id	sid	tid	token	lemma	pos
cana-835	1	1	communications	communication	NOUN
cana-835	1	2	on	on	ADP
cana-835	1	3	applied	apply	VERB
cana-835	1	4	nonlinear	nonlinear	ADJ
cana-835	1	5	analysis	analysis	NOUN
cana-835	1	6	issn	issn	NOUN
cana-835	1	7	:	:	PUNCT
cana-835	1	8	1074	1074	NUM
cana-835	1	9	-	-	PUNCT
cana-835	1	10	133x	133x	NUM
cana-835	1	11	vol	vol	NOUN
cana-835	1	12	31	31	NUM
cana-835	1	13	no	no	NOUN
cana-835	1	14	.	.	PUNCT
cana-835	2	1	4s	4s	NUM
cana-835	2	2	(	(	PUNCT
cana-835	2	3	2024	2024	NUM
cana-835	2	4	)	)	PUNCT
cana-835	2	5	182	182	NUM
cana-835	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	2	7	solving	solve	VERB
cana-835	2	8	intuitionistic	intuitionistic	ADJ
cana-835	2	9	fuzzy	fuzzy	ADJ
cana-835	2	10	unconstrained	unconstrained	ADJ
cana-835	2	11	optimization	optimization	NOUN
cana-835	2	12	problems	problem	NOUN
cana-835	2	13	using	use	VERB
cana-835	2	14	interval	interval	PROPN
cana-835	2	15	newton	newton	PROPN
cana-835	2	16	’s	’s	PART
cana-835	2	17	method	method	PROPN
cana-835	2	18	s.	s.	PROPN
cana-835	2	19	shilpa	shilpa	PROPN
cana-835	2	20	ivin	ivin	PROPN
cana-835	2	21	emimal1	emimal1	PROPN
cana-835	2	22	,	,	PUNCT
cana-835	2	23	r.	r.	PROPN
cana-835	2	24	irene	irene	PROPN
cana-835	2	25	hepzibah	hepzibah	PROPN
cana-835	2	26	2	2	NUM
cana-835	2	27	*	*	PUNCT
cana-835	2	28	1&2	1&2	NUM
cana-835	2	29	*	*	PUNCT
cana-835	2	30	(	(	PUNCT
cana-835	2	31	affiliated	affiliate	VERB
cana-835	2	32	to	to	PART
cana-835	2	33	bharathidasan	bharathidasan	VERB
cana-835	2	34	university	university	NOUN
cana-835	2	35	)	)	PUNCT
cana-835	2	36	,	,	PUNCT
cana-835	2	37	t.b.m.l.college	t.b.m.l.college	NOUN
cana-835	2	38	(	(	PUNCT
cana-835	2	39	post	post	VERB
cana-835	2	40	graduate	graduate	NOUN
cana-835	2	41	and	and	CCONJ
cana-835	2	42	research	research	NOUN
cana-835	2	43	department	department	PROPN
cana-835	2	44	of	of	ADP
cana-835	2	45	mathematics	mathematic	NOUN
cana-835	2	46	)	)	PUNCT
cana-835	2	47	,	,	PUNCT
cana-835	2	48	porayar	porayar	NOUN
cana-835	2	49	609	609	NUM
cana-835	2	50	307	307	NUM
cana-835	2	51	,	,	PUNCT
cana-835	2	52	tamil	tamil	PROPN
cana-835	2	53	nadu	nadu	PROPN
cana-835	2	54	,	,	PUNCT
cana-835	2	55	india	india	PROPN
cana-835	2	56	e	e	PROPN
cana-835	2	57	-	-	NOUN
cana-835	2	58	mail	mail	NOUN
cana-835	2	59	:	:	PUNCT
cana-835	2	60	1shilpaivins@gmail.com	1shilpaivins@gmail.com	NUM
cana-835	2	61	,	,	PUNCT
cana-835	2	62	2	2	NUM
cana-835	2	63	*	*	SYM
cana-835	2	64	ireneraj74@gmail.com	ireneraj74@gmail.com	X
cana-835	2	65	article	article	NOUN
cana-835	2	66	history	history	NOUN
cana-835	2	67	:	:	PUNCT
cana-835	2	68	received	receive	VERB
cana-835	2	69	:	:	PUNCT
cana-835	2	70	19	19	NUM
cana-835	2	71	-	-	PUNCT
cana-835	2	72	04	04	NUM
cana-835	2	73	-	-	PUNCT
cana-835	2	74	2024	2024	NUM
cana-835	2	75	revised	revise	VERB
cana-835	2	76	:	:	PUNCT
cana-835	2	77	08	08	NUM
cana-835	2	78	-	-	SYM
cana-835	2	79	06	06	NUM
cana-835	2	80	-	-	PUNCT
cana-835	2	81	2024	2024	NUM
cana-835	2	82	accepted	accept	VERB
cana-835	2	83	:	:	PUNCT
cana-835	2	84	21	21	NUM
cana-835	2	85	-	-	SYM
cana-835	2	86	06	06	NUM
cana-835	2	87	-	-	PUNCT
cana-835	2	88	2024	2024	NUM
cana-835	2	89	abstract	abstract	NOUN
cana-835	2	90	:	:	PUNCT
cana-835	2	91	this	this	DET
cana-835	2	92	research	research	NOUN
cana-835	2	93	work	work	NOUN
cana-835	2	94	studies	study	NOUN
cana-835	2	95	the	the	DET
cana-835	2	96	optimization	optimization	NOUN
cana-835	2	97	of	of	ADP
cana-835	2	98	intuitionistic	intuitionistic	ADJ
cana-835	2	99	fuzzy	fuzzy	ADJ
cana-835	2	100	valued	value	VERB
cana-835	2	101	functions	function	NOUN
cana-835	2	102	in	in	ADP
cana-835	2	103	unconstrained	unconstrained	ADJ
cana-835	2	104	problems	problem	NOUN
cana-835	2	105	.	.	PUNCT
cana-835	3	1	the	the	DET
cana-835	3	2	interval	interval	NOUN
cana-835	3	3	newton	newton	PROPN
cana-835	3	4	's	's	PART
cana-835	3	5	method	method	NOUN
cana-835	3	6	using	use	VERB
cana-835	3	7	an	an	DET
cana-835	3	8	intuitionistic	intuitionistic	ADJ
cana-835	3	9	approach	approach	NOUN
cana-835	3	10	addresses	address	NOUN
cana-835	3	11	both	both	DET
cana-835	3	12	single	single	ADJ
cana-835	3	13	and	and	CCONJ
cana-835	3	14	multivariable	multivariable	ADJ
cana-835	3	15	optimization	optimization	NOUN
cana-835	3	16	problems	problem	NOUN
cana-835	3	17	.	.	PUNCT
cana-835	4	1	the	the	DET
cana-835	4	2	study	study	NOUN
cana-835	4	3	incorporates	incorporate	VERB
cana-835	4	4	a	a	DET
cana-835	4	5	mathematical	mathematical	ADJ
cana-835	4	6	comprehension	comprehension	NOUN
cana-835	4	7	of	of	ADP
cana-835	4	8	interval	interval	NOUN
cana-835	4	9	intuitionistic	intuitionistic	ADJ
cana-835	4	10	fuzzy	fuzzy	ADJ
cana-835	4	11	valued	value	VERB
cana-835	4	12	problems	problem	NOUN
cana-835	4	13	,	,	PUNCT
cana-835	4	14	as	as	ADV
cana-835	4	15	well	well	ADV
cana-835	4	16	as	as	ADP
cana-835	4	17	realworld	realworld	PROPN
cana-835	4	18	examples	example	NOUN
cana-835	4	19	to	to	PART
cana-835	4	20	demonstrate	demonstrate	VERB
cana-835	4	21	their	their	PRON
cana-835	4	22	effectiveness	effectiveness	NOUN
cana-835	4	23	.	.	PUNCT
cana-835	5	1	furthermore	furthermore	ADV
cana-835	5	2	,	,	PUNCT
cana-835	5	3	matlab	matlab	PROPN
cana-835	5	4	code	code	PROPN
cana-835	5	5	is	be	AUX
cana-835	5	6	provided	provide	VERB
cana-835	5	7	to	to	PART
cana-835	5	8	demonstrate	demonstrate	VERB
cana-835	5	9	the	the	DET
cana-835	5	10	implementation	implementation	NOUN
cana-835	5	11	of	of	ADP
cana-835	5	12	the	the	DET
cana-835	5	13	interval	interval	NOUN
cana-835	5	14	newton	newton	PROPN
cana-835	5	15	's	's	PART
cana-835	5	16	method	method	NOUN
cana-835	5	17	.	.	PUNCT
cana-835	6	1	keywords	keyword	NOUN
cana-835	6	2	:	:	PUNCT
cana-835	6	3	unconstrained	unconstrained	ADJ
cana-835	6	4	optimization	optimization	NOUN
cana-835	6	5	problems	problem	NOUN
cana-835	6	6	,	,	PUNCT
cana-835	6	7	interval	interval	NOUN
cana-835	6	8	newton	newton	PROPN
cana-835	6	9	's	's	PART
cana-835	6	10	meth0d(inm	meth0d(inm	ADJ
cana-835	6	11	)	)	PUNCT
cana-835	6	12	,	,	PUNCT
cana-835	6	13	intuitionistic	intuitionistic	ADJ
cana-835	6	14	fuzzy	fuzzy	ADJ
cana-835	6	15	numbers	number	NOUN
cana-835	6	16	.	.	PUNCT
cana-835	7	1	1	1	X
cana-835	7	2	.	.	X
cana-835	7	3	introduction	introduction	NOUN
cana-835	7	4	this	this	DET
cana-835	7	5	paper	paper	NOUN
cana-835	7	6	focuses	focus	VERB
cana-835	7	7	on	on	ADP
cana-835	7	8	unconstrained	unconstrained	ADJ
cana-835	7	9	optimization	optimization	NOUN
cana-835	7	10	problems	problem	NOUN
cana-835	7	11	ἰnvolving	ἰnvolve	VERB
cana-835	7	12	intuitἰonistic	intuitἰonistic	ADJ
cana-835	7	13	fuzzy	fuzzy	ADV
cana-835	7	14	-	-	PUNCT
cana-835	7	15	valued	value	VERB
cana-835	7	16	functions	function	NOUN
cana-835	7	17	.	.	PUNCT
cana-835	8	1	it	it	PRON
cana-835	8	2	delves	delve	VERB
cana-835	8	3	into	into	ADP
cana-835	8	4	both	both	DET
cana-835	8	5	single	single	ADJ
cana-835	8	6	-	-	PUNCT
cana-835	8	7	variable	variable	ADJ
cana-835	8	8	and	and	CCONJ
cana-835	8	9	multi	multi	ADJ
cana-835	8	10	-	-	ADJ
cana-835	8	11	variable	variable	ADJ
cana-835	8	12	scenarios	scenario	NOUN
cana-835	8	13	,	,	PUNCT
cana-835	8	14	providing	provide	VERB
cana-835	8	15	explanations	explanation	NOUN
cana-835	8	16	and	and	CCONJ
cana-835	8	17	illustrations	illustration	NOUN
cana-835	8	18	to	to	PART
cana-835	8	19	demonstrate	demonstrate	VERB
cana-835	8	20	the	the	DET
cana-835	8	21	application	application	NOUN
cana-835	8	22	of	of	ADP
cana-835	8	23	the	the	DET
cana-835	8	24	interval	interval	NOUN
cana-835	8	25	newt0n	newt0n	PROPN
cana-835	8	26	method	method	NOUN
cana-835	8	27	in	in	ADP
cana-835	8	28	tackling	tackle	VERB
cana-835	8	29	these	these	DET
cana-835	8	30	optimization	optimization	NOUN
cana-835	8	31	problems	problem	NOUN
cana-835	8	32	.	.	PUNCT
cana-835	9	1	helmut	helmut	PROPN
cana-835	9	2	ratschek[4]explored	ratschek[4]explored	ADJ
cana-835	9	3	interval	interval	NOUN
cana-835	9	4	methods	method	NOUN
cana-835	9	5	in	in	ADP
cana-835	9	6	global	global	ADJ
cana-835	9	7	optimization	optimization	NOUN
cana-835	9	8	,	,	PUNCT
cana-835	9	9	providing	provide	VERB
cana-835	9	10	solutions	solution	NOUN
cana-835	9	11	for	for	ADP
cana-835	9	12	diverse	diverse	ADJ
cana-835	9	13	optimization	optimization	NOUN
cana-835	9	14	scenarios	scenario	NOUN
cana-835	9	15	,	,	PUNCT
cana-835	9	16	including	include	VERB
cana-835	9	17	unc0nstrained	unc0nstrained	PROPN
cana-835	9	18	,	,	PUNCT
cana-835	9	19	constrained	constrain	VERB
cana-835	9	20	,	,	PUNCT
cana-835	9	21	and	and	CCONJ
cana-835	9	22	n0nsmooth	n0nsmooth	NUM
cana-835	9	23	optimization	optimization	NOUN
cana-835	9	24	.	.	PUNCT
cana-835	10	1	it	it	PRON
cana-835	10	2	underscores	underscore	VERB
cana-835	10	3	the	the	DET
cana-835	10	4	importance	importance	NOUN
cana-835	10	5	of	of	ADP
cana-835	10	6	bisection	bisection	NOUN
cana-835	10	7	techniques	technique	NOUN
cana-835	10	8	in	in	ADP
cana-835	10	9	interval	interval	NOUN
cana-835	10	10	-	-	PUNCT
cana-835	10	11	based	base	VERB
cana-835	10	12	global	global	ADJ
cana-835	10	13	optimization	optimization	NOUN
cana-835	10	14	algorithms	algorithm	NOUN
cana-835	10	15	,	,	PUNCT
cana-835	10	16	where	where	SCONJ
cana-835	10	17	the	the	DET
cana-835	10	18	problem	problem	NOUN
cana-835	10	19	domain	domain	NOUN
cana-835	10	20	is	be	AUX
cana-835	10	21	recursively	recursively	ADV
cana-835	10	22	divided	divide	VERB
cana-835	10	23	and	and	CCONJ
cana-835	10	24	also	also	ADV
cana-835	10	25	acknowledges	acknowledge	VERB
cana-835	10	26	advancements	advancement	NOUN
cana-835	10	27	in	in	ADP
cana-835	10	28	bisection	bisection	NOUN
cana-835	10	29	strategies	strategy	NOUN
cana-835	10	30	over	over	ADP
cana-835	10	31	the	the	DET
cana-835	10	32	last	last	ADJ
cana-835	10	33	decade	decade	NOUN
cana-835	10	34	.	.	PUNCT
cana-835	11	1	furthermore	furthermore	ADV
cana-835	11	2	,	,	PUNCT
cana-835	11	3	it	it	PRON
cana-835	11	4	emphasized	emphasize	VERB
cana-835	11	5	the	the	DET
cana-835	11	6	significance	significance	NOUN
cana-835	11	7	of	of	ADP
cana-835	11	8	interval	interval	NOUN
cana-835	11	9	arithmetic	arithmetic	ADJ
cana-835	11	10	in	in	ADP
cana-835	11	11	handling	handle	VERB
cana-835	11	12	global	global	ADJ
cana-835	11	13	optimization	optimization	NOUN
cana-835	11	14	problems	problem	NOUN
cana-835	11	15	,	,	PUNCT
cana-835	11	16	as	as	SCONJ
cana-835	11	17	it	it	PRON
cana-835	11	18	offers	offer	VERB
cana-835	11	19	global	global	ADJ
cana-835	11	20	information	information	NOUN
cana-835	11	21	compared	compare	VERB
cana-835	11	22	to	to	ADP
cana-835	11	23	local	local	ADJ
cana-835	11	24	optimization	optimization	NOUN
cana-835	11	25	meth0ds	meth0ds	NOUN
cana-835	11	26	that	that	PRON
cana-835	11	27	rely	rely	VERB
cana-835	11	28	on	on	ADP
cana-835	11	29	limited	limited	ADJ
cana-835	11	30	,	,	PUNCT
cana-835	11	31	local	local	ADJ
cana-835	11	32	data	datum	NOUN
cana-835	11	33	.	.	PUNCT
cana-835	12	1	recently	recently	ADV
cana-835	12	2	,	,	PUNCT
cana-835	12	3	we	we	PRON
cana-835	12	4	have	have	AUX
cana-835	12	5	had	have	VERB
cana-835	12	6	to	to	PART
cana-835	12	7	optimize	optimize	VERB
cana-835	12	8	provided	provide	VERB
cana-835	12	9	systems	system	NOUN
cana-835	12	10	and	and	CCONJ
cana-835	12	11	deal	deal	VERB
cana-835	12	12	with	with	ADP
cana-835	12	13	linear	linear	PROPN
cana-835	12	14	and	and	CCONJ
cana-835	12	15	nlpp	nlpp	NOUN
cana-835	12	16	.	.	PUNCT
cana-835	13	1	the	the	DET
cana-835	13	2	phrase	phrase	NOUN
cana-835	13	3	optimization	optimization	NOUN
cana-835	13	4	refers	refer	VERB
cana-835	13	5	to	to	ADP
cana-835	13	6	reaching	reach	VERB
cana-835	13	7	the	the	DET
cana-835	13	8	best	good	ADJ
cana-835	13	9	possible	possible	ADJ
cana-835	13	10	outcome	outcome	NOUN
cana-835	13	11	.	.	PUNCT
cana-835	14	1	the	the	DET
cana-835	14	2	interval	interval	NOUN
cana-835	14	3	analysis	analysis	NOUN
cana-835	14	4	appr0ach	appr0ach	NOUN
cana-835	14	5	emerged	emerge	VERB
cana-835	14	6	between	between	ADP
cana-835	14	7	1950	1950	NUM
cana-835	14	8	and	and	CCONJ
cana-835	14	9	1960	1960	NUM
cana-835	14	10	.	.	PUNCT
cana-835	15	1	interval	interval	NOUN
cana-835	15	2	analysis	analysis	NOUN
cana-835	15	3	,	,	PUNCT
cana-835	15	4	intr0duced	intr0duce	VERB
cana-835	15	5	with	with	ADP
cana-835	15	6	the	the	DET
cana-835	15	7	devel0pment	devel0pment	NOUN
cana-835	15	8	of	of	ADP
cana-835	15	9	c0mputational	c0mputational	ADJ
cana-835	15	10	mathematics	mathematic	NOUN
cana-835	15	11	,	,	PUNCT
cana-835	15	12	is	be	AUX
cana-835	15	13	a	a	DET
cana-835	15	14	meth0d	meth0d	PROPN
cana-835	15	15	of	of	ADP
cana-835	15	16	describing	describe	VERB
cana-835	15	17	by	by	ADP
cana-835	15	18	substituting	substitute	VERB
cana-835	15	19	a	a	DET
cana-835	15	20	sἰngle	sἰngle	ADV
cana-835	15	21	fἰxed	fἰxe	VERB
cana-835	15	22	p0int	p0int	NOUN
cana-835	15	23	with	with	ADP
cana-835	15	24	an	an	DET
cana-835	15	25	ἰnterval	ἰnterval	NOUN
cana-835	15	26	.	.	PUNCT
cana-835	16	1	in	in	ADP
cana-835	16	2	general	general	ADJ
cana-835	16	3	,	,	PUNCT
cana-835	16	4	we	we	PRON
cana-835	16	5	tackle	tackle	VERB
cana-835	16	6	n0nlinear	n0nlinear	PROPN
cana-835	16	7	pr0gramming	pr0gramme	VERB
cana-835	16	8	pr0blems	pr0blem	NOUN
cana-835	16	9	that	that	PRON
cana-835	16	10	require	require	VERB
cana-835	16	11	only	only	ADV
cana-835	16	12	crisp	crisp	ADJ
cana-835	16	13	integers	integer	NOUN
cana-835	16	14	in	in	ADP
cana-835	16	15	the	the	DET
cana-835	16	16	goal	goal	NOUN
cana-835	16	17	and	and	CCONJ
cana-835	16	18	a	a	DET
cana-835	16	19	limited	limited	ADJ
cana-835	16	20	c0	c0	NOUN
cana-835	16	21	-	-	PUNCT
cana-835	16	22	efficient	efficient	ADJ
cana-835	16	23	.	.	PUNCT
cana-835	17	1	when	when	SCONJ
cana-835	17	2	dealing	deal	VERB
cana-835	17	3	with	with	ADP
cana-835	17	4	such	such	ADJ
cana-835	17	5	natural	natural	ADJ
cana-835	17	6	situations	situation	NOUN
cana-835	17	7	,	,	PUNCT
cana-835	17	8	challenges	challenge	NOUN
cana-835	17	9	exist	exist	VERB
cana-835	17	10	because	because	SCONJ
cana-835	17	11	of	of	ADP
cana-835	17	12	uncertainty	uncertainty	NOUN
cana-835	17	13	and	and	CCONJ
cana-835	17	14	inexactness	inexactness	ADJ
cana-835	17	15	ἰn	ἰn	ADP
cana-835	17	16	the	the	DET
cana-835	17	17	derived	derive	VERB
cana-835	17	18	parameters	parameter	NOUN
cana-835	17	19	.	.	PUNCT
cana-835	18	1	since	since	SCONJ
cana-835	18	2	0ccurrence	0ccurrence	NUM
cana-835	18	3	of	of	ADP
cana-835	18	4	the	the	DET
cana-835	18	5	uncertainty	uncertainty	NOUN
cana-835	18	6	and	and	CCONJ
cana-835	18	7	inexactness	inexactness	NOUN
cana-835	18	8	,	,	PUNCT
cana-835	18	9	it	it	PRON
cana-835	18	10	is	be	AUX
cana-835	18	11	inadequate	inadequate	ADJ
cana-835	18	12	to	to	PART
cana-835	18	13	apply	apply	VERB
cana-835	18	14	the	the	DET
cana-835	18	15	classic	classic	ADJ
cana-835	18	16	meth0d	meth0d	PROPN
cana-835	18	17	to	to	PART
cana-835	18	18	handle	handle	VERB
cana-835	18	19	such	such	ADJ
cana-835	18	20	problems	problem	NOUN
cana-835	18	21	.	.	PUNCT
cana-835	19	1	karl	karl	PROPN
cana-835	19	2	nickel	nickel	PROPN
cana-835	19	3	[	[	X
cana-835	19	4	6]explained	6]explaine	VERB
cana-835	19	5	the	the	DET
cana-835	19	6	application	application	NOUN
cana-835	19	7	of	of	ADP
cana-835	19	8	the	the	DET
cana-835	19	9	newt0n	newt0n	PROPN
cana-835	19	10	technique	technique	NOUN
cana-835	19	11	and	and	CCONJ
cana-835	19	12	interval	interval	NOUN
cana-835	19	13	arithmetic	arithmetic	NOUN
cana-835	19	14	in	in	ADP
cana-835	19	15	solving	solve	VERB
cana-835	19	16	ndimensional	ndimensional	ADJ
cana-835	19	17	vector	vector	NOUN
cana-835	19	18	problems	problem	NOUN
cana-835	19	19	.	.	PUNCT
cana-835	20	1	it	it	PRON
cana-835	20	2	delves	delve	VERB
cana-835	20	3	into	into	ADP
cana-835	20	4	the	the	DET
cana-835	20	5	characteristics	characteristic	NOUN
cana-835	20	6	of	of	ADP
cana-835	20	7	the	the	DET
cana-835	20	8	newt0n	newt0n	PROPN
cana-835	20	9	operator	operator	NOUN
cana-835	20	10	,	,	PUNCT
cana-835	20	11	conditions	condition	NOUN
cana-835	20	12	for	for	ADP
cana-835	20	13	solution	solution	NOUN
cana-835	20	14	existence	existence	NOUN
cana-835	20	15	,	,	PUNCT
cana-835	20	16	and	and	CCONJ
cana-835	20	17	limitations	limitation	NOUN
cana-835	20	18	on	on	ADP
cana-835	20	19	error	error	NOUN
cana-835	20	20	tolerances	tolerance	NOUN
cana-835	20	21	for	for	ADP
cana-835	20	22	convergent	convergent	ADJ
cana-835	20	23	sequences	sequence	NOUN
cana-835	20	24	.	.	PUNCT
cana-835	21	1	the	the	DET
cana-835	21	2	concept	concept	NOUN
cana-835	21	3	is	be	AUX
cana-835	21	4	further	far	ADV
cana-835	21	5	illustrated	illustrate	VERB
cana-835	21	6	through	through	ADP
cana-835	21	7	an	an	DET
cana-835	21	8	example	example	NOUN
cana-835	21	9	in	in	ADP
cana-835	21	10	convex	convex	PROPN
cana-835	21	11	programming	programming	NOUN
cana-835	21	12	,	,	PUNCT
cana-835	21	13	showcasing	showcase	VERB
cana-835	21	14	its	its	PRON
cana-835	21	15	real	real	ADJ
cana-835	21	16	-	-	PUNCT
cana-835	21	17	world	world	NOUN
cana-835	21	18	implications	implication	NOUN
cana-835	21	19	.	.	PUNCT
cana-835	22	1	ved	ve	VERB
cana-835	22	2	https://link.springer.com/chapter/10.1007/978-1-4615-2025-2_14#auth-helmut-ratschek	https://link.springer.com/chapter/10.1007/978-1-4615-2025-2_14#auth-helmut-ratschek	PROPN
cana-835	22	3	communications	communication	NOUN
cana-835	22	4	on	on	ADP
cana-835	22	5	applied	apply	VERB
cana-835	22	6	nonlinear	nonlinear	ADJ
cana-835	22	7	analysis	analysis	NOUN
cana-835	22	8	issn	issn	NOUN
cana-835	22	9	:	:	PUNCT
cana-835	22	10	1074	1074	NUM
cana-835	22	11	-	-	PUNCT
cana-835	22	12	133x	133x	NUM
cana-835	22	13	vol	vol	NOUN
cana-835	22	14	31	31	NUM
cana-835	22	15	no	no	NOUN
cana-835	22	16	.	.	PUNCT
cana-835	23	1	4s	4s	NUM
cana-835	23	2	(	(	PUNCT
cana-835	23	3	2024	2024	NUM
cana-835	23	4	)	)	PUNCT
cana-835	23	5	183	183	NUM
cana-835	23	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	24	1	p.	p.	NOUN
cana-835	24	2	madan	madan	PROPN
cana-835	25	1	[	[	X
cana-835	25	2	15]the	15]the	DET
cana-835	25	3	interval	interval	NOUN
cana-835	25	4	newt0n	newt0n	PROPN
cana-835	25	5	meth0d	meth0d	PROPN
cana-835	25	6	,	,	PUNCT
cana-835	25	7	especially	especially	ADV
cana-835	25	8	the	the	DET
cana-835	25	9	hansen	hansen	PROPN
cana-835	25	10	-	-	PUNCT
cana-835	25	11	greenberg	greenberg	PROPN
cana-835	25	12	appr0ach	appr0ach	NOUN
cana-835	25	13	,	,	PUNCT
cana-835	25	14	is	be	AUX
cana-835	25	15	a	a	DET
cana-835	25	16	technique	technique	NOUN
cana-835	25	17	for	for	ADP
cana-835	25	18	solving	solve	VERB
cana-835	25	19	systems	system	NOUN
cana-835	25	20	of	of	ADP
cana-835	25	21	n0nlinear	n0nlinear	PROPN
cana-835	25	22	equations	equation	NOUN
cana-835	25	23	by	by	ADP
cana-835	25	24	linearizing	linearize	VERB
cana-835	25	25	the	the	DET
cana-835	25	26	system	system	NOUN
cana-835	25	27	and	and	CCONJ
cana-835	25	28	making	make	VERB
cana-835	25	29	different	different	ADJ
cana-835	25	30	changes	change	NOUN
cana-835	25	31	t0	t0	PROPN
cana-835	25	32	enhance	enhance	VERB
cana-835	25	33	efficiency	efficiency	NOUN
cana-835	25	34	.	.	PUNCT
cana-835	26	1	this	this	DET
cana-835	26	2	appr0ach	appr0ach	NOUN
cana-835	26	3	uses	use	VERB
cana-835	26	4	preconditioning	precondition	VERB
cana-835	26	5	,	,	PUNCT
cana-835	26	6	the	the	DET
cana-835	26	7	hansen	hansen	ADJ
cana-835	26	8	-	-	PUNCT
cana-835	26	9	sengupta	sengupta	NOUN
cana-835	26	10	step	step	NOUN
cana-835	26	11	,	,	PUNCT
cana-835	26	12	and	and	CCONJ
cana-835	26	13	interval	interval	NOUN
cana-835	26	14	iterations	iteration	NOUN
cana-835	26	15	to	to	PART
cana-835	26	16	provide	provide	VERB
cana-835	26	17	more	more	ADV
cana-835	26	18	accurate	accurate	ADJ
cana-835	26	19	and	and	CCONJ
cana-835	26	20	efficient	efficient	ADJ
cana-835	26	21	solutions	solution	NOUN
cana-835	26	22	for	for	ADP
cana-835	26	23	solving	solve	VERB
cana-835	26	24	complicated	complicated	ADJ
cana-835	26	25	mathematical	mathematical	ADJ
cana-835	26	26	problems	problem	NOUN
cana-835	26	27	.	.	PUNCT
cana-835	27	1	the	the	DET
cana-835	27	2	paper	paper	NOUN
cana-835	27	3	's	's	PART
cana-835	27	4	proposed	propose	VERB
cana-835	27	5	procedural	procedural	ADJ
cana-835	27	6	enhancements	enhancement	NOUN
cana-835	27	7	attempt	attempt	VERB
cana-835	27	8	to	to	PART
cana-835	27	9	increase	increase	VERB
cana-835	27	10	algorithm	algorithm	NOUN
cana-835	27	11	performance	performance	NOUN
cana-835	27	12	by	by	ADP
cana-835	27	13	adding	add	VERB
cana-835	27	14	improved	improved	ADJ
cana-835	27	15	approximations	approximation	NOUN
cana-835	27	16	,	,	PUNCT
cana-835	27	17	a	a	DET
cana-835	27	18	sequential	sequential	ADJ
cana-835	27	19	overrelaxation	overrelaxation	NOUN
cana-835	27	20	methodology	methodology	NOUN
cana-835	27	21	,	,	PUNCT
cana-835	27	22	and	and	CCONJ
cana-835	27	23	interval	interval	NOUN
cana-835	27	24	iterations	iteration	NOUN
cana-835	27	25	as	as	ADP
cana-835	27	26	alternatives	alternative	NOUN
cana-835	27	27	to	to	ADP
cana-835	27	28	existing	exist	VERB
cana-835	27	29	methods	method	NOUN
cana-835	27	30	.	.	PUNCT
cana-835	28	1	the	the	DET
cana-835	28	2	discussed	discuss	VERB
cana-835	28	3	interval	interval	NOUN
cana-835	28	4	newt0n	newt0n	PROPN
cana-835	28	5	meth0d	meth0d	PROPN
cana-835	28	6	aims	aim	VERB
cana-835	28	7	to	to	PART
cana-835	28	8	efficiently	efficiently	ADV
cana-835	28	9	solve	solve	VERB
cana-835	28	10	systems	system	NOUN
cana-835	28	11	of	of	ADP
cana-835	28	12	nonlinear	nonlinear	ADJ
cana-835	28	13	equations	equation	NOUN
cana-835	28	14	by	by	ADP
cana-835	28	15	integrating	integrate	VERB
cana-835	28	16	three	three	NUM
cana-835	28	17	subalg0rithms	subalg0rithm	NOUN
cana-835	28	18	:	:	PUNCT
cana-835	28	19	a	a	DET
cana-835	28	20	gauss	gauss	ADJ
cana-835	28	21	-	-	PUNCT
cana-835	28	22	seidel	seidel	NOUN
cana-835	28	23	-	-	PUNCT
cana-835	28	24	type	type	NOUN
cana-835	28	25	step	step	NOUN
cana-835	28	26	,	,	PUNCT
cana-835	28	27	a	a	DET
cana-835	28	28	real	real	ADJ
cana-835	28	29	newton	newton	PROPN
cana-835	28	30	iteration	iteration	NOUN
cana-835	28	31	,	,	PUNCT
cana-835	28	32	and	and	CCONJ
cana-835	28	33	linearized	linearize	VERB
cana-835	28	34	equation	equation	NOUN
cana-835	28	35	solving	solve	VERB
cana-835	28	36	via	via	ADP
cana-835	28	37	elimination	elimination	NOUN
cana-835	28	38	.	.	PUNCT
cana-835	29	1	this	this	DET
cana-835	29	2	approach	approach	NOUN
cana-835	29	3	improves	improve	VERB
cana-835	29	4	upon	upon	SCONJ
cana-835	29	5	existing	exist	VERB
cana-835	29	6	techniques	technique	NOUN
cana-835	29	7	like	like	ADP
cana-835	29	8	krawczyk	krawczyk	PROPN
cana-835	29	9	's	's	PART
cana-835	29	10	method	method	NOUN
cana-835	29	11	,	,	PUNCT
cana-835	29	12	offering	offer	VERB
cana-835	29	13	better	well	ADJ
cana-835	29	14	solution	solution	NOUN
cana-835	29	15	efficiency	efficiency	NOUN
cana-835	29	16	.	.	PUNCT
cana-835	30	1	the	the	DET
cana-835	30	2	newt0n	newt0n	PROPN
cana-835	30	3	method	method	NOUN
cana-835	30	4	is	be	AUX
cana-835	30	5	a	a	DET
cana-835	30	6	numerical	numerical	ADJ
cana-835	30	7	method	method	NOUN
cana-835	30	8	for	for	ADP
cana-835	30	9	solving	solve	VERB
