5350	84	134	,	,	PUNCT
cana-5350	84	135	𝑡	𝑡	PROPN
cana-5350	84	136	)	)	PUNCT
cana-5350	84	137	,	,	PUNCT
cana-5350	84	138	𝑀(𝑇𝑦	𝑀(𝑇𝑦	PROPN
cana-5350	84	139	,	,	PUNCT
cana-5350	84	140	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	84	141	,	,	PUNCT
cana-5350	84	142	𝑡	𝑡	NOUN
cana-5350	84	143	)	)	PUNCT
cana-5350	84	144	,	,	PUNCT
cana-5350	84	145	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	84	146	,	,	PUNCT
cana-5350	84	147	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	84	148	,	,	PUNCT
cana-5350	84	149	𝑡	𝑡	NOUN
cana-5350	84	150	)	)	PUNCT
cana-5350	84	151	,	,	PUNCT
cana-5350	84	152	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	84	153	,	,	PUNCT
cana-5350	84	154	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	84	155	,	,	PUNCT
cana-5350	84	156	𝑡	𝑡	NOUN
cana-5350	84	157	)	)	PUNCT
cana-5350	84	158	}	}	PUNCT
cana-5350	84	159	=	=	SYM
cana-5350	84	160	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5350	84	161	{	{	PUNCT
cana-5350	84	162	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	84	163	,	,	PUNCT
cana-5350	84	164	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	84	165	,	,	PUNCT
cana-5350	84	166	𝑡	𝑡	NOUN
cana-5350	84	167	)	)	PUNCT
cana-5350	84	168	,	,	PUNCT
cana-5350	84	169	1,1	1,1	NUM
cana-5350	84	170	,	,	PUNCT
cana-5350	84	171	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	84	172	,	,	PUNCT
cana-5350	84	173	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	84	174	,	,	PUNCT
cana-5350	84	175	𝑡	𝑡	NOUN
cana-5350	84	176	)	)	PUNCT
cana-5350	84	177	,	,	PUNCT
cana-5350	84	178	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	84	179	,	,	PUNCT
cana-5350	84	180	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	84	181	,	,	PUNCT
cana-5350	84	182	𝑡	𝑡	NOUN
cana-5350	84	183	)	)	PUNCT
cana-5350	84	184	}	}	PUNCT
cana-5350	84	185	=	=	PUNCT
cana-5350	84	186	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	84	187	,	,	PUNCT
cana-5350	84	188	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	84	189	,	,	PUNCT
cana-5350	84	190	𝑡	𝑡	NOUN
cana-5350	84	191	)	)	PUNCT
cana-5350	84	192	⟹	⟹	PUNCT
cana-5350	85	1	𝑆𝑥	𝑆𝑥	NOUN
cana-5350	85	2	=	=	PUNCT
cana-5350	85	3	𝑇𝑦	𝑇𝑦	PROPN
cana-5350	85	4	⇒	⇒	NOUN
cana-5350	85	5	𝑆𝑥	𝑆𝑥	PROPN
cana-5350	85	6	=	=	PUNCT
cana-5350	85	7	𝑇𝑥	𝑇𝑥	PROPN
cana-5350	85	8	also	also	ADV
cana-5350	85	9	by	by	ADP
cana-5350	85	10	condition	condition	NOUN
cana-5350	85	11	(	(	PUNCT
cana-5350	85	12	ii	ii	NOUN
cana-5350	85	13	)	)	PUNCT
cana-5350	85	14	we	we	PRON
cana-5350	85	15	have	have	VERB
cana-5350	85	16	,	,	PUNCT
cana-5350	85	17	𝑥	𝑥	X
cana-5350	85	18	=	=	SYM
cana-5350	85	19	𝐵(𝑥	𝐵(𝑥	PROPN
cana-5350	85	20	,	,	PUNCT
cana-5350	85	21	𝑥	𝑥	PROPN
cana-5350	85	22	,	,	PUNCT
cana-5350	85	23	𝑥	𝑥	NOUN
cana-5350	85	24	,	,	PUNCT
cana-5350	85	25	𝑥	𝑥	NOUN
cana-5350	85	26	)	)	PUNCT
cana-5350	85	27	thus	thus	ADV
cana-5350	85	28	𝐴(𝑥	𝐴(𝑥	ADP
cana-5350	85	29	,	,	PUNCT
cana-5350	85	30	𝑥	𝑥	NOUN
cana-5350	85	31	)	)	PUNCT
cana-5350	85	32	=	=	SYM
cana-5350	86	1	𝑇(𝑥	𝑇(𝑥	X
cana-5350	86	2	)	)	PUNCT
cana-5350	86	3	=	=	SYM
cana-5350	87	1	𝐵(𝑥	𝐵(𝑥	PROPN
cana-5350	87	2	,	,	PUNCT
cana-5350	87	3	𝑥	𝑥	NOUN
cana-5350	87	4	)	)	PUNCT
cana-5350	87	5	=	=	SYM
cana-5350	87	6	𝑆(𝑥	𝑆(𝑥	X
cana-5350	87	7	)	)	PUNCT
cana-5350	87	8	=	=	PUNCT
cana-5350	88	1	𝑥.	𝑥.	PRON
cana-5350	88	2	example	example	NOUN
cana-5350	88	3	3.1.1	3.1.1	NUM
cana-5350	88	4	let	let	VERB
cana-5350	88	5	𝑋	𝑋	NOUN
cana-5350	88	6	=	=	PUNCT
cana-5350	89	1	[	[	X
cana-5350	89	2	0,1	0,1	NUM
cana-5350	89	3	]	]	PUNCT
cana-5350	89	4	with	with	ADP
cana-5350	89	5	the	the	DET
cana-5350	89	6	metric	metric	NOUN
cana-5350	89	7	𝑑	𝑑	AUX
cana-5350	89	8	defined	define	VERB
cana-5350	89	9	by	by	ADP
cana-5350	89	10	𝑑(𝑥	𝑑(𝑥	PROPN
cana-5350	89	11	,	,	PUNCT
cana-5350	89	12	𝑦	𝑦	X
cana-5350	89	13	)	)	PUNCT
cana-5350	89	14	=	=	SYM
cana-5350	89	15	|𝑥	|𝑥	ADP
cana-5350	89	16	−	−	PROPN
cana-5350	89	17	𝑦|	𝑦|	PROPN
cana-5350	89	18	and	and	CCONJ
cana-5350	89	19	for	for	ADP
cana-5350	89	20	each	each	DET
cana-5350	89	21	𝑡	𝑡	PROPN
cana-5350	89	22	∈	∈	PROPN
cana-5350	89	23	[	[	X
cana-5350	89	24	0,1	0,1	NUM
cana-5350	89	25	]	]	PUNCT
cana-5350	89	26	,	,	PUNCT
cana-5350	89	27	define	define	VERB
cana-5350	89	28	m(x	m(x	PROPN
cana-5350	89	29	,	,	PUNCT
cana-5350	89	30	y	y	PROPN
cana-5350	89	31	,	,	PUNCT
cana-5350	89	32	t	t	PROPN
cana-5350	89	33	)	)	PUNCT
cana-5350	89	34	=	=	PRON
cana-5350	89	35	{	{	PUNCT
cana-5350	89	36	t	t	NOUN
cana-5350	89	37	t	t	PROPN
cana-5350	89	38	+	+	CCONJ
cana-5350	89	39	|x	|x	NOUN
cana-5350	89	40	−	−	VERB
cana-5350	89	41	y|	y|	NOUN
cana-5350	89	42	,	,	PUNCT
cana-5350	89	43	if	if	SCONJ
cana-5350	89	44	t	t	PROPN
cana-5350	89	45	>	>	X
cana-5350	89	46	0	0	NUM
cana-5350	89	47	;	;	PUNCT
cana-5350	89	48	0	0	NUM
cana-5350	89	49	,	,	PUNCT
cana-5350	89	50	if	if	SCONJ
cana-5350	89	51	t	t	PROPN
cana-5350	89	52	=	=	SYM
cana-5350	89	53	0	0	NUM
