id	sid	tid	token	lemma	pos
cana-2978	1	1	communications	communication	NOUN
cana-2978	1	2	on	on	ADP
cana-2978	1	3	applied	apply	VERB
cana-2978	1	4	nonlinear	nonlinear	ADJ
cana-2978	1	5	analysis	analysis	NOUN
cana-2978	1	6	issn	issn	NOUN
cana-2978	1	7	:	:	PUNCT
cana-2978	1	8	1074	1074	NUM
cana-2978	1	9	-	-	PUNCT
cana-2978	1	10	133x	133x	NUM
cana-2978	1	11	vol	vol	NOUN
cana-2978	1	12	32	32	NUM
cana-2978	1	13	no	no	NOUN
cana-2978	1	14	.	.	PUNCT
cana-2978	2	1	5s	5s	NUM
cana-2978	2	2	(	(	PUNCT
cana-2978	2	3	2025	2025	NUM
cana-2978	2	4	)	)	PUNCT
cana-2978	2	5	complex	complex	ADJ
cana-2978	2	6	tangent	tangent	NOUN
cana-2978	2	7	trigonometric	trigonometric	ADJ
cana-2978	2	8	approach	approach	NOUN
cana-2978	2	9	applied	apply	VERB
cana-2978	2	10	to	to	ADP
cana-2978	2	11	(	(	PUNCT
cana-2978	2	12	γ	γ	PROPN
cana-2978	2	13	,	,	PUNCT
cana-2978	2	14	τ)-rung	τ)-rung	X
cana-2978	2	15	fuzzy	fuzzy	ADJ
cana-2978	2	16	set	set	VERB
cana-2978	2	17	using	use	VERB
cana-2978	2	18	weighted	weight	VERB
cana-2978	2	19	averaging	averaging	NOUN
cana-2978	2	20	,	,	PUNCT
cana-2978	2	21	geometric	geometric	ADJ
cana-2978	2	22	operators	operator	NOUN
cana-2978	2	23	and	and	CCONJ
cana-2978	2	24	its	its	PRON
cana-2978	2	25	extension	extension	NOUN
cana-2978	2	26	raed	raed	NOUN
cana-2978	2	27	hatamleh1	hatamleh1	PROPN
cana-2978	2	28	,	,	PUNCT
cana-2978	2	29	abdallah	abdallah	PROPN
cana-2978	2	30	al	al	PROPN
cana-2978	2	31	-	-	PUNCT
cana-2978	2	32	husban2,3	husban2,3	PROPN
cana-2978	2	33	,	,	PUNCT
cana-2978	2	34	k.	k.	NOUN
cana-2978	2	35	sundareswari4,∗	sundareswari4,∗	PROPN
cana-2978	2	36	,	,	PUNCT
cana-2978	2	37	g.balaj5	g.balaj5	NOUN
cana-2978	2	38	,	,	PUNCT
cana-2978	2	39	m.palanikumar6	m.palanikumar6	PROPN
cana-2978	2	40	1department	1department	NUM
cana-2978	2	41	of	of	ADP
cana-2978	2	42	mathematics	mathematic	NOUN
cana-2978	2	43	,	,	PUNCT
cana-2978	2	44	faculty	faculty	NOUN
cana-2978	2	45	of	of	ADP
cana-2978	2	46	science	science	NOUN
cana-2978	2	47	,	,	PUNCT
cana-2978	2	48	jadara	jadara	PROPN
cana-2978	2	49	university	university	PROPN
cana-2978	2	50	,	,	PUNCT
cana-2978	2	51	p.o	p.o	PROPN
cana-2978	2	52	.	.	PROPN
cana-2978	2	53	box	box	PROPN
cana-2978	2	54	733	733	NUM
cana-2978	2	55	,	,	PUNCT
cana-2978	2	56	irbid	irbid	ADJ
cana-2978	2	57	21110	21110	NUM
cana-2978	2	58	,	,	PUNCT
cana-2978	2	59	jordan	jordan	PROPN
cana-2978	2	60	.	.	PUNCT
cana-2978	3	1	2department	2department	NUM
cana-2978	3	2	of	of	ADP
cana-2978	3	3	mathematics	mathematic	NOUN
cana-2978	3	4	,	,	PUNCT
cana-2978	3	5	faculty	faculty	NOUN
cana-2978	3	6	of	of	ADP
cana-2978	3	7	science	science	NOUN
cana-2978	3	8	,	,	PUNCT
cana-2978	3	9	irbid	irbid	VERB
cana-2978	3	10	national	national	ADJ
cana-2978	3	11	university	university	PROPN
cana-2978	3	12	,	,	PUNCT
cana-2978	3	13	p.o	p.o	PROPN
cana-2978	3	14	.	.	PROPN
cana-2978	3	15	box	box	PROPN
cana-2978	3	16	:	:	PUNCT
cana-2978	3	17	2600	2600	NUM
cana-2978	3	18	irbid	irbid	PROPN
cana-2978	3	19	,	,	PUNCT
cana-2978	3	20	jordan	jordan	PROPN
cana-2978	3	21	.	.	PUNCT
cana-2978	4	1	3jadara	3jadara	NUM
cana-2978	4	2	research	research	NOUN
cana-2978	4	3	center	center	NOUN
cana-2978	4	4	,	,	PUNCT
cana-2978	4	5	jadara	jadara	PROPN
cana-2978	4	6	university	university	PROPN
cana-2978	4	7	,	,	PUNCT
cana-2978	4	8	irbid	irbid	VERB
cana-2978	4	9	21110	21110	NUM
cana-2978	4	10	,	,	PUNCT
cana-2978	4	11	jordan	jordan	PROPN
cana-2978	4	12	.	.	PUNCT
cana-2978	5	1	4,5department	4,5department	NUM
cana-2978	5	2	of	of	ADP
cana-2978	5	3	mathematics	mathematic	NOUN
cana-2978	5	4	,	,	PUNCT
cana-2978	5	5	alameen	alameen	VERB
cana-2978	5	6	engineering	engineering	NOUN
cana-2978	5	7	college	college	NOUN
cana-2978	5	8	,	,	PUNCT
cana-2978	5	9	erode	erode	VERB
cana-2978	5	10	.	.	PUNCT
cana-2978	6	1	6department	6department	NUM
cana-2978	6	2	of	of	ADP
cana-2978	6	3	mathematics	mathematic	NOUN
cana-2978	6	4	,	,	PUNCT
cana-2978	6	5	saveetha	saveetha	PROPN
cana-2978	6	6	school	school	PROPN
cana-2978	6	7	of	of	ADP
cana-2978	6	8	engineering	engineering	PROPN
cana-2978	6	9	,	,	PUNCT
cana-2978	6	10	saveetha	saveetha	PROPN
cana-2978	6	11	institute	institute	PROPN
cana-2978	6	12	of	of	ADP
cana-2978	6	13	medical	medical	ADJ
cana-2978	6	14	and	and	CCONJ
cana-2978	6	15	technical	technical	ADJ
cana-2978	6	16	sciences	science	NOUN
cana-2978	6	17	,	,	PUNCT
cana-2978	6	18	chennai-602105	chennai-602105	ADJ
cana-2978	6	19	,	,	PUNCT
cana-2978	6	20	india	india	PROPN
cana-2978	6	21	.	.	PUNCT
cana-2978	7	1	e-mails:1raed@jadara.edu.jo	e-mails:1raed@jadara.edu.jo	PROPN
cana-2978	7	2	,	,	PUNCT
cana-2978	7	3	3dralhosban@inu.edu.jo	3dralhosban@inu.edu.jo	NUM
cana-2978	7	4	,	,	PUNCT
cana-2978	7	5	4sundarimaths@gmail.com	4sundarimaths@gmail.com	PROPN
cana-2978	7	6	,	,	PUNCT
cana-2978	7	7	5balajivaithesh@gmail.com	5balajivaithesh@gmail.com	NUM
cana-2978	7	8	,	,	PUNCT
cana-2978	7	9	6palanimaths86@gmail.com	6palanimaths86@gmail.com	NOUN
cana-2978	7	10	,	,	PUNCT
cana-2978	7	11	∗corresponding	∗corresponde	VERB
cana-2978	7	12	author	author	NOUN
cana-2978	7	13	:	:	PUNCT
cana-2978	7	14	k.	k.	PROPN
cana-2978	7	15	sundareswari	sundareswari	PROPN
cana-2978	7	16	.	.	PUNCT
cana-2978	8	1	received	receive	VERB
cana-2978	8	2	:	:	PUNCT
cana-2978	8	3	04	04	NUM
cana-2978	8	4	-	-	SYM
cana-2978	8	5	10	10	NUM
cana-2978	8	6	-	-	PUNCT
cana-2978	8	7	2024	2024	NUM
cana-2978	8	8	revised	revise	VERB
cana-2978	8	9	:	:	PUNCT
cana-2978	8	10	26	26	NUM
cana-2978	8	11	-	-	SYM
cana-2978	8	12	11	11	NUM
cana-2978	8	13	-	-	PUNCT
cana-2978	8	14	2024	2024	NUM
cana-2978	8	15	accepted	accept	VERB
cana-2978	8	16	:	:	PUNCT
cana-2978	8	17	04	04	NUM
cana-2978	8	18	-	-	SYM
cana-2978	8	19	12	12	NUM
cana-2978	8	20	-	-	PUNCT
cana-2978	8	21	2024	2024	NUM
cana-2978	8	22	.	.	PUNCT
cana-2978	9	1	abstract	abstract	ADJ
cana-2978	9	2	this	this	DET
cana-2978	9	3	paper	paper	NOUN
cana-2978	9	4	presents	present	VERB
cana-2978	9	5	a	a	DET
cana-2978	9	6	new	new	ADJ
cana-2978	9	7	method	method	NOUN
cana-2978	9	8	that	that	PRON
cana-2978	9	9	generates	generate	VERB
cana-2978	9	10	complex	complex	ADJ
cana-2978	9	11	tangent	tangent	NOUN
cana-2978	9	12	trigonometric	trigonometric	NOUN
cana-2978	9	13	(	(	PUNCT
cana-2978	9	14	γ	γ	PROPN
cana-2978	9	15	,	,	PUNCT
cana-2978	9	16	τ)-rung	τ)-rung	PUNCT
cana-2978	9	17	fuzzy	fuzzy	ADJ
cana-2978	9	18	sets	set	NOUN
cana-2978	9	19	.	.	PUNCT
cana-2978	10	1	this	this	DET
cana-2978	10	2	article	article	NOUN
cana-2978	10	3	will	will	AUX
cana-2978	10	4	deal	deal	VERB
cana-2978	10	5	with	with	ADP
cana-2978	10	6	averaging	averaging	NOUN
cana-2978	10	7	,	,	PUNCT
cana-2978	10	8	geometric	geometric	ADJ
cana-2978	10	9	,	,	PUNCT
cana-2978	10	10	generalized	generalize	VERB
cana-2978	10	11	weighted	weighted	ADJ
cana-2978	10	12	averaging	averaging	NOUN
cana-2978	10	13	,	,	PUNCT
cana-2978	11	1	generalized	generalize	VERB
cana-2978	11	2	weighted	weight	VERB
cana-2978	11	3	geometric	geometric	ADJ
cana-2978	11	4	using	use	VERB
cana-2978	11	5	complex	complex	ADJ
cana-2978	11	6	tangent	tangent	NOUN
cana-2978	11	7	trigonometric	trigonometric	NOUN
cana-2978	11	8	(	(	PUNCT
cana-2978	11	9	γ	γ	PROPN
cana-2978	11	10	,	,	PUNCT
cana-2978	11	11	τ)-rung	τ)-rung	X
cana-2978	11	12	fuzzy	fuzzy	ADJ
cana-2978	11	13	set	set	NOUN
cana-2978	11	14	.	.	PUNCT
cana-2978	12	1	we	we	PRON
cana-2978	12	2	used	use	VERB
cana-2978	12	3	an	an	DET
cana-2978	12	4	aggregating	aggregate	VERB
cana-2978	12	5	model	model	NOUN
cana-2978	12	6	to	to	PART
cana-2978	12	7	get	get	VERB
cana-2978	12	8	the	the	DET
cana-2978	12	9	weighted	weighted	ADJ
cana-2978	12	10	average	average	ADJ
cana-2978	12	11	and	and	CCONJ
cana-2978	12	12	geometric	geometric	ADJ
cana-2978	12	13	.	.	PUNCT
cana-2978	13	1	several	several	ADJ
cana-2978	13	2	sets	set	NOUN
cana-2978	13	3	with	with	ADP
cana-2978	13	4	significant	significant	ADJ
cana-2978	13	5	characteristics	characteristic	NOUN
cana-2978	13	6	will	will	AUX
cana-2978	13	7	be	be	AUX
cana-2978	13	8	further	far	ADV
cana-2978	13	9	studied	study	VERB
cana-2978	13	10	using	use	VERB
cana-2978	13	11	the	the	DET
cana-2978	13	12	algebraic	algebraic	ADJ
cana-2978	13	13	approaches	approach	NOUN
cana-2978	13	14	.	.	PUNCT
cana-2978	14	1	keywords	keyword	NOUN
cana-2978	14	2	:	:	PUNCT
cana-2978	14	3	(	(	PUNCT
cana-2978	14	4	γ	γ	X
cana-2978	14	5	,	,	PUNCT
cana-2978	14	6	τ)-rung	τ)-rung	PUNCT
cana-2978	14	7	,	,	PUNCT
cana-2978	14	8	wa	wa	PROPN
cana-2978	14	9	,	,	PUNCT
cana-2978	14	10	wg	wg	PROPN
cana-2978	14	11	,	,	PUNCT
cana-2978	14	12	gwa	gwa	PROPN
cana-2978	14	13	,	,	PUNCT
cana-2978	14	14	gwg	gwg	PROPN
cana-2978	14	15	.	.	PROPN
cana-2978	14	16	1	1	NUM
cana-2978	14	17	introduction	introduction	NOUN
cana-2978	14	18	numerous	numerous	ADJ
cana-2978	14	19	ideas	idea	NOUN
cana-2978	14	20	have	have	AUX
cana-2978	14	21	been	be	AUX
cana-2978	14	22	put	put	VERB
cana-2978	14	23	out	out	ADP
cana-2978	14	24	to	to	PART
cana-2978	14	25	explain	explain	VERB
cana-2978	14	26	uncertainty	uncertainty	NOUN
cana-2978	14	27	,	,	PUNCT
cana-2978	14	28	including	include	VERB
cana-2978	14	29	fuzzy	fuzzy	ADJ
cana-2978	14	30	sets	set	NOUN
cana-2978	14	31	(	(	PUNCT
cana-2978	14	32	fs),1	fs),1	X
cana-2978	14	33	which	which	PRON
cana-2978	14	34	have	have	VERB
cana-2978	14	35	membership	membership	NOUN
cana-2978	14	36	grades	grade	NOUN
cana-2978	14	37	(	(	PUNCT
cana-2978	14	38	mg	mg	ADJ
cana-2978	14	39	)	)	PUNCT
cana-2978	14	40	ranging	range	VERB
cana-2978	14	41	from	from	ADP
cana-2978	14	42	zero	zero	NUM
cana-2978	14	43	to	to	ADP
cana-2978	14	44	one	one	NUM
cana-2978	14	45	.	.	PUNCT
cana-2978	15	1	atanassov.2	atanassov.2	NOUN
cana-2978	15	2	for	for	ADP
cana-2978	15	3	$	$	SYM
cana-2978	15	4	,	,	PUNCT
cana-2978	15	5	κ	κ	PROPN
cana-2978	15	6	∈	∈	PROPN
cana-2978	16	1	[	[	X
cana-2978	16	2	0	0	NUM
cana-2978	16	3	,	,	PUNCT
cana-2978	16	4	1	1	NUM
cana-2978	16	5	]	]	PUNCT
cana-2978	16	6	created	create	VERB
cana-2978	16	7	an	an	DET
cana-2978	16	8	intuitionistic	intuitionistic	ADJ
cana-2978	16	9	fs	fs	X
cana-2978	16	10	(	(	PUNCT
cana-2978	16	11	ifs	ifs	PROPN
cana-2978	16	12	)	)	PUNCT
cana-2978	16	13	in	in	ADP
cana-2978	16	14	which	which	PRON
cana-2978	16	15	each	each	DET
cana-2978	16	16	element	element	NOUN
cana-2978	16	17	has	have	VERB
cana-2978	16	18	two	two	NUM
cana-2978	16	19	mgs	mgs	NOUN
cana-2978	16	20	:	:	PUNCT
cana-2978	16	21	positive	positive	ADJ
cana-2978	16	22	$	$	NOUN
cana-2978	16	23	and	and	CCONJ
cana-2978	16	24	negative	negative	ADJ
cana-2978	16	25	κ	κ	NOUN
cana-2978	16	26	,	,	PUNCT
cana-2978	16	27	and	and	CCONJ
cana-2978	16	28	0	0	NUM
cana-2978	16	29	≤	≤	NOUN
cana-2978	16	30	$	$	SYM
cana-2978	16	31	+	+	NUM
cana-2978	16	32	κ	κ	X
cana-2978	16	33	≤	≤	NUM
cana-2978	16	34	1	1	NUM
cana-2978	16	35	.	.	PUNCT
cana-2978	17	1	the	the	DET
cana-2978	17	2	pythagorean	pythagorean	PROPN
cana-2978	17	3	fss	fss	PROPN
cana-2978	17	4	(	(	PUNCT
cana-2978	17	5	pfs	pfs	PROPN
cana-2978	17	6	)	)	PUNCT
cana-2978	17	7	idea	idea	NOUN
cana-2978	17	8	was	be	AUX
cana-2978	17	9	developed	develop	VERB
cana-2978	17	10	by	by	ADP
cana-2978	17	11	yager3	yager3	PROPN
cana-2978	17	12	and	and	CCONJ
cana-2978	17	13	is	be	AUX
cana-2978	17	14	distinguished	distinguish	VERB
cana-2978	17	15	by	by	ADP
cana-2978	17	16	its	its	PRON
cana-2978	17	17	mg	mg	PROPN
cana-2978	17	18	and	and	CCONJ
cana-2978	17	19	non	non	ADJ
cana-2978	17	20	-	-	ADJ
cana-2978	17	21	mg	mg	ADJ
cana-2978	17	22	(	(	PUNCT
cana-2978	17	23	nmg	nmg	NOUN
cana-2978	17	24	)	)	PUNCT
cana-2978	17	25	with	with	ADP
cana-2978	17	26	$	$	SYM
cana-2978	17	27	+	+	NUM
cana-2978	17	28	κ	κ	X
cana-2978	17	29	≥	≥	NOUN
cana-2978	17	30	1	1	NUM
cana-2978	17	31	to$2+κ2	to$2+κ2	ADP
cana-2978	17	32	≤	≤	NUM
cana-2978	17	33	1	1	NUM
cana-2978	17	34	.	.	PUNCT
cana-2978	18	1	the	the	DET
cana-2978	18	2	three	three	NUM
cana-2978	18	3	main	main	ADJ
cana-2978	18	4	concepts	concept	NOUN
cana-2978	18	5	of	of	ADP
cana-2978	18	6	the	the	DET
cana-2978	18	7	picture	picture	NOUN
cana-2978	18	8	fs	fs	PART
cana-2978	18	9	are	be	AUX
cana-2978	18	10	positive	positive	ADJ
cana-2978	18	11	mg	mg	PROPN
cana-2978	18	12	(	(	PUNCT
cana-2978	18	13	$	$	NOUN
cana-2978	18	14	)	)	PUNCT
cana-2978	18	15	,	,	PUNCT
cana-2978	18	16	neutral	neutral	ADJ
cana-2978	18	17	mg	mg	PROPN
cana-2978	18	18	(	(	PUNCT
cana-2978	18	19	γ	γ	NOUN
cana-2978	18	20	)	)	PUNCT
cana-2978	18	21	,	,	PUNCT
cana-2978	18	22	and	and	CCONJ
cana-2978	18	23	negative	negative	ADJ
cana-2978	18	24	mg	mg	PROPN
cana-2978	18	25	(	(	PUNCT
cana-2978	18	26	κ	κ	NOUN
cana-2978	18	27	)	)	PUNCT
cana-2978	18	28	,	,	PUNCT
cana-2978	18	29	as	as	SCONJ
cana-2978	18	30	stated	state	VERB
cana-2978	18	31	by	by	ADP
cana-2978	18	32	cuong	cuong	PROPN
cana-2978	18	33	et	et	PROPN
cana-2978	19	1	al.4	al.4	PROPN
cana-2978	19	2	it	it	PRON
cana-2978	19	3	also	also	ADV
cana-2978	19	4	provides	provide	VERB
cana-2978	19	5	more	more	ADJ
cana-2978	19	6	advantages	advantage	NOUN
cana-2978	19	7	than	than	ADP
cana-2978	19	8	pfs	pfs	PROPN
cana-2978	19	9	and	and	CCONJ
cana-2978	19	10	ifs	ifs	PROPN
cana-2978	19	11	with	with	ADP
cana-2978	19	12	0	0	NUM
cana-2978	19	13	≤	≤	NUM
cana-2978	19	14	$	$	SYM
cana-2978	19	15	+	+	NOUN
cana-2978	19	16	γ+κ	γ+κ	NOUN
cana-2978	19	17	≤	≤	NOUN
cana-2978	19	18	1	1	NUM
cana-2978	19	19	since$	since$	PROPN
cana-2978	19	20	,	,	PUNCT
cana-2978	19	21	γ	γ	X
cana-2978	19	22	,	,	PUNCT
cana-2978	19	23	κ	κ	PROPN
cana-2978	19	24	∈	∈	PROPN
cana-2978	20	1	[	[	X
cana-2978	20	2	0	0	NUM
cana-2978	20	3	,	,	PUNCT
cana-2978	20	4	1	1	NUM
cana-2978	20	5	]	]	PUNCT
cana-2978	20	6	.	.	PUNCT
cana-2978	21	1	expert	expert	ADJ
cana-2978	21	2	comments	comment	NOUN
cana-2978	21	3	such	such	ADJ
cana-2978	21	4	as	as	ADP
cana-2978	21	5	”	"	PUNCT
cana-2978	21	6	yes	yes	INTJ
cana-2978	21	7	,	,	PUNCT
cana-2978	21	8	”	"	PUNCT
cana-2978	21	9	”	"	PUNCT
cana-2978	21	10	abstain	abstain	NOUN
cana-2978	21	11	,	,	PUNCT
cana-2978	21	12	”	"	PUNCT
cana-2978	21	13	”	"	PUNCT
cana-2978	21	14	no	no	INTJ
cana-2978	21	15	,	,	PUNCT
cana-2978	21	16	”	"	PUNCT
cana-2978	21	17	and	and	CCONJ
cana-2978	21	18	”	"	PUNCT
cana-2978	21	19	refusal	refusal	NOUN
cana-2978	21	20	”	"	PUNCT
cana-2978	21	21	will	will	AUX
cana-2978	21	22	be	be	AUX
cana-2978	21	23	sent	send	VERB
cana-2978	21	24	,	,	PUNCT
cana-2978	21	25	in	in	ADP
cana-2978	21	26	accordance	accordance	NOUN
cana-2978	21	27	with	with	ADP
cana-2978	21	28	the	the	DET
cana-2978	21	29	image	image	NOUN
cana-2978	21	30	fs	fs	ADP
cana-2978	21	31	description	description	NOUN
cana-2978	21	32	.	.	PUNCT
cana-2978	22	1	shahzaib	shahzaib	PROPN
cana-2978	22	2	et	et	PROPN
cana-2978	22	3	al.5	al.5	PROPN
cana-2978	22	4	used	use	VERB
cana-2978	22	5	madm	madm	NOUN
cana-2978	22	6	to	to	PART
cana-2978	22	7	define	define	VERB
cana-2978	22	8	the	the	DET
cana-2978	22	9	sfs	sfs	NOUN
cana-2978	22	10	for	for	ADP
cana-2978	22	11	certain	certain	ADJ
cana-2978	22	12	aos	aos	PROPN
cana-2978	22	13	.	.	PUNCT
cana-2978	23	1	instead	instead	ADV
cana-2978	23	2	of	of	ADP
cana-2978	23	3	0	0	NUM
cana-2978	23	4	≤	≤	NUM
cana-2978	23	5	$	$	SYM
cana-2978	23	6	+	+	NUM
cana-2978	23	7	γ	γ	X
cana-2978	23	8	+	+	X
cana-2978	23	9	κ	κ	X
cana-2978	23	10	≤	≤	NUM
cana-2978	23	11	1	1	NUM
cana-2978	23	12	,	,	PUNCT
cana-2978	23	13	sfs	sfs	ADJ
cana-2978	23	14	demands	demand	VERB
cana-2978	23	15	that	that	SCONJ
cana-2978	23	16	0	0	NUM
cana-2978	23	17	≤	≤	NUM
cana-2978	23	18	$	$	SYM
cana-2978	23	19	2	2	NUM
cana-2978	23	20	+	+	CCONJ
cana-2978	23	21	γ2	γ2	ADJ
cana-2978	23	22	+	+	CCONJ
cana-2978	23	23	κ2	κ2	NOUN
cana-2978	23	24	≤	≤	ADV
cana-2978	23	25	1	1	NUM
cana-2978	23	26	.	.	PUNCT
cana-2978	24	1	the	the	DET
cana-2978	24	2	idea	idea	NOUN
cana-2978	24	3	of	of	ADP
cana-2978	24	4	an	an	DET
cana-2978	24	5	intelligent	intelligent	ADJ
cana-2978	24	6	decision	decision	NOUN
cana-2978	24	7	support	support	NOUN
cana-2978	24	8	system	system	NOUN
cana-2978	24	9	for	for	ADP
cana-2978	24	10	sfs	sfs	PROPN
cana-2978	24	11	was	be	AUX
cana-2978	24	12	initially	initially	ADV
cana-2978	24	13	put	put	VERB
cana-2978	24	14	out	out	ADP
cana-2978	24	15	by	by	ADP
cana-2978	24	16	hussain	hussain	PROPN
cana-2978	24	17	et	et	PROPN
cana-2978	24	18	al.6	al.6	PROPN
cana-2978	24	19	both	both	CCONJ
cana-2978	24	20	the	the	DET
cana-2978	24	21	mg	mg	PROPN
cana-2978	24	22	and	and	CCONJ
cana-2978	24	23	the	the	DET
cana-2978	24	24	nmg	nmg	NOUN
cana-2978	24	25	have	have	VERB
cana-2978	24	26	power	power	NOUN
cana-2978	24	27	q	q	PROPN
cana-2978	24	28	in	in	ADP
cana-2978	24	29	the	the	DET
cana-2978	24	30	q	q	ADJ
cana-2978	24	31	-	-	PUNCT
cana-2978	24	32	rung	rung	ADJ
cana-2978	24	33	orthogonal	orthogonal	ADJ
cana-2978	24	34	pair	pair	NOUN
cana-2978	24	35	fs	fs	ADP
cana-2978	24	36	(	(	PUNCT
cana-2978	24	37	q	q	NOUN
cana-2978	24	38	-	-	PUNCT
cana-2978	24	39	rofs	rofs	NOUN
cana-2978	24	40	)	)	PUNCT
cana-2978	24	41	,	,	PUNCT
cana-2978	24	42	but	but	CCONJ
cana-2978	24	43	their	their	PRON
cana-2978	24	44	sum	sum	NOUN
cana-2978	24	45	can	can	AUX
cana-2978	24	46	never	never	ADV
cana-2978	24	47	be	be	AUX
cana-2978	24	48	more	more	ADJ
cana-2978	24	49	than	than	ADP
cana-2978	24	50	one	one	NUM
cana-2978	24	51	.	.	PUNCT
cana-2978	25	1	xu	xu	PROPN
cana-2978	25	2	et	et	PROPN
cana-2978	25	3	al	al	PROPN
cana-2978	25	4	.	.	PROPN
cana-2978	25	5	developed	develop	VERB
cana-2978	25	6	geometric	geometric	ADJ
cana-2978	25	7	operators	operator	NOUN
cana-2978	25	8	,	,	PUNCT
cana-2978	25	9	including	include	VERB
cana-2978	25	10	weighted	weight	VERB
cana-2978	25	11	,	,	PUNCT
cana-2978	25	12	ordered	order	VERB
cana-2978	25	13	weighted	weight	VERB
cana-2978	25	14	,	,	PUNCT
cana-2978	25	15	and	and	CCONJ
cana-2978	26	1	hybrid	hybrid	ADJ
cana-2978	26	2	operators	operator	NOUN
cana-2978	26	3	,	,	PUNCT
cana-2978	26	4	that	that	PRON
cana-2978	26	5	were	be	AUX
cana-2978	26	6	derived	derive	VERB
cana-2978	26	7	from	from	ADP
cana-2978	26	8	ifss.7	ifss.7	NOUN
cana-2978	26	9	generalized	generalized	ADJ
cana-2978	26	10	ordered	order	VERB
cana-2978	26	11	weighted	weight	VERB
cana-2978	26	12	averaging	average	VERB
cana-2978	26	13	operators	operator	NOUN
cana-2978	26	14	(	(	PUNCT
cana-2978	26	15	gows	gow	NOUN
cana-2978	26	16	)	)	PUNCT
cana-2978	26	17	were	be	AUX
cana-2978	26	18	suggested	suggest	VERB
cana-2978	26	19	by	by	ADP
cana-2978	26	20	li	li	PROPN
cana-2978	26	21	et	et	PROPN
cana-2978	26	22	al.8	al.8	PROPN
cana-2978	26	23	in	in	ADP
cana-2978	26	24	2002	2002	NUM
cana-2978	26	25	.	.	PUNCT
cana-2978	27	1	al	al	PROPN
cana-2978	27	2	-	-	PUNCT
cana-2978	27	3	husband	husband	PROPN
cana-2978	27	4	et	et	PROPN
cana-2978	27	5	al.9	al.9	PROPN
cana-2978	27	6	-	-	PUNCT
cana-2978	27	7	14	14	NUM
cana-2978	27	8	and20	and20	NOUN
cana-2978	27	9	-	-	PUNCT
cana-2978	27	10	30	30	NUM
cana-2978	27	11	discussed	discuss	VERB
cana-2978	27	12	the	the	DET
cana-2978	27	13	concept	concept	NOUN
cana-2978	27	14	of	of	ADP
cana-2978	27	15	various	various	ADJ
cana-2978	27	16	fs	f	NOUN
cana-2978	27	17	and	and	CCONJ
cana-2978	27	18	its	its	PRON
cana-2978	27	19	extension	extension	NOUN
cana-2978	27	20	.	.	PUNCT
cana-2978	28	1	zeng	zeng	PROPN
cana-2978	28	2	et	et	PROPN
cana-2978	28	3	al.15	al.15	PROPN
cana-2978	28	4	explained	explain	VERB
cana-2978	28	5	how	how	SCONJ
cana-2978	28	6	to	to	PART
cana-2978	28	7	compute	compute	VERB
cana-2978	28	8	ordered	order	VERB
cana-2978	28	9	weighted	weight	VERB
cana-2978	28	10	distances	distance	NOUN
cana-2978	28	11	using	use	VERB
cana-2978	28	12	aos	aos	PROPN
cana-2978	28	13	and	and	CCONJ
cana-2978	28	14	distance	distance	NOUN
cana-2978	28	15	measurements	measurement	NOUN
cana-2978	28	16	.	.	PUNCT
cana-2978	29	1	based	base	VERB
cana-2978	29	2	on	on	ADP
cana-2978	29	3	the	the	DET
cana-2978	29	4	features	feature	NOUN
cana-2978	29	5	of	of	ADP
cana-2978	29	6	aos	aos	PROPN
cana-2978	29	7	,	,	PUNCT
cana-2978	29	8	peng	peng	PROPN
cana-2978	29	9	et	et	PROPN
cana-2978	29	10	al	al	PROPN
cana-2978	29	11	.	.	PROPN
cana-2978	29	12	investigated	investigate	VERB
cana-2978	29	13	a	a	DET
cana-2978	29	14	simple	simple	ADJ
cana-2978	29	15	pfs.16	pfs.16	NOUN
cana-2978	29	16	various	various	ADJ
cana-2978	29	17	algebraic	algebraic	ADJ
cana-2978	29	18	structures	structure	NOUN
cana-2978	29	19	and	and	CCONJ
cana-2978	29	20	aggregation	aggregation	NOUN
cana-2978	29	21	techniques	technique	NOUN
cana-2978	29	22	with	with	ADP
cana-2978	29	23	applications	application	NOUN
cana-2978	29	24	were	be	AUX
cana-2978	29	25	studied	study	VERB
cana-2978	29	26	by	by	ADP
cana-2978	29	27	palanikumar	palanikumar	PROPN
cana-2978	29	28	et	et	NOUN
cana-2978	29	29	al.17–19	al.17–19	NOUN
cana-2978	29	30	for	for	ADP
cana-2978	29	31	the	the	DET
cana-2978	29	32	rest	rest	NOUN
cana-2978	29	33	of	of	ADP
cana-2978	29	34	my	my	PRON
cana-2978	29	35	work	work	NOUN
cana-2978	29	36	,	,	PUNCT
cana-2978	29	37	i	i	PRON
cana-2978	29	38	will	will	AUX
cana-2978	29	39	keep	keep	VERB
cana-2978	29	40	to	to	ADP
cana-2978	29	41	the	the	DET
cana-2978	29	42	format	format	NOUN
cana-2978	29	43	provided	provide	VERB
cana-2978	29	44	here	here	ADV
cana-2978	29	45	.	.	PUNCT
cana-2978	30	1	in	in	ADP
cana-2978	30	2	section	section	NOUN
cana-2978	30	3	2	2	NUM
cana-2978	30	4	deals	deal	NOUN
cana-2978	30	5	that	that	PRON
cana-2978	30	6	pfs	pf	VERB
cana-2978	30	7	and	and	CCONJ
cana-2978	30	8	ns	ns	NUM
cana-2978	30	9	were	be	AUX
cana-2978	30	10	discussed	discuss	VERB
cana-2978	30	11	.	.	PUNCT
cana-2978	31	1	section	section	NOUN
cana-2978	31	2	3	3	NUM
cana-2978	31	3	describes	describe	VERB
cana-2978	31	4	numerous	numerous	ADJ
cana-2978	31	5	methods	method	NOUN
cana-2978	31	6	on	on	ADP
cana-2978	31	7	(	(	PUNCT
cana-2978	31	8	γ	γ	PROPN
cana-2978	31	9	,	,	PUNCT
cana-2978	31	10	τ)-rung	τ)-rung	PROPN
cana-2978	31	11	fns	fns	PROPN
cana-2978	31	12	.	.	PUNCT
cana-2978	32	1	in	in	ADP
cana-2978	32	2	section	section	NOUN
cana-2978	32	3	4	4	NUM
cana-2978	32	4	,	,	PUNCT
cana-2978	32	5	the	the	DET
cana-2978	32	6	aos	aos	NOUN
cana-2978	32	7	based	base	VERB
cana-2978	32	8	on	on	ADP
cana-2978	32	9	ct	ct	PROPN
cana-2978	32	10	(	(	PUNCT
cana-2978	32	11	γ	γ	PROPN
cana-2978	32	12	,	,	PUNCT
cana-2978	32	13	τ)-rung	τ)-rung	VERB
cana-2978	32	14	fn	fn	PROPN
cana-2978	32	15	are	be	AUX
cana-2978	32	16	discussed	discuss	VERB
cana-2978	32	17	.	.	PUNCT
cana-2978	33	1	2	2	NUM
cana-2978	33	2	background	background	NOUN
cana-2978	33	3	many	many	ADJ
cana-2978	33	4	important	important	ADJ
cana-2978	33	5	definitions	definition	NOUN
cana-2978	33	6	that	that	PRON
cana-2978	33	7	we	we	PRON
cana-2978	33	8	should	should	AUX
cana-2978	33	9	review	review	VERB
cana-2978	33	10	for	for	ADP
cana-2978	33	11	future	future	ADJ
cana-2978	33	12	learning	learning	NOUN
cana-2978	33	13	are	be	AUX
cana-2978	33	14	included	include	VERB
cana-2978	33	15	in	in	ADP
cana-2978	33	16	this	this	DET
cana-2978	33	17	section	section	NOUN
cana-2978	33	18	.	.	PUNCT
cana-2978	34	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	34	2	133	133	NUM
cana-2978	34	3	communications	communication	NOUN
cana-2978	34	4	on	on	ADP
cana-2978	34	5	applied	apply	VERB
cana-2978	34	6	nonlinear	nonlinear	ADJ
cana-2978	34	7	analysis	analysis	NOUN
cana-2978	34	8	issn	issn	NOUN
cana-2978	34	9	:	:	PUNCT
cana-2978	34	10	1074	1074	NUM
cana-2978	34	11	-	-	PUNCT
cana-2978	34	12	133x	133x	NUM
cana-2978	34	13	vol	vol	NOUN
cana-2978	34	14	32	32	NUM
cana-2978	34	15	no	no	NOUN
cana-2978	34	16	.	.	PUNCT
cana-2978	35	1	5s	5s	NUM
cana-2978	35	2	(	(	PUNCT
cana-2978	35	3	2025	2025	NUM
cana-2978	35	4	)	)	PUNCT
cana-2978	35	5	definition	definition	NOUN
cana-2978	35	6	2	2	NUM
cana-2978	35	7	.1	.1	NOUN
cana-2978	35	8	.	.	PUNCT
cana-2978	36	1	let	let	VERB
cana-2978	36	2	a	a	PRON
cana-2978	36	3	be	be	AUX
cana-2978	36	4	a	a	DET
cana-2978	36	5	universal	universal	NOUN
cana-2978	36	6	.	.	PUNCT
cana-2978	37	1	the	the	DET
cana-2978	37	2	pfs	pfs	PROPN
cana-2978	37	3	θ	θ	PROPN
cana-2978	37	4	=	=	SYM
cana-2978	37	5	{	{	PUNCT
cana-2978	37	6	δ	δ	PROPN
cana-2978	37	7	,	,	PUNCT
cana-2978	37	8	〈	〈	PROPN
cana-2978	37	9	m	m	NOUN
cana-2978	37	10	ᵀ(δ),m	ᵀ(δ),m	NOUN
cana-2978	37	11	`	`	PUNCT
cana-2978	37	12	(	(	PUNCT
cana-2978	37	13	δ	δ	NOUN
cana-2978	37	14	)	)	PUNCT
cana-2978	37	15	〉	〉	PROPN
cana-2978	37	16	∣∣δ	∣∣δ	PROPN
cana-2978	37	17	∈	∈	PROPN
cana-2978	37	18	a	a	PRON
cana-2978	37	19	}	}	PUNCT
cana-2978	37	20	,	,	PUNCT
cana-2978	37	21	m	m	VERB
cana-2978	37	22	ᵀ	ᵀ	NOUN
cana-2978	37	23	:	:	PUNCT
cana-2978	37	24	a	a	DET
cana-2978	37	25	→	→	SYM
cana-2978	37	26	(	(	PUNCT
cana-2978	37	27	0	0	NUM
cana-2978	37	28	,	,	PUNCT
cana-2978	37	29	1	1	NUM
cana-2978	37	30	)	)	PUNCT
cana-2978	37	31	and	and	CCONJ
cana-2978	37	32	m	m	VERB
cana-2978	37	33	`	`	PUNCT
cana-2978	37	34	:	:	PUNCT
cana-2978	37	35	a	a	X
cana-2978	37	36	→	→	SYM
cana-2978	37	37	(	(	PUNCT
cana-2978	37	38	0	0	NUM
cana-2978	37	39	,	,	PUNCT
cana-2978	37	40	1	1	NUM
cana-2978	37	41	)	)	PUNCT
cana-2978	37	42	called	call	VERB
cana-2978	37	43	the	the	DET
cana-2978	37	44	mg	mg	PROPN
cana-2978	37	45	and	and	CCONJ
cana-2978	37	46	nmg	nmg	NOUN
cana-2978	37	47	of	of	ADP
cana-2978	37	48	δ	δ	PROPN
cana-2978	37	49	∈	∈	PROPN
cana-2978	37	50	a	a	DET
cana-2978	37	51	to	to	ADP
cana-2978	37	52	θ	θ	NOUN
cana-2978	37	53	,	,	PUNCT
cana-2978	37	54	respectively	respectively	ADV
cana-2978	37	55	and	and	CCONJ
cana-2978	37	56	0	0	NUM
cana-2978	37	57	�	�	PROPN
cana-2978	37	58	(	(	PUNCT
cana-2978	37	59	m	m	PROPN
cana-2978	37	60	ᵀ(δ))2+(m	ᵀ(δ))2+(m	NOUN
cana-2978	37	61	`	`	PUNCT
cana-2978	37	62	(	(	PUNCT
cana-2978	37	63	δ))2	δ))2	PROPN
cana-2978	37	64	�	�	PROPN
cana-2978	37	65	1	1	NUM
cana-2978	37	66	.	.	PUNCT
cana-2978	38	1	for	for	ADP
cana-2978	38	2	θ	θ	PROPN
cana-2978	38	3	=	=	SYM
cana-2978	38	4	〈	〈	PROPN
cana-2978	38	5	m	m	NOUN
cana-2978	38	6	ᵀ,m	ᵀ,m	NOUN
cana-2978	38	7	`	`	PUNCT
cana-2978	38	8	〉	〉	NOUN
cana-2978	38	9	is	be	AUX
cana-2978	38	10	called	call	VERB
cana-2978	38	11	a	a	DET
cana-2978	38	12	pythagorean	pythagorean	ADJ
cana-2978	38	13	fuzzy	fuzzy	ADJ
cana-2978	38	14	number	number	NOUN
cana-2978	38	15	(	(	PUNCT
cana-2978	38	16	pfn	pfn	PROPN
cana-2978	38	17	)	)	PUNCT
cana-2978	38	18	.	.	PUNCT
cana-2978	39	1	definition	definition	NOUN
cana-2978	39	2	2.2	2.2	NUM
cana-2978	39	3	.	.	PUNCT
cana-2978	40	1	the	the	DET
cana-2978	40	2	ns	ns	NUM
cana-2978	40	3	θ	θ	PROPN
cana-2978	40	4	=	=	SYM
cana-2978	40	5	{	{	PUNCT
cana-2978	40	6	δ	δ	PROPN
cana-2978	40	7	,	,	PUNCT
cana-2978	40	8	〈	〈	PROPN
cana-2978	40	9	m	m	VERB
cana-2978	40	10	ᵀ(δ),mi(δ),m	ᵀ(δ),mi(δ),m	ADJ
cana-2978	40	11	`	`	PUNCT
cana-2978	40	12	(	(	PUNCT
cana-2978	40	13	δ	δ	NOUN
cana-2978	40	14	)	)	PUNCT
cana-2978	40	15	〉	〉	PROPN
cana-2978	40	16	∣∣δ	∣∣δ	PROPN
cana-2978	40	17	∈	∈	PROPN
cana-2978	40	18	a	a	PRON
cana-2978	40	19	}	}	PUNCT
cana-2978	40	20	,	,	PUNCT
cana-2978	40	21	where	where	SCONJ
cana-2978	40	22	m	m	VERB
cana-2978	40	23	ᵀ,mi	ᵀ,mi	VERB
cana-2978	40	24	,	,	PUNCT
cana-2978	40	25	m	m	VERB
cana-2978	40	26	`	`	PUNCT
cana-2978	40	27	:	:	PUNCT
cana-2978	40	28	a	a	X
cana-2978	40	29	→	→	SYM
cana-2978	40	30	(	(	PUNCT
cana-2978	40	31	0	0	NUM
cana-2978	40	32	,	,	PUNCT
cana-2978	40	33	1	1	NUM
cana-2978	40	34	)	)	PUNCT
cana-2978	40	35	is	be	AUX
cana-2978	40	36	denote	denote	VERB
cana-2978	40	37	the	the	DET
cana-2978	40	38	mg	mg	PROPN
cana-2978	40	39	,	,	PUNCT
cana-2978	40	40	img	img	PUNCT
cana-2978	40	41	and	and	CCONJ
cana-2978	40	42	nmg	nmg	NOUN
cana-2978	40	43	of	of	ADP
cana-2978	40	44	δ	δ	PROPN
cana-2978	40	45	∈	∈	PROPN
cana-2978	40	46	a	a	PRON
cana-2978	40	47	,	,	PUNCT
cana-2978	40	48	respectively	respectively	ADV
cana-2978	40	49	and	and	CCONJ
cana-2978	40	50	0	0	NUM
cana-2978	40	51	≤	≤	NUM
cana-2978	40	52	(	(	PUNCT
cana-2978	40	53	m	m	NOUN
cana-2978	40	54	ᵀ(δ	ᵀ(δ	ADJ
cana-2978	40	55	)	)	PUNCT
cana-2978	40	56	)	)	PUNCT
cana-2978	41	1	+	+	CCONJ
cana-2978	41	2	(	(	PUNCT
cana-2978	41	3	mi(δ	mi(δ	NOUN
cana-2978	41	4	)	)	PUNCT
cana-2978	41	5	)	)	PUNCT
cana-2978	42	1	+	+	CCONJ
cana-2978	42	2	(	(	PUNCT
cana-2978	42	3	m	m	VERB
cana-2978	42	4	`	`	PUNCT
cana-2978	42	5	(	(	PUNCT
cana-2978	42	6	δ	δ	NOUN
cana-2978	42	7	)	)	PUNCT
cana-2978	42	8	)	)	PUNCT
cana-2978	42	9	≤	≤	NUM
cana-2978	42	10	2	2	NUM
cana-2978	42	11	.	.	X
cana-2978	43	1	for	for	ADP
cana-2978	43	2	m	m	PROPN
cana-2978	43	3	=	=	VERB
cana-2978	43	4	〈	〈	PROPN
cana-2978	43	5	m	m	NOUN
cana-2978	43	6	ᵀ,mi	ᵀ,mi	NUM
cana-2978	43	7	,	,	PUNCT
cana-2978	43	8	m	m	AUX
cana-2978	43	9	`	`	PUNCT
cana-2978	43	10	〉	〉	NOUN
cana-2978	43	11	is	be	AUX
cana-2978	43	12	called	call	VERB
cana-2978	43	13	a	a	DET
cana-2978	43	14	neutrosophic	neutrosophic	ADJ
cana-2978	43	15	number	number	NOUN
cana-2978	43	16	(	(	PUNCT
cana-2978	43	17	-rung	-rung	PROPN
cana-2978	43	18	fn	fn	NOUN
cana-2978	43	19	)	)	PUNCT
cana-2978	43	20	.	.	PUNCT
cana-2978	44	1	definition	definition	NOUN
cana-2978	44	2	2.3	2.3	NUM
cana-2978	44	3	.	.	PUNCT
cana-2978	45	1	the	the	DET
cana-2978	45	2	pythagorean	pythagorean	PROPN
cana-2978	45	3	ns	ns	NUM
cana-2978	45	4	θ	θ	PROPN
cana-2978	45	5	=	=	SYM
cana-2978	45	6	{	{	PUNCT
cana-2978	45	7	δ	δ	PROPN
cana-2978	45	8	,	,	PUNCT
cana-2978	45	9	〈	〈	PROPN
cana-2978	45	10	m	m	VERB
cana-2978	45	11	ᵀ(δ),mi(δ),m	ᵀ(δ),mi(δ),m	ADJ
cana-2978	45	12	`	`	PUNCT
cana-2978	45	13	(	(	PUNCT
cana-2978	45	14	δ	δ	NOUN
cana-2978	45	15	)	)	PUNCT
cana-2978	45	16	〉	〉	PROPN
cana-2978	45	17	∣∣δ	∣∣δ	PROPN
cana-2978	45	18	∈	∈	PROPN
cana-2978	45	19	a	a	PRON
cana-2978	45	20	}	}	PUNCT
cana-2978	45	21	,	,	PUNCT
cana-2978	45	22	where	where	SCONJ
cana-2978	45	23	m	m	VERB
cana-2978	45	24	ᵀ,mi	ᵀ,mi	VERB
cana-2978	45	25	,	,	PUNCT
cana-2978	45	26	m	m	VERB
cana-2978	45	27	`	`	PUNCT
cana-2978	45	28	:	:	PUNCT
cana-2978	45	29	a	a	X
cana-2978	45	30	→	→	SYM
cana-2978	45	31	(	(	PUNCT
cana-2978	45	32	0	0	NUM
cana-2978	45	33	,	,	PUNCT
cana-2978	45	34	1	1	NUM
cana-2978	45	35	)	)	PUNCT
cana-2978	45	36	is	be	AUX
cana-2978	45	37	called	call	VERB
cana-2978	45	38	the	the	DET
cana-2978	45	39	mg	mg	PROPN
cana-2978	45	40	,	,	PUNCT
cana-2978	45	41	img	img	PUNCT
cana-2978	45	42	and	and	CCONJ
cana-2978	45	43	nmg	nmg	NOUN
cana-2978	45	44	of	of	ADP
cana-2978	45	45	δ	δ	PROPN
cana-2978	45	46	∈	∈	PROPN
cana-2978	45	47	a	a	PRON
cana-2978	45	48	,	,	PUNCT
cana-2978	45	49	respectively	respectively	ADV
cana-2978	45	50	and	and	CCONJ
cana-2978	45	51	0	0	NUM
cana-2978	45	52	≤	≤	NUM
cana-2978	45	53	(	(	PUNCT
cana-2978	45	54	m	m	VERB
cana-2978	45	55	ᵀ(δ))2	ᵀ(δ))2	NOUN
cana-2978	45	56	+	+	CCONJ
cana-2978	45	57	(	(	PUNCT
cana-2978	45	58	mi(δ))2	mi(δ))2	X
cana-2978	45	59	+	+	CCONJ
cana-2978	45	60	(	(	PUNCT
cana-2978	45	61	m	m	VERB
cana-2978	45	62	`	`	PUNCT
cana-2978	45	63	(	(	PUNCT
cana-2978	45	64	δ))2	δ))2	PROPN
cana-2978	45	65	≤	≤	NOUN
cana-2978	45	66	2	2	NUM
cana-2978	45	67	.	.	PUNCT
cana-2978	46	1	for	for	ADP
cana-2978	46	2	m	m	PROPN
cana-2978	46	3	=	=	VERB
cana-2978	46	4	〈	〈	PROPN
cana-2978	46	5	m	m	NOUN
cana-2978	46	6	ᵀ,mi	ᵀ,mi	NUM
cana-2978	46	7	,	,	PUNCT
cana-2978	46	8	m	m	VERB
cana-2978	46	9	`	`	PUNCT
cana-2978	46	10	〉	〉	NOUN
cana-2978	46	11	is	be	AUX
cana-2978	46	12	called	call	VERB
cana-2978	46	13	a	a	DET
cana-2978	46	14	pythagorean	pythagorean	ADJ
cana-2978	46	15	neutrosophic	neutrosophic	ADJ
cana-2978	46	16	number	number	NOUN
cana-2978	46	17	(	(	PUNCT
cana-2978	46	18	py	py	NOUN
cana-2978	46	19	-	-	PUNCT
cana-2978	46	20	rung	rung	NOUN
cana-2978	46	21	fn	fn	NOUN
cana-2978	46	22	)	)	PUNCT
cana-2978	46	23	.	.	PUNCT
cana-2978	47	1	definition	definition	NOUN
cana-2978	47	2	2.4	2.4	NUM
cana-2978	47	3	.	.	PUNCT
cana-2978	48	1	let	let	VERB
cana-2978	48	2	θ1	θ1	PROPN
cana-2978	48	3	=	=	SYM
cana-2978	48	4	(	(	PUNCT
cana-2978	48	5	a1	a1	PROPN
cana-2978	48	6	,	,	PUNCT
cana-2978	48	7	b1	b1	NOUN
cana-2978	48	8	)	)	PUNCT
cana-2978	48	9	∈	∈	PROPN
cana-2978	48	10	nand	nand	NOUN
cana-2978	48	11	θ2	θ2	PROPN
cana-2978	48	12	=	=	SYM
