id	sid	tid	token	lemma	pos
cana-2015	1	1	communications	communication	NOUN
cana-2015	1	2	on	on	ADP
cana-2015	1	3	applied	apply	VERB
cana-2015	1	4	nonlinear	nonlinear	ADJ
cana-2015	1	5	analysis	analysis	NOUN
cana-2015	1	6	issn	issn	NOUN
cana-2015	1	7	:	:	PUNCT
cana-2015	1	8	1074	1074	NUM
cana-2015	1	9	-	-	PUNCT
cana-2015	1	10	133x	133x	NUM
cana-2015	1	11	vol	vol	NOUN
cana-2015	1	12	32	32	NUM
cana-2015	1	13	no	no	NOUN
cana-2015	1	14	.	.	NOUN
cana-2015	1	15	3	3	NUM
cana-2015	1	16	(	(	PUNCT
cana-2015	1	17	2025	2025	NUM
cana-2015	1	18	)	)	PUNCT
cana-2015	1	19	new	new	ADJ
cana-2015	1	20	algebraic	algebraic	ADJ
cana-2015	1	21	structures	structure	NOUN
cana-2015	1	22	such	such	ADJ
cana-2015	1	23	as	as	ADP
cana-2015	1	24	q	q	ADJ
cana-2015	1	25	-	-	PUNCT
cana-2015	1	26	rung	rung	ADJ
cana-2015	1	27	interval	interval	NOUN
cana-2015	1	28	-	-	PUNCT
cana-2015	1	29	valued	value	VERB
cana-2015	1	30	intuitionistic	intuitionistic	ADJ
cana-2015	1	31	fuzzy	fuzzy	ADJ
cana-2015	1	32	set	set	NOUN
cana-2015	1	33	applied	apply	VERB
cana-2015	1	34	to	to	ADP
cana-2015	1	35	logarithm	logarithm	NOUN
cana-2015	1	36	operator	operator	NOUN
cana-2015	1	37	and	and	CCONJ
cana-2015	1	38	its	its	PRON
cana-2015	1	39	extension	extension	NOUN
cana-2015	1	40	g.	g.	PROPN
cana-2015	1	41	shanmugam1	shanmugam1	PROPN
cana-2015	1	42	,	,	PUNCT
cana-2015	1	43	m.	m.	NOUN
cana-2015	1	44	palanikumar2	palanikumar2	PROPN
cana-2015	1	45	,	,	PUNCT
cana-2015	1	46	aiyared	aiyare	VERB
cana-2015	1	47	iampan3,∗	iampan3,∗	ADJ
cana-2015	1	48	1,2department	1,2department	NUM
cana-2015	1	49	of	of	ADP
cana-2015	1	50	mathematics	mathematic	NOUN
cana-2015	1	51	,	,	PUNCT
cana-2015	1	52	saveetha	saveetha	PROPN
cana-2015	1	53	school	school	PROPN
cana-2015	1	54	of	of	ADP
cana-2015	1	55	engineering	engineering	PROPN
cana-2015	1	56	,	,	PUNCT
cana-2015	1	57	saveetha	saveetha	PROPN
cana-2015	1	58	institute	institute	PROPN
cana-2015	1	59	of	of	ADP
cana-2015	1	60	medical	medical	ADJ
cana-2015	1	61	and	and	CCONJ
cana-2015	1	62	technical	technical	ADJ
cana-2015	1	63	sciences	science	NOUN
cana-2015	1	64	,	,	PUNCT
cana-2015	1	65	chennai-602105	chennai-602105	ADJ
cana-2015	1	66	,	,	PUNCT
cana-2015	1	67	india	india	PROPN
cana-2015	1	68	.	.	PUNCT
cana-2015	2	1	3department	3department	NUM
cana-2015	2	2	of	of	ADP
cana-2015	2	3	mathematics	mathematic	NOUN
cana-2015	2	4	,	,	PUNCT
cana-2015	2	5	school	school	NOUN
cana-2015	2	6	of	of	ADP
cana-2015	2	7	science	science	NOUN
cana-2015	2	8	,	,	PUNCT
cana-2015	2	9	university	university	NOUN
cana-2015	2	10	of	of	ADP
cana-2015	2	11	phayao	phayao	NOUN
cana-2015	2	12	,	,	PUNCT
cana-2015	2	13	19	19	NUM
cana-2015	2	14	moo	moo	NOUN
cana-2015	2	15	2,tambon	2,tambon	NUM
cana-2015	2	16	mae	mae	PROPN
cana-2015	2	17	ka	ka	PROPN
cana-2015	2	18	,	,	PUNCT
cana-2015	2	19	amphur	amphur	PROPN
cana-2015	2	20	mueang	mueang	NOUN
cana-2015	2	21	,	,	PUNCT
cana-2015	2	22	phayao	phayao	NOUN
cana-2015	2	23	56000	56000	NUM
cana-2015	2	24	,	,	PUNCT
cana-2015	2	25	thailand	thailand	PROPN
cana-2015	2	26	.	.	PUNCT
cana-2015	3	1	e-mails:1gsm.maths@gmail.com	e-mails:1gsm.maths@gmail.com	PROPN
cana-2015	3	2	,	,	PUNCT
cana-2015	3	3	2palanimaths86@gmail.com	2palanimaths86@gmail.com	NUM
cana-2015	3	4	,	,	PUNCT
cana-2015	3	5	3aiyared.ia@up.ac.th	3aiyared.ia@up.ac.th	NUM
cana-2015	3	6	,	,	PUNCT
cana-2015	3	7	∗corresponding	∗corresponde	VERB
cana-2015	3	8	author	author	NOUN
cana-2015	3	9	:	:	PUNCT
cana-2015	3	10	aiyared	aiyared	PROPN
cana-2015	3	11	iampan	iampan	PROPN
cana-2015	3	12	.	.	PUNCT
cana-2015	4	1	received	receive	VERB
cana-2015	4	2	:	:	PUNCT
cana-2015	4	3	09	09	NUM
cana-2015	4	4	-	-	PUNCT
cana-2015	4	5	03	03	NUM
cana-2015	4	6	-	-	PUNCT
cana-2015	4	7	2024	2024	NUM
cana-2015	4	8	revised	revise	VERB
cana-2015	4	9	:	:	PUNCT
cana-2015	4	10	26	26	NUM
cana-2015	4	11	-	-	SYM
cana-2015	4	12	07	07	NUM
cana-2015	4	13	-	-	PUNCT
cana-2015	4	14	2024	2024	NUM
cana-2015	4	15	accepted	accept	VERB
cana-2015	4	16	:	:	PUNCT
cana-2015	4	17	16	16	NUM
cana-2015	4	18	-	-	SYM
cana-2015	4	19	09	09	NUM
cana-2015	4	20	-	-	PUNCT
cana-2015	4	21	2024	2024	NUM
cana-2015	4	22	.	.	PUNCT
cana-2015	5	1	abstract	abstract	ADV
cana-2015	5	2	we	we	PRON
cana-2015	5	3	introduce	introduce	VERB
cana-2015	5	4	the	the	DET
cana-2015	5	5	interval	interval	NOUN
cana-2015	5	6	-	-	PUNCT
cana-2015	5	7	valued	value	VERB
cana-2015	5	8	intuitionistic	intuitionistic	ADJ
cana-2015	5	9	fuzzy	fuzzy	ADJ
cana-2015	5	10	set	set	NOUN
cana-2015	5	11	used	use	VERB
cana-2015	5	12	with	with	ADP
cana-2015	5	13	the	the	DET
cana-2015	5	14	q	q	NOUN
cana-2015	5	15	-	-	PUNCT
cana-2015	5	16	rung	rung	ADJ
cana-2015	5	17	logarithimic	logarithimic	ADJ
cana-2015	5	18	operator	operator	NOUN
cana-2015	5	19	(	(	PUNCT
cana-2015	5	20	q	q	NOUN
cana-2015	5	21	-	-	PUNCT
cana-2015	5	22	livifs	livif	NOUN
cana-2015	5	23	)	)	PUNCT
cana-2015	5	24	.	.	PUNCT
cana-2015	6	1	a	a	DET
cana-2015	6	2	q	q	ADJ
cana-2015	6	3	-	-	PUNCT
cana-2015	6	4	rung	rung	ADJ
cana-2015	6	5	interval	interval	NOUN
cana-2015	6	6	-	-	PUNCT
cana-2015	6	7	valued	value	VERB
cana-2015	6	8	intuitionistic	intuitionistic	ADJ
cana-2015	6	9	fuzzy	fuzzy	ADJ
cana-2015	6	10	set	set	NOUN
cana-2015	6	11	may	may	AUX
cana-2015	6	12	be	be	AUX
cana-2015	6	13	developed	develop	VERB
cana-2015	6	14	by	by	ADP
cana-2015	6	15	expanding	expand	VERB
cana-2015	6	16	the	the	DET
cana-2015	6	17	pythagorean	pythagorean	PROPN
cana-2015	6	18	intervalvalued	intervalvalue	VERB
cana-2015	6	19	fuzzy	fuzzy	ADJ
cana-2015	6	20	set	set	NOUN
cana-2015	6	21	(	(	PUNCT
cana-2015	6	22	pivfs	pivfs	NOUN
cana-2015	6	23	)	)	PUNCT
cana-2015	6	24	.	.	PUNCT
cana-2015	7	1	we	we	PRON
cana-2015	7	2	discuss	discuss	VERB
cana-2015	7	3	the	the	DET
cana-2015	7	4	q	q	ADJ
cana-2015	7	5	-	-	ADJ
cana-2015	7	6	logarithimic	logarithimic	ADJ
cana-2015	7	7	operator	operator	NOUN
cana-2015	7	8	applied	apply	VERB
cana-2015	7	9	to	to	ADP
cana-2015	7	10	interval	interval	NOUN
cana-2015	7	11	-	-	PUNCT
cana-2015	7	12	valued	value	VERB
cana-2015	7	13	intuitionistic	intuitionistic	ADJ
cana-2015	7	14	fuzzy	fuzzy	ADJ
cana-2015	7	15	weighted	weight	VERB
cana-2015	7	16	averaging	average	VERB
cana-2015	7	17	(	(	PUNCT
cana-2015	7	18	q	q	NOUN
cana-2015	7	19	-	-	PUNCT
cana-2015	7	20	livifwa	livifwa	NOUN
cana-2015	7	21	)	)	PUNCT
cana-2015	7	22	,	,	PUNCT
cana-2015	7	23	interval	interval	NOUN
cana-2015	7	24	-	-	PUNCT
cana-2015	7	25	valued	value	VERB
cana-2015	7	26	intuitionistic	intuitionistic	ADJ
cana-2015	7	27	fuzzy	fuzzy	ADJ
cana-2015	7	28	weighted	weight	VERB
cana-2015	7	29	geometric	geometric	ADJ
cana-2015	7	30	(	(	PUNCT
cana-2015	7	31	q	q	NOUN
cana-2015	7	32	-	-	PUNCT
cana-2015	7	33	livifwg	livifwg	NOUN
cana-2015	7	34	)	)	PUNCT
cana-2015	7	35	,	,	PUNCT
cana-2015	7	36	extended	extend	VERB
cana-2015	7	37	q	q	ADJ
cana-2015	7	38	-	-	ADJ
cana-2015	7	39	logarithimic	logarithimic	ADJ
cana-2015	7	40	operator	operator	NOUN
cana-2015	7	41	applied	apply	VERB
cana-2015	7	42	to	to	ADP
cana-2015	7	43	interval	interval	NOUN
cana-2015	7	44	-	-	PUNCT
cana-2015	7	45	valued	value	VERB
cana-2015	7	46	intuitionistic	intuitionistic	ADJ
cana-2015	7	47	fuzzy	fuzzy	ADJ
cana-2015	7	48	weighted	weight	VERB
cana-2015	7	49	averaging	average	VERB
cana-2015	7	50	(	(	PUNCT
cana-2015	7	51	q	q	NOUN
cana-2015	7	52	-	-	PUNCT
cana-2015	7	53	elivifwa	elivifwa	NOUN
cana-2015	7	54	)	)	PUNCT
cana-2015	7	55	,	,	PUNCT
cana-2015	7	56	and	and	CCONJ
cana-2015	7	57	extended	extend	VERB
cana-2015	7	58	q	q	ADJ
cana-2015	7	59	-	-	ADJ
cana-2015	7	60	logarithimic	logarithimic	ADJ
cana-2015	7	61	operator	operator	NOUN
cana-2015	7	62	applied	apply	VERB
cana-2015	7	63	to	to	ADP
cana-2015	7	64	interval	interval	NOUN
cana-2015	7	65	-	-	PUNCT
cana-2015	7	66	valued	value	VERB
cana-2015	7	67	intuitionistic	intuitionistic	ADJ
cana-2015	7	68	fuzzy	fuzzy	ADJ
cana-2015	7	69	weighted	weight	VERB
cana-2015	7	70	geometric	geometric	ADJ
cana-2015	7	71	(	(	PUNCT
cana-2015	7	72	qelivifwg	qelivifwg	NOUN
cana-2015	7	73	)	)	PUNCT
cana-2015	7	74	.	.	PUNCT
cana-2015	8	1	several	several	ADJ
cana-2015	8	2	algebraic	algebraic	ADJ
cana-2015	8	3	properties	property	NOUN
cana-2015	8	4	of	of	ADP
cana-2015	8	5	q	q	NOUN
cana-2015	8	6	-	-	PUNCT
cana-2015	8	7	livifss	livifss	ADJ
cana-2015	8	8	,	,	PUNCT
cana-2015	8	9	such	such	ADJ
cana-2015	8	10	as	as	ADP
cana-2015	8	11	distributivity	distributivity	NOUN
cana-2015	8	12	,	,	PUNCT
cana-2015	8	13	idempotency	idempotency	NOUN
cana-2015	8	14	,	,	PUNCT
cana-2015	8	15	and	and	CCONJ
cana-2015	8	16	associativity	associativity	NOUN
cana-2015	8	17	,	,	PUNCT
cana-2015	8	18	have	have	AUX
cana-2015	8	19	been	be	AUX
cana-2015	8	20	identified	identify	VERB
cana-2015	8	21	.	.	PUNCT
cana-2015	9	1	keywords	keyword	NOUN
cana-2015	9	2	:	:	PUNCT
cana-2015	9	3	q	q	X
cana-2015	9	4	-	-	PUNCT
cana-2015	9	5	livifwa	livifwa	NOUN
cana-2015	9	6	;	;	PUNCT
cana-2015	9	7	q	q	X
cana-2015	9	8	-	-	PUNCT
cana-2015	9	9	livifwg	livifwg	NOUN
cana-2015	9	10	;	;	PUNCT
cana-2015	9	11	q	q	X
cana-2015	9	12	-	-	PUNCT
cana-2015	9	13	elivifwa	elivifwa	NOUN
cana-2015	9	14	;	;	PUNCT
cana-2015	9	15	q	q	X
cana-2015	9	16	-	-	PUNCT
cana-2015	9	17	elivifwg	elivifwg	NOUN
cana-2015	9	18	.	.	PUNCT
cana-2015	10	1	1	1	NUM
cana-2015	10	2	introduction	introduction	NOUN
cana-2015	10	3	several	several	ADJ
cana-2015	10	4	authors	author	NOUN
cana-2015	10	5	have	have	AUX
cana-2015	10	6	contributed	contribute	VERB
cana-2015	10	7	to	to	ADP
cana-2015	10	8	this	this	DET
cana-2015	10	9	field	field	NOUN
cana-2015	10	10	of	of	ADP
cana-2015	10	11	research	research	NOUN
cana-2015	10	12	using	use	VERB
cana-2015	10	13	a	a	DET
cana-2015	10	14	variety	variety	NOUN
cana-2015	10	15	of	of	ADP
cana-2015	10	16	methods	method	NOUN
cana-2015	10	17	.	.	PUNCT
cana-2015	11	1	fuzzy	fuzzy	ADJ
cana-2015	11	2	set	set	NOUN
cana-2015	11	3	(	(	PUNCT
cana-2015	11	4	fs),1	fs),1	X
cana-2015	11	5	intuitionistic	intuitionistic	ADJ
cana-2015	11	6	fs	fs	X
cana-2015	11	7	(	(	PUNCT
cana-2015	11	8	ifs),2	ifs),2	PROPN
cana-2015	11	9	interval	interval	NOUN
cana-2015	11	10	valued	value	VERB
cana-2015	11	11	fs	fs	ADP
cana-2015	11	12	(	(	PUNCT
cana-2015	11	13	ivfs),3	ivfs),3	PROPN
cana-2015	11	14	vague	vague	ADJ
cana-2015	11	15	set	set	NOUN
cana-2015	11	16	(	(	PUNCT
cana-2015	11	17	vs),4	vs),4	NOUN
cana-2015	11	18	pythagorean	pythagorean	NOUN
cana-2015	11	19	fs	fs	X
cana-2015	11	20	(	(	PUNCT
cana-2015	11	21	pfs),5	pfs),5	PROPN
cana-2015	11	22	ivpfs,6	ivpfs,6	X
cana-2015	11	23	spherical	spherical	ADJ
cana-2015	11	24	fs	fs	X
cana-2015	11	25	(	(	PUNCT
cana-2015	11	26	sfs),7	sfs),7	PROPN
cana-2015	11	27	neutrosophic	neutrosophic	ADJ
cana-2015	11	28	set	set	NOUN
cana-2015	11	29	(	(	PUNCT
cana-2015	11	30	ns)8	ns)8	PROPN
cana-2015	11	31	can	can	AUX
cana-2015	11	32	all	all	PRON
cana-2015	11	33	arise	arise	VERB
cana-2015	11	34	from	from	ADP
cana-2015	11	35	uncertainties	uncertainty	NOUN
cana-2015	11	36	.	.	PUNCT
cana-2015	12	1	there	there	PRON
cana-2015	12	2	are	be	VERB
cana-2015	12	3	several	several	ADJ
cana-2015	12	4	theories	theory	NOUN
cana-2015	12	5	about	about	ADP
cana-2015	12	6	uncertainty	uncertainty	NOUN
cana-2015	12	7	that	that	PRON
cana-2015	12	8	have	have	AUX
cana-2015	12	9	been	be	AUX
cana-2015	12	10	proposed	propose	VERB
cana-2015	12	11	.	.	PUNCT
cana-2015	13	1	for	for	ADP
cana-2015	13	2	example	example	NOUN
cana-2015	13	3	,	,	PUNCT
cana-2015	13	4	fuzzy	fuzzy	ADJ
cana-2015	13	5	set	set	NOUN
cana-2015	13	6	(	(	PUNCT
cana-2015	13	7	fs)1	fs)1	PROPN
cana-2015	13	8	has	have	AUX
cana-2015	13	9	membership	membership	NOUN
cana-2015	13	10	grade	grade	NOUN
cana-2015	13	11	(	(	PUNCT
cana-2015	13	12	mg	mg	ADJ
cana-2015	13	13	)	)	PUNCT
cana-2015	13	14	ranging	range	VERB
cana-2015	13	15	from	from	ADP
cana-2015	13	16	0	0	NUM
cana-2015	13	17	to	to	ADP
cana-2015	13	18	1	1	NUM
cana-2015	13	19	.	.	PUNCT
cana-2015	14	1	atanassov2	atanassov2	PROPN
cana-2015	14	2	developed	develop	VERB
cana-2015	14	3	an	an	DET
cana-2015	14	4	intuitionistic	intuitionistic	ADJ
cana-2015	14	5	fuzzy	fuzzy	ADJ
cana-2015	14	6	set	set	NOUN
cana-2015	14	7	(	(	PUNCT
cana-2015	14	8	ifs	ifs	PROPN
cana-2015	14	9	)	)	PUNCT
cana-2015	14	10	where	where	SCONJ
cana-2015	14	11	the	the	DET
cana-2015	14	12	two	two	NUM
cana-2015	14	13	mgs	mgs	NOUN
cana-2015	14	14	of	of	ADP
cana-2015	14	15	each	each	DET
cana-2015	14	16	component	component	NOUN
cana-2015	14	17	,	,	PUNCT
cana-2015	14	18	positive	positive	ADJ
cana-2015	14	19	β	β	X
cana-2015	14	20	and	and	CCONJ
cana-2015	14	21	negative	negative	ADJ
cana-2015	14	22	α	α	NOUN
cana-2015	14	23	,	,	PUNCT
cana-2015	14	24	satisfy	satisfy	NOUN
cana-2015	14	25	0	0	NUM
cana-2015	14	26	≤	≤	NUM
cana-2015	14	27	β	β	X
cana-2015	15	1	+	+	X
cana-2015	15	2	α	α	PROPN
cana-2015	15	3	≤	≤	NUM
cana-2015	15	4	1	1	NUM
cana-2015	15	5	,	,	PUNCT
cana-2015	15	6	for	for	ADP
cana-2015	15	7	β	β	X
cana-2015	15	8	,	,	PUNCT
cana-2015	15	9	α	α	PROPN
cana-2015	15	10	∈	∈	PROPN
cana-2015	16	1	[	[	X
cana-2015	16	2	0	0	NUM
cana-2015	16	3	,	,	PUNCT
cana-2015	16	4	1	1	NUM
cana-2015	16	5	]	]	PUNCT
cana-2015	16	6	.	.	PUNCT
cana-2015	17	1	yager5	yager5	PROPN
cana-2015	17	2	invented	invent	VERB
cana-2015	17	3	pythagorean	pythagorean	PROPN
cana-2015	17	4	fuzzy	fuzzy	ADJ
cana-2015	17	5	sets	set	NOUN
cana-2015	17	6	(	(	PUNCT
cana-2015	17	7	pfs	pfs	PROPN
cana-2015	17	8	)	)	PUNCT
cana-2015	17	9	.	.	PUNCT
cana-2015	18	1	with	with	ADP
cana-2015	18	2	the	the	DET
cana-2015	18	3	assumption	assumption	NOUN
cana-2015	18	4	that	that	SCONJ
cana-2015	18	5	β	β	PROPN
cana-2015	18	6	+	+	X
cana-2015	18	7	α	α	PRON
cana-2015	18	8	≥	≥	NOUN
cana-2015	18	9	1	1	NUM
cana-2015	18	10	to	to	ADP
cana-2015	18	11	β2	β2	NOUN
cana-2015	18	12	+	+	CCONJ
cana-2015	18	13	α2	α2	ADJ
cana-2015	18	14	≤	≤	ADV
cana-2015	18	15	1	1	NUM
cana-2015	18	16	,	,	PUNCT
cana-2015	18	17	they	they	PRON
cana-2015	18	18	are	be	AUX
cana-2015	18	19	distinguished	distinguish	VERB
cana-2015	18	20	by	by	ADP
cana-2015	18	21	their	their	PRON
cana-2015	18	22	mg	mg	PROPN
cana-2015	18	23	and	and	CCONJ
cana-2015	18	24	non	non	ADJ
cana-2015	18	25	-	-	ADJ
cana-2015	18	26	membership	membership	ADJ
cana-2015	18	27	grade	grade	NOUN
cana-2015	18	28	(	(	PUNCT
cana-2015	18	29	nmg	nmg	NOUN
cana-2015	18	30	)	)	PUNCT
cana-2015	18	31	.	.	PUNCT
cana-2015	19	1	numerous	numerous	ADJ
cana-2015	19	2	studies	study	NOUN
cana-2015	19	3	have	have	AUX
cana-2015	19	4	been	be	AUX
cana-2015	19	5	conducted	conduct	VERB
cana-2015	19	6	on	on	ADP
cana-2015	19	7	the	the	DET
cana-2015	19	8	use	use	NOUN
cana-2015	19	9	of	of	ADP
cana-2015	19	10	pfss	pfss	NOUN
cana-2015	19	11	and	and	CCONJ
cana-2015	19	12	ifss	ifss	ADJ
cana-2015	19	13	in	in	ADP
cana-2015	19	14	different	different	ADJ
cana-2015	19	15	fields	field	NOUN
cana-2015	19	16	of	of	ADP
cana-2015	19	17	research	research	NOUN
cana-2015	19	18	.	.	PUNCT
cana-2015	20	1	they	they	PRON
cana-2015	20	2	are	be	AUX
cana-2015	20	3	still	still	ADV
cana-2015	20	4	not	not	PART
cana-2015	20	5	adept	adept	ADJ
cana-2015	20	6	at	at	ADP
cana-2015	20	7	explaining	explain	VERB
cana-2015	20	8	concepts	concept	NOUN
cana-2015	20	9	.	.	PUNCT
cana-2015	21	1	because	because	SCONJ
cana-2015	21	2	of	of	ADP
cana-2015	21	3	this	this	PRON
cana-2015	21	4	,	,	PUNCT
cana-2015	21	5	the	the	DET
cana-2015	21	6	experts	expert	NOUN
cana-2015	21	7	were	be	AUX
cana-2015	21	8	still	still	ADV
cana-2015	21	9	having	have	VERB
cana-2015	21	10	problems	problem	NOUN
cana-2015	21	11	interpreting	interpret	VERB
cana-2015	21	12	the	the	DET
cana-2015	21	13	data	datum	NOUN
cana-2015	21	14	in	in	ADP
cana-2015	21	15	these	these	DET
cana-2015	21	16	sets	set	NOUN
cana-2015	21	17	and	and	CCONJ
cana-2015	21	18	the	the	DET
cana-2015	21	19	supporting	support	VERB
cana-2015	21	20	data	datum	NOUN
cana-2015	21	21	.	.	PUNCT
cana-2015	22	1	cuong	cuong	PROPN
cana-2015	22	2	et	et	PROPN
cana-2015	22	3	al.9	al.9	PROPN
cana-2015	22	4	developed	develop	VERB
cana-2015	22	5	the	the	DET
cana-2015	22	6	concept	concept	NOUN
cana-2015	22	7	of	of	ADP
cana-2015	22	8	a	a	DET
cana-2015	22	9	picture	picture	NOUN
cana-2015	22	10	fuzzy	fuzzy	ADJ
cana-2015	22	11	set	set	VERB
cana-2015	22	12	as	as	ADP
cana-2015	22	13	an	an	DET
cana-2015	22	14	alternative	alternative	NOUN
cana-2015	22	15	for	for	ADP
cana-2015	22	16	this	this	DET
cana-2015	22	17	information	information	NOUN
cana-2015	22	18	.	.	PUNCT
cana-2015	23	1	as	as	ADP
cana-2015	23	2	a	a	DET
cana-2015	23	3	result	result	NOUN
cana-2015	23	4	,	,	PUNCT
cana-2015	23	5	it	it	PRON
cana-2015	23	6	has	have	AUX
cana-2015	23	7	been	be	AUX
cana-2015	23	8	noted	note	VERB
cana-2015	23	9	that	that	SCONJ
cana-2015	23	10	the	the	DET
cana-2015	23	11	picture	picture	NOUN
cana-2015	23	12	fuzzy	fuzzy	ADJ
cana-2015	23	13	set	set	NOUN
cana-2015	23	14	is	be	AUX
cana-2015	23	15	an	an	DET
cana-2015	23	16	expanded	expand	VERB
cana-2015	23	17	version	version	NOUN
cana-2015	23	18	of	of	ADP
cana-2015	23	19	ifs	ifs	PROPN
cana-2015	23	20	with	with	ADP
cana-2015	23	21	more	more	ADJ
cana-2015	23	22	ambiguity	ambiguity	NOUN
cana-2015	23	23	handling	handle	VERB
cana-2015	23	24	capabilities	capability	NOUN
cana-2015	23	25	.	.	PUNCT
cana-2015	24	1	as	as	SCONJ
cana-2015	24	2	0	0	NUM
cana-2015	24	3	≤	≤	NUM
cana-2015	24	4	β+α+ζ	β+α+ζ	NOUN
cana-2015	24	5	≤	≤	NUM
cana-2015	24	6	1	1	NUM
cana-2015	24	7	,	,	PUNCT
cana-2015	24	8	it	it	PRON
cana-2015	24	9	was	be	AUX
cana-2015	24	10	noted	note	VERB
cana-2015	24	11	that	that	SCONJ
cana-2015	24	12	in	in	ADP
cana-2015	24	13	the	the	DET
cana-2015	24	14	picture	picture	NOUN
cana-2015	24	15	fuzzy	fuzzy	ADJ
cana-2015	24	16	set	set	NOUN
cana-2015	24	17	,	,	PUNCT
cana-2015	24	18	mg	mg	PROPN
cana-2015	24	19	β	β	PROPN
cana-2015	24	20	,	,	PUNCT
cana-2015	24	21	nmg	nmg	NOUN
cana-2015	24	22	ζ	ζ	PROPN
cana-2015	24	23	,	,	PUNCT
cana-2015	24	24	and	and	CCONJ
cana-2015	24	25	neutral	neutral	ADJ
cana-2015	24	26	grade	grade	NOUN
cana-2015	24	27	α	α	NOUN
cana-2015	24	28	;	;	PUNCT
cana-2015	24	29	for	for	ADP
cana-2015	24	30	β	β	X
cana-2015	24	31	,	,	PUNCT
cana-2015	24	32	α	α	PROPN
cana-2015	24	33	,	,	PUNCT
cana-2015	24	34	ζ	ζ	PROPN
cana-2015	24	35	∈	∈	NOUN
cana-2015	25	1	[	[	X
cana-2015	25	2	0	0	NUM
cana-2015	25	3	,	,	PUNCT
cana-2015	25	4	1	1	NUM
cana-2015	25	5	]	]	PUNCT
cana-2015	25	6	.	.	PUNCT
cana-2015	26	1	it	it	PRON
cana-2015	26	2	will	will	AUX
cana-2015	26	3	be	be	AUX
cana-2015	26	4	feasible	feasible	ADJ
cana-2015	26	5	to	to	PART
cana-2015	26	6	ensure	ensure	VERB
cana-2015	26	7	that	that	SCONJ
cana-2015	26	8	expert	expert	NOUN
cana-2015	26	9	assessments	assessment	NOUN
cana-2015	26	10	like	like	ADP
cana-2015	26	11	”	"	PUNCT
cana-2015	26	12	yes	yes	INTJ
cana-2015	26	13	,	,	PUNCT
cana-2015	26	14	”	"	PUNCT
cana-2015	26	15	”	"	PUNCT
cana-2015	26	16	abstain	abstain	NOUN
cana-2015	26	17	,	,	PUNCT
cana-2015	26	18	”	"	PUNCT
cana-2015	26	19	”	"	PUNCT
cana-2015	26	20	no	no	INTJ
cana-2015	26	21	,	,	PUNCT
cana-2015	26	22	”	"	PUNCT
cana-2015	26	23	and	and	CCONJ
cana-2015	26	24	”	"	PUNCT
cana-2015	26	25	refusal	refusal	NOUN
cana-2015	26	26	”	"	PUNCT
cana-2015	26	27	are	be	AUX
cana-2015	26	28	expressed	express	VERB
cana-2015	26	29	by	by	ADP
cana-2015	26	30	following	follow	VERB
cana-2015	26	31	to	to	ADP
cana-2015	26	32	the	the	DET
cana-2015	26	33	pfs	pfs	PROPN
cana-2015	26	34	definition	definition	NOUN
cana-2015	26	35	.	.	PUNCT
cana-2015	27	1	furthermore	furthermore	ADV
cana-2015	27	2	,	,	PUNCT
cana-2015	27	3	there	there	PRON
cana-2015	27	4	will	will	AUX
cana-2015	27	5	be	be	AUX
cana-2015	27	6	consistency	consistency	NOUN
cana-2015	27	7	between	between	ADP
cana-2015	27	8	the	the	DET
cana-2015	27	9	outcome	outcome	NOUN
cana-2015	27	10	data	datum	NOUN
cana-2015	27	11	and	and	CCONJ
cana-2015	27	12	the	the	DET
cana-2015	27	13	actual	actual	ADJ
cana-2015	27	14	decision	decision	NOUN
cana-2015	27	15	-	-	PUNCT
cana-2015	27	16	making	make	VERB
cana-2015	27	17	environment	environment	NOUN
cana-2015	27	18	,	,	PUNCT
cana-2015	27	19	and	and	CCONJ
cana-2015	27	20	no	no	DET
cana-2015	27	21	evaluative	evaluative	ADJ
cana-2015	27	22	detail	detail	NOUN
cana-2015	27	23	will	will	AUX
cana-2015	27	24	be	be	AUX
cana-2015	27	25	missed	miss	VERB
cana-2015	27	26	.	.	PUNCT
cana-2015	28	1	although	although	SCONJ
cana-2015	28	2	picture	picture	NOUN
cana-2015	28	3	fuzzy	fuzzy	ADJ
cana-2015	28	4	sets	set	NOUN
cana-2015	28	5	have	have	AUX
cana-2015	28	6	been	be	AUX
cana-2015	28	7	used	use	VERB
cana-2015	28	8	and	and	CCONJ
cana-2015	28	9	studied	study	VERB
cana-2015	28	10	extensively	extensively	ADV
cana-2015	28	11	,	,	PUNCT
cana-2015	28	12	less	less	ADJ
cana-2015	28	13	emphasis	emphasis	NOUN
cana-2015	28	14	has	have	AUX
cana-2015	28	15	been	be	AUX
cana-2015	28	16	dedicated	dedicate	VERB
cana-2015	28	17	to	to	ADP
cana-2015	28	18	their	their	PRON
cana-2015	28	19	concept	concept	NOUN
cana-2015	28	20	.	.	PUNCT
cana-2015	29	1	in	in	ADP
cana-2015	29	2	their	their	PRON
cana-2015	29	3	discussion	discussion	NOUN
cana-2015	29	4	of	of	ADP
cana-2015	29	5	the	the	DET
cana-2015	29	6	new	new	ADJ
cana-2015	29	7	aggregating	aggregating	NOUN
cana-2015	29	8	operator	operator	NOUN
cana-2015	29	9	,	,	PUNCT
cana-2015	29	10	palanikumar	palanikumar	PROPN
cana-2015	29	11	et	et	PROPN
cana-2015	29	12	al.10-.15	al.10-.15	PROPN
cana-2015	29	13	aggregation	aggregation	NOUN
cana-2015	29	14	operators	operator	NOUN
cana-2015	29	15	(	(	PUNCT
cana-2015	29	16	ao	ao	PROPN
cana-2015	29	17	)	)	PUNCT
cana-2015	29	18	were	be	AUX
cana-2015	29	19	introduced	introduce	VERB
cana-2015	29	20	in	in	ADP
cana-2015	29	21	addition	addition	NOUN
cana-2015	29	22	to	to	ADP
cana-2015	29	23	extended	extend	VERB
cana-2015	29	24	pfs	pfs	PROPN
cana-2015	29	25	to	to	PART
cana-2015	29	26	handle	handle	VERB
cana-2015	29	27	issues	issue	NOUN
cana-2015	29	28	with	with	ADP
cana-2015	29	29	multiple	multiple	ADJ
cana-2015	29	30	truth	truth	NOUN
cana-2015	29	31	membership	membership	NOUN
cana-2015	29	32	values	value	NOUN
cana-2015	29	33	(	(	PUNCT
cana-2015	29	34	tmd	tmd	NOUN
cana-2015	29	35	)	)	PUNCT
cana-2015	29	36	,	,	PUNCT
cana-2015	29	37	false	false	ADJ
cana-2015	29	38	membership	membership	NOUN
cana-2015	29	39	values	value	NOUN
cana-2015	29	40	(	(	PUNCT
cana-2015	29	41	fmd	fmd	NOUN
cana-2015	29	42	)	)	PUNCT
cana-2015	29	43	,	,	PUNCT
cana-2015	29	44	and	and	CCONJ
cana-2015	29	45	indeterminacy	indeterminacy	NOUN
cana-2015	29	46	membership	membership	NOUN
cana-2015	29	47	values	value	NOUN
cana-2015	29	48	(	(	PUNCT
cana-2015	29	49	imd	imd	PROPN
cana-2015	29	50	)	)	PUNCT
cana-2015	29	51	that	that	PRON
cana-2015	29	52	are	be	AUX
cana-2015	29	53	handled	handle	VERB
cana-2015	29	54	by	by	ADP
cana-2015	29	55	the	the	DET
cana-2015	29	56	dm	dm	PROPN
cana-2015	29	57	method	method	NOUN
cana-2015	29	58	,	,	PUNCT
cana-2015	29	59	as	as	SCONJ
cana-2015	29	60	explained	explain	VERB
cana-2015	29	61	by	by	ADP
cana-2015	29	62	liu	liu	PROPN
cana-2015	29	63	et	et	PROPN
cana-2015	29	64	al.16	al.16	PROPN
cana-2015	29	65	the	the	DET
cana-2015	29	66	novel	novel	ADJ
cana-2015	29	67	aggregating	aggregate	VERB
cana-2015	29	68	operators	operator	NOUN
cana-2015	29	69	have	have	AUX
cana-2015	29	70	been	be	AUX
cana-2015	29	71	studied	study	VERB
cana-2015	29	72	by	by	ADP
cana-2015	29	73	palanikumar	palanikumar	PROPN
cana-2015	29	74	et	et	PROPN
cana-2015	29	75	al.17-.18	al.17-.18	VERB
cana-2015	29	76	the	the	DET
cana-2015	29	77	concept	concept	NOUN
cana-2015	29	78	of	of	ADP
cana-2015	29	79	neutrosophic	neutrosophic	ADJ
cana-2015	29	80	sets	set	NOUN
cana-2015	29	81	was	be	AUX
cana-2015	29	82	proposed	propose	VERB
cana-2015	29	83	by	by	ADP
cana-2015	29	84	smarandache	smarandache	PROPN
cana-2015	29	85	et	et	PROPN
cana-2015	29	86	al.19	al.19	AUX
cana-2015	29	87	the	the	DET
cana-2015	29	88	capacity	capacity	NOUN
cana-2015	29	89	for	for	ADP
cana-2015	29	90	impartial	impartial	ADJ
cana-2015	29	91	thought	thought	NOUN
cana-2015	29	92	is	be	AUX
cana-2015	29	93	one	one	NUM
cana-2015	29	94	of	of	ADP
cana-2015	29	95	the	the	DET
cana-2015	29	96	primary	primary	ADJ
cana-2015	29	97	differences	difference	NOUN
cana-2015	29	98	between	between	ADP
cana-2015	29	99	fs	f	NOUN
cana-2015	29	100	and	and	CCONJ
cana-2015	29	101	ifs	ifs	PROPN
cana-2015	29	102	.	.	PUNCT
cana-2015	30	1	neutroposophy	neutroposophy	PROPN
cana-2015	30	2	is	be	AUX
cana-2015	30	3	the	the	DET
cana-2015	30	4	study	study	NOUN
cana-2015	30	5	of	of	ADP
cana-2015	30	6	neutral	neutral	ADJ
cana-2015	30	7	cognition	cognition	NOUN
cana-2015	30	8	.	.	PUNCT
cana-2015	31	1	tmd	tmd	INTJ
cana-2015	31	2	,	,	PUNCT
cana-2015	31	3	imd	imd	PROPN
cana-2015	31	4	,	,	PUNCT
cana-2015	31	5	and	and	CCONJ
cana-2015	31	6	fd	fd	PROPN
cana-2015	31	7	are	be	AUX
cana-2015	31	8	used	use	VERB
cana-2015	31	9	in	in	ADP
cana-2015	31	10	this	this	DET
cana-2015	31	11	reasoning	reasoning	NOUN
cana-2015	31	12	to	to	PART
cana-2015	31	13	calculate	calculate	VERB
cana-2015	31	14	a	a	DET
cana-2015	31	15	value	value	NOUN
cana-2015	31	16	for	for	ADP
cana-2015	31	17	every	every	DET
cana-2015	31	18	proposition	proposition	NOUN
cana-2015	31	19	.	.	PUNCT
cana-2015	32	1	a	a	DET
cana-2015	32	2	strategy	strategy	NOUN
cana-2015	32	3	for	for	ADP
cana-2015	32	4	mcdm	mcdm	ADJ
cana-2015	32	5	under	under	ADP
cana-2015	32	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2015	32	7	539	539	NUM
cana-2015	32	8	communications	communication	NOUN
cana-2015	32	9	on	on	ADP
cana-2015	32	10	applied	apply	VERB
cana-2015	32	11	nonlinear	nonlinear	ADJ
cana-2015	32	12	analysis	analysis	NOUN
cana-2015	32	13	issn	issn	NOUN
cana-2015	32	14	:	:	PUNCT
cana-2015	32	15	1074	1074	NUM
cana-2015	32	16	-	-	PUNCT
cana-2015	32	17	133x	133x	NUM
cana-2015	32	18	vol	vol	NOUN
cana-2015	32	19	32	32	NUM
cana-2015	32	20	no	no	NOUN
cana-2015	32	21	.	.	NOUN
cana-2015	32	22	3	3	NUM
cana-2015	32	23	(	(	PUNCT
cana-2015	32	24	2025	2025	NUM
cana-2015	32	25	)	)	PUNCT
cana-2015	32	26	interval	interval	NOUN
cana-2015	32	27	ns	ns	NUM
cana-2015	32	28	based	base	VERB
cana-2015	32	29	on	on	ADP
cana-2015	32	30	aos	aos	PROPN
cana-2015	32	31	was	be	AUX
cana-2015	32	32	given	give	VERB
cana-2015	32	33	by.20	by.20	PROPN
cana-2015	32	34	this	this	DET
cana-2015	32	35	universe	universe	NOUN
cana-2015	32	36	has	have	VERB
cana-2015	32	37	all	all	DET
cana-2015	32	38	elements	element	NOUN
cana-2015	32	39	with	with	ADP
cana-2015	32	40	values	value	NOUN
cana-2015	32	41	between	between	ADP
cana-2015	32	42	0	0	NUM
cana-2015	32	43	and	and	CCONJ
cana-2015	32	44	1	1	NUM
cana-2015	32	45	,	,	PUNCT
cana-2015	32	46	totaling	total	VERB
cana-2015	32	47	1	1	NUM
cana-2015	32	48	.	.	PUNCT
cana-2015	33	1	in	in	ADP
cana-2015	33	2	several	several	ADJ
cana-2015	33	3	applications	application	NOUN
cana-2015	33	4	,	,	PUNCT
cana-2015	33	5	aos	aos	PROPN
cana-2015	33	6	and	and	CCONJ
cana-2015	33	7	their	their	PRON
cana-2015	33	8	algebraic	algebraic	ADJ
cana-2015	33	9	structures	structure	NOUN
cana-2015	33	10	are	be	AUX
cana-2015	33	11	explained	explain	VERB
cana-2015	33	12	by	by	ADP
cana-2015	33	13	palanikumar	palanikumar	PROPN
cana-2015	33	14	et	et	PROPN
cana-2015	33	15	al.21	al.21	PROPN
cana-2015	33	16	xu	xu	PROPN
cana-2015	33	17	et	et	PROPN
cana-2015	33	18	al.22	al.22	PROPN
cana-2015	33	19	proposed	propose	VERB
cana-2015	33	20	using	use	VERB
cana-2015	33	21	various	various	ADJ
cana-2015	33	22	ifs	ifs	PROPN
cana-2015	33	23	averaging	average	VERB
cana-2015	33	24	operators	operator	NOUN
cana-2015	33	25	to	to	PART
cana-2015	33	26	manage	manage	VERB
cana-2015	33	27	ifs	ifs	PROPN
cana-2015	33	28	data	datum	NOUN
cana-2015	33	29	.	.	PUNCT
cana-2015	34	1	in	in	ADP
cana-2015	34	2	addition	addition	NOUN
cana-2015	34	3	,	,	PUNCT
cana-2015	34	4	weighted	weight	VERB
cana-2015	34	5	,	,	PUNCT
cana-2015	34	6	ordered	order	VERB
cana-2015	34	7	weighted	weight	VERB
cana-2015	34	8	,	,	PUNCT
cana-2015	34	9	and	and	CCONJ
cana-2015	34	10	hybrid	hybrid	ADJ
cana-2015	34	11	geometric	geometric	ADJ
cana-2015	34	12	operators	operator	NOUN
cana-2015	34	13	based	base	VERB
cana-2015	34	14	on	on	ADP
cana-2015	34	15	ifss	ifss	NOUN
cana-2015	34	16	were	be	AUX
cana-2015	34	17	developed	develop	VERB
cana-2015	34	18	by	by	ADP
cana-2015	34	19	xu	xu	PROPN
cana-2015	34	20	et	et	PROPN
cana-2015	34	21	al.23	al.23	NOUN
cana-2015	34	22	in	in	ADP
cana-2015	34	23	order	order	NOUN
cana-2015	34	24	to	to	PART
cana-2015	34	25	construct	construct	VERB
cana-2015	34	26	the	the	DET
cana-2015	34	27	if	if	SCONJ
cana-2015	34	28	ordered	order	VERB
cana-2015	34	29	weighted	weight	VERB
cana-2015	34	30	distance	distance	NOUN
cana-2015	34	31	(	(	PUNCT
cana-2015	34	32	ifowd	ifowd	NOUN
cana-2015	34	33	)	)	PUNCT
cana-2015	34	34	operators	operator	NOUN
cana-2015	34	35	that	that	PRON
cana-2015	34	36	are	be	AUX
cana-2015	34	37	covered	cover	VERB
cana-2015	34	38	in25	in25	PROPN
cana-2015	34	39	by	by	ADP
cana-2015	34	40	zeng	zeng	PROPN
cana-2015	34	41	et	et	PROPN
cana-2015	34	42	al	al	PROPN
cana-2015	34	43	.	.	PROPN
cana-2015	34	44	,	,	PUNCT
cana-2015	34	45	li	li	PROPN
cana-2015	34	46	et	et	PROPN
cana-2015	34	47	al.24	al.24	PROPN
cana-2015	34	48	introduced	introduce	VERB
cana-2015	34	49	the	the	DET
cana-2015	34	50	generalized	generalize	VERB
cana-2015	34	51	ordered	order	VERB
cana-2015	34	52	weighted	weight	VERB
cana-2015	34	53	averaging	average	VERB
cana-2015	34	54	(	(	PUNCT
cana-2015	34	55	gowa	gowa	NOUN
cana-2015	34	56	)	)	PUNCT
cana-2015	34	57	operators	operator	NOUN
cana-2015	34	58	.	.	PUNCT
cana-2015	35	1	peng	peng	PROPN
cana-2015	35	2	et	et	PROPN
cana-2015	35	3	al.26	al.26	PROPN
cana-2015	35	4	used	use	VERB
cana-2015	35	5	aos	aos	PROPN
cana-2015	35	6	to	to	PART
cana-2015	35	7	study	study	VERB
cana-2015	35	8	the	the	DET
cana-2015	35	9	basic	basic	ADJ
cana-2015	35	10	characteristics	characteristic	NOUN
cana-2015	35	11	of	of	ADP
cana-2015	35	12	pfs	pfs	PROPN
cana-2015	35	13	.	.	PUNCT
cana-2015	36	1	spherical	spherical	ADJ
cana-2015	36	2	fuzzy	fuzzy	ADJ
cana-2015	36	3	dombi	dombi	PROPN
cana-2015	36	4	aos	aos	PROPN
cana-2015	36	5	have	have	AUX
cana-2015	36	6	recently	recently	ADV
cana-2015	36	7	been	be	AUX
cana-2015	36	8	suggested	suggest	VERB
cana-2015	36	9	by	by	ADP
cana-2015	36	10	ashraf	ashraf	PROPN
cana-2015	36	11	et	et	PROPN
cana-2015	36	12	al.27	al.27	PROPN
cana-2015	36	13	this	this	DET
cana-2015	36	14	new	new	ADJ
cana-2015	36	15	power	power	NOUN
cana-2015	36	16	-	-	PUNCT
cana-2015	36	17	moirhead	moirhead	NOUN
cana-2015	36	18	mean	mean	NOUN
cana-2015	36	19	was	be	AUX
cana-2015	36	20	defined	define	VERB
cana-2015	36	21	in	in	ADP
cana-2015	36	22	the	the	DET
cana-2015	36	23	sfs	sfs	NOUN
cana-2015	36	24	in	in	ADP
cana-2015	36	25	2022	2022	NUM
cana-2015	36	26	by	by	ADP
cana-2015	36	27	temel	temel	NOUN
cana-2015	36	28	et	et	PROPN
cana-2015	36	29	al	al	PROPN
cana-2015	36	30	.	.	PROPN
cana-2015	36	31	,28	,28	PUNCT
cana-2015	36	32	and	and	CCONJ
cana-2015	36	33	it	it	PRON
cana-2015	36	34	also	also	ADV
cana-2015	36	35	applies	apply	VERB
cana-2015	36	36	to	to	PART
cana-2015	36	37	madm	madm	VERB
cana-2015	36	38	.	.	PUNCT
cana-2015	37	1	new	new	ADJ
cana-2015	37	2	aggregating	aggregate	VERB
cana-2015	37	3	operators	operator	NOUN
cana-2015	37	4	have	have	AUX
cana-2015	37	5	been	be	AUX
cana-2015	37	6	developed	develop	VERB
cana-2015	37	7	recently	recently	ADV
cana-2015	37	8	by.29–31	by.29–31	ADJ
cana-2015	37	9	section	section	NOUN
cana-2015	37	10	1	1	NUM
cana-2015	37	11	has	have	VERB
cana-2015	37	12	an	an	DET
cana-2015	37	13	introduction	introduction	NOUN
cana-2015	37	14	.	.	PUNCT
cana-2015	38	1	section	section	NOUN
cana-2015	38	2	2	2	NUM
cana-2015	38	3	for	for	ADP
cana-2015	38	4	information	information	NOUN
cana-2015	38	5	on	on	ADP
cana-2015	38	6	fs	f	NOUN
cana-2015	38	7	and	and	CCONJ
cana-2015	38	8	pns	pns	PROPN
cana-2015	38	9	.	.	PROPN
cana-2015	38	10	section	section	PROPN
cana-2015	38	11	3	3	NUM
cana-2015	38	12	contains	contain	VERB
cana-2015	38	13	a	a	DET
cana-2015	38	14	definition	definition	NOUN
cana-2015	38	15	and	and	CCONJ
cana-2015	38	16	an	an	DET
cana-2015	38	17	explanation	explanation	NOUN
cana-2015	38	18	of	of	ADP
cana-2015	38	19	some	some	PRON
cana-2015	38	20	of	of	ADP
cana-2015	38	21	the	the	DET
cana-2015	38	22	uses	use	NOUN
cana-2015	38	23	for	for	ADP
cana-2015	38	24	q	q	NOUN
cana-2015	38	25	-	-	PUNCT
cana-2015	38	26	livifns	livifns	NOUN
cana-2015	38	27	.	.	PUNCT
cana-2015	39	1	the	the	DET
cana-2015	39	2	article	article	NOUN
cana-2015	39	3	draws	draw	VERB
cana-2015	39	4	two	two	NUM
cana-2015	39	5	main	main	ADJ
cana-2015	39	6	conclusions	conclusion	NOUN
cana-2015	39	7	:	:	PUNCT
cana-2015	39	8	1	1	X
cana-2015	39	9	)	)	PUNCT
cana-2015	39	10	it	it	PRON
cana-2015	39	11	has	have	AUX
cana-2015	39	12	been	be	AUX
cana-2015	39	13	shown	show	VERB
cana-2015	39	14	that	that	SCONJ
cana-2015	39	15	the	the	DET
cana-2015	39	16	q	q	NOUN
cana-2015	39	17	-	-	PUNCT
cana-2015	39	18	rungs	rung	NOUN
cana-2015	39	19	of	of	ADP
cana-2015	39	20	livifs	livif	NOUN
cana-2015	39	21	exhibit	exhibit	VERB
cana-2015	39	22	the	the	DET
cana-2015	39	23	following	follow	VERB
cana-2015	39	24	algebraic	algebraic	ADJ
cana-2015	39	25	properties	property	NOUN
cana-2015	39	26	:	:	PUNCT
cana-2015	39	27	distributive	distributive	ADJ
cana-2015	39	28	,	,	PUNCT
cana-2015	39	29	idempotent	idempotent	ADJ
cana-2015	39	30	and	and	CCONJ
cana-2015	39	31	associative	associative	ADJ
cana-2015	39	32	.	.	PUNCT
cana-2015	40	1	(	(	PUNCT
cana-2015	40	2	2	2	X
cana-2015	40	3	)	)	PUNCT
cana-2015	40	4	we	we	PRON
cana-2015	40	5	examine	examine	VERB
cana-2015	40	6	the	the	DET
cana-2015	40	7	q	q	NOUN
cana-2015	40	8	-	-	PUNCT
cana-2015	40	9	livifwa	livifwa	NOUN
cana-2015	40	10	,	,	PUNCT
cana-2015	40	11	q	q	NOUN
cana-2015	40	12	-	-	PUNCT
cana-2015	40	13	livifwg	livifwg	NOUN
cana-2015	40	14	,	,	PUNCT
cana-2015	40	15	q	q	NOUN