cana-5350	89	54	for	for	ADP
cana-5350	89	55	all	all	PRON
cana-5350	89	56	𝑥	𝑥	PROPN
cana-5350	89	57	,	,	PUNCT
cana-5350	89	58	𝑦	𝑦	PRON
cana-5350	89	59	∈	∈	PROPN
cana-5350	89	60	𝑋.	𝑋.	PROPN
cana-5350	89	61	clearly	clearly	ADV
cana-5350	89	62	(	(	PUNCT
cana-5350	89	63	x	x	X
cana-5350	89	64	,	,	PUNCT
cana-5350	89	65	ℱ,∗	ℱ,∗	NUM
cana-5350	89	66	)	)	PUNCT
cana-5350	89	67	be	be	VERB
cana-5350	89	68	a	a	DET
cana-5350	89	69	fuzzy	fuzzy	ADJ
cana-5350	89	70	metric	metric	ADJ
cana-5350	89	71	space	space	NOUN
cana-5350	89	72	,	,	PUNCT
cana-5350	89	73	with	with	ADP
cana-5350	89	74	𝑎	𝑎	DET
cana-5350	89	75	∗	∗	NOUN
cana-5350	89	76	𝑏	𝑏	NOUN
cana-5350	89	77	=	=	SYM
cana-5350	89	78	min{𝑎	min{𝑎	PROPN
cana-5350	89	79	,	,	PUNCT
cana-5350	89	80	𝑏	𝑏	NOUN
cana-5350	89	81	}	}	PUNCT
cana-5350	89	82	.	.	PUNCT
cana-5350	90	1	let	let	VERB
cana-5350	90	2	𝑆	𝑆	PROPN
cana-5350	90	3	,	,	PUNCT
cana-5350	90	4	𝑇	𝑇	PROPN
cana-5350	90	5	:	:	PUNCT
cana-5350	90	6	𝑋	𝑋	PROPN
cana-5350	90	7	→	→	SYM
cana-5350	90	8	𝑋	𝑋	PROPN
cana-5350	90	9	and	and	CCONJ
cana-5350	90	10	𝐴	𝐴	PROPN
cana-5350	90	11	,	,	PUNCT
cana-5350	90	12	𝐵	𝐵	NOUN
cana-5350	90	13	:	:	PUNCT
cana-5350	90	14	𝑋	𝑋	NOUN
cana-5350	90	15	×	×	NOUN
cana-5350	90	16	𝑋	𝑋	PROPN
cana-5350	90	17	×	×	NOUN
cana-5350	90	18	𝑋	𝑋	NOUN
cana-5350	90	19	×	×	NOUN
cana-5350	90	20	𝑋	𝑋	PROPN
cana-5350	90	21	→	→	SYM
cana-5350	90	22	𝑋	𝑋	PROPN
cana-5350	90	23	defined	define	VERB
cana-5350	90	24	by	by	ADP
cana-5350	90	25	a(x	a(x	NOUN
cana-5350	90	26	,	,	PUNCT
cana-5350	90	27	y	y	PROPN
cana-5350	90	28	,	,	PUNCT
cana-5350	90	29	z	z	PROPN
cana-5350	90	30	,	,	PUNCT
cana-5350	90	31	w	w	PROPN
cana-5350	90	32	)	)	PUNCT
cana-5350	90	33	=	=	SYM
cana-5350	90	34	2x+y+2z+w	2x+y+2z+w	NUM
cana-5350	90	35	2	2	NUM
cana-5350	90	36	s(x	s(x	NOUN
cana-5350	90	37	)	)	PUNCT
cana-5350	90	38	=	=	PRON
cana-5350	91	1	{	{	PUNCT
cana-5350	91	2	x	x	X
cana-5350	91	3	,	,	PUNCT
cana-5350	91	4	if	if	SCONJ
cana-5350	91	5	0	0	NUM
cana-5350	91	6	≤	≤	NUM
cana-5350	91	7	x	x	X
cana-5350	91	8	<	<	X
cana-5350	91	9	1	1	NUM
cana-5350	91	10	;	;	PUNCT
cana-5350	91	11	7	7	NUM
cana-5350	91	12	2	2	NUM
cana-5350	91	13	,	,	PUNCT
cana-5350	91	14	if	if	SCONJ
cana-5350	91	15	x	x	X
cana-5350	91	16	≥	≥	NOUN
cana-5350	91	17	1	1	NUM
cana-5350	91	18	.	.	PUNCT
cana-5350	92	1	b(x	b(x	NOUN
cana-5350	92	2	,	,	PUNCT
cana-5350	92	3	y	y	PROPN
cana-5350	92	4	,	,	PUNCT
cana-5350	92	5	z	z	PROPN
cana-5350	92	6	,	,	PUNCT
cana-5350	92	7	w	w	PROPN
cana-5350	92	8	)	)	PUNCT
cana-5350	92	9	=	=	SYM
cana-5350	92	10	y	y	PROPN
cana-5350	92	11	t(x	t(x	PROPN
cana-5350	92	12	)	)	PUNCT
cana-5350	92	13	=	=	PRON
cana-5350	92	14	{	{	PUNCT
cana-5350	92	15	x	x	X
cana-5350	92	16	,	,	PUNCT
cana-5350	92	17	if	if	SCONJ
cana-5350	92	18	0	0	NUM
cana-5350	92	19	≤	≤	NUM
cana-5350	92	20	x	x	X
cana-5350	92	21	<	<	X
cana-5350	92	22	1	1	NUM
cana-5350	92	23	;	;	PUNCT
cana-5350	92	24	5	5	NUM
cana-5350	92	25	,	,	PUNCT
cana-5350	92	26	if	if	SCONJ
cana-5350	92	27	x	x	PRON
cana-5350	92	28	≥	≥	NUM
cana-5350	92	29	1	1	NUM
cana-5350	92	30	.	.	PUNCT
cana-5350	92	31	clearly	clearly	ADV
cana-5350	92	32	all	all	DET
cana-5350	92	33	the	the	DET
cana-5350	92	34	conditions	condition	NOUN
cana-5350	92	35	of	of	ADP
cana-5350	92	36	the	the	DET
cana-5350	92	37	above	above	ADJ
cana-5350	92	38	theorem	theorem	NOUN
cana-5350	92	39	are	be	AUX
cana-5350	92	40	satisfied	satisfied	ADJ
cana-5350	92	41	.	.	PUNCT
cana-5350	93	1	also	also	ADV
cana-5350	93	2	𝑆𝐴(0,0,0,0	𝑆𝐴(0,0,0,0	NOUN
cana-5350	93	3	)	)	PUNCT
cana-5350	93	4	=	=	SYM
cana-5350	93	5	𝐴(𝑆0	𝐴(𝑆0	PROPN
cana-5350	93	6	,	,	PUNCT
cana-5350	93	7	𝑆0	𝑆0	PROPN
cana-5350	93	8	,	,	PUNCT
cana-5350	93	9	𝑆0	𝑆0	PROPN
cana-5350	93	10	,	,	PUNCT
cana-5350	93	11	𝑆0	𝑆0	NOUN
cana-5350	93	12	)	)	PUNCT
cana-5350	93	13	and	and	CCONJ
cana-5350	93	14	𝑇𝐵(0,0,0,0	𝑇𝐵(0,0,0,0	NOUN
cana-5350	93	15	)	)	PUNCT
cana-5350	93	16	=	=	SYM
cana-5350	94	1	𝐵(𝑇0	𝐵(𝑇0	PROPN
cana-5350	94	2	,	,	PUNCT
cana-5350	94	3	𝑇0	𝑇0	NOUN
cana-5350	94	4	,	,	PUNCT
cana-5350	94	5	𝑇0	𝑇0	NOUN
cana-5350	94	6	,	,	PUNCT
cana-5350	94	7	𝑇0	𝑇0	NOUN
cana-5350	94	8	)	)	PUNCT
cana-5350	95	1	so	so	ADV
cana-5350	95	2	,	,	PUNCT
cana-5350	95	3	(	(	PUNCT
cana-5350	95	4	a	a	PRON
cana-5350	95	5	,	,	PUNCT
cana-5350	95	6	s	s	NOUN
cana-5350	95	7	)	)	PUNCT
cana-5350	95	8	and	and	CCONJ
cana-5350	95	9	(	(	PUNCT
cana-5350	95	10	b	b	PROPN
cana-5350	95	11	,	,	PUNCT
cana-5350	95	12	t	t	PROPN
cana-5350	95	13	)	)	PUNCT
cana-5350	95	14	are	be	AUX
cana-5350	95	15	owc	owc	NUM
cana-5350	95	16	maps	map	NOUN
cana-5350	95	17	and	and	CCONJ
cana-5350	95	18	(	(	PUNCT
cana-5350	95	19	0	0	NUM
cana-5350	95	20	,	,	PUNCT
cana-5350	95	21	0	0	NUM
cana-5350	95	22	,	,	PUNCT
cana-5350	95	23	0	0	NUM
cana-5350	95	24	,	,	PUNCT
cana-5350	95	25	0	0	NUM
cana-5350	95	26	)	)	PUNCT
cana-5350	96	1	is	be	AUX
cana-5350	96	2	the	the	DET
cana-5350	96	3	common	common	ADJ
cana-5350	96	4	quadruple	quadruple	NOUN