cana-2978	48	13	(	(	PUNCT
cana-2978	48	14	a2	a2	PROPN
cana-2978	48	15	,	,	PUNCT
cana-2978	48	16	b2	b2	NOUN
cana-2978	48	17	)	)	PUNCT
cana-2978	48	18	∈	∈	PROPN
cana-2978	48	19	n	n	NOUN
cana-2978	48	20	.	.	PUNCT
cana-2978	49	1	then	then	ADV
cana-2978	49	2	the	the	DET
cana-2978	49	3	distance	distance	NOUN
cana-2978	49	4	between	between	ADP
cana-2978	49	5	θ1	θ1	NOUN
cana-2978	49	6	and	and	CCONJ
cana-2978	49	7	θ2	θ2	PROPN
cana-2978	49	8	is	be	AUX
cana-2978	49	9	defined	define	VERB
cana-2978	49	10	as	as	ADP
cana-2978	49	11	d(θ1,θ2	d(θ1,θ2	PROPN
cana-2978	49	12	)	)	PUNCT
cana-2978	49	13	=	=	PUNCT
cana-2978	50	1	√	√	PROPN
cana-2978	50	2	(	(	PUNCT
cana-2978	50	3	a1	a1	NOUN
cana-2978	50	4	−	−	PROPN
cana-2978	50	5	a2)2	a2)2	PUNCT
cana-2978	50	6	+	+	NUM
cana-2978	50	7	1	1	NUM
cana-2978	50	8	2	2	NUM
cana-2978	50	9	(	(	PUNCT
cana-2978	50	10	b1	b1	NOUN
cana-2978	50	11	−	−	PROPN
cana-2978	50	12	b2)2	b2)2	ADP
cana-2978	50	13	,	,	PUNCT
cana-2978	50	14	where	where	SCONJ
cana-2978	50	15	n	n	PRON
cana-2978	50	16	is	be	AUX
cana-2978	50	17	a	a	DET
cana-2978	50	18	natural	natural	ADJ
cana-2978	50	19	number	number	NOUN
cana-2978	50	20	.	.	PUNCT
cana-2978	51	1	3	3	NUM
cana-2978	51	2	operations	operation	NOUN
cana-2978	51	3	for	for	ADP
cana-2978	51	4	ct	ct	PROPN
cana-2978	51	5	(	(	PUNCT
cana-2978	51	6	γ	γ	PROPN
cana-2978	51	7	,	,	PUNCT
cana-2978	51	8	τ)-rung	τ)-rung	PUNCT
cana-2978	51	9	fn	fn	NOUN
cana-2978	51	10	we	we	PRON
cana-2978	51	11	introduce	introduce	VERB
cana-2978	51	12	the	the	DET
cana-2978	51	13	notion	notion	NOUN
cana-2978	51	14	of	of	ADP
cana-2978	51	15	a	a	DET
cana-2978	51	16	complex	complex	ADJ
cana-2978	51	17	tangent	tangent	NOUN
cana-2978	51	18	trigonometric	trigonometric	NOUN
cana-2978	51	19	,	,	PUNCT
cana-2978	51	20	the	the	DET
cana-2978	51	21	(	(	PUNCT
cana-2978	51	22	γ	γ	PROPN
cana-2978	51	23	,	,	PUNCT
cana-2978	51	24	τ)-rung	τ)-rung	PUNCT
cana-2978	51	25	fn	fn	NOUN
cana-2978	51	26	.	.	PUNCT
cana-2978	52	1	consequently	consequently	ADV
cana-2978	52	2	,	,	PUNCT
cana-2978	52	3	tanπ/2	tanπ/2	PROPN
cana-2978	52	4	=	=	PUNCT
cana-2978	52	5	a	a	PRON
cana-2978	52	6	and	and	CCONJ
cana-2978	52	7	the	the	DET
cana-2978	52	8	ct	ct	PROPN
cana-2978	52	9	(	(	PUNCT
cana-2978	52	10	γ	γ	PROPN
cana-2978	52	11	,	,	PUNCT
cana-2978	52	12	τ)-rung	τ)-rung	NOUN
cana-2978	52	13	fn	fn	NOUN
cana-2978	52	14	and	and	CCONJ
cana-2978	52	15	its	its	PRON
cana-2978	52	16	operations	operation	NOUN
cana-2978	52	17	were	be	AUX
cana-2978	52	18	established	establish	VERB
cana-2978	52	19	.	.	PUNCT
cana-2978	53	1	definition	definition	NOUN
cana-2978	53	2	3.1	3.1	NUM
cana-2978	53	3	.	.	PUNCT
cana-2978	54	1	the	the	DET
cana-2978	54	2	(	(	PUNCT
cana-2978	54	3	γ	γ	PROPN
cana-2978	54	4	,	,	PUNCT
cana-2978	54	5	τ	τ	NOUN
cana-2978	54	6	)	)	PUNCT
cana-2978	54	7	ns	ns	NUM
cana-2978	54	8	θ	θ	NOUN
cana-2978	54	9	=	=	SYM
cana-2978	54	10	{	{	PUNCT
cana-2978	54	11	δ	δ	PROPN
cana-2978	54	12	,	,	PUNCT
cana-2978	54	13	〈	〈	PROPN
cana-2978	54	14	(	(	PUNCT
cana-2978	54	15	(	(	PUNCT
cana-2978	54	16	a	a	DET
cana-2978	54	17	·	·	PUNCT
cana-2978	54	18	rᵀ)(δ	rᵀ)(δ	PROPN
cana-2978	54	19	)	)	PUNCT
cana-2978	54	20	·	·	PUNCT
cana-2978	55	1	e(a·i	e(a·i	NOUN
cana-2978	55	2	ᵀ)(δ	ᵀ)(δ	PRON
cana-2978	55	3	)	)	PUNCT
cana-2978	55	4	,	,	PUNCT
cana-2978	55	5	(	(	PUNCT
cana-2978	55	6	a	a	DET
cana-2978	55	7	·	·	PUNCT
cana-2978	55	8	r`)(δ	r`)(δ	NOUN
cana-2978	55	9	)	)	PUNCT
cana-2978	55	10	·	·	PUNCT
cana-2978	56	1	e(a·i	e(a·i	NOUN
cana-2978	56	2	`	`	PUNCT
cana-2978	56	3	)	)	PUNCT
cana-2978	56	4	(	(	PUNCT
cana-2978	56	5	δ	δ	NOUN
cana-2978	56	6	)	)	PUNCT
cana-2978	56	7	)	)	PUNCT
cana-2978	56	8	〉	〉	PROPN
cana-2978	56	9	∣∣∣δ	∣∣∣δ	PROPN
cana-2978	56	10	∈	∈	PROPN
cana-2978	56	11	a	a	PRON
cana-2978	56	12	}	}	PUNCT
cana-2978	56	13	,	,	PUNCT
cana-2978	56	14	where	where	SCONJ
cana-2978	56	15	(	(	PUNCT
cana-2978	56	16	a	a	DET
cana-2978	56	17	·	·	PUNCT
cana-2978	56	18	rᵀ	rᵀ	NOUN
cana-2978	56	19	)	)	PUNCT
cana-2978	56	20	,	,	PUNCT
cana-2978	56	21	(	(	PUNCT
cana-2978	56	22	a	a	DET
cana-2978	56	23	·	·	PUNCT
cana-2978	56	24	r	r	NOUN
cana-2978	56	25	`	`	PROPN
cana-2978	56	26	)	)	PUNCT
cana-2978	56	27	:	:	PUNCT
cana-2978	56	28	a	a	X
cana-2978	56	29	→	→	SYM
cana-2978	56	30	(	(	PUNCT
cana-2978	56	31	0	0	NUM
cana-2978	56	32	,	,	PUNCT
cana-2978	56	33	1	1	NUM
cana-2978	56	34	)	)	PUNCT
cana-2978	56	35	denote	denote	VERB
cana-2978	56	36	the	the	DET
cana-2978	56	37	mg	mg	PROPN
cana-2978	56	38	and	and	CCONJ
cana-2978	56	39	nmg	nmg	NOUN
cana-2978	56	40	of	of	ADP
cana-2978	56	41	δ	δ	PROPN
cana-2978	56	42	∈	∈	PROPN
cana-2978	56	43	a	a	DET
cana-2978	56	44	to	to	ADP
cana-2978	56	45	θ	θ	NOUN
cana-2978	56	46	,	,	PUNCT
cana-2978	56	47	respectively	respectively	ADV
cana-2978	56	48	and	and	CCONJ
cana-2978	56	49	0	0	NUM
cana-2978	56	50	≤	≤	NOUN
cana-2978	56	51	(	(	PUNCT
cana-2978	56	52	(	(	PUNCT
cana-2978	56	53	a	a	DET
cana-2978	56	54	·	·	PUNCT
cana-2978	56	55	rᵀ)(δ))γ	rᵀ)(δ))γ	NOUN
cana-2978	56	56	+	+	CCONJ
cana-2978	56	57	(	(	PUNCT
cana-2978	56	58	(	(	PUNCT
cana-2978	56	59	a	a	DET
cana-2978	56	60	·	·	PUNCT
cana-2978	56	61	r`)(δ))τ	r`)(δ))τ	NOUN
cana-2978	56	62	≤	≤	NUM
cana-2978	56	63	1	1	NUM
cana-2978	56	64	and	and	CCONJ
cana-2978	56	65	0	0	NUM
cana-2978	56	66	≤	≤	NOUN
cana-2978	56	67	(	(	PUNCT
cana-2978	56	68	(	(	PUNCT
cana-2978	56	69	a	a	PRON
cana-2978	56	70	·	·	PUNCT
cana-2978	56	71	i	i	PRON
cana-2978	56	72	ᵀ)(δ))γ	ᵀ)(δ))γ	VERB
cana-2978	56	73	+	+	CCONJ
cana-2978	56	74	(	(	PUNCT
cana-2978	56	75	(	(	PUNCT
cana-2978	56	76	a	a	DET
cana-2978	56	77	·	·	PUNCT
cana-2978	56	78	i	i	PRON
cana-2978	56	79	`	`	PUNCT
cana-2978	56	80	)	)	PUNCT
cana-2978	56	81	(	(	PUNCT
cana-2978	56	82	δ))τ	δ))τ	VERB
cana-2978	56	83	≤	≤	NUM
cana-2978	56	84	1	1	NUM
cana-2978	56	85	.	.	PUNCT
cana-2978	57	1	for	for	ADP
cana-2978	57	2	,	,	PUNCT
cana-2978	57	3	θ	θ	PROPN
cana-2978	57	4	=	=	SYM
cana-2978	57	5	〈	〈	PROPN
cana-2978	57	6	(	(	PUNCT
cana-2978	57	7	(	(	PUNCT
cana-2978	57	8	a	a	DET
cana-2978	57	9	·	·	SYM
cana-2978	57	10	rᵀ	rᵀ	NOUN
cana-2978	57	11	)	)	PUNCT
cana-2978	57	12	·	·	PUNCT
cana-2978	57	13	e(a·i	e(a·i	PROPN
cana-2978	57	14	ᵀ	ᵀ	NUM
cana-2978	57	15	)	)	PUNCT
cana-2978	57	16	,	,	PUNCT
cana-2978	57	17	(	(	PUNCT
cana-2978	57	18	a	a	DET
cana-2978	57	19	·	·	SYM
cana-2978	57	20	r	r	NOUN
cana-2978	57	21	`	`	PUNCT
cana-2978	57	22	)	)	PUNCT
cana-2978	57	23	·	·	PUNCT
cana-2978	57	24	e(a·i	e(a·i	NOUN
cana-2978	57	25	`	`	PUNCT
cana-2978	57	26	)	)	PUNCT
cana-2978	57	27	)	)	PUNCT
cana-2978	57	28	〉	〉	NOUN
cana-2978	57	29	is	be	AUX
cana-2978	57	30	represent	represent	VERB
cana-2978	57	31	a	a	DET
cana-2978	57	32	ct	ct	PROPN
cana-2978	57	33	(	(	PUNCT
cana-2978	57	34	γ	γ	PROPN
cana-2978	57	35	,	,	PUNCT
cana-2978	57	36	τ)-rung	τ)-rung	PUNCT
cana-2978	57	37	fn	fn	PROPN
cana-2978	57	38	.	.	PUNCT
cana-2978	57	39	definition	definition	NOUN
cana-2978	57	40	3.2	3.2	NUM
cana-2978	57	41	.	.	PUNCT
cana-2978	58	1	let	let	VERB
cana-2978	58	2	θ	θ	NOUN
cana-2978	58	3	=	=	SYM
cana-2978	58	4	〈	〈	PROPN
cana-2978	58	5	(	(	PUNCT
cana-2978	58	6	(	(	PUNCT
cana-2978	58	7	a	a	DET
cana-2978	58	8	·	·	SYM
cana-2978	58	9	rᵀ	rᵀ	NOUN
cana-2978	58	10	)	)	PUNCT
cana-2978	58	11	·	·	PUNCT
cana-2978	59	1	e(a·i	e(a·i	PROPN
cana-2978	59	2	ᵀ	ᵀ	NUM
cana-2978	59	3	)	)	PUNCT
cana-2978	59	4	,	,	PUNCT
cana-2978	59	5	(	(	PUNCT
cana-2978	59	6	(	(	PUNCT
cana-2978	59	7	a	a	DET
cana-2978	59	8	·	·	SYM
cana-2978	59	9	r	r	NOUN
cana-2978	59	10	`	`	NOUN
cana-2978	59	11	)	)	PUNCT
cana-2978	59	12	)	)	PUNCT
cana-2978	59	13	·	·	PUNCT
cana-2978	60	1	e(a·i	e(a·i	NOUN
cana-2978	60	2	`	`	PUNCT
cana-2978	60	3	)	)	PUNCT
cana-2978	60	4	)	)	PUNCT
cana-2978	60	5	〉	〉	PROPN
cana-2978	60	6	,	,	PUNCT
cana-2978	60	7	θ1	θ1	NOUN
cana-2978	60	8	=	=	SYM
cana-2978	60	9	〈	〈	PROPN
cana-2978	60	10	(	(	PUNCT
cana-2978	60	11	(	(	PUNCT
cana-2978	60	12	a	a	DET
cana-2978	60	13	·	·	PUNCT
cana-2978	60	14	rᵀ	rᵀ	NOUN
cana-2978	60	15	1	1	NUM
cana-2978	60	16	)	)	PUNCT
cana-2978	60	17	·	·	PUNCT
cana-2978	61	1	e(a·i	e(a·i	NOUN
cana-2978	61	2	ᵀ	ᵀ	ADP
cana-2978	61	3	1	1	NUM
cana-2978	61	4	)	)	PUNCT
cana-2978	61	5	,	,	PUNCT
cana-2978	61	6	(	(	PUNCT
cana-2978	61	7	a	a	DET
cana-2978	61	8	·	·	SYM
cana-2978	61	9	r	r	NOUN
cana-2978	61	10	`	`	SYM
cana-2978	61	11	1	1	NUM
cana-2978	61	12	)	)	PUNCT
cana-2978	61	13	·	·	PUNCT
cana-2978	62	1	e(a·i	e(a·i	NOUN
cana-2978	62	2	`	`	PUNCT
cana-2978	62	3	1	1	NUM
cana-2978	62	4	)	)	PUNCT
cana-2978	62	5	)	)	PUNCT
cana-2978	62	6	〉	〉	PROPN
cana-2978	62	7	,	,	PUNCT
cana-2978	62	8	θ2	θ2	PROPN
cana-2978	62	9	=	=	SYM
cana-2978	62	10	〈	〈	PROPN
cana-2978	62	11	(	(	PUNCT
cana-2978	62	12	(	(	PUNCT
cana-2978	62	13	a	a	DET
cana-2978	62	14	·	·	PUNCT
cana-2978	62	15	rᵀ	rᵀ	NOUN
cana-2978	62	16	2	2	NUM
cana-2978	62	17	)	)	PUNCT
cana-2978	62	18	·	·	PUNCT
cana-2978	63	1	e(a·i	e(a·i	NOUN
cana-2978	63	2	ᵀ	ᵀ	ADP
cana-2978	63	3	2	2	NUM
cana-2978	63	4	)	)	PUNCT
cana-2978	63	5	,	,	PUNCT
cana-2978	63	6	(	(	PUNCT
cana-2978	63	7	a	a	DET
cana-2978	63	8	·	·	SYM
cana-2978	63	9	r	r	NOUN
cana-2978	63	10	`	`	SYM
cana-2978	63	11	2	2	NUM
cana-2978	63	12	)	)	PUNCT
cana-2978	63	13	·	·	PUNCT
cana-2978	64	1	e(a·i	e(a·i	NOUN
cana-2978	64	2	`	`	PUNCT
cana-2978	64	3	2	2	NUM
cana-2978	64	4	)	)	PUNCT
cana-2978	64	5	)	)	PUNCT
cana-2978	65	1	〉	〉	NOUN
cana-2978	65	2	be	be	AUX
cana-2978	65	3	any	any	DET
cana-2978	65	4	three	three	NUM
cana-2978	65	5	ct	ct	NUM
cana-2978	65	6	(	(	PUNCT
cana-2978	65	7	γ	γ	PROPN
cana-2978	65	8	,	,	PUNCT
cana-2978	65	9	τ)-rung	τ)-rung	PROPN
cana-2978	65	10	fns	fns	PROPN
cana-2978	65	11	,	,	PUNCT
cana-2978	65	12	and	and	CCONJ
cana-2978	65	13	(	(	PUNCT
cana-2978	65	14	γ	γ	PROPN
cana-2978	65	15	,	,	PUNCT
cana-2978	65	16	τ	τ	PROPN
cana-2978	65	17	)	)	PUNCT
cana-2978	65	18	>	>	X
cana-2978	65	19	0	0	X
cana-2978	65	20	.	.	PUNCT
cana-2978	66	1	then	then	ADV
cana-2978	66	2	1	1	X
cana-2978	66	3	.	.	PUNCT
cana-2978	66	4	θ1	θ1	PROPN
cana-2978	66	5	⊕	⊕	PROPN
cana-2978	66	6	θ2	θ2	PROPN
cana-2978	66	7	=	=	SYM
cana-2978	66	8			PROPN
cana-2978	66	9	γ	γ	NOUN
cana-2978	66	10	√	√	PROPN
cana-2978	66	11	(	(	PUNCT
cana-2978	66	12	(	(	PUNCT
cana-2978	66	13	a	a	DET
cana-2978	66	14	·	·	PUNCT
cana-2978	66	15	rᵀ	rᵀ	NOUN
cana-2978	66	16	1	1	NUM
cana-2978	66	17	)	)	PUNCT
cana-2978	66	18	)	)	PUNCT
cana-2978	67	1	γ	γ	X
cana-2978	67	2	+	+	X
cana-2978	67	3	(	(	PUNCT
cana-2978	67	4	(	(	PUNCT
cana-2978	67	5	a	a	DET
cana-2978	67	6	·	·	PUNCT
cana-2978	67	7	rᵀ	rᵀ	NOUN
cana-2978	67	8	2	2	NUM
cana-2978	67	9	)	)	PUNCT
cana-2978	67	10	)	)	PUNCT
cana-2978	67	11	γ	γ	X
cana-2978	67	12	−((a	−((a	NUM
cana-2978	67	13	·	·	PUNCT
cana-2978	67	14	rᵀ	rᵀ	NOUN
cana-2978	67	15	1	1	NUM
cana-2978	67	16	)	)	PUNCT
cana-2978	67	17	)	)	PUNCT
cana-2978	67	18	γ	γ	X
cana-2978	67	19	·	·	PUNCT
cana-2978	67	20	(	(	PUNCT
cana-2978	67	21	(	(	PUNCT
cana-2978	67	22	a	a	PRON
cana-2978	67	23	·	·	PUNCT
cana-2978	67	24	rᵀ	rᵀ	NOUN
cana-2978	67	25	2	2	NUM
cana-2978	67	26	)	)	PUNCT
cana-2978	67	27	)	)	PUNCT
cana-2978	67	28	γ	γ	X
cana-2978	67	29	·	·	PUNCT
cana-2978	67	30	e	e	X
cana-2978	67	31	γ	γ	X
cana-2978	67	32	√√√√√	√√√√√	PROPN
cana-2978	67	33	(	(	PUNCT
cana-2978	67	34	(	(	PUNCT
cana-2978	67	35	a	a	PRON
cana-2978	67	36	·	·	PUNCT
cana-2978	67	37	i	i	PRON
cana-2978	67	38	ᵀ	ᵀ	ADJ
cana-2978	67	39	1	1	NUM
cana-2978	67	40	)	)	PUNCT
cana-2978	67	41	)	)	PUNCT
cana-2978	67	42	γ	γ	X
cana-2978	67	43	+	+	X
cana-2978	67	44	(	(	PUNCT
cana-2978	67	45	(	(	PUNCT
cana-2978	67	46	a	a	DET
cana-2978	67	47	·	·	PUNCT
cana-2978	67	48	i	i	PRON
cana-2978	67	49	ᵀ	ᵀ	ADJ
cana-2978	67	50	2	2	NUM
cana-2978	67	51	)	)	PUNCT
cana-2978	67	52	)	)	PUNCT
cana-2978	67	53	γ	γ	X
cana-2978	67	54	−((a	−((a	NUM
cana-2978	67	55	·	·	PUNCT
cana-2978	67	56	i	i	PRON
cana-2978	67	57	ᵀ	ᵀ	VERB
cana-2978	67	58	1	1	NUM
cana-2978	67	59	)	)	PUNCT
cana-2978	67	60	)	)	PUNCT
cana-2978	67	61	γ	γ	X
cana-2978	67	62	·	·	PUNCT
cana-2978	67	63	(	(	PUNCT
cana-2978	67	64	(	(	PUNCT
cana-2978	67	65	a	a	PRON
cana-2978	67	66	·	·	PUNCT
cana-2978	67	67	i	i	PRON
cana-2978	67	68	ᵀ	ᵀ	ADJ
cana-2978	67	69	2	2	NUM
cana-2978	67	70	)	)	PUNCT
cana-2978	67	71	)	)	PUNCT
cana-2978	67	72	γ	γ	X
cana-2978	67	73	,	,	PUNCT
cana-2978	67	74	(	(	PUNCT
cana-2978	67	75	(	(	PUNCT
cana-2978	67	76	a	a	DET
cana-2978	67	77	·	·	SYM
cana-2978	67	78	r	r	NOUN
cana-2978	67	79	`	`	PUNCT
cana-2978	67	80	1	1	NUM
cana-2978	67	81	)	)	PUNCT
cana-2978	67	82	)	)	PUNCT
cana-2978	67	83	τ	τ	PROPN
cana-2978	67	84	(	(	PUNCT
cana-2978	67	85	(	(	PUNCT
cana-2978	67	86	a	a	DET
cana-2978	67	87	·	·	SYM
cana-2978	67	88	r	r	NOUN
cana-2978	67	89	`	`	SYM
cana-2978	67	90	2	2	NUM
cana-2978	67	91	)	)	PUNCT
cana-2978	67	92	)	)	PUNCT
cana-2978	67	93	τ	τ	X
cana-2978	67	94	·	·	PUNCT
cana-2978	67	95	e((a·i	e((a·i	PUNCT
cana-2978	67	96	`	`	PUNCT
cana-2978	67	97	1	1	NUM
cana-2978	67	98	)	)	PUNCT
cana-2978	67	99	)	)	PUNCT
cana-2978	68	1	τ	τ	PROPN
cana-2978	68	2	(	(	PUNCT
cana-2978	68	3	(	(	PUNCT
cana-2978	68	4	a·i	a·i	NOUN
cana-2978	68	5	`	`	PUNCT
cana-2978	68	6	2	2	NUM
cana-2978	68	7	)	)	PUNCT
cana-2978	68	8	)	)	PUNCT
cana-2978	69	1	τ	τ	PROPN
cana-2978	69	2			VERB
cana-2978	69	3	,	,	PUNCT
cana-2978	69	4	2	2	X
cana-2978	69	5	.	.	X
cana-2978	69	6	θ1	θ1	PROPN
cana-2978	69	7	�	�	PROPN
cana-2978	69	8	θ2	θ2	PROPN
cana-2978	69	9	=	=	SYM
cana-2978	69	10			PROPN
cana-2978	69	11	(	(	PUNCT
cana-2978	69	12	(	(	PUNCT
cana-2978	69	13	a	a	DET
cana-2978	69	14	·	·	PUNCT
cana-2978	69	15	rᵀ	rᵀ	NOUN
cana-2978	69	16	1	1	NUM
cana-2978	69	17	)	)	PUNCT
cana-2978	69	18	)	)	PUNCT
cana-2978	69	19	γ((a	γ((a	PUNCT
cana-2978	70	1	·	·	PUNCT
cana-2978	70	2	rᵀ	rᵀ	NOUN
cana-2978	70	3	2	2	NUM
cana-2978	70	4	)	)	PUNCT
cana-2978	70	5	)	)	PUNCT
cana-2978	70	6	γ	γ	X
cana-2978	70	7	·	·	PUNCT
cana-2978	70	8	e((a·i	e((a·i	PUNCT
cana-2978	70	9	ᵀ	ᵀ	ADP
cana-2978	70	10	1	1	NUM
cana-2978	70	11	)	)	PUNCT
cana-2978	70	12	)	)	PUNCT
cana-2978	70	13	γ((a·i	γ((a·i	PUNCT
cana-2978	70	14	ᵀ	ᵀ	NUM
cana-2978	70	15	2	2	NUM
cana-2978	70	16	)	)	PUNCT
cana-2978	70	17	)	)	PUNCT
cana-2978	70	18	γ	γ	PROPN
cana-2978	70	19	,	,	PUNCT
cana-2978	70	20	τ	τ	PROPN
cana-2978	70	21	√	√	PROPN
cana-2978	70	22	(	(	PUNCT
cana-2978	70	23	(	(	PUNCT
cana-2978	70	24	a	a	DET
cana-2978	70	25	·	·	SYM
cana-2978	70	26	r	r	NOUN
cana-2978	70	27	`	`	PUNCT
cana-2978	70	28	1	1	NUM
cana-2978	70	29	)	)	PUNCT
cana-2978	70	30	)	)	PUNCT
cana-2978	70	31	τ	τ	PROPN
cana-2978	71	1	+	+	PUNCT
cana-2978	71	2	(	(	PUNCT
cana-2978	71	3	(	(	PUNCT
cana-2978	71	4	a	a	DET
cana-2978	71	5	·	·	SYM
cana-2978	71	6	r	r	NOUN
cana-2978	71	7	`	`	SYM
cana-2978	71	8	2	2	NUM
cana-2978	71	9	)	)	PUNCT
cana-2978	71	10	)	)	PUNCT
cana-2978	72	1	τ	τ	X
cana-2978	72	2	−((a	−((a	NUM
cana-2978	72	3	·	·	PUNCT
cana-2978	72	4	r	r	NOUN
cana-2978	72	5	`	`	PUNCT
cana-2978	72	6	1	1	NUM
cana-2978	72	7	)	)	PUNCT
cana-2978	72	8	)	)	PUNCT
cana-2978	73	1	τ	τ	X
cana-2978	73	2	·	·	PUNCT
cana-2978	73	3	(	(	PUNCT
cana-2978	73	4	(	(	PUNCT
cana-2978	73	5	a	a	DET
cana-2978	73	6	·	·	SYM
cana-2978	73	7	r	r	NOUN
cana-2978	73	8	`	`	SYM
cana-2978	73	9	2	2	NUM
cana-2978	73	10	)	)	PUNCT
cana-2978	73	11	)	)	PUNCT
cana-2978	74	1	τ	τ	X
cana-2978	74	2	·	·	PUNCT
cana-2978	74	3	e	e	X
cana-2978	74	4	τ	τ	X
cana-2978	74	5	√√√√√	√√√√√	PROPN
cana-2978	74	6	(	(	PUNCT
cana-2978	74	7	(	(	PUNCT
cana-2978	74	8	a	a	DET
cana-2978	74	9	·	·	SYM
cana-2978	74	10	r	r	NOUN
cana-2978	74	11	`	`	PUNCT
cana-2978	74	12	1	1	NUM
cana-2978	74	13	)	)	PUNCT
cana-2978	74	14	)	)	PUNCT
cana-2978	74	15	τ	τ	PROPN
cana-2978	75	1	+	+	PUNCT
cana-2978	75	2	(	(	PUNCT
cana-2978	75	3	(	(	PUNCT
cana-2978	75	4	a	a	DET
cana-2978	75	5	·	·	PUNCT
cana-2978	75	6	i	i	NOUN
cana-2978	75	7	`	`	PUNCT
cana-2978	75	8	2	2	NUM
cana-2978	75	9	)	)	PUNCT
cana-2978	75	10	)	)	PUNCT
cana-2978	75	11	τ	τ	X
cana-2978	75	12	−((a	−((a	NUM
cana-2978	75	13	·	·	PUNCT
cana-2978	75	14	r	r	NOUN
cana-2978	75	15	`	`	PUNCT
cana-2978	75	16	1	1	NUM
cana-2978	75	17	)	)	PUNCT
cana-2978	75	18	)	)	PUNCT
cana-2978	76	1	τ	τ	X
cana-2978	76	2	·	·	PUNCT
cana-2978	76	3	(	(	PUNCT
cana-2978	76	4	(	(	PUNCT
cana-2978	76	5	a	a	DET
cana-2978	76	6	·	·	PUNCT
cana-2978	76	7	i	i	NOUN
cana-2978	76	8	`	`	PUNCT
cana-2978	76	9	2	2	NUM
cana-2978	76	10	)	)	PUNCT
cana-2978	76	11	)	)	PUNCT
cana-2978	77	1	τ	τ	PROPN
cana-2978	77	2			ADJ
cana-2978	77	3	3	3	NUM
cana-2978	77	4	.	.	PUNCT
cana-2978	77	5	∂	∂	NUM
cana-2978	77	6	·	·	PUNCT
cana-2978	77	7	θ	θ	X
cana-2978	77	8	=	=	SYM
cana-2978	77	9			PROPN
cana-2978	77	10	γ	γ	NOUN
cana-2978	77	11	√	√	ADP
cana-2978	77	12	1−	1−	NUM
cana-2978	77	13	(	(	PUNCT
cana-2978	77	14	1−	1−	NUM
cana-2978	77	15	(	(	PUNCT
cana-2978	77	16	a	a	DET
cana-2978	77	17	·	·	PUNCT
cana-2978	77	18	(	(	PUNCT
cana-2978	77	19	rᵀ)γ	rᵀ)γ	PROPN
cana-2978	77	20	)	)	PUNCT
cana-2978	77	21	∂	∂	NUM
cana-2978	77	22	·	·	PUNCT
cana-2978	78	1	e	e	X
cana-2978	78	2	γ√1−	γ√1−	X
cana-2978	78	3	(	(	PUNCT
cana-2978	78	4	1−(a·(i	1−(a·(i	NUM
cana-2978	78	5	ᵀ)γ	ᵀ)γ	NOUN
cana-2978	78	6	)	)	PUNCT
cana-2978	78	7	∂	∂	NUM
cana-2978	78	8	,	,	PUNCT
cana-2978	78	9	(	(	PUNCT
cana-2978	78	10	(	(	PUNCT
cana-2978	78	11	a	a	PRON
cana-2978	78	12	·	·	PUNCT
cana-2978	78	13	(	(	PUNCT
cana-2978	78	14	r`)τ	r`)τ	NOUN
cana-2978	78	15	)	)	PUNCT
cana-2978	78	16	∂	∂	NUM
cana-2978	78	17	·	·	PUNCT
cana-2978	78	18	e((a·(i	e((a·(i	NUM
cana-2978	78	19	`	`	PUNCT
cana-2978	78	20	)	)	PUNCT
cana-2978	78	21	τ	τ	PROPN
cana-2978	78	22	)	)	PUNCT
cana-2978	78	23	∂	∂	NUM
cana-2978	78	24			NOUN
cana-2978	78	25	4	4	NUM
cana-2978	78	26	.	.	X
cana-2978	78	27	θ∂	θ∂	PROPN
cana-2978	78	28	=	=	SYM
cana-2978	78	29			PROPN
cana-2978	78	30	(	(	PUNCT
cana-2978	78	31	(	(	PUNCT
cana-2978	78	32	a	a	PRON
cana-2978	78	33	·	·	PUNCT
cana-2978	78	34	(	(	PUNCT
cana-2978	78	35	rᵀ)γ)∂	rᵀ)γ)∂	X
cana-2978	78	36	·	·	PUNCT
cana-2978	79	1	e((a·(i	e((a·(i	PRON
cana-2978	79	2	ᵀ)γ)∂	ᵀ)γ)∂	ADV
cana-2978	79	3	,	,	PUNCT
cana-2978	79	4	τ	τ	PROPN
cana-2978	79	5	√	√	PROPN
cana-2978	79	6	1−	1−	NUM
cana-2978	79	7	(	(	PUNCT
cana-2978	79	8	1−	1−	NUM
cana-2978	79	9	(	(	PUNCT
cana-2978	79	10	a	a	PRON
cana-2978	79	11	·	·	PUNCT
cana-2978	79	12	(	(	PUNCT
cana-2978	79	13	r`)τ	r`)τ	NOUN
cana-2978	79	14	)	)	PUNCT
cana-2978	79	15	∂	∂	NUM
cana-2978	79	16	·	·	PUNCT
cana-2978	79	17	e	e	X
cana-2978	79	18	τ√1−	τ√1−	NOUN
cana-2978	79	19	(	(	PUNCT
cana-2978	79	20	1−(a·(i	1−(a·(i	NUM
cana-2978	79	21	`	`	PUNCT
cana-2978	79	22	)	)	PUNCT
cana-2978	79	23	τ	τ	PROPN
cana-2978	79	24	)	)	PUNCT
cana-2978	79	25	∂	∂	NUM
cana-2978	79	26			NOUN
cana-2978	79	27	.	.	PUNCT
cana-2978	80	1	definition	definition	NOUN
cana-2978	80	2	3.3	3.3	NUM
cana-2978	80	3	.	.	PUNCT
cana-2978	81	1	for	for	ADP
cana-2978	81	2	any	any	DET
cana-2978	81	3	two	two	NUM
cana-2978	81	4	ct	ct	NUM
cana-2978	81	5	(	(	PUNCT
cana-2978	81	6	γ	γ	PROPN
cana-2978	81	7	,	,	PUNCT
cana-2978	81	8	τ)-rung	τ)-rung	PROPN
cana-2978	81	9	fns	fns	PROPN
cana-2978	81	10	θ1	θ1	PROPN
cana-2978	81	11	=	=	SYM
cana-2978	81	12	〈	〈	PROPN
cana-2978	81	13	(	(	PUNCT
cana-2978	81	14	(	(	PUNCT
cana-2978	81	15	(	(	PUNCT
cana-2978	81	16	a	a	DET
cana-2978	81	17	·	·	PUNCT
cana-2978	81	18	rᵀ	rᵀ	NOUN
cana-2978	81	19	1	1	NUM
cana-2978	81	20	)	)	PUNCT
cana-2978	81	21	,	,	PUNCT
cana-2978	81	22	(	(	PUNCT
cana-2978	81	23	a	a	DET
cana-2978	81	24	·	·	SYM
cana-2978	81	25	r	r	NOUN
cana-2978	81	26	`	`	PUNCT
cana-2978	81	27	1	1	NUM
cana-2978	81	28	)	)	PUNCT
cana-2978	81	29	)	)	PUNCT
cana-2978	81	30	)	)	PUNCT
cana-2978	81	31	〉	〉	PROPN
cana-2978	81	32	and	and	CCONJ
cana-2978	81	33	θ2	θ2	PROPN
cana-2978	81	34	=	=	SYM
cana-2978	81	35	〈	〈	PROPN
cana-2978	81	36	(	(	PUNCT
cana-2978	81	37	(	(	PUNCT
cana-2978	81	38	(	(	PUNCT
cana-2978	81	39	a	a	DET
cana-2978	81	40	·	·	PUNCT
cana-2978	81	41	rᵀ	rᵀ	NOUN
cana-2978	81	42	2	2	NUM
cana-2978	81	43	)	)	PUNCT
cana-2978	81	44	,	,	PUNCT
cana-2978	81	45	(	(	PUNCT
cana-2978	81	46	a	a	DET
cana-2978	81	47	·	·	PUNCT
cana-2978	81	48	r	r	NOUN
cana-2978	81	49	`	`	SYM
cana-2978	81	50	2	2	NUM
cana-2978	81	51	)	)	PUNCT
cana-2978	81	52	)	)	PUNCT
cana-2978	81	53	)	)	PUNCT
cana-2978	81	54	〉	〉	PROPN
cana-2978	81	55	.	.	PUNCT
cana-2978	82	1	then	then	ADV
cana-2978	82	2	de(θ1,θ2	de(θ1,θ2	PROPN
cana-2978	82	3	)	)	PUNCT
cana-2978	82	4	=	=	SYM
cana-2978	83	1	√	√	NUM
cana-2978	83	2	1	1	NUM
cana-2978	83	3	2	2	NUM
cana-2978	83	4	[	[	PUNCT
cana-2978	83	5	[	[	PUNCT
cana-2978	83	6	1	1	NUM
cana-2978	83	7	+	+	CCONJ
cana-2978	83	8	(	(	PUNCT
cana-2978	83	9	(	(	PUNCT
cana-2978	83	10	a	a	DET
cana-2978	83	11	·	·	PUNCT
cana-2978	83	12	rᵀ	rᵀ	NOUN
cana-2978	83	13	1	1	NUM
cana-2978	83	14	)	)	PUNCT
cana-2978	83	15	)	)	PUNCT
cana-2978	83	16	2	2	NUM
cana-2978	83	17	−	−	PROPN
cana-2978	83	18	(	(	PUNCT
cana-2978	83	19	(	(	PUNCT
cana-2978	83	20	a	a	DET
cana-2978	83	21	·	·	SYM
cana-2978	83	22	r	r	NOUN
cana-2978	83	23	`	`	PUNCT
cana-2978	83	24	1	1	NUM
cana-2978	83	25	)	)	PUNCT
cana-2978	83	26	)	)	PUNCT
cana-2978	83	27	2	2	NUM
cana-2978	83	28	−	−	NOUN
cana-2978	83	29	(	(	PUNCT
cana-2978	83	30	1	1	NUM
cana-2978	83	31	+	+	CCONJ
cana-2978	83	32	(	(	PUNCT
cana-2978	83	33	(	(	PUNCT
cana-2978	83	34	a	a	DET
cana-2978	83	35	·	·	PUNCT
cana-2978	83	36	rᵀ	rᵀ	NOUN
cana-2978	83	37	2	2	NUM
cana-2978	83	38	)	)	PUNCT
cana-2978	83	39	)	)	PUNCT
cana-2978	83	40	2	2	NUM
cana-2978	83	41	−	−	PROPN
cana-2978	83	42	(	(	PUNCT
cana-2978	83	43	(	(	PUNCT
cana-2978	83	44	a	a	DET
cana-2978	83	45	·	·	SYM
cana-2978	83	46	r	r	NOUN
cana-2978	83	47	`	`	SYM
cana-2978	83	48	2	2	NUM
cana-2978	83	49	)	)	PUNCT
cana-2978	83	50	)	)	PUNCT
cana-2978	83	51	2	2	NUM
cana-2978	83	52	)	)	PUNCT
cana-2978	83	53	]	]	X
cana-2978	83	54	2	2	X
cana-2978	84	1	+	+	CCONJ
cana-2978	84	2	[	[	PUNCT
cana-2978	84	3	(	(	PUNCT
cana-2978	84	4	(	(	PUNCT
cana-2978	84	5	a	a	DET
cana-2978	84	6	·	·	PUNCT
cana-2978	84	7	i	i	PRON
cana-2978	84	8	ᵀ	ᵀ	ADJ
cana-2978	84	9	1	1	NUM
cana-2978	84	10	)	)	PUNCT
cana-2978	84	11	)	)	PUNCT
cana-2978	84	12	2	2	NUM
cana-2978	84	13	−	−	PROPN
cana-2978	84	14	(	(	PUNCT
cana-2978	84	15	(	(	PUNCT
cana-2978	84	16	a	a	DET
cana-2978	84	17	·	·	PUNCT
cana-2978	84	18	i	i	NOUN
cana-2978	84	19	`	`	PUNCT
cana-2978	84	20	1	1	NUM
cana-2978	84	21	)	)	PUNCT
cana-2978	84	22	)	)	PUNCT
cana-2978	84	23	2	2	NUM
cana-2978	84	24	−	−	PROPN
cana-2978	84	25	(	(	PUNCT
cana-2978	84	26	(	(	PUNCT
cana-2978	84	27	(	(	PUNCT
cana-2978	84	28	a	a	DET
cana-2978	84	29	·	·	PUNCT
cana-2978	84	30	i	i	PRON
cana-2978	84	31	ᵀ	ᵀ	ADJ
cana-2978	84	32	2	2	NUM
cana-2978	84	33	)	)	PUNCT
cana-2978	84	34	)	)	PUNCT
cana-2978	84	35	2	2	NUM
cana-2978	84	36	−	−	PROPN
cana-2978	84	37	(	(	PUNCT
cana-2978	84	38	(	(	PUNCT
cana-2978	84	39	a	a	DET
cana-2978	84	40	·	·	PUNCT
cana-2978	84	41	i	i	NOUN
cana-2978	84	42	`	`	PUNCT
cana-2978	84	43	2	2	NUM
cana-2978	84	44	)	)	PUNCT
cana-2978	84	45	)	)	PUNCT
cana-2978	84	46	2	2	NUM
cana-2978	84	47	)	)	PUNCT
cana-2978	84	48	]	]	X
cana-2978	84	49	2	2	X
cana-2978	84	50	]	]	PUNCT
cana-2978	84	51	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	84	52	134	134	NUM
cana-2978	84	53	communications	communication	NOUN
cana-2978	84	54	on	on	ADP
cana-2978	84	55	applied	apply	VERB
cana-2978	84	56	nonlinear	nonlinear	ADJ
cana-2978	84	57	analysis	analysis	NOUN
cana-2978	84	58	issn	issn	NOUN
cana-2978	84	59	:	:	PUNCT
cana-2978	84	60	1074	1074	NUM
cana-2978	84	61	-	-	PUNCT
cana-2978	84	62	133x	133x	NUM
cana-2978	84	63	vol	vol	NOUN
cana-2978	84	64	32	32	NUM
cana-2978	84	65	no	no	NOUN
cana-2978	84	66	.	.	PUNCT
cana-2978	85	1	5s	5s	NUM
cana-2978	85	2	(	(	PUNCT
cana-2978	85	3	2025	2025	NUM
cana-2978	85	4	)	)	PUNCT
cana-2978	85	5	where	where	SCONJ
cana-2978	85	6	de(θ1	de(θ1	PROPN
cana-2978	85	7	,	,	PUNCT
cana-2978	85	8	θ2	θ2	PROPN
cana-2978	85	9	)	)	PUNCT
cana-2978	85	10	is	be	AUX
cana-2978	85	11	called	call	VERB
cana-2978	85	12	the	the	DET
cana-2978	85	13	ed	ed	NOUN
cana-2978	85	14	between	between	ADP
cana-2978	85	15	θ1	θ1	PROPN
cana-2978	85	16	and	and	CCONJ
cana-2978	85	17	θ2	θ2	PROPN
cana-2978	85	18	.	.	PUNCT
cana-2978	86	1	dh(θ1,θ2	dh(θ1,θ2	X
cana-2978	86	2	)	)	PUNCT
cana-2978	87	1	=	=	SYM
cana-2978	87	2	1	1	NUM
cana-2978	87	3	2	2	NUM
cana-2978	88	1	[	[	X
cana-2978	88	2	∣∣∣∣∣	∣∣∣∣∣	NOUN
cana-2978	88	3	1	1	NUM
cana-2978	88	4	+	+	CCONJ
cana-2978	88	5	(	(	PUNCT
cana-2978	88	6	(	(	PUNCT
cana-2978	88	7	a	a	DET
cana-2978	88	8	·	·	PUNCT
cana-2978	88	9	rᵀ	rᵀ	NOUN
cana-2978	88	10	1	1	NUM
cana-2978	88	11	)	)	PUNCT
cana-2978	88	12	)	)	PUNCT
cana-2978	88	13	2	2	NUM
cana-2978	88	14	−	−	PROPN
cana-2978	88	15	(	(	PUNCT
cana-2978	88	16	(	(	PUNCT
cana-2978	88	17	a	a	DET
cana-2978	88	18	·	·	SYM
cana-2978	88	19	r	r	NOUN
cana-2978	88	20	`	`	PUNCT
cana-2978	88	21	1	1	NUM
cana-2978	88	22	)	)	PUNCT
cana-2978	88	23	)	)	PUNCT
cana-2978	88	24	2	2	NUM
cana-2978	88	25	−	−	NOUN
cana-2978	88	26	(	(	PUNCT
cana-2978	88	27	1	1	NUM
cana-2978	88	28	+	+	CCONJ
cana-2978	88	29	(	(	PUNCT
cana-2978	88	30	(	(	PUNCT
cana-2978	88	31	a	a	DET
cana-2978	88	32	·	·	PUNCT
cana-2978	88	33	rᵀ	rᵀ	NOUN
cana-2978	88	34	2	2	NUM
cana-2978	88	35	)	)	PUNCT
cana-2978	88	36	)	)	PUNCT
cana-2978	88	37	2	2	NUM
cana-2978	88	38	−	−	PROPN
cana-2978	88	39	(	(	PUNCT
cana-2978	88	40	(	(	PUNCT
cana-2978	88	41	a	a	DET
cana-2978	88	42	·	·	SYM
cana-2978	88	43	r	r	NOUN
cana-2978	88	44	`	`	SYM
cana-2978	88	45	2	2	NUM
cana-2978	88	46	)	)	PUNCT
cana-2978	88	47	)	)	PUNCT
cana-2978	88	48	2	2	X
cana-2978	88	49	)	)	PUNCT
cana-2978	88	50	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
cana-2978	88	51	∣∣∣∣∣	∣∣∣∣∣	PROPN
cana-2978	88	52	(	(	PUNCT
cana-2978	88	53	(	(	PUNCT
cana-2978	88	54	a	a	PRON
cana-2978	88	55	·	·	PUNCT
cana-2978	88	56	i	i	PRON
cana-2978	88	57	ᵀ	ᵀ	ADJ
cana-2978	88	58	1	1	NUM
cana-2978	88	59	)	)	PUNCT
cana-2978	88	60	)	)	PUNCT
cana-2978	88	61	2	2	NUM
cana-2978	88	62	−	−	PROPN
cana-2978	88	63	(	(	PUNCT
cana-2978	88	64	(	(	PUNCT
cana-2978	88	65	a	a	DET
cana-2978	88	66	·	·	PUNCT
cana-2978	88	67	i	i	NOUN
cana-2978	88	68	`	`	PUNCT
cana-2978	88	69	1	1	NUM
cana-2978	88	70	)	)	PUNCT
cana-2978	88	71	)	)	PUNCT
cana-2978	88	72	2	2	NUM
cana-2978	88	73	(	(	PUNCT
cana-2978	88	74	−((a	−((a	VERB
cana-2978	88	75	·	·	PUNCT
cana-2978	88	76	i	i	PRON
cana-2978	88	77	ᵀ	ᵀ	VERB
cana-2978	88	78	2	2	NUM
cana-2978	88	79	)	)	PUNCT
cana-2978	88	80	)	)	PUNCT
cana-2978	88	81	2	2	NUM
cana-2978	88	82	−	−	PROPN
cana-2978	88	83	(	(	PUNCT
cana-2978	88	84	(	(	PUNCT
cana-2978	88	85	a	a	DET
cana-2978	88	86	·	·	PUNCT
cana-2978	88	87	i	i	NOUN
cana-2978	88	88	`	`	PUNCT
cana-2978	88	89	2	2	NUM
cana-2978	88	90	)	)	PUNCT
cana-2978	88	91	)	)	PUNCT
cana-2978	88	92	2	2	NUM
cana-2978	88	93	)	)	PUNCT
cana-2978	88	94	∣∣∣∣∣	∣∣∣∣∣	ADP
cana-2978	88	95	]	]	PUNCT
cana-2978	88	96	where	where	SCONJ
cana-2978	88	97	dh(θ1,θ2	dh(θ1,θ2	NUM
cana-2978	88	98	)	)	PUNCT
cana-2978	88	99	is	be	AUX
cana-2978	88	100	called	call	VERB
cana-2978	88	101	the	the	DET
cana-2978	88	102	hd	hd	NOUN
cana-2978	88	103	between	between	ADP
cana-2978	88	104	θ1	θ1	PROPN
cana-2978	88	105	and	and	CCONJ
cana-2978	88	106	θ2	θ2	PROPN
cana-2978	88	107	.	.	PROPN
cana-2978	88	108	4	4	NUM
cana-2978	88	109	aos	aos	PROPN
cana-2978	88	110	based	base	VERB
cana-2978	88	111	on	on	ADP
cana-2978	88	112	ct	ct	PROPN
cana-2978	88	113	(	(	PUNCT
cana-2978	88	114	γ	γ	PROPN
cana-2978	88	115	,	,	PUNCT
cana-2978	88	116	τ)-rung	τ)-rung	PUNCT
cana-2978	88	117	fn	fn	NOUN
cana-2978	89	1	we	we	PRON
cana-2978	89	2	use	use	VERB
cana-2978	89	3	ct	ct	PROPN
cana-2978	89	4	(	(	PUNCT
cana-2978	89	5	γ	γ	PROPN
cana-2978	89	6	,	,	PUNCT
cana-2978	89	7	τ)-rung	τ)-rung	NOUN
cana-2978	89	8	fnwa	fnwa	VERB
cana-2978	89	9	,	,	PUNCT
cana-2978	89	10	ct	ct	PROPN
cana-2978	89	11	(	(	PUNCT
cana-2978	89	12	γ	γ	PROPN
cana-2978	89	13	,	,	PUNCT
cana-2978	89	14	τ)-rung	τ)-rung	VERB
cana-2978	89	15	fnwg	fnwg	PROPN
cana-2978	89	16	,	,	PUNCT
cana-2978	89	17	gct	gct	PROPN
cana-2978	89	18	(	(	PUNCT
cana-2978	89	19	γ	γ	PROPN
cana-2978	89	20	,	,	PUNCT
cana-2978	89	21	τ)-rung	τ)-rung	NOUN
cana-2978	89	22	fnwa	fnwa	VERB
cana-2978	89	23	,	,	PUNCT
cana-2978	89	24	and	and	CCONJ
cana-2978	89	25	gct	gct	PROPN
cana-2978	89	26	(	(	PUNCT
cana-2978	89	27	γ	γ	PROPN
cana-2978	89	28	,	,	PUNCT
cana-2978	89	29	τ)-rung	τ)-rung	PUNCT
cana-2978	89	30	fnwg	fnwg	ADJ
cana-2978	89	31	to	to	PART
cana-2978	89	32	describe	describe	VERB
cana-2978	89	33	the	the	DET
cana-2978	89	34	aos	aos	PROPN
cana-2978	89	35	.	.	PROPN
cana-2978	89	36	4.1	4.1	NUM
cana-2978	89	37	ct	ct	PROPN
cana-2978	89	38	(	(	PUNCT
cana-2978	89	39	γ	γ	X
cana-2978	89	40	,	,	PUNCT
cana-2978	89	41	τ)nwa	τ)nwa	ADJ
cana-2978	89	42	definition	definition	NOUN
cana-2978	89	43	4.1	4.1	NUM
cana-2978	89	44	.	.	PUNCT
cana-2978	90	1	let	let	VERB
cana-2978	90	2	θi	θi	X
cana-2978	90	3	=	=	SYM
cana-2978	90	4	〈	〈	PROPN
cana-2978	90	5	(	(	PUNCT
cana-2978	90	6	(	(	PUNCT
cana-2978	90	7	(	(	PUNCT
cana-2978	90	8	a	a	DET
cana-2978	90	9	·	·	PUNCT
cana-2978	90	10	rᵀ	rᵀ	NOUN
cana-2978	90	11	i	i	NOUN
cana-2978	90	12	)	)	PUNCT
cana-2978	90	13	·	·	PUNCT
cana-2978	91	1	e(a·i	e(a·i	NOUN
cana-2978	91	2	ᵀ	ᵀ	VERB
cana-2978	91	3	i	i	PROPN
cana-2978	91	4	)	)	PUNCT
cana-2978	91	5	,	,	PUNCT
cana-2978	91	6	(	(	PUNCT
cana-2978	91	7	a	a	PRON
cana-2978	91	8	·	·	PUNCT
cana-2978	91	9	r	r	NOUN
cana-2978	91	10	`	`	PUNCT
cana-2978	91	11	i	i	NOUN
cana-2978	91	12	)	)	PUNCT
cana-2978	91	13	·	·	PUNCT
cana-2978	92	1	e(a·i	e(a·i	NOUN
cana-2978	92	2	`	`	PUNCT
cana-2978	92	3	i	i	PROPN
cana-2978	92	4	)	)	PUNCT
cana-2978	92	5	)	)	PUNCT
cana-2978	92	6	)	)	PUNCT
cana-2978	93	1	〉	〉	NOUN
cana-2978	93	2	be	be	AUX
cana-2978	93	3	the	the	DET
cana-2978	93	4	ct	ct	PROPN
cana-2978	93	5	(	(	PUNCT
cana-2978	93	6	γ	γ	PROPN
cana-2978	93	7	,	,	PUNCT
cana-2978	93	8	τ)-rung	τ)-rung	PROPN
cana-2978	93	9	fns	fns	PROPN
cana-2978	93	10	,	,	PUNCT
cana-2978	93	11	w	w	PROPN
cana-2978	93	12	=	=	SYM
cana-2978	93	13	(	(	PUNCT
cana-2978	93	14	ω1	ω1	PROPN
cana-2978	93	15	,	,	PUNCT
cana-2978	93	16	ω2	ω2	ADJ
cana-2978	93	17	,	,	PUNCT
cana-2978	93	18	...	...	PUNCT
cana-2978	93	19	,	,	PUNCT
cana-2978	93	20	ω	ω	X
cana-2978	93	21	`	`	PUNCT
cana-2978	93	22	)	)	PUNCT
cana-2978	93	23	be	be	AUX
cana-2978	93	24	the	the	DET
cana-2978	93	25	weight	weight	NOUN
cana-2978	93	26	of	of	ADP
cana-2978	93	27	θi	θi	PROPN
cana-2978	93	28	,	,	PUNCT
cana-2978	93	29	ωi	ωi	X
cana-2978	93	30	≥	≥	NOUN
cana-2978	93	31	0	0	NUM
cana-2978	93	32	and	and	CCONJ
cana-2978	93	33	⊕	⊕	PROPN
cana-2978	93	34	`	`	PUNCT
cana-2978	93	35	i=1	i=1	PROPN
cana-2978	93	36	ωi	ωi	PROPN
cana-2978	93	37	=	=	ADJ
cana-2978	93	38	1	1	X
cana-2978	93	39	.	.	PUNCT
cana-2978	94	1	then	then	ADV
cana-2978	94	2	ct	ct	PRON
cana-2978	94	3	(	(	PUNCT
cana-2978	94	4	γ	γ	PROPN
cana-2978	94	5	,	,	PUNCT
cana-2978	94	6	τ)-rung	τ)-rung	NOUN
cana-2978	94	7	fnwa	fnwa	PROPN
cana-2978	94	8	(	(	PUNCT
cana-2978	94	9	θ1,θ2	θ1,θ2	PROPN
cana-2978	94	10	,	,	PUNCT
cana-2978	94	11	...	...	PUNCT
cana-2978	94	12	,	,	PUNCT
cana-2978	94	13	θ	θ	NOUN
cana-2978	94	14	`	`	PUNCT
cana-2978	94	15	)	)	PUNCT
cana-2978	95	1	=	=	VERB
cana-2978	95	2	⊕	⊕	PROPN
cana-2978	95	3	`	`	PUNCT
cana-2978	95	4	i=1	i=1	PROPN
cana-2978	95	5	ωiθi	ωiθi	PROPN
cana-2978	95	6	.	.	PUNCT
cana-2978	96	1	theorem	theorem	VERB
cana-2978	96	2	4.2	4.2	NUM
cana-2978	96	3	.	.	PUNCT
cana-2978	97	1	let	let	VERB
cana-2978	97	2	θi	θi	X
cana-2978	97	3	=	=	PROPN
cana-2978	97	4	〈	〈	PROPN
cana-2978	97	5	(	(	PUNCT
cana-2978	97	6	(	(	PUNCT
cana-2978	97	7	(	(	PUNCT
cana-2978	97	8	a	a	DET
cana-2978	97	9	·	·	PUNCT
cana-2978	97	10	rᵀ	rᵀ	NOUN
cana-2978	97	11	i	i	NOUN
cana-2978	97	12	)	)	PUNCT
cana-2978	97	13	·	·	PUNCT
cana-2978	98	1	e(a·i	e(a·i	NOUN
cana-2978	98	2	ᵀ	ᵀ	VERB
cana-2978	98	3	i	i	PROPN
cana-2978	98	4	)	)	PUNCT
cana-2978	98	5	,	,	PUNCT
cana-2978	98	6	(	(	PUNCT
cana-2978	98	7	a	a	DET
cana-2978	98	8	·	·	SYM
cana-2978	98	9	r	r	NOUN
cana-2978	98	10	`	`	PUNCT
cana-2978	98	11	i	i	PROPN
cana-2978	98	12	)	)	PUNCT
cana-2978	98	13	·	·	PUNCT
cana-2978	99	1	e(a·i	e(a·i	NOUN
cana-2978	99	2	`	`	PUNCT
cana-2978	99	3	i	i	PROPN
cana-2978	99	4	)	)	PUNCT