cana-2015	40	16	-	-	PUNCT
cana-2015	40	17	elivifwa	elivifwa	NOUN
cana-2015	40	18	and	and	CCONJ
cana-2015	40	19	q	q	NOUN
cana-2015	40	20	-	-	NOUN
cana-2015	40	21	elivifwg	elivifwg	NOUN
cana-2015	40	22	.	.	PUNCT
cana-2015	41	1	2	2	NUM
cana-2015	41	2	preliminaries	preliminary	NOUN
cana-2015	41	3	in	in	ADP
cana-2015	41	4	this	this	DET
cana-2015	41	5	section	section	NOUN
cana-2015	41	6	,	,	PUNCT
cana-2015	41	7	we	we	PRON
cana-2015	41	8	will	will	AUX
cana-2015	41	9	go	go	VERB
cana-2015	41	10	over	over	ADP
cana-2015	41	11	pfs	pfs	PROPN
cana-2015	41	12	and	and	CCONJ
cana-2015	41	13	pivfs	pivfs	PROPN
cana-2015	41	14	concepts	concept	NOUN
cana-2015	41	15	.	.	PUNCT
cana-2015	42	1	definition	definition	NOUN
cana-2015	42	2	2.1	2.1	NUM
cana-2015	42	3	.	.	PUNCT
cana-2015	42	4	5	5	NUM
cana-2015	42	5	let	let	VERB
cana-2015	42	6	x	x	PRON
cana-2015	42	7	be	be	AUX
cana-2015	42	8	the	the	DET
cana-2015	42	9	universal	universal	ADJ
cana-2015	42	10	set	set	NOUN
cana-2015	42	11	.	.	PUNCT
cana-2015	43	1	the	the	DET
cana-2015	43	2	pfs	pfs	PROPN
cana-2015	43	3	m	m	PROPN
cana-2015	43	4	=	=	SYM
cana-2015	43	5	{	{	PUNCT
cana-2015	43	6	u	u	NOUN
cana-2015	43	7	,	,	PUNCT
cana-2015	43	8	〈	〈	PROPN
cana-2015	43	9	µt	µt	INTJ
cana-2015	43	10	m	m	PROPN
cana-2015	43	11	(	(	PUNCT
cana-2015	43	12	u	u	NOUN
cana-2015	43	13	)	)	PUNCT
cana-2015	43	14	,	,	PUNCT
cana-2015	43	15	µf	µf	ADP
cana-2015	43	16	m	m	PROPN
cana-2015	43	17	(	(	PUNCT
cana-2015	43	18	u	u	NOUN
cana-2015	43	19	)	)	PUNCT
cana-2015	43	20	〉	〉	NOUN
cana-2015	43	21	∣∣u	∣∣u	X
cana-2015	43	22	∈	∈	PROPN
cana-2015	43	23	x	x	PUNCT
cana-2015	43	24	}	}	PUNCT
cana-2015	43	25	,	,	PUNCT
cana-2015	43	26	µt	µt	ADV
cana-2015	43	27	m	m	VERB
cana-2015	43	28	:	:	PUNCT
cana-2015	43	29	x	x	X
cana-2015	43	30	→	→	SYM
cana-2015	43	31	(	(	PUNCT
cana-2015	43	32	0	0	NUM
cana-2015	43	33	,	,	PUNCT
cana-2015	43	34	1	1	NUM
cana-2015	43	35	)	)	PUNCT
cana-2015	43	36	and	and	CCONJ
cana-2015	43	37	µf	µf	ADP
cana-2015	43	38	m	m	ADJ
cana-2015	43	39	:	:	PUNCT
cana-2015	43	40	x	x	X
cana-2015	43	41	→	→	SYM
cana-2015	43	42	(	(	PUNCT
cana-2015	43	43	0	0	NUM
cana-2015	43	44	,	,	PUNCT
cana-2015	43	45	1	1	X
cana-2015	43	46	)	)	PUNCT
cana-2015	43	47	denotes	denote	NOUN
cana-2015	43	48	md	md	PROPN
cana-2015	43	49	and	and	CCONJ
cana-2015	43	50	nmd	nmd	PROPN
cana-2015	43	51	of	of	ADP
cana-2015	43	52	u	u	PROPN
cana-2015	43	53	∈	∈	PROPN
cana-2015	43	54	x	x	PUNCT
cana-2015	43	55	to	to	ADP
cana-2015	43	56	m	m	PRON
cana-2015	43	57	,	,	PUNCT
cana-2015	43	58	respectively	respectively	ADV
cana-2015	43	59	and	and	CCONJ
cana-2015	43	60	0	0	NUM
cana-2015	43	61	≤	≤	NUM
cana-2015	43	62	(	(	PUNCT
cana-2015	43	63	µt	µt	INTJ
cana-2015	43	64	m	m	VERB
cana-2015	43	65	(	(	PUNCT
cana-2015	43	66	u))2	u))2	X
cana-2015	44	1	+	+	CCONJ
cana-2015	44	2	(	(	PUNCT
cana-2015	44	3	µf	µf	PART
cana-2015	44	4	m	m	PROPN
cana-2015	44	5	(	(	PUNCT
cana-2015	44	6	u))2	u))2	PROPN
cana-2015	44	7	≤	≤	NUM
cana-2015	44	8	1	1	NUM
cana-2015	44	9	.	.	PUNCT
cana-2015	45	1	for	for	ADP
cana-2015	45	2	convenience	convenience	NOUN
cana-2015	45	3	,	,	PUNCT
cana-2015	45	4	m	m	VERB
cana-2015	45	5	=	=	VERB
cana-2015	45	6	〈	〈	PROPN
cana-2015	45	7	µt	µt	INTJ
cana-2015	45	8	m	m	PROPN
cana-2015	45	9	,	,	PUNCT
cana-2015	45	10	µ	µ	PROPN
cana-2015	45	11	f	f	X
cana-2015	45	12	m	m	VERB
cana-2015	45	13	〉	〉	NOUN
cana-2015	45	14	is	be	AUX
cana-2015	45	15	called	call	VERB
cana-2015	45	16	the	the	DET
cana-2015	45	17	pythagorean	pythagorean	ADJ
cana-2015	45	18	fuzzy	fuzzy	PROPN
cana-2015	45	19	number(pfn	number(pfn	PROPN
cana-2015	45	20	)	)	PUNCT
cana-2015	45	21	.	.	PUNCT
cana-2015	46	1	definition	definition	NOUN
cana-2015	46	2	2.2	2.2	NUM
cana-2015	46	3	.	.	NOUN
cana-2015	46	4	6	6	NUM
cana-2015	46	5	the	the	DET
cana-2015	46	6	pythagorean	pythagorean	PROPN
cana-2015	46	7	ivfs	ivfs	NOUN
cana-2015	46	8	(	(	PUNCT
cana-2015	46	9	pivfs	pivfs	NOUN
cana-2015	46	10	)	)	PUNCT
cana-2015	47	1	m	m	VERB
cana-2015	47	2	=	=	SYM
cana-2015	47	3	{	{	PUNCT
cana-2015	47	4	u	u	NOUN
cana-2015	47	5	,	,	PUNCT
cana-2015	47	6	〈	〈	PROPN
cana-2015	47	7	µ̃t	µ̃t	VERB
cana-2015	47	8	m	m	PROPN
cana-2015	47	9	(	(	PUNCT
cana-2015	47	10	u	u	NOUN
cana-2015	47	11	)	)	PUNCT
cana-2015	47	12	,	,	PUNCT
cana-2015	47	13	µ̃f	µ̃f	ADJ
cana-2015	47	14	m	m	PROPN
cana-2015	47	15	(	(	PUNCT
cana-2015	47	16	u	u	NOUN
cana-2015	47	17	)	)	PUNCT
cana-2015	47	18	〉	〉	NOUN
cana-2015	47	19	∣∣∣u	∣∣∣u	PROPN
cana-2015	47	20	∈	∈	PROPN
cana-2015	47	21	x	x	PUNCT
cana-2015	47	22	}	}	PUNCT
cana-2015	47	23	,	,	PUNCT
cana-2015	47	24	where	where	SCONJ
cana-2015	47	25	µ̃t	µ̃t	VERB
cana-2015	47	26	m	m	VERB
cana-2015	47	27	:	:	PUNCT
cana-2015	47	28	x	x	X
cana-2015	47	29	→	→	SYM
cana-2015	47	30	int((0	int((0	NOUN
cana-2015	47	31	,	,	PUNCT
cana-2015	47	32	1	1	NUM
cana-2015	47	33	)	)	PUNCT
cana-2015	47	34	)	)	PUNCT
cana-2015	47	35	and	and	CCONJ
cana-2015	47	36	µ̃f	µ̃f	ADJ
cana-2015	47	37	m	m	NOUN
cana-2015	47	38	:	:	PUNCT
cana-2015	48	1	x	x	X
cana-2015	48	2	→	→	SYM
cana-2015	48	3	int((0	int((0	NOUN
cana-2015	48	4	,	,	PUNCT
cana-2015	48	5	1	1	NUM
cana-2015	48	6	)	)	PUNCT
cana-2015	48	7	)	)	PUNCT
cana-2015	48	8	denotes	denote	VERB
cana-2015	48	9	md	md	PROPN
cana-2015	48	10	and	and	CCONJ
cana-2015	48	11	nmd	nmd	PROPN
cana-2015	48	12	of	of	ADP
cana-2015	48	13	u	u	PROPN
cana-2015	48	14	∈	∈	PROPN
cana-2015	48	15	x	x	PUNCT
cana-2015	48	16	to	to	ADP
cana-2015	48	17	m	m	PRON
cana-2015	48	18	,	,	PUNCT
cana-2015	48	19	respectively	respectively	ADV
cana-2015	48	20	,	,	PUNCT
cana-2015	48	21	and	and	CCONJ
cana-2015	48	22	0	0	NUM
cana-2015	48	23	≤	≤	NOUN
cana-2015	48	24	(	(	PUNCT
cana-2015	48	25	µt	µt	X
cana-2015	49	1	+	+	NOUN
cana-2015	49	2	m	m	AUX
cana-2015	49	3	(	(	PUNCT
cana-2015	49	4	u))2	u))2	X
cana-2015	49	5	+	+	CCONJ
cana-2015	49	6	(	(	PUNCT
cana-2015	49	7	µf+	µf+	NOUN
cana-2015	49	8	m	m	VERB
cana-2015	49	9	(	(	PUNCT
cana-2015	49	10	u))2	u))2	PROPN
cana-2015	49	11	≤	≤	NUM
cana-2015	49	12	1	1	NUM
cana-2015	49	13	.	.	PUNCT
cana-2015	50	1	for	for	ADP
cana-2015	50	2	convenience	convenience	NOUN
cana-2015	50	3	,	,	PUNCT
cana-2015	50	4	m	m	VERB
cana-2015	50	5	=	=	SYM
cana-2015	50	6	〈	〈	PROPN
cana-2015	50	7	(	(	PUNCT
cana-2015	50	8	µt	µt	INTJ
cana-2015	50	9	−	−	PROPN
cana-2015	50	10	m	m	INTJ
cana-2015	50	11	,	,	PUNCT
cana-2015	50	12	µt	µt	X
cana-2015	50	13	+	+	NOUN
cana-2015	50	14	m	m	VERB
cana-2015	50	15	)	)	PUNCT
cana-2015	50	16	,	,	PUNCT
cana-2015	50	17	(	(	PUNCT
cana-2015	50	18	µf−	µf−	X
cana-2015	50	19	m	m	NOUN
cana-2015	50	20	,	,	PUNCT
cana-2015	50	21	µf+	µf+	NOUN
cana-2015	50	22	m	m	NOUN
cana-2015	50	23	)	)	PUNCT
cana-2015	50	24	〉	〉	NOUN
cana-2015	50	25	is	be	AUX
cana-2015	50	26	called	call	VERB
cana-2015	50	27	the	the	DET
cana-2015	50	28	pivfn	pivfn	NOUN
cana-2015	50	29	.	.	PUNCT
cana-2015	51	1	definition	definition	NOUN
cana-2015	51	2	2.3	2.3	NUM
cana-2015	51	3	.	.	PUNCT
cana-2015	52	1	the	the	DET
cana-2015	52	2	pythagorean	pythagorean	PROPN
cana-2015	52	3	nsm	nsm	PROPN
cana-2015	52	4	=	=	PUNCT
cana-2015	52	5	{	{	PUNCT
cana-2015	52	6	u	u	PROPN
cana-2015	52	7	,	,	PUNCT
cana-2015	52	8	〈	〈	PROPN
cana-2015	52	9	µt	µt	INTJ
cana-2015	52	10	m	m	PROPN
cana-2015	52	11	(	(	PUNCT
cana-2015	52	12	u	u	NOUN
cana-2015	52	13	)	)	PUNCT
cana-2015	52	14	,	,	PUNCT
cana-2015	52	15	µim	µim	PROPN
cana-2015	52	16	(	(	PUNCT
cana-2015	52	17	u	u	NOUN
cana-2015	52	18	)	)	PUNCT
cana-2015	52	19	,	,	PUNCT
cana-2015	52	20	µf	µf	ADP
cana-2015	52	21	m	m	PROPN
cana-2015	52	22	(	(	PUNCT
cana-2015	52	23	u	u	NOUN
cana-2015	52	24	)	)	PUNCT
cana-2015	52	25	〉	〉	NOUN
cana-2015	52	26	∣∣u	∣∣u	NOUN
cana-2015	52	27	∈x	∈x	NOUN
cana-2015	52	28	}	}	PUNCT
cana-2015	52	29	,	,	PUNCT
cana-2015	52	30	where	where	SCONJ
cana-2015	52	31	µt	µt	PRON
cana-2015	52	32	m	m	VERB
cana-2015	52	33	:	:	PUNCT
cana-2015	52	34	x	x	X
cana-2015	52	35	→	→	SYM
cana-2015	52	36	(	(	PUNCT
cana-2015	52	37	0	0	NUM
cana-2015	52	38	,	,	PUNCT
cana-2015	52	39	1	1	NUM
cana-2015	52	40	)	)	PUNCT
cana-2015	52	41	,	,	PUNCT
cana-2015	52	42	µim	µim	NOUN
cana-2015	52	43	:	:	PUNCT
cana-2015	52	44	x	x	X
cana-2015	52	45	→	→	X
cana-2015	52	46	(	(	PUNCT
cana-2015	52	47	0	0	NUM
cana-2015	52	48	,	,	PUNCT
cana-2015	52	49	1	1	NUM
cana-2015	52	50	)	)	PUNCT
cana-2015	52	51	and	and	CCONJ
cana-2015	52	52	µf	µf	ADP
cana-2015	52	53	m	m	ADJ
cana-2015	52	54	:	:	PUNCT
cana-2015	52	55	x	x	X
cana-2015	52	56	→	→	SYM
cana-2015	52	57	(	(	PUNCT
cana-2015	52	58	0	0	NUM
cana-2015	52	59	,	,	PUNCT
cana-2015	52	60	1	1	X
cana-2015	52	61	)	)	PUNCT
cana-2015	52	62	denotes	denote	NOUN
cana-2015	52	63	tmd	tmd	PROPN
cana-2015	52	64	,	,	PUNCT
cana-2015	52	65	imd	imd	PROPN
cana-2015	52	66	and	and	CCONJ
cana-2015	52	67	fmd	fmd	NOUN
cana-2015	52	68	of	of	ADP
cana-2015	52	69	u	u	PROPN
cana-2015	52	70	∈	∈	PROPN
cana-2015	52	71	x	x	PUNCT
cana-2015	52	72	to	to	ADP
cana-2015	52	73	m	m	PRON
cana-2015	52	74	,	,	PUNCT
cana-2015	52	75	respectively	respectively	ADV
cana-2015	52	76	and	and	CCONJ
cana-2015	52	77	0	0	NUM
cana-2015	52	78	≤	≤	NUM
cana-2015	52	79	(	(	PUNCT
cana-2015	52	80	µt	µt	NOUN
cana-2015	52	81	m	m	PROPN
cana-2015	52	82	(	(	PUNCT
cana-2015	52	83	u))2+(µim	u))2+(µim	PROPN
cana-2015	52	84	(	(	PUNCT
cana-2015	52	85	u))2+(µf	u))2+(µf	PROPN
cana-2015	52	86	m	m	PROPN
cana-2015	52	87	(	(	PUNCT
cana-2015	52	88	u))2	u))2	PROPN
cana-2015	52	89	≤	≤	NUM
cana-2015	52	90	2	2	NUM
cana-2015	52	91	.	.	PUNCT
cana-2015	52	92	for	for	ADP
cana-2015	52	93	convenience	convenience	NOUN
cana-2015	52	94	,	,	PUNCT
cana-2015	52	95	m	m	VERB
cana-2015	52	96	=	=	VERB
cana-2015	52	97	〈	〈	PROPN
cana-2015	52	98	µt	µt	INTJ
cana-2015	52	99	m	m	PROPN
cana-2015	52	100	,	,	PUNCT
cana-2015	52	101	µ	µ	VERB
cana-2015	52	102	i	i	PRON
cana-2015	52	103	m	m	VERB
cana-2015	52	104	,	,	PUNCT
cana-2015	52	105	µ	µ	PROPN
cana-2015	52	106	f	f	X
cana-2015	52	107	m	m	VERB
cana-2015	52	108	〉	〉	NOUN
cana-2015	52	109	is	be	AUX
cana-2015	52	110	called	call	VERB
cana-2015	52	111	the	the	DET
cana-2015	52	112	pythagorean	pythagorean	ADJ
cana-2015	52	113	neutrosophic	neutrosophic	ADJ
cana-2015	52	114	number	number	NOUN
cana-2015	52	115	.	.	PUNCT
cana-2015	53	1	3	3	NUM
cana-2015	53	2	q	q	NOUN
cana-2015	53	3	-	-	PUNCT
cana-2015	53	4	livifn	livifn	NOUN
cana-2015	53	5	and	and	CCONJ
cana-2015	53	6	its	its	PRON
cana-2015	53	7	fundamental	fundamental	ADJ
cana-2015	53	8	operations	operation	NOUN
cana-2015	53	9	the	the	DET
cana-2015	53	10	q	q	NOUN
cana-2015	53	11	-	-	PUNCT
cana-2015	53	12	livifn	livifn	NOUN
cana-2015	53	13	has	have	VERB
cana-2015	53	14	several	several	ADJ
cana-2015	53	15	intriguing	intriguing	ADJ
cana-2015	53	16	basic	basic	ADJ
cana-2015	53	17	operations	operation	NOUN
cana-2015	53	18	connected	connect	VERB
cana-2015	53	19	to	to	ADP
cana-2015	53	20	it	it	PRON
cana-2015	53	21	.	.	PUNCT
cana-2015	54	1	definition	definition	NOUN
cana-2015	54	2	3.1	3.1	NUM
cana-2015	54	3	.	.	PUNCT
cana-2015	55	1	the	the	DET
cana-2015	55	2	q	q	NOUN
cana-2015	55	3	-	-	PUNCT
cana-2015	55	4	livifs	livifs	NOUN
cana-2015	55	5	m	m	NOUN
cana-2015	55	6	=	=	SYM
cana-2015	55	7	{	{	PUNCT
cana-2015	55	8	u	u	NOUN
cana-2015	55	9	,	,	PUNCT
cana-2015	55	10	〈	〈	PROPN
cana-2015	55	11	(	(	PUNCT
cana-2015	55	12	logt	logt	PROPN
cana-2015	55	13	l	l	NOUN
cana-2015	55	14	m	m	PROPN
cana-2015	55	15	(	(	PUNCT
cana-2015	55	16	u	u	NOUN
cana-2015	55	17	)	)	PUNCT
cana-2015	55	18	,	,	PUNCT
cana-2015	55	19	log(t	log(t	PROPN
cana-2015	55	20	u	u	NOUN
cana-2015	55	21	m	m	PROPN
cana-2015	55	22	(	(	PUNCT
cana-2015	55	23	u	u	NOUN
cana-2015	55	24	)	)	PUNCT
cana-2015	55	25	)	)	PUNCT
cana-2015	55	26	)	)	PUNCT
cana-2015	56	1	(	(	PUNCT
cana-2015	56	2	logf	logf	INTJ
cana-2015	56	3	l	l	NOUN
cana-2015	56	4	m	m	PROPN
cana-2015	56	5	(	(	PUNCT
cana-2015	56	6	u	u	NOUN
cana-2015	56	7	)	)	PUNCT
cana-2015	56	8	,	,	PUNCT
cana-2015	56	9	log(fu	log(fu	VERB
cana-2015	56	10	m	m	PROPN
cana-2015	56	11	(	(	PUNCT
cana-2015	56	12	u	u	NOUN
cana-2015	56	13	)	)	PUNCT
cana-2015	56	14	)	)	PUNCT
cana-2015	56	15	)	)	PUNCT
cana-2015	56	16	〉	〉	NOUN
cana-2015	56	17	∣∣∣u	∣∣∣u	PROPN
cana-2015	56	18	∈	∈	PROPN
cana-2015	56	19	x	x	PUNCT
cana-2015	56	20	}	}	PUNCT
cana-2015	56	21	,	,	PUNCT
cana-2015	56	22	µ̃t	µ̃t	VERB
cana-2015	56	23	m	m	VERB
cana-2015	56	24	:	:	PUNCT
cana-2015	56	25	x	x	X
cana-2015	56	26	→	→	SYM
cana-2015	56	27	int((0	int((0	NOUN
cana-2015	56	28	,	,	PUNCT
cana-2015	56	29	1	1	NUM
cana-2015	56	30	)	)	PUNCT
cana-2015	56	31	)	)	PUNCT
cana-2015	56	32	and	and	CCONJ
cana-2015	56	33	µ̃f	µ̃f	ADJ
cana-2015	56	34	m	m	NOUN
cana-2015	56	35	:	:	PUNCT
cana-2015	56	36	x	x	X
cana-2015	56	37	→	→	SYM
cana-2015	56	38	int((0	int((0	NOUN
cana-2015	56	39	,	,	PUNCT
cana-2015	56	40	1	1	NUM
cana-2015	56	41	)	)	PUNCT
cana-2015	56	42	)	)	PUNCT
cana-2015	56	43	denotes	denote	VERB
cana-2015	56	44	tmd	tmd	NOUN
cana-2015	56	45	and	and	CCONJ
cana-2015	56	46	fmd	fmd	NOUN
cana-2015	56	47	of	of	ADP
cana-2015	56	48	u	u	NOUN
cana-2015	56	49	∈x	∈x	NOUN
cana-2015	56	50	tom	tom	PROPN
cana-2015	56	51	,	,	PUNCT
cana-2015	56	52	respectively	respectively	ADV
cana-2015	56	53	and	and	CCONJ
cana-2015	56	54	0	0	NUM
cana-2015	56	55	≤	≤	NOUN
cana-2015	56	56	(	(	PUNCT
cana-2015	56	57	log∏	log∏	NOUN
cana-2015	57	1	i	i	PRON
cana-2015	57	2	t	t	VERB
cana-2015	57	3	u	u	X
cana-2015	57	4	m	m	VERB
cana-2015	57	5	(	(	PUNCT
cana-2015	57	6	u))q+(log∏	u))q+(log∏	INTJ
cana-2015	57	7	i	i	PROPN
cana-2015	57	8	fu	fu	PROPN
cana-2015	57	9	m	m	PROPN
cana-2015	58	1	(	(	PUNCT
cana-2015	58	2	u))q	u))q	ADJ
cana-2015	58	3	≤	≤	PROPN
cana-2015	58	4	1	1	NUM
cana-2015	58	5	,	,	PUNCT
cana-2015	58	6	where	where	SCONJ
cana-2015	58	7	q	q	NOUN
cana-2015	58	8	are	be	AUX
cana-2015	58	9	positive	positive	ADJ
cana-2015	58	10	integers	integer	NOUN
cana-2015	58	11	and	and	CCONJ
cana-2015	58	12	∏	∏	PROPN
cana-2015	58	13	=	=	SYM
cana-2015	58	14	�	�	PROPN
cana-2015	58	15	(	(	PUNCT
cana-2015	58	16	t	t	PROPN
cana-2015	58	17	l	l	NOUN
cana-2015	58	18	m	m	PROPN
cana-2015	58	19	,	,	PUNCT
cana-2015	58	20	t	t	PROPN
cana-2015	58	21	u	u	X
cana-2015	58	22	m	m	PROPN
cana-2015	58	23	)	)	PUNCT
cana-2015	58	24	,	,	PUNCT
cana-2015	58	25	(	(	PUNCT
cana-2015	58	26	f	f	X
cana-2015	58	27	l	l	NOUN
cana-2015	58	28	m	m	PROPN
cana-2015	58	29	,	,	PUNCT
cana-2015	58	30	f	f	PROPN
cana-2015	58	31	u	u	X
cana-2015	58	32	m	m	PROPN
cana-2015	58	33	)	)	PUNCT
cana-2015	58	34	.	.	PUNCT
cana-2015	59	1	for	for	ADP
cana-2015	59	2	convenience	convenience	NOUN
cana-2015	59	3	,	,	PUNCT
cana-2015	59	4	m	m	VERB
cana-2015	59	5	=	=	SYM
cana-2015	59	6	〈	〈	PROPN
cana-2015	59	7	(	(	PUNCT
cana-2015	59	8	logt	logt	PROPN
cana-2015	59	9	l	l	PROPN
cana-2015	59	10	m	m	NOUN
cana-2015	59	11	,	,	PUNCT
cana-2015	59	12	log(t	log(t	PROPN
cana-2015	59	13	u	u	NOUN
cana-2015	59	14	m	m	NOUN
cana-2015	59	15	)	)	PUNCT
cana-2015	59	16	)	)	PUNCT
cana-2015	59	17	,	,	PUNCT
cana-2015	59	18	(	(	PUNCT
cana-2015	59	19	logf	logf	INTJ
cana-2015	59	20	l	l	NOUN
cana-2015	59	21	m	m	VERB
cana-2015	59	22	,	,	PUNCT
cana-2015	59	23	log(f	log(f	PROPN
cana-2015	59	24	u	u	NOUN
cana-2015	59	25	m	m	VERB
cana-2015	59	26	)	)	PUNCT
cana-2015	59	27	)	)	PUNCT
cana-2015	59	28	〉	〉	NOUN
cana-2015	59	29	is	be	AUX
cana-2015	59	30	called	call	VERB
cana-2015	59	31	the	the	DET
cana-2015	59	32	q	q	NOUN
cana-2015	59	33	-	-	NOUN
cana-2015	59	34	livifn	livifn	ADJ
cana-2015	59	35	,	,	PUNCT
cana-2015	59	36	where	where	SCONJ
cana-2015	59	37	q	q	PROPN
cana-2015	59	38	≥	≥	NUM
cana-2015	59	39	1	1	NUM
cana-2015	59	40	.	.	PUNCT
cana-2015	60	1	definition	definition	NOUN
cana-2015	60	2	3.2	3.2	NUM
cana-2015	60	3	.	.	PUNCT
cana-2015	61	1	let	let	VERB
cana-2015	61	2	m	m	NOUN
cana-2015	61	3	=	=	VERB
cana-2015	61	4	〈	〈	PROPN
cana-2015	61	5	(	(	PUNCT
cana-2015	61	6	logt	logt	PROPN
cana-2015	61	7	l	l	PROPN
cana-2015	61	8	m	m	NOUN
cana-2015	61	9	,	,	PUNCT
cana-2015	61	10	log(t	log(t	PROPN
cana-2015	61	11	u	u	NOUN
cana-2015	61	12	m	m	NOUN
cana-2015	61	13	)	)	PUNCT
cana-2015	61	14	)	)	PUNCT
cana-2015	62	1	,	,	PUNCT
cana-2015	62	2	(	(	PUNCT
cana-2015	62	3	logf	logf	INTJ
cana-2015	62	4	l	l	NOUN
cana-2015	62	5	m	m	VERB
cana-2015	62	6	,	,	PUNCT
cana-2015	62	7	log(f	log(f	PROPN
cana-2015	62	8	u	u	NOUN
cana-2015	62	9	m	m	VERB
cana-2015	62	10	)	)	PUNCT
cana-2015	62	11	)	)	PUNCT
cana-2015	62	12	〉	〉	NOUN
cana-2015	62	13	be	be	VERB
cana-2015	62	14	the	the	DET
cana-2015	62	15	q	q	NOUN
cana-2015	62	16	-	-	NOUN
cana-2015	62	17	livifn	livifn	NOUN
cana-2015	62	18	,	,	PUNCT
cana-2015	62	19	the	the	DET
cana-2015	62	20	score	score	NOUN
cana-2015	62	21	function	function	NOUN
cana-2015	62	22	of	of	ADP
cana-2015	62	23	m	m	PROPN
cana-2015	62	24	is	be	AUX
cana-2015	62	25	defined	define	VERB
cana-2015	62	26	as	as	ADP
cana-2015	62	27	s(m	s(m	NOUN
cana-2015	62	28	)	)	PUNCT
cana-2015	63	1	=	=	SYM
cana-2015	63	2	s1(m)+s2(m	s1(m)+s2(m	NOUN
cana-2015	63	3	)	)	PUNCT
cana-2015	63	4	2	2	NUM
cana-2015	63	5	,	,	PUNCT
cana-2015	63	6	−1	−1	NOUN
cana-2015	63	7	≤	≤	NUM
cana-2015	63	8	s(m	s(m	NOUN
cana-2015	63	9	)	)	PUNCT
cana-2015	63	10	≤	≤	NOUN
cana-2015	63	11	1	1	NUM
cana-2015	63	12	.	.	PUNCT
cana-2015	64	1	where	where	SCONJ
cana-2015	64	2	s1(m	s1(m	NOUN
cana-2015	64	3	)	)	PUNCT
cana-2015	64	4	=	=	SYM
cana-2015	64	5	(	(	PUNCT
cana-2015	64	6	l1	l1	PROPN
cana-2015	64	7	2	2	NUM
cana-2015	64	8	+	+	CCONJ
cana-2015	64	9	1−	1−	NUM
cana-2015	64	10	l2	l2	NOUN
cana-2015	64	11	2	2	NUM
cana-2015	64	12	)	)	PUNCT
cana-2015	64	13	,	,	PUNCT
cana-2015	64	14	s2(m	s2(m	PROPN
cana-2015	64	15	)	)	PUNCT
cana-2015	64	16	=	=	SYM
cana-2015	64	17	(	(	PUNCT
cana-2015	64	18	l1	l1	PROPN
cana-2015	64	19	2	2	NUM
cana-2015	64	20	+	+	CCONJ
cana-2015	64	21	1−	1−	NUM
cana-2015	64	22	l2	l2	NOUN
cana-2015	64	23	2	2	NUM
cana-2015	64	24	)	)	PUNCT
cana-2015	64	25	,	,	PUNCT
cana-2015	64	26	the	the	DET
cana-2015	64	27	accuracy	accuracy	NOUN
cana-2015	64	28	function	function	NOUN
cana-2015	64	29	of	of	ADP
cana-2015	64	30	m	m	PROPN
cana-2015	64	31	is	be	AUX
cana-2015	64	32	a(m	a(m	ADV
cana-2015	64	33	)	)	PUNCT
cana-2015	64	34	=	=	SYM
cana-2015	64	35	a1(m)+a2(m	a1(m)+a2(m	NOUN
cana-2015	64	36	)	)	PUNCT
cana-2015	64	37	2	2	NUM
cana-2015	64	38	,	,	PUNCT
cana-2015	64	39	where	where	SCONJ
cana-2015	64	40	0	0	NUM
cana-2015	64	41	≤	≤	NUM
cana-2015	64	42	a(m	a(m	NOUN
cana-2015	64	43	)	)	PUNCT
cana-2015	64	44	≤	≤	NUM
cana-2015	64	45	1	1	NUM
cana-2015	64	46	.	.	PUNCT
cana-2015	65	1	a1(m	a1(m	X
cana-2015	65	2	)	)	PUNCT
cana-2015	66	1	=	=	SYM
cana-2015	66	2	(	(	PUNCT
cana-2015	66	3	l1	l1	PROPN
cana-2015	66	4	2	2	NUM
cana-2015	67	1	+	+	CCONJ
cana-2015	67	2	1	1	NUM
cana-2015	67	3	+	+	NUM
cana-2015	67	4	l2	l2	NOUN
cana-2015	67	5	2	2	NUM
cana-2015	67	6	)	)	PUNCT
cana-2015	67	7	,	,	PUNCT
cana-2015	67	8	a2(m	a2(m	PROPN
cana-2015	67	9	)	)	PUNCT
cana-2015	67	10	=	=	SYM
cana-2015	67	11	(	(	PUNCT
cana-2015	67	12	l1	l1	PROPN
cana-2015	67	13	2	2	NUM
cana-2015	67	14	+	+	CCONJ
cana-2015	67	15	1	1	NUM
cana-2015	67	16	+	+	NUM
cana-2015	67	17	l2	l2	NOUN
cana-2015	67	18	2	2	NUM
cana-2015	67	19	)	)	PUNCT
cana-2015	67	20	,	,	PUNCT
cana-2015	67	21	where	where	SCONJ
cana-2015	67	22	l1	l1	PROPN
cana-2015	67	23	=	=	PROPN
cana-2015	67	24	(	(	PUNCT
cana-2015	67	25	log∏	log∏	PROPN
cana-2015	67	26	i	i	NOUN
cana-2015	67	27	t	t	VERB
cana-2015	67	28	l	l	NOUN
cana-2015	67	29	m	m	VERB
cana-2015	67	30	)	)	PUNCT
cana-2015	67	31	2	2	NUM
cana-2015	67	32	+	+	CCONJ
cana-2015	67	33	(	(	PUNCT
cana-2015	67	34	log∏	log∏	PROPN
cana-2015	67	35	i	i	PRON
cana-2015	67	36	(	(	PUNCT
cana-2015	67	37	t	t	PROPN
cana-2015	67	38	u	u	X
cana-2015	67	39	m	m	PROPN
cana-2015	67	40	)	)	PUNCT
cana-2015	67	41	)	)	PUNCT
cana-2015	67	42	2	2	NUM
cana-2015	67	43	,	,	PUNCT
cana-2015	67	44	l2	l2	NOUN
cana-2015	67	45	=	=	SYM
cana-2015	67	46	(	(	PUNCT
cana-2015	67	47	log∏	log∏	PROPN
cana-2015	67	48	i	i	NOUN
cana-2015	67	49	f	f	PROPN
cana-2015	67	50	l	l	NOUN
cana-2015	67	51	m	m	VERB
cana-2015	67	52	)	)	PUNCT
cana-2015	67	53	2	2	NUM
cana-2015	67	54	+	+	CCONJ
cana-2015	67	55	(	(	PUNCT
cana-2015	67	56	log∏	log∏	PROPN
cana-2015	67	57	i	i	PRON
cana-2015	67	58	(	(	PUNCT
cana-2015	67	59	fu	fu	NOUN
cana-2015	67	60	m	m	PROPN
cana-2015	67	61	)	)	PUNCT
cana-2015	67	62	)	)	PUNCT
cana-2015	67	63	2	2	NUM
cana-2015	67	64	https://internationalpubls.com	https://internationalpubls.com	X
cana-2015	67	65	540	540	NUM
cana-2015	67	66	communications	communication	NOUN
cana-2015	67	67	on	on	ADP
cana-2015	67	68	applied	apply	VERB
cana-2015	67	69	nonlinear	nonlinear	ADJ
cana-2015	67	70	analysis	analysis	NOUN
cana-2015	67	71	issn	issn	NOUN
cana-2015	67	72	:	:	PUNCT
cana-2015	67	73	1074	1074	NUM
cana-2015	67	74	-	-	PUNCT
cana-2015	67	75	133x	133x	NUM
cana-2015	67	76	vol	vol	NOUN
cana-2015	67	77	32	32	NUM
cana-2015	67	78	no	no	NOUN
cana-2015	67	79	.	.	NOUN
cana-2015	67	80	3	3	NUM
cana-2015	67	81	(	(	PUNCT
cana-2015	67	82	2025	2025	NUM
cana-2015	67	83	)	)	PUNCT
cana-2015	67	84	definition	definition	NOUN
cana-2015	67	85	3.3	3.3	NUM
cana-2015	67	86	.	.	PUNCT
cana-2015	68	1	let	let	VERB
cana-2015	68	2	m	m	PROPN
cana-2015	68	3	=	=	VERB
cana-2015	68	4	〈	〈	PROPN
cana-2015	68	5	(	(	PUNCT
cana-2015	68	6	logt	logt	NOUN
cana-2015	68	7	l	l	PROPN
cana-2015	68	8	m	m	NOUN
cana-2015	68	9	,	,	PUNCT
cana-2015	68	10	log(t	log(t	PROPN
cana-2015	68	11	u	u	NOUN
cana-2015	68	12	m	m	NOUN
cana-2015	68	13	)	)	PUNCT
cana-2015	68	14	)	)	PUNCT
cana-2015	68	15	,	,	PUNCT
cana-2015	68	16	(	(	PUNCT
cana-2015	68	17	logf	logf	ADV
cana-2015	68	18	l	l	NOUN
cana-2015	68	19	m	m	VERB
cana-2015	68	20	,	,	PUNCT
cana-2015	68	21	log(f	log(f	PROPN
cana-2015	68	22	u	u	NOUN
cana-2015	68	23	m	m	VERB
cana-2015	68	24	)	)	PUNCT
cana-2015	68	25	)	)	PUNCT
cana-2015	68	26	〉	〉	NOUN
cana-2015	68	27	,	,	PUNCT
cana-2015	68	28	b	b	NOUN
cana-2015	68	29	=	=	SYM
cana-2015	68	30	〈	〈	PROPN
cana-2015	68	31	(	(	PUNCT
cana-2015	68	32	logt	logt	NOUN
cana-2015	68	33	l	l	PROPN
cana-2015	68	34	b	b	PROPN
cana-2015	68	35	,	,	PUNCT
cana-2015	68	36	log(t	log(t	PROPN
cana-2015	68	37	u	u	NOUN
cana-2015	68	38	b	b	PROPN
cana-2015	68	39	)	)	PUNCT
cana-2015	68	40	)	)	PUNCT
cana-2015	68	41	,	,	PUNCT
cana-2015	68	42	(	(	PUNCT
cana-2015	68	43	logf	logf	ADP
cana-2015	68	44	l	l	PROPN
cana-2015	68	45	b	b	PROPN
cana-2015	68	46	,	,	PUNCT
cana-2015	68	47	log(f	log(f	PROPN
cana-2015	68	48	u	u	NOUN
cana-2015	68	49	b	b	NOUN
cana-2015	68	50	)	)	PUNCT
cana-2015	68	51	)	)	PUNCT
cana-2015	68	52	〉	〉	NOUN
cana-2015	68	53	and	and	CCONJ
cana-2015	68	54	c	c	NOUN
cana-2015	68	55	=	=	SYM
cana-2015	68	56	〈	〈	PROPN
cana-2015	68	57	(	(	PUNCT
cana-2015	68	58	logt	logt	NOUN
cana-2015	68	59	l	l	PROPN
cana-2015	68	60	c	c	NOUN
cana-2015	68	61	,	,	PUNCT
cana-2015	68	62	log(t	log(t	PROPN
cana-2015	68	63	u	u	NOUN
cana-2015	68	64	c	c	PROPN
cana-2015	68	65	)	)	PUNCT
cana-2015	68	66	)	)	PUNCT
cana-2015	68	67	,	,	PUNCT
cana-2015	68	68	(	(	PUNCT
cana-2015	68	69	logf	logf	INTJ
cana-2015	68	70	l	l	NOUN
cana-2015	68	71	c	c	NOUN
cana-2015	68	72	,	,	PUNCT
cana-2015	68	73	log(f	log(f	PROPN
cana-2015	68	74	u	u	NOUN
cana-2015	68	75	c	c	NOUN
cana-2015	68	76	)	)	PUNCT
cana-2015	68	77	)	)	PUNCT
cana-2015	68	78	〉	〉	NOUN
cana-2015	68	79	be	be	VERB
cana-2015	68	80	any	any	DET
cana-2015	68	81	three	three	NUM
cana-2015	68	82	q	q	ADJ
cana-2015	68	83	-	-	PUNCT
cana-2015	68	84	livifns	livifns	NOUN
cana-2015	68	85	and∏	and∏	PROPN
cana-2015	68	86	=	=	SYM
cana-2015	68	87	�	�	PROPN
cana-2015	68	88	(	(	PUNCT
cana-2015	68	89	tmi	tmi	PROPN
cana-2015	68	90	,	,	PUNCT
cana-2015	68	91	t	t	PROPN
cana-2015	68	92	u	u	PROPN
cana-2015	68	93	mi	mi	PROPN
cana-2015	68	94	)	)	PUNCT
cana-2015	68	95	,	,	PUNCT
cana-2015	68	96	(	(	PUNCT
cana-2015	68	97	fmi	fmi	PROPN
cana-2015	68	98	,	,	PUNCT
cana-2015	68	99	fu	fu	PROPN
cana-2015	68	100	mi	mi	PROPN
cana-2015	68	101	)	)	PUNCT
cana-2015	68	102	.	.	PUNCT
cana-2015	69	1	their	their	PRON
cana-2015	69	2	following	follow	VERB
cana-2015	69	3	operations	operation	NOUN
cana-2015	69	4	are	be	AUX
cana-2015	69	5	defined	define	VERB
cana-2015	69	6	as	as	SCONJ
cana-2015	69	7	follows	follow	VERB
cana-2015	69	8	:	:	PUNCT
cana-2015	69	9	1	1	NUM
cana-2015	69	10	.	.	X
cana-2015	70	1	b	b	X
cana-2015	70	2	∨	∨	NUM
cana-2015	70	3	c	c	X
cana-2015	71	1	=	=	NOUN
cana-2015	71	2			NOUN
cana-2015	71	3			PROPN
cana-2015	71	4	q	q	PROPN
cana-2015	71	5	√	√	PROPN
cana-2015	71	6	(	(	PUNCT
cana-2015	71	7	log∏	log∏	PROPN
cana-2015	71	8	i	i	PRON
cana-2015	71	9	t	t	VERB
cana-2015	71	10	l	l	NOUN
cana-2015	71	11	b	b	X
cana-2015	71	12	)	)	PUNCT
cana-2015	71	13	q	q	NOUN
cana-2015	72	1	+	+	CCONJ
cana-2015	72	2	(	(	PUNCT
cana-2015	72	3	log∏	log∏	PROPN
cana-2015	72	4	i	i	NOUN
cana-2015	72	5	t	t	VERB
cana-2015	72	6	l	l	NOUN
cana-2015	72	7	c	c	X
cana-2015	72	8	)	)	PUNCT
cana-2015	72	9	q	q	NOUN
cana-2015	72	10	−	−	PROPN
cana-2015	72	11	(	(	PUNCT
cana-2015	72	12	log∏	log∏	PROPN
cana-2015	72	13	i	i	PRON
cana-2015	72	14	t	t	VERB
cana-2015	72	15	l	l	NOUN
cana-2015	72	16	b	b	X
cana-2015	72	17	)	)	PUNCT
cana-2015	72	18	q	q	NOUN
cana-2015	72	19	·	·	PUNCT
cana-2015	72	20	(	(	PUNCT
cana-2015	72	21	log∏	log∏	NOUN
cana-2015	72	22	i	i	NOUN
cana-2015	72	23	t	t	VERB
cana-2015	72	24	l	l	NOUN
cana-2015	72	25	c	c	X
cana-2015	72	26	)	)	PUNCT
cana-2015	72	27	q	q	NOUN
cana-2015	72	28	,	,	PUNCT
cana-2015	72	29	q	q	NOUN
cana-2015	72	30	√	√	PROPN
cana-2015	72	31	(	(	PUNCT
cana-2015	72	32	log∏	log∏	PROPN
cana-2015	72	33	i	i	PRON
cana-2015	72	34	(	(	PUNCT
cana-2015	72	35	t	t	PROPN
cana-2015	72	36	u	u	PROPN
cana-2015	72	37	b	b	PROPN
cana-2015	72	38	)	)	PUNCT
cana-2015	72	39	)	)	PUNCT
cana-2015	72	40	q	q	PROPN
cana-2015	73	1	+	+	CCONJ
cana-2015	73	2	(	(	PUNCT
cana-2015	73	3	log∏	log∏	PROPN
cana-2015	73	4	i	i	PRON
cana-2015	73	5	(	(	PUNCT
cana-2015	73	6	t	t	PROPN
cana-2015	73	7	u	u	X
cana-2015	73	8	c	c	PROPN
cana-2015	73	9	)	)	PUNCT
cana-2015	73	10	)	)	PUNCT
cana-2015	73	11	q	q	NOUN
cana-2015	73	12	−	−	PROPN
cana-2015	73	13	(	(	PUNCT
cana-2015	73	14	log∏	log∏	PROPN
cana-2015	73	15	i	i	PRON
cana-2015	73	16	(	(	PUNCT
cana-2015	73	17	t	t	PROPN
cana-2015	73	18	u	u	PROPN
cana-2015	73	19	b	b	PROPN
cana-2015	73	20	)	)	PUNCT
cana-2015	73	21	)	)	PUNCT
cana-2015	73	22	q	q	X
cana-2015	73	23	·	·	PUNCT
cana-2015	73	24	(	(	PUNCT
cana-2015	73	25	log∏	log∏	NOUN
cana-2015	73	26	i	i	PRON
cana-2015	73	27	(	(	PUNCT
cana-2015	73	28	t	t	PROPN
cana-2015	73	29	u	u	X
cana-2015	73	30	c	c	PROPN
cana-2015	73	31	)	)	PUNCT
cana-2015	73	32	)	)	PUNCT
cana-2015	73	33	q	q	PROPN
cana-2015	74	1			PROPN
cana-2015	74	2	,	,	PUNCT
cana-2015	74	3	(	(	PUNCT
cana-2015	74	4	log∏	log∏	PROPN
cana-2015	74	5	i	i	PRON
cana-2015	74	6	(	(	PUNCT
cana-2015	74	7	f	f	PROPN
cana-2015	74	8	l	l	PROPN
cana-2015	74	9	b	b	X
cana-2015	74	10	)	)	PUNCT
cana-2015	74	11	q	q	NOUN
cana-2015	74	12	·	·	PUNCT
cana-2015	74	13	log∏	log∏	NOUN
cana-2015	74	14	i	i	PRON
cana-2015	74	15	(	(	PUNCT
cana-2015	74	16	f	f	X
cana-2015	74	17	l	l	NOUN
cana-2015	74	18	c	c	X
cana-2015	74	19	)	)	PUNCT
cana-2015	74	20	q	q	NOUN
cana-2015	74	21	,	,	PUNCT
cana-2015	74	22	log∏	log∏	PROPN
cana-2015	74	23	i	i	PRON
cana-2015	74	24	(	(	PUNCT
cana-2015	74	25	fu	fu	NOUN
cana-2015	74	26	b	b	PROPN
cana-2015	74	27	)	)	PUNCT
cana-2015	74	28	q	q	NOUN
cana-2015	74	29	·	·	PUNCT
cana-2015	74	30	log∏	log∏	NOUN
cana-2015	74	31	i	i	PRON
cana-2015	74	32	(	(	PUNCT
cana-2015	74	33	fu	fu	NOUN
cana-2015	74	34	c	c	NOUN
cana-2015	74	35	)	)	PUNCT
cana-2015	74	36	q	q	NOUN
cana-2015	74	37	)	)	PUNCT
cana-2015	74	38			NOUN
cana-2015	74	39	,	,	PUNCT
cana-2015	74	40	2	2	NUM
cana-2015	74	41	.	.	X
cana-2015	75	1	b	b	X
cana-2015	75	2	∧	∧	NOUN
cana-2015	75	3	c	c	NOUN
cana-2015	75	4	=	=	NOUN
cana-2015	75	5			NOUN
cana-2015	75	6	(	(	PUNCT
cana-2015	75	7	log∏	log∏	PROPN
cana-2015	75	8	i	i	PRON
cana-2015	75	9	(	(	PUNCT
cana-2015	75	10	t	t	PROPN
cana-2015	75	11	l	l	NOUN
cana-2015	75	12	b	b	X
cana-2015	75	13	)	)	PUNCT
cana-2015	75	14	q	q	NOUN
cana-2015	76	1	·	·	PUNCT
cana-2015	76	2	log∏	log∏	NOUN
cana-2015	76	3	i	i	PRON
cana-2015	76	4	(	(	PUNCT
cana-2015	76	5	t	t	NOUN
cana-2015	76	6	l	l	NOUN
cana-2015	76	7	c	c	X
cana-2015	76	8	)	)	PUNCT
cana-2015	76	9	q	q	NOUN
cana-2015	76	10	,	,	PUNCT
cana-2015	76	11	log∏	log∏	PROPN
cana-2015	76	12	i	i	PRON
cana-2015	76	13	(	(	PUNCT
cana-2015	76	14	t	t	PROPN
cana-2015	76	15	u	u	PROPN
cana-2015	76	16	b	b	PROPN
cana-2015	76	17	)	)	PUNCT
cana-2015	76	18	q	q	NOUN
cana-2015	76	19	·	·	PUNCT
cana-2015	76	20	log∏	log∏	NOUN
cana-2015	76	21	i	i	PRON
cana-2015	76	22	(	(	PUNCT
cana-2015	76	23	t	t	PROPN
cana-2015	76	24	u	u	X
cana-2015	76	25	c	c	PROPN
cana-2015	76	26	)	)	PUNCT
cana-2015	76	27	q	q	NOUN
cana-2015	76	28	)	)	PUNCT
cana-2015	76	29	,	,	PUNCT
cana-2015	76	30			PROPN
cana-2015	76	31	q	q	PROPN
cana-2015	76	32	√	√	PROPN
cana-2015	76	33	(	(	PUNCT
cana-2015	76	34	log∏	log∏	NOUN
cana-2015	76	35	i	i	NOUN
cana-2015	76	36	f	f	PROPN
cana-2015	76	37	l	l	NOUN
cana-2015	76	38	b	b	X
cana-2015	76	39	)	)	PUNCT
cana-2015	76	40	q	q	NOUN
cana-2015	77	1	+	+	CCONJ
cana-2015	77	2	(	(	PUNCT
cana-2015	77	3	log∏	log∏	NOUN
cana-2015	77	4	i	i	NOUN
cana-2015	77	5	f	f	NOUN
cana-2015	77	6	l	l	NOUN
cana-2015	77	7	c	c	X
cana-2015	77	8	)	)	PUNCT
cana-2015	77	9	q	q	NOUN
cana-2015	78	1	−	−	PROPN
cana-2015	79	1	(	(	PUNCT
cana-2015	79	2	log∏	log∏	NOUN
cana-2015	79	3	i	i	NOUN
cana-2015	79	4	f	f	PROPN
cana-2015	79	5	l	l	NOUN
cana-2015	79	6	b	b	X
cana-2015	79	7	)	)	PUNCT
cana-2015	79	8	q	q	NOUN
cana-2015	79	9	·	·	PUNCT
cana-2015	79	10	(	(	PUNCT
cana-2015	79	11	log∏	log∏	NOUN
cana-2015	79	12	i	i	PRON
cana-2015	79	13	f	f	NOUN
cana-2015	79	14	l	l	NOUN
cana-2015	79	15	c	c	X
cana-2015	79	16	)	)	PUNCT
cana-2015	79	17	q	q	NOUN
cana-2015	79	18	,	,	PUNCT
cana-2015	79	19	q	q	NOUN
cana-2015	79	20	√	√	PROPN
cana-2015	79	21	(	(	PUNCT
cana-2015	79	22	log∏	log∏	PROPN
cana-2015	79	23	i	i	PRON
cana-2015	79	24	(	(	PUNCT
cana-2015	79	25	fu	fu	PROPN
cana-2015	79	26	b	b	PROPN
cana-2015	79	27	)	)	PUNCT
cana-2015	79	28	)	)	PUNCT
cana-2015	79	29	q	q	NOUN
cana-2015	80	1	+	+	CCONJ
cana-2015	80	2	(	(	PUNCT
cana-2015	80	3	log∏	log∏	PROPN
cana-2015	80	4	i	i	PRON
cana-2015	80	5	(	(	PUNCT
cana-2015	80	6	fu	fu	NOUN
cana-2015	80	7	c	c	NOUN
cana-2015	80	8	)	)	PUNCT
cana-2015	80	9	)	)	PUNCT
cana-2015	81	1	q	q	NOUN
cana-2015	82	1	−	−	PROPN
cana-2015	82	2	(	(	PUNCT
cana-2015	82	3	log∏	log∏	PROPN
cana-2015	82	4	i	i	PRON
cana-2015	82	5	(	(	PUNCT
cana-2015	82	6	fu	fu	PROPN
cana-2015	82	7	b	b	PROPN
cana-2015	82	8	)	)	PUNCT
cana-2015	82	9	)	)	PUNCT
cana-2015	82	10	q	q	X
cana-2015	83	1	·	·	PUNCT
cana-2015	83	2	(	(	PUNCT
cana-2015	83	3	log∏	log∏	NOUN
cana-2015	83	4	i	i	PRON
cana-2015	83	5	(	(	PUNCT
cana-2015	83	6	fu	fu	NOUN
cana-2015	83	7	c	c	NOUN
cana-2015	83	8	)	)	PUNCT
cana-2015	83	9	)	)	PUNCT
cana-2015	84	1	q	q	PROPN
cana-2015	85	1			PROPN
cana-2015	85	2			X
cana-2015	85	3	,	,	PUNCT
cana-2015	85	4	3	3	NUM
cana-2015	85	5	.	.	NOUN
cana-2015	85	6	ℵ	ℵ	X
cana-2015	85	7	·	·	SYM
cana-2015	85	8	m	m	PROPN
cana-2015	85	9	=	=	SYM
cana-2015	85	10			PROPN
cana-2015	85	11	(	(	PUNCT
cana-2015	85	12	q	q	NOUN
cana-2015	85	13	√	√	NUM
cana-2015	85	14	1−	1−	NUM
cana-2015	85	15	(	(	PUNCT
cana-2015	85	16	1−	1−	NUM
cana-2015	85	17	(	(	PUNCT
cana-2015	85	18	log∏	log∏	NOUN
cana-2015	86	1	i	i	NOUN
cana-2015	86	2	t	t	VERB
cana-2015	86	3	l	l	NOUN
cana-2015	86	4	m	m	NOUN
cana-2015	86	5	)	)	PUNCT
cana-2015	86	6	q	q	NOUN
cana-2015	86	7	)	)	PUNCT
cana-2015	86	8	ℵ	ℵ	NOUN
cana-2015	86	9	,	,	PUNCT
cana-2015	86	10	q	q	NOUN
cana-2015	86	11	√	√	NUM
cana-2015	86	12	1−	1−	NUM
cana-2015	87	1	(	(	PUNCT
cana-2015	87	2	1−	1−	NUM
cana-2015	87	3	(	(	PUNCT
cana-2015	87	4	log∏	log∏	NOUN
cana-2015	87	5	i	i	PRON
cana-2015	87	6	(	(	PUNCT
cana-2015	87	7	t	t	PROPN
cana-2015	87	8	u	u	X
cana-2015	87	9	m	m	NOUN
cana-2015	87	10	)	)	PUNCT
cana-2015	87	11	)	)	PUNCT
cana-2015	87	12	q	q	X
cana-2015	87	13	)	)	PUNCT
cana-2015	87	14	ℵ	ℵ	NOUN
cana-2015	87	15	)	)	PUNCT
cana-2015	87	16	,	,	PUNCT
cana-2015	87	17	(	(	PUNCT
cana-2015	87	18	(	(	PUNCT
cana-2015	87	19	log∏	log∏	NOUN
cana-2015	87	20	i	i	NOUN
cana-2015	87	21	f	f	PROPN
cana-2015	87	22	l	l	NOUN
cana-2015	87	23	m	m	NOUN
cana-2015	87	24	)	)	PUNCT
cana-2015	87	25	qℵ	qℵ	PROPN
cana-2015	87	26	,	,	PUNCT
cana-2015	87	27	(	(	PUNCT
cana-2015	87	28	log∏	log∏	PROPN
cana-2015	87	29	i	i	PRON
cana-2015	87	30	(	(	PUNCT
cana-2015	87	31	fu	fu	NOUN
cana-2015	87	32	m	m	PROPN
cana-2015	87	33	)	)	PUNCT
cana-2015	87	34	)	)	PUNCT
cana-2015	87	35	qℵ	qℵ	X
cana-2015	87	36	)	)	PUNCT
cana-2015	88	1			PROPN
cana-2015	88	2	,	,	PUNCT
cana-2015	88	3	4	4	X
cana-2015	88	4	.	.	PUNCT
cana-2015	88	5	mℵ	mℵ	NOUN
cana-2015	89	1	=	=	PUNCT
cana-2015	89	2			PROPN
cana-2015	89	3	(	(	PUNCT
cana-2015	89	4	(	(	PUNCT
cana-2015	89	5	log∏	log∏	NOUN
cana-2015	89	6	i	i	NOUN
cana-2015	89	7	t	t	VERB
cana-2015	89	8	l	l	NOUN
cana-2015	89	9	m	m	NOUN
cana-2015	89	10	)	)	PUNCT
cana-2015	89	11	qℵ	qℵ	PROPN
cana-2015	89	12	,	,	PUNCT
cana-2015	89	13	(	(	PUNCT
cana-2015	89	14	log∏	log∏	PROPN
cana-2015	89	15	i	i	PRON
cana-2015	89	16	(	(	PUNCT
cana-2015	89	17	t	t	PROPN
cana-2015	89	18	u	u	X
cana-2015	89	19	m	m	PROPN
cana-2015	89	20	)	)	PUNCT
cana-2015	89	21	)	)	PUNCT
cana-2015	89	22	qℵ	qℵ	X
cana-2015	89	23	)	)	PUNCT
cana-2015	89	24	,	,	PUNCT
cana-2015	89	25	(	(	PUNCT
cana-2015	89	26	q	q	NOUN
cana-2015	89	27	√	√	NUM
cana-2015	89	28	1−	1−	NUM
cana-2015	89	29	(	(	PUNCT
cana-2015	89	30	1−	1−	NUM
cana-2015	89	31	(	(	PUNCT
cana-2015	89	32	log∏	log∏	NOUN
cana-2015	89	33	i	i	NOUN
cana-2015	89	34	f	f	PROPN
cana-2015	89	35	l	l	NOUN
cana-2015	89	36	m	m	NOUN
cana-2015	89	37	)	)	PUNCT
cana-2015	89	38	q	q	NOUN
cana-2015	89	39	)	)	PUNCT
cana-2015	89	40	ℵ	ℵ	NOUN
cana-2015	89	41	,	,	PUNCT
cana-2015	89	42	q	q	NOUN
cana-2015	89	43	√	√	NUM
cana-2015	89	44	1−	1−	NUM
cana-2015	89	45	(	(	PUNCT
cana-2015	89	46	1−	1−	NUM
cana-2015	89	47	(	(	PUNCT
cana-2015	89	48	log∏	log∏	NOUN
cana-2015	89	49	i	i	PRON
cana-2015	89	50	(	(	PUNCT
cana-2015	89	51	fu	fu	NOUN
cana-2015	89	52	m	m	PROPN
cana-2015	89	53	)	)	PUNCT