cana-5350	96	5	fixed	fix	VERB
cana-5350	96	6	point	point	NOUN
cana-5350	96	7	of	of	ADP
cana-5350	96	8	a	a	DET
cana-5350	96	9	,	,	PUNCT
cana-5350	96	10	b	b	NOUN
cana-5350	96	11	,	,	PUNCT
cana-5350	96	12	s	s	PART
cana-5350	96	13	and	and	CCONJ
cana-5350	96	14	t.	t.	NOUN
cana-5350	96	15	communications	communication	NOUN
cana-5350	96	16	on	on	ADP
cana-5350	96	17	applied	apply	VERB
cana-5350	96	18	nonlinear	nonlinear	ADJ
cana-5350	96	19	analysis	analysis	NOUN
cana-5350	96	20	issn	issn	NOUN
cana-5350	96	21	:	:	PUNCT
cana-5350	96	22	1074	1074	NUM
cana-5350	96	23	-	-	PUNCT
cana-5350	96	24	133x	133x	NUM
cana-5350	96	25	vol	vol	VERB
cana-5350	96	26	32	32	NUM
cana-5350	96	27	no	no	NOUN
cana-5350	96	28	.	.	PUNCT
cana-5350	97	1	10s	10	NOUN
cana-5350	97	2	(	(	PUNCT
cana-5350	97	3	2025	2025	NUM
cana-5350	97	4	)	)	PUNCT
cana-5350	97	5	1801	1801	NUM
cana-5350	97	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5350	97	7	all	all	DET
cana-5350	97	8	conditions	condition	NOUN
cana-5350	97	9	of	of	ADP
cana-5350	97	10	the	the	DET
cana-5350	97	11	theorem	theorem	NOUN
cana-5350	97	12	are	be	AUX
cana-5350	97	13	satisfied	satisfied	ADJ
cana-5350	97	14	.	.	PUNCT
cana-5350	98	1	common	common	ADJ
cana-5350	98	2	quadruple	quadruple	NOUN
cana-5350	98	3	fixed	fix	VERB
cana-5350	98	4	point	point	NOUN
cana-5350	98	5	is	be	AUX
cana-5350	98	6	(	(	PUNCT
cana-5350	98	7	0	0	NUM
cana-5350	98	8	,	,	PUNCT
cana-5350	98	9	0	0	NUM
cana-5350	98	10	,	,	PUNCT
cana-5350	98	11	0	0	NUM
cana-5350	98	12	,	,	PUNCT
cana-5350	98	13	0	0	NUM
cana-5350	98	14	)	)	PUNCT
cana-5350	98	15	.	.	PUNCT
cana-5350	99	1	theorem	theorem	VERB
cana-5350	99	2	:	:	PUNCT
cana-5350	99	3	3.2	3.2	NUM
cana-5350	99	4	let	let	VERB
cana-5350	99	5	(	(	PUNCT
cana-5350	99	6	𝑋	𝑋	PROPN
cana-5350	99	7	,	,	PUNCT
cana-5350	99	8	𝑀	𝑀	PROPN
cana-5350	99	9	,	,	PUNCT
cana-5350	99	10			PROPN
cana-5350	99	11	)	)	PUNCT
cana-5350	99	12	be	be	AUX
cana-5350	99	13	a	a	DET
cana-5350	99	14	fuzzy	fuzzy	ADJ
cana-5350	99	15	metric	metric	ADJ
cana-5350	99	16	space	space	NOUN
cana-5350	99	17	with	with	ADP
cana-5350	99	18	𝑡	𝑡	PROPN
cana-5350	99	19	∗	∗	NOUN
cana-5350	99	20	𝑡	𝑡	X
cana-5350	99	21	=	=	PUNCT
cana-5350	99	22	𝑡	𝑡	PROPN
cana-5350	99	23	for	for	ADP
cana-5350	99	24	all	all	DET
cana-5350	99	25	𝑡	𝑡	ADP
cana-5350	99	26	∈	∈	PROPN
cana-5350	100	1	[	[	X
cana-5350	100	2	0,1	0,1	NUM
cana-5350	100	3	]	]	PUNCT
cana-5350	100	4	.	.	PUNCT
cana-5350	101	1	let	let	VERB
cana-5350	101	2	𝐴	𝐴	PROPN
cana-5350	101	3	,	,	PUNCT
cana-5350	101	4	𝐵	𝐵	PROPN
cana-5350	101	5	:	:	PUNCT
cana-5350	101	6	𝑋	𝑋	NOUN
cana-5350	101	7	×	×	NOUN
cana-5350	101	8	𝑋	𝑋	PROPN
cana-5350	101	9	×	×	NOUN
cana-5350	101	10	𝑋	𝑋	NOUN
cana-5350	101	11	×	×	NOUN
cana-5350	101	12	𝑋	𝑋	PROPN
cana-5350	101	13	→	→	SYM
cana-5350	101	14	𝑋	𝑋	PROPN
cana-5350	101	15	and	and	CCONJ
cana-5350	101	16	𝑆	𝑆	PROPN
cana-5350	101	17	,	,	PUNCT
cana-5350	101	18	𝑇	𝑇	PROPN
cana-5350	101	19	:	:	PUNCT
cana-5350	101	20	𝑋	𝑋	PROPN
cana-5350	101	21	→	→	SYM
cana-5350	101	22	𝑋	𝑋	PROPN
cana-5350	101	23	be	be	VERB
cana-5350	101	24	four	four	NUM
cana-5350	101	25	self	self	NOUN
cana-5350	101	26	-	-	PUNCT
cana-5350	101	27	mappings	mapping	NOUN
cana-5350	101	28	satisfying	satisfy	VERB
cana-5350	101	29	the	the	DET
cana-5350	101	30	following	follow	VERB
cana-5350	101	31	conditions	condition	NOUN
cana-5350	101	32	:	:	PUNCT
cana-5350	101	33	(	(	PUNCT
cana-5350	101	34	i	i	NOUN
cana-5350	101	35	)	)	PUNCT
cana-5350	101	36	𝑀(𝐴(𝑥	𝑀(𝐴(𝑥	NOUN
cana-5350	101	37	,	,	PUNCT
cana-5350	101	38	𝑦	𝑦	NOUN
cana-5350	101	39	,	,	PUNCT
cana-5350	101	40	𝑧	𝑧	NOUN
cana-5350	101	41	,	,	PUNCT
cana-5350	101	42	𝑝	𝑝	NOUN
cana-5350	101	43	)	)	PUNCT
cana-5350	101	44	,	,	PUNCT
cana-5350	101	45	𝐵(𝑢	𝐵(𝑢	PROPN
cana-5350	101	46	,	,	PUNCT
cana-5350	101	47	𝑣	𝑣	NOUN
cana-5350	101	48	,	,	PUNCT
cana-5350	101	49	𝑤	𝑤	ADP
cana-5350	101	50	,	,	PUNCT
cana-5350	101	51	𝑟	𝑟	NOUN
cana-5350	101	52	)	)	PUNCT
cana-5350	101	53	,	,	PUNCT
cana-5350	101	54	𝑞𝑡	𝑞𝑡	PRON
cana-5350	101	55	)	)	PUNCT
cana-5350	101	56	≥	≥	PROPN
cana-5350	101	57	{	{	PUNCT
cana-5350	101	58	𝑀(𝐵(𝑢,𝑣,𝑤,𝑟),𝑆𝑥,𝑡).𝑀(𝐵(𝑢,𝑣,𝑤,𝑟),𝑇𝑢,𝑡)+𝑀(𝑆𝑥,𝐵(𝑢,𝑣,𝑤,𝑟),𝑡	𝑀(𝐵(𝑢,𝑣,𝑤,𝑟),𝑆𝑥,𝑡).𝑀(𝐵(𝑢,𝑣,𝑤,𝑟),𝑇𝑢,𝑡)+𝑀(𝑆𝑥,𝐵(𝑢,𝑣,𝑤,𝑟),𝑡	PROPN
cana-5350	101	59	)	)	PUNCT
cana-5350	101	60	.	.	PUNCT
cana-5350	102	1	𝑀(𝐵(𝑢,𝑣,𝑤,𝑟),𝑇𝑢,𝑡	𝑀(𝐵(𝑢,𝑣,𝑤,𝑟),𝑇𝑢,𝑡	NUM
cana-5350	102	2	)	)	PUNCT
cana-5350	102	3	2	2	NUM
cana-5350	102	4	}	}	PUNCT
cana-5350	102	5	for	for	ADP
cana-5350	102	6	all	all	PRON
cana-5350	102	7	𝑥	𝑥	PROPN
cana-5350	102	8	,	,	PUNCT
cana-5350	102	9	𝑦	𝑦	NOUN
cana-5350	102	10	,	,	PUNCT
cana-5350	102	11	𝑧	𝑧	PROPN
cana-5350	102	12	,	,	PUNCT
cana-5350	102	13	𝑝	𝑝	NOUN
cana-5350	102	14	,	,	PUNCT
cana-5350	102	15	𝑢	𝑢	PROPN
cana-5350	102	16	,	,	PUNCT
cana-5350	102	17	𝑣	𝑣	NOUN
cana-5350	102	18	,	,	PUNCT
cana-5350	102	19	𝑤	𝑤	ADP
cana-5350	102	20	,	,	PUNCT
cana-5350	102	21	𝑟	𝑟	X
cana-5350	102	22	∈	∈	PROPN