cana-2978	99	5	)	)	PUNCT
cana-2978	99	6	)	)	PUNCT
cana-2978	99	7	〉	〉	NOUN
cana-2978	99	8	be	be	VERB
cana-2978	99	9	the	the	DET
cana-2978	99	10	ct	ct	PROPN
cana-2978	99	11	(	(	PUNCT
cana-2978	99	12	γ	γ	PROPN
cana-2978	99	13	,	,	PUNCT
cana-2978	99	14	τ)-rung	τ)-rung	PROPN
cana-2978	99	15	fns	fns	PROPN
cana-2978	99	16	.	.	PUNCT
cana-2978	100	1	then	then	ADV
cana-2978	100	2	ct	ct	PRON
cana-2978	100	3	(	(	PUNCT
cana-2978	100	4	γ	γ	X
cana-2978	100	5	,	,	PUNCT
cana-2978	100	6	τ)nwa(θ1,θ2	τ)nwa(θ1,θ2	PROPN
cana-2978	100	7	,	,	PUNCT
cana-2978	100	8	...	...	PUNCT
cana-2978	100	9	,	,	PUNCT
cana-2978	100	10	θ	θ	NOUN
cana-2978	100	11	`	`	PUNCT
cana-2978	100	12	)	)	PUNCT
cana-2978	101	1	=	=	VERB
cana-2978	101	2			NUM
cana-2978	101	3	γ	γ	NOUN
cana-2978	101	4	√	√	PROPN
cana-2978	101	5	1−	1−	NUM
cana-2978	101	6	⊗	⊗	NUM
cana-2978	101	7	`	`	PUNCT
cana-2978	101	8	i=1	i=1	PROPN
cana-2978	101	9	(	(	PUNCT
cana-2978	101	10	1−	1−	NUM
cana-2978	101	11	(	(	PUNCT
cana-2978	101	12	(	(	PUNCT
cana-2978	101	13	a	a	DET
cana-2978	101	14	·	·	PUNCT
cana-2978	101	15	rᵀ	rᵀ	NOUN
cana-2978	101	16	i	i	NOUN
cana-2978	101	17	)	)	PUNCT
cana-2978	101	18	)	)	PUNCT
cana-2978	101	19	γ	γ	X
cana-2978	101	20	)	)	PUNCT
cana-2978	101	21	ωi	ωi	X
cana-2978	101	22	·	·	PUNCT
cana-2978	101	23	e	e	X
cana-2978	101	24	γ	γ	X
cana-2978	101	25	√	√	PROPN
cana-2978	101	26	1−	1−	NUM
cana-2978	101	27	⊗	⊗	NUM
cana-2978	101	28	`	`	PUNCT
cana-2978	101	29	i=1	i=1	PROPN
cana-2978	101	30	(	(	PUNCT
cana-2978	101	31	1−((a·i	1−((a·i	NUM
cana-2978	101	32	ᵀ	ᵀ	NOUN
cana-2978	101	33	i	i	NOUN
cana-2978	101	34	)	)	PUNCT
cana-2978	101	35	)	)	PUNCT
cana-2978	101	36	γ	γ	X
cana-2978	101	37	)	)	PUNCT
cana-2978	101	38	ωi	ωi	PROPN
cana-2978	101	39	,	,	PUNCT
cana-2978	101	40	⊗	⊗	PROPN
cana-2978	101	41	`	`	PUNCT
cana-2978	101	42	i=1(((a	i=1(((a	PROPN
cana-2978	101	43	·	·	PUNCT
cana-2978	101	44	r	r	NOUN
cana-2978	101	45	`	`	PUNCT
cana-2978	101	46	i	i	PROPN
cana-2978	101	47	)	)	PUNCT
cana-2978	101	48	)	)	PUNCT
cana-2978	101	49	τ	τ	X
cana-2978	101	50	)	)	PUNCT
cana-2978	101	51	ωi	ωi	X
cana-2978	101	52	·	·	PUNCT
cana-2978	101	53	e	e	X
cana-2978	101	54	⊗	⊗	PROPN
cana-2978	101	55	`	`	PUNCT
cana-2978	101	56	i=1(((a·i	i=1(((a·i	PROPN
cana-2978	101	57	`	`	PUNCT
cana-2978	101	58	i	i	NOUN
cana-2978	101	59	)	)	PUNCT
cana-2978	101	60	)	)	PUNCT
cana-2978	101	61	τ	τ	X
cana-2978	101	62	)	)	PUNCT
cana-2978	101	63	ωi	ωi	X
cana-2978	101	64			NUM
cana-2978	101	65	.	.	PUNCT
cana-2978	102	1	proof	proof	NOUN
cana-2978	102	2	.	.	PUNCT
cana-2978	103	1	if	if	SCONJ
cana-2978	103	2	`	`	PUNCT
cana-2978	103	3	=	=	SYM
cana-2978	103	4	2	2	NUM
cana-2978	103	5	,	,	PUNCT
cana-2978	103	6	then	then	ADV
cana-2978	103	7	ct	ct	PRON
cana-2978	103	8	(	(	PUNCT
cana-2978	103	9	γ	γ	PROPN
cana-2978	103	10	,	,	PUNCT
cana-2978	103	11	τ)-rung	τ)-rung	PUNCT
cana-2978	103	12	fnwa(θ1,θ2	fnwa(θ1,θ2	PROPN
cana-2978	103	13	)	)	PUNCT
cana-2978	103	14	=	=	SYM
cana-2978	104	1	ω1θ1	ω1θ1	PUNCT
cana-2978	104	2	⊕	⊕	PROPN
cana-2978	104	3	ω2θ2	ω2θ2	NOUN
cana-2978	104	4	,	,	PUNCT
cana-2978	104	5	where	where	SCONJ
cana-2978	104	6	ω1θ1	ω1θ1	PUNCT
cana-2978	104	7	=	=	SYM
cana-2978	104	8			NUM
cana-2978	104	9	γ	γ	NOUN
cana-2978	104	10	√	√	PROPN
cana-2978	104	11	1−	1−	NUM
cana-2978	104	12	(	(	PUNCT
cana-2978	104	13	1−	1−	NUM
cana-2978	104	14	(	(	PUNCT
cana-2978	104	15	(	(	PUNCT
cana-2978	104	16	a	a	DET
cana-2978	104	17	·	·	PUNCT
cana-2978	104	18	rᵀ	rᵀ	NOUN
cana-2978	104	19	1	1	NUM
cana-2978	104	20	)	)	PUNCT
cana-2978	104	21	)	)	PUNCT
cana-2978	104	22	γ	γ	PROPN
cana-2978	104	23	)	)	PUNCT
cana-2978	104	24	ω1	ω1	PROPN
cana-2978	104	25	·	·	PUNCT
cana-2978	104	26	e	e	NOUN
cana-2978	104	27	γ	γ	X
cana-2978	104	28	√	√	PROPN
cana-2978	104	29	1−	1−	NUM
cana-2978	104	30	(	(	PUNCT
cana-2978	104	31	1−((a·i	1−((a·i	NUM
cana-2978	104	32	ᵀ	ᵀ	NOUN
cana-2978	104	33	1	1	NUM
cana-2978	104	34	)	)	PUNCT
cana-2978	104	35	)	)	PUNCT
cana-2978	104	36	γ	γ	PROPN
cana-2978	104	37	)	)	PUNCT
cana-2978	104	38	ω1	ω1	PROPN
cana-2978	104	39	,	,	PUNCT
cana-2978	104	40	(	(	PUNCT
cana-2978	104	41	(	(	PUNCT
cana-2978	104	42	(	(	PUNCT
cana-2978	104	43	a	a	DET
cana-2978	104	44	·	·	SYM
cana-2978	104	45	r	r	NOUN
cana-2978	104	46	`	`	PUNCT
cana-2978	104	47	1	1	NUM
cana-2978	104	48	)	)	PUNCT
cana-2978	104	49	)	)	PUNCT
cana-2978	104	50	τ	τ	PROPN
cana-2978	104	51	)	)	PUNCT
cana-2978	104	52	ω1	ω1	PROPN
cana-2978	104	53	·	·	PUNCT
cana-2978	105	1	e(((a·i	e(((a·i	ADJ
cana-2978	105	2	`	`	PUNCT
cana-2978	105	3	1	1	NUM
cana-2978	105	4	)	)	PUNCT
cana-2978	105	5	)	)	PUNCT
cana-2978	105	6	τ	τ	X
cana-2978	105	7	)	)	PUNCT
cana-2978	105	8	ω1	ω1	PROPN
cana-2978	105	9			NUM
cana-2978	105	10	ω2θ2	ω2θ2	SYM
cana-2978	105	11	=	=	SYM
cana-2978	105	12			X
cana-2978	105	13	γ	γ	NOUN
cana-2978	105	14	√	√	PROPN
cana-2978	105	15	1−	1−	NUM
cana-2978	105	16	(	(	PUNCT
cana-2978	105	17	1−	1−	NUM
cana-2978	105	18	(	(	PUNCT
cana-2978	105	19	(	(	PUNCT
cana-2978	105	20	a	a	PRON
cana-2978	105	21	·	·	PUNCT
cana-2978	105	22	rᵀ	rᵀ	NOUN
cana-2978	105	23	2	2	NUM
cana-2978	105	24	)	)	PUNCT
cana-2978	105	25	)	)	PUNCT
cana-2978	105	26	γ	γ	NOUN
cana-2978	105	27	)	)	PUNCT
cana-2978	105	28	ω2	ω2	NOUN
cana-2978	105	29	·	·	PUNCT
cana-2978	106	1	e	e	X
cana-2978	106	2	γ	γ	X
cana-2978	106	3	√	√	PROPN
cana-2978	106	4	1−	1−	NUM
cana-2978	106	5	(	(	PUNCT
cana-2978	106	6	1−((a·i	1−((a·i	NUM
cana-2978	106	7	ᵀ	ᵀ	NOUN
cana-2978	106	8	2	2	NUM
cana-2978	106	9	)	)	PUNCT
cana-2978	106	10	)	)	PUNCT
cana-2978	106	11	γ	γ	NOUN
cana-2978	106	12	)	)	PUNCT
cana-2978	106	13	ω2	ω2	ADV
cana-2978	106	14	,	,	PUNCT
cana-2978	106	15	(	(	PUNCT
cana-2978	106	16	(	(	PUNCT
cana-2978	106	17	(	(	PUNCT
cana-2978	106	18	a	a	DET
cana-2978	106	19	·	·	SYM
cana-2978	106	20	r	r	NOUN
cana-2978	106	21	`	`	SYM
cana-2978	106	22	2	2	NUM
cana-2978	106	23	)	)	PUNCT
cana-2978	106	24	)	)	PUNCT
cana-2978	106	25	τ	τ	X
cana-2978	106	26	)	)	PUNCT
cana-2978	106	27	ω2	ω2	ADP
cana-2978	106	28	·	·	PUNCT
cana-2978	106	29	e(((a·i	e(((a·i	ADJ
cana-2978	106	30	`	`	PUNCT
cana-2978	106	31	2	2	NUM
cana-2978	106	32	)	)	PUNCT
cana-2978	106	33	)	)	PUNCT
cana-2978	106	34	τ	τ	X
cana-2978	106	35	)	)	PUNCT
cana-2978	106	36	ω2	ω2	ADV
cana-2978	106	37			NUM
cana-2978	106	38	.	.	PUNCT
cana-2978	107	1	now	now	ADV
cana-2978	107	2	,	,	PUNCT
cana-2978	107	3	ω1θ1	ω1θ1	X
cana-2978	107	4	⊕	⊕	NUM
cana-2978	107	5	ω2θ2	ω2θ2	NOUN
cana-2978	107	6	=	=	X
cana-2978	107	7			ADJ
cana-2978	107	8	γ	γ	PROPN
cana-2978	107	9	√√√√√√√√√√√√√	√√√√√√√√√√√√√	NOUN
cana-2978	107	10	(	(	PUNCT
cana-2978	107	11	1−	1−	NUM
cana-2978	107	12	(	(	PUNCT
cana-2978	107	13	1−	1−	NUM
cana-2978	107	14	(	(	PUNCT
cana-2978	107	15	(	(	PUNCT
cana-2978	107	16	a	a	PRON
cana-2978	107	17	·	·	PUNCT
cana-2978	107	18	rᵀ	rᵀ	NOUN
cana-2978	107	19	1	1	NUM
cana-2978	107	20	)	)	PUNCT
cana-2978	107	21	)	)	PUNCT
cana-2978	107	22	γ	γ	PROPN
cana-2978	107	23	)	)	PUNCT
cana-2978	107	24	ω1	ω1	PROPN
cana-2978	107	25	)	)	PUNCT
cana-2978	108	1	+	+	PROPN
cana-2978	108	2	(	(	PUNCT
cana-2978	108	3	1−	1−	NUM
cana-2978	108	4	(	(	PUNCT
cana-2978	108	5	1−	1−	NUM
cana-2978	108	6	(	(	PUNCT
cana-2978	108	7	(	(	PUNCT
cana-2978	108	8	a	a	PRON
cana-2978	108	9	·	·	PUNCT
cana-2978	108	10	rᵀ	rᵀ	NOUN
cana-2978	108	11	2	2	NUM
cana-2978	108	12	)	)	PUNCT
cana-2978	108	13	)	)	PUNCT
cana-2978	108	14	γ	γ	NOUN
cana-2978	108	15	)	)	PUNCT
cana-2978	108	16	ω2	ω2	ADJ
cana-2978	108	17	)	)	PUNCT
cana-2978	108	18	−	−	PROPN
cana-2978	109	1	(	(	PUNCT
cana-2978	109	2	1−	1−	NUM
cana-2978	109	3	(	(	PUNCT
cana-2978	109	4	1−	1−	NUM
cana-2978	109	5	(	(	PUNCT
cana-2978	109	6	(	(	PUNCT
cana-2978	109	7	a	a	PRON
cana-2978	109	8	·	·	PUNCT
cana-2978	109	9	rᵀ	rᵀ	NOUN
cana-2978	109	10	1	1	NUM
cana-2978	109	11	)	)	PUNCT
cana-2978	109	12	)	)	PUNCT
cana-2978	109	13	γ	γ	PROPN
cana-2978	109	14	)	)	PUNCT
cana-2978	109	15	ω1	ω1	PROPN
cana-2978	109	16	)	)	PUNCT
cana-2978	109	17	·	·	PUNCT
cana-2978	109	18	(	(	PUNCT
cana-2978	109	19	1−	1−	NUM
cana-2978	109	20	(	(	PUNCT
cana-2978	109	21	1−	1−	NUM
cana-2978	109	22	(	(	PUNCT
cana-2978	109	23	(	(	PUNCT
cana-2978	109	24	a	a	PRON
cana-2978	109	25	·	·	PUNCT
cana-2978	109	26	rᵀ	rᵀ	NOUN
cana-2978	109	27	2	2	NUM
cana-2978	109	28	)	)	PUNCT
cana-2978	109	29	)	)	PUNCT
cana-2978	109	30	γ	γ	NOUN
cana-2978	109	31	)	)	PUNCT
cana-2978	109	32	ω2	ω2	NUM
cana-2978	109	33	)	)	PUNCT
cana-2978	109	34	,	,	PUNCT
cana-2978	109	35	·	·	PUNCT
cana-2978	109	36	e	e	X
cana-2978	109	37	γ	γ	X
cana-2978	109	38	√√√√√√√√√√√√√√√√√√	√√√√√√√√√√√√√√√√√√	X
cana-2978	109	39	(	(	PUNCT
cana-2978	109	40	1−	1−	NUM
cana-2978	109	41	(	(	PUNCT
cana-2978	109	42	1−	1−	NUM
cana-2978	109	43	(	(	PUNCT
cana-2978	109	44	(	(	PUNCT
cana-2978	109	45	a	a	PRON
cana-2978	109	46	·	·	PUNCT
cana-2978	109	47	i	i	PRON
cana-2978	109	48	ᵀ	ᵀ	ADJ
cana-2978	109	49	1	1	NUM
cana-2978	109	50	)	)	PUNCT
cana-2978	109	51	)	)	PUNCT
cana-2978	109	52	γ	γ	PROPN
cana-2978	109	53	)	)	PUNCT
cana-2978	109	54	ω1	ω1	PROPN
cana-2978	109	55	)	)	PUNCT
cana-2978	110	1	+	+	PROPN
cana-2978	110	2	(	(	PUNCT
cana-2978	110	3	1−	1−	NUM
cana-2978	110	4	(	(	PUNCT
cana-2978	110	5	1−	1−	NUM
cana-2978	110	6	(	(	PUNCT
cana-2978	110	7	(	(	PUNCT
cana-2978	110	8	a	a	PRON
cana-2978	110	9	·	·	PUNCT
cana-2978	110	10	i	i	PRON
cana-2978	110	11	ᵀ	ᵀ	ADJ
cana-2978	110	12	2	2	NUM
cana-2978	110	13	)	)	PUNCT
cana-2978	110	14	)	)	PUNCT
cana-2978	110	15	γ	γ	NOUN
cana-2978	110	16	)	)	PUNCT
cana-2978	110	17	ω2	ω2	ADJ
cana-2978	110	18	)	)	PUNCT
cana-2978	110	19	−	−	PROPN
cana-2978	110	20	(	(	PUNCT
cana-2978	110	21	1−	1−	NUM
cana-2978	110	22	(	(	PUNCT
cana-2978	110	23	1−	1−	NUM
cana-2978	110	24	(	(	PUNCT
cana-2978	110	25	(	(	PUNCT
cana-2978	110	26	a	a	PRON
cana-2978	110	27	·	·	PUNCT
cana-2978	110	28	i	i	PRON
cana-2978	110	29	ᵀ	ᵀ	ADJ
cana-2978	110	30	1	1	NUM
cana-2978	110	31	)	)	PUNCT
cana-2978	110	32	)	)	PUNCT
cana-2978	110	33	γ	γ	PROPN
cana-2978	110	34	)	)	PUNCT
cana-2978	110	35	ω1	ω1	PROPN
cana-2978	110	36	)	)	PUNCT
cana-2978	110	37	·	·	PUNCT
cana-2978	110	38	(	(	PUNCT
cana-2978	110	39	1−	1−	NUM
cana-2978	110	40	(	(	PUNCT
cana-2978	110	41	1−	1−	NUM
cana-2978	110	42	(	(	PUNCT
cana-2978	110	43	(	(	PUNCT
cana-2978	110	44	a	a	PRON
cana-2978	110	45	·	·	PUNCT
cana-2978	110	46	i	i	PRON
cana-2978	110	47	ᵀ	ᵀ	ADJ
cana-2978	110	48	2	2	NUM
cana-2978	110	49	)	)	PUNCT
cana-2978	110	50	)	)	PUNCT
cana-2978	110	51	γ	γ	NOUN
cana-2978	110	52	)	)	PUNCT
cana-2978	110	53	ω2	ω2	NUM
cana-2978	110	54	)	)	PUNCT
cana-2978	110	55	,	,	PUNCT
cana-2978	110	56	(	(	PUNCT
cana-2978	110	57	(	(	PUNCT
cana-2978	110	58	(	(	PUNCT
cana-2978	110	59	a	a	DET
cana-2978	110	60	·	·	SYM
cana-2978	110	61	r	r	NOUN
cana-2978	110	62	`	`	PUNCT
cana-2978	110	63	1	1	NUM
cana-2978	110	64	)	)	PUNCT
cana-2978	110	65	)	)	PUNCT
cana-2978	110	66	τ	τ	PROPN
cana-2978	110	67	)	)	PUNCT
cana-2978	110	68	ω1	ω1	PROPN
cana-2978	110	69	·	·	PUNCT
cana-2978	110	70	(	(	PUNCT
cana-2978	110	71	(	(	PUNCT
cana-2978	110	72	(	(	PUNCT
cana-2978	110	73	a	a	DET
cana-2978	110	74	·	·	SYM
cana-2978	110	75	r	r	NOUN
cana-2978	110	76	`	`	SYM
cana-2978	110	77	2	2	NUM
cana-2978	110	78	)	)	PUNCT
cana-2978	110	79	)	)	PUNCT
cana-2978	110	80	τ	τ	X
cana-2978	110	81	)	)	PUNCT
cana-2978	110	82	ω2	ω2	ADP
cana-2978	110	83	·	·	PUNCT
cana-2978	110	84	e(((a·i	e(((a·i	ADJ
cana-2978	110	85	`	`	PUNCT
cana-2978	110	86	1	1	NUM
cana-2978	110	87	)	)	PUNCT
cana-2978	110	88	)	)	PUNCT
cana-2978	110	89	τ	τ	PROPN
cana-2978	110	90	)	)	PUNCT
cana-2978	110	91	ω1	ω1	PROPN
cana-2978	110	92	·	·	PUNCT
cana-2978	110	93	(	(	PUNCT
cana-2978	110	94	(	(	PUNCT
cana-2978	110	95	(	(	PUNCT
cana-2978	110	96	a·i	a·i	NOUN
cana-2978	110	97	`	`	PUNCT
cana-2978	110	98	2	2	NUM
cana-2978	110	99	)	)	PUNCT
cana-2978	110	100	)	)	PUNCT
cana-2978	110	101	τ	τ	X
cana-2978	110	102	)	)	PUNCT
cana-2978	111	1	ω2	ω2	ADV
cana-2978	111	2			NUM
cana-2978	111	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	111	4	135	135	NUM
cana-2978	111	5	communications	communication	NOUN
cana-2978	111	6	on	on	ADP
cana-2978	111	7	applied	apply	VERB
cana-2978	111	8	nonlinear	nonlinear	ADJ
cana-2978	111	9	analysis	analysis	NOUN
cana-2978	111	10	issn	issn	NOUN
cana-2978	111	11	:	:	PUNCT
cana-2978	111	12	1074	1074	NUM
cana-2978	111	13	-	-	PUNCT
cana-2978	111	14	133x	133x	NUM
cana-2978	111	15	vol	vol	NOUN
cana-2978	111	16	32	32	NUM
cana-2978	111	17	no	no	NOUN
cana-2978	111	18	.	.	PUNCT
cana-2978	112	1	5s	5s	NUM
cana-2978	112	2	(	(	PUNCT
cana-2978	112	3	2025	2025	NUM
cana-2978	112	4	)	)	PUNCT
cana-2978	112	5	=	=	SYM
cana-2978	112	6			NOUN
cana-2978	112	7	γ	γ	NOUN
cana-2978	112	8	√	√	PROPN
cana-2978	112	9	1−	1−	NUM
cana-2978	112	10	(	(	PUNCT
cana-2978	112	11	1−	1−	NUM
cana-2978	112	12	(	(	PUNCT
cana-2978	112	13	(	(	PUNCT
cana-2978	112	14	a	a	DET
cana-2978	112	15	·	·	PUNCT
cana-2978	112	16	rᵀ	rᵀ	NOUN
cana-2978	112	17	1	1	NUM
cana-2978	112	18	)	)	PUNCT
cana-2978	112	19	)	)	PUNCT
cana-2978	112	20	γ	γ	PROPN
cana-2978	112	21	)	)	PUNCT
cana-2978	112	22	ω1	ω1	PROPN
cana-2978	112	23	(	(	PUNCT
cana-2978	112	24	1−	1−	NUM
cana-2978	112	25	(	(	PUNCT
cana-2978	112	26	(	(	PUNCT
cana-2978	112	27	a	a	PRON
cana-2978	112	28	·	·	PUNCT
cana-2978	112	29	rᵀ	rᵀ	NOUN
cana-2978	112	30	2	2	NUM
cana-2978	112	31	)	)	PUNCT
cana-2978	112	32	)	)	PUNCT
cana-2978	112	33	γ	γ	NOUN
cana-2978	112	34	)	)	PUNCT
cana-2978	112	35	ω2	ω2	NOUN
cana-2978	112	36	·	·	PUNCT
cana-2978	112	37	e	e	X
cana-2978	112	38	γ	γ	X
cana-2978	112	39	√	√	PROPN
cana-2978	112	40	1−	1−	NUM
cana-2978	112	41	(	(	PUNCT
cana-2978	112	42	1−	1−	NUM
cana-2978	112	43	(	(	PUNCT
cana-2978	112	44	(	(	PUNCT
cana-2978	112	45	a	a	DET
cana-2978	112	46	·	·	PUNCT
cana-2978	112	47	i	i	PRON
cana-2978	112	48	ᵀ	ᵀ	ADJ
cana-2978	112	49	1	1	NUM
cana-2978	112	50	)	)	PUNCT
cana-2978	112	51	)	)	PUNCT
cana-2978	112	52	γ	γ	PROPN
cana-2978	112	53	)	)	PUNCT
cana-2978	112	54	ω1	ω1	PROPN
cana-2978	112	55	(	(	PUNCT
cana-2978	112	56	1−	1−	NUM
cana-2978	112	57	(	(	PUNCT
cana-2978	112	58	(	(	PUNCT
cana-2978	112	59	a	a	PRON
cana-2978	112	60	·	·	PUNCT
cana-2978	112	61	i	i	PRON
cana-2978	112	62	ᵀ	ᵀ	ADJ
cana-2978	112	63	2	2	NUM
cana-2978	112	64	)	)	PUNCT
cana-2978	112	65	)	)	PUNCT
cana-2978	112	66	γ	γ	NOUN
cana-2978	112	67	)	)	PUNCT
cana-2978	112	68	ω2	ω2	ADV
cana-2978	112	69	,	,	PUNCT
cana-2978	112	70	(	(	PUNCT
cana-2978	112	71	(	(	PUNCT
cana-2978	112	72	(	(	PUNCT
cana-2978	112	73	a	a	DET
cana-2978	112	74	·	·	SYM
cana-2978	112	75	r	r	NOUN
cana-2978	112	76	`	`	PUNCT
cana-2978	112	77	1	1	NUM
cana-2978	112	78	)	)	PUNCT
cana-2978	112	79	)	)	PUNCT
cana-2978	112	80	τ	τ	PROPN
cana-2978	112	81	)	)	PUNCT
cana-2978	112	82	ω1	ω1	PROPN
cana-2978	112	83	·	·	PUNCT
cana-2978	112	84	(	(	PUNCT
cana-2978	112	85	(	(	PUNCT
cana-2978	112	86	(	(	PUNCT
cana-2978	112	87	a	a	DET
cana-2978	112	88	·	·	SYM
cana-2978	112	89	r	r	NOUN
cana-2978	112	90	`	`	SYM
cana-2978	112	91	2	2	NUM
cana-2978	112	92	)	)	PUNCT
cana-2978	112	93	)	)	PUNCT
cana-2978	112	94	τ	τ	X
cana-2978	112	95	)	)	PUNCT
cana-2978	112	96	ω2	ω2	ADP
cana-2978	112	97	·	·	PUNCT
cana-2978	113	1	e(((a·i	e(((a·i	ADJ
cana-2978	113	2	`	`	PUNCT
cana-2978	113	3	1	1	NUM
cana-2978	113	4	)	)	PUNCT
cana-2978	113	5	)	)	PUNCT
cana-2978	113	6	τ	τ	PROPN
cana-2978	113	7	)	)	PUNCT
cana-2978	113	8	ω1	ω1	PROPN
cana-2978	113	9	·	·	PUNCT
cana-2978	113	10	(	(	PUNCT
cana-2978	113	11	(	(	PUNCT
cana-2978	113	12	(	(	PUNCT
cana-2978	113	13	a·i	a·i	NOUN
cana-2978	113	14	`	`	PUNCT
cana-2978	113	15	2	2	NUM
cana-2978	113	16	)	)	PUNCT
cana-2978	113	17	)	)	PUNCT
cana-2978	114	1	τ	τ	X
cana-2978	114	2	)	)	PUNCT
cana-2978	114	3	ω2	ω2	ADJ
cana-2978	114	4			VERB
cana-2978	114	5	hence	hence	ADV
cana-2978	114	6	,	,	PUNCT
cana-2978	114	7	ct	ct	PROPN
cana-2978	114	8	(	(	PUNCT
cana-2978	114	9	γ	γ	X
cana-2978	114	10	,	,	PUNCT
cana-2978	114	11	τ)nwa(θ1,θ2	τ)nwa(θ1,θ2	PROPN
cana-2978	114	12	)	)	PUNCT
cana-2978	114	13	=	=	NOUN
cana-2978	115	1			NUM
cana-2978	115	2	γ	γ	NOUN
cana-2978	115	3	√	√	PROPN
cana-2978	115	4	1−	1−	NUM
cana-2978	115	5	⊗2	⊗2	NUM
cana-2978	115	6	i=1	i=1	PROPN
cana-2978	116	1	(	(	PUNCT
cana-2978	116	2	1−	1−	NUM
cana-2978	116	3	(	(	PUNCT
cana-2978	116	4	(	(	PUNCT
cana-2978	116	5	a	a	PRON
cana-2978	116	6	·	·	PUNCT
cana-2978	116	7	rᵀ	rᵀ	NOUN
cana-2978	116	8	i	i	NOUN
cana-2978	116	9	)	)	PUNCT
cana-2978	116	10	)	)	PUNCT
cana-2978	116	11	γ	γ	X
cana-2978	116	12	)	)	PUNCT
cana-2978	116	13	ωi	ωi	X
cana-2978	116	14	·	·	PUNCT
cana-2978	116	15	e	e	X
cana-2978	116	16	γ	γ	X
cana-2978	116	17	√	√	ADP
cana-2978	116	18	1−	1−	NUM
cana-2978	116	19	⊗2	⊗2	NUM
cana-2978	116	20	i=1	i=1	PROPN
cana-2978	117	1	(	(	PUNCT
cana-2978	117	2	1−((a·i	1−((a·i	NUM
cana-2978	117	3	ᵀ	ᵀ	NOUN
cana-2978	117	4	i	i	NOUN
cana-2978	117	5	)	)	PUNCT
cana-2978	117	6	)	)	PUNCT
cana-2978	117	7	γ	γ	X
cana-2978	117	8	)	)	PUNCT
cana-2978	117	9	ωi	ωi	PROPN
cana-2978	117	10	,	,	PUNCT
cana-2978	117	11	⊗2	⊗2	NUM
cana-2978	117	12	i=1(((a	i=1(((a	NOUN
cana-2978	117	13	·	·	PUNCT
cana-2978	117	14	r	r	NOUN
cana-2978	117	15	`	`	PUNCT
cana-2978	117	16	i	i	PROPN
cana-2978	117	17	)	)	PUNCT
cana-2978	117	18	)	)	PUNCT
cana-2978	118	1	τ	τ	X
cana-2978	118	2	)	)	PUNCT
cana-2978	118	3	ωi	ωi	X
cana-2978	118	4	·	·	PUNCT
cana-2978	118	5	e	e	X
cana-2978	118	6	⊗2	⊗2	NUM
cana-2978	118	7	i=1(((a·i	i=1(((a·i	ADJ
cana-2978	118	8	`	`	PUNCT
cana-2978	118	9	i	i	PROPN
cana-2978	118	10	)	)	PUNCT
cana-2978	118	11	)	)	PUNCT
cana-2978	119	1	τ	τ	X
cana-2978	119	2	)	)	PUNCT
cana-2978	119	3	ωi	ωi	X
cana-2978	119	4			NUM
cana-2978	119	5	.	.	PUNCT
cana-2978	120	1	it	it	PRON
cana-2978	120	2	valid	valid	ADJ
cana-2978	120	3	for	for	ADP
cana-2978	120	4	`	`	PUNCT
cana-2978	120	5	≥	≥	NUM
cana-2978	120	6	3	3	NUM
cana-2978	120	7	,	,	PUNCT
cana-2978	120	8	thus	thus	ADV
cana-2978	120	9	,	,	PUNCT
cana-2978	120	10	ct	ct	PROPN
cana-2978	120	11	(	(	PUNCT
cana-2978	120	12	γ	γ	X
cana-2978	120	13	,	,	PUNCT
cana-2978	120	14	τ)nwa(θ1,θ2	τ)nwa(θ1,θ2	PROPN
cana-2978	120	15	,	,	PUNCT
cana-2978	120	16	...	...	PUNCT
cana-2978	120	17	,	,	PUNCT
cana-2978	120	18	θ	θ	NOUN
cana-2978	120	19	`	`	PUNCT
cana-2978	120	20	)	)	PUNCT
cana-2978	120	21	=	=	VERB
cana-2978	120	22			NUM
cana-2978	120	23	γ	γ	NOUN
cana-2978	120	24	√	√	PROPN
cana-2978	120	25	1−	1−	NUM
cana-2978	120	26	⊗	⊗	NUM
cana-2978	120	27	`	`	PUNCT
cana-2978	120	28	i=1	i=1	PROPN
cana-2978	120	29	(	(	PUNCT
cana-2978	120	30	1−	1−	NUM
cana-2978	120	31	(	(	PUNCT
cana-2978	120	32	(	(	PUNCT
cana-2978	120	33	a	a	DET
cana-2978	120	34	·	·	PUNCT
cana-2978	120	35	rᵀ	rᵀ	NOUN
cana-2978	120	36	i	i	NOUN
cana-2978	120	37	)	)	PUNCT
cana-2978	120	38	)	)	PUNCT
cana-2978	120	39	γ	γ	X
cana-2978	120	40	)	)	PUNCT
cana-2978	120	41	ωi	ωi	X
cana-2978	120	42	·	·	PUNCT
cana-2978	120	43	e	e	X
cana-2978	120	44	γ	γ	X
cana-2978	120	45	√	√	PROPN
cana-2978	120	46	1−	1−	NUM
cana-2978	120	47	⊗	⊗	NUM
cana-2978	120	48	`	`	PUNCT
cana-2978	120	49	i=1	i=1	PROPN
cana-2978	120	50	(	(	PUNCT
cana-2978	120	51	1−((a·i	1−((a·i	NUM
cana-2978	120	52	ᵀ	ᵀ	NOUN
cana-2978	120	53	i	i	NOUN
cana-2978	120	54	)	)	PUNCT
cana-2978	120	55	)	)	PUNCT
cana-2978	121	1	γ	γ	X
cana-2978	121	2	)	)	PUNCT
cana-2978	121	3	ωi	ωi	PROPN
cana-2978	121	4	,	,	PUNCT
cana-2978	121	5	⊗	⊗	PROPN
cana-2978	121	6	`	`	PUNCT
cana-2978	121	7	i=1(((a	i=1(((a	PROPN
cana-2978	121	8	·	·	PUNCT
cana-2978	121	9	r	r	NOUN
cana-2978	121	10	`	`	PUNCT
cana-2978	121	11	i	i	PROPN
cana-2978	121	12	)	)	PUNCT
cana-2978	121	13	)	)	PUNCT
cana-2978	122	1	τ	τ	X
cana-2978	122	2	)	)	PUNCT
cana-2978	122	3	ωi	ωi	X
cana-2978	122	4	·	·	PUNCT
cana-2978	122	5	e	e	X
cana-2978	122	6	⊗	⊗	PROPN
cana-2978	122	7	`	`	PUNCT
cana-2978	122	8	i=1(((a·i	i=1(((a·i	PROPN
cana-2978	122	9	`	`	PUNCT
cana-2978	122	10	i	i	NOUN
cana-2978	122	11	)	)	PUNCT
cana-2978	122	12	)	)	PUNCT
cana-2978	123	1	τ	τ	X
cana-2978	123	2	)	)	PUNCT
cana-2978	123	3	ωi	ωi	X
cana-2978	123	4			ADP
cana-2978	123	5	.	.	PUNCT
cana-2978	124	1	if	if	SCONJ
cana-2978	124	2	`	`	PUNCT
cana-2978	124	3	=	=	PUNCT
cana-2978	124	4	`	`	PUNCT
cana-2978	124	5	+	+	NUM
cana-2978	124	6	1	1	NUM
cana-2978	124	7	,	,	PUNCT
cana-2978	124	8	then	then	ADV
cana-2978	124	9	ct	ct	PRON
cana-2978	124	10	(	(	PUNCT
cana-2978	124	11	γ	γ	PROPN
cana-2978	124	12	,	,	PUNCT
cana-2978	124	13	τ)-rung	τ)-rung	NOUN
cana-2978	124	14	fnwa	fnwa	PROPN
cana-2978	124	15	(	(	PUNCT
cana-2978	124	16	θ1,θ2	θ1,θ2	PROPN
cana-2978	124	17	,	,	PUNCT
cana-2978	124	18	...	...	PUNCT
cana-2978	124	19	,	,	PUNCT
cana-2978	124	20	θ`,θ`+1	θ`,θ`+1	X
cana-2978	124	21	)	)	PUNCT
cana-2978	125	1	=	=	SYM
cana-2978	125	2			NOUN
cana-2978	125	3	γ	γ	PROPN
cana-2978	125	4	√√√√√√√√√√	√√√√√√√√√√	PROPN
cana-2978	125	5	⊕̀	⊕̀	VERB
cana-2978	125	6	i=1	i=1	PROPN
cana-2978	126	1	(	(	PUNCT
cana-2978	126	2	1−	1−	NUM
cana-2978	126	3	(	(	PUNCT
cana-2978	126	4	1−	1−	NUM
cana-2978	126	5	(	(	PUNCT
cana-2978	126	6	(	(	PUNCT
cana-2978	126	7	a	a	PRON
cana-2978	126	8	·	·	PUNCT
cana-2978	126	9	rᵀ	rᵀ	NOUN
cana-2978	126	10	i	i	NOUN
cana-2978	126	11	)	)	PUNCT
cana-2978	126	12	)	)	PUNCT
cana-2978	126	13	γ	γ	X
cana-2978	126	14	)	)	PUNCT
cana-2978	126	15	ωi	ωi	PROPN
cana-2978	126	16	)	)	PUNCT
cana-2978	127	1	+	+	CCONJ
cana-2978	127	2	(	(	PUNCT
cana-2978	127	3	1−	1−	NUM
cana-2978	127	4	(	(	PUNCT
cana-2978	127	5	1−	1−	NUM
cana-2978	127	6	(	(	PUNCT
cana-2978	127	7	rᵀ	rᵀ	NOUN
cana-2978	127	8	`	`	PUNCT
cana-2978	127	9	+1)γ	+1)γ	PROPN
cana-2978	127	10	)	)	PUNCT
cana-2978	127	11	ω`+1	ω`+1	PUNCT
cana-2978	127	12	)	)	PUNCT
cana-2978	128	1	−	−	PROPN
cana-2978	129	1	⊗̀	⊗̀	VERB
cana-2978	129	2	i=1	i=1	X
cana-2978	130	1	(	(	PUNCT
cana-2978	130	2	1−	1−	NUM
cana-2978	130	3	(	(	PUNCT
cana-2978	130	4	1−	1−	NUM
cana-2978	130	5	(	(	PUNCT
cana-2978	130	6	(	(	PUNCT
cana-2978	130	7	a	a	PRON
cana-2978	130	8	·	·	PUNCT
cana-2978	130	9	rᵀ	rᵀ	NOUN
cana-2978	130	10	i	i	NOUN
cana-2978	130	11	)	)	PUNCT
cana-2978	130	12	)	)	PUNCT
cana-2978	130	13	γ	γ	X
cana-2978	130	14	)	)	PUNCT
cana-2978	130	15	ωi	ωi	PROPN
cana-2978	130	16	)	)	PUNCT
cana-2978	130	17	·	·	PUNCT
cana-2978	131	1	(	(	PUNCT
cana-2978	131	2	1−	1−	NUM
cana-2978	131	3	(	(	PUNCT
cana-2978	131	4	1−	1−	NUM
cana-2978	131	5	(	(	PUNCT
cana-2978	131	6	rᵀ	rᵀ	NOUN
cana-2978	131	7	`	`	PUNCT
cana-2978	131	8	+1)γ	+1)γ	PROPN
cana-2978	131	9	)	)	PUNCT
cana-2978	131	10	ω`+1	ω`+1	PROPN
cana-2978	131	11	)	)	PUNCT
cana-2978	131	12	·	·	PUNCT
cana-2978	132	1	e	e	X
cana-2978	132	2	γ	γ	PROPN
cana-2978	132	3	√√√√√√√√√√√√√√	√√√√√√√√√√√√√√	PROPN
cana-2978	132	4	⊕̀	⊕̀	VERB
cana-2978	132	5	i=1	i=1	PROPN
cana-2978	132	6	(	(	PUNCT
cana-2978	132	7	1−	1−	NUM
cana-2978	132	8	(	(	PUNCT
cana-2978	132	9	1−	1−	NUM
cana-2978	132	10	(	(	PUNCT
cana-2978	132	11	(	(	PUNCT
cana-2978	132	12	a	a	PRON
cana-2978	132	13	·	·	PUNCT
cana-2978	132	14	i	i	PRON
cana-2978	132	15	ᵀ	ᵀ	NOUN
cana-2978	132	16	i	i	NOUN
cana-2978	132	17	)	)	PUNCT
cana-2978	132	18	)	)	PUNCT
cana-2978	132	19	γ	γ	X
cana-2978	132	20	)	)	PUNCT
cana-2978	132	21	ωi	ωi	PROPN
cana-2978	132	22	)	)	PUNCT
cana-2978	132	23	+	+	CCONJ
cana-2978	132	24	(	(	PUNCT
cana-2978	132	25	1−	1−	NUM
cana-2978	132	26	(	(	PUNCT
cana-2978	132	27	1−	1−	NUM
cana-2978	132	28	(	(	PUNCT
cana-2978	132	29	i	i	PRON
cana-2978	132	30	ᵀ	ᵀ	VERB
cana-2978	132	31	`	`	PUNCT
cana-2978	132	32	+1)γ	+1)γ	PROPN
cana-2978	132	33	)	)	PUNCT
cana-2978	132	34	ω`+1	ω`+1	PUNCT
cana-2978	132	35	)	)	PUNCT
cana-2978	133	1	−	−	PROPN
cana-2978	134	1	⊗̀	⊗̀	VERB
cana-2978	134	2	i=1	i=1	X
cana-2978	135	1	(	(	PUNCT
cana-2978	135	2	1−	1−	NUM
cana-2978	135	3	(	(	PUNCT
cana-2978	135	4	1−	1−	NUM
cana-2978	135	5	(	(	PUNCT
cana-2978	135	6	(	(	PUNCT
cana-2978	135	7	a	a	PRON
cana-2978	135	8	·	·	PUNCT
cana-2978	135	9	i	i	PRON
cana-2978	135	10	ᵀ	ᵀ	NOUN
cana-2978	135	11	i	i	NOUN
cana-2978	135	12	)	)	PUNCT
cana-2978	135	13	)	)	PUNCT
cana-2978	135	14	γ	γ	X
cana-2978	135	15	)	)	PUNCT
cana-2978	135	16	ωi	ωi	PROPN
cana-2978	135	17	)	)	PUNCT
cana-2978	135	18	·	·	PUNCT
cana-2978	135	19	(	(	PUNCT
cana-2978	135	20	1−	1−	NUM
cana-2978	135	21	(	(	PUNCT
cana-2978	135	22	1−	1−	NUM
cana-2978	135	23	(	(	PUNCT
cana-2978	135	24	i	i	PRON
cana-2978	135	25	ᵀ	ᵀ	VERB
cana-2978	135	26	`	`	PUNCT
cana-2978	135	27	+1)γ	+1)γ	PROPN
cana-2978	135	28	)	)	PUNCT
cana-2978	135	29	ω`+1	ω`+1	PROPN
cana-2978	135	30	)	)	PUNCT
cana-2978	135	31	,	,	PUNCT
cana-2978	135	32	⊗	⊗	PROPN
cana-2978	135	33	`	`	PUNCT
cana-2978	135	34	i=1(((a	i=1(((a	PROPN
cana-2978	135	35	·	·	PUNCT
cana-2978	135	36	r	r	NOUN
cana-2978	135	37	`	`	PUNCT
cana-2978	135	38	i	i	PROPN
cana-2978	135	39	)	)	PUNCT
cana-2978	135	40	)	)	PUNCT
cana-2978	135	41	τ	τ	X
cana-2978	135	42	)	)	PUNCT
cana-2978	135	43	ωi	ωi	X
cana-2978	135	44	·	·	PUNCT
cana-2978	135	45	(	(	PUNCT
cana-2978	135	46	(	(	PUNCT
cana-2978	135	47	r	r	NOUN
cana-2978	135	48	`	`	PUNCT
cana-2978	135	49	`	`	PUNCT
cana-2978	135	50	+1)τ	+1)τ	PROPN
cana-2978	135	51	)	)	PUNCT
cana-2978	135	52	ω`+1	ω`+1	NOUN
cana-2978	135	53	·	·	PUNCT
cana-2978	136	1	e	e	X
cana-2978	136	2	⊗	⊗	PROPN
cana-2978	136	3	`	`	PUNCT
cana-2978	136	4	i=1(((a·i	i=1(((a·i	PROPN
cana-2978	136	5	`	`	PUNCT
cana-2978	136	6	i	i	NOUN
cana-2978	136	7	)	)	PUNCT
cana-2978	136	8	)	)	PUNCT
cana-2978	136	9	τ	τ	X
cana-2978	136	10	)	)	PUNCT
cana-2978	136	11	ωi	ωi	X
cana-2978	136	12	·	·	PUNCT
cana-2978	136	13	(	(	PUNCT
cana-2978	136	14	(	(	PUNCT
cana-2978	136	15	i	i	PRON
cana-2978	136	16	`	`	PUNCT
cana-2978	136	17	`	`	PUNCT
cana-2978	136	18	+1	+1	ADJ
cana-2978	136	19	)	)	PUNCT
cana-2978	136	20	τ	τ	PROPN
cana-2978	136	21	)	)	PUNCT
cana-2978	136	22	ω`+1	ω`+1	NOUN
cana-2978	136	23			PUNCT
cana-2978	137	1	=	=	X
cana-2978	137	2			ADJ
cana-2978	137	3	γ	γ	NOUN
cana-2978	137	4	√√√√	√√√√	ADV
cana-2978	137	5	1−	1−	NUM
cana-2978	137	6	`	`	PUNCT
cana-2978	137	7	+1⊗	+1⊗	NUM
cana-2978	137	8	i=1	i=1	X
cana-2978	137	9	(	(	PUNCT
cana-2978	137	10	1−	1−	NUM
cana-2978	137	11	(	(	PUNCT
cana-2978	137	12	(	(	PUNCT
cana-2978	137	13	a	a	DET
cana-2978	137	14	·	·	PUNCT
cana-2978	137	15	rᵀ	rᵀ	NOUN
cana-2978	137	16	i	i	NOUN
cana-2978	137	17	)	)	PUNCT
cana-2978	137	18	)	)	PUNCT
cana-2978	137	19	γ	γ	X
cana-2978	137	20	)	)	PUNCT
cana-2978	137	21	ωi	ωi	X
cana-2978	137	22	·	·	PUNCT
cana-2978	137	23	e	e	X
cana-2978	137	24	γ	γ	X
cana-2978	137	25	√√√√√√1−	√√√√√√1−	PRON
cana-2978	137	26	`	`	PUNCT
cana-2978	137	27	+1⊗	+1⊗	NUM
cana-2978	137	28	i=1	i=1	X
cana-2978	137	29	(	(	PUNCT
cana-2978	137	30	1−	1−	NUM
cana-2978	137	31	(	(	PUNCT
cana-2978	137	32	(	(	PUNCT
cana-2978	137	33	a	a	PRON
cana-2978	137	34	·	·	PUNCT
cana-2978	137	35	i	i	PRON
cana-2978	137	36	ᵀ	ᵀ	NOUN
cana-2978	137	37	i	i	NOUN
cana-2978	137	38	)	)	PUNCT
cana-2978	137	39	)	)	PUNCT
cana-2978	137	40	γ	γ	X
cana-2978	137	41	)	)	PUNCT
cana-2978	137	42	ωi	ωi	PROPN
cana-2978	137	43	,	,	PUNCT
cana-2978	137	44	⊗`+1	⊗`+1	PROPN
cana-2978	137	45	i=1(((a	i=1(((a	NOUN
cana-2978	137	46	·	·	PUNCT
cana-2978	137	47	r	r	NOUN
cana-2978	137	48	`	`	PUNCT
cana-2978	137	49	i	i	PROPN
cana-2978	137	50	)	)	PUNCT
cana-2978	137	51	)	)	PUNCT
cana-2978	138	1	τ	τ	X
cana-2978	138	2	)	)	PUNCT
cana-2978	138	3	ωi	ωi	X
cana-2978	138	4	·	·	PUNCT
cana-2978	138	5	e	e	X
cana-2978	138	6	⊗`+1	⊗`+1	PROPN
cana-2978	138	7	i=1(((a·i	i=1(((a·i	X
cana-2978	138	8	`	`	PUNCT
cana-2978	138	9	i	i	PROPN
cana-2978	138	10	)	)	PUNCT
cana-2978	138	11	)	)	PUNCT
cana-2978	139	1	τ	τ	X
cana-2978	139	2	)	)	PUNCT
cana-2978	139	3	ωi	ωi	PROPN
cana-2978	139	4			NOUN
cana-2978	139	5	.	.	PUNCT
cana-2978	140	1	theorem	theorem	VERB
cana-2978	140	2	4.3	4.3	NUM
cana-2978	140	3	.	.	PUNCT
cana-2978	141	1	let	let	VERB
cana-2978	141	2	θi	θi	X
cana-2978	141	3	=	=	PROPN
cana-2978	141	4	〈	〈	PROPN
cana-2978	141	5	(	(	PUNCT
cana-2978	141	6	(	(	PUNCT
cana-2978	141	7	(	(	PUNCT
cana-2978	141	8	a	a	DET
cana-2978	141	9	·	·	PUNCT
cana-2978	141	10	rᵀ	rᵀ	NOUN
cana-2978	141	11	i	i	NOUN
cana-2978	141	12	)	)	PUNCT
cana-2978	141	13	·	·	PUNCT
cana-2978	142	1	e(a·i	e(a·i	NOUN
cana-2978	142	2	ᵀ	ᵀ	VERB
cana-2978	142	3	i	i	PROPN
cana-2978	142	4	)	)	PUNCT
cana-2978	142	5	,	,	PUNCT
cana-2978	142	6	(	(	PUNCT
cana-2978	142	7	a	a	DET
cana-2978	142	8	·	·	SYM
cana-2978	142	9	r	r	NOUN
cana-2978	142	10	`	`	PUNCT
cana-2978	142	11	i	i	PROPN
cana-2978	142	12	)	)	PUNCT
cana-2978	142	13	·	·	PUNCT
cana-2978	143	1	e(a·i	e(a·i	NOUN
cana-2978	143	2	`	`	PUNCT
cana-2978	143	3	i	i	PROPN
cana-2978	143	4	)	)	PUNCT
cana-2978	143	5	)	)	PUNCT
cana-2978	143	6	)	)	PUNCT
cana-2978	143	7	〉	〉	NOUN
cana-2978	143	8	be	be	VERB
cana-2978	143	9	the	the	DET
cana-2978	143	10	ct	ct	PROPN
cana-2978	143	11	(	(	PUNCT
cana-2978	143	12	γ	γ	PROPN
cana-2978	143	13	,	,	PUNCT
cana-2978	143	14	τ)-rung	τ)-rung	PROPN
cana-2978	143	15	fns	fns	PROPN
cana-2978	143	16	.	.	PUNCT
cana-2978	144	1	then	then	ADV
cana-2978	144	2	ct	ct	PRON
cana-2978	144	3	(	(	PUNCT
cana-2978	144	4	γ	γ	PROPN
cana-2978	144	5	,	,	PUNCT
cana-2978	144	6	τ)-rung	τ)-rung	NOUN
cana-2978	144	7	fnwa	fnwa	PROPN
cana-2978	144	8	(	(	PUNCT
cana-2978	144	9	θ1,θ2	θ1,θ2	PROPN
cana-2978	144	10	,	,	PUNCT
cana-2978	144	11	...	...	PUNCT
cana-2978	144	12	,	,	PUNCT
cana-2978	144	13	θ	θ	NOUN
cana-2978	144	14	`	`	PUNCT
cana-2978	144	15	)	)	PUNCT
cana-2978	144	16	=	=	SYM
cana-2978	144	17	θ	θ	PROPN
cana-2978	144	18	(	(	PUNCT
cana-2978	144	19	idempotency	idempotency	NOUN
cana-2978	144	20	property	property	NOUN
cana-2978	144	21	)	)	PUNCT
cana-2978	144	22	.	.	PUNCT
cana-2978	145	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	145	2	136	136	NUM
cana-2978	145	3	communications	communication	NOUN
cana-2978	145	4	on	on	ADP
cana-2978	145	5	applied	apply	VERB
cana-2978	145	6	nonlinear	nonlinear	ADJ
cana-2978	145	7	analysis	analysis	NOUN
cana-2978	145	8	issn	issn	NOUN
cana-2978	145	9	:	:	PUNCT
cana-2978	145	10	1074	1074	NUM
cana-2978	145	11	-	-	PUNCT
cana-2978	145	12	133x	133x	NUM
cana-2978	145	13	vol	vol	NOUN
cana-2978	145	14	32	32	NUM
cana-2978	145	15	no	no	NOUN
cana-2978	145	16	.	.	PUNCT
cana-2978	146	1	5s	5s	NUM
cana-2978	146	2	(	(	PUNCT
cana-2978	146	3	2025	2025	NUM
cana-2978	146	4	)	)	PUNCT
cana-2978	146	5	proof	proof	NOUN
cana-2978	146	6	.	.	PUNCT
cana-2978	147	1	since	since	SCONJ
cana-2978	147	2	(	(	PUNCT
cana-2978	147	3	a	a	DET
cana-2978	147	4	·	·	PUNCT
cana-2978	147	5	rᵀ	rᵀ	NOUN
cana-2978	147	6	i	i	NOUN
cana-2978	147	7	)	)	PUNCT
cana-2978	147	8	=	=	SYM
cana-2978	147	9	(	(	PUNCT
cana-2978	147	10	a	a	DET
cana-2978	147	11	·	·	SYM
cana-2978	147	12	rᵀ	rᵀ	NOUN
cana-2978	147	13	)	)	PUNCT
cana-2978	147	14	,	,	PUNCT
cana-2978	147	15	(	(	PUNCT
cana-2978	147	16	a	a	DET
cana-2978	147	17	·	·	SYM
cana-2978	147	18	r	r	NOUN
cana-2978	147	19	`	`	PUNCT
cana-2978	147	20	i	i	NOUN
cana-2978	147	21	)	)	PUNCT
cana-2978	148	1	=	=	SYM
cana-2978	148	2	(	(	PUNCT
cana-2978	148	3	a	a	DET
cana-2978	148	4	·	·	SYM
cana-2978	148	5	r	r	NOUN
cana-2978	148	6	`	`	PUNCT
cana-2978	148	7	)	)	PUNCT
cana-2978	148	8	and	and	CCONJ
cana-2978	148	9	(	(	PUNCT
cana-2978	148	10	a	a	PRON
cana-2978	148	11	·	·	PUNCT
cana-2978	148	12	i	i	PRON
cana-2978	148	13	ᵀ	ᵀ	NOUN
cana-2978	148	14	i	i	NOUN
cana-2978	148	15	)	)	PUNCT
cana-2978	149	1	=	=	PRON
cana-2978	149	2	(	(	PUNCT
cana-2978	149	3	a	a	DET
cana-2978	149	4	·	·	PUNCT
cana-2978	149	5	i	i	PRON
cana-2978	149	6	ᵀ	ᵀ	NOUN
cana-2978	149	7	)	)	PUNCT
cana-2978	149	8	,	,	PUNCT
cana-2978	149	9	(	(	PUNCT
cana-2978	149	10	a	a	DET
cana-2978	149	11	·	·	PUNCT
cana-2978	149	12	i	i	PRON
cana-2978	149	13	`	`	PUNCT
cana-2978	149	14	i	i	NOUN
cana-2978	149	15	)	)	PUNCT
cana-2978	150	1	=	=	SYM
cana-2978	150	2	(	(	PUNCT
cana-2978	150	3	a	a	DET
cana-2978	150	4	·	·	PUNCT
cana-2978	150	5	i	i	PRON
cana-2978	150	6	`	`	PUNCT
cana-2978	150	7	)	)	PUNCT
cana-2978	150	8	and	and	CCONJ
cana-2978	150	9	⊕	⊕	NUM
cana-2978	150	10	`	`	PUNCT
cana-2978	150	11	i=1	i=1	PROPN
cana-2978	150	12	ωi	ωi	PROPN
cana-2978	150	13	=	=	NOUN
cana-2978	150	14	1	1	X
cana-2978	150	15	.	.	PUNCT
cana-2978	151	1	now	now	ADV
cana-2978	151	2	,	,	PUNCT
cana-2978	151	3	ct	ct	PROPN
cana-2978	151	4	(	(	PUNCT
cana-2978	151	5	γ	γ	X
cana-2978	151	6	,	,	PUNCT
cana-2978	151	7	τ)nwa(θ1,θ2	τ)nwa(θ1,θ2	PROPN