cana-2015	89	54	)	)	PUNCT
cana-2015	89	55	q	q	X
cana-2015	89	56	)	)	PUNCT
cana-2015	89	57	ℵ	ℵ	NOUN
cana-2015	89	58	)	)	PUNCT
cana-2015	89	59			PROPN
cana-2015	89	60	.	.	PUNCT
cana-2015	90	1	4	4	NUM
cana-2015	90	2	q	q	NOUN
cana-2015	90	3	-	-	PUNCT
cana-2015	90	4	livifs	livif	NOUN
cana-2015	90	5	concept	concept	NOUN
cana-2015	90	6	the	the	DET
cana-2015	90	7	weighed	weighed	ADJ
cana-2015	90	8	averaging	average	VERB
cana-2015	90	9	operators	operator	NOUN
cana-2015	90	10	for	for	ADP
cana-2015	90	11	q	q	NOUN
cana-2015	90	12	-	-	PUNCT
cana-2015	90	13	livifn	livifn	NOUN
cana-2015	90	14	are	be	AUX
cana-2015	90	15	given	give	VERB
cana-2015	90	16	,	,	PUNCT
cana-2015	90	17	based	base	VERB
cana-2015	90	18	on	on	ADP
cana-2015	90	19	the	the	DET
cana-2015	90	20	operational	operational	ADJ
cana-2015	90	21	rules	rule	NOUN
cana-2015	90	22	of	of	ADP
cana-2015	90	23	q	q	NOUN
cana-2015	90	24	-	-	PUNCT
cana-2015	90	25	livifns	livifns	NOUN
cana-2015	90	26	.	.	PUNCT
cana-2015	91	1	4.1	4.1	NUM
cana-2015	91	2	q	q	NOUN
cana-2015	91	3	-	-	PUNCT
cana-2015	91	4	livif	livif	NOUN
cana-2015	91	5	weighted	weight	VERB
cana-2015	91	6	averaging	average	VERB
cana-2015	91	7	(	(	PUNCT
cana-2015	91	8	q	q	ADJ
cana-2015	91	9	-	-	PUNCT
cana-2015	91	10	livifwa	livifwa	NOUN
cana-2015	91	11	)	)	PUNCT
cana-2015	91	12	operator	operator	NOUN
cana-2015	91	13	definition	definition	NOUN
cana-2015	91	14	4.1	4.1	NUM
cana-2015	91	15	.	.	PUNCT
cana-2015	92	1	let	let	VERB
cana-2015	92	2	mi	mi	PROPN
cana-2015	92	3	=	=	PROPN
cana-2015	92	4	〈	〈	PROPN
cana-2015	92	5	(	(	PUNCT
cana-2015	92	6	logt	logt	NOUN
cana-2015	92	7	l	l	NOUN
cana-2015	92	8	m	m	VERB
cana-2015	92	9	i	i	PRON
cana-2015	92	10	,	,	PUNCT
cana-2015	92	11	logt	logt	PROPN
cana-2015	92	12	u	u	PROPN
cana-2015	92	13	mi	mi	PROPN
cana-2015	92	14	)	)	PUNCT
cana-2015	92	15	,	,	PUNCT
cana-2015	92	16	(	(	PUNCT
cana-2015	92	17	logf	logf	INTJ
cana-2015	92	18	l	l	NOUN
cana-2015	92	19	m	m	VERB
cana-2015	92	20	i	i	PRON
cana-2015	92	21	,	,	PUNCT
cana-2015	92	22	logf	logf	VERB
cana-2015	92	23	u	u	PROPN
cana-2015	92	24	mi	mi	PROPN
cana-2015	92	25	)	)	PUNCT
cana-2015	92	26	〉	〉	NOUN
cana-2015	92	27	be	be	VERB
cana-2015	92	28	the	the	DET
cana-2015	92	29	collection	collection	NOUN
cana-2015	92	30	of	of	ADP
cana-2015	92	31	q	q	NOUN
cana-2015	92	32	-	-	PUNCT
cana-2015	92	33	livifns	livifns	ADJ
cana-2015	92	34	,	,	PUNCT
cana-2015	92	35	ω	ω	NUM
cana-2015	92	36	=	=	SYM
cana-2015	92	37	(	(	PUNCT
cana-2015	92	38	ω1	ω1	PROPN
cana-2015	92	39	,	,	PUNCT
cana-2015	92	40	ω2	ω2	ADJ
cana-2015	92	41	,	,	PUNCT
cana-2015	92	42	...	...	PUNCT
cana-2015	92	43	,	,	PUNCT
cana-2015	92	44	ωn	ωn	X
cana-2015	92	45	)	)	PUNCT
cana-2015	92	46	be	be	VERB
cana-2015	92	47	the	the	DET
cana-2015	92	48	weight	weight	NOUN
cana-2015	92	49	of	of	ADP
cana-2015	92	50	mi	mi	PROPN
cana-2015	92	51	,	,	PUNCT
cana-2015	92	52	ωi	ωi	NUM
cana-2015	92	53	≥	≥	NOUN
cana-2015	92	54	0	0	NUM
cana-2015	92	55	and	and	CCONJ
cana-2015	92	56	�	�	PROPN
cana-2015	92	57	n	n	CCONJ
cana-2015	92	58	i=1ωi	i=1ωi	NOUN
cana-2015	92	59	=	=	SYM
cana-2015	92	60	1	1	NUM
cana-2015	92	61	and∏	and∏	PROPN
cana-2015	92	62	=	=	SYM
cana-2015	92	63	�	�	PROPN
cana-2015	92	64	(	(	PUNCT
cana-2015	92	65	t	t	PROPN
cana-2015	92	66	l	l	PROPN
cana-2015	92	67	mi	mi	PROPN
cana-2015	92	68	,	,	PUNCT
cana-2015	92	69	t	t	PROPN
cana-2015	92	70	u	u	PROPN
cana-2015	92	71	mi	mi	PROPN
cana-2015	92	72	)	)	PUNCT
cana-2015	92	73	,	,	PUNCT
cana-2015	92	74	(	(	PUNCT
cana-2015	92	75	fmi	fmi	PROPN
cana-2015	92	76	,	,	PUNCT
cana-2015	92	77	fu	fu	PROPN
cana-2015	92	78	mi	mi	PROPN
cana-2015	92	79	)	)	PUNCT
cana-2015	92	80	.	.	PUNCT
cana-2015	93	1	then	then	ADV
cana-2015	93	2	q	q	X
cana-2015	93	3	-	-	PUNCT
cana-2015	93	4	livifwa	livifwa	NOUN
cana-2015	93	5	operator	operator	NOUN
cana-2015	93	6	is	be	AUX
cana-2015	93	7	q	q	ADJ
cana-2015	93	8	-	-	PUNCT
cana-2015	93	9	livifwa	livifwa	NOUN
cana-2015	93	10	(	(	PUNCT
cana-2015	93	11	m1,m2	m1,m2	PROPN
cana-2015	93	12	,	,	PUNCT
cana-2015	93	13	...	...	PUNCT
cana-2015	93	14	,	,	PUNCT
cana-2015	93	15	mn	mn	PROPN
cana-2015	93	16	)	)	PUNCT
cana-2015	93	17	=	=	SYM
cana-2015	93	18	�	�	PROPN
cana-2015	93	19	n	n	PROPN
cana-2015	93	20	i=1ωimi	i=1ωimi	PROPN
cana-2015	93	21	for	for	ADP
cana-2015	93	22	i	i	PRON
cana-2015	93	23	=	=	NOUN
cana-2015	93	24	1	1	NUM
cana-2015	93	25	,	,	PUNCT
cana-2015	93	26	2	2	NUM
cana-2015	93	27	,	,	PUNCT
cana-2015	93	28	...	...	PUNCT
cana-2015	93	29	,	,	PUNCT
cana-2015	93	30	n.	n.	PROPN
cana-2015	93	31	theorem	theorem	VERB
cana-2015	93	32	4.2	4.2	NUM
cana-2015	93	33	.	.	PUNCT
cana-2015	94	1	let	let	VERB
cana-2015	94	2	mi	mi	PROPN
cana-2015	94	3	=	=	PROPN
cana-2015	94	4	〈	〈	PROPN
cana-2015	94	5	(	(	PUNCT
cana-2015	94	6	logt	logt	NOUN
cana-2015	94	7	l	l	NOUN
cana-2015	94	8	m	m	VERB
cana-2015	94	9	i	i	PRON
cana-2015	94	10	,	,	PUNCT
cana-2015	94	11	logt	logt	PROPN
cana-2015	94	12	u	u	PROPN
cana-2015	94	13	mi	mi	PROPN
cana-2015	94	14	)	)	PUNCT
cana-2015	94	15	,	,	PUNCT
cana-2015	94	16	(	(	PUNCT
cana-2015	94	17	logf	logf	INTJ
cana-2015	94	18	l	l	NOUN
cana-2015	94	19	m	m	VERB
cana-2015	94	20	i	i	PRON
cana-2015	94	21	,	,	PUNCT
cana-2015	94	22	logf	logf	VERB
cana-2015	94	23	u	u	PROPN
cana-2015	94	24	mi	mi	PROPN
cana-2015	94	25	)	)	PUNCT
cana-2015	94	26	〉	〉	NOUN
cana-2015	94	27	be	be	VERB
cana-2015	94	28	the	the	DET
cana-2015	94	29	collection	collection	NOUN
cana-2015	94	30	of	of	ADP
cana-2015	94	31	q	q	NOUN
cana-2015	94	32	-	-	PUNCT
cana-2015	94	33	livifns	livifns	NOUN
cana-2015	94	34	.	.	PUNCT
cana-2015	95	1	then	then	ADV
cana-2015	95	2	q	q	X
cana-2015	95	3	-	-	PUNCT
cana-2015	95	4	livifwa	livifwa	NOUN
cana-2015	95	5	(	(	PUNCT
cana-2015	95	6	m1,m2	m1,m2	PROPN
cana-2015	95	7	,	,	PUNCT
cana-2015	95	8	...	...	PUNCT
cana-2015	95	9	,	,	PUNCT
cana-2015	95	10	mn	mn	PROPN
cana-2015	95	11	)	)	PUNCT
cana-2015	95	12	=	=	PRON
cana-2015	95	13	(	(	PUNCT
cana-2015	95	14	associativity	associativity	NOUN
cana-2015	95	15	property).	property).	NOUN
cana-2015	95	16	(	(	PUNCT
cana-2015	95	17	q	q	NOUN
cana-2015	95	18	√	√	NUM
cana-2015	95	19	1−	1−	NUM
cana-2015	95	20	�	�	PROPN
cana-2015	95	21	n	n	PRON
cana-2015	95	22	i=1	i=1	PROPN
cana-2015	95	23	(	(	PUNCT
cana-2015	95	24	1−	1−	NUM
cana-2015	95	25	(	(	PUNCT
cana-2015	95	26	log∏	log∏	NOUN
cana-2015	95	27	i	i	NOUN
cana-2015	95	28	t	t	VERB
cana-2015	95	29	l	l	NOUN
cana-2015	95	30	m	m	VERB
cana-2015	95	31	i	i	NOUN
cana-2015	95	32	)	)	PUNCT
cana-2015	95	33	q	q	NOUN
cana-2015	95	34	)	)	PUNCT
cana-2015	95	35	ωi	ωi	NOUN
cana-2015	95	36	,	,	PUNCT
cana-2015	95	37	q	q	NOUN
cana-2015	95	38	√	√	NUM
cana-2015	95	39	1−	1−	NUM
cana-2015	95	40	�	�	PROPN
cana-2015	95	41	n	n	PRON
cana-2015	95	42	i=1	i=1	PROPN
cana-2015	95	43	(	(	PUNCT
cana-2015	95	44	1−	1−	NUM
cana-2015	95	45	(	(	PUNCT
cana-2015	95	46	log∏	log∏	NOUN
cana-2015	95	47	i	i	PRON
cana-2015	95	48	(	(	PUNCT
cana-2015	95	49	t	t	PROPN
cana-2015	95	50	u	u	PROPN
cana-2015	95	51	mi	mi	PROPN
cana-2015	95	52	)	)	PUNCT
cana-2015	95	53	)	)	PUNCT
cana-2015	95	54	q	q	NOUN
cana-2015	95	55	)	)	PUNCT
cana-2015	95	56	ωi	ωi	PROPN
cana-2015	95	57	)	)	PUNCT
cana-2015	95	58	,	,	PUNCT
cana-2015	95	59	(	(	PUNCT
cana-2015	95	60	�	�	PROPN
cana-2015	95	61	n	n	CCONJ
cana-2015	95	62	i=1	i=1	PROPN
cana-2015	95	63	(	(	PUNCT
cana-2015	95	64	log	log	VERB
cana-2015	95	65	∏	∏	NUM
cana-2015	96	1	i	i	PRON
cana-2015	96	2	f	f	PROPN
cana-2015	96	3	l	l	NOUN
cana-2015	96	4	m	m	VERB
cana-2015	96	5	i	i	NOUN
cana-2015	96	6	)	)	PUNCT
cana-2015	96	7	qωi	qωi	PROPN
cana-2015	96	8	,	,	PUNCT
cana-2015	96	9	�	�	PROPN
cana-2015	96	10	n	n	CCONJ
cana-2015	96	11	i=1(log	i=1(log	PROPN
cana-2015	96	12	∏	∏	PROPN
cana-2015	96	13	i	i	PROPN
cana-2015	96	14	(	(	PUNCT
cana-2015	96	15	fu	fu	PROPN
cana-2015	96	16	mi	mi	PROPN
cana-2015	96	17	)	)	PUNCT
cana-2015	96	18	)	)	PUNCT
cana-2015	96	19	qωi	qωi	NOUN
cana-2015	96	20	)	)	PUNCT
cana-2015	96	21			NOUN
cana-2015	96	22	.	.	PUNCT
cana-2015	97	1	proof	proof	NOUN
cana-2015	97	2	.	.	PUNCT
cana-2015	98	1	if	if	SCONJ
cana-2015	98	2	n	n	NOUN
cana-2015	98	3	=	=	SYM
cana-2015	98	4	2	2	NUM
cana-2015	98	5	,	,	PUNCT
cana-2015	98	6	then	then	ADV
cana-2015	98	7	q	q	NOUN
cana-2015	98	8	-	-	PUNCT
cana-2015	98	9	livifwa	livifwa	NOUN
cana-2015	98	10	(	(	PUNCT
cana-2015	98	11	m1	m1	PROPN
cana-2015	98	12	=	=	SYM
cana-2015	98	13	b	b	PROPN
cana-2015	98	14	,	,	PUNCT
cana-2015	99	1	m2	m2	PROPN
cana-2015	99	2	=	=	SYM
cana-2015	99	3	c	c	X
cana-2015	99	4	)	)	PUNCT
cana-2015	99	5	=	=	SYM
cana-2015	99	6	ω1b	ω1b	X
cana-2015	99	7	∨	∨	NUM
cana-2015	99	8	ω2c	ω2c	NOUN
cana-2015	99	9	,	,	PUNCT
cana-2015	99	10	where	where	SCONJ
cana-2015	99	11	ω1b	ω1b	ADV
cana-2015	99	12	=	=	SYM
cana-2015	99	13			PROPN
cana-2015	99	14	(	(	PUNCT
cana-2015	99	15	q	q	SYM
cana-2015	99	16	√	√	NUM
cana-2015	99	17	1−	1−	NUM
cana-2015	99	18	(	(	PUNCT
cana-2015	99	19	1−	1−	NUM
cana-2015	99	20	(	(	PUNCT
cana-2015	99	21	log∏	log∏	NOUN
cana-2015	99	22	i	i	PRON
cana-2015	99	23	t	t	VERB
cana-2015	99	24	l	l	NOUN
cana-2015	99	25	b	b	X
cana-2015	99	26	)	)	PUNCT
cana-2015	99	27	q	q	NOUN
cana-2015	99	28	)	)	PUNCT
cana-2015	99	29	ω1	ω1	PROPN
cana-2015	99	30	,	,	PUNCT
cana-2015	99	31	q	q	PROPN
cana-2015	99	32	√	√	NUM
cana-2015	99	33	1−	1−	NUM
cana-2015	99	34	(	(	PUNCT
cana-2015	99	35	1−	1−	NUM
cana-2015	99	36	(	(	PUNCT
cana-2015	99	37	log∏	log∏	NOUN
cana-2015	99	38	i	i	PRON
cana-2015	99	39	(	(	PUNCT
cana-2015	99	40	t	t	PROPN
cana-2015	99	41	u	u	PROPN
cana-2015	99	42	b	b	PROPN
cana-2015	99	43	)	)	PUNCT
cana-2015	99	44	)	)	PUNCT
cana-2015	99	45	q	q	X
cana-2015	99	46	)	)	PUNCT
cana-2015	99	47	ω1	ω1	PROPN
cana-2015	99	48	)	)	PUNCT
cana-2015	99	49	,	,	PUNCT
cana-2015	99	50	(	(	PUNCT
cana-2015	99	51	(	(	PUNCT
cana-2015	99	52	log∏	log∏	NOUN
cana-2015	99	53	i	i	NOUN
cana-2015	99	54	f	f	PROPN
cana-2015	99	55	l	l	NOUN
cana-2015	99	56	b	b	X
cana-2015	99	57	)	)	PUNCT
cana-2015	99	58	qω1	qω1	NOUN
cana-2015	99	59	,	,	PUNCT
cana-2015	99	60	(	(	PUNCT
cana-2015	99	61	log∏	log∏	PROPN
cana-2015	99	62	i	i	PRON
cana-2015	99	63	(	(	PUNCT
cana-2015	99	64	fu	fu	PROPN
cana-2015	99	65	b	b	NOUN
cana-2015	99	66	)	)	PUNCT
cana-2015	99	67	)	)	PUNCT
cana-2015	99	68	qω1	qω1	NOUN
cana-2015	99	69	)	)	PUNCT
cana-2015	99	70			NOUN
cana-2015	99	71	https://internationalpubls.com	https://internationalpubls.com	X
cana-2015	99	72	541	541	NUM
cana-2015	99	73	communications	communication	NOUN
cana-2015	99	74	on	on	ADP
cana-2015	99	75	applied	apply	VERB
cana-2015	99	76	nonlinear	nonlinear	ADJ
cana-2015	99	77	analysis	analysis	NOUN
cana-2015	99	78	issn	issn	NOUN
cana-2015	99	79	:	:	PUNCT
cana-2015	99	80	1074	1074	NUM
cana-2015	99	81	-	-	PUNCT
cana-2015	99	82	133x	133x	NUM
cana-2015	99	83	vol	vol	NOUN
cana-2015	99	84	32	32	NUM
cana-2015	99	85	no	no	NOUN
cana-2015	99	86	.	.	NOUN
cana-2015	99	87	3	3	NUM
cana-2015	99	88	(	(	PUNCT
cana-2015	99	89	2025	2025	NUM
cana-2015	99	90	)	)	PUNCT
cana-2015	99	91	and	and	CCONJ
cana-2015	99	92	ω2c	ω2c	NOUN
cana-2015	99	93	=	=	PUNCT
cana-2015	99	94			PROPN
cana-2015	99	95	(	(	PUNCT
cana-2015	99	96	q	q	SYM
cana-2015	99	97	√	√	NUM
cana-2015	99	98	1−	1−	NUM
cana-2015	99	99	(	(	PUNCT
cana-2015	99	100	1−	1−	NUM
cana-2015	99	101	(	(	PUNCT
cana-2015	99	102	log∏	log∏	NOUN
cana-2015	99	103	i	i	NOUN
cana-2015	99	104	t	t	VERB
cana-2015	99	105	l	l	NOUN
cana-2015	99	106	c	c	X
cana-2015	99	107	)	)	PUNCT
cana-2015	99	108	q	q	NOUN
cana-2015	99	109	)	)	PUNCT
cana-2015	99	110	ω2	ω2	ADJ
cana-2015	99	111	,	,	PUNCT
cana-2015	99	112	q	q	PROPN
cana-2015	99	113	√	√	NUM
cana-2015	99	114	1−	1−	NUM
cana-2015	99	115	(	(	PUNCT
cana-2015	99	116	1−	1−	NUM
cana-2015	99	117	(	(	PUNCT
cana-2015	99	118	log∏	log∏	NOUN
cana-2015	99	119	i	i	PRON
cana-2015	99	120	(	(	PUNCT
cana-2015	99	121	t	t	PROPN
cana-2015	99	122	u	u	X
cana-2015	99	123	c	c	PROPN
cana-2015	99	124	)	)	PUNCT
cana-2015	99	125	)	)	PUNCT
cana-2015	99	126	q	q	X
cana-2015	99	127	)	)	PUNCT
cana-2015	99	128	ω2	ω2	ADJ
cana-2015	99	129	)	)	PUNCT
cana-2015	99	130	,	,	PUNCT
cana-2015	99	131	(	(	PUNCT
cana-2015	99	132	(	(	PUNCT
cana-2015	99	133	log∏	log∏	NOUN
cana-2015	99	134	i	i	NOUN
cana-2015	99	135	f	f	NOUN
cana-2015	99	136	l	l	NOUN
cana-2015	99	137	c	c	X
cana-2015	99	138	)	)	PUNCT
cana-2015	99	139	qω2	qω2	NOUN
cana-2015	99	140	,	,	PUNCT
cana-2015	99	141	(	(	PUNCT
cana-2015	99	142	log∏	log∏	PROPN
cana-2015	99	143	i	i	PRON
cana-2015	99	144	(	(	PUNCT
cana-2015	99	145	fu	fu	NOUN
cana-2015	99	146	c	c	NOUN
cana-2015	99	147	)	)	PUNCT
cana-2015	99	148	)	)	PUNCT
cana-2015	99	149	qω2	qω2	NOUN
cana-2015	99	150	)	)	PUNCT
cana-2015	99	151			NOUN
cana-2015	99	152	.	.	PUNCT
cana-2015	100	1	hence	hence	ADV
cana-2015	100	2	,	,	PUNCT
cana-2015	100	3	ω1b	ω1b	X
cana-2015	100	4	∨	∨	NUM
cana-2015	100	5	ω2c	ω2c	ADJ
cana-2015	100	6	=	=	SYM
cana-2015	100	7			NOUN
cana-2015	100	8			ADJ
cana-2015	100	9	q	q	X
cana-2015	100	10	√√√√√	√√√√√	PROPN
cana-2015	100	11	(	(	PUNCT
cana-2015	100	12	1−	1−	NUM
cana-2015	100	13	(	(	PUNCT
cana-2015	100	14	1−	1−	NUM
cana-2015	100	15	(	(	PUNCT
cana-2015	100	16	log∏	log∏	NOUN
cana-2015	100	17	i	i	PRON
cana-2015	100	18	t	t	VERB
cana-2015	100	19	l	l	NOUN
cana-2015	100	20	b	b	X
cana-2015	100	21	)	)	PUNCT
cana-2015	100	22	q	q	NOUN
cana-2015	100	23	)	)	PUNCT
cana-2015	100	24	ω1	ω1	PROPN
cana-2015	100	25	)	)	PUNCT
cana-2015	101	1	+	+	CCONJ
cana-2015	101	2	(	(	PUNCT
cana-2015	101	3	1−	1−	NUM
cana-2015	101	4	(	(	PUNCT
cana-2015	101	5	1−	1−	NUM
cana-2015	101	6	(	(	PUNCT
cana-2015	101	7	log∏	log∏	NOUN
cana-2015	101	8	i	i	NOUN
cana-2015	101	9	t	t	VERB
cana-2015	101	10	l	l	NOUN
cana-2015	101	11	c	c	X
cana-2015	101	12	)	)	PUNCT
cana-2015	101	13	q	q	NOUN
cana-2015	101	14	)	)	PUNCT
cana-2015	101	15	ω2	ω2	ADJ
cana-2015	101	16	)	)	PUNCT
cana-2015	101	17	−	−	PROPN
cana-2015	102	1	(	(	PUNCT
cana-2015	102	2	1−	1−	NUM
cana-2015	102	3	(	(	PUNCT
cana-2015	102	4	1−	1−	NUM
cana-2015	102	5	(	(	PUNCT
cana-2015	102	6	log∏	log∏	NOUN
cana-2015	102	7	i	i	PRON
cana-2015	102	8	t	t	VERB
cana-2015	102	9	l	l	NOUN
cana-2015	102	10	b	b	X
cana-2015	102	11	)	)	PUNCT
cana-2015	102	12	q	q	NOUN
cana-2015	102	13	)	)	PUNCT
cana-2015	102	14	ω1	ω1	PROPN
cana-2015	102	15	)	)	PUNCT
cana-2015	102	16	·	·	PUNCT
cana-2015	103	1	(	(	PUNCT
cana-2015	103	2	1−	1−	NUM
cana-2015	103	3	(	(	PUNCT
cana-2015	103	4	1−	1−	NUM
cana-2015	103	5	(	(	PUNCT
cana-2015	103	6	log∏	log∏	NOUN
cana-2015	103	7	i	i	NOUN
cana-2015	103	8	t	t	VERB
cana-2015	103	9	l	l	NOUN
cana-2015	103	10	c	c	X
cana-2015	103	11	)	)	PUNCT
cana-2015	103	12	q	q	NOUN
cana-2015	103	13	)	)	PUNCT
cana-2015	103	14	ω2	ω2	ADJ
cana-2015	103	15	)	)	PUNCT
cana-2015	104	1	,	,	PUNCT
cana-2015	104	2	q	q	PROPN
cana-2015	104	3	√√√√√	√√√√√	PROPN
cana-2015	104	4	(	(	PUNCT
cana-2015	104	5	1−	1−	NUM
cana-2015	104	6	(	(	PUNCT
cana-2015	104	7	1−	1−	NUM
cana-2015	104	8	(	(	PUNCT
cana-2015	104	9	log∏	log∏	NOUN
cana-2015	104	10	i	i	PRON
cana-2015	104	11	(	(	PUNCT
cana-2015	104	12	t	t	PROPN
cana-2015	104	13	u	u	PROPN
cana-2015	104	14	b	b	PROPN
cana-2015	104	15	)	)	PUNCT
cana-2015	104	16	)	)	PUNCT
cana-2015	104	17	q	q	X
cana-2015	104	18	)	)	PUNCT
cana-2015	104	19	ω1	ω1	PROPN
cana-2015	104	20	)	)	PUNCT
cana-2015	105	1	+	+	CCONJ
cana-2015	105	2	(	(	PUNCT
cana-2015	105	3	1−	1−	NUM
cana-2015	105	4	(	(	PUNCT
cana-2015	105	5	1−	1−	NUM
cana-2015	105	6	(	(	PUNCT
cana-2015	105	7	log∏	log∏	NOUN
cana-2015	105	8	i	i	PRON
cana-2015	105	9	(	(	PUNCT
cana-2015	105	10	t	t	PROPN
cana-2015	105	11	u	u	X
cana-2015	105	12	c	c	PROPN
cana-2015	105	13	)	)	PUNCT
cana-2015	105	14	)	)	PUNCT
cana-2015	105	15	q	q	X
cana-2015	105	16	)	)	PUNCT
cana-2015	105	17	ω2	ω2	ADJ
cana-2015	105	18	)	)	PUNCT
cana-2015	105	19	−	−	PROPN
cana-2015	106	1	(	(	PUNCT
cana-2015	106	2	1−	1−	NUM
cana-2015	106	3	(	(	PUNCT
cana-2015	106	4	1−	1−	NUM
cana-2015	106	5	(	(	PUNCT
cana-2015	106	6	log∏	log∏	NOUN
cana-2015	106	7	i	i	PRON
cana-2015	106	8	(	(	PUNCT
cana-2015	106	9	t	t	PROPN
cana-2015	106	10	u	u	PROPN
cana-2015	106	11	b	b	PROPN
cana-2015	106	12	)	)	PUNCT
cana-2015	106	13	)	)	PUNCT
cana-2015	106	14	q	q	X
cana-2015	106	15	)	)	PUNCT
cana-2015	106	16	ω1	ω1	PROPN
cana-2015	106	17	)	)	PUNCT
cana-2015	106	18	·	·	PUNCT
cana-2015	107	1	(	(	PUNCT
cana-2015	107	2	1−	1−	NUM
cana-2015	107	3	(	(	PUNCT
cana-2015	107	4	1−	1−	NUM
cana-2015	107	5	(	(	PUNCT
cana-2015	107	6	log∏	log∏	NOUN
cana-2015	107	7	i	i	PRON
cana-2015	107	8	(	(	PUNCT
cana-2015	107	9	t	t	PROPN
cana-2015	107	10	u	u	X
cana-2015	107	11	c	c	PROPN
cana-2015	107	12	)	)	PUNCT
cana-2015	107	13	)	)	PUNCT
cana-2015	107	14	q	q	X
cana-2015	107	15	)	)	PUNCT
cana-2015	107	16	ω2	ω2	ADJ
cana-2015	107	17	)	)	PUNCT
cana-2015	107	18			NOUN
cana-2015	107	19	,	,	PUNCT
cana-2015	107	20	(	(	PUNCT
cana-2015	107	21	(	(	PUNCT
cana-2015	107	22	log∏	log∏	NOUN
cana-2015	107	23	i	i	NOUN
cana-2015	107	24	f	f	PROPN
cana-2015	107	25	l	l	NOUN
cana-2015	107	26	b	b	X
cana-2015	107	27	)	)	PUNCT
cana-2015	107	28	qω1	qω1	NOUN
cana-2015	107	29	·	·	PUNCT
cana-2015	107	30	(	(	PUNCT
cana-2015	107	31	log∏	log∏	NOUN
cana-2015	107	32	i	i	PRON
cana-2015	107	33	f	f	NOUN
cana-2015	107	34	l	l	NOUN
cana-2015	107	35	c	c	X
cana-2015	107	36	)	)	PUNCT
cana-2015	107	37	qω2	qω2	NOUN
cana-2015	107	38	,	,	PUNCT
cana-2015	107	39	(	(	PUNCT
cana-2015	107	40	log∏	log∏	PROPN
cana-2015	107	41	i	i	PRON
cana-2015	107	42	(	(	PUNCT
cana-2015	107	43	fu	fu	PROPN
cana-2015	107	44	b	b	NOUN
cana-2015	107	45	)	)	PUNCT
cana-2015	107	46	)	)	PUNCT
cana-2015	107	47	qω1	qω1	NOUN
cana-2015	107	48	·	·	PUNCT
cana-2015	107	49	(	(	PUNCT
cana-2015	107	50	log∏	log∏	NOUN
cana-2015	107	51	i	i	PRON
cana-2015	107	52	(	(	PUNCT
cana-2015	107	53	fu	fu	NOUN
cana-2015	107	54	c	c	NOUN
cana-2015	107	55	)	)	PUNCT
cana-2015	107	56	)	)	PUNCT
cana-2015	107	57	qω2	qω2	NOUN
cana-2015	107	58	)	)	PUNCT
cana-2015	107	59			X
cana-2015	108	1	=	=	PUNCT
cana-2015	108	2			ADJ
cana-2015	108	3			PROPN
cana-2015	108	4	q	q	PUNCT
cana-2015	108	5	√	√	NUM
cana-2015	108	6	1−	1−	NUM
cana-2015	109	1	(	(	PUNCT
cana-2015	109	2	1−	1−	NUM
cana-2015	109	3	(	(	PUNCT
cana-2015	109	4	log∏	log∏	NOUN
cana-2015	109	5	i	i	PRON
cana-2015	109	6	t	t	VERB
cana-2015	109	7	l	l	NOUN
cana-2015	109	8	b	b	X
cana-2015	109	9	)	)	PUNCT
cana-2015	109	10	q	q	NOUN
cana-2015	109	11	)	)	PUNCT
cana-2015	109	12	ω1	ω1	PROPN
cana-2015	109	13	·	·	PUNCT
cana-2015	109	14	(	(	PUNCT
cana-2015	109	15	1−	1−	NUM
cana-2015	109	16	(	(	PUNCT
cana-2015	109	17	log∏	log∏	NOUN
cana-2015	109	18	i	i	NOUN
cana-2015	109	19	t	t	VERB
cana-2015	109	20	l	l	NOUN
cana-2015	109	21	c	c	X
cana-2015	109	22	)	)	PUNCT
cana-2015	109	23	q	q	NOUN
cana-2015	109	24	)	)	PUNCT
cana-2015	109	25	ω2	ω2	ADJ
cana-2015	109	26	,	,	PUNCT
cana-2015	109	27	q	q	PROPN
cana-2015	109	28	√	√	NUM
cana-2015	109	29	1−	1−	NUM
cana-2015	109	30	(	(	PUNCT
cana-2015	109	31	1−	1−	NUM
cana-2015	109	32	(	(	PUNCT
cana-2015	109	33	log∏	log∏	NOUN
cana-2015	109	34	i	i	PRON
cana-2015	109	35	(	(	PUNCT
cana-2015	109	36	t	t	PROPN
cana-2015	109	37	u	u	PROPN
cana-2015	109	38	b	b	PROPN
cana-2015	109	39	)	)	PUNCT
cana-2015	109	40	)	)	PUNCT
cana-2015	109	41	q	q	X
cana-2015	109	42	)	)	PUNCT
cana-2015	109	43	ω1	ω1	PROPN
cana-2015	109	44	·	·	PUNCT
cana-2015	109	45	(	(	PUNCT
cana-2015	109	46	1−	1−	NUM
cana-2015	109	47	(	(	PUNCT
cana-2015	109	48	log∏	log∏	NOUN
cana-2015	109	49	i	i	PRON
cana-2015	109	50	(	(	PUNCT
cana-2015	109	51	t	t	PROPN
cana-2015	109	52	u	u	X
cana-2015	109	53	c	c	PROPN
cana-2015	109	54	)	)	PUNCT
cana-2015	109	55	)	)	PUNCT
cana-2015	109	56	q	q	X
cana-2015	109	57	)	)	PUNCT
cana-2015	109	58	ω2	ω2	ADJ
cana-2015	109	59			NOUN
cana-2015	109	60	,	,	PUNCT
cana-2015	109	61	(	(	PUNCT
cana-2015	109	62	(	(	PUNCT
cana-2015	109	63	log∏	log∏	NOUN
cana-2015	109	64	i	i	NOUN
cana-2015	109	65	f	f	PROPN
cana-2015	109	66	l	l	NOUN
cana-2015	109	67	b	b	X
cana-2015	109	68	)	)	PUNCT
cana-2015	109	69	qω1	qω1	NOUN
cana-2015	109	70	·	·	PUNCT
cana-2015	110	1	(	(	PUNCT
cana-2015	110	2	log∏	log∏	NOUN
cana-2015	110	3	i	i	PRON
cana-2015	110	4	f	f	NOUN
cana-2015	110	5	l	l	NOUN
cana-2015	110	6	c	c	X
cana-2015	110	7	)	)	PUNCT
cana-2015	110	8	qω2	qω2	NOUN
cana-2015	110	9	,	,	PUNCT
cana-2015	110	10	(	(	PUNCT
cana-2015	110	11	log∏	log∏	PROPN
cana-2015	110	12	i	i	PRON
cana-2015	110	13	(	(	PUNCT
cana-2015	110	14	fu	fu	PROPN
cana-2015	110	15	b	b	NOUN
cana-2015	110	16	)	)	PUNCT
cana-2015	110	17	)	)	PUNCT
cana-2015	110	18	qω1	qω1	NOUN
cana-2015	110	19	·	·	PUNCT
cana-2015	110	20	(	(	PUNCT
cana-2015	110	21	log∏	log∏	NOUN
cana-2015	110	22	i	i	PRON
cana-2015	110	23	(	(	PUNCT
cana-2015	110	24	fu	fu	NOUN
cana-2015	110	25	c	c	NOUN
cana-2015	110	26	)	)	PUNCT
cana-2015	110	27	)	)	PUNCT
cana-2015	110	28	qω2	qω2	NOUN
cana-2015	110	29	)	)	PUNCT
cana-2015	110	30			PROPN
cana-2015	110	31	.	.	PUNCT
cana-2015	111	1	thus	thus	ADV
cana-2015	111	2	,	,	PUNCT
cana-2015	111	3	q	q	NOUN
cana-2015	111	4	-	-	PUNCT
cana-2015	111	5	livifwa	livifwa	NOUN
cana-2015	111	6	(	(	PUNCT
cana-2015	111	7	m1	m1	PROPN
cana-2015	111	8	=	=	SYM
cana-2015	111	9	b	b	PROPN
cana-2015	111	10	,	,	PUNCT
cana-2015	111	11	m2	m2	PROPN
cana-2015	111	12	=	=	SYM
cana-2015	111	13	c	c	X
cana-2015	111	14	)	)	PUNCT
cana-2015	111	15	=	=	SYM
cana-2015	112	1			NOUN
cana-2015	112	2	(	(	PUNCT
cana-2015	112	3	q	q	NOUN
cana-2015	112	4	√	√	NUM
cana-2015	112	5	1−	1−	NUM
cana-2015	112	6	�	�	PROPN
cana-2015	112	7	n	n	PRON
cana-2015	112	8	i=1	i=1	PROPN
cana-2015	112	9	(	(	PUNCT
cana-2015	112	10	1−	1−	NUM
cana-2015	112	11	(	(	PUNCT
cana-2015	112	12	log∏	log∏	NOUN
cana-2015	112	13	i	i	NOUN
cana-2015	112	14	t	t	VERB
cana-2015	113	1	l	l	NOUN
cana-2015	114	1	m	m	VERB
cana-2015	114	2	i	i	NOUN
cana-2015	114	3	)	)	PUNCT
cana-2015	114	4	q	q	NOUN
cana-2015	114	5	)	)	PUNCT
cana-2015	114	6	ωi	ωi	NOUN
cana-2015	114	7	,	,	PUNCT
cana-2015	114	8	q	q	NOUN
cana-2015	114	9	√	√	NUM
cana-2015	114	10	1−	1−	NUM
cana-2015	114	11	�	�	PROPN
cana-2015	114	12	n	n	PRON
cana-2015	114	13	i=1	i=1	PROPN
cana-2015	114	14	(	(	PUNCT
cana-2015	114	15	1−	1−	NUM
cana-2015	114	16	(	(	PUNCT
cana-2015	114	17	log∏	log∏	NOUN
cana-2015	114	18	i	i	PRON
cana-2015	114	19	(	(	PUNCT
cana-2015	114	20	t	t	PROPN
cana-2015	114	21	u	u	PROPN
cana-2015	114	22	mi	mi	PROPN
cana-2015	114	23	)	)	PUNCT
cana-2015	114	24	)	)	PUNCT
cana-2015	114	25	q	q	NOUN
cana-2015	114	26	)	)	PUNCT
cana-2015	114	27	ωi	ωi	PROPN
cana-2015	114	28	)	)	PUNCT
cana-2015	114	29	,	,	PUNCT
cana-2015	114	30	(	(	PUNCT
cana-2015	114	31	�	�	PROPN
cana-2015	114	32	n	n	CCONJ
cana-2015	114	33	i=1	i=1	PROPN
cana-2015	114	34	(	(	PUNCT
cana-2015	114	35	log	log	VERB
cana-2015	114	36	∏	∏	NUM
cana-2015	115	1	i	i	PRON
cana-2015	115	2	f	f	PROPN
cana-2015	115	3	l	l	NOUN
cana-2015	115	4	m	m	VERB
cana-2015	115	5	i	i	NOUN
cana-2015	115	6	)	)	PUNCT
cana-2015	115	7	qωi	qωi	PROPN
cana-2015	115	8	,	,	PUNCT
cana-2015	115	9	�	�	PROPN
cana-2015	115	10	n	n	CCONJ
cana-2015	115	11	i=1(log	i=1(log	PROPN
cana-2015	115	12	∏	∏	PROPN
cana-2015	115	13	i	i	PROPN
cana-2015	115	14	(	(	PUNCT
cana-2015	115	15	fu	fu	PROPN
cana-2015	115	16	mi	mi	PROPN
cana-2015	115	17	)	)	PUNCT
cana-2015	115	18	)	)	PUNCT
cana-2015	115	19	qωi	qωi	NOUN
cana-2015	115	20	)	)	PUNCT
cana-2015	115	21			NOUN
cana-2015	115	22	.	.	PUNCT
cana-2015	116	1	it	it	PRON
cana-2015	116	2	is	be	AUX
cana-2015	116	3	valid	valid	ADJ
cana-2015	116	4	for	for	ADP
cana-2015	116	5	n	n	NOUN
cana-2015	116	6	=	=	SYM
cana-2015	116	7	m	m	PROPN
cana-2015	116	8	and	and	CCONJ
cana-2015	116	9	m	m	PRON
cana-2015	116	10	≥	≥	NOUN
cana-2015	116	11	3	3	NUM
cana-2015	116	12	.	.	PUNCT
cana-2015	117	1	hence	hence	ADV
cana-2015	117	2	,	,	PUNCT
cana-2015	117	3	q	q	NOUN
cana-2015	117	4	-	-	PUNCT
cana-2015	117	5	livifwa	livifwa	NOUN
cana-2015	117	6	(	(	PUNCT
cana-2015	117	7	m1,m2	m1,m2	PROPN
cana-2015	117	8	,	,	PUNCT
cana-2015	117	9	...	...	PUNCT
cana-2015	117	10	,	,	PUNCT
cana-2015	117	11	mm	mm	X
cana-2015	117	12	)	)	PUNCT
cana-2015	117	13	=	=	SYM
cana-2015	117	14			PROPN
cana-2015	117	15	(	(	PUNCT
cana-2015	117	16	q	q	NOUN
cana-2015	117	17	√	√	NUM
cana-2015	117	18	1−	1−	NUM
cana-2015	117	19	�	�	PROPN
cana-2015	117	20	m	m	PROPN
cana-2015	117	21	i=1	i=1	PROPN
cana-2015	117	22	(	(	PUNCT
cana-2015	117	23	1−	1−	NUM
cana-2015	117	24	(	(	PUNCT
cana-2015	117	25	log∏	log∏	NOUN
cana-2015	117	26	i	i	NOUN
cana-2015	117	27	t	t	VERB
cana-2015	118	1	l	l	NOUN
cana-2015	118	2	m	m	VERB
cana-2015	118	3	i	i	NOUN
cana-2015	118	4	)	)	PUNCT
cana-2015	118	5	q	q	NOUN
cana-2015	118	6	)	)	PUNCT
cana-2015	118	7	ωi	ωi	NOUN
cana-2015	118	8	,	,	PUNCT
cana-2015	118	9	q	q	NOUN
cana-2015	118	10	√	√	NUM
cana-2015	118	11	1−	1−	NUM
cana-2015	118	12	�	�	PROPN
cana-2015	118	13	m	m	PROPN
cana-2015	118	14	i=1	i=1	PROPN
cana-2015	118	15	(	(	PUNCT
cana-2015	118	16	1−	1−	NUM
cana-2015	118	17	(	(	PUNCT
cana-2015	118	18	log∏	log∏	NOUN
cana-2015	118	19	i	i	PRON
cana-2015	118	20	(	(	PUNCT
cana-2015	118	21	t	t	PROPN
cana-2015	118	22	u	u	PROPN
cana-2015	118	23	mi	mi	PROPN
cana-2015	118	24	)	)	PUNCT
cana-2015	118	25	)	)	PUNCT
cana-2015	118	26	q	q	NOUN
cana-2015	118	27	)	)	PUNCT
cana-2015	118	28	ωi	ωi	PROPN
cana-2015	118	29	)	)	PUNCT
cana-2015	118	30	,	,	PUNCT
cana-2015	118	31	(	(	PUNCT
cana-2015	118	32	�	�	PROPN
cana-2015	118	33	m	m	VERB
cana-2015	118	34	i=1	i=1	PROPN
cana-2015	118	35	(	(	PUNCT
cana-2015	118	36	log	log	VERB
cana-2015	118	37	∏	∏	NUM
cana-2015	119	1	i	i	PRON
cana-2015	119	2	f	f	PROPN
cana-2015	119	3	l	l	NOUN
cana-2015	119	4	m	m	VERB
cana-2015	119	5	i	i	NOUN
cana-2015	119	6	)	)	PUNCT
cana-2015	119	7	qωi	qωi	PROPN
cana-2015	119	8	,	,	PUNCT
cana-2015	119	9	�	�	PROPN
cana-2015	119	10	m	m	NOUN
cana-2015	119	11	i=1(log	i=1(log	PROPN
cana-2015	119	12	∏	∏	PROPN
cana-2015	120	1	i	i	PROPN
cana-2015	120	2	(	(	PUNCT
cana-2015	120	3	fu	fu	PROPN
cana-2015	120	4	mi	mi	PROPN
cana-2015	120	5	)	)	PUNCT
cana-2015	120	6	)	)	PUNCT
cana-2015	120	7	qωi	qωi	NOUN
cana-2015	120	8	)	)	PUNCT
cana-2015	120	9			NOUN
cana-2015	120	10	.	.	PUNCT
cana-2015	121	1	if	if	SCONJ
cana-2015	121	2	n	n	NOUN
cana-2015	121	3	=	=	SYM
cana-2015	121	4	l	l	NOUN
cana-2015	121	5	+	+	CCONJ
cana-2015	121	6	1	1	NUM
cana-2015	121	7	and	and	CCONJ
cana-2015	121	8	we	we	PRON
cana-2015	121	9	apply	apply	VERB
cana-2015	121	10	,	,	PUNCT
cana-2015	121	11	q	q	NOUN
cana-2015	121	12	-	-	PUNCT
cana-2015	121	13	livifwa	livifwa	NOUN
cana-2015	121	14	(	(	PUNCT
cana-2015	121	15	m1,m2	m1,m2	PROPN
cana-2015	121	16	,	,	PUNCT
cana-2015	121	17	...	...	PUNCT
cana-2015	121	18	,	,	PUNCT
cana-2015	121	19	mm	mm	PROPN
cana-2015	121	20	,	,	PUNCT
cana-2015	121	21	mm+1	mm+1	X
cana-2015	121	22	)	)	PUNCT
cana-2015	121	23	=	=	SYM
cana-2015	122	1			NOUN
cana-2015	122	2			ADJ
cana-2015	122	3	q	q	X
cana-2015	122	4	√√√√√	√√√√√	PROPN
cana-2015	122	5	�	�	PROPN
cana-2015	122	6	m	m	PROPN
cana-2015	122	7	i=1	i=1	PROPN
cana-2015	122	8	(	(	PUNCT
cana-2015	122	9	1−	1−	NUM
cana-2015	122	10	(	(	PUNCT
cana-2015	122	11	1−	1−	NUM
cana-2015	122	12	(	(	PUNCT
cana-2015	122	13	log∏	log∏	NOUN
cana-2015	122	14	i	i	NOUN
cana-2015	122	15	t	t	VERB
cana-2015	122	16	l	l	NOUN
cana-2015	122	17	m	m	VERB
cana-2015	122	18	i	i	NOUN
cana-2015	122	19	)	)	PUNCT
cana-2015	122	20	q	q	NOUN
cana-2015	122	21	)	)	PUNCT
cana-2015	122	22	ωi	ωi	X
cana-2015	122	23	)	)	PUNCT
cana-2015	123	1	+	+	CCONJ
cana-2015	123	2	(	(	PUNCT
cana-2015	123	3	1−	1−	NUM
cana-2015	123	4	(	(	PUNCT
cana-2015	123	5	1−	1−	NUM
cana-2015	123	6	(	(	PUNCT
cana-2015	123	7	log∏	log∏	NOUN
cana-2015	123	8	i	i	NOUN
cana-2015	123	9	t	t	NOUN
cana-2015	123	10	l	l	NOUN
cana-2015	123	11	mm+1	mm+1	X
cana-2015	123	12	)	)	PUNCT
cana-2015	123	13	q	q	NOUN
cana-2015	123	14	)	)	PUNCT
cana-2015	123	15	ωm+1	ωm+1	NUM
cana-2015	123	16	)	)	PUNCT
cana-2015	123	17	−	−	NUM
cana-2015	123	18	�	�	PROPN
cana-2015	123	19	m	m	VERB
cana-2015	123	20	i=1	i=1	PROPN
cana-2015	123	21	(	(	PUNCT
cana-2015	123	22	1−	1−	NUM
cana-2015	123	23	(	(	PUNCT
cana-2015	123	24	1−	1−	NUM
cana-2015	123	25	(	(	PUNCT
cana-2015	123	26	log∏	log∏	NOUN
cana-2015	123	27	i	i	NOUN
cana-2015	123	28	t	t	VERB
cana-2015	124	1	l	l	NOUN
cana-2015	124	2	m	m	VERB
cana-2015	124	3	i	i	NOUN
cana-2015	124	4	)	)	PUNCT
cana-2015	124	5	q	q	NOUN
cana-2015	124	6	)	)	PUNCT
cana-2015	124	7	ωi	ωi	PROPN
cana-2015	124	8	)	)	PUNCT
cana-2015	124	9	·	·	PUNCT
cana-2015	125	1	(	(	PUNCT
cana-2015	125	2	1−	1−	NUM
cana-2015	125	3	(	(	PUNCT
cana-2015	125	4	1−	1−	NUM
cana-2015	125	5	(	(	PUNCT
cana-2015	125	6	log∏	log∏	NOUN
cana-2015	125	7	i	i	NOUN
cana-2015	125	8	t	t	NOUN
cana-2015	125	9	l	l	NOUN
cana-2015	125	10	mm+1	mm+1	X
cana-2015	125	11	)	)	PUNCT
cana-2015	125	12	q	q	NOUN
cana-2015	125	13	)	)	PUNCT
cana-2015	125	14	ωm+1	ωm+1	NUM
cana-2015	125	15	)	)	PUNCT
cana-2015	126	1	,	,	PUNCT
cana-2015	126	2	q	q	PROPN
cana-2015	126	3	√√√√√	√√√√√	PROPN
cana-2015	126	4	�	�	PROPN
cana-2015	126	5	m	m	PROPN
cana-2015	126	6	i=1	i=1	PROPN
cana-2015	126	7	(	(	PUNCT
cana-2015	126	8	1−	1−	NUM
cana-2015	126	9	(	(	PUNCT
cana-2015	126	10	1−	1−	NUM
cana-2015	126	11	(	(	PUNCT
cana-2015	126	12	log∏	log∏	NOUN
cana-2015	126	13	i	i	PRON
cana-2015	126	14	(	(	PUNCT
cana-2015	126	15	t	t	PROPN
cana-2015	126	16	u	u	PROPN
cana-2015	126	17	mi	mi	PROPN
cana-2015	126	18	)	)	PUNCT
cana-2015	126	19	)	)	PUNCT
cana-2015	126	20	q	q	X
cana-2015	126	21	)	)	PUNCT
cana-2015	126	22	ωi	ωi	PROPN
cana-2015	126	23	)	)	PUNCT
cana-2015	127	1	+	+	CCONJ
cana-2015	127	2	(	(	PUNCT
cana-2015	127	3	1−	1−	NUM
cana-2015	127	4	(	(	PUNCT
cana-2015	127	5	1−	1−	NUM
cana-2015	127	6	(	(	PUNCT
cana-2015	127	7	log∏	log∏	NOUN
cana-2015	127	8	i	i	PRON
cana-2015	127	9	(	(	PUNCT
cana-2015	127	10	t	t	PROPN
cana-2015	127	11	u	u	PROPN
cana-2015	127	12	mm+1	mm+1	PROPN
cana-2015	127	13	)	)	PUNCT
cana-2015	127	14	)	)	PUNCT
cana-2015	127	15	q	q	X
cana-2015	127	16	)	)	PUNCT
cana-2015	127	17	ωm+1	ωm+1	NUM
cana-2015	127	18	)	)	PUNCT
cana-2015	127	19	−	−	NUM
cana-2015	127	20	�	�	PROPN
cana-2015	127	21	m	m	VERB
cana-2015	127	22	i=1	i=1	PROPN
cana-2015	127	23	(	(	PUNCT
cana-2015	127	24	1−	1−	NUM
cana-2015	127	25	(	(	PUNCT
cana-2015	127	26	1−	1−	NUM
cana-2015	127	27	(	(	PUNCT
cana-2015	127	28	log∏	log∏	NOUN
cana-2015	127	29	i	i	PRON
cana-2015	127	30	(	(	PUNCT
cana-2015	127	31	t	t	PROPN
cana-2015	127	32	u	u	PROPN
cana-2015	127	33	mi	mi	PROPN
cana-2015	127	34	)	)	PUNCT
cana-2015	127	35	)	)	PUNCT
cana-2015	127	36	q	q	NOUN
cana-2015	127	37	)	)	PUNCT
cana-2015	127	38	ωi	ωi	PROPN
cana-2015	127	39	)	)	PUNCT
cana-2015	127	40	·	·	PUNCT
cana-2015	128	1	(	(	PUNCT
cana-2015	128	2	1−	1−	NUM
cana-2015	128	3	(	(	PUNCT
cana-2015	128	4	1−	1−	NUM
cana-2015	128	5	(	(	PUNCT
cana-2015	128	6	log∏	log∏	NOUN
cana-2015	128	7	i	i	PRON
cana-2015	128	8	(	(	PUNCT
cana-2015	128	9	t	t	PROPN
cana-2015	128	10	u	u	PROPN
cana-2015	128	11	mm+1	mm+1	PROPN
cana-2015	128	12	)	)	PUNCT
cana-2015	128	13	)	)	PUNCT
cana-2015	128	14	q	q	X
cana-2015	128	15	)	)	PUNCT
cana-2015	128	16	ωm+1	ωm+1	NUM
cana-2015	128	17	)	)	PUNCT
cana-2015	128	18			NOUN
cana-2015	128	19	,	,	PUNCT
cana-2015	128	20	(	(	PUNCT
cana-2015	128	21	�	�	PROPN
cana-2015	128	22	m	m	VERB
cana-2015	128	23	i=1	i=1	PROPN
cana-2015	128	24	(	(	PUNCT
cana-2015	128	25	log	log	VERB
cana-2015	128	26	∏	∏	NUM
cana-2015	129	1	i	i	PRON
cana-2015	129	2	f	f	PROPN
cana-2015	129	3	l	l	NOUN
cana-2015	129	4	m	m	VERB
cana-2015	129	5	i	i	NOUN
cana-2015	129	6	)	)	PUNCT
cana-2015	129	7	qωi	qωi	NOUN
cana-2015	129	8	·	·	PUNCT
cana-2015	129	9	(	(	PUNCT
cana-2015	129	10	log∏	log∏	NOUN
cana-2015	129	11	i	i	NOUN
cana-2015	129	12	f	f	PROPN
cana-2015	129	13	l	l	NOUN
cana-2015	129	14	mm+1	mm+1	X
cana-2015	129	15	)	)	PUNCT
cana-2015	129	16	qωm+1	qωm+1	PROPN
cana-2015	129	17	,	,	PUNCT
cana-2015	129	18	�	�	PROPN
cana-2015	129	19	m	m	NOUN
cana-2015	129	20	i=1(log	i=1(log	PROPN
cana-2015	129	21	∏	∏	PROPN
cana-2015	130	1	i	i	PROPN
cana-2015	130	2	(	(	PUNCT
cana-2015	130	3	fu	fu	PROPN
cana-2015	130	4	mi	mi	PROPN
cana-2015	130	5	)	)	PUNCT
cana-2015	130	6	)	)	PUNCT
cana-2015	130	7	qωi	qωi	NOUN
cana-2015	130	8	·	·	PUNCT
cana-2015	130	9	(	(	PUNCT
cana-2015	130	10	log∏	log∏	NOUN
cana-2015	130	11	i	i	PRON
cana-2015	130	12	(	(	PUNCT
cana-2015	130	13	fu	fu	PROPN
cana-2015	130	14	mm+1	mm+1	PROPN
cana-2015	130	15	)	)	PUNCT
cana-2015	130	16	)	)	PUNCT
cana-2015	130	17	qωm+1	qωm+1	NOUN
cana-2015	130	18	)	)	PUNCT
cana-2015	130	19			X
cana-2015	131	1	=	=	PRON
cana-2015	131	2			X
cana-2015	131	3	(	(	PUNCT
cana-2015	131	4	q	q	NOUN
cana-2015	131	5	√	√	NUM
cana-2015	131	6	1−	1−	NUM
cana-2015	131	7	�	�	PROPN
cana-2015	131	8	m+1	m+1	NUM
cana-2015	131	9	i=1	i=1	PROPN
cana-2015	131	10	(	(	PUNCT
cana-2015	131	11	1−	1−	NUM
cana-2015	131	12	(	(	PUNCT
cana-2015	131	13	log∏	log∏	NOUN
cana-2015	131	14	i	i	NOUN
cana-2015	131	15	t	t	VERB
cana-2015	131	16	l	l	NOUN
cana-2015	131	17	m	m	VERB
cana-2015	131	18	i	i	NOUN
cana-2015	131	19	)	)	PUNCT
cana-2015	131	20	q	q	NOUN
cana-2015	131	21	)	)	PUNCT
cana-2015	131	22	ωi	ωi	NOUN
cana-2015	131	23	,	,	PUNCT
cana-2015	131	24	q	q	NOUN
cana-2015	131	25	√	√	NUM
cana-2015	131	26	1−	1−	NUM
cana-2015	131	27	�	�	PROPN
cana-2015	131	28	m+1	m+1	NUM
cana-2015	131	29	i=1	i=1	PROPN
cana-2015	131	30	(	(	PUNCT
cana-2015	131	31	1−	1−	NUM
cana-2015	131	32	(	(	PUNCT
cana-2015	131	33	log∏	log∏	NOUN
cana-2015	131	34	i	i	PRON
cana-2015	131	35	(	(	PUNCT
cana-2015	131	36	t	t	PROPN
cana-2015	131	37	u	u	PROPN
cana-2015	131	38	mi	mi	PROPN
cana-2015	131	39	)	)	PUNCT
cana-2015	131	40	)	)	PUNCT
cana-2015	131	41	q	q	NOUN
cana-2015	131	42	)	)	PUNCT
cana-2015	131	43	ωi	ωi	PROPN
cana-2015	131	44	)	)	PUNCT
cana-2015	131	45	,	,	PUNCT
cana-2015	131	46	(	(	PUNCT
cana-2015	131	47	�	�	ADP
cana-2015	131	48	m+1	m+1	PRON
cana-2015	131	49	i=1	i=1	PROPN
cana-2015	132	1	(	(	PUNCT
cana-2015	132	2	log∏	log∏	NOUN
cana-2015	132	3	i	i	PRON
cana-2015	132	4	f	f	VERB
cana-2015	132	5	l	l	NOUN
cana-2015	132	6	m	m	VERB
cana-2015	132	7	i	i	NOUN
cana-2015	132	8	)	)	PUNCT
cana-2015	132	9	qωi	qωi	NOUN
cana-2015	132	10	,	,	PUNCT
cana-2015	132	11	�	�	PROPN