cana-5350	102	23	𝑋	𝑋	PROPN
cana-5350	102	24	(	(	PUNCT
cana-5350	102	25	ii	ii	PROPN
cana-5350	102	26	)	)	PUNCT
cana-5350	102	27	𝑦	𝑦	NOUN
cana-5350	102	28	=	=	SYM
cana-5350	102	29	𝐵(𝑥	𝐵(𝑥	PROPN
cana-5350	102	30	,	,	PUNCT
cana-5350	102	31	𝑦	𝑦	NOUN
cana-5350	102	32	,	,	PUNCT
cana-5350	102	33	𝑧	𝑧	NOUN
cana-5350	102	34	,	,	PUNCT
cana-5350	102	35	𝑝	𝑝	NOUN
cana-5350	102	36	)	)	PUNCT
cana-5350	102	37	moreover	moreover	ADV
cana-5350	102	38	if	if	SCONJ
cana-5350	102	39	the	the	DET
cana-5350	102	40	pairs	pair	NOUN
cana-5350	102	41	(	(	PUNCT
cana-5350	102	42	𝐴	𝐴	PROPN
cana-5350	102	43	,	,	PUNCT
cana-5350	102	44	𝑆	𝑆	PROPN
cana-5350	102	45	)	)	PUNCT
cana-5350	102	46	and	and	CCONJ
cana-5350	102	47	(	(	PUNCT
cana-5350	102	48	𝐵	𝐵	PROPN
cana-5350	102	49	,	,	PUNCT
cana-5350	102	50	𝑇	𝑇	PROPN
cana-5350	102	51	)	)	PUNCT
cana-5350	102	52	are	be	AUX
cana-5350	102	53	owc	owc	NUM
cana-5350	102	54	,	,	PUNCT
cana-5350	102	55	then	then	ADV
cana-5350	102	56	there	there	PRON
cana-5350	102	57	exists	exist	VERB
cana-5350	102	58	a	a	DET
cana-5350	102	59	unique	unique	ADJ
cana-5350	102	60	point	point	NOUN
cana-5350	102	61	𝑥	𝑥	NOUN
cana-5350	102	62	in	in	ADP
cana-5350	102	63	𝑋	𝑋	NOUN
cana-5350	103	1	such	such	ADJ
cana-5350	103	2	that	that	SCONJ
cana-5350	103	3	𝐴(𝑥	𝐴(𝑥	NOUN
cana-5350	103	4	,	,	PUNCT
cana-5350	103	5	𝑥	𝑥	PRON
cana-5350	103	6	,	,	PUNCT
cana-5350	103	7	𝑥	𝑥	NOUN
cana-5350	103	8	,	,	PUNCT
cana-5350	103	9	𝑥	𝑥	NOUN
cana-5350	103	10	)	)	PUNCT
cana-5350	103	11	=	=	SYM
cana-5350	103	12	𝑇(𝑥	𝑇(𝑥	X
cana-5350	103	13	)	)	PUNCT
cana-5350	103	14	=	=	SYM
cana-5350	103	15	𝐵(𝑥	𝐵(𝑥	PROPN
cana-5350	103	16	,	,	PUNCT
cana-5350	103	17	𝑥	𝑥	PROPN
cana-5350	103	18	,	,	PUNCT
cana-5350	103	19	𝑥	𝑥	NOUN
cana-5350	103	20	,	,	PUNCT
cana-5350	103	21	𝑥	𝑥	NOUN
cana-5350	103	22	)	)	PUNCT
cana-5350	103	23	=	=	SYM
cana-5350	103	24	𝑆(𝑥	𝑆(𝑥	X
cana-5350	103	25	)	)	PUNCT
cana-5350	103	26	=	=	PUNCT
cana-5350	103	27	𝑥.	𝑥.	NOUN
cana-5350	103	28	theorem	theorem	VERB
cana-5350	103	29	:	:	PUNCT
cana-5350	103	30	3.3	3.3	NUM
cana-5350	103	31	let	let	VERB
cana-5350	103	32	(	(	PUNCT
cana-5350	103	33	𝑋	𝑋	PROPN
cana-5350	103	34	,	,	PUNCT
cana-5350	103	35	𝑀	𝑀	PROPN
cana-5350	103	36	,	,	PUNCT
cana-5350	103	37			PROPN
cana-5350	103	38	)	)	PUNCT
cana-5350	103	39	be	be	AUX
cana-5350	103	40	a	a	DET
cana-5350	103	41	fuzzy	fuzzy	ADJ
cana-5350	103	42	metric	metric	ADJ
cana-5350	103	43	space	space	NOUN
cana-5350	103	44	with	with	ADP
cana-5350	103	45	𝑡	𝑡	PROPN
cana-5350	103	46	∗	∗	NOUN
cana-5350	103	47	𝑡	𝑡	X
cana-5350	103	48	=	=	PUNCT
cana-5350	103	49	𝑡	𝑡	PROPN
cana-5350	103	50	for	for	ADP
cana-5350	103	51	all	all	DET
cana-5350	103	52	𝑡	𝑡	ADP
cana-5350	103	53	∈	∈	PROPN
cana-5350	104	1	[	[	X
cana-5350	104	2	0,1	0,1	NUM
cana-5350	104	3	]	]	PUNCT
cana-5350	104	4	.	.	PUNCT
cana-5350	105	1	let	let	VERB
cana-5350	105	2	𝐴	𝐴	PROPN
cana-5350	105	3	,	,	PUNCT
cana-5350	105	4	𝐵	𝐵	PROPN
cana-5350	105	5	:	:	PUNCT
cana-5350	105	6	𝑋	𝑋	NOUN
cana-5350	105	7	×	×	NOUN
cana-5350	105	8	𝑋	𝑋	PROPN
cana-5350	105	9	×	×	NOUN
cana-5350	105	10	𝑋	𝑋	NOUN
cana-5350	105	11	×	×	NOUN
cana-5350	105	12	𝑋	𝑋	PROPN
cana-5350	105	13	→	→	SYM
cana-5350	105	14	𝑋	𝑋	PROPN
cana-5350	105	15	and	and	CCONJ
cana-5350	105	16	𝑆	𝑆	PROPN
cana-5350	105	17	,	,	PUNCT
cana-5350	105	18	𝑇	𝑇	PROPN
cana-5350	105	19	:	:	PUNCT
cana-5350	105	20	𝑋	𝑋	PROPN
cana-5350	105	21	→	→	SYM
cana-5350	105	22	𝑋	𝑋	PROPN
cana-5350	105	23	be	be	VERB
cana-5350	105	24	four	four	NUM
cana-5350	105	25	self	self	NOUN
cana-5350	105	26	-	-	PUNCT
cana-5350	105	27	mappings	mapping	NOUN
cana-5350	105	28	satisfying	satisfy	VERB
cana-5350	105	29	the	the	DET
cana-5350	105	30	following	follow	VERB
cana-5350	105	31	conditions	condition	NOUN
cana-5350	105	32	:	:	PUNCT
cana-5350	105	33	(	(	PUNCT
cana-5350	105	34	i	i	NOUN
cana-5350	105	35	)	)	PUNCT
cana-5350	105	36	𝑀(𝐴(𝑥	𝑀(𝐴(𝑥	NOUN
cana-5350	105	37	,	,	PUNCT
cana-5350	105	38	𝑦	𝑦	NOUN
cana-5350	105	39	,	,	PUNCT
cana-5350	105	40	𝑧	𝑧	NOUN
cana-5350	105	41	,	,	PUNCT
cana-5350	105	42	𝑝	𝑝	NOUN
cana-5350	105	43	)	)	PUNCT
cana-5350	105	44	,	,	PUNCT
cana-5350	105	45	𝐵(𝑢	𝐵(𝑢	PROPN
cana-5350	105	46	,	,	PUNCT
cana-5350	105	47	𝑣	𝑣	NOUN
cana-5350	105	48	,	,	PUNCT
cana-5350	105	49	𝑤	𝑤	ADP
cana-5350	105	50	,	,	PUNCT
cana-5350	105	51	𝑟	𝑟	NOUN
cana-5350	105	52	)	)	PUNCT
cana-5350	105	53	,	,	PUNCT
cana-5350	105	54	𝑞𝑡	𝑞𝑡	PRON
cana-5350	105	55	)	)	PUNCT
cana-5350	105	56	≥	≥	PROPN
cana-5350	105	57	𝑚𝑖𝑛	𝑚𝑖𝑛	NOUN
cana-5350	105	58	{	{	PUNCT
cana-5350	105	59	𝑀(𝑆𝑥	𝑀(𝑆𝑥	ADJ
cana-5350	105	60	,	,	PUNCT
cana-5350	105	61	𝑇𝑢	𝑇𝑢	PROPN
cana-5350	105	62	,	,	PUNCT
cana-5350	105	63	𝑡	𝑡	PROPN
cana-5350	105	64	)	)	PUNCT
cana-5350	105	65	,	,	PUNCT
cana-5350	105	66	(	(	PUNCT
cana-5350	105	67	1+𝑀(𝐴(𝑥,𝑦,𝑧,𝑝),𝑆𝑥,𝑡	1+𝑀(𝐴(𝑥,𝑦,𝑧,𝑝),𝑆𝑥,𝑡	NUM
cana-5350	105	68	)	)	PUNCT
cana-5350	105	69	1+𝑀(𝐵(𝑢,𝑣,𝑤,𝑟),𝑇𝑢,𝑡	1+𝑀(𝐵(𝑢,𝑣,𝑤,𝑟),𝑇𝑢,𝑡	NUM
cana-5350	105	70	)	)	PUNCT