cana-2978	151	8	,	,	PUNCT
cana-2978	151	9	...	...	PUNCT
cana-2978	151	10	,	,	PUNCT
cana-2978	151	11	θ	θ	NOUN
cana-2978	151	12	`	`	PUNCT
cana-2978	151	13	)	)	PUNCT
cana-2978	151	14	=	=	PUNCT
cana-2978	151	15			NOUN
cana-2978	151	16	γ	γ	NOUN
cana-2978	151	17	√√√√	√√√√	ADP
cana-2978	151	18	1−	1−	NUM
cana-2978	151	19	⊗̀	⊗̀	NOUN
cana-2978	151	20	i=1	i=1	X
cana-2978	152	1	(	(	PUNCT
cana-2978	152	2	1−	1−	NUM
cana-2978	152	3	(	(	PUNCT
cana-2978	152	4	(	(	PUNCT
cana-2978	152	5	a	a	PRON
cana-2978	152	6	·	·	PUNCT
cana-2978	152	7	rᵀ	rᵀ	NOUN
cana-2978	152	8	i	i	NOUN
cana-2978	152	9	)	)	PUNCT
cana-2978	152	10	)	)	PUNCT
cana-2978	152	11	γ	γ	X
cana-2978	152	12	)	)	PUNCT
cana-2978	152	13	ωi	ωi	X
cana-2978	152	14	·	·	PUNCT
cana-2978	152	15	e	e	X
cana-2978	152	16	γ	γ	X
cana-2978	152	17	√√√√√√1−	√√√√√√1−	ADV
cana-2978	152	18	⊗̀	⊗̀	NOUN
cana-2978	152	19	i=1	i=1	PROPN
cana-2978	153	1	(	(	PUNCT
cana-2978	153	2	1−	1−	NUM
cana-2978	153	3	(	(	PUNCT
cana-2978	153	4	(	(	PUNCT
cana-2978	153	5	a	a	PRON
cana-2978	153	6	·	·	PUNCT
cana-2978	153	7	i	i	PRON
cana-2978	153	8	ᵀ	ᵀ	NOUN
cana-2978	153	9	i	i	NOUN
cana-2978	153	10	)	)	PUNCT
cana-2978	153	11	)	)	PUNCT
cana-2978	153	12	γ	γ	X
cana-2978	153	13	)	)	PUNCT
cana-2978	153	14	ωi	ωi	PROPN
cana-2978	153	15	,	,	PUNCT
cana-2978	153	16	⊗	⊗	PROPN
cana-2978	153	17	`	`	PUNCT
cana-2978	153	18	i=1(((a	i=1(((a	PROPN
cana-2978	153	19	·	·	PUNCT
cana-2978	153	20	r	r	NOUN
cana-2978	153	21	`	`	PUNCT
cana-2978	153	22	i	i	PROPN
cana-2978	153	23	)	)	PUNCT
cana-2978	153	24	)	)	PUNCT
cana-2978	154	1	τ	τ	X
cana-2978	154	2	)	)	PUNCT
cana-2978	154	3	ωi	ωi	X
cana-2978	154	4	·	·	PUNCT
cana-2978	154	5	e	e	X
cana-2978	154	6	⊗	⊗	PROPN
cana-2978	154	7	`	`	PUNCT
cana-2978	154	8	i=1(((a·i	i=1(((a·i	PROPN
cana-2978	154	9	`	`	PUNCT
cana-2978	154	10	i	i	NOUN
cana-2978	154	11	)	)	PUNCT
cana-2978	154	12	)	)	PUNCT
cana-2978	155	1	τ	τ	X
cana-2978	155	2	)	)	PUNCT
cana-2978	155	3	ωi	ωi	PROPN
cana-2978	155	4			NOUN
cana-2978	155	5	=	=	PUNCT
cana-2978	155	6			NOUN
cana-2978	155	7	γ	γ	NOUN
cana-2978	155	8	√	√	VERB
cana-2978	155	9	1−	1−	NUM
cana-2978	155	10	(	(	PUNCT
cana-2978	155	11	1−	1−	NUM
cana-2978	155	12	(	(	PUNCT
cana-2978	155	13	a	a	PRON
cana-2978	155	14	·	·	PUNCT
cana-2978	155	15	(	(	PUNCT
cana-2978	155	16	rᵀ)γ	rᵀ)γ	PROPN
cana-2978	155	17	)	)	PUNCT
cana-2978	155	18	⊕	⊕	PROPN
cana-2978	155	19	`	`	PUNCT
cana-2978	155	20	i=1	i=1	PROPN
cana-2978	155	21	ωi	ωi	X
cana-2978	155	22	·	·	PUNCT
cana-2978	155	23	e	e	X
cana-2978	155	24	γ	γ	X
cana-2978	155	25	√√√√1−	√√√√1−	X
cana-2978	155	26	(	(	PUNCT
cana-2978	155	27	1−	1−	NUM
cana-2978	155	28	(	(	PUNCT
cana-2978	155	29	a	a	PRON
cana-2978	155	30	·	·	PUNCT
cana-2978	155	31	(	(	PUNCT
cana-2978	155	32	i	i	PRON
cana-2978	155	33	ᵀ)γ	ᵀ)γ	PUNCT
cana-2978	155	34	)	)	PUNCT
cana-2978	156	1	⊕	⊕	PROPN
cana-2978	156	2	`	`	PUNCT
cana-2978	156	3	i=1	i=1	PROPN
cana-2978	156	4	ωi	ωi	X
cana-2978	156	5	,	,	PUNCT
cana-2978	156	6	(	(	PUNCT
cana-2978	156	7	(	(	PUNCT
cana-2978	156	8	a	a	PRON
cana-2978	156	9	·	·	PUNCT
cana-2978	156	10	(	(	PUNCT
cana-2978	156	11	r`)τ	r`)τ	PROPN
cana-2978	156	12	)	)	PUNCT
cana-2978	156	13	⊕	⊕	PROPN
cana-2978	156	14	`	`	PUNCT
cana-2978	156	15	i=1	i=1	PROPN
cana-2978	156	16	ωi	ωi	X
cana-2978	156	17	·	·	PUNCT
cana-2978	156	18	e((a·(i	e((a·(i	NUM
cana-2978	156	19	`	`	PUNCT
cana-2978	156	20	)	)	PUNCT
cana-2978	156	21	τ	τ	PROPN
cana-2978	156	22	)	)	PUNCT
cana-2978	156	23	⊕	⊕	PROPN
cana-2978	156	24	`	`	PUNCT
cana-2978	156	25	i=1	i=1	PROPN
cana-2978	156	26	ωi	ωi	X
cana-2978	156	27			NOUN
cana-2978	156	28	=	=	PUNCT
cana-2978	156	29			X
cana-2978	156	30	γ	γ	NOUN
cana-2978	156	31	√	√	PROPN
cana-2978	156	32	1−	1−	NUM
cana-2978	156	33	(	(	PUNCT
cana-2978	156	34	1−	1−	NUM
cana-2978	156	35	(	(	PUNCT
cana-2978	156	36	a	a	DET
cana-2978	156	37	·	·	PUNCT
cana-2978	156	38	(	(	PUNCT
cana-2978	156	39	rᵀ)γ	rᵀ)γ	PROPN
cana-2978	156	40	)	)	PUNCT
cana-2978	156	41	·	·	PUNCT
cana-2978	157	1	e	e	X
cana-2978	157	2	γ	γ	X
cana-2978	157	3	√	√	PROPN
cana-2978	157	4	1−	1−	NUM
cana-2978	157	5	(	(	PUNCT
cana-2978	157	6	1−	1−	NUM
cana-2978	157	7	(	(	PUNCT
cana-2978	157	8	a	a	PRON
cana-2978	157	9	·	·	PUNCT
cana-2978	157	10	(	(	PUNCT
cana-2978	157	11	i	i	PRON
cana-2978	157	12	ᵀ)γ	ᵀ)γ	PUNCT
cana-2978	157	13	)	)	PUNCT
cana-2978	157	14	,	,	PUNCT
cana-2978	157	15	(	(	PUNCT
cana-2978	157	16	a	a	PRON
cana-2978	157	17	·	·	PUNCT
cana-2978	157	18	(	(	PUNCT
cana-2978	157	19	r`)τ	r`)τ	X
cana-2978	157	20	·	·	PUNCT
cana-2978	157	21	e(a·(i	e(a·(i	PROPN
cana-2978	157	22	`	`	PUNCT
cana-2978	157	23	)	)	PUNCT
cana-2978	157	24	τ	τ	PROPN
cana-2978	157	25			NUM
cana-2978	157	26	=	=	SYM
cana-2978	157	27	θ	θ	PROPN
cana-2978	157	28	.	.	PUNCT
cana-2978	157	29	theorem	theorem	VERB
cana-2978	157	30	4.4	4.4	NUM
cana-2978	157	31	.	.	PUNCT
cana-2978	158	1	let	let	VERB
cana-2978	158	2	θi	θi	X
cana-2978	158	3	=	=	PROPN
cana-2978	158	4	〈	〈	PROPN
cana-2978	158	5	(	(	PUNCT
cana-2978	158	6	(	(	PUNCT
cana-2978	158	7	(	(	PUNCT
cana-2978	158	8	a	a	DET
cana-2978	158	9	·	·	PUNCT
cana-2978	158	10	rᵀ	rᵀ	NOUN
cana-2978	158	11	i	i	NOUN
cana-2978	158	12	)	)	PUNCT
cana-2978	158	13	·	·	PUNCT
cana-2978	159	1	e(a·i	e(a·i	NOUN
cana-2978	159	2	ᵀ	ᵀ	VERB
cana-2978	159	3	i	i	PROPN
cana-2978	159	4	)	)	PUNCT
cana-2978	159	5	,	,	PUNCT
cana-2978	159	6	(	(	PUNCT
cana-2978	159	7	a	a	DET
cana-2978	159	8	·	·	SYM
cana-2978	159	9	r	r	NOUN
cana-2978	159	10	`	`	PUNCT
cana-2978	159	11	i	i	PROPN
cana-2978	159	12	)	)	PUNCT
cana-2978	159	13	·	·	PUNCT
cana-2978	160	1	e(a·i	e(a·i	NOUN
cana-2978	160	2	`	`	PUNCT
cana-2978	160	3	i	i	PROPN
cana-2978	160	4	)	)	PUNCT
cana-2978	160	5	)	)	PUNCT
cana-2978	160	6	)	)	PUNCT
cana-2978	160	7	〉	〉	NOUN
cana-2978	160	8	be	be	VERB
cana-2978	160	9	the	the	DET
cana-2978	160	10	ct	ct	PROPN
cana-2978	160	11	(	(	PUNCT
cana-2978	160	12	γ	γ	PROPN
cana-2978	160	13	,	,	PUNCT
cana-2978	160	14	τ)-rung	τ)-rung	PROPN
cana-2978	160	15	fns	fns	PROPN
cana-2978	160	16	.	.	PUNCT
cana-2978	161	1	then	then	ADV
cana-2978	161	2	ct	ct	PRON
cana-2978	161	3	(	(	PUNCT
cana-2978	161	4	γ	γ	PROPN
cana-2978	161	5	,	,	PUNCT
cana-2978	161	6	τ)-rung	τ)-rung	PUNCT
cana-2978	161	7	fnwa(θ1,θ2	fnwa(θ1,θ2	PROPN
cana-2978	161	8	,	,	PUNCT
cana-2978	161	9	...	...	PUNCT
cana-2978	161	10	,	,	PUNCT
cana-2978	161	11	θ	θ	NOUN
cana-2978	161	12	`	`	PROPN
cana-2978	161	13	)	)	PUNCT
cana-2978	161	14	,	,	PUNCT
cana-2978	161	15	where	where	SCONJ
cana-2978	161	16	←−−−−−	←−−−−−	PROPN
cana-2978	161	17	(	(	PUNCT
cana-2978	161	18	a	a	DET
cana-2978	161	19	·	·	SYM
cana-2978	161	20	rᵀ	rᵀ	NOUN
cana-2978	161	21	)	)	PUNCT
cana-2978	161	22	=	=	SYM
cana-2978	161	23	min(a	min(a	PROPN
cana-2978	161	24	·	·	PUNCT
cana-2978	161	25	rᵀ	rᵀ	NOUN
cana-2978	161	26	ij	ij	NOUN
cana-2978	161	27	)	)	PUNCT
cana-2978	161	28	,	,	PUNCT
cana-2978	161	29	̂(a	̂(a	NOUN
cana-2978	161	30	·	·	SYM
cana-2978	161	31	rᵀ	rᵀ	NOUN
cana-2978	161	32	)	)	PUNCT
cana-2978	161	33	=	=	SYM
cana-2978	161	34	max(a	max(a	PROPN
cana-2978	161	35	·	·	PUNCT
cana-2978	161	36	rᵀ	rᵀ	NOUN
cana-2978	161	37	ij	ij	NOUN
cana-2978	161	38	)	)	PUNCT
cana-2978	161	39	,	,	PUNCT
cana-2978	161	40	←−−−−−	←−−−−−	PROPN
cana-2978	161	41	(	(	PUNCT
cana-2978	161	42	a	a	DET
cana-2978	161	43	·	·	SYM
cana-2978	161	44	r	r	NOUN
cana-2978	161	45	`	`	PUNCT
cana-2978	161	46	)	)	PUNCT
cana-2978	161	47	=	=	PUNCT
cana-2978	161	48	min(a	min(a	PROPN
cana-2978	161	49	·	·	SYM
cana-2978	161	50	r	r	NOUN
cana-2978	161	51	`	`	PUNCT
cana-2978	161	52	ij	ij	NOUN
cana-2978	161	53	)	)	PUNCT
cana-2978	161	54	,	,	PUNCT
cana-2978	161	55	̂(a	̂(a	NOUN
cana-2978	161	56	·	·	PUNCT
cana-2978	161	57	r	r	NOUN
cana-2978	161	58	`	`	PUNCT
cana-2978	161	59	)	)	PUNCT
cana-2978	162	1	=	=	SYM
cana-2978	162	2	max(a	max(a	X
cana-2978	162	3	·	·	PUNCT
cana-2978	162	4	r	r	NOUN
cana-2978	162	5	`	`	PUNCT
cana-2978	162	6	ij	ij	NOUN
cana-2978	162	7	)	)	PUNCT
cana-2978	162	8	and	and	CCONJ
cana-2978	162	9	←−−−−−	←−−−−−	NUM
cana-2978	162	10	(	(	PUNCT
cana-2978	162	11	a	a	DET
cana-2978	162	12	·	·	PUNCT
cana-2978	162	13	i	i	PRON
cana-2978	162	14	ᵀ	ᵀ	NOUN
cana-2978	162	15	)	)	PUNCT
cana-2978	163	1	=	=	SYM
cana-2978	163	2	min(a	min(a	PROPN
cana-2978	163	3	·	·	PUNCT
cana-2978	163	4	i	i	PRON
cana-2978	163	5	ᵀ	ᵀ	VERB
cana-2978	163	6	ij	ij	NOUN
cana-2978	163	7	)	)	PUNCT
cana-2978	163	8	,	,	PUNCT
cana-2978	163	9	̂(a	̂(a	NOUN
cana-2978	163	10	·	·	PUNCT
cana-2978	163	11	i	i	PRON
cana-2978	163	12	ᵀ	ᵀ	NOUN
cana-2978	163	13	)	)	PUNCT
cana-2978	163	14	=	=	SYM
cana-2978	164	1	max(a	max(a	PROPN
cana-2978	164	2	·	·	PUNCT
cana-2978	164	3	i	i	PRON
cana-2978	164	4	ᵀ	ᵀ	VERB
cana-2978	164	5	ij	ij	NOUN
cana-2978	164	6	)	)	PUNCT
cana-2978	164	7	,	,	PUNCT
cana-2978	164	8	←−−−−−	←−−−−−	PROPN
cana-2978	164	9	(	(	PUNCT
cana-2978	164	10	a	a	DET
cana-2978	164	11	·	·	PUNCT
cana-2978	164	12	i	i	PRON
cana-2978	164	13	`	`	PUNCT
cana-2978	164	14	)	)	PUNCT
cana-2978	164	15	=	=	SYM
cana-2978	164	16	min(a	min(a	PROPN
cana-2978	164	17	·	·	PUNCT
cana-2978	164	18	i	i	PRON
cana-2978	164	19	`	`	PUNCT
cana-2978	164	20	ij	ij	INTJ
cana-2978	164	21	)	)	PUNCT
cana-2978	164	22	,	,	PUNCT
cana-2978	164	23	̂(a	̂(a	NOUN
cana-2978	164	24	·	·	PUNCT
cana-2978	164	25	i	i	PRON
cana-2978	164	26	`	`	PUNCT
cana-2978	164	27	)	)	PUNCT
cana-2978	165	1	=	=	SYM
cana-2978	166	1	max(a	max(a	PROPN
cana-2978	166	2	·	·	PUNCT
cana-2978	166	3	i	i	PRON
cana-2978	166	4	`	`	PUNCT
cana-2978	166	5	ij	ij	INTJ
cana-2978	166	6	)	)	PUNCT
cana-2978	166	7	and	and	CCONJ
cana-2978	166	8	where	where	SCONJ
cana-2978	166	9	1	1	NUM
cana-2978	166	10	≤	≤	NUM
cana-2978	166	11	i	i	PRON
cana-2978	166	12	≤	≤	PROPN
cana-2978	166	13	n	n	CCONJ
cana-2978	166	14	,	,	PUNCT
cana-2978	166	15	j	j	PROPN
cana-2978	166	16	=	=	SYM
cana-2978	166	17	1	1	NUM
cana-2978	166	18	,	,	PUNCT
cana-2978	166	19	2	2	NUM
cana-2978	166	20	,	,	PUNCT
cana-2978	166	21	...	...	PUNCT
cana-2978	166	22	,	,	PUNCT
cana-2978	166	23	ij	ij	INTJ
cana-2978	166	24	.	.	PUNCT
cana-2978	167	1	then,〈←−−−−−−−−−−−−	then,〈←−−−−−−−−−−−−	PROPN
cana-2978	167	2	(	(	PUNCT
cana-2978	167	3	a	a	DET
cana-2978	167	4	·	·	SYM
cana-2978	167	5	rᵀ	rᵀ	NOUN
cana-2978	167	6	)	)	PUNCT
cana-2978	167	7	·	·	PUNCT
cana-2978	168	1	e(a·i	e(a·i	PROPN
cana-2978	168	2	ᵀ	ᵀ	NUM
cana-2978	168	3	)	)	PUNCT
cana-2978	168	4	,	,	PUNCT
cana-2978	168	5	̂(a	̂(a	NOUN
cana-2978	168	6	·	·	PUNCT
cana-2978	168	7	r	r	NOUN
cana-2978	168	8	`	`	PUNCT
cana-2978	168	9	)	)	PUNCT
cana-2978	168	10	·	·	PUNCT
cana-2978	169	1	e(a·i	e(a·i	NOUN
cana-2978	169	2	`	`	PUNCT
cana-2978	169	3	)	)	PUNCT
cana-2978	169	4	〉	〉	NOUN
cana-2978	169	5	≤	≤	NUM
cana-2978	169	6	ct	ct	NUM
cana-2978	169	7	(	(	PUNCT
cana-2978	169	8	γ	γ	X
cana-2978	169	9	,	,	PUNCT
cana-2978	169	10	τ)nwa(θ1,θ2	τ)nwa(θ1,θ2	PROPN
cana-2978	169	11	,	,	PUNCT
cana-2978	169	12	...	...	PUNCT
cana-2978	169	13	,	,	PUNCT
cana-2978	169	14	θ	θ	NOUN
cana-2978	169	15	`	`	PUNCT
cana-2978	169	16	)	)	PUNCT
cana-2978	169	17	≤	≤	NUM
cana-2978	170	1	〈	〈	PROPN
cana-2978	170	2	̂(a	̂(a	NOUN
cana-2978	170	3	·	·	PUNCT
cana-2978	170	4	rᵀ	rᵀ	NOUN
cana-2978	170	5	)	)	PUNCT
cana-2978	170	6	·	·	PUNCT
cana-2978	170	7	e(a·i	e(a·i	PROPN
cana-2978	170	8	ᵀ	ᵀ	NUM
cana-2978	170	9	)	)	PUNCT
cana-2978	170	10	,	,	PUNCT
cana-2978	170	11	←−−−−−−−−−−−−	←−−−−−−−−−−−−	PROPN
cana-2978	170	12	(	(	PUNCT
cana-2978	170	13	a	a	DET
cana-2978	170	14	·	·	SYM
cana-2978	170	15	r	r	NOUN
cana-2978	170	16	`	`	PUNCT
cana-2978	170	17	)	)	PUNCT
cana-2978	170	18	·	·	PUNCT
cana-2978	171	1	e(a·i	e(a·i	NOUN
cana-2978	171	2	`	`	PUNCT
cana-2978	171	3	)	)	PUNCT
cana-2978	171	4	〉	〉	NOUN
cana-2978	171	5	.	.	PUNCT
cana-2978	172	1	(	(	PUNCT
cana-2978	172	2	boundedness	boundedness	NOUN
cana-2978	172	3	property	property	NOUN
cana-2978	172	4	)	)	PUNCT
cana-2978	172	5	.	.	PUNCT
cana-2978	173	1	proof	proof	NOUN
cana-2978	173	2	.	.	PUNCT
cana-2978	174	1	since	since	SCONJ
cana-2978	174	2	,	,	PUNCT
cana-2978	174	3	←−−−−−	←−−−−−	PROPN
cana-2978	174	4	(	(	PUNCT
cana-2978	174	5	a	a	DET
cana-2978	174	6	·	·	SYM
cana-2978	174	7	rᵀ	rᵀ	NOUN
cana-2978	174	8	)	)	PUNCT
cana-2978	174	9	=	=	SYM
cana-2978	174	10	min(a	min(a	PROPN
cana-2978	174	11	·	·	PUNCT
cana-2978	174	12	rᵀ	rᵀ	NOUN
cana-2978	174	13	ij	ij	NOUN
cana-2978	174	14	)	)	PUNCT
cana-2978	174	15	,	,	PUNCT
cana-2978	174	16	̂(a	̂(a	NOUN
cana-2978	174	17	·	·	SYM
cana-2978	174	18	rᵀ	rᵀ	NOUN
cana-2978	174	19	)	)	PUNCT
cana-2978	174	20	=	=	SYM
cana-2978	174	21	max(a	max(a	PROPN
cana-2978	174	22	·	·	PUNCT
cana-2978	174	23	rᵀ	rᵀ	NOUN
cana-2978	174	24	ij	ij	NOUN
cana-2978	174	25	)	)	PUNCT
cana-2978	174	26	and	and	CCONJ
cana-2978	174	27	←−−−−−	←−−−−−	NUM
cana-2978	174	28	(	(	PUNCT
cana-2978	174	29	a	a	DET
cana-2978	174	30	·	·	SYM
cana-2978	174	31	rᵀ	rᵀ	NOUN
cana-2978	174	32	)	)	PUNCT
cana-2978	174	33	≤	≤	NOUN
cana-2978	174	34	(	(	PUNCT
cana-2978	174	35	a	a	DET
cana-2978	174	36	·	·	PUNCT
cana-2978	174	37	rᵀ	rᵀ	NOUN
cana-2978	174	38	ij	ij	NOUN
cana-2978	174	39	)	)	PUNCT
cana-2978	174	40	≤	≤	NOUN
cana-2978	174	41	̂(a	̂(a	NOUN
cana-2978	174	42	·	·	SYM
cana-2978	174	43	rᵀ	rᵀ	NOUN
cana-2978	174	44	)	)	PUNCT
cana-2978	174	45	and	and	CCONJ
cana-2978	174	46	←−−−−−	←−−−−−	NUM
cana-2978	174	47	(	(	PUNCT
cana-2978	174	48	a	a	DET
cana-2978	174	49	·	·	PUNCT
cana-2978	174	50	i	i	PRON
cana-2978	174	51	ᵀ	ᵀ	NOUN
cana-2978	174	52	)	)	PUNCT
cana-2978	174	53	=	=	SYM
cana-2978	174	54	min(a	min(a	PROPN
cana-2978	174	55	·	·	PUNCT
cana-2978	174	56	i	i	PRON
cana-2978	174	57	ᵀ	ᵀ	VERB
cana-2978	174	58	ij	ij	NOUN
cana-2978	174	59	)	)	PUNCT
cana-2978	174	60	,	,	PUNCT
cana-2978	174	61	̂(a	̂(a	NOUN
cana-2978	174	62	·	·	PUNCT
cana-2978	174	63	i	i	PRON
cana-2978	174	64	ᵀ	ᵀ	NOUN
cana-2978	174	65	)	)	PUNCT
cana-2978	174	66	=	=	SYM
cana-2978	175	1	max(a	max(a	PROPN
cana-2978	175	2	·	·	PUNCT
cana-2978	175	3	i	i	PRON
cana-2978	175	4	ᵀ	ᵀ	X
cana-2978	175	5	ij	ij	NOUN
cana-2978	175	6	)	)	PUNCT
cana-2978	175	7	and	and	CCONJ
cana-2978	175	8	←−−−−−	←−−−−−	NUM
cana-2978	175	9	(	(	PUNCT
cana-2978	175	10	a	a	DET
cana-2978	175	11	·	·	PUNCT
cana-2978	175	12	i	i	PRON
cana-2978	175	13	ᵀ	ᵀ	NOUN
cana-2978	175	14	)	)	PUNCT
cana-2978	175	15	≤	≤	NOUN
cana-2978	175	16	(	(	PUNCT
cana-2978	175	17	a	a	PRON
cana-2978	175	18	·	·	PUNCT
cana-2978	175	19	i	i	PRON
cana-2978	175	20	ᵀ	ᵀ	X
cana-2978	175	21	ij	ij	NOUN
cana-2978	175	22	)	)	PUNCT
cana-2978	175	23	≤	≤	NOUN
cana-2978	175	24	̂(a	̂(a	NOUN
cana-2978	175	25	·	·	PUNCT
cana-2978	175	26	i	i	PRON
cana-2978	175	27	ᵀ	ᵀ	VERB
cana-2978	175	28	)	)	PUNCT
cana-2978	175	29	.	.	PUNCT
cana-2978	176	1	now	now	ADV
cana-2978	176	2	←−−−−−	←−−−−−	PROPN
cana-2978	176	3	(	(	PUNCT
cana-2978	176	4	a	a	DET
cana-2978	176	5	·	·	SYM
cana-2978	176	6	rᵀ	rᵀ	NOUN
cana-2978	176	7	)	)	PUNCT
cana-2978	176	8	·	·	PUNCT
cana-2978	176	9	e	e	X
cana-2978	176	10	←−−−−−	←−−−−−	PROPN
cana-2978	176	11	(	(	PUNCT
cana-2978	176	12	a·i	a·i	NOUN
cana-2978	176	13	ᵀ	ᵀ	NUM
cana-2978	176	14	)	)	PUNCT
cana-2978	176	15	=	=	NOUN
cana-2978	176	16	γ	γ	X
cana-2978	176	17	√√√√1−	√√√√1−	ADV
cana-2978	176	18	⊗̀	⊗̀	NOUN
cana-2978	176	19	i=1	i=1	X
cana-2978	177	1	(	(	PUNCT
cana-2978	177	2	1−	1−	NUM
cana-2978	177	3	(	(	PUNCT
cana-2978	177	4	←−−−−−	←−−−−−	PROPN
cana-2978	177	5	(	(	PUNCT
cana-2978	177	6	a	a	DET
cana-2978	177	7	·	·	SYM
cana-2978	177	8	rᵀ))γ	rᵀ))γ	NOUN
cana-2978	177	9	)	)	PUNCT
cana-2978	177	10	ωi	ωi	X
cana-2978	177	11	·	·	PUNCT
cana-2978	177	12	e	e	X
cana-2978	177	13	γ	γ	X
cana-2978	177	14	√	√	PROPN
cana-2978	177	15	1−	1−	NUM
cana-2978	177	16	⊗	⊗	NUM
cana-2978	177	17	`	`	PUNCT
cana-2978	177	18	i=1	i=1	PROPN
cana-2978	177	19	(	(	PUNCT
cana-2978	177	20	1−	1−	NUM
cana-2978	177	21	(	(	PUNCT
cana-2978	177	22	←−−−−−	←−−−−−	PROPN
cana-2978	177	23	(	(	PUNCT
cana-2978	177	24	a·i	a·i	PROPN
cana-2978	177	25	ᵀ))γ	ᵀ))γ	NOUN
cana-2978	177	26	)	)	PUNCT
cana-2978	177	27	ωi	ωi	PROPN
cana-2978	177	28	≤	≤	ADV
cana-2978	177	29	γ	γ	X
cana-2978	177	30	√√√√1−	√√√√1−	ADV
cana-2978	177	31	⊗̀	⊗̀	NOUN
cana-2978	177	32	i=1	i=1	X
cana-2978	178	1	(	(	PUNCT
cana-2978	178	2	1−	1−	NUM
cana-2978	178	3	(	(	PUNCT
cana-2978	178	4	(	(	PUNCT
cana-2978	178	5	(	(	PUNCT
cana-2978	178	6	a	a	DET
cana-2978	178	7	·	·	PUNCT
cana-2978	178	8	rᵀ	rᵀ	NOUN
cana-2978	178	9	ij	ij	NOUN
cana-2978	178	10	)	)	PUNCT
cana-2978	178	11	)	)	PUNCT
cana-2978	178	12	)	)	PUNCT
cana-2978	178	13	γ	γ	X
cana-2978	178	14	)	)	PUNCT
cana-2978	178	15	ωi	ωi	X
cana-2978	178	16	·	·	PUNCT
cana-2978	178	17	e	e	X
cana-2978	178	18	γ	γ	X
cana-2978	178	19	√	√	PROPN
cana-2978	178	20	1−	1−	NUM
cana-2978	178	21	⊗	⊗	NUM
cana-2978	178	22	`	`	PUNCT
cana-2978	178	23	i=1	i=1	PROPN
cana-2978	178	24	(	(	PUNCT
cana-2978	178	25	1−(((a·i	1−(((a·i	NUM
cana-2978	178	26	ᵀ	ᵀ	NOUN
cana-2978	178	27	ij	ij	NOUN
cana-2978	178	28	)	)	PUNCT
cana-2978	178	29	)	)	PUNCT
cana-2978	178	30	)	)	PUNCT
cana-2978	179	1	γ	γ	X
cana-2978	179	2	)	)	PUNCT
cana-2978	179	3	ωi	ωi	PROPN
cana-2978	179	4	≤	≤	ADV
cana-2978	179	5	γ	γ	X
cana-2978	179	6	√√√√1−	√√√√1−	ADV
cana-2978	179	7	⊗̀	⊗̀	NOUN
cana-2978	179	8	i=1	i=1	X
cana-2978	180	1	(	(	PUNCT
cana-2978	180	2	1−	1−	NUM
cana-2978	180	3	(	(	PUNCT
cana-2978	180	4	̂(a	̂(a	NOUN
cana-2978	180	5	·	·	PUNCT
cana-2978	180	6	rᵀ))γ	rᵀ))γ	NOUN
cana-2978	180	7	)	)	PUNCT
cana-2978	180	8	ωi	ωi	X
cana-2978	180	9	·	·	PUNCT
cana-2978	180	10	e	e	X
cana-2978	180	11	γ	γ	X
cana-2978	180	12	√	√	PROPN
cana-2978	180	13	1−	1−	NUM
cana-2978	180	14	⊗	⊗	NUM
cana-2978	180	15	`	`	PUNCT
cana-2978	180	16	i=1	i=1	PROPN
cana-2978	180	17	(	(	PUNCT
cana-2978	180	18	1−	1−	NUM
cana-2978	180	19	(	(	PUNCT
cana-2978	180	20	̂(a·i	̂(a·i	NOUN
cana-2978	180	21	ᵀ))γ	ᵀ))γ	NOUN
cana-2978	180	22	)	)	PUNCT
cana-2978	180	23	ωi	ωi	PROPN
cana-2978	180	24	=	=	PUNCT
cana-2978	180	25	̂(a	̂(a	NOUN
cana-2978	180	26	·	·	PUNCT
cana-2978	180	27	rᵀ	rᵀ	NOUN
cana-2978	180	28	)	)	PUNCT
cana-2978	180	29	.	.	PUNCT
cana-2978	181	1	since	since	SCONJ
cana-2978	181	2	,	,	PUNCT
cana-2978	181	3	←−−−−−−−	←−−−−−−−	PROPN
cana-2978	181	4	(	(	PUNCT
cana-2978	181	5	a	a	PRON
cana-2978	181	6	·	·	PUNCT
cana-2978	181	7	(	(	PUNCT
cana-2978	181	8	r`)τ	r`)τ	PROPN
cana-2978	181	9	)	)	PUNCT
cana-2978	181	10	=	=	SYM
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cana-2978	181	12	·	·	SYM
cana-2978	181	13	r	r	NOUN
cana-2978	181	14	`	`	PUNCT
cana-2978	181	15	ij	ij	NOUN
cana-2978	181	16	)	)	PUNCT
cana-2978	181	17	)	)	PUNCT
cana-2978	182	1	τ	τ	PROPN
cana-2978	182	2	,	,	PUNCT
cana-2978	182	3	̂(a	̂(a	NOUN
cana-2978	182	4	·	·	PUNCT
cana-2978	182	5	(	(	PUNCT
cana-2978	182	6	r`)τ	r`)τ	PROPN
cana-2978	182	7	)	)	PUNCT
cana-2978	183	1	=	=	SYM
cana-2978	183	2	max((a	max((a	X
cana-2978	183	3	·	·	SYM
cana-2978	183	4	r	r	NOUN
cana-2978	183	5	`	`	PUNCT
cana-2978	183	6	ij	ij	NOUN
cana-2978	183	7	)	)	PUNCT
cana-2978	183	8	)	)	PUNCT
cana-2978	184	1	τ	τ	PROPN
cana-2978	184	2	and	and	CCONJ
cana-2978	184	3	←−−−−−−−	←−−−−−−−	PROPN
cana-2978	184	4	(	(	PUNCT
cana-2978	184	5	a	a	PRON
cana-2978	184	6	·	·	PUNCT
cana-2978	184	7	(	(	PUNCT
cana-2978	184	8	r`)τ	r`)τ	PROPN
cana-2978	184	9	)	)	PUNCT
cana-2978	184	10	≤	≤	NOUN
cana-2978	184	11	(	(	PUNCT
cana-2978	184	12	(	(	PUNCT
cana-2978	184	13	a	a	DET
cana-2978	184	14	·	·	SYM
cana-2978	184	15	r	r	NOUN
cana-2978	184	16	`	`	PUNCT
cana-2978	184	17	ij	ij	NOUN
cana-2978	184	18	)	)	PUNCT
cana-2978	184	19	)	)	PUNCT
cana-2978	185	1	τ	τ	PROPN
cana-2978	185	2	≤	≤	PROPN
cana-2978	185	3	̂(a	̂(a	NOUN
cana-2978	185	4	·	·	PUNCT
cana-2978	185	5	(	(	PUNCT
cana-2978	185	6	r`)τ	r`)τ	PROPN
cana-2978	185	7	)	)	PUNCT
cana-2978	185	8	and	and	CCONJ
cana-2978	185	9	←−−−−−−−−	←−−−−−−−−	PROPN
cana-2978	185	10	(	(	PUNCT
cana-2978	185	11	a	a	PRON
cana-2978	185	12	·	·	PUNCT
cana-2978	185	13	(	(	PUNCT
cana-2978	185	14	i	i	PRON
cana-2978	185	15	`	`	VERB
cana-2978	185	16	)	)	PUNCT
cana-2978	185	17	τ	τ	X
cana-2978	185	18	)	)	PUNCT
cana-2978	185	19	=	=	SYM
cana-2978	186	1	min((a	min((a	NOUN
cana-2978	186	2	·	·	PUNCT
cana-2978	186	3	i	i	PRON
cana-2978	186	4	`	`	PUNCT
cana-2978	186	5	ij	ij	NOUN
cana-2978	186	6	)	)	PUNCT
cana-2978	186	7	)	)	PUNCT
cana-2978	187	1	τ	τ	PROPN
cana-2978	187	2	,	,	PUNCT
cana-2978	187	3	̂(a	̂(a	NOUN
cana-2978	187	4	·	·	PUNCT
cana-2978	187	5	(	(	PUNCT
cana-2978	187	6	i	i	PRON
cana-2978	187	7	`	`	VERB
cana-2978	187	8	)	)	PUNCT
cana-2978	187	9	τ	τ	X
cana-2978	187	10	)	)	PUNCT
cana-2978	188	1	=	=	SYM
cana-2978	188	2	max((a	max((a	X
cana-2978	188	3	·	·	PUNCT
cana-2978	189	1	i	i	PRON
cana-2978	189	2	`	`	PUNCT
cana-2978	189	3	ij	ij	NOUN
cana-2978	189	4	)	)	PUNCT
cana-2978	189	5	)	)	PUNCT
cana-2978	190	1	τ	τ	PROPN
cana-2978	190	2	and	and	CCONJ
cana-2978	190	3	←−−−−−−−−	←−−−−−−−−	PROPN
cana-2978	190	4	(	(	PUNCT
cana-2978	190	5	a	a	PRON
cana-2978	190	6	·	·	PUNCT
cana-2978	190	7	(	(	PUNCT
cana-2978	190	8	i	i	PRON
cana-2978	190	9	`	`	VERB
cana-2978	190	10	)	)	PUNCT
cana-2978	190	11	τ	τ	PROPN
cana-2978	190	12	)	)	PUNCT
cana-2978	190	13	≤	≤	NOUN
cana-2978	190	14	(	(	PUNCT
cana-2978	190	15	(	(	PUNCT
cana-2978	190	16	a	a	PRON
cana-2978	190	17	·	·	PUNCT
cana-2978	190	18	i	i	PRON
cana-2978	190	19	`	`	PUNCT
cana-2978	190	20	ij	ij	NOUN
cana-2978	190	21	)	)	PUNCT
cana-2978	190	22	)	)	PUNCT
cana-2978	191	1	τ	τ	PROPN
cana-2978	191	2	≤	≤	PROPN
cana-2978	191	3	̂(a	̂(a	NOUN
cana-2978	191	4	·	·	PUNCT
cana-2978	191	5	(	(	PUNCT
cana-2978	191	6	i	i	PRON
cana-2978	191	7	`	`	VERB
cana-2978	191	8	)	)	PUNCT
cana-2978	191	9	τ	τ	PROPN
cana-2978	191	10	)	)	PUNCT
cana-2978	191	11	.	.	PUNCT
cana-2978	192	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	192	2	137	137	NUM
cana-2978	192	3	communications	communication	NOUN
cana-2978	192	4	on	on	ADP
cana-2978	192	5	applied	apply	VERB
cana-2978	192	6	nonlinear	nonlinear	ADJ
cana-2978	192	7	analysis	analysis	NOUN
cana-2978	192	8	issn	issn	NOUN
cana-2978	192	9	:	:	PUNCT
cana-2978	192	10	1074	1074	NUM
cana-2978	192	11	-	-	PUNCT
cana-2978	192	12	133x	133x	NUM
cana-2978	192	13	vol	vol	NOUN
cana-2978	192	14	32	32	NUM
cana-2978	192	15	no	no	NOUN
cana-2978	192	16	.	.	PUNCT
cana-2978	193	1	5s	5s	NUM
cana-2978	193	2	(	(	PUNCT
cana-2978	193	3	2025	2025	NUM
cana-2978	193	4	)	)	PUNCT
cana-2978	193	5	we	we	PRON
cana-2978	193	6	have	have	VERB
cana-2978	193	7	,	,	PUNCT
cana-2978	194	1	←−−−−−−−	←−−−−−−−	PROPN
cana-2978	194	2	(	(	PUNCT
cana-2978	194	3	a	a	PRON
cana-2978	194	4	·	·	PUNCT
cana-2978	194	5	(	(	PUNCT
cana-2978	194	6	r`)τ	r`)τ	X
cana-2978	194	7	=	=	PUNCT
cana-2978	194	8	⊗̀	⊗̀	NOUN
cana-2978	194	9	i=1	i=1	PROPN
cana-2978	195	1	←−−−−−−−	←−−−−−−−	PROPN
cana-2978	195	2	(	(	PUNCT
cana-2978	195	3	a	a	DET
cana-2978	195	4	·	·	PUNCT
cana-2978	195	5	(	(	PUNCT
cana-2978	195	6	r`)τ	r`)τ	PROPN
cana-2978	195	7	)	)	PUNCT
cana-2978	195	8	ωi	ωi	X
cana-2978	195	9	·	·	PUNCT
cana-2978	195	10	e	e	X
cana-2978	195	11	⊗	⊗	NUM
cana-2978	195	12	`	`	PUNCT
cana-2978	195	13	i=1	i=1	PROPN
cana-2978	195	14	←−−−−−−−	←−−−−−−−	PROPN
cana-2978	195	15	(	(	PUNCT
cana-2978	195	16	a·(i	a·(i	NOUN
cana-2978	195	17	`	`	PUNCT
cana-2978	195	18	)	)	PUNCT
cana-2978	195	19	τ	τ	X
cana-2978	195	20	)	)	PUNCT
cana-2978	195	21	ωi	ωi	PROPN
cana-2978	195	22	≤	≤	ADJ
cana-2978	195	23	⊗̀	⊗̀	NOUN
cana-2978	195	24	i=1	i=1	X
cana-2978	196	1	(	(	PUNCT
cana-2978	196	2	(	(	PUNCT
cana-2978	196	3	(	(	PUNCT
cana-2978	196	4	a	a	DET
cana-2978	196	5	·	·	SYM
cana-2978	196	6	r	r	NOUN
cana-2978	196	7	`	`	PUNCT
cana-2978	196	8	ij	ij	NOUN
cana-2978	196	9	)	)	PUNCT
cana-2978	196	10	)	)	PUNCT
cana-2978	197	1	τ	τ	PROPN
cana-2978	197	2	)	)	PUNCT
cana-2978	197	3	ωi	ωi	X
cana-2978	197	4	·	·	PUNCT
cana-2978	197	5	e	e	X
cana-2978	197	6	⊗	⊗	PROPN
cana-2978	197	7	`	`	PUNCT
cana-2978	197	8	i=1(((a·i	i=1(((a·i	PROPN
cana-2978	197	9	`	`	PUNCT
cana-2978	197	10	ij	ij	NOUN
cana-2978	197	11	)	)	PUNCT
cana-2978	197	12	)	)	PUNCT
cana-2978	198	1	τ	τ	PROPN
cana-2978	198	2	)	)	PUNCT
cana-2978	198	3	ωi	ωi	PROPN
cana-2978	198	4	≤	≤	ADJ
cana-2978	198	5	⊗̀	⊗̀	NOUN
cana-2978	198	6	i=1	i=1	PROPN
cana-2978	198	7	̂(a	̂(a	NOUN
cana-2978	198	8	·	·	PUNCT
cana-2978	198	9	(	(	PUNCT
cana-2978	198	10	r`)τ	r`)τ	PROPN
cana-2978	198	11	)	)	PUNCT
cana-2978	198	12	ωi	ωi	X
cana-2978	198	13	·	·	PUNCT
cana-2978	198	14	e	e	X
cana-2978	198	15	⊗	⊗	PROPN
cana-2978	198	16	`	`	PUNCT
cana-2978	198	17	i=1	i=1	PROPN
cana-2978	198	18	̂(a·(i	̂(a·(i	PROPN
cana-2978	199	1	`	`	PUNCT
cana-2978	199	2	)	)	PUNCT
cana-2978	199	3	τ	τ	PROPN
cana-2978	199	4	)	)	PUNCT
cana-2978	199	5	ωi	ωi	PROPN
cana-2978	199	6	=	=	SYM
cana-2978	199	7	̂(a	̂(a	NOUN
cana-2978	199	8	·	·	PUNCT
cana-2978	199	9	(	(	PUNCT
cana-2978	199	10	r`)τ	r`)τ	PROPN
cana-2978	199	11	)	)	PUNCT
cana-2978	199	12	·	·	PUNCT
cana-2978	200	1	e	e	X
cana-2978	200	2	̂(a·(i	̂(a·(i	PROPN
cana-2978	200	3	`	`	PUNCT
cana-2978	200	4	)	)	PUNCT
cana-2978	200	5	τ	τ	PROPN
cana-2978	200	6	)	)	PUNCT
cana-2978	200	7	.	.	PUNCT
cana-2978	201	1	therefore	therefore	ADV
cana-2978	201	2	,	,	PUNCT
cana-2978	201	3	1	1	NUM
cana-2978	201	4	2	2	NUM
cana-2978	201	5	×	×	NOUN
cana-2978	201	6			NOUN
cana-2978	201	7			VERB
cana-2978	201	8	γ	γ	X
cana-2978	201	9	√√√√	√√√√	ADP
cana-2978	201	10	1−	1−	NUM
cana-2978	201	11	⊗̀	⊗̀	NOUN
cana-2978	201	12	i=1	i=1	X
cana-2978	202	1	(	(	PUNCT
cana-2978	202	2	1−	1−	NUM
cana-2978	202	3	(	(	PUNCT
cana-2978	202	4	←−−−−−	←−−−−−	PROPN
cana-2978	202	5	(	(	PUNCT
cana-2978	202	6	a	a	DET
cana-2978	202	7	·	·	SYM
cana-2978	202	8	rᵀ))γ	rᵀ))γ	NOUN
cana-2978	202	9	)	)	PUNCT
cana-2978	202	10	ωi2	ωi2	VERB
cana-2978	203	1	+	+	X
cana-2978	203	2	1−	1−	NUM
cana-2978	203	3	(	(	PUNCT
cana-2978	203	4	⊗	⊗	PROPN
cana-2978	203	5	`	`	PUNCT
cana-2978	203	6	i=1	i=1	X
cana-2978	203	7	(	(	PUNCT
cana-2978	203	8	(	(	PUNCT
cana-2978	203	9	̂(a	̂(a	NOUN
cana-2978	203	10	·	·	SYM
cana-2978	203	11	r`))τ	r`))τ	NOUN
cana-2978	203	12	)	)	PUNCT
cana-2978	203	13	ωi	ωi	PROPN
cana-2978	203	14	)	)	PUNCT
cana-2978	203	15	2	2	PROPN
cana-2978	204	1	+	+	CCONJ
cana-2978	204	2			VERB
cana-2978	204	3	γ	γ	X
cana-2978	204	4	√√√√	√√√√	ADP
cana-2978	204	5	1−	1−	NUM
cana-2978	204	6	⊗̀	⊗̀	NOUN
cana-2978	204	7	i=1	i=1	X
cana-2978	204	8	(	(	PUNCT
cana-2978	204	9	1−	1−	NUM
cana-2978	204	10	(	(	PUNCT
cana-2978	204	11	←−−−−−	←−−−−−	PROPN
cana-2978	204	12	(	(	PUNCT
cana-2978	204	13	a	a	DET
cana-2978	204	14	·	·	PUNCT
cana-2978	204	15	i	i	NOUN
cana-2978	204	16	ᵀ))γ	ᵀ))γ	NOUN
cana-2978	204	17	)	)	PUNCT
cana-2978	204	18	ωi2	ωi2	VERB
cana-2978	204	19	−	−	PROPN
cana-2978	205	1	(	(	PUNCT
cana-2978	205	2	⊗	⊗	PROPN
cana-2978	205	3	`	`	PUNCT
cana-2978	205	4	i=1	i=1	X
cana-2978	205	5	(	(	PUNCT
cana-2978	205	6	(	(	PUNCT
cana-2978	205	7	̂(a	̂(a	NOUN
cana-2978	205	8	·	·	PUNCT
cana-2978	205	9	i	i	PRON
cana-2978	205	10	`	`	PUNCT
cana-2978	205	11	)	)	PUNCT
cana-2978	205	12	)	)	PUNCT
cana-2978	205	13	τ	τ	X
cana-2978	205	14	)	)	PUNCT
cana-2978	205	15	ωi	ωi	PROPN
cana-2978	205	16	)	)	PUNCT
cana-2978	206	1	2	2	PROPN
cana-2978	206	2			VERB
cana-2978	206	3	≤	≤	NUM
cana-2978	206	4	1	1	NUM
cana-2978	206	5	2	2	NUM
cana-2978	206	6	×	×	NOUN
cana-2978	206	7			NOUN
cana-2978	206	8			VERB
cana-2978	206	9	γ	γ	X
cana-2978	206	10	√√√√	√√√√	ADP
cana-2978	206	11	1−	1−	NUM
cana-2978	206	12	⊗̀	⊗̀	NOUN
cana-2978	206	13	i=1	i=1	X
cana-2978	207	1	(	(	PUNCT
cana-2978	207	2	1−	1−	NUM
cana-2978	207	3	(	(	PUNCT
cana-2978	207	4	(	(	PUNCT
cana-2978	207	5	a	a	PRON
cana-2978	207	6	·	·	PUNCT
cana-2978	207	7	(	(	PUNCT
cana-2978	207	8	a	a	DET
cana-2978	207	9	·	·	PUNCT
cana-2978	207	10	rᵀ	rᵀ	NOUN
cana-2978	207	11	ij	ij	NOUN
cana-2978	207	12	)	)	PUNCT
cana-2978	207	13	)	)	PUNCT
cana-2978	207	14	)	)	PUNCT
cana-2978	207	15	γ	γ	PROPN
cana-2978	207	16	)	)	PUNCT
cana-2978	207	17	ωi2	ωi2	VERB
cana-2978	208	1	+	+	X
cana-2978	209	1	1−	1−	NUM
cana-2978	209	2	(	(	PUNCT
cana-2978	209	3	⊗	⊗	PROPN
cana-2978	209	4	`	`	PUNCT
cana-2978	209	5	i=1(((a	i=1(((a	PROPN
cana-2978	209	6	·	·	PUNCT
cana-2978	209	7	r	r	NOUN
cana-2978	209	8	`	`	PUNCT
cana-2978	209	9	ij	ij	NOUN
cana-2978	209	10	)	)	PUNCT
cana-2978	209	11	)	)	PUNCT
cana-2978	210	1	τ	τ	PROPN
cana-2978	210	2	)	)	PUNCT
cana-2978	210	3	ωi	ωi	PROPN
cana-2978	210	4	)	)	PUNCT
cana-2978	210	5	2	2	PROPN
cana-2978	211	1	+	+	CCONJ
cana-2978	211	2			VERB
cana-2978	211	3	γ	γ	X
cana-2978	211	4	√√√√	√√√√	ADP
cana-2978	211	5	1−	1−	NUM
cana-2978	211	6	⊗̀	⊗̀	NOUN
cana-2978	211	7	i=1	i=1	X
cana-2978	211	8	(	(	PUNCT
cana-2978	211	9	1−	1−	NUM
cana-2978	211	10	(	(	PUNCT
cana-2978	211	11	(	(	PUNCT
cana-2978	211	12	a	a	PRON
cana-2978	211	13	·	·	PUNCT
cana-2978	211	14	(	(	PUNCT
cana-2978	211	15	a	a	PRON
cana-2978	211	16	·	·	PUNCT
cana-2978	211	17	i	i	PRON
cana-2978	211	18	ᵀ	ᵀ	X
cana-2978	211	19	ij	ij	NOUN
cana-2978	211	20	)	)	PUNCT
cana-2978	211	21	)	)	PUNCT
cana-2978	211	22	)	)	PUNCT
cana-2978	212	1	γ	γ	PROPN
cana-2978	212	2	)	)	PUNCT
cana-2978	212	3	ωi2	ωi2	VERB
cana-2978	212	4	−	−	PROPN
cana-2978	213	1	(	(	PUNCT
cana-2978	213	2	⊗	⊗	PROPN
cana-2978	213	3	`	`	PUNCT
cana-2978	213	4	i=1(((a	i=1(((a	PROPN
cana-2978	213	5	·	·	PUNCT
cana-2978	213	6	i	i	PRON
cana-2978	213	7	`	`	PUNCT
cana-2978	213	8	ij	ij	NOUN
cana-2978	213	9	)	)	PUNCT
cana-2978	213	10	)	)	PUNCT
cana-2978	214	1	τ	τ	PROPN
cana-2978	214	2	)	)	PUNCT
cana-2978	214	3	ωi	ωi	PROPN
cana-2978	214	4	)	)	PUNCT
cana-2978	214	5	2	2	PROPN
cana-2978	214	6			VERB
cana-2978	214	7	≤	≤	NUM
cana-2978	214	8	1	1	NUM
cana-2978	214	9	2	2	NUM
cana-2978	214	10	×	×	NOUN
cana-2978	214	11			NOUN
cana-2978	214	12			VERB
cana-2978	214	13	γ	γ	X
cana-2978	214	14	√√√√	√√√√	ADP
cana-2978	214	15	1−	1−	NUM
cana-2978	214	16	⊗̀	⊗̀	NOUN
cana-2978	214	17	i=1	i=1	X
cana-2978	215	1	(	(	PUNCT
cana-2978	215	2	1−	1−	NUM
cana-2978	215	3	(	(	PUNCT
cana-2978	215	4	̂(a	̂(a	NOUN
cana-2978	215	5	·	·	PUNCT
cana-2978	215	6	rᵀ))γ	rᵀ))γ	NOUN
cana-2978	215	7	)	)	PUNCT
cana-2978	215	8	ωi2	ωi2	VERB
cana-2978	216	1	+	+	X
cana-2978	216	2	1−	1−	NUM
cana-2978	216	3	(	(	PUNCT
cana-2978	216	4	⊗	⊗	PROPN
cana-2978	216	5	`	`	PUNCT
cana-2978	216	6	i=1	i=1	X
cana-2978	216	7	(	(	PUNCT
cana-2978	216	8	←−−−−−	←−−−−−	PROPN
cana-2978	216	9	(	(	PUNCT
cana-2978	216	10	a	a	DET
cana-2978	216	11	·	·	SYM
cana-2978	216	12	r`))τ	r`))τ	NOUN
cana-2978	216	13	)	)	PUNCT
cana-2978	216	14	ωi	ωi	PROPN
cana-2978	216	15	)	)	PUNCT
cana-2978	216	16	2	2	PROPN
cana-2978	217	1	+	+	CCONJ
cana-2978	217	2			VERB
cana-2978	217	3	γ	γ	X
cana-2978	217	4	√√√√	√√√√	ADP
cana-2978	217	5	1−	1−	NUM
cana-2978	217	6	⊗̀	⊗̀	NOUN
cana-2978	217	7	i=1	i=1	X
cana-2978	217	8	(	(	PUNCT
cana-2978	217	9	1−	1−	NUM
cana-2978	217	10	(	(	PUNCT
cana-2978	217	11	̂(a	̂(a	NOUN
cana-2978	217	12	·	·	PUNCT
cana-2978	217	13	i	i	PRON
cana-2978	217	14	ᵀ))γ	ᵀ))γ	NOUN
cana-2978	217	15	)	)	PUNCT
cana-2978	217	16	ωi2	ωi2	VERB
cana-2978	217	17	−	−	PROPN
cana-2978	218	1	(	(	PUNCT
cana-2978	218	2	⊗	⊗	PROPN
cana-2978	218	3	`	`	PUNCT
cana-2978	218	4	i=1	i=1	X
cana-2978	218	5	(	(	PUNCT
cana-2978	218	6	←−−−−−	←−−−−−	PROPN
cana-2978	218	7	(	(	PUNCT
cana-2978	218	8	a	a	DET
cana-2978	218	9	·	·	PUNCT
cana-2978	218	10	i	i	PRON
cana-2978	218	11	`	`	PUNCT
cana-2978	218	12	)	)	PUNCT
cana-2978	218	13	)	)	PUNCT
cana-2978	218	14	τ	τ	X
cana-2978	218	15	)	)	PUNCT
cana-2978	218	16	ωi	ωi	PROPN
cana-2978	218	17	)	)	PUNCT
cana-2978	218	18	2	2	PROPN
cana-2978	218	19			VERB
cana-2978	218	20	.	.	PUNCT
cana-2978	219	1	hence	hence	ADV
cana-2978	219	2	,	,	PUNCT
cana-2978	219	3	〈	〈	NOUN
cana-2978	219	4	←−−−−−−−−−−−−	←−−−−−−−−−−−−	PROPN
cana-2978	219	5	(	(	PUNCT
cana-2978	219	6	a	a	DET
cana-2978	219	7	·	·	SYM
cana-2978	219	8	rᵀ	rᵀ	NOUN
cana-2978	219	9	)	)	PUNCT
cana-2978	219	10	·	·	PUNCT
cana-2978	219	11	e(a·i	e(a·i	PROPN
cana-2978	219	12	ᵀ	ᵀ	NUM
cana-2978	219	13	)	)	PUNCT
cana-2978	219	14	,	,	PUNCT
cana-2978	219	15	̂(a	̂(a	NOUN
cana-2978	219	16	·	·	PUNCT
cana-2978	219	17	r	r	NOUN
cana-2978	219	18	`	`	PUNCT
cana-2978	219	19	)	)	PUNCT
cana-2978	219	20	·	·	PUNCT
cana-2978	220	1	e(a·i	e(a·i	NOUN
cana-2978	220	2	`	`	PUNCT
cana-2978	220	3	)	)	PUNCT
cana-2978	220	4	〉	〉	NOUN
cana-2978	220	5	≤	≤	NUM
cana-2978	220	6	ct	ct	NUM
cana-2978	220	7	(	(	PUNCT