cana-2015	132	12	m+1	m+1	PRON
cana-2015	132	13	i=1	i=1	PROPN
cana-2015	133	1	(	(	PUNCT
cana-2015	133	2	log∏	log∏	PROPN
cana-2015	133	3	i	i	PROPN
cana-2015	133	4	(	(	PUNCT
cana-2015	133	5	fu	fu	PROPN
cana-2015	133	6	mi	mi	PROPN
cana-2015	133	7	)	)	PUNCT
cana-2015	133	8	)	)	PUNCT
cana-2015	133	9	qωi	qωi	NOUN
cana-2015	133	10	)	)	PUNCT
cana-2015	133	11			PROPN
cana-2015	133	12	.	.	PUNCT
cana-2015	134	1	theorem	theorem	VERB
cana-2015	134	2	4.3	4.3	NUM
cana-2015	134	3	.	.	PUNCT
cana-2015	135	1	(	(	PUNCT
cana-2015	135	2	idempotency	idempotency	NOUN
cana-2015	135	3	property	property	NOUN
cana-2015	135	4	)	)	PUNCT
cana-2015	135	5	if	if	SCONJ
cana-2015	135	6	allmi	allmi	NOUN
cana-2015	135	7	=	=	SYM
cana-2015	135	8	〈	〈	PROPN
cana-2015	135	9	(	(	PUNCT
cana-2015	135	10	logt	logt	NOUN
cana-2015	135	11	l	l	NOUN
cana-2015	136	1	m	m	VERB
cana-2015	136	2	i	i	PRON
cana-2015	136	3	,	,	PUNCT
cana-2015	136	4	logt	logt	PROPN
cana-2015	136	5	u	u	PROPN
cana-2015	136	6	mi	mi	PROPN
cana-2015	136	7	)	)	PUNCT
cana-2015	136	8	,	,	PUNCT
cana-2015	136	9	(	(	PUNCT
cana-2015	136	10	logf	logf	INTJ
cana-2015	136	11	l	l	NOUN
cana-2015	136	12	m	m	VERB
cana-2015	136	13	i	i	PRON
cana-2015	136	14	,	,	PUNCT
cana-2015	136	15	logf	logf	VERB
cana-2015	136	16	u	u	PROPN
cana-2015	136	17	mi	mi	PROPN
cana-2015	136	18	)	)	PUNCT
cana-2015	136	19	〉	〉	NOUN
cana-2015	136	20	(	(	PUNCT
cana-2015	136	21	i	i	NOUN
cana-2015	136	22	=	=	NOUN
cana-2015	136	23	1	1	NUM
cana-2015	136	24	,	,	PUNCT
cana-2015	136	25	2	2	NUM
cana-2015	136	26	,	,	PUNCT
cana-2015	136	27	...	...	PUNCT
cana-2015	136	28	,	,	PUNCT
cana-2015	136	29	n	n	CCONJ
cana-2015	136	30	)	)	PUNCT
cana-2015	136	31	are	be	AUX
cana-2015	136	32	equal	equal	ADJ
cana-2015	136	33	and	and	CCONJ
cana-2015	136	34	mi	mi	X
cana-2015	137	1	=	=	NOUN
cana-2015	137	2	m	m	PROPN
cana-2015	137	3	.	.	PUNCT
cana-2015	138	1	then	then	ADV
cana-2015	138	2	q	q	X
cana-2015	138	3	-	-	PUNCT
cana-2015	138	4	livifwa	livifwa	NOUN
cana-2015	138	5	(	(	PUNCT
cana-2015	138	6	m1,m2	m1,m2	PROPN
cana-2015	138	7	,	,	PUNCT
cana-2015	138	8	...	...	PUNCT
cana-2015	138	9	,	,	PUNCT
cana-2015	138	10	mn	mn	PROPN
cana-2015	138	11	)	)	PUNCT
cana-2015	139	1	=	=	NOUN
cana-2015	139	2	m	m	NOUN
cana-2015	139	3	.	.	PUNCT
cana-2015	140	1	proof	proof	NOUN
cana-2015	140	2	.	.	PUNCT
cana-2015	141	1	given	give	VERB
cana-2015	141	2	that	that	PRON
cana-2015	141	3	(	(	PUNCT
cana-2015	141	4	logt	logt	NOUN
cana-2015	141	5	l	l	NOUN
cana-2015	141	6	m	m	VERB
cana-2015	141	7	i	i	PRON
cana-2015	141	8	,	,	PUNCT
cana-2015	141	9	logt	logt	PROPN
cana-2015	141	10	u	u	PROPN
cana-2015	141	11	mi	mi	PROPN
cana-2015	141	12	)	)	PUNCT
cana-2015	141	13	=	=	PRON
cana-2015	142	1	(	(	PUNCT
cana-2015	142	2	logt	logt	NOUN
cana-2015	142	3	l	l	NOUN
cana-2015	142	4	m	m	NOUN
cana-2015	142	5	,	,	PUNCT
cana-2015	142	6	log(t	log(t	PROPN
cana-2015	142	7	u	u	NOUN
cana-2015	142	8	m	m	NOUN
cana-2015	142	9	)	)	PUNCT
cana-2015	142	10	)	)	PUNCT
cana-2015	143	1	and	and	CCONJ
cana-2015	143	2	(	(	PUNCT
cana-2015	143	3	logf	logf	INTJ
cana-2015	143	4	l	l	NOUN
cana-2015	143	5	m	m	VERB
cana-2015	143	6	i	i	PRON
cana-2015	143	7	,	,	PUNCT
cana-2015	143	8	logf	logf	VERB
cana-2015	143	9	u	u	PROPN
cana-2015	143	10	mi	mi	PROPN
cana-2015	143	11	)	)	PUNCT
cana-2015	143	12	=	=	PUNCT
cana-2015	143	13	(	(	PUNCT
cana-2015	143	14	logf	logf	INTJ
cana-2015	143	15	l	l	NOUN
cana-2015	143	16	m	m	VERB
cana-2015	143	17	,	,	PUNCT
cana-2015	143	18	log(f	log(f	PROPN
cana-2015	143	19	u	u	NOUN
cana-2015	143	20	m	m	NOUN
cana-2015	143	21	)	)	PUNCT
cana-2015	143	22	)	)	PUNCT
cana-2015	143	23	,	,	PUNCT
cana-2015	143	24	https://internationalpubls.com	https://internationalpubls.com	X
cana-2015	143	25	542	542	NUM
cana-2015	143	26	communications	communication	NOUN
cana-2015	143	27	on	on	ADP
cana-2015	143	28	applied	apply	VERB
cana-2015	143	29	nonlinear	nonlinear	ADJ
cana-2015	143	30	analysis	analysis	NOUN
cana-2015	143	31	issn	issn	NOUN
cana-2015	143	32	:	:	PUNCT
cana-2015	143	33	1074	1074	NUM
cana-2015	143	34	-	-	PUNCT
cana-2015	143	35	133x	133x	NUM
cana-2015	143	36	vol	vol	NOUN
cana-2015	143	37	32	32	NUM
cana-2015	143	38	no	no	NOUN
cana-2015	143	39	.	.	NOUN
cana-2015	143	40	3	3	NUM
cana-2015	143	41	(	(	PUNCT
cana-2015	143	42	2025	2025	NUM
cana-2015	143	43	)	)	PUNCT
cana-2015	143	44	for	for	ADP
cana-2015	143	45	i	i	PROPN
cana-2015	143	46	=	=	SYM
cana-2015	143	47	1	1	NUM
cana-2015	143	48	,	,	PUNCT
cana-2015	143	49	2	2	NUM
cana-2015	143	50	,	,	PUNCT
cana-2015	143	51	...	...	PUNCT
cana-2015	143	52	,	,	PUNCT
cana-2015	143	53	n	n	PROPN
cana-2015	143	54	and	and	CCONJ
cana-2015	143	55	�	�	PROPN
cana-2015	143	56	n	n	CCONJ
cana-2015	143	57	i=1ωi	i=1ωi	NOUN
cana-2015	143	58	=	=	NOUN
cana-2015	143	59	1	1	X
cana-2015	143	60	.	.	PUNCT
cana-2015	144	1	now	now	ADV
cana-2015	144	2	,	,	PUNCT
cana-2015	144	3	q	q	NOUN
cana-2015	144	4	-	-	PUNCT
cana-2015	144	5	livifwa	livifwa	NOUN
cana-2015	144	6	(	(	PUNCT
cana-2015	144	7	m1,m2	m1,m2	PROPN
cana-2015	144	8	,	,	PUNCT
cana-2015	144	9	...	...	PUNCT
cana-2015	144	10	,	,	PUNCT
cana-2015	144	11	mn	mn	PROPN
cana-2015	144	12	)	)	PUNCT
cana-2015	144	13	=	=	PRON
cana-2015	144	14			X
cana-2015	144	15	(	(	PUNCT
cana-2015	144	16	q	q	NOUN
cana-2015	144	17	√	√	NUM
cana-2015	144	18	1−	1−	NUM
cana-2015	144	19	�	�	PROPN
cana-2015	144	20	n	n	PRON
cana-2015	144	21	i=1	i=1	PROPN
cana-2015	144	22	(	(	PUNCT
cana-2015	144	23	1−	1−	NUM
cana-2015	144	24	(	(	PUNCT
cana-2015	144	25	log∏	log∏	NOUN
cana-2015	144	26	i	i	NOUN
cana-2015	144	27	t	t	VERB
cana-2015	144	28	l	l	NOUN
cana-2015	144	29	m	m	VERB
cana-2015	144	30	i	i	NOUN
cana-2015	144	31	)	)	PUNCT
cana-2015	144	32	q	q	NOUN
cana-2015	144	33	)	)	PUNCT
cana-2015	144	34	ωi	ωi	NOUN
cana-2015	144	35	,	,	PUNCT
cana-2015	144	36	q	q	NOUN
cana-2015	144	37	√	√	NUM
cana-2015	144	38	1−	1−	NUM
cana-2015	144	39	�	�	PROPN
cana-2015	144	40	n	n	PRON
cana-2015	144	41	i=1	i=1	PROPN
cana-2015	144	42	(	(	PUNCT
cana-2015	144	43	1−	1−	NUM
cana-2015	144	44	(	(	PUNCT
cana-2015	144	45	log∏	log∏	NOUN
cana-2015	144	46	i	i	PRON
cana-2015	144	47	(	(	PUNCT
cana-2015	144	48	t	t	PROPN
cana-2015	144	49	u	u	PROPN
cana-2015	144	50	mi	mi	PROPN
cana-2015	144	51	)	)	PUNCT
cana-2015	144	52	)	)	PUNCT
cana-2015	144	53	q	q	NOUN
cana-2015	144	54	)	)	PUNCT
cana-2015	144	55	ωi	ωi	PROPN
cana-2015	144	56	)	)	PUNCT
cana-2015	144	57	,	,	PUNCT
cana-2015	144	58	(	(	PUNCT
cana-2015	144	59	�	�	PROPN
cana-2015	144	60	n	n	CCONJ
cana-2015	144	61	i=1	i=1	PROPN
cana-2015	144	62	(	(	PUNCT
cana-2015	144	63	log	log	VERB
cana-2015	144	64	∏	∏	NUM
cana-2015	145	1	i	i	PRON
cana-2015	145	2	f	f	PROPN
cana-2015	145	3	l	l	NOUN
cana-2015	145	4	m	m	VERB
cana-2015	145	5	i	i	NOUN
cana-2015	145	6	)	)	PUNCT
cana-2015	145	7	qωi	qωi	PROPN
cana-2015	145	8	,	,	PUNCT
cana-2015	145	9	�	�	PROPN
cana-2015	145	10	n	n	CCONJ
cana-2015	145	11	i=1(log	i=1(log	PROPN
cana-2015	145	12	∏	∏	PROPN
cana-2015	145	13	i	i	PROPN
cana-2015	145	14	(	(	PUNCT
cana-2015	145	15	fu	fu	PROPN
cana-2015	145	16	mi	mi	PROPN
cana-2015	145	17	)	)	PUNCT
cana-2015	145	18	)	)	PUNCT
cana-2015	145	19	qωi	qωi	NOUN
cana-2015	145	20	)	)	PUNCT
cana-2015	145	21			PUNCT
cana-2015	146	1	=	=	PUNCT
cana-2015	146	2			PROPN
cana-2015	146	3	(	(	PUNCT
cana-2015	146	4	q	q	NOUN
cana-2015	146	5	√	√	NUM
cana-2015	146	6	1−	1−	NUM
cana-2015	146	7	(	(	PUNCT
cana-2015	146	8	1−	1−	NUM
cana-2015	146	9	(	(	PUNCT
cana-2015	146	10	log∏	log∏	NOUN
cana-2015	146	11	i	i	NOUN
cana-2015	146	12	t	t	VERB
cana-2015	146	13	l	l	NOUN
cana-2015	146	14	m	m	NOUN
cana-2015	146	15	)	)	PUNCT
cana-2015	146	16	q	q	NOUN
cana-2015	146	17	)	)	PUNCT
cana-2015	146	18	�	�	PROPN
cana-2015	146	19	n	n	NUM
cana-2015	146	20	i=1ωi	i=1ωi	NOUN
cana-2015	146	21	,	,	PUNCT
cana-2015	146	22	q	q	NOUN
cana-2015	146	23	√	√	ADJ
cana-2015	146	24	1	1	NUM
cana-2015	146	25	(	(	PUNCT
cana-2015	146	26	1−	1−	NUM
cana-2015	146	27	(	(	PUNCT
cana-2015	146	28	log∏	log∏	NOUN
cana-2015	146	29	i	i	PRON
cana-2015	146	30	(	(	PUNCT
cana-2015	146	31	t	t	PROPN
cana-2015	146	32	u	u	X
cana-2015	146	33	m	m	NOUN
cana-2015	146	34	)	)	PUNCT
cana-2015	146	35	)	)	PUNCT
cana-2015	146	36	q	q	X
cana-2015	146	37	)	)	PUNCT
cana-2015	146	38	�	�	PROPN
cana-2015	146	39	n	n	NUM
cana-2015	146	40	i=1ωi	i=1ωi	PRON
cana-2015	146	41	)	)	PUNCT
cana-2015	146	42	,	,	PUNCT
cana-2015	146	43	(	(	PUNCT
cana-2015	146	44	(	(	PUNCT
cana-2015	146	45	log∏	log∏	NOUN
cana-2015	146	46	i	i	NOUN
cana-2015	146	47	f	f	PROPN
cana-2015	146	48	l	l	NOUN
cana-2015	146	49	m	m	NOUN
cana-2015	146	50	)	)	PUNCT
cana-2015	146	51	�	�	PROPN
cana-2015	146	52	n	n	CCONJ
cana-2015	146	53	i=1qωi	i=1qωi	NOUN
cana-2015	146	54	,	,	PUNCT
cana-2015	146	55	(	(	PUNCT
cana-2015	146	56	log∏	log∏	PROPN
cana-2015	146	57	i	i	PRON
cana-2015	146	58	(	(	PUNCT
cana-2015	146	59	fu	fu	NOUN
cana-2015	146	60	m	m	PROPN
cana-2015	146	61	)	)	PUNCT
cana-2015	146	62	)	)	PUNCT
cana-2015	146	63	�	�	PROPN
cana-2015	146	64	n	n	CCONJ
cana-2015	146	65	i=1qωi	i=1qωi	NOUN
cana-2015	146	66	)	)	PUNCT
cana-2015	147	1			PROPN
cana-2015	147	2	=	=	SYM
cana-2015	147	3			X
cana-2015	147	4	(	(	PUNCT
cana-2015	147	5	q	q	SYM
cana-2015	147	6	√	√	NUM
cana-2015	147	7	1−	1−	NUM
cana-2015	147	8	(	(	PUNCT
cana-2015	147	9	1−	1−	NUM
cana-2015	147	10	(	(	PUNCT
cana-2015	147	11	log∏	log∏	NOUN
cana-2015	147	12	i	i	NOUN
cana-2015	147	13	t	t	VERB
cana-2015	147	14	l	l	NOUN
cana-2015	147	15	m	m	NOUN
cana-2015	147	16	)	)	PUNCT
cana-2015	147	17	q	q	PUNCT
cana-2015	147	18	)	)	PUNCT
cana-2015	147	19	,	,	PUNCT
cana-2015	147	20	q	q	PROPN
cana-2015	147	21	√	√	NUM
cana-2015	147	22	1−	1−	NUM
cana-2015	147	23	(	(	PUNCT
cana-2015	147	24	1−	1−	NUM
cana-2015	147	25	(	(	PUNCT
cana-2015	147	26	log∏	log∏	NOUN
cana-2015	147	27	i	i	PRON
cana-2015	147	28	(	(	PUNCT
cana-2015	147	29	t	t	PROPN
cana-2015	147	30	u	u	X
cana-2015	147	31	m	m	NOUN
cana-2015	147	32	)	)	PUNCT
cana-2015	147	33	)	)	PUNCT
cana-2015	147	34	q	q	NOUN
cana-2015	147	35	)	)	PUNCT
cana-2015	147	36	)	)	PUNCT
cana-2015	147	37	,	,	PUNCT
cana-2015	147	38	(	(	PUNCT
cana-2015	147	39	(	(	PUNCT
cana-2015	147	40	log∏	log∏	NOUN
cana-2015	147	41	i	i	NOUN
cana-2015	147	42	f	f	PROPN
cana-2015	147	43	l	l	NOUN
cana-2015	147	44	m	m	NOUN
cana-2015	147	45	)	)	PUNCT
cana-2015	147	46	q	q	NOUN
cana-2015	147	47	,	,	PUNCT
cana-2015	147	48	(	(	PUNCT
cana-2015	147	49	log∏	log∏	PROPN
cana-2015	147	50	i	i	PRON
cana-2015	147	51	(	(	PUNCT
cana-2015	147	52	fu	fu	NOUN
cana-2015	147	53	m	m	PROPN
cana-2015	147	54	)	)	PUNCT
cana-2015	147	55	)	)	PUNCT
cana-2015	147	56	q	q	X
cana-2015	147	57	)	)	PUNCT
cana-2015	147	58			NOUN
cana-2015	147	59	=	=	SYM
cana-2015	147	60	m.	m.	NOUN
cana-2015	147	61	theorem	theorem	VERB
cana-2015	147	62	4.4	4.4	NUM
cana-2015	147	63	.	.	PUNCT
cana-2015	148	1	let	let	VERB
cana-2015	148	2	mi	mi	PROPN
cana-2015	148	3	=	=	PROPN
cana-2015	148	4	〈	〈	PROPN
cana-2015	148	5	(	(	PUNCT
cana-2015	148	6	logt	logt	NOUN
cana-2015	148	7	l	l	NOUN
cana-2015	148	8	m	m	VERB
cana-2015	148	9	ij	ij	INTJ
cana-2015	148	10	,	,	PUNCT
cana-2015	148	11	log(t	log(t	PROPN
cana-2015	148	12	u	u	NOUN
cana-2015	148	13	mij	mij	NOUN
cana-2015	148	14	)	)	PUNCT
cana-2015	148	15	)	)	PUNCT
cana-2015	148	16	,	,	PUNCT
cana-2015	148	17	(	(	PUNCT
cana-2015	148	18	logf	logf	INTJ
cana-2015	148	19	l	l	NOUN
cana-2015	148	20	m	m	VERB
cana-2015	148	21	ij	ij	INTJ
cana-2015	148	22	,	,	PUNCT
cana-2015	148	23	log(f	log(f	PROPN
cana-2015	148	24	u	u	NOUN
cana-2015	148	25	mij	mij	NOUN
cana-2015	148	26	)	)	PUNCT
cana-2015	148	27	)	)	PUNCT
cana-2015	148	28	〉	〉	NOUN
cana-2015	148	29	(	(	PUNCT
cana-2015	148	30	i	i	NOUN
cana-2015	148	31	=	=	NOUN
cana-2015	148	32	1	1	NUM
cana-2015	148	33	,	,	PUNCT
cana-2015	148	34	2	2	NUM
cana-2015	148	35	,	,	PUNCT
cana-2015	148	36	...	...	PUNCT
cana-2015	148	37	,	,	PUNCT
cana-2015	148	38	n	n	CCONJ
cana-2015	148	39	)	)	PUNCT
cana-2015	148	40	;	;	PUNCT
cana-2015	148	41	(	(	PUNCT
cana-2015	148	42	j	j	NOUN
cana-2015	148	43	=	=	SYM
cana-2015	148	44	1	1	NUM
cana-2015	148	45	,	,	PUNCT
cana-2015	148	46	2	2	NUM
cana-2015	148	47	,	,	PUNCT
cana-2015	148	48	...	...	PUNCT
cana-2015	148	49	,	,	PUNCT
cana-2015	148	50	ij	ij	X
cana-2015	148	51	)	)	PUNCT
cana-2015	148	52	be	be	AUX
cana-2015	148	53	the	the	DET
cana-2015	148	54	collection	collection	NOUN
cana-2015	148	55	of	of	ADP
cana-2015	148	56	q	q	NOUN
cana-2015	148	57	-	-	PUNCT
cana-2015	148	58	livifwa	livifwa	NOUN
cana-2015	148	59	,	,	PUNCT
cana-2015	149	1	where	where	SCONJ
cana-2015	149	2	log∏	log∏	PROPN
cana-2015	149	3	i	i	PROPN
cana-2015	149	4	t	t	NOUN
cana-2015	149	5	l	l	NOUN
cana-2015	149	6	m︸	m︸	X
cana-2015	149	7	︷︷	︷︷	PROPN
cana-2015	149	8	︸	︸	X
cana-2015	149	9	=	=	SYM
cana-2015	149	10	min	min	NOUN
cana-2015	149	11	log∏	log∏	PROPN
cana-2015	149	12	i	i	PRON
cana-2015	149	13	t	t	VERB
cana-2015	149	14	l	l	NOUN
cana-2015	149	15	m	m	VERB
cana-2015	149	16	ij	ij	INTJ
cana-2015	149	17	,	,	PUNCT
cana-2015	149	18	︷	︷	PROPN
cana-2015	149	19	︸︸	︸︸	ADJ
cana-2015	149	20	︷	︷	PUNCT
cana-2015	150	1	log∏	log∏	NOUN
cana-2015	151	1	i	i	PRON
cana-2015	151	2	t	t	VERB
cana-2015	151	3	l	l	NOUN
cana-2015	151	4	m	m	PROPN
cana-2015	151	5	=	=	SYM
cana-2015	151	6	max	max	PROPN
cana-2015	151	7	log∏	log∏	PROPN
cana-2015	152	1	i	i	PRON
cana-2015	152	2	t	t	AUX
cana-2015	152	3	l	l	NOUN
cana-2015	152	4	m	m	VERB
cana-2015	152	5	ij	ij	INTJ
cana-2015	152	6	,	,	PUNCT
cana-2015	152	7	log	log	VERB
cana-2015	152	8	∏	∏	PROPN
cana-2015	153	1	i	i	INTJ
cana-2015	153	2	(	(	PUNCT
cana-2015	153	3	t	t	PROPN
cana-2015	153	4	u	u	X
cana-2015	153	5	m	m	NOUN
cana-2015	153	6	)	)	PUNCT
cana-2015	153	7	︸	︸	NOUN
cana-2015	153	8	︷︷	︷︷	NOUN
cana-2015	153	9	︸	︸	X
cana-2015	153	10	=	=	SYM
cana-2015	153	11	min	min	NOUN
cana-2015	153	12	log∏	log∏	PROPN
cana-2015	153	13	i	i	PRON
cana-2015	153	14	(	(	PUNCT
cana-2015	153	15	t	t	PROPN
cana-2015	153	16	u	u	NOUN
cana-2015	153	17	mij	mij	NOUN
cana-2015	153	18	)	)	PUNCT
cana-2015	153	19	,	,	PUNCT
cana-2015	153	20	︷	︷	X
cana-2015	153	21	︸︸	︸︸	ADJ
cana-2015	153	22	︷	︷	PUNCT
cana-2015	154	1	log∏	log∏	PROPN
cana-2015	154	2	i	i	PRON
cana-2015	154	3	(	(	PUNCT
cana-2015	154	4	t	t	PROPN
cana-2015	154	5	u	u	X
cana-2015	154	6	m	m	NOUN
cana-2015	154	7	)	)	PUNCT
cana-2015	155	1	=	=	SYM
cana-2015	155	2	max	max	PROPN
cana-2015	155	3	log∏	log∏	PROPN
cana-2015	155	4	i	i	PROPN
cana-2015	155	5	(	(	PUNCT
cana-2015	155	6	t	t	PROPN
cana-2015	155	7	u	u	NOUN
cana-2015	155	8	mij	mij	NOUN
cana-2015	155	9	)	)	PUNCT
cana-2015	155	10	,	,	PUNCT
cana-2015	155	11	log	log	VERB
cana-2015	155	12	∏	∏	PROPN
cana-2015	156	1	i	i	PRON
cana-2015	156	2	f	f	PROPN
cana-2015	156	3	l	l	NOUN
cana-2015	156	4	m︸	m︸	X
cana-2015	156	5	︷︷	︷︷	PROPN
cana-2015	156	6	︸	︸	X
cana-2015	156	7	=	=	SYM
cana-2015	156	8	min	min	NOUN
cana-2015	156	9	log∏	log∏	PROPN
cana-2015	157	1	i	i	PRON
cana-2015	157	2	f	f	PROPN
cana-2015	157	3	l	l	NOUN
cana-2015	157	4	m	m	VERB
cana-2015	157	5	ij	ij	INTJ
cana-2015	157	6	,	,	PUNCT
cana-2015	157	7	︷	︷	PROPN
cana-2015	157	8	︸︸	︸︸	ADJ
cana-2015	157	9	︷	︷	PUNCT
cana-2015	158	1	log∏	log∏	NOUN
cana-2015	159	1	i	i	PRON
cana-2015	159	2	f	f	VERB
cana-2015	159	3	l	l	NOUN
cana-2015	159	4	m	m	PROPN
cana-2015	159	5	=	=	SYM
cana-2015	159	6	max	max	PROPN
cana-2015	159	7	log∏	log∏	PROPN
cana-2015	160	1	i	i	PRON
cana-2015	160	2	f	f	PROPN
cana-2015	160	3	l	l	NOUN
cana-2015	160	4	m	m	VERB
cana-2015	160	5	ij	ij	INTJ
cana-2015	160	6	,	,	PUNCT
cana-2015	160	7	log∏	log∏	PROPN
cana-2015	160	8	i	i	PROPN
cana-2015	160	9	(	(	PUNCT
cana-2015	160	10	fu	fu	NOUN
cana-2015	160	11	m	m	PROPN
cana-2015	160	12	)	)	PUNCT
cana-2015	160	13	︸	︸	NOUN
cana-2015	160	14	︷︷	︷︷	NOUN
cana-2015	160	15	︸	︸	X
cana-2015	160	16	=	=	SYM
cana-2015	160	17	min	min	NOUN
cana-2015	160	18	log∏	log∏	PROPN
cana-2015	160	19	i	i	PRON
cana-2015	160	20	(	(	PUNCT
cana-2015	160	21	fu	fu	NOUN
cana-2015	160	22	mij	mij	NOUN
cana-2015	160	23	)	)	PUNCT
cana-2015	160	24	,	,	PUNCT
cana-2015	160	25	︷	︷	X
cana-2015	160	26	︸︸	︸︸	ADJ
cana-2015	160	27	︷	︷	PUNCT
cana-2015	161	1	log∏	log∏	PROPN
cana-2015	161	2	i	i	PRON
cana-2015	161	3	(	(	PUNCT
cana-2015	161	4	fu	fu	NOUN
cana-2015	161	5	m	m	PROPN
cana-2015	161	6	)	)	PUNCT
cana-2015	162	1	=	=	SYM
cana-2015	162	2	max	max	PROPN
cana-2015	162	3	log∏	log∏	PROPN
cana-2015	162	4	i	i	PROPN
cana-2015	162	5	(	(	PUNCT
cana-2015	162	6	fu	fu	NOUN
cana-2015	162	7	mij	mij	NOUN
cana-2015	162	8	)	)	PUNCT
cana-2015	162	9	.	.	PUNCT
cana-2015	163	1	then	then	ADV
cana-2015	163	2	,	,	PUNCT
cana-2015	163	3	〈	〈	PROPN
cana-2015	163	4	(	(	PUNCT
cana-2015	163	5	log∏	log∏	PROPN
cana-2015	163	6	i	i	NOUN
cana-2015	163	7	t	t	NOUN
cana-2015	163	8	l	l	NOUN
cana-2015	163	9	m︸	m︸	X
cana-2015	163	10	︷︷	︷︷	PROPN
cana-2015	163	11	︸	︸	X
cana-2015	163	12	,	,	PUNCT
cana-2015	163	13	log∏i	log∏i	ADJ
cana-2015	163	14	(	(	PUNCT
cana-2015	163	15	t	t	NOUN
cana-2015	163	16	u	u	X
cana-2015	163	17	m	m	NOUN
cana-2015	163	18	)	)	PUNCT
cana-2015	163	19	︸	︸	NOUN
cana-2015	163	20	︷︷	︷︷	PROPN
cana-2015	163	21	︸	︸	NOUN
cana-2015	163	22	)	)	PUNCT
cana-2015	163	23	,	,	PUNCT
cana-2015	163	24	(	(	PUNCT
cana-2015	163	25	︷	︷	ADV
cana-2015	163	26	︸︸	︸︸	ADJ
cana-2015	163	27	︷	︷	PUNCT
cana-2015	164	1	log∏	log∏	NOUN
cana-2015	165	1	i	i	PRON
cana-2015	165	2	f	f	PROPN
cana-2015	166	1	l	l	NOUN
cana-2015	166	2	m	m	PROPN
cana-2015	166	3	,	,	PUNCT
cana-2015	166	4	︷	︷	ADJ
cana-2015	166	5	︸︸	︸︸	ADJ
cana-2015	166	6	︷	︷	PUNCT
cana-2015	167	1	log∏	log∏	PROPN
cana-2015	167	2	i	i	PRON
cana-2015	167	3	(	(	PUNCT
cana-2015	167	4	fu	fu	NOUN
cana-2015	167	5	m	m	PROPN
cana-2015	167	6	)	)	PUNCT
cana-2015	167	7	)	)	PUNCT
cana-2015	167	8	〉	〉	NOUN
cana-2015	167	9	≤	≤	VERB
cana-2015	167	10	new	new	ADJ
cana-2015	167	11	type	type	NOUN
cana-2015	167	12	liv	liv	PROPN
cana-2015	167	13	ifwa(m1,m2	ifwa(m1,m2	NOUN
cana-2015	167	14	,	,	PUNCT
cana-2015	167	15	...	...	PUNCT
cana-2015	167	16	,	,	PUNCT
cana-2015	167	17	mn	mn	PROPN
cana-2015	167	18	)	)	PUNCT
cana-2015	167	19	≤	≤	NOUN
cana-2015	168	1	〈	〈	PROPN
cana-2015	168	2	(	(	PUNCT
cana-2015	168	3	︷	︷	ADJ
cana-2015	168	4	︸︸	︸︸	PUNCT
cana-2015	168	5	︷	︷	PUNCT
cana-2015	169	1	log∏	log∏	NOUN
cana-2015	170	1	i	i	PRON
cana-2015	170	2	t	t	VERB
cana-2015	170	3	l	l	NOUN
cana-2015	170	4	m	m	PROPN
cana-2015	170	5	,	,	PUNCT
cana-2015	170	6	︷	︷	ADJ
cana-2015	170	7	︸︸	︸︸	ADJ
cana-2015	170	8	︷	︷	PUNCT
cana-2015	171	1	log∏	log∏	PROPN
cana-2015	171	2	i	i	PRON
cana-2015	171	3	(	(	PUNCT
cana-2015	171	4	t	t	PROPN
cana-2015	171	5	u	u	X
cana-2015	171	6	m	m	PROPN
cana-2015	171	7	)	)	PUNCT
cana-2015	171	8	)	)	PUNCT
cana-2015	171	9	,	,	PUNCT
cana-2015	171	10	(	(	PUNCT
cana-2015	171	11	log∏	log∏	NOUN
cana-2015	171	12	i	i	NOUN
cana-2015	171	13	f	f	PROPN
cana-2015	171	14	l	l	NOUN
cana-2015	171	15	m︸	m︸	X
cana-2015	171	16	︷︷	︷︷	PROPN
cana-2015	171	17	︸	︸	X
cana-2015	171	18	,	,	PUNCT
cana-2015	171	19	log∏i	log∏i	ADJ
cana-2015	171	20	(	(	PUNCT
cana-2015	171	21	fu	fu	NOUN
cana-2015	171	22	m	m	PROPN
cana-2015	171	23	)	)	PUNCT
cana-2015	171	24	︸	︸	NOUN
cana-2015	171	25	︷︷	︷︷	NOUN
cana-2015	171	26	︸	︸	NOUN
cana-2015	171	27	)	)	PUNCT
cana-2015	171	28	〉	〉	NOUN
cana-2015	171	29	.	.	PUNCT
cana-2015	172	1	where	where	SCONJ
cana-2015	172	2	1	1	NUM
cana-2015	172	3	≤	≤	NUM
cana-2015	172	4	i	i	PRON
cana-2015	172	5	≤	≤	PROPN
cana-2015	172	6	n	n	CCONJ
cana-2015	172	7	,	,	PUNCT
cana-2015	172	8	j	j	PROPN
cana-2015	172	9	=	=	SYM
cana-2015	172	10	1	1	NUM
cana-2015	172	11	,	,	PUNCT
cana-2015	172	12	2	2	NUM
cana-2015	172	13	,	,	PUNCT
cana-2015	172	14	...	...	PUNCT
cana-2015	172	15	,	,	PUNCT
cana-2015	172	16	ij	ij	INTJ
cana-2015	172	17	,	,	PUNCT
cana-2015	172	18	(	(	PUNCT
cana-2015	172	19	boundedness	boundedness	NOUN
cana-2015	172	20	property	property	NOUN
cana-2015	172	21	)	)	PUNCT
cana-2015	172	22	.	.	PUNCT
cana-2015	173	1	proof	proof	NOUN
cana-2015	173	2	.	.	PUNCT
cana-2015	174	1	since	since	SCONJ
cana-2015	174	2	,	,	PUNCT
cana-2015	174	3	log∏	log∏	PROPN
cana-2015	175	1	i	i	PROPN
cana-2015	175	2	t	t	NOUN
cana-2015	175	3	l	l	NOUN
cana-2015	175	4	m︸	m︸	X
cana-2015	175	5	︷︷	︷︷	PROPN
cana-2015	175	6	︸	︸	X
cana-2015	175	7	=	=	SYM
cana-2015	175	8	min	min	NOUN
cana-2015	175	9	log∏	log∏	PROPN
cana-2015	175	10	i	i	PRON
cana-2015	175	11	t	t	VERB
cana-2015	175	12	l	l	NOUN
cana-2015	175	13	m	m	VERB
cana-2015	175	14	ij	ij	INTJ
cana-2015	175	15	,	,	PUNCT
cana-2015	175	16	︷	︷	PROPN
cana-2015	175	17	︸︸	︸︸	ADJ
cana-2015	175	18	︷	︷	PUNCT
cana-2015	176	1	log∏	log∏	NOUN
cana-2015	177	1	i	i	PRON
cana-2015	177	2	t	t	VERB
cana-2015	177	3	l	l	NOUN
cana-2015	177	4	m	m	PROPN
cana-2015	177	5	=	=	SYM
cana-2015	177	6	max	max	PROPN
cana-2015	177	7	log∏	log∏	PROPN
cana-2015	178	1	i	i	PRON
cana-2015	178	2	t	t	VERB
cana-2015	178	3	l	l	NOUN
cana-2015	178	4	m	m	VERB
cana-2015	178	5	ij	ij	INTJ
cana-2015	178	6	log	log	NOUN
cana-2015	178	7	∏	∏	PROPN
cana-2015	179	1	i	i	INTJ
cana-2015	179	2	(	(	PUNCT
cana-2015	179	3	t	t	PROPN
cana-2015	179	4	u	u	X
cana-2015	179	5	m	m	NOUN
cana-2015	179	6	)	)	PUNCT
cana-2015	179	7	︸	︸	NOUN
cana-2015	179	8	︷︷	︷︷	NOUN
cana-2015	179	9	︸	︸	X
cana-2015	179	10	=	=	SYM
cana-2015	179	11	min	min	NOUN
cana-2015	179	12	log∏	log∏	PROPN
cana-2015	179	13	i	i	PRON
cana-2015	179	14	(	(	PUNCT
cana-2015	179	15	t	t	PROPN
cana-2015	179	16	u	u	PROPN
cana-2015	179	17	mij),︷	mij),︷	PROPN
cana-2015	179	18	︸︸	︸︸	PRON
cana-2015	179	19	︷	︷	PUNCT
cana-2015	180	1	log∏	log∏	PROPN
cana-2015	180	2	i	i	PRON
cana-2015	180	3	(	(	PUNCT
cana-2015	180	4	t	t	PROPN
cana-2015	180	5	u	u	X
cana-2015	180	6	m	m	NOUN
cana-2015	180	7	)	)	PUNCT
cana-2015	181	1	=	=	SYM
cana-2015	181	2	max	max	PROPN
cana-2015	181	3	log∏	log∏	PROPN
cana-2015	181	4	i	i	PROPN
cana-2015	181	5	(	(	PUNCT
cana-2015	181	6	t	t	PROPN
cana-2015	181	7	u	u	NOUN
cana-2015	181	8	mij	mij	NOUN
cana-2015	181	9	)	)	PUNCT
cana-2015	181	10	and	and	CCONJ
cana-2015	181	11	log∏	log∏	PROPN
cana-2015	182	1	i	i	PROPN
cana-2015	182	2	t	t	NOUN
cana-2015	182	3	l	l	NOUN
cana-2015	182	4	m︸	m︸	PROPN
cana-2015	182	5	︷︷	︷︷	PROPN
cana-2015	182	6	︸	︸	ADP
cana-2015	182	7	≤	≤	NUM
cana-2015	183	1	log∏i	log∏i	PROPN
cana-2015	183	2	t	t	PROPN
cana-2015	183	3	l	l	NOUN
cana-2015	183	4	m	m	VERB
cana-2015	183	5	ij	ij	X
cana-2015	183	6	≤	≤	NUM
cana-2015	183	7	︷	︷	X
cana-2015	183	8	︸︸	︸︸	PUNCT
cana-2015	183	9	︷	︷	PUNCT
cana-2015	184	1	log∏	log∏	NOUN
cana-2015	185	1	i	i	PRON
cana-2015	185	2	t	t	VERB
cana-2015	185	3	l	l	NOUN
cana-2015	185	4	m	m	PROPN
cana-2015	185	5	and	and	CCONJ
cana-2015	185	6	log∏	log∏	PROPN
cana-2015	186	1	i	i	PRON
cana-2015	186	2	(	(	PUNCT
cana-2015	186	3	t	t	PROPN
cana-2015	186	4	u	u	X
cana-2015	186	5	m	m	NOUN
cana-2015	186	6	)	)	PUNCT
cana-2015	186	7	︸	︸	NOUN
cana-2015	186	8	︷︷	︷︷	NOUN
cana-2015	186	9	︸	︸	ADP
cana-2015	186	10	≤	≤	NUM
cana-2015	186	11	log∏i	log∏i	ADJ
cana-2015	186	12	(	(	PUNCT
cana-2015	186	13	t	t	NOUN
cana-2015	186	14	u	u	X
cana-2015	186	15	m	m	NOUN
cana-2015	186	16	)	)	PUNCT
cana-2015	186	17	ij	ij	NOUN
cana-2015	186	18	≤︷	≤︷	VERB
cana-2015	186	19	︸︸	︸︸	NUM
cana-2015	186	20	︷	︷	PUNCT
cana-2015	187	1	log∏	log∏	PROPN
cana-2015	187	2	i	i	PRON
cana-2015	187	3	(	(	PUNCT
cana-2015	187	4	t	t	PROPN
cana-2015	187	5	u	u	X
cana-2015	187	6	m	m	PROPN
cana-2015	187	7	)	)	PUNCT
cana-2015	187	8	.	.	PUNCT
cana-2015	188	1	now	now	ADV
cana-2015	188	2	,	,	PUNCT
cana-2015	188	3	log∏	log∏	PROPN
cana-2015	188	4	i	i	NOUN
cana-2015	188	5	t	t	NOUN
cana-2015	188	6	l	l	NOUN
cana-2015	188	7	m︸	m︸	PROPN
cana-2015	189	1	︷︷	︷︷	PROPN
cana-2015	189	2	︸+	︸+	PROPN
cana-2015	189	3	log∏	log∏	PROPN
cana-2015	189	4	i	i	PRON
cana-2015	189	5	(	(	PUNCT
cana-2015	189	6	t	t	PROPN
cana-2015	189	7	u	u	X
cana-2015	189	8	m	m	NOUN
cana-2015	189	9	)	)	PUNCT
cana-2015	189	10	︸	︸	NOUN
cana-2015	189	11	︷︷	︷︷	NOUN
cana-2015	189	12	︸	︸	X
cana-2015	190	1	=	=	PUNCT
cana-2015	190	2	q	q	NOUN
cana-2015	190	3	√	√	NUM
cana-2015	190	4	1−	1−	NUM
cana-2015	190	5	�	�	PROPN
cana-2015	190	6	n	n	PRON
cana-2015	190	7	i=1	i=1	PROPN
cana-2015	190	8	(	(	PUNCT
cana-2015	190	9	1−	1−	NUM
cana-2015	190	10	(	(	PUNCT
cana-2015	190	11	log∏	log∏	NOUN
cana-2015	191	1	i	i	NOUN
cana-2015	191	2	t	t	NOUN
cana-2015	191	3	l	l	NOUN
cana-2015	191	4	m︸	m︸	PROPN
cana-2015	191	5	︷︷	︷︷	PROPN
cana-2015	191	6	︸)q	︸)q	PROPN
cana-2015	191	7	)	)	PUNCT
cana-2015	191	8	ωi	ωi	PROPN
cana-2015	192	1	+	+	CCONJ
cana-2015	192	2	q	q	ADJ
cana-2015	192	3	√	√	NUM
cana-2015	192	4	1−	1−	NUM
cana-2015	192	5	�	�	PROPN
cana-2015	192	6	n	n	PRON
cana-2015	192	7	i=1	i=1	PROPN
cana-2015	192	8	(	(	PUNCT
cana-2015	192	9	1−	1−	NUM
cana-2015	192	10	(	(	PUNCT
cana-2015	192	11	log∏	log∏	NOUN
cana-2015	192	12	i	i	PRON
cana-2015	192	13	(	(	PUNCT
cana-2015	192	14	t	t	PROPN
cana-2015	192	15	u	u	X
cana-2015	192	16	m	m	NOUN
cana-2015	192	17	)	)	PUNCT
cana-2015	192	18	︸	︸	NOUN
cana-2015	192	19	︷︷	︷︷	PROPN
cana-2015	192	20	︸)q	︸)q	PROPN
cana-2015	192	21	)	)	PUNCT
cana-2015	192	22	ωi	ωi	PROPN
cana-2015	192	23	≤	≤	PROPN
cana-2015	192	24	q	q	ADJ
cana-2015	192	25	√	√	NUM
cana-2015	192	26	1−	1−	NUM
cana-2015	192	27	�	�	PROPN
cana-2015	192	28	n	n	PRON
cana-2015	192	29	i=1	i=1	PROPN
cana-2015	192	30	(	(	PUNCT
cana-2015	192	31	1−	1−	NUM
cana-2015	192	32	(	(	PUNCT
cana-2015	192	33	log∏	log∏	NOUN
cana-2015	192	34	i	i	NOUN
cana-2015	192	35	t	t	VERB
cana-2015	192	36	l	l	NOUN
cana-2015	192	37	m	m	VERB
cana-2015	192	38	ij	ij	NOUN
cana-2015	192	39	)	)	PUNCT
cana-2015	192	40	q	q	NOUN
cana-2015	192	41	)	)	PUNCT
cana-2015	192	42	ωi	ωi	PROPN
cana-2015	193	1	+	+	CCONJ
cana-2015	193	2	q	q	ADJ
cana-2015	193	3	√	√	NUM
cana-2015	193	4	1−	1−	NUM
cana-2015	193	5	�	�	PROPN
cana-2015	193	6	n	n	PRON
cana-2015	193	7	i=1	i=1	PROPN
cana-2015	193	8	(	(	PUNCT
cana-2015	193	9	1−	1−	NUM
cana-2015	193	10	(	(	PUNCT
cana-2015	193	11	log∏	log∏	NOUN
cana-2015	193	12	i	i	PRON
cana-2015	193	13	(	(	PUNCT
cana-2015	193	14	t	t	PROPN
cana-2015	193	15	u	u	NOUN
cana-2015	193	16	mij	mij	NOUN
cana-2015	193	17	)	)	PUNCT
cana-2015	193	18	)	)	PUNCT
cana-2015	193	19	q	q	X
cana-2015	193	20	)	)	PUNCT
cana-2015	193	21	ωi	ωi	PROPN
cana-2015	193	22	≤	≤	PROPN
cana-2015	193	23	q	q	ADJ
cana-2015	193	24	√	√	NUM
cana-2015	193	25	1−	1−	NUM
cana-2015	193	26	�	�	PROPN
cana-2015	193	27	n	n	PRON
cana-2015	193	28	i=1	i=1	PROPN
cana-2015	193	29	(	(	PUNCT
cana-2015	193	30	1−	1−	NUM
cana-2015	193	31	(	(	PUNCT
cana-2015	193	32	︷	︷	X
cana-2015	193	33	︸︸	︸︸	PUNCT
cana-2015	193	34	︷	︷	PUNCT
cana-2015	194	1	log∏	log∏	NOUN
cana-2015	195	1	i	i	PRON
cana-2015	195	2	t	t	VERB
cana-2015	195	3	l	l	NOUN
cana-2015	195	4	m	m	NOUN
cana-2015	195	5	)	)	PUNCT
cana-2015	195	6	q	q	NOUN
cana-2015	195	7	)	)	PUNCT
cana-2015	195	8	ωi	ωi	PROPN
cana-2015	196	1	+	+	CCONJ
cana-2015	196	2	q	q	ADJ
cana-2015	196	3	√	√	NUM
cana-2015	196	4	1−	1−	NUM
cana-2015	196	5	�	�	PROPN
cana-2015	196	6	n	n	PRON
cana-2015	196	7	i=1	i=1	PROPN
cana-2015	196	8	(	(	PUNCT
cana-2015	196	9	1−	1−	NUM
cana-2015	196	10	(	(	PUNCT
cana-2015	196	11	︷	︷	X
cana-2015	196	12	︸︸	︸︸	PUNCT
cana-2015	196	13	︷	︷	PUNCT
cana-2015	197	1	log∏	log∏	PROPN
cana-2015	197	2	i	i	PRON
cana-2015	197	3	(	(	PUNCT
cana-2015	197	4	t	t	PROPN
cana-2015	197	5	u	u	X
cana-2015	197	6	m	m	NOUN
cana-2015	197	7	)	)	PUNCT
cana-2015	197	8	)	)	PUNCT
cana-2015	197	9	q	q	X
cana-2015	197	10	)	)	PUNCT
cana-2015	197	11	ωi	ωi	PROPN
cana-2015	198	1	=	=	PUNCT
cana-2015	198	2	︷	︷	X
cana-2015	198	3	︸︸	︸︸	ADJ
cana-2015	198	4	︷	︷	PUNCT
cana-2015	199	1	log∏	log∏	NOUN
cana-2015	200	1	i	i	PRON
cana-2015	200	2	t	t	VERB
cana-2015	200	3	l	l	NOUN
cana-2015	200	4	m	m	VERB
cana-2015	201	1	+	+	ADJ
cana-2015	201	2	︷	︷	PUNCT
cana-2015	201	3	︸︸	︸︸	ADJ
cana-2015	201	4	︷	︷	PUNCT
cana-2015	202	1	log∏	log∏	PROPN
cana-2015	202	2	i	i	PRON
cana-2015	202	3	(	(	PUNCT
cana-2015	202	4	t	t	PROPN
cana-2015	202	5	u	u	X
cana-2015	202	6	m	m	PROPN
cana-2015	202	7	)	)	PUNCT
cana-2015	202	8	.	.	PUNCT
cana-2015	203	1	since	since	SCONJ
cana-2015	203	2	,	,	PUNCT
cana-2015	203	3	log∏	log∏	PROPN
cana-2015	203	4	i	i	PROPN
cana-2015	203	5	f	f	PROPN
cana-2015	203	6	l	l	NOUN
cana-2015	203	7	m︸	m︸	X
cana-2015	203	8	︷︷	︷︷	PROPN
cana-2015	203	9	︸	︸	X
cana-2015	203	10	=	=	SYM
cana-2015	203	11	min	min	NOUN
cana-2015	203	12	log∏	log∏	PROPN
cana-2015	204	1	i	i	PRON
cana-2015	204	2	f	f	PROPN
cana-2015	204	3	l	l	NOUN
cana-2015	204	4	m	m	VERB
cana-2015	204	5	ij	ij	INTJ
cana-2015	204	6	,	,	PUNCT
cana-2015	204	7	︷	︷	PROPN
cana-2015	204	8	︸︸	︸︸	ADJ
cana-2015	204	9	︷	︷	PUNCT
cana-2015	205	1	log∏	log∏	NOUN
cana-2015	206	1	i	i	PRON
cana-2015	206	2	f	f	VERB
cana-2015	206	3	l	l	NOUN
cana-2015	206	4	m	m	PROPN
cana-2015	206	5	=	=	SYM
cana-2015	206	6	max	max	PROPN
cana-2015	206	7	log∏	log∏	PROPN
cana-2015	207	1	i	i	PRON
cana-2015	207	2	f	f	VERB
cana-2015	207	3	l	l	NOUN
cana-2015	207	4	m	m	VERB
cana-2015	207	5	ij	ij	INTJ
cana-2015	207	6	log	log	NOUN
cana-2015	207	7	∏	∏	PROPN
cana-2015	208	1	i	i	INTJ
cana-2015	208	2	(	(	PUNCT
cana-2015	208	3	fu	fu	NOUN
cana-2015	208	4	m	m	PROPN
cana-2015	208	5	)	)	PUNCT
cana-2015	208	6	︸	︸	NOUN
cana-2015	208	7	︷︷	︷︷	NOUN
cana-2015	208	8	︸	︸	X
cana-2015	208	9	=	=	SYM
cana-2015	208	10	min	min	NOUN
cana-2015	208	11	log∏	log∏	PROPN
cana-2015	208	12	i	i	PRON
cana-2015	208	13	(	(	PUNCT
cana-2015	208	14	fu	fu	PROPN
cana-2015	208	15	mij),︷	mij),︷	PROPN
cana-2015	208	16	︸︸	︸︸	PRON
cana-2015	208	17	︷	︷	PUNCT
cana-2015	209	1	log∏	log∏	PROPN
cana-2015	209	2	i	i	PRON
cana-2015	209	3	(	(	PUNCT
cana-2015	209	4	fu	fu	NOUN
cana-2015	209	5	m	m	PROPN
cana-2015	209	6	)	)	PUNCT
cana-2015	210	1	=	=	SYM
cana-2015	210	2	max	max	PROPN
cana-2015	210	3	log∏	log∏	PROPN
cana-2015	210	4	i	i	PROPN
cana-2015	210	5	(	(	PUNCT
cana-2015	210	6	fu	fu	NOUN
cana-2015	210	7	mij	mij	NOUN
cana-2015	210	8	)	)	PUNCT
cana-2015	210	9	and	and	CCONJ
cana-2015	210	10	log∏	log∏	PROPN
cana-2015	210	11	i	i	PROPN
cana-2015	210	12	f	f	PROPN
cana-2015	210	13	l	l	NOUN
cana-2015	210	14	m︸	m︸	PROPN
cana-2015	210	15	︷︷	︷︷	PROPN
cana-2015	210	16	︸	︸	ADP
cana-2015	210	17	≤	≤	NUM
cana-2015	210	18	log∏i	log∏i	ADJ
cana-2015	210	19	f	f	X
cana-2015	210	20	l	l	NOUN
cana-2015	210	21	m	m	VERB
cana-2015	210	22	ij	ij	X
cana-2015	210	23	≤	≤	PUNCT
cana-2015	210	24	︷	︷	X
cana-2015	210	25	︸︸	︸︸	PUNCT
cana-2015	210	26	︷	︷	PUNCT
cana-2015	211	1	log∏	log∏	NOUN
cana-2015	212	1	i	i	PRON
cana-2015	212	2	f	f	VERB
cana-2015	212	3	l	l	NOUN
cana-2015	212	4	m	m	VERB
cana-2015	212	5	and	and	CCONJ
cana-2015	212	6	log∏	log∏	PROPN
cana-2015	212	7	i	i	PROPN
cana-2015	212	8	(	(	PUNCT
cana-2015	212	9	fu	fu	NOUN
cana-2015	212	10	m	m	PROPN
cana-2015	212	11	)	)	PUNCT
cana-2015	212	12	︸	︸	NOUN
cana-2015	212	13	︷︷	︷︷	NOUN
cana-2015	212	14	︸	︸	ADP
cana-2015	212	15	≤	≤	PROPN
cana-2015	212	16	log∏i	log∏i	ADJ
cana-2015	212	17	(	(	PUNCT
cana-2015	212	18	fu	fu	NOUN
cana-2015	212	19	mij	mij	NOUN
cana-2015	212	20	)	)	PUNCT
cana-2015	212	21	≤	≤	NOUN
cana-2015	212	22	https://internationalpubls.com	https://internationalpubls.com	X
cana-2015	212	23	543	543	NUM
cana-2015	212	24	communications	communication	NOUN
cana-2015	212	25	on	on	ADP
cana-2015	212	26	applied	apply	VERB
cana-2015	212	27	nonlinear	nonlinear	ADJ
cana-2015	212	28	analysis	analysis	NOUN
cana-2015	212	29	issn	issn	NOUN
cana-2015	212	30	:	:	PUNCT
cana-2015	212	31	1074	1074	NUM
cana-2015	212	32	-	-	PUNCT
cana-2015	212	33	133x	133x	NUM
cana-2015	212	34	vol	vol	NOUN
cana-2015	212	35	32	32	NUM
cana-2015	212	36	no	no	NOUN
cana-2015	212	37	.	.	NOUN
cana-2015	212	38	3	3	NUM
cana-2015	212	39	(	(	PUNCT
cana-2015	212	40	2025	2025	NUM
cana-2015	212	41	)	)	PUNCT
cana-2015	212	42	︷	︷	X
cana-2015	213	1	︸︸	︸︸	PRON
cana-2015	213	2	︷	︷	PUNCT
cana-2015	214	1	log∏	log∏	PROPN
cana-2015	214	2	i	i	PRON
cana-2015	214	3	(	(	PUNCT
cana-2015	214	4	fu	fu	NOUN
cana-2015	214	5	m	m	PROPN
cana-2015	214	6	)	)	PUNCT
cana-2015	214	7	.	.	PUNCT
cana-2015	215	1	now	now	ADV
cana-2015	215	2	,	,	PUNCT
cana-2015	215	3	log∏	log∏	PROPN
cana-2015	215	4	i	i	NOUN
cana-2015	215	5	f	f	PROPN
cana-2015	215	6	l	l	NOUN
cana-2015	215	7	m︸	m︸	PROPN
cana-2015	215	8	︷︷	︷︷	PROPN
cana-2015	215	9	︸+	︸+	PROPN
cana-2015	215	10	log∏	log∏	PROPN
cana-2015	215	11	i	i	PROPN
cana-2015	215	12	(	(	PUNCT
cana-2015	215	13	fu	fu	NOUN
cana-2015	215	14	m	m	PROPN
cana-2015	215	15	)	)	PUNCT
cana-2015	215	16	︸	︸	NOUN
cana-2015	215	17	︷︷	︷︷	NOUN
cana-2015	215	18	︸	︸	X
cana-2015	215	19	=	=	PUNCT
cana-2015	215	20	�	�	PROPN
cana-2015	215	21	n	n	CCONJ
cana-2015	215	22	i=1(log	i=1(log	PROPN
cana-2015	215	23	∏	∏	PROPN
cana-2015	216	1	i	i	NOUN
cana-2015	216	2	f	f	PROPN
cana-2015	216	3	l	l	NOUN
cana-2015	216	4	m︸	m︸	PROPN
cana-2015	216	5	︷︷	︷︷	PROPN
cana-2015	216	6	︸)qωi	︸)qωi	PROPN
cana-2015	217	1	+	+	NOUN
cana-2015	217	2	�	�	PROPN
cana-2015	217	3	n	n	CCONJ
cana-2015	217	4	i=1(log	i=1(log	PROPN
cana-2015	217	5	∏	∏	PROPN
cana-2015	217	6	i	i	INTJ
cana-2015	217	7	(	(	PUNCT
cana-2015	217	8	fu	fu	NOUN
cana-2015	217	9	m	m	PROPN
cana-2015	217	10	)	)	PUNCT
cana-2015	217	11	︸	︸	NOUN
cana-2015	217	12	︷︷	︷︷	VERB
cana-2015	217	13	︸)qωi	︸)qωi	PROPN
cana-2015	217	14	≤	≤	PROPN
cana-2015	217	15	�	�	PROPN
cana-2015	217	16	n	n	CCONJ
cana-2015	217	17	i=1(log	i=1(log	PROPN
cana-2015	217	18	∏	∏	PROPN
cana-2015	218	1	i	i	PRON
cana-2015	218	2	f	f	PROPN
cana-2015	218	3	l	l	NOUN
cana-2015	218	4	m	m	VERB
cana-2015	218	5	ij	ij	ADJ
cana-2015	218	6	)	)	PUNCT
cana-2015	218	7	qωi	qωi	VERB
cana-2015	218	8	+	+	PROPN
cana-2015	218	9	�	�	PROPN
cana-2015	218	10	n	n	CCONJ
cana-2015	218	11	i=1(log	i=1(log	PROPN
cana-2015	218	12	∏	∏	PROPN
cana-2015	218	13	i	i	PROPN
cana-2015	218	14	(	(	PUNCT
cana-2015	218	15	fu	fu	NOUN
cana-2015	218	16	mij	mij	NOUN
cana-2015	218	17	)	)	PUNCT
cana-2015	218	18	)	)	PUNCT
cana-2015	219	1	qωi	qωi	VERB
cana-2015	219	2	≤	≤	NUM
cana-2015	219	3	�	�	PROPN
cana-2015	219	4	n	n	CCONJ
cana-2015	219	5	i=1	i=1	PROPN
cana-2015	219	6	(	(	PUNCT
cana-2015	219	7	︷	︷	PROPN
cana-2015	219	8	︸︸	︸︸	PUNCT
cana-2015	219	9	︷	︷	PUNCT
cana-2015	220	1	log∏	log∏	NOUN
cana-2015	221	1	i	i	PRON
cana-2015	221	2	f	f	PROPN