cana-835	30	10	equations	equation	NOUN
cana-835	30	11	that	that	PRON
cana-835	30	12	starts	start	VERB
cana-835	30	13	with	with	ADP
cana-835	30	14	an	an	DET
cana-835	30	15	initial	initial	ADJ
cana-835	30	16	guess	guess	NOUN
cana-835	30	17	and	and	CCONJ
cana-835	30	18	then	then	ADV
cana-835	30	19	uses	use	VERB
cana-835	30	20	iterative	iterative	NOUN
cana-835	30	21	steps	step	NOUN
cana-835	30	22	to	to	PART
cana-835	30	23	c0nverge	c0nverge	VERB
cana-835	30	24	t0wards	t0wards	SCONJ
cana-835	30	25	the	the	DET
cana-835	30	26	true	true	ADJ
cana-835	30	27	solution	solution	NOUN
cana-835	30	28	.	.	PUNCT
cana-835	31	1	it	it	PRON
cana-835	31	2	is	be	AUX
cana-835	31	3	based	base	VERB
cana-835	31	4	on	on	ADP
cana-835	31	5	the	the	DET
cana-835	31	6	idea	idea	NOUN
cana-835	31	7	of	of	ADP
cana-835	31	8	appr0ximating	appr0ximate	VERB
cana-835	31	9	a	a	DET
cana-835	31	10	function	function	NOUN
cana-835	31	11	as	as	ADP
cana-835	31	12	a	a	DET
cana-835	31	13	straight	straight	ADJ
cana-835	31	14	line	line	NOUN
cana-835	31	15	tangent	tangent	NOUN
cana-835	31	16	to	to	ADP
cana-835	31	17	the	the	DET
cana-835	31	18	curve	curve	NOUN
cana-835	31	19	at	at	ADP
cana-835	31	20	a	a	DET
cana-835	31	21	given	give	VERB
cana-835	31	22	point	point	NOUN
cana-835	31	23	.	.	PUNCT
cana-835	32	1	to	to	PART
cana-835	32	2	implement	implement	VERB
cana-835	32	3	the	the	DET
cana-835	32	4	interval	interval	NOUN
cana-835	32	5	newt0n	newt0n	PROPN
cana-835	32	6	method	method	NOUN
cana-835	32	7	,	,	PUNCT
cana-835	32	8	we	we	PRON
cana-835	32	9	will	will	AUX
cana-835	32	10	make	make	VERB
cana-835	32	11	use	use	NOUN
cana-835	32	12	of	of	ADP
cana-835	32	13	interval	interval	NOUN
cana-835	32	14	arithmetic	arithmetic	ADJ
cana-835	32	15	,	,	PUNCT
cana-835	32	16	where	where	SCONJ
cana-835	32	17	the	the	DET
cana-835	32	18	result	result	NOUN
cana-835	32	19	of	of	ADP
cana-835	32	20	an	an	DET
cana-835	32	21	0peration	0peration	PROPN
cana-835	32	22	on	on	ADP
cana-835	32	23	intervals	interval	NOUN
cana-835	32	24	is	be	AUX
cana-835	32	25	an	an	DET
cana-835	32	26	interval	interval	NOUN
cana-835	32	27	that	that	PRON
cana-835	32	28	bounds	bound	VERB
cana-835	32	29	the	the	DET
cana-835	32	30	possible	possible	ADJ
cana-835	32	31	values	value	NOUN
cana-835	32	32	of	of	ADP
cana-835	32	33	the	the	DET
cana-835	32	34	output	output	NOUN
cana-835	32	35	.	.	PUNCT
cana-835	33	1	this	this	PRON
cana-835	33	2	allows	allow	VERB
cana-835	33	3	to	to	PART
cana-835	33	4	compute	compute	VERB
cana-835	33	5	rigorous	rigorous	ADJ
cana-835	33	6	bounds	bound	NOUN
cana-835	33	7	on	on	ADP
cana-835	33	8	the	the	DET
cana-835	33	9	solution	solution	NOUN
cana-835	33	10	of	of	ADP
cana-835	33	11	an	an	DET
cana-835	33	12	equation	equation	NOUN
cana-835	33	13	.	.	PUNCT
cana-835	34	1	in	in	ADP
cana-835	34	2	this	this	DET
cana-835	34	3	implementation	implementation	NOUN
cana-835	34	4	,	,	PUNCT
cana-835	34	5	the	the	DET
cana-835	34	6	`	`	PUNCT
cana-835	34	7	f	f	X
cana-835	34	8	`	`	PUNCT
cana-835	34	9	and	and	CCONJ
cana-835	34	10	`	`	PUNCT
cana-835	34	11	df	df	NOUN
cana-835	34	12	`	`	PUNCT
cana-835	34	13	arguments	argument	NOUN
cana-835	34	14	are	be	AUX
cana-835	34	15	functions	function	NOUN
cana-835	34	16	that	that	PRON
cana-835	34	17	represent	represent	VERB
cana-835	34	18	the	the	DET
cana-835	34	19	original	original	ADJ
cana-835	34	20	function	function	NOUN
cana-835	34	21	and	and	CCONJ
cana-835	34	22	its	its	PRON
cana-835	34	23	derivative	derivative	NOUN
cana-835	34	24	,	,	PUNCT
cana-835	34	25	respectively	respectively	ADV
cana-835	34	26	.	.	PUNCT
cana-835	35	1	the	the	DET
cana-835	35	2	`	`	PUNCT
cana-835	35	3	x0	x0	NUM
cana-835	35	4	`	`	PUNCT
cana-835	35	5	argument	argument	NOUN
cana-835	35	6	is	be	AUX
cana-835	35	7	the	the	DET
cana-835	35	8	initial	initial	ADJ
cana-835	35	9	guess	guess	NOUN
cana-835	35	10	for	for	ADP
cana-835	35	11	the	the	DET
cana-835	35	12	root	root	NOUN
cana-835	35	13	of	of	ADP
cana-835	35	14	the	the	DET
cana-835	35	15	equation	equation	NOUN
cana-835	35	16	.	.	PUNCT
cana-835	36	1	the	the	DET
cana-835	36	2	`	`	PUNCT
cana-835	36	3	epsilon	epsilon	PROPN
cana-835	36	4	`	`	PUNCT
cana-835	36	5	argument	argument	NOUN
cana-835	36	6	specifies	specify	VERB
cana-835	36	7	the	the	DET
cana-835	36	8	desired	desire	VERB
cana-835	36	9	precision	precision	NOUN
cana-835	36	10	of	of	ADP
cana-835	36	11	the	the	DET
cana-835	36	12	solution	solution	NOUN
cana-835	36	13	.	.	PUNCT
cana-835	37	1	the	the	DET
cana-835	37	2	`	`	PUNCT
cana-835	37	3	interval	interval	NOUN
cana-835	37	4	`	`	PUNCT
cana-835	37	5	function	function	NOUN
cana-835	37	6	is	be	AUX
cana-835	37	7	used	use	VERB
cana-835	37	8	to	to	PART
cana-835	37	9	compute	compute	VERB
cana-835	37	10	an	an	DET
cana-835	37	11	interval	interval	NOUN
cana-835	37	12	from	from	ADP
cana-835	37	13	a	a	DET
cana-835	37	14	single	single	ADJ
cana-835	37	15	value	value	NOUN
cana-835	37	16	.	.	PUNCT
cana-835	38	1	the	the	DET
cana-835	38	2	method	method	NOUN
cana-835	38	3	iteratively	iteratively	ADV
cana-835	38	4	updates	update	VERB
cana-835	38	5	the	the	DET
cana-835	38	6	value	value	NOUN
cana-835	38	7	of	of	ADP
cana-835	38	8	`	`	PUNCT
cana-835	38	9	x	x	PUNCT
cana-835	38	10	`	`	PUNCT
cana-835	38	11	using	use	VERB
cana-835	38	12	the	the	DET
cana-835	38	13	interval	interval	NOUN
cana-835	38	14	newt0n	newt0n	PROPN
cana-835	38	15	iteration	iteration	NOUN
cana-835	38	16	formula	formula	NOUN
cana-835	38	17	until	until	ADP
cana-835	38	18	the	the	DET
cana-835	38	19	absolute	absolute	ADJ
cana-835	38	20	value	value	NOUN
cana-835	38	21	of	of	ADP
cana-835	38	22	`	`	PUNCT
cana-835	38	23	f(x	f(x	PROPN
cana-835	38	24	)	)	PUNCT
cana-835	38	25	`	`	PUNCT
cana-835	38	26	is	be	AUX
cana-835	38	27	less	less	ADJ
cana-835	38	28	than	than	ADP
cana-835	38	29	`	`	PUNCT
cana-835	38	30	epsilon	epsilon	PROPN
cana-835	38	31	`	`	PUNCT
cana-835	38	32	,	,	PUNCT
cana-835	38	33	indicating	indicate	VERB
cana-835	38	34	a	a	DET
cana-835	38	35	suitable	suitable	ADJ
cana-835	38	36	approximation	approximation	NOUN
cana-835	38	37	has	have	AUX
cana-835	38	38	been	be	AUX
cana-835	38	39	found	find	VERB
cana-835	38	40	.	.	PUNCT
cana-835	39	1	the	the	DET
cana-835	39	2	`	`	PUNCT
cana-835	39	3	df	df	NOUN
cana-835	39	4	interval	interval	NOUN
cana-835	39	5	`	`	PUNCT
cana-835	39	6	is	be	AUX
cana-835	39	7	used	use	VERB
cana-835	39	8	to	to	PART
cana-835	39	9	compute	compute	VERB
cana-835	39	10	the	the	DET
cana-835	39	11	slope	slope	NOUN
cana-835	39	12	of	of	ADP
cana-835	39	13	the	the	DET
cana-835	39	14	tangent	tangent	ADJ
cana-835	39	15	line	line	NOUN
cana-835	39	16	at	at	ADP
cana-835	39	17	each	each	DET
cana-835	39	18	iteration	iteration	NOUN
cana-835	39	19	.	.	PUNCT
cana-835	40	1	the	the	DET
cana-835	40	2	impact	impact	NOUN
cana-835	40	3	of	of	ADP
cana-835	40	4	employing	employ	VERB
cana-835	40	5	a	a	DET
cana-835	40	6	local	local	ADJ
cana-835	40	7	minimizer	minimizer	NOUN
cana-835	40	8	to	to	PART
cana-835	40	9	update	update	VERB
cana-835	40	10	the	the	DET
cana-835	40	11	upper	upper	ADJ
cana-835	40	12	bound	bind	VERB
cana-835	40	13	on	on	ADP
cana-835	40	14	the	the	DET
cana-835	40	15	global	global	ADJ
cana-835	40	16	minimum	minimum	NOUN
cana-835	40	17	is	be	AUX
cana-835	40	18	also	also	ADV
cana-835	40	19	considered	consider	VERB
cana-835	40	20	.	.	PUNCT
cana-835	41	1	this	this	DET
cana-835	41	2	approach	approach	NOUN
cana-835	41	3	,	,	PUNCT
cana-835	41	4	named	name	VERB
cana-835	41	5	liss_lp	liss_lp	ADJ
cana-835	41	6	,	,	PUNCT
cana-835	41	7	is	be	AUX
cana-835	41	8	demonstrated	demonstrate	VERB
cana-835	41	9	through	through	ADP
cana-835	41	10	various	various	ADJ
cana-835	41	11	global	global	ADJ
cana-835	41	12	optimization	optimization	NOUN
cana-835	41	13	problems	problem	NOUN
cana-835	41	14	,	,	PUNCT
cana-835	41	15	particularly	particularly	ADV
cana-835	41	16	focusing	focus	VERB
cana-835	41	17	on	on	ADP
cana-835	41	18	those	those	PRON
cana-835	41	19	originating	originate	VERB
cana-835	41	20	from	from	ADP
cana-835	41	21	chemical	chemical	ADJ
cana-835	41	22	engineering	engineering	NOUN
cana-835	41	23	.	.	PUNCT
cana-835	42	1	liss_lp	liss_lp	PROPN
cana-835	42	2	proves	prove	VERB
cana-835	42	3	effective	effective	ADJ
cana-835	42	4	in	in	ADP
cana-835	42	5	solving	solve	VERB
cana-835	42	6	problems	problem	NOUN
cana-835	42	7	with	with	ADP
cana-835	42	8	a	a	DET
cana-835	42	9	vast	vast	ADJ
cana-835	42	10	number	number	NOUN
cana-835	42	11	of	of	ADP
cana-835	42	12	local	local	ADJ
cana-835	42	13	optima	optima	NOUN
cana-835	42	14	and	and	CCONJ
cana-835	42	15	those	those	PRON
cana-835	42	16	involving	involve	VERB
cana-835	42	17	a	a	DET
cana-835	42	18	relatively	relatively	ADV
cana-835	42	19	large	large	ADJ
cana-835	42	20	number	number	NOUN
cana-835	42	21	of	of	ADP
cana-835	42	22	variables	variable	NOUN
cana-835	42	23	.	.	PUNCT
cana-835	43	1	in	in	ADP
cana-835	43	2	2017	2017	NUM
cana-835	43	3	,	,	PUNCT
cana-835	43	4	lei	lei	PROPN
cana-835	43	5	wang	wang	PROPN
cana-835	43	6	described	describe	VERB
cana-835	43	7	the	the	DET
cana-835	43	8	newt0n	newt0n	PROPN
cana-835	43	9	iteration	iteration	NOUN
cana-835	43	10	-	-	PUNCT
cana-835	43	11	based	base	VERB
cana-835	43	12	interval	interval	NOUN
cana-835	43	13	uncertainty	uncertainty	NOUN
cana-835	43	14	analysis	analysis	NOUN
cana-835	43	15	approach	approach	NOUN
cana-835	43	16	for	for	ADP
cana-835	43	17	interdisciplinary	interdisciplinary	ADJ
cana-835	43	18	systems	system	NOUN
cana-835	43	19	,	,	PUNCT
cana-835	43	20	known	know	VERB
cana-835	43	21	as	as	ADP
cana-835	43	22	ni	ni	NOUN
cana-835	43	23	-	-	PUNCT
cana-835	43	24	iuam	iuam	ADJ
cana-835	43	25	,	,	PUNCT
cana-835	43	26	this	this	DET
cana-835	43	27	technique	technique	NOUN
cana-835	43	28	divides	divide	VERB
cana-835	43	29	complicated	complicated	ADJ
cana-835	43	30	systems	system	NOUN
cana-835	43	31	into	into	ADP
cana-835	43	32	distinct	distinct	ADJ
cana-835	43	33	disciplines	discipline	NOUN
cana-835	43	34	and	and	CCONJ
cana-835	43	35	uses	use	VERB
cana-835	43	36	newton	newton	PROPN
cana-835	43	37	iteration	iteration	PROPN
cana-835	43	38	equations	equation	NOUN
cana-835	43	39	to	to	PART
cana-835	43	40	calculate	calculate	VERB
cana-835	43	41	the	the	DET
cana-835	43	42	upperi	upperi	PROPN
cana-835	43	43	and	and	CCONJ
cana-835	43	44	l0wer	l0w	ADJ
cana-835	43	45	limits	limit	NOUN
cana-835	43	46	of	of	ADP
cana-835	43	47	connected	connected	ADJ
cana-835	43	48	state	state	NOUN
cana-835	43	49	variables	variable	NOUN
cana-835	43	50	at	at	ADP
cana-835	43	51	each	each	DET
cana-835	43	52	iterative	iterative	ADJ
cana-835	43	53	step	step	NOUN
cana-835	43	54	.	.	PUNCT
cana-835	44	1	ni	ni	ADJ
cana-835	44	2	-	-	ADJ
cana-835	44	3	iuam	iuam	PROPN
cana-835	44	4	requires	require	VERB
cana-835	44	5	simply	simply	ADV
cana-835	44	6	the	the	DET
cana-835	44	7	boundaries	boundary	NOUN
cana-835	44	8	of	of	ADP
cana-835	44	9	unknown	unknown	ADJ
cana-835	44	10	parameters	parameter	NOUN
cana-835	44	11	,	,	PUNCT
cana-835	44	12	removing	remove	VERB
cana-835	44	13	the	the	DET
cana-835	44	14	requirement	requirement	NOUN
cana-835	44	15	for	for	ADP
cana-835	44	16	particular	particular	ADJ
cana-835	44	17	distribution	distribution	NOUN
cana-835	44	18	formats	format	NOUN
cana-835	44	19	and	and	CCONJ
cana-835	44	20	perhaps	perhaps	ADV
cana-835	44	21	reducing	reduce	VERB
cana-835	44	22	the	the	DET
cana-835	44	23	need	need	NOUN
cana-835	44	24	for	for	ADP
cana-835	44	25	raw	raw	ADJ
cana-835	44	26	data	datum	NOUN
cana-835	44	27	.	.	PUNCT
cana-835	45	1	additionally	additionally	ADV
cana-835	45	2	,	,	PUNCT
cana-835	45	3	ni	ni	ADJ
cana-835	45	4	-	-	PUNCT
cana-835	45	5	iuam	iuam	ADJ
cana-835	45	6	benefits	benefit	NOUN
cana-835	45	7	from	from	ADP
cana-835	45	8	newton	newton	PROPN
cana-835	45	9	iteration	iteration	PROPN
cana-835	45	10	's	's	PART
cana-835	45	11	super	super	ADJ
cana-835	45	12	-	-	ADJ
cana-835	45	13	linear	linear	ADJ
cana-835	45	14	convergence	convergence	NOUN
cana-835	45	15	,	,	PUNCT
cana-835	45	16	which	which	PRON
cana-835	45	17	accelerates	accelerate	VERB
cana-835	45	18	the	the	DET
cana-835	45	19	convergence	convergence	NOUN
cana-835	45	20	process	process	NOUN
cana-835	45	21	.	.	PUNCT
cana-835	46	1	in	in	ADP
cana-835	46	2	2021	2021	NUM
cana-835	46	3	,	,	PUNCT
cana-835	46	4	zhiping	zhipe	VERB
cana-835	46	5	f0cused	f0cuse	VERB
cana-835	46	6	on	on	ADP
cana-835	46	7	studying	study	VERB
cana-835	46	8	the	the	DET
cana-835	46	9	impact	impact	NOUN
cana-835	46	10	of	of	ADP
cana-835	46	11	uncertainties	uncertainty	NOUN
cana-835	46	12	in	in	ADP
cana-835	46	13	n0nlinear	n0nlinear	PROPN
cana-835	46	14	structural	structural	ADJ
cana-835	46	15	system	system	NOUN
cana-835	46	16	,	,	PUNCT
cana-835	46	17	a	a	DET
cana-835	46	18	newt0n	newt0n	PROPN
cana-835	46	19	iteration	iteration	NOUN
cana-835	46	20	-	-	PUNCT
cana-835	46	21	based	base	VERB
cana-835	46	22	interval	interval	NOUN
cana-835	46	23	analysis	analysis	NOUN
cana-835	46	24	meth0d	meth0d	PROPN
cana-835	46	25	(	(	PUNCT
cana-835	46	26	ni	ni	PROPN
cana-835	46	27	-	-	PUNCT
cana-835	46	28	iam	iam	PROPN
cana-835	46	29	)	)	PUNCT
cana-835	46	30	to	to	PART
cana-835	46	31	quantify	quantify	VERB
cana-835	46	32	these	these	DET
cana-835	46	33	uncertainties	uncertainty	NOUN
cana-835	46	34	by	by	ADP
cana-835	46	35	considering	consider	VERB
cana-835	46	36	uncertain	uncertain	ADJ
cana-835	46	37	-	-	PUNCT
cana-835	46	38	but	but	CCONJ
cana-835	46	39	-	-	PUNCT
cana-835	46	40	b0unded	b0unde	VERB
cana-835	46	41	parameters	parameter	NOUN
cana-835	46	42	as	as	ADP
cana-835	46	43	interval	interval	NOUN
cana-835	46	44	variables	variable	NOUN
cana-835	46	45	.	.	PUNCT
cana-835	47	1	the	the	DET
cana-835	47	2	meth0d	meth0d	PROPN
cana-835	47	3	simplifies	simplify	VERB
cana-835	47	4	the	the	DET
cana-835	47	5	uncertain	uncertain	ADJ
cana-835	47	6	0nlinear	0nlinear	PROPN
cana-835	47	7	pr0blem	pr0blem	NOUN
cana-835	47	8	into	into	ADP
cana-835	47	9	a	a	DET
cana-835	47	10	series	series	NOUN
cana-835	47	11	of	of	ADP
cana-835	47	12	uncertain	uncertain	ADJ
cana-835	47	13	linear	linear	ADJ
cana-835	47	14	issues	issue	NOUN
cana-835	47	15	through	through	ADP
cana-835	47	16	interval	interval	NOUN
cana-835	47	17	iteration	iteration	NOUN
cana-835	47	18	schemes	scheme	NOUN
cana-835	47	19	,	,	PUNCT
cana-835	47	20	taylorseriesexpansion	taylorseriesexpansion	NOUN
cana-835	47	21	,	,	PUNCT
cana-835	47	22	and	and	CCONJ
cana-835	47	23	the	the	DET
cana-835	47	24	lagrangianmultipliermethod	lagrangianmultipliermethod	NOUN
cana-835	47	25	.	.	PUNCT
cana-835	48	1	numerical	numerical	ADJ
cana-835	48	2	examples	example	NOUN
cana-835	48	3	dem0nstrate	dem0nstrate	VERB
cana-835	48	4	the	the	DET
cana-835	48	5	effectiveness	effectiveness	NOUN
cana-835	48	6	and	and	CCONJ
cana-835	48	7	applicability	applicability	NOUN
cana-835	48	8	of	of	ADP
cana-835	48	9	the	the	DET
cana-835	48	10	prop0sed	prop0se	VERB
cana-835	48	11	meth0d	meth0d	PROPN
cana-835	48	12	,	,	PUNCT
cana-835	48	13	and	and	CCONJ
cana-835	48	14	its	its	PRON
cana-835	48	15	compatibility	compatibility	NOUN
cana-835	48	16	with	with	ADP
cana-835	48	17	the	the	DET
cana-835	48	18	perturbati0n	perturbati0n	PROPN
cana-835	48	19	-	-	PUNCT
cana-835	48	20	based	base	VERB
cana-835	48	21	pr0babilistic	pr0babilistic	ADJ
cana-835	48	22	method	method	NOUN
cana-835	48	23	is	be	AUX
cana-835	48	24	also	also	ADV
cana-835	48	25	studied	study	VERB
cana-835	48	26	.	.	PUNCT
cana-835	49	1	https://link.springer.com/article/10.1007/s11433-017-9068-5#auth-lei-wang-aff1	https://link.springer.com/article/10.1007/s11433-017-9068-5#auth-lei-wang-aff1	PROPN
cana-835	49	2	https://link.springer.com/article/10.1007/s11433-017-9068-5#auth-lei-wang-aff1	https://link.springer.com/article/10.1007/s11433-017-9068-5#auth-lei-wang-aff1	PROPN
cana-835	49	3	communications	communication	NOUN
cana-835	49	4	on	on	ADP
cana-835	49	5	applied	apply	VERB
cana-835	49	6	nonlinear	nonlinear	ADJ
cana-835	49	7	analysis	analysis	NOUN
cana-835	49	8	issn	issn	NOUN
cana-835	49	9	:	:	PUNCT
cana-835	49	10	1074	1074	NUM
cana-835	49	11	-	-	PUNCT
cana-835	49	12	133x	133x	NUM
cana-835	49	13	vol	vol	NOUN
cana-835	49	14	31	31	NUM
cana-835	49	15	no	no	NOUN
cana-835	49	16	.	.	PUNCT
cana-835	50	1	4s	4s	NUM
cana-835	50	2	(	(	PUNCT
cana-835	50	3	2024	2024	NUM
cana-835	50	4	)	)	PUNCT
cana-835	50	5	184	184	NUM
cana-835	50	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	50	7	fuzzy	fuzzy	ADJ
cana-835	50	8	sets	set	NOUN
cana-835	50	9	,	,	PUNCT
cana-835	50	10	initially	initially	ADV
cana-835	50	11	introduced	introduce	VERB
cana-835	50	12	by	by	ADP
cana-835	50	13	zadeh	zadeh	PROPN
cana-835	50	14	in	in	ADP
cana-835	50	15	1965	1965	NUM
cana-835	50	16	,	,	PUNCT
cana-835	50	17	have	have	AUX
cana-835	50	18	significantly	significantly	ADV
cana-835	50	19	impacted	impact	VERB
cana-835	50	20	various	various	ADJ
cana-835	50	21	fields	field	NOUN
cana-835	50	22	due	due	ADP
cana-835	50	23	to	to	ADP
cana-835	50	24	their	their	PRON
cana-835	50	25	ability	ability	NOUN
cana-835	50	26	to	to	PART
cana-835	50	27	represent	represent	VERB
cana-835	50	28	the	the	DET
cana-835	50	29	ambiguity	ambiguity	NOUN
cana-835	50	30	in	in	ADP
cana-835	50	31	real	real	ADJ
cana-835	50	32	-	-	PUNCT
cana-835	50	33	world	world	NOUN
cana-835	50	34	scenarios	scenario	NOUN
cana-835	50	35	.	.	PUNCT
cana-835	51	1	triangular	triangular	ADJ
cana-835	51	2	fuzzy	fuzzy	ADJ
cana-835	51	3	numbers	number	NOUN
cana-835	51	4	,	,	PUNCT
cana-835	51	5	a	a	DET
cana-835	51	6	crucial	crucial	ADJ
cana-835	51	7	aspect	aspect	NOUN
cana-835	51	8	of	of	ADP
cana-835	51	9	fuzzy	fuzzy	ADJ
cana-835	51	10	set	set	NOUN
cana-835	51	11	theory	theory	NOUN
cana-835	51	12	,	,	PUNCT
cana-835	51	13	have	have	AUX
cana-835	51	14	been	be	AUX
cana-835	51	15	discussed	discuss	VERB
cana-835	51	16	in	in	ADP
cana-835	51	17	detail	detail	NOUN
cana-835	51	18	,	,	PUNCT
cana-835	51	19	along	along	ADP
cana-835	51	20	with	with	ADP
cana-835	51	21	their	their	PRON
cana-835	51	22	operations	operation	NOUN
cana-835	51	23	.	.	PUNCT
cana-835	52	1	later	later	ADV
cana-835	52	2	,	,	PUNCT
cana-835	52	3	krassimir	krassimir	PROPN
cana-835	52	4	atanassov	atanassov	PROPN
cana-835	52	5	introduced	introduce	VERB
cana-835	52	6	intuitionistic	intuitionistic	ADJ
cana-835	52	7	fuzzy	fuzzy	ADJ
cana-835	52	8	sets	set	NOUN
cana-835	52	9	in	in	ADP
cana-835	52	10	1983	1983	NUM
cana-835	52	11	,	,	PUNCT
cana-835	52	12	further	far	ADV
cana-835	52	13	expanding	expand	VERB
cana-835	52	14	upon	upon	SCONJ
cana-835	52	15	zadeh	zadeh	PROPN
cana-835	52	16	's	's	PART
cana-835	52	17	foundation	foundation	NOUN
cana-835	52	18	.	.	PUNCT
cana-835	53	1	in	in	ADP
cana-835	53	2	addition	addition	NOUN
cana-835	53	3	to	to	ADP
cana-835	53	4	degrees	degree	NOUN
cana-835	53	5	of	of	ADP
cana-835	53	6	membership	membership	NOUN
cana-835	53	7	,	,	PUNCT
cana-835	53	8	intuitionistic	intuitionistic	ADJ
cana-835	53	9	fuzzy	fuzzy	ADJ
cana-835	53	10	sets	set	NOUN
cana-835	53	11	also	also	ADV
cana-835	53	12	incorporate	incorporate	VERB
cana-835	53	13	degrees	degree	NOUN
cana-835	53	14	of	of	ADP
cana-835	53	15	nonmembership	nonmembership	NOUN
cana-835	53	16	.	.	PUNCT
cana-835	54	1	this	this	PRON
cana-835	54	2	means	mean	VERB
cana-835	54	3	that	that	SCONJ
cana-835	54	4	for	for	ADP
cana-835	54	5	each	each	DET
cana-835	54	6	element	element	NOUN
cana-835	54	7	,	,	PUNCT
cana-835	54	8	there	there	PRON
cana-835	54	9	are	be	VERB
cana-835	54	10	not	not	PART
cana-835	54	11	only	only	ADV
cana-835	54	12	measures	measure	NOUN
cana-835	54	13	of	of	ADP
cana-835	54	14	how	how	SCONJ
cana-835	54	15	much	much	ADJ
cana-835	54	16	it	it	PRON
cana-835	54	17	belongs	belong	VERB
cana-835	54	18	to	to	ADP
cana-835	54	19	the	the	DET
cana-835	54	20	set	set	NOUN
cana-835	54	21	,	,	PUNCT
cana-835	54	22	but	but	CCONJ
cana-835	54	23	also	also	ADV
cana-835	54	24	measures	measure	NOUN
cana-835	54	25	of	of	ADP
cana-835	54	26	how	how	SCONJ
cana-835	54	27	much	much	ADJ
cana-835	54	28	it	it	PRON
cana-835	54	29	does	do	AUX
cana-835	54	30	not	not	PART
cana-835	54	31	belong	belong	VERB
cana-835	54	32	to	to	ADP
cana-835	54	33	the	the	DET
cana-835	54	34	set	set	NOUN
cana-835	54	35	.	.	PUNCT
cana-835	55	1	this	this	DET
cana-835	55	2	dual	dual	ADJ
cana-835	55	3	perspective	perspective	NOUN
cana-835	55	4	offers	offer	VERB
cana-835	55	5	a	a	DET
cana-835	55	6	more	more	ADV
cana-835	55	7	comprehensive	comprehensive	ADJ
cana-835	55	8	representation	representation	NOUN
cana-835	55	9	of	of	ADP
cana-835	55	10	uncertainty	uncertainty	NOUN
cana-835	55	11	and	and	CCONJ
cana-835	55	12	ambiguity	ambiguity	NOUN
cana-835	55	13	in	in	ADP
cana-835	55	14	real	real	ADJ
cana-835	55	15	-	-	PUNCT
cana-835	55	16	world	world	NOUN
cana-835	55	17	situations	situation	NOUN
cana-835	55	18	.	.	PUNCT
cana-835	56	1	intuitionistic	intuitionistic	ADJ
cana-835	56	2	fuzzy	fuzzy	ADJ
cana-835	56	3	sets	set	NOUN
cana-835	56	4	have	have	AUX
cana-835	56	5	found	find	VERB
cana-835	56	6	applicati0ns	applicati0ns	VERB
cana-835	56	7	in	in	ADP
cana-835	56	8	vari0us	vari0us	PROPN
cana-835	56	9	fields	field	NOUN
cana-835	56	10	,	,	PUNCT
cana-835	56	11	including	include	VERB
cana-835	56	12	decisi0n	decisi0n	NOUN
cana-835	56	13	-	-	PUNCT
cana-835	56	14	making	making	NOUN
cana-835	56	15	,	,	PUNCT
cana-835	56	16	pattern	pattern	NOUN
cana-835	56	17	rec0gnition	rec0gnition	PROPN
cana-835	56	18	,	,	PUNCT
cana-835	56	19	image	image	NOUN
cana-835	56	20	pr0cessing	pr0cessing	NOUN
cana-835	56	21	,	,	PUNCT
cana-835	56	22	medical	medical	ADJ
cana-835	56	23	diagnosis	diagnosis	NOUN
cana-835	56	24	,	,	PUNCT
cana-835	56	25	and	and	CCONJ
cana-835	56	26	more	more	ADJ
cana-835	56	27	.	.	PUNCT
cana-835	57	1	they	they	PRON
cana-835	57	2	provide	provide	VERB
cana-835	57	3	a	a	DET
cana-835	57	4	powerful	powerful	ADJ
cana-835	57	5	framework	framework	NOUN
cana-835	57	6	for	for	ADP
cana-835	57	7	modeling	modeling	NOUN
cana-835	57	8	and	and	CCONJ
cana-835	57	9	reasoning	reasoning	NOUN
cana-835	57	10	with	with	ADP
cana-835	57	11	uncertain	uncertain	ADJ
cana-835	57	12	and	and	CCONJ
cana-835	57	13	imprecise	imprecise	ADJ
cana-835	57	14	information	information	NOUN
cana-835	57	15	,	,	PUNCT
cana-835	57	16	offering	offer	VERB
cana-835	57	17	more	more	ADV
cana-835	57	18	nuanced	nuanced	ADJ
cana-835	57	19	solutions	solution	NOUN
cana-835	57	20	to	to	ADP
cana-835	57	21	problems	problem	NOUN
cana-835	57	22	where	where	SCONJ
cana-835	57	23	traditional	traditional	ADJ
cana-835	57	24	crisp	crisp	ADJ
cana-835	57	25	sets	set	NOUN
cana-835	57	26	or	or	CCONJ
cana-835	57	27	classical	classical	ADJ
cana-835	57	28	fuzzy	fuzzy	ADJ
cana-835	57	29	sets	set	NOUN
cana-835	57	30	may	may	AUX
cana-835	57	31	fall	fall	VERB
cana-835	57	32	short	short	ADJ
cana-835	57	33	.	.	PUNCT
cana-835	58	1	throughout	throughout	ADP
cana-835	58	2	the	the	DET
cana-835	58	3	last	last	ADJ
cana-835	58	4	few	few	ADJ
cana-835	58	5	decades	decade	NOUN
cana-835	58	6	,	,	PUNCT
cana-835	58	7	various	various	ADJ