cana-5350	105	71	)	)	PUNCT
cana-5350	105	72	,	,	PUNCT
cana-5350	105	73	𝑀(𝐴(𝑥,𝑦,𝑧,𝑝),𝑆𝑥,𝑡	𝑀(𝐴(𝑥,𝑦,𝑧,𝑝),𝑆𝑥,𝑡	NOUN
cana-5350	105	74	)	)	PUNCT
cana-5350	105	75	𝑀(𝐵(𝑢,𝑣,𝑤,𝑟),𝑇𝑢,𝑡	𝑀(𝐵(𝑢,𝑣,𝑤,𝑟),𝑇𝑢,𝑡	NUM
cana-5350	105	76	)	)	PUNCT
cana-5350	105	77	}	}	PUNCT
cana-5350	105	78	for	for	ADP
cana-5350	105	79	all	all	DET
cana-5350	105	80	𝑥	𝑥	PROPN
cana-5350	105	81	,	,	PUNCT
cana-5350	105	82	𝑦	𝑦	NOUN
cana-5350	105	83	,	,	PUNCT
cana-5350	105	84	𝑧	𝑧	PROPN
cana-5350	105	85	,	,	PUNCT
cana-5350	105	86	𝑝	𝑝	NOUN
cana-5350	105	87	,	,	PUNCT
cana-5350	105	88	𝑢	𝑢	PROPN
cana-5350	105	89	,	,	PUNCT
cana-5350	105	90	𝑣	𝑣	NOUN
cana-5350	105	91	,	,	PUNCT
cana-5350	105	92	𝑤	𝑤	ADP
cana-5350	105	93	,	,	PUNCT
cana-5350	105	94	𝑟	𝑟	X
cana-5350	105	95	∈	∈	PROPN
cana-5350	105	96	𝑋	𝑋	PROPN
cana-5350	105	97	(	(	PUNCT
cana-5350	105	98	ii	ii	PROPN
cana-5350	105	99	)	)	PUNCT
cana-5350	105	100	𝑦	𝑦	NOUN
cana-5350	105	101	=	=	SYM
cana-5350	105	102	𝐵(𝑥	𝐵(𝑥	PROPN
cana-5350	105	103	,	,	PUNCT
cana-5350	105	104	𝑦	𝑦	NOUN
cana-5350	105	105	,	,	PUNCT
cana-5350	105	106	𝑧	𝑧	NOUN
cana-5350	105	107	,	,	PUNCT
cana-5350	105	108	𝑝	𝑝	NOUN
cana-5350	105	109	)	)	PUNCT
cana-5350	105	110	communications	communication	NOUN
cana-5350	105	111	on	on	ADP
cana-5350	105	112	applied	apply	VERB
cana-5350	105	113	nonlinear	nonlinear	ADJ
cana-5350	105	114	analysis	analysis	NOUN
cana-5350	105	115	issn	issn	NOUN
cana-5350	105	116	:	:	PUNCT
cana-5350	105	117	1074	1074	NUM
cana-5350	105	118	-	-	PUNCT
cana-5350	105	119	133x	133x	NUM
cana-5350	105	120	vol	vol	VERB
cana-5350	105	121	32	32	NUM
cana-5350	105	122	no	no	NOUN
cana-5350	105	123	.	.	PUNCT
cana-5350	106	1	10s	10	NOUN
cana-5350	106	2	(	(	PUNCT
cana-5350	106	3	2025	2025	NUM
cana-5350	106	4	)	)	PUNCT
cana-5350	106	5	1802	1802	NUM
cana-5350	106	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5350	107	1	moreover	moreover	ADV
cana-5350	107	2	if	if	SCONJ
cana-5350	107	3	the	the	DET
cana-5350	107	4	pairs	pair	NOUN
cana-5350	107	5	(	(	PUNCT
cana-5350	107	6	𝐴	𝐴	PROPN
cana-5350	107	7	,	,	PUNCT
cana-5350	107	8	𝑆	𝑆	PROPN
cana-5350	107	9	)	)	PUNCT
cana-5350	107	10	and	and	CCONJ
cana-5350	107	11	(	(	PUNCT
cana-5350	107	12	𝐵	𝐵	PROPN
cana-5350	107	13	,	,	PUNCT
cana-5350	107	14	𝑇	𝑇	PROPN
cana-5350	107	15	)	)	PUNCT
cana-5350	107	16	are	be	AUX
cana-5350	107	17	owc	owc	NUM
cana-5350	107	18	,	,	PUNCT
cana-5350	107	19	then	then	ADV
cana-5350	107	20	there	there	PRON
cana-5350	107	21	exists	exist	VERB
cana-5350	107	22	a	a	DET
cana-5350	107	23	unique	unique	ADJ
cana-5350	107	24	point	point	NOUN
cana-5350	107	25	𝑥	𝑥	NOUN
cana-5350	107	26	in	in	ADP
cana-5350	107	27	𝑋	𝑋	NOUN
cana-5350	107	28	such	such	ADJ
cana-5350	107	29	that	that	SCONJ
cana-5350	107	30	𝐴(𝑥	𝐴(𝑥	NOUN
cana-5350	107	31	,	,	PUNCT
cana-5350	107	32	𝑥	𝑥	PRON
cana-5350	107	33	,	,	PUNCT
cana-5350	107	34	𝑥	𝑥	NOUN
cana-5350	107	35	,	,	PUNCT
cana-5350	107	36	𝑥	𝑥	NOUN
cana-5350	107	37	)	)	PUNCT
cana-5350	107	38	=	=	SYM
cana-5350	107	39	𝑇(𝑥	𝑇(𝑥	X
cana-5350	107	40	)	)	PUNCT
cana-5350	107	41	=	=	SYM
cana-5350	108	1	𝐵(𝑥	𝐵(𝑥	PROPN
cana-5350	108	2	,	,	PUNCT
cana-5350	108	3	𝑥	𝑥	PROPN
cana-5350	108	4	,	,	PUNCT
cana-5350	108	5	𝑥	𝑥	NOUN
cana-5350	108	6	,	,	PUNCT
cana-5350	108	7	𝑥	𝑥	NOUN
cana-5350	108	8	)	)	PUNCT
cana-5350	108	9	=	=	SYM
cana-5350	108	10	𝑆(𝑥	𝑆(𝑥	X
cana-5350	108	11	)	)	PUNCT
cana-5350	108	12	=	=	PUNCT
cana-5350	109	1	𝑥.	𝑥.	ADJ
cana-5350	109	2	references	reference	NOUN
cana-5350	109	3	[	[	X
cana-5350	109	4	1	1	NUM
cana-5350	109	5	]	]	X
cana-5350	109	6	h.	h.	PROPN
cana-5350	109	7	aydi	aydi	PROPN
cana-5350	109	8	,	,	PUNCT
cana-5350	109	9	e.	e.	PROPN
cana-5350	109	10	karapınar	karapınar	PROPN
cana-5350	109	11	,	,	PUNCT
cana-5350	109	12	and	and	CCONJ
cana-5350	109	13	i̇.	i̇.	VERB
cana-5350	109	14	savaş	savaş	ADJ
cana-5350	109	15	yüce	yüce	NOUN
cana-5350	109	16	,	,	PUNCT
cana-5350	109	17	"	"	PUNCT
cana-5350	109	18	quadruple	quadruple	ADJ
cana-5350	109	19	fixed	fix	VERB
cana-5350	109	20	point	point	NOUN
cana-5350	109	21	theorems	theorem	NOUN
cana-5350	109	22	in	in	ADP
cana-5350	109	23	partially	partially	ADV
cana-5350	109	24	ordered	order	VERB
cana-5350	109	25	metric	metric	ADJ
cana-5350	109	26	spaces	space	NOUN
cana-5350	109	27	depending	depend	VERB
cana-5350	109	28	on	on	ADP
cana-5350	109	29	another	another	DET
cana-5350	109	30	function	function	NOUN
cana-5350	109	31	,	,	PUNCT
cana-5350	109	32	"	"	PUNCT
cana-5350	109	33	isrn	isrn	NOUN
cana-5350	109	34	applied	apply	VERB
cana-5350	109	35	mathematics	mathematic	NOUN
cana-5350	109	36	,	,	PUNCT
cana-5350	109	37	vol	vol	NOUN
cana-5350	109	38	.	.	PROPN
cana-5350	109	39	2012	2012	NUM
cana-5350	109	40	,	,	PUNCT
cana-5350	109	41	article	article	NOUN
cana-5350	109	42	i	i	PROPN
cana-5350	109	43	d	d	PROPN
cana-5350	109	44	539125	539125	NUM
cana-5350	109	45	,	,	PUNCT
cana-5350	109	46	16	16	NUM
cana-5350	109	47	pages	page	NOUN
cana-5350	109	48	,	,	PUNCT