cana-2978	220	8	γ	γ	X
cana-2978	220	9	,	,	PUNCT
cana-2978	220	10	τ)nwa(θ1,θ2	τ)nwa(θ1,θ2	PROPN
cana-2978	220	11	,	,	PUNCT
cana-2978	220	12	...	...	PUNCT
cana-2978	220	13	,	,	PUNCT
cana-2978	220	14	θ	θ	NOUN
cana-2978	220	15	`	`	PUNCT
cana-2978	220	16	)	)	PUNCT
cana-2978	220	17	≤	≤	PUNCT
cana-2978	221	1	〈	〈	PROPN
cana-2978	221	2	̂(a	̂(a	NOUN
cana-2978	221	3	·	·	PUNCT
cana-2978	221	4	rᵀ	rᵀ	NOUN
cana-2978	221	5	)	)	PUNCT
cana-2978	221	6	·	·	PUNCT
cana-2978	221	7	e(a·i	e(a·i	PROPN
cana-2978	221	8	ᵀ	ᵀ	NUM
cana-2978	221	9	)	)	PUNCT
cana-2978	221	10	,	,	PUNCT
cana-2978	221	11	←−−−−−−−−−−−−	←−−−−−−−−−−−−	PROPN
cana-2978	221	12	(	(	PUNCT
cana-2978	221	13	a	a	DET
cana-2978	221	14	·	·	SYM
cana-2978	221	15	r	r	NOUN
cana-2978	221	16	`	`	PUNCT
cana-2978	221	17	)	)	PUNCT
cana-2978	221	18	·	·	PUNCT
cana-2978	222	1	e(a·i	e(a·i	NOUN
cana-2978	222	2	`	`	PUNCT
cana-2978	222	3	)	)	PUNCT
cana-2978	222	4	〉	〉	PROPN
cana-2978	222	5	.	.	PUNCT
cana-2978	223	1	theorem	theorem	VERB
cana-2978	223	2	4.5	4.5	NUM
cana-2978	223	3	.	.	PUNCT
cana-2978	224	1	let	let	VERB
cana-2978	224	2	θi	θi	X
cana-2978	224	3	=	=	SYM
cana-2978	224	4	〈	〈	PROPN
cana-2978	224	5	(	(	PUNCT
cana-2978	224	6	(	(	PUNCT
cana-2978	224	7	a	a	DET
cana-2978	224	8	·	·	PUNCT
cana-2978	224	9	rᵀ	rᵀ	NOUN
cana-2978	224	10	tij	tij	PROPN
cana-2978	224	11	)	)	PUNCT
cana-2978	224	12	·	·	PUNCT
cana-2978	225	1	e	e	X
cana-2978	225	2	(	(	PUNCT
cana-2978	225	3	a·i	a·i	X
cana-2978	225	4	ᵀ	ᵀ	X
cana-2978	225	5	tij	tij	PROPN
cana-2978	225	6	)	)	PUNCT
cana-2978	225	7	,	,	PUNCT
cana-2978	225	8	(	(	PUNCT
cana-2978	225	9	a	a	DET
cana-2978	225	10	·	·	SYM
cana-2978	225	11	r	r	NOUN
cana-2978	225	12	`	`	PUNCT
cana-2978	225	13	tij	tij	PROPN
cana-2978	225	14	)	)	PUNCT
cana-2978	225	15	·	·	PUNCT
cana-2978	226	1	e	e	X
cana-2978	226	2	(	(	PUNCT
cana-2978	226	3	a·i	a·i	NOUN
cana-2978	226	4	`	`	PUNCT
cana-2978	226	5	tij	tij	PROPN
cana-2978	226	6	)	)	PUNCT
cana-2978	226	7	)	)	PUNCT
cana-2978	227	1	〉	〉	PROPN
cana-2978	227	2	and	and	CCONJ
cana-2978	227	3	wi	wi	PROPN
cana-2978	227	4	=	=	SYM
cana-2978	227	5	〈	〈	PROPN
cana-2978	227	6	(	(	PUNCT
cana-2978	227	7	(	(	PUNCT
cana-2978	227	8	a	a	DET
cana-2978	227	9	·	·	PUNCT
cana-2978	227	10	rᵀ	rᵀ	NOUN
cana-2978	227	11	hij	hij	NOUN
cana-2978	227	12	)	)	PUNCT
cana-2978	227	13	·	·	PUNCT
cana-2978	228	1	e(a·i	e(a·i	NOUN
cana-2978	228	2	ᵀ	ᵀ	X
cana-2978	228	3	hij	hij	PROPN
cana-2978	228	4	)	)	PUNCT
cana-2978	228	5	,	,	PUNCT
cana-2978	228	6	(	(	PUNCT
cana-2978	228	7	a	a	DET
cana-2978	228	8	·	·	SYM
cana-2978	228	9	r	r	NOUN
cana-2978	228	10	`	`	PUNCT
cana-2978	228	11	hij	hij	NOUN
cana-2978	228	12	)	)	PUNCT
cana-2978	228	13	·	·	PUNCT
cana-2978	229	1	e(a·i	e(a·i	NOUN
cana-2978	229	2	`	`	PUNCT
cana-2978	229	3	hij	hij	PROPN
cana-2978	229	4	)	)	PUNCT
cana-2978	229	5	)	)	PUNCT
cana-2978	230	1	〉	〉	NOUN
cana-2978	230	2	,	,	PUNCT
cana-2978	230	3	be	be	AUX
cana-2978	230	4	the	the	DET
cana-2978	230	5	ct	ct	PROPN
cana-2978	230	6	(	(	PUNCT
cana-2978	230	7	γ	γ	PROPN
cana-2978	230	8	,	,	PUNCT
cana-2978	230	9	τ)-rung	τ)-rung	PUNCT
cana-2978	230	10	fnwas	fnwas	PROPN
cana-2978	230	11	.	.	PUNCT
cana-2978	231	1	for	for	ADP
cana-2978	231	2	any	any	DET
cana-2978	231	3	i	i	PRON
cana-2978	231	4	,	,	PUNCT
cana-2978	231	5	if	if	SCONJ
cana-2978	231	6	there	there	PRON
cana-2978	231	7	is	be	VERB
cana-2978	231	8	(	(	PUNCT
cana-2978	231	9	a	a	DET
cana-2978	231	10	·	·	PUNCT
cana-2978	231	11	rᵀ	rᵀ	NOUN
cana-2978	231	12	tij	tij	NOUN
cana-2978	231	13	)	)	PUNCT
cana-2978	231	14	2	2	NUM
cana-2978	231	15	≤	≤	NOUN
cana-2978	231	16	(	(	PUNCT
cana-2978	231	17	a	a	DET
cana-2978	231	18	·	·	PUNCT
cana-2978	231	19	rᵀ	rᵀ	NOUN
cana-2978	231	20	hij	hij	NOUN
cana-2978	231	21	)	)	PUNCT
cana-2978	231	22	2	2	NUM
cana-2978	231	23	and	and	CCONJ
cana-2978	231	24	(	(	PUNCT
cana-2978	231	25	a	a	DET
cana-2978	231	26	·	·	SYM
cana-2978	231	27	r	r	NOUN
cana-2978	231	28	`	`	PUNCT
cana-2978	231	29	tij	tij	PROPN
cana-2978	231	30	)	)	PUNCT
cana-2978	231	31	2	2	NUM
cana-2978	231	32	≥	≥	NOUN
cana-2978	231	33	(	(	PUNCT
cana-2978	231	34	a	a	DET
cana-2978	231	35	·	·	SYM
cana-2978	231	36	r	r	NOUN
cana-2978	231	37	`	`	PUNCT
cana-2978	231	38	hij	hij	NOUN
cana-2978	231	39	)	)	PUNCT
cana-2978	231	40	2	2	NUM
cana-2978	231	41	and	and	CCONJ
cana-2978	231	42	(	(	PUNCT
cana-2978	231	43	a	a	PRON
cana-2978	231	44	·	·	PUNCT
cana-2978	231	45	i	i	PRON
cana-2978	231	46	ᵀ	ᵀ	VERB
cana-2978	231	47	tij	tij	NOUN
cana-2978	231	48	)	)	PUNCT
cana-2978	231	49	2	2	NUM
cana-2978	231	50	≤	≤	NOUN
cana-2978	231	51	(	(	PUNCT
cana-2978	231	52	a	a	DET
cana-2978	231	53	·	·	PUNCT
cana-2978	231	54	i	i	PRON
cana-2978	231	55	ᵀ	ᵀ	PRON
cana-2978	231	56	hij	hij	NOUN
cana-2978	231	57	)	)	PUNCT
cana-2978	231	58	2	2	NUM
cana-2978	231	59	and	and	CCONJ
cana-2978	231	60	(	(	PUNCT
cana-2978	231	61	a	a	PRON
cana-2978	231	62	·	·	PUNCT
cana-2978	231	63	i	i	PRON
cana-2978	231	64	`	`	PUNCT
cana-2978	231	65	tij	tij	PROPN
cana-2978	231	66	)	)	PUNCT
cana-2978	231	67	2	2	NUM
cana-2978	231	68	≥	≥	NOUN
cana-2978	231	69	(	(	PUNCT
cana-2978	231	70	a	a	PRON
cana-2978	231	71	·	·	PUNCT
cana-2978	231	72	i	i	PRON
cana-2978	231	73	`	`	PUNCT
cana-2978	231	74	hij	hij	PROPN
cana-2978	231	75	)	)	PUNCT
cana-2978	231	76	2or	2or	NOUN
cana-2978	231	77	θi	θi	ADP
cana-2978	231	78	≤	≤	PROPN
cana-2978	231	79	wi	wi	PROPN
cana-2978	231	80	.	.	PUNCT
cana-2978	231	81	prove	prove	VERB
cana-2978	231	82	that	that	SCONJ
cana-2978	231	83	ct	ct	PROPN
cana-2978	231	84	(	(	PUNCT
cana-2978	231	85	γ	γ	PROPN
cana-2978	231	86	,	,	PUNCT
cana-2978	231	87	τ)nwa(θ1,θ2	τ)nwa(θ1,θ2	PROPN
cana-2978	231	88	,	,	PUNCT
cana-2978	231	89	...	...	PUNCT
cana-2978	231	90	,	,	PUNCT
cana-2978	231	91	θ	θ	NOUN
cana-2978	231	92	`	`	PUNCT
cana-2978	231	93	)	)	PUNCT
cana-2978	231	94	≤	≤	NUM
cana-2978	232	1	ct	ct	PROPN
cana-2978	232	2	(	(	PUNCT
cana-2978	232	3	γ	γ	X
cana-2978	232	4	,	,	PUNCT
cana-2978	232	5	τ)nwa(w1,w2	τ)nwa(w1,w2	PROPN
cana-2978	232	6	,	,	PUNCT
cana-2978	232	7	...	...	PUNCT
cana-2978	232	8	,	,	PUNCT
cana-2978	232	9	w	w	NOUN
cana-2978	232	10	`	`	PUNCT
cana-2978	232	11	)	)	PUNCT
cana-2978	232	12	,	,	PUNCT
cana-2978	232	13	where	where	SCONJ
cana-2978	232	14	(	(	PUNCT
cana-2978	232	15	i	i	NOUN
cana-2978	232	16	=	=	NOUN
cana-2978	232	17	1	1	NUM
cana-2978	232	18	,	,	PUNCT
cana-2978	232	19	2	2	NUM
cana-2978	232	20	,	,	PUNCT
cana-2978	232	21	...	...	PUNCT
cana-2978	232	22	,	,	PUNCT
cana-2978	232	23	`	`	PUNCT
cana-2978	232	24	)	)	PUNCT
cana-2978	232	25	;	;	PUNCT
cana-2978	232	26	(	(	PUNCT
cana-2978	232	27	j	j	NOUN
cana-2978	232	28	=	=	SYM
cana-2978	232	29	1	1	NUM
cana-2978	232	30	,	,	PUNCT
cana-2978	232	31	2	2	NUM
cana-2978	232	32	,	,	PUNCT
cana-2978	232	33	...	...	PUNCT
cana-2978	232	34	,	,	PUNCT
cana-2978	232	35	ij	ij	X
cana-2978	232	36	)	)	PUNCT
cana-2978	232	37	(	(	PUNCT
cana-2978	232	38	monotonicity	monotonicity	NOUN
cana-2978	232	39	property	property	NOUN
cana-2978	232	40	)	)	PUNCT
cana-2978	232	41	.	.	PUNCT
cana-2978	233	1	proof	proof	NOUN
cana-2978	233	2	.	.	PUNCT
cana-2978	234	1	for	for	ADP
cana-2978	234	2	any	any	DET
cana-2978	234	3	i	i	PROPN
cana-2978	234	4	,	,	PUNCT
cana-2978	234	5	(	(	PUNCT
cana-2978	234	6	a	a	DET
cana-2978	234	7	·	·	PUNCT
cana-2978	234	8	rᵀ	rᵀ	NOUN
cana-2978	234	9	tij	tij	NOUN
cana-2978	234	10	)	)	PUNCT
cana-2978	234	11	2	2	NUM
cana-2978	234	12	≤	≤	NOUN
cana-2978	234	13	(	(	PUNCT
cana-2978	234	14	a	a	DET
cana-2978	234	15	·	·	PUNCT
cana-2978	234	16	rᵀ	rᵀ	NOUN
cana-2978	234	17	hij	hij	NOUN
cana-2978	234	18	)	)	PUNCT
cana-2978	234	19	2	2	X
cana-2978	234	20	.	.	X
cana-2978	235	1	therefore	therefore	ADV
cana-2978	235	2	,	,	PUNCT
cana-2978	235	3	1−	1−	NUM
cana-2978	235	4	(	(	PUNCT
cana-2978	235	5	(	(	PUNCT
cana-2978	235	6	a	a	DET
cana-2978	235	7	·	·	PUNCT
cana-2978	235	8	rᵀ	rᵀ	NOUN
cana-2978	235	9	ti	ti	NOUN
cana-2978	235	10	)	)	PUNCT
cana-2978	235	11	)	)	PUNCT
cana-2978	235	12	2	2	NUM
cana-2978	235	13	≥	≥	NOUN
cana-2978	235	14	1−	1−	NUM
cana-2978	235	15	(	(	PUNCT
cana-2978	235	16	(	(	PUNCT
cana-2978	235	17	a	a	DET
cana-2978	235	18	·	·	PUNCT
cana-2978	235	19	rᵀ	rᵀ	NOUN
cana-2978	235	20	hi	hi	INTJ
cana-2978	235	21	)	)	PUNCT
cana-2978	235	22	)	)	PUNCT
cana-2978	235	23	2	2	X
cana-2978	235	24	.	.	X
cana-2978	235	25	hence	hence	ADV
cana-2978	235	26	,	,	PUNCT
cana-2978	235	27	⊗	⊗	PROPN
cana-2978	235	28	`	`	PUNCT
cana-2978	235	29	i=1	i=1	PROPN
cana-2978	235	30	(	(	PUNCT
cana-2978	235	31	1−	1−	NUM
cana-2978	235	32	(	(	PUNCT
cana-2978	235	33	(	(	PUNCT
cana-2978	235	34	a	a	DET
cana-2978	235	35	·	·	PUNCT
cana-2978	235	36	rᵀ	rᵀ	NOUN
cana-2978	235	37	ti	ti	NOUN
cana-2978	235	38	)	)	PUNCT
cana-2978	235	39	)	)	PUNCT
cana-2978	236	1	2)ωi	2)ωi	NUM
cana-2978	236	2	≥⊗	≥⊗	PROPN
cana-2978	236	3	`	`	PUNCT
cana-2978	236	4	i=1	i=1	PROPN
cana-2978	236	5	(	(	PUNCT
cana-2978	236	6	1−	1−	NUM
cana-2978	236	7	(	(	PUNCT
cana-2978	236	8	(	(	PUNCT
cana-2978	236	9	a	a	DET
cana-2978	236	10	·	·	PUNCT
cana-2978	236	11	rᵀ	rᵀ	NOUN
cana-2978	236	12	hi	hi	INTJ
cana-2978	236	13	)	)	PUNCT
cana-2978	236	14	)	)	PUNCT
cana-2978	236	15	2)ωi	2)ωi	PROPN
cana-2978	236	16	and	and	CCONJ
cana-2978	236	17	γ	γ	PROPN
cana-2978	236	18	√	√	PROPN
cana-2978	236	19	1−	1−	NUM
cana-2978	236	20	⊗	⊗	NUM
cana-2978	236	21	`	`	PUNCT
cana-2978	236	22	i=1	i=1	PROPN
cana-2978	236	23	(	(	PUNCT
cana-2978	236	24	1−	1−	NUM
cana-2978	236	25	(	(	PUNCT
cana-2978	236	26	(	(	PUNCT
cana-2978	236	27	a	a	DET
cana-2978	236	28	·	·	PUNCT
cana-2978	236	29	rᵀ	rᵀ	NOUN
cana-2978	236	30	ti	ti	NOUN
cana-2978	236	31	)	)	PUNCT
cana-2978	236	32	)	)	PUNCT
cana-2978	237	1	γ)ωi	γ)ωi	PROPN
cana-2978	237	2	≤	≤	NOUN
cana-2978	237	3	γ	γ	X
cana-2978	237	4	√	√	PROPN
cana-2978	237	5	1−	1−	NUM
cana-2978	237	6	⊗	⊗	NUM
cana-2978	237	7	`	`	PUNCT
cana-2978	237	8	i=1	i=1	PROPN
cana-2978	237	9	(	(	PUNCT
cana-2978	237	10	1−	1−	NUM
cana-2978	237	11	(	(	PUNCT
cana-2978	237	12	(	(	PUNCT
cana-2978	237	13	a	a	DET
cana-2978	237	14	·	·	PUNCT
cana-2978	237	15	rᵀ	rᵀ	NOUN
cana-2978	237	16	hi	hi	INTJ
cana-2978	237	17	)	)	PUNCT
cana-2978	237	18	)	)	PUNCT
cana-2978	238	1	γ)ωi	γ)ωi	PROPN
cana-2978	238	2	.	.	PUNCT
cana-2978	239	1	similarly	similarly	ADV
cana-2978	239	2	,	,	PUNCT
cana-2978	239	3	(	(	PUNCT
cana-2978	239	4	a	a	PRON
cana-2978	239	5	·	·	PUNCT
cana-2978	239	6	i	i	PRON
cana-2978	239	7	ᵀ	ᵀ	VERB
cana-2978	239	8	tij	tij	NOUN
cana-2978	239	9	)	)	PUNCT
cana-2978	239	10	2	2	NUM
cana-2978	239	11	≤	≤	NOUN
cana-2978	239	12	(	(	PUNCT
cana-2978	239	13	a	a	DET
cana-2978	239	14	·	·	PUNCT
cana-2978	239	15	i	i	PRON
cana-2978	239	16	ᵀ	ᵀ	PRON
cana-2978	239	17	hij	hij	NOUN
cana-2978	239	18	)	)	PUNCT
cana-2978	239	19	2	2	X
cana-2978	239	20	.	.	X
cana-2978	240	1	therefore	therefore	ADV
cana-2978	240	2	,	,	PUNCT
cana-2978	240	3	1−	1−	NUM
cana-2978	240	4	(	(	PUNCT
cana-2978	240	5	(	(	PUNCT
cana-2978	240	6	a	a	DET
cana-2978	240	7	·	·	PUNCT
cana-2978	240	8	i	i	PRON
cana-2978	240	9	ᵀ	ᵀ	NOUN
cana-2978	240	10	ti	ti	NOUN
cana-2978	240	11	)	)	PUNCT
cana-2978	240	12	)	)	PUNCT
cana-2978	240	13	2	2	NUM
cana-2978	240	14	≥	≥	NOUN
cana-2978	240	15	1−	1−	NUM
cana-2978	240	16	(	(	PUNCT
cana-2978	240	17	(	(	PUNCT
cana-2978	240	18	a	a	PRON
cana-2978	240	19	·	·	PUNCT
cana-2978	240	20	i	i	PRON
cana-2978	240	21	ᵀ	ᵀ	VERB
cana-2978	240	22	hi	hi	INTJ
cana-2978	240	23	)	)	PUNCT
cana-2978	240	24	)	)	PUNCT
cana-2978	241	1	2	2	X
cana-2978	241	2	.	.	X
cana-2978	242	1	hence	hence	ADV
cana-2978	242	2	,	,	PUNCT
cana-2978	242	3	⊗	⊗	PROPN
cana-2978	242	4	`	`	PUNCT
cana-2978	242	5	i=1	i=1	PROPN
cana-2978	242	6	(	(	PUNCT
cana-2978	242	7	1−	1−	NUM
cana-2978	242	8	(	(	PUNCT
cana-2978	242	9	(	(	PUNCT
cana-2978	242	10	a	a	PRON
cana-2978	242	11	·	·	PUNCT
cana-2978	242	12	i	i	PRON
cana-2978	242	13	ᵀ	ᵀ	X
cana-2978	242	14	ti	ti	NOUN
cana-2978	242	15	)	)	PUNCT
cana-2978	242	16	)	)	PUNCT
cana-2978	243	1	2)ωi	2)ωi	NUM
cana-2978	243	2	≥⊗	≥⊗	PROPN
cana-2978	243	3	`	`	PUNCT
cana-2978	243	4	i=1	i=1	PROPN
cana-2978	243	5	(	(	PUNCT
cana-2978	243	6	1−	1−	NUM
cana-2978	243	7	(	(	PUNCT
cana-2978	243	8	(	(	PUNCT
cana-2978	243	9	a	a	PRON
cana-2978	243	10	·	·	PUNCT
cana-2978	243	11	i	i	PRON
cana-2978	243	12	ᵀ	ᵀ	VERB
cana-2978	243	13	hi	hi	INTJ
cana-2978	243	14	)	)	PUNCT
cana-2978	243	15	)	)	PUNCT
cana-2978	244	1	2)ωi	2)ωi	NUM
cana-2978	244	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	244	3	138	138	NUM
cana-2978	244	4	communications	communication	NOUN
cana-2978	244	5	on	on	ADP
cana-2978	244	6	applied	apply	VERB
cana-2978	244	7	nonlinear	nonlinear	ADJ
cana-2978	244	8	analysis	analysis	NOUN
cana-2978	244	9	issn	issn	NOUN
cana-2978	244	10	:	:	PUNCT
cana-2978	244	11	1074	1074	NUM
cana-2978	244	12	-	-	PUNCT
cana-2978	244	13	133x	133x	NUM
cana-2978	244	14	vol	vol	NOUN
cana-2978	244	15	32	32	NUM
cana-2978	244	16	no	no	NOUN
cana-2978	244	17	.	.	PUNCT
cana-2978	245	1	5s	5s	NUM
cana-2978	245	2	(	(	PUNCT
cana-2978	245	3	2025	2025	NUM
cana-2978	245	4	)	)	PUNCT
cana-2978	245	5	and	and	CCONJ
cana-2978	245	6	γ	γ	X
cana-2978	245	7	√	√	PROPN
cana-2978	245	8	1−	1−	NUM
cana-2978	245	9	⊗	⊗	NUM
cana-2978	245	10	`	`	PUNCT
cana-2978	245	11	i=1	i=1	PROPN
cana-2978	245	12	(	(	PUNCT
cana-2978	245	13	1−	1−	NUM
cana-2978	245	14	(	(	PUNCT
cana-2978	245	15	(	(	PUNCT
cana-2978	245	16	a	a	PRON
cana-2978	245	17	·	·	PUNCT
cana-2978	245	18	i	i	PRON
cana-2978	245	19	ᵀ	ᵀ	X
cana-2978	245	20	ti	ti	NOUN
cana-2978	245	21	)	)	PUNCT
cana-2978	245	22	)	)	PUNCT
cana-2978	246	1	γ)ωi	γ)ωi	PROPN
cana-2978	246	2	≤	≤	NOUN
cana-2978	246	3	γ	γ	X
cana-2978	246	4	√	√	PROPN
cana-2978	246	5	1−	1−	NUM
cana-2978	246	6	⊗	⊗	NUM
cana-2978	246	7	`	`	PUNCT
cana-2978	246	8	i=1	i=1	PROPN
cana-2978	246	9	(	(	PUNCT
cana-2978	246	10	1−	1−	NUM
cana-2978	246	11	(	(	PUNCT
cana-2978	246	12	(	(	PUNCT
cana-2978	246	13	a	a	PRON
cana-2978	246	14	·	·	PUNCT
cana-2978	246	15	i	i	PRON
cana-2978	246	16	ᵀ	ᵀ	VERB
cana-2978	246	17	hi	hi	INTJ
cana-2978	246	18	)	)	PUNCT
cana-2978	246	19	)	)	PUNCT
cana-2978	247	1	γ)ωi	γ)ωi	PROPN
cana-2978	247	2	.	.	PUNCT
cana-2978	248	1	for	for	ADP
cana-2978	248	2	any	any	DET
cana-2978	248	3	i	i	PROPN
cana-2978	248	4	,	,	PUNCT
cana-2978	248	5	(	(	PUNCT
cana-2978	248	6	(	(	PUNCT
cana-2978	248	7	a	a	DET
cana-2978	248	8	·	·	SYM
cana-2978	248	9	r	r	NOUN
cana-2978	248	10	`	`	PUNCT
cana-2978	248	11	tij	tij	PROPN
cana-2978	248	12	)	)	PUNCT
cana-2978	248	13	)	)	PUNCT
cana-2978	248	14	2	2	NUM
cana-2978	248	15	≥	≥	NOUN
cana-2978	248	16	(	(	PUNCT
cana-2978	248	17	(	(	PUNCT
cana-2978	248	18	a	a	DET
cana-2978	248	19	·	·	SYM
cana-2978	248	20	r	r	NOUN
cana-2978	248	21	`	`	PUNCT
cana-2978	248	22	hij	hij	NOUN
cana-2978	248	23	)	)	PUNCT
cana-2978	248	24	)	)	PUNCT
cana-2978	248	25	2	2	NUM
cana-2978	248	26	and	and	CCONJ
cana-2978	248	27	(	(	PUNCT
cana-2978	248	28	(	(	PUNCT
cana-2978	248	29	a	a	DET
cana-2978	248	30	·	·	SYM
cana-2978	248	31	r	r	NOUN
cana-2978	248	32	`	`	PUNCT
cana-2978	248	33	tij	tij	PROPN
cana-2978	248	34	)	)	PUNCT
cana-2978	248	35	)	)	PUNCT
cana-2978	248	36	τ	τ	PROPN
cana-2978	248	37	≥	≥	NUM
cana-2978	248	38	(	(	PUNCT
cana-2978	248	39	(	(	PUNCT
cana-2978	248	40	a	a	DET
cana-2978	248	41	·	·	SYM
cana-2978	248	42	r	r	NOUN
cana-2978	248	43	`	`	PUNCT
cana-2978	248	44	hij	hij	NOUN
cana-2978	248	45	)	)	PUNCT
cana-2978	248	46	)	)	PUNCT
cana-2978	249	1	τ	τ	PROPN
cana-2978	249	2	.	.	PUNCT
cana-2978	250	1	therefore	therefore	ADV
cana-2978	250	2	,	,	PUNCT
cana-2978	250	3	1−	1−	NUM
cana-2978	250	4	(	(	PUNCT
cana-2978	250	5	⊗	⊗	PROPN
cana-2978	250	6	`	`	PUNCT
cana-2978	250	7	i=1(a	i=1(a	PROPN
cana-2978	250	8	·	·	PUNCT
cana-2978	250	9	r	r	NOUN
cana-2978	250	10	`	`	PUNCT
cana-2978	250	11	tij	tij	PROPN
cana-2978	250	12	)	)	PUNCT
cana-2978	250	13	)	)	PUNCT
cana-2978	251	1	τ	τ	PROPN
cana-2978	251	2	≤	≤	PROPN
cana-2978	251	3	1−	1−	NUM
cana-2978	251	4	(	(	PUNCT
cana-2978	251	5	⊗	⊗	PROPN
cana-2978	251	6	`	`	PUNCT
cana-2978	251	7	i=1(a	i=1(a	PROPN
cana-2978	251	8	·	·	SYM
cana-2978	251	9	r	r	NOUN
cana-2978	251	10	`	`	PUNCT
cana-2978	251	11	hij	hij	NOUN
cana-2978	251	12	)	)	PUNCT
cana-2978	251	13	)	)	PUNCT
cana-2978	252	1	τ	τ	PROPN
cana-2978	252	2	.	.	PUNCT
cana-2978	253	1	similarly	similarly	ADV
cana-2978	253	2	,	,	PUNCT
cana-2978	253	3	for	for	ADP
cana-2978	253	4	any	any	DET
cana-2978	253	5	i	i	PRON
cana-2978	253	6	,	,	PUNCT
cana-2978	253	7	(	(	PUNCT
cana-2978	253	8	(	(	PUNCT
cana-2978	253	9	a	a	DET
cana-2978	253	10	·	·	PUNCT
cana-2978	253	11	i	i	PRON
cana-2978	253	12	`	`	PUNCT
cana-2978	253	13	tij	tij	PROPN
cana-2978	253	14	)	)	PUNCT
cana-2978	253	15	)	)	PUNCT
cana-2978	253	16	2	2	NUM
cana-2978	253	17	≥	≥	NOUN
cana-2978	253	18	(	(	PUNCT
cana-2978	253	19	(	(	PUNCT
cana-2978	253	20	a	a	DET
cana-2978	253	21	·	·	PUNCT
cana-2978	253	22	i	i	PRON
cana-2978	253	23	`	`	PUNCT
cana-2978	253	24	hij	hij	PROPN
cana-2978	253	25	)	)	PUNCT
cana-2978	253	26	)	)	PUNCT
cana-2978	253	27	2	2	NUM
cana-2978	253	28	and	and	CCONJ
cana-2978	253	29	(	(	PUNCT
cana-2978	253	30	(	(	PUNCT
cana-2978	253	31	a	a	DET
cana-2978	253	32	·	·	PUNCT
cana-2978	253	33	i	i	PRON
cana-2978	253	34	`	`	PUNCT
cana-2978	253	35	tij	tij	PROPN
cana-2978	253	36	)	)	PUNCT
cana-2978	253	37	)	)	PUNCT
cana-2978	253	38	τ	τ	PROPN
cana-2978	253	39	≥	≥	NUM
cana-2978	253	40	(	(	PUNCT
cana-2978	253	41	(	(	PUNCT
cana-2978	253	42	a	a	DET
cana-2978	253	43	·	·	PUNCT
cana-2978	253	44	i	i	PRON
cana-2978	253	45	`	`	PUNCT
cana-2978	253	46	hij	hij	PROPN
cana-2978	253	47	)	)	PUNCT
cana-2978	253	48	)	)	PUNCT
cana-2978	254	1	τ	τ	PROPN
cana-2978	254	2	.	.	PUNCT
cana-2978	255	1	therefore	therefore	ADV
cana-2978	255	2	,	,	PUNCT
cana-2978	255	3	−	−	PROPN
cana-2978	255	4	(	(	PUNCT
cana-2978	255	5	⊗	⊗	PROPN
cana-2978	255	6	`	`	PUNCT
cana-2978	255	7	i=1(a	i=1(a	PROPN
cana-2978	255	8	·	·	PUNCT
cana-2978	255	9	i	i	PRON
cana-2978	255	10	`	`	PUNCT
cana-2978	255	11	tij	tij	PROPN
cana-2978	255	12	)	)	PUNCT
cana-2978	255	13	)	)	PUNCT
cana-2978	255	14	τ	τ	PROPN
cana-2978	255	15	≤	≤	ADV
cana-2978	255	16	−	−	PROPN
cana-2978	255	17	(	(	PUNCT
cana-2978	255	18	⊗	⊗	PROPN
cana-2978	255	19	`	`	PUNCT
cana-2978	255	20	i=1(a	i=1(a	PROPN
cana-2978	255	21	·	·	PUNCT
cana-2978	255	22	i	i	PRON
cana-2978	255	23	`	`	PUNCT
cana-2978	255	24	hij	hij	PROPN
cana-2978	255	25	)	)	PUNCT
cana-2978	255	26	)	)	PUNCT
cana-2978	256	1	τ	τ	PROPN
cana-2978	256	2	.	.	PUNCT
cana-2978	257	1	hence	hence	ADV
cana-2978	257	2	,	,	PUNCT
cana-2978	257	3	1	1	NUM
cana-2978	257	4	2	2	NUM
cana-2978	257	5	×	×	NOUN
cana-2978	257	6			NOUN
cana-2978	257	7			NOUN
cana-2978	257	8			PROPN
cana-2978	257	9	γ	γ	NOUN
cana-2978	257	10	√√√√	√√√√	DET
cana-2978	257	11	1−	1−	NUM
cana-2978	257	12	⊗̀	⊗̀	NOUN
cana-2978	257	13	i=1	i=1	X
cana-2978	258	1	(	(	PUNCT
cana-2978	258	2	1−	1−	NUM
cana-2978	258	3	(	(	PUNCT
cana-2978	258	4	(	(	PUNCT
cana-2978	258	5	a	a	DET
cana-2978	258	6	·	·	PUNCT
cana-2978	258	7	rᵀ	rᵀ	NOUN
cana-2978	258	8	ti	ti	NOUN
cana-2978	258	9	)	)	PUNCT
cana-2978	258	10	)	)	PUNCT
cana-2978	258	11	γ	γ	PROPN
cana-2978	258	12	)	)	PUNCT
cana-2978	258	13	ωi2	ωi2	VERB
cana-2978	258	14	+1−	+1−	PROPN
cana-2978	258	15	(	(	PUNCT
cana-2978	258	16	⊗	⊗	PROPN
cana-2978	258	17	`	`	PUNCT
cana-2978	258	18	i=1((a	i=1((a	NOUN
cana-2978	258	19	·	·	PUNCT
cana-2978	258	20	r	r	NOUN
cana-2978	258	21	`	`	PUNCT
cana-2978	258	22	ti	ti	NOUN
cana-2978	258	23	)	)	PUNCT
cana-2978	258	24	)	)	PUNCT
cana-2978	259	1	τ	τ	PROPN
cana-2978	259	2	)	)	PUNCT
cana-2978	259	3	2	2	NUM
cana-2978	259	4	+	+	VERB
cana-2978	259	5			PROPN
cana-2978	259	6			PROPN
cana-2978	259	7	γ	γ	NOUN
cana-2978	259	8	√√√√	√√√√	DET
cana-2978	259	9	1−	1−	NUM
cana-2978	259	10	⊗̀	⊗̀	NOUN
cana-2978	259	11	i=1	i=1	X
cana-2978	260	1	(	(	PUNCT
cana-2978	260	2	1−	1−	NUM
cana-2978	260	3	(	(	PUNCT
cana-2978	260	4	(	(	PUNCT
cana-2978	260	5	a	a	PRON
cana-2978	260	6	·	·	PUNCT
cana-2978	260	7	i	i	PRON
cana-2978	260	8	ᵀ	ᵀ	NOUN
cana-2978	260	9	ti	ti	NOUN
cana-2978	260	10	)	)	PUNCT
cana-2978	260	11	)	)	PUNCT
cana-2978	260	12	γ	γ	PROPN
cana-2978	260	13	)	)	PUNCT
cana-2978	260	14	ωi2	ωi2	VERB
cana-2978	260	15	−	−	PROPN
cana-2978	261	1	(	(	PUNCT
cana-2978	261	2	⊗	⊗	PROPN
cana-2978	261	3	`	`	PUNCT
cana-2978	261	4	i=1((a	i=1((a	PROPN
cana-2978	261	5	·	·	PUNCT
cana-2978	261	6	i	i	PRON
cana-2978	261	7	`	`	PUNCT
cana-2978	261	8	ti	ti	NOUN
cana-2978	261	9	)	)	PUNCT
cana-2978	261	10	)	)	PUNCT
cana-2978	262	1	τ	τ	X
cana-2978	262	2	)	)	PUNCT
cana-2978	262	3	2	2	NUM
cana-2978	262	4			VERB
cana-2978	262	5			VERB
cana-2978	262	6	≤	≤	NUM
cana-2978	262	7	1	1	NUM
cana-2978	262	8	2	2	NUM
cana-2978	262	9	×	×	NOUN
cana-2978	262	10			NOUN
cana-2978	262	11			NOUN
cana-2978	262	12			PROPN
cana-2978	262	13	γ	γ	NOUN
cana-2978	262	14	√√√√	√√√√	DET
cana-2978	262	15	1−	1−	NUM
cana-2978	262	16	⊗̀	⊗̀	NOUN
cana-2978	262	17	i=1	i=1	X
cana-2978	263	1	(	(	PUNCT
cana-2978	263	2	1−	1−	NUM
cana-2978	263	3	(	(	PUNCT
cana-2978	263	4	(	(	PUNCT
cana-2978	263	5	a	a	DET
cana-2978	263	6	·	·	PUNCT
cana-2978	263	7	rᵀ	rᵀ	NOUN
cana-2978	263	8	hi	hi	NOUN
cana-2978	263	9	)	)	PUNCT
cana-2978	263	10	)	)	PUNCT
cana-2978	263	11	γ	γ	PROPN
cana-2978	263	12	)	)	PUNCT
cana-2978	263	13	ωi2	ωi2	VERB
cana-2978	263	14	+1−	+1−	PROPN
cana-2978	263	15	(	(	PUNCT
cana-2978	263	16	⊗	⊗	PROPN
cana-2978	263	17	`	`	PUNCT
cana-2978	263	18	i=1((a	i=1((a	NOUN
cana-2978	263	19	·	·	PUNCT
cana-2978	263	20	r	r	NOUN
cana-2978	263	21	`	`	PUNCT
cana-2978	263	22	hi	hi	INTJ
cana-2978	263	23	)	)	PUNCT
cana-2978	263	24	)	)	PUNCT
cana-2978	264	1	τ	τ	X
cana-2978	264	2	)	)	PUNCT
cana-2978	264	3	2	2	NUM
cana-2978	264	4	+	+	VERB
cana-2978	264	5			PROPN
cana-2978	264	6			PROPN
cana-2978	264	7	γ	γ	NOUN
cana-2978	264	8	√√√√	√√√√	DET
cana-2978	264	9	1−	1−	NUM
cana-2978	264	10	⊗̀	⊗̀	NOUN
cana-2978	264	11	i=1	i=1	X
cana-2978	265	1	(	(	PUNCT
cana-2978	265	2	1−	1−	NUM
cana-2978	265	3	(	(	PUNCT
cana-2978	265	4	(	(	PUNCT
cana-2978	265	5	a	a	PRON
cana-2978	265	6	·	·	PUNCT
cana-2978	265	7	i	i	PRON
cana-2978	265	8	ᵀ	ᵀ	VERB
cana-2978	265	9	hi	hi	INTJ
cana-2978	265	10	)	)	PUNCT
cana-2978	265	11	)	)	PUNCT
cana-2978	265	12	γ	γ	PROPN
cana-2978	265	13	)	)	PUNCT
cana-2978	265	14	ωi2	ωi2	VERB
cana-2978	265	15	−	−	PROPN
cana-2978	266	1	(	(	PUNCT
cana-2978	266	2	⊗	⊗	PROPN
cana-2978	266	3	`	`	PUNCT
cana-2978	266	4	i=1((a	i=1((a	PROPN
cana-2978	266	5	·	·	PUNCT
cana-2978	266	6	i	i	PRON
cana-2978	266	7	`	`	PUNCT
cana-2978	266	8	hi	hi	INTJ
cana-2978	266	9	)	)	PUNCT
cana-2978	266	10	)	)	PUNCT
cana-2978	266	11	τ	τ	X
cana-2978	266	12	)	)	PUNCT
cana-2978	266	13	2	2	NUM
cana-2978	266	14			NOUN
cana-2978	266	15			VERB
cana-2978	266	16	.	.	PUNCT
cana-2978	267	1	hence	hence	ADV
cana-2978	267	2	,	,	PUNCT
cana-2978	267	3	ct	ct	PROPN
cana-2978	267	4	(	(	PUNCT
cana-2978	267	5	γ	γ	X
cana-2978	267	6	,	,	PUNCT
cana-2978	267	7	τ)nwa	τ)nwa	PROPN
cana-2978	267	8	(	(	PUNCT
cana-2978	267	9	θ1,θ2	θ1,θ2	PROPN
cana-2978	267	10	,	,	PUNCT
cana-2978	267	11	...	...	PUNCT
cana-2978	267	12	,	,	PUNCT
cana-2978	267	13	θ	θ	NOUN
cana-2978	267	14	`	`	PUNCT
cana-2978	267	15	)	)	PUNCT
cana-2978	267	16	≤	≤	NUM
cana-2978	267	17	ct	ct	PROPN
cana-2978	267	18	(	(	PUNCT
cana-2978	267	19	γ	γ	X
cana-2978	267	20	,	,	PUNCT
cana-2978	267	21	τ)nwa	τ)nwa	PROPN
cana-2978	267	22	(	(	PUNCT
cana-2978	267	23	w1,w2	w1,w2	PROPN
cana-2978	267	24	,	,	PUNCT
cana-2978	267	25	...	...	PUNCT
cana-2978	267	26	,	,	PUNCT
cana-2978	267	27	w	w	NOUN
cana-2978	267	28	`	`	PUNCT
cana-2978	267	29	)	)	PUNCT
cana-2978	267	30	.	.	PUNCT
cana-2978	268	1	4.2	4.2	NUM
cana-2978	268	2	ct	ct	NUM
cana-2978	268	3	(	(	PUNCT
cana-2978	268	4	γ	γ	PROPN
cana-2978	268	5	,	,	PUNCT
cana-2978	268	6	τ)-rung	τ)-rung	PUNCT
cana-2978	268	7	fnwg	fnwg	ADJ
cana-2978	268	8	definition	definition	NOUN
cana-2978	268	9	4.6	4.6	NUM
cana-2978	268	10	.	.	PUNCT
cana-2978	269	1	let	let	VERB
cana-2978	269	2	θi	θi	X
cana-2978	269	3	=	=	PROPN
cana-2978	269	4	〈	〈	PROPN
cana-2978	269	5	(	(	PUNCT
cana-2978	269	6	(	(	PUNCT
cana-2978	269	7	(	(	PUNCT
cana-2978	269	8	a	a	DET
cana-2978	269	9	·	·	PUNCT
cana-2978	269	10	rᵀ	rᵀ	NOUN
cana-2978	269	11	i	i	NOUN
cana-2978	269	12	)	)	PUNCT
cana-2978	269	13	·	·	PUNCT
cana-2978	270	1	e(a·i	e(a·i	NOUN
cana-2978	270	2	ᵀ	ᵀ	VERB
cana-2978	270	3	i	i	PROPN
cana-2978	270	4	)	)	PUNCT
cana-2978	270	5	,	,	PUNCT
cana-2978	270	6	(	(	PUNCT
cana-2978	270	7	a	a	PRON
cana-2978	270	8	·	·	PUNCT
cana-2978	270	9	r	r	NOUN
cana-2978	270	10	`	`	PUNCT
cana-2978	270	11	i	i	NOUN
cana-2978	270	12	)	)	PUNCT
cana-2978	270	13	·	·	PUNCT
cana-2978	271	1	e(a·i	e(a·i	NOUN
cana-2978	271	2	`	`	PUNCT
cana-2978	271	3	i	i	PROPN
cana-2978	271	4	)	)	PUNCT
cana-2978	271	5	)	)	PUNCT
cana-2978	271	6	)	)	PUNCT
cana-2978	271	7	〉	〉	NOUN
cana-2978	271	8	be	be	VERB
cana-2978	271	9	the	the	DET
cana-2978	271	10	ct	ct	PROPN
cana-2978	271	11	(	(	PUNCT
cana-2978	271	12	γ	γ	PROPN
cana-2978	271	13	,	,	PUNCT
cana-2978	271	14	τ)-rung	τ)-rung	PROPN
cana-2978	271	15	fns	fns	PROPN
cana-2978	271	16	.	.	PUNCT
cana-2978	272	1	then	then	ADV
cana-2978	272	2	(	(	PUNCT
cana-2978	272	3	γ	γ	X
cana-2978	272	4	,	,	PUNCT
cana-2978	272	5	τ)-rung	τ)-rung	PUNCT
cana-2978	272	6	fnwg	fnwg	ADJ
cana-2978	272	7	(	(	PUNCT
cana-2978	272	8	θ1,θ2	θ1,θ2	PROPN
cana-2978	272	9	,	,	PUNCT
cana-2978	272	10	...	...	PUNCT
cana-2978	272	11	,	,	PUNCT
cana-2978	272	12	θ	θ	NOUN
cana-2978	272	13	`	`	PUNCT
cana-2978	272	14	)	)	PUNCT
cana-2978	272	15	=	=	SYM
cana-2978	273	1	⊗	⊗	NUM
cana-2978	273	2	`	`	PUNCT
cana-2978	273	3	i=1	i=1	PRON
cana-2978	273	4	θωi	θωi	VERB
cana-2978	273	5	i	i	PRON
cana-2978	273	6	.	.	PUNCT
cana-2978	274	1	corollary	corollary	ADJ
cana-2978	274	2	4.7	4.7	NUM
cana-2978	274	3	.	.	PUNCT
cana-2978	275	1	let	let	VERB
cana-2978	275	2	θi	θi	X
cana-2978	275	3	=	=	PROPN
cana-2978	275	4	〈	〈	PROPN
cana-2978	275	5	(	(	PUNCT
cana-2978	275	6	(	(	PUNCT
cana-2978	275	7	(	(	PUNCT
cana-2978	275	8	a	a	PRON
cana-2978	275	9	·	·	PUNCT
cana-2978	275	10	rᵀ	rᵀ	NOUN
cana-2978	275	11	i	i	NOUN
cana-2978	275	12	)	)	PUNCT
cana-2978	275	13	·	·	PUNCT
cana-2978	276	1	e(a·i	e(a·i	NOUN
cana-2978	276	2	ᵀ	ᵀ	VERB
cana-2978	276	3	i	i	PROPN
cana-2978	276	4	)	)	PUNCT
cana-2978	276	5	,	,	PUNCT
cana-2978	276	6	(	(	PUNCT
cana-2978	276	7	a	a	DET
cana-2978	276	8	·	·	SYM
cana-2978	276	9	r	r	NOUN
cana-2978	276	10	`	`	PUNCT
cana-2978	276	11	i	i	PROPN
cana-2978	276	12	)	)	PUNCT
cana-2978	276	13	·	·	PUNCT
cana-2978	277	1	e(a·i	e(a·i	NOUN
cana-2978	277	2	`	`	PUNCT
cana-2978	277	3	i	i	PROPN
cana-2978	277	4	)	)	PUNCT
cana-2978	277	5	)	)	PUNCT
cana-2978	277	6	)	)	PUNCT
cana-2978	277	7	〉	〉	NOUN
cana-2978	277	8	be	be	VERB
cana-2978	277	9	the	the	DET
cana-2978	277	10	ct	ct	PROPN
cana-2978	277	11	(	(	PUNCT
cana-2978	277	12	γ	γ	PROPN
cana-2978	277	13	,	,	PUNCT
cana-2978	277	14	τ)-rung	τ)-rung	PROPN
cana-2978	277	15	fns	fns	PROPN
cana-2978	277	16	.	.	PUNCT
cana-2978	278	1	then	then	ADV
cana-2978	278	2	ct	ct	PRON
cana-2978	278	3	(	(	PUNCT
cana-2978	278	4	γ	γ	PROPN
cana-2978	278	5	,	,	PUNCT
cana-2978	278	6	τ)-rung	τ)-rung	PUNCT
cana-2978	278	7	fnwg	fnwg	ADJ
cana-2978	278	8	(	(	PUNCT
cana-2978	278	9	θ1,θ2	θ1,θ2	PROPN
cana-2978	278	10	,	,	PUNCT
cana-2978	278	11	...	...	PUNCT
cana-2978	278	12	,	,	PUNCT
cana-2978	278	13	θ	θ	NOUN
cana-2978	278	14	`	`	PUNCT
cana-2978	278	15	)	)	PUNCT
cana-2978	278	16	=	=	SYM
cana-2978	278	17			NUM
cana-2978	278	18	⊗	⊗	PROPN
cana-2978	278	19	`	`	PUNCT
cana-2978	278	20	i=1(((a	i=1(((a	PROPN
cana-2978	278	21	·	·	PUNCT
cana-2978	278	22	rᵀ	rᵀ	NOUN
cana-2978	278	23	i	i	NOUN
cana-2978	278	24	)	)	PUNCT
cana-2978	278	25	)	)	PUNCT
cana-2978	279	1	γ)ωi	γ)ωi	PROPN
cana-2978	279	2	·	·	PUNCT
cana-2978	279	3	e	e	X
cana-2978	279	4	⊗	⊗	PROPN
cana-2978	279	5	`	`	PROPN
cana-2978	279	6	i=1(((a·i	i=1(((a·i	NOUN
cana-2978	279	7	ᵀ	ᵀ	X
cana-2978	279	8	i	i	NOUN
cana-2978	279	9	)	)	PUNCT
cana-2978	279	10	)	)	PUNCT
cana-2978	280	1	γ)ωi	γ)ωi	PROPN
cana-2978	280	2	τ	τ	PROPN
cana-2978	280	3	√	√	NOUN
cana-2978	280	4	1−	1−	NUM
cana-2978	280	5	⊗	⊗	NUM
cana-2978	280	6	`	`	PUNCT
cana-2978	280	7	i=1	i=1	PROPN
cana-2978	280	8	(	(	PUNCT
cana-2978	280	9	1−	1−	NUM
cana-2978	280	10	(	(	PUNCT
cana-2978	280	11	(	(	PUNCT
cana-2978	280	12	a	a	DET
cana-2978	280	13	·	·	SYM
cana-2978	280	14	r	r	NOUN
cana-2978	280	15	`	`	PUNCT
cana-2978	280	16	i	i	PROPN
cana-2978	280	17	)	)	PUNCT
cana-2978	280	18	)	)	PUNCT
cana-2978	281	1	τ	τ	X
cana-2978	281	2	)	)	PUNCT
cana-2978	281	3	ωi	ωi	X
cana-2978	281	4	·	·	PUNCT
cana-2978	281	5	e	e	X
cana-2978	281	6	τ	τ	X
cana-2978	281	7	√	√	PROPN
cana-2978	281	8	1−	1−	NUM
cana-2978	281	9	⊗	⊗	NUM
cana-2978	281	10	`	`	PUNCT
cana-2978	281	11	i=1	i=1	PROPN
cana-2978	281	12	(	(	PUNCT
cana-2978	281	13	1−((a·i	1−((a·i	NUM
cana-2978	281	14	`	`	PUNCT
cana-2978	281	15	i	i	PROPN
cana-2978	281	16	)	)	PUNCT
cana-2978	281	17	)	)	PUNCT
cana-2978	281	18	τ	τ	X
cana-2978	281	19	)	)	PUNCT
cana-2978	281	20	ωi	ωi	NOUN
cana-2978	281	21	.	.	PUNCT
cana-2978	282	1	corollary	corollary	ADJ
cana-2978	282	2	4.8	4.8	NUM
cana-2978	282	3	.	.	PUNCT
cana-2978	283	1	(	(	PUNCT
cana-2978	283	2	i	i	NOUN
cana-2978	283	3	)	)	PUNCT
cana-2978	283	4	let	let	VERB
cana-2978	283	5	θi	θi	X
cana-2978	283	6	=	=	PROPN
cana-2978	283	7	〈	〈	PROPN
cana-2978	283	8	(	(	PUNCT
cana-2978	283	9	(	(	PUNCT
cana-2978	283	10	(	(	PUNCT
cana-2978	283	11	a	a	DET
cana-2978	283	12	·	·	PUNCT
cana-2978	283	13	rᵀ	rᵀ	NOUN
cana-2978	283	14	i	i	NOUN
cana-2978	283	15	)	)	PUNCT
cana-2978	283	16	·	·	PUNCT
cana-2978	284	1	e(a·i	e(a·i	NOUN
cana-2978	284	2	ᵀ	ᵀ	VERB
cana-2978	284	3	i	i	PROPN
cana-2978	284	4	)	)	PUNCT
cana-2978	284	5	,	,	PUNCT
cana-2978	284	6	(	(	PUNCT
cana-2978	284	7	a	a	DET
cana-2978	284	8	·	·	SYM
cana-2978	284	9	r	r	NOUN
cana-2978	284	10	`	`	PUNCT
cana-2978	284	11	i	i	PROPN
cana-2978	284	12	)	)	PUNCT
cana-2978	284	13	·	·	PUNCT
cana-2978	285	1	e(a·i	e(a·i	NOUN
cana-2978	285	2	`	`	PUNCT
cana-2978	285	3	i	i	PROPN
cana-2978	285	4	)	)	PUNCT
cana-2978	285	5	)	)	PUNCT
cana-2978	285	6	)	)	PUNCT
cana-2978	285	7	〉	〉	NOUN
cana-2978	285	8	be	be	VERB
cana-2978	285	9	the	the	DET
cana-2978	285	10	ct	ct	PROPN
cana-2978	285	11	(	(	PUNCT
cana-2978	285	12	γ	γ	PROPN
cana-2978	285	13	,	,	PUNCT
cana-2978	285	14	τ)-rung	τ)-rung	PROPN
cana-2978	285	15	fns	fns	PROPN
cana-2978	285	16	and	and	CCONJ
cana-2978	285	17	all	all	PRON
cana-2978	285	18	are	be	AUX
cana-2978	285	19	equal	equal	ADJ
cana-2978	285	20	.	.	PUNCT
cana-2978	286	1	then	then	ADV
cana-2978	286	2	(	(	PUNCT
cana-2978	286	3	γ	γ	X
cana-2978	286	4	,	,	PUNCT
cana-2978	286	5	τ)-rung	τ)-rung	PUNCT
cana-2978	286	6	fnwg(θ1,θ2	fnwg(θ1,θ2	PROPN
cana-2978	286	7	,	,	PUNCT
cana-2978	286	8	...	...	PUNCT
cana-2978	286	9	,	,	PUNCT
cana-2978	286	10	θ	θ	NOUN
cana-2978	286	11	`	`	PUNCT
cana-2978	286	12	)	)	PUNCT
cana-2978	286	13	=	=	SYM
cana-2978	286	14	θ	θ	X
cana-2978	286	15	.	.	PUNCT
cana-2978	286	16	(	(	PUNCT
cana-2978	286	17	ii	ii	NOUN
cana-2978	286	18	)	)	PUNCT
cana-2978	286	19	it	it	PRON
cana-2978	286	20	has	have	VERB
cana-2978	286	21	other	other	ADJ
cana-2978	286	22	properties	property	NOUN
cana-2978	286	23	,	,	PUNCT
cana-2978	286	24	including	include	VERB
cana-2978	286	25	boundedness	boundedness	NOUN
cana-2978	286	26	and	and	CCONJ
cana-2978	286	27	monotonicity	monotonicity	NOUN
cana-2978	286	28	,	,	PUNCT
cana-2978	286	29	as	as	ADV
cana-2978	286	30	well	well	ADV
cana-2978	286	31	as	as	ADP
cana-2978	286	32	having	have	VERB
cana-2978	286	33	(	(	PUNCT
cana-2978	286	34	γ	γ	X
cana-2978	286	35	,	,	PUNCT
cana-2978	286	36	τ)-rung	τ)-rung	PUNCT
cana-2978	286	37	fnwg	fnwg	PROPN
cana-2978	286	38	.	.	PUNCT
cana-2978	287	1	4.3	4.3	NUM
cana-2978	287	2	generalized	generalize	VERB
cana-2978	287	3	ct	ct	PROPN
cana-2978	287	4	(	(	PUNCT
cana-2978	287	5	γ	γ	PROPN
cana-2978	287	6	,	,	PUNCT
cana-2978	287	7	τ)-rung	τ)-rung	NOUN
cana-2978	287	8	fnwa	fnwa	PROPN
cana-2978	287	9	(	(	PUNCT
cana-2978	287	10	gct(γ	gct(γ	PROPN
cana-2978	287	11	,	,	PUNCT
cana-2978	287	12	τ)-rung	τ)-rung	NOUN
cana-2978	287	13	fnwa	fnwa	NOUN
cana-2978	287	14	)	)	PUNCT