cana-2015	221	3	l	l	NOUN
cana-2015	221	4	m	m	NOUN
cana-2015	221	5	)	)	PUNCT
cana-2015	221	6	qωi	qωi	PROPN
cana-2015	221	7	+	+	NOUN
cana-2015	221	8	�	�	PROPN
cana-2015	221	9	n	n	CCONJ
cana-2015	221	10	i=1	i=1	PROPN
cana-2015	221	11	(	(	PUNCT
cana-2015	221	12	︷	︷	PROPN
cana-2015	221	13	︸︸	︸︸	PUNCT
cana-2015	221	14	︷	︷	PUNCT
cana-2015	222	1	log∏	log∏	PROPN
cana-2015	222	2	i	i	PRON
cana-2015	222	3	(	(	PUNCT
cana-2015	222	4	fu	fu	NOUN
cana-2015	222	5	m	m	PROPN
cana-2015	222	6	)	)	PUNCT
cana-2015	222	7	)	)	PUNCT
cana-2015	222	8	qωi	qωi	PRON
cana-2015	222	9	=	=	SYM
cana-2015	222	10	︷	︷	X
cana-2015	222	11	︸︸	︸︸	ADJ
cana-2015	222	12	︷	︷	PUNCT
cana-2015	223	1	log∏	log∏	NOUN
cana-2015	224	1	i	i	PRON
cana-2015	224	2	f	f	VERB
cana-2015	224	3	l	l	NOUN
cana-2015	224	4	m	m	VERB
cana-2015	225	1	+	+	ADJ
cana-2015	225	2	︷	︷	PUNCT
cana-2015	225	3	︸︸	︸︸	ADJ
cana-2015	225	4	︷	︷	PUNCT
cana-2015	226	1	log∏	log∏	PROPN
cana-2015	226	2	i	i	PRON
cana-2015	226	3	(	(	PUNCT
cana-2015	226	4	fu	fu	NOUN
cana-2015	226	5	m	m	PROPN
cana-2015	226	6	)	)	PUNCT
cana-2015	226	7	.	.	PUNCT
cana-2015	227	1	therefore,	therefore,	PROPN
cana-2015	228	1			PROPN
cana-2015	228	2	q	q	NOUN
cana-2015	228	3	√√√√1−	√√√√1−	NUM
cana-2015	228	4	�	�	PROPN
cana-2015	228	5	n	n	PRON
cana-2015	228	6	i=1	i=1	PROPN
cana-2015	228	7	(	(	PUNCT
cana-2015	228	8	1−	1−	NUM
cana-2015	228	9	(	(	PUNCT
cana-2015	228	10	log∏	log∏	NOUN
cana-2015	228	11	i	i	NOUN
cana-2015	228	12	t	t	NOUN
cana-2015	228	13	l	l	NOUN
cana-2015	228	14	m︸	m︸	PROPN
cana-2015	228	15	︷︷	︷︷	PROPN
cana-2015	228	16	︸)q	︸)q	PROPN
cana-2015	228	17	)	)	PUNCT
cana-2015	228	18	ωi	ωi	PROPN
cana-2015	228	19	2	2	NOUN
cana-2015	229	1	+	+	CCONJ
cana-2015	229	2			PROPN
cana-2015	229	3	q	q	ADJ
cana-2015	229	4	√√√√1−	√√√√1−	NUM
cana-2015	229	5	�	�	NOUN
cana-2015	229	6	n	n	PRON
cana-2015	229	7	i=1	i=1	PROPN
cana-2015	229	8	(	(	PUNCT
cana-2015	229	9	1−	1−	NUM
cana-2015	229	10	(	(	PUNCT
cana-2015	229	11	log∏	log∏	NOUN
cana-2015	229	12	i	i	PRON
cana-2015	229	13	(	(	PUNCT
cana-2015	229	14	t	t	PROPN
cana-2015	229	15	u	u	X
cana-2015	229	16	m	m	NOUN
cana-2015	229	17	)	)	PUNCT
cana-2015	229	18	︸	︸	NOUN
cana-2015	229	19	︷︷	︷︷	PROPN
cana-2015	229	20	︸)q	︸)q	PROPN
cana-2015	229	21	)	)	PUNCT
cana-2015	229	22	ωi	ωi	NOUN
cana-2015	229	23	2	2	ADV
cana-2015	229	24	2	2	NUM
cana-2015	229	25	+1−	+1−	PROPN
cana-2015	229	26			PROPN
cana-2015	229	27	�	�	PROPN
cana-2015	229	28	n	n	PRON
cana-2015	229	29	i=1	i=1	PROPN
cana-2015	229	30	(	(	PUNCT
cana-2015	229	31	︷	︷	PROPN
cana-2015	229	32	︸︸	︸︸	PUNCT
cana-2015	229	33	︷	︷	PUNCT
cana-2015	230	1	log∏	log∏	NOUN
cana-2015	231	1	i	i	PRON
cana-2015	231	2	f	f	PROPN
cana-2015	231	3	l	l	NOUN
cana-2015	231	4	m	m	NOUN
cana-2015	231	5	)	)	PUNCT
cana-2015	231	6	qωi	qωi	VERB
cana-2015	231	7	2	2	ADJ
cana-2015	232	1	+	+	CCONJ
cana-2015	232	2			PROPN
cana-2015	232	3	�	�	PROPN
cana-2015	232	4	n	n	NOUN
cana-2015	232	5	i=1	i=1	PROPN
cana-2015	232	6	(	(	PUNCT
cana-2015	232	7	︷	︷	PROPN
cana-2015	232	8	︸︸	︸︸	PUNCT
cana-2015	232	9	︷	︷	PUNCT
cana-2015	233	1	log∏	log∏	PROPN
cana-2015	233	2	i	i	PRON
cana-2015	233	3	(	(	PUNCT
cana-2015	233	4	fu	fu	NOUN
cana-2015	233	5	m	m	PROPN
cana-2015	233	6	)	)	PUNCT
cana-2015	233	7	)	)	PUNCT
cana-2015	233	8	qωi	qωi	VERB
cana-2015	233	9	2	2	ADJ
cana-2015	233	10	2	2	X
cana-2015	233	11			NOUN
cana-2015	233	12	=	=	PRON
cana-2015	234	1			PROPN
cana-2015	234	2	(	(	PUNCT
cana-2015	234	3	q	q	NOUN
cana-2015	234	4	√	√	NUM
cana-2015	234	5	1−	1−	NUM
cana-2015	234	6	�	�	PROPN
cana-2015	234	7	n	n	PRON
cana-2015	234	8	i=1	i=1	PROPN
cana-2015	234	9	(	(	PUNCT
cana-2015	234	10	1−	1−	NUM
cana-2015	234	11	(	(	PUNCT
cana-2015	234	12	log∏	log∏	NOUN
cana-2015	234	13	i	i	NOUN
cana-2015	234	14	t	t	VERB
cana-2015	235	1	l	l	NOUN
cana-2015	235	2	m	m	VERB
cana-2015	235	3	ij	ij	NOUN
cana-2015	235	4	)	)	PUNCT
cana-2015	235	5	q	q	NOUN
cana-2015	235	6	)	)	PUNCT
cana-2015	235	7	ωi	ωi	PROPN
cana-2015	235	8	)	)	PUNCT
cana-2015	235	9	2	2	NUM
cana-2015	236	1	+	+	CCONJ
cana-2015	236	2	(	(	PUNCT
cana-2015	236	3	q	q	NOUN
cana-2015	236	4	√	√	NUM
cana-2015	236	5	1−	1−	NUM
cana-2015	236	6	�	�	PROPN
cana-2015	236	7	n	n	PRON
cana-2015	236	8	i=1	i=1	PROPN
cana-2015	236	9	(	(	PUNCT
cana-2015	236	10	1−	1−	NUM
cana-2015	236	11	(	(	PUNCT
cana-2015	236	12	log∏	log∏	NOUN
cana-2015	236	13	i	i	PRON
cana-2015	236	14	(	(	PUNCT
cana-2015	236	15	t	t	PROPN
cana-2015	236	16	u	u	NOUN
cana-2015	236	17	mij	mij	NOUN
cana-2015	236	18	)	)	PUNCT
cana-2015	236	19	)	)	PUNCT
cana-2015	236	20	q	q	X
cana-2015	236	21	)	)	PUNCT
cana-2015	236	22	ωi	ωi	X
cana-2015	236	23	)	)	PUNCT
cana-2015	236	24	2	2	NUM
cana-2015	236	25	2	2	NUM
cana-2015	236	26	+1−	+1−	PROPN
cana-2015	236	27	(	(	PUNCT
cana-2015	236	28	�	�	PROPN
cana-2015	236	29	n	n	CCONJ
cana-2015	236	30	i=1(log	i=1(log	PROPN
cana-2015	236	31	∏	∏	PROPN
cana-2015	236	32	i	i	PRON
cana-2015	236	33	f	f	PROPN
cana-2015	236	34	l	l	NOUN
cana-2015	236	35	mij	mij	X
cana-2015	236	36	)	)	PUNCT
cana-2015	236	37	qωi	qωi	NOUN
cana-2015	236	38	)	)	PUNCT
cana-2015	236	39	2	2	NUM
cana-2015	237	1	+	+	NOUN
cana-2015	237	2	(	(	PUNCT
cana-2015	237	3	�	�	PROPN
cana-2015	237	4	n	n	CCONJ
cana-2015	237	5	i=1(log	i=1(log	PROPN
cana-2015	237	6	∏	∏	PROPN
cana-2015	237	7	i	i	INTJ
cana-2015	237	8	(	(	PUNCT
cana-2015	237	9	fu	fu	NOUN
cana-2015	237	10	mij	mij	NOUN
cana-2015	237	11	)	)	PUNCT
cana-2015	237	12	)	)	PUNCT
cana-2015	237	13	qωi	qωi	X
cana-2015	237	14	)	)	PUNCT
cana-2015	237	15	2	2	NUM
cana-2015	237	16	2	2	NUM
cana-2015	237	17			NOUN
cana-2015	237	18	=	=	PUNCT
cana-2015	237	19			ADJ
cana-2015	237	20			PROPN
cana-2015	237	21	q	q	NOUN
cana-2015	237	22	√√√√1−	√√√√1−	NUM
cana-2015	237	23	�	�	NOUN
cana-2015	237	24	n	n	PRON
cana-2015	237	25	i=1	i=1	PROPN
cana-2015	237	26	(	(	PUNCT
cana-2015	237	27	1−	1−	NUM
cana-2015	237	28	(	(	PUNCT
cana-2015	237	29	︷	︷	X
cana-2015	237	30	︸︸	︸︸	PUNCT
cana-2015	237	31	︷	︷	PUNCT
cana-2015	238	1	log∏	log∏	NOUN
cana-2015	239	1	i	i	PRON
cana-2015	239	2	t	t	VERB
cana-2015	239	3	l	l	NOUN
cana-2015	239	4	m	m	NOUN
cana-2015	239	5	)	)	PUNCT
cana-2015	239	6	q	q	X
cana-2015	239	7	)	)	PUNCT
cana-2015	239	8	ωi	ωi	NOUN
cana-2015	240	1	2	2	NOUN
cana-2015	241	1	+	+	CCONJ
cana-2015	241	2			PROPN
cana-2015	241	3	q	q	ADJ
cana-2015	241	4	√√√√1−	√√√√1−	NUM
cana-2015	241	5	�	�	NOUN
cana-2015	241	6	n	n	PRON
cana-2015	241	7	i=1	i=1	PROPN
cana-2015	241	8	(	(	PUNCT
cana-2015	241	9	1−	1−	NUM
cana-2015	241	10	(	(	PUNCT
cana-2015	241	11	︷	︷	X
cana-2015	241	12	︸︸	︸︸	PUNCT
cana-2015	241	13	︷	︷	PUNCT
cana-2015	242	1	log∏	log∏	PROPN
cana-2015	242	2	i	i	PRON
cana-2015	242	3	(	(	PUNCT
cana-2015	242	4	t	t	PROPN
cana-2015	242	5	u	u	X
cana-2015	242	6	m	m	NOUN
cana-2015	242	7	)	)	PUNCT
cana-2015	242	8	)	)	PUNCT
cana-2015	242	9	q	q	X
cana-2015	242	10	)	)	PUNCT
cana-2015	242	11	ωi	ωi	NOUN
cana-2015	242	12	2	2	ADV
cana-2015	242	13	2	2	NUM
cana-2015	243	1	+1−	+1−	PROPN
cana-2015	243	2			PROPN
cana-2015	243	3	�	�	PROPN
cana-2015	243	4	n	n	CCONJ
cana-2015	243	5	i=1(log	i=1(log	PROPN
cana-2015	243	6	∏	∏	PROPN
cana-2015	244	1	i	i	NOUN
cana-2015	244	2	f	f	PROPN
cana-2015	244	3	l	l	NOUN
cana-2015	244	4	m︸	m︸	PROPN
cana-2015	244	5	︷︷	︷︷	PROPN
cana-2015	244	6	︸)qωi	︸)qωi	PROPN
cana-2015	244	7	2	2	ADJ
cana-2015	245	1	+	+	CCONJ
cana-2015	245	2			PROPN
cana-2015	245	3	�	�	PROPN
cana-2015	245	4	n	n	CCONJ
cana-2015	245	5	i=1(log	i=1(log	PROPN
cana-2015	245	6	∏	∏	PROPN
cana-2015	245	7	i	i	INTJ
cana-2015	245	8	(	(	PUNCT
cana-2015	245	9	fu	fu	NOUN
cana-2015	245	10	m	m	PROPN
cana-2015	245	11	)	)	PUNCT
cana-2015	245	12	︸	︸	NOUN
cana-2015	245	13	︷︷	︷︷	VERB
cana-2015	245	14	︸)qωi	︸)qωi	PROPN
cana-2015	245	15	2	2	ADV
cana-2015	245	16	2	2	X
cana-2015	245	17			NOUN
cana-2015	245	18	.	.	PUNCT
cana-2015	246	1	hence	hence	ADV
cana-2015	246	2	,	,	PUNCT
cana-2015	246	3	〈	〈	PROPN
cana-2015	246	4	(	(	PUNCT
cana-2015	246	5	logt	logt	PROPN
cana-2015	246	6	l	l	PROPN
cana-2015	246	7	m︸	m︸	PROPN
cana-2015	246	8	︷︷	︷︷	PROPN
cana-2015	246	9	︸	︸	X
cana-2015	246	10	,	,	PUNCT
cana-2015	246	11	log(t	log(t	PROPN
cana-2015	246	12	u	u	NOUN
cana-2015	246	13	m	m	NOUN
cana-2015	246	14	)	)	PUNCT
cana-2015	246	15	︸	︸	NOUN
cana-2015	246	16	︷︷	︷︷	PROPN
cana-2015	246	17	︸	︸	NOUN
cana-2015	246	18	)	)	PUNCT
cana-2015	246	19	,	,	PUNCT
cana-2015	246	20	(	(	PUNCT
cana-2015	246	21	︷	︷	ADJ
cana-2015	246	22	︸︸	︸︸	ADJ
cana-2015	246	23	︷	︷	X
cana-2015	246	24	logf	logf	INTJ
cana-2015	247	1	l	l	NOUN
cana-2015	247	2	m	m	VERB
cana-2015	247	3	,	,	PUNCT
cana-2015	247	4	︷	︷	X
cana-2015	247	5	︸︸	︸︸	ADJ
cana-2015	247	6	︷	︷	PROPN
cana-2015	247	7	log(fu	log(fu	VERB
cana-2015	247	8	m	m	PROPN
cana-2015	247	9	)	)	PUNCT
cana-2015	247	10	)	)	PUNCT
cana-2015	247	11	〉	〉	NOUN
cana-2015	247	12	≤	≤	NOUN
cana-2015	247	13	q	q	NOUN
cana-2015	247	14	−	−	PROPN
cana-2015	247	15	liv	liv	PROPN
cana-2015	247	16	ifwa(m1,m2	ifwa(m1,m2	NOUN
cana-2015	247	17	,	,	PUNCT
cana-2015	247	18	...	...	PUNCT
cana-2015	247	19	,	,	PUNCT
cana-2015	247	20	mn	mn	PROPN
cana-2015	247	21	)	)	PUNCT
cana-2015	247	22	≤	≤	NOUN
cana-2015	248	1	〈	〈	PROPN
cana-2015	248	2	(	(	PUNCT
cana-2015	248	3	︷	︷	NOUN
cana-2015	248	4	︸︸	︸︸	ADJ
cana-2015	248	5	︷	︷	PROPN
cana-2015	249	1	logt	logt	INTJ
cana-2015	250	1	l	l	PROPN
cana-2015	250	2	m	m	PROPN
cana-2015	250	3	,	,	PUNCT
cana-2015	250	4	︷	︷	ADJ
cana-2015	250	5	︸︸	︸︸	ADJ
cana-2015	250	6	︷	︷	PUNCT
cana-2015	251	1	log(t	log(t	NOUN
cana-2015	251	2	u	u	NOUN
cana-2015	251	3	m	m	PROPN
cana-2015	251	4	)	)	PUNCT
cana-2015	251	5	)	)	PUNCT
cana-2015	251	6	,	,	PUNCT
cana-2015	251	7	(	(	PUNCT
cana-2015	251	8	logf	logf	PROPN
cana-2015	251	9	l	l	PROPN
cana-2015	251	10	m︸	m︸	X
cana-2015	251	11	︷︷	︷︷	PROPN
cana-2015	251	12	︸	︸	X
cana-2015	251	13	,	,	PUNCT
cana-2015	251	14	log(fu	log(fu	VERB
cana-2015	251	15	m	m	NOUN
cana-2015	251	16	)	)	PUNCT
cana-2015	252	1	︸	︸	X
cana-2015	252	2	︷︷	︷︷	PROPN
cana-2015	252	3	︸	︸	NOUN
cana-2015	252	4	)	)	PUNCT
cana-2015	252	5	〉	〉	NOUN
cana-2015	252	6	.	.	PUNCT
cana-2015	253	1	theorem	theorem	VERB
cana-2015	253	2	4.5	4.5	NUM
cana-2015	253	3	.	.	PUNCT
cana-2015	254	1	(	(	PUNCT
cana-2015	254	2	monotonicity	monotonicity	NOUN
cana-2015	254	3	property	property	NOUN
cana-2015	254	4	)	)	PUNCT
cana-2015	254	5	let	let	VERB
cana-2015	254	6	mi	mi	PROPN
cana-2015	254	7	=	=	PROPN
cana-2015	254	8	〈	〈	PROPN
cana-2015	254	9	(	(	PUNCT
cana-2015	254	10	logt	logt	NOUN
cana-2015	254	11	l	l	NOUN
cana-2015	254	12	m	m	VERB
cana-2015	254	13	tij	tij	NOUN
cana-2015	254	14	,	,	PUNCT
cana-2015	254	15	log(t	log(t	PROPN
cana-2015	254	16	u	u	PROPN
cana-2015	254	17	mtij	mtij	PROPN
cana-2015	254	18	)	)	PUNCT
cana-2015	254	19	)	)	PUNCT
cana-2015	254	20	,	,	PUNCT
cana-2015	254	21	(	(	PUNCT
cana-2015	254	22	logf	logf	INTJ
cana-2015	254	23	l	l	NOUN
cana-2015	254	24	m	m	VERB
cana-2015	254	25	tij	tij	NOUN
cana-2015	254	26	,	,	PUNCT
cana-2015	254	27	log(fu	log(fu	CCONJ
cana-2015	254	28	mtij	mtij	NOUN
cana-2015	254	29	)	)	PUNCT
cana-2015	254	30	)	)	PUNCT
cana-2015	254	31	〉	〉	NOUN
cana-2015	254	32	and	and	CCONJ
cana-2015	254	33	ωi	ωi	NOUN
cana-2015	254	34	=	=	SYM
cana-2015	254	35	〈	〈	PROPN
cana-2015	254	36	(	(	PUNCT
cana-2015	254	37	logt	logt	NOUN
cana-2015	254	38	l	l	PROPN
cana-2015	254	39	mhij	mhij	NOUN
cana-2015	254	40	,	,	PUNCT
cana-2015	254	41	log(t	log(t	NOUN
cana-2015	254	42	u	u	NOUN
cana-2015	254	43	mhij	mhij	NOUN
cana-2015	254	44	)	)	PUNCT
cana-2015	254	45	)	)	PUNCT
cana-2015	254	46	,	,	PUNCT
cana-2015	254	47	(	(	PUNCT
cana-2015	254	48	logf	logf	NOUN
cana-2015	254	49	l	l	NOUN
cana-2015	254	50	mhij	mhij	NOUN
cana-2015	254	51	,	,	PUNCT
cana-2015	254	52	log(fu	log(fu	CCONJ
cana-2015	254	53	mhij	mhij	NOUN
cana-2015	254	54	)	)	PUNCT
cana-2015	254	55	)	)	PUNCT
cana-2015	255	1	〉	〉	NOUN
cana-2015	255	2	(	(	PUNCT
cana-2015	255	3	i	i	NOUN
cana-2015	255	4	=	=	NOUN
cana-2015	255	5	1	1	NUM
cana-2015	255	6	,	,	PUNCT
cana-2015	255	7	2	2	NUM
cana-2015	255	8	,	,	PUNCT
cana-2015	255	9	...	...	PUNCT
cana-2015	255	10	,	,	PUNCT
cana-2015	255	11	n	n	CCONJ
cana-2015	255	12	)	)	PUNCT
cana-2015	255	13	;	;	PUNCT
cana-2015	255	14	(	(	PUNCT
cana-2015	255	15	j	j	NOUN
cana-2015	255	16	=	=	SYM
cana-2015	255	17	1	1	NUM
cana-2015	255	18	,	,	PUNCT
cana-2015	255	19	2	2	NUM
cana-2015	255	20	,	,	PUNCT
cana-2015	255	21	...	...	PUNCT
cana-2015	255	22	,	,	PUNCT
cana-2015	255	23	ij	ij	X
cana-2015	255	24	)	)	PUNCT
cana-2015	255	25	be	be	AUX
cana-2015	255	26	the	the	DET
cana-2015	255	27	families	family	NOUN
cana-2015	255	28	of	of	ADP
cana-2015	255	29	q	q	NOUN
cana-2015	255	30	-	-	PUNCT
cana-2015	255	31	livifwas	livifwa	VERB
cana-2015	255	32	.	.	PUNCT
cana-2015	256	1	for	for	ADP
cana-2015	256	2	any	any	DET
cana-2015	256	3	i	i	PRON
cana-2015	256	4	,	,	PUNCT
cana-2015	256	5	if	if	SCONJ
cana-2015	256	6	there	there	PRON
cana-2015	256	7	is	be	VERB
cana-2015	256	8	(	(	PUNCT
cana-2015	256	9	log∏	log∏	PROPN
cana-2015	256	10	i	i	NOUN
cana-2015	256	11	t	t	VERB
cana-2015	256	12	l	l	NOUN
cana-2015	256	13	m	m	VERB
cana-2015	256	14	tij	tij	NOUN
cana-2015	256	15	)	)	PUNCT
cana-2015	256	16	2	2	X
cana-2015	257	1	+	+	NOUN
cana-2015	257	2	(	(	PUNCT
cana-2015	257	3	log∏	log∏	PROPN
cana-2015	257	4	i	i	PRON
cana-2015	257	5	(	(	PUNCT
cana-2015	257	6	t	t	PROPN
cana-2015	257	7	u	u	PROPN
cana-2015	257	8	mtij	mtij	PROPN
cana-2015	257	9	)	)	PUNCT
cana-2015	257	10	)	)	PUNCT
cana-2015	257	11	2	2	NUM
cana-2015	257	12	≤	≤	NOUN
cana-2015	257	13	(	(	PUNCT
cana-2015	257	14	log∏	log∏	PROPN
cana-2015	257	15	i	i	NOUN
cana-2015	257	16	t	t	NOUN
cana-2015	257	17	l	l	NOUN
cana-2015	257	18	mhij	mhij	NOUN
cana-2015	257	19	)	)	PUNCT
cana-2015	257	20	2	2	NUM
cana-2015	257	21	+	+	CCONJ
cana-2015	257	22	(	(	PUNCT
cana-2015	257	23	log∏	log∏	PROPN
cana-2015	257	24	i	i	PRON
cana-2015	257	25	(	(	PUNCT
cana-2015	257	26	t	t	NOUN
cana-2015	257	27	u	u	NOUN
cana-2015	257	28	mhij	mhij	NOUN
cana-2015	257	29	)	)	PUNCT
cana-2015	257	30	)	)	PUNCT
cana-2015	257	31	2	2	NUM
cana-2015	257	32	and	and	CCONJ
cana-2015	257	33	(	(	PUNCT
cana-2015	257	34	log∏	log∏	PROPN
cana-2015	257	35	i	i	NOUN
cana-2015	257	36	f	f	VERB
cana-2015	257	37	l	l	NOUN
cana-2015	257	38	m	m	VERB
cana-2015	257	39	tij	tij	NOUN
cana-2015	257	40	)	)	PUNCT
cana-2015	257	41	2	2	NUM
cana-2015	257	42	+	+	CCONJ
cana-2015	257	43	(	(	PUNCT
cana-2015	257	44	log∏	log∏	PROPN
cana-2015	257	45	i	i	PRON
cana-2015	257	46	(	(	PUNCT
cana-2015	257	47	fu	fu	PROPN
cana-2015	257	48	m	m	PROPN
cana-2015	257	49	)	)	PUNCT
cana-2015	257	50	tij	tij	NOUN
cana-2015	257	51	)	)	PUNCT
cana-2015	257	52	2	2	NUM
cana-2015	257	53	≥	≥	NUM
cana-2015	257	54	(	(	PUNCT
cana-2015	257	55	log∏	log∏	NOUN
cana-2015	257	56	i	i	NOUN
cana-2015	257	57	f	f	NOUN
cana-2015	257	58	l	l	NOUN
cana-2015	257	59	mhij	mhij	NOUN
cana-2015	257	60	)	)	PUNCT
cana-2015	257	61	2	2	NUM
cana-2015	257	62	+	+	CCONJ
cana-2015	257	63	(	(	PUNCT
cana-2015	257	64	log∏	log∏	PROPN
cana-2015	257	65	i	i	PRON
cana-2015	257	66	(	(	PUNCT
cana-2015	257	67	fu	fu	PROPN
cana-2015	257	68	mhij	mhij	NOUN
cana-2015	257	69	)	)	PUNCT
cana-2015	257	70	)	)	PUNCT
cana-2015	257	71	2	2	NUM
cana-2015	257	72	or	or	CCONJ
cana-2015	257	73	mi	mi	PROPN
cana-2015	257	74	≤	≤	PROPN
cana-2015	257	75	wi	wi	PROPN
cana-2015	257	76	.	.	PUNCT
cana-2015	258	1	then	then	ADV
cana-2015	258	2	q	q	X
cana-2015	258	3	-	-	PUNCT
cana-2015	258	4	livifwa	livifwa	NOUN
cana-2015	258	5	(	(	PUNCT
cana-2015	258	6	m1,m2	m1,m2	PROPN
cana-2015	258	7	,	,	PUNCT
cana-2015	258	8	...	...	PUNCT
cana-2015	258	9	,	,	PUNCT
cana-2015	258	10	mn	mn	PROPN
cana-2015	258	11	)	)	PUNCT
cana-2015	258	12	≤	≤	NOUN
cana-2015	258	13	q	q	NOUN
cana-2015	258	14	-	-	PUNCT
cana-2015	258	15	livifwa	livifwa	NOUN
cana-2015	258	16	(	(	PUNCT
cana-2015	258	17	w1,w2	w1,w2	PROPN
cana-2015	258	18	,	,	PUNCT
cana-2015	258	19	...	...	PUNCT
cana-2015	258	20	,	,	PUNCT
cana-2015	258	21	wn	wn	PROPN
cana-2015	258	22	)	)	PUNCT
cana-2015	258	23	.	.	PUNCT
cana-2015	259	1	proof	proof	NOUN
cana-2015	259	2	.	.	PUNCT
cana-2015	260	1	for	for	ADP
cana-2015	260	2	any	any	DET
cana-2015	260	3	i	i	PROPN
cana-2015	260	4	,	,	PUNCT
cana-2015	260	5	(	(	PUNCT
cana-2015	260	6	log∏	log∏	PROPN
cana-2015	260	7	i	i	NOUN
cana-2015	260	8	t	t	VERB
cana-2015	260	9	l	l	NOUN
cana-2015	260	10	m	m	VERB
cana-2015	260	11	tij	tij	NOUN
cana-2015	260	12	)	)	PUNCT
cana-2015	260	13	q	q	PROPN
cana-2015	261	1	+	+	CCONJ
cana-2015	261	2	(	(	PUNCT
cana-2015	261	3	log∏	log∏	PROPN
cana-2015	261	4	i	i	PRON
cana-2015	261	5	(	(	PUNCT
cana-2015	261	6	t	t	PROPN
cana-2015	261	7	u	u	PROPN
cana-2015	261	8	mtij	mtij	PROPN
cana-2015	261	9	)	)	PUNCT
cana-2015	261	10	)	)	PUNCT
cana-2015	262	1	q	q	PROPN
cana-2015	262	2	≤	≤	NOUN
cana-2015	262	3	(	(	PUNCT
cana-2015	262	4	log∏	log∏	PROPN
cana-2015	262	5	i	i	NOUN
cana-2015	262	6	t	t	NOUN
cana-2015	262	7	l	l	NOUN
cana-2015	262	8	mhij	mhij	NOUN
cana-2015	262	9	)	)	PUNCT
cana-2015	262	10	q	q	PROPN
cana-2015	263	1	+	+	CCONJ
cana-2015	263	2	(	(	PUNCT
cana-2015	263	3	log∏	log∏	PROPN
cana-2015	263	4	i	i	PRON
cana-2015	263	5	(	(	PUNCT
cana-2015	263	6	t	t	NOUN
cana-2015	263	7	u	u	NOUN
cana-2015	263	8	mhij	mhij	NOUN
cana-2015	263	9	)	)	PUNCT
cana-2015	263	10	)	)	PUNCT
cana-2015	263	11	q	q	NOUN
cana-2015	263	12	.	.	PUNCT
cana-2015	264	1	therefore	therefore	ADV
cana-2015	264	2	,	,	PUNCT
cana-2015	264	3	1−	1−	NUM
cana-2015	264	4	(	(	PUNCT
cana-2015	264	5	log∏	log∏	NOUN
cana-2015	265	1	i	i	NOUN
cana-2015	265	2	t	t	VERB
cana-2015	265	3	l	l	NOUN
cana-2015	265	4	m	m	VERB
cana-2015	265	5	ti	ti	NOUN
cana-2015	265	6	)	)	PUNCT
cana-2015	265	7	q	q	PROPN
cana-2015	266	1	+	+	NUM
cana-2015	266	2	1−	1−	NUM
cana-2015	266	3	(	(	PUNCT
cana-2015	266	4	log∏	log∏	PROPN
cana-2015	266	5	i	i	PRON
cana-2015	266	6	(	(	PUNCT
cana-2015	266	7	t	t	PROPN
cana-2015	266	8	u	u	NOUN
cana-2015	266	9	mti	mti	PROPN
cana-2015	266	10	)	)	PUNCT
cana-2015	266	11	)	)	PUNCT
cana-2015	266	12	q	q	NOUN
cana-2015	266	13	≥	≥	NOUN
cana-2015	266	14	1−	1−	NUM
cana-2015	266	15	(	(	PUNCT
cana-2015	266	16	log∏	log∏	NOUN
cana-2015	267	1	i	i	PROPN
cana-2015	267	2	t	t	PROPN
cana-2015	267	3	l	l	PROPN
cana-2015	267	4	mhi	mhi	PROPN
cana-2015	267	5	)	)	PUNCT
cana-2015	267	6	q	q	PROPN
cana-2015	268	1	+	+	NUM
cana-2015	268	2	1−	1−	NUM
cana-2015	268	3	(	(	PUNCT
cana-2015	268	4	log∏	log∏	PROPN
cana-2015	268	5	i	i	PRON
cana-2015	268	6	(	(	PUNCT
cana-2015	268	7	t	t	PROPN
cana-2015	268	8	u	u	PROPN
cana-2015	268	9	mhi	mhi	PROPN
cana-2015	268	10	)	)	PUNCT
cana-2015	268	11	)	)	PUNCT
cana-2015	269	1	q	q	NOUN
cana-2015	269	2	.	.	PUNCT
cana-2015	270	1	hence	hence	ADV
cana-2015	270	2	,	,	PUNCT
cana-2015	270	3	�	�	PROPN
cana-2015	270	4	n	n	CCONJ
cana-2015	270	5	i=1	i=1	PROPN
cana-2015	270	6	(	(	PUNCT
cana-2015	270	7	1−	1−	NUM
cana-2015	270	8	(	(	PUNCT
cana-2015	270	9	log∏	log∏	NOUN
cana-2015	271	1	i	i	NOUN
cana-2015	271	2	t	t	VERB
cana-2015	271	3	l	l	NOUN
cana-2015	271	4	m	m	VERB
cana-2015	271	5	ti	ti	NOUN
cana-2015	271	6	)	)	PUNCT
cana-2015	272	1	q)ωi	q)ωi	PROPN
cana-2015	272	2	+	+	PROPN
cana-2015	272	3	�	�	PROPN
cana-2015	272	4	n	n	PRON
cana-2015	272	5	i=1	i=1	PROPN
cana-2015	272	6	(	(	PUNCT
cana-2015	272	7	1−	1−	NUM
cana-2015	272	8	(	(	PUNCT
cana-2015	272	9	log∏	log∏	PROPN
cana-2015	272	10	i	i	PRON
cana-2015	272	11	(	(	PUNCT
cana-2015	272	12	t	t	PROPN
cana-2015	272	13	u	u	NOUN
cana-2015	272	14	mti	mti	PROPN
cana-2015	272	15	)	)	PUNCT
cana-2015	272	16	)	)	PUNCT
cana-2015	273	1	q)ωi	q)ωi	PROPN
cana-2015	273	2	≥	≥	NUM
cana-2015	273	3	�	�	PROPN
cana-2015	273	4	n	n	PRON
cana-2015	273	5	i=1	i=1	PROPN
cana-2015	273	6	(	(	PUNCT
cana-2015	273	7	1−	1−	NUM
cana-2015	273	8	(	(	PUNCT
cana-2015	273	9	log∏	log∏	NOUN
cana-2015	273	10	i	i	PROPN
cana-2015	273	11	t	t	PROPN
cana-2015	273	12	l	l	PROPN
cana-2015	273	13	mhi	mhi	PROPN
cana-2015	273	14	)	)	PUNCT
cana-2015	274	1	q)ωi	q)ωi	PROPN
cana-2015	274	2	+	+	PROPN
cana-2015	274	3	�	�	PROPN
cana-2015	274	4	n	n	PRON
cana-2015	274	5	i=1	i=1	PROPN
cana-2015	274	6	(	(	PUNCT
cana-2015	274	7	1−	1−	NUM
cana-2015	274	8	(	(	PUNCT
cana-2015	274	9	log∏	log∏	PROPN
cana-2015	274	10	i	i	PRON
cana-2015	274	11	(	(	PUNCT
cana-2015	274	12	t	t	PROPN
cana-2015	274	13	u	u	PROPN
cana-2015	274	14	mhi	mhi	PROPN
cana-2015	274	15	)	)	PUNCT
cana-2015	274	16	)	)	PUNCT
cana-2015	275	1	q)ωi	q)ωi	PROPN
cana-2015	275	2	and	and	CCONJ
cana-2015	275	3	q	q	NOUN
cana-2015	275	4	√	√	NUM
cana-2015	275	5	1−	1−	NUM
cana-2015	275	6	�	�	PROPN
cana-2015	275	7	n	n	PRON
cana-2015	275	8	i=1	i=1	PROPN
cana-2015	275	9	(	(	PUNCT
cana-2015	275	10	1−	1−	NUM
cana-2015	275	11	(	(	PUNCT
cana-2015	275	12	log∏	log∏	NOUN
cana-2015	275	13	i	i	NOUN
cana-2015	275	14	t	t	VERB
cana-2015	275	15	l	l	NOUN
cana-2015	275	16	m	m	VERB
cana-2015	275	17	ti	ti	NOUN
cana-2015	275	18	)	)	PUNCT
cana-2015	276	1	q)ωi	q)ωi	PROPN
cana-2015	276	2	+	+	CCONJ
cana-2015	276	3	q	q	ADJ
cana-2015	276	4	√	√	NUM
cana-2015	276	5	1−	1−	NUM
cana-2015	276	6	�	�	PROPN
cana-2015	276	7	n	n	PRON
cana-2015	276	8	i=1	i=1	PROPN
cana-2015	276	9	(	(	PUNCT
cana-2015	276	10	1−	1−	NUM
cana-2015	276	11	(	(	PUNCT
cana-2015	276	12	log∏	log∏	PROPN
cana-2015	276	13	i	i	PRON
cana-2015	276	14	(	(	PUNCT
cana-2015	276	15	t	t	PROPN
cana-2015	276	16	u	u	PROPN
cana-2015	276	17	mti	mti	NOUN
cana-2015	276	18	)	)	PUNCT
cana-2015	276	19	)	)	PUNCT
cana-2015	277	1	q)ωi	q)ωi	PROPN
cana-2015	277	2	≤	≤	PRON
cana-2015	277	3	q	q	ADJ
cana-2015	277	4	√	√	NUM
cana-2015	277	5	1−	1−	NUM
cana-2015	277	6	�	�	PROPN
cana-2015	277	7	n	n	PRON
cana-2015	277	8	i=1	i=1	PROPN
cana-2015	277	9	(	(	PUNCT
cana-2015	277	10	1−	1−	NUM
cana-2015	277	11	(	(	PUNCT
cana-2015	277	12	log∏	log∏	NOUN
cana-2015	277	13	i	i	PROPN
cana-2015	277	14	t	t	PROPN
cana-2015	277	15	l	l	PROPN
cana-2015	277	16	mhi	mhi	PROPN
cana-2015	277	17	)	)	PUNCT
cana-2015	278	1	q)ωi	q)ωi	PROPN
cana-2015	278	2	+	+	CCONJ
cana-2015	278	3	q	q	ADJ
cana-2015	278	4	√	√	NUM
cana-2015	278	5	1−	1−	NUM
cana-2015	278	6	�	�	PROPN
cana-2015	278	7	n	n	PRON
cana-2015	278	8	i=1	i=1	PROPN
cana-2015	278	9	(	(	PUNCT
cana-2015	278	10	1−	1−	NUM
cana-2015	278	11	(	(	PUNCT
cana-2015	278	12	log∏	log∏	PROPN
cana-2015	278	13	i	i	PRON
cana-2015	278	14	(	(	PUNCT
cana-2015	278	15	t	t	PROPN
cana-2015	278	16	u	u	PROPN
cana-2015	278	17	mhi	mhi	PROPN
cana-2015	278	18	)	)	PUNCT
cana-2015	278	19	)	)	PUNCT
cana-2015	279	1	q)ωi	q)ωi	PROPN
cana-2015	279	2	.	.	PUNCT
cana-2015	280	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2015	280	2	544	544	NUM
cana-2015	280	3	communications	communication	NOUN
cana-2015	280	4	on	on	ADP
cana-2015	280	5	applied	apply	VERB
cana-2015	280	6	nonlinear	nonlinear	ADJ
cana-2015	280	7	analysis	analysis	NOUN
cana-2015	280	8	issn	issn	NOUN
cana-2015	280	9	:	:	PUNCT
cana-2015	280	10	1074	1074	NUM
cana-2015	280	11	-	-	PUNCT
cana-2015	280	12	133x	133x	NUM
cana-2015	280	13	vol	vol	NOUN
cana-2015	280	14	32	32	NUM
cana-2015	280	15	no	no	NOUN
cana-2015	280	16	.	.	NOUN
cana-2015	280	17	3	3	NUM
cana-2015	280	18	(	(	PUNCT
cana-2015	280	19	2025	2025	NUM
cana-2015	280	20	)	)	PUNCT
cana-2015	280	21	for	for	ADP
cana-2015	280	22	any	any	DET
cana-2015	280	23	i	i	PROPN
cana-2015	280	24	,	,	PUNCT
cana-2015	280	25	(	(	PUNCT
cana-2015	280	26	log∏	log∏	NOUN
cana-2015	280	27	i	i	PRON
cana-2015	280	28	f	f	VERB
cana-2015	280	29	l	l	NOUN
cana-2015	280	30	m	m	VERB
cana-2015	280	31	tij	tij	NOUN
cana-2015	280	32	)	)	PUNCT
cana-2015	280	33	q	q	PROPN
cana-2015	281	1	+	+	CCONJ
cana-2015	281	2	(	(	PUNCT
cana-2015	281	3	log∏	log∏	PROPN
cana-2015	281	4	i	i	PROPN
cana-2015	281	5	(	(	PUNCT
cana-2015	281	6	fu	fu	PROPN
cana-2015	281	7	mtij	mtij	PROPN
cana-2015	281	8	)	)	PUNCT
cana-2015	281	9	)	)	PUNCT
cana-2015	281	10	q	q	NOUN
cana-2015	282	1	≥	≥	NOUN
cana-2015	282	2	(	(	PUNCT
cana-2015	282	3	log∏	log∏	NOUN
cana-2015	282	4	i	i	NOUN
cana-2015	282	5	f	f	NOUN
cana-2015	282	6	l	l	NOUN
cana-2015	282	7	mhij	mhij	NOUN
cana-2015	282	8	)	)	PUNCT
cana-2015	282	9	q	q	PROPN
cana-2015	283	1	+	+	CCONJ
cana-2015	283	2	(	(	PUNCT
cana-2015	283	3	log∏	log∏	PROPN
cana-2015	283	4	i	i	PRON
cana-2015	283	5	(	(	PUNCT
cana-2015	283	6	fu	fu	PROPN
cana-2015	283	7	mhij	mhij	NOUN
cana-2015	283	8	)	)	PUNCT
cana-2015	283	9	)	)	PUNCT
cana-2015	283	10	q	q	NOUN
cana-2015	283	11	.	.	PUNCT
cana-2015	284	1	therefore	therefore	ADV
cana-2015	284	2	,	,	PUNCT
cana-2015	284	3	1−	1−	NUM
cana-2015	284	4	(	(	PUNCT
cana-2015	284	5	�	�	PROPN
cana-2015	284	6	n	n	CCONJ
cana-2015	284	7	i=1log	i=1log	PROPN
cana-2015	284	8	∏	∏	PROPN
cana-2015	284	9	i	i	PRON
cana-2015	284	10	f	f	PROPN
cana-2015	284	11	l	l	NOUN
cana-2015	284	12	mtij	mtij	NOUN
cana-2015	284	13	)	)	PUNCT
cana-2015	284	14	q	q	PROPN
cana-2015	285	1	+	+	CCONJ
cana-2015	285	2	(	(	PUNCT
cana-2015	285	3	�	�	PROPN
cana-2015	285	4	n	n	CCONJ
cana-2015	285	5	i=1log	i=1log	PROPN
cana-2015	285	6	∏	∏	PROPN
cana-2015	285	7	i	i	PROPN
cana-2015	285	8	(	(	PUNCT
cana-2015	285	9	fu	fu	PROPN
cana-2015	285	10	mtij	mtij	PROPN
cana-2015	285	11	)	)	PUNCT
cana-2015	285	12	)	)	PUNCT
cana-2015	285	13	q	q	NOUN
cana-2015	285	14	2	2	NUM
cana-2015	285	15	≤	≤	NUM
cana-2015	285	16	1−	1−	NUM
cana-2015	285	17	(	(	PUNCT
cana-2015	285	18	�	�	PROPN
cana-2015	285	19	n	n	CCONJ
cana-2015	285	20	i=1log	i=1log	PROPN
cana-2015	285	21	∏	∏	PROPN
cana-2015	286	1	i	i	PRON
cana-2015	286	2	f	f	NOUN
cana-2015	286	3	l	l	NOUN
cana-2015	286	4	mhij	mhij	NOUN
cana-2015	286	5	)	)	PUNCT
cana-2015	286	6	q	q	PROPN
cana-2015	287	1	+	+	CCONJ
cana-2015	287	2	(	(	PUNCT
cana-2015	287	3	�	�	PROPN
cana-2015	287	4	n	n	CCONJ
cana-2015	287	5	i=1log	i=1log	PROPN
cana-2015	287	6	∏	∏	PROPN
cana-2015	287	7	i	i	PROPN
cana-2015	287	8	(	(	PUNCT
cana-2015	287	9	fu	fu	PROPN
cana-2015	287	10	mhij	mhij	NOUN
cana-2015	287	11	)	)	PUNCT
cana-2015	287	12	)	)	PUNCT
cana-2015	287	13	q	q	NOUN
cana-2015	287	14	2	2	NUM
cana-2015	287	15	.	.	PUNCT
cana-2015	287	16	=	=	PRON
cana-2015	288	1			PROPN
cana-2015	288	2	(	(	PUNCT
cana-2015	288	3	q	q	NOUN
cana-2015	288	4	√	√	NUM
cana-2015	288	5	1−	1−	NUM
cana-2015	288	6	�	�	PROPN
cana-2015	288	7	n	n	PRON
cana-2015	288	8	i=1	i=1	PROPN
cana-2015	288	9	(	(	PUNCT
cana-2015	288	10	1−	1−	NUM
cana-2015	288	11	(	(	PUNCT
cana-2015	288	12	log∏	log∏	NOUN
cana-2015	288	13	i	i	NOUN
cana-2015	288	14	t	t	VERB
cana-2015	288	15	l	l	NOUN
cana-2015	288	16	m	m	VERB
cana-2015	288	17	ti	ti	NOUN
cana-2015	288	18	)	)	PUNCT
cana-2015	288	19	q	q	NOUN
cana-2015	288	20	)	)	PUNCT
cana-2015	288	21	ωi	ωi	PROPN
cana-2015	288	22	)	)	PUNCT
cana-2015	288	23	2	2	NUM
cana-2015	288	24	+	+	CCONJ
cana-2015	288	25	(	(	PUNCT
cana-2015	288	26	q	q	NOUN
cana-2015	288	27	√	√	NUM
cana-2015	288	28	1−	1−	NUM
cana-2015	288	29	�	�	PROPN
cana-2015	288	30	n	n	PRON
cana-2015	288	31	i=1	i=1	PROPN
cana-2015	289	1	(	(	PUNCT
cana-2015	289	2	1−	1−	NUM
cana-2015	289	3	(	(	PUNCT
cana-2015	289	4	log∏	log∏	NOUN
cana-2015	289	5	i	i	PRON
cana-2015	289	6	(	(	PUNCT
cana-2015	289	7	t	t	PROPN
cana-2015	289	8	u	u	PROPN
cana-2015	289	9	mti	mti	NOUN
cana-2015	289	10	)	)	PUNCT
cana-2015	289	11	)	)	PUNCT
cana-2015	289	12	q	q	X
cana-2015	289	13	)	)	PUNCT
cana-2015	289	14	ωi	ωi	X
cana-2015	289	15	)	)	PUNCT
cana-2015	289	16	2	2	NUM
cana-2015	289	17	2	2	NUM
cana-2015	289	18	+1−	+1−	PROPN
cana-2015	289	19	(	(	PUNCT
cana-2015	289	20	�	�	PROPN
cana-2015	289	21	n	n	CCONJ
cana-2015	289	22	i=1(log	i=1(log	PROPN
cana-2015	289	23	∏	∏	PROPN
cana-2015	289	24	i	i	PRON
cana-2015	289	25	f	f	PROPN
cana-2015	289	26	l	l	NOUN
cana-2015	289	27	mtij	mtij	PROPN
cana-2015	289	28	)	)	PUNCT
cana-2015	289	29	)	)	PUNCT
cana-2015	289	30	2	2	NUM
cana-2015	290	1	+	+	NOUN
cana-2015	290	2	(	(	PUNCT
cana-2015	290	3	�	�	PROPN
cana-2015	290	4	n	n	CCONJ
cana-2015	290	5	i=1(log	i=1(log	PROPN
cana-2015	290	6	∏	∏	PROPN
cana-2015	290	7	i	i	PROPN
cana-2015	290	8	(	(	PUNCT
cana-2015	290	9	fu	fu	PROPN
cana-2015	290	10	mtij	mtij	NOUN
cana-2015	290	11	)	)	PUNCT
cana-2015	290	12	)	)	PUNCT
cana-2015	290	13	)	)	PUNCT
cana-2015	290	14	2	2	NUM
cana-2015	290	15	2	2	NUM
cana-2015	290	16			NOUN
cana-2015	290	17	=	=	SYM
cana-2015	290	18			PROPN
cana-2015	290	19	(	(	PUNCT
cana-2015	290	20	q	q	NOUN
cana-2015	290	21	√	√	NUM
cana-2015	290	22	1−	1−	NUM
cana-2015	290	23	�	�	PROPN
cana-2015	290	24	n	n	PRON
cana-2015	290	25	i=1	i=1	PROPN
cana-2015	290	26	(	(	PUNCT
cana-2015	290	27	1−	1−	NUM
cana-2015	290	28	(	(	PUNCT
cana-2015	290	29	log∏	log∏	NOUN
cana-2015	290	30	i	i	NOUN
cana-2015	290	31	t	t	PROPN
cana-2015	290	32	l	l	PROPN
cana-2015	290	33	mhi	mhi	PROPN
cana-2015	290	34	)	)	PUNCT
cana-2015	290	35	q	q	NOUN
cana-2015	290	36	)	)	PUNCT
cana-2015	290	37	ωi	ωi	PROPN
cana-2015	290	38	)	)	PUNCT
cana-2015	290	39	2	2	NUM
cana-2015	290	40	+	+	CCONJ
cana-2015	290	41	(	(	PUNCT
cana-2015	290	42	q	q	NOUN
cana-2015	290	43	√	√	NUM
cana-2015	290	44	1−	1−	NUM
cana-2015	290	45	�	�	PROPN
cana-2015	290	46	n	n	PRON
cana-2015	290	47	i=1	i=1	PROPN
cana-2015	290	48	(	(	PUNCT
cana-2015	290	49	1−	1−	NUM
cana-2015	290	50	(	(	PUNCT
cana-2015	290	51	log∏	log∏	NOUN
cana-2015	290	52	i	i	PRON
cana-2015	290	53	(	(	PUNCT
cana-2015	290	54	t	t	PROPN
cana-2015	290	55	u	u	PROPN
cana-2015	290	56	mhi	mhi	PROPN
cana-2015	290	57	)	)	PUNCT
cana-2015	290	58	)	)	PUNCT
cana-2015	290	59	q	q	X
cana-2015	290	60	)	)	PUNCT
cana-2015	290	61	ωi	ωi	X
cana-2015	290	62	)	)	PUNCT
cana-2015	290	63	2	2	NUM
cana-2015	290	64	2	2	NUM
cana-2015	290	65	+1−	+1−	PROPN
cana-2015	290	66	(	(	PUNCT
cana-2015	290	67	�	�	PROPN
cana-2015	290	68	n	n	CCONJ
cana-2015	290	69	i=1(log	i=1(log	PROPN
cana-2015	290	70	∏	∏	PROPN
cana-2015	290	71	i	i	NOUN
cana-2015	290	72	f	f	NOUN
cana-2015	290	73	l	l	NOUN
cana-2015	290	74	mhij	mhij	NOUN
cana-2015	290	75	)	)	PUNCT
cana-2015	290	76	)	)	PUNCT
cana-2015	290	77	2	2	NUM
cana-2015	291	1	+	+	NOUN
cana-2015	291	2	(	(	PUNCT
cana-2015	291	3	�	�	PROPN
cana-2015	291	4	n	n	CCONJ
cana-2015	291	5	i=1(log	i=1(log	PROPN
cana-2015	291	6	∏	∏	PROPN
cana-2015	291	7	i	i	PROPN
cana-2015	291	8	(	(	PUNCT
cana-2015	291	9	fu	fu	NOUN
cana-2015	291	10	mhij	mhij	NOUN
cana-2015	291	11	)	)	PUNCT
cana-2015	291	12	)	)	PUNCT
cana-2015	291	13	)	)	PUNCT
cana-2015	291	14	2	2	NUM
cana-2015	291	15	2	2	NUM
cana-2015	291	16			NOUN
cana-2015	291	17	.	.	PUNCT
cana-2015	292	1	hence	hence	ADV
cana-2015	292	2	,	,	PUNCT
cana-2015	292	3	q	q	NOUN
cana-2015	292	4	-	-	PUNCT
cana-2015	292	5	livifwa	livifwa	NOUN
cana-2015	292	6	(	(	PUNCT
cana-2015	292	7	m1,m2	m1,m2	PROPN
cana-2015	292	8	,	,	PUNCT
cana-2015	292	9	...	...	PUNCT
cana-2015	292	10	,	,	PUNCT
cana-2015	292	11	mn	mn	PROPN
cana-2015	292	12	)	)	PUNCT
cana-2015	292	13	≤	≤	NOUN
cana-2015	293	1	q	q	NOUN
cana-2015	293	2	-	-	PUNCT
cana-2015	293	3	livifwa	livifwa	NOUN
cana-2015	293	4	(	(	PUNCT
cana-2015	293	5	w1,w2	w1,w2	PROPN
cana-2015	293	6	,	,	PUNCT
cana-2015	293	7	...	...	PUNCT
cana-2015	293	8	,	,	PUNCT
cana-2015	293	9	wn	wn	PROPN
cana-2015	293	10	)	)	PUNCT
cana-2015	293	11	.	.	PUNCT
cana-2015	294	1	4.2	4.2	NUM
cana-2015	294	2	q	q	NOUN
cana-2015	294	3	-	-	PUNCT
cana-2015	294	4	livif	livif	NOUN
cana-2015	294	5	weighted	weight	VERB
cana-2015	294	6	geometric	geometric	ADJ
cana-2015	294	7	(	(	PUNCT
cana-2015	294	8	q	q	NOUN
cana-2015	294	9	-	-	PUNCT
cana-2015	294	10	livifwg	livifwg	NOUN
cana-2015	294	11	)	)	PUNCT
cana-2015	294	12	operator	operator	NOUN
cana-2015	294	13	definition	definition	NOUN
cana-2015	294	14	4.6	4.6	NUM
cana-2015	294	15	.	.	PUNCT
cana-2015	295	1	let	let	VERB
cana-2015	295	2	mi	mi	PROPN
cana-2015	295	3	=	=	PROPN
cana-2015	295	4	〈	〈	PROPN
cana-2015	295	5	(	(	PUNCT
cana-2015	295	6	logt	logt	NOUN
cana-2015	295	7	l	l	NOUN
cana-2015	295	8	m	m	VERB
cana-2015	295	9	i	i	PRON
cana-2015	295	10	,	,	PUNCT
cana-2015	295	11	logt	logt	PROPN
cana-2015	295	12	u	u	PROPN
cana-2015	295	13	mi	mi	PROPN
cana-2015	295	14	)	)	PUNCT
cana-2015	295	15	,	,	PUNCT
cana-2015	295	16	(	(	PUNCT
cana-2015	295	17	logf	logf	INTJ
cana-2015	295	18	l	l	NOUN
cana-2015	295	19	m	m	VERB
cana-2015	295	20	i	i	PRON
cana-2015	295	21	,	,	PUNCT
cana-2015	295	22	logf	logf	VERB
cana-2015	295	23	u	u	PROPN
cana-2015	295	24	mi	mi	PROPN
cana-2015	295	25	)	)	PUNCT
cana-2015	295	26	〉	〉	NOUN
cana-2015	295	27	be	be	VERB
cana-2015	295	28	the	the	DET
cana-2015	295	29	collection	collection	NOUN
cana-2015	295	30	of	of	ADP
cana-2015	295	31	q	q	NOUN
cana-2015	295	32	-	-	PUNCT
cana-2015	295	33	livifns	livifns	NOUN
cana-2015	295	34	.	.	PUNCT
cana-2015	296	1	then	then	ADV
cana-2015	296	2	q	q	ADJ
cana-2015	296	3	-	-	PUNCT
cana-2015	296	4	livifwg	livifwg	NOUN
cana-2015	296	5	operator	operator	NOUN
cana-2015	296	6	is	be	AUX
cana-2015	296	7	q	q	NOUN
cana-2015	296	8	-	-	PUNCT
cana-2015	296	9	livifwg	livifwg	NOUN
cana-2015	296	10	(	(	PUNCT
cana-2015	296	11	m1,m2	m1,m2	PROPN
cana-2015	296	12	,	,	PUNCT
cana-2015	296	13	...	...	PUNCT
cana-2015	296	14	,	,	PUNCT
cana-2015	296	15	mn	mn	PROPN
cana-2015	296	16	)	)	PUNCT
cana-2015	296	17	=	=	SYM
cana-2015	296	18	�	�	PROPN
cana-2015	296	19	n	n	CCONJ
cana-2015	296	20	i=1	i=1	X
cana-2015	296	21	m	m	VERB
cana-2015	296	22	ωi	ωi	INTJ
cana-2015	297	1	i	i	PRON
cana-2015	297	2	(	(	PUNCT
cana-2015	297	3	i	i	NOUN
cana-2015	297	4	=	=	NOUN
cana-2015	297	5	1	1	NUM
cana-2015	297	6	,	,	PUNCT
cana-2015	297	7	2	2	NUM
cana-2015	297	8	,	,	PUNCT
cana-2015	297	9	...	...	PUNCT
cana-2015	297	10	,	,	PUNCT
cana-2015	297	11	n	n	CCONJ
cana-2015	297	12	)	)	PUNCT
cana-2015	297	13	.	.	PUNCT
cana-2015	298	1	theorem	theorem	NOUN
cana-2015	298	2	4.7	4.7	NUM
cana-2015	298	3	.	.	PUNCT
cana-2015	299	1	let	let	VERB
cana-2015	299	2	mi	mi	PROPN
cana-2015	299	3	=	=	PROPN
cana-2015	299	4	〈	〈	PROPN
cana-2015	299	5	(	(	PUNCT
cana-2015	299	6	logt	logt	NOUN
cana-2015	299	7	l	l	NOUN
cana-2015	299	8	m	m	VERB
cana-2015	299	9	i	i	PRON
cana-2015	299	10	,	,	PUNCT
cana-2015	299	11	logt	logt	PROPN
cana-2015	299	12	u	u	PROPN
cana-2015	299	13	mi	mi	PROPN
cana-2015	299	14	)	)	PUNCT
cana-2015	299	15	,	,	PUNCT
cana-2015	299	16	(	(	PUNCT
cana-2015	299	17	logf	logf	INTJ
cana-2015	299	18	l	l	NOUN
cana-2015	299	19	m	m	VERB