cana-835	58	8	academics	academic	NOUN
cana-835	58	9	have	have	AUX
cana-835	58	10	created	create	VERB
cana-835	58	11	0ptimization	0ptimization	NUM
cana-835	58	12	pr0blems	pr0blem	NOUN
cana-835	58	13	with	with	ADP
cana-835	58	14	fuzzy	fuzzy	ADJ
cana-835	58	15	valued	value	VERB
cana-835	58	16	0bjective	0bjective	NUM
cana-835	58	17	issues	issue	NOUN
cana-835	58	18	.	.	PUNCT
cana-835	59	1	ganesan	ganesan	PROPN
cana-835	59	2	et	et	PROPN
cana-835	59	3	al	al	PROPN
cana-835	59	4	.	.	PROPN
cana-835	60	1	(	(	PUNCT
cana-835	60	2	2017	2017	NUM
cana-835	60	3	)	)	PUNCT
cana-835	60	4	presented	present	VERB
cana-835	60	5	a	a	DET
cana-835	60	6	c0mparable	c0mparable	ADJ
cana-835	60	7	solutἰ0n	solutἰ0n	NOUN
cana-835	60	8	to	to	ADP
cana-835	60	9	fuzzy	fuzzy	ADJ
cana-835	60	10	unc0nstraἰned	unc0nstraἰned	ADJ
cana-835	60	11	optimἰzati0n	optimἰzati0n	NOUN
cana-835	60	12	problems	problem	NOUN
cana-835	60	13	using	use	VERB
cana-835	60	14	trἰangular	trἰangular	ADJ
cana-835	60	15	fuzzy	fuzzy	ADJ
cana-835	60	16	numbers	number	NOUN
cana-835	60	17	(	(	PUNCT
cana-835	60	18	2020	2020	NUM
cana-835	60	19	)	)	PUNCT
cana-835	60	20	.	.	PUNCT
cana-835	61	1	through0ut	through0ut	NOUN
cana-835	61	2	the	the	DET
cana-835	61	3	last	last	ADJ
cana-835	61	4	few	few	ADJ
cana-835	61	5	decades	decade	NOUN
cana-835	61	6	,	,	PUNCT
cana-835	61	7	different	different	ADJ
cana-835	61	8	researchers	researcher	NOUN
cana-835	61	9	have	have	AUX
cana-835	61	10	created	create	VERB
cana-835	61	11	0ptimization	0ptimization	NUM
cana-835	61	12	pr0blems	pr0blem	NOUN
cana-835	61	13	with	with	ADP
cana-835	61	14	fuzzy	fuzzy	ADJ
cana-835	61	15	valued	value	VERB
cana-835	61	16	objective	objective	ADJ
cana-835	61	17	problems	problem	NOUN
cana-835	61	18	.	.	PUNCT
cana-835	62	1	[	[	X
cana-835	62	2	ben	ben	PROPN
cana-835	62	3	et	et	PROPN
cana-835	62	4	al	al	PROPN
cana-835	62	5	.	.	PUNCT
cana-835	63	1	[	[	X
cana-835	63	2	1	1	NUM
cana-835	63	3	]	]	PUNCT
cana-835	63	4	.	.	PUNCT
cana-835	64	1	debski	debski	PROPN
cana-835	65	1	[	[	X
cana-835	65	2	2	2	NUM
cana-835	65	3	]	]	PUNCT
cana-835	65	4	,	,	PUNCT
cana-835	65	5	dennis	dennis	PROPN
cana-835	65	6	and	and	CCONJ
cana-835	65	7	shanable	shanable	VERB
cana-835	65	8	[	[	X
cana-835	65	9	3	3	NUM
cana-835	65	10	]	]	PUNCT
cana-835	65	11	,	,	PUNCT
cana-835	65	12	chenghand	chenghand	NOUN
cana-835	65	13	k0valyov	k0valyov	VERB
cana-835	66	1	[	[	X
cana-835	66	2	10	10	NUM
cana-835	66	3	]	]	PUNCT
cana-835	66	4	,	,	PUNCT
cana-835	66	5	timothy	timothy	PROPN
cana-835	67	1	[	[	X
cana-835	67	2	11	11	NUM
cana-835	67	3	]	]	PUNCT
cana-835	67	4	,	,	PUNCT
cana-835	67	5	shi	shi	PROPN
cana-835	68	1	[	[	X
cana-835	68	2	21	21	NUM
cana-835	68	3	]	]	PUNCT
cana-835	68	4	.	.	PUNCT
cana-835	69	1	m	m	AUX
cana-835	69	2	furthermore	furthermore	ADV
cana-835	69	3	,	,	PUNCT
cana-835	69	4	unc0nstrained	unc0nstrained	ADJ
cana-835	69	5	pr0blems	pr0blem	NOUN
cana-835	69	6	are	be	AUX
cana-835	69	7	s0lvedhusinghdifferential	s0lvedhusinghdifferential	ADJ
cana-835	69	8	calculus	calculus	NOUN
cana-835	69	9	.	.	PUNCT
cana-835	70	1	ganesan	ganesan	PROPN
cana-835	70	2	et	et	PROPN
cana-835	70	3	al	al	PROPN
cana-835	70	4	.	.	PROPN
cana-835	70	5	,[12	,[12	PROPN
cana-835	70	6	]	]	PUNCT
cana-835	70	7	propose	propose	VERB
cana-835	70	8	a	a	DET
cana-835	70	9	novel	novel	ADJ
cana-835	70	10	methodology	methodology	NOUN
cana-835	70	11	for	for	ADP
cana-835	70	12	addressing	address	VERB
cana-835	70	13	single	single	ADJ
cana-835	70	14	-	-	PUNCT
cana-835	70	15	variable	variable	ADJ
cana-835	70	16	problems	problem	NOUN
cana-835	70	17	without	without	ADP
cana-835	70	18	constraints	constraint	NOUN
cana-835	70	19	using	use	VERB
cana-835	70	20	newton	newton	PROPN
cana-835	70	21	's	's	PART
cana-835	70	22	interval	interval	NOUN
cana-835	70	23	analysis	analysis	NOUN
cana-835	70	24	method	method	NOUN
cana-835	70	25	,	,	PUNCT
cana-835	70	26	which	which	PRON
cana-835	70	27	differs	differ	VERB
cana-835	70	28	from	from	ADP
cana-835	70	29	the	the	DET
cana-835	70	30	standard	standard	ADJ
cana-835	70	31	method	method	NOUN
cana-835	70	32	of	of	ADP
cana-835	70	33	employing	employ	VERB
cana-835	70	34	calculus	calculus	NOUN
cana-835	70	35	..	..	PUNCT
cana-835	70	36	sophia	sophia	PROPN
cana-835	70	37	porchelvihet	porchelvihet	PROPN
cana-835	70	38	al[8	al[8	X
cana-835	70	39	]	]	PUNCT
cana-835	70	40	extended	extend	VERB
cana-835	70	41	to	to	PART
cana-835	70	42	bivariate	bivariate	VERB
cana-835	70	43	pr0blems	pr0blem	NOUN
cana-835	70	44	using	use	VERB
cana-835	70	45	newt0n	newt0n	PROPN
cana-835	70	46	’s	’s	PART
cana-835	70	47	meth0d	meth0d	PROPN
cana-835	70	48	.	.	PUNCT
cana-835	71	1	irene	irene	PROPN
cana-835	71	2	hepzibah	hepzibah	PROPN
cana-835	71	3	,	,	PUNCT
cana-835	71	4	shilpa[5	shilpa[5	PRON
cana-835	71	5	]	]	PUNCT
cana-835	71	6	extended	extend	VERB
cana-835	71	7	into	into	ADP
cana-835	71	8	fuzzy	fuzzy	ADJ
cana-835	71	9	single	single	ADJ
cana-835	71	10	and	and	CCONJ
cana-835	71	11	bivariate	bivariate	ADJ
cana-835	71	12	unconstrained	unconstrained	ADJ
cana-835	71	13	problems	problem	NOUN
cana-835	71	14	by	by	ADP
cana-835	71	15	using	use	VERB
cana-835	71	16	fuzzy	fuzzy	ADJ
cana-835	71	17	newt0n	newt0n	PROPN
cana-835	71	18	's	's	PART
cana-835	71	19	interval	interval	NOUN
cana-835	71	20	analysis	analysis	NOUN
cana-835	71	21	meth0d	meth0d	PROPN
cana-835	71	22	.	.	PUNCT
cana-835	72	1	this	this	DET
cana-835	72	2	paper	paper	NOUN
cana-835	72	3	presents	present	VERB
cana-835	72	4	a	a	DET
cana-835	72	5	novel	novel	ADJ
cana-835	72	6	approach	approach	NOUN
cana-835	72	7	to	to	ADP
cana-835	72	8	solving	solve	VERB
cana-835	72	9	non	non	ADJ
cana-835	72	10	-	-	ADJ
cana-835	72	11	linear	linear	ADJ
cana-835	72	12	,	,	PUNCT
cana-835	72	13	unc0nstrained	unc0nstrained	PROPN
cana-835	72	14	0ptimization	0ptimization	PROPN
cana-835	72	15	problems	problem	NOUN
cana-835	72	16	using	use	VERB
cana-835	72	17	the	the	DET
cana-835	72	18	intuitionistic	intuitionistic	ADJ
cana-835	72	19	newt0n	newt0n	ADJ
cana-835	72	20	meth0d	meth0d	PROPN
cana-835	72	21	and	and	CCONJ
cana-835	72	22	interval	interval	NOUN
cana-835	72	23	analysis	analysis	NOUN
cana-835	72	24	.	.	PUNCT
cana-835	73	1	it	it	PRON
cana-835	73	2	intr0duces	intr0duce	VERB
cana-835	73	3	interval	interval	NOUN
cana-835	73	4	arithmetic	arithmetic	ADJ
cana-835	73	5	operations	operation	NOUN
cana-835	73	6	for	for	ADP
cana-835	73	7	addressing	address	VERB
cana-835	73	8	intuitionistic	intuitionistic	ADJ
cana-835	73	9	fuzzy	fuzzy	ADJ
cana-835	73	10	unconstrained	unconstrained	ADJ
cana-835	73	11	optimization	optimization	NOUN
cana-835	73	12	issues	issue	NOUN
cana-835	73	13	.	.	PUNCT
cana-835	74	1	section	section	NOUN
cana-835	74	2	3	3	NUM
cana-835	74	3	focuses	focus	VERB
cana-835	74	4	on	on	ADP
cana-835	74	5	applying	apply	VERB
cana-835	74	6	newton	newton	PROPN
cana-835	74	7	's	's	PART
cana-835	74	8	method	method	NOUN
cana-835	74	9	and	and	CCONJ
cana-835	74	10	interval	interval	NOUN
cana-835	74	11	newt0n	newt0n	PROPN
cana-835	74	12	's	's	PART
cana-835	74	13	method	method	NOUN
cana-835	74	14	for	for	ADP
cana-835	74	15	unc0nstrained	unc0nstrained	PROPN
cana-835	74	16	0ptimization	0ptimization	PROPN
cana-835	74	17	,	,	PUNCT
cana-835	74	18	while	while	SCONJ
cana-835	74	19	secti0n	secti0n	NOUN
cana-835	74	20	4	4	NUM
cana-835	74	21	provides	provide	VERB
cana-835	74	22	illustrative	illustrative	ADJ
cana-835	74	23	examples	example	NOUN
cana-835	74	24	.	.	PUNCT
cana-835	75	1	the	the	DET
cana-835	75	2	study	study	NOUN
cana-835	75	3	concludes	conclude	VERB
cana-835	75	4	with	with	ADP
cana-835	75	5	some	some	DET
cana-835	75	6	remarks	remark	NOUN
cana-835	75	7	in	in	ADP
cana-835	75	8	section	section	NOUN
cana-835	75	9	5	5	NUM
cana-835	75	10	.	.	NOUN
cana-835	75	11	2	2	NUM
cana-835	75	12	.	.	X
cana-835	75	13	preliminariesl	preliminariesl	VERB
cana-835	75	14	in	in	ADP
cana-835	75	15	this	this	DET
cana-835	75	16	section	section	NOUN
cana-835	75	17	,	,	PUNCT
cana-835	75	18	some	some	DET
cana-835	75	19	important	important	ADJ
cana-835	75	20	definiti0ns	definiti0ns	PROPN
cana-835	75	21	are	be	AUX
cana-835	75	22	provided	provide	VERB
cana-835	75	23	definition	definition	NOUN
cana-835	75	24	1	1	NUM
cana-835	75	25	:	:	PUNCT
cana-835	76	1	[	[	X
cana-835	76	2	13	13	NUM
cana-835	76	3	]	]	X
cana-835	76	4	:	:	PUNCT
cana-835	76	5	a	a	DET
cana-835	76	6	fuzzy	fuzzy	ADJ
cana-835	76	7	set	set	NOUN
cana-835	76	8	ã	ã	PROPN
cana-835	76	9	can	can	AUX
cana-835	76	10	be	be	AUX
cana-835	76	11	expressed	express	VERB
cana-835	76	12	as	as	ADP
cana-835	76	13	the	the	DET
cana-835	76	14	pair	pair	NOUN
cana-835	76	15	𝓍	𝓍	X
cana-835	76	16	,	,	PUNCT
cana-835	76	17	𝜇	𝜇	PROPN
cana-835	76	18	�	�	PROPN
cana-835	76	19	̃	̃	NOUN
cana-835	76	20	�	�	PROPN
cana-835	76	21	(𝓍	(𝓍	NOUN
cana-835	76	22	)	)	PUNCT
cana-835	76	23	,	,	PUNCT
cana-835	76	24	where	where	SCONJ
cana-835	76	25	x	x	PRON
cana-835	76	26	is	be	AUX
cana-835	76	27	an	an	DET
cana-835	76	28	element	element	NOUN
cana-835	76	29	from	from	ADP
cana-835	76	30	a	a	DET
cana-835	76	31	classical	classical	ADJ
cana-835	76	32	set	set	NOUN
cana-835	76	33	a	a	DET
cana-835	76	34	and	and	CCONJ
cana-835	76	35	𝜇	𝜇	ADP
cana-835	76	36	�	�	PROPN
cana-835	76	37	̃	̃	PROPN
cana-835	76	38	�	�	NOUN
cana-835	76	39	(𝓍	(𝓍	NOUN
cana-835	76	40	)	)	PUNCT
cana-835	76	41	is	be	AUX
cana-835	76	42	the	the	DET
cana-835	76	43	membershℹp	membershℹp	NOUN
cana-835	76	44	functi0n	functi0n	NOUN
cana-835	76	45	associated	associate	VERB
cana-835	76	46	with	with	ADP
cana-835	76	47	x.	x.	NOUN
cana-835	76	48	this	this	DET
cana-835	76	49	functi0n	functi0n	NOUN
cana-835	76	50	takes	take	VERB
cana-835	76	51	values	value	NOUN
cana-835	76	52	within	within	ADP
cana-835	76	53	the	the	DET
cana-835	76	54	interval	interval	NOUN
cana-835	76	55	[	[	X
cana-835	76	56	0	0	NUM
cana-835	76	57	,	,	PUNCT
cana-835	76	58	1	1	NUM
cana-835	76	59	]	]	PUNCT
cana-835	76	60	and	and	CCONJ
cana-835	76	61	indicates	indicate	VERB
cana-835	76	62	x	x	NOUN
cana-835	76	63	's	's	PART
cana-835	76	64	degree	degree	NOUN
cana-835	76	65	of	of	ADP
cana-835	76	66	membershℹp	membershℹp	NOUN
cana-835	76	67	in	in	ADP
cana-835	76	68	the	the	DET
cana-835	76	69	fuzzy	fuzzy	ADJ
cana-835	76	70	set	set	VERB
cana-835	76	71	a.the	a.the	DET
cana-835	76	72	fuzzy	fuzzy	ADJ
cana-835	76	73	set	set	NOUN
cana-835	76	74	ã	ã	PROPN
cana-835	76	75	can	can	AUX
cana-835	76	76	be	be	AUX
cana-835	76	77	symbolized	symbolize	VERB
cana-835	76	78	by	by	ADP
cana-835	76	79	the	the	DET
cana-835	76	80	notation	notation	NOUN
cana-835	76	81	{	{	PUNCT
cana-835	76	82	𝓍	𝓍	NOUN
cana-835	76	83	,	,	PUNCT
cana-835	76	84	𝜇	𝜇	PROPN
cana-835	76	85	�	�	PROPN
cana-835	76	86	̃	̃	NOUN
cana-835	76	87	�	�	NOUN
cana-835	76	88	(𝓍	(𝓍	NOUN
cana-835	76	89	):	):	PUNCT
cana-835	76	90	𝓍	𝓍	PROPN
cana-835	76	91	∈	∈	PROPN
cana-835	76	92	𝜇	𝜇	ADP
cana-835	76	93	�	�	PROPN
cana-835	76	94	̃	̃	PROPN
cana-835	76	95	�	�	PROPN
cana-835	76	96	(𝓍	(𝓍	NOUN
cana-835	76	97	)	)	PUNCT
cana-835	76	98	∈	∈	PROPN
cana-835	77	1	[	[	X
cana-835	77	2	0,1	0,1	NUM
cana-835	77	3	]	]	PUNCT
cana-835	77	4	}	}	PUNCT
cana-835	77	5	.	.	PUNCT
cana-835	78	1	this	this	DET
cana-835	78	2	notation	notation	NOUN
cana-835	78	3	emphasizes	emphasize	VERB
cana-835	78	4	the	the	DET
cana-835	78	5	link	link	NOUN
cana-835	78	6	between	between	ADP
cana-835	78	7	the	the	DET
cana-835	78	8	classical	classical	ADJ
cana-835	78	9	set	set	NOUN
cana-835	78	10	a	a	PRON
cana-835	78	11	and	and	CCONJ
cana-835	78	12	the	the	DET
cana-835	78	13	membershℹp	membershℹp	NOUN
cana-835	78	14	functi0n	functi0n	PROPN
cana-835	78	15	𝜇	𝜇	ADP
cana-835	78	16	�	�	PROPN
cana-835	78	17	̃	̃	NOUN
cana-835	78	18	�	�	PROPN
cana-835	78	19	(𝓍	(𝓍	NOUN
cana-835	78	20	)	)	PUNCT
cana-835	78	21	.	.	PUNCT
cana-835	79	1	communications	communication	NOUN
cana-835	79	2	on	on	ADP
cana-835	79	3	applied	apply	VERB
cana-835	79	4	nonlinear	nonlinear	ADJ
cana-835	79	5	analysis	analysis	NOUN
cana-835	79	6	issn	issn	NOUN
cana-835	79	7	:	:	PUNCT
cana-835	79	8	1074	1074	NUM
cana-835	79	9	-	-	PUNCT
cana-835	79	10	133x	133x	NUM
cana-835	79	11	vol	vol	NOUN
cana-835	79	12	31	31	NUM
cana-835	79	13	no	no	NOUN
cana-835	79	14	.	.	PUNCT
cana-835	80	1	4s	4s	NUM
cana-835	80	2	(	(	PUNCT
cana-835	80	3	2024	2024	NUM
cana-835	80	4	)	)	PUNCT
cana-835	80	5	185	185	NUM
cana-835	80	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	80	7	definition	definition	NOUN
cana-835	80	8	2	2	NUM
cana-835	80	9	:	:	PUNCT
cana-835	80	10	l	l	ADJ
cana-835	80	11	-	-	PUNCT
cana-835	80	12	u	u	NOUN
cana-835	80	13	parametrℹc	parametrℹc	NOUN
cana-835	80	14	representation	representation	NOUN
cana-835	80	15	of	of	ADP
cana-835	80	16	intuiti0nℹstic	intuiti0nℹstic	ADJ
cana-835	80	17	trℹangular	trℹangular	ADJ
cana-835	80	18	fuzzy	fuzzy	ADJ
cana-835	80	19	number	number	NOUN
cana-835	80	20	a	a	DET
cana-835	80	21	intuiti0nistℹc	intuiti0nistℹc	NUM
cana-835	80	22	triangular	triangular	NOUN
cana-835	80	23	fuzzy	fuzzy	ADJ
cana-835	80	24	number	number	NOUN
cana-835	80	25	�	�	PROPN
cana-835	80	26	̃	̃	PROPN
cana-835	80	27	�	�	PROPN
cana-835	80	28	𝐼	𝐼	NOUN
cana-835	80	29	𝐿𝑈	𝐿𝑈	PROPN
cana-835	80	30	=	=	SYM
cana-835	80	31	(	(	PUNCT
cana-835	80	32	𝑚	𝑚	PROPN
cana-835	80	33	,	,	PUNCT
cana-835	80	34	𝛼	𝛼	X
cana-835	80	35	,	,	PUNCT
cana-835	80	36	𝛽	𝛽	NOUN
cana-835	80	37	)	)	PUNCT
cana-835	80	38	;	;	PUNCT
cana-835	80	39	(	(	PUNCT
cana-835	80	40	𝑚′	𝑚′	NUM
cana-835	80	41	,	,	PUNCT
cana-835	80	42	𝛼′	𝛼′	PROPN
cana-835	80	43	,	,	PUNCT
cana-835	80	44	𝛽′	𝛽′	PROPN
cana-835	80	45	)	)	PUNCT
cana-835	80	46	where	where	SCONJ
cana-835	80	47	𝑚	𝑚	NOUN
cana-835	80	48	=	=	SYM
cana-835	80	49	𝑏	𝑏	PROPN
cana-835	80	50	,	,	PUNCT
cana-835	80	51	𝛼	𝛼	NOUN
cana-835	80	52	=	=	NOUN
cana-835	80	53	𝑏	𝑏	PROPN
cana-835	80	54	−	−	PROPN
cana-835	80	55	𝑎	𝑎	PRON
cana-835	80	56	≥	≥	NOUN
cana-835	80	57	0	0	NUM
cana-835	80	58	,	,	PUNCT
cana-835	80	59	𝛽	𝛽	NOUN
cana-835	80	60	=	=	SYM
cana-835	80	61	𝑐	𝑐	PROPN
cana-835	80	62	−	−	PROPN
cana-835	80	63	𝑏	𝑏	PRON
cana-835	80	64	≥	≥	NOUN
cana-835	80	65	0.𝑚′	0.𝑚′	NOUN
cana-835	80	66	=	=	SYM
cana-835	80	67	𝑏′	𝑏′	PROPN
cana-835	80	68	,	,	PUNCT
cana-835	80	69	𝛼′	𝛼′	PROPN
cana-835	80	70	=	=	SYM
cana-835	80	71	𝑏′	𝑏′	PROPN
cana-835	80	72	−	−	PROPN
cana-835	80	73	𝑎′	𝑎′	NUM
cana-835	80	74	≥	≥	NOUN
cana-835	80	75	0	0	NUM
cana-835	80	76	,	,	PUNCT
cana-835	80	77	𝛽′	𝛽′	PUNCT
cana-835	80	78	=	=	SYM
cana-835	80	79	𝑐′	𝑐′	ADP
cana-835	80	80	−	−	PROPN
cana-835	80	81	𝑏′	𝑏′	NUM
cana-835	80	82	≥	≥	PROPN
cana-835	80	83	0	0	NUM
cana-835	80	84	.	.	PUNCT
cana-835	81	1	𝜇	𝜇	ADP
cana-835	81	2	�	�	PROPN
cana-835	81	3	̃	̃	PROPN
cana-835	81	4	�	�	PROPN
cana-835	81	5	𝐿𝑅	𝐿𝑅	PROPN
cana-835	81	6	(	(	PUNCT
cana-835	81	7	x	x	NOUN
cana-835	81	8	)	)	PUNCT
cana-835	81	9	=	=	SYM
cana-835	81	10	{	{	PUNCT
cana-835	81	11	0	0	NUM
cana-835	81	12	;	;	PUNCT
cana-835	81	13	−∞	−∞	ADP
cana-835	81	14	<	<	X
cana-835	81	15	𝑥	𝑥	X
cana-835	81	16	≤	≤	NUM
cana-835	81	17	𝑚	𝑚	ADP
cana-835	81	18	∝	∝	PROPN
cana-835	81	19	1	1	NUM
cana-835	81	20	−	−	PROPN
cana-835	81	21	𝑚−𝑥	𝑚−𝑥	NOUN
cana-835	81	22	𝛼	𝛼	VERB
cana-835	81	23	;	;	PUNCT
cana-835	81	24	𝑚	𝑚	ADP
cana-835	81	25	−	−	PROPN
cana-835	81	26	𝑑	𝑑	PROPN
cana-835	81	27	≤	≤	NUM
cana-835	81	28	𝑥	𝑥	PART
cana-835	81	29	<	<	X
cana-835	81	30	𝑚	𝑚	PROPN
cana-835	81	31	1	1	NUM
cana-835	81	32	−	−	NOUN
cana-835	81	33	𝑥−𝑚	𝑥−𝑚	NOUN
cana-835	81	34	𝛽	𝛽	NOUN
cana-835	81	35	;	;	PUNCT
cana-835	81	36	𝑚	𝑚	ADP
cana-835	81	37	≤	≤	NUM
cana-835	82	1	𝑥	𝑥	PART
cana-835	82	2	<	<	X
cana-835	82	3	𝑥	𝑥	X
cana-835	82	4	+	+	PUNCT
cana-835	82	5	𝛽	𝛽	NOUN
cana-835	82	6	0	0	NUM
cana-835	82	7	;	;	PUNCT
cana-835	82	8	𝑚	𝑚	PROPN
cana-835	82	9	+	+	X
cana-835	82	10	𝛽	𝛽	NOUN
cana-835	82	11	≤	≤	NOUN
cana-835	82	12	𝑥	𝑥	ADP
cana-835	82	13	<	<	X
cana-835	82	14	∞	∞	PROPN
cana-835	82	15	𝛾	𝛾	ADP
cana-835	82	16	�	�	PROPN
cana-835	82	17	̃	̃	PROPN
cana-835	82	18	�	�	PROPN
cana-835	82	19	𝐿𝑈	𝐿𝑈	PROPN
cana-835	82	20	(	(	PUNCT
cana-835	82	21	x	x	NOUN
cana-835	82	22	)	)	PUNCT
cana-835	82	23	=	=	SYM
cana-835	82	24	{	{	PUNCT
cana-835	82	25	1	1	NUM
cana-835	82	26	;	;	PUNCT
cana-835	82	27	−∞	−∞	ADP
cana-835	82	28	<	<	X
cana-835	82	29	𝑥	𝑥	X
cana-835	82	30	≤	≤	NUM
cana-835	82	31	𝑚	𝑚	ADP
cana-835	82	32	∝	∝	PROPN
cana-835	82	33	𝑚−𝑥	𝑚−𝑥	NOUN
cana-835	82	34	𝛼	𝛼	NOUN
cana-835	82	35	;	;	PUNCT
cana-835	82	36	𝑚	𝑚	ADP
cana-835	82	37	−	−	PROPN
cana-835	82	38	𝑑	𝑑	PROPN
cana-835	82	39	≤	≤	NUM
cana-835	82	40	𝑥	𝑥	ADP
cana-835	82	41	<	<	X
cana-835	82	42	𝑚	𝑚	ADP
cana-835	82	43	𝑥−𝑚	𝑥−𝑚	NOUN
cana-835	82	44	𝛽	𝛽	NOUN
cana-835	82	45	;	;	PUNCT
cana-835	82	46	𝑚	𝑚	ADP
cana-835	82	47	≤	≤	NUM
cana-835	83	1	𝑥	𝑥	ADP
cana-835	83	2	<	<	X
cana-835	83	3	𝑥	𝑥	X
cana-835	83	4	+	+	PUNCT
cana-835	83	5	𝛽	𝛽	NOUN
cana-835	83	6	1	1	NUM
cana-835	83	7	;	;	PUNCT
cana-835	83	8	𝑚	𝑚	PROPN
cana-835	83	9	+	+	X
cana-835	83	10	𝛽	𝛽	NOUN
cana-835	83	11	≤	≤	NOUN
cana-835	83	12	𝑥	𝑥	ADP
cana-835	83	13	<	<	X
cana-835	83	14	∞	∞	PROPN
cana-835	83	15	𝛾	𝛾	ADP
cana-835	83	16	�	�	PROPN
cana-835	83	17	̃	̃	PROPN
cana-835	83	18	�	�	PROPN
cana-835	83	19	𝐿𝑈	𝐿𝑈	PROPN
cana-835	83	20	(	(	PUNCT
cana-835	83	21	x	x	NOUN
cana-835	83	22	)	)	PUNCT
cana-835	83	23	1	1	NUM
cana-835	83	24	o	o	NOUN
cana-835	83	25	m	m	NOUN
cana-835	83	26	𝛼	𝛼	NOUN
cana-835	83	27	𝛽	𝛽	NOUN
cana-835	83	28	definition	definition	NOUN
cana-835	83	29	3	3	NUM
cana-835	83	30	:	:	PUNCT
cana-835	83	31	ranking	rank	VERB
cana-835	83	32	function	function	NOUN
cana-835	83	33	an	an	DET
cana-835	83	34	efficient	efficient	ADJ
cana-835	83	35	method	method	NOUN
cana-835	83	36	for	for	ADP
cana-835	83	37	computing	compute	VERB
cana-835	83	38	intuℹti0nistic	intuℹti0nistic	ADJ
cana-835	83	39	fuzzy	fuzzy	ADJ
cana-835	83	40	numbers	number	NOUN
cana-835	83	41	inv0lves	inv0lve	VERB
cana-835	83	42	the	the	DET
cana-835	83	43	use	use	NOUN
cana-835	83	44	of	of	ADP
cana-835	83	45	a	a	DET
cana-835	83	46	ranking	rank	VERB
cana-835	83	47	function	function	NOUN
cana-835	83	48	r	r	NOUN
cana-835	83	49	,	,	PUNCT
cana-835	83	50	which	which	PRON
cana-835	83	51	maps	map	VERB
cana-835	83	52	intuiti0nistℹc	intuiti0nistℹc	X
cana-835	83	53	fuzzy	fuzzy	ADJ
cana-835	83	54	numbers	number	NOUN
cana-835	83	55	(	(	PUNCT
cana-835	83	56	f	f	X
cana-835	83	57	)	)	PUNCT
cana-835	83	58	to	to	ADP
cana-835	83	59	the	the	DET
cana-835	83	60	real	real	ADJ
cana-835	83	61	line	line	NOUN
cana-835	83	62	(	(	PUNCT
cana-835	83	63	r	r	NOUN
cana-835	83	64	)	)	PUNCT
cana-835	83	65	,	,	PUNCT
cana-835	83	66	ℜ:f(r)→r	ℜ:f(r)→r	PROPN
cana-835	83	67	.	.	PUNCT
cana-835	84	1	this	this	DET
cana-835	84	2	function	function	NOUN
cana-835	84	3	enables	enable	VERB
cana-835	84	4	the	the	DET
cana-835	84	5	establishment	establishment	NOUN
cana-835	84	6	of	of	ADP
cana-835	84	7	a	a	DET
cana-835	84	8	natural	natural	ADJ
cana-835	84	9	order	order	NOUN
cana-835	84	10	within	within	ADP
cana-835	84	11	the	the	DET
cana-835	84	12	set	set	NOUN
cana-835	84	13	f(r	f(r	NOUN
cana-835	84	14	)	)	PUNCT
cana-835	84	15	of	of	ADP
cana-835	84	16	intuitionistic	intuitionistic	ADJ
cana-835	84	17	fuzzy	fuzzy	ADJ
cana-835	84	18	numbers	number	NOUN
cana-835	84	19	defined	define	VERB
cana-835	84	20	on	on	ADP
cana-835	84	21	the	the	DET
cana-835	84	22	real	real	ADJ
cana-835	84	23	number	number	NOUN
cana-835	84	24	set	set	VERB
cana-835	84	25	.	.	PUNCT
cana-835	85	1	with	with	ADP
cana-835	85	2	this	this	DET
cana-835	85	3	ranking	rank	VERB
cana-835	85	4	function	function	NOUN
cana-835	85	5	,	,	PUNCT
cana-835	85	6	comparisons	comparison	NOUN
cana-835	85	7	and	and	CCONJ
cana-835	85	8	ordering	ordering	NOUN
cana-835	85	9	of	of	ADP
cana-835	85	10	intuiti0nistic	intuiti0nistic	ADJ
cana-835	85	11	fuzzy	fuzzy	ADJ
cana-835	85	12	numbers	number	NOUN
cana-835	85	13	can	can	AUX
cana-835	85	14	be	be	AUX
cana-835	85	15	effectively	effectively	ADV
cana-835	85	16	performed	perform	VERB
cana-835	85	17	.	.	PUNCT
cana-835	86	1	r(a	r(a	X
cana-835	86	2	)	)	PUNCT
cana-835	87	1	=	=	SYM
cana-835	87	2	m+[(𝛽	m+[(𝛽	NUM
cana-835	88	1	−	−	NOUN
cana-835	88	2	𝛼)]/4	𝛼)]/4	NOUN
cana-835	88	3	+	+	PROPN
cana-835	88	4	(	(	PUNCT
cana-835	88	5	4𝑚′	4𝑚′	NUM
cana-835	88	6	+	+	CCONJ
cana-835	88	7	(	(	PUNCT
cana-835	88	8	𝛽′	𝛽′	PROPN
cana-835	88	9	−	−	NOUN
cana-835	88	10	𝛼′))/4	𝛼′))/4	NUM
cana-835	88	11	)	)	PUNCT
cana-835	88	12	2.2	2.2	NUM
cana-835	88	13	arithmetic	arithmetic	ADJ
cana-835	88	14	operation	operation	NOUN
cana-835	88	15	for	for	ADP
cana-835	88	16	triangular	triangular	NOUN
cana-835	88	17	intuiti0nistic	intuiti0nistic	ADJ
cana-835	88	18	fuzzy	fuzzy	ADJ
cana-835	88	19	numbers	number	NOUN
cana-835	88	20	:	:	PUNCT
cana-835	88	21	let	let	VERB
cana-835	88	22	�	�	PROPN
cana-835	88	23	̃	̃	NOUN
cana-835	88	24	�	�	PROPN
cana-835	88	25	𝐼	𝐼	NOUN
cana-835	88	26	=	=	SYM
cana-835	88	27	{	{	PUNCT
cana-835	88	28	(	(	PUNCT
cana-835	88	29	𝑎1	𝑎1	PROPN
cana-835	88	30	,	,	PUNCT
cana-835	88	31	𝑎2	𝑎2	PROPN
cana-835	88	32	,	,	PUNCT
cana-835	88	33	𝑎3	𝑎3	PROPN
cana-835	88	34	)	)	PUNCT
cana-835	88	35	;	;	PUNCT
cana-835	88	36	(	(	PUNCT
cana-835	88	37	𝑎1	𝑎1	INTJ
cana-835	88	38	,	,	PUNCT
cana-835	88	39	,	,	PUNCT
cana-835	88	40	𝑎2	𝑎2	PROPN
cana-835	88	41	′	′	PROPN
cana-835	88	42	,	,	PUNCT
cana-835	88	43	𝑎3	𝑎3	PROPN
cana-835	88	44	,	,	PUNCT
cana-835	88	45	)	)	PUNCT
cana-835	88	46	}	}	PUNCT
cana-835	88	47	and	and	CCONJ
cana-835	88	48	�	�	PROPN
cana-835	88	49	̃	̃	NOUN
cana-835	88	50	�	�	PROPN
cana-835	88	51	𝐼	𝐼	NOUN
cana-835	88	52	=	=	SYM
cana-835	88	53	{	{	PUNCT
cana-835	88	54	(	(	PUNCT
cana-835	88	55	𝑏1	𝑏1	NOUN
cana-835	88	56	,	,	PUNCT
cana-835	88	57	𝑏2	𝑏2	NOUN
cana-835	88	58	,	,	PUNCT
cana-835	88	59	𝑏3	𝑏3	NOUN
cana-835	88	60	)	)	PUNCT
cana-835	88	61	;	;	PUNCT
cana-835	88	62	(	(	PUNCT
cana-835	88	63	𝑏1	𝑏1	VERB
cana-835	88	64	,	,	PUNCT
cana-835	88	65	,	,	PUNCT
cana-835	88	66	𝑏2	𝑏2	PROPN
cana-835	88	67	,	,	PUNCT
cana-835	88	68	𝑏3	𝑏3	NOUN
cana-835	88	69	,	,	PUNCT
cana-835	88	70	)	)	PUNCT
cana-835	88	71	}	}	PUNCT
cana-835	88	72	are	be	AUX
cana-835	88	73	two	two	NUM
cana-835	88	74	tifn	tifn	NOUN
cana-835	88	75	,	,	PUNCT
cana-835	88	76	addition	addition	NOUN
cana-835	88	77	:	:	PUNCT
cana-835	88	78	�	�	PROPN
cana-835	88	79	̃	̃	NOUN
cana-835	88	80	�	�	PROPN
cana-835	88	81	𝐼	𝐼	ADP
cana-835	88	82	+	+	PROPN
cana-835	88	83	�	�	PROPN
cana-835	88	84	̃	̃	NOUN
cana-835	88	85	�	�	NOUN
cana-835	88	86	𝐼	𝐼	NOUN
cana-835	88	87	=	=	PUNCT
cana-835	88	88	{	{	PUNCT
cana-835	89	1	𝑎1	𝑎1	NOUN
cana-835	89	2	+	+	CCONJ
cana-835	89	3	𝑏1	𝑏1	ADJ
cana-835	89	4	,	,	PUNCT
cana-835	89	5	𝑎2	𝑎2	PROPN
cana-835	89	6	+	+	CCONJ
cana-835	89	7	𝑏2	𝑏2	PROPN
cana-835	89	8	,	,	PUNCT
cana-835	89	9	𝑎3	𝑎3	PROPN
cana-835	89	10	+	+	CCONJ
cana-835	89	11	𝑏3	𝑏3	NOUN
cana-835	89	12	)	)	PUNCT
cana-835	90	1	;	;	PUNCT
cana-835	90	2	(	(	PUNCT
cana-835	90	3	𝑎1	𝑎1	INTJ
cana-835	90	4	,	,	PUNCT
cana-835	90	5	+	+	CCONJ
cana-835	90	6	𝑏1	𝑏1	ADJ
cana-835	90	7	,	,	PUNCT
cana-835	90	8	,	,	PUNCT
cana-835	90	9	𝑎2	𝑎2	NOUN
cana-835	90	10	′	′	NUM
cana-835	90	11	+	+	CCONJ
cana-835	90	12	𝑏2	𝑏2	PROPN
cana-835	90	13	′	′	PROPN
cana-835	90	14	,	,	PUNCT
cana-835	90	15	𝑎3	𝑎3	PROPN
cana-835	90	16	,	,	PUNCT