cana-2978	287	15	definition	definition	NOUN
cana-2978	287	16	4.9	4.9	NUM
cana-2978	287	17	.	.	PUNCT
cana-2978	288	1	let	let	VERB
cana-2978	288	2	θi	θi	X
cana-2978	288	3	=	=	PROPN
cana-2978	288	4	〈	〈	PROPN
cana-2978	288	5	(	(	PUNCT
cana-2978	288	6	(	(	PUNCT
cana-2978	288	7	(	(	PUNCT
cana-2978	288	8	a	a	DET
cana-2978	288	9	·	·	PUNCT
cana-2978	288	10	rᵀ	rᵀ	NOUN
cana-2978	288	11	i	i	NOUN
cana-2978	288	12	)	)	PUNCT
cana-2978	288	13	,	,	PUNCT
cana-2978	288	14	(	(	PUNCT
cana-2978	288	15	a	a	DET
cana-2978	288	16	·	·	SYM
cana-2978	288	17	r	r	NOUN
cana-2978	288	18	`	`	PUNCT
cana-2978	288	19	i	i	NOUN
cana-2978	288	20	)	)	PUNCT
cana-2978	288	21	)	)	PUNCT
cana-2978	288	22	)	)	PUNCT
cana-2978	288	23	〉	〉	NOUN
cana-2978	288	24	be	be	VERB
cana-2978	288	25	the	the	DET
cana-2978	288	26	ct	ct	PROPN
cana-2978	288	27	(	(	PUNCT
cana-2978	288	28	γ	γ	PROPN
cana-2978	288	29	,	,	PUNCT
cana-2978	288	30	τ)-rung	τ)-rung	PUNCT
cana-2978	289	1	fn	fn	PROPN
cana-2978	289	2	.	.	PUNCT
cana-2978	290	1	then	then	ADV
cana-2978	290	2	gct	gct	PROPN
cana-2978	290	3	(	(	PUNCT
cana-2978	290	4	γ	γ	PROPN
cana-2978	290	5	,	,	PUNCT
cana-2978	290	6	τ)-rung	τ)-rung	NOUN
cana-2978	290	7	fnwa	fnwa	PROPN
cana-2978	290	8	(	(	PUNCT
cana-2978	290	9	θ1,θ2	θ1,θ2	PROPN
cana-2978	290	10	,	,	PUNCT
cana-2978	290	11	...	...	PUNCT
cana-2978	290	12	,	,	PUNCT
cana-2978	290	13	θ	θ	NOUN
cana-2978	290	14	`	`	PUNCT
cana-2978	290	15	)	)	PUNCT
cana-2978	290	16	=	=	SYM
cana-2978	290	17	(	(	PUNCT
cana-2978	290	18	⊕	⊕	NOUN
cana-2978	290	19	`	`	PUNCT
cana-2978	290	20	i=1	i=1	PROPN
cana-2978	290	21	ωiθ	ωiθ	PROPN
cana-2978	290	22	∂	∂	NUM
cana-2978	291	1	i	i	NOUN
cana-2978	291	2	)	)	PUNCT
cana-2978	291	3	1/∂	1/∂	PROPN
cana-2978	291	4	.	.	PUNCT
cana-2978	292	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	292	2	139	139	NUM
cana-2978	292	3	communications	communication	NOUN
cana-2978	292	4	on	on	ADP
cana-2978	292	5	applied	apply	VERB
cana-2978	292	6	nonlinear	nonlinear	ADJ
cana-2978	292	7	analysis	analysis	NOUN
cana-2978	292	8	issn	issn	NOUN
cana-2978	292	9	:	:	PUNCT
cana-2978	292	10	1074	1074	NUM
cana-2978	292	11	-	-	PUNCT
cana-2978	292	12	133x	133x	NUM
cana-2978	292	13	vol	vol	NOUN
cana-2978	292	14	32	32	NUM
cana-2978	292	15	no	no	NOUN
cana-2978	292	16	.	.	PUNCT
cana-2978	293	1	5s	5s	NUM
cana-2978	293	2	(	(	PUNCT
cana-2978	293	3	2025	2025	NUM
cana-2978	293	4	)	)	PUNCT
cana-2978	293	5	theorem	theorem	VERB
cana-2978	293	6	4.10	4.10	NUM
cana-2978	293	7	.	.	PUNCT
cana-2978	294	1	let	let	VERB
cana-2978	294	2	θi	θi	X
cana-2978	294	3	=	=	PROPN
cana-2978	294	4	〈	〈	PROPN
cana-2978	294	5	(	(	PUNCT
cana-2978	294	6	(	(	PUNCT
cana-2978	294	7	(	(	PUNCT
cana-2978	294	8	a	a	DET
cana-2978	294	9	·	·	PUNCT
cana-2978	294	10	rᵀ	rᵀ	NOUN
cana-2978	294	11	i	i	NOUN
cana-2978	294	12	)	)	PUNCT
cana-2978	294	13	,	,	PUNCT
cana-2978	294	14	(	(	PUNCT
cana-2978	294	15	a	a	DET
cana-2978	294	16	·	·	SYM
cana-2978	294	17	r	r	NOUN
cana-2978	294	18	`	`	PUNCT
cana-2978	294	19	i	i	NOUN
cana-2978	294	20	)	)	PUNCT
cana-2978	294	21	)	)	PUNCT
cana-2978	294	22	)	)	PUNCT
cana-2978	294	23	〉	〉	NOUN
cana-2978	294	24	be	be	VERB
cana-2978	294	25	the	the	DET
cana-2978	294	26	ct	ct	PROPN
cana-2978	294	27	(	(	PUNCT
cana-2978	294	28	γ	γ	PROPN
cana-2978	294	29	,	,	PUNCT
cana-2978	294	30	τ)-rung	τ)-rung	PROPN
cana-2978	294	31	fns	fns	PROPN
cana-2978	294	32	.	.	PUNCT
cana-2978	295	1	then	then	ADV
cana-2978	295	2	gct	gct	PROPN
cana-2978	295	3	(	(	PUNCT
cana-2978	295	4	γ	γ	PROPN
cana-2978	295	5	,	,	PUNCT
cana-2978	295	6	τ)-rung	τ)-rung	NOUN
cana-2978	295	7	fnwa	fnwa	PROPN
cana-2978	295	8	(	(	PUNCT
cana-2978	295	9	θ1,θ2	θ1,θ2	PROPN
cana-2978	295	10	,	,	PUNCT
cana-2978	295	11	...	...	PUNCT
cana-2978	295	12	,	,	PUNCT
cana-2978	295	13	θ	θ	NOUN
cana-2978	295	14	`	`	PUNCT
cana-2978	295	15	)	)	PUNCT
cana-2978	295	16	=	=	SYM
cana-2978	295	17			NOUN
cana-2978	295	18	(	(	PUNCT
cana-2978	295	19	γ	γ	X
cana-2978	295	20	√√√√	√√√√	PRON
cana-2978	295	21	1−	1−	NUM
cana-2978	295	22	⊗̀	⊗̀	NOUN
cana-2978	295	23	i=1	i=1	X
cana-2978	296	1	(	(	PUNCT
cana-2978	296	2	1−	1−	NUM
cana-2978	296	3	(	(	PUNCT
cana-2978	296	4	(	(	PUNCT
cana-2978	296	5	(	(	PUNCT
cana-2978	296	6	a	a	DET
cana-2978	296	7	·	·	PUNCT
cana-2978	296	8	rᵀ	rᵀ	NOUN
cana-2978	296	9	i	i	NOUN
cana-2978	296	10	)	)	PUNCT
cana-2978	296	11	)	)	PUNCT
cana-2978	297	1	γ	γ	X
cana-2978	297	2	)	)	PUNCT
cana-2978	297	3	γ)ωi	γ)ωi	PROPN
cana-2978	297	4	)	)	PUNCT
cana-2978	297	5	1	1	NUM
cana-2978	297	6	/	/	SYM
cana-2978	297	7	γ	γ	X
cana-2978	297	8	·	·	PUNCT
cana-2978	297	9	e	e	X
cana-2978	297	10	(	(	PUNCT
cana-2978	297	11	γ	γ	X
cana-2978	297	12	√√√√√√1−	√√√√√√1−	NUM
cana-2978	297	13	⊗̀	⊗̀	NOUN
cana-2978	297	14	i=1	i=1	PROPN
cana-2978	298	1	(	(	PUNCT
cana-2978	298	2	1−	1−	NUM
cana-2978	298	3	(	(	PUNCT
cana-2978	298	4	(	(	PUNCT
cana-2978	298	5	(	(	PUNCT
cana-2978	298	6	a	a	PRON
cana-2978	298	7	·	·	PUNCT
cana-2978	298	8	i	i	PRON
cana-2978	298	9	ᵀ	ᵀ	NOUN
cana-2978	298	10	i	i	NOUN
cana-2978	298	11	)	)	PUNCT
cana-2978	298	12	)	)	PUNCT
cana-2978	298	13	γ	γ	X
cana-2978	298	14	)	)	PUNCT
cana-2978	298	15	γ)ωi	γ)ωi	PROPN
cana-2978	298	16	)	)	PUNCT
cana-2978	298	17	1	1	NUM
cana-2978	298	18	/	/	SYM
cana-2978	298	19	γ	γ	NOUN
cana-2978	298	20	,	,	PUNCT
cana-2978	298	21	τ	τ	X
cana-2978	298	22	√√√√1−	√√√√1−	X
cana-2978	298	23	(	(	PUNCT
cana-2978	298	24	1−	1−	NUM
cana-2978	298	25	(	(	PUNCT
cana-2978	298	26	⊗̀	⊗̀	NOUN
cana-2978	298	27	i=1	i=1	X
cana-2978	299	1	(	(	PUNCT
cana-2978	299	2	τ	τ	PROPN
cana-2978	299	3	√	√	PROPN
cana-2978	299	4	1−	1−	NUM
cana-2978	299	5	(	(	PUNCT
cana-2978	299	6	1−	1−	NUM
cana-2978	299	7	(	(	PUNCT
cana-2978	299	8	(	(	PUNCT
cana-2978	299	9	a	a	DET
cana-2978	299	10	·	·	SYM
cana-2978	299	11	r	r	NOUN
cana-2978	299	12	`	`	PUNCT
cana-2978	299	13	i	i	PROPN
cana-2978	299	14	)	)	PUNCT
cana-2978	299	15	)	)	PUNCT
cana-2978	299	16	τ	τ	PROPN
cana-2978	299	17	)	)	PUNCT
cana-2978	300	1	τ)ωi	τ)ωi	PROPN
cana-2978	300	2	)	)	PUNCT
cana-2978	300	3	τ)1	τ)1	NOUN
cana-2978	300	4	/	/	SYM
cana-2978	300	5	τ	τ	PROPN
cana-2978	300	6	·	·	PUNCT
cana-2978	300	7	e	e	X
cana-2978	300	8	τ	τ	X
cana-2978	300	9	√√√√√√1−	√√√√√√1−	NUM
cana-2978	300	10	(	(	PUNCT
cana-2978	300	11	1−	1−	NUM
cana-2978	300	12	(	(	PUNCT
cana-2978	300	13	⊗̀	⊗̀	NOUN
cana-2978	300	14	i=1	i=1	X
cana-2978	301	1	(	(	PUNCT
cana-2978	301	2	τ	τ	PROPN
cana-2978	301	3	√	√	PROPN
cana-2978	301	4	1−	1−	NUM
cana-2978	301	5	(	(	PUNCT
cana-2978	301	6	1−	1−	NUM
cana-2978	301	7	(	(	PUNCT
cana-2978	301	8	(	(	PUNCT
cana-2978	301	9	a	a	DET
cana-2978	301	10	·	·	PUNCT
cana-2978	301	11	i	i	PRON
cana-2978	301	12	`	`	PUNCT
cana-2978	301	13	i	i	PROPN
cana-2978	301	14	)	)	PUNCT
cana-2978	301	15	)	)	PUNCT
cana-2978	301	16	τ	τ	PROPN
cana-2978	301	17	)	)	PUNCT
cana-2978	301	18	τ)ωi	τ)ωi	PROPN
cana-2978	301	19	)	)	PUNCT
cana-2978	301	20	τ)1	τ)1	NOUN
cana-2978	301	21	/	/	SYM
cana-2978	301	22	τ	τ	PROPN
cana-2978	301	23			NUM
cana-2978	301	24	.	.	PUNCT
cana-2978	302	1	proof	proof	NOUN
cana-2978	302	2	.	.	PUNCT
cana-2978	303	1	to	to	PART
cana-2978	303	2	illustrate	illustrate	VERB
cana-2978	303	3	this	this	PRON
cana-2978	303	4	,	,	PUNCT
cana-2978	303	5	we	we	PRON
cana-2978	303	6	may	may	AUX
cana-2978	303	7	first	first	ADV
cana-2978	303	8	show	show	VERB
cana-2978	303	9	that	that	SCONJ
cana-2978	303	10	,	,	PUNCT
cana-2978	303	11	⊕	⊕	PROPN
cana-2978	303	12	`	`	PUNCT
cana-2978	303	13	i=1	i=1	PROPN
cana-2978	303	14	ωiθ	ωiθ	PROPN
cana-2978	303	15	γ	γ	X
cana-2978	303	16	i	i	PROPN
cana-2978	303	17	=	=	SYM
cana-2978	303	18			PROPN
cana-2978	303	19	γ	γ	PROPN
cana-2978	303	20	√√√√	√√√√	ADP
cana-2978	303	21	1−	1−	NUM
cana-2978	303	22	⊗̀	⊗̀	NOUN
cana-2978	303	23	i=1	i=1	X
cana-2978	304	1	(	(	PUNCT
cana-2978	304	2	1−	1−	NUM
cana-2978	304	3	(	(	PUNCT
cana-2978	304	4	(	(	PUNCT
cana-2978	304	5	(	(	PUNCT
cana-2978	304	6	a	a	DET
cana-2978	304	7	·	·	PUNCT
cana-2978	304	8	rᵀ	rᵀ	NOUN
cana-2978	304	9	i	i	NOUN
cana-2978	304	10	)	)	PUNCT
cana-2978	304	11	)	)	PUNCT
cana-2978	305	1	γ	γ	X
cana-2978	305	2	)	)	PUNCT
cana-2978	305	3	γ)ωi	γ)ωi	PROPN
cana-2978	305	4	·	·	PUNCT
cana-2978	305	5	e	e	X
cana-2978	305	6	γ	γ	X
cana-2978	305	7	√√√√√√√√√√	√√√√√√√√√√	PRON
cana-2978	305	8	1−	1−	NUM
cana-2978	305	9	⊗̀	⊗̀	NOUN
cana-2978	305	10	i=1	i=1	X
cana-2978	305	11	(	(	PUNCT
cana-2978	305	12	1−	1−	NUM
cana-2978	305	13	(	(	PUNCT
cana-2978	305	14	(	(	PUNCT
cana-2978	305	15	(	(	PUNCT
cana-2978	305	16	a	a	PRON
cana-2978	305	17	·	·	PUNCT
cana-2978	305	18	i	i	PRON
cana-2978	305	19	ᵀ	ᵀ	NOUN
cana-2978	305	20	i	i	NOUN
cana-2978	305	21	)	)	PUNCT
cana-2978	305	22	)	)	PUNCT
cana-2978	305	23	γ	γ	X
cana-2978	305	24	)	)	PUNCT
cana-2978	306	1	γ)ωi	γ)ωi	PROPN
cana-2978	306	2	⊗	⊗	PROPN
cana-2978	306	3	`	`	PUNCT
cana-2978	306	4	i=1	i=1	PROPN
cana-2978	306	5	(	(	PUNCT
cana-2978	306	6	τ	τ	PROPN
cana-2978	306	7	√	√	PROPN
cana-2978	306	8	1−	1−	NUM
cana-2978	306	9	(	(	PUNCT
cana-2978	306	10	1−	1−	NUM
cana-2978	306	11	(	(	PUNCT
cana-2978	306	12	(	(	PUNCT
cana-2978	306	13	a	a	DET
cana-2978	306	14	·	·	SYM
cana-2978	306	15	r	r	NOUN
cana-2978	306	16	`	`	PUNCT
cana-2978	306	17	i	i	PROPN
cana-2978	306	18	)	)	PUNCT
cana-2978	306	19	)	)	PUNCT
cana-2978	306	20	τ	τ	PROPN
cana-2978	306	21	)	)	PUNCT
cana-2978	307	1	τ)ωi	τ)ωi	PROPN
cana-2978	307	2	·	·	PUNCT
cana-2978	307	3	e	e	NOUN
cana-2978	307	4	⊗̀	⊗̀	NOUN
cana-2978	307	5	i=1	i=1	PROPN
cana-2978	308	1	(	(	PUNCT
cana-2978	308	2	τ	τ	PROPN
cana-2978	308	3	√	√	PROPN
cana-2978	308	4	1−	1−	NUM
cana-2978	308	5	(	(	PUNCT
cana-2978	308	6	1−	1−	NUM
cana-2978	308	7	(	(	PUNCT
cana-2978	308	8	(	(	PUNCT
cana-2978	308	9	a	a	DET
cana-2978	308	10	·	·	PUNCT
cana-2978	308	11	i	i	PRON
cana-2978	308	12	`	`	PUNCT
cana-2978	308	13	i	i	PROPN
cana-2978	308	14	)	)	PUNCT
cana-2978	308	15	)	)	PUNCT
cana-2978	308	16	τ	τ	PROPN
cana-2978	308	17	)	)	PUNCT
cana-2978	309	1	τ)ωi	τ)ωi	PROPN
cana-2978	309	2			NUM
cana-2978	309	3	.	.	PUNCT
cana-2978	310	1	put	put	VERB
cana-2978	310	2	`	`	PUNCT
cana-2978	310	3	=	=	SYM
cana-2978	310	4	2	2	NUM
cana-2978	310	5	,	,	PUNCT
cana-2978	310	6	ω1θ1	ω1θ1	X
cana-2978	310	7	⊕	⊕	NUM
cana-2978	310	8	ω2θ2	ω2θ2	NOUN
cana-2978	310	9	=	=	SYM
cana-2978	310	10			NOUN
cana-2978	310	11	γ	γ	X
cana-2978	310	12	√√√√√√√√√√	√√√√√√√√√√	PROPN
cana-2978	310	13	(	(	PUNCT
cana-2978	310	14	γ	γ	X
cana-2978	310	15	√	√	PROPN
cana-2978	310	16	1−	1−	NUM
cana-2978	310	17	(	(	PUNCT
cana-2978	310	18	1−	1−	NUM
cana-2978	310	19	(	(	PUNCT
cana-2978	310	20	(	(	PUNCT
cana-2978	310	21	(	(	PUNCT
cana-2978	310	22	a	a	DET
cana-2978	310	23	·	·	PUNCT
cana-2978	310	24	rᵀ	rᵀ	NOUN
cana-2978	310	25	1	1	NUM
cana-2978	310	26	)	)	PUNCT
cana-2978	310	27	)	)	PUNCT
cana-2978	310	28	γ	γ	X
cana-2978	310	29	)	)	PUNCT
cana-2978	310	30	γ)ω1	γ)ω1	PROPN
cana-2978	310	31	)	)	PUNCT
cana-2978	310	32	γ	γ	PROPN
cana-2978	310	33	+	+	X
cana-2978	310	34	(	(	PUNCT
cana-2978	310	35	γ	γ	X
cana-2978	310	36	√	√	PROPN
cana-2978	310	37	1−	1−	NUM
cana-2978	310	38	(	(	PUNCT
cana-2978	310	39	1−	1−	NUM
cana-2978	310	40	(	(	PUNCT
cana-2978	310	41	(	(	PUNCT
cana-2978	310	42	(	(	PUNCT
cana-2978	310	43	a	a	DET
cana-2978	310	44	·	·	PUNCT
cana-2978	310	45	rᵀ	rᵀ	NOUN
cana-2978	310	46	2	2	NUM
cana-2978	310	47	)	)	PUNCT
cana-2978	310	48	)	)	PUNCT
cana-2978	310	49	γ	γ	X
cana-2978	310	50	)	)	PUNCT
cana-2978	310	51	γ)ω1	γ)ω1	PROPN
cana-2978	310	52	)	)	PUNCT
cana-2978	310	53	γ	γ	NOUN
cana-2978	310	54	−	−	PROPN
cana-2978	310	55	(	(	PUNCT
cana-2978	310	56	γ	γ	X
cana-2978	310	57	√	√	PROPN
cana-2978	310	58	1−	1−	NUM
cana-2978	310	59	(	(	PUNCT
cana-2978	310	60	1−	1−	NUM
cana-2978	310	61	(	(	PUNCT
cana-2978	310	62	(	(	PUNCT
cana-2978	310	63	(	(	PUNCT
cana-2978	310	64	a	a	DET
cana-2978	310	65	·	·	PUNCT
cana-2978	310	66	rᵀ	rᵀ	NOUN
cana-2978	310	67	1	1	NUM
cana-2978	310	68	)	)	PUNCT
cana-2978	310	69	)	)	PUNCT
cana-2978	310	70	γ	γ	X
cana-2978	310	71	)	)	PUNCT
cana-2978	310	72	γ)ω1	γ)ω1	PROPN
cana-2978	310	73	)	)	PUNCT
cana-2978	310	74	γ	γ	X
cana-2978	310	75	·	·	PUNCT
cana-2978	310	76	(	(	PUNCT
cana-2978	310	77	γ	γ	X
cana-2978	310	78	√	√	PROPN
cana-2978	310	79	1−	1−	NUM
cana-2978	310	80	(	(	PUNCT
cana-2978	310	81	1−	1−	NUM
cana-2978	310	82	(	(	PUNCT
cana-2978	310	83	(	(	PUNCT
cana-2978	310	84	(	(	PUNCT
cana-2978	310	85	a	a	DET
cana-2978	310	86	·	·	PUNCT
cana-2978	310	87	rᵀ	rᵀ	NOUN
cana-2978	310	88	2	2	NUM
cana-2978	310	89	)	)	PUNCT
cana-2978	310	90	)	)	PUNCT
cana-2978	310	91	γ	γ	X
cana-2978	310	92	)	)	PUNCT
cana-2978	310	93	γ)ω1	γ)ω1	PROPN
cana-2978	310	94	)	)	PUNCT
cana-2978	310	95	γ	γ	X
cana-2978	310	96	·	·	PUNCT
cana-2978	310	97	e	e	X
cana-2978	310	98	γ	γ	X
cana-2978	310	99	√√√√√√√√√√√√√√	√√√√√√√√√√√√√√	PROPN
cana-2978	310	100	(	(	PUNCT
cana-2978	310	101	γ	γ	X
cana-2978	310	102	√	√	PROPN
cana-2978	310	103	1−	1−	NUM
cana-2978	310	104	(	(	PUNCT
cana-2978	310	105	1−	1−	NUM
cana-2978	310	106	(	(	PUNCT
cana-2978	310	107	(	(	PUNCT
cana-2978	310	108	(	(	PUNCT
cana-2978	310	109	a	a	PRON
cana-2978	310	110	·	·	PUNCT
cana-2978	310	111	i	i	PRON
cana-2978	310	112	ᵀ	ᵀ	ADJ
cana-2978	310	113	1	1	NUM
cana-2978	310	114	)	)	PUNCT
cana-2978	310	115	)	)	PUNCT
cana-2978	310	116	γ	γ	X
cana-2978	310	117	)	)	PUNCT
cana-2978	310	118	γ)ω1	γ)ω1	PROPN
cana-2978	310	119	)	)	PUNCT
cana-2978	310	120	γ	γ	PROPN
cana-2978	310	121	+	+	X
cana-2978	310	122	(	(	PUNCT
cana-2978	310	123	γ	γ	X
cana-2978	310	124	√	√	PROPN
cana-2978	310	125	1−	1−	NUM
cana-2978	310	126	(	(	PUNCT
cana-2978	310	127	1−	1−	NUM
cana-2978	310	128	(	(	PUNCT
cana-2978	310	129	(	(	PUNCT
cana-2978	310	130	(	(	PUNCT
cana-2978	310	131	a	a	DET
cana-2978	310	132	·	·	PUNCT
cana-2978	310	133	i	i	PRON
cana-2978	310	134	ᵀ	ᵀ	ADJ
cana-2978	310	135	2	2	NUM
cana-2978	310	136	)	)	PUNCT
cana-2978	310	137	)	)	PUNCT
cana-2978	310	138	γ	γ	X
cana-2978	310	139	)	)	PUNCT
cana-2978	310	140	γ)ω1	γ)ω1	PROPN
cana-2978	310	141	)	)	PUNCT
cana-2978	310	142	γ	γ	NOUN
cana-2978	310	143	−	−	PROPN
cana-2978	310	144	(	(	PUNCT
cana-2978	310	145	γ	γ	X
cana-2978	310	146	√	√	PROPN
cana-2978	310	147	1−	1−	NUM
cana-2978	310	148	(	(	PUNCT
cana-2978	310	149	1−	1−	NUM
cana-2978	310	150	(	(	PUNCT
cana-2978	310	151	(	(	PUNCT
cana-2978	310	152	(	(	PUNCT
cana-2978	310	153	a	a	DET
cana-2978	310	154	·	·	PUNCT
cana-2978	310	155	i	i	PRON
cana-2978	310	156	ᵀ	ᵀ	ADJ
cana-2978	310	157	1	1	NUM
cana-2978	310	158	)	)	PUNCT
cana-2978	310	159	)	)	PUNCT
cana-2978	310	160	γ	γ	X
cana-2978	310	161	)	)	PUNCT
cana-2978	310	162	γ)ω1	γ)ω1	PROPN
cana-2978	310	163	)	)	PUNCT
cana-2978	310	164	γ	γ	X
cana-2978	310	165	·	·	PUNCT
cana-2978	310	166	(	(	PUNCT
cana-2978	310	167	γ	γ	X
cana-2978	310	168	√	√	PROPN
cana-2978	310	169	1−	1−	NUM
cana-2978	310	170	(	(	PUNCT
cana-2978	310	171	1−	1−	NUM
cana-2978	310	172	(	(	PUNCT
cana-2978	310	173	(	(	PUNCT
cana-2978	310	174	(	(	PUNCT
cana-2978	310	175	a	a	DET
cana-2978	310	176	·	·	PUNCT
cana-2978	310	177	i	i	PRON
cana-2978	310	178	ᵀ	ᵀ	ADJ
cana-2978	310	179	2	2	NUM
cana-2978	310	180	)	)	PUNCT
cana-2978	310	181	)	)	PUNCT
cana-2978	310	182	γ	γ	X
cana-2978	310	183	)	)	PUNCT
cana-2978	310	184	γ)ω1	γ)ω1	PROPN
cana-2978	310	185	)	)	PUNCT
cana-2978	310	186	γ	γ	X
cana-2978	310	187	,	,	PUNCT
cana-2978	310	188	(	(	PUNCT
cana-2978	310	189	τ	τ	X
cana-2978	310	190	√	√	PROPN
cana-2978	310	191	1−	1−	NUM
cana-2978	310	192	(	(	PUNCT
cana-2978	310	193	1−	1−	NUM
cana-2978	310	194	(	(	PUNCT
cana-2978	310	195	(	(	PUNCT
cana-2978	310	196	a	a	DET
cana-2978	310	197	·	·	SYM
cana-2978	310	198	r	r	NOUN
cana-2978	310	199	`	`	PUNCT
cana-2978	310	200	1	1	NUM
cana-2978	310	201	)	)	PUNCT
cana-2978	310	202	)	)	PUNCT
cana-2978	310	203	τ	τ	X
cana-2978	310	204	)	)	PUNCT
cana-2978	310	205	τ)ω1	τ)ω1	PROPN
cana-2978	310	206	·	·	PUNCT
cana-2978	311	1	(	(	PUNCT
cana-2978	311	2	τ	τ	X
cana-2978	311	3	√	√	VERB
cana-2978	311	4	1−	1−	NUM
cana-2978	311	5	(	(	PUNCT
cana-2978	311	6	1−	1−	NUM
cana-2978	311	7	(	(	PUNCT
cana-2978	311	8	(	(	PUNCT
cana-2978	311	9	a	a	DET
cana-2978	311	10	·	·	SYM
cana-2978	311	11	r	r	NOUN
cana-2978	311	12	`	`	SYM
cana-2978	311	13	2	2	NUM
cana-2978	311	14	)	)	PUNCT
cana-2978	311	15	)	)	PUNCT
cana-2978	312	1	τ	τ	PROPN
cana-2978	312	2	)	)	PUNCT
cana-2978	312	3	τ)ω1	τ)ω1	PROPN
cana-2978	312	4	·	·	PUNCT
cana-2978	312	5	e	e	X
cana-2978	312	6	(	(	PUNCT
cana-2978	312	7	τ	τ	PROPN
cana-2978	312	8	√	√	PROPN
cana-2978	312	9	1−	1−	NUM
cana-2978	312	10	(	(	PUNCT
cana-2978	312	11	1−	1−	NUM
cana-2978	312	12	(	(	PUNCT
cana-2978	312	13	(	(	PUNCT
cana-2978	312	14	a	a	DET
cana-2978	312	15	·	·	PUNCT
cana-2978	312	16	i	i	NOUN
cana-2978	312	17	`	`	PUNCT
cana-2978	312	18	1	1	NUM
cana-2978	312	19	)	)	PUNCT
cana-2978	312	20	)	)	PUNCT
cana-2978	312	21	τ	τ	X
cana-2978	312	22	)	)	PUNCT
cana-2978	312	23	τ)ω1	τ)ω1	PROPN
cana-2978	312	24	·	·	PUNCT
cana-2978	312	25	(	(	PUNCT
cana-2978	312	26	τ	τ	X
cana-2978	312	27	√	√	VERB
cana-2978	312	28	1−	1−	NUM
cana-2978	312	29	(	(	PUNCT
cana-2978	312	30	1−	1−	NUM
cana-2978	312	31	(	(	PUNCT
cana-2978	312	32	(	(	PUNCT
cana-2978	312	33	a	a	DET
cana-2978	312	34	·	·	PUNCT
cana-2978	312	35	i	i	NOUN
cana-2978	312	36	`	`	PUNCT
cana-2978	312	37	2	2	NUM
cana-2978	312	38	)	)	PUNCT
cana-2978	312	39	)	)	PUNCT
cana-2978	312	40	τ	τ	X
cana-2978	312	41	)	)	PUNCT
cana-2978	312	42	τ)ω1	τ)ω1	PROPN
cana-2978	312	43			X
cana-2978	312	44	=	=	SYM
cana-2978	312	45			NOUN
cana-2978	312	46	γ	γ	NOUN
cana-2978	312	47	√	√	NUM
cana-2978	312	48	1−	1−	NUM
cana-2978	312	49	⊗2	⊗2	NUM
cana-2978	312	50	i=1	i=1	PROPN
cana-2978	313	1	(	(	PUNCT
cana-2978	313	2	1−	1−	NUM
cana-2978	313	3	(	(	PUNCT
cana-2978	313	4	(	(	PUNCT
cana-2978	313	5	(	(	PUNCT
cana-2978	313	6	a	a	DET
cana-2978	313	7	·	·	PUNCT
cana-2978	313	8	rᵀ	rᵀ	NOUN
cana-2978	313	9	1	1	NUM
cana-2978	313	10	)	)	PUNCT
cana-2978	313	11	)	)	PUNCT
cana-2978	314	1	γ	γ	X
cana-2978	314	2	)	)	PUNCT
cana-2978	314	3	γ)ωi	γ)ωi	PROPN
cana-2978	314	4	·	·	PUNCT
cana-2978	314	5	e	e	X
cana-2978	314	6	γ	γ	X
cana-2978	314	7	√√√√1−	√√√√1−	X
cana-2978	314	8	⊗2	⊗2	X
cana-2978	314	9	i=1	i=1	PROPN
cana-2978	315	1	(	(	PUNCT
cana-2978	315	2	1−	1−	NUM
cana-2978	315	3	(	(	PUNCT
cana-2978	315	4	(	(	PUNCT
cana-2978	315	5	(	(	PUNCT
cana-2978	315	6	a·i	a·i	X
cana-2978	315	7	ᵀ	ᵀ	PROPN
cana-2978	315	8	1	1	NUM
cana-2978	315	9	)	)	PUNCT
cana-2978	315	10	)	)	PUNCT
cana-2978	315	11	γ	γ	X
cana-2978	315	12	)	)	PUNCT
cana-2978	315	13	γ)ωi	γ)ωi	PROPN
cana-2978	315	14	⊗2	⊗2	NUM
cana-2978	315	15	i=1	i=1	PROPN
cana-2978	316	1	(	(	PUNCT
cana-2978	316	2	τ	τ	PROPN
cana-2978	316	3	√	√	PROPN
cana-2978	316	4	1−	1−	NUM
cana-2978	316	5	(	(	PUNCT
cana-2978	316	6	1−	1−	NUM
cana-2978	316	7	(	(	PUNCT
cana-2978	316	8	(	(	PUNCT
cana-2978	316	9	a	a	DET
cana-2978	316	10	·	·	SYM
cana-2978	316	11	r	r	NOUN
cana-2978	316	12	`	`	PUNCT
cana-2978	316	13	i	i	PROPN
cana-2978	316	14	)	)	PUNCT
cana-2978	316	15	)	)	PUNCT
cana-2978	316	16	τ	τ	PROPN
cana-2978	316	17	)	)	PUNCT
cana-2978	317	1	τ)ωi	τ)ωi	PROPN
cana-2978	317	2	·	·	PUNCT
cana-2978	317	3	⊗2	⊗2	X
cana-2978	317	4	i=1	i=1	PROPN
cana-2978	317	5	(	(	PUNCT
cana-2978	317	6	τ	τ	PROPN
cana-2978	317	7	√	√	PROPN
cana-2978	317	8	1−	1−	NUM
cana-2978	317	9	(	(	PUNCT
cana-2978	317	10	1−	1−	NUM
cana-2978	317	11	(	(	PUNCT
cana-2978	317	12	(	(	PUNCT
cana-2978	317	13	a	a	DET
cana-2978	317	14	·	·	PUNCT
cana-2978	317	15	i	i	PRON
cana-2978	317	16	`	`	PUNCT
cana-2978	317	17	i	i	PROPN
cana-2978	317	18	)	)	PUNCT
cana-2978	317	19	)	)	PUNCT
cana-2978	317	20	τ	τ	PROPN
cana-2978	317	21	)	)	PUNCT
cana-2978	318	1	τ)ωi	τ)ωi	PROPN
cana-2978	318	2			NOUN
cana-2978	318	3	.	.	PUNCT
cana-2978	319	1	hence	hence	ADV
cana-2978	319	2	,	,	PUNCT
cana-2978	319	3	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	319	4	140	140	NUM
cana-2978	319	5	communications	communication	NOUN
cana-2978	319	6	on	on	ADP
cana-2978	319	7	applied	apply	VERB
cana-2978	319	8	nonlinear	nonlinear	ADJ
cana-2978	319	9	analysis	analysis	NOUN
cana-2978	319	10	issn	issn	NOUN
cana-2978	319	11	:	:	PUNCT
cana-2978	319	12	1074	1074	NUM
cana-2978	319	13	-	-	PUNCT
cana-2978	319	14	133x	133x	NUM
cana-2978	319	15	vol	vol	NOUN
cana-2978	319	16	32	32	NUM
cana-2978	319	17	no	no	NOUN
cana-2978	319	18	.	.	PUNCT
cana-2978	320	1	5s	5s	NUM
cana-2978	320	2	(	(	PUNCT
cana-2978	320	3	2025	2025	NUM
cana-2978	320	4	)	)	PUNCT
cana-2978	320	5	⊕̀	⊕̀	VERB
cana-2978	320	6	i=1	i=1	PROPN
cana-2978	320	7	ωiθ	ωiθ	PROPN
cana-2978	320	8	∂	∂	NUM
cana-2978	321	1	i	i	NOUN
cana-2978	321	2	=	=	PUNCT
cana-2978	321	3			ADJ
cana-2978	321	4	γ	γ	PROPN
cana-2978	321	5	√	√	PROPN
cana-2978	321	6	1−	1−	NUM
cana-2978	321	7	⊗	⊗	NUM
cana-2978	321	8	`	`	PUNCT
cana-2978	321	9	i=1	i=1	PROPN
cana-2978	321	10	(	(	PUNCT
cana-2978	321	11	1−	1−	NUM
cana-2978	321	12	(	(	PUNCT
cana-2978	321	13	(	(	PUNCT
cana-2978	321	14	(	(	PUNCT
cana-2978	321	15	a	a	DET
cana-2978	321	16	·	·	PUNCT
cana-2978	321	17	rᵀ	rᵀ	NOUN
cana-2978	321	18	1	1	NUM
cana-2978	321	19	)	)	PUNCT
cana-2978	321	20	)	)	PUNCT
cana-2978	321	21	γ	γ	X
cana-2978	321	22	)	)	PUNCT
cana-2978	321	23	γ)ωi	γ)ωi	PROPN
cana-2978	321	24	·	·	PUNCT
cana-2978	321	25	e	e	X
cana-2978	321	26	γ	γ	PROPN
cana-2978	321	27	√√√√1−	√√√√1−	PROPN
cana-2978	321	28	⊗	⊗	PROPN
cana-2978	321	29	`	`	PUNCT
cana-2978	321	30	i=1	i=1	PROPN
cana-2978	321	31	(	(	PUNCT
cana-2978	321	32	1−	1−	NUM
cana-2978	321	33	(	(	PUNCT
cana-2978	321	34	(	(	PUNCT
cana-2978	321	35	(	(	PUNCT
cana-2978	321	36	a·i	a·i	X
cana-2978	321	37	ᵀ	ᵀ	PROPN
cana-2978	321	38	1	1	NUM
cana-2978	321	39	)	)	PUNCT
cana-2978	321	40	)	)	PUNCT
cana-2978	321	41	γ	γ	X
cana-2978	321	42	)	)	PUNCT
cana-2978	321	43	γ)ωi	γ)ωi	PROPN
cana-2978	321	44	⊗	⊗	PROPN
cana-2978	321	45	`	`	PUNCT
cana-2978	321	46	i=1	i=1	PROPN
cana-2978	321	47	(	(	PUNCT
cana-2978	321	48	τ	τ	PROPN
cana-2978	321	49	√	√	PROPN
cana-2978	321	50	1−	1−	NUM
cana-2978	321	51	(	(	PUNCT
cana-2978	321	52	1−	1−	NUM
cana-2978	321	53	(	(	PUNCT
cana-2978	321	54	(	(	PUNCT
cana-2978	321	55	a	a	DET
cana-2978	321	56	·	·	SYM
cana-2978	321	57	r	r	NOUN
cana-2978	321	58	`	`	PUNCT
cana-2978	321	59	i	i	PROPN
cana-2978	321	60	)	)	PUNCT
cana-2978	321	61	)	)	PUNCT
cana-2978	321	62	τ	τ	PROPN
cana-2978	321	63	)	)	PUNCT
cana-2978	321	64	τ)ωi	τ)ωi	PROPN
cana-2978	321	65	·	·	PUNCT
cana-2978	321	66	e	e	X
cana-2978	321	67	⊗	⊗	PROPN
cana-2978	321	68	`	`	PUNCT
cana-2978	321	69	i=1	i=1	PROPN
cana-2978	321	70	(	(	PUNCT
cana-2978	321	71	τ	τ	PROPN
cana-2978	321	72	√	√	PROPN
cana-2978	321	73	1−	1−	NUM
cana-2978	321	74	(	(	PUNCT
cana-2978	321	75	1−((a·i	1−((a·i	NUM
cana-2978	321	76	`	`	PUNCT
cana-2978	321	77	i	i	PROPN
cana-2978	321	78	)	)	PUNCT
cana-2978	321	79	)	)	PUNCT
cana-2978	321	80	τ	τ	X
cana-2978	321	81	)	)	PUNCT
cana-2978	322	1	τ)ωi	τ)ωi	PROPN
cana-2978	322	2			VERB
cana-2978	322	3	.	.	PUNCT
cana-2978	323	1	if	if	SCONJ
cana-2978	323	2	`	`	PUNCT
cana-2978	323	3	=	=	PUNCT
cana-2978	323	4	`	`	PUNCT
cana-2978	323	5	+	+	NUM
cana-2978	323	6	1	1	NUM
cana-2978	323	7	,	,	PUNCT
cana-2978	323	8	then	then	ADV
cana-2978	323	9	⊕	⊕	PROPN
cana-2978	323	10	`	`	PUNCT
cana-2978	323	11	i=1	i=1	PROPN
cana-2978	323	12	ωiθ	ωiθ	PROPN
cana-2978	323	13	∂	∂	NUM
cana-2978	324	1	i	i	PRON
cana-2978	324	2	+	+	CCONJ
cana-2978	324	3	ω`+1θ∂	ω`+1θ∂	NUM
cana-2978	324	4	`	`	PUNCT
cana-2978	324	5	+1	+1	PROPN
cana-2978	324	6	=	=	SYM
cana-2978	324	7	⊕`+1	⊕`+1	NUM
cana-2978	324	8	i=1	i=1	PROPN
cana-2978	324	9	ωiθ	ωiθ	PROPN
cana-2978	324	10	∂	∂	NUM
cana-2978	325	1	i	i	PRON
cana-2978	325	2	.	.	PUNCT
cana-2978	326	1	now	now	ADV
cana-2978	326	2	,	,	PUNCT
cana-2978	326	3	⊕	⊕	PROPN
cana-2978	326	4	`	`	PUNCT
cana-2978	326	5	i=1	i=1	PROPN
cana-2978	326	6	ωiθ	ωiθ	PROPN
cana-2978	326	7	∂	∂	NUM
cana-2978	327	1	i	i	PRON
cana-2978	327	2	+	+	CCONJ
cana-2978	327	3	ω`+1θ∂	ω`+1θ∂	NUM
cana-2978	327	4	`	`	PUNCT
cana-2978	327	5	+1	+1	NOUN
cana-2978	327	6	=	=	PUNCT
cana-2978	327	7	ω1θ∂	ω1θ∂	ADJ
cana-2978	327	8	1	1	NUM
cana-2978	327	9	⊕	⊕	PROPN
cana-2978	327	10	ω2θ∂	ω2θ∂	NUM
cana-2978	327	11	2	2	NUM
cana-2978	327	12	⊕	⊕	PROPN
cana-2978	327	13	...	...	PUNCT
cana-2978	328	1	⊕	⊕	PROPN
cana-2978	328	2	ω`θ	ω`θ	NOUN
cana-2978	328	3	∂	∂	NUM
cana-2978	328	4	`	`	PUNCT
cana-2978	328	5	⊕	⊕	PROPN
cana-2978	328	6	ω`+1θ∂	ω`+1θ∂	NUM
cana-2978	328	7	`	`	PUNCT
cana-2978	328	8	+1	+1	ADJ
cana-2978	328	9	=	=	SYM
cana-2978	328	10			NOUN
cana-2978	328	11	γ	γ	NOUN
cana-2978	328	12	√√√√√√√√√√√	√√√√√√√√√√√	PROPN
cana-2978	328	13	(	(	PUNCT
cana-2978	328	14	γ	γ	X
cana-2978	328	15	√√√√	√√√√	ADP
cana-2978	328	16	1	1	NUM
cana-2978	328	17	−	−	PROPN
cana-2978	328	18	⊗̀	⊗̀	NOUN
cana-2978	328	19	i=1	i=1	X
cana-2978	329	1	(	(	PUNCT
cana-2978	329	2	1	1	NUM
cana-2978	329	3	−	−	PROPN
cana-2978	329	4	(	(	PUNCT
cana-2978	329	5	(	(	PUNCT
cana-2978	329	6	(	(	PUNCT
cana-2978	329	7	a	a	PRON
cana-2978	329	8	·	·	PUNCT
cana-2978	329	9	rᵀ	rᵀ	NOUN
cana-2978	329	10	i	i	NOUN
cana-2978	329	11	)	)	PUNCT
cana-2978	329	12	)	)	PUNCT
cana-2978	330	1	γ	γ	X
cana-2978	330	2	)	)	PUNCT
cana-2978	330	3	γ)ωi	γ)ωi	PROPN
cana-2978	330	4	)	)	PUNCT
cana-2978	330	5	γ	γ	PROPN
cana-2978	330	6	+	+	X
cana-2978	330	7	(	(	PUNCT
cana-2978	330	8	γ	γ	NOUN
cana-2978	330	9	√	√	PROPN
cana-2978	330	10	1	1	NUM
cana-2978	330	11	−	−	PROPN
cana-2978	330	12	(	(	PUNCT
cana-2978	330	13	1	1	NUM
cana-2978	330	14	−	−	PROPN
cana-2978	330	15	(	(	PUNCT
cana-2978	330	16	(	(	PUNCT
cana-2978	330	17	rᵀ	rᵀ	NOUN
cana-2978	330	18	`	`	PUNCT
cana-2978	330	19	+1)γ	+1)γ	PROPN
cana-2978	330	20	)	)	PUNCT
cana-2978	330	21	γ)ω1	γ)ω1	PROPN
cana-2978	330	22	)	)	PUNCT
cana-2978	330	23	γ	γ	NOUN
cana-2978	330	24	−	−	PROPN
cana-2978	330	25	(	(	PUNCT
cana-2978	330	26	γ	γ	X
cana-2978	330	27	√√√√	√√√√	ADP
cana-2978	330	28	1	1	NUM
cana-2978	330	29	−	−	PROPN
cana-2978	330	30	⊗̀	⊗̀	NOUN
cana-2978	330	31	i=1	i=1	X
cana-2978	331	1	(	(	PUNCT
cana-2978	331	2	1	1	NUM
cana-2978	331	3	−	−	PROPN
cana-2978	331	4	(	(	PUNCT
cana-2978	331	5	(	(	PUNCT
cana-2978	331	6	(	(	PUNCT
cana-2978	331	7	a	a	PRON
cana-2978	331	8	·	·	PUNCT
cana-2978	331	9	rᵀ	rᵀ	NOUN
cana-2978	331	10	i	i	NOUN
cana-2978	331	11	)	)	PUNCT
cana-2978	331	12	)	)	PUNCT
cana-2978	331	13	γ	γ	X
cana-2978	331	14	)	)	PUNCT
cana-2978	331	15	γ)ωi	γ)ωi	PROPN
cana-2978	331	16	)	)	PUNCT
cana-2978	331	17	γ	γ	X
cana-2978	331	18	·	·	PUNCT
cana-2978	331	19	(	(	PUNCT
cana-2978	331	20	γ	γ	X
cana-2978	331	21	√	√	PROPN
cana-2978	331	22	1	1	NUM
cana-2978	331	23	−	−	PROPN
cana-2978	331	24	(	(	PUNCT
cana-2978	331	25	1	1	NUM
cana-2978	331	26	−	−	PROPN
cana-2978	331	27	(	(	PUNCT
cana-2978	331	28	(	(	PUNCT
cana-2978	331	29	rᵀ	rᵀ	NOUN
cana-2978	331	30	`	`	PUNCT
cana-2978	331	31	+1)γ	+1)γ	PROPN
cana-2978	331	32	)	)	PUNCT
cana-2978	331	33	γ)ω1	γ)ω1	PROPN
cana-2978	331	34	)	)	PUNCT
cana-2978	331	35	γ	γ	X
cana-2978	331	36	·	·	PUNCT
cana-2978	331	37	e	e	X
cana-2978	331	38	γ	γ	X
cana-2978	331	39	√√√√√√√√√√√√√√√√√√	√√√√√√√√√√√√√√√√√√	X
cana-2978	331	40	(	(	PUNCT
cana-2978	331	41	γ	γ	X
cana-2978	331	42	√√√√	√√√√	ADP
cana-2978	331	43	1	1	NUM
cana-2978	331	44	−	−	PROPN
cana-2978	331	45	⊗̀	⊗̀	NOUN
cana-2978	331	46	i=1	i=1	X
cana-2978	332	1	(	(	PUNCT
cana-2978	332	2	1	1	NUM
cana-2978	332	3	−	−	PROPN
cana-2978	332	4	(	(	PUNCT
cana-2978	332	5	(	(	PUNCT
cana-2978	332	6	(	(	PUNCT
cana-2978	332	7	a	a	PRON
cana-2978	332	8	·	·	PUNCT
cana-2978	332	9	i	i	PRON
cana-2978	332	10	ᵀ	ᵀ	VERB
cana-2978	332	11	i	i	NOUN
cana-2978	332	12	)	)	PUNCT
cana-2978	332	13	)	)	PUNCT
cana-2978	333	1	γ	γ	X
cana-2978	333	2	)	)	PUNCT
cana-2978	333	3	γ)ωi	γ)ωi	PROPN
cana-2978	333	4	)	)	PUNCT
cana-2978	333	5	γ	γ	PROPN
cana-2978	333	6	+	+	X
cana-2978	333	7	(	(	PUNCT
cana-2978	333	8	γ	γ	NOUN
cana-2978	333	9	√	√	PROPN
cana-2978	333	10	1	1	NUM
cana-2978	333	11	−	−	PROPN
cana-2978	333	12	(	(	PUNCT
cana-2978	333	13	1	1	NUM
cana-2978	333	14	−	−	PROPN
cana-2978	333	15	(	(	PUNCT
cana-2978	333	16	(	(	PUNCT
cana-2978	333	17	i	i	PRON
cana-2978	333	18	ᵀ	ᵀ	VERB
cana-2978	333	19	`	`	PUNCT
cana-2978	333	20	+1)γ	+1)γ	PROPN
cana-2978	333	21	)	)	PUNCT
cana-2978	333	22	γ)ω1	γ)ω1	PROPN
cana-2978	333	23	)	)	PUNCT
cana-2978	333	24	γ	γ	NOUN
cana-2978	333	25	−	−	PROPN
cana-2978	333	26	(	(	PUNCT
cana-2978	333	27	γ	γ	X
cana-2978	333	28	√√√√	√√√√	ADP
cana-2978	333	29	1	1	NUM
cana-2978	333	30	−	−	PROPN
cana-2978	333	31	⊗̀	⊗̀	NOUN
cana-2978	333	32	i=1	i=1	X
cana-2978	334	1	(	(	PUNCT
cana-2978	334	2	1	1	NUM
cana-2978	334	3	−	−	PROPN
cana-2978	334	4	(	(	PUNCT
cana-2978	334	5	(	(	PUNCT
cana-2978	334	6	(	(	PUNCT
cana-2978	334	7	a	a	PRON
cana-2978	334	8	·	·	PUNCT
cana-2978	334	9	i	i	PRON
cana-2978	334	10	ᵀ	ᵀ	VERB
cana-2978	334	11	i	i	NOUN
cana-2978	334	12	)	)	PUNCT
cana-2978	334	13	)	)	PUNCT
cana-2978	335	1	γ	γ	X
cana-2978	335	2	)	)	PUNCT
cana-2978	335	3	γ)ωi	γ)ωi	PROPN
cana-2978	335	4	)	)	PUNCT
cana-2978	335	5	γ	γ	X
cana-2978	335	6	·	·	PUNCT
cana-2978	335	7	(	(	PUNCT
cana-2978	335	8	γ	γ	X
cana-2978	335	9	√	√	PROPN
cana-2978	335	10	1	1	NUM
cana-2978	335	11	−	−	PROPN
cana-2978	335	12	(	(	PUNCT
cana-2978	335	13	1	1	NUM
cana-2978	335	14	−	−	PROPN
cana-2978	335	15	(	(	PUNCT
cana-2978	335	16	(	(	PUNCT
cana-2978	335	17	i	i	PRON
cana-2978	335	18	ᵀ	ᵀ	VERB
cana-2978	335	19	`	`	PUNCT
cana-2978	335	20	+1)γ	+1)γ	PROPN
cana-2978	335	21	)	)	PUNCT
cana-2978	335	22	γ)ω1	γ)ω1	PROPN
cana-2978	335	23	)	)	PUNCT
cana-2978	335	24	γ	γ	NOUN
cana-2978	335	25	⊗̀	⊗̀	NOUN
cana-2978	335	26	i=1	i=1	PROPN
cana-2978	336	1	(	(	PUNCT
cana-2978	336	2	τ	τ	NOUN
cana-2978	336	3	√	√	PROPN
cana-2978	336	4	1	1	NUM
cana-2978	336	5	−	−	PROPN
cana-2978	336	6	(	(	PUNCT
cana-2978	336	7	1	1	NUM
cana-2978	336	8	−	−	PROPN
cana-2978	336	9	(	(	PUNCT
cana-2978	336	10	(	(	PUNCT
cana-2978	336	11	a	a	DET
cana-2978	336	12	·	·	PUNCT
cana-2978	336	13	r	r	NOUN
cana-2978	336	14	`	`	PUNCT
cana-2978	336	15	i	i	PROPN
cana-2978	336	16	)	)	PUNCT
cana-2978	336	17	)	)	PUNCT
cana-2978	336	18	τ	τ	PROPN
cana-2978	336	19	)	)	PUNCT
cana-2978	337	1	τ)ωi	τ)ωi	PROPN
cana-2978	337	2	·	·	PUNCT
cana-2978	337	3	(	(	PUNCT
cana-2978	337	4	τ	τ	X
cana-2978	337	5	√	√	PROPN
cana-2978	337	6	1	1	NUM
cana-2978	337	7	−	−	PROPN
cana-2978	337	8	(	(	PUNCT
cana-2978	337	9	1	1	NUM
cana-2978	337	10	−	−	NOUN
cana-2978	337	11	(	(	PUNCT
cana-2978	337	12	r	r	NOUN
cana-2978	337	13	`	`	PUNCT
cana-2978	337	14	`	`	PUNCT
cana-2978	337	15	+1)τ	+1)τ	PROPN
cana-2978	337	16	)	)	PUNCT
cana-2978	337	17	τ)ω1	τ)ω1	PROPN
cana-2978	337	18	·	·	PUNCT
cana-2978	337	19	e	e	PROPN
cana-2978	337	20	⊗̀	⊗̀	NOUN
cana-2978	337	21	i=1	i=1	PROPN
cana-2978	337	22	(	(	PUNCT
cana-2978	337	23	τ	τ	NOUN
cana-2978	337	24	√	√	PROPN
cana-2978	337	25	1	1	NUM
cana-2978	337	26	−	−	PROPN
cana-2978	337	27	(	(	PUNCT
cana-2978	337	28	1	1	NUM
cana-2978	337	29	−	−	PROPN
cana-2978	337	30	(	(	PUNCT
cana-2978	337	31	(	(	PUNCT
cana-2978	337	32	a	a	PRON
cana-2978	337	33	·	·	PUNCT
cana-2978	337	34	i	i	PRON
cana-2978	337	35	`	`	PUNCT
cana-2978	337	36	i	i	PROPN
cana-2978	337	37	)	)	PUNCT
cana-2978	337	38	)	)	PUNCT
cana-2978	337	39	τ	τ	PROPN
cana-2978	337	40	)	)	PUNCT
cana-2978	338	1	τ)ωi	τ)ωi	PROPN
cana-2978	338	2	·	·	PUNCT
cana-2978	338	3	(	(	PUNCT
cana-2978	338	4	τ	τ	X
cana-2978	338	5	√	√	PROPN
cana-2978	338	6	1	1	NUM
cana-2978	338	7	−	−	PROPN
cana-2978	338	8	(	(	PUNCT
cana-2978	338	9	1	1	NUM
cana-2978	338	10	−	−	PROPN
cana-2978	338	11	(	(	PUNCT
cana-2978	338	12	i	i	PRON
cana-2978	338	13	`	`	PUNCT
cana-2978	338	14	`	`	PUNCT
cana-2978	338	15	+1)τ	+1)τ	PROPN
cana-2978	338	16	)	)	PUNCT
cana-2978	338	17	τ)ω1	τ)ω1	PROPN
cana-2978	338	18			NUM
cana-2978	338	19	`	`	PUNCT
cana-2978	338	20	+1⊕	+1⊕	PROPN
cana-2978	338	21	i=1	i=1	PROPN
cana-2978	338	22	ωiθ	ωiθ	PROPN
cana-2978	338	23	γ	γ	X
cana-2978	338	24	i	i	NOUN
cana-2978	338	25	=	=	PUNCT
cana-2978	338	26			NOUN
cana-2978	338	27	γ	γ	NOUN
cana-2978	338	28	√	√	VERB
cana-2978	338	29	1	1	NUM
cana-2978	338	30	−	−	NOUN
cana-2978	338	31	⊗`+1	⊗`+1	NOUN
cana-2978	338	32	i=1	i=1	X
cana-2978	339	1	(	(	PUNCT
cana-2978	339	2	1	1	NUM
cana-2978	339	3	−	−	PROPN
cana-2978	339	4	(	(	PUNCT
cana-2978	339	5	(	(	PUNCT
cana-2978	339	6	(	(	PUNCT