cana-5350	109	49	2012	2012	NUM
cana-5350	109	50	.	.	PUNCT
cana-5350	110	1	[	[	X
cana-5350	110	2	2	2	X
cana-5350	110	3	]	]	PUNCT
cana-5350	110	4	t.	t.	NOUN
cana-5350	110	5	g.	g.	PROPN
cana-5350	110	6	bhaskar	bhaskar	PROPN
cana-5350	110	7	and	and	CCONJ
cana-5350	110	8	v.	v.	ADP
cana-5350	110	9	lakshmikantham	lakshmikantham	NOUN
cana-5350	110	10	,	,	PUNCT
cana-5350	110	11	"	"	PUNCT
cana-5350	110	12	fixed	fixed	ADJ
cana-5350	110	13	point	point	NOUN
cana-5350	110	14	theorems	theorem	NOUN
cana-5350	110	15	in	in	ADP
cana-5350	110	16	partially	partially	ADV
cana-5350	110	17	ordered	order	VERB
cana-5350	110	18	metric	metric	ADJ
cana-5350	110	19	spaces	space	NOUN
cana-5350	110	20	and	and	CCONJ
cana-5350	110	21	applications	application	NOUN
cana-5350	110	22	,	,	PUNCT
cana-5350	110	23	"	"	PUNCT
cana-5350	110	24	nonlinear	nonlinear	ADJ
cana-5350	110	25	analysis	analysis	NOUN
cana-5350	110	26	:	:	PUNCT
cana-5350	110	27	theory	theory	NOUN
cana-5350	110	28	,	,	PUNCT
cana-5350	110	29	methods	method	NOUN
cana-5350	110	30	and	and	CCONJ
cana-5350	110	31	applications	application	NOUN
cana-5350	110	32	,	,	PUNCT
cana-5350	110	33	vol	vol	NOUN
cana-5350	110	34	.	.	PROPN
cana-5350	111	1	65	65	NUM
cana-5350	111	2	,	,	PUNCT
cana-5350	111	3	no	no	INTJ
cana-5350	111	4	.	.	NOUN
cana-5350	111	5	7	7	NUM
cana-5350	111	6	,	,	PUNCT
cana-5350	111	7	pp	pp	ADJ
cana-5350	111	8	.	.	PUNCT
cana-5350	112	1	1379	1379	NUM
cana-5350	112	2	–	–	PUNCT
cana-5350	112	3	1393	1393	NUM
cana-5350	112	4	,	,	PUNCT
cana-5350	112	5	2006	2006	NUM
cana-5350	112	6	.	.	PUNCT
cana-5350	113	1	[	[	X
cana-5350	113	2	3	3	X
cana-5350	113	3	]	]	X
cana-5350	113	4	j.	j.	PROPN
cana-5350	113	5	chen	chen	PROPN
cana-5350	113	6	and	and	CCONJ
cana-5350	113	7	x.	x.	PROPN
cana-5350	113	8	huang	huang	PROPN
cana-5350	113	9	,	,	PUNCT
cana-5350	113	10	"	"	PUNCT
cana-5350	113	11	quadruple	quadruple	ADJ
cana-5350	113	12	fixed	fix	VERB
cana-5350	113	13	point	point	NOUN
cana-5350	113	14	theorems	theorem	NOUN
cana-5350	113	15	under	under	ADP
cana-5350	113	16	(	(	PUNCT
cana-5350	113	17	ϕ	ϕ	NOUN
cana-5350	113	18	,	,	PUNCT
cana-5350	113	19	ψ)-contractive	ψ)-contractive	ADJ
cana-5350	113	20	conditions	condition	NOUN
cana-5350	113	21	in	in	ADP
cana-5350	113	22	partially	partially	ADV
cana-5350	113	23	ordered	order	VERB
cana-5350	113	24	g	g	NOUN
cana-5350	113	25	-	-	PUNCT
cana-5350	113	26	metric	metric	ADJ
cana-5350	113	27	spaces	space	NOUN
cana-5350	113	28	,	,	PUNCT
cana-5350	113	29	"	"	PUNCT
cana-5350	113	30	journal	journal	NOUN
cana-5350	113	31	of	of	ADP
cana-5350	113	32	nonlinear	nonlinear	ADJ
cana-5350	113	33	science	science	NOUN
cana-5350	113	34	and	and	CCONJ
cana-5350	113	35	applications	application	NOUN
cana-5350	113	36	,	,	PUNCT
cana-5350	113	37	vol	vol	NOUN
cana-5350	113	38	.	.	PROPN
cana-5350	113	39	8	8	NUM
cana-5350	113	40	,	,	PUNCT
cana-5350	113	41	pp	pp	ADJ
cana-5350	113	42	.	.	PUNCT
cana-5350	113	43	285	285	NUM
cana-5350	113	44	–	–	PUNCT
cana-5350	113	45	300	300	NUM
cana-5350	113	46	,	,	PUNCT
cana-5350	113	47	2015	2015	NUM
cana-5350	113	48	.	.	PUNCT
cana-5350	114	1	[	[	X
cana-5350	114	2	4	4	X
cana-5350	114	3	]	]	PUNCT
cana-5350	114	4	j.	j.	PROPN
cana-5350	114	5	x.	x.	PROPN
cana-5350	114	6	fang	fang	PROPN
cana-5350	114	7	,	,	PUNCT
cana-5350	114	8	"	"	PUNCT
cana-5350	114	9	common	common	ADJ
cana-5350	114	10	fixed	fix	VERB
cana-5350	114	11	point	point	NOUN
cana-5350	114	12	theorems	theorem	NOUN
cana-5350	114	13	of	of	ADP
cana-5350	114	14	compatible	compatible	ADJ
cana-5350	114	15	and	and	CCONJ
cana-5350	114	16	weakly	weakly	ADJ
cana-5350	114	17	compatible	compatible	ADJ
cana-5350	114	18	maps	map	NOUN
cana-5350	114	19	in	in	ADP
cana-5350	114	20	menger	menger	PROPN
cana-5350	114	21	spaces	space	NOUN
cana-5350	114	22	,	,	PUNCT
cana-5350	114	23	"	"	PUNCT
cana-5350	114	24	nonlinear	nonlinear	ADJ
cana-5350	114	25	analysis	analysis	NOUN
cana-5350	114	26	:	:	PUNCT
cana-5350	114	27	theory	theory	NOUN
cana-5350	114	28	,	,	PUNCT
cana-5350	114	29	methods	method	NOUN
cana-5350	114	30	and	and	CCONJ
cana-5350	114	31	applications	application	NOUN
cana-5350	114	32	,	,	PUNCT
cana-5350	114	33	vol	vol	NOUN
cana-5350	114	34	.	.	PROPN
cana-5350	114	35	71	71	NUM
cana-5350	114	36	,	,	PUNCT
cana-5350	114	37	no	no	INTJ
cana-5350	114	38	.	.	PUNCT
cana-5350	115	1	5–6	5–6	NUM
cana-5350	115	2	,	,	PUNCT
cana-5350	115	3	pp	pp	ADJ
cana-5350	115	4	.	.	PUNCT
cana-5350	116	1	1833–1843	1833–1843	NUM
cana-5350	116	2	,	,	PUNCT
cana-5350	116	3	2009	2009	NUM
cana-5350	116	4	.	.	PUNCT
cana-5350	117	1	[	[	X
cana-5350	117	2	5	5	NUM
cana-5350	117	3	]	]	PUNCT
cana-5350	117	4	a.	a.	NOUN
cana-5350	117	5	george	george	PROPN
cana-5350	117	6	and	and	CCONJ
cana-5350	117	7	p.	p.	PROPN
cana-5350	117	8	veeramani	veeramani	PROPN
cana-5350	117	9	,	,	PUNCT
cana-5350	117	10	"	"	PUNCT
cana-5350	117	11	on	on	ADP