cana-835	90	17	+	+	NUM
cana-835	90	18	𝑏3	𝑏3	NOUN
cana-835	90	19	,	,	PUNCT
cana-835	90	20	)	)	PUNCT
cana-835	90	21	is	be	AUX
cana-835	90	22	also	also	ADV
cana-835	90	23	a	a	DET
cana-835	90	24	tifn	tifn	NOUN
cana-835	90	25	communications	communication	NOUN
cana-835	90	26	on	on	ADP
cana-835	90	27	applied	apply	VERB
cana-835	90	28	nonlinear	nonlinear	ADJ
cana-835	90	29	analysis	analysis	NOUN
cana-835	90	30	issn	issn	NOUN
cana-835	90	31	:	:	PUNCT
cana-835	90	32	1074	1074	NUM
cana-835	90	33	-	-	PUNCT
cana-835	90	34	133x	133x	NUM
cana-835	90	35	vol	vol	NOUN
cana-835	90	36	31	31	NUM
cana-835	90	37	no	no	NOUN
cana-835	90	38	.	.	PUNCT
cana-835	91	1	4s	4s	NUM
cana-835	91	2	(	(	PUNCT
cana-835	91	3	2024	2024	NUM
cana-835	91	4	)	)	PUNCT
cana-835	91	5	186	186	NUM
cana-835	91	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	91	7	subtraction	subtraction	NOUN
cana-835	91	8	�	�	PROPN
cana-835	91	9	̃	̃	PROPN
cana-835	91	10	�	�	PROPN
cana-835	91	11	𝐼	𝐼	ADP
cana-835	91	12	−	−	PROPN
cana-835	91	13	�	�	PROPN
cana-835	91	14	̃	̃	NOUN
cana-835	91	15	�	�	PROPN
cana-835	91	16	𝐼	𝐼	NOUN
cana-835	91	17	=	=	PUNCT
cana-835	91	18	{	{	PUNCT
cana-835	91	19	𝑎1	𝑎1	NOUN
cana-835	91	20	−	−	PROPN
cana-835	91	21	𝑏3	𝑏3	NOUN
cana-835	91	22	,	,	PUNCT
cana-835	91	23	𝑎2	𝑎2	NOUN
cana-835	91	24	−	−	PROPN
cana-835	91	25	𝑏2	𝑏2	PROPN
cana-835	91	26	,	,	PUNCT
cana-835	91	27	𝑎3	𝑎3	ADJ
cana-835	91	28	−	−	NOUN
cana-835	91	29	𝑏1	𝑏1	NOUN
cana-835	91	30	)	)	PUNCT
cana-835	91	31	;	;	PUNCT
cana-835	91	32	(	(	PUNCT
cana-835	91	33	𝑎1	𝑎1	INTJ
cana-835	91	34	,	,	PUNCT
cana-835	91	35	−	−	NOUN
cana-835	91	36	𝑏3	𝑏3	NOUN
cana-835	91	37	,	,	PUNCT
cana-835	91	38	,	,	PUNCT
cana-835	91	39	𝑎2	𝑎2	NOUN
cana-835	91	40	′	′	NUM
cana-835	91	41	−	−	PROPN
cana-835	91	42	𝑏2	𝑏2	PROPN
cana-835	91	43	′	′	PROPN
cana-835	91	44	,	,	PUNCT
cana-835	91	45	𝑎3	𝑎3	NOUN
cana-835	91	46	,	,	PUNCT
cana-835	91	47	−	−	ADP
cana-835	91	48	𝑏1	𝑏1	NOUN
cana-835	91	49	,	,	PUNCT
cana-835	91	50	)	)	PUNCT
cana-835	91	51	is	be	AUX
cana-835	91	52	also	also	ADV
cana-835	91	53	a	a	DET
cana-835	91	54	tifn	tifn	NOUN
cana-835	91	55	multiplication	multiplication	NOUN
cana-835	91	56	�	�	PROPN
cana-835	91	57	̃	̃	NOUN
cana-835	91	58	�	�	NOUN
cana-835	91	59	𝐼	𝐼	PROPN
cana-835	91	60	.	.	PUNCT
cana-835	92	1	�	�	PROPN
cana-835	92	2	̃	̃	NOUN
cana-835	92	3	�	�	PROPN
cana-835	92	4	𝐼	𝐼	NOUN
cana-835	92	5	=	=	PUNCT
cana-835	92	6	(	(	PUNCT
cana-835	92	7	𝑎1	𝑎1	PROPN
cana-835	92	8	.	.	PUNCT
cana-835	92	9	𝑅(	𝑅(	PROPN
cana-835	92	10	�	�	PROPN
cana-835	92	11	̃	̃	PROPN
cana-835	92	12	�	�	PROPN
cana-835	92	13	𝐼	𝐼	PROPN
cana-835	92	14	)	)	PUNCT
cana-835	92	15	,	,	PUNCT
cana-835	92	16	𝑎2	𝑎2	PROPN
cana-835	92	17	.	.	PUNCT
cana-835	92	18	𝑅(	𝑅(	PROPN
cana-835	92	19	�	�	PROPN
cana-835	92	20	̃	̃	PROPN
cana-835	92	21	�	�	PROPN
cana-835	92	22	𝐼	𝐼	PROPN
cana-835	92	23	)	)	PUNCT
cana-835	92	24	,	,	PUNCT
cana-835	92	25	𝑎3	𝑎3	PROPN
cana-835	92	26	.	.	PROPN
cana-835	92	27	𝑅(	𝑅(	PROPN
cana-835	92	28	�	�	PROPN
cana-835	92	29	̃	̃	PROPN
cana-835	92	30	�	�	PROPN
cana-835	92	31	𝐼	𝐼	PROPN
cana-835	92	32	)	)	PUNCT
cana-835	92	33	)	)	PUNCT
cana-835	93	1	;	;	PUNCT
cana-835	93	2	(	(	PUNCT
cana-835	93	3	𝑎1	𝑎1	INTJ
cana-835	93	4	,	,	PUNCT
cana-835	93	5	.	.	PUNCT
cana-835	93	6	𝑅(	𝑅(	PROPN
cana-835	93	7	�	�	PROPN
cana-835	93	8	̃	̃	PROPN
cana-835	93	9	�	�	PROPN
cana-835	93	10	𝐼	𝐼	NOUN
cana-835	93	11	)	)	PUNCT
cana-835	93	12	,	,	PUNCT
cana-835	93	13	𝑎2	𝑎2	PROPN
cana-835	93	14	′.	′.	PROPN
cana-835	93	15	𝑅(	𝑅(	PROPN
cana-835	93	16	�	�	PROPN
cana-835	93	17	̃	̃	PROPN
cana-835	93	18	�	�	PROPN
cana-835	93	19	𝐼	𝐼	NOUN
cana-835	93	20	)	)	PUNCT
cana-835	93	21	,	,	PUNCT
cana-835	93	22	𝑎3	𝑎3	PROPN
cana-835	93	23	,	,	PUNCT
cana-835	93	24	.	.	PUNCT
cana-835	93	25	𝑅(	𝑅(	PROPN
cana-835	93	26	�	�	PROPN
cana-835	93	27	̃	̃	PROPN
cana-835	93	28	�	�	PROPN
cana-835	93	29	𝐼	𝐼	NOUN
cana-835	93	30	)	)	PUNCT
cana-835	93	31	)	)	PUNCT
cana-835	93	32	is	be	AUX
cana-835	93	33	also	also	ADV
cana-835	93	34	a	a	DET
cana-835	93	35	tifn	tifn	NOUN
cana-835	93	36	,	,	PUNCT
cana-835	93	37	where	where	SCONJ
cana-835	93	38	𝑅(	𝑅(	PROPN
cana-835	93	39	�	�	PROPN
cana-835	93	40	̃	̃	PROPN
cana-835	93	41	�	�	PROPN
cana-835	93	42	𝐼	𝐼	NOUN
cana-835	93	43	)	)	PUNCT
cana-835	93	44	=	=	PUNCT
cana-835	93	45	(	(	PUNCT
cana-835	93	46	𝑎1	𝑎1	X
cana-835	93	47	+	+	X
cana-835	94	1	[	[	X
cana-835	94	2	(	(	PUNCT
cana-835	94	3	𝑎2	𝑎2	NOUN
cana-835	94	4	−	−	PROPN
cana-835	94	5	𝑎1)]/4	𝑎1)]/4	NUM
cana-835	94	6	)	)	PUNCT
cana-835	94	7	+	+	CCONJ
cana-835	94	8	(	(	PUNCT
cana-835	94	9	4𝑎1′	4𝑎1′	NOUN
cana-835	94	10	+	+	CCONJ
cana-835	94	11	(	(	PUNCT
cana-835	94	12	𝑎2′	𝑎2′	NOUN
cana-835	94	13	−	−	NOUN
cana-835	94	14	𝑎3′))/4	𝑎3′))/4	NOUN
cana-835	94	15	)	)	PUNCT
cana-835	94	16	division	division	NOUN
cana-835	94	17	�	�	PROPN
cana-835	94	18	̃	̃	PROPN
cana-835	94	19	�	�	NOUN
cana-835	94	20	𝐼/	𝐼/	NOUN
cana-835	94	21	�	�	NOUN
cana-835	94	22	̃	̃	NOUN
cana-835	94	23	�	�	NOUN
cana-835	94	24	𝐼	𝐼	NOUN
cana-835	94	25	=	=	SYM
cana-835	94	26	(	(	PUNCT
cana-835	94	27	𝑎1/𝑅(	𝑎1/𝑅(	PROPN
cana-835	94	28	�	�	PROPN
cana-835	94	29	̃	̃	PROPN
cana-835	94	30	�	�	PROPN
cana-835	94	31	𝐼	𝐼	PROPN
cana-835	94	32	)	)	PUNCT
cana-835	94	33	,	,	PUNCT
cana-835	94	34	𝑎2/𝑅(	𝑎2/𝑅(	PROPN
cana-835	94	35	�	�	PROPN
cana-835	94	36	̃	̃	PROPN
cana-835	94	37	�	�	PROPN
cana-835	94	38	𝐼	𝐼	PROPN
cana-835	94	39	)	)	PUNCT
cana-835	94	40	,	,	PUNCT
cana-835	94	41	𝑎3/𝑅(	𝑎3/𝑅(	PROPN
cana-835	94	42	�	�	PROPN
cana-835	94	43	̃	̃	PROPN
cana-835	94	44	�	�	PROPN
cana-835	94	45	𝐼	𝐼	PROPN
cana-835	94	46	)	)	PUNCT
cana-835	94	47	)	)	PUNCT
cana-835	95	1	;	;	PUNCT
cana-835	95	2	(	(	PUNCT
cana-835	95	3	𝑎1	𝑎1	INTJ
cana-835	95	4	,	,	PUNCT
cana-835	95	5	/𝑅(	/𝑅(	NOUN
cana-835	95	6	�	�	PROPN
cana-835	95	7	̃	̃	NOUN
cana-835	95	8	�	�	NOUN
cana-835	95	9	𝐼	𝐼	NOUN
cana-835	95	10	)	)	PUNCT
cana-835	95	11	,	,	PUNCT
cana-835	95	12	𝑎2	𝑎2	PROPN
cana-835	95	13	/𝑅(	/𝑅(	SYM
cana-835	95	14	�	�	PROPN
cana-835	95	15	̃	̃	NOUN
cana-835	95	16	�	�	NOUN
cana-835	95	17	𝐼	𝐼	NOUN
cana-835	95	18	)	)	PUNCT
cana-835	95	19	,	,	PUNCT
cana-835	95	20	𝑎3	𝑎3	PROPN
cana-835	95	21	,	,	PUNCT
cana-835	95	22	/𝑅(	/𝑅(	SYM
cana-835	95	23	�	�	PROPN
cana-835	95	24	̃	̃	NOUN
cana-835	95	25	�	�	NOUN
cana-835	95	26	𝐼	𝐼	NOUN
cana-835	95	27	)	)	PUNCT
cana-835	95	28	)	)	PUNCT
cana-835	95	29	is	be	AUX
cana-835	95	30	also	also	ADV
cana-835	95	31	a	a	DET
cana-835	95	32	tifn	tifn	NOUN
cana-835	95	33	,	,	PUNCT
cana-835	95	34	where	where	SCONJ
cana-835	95	35	𝑅(	𝑅(	PROPN
cana-835	95	36	�	�	PROPN
cana-835	95	37	̃	̃	PROPN
cana-835	95	38	�	�	PROPN
cana-835	95	39	𝐼	𝐼	NOUN
cana-835	95	40	)	)	PUNCT
cana-835	95	41	=	=	PUNCT
cana-835	95	42	(	(	PUNCT
cana-835	95	43	𝑎1	𝑎1	X
cana-835	95	44	+	+	X
cana-835	96	1	[	[	X
cana-835	96	2	(	(	PUNCT
cana-835	96	3	𝑎2	𝑎2	NOUN
cana-835	96	4	−	−	PROPN
cana-835	96	5	𝑎1)]/4	𝑎1)]/4	NUM
cana-835	96	6	)	)	PUNCT
cana-835	96	7	+	+	CCONJ
cana-835	96	8	(	(	PUNCT
cana-835	96	9	4𝑎1′	4𝑎1′	NOUN
cana-835	96	10	+	+	CCONJ
cana-835	96	11	(	(	PUNCT
cana-835	96	12	𝑎2′	𝑎2′	NOUN
cana-835	96	13	−	−	NOUN
cana-835	96	14	𝑎3′))/4	𝑎3′))/4	NOUN
cana-835	96	15	)	)	PUNCT
cana-835	96	16	2.3	2.3	NUM
cana-835	96	17	interval	interval	NOUN
cana-835	96	18	valued	value	VERB
cana-835	96	19	intuiti0nistic	intuiti0nistic	ADJ
cana-835	96	20	fuzzy	fuzzy	ADJ
cana-835	96	21	number	number	NOUN
cana-835	96	22	a	a	DET
cana-835	96	23	interval	interval	NOUN
cana-835	96	24	valued	value	VERB
cana-835	96	25	intuiti0nℹstic	intuiti0nℹstic	ADJ
cana-835	96	26	fuzzy	fuzzy	ADJ
cana-835	96	27	number	number	NOUN
cana-835	96	28	�	�	PROPN
cana-835	96	29	̃	̃	PROPN
cana-835	96	30	�	�	NOUN
cana-835	96	31	𝐼	𝐼	PROPN
cana-835	96	32	is	be	AUX
cana-835	96	33	pair	pair	NOUN
cana-835	96	34	of	of	ADP
cana-835	96	35	[	[	X
cana-835	96	36	𝑢	𝑢	X
cana-835	96	37	,	,	PUNCT
cana-835	96	38	�	�	NOUN
cana-835	96	39	̅	̅	NOUN
cana-835	96	40	�	�	NOUN
cana-835	96	41	]	]	PUNCT
cana-835	96	42	of	of	ADP
cana-835	96	43	𝑢(𝑟	𝑢(𝑟	PROPN
cana-835	96	44	)	)	PUNCT
cana-835	96	45	,	,	PUNCT
cana-835	96	46	�	�	PROPN
cana-835	96	47	̅	̅	NOUN
cana-835	96	48	�	�	NOUN
cana-835	96	49	(𝑟	(𝑟	NOUN
cana-835	96	50	)	)	PUNCT
cana-835	96	51	;	;	PUNCT
cana-835	96	52	0	0	NUM
cana-835	96	53	≤	≤	NUM
cana-835	96	54	𝑟	𝑟	X
cana-835	96	55	≤	≤	NUM
cana-835	96	56	1	1	NUM
cana-835	96	57	which	which	PRON
cana-835	96	58	satisfies	satisfy	VERB
cana-835	96	59	the	the	DET
cana-835	96	60	following	follow	VERB
cana-835	96	61	conditi0ns	conditi0ns	PROPN
cana-835	96	62	:	:	PUNCT
cana-835	96	63	stefen	stefen	PROPN
cana-835	96	64	et	et	PROPN
cana-835	96	65	al	al	PROPN
cana-835	96	66	enhancing	enhance	VERB
cana-835	96	67	the	the	DET
cana-835	96	68	efficiency	efficiency	NOUN
cana-835	96	69	of	of	ADP
cana-835	96	70	a	a	DET
cana-835	96	71	n0nlℹnear	n0nlℹnear	ADJ
cana-835	96	72	-	-	PUNCT
cana-835	96	73	system	system	NOUN
cana-835	96	74	-	-	PUNCT
cana-835	96	75	s0lver	s0lver	NOUN
cana-835	96	76	using	use	VERB
cana-835	96	77	a	a	DET
cana-835	96	78	comp0nentwℹse	comp0nentwℹse	NUM
cana-835	96	79	newt0n	newt0n	PROPN
cana-835	96	80	meth0d	meth0d	PROPN
cana-835	96	81	,	,	PUNCT
cana-835	96	82	intr0duce	intr0duce	VERB
cana-835	96	83	impr0vements	impr0vement	NOUN
cana-835	96	84	to	to	ADP
cana-835	96	85	the	the	DET
cana-835	96	86	meth0d	meth0d	PROPN
cana-835	96	87	,	,	PUNCT
cana-835	96	88	such	such	ADJ
cana-835	96	89	as	as	ADP
cana-835	96	90	utilizing	utilize	VERB
cana-835	96	91	ℹndexlists	ℹndexlist	NOUN
cana-835	96	92	,	,	PUNCT
cana-835	96	93	combining	combine	VERB
cana-835	96	94	with	with	ADP
cana-835	96	95	an	an	DET
cana-835	96	96	interval	interval	NOUN
cana-835	96	97	newt0n	newt0n	PROPN
cana-835	96	98	gauss	gaus	VERB
cana-835	96	99	-	-	PUNCT
cana-835	96	100	seℹdel	seℹdel	NOUN
cana-835	96	101	step	step	NOUN
cana-835	96	102	,	,	PUNCT
cana-835	96	103	and	and	CCONJ
cana-835	96	104	verifying	verifying	NOUN
cana-835	96	105	solution	solution	NOUN
cana-835	96	106	unℹqueness	unℹqueness	NOUN
cana-835	96	107	and	and	CCONJ
cana-835	96	108	it	it	PRON
cana-835	96	109	pr0vides	pr0vide	VERB
cana-835	97	1	alg0rithmic	alg0rithmic	ADJ
cana-835	97	2	descriptions	description	NOUN
cana-835	97	3	,	,	PUNCT
cana-835	97	4	pr0perties	pr0pertie	NOUN
cana-835	97	5	0f	0f	VERB
cana-835	97	6	the	the	DET
cana-835	97	7	meth0d	meth0d	PROPN
cana-835	97	8	,	,	PUNCT
cana-835	97	9	examples	example	NOUN
cana-835	97	10	,	,	PUNCT
cana-835	97	11	and	and	CCONJ
cana-835	97	12	results	result	NOUN
cana-835	97	13	to	to	AUX
cana-835	97	14	dem0nstrate	dem0nstrate	VERB
cana-835	97	15	the	the	DET
cana-835	97	16	effectiveness	effectiveness	NOUN
cana-835	97	17	of	of	ADP
cana-835	97	18	the	the	DET
cana-835	97	19	pr0p0sed	pr0p0sed	ADJ
cana-835	97	20	appr0ach	appr0ach	NOUN
cana-835	97	21	in	in	ADP
cana-835	97	22	solving	solve	VERB
cana-835	97	23	n0nlℹnear	n0nlℹnear	ADJ
cana-835	97	24	equations	equation	NOUN
cana-835	97	25	let	let	VERB
cana-835	97	26	�	�	PROPN
cana-835	97	27	̃	̃	NOUN
cana-835	97	28	�	�	NOUN
cana-835	97	29	=	=	PUNCT
cana-835	98	1	[	[	X
cana-835	98	2	𝑣(𝑟	𝑣(𝑟	NOUN
cana-835	98	3	)	)	PUNCT
cana-835	98	4	,	,	PUNCT
cana-835	98	5	�	�	PROPN
cana-835	98	6	̅	̅	NOUN
cana-835	98	7	�	�	NOUN
cana-835	98	8	(𝑟	(𝑟	NOUN
cana-835	98	9	)	)	PUNCT
cana-835	98	10	]	]	PUNCT
cana-835	99	1	x	x	X
cana-835	99	2	>	>	X
cana-835	99	3	0	0	NUM
cana-835	99	4	;	;	PUNCT
cana-835	99	5	𝑥	𝑥	PROPN
cana-835	99	6	=	=	SYM
cana-835	100	1	[	[	X
cana-835	100	2	𝑥𝑣(𝑟	𝑥𝑣(𝑟	NUM
cana-835	100	3	)	)	PUNCT
cana-835	100	4	,	,	PUNCT
cana-835	100	5	𝑥	𝑥	NOUN
cana-835	100	6	�	�	NOUN
cana-835	100	7	̅	̅	NOUN
cana-835	100	8	�	�	NOUN
cana-835	100	9	(𝑟	(𝑟	NOUN
cana-835	100	10	)	)	PUNCT
cana-835	100	11	]	]	PUNCT
cana-835	101	1	and	and	CCONJ
cana-835	101	2	x	x	X
cana-835	101	3	<	<	X
cana-835	101	4	0	0	NUM
cana-835	101	5	;	;	PUNCT
cana-835	101	6	𝑥	𝑥	ADP
cana-835	101	7	=	=	PUNCT
cana-835	101	8	[	[	PUNCT
cana-835	101	9	𝑥	𝑥	NOUN
cana-835	101	10	�	�	PROPN
cana-835	101	11	̅	̅	NOUN
cana-835	101	12	�	�	NOUN
cana-835	101	13	(𝑟	(𝑟	NOUN
cana-835	101	14	)	)	PUNCT
cana-835	101	15	,	,	PUNCT
cana-835	101	16	x𝑣(𝑟	x𝑣(𝑟	NUM
cana-835	101	17	)	)	PUNCT
cana-835	101	18	]	]	PUNCT
cana-835	101	19	3	3	X
cana-835	101	20	.	.	X
cana-835	101	21	newt0n	newt0n	PROPN
cana-835	101	22	’s	’s	PART
cana-835	101	23	meth0d	meth0d	PROPN
cana-835	101	24	for	for	ADP
cana-835	101	25	unc0nstraℹned	unc0nstraℹned	ADJ
cana-835	101	26	intuiti0nℹstic	intuiti0nℹstic	ADJ
cana-835	101	27	fuzzy	fuzzy	ADJ
cana-835	101	28	optℹmizati0n	optℹmizati0n	NOUN
cana-835	101	29	now	now	ADV
cana-835	101	30	we	we	PRON
cana-835	101	31	consider	consider	VERB
cana-835	101	32	an	an	DET
cana-835	101	33	unc0nstrained	unc0nstrained	PROPN
cana-835	101	34	ℹntuiti0nistic	ℹntuiti0nistic	ADJ
cana-835	101	35	fuzzy	fuzzy	ADJ
cana-835	101	36	0ptimℹzation	0ptimℹzation	NUM
cana-835	101	37	pr0blem	pr0blem	NOUN
cana-835	101	38	𝑥∈𝑋	𝑥∈𝑋	PROPN
cana-835	101	39	𝑚𝑖𝑛	𝑚𝑖𝑛	PROPN
cana-835	101	40	�	�	PROPN
cana-835	101	41	̃	̃	PROPN
cana-835	101	42	�	�	PROPN
cana-835	101	43	(𝑥	(𝑥	NOUN
cana-835	101	44	)	)	PUNCT
cana-835	101	45	where	where	SCONJ
cana-835	101	46	�	�	PROPN
cana-835	101	47	̃	̃	PROPN
cana-835	101	48	�	�	PROPN
cana-835	101	49	:	:	PUNCT
cana-835	101	50	𝑋	𝑋	PROPN
cana-835	101	51	→	→	SYM
cana-835	101	52	𝐹(ℜ	𝐹(ℜ	NUM
cana-835	101	53	)	)	PUNCT
cana-835	101	54	is	be	AUX
cana-835	101	55	a	a	DET
cana-835	101	56	fuzzy	fuzzy	ADJ
cana-835	101	57	valued	value	VERB
cana-835	101	58	functi0n	functi0n	NOUN
cana-835	101	59	defined	define	VERB
cana-835	101	60	on	on	ADP
cana-835	101	61	𝑋	𝑋	PROPN
cana-835	101	62	⊆	⊆	NUM
cana-835	101	63	ℜ𝑛.	ℜ𝑛.	PROPN
cana-835	101	64	the	the	DET
cana-835	101	65	newt0n	newt0n	PROPN
cana-835	101	66	meth0d	meth0d	PROPN
cana-835	101	67	is	be	AUX
cana-835	101	68	an	an	DET
cana-835	101	69	iterative	iterative	NOUN
cana-835	101	70	appr0ach	appr0ach	NOUN
cana-835	101	71	for	for	ADP
cana-835	101	72	determining	determine	VERB
cana-835	101	73	the	the	DET
cana-835	101	74	r00	r00	PROPN
cana-835	101	75	t	t	PROPN
cana-835	101	76	of	of	ADP
cana-835	101	77	a	a	DET
cana-835	101	78	function	function	NOUN
cana-835	101	79	f(x	f(x	PROPN
cana-835	101	80	)	)	PUNCT
cana-835	101	81	.	.	PUNCT
cana-835	102	1	following	follow	VERB
cana-835	102	2	an	an	DET
cana-835	102	3	ℹnitial	ℹnitial	ADJ
cana-835	102	4	estimate	estimate	NOUN
cana-835	102	5	to	to	ADP
cana-835	102	6	the	the	DET
cana-835	102	7	root	root	NOUN
cana-835	102	8	x_0	x_0	PROPN
cana-835	102	9	,	,	PUNCT
cana-835	102	10	better	well	ADJ
cana-835	102	11	guesses	guess	NOUN
cana-835	102	12	are	be	AUX
cana-835	102	13	provided	provide	VERB
cana-835	102	14	.	.	PUNCT
cana-835	103	1	the	the	DET
cana-835	103	2	newt0n	newt0n	PROPN
cana-835	103	3	approach	approach	NOUN
cana-835	103	4	for	for	ADP
cana-835	103	5	single	single	ADJ
cana-835	103	6	variable	variable	NOUN
cana-835	103	7	0ptimization[12	0ptimization[12	X
cana-835	103	8	]	]	PUNCT
cana-835	103	9	is	be	AUX
cana-835	103	10	used	use	VERB
cana-835	103	11	to	to	PART
cana-835	103	12	find	find	VERB
cana-835	103	13	the	the	DET
cana-835	103	14	root	root	NOUN
cana-835	103	15	.	.	PUNCT
cana-835	104	1	the	the	DET
cana-835	104	2	newt0n	newt0n	PROPN
cana-835	104	3	meth0d	meth0d	PROPN
cana-835	104	4	can	can	AUX
cana-835	104	5	be	be	AUX
cana-835	104	6	adapted	adapt	VERB
cana-835	104	7	to	to	PART
cana-835	104	8	solve	solve	VERB
cana-835	104	9	unc0nstraℹned	unc0nstraℹned	ADJ
cana-835	104	10	intuiti0nℹstic	intuiti0nℹstic	ADJ
cana-835	104	11	fuzzy	fuzzy	ADJ
cana-835	104	12	optimizati0n	optimizati0n	NOUN
cana-835	104	13	pr0blems	pr0blem	NOUN
cana-835	104	14	,	,	PUNCT
cana-835	104	15	taking	take	VERB
cana-835	104	16	into	into	ADP
cana-835	104	17	account	account	NOUN
cana-835	104	18	the	the	DET
cana-835	104	19	unique	unique	ADJ
cana-835	104	20	characteristics	characteristic	NOUN
cana-835	104	21	of	of	ADP
cana-835	104	22	intuiti0nistic	intuiti0nistic	ADJ
cana-835	104	23	fuzzy	fuzzy	ADJ
cana-835	104	24	numbers	number	NOUN
cana-835	104	25	and	and	CCONJ
cana-835	104	26	their	their	PRON
cana-835	104	27	associated	associated	ADJ
cana-835	104	28	membership	membership	NOUN
cana-835	104	29	functions	function	NOUN
cana-835	104	30	.	.	PUNCT
cana-835	105	1	𝑥𝑘+1	𝑥𝑘+1	NOUN
cana-835	105	2	=	=	SYM
cana-835	105	3	𝑥𝑘	𝑥𝑘	X
cana-835	105	4	−	−	X
cana-835	105	5	[	[	PUNCT
cana-835	105	6	𝑓′(𝑥𝑘	𝑓′(𝑥𝑘	ADJ
cana-835	105	7	)	)	PUNCT
cana-835	105	8	𝑓′′(𝑥𝑘	𝑓′′(𝑥𝑘	ADJ
cana-835	105	9	)	)	PUNCT
cana-835	105	10	]	]	PUNCT
cana-835	105	11	𝑢𝑛𝑡𝑖𝑙	𝑢𝑛𝑡𝑖𝑙	NOUN
cana-835	105	12	|𝑥𝑘+1	|𝑥𝑘+1	NOUN
cana-835	105	13	−	−	PROPN
cana-835	105	14	𝑥𝑘|	𝑥𝑘|	PROPN
cana-835	105	15	<	<	X
cana-835	105	16	∈	∈	PROPN
cana-835	105	17	newton	newton	PROPN
cana-835	105	18	method	method	NOUN
cana-835	105	19	for	for	ADP
cana-835	105	20	tw0	tw0	PROPN
cana-835	105	21	variable	variable	ADJ
cana-835	105	22	0ptimization[5	0ptimization[5	NOUN
cana-835	105	23	]	]	PUNCT
cana-835	105	24	for	for	ADP
cana-835	105	25	0btaining	0btaine	VERB
cana-835	105	26	the	the	DET
cana-835	105	27	root	root	NOUN
cana-835	105	28	,	,	PUNCT
cana-835	105	29	communications	communication	NOUN
cana-835	105	30	on	on	ADP
cana-835	105	31	applied	apply	VERB
cana-835	105	32	nonlinear	nonlinear	ADJ
cana-835	105	33	analysis	analysis	NOUN
cana-835	105	34	issn	issn	NOUN
cana-835	105	35	:	:	PUNCT
cana-835	105	36	1074	1074	NUM
cana-835	105	37	-	-	PUNCT
cana-835	105	38	133x	133x	NUM
cana-835	105	39	vol	vol	NOUN
cana-835	105	40	31	31	NUM
cana-835	105	41	no	no	NOUN
cana-835	105	42	.	.	PUNCT
cana-835	106	1	4s	4s	NUM
cana-835	106	2	(	(	PUNCT
cana-835	106	3	2024	2024	NUM
cana-835	106	4	)	)	PUNCT
cana-835	106	5	187	187	NUM
cana-835	106	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	106	7	newton	newton	PROPN
cana-835	106	8	's	's	PART
cana-835	106	9	approach	approach	NOUN
cana-835	106	10	for	for	ADP
cana-835	106	11	determining	determine	VERB
cana-835	106	12	a	a	DET
cana-835	106	13	function	function	NOUN
cana-835	106	14	's	's	PART
cana-835	106	15	critical	critical	ADJ
cana-835	106	16	points	point	NOUN
cana-835	106	17	requires	require	VERB
cana-835	106	18	the	the	DET
cana-835	106	19	existence	existence	NOUN
cana-835	106	20	of	of	ADP
cana-835	106	21	its	its	PRON
cana-835	106	22	first	first	ADJ
cana-835	106	23	and	and	CCONJ
cana-835	106	24	second	second	ADJ
cana-835	106	25	derivatives	derivative	NOUN
cana-835	106	26	.	.	PUNCT
cana-835	107	1	newton	newton	PROPN
cana-835	107	2	's	's	PART
cana-835	107	3	approach	approach	NOUN
cana-835	107	4	to	to	ADP
cana-835	107	5	finding	find	VERB
cana-835	107	6	critical	critical	ADJ
cana-835	107	7	p0ints	p0int	NOUN
cana-835	107	8	of	of	ADP
cana-835	107	9	a	a	DET
cana-835	107	10	functi0n	functi0n	NOUN
cana-835	107	11	involves	involve	VERB
cana-835	107	12	analyzing	analyze	VERB
cana-835	107	13	the	the	DET
cana-835	107	14	behavi0r	behavi0r	PROPN
cana-835	107	15	of	of	ADP
cana-835	107	16	its	its	PRON
cana-835	107	17	first	first	ADJ
cana-835	107	18	and	and	CCONJ
cana-835	107	19	sec0nd	sec0nd	PROPN
cana-835	107	20	derivatives	derivative	NOUN
cana-835	107	21	.	.	PUNCT
cana-835	108	1	critical	critical	ADJ
cana-835	108	2	points	point	NOUN
cana-835	108	3	are	be	AUX
cana-835	108	4	l0cations	l0cation	NOUN
cana-835	108	5	where	where	SCONJ
cana-835	108	6	the	the	DET
cana-835	108	7	function	function	NOUN
cana-835	108	8	's	's	PART
cana-835	108	9	rate	rate	NOUN
cana-835	108	10	of	of	ADP
cana-835	108	11	change	change	NOUN
cana-835	108	12	,	,	PUNCT
cana-835	108	13	represented	represent	VERB
cana-835	108	14	by	by	ADP
cana-835	108	15	the	the	DET
cana-835	108	16	first	first	ADJ
cana-835	108	17	derivative	derivative	NOUN
cana-835	108	18	(	(	PUNCT
cana-835	108	19	also	also	ADV
cana-835	108	20	known	know	VERB
cana-835	108	21	as	as	ADP
cana-835	108	22	the	the	DET
cana-835	108	23	derivative	derivative	ADJ
cana-835	108	24	or	or	CCONJ
cana-835	108	25	slope	slope	NOUN
cana-835	108	26	)	)	PUNCT
cana-835	108	27	,	,	PUNCT
cana-835	108	28	either	either	CCONJ
cana-835	108	29	changes	change	VERB
cana-835	108	30	its	its	PRON
cana-835	108	31	sign	sign	NOUN
cana-835	108	32	or	or	CCONJ
cana-835	108	33	becomes	become	VERB
cana-835	108	34	zero	zero	NUM
cana-835	108	35	.	.	PUNCT
cana-835	109	1	to	to	PART
cana-835	109	2	determine	determine	VERB
cana-835	109	3	these	these	DET
cana-835	109	4	points	point	NOUN
cana-835	109	5	,	,	PUNCT
cana-835	109	6	we	we	PRON
cana-835	109	7	need	need	VERB
cana-835	109	8	the	the	DET
cana-835	109	9	first	first	ADJ
cana-835	109	10	derivative	derivative	NOUN
cana-835	109	11	to	to	PART
cana-835	109	12	identify	identify	VERB
cana-835	109	13	where	where	SCONJ
cana-835	109	14	changes	change	NOUN
cana-835	109	15	in	in	ADP
cana-835	109	16	the	the	DET
cana-835	109	17	function	function	NOUN
cana-835	109	18	's	's	PART
cana-835	109	19	rate	rate	NOUN
cana-835	109	20	of	of	ADP
cana-835	109	21	change	change	NOUN
cana-835	109	22	occur	occur	VERB
cana-835	109	23	.	.	PUNCT
cana-835	110	1	additionally	additionally	ADV
cana-835	110	2	,	,	PUNCT
cana-835	110	3	newton	newton	PROPN
cana-835	110	4	's	's	PART
cana-835	110	5	method	method	NOUN
cana-835	110	6	requires	require	VERB
cana-835	110	7	the	the	DET
cana-835	110	8	second	second	ADJ
cana-835	110	9	derivative	derivative	NOUN
cana-835	110	10	(	(	PUNCT
cana-835	110	11	the	the	DET
cana-835	110	12	derivative	derivative	NOUN
cana-835	110	13	of	of	ADP
cana-835	110	14	the	the	DET
cana-835	110	15	first	first	ADJ
cana-835	110	16	derivative	derivative	NOUN
cana-835	110	17	)	)	PUNCT
cana-835	110	18	to	to	PART
cana-835	110	19	assess	assess	VERB
cana-835	110	20	the	the	DET
cana-835	110	21	concavity	concavity	NOUN
cana-835	110	22	of	of	ADP
cana-835	110	23	the	the	DET
cana-835	110	24	function	function	NOUN
cana-835	110	25	at	at	ADP
cana-835	110	26	these	these	DET
cana-835	110	27	critical	critical	ADJ
cana-835	110	28	points	point	NOUN
cana-835	110	29	.	.	PUNCT
cana-835	111	1	if	if	SCONJ
cana-835	111	2	the	the	DET
cana-835	111	3	second	second	ADJ
cana-835	111	4	derivative	derivative	NOUN
cana-835	111	5	is	be	AUX
cana-835	111	6	positive	positive	ADJ
cana-835	111	7	,	,	PUNCT
cana-835	111	8	the	the	DET
cana-835	111	9	function	function	NOUN
cana-835	111	10	is	be	AUX
cana-835	111	11	concave	concave	VERB
cana-835	111	12	up	up	ADP
cana-835	111	13	,	,	PUNCT
cana-835	111	14	and	and	CCONJ
cana-835	111	15	if	if	SCONJ
cana-835	111	16	it	it	PRON
cana-835	111	17	's	be	AUX
cana-835	111	18	negative	negative	ADJ
cana-835	111	19	,	,	PUNCT
cana-835	111	20	the	the	DET
cana-835	111	21	function	function	NOUN
cana-835	111	22	is	be	AUX
cana-835	111	23	concave	concave	VERB
cana-835	111	24	down	down	ADP
cana-835	111	25	.	.	PUNCT
cana-835	112	1	this	this	DET
cana-835	112	2	information	information	NOUN
cana-835	112	3	helps	help	VERB
cana-835	112	4	in	in	ADP
cana-835	112	5	classifying	classify	VERB
cana-835	112	6	critical	critical	ADJ
cana-835	112	7	points	point	NOUN
cana-835	112	8	as	as	ADP
cana-835	112	9	local	local	ADJ
cana-835	112	10	maxℹma	maxℹma	NOUN
cana-835	112	11	(	(	PUNCT
cana-835	112	12	concave	concave	VERB
cana-835	112	13	up	up	ADP
cana-835	112	14	and	and	CCONJ