cana-2978	339	7	a	a	DET
cana-2978	339	8	·	·	PUNCT
cana-2978	339	9	rᵀ	rᵀ	NOUN
cana-2978	339	10	1	1	NUM
cana-2978	339	11	)	)	PUNCT
cana-2978	339	12	)	)	PUNCT
cana-2978	339	13	γ	γ	X
cana-2978	339	14	)	)	PUNCT
cana-2978	339	15	γ)ωi	γ)ωi	PROPN
cana-2978	339	16	·	·	PUNCT
cana-2978	339	17	e	e	X
cana-2978	339	18	γ	γ	X
cana-2978	339	19	√√√√√1−	√√√√√1−	NUM
cana-2978	339	20	⊗`+1	⊗`+1	NOUN
cana-2978	339	21	i=1	i=1	PROPN
cana-2978	339	22	(	(	PUNCT
cana-2978	339	23	1−	1−	NUM
cana-2978	339	24	(	(	PUNCT
cana-2978	339	25	(	(	PUNCT
cana-2978	339	26	(	(	PUNCT
cana-2978	339	27	a·iᵀ	a·iᵀ	PROPN
cana-2978	339	28	1	1	NUM
cana-2978	339	29	)	)	PUNCT
cana-2978	339	30	)	)	PUNCT
cana-2978	339	31	γ	γ	X
cana-2978	339	32	)	)	PUNCT
cana-2978	339	33	γ)ωi	γ)ωi	PROPN
cana-2978	339	34	⊗`+1	⊗`+1	NOUN
cana-2978	340	1	i=1	i=1	X
cana-2978	340	2	(	(	PUNCT
cana-2978	340	3	τ	τ	NOUN
cana-2978	340	4	√	√	PROPN
cana-2978	340	5	1	1	NUM
cana-2978	340	6	−	−	PROPN
cana-2978	340	7	(	(	PUNCT
cana-2978	340	8	1	1	NUM
cana-2978	340	9	−	−	PROPN
cana-2978	340	10	(	(	PUNCT
cana-2978	340	11	(	(	PUNCT
cana-2978	340	12	a	a	DET
cana-2978	340	13	·	·	PUNCT
cana-2978	340	14	r	r	NOUN
cana-2978	340	15	`	`	PUNCT
cana-2978	340	16	i	i	PROPN
cana-2978	340	17	)	)	PUNCT
cana-2978	340	18	)	)	PUNCT
cana-2978	340	19	τ	τ	PROPN
cana-2978	340	20	)	)	PUNCT
cana-2978	341	1	τ)ωi	τ)ωi	PROPN
cana-2978	341	2	·	·	PUNCT
cana-2978	341	3	e	e	X
cana-2978	341	4	⊗`+1	⊗`+1	PROPN
cana-2978	341	5	i=1	i=1	PROPN
cana-2978	342	1	(	(	PUNCT
cana-2978	342	2	τ	τ	PROPN
cana-2978	342	3	√	√	PROPN
cana-2978	342	4	1−	1−	NUM
cana-2978	342	5	(	(	PUNCT
cana-2978	342	6	1−((a·i	1−((a·i	NUM
cana-2978	342	7	`	`	PUNCT
cana-2978	342	8	i	i	PROPN
cana-2978	342	9	)	)	PUNCT
cana-2978	342	10	)	)	PUNCT
cana-2978	343	1	τ	τ	PROPN
cana-2978	343	2	)	)	PUNCT
cana-2978	344	1	τ)ωi	τ)ωi	PROPN
cana-2978	344	2			NUM
cana-2978	344	3	.	.	PUNCT
cana-2978	345	1	(	(	PUNCT
cana-2978	345	2	`	`	PUNCT
cana-2978	345	3	+1⊕	+1⊕	ADJ
cana-2978	345	4	i=1	i=1	PROPN
cana-2978	345	5	ωiθ	ωiθ	PROPN
cana-2978	345	6	∂	∂	NUM
cana-2978	345	7	i	i	NOUN
cana-2978	345	8	)	)	PUNCT
cana-2978	345	9	1/∂	1/∂	NUM
cana-2978	345	10	=	=	SYM
cana-2978	345	11			NOUN
cana-2978	345	12	(	(	PUNCT
cana-2978	345	13	γ	γ	X
cana-2978	345	14	√√√√	√√√√	ADP
cana-2978	345	15	1	1	NUM
cana-2978	345	16	−	−	NOUN
cana-2978	345	17	`	`	PUNCT
cana-2978	345	18	+1⊗	+1⊗	NUM
cana-2978	345	19	i=1	i=1	X
cana-2978	345	20	(	(	PUNCT
cana-2978	345	21	1	1	NUM
cana-2978	345	22	−	−	PROPN
cana-2978	345	23	(	(	PUNCT
cana-2978	345	24	(	(	PUNCT
cana-2978	345	25	(	(	PUNCT
cana-2978	345	26	a	a	PRON
cana-2978	345	27	·	·	PUNCT
cana-2978	345	28	rᵀ	rᵀ	NOUN
cana-2978	345	29	i	i	NOUN
cana-2978	345	30	)	)	PUNCT
cana-2978	345	31	)	)	PUNCT
cana-2978	345	32	γ	γ	X
cana-2978	345	33	)	)	PUNCT
cana-2978	345	34	γ)ωi	γ)ωi	PROPN
cana-2978	345	35	)	)	PUNCT
cana-2978	345	36	1	1	NUM
cana-2978	345	37	/	/	SYM
cana-2978	345	38	γ	γ	X
cana-2978	345	39	·	·	PUNCT
cana-2978	345	40	e	e	X
cana-2978	345	41	(	(	PUNCT
cana-2978	345	42	γ	γ	X
cana-2978	345	43	√√√√√√1	√√√√√√1	VERB
cana-2978	345	44	−	−	NOUN
cana-2978	345	45	`	`	PUNCT
cana-2978	345	46	+1⊗	+1⊗	NUM
cana-2978	345	47	i=1	i=1	X
cana-2978	345	48	(	(	PUNCT
cana-2978	345	49	1	1	NUM
cana-2978	345	50	−	−	PROPN
cana-2978	345	51	(	(	PUNCT
cana-2978	345	52	(	(	PUNCT
cana-2978	345	53	(	(	PUNCT
cana-2978	345	54	a	a	PRON
cana-2978	345	55	·	·	PUNCT
cana-2978	345	56	i	i	PRON
cana-2978	345	57	ᵀ	ᵀ	VERB
cana-2978	345	58	i	i	NOUN
cana-2978	345	59	)	)	PUNCT
cana-2978	345	60	)	)	PUNCT
cana-2978	345	61	γ	γ	X
cana-2978	345	62	)	)	PUNCT
cana-2978	345	63	γ)ωi	γ)ωi	PROPN
cana-2978	345	64	)	)	PUNCT
cana-2978	345	65	1	1	NUM
cana-2978	345	66	/	/	SYM
cana-2978	345	67	γ	γ	X
cana-2978	345	68	τ	τ	X
cana-2978	345	69	√√√√1	√√√√1	NOUN
cana-2978	345	70	−	−	PROPN
cana-2978	345	71	(	(	PUNCT
cana-2978	345	72	1	1	NUM
cana-2978	345	73	−	−	PROPN
cana-2978	345	74	(	(	PUNCT
cana-2978	345	75	`	`	PUNCT
cana-2978	345	76	+1⊗	+1⊗	NUM
cana-2978	345	77	i=1	i=1	X
cana-2978	345	78	(	(	PUNCT
cana-2978	345	79	τ	τ	PROPN
cana-2978	345	80	√	√	PROPN
cana-2978	345	81	1	1	NUM
cana-2978	345	82	−	−	PROPN
cana-2978	345	83	(	(	PUNCT
cana-2978	345	84	1	1	NUM
cana-2978	345	85	−	−	PROPN
cana-2978	345	86	(	(	PUNCT
cana-2978	345	87	(	(	PUNCT
cana-2978	345	88	a	a	DET
cana-2978	345	89	·	·	PUNCT
cana-2978	345	90	r	r	NOUN
cana-2978	345	91	`	`	PUNCT
cana-2978	345	92	i	i	PROPN
cana-2978	345	93	)	)	PUNCT
cana-2978	345	94	)	)	PUNCT
cana-2978	345	95	τ	τ	PROPN
cana-2978	345	96	)	)	PUNCT
cana-2978	345	97	τ)ωi	τ)ωi	PROPN
cana-2978	345	98	)	)	PUNCT
cana-2978	345	99	2)1	2)1	NUM
cana-2978	345	100	/	/	SYM
cana-2978	345	101	τ	τ	X
cana-2978	345	102	·	·	PUNCT
cana-2978	345	103	e	e	X
cana-2978	345	104	τ	τ	X
cana-2978	345	105	√√√√√√√1−	√√√√√√√1−	NUM
cana-2978	345	106	(	(	PUNCT
cana-2978	345	107	1	1	NUM
cana-2978	345	108	−	−	PROPN
cana-2978	345	109	(	(	PUNCT
cana-2978	345	110	`	`	PUNCT
cana-2978	345	111	+1⊗	+1⊗	NUM
cana-2978	345	112	i=1	i=1	X
cana-2978	345	113	(	(	PUNCT
cana-2978	345	114	τ	τ	PROPN
cana-2978	345	115	√	√	PROPN
cana-2978	345	116	1	1	NUM
cana-2978	345	117	−	−	PROPN
cana-2978	345	118	(	(	PUNCT
cana-2978	345	119	1	1	NUM
cana-2978	345	120	−	−	PROPN
cana-2978	345	121	(	(	PUNCT
cana-2978	345	122	(	(	PUNCT
cana-2978	345	123	a	a	PRON
cana-2978	345	124	·	·	PUNCT
cana-2978	345	125	i	i	PRON
cana-2978	345	126	`	`	PUNCT
cana-2978	345	127	i	i	PROPN
cana-2978	345	128	)	)	PUNCT
cana-2978	345	129	)	)	PUNCT
cana-2978	345	130	τ	τ	PROPN
cana-2978	345	131	)	)	PUNCT
cana-2978	345	132	τ)ωi	τ)ωi	PROPN
cana-2978	345	133	)	)	PUNCT
cana-2978	345	134	2)1	2)1	NUM
cana-2978	345	135	/	/	SYM
cana-2978	345	136	τ	τ	PROPN
cana-2978	345	137			NUM
cana-2978	345	138	corollary	corollary	NOUN
cana-2978	345	139	4.11	4.11	NUM
cana-2978	345	140	.	.	PUNCT
cana-2978	346	1	(	(	PUNCT
cana-2978	346	2	i	i	NOUN
cana-2978	346	3	)	)	PUNCT
cana-2978	346	4	if	if	SCONJ
cana-2978	346	5	(	(	PUNCT
cana-2978	346	6	γ	γ	X
cana-2978	346	7	,	,	PUNCT
cana-2978	346	8	τ	τ	X
cana-2978	346	9	)	)	PUNCT
cana-2978	346	10	=	=	SYM
cana-2978	346	11	(	(	PUNCT
cana-2978	346	12	1	1	NUM
cana-2978	346	13	,	,	PUNCT
cana-2978	346	14	1	1	NUM
cana-2978	346	15	)	)	PUNCT
cana-2978	346	16	,	,	PUNCT
cana-2978	346	17	then	then	ADV
cana-2978	346	18	ct	ct	PRON
cana-2978	346	19	(	(	PUNCT
cana-2978	346	20	γ	γ	PROPN
cana-2978	346	21	,	,	PUNCT
cana-2978	346	22	τ)-rung	τ)-rung	NOUN
cana-2978	346	23	fnwa	fnwa	NOUN
cana-2978	346	24	operator	operator	NOUN
cana-2978	346	25	is	be	AUX
cana-2978	346	26	used	use	VERB
cana-2978	346	27	instead	instead	ADV
cana-2978	346	28	of	of	ADP
cana-2978	346	29	the	the	DET
cana-2978	346	30	gct	gct	PROPN
cana-2978	346	31	(	(	PUNCT
cana-2978	346	32	γ	γ	PROPN
cana-2978	346	33	,	,	PUNCT
cana-2978	346	34	τ)rung	τ)rung	PROPN
cana-2978	346	35	fnwa	fnwa	NOUN
cana-2978	346	36	operator	operator	NOUN
cana-2978	346	37	.	.	PUNCT
cana-2978	347	1	(	(	PUNCT
cana-2978	347	2	ii	ii	NOUN
cana-2978	347	3	)	)	PUNCT
cana-2978	347	4	if	if	SCONJ
cana-2978	347	5	all	all	DET
cana-2978	347	6	θi	θi	ADP
cana-2978	347	7	=	=	SYM
cana-2978	347	8	〈	〈	PROPN
cana-2978	347	9	(	(	PUNCT
cana-2978	347	10	(	(	PUNCT
cana-2978	347	11	(	(	PUNCT
cana-2978	347	12	a	a	DET
cana-2978	347	13	·	·	PUNCT
cana-2978	347	14	rᵀ	rᵀ	NOUN
cana-2978	347	15	i	i	NOUN
cana-2978	347	16	)	)	PUNCT
cana-2978	347	17	·	·	PUNCT
cana-2978	348	1	e(a·i	e(a·i	NOUN
cana-2978	348	2	ᵀ	ᵀ	VERB
cana-2978	348	3	i	i	PROPN
cana-2978	348	4	)	)	PUNCT
cana-2978	348	5	,	,	PUNCT
cana-2978	348	6	(	(	PUNCT
cana-2978	348	7	a	a	PRON
cana-2978	348	8	·	·	PUNCT
cana-2978	348	9	r	r	NOUN
cana-2978	348	10	`	`	PUNCT
cana-2978	348	11	i	i	NOUN
cana-2978	348	12	)	)	PUNCT
cana-2978	348	13	·	·	PUNCT
cana-2978	349	1	e(a·i	e(a·i	NOUN
cana-2978	349	2	`	`	PUNCT
cana-2978	349	3	i	i	PROPN
cana-2978	349	4	)	)	PUNCT
cana-2978	349	5	)	)	PUNCT
cana-2978	349	6	)	)	PUNCT
cana-2978	349	7	〉	〉	NOUN
cana-2978	349	8	and	and	CCONJ
cana-2978	349	9	all	all	PRON
cana-2978	349	10	are	be	AUX
cana-2978	349	11	equal	equal	ADJ
cana-2978	349	12	.	.	PUNCT
cana-2978	350	1	then	then	ADV
cana-2978	350	2	gct	gct	PROPN
cana-2978	350	3	(	(	PUNCT
cana-2978	350	4	γ	γ	PROPN
cana-2978	350	5	,	,	PUNCT
cana-2978	350	6	τ)-rung	τ)-rung	PUNCT
cana-2978	350	7	fnwa(θ1,θ2	fnwa(θ1,θ2	PROPN
cana-2978	350	8	,	,	PUNCT
cana-2978	350	9	...	...	PUNCT
cana-2978	350	10	,	,	PUNCT
cana-2978	350	11	θ	θ	NOUN
cana-2978	350	12	`	`	PUNCT
cana-2978	350	13	)	)	PUNCT
cana-2978	350	14	=	=	SYM
cana-2978	350	15	θ	θ	X
cana-2978	350	16	.	.	PUNCT
cana-2978	350	17	(	(	PUNCT
cana-2978	350	18	iii	iii	X
cana-2978	350	19	)	)	PUNCT
cana-2978	350	20	the	the	DET
cana-2978	350	21	gct	gct	PROPN
cana-2978	350	22	(	(	PUNCT
cana-2978	350	23	γ	γ	PROPN
cana-2978	350	24	,	,	PUNCT
cana-2978	350	25	τ)-rung	τ)-rung	NOUN
cana-2978	350	26	fnwa	fnwa	NOUN
cana-2978	350	27	operator	operator	NOUN
cana-2978	350	28	meets	meet	VERB
cana-2978	350	29	both	both	CCONJ
cana-2978	350	30	boundedness	boundedness	NOUN
cana-2978	350	31	and	and	CCONJ
cana-2978	350	32	monotonicity	monotonicity	NOUN
cana-2978	350	33	constraints	constraint	NOUN
cana-2978	350	34	.	.	PUNCT
cana-2978	351	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	351	2	141	141	NUM
cana-2978	351	3	communications	communication	NOUN
cana-2978	351	4	on	on	ADP
cana-2978	351	5	applied	apply	VERB
cana-2978	351	6	nonlinear	nonlinear	ADJ
cana-2978	351	7	analysis	analysis	NOUN
cana-2978	351	8	issn	issn	NOUN
cana-2978	351	9	:	:	PUNCT
cana-2978	351	10	1074	1074	NUM
cana-2978	351	11	-	-	PUNCT
cana-2978	351	12	133x	133x	NUM
cana-2978	351	13	vol	vol	NOUN
cana-2978	351	14	32	32	NUM
cana-2978	351	15	no	no	NOUN
cana-2978	351	16	.	.	PUNCT
cana-2978	352	1	5s	5s	NUM
cana-2978	352	2	(	(	PUNCT
cana-2978	352	3	2025	2025	NUM
cana-2978	352	4	)	)	PUNCT
cana-2978	352	5	4.4	4.4	NUM
cana-2978	352	6	generalized	generalize	VERB
cana-2978	352	7	ct	ct	PROPN
cana-2978	352	8	(	(	PUNCT
cana-2978	352	9	γ	γ	PROPN
cana-2978	352	10	,	,	PUNCT
cana-2978	352	11	τ)-rung	τ)-rung	PUNCT
cana-2978	352	12	fnwg	fnwg	PROPN
cana-2978	352	13	(	(	PUNCT
cana-2978	352	14	gct	gct	PROPN
cana-2978	352	15	(	(	PUNCT
cana-2978	352	16	γ	γ	PROPN
cana-2978	352	17	,	,	PUNCT
cana-2978	352	18	τ)-rung	τ)-rung	VERB
cana-2978	352	19	fnwg	fnwg	ADJ
cana-2978	352	20	)	)	PUNCT
cana-2978	352	21	definition	definition	NOUN
cana-2978	352	22	4.12	4.12	NUM
cana-2978	352	23	.	.	PUNCT
cana-2978	353	1	let	let	VERB
cana-2978	353	2	θi	θi	X
cana-2978	353	3	=	=	PROPN
cana-2978	353	4	〈	〈	PROPN
cana-2978	353	5	(	(	PUNCT
cana-2978	353	6	(	(	PUNCT
cana-2978	353	7	(	(	PUNCT
cana-2978	353	8	a	a	PRON
cana-2978	353	9	·	·	PUNCT
cana-2978	353	10	rᵀ	rᵀ	NOUN
cana-2978	353	11	i	i	NOUN
cana-2978	353	12	)	)	PUNCT
cana-2978	353	13	·	·	PUNCT
cana-2978	354	1	e(a·i	e(a·i	NOUN
cana-2978	354	2	ᵀ	ᵀ	VERB
cana-2978	354	3	i	i	PROPN
cana-2978	354	4	)	)	PUNCT
cana-2978	354	5	,	,	PUNCT
cana-2978	354	6	(	(	PUNCT
cana-2978	354	7	a	a	DET
cana-2978	354	8	·	·	SYM
cana-2978	354	9	r	r	NOUN
cana-2978	354	10	`	`	PUNCT
cana-2978	354	11	i	i	PROPN
cana-2978	354	12	)	)	PUNCT
cana-2978	354	13	·	·	PUNCT
cana-2978	355	1	e(a·i	e(a·i	NOUN
cana-2978	355	2	`	`	PUNCT
cana-2978	355	3	i	i	PROPN
cana-2978	355	4	)	)	PUNCT
cana-2978	355	5	)	)	PUNCT
cana-2978	355	6	)	)	PUNCT
cana-2978	355	7	〉	〉	NOUN
cana-2978	355	8	be	be	VERB
cana-2978	355	9	the	the	DET
cana-2978	355	10	ct	ct	PROPN
cana-2978	355	11	(	(	PUNCT
cana-2978	355	12	γ	γ	PROPN
cana-2978	355	13	,	,	PUNCT
cana-2978	355	14	τ)-rung	τ)-rung	PROPN
cana-2978	355	15	fns	fns	PROPN
cana-2978	355	16	.	.	PUNCT
cana-2978	356	1	then	then	ADV
cana-2978	356	2	gct(γ	gct(γ	PROPN
cana-2978	356	3	,	,	PUNCT
cana-2978	356	4	τ)-rung	τ)-rung	PUNCT
cana-2978	356	5	fnwg	fnwg	ADJ
cana-2978	356	6	(	(	PUNCT
cana-2978	356	7	θ1,θ2	θ1,θ2	PROPN
cana-2978	356	8	,	,	PUNCT
cana-2978	356	9	...	...	PUNCT
cana-2978	356	10	,	,	PUNCT
cana-2978	356	11	θ	θ	NOUN
cana-2978	356	12	`	`	PUNCT
cana-2978	356	13	)	)	PUNCT
cana-2978	356	14	=	=	SYM
cana-2978	357	1	1	1	NUM
cana-2978	357	2	∂	∂	NUM
cana-2978	357	3	(	(	PUNCT
cana-2978	357	4	⊗	⊗	PROPN
cana-2978	357	5	`	`	PUNCT
cana-2978	357	6	i=1(∂θi	i=1(∂θi	PROPN
cana-2978	357	7	)	)	PUNCT
cana-2978	357	8	ωi	ωi	NUM
cana-2978	357	9	)	)	PUNCT
cana-2978	357	10	.	.	PUNCT
cana-2978	358	1	corollary	corollary	ADJ
cana-2978	358	2	4.13	4.13	NUM
cana-2978	358	3	.	.	PUNCT
cana-2978	359	1	let	let	VERB
cana-2978	359	2	θi	θi	X
cana-2978	359	3	=	=	PROPN
cana-2978	359	4	〈	〈	PROPN
cana-2978	359	5	(	(	PUNCT
cana-2978	359	6	(	(	PUNCT
cana-2978	359	7	(	(	PUNCT
cana-2978	359	8	a	a	DET
cana-2978	359	9	·	·	PUNCT
cana-2978	359	10	rᵀ	rᵀ	NOUN
cana-2978	359	11	i	i	NOUN
cana-2978	359	12	)	)	PUNCT
cana-2978	359	13	·	·	PUNCT
cana-2978	360	1	e(a·i	e(a·i	NOUN
cana-2978	360	2	ᵀ	ᵀ	VERB
cana-2978	360	3	i	i	PROPN
cana-2978	360	4	)	)	PUNCT
cana-2978	360	5	,	,	PUNCT
cana-2978	360	6	(	(	PUNCT
cana-2978	360	7	a	a	PRON
cana-2978	360	8	·	·	PUNCT
cana-2978	360	9	r	r	NOUN
cana-2978	360	10	`	`	PUNCT
cana-2978	360	11	i	i	NOUN
cana-2978	360	12	)	)	PUNCT
cana-2978	360	13	·	·	PUNCT
cana-2978	361	1	e(a·i	e(a·i	NOUN
cana-2978	361	2	`	`	PUNCT
cana-2978	361	3	i	i	PROPN
cana-2978	361	4	)	)	PUNCT
cana-2978	361	5	)	)	PUNCT
cana-2978	361	6	)	)	PUNCT
cana-2978	361	7	〉	〉	NOUN
cana-2978	361	8	be	be	VERB
cana-2978	361	9	the	the	DET
cana-2978	361	10	ct	ct	PROPN
cana-2978	361	11	(	(	PUNCT
cana-2978	361	12	γ	γ	PROPN
cana-2978	361	13	,	,	PUNCT
cana-2978	361	14	τ)-rung	τ)-rung	PROPN
cana-2978	361	15	fns	fns	PROPN
cana-2978	361	16	.	.	PUNCT
cana-2978	362	1	then	then	ADV
cana-2978	362	2	gct(γ	gct(γ	PROPN
cana-2978	362	3	,	,	PUNCT
cana-2978	362	4	τ)-rung	τ)-rung	PUNCT
cana-2978	363	1	fnwg(θ1,θ2	fnwg(θ1,θ2	PROPN
cana-2978	363	2	,	,	PUNCT
cana-2978	363	3	...	...	PUNCT
cana-2978	363	4	,	,	PUNCT
cana-2978	363	5	θ	θ	NOUN
cana-2978	363	6	`	`	PUNCT
cana-2978	363	7	)	)	PUNCT
cana-2978	363	8	=	=	SYM
cana-2978	363	9			NOUN
cana-2978	363	10	γ	γ	X
cana-2978	363	11	√√√√1−	√√√√1−	X
cana-2978	363	12	(	(	PUNCT
cana-2978	363	13	1−	1−	NUM
cana-2978	363	14	(	(	PUNCT
cana-2978	363	15	⊗̀	⊗̀	NOUN
cana-2978	363	16	i=1	i=1	X
cana-2978	363	17	(	(	PUNCT
cana-2978	363	18	γ	γ	X
cana-2978	363	19	√	√	PROPN
cana-2978	363	20	1−	1−	NUM
cana-2978	363	21	(	(	PUNCT
cana-2978	363	22	1−	1−	NUM
cana-2978	363	23	(	(	PUNCT
cana-2978	363	24	(	(	PUNCT
cana-2978	363	25	a	a	DET
cana-2978	363	26	·	·	PUNCT
cana-2978	363	27	rᵀ	rᵀ	NOUN
cana-2978	363	28	i	i	NOUN
cana-2978	363	29	)	)	PUNCT
cana-2978	363	30	)	)	PUNCT
cana-2978	363	31	γ	γ	X
cana-2978	363	32	)	)	PUNCT
cana-2978	363	33	γ)ωi	γ)ωi	PROPN
cana-2978	363	34	)	)	PUNCT
cana-2978	363	35	γ)1	γ)1	NOUN
cana-2978	363	36	/	/	SYM
cana-2978	363	37	γ	γ	X
cana-2978	363	38	·	·	PUNCT
cana-2978	363	39	e	e	X
cana-2978	363	40	γ	γ	X
cana-2978	363	41	√√√√√√1−	√√√√√√1−	NUM
cana-2978	363	42	(	(	PUNCT
cana-2978	363	43	1−	1−	NUM
cana-2978	363	44	(	(	PUNCT
cana-2978	363	45	⊗̀	⊗̀	NOUN
cana-2978	363	46	i=1	i=1	X
cana-2978	364	1	(	(	PUNCT
cana-2978	364	2	γ	γ	X
cana-2978	364	3	√	√	PROPN
cana-2978	364	4	1−	1−	NUM
cana-2978	364	5	(	(	PUNCT
cana-2978	364	6	1−	1−	NUM
cana-2978	364	7	(	(	PUNCT
cana-2978	364	8	(	(	PUNCT
cana-2978	364	9	a	a	PRON
cana-2978	364	10	·	·	PUNCT
cana-2978	364	11	i	i	PRON
cana-2978	364	12	ᵀ	ᵀ	NOUN
cana-2978	364	13	i	i	NOUN
cana-2978	364	14	)	)	PUNCT
cana-2978	364	15	)	)	PUNCT
cana-2978	365	1	γ	γ	X
cana-2978	365	2	)	)	PUNCT
cana-2978	365	3	γ)ωi	γ)ωi	PROPN
cana-2978	365	4	)	)	PUNCT
cana-2978	365	5	γ)1	γ)1	NOUN
cana-2978	365	6	/	/	SYM
cana-2978	365	7	γ	γ	X
cana-2978	365	8	(	(	PUNCT
cana-2978	365	9	τ	τ	X
cana-2978	365	10	√√√√	√√√√	NOUN
cana-2978	365	11	1−	1−	NUM
cana-2978	365	12	⊗̀	⊗̀	NOUN
cana-2978	365	13	i=1	i=1	X
cana-2978	366	1	(	(	PUNCT
cana-2978	366	2	1−	1−	NUM
cana-2978	366	3	(	(	PUNCT
cana-2978	366	4	(	(	PUNCT
cana-2978	366	5	(	(	PUNCT
cana-2978	366	6	a	a	DET
cana-2978	366	7	·	·	SYM
cana-2978	366	8	r	r	NOUN
cana-2978	366	9	`	`	PUNCT
cana-2978	366	10	i	i	PROPN
cana-2978	366	11	)	)	PUNCT
cana-2978	366	12	)	)	PUNCT
cana-2978	367	1	τ	τ	PROPN
cana-2978	367	2	)	)	PUNCT
cana-2978	368	1	τ)ωi	τ)ωi	PROPN
cana-2978	368	2	)	)	PUNCT
cana-2978	368	3	1	1	NUM
cana-2978	368	4	/	/	SYM
cana-2978	368	5	τ	τ	X
cana-2978	368	6	·	·	PUNCT
cana-2978	368	7	e	e	X
cana-2978	368	8	(	(	PUNCT
cana-2978	368	9	τ	τ	X
cana-2978	368	10	√√√√√√1−	√√√√√√1−	NUM
cana-2978	368	11	⊗̀	⊗̀	NOUN
cana-2978	368	12	i=1	i=1	PROPN
cana-2978	368	13	(	(	PUNCT
cana-2978	368	14	1−	1−	NUM
cana-2978	368	15	(	(	PUNCT
cana-2978	368	16	(	(	PUNCT
cana-2978	368	17	(	(	PUNCT
cana-2978	368	18	a	a	PRON
cana-2978	368	19	·	·	PUNCT
cana-2978	368	20	i	i	PRON
cana-2978	368	21	`	`	PUNCT
cana-2978	368	22	i	i	PROPN
cana-2978	368	23	)	)	PUNCT
cana-2978	368	24	)	)	PUNCT
cana-2978	368	25	τ	τ	PROPN
cana-2978	368	26	)	)	PUNCT
cana-2978	368	27	τ)ωi	τ)ωi	PROPN
cana-2978	368	28	)	)	PUNCT
cana-2978	368	29	1	1	NUM
cana-2978	368	30	/	/	SYM
cana-2978	368	31	τ	τ	PROPN
cana-2978	368	32			NUM
cana-2978	368	33	.	.	PUNCT
cana-2978	369	1	corollary	corollary	ADJ
cana-2978	369	2	4.14	4.14	NUM
cana-2978	369	3	.	.	PUNCT
cana-2978	370	1	(	(	PUNCT
cana-2978	370	2	i	i	NOUN
cana-2978	370	3	)	)	PUNCT
cana-2978	370	4	when	when	SCONJ
cana-2978	370	5	∂	∂	ADV
cana-2978	370	6	=	=	SYM
cana-2978	370	7	1	1	NUM
cana-2978	370	8	,	,	PUNCT
cana-2978	370	9	the	the	DET
cana-2978	370	10	gct	gct	PROPN
cana-2978	370	11	(	(	PUNCT
cana-2978	370	12	γ	γ	PROPN
cana-2978	370	13	,	,	PUNCT
cana-2978	370	14	τ)-rung	τ)-rung	PUNCT
cana-2978	370	15	fnwg	fnwg	PROPN
cana-2978	370	16	is	be	AUX
cana-2978	370	17	converted	convert	VERB
cana-2978	370	18	to	to	ADP
cana-2978	370	19	the	the	DET
cana-2978	370	20	(	(	PUNCT
cana-2978	370	21	γ	γ	PROPN
cana-2978	370	22	,	,	PUNCT
cana-2978	370	23	τ)-rung	τ)-rung	PUNCT
cana-2978	370	24	fnwg	fnwg	ADJ
cana-2978	370	25	.	.	PUNCT
cana-2978	371	1	(	(	PUNCT
cana-2978	371	2	ii	ii	X
cana-2978	371	3	)	)	PUNCT
cana-2978	371	4	gct(γ	gct(γ	PROPN
cana-2978	371	5	,	,	PUNCT
cana-2978	371	6	τ)-rung	τ)-rung	PUNCT
cana-2978	371	7	fnwg	fnwg	PROPN
cana-2978	371	8	operators	operator	NOUN
cana-2978	371	9	satisfy	satisfy	VERB
cana-2978	371	10	the	the	DET
cana-2978	371	11	boundedness	boundedness	NOUN
cana-2978	371	12	and	and	CCONJ
cana-2978	371	13	monotonicity	monotonicity	NOUN
cana-2978	371	14	characteristics	characteristic	NOUN
cana-2978	371	15	.	.	PUNCT
cana-2978	372	1	(	(	PUNCT
cana-2978	372	2	iii	iii	X
cana-2978	372	3	)	)	PUNCT
cana-2978	372	4	if	if	SCONJ
cana-2978	372	5	all	all	DET
cana-2978	372	6	θi	θi	ADP
cana-2978	372	7	=	=	SYM
cana-2978	372	8	〈	〈	PROPN
cana-2978	372	9	(	(	PUNCT
cana-2978	372	10	(	(	PUNCT
cana-2978	372	11	(	(	PUNCT
cana-2978	372	12	a	a	DET
cana-2978	372	13	·	·	PUNCT
cana-2978	372	14	rᵀ	rᵀ	NOUN
cana-2978	372	15	i	i	NOUN
cana-2978	372	16	)	)	PUNCT
cana-2978	372	17	·	·	PUNCT
cana-2978	373	1	e(a·i	e(a·i	NOUN
cana-2978	373	2	ᵀ	ᵀ	VERB
cana-2978	373	3	i	i	PROPN
cana-2978	373	4	)	)	PUNCT
cana-2978	373	5	,	,	PUNCT
cana-2978	373	6	(	(	PUNCT
cana-2978	373	7	a	a	DET
cana-2978	373	8	·	·	SYM
cana-2978	373	9	r	r	NOUN
cana-2978	373	10	`	`	PUNCT
cana-2978	373	11	i	i	PROPN
cana-2978	373	12	)	)	PUNCT
cana-2978	373	13	·	·	PUNCT
cana-2978	374	1	e(a·i	e(a·i	NOUN
cana-2978	374	2	`	`	PUNCT
cana-2978	374	3	i	i	PROPN
cana-2978	374	4	)	)	PUNCT
cana-2978	374	5	)	)	PUNCT
cana-2978	374	6	)	)	PUNCT
cana-2978	374	7	〉	〉	NOUN
cana-2978	374	8	are	be	AUX
cana-2978	374	9	equal	equal	ADJ
cana-2978	374	10	.	.	PUNCT
cana-2978	375	1	then	then	ADV
cana-2978	375	2	gct(γ	gct(γ	PROPN
cana-2978	375	3	,	,	PUNCT
cana-2978	375	4	τ)-rung	τ)-rung	PUNCT
cana-2978	376	1	fnwg(θ1,θ2	fnwg(θ1,θ2	PROPN
cana-2978	376	2	,	,	PUNCT
cana-2978	376	3	...	...	PUNCT
cana-2978	376	4	,	,	PUNCT
cana-2978	376	5	θ	θ	NOUN
cana-2978	376	6	`	`	PUNCT
cana-2978	376	7	)	)	PUNCT
cana-2978	376	8	=	=	SYM
cana-2978	376	9	θ	θ	X
cana-2978	376	10	.	.	PUNCT
cana-2978	376	11	references	reference	NOUN
cana-2978	376	12	[	[	X
cana-2978	376	13	1	1	NUM
cana-2978	376	14	]	]	PUNCT
cana-2978	376	15	l.	l.	PROPN
cana-2978	376	16	a.	a.	PROPN
cana-2978	376	17	zadeh	zadeh	PROPN
cana-2978	376	18	,	,	PUNCT
cana-2978	376	19	fuzzy	fuzzy	ADJ
cana-2978	376	20	sets	set	NOUN
cana-2978	376	21	,	,	PUNCT
cana-2978	376	22	information	information	NOUN
cana-2978	376	23	and	and	CCONJ
cana-2978	376	24	control	control	NOUN
cana-2978	376	25	,	,	PUNCT
cana-2978	376	26	8(3	8(3	NUM
cana-2978	376	27	)	)	PUNCT
cana-2978	376	28	,	,	PUNCT
cana-2978	376	29	(	(	PUNCT
cana-2978	376	30	1965	1965	NUM
cana-2978	376	31	)	)	PUNCT
cana-2978	376	32	,	,	PUNCT
cana-2978	376	33	338	338	NUM
cana-2978	376	34	-	-	SYM
cana-2978	376	35	353	353	NUM
cana-2978	376	36	.	.	PUNCT
cana-2978	377	1	[	[	X
cana-2978	377	2	2	2	NUM
cana-2978	377	3	]	]	PUNCT
cana-2978	377	4	k.	k.	PROPN
cana-2978	377	5	atanassov	atanassov	PROPN
cana-2978	377	6	,	,	PUNCT
cana-2978	377	7	intuitionistic	intuitionistic	ADJ
cana-2978	377	8	fuzzy	fuzzy	ADJ
cana-2978	377	9	sets	set	NOUN
cana-2978	377	10	,	,	PUNCT
cana-2978	377	11	fuzzy	fuzzy	ADJ
cana-2978	377	12	sets	set	NOUN
cana-2978	377	13	and	and	CCONJ
cana-2978	377	14	systems	system	NOUN
cana-2978	377	15	,	,	PUNCT
cana-2978	377	16	20(1	20(1	NUM
cana-2978	377	17	)	)	PUNCT
cana-2978	377	18	,	,	PUNCT
cana-2978	377	19	(	(	PUNCT
cana-2978	377	20	1986	1986	NUM
cana-2978	377	21	)	)	PUNCT
cana-2978	377	22	,	,	PUNCT
cana-2978	377	23	87–96	87–96	NUM
cana-2978	377	24	.	.	PUNCT
cana-2978	378	1	[	[	X
cana-2978	378	2	3	3	X
cana-2978	378	3	]	]	X
cana-2978	378	4	r.	r.	PROPN
cana-2978	378	5	r.	r.	PROPN
cana-2978	378	6	yager	yager	PROPN
cana-2978	378	7	,	,	PUNCT
cana-2978	378	8	pythagorean	pythagorean	PROPN
cana-2978	378	9	membership	membership	NOUN
cana-2978	378	10	grades	grade	NOUN
cana-2978	378	11	in	in	ADP
cana-2978	378	12	multi	multi	ADJ
cana-2978	378	13	criteria	criterion	NOUN
cana-2978	378	14	decision	decision	NOUN
cana-2978	378	15	-	-	PUNCT
cana-2978	378	16	making	making	NOUN
cana-2978	378	17	,	,	PUNCT
cana-2978	378	18	ieee	ieee	NOUN
cana-2978	378	19	trans	tran	NOUN
cana-2978	378	20	.	.	PUNCT
cana-2978	379	1	fuzzy	fuzzy	ADJ
cana-2978	379	2	systems	system	NOUN
cana-2978	379	3	,	,	PUNCT
cana-2978	379	4	22	22	NUM
cana-2978	379	5	,	,	PUNCT
cana-2978	379	6	(	(	PUNCT
cana-2978	379	7	2014	2014	NUM
cana-2978	379	8	)	)	PUNCT
cana-2978	379	9	,	,	PUNCT
cana-2978	379	10	958–965	958–965	NUM
cana-2978	379	11	.	.	PUNCT
cana-2978	380	1	[	[	X
cana-2978	380	2	4	4	NUM
cana-2978	380	3	]	]	SYM
cana-2978	380	4	b.c	b.c	PROPN
cana-2978	380	5	.	.	PROPN
cana-2978	380	6	cuong	cuong	PROPN
cana-2978	380	7	and	and	CCONJ
cana-2978	380	8	v.	v.	ADP
cana-2978	380	9	kreinovich	kreinovich	ADJ
cana-2978	380	10	,	,	PUNCT
cana-2978	380	11	picture	picture	NOUN
cana-2978	380	12	fuzzy	fuzzy	ADJ
cana-2978	380	13	sets	set	VERB
cana-2978	380	14	a	a	DET
cana-2978	380	15	new	new	ADJ
cana-2978	380	16	concept	concept	NOUN
cana-2978	380	17	for	for	ADP
cana-2978	380	18	computational	computational	ADJ
cana-2978	380	19	intelligence	intelligence	NOUN
cana-2978	380	20	problems	problem	NOUN
cana-2978	380	21	,	,	PUNCT
cana-2978	380	22	in	in	ADP
cana-2978	380	23	proceedings	proceeding	NOUN
cana-2978	380	24	of	of	ADP
cana-2978	380	25	2013	2013	NUM
cana-2978	380	26	third	third	ADJ
cana-2978	380	27	world	world	NOUN
cana-2978	380	28	congress	congress	PROPN
cana-2978	380	29	on	on	ADP
cana-2978	380	30	information	information	NOUN
cana-2978	380	31	and	and	CCONJ
cana-2978	380	32	communication	communication	NOUN
cana-2978	380	33	technologies	technology	NOUN
cana-2978	380	34	(	(	PUNCT
cana-2978	380	35	wict	wict	NOUN
cana-2978	380	36	2013	2013	NUM
cana-2978	380	37	)	)	PUNCT
cana-2978	380	38	,	,	PUNCT
cana-2978	380	39	ieee	ieee	NOUN
cana-2978	380	40	,	,	PUNCT
cana-2978	380	41	(	(	PUNCT
cana-2978	380	42	2013	2013	NUM
cana-2978	380	43	)	)	PUNCT
cana-2978	380	44	,	,	PUNCT
cana-2978	380	45	1–6	1–6	X
cana-2978	380	46	.	.	PUNCT
cana-2978	381	1	[	[	X
cana-2978	381	2	5	5	X
cana-2978	381	3	]	]	PUNCT
cana-2978	381	4	s.	s.	PROPN
cana-2978	381	5	ashraf	ashraf	PROPN
cana-2978	381	6	,	,	PUNCT
cana-2978	381	7	s.	s.	PROPN
cana-2978	381	8	abdullah	abdullah	PROPN
cana-2978	381	9	,	,	PUNCT
cana-2978	381	10	t.	t.	PROPN
cana-2978	381	11	mahmood	mahmood	PROPN
cana-2978	381	12	,	,	PUNCT
cana-2978	381	13	f.	f.	PROPN
cana-2978	381	14	ghani	ghani	PROPN
cana-2978	381	15	and	and	CCONJ
cana-2978	381	16	t.	t.	PROPN
cana-2978	381	17	mahmood	mahmood	PROPN
cana-2978	381	18	,	,	PUNCT
cana-2978	381	19	spherical	spherical	ADJ
cana-2978	381	20	fuzzy	fuzzy	ADJ
cana-2978	381	21	sets	set	NOUN
cana-2978	381	22	and	and	CCONJ
cana-2978	381	23	their	their	PRON
cana-2978	381	24	applications	application	NOUN
cana-2978	381	25	in	in	ADP
cana-2978	381	26	multi	multi	ADJ
cana-2978	381	27	-	-	ADJ
cana-2978	381	28	attribute	attribute	NOUN
cana-2978	381	29	decision	decision	NOUN
cana-2978	381	30	making	make	VERB
cana-2978	381	31	problems	problem	NOUN
cana-2978	381	32	,	,	PUNCT
cana-2978	381	33	journal	journal	NOUN
cana-2978	381	34	of	of	ADP
cana-2978	381	35	intelligent	intelligent	ADJ
cana-2978	381	36	and	and	CCONJ
cana-2978	381	37	fuzzy	fuzzy	ADJ
cana-2978	381	38	systems	system	NOUN
cana-2978	381	39	,	,	PUNCT
cana-2978	381	40	36	36	NUM
cana-2978	381	41	,	,	PUNCT
cana-2978	381	42	(	(	PUNCT
cana-2978	381	43	2019	2019	NUM
cana-2978	381	44	)	)	PUNCT
cana-2978	381	45	,	,	PUNCT
cana-2978	381	46	2829–284	2829–284	NOUN
cana-2978	381	47	.	.	PUNCT
cana-2978	382	1	[	[	X
cana-2978	382	2	6	6	NUM
cana-2978	382	3	]	]	SYM
cana-2978	382	4	hussain	hussain	PROPN
cana-2978	382	5	,	,	PUNCT
cana-2978	382	6	a.	a.	PROPN
cana-2978	382	7	,	,	PUNCT
cana-2978	382	8	&	&	CCONJ
cana-2978	382	9	ullah	ullah	PROPN
cana-2978	382	10	,	,	PUNCT
cana-2978	382	11	k.	k.	PROPN
cana-2978	383	1	an	an	DET
cana-2978	383	2	intelligent	intelligent	ADJ
cana-2978	383	3	decision	decision	NOUN
cana-2978	383	4	support	support	NOUN
cana-2978	383	5	system	system	NOUN
cana-2978	383	6	for	for	ADP
cana-2978	383	7	spherical	spherical	ADJ
cana-2978	383	8	fuzzy	fuzzy	ADJ
cana-2978	383	9	sugeno	sugeno	NOUN
cana-2978	383	10	-	-	PUNCT
cana-2978	383	11	weber	weber	PROPN
cana-2978	383	12	aggregation	aggregation	NOUN
cana-2978	383	13	operators	operator	NOUN
cana-2978	383	14	and	and	CCONJ
cana-2978	383	15	real	real	ADJ
cana-2978	383	16	-	-	PUNCT
cana-2978	383	17	life	life	NOUN
cana-2978	383	18	applications	application	NOUN
cana-2978	383	19	.	.	PUNCT
cana-2978	384	1	spectrum	spectrum	NOUN
cana-2978	384	2	of	of	ADP
cana-2978	384	3	mechanical	mechanical	ADJ
cana-2978	384	4	engineering	engineering	NOUN
cana-2978	384	5	and	and	CCONJ
cana-2978	384	6	operational	operational	ADJ
cana-2978	384	7	research	research	NOUN
cana-2978	384	8	,	,	PUNCT
cana-2978	384	9	1(1	1(1	NUM
cana-2978	384	10	)	)	PUNCT
cana-2978	384	11	,	,	PUNCT
cana-2978	384	12	(	(	PUNCT
cana-2978	384	13	2024	2024	NUM
cana-2978	384	14	)	)	PUNCT
cana-2978	384	15	,	,	PUNCT
cana-2978	384	16	177	177	NUM
cana-2978	384	17	-	-	SYM
cana-2978	384	18	188	188	NUM
cana-2978	384	19	.	.	PUNCT
cana-2978	385	1	[	[	X
cana-2978	385	2	7	7	X
cana-2978	385	3	]	]	PUNCT
cana-2978	385	4	z.	z.	PROPN
cana-2978	385	5	xu	xu	PROPN
cana-2978	385	6	,	,	PUNCT
cana-2978	385	7	r.r	r.r	PROPN
cana-2978	385	8	.	.	PROPN
cana-2978	385	9	yager	yager	PROPN
cana-2978	385	10	,	,	PUNCT
cana-2978	385	11	some	some	DET
cana-2978	385	12	geometric	geometric	ADJ
cana-2978	385	13	aggregation	aggregation	NOUN
cana-2978	385	14	operators	operator	NOUN
cana-2978	385	15	based	base	VERB
cana-2978	385	16	on	on	ADP
cana-2978	385	17	intuitionistic	intuitionistic	ADJ
cana-2978	385	18	fuzzy	fuzzy	ADJ
cana-2978	385	19	sets	set	NOUN
cana-2978	385	20	,	,	PUNCT
cana-2978	385	21	int	int	NOUN
cana-2978	385	22	.	.	PUNCT
cana-2978	386	1	j.	j.	PROPN
cana-2978	386	2	gen	gen	PROPN
cana-2978	386	3	.	.	PROPN
cana-2978	386	4	syst	syst	PROPN
cana-2978	386	5	.	.	PROPN
cana-2978	386	6	35	35	NUM
cana-2978	386	7	,	,	PUNCT
cana-2978	386	8	(	(	PUNCT
cana-2978	386	9	2006	2006	NUM
cana-2978	386	10	)	)	PUNCT
cana-2978	386	11	,	,	PUNCT
cana-2978	386	12	417–433	417–433	NUM
cana-2978	386	13	.	.	PUNCT
cana-2978	387	1	[	[	X
cana-2978	387	2	8	8	NUM
cana-2978	387	3	]	]	X
cana-2978	387	4	d.f	d.f	PROPN
cana-2978	387	5	.	.	PROPN
cana-2978	387	6	li	li	PROPN
cana-2978	387	7	,	,	PUNCT
cana-2978	387	8	multi	multi	ADJ
cana-2978	387	9	-	-	ADJ
cana-2978	387	10	attribute	attribute	ADJ
cana-2978	387	11	decision	decision	NOUN
cana-2978	387	12	making	make	VERB
cana-2978	387	13	method	method	NOUN
cana-2978	387	14	based	base	VERB
cana-2978	387	15	on	on	ADP
cana-2978	387	16	generalized	generalized	ADJ
cana-2978	387	17	owa	owa	PROPN
cana-2978	387	18	operators	operator	NOUN
cana-2978	387	19	with	with	ADP
cana-2978	387	20	intuitionistic	intuitionistic	ADJ
cana-2978	387	21	fuzzy	fuzzy	ADJ
cana-2978	387	22	sets	set	NOUN
cana-2978	387	23	,	,	PUNCT
cana-2978	387	24	expert	expert	NOUN
cana-2978	387	25	syst	syst	NOUN
cana-2978	387	26	.	.	PUNCT
cana-2978	388	1	appl	appl	PROPN
cana-2978	388	2	.	.	PUNCT
cana-2978	389	1	37	37	NUM
cana-2978	389	2	,	,	PUNCT
cana-2978	389	3	(	(	PUNCT
cana-2978	389	4	2010	2010	NUM
cana-2978	389	5	)	)	PUNCT
cana-2978	389	6	,	,	PUNCT
cana-2978	389	7	8673–8678	8673–8678	NUM
cana-2978	389	8	.	.	PUNCT
cana-2978	390	1	[	[	X
cana-2978	390	2	9	9	NUM
cana-2978	390	3	]	]	X
cana-2978	390	4	abdallah	abdallah	PROPN
cana-2978	390	5	shihadeh	shihadeh	PROPN
cana-2978	390	6	,	,	PUNCT
cana-2978	390	7	khaled	khaled	PROPN
cana-2978	390	8	ahmad	ahmad	PROPN
cana-2978	390	9	mohammad	mohammad	PROPN
cana-2978	390	10	matarneh	matarneh	PROPN
cana-2978	390	11	,	,	PUNCT
cana-2978	390	12	raed	raed	PROPN
cana-2978	390	13	hatamleh	hatamleh	PROPN
cana-2978	390	14	,	,	PUNCT
cana-2978	390	15	randa	randa	PROPN
cana-2978	390	16	bashir	bashir	PROPN
cana-2978	390	17	yousef	yousef	PROPN
cana-2978	390	18	hijazeen	hijazeen	PROPN
cana-2978	390	19	,	,	PUNCT
cana-2978	390	20	mowafaq	mowafaq	PROPN
cana-2978	390	21	omar	omar	PROPN
cana-2978	390	22	al	al	PROPN
cana-2978	390	23	-	-	PUNCT
cana-2978	390	24	qadri	qadri	PROPN
cana-2978	390	25	,	,	PUNCT
cana-2978	390	26	abdallah	abdallah	PROPN
cana-2978	390	27	al	al	PROPN
cana-2978	390	28	-	-	PUNCT
cana-2978	390	29	husban	husban	PROPN
cana-2978	390	30	,	,	PUNCT
cana-2978	390	31	an	an	DET
cana-2978	390	32	example	example	NOUN
cana-2978	390	33	of	of	ADP
cana-2978	390	34	two	two	NUM
cana-2978	390	35	-	-	PUNCT
cana-2978	390	36	fold	fold	ADJ
cana-2978	390	37	fuzzy	fuzzy	ADJ
cana-2978	390	38	algebras	algebra	NOUN
cana-2978	390	39	based	base	VERB
cana-2978	390	40	on	on	ADP
cana-2978	390	41	neutrosophic	neutrosophic	ADJ
cana-2978	390	42	real	real	ADJ
cana-2978	390	43	numbers	number	NOUN
cana-2978	390	44	,	,	PUNCT
cana-2978	390	45	neutrosophic	neutrosophic	ADJ
cana-2978	390	46	sets	set	NOUN
cana-2978	390	47	and	and	CCONJ
cana-2978	390	48	systems	system	NOUN
cana-2978	390	49	,	,	PUNCT
cana-2978	390	50	67	67	NUM
cana-2978	390	51	,	,	PUNCT
cana-2978	390	52	(	(	PUNCT
cana-2978	390	53	2024	2024	NUM
cana-2978	390	54	)	)	PUNCT
cana-2978	390	55	,	,	PUNCT
cana-2978	390	56	169	169	NUM
cana-2978	390	57	-	-	SYM
cana-2978	390	58	178	178	NUM
cana-2978	390	59	.	.	PUNCT
cana-2978	391	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	391	2	142	142	NUM
cana-2978	391	3	communications	communication	NOUN
cana-2978	391	4	on	on	ADP
cana-2978	391	5	applied	apply	VERB
cana-2978	391	6	nonlinear	nonlinear	ADJ
cana-2978	391	7	analysis	analysis	NOUN
cana-2978	391	8	issn	issn	NOUN
cana-2978	391	9	:	:	PUNCT
cana-2978	391	10	1074	1074	NUM
cana-2978	391	11	-	-	PUNCT
cana-2978	391	12	133x	133x	NUM
cana-2978	391	13	vol	vol	NOUN
cana-2978	391	14	32	32	NUM
cana-2978	391	15	no	no	NOUN
cana-2978	391	16	.	.	PUNCT
cana-2978	392	1	5s	5s	NUM
cana-2978	392	2	(	(	PUNCT
cana-2978	392	3	2025	2025	NUM
cana-2978	392	4	)	)	PUNCT
cana-2978	393	1	[	[	X