cana-2015	299	20	i	i	PRON
cana-2015	299	21	,	,	PUNCT
cana-2015	299	22	logf	logf	VERB
cana-2015	299	23	u	u	PROPN
cana-2015	299	24	mi	mi	PROPN
cana-2015	299	25	)	)	PUNCT
cana-2015	299	26	〉	〉	NOUN
cana-2015	299	27	be	be	VERB
cana-2015	299	28	the	the	DET
cana-2015	299	29	collection	collection	NOUN
cana-2015	299	30	of	of	ADP
cana-2015	299	31	q	q	NOUN
cana-2015	299	32	-	-	PUNCT
cana-2015	299	33	livifns	livifns	NOUN
cana-2015	299	34	.	.	PUNCT
cana-2015	300	1	then	then	ADV
cana-2015	300	2	q	q	NOUN
cana-2015	300	3	-	-	PUNCT
cana-2015	300	4	livifwg	livifwg	NOUN
cana-2015	300	5	(	(	PUNCT
cana-2015	300	6	m1,m2	m1,m2	PROPN
cana-2015	300	7	,	,	PUNCT
cana-2015	300	8	...	...	PUNCT
cana-2015	300	9	,	,	PUNCT
cana-2015	300	10	mn	mn	PROPN
cana-2015	300	11	)	)	PUNCT
cana-2015	300	12	=	=	SYM
cana-2015	301	1			PROPN
cana-2015	301	2	(	(	PUNCT
cana-2015	301	3	�	�	PROPN
cana-2015	301	4	n	n	CCONJ
cana-2015	301	5	i=1(log	i=1(log	PROPN
cana-2015	301	6	∏	∏	PROPN
cana-2015	302	1	i	i	PRON
cana-2015	302	2	t	t	X
cana-2015	302	3	l	l	NOUN
cana-2015	302	4	m	m	VERB
cana-2015	302	5	i	i	NOUN
cana-2015	302	6	)	)	PUNCT
cana-2015	302	7	qωi	qωi	PROPN
cana-2015	302	8	,	,	PUNCT
cana-2015	302	9	�	�	PROPN
cana-2015	302	10	n	n	CCONJ
cana-2015	302	11	i=1(log	i=1(log	PROPN
cana-2015	302	12	∏	∏	PROPN
cana-2015	303	1	i	i	INTJ
cana-2015	303	2	(	(	PUNCT
cana-2015	303	3	t	t	PROPN
cana-2015	303	4	u	u	PROPN
cana-2015	303	5	mi	mi	PROPN
cana-2015	303	6	)	)	PUNCT
cana-2015	303	7	)	)	PUNCT
cana-2015	303	8	qωi	qωi	NOUN
cana-2015	303	9	)	)	PUNCT
cana-2015	303	10	,	,	PUNCT
cana-2015	303	11	(	(	PUNCT
cana-2015	303	12	q	q	NOUN
cana-2015	303	13	√	√	NUM
cana-2015	303	14	1−	1−	NUM
cana-2015	303	15	�	�	PROPN
cana-2015	303	16	n	n	PRON
cana-2015	303	17	i=1	i=1	PROPN
cana-2015	304	1	(	(	PUNCT
cana-2015	304	2	1−	1−	NUM
cana-2015	304	3	(	(	PUNCT
cana-2015	304	4	log∏	log∏	NOUN
cana-2015	304	5	i	i	PRON
cana-2015	304	6	f	f	VERB
cana-2015	304	7	l	l	NOUN
cana-2015	304	8	m	m	VERB
cana-2015	304	9	i	i	NOUN
cana-2015	304	10	)	)	PUNCT
cana-2015	304	11	q	q	NOUN
cana-2015	304	12	)	)	PUNCT
cana-2015	304	13	ωi	ωi	NOUN
cana-2015	304	14	,	,	PUNCT
cana-2015	304	15	q	q	NOUN
cana-2015	304	16	√	√	NUM
cana-2015	304	17	1−	1−	NUM
cana-2015	304	18	�	�	PROPN
cana-2015	304	19	n	n	PRON
cana-2015	304	20	i=1	i=1	PROPN
cana-2015	304	21	(	(	PUNCT
cana-2015	304	22	1−	1−	NUM
cana-2015	304	23	(	(	PUNCT
cana-2015	304	24	log∏	log∏	PROPN
cana-2015	304	25	i	i	PRON
cana-2015	304	26	(	(	PUNCT
cana-2015	304	27	fu	fu	PROPN
cana-2015	304	28	mi	mi	PROPN
cana-2015	304	29	)	)	PUNCT
cana-2015	304	30	)	)	PUNCT
cana-2015	304	31	q	q	X
cana-2015	304	32	)	)	PUNCT
cana-2015	304	33	ωi	ωi	X
cana-2015	304	34	)	)	PUNCT
cana-2015	304	35			PROPN
cana-2015	304	36	.	.	PUNCT
cana-2015	305	1	theorem	theorem	VERB
cana-2015	305	2	4.8	4.8	NUM
cana-2015	305	3	.	.	PUNCT
cana-2015	306	1	if	if	SCONJ
cana-2015	306	2	all	all	PRON
cana-2015	306	3	mi	mi	PROPN
cana-2015	306	4	=	=	PROPN
cana-2015	306	5	〈	〈	PROPN
cana-2015	306	6	(	(	PUNCT
cana-2015	306	7	logt	logt	NOUN
cana-2015	306	8	l	l	NOUN
cana-2015	306	9	m	m	VERB
cana-2015	306	10	i	i	PRON
cana-2015	306	11	,	,	PUNCT
cana-2015	306	12	logt	logt	PROPN
cana-2015	306	13	u	u	PROPN
cana-2015	306	14	mi	mi	PROPN
cana-2015	306	15	)	)	PUNCT
cana-2015	306	16	,	,	PUNCT
cana-2015	306	17	(	(	PUNCT
cana-2015	306	18	logf	logf	INTJ
cana-2015	306	19	l	l	NOUN
cana-2015	306	20	m	m	VERB
cana-2015	306	21	i	i	PRON
cana-2015	306	22	,	,	PUNCT
cana-2015	306	23	logf	logf	VERB
cana-2015	306	24	u	u	PROPN
cana-2015	306	25	mi	mi	PROPN
cana-2015	306	26	)	)	PUNCT
cana-2015	306	27	〉	〉	NOUN
cana-2015	306	28	are	be	AUX
cana-2015	306	29	equal	equal	ADJ
cana-2015	306	30	and	and	CCONJ
cana-2015	306	31	mi	mi	X
cana-2015	307	1	=	=	PROPN
cana-2015	307	2	m	m	PROPN
cana-2015	307	3	,	,	PUNCT
cana-2015	307	4	for	for	ADP
cana-2015	307	5	i	i	PROPN
cana-2015	307	6	=	=	SYM
cana-2015	307	7	1	1	NUM
cana-2015	307	8	,	,	PUNCT
cana-2015	307	9	2	2	NUM
cana-2015	307	10	,	,	PUNCT
cana-2015	307	11	...	...	PUNCT
cana-2015	307	12	,	,	PUNCT
cana-2015	308	1	n.	n.	PROPN
cana-2015	308	2	then	then	ADV
cana-2015	308	3	q	q	NOUN
cana-2015	308	4	-	-	PUNCT
cana-2015	308	5	livifwg	livifwg	NOUN
cana-2015	308	6	(	(	PUNCT
cana-2015	308	7	m1,m2	m1,m2	PROPN
cana-2015	308	8	,	,	PUNCT
cana-2015	308	9	...	...	PUNCT
cana-2015	308	10	,	,	PUNCT
cana-2015	308	11	mn	mn	PROPN
cana-2015	308	12	)	)	PUNCT
cana-2015	309	1	=	=	NOUN
cana-2015	309	2	m	m	NOUN
cana-2015	309	3	.	.	PUNCT
cana-2015	310	1	corollary	corollary	ADJ
cana-2015	310	2	4.9	4.9	NUM
cana-2015	310	3	.	.	PUNCT
cana-2015	311	1	the	the	DET
cana-2015	311	2	q	q	ADJ
cana-2015	311	3	-	-	PUNCT
cana-2015	311	4	livifwg	livifwg	NOUN
cana-2015	311	5	operator	operator	NOUN
cana-2015	311	6	is	be	AUX
cana-2015	311	7	used	use	VERB
cana-2015	311	8	to	to	PART
cana-2015	311	9	satisfy	satisfy	VERB
cana-2015	311	10	the	the	DET
cana-2015	311	11	boundedness	boundedness	NOUN
cana-2015	311	12	and	and	CCONJ
cana-2015	311	13	monotonicity	monotonicity	NOUN
cana-2015	311	14	properties	property	NOUN
cana-2015	311	15	.	.	PUNCT
cana-2015	312	1	4.3	4.3	NUM
cana-2015	312	2	extended	extend	VERB
cana-2015	312	3	q	q	NOUN
cana-2015	312	4	-	-	PUNCT
cana-2015	312	5	livifwa	livifwa	NOUN
cana-2015	312	6	(	(	PUNCT
cana-2015	312	7	q	q	NOUN
cana-2015	312	8	-	-	PUNCT
cana-2015	312	9	elivifwa	elivifwa	NOUN
cana-2015	312	10	)	)	PUNCT
cana-2015	312	11	operator	operator	NOUN
cana-2015	312	12	definition	definition	NOUN
cana-2015	312	13	4.10	4.10	NUM
cana-2015	312	14	.	.	PUNCT
cana-2015	313	1	let	let	VERB
cana-2015	313	2	mi	mi	PROPN
cana-2015	313	3	=	=	PROPN
cana-2015	313	4	〈	〈	PROPN
cana-2015	313	5	(	(	PUNCT
cana-2015	313	6	logt	logt	NOUN
cana-2015	313	7	l	l	NOUN
cana-2015	313	8	m	m	VERB
cana-2015	313	9	i	i	PRON
cana-2015	313	10	,	,	PUNCT
cana-2015	313	11	logt	logt	PROPN
cana-2015	313	12	u	u	PROPN
cana-2015	313	13	mi	mi	PROPN
cana-2015	313	14	)	)	PUNCT
cana-2015	313	15	,	,	PUNCT
cana-2015	313	16	(	(	PUNCT
cana-2015	313	17	logf	logf	INTJ
cana-2015	313	18	l	l	NOUN
cana-2015	313	19	m	m	VERB
cana-2015	313	20	i	i	PRON
cana-2015	313	21	,	,	PUNCT
cana-2015	313	22	logf	logf	VERB
cana-2015	313	23	u	u	PROPN
cana-2015	313	24	mi	mi	PROPN
cana-2015	313	25	)	)	PUNCT
cana-2015	313	26	〉	〉	NOUN
cana-2015	313	27	be	be	VERB
cana-2015	313	28	the	the	DET
cana-2015	313	29	collection	collection	NOUN
cana-2015	313	30	of	of	ADP
cana-2015	313	31	q	q	NOUN
cana-2015	313	32	-	-	NOUN
cana-2015	313	33	livifn	livifn	NOUN
cana-2015	313	34	.	.	PUNCT
cana-2015	314	1	then	then	ADV
cana-2015	314	2	q	q	X
cana-2015	314	3	-	-	PUNCT
cana-2015	314	4	elivifwa	elivifwa	NOUN
cana-2015	314	5	(	(	PUNCT
cana-2015	314	6	m1,m2	m1,m2	PROPN
cana-2015	314	7	,	,	PUNCT
cana-2015	314	8	...	...	PUNCT
cana-2015	314	9	,	,	PUNCT
cana-2015	314	10	mn	mn	PROPN
cana-2015	314	11	)	)	PUNCT
cana-2015	314	12	=	=	PRON
cana-2015	314	13	(	(	PUNCT
cana-2015	314	14	�	�	PROPN
cana-2015	314	15	n	n	CCONJ
cana-2015	314	16	i=1	i=1	PROPN
cana-2015	314	17	ωim	ωim	PROPN
cana-2015	314	18	ℵ	ℵ	PROPN
cana-2015	314	19	i	i	PROPN
cana-2015	314	20	)	)	PUNCT
cana-2015	314	21	1/ℵ	1/ℵ	NUM
cana-2015	314	22	is	be	AUX
cana-2015	314	23	called	call	VERB
cana-2015	314	24	the	the	DET
cana-2015	314	25	q	q	ADJ
cana-2015	314	26	-	-	PUNCT
cana-2015	314	27	elivifwa	elivifwa	NOUN
cana-2015	314	28	operator	operator	NOUN
cana-2015	314	29	.	.	PUNCT
cana-2015	315	1	theorem	theorem	VERB
cana-2015	315	2	4.11	4.11	NUM
cana-2015	315	3	.	.	PUNCT
cana-2015	316	1	let	let	VERB
cana-2015	316	2	mi	mi	PROPN
cana-2015	316	3	=	=	PROPN
cana-2015	316	4	〈	〈	PROPN
cana-2015	316	5	(	(	PUNCT
cana-2015	316	6	logt	logt	NOUN
cana-2015	316	7	l	l	NOUN
cana-2015	316	8	m	m	VERB
cana-2015	316	9	i	i	PRON
cana-2015	316	10	,	,	PUNCT
cana-2015	316	11	logt	logt	PROPN
cana-2015	316	12	u	u	PROPN
cana-2015	316	13	mi	mi	PROPN
cana-2015	316	14	)	)	PUNCT
cana-2015	316	15	,	,	PUNCT
cana-2015	316	16	(	(	PUNCT
cana-2015	316	17	logf	logf	INTJ
cana-2015	316	18	l	l	NOUN
cana-2015	316	19	m	m	VERB
cana-2015	316	20	i	i	PRON
cana-2015	316	21	,	,	PUNCT
cana-2015	316	22	logf	logf	VERB
cana-2015	316	23	u	u	PROPN
cana-2015	316	24	mi	mi	PROPN
cana-2015	316	25	)	)	PUNCT
cana-2015	316	26	〉	〉	NOUN
cana-2015	316	27	be	be	VERB
cana-2015	316	28	the	the	DET
cana-2015	316	29	collection	collection	NOUN
cana-2015	316	30	of	of	ADP
cana-2015	316	31	q	q	NOUN
cana-2015	316	32	-	-	PUNCT
cana-2015	316	33	livifns	livifns	NOUN
cana-2015	316	34	.	.	PUNCT
cana-2015	317	1	then	then	ADV
cana-2015	317	2	q	q	X
cana-2015	317	3	-	-	PUNCT
cana-2015	317	4	elivifwa	elivifwa	NOUN
cana-2015	317	5	(	(	PUNCT
cana-2015	317	6	m1,m2	m1,m2	PROPN
cana-2015	317	7	,	,	PUNCT
cana-2015	317	8	...	...	PUNCT
cana-2015	317	9	,	,	PUNCT
cana-2015	317	10	mn	mn	PROPN
cana-2015	317	11	)	)	PUNCT
cana-2015	317	12	=	=	PRON
cana-2015	317	13			VERB
cana-2015	317	14			PROPN
cana-2015	317	15	(	(	PUNCT
cana-2015	317	16	q	q	NOUN
cana-2015	317	17	√√√√	√√√√	PRON
cana-2015	317	18	1−	1−	NUM
cana-2015	317	19	�	�	NOUN
cana-2015	317	20	n	n	PRON
cana-2015	317	21	i=1	i=1	PROPN
cana-2015	317	22	(	(	PUNCT
cana-2015	317	23	1−	1−	NUM
cana-2015	317	24	(	(	PUNCT
cana-2015	317	25	(	(	PUNCT
cana-2015	317	26	log∏	log∏	NOUN
cana-2015	317	27	i	i	NOUN
cana-2015	317	28	t	t	VERB
cana-2015	317	29	l	l	NOUN
cana-2015	317	30	m	m	VERB
cana-2015	317	31	i	i	NOUN
cana-2015	317	32	)	)	PUNCT
cana-2015	317	33	q	q	NOUN
cana-2015	317	34	)	)	PUNCT
cana-2015	318	1	q)ωi	q)ωi	PROPN
cana-2015	318	2	)	)	PUNCT
cana-2015	318	3	1/ℵ	1/ℵ	NUM
cana-2015	318	4	,	,	PUNCT
cana-2015	318	5	(	(	PUNCT
cana-2015	318	6	q	q	NOUN
cana-2015	318	7	√√√√	√√√√	PRON
cana-2015	318	8	1−	1−	NUM
cana-2015	318	9	�	�	NOUN
cana-2015	318	10	n	n	PRON
cana-2015	318	11	i=1	i=1	PROPN
cana-2015	318	12	(	(	PUNCT
cana-2015	318	13	1−	1−	NUM
cana-2015	318	14	(	(	PUNCT
cana-2015	318	15	(	(	PUNCT
cana-2015	318	16	log∏	log∏	NOUN
cana-2015	318	17	i	i	PRON
cana-2015	318	18	(	(	PUNCT
cana-2015	318	19	t	t	PROPN
cana-2015	318	20	u	u	PROPN
cana-2015	318	21	mi	mi	PROPN
cana-2015	318	22	)	)	PUNCT
cana-2015	318	23	)	)	PUNCT
cana-2015	318	24	q	q	NOUN
cana-2015	318	25	)	)	PUNCT
cana-2015	318	26	q)ωi	q)ωi	PROPN
cana-2015	318	27	)	)	PUNCT
cana-2015	318	28	1/ℵ	1/ℵ	PROPN
cana-2015	318	29			PROPN
cana-2015	318	30	,	,	PUNCT
cana-2015	318	31			VERB
cana-2015	318	32	q	q	NOUN
cana-2015	318	33	√√√√1−	√√√√1−	X
cana-2015	318	34	(	(	PUNCT
cana-2015	318	35	1−	1−	NUM
cana-2015	318	36	(	(	PUNCT
cana-2015	318	37	�	�	PROPN
cana-2015	318	38	n	n	CCONJ
cana-2015	318	39	i=1	i=1	PROPN
cana-2015	318	40	(	(	PUNCT
cana-2015	318	41	q	q	NOUN
cana-2015	318	42	√	√	NUM
cana-2015	318	43	1−	1−	NUM
cana-2015	318	44	(	(	PUNCT
cana-2015	318	45	1−	1−	NUM
cana-2015	318	46	(	(	PUNCT
cana-2015	318	47	log∏	log∏	NOUN
cana-2015	318	48	i	i	PRON
cana-2015	318	49	f	f	PROPN
cana-2015	318	50	l	l	NOUN
cana-2015	318	51	m	m	VERB
cana-2015	318	52	i	i	NOUN
cana-2015	318	53	)	)	PUNCT
cana-2015	318	54	q	q	X
cana-2015	318	55	)	)	PUNCT
cana-2015	319	1	q)ωi	q)ωi	PROPN
cana-2015	319	2	)	)	PUNCT
cana-2015	319	3	q)1/ℵ	q)1/ℵ	PROPN
cana-2015	319	4	,	,	PUNCT
cana-2015	319	5	q	q	X
cana-2015	319	6	√√√√1−	√√√√1−	X
cana-2015	319	7	(	(	PUNCT
cana-2015	319	8	1−	1−	NUM
cana-2015	319	9	(	(	PUNCT
cana-2015	319	10	�	�	PROPN
cana-2015	319	11	n	n	CCONJ
cana-2015	319	12	i=1	i=1	PROPN
cana-2015	319	13	(	(	PUNCT
cana-2015	319	14	q	q	NOUN
cana-2015	319	15	√	√	NUM
cana-2015	319	16	1−	1−	NUM
cana-2015	319	17	(	(	PUNCT
cana-2015	319	18	1−	1−	NUM
cana-2015	319	19	(	(	PUNCT
cana-2015	319	20	log∏	log∏	PROPN
cana-2015	319	21	i	i	PRON
cana-2015	319	22	(	(	PUNCT
cana-2015	319	23	fu	fu	PROPN
cana-2015	319	24	mi	mi	PROPN
cana-2015	319	25	)	)	PUNCT
cana-2015	319	26	)	)	PUNCT
cana-2015	319	27	q	q	X
cana-2015	319	28	)	)	PUNCT
cana-2015	319	29	q)ωi	q)ωi	PROPN
cana-2015	319	30	)	)	PUNCT
cana-2015	319	31	q)1/ℵ	q)1/ℵ	NOUN
cana-2015	319	32			ADP
cana-2015	319	33			NOUN
cana-2015	319	34	.	.	PUNCT
cana-2015	320	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2015	320	2	545	545	NUM
cana-2015	320	3	communications	communication	NOUN
cana-2015	320	4	on	on	ADP
cana-2015	320	5	applied	apply	VERB
cana-2015	320	6	nonlinear	nonlinear	ADJ
cana-2015	320	7	analysis	analysis	NOUN
cana-2015	320	8	issn	issn	NOUN
cana-2015	320	9	:	:	PUNCT
cana-2015	320	10	1074	1074	NUM
cana-2015	320	11	-	-	PUNCT
cana-2015	320	12	133x	133x	NUM
cana-2015	320	13	vol	vol	NOUN
cana-2015	320	14	32	32	NUM
cana-2015	320	15	no	no	NOUN
cana-2015	320	16	.	.	NOUN
cana-2015	320	17	3	3	NUM
cana-2015	320	18	(	(	PUNCT
cana-2015	320	19	2025	2025	NUM
cana-2015	320	20	)	)	PUNCT
cana-2015	320	21	proof	proof	NOUN
cana-2015	320	22	.	.	PUNCT
cana-2015	321	1	we	we	PRON
cana-2015	321	2	have	have	VERB
cana-2015	321	3	,	,	PUNCT
cana-2015	321	4	�	�	PROPN
cana-2015	321	5	n	n	PROPN
cana-2015	321	6	i=1ωim	i=1ωim	NOUN
cana-2015	321	7	ℵ	ℵ	PROPN
cana-2015	321	8	i	i	NOUN
cana-2015	321	9	=	=	PUNCT
cana-2015	322	1			ADJ
cana-2015	322	2			PROPN
cana-2015	322	3	q	q	NOUN
cana-2015	322	4	√√√√	√√√√	PRON
cana-2015	322	5	1−	1−	NUM
cana-2015	322	6	�	�	NOUN
cana-2015	322	7	n	n	PRON
cana-2015	322	8	i=1	i=1	PROPN
cana-2015	322	9	(	(	PUNCT
cana-2015	322	10	1−	1−	NUM
cana-2015	322	11	(	(	PUNCT
cana-2015	322	12	(	(	PUNCT
cana-2015	322	13	log∏	log∏	NOUN
cana-2015	322	14	i	i	NOUN
cana-2015	322	15	t	t	VERB
cana-2015	322	16	l	l	NOUN
cana-2015	322	17	m	m	VERB
cana-2015	322	18	i	i	NOUN
cana-2015	322	19	)	)	PUNCT
cana-2015	322	20	q	q	NOUN
cana-2015	323	1	)	)	PUNCT
cana-2015	323	2	q)ωi	q)ωi	PROPN
cana-2015	323	3	,	,	PUNCT
cana-2015	323	4	q	q	PRON
cana-2015	323	5	√√√√	√√√√	ADP
cana-2015	323	6	1−	1−	NUM
cana-2015	323	7	�	�	NOUN
cana-2015	323	8	n	n	PRON
cana-2015	323	9	i=1	i=1	PROPN
cana-2015	323	10	(	(	PUNCT
cana-2015	323	11	1−	1−	NUM
cana-2015	323	12	(	(	PUNCT
cana-2015	323	13	(	(	PUNCT
cana-2015	323	14	log∏	log∏	NOUN
cana-2015	323	15	i	i	PRON
cana-2015	323	16	(	(	PUNCT
cana-2015	323	17	t	t	PROPN
cana-2015	323	18	u	u	PROPN
cana-2015	323	19	mi	mi	PROPN
cana-2015	323	20	)	)	PUNCT
cana-2015	323	21	)	)	PUNCT
cana-2015	323	22	q	q	NOUN
cana-2015	323	23	)	)	PUNCT
cana-2015	323	24	q)ωi	q)ωi	PROPN
cana-2015	323	25			PROPN
cana-2015	323	26	,	,	PUNCT
cana-2015	323	27	(	(	PUNCT
cana-2015	323	28	�	�	PROPN
cana-2015	323	29	n	n	CCONJ
cana-2015	323	30	i=1	i=1	PROPN
cana-2015	323	31	(	(	PUNCT
cana-2015	323	32	q	q	NOUN
cana-2015	323	33	√	√	NUM
cana-2015	323	34	1−	1−	NUM
cana-2015	323	35	(	(	PUNCT
cana-2015	323	36	1−	1−	NUM
cana-2015	323	37	(	(	PUNCT
cana-2015	323	38	log∏	log∏	NOUN
cana-2015	323	39	i	i	PRON
cana-2015	323	40	f	f	VERB
cana-2015	323	41	l	l	NOUN
cana-2015	323	42	m	m	VERB
cana-2015	323	43	i	i	NOUN
cana-2015	323	44	)	)	PUNCT
cana-2015	323	45	q	q	NOUN
cana-2015	323	46	)	)	PUNCT
cana-2015	324	1	q)ωi	q)ωi	PROPN
cana-2015	324	2	,	,	PUNCT
cana-2015	324	3	�	�	PROPN
cana-2015	324	4	n	n	CCONJ
cana-2015	324	5	i=1	i=1	PROPN
cana-2015	324	6	(	(	PUNCT
cana-2015	324	7	q	q	NOUN
cana-2015	324	8	√	√	NUM
cana-2015	324	9	1−	1−	NUM
cana-2015	324	10	(	(	PUNCT
cana-2015	324	11	1−	1−	NUM
cana-2015	324	12	(	(	PUNCT
cana-2015	324	13	log∏	log∏	PROPN
cana-2015	324	14	i	i	PRON
cana-2015	324	15	(	(	PUNCT
cana-2015	324	16	fu	fu	PROPN
cana-2015	324	17	mi	mi	PROPN
cana-2015	324	18	)	)	PUNCT
cana-2015	324	19	)	)	PUNCT
cana-2015	324	20	q	q	NOUN
cana-2015	324	21	)	)	PUNCT
cana-2015	324	22	q)ωi	q)ωi	PROPN
cana-2015	324	23	)	)	PUNCT
cana-2015	324	24			PROPN
cana-2015	324	25	.	.	PUNCT
cana-2015	325	1	if	if	SCONJ
cana-2015	325	2	n	n	NOUN
cana-2015	325	3	=	=	SYM
cana-2015	325	4	2	2	NUM
cana-2015	325	5	,	,	PUNCT
cana-2015	325	6	then	then	ADV
cana-2015	325	7	ω1b	ω1b	NUM
cana-2015	325	8	∨	∨	X
cana-2015	325	9	ω2c	ω2c	ADJ
cana-2015	325	10	=	=	SYM
cana-2015	325	11			NOUN
cana-2015	325	12			NOUN
cana-2015	325	13	q	q	X
cana-2015	325	14	√√√√√√√√√√	√√√√√√√√√√	NOUN
cana-2015	325	15	(	(	PUNCT
cana-2015	325	16	q	q	NOUN
cana-2015	325	17	√	√	NUM
cana-2015	325	18	1−	1−	NUM
cana-2015	325	19	(	(	PUNCT
cana-2015	325	20	1−	1−	NUM
cana-2015	325	21	(	(	PUNCT
cana-2015	325	22	(	(	PUNCT
cana-2015	325	23	log∏	log∏	NOUN
cana-2015	325	24	i	i	NOUN
cana-2015	325	25	t	t	VERB
cana-2015	325	26	l	l	NOUN
cana-2015	325	27	b	b	X
cana-2015	325	28	)	)	PUNCT
cana-2015	325	29	q	q	NOUN
cana-2015	325	30	)	)	PUNCT
cana-2015	325	31	q)ω1	q)ω1	NOUN
cana-2015	325	32	)	)	PUNCT
cana-2015	325	33	q	q	NOUN
cana-2015	326	1	+	+	CCONJ
cana-2015	326	2	(	(	PUNCT
cana-2015	326	3	q	q	PART
cana-2015	326	4	√	√	NUM
cana-2015	326	5	1−	1−	NUM
cana-2015	326	6	(	(	PUNCT
cana-2015	326	7	1−	1−	NUM
cana-2015	326	8	(	(	PUNCT
cana-2015	326	9	(	(	PUNCT
cana-2015	326	10	log∏	log∏	NOUN
cana-2015	326	11	i	i	NOUN
cana-2015	326	12	t	t	VERB
cana-2015	326	13	l	l	NOUN
cana-2015	326	14	c	c	X
cana-2015	326	15	)	)	PUNCT
cana-2015	326	16	q	q	NOUN
cana-2015	326	17	)	)	PUNCT
cana-2015	326	18	q)ω1	q)ω1	NOUN
cana-2015	326	19	)	)	PUNCT
cana-2015	326	20	q	q	NOUN
cana-2015	326	21	,	,	PUNCT
cana-2015	326	22	−	−	PROPN
cana-2015	326	23	(	(	PUNCT
cana-2015	326	24	q	q	NOUN
cana-2015	326	25	√	√	NUM
cana-2015	326	26	1−	1−	NUM
cana-2015	326	27	(	(	PUNCT
cana-2015	326	28	1−	1−	NUM
cana-2015	326	29	(	(	PUNCT
cana-2015	326	30	(	(	PUNCT
cana-2015	326	31	log∏	log∏	NOUN
cana-2015	326	32	i	i	NOUN
cana-2015	326	33	t	t	VERB
cana-2015	326	34	l	l	NOUN
cana-2015	326	35	b	b	X
cana-2015	326	36	)	)	PUNCT
cana-2015	326	37	q	q	NOUN
cana-2015	326	38	)	)	PUNCT
cana-2015	326	39	q)ω1	q)ω1	NOUN
cana-2015	326	40	)	)	PUNCT
cana-2015	326	41	q	q	NOUN
cana-2015	326	42	·	·	PUNCT
cana-2015	326	43	(	(	PUNCT
cana-2015	326	44	q	q	SYM
cana-2015	326	45	√	√	NUM
cana-2015	326	46	1−	1−	NUM
cana-2015	326	47	(	(	PUNCT
cana-2015	326	48	1−	1−	NUM
cana-2015	326	49	(	(	PUNCT
cana-2015	326	50	(	(	PUNCT
cana-2015	326	51	log∏	log∏	NOUN
cana-2015	326	52	i	i	NOUN
cana-2015	326	53	t	t	VERB
cana-2015	326	54	l	l	NOUN
cana-2015	326	55	c	c	X
cana-2015	326	56	)	)	PUNCT
cana-2015	326	57	q	q	NOUN
cana-2015	326	58	)	)	PUNCT
cana-2015	326	59	q)ω1	q)ω1	NOUN
cana-2015	326	60	)	)	PUNCT
cana-2015	326	61	q	q	NOUN
cana-2015	326	62	q	q	NOUN
cana-2015	326	63	√√√√√√√√√√	√√√√√√√√√√	NOUN
cana-2015	326	64	(	(	PUNCT
cana-2015	326	65	q	q	NOUN
cana-2015	326	66	√	√	NUM
cana-2015	326	67	1−	1−	NUM
cana-2015	326	68	(	(	PUNCT
cana-2015	326	69	1−	1−	NUM
cana-2015	326	70	(	(	PUNCT
cana-2015	326	71	(	(	PUNCT
cana-2015	326	72	log∏	log∏	NOUN
cana-2015	326	73	i	i	PRON
cana-2015	326	74	(	(	PUNCT
cana-2015	326	75	t	t	PROPN
cana-2015	326	76	u	u	PROPN
cana-2015	326	77	b	b	PROPN
cana-2015	326	78	)	)	PUNCT
cana-2015	326	79	)	)	PUNCT
cana-2015	326	80	q	q	NOUN
cana-2015	326	81	)	)	PUNCT
cana-2015	326	82	q)ω1	q)ω1	NOUN
cana-2015	326	83	)	)	PUNCT
cana-2015	326	84	q	q	NOUN
cana-2015	327	1	+	+	CCONJ
cana-2015	327	2	(	(	PUNCT
cana-2015	327	3	q	q	PART
cana-2015	327	4	√	√	NUM
cana-2015	327	5	1−	1−	NUM
cana-2015	327	6	(	(	PUNCT
cana-2015	327	7	1−	1−	NUM
cana-2015	327	8	(	(	PUNCT
cana-2015	327	9	(	(	PUNCT
cana-2015	327	10	log∏	log∏	NOUN
cana-2015	327	11	i	i	PRON
cana-2015	327	12	(	(	PUNCT
cana-2015	327	13	t	t	PROPN
cana-2015	327	14	u	u	X
cana-2015	327	15	c	c	PROPN
cana-2015	327	16	)	)	PUNCT
cana-2015	327	17	)	)	PUNCT
cana-2015	327	18	q	q	X
cana-2015	327	19	)	)	PUNCT
cana-2015	327	20	q)ω1	q)ω1	NOUN
cana-2015	327	21	)	)	PUNCT
cana-2015	327	22	q	q	NOUN
cana-2015	327	23	−	−	PROPN
cana-2015	328	1	(	(	PUNCT
cana-2015	328	2	q	q	NOUN
cana-2015	328	3	√	√	NUM
cana-2015	328	4	1−	1−	NUM
cana-2015	328	5	(	(	PUNCT
cana-2015	328	6	1−	1−	NUM
cana-2015	328	7	(	(	PUNCT
cana-2015	328	8	(	(	PUNCT
cana-2015	328	9	log∏	log∏	NOUN
cana-2015	328	10	i	i	PRON
cana-2015	328	11	(	(	PUNCT
cana-2015	328	12	t	t	PROPN
cana-2015	328	13	u	u	PROPN
cana-2015	328	14	b	b	PROPN
cana-2015	328	15	)	)	PUNCT
cana-2015	328	16	)	)	PUNCT
cana-2015	328	17	q	q	NOUN
cana-2015	328	18	)	)	PUNCT
cana-2015	328	19	q)ω1	q)ω1	NOUN
cana-2015	328	20	)	)	PUNCT
cana-2015	328	21	q	q	NOUN
cana-2015	328	22	·	·	PUNCT
cana-2015	328	23	(	(	PUNCT
cana-2015	328	24	q	q	SYM
cana-2015	328	25	√	√	NUM
cana-2015	328	26	1−	1−	NUM
cana-2015	328	27	(	(	PUNCT
cana-2015	328	28	1−	1−	NUM
cana-2015	328	29	(	(	PUNCT
cana-2015	328	30	(	(	PUNCT
cana-2015	328	31	log∏	log∏	NOUN
cana-2015	328	32	i	i	PRON
cana-2015	328	33	(	(	PUNCT
cana-2015	328	34	t	t	PROPN
cana-2015	328	35	u	u	X
cana-2015	328	36	c	c	PROPN
cana-2015	328	37	)	)	PUNCT
cana-2015	328	38	)	)	PUNCT
cana-2015	328	39	q	q	X
cana-2015	328	40	)	)	PUNCT
cana-2015	328	41	q)ω1	q)ω1	NOUN
cana-2015	328	42	)	)	PUNCT
cana-2015	328	43	q	q	NOUN
cana-2015	328	44			NOUN
cana-2015	328	45	,	,	PUNCT
cana-2015	328	46			NOUN
cana-2015	328	47	(	(	PUNCT
cana-2015	328	48	q	q	NOUN
cana-2015	328	49	√	√	NUM
cana-2015	328	50	1−	1−	NUM
cana-2015	328	51	(	(	PUNCT
cana-2015	328	52	1−	1−	NUM
cana-2015	328	53	(	(	PUNCT
cana-2015	328	54	log∏	log∏	NOUN
cana-2015	328	55	i	i	NOUN
cana-2015	328	56	f	f	PROPN
cana-2015	328	57	l	l	NOUN
cana-2015	328	58	b	b	X
cana-2015	328	59	)	)	PUNCT
cana-2015	328	60	q	q	NOUN
cana-2015	328	61	)	)	PUNCT
cana-2015	328	62	q)ω1	q)ω1	NOUN
cana-2015	328	63	·	·	PUNCT
cana-2015	328	64	(	(	PUNCT
cana-2015	328	65	q	q	SYM
cana-2015	328	66	√	√	NUM
cana-2015	328	67	1−	1−	NUM
cana-2015	328	68	(	(	PUNCT
cana-2015	328	69	1−	1−	NUM
cana-2015	328	70	(	(	PUNCT
cana-2015	328	71	log∏	log∏	NOUN
cana-2015	328	72	i	i	NOUN
cana-2015	328	73	f	f	NOUN
cana-2015	328	74	l	l	NOUN
cana-2015	328	75	c	c	X
cana-2015	328	76	)	)	PUNCT
cana-2015	328	77	q	q	NOUN
cana-2015	328	78	)	)	PUNCT
cana-2015	328	79	q)ω1	q)ω1	NOUN
cana-2015	328	80	,	,	PUNCT
cana-2015	328	81	(	(	PUNCT
cana-2015	328	82	q	q	NOUN
cana-2015	328	83	√	√	NUM
cana-2015	328	84	1−	1−	NUM
cana-2015	328	85	(	(	PUNCT
cana-2015	328	86	1−	1−	NUM
cana-2015	328	87	(	(	PUNCT
cana-2015	328	88	log∏	log∏	NOUN
cana-2015	328	89	i	i	PRON
cana-2015	328	90	(	(	PUNCT
cana-2015	328	91	fu	fu	PROPN
cana-2015	328	92	b	b	PROPN
cana-2015	328	93	)	)	PUNCT
cana-2015	328	94	)	)	PUNCT
cana-2015	328	95	q	q	NOUN
cana-2015	328	96	)	)	PUNCT
cana-2015	328	97	q)ω1	q)ω1	NOUN
cana-2015	328	98	·	·	PUNCT
cana-2015	328	99	(	(	PUNCT
cana-2015	328	100	q	q	SYM
cana-2015	328	101	√	√	NUM
cana-2015	328	102	1−	1−	NUM
cana-2015	328	103	(	(	PUNCT
cana-2015	328	104	1−	1−	NUM
cana-2015	328	105	(	(	PUNCT
cana-2015	328	106	log∏	log∏	NOUN
cana-2015	328	107	i	i	PRON
cana-2015	328	108	(	(	PUNCT
cana-2015	328	109	fu	fu	NOUN
cana-2015	328	110	c	c	NOUN
cana-2015	328	111	)	)	PUNCT
cana-2015	328	112	)	)	PUNCT
cana-2015	328	113	q	q	NOUN
cana-2015	328	114	)	)	PUNCT
cana-2015	328	115	q)ω1	q)ω1	ADJ
cana-2015	328	116			NOUN
cana-2015	328	117			NOUN
cana-2015	328	118	=	=	NOUN
cana-2015	328	119			NOUN
cana-2015	328	120	(	(	PUNCT
cana-2015	328	121	q	q	NOUN
cana-2015	328	122	√	√	NUM
cana-2015	328	123	1−	1−	NUM
cana-2015	328	124	�	�	PROPN
cana-2015	328	125	q	q	NOUN
cana-2015	328	126	i=1	i=1	PROPN
cana-2015	328	127	(	(	PUNCT
cana-2015	328	128	1−	1−	NUM
cana-2015	328	129	(	(	PUNCT
cana-2015	328	130	(	(	PUNCT
cana-2015	328	131	log∏	log∏	NOUN
cana-2015	329	1	i	i	NOUN
cana-2015	329	2	t	t	VERB
cana-2015	329	3	l	l	NOUN
cana-2015	329	4	b	b	X
cana-2015	329	5	)	)	PUNCT
cana-2015	329	6	q	q	NOUN
cana-2015	330	1	)	)	PUNCT
cana-2015	331	1	q)ωi	q)ωi	PROPN
cana-2015	331	2	,	,	PUNCT
cana-2015	331	3	q	q	PROPN
cana-2015	331	4	√	√	NUM
cana-2015	331	5	1−	1−	NUM
cana-2015	331	6	�	�	PROPN
cana-2015	331	7	q	q	NOUN
cana-2015	331	8	i=1	i=1	PROPN
cana-2015	331	9	(	(	PUNCT
cana-2015	331	10	1−	1−	NUM
cana-2015	331	11	(	(	PUNCT
cana-2015	331	12	(	(	PUNCT
cana-2015	331	13	log∏	log∏	NOUN
cana-2015	331	14	i	i	PRON
cana-2015	331	15	(	(	PUNCT
cana-2015	331	16	t	t	PROPN
cana-2015	331	17	u	u	PROPN
cana-2015	331	18	b	b	PROPN
cana-2015	331	19	)	)	PUNCT
cana-2015	331	20	)	)	PUNCT
cana-2015	331	21	q	q	X
cana-2015	331	22	)	)	PUNCT
cana-2015	331	23	q)ωi	q)ωi	PROPN
cana-2015	331	24	)	)	PUNCT
cana-2015	331	25	,	,	PUNCT
cana-2015	331	26	(	(	PUNCT
cana-2015	331	27	�	�	PROPN
cana-2015	331	28	q	q	X
cana-2015	331	29	i=1	i=1	PROPN
cana-2015	331	30	(	(	PUNCT
cana-2015	331	31	q	q	NOUN
cana-2015	331	32	√	√	NUM
cana-2015	331	33	1−	1−	NUM
cana-2015	331	34	(	(	PUNCT
cana-2015	331	35	1−	1−	NUM
cana-2015	331	36	(	(	PUNCT
cana-2015	331	37	log∏	log∏	NOUN
cana-2015	331	38	i	i	PRON
cana-2015	331	39	f	f	VERB
cana-2015	331	40	l	l	NOUN
cana-2015	331	41	m	m	VERB
cana-2015	331	42	i	i	NOUN
cana-2015	331	43	)	)	PUNCT
cana-2015	331	44	q	q	NOUN
cana-2015	331	45	)	)	PUNCT
cana-2015	332	1	q)ωi	q)ωi	PROPN
cana-2015	332	2	,	,	PUNCT
cana-2015	332	3	�	�	PROPN
cana-2015	332	4	q	q	PROPN
cana-2015	332	5	i=1	i=1	PROPN
cana-2015	332	6	(	(	PUNCT
cana-2015	332	7	q	q	NOUN
cana-2015	332	8	√	√	NUM
cana-2015	332	9	1−	1−	NUM
cana-2015	332	10	(	(	PUNCT
cana-2015	332	11	1−	1−	NUM
cana-2015	332	12	(	(	PUNCT
cana-2015	332	13	log∏	log∏	PROPN
cana-2015	332	14	i	i	PRON
cana-2015	332	15	(	(	PUNCT
cana-2015	332	16	fu	fu	PROPN
cana-2015	332	17	mi	mi	PROPN
cana-2015	332	18	)	)	PUNCT
cana-2015	332	19	)	)	PUNCT
cana-2015	332	20	q	q	NOUN
cana-2015	332	21	)	)	PUNCT
cana-2015	332	22	q)ωi	q)ωi	PROPN
cana-2015	332	23	)	)	PUNCT
cana-2015	332	24			NOUN
cana-2015	332	25	.	.	PUNCT
cana-2015	333	1	it	it	PRON
cana-2015	333	2	is	be	AUX
cana-2015	333	3	valid	valid	ADJ
cana-2015	333	4	for	for	ADP
cana-2015	333	5	n	n	NOUN
cana-2015	333	6	=	=	SYM
cana-2015	333	7	m	m	PROPN
cana-2015	333	8	and	and	CCONJ
cana-2015	333	9	m	m	PRON
cana-2015	333	10	≥	≥	NOUN
cana-2015	333	11	3	3	NUM
cana-2015	333	12	.	.	PUNCT
cana-2015	334	1	hence	hence	ADV
cana-2015	334	2	,	,	PUNCT
cana-2015	334	3	�	�	PROPN
cana-2015	334	4	m	m	NOUN
cana-2015	334	5	i=1ωim	i=1ωim	ADJ
cana-2015	334	6	ℵ	ℵ	NOUN
cana-2015	334	7	i	i	NOUN
cana-2015	334	8	=	=	NOUN
cana-2015	334	9			NOUN
cana-2015	334	10	(	(	PUNCT
cana-2015	334	11	q	q	NOUN
cana-2015	334	12	√	√	NUM
cana-2015	334	13	1−	1−	NUM
cana-2015	334	14	�	�	PROPN
cana-2015	334	15	m	m	PROPN
cana-2015	334	16	i=1	i=1	PROPN
cana-2015	334	17	(	(	PUNCT
cana-2015	334	18	1−	1−	NUM
cana-2015	334	19	(	(	PUNCT
cana-2015	334	20	(	(	PUNCT
cana-2015	334	21	log∏	log∏	NOUN
cana-2015	334	22	i	i	NOUN
cana-2015	334	23	t	t	VERB
cana-2015	334	24	l	l	NOUN
cana-2015	334	25	b	b	X
cana-2015	334	26	)	)	PUNCT
cana-2015	334	27	q	q	NOUN
cana-2015	334	28	)	)	PUNCT
cana-2015	335	1	q)ωi	q)ωi	PROPN
cana-2015	335	2	,	,	PUNCT
cana-2015	335	3	q	q	ADJ
cana-2015	335	4	√	√	NUM
cana-2015	335	5	1−	1−	NUM
cana-2015	335	6	�	�	PROPN
cana-2015	335	7	m	m	PROPN
cana-2015	335	8	i=1	i=1	PROPN
cana-2015	335	9	(	(	PUNCT
cana-2015	335	10	1−	1−	NUM
cana-2015	335	11	(	(	PUNCT
cana-2015	335	12	(	(	PUNCT
cana-2015	335	13	log∏	log∏	NOUN
cana-2015	335	14	i	i	PRON
cana-2015	335	15	(	(	PUNCT
cana-2015	335	16	t	t	PROPN
cana-2015	335	17	u	u	PROPN
cana-2015	335	18	b	b	PROPN
cana-2015	335	19	)	)	PUNCT
cana-2015	335	20	)	)	PUNCT
cana-2015	335	21	q	q	X
cana-2015	335	22	)	)	PUNCT
cana-2015	335	23	q)ωi	q)ωi	PROPN
cana-2015	335	24	)	)	PUNCT
cana-2015	335	25	,	,	PUNCT
cana-2015	335	26	(	(	PUNCT
cana-2015	335	27	�	�	PROPN
cana-2015	335	28	m	m	VERB
cana-2015	335	29	i=1	i=1	PROPN
cana-2015	335	30	(	(	PUNCT
cana-2015	335	31	q	q	NOUN
cana-2015	335	32	√	√	NUM
cana-2015	335	33	1−	1−	NUM
cana-2015	335	34	(	(	PUNCT
cana-2015	335	35	1−	1−	NUM
cana-2015	335	36	(	(	PUNCT
cana-2015	335	37	log∏	log∏	NOUN
cana-2015	335	38	i	i	PRON
cana-2015	335	39	f	f	VERB
cana-2015	335	40	l	l	NOUN
cana-2015	335	41	m	m	VERB
cana-2015	335	42	i	i	NOUN
cana-2015	335	43	)	)	PUNCT
cana-2015	335	44	q	q	NOUN
cana-2015	335	45	)	)	PUNCT
cana-2015	336	1	q)ωi	q)ωi	PROPN
cana-2015	336	2	,	,	PUNCT
cana-2015	336	3	�	�	PROPN
cana-2015	336	4	m	m	VERB
cana-2015	336	5	i=1	i=1	PROPN
cana-2015	336	6	(	(	PUNCT
cana-2015	336	7	q	q	NOUN
cana-2015	336	8	√	√	NUM
cana-2015	336	9	1−	1−	NUM
cana-2015	336	10	(	(	PUNCT
cana-2015	336	11	1−	1−	NUM
cana-2015	336	12	(	(	PUNCT
cana-2015	336	13	log∏	log∏	NOUN
cana-2015	336	14	i	i	PRON
cana-2015	336	15	f	f	VERB
cana-2015	336	16	l	l	NOUN
cana-2015	336	17	m	m	VERB
cana-2015	336	18	i	i	NOUN
cana-2015	336	19	)	)	PUNCT
cana-2015	336	20	q	q	NOUN
cana-2015	336	21	)	)	PUNCT
cana-2015	336	22	q)ωi	q)ωi	PROPN
cana-2015	336	23	)	)	PUNCT
cana-2015	336	24	.	.	NOUN
cana-2015	336	25	if	if	SCONJ
cana-2015	336	26	n	n	NOUN
cana-2015	336	27	=	=	SYM
cana-2015	336	28	m+	m+	NUM
cana-2015	336	29	1	1	NUM
cana-2015	337	1	and	and	CCONJ
cana-2015	337	2	we	we	PRON
cana-2015	337	3	apply	apply	VERB
cana-2015	337	4	,	,	PUNCT
cana-2015	337	5	then	then	ADV
cana-2015	337	6	�	�	PROPN
cana-2015	337	7	m	m	PROPN
cana-2015	337	8	i=1ωim	i=1ωim	ADJ
cana-2015	337	9	ℵ	ℵ	ADP
cana-2015	337	10	i	i	PROPN
cana-2015	337	11	+	+	CCONJ
cana-2015	337	12	ωm+1	ωm+1	NUM
cana-2015	337	13	m	m	NOUN
cana-2015	337	14	ℵ	ℵ	NOUN
cana-2015	337	15	m+1	m+1	X
cana-2015	337	16	=	=	SYM
cana-2015	337	17	�	�	PROPN
cana-2015	337	18	m+1	m+1	PROPN
cana-2015	337	19	i=1	i=1	PROPN
cana-2015	337	20	ωim	ωim	PROPN
cana-2015	337	21	ℵ	ℵ	PROPN
cana-2015	337	22	i	i	PROPN
cana-2015	337	23	.	.	PUNCT
cana-2015	338	1	now,	now,	PROPN
cana-2015	338	2	�	�	PROPN
cana-2015	338	3	m	m	PROPN
cana-2015	338	4	i=1ωim	i=1ωim	ADJ
cana-2015	338	5	ℵ	ℵ	ADP
cana-2015	338	6	i	i	PROPN
cana-2015	338	7	+	+	CCONJ
cana-2015	338	8	ωm+1	ωm+1	NUM
cana-2015	338	9	m	m	NOUN
cana-2015	338	10	ℵ	ℵ	ADJ
cana-2015	338	11	m+1	m+1	X
cana-2015	338	12	=	=	SYM
cana-2015	338	13	ω1	ω1	PROPN
cana-2015	338	14	m	m	PROPN
cana-2015	338	15	ℵ	ℵ	ADJ
cana-2015	338	16	1	1	NUM
cana-2015	338	17	∨	∨	NUM
cana-2015	338	18	ω2	ω2	NUM
cana-2015	338	19	m	m	PROPN
cana-2015	338	20	ℵ	ℵ	ADP
cana-2015	338	21	2	2	NUM
cana-2015	338	22	∨	∨	NUM
cana-2015	338	23	...	...	PUNCT
cana-2015	338	24	∨	∨	NUM
cana-2015	338	25	ωmmℵ	ωmmℵ	NOUN
cana-2015	338	26	m	m	PROPN
cana-2015	338	27	∨	∨	NUM
cana-2015	338	28	ωm+1	ωm+1	NUM
cana-2015	338	29	m	m	PROPN
cana-2015	338	30	ℵ	ℵ	NOUN
cana-2015	338	31	m+1	m+1	X
cana-2015	338	32	=	=	SYM
cana-2015	338	33			ADJ
cana-2015	338	34			NOUN
cana-2015	338	35	q	q	PROPN
cana-2015	338	36	√√√√√√√√√√	√√√√√√√√√√	PROPN
cana-2015	338	37	(	(	PUNCT
cana-2015	338	38	q	q	NOUN
cana-2015	338	39	√	√	NUM
cana-2015	338	40	1−	1−	NUM
cana-2015	338	41	�	�	PROPN
cana-2015	338	42	m	m	PROPN
cana-2015	338	43	i=1	i=1	PROPN
cana-2015	338	44	(	(	PUNCT
cana-2015	338	45	1−	1−	NUM
cana-2015	338	46	(	(	PUNCT
cana-2015	338	47	(	(	PUNCT
cana-2015	338	48	log∏	log∏	NOUN
cana-2015	338	49	i	i	NOUN
cana-2015	338	50	t	t	VERB
cana-2015	338	51	l	l	NOUN
cana-2015	338	52	m	m	VERB
cana-2015	338	53	i	i	NOUN
cana-2015	338	54	)	)	PUNCT
cana-2015	338	55	q	q	NOUN
cana-2015	338	56	)	)	PUNCT
cana-2015	338	57	q)ωi	q)ωi	PROPN
cana-2015	338	58	)	)	PUNCT
cana-2015	338	59	q	q	PROPN
cana-2015	339	1	+	+	CCONJ
cana-2015	339	2	(	(	PUNCT
cana-2015	339	3	q	q	PART
cana-2015	339	4	√	√	NUM
cana-2015	339	5	1−	1−	NUM
cana-2015	339	6	(	(	PUNCT
cana-2015	339	7	1−	1−	NUM
cana-2015	339	8	(	(	PUNCT
cana-2015	339	9	(	(	PUNCT
cana-2015	339	10	log∏	log∏	NOUN
cana-2015	339	11	i	i	NOUN
cana-2015	339	12	t	t	NOUN
cana-2015	339	13	l	l	NOUN
cana-2015	339	14	mm+1	mm+1	X
cana-2015	339	15	)	)	PUNCT
cana-2015	339	16	q	q	NOUN
cana-2015	339	17	)	)	PUNCT
cana-2015	339	18	q)ω1	q)ω1	NOUN
cana-2015	339	19	)	)	PUNCT
cana-2015	339	20	q	q	NOUN
cana-2015	339	21	,	,	PUNCT
cana-2015	339	22	−	−	PROPN
cana-2015	339	23	(	(	PUNCT
cana-2015	339	24	q	q	NOUN
cana-2015	339	25	√	√	NUM
cana-2015	339	26	1−	1−	NUM
cana-2015	339	27	�	�	PROPN
cana-2015	339	28	m	m	PROPN
cana-2015	339	29	i=1	i=1	PROPN
cana-2015	339	30	(	(	PUNCT
cana-2015	339	31	1−	1−	NUM
cana-2015	339	32	(	(	PUNCT
cana-2015	339	33	(	(	PUNCT
cana-2015	339	34	log∏	log∏	NOUN
cana-2015	339	35	i	i	NOUN
cana-2015	339	36	t	t	VERB
cana-2015	339	37	l	l	NOUN
cana-2015	339	38	m	m	VERB
cana-2015	339	39	i	i	NOUN
cana-2015	339	40	)	)	PUNCT
cana-2015	339	41	q	q	NOUN
cana-2015	339	42	)	)	PUNCT
cana-2015	340	1	q)ωi	q)ωi	PROPN
cana-2015	340	2	)	)	PUNCT
cana-2015	340	3	q	q	X
cana-2015	340	4	·	·	PUNCT
cana-2015	340	5	(	(	PUNCT
cana-2015	340	6	q	q	SYM
cana-2015	340	7	√	√	NUM
cana-2015	340	8	1−	1−	NUM
cana-2015	340	9	(	(	PUNCT
cana-2015	340	10	1−	1−	NUM
cana-2015	340	11	(	(	PUNCT
cana-2015	340	12	(	(	PUNCT
cana-2015	340	13	log∏	log∏	NOUN
cana-2015	341	1	i	i	NOUN
cana-2015	341	2	t	t	NOUN
cana-2015	341	3	l	l	NOUN
cana-2015	341	4	mm+1	mm+1	X
cana-2015	341	5	)	)	PUNCT
cana-2015	341	6	q	q	NOUN
cana-2015	341	7	)	)	PUNCT
cana-2015	341	8	q)ω1	q)ω1	NOUN
cana-2015	341	9	)	)	PUNCT
cana-2015	341	10	q	q	NOUN
cana-2015	341	11	q	q	NOUN
cana-2015	341	12	√√√√√√√√√√	√√√√√√√√√√	NOUN
cana-2015	341	13	(	(	PUNCT
cana-2015	341	14	q	q	NOUN
cana-2015	341	15	√	√	NUM
cana-2015	341	16	1−	1−	NUM
cana-2015	341	17	�	�	PROPN
cana-2015	341	18	m	m	PROPN
cana-2015	341	19	i=1	i=1	PROPN
cana-2015	341	20	(	(	PUNCT
cana-2015	341	21	1−	1−	NUM
cana-2015	341	22	(	(	PUNCT
cana-2015	341	23	(	(	PUNCT
cana-2015	341	24	log∏	log∏	NOUN
cana-2015	341	25	i	i	PRON
cana-2015	341	26	(	(	PUNCT
cana-2015	341	27	t	t	PROPN
cana-2015	341	28	u	u	PROPN
cana-2015	341	29	mi	mi	PROPN
cana-2015	341	30	)	)	PUNCT
cana-2015	341	31	)	)	PUNCT
cana-2015	341	32	q	q	NOUN
cana-2015	341	33	)	)	PUNCT
cana-2015	342	1	q)ωi	q)ωi	PROPN
cana-2015	342	2	)	)	PUNCT
cana-2015	342	3	q	q	PROPN
cana-2015	343	1	+	+	CCONJ
cana-2015	343	2	(	(	PUNCT
cana-2015	343	3	q	q	PART
cana-2015	343	4	√	√	NUM
cana-2015	343	5	1−	1−	NUM
cana-2015	343	6	(	(	PUNCT
cana-2015	343	7	1−	1−	NUM
cana-2015	343	8	(	(	PUNCT
cana-2015	343	9	(	(	PUNCT
cana-2015	343	10	log∏	log∏	NOUN
cana-2015	343	11	i	i	PRON
cana-2015	343	12	(	(	PUNCT
cana-2015	343	13	t	t	PROPN
cana-2015	343	14	u	u	PROPN
cana-2015	343	15	mm+1	mm+1	PROPN
cana-2015	343	16	)	)	PUNCT
cana-2015	343	17	)	)	PUNCT
cana-2015	343	18	q	q	NOUN
cana-2015	343	19	)	)	PUNCT
cana-2015	343	20	q)ω1	q)ω1	NOUN
cana-2015	343	21	)	)	PUNCT
cana-2015	343	22	q	q	NOUN
cana-2015	343	23	−	−	PROPN
cana-2015	343	24	(	(	PUNCT
cana-2015	343	25	q	q	NOUN
cana-2015	343	26	√	√	NUM
cana-2015	343	27	1−	1−	NUM
cana-2015	343	28	�	�	PROPN
cana-2015	343	29	m	m	PROPN