cana-835	112	15	negative	negative	ADJ
cana-835	112	16	first	first	ADJ
cana-835	112	17	derivative	derivative	NOUN
cana-835	112	18	)	)	PUNCT
cana-835	112	19	,	,	PUNCT
cana-835	112	20	local	local	ADJ
cana-835	112	21	minℹma	minℹma	NOUN
cana-835	112	22	(	(	PUNCT
cana-835	112	23	concave	concave	VERB
cana-835	112	24	down	down	ADP
cana-835	112	25	and	and	CCONJ
cana-835	112	26	positive	positive	ADJ
cana-835	112	27	first	first	ADJ
cana-835	112	28	derivative	derivative	NOUN
cana-835	112	29	)	)	PUNCT
cana-835	112	30	,	,	PUNCT
cana-835	112	31	or	or	CCONJ
cana-835	112	32	points	point	NOUN
cana-835	112	33	of	of	ADP
cana-835	112	34	inflection	inflection	NOUN
cana-835	112	35	(	(	PUNCT
cana-835	112	36	concave	concave	VERB
cana-835	112	37	up	up	ADP
cana-835	112	38	and	and	CCONJ
cana-835	112	39	positive	positive	ADJ
cana-835	112	40	or	or	CCONJ
cana-835	112	41	concave	concave	VERB
cana-835	112	42	down	down	ADP
cana-835	112	43	and	and	CCONJ
cana-835	112	44	negative	negative	ADJ
cana-835	112	45	first	first	ADJ
cana-835	112	46	derivative	derivative	NOUN
cana-835	112	47	)	)	PUNCT
cana-835	112	48	if	if	SCONJ
cana-835	112	49	the	the	DET
cana-835	112	50	second	second	ADJ
cana-835	112	51	-	-	PUNCT
cana-835	112	52	order	order	NOUN
cana-835	112	53	derivatives	derivative	NOUN
cana-835	112	54	at	at	ADP
cana-835	112	55	iteration	iteration	NOUN
cana-835	112	56	𝑥𝑖+1are	𝑥𝑖+1are	PROPN
cana-835	112	57	zero	zero	NUM
cana-835	112	58	,	,	PUNCT
cana-835	112	59	the	the	DET
cana-835	112	60	technique	technique	NOUN
cana-835	112	61	fails	fail	VERB
cana-835	112	62	.	.	PUNCT
cana-835	113	1	the	the	DET
cana-835	113	2	newton	newton	PROPN
cana-835	113	3	method	method	NOUN
cana-835	113	4	's	's	PART
cana-835	113	5	initial	initial	ADJ
cana-835	113	6	derivatives	derivative	NOUN
cana-835	113	7	are	be	AUX
cana-835	113	8	employed	employ	VERB
cana-835	113	9	only	only	ADV
cana-835	113	10	to	to	PART
cana-835	113	11	find	find	VERB
cana-835	113	12	the	the	DET
cana-835	113	13	functions	function	NOUN
cana-835	113	14	'	'	PART
cana-835	113	15	roots	root	NOUN
cana-835	113	16	.	.	PUNCT
cana-835	114	1	the	the	DET
cana-835	114	2	sec0nd	sec0nd	PROPN
cana-835	114	3	derivatives	derivative	NOUN
cana-835	114	4	of	of	ADP
cana-835	114	5	the	the	DET
cana-835	114	6	newt0n	newt0n	PROPN
cana-835	114	7	method	method	NOUN
cana-835	114	8	determine	determine	VERB
cana-835	114	9	the	the	DET
cana-835	114	10	maximum	maximum	ADJ
cana-835	114	11	and	and	CCONJ
cana-835	114	12	least	least	ADJ
cana-835	114	13	of	of	ADP
cana-835	114	14	a	a	DET
cana-835	114	15	given	give	VERB
cana-835	114	16	functi0n	functi0n	NOUN
cana-835	114	17	.	.	NOUN
cana-835	114	18	3.1	3.1	NUM
cana-835	114	19	interval	interval	NOUN
cana-835	114	20	newton	newton	PROPN
cana-835	114	21	method	method	VERB
cana-835	114	22	the	the	DET
cana-835	114	23	interval	interval	NOUN
cana-835	114	24	newt0n	newt0n	PROPN
cana-835	114	25	meth0d	meth0d	PROPN
cana-835	114	26	shares	share	NOUN
cana-835	114	27	simℹlarities	simℹlaritie	NOUN
cana-835	114	28	with	with	ADP
cana-835	114	29	the	the	DET
cana-835	114	30	bℹsection	bℹsection	NOUN
cana-835	114	31	method	method	NOUN
cana-835	114	32	,	,	PUNCT
cana-835	114	33	as	as	SCONJ
cana-835	114	34	it	it	PRON
cana-835	114	35	also	also	ADV
cana-835	114	36	begins	begin	VERB
cana-835	114	37	with	with	ADP
cana-835	114	38	a	a	DET
cana-835	114	39	bracketing	bracket	VERB
cana-835	114	40	ℹnterval	ℹnterval	NOUN
cana-835	114	41	.	.	PUNCT
cana-835	115	1	in	in	ADP
cana-835	115	2	each	each	DET
cana-835	115	3	iterati0n	iterati0n	NOUN
cana-835	115	4	,	,	PUNCT
cana-835	115	5	it	it	PRON
cana-835	115	6	generates	generate	VERB
cana-835	115	7	smaller	small	ADJ
cana-835	115	8	and	and	CCONJ
cana-835	115	9	smaller	small	ADJ
cana-835	115	10	intervals	interval	NOUN
cana-835	115	11	,	,	PUNCT
cana-835	115	12	all	all	PRON
cana-835	115	13	b0unded	b0unde	VERB
cana-835	115	14	by	by	ADP
cana-835	115	15	the	the	DET
cana-835	115	16	intersecti0n	intersecti0n	NOUN
cana-835	115	17	with	with	ADP
cana-835	115	18	previ0us	previ0us	PROPN
cana-835	115	19	ℹterati0ns	ℹterati0ns	PROPN
cana-835	115	20	.	.	PUNCT
cana-835	116	1	the	the	DET
cana-835	116	2	f0rmula	f0rmula	PROPN
cana-835	116	3	is	be	AUX
cana-835	116	4	as	as	ADP
cana-835	116	5	foll0ws	foll0ws	NOUN
cana-835	116	6	𝑥𝑘+1	𝑥𝑘+1	NOUN
cana-835	116	7	=	=	SYM
cana-835	117	1	[	[	X
cana-835	117	2	𝑚(𝑥𝑘	𝑚(𝑥𝑘	NUM
cana-835	117	3	)	)	PUNCT
cana-835	117	4	−	−	NOUN
cana-835	117	5	𝑓′(𝑚(𝑥𝑘	𝑓′(𝑚(𝑥𝑘	ADJ
cana-835	117	6	)	)	PUNCT
cana-835	117	7	)	)	PUNCT
cana-835	117	8	𝑓′′(𝑥𝑘	𝑓′′(𝑥𝑘	ADJ
cana-835	117	9	)	)	PUNCT
cana-835	117	10	]	]	PUNCT
cana-835	118	1	∩	∩	NOUN
cana-835	118	2	(	(	PUNCT
cana-835	118	3	𝑥𝑘	𝑥𝑘	X
cana-835	118	4	)	)	PUNCT
cana-835	118	5	(	(	PUNCT
cana-835	118	6	3.1.1	3.1.1	X
cana-835	118	7	)	)	PUNCT
cana-835	118	8	where	where	SCONJ
cana-835	118	9	x	x	X
cana-835	118	10	’s	’s	X
cana-835	118	11	are	be	AUX
cana-835	118	12	the	the	DET
cana-835	118	13	ℹnterval	ℹnterval	NOUN
cana-835	118	14	m(x	m(x	PROPN
cana-835	118	15	)	)	PUNCT
cana-835	118	16	is	be	AUX
cana-835	118	17	the	the	DET
cana-835	118	18	mℹdp0int	mℹdp0int	NOUN
cana-835	118	19	of	of	ADP
cana-835	118	20	interval	interval	NOUN
cana-835	118	21	x	x	NOUN
cana-835	118	22	,	,	PUNCT
cana-835	118	23	and	and	CCONJ
cana-835	118	24	f	f	PROPN
cana-835	118	25	is	be	AUX
cana-835	118	26	unc0nstrained	unc0nstrained	PROPN
cana-835	118	27	0ptℹmization	0ptℹmization	NUM
cana-835	118	28	function	function	NOUN
cana-835	118	29	.	.	PUNCT
cana-835	119	1	for	for	ADP
cana-835	119	2	an	an	DET
cana-835	119	3	fuzzy	fuzzy	ADJ
cana-835	119	4	unc0nstraℹned	unc0nstraℹned	ADJ
cana-835	119	5	optimizati0n	optimizati0n	NOUN
cana-835	119	6	problem	problem	NOUN
cana-835	119	7	then	then	ADV
cana-835	119	8	(	(	PUNCT
cana-835	119	9	3.1.1	3.1.1	X
cana-835	119	10	)	)	PUNCT
cana-835	119	11	takes	take	VERB
cana-835	119	12	the	the	DET
cana-835	119	13	f0rm	f0rm	ADJ
cana-835	119	14	�	�	PROPN
cana-835	119	15	̃	̃	NOUN
cana-835	119	16	�	�	NOUN
cana-835	119	17	𝑘+1	𝑘+1	PRON
cana-835	119	18	𝐼	𝐼	NOUN
cana-835	119	19	=	=	SYM
cana-835	119	20	[	[	X
cana-835	119	21	𝑚(	𝑚(	NUM
cana-835	119	22	�	�	SYM
cana-835	119	23	̃	̃	PROPN
cana-835	119	24	�	�	NOUN
cana-835	119	25	𝑘	𝑘	NOUN
cana-835	119	26	)	)	PUNCT
cana-835	119	27	𝐼	𝐼	ADP
cana-835	119	28	−	−	PROPN
cana-835	119	29	𝑓′(𝑚(	𝑓′(𝑚(	PROPN
cana-835	119	30	�	�	PROPN
cana-835	119	31	̃	̃	PROPN
cana-835	119	32	�	�	NOUN
cana-835	119	33	𝑘	𝑘	NOUN
cana-835	119	34	)	)	PUNCT
cana-835	119	35	𝐼	𝐼	ADP
cana-835	119	36	𝑓′′(	𝑓′′(	PROPN
cana-835	119	37	�	�	PROPN
cana-835	119	38	̃	̃	PROPN
cana-835	119	39	�	�	PROPN
cana-835	119	40	𝑘	𝑘	NOUN
cana-835	119	41	)	)	PUNCT
cana-835	119	42	𝐼	𝐼	PROPN
cana-835	119	43	]	]	PUNCT
cana-835	119	44	∩	∩	NOUN
cana-835	119	45	(	(	PUNCT
cana-835	119	46	�	�	PROPN
cana-835	119	47	̃	̃	PROPN
cana-835	119	48	�	�	NOUN
cana-835	119	49	𝑘	𝑘	NOUN
cana-835	119	50	)	)	PUNCT
cana-835	119	51	𝐼	𝐼	PROPN
cana-835	119	52	(	(	PUNCT
cana-835	119	53	3.1.2	3.1.2	NUM
cana-835	119	54	)	)	PUNCT
cana-835	119	55	�	�	PROPN
cana-835	119	56	̃	̃	PROPN
cana-835	119	57	�	�	NOUN
cana-835	119	58	𝑘+1	𝑘+1	PRON
cana-835	119	59	𝐼	𝐼	NOUN
cana-835	119	60	=	=	SYM
cana-835	120	1	[	[	X
cana-835	120	2	(	(	PUNCT
cana-835	120	3	𝑚(	𝑚(	NUM
cana-835	120	4	�	�	PROPN
cana-835	120	5	̃	̃	PROPN
cana-835	120	6	�	�	NOUN
cana-835	120	7	𝑇1	𝑇1	NOUN
cana-835	120	8	)	)	PUNCT
cana-835	120	9	,	,	PUNCT
cana-835	120	10	𝑚(	𝑚(	PROPN
cana-835	120	11	�	�	PROPN
cana-835	120	12	̃	̃	PROPN
cana-835	120	13	�	�	NOUN
cana-835	120	14	𝑇2	𝑇2	NOUN
cana-835	120	15	)	)	PUNCT
cana-835	120	16	,	,	PUNCT
cana-835	120	17	…	…	PUNCT
cana-835	120	18	,	,	PUNCT
cana-835	120	19	𝑚(	𝑚(	PROPN
cana-835	120	20	�	�	SYM
cana-835	120	21	̃	̃	PROPN
cana-835	120	22	�	�	PROPN
cana-835	120	23	𝑇𝑛	𝑇𝑛	NOUN
cana-835	120	24	)	)	PUNCT
cana-835	120	25	)	)	PUNCT
cana-835	121	1	;	;	PUNCT
cana-835	121	2	(	(	PUNCT
cana-835	121	3	𝑚(	𝑚(	NUM
cana-835	121	4	�	�	SYM
cana-835	121	5	̃	̃	PROPN
cana-835	121	6	�	�	NOUN
cana-835	121	7	𝐹1	𝐹1	NOUN
cana-835	121	8	)	)	PUNCT
cana-835	121	9	,	,	PUNCT
cana-835	121	10	𝑚(	𝑚(	PROPN
cana-835	121	11	�	�	PROPN
cana-835	121	12	̃	̃	PROPN
cana-835	121	13	�	�	NOUN
cana-835	121	14	𝐹2	𝐹2	NOUN
cana-835	121	15	)	)	PUNCT
cana-835	121	16	,	,	PUNCT
cana-835	121	17	…	…	PUNCT
cana-835	121	18	,	,	PUNCT
cana-835	121	19	𝑚(	𝑚(	PROPN
cana-835	121	20	�	�	SYM
cana-835	121	21	̃	̃	PROPN
cana-835	121	22	�	�	NOUN
cana-835	121	23	𝐹𝑛	𝐹𝑛	PROPN
cana-835	121	24	)	)	PUNCT
cana-835	121	25	)	)	PUNCT
cana-835	122	1	]	]	PUNCT
cana-835	123	1	−	−	PROPN
cana-835	123	2	[	[	PUNCT
cana-835	123	3	𝑓′[(𝑚(	𝑓′[(𝑚(	PROPN
cana-835	123	4	�	�	PROPN
cana-835	123	5	̃	̃	PROPN
cana-835	123	6	�	�	NOUN
cana-835	123	7	𝑇1	𝑇1	NOUN
cana-835	123	8	)	)	PUNCT
cana-835	123	9	,	,	PUNCT
cana-835	123	10	𝑚(	𝑚(	PROPN
cana-835	123	11	�	�	PROPN
cana-835	123	12	̃	̃	PROPN
cana-835	123	13	�	�	NOUN
cana-835	123	14	𝑇2	𝑇2	NOUN
cana-835	123	15	)	)	PUNCT
cana-835	123	16	,	,	PUNCT
cana-835	123	17	…	…	PUNCT
cana-835	123	18	,	,	PUNCT
cana-835	123	19	𝑚(	𝑚(	PROPN
cana-835	123	20	�	�	PROPN
cana-835	123	21	̃	̃	PROPN
cana-835	123	22	�	�	PROPN
cana-835	123	23	𝑇𝑛	𝑇𝑛	NOUN
cana-835	123	24	)	)	PUNCT
cana-835	123	25	)	)	PUNCT
cana-835	123	26	;	;	PUNCT
cana-835	123	27	(	(	PUNCT
cana-835	123	28	𝑚(	𝑚(	NUM
cana-835	123	29	�	�	SYM
cana-835	123	30	̃	̃	PROPN
cana-835	123	31	�	�	NOUN
cana-835	123	32	𝐹1	𝐹1	NOUN
cana-835	123	33	)	)	PUNCT
cana-835	123	34	,	,	PUNCT
cana-835	123	35	𝑚(	𝑚(	PROPN
cana-835	123	36	�	�	PROPN
cana-835	123	37	̃	̃	PROPN
cana-835	123	38	�	�	NOUN
cana-835	123	39	𝐹2	𝐹2	NOUN
cana-835	123	40	)	)	PUNCT
cana-835	123	41	,	,	PUNCT
cana-835	123	42	…	…	PUNCT
cana-835	123	43	,	,	PUNCT
cana-835	123	44	𝑚(	𝑚(	PROPN
cana-835	123	45	�	�	SYM
cana-835	123	46	̃	̃	PROPN
cana-835	123	47	�	�	NOUN
cana-835	123	48	𝐹𝑛	𝐹𝑛	PROPN
cana-835	123	49	)	)	PUNCT
cana-835	123	50	)	)	PUNCT
cana-835	123	51	]	]	PUNCT
cana-835	123	52	𝑓′′([((	𝑓′′([((	PROPN
cana-835	123	53	�	�	PROPN
cana-835	123	54	̃	̃	PROPN
cana-835	123	55	�	�	NOUN
cana-835	123	56	𝑇1	𝑇1	NOUN
cana-835	123	57	)	)	PUNCT
cana-835	123	58	,	,	PUNCT
cana-835	123	59	(	(	PUNCT
cana-835	123	60	�	�	PROPN
cana-835	123	61	̃	̃	PROPN
cana-835	123	62	�	�	NOUN
cana-835	123	63	𝑇2	𝑇2	NOUN
cana-835	123	64	)	)	PUNCT
cana-835	123	65	,	,	PUNCT
cana-835	123	66	…	…	PUNCT
cana-835	123	67	,	,	PUNCT
cana-835	123	68	(	(	PUNCT
cana-835	123	69	�	�	PROPN
cana-835	123	70	̃	̃	PROPN
cana-835	123	71	�	�	PROPN
cana-835	123	72	𝑇𝑛	𝑇𝑛	NOUN
cana-835	123	73	)	)	PUNCT
cana-835	123	74	)	)	PUNCT
cana-835	123	75	;	;	PUNCT
cana-835	123	76	(	(	PUNCT
cana-835	123	77	(	(	PUNCT
cana-835	123	78	�	�	PROPN
cana-835	123	79	̃	̃	NOUN
cana-835	123	80	�	�	NOUN
cana-835	123	81	𝐹1	𝐹1	NOUN
cana-835	123	82	)	)	PUNCT
cana-835	123	83	,	,	PUNCT
cana-835	123	84	(	(	PUNCT
cana-835	123	85	�	�	PROPN
cana-835	123	86	̃	̃	PROPN
cana-835	123	87	�	�	NOUN
cana-835	123	88	𝐹2	𝐹2	NOUN
cana-835	123	89	)	)	PUNCT
cana-835	123	90	,	,	PUNCT
cana-835	123	91	…	…	PUNCT
cana-835	123	92	,	,	PUNCT
cana-835	123	93	(	(	PUNCT
cana-835	123	94	�	�	PROPN
cana-835	123	95	̃	̃	NUM
cana-835	123	96	�	�	NOUN
cana-835	123	97	𝐹𝑛	𝐹𝑛	PROPN
cana-835	123	98	)	)	PUNCT
cana-835	123	99	)	)	PUNCT
cana-835	124	1	]	]	PUNCT
cana-835	124	2	)	)	PUNCT
cana-835	124	3	]	]	PUNCT
cana-835	125	1	∩	∩	NOUN
cana-835	125	2	(	(	PUNCT
cana-835	125	3	[	[	X
cana-835	125	4	(	(	PUNCT
cana-835	125	5	(	(	PUNCT
cana-835	125	6	�	�	PROPN
cana-835	125	7	̃	̃	NOUN
cana-835	125	8	�	�	NOUN
cana-835	125	9	𝑇1	𝑇1	NOUN
cana-835	125	10	)	)	PUNCT
cana-835	125	11	,	,	PUNCT
cana-835	125	12	(	(	PUNCT
cana-835	125	13	�	�	PROPN
cana-835	125	14	̃	̃	PROPN
cana-835	125	15	�	�	NOUN
cana-835	125	16	𝑇2	𝑇2	NOUN
cana-835	125	17	)	)	PUNCT
cana-835	125	18	,	,	PUNCT
cana-835	125	19	…	…	PUNCT
cana-835	125	20	,	,	PUNCT
cana-835	125	21	(	(	PUNCT
cana-835	125	22	�	�	PROPN
cana-835	125	23	̃	̃	PROPN
cana-835	125	24	�	�	PROPN
cana-835	125	25	𝑇𝑛	𝑇𝑛	NOUN
cana-835	125	26	)	)	PUNCT
cana-835	125	27	)	)	PUNCT
cana-835	125	28	;	;	PUNCT
cana-835	125	29	(	(	PUNCT
cana-835	125	30	(	(	PUNCT
cana-835	125	31	�	�	PROPN
cana-835	125	32	̃	̃	NOUN
cana-835	125	33	�	�	NOUN
cana-835	125	34	𝐹1	𝐹1	NOUN
cana-835	125	35	)	)	PUNCT
cana-835	125	36	,	,	PUNCT
cana-835	125	37	(	(	PUNCT
cana-835	125	38	�	�	PROPN
cana-835	125	39	̃	̃	PROPN
cana-835	125	40	�	�	NOUN
cana-835	125	41	𝐹2	𝐹2	NOUN
cana-835	125	42	)	)	PUNCT
cana-835	125	43	,	,	PUNCT
cana-835	125	44	…	…	PUNCT
cana-835	125	45	,	,	PUNCT
cana-835	125	46	(	(	PUNCT
cana-835	125	47	�	�	PROPN
cana-835	125	48	̃	̃	NOUN
cana-835	125	49	�	�	NOUN
cana-835	125	50	𝐹𝑛	𝐹𝑛	PROPN
cana-835	125	51	)	)	PUNCT
cana-835	125	52	)	)	PUNCT
cana-835	125	53	]	]	PUNCT
cana-835	125	54	)	)	PUNCT
cana-835	125	55	where	where	SCONJ
cana-835	125	56	n	n	PRON
cana-835	125	57	den0tes	den0te	VERB
cana-835	125	58	the	the	DET
cana-835	125	59	ℹntuiti0nistic	ℹntuiti0nistic	ADJ
cana-835	125	60	fuzzy	fuzzy	ADJ
cana-835	125	61	number	number	NOUN
cana-835	125	62	.	.	PUNCT
cana-835	126	1	if	if	SCONJ
cana-835	126	2	n=3	n=3	VERB
cana-835	126	3	,	,	PUNCT
cana-835	126	4	it	it	PRON
cana-835	126	5	is	be	AUX
cana-835	126	6	denoted	denote	VERB
cana-835	126	7	as	as	ADP
cana-835	126	8	ℹntuiti0nistic	ℹntuiti0nistic	ADJ
cana-835	126	9	trℹangular	trℹangular	ADJ
cana-835	126	10	fuzzy	fuzzy	ADJ
cana-835	126	11	number	number	NOUN
cana-835	126	12	,	,	PUNCT
cana-835	126	13	if	if	SCONJ
cana-835	126	14	n=4	n=4	NOUN
cana-835	126	15	,	,	PUNCT
cana-835	126	16	it	it	PRON
cana-835	126	17	is	be	AUX
cana-835	126	18	denoted	denote	VERB
cana-835	126	19	as	as	ADP
cana-835	126	20	ℹntuiti0nistic	ℹntuiti0nistic	ADJ
cana-835	126	21	trapez0idal	trapez0idal	ADJ
cana-835	126	22	fuzzy	fuzzy	ADJ
cana-835	126	23	number	number	NOUN
cana-835	126	24	and	and	CCONJ
cana-835	126	25	so	so	ADV
cana-835	126	26	on	on	ADV
cana-835	126	27	.	.	PUNCT
cana-835	127	1	�	�	PROPN
cana-835	127	2	̃	̃	PROPN
cana-835	127	3	�	�	NOUN
cana-835	127	4	𝑘+1	𝑘+1	PRON
cana-835	127	5	𝐼	𝐼	NOUN
cana-835	127	6	=	=	SYM
cana-835	128	1	[	[	X
cana-835	128	2	(	(	PUNCT
cana-835	128	3	(	(	PUNCT
cana-835	128	4	�	�	PROPN
cana-835	128	5	̃	̃	PROPN
cana-835	128	6	�	�	PROPN
cana-835	128	7	𝑇1𝐿	𝑇1𝐿	PROPN
cana-835	128	8	+	+	CCONJ
cana-835	128	9	�	�	PROPN
cana-835	128	10	̃	̃	PROPN
cana-835	128	11	�	�	NOUN
cana-835	128	12	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	128	13	2	2	NUM
cana-835	128	14	)	)	PUNCT
cana-835	128	15	,	,	PUNCT
cana-835	128	16	(	(	PUNCT
cana-835	128	17	�	�	PROPN
cana-835	128	18	̃	̃	NOUN
cana-835	128	19	�	�	PROPN
cana-835	128	20	𝑇2𝐿	𝑇2𝐿	PROPN
cana-835	128	21	+	+	SYM
cana-835	128	22	�	�	PROPN
cana-835	128	23	̃	̃	PROPN
cana-835	128	24	�	�	NOUN
cana-835	128	25	𝑇2𝑈	𝑇2𝑈	PROPN
cana-835	128	26	2	2	NUM
cana-835	128	27	)	)	PUNCT
cana-835	128	28	,	,	PUNCT
cana-835	128	29	…	…	PUNCT
cana-835	128	30	,	,	PUNCT
cana-835	128	31	(	(	PUNCT
cana-835	128	32	�	�	PROPN
cana-835	128	33	̃	̃	NOUN
cana-835	128	34	�	�	PROPN
cana-835	128	35	𝑇𝑛𝐿	𝑇𝑛𝐿	PROPN
cana-835	128	36	+	+	SYM
cana-835	128	37	�	�	PROPN
cana-835	128	38	̃	̃	PROPN
cana-835	128	39	�	�	NOUN
cana-835	128	40	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	128	41	2	2	NUM
cana-835	128	42	)	)	PUNCT
cana-835	128	43	)	)	PUNCT
cana-835	129	1	;	;	PUNCT
cana-835	129	2	(	(	PUNCT
cana-835	129	3	(	(	PUNCT
cana-835	129	4	�	�	PROPN
cana-835	129	5	̃	̃	NOUN
cana-835	129	6	�	�	PROPN
cana-835	129	7	𝐹1𝐿	𝐹1𝐿	PRON
cana-835	129	8	+	+	NUM
cana-835	129	9	�	�	PROPN
cana-835	129	10	̃	̃	PROPN
cana-835	129	11	�	�	NOUN
cana-835	129	12	𝐹1𝑈	𝐹1𝑈	ADP
cana-835	129	13	2	2	NUM
cana-835	129	14	)	)	PUNCT
cana-835	129	15	,	,	PUNCT
cana-835	129	16	(	(	PUNCT
cana-835	129	17	�	�	PROPN
cana-835	129	18	̃	̃	NOUN
cana-835	129	19	�	�	PROPN
cana-835	129	20	𝐹2𝐿	𝐹2𝐿	PROPN
cana-835	129	21	+	+	NUM
cana-835	129	22	�	�	PROPN
cana-835	129	23	̃	̃	PROPN
cana-835	129	24	�	�	PROPN
cana-835	129	25	𝐹2𝑈	𝐹2𝑈	ADP
cana-835	129	26	2	2	NUM
cana-835	129	27	)	)	PUNCT
cana-835	129	28	,	,	PUNCT
cana-835	129	29	…	…	PUNCT
cana-835	129	30	,	,	PUNCT
cana-835	129	31	(	(	PUNCT
cana-835	129	32	�	�	PROPN
cana-835	129	33	̃	̃	NOUN
cana-835	129	34	�	�	NOUN
cana-835	129	35	𝐹𝑛𝐿	𝐹𝑛𝐿	PROPN
cana-835	129	36	+	+	SYM
cana-835	129	37	�	�	PROPN
cana-835	129	38	̃	̃	PROPN
cana-835	129	39	�	�	NOUN
cana-835	129	40	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	129	41	2	2	NUM
cana-835	129	42	)	)	PUNCT
cana-835	129	43	)	)	PUNCT
cana-835	130	1	communications	communication	NOUN
cana-835	130	2	on	on	ADP
cana-835	130	3	applied	apply	VERB
cana-835	130	4	nonlinear	nonlinear	ADJ
cana-835	130	5	analysis	analysis	NOUN
cana-835	130	6	issn	issn	NOUN
cana-835	130	7	:	:	PUNCT
cana-835	130	8	1074	1074	NUM
cana-835	130	9	-	-	PUNCT
cana-835	130	10	133x	133x	NUM
cana-835	130	11	vol	vol	NOUN
cana-835	130	12	31	31	NUM
cana-835	130	13	no	no	NOUN
cana-835	130	14	.	.	PUNCT
cana-835	131	1	4s	4s	NUM
cana-835	131	2	(	(	PUNCT
cana-835	131	3	2024	2024	NUM
cana-835	131	4	)	)	PUNCT
cana-835	131	5	188	188	NUM
cana-835	131	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	131	7	−	−	PROPN
cana-835	131	8	[	[	PUNCT
cana-835	131	9	𝑓′	𝑓′	X
cana-835	131	10	[	[	PUNCT
cana-835	131	11	(	(	PUNCT
cana-835	131	12	(	(	PUNCT
cana-835	131	13	�	�	PROPN
cana-835	131	14	̃	̃	PROPN
cana-835	131	15	�	�	PROPN
cana-835	131	16	𝑇1𝐿	𝑇1𝐿	PROPN
cana-835	131	17	+	+	CCONJ
cana-835	131	18	�	�	PROPN
cana-835	131	19	̃	̃	PROPN
cana-835	131	20	�	�	NOUN
cana-835	131	21	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	131	22	2	2	NUM
cana-835	131	23	)	)	PUNCT
cana-835	131	24	,	,	PUNCT
cana-835	131	25	(	(	PUNCT
cana-835	131	26	�	�	PROPN
cana-835	131	27	̃	̃	NOUN
cana-835	131	28	�	�	PROPN
cana-835	131	29	𝑇2𝐿	𝑇2𝐿	PROPN
cana-835	131	30	+	+	SYM
cana-835	131	31	�	�	PROPN
cana-835	131	32	̃	̃	PROPN
cana-835	131	33	�	�	NOUN
cana-835	131	34	𝑇2𝑈	𝑇2𝑈	NOUN
cana-835	131	35	2	2	NUM
cana-835	131	36	)	)	PUNCT
cana-835	131	37	,	,	PUNCT
cana-835	131	38	…	…	PUNCT
cana-835	131	39	,	,	PUNCT
cana-835	131	40	(	(	PUNCT
cana-835	131	41	�	�	PROPN
cana-835	131	42	̃	̃	NOUN
cana-835	131	43	�	�	PROPN
cana-835	131	44	𝑇𝑛𝐿	𝑇𝑛𝐿	PROPN
cana-835	131	45	+	+	SYM
cana-835	131	46	�	�	PROPN
cana-835	131	47	̃	̃	PROPN
cana-835	131	48	�	�	NOUN
cana-835	131	49	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	131	50	2	2	NUM
cana-835	131	51	)	)	PUNCT
cana-835	131	52	)	)	PUNCT
cana-835	131	53	;	;	PUNCT
cana-835	131	54	(	(	PUNCT
cana-835	131	55	(	(	PUNCT
cana-835	131	56	�	�	PROPN
cana-835	131	57	̃	̃	NOUN
cana-835	131	58	�	�	PROPN
cana-835	131	59	𝐹1𝐿	𝐹1𝐿	PRON
cana-835	131	60	+	+	NUM
cana-835	131	61	�	�	PROPN
cana-835	131	62	̃	̃	PROPN
cana-835	131	63	�	�	NOUN
cana-835	131	64	𝐹1𝑈	𝐹1𝑈	ADP
cana-835	131	65	2	2	NUM
cana-835	131	66	)	)	PUNCT
cana-835	131	67	,	,	PUNCT
cana-835	131	68	(	(	PUNCT
cana-835	131	69	�	�	PROPN
cana-835	131	70	̃	̃	NOUN
cana-835	131	71	�	�	PROPN
cana-835	131	72	𝐹2𝐿	𝐹2𝐿	PROPN
cana-835	131	73	+	+	NUM
cana-835	131	74	�	�	PROPN
cana-835	131	75	̃	̃	PROPN
cana-835	131	76	�	�	PROPN
cana-835	131	77	𝐹2𝑈	𝐹2𝑈	ADP
cana-835	131	78	2	2	NUM
cana-835	131	79	)	)	PUNCT
cana-835	131	80	,	,	PUNCT
cana-835	131	81	…	…	PUNCT
cana-835	131	82	,	,	PUNCT
cana-835	131	83	(	(	PUNCT
cana-835	131	84	�	�	PROPN
cana-835	131	85	̃	̃	NOUN
cana-835	131	86	�	�	NOUN
cana-835	131	87	𝐹𝑛𝐿	𝐹𝑛𝐿	PROPN
cana-835	131	88	+	+	SYM
cana-835	131	89	�	�	PROPN
cana-835	131	90	̃	̃	PROPN
cana-835	131	91	�	�	NOUN
cana-835	131	92	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	131	93	2	2	NUM
cana-835	131	94	)	)	PUNCT
cana-835	131	95	)	)	PUNCT
cana-835	131	96	]	]	PUNCT
cana-835	132	1	𝑓′′	𝑓′′	PROPN
cana-835	132	2	(	(	PUNCT
cana-835	132	3	[	[	PUNCT
cana-835	132	4	(	(	PUNCT
cana-835	132	5	(	(	PUNCT
cana-835	132	6	�	�	PROPN
cana-835	132	7	̃	̃	PROPN
cana-835	132	8	�	�	PROPN
cana-835	132	9	𝑇1𝐿	𝑇1𝐿	PROPN
cana-835	132	10	,	,	PUNCT
cana-835	132	11	�	�	PROPN
cana-835	132	12	̃	̃	PROPN
cana-835	132	13	�	�	NOUN
cana-835	132	14	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	132	15	)	)	PUNCT
cana-835	132	16	,	,	PUNCT
cana-835	132	17	(	(	PUNCT
cana-835	132	18	�	�	PROPN
cana-835	132	19	̃	̃	PROPN
cana-835	132	20	�	�	PROPN
cana-835	132	21	𝑇2𝐿	𝑇2𝐿	PROPN
cana-835	132	22	,	,	PUNCT
cana-835	132	23	�	�	PROPN
cana-835	132	24	̃	̃	PROPN
cana-835	132	25	�	�	NOUN
cana-835	132	26	𝑇2𝑈	𝑇2𝑈	NOUN
cana-835	132	27	)	)	PUNCT
cana-835	132	28	,	,	PUNCT
cana-835	132	29	…	…	PUNCT
cana-835	132	30	,	,	PUNCT
cana-835	132	31	(	(	PUNCT
cana-835	132	32	�	�	PROPN
cana-835	132	33	̃	̃	NOUN
cana-835	132	34	�	�	NOUN
cana-835	132	35	𝑇𝑛𝐿	𝑇𝑛𝐿	NOUN
cana-835	132	36	,	,	PUNCT
cana-835	132	37	�	�	PROPN
cana-835	132	38	̃	̃	PROPN
cana-835	132	39	�	�	NOUN
cana-835	132	40	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	132	41	)	)	PUNCT
cana-835	132	42	)	)	PUNCT
cana-835	133	1	;	;	PUNCT
cana-835	133	2	(	(	PUNCT
cana-835	133	3	(	(	PUNCT
cana-835	133	4	�	�	PROPN
cana-835	133	5	̃	̃	NOUN
cana-835	133	6	�	�	PROPN
cana-835	133	7	𝐹1𝐿	𝐹1𝐿	PROPN
cana-835	133	8	,	,	PUNCT
cana-835	133	9	�	�	PROPN
cana-835	133	10	̃	̃	PROPN
cana-835	133	11	�	�	NOUN
cana-835	133	12	𝐹1𝑈	𝐹1𝑈	NOUN
cana-835	133	13	)	)	PUNCT
cana-835	133	14	,	,	PUNCT
cana-835	133	15	(	(	PUNCT
cana-835	133	16	�	�	PROPN
cana-835	133	17	̃	̃	PROPN
cana-835	133	18	�	�	PROPN
cana-835	133	19	𝐹2𝐿	𝐹2𝐿	PROPN
cana-835	133	20	,	,	PUNCT
cana-835	133	21	�	�	PROPN
cana-835	133	22	̃	̃	PROPN
cana-835	133	23	�	�	NOUN
cana-835	133	24	𝐹2𝑈	𝐹2𝑈	NUM
cana-835	133	25	)	)	PUNCT
cana-835	133	26	,	,	PUNCT
cana-835	133	27	…	…	PUNCT
cana-835	133	28	,	,	PUNCT
cana-835	133	29	(	(	PUNCT
cana-835	133	30	�	�	PROPN
cana-835	133	31	̃	̃	PROPN
cana-835	133	32	�	�	NOUN
cana-835	133	33	𝐹𝑛𝐿	𝐹𝑛𝐿	PROPN
cana-835	133	34	,	,	PUNCT
cana-835	133	35	�	�	PROPN
cana-835	133	36	̃	̃	PROPN
cana-835	133	37	�	�	NOUN
cana-835	133	38	𝐹𝑛𝑈	𝐹𝑛𝑈	PROPN
cana-835	133	39	)	)	PUNCT
cana-835	133	40	)	)	PUNCT
cana-835	134	1	]	]	PUNCT
cana-835	134	2	)	)	PUNCT
cana-835	134	3	]	]	PUNCT
cana-835	134	4	∩	∩	NOUN
cana-835	134	5	(	(	PUNCT
cana-835	134	6	[	[	PUNCT
cana-835	134	7	(	(	PUNCT
cana-835	134	8	(	(	PUNCT
cana-835	134	9	�	�	PROPN
cana-835	134	10	̃	̃	NOUN
cana-835	134	11	�	�	NOUN
cana-835	134	12	𝑇1	𝑇1	NOUN
cana-835	134	13	)	)	PUNCT
cana-835	134	14	,	,	PUNCT
cana-835	134	15	(	(	PUNCT
cana-835	134	16	�	�	PROPN
cana-835	134	17	̃	̃	PROPN
cana-835	134	18	�	�	NOUN
cana-835	134	19	𝑇2	𝑇2	NOUN
cana-835	134	20	)	)	PUNCT
cana-835	134	21	,	,	PUNCT
cana-835	134	22	…	…	PUNCT
cana-835	134	23	,	,	PUNCT
cana-835	134	24	(	(	PUNCT
cana-835	134	25	�	�	PROPN
cana-835	134	26	̃	̃	PROPN
cana-835	134	27	�	�	PROPN
cana-835	134	28	𝑇𝑛	𝑇𝑛	NOUN
cana-835	134	29	)	)	PUNCT
cana-835	134	30	)	)	PUNCT
cana-835	134	31	;	;	PUNCT
cana-835	134	32	(	(	PUNCT
cana-835	134	33	(	(	PUNCT
cana-835	134	34	�	�	PROPN
cana-835	134	35	̃	̃	NOUN
cana-835	134	36	�	�	NOUN
cana-835	134	37	𝐹1	𝐹1	NOUN
cana-835	134	38	)	)	PUNCT
cana-835	134	39	,	,	PUNCT
cana-835	134	40	(	(	PUNCT
cana-835	134	41	�	�	PROPN
cana-835	134	42	̃	̃	PROPN
cana-835	134	43	�	�	NOUN
cana-835	134	44	𝐹2	𝐹2	NOUN
cana-835	134	45	)	)	PUNCT
cana-835	134	46	,	,	PUNCT
cana-835	134	47	…	…	PUNCT
cana-835	134	48	,	,	PUNCT
cana-835	134	49	(	(	PUNCT
cana-835	134	50	�	�	PROPN
cana-835	134	51	̃	̃	NOUN