cana-5350	117	12	some	some	DET
cana-5350	117	13	results	result	NOUN
cana-5350	117	14	in	in	ADP
cana-5350	117	15	fuzzy	fuzzy	ADJ
cana-5350	117	16	metric	metric	ADJ
cana-5350	117	17	spaces	space	NOUN
cana-5350	117	18	,	,	PUNCT
cana-5350	117	19	"	"	PUNCT
cana-5350	117	20	fuzzy	fuzzy	ADJ
cana-5350	117	21	sets	set	NOUN
cana-5350	117	22	and	and	CCONJ
cana-5350	117	23	systems	system	NOUN
cana-5350	117	24	,	,	PUNCT
cana-5350	117	25	vol	vol	NOUN
cana-5350	117	26	.	.	PROPN
cana-5350	117	27	64	64	NUM
cana-5350	117	28	,	,	PUNCT
cana-5350	117	29	pp	pp	ADJ
cana-5350	117	30	.	.	PUNCT
cana-5350	118	1	395–399	395–399	NUM
cana-5350	118	2	,	,	PUNCT
cana-5350	118	3	1994	1994	NUM
cana-5350	118	4	.	.	PUNCT
cana-5350	119	1	[	[	X
cana-5350	119	2	6	6	NUM
cana-5350	119	3	]	]	PUNCT
cana-5350	119	4	g.	g.	PROPN
cana-5350	119	5	jungck	jungck	PROPN
cana-5350	119	6	,	,	PUNCT
cana-5350	119	7	"	"	PUNCT
cana-5350	119	8	compatible	compatible	ADJ
cana-5350	119	9	mappings	mapping	NOUN
cana-5350	119	10	and	and	CCONJ
cana-5350	119	11	common	common	ADJ
cana-5350	119	12	fixed	fix	VERB
cana-5350	119	13	points	point	NOUN
cana-5350	119	14	,	,	PUNCT
cana-5350	119	15	"	"	PUNCT
cana-5350	119	16	international	international	ADJ
cana-5350	119	17	journal	journal	NOUN
cana-5350	119	18	of	of	ADP
cana-5350	119	19	mathematics	mathematics	PROPN
cana-5350	119	20	and	and	CCONJ
cana-5350	119	21	mathematical	mathematical	ADJ
cana-5350	119	22	sciences	science	NOUN
cana-5350	119	23	,	,	PUNCT
cana-5350	119	24	vol	vol	NOUN
cana-5350	119	25	.	.	NOUN
cana-5350	119	26	9	9	NUM
cana-5350	119	27	,	,	PUNCT
cana-5350	119	28	no	no	INTJ
cana-5350	119	29	.	.	NOUN
cana-5350	119	30	4	4	NUM
cana-5350	119	31	,	,	PUNCT
cana-5350	119	32	pp	pp	ADJ
cana-5350	119	33	.	.	PUNCT
cana-5350	120	1	771–779	771–779	NUM
cana-5350	120	2	,	,	PUNCT
cana-5350	120	3	1986	1986	NUM
cana-5350	120	4	.	.	PUNCT
cana-5350	121	1	[	[	X
cana-5350	121	2	7	7	X
cana-5350	121	3	]	]	X
cana-5350	121	4	g.	g.	PROPN
cana-5350	121	5	jungck	jungck	PROPN
cana-5350	121	6	,	,	PUNCT
cana-5350	121	7	"	"	PUNCT
cana-5350	121	8	common	common	ADJ
cana-5350	121	9	fixed	fix	VERB
cana-5350	121	10	points	point	NOUN
cana-5350	121	11	for	for	ADP
cana-5350	121	12	non	non	ADJ
cana-5350	121	13	-	-	ADJ
cana-5350	121	14	continuous	continuous	ADJ
cana-5350	121	15	nonself	nonself	NOUN
cana-5350	121	16	maps	map	NOUN
cana-5350	121	17	on	on	ADP
cana-5350	121	18	nonmetric	nonmetric	ADJ
cana-5350	121	19	spaces	space	NOUN
cana-5350	121	20	,	,	PUNCT
cana-5350	121	21	"	"	PUNCT
cana-5350	121	22	far	far	PROPN
cana-5350	121	23	east	east	PROPN
cana-5350	121	24	journal	journal	PROPN
cana-5350	121	25	of	of	ADP
cana-5350	121	26	mathematical	mathematical	ADJ
cana-5350	121	27	sciences	sciences	PROPN
cana-5350	121	28	,	,	PUNCT
cana-5350	121	29	vol	vol	NOUN
cana-5350	121	30	.	.	PROPN
cana-5350	121	31	4	4	NUM
cana-5350	121	32	,	,	PUNCT
cana-5350	121	33	no	no	INTJ
cana-5350	121	34	.	.	NOUN
cana-5350	121	35	2	2	NUM
cana-5350	121	36	,	,	PUNCT
cana-5350	121	37	pp	pp	ADJ
cana-5350	121	38	.	.	PUNCT
cana-5350	122	1	199–215	199–215	NUM
cana-5350	122	2	,	,	PUNCT
cana-5350	122	3	1996	1996	NUM
cana-5350	122	4	.	.	PUNCT
cana-5350	123	1	[	[	X
cana-5350	123	2	8	8	NUM
cana-5350	123	3	]	]	X
cana-5350	123	4	g.	g.	PROPN
cana-5350	123	5	jungck	jungck	PROPN
cana-5350	123	6	and	and	CCONJ
cana-5350	123	7	b.	b.	PROPN
cana-5350	123	8	e.	e.	PROPN
cana-5350	123	9	rhoades	rhoades	PROPN
cana-5350	123	10	,	,	PUNCT
cana-5350	123	11	"	"	PUNCT
cana-5350	123	12	fixed	fix	VERB
cana-5350	123	13	point	point	NOUN
cana-5350	123	14	theorems	theorem	NOUN
cana-5350	123	15	for	for	ADP
cana-5350	123	16	occasionally	occasionally	ADV
cana-5350	123	17	weakly	weakly	ADJ
cana-5350	123	18	compatible	compatible	ADJ
cana-5350	123	19	mappings	mapping	NOUN
cana-5350	123	20	,	,	PUNCT
cana-5350	123	21	"	"	PUNCT
cana-5350	123	22	fixed	fix	VERB
cana-5350	123	23	point	point	NOUN
cana-5350	123	24	theory	theory	NOUN
cana-5350	123	25	,	,	PUNCT
cana-5350	123	26	vol	vol	NOUN
cana-5350	123	27	.	.	PROPN
cana-5350	124	1	7	7	NUM
cana-5350	124	2	,	,	PUNCT
cana-5350	124	3	no	no	INTJ
cana-5350	124	4	.	.	NOUN
cana-5350	124	5	2	2	NUM
cana-5350	124	6	,	,	PUNCT
cana-5350	124	7	pp	pp	ADJ
cana-5350	124	8	.	.	PUNCT
cana-5350	125	1	287–296	287–296	NUM
cana-5350	125	2	,	,	PUNCT
cana-5350	125	3	2006	2006	NUM
cana-5350	125	4	.	.	PUNCT
cana-5350	126	1	[	[	X
cana-5350	126	2	9	9	NUM
cana-5350	126	3	]	]	PUNCT
cana-5350	126	4	e.	e.	PROPN
cana-5350	126	5	karapınar	karapınar	PROPN
cana-5350	126	6	and	and	CCONJ
cana-5350	126	7	n.	n.	PROPN
cana-5350	126	8	v.	v.	PROPN
cana-5350	126	9	luong	luong	PROPN
cana-5350	126	10	,	,	PUNCT
cana-5350	126	11	"	"	PUNCT
cana-5350	126	12	quadruple	quadruple	ADJ
cana-5350	126	13	fixed	fix	VERB
cana-5350	126	14	point	point	NOUN
cana-5350	126	15	theorems	theorem	NOUN
cana-5350	126	16	for	for	ADP