cana-2015	343	30	i=1	i=1	PROPN
cana-2015	344	1	(	(	PUNCT
cana-2015	344	2	1−	1−	NUM
cana-2015	344	3	(	(	PUNCT
cana-2015	344	4	(	(	PUNCT
cana-2015	344	5	log∏	log∏	NOUN
cana-2015	344	6	i	i	PRON
cana-2015	344	7	(	(	PUNCT
cana-2015	344	8	t	t	PROPN
cana-2015	344	9	u	u	PROPN
cana-2015	344	10	mi	mi	PROPN
cana-2015	344	11	)	)	PUNCT
cana-2015	344	12	)	)	PUNCT
cana-2015	344	13	q	q	NOUN
cana-2015	345	1	)	)	PUNCT
cana-2015	345	2	q)ωi	q)ωi	PROPN
cana-2015	345	3	)	)	PUNCT
cana-2015	345	4	q	q	X
cana-2015	345	5	·	·	PUNCT
cana-2015	345	6	(	(	PUNCT
cana-2015	345	7	q	q	SYM
cana-2015	345	8	√	√	NUM
cana-2015	345	9	1−	1−	NUM
cana-2015	345	10	(	(	PUNCT
cana-2015	345	11	1−	1−	NUM
cana-2015	345	12	(	(	PUNCT
cana-2015	345	13	(	(	PUNCT
cana-2015	345	14	log∏	log∏	NOUN
cana-2015	345	15	i	i	PRON
cana-2015	345	16	(	(	PUNCT
cana-2015	345	17	t	t	PROPN
cana-2015	345	18	u	u	PROPN
cana-2015	345	19	mm+1	mm+1	PROPN
cana-2015	345	20	)	)	PUNCT
cana-2015	345	21	)	)	PUNCT
cana-2015	345	22	q	q	NOUN
cana-2015	345	23	)	)	PUNCT
cana-2015	345	24	q)ω1	q)ω1	NOUN
cana-2015	345	25	)	)	PUNCT
cana-2015	345	26	q	q	NOUN
cana-2015	345	27			NOUN
cana-2015	345	28	,	,	PUNCT
cana-2015	345	29			NOUN
cana-2015	345	30	�	�	PROPN
cana-2015	345	31	m	m	VERB
cana-2015	345	32	i=1	i=1	PROPN
cana-2015	345	33	(	(	PUNCT
cana-2015	345	34	q	q	NOUN
cana-2015	345	35	√	√	NUM
cana-2015	345	36	1−	1−	NUM
cana-2015	345	37	(	(	PUNCT
cana-2015	345	38	1−	1−	NUM
cana-2015	345	39	(	(	PUNCT
cana-2015	345	40	log∏	log∏	NOUN
cana-2015	345	41	i	i	PRON
cana-2015	345	42	f	f	PROPN
cana-2015	345	43	l	l	NOUN
cana-2015	345	44	m	m	VERB
cana-2015	345	45	i	i	NOUN
cana-2015	345	46	)	)	PUNCT
cana-2015	345	47	q	q	X
cana-2015	345	48	)	)	PUNCT
cana-2015	346	1	q)ωi	q)ωi	PROPN
cana-2015	346	2	·	·	PUNCT
cana-2015	346	3	(	(	PUNCT
cana-2015	346	4	q	q	SYM
cana-2015	346	5	√	√	NUM
cana-2015	346	6	1−	1−	NUM
cana-2015	346	7	(	(	PUNCT
cana-2015	346	8	1−	1−	NUM
cana-2015	346	9	(	(	PUNCT
cana-2015	346	10	log∏	log∏	NOUN
cana-2015	346	11	i	i	NOUN
cana-2015	346	12	f	f	PROPN
cana-2015	346	13	l	l	NOUN
cana-2015	346	14	mm+1	mm+1	PROPN
cana-2015	346	15	)	)	PUNCT
cana-2015	346	16	q	q	NOUN
cana-2015	346	17	)	)	PUNCT
cana-2015	346	18	q)ω1	q)ω1	PROPN
cana-2015	346	19	,	,	PUNCT
cana-2015	346	20	�	�	PROPN
cana-2015	346	21	m	m	VERB
cana-2015	346	22	i=1	i=1	PROPN
cana-2015	346	23	(	(	PUNCT
cana-2015	346	24	q	q	NOUN
cana-2015	346	25	√	√	NUM
cana-2015	346	26	1−	1−	NUM
cana-2015	346	27	(	(	PUNCT
cana-2015	346	28	1−	1−	NUM
cana-2015	346	29	(	(	PUNCT
cana-2015	346	30	log∏	log∏	PROPN
cana-2015	346	31	i	i	PRON
cana-2015	346	32	(	(	PUNCT
cana-2015	346	33	fu	fu	PROPN
cana-2015	346	34	mi	mi	PROPN
cana-2015	346	35	)	)	PUNCT
cana-2015	346	36	)	)	PUNCT
cana-2015	346	37	q	q	X
cana-2015	346	38	)	)	PUNCT
cana-2015	347	1	q)ωi	q)ωi	PROPN
cana-2015	347	2	·	·	PUNCT
cana-2015	347	3	(	(	PUNCT
cana-2015	347	4	q	q	SYM
cana-2015	347	5	√	√	NUM
cana-2015	347	6	1−	1−	NUM
cana-2015	347	7	(	(	PUNCT
cana-2015	347	8	1−	1−	NUM
cana-2015	347	9	(	(	PUNCT
cana-2015	347	10	log∏	log∏	PROPN
cana-2015	347	11	i	i	PRON
cana-2015	347	12	(	(	PUNCT
cana-2015	347	13	fu	fu	NOUN
cana-2015	347	14	mm+1	mm+1	PROPN
cana-2015	347	15	)	)	PUNCT
cana-2015	347	16	)	)	PUNCT
cana-2015	347	17	q	q	X
cana-2015	347	18	)	)	PUNCT
cana-2015	347	19	q)ω1	q)ω1	ADJ
cana-2015	347	20			NOUN
cana-2015	347	21			NOUN
cana-2015	347	22	.	.	PUNCT
cana-2015	348	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2015	348	2	546	546	NUM
cana-2015	348	3	communications	communication	NOUN
cana-2015	348	4	on	on	ADP
cana-2015	348	5	applied	apply	VERB
cana-2015	348	6	nonlinear	nonlinear	ADJ
cana-2015	348	7	analysis	analysis	NOUN
cana-2015	348	8	issn	issn	NOUN
cana-2015	348	9	:	:	PUNCT
cana-2015	348	10	1074	1074	NUM
cana-2015	348	11	-	-	PUNCT
cana-2015	348	12	133x	133x	NUM
cana-2015	348	13	vol	vol	NOUN
cana-2015	348	14	32	32	NUM
cana-2015	348	15	no	no	NOUN
cana-2015	348	16	.	.	NOUN
cana-2015	348	17	3	3	NUM
cana-2015	348	18	(	(	PUNCT
cana-2015	348	19	2025	2025	NUM
cana-2015	348	20	)	)	PUNCT
cana-2015	348	21	thus	thus	ADV
cana-2015	348	22	,	,	PUNCT
cana-2015	348	23	�	�	VERB
cana-2015	348	24	m+1	m+1	PROPN
cana-2015	349	1	i=1	i=1	PROPN
cana-2015	349	2	ωim	ωim	PROPN
cana-2015	349	3	ℵ	ℵ	PROPN
cana-2015	349	4	i	i	PROPN
cana-2015	350	1	=	=	NOUN
cana-2015	351	1			NOUN
cana-2015	352	1	(	(	PUNCT
cana-2015	352	2	q	q	NOUN
cana-2015	352	3	√	√	NUM
cana-2015	352	4	1−	1−	NUM
cana-2015	352	5	�	�	PROPN
cana-2015	352	6	m+1	m+1	NUM
cana-2015	352	7	i=1	i=1	PROPN
cana-2015	353	1	(	(	PUNCT
cana-2015	353	2	1−	1−	NUM
cana-2015	353	3	(	(	PUNCT
cana-2015	353	4	(	(	PUNCT
cana-2015	353	5	log∏	log∏	NOUN
cana-2015	353	6	i	i	NOUN
cana-2015	353	7	t	t	PROPN
cana-2015	353	8	l	l	PROPN
cana-2015	353	9	mi	mi	PROPN
cana-2015	353	10	)	)	PUNCT
cana-2015	353	11	q	q	NOUN
cana-2015	353	12	)	)	PUNCT
cana-2015	354	1	q)ωi	q)ωi	PROPN
cana-2015	354	2	,	,	PUNCT
cana-2015	354	3	q	q	ADJ
cana-2015	354	4	√	√	NUM
cana-2015	354	5	1−	1−	NUM
cana-2015	354	6	�	�	PROPN
cana-2015	354	7	m+1	m+1	NUM
cana-2015	354	8	i=1	i=1	PROPN
cana-2015	354	9	(	(	PUNCT
cana-2015	354	10	1−	1−	NUM
cana-2015	354	11	(	(	PUNCT
cana-2015	354	12	(	(	PUNCT
cana-2015	354	13	log∏	log∏	NOUN
cana-2015	354	14	i	i	PRON
cana-2015	354	15	(	(	PUNCT
cana-2015	354	16	t	t	PROPN
cana-2015	354	17	u	u	PROPN
cana-2015	354	18	mi	mi	PROPN
cana-2015	354	19	)	)	PUNCT
cana-2015	354	20	)	)	PUNCT
cana-2015	354	21	q	q	NOUN
cana-2015	354	22	)	)	PUNCT
cana-2015	354	23	q)ωi	q)ωi	PROPN
cana-2015	354	24	)	)	PUNCT
cana-2015	354	25	,	,	PUNCT
cana-2015	354	26	�	�	X
cana-2015	354	27	m+1	m+1	PRON
cana-2015	354	28	i=1	i=1	PROPN
cana-2015	355	1	(	(	PUNCT
cana-2015	355	2	q	q	NOUN
cana-2015	355	3	√	√	NUM
cana-2015	355	4	1−	1−	NUM
cana-2015	355	5	(	(	PUNCT
cana-2015	355	6	1−	1−	NUM
cana-2015	355	7	(	(	PUNCT
cana-2015	355	8	log∏	log∏	NOUN
cana-2015	355	9	i	i	PRON
cana-2015	355	10	f	f	VERB
cana-2015	355	11	l	l	NOUN
cana-2015	355	12	m	m	VERB
cana-2015	355	13	i	i	NOUN
cana-2015	355	14	)	)	PUNCT
cana-2015	355	15	q	q	NOUN
cana-2015	355	16	)	)	PUNCT
cana-2015	356	1	q)ωi	q)ωi	PROPN
cana-2015	356	2	,	,	PUNCT
cana-2015	356	3	�	�	PROPN
cana-2015	356	4	m+1	m+1	NUM
cana-2015	356	5	i=1	i=1	PROPN
cana-2015	357	1	(	(	PUNCT
cana-2015	357	2	q	q	NOUN
cana-2015	357	3	√	√	NUM
cana-2015	357	4	1−	1−	NUM
cana-2015	357	5	(	(	PUNCT
cana-2015	357	6	1−	1−	NUM
cana-2015	357	7	(	(	PUNCT
cana-2015	357	8	log∏	log∏	NOUN
cana-2015	357	9	i	i	PRON
cana-2015	357	10	f	f	VERB
cana-2015	357	11	l	l	NOUN
cana-2015	357	12	m	m	VERB
cana-2015	357	13	i	i	NOUN
cana-2015	357	14	)	)	PUNCT
cana-2015	357	15	q	q	NOUN
cana-2015	357	16	)	)	PUNCT
cana-2015	358	1	q)ωi	q)ωi	ADJ
cana-2015	358	2			NOUN
cana-2015	358	3	.	.	PUNCT
cana-2015	359	1	hence	hence	ADV
cana-2015	359	2	,	,	PUNCT
cana-2015	359	3	(	(	PUNCT
cana-2015	359	4	�	�	ADP
cana-2015	359	5	m+1	m+1	X
cana-2015	359	6	i=1	i=1	PROPN
cana-2015	359	7	ωim	ωim	PROPN
cana-2015	359	8	ℵ	ℵ	PROPN
cana-2015	359	9	i	i	PROPN
cana-2015	359	10	)	)	PUNCT
cana-2015	359	11	1/ℵ	1/ℵ	NUM
cana-2015	359	12	=	=	NOUN
cana-2015	359	13			VERB
cana-2015	360	1			PROPN
cana-2015	360	2	(	(	PUNCT
cana-2015	360	3	q	q	NOUN
cana-2015	360	4	√√√√	√√√√	PRON
cana-2015	360	5	1−	1−	NUM
cana-2015	360	6	�	�	NOUN
cana-2015	360	7	m+1	m+1	PRON
cana-2015	360	8	i=1	i=1	PROPN
cana-2015	361	1	(	(	PUNCT
cana-2015	361	2	1−	1−	NUM
cana-2015	361	3	(	(	PUNCT
cana-2015	361	4	(	(	PUNCT
cana-2015	361	5	log∏	log∏	NOUN
cana-2015	361	6	i	i	NOUN
cana-2015	361	7	t	t	VERB
cana-2015	361	8	l	l	NOUN
cana-2015	361	9	m	m	VERB
cana-2015	361	10	i	i	NOUN
cana-2015	361	11	)	)	PUNCT
cana-2015	361	12	q	q	NOUN
cana-2015	362	1	)	)	PUNCT
cana-2015	362	2	q)ωi	q)ωi	PROPN
cana-2015	362	3	)	)	PUNCT
cana-2015	362	4	1/ℵ	1/ℵ	NUM
cana-2015	362	5	,	,	PUNCT
cana-2015	362	6	(	(	PUNCT
cana-2015	362	7	q	q	NOUN
cana-2015	362	8	√√√√	√√√√	ADP
cana-2015	362	9	1−	1−	NUM
cana-2015	362	10	�	�	NOUN
cana-2015	362	11	m+1	m+1	PRON
cana-2015	362	12	i=1	i=1	PROPN
cana-2015	362	13	(	(	PUNCT
cana-2015	362	14	1−	1−	NUM
cana-2015	362	15	(	(	PUNCT
cana-2015	362	16	(	(	PUNCT
cana-2015	362	17	log∏	log∏	NOUN
cana-2015	362	18	i	i	PRON
cana-2015	362	19	(	(	PUNCT
cana-2015	362	20	t	t	PROPN
cana-2015	362	21	u	u	PROPN
cana-2015	362	22	mi	mi	PROPN
cana-2015	362	23	)	)	PUNCT
cana-2015	362	24	)	)	PUNCT
cana-2015	362	25	q	q	NOUN
cana-2015	362	26	)	)	PUNCT
cana-2015	362	27	q)ωi	q)ωi	PROPN
cana-2015	362	28	)	)	PUNCT
cana-2015	362	29	1/ℵ	1/ℵ	PROPN
cana-2015	362	30			PROPN
cana-2015	362	31	,	,	PUNCT
cana-2015	362	32			VERB
cana-2015	362	33	q	q	NOUN
cana-2015	362	34	√√√√1−	√√√√1−	X
cana-2015	362	35	(	(	PUNCT
cana-2015	362	36	1−	1−	NUM
cana-2015	362	37	(	(	PUNCT
cana-2015	362	38	�	�	PROPN
cana-2015	362	39	m+1	m+1	PRON
cana-2015	362	40	i=1	i=1	PROPN
cana-2015	362	41	(	(	PUNCT
cana-2015	362	42	q	q	NOUN
cana-2015	362	43	√	√	NUM
cana-2015	362	44	1−	1−	NUM
cana-2015	362	45	(	(	PUNCT
cana-2015	362	46	1−	1−	NUM
cana-2015	362	47	(	(	PUNCT
cana-2015	362	48	log∏	log∏	NOUN
cana-2015	362	49	i	i	PRON
cana-2015	362	50	f	f	VERB
cana-2015	363	1	l	l	NOUN
cana-2015	363	2	m	m	VERB
cana-2015	363	3	i	i	NOUN
cana-2015	363	4	)	)	PUNCT
cana-2015	363	5	q	q	NOUN
cana-2015	364	1	)	)	PUNCT
cana-2015	364	2	q)ωi	q)ωi	PROPN
cana-2015	364	3	)	)	PUNCT
cana-2015	364	4	q)1/ℵ	q)1/ℵ	PROPN
cana-2015	364	5	,	,	PUNCT
cana-2015	364	6	q	q	X
cana-2015	364	7	√√√√1−	√√√√1−	X
cana-2015	364	8	(	(	PUNCT
cana-2015	364	9	1−	1−	NUM
cana-2015	364	10	(	(	PUNCT
cana-2015	364	11	�	�	PROPN
cana-2015	364	12	m+1	m+1	PRON
cana-2015	364	13	i=1	i=1	PROPN
cana-2015	364	14	(	(	PUNCT
cana-2015	364	15	q	q	NOUN
cana-2015	364	16	√	√	NUM
cana-2015	364	17	1−	1−	NUM
cana-2015	364	18	(	(	PUNCT
cana-2015	364	19	1−	1−	NUM
cana-2015	364	20	(	(	PUNCT
cana-2015	364	21	log∏	log∏	PROPN
cana-2015	364	22	i	i	PRON
cana-2015	364	23	(	(	PUNCT
cana-2015	364	24	fu	fu	PROPN
cana-2015	364	25	mi	mi	PROPN
cana-2015	364	26	)	)	PUNCT
cana-2015	364	27	)	)	PUNCT
cana-2015	364	28	q	q	NOUN
cana-2015	364	29	)	)	PUNCT
cana-2015	365	1	q)ωi	q)ωi	PROPN
cana-2015	365	2	)	)	PUNCT
cana-2015	365	3	q)1/ℵ	q)1/ℵ	NOUN
cana-2015	365	4			ADP
cana-2015	365	5			NOUN
cana-2015	365	6	.	.	PUNCT
cana-2015	366	1	it	it	PRON
cana-2015	366	2	is	be	AUX
cana-2015	366	3	valid	valid	ADJ
cana-2015	366	4	for	for	ADP
cana-2015	366	5	m	m	PROPN
cana-2015	366	6	≥	≥	NOUN
cana-2015	366	7	1	1	NUM
cana-2015	366	8	.	.	PUNCT
cana-2015	366	9	remark	remark	PROPN
cana-2015	366	10	4.12	4.12	NUM
cana-2015	366	11	.	.	PUNCT
cana-2015	367	1	if	if	SCONJ
cana-2015	367	2	ωi	ωi	NUM
cana-2015	367	3	=	=	SYM
cana-2015	367	4	1	1	NUM
cana-2015	367	5	,	,	PUNCT
cana-2015	367	6	then	then	ADV
cana-2015	367	7	q	q	ADJ
cana-2015	367	8	-	-	PUNCT
cana-2015	367	9	elivifwa	elivifwa	NOUN
cana-2015	367	10	operator	operator	NOUN
cana-2015	367	11	is	be	AUX
cana-2015	367	12	modified	modify	VERB
cana-2015	367	13	to	to	ADP
cana-2015	367	14	the	the	DET
cana-2015	367	15	q	q	NOUN
cana-2015	367	16	-	-	PUNCT
cana-2015	367	17	livifwa	livifwa	NOUN
cana-2015	367	18	operator	operator	NOUN
cana-2015	367	19	.	.	PUNCT
cana-2015	368	1	theorem	theorem	VERB
cana-2015	368	2	4.13	4.13	NUM
cana-2015	368	3	.	.	PUNCT
cana-2015	369	1	if	if	SCONJ
cana-2015	369	2	all	all	PRON
cana-2015	369	3	mi	mi	PROPN
cana-2015	369	4	=	=	PROPN
cana-2015	369	5	〈	〈	PROPN
cana-2015	369	6	(	(	PUNCT
cana-2015	369	7	logt	logt	NOUN
cana-2015	369	8	l	l	NOUN
cana-2015	369	9	m	m	VERB
cana-2015	369	10	i	i	PRON
cana-2015	369	11	,	,	PUNCT
cana-2015	369	12	logt	logt	PROPN
cana-2015	369	13	u	u	PROPN
cana-2015	369	14	mi	mi	PROPN
cana-2015	369	15	)	)	PUNCT
cana-2015	369	16	,	,	PUNCT
cana-2015	369	17	(	(	PUNCT
cana-2015	369	18	logf	logf	INTJ
cana-2015	369	19	l	l	NOUN
cana-2015	369	20	m	m	VERB
cana-2015	369	21	i	i	PRON
cana-2015	369	22	,	,	PUNCT
cana-2015	369	23	logf	logf	VERB
cana-2015	369	24	u	u	PROPN
cana-2015	369	25	mi	mi	PROPN
cana-2015	369	26	)	)	PUNCT
cana-2015	369	27	〉	〉	NOUN
cana-2015	369	28	are	be	AUX
cana-2015	369	29	equal	equal	ADJ
cana-2015	369	30	and	and	CCONJ
cana-2015	369	31	mi	mi	X
cana-2015	370	1	=	=	NOUN
cana-2015	370	2	m	m	PROPN
cana-2015	370	3	.	.	PUNCT
cana-2015	371	1	then	then	ADV
cana-2015	371	2	qelivifwa	qelivifwa	PROPN
cana-2015	371	3	(	(	PUNCT
cana-2015	371	4	m1,m2	m1,m2	PROPN
cana-2015	371	5	,	,	PUNCT
cana-2015	371	6	...	...	PUNCT
cana-2015	371	7	,	,	PUNCT
cana-2015	371	8	mn	mn	PROPN
cana-2015	371	9	)	)	PUNCT
cana-2015	371	10	=	=	NOUN
cana-2015	371	11	m	m	NOUN
cana-2015	371	12	.	.	PUNCT
cana-2015	371	13	remark	remark	VERB
cana-2015	371	14	4.14	4.14	NUM
cana-2015	371	15	.	.	PUNCT
cana-2015	372	1	we	we	PRON
cana-2015	372	2	use	use	VERB
cana-2015	372	3	the	the	DET
cana-2015	372	4	q	q	NOUN
cana-2015	372	5	-	-	PUNCT
cana-2015	372	6	elivifwa	elivifwa	NOUN
cana-2015	372	7	operator	operator	NOUN
cana-2015	372	8	to	to	PART
cana-2015	372	9	satisfy	satisfy	VERB
cana-2015	372	10	boundedness	boundedness	PROPN
cana-2015	372	11	and	and	CCONJ
cana-2015	372	12	monotonicity	monotonicity	NOUN
cana-2015	372	13	conditions	condition	NOUN
cana-2015	372	14	.	.	PUNCT
cana-2015	373	1	4.4	4.4	NUM
cana-2015	373	2	extended	extend	VERB
cana-2015	373	3	q	q	NOUN
cana-2015	373	4	-	-	PUNCT
cana-2015	373	5	livifwg	livifwg	NOUN
cana-2015	373	6	(	(	PUNCT
cana-2015	373	7	q	q	NOUN
cana-2015	373	8	-	-	PUNCT
cana-2015	373	9	elivifwg	elivifwg	NOUN
cana-2015	373	10	)	)	PUNCT
cana-2015	373	11	operator	operator	NOUN
cana-2015	373	12	definition	definition	NOUN
cana-2015	373	13	4.15	4.15	NUM
cana-2015	373	14	.	.	PUNCT
cana-2015	374	1	let	let	VERB
cana-2015	374	2	mi	mi	PROPN
cana-2015	374	3	=	=	PROPN
cana-2015	374	4	〈	〈	PROPN
cana-2015	374	5	(	(	PUNCT
cana-2015	374	6	logt	logt	NOUN
cana-2015	374	7	l	l	NOUN
cana-2015	374	8	m	m	VERB
cana-2015	374	9	i	i	PRON
cana-2015	374	10	,	,	PUNCT
cana-2015	374	11	logt	logt	PROPN
cana-2015	374	12	u	u	PROPN
cana-2015	374	13	mi	mi	PROPN
cana-2015	374	14	)	)	PUNCT
cana-2015	374	15	,	,	PUNCT
cana-2015	374	16	(	(	PUNCT
cana-2015	374	17	logf	logf	INTJ
cana-2015	374	18	l	l	NOUN
cana-2015	374	19	m	m	VERB
cana-2015	374	20	i	i	PRON
cana-2015	374	21	,	,	PUNCT
cana-2015	374	22	logf	logf	VERB
cana-2015	374	23	u	u	PROPN
cana-2015	374	24	mi	mi	PROPN
cana-2015	374	25	)	)	PUNCT
cana-2015	374	26	〉	〉	NOUN
cana-2015	374	27	be	be	VERB
cana-2015	374	28	the	the	DET
cana-2015	374	29	collection	collection	NOUN
cana-2015	374	30	of	of	ADP
cana-2015	374	31	q	q	NOUN
cana-2015	374	32	-	-	PUNCT
cana-2015	374	33	livifns	livifns	NOUN
cana-2015	374	34	.	.	PUNCT
cana-2015	375	1	then	then	ADV
cana-2015	375	2	q	q	X
cana-2015	375	3	-	-	PUNCT
cana-2015	375	4	elivifwg	elivifwg	NOUN
cana-2015	375	5	(	(	PUNCT
cana-2015	375	6	m1,m2	m1,m2	PROPN
cana-2015	375	7	,	,	PUNCT
cana-2015	375	8	...	...	PUNCT
cana-2015	375	9	,	,	PUNCT
cana-2015	375	10	mn	mn	PROPN
cana-2015	375	11	)	)	PUNCT
cana-2015	375	12	=	=	SYM
cana-2015	375	13	1	1	NUM
cana-2015	375	14	ℵ	ℵ	NOUN
cana-2015	375	15	(	(	PUNCT
cana-2015	375	16	�	�	PROPN
cana-2015	375	17	n	n	CCONJ
cana-2015	375	18	i=1	i=1	PROPN
cana-2015	375	19	(	(	PUNCT
cana-2015	375	20	ℵmi	ℵmi	PROPN
cana-2015	375	21	)	)	PUNCT
cana-2015	375	22	ωi	ωi	X
cana-2015	375	23	)	)	PUNCT
cana-2015	375	24	is	be	AUX
cana-2015	375	25	called	call	VERB
cana-2015	375	26	the	the	DET
cana-2015	375	27	q	q	ADJ
cana-2015	375	28	-	-	PUNCT
cana-2015	375	29	elivifwg	elivifwg	NOUN
cana-2015	375	30	operator	operator	NOUN
cana-2015	375	31	.	.	PUNCT
cana-2015	376	1	theorem	theorem	VERB
cana-2015	376	2	4.16	4.16	NUM
cana-2015	376	3	.	.	PUNCT
cana-2015	377	1	let	let	VERB
cana-2015	377	2	mi	mi	PROPN
cana-2015	377	3	=	=	PROPN
cana-2015	377	4	〈	〈	PROPN
cana-2015	377	5	(	(	PUNCT
cana-2015	377	6	logt	logt	NOUN
cana-2015	377	7	l	l	NOUN
cana-2015	377	8	m	m	VERB
cana-2015	377	9	i	i	PRON
cana-2015	377	10	,	,	PUNCT
cana-2015	377	11	logt	logt	PROPN
cana-2015	377	12	u	u	PROPN
cana-2015	377	13	mi	mi	PROPN
cana-2015	377	14	)	)	PUNCT
cana-2015	377	15	,	,	PUNCT
cana-2015	377	16	(	(	PUNCT
cana-2015	377	17	logf	logf	INTJ
cana-2015	377	18	l	l	NOUN
cana-2015	377	19	m	m	VERB
cana-2015	377	20	i	i	PRON
cana-2015	377	21	,	,	PUNCT
cana-2015	377	22	logf	logf	VERB
cana-2015	377	23	u	u	PROPN
cana-2015	377	24	mi	mi	PROPN
cana-2015	377	25	)	)	PUNCT
cana-2015	377	26	〉	〉	NOUN
cana-2015	377	27	be	be	VERB
cana-2015	377	28	the	the	DET
cana-2015	377	29	collection	collection	NOUN
cana-2015	377	30	of	of	ADP
cana-2015	377	31	q	q	NOUN
cana-2015	377	32	-	-	PUNCT
cana-2015	377	33	livifns	livifns	NOUN
cana-2015	377	34	.	.	PUNCT
cana-2015	378	1	then	then	ADV
cana-2015	378	2	q	q	X
cana-2015	378	3	-	-	PUNCT
cana-2015	378	4	elivifwg(m1,m2	elivifwg(m1,m2	NOUN
cana-2015	378	5	,	,	PUNCT
cana-2015	378	6	...	...	PUNCT
cana-2015	378	7	,	,	PUNCT
cana-2015	378	8	mn	mn	PROPN
cana-2015	378	9	)	)	PUNCT
cana-2015	378	10	=	=	PRON
cana-2015	378	11			ADJ
cana-2015	378	12			VERB
cana-2015	378	13	q	q	PUNCT
cana-2015	378	14	√√√√1−	√√√√1−	X
cana-2015	378	15	(	(	PUNCT
cana-2015	378	16	1−	1−	NUM
cana-2015	378	17	(	(	PUNCT
cana-2015	378	18	�	�	PROPN
cana-2015	378	19	n	n	CCONJ
cana-2015	378	20	i=1	i=1	PROPN
cana-2015	378	21	(	(	PUNCT
cana-2015	378	22	q	q	NOUN
cana-2015	378	23	√	√	NUM
cana-2015	378	24	1−	1−	NUM
cana-2015	378	25	(	(	PUNCT
cana-2015	378	26	1−	1−	NUM
cana-2015	378	27	(	(	PUNCT
cana-2015	378	28	log∏	log∏	NOUN
cana-2015	379	1	i	i	NOUN
cana-2015	379	2	t	t	VERB
cana-2015	379	3	l	l	NOUN
cana-2015	379	4	m	m	VERB
cana-2015	379	5	i	i	NOUN
cana-2015	379	6	)	)	PUNCT
cana-2015	379	7	q	q	NOUN
cana-2015	380	1	)	)	PUNCT
cana-2015	380	2	q)ωi	q)ωi	PROPN
cana-2015	380	3	)	)	PUNCT
cana-2015	380	4	q)1/ℵ	q)1/ℵ	PROPN
cana-2015	380	5	,	,	PUNCT
cana-2015	380	6	q	q	X
cana-2015	380	7	√√√√1−	√√√√1−	X
cana-2015	380	8	(	(	PUNCT
cana-2015	380	9	1−	1−	NUM
cana-2015	380	10	(	(	PUNCT
cana-2015	380	11	�	�	PROPN
cana-2015	380	12	n	n	CCONJ
cana-2015	380	13	i=1	i=1	PROPN
cana-2015	380	14	(	(	PUNCT
cana-2015	380	15	q	q	NOUN
cana-2015	380	16	√	√	NUM
cana-2015	380	17	1−	1−	NUM
cana-2015	380	18	(	(	PUNCT
cana-2015	380	19	1−	1−	NUM
cana-2015	380	20	(	(	PUNCT
cana-2015	380	21	log∏	log∏	NOUN
cana-2015	380	22	i	i	PRON
cana-2015	380	23	(	(	PUNCT
cana-2015	380	24	t	t	PROPN
cana-2015	380	25	u	u	PROPN
cana-2015	380	26	mi	mi	PROPN
cana-2015	380	27	)	)	PUNCT
cana-2015	380	28	)	)	PUNCT
cana-2015	380	29	q	q	NOUN
cana-2015	380	30	)	)	PUNCT
cana-2015	381	1	q)ωi	q)ωi	PROPN
cana-2015	381	2	)	)	PUNCT
cana-2015	381	3	q)1/ℵ	q)1/ℵ	PROPN
cana-2015	381	4			PROPN
cana-2015	381	5	,	,	PUNCT
cana-2015	381	6			PROPN
cana-2015	381	7	(	(	PUNCT
cana-2015	381	8	q	q	NOUN
cana-2015	381	9	√√√√	√√√√	PRON
cana-2015	381	10	1−	1−	NUM
cana-2015	381	11	�	�	NOUN
cana-2015	381	12	n	n	PRON
cana-2015	381	13	i=1	i=1	PROPN
cana-2015	381	14	(	(	PUNCT
cana-2015	381	15	1−	1−	NUM
cana-2015	381	16	(	(	PUNCT
cana-2015	381	17	(	(	PUNCT
cana-2015	381	18	log∏	log∏	NOUN
cana-2015	381	19	i	i	NOUN
cana-2015	381	20	f	f	VERB
cana-2015	381	21	l	l	NOUN
cana-2015	381	22	m	m	VERB
cana-2015	381	23	i	i	NOUN
cana-2015	381	24	)	)	PUNCT
cana-2015	381	25	q	q	NOUN
cana-2015	381	26	)	)	PUNCT
cana-2015	381	27	q)ωi	q)ωi	PROPN
cana-2015	381	28	)	)	PUNCT
cana-2015	381	29	1/ℵ	1/ℵ	NUM
cana-2015	381	30	,	,	PUNCT
cana-2015	381	31	(	(	PUNCT
cana-2015	381	32	q	q	NOUN
cana-2015	381	33	√√√√	√√√√	PRON
cana-2015	381	34	1−	1−	NUM
cana-2015	381	35	�	�	NOUN
cana-2015	381	36	n	n	PRON
cana-2015	381	37	i=1	i=1	PROPN
cana-2015	381	38	(	(	PUNCT
cana-2015	381	39	1−	1−	NUM
cana-2015	381	40	(	(	PUNCT
cana-2015	381	41	(	(	PUNCT
cana-2015	381	42	log∏	log∏	NOUN
cana-2015	381	43	i	i	PRON
cana-2015	381	44	(	(	PUNCT
cana-2015	381	45	fu	fu	PROPN
cana-2015	381	46	mi	mi	PROPN
cana-2015	381	47	)	)	PUNCT
cana-2015	381	48	)	)	PUNCT
cana-2015	381	49	q	q	NOUN
cana-2015	381	50	)	)	PUNCT
cana-2015	381	51	q)ωi	q)ωi	PROPN
cana-2015	381	52	)	)	PUNCT
cana-2015	381	53	1/ℵ	1/ℵ	NUM
cana-2015	381	54			PROPN
cana-2015	381	55			PROPN
cana-2015	381	56	.	.	PUNCT
cana-2015	382	1	remark	remark	VERB
cana-2015	382	2	4.17	4.17	NUM
cana-2015	382	3	.	.	PUNCT
cana-2015	383	1	if	if	SCONJ
cana-2015	383	2	ωi	ωi	NUM
cana-2015	383	3	=	=	SYM
cana-2015	383	4	1	1	NUM
cana-2015	383	5	,	,	PUNCT
cana-2015	383	6	then	then	ADV
cana-2015	383	7	q	q	ADJ
cana-2015	383	8	-	-	PUNCT
cana-2015	383	9	elivifwg	elivifwg	NOUN
cana-2015	383	10	operator	operator	NOUN
cana-2015	383	11	is	be	AUX
cana-2015	383	12	converted	convert	VERB
cana-2015	383	13	to	to	ADP
cana-2015	383	14	the	the	DET
cana-2015	383	15	q	q	ADJ
cana-2015	383	16	-	-	PUNCT
cana-2015	383	17	livifwg	livifwg	NOUN
cana-2015	383	18	operator	operator	NOUN
cana-2015	383	19	.	.	PUNCT
cana-2015	384	1	remark	remark	PROPN
cana-2015	384	2	4.18	4.18	NUM
cana-2015	384	3	.	.	PUNCT
cana-2015	385	1	q	q	X
cana-2015	385	2	-	-	PUNCT
cana-2015	385	3	elivifwg	elivifwg	NOUN
cana-2015	385	4	operators	operator	NOUN
cana-2015	385	5	satisfy	satisfy	VERB
cana-2015	385	6	boundedness	boundedness	PROPN
cana-2015	385	7	and	and	CCONJ
cana-2015	385	8	monotonicity	monotonicity	NOUN
cana-2015	385	9	properties	property	NOUN
cana-2015	385	10	.	.	PUNCT
cana-2015	386	1	corollary	corollary	ADJ
cana-2015	386	2	4.19	4.19	NUM
cana-2015	386	3	.	.	PUNCT
cana-2015	387	1	if	if	SCONJ
cana-2015	387	2	all	all	PRON
cana-2015	387	3	mi	mi	PROPN
cana-2015	387	4	=	=	PROPN
cana-2015	387	5	〈	〈	PROPN
cana-2015	387	6	(	(	PUNCT
cana-2015	387	7	logt	logt	NOUN
cana-2015	387	8	l	l	NOUN
cana-2015	387	9	m	m	VERB
cana-2015	387	10	i	i	PRON
cana-2015	387	11	,	,	PUNCT
cana-2015	387	12	logt	logt	PROPN
cana-2015	387	13	u	u	PROPN
cana-2015	387	14	mi	mi	PROPN
cana-2015	387	15	)	)	PUNCT
cana-2015	387	16	,	,	PUNCT
cana-2015	387	17	(	(	PUNCT
cana-2015	387	18	logf	logf	INTJ
cana-2015	387	19	l	l	NOUN
cana-2015	387	20	m	m	VERB
cana-2015	387	21	i	i	PRON
cana-2015	387	22	,	,	PUNCT
cana-2015	387	23	logf	logf	VERB
cana-2015	387	24	u	u	PROPN
cana-2015	387	25	mi	mi	PROPN
cana-2015	387	26	)	)	PUNCT
cana-2015	387	27	〉	〉	NOUN
cana-2015	387	28	are	be	AUX
cana-2015	387	29	equal	equal	ADJ
cana-2015	387	30	and	and	CCONJ
cana-2015	387	31	mi	mi	X
cana-2015	388	1	=	=	PROPN
cana-2015	388	2	m	m	PROPN
cana-2015	388	3	,	,	PUNCT
cana-2015	388	4	for	for	ADP
cana-2015	388	5	i	i	PROPN
cana-2015	388	6	=	=	SYM
cana-2015	388	7	1	1	NUM
cana-2015	388	8	,	,	PUNCT
cana-2015	388	9	2	2	NUM
cana-2015	388	10	,	,	PUNCT
cana-2015	388	11	...	...	PUNCT
cana-2015	388	12	,	,	PUNCT
cana-2015	389	1	n.	n.	PROPN
cana-2015	389	2	then	then	ADV
cana-2015	389	3	q	q	NOUN
cana-2015	389	4	-	-	PUNCT
cana-2015	389	5	elivifwg(m1,m2	elivifwg(m1,m2	NOUN
cana-2015	389	6	,	,	PUNCT
cana-2015	389	7	...	...	PUNCT
cana-2015	389	8	,	,	PUNCT
cana-2015	389	9	mn	mn	PROPN
cana-2015	389	10	)	)	PUNCT
cana-2015	389	11	=	=	NOUN
cana-2015	389	12	m	m	NOUN
cana-2015	389	13	.	.	PUNCT
cana-2015	390	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2015	390	2	547	547	NUM
cana-2015	390	3	communications	communication	NOUN
cana-2015	390	4	on	on	ADP
cana-2015	390	5	applied	apply	VERB
cana-2015	390	6	nonlinear	nonlinear	ADJ
cana-2015	390	7	analysis	analysis	NOUN
cana-2015	390	8	issn	issn	NOUN
cana-2015	390	9	:	:	PUNCT
cana-2015	390	10	1074	1074	NUM
cana-2015	390	11	-	-	PUNCT
cana-2015	390	12	133x	133x	NUM
cana-2015	390	13	vol	vol	NOUN
cana-2015	390	14	32	32	NUM
cana-2015	390	15	no	no	NOUN
cana-2015	390	16	.	.	NOUN
cana-2015	390	17	3	3	NUM
cana-2015	390	18	(	(	PUNCT
cana-2015	390	19	2025	2025	NUM
cana-2015	390	20	)	)	PUNCT
cana-2015	390	21	acknowledgment	acknowledgment	NOUN
cana-2015	390	22	.	.	PUNCT
cana-2015	391	1	this	this	DET
cana-2015	391	2	research	research	NOUN
cana-2015	391	3	was	be	AUX
cana-2015	391	4	supported	support	VERB
cana-2015	391	5	by	by	ADP
cana-2015	391	6	the	the	DET
cana-2015	391	7	university	university	NOUN
cana-2015	391	8	of	of	ADP
cana-2015	391	9	phayao	phayao	NOUN
cana-2015	391	10	and	and	CCONJ
cana-2015	391	11	the	the	DET
cana-2015	391	12	thailand	thailand	PROPN
cana-2015	391	13	science	science	PROPN
cana-2015	391	14	research	research	PROPN
cana-2015	391	15	and	and	CCONJ
cana-2015	391	16	innovation	innovation	NOUN
cana-2015	391	17	fund	fund	NOUN
cana-2015	391	18	(	(	PUNCT
cana-2015	391	19	fundamental	fundamental	ADJ
cana-2015	391	20	fund	fund	NOUN
cana-2015	391	21	2025	2025	NUM
cana-2015	391	22	)	)	PUNCT
cana-2015	391	23	.	.	PUNCT
cana-2015	392	1	conflicts	conflict	NOUN
cana-2015	392	2	of	of	ADP
cana-2015	392	3	interest	interest	NOUN
cana-2015	392	4	the	the	DET
cana-2015	392	5	author(s	author(s	NOUN
cana-2015	392	6	)	)	PUNCT
cana-2015	392	7	declare	declare	VERB
cana-2015	392	8	that	that	SCONJ
cana-2015	392	9	there	there	PRON
cana-2015	392	10	are	be	VERB
cana-2015	392	11	no	no	DET
cana-2015	392	12	conflicts	conflict	NOUN
cana-2015	392	13	of	of	ADP
cana-2015	392	14	interest	interest	NOUN
cana-2015	392	15	regarding	regard	VERB
cana-2015	392	16	the	the	DET
cana-2015	392	17	publication	publication	NOUN
cana-2015	392	18	of	of	ADP
cana-2015	392	19	this	this	DET
cana-2015	392	20	paper	paper	NOUN
cana-2015	392	21	.	.	PUNCT
cana-2015	393	1	references	reference	NOUN
cana-2015	393	2	[	[	X
cana-2015	393	3	1	1	NUM
cana-2015	393	4	]	]	X
cana-2015	393	5	zadeh	zadeh	PROPN
cana-2015	393	6	,	,	PUNCT
cana-2015	393	7	l.a	l.a	PROPN
cana-2015	393	8	.	.	PROPN
cana-2015	393	9	(	(	PUNCT
cana-2015	393	10	1965	1965	NUM
cana-2015	393	11	)	)	PUNCT
cana-2015	393	12	.	.	PUNCT
cana-2015	394	1	fuzzy	fuzzy	ADJ
cana-2015	394	2	sets	set	NOUN
cana-2015	394	3	.	.	PUNCT
cana-2015	395	1	information	information	NOUN
cana-2015	395	2	and	and	CCONJ
cana-2015	395	3	control	control	NOUN
cana-2015	395	4	,	,	PUNCT
cana-2015	395	5	8(3	8(3	NUM
cana-2015	395	6	)	)	PUNCT
cana-2015	395	7	,	,	PUNCT
cana-2015	395	8	338	338	NUM
cana-2015	395	9	-	-	SYM
cana-2015	395	10	353	353	NUM
cana-2015	395	11	.	.	PUNCT
cana-2015	396	1	[	[	X
cana-2015	396	2	2	2	NUM
cana-2015	396	3	]	]	PUNCT
cana-2015	396	4	atanassov	atanassov	NOUN
cana-2015	396	5	,	,	PUNCT
cana-2015	396	6	k.	k.	PROPN
cana-2015	396	7	(	(	PUNCT
cana-2015	396	8	1986	1986	NUM
cana-2015	396	9	)	)	PUNCT
cana-2015	396	10	.	.	PUNCT
cana-2015	397	1	intuitionistic	intuitionistic	ADJ
cana-2015	397	2	fuzzy	fuzzy	ADJ
cana-2015	397	3	sets	set	NOUN
cana-2015	397	4	.	.	PUNCT
cana-2015	398	1	fuzzy	fuzzy	ADJ
cana-2015	398	2	sets	set	NOUN
cana-2015	398	3	and	and	CCONJ
cana-2015	398	4	systems	system	NOUN
cana-2015	398	5	,	,	PUNCT
cana-2015	398	6	20(1	20(1	NUM
cana-2015	398	7	)	)	PUNCT
cana-2015	398	8	,	,	PUNCT
cana-2015	398	9	87	87	NUM
cana-2015	398	10	-	-	SYM
cana-2015	398	11	96	96	NUM
cana-2015	398	12	.	.	PUNCT
cana-2015	399	1	[	[	X
cana-2015	399	2	3	3	NUM
cana-2015	399	3	]	]	X
cana-2015	399	4	gorzalczany	gorzalczany	NOUN
cana-2015	399	5	,	,	PUNCT
cana-2015	399	6	m.	m.	NOUN
cana-2015	399	7	(	(	PUNCT
cana-2015	399	8	1987	1987	NUM
cana-2015	399	9	)	)	PUNCT
cana-2015	399	10	.	.	PUNCT
cana-2015	400	1	a	a	DET
cana-2015	400	2	method	method	NOUN
cana-2015	400	3	of	of	ADP
cana-2015	400	4	inference	inference	NOUN
cana-2015	400	5	in	in	ADP
cana-2015	400	6	approximate	approximate	ADJ
cana-2015	400	7	reasoning	reasoning	NOUN
cana-2015	400	8	based	base	VERB
cana-2015	400	9	on	on	ADP
cana-2015	400	10	interval	interval	NOUN
cana-2015	400	11	valued	value	VERB
cana-2015	400	12	fuzzy	fuzzy	ADJ
cana-2015	400	13	sets	set	NOUN
cana-2015	400	14	.	.	PUNCT
cana-2015	401	1	fuzzy	fuzzy	ADJ
cana-2015	401	2	sets	set	NOUN
cana-2015	401	3	and	and	CCONJ
cana-2015	401	4	systems	system	NOUN
cana-2015	401	5	,	,	PUNCT
cana-2015	401	6	21	21	NUM
cana-2015	401	7	,	,	PUNCT
cana-2015	401	8	1	1	NUM
cana-2015	401	9	-	-	SYM
cana-2015	401	10	17	17	NUM
cana-2015	401	11	.	.	PUNCT
cana-2015	402	1	[	[	X
cana-2015	402	2	4	4	NUM
cana-2015	402	3	]	]	X
cana-2015	402	4	biswas	biswas	PROPN
cana-2015	402	5	,	,	PUNCT
cana-2015	402	6	r.	r.	PROPN
cana-2015	402	7	(	(	PUNCT
cana-2015	402	8	2006	2006	NUM
cana-2015	402	9	)	)	PUNCT
cana-2015	402	10	.	.	PUNCT
cana-2015	403	1	vague	vague	ADJ
cana-2015	403	2	groups	group	NOUN
cana-2015	403	3	.	.	PUNCT
cana-2015	404	1	international	international	ADJ
cana-2015	404	2	journal	journal	NOUN
cana-2015	404	3	of	of	ADP
cana-2015	404	4	computational	computational	ADJ
cana-2015	404	5	cognition	cognition	NOUN
cana-2015	404	6	,	,	PUNCT
cana-2015	404	7	4(2	4(2	NUM
cana-2015	404	8	)	)	PUNCT
cana-2015	404	9	,	,	PUNCT
cana-2015	404	10	20	20	NUM
cana-2015	404	11	-	-	SYM
cana-2015	404	12	23	23	NUM
cana-2015	404	13	.	.	PUNCT
cana-2015	405	1	[	[	X
cana-2015	405	2	5	5	NUM
cana-2015	405	3	]	]	SYM
cana-2015	405	4	yager	yager	NOUN
cana-2015	405	5	,	,	PUNCT
cana-2015	405	6	r.r	r.r	PROPN
cana-2015	405	7	.	.	PROPN
cana-2015	405	8	(	(	PUNCT
cana-2015	405	9	2014	2014	NUM
cana-2015	405	10	)	)	PUNCT
cana-2015	405	11	.	.	PUNCT
cana-2015	406	1	pythagorean	pythagorean	PROPN
cana-2015	406	2	membership	membership	NOUN
cana-2015	406	3	grades	grade	NOUN
cana-2015	406	4	in	in	ADP
cana-2015	406	5	multi	multi	ADJ
cana-2015	406	6	criteria	criterion	NOUN
cana-2015	406	7	decision	decision	NOUN
cana-2015	406	8	-	-	PUNCT
cana-2015	406	9	making	making	NOUN
cana-2015	406	10	.	.	PUNCT
cana-2015	407	1	ieee	ieee	PROPN
cana-2015	407	2	trans	trans	PROPN
cana-2015	407	3	.	.	PUNCT
cana-2015	407	4	fuzzy	fuzzy	ADJ
cana-2015	407	5	systems	system	NOUN
cana-2015	407	6	,	,	PUNCT
cana-2015	407	7	22	22	NUM
cana-2015	407	8	,	,	PUNCT
cana-2015	407	9	958	958	NUM
cana-2015	407	10	-	-	SYM
cana-2015	407	11	965	965	NUM
cana-2015	407	12	.	.	PUNCT
cana-2015	408	1	[	[	X
cana-2015	408	2	6	6	NUM
cana-2015	408	3	]	]	X
cana-2015	408	4	peng	peng	PROPN
cana-2015	408	5	,	,	PUNCT
cana-2015	408	6	x.	x.	PROPN
cana-2015	408	7	,	,	PUNCT
cana-2015	408	8	yang	yang	PROPN
cana-2015	408	9	,	,	PUNCT
cana-2015	408	10	y.	y.	PROPN
cana-2015	408	11	(	(	PUNCT
cana-2015	408	12	2016	2016	NUM
cana-2015	408	13	)	)	PUNCT
cana-2015	408	14	.	.	PUNCT
cana-2015	409	1	fundamental	fundamental	ADJ
cana-2015	409	2	properties	property	NOUN
cana-2015	409	3	of	of	ADP
cana-2015	409	4	interval	interval	NOUN
cana-2015	409	5	valued	value	VERB
cana-2015	409	6	pythagorean	pythagorean	PROPN
cana-2015	409	7	fuzzy	fuzzy	ADJ
cana-2015	409	8	aggregation	aggregation	NOUN
cana-2015	409	9	operators	operator	NOUN
cana-2015	409	10	.	.	PUNCT
cana-2015	410	1	international	international	ADJ
cana-2015	410	2	journal	journal	NOUN
cana-2015	410	3	of	of	ADP
cana-2015	410	4	intelligent	intelligent	ADJ
cana-2015	410	5	systems	system	NOUN
cana-2015	410	6	,	,	PUNCT
cana-2015	410	7	31(5	31(5	NUM
cana-2015	410	8	)	)	PUNCT
cana-2015	410	9	(	(	PUNCT
cana-2015	410	10	2016	2016	NUM
cana-2015	410	11	)	)	PUNCT
cana-2015	410	12	,	,	PUNCT
cana-2015	410	13	444	444	NUM
cana-2015	410	14	-	-	SYM
cana-2015	410	15	487	487	NUM
cana-2015	410	16	.	.	PUNCT
cana-2015	411	1	[	[	X
cana-2015	411	2	7	7	NUM
cana-2015	411	3	]	]	PUNCT
cana-2015	411	4	ashraf	ashraf	NOUN
cana-2015	411	5	,	,	PUNCT
cana-2015	411	6	s.	s.	PROPN
cana-2015	411	7	,	,	PUNCT
cana-2015	411	8	abdullah	abdullah	PROPN
cana-2015	411	9	,	,	PUNCT
cana-2015	411	10	s.	s.	PROPN
cana-2015	411	11	,	,	PUNCT
cana-2015	411	12	mahmood	mahmood	PROPN
cana-2015	411	13	,	,	PUNCT
cana-2015	411	14	t.	t.	PROPN
cana-2015	411	15	,	,	PUNCT
cana-2015	411	16	ghani	ghani	PROPN
cana-2015	411	17	,	,	PUNCT
cana-2015	411	18	f.	f.	PROPN
cana-2015	411	19	,	,	PUNCT
cana-2015	411	20	mahmood	mahmood	PROPN
cana-2015	411	21	,	,	PUNCT
cana-2015	411	22	t.	t.	PROPN
cana-2015	411	23	(	(	PUNCT
cana-2015	411	24	2019	2019	NUM
cana-2015	411	25	)	)	PUNCT
cana-2015	411	26	.	.	PUNCT
cana-2015	412	1	spherical	spherical	ADJ
cana-2015	412	2	fuzzy	fuzzy	ADJ
cana-2015	412	3	sets	set	NOUN
cana-2015	412	4	and	and	CCONJ
cana-2015	412	5	their	their	PRON
cana-2015	412	6	applications	application	NOUN
cana-2015	412	7	in	in	ADP
cana-2015	412	8	multi	multi	ADJ
cana-2015	412	9	-	-	ADJ
cana-2015	412	10	attribute	attribute	NOUN
cana-2015	412	11	decision	decision	NOUN
cana-2015	412	12	making	make	VERB
cana-2015	412	13	problems	problem	NOUN
cana-2015	412	14	.	.	PUNCT
cana-2015	413	1	j.	j.	PROPN
cana-2015	413	2	intell	intell	PROPN
cana-2015	413	3	.	.	PUNCT
cana-2015	414	1	fuzzy	fuzzy	ADJ
cana-2015	414	2	syst	syst	PROPN
cana-2015	414	3	.	.	PUNCT
cana-2015	414	4	,	,	PUNCT
cana-2015	414	5	36	36	NUM
cana-2015	414	6	,	,	PUNCT
cana-2015	414	7	2829	2829	NUM
cana-2015	414	8	-	-	SYM
cana-2015	414	9	284	284	NUM
cana-2015	414	10	.	.	PUNCT
cana-2015	415	1	[	[	X
cana-2015	415	2	8	8	NUM
cana-2015	415	3	]	]	X
cana-2015	415	4	smarandache	smarandache	NOUN
cana-2015	415	5	,	,	PUNCT
cana-2015	415	6	f.	f.	PROPN
cana-2015	415	7	,	,	PUNCT
cana-2015	415	8	unifying	unifying	NOUN
cana-2015	415	9	,	,	PUNCT
cana-2015	415	10	a.	a.	NOUN
cana-2015	415	11	(	(	PUNCT
cana-2015	415	12	2002	2002	NUM
cana-2015	415	13	)	)	PUNCT
cana-2015	415	14	.	.	PUNCT
cana-2015	416	1	field	field	NOUN
cana-2015	416	2	in	in	ADP
cana-2015	416	3	logics	logic	NOUN
cana-2015	416	4	neutrosophic	neutrosophic	ADJ
cana-2015	416	5	logic	logic	NOUN
cana-2015	416	6	,	,	PUNCT
cana-2015	416	7	multiple	multiple	ADJ
cana-2015	416	8	valued	value	VERB
cana-2015	416	9	logic	logic	NOUN
cana-2015	416	10	.	.	PUNCT
cana-2015	417	1	an	an	DET
cana-2015	417	2	international	international	ADJ
cana-2015	417	3	journal	journal	NOUN
cana-2015	417	4	,	,	PUNCT
cana-2015	417	5	8(3	8(3	NUM
cana-2015	417	6	)	)	PUNCT
cana-2015	417	7	,	,	PUNCT
cana-2015	417	8	385	385	NUM
cana-2015	417	9	-	-	SYM
cana-2015	417	10	438	438	NUM
cana-2015	417	11	.	.	PUNCT
cana-2015	418	1	[	[	X
cana-2015	418	2	9	9	NUM
cana-2015	418	3	]	]	X
cana-2015	418	4	cuong	cuong	PROPN
cana-2015	418	5	,	,	PUNCT
cana-2015	418	6	b.	b.	PROPN
cana-2015	418	7	c.	c.	PROPN
cana-2015	418	8	,	,	PUNCT
cana-2015	418	9	kreinovich	kreinovich	PROPN
cana-2015	418	10	,	,	PUNCT
cana-2015	418	11	v.	v.	PROPN
cana-2015	418	12	(	(	PUNCT
cana-2015	418	13	2013	2013	NUM
cana-2015	418	14	)	)	PUNCT
cana-2015	418	15	.	.	PUNCT
cana-2015	419	1	picture	picture	NOUN
cana-2015	419	2	fuzzy	fuzzy	ADJ