cana-835	134	52	�	�	NOUN
cana-835	134	53	𝐹𝑛	𝐹𝑛	PROPN
cana-835	134	54	)	)	PUNCT
cana-835	134	55	)	)	PUNCT
cana-835	134	56	]	]	PUNCT
cana-835	134	57	)	)	PUNCT
cana-835	134	58	for	for	ADP
cana-835	134	59	bivariate	bivariate	ADJ
cana-835	134	60	,	,	PUNCT
cana-835	134	61	the	the	DET
cana-835	134	62	f0rmula	f0rmula	PROPN
cana-835	134	63	𝑋𝑘+1	𝑋𝑘+1	NOUN
cana-835	134	64	=	=	SYM
cana-835	134	65	𝑁𝑘((𝑋𝑘	𝑁𝑘((𝑋𝑘	NOUN
cana-835	134	66	,	,	PUNCT
cana-835	134	67	𝑌𝑘	𝑌𝑘	PROPN
cana-835	134	68	)	)	PUNCT
cana-835	134	69	)	)	PUNCT
cana-835	134	70	∩	∩	NOUN
cana-835	134	71	(	(	PUNCT
cana-835	134	72	𝑋𝐾	𝑋𝐾	PROPN
cana-835	134	73	)	)	PUNCT
cana-835	134	74	where	where	SCONJ
cana-835	134	75	𝑁𝑘((𝑋𝑘	𝑁𝑘((𝑋𝑘	NOUN
cana-835	134	76	,	,	PUNCT
cana-835	134	77	𝑌𝑘	𝑌𝑘	PROPN
cana-835	134	78	)	)	PUNCT
cana-835	134	79	)	)	PUNCT
cana-835	135	1	=	=	PUNCT
cana-835	136	1	[	[	X
cana-835	136	2	𝑚(𝑋𝑘	𝑚(𝑋𝑘	NOUN
cana-835	136	3	)	)	PUNCT
cana-835	136	4	−	−	PROPN
cana-835	136	5	𝑓′(𝑚(𝑋𝑘),𝑚(𝑌𝑘	𝑓′(𝑚(𝑋𝑘),𝑚(𝑌𝑘	NOUN
cana-835	136	6	)	)	PUNCT
cana-835	136	7	)	)	PUNCT
cana-835	136	8	𝑓′′((𝑋𝑘,𝑌𝑘	𝑓′′((𝑋𝑘,𝑌𝑘	PROPN
cana-835	136	9	)	)	PUNCT
cana-835	136	10	]	]	PUNCT
cana-835	136	11	𝑋𝑘+1	𝑋𝑘+1	X
cana-835	137	1	=	=	X
cana-835	138	1	[	[	X
cana-835	138	2	𝑚(𝑋𝑘	𝑚(𝑋𝑘	NOUN
cana-835	138	3	)	)	PUNCT
cana-835	138	4	−	−	PROPN
cana-835	138	5	𝑓′(𝑚(𝑋𝑘),𝑚(𝑌𝑘	𝑓′(𝑚(𝑋𝑘),𝑚(𝑌𝑘	NOUN
cana-835	138	6	)	)	PUNCT
cana-835	138	7	)	)	PUNCT
cana-835	139	1	𝑓′′(𝑋𝑘,𝑌𝑘	𝑓′′(𝑋𝑘,𝑌𝑘	PROPN
cana-835	139	2	)	)	PUNCT
cana-835	139	3	]	]	PUNCT
cana-835	140	1	∩	∩	NOUN
cana-835	140	2	(	(	PUNCT
cana-835	140	3	𝑋𝑘	𝑋𝑘	PROPN
cana-835	140	4	)	)	PUNCT
cana-835	140	5	,	,	PUNCT
cana-835	140	6	𝑓′′(𝑋𝑘	𝑓′′(𝑋𝑘	ADV
cana-835	140	7	,	,	PUNCT
cana-835	140	8	𝑌𝑘	𝑌𝑘	PROPN
cana-835	140	9	)	)	PUNCT
cana-835	140	10	≠	≠	PROPN
cana-835	140	11	0	0	NUM
cana-835	140	12	(	(	PUNCT
cana-835	140	13	3.1.3	3.1.3	NUM
cana-835	140	14	)	)	PUNCT
cana-835	140	15	and	and	CCONJ
cana-835	140	16	𝑌𝑖+1	𝑌𝑖+1	X
cana-835	140	17	=	=	PUNCT
cana-835	140	18	𝑁𝑘((𝑋𝑘	𝑁𝑘((𝑋𝑘	ADJ
cana-835	140	19	,	,	PUNCT
cana-835	140	20	𝑌𝑘	𝑌𝑘	PROPN
cana-835	140	21	)	)	PUNCT
cana-835	140	22	)	)	PUNCT
cana-835	140	23	∩	∩	NOUN
cana-835	140	24	(	(	PUNCT
cana-835	140	25	𝑌𝐾	𝑌𝐾	PROPN
cana-835	140	26	)	)	PUNCT
cana-835	140	27	where	where	SCONJ
cana-835	140	28	𝑁𝑘((𝑋𝑘	𝑁𝑘((𝑋𝑘	NOUN
cana-835	140	29	,	,	PUNCT
cana-835	140	30	𝑌𝑘	𝑌𝑘	PROPN
cana-835	140	31	)	)	PUNCT
cana-835	140	32	)	)	PUNCT
cana-835	141	1	=	=	PUNCT
cana-835	142	1	[	[	X
cana-835	142	2	𝑚(𝑌𝑘	𝑚(𝑌𝑘	NOUN
cana-835	142	3	)	)	PUNCT
cana-835	142	4	−	−	PROPN
cana-835	142	5	𝑓′(𝑚(𝑋𝑘),𝑚(𝑌𝑘	𝑓′(𝑚(𝑋𝑘),𝑚(𝑌𝑘	NOUN
cana-835	142	6	)	)	PUNCT
cana-835	142	7	)	)	PUNCT
cana-835	142	8	𝑓′′((𝑋𝑘,𝑌𝑘	𝑓′′((𝑋𝑘,𝑌𝑘	PROPN
cana-835	142	9	)	)	PUNCT
cana-835	142	10	]	]	PUNCT
cana-835	142	11	𝑌𝑘+1	𝑌𝑘+1	X
cana-835	143	1	=	=	PUNCT
cana-835	144	1	[	[	X
cana-835	144	2	𝑚	𝑚	X
cana-835	144	3	(	(	PUNCT
cana-835	144	4	,	,	PUNCT
cana-835	144	5	𝑌𝑘	𝑌𝑘	PROPN
cana-835	144	6	)	)	PUNCT
cana-835	144	7	−	−	PROPN
cana-835	144	8	𝑓′(𝑚(𝑋𝑘),𝑚(𝑌𝑘	𝑓′(𝑚(𝑋𝑘),𝑚(𝑌𝑘	NOUN
cana-835	144	9	)	)	PUNCT
cana-835	144	10	)	)	PUNCT
cana-835	144	11	𝑓′′((𝑋𝑘,𝑌𝑘	𝑓′′((𝑋𝑘,𝑌𝑘	PROPN
cana-835	144	12	)	)	PUNCT
cana-835	144	13	]	]	PUNCT
cana-835	145	1	∩	∩	NOUN
cana-835	145	2	(	(	PUNCT
cana-835	145	3	𝑌𝑘	𝑌𝑘	PROPN
cana-835	145	4	)	)	PUNCT
cana-835	145	5	,	,	PUNCT
cana-835	145	6	𝑓′′(𝑋𝑘	𝑓′′(𝑋𝑘	ADV
cana-835	145	7	,	,	PUNCT
cana-835	145	8	𝑌𝑘	𝑌𝑘	PROPN
cana-835	145	9	)	)	PUNCT
cana-835	145	10	≠	≠	PROPN
cana-835	145	11	0	0	NUM
cana-835	145	12	(	(	PUNCT
cana-835	145	13	3.1.4	3.1.4	NUM
cana-835	145	14	)	)	PUNCT
cana-835	145	15	where	where	SCONJ
cana-835	145	16	x	x	X
cana-835	145	17	’s	’s	X
cana-835	145	18	are	be	AUX
cana-835	145	19	the	the	DET
cana-835	145	20	ℹnterval	ℹnterval	NOUN
cana-835	145	21	m(x	m(x	PROPN
cana-835	145	22	)	)	PUNCT
cana-835	145	23	is	be	AUX
cana-835	145	24	the	the	DET
cana-835	145	25	mℹdp0int	mℹdp0int	NOUN
cana-835	145	26	of	of	ADP
cana-835	145	27	interval	interval	NOUN
cana-835	145	28	x	x	NOUN
cana-835	145	29	,	,	PUNCT
cana-835	145	30	and	and	CCONJ
cana-835	145	31	f	f	PROPN
cana-835	145	32	is	be	AUX
cana-835	145	33	unc0nstraℹned	unc0nstraℹned	ADJ
cana-835	145	34	0ptimization	0ptimization	NOUN
cana-835	145	35	function	function	NOUN
cana-835	145	36	.	.	PUNCT
cana-835	146	1	�	�	PROPN
cana-835	146	2	̃	̃	PROPN
cana-835	146	3	�	�	NOUN
cana-835	146	4	𝑘+1	𝑘+1	PRON
cana-835	146	5	𝐼	𝐼	NOUN
cana-835	146	6	=	=	PUNCT
cana-835	146	7	(	(	PUNCT
cana-835	146	8	[	[	PUNCT
cana-835	146	9	(	(	PUNCT
cana-835	146	10	𝑚(	𝑚(	NUM
cana-835	146	11	�	�	PROPN
cana-835	146	12	̃	̃	PROPN
cana-835	146	13	�	�	NOUN
cana-835	146	14	𝑇1	𝑇1	NOUN
cana-835	146	15	)	)	PUNCT
cana-835	146	16	,	,	PUNCT
cana-835	146	17	𝑚(	𝑚(	PROPN
cana-835	146	18	�	�	PROPN
cana-835	146	19	̃	̃	PROPN
cana-835	146	20	�	�	NOUN
cana-835	146	21	𝑇2	𝑇2	NOUN
cana-835	146	22	)	)	PUNCT
cana-835	146	23	,	,	PUNCT
cana-835	146	24	…	…	PUNCT
cana-835	146	25	,	,	PUNCT
cana-835	146	26	𝑚(	𝑚(	PROPN
cana-835	146	27	�	�	SYM
cana-835	146	28	̃	̃	PROPN
cana-835	146	29	�	�	PROPN
cana-835	146	30	𝑇𝑛	𝑇𝑛	NOUN
cana-835	146	31	)	)	PUNCT
cana-835	146	32	)	)	PUNCT
cana-835	147	1	;	;	PUNCT
cana-835	147	2	(	(	PUNCT
cana-835	147	3	𝑚(	𝑚(	NUM
cana-835	147	4	�	�	SYM
cana-835	147	5	̃	̃	PROPN
cana-835	147	6	�	�	NOUN
cana-835	147	7	𝐹1	𝐹1	NOUN
cana-835	147	8	)	)	PUNCT
cana-835	147	9	,	,	PUNCT
cana-835	147	10	𝑚(	𝑚(	PROPN
cana-835	147	11	�	�	PROPN
cana-835	147	12	̃	̃	PROPN
cana-835	147	13	�	�	NOUN
cana-835	147	14	𝐹2	𝐹2	NOUN
cana-835	147	15	)	)	PUNCT
cana-835	147	16	,	,	PUNCT
cana-835	147	17	…	…	PUNCT
cana-835	147	18	,	,	PUNCT
cana-835	147	19	𝑚(	𝑚(	PROPN
cana-835	147	20	�	�	SYM
cana-835	147	21	̃	̃	PROPN
cana-835	147	22	�	�	NOUN
cana-835	147	23	𝐹𝑛	𝐹𝑛	PROPN
cana-835	147	24	)	)	PUNCT
cana-835	147	25	)	)	PUNCT
cana-835	147	26	]	]	PUNCT
cana-835	148	1	−	−	PROPN
cana-835	148	2	[	[	PUNCT
cana-835	148	3	𝑓′	𝑓′	X
cana-835	148	4	[	[	PUNCT
cana-835	148	5	(	(	PUNCT
cana-835	148	6	𝑚(	𝑚(	NUM
cana-835	148	7	�	�	PROPN
cana-835	148	8	̃	̃	PROPN
cana-835	148	9	�	�	NOUN
cana-835	148	10	𝑇1	𝑇1	NOUN
cana-835	148	11	,	,	PUNCT
cana-835	148	12	�	�	PROPN
cana-835	148	13	̃	̃	PROPN
cana-835	148	14	�	�	NOUN
cana-835	148	15	𝑇1	𝑇1	NOUN
cana-835	148	16	)	)	PUNCT
cana-835	148	17	,	,	PUNCT
cana-835	148	18	𝑚(	𝑚(	PROPN
cana-835	148	19	�	�	PROPN
cana-835	148	20	̃	̃	PROPN
cana-835	148	21	�	�	NOUN
cana-835	148	22	𝑇2	𝑇2	PROPN
cana-835	148	23	,	,	PUNCT
cana-835	148	24	�	�	PROPN
cana-835	148	25	̃	̃	PROPN
cana-835	148	26	�	�	NOUN
cana-835	148	27	𝑇2	𝑇2	NOUN
cana-835	148	28	)	)	PUNCT
cana-835	148	29	,	,	PUNCT
cana-835	148	30	…	…	PUNCT
cana-835	148	31	,	,	PUNCT
cana-835	148	32	𝑚(	𝑚(	PROPN
cana-835	148	33	�	�	SYM
cana-835	148	34	̃	̃	PROPN
cana-835	148	35	�	�	PROPN
cana-835	148	36	𝑇𝑛	𝑇𝑛	PROPN
cana-835	148	37	,	,	PUNCT
cana-835	148	38	�	�	PROPN
cana-835	148	39	̃	̃	PROPN
cana-835	148	40	�	�	PROPN
cana-835	148	41	𝑇𝑛	𝑇𝑛	NOUN
cana-835	148	42	)	)	PUNCT
cana-835	148	43	)	)	PUNCT
cana-835	148	44	;	;	PUNCT
cana-835	148	45	(	(	PUNCT
cana-835	148	46	𝑚(	𝑚(	NUM
cana-835	148	47	�	�	SYM
cana-835	148	48	̃	̃	PROPN
cana-835	148	49	�	�	NOUN
cana-835	148	50	𝐹1	𝐹1	PROPN
cana-835	148	51	,	,	PUNCT
cana-835	148	52	�	�	PROPN
cana-835	148	53	̃	̃	PROPN
cana-835	148	54	�	�	NOUN
cana-835	148	55	𝑇1	𝑇1	NOUN
cana-835	148	56	)	)	PUNCT
cana-835	148	57	,	,	PUNCT
cana-835	148	58	𝑚(	𝑚(	PROPN
cana-835	148	59	�	�	PROPN
cana-835	148	60	̃	̃	PROPN
cana-835	148	61	�	�	NOUN
cana-835	148	62	𝐹2	𝐹2	NOUN
cana-835	148	63	,	,	PUNCT
cana-835	148	64	�	�	PROPN
cana-835	148	65	̃	̃	PROPN
cana-835	148	66	�	�	NOUN
cana-835	148	67	𝑇1	𝑇1	NOUN
cana-835	148	68	)	)	PUNCT
cana-835	148	69	,	,	PUNCT
cana-835	148	70	…	…	PUNCT
cana-835	148	71	,	,	PUNCT
cana-835	148	72	𝑚(	𝑚(	PROPN
cana-835	148	73	�	�	SYM
cana-835	148	74	̃	̃	PROPN
cana-835	148	75	�	�	NOUN
cana-835	148	76	𝐹𝑛,	𝐹𝑛,	SYM
cana-835	148	77	�	�	PROPN
cana-835	148	78	̃	̃	PROPN
cana-835	148	79	�	�	NOUN
cana-835	148	80	𝑇1	𝑇1	NOUN
cana-835	148	81	)	)	PUNCT
cana-835	148	82	)	)	PUNCT
cana-835	148	83	]	]	PUNCT
cana-835	149	1	𝑓′′	𝑓′′	PROPN
cana-835	149	2	(	(	PUNCT
cana-835	149	3	[	[	PUNCT
cana-835	149	4	(	(	PUNCT
cana-835	149	5	(	(	PUNCT
cana-835	149	6	�	�	PROPN
cana-835	149	7	̃	̃	NOUN
cana-835	149	8	�	�	NOUN
cana-835	149	9	𝑇1	𝑇1	NOUN
cana-835	149	10	,	,	PUNCT
cana-835	149	11	�	�	PROPN
cana-835	149	12	̃	̃	PROPN
cana-835	149	13	�	�	NOUN
cana-835	149	14	𝑇1	𝑇1	NOUN
cana-835	149	15	)	)	PUNCT
cana-835	149	16	,	,	PUNCT
cana-835	149	17	(	(	PUNCT
cana-835	149	18	�	�	PROPN
cana-835	149	19	̃	̃	PROPN
cana-835	149	20	�	�	NOUN
cana-835	149	21	𝑇2	𝑇2	PROPN
cana-835	149	22	,	,	PUNCT
cana-835	149	23	�	�	PROPN
cana-835	149	24	̃	̃	PROPN
cana-835	149	25	�	�	NOUN
cana-835	149	26	𝑇2	𝑇2	NOUN
cana-835	149	27	)	)	PUNCT
cana-835	149	28	,	,	PUNCT
cana-835	149	29	…	…	PUNCT
cana-835	149	30	,	,	PUNCT
cana-835	149	31	(	(	PUNCT
cana-835	149	32	�	�	PROPN
cana-835	149	33	̃	̃	PROPN
cana-835	149	34	�	�	PROPN
cana-835	149	35	𝑇𝑛	𝑇𝑛	PROPN
cana-835	149	36	,	,	PUNCT
cana-835	149	37	�	�	PROPN
cana-835	149	38	̃	̃	PROPN
cana-835	149	39	�	�	PROPN
cana-835	149	40	𝑇𝑛	𝑇𝑛	NOUN
cana-835	149	41	)	)	PUNCT
cana-835	149	42	)	)	PUNCT
cana-835	149	43	;	;	PUNCT
cana-835	149	44	(	(	PUNCT
cana-835	149	45	(	(	PUNCT
cana-835	149	46	�	�	PROPN
cana-835	149	47	̃	̃	PROPN
cana-835	149	48	�	�	NOUN
cana-835	149	49	𝐹1	𝐹1	PROPN
cana-835	149	50	,	,	PUNCT
cana-835	149	51	�	�	PROPN
cana-835	149	52	̃	̃	PROPN
cana-835	149	53	�	�	NOUN
cana-835	149	54	𝐹1	𝐹1	NOUN
cana-835	149	55	)	)	PUNCT
cana-835	149	56	,	,	PUNCT
cana-835	149	57	(	(	PUNCT
cana-835	149	58	�	�	PROPN
cana-835	149	59	̃	̃	PROPN
cana-835	149	60	�	�	NOUN
cana-835	149	61	𝐹2	𝐹2	NOUN
cana-835	149	62	,	,	PUNCT
cana-835	149	63	�	�	PROPN
cana-835	149	64	̃	̃	PROPN
cana-835	149	65	�	�	NOUN
cana-835	149	66	𝐹2	𝐹2	NOUN
cana-835	149	67	)	)	PUNCT
cana-835	149	68	,	,	PUNCT
cana-835	149	69	…	…	PUNCT
cana-835	149	70	,	,	PUNCT
cana-835	149	71	(	(	PUNCT
cana-835	149	72	�	�	PROPN
cana-835	149	73	̃	̃	NOUN
cana-835	149	74	�	�	NOUN
cana-835	149	75	𝐹𝑛,	𝐹𝑛,	SYM
cana-835	149	76	�	�	PROPN
cana-835	149	77	̃	̃	PROPN
cana-835	149	78	�	�	NOUN
cana-835	149	79	𝐹𝑛	𝐹𝑛	PROPN
cana-835	149	80	)	)	PUNCT
cana-835	149	81	)	)	PUNCT
cana-835	149	82	]	]	PUNCT
cana-835	149	83	)	)	PUNCT
cana-835	149	84	]	]	PUNCT
cana-835	149	85	)	)	PUNCT
cana-835	149	86	∩	∩	NOUN
cana-835	149	87	[	[	PUNCT
cana-835	149	88	(	(	PUNCT
cana-835	149	89	(	(	PUNCT
cana-835	149	90	�	�	PROPN
cana-835	149	91	̃	̃	PROPN
cana-835	149	92	�	�	PROPN
cana-835	149	93	𝑇1𝐿	𝑇1𝐿	PROPN
cana-835	149	94	,	,	PUNCT
cana-835	149	95	�	�	PROPN
cana-835	149	96	̃	̃	PROPN
cana-835	149	97	�	�	NOUN
cana-835	149	98	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	149	99	)	)	PUNCT
cana-835	149	100	,	,	PUNCT
cana-835	149	101	(	(	PUNCT
cana-835	149	102	�	�	PROPN
cana-835	149	103	̃	̃	PROPN
cana-835	149	104	�	�	PROPN
cana-835	149	105	𝑇2𝐿	𝑇2𝐿	PROPN
cana-835	149	106	,	,	PUNCT
cana-835	149	107	�	�	PROPN
cana-835	149	108	̃	̃	PROPN
cana-835	149	109	�	�	NOUN
cana-835	149	110	𝑇2𝑈	𝑇2𝑈	NOUN
cana-835	149	111	)	)	PUNCT
cana-835	149	112	,	,	PUNCT
cana-835	149	113	…	…	PUNCT
cana-835	149	114	,	,	PUNCT
cana-835	149	115	(	(	PUNCT
cana-835	149	116	�	�	PROPN
cana-835	149	117	̃	̃	NOUN
cana-835	149	118	�	�	NOUN
cana-835	149	119	𝑇𝑛𝐿	𝑇𝑛𝐿	NOUN
cana-835	149	120	,	,	PUNCT
cana-835	149	121	�	�	PROPN
cana-835	149	122	̃	̃	PROPN
cana-835	149	123	�	�	NOUN
cana-835	149	124	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	149	125	)	)	PUNCT
cana-835	149	126	)	)	PUNCT
cana-835	149	127	;	;	PUNCT
cana-835	149	128	(	(	PUNCT
cana-835	149	129	(	(	PUNCT
cana-835	149	130	�	�	PROPN
cana-835	149	131	̃	̃	NOUN
cana-835	149	132	�	�	NOUN
cana-835	149	133	𝐹1𝐿	𝐹1𝐿	NOUN
cana-835	149	134	,	,	PUNCT
cana-835	149	135	�	�	PROPN
cana-835	149	136	̃	̃	PROPN
cana-835	149	137	�	�	NOUN
cana-835	149	138	𝐹1𝑈	𝐹1𝑈	NOUN
cana-835	149	139	)	)	PUNCT
cana-835	149	140	,	,	PUNCT
cana-835	149	141	(	(	PUNCT
cana-835	149	142	�	�	PROPN
cana-835	149	143	̃	̃	PROPN
cana-835	149	144	�	�	PROPN
cana-835	149	145	𝐹2𝐿	𝐹2𝐿	PROPN
cana-835	149	146	,	,	PUNCT
cana-835	149	147	�	�	PROPN
cana-835	149	148	̃	̃	PROPN
cana-835	149	149	�	�	NOUN
cana-835	149	150	𝐹2𝑈	𝐹2𝑈	NUM
cana-835	149	151	)	)	PUNCT
cana-835	149	152	,	,	PUNCT
cana-835	149	153	…	…	PUNCT
cana-835	149	154	,	,	PUNCT
cana-835	149	155	(	(	PUNCT
cana-835	149	156	�	�	PROPN
cana-835	149	157	̃	̃	PROPN
cana-835	149	158	�	�	NOUN
cana-835	149	159	𝐹𝑛𝐿	𝐹𝑛𝐿	PROPN
cana-835	149	160	,	,	PUNCT
cana-835	149	161	�	�	PROPN
cana-835	149	162	̃	̃	PROPN
cana-835	149	163	�	�	NOUN
cana-835	149	164	𝐹𝑛𝑈	𝐹𝑛𝑈	PROPN
cana-835	149	165	)	)	PUNCT
cana-835	149	166	)	)	PUNCT
cana-835	149	167	]	]	PUNCT
cana-835	150	1	communications	communication	NOUN
cana-835	150	2	on	on	ADP
cana-835	150	3	applied	apply	VERB
cana-835	150	4	nonlinear	nonlinear	ADJ
cana-835	150	5	analysis	analysis	NOUN
cana-835	150	6	issn	issn	NOUN
cana-835	150	7	:	:	PUNCT
cana-835	150	8	1074	1074	NUM
cana-835	150	9	-	-	PUNCT
cana-835	150	10	133x	133x	NUM
cana-835	150	11	vol	vol	NOUN
cana-835	150	12	31	31	NUM
cana-835	150	13	no	no	NOUN
cana-835	150	14	.	.	PUNCT
cana-835	151	1	4s	4s	NUM
cana-835	151	2	(	(	PUNCT
cana-835	151	3	2024	2024	NUM
cana-835	151	4	)	)	PUNCT
cana-835	151	5	189	189	NUM
cana-835	151	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	151	7	�	�	PROPN
cana-835	151	8	̃	̃	PROPN
cana-835	151	9	�	�	NOUN
cana-835	151	10	𝑘+1	𝑘+1	PRON
cana-835	151	11	𝐼	𝐼	NOUN
cana-835	151	12	=	=	PUNCT
cana-835	151	13	[	[	PUNCT
cana-835	151	14	[	[	PUNCT
cana-835	151	15	(	(	PUNCT
cana-835	151	16	(	(	PUNCT
cana-835	151	17	�	�	PROPN
cana-835	151	18	̃	̃	PROPN
cana-835	151	19	�	�	PROPN
cana-835	151	20	𝑇1𝐿	𝑇1𝐿	PROPN
cana-835	151	21	+	+	CCONJ
cana-835	151	22	�	�	PROPN
cana-835	151	23	̃	̃	PROPN
cana-835	151	24	�	�	NOUN
cana-835	151	25	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	151	26	2	2	NUM
cana-835	151	27	)	)	PUNCT
cana-835	151	28	,	,	PUNCT
cana-835	151	29	(	(	PUNCT
cana-835	151	30	�	�	PROPN
cana-835	151	31	̃	̃	NOUN
cana-835	151	32	�	�	PROPN
cana-835	151	33	𝑇2𝐿	𝑇2𝐿	PROPN
cana-835	151	34	+	+	SYM
cana-835	151	35	�	�	PROPN
cana-835	151	36	̃	̃	PROPN
cana-835	151	37	�	�	NOUN
cana-835	151	38	𝑇2𝑈	𝑇2𝑈	PROPN
cana-835	151	39	2	2	NUM
cana-835	151	40	)	)	PUNCT
cana-835	151	41	,	,	PUNCT
cana-835	151	42	…	…	PUNCT
cana-835	151	43	,	,	PUNCT
cana-835	151	44	(	(	PUNCT
cana-835	151	45	�	�	PROPN
cana-835	151	46	̃	̃	NOUN
cana-835	151	47	�	�	PROPN
cana-835	151	48	𝑇𝑛𝐿	𝑇𝑛𝐿	PROPN
cana-835	151	49	+	+	SYM
cana-835	151	50	�	�	PROPN
cana-835	151	51	̃	̃	PROPN
cana-835	151	52	�	�	NOUN
cana-835	151	53	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	151	54	2	2	NUM
cana-835	151	55	)	)	PUNCT
cana-835	151	56	)	)	PUNCT
cana-835	152	1	;	;	PUNCT
cana-835	152	2	(	(	PUNCT
cana-835	152	3	(	(	PUNCT
cana-835	152	4	�	�	PROPN
cana-835	152	5	̃	̃	NOUN
cana-835	152	6	�	�	PROPN
cana-835	152	7	𝐹1𝐿	𝐹1𝐿	PRON
cana-835	152	8	+	+	NUM
cana-835	152	9	�	�	PROPN
cana-835	152	10	̃	̃	PROPN
cana-835	152	11	�	�	NOUN
cana-835	152	12	𝐹1𝑈	𝐹1𝑈	ADP
cana-835	152	13	2	2	NUM
cana-835	152	14	)	)	PUNCT
cana-835	152	15	,	,	PUNCT
cana-835	152	16	(	(	PUNCT
cana-835	152	17	�	�	PROPN
cana-835	152	18	̃	̃	NOUN
cana-835	152	19	�	�	PROPN
cana-835	152	20	𝐹2𝐿	𝐹2𝐿	PROPN
cana-835	152	21	+	+	NUM
cana-835	152	22	�	�	PROPN
cana-835	152	23	̃	̃	PROPN
cana-835	152	24	�	�	PROPN
cana-835	152	25	𝐹2𝑈	𝐹2𝑈	ADP
cana-835	152	26	2	2	NUM
cana-835	152	27	)	)	PUNCT
cana-835	152	28	,	,	PUNCT
cana-835	152	29	…	…	PUNCT
cana-835	152	30	,	,	PUNCT
cana-835	152	31	(	(	PUNCT
cana-835	152	32	�	�	PROPN
cana-835	152	33	̃	̃	NOUN
cana-835	152	34	�	�	NOUN
cana-835	152	35	𝐹𝑛𝐿	𝐹𝑛𝐿	PROPN
cana-835	152	36	+	+	SYM
cana-835	152	37	�	�	PROPN
cana-835	152	38	̃	̃	PROPN
cana-835	152	39	�	�	NOUN
cana-835	152	40	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	152	41	2	2	NUM
cana-835	152	42	)	)	PUNCT
cana-835	152	43	)	)	PUNCT
cana-835	152	44	]	]	PUNCT
cana-835	153	1	−	−	PROPN
cana-835	153	2	𝑓′	𝑓′	NOUN
cana-835	154	1	′	′	NUM
cana-835	155	1	[	[	PUNCT
cana-835	155	2	(	(	PUNCT
cana-835	155	3	(	(	PUNCT
cana-835	155	4	(	(	PUNCT
cana-835	155	5	�	�	PROPN
cana-835	155	6	̃	̃	PROPN
cana-835	155	7	�	�	PROPN
cana-835	155	8	𝑇1𝐿+	𝑇1𝐿+	PROPN
cana-835	155	9	�	�	PROPN
cana-835	155	10	̃	̃	NOUN
cana-835	155	11	�	�	NOUN
cana-835	155	12	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	155	13	2	2	NUM
cana-835	155	14	)	)	PUNCT
cana-835	155	15	,	,	PUNCT
cana-835	155	16	(	(	PUNCT
cana-835	155	17	�	�	PROPN
cana-835	155	18	̃	̃	NOUN
cana-835	155	19	�	�	PROPN
cana-835	155	20	𝑇1𝐿+	𝑇1𝐿+	PROPN
cana-835	155	21	�	�	PROPN
cana-835	155	22	̃	̃	NOUN
cana-835	155	23	�	�	NOUN
cana-835	155	24	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	155	25	2	2	NUM
cana-835	155	26	)	)	PUNCT
cana-835	155	27	)	)	PUNCT
cana-835	155	28	,	,	PUNCT
cana-835	155	29	(	(	PUNCT
cana-835	155	30	(	(	PUNCT
cana-835	155	31	�	�	PROPN
cana-835	155	32	̃	̃	NOUN
cana-835	155	33	�	�	NOUN
cana-835	155	34	𝑇2𝐿+	𝑇2𝐿+	NUM
cana-835	155	35	�	�	SYM
cana-835	155	36	̃	̃	NOUN
cana-835	155	37	�	�	NOUN
cana-835	155	38	𝑇2𝑈	𝑇2𝑈	PROPN
cana-835	155	39	2	2	NUM
cana-835	155	40	)	)	PUNCT
cana-835	155	41	,	,	PUNCT
cana-835	155	42	(	(	PUNCT
cana-835	155	43	�	�	PROPN
cana-835	155	44	̃	̃	NOUN
cana-835	155	45	�	�	NOUN
cana-835	155	46	𝑇2𝐿+	𝑇2𝐿+	NUM
cana-835	155	47	�	�	SYM
cana-835	155	48	̃	̃	NOUN
cana-835	155	49	�	�	NOUN
cana-835	155	50	𝑇2𝑈	𝑇2𝑈	PROPN
cana-835	155	51	2	2	NUM
cana-835	155	52	)	)	PUNCT
cana-835	155	53	)	)	PUNCT
cana-835	156	1	,	,	PUNCT
cana-835	156	2	…	…	PUNCT
cana-835	156	3	(	(	PUNCT
cana-835	156	4	(	(	PUNCT
cana-835	156	5	�	�	PROPN
cana-835	156	6	̃	̃	NOUN
cana-835	156	7	�	�	NOUN
cana-835	156	8	𝑇𝑛𝐿+	𝑇𝑛𝐿+	NOUN
cana-835	156	9	�	�	PROPN
cana-835	156	10	̃	̃	PROPN
cana-835	156	11	�	�	PROPN
cana-835	156	12	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	156	13	2	2	NUM
cana-835	156	14	)	)	PUNCT
cana-835	156	15	,	,	PUNCT
cana-835	156	16	(	(	PUNCT
cana-835	156	17	�	�	PROPN
cana-835	156	18	̃	̃	NOUN
cana-835	156	19	�	�	NOUN
cana-835	156	20	𝑇𝑛𝐿+	𝑇𝑛𝐿+	NOUN
cana-835	156	21	�	�	PROPN
cana-835	156	22	̃	̃	PROPN
cana-835	156	23	�	�	PROPN
cana-835	156	24	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	156	25	2	2	NUM
cana-835	156	26	)	)	PUNCT
cana-835	156	27	)	)	PUNCT
cana-835	156	28	;	;	PUNCT
cana-835	156	29	)	)	PUNCT
cana-835	156	30	,	,	PUNCT
cana-835	156	31	(	(	PUNCT
cana-835	156	32	(	(	PUNCT
cana-835	156	33	(	(	PUNCT
cana-835	156	34	�	�	PROPN
cana-835	156	35	̃	̃	PROPN
cana-835	156	36	�	�	PROPN
cana-835	156	37	𝐹1𝐿+	𝐹1𝐿+	NOUN
cana-835	156	38	�	�	PROPN
cana-835	156	39	̃	̃	NOUN
cana-835	156	40	�	�	NOUN
cana-835	156	41	𝐹1𝑈	𝐹1𝑈	ADP
cana-835	156	42	2	2	NUM
cana-835	156	43	)	)	PUNCT
cana-835	156	44	,	,	PUNCT
cana-835	156	45	(	(	PUNCT
cana-835	156	46	�	�	PROPN
cana-835	156	47	̃	̃	PROPN
cana-835	156	48	�	�	PROPN
cana-835	156	49	𝐹1𝐿+	𝐹1𝐿+	NOUN
cana-835	156	50	�	�	PROPN
cana-835	156	51	̃	̃	NOUN
cana-835	156	52	�	�	NOUN
cana-835	156	53	𝐹1𝑈	𝐹1𝑈	ADP
cana-835	156	54	2	2	NUM
cana-835	156	55	)	)	PUNCT
cana-835	156	56	)	)	PUNCT
cana-835	156	57	,	,	PUNCT
cana-835	156	58	(	(	PUNCT
cana-835	156	59	(	(	PUNCT
cana-835	156	60	�	�	PROPN
cana-835	156	61	̃	̃	NOUN
cana-835	156	62	�	�	NOUN
cana-835	156	63	𝐹𝑛𝐿+	𝐹𝑛𝐿+	NOUN
cana-835	156	64	�	�	PROPN
cana-835	156	65	̃	̃	NOUN
cana-835	156	66	�	�	NOUN
cana-835	156	67	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	156	68	2	2	NUM
cana-835	156	69	)	)	PUNCT
cana-835	156	70	,	,	PUNCT
cana-835	156	71	(	(	PUNCT
cana-835	156	72	�	�	PROPN
cana-835	156	73	̃	̃	NOUN
cana-835	156	74	�	�	NOUN
cana-835	156	75	𝐹𝑛𝐿+	𝐹𝑛𝐿+	NOUN
cana-835	156	76	�	�	PROPN
cana-835	156	77	̃	̃	NOUN
cana-835	156	78	�	�	NOUN
cana-835	156	79	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	156	80	2	2	NUM
cana-835	156	81	)	)	PUNCT
cana-835	156	82	)	)	PUNCT
cana-835	156	83	…	…	PUNCT
cana-835	156	84	.	.	PUNCT
cana-835	157	1	(	(	PUNCT
cana-835	157	2	(	(	PUNCT
cana-835	157	3	�	�	PROPN
cana-835	157	4	̃	̃	NOUN
cana-835	157	5	�	�	NOUN
cana-835	157	6	𝐹𝑛𝐿+	𝐹𝑛𝐿+	NOUN
cana-835	157	7	�	�	PROPN
cana-835	157	8	̃	̃	NOUN
cana-835	157	9	�	�	NOUN
cana-835	157	10	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	157	11	2	2	NUM
cana-835	157	12	)	)	PUNCT
cana-835	157	13	,	,	PUNCT
cana-835	157	14	(	(	PUNCT
cana-835	157	15	�	�	PROPN
cana-835	157	16	̃	̃	NOUN
cana-835	157	17	�	�	NOUN
cana-835	157	18	𝐹𝑛𝐿+	𝐹𝑛𝐿+	NOUN
cana-835	157	19	�	�	PROPN
cana-835	157	20	̃	̃	NOUN
cana-835	157	21	�	�	NOUN
cana-835	157	22	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	157	23	2	2	NUM
cana-835	157	24	)	)	PUNCT
cana-835	157	25	)	)	PUNCT
cana-835	157	26	)	)	PUNCT
cana-835	158	1	]	]	PUNCT
cana-835	159	1	𝑓′′	𝑓′′	PROPN
cana-835	159	2	(	(	PUNCT
cana-835	159	3	(	(	PUNCT
cana-835	159	4	[	[	PUNCT
cana-835	159	5	(	(	PUNCT
cana-835	159	6	(	(	PUNCT
cana-835	159	7	�	�	PROPN
cana-835	159	8	̃	̃	NOUN
cana-835	159	9	�	�	NOUN
cana-835	159	10	𝑇1	𝑇1	NOUN
cana-835	159	11	,	,	PUNCT
cana-835	159	12	�	�	PROPN
cana-835	159	13	̃	̃	PROPN
cana-835	159	14	�	�	NOUN
cana-835	159	15	𝑇1	𝑇1	NOUN
cana-835	159	16	)	)	PUNCT
cana-835	159	17	,	,	PUNCT
cana-835	159	18	(	(	PUNCT
cana-835	159	19	�	�	PROPN
cana-835	159	20	̃	̃	PROPN
cana-835	159	21	�	�	NOUN
cana-835	159	22	𝑇2	𝑇2	PROPN
cana-835	159	23	,	,	PUNCT
cana-835	159	24	�	�	PROPN
cana-835	159	25	̃	̃	PROPN
cana-835	159	26	�	�	NOUN
cana-835	159	27	𝑇2	𝑇2	NOUN
cana-835	159	28	)	)	PUNCT
cana-835	159	29	,	,	PUNCT
cana-835	159	30	…	…	PUNCT
cana-835	159	31	,	,	PUNCT
cana-835	159	32	(	(	PUNCT
cana-835	159	33	�	�	PROPN
cana-835	159	34	̃	̃	PROPN
cana-835	159	35	�	�	PROPN
cana-835	159	36	𝑇𝑛	𝑇𝑛	PROPN
cana-835	159	37	,	,	PUNCT
cana-835	159	38	�	�	PROPN
cana-835	159	39	̃	̃	PROPN
cana-835	159	40	�	�	PROPN
cana-835	159	41	𝑇𝑛	𝑇𝑛	NOUN
cana-835	159	42	)	)	PUNCT
cana-835	159	43	)	)	PUNCT
cana-835	159	44	;	;	PUNCT
cana-835	159	45	(	(	PUNCT
cana-835	159	46	(	(	PUNCT
cana-835	159	47	�	�	PROPN
cana-835	159	48	̃	̃	PROPN
cana-835	159	49	�	�	NOUN
cana-835	159	50	𝐹1	𝐹1	PROPN
cana-835	159	51	,	,	PUNCT
cana-835	159	52	�	�	PROPN
cana-835	159	53	̃	̃	PROPN
cana-835	159	54	�	�	NOUN
cana-835	159	55	𝐹1	𝐹1	NOUN
cana-835	159	56	)	)	PUNCT
cana-835	159	57	,	,	PUNCT
cana-835	159	58	(	(	PUNCT
cana-835	159	59	�	�	PROPN
cana-835	159	60	̃	̃	PROPN
cana-835	159	61	�	�	NOUN
cana-835	159	62	𝐹2	𝐹2	NOUN
cana-835	159	63	,	,	PUNCT
cana-835	159	64	�	�	PROPN
cana-835	159	65	̃	̃	PROPN
cana-835	159	66	�	�	NOUN
cana-835	159	67	𝐹2	𝐹2	NOUN
cana-835	159	68	)	)	PUNCT
cana-835	159	69	,	,	PUNCT
cana-835	159	70	…	…	PUNCT
cana-835	159	71	,	,	PUNCT
cana-835	159	72	(	(	PUNCT
cana-835	159	73	�	�	PROPN
cana-835	159	74	̃	̃	NOUN
cana-835	159	75	�	�	NOUN
cana-835	159	76	𝐹𝑛,	𝐹𝑛,	SYM
cana-835	159	77	�	�	PROPN
cana-835	159	78	̃	̃	PROPN
cana-835	159	79	�	�	NOUN
cana-835	159	80	𝐹𝑛	𝐹𝑛	PROPN
cana-835	159	81	)	)	PUNCT
cana-835	159	82	)	)	PUNCT
cana-835	159	83	]	]	PUNCT
cana-835	159	84	)	)	PUNCT
cana-835	159	85	)	)	PUNCT
cana-835	159	86	]	]	PUNCT
cana-835	160	1	∩	∩	NOUN
cana-835	160	2	(	(	PUNCT
cana-835	160	3	[	[	PUNCT
cana-835	160	4	(	(	PUNCT
cana-835	160	5	(	(	PUNCT
cana-835	160	6	�	�	PROPN
cana-835	160	7	̃	̃	PROPN
cana-835	160	8	�	�	PROPN
cana-835	160	9	𝑇1𝐿	𝑇1𝐿	PROPN