cana-5350	126	17	nonlinear	nonlinear	ADJ
cana-5350	126	18	contractions	contraction	NOUN
cana-5350	126	19	,	,	PUNCT
cana-5350	126	20	"	"	PUNCT
cana-5350	126	21	computers	computer	NOUN
cana-5350	126	22	and	and	CCONJ
cana-5350	126	23	mathematics	mathematic	NOUN
cana-5350	126	24	with	with	ADP
cana-5350	126	25	applications	application	NOUN
cana-5350	126	26	,	,	PUNCT
cana-5350	126	27	vol	vol	NOUN
cana-5350	126	28	.	.	PROPN
cana-5350	126	29	64	64	NUM
cana-5350	126	30	,	,	PUNCT
cana-5350	126	31	pp	pp	ADJ
cana-5350	126	32	.	.	PUNCT
cana-5350	127	1	1839–1848	1839–1848	NUM
cana-5350	127	2	,	,	PUNCT
cana-5350	127	3	2012	2012	NUM
cana-5350	127	4	.	.	PUNCT
cana-5350	128	1	[	[	X
cana-5350	128	2	10	10	NUM
cana-5350	128	3	]	]	X
cana-5350	128	4	e.	e.	PROPN
cana-5350	128	5	karapınar	karapınar	PROPN
cana-5350	128	6	and	and	CCONJ
cana-5350	128	7	k.	k.	PROPN
cana-5350	128	8	tas	tas	PROPN
cana-5350	128	9	,	,	PUNCT
cana-5350	128	10	"	"	PUNCT
cana-5350	128	11	quadruple	quadruple	ADJ
cana-5350	128	12	fixed	fix	VERB
cana-5350	128	13	point	point	NOUN
cana-5350	128	14	theorems	theorem	NOUN
cana-5350	128	15	for	for	ADP
cana-5350	128	16	nonlinear	nonlinear	ADJ
cana-5350	128	17	contractions	contraction	NOUN
cana-5350	128	18	on	on	ADP
cana-5350	128	19	partial	partial	ADJ
cana-5350	128	20	metric	metric	ADJ
cana-5350	128	21	spaces	space	NOUN
cana-5350	128	22	,	,	PUNCT
cana-5350	128	23	"	"	PUNCT
cana-5350	128	24	applied	apply	VERB
cana-5350	128	25	general	general	ADJ
cana-5350	128	26	topology	topology	NOUN
cana-5350	128	27	,	,	PUNCT
cana-5350	128	28	vol	vol	NOUN
cana-5350	128	29	.	.	PROPN
cana-5350	128	30	15	15	NUM
cana-5350	128	31	,	,	PUNCT
cana-5350	128	32	no	no	INTJ
cana-5350	128	33	.	.	NOUN
cana-5350	128	34	1	1	NUM
cana-5350	128	35	,	,	PUNCT
cana-5350	128	36	pp	pp	ADJ
cana-5350	128	37	.	.	PUNCT
cana-5350	129	1	11–24	11–24	NUM
cana-5350	129	2	,	,	PUNCT
cana-5350	129	3	2014	2014	NUM
cana-5350	129	4	.	.	PUNCT
cana-5350	130	1	[	[	X
cana-5350	130	2	11	11	NUM
cana-5350	130	3	]	]	X
cana-5350	130	4	o.	o.	NOUN
cana-5350	130	5	kramosil	kramosil	PROPN
cana-5350	130	6	and	and	CCONJ
cana-5350	130	7	j.	j.	PROPN
cana-5350	130	8	michalek	michalek	PROPN
cana-5350	130	9	,	,	PUNCT
cana-5350	130	10	"	"	PUNCT
cana-5350	130	11	fuzzy	fuzzy	ADJ
cana-5350	130	12	metric	metric	ADJ
cana-5350	130	13	and	and	CCONJ
cana-5350	130	14	statistical	statistical	ADJ
cana-5350	130	15	metric	metric	ADJ
cana-5350	130	16	spaces	space	NOUN
cana-5350	130	17	,	,	PUNCT
cana-5350	130	18	"	"	PUNCT
cana-5350	130	19	kybernetika	kybernetika	NOUN
cana-5350	130	20	,	,	PUNCT
cana-5350	130	21	vol	vol	NOUN
cana-5350	130	22	.	.	PROPN
cana-5350	130	23	11	11	NUM
cana-5350	130	24	,	,	PUNCT
cana-5350	130	25	pp	pp	ADJ
cana-5350	130	26	.	.	PUNCT
cana-5350	131	1	326–334	326–334	NUM
cana-5350	131	2	,	,	PUNCT
cana-5350	131	3	1975	1975	NUM
cana-5350	131	4	.	.	PUNCT
cana-5350	132	1	[	[	X
cana-5350	132	2	13	13	NUM
cana-5350	132	3	]	]	PUNCT
cana-5350	132	4	s.	s.	PROPN
cana-5350	132	5	sessa	sessa	PROPN
cana-5350	132	6	,	,	PUNCT
cana-5350	132	7	"	"	PUNCT
cana-5350	132	8	on	on	ADP
cana-5350	132	9	a	a	DET
cana-5350	132	10	weak	weak	ADJ
cana-5350	132	11	commutativity	commutativity	NOUN
cana-5350	132	12	condition	condition	NOUN
cana-5350	132	13	of	of	ADP
cana-5350	132	14	mappings	mapping	NOUN
cana-5350	132	15	in	in	ADP
cana-5350	132	16	fixed	fix	VERB
cana-5350	132	17	point	point	NOUN
cana-5350	132	18	considerations	consideration	NOUN
cana-5350	132	19	,	,	PUNCT
cana-5350	132	20	"	"	PUNCT
cana-5350	132	21	publications	publication	NOUN
cana-5350	132	22	de	de	X
cana-5350	132	23	l’institute	l’institute	X
cana-5350	132	24	mathématique	mathématique	NOUN
cana-5350	132	25	,	,	PUNCT
cana-5350	132	26	vol	vol	NOUN
cana-5350	132	27	.	.	PROPN
cana-5350	132	28	32	32	NUM
cana-5350	132	29	,	,	PUNCT
cana-5350	132	30	no	no	INTJ
cana-5350	132	31	.	.	NOUN
cana-5350	132	32	46	46	NUM
cana-5350	132	33	,	,	PUNCT
cana-5350	132	34	pp	pp	ADJ
cana-5350	132	35	.	.	PUNCT
cana-5350	133	1	149–153	149–153	NUM
cana-5350	133	2	,	,	PUNCT
cana-5350	133	3	1982	1982	NUM
cana-5350	133	4	.	.	PUNCT
cana-5350	134	1	[	[	X
cana-5350	134	2	14	14	NUM
cana-5350	134	3	]	]	X
cana-5350	134	4	l.	l.	PROPN
cana-5350	134	5	a.	a.	PROPN
cana-5350	134	6	zadeh	zadeh	PROPN
cana-5350	134	7	,	,	PUNCT
cana-5350	134	8	"	"	PUNCT
cana-5350	134	9	fuzzy	fuzzy	ADJ
cana-5350	134	10	sets	set	NOUN
cana-5350	134	11	,	,	PUNCT
cana-5350	134	12	"	"	PUNCT
cana-5350	134	13	information	information	NOUN
cana-5350	134	14	and	and	CCONJ
cana-5350	134	15	control	control	NOUN
cana-5350	134	16	,	,	PUNCT
cana-5350	134	17	vol	vol	NOUN
cana-5350	134	18	.	.	PROPN
cana-5350	134	19	8	8	NUM
cana-5350	134	20	,	,	PUNCT
cana-5350	134	21	pp	pp	ADJ
cana-5350	134	22	.	.	PUNCT
cana-5350	135	1	338–353	338–353	NUM
cana-5350	135	2	,	,	PUNCT
cana-5350	135	3	1965	1965	NUM
cana-5350	135	4	.	.	PUNCT