cana-2978	393	2	10	10	NUM
cana-2978	393	3	]	]	PUNCT
cana-2978	393	4	a.	a.	NOUN
cana-2978	393	5	rajalakshmi	rajalakshmi	NOUN
cana-2978	393	6	,	,	PUNCT
cana-2978	393	7	raed	raed	PROPN
cana-2978	393	8	hatamleh	hatamleh	PROPN
cana-2978	393	9	,	,	PUNCT
cana-2978	393	10	abdallah	abdallah	PROPN
cana-2978	393	11	al	al	PROPN
cana-2978	393	12	-	-	PUNCT
cana-2978	393	13	husban	husban	PROPN
cana-2978	393	14	,	,	PUNCT
cana-2978	393	15	k.	k.	PROPN
cana-2978	393	16	lenin	lenin	PROPN
cana-2978	393	17	muthu	muthu	PROPN
cana-2978	393	18	kumaran	kumaran	PROPN
cana-2978	393	19	,	,	PUNCT
cana-2978	393	20	m.	m.	PROPN
cana-2978	393	21	s.	s.	PROPN
cana-2978	393	22	malchijah	malchijah	PROPN
cana-2978	393	23	raj	raj	PROPN
cana-2978	393	24	,	,	PUNCT
cana-2978	393	25	various	various	ADJ
cana-2978	393	26	neutrosophic	neutrosophic	ADJ
cana-2978	393	27	ideals	ideal	NOUN
cana-2978	393	28	of	of	ADP
cana-2978	393	29	an	an	DET
cana-2978	393	30	ordered	order	VERB
cana-2978	393	31	ternary	ternary	ADJ
cana-2978	393	32	semigroups	semigroup	NOUN
cana-2978	393	33	.	.	PUNCT
cana-2978	394	1	32	32	NUM
cana-2978	394	2	(	(	PUNCT
cana-2978	394	3	3	3	NUM
cana-2978	394	4	)	)	PUNCT
cana-2978	394	5	,	,	PUNCT
cana-2978	394	6	(	(	PUNCT
cana-2978	394	7	2025	2025	NUM
cana-2978	394	8	)	)	PUNCT
cana-2978	394	9	,	,	PUNCT
cana-2978	394	10	400	400	NUM
cana-2978	394	11	-	-	SYM
cana-2978	394	12	417	417	NUM
cana-2978	394	13	.	.	PUNCT
cana-2978	395	1	[	[	X
cana-2978	395	2	11	11	NUM
cana-2978	395	3	]	]	PUNCT
cana-2978	395	4	abdallah	abdallah	PROPN
cana-2978	395	5	al	al	PROPN
cana-2978	395	6	-	-	PROPN
cana-2978	395	7	husban	husban	PROPN
cana-2978	395	8	&	&	CCONJ
cana-2978	395	9	abdul	abdul	PROPN
cana-2978	395	10	razak	razak	PROPN
cana-2978	395	11	salleh	salleh	PROPN
cana-2978	395	12	,	,	PUNCT
cana-2978	395	13	complex	complex	ADJ
cana-2978	395	14	fuzzy	fuzzy	ADJ
cana-2978	395	15	ring	ring	NOUN
cana-2978	395	16	.	.	PUNCT
cana-2978	396	1	proceedings	proceeding	NOUN
cana-2978	396	2	of	of	ADP
cana-2978	396	3	2nd	2nd	ADJ
cana-2978	396	4	international	international	ADJ
cana-2978	396	5	conference	conference	NOUN
cana-2978	396	6	on	on	ADP
cana-2978	396	7	computing	computing	NOUN
cana-2978	396	8	,	,	PUNCT
cana-2978	396	9	mathematics	mathematic	NOUN
cana-2978	396	10	and	and	CCONJ
cana-2978	396	11	statistics	statistic	NOUN
cana-2978	396	12	,	,	PUNCT
cana-2978	396	13	(	(	PUNCT
cana-2978	396	14	2015	2015	NUM
cana-2978	396	15	)	)	PUNCT
cana-2978	396	16	,	,	PUNCT
cana-2978	396	17	241	241	NUM
cana-2978	396	18	-	-	SYM
cana-2978	396	19	245	245	NUM
cana-2978	396	20	.	.	PUNCT
cana-2978	397	1	[	[	X
cana-2978	397	2	12	12	NUM
cana-2978	397	3	]	]	PUNCT
cana-2978	397	4	.	.	PUNCT
cana-2978	398	1	abdallah	abdallah	PROPN
cana-2978	398	2	al	al	PROPN
cana-2978	398	3	-	-	PROPN
cana-2978	398	4	husban	husban	PROPN
cana-2978	398	5	&	&	CCONJ
cana-2978	398	6	abdul	abdul	PROPN
cana-2978	398	7	razak	razak	PROPN
cana-2978	398	8	salleh	salleh	PROPN
cana-2978	398	9	2015	2015	NUM
cana-2978	398	10	.	.	PUNCT
cana-2978	399	1	complex	complex	ADJ
cana-2978	399	2	fuzzy	fuzzy	ADJ
cana-2978	399	3	hyperring	hyperring	NOUN
cana-2978	399	4	based	base	VERB
cana-2978	399	5	on	on	ADP
cana-2978	399	6	complex	complex	ADJ
cana-2978	399	7	fuzzy	fuzzy	ADJ
cana-2978	399	8	spaces	space	NOUN
cana-2978	399	9	.	.	PUNCT
cana-2978	400	1	proceedings	proceeding	NOUN
cana-2978	400	2	of	of	ADP
cana-2978	400	3	2nd	2nd	ADJ
cana-2978	400	4	innovation	innovation	NOUN
cana-2978	400	5	and	and	CCONJ
cana-2978	400	6	analytics	analytic	NOUN
cana-2978	400	7	conference	conference	NOUN
cana-2978	400	8	&	&	CCONJ
cana-2978	400	9	exhibition	exhibition	PROPN
cana-2978	400	10	(	(	PUNCT
cana-2978	400	11	iace	iace	NOUN
cana-2978	400	12	)	)	PUNCT
cana-2978	400	13	,	,	PUNCT
cana-2978	400	14	1691	1691	NUM
cana-2978	400	15	,	,	PUNCT
cana-2978	400	16	aip	aip	PROPN
cana-2978	400	17	publishing	publish	VERB
cana-2978	400	18	2015	2015	NUM
cana-2978	400	19	,	,	PUNCT
cana-2978	400	20	040009	040009	NUM
cana-2978	400	21	-	-	SYM
cana-2978	400	22	040017	040017	NUM
cana-2978	400	23	.	.	PUNCT
cana-2978	401	1	[	[	X
cana-2978	401	2	13	13	NUM
cana-2978	401	3	]	]	X
cana-2978	401	4	al	al	PROPN
cana-2978	401	5	-	-	PUNCT
cana-2978	401	6	husban	husban	PROPN
cana-2978	401	7	,	,	PUNCT
cana-2978	401	8	a.	a.	PROPN
cana-2978	401	9	,	,	PUNCT
cana-2978	401	10	&	&	CCONJ
cana-2978	401	11	salleh	salleh	PROPN
cana-2978	401	12	,	,	PUNCT
cana-2978	401	13	a.	a.	PROPN
cana-2978	401	14	r.	r.	PROPN
cana-2978	401	15	complex	complex	PROPN
cana-2978	401	16	fuzzy	fuzzy	ADJ
cana-2978	401	17	hypergroups	hypergroup	NOUN
cana-2978	401	18	based	base	VERB
cana-2978	401	19	on	on	ADP
cana-2978	401	20	complex	complex	ADJ
cana-2978	401	21	fuzzy	fuzzy	ADJ
cana-2978	401	22	spaces	space	NOUN
cana-2978	401	23	.	.	PUNCT
cana-2978	402	1	international	international	ADJ
cana-2978	402	2	journal	journal	NOUN
cana-2978	402	3	of	of	ADP
cana-2978	402	4	pure	pure	ADJ
cana-2978	402	5	and	and	CCONJ
cana-2978	402	6	applied	applied	ADJ
cana-2978	402	7	mathematics	mathematic	NOUN
cana-2978	402	8	,	,	PUNCT
cana-2978	402	9	107(4	107(4	NUM
cana-2978	402	10	)	)	PUNCT
cana-2978	402	11	,	,	PUNCT
cana-2978	402	12	(	(	PUNCT
cana-2978	402	13	2016	2016	NUM
cana-2978	402	14	)	)	PUNCT
cana-2978	402	15	,	,	PUNCT
cana-2978	402	16	949	949	NUM
cana-2978	402	17	-	-	SYM
cana-2978	402	18	958	958	NUM
cana-2978	402	19	.	.	PUNCT
cana-2978	403	1	[	[	X
cana-2978	403	2	14	14	NUM
cana-2978	403	3	]	]	X
cana-2978	403	4	al	al	PROPN
cana-2978	403	5	-	-	PUNCT
cana-2978	403	6	husban	husban	PROPN
cana-2978	403	7	,	,	PUNCT
cana-2978	403	8	a.	a.	PROPN
cana-2978	403	9	,	,	PUNCT
cana-2978	403	10	amourah	amourah	PROPN
cana-2978	403	11	,	,	PUNCT
cana-2978	403	12	a.	a.	PROPN
cana-2978	403	13	,	,	PUNCT
cana-2978	403	14	&	&	CCONJ
cana-2978	403	15	jaber	jaber	PROPN
cana-2978	403	16	,	,	PUNCT
cana-2978	403	17	j.	j.	PROPN
cana-2978	403	18	j.	j.	PROPN
cana-2978	403	19	bipolar	bipolar	PROPN
cana-2978	403	20	complex	complex	ADJ
cana-2978	403	21	fuzzy	fuzzy	ADJ
cana-2978	403	22	sets	set	NOUN
cana-2978	403	23	and	and	CCONJ
cana-2978	403	24	their	their	PRON
cana-2978	403	25	properties	property	NOUN
cana-2978	403	26	.	.	PUNCT
cana-2978	404	1	italian	italian	ADJ
cana-2978	404	2	journal	journal	NOUN
cana-2978	404	3	of	of	ADP
cana-2978	404	4	pure	pure	ADJ
cana-2978	404	5	and	and	CCONJ
cana-2978	404	6	applied	applied	ADJ
cana-2978	404	7	mathematics	mathematic	NOUN
cana-2978	404	8	,	,	PUNCT
cana-2978	404	9	43	43	NUM
cana-2978	404	10	,	,	PUNCT
cana-2978	404	11	2020	2020	NUM
cana-2978	404	12	,	,	PUNCT
cana-2978	404	13	754	754	NUM
cana-2978	404	14	-	-	SYM
cana-2978	404	15	761	761	NUM
cana-2978	404	16	.	.	PUNCT
cana-2978	405	1	[	[	X
cana-2978	405	2	15	15	NUM
cana-2978	405	3	]	]	X
cana-2978	405	4	s.	s.	PROPN
cana-2978	405	5	zeng	zeng	PROPN
cana-2978	405	6	,	,	PUNCT
cana-2978	405	7	w.	w.	PROPN
cana-2978	405	8	sua	sua	PROPN
cana-2978	405	9	,	,	PUNCT
cana-2978	405	10	intuitionistic	intuitionistic	ADJ
cana-2978	405	11	fuzzy	fuzzy	ADJ
cana-2978	405	12	ordered	order	VERB
cana-2978	405	13	weighted	weight	VERB
cana-2978	405	14	distance	distance	NOUN
cana-2978	405	15	operator	operator	NOUN
cana-2978	405	16	,	,	PUNCT
cana-2978	405	17	knowl	knowl	NOUN
cana-2978	405	18	.	.	PUNCT
cana-2978	405	19	based	base	VERB
cana-2978	405	20	syst	syst	PROPN
cana-2978	405	21	.	.	PUNCT
cana-2978	406	1	24	24	NUM
cana-2978	406	2	,	,	PUNCT
cana-2978	406	3	(	(	PUNCT
cana-2978	406	4	2011	2011	NUM
cana-2978	406	5	)	)	PUNCT
cana-2978	406	6	,	,	PUNCT
cana-2978	406	7	1224–1232	1224–1232	NOUN
cana-2978	406	8	.	.	PUNCT
cana-2978	407	1	[	[	X
cana-2978	407	2	16	16	NUM
cana-2978	407	3	]	]	PUNCT
cana-2978	407	4	x.	x.	PROPN
cana-2978	407	5	peng	peng	PROPN
cana-2978	407	6	,	,	PUNCT
cana-2978	407	7	h.	h.	PROPN
cana-2978	407	8	yuan	yuan	PROPN
cana-2978	407	9	,	,	PUNCT
cana-2978	407	10	fundamental	fundamental	ADJ
cana-2978	407	11	properties	property	NOUN
cana-2978	407	12	of	of	ADP
cana-2978	407	13	pythagorean	pythagorean	ADJ
cana-2978	407	14	fuzzy	fuzzy	ADJ
cana-2978	407	15	aggregation	aggregation	NOUN
cana-2978	407	16	operators	operator	NOUN
cana-2978	407	17	,	,	PUNCT
cana-2978	407	18	fundam	fundam	ADJ
cana-2978	407	19	.	.	PUNCT
cana-2978	408	1	inform	inform	NOUN
cana-2978	408	2	.	.	PUNCT
cana-2978	409	1	147	147	NUM
cana-2978	409	2	,	,	PUNCT
cana-2978	409	3	(	(	PUNCT
cana-2978	409	4	2016	2016	NUM
cana-2978	409	5	)	)	PUNCT
cana-2978	409	6	,	,	PUNCT
cana-2978	410	1	415–446	415–446	NUM
cana-2978	410	2	.	.	PUNCT
cana-2978	411	1	[	[	X
cana-2978	411	2	17	17	NUM
cana-2978	411	3	]	]	PUNCT
cana-2978	411	4	m.	m.	NOUN
cana-2978	411	5	palanikumar	palanikumar	PROPN
cana-2978	411	6	,	,	PUNCT
cana-2978	411	7	k.	k.	PROPN
cana-2978	411	8	arulmozhi	arulmozhi	PROPN
cana-2978	411	9	,	,	PUNCT
cana-2978	411	10	a	a	DET
cana-2978	411	11	iampan	iampan	NOUN
cana-2978	411	12	,	,	PUNCT
cana-2978	411	13	multi	multi	X
cana-2978	411	14	criteria	criterion	NOUN
cana-2978	411	15	group	group	NOUN
cana-2978	411	16	decision	decision	NOUN
cana-2978	411	17	making	making	NOUN
cana-2978	411	18	based	base	VERB
cana-2978	411	19	on	on	ADP
cana-2978	411	20	vikorand	vikorand	NOUN
cana-2978	411	21	topsis	topsis	NOUN
cana-2978	411	22	methods	method	NOUN
cana-2978	411	23	for	for	ADP
cana-2978	411	24	fermatean	fermatean	ADJ
cana-2978	411	25	fuzzy	fuzzy	ADJ
cana-2978	411	26	soft	soft	ADJ
cana-2978	411	27	with	with	ADP
cana-2978	411	28	aggregation	aggregation	NOUN
cana-2978	411	29	operators	operator	NOUN
cana-2978	411	30	,	,	PUNCT
cana-2978	411	31	icic	icic	PROPN
cana-2978	411	32	express	express	PROPN
cana-2978	411	33	letters	letter	NOUN
cana-2978	411	34	16	16	NUM
cana-2978	411	35	(	(	PUNCT
cana-2978	411	36	10	10	NUM
cana-2978	411	37	)	)	PUNCT
cana-2978	411	38	,	,	PUNCT
cana-2978	411	39	(	(	PUNCT
cana-2978	411	40	2022	2022	NUM
cana-2978	411	41	)	)	PUNCT
cana-2978	411	42	,	,	PUNCT
cana-2978	411	43	1129–1138	1129–1138	NUM
cana-2978	411	44	.	.	PUNCT
cana-2978	412	1	[	[	X
cana-2978	412	2	18	18	NUM
cana-2978	412	3	]	]	PUNCT
cana-2978	412	4	m.	m.	NOUN
cana-2978	412	5	palanikumar	palanikumar	PROPN
cana-2978	412	6	,	,	PUNCT
cana-2978	412	7	k.	k.	PROPN
cana-2978	412	8	arulmozhi	arulmozhi	PROPN
cana-2978	412	9	,	,	PUNCT
cana-2978	412	10	mcgdm	mcgdm	NOUN
cana-2978	412	11	based	base	VERB
cana-2978	412	12	on	on	ADP
cana-2978	412	13	topsis	topsis	NOUN
cana-2978	412	14	and	and	CCONJ
cana-2978	412	15	vikorusing	vikoruse	VERB
cana-2978	412	16	pythagorean	pythagorean	PROPN
cana-2978	412	17	neutrosophic	neutrosophic	PROPN
cana-2978	412	18	soft	soft	ADJ
cana-2978	412	19	with	with	ADP
cana-2978	412	20	aggregation	aggregation	NOUN
cana-2978	412	21	operators	operator	NOUN
cana-2978	412	22	,	,	PUNCT
cana-2978	412	23	neutrosophic	neutrosophic	ADJ
cana-2978	412	24	sets	set	NOUN
cana-2978	412	25	and	and	CCONJ
cana-2978	412	26	systems	system	NOUN
cana-2978	412	27	,	,	PUNCT
cana-2978	412	28	(	(	PUNCT
cana-2978	412	29	2022	2022	NUM
cana-2978	412	30	)	)	PUNCT
cana-2978	412	31	,	,	PUNCT
cana-2978	412	32	538–555	538–555	NUM
cana-2978	412	33	.	.	PUNCT
cana-2978	413	1	[	[	X
cana-2978	413	2	19	19	NUM
cana-2978	413	3	]	]	PUNCT
cana-2978	413	4	m.	m.	NOUN
cana-2978	413	5	palanikumar	palanikumar	PROPN
cana-2978	413	6	,	,	PUNCT
cana-2978	413	7	n.	n.	PROPN
cana-2978	413	8	kausar	kausar	PROPN
cana-2978	413	9	,	,	PUNCT
cana-2978	413	10	h.	h.	PROPN
cana-2978	413	11	garg	garg	PROPN
cana-2978	413	12	,	,	PUNCT
cana-2978	413	13	a.	a.	NOUN
cana-2978	413	14	iampan	iampan	PROPN
cana-2978	413	15	,	,	PUNCT
cana-2978	413	16	s.	s.	PROPN
cana-2978	413	17	kadry	kadry	PROPN
cana-2978	413	18	,	,	PUNCT
cana-2978	413	19	m.	m.	NOUN
cana-2978	413	20	sharaf	sharaf	PROPN
cana-2978	413	21	,	,	PUNCT
cana-2978	413	22	medical	medical	ADJ
cana-2978	413	23	robotic	robotic	ADJ
cana-2978	413	24	engineering	engineering	NOUN
cana-2978	413	25	selection	selection	NOUN
cana-2978	413	26	based	base	VERB
cana-2978	413	27	on	on	ADP
cana-2978	413	28	square	square	ADJ
cana-2978	413	29	root	root	NOUN
cana-2978	413	30	neutrosophic	neutrosophic	ADJ
cana-2978	413	31	normal	normal	ADJ
cana-2978	413	32	interval	interval	NOUN
cana-2978	413	33	-	-	PUNCT
cana-2978	413	34	valued	value	VERB
cana-2978	413	35	sets	set	NOUN
cana-2978	413	36	and	and	CCONJ
cana-2978	413	37	their	their	PRON
cana-2978	413	38	aggregated	aggregate	VERB
cana-2978	413	39	operators	operator	NOUN
cana-2978	413	40	,	,	PUNCT
cana-2978	413	41	aims	aim	VERB
cana-2978	413	42	mathematics	mathematic	NOUN
cana-2978	413	43	,	,	PUNCT
cana-2978	413	44	8(8	8(8	NUM
cana-2978	413	45	)	)	PUNCT
cana-2978	413	46	,	,	PUNCT
cana-2978	413	47	(	(	PUNCT
cana-2978	413	48	2023	2023	NUM
cana-2978	413	49	)	)	PUNCT
cana-2978	413	50	,	,	PUNCT
cana-2978	413	51	17402–17432	17402–17432	NUM
cana-2978	413	52	.	.	PUNCT
cana-2978	414	1	[	[	X
cana-2978	414	2	20	20	NUM
cana-2978	414	3	]	]	X
cana-2978	414	4	r.	r.	PROPN
cana-2978	414	5	hatamleh	hatamleh	PROPN
cana-2978	414	6	,	,	PUNCT
cana-2978	414	7	on	on	ADP
cana-2978	414	8	the	the	DET
cana-2978	414	9	compactness	compactness	NOUN
cana-2978	414	10	and	and	CCONJ
cana-2978	414	11	continuity	continuity	NOUN
cana-2978	414	12	of	of	ADP
cana-2978	414	13	uryson	uryson	PROPN
cana-2978	414	14	’s	’s	PART
cana-2978	414	15	operator	operator	NOUN
cana-2978	414	16	in	in	ADP
cana-2978	414	17	orlicz	orlicz	ADJ
cana-2978	414	18	space	space	NOUN
cana-2978	414	19	,	,	PUNCT
cana-2978	414	20	international	international	ADJ
cana-2978	414	21	journal	journal	NOUN
cana-2978	414	22	of	of	ADP
cana-2978	414	23	neutrosophic	neutrosophic	ADJ
cana-2978	414	24	science	science	NOUN
cana-2978	414	25	,	,	PUNCT
cana-2978	414	26	24	24	NUM
cana-2978	414	27	(	(	PUNCT
cana-2978	414	28	3	3	NUM
cana-2978	414	29	)	)	PUNCT
cana-2978	414	30	,	,	PUNCT
cana-2978	414	31	(	(	PUNCT
cana-2978	414	32	2024	2024	NUM
cana-2978	414	33	)	)	PUNCT
cana-2978	414	34	,	,	PUNCT
cana-2978	414	35	233	233	NUM
cana-2978	414	36	-	-	SYM
cana-2978	414	37	239	239	NUM
cana-2978	414	38	.	.	PUNCT
cana-2978	415	1	[	[	X
cana-2978	415	2	21	21	NUM
cana-2978	415	3	]	]	X
cana-2978	415	4	r.	r.	PROPN
cana-2978	415	5	hatamleh	hatamleh	PROPN
cana-2978	415	6	,	,	PUNCT
cana-2978	415	7	on	on	ADP
cana-2978	415	8	the	the	DET
cana-2978	415	9	numerical	numerical	ADJ
cana-2978	415	10	solutions	solution	NOUN
cana-2978	415	11	of	of	ADP
cana-2978	415	12	the	the	DET
cana-2978	415	13	neutrosophic	neutrosophic	ADJ
cana-2978	415	14	one	one	NUM
cana-2978	415	15	-	-	PUNCT
cana-2978	415	16	dimensional	dimensional	ADJ
cana-2978	415	17	sine	sine	NOUN
cana-2978	415	18	-	-	PUNCT
cana-2978	415	19	gordon	gordon	NOUN
cana-2978	415	20	system	system	NOUN
cana-2978	415	21	,	,	PUNCT
cana-2978	415	22	international	international	ADJ
cana-2978	415	23	journal	journal	NOUN
cana-2978	415	24	of	of	ADP
cana-2978	415	25	neutrosophic	neutrosophic	ADJ
cana-2978	415	26	science	science	NOUN
cana-2978	415	27	,	,	PUNCT
cana-2978	415	28	25	25	NUM
cana-2978	415	29	(	(	PUNCT
cana-2978	415	30	3	3	NUM
cana-2978	415	31	)	)	PUNCT
cana-2978	415	32	,	,	PUNCT
cana-2978	415	33	(	(	PUNCT
cana-2978	415	34	2024	2024	NUM
cana-2978	415	35	)	)	PUNCT
cana-2978	415	36	,	,	PUNCT
cana-2978	415	37	25	25	NUM
cana-2978	415	38	-	-	SYM
cana-2978	415	39	36	36	NUM
cana-2978	415	40	.	.	PUNCT
cana-2978	416	1	[	[	X
cana-2978	416	2	22	22	NUM
cana-2978	416	3	]	]	X
cana-2978	416	4	r.	r.	PROPN
cana-2978	416	5	hatamleh	hatamleh	PROPN
cana-2978	416	6	,	,	PUNCT
cana-2978	416	7	on	on	ADP
cana-2978	416	8	the	the	DET
cana-2978	416	9	continuous	continuous	ADJ
cana-2978	416	10	and	and	CCONJ
cana-2978	416	11	differentiable	differentiable	ADJ
cana-2978	416	12	two	two	NUM
cana-2978	416	13	-	-	PUNCT
cana-2978	416	14	fold	fold	ADJ
cana-2978	416	15	neutrosophic	neutrosophic	ADJ
cana-2978	416	16	and	and	CCONJ
cana-2978	416	17	fuzzy	fuzzy	ADJ
cana-2978	416	18	real	real	ADJ
cana-2978	416	19	functions	function	NOUN
cana-2978	416	20	,	,	PUNCT
cana-2978	416	21	neutrosophic	neutrosophic	ADJ
cana-2978	416	22	sets	set	NOUN
cana-2978	416	23	and	and	CCONJ
cana-2978	416	24	systems	system	NOUN
cana-2978	416	25	,	,	PUNCT
cana-2978	416	26	75,(2025	75,(2025	NUM
cana-2978	416	27	)	)	PUNCT
cana-2978	416	28	,	,	PUNCT
cana-2978	416	29	196	196	NUM
cana-2978	416	30	-	-	SYM
cana-2978	416	31	209	209	NUM
cana-2978	416	32	.	.	PUNCT
cana-2978	417	1	[	[	X
cana-2978	417	2	23	23	NUM
cana-2978	417	3	]	]	PUNCT
cana-2978	417	4	shihadeh	shihadeh	NOUN
cana-2978	417	5	,	,	PUNCT
cana-2978	417	6	a.	a.	NOUN
cana-2978	417	7	,	,	PUNCT
cana-2978	417	8	matarneh	matarneh	PROPN
cana-2978	417	9	,	,	PUNCT
cana-2978	417	10	k.	k.	PROPN
cana-2978	417	11	a.	a.	PROPN
cana-2978	417	12	m.	m.	PROPN
cana-2978	417	13	,	,	PUNCT
cana-2978	417	14	hatamleh	hatamleh	PROPN
cana-2978	417	15	,	,	PUNCT
cana-2978	417	16	r.	r.	PROPN
cana-2978	417	17	,	,	PUNCT
cana-2978	417	18	al	al	PROPN
cana-2978	417	19	-	-	PUNCT
cana-2978	417	20	qadri	qadri	PROPN
cana-2978	417	21	,	,	PUNCT
cana-2978	417	22	m.	m.	NOUN
cana-2978	417	23	o.	o.	PROPN
cana-2978	417	24	,	,	PUNCT
cana-2978	417	25	&	&	CCONJ
cana-2978	417	26	al	al	PROPN
cana-2978	417	27	-	-	PUNCT
cana-2978	417	28	husban	husban	PROPN
cana-2978	417	29	,	,	PUNCT
cana-2978	417	30	a.	a.	NOUN
cana-2978	417	31	(	(	PUNCT
cana-2978	417	32	2024	2024	NUM
cana-2978	417	33	)	)	PUNCT
cana-2978	417	34	.	.	PUNCT
cana-2978	418	1	on	on	ADP
cana-2978	418	2	the	the	DET
cana-2978	418	3	two	two	NUM
cana-2978	418	4	-	-	ADJ
cana-2978	418	5	fold	fold	ADJ
cana-2978	418	6	fuzzy	fuzzy	ADJ
cana-2978	418	7	n	n	CCONJ
cana-2978	418	8	-	-	PUNCT
cana-2978	418	9	refined	refine	VERB
cana-2978	418	10	neutrosophic	neutrosophic	ADJ
cana-2978	418	11	rings	ring	NOUN
cana-2978	418	12	for	for	ADP
cana-2978	418	13	2=	2=	NUM
cana-2978	418	14	3	3	NUM
cana-2978	418	15	.	.	NUM
cana-2978	418	16	neutrosophic	neutrosophic	ADJ
cana-2978	418	17	sets	set	NOUN
cana-2978	418	18	and	and	CCONJ
cana-2978	418	19	systems	system	NOUN
cana-2978	418	20	,	,	PUNCT
cana-2978	418	21	68	68	NUM
cana-2978	418	22	,	,	PUNCT
cana-2978	418	23	8	8	NUM
cana-2978	418	24	-	-	SYM
cana-2978	418	25	25	25	NUM
cana-2978	418	26	.	.	PUNCT
cana-2978	419	1	[	[	X
cana-2978	419	2	24	24	NUM
cana-2978	419	3	]	]	X
cana-2978	419	4	abdallah	abdallah	PROPN
cana-2978	419	5	shihadeh	shihadeh	PROPN
cana-2978	419	6	,	,	PUNCT
cana-2978	419	7	khaled	khaled	PROPN
cana-2978	419	8	ahmad	ahmad	PROPN
cana-2978	419	9	mohammad	mohammad	PROPN
cana-2978	419	10	matarneh	matarneh	PROPN
cana-2978	419	11	,	,	PUNCT
cana-2978	419	12	raed	raed	PROPN
cana-2978	419	13	hatamleh	hatamleh	PROPN
cana-2978	419	14	,	,	PUNCT
cana-2978	419	15	randa	randa	PROPN
cana-2978	419	16	bashir	bashir	PROPN
cana-2978	419	17	yousef	yousef	PROPN
cana-2978	420	1	hijazeen	hijazeen	PROPN
cana-2978	420	2	,	,	PUNCT
cana-2978	420	3	mowafaq	mowafaq	PROPN
cana-2978	420	4	omar	omar	PROPN
cana-2978	420	5	al	al	PROPN
cana-2978	420	6	-	-	PUNCT
cana-2978	420	7	qadri	qadri	PROPN
cana-2978	420	8	,	,	PUNCT
cana-2978	420	9	abdallah	abdallah	PROPN
cana-2978	420	10	al	al	PROPN
cana-2978	420	11	-	-	PUNCT
cana-2978	420	12	husban.(2024	husban.(2024	NOUN
cana-2978	420	13	)	)	PUNCT
cana-2978	420	14	.	.	PUNCT
cana-2978	421	1	an	an	DET
cana-2978	421	2	example	example	NOUN
cana-2978	421	3	of	of	ADP
cana-2978	421	4	two	two	NUM
cana-2978	421	5	-	-	PUNCT
cana-2978	421	6	fold	fold	ADJ
cana-2978	421	7	fuzzy	fuzzy	ADJ
cana-2978	421	8	algebras	algebra	NOUN
cana-2978	421	9	based	base	VERB
cana-2978	421	10	on	on	ADP
cana-2978	421	11	neutrosophic	neutrosophic	ADJ
cana-2978	421	12	real	real	ADJ
cana-2978	421	13	numbers	number	NOUN
cana-2978	421	14	,	,	PUNCT
cana-2978	421	15	neutrosophic	neutrosophic	ADJ
cana-2978	421	16	sets	set	NOUN
cana-2978	421	17	and	and	CCONJ
cana-2978	421	18	systems	system	NOUN
cana-2978	421	19	,	,	PUNCT
cana-2978	421	20	67,169	67,169	NUM
cana-2978	421	21	-	-	SYM
cana-2978	421	22	178	178	NUM
cana-2978	421	23	.	.	PUNCT
cana-2978	422	1	[	[	X
cana-2978	422	2	25	25	NUM
cana-2978	422	3	]	]	PUNCT
cana-2978	422	4	raed	raed	PROPN
cana-2978	422	5	hatamleh	hatamleh	PROPN
cana-2978	422	6	,	,	PUNCT
cana-2978	422	7	abdallah	abdallah	PROPN
cana-2978	422	8	al	al	PROPN
cana-2978	422	9	-	-	PUNCT
cana-2978	422	10	husban	husban	PROPN
cana-2978	422	11	,	,	PUNCT
cana-2978	422	12	n.	n.	NOUN
cana-2978	422	13	sundarakannan	sundarakannan	NOUN
cana-2978	422	14	,	,	PUNCT
cana-2978	422	15	m.	m.	NOUN
cana-2978	422	16	s.	s.	PROPN
cana-2978	422	17	malchijah	malchijah	PROPN
cana-2978	422	18	raj	raj	PROPN
cana-2978	422	19	.	.	PUNCT
cana-2978	423	1	(	(	PUNCT
cana-2978	423	2	2025	2025	NUM
cana-2978	423	3	)	)	PUNCT
cana-2978	423	4	.	.	PUNCT
cana-2978	424	1	complex	complex	ADJ
cana-2978	424	2	cubic	cubic	ADJ
cana-2978	424	3	intuitionistic	intuitionistic	ADJ
cana-2978	424	4	fuzzy	fuzzy	ADJ
cana-2978	424	5	set	set	NOUN
cana-2978	424	6	applied	apply	VERB
cana-2978	424	7	to	to	ADP
cana-2978	424	8	subbisemirings	subbisemiring	NOUN
cana-2978	424	9	of	of	ADP
cana-2978	424	10	bisemirings	bisemiring	NOUN
cana-2978	424	11	using	use	VERB
cana-2978	424	12	homomorphism	homomorphism	NOUN
cana-2978	424	13	.	.	PUNCT
cana-2978	425	1	32	32	NUM
cana-2978	425	2	(	(	PUNCT
cana-2978	425	3	3	3	NUM
cana-2978	425	4	)	)	PUNCT
cana-2978	425	5	,	,	PUNCT
cana-2978	425	6	pp	pp	ADP
cana-2978	425	7	:	:	PUNCT
cana-2978	425	8	418435	418435	NUM
cana-2978	425	9	.	.	PUNCT
cana-2978	426	1	[	[	X
cana-2978	426	2	26	26	NUM
cana-2978	426	3	]	]	SYM
cana-2978	426	4	abubaker	abubaker	X
cana-2978	426	5	,	,	PUNCT
cana-2978	426	6	ahmad	ahmad	PROPN
cana-2978	426	7	a	a	DET
cana-2978	426	8	,	,	PUNCT
cana-2978	426	9	hatamleh	hatamleh	ADJ
cana-2978	426	10	,	,	PUNCT
cana-2978	426	11	raed	raed	PROPN
cana-2978	426	12	,	,	PUNCT
cana-2978	426	13	matarneh	matarneh	PROPN
cana-2978	426	14	,	,	PUNCT
cana-2978	426	15	khaled	khaled	PROPN
cana-2978	426	16	,	,	PUNCT
cana-2978	426	17	al	al	PROPN
cana-2978	426	18	-	-	PUNCT
cana-2978	426	19	husban	husban	ADJ
cana-2978	426	20	,	,	PUNCT
cana-2978	426	21	abdallah.(2024	abdallah.(2024	NOUN
cana-2978	426	22	)	)	PUNCT
cana-2978	426	23	.	.	PUNCT
cana-2978	427	1	on	on	ADP
cana-2978	427	2	the	the	DET
cana-2978	427	3	numerica	numerica	PROPN
cana-2978	427	4	solutions	solution	NOUN
cana-2978	427	5	for	for	ADP
cana-2978	427	6	some	some	DET
cana-2978	427	7	neutrosophic	neutrosophic	ADJ
cana-2978	427	8	singular	singular	ADJ
cana-2978	427	9	boundary	boundary	ADJ
cana-2978	427	10	value	value	NOUN
cana-2978	427	11	problems	problem	NOUN
cana-2978	427	12	by	by	ADP
cana-2978	427	13	using	use	VERB
cana-2978	427	14	(	(	PUNCT
cana-2978	427	15	lpm	lpm	NOUN
cana-2978	427	16	)	)	PUNCT
cana-2978	427	17	polynomials	polynomial	NOUN
cana-2978	427	18	,	,	PUNCT
cana-2978	427	19	international	international	ADJ
cana-2978	427	20	journal	journal	NOUN
cana-2978	427	21	of	of	ADP
cana-2978	427	22	neutrosophic	neutrosophic	ADJ
cana-2978	427	23	science,25(2),197	science,25(2),197	PROPN
cana-2978	427	24	-	-	PUNCT
cana-2978	427	25	205	205	NUM
cana-2978	427	26	.	.	PUNCT
cana-2978	428	1	[	[	X
cana-2978	428	2	27	27	NUM
cana-2978	428	3	]	]	SYM
cana-2978	428	4	a.	a.	NOUN
cana-2978	428	5	,	,	PUNCT
cana-2978	428	6	ahmad	ahmad	PROPN
cana-2978	428	7	.	.	PROPN
cana-2978	428	8	,	,	PUNCT
cana-2978	428	9	hatamleh	hatamleh	ADJ
cana-2978	428	10	,	,	PUNCT
cana-2978	428	11	raed	raed	PROPN
cana-2978	428	12	.	.	PROPN
cana-2978	428	13	,	,	PUNCT
cana-2978	428	14	matarneh	matarneh	PROPN
cana-2978	428	15	,	,	PUNCT
cana-2978	428	16	khaled	khaled	PROPN
cana-2978	428	17	.	.	PUNCT
cana-2978	428	18	,	,	PUNCT
cana-2978	428	19	al	al	PROPN
cana-2978	428	20	-	-	PUNCT
cana-2978	428	21	husban	husban	PROPN
cana-2978	428	22	,	,	PUNCT
cana-2978	428	23	abdallah	abdallah	PROPN
cana-2978	428	24	.	.	PUNCT
cana-2978	429	1	on	on	ADP
cana-2978	429	2	the	the	DET
cana-2978	429	3	irreversible	irreversible	ADJ
cana-2978	429	4	kthreshold	kthreshold	ADJ
cana-2978	429	5	conversion	conversion	NOUN
cana-2978	429	6	number	number	NOUN
cana-2978	429	7	for	for	ADP
cana-2978	429	8	some	some	DET
cana-2978	429	9	graph	graph	NOUN
cana-2978	429	10	products	product	NOUN
cana-2978	429	11	and	and	CCONJ
cana-2978	429	12	neutrosophic	neutrosophic	ADJ
cana-2978	429	13	graphs	graph	NOUN
cana-2978	429	14	.	.	PUNCT
cana-2978	430	1	(	(	PUNCT
cana-2978	430	2	2025	2025	NUM
cana-2978	430	3	)	)	PUNCT
cana-2978	430	4	.	.	PUNCT
cana-2978	431	1	international	international	ADJ
cana-2978	431	2	journal	journal	PROPN
cana-2978	431	3	of	of	ADP
cana-2978	431	4	neutrosophic	neutrosophic	ADJ
cana-2978	431	5	science	science	NOUN
cana-2978	431	6	,	,	PUNCT
cana-2978	431	7	25(2	25(2	NUM
cana-2978	431	8	)	)	PUNCT
cana-2978	431	9	,	,	PUNCT
cana-2978	431	10	pp	pp	ADP
cana-2978	431	11	.	.	PUNCT
cana-2978	432	1	183	183	NUM
cana-2978	432	2	-	-	SYM
cana-2978	432	3	196	196	NUM
cana-2978	432	4	[	[	X
cana-2978	432	5	28	28	NUM
cana-2978	432	6	]	]	X
cana-2978	432	7	r.	r.	PROPN
cana-2978	432	8	hatamleh	hatamleh	PROPN
cana-2978	432	9	,	,	PUNCT
cana-2978	432	10	v.a	v.a	PROPN
cana-2978	432	11	.	.	PROPN
cana-2978	432	12	zolotarev	zolotarev	PROPN
cana-2978	432	13	,	,	PUNCT
cana-2978	432	14	on	on	ADP
cana-2978	432	15	the	the	DET
cana-2978	432	16	universal	universal	ADJ
cana-2978	432	17	models	model	NOUN
cana-2978	432	18	of	of	ADP
cana-2978	432	19	commutative	commutative	ADJ
cana-2978	432	20	systems	system	NOUN
cana-2978	432	21	of	of	ADP
cana-2978	432	22	linear	linear	PROPN
cana-2978	432	23	operators.journal	operators.journal	PROPN
cana-2978	432	24	of	of	ADP
cana-2978	432	25	mathematical	mathematical	ADJ
cana-2978	432	26	physics	physics	NOUN
cana-2978	432	27	,	,	PUNCT
cana-2978	432	28	analysis	analysis	NOUN
cana-2978	432	29	,	,	PUNCT
cana-2978	432	30	geometry	geometry	NOUN
cana-2978	432	31	,	,	PUNCT
cana-2978	432	32	8(3	8(3	NUM
cana-2978	432	33	)	)	PUNCT
cana-2978	432	34	,	,	PUNCT
cana-2978	432	35	(	(	PUNCT
cana-2978	432	36	2012	2012	NUM
cana-2978	432	37	)	)	PUNCT
cana-2978	432	38	,	,	PUNCT
cana-2978	432	39	248	248	NUM
cana-2978	432	40	-	-	SYM
cana-2978	432	41	259	259	NUM
cana-2978	432	42	.	.	PUNCT
cana-2978	433	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	433	2	143	143	NUM
cana-2978	433	3	communications	communication	NOUN
cana-2978	433	4	on	on	ADP
cana-2978	433	5	applied	apply	VERB
cana-2978	433	6	nonlinear	nonlinear	ADJ
cana-2978	433	7	analysis	analysis	NOUN
cana-2978	433	8	issn	issn	NOUN
cana-2978	433	9	:	:	PUNCT
cana-2978	433	10	1074	1074	NUM
cana-2978	433	11	-	-	PUNCT
cana-2978	433	12	133x	133x	NUM
cana-2978	433	13	vol	vol	NOUN
cana-2978	433	14	32	32	NUM
cana-2978	433	15	no	no	NOUN
cana-2978	433	16	.	.	PUNCT
cana-2978	434	1	5s	5s	NUM
cana-2978	434	2	(	(	PUNCT
cana-2978	434	3	2025	2025	NUM
cana-2978	434	4	)	)	PUNCT
cana-2978	435	1	[	[	X
cana-2978	435	2	29	29	NUM
cana-2978	435	3	]	]	X
cana-2978	435	4	r.	r.	PROPN
cana-2978	435	5	hatamleh	hatamleh	PROPN
cana-2978	435	6	,	,	PUNCT
cana-2978	435	7	v.a	v.a	PROPN
cana-2978	435	8	.	.	PROPN
cana-2978	435	9	zolotarev	zolotarev	PROPN
cana-2978	435	10	,	,	PUNCT
cana-2978	435	11	on	on	ADP
cana-2978	435	12	the	the	DET
cana-2978	435	13	abstract	abstract	ADJ
cana-2978	435	14	inverse	inverse	NOUN
cana-2978	435	15	scattering	scattering	NOUN
cana-2978	435	16	problem	problem	NOUN
cana-2978	435	17	for	for	ADP
cana-2978	435	18	traces	trace	NOUN
cana-2978	435	19	class	class	NOUN
cana-2978	435	20	pertubations	pertubation	NOUN
cana-2978	435	21	.	.	PUNCT
cana-2978	436	1	journal	journal	PROPN
cana-2978	436	2	of	of	ADP
cana-2978	436	3	mathematical	mathematical	ADJ
cana-2978	436	4	physics	physics	NOUN
cana-2978	436	5	,	,	PUNCT
cana-2978	436	6	analysis	analysis	NOUN
cana-2978	436	7	,	,	PUNCT
cana-2978	436	8	geometry	geometry	NOUN
cana-2978	436	9	,	,	PUNCT
cana-2978	436	10	13(1	13(1	NUM
cana-2978	436	11	)	)	PUNCT
cana-2978	436	12	,	,	PUNCT
cana-2978	436	13	(	(	PUNCT
cana-2978	436	14	2017	2017	NUM
cana-2978	436	15	)	)	PUNCT
cana-2978	436	16	,	,	PUNCT
cana-2978	436	17	1	1	NUM
cana-2978	436	18	-	-	SYM
cana-2978	436	19	32	32	NUM
cana-2978	436	20	.	.	PUNCT
cana-2978	437	1	[	[	X
cana-2978	437	2	30	30	NUM
cana-2978	437	3	]	]	X
cana-2978	437	4	r.	r.	PROPN
cana-2978	437	5	hatamleh	hatamleh	PROPN
cana-2978	437	6	,	,	PUNCT
cana-2978	437	7	on	on	ADP
cana-2978	437	8	a	a	DET
cana-2978	437	9	novel	novel	ADJ
cana-2978	437	10	topological	topological	ADJ
cana-2978	437	11	space	space	NOUN
cana-2978	437	12	based	base	VERB
cana-2978	437	13	on	on	ADP
cana-2978	437	14	partially	partially	ADV
cana-2978	437	15	ordered	order	VERB
cana-2978	437	16	ring	ring	NOUN
cana-2978	437	17	of	of	ADP
cana-2978	437	18	weak	weak	ADJ
cana-2978	437	19	fuzzy	fuzzy	ADJ
cana-2978	437	20	complex	complex	ADJ
cana-2978	437	21	numbers	number	NOUN
cana-2978	437	22	and	and	CCONJ
cana-2978	437	23	its	its	PRON
cana-2978	437	24	relation	relation	NOUN
cana-2978	437	25	with	with	ADP
cana-2978	437	26	the	the	DET
cana-2978	437	27	partially	partially	ADV
cana-2978	437	28	ordered	order	VERB
cana-2978	437	29	neutrosophic	neutrosophic	ADJ
cana-2978	437	30	ring	ring	NOUN
cana-2978	437	31	of	of	ADP
cana-2978	437	32	real	real	ADJ
cana-2978	437	33	numbers	number	NOUN
cana-2978	437	34	,	,	PUNCT
cana-2978	437	35	neutrosophic	neutrosophic	ADJ
cana-2978	437	36	sets	set	NOUN
cana-2978	437	37	and	and	CCONJ
cana-2978	437	38	systems	system	NOUN
cana-2978	437	39	,	,	PUNCT
cana-2978	437	40	78	78	NUM
cana-2978	437	41	,	,	PUNCT
cana-2978	437	42	(	(	PUNCT
cana-2978	437	43	2025	2025	NUM
cana-2978	437	44	)	)	PUNCT
cana-2978	437	45	,	,	PUNCT
cana-2978	437	46	578	578	NUM
cana-2978	437	47	-	-	SYM
cana-2978	437	48	590	590	NUM
cana-2978	437	49	.	.	PUNCT
cana-2978	438	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2978	438	2	144	144	NUM
cana-2978	438	3	1	1	NUM
cana-2978	438	4	introduction	introduction	NOUN
cana-2978	438	5	2	2	NUM
cana-2978	438	6	background	background	NOUN
cana-2978	438	7	3	3	NUM
cana-2978	438	8	operations	operation	NOUN
cana-2978	438	9	for	for	ADP
cana-2978	438	10	ct	ct	PROPN
cana-2978	438	11	(	(	PUNCT
cana-2978	438	12	,	,	PUNCT
cana-2978	438	13	)	)	PUNCT
cana-2978	438	14	-rung	-rung	PROPN
cana-2978	438	15	fn	fn	PROPN
cana-2978	438	16	4	4	NUM
cana-2978	438	17	aos	aos	NOUN
cana-2978	438	18	based	base	VERB
cana-2978	438	19	on	on	ADP
cana-2978	438	20	ct	ct	PROPN
cana-2978	438	21	(	(	PUNCT
cana-2978	438	22	,	,	PUNCT
cana-2978	438	23	)	)	PUNCT
cana-2978	438	24	-rung	-rung	PROPN
cana-2978	438	25	fn	fn	PROPN
cana-2978	438	26	4.1	4.1	NUM
cana-2978	438	27	ct	ct	NOUN
cana-2978	438	28	(	(	PUNCT
cana-2978	438	29	,	,	PUNCT
cana-2978	438	30	)	)	PUNCT
cana-2978	438	31	nwa	nwa	PROPN
cana-2978	438	32	4.2	4.2	NUM
cana-2978	438	33	ct	ct	PROPN
cana-2978	438	34	(	(	PUNCT
cana-2978	438	35	,	,	PUNCT
cana-2978	438	36	)	)	PUNCT
cana-2978	438	37	-rung	-rung	PROPN
cana-2978	438	38	fnwg	fnwg	ADJ
cana-2978	438	39	4.3	4.3	NUM
cana-2978	438	40	generalized	generalized	ADJ
cana-2978	438	41	ct	ct	PROPN
cana-2978	438	42	(	(	PUNCT
cana-2978	438	43	,	,	PUNCT
cana-2978	438	44	)	)	PUNCT
cana-2978	438	45	-rung	-rung	PROPN
cana-2978	438	46	fnwa	fnwa	PROPN
cana-2978	438	47	(	(	PUNCT
cana-2978	438	48	gct	gct	PROPN
cana-2978	438	49	(	(	PUNCT
cana-2978	438	50	,	,	PUNCT
cana-2978	438	51	)	)	PUNCT
cana-2978	438	52	-rung	-rung	PROPN
cana-2978	438	53	fnwa	fnwa	NOUN
cana-2978	438	54	)	)	PUNCT
cana-2978	438	55	4.4	4.4	NUM
cana-2978	438	56	generalized	generalize	VERB
cana-2978	438	57	ct	ct	PROPN
cana-2978	438	58	(	(	PUNCT
cana-2978	438	59	,	,	PUNCT
cana-2978	438	60	)	)	PUNCT
cana-2978	438	61	-rung	-rung	PROPN
cana-2978	438	62	fnwg	fnwg	ADJ
cana-2978	438	63	(	(	PUNCT
cana-2978	438	64	gct	gct	PROPN
cana-2978	438	65	(	(	PUNCT
cana-2978	438	66	,	,	PUNCT
cana-2978	438	67	)	)	PUNCT
cana-2978	438	68	-rung	-rung	PROPN
cana-2978	438	69	fnwg	fnwg	ADJ
cana-2978	438	70	)	)	PUNCT