cana-835	160	10	,	,	PUNCT
cana-835	160	11	�	�	PROPN
cana-835	160	12	̃	̃	PROPN
cana-835	160	13	�	�	NOUN
cana-835	160	14	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	160	15	)	)	PUNCT
cana-835	160	16	,	,	PUNCT
cana-835	160	17	(	(	PUNCT
cana-835	160	18	�	�	PROPN
cana-835	160	19	̃	̃	PROPN
cana-835	160	20	�	�	PROPN
cana-835	160	21	𝑇2𝐿	𝑇2𝐿	PROPN
cana-835	160	22	,	,	PUNCT
cana-835	160	23	�	�	PROPN
cana-835	160	24	̃	̃	PROPN
cana-835	160	25	�	�	NOUN
cana-835	160	26	𝑇2𝑈	𝑇2𝑈	NOUN
cana-835	160	27	)	)	PUNCT
cana-835	160	28	,	,	PUNCT
cana-835	160	29	…	…	PUNCT
cana-835	160	30	,	,	PUNCT
cana-835	160	31	(	(	PUNCT
cana-835	160	32	�	�	PROPN
cana-835	160	33	̃	̃	NOUN
cana-835	160	34	�	�	NOUN
cana-835	160	35	𝑇𝑛𝐿	𝑇𝑛𝐿	NOUN
cana-835	160	36	,	,	PUNCT
cana-835	160	37	�	�	PROPN
cana-835	160	38	̃	̃	PROPN
cana-835	160	39	�	�	NOUN
cana-835	160	40	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	160	41	)	)	PUNCT
cana-835	160	42	)	)	PUNCT
cana-835	160	43	;	;	PUNCT
cana-835	160	44	(	(	PUNCT
cana-835	160	45	(	(	PUNCT
cana-835	160	46	�	�	PROPN
cana-835	160	47	̃	̃	NOUN
cana-835	160	48	�	�	NOUN
cana-835	160	49	𝐹1𝐿	𝐹1𝐿	NOUN
cana-835	160	50	,	,	PUNCT
cana-835	160	51	�	�	PROPN
cana-835	160	52	̃	̃	PROPN
cana-835	160	53	�	�	NOUN
cana-835	160	54	𝐹1𝑈	𝐹1𝑈	NOUN
cana-835	160	55	)	)	PUNCT
cana-835	160	56	,	,	PUNCT
cana-835	160	57	(	(	PUNCT
cana-835	160	58	�	�	PROPN
cana-835	160	59	̃	̃	PROPN
cana-835	160	60	�	�	PROPN
cana-835	160	61	𝐹2𝐿	𝐹2𝐿	PROPN
cana-835	160	62	,	,	PUNCT
cana-835	160	63	�	�	PROPN
cana-835	160	64	̃	̃	PROPN
cana-835	160	65	�	�	NOUN
cana-835	160	66	𝐹2𝑈	𝐹2𝑈	NUM
cana-835	160	67	)	)	PUNCT
cana-835	160	68	,	,	PUNCT
cana-835	160	69	…	…	PUNCT
cana-835	160	70	,	,	PUNCT
cana-835	160	71	(	(	PUNCT
cana-835	160	72	�	�	PROPN
cana-835	160	73	̃	̃	PROPN
cana-835	160	74	�	�	NOUN
cana-835	160	75	𝐹𝑛𝐿	𝐹𝑛𝐿	PROPN
cana-835	160	76	,	,	PUNCT
cana-835	160	77	�	�	PROPN
cana-835	160	78	̃	̃	PROPN
cana-835	160	79	�	�	NOUN
cana-835	160	80	𝐹𝑛𝑈	𝐹𝑛𝑈	PROPN
cana-835	160	81	)	)	PUNCT
cana-835	160	82	)	)	PUNCT
cana-835	161	1	]	]	PUNCT
cana-835	161	2	)	)	PUNCT
cana-835	161	3	�	�	PROPN
cana-835	161	4	̃	̃	PROPN
cana-835	161	5	�	�	NOUN
cana-835	161	6	𝑘+1	𝑘+1	PRON
cana-835	161	7	𝐼	𝐼	NOUN
cana-835	161	8	=	=	PUNCT
cana-835	161	9	(	(	PUNCT
cana-835	161	10	[	[	PUNCT
cana-835	161	11	(	(	PUNCT
cana-835	161	12	𝑚(	𝑚(	NUM
cana-835	161	13	�	�	PROPN
cana-835	161	14	̃	̃	PROPN
cana-835	161	15	�	�	NOUN
cana-835	161	16	𝑇1	𝑇1	NOUN
cana-835	161	17	)	)	PUNCT
cana-835	161	18	,	,	PUNCT
cana-835	161	19	𝑚(	𝑚(	PROPN
cana-835	161	20	�	�	PROPN
cana-835	161	21	̃	̃	PROPN
cana-835	161	22	�	�	NOUN
cana-835	161	23	𝑇2	𝑇2	NOUN
cana-835	161	24	)	)	PUNCT
cana-835	161	25	,	,	PUNCT
cana-835	161	26	…	…	PUNCT
cana-835	161	27	,	,	PUNCT
cana-835	161	28	𝑚(	𝑚(	PROPN
cana-835	161	29	�	�	SYM
cana-835	161	30	̃	̃	PROPN
cana-835	161	31	�	�	PROPN
cana-835	161	32	𝑇𝑛	𝑇𝑛	NOUN
cana-835	161	33	)	)	PUNCT
cana-835	161	34	)	)	PUNCT
cana-835	161	35	;	;	PUNCT
cana-835	161	36	(	(	PUNCT
cana-835	161	37	𝑚(	𝑚(	NUM
cana-835	161	38	�	�	SYM
cana-835	161	39	̃	̃	PROPN
cana-835	161	40	�	�	NOUN
cana-835	161	41	𝐹1	𝐹1	NOUN
cana-835	161	42	)	)	PUNCT
cana-835	161	43	,	,	PUNCT
cana-835	161	44	𝑚(	𝑚(	PROPN
cana-835	161	45	�	�	PROPN
cana-835	161	46	̃	̃	PROPN
cana-835	161	47	�	�	NOUN
cana-835	161	48	𝐹2	𝐹2	NOUN
cana-835	161	49	)	)	PUNCT
cana-835	161	50	,	,	PUNCT
cana-835	161	51	…	…	PUNCT
cana-835	161	52	,	,	PUNCT
cana-835	161	53	𝑚(	𝑚(	PROPN
cana-835	161	54	�	�	SYM
cana-835	161	55	̃	̃	PROPN
cana-835	161	56	�	�	NOUN
cana-835	161	57	𝐹𝑛	𝐹𝑛	PROPN
cana-835	161	58	)	)	PUNCT
cana-835	161	59	)	)	PUNCT
cana-835	162	1	]	]	PUNCT
cana-835	163	1	−	−	PROPN
cana-835	163	2	[	[	PUNCT
cana-835	163	3	𝑓′	𝑓′	X
cana-835	163	4	[	[	PUNCT
cana-835	163	5	(	(	PUNCT
cana-835	163	6	𝑚(	𝑚(	NUM
cana-835	163	7	�	�	PROPN
cana-835	163	8	̃	̃	PROPN
cana-835	163	9	�	�	NOUN
cana-835	163	10	𝑇1	𝑇1	NOUN
cana-835	163	11	,	,	PUNCT
cana-835	163	12	�	�	PROPN
cana-835	163	13	̃	̃	PROPN
cana-835	163	14	�	�	NOUN
cana-835	163	15	𝑇1	𝑇1	NOUN
cana-835	163	16	)	)	PUNCT
cana-835	163	17	,	,	PUNCT
cana-835	163	18	𝑚(	𝑚(	PROPN
cana-835	163	19	�	�	PROPN
cana-835	163	20	̃	̃	PROPN
cana-835	163	21	�	�	NOUN
cana-835	163	22	𝑇2	𝑇2	PROPN
cana-835	163	23	,	,	PUNCT
cana-835	163	24	�	�	PROPN
cana-835	163	25	̃	̃	PROPN
cana-835	163	26	�	�	NOUN
cana-835	163	27	𝑇2	𝑇2	NOUN
cana-835	163	28	)	)	PUNCT
cana-835	163	29	,	,	PUNCT
cana-835	163	30	…	…	PUNCT
cana-835	163	31	,	,	PUNCT
cana-835	163	32	𝑚(	𝑚(	PROPN
cana-835	163	33	�	�	SYM
cana-835	163	34	̃	̃	PROPN
cana-835	163	35	�	�	PROPN
cana-835	163	36	𝑇𝑛	𝑇𝑛	PROPN
cana-835	163	37	,	,	PUNCT
cana-835	163	38	�	�	PROPN
cana-835	163	39	̃	̃	PROPN
cana-835	163	40	�	�	PROPN
cana-835	163	41	𝑇𝑛	𝑇𝑛	NOUN
cana-835	163	42	)	)	PUNCT
cana-835	163	43	)	)	PUNCT
cana-835	163	44	;	;	PUNCT
cana-835	163	45	(	(	PUNCT
cana-835	163	46	𝑚(	𝑚(	NUM
cana-835	163	47	�	�	SYM
cana-835	163	48	̃	̃	PROPN
cana-835	163	49	�	�	NOUN
cana-835	163	50	𝐹1	𝐹1	PROPN
cana-835	163	51	,	,	PUNCT
cana-835	163	52	�	�	PROPN
cana-835	163	53	̃	̃	PROPN
cana-835	163	54	�	�	NOUN
cana-835	163	55	𝑇1	𝑇1	NOUN
cana-835	163	56	)	)	PUNCT
cana-835	163	57	,	,	PUNCT
cana-835	163	58	𝑚(	𝑚(	PROPN
cana-835	163	59	�	�	PROPN
cana-835	163	60	̃	̃	PROPN
cana-835	163	61	�	�	NOUN
cana-835	163	62	𝐹2	𝐹2	NOUN
cana-835	163	63	,	,	PUNCT
cana-835	163	64	�	�	PROPN
cana-835	163	65	̃	̃	PROPN
cana-835	163	66	�	�	NOUN
cana-835	163	67	𝑇1	𝑇1	NOUN
cana-835	163	68	)	)	PUNCT
cana-835	163	69	,	,	PUNCT
cana-835	163	70	…	…	PUNCT
cana-835	163	71	,	,	PUNCT
cana-835	163	72	𝑚(	𝑚(	PROPN
cana-835	163	73	�	�	SYM
cana-835	163	74	̃	̃	PROPN
cana-835	163	75	�	�	NOUN
cana-835	163	76	𝐹𝑛,	𝐹𝑛,	SYM
cana-835	163	77	�	�	PROPN
cana-835	163	78	̃	̃	PROPN
cana-835	163	79	�	�	NOUN
cana-835	163	80	𝑇1	𝑇1	NOUN
cana-835	163	81	)	)	PUNCT
cana-835	163	82	)	)	PUNCT
cana-835	163	83	]	]	PUNCT
cana-835	164	1	𝑓′′	𝑓′′	PROPN
cana-835	164	2	(	(	PUNCT
cana-835	164	3	[	[	PUNCT
cana-835	164	4	(	(	PUNCT
cana-835	164	5	(	(	PUNCT
cana-835	164	6	�	�	PROPN
cana-835	164	7	̃	̃	NOUN
cana-835	164	8	�	�	NOUN
cana-835	164	9	𝑇1	𝑇1	NOUN
cana-835	164	10	,	,	PUNCT
cana-835	164	11	�	�	PROPN
cana-835	164	12	̃	̃	PROPN
cana-835	164	13	�	�	NOUN
cana-835	164	14	𝑇1	𝑇1	NOUN
cana-835	164	15	)	)	PUNCT
cana-835	164	16	,	,	PUNCT
cana-835	164	17	(	(	PUNCT
cana-835	164	18	�	�	PROPN
cana-835	164	19	̃	̃	PROPN
cana-835	164	20	�	�	NOUN
cana-835	164	21	𝑇2	𝑇2	PROPN
cana-835	164	22	,	,	PUNCT
cana-835	164	23	�	�	PROPN
cana-835	164	24	̃	̃	PROPN
cana-835	164	25	�	�	NOUN
cana-835	164	26	𝑇2	𝑇2	NOUN
cana-835	164	27	)	)	PUNCT
cana-835	164	28	,	,	PUNCT
cana-835	164	29	…	…	PUNCT
cana-835	164	30	,	,	PUNCT
cana-835	164	31	(	(	PUNCT
cana-835	164	32	�	�	PROPN
cana-835	164	33	̃	̃	PROPN
cana-835	164	34	�	�	PROPN
cana-835	164	35	𝑇𝑛	𝑇𝑛	PROPN
cana-835	164	36	,	,	PUNCT
cana-835	164	37	�	�	PROPN
cana-835	164	38	̃	̃	PROPN
cana-835	164	39	�	�	PROPN
cana-835	164	40	𝑇𝑛	𝑇𝑛	NOUN
cana-835	164	41	)	)	PUNCT
cana-835	164	42	)	)	PUNCT
cana-835	164	43	;	;	PUNCT
cana-835	164	44	(	(	PUNCT
cana-835	164	45	(	(	PUNCT
cana-835	164	46	�	�	PROPN
cana-835	164	47	̃	̃	PROPN
cana-835	164	48	�	�	NOUN
cana-835	164	49	𝐹1	𝐹1	PROPN
cana-835	164	50	,	,	PUNCT
cana-835	164	51	�	�	PROPN
cana-835	164	52	̃	̃	PROPN
cana-835	164	53	�	�	NOUN
cana-835	164	54	𝐹1	𝐹1	NOUN
cana-835	164	55	)	)	PUNCT
cana-835	164	56	,	,	PUNCT
cana-835	164	57	(	(	PUNCT
cana-835	164	58	�	�	PROPN
cana-835	164	59	̃	̃	PROPN
cana-835	164	60	�	�	NOUN
cana-835	164	61	𝐹2	𝐹2	NOUN
cana-835	164	62	,	,	PUNCT
cana-835	164	63	�	�	PROPN
cana-835	164	64	̃	̃	PROPN
cana-835	164	65	�	�	NOUN
cana-835	164	66	𝐹2	𝐹2	NOUN
cana-835	164	67	)	)	PUNCT
cana-835	164	68	,	,	PUNCT
cana-835	164	69	…	…	PUNCT
cana-835	164	70	,	,	PUNCT
cana-835	164	71	(	(	PUNCT
cana-835	164	72	�	�	PROPN
cana-835	164	73	̃	̃	NOUN
cana-835	164	74	�	�	NOUN
cana-835	164	75	𝐹𝑛,	𝐹𝑛,	SYM
cana-835	164	76	�	�	PROPN
cana-835	164	77	̃	̃	PROPN
cana-835	164	78	�	�	NOUN
cana-835	164	79	𝐹𝑛	𝐹𝑛	PROPN
cana-835	164	80	)	)	PUNCT
cana-835	164	81	)	)	PUNCT
cana-835	164	82	]	]	PUNCT
cana-835	164	83	)	)	PUNCT
cana-835	164	84	]	]	PUNCT
cana-835	164	85	)	)	PUNCT
cana-835	164	86	∩	∩	NOUN
cana-835	164	87	[	[	PUNCT
cana-835	164	88	(	(	PUNCT
cana-835	164	89	(	(	PUNCT
cana-835	164	90	�	�	PROPN
cana-835	164	91	̃	̃	PROPN
cana-835	164	92	�	�	PROPN
cana-835	164	93	𝑇1𝐿	𝑇1𝐿	PROPN
cana-835	164	94	,	,	PUNCT
cana-835	164	95	�	�	PROPN
cana-835	164	96	̃	̃	PROPN
cana-835	164	97	�	�	NOUN
cana-835	164	98	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	164	99	)	)	PUNCT
cana-835	164	100	,	,	PUNCT
cana-835	164	101	(	(	PUNCT
cana-835	164	102	�	�	PROPN
cana-835	164	103	̃	̃	PROPN
cana-835	164	104	�	�	PROPN
cana-835	164	105	𝑇2𝐿	𝑇2𝐿	PROPN
cana-835	164	106	,	,	PUNCT
cana-835	164	107	�	�	PROPN
cana-835	164	108	̃	̃	PROPN
cana-835	164	109	�	�	NOUN
cana-835	164	110	𝑇2𝑈	𝑇2𝑈	NOUN
cana-835	164	111	)	)	PUNCT
cana-835	164	112	,	,	PUNCT
cana-835	164	113	…	…	PUNCT
cana-835	164	114	,	,	PUNCT
cana-835	164	115	(	(	PUNCT
cana-835	164	116	�	�	PROPN
cana-835	164	117	̃	̃	NOUN
cana-835	164	118	�	�	NOUN
cana-835	164	119	𝑇𝑛𝐿	𝑇𝑛𝐿	NOUN
cana-835	164	120	,	,	PUNCT
cana-835	164	121	�	�	PROPN
cana-835	164	122	̃	̃	PROPN
cana-835	164	123	�	�	NOUN
cana-835	164	124	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	164	125	)	)	PUNCT
cana-835	164	126	)	)	PUNCT
cana-835	164	127	;	;	PUNCT
cana-835	164	128	(	(	PUNCT
cana-835	164	129	(	(	PUNCT
cana-835	164	130	�	�	PROPN
cana-835	164	131	̃	̃	NOUN
cana-835	164	132	�	�	PROPN
cana-835	164	133	𝐹1𝐿	𝐹1𝐿	PROPN
cana-835	164	134	,	,	PUNCT
cana-835	164	135	�	�	PROPN
cana-835	164	136	̃	̃	PROPN
cana-835	164	137	�	�	NOUN
cana-835	164	138	𝐹1𝑈	𝐹1𝑈	NOUN
cana-835	164	139	)	)	PUNCT
cana-835	164	140	,	,	PUNCT
cana-835	164	141	(	(	PUNCT
cana-835	164	142	�	�	PROPN
cana-835	164	143	̃	̃	PROPN
cana-835	164	144	�	�	PROPN
cana-835	164	145	𝐹2𝐿	𝐹2𝐿	PROPN
cana-835	164	146	,	,	PUNCT
cana-835	164	147	�	�	PROPN
cana-835	164	148	̃	̃	PROPN
cana-835	164	149	�	�	NOUN
cana-835	164	150	𝐹2𝑈	𝐹2𝑈	NUM
cana-835	164	151	)	)	PUNCT
cana-835	164	152	,	,	PUNCT
cana-835	164	153	…	…	PUNCT
cana-835	164	154	,	,	PUNCT
cana-835	164	155	(	(	PUNCT
cana-835	164	156	�	�	PROPN
cana-835	164	157	̃	̃	PROPN
cana-835	164	158	�	�	NOUN
cana-835	164	159	𝐹𝑛𝐿	𝐹𝑛𝐿	PROPN
cana-835	164	160	,	,	PUNCT
cana-835	164	161	�	�	PROPN
cana-835	164	162	̃	̃	PROPN
cana-835	164	163	�	�	NOUN
cana-835	164	164	𝐹𝑛𝑈	𝐹𝑛𝑈	PROPN
cana-835	164	165	)	)	PUNCT
cana-835	164	166	)	)	PUNCT
cana-835	164	167	]	]	PUNCT
cana-835	165	1	communications	communication	NOUN
cana-835	165	2	on	on	ADP
cana-835	165	3	applied	apply	VERB
cana-835	165	4	nonlinear	nonlinear	ADJ
cana-835	165	5	analysis	analysis	NOUN
cana-835	165	6	issn	issn	NOUN
cana-835	165	7	:	:	PUNCT
cana-835	165	8	1074	1074	NUM
cana-835	165	9	-	-	PUNCT
cana-835	165	10	133x	133x	NUM
cana-835	165	11	vol	vol	NOUN
cana-835	165	12	31	31	NUM
cana-835	165	13	no	no	NOUN
cana-835	165	14	.	.	PUNCT
cana-835	166	1	4s	4s	NUM
cana-835	166	2	(	(	PUNCT
cana-835	166	3	2024	2024	NUM
cana-835	166	4	)	)	PUNCT
cana-835	166	5	190	190	NUM
cana-835	166	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	166	7	�	�	PROPN
cana-835	166	8	̃	̃	PROPN
cana-835	166	9	�	�	NOUN
cana-835	166	10	𝑘+1	𝑘+1	PRON
cana-835	166	11	𝐼	𝐼	NOUN
cana-835	166	12	=	=	PUNCT
cana-835	166	13	[	[	PUNCT
cana-835	166	14	[	[	PUNCT
cana-835	166	15	(	(	PUNCT
cana-835	166	16	(	(	PUNCT
cana-835	166	17	�	�	PROPN
cana-835	166	18	̃	̃	PROPN
cana-835	166	19	�	�	PROPN
cana-835	166	20	𝑇1𝐿	𝑇1𝐿	PROPN
cana-835	166	21	+	+	CCONJ
cana-835	166	22	�	�	PROPN
cana-835	166	23	̃	̃	PROPN
cana-835	166	24	�	�	NOUN
cana-835	166	25	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	166	26	2	2	NUM
cana-835	166	27	)	)	PUNCT
cana-835	166	28	,	,	PUNCT
cana-835	166	29	(	(	PUNCT
cana-835	166	30	�	�	PROPN
cana-835	166	31	̃	̃	NOUN
cana-835	166	32	�	�	PROPN
cana-835	166	33	𝑇2𝐿	𝑇2𝐿	PROPN
cana-835	166	34	+	+	SYM
cana-835	166	35	�	�	PROPN
cana-835	166	36	̃	̃	PROPN
cana-835	166	37	�	�	NOUN
cana-835	166	38	𝑇2𝑈	𝑇2𝑈	PROPN
cana-835	166	39	2	2	NUM
cana-835	166	40	)	)	PUNCT
cana-835	166	41	,	,	PUNCT
cana-835	166	42	…	…	PUNCT
cana-835	166	43	,	,	PUNCT
cana-835	166	44	(	(	PUNCT
cana-835	166	45	�	�	PROPN
cana-835	166	46	̃	̃	NOUN
cana-835	166	47	�	�	PROPN
cana-835	166	48	𝑇𝑛𝐿	𝑇𝑛𝐿	PROPN
cana-835	166	49	+	+	SYM
cana-835	166	50	�	�	PROPN
cana-835	166	51	̃	̃	PROPN
cana-835	166	52	�	�	NOUN
cana-835	166	53	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	166	54	2	2	NUM
cana-835	166	55	)	)	PUNCT
cana-835	166	56	)	)	PUNCT
cana-835	167	1	;	;	PUNCT
cana-835	167	2	(	(	PUNCT
cana-835	167	3	(	(	PUNCT
cana-835	167	4	�	�	PROPN
cana-835	167	5	̃	̃	NOUN
cana-835	167	6	�	�	PROPN
cana-835	167	7	𝐹1𝐿	𝐹1𝐿	PRON
cana-835	167	8	+	+	NUM
cana-835	167	9	�	�	PROPN
cana-835	167	10	̃	̃	PROPN
cana-835	167	11	�	�	NOUN
cana-835	167	12	𝐹1𝑈	𝐹1𝑈	ADP
cana-835	167	13	2	2	NUM
cana-835	167	14	)	)	PUNCT
cana-835	167	15	,	,	PUNCT
cana-835	167	16	(	(	PUNCT
cana-835	167	17	�	�	PROPN
cana-835	167	18	̃	̃	NOUN
cana-835	167	19	�	�	PROPN
cana-835	167	20	𝐹2𝐿	𝐹2𝐿	PROPN
cana-835	167	21	+	+	NUM
cana-835	167	22	�	�	PROPN
cana-835	167	23	̃	̃	PROPN
cana-835	167	24	�	�	PROPN
cana-835	167	25	𝐹2𝑈	𝐹2𝑈	ADP
cana-835	167	26	2	2	NUM
cana-835	167	27	)	)	PUNCT
cana-835	167	28	,	,	PUNCT
cana-835	167	29	…	…	PUNCT
cana-835	167	30	,	,	PUNCT
cana-835	167	31	(	(	PUNCT
cana-835	167	32	�	�	PROPN
cana-835	167	33	̃	̃	NOUN
cana-835	167	34	�	�	NOUN
cana-835	167	35	𝐹𝑛𝐿	𝐹𝑛𝐿	PROPN
cana-835	167	36	+	+	SYM
cana-835	167	37	�	�	PROPN
cana-835	167	38	̃	̃	PROPN
cana-835	167	39	�	�	NOUN
cana-835	167	40	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	167	41	2	2	NUM
cana-835	167	42	)	)	PUNCT
cana-835	167	43	)	)	PUNCT
cana-835	167	44	]	]	PUNCT
cana-835	168	1	−	−	PROPN
cana-835	169	1	𝑓	𝑓	PRON
cana-835	169	2	′	′	NUM
cana-835	169	3	[	[	PUNCT
cana-835	169	4	(	(	PUNCT
cana-835	169	5	(	(	PUNCT
cana-835	169	6	(	(	PUNCT
cana-835	169	7	�	�	PROPN
cana-835	169	8	̃	̃	PROPN
cana-835	169	9	�	�	PROPN
cana-835	169	10	𝑇1𝐿+	𝑇1𝐿+	PROPN
cana-835	169	11	�	�	PROPN
cana-835	169	12	̃	̃	NOUN
cana-835	169	13	�	�	NOUN
cana-835	169	14	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	169	15	2	2	NUM
cana-835	169	16	)	)	PUNCT
cana-835	169	17	,	,	PUNCT
cana-835	169	18	(	(	PUNCT
cana-835	169	19	�	�	PROPN
cana-835	169	20	̃	̃	NOUN
cana-835	169	21	�	�	PROPN
cana-835	169	22	𝑇1𝐿+	𝑇1𝐿+	PROPN
cana-835	169	23	�	�	PROPN
cana-835	169	24	̃	̃	NOUN
cana-835	169	25	�	�	NOUN
cana-835	169	26	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	169	27	2	2	NUM
cana-835	169	28	)	)	PUNCT
cana-835	169	29	)	)	PUNCT
cana-835	169	30	,	,	PUNCT
cana-835	169	31	(	(	PUNCT
cana-835	169	32	(	(	PUNCT
cana-835	169	33	�	�	PROPN
cana-835	169	34	̃	̃	NOUN
cana-835	169	35	�	�	NOUN
cana-835	169	36	𝑇2𝐿+	𝑇2𝐿+	NUM
cana-835	169	37	�	�	SYM
cana-835	169	38	̃	̃	NOUN
cana-835	169	39	�	�	NOUN
cana-835	169	40	𝑇2𝑈	𝑇2𝑈	PROPN
cana-835	169	41	2	2	NUM
cana-835	169	42	)	)	PUNCT
cana-835	169	43	,	,	PUNCT
cana-835	169	44	(	(	PUNCT
cana-835	169	45	�	�	PROPN
cana-835	169	46	̃	̃	NOUN
cana-835	169	47	�	�	NOUN
cana-835	169	48	𝑇2𝐿+	𝑇2𝐿+	NUM
cana-835	169	49	�	�	SYM
cana-835	169	50	̃	̃	NOUN
cana-835	169	51	�	�	NOUN
cana-835	169	52	𝑇2𝑈	𝑇2𝑈	PROPN
cana-835	169	53	2	2	NUM
cana-835	169	54	)	)	PUNCT
cana-835	169	55	)	)	PUNCT
cana-835	169	56	,	,	PUNCT
cana-835	169	57	…	…	PUNCT
cana-835	169	58	(	(	PUNCT
cana-835	169	59	(	(	PUNCT
cana-835	169	60	�	�	PROPN
cana-835	169	61	̃	̃	NOUN
cana-835	169	62	�	�	NOUN
cana-835	169	63	𝑇𝑛𝐿+	𝑇𝑛𝐿+	NOUN
cana-835	169	64	�	�	PROPN
cana-835	169	65	̃	̃	PROPN
cana-835	169	66	�	�	PROPN
cana-835	169	67	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	169	68	2	2	NUM
cana-835	169	69	)	)	PUNCT
cana-835	169	70	,	,	PUNCT
cana-835	169	71	(	(	PUNCT
cana-835	169	72	�	�	PROPN
cana-835	169	73	̃	̃	NOUN
cana-835	169	74	�	�	NOUN
cana-835	169	75	𝑇𝑛𝐿+	𝑇𝑛𝐿+	NOUN
cana-835	169	76	�	�	PROPN
cana-835	169	77	̃	̃	PROPN
cana-835	169	78	�	�	PROPN
cana-835	169	79	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	169	80	2	2	NUM
cana-835	169	81	)	)	PUNCT
cana-835	169	82	)	)	PUNCT
cana-835	169	83	;	;	PUNCT
cana-835	169	84	)	)	PUNCT
cana-835	169	85	,	,	PUNCT
cana-835	169	86	(	(	PUNCT
cana-835	169	87	(	(	PUNCT
cana-835	169	88	(	(	PUNCT
cana-835	169	89	�	�	PROPN
cana-835	169	90	̃	̃	PROPN
cana-835	169	91	�	�	PROPN
cana-835	169	92	𝐹1𝐿+	𝐹1𝐿+	NOUN
cana-835	169	93	�	�	PROPN
cana-835	169	94	̃	̃	NOUN
cana-835	169	95	�	�	NOUN
cana-835	169	96	𝐹1𝑈	𝐹1𝑈	ADP
cana-835	169	97	2	2	NUM
cana-835	169	98	)	)	PUNCT
cana-835	169	99	,	,	PUNCT
cana-835	169	100	(	(	PUNCT
cana-835	169	101	�	�	PROPN
cana-835	169	102	̃	̃	PROPN
cana-835	169	103	�	�	PROPN
cana-835	169	104	𝐹1𝐿+	𝐹1𝐿+	NOUN
cana-835	169	105	�	�	PROPN
cana-835	169	106	̃	̃	NOUN
cana-835	169	107	�	�	NOUN
cana-835	169	108	𝐹1𝑈	𝐹1𝑈	ADP
cana-835	169	109	2	2	NUM
cana-835	169	110	)	)	PUNCT
cana-835	169	111	)	)	PUNCT
cana-835	169	112	,	,	PUNCT
cana-835	169	113	(	(	PUNCT
cana-835	169	114	(	(	PUNCT
cana-835	169	115	�	�	PROPN
cana-835	169	116	̃	̃	NOUN
cana-835	169	117	�	�	NOUN
cana-835	169	118	𝐹𝑛𝐿+	𝐹𝑛𝐿+	NOUN
cana-835	169	119	�	�	PROPN
cana-835	169	120	̃	̃	NOUN
cana-835	169	121	�	�	NOUN
cana-835	169	122	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	169	123	2	2	NUM
cana-835	169	124	)	)	PUNCT
cana-835	169	125	,	,	PUNCT
cana-835	169	126	(	(	PUNCT
cana-835	169	127	�	�	PROPN
cana-835	169	128	̃	̃	NOUN
cana-835	169	129	�	�	NOUN
cana-835	169	130	𝐹𝑛𝐿+	𝐹𝑛𝐿+	NOUN
cana-835	169	131	�	�	PROPN
cana-835	169	132	̃	̃	NOUN
cana-835	169	133	�	�	NOUN
cana-835	169	134	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	169	135	2	2	NUM
cana-835	169	136	)	)	PUNCT
cana-835	169	137	)	)	PUNCT
cana-835	169	138	…	…	PUNCT
cana-835	169	139	.	.	PUNCT
cana-835	170	1	(	(	PUNCT
cana-835	170	2	(	(	PUNCT
cana-835	170	3	�	�	PROPN
cana-835	170	4	̃	̃	NOUN
cana-835	170	5	�	�	NOUN
cana-835	170	6	𝐹𝑛𝐿+	𝐹𝑛𝐿+	NOUN
cana-835	170	7	�	�	PROPN
cana-835	170	8	̃	̃	NOUN
cana-835	170	9	�	�	NOUN
cana-835	170	10	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	170	11	2	2	NUM
cana-835	170	12	)	)	PUNCT
cana-835	170	13	,	,	PUNCT
cana-835	170	14	(	(	PUNCT
cana-835	170	15	�	�	PROPN
cana-835	170	16	̃	̃	NOUN
cana-835	170	17	�	�	NOUN
cana-835	170	18	𝐹𝑛𝐿+	𝐹𝑛𝐿+	NOUN
cana-835	170	19	�	�	PROPN
cana-835	170	20	̃	̃	NOUN
cana-835	170	21	�	�	NOUN
cana-835	170	22	𝐹𝑛𝑈	𝐹𝑛𝑈	NOUN
cana-835	170	23	2	2	NUM
cana-835	170	24	)	)	PUNCT
cana-835	170	25	)	)	PUNCT
cana-835	170	26	)	)	PUNCT
cana-835	171	1	]	]	PUNCT
cana-835	172	1	𝑓′′	𝑓′′	PROPN
cana-835	172	2	(	(	PUNCT
cana-835	172	3	(	(	PUNCT
cana-835	172	4	[	[	PUNCT
cana-835	172	5	(	(	PUNCT
cana-835	172	6	(	(	PUNCT
cana-835	172	7	�	�	PROPN
cana-835	172	8	̃	̃	NOUN
cana-835	172	9	�	�	NOUN
cana-835	172	10	𝑇1	𝑇1	NOUN
cana-835	172	11	,	,	PUNCT
cana-835	172	12	�	�	PROPN
cana-835	172	13	̃	̃	PROPN
cana-835	172	14	�	�	NOUN
cana-835	172	15	𝑇1	𝑇1	NOUN
cana-835	172	16	)	)	PUNCT
cana-835	172	17	,	,	PUNCT
cana-835	172	18	(	(	PUNCT
cana-835	172	19	�	�	PROPN
cana-835	172	20	̃	̃	PROPN
cana-835	172	21	�	�	NOUN
cana-835	172	22	𝑇2	𝑇2	PROPN
cana-835	172	23	,	,	PUNCT
cana-835	172	24	�	�	PROPN
cana-835	172	25	̃	̃	PROPN
cana-835	172	26	�	�	NOUN
cana-835	172	27	𝑇2	𝑇2	NOUN
cana-835	172	28	)	)	PUNCT
cana-835	172	29	,	,	PUNCT
cana-835	172	30	…	…	PUNCT
cana-835	172	31	,	,	PUNCT
cana-835	172	32	(	(	PUNCT
cana-835	172	33	�	�	PROPN
cana-835	172	34	̃	̃	PROPN
cana-835	172	35	�	�	PROPN
cana-835	172	36	𝑇𝑛	𝑇𝑛	PROPN
cana-835	172	37	,	,	PUNCT
cana-835	172	38	�	�	PROPN
cana-835	172	39	̃	̃	PROPN
cana-835	172	40	�	�	PROPN
cana-835	172	41	𝑇𝑛	𝑇𝑛	NOUN
cana-835	172	42	)	)	PUNCT
cana-835	172	43	)	)	PUNCT
cana-835	172	44	;	;	PUNCT
cana-835	172	45	(	(	PUNCT
cana-835	172	46	(	(	PUNCT
cana-835	172	47	�	�	PROPN
cana-835	172	48	̃	̃	PROPN
cana-835	172	49	�	�	NOUN
cana-835	172	50	𝐹1	𝐹1	PROPN
cana-835	172	51	,	,	PUNCT
cana-835	172	52	�	�	PROPN
cana-835	172	53	̃	̃	PROPN
cana-835	172	54	�	�	NOUN
cana-835	172	55	𝐹1	𝐹1	NOUN
cana-835	172	56	)	)	PUNCT
cana-835	172	57	,	,	PUNCT
cana-835	172	58	(	(	PUNCT
cana-835	172	59	�	�	PROPN
cana-835	172	60	̃	̃	PROPN
cana-835	172	61	�	�	NOUN
cana-835	172	62	𝐹2	𝐹2	NOUN
cana-835	172	63	,	,	PUNCT
cana-835	172	64	�	�	PROPN
cana-835	172	65	̃	̃	PROPN
cana-835	172	66	�	�	NOUN
cana-835	172	67	𝐹2	𝐹2	NOUN
cana-835	172	68	)	)	PUNCT
cana-835	172	69	,	,	PUNCT
cana-835	172	70	…	…	PUNCT
cana-835	172	71	,	,	PUNCT
cana-835	172	72	(	(	PUNCT
cana-835	172	73	�	�	PROPN
cana-835	172	74	̃	̃	NOUN
cana-835	172	75	�	�	NOUN
cana-835	172	76	𝐹𝑛,	𝐹𝑛,	SYM
cana-835	172	77	�	�	PROPN
cana-835	172	78	̃	̃	PROPN
cana-835	172	79	�	�	NOUN
cana-835	172	80	𝐹𝑛	𝐹𝑛	PROPN
cana-835	172	81	)	)	PUNCT
cana-835	172	82	)	)	PUNCT
cana-835	172	83	]	]	PUNCT
cana-835	172	84	)	)	PUNCT
cana-835	172	85	)	)	PUNCT
cana-835	172	86	]	]	PUNCT
cana-835	173	1	∩	∩	NOUN
cana-835	173	2	(	(	PUNCT
cana-835	173	3	[	[	PUNCT
cana-835	173	4	(	(	PUNCT
cana-835	173	5	(	(	PUNCT
cana-835	173	6	�	�	PROPN
cana-835	173	7	̃	̃	PROPN
cana-835	173	8	�	�	PROPN
cana-835	173	9	𝑇1𝐿	𝑇1𝐿	PROPN
cana-835	173	10	,	,	PUNCT
cana-835	173	11	�	�	PROPN
cana-835	173	12	̃	̃	PROPN
cana-835	173	13	�	�	NOUN
cana-835	173	14	𝑇1𝑈	𝑇1𝑈	NOUN
cana-835	173	15	)	)	PUNCT
cana-835	173	16	,	,	PUNCT
cana-835	173	17	(	(	PUNCT
cana-835	173	18	�	�	PROPN
cana-835	173	19	̃	̃	PROPN
cana-835	173	20	�	�	PROPN
cana-835	173	21	𝑇2𝐿	𝑇2𝐿	PROPN
cana-835	173	22	,	,	PUNCT
cana-835	173	23	�	�	PROPN
cana-835	173	24	̃	̃	PROPN
cana-835	173	25	�	�	NOUN
cana-835	173	26	𝑇2𝑈	𝑇2𝑈	NOUN
cana-835	173	27	)	)	PUNCT
cana-835	173	28	,	,	PUNCT
cana-835	173	29	…	…	PUNCT
cana-835	173	30	,	,	PUNCT
cana-835	173	31	(	(	PUNCT
cana-835	173	32	�	�	PROPN
cana-835	173	33	̃	̃	NOUN
cana-835	173	34	�	�	NOUN
cana-835	173	35	𝑇𝑛𝐿	𝑇𝑛𝐿	NOUN
cana-835	173	36	,	,	PUNCT
cana-835	173	37	�	�	PROPN
cana-835	173	38	̃	̃	PROPN
cana-835	173	39	�	�	NOUN
cana-835	173	40	𝑇𝑛𝑈	𝑇𝑛𝑈	NOUN
cana-835	173	41	)	)	PUNCT
cana-835	173	42	)	)	PUNCT
cana-835	173	43	;	;	PUNCT
cana-835	173	44	(	(	PUNCT
cana-835	173	45	(	(	PUNCT
cana-835	173	46	�	�	PROPN
cana-835	173	47	̃	̃	NOUN
cana-835	173	48	�	�	PROPN
cana-835	173	49	𝐹1𝐿	𝐹1𝐿	PROPN
cana-835	173	50	,	,	PUNCT
cana-835	173	51	�	�	PROPN
cana-835	173	52	̃	̃	PROPN
cana-835	173	53	�	�	NOUN
cana-835	173	54	𝐹1𝑈	𝐹1𝑈	NOUN
cana-835	173	55	)	)	PUNCT
cana-835	173	56	,	,	PUNCT
cana-835	173	57	(	(	PUNCT
cana-835	173	58	�	�	PROPN
cana-835	173	59	̃	̃	PROPN
cana-835	173	60	�	�	PROPN
cana-835	173	61	𝐹2𝐿	𝐹2𝐿	PROPN
cana-835	173	62	,	,	PUNCT
cana-835	173	63	�	�	PROPN
cana-835	173	64	̃	̃	PROPN
cana-835	173	65	�	�	NOUN
cana-835	173	66	𝐹2𝑈	𝐹2𝑈	NUM
cana-835	173	67	)	)	PUNCT
cana-835	173	68	,	,	PUNCT
cana-835	173	69	…	…	PUNCT
cana-835	173	70	,	,	PUNCT
cana-835	173	71	(	(	PUNCT
cana-835	173	72	�	�	PROPN
cana-835	173	73	̃	̃	PROPN
cana-835	173	74	�	�	NOUN
cana-835	173	75	𝐹𝑛𝐿	𝐹𝑛𝐿	PROPN
cana-835	173	76	,	,	PUNCT
cana-835	173	77	�	�	PROPN
cana-835	173	78	̃	̃	PROPN
cana-835	173	79	�	�	NOUN
cana-835	173	80	𝐹𝑛𝑈	𝐹𝑛𝑈	PROPN
cana-835	173	81	)	)	PUNCT
cana-835	173	82	)	)	PUNCT
cana-835	173	83	]	]	PUNCT
cana-835	173	84	)	)	PUNCT
cana-835	173	85	𝑓′′	𝑓′′	PROPN
cana-835	173	86	(	(	PUNCT
cana-835	173	87	(	(	PUNCT