cana-2015	419	3	sets	set	VERB
cana-2015	419	4	a	a	DET
cana-2015	419	5	new	new	ADJ
cana-2015	419	6	concept	concept	NOUN
cana-2015	419	7	for	for	ADP
cana-2015	419	8	computational	computational	ADJ
cana-2015	419	9	intelligence	intelligence	NOUN
cana-2015	419	10	problems	problem	NOUN
cana-2015	419	11	,	,	PUNCT
cana-2015	419	12	in	in	ADP
cana-2015	419	13	proceedings	proceeding	NOUN
cana-2015	419	14	of	of	ADP
cana-2015	419	15	2013	2013	NUM
cana-2015	419	16	third	third	ADJ
cana-2015	419	17	world	world	NOUN
cana-2015	419	18	congress	congress	PROPN
cana-2015	419	19	on	on	ADP
cana-2015	419	20	information	information	NOUN
cana-2015	419	21	and	and	CCONJ
cana-2015	419	22	communication	communication	NOUN
cana-2015	419	23	technologies	technology	NOUN
cana-2015	419	24	(	(	PUNCT
cana-2015	419	25	wict	wict	NOUN
cana-2015	419	26	2013	2013	NUM
cana-2015	419	27	)	)	PUNCT
cana-2015	419	28	,	,	PUNCT
cana-2015	419	29	ieee	ieee	NOUN
cana-2015	419	30	,	,	PUNCT
cana-2015	419	31	1	1	NUM
cana-2015	419	32	-	-	SYM
cana-2015	419	33	6	6	NUM
cana-2015	419	34	.	.	PUNCT
cana-2015	420	1	[	[	X
cana-2015	420	2	10	10	NUM
cana-2015	420	3	]	]	X
cana-2015	420	4	palanikumar	palanikumar	PROPN
cana-2015	420	5	,	,	PUNCT
cana-2015	420	6	m.	m.	NOUN
cana-2015	420	7	,	,	PUNCT
cana-2015	420	8	arulmozhi	arulmozhi	PROPN
cana-2015	420	9	,	,	PUNCT
cana-2015	420	10	k.	k.	PROPN
cana-2015	420	11	,	,	PUNCT
cana-2015	420	12	jana	jana	PROPN
cana-2015	420	13	,	,	PUNCT
cana-2015	420	14	c	c	X
cana-2015	420	15	,	,	PUNCT
cana-2015	420	16	multiple	multiple	ADJ
cana-2015	420	17	attribute	attribute	NOUN
cana-2015	420	18	decision	decision	NOUN
cana-2015	420	19	-	-	PUNCT
cana-2015	420	20	making	make	VERB
cana-2015	420	21	approach	approach	NOUN
cana-2015	420	22	for	for	ADP
cana-2015	420	23	pythagorean	pythagorean	PROPN
cana-2015	420	24	neutrosophic	neutrosophic	ADJ
cana-2015	420	25	normal	normal	ADJ
cana-2015	420	26	interval	interval	NOUN
cana-2015	420	27	-	-	PUNCT
cana-2015	420	28	valued	value	VERB
cana-2015	420	29	fuzzy	fuzzy	ADJ
cana-2015	420	30	aggregation	aggregation	NOUN
cana-2015	420	31	operators	operator	NOUN
cana-2015	420	32	,	,	PUNCT
cana-2015	420	33	computational	computational	ADJ
cana-2015	420	34	and	and	CCONJ
cana-2015	420	35	applied	applied	ADJ
cana-2015	420	36	mathematics	mathematic	NOUN
cana-2015	420	37	41	41	NUM
cana-2015	420	38	(	(	PUNCT
cana-2015	420	39	3	3	NUM
cana-2015	420	40	)	)	PUNCT
cana-2015	420	41	,	,	PUNCT
cana-2015	420	42	90	90	NUM
cana-2015	420	43	,	,	PUNCT
cana-2015	420	44	2022	2022	NUM
cana-2015	420	45	.	.	PUNCT
cana-2015	421	1	[	[	X
cana-2015	421	2	11	11	NUM
cana-2015	421	3	]	]	X
cana-2015	421	4	palanikumar	palanikumar	PROPN
cana-2015	421	5	,	,	PUNCT
cana-2015	421	6	m.	m.	NOUN
cana-2015	421	7	,	,	PUNCT
cana-2015	421	8	arulmozhi	arulmozhi	PROPN
cana-2015	421	9	,	,	PUNCT
cana-2015	421	10	k.	k.	PROPN
cana-2015	421	11	,	,	PUNCT
cana-2015	421	12	jana	jana	PROPN
cana-2015	421	13	,	,	PUNCT
cana-2015	421	14	c	c	PROPN
cana-2015	421	15	,	,	PUNCT
cana-2015	421	16	pal	pal	NOUN
cana-2015	421	17	,	,	PUNCT
cana-2015	421	18	m.	m.	NOUN
cana-2015	421	19	,	,	PUNCT
cana-2015	421	20	multiple	multiple	ADJ
cana-2015	421	21	attribute	attribute	NOUN
cana-2015	421	22	decision	decision	NOUN
cana-2015	421	23	making	make	VERB
cana-2015	421	24	spherical	spherical	ADJ
cana-2015	421	25	vague	vague	ADJ
cana-2015	421	26	normal	normal	ADJ
cana-2015	421	27	operators	operator	NOUN
cana-2015	421	28	and	and	CCONJ
cana-2015	421	29	their	their	PRON
cana-2015	421	30	applications	application	NOUN
cana-2015	421	31	for	for	ADP
cana-2015	421	32	the	the	DET
cana-2015	421	33	selection	selection	NOUN
cana-2015	421	34	of	of	ADP
cana-2015	421	35	farmers	farmer	NOUN
cana-2015	421	36	,	,	PUNCT
cana-2015	421	37	expert	expert	NOUN
cana-2015	421	38	systems	system	NOUN
cana-2015	421	39	40	40	NUM
cana-2015	421	40	(	(	PUNCT
cana-2015	421	41	3	3	NUM
cana-2015	421	42	)	)	PUNCT
cana-2015	421	43	,	,	PUNCT
cana-2015	421	44	e13188	e13188	ADJ
cana-2015	421	45	,	,	PUNCT
cana-2015	421	46	2022	2022	NUM
cana-2015	421	47	.	.	PUNCT
cana-2015	422	1	[	[	X
cana-2015	422	2	12	12	NUM
cana-2015	422	3	]	]	X
cana-2015	422	4	palanikumar	palanikumar	PROPN
cana-2015	422	5	,	,	PUNCT
cana-2015	422	6	m.	m.	NOUN
cana-2015	422	7	,	,	PUNCT
cana-2015	422	8	arulmozhi	arulmozhi	PROPN
cana-2015	422	9	,	,	PUNCT
cana-2015	422	10	k.	k.	PROPN
cana-2015	422	11	,	,	PUNCT
cana-2015	422	12	mcgdm	mcgdm	NOUN
cana-2015	422	13	based	base	VERB
cana-2015	422	14	on	on	ADP
cana-2015	422	15	topsis	topsis	NOUN
cana-2015	422	16	and	and	CCONJ
cana-2015	422	17	vikor	vikor	ADJ
cana-2015	422	18	using	use	VERB
cana-2015	422	19	pythagorean	pythagorean	PROPN
cana-2015	422	20	neutrosophic	neutrosophic	PROPN
cana-2015	422	21	soft	soft	ADJ
cana-2015	422	22	with	with	ADP
cana-2015	422	23	aggregation	aggregation	NOUN
cana-2015	422	24	operators	operator	NOUN
cana-2015	422	25	,	,	PUNCT
cana-2015	422	26	neutrosophic	neutrosophic	ADJ
cana-2015	422	27	sets	set	NOUN
cana-2015	422	28	and	and	CCONJ
cana-2015	422	29	systems	system	NOUN
cana-2015	422	30	,	,	PUNCT
cana-2015	422	31	,	,	PUNCT
cana-2015	422	32	538	538	NUM
cana-2015	422	33	-	-	SYM
cana-2015	422	34	555	555	NUM
cana-2015	422	35	,	,	PUNCT
cana-2015	422	36	2022	2022	NUM
cana-2015	422	37	.	.	PUNCT
cana-2015	423	1	[	[	X
cana-2015	423	2	13	13	NUM
cana-2015	423	3	]	]	PUNCT
cana-2015	423	4	n	n	PRON
cana-2015	423	5	kausar	kausar	NOUN
cana-2015	423	6	,	,	PUNCT
cana-2015	423	7	h	h	NOUN
cana-2015	423	8	garg	garg	NOUN
cana-2015	423	9	,	,	PUNCT
cana-2015	423	10	a	a	DET
cana-2015	423	11	iampan	iampan	NOUN
cana-2015	423	12	,	,	PUNCT
cana-2015	423	13	s	s	NOUN
cana-2015	423	14	kadry	kadry	NOUN
cana-2015	423	15	,	,	PUNCT
cana-2015	423	16	m	m	VERB
cana-2015	423	17	sharaf	sharaf	NOUN
cana-2015	423	18	,	,	PUNCT
cana-2015	423	19	medical	medical	ADJ
cana-2015	423	20	robotic	robotic	ADJ
cana-2015	423	21	engineering	engineering	NOUN
cana-2015	423	22	selection	selection	NOUN
cana-2015	423	23	based	base	VERB
cana-2015	423	24	on	on	ADP
cana-2015	423	25	square	square	ADJ
cana-2015	423	26	root	root	NOUN
cana-2015	423	27	neutrosophic	neutrosophic	ADJ
cana-2015	423	28	normal	normal	ADJ
cana-2015	423	29	interval	interval	NOUN
cana-2015	423	30	-	-	PUNCT
cana-2015	423	31	valued	value	VERB
cana-2015	423	32	sets	set	NOUN
cana-2015	423	33	and	and	CCONJ
cana-2015	423	34	their	their	PRON
cana-2015	423	35	aggregated	aggregate	VERB
cana-2015	423	36	operators	operator	NOUN
cana-2015	423	37	,	,	PUNCT
cana-2015	423	38	aims	aim	VERB
cana-2015	423	39	mathematics	mathematic	NOUN
cana-2015	423	40	,	,	PUNCT
cana-2015	423	41	8(8	8(8	NUM
cana-2015	423	42	)	)	PUNCT
cana-2015	423	43	,	,	PUNCT
cana-2015	423	44	2023	2023	NUM
cana-2015	423	45	,	,	PUNCT
cana-2015	423	46	17402	17402	NUM
cana-2015	423	47	-	-	SYM
cana-2015	423	48	17432	17432	NUM
cana-2015	423	49	.	.	PUNCT
cana-2015	424	1	[	[	X
cana-2015	424	2	14	14	NUM
cana-2015	424	3	]	]	X
cana-2015	424	4	palanikumar	palanikumar	PROPN
cana-2015	424	5	,	,	PUNCT
cana-2015	424	6	m.	m.	NOUN
cana-2015	424	7	,	,	PUNCT
cana-2015	424	8	iampan	iampan	PROPN
cana-2015	424	9	,	,	PUNCT
cana-2015	424	10	a	a	DET
cana-2015	424	11	,	,	PUNCT
cana-2015	424	12	spherical	spherical	ADJ
cana-2015	424	13	fermatean	fermatean	NOUN
cana-2015	424	14	interval	interval	NOUN
cana-2015	424	15	valued	value	VERB
cana-2015	424	16	fuzzy	fuzzy	ADJ
cana-2015	424	17	soft	soft	ADJ
cana-2015	424	18	set	set	NOUN
cana-2015	424	19	based	base	VERB
cana-2015	424	20	on	on	ADP
cana-2015	424	21	multi	multi	ADJ
cana-2015	424	22	criteria	criterion	NOUN
cana-2015	424	23	group	group	NOUN
cana-2015	424	24	decision	decision	NOUN
cana-2015	424	25	making	making	NOUN
cana-2015	424	26	,	,	PUNCT
cana-2015	424	27	international	international	ADJ
cana-2015	424	28	journal	journal	NOUN
cana-2015	424	29	of	of	ADP
cana-2015	424	30	innovative	innovative	ADJ
cana-2015	424	31	computing	computing	NOUN
cana-2015	424	32	,	,	PUNCT
cana-2015	424	33	information	information	NOUN
cana-2015	424	34	and	and	CCONJ
cana-2015	424	35	control	control	NOUN
cana-2015	424	36	2022	2022	NUM
cana-2015	424	37	,	,	PUNCT
cana-2015	424	38	18(2	18(2	NUM
cana-2015	424	39	)	)	PUNCT
cana-2015	424	40	,	,	PUNCT
cana-2015	424	41	607–619	607–619	NUM
cana-2015	424	42	.	.	PUNCT
cana-2015	425	1	[	[	X
cana-2015	425	2	15	15	NUM
cana-2015	425	3	]	]	X
cana-2015	425	4	palanikumar	palanikumar	PROPN
cana-2015	425	5	,	,	PUNCT
cana-2015	425	6	m.	m.	NOUN
cana-2015	425	7	,	,	PUNCT
cana-2015	425	8	iampan	iampan	PROPN
cana-2015	425	9	,	,	PUNCT
cana-2015	425	10	a	a	DET
cana-2015	425	11	,	,	PUNCT
cana-2015	425	12	novel	novel	ADJ
cana-2015	425	13	approach	approach	NOUN
cana-2015	425	14	to	to	ADP
cana-2015	425	15	decision	decision	NOUN
cana-2015	425	16	making	making	NOUN
cana-2015	425	17	based	base	VERB
cana-2015	425	18	on	on	ADP
cana-2015	425	19	type	type	NOUN
cana-2015	425	20	-	-	PUNCT
cana-2015	425	21	ii	ii	NOUN
cana-2015	425	22	extended	extend	VERB
cana-2015	425	23	fermatean	fermatean	ADJ
cana-2015	425	24	bipolar	bipolar	ADJ
cana-2015	425	25	fuzzy	fuzzy	ADJ
cana-2015	425	26	soft	soft	ADJ
cana-2015	425	27	sets	set	NOUN
cana-2015	425	28	,	,	PUNCT
cana-2015	425	29	international	international	ADJ
cana-2015	425	30	journal	journal	NOUN
cana-2015	425	31	of	of	ADP
cana-2015	425	32	innovative	innovative	ADJ
cana-2015	425	33	computing	computing	NOUN
cana-2015	425	34	,	,	PUNCT
cana-2015	425	35	information	information	NOUN
cana-2015	425	36	and	and	CCONJ
cana-2015	425	37	control	control	NOUN
cana-2015	425	38	2022	2022	NUM
cana-2015	425	39	,	,	PUNCT
cana-2015	425	40	18(3	18(3	NUM
cana-2015	425	41	)	)	PUNCT
cana-2015	425	42	,	,	PUNCT
cana-2015	425	43	769–781	769–781	NUM
cana-2015	425	44	.	.	PUNCT
cana-2015	426	1	[	[	X
cana-2015	426	2	16	16	NUM
cana-2015	426	3	]	]	X
cana-2015	426	4	liu	liu	PROPN
cana-2015	426	5	,	,	PUNCT
cana-2015	426	6	w.f	w.f	PROPN
cana-2015	426	7	.	.	PROPN
cana-2015	426	8	,	,	PUNCT
cana-2015	426	9	chang	chang	PROPN
cana-2015	426	10	,	,	PUNCT
cana-2015	426	11	j.	j.	PROPN
cana-2015	426	12	,	,	PUNCT
cana-2015	426	13	he	he	PRON
cana-2015	426	14	,	,	PUNCT
cana-2015	426	15	x.	x.	NOUN
cana-2015	426	16	(	(	PUNCT
cana-2015	426	17	2016	2016	NUM
cana-2015	426	18	)	)	PUNCT
cana-2015	426	19	.	.	PUNCT
cana-2015	426	20	extended	extend	VERB
cana-2015	426	21	pythagorean	pythagorean	PROPN
cana-2015	426	22	fuzzy	fuzzy	ADJ
cana-2015	426	23	aggregation	aggregation	NOUN
cana-2015	426	24	operators	operator	NOUN
cana-2015	426	25	and	and	CCONJ
cana-2015	426	26	applications	application	NOUN
cana-2015	426	27	in	in	ADP
cana-2015	426	28	decision	decision	NOUN
cana-2015	426	29	making	making	NOUN
cana-2015	426	30	.	.	PUNCT
cana-2015	427	1	control	control	PROPN
cana-2015	427	2	decis	decis	PROPN
cana-2015	427	3	.	.	PROPN
cana-2015	427	4	31	31	NUM
cana-2015	427	5	,	,	PUNCT
cana-2015	427	6	2280	2280	NUM
cana-2015	427	7	-	-	SYM
cana-2015	427	8	2286	2286	NUM
cana-2015	427	9	.	.	PUNCT
cana-2015	428	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2015	428	2	548	548	NUM
cana-2015	428	3	communications	communication	NOUN
cana-2015	428	4	on	on	ADP
cana-2015	428	5	applied	apply	VERB
cana-2015	428	6	nonlinear	nonlinear	ADJ
cana-2015	428	7	analysis	analysis	NOUN
cana-2015	428	8	issn	issn	NOUN
cana-2015	428	9	:	:	PUNCT
cana-2015	428	10	1074	1074	NUM
cana-2015	428	11	-	-	PUNCT
cana-2015	428	12	133x	133x	NUM
cana-2015	428	13	vol	vol	NOUN
cana-2015	428	14	32	32	NUM
cana-2015	428	15	no	no	NOUN
cana-2015	428	16	.	.	NOUN
cana-2015	428	17	3	3	NUM
cana-2015	428	18	(	(	PUNCT
cana-2015	428	19	2025	2025	NUM
cana-2015	428	20	)	)	PUNCT
cana-2015	429	1	[	[	X
cana-2015	429	2	17	17	NUM
cana-2015	429	3	]	]	X
cana-2015	429	4	palanikumar	palanikumar	PROPN
cana-2015	429	5	,	,	PUNCT
cana-2015	429	6	m.	m.	NOUN
cana-2015	429	7	,	,	PUNCT
cana-2015	429	8	arulmozhi	arulmozhi	PROPN
cana-2015	429	9	,	,	PUNCT
cana-2015	429	10	k.	k.	PROPN
cana-2015	429	11	,	,	PUNCT
cana-2015	429	12	iampan	iampan	PROPN
cana-2015	429	13	,	,	PUNCT
cana-2015	429	14	a.	a.	NOUN
cana-2015	429	15	,	,	PUNCT
cana-2015	429	16	multi	multi	X
cana-2015	429	17	criteria	criterion	NOUN
cana-2015	429	18	group	group	NOUN
cana-2015	429	19	decision	decision	NOUN
cana-2015	429	20	making	making	NOUN
cana-2015	429	21	based	base	VERB
cana-2015	429	22	on	on	ADP
cana-2015	429	23	vikor	vikor	ADJ
cana-2015	429	24	and	and	CCONJ
cana-2015	429	25	topsis	topsis	NOUN
cana-2015	429	26	methods	method	NOUN
cana-2015	429	27	for	for	ADP
cana-2015	429	28	fermatean	fermatean	ADJ
cana-2015	429	29	fuzzy	fuzzy	ADJ
cana-2015	429	30	soft	soft	ADJ
cana-2015	429	31	with	with	ADP
cana-2015	429	32	aggregation	aggregation	NOUN
cana-2015	429	33	operators	operator	NOUN
cana-2015	429	34	,	,	PUNCT
cana-2015	429	35	icic	icic	PROPN
cana-2015	429	36	express	express	PROPN
cana-2015	429	37	letters	letter	NOUN
cana-2015	429	38	16	16	NUM
cana-2015	429	39	(	(	PUNCT
cana-2015	429	40	10	10	NUM
cana-2015	429	41	)	)	PUNCT
cana-2015	429	42	,	,	PUNCT
cana-2015	429	43	1129	1129	NUM
cana-2015	429	44	-	-	SYM
cana-2015	429	45	1138	1138	NUM
cana-2015	429	46	,	,	PUNCT
cana-2015	429	47	2022	2022	NUM
cana-2015	429	48	.	.	PUNCT
cana-2015	430	1	[	[	X
cana-2015	430	2	18	18	NUM
cana-2015	430	3	]	]	X
cana-2015	430	4	sg	sg	PROPN
cana-2015	430	5	quek	quek	PROPN
cana-2015	430	6	,	,	PUNCT
cana-2015	430	7	h	h	PROPN
cana-2015	430	8	garg	garg	NOUN
cana-2015	430	9	,	,	PUNCT
cana-2015	430	10	g	g	PROPN
cana-2015	430	11	selvachandran	selvachandran	VERB
cana-2015	430	12	,	,	PUNCT
cana-2015	430	13	m	m	NOUN
cana-2015	430	14	palanikumar	palanikumar	PROPN
cana-2015	430	15	,	,	PUNCT
cana-2015	430	16	k	k	PROPN
cana-2015	430	17	arulmozhi	arulmozhi	PROPN
cana-2015	430	18	,	,	PUNCT
cana-2015	430	19	vikor	vikor	ADJ
cana-2015	430	20	and	and	CCONJ
cana-2015	430	21	topsis	topsis	NOUN
cana-2015	430	22	framework	framework	NOUN
cana-2015	430	23	with	with	ADP
cana-2015	430	24	a	a	DET
cana-2015	430	25	truthful	truthful	ADJ
cana-2015	430	26	-	-	PUNCT
cana-2015	430	27	distance	distance	NOUN
cana-2015	430	28	measure	measure	NOUN
cana-2015	430	29	for	for	ADP
cana-2015	430	30	the	the	DET
cana-2015	430	31	(	(	PUNCT
cana-2015	430	32	t	t	PROPN
cana-2015	430	33	,	,	PUNCT
cana-2015	430	34	s)-regulated	s)-regulate	VERB
cana-2015	430	35	interval	interval	NOUN
cana-2015	430	36	-	-	PUNCT
cana-2015	430	37	valued	value	VERB
cana-2015	430	38	neutrosophic	neutrosophic	ADJ
cana-2015	430	39	soft	soft	ADJ
cana-2015	430	40	set	set	NOUN
cana-2015	430	41	,	,	PUNCT
cana-2015	430	42	soft	soft	ADJ
cana-2015	430	43	computing	computing	NOUN
cana-2015	430	44	,	,	PUNCT
cana-2015	430	45	1	1	NUM
cana-2015	430	46	-	-	SYM
cana-2015	430	47	27	27	NUM
cana-2015	430	48	,	,	PUNCT
cana-2015	430	49	2023	2023	NUM
cana-2015	430	50	.	.	PUNCT
cana-2015	431	1	[	[	X
cana-2015	431	2	19	19	NUM
cana-2015	431	3	]	]	X
cana-2015	431	4	smarandache	smarandache	NOUN
cana-2015	431	5	,	,	PUNCT
cana-2015	431	6	f.	f.	PROPN
cana-2015	431	7	(	(	PUNCT
cana-2015	431	8	1999	1999	NUM
cana-2015	431	9	)	)	PUNCT
cana-2015	431	10	.	.	PUNCT
cana-2015	432	1	a	a	DET
cana-2015	432	2	unifying	unifying	ADJ
cana-2015	432	3	field	field	NOUN
cana-2015	432	4	in	in	ADP
cana-2015	432	5	logics	logic	NOUN
cana-2015	432	6	,	,	PUNCT
cana-2015	432	7	neutrosophy	neutrosophy	NOUN
cana-2015	432	8	neutrosophic	neutrosophic	ADJ
cana-2015	432	9	probability	probability	NOUN
cana-2015	432	10	,	,	PUNCT
cana-2015	432	11	set	set	NOUN
cana-2015	432	12	and	and	CCONJ
cana-2015	432	13	logic	logic	NOUN
cana-2015	432	14	.	.	PUNCT
cana-2015	433	1	american	american	ADJ
cana-2015	433	2	research	research	PROPN
cana-2015	433	3	press	press	PROPN
cana-2015	433	4	,	,	PUNCT
cana-2015	433	5	rehoboth	rehoboth	NOUN
cana-2015	433	6	.	.	PUNCT
cana-2015	434	1	[	[	X
cana-2015	434	2	20	20	NUM
cana-2015	434	3	]	]	SYM
cana-2015	434	4	ye	ye	PROPN
cana-2015	434	5	,	,	PUNCT
cana-2015	434	6	j.	j.	PROPN
cana-2015	434	7	,	,	PUNCT
cana-2015	434	8	similarity	similarity	NOUN
cana-2015	434	9	measures	measure	NOUN
cana-2015	434	10	between	between	ADP
cana-2015	434	11	interval	interval	NOUN
cana-2015	434	12	neutrosophic	neutrosophic	ADJ
cana-2015	434	13	sets	set	NOUN
cana-2015	434	14	and	and	CCONJ
cana-2015	434	15	their	their	PRON
cana-2015	434	16	applications	application	NOUN
cana-2015	434	17	in	in	ADP
cana-2015	434	18	multi	multi	ADJ
cana-2015	434	19	-	-	ADJ
cana-2015	434	20	criteria	criterion	NOUN
cana-2015	434	21	decision	decision	NOUN
cana-2015	434	22	-	-	PUNCT
cana-2015	434	23	making	making	NOUN
cana-2015	434	24	.	.	PUNCT
cana-2015	435	1	journal	journal	NOUN
cana-2015	435	2	of	of	ADP
cana-2015	435	3	intelligent	intelligent	ADJ
cana-2015	435	4	and	and	CCONJ
cana-2015	435	5	fuzzy	fuzzy	ADJ
cana-2015	435	6	systems	system	NOUN
cana-2015	435	7	,	,	PUNCT
cana-2015	435	8	2014	2014	NUM
cana-2015	435	9	,	,	PUNCT
cana-2015	435	10	26	26	NUM
cana-2015	435	11	,	,	PUNCT
cana-2015	435	12	165	165	NUM
cana-2015	435	13	-	-	SYM
cana-2015	435	14	172	172	NUM
cana-2015	435	15	.	.	PUNCT
cana-2015	436	1	[	[	X
cana-2015	436	2	21	21	NUM
cana-2015	436	3	]	]	X
cana-2015	436	4	palanikumar	palanikumar	PROPN
cana-2015	436	5	,	,	PUNCT
cana-2015	436	6	m.	m.	NOUN
cana-2015	436	7	,	,	PUNCT
cana-2015	436	8	arulmozhi	arulmozhi	ADJ
cana-2015	436	9	,	,	PUNCT
cana-2015	436	10	k	k	PROPN
cana-2015	436	11	,	,	PUNCT
cana-2015	436	12	on	on	ADP
cana-2015	436	13	intuitionistic	intuitionistic	ADJ
cana-2015	436	14	fuzzy	fuzzy	ADJ
cana-2015	436	15	normal	normal	ADJ
cana-2015	436	16	subbisemiring	subbisemiring	NOUN
cana-2015	436	17	of	of	ADP
cana-2015	436	18	bisemiring	bisemiring	NOUN
cana-2015	436	19	,	,	PUNCT
cana-2015	436	20	nonlinear	nonlinear	ADJ
cana-2015	436	21	studies	study	NOUN
cana-2015	436	22	2021	2021	NUM
cana-2015	436	23	,	,	PUNCT
cana-2015	436	24	28(3	28(3	NUM
cana-2015	436	25	)	)	PUNCT
cana-2015	436	26	,	,	PUNCT
cana-2015	436	27	717	717	NUM
cana-2015	436	28	-	-	SYM
cana-2015	436	29	721	721	NUM
cana-2015	436	30	.	.	PUNCT
cana-2015	437	1	[	[	X
cana-2015	437	2	22	22	NUM
cana-2015	437	3	]	]	X
cana-2015	437	4	r.n	r.n	PROPN
cana-2015	437	5	.	.	PROPN
cana-2015	437	6	xu	xu	PROPN
cana-2015	437	7	and	and	CCONJ
cana-2015	437	8	c.l	c.l	PROPN
cana-2015	437	9	.	.	PROPN
cana-2015	437	10	li	li	PROPN
cana-2015	437	11	,	,	PUNCT
cana-2015	437	12	regression	regression	NOUN
cana-2015	437	13	prediction	prediction	NOUN
cana-2015	437	14	for	for	ADP
cana-2015	437	15	fuzzy	fuzzy	ADJ
cana-2015	437	16	time	time	NOUN
cana-2015	437	17	series	series	PROPN
cana-2015	437	18	,	,	PUNCT
cana-2015	437	19	appl	appl	PROPN
cana-2015	437	20	.	.	PROPN
cana-2015	437	21	math	math	PROPN
cana-2015	437	22	.	.	PUNCT
cana-2015	438	1	j.	j.	PROPN
cana-2015	438	2	chinese	chinese	PROPN
cana-2015	438	3	univ	univ	PROPN
cana-2015	438	4	.	.	PROPN
cana-2015	438	5	,	,	PUNCT
cana-2015	438	6	16	16	NUM
cana-2015	438	7	,	,	PUNCT
cana-2015	438	8	(	(	PUNCT
cana-2015	438	9	2001	2001	NUM
cana-2015	438	10	)	)	PUNCT
cana-2015	438	11	,	,	PUNCT
cana-2015	438	12	451	451	NUM
cana-2015	438	13	-	-	SYM
cana-2015	438	14	461	461	NUM
cana-2015	438	15	.	.	PUNCT
cana-2015	439	1	[	[	X
cana-2015	439	2	23	23	NUM
cana-2015	439	3	]	]	PUNCT
cana-2015	439	4	z.	z.	PROPN
cana-2015	439	5	xu	xu	PROPN
cana-2015	439	6	,	,	PUNCT
cana-2015	439	7	r.r	r.r	PROPN
cana-2015	439	8	.	.	PROPN
cana-2015	439	9	yager	yager	PROPN
cana-2015	439	10	,	,	PUNCT
cana-2015	439	11	some	some	DET
cana-2015	439	12	geometric	geometric	ADJ
cana-2015	439	13	aggregation	aggregation	NOUN
cana-2015	439	14	operators	operator	NOUN
cana-2015	439	15	based	base	VERB
cana-2015	439	16	on	on	ADP
cana-2015	439	17	intuitionistic	intuitionistic	ADJ
cana-2015	439	18	fuzzy	fuzzy	ADJ
cana-2015	439	19	sets	set	NOUN
cana-2015	439	20	,	,	PUNCT
cana-2015	439	21	int	int	NOUN
cana-2015	439	22	.	.	PUNCT
cana-2015	440	1	j.	j.	PROPN
cana-2015	440	2	gen	gen	PROPN
cana-2015	440	3	.	.	PROPN
cana-2015	440	4	syst	syst	PROPN
cana-2015	440	5	.	.	PROPN
cana-2015	440	6	35	35	NUM
cana-2015	440	7	,	,	PUNCT
cana-2015	440	8	(	(	PUNCT
cana-2015	440	9	2006	2006	NUM
cana-2015	440	10	)	)	PUNCT
cana-2015	440	11	,	,	PUNCT
cana-2015	440	12	417	417	NUM
cana-2015	440	13	-	-	SYM
cana-2015	440	14	433	433	NUM
cana-2015	440	15	.	.	PUNCT
cana-2015	441	1	[	[	X
cana-2015	441	2	24	24	NUM
cana-2015	441	3	]	]	X
cana-2015	441	4	d.f	d.f	PROPN
cana-2015	441	5	.	.	PROPN
cana-2015	441	6	li	li	PROPN
cana-2015	441	7	,	,	PUNCT
cana-2015	441	8	multi	multi	ADJ
cana-2015	441	9	-	-	ADJ
cana-2015	441	10	attribute	attribute	ADJ
cana-2015	441	11	decision	decision	NOUN
cana-2015	441	12	-	-	PUNCT
cana-2015	441	13	making	make	VERB
cana-2015	441	14	method	method	NOUN
cana-2015	441	15	based	base	VERB
cana-2015	441	16	on	on	ADP
cana-2015	441	17	generalized	generalized	ADJ
cana-2015	441	18	owa	owa	PROPN
cana-2015	441	19	operators	operator	NOUN
cana-2015	441	20	with	with	ADP
cana-2015	441	21	intuitionistic	intuitionistic	ADJ
cana-2015	441	22	fuzzy	fuzzy	ADJ
cana-2015	441	23	sets	set	NOUN
cana-2015	441	24	,	,	PUNCT
cana-2015	441	25	expert	expert	NOUN
cana-2015	441	26	syst	syst	NOUN
cana-2015	441	27	.	.	PUNCT
cana-2015	442	1	appl	appl	PROPN
cana-2015	442	2	.	.	PUNCT
cana-2015	443	1	37	37	NUM
cana-2015	443	2	,	,	PUNCT
cana-2015	443	3	(	(	PUNCT
cana-2015	443	4	2010	2010	NUM
cana-2015	443	5	)	)	PUNCT
cana-2015	443	6	,	,	PUNCT
cana-2015	443	7	8673	8673	NUM
cana-2015	443	8	-	-	SYM
cana-2015	443	9	8678	8678	NUM
cana-2015	443	10	.	.	PUNCT
cana-2015	444	1	[	[	X
cana-2015	444	2	25	25	NUM
cana-2015	444	3	]	]	PUNCT
cana-2015	444	4	s.	s.	PROPN
cana-2015	444	5	zeng	zeng	PROPN
cana-2015	444	6	,	,	PUNCT
cana-2015	444	7	w.	w.	PROPN
cana-2015	444	8	sua	sua	PROPN
cana-2015	444	9	,	,	PUNCT
cana-2015	444	10	intuitionistic	intuitionistic	ADJ
cana-2015	444	11	fuzzy	fuzzy	ADJ
cana-2015	444	12	ordered	order	VERB
cana-2015	444	13	weighted	weight	VERB
cana-2015	444	14	distance	distance	NOUN
cana-2015	444	15	operator	operator	NOUN
cana-2015	444	16	,	,	PUNCT
cana-2015	444	17	knowl	knowl	NOUN
cana-2015	444	18	.	.	PUNCT
cana-2015	444	19	based	base	VERB
cana-2015	444	20	syst	syst	PROPN
cana-2015	444	21	.	.	PUNCT
cana-2015	444	22	24	24	NUM
cana-2015	444	23	,	,	PUNCT
cana-2015	444	24	(	(	PUNCT
cana-2015	444	25	2011	2011	NUM
cana-2015	444	26	)	)	PUNCT
cana-2015	444	27	,	,	PUNCT
cana-2015	444	28	1224	1224	NUM
cana-2015	444	29	-	-	SYM
cana-2015	444	30	1232	1232	NUM
cana-2015	444	31	.	.	PUNCT
cana-2015	445	1	[	[	X
cana-2015	445	2	26	26	NUM
cana-2015	445	3	]	]	PUNCT
cana-2015	445	4	x.	x.	PROPN
cana-2015	445	5	peng	peng	PROPN
cana-2015	445	6	,	,	PUNCT
cana-2015	445	7	h.	h.	PROPN
cana-2015	445	8	yuan	yuan	PROPN
cana-2015	445	9	,	,	PUNCT
cana-2015	445	10	fundamental	fundamental	ADJ
cana-2015	445	11	properties	property	NOUN
cana-2015	445	12	of	of	ADP
cana-2015	445	13	pythagorean	pythagorean	ADJ
cana-2015	445	14	fuzzy	fuzzy	ADJ
cana-2015	445	15	aggregation	aggregation	NOUN
cana-2015	445	16	operators	operator	NOUN
cana-2015	445	17	,	,	PUNCT
cana-2015	445	18	fundam	fundam	ADJ
cana-2015	445	19	.	.	PUNCT
cana-2015	445	20	inform	inform	NOUN
cana-2015	445	21	.	.	PUNCT
cana-2015	446	1	147	147	NUM
cana-2015	446	2	,	,	PUNCT
cana-2015	446	3	(	(	PUNCT
cana-2015	446	4	2016	2016	NUM
cana-2015	446	5	)	)	PUNCT
cana-2015	446	6	,	,	PUNCT
cana-2015	446	7	415	415	NUM
cana-2015	446	8	-	-	SYM
cana-2015	446	9	446	446	NUM
cana-2015	446	10	.	.	PUNCT
cana-2015	447	1	[	[	X
cana-2015	447	2	27	27	NUM
cana-2015	447	3	]	]	X
cana-2015	447	4	s.	s.	PROPN
cana-2015	447	5	ashraf	ashraf	PROPN
cana-2015	447	6	,	,	PUNCT
cana-2015	447	7	s.	s.	PROPN
cana-2015	447	8	abdullah	abdullah	PROPN
cana-2015	447	9	,	,	PUNCT
cana-2015	447	10	t.	t.	PROPN
cana-2015	447	11	mahmood	mahmood	PROPN
cana-2015	447	12	,	,	PUNCT
cana-2015	447	13	spherical	spherical	ADJ
cana-2015	447	14	fuzzy	fuzzy	ADJ
cana-2015	447	15	dombi	dombi	NOUN
cana-2015	447	16	aggregation	aggregation	NOUN
cana-2015	447	17	operators	operator	NOUN
cana-2015	447	18	and	and	CCONJ
cana-2015	447	19	their	their	PRON
cana-2015	447	20	application	application	NOUN
cana-2015	447	21	in	in	ADP
cana-2015	447	22	group	group	NOUN
cana-2015	447	23	decision	decision	NOUN
cana-2015	447	24	-	-	PUNCT
cana-2015	447	25	making	make	VERB
cana-2015	447	26	problems	problem	NOUN
cana-2015	447	27	,	,	PUNCT
cana-2015	447	28	j.	j.	PROPN
cana-2015	447	29	amb	amb	PROPN
cana-2015	447	30	.	.	PROPN
cana-2015	447	31	intell	intell	PROPN
cana-2015	447	32	.	.	PUNCT
cana-2015	448	1	hum	hum	ADJ
cana-2015	448	2	.	.	PUNCT
cana-2015	449	1	comput	comput	NOUN
cana-2015	449	2	.	.	PUNCT
cana-2015	450	1	11	11	NUM
cana-2015	450	2	,	,	PUNCT
cana-2015	450	3	(	(	PUNCT
cana-2015	450	4	2020	2020	NUM
cana-2015	450	5	)	)	PUNCT
cana-2015	450	6	,	,	PUNCT
cana-2015	450	7	2731	2731	NUM
cana-2015	450	8	-	-	SYM
cana-2015	450	9	2749	2749	NUM
cana-2015	450	10	.	.	PUNCT
cana-2015	451	1	[	[	X
cana-2015	451	2	28	28	NUM
cana-2015	451	3	]	]	X
cana-2015	451	4	tansu	tansu	PROPN
cana-2015	451	5	temel	temel	PROPN
cana-2015	451	6	,	,	PUNCT
cana-2015	451	7	salih	salih	PROPN
cana-2015	451	8	berkan	berkan	PROPN
cana-2015	451	9	aydemir	aydemir	PROPN
cana-2015	451	10	,	,	PUNCT
cana-2015	451	11	yasar	yasar	PROPN
cana-2015	451	12	hoscan	hoscan	PROPN
cana-2015	451	13	,	,	PUNCT
cana-2015	451	14	power	power	NOUN
cana-2015	451	15	muirhead	muirhead	NOUN
cana-2015	451	16	mean	mean	VERB
cana-2015	451	17	in	in	ADP
cana-2015	451	18	spherical	spherical	ADJ
cana-2015	451	19	normal	normal	ADJ
cana-2015	451	20	fuzzy	fuzzy	ADJ
cana-2015	451	21	environment	environment	NOUN
cana-2015	451	22	and	and	CCONJ
cana-2015	451	23	its	its	PRON
cana-2015	451	24	applications	application	NOUN
cana-2015	451	25	to	to	ADP
cana-2015	451	26	multi	multi	ADJ
cana-2015	451	27	-	-	ADJ
cana-2015	451	28	attribute	attribute	NOUN
cana-2015	451	29	decision	decision	NOUN
cana-2015	451	30	-	-	PUNCT
cana-2015	451	31	making	making	NOUN
cana-2015	451	32	,	,	PUNCT
cana-2015	451	33	complex	complex	ADJ
cana-2015	451	34	and	and	CCONJ
cana-2015	451	35	intelligent	intelligent	ADJ
cana-2015	451	36	systems	system	NOUN
cana-2015	451	37	,	,	PUNCT
cana-2015	451	38	(	(	PUNCT
cana-2015	451	39	2022	2022	NUM
cana-2015	451	40	)	)	PUNCT
cana-2015	451	41	,	,	PUNCT
cana-2015	451	42	1	1	NUM
cana-2015	451	43	-	-	SYM
cana-2015	451	44	19	19	NUM
cana-2015	451	45	.	.	PUNCT
cana-2015	452	1	[	[	X
cana-2015	452	2	29	29	NUM
cana-2015	452	3	]	]	X
cana-2015	452	4	qiu	qiu	PROPN
cana-2015	452	5	,	,	PUNCT
cana-2015	452	6	y.	y.	PROPN
cana-2015	452	7	j.	j.	PROPN
cana-2015	452	8	,	,	PUNCT
cana-2015	452	9	bouraima	bouraima	PROPN
cana-2015	452	10	,	,	PUNCT
cana-2015	452	11	m.	m.	PROPN
cana-2015	452	12	b.	b.	PROPN
cana-2015	452	13	,	,	PUNCT
cana-2015	452	14	kiptum	kiptum	PROPN
cana-2015	452	15	,	,	PUNCT
cana-2015	452	16	c.	c.	PROPN
cana-2015	452	17	k.	k.	PROPN
cana-2015	452	18	,	,	PUNCT
cana-2015	452	19	ayyildiz	ayyildiz	PROPN
cana-2015	452	20	,	,	PUNCT
cana-2015	452	21	e.	e.	PROPN
cana-2015	452	22	,	,	PUNCT
cana-2015	452	23	stević	stević	ADV
cana-2015	452	24	,	,	PUNCT
cana-2015	452	25	ž.	ž.	PRON
cana-2015	452	26	,	,	PUNCT
cana-2015	452	27	badi	badi	NOUN
cana-2015	452	28	,	,	PUNCT
cana-2015	452	29	i.	i.	PROPN
cana-2015	452	30	,	,	PUNCT
cana-2015	452	31	&	&	CCONJ
cana-2015	452	32	ndiema	ndiema	PROPN
cana-2015	452	33	,	,	PUNCT
cana-2015	452	34	k.	k.	PROPN
cana-2015	452	35	m.	m.	PROPN
cana-2015	452	36	(	(	PUNCT
cana-2015	452	37	2023	2023	NUM
cana-2015	452	38	)	)	PUNCT
cana-2015	452	39	.	.	PUNCT
cana-2015	453	1	strategies	strategy	NOUN
cana-2015	453	2	for	for	ADP
cana-2015	453	3	enhancing	enhance	VERB
cana-2015	453	4	industry	industry	NOUN
cana-2015	453	5	4.0	4.0	NUM
cana-2015	453	6	adoption	adoption	NOUN
cana-2015	453	7	in	in	ADP
cana-2015	453	8	east	east	PROPN
cana-2015	453	9	africa	africa	PROPN
cana-2015	453	10	:	:	PUNCT
cana-2015	453	11	an	an	DET
cana-2015	453	12	integrated	integrate	VERB
cana-2015	453	13	spherical	spherical	ADJ
cana-2015	453	14	fuzzy	fuzzy	ADJ
cana-2015	453	15	swarawaspas	swarawaspas	NOUN
cana-2015	453	16	approach	approach	NOUN
cana-2015	453	17	.	.	PUNCT
cana-2015	454	1	j.	j.	PROPN
cana-2015	454	2	ind	ind	PROPN
cana-2015	454	3	intell	intell	PROPN
cana-2015	454	4	.	.	PUNCT
cana-2015	454	5	,	,	PUNCT
cana-2015	454	6	1(2	1(2	NUM
cana-2015	454	7	)	)	PUNCT
cana-2015	454	8	,	,	PUNCT
cana-2015	454	9	87	87	NUM
cana-2015	454	10	-	-	SYM
cana-2015	454	11	100	100	NUM
cana-2015	454	12	.	.	PUNCT
cana-2015	455	1	https://doi.org/10.56578/jii010202	https://doi.org/10.56578/jii010202	PROPN
cana-2015	456	1	[	[	X
cana-2015	456	2	30	30	NUM
cana-2015	456	3	]	]	X
cana-2015	456	4	choudhary	choudhary	PROPN
cana-2015	456	5	,	,	PUNCT
cana-2015	456	6	r.	r.	PROPN
cana-2015	456	7	,	,	PUNCT
cana-2015	456	8	ashraf	ashraf	PROPN
cana-2015	456	9	,	,	PUNCT
cana-2015	456	10	s.	s.	PROPN
cana-2015	456	11	,	,	PUNCT
cana-2015	456	12	&	&	CCONJ
cana-2015	456	13	anafi	anafi	PROPN
cana-2015	456	14	,	,	PUNCT
cana-2015	456	15	j.	j.	PROPN
cana-2015	456	16	(	(	PUNCT
cana-2015	456	17	2023	2023	NUM
cana-2015	456	18	)	)	PUNCT
cana-2015	456	19	.	.	PUNCT
cana-2015	456	20	enhanced	enhance	VERB
cana-2015	456	21	industrial	industrial	ADJ
cana-2015	456	22	control	control	NOUN
cana-2015	456	23	system	system	NOUN
cana-2015	456	24	of	of	ADP
cana-2015	456	25	decision	decision	NOUN
cana-2015	456	26	-	-	PUNCT
cana-2015	456	27	making	making	NOUN
cana-2015	456	28	using	use	VERB
cana-2015	456	29	spherical	spherical	ADJ
cana-2015	456	30	hesitant	hesitant	ADJ
cana-2015	456	31	fuzzy	fuzzy	ADJ
cana-2015	456	32	soft	soft	ADJ
cana-2015	456	33	yager	yager	NOUN
cana-2015	456	34	aggregation	aggregation	NOUN
cana-2015	456	35	information	information	NOUN
cana-2015	456	36	.	.	PUNCT
cana-2015	457	1	acadlore	acadlore	PROPN
cana-2015	457	2	trans	trans	PROPN
cana-2015	457	3	.	.	PROPN
cana-2015	458	1	appl	appl	PROPN
cana-2015	458	2	math	math	PROPN
cana-2015	458	3	.	.	PUNCT
cana-2015	459	1	stat	stat	PROPN
cana-2015	459	2	,	,	PUNCT
cana-2015	459	3	1(3	1(3	NUM
cana-2015	459	4	)	)	PUNCT
cana-2015	459	5	,	,	PUNCT
cana-2015	459	6	161	161	NUM
cana-2015	459	7	-	-	SYM
cana-2015	459	8	180	180	NUM
cana-2015	459	9	.	.	PUNCT
cana-2015	460	1	[	[	X
cana-2015	460	2	31	31	NUM
cana-2015	460	3	]	]	X
cana-2015	460	4	khan	khan	PROPN
cana-2015	460	5	,	,	PUNCT
cana-2015	460	6	a.	a.	NOUN
cana-2015	460	7	a.	a.	PROPN
cana-2015	460	8	,	,	PUNCT
cana-2015	460	9	mashat	mashat	PROPN
cana-2015	460	10	,	,	PUNCT
cana-2015	460	11	d.	d.	PROPN
cana-2015	460	12	s.	s.	PROPN
cana-2015	460	13	,	,	PUNCT
cana-2015	460	14	&	&	CCONJ
cana-2015	460	15	dong	dong	PROPN
cana-2015	460	16	,	,	PUNCT
cana-2015	460	17	k.	k.	PROPN
cana-2015	460	18	(	(	PUNCT
cana-2015	460	19	2024	2024	NUM
cana-2015	460	20	)	)	PUNCT
cana-2015	460	21	.	.	PUNCT
cana-2015	461	1	evaluating	evaluate	VERB
cana-2015	461	2	sustainable	sustainable	ADJ
cana-2015	461	3	urban	urban	ADJ
cana-2015	461	4	development	development	NOUN
cana-2015	461	5	strategies	strategy	NOUN
cana-2015	461	6	through	through	ADP
cana-2015	461	7	spherical	spherical	ADJ
cana-2015	461	8	critic	critic	NOUN
cana-2015	461	9	-	-	PUNCT
cana-2015	461	10	waspas	waspas	NOUN
cana-2015	461	11	analysis	analysis	NOUN
cana-2015	461	12	.	.	PUNCT
cana-2015	462	1	j.	j.	PROPN
cana-2015	462	2	urban	urban	PROPN
cana-2015	462	3	dev	dev	PROPN
cana-2015	462	4	.	.	PROPN
cana-2015	462	5	manag	manag	PROPN
cana-2015	462	6	.	.	PROPN
cana-2015	462	7	,	,	PUNCT
cana-2015	462	8	3(1	3(1	NUM
cana-2015	462	9	)	)	PUNCT
cana-2015	462	10	,	,	PUNCT
cana-2015	462	11	1	1	NUM
cana-2015	462	12	-	-	SYM
cana-2015	462	13	17	17	NUM
cana-2015	462	14	.	.	PUNCT
cana-2015	463	1	https://doi.org/10.56578/judm030101	https://doi.org/10.56578/judm030101	PROPN
cana-2015	463	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-2015	463	3	549	549	NUM
cana-2015	463	4	1	1	NUM
cana-2015	463	5	introduction	introduction	NOUN
cana-2015	463	6	2	2	NUM
cana-2015	463	7	preliminaries	preliminary	NOUN
cana-2015	463	8	3	3	NUM
cana-2015	463	9	q	q	NOUN
cana-2015	463	10	-	-	PUNCT
cana-2015	463	11	livifn	livifn	NOUN
cana-2015	463	12	and	and	CCONJ
cana-2015	463	13	its	its	PRON
cana-2015	463	14	fundamental	fundamental	ADJ
cana-2015	463	15	operations	operation	NOUN
cana-2015	463	16	4	4	NUM
cana-2015	463	17	q	q	NOUN
cana-2015	463	18	-	-	PUNCT
cana-2015	463	19	livifs	livif	NOUN
cana-2015	463	20	concept	concept	NOUN
cana-2015	463	21	4.1	4.1	NUM
cana-2015	463	22	q	q	NOUN
cana-2015	463	23	-	-	PUNCT
cana-2015	463	24	livif	livif	NOUN
cana-2015	463	25	weighted	weight	VERB
cana-2015	463	26	averaging	average	VERB
cana-2015	463	27	(	(	PUNCT
cana-2015	463	28	q	q	ADJ
cana-2015	463	29	-	-	PUNCT
cana-2015	463	30	livifwa	livifwa	NOUN
cana-2015	463	31	)	)	PUNCT
cana-2015	463	32	operator	operator	NOUN
cana-2015	463	33	4.2	4.2	NUM
cana-2015	463	34	q	q	NOUN
cana-2015	463	35	-	-	PUNCT
cana-2015	463	36	livif	livif	NOUN
cana-2015	463	37	weighted	weight	VERB
cana-2015	463	38	geometric	geometric	ADJ
cana-2015	463	39	(	(	PUNCT
cana-2015	463	40	q	q	NOUN
cana-2015	463	41	-	-	PUNCT
cana-2015	463	42	livifwg	livifwg	NOUN
cana-2015	463	43	)	)	PUNCT
cana-2015	463	44	operator	operator	NOUN
cana-2015	463	45	4.3	4.3	NUM
cana-2015	463	46	extended	extended	ADJ
cana-2015	463	47	q	q	NOUN
cana-2015	463	48	-	-	PUNCT
cana-2015	463	49	livifwa	livifwa	NOUN
cana-2015	463	50	(	(	PUNCT
cana-2015	463	51	q	q	NOUN
cana-2015	463	52	-	-	PUNCT
cana-2015	463	53	elivifwa	elivifwa	NOUN
cana-2015	463	54	)	)	PUNCT
cana-2015	463	55	operator	operator	NOUN
cana-2015	463	56	4.4	4.4	NUM
cana-2015	463	57	extended	extend	VERB
cana-2015	463	58	q	q	NOUN
cana-2015	463	59	-	-	PUNCT
cana-2015	463	60	livifwg	livifwg	NOUN
cana-2015	463	61	(	(	PUNCT
cana-2015	463	62	q	q	NOUN
cana-2015	463	63	-	-	PUNCT
cana-2015	463	64	elivifwg	elivifwg	NOUN
cana-2015	463	65	)	)	PUNCT
cana-2015	463	66	operator	operator	NOUN