cana-835	173	88	[	[	PUNCT
cana-835	173	89	(	(	PUNCT
cana-835	173	90	(	(	PUNCT
cana-835	173	91	�	�	PROPN
cana-835	173	92	̃	̃	NOUN
cana-835	173	93	�	�	NOUN
cana-835	173	94	𝑇1	𝑇1	NOUN
cana-835	173	95	,	,	PUNCT
cana-835	173	96	�	�	PROPN
cana-835	173	97	̃	̃	PROPN
cana-835	173	98	�	�	NOUN
cana-835	173	99	𝑇1	𝑇1	NOUN
cana-835	173	100	)	)	PUNCT
cana-835	173	101	,	,	PUNCT
cana-835	173	102	(	(	PUNCT
cana-835	173	103	�	�	PROPN
cana-835	173	104	̃	̃	PROPN
cana-835	173	105	�	�	NOUN
cana-835	173	106	𝑇2	𝑇2	PROPN
cana-835	173	107	,	,	PUNCT
cana-835	173	108	�	�	PROPN
cana-835	173	109	̃	̃	PROPN
cana-835	173	110	�	�	NOUN
cana-835	173	111	𝑇2	𝑇2	NOUN
cana-835	173	112	)	)	PUNCT
cana-835	173	113	,	,	PUNCT
cana-835	173	114	…	…	PUNCT
cana-835	173	115	,	,	PUNCT
cana-835	173	116	(	(	PUNCT
cana-835	173	117	�	�	PROPN
cana-835	173	118	̃	̃	PROPN
cana-835	173	119	�	�	PROPN
cana-835	173	120	𝑇𝑛	𝑇𝑛	PROPN
cana-835	173	121	,	,	PUNCT
cana-835	173	122	�	�	PROPN
cana-835	173	123	̃	̃	PROPN
cana-835	173	124	�	�	PROPN
cana-835	173	125	𝑇𝑛	𝑇𝑛	NOUN
cana-835	173	126	)	)	PUNCT
cana-835	173	127	)	)	PUNCT
cana-835	173	128	;	;	PUNCT
cana-835	173	129	(	(	PUNCT
cana-835	173	130	(	(	PUNCT
cana-835	173	131	�	�	PROPN
cana-835	173	132	̃	̃	PROPN
cana-835	173	133	�	�	NOUN
cana-835	173	134	𝐹1	𝐹1	PROPN
cana-835	173	135	,	,	PUNCT
cana-835	173	136	�	�	PROPN
cana-835	173	137	̃	̃	PROPN
cana-835	173	138	�	�	NOUN
cana-835	173	139	𝐹1	𝐹1	NOUN
cana-835	173	140	)	)	PUNCT
cana-835	173	141	,	,	PUNCT
cana-835	173	142	(	(	PUNCT
cana-835	173	143	�	�	PROPN
cana-835	173	144	̃	̃	PROPN
cana-835	173	145	�	�	NOUN
cana-835	173	146	𝐹2	𝐹2	NOUN
cana-835	173	147	,	,	PUNCT
cana-835	173	148	�	�	PROPN
cana-835	173	149	̃	̃	PROPN
cana-835	173	150	�	�	NOUN
cana-835	173	151	𝐹2	𝐹2	NOUN
cana-835	173	152	)	)	PUNCT
cana-835	173	153	,	,	PUNCT
cana-835	173	154	…	…	PUNCT
cana-835	173	155	,	,	PUNCT
cana-835	173	156	(	(	PUNCT
cana-835	173	157	�	�	PROPN
cana-835	173	158	̃	̃	NOUN
cana-835	173	159	�	�	NOUN
cana-835	173	160	𝐹𝑛,	𝐹𝑛,	SYM
cana-835	173	161	�	�	PROPN
cana-835	173	162	̃	̃	PROPN
cana-835	173	163	�	�	NOUN
cana-835	173	164	𝐹𝑛	𝐹𝑛	PROPN
cana-835	173	165	)	)	PUNCT
cana-835	173	166	)	)	PUNCT
cana-835	173	167	]	]	PUNCT
cana-835	173	168	)	)	PUNCT
cana-835	173	169	)	)	PUNCT
cana-835	174	1	≠	≠	PROPN
cana-835	174	2	0𝐼	0𝐼	NOUN
cana-835	174	3	for	for	ADP
cana-835	174	4	ℹntuiti0nistic	ℹntuiti0nistic	ADJ
cana-835	174	5	fuzzy	fuzzy	ADJ
cana-835	174	6	unc0nstraℹned	unc0nstraℹned	PROPN
cana-835	174	7	0ptimization	0ptimization	PROPN
cana-835	174	8	pr0blem	pr0blem	NOUN
cana-835	174	9	then	then	ADV
cana-835	174	10	(	(	PUNCT
cana-835	174	11	3.1.3	3.1.3	NUM
cana-835	174	12	)	)	PUNCT
cana-835	174	13	and	and	CCONJ
cana-835	174	14	(	(	PUNCT
cana-835	174	15	3.1.4	3.1.4	NUM
cana-835	174	16	)	)	PUNCT
cana-835	174	17	takes	take	VERB
cana-835	174	18	the	the	DET
cana-835	174	19	form	form	NOUN
cana-835	174	20	�	�	PROPN
cana-835	174	21	̃	̃	NOUN
cana-835	174	22	�	�	NOUN
cana-835	174	23	𝑘+1	𝑘+1	PRON
cana-835	174	24	𝐼	𝐼	PROPN
cana-835	174	25	=	=	SYM
cana-835	174	26	𝑁𝑘	𝑁𝑘	PROPN
cana-835	174	27	𝐼	𝐼	PROPN
cana-835	174	28	(	(	PUNCT
cana-835	174	29	(	(	PUNCT
cana-835	174	30	�	�	PROPN
cana-835	174	31	̃	̃	PROPN
cana-835	174	32	�	�	PROPN
cana-835	174	33	𝑘	𝑘	NOUN
cana-835	174	34	,	,	PUNCT
cana-835	174	35	�	�	PROPN
cana-835	174	36	̃	̃	PROPN
cana-835	174	37	�	�	PROPN
cana-835	174	38	𝑘	𝑘	NOUN
cana-835	174	39	)	)	PUNCT
cana-835	174	40	)	)	PUNCT
cana-835	175	1	𝐼	𝐼	ADP
cana-835	175	2	∩	∩	NOUN
cana-835	175	3	(	(	PUNCT
cana-835	175	4	�	�	PROPN
cana-835	175	5	̃	̃	PROPN
cana-835	175	6	�	�	PROPN
cana-835	175	7	𝐾	𝐾	NOUN
cana-835	175	8	)	)	PUNCT
cana-835	175	9	𝐼	𝐼	PROPN
cana-835	175	10	(	(	PUNCT
cana-835	175	11	3.1.5	3.1.5	NOUN
cana-835	175	12	)	)	PUNCT
cana-835	175	13	and	and	CCONJ
cana-835	175	14	�	�	PROPN
cana-835	175	15	̃	̃	PROPN
cana-835	175	16	�	�	NOUN
cana-835	175	17	𝑘+1	𝑘+1	PRON
cana-835	175	18	𝐼	𝐼	PROPN
cana-835	175	19	=	=	SYM
cana-835	175	20	𝑁𝑘	𝑁𝑘	PROPN
cana-835	175	21	𝐼	𝐼	PROPN
cana-835	175	22	(	(	PUNCT
cana-835	175	23	(	(	PUNCT
cana-835	175	24	�	�	PROPN
cana-835	175	25	̃	̃	PROPN
cana-835	175	26	�	�	PROPN
cana-835	175	27	𝑘	𝑘	NOUN
cana-835	175	28	,	,	PUNCT
cana-835	175	29	�	�	PROPN
cana-835	175	30	̃	̃	PROPN
cana-835	175	31	�	�	PROPN
cana-835	175	32	𝑘	𝑘	NOUN
cana-835	175	33	)	)	PUNCT
cana-835	175	34	)	)	PUNCT
cana-835	176	1	𝐼	𝐼	ADP
cana-835	176	2	∩	∩	NOUN
cana-835	176	3	(	(	PUNCT
cana-835	176	4	�	�	PROPN
cana-835	176	5	̃	̃	PROPN
cana-835	176	6	�	�	PROPN
cana-835	176	7	𝐾	𝐾	NOUN
cana-835	176	8	)	)	PUNCT
cana-835	176	9	𝐼	𝐼	PROPN
cana-835	176	10	(	(	PUNCT
cana-835	176	11	3.1.6	3.1.6	NOUN
cana-835	176	12	)	)	PUNCT
cana-835	176	13	communications	communication	NOUN
cana-835	176	14	on	on	ADP
cana-835	176	15	applied	apply	VERB
cana-835	176	16	nonlinear	nonlinear	ADJ
cana-835	176	17	analysis	analysis	NOUN
cana-835	176	18	issn	issn	NOUN
cana-835	176	19	:	:	PUNCT
cana-835	176	20	1074	1074	NUM
cana-835	176	21	-	-	PUNCT
cana-835	176	22	133x	133x	NUM
cana-835	176	23	vol	vol	NOUN
cana-835	176	24	31	31	NUM
cana-835	176	25	no	no	NOUN
cana-835	176	26	.	.	PUNCT
cana-835	177	1	4s	4s	NUM
cana-835	177	2	(	(	PUNCT
cana-835	177	3	2024	2024	NUM
cana-835	177	4	)	)	PUNCT
cana-835	177	5	191	191	NUM
cana-835	177	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	177	7	3.2	3.2	NUM
cana-835	177	8	algorithms	algorithm	VERB
cana-835	177	9	3.2.1	3.2.1	NUM
cana-835	177	10	algorithmi	algorithmi	NOUN
cana-835	177	11	for	for	ADP
cana-835	177	12	singlei	singlei	PROPN
cana-835	177	13	variablei	variablei	VERB
cana-835	177	14	fuzzy	fuzzy	ADJ
cana-835	177	15	intuitionℹstici	intuitionℹstici	PROPN
cana-835	177	16	intervali	intervali	VERB
cana-835	177	17	newton’si	newton’si	PROPN
cana-835	177	18	methodi	methodi	PROPN
cana-835	177	19	3.2.2	3.2.2	NUM
cana-835	177	20	algorithmi	algorithmi	NOUN
cana-835	177	21	for	for	ADP
cana-835	177	22	bivariatei	bivariatei	NOUN
cana-835	177	23	intuitionistici	intuitionistici	NOUN
cana-835	177	24	fuzzyi	fuzzyi	NOUN
cana-835	177	25	intervali	intervali	VERB
cana-835	177	26	newton’si	newton’si	PROPN
cana-835	177	27	methodi	methodi	NOUN
cana-835	177	28	:	:	PUNCT
cana-835	177	29	4	4	NUM
cana-835	177	30	.	.	NOUN
cana-835	177	31	numerical	numerical	PROPN
cana-835	177	32	illustrations	illustrations	PROPN
cana-835	177	33	example	example	VERB
cana-835	177	34	4.1	4.1	NUM
cana-835	177	35	:	:	PUNCT
cana-835	177	36	let	let	VERB
cana-835	177	37	us	we	PRON
cana-835	177	38	c0nsider	c0nsider	VERB
cana-835	177	39	the	the	DET
cana-835	177	40	f0llowing	f0llowe	VERB
cana-835	177	41	unc0nstrained	unc0nstraine	VERB
cana-835	177	42	fuzzy	fuzzy	ADJ
cana-835	177	43	0ptimization	0ptimization	NOUN
cana-835	177	44	pr0blem	pr0blem	ADP
cana-835	177	45	(	(	PUNCT
cana-835	177	46	𝑓(	𝑓(	PROPN
cana-835	177	47	�	�	PROPN
cana-835	177	48	̃	̃	PROPN
cana-835	177	49	�	�	PROPN
cana-835	177	50	)	)	PUNCT
cana-835	177	51	𝐼	𝐼	PROPN
cana-835	177	52	)	)	PUNCT
cana-835	177	53	=	=	SYM
cana-835	177	54	(	(	PUNCT
cana-835	177	55	�	�	PROPN
cana-835	177	56	̃	̃	NOUN
cana-835	177	57	�	�	NOUN
cana-835	177	58	4)𝐼	4)𝐼	NOUN
cana-835	177	59	−	−	PROPN
cana-835	177	60	(	(	PUNCT
cana-835	177	61	48	48	NUM
cana-835	177	62	�	�	PROPN
cana-835	177	63	̃	̃	PROPN
cana-835	177	64	�	�	PROPN
cana-835	177	65	)𝐼	)𝐼	PUNCT
cana-835	178	1	+	+	CCONJ
cana-835	178	2	(	(	PUNCT
cana-835	178	3	12)𝐼	12)𝐼	NUM
cana-835	178	4	𝑓(	𝑓(	PROPN
cana-835	178	5	�	�	PROPN
cana-835	178	6	̃	̃	PROPN
cana-835	178	7	�	�	PROPN
cana-835	178	8	)	)	PUNCT
cana-835	178	9	=	=	SYM
cana-835	178	10	(	(	PUNCT
cana-835	178	11	(	(	PUNCT
cana-835	178	12	−1,1,3	−1,1,3	NUM
cana-835	178	13	)	)	PUNCT
cana-835	178	14	;	;	PUNCT
cana-835	178	15	(	(	PUNCT
cana-835	178	16	−1.1,1,2.9))𝑋4	−1.1,1,2.9))𝑋4	NOUN
cana-835	178	17	−	−	PROPN
cana-835	178	18	(	(	PUNCT
cana-835	178	19	(	(	PUNCT
cana-835	178	20	47,48,49	47,48,49	NUM
cana-835	178	21	)	)	PUNCT
cana-835	178	22	;	;	PUNCT
cana-835	178	23	(	(	PUNCT
cana-835	178	24	46.9,48,49.1))𝑋	46.9,48,49.1))𝑋	X
cana-835	178	25	+	+	X
cana-835	178	26	(	(	PUNCT
cana-835	178	27	(	(	PUNCT
cana-835	178	28	10,12,14	10,12,14	NUM
cana-835	178	29	)	)	PUNCT
cana-835	178	30	;	;	PUNCT
cana-835	178	31	(	(	PUNCT
cana-835	178	32	10.5,12,13.5	10.5,12,13.5	NUM
cana-835	178	33	)	)	PUNCT
cana-835	178	34	where	where	SCONJ
cana-835	178	35	𝑋	𝑋	PROPN
cana-835	178	36	∈	∈	NOUN
cana-835	178	37	ℜ.	ℜ.	VERB
cana-835	178	38	by	by	ADP
cana-835	178	39	empl0ying	empl0ye	VERB
cana-835	178	40	0ur	0ur	NOUN
cana-835	178	41	pr0posed	pr0posed	ADJ
cana-835	178	42	arithmetic	arithmetic	ADJ
cana-835	178	43	operati0ns	operati0ns	PROPN
cana-835	178	44	,	,	PUNCT
cana-835	178	45	we	we	PRON
cana-835	178	46	first	first	ADV
cana-835	178	47	transf0rm	transf0rm	ADV
cana-835	178	48	all	all	DET
cana-835	178	49	intuℹti0nistic	intuℹti0nistic	ADJ
cana-835	178	50	triangular	triangular	NOUN
cana-835	178	51	fuzzy	fuzzy	ADJ
cana-835	178	52	numbers	number	NOUN
cana-835	178	53	into	into	ADP
cana-835	178	54	their	their	PRON
cana-835	178	55	l0catℹon	l0catℹon	NOUN
cana-835	178	56	ℹndex	ℹndex	NOUN
cana-835	178	57	and	and	CCONJ
cana-835	178	58	fuzzℹness	fuzzℹness	ADJ
cana-835	178	59	ℹndex	ℹndex	NOUN
cana-835	178	60	functℹ0ns	functℹ0ns	PROPN
cana-835	178	61	.	.	PROPN
cana-835	179	1	then	then	ADV
cana-835	179	2	the	the	DET
cana-835	179	3	parametric	parametric	ADJ
cana-835	179	4	form	form	NOUN
cana-835	179	5	for	for	ADP
cana-835	179	6	unc0nstraℹned	unc0nstraℹned	PROPN
cana-835	179	7	0ptimℹzation	0ptimℹzation	PROPN
cana-835	179	8	pr0blem	pr0blem	ADP
cana-835	179	9	is	be	AUX
cana-835	179	10	written	write	VERB
cana-835	179	11	as	as	ADP
cana-835	179	12	𝑓(	𝑓(	PROPN
cana-835	179	13	�	�	PROPN
cana-835	179	14	̃	̃	PROPN
cana-835	179	15	�	�	PROPN
cana-835	179	16	)	)	PUNCT
cana-835	179	17	=	=	SYM
cana-835	180	1	(	(	PUNCT
cana-835	180	2	(	(	PUNCT
cana-835	180	3	−1,1,3	−1,1,3	NUM
cana-835	180	4	)	)	PUNCT
cana-835	181	1	;	;	PUNCT
cana-835	181	2	(	(	PUNCT
cana-835	181	3	−1.1,1,2.9))𝑋3	−1.1,1,2.9))𝑋3	ADJ
cana-835	181	4	−	−	PROPN
cana-835	181	5	(	(	PUNCT
cana-835	181	6	(	(	PUNCT
cana-835	181	7	47,48,49	47,48,49	NUM
cana-835	181	8	)	)	PUNCT
cana-835	181	9	;	;	PUNCT
cana-835	181	10	(	(	PUNCT
cana-835	181	11	46.9,48,49.1))𝑋	46.9,48,49.1))𝑋	X
cana-835	181	12	+	+	X
cana-835	181	13	(	(	PUNCT
cana-835	181	14	(	(	PUNCT
cana-835	181	15	10,12,14	10,12,14	NUM
cana-835	181	16	)	)	PUNCT
cana-835	181	17	;	;	PUNCT
cana-835	181	18	(	(	PUNCT
cana-835	181	19	10.5,12,13.5	10.5,12,13.5	NUM
cana-835	181	20	)	)	PUNCT
cana-835	181	21	communications	communication	NOUN
cana-835	181	22	on	on	ADP
cana-835	181	23	applied	apply	VERB
cana-835	181	24	nonlinear	nonlinear	ADJ
cana-835	181	25	analysis	analysis	NOUN
cana-835	181	26	issn	issn	NOUN
cana-835	181	27	:	:	PUNCT
cana-835	181	28	1074	1074	NUM
cana-835	181	29	-	-	PUNCT
cana-835	181	30	133x	133x	NUM
cana-835	181	31	vol	vol	NOUN
cana-835	181	32	31	31	NUM
cana-835	181	33	no	no	NOUN
cana-835	181	34	.	.	PUNCT
cana-835	182	1	4s	4s	NUM
cana-835	182	2	(	(	PUNCT
cana-835	182	3	2024	2024	NUM
cana-835	182	4	)	)	PUNCT
cana-835	182	5	192	192	NUM
cana-835	182	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	182	7	𝑓′(	𝑓′(	PROPN
cana-835	182	8	�	�	PROPN
cana-835	182	9	̃	̃	NOUN
cana-835	182	10	�	�	PROPN
cana-835	182	11	)	)	PUNCT
cana-835	182	12	=	=	SYM
cana-835	182	13	4((−1,1,3	4((−1,1,3	NOUN
cana-835	182	14	)	)	PUNCT
cana-835	182	15	;	;	PUNCT
cana-835	182	16	(	(	PUNCT
cana-835	182	17	−1.1,1,2.9))𝑋3	−1.1,1,2.9))𝑋3	ADJ
cana-835	182	18	−	−	PROPN
cana-835	182	19	(	(	PUNCT
cana-835	182	20	(	(	PUNCT
cana-835	182	21	47,48,49	47,48,49	NUM
cana-835	182	22	)	)	PUNCT
cana-835	182	23	;	;	PUNCT
cana-835	182	24	(	(	PUNCT
cana-835	182	25	46.9,48,49.1	46.9,48,49.1	NUM
cana-835	182	26	)	)	PUNCT
cana-835	182	27	)	)	PUNCT
cana-835	183	1	𝑓′(	𝑓′(	PROPN
cana-835	183	2	�	�	PROPN
cana-835	183	3	̃	̃	NOUN
cana-835	183	4	�	�	NOUN
cana-835	183	5	)=((−1,1,3	)=((−1,1,3	NUM
cana-835	183	6	)	)	PUNCT
cana-835	183	7	;	;	PUNCT
cana-835	183	8	(	(	PUNCT
cana-835	183	9	−1.1,1,2.9))𝑋3	−1.1,1,2.9))𝑋3	ADJ
cana-835	183	10	−	−	PROPN
cana-835	183	11	(	(	PUNCT
cana-835	183	12	(	(	PUNCT
cana-835	183	13	11.75,12,12.25	11.75,12,12.25	NOUN
cana-835	183	14	)	)	PUNCT
cana-835	183	15	;	;	PUNCT
cana-835	183	16	(	(	PUNCT
cana-835	183	17	11.725,12,12.2750	11.725,12,12.2750	X
cana-835	183	18	)	)	PUNCT
cana-835	183	19	𝑓′′(	𝑓′′(	PROPN
cana-835	183	20	�	�	PROPN
cana-835	183	21	̃	̃	PROPN
cana-835	183	22	�	�	PROPN
cana-835	183	23	)	)	PUNCT
cana-835	183	24	=	=	NOUN
cana-835	183	25	3((−1,1,3	3((−1,1,3	NUM
cana-835	183	26	)	)	PUNCT
cana-835	183	27	;	;	PUNCT
cana-835	183	28	(	(	PUNCT
cana-835	183	29	−1.1,1,2.9))𝑋2	−1.1,1,2.9))𝑋2	NOUN
cana-835	183	30	the	the	DET
cana-835	183	31	interval	interval	NOUN
cana-835	183	32	analysis	analysis	NOUN
cana-835	183	33	of	of	ADP
cana-835	183	34	newt0n	newt0n	PROPN
cana-835	183	35	meth0d	meth0d	PROPN
cana-835	183	36	for	for	ADP
cana-835	183	37	unc0nstrained	unc0nstrained	PROPN
cana-835	183	38	fuzzy	fuzzy	ADJ
cana-835	183	39	0ptimization	0ptimization	NOUN
cana-835	183	40	is	be	AUX
cana-835	183	41	(	(	PUNCT
cana-835	183	42	�	�	PROPN
cana-835	183	43	̃	̃	NOUN
cana-835	183	44	�	�	NOUN
cana-835	183	45	𝑖+1	𝑖+1	NUM
cana-835	183	46	)	)	PUNCT
cana-835	183	47	𝐼	𝐼	ADP
cana-835	183	48	=	=	PUNCT
cana-835	183	49	𝑁(	𝑁(	X
cana-835	183	50	�	�	PROPN
cana-835	183	51	̃	̃	PROPN
cana-835	183	52	�	�	PROPN
cana-835	183	53	)	)	PUNCT
cana-835	183	54	𝐼	𝐼	ADP
cana-835	183	55	∩	∩	NOUN
cana-835	183	56	(	(	PUNCT
cana-835	183	57	�	�	PROPN
cana-835	183	58	̃	̃	PROPN
cana-835	183	59	�	�	NOUN
cana-835	183	60	𝑖	𝑖	NOUN
cana-835	183	61	)	)	PUNCT
cana-835	183	62	𝐼	𝐼	ADP
cana-835	183	63	here	here	ADV
cana-835	183	64	𝑁(	𝑁(	PUNCT
cana-835	183	65	�	�	PROPN
cana-835	183	66	̃	̃	PROPN
cana-835	183	67	�	�	PROPN
cana-835	183	68	)	)	PUNCT
cana-835	183	69	𝐼	𝐼	NOUN
cana-835	183	70	=	=	SYM
cana-835	184	1	[	[	X
cana-835	184	2	𝑚(	𝑚(	NUM
cana-835	184	3	�	�	SYM
cana-835	184	4	̃	̃	NOUN
cana-835	184	5	�	�	PROPN
cana-835	184	6	)	)	PUNCT
cana-835	185	1	𝐼	𝐼	ADP
cana-835	185	2	−	−	PROPN
cana-835	185	3	𝑓′(𝑚(	𝑓′(𝑚(	PROPN
cana-835	185	4	�	�	PROPN
cana-835	185	5	̃	̃	NOUN
cana-835	185	6	�	�	PROPN
cana-835	185	7	)	)	PUNCT
cana-835	186	1	𝐼	𝐼	ADP
cana-835	186	2	𝑓′′(	𝑓′′(	PROPN
cana-835	186	3	�	�	PROPN
cana-835	186	4	̃	̃	PROPN
cana-835	186	5	�	�	PROPN
cana-835	186	6	)	)	PUNCT
cana-835	186	7	𝐼	𝐼	PROPN
cana-835	186	8	]	]	PUNCT
cana-835	186	9	let	let	VERB
cana-835	186	10	us	we	PRON
cana-835	186	11	take	take	VERB
cana-835	186	12	the	the	DET
cana-835	186	13	ℹnitial	ℹnitial	ADJ
cana-835	186	14	ℹnterval	ℹnterval	PROPN
cana-835	186	15	�	�	PROPN
cana-835	186	16	̃	̃	PROPN
cana-835	186	17	�	�	NOUN
cana-835	186	18	0	0	NUM
cana-835	186	19	=	=	SYM
cana-835	187	1	[	[	X
cana-835	187	2	(	(	PUNCT
cana-835	187	3	(	(	PUNCT
cana-835	187	4	1,2,3	1,2,3	NUM
cana-835	187	5	)	)	PUNCT
cana-835	187	6	;	;	PUNCT
cana-835	187	7	(	(	PUNCT
cana-835	187	8	1.1,2,2.9	1.1,2,2.9	NUM
cana-835	187	9	)	)	PUNCT
cana-835	187	10	)	)	PUNCT
cana-835	187	11	,	,	PUNCT
cana-835	187	12	(	(	PUNCT
cana-835	187	13	(	(	PUNCT
cana-835	187	14	3,4,5	3,4,5	NUM
cana-835	187	15	)	)	PUNCT
cana-835	187	16	;	;	PUNCT
cana-835	187	17	(	(	PUNCT
cana-835	187	18	3.1,4,4.9	3.1,4,4.9	NUM
cana-835	187	19	)	)	PUNCT
cana-835	187	20	)	)	PUNCT
cana-835	187	21	]	]	PUNCT
cana-835	187	22	in	in	ADP
cana-835	187	23	intuℹti0nistic	intuℹti0nistic	ADJ
cana-835	187	24	triangular	triangular	NOUN
cana-835	187	25	fuzzy	fuzzy	ADJ
cana-835	187	26	number	number	NOUN
cana-835	187	27	.	.	PUNCT
cana-835	188	1	𝑚(	𝑚(	PROPN
cana-835	188	2	�	�	PROPN
cana-835	188	3	̃	̃	PROPN
cana-835	188	4	�	�	NOUN
cana-835	188	5	0	0	NUM
cana-835	188	6	)	)	PUNCT
cana-835	189	1	𝐼	𝐼	NOUN
cana-835	189	2	=	=	SYM
cana-835	190	1	[	[	X
cana-835	190	2	(	(	PUNCT
cana-835	190	3	2,3,4	2,3,4	NUM
cana-835	190	4	)	)	PUNCT
cana-835	190	5	;	;	PUNCT
cana-835	190	6	(	(	PUNCT
cana-835	190	7	2.1,3,2.9	2.1,3,2.9	NUM
cana-835	190	8	)	)	PUNCT
cana-835	190	9	]	]	PUNCT
cana-835	190	10	𝑁(	𝑁(	NUM
cana-835	190	11	�	�	PROPN
cana-835	190	12	̃	̃	NOUN
cana-835	190	13	�	�	PROPN
cana-835	190	14	)	)	PUNCT
cana-835	190	15	𝐼	𝐼	PROPN
cana-835	190	16	=	=	PUNCT
cana-835	190	17	𝑚(	𝑚(	PROPN
cana-835	190	18	�	�	PROPN
cana-835	190	19	̃	̃	PROPN
cana-835	190	20	�	�	NOUN
cana-835	190	21	0	0	NUM
cana-835	190	22	)	)	PUNCT
cana-835	191	1	𝐼	𝐼	ADP
cana-835	191	2	−	−	PROPN
cana-835	191	3	[	[	PUNCT
cana-835	191	4	(	(	PUNCT
cana-835	191	5	(	(	PUNCT
cana-835	191	6	(	(	PUNCT
cana-835	191	7	−1,1,3	−1,1,3	NUM
cana-835	191	8	)	)	PUNCT
cana-835	191	9	;	;	PUNCT
cana-835	191	10	(	(	PUNCT
cana-835	191	11	−1.1,1,2.9	−1.1,1,2.9	NOUN
cana-835	191	12	)	)	PUNCT
cana-835	191	13	)	)	PUNCT
cana-835	191	14	∗	∗	NOUN
cana-835	191	15	[	[	X
cana-835	191	16	(	(	PUNCT
cana-835	191	17	2,3,4	2,3,4	NUM
cana-835	191	18	)	)	PUNCT
cana-835	191	19	;	;	PUNCT
cana-835	191	20	(	(	PUNCT
cana-835	191	21	2.1,3,3.9)]3	2.1,3,3.9)]3	NUM
cana-835	191	22	−((11.75,12,12.25	−((11.75,12,12.25	NOUN
cana-835	191	23	)	)	PUNCT
cana-835	191	24	;	;	PUNCT
cana-835	191	25	(	(	PUNCT
cana-835	191	26	11.725,12,12.2750	11.725,12,12.2750	NUM
cana-835	191	27	)	)	PUNCT
cana-835	191	28	3[((1,2,3	3[((1,2,3	NUM
cana-835	191	29	)	)	PUNCT
cana-835	191	30	;	;	PUNCT
cana-835	191	31	(	(	PUNCT
cana-835	191	32	1.1,2,2.9	1.1,2,2.9	NUM
cana-835	191	33	)	)	PUNCT
cana-835	191	34	)	)	PUNCT
cana-835	191	35	,	,	PUNCT
cana-835	191	36	(	(	PUNCT
cana-835	191	37	(	(	PUNCT
cana-835	191	38	3,4,5	3,4,5	NUM
cana-835	191	39	)	)	PUNCT
cana-835	191	40	;	;	PUNCT
cana-835	191	41	(	(	PUNCT
cana-835	191	42	3.1,4,4.9	3.1,4,4.9	NUM
cana-835	191	43	)	)	PUNCT
cana-835	191	44	)	)	PUNCT
cana-835	191	45	]	]	PUNCT
cana-835	192	1	2	2	X
cana-835	192	2	]	]	PUNCT
cana-835	192	3	=	=	PUNCT
cana-835	193	1	[	[	X
cana-835	193	2	(	(	PUNCT
cana-835	193	3	2,3,4	2,3,4	NUM
cana-835	193	4	)	)	PUNCT
cana-835	193	5	;	;	PUNCT
cana-835	193	6	(	(	PUNCT
cana-835	193	7	2.1,3,2.9	2.1,3,2.9	NUM
cana-835	193	8	)	)	PUNCT
cana-835	193	9	]	]	PUNCT
cana-835	194	1	−	−	PROPN
cana-835	194	2	[	[	PUNCT
cana-835	194	3	(	(	PUNCT
cana-835	194	4	(	(	PUNCT
cana-835	194	5	(	(	PUNCT
cana-835	194	6	−1,1,3	−1,1,3	NUM
cana-835	194	7	)	)	PUNCT
cana-835	194	8	;	;	PUNCT
cana-835	194	9	(	(	PUNCT
cana-835	194	10	−1.1,1,2.9	−1.1,1,2.9	NOUN
cana-835	194	11	)	)	PUNCT
cana-835	194	12	)	)	PUNCT
cana-835	194	13	∗	∗	NOUN
cana-835	195	1	[	[	X
cana-835	195	2	(	(	PUNCT
cana-835	195	3	2,3,4	2,3,4	NUM
cana-835	195	4	)	)	PUNCT
cana-835	195	5	;	;	PUNCT
cana-835	195	6	(	(	PUNCT
cana-835	195	7	2.1,3,3.9)]3	2.1,3,3.9)]3	NUM
cana-835	195	8	−((11.75,12,12.25	−((11.75,12,12.25	NOUN
cana-835	195	9	)	)	PUNCT
cana-835	195	10	;	;	PUNCT
cana-835	195	11	(	(	PUNCT
cana-835	195	12	11.725,12,12.2750	11.725,12,12.2750	NUM
cana-835	195	13	)	)	PUNCT
cana-835	195	14	3[((2,4,6	3[((2,4,6	NUM
cana-835	195	15	)	)	PUNCT
cana-835	195	16	;	;	PUNCT
cana-835	195	17	(	(	PUNCT
cana-835	195	18	2.2,4,5.8	2.2,4,5.8	NOUN
cana-835	195	19	)	)	PUNCT
cana-835	195	20	,	,	PUNCT
cana-835	195	21	(	(	PUNCT
cana-835	195	22	12,16,20	12,16,20	NUM
cana-835	195	23	)	)	PUNCT
cana-835	195	24	;	;	PUNCT
cana-835	195	25	(	(	PUNCT
cana-835	195	26	12.4,16,19.6	12.4,16,19.6	NUM
cana-835	195	27	)	)	PUNCT
cana-835	195	28	]	]	PUNCT
cana-835	196	1	]	]	PUNCT
cana-835	196	2	=[	=[	X
cana-835	196	3	(	(	PUNCT
cana-835	196	4	(	(	PUNCT
cana-835	196	5	0.5208,1.25,1.9791	0.5208,1.25,1.9791	NUM
cana-835	196	6	)	)	PUNCT
cana-835	196	7	;	;	PUNCT
cana-835	196	8	(	(	PUNCT
cana-835	196	9	0.59791,1.25,1.9020	0.59791,1.25,1.9020	NUM
cana-835	196	10	)	)	PUNCT
cana-835	196	11	)	)	PUNCT
cana-835	196	12	,	,	PUNCT
cana-835	196	13	(	(	PUNCT
cana-835	196	14	0.13021,0.31250.49479	0.13021,0.31250.49479	NOUN
cana-835	196	15	)	)	PUNCT
cana-835	196	16	;	;	PUNCT
cana-835	196	17	(	(	PUNCT
cana-835	196	18	0.14947,0.3125,0.4755	0.14947,0.3125,0.4755	NOUN
cana-835	196	19	)	)	PUNCT
cana-835	196	20	)	)	PUNCT
cana-835	196	21	]	]	PUNCT
cana-835	196	22	(	(	PUNCT
cana-835	196	23	�	�	PROPN
cana-835	196	24	̃	̃	NOUN
cana-835	196	25	�	�	NOUN
cana-835	196	26	1	1	NUM
cana-835	196	27	)	)	PUNCT
cana-835	196	28	𝐼	𝐼	NOUN
cana-835	196	29	=	=	SYM
cana-835	197	1	[	[	X
cana-835	197	2	(	(	PUNCT
cana-835	197	3	(	(	PUNCT
cana-835	197	4	1,2,3	1,2,3	NUM
cana-835	197	5	)	)	PUNCT
cana-835	197	6	;	;	PUNCT
cana-835	197	7	(	(	PUNCT
cana-835	197	8	1.1,2,2.9	1.1,2,2.9	NUM
cana-835	197	9	)	)	PUNCT
cana-835	197	10	)	)	PUNCT
cana-835	197	11	,	,	PUNCT
cana-835	197	12	(	(	PUNCT
cana-835	197	13	(	(	PUNCT
cana-835	197	14	3,4,5	3,4,5	NUM
cana-835	197	15	)	)	PUNCT
cana-835	197	16	;	;	PUNCT
cana-835	197	17	(	(	PUNCT
cana-835	197	18	3.1,4,4.9	3.1,4,4.9	NUM
cana-835	197	19	)	)	PUNCT
cana-835	197	20	)	)	PUNCT
cana-835	197	21	]	]	PUNCT
cana-835	198	1	∩	∩	NOUN
cana-835	198	2	[	[	PUNCT
cana-835	198	3	(	(	PUNCT
cana-835	198	4	(	(	PUNCT
cana-835	198	5	0.5208,1.25,1.9791	0.5208,1.25,1.9791	NUM
cana-835	198	6	)	)	PUNCT
cana-835	198	7	;	;	PUNCT
cana-835	198	8	(	(	PUNCT
cana-835	198	9	0.59791,1.25,1.9020	0.59791,1.25,1.9020	NUM
cana-835	198	10	)	)	PUNCT
cana-835	198	11	)	)	PUNCT
cana-835	198	12	,	,	PUNCT
cana-835	198	13	(	(	PUNCT
cana-835	198	14	0.13021,0.31250.49479	0.13021,0.31250.49479	NOUN
cana-835	198	15	)	)	PUNCT
cana-835	198	16	;	;	PUNCT
cana-835	198	17	(	(	PUNCT
cana-835	198	18	0.14947,0.3125,0.4755	0.14947,0.3125,0.4755	NOUN
cana-835	198	19	)	)	PUNCT
cana-835	198	20	)	)	PUNCT
cana-835	198	21	]	]	PUNCT
cana-835	198	22	(	(	PUNCT
cana-835	198	23	�	�	PROPN
cana-835	198	24	̃	̃	NOUN
cana-835	198	25	�	�	NOUN
cana-835	198	26	1)=	1)=	NUM
cana-835	198	27	[	[	PUNCT
cana-835	198	28	(	(	PUNCT
cana-835	198	29	(	(	PUNCT
cana-835	198	30	1,2,3	1,2,3	NUM
cana-835	198	31	)	)	PUNCT
cana-835	198	32	;	;	PUNCT
cana-835	198	33	(	(	PUNCT
cana-835	198	34	1.1,2,2.9	1.1,2,2.9	NUM
cana-835	198	35	)	)	PUNCT
cana-835	198	36	)	)	PUNCT
cana-835	198	37	,	,	PUNCT
cana-835	198	38	(	(	PUNCT
cana-835	198	39	(	(	PUNCT
cana-835	198	40	3,4,5	3,4,5	NUM
cana-835	198	41	)	)	PUNCT
cana-835	198	42	;	;	PUNCT
cana-835	198	43	(	(	PUNCT
cana-835	198	44	3.1,4,4.9	3.1,4,4.9	NUM
cana-835	198	45	)	)	PUNCT
cana-835	198	46	)	)	PUNCT
cana-835	198	47	]	]	PUNCT
cana-835	199	1	∩	∩	NOUN
cana-835	199	2	[	[	PUNCT
cana-835	199	3	(	(	PUNCT
cana-835	199	4	1.375,1.75,2.125	1.375,1.75,2.125	NUM
cana-835	199	5	)	)	PUNCT
cana-835	199	6	;	;	PUNCT
cana-835	199	7	(	(	PUNCT
cana-835	199	8	1.4,1.75,2.1	1.4,1.75,2.1	NUM
cana-835	199	9	)	)	PUNCT
cana-835	199	10	,	,	PUNCT
cana-835	199	11	(	(	PUNCT
cana-835	199	12	1.4687,2.6875,3.9062	1.4687,2.6875,3.9062	NUM
cana-835	199	13	)	)	PUNCT
cana-835	199	14	;	;	PUNCT
cana-835	199	15	(	(	PUNCT
cana-835	199	16	1.55,2.6875,3.825	1.55,2.6875,3.825	NUM
cana-835	199	17	)	)	PUNCT
cana-835	199	18	]	]	PUNCT
cana-835	199	19	(	(	PUNCT
cana-835	199	20	�	�	PROPN
cana-835	199	21	̃	̃	NOUN
cana-835	199	22	�	�	NOUN
cana-835	199	23	1	1	NUM
cana-835	199	24	)	)	PUNCT
cana-835	199	25	=	=	NOUN
cana-835	199	26	[	[	PUNCT
cana-835	199	27	(	(	PUNCT
cana-835	199	28	1,2,3	1,2,3	NUM
cana-835	199	29	)	)	PUNCT
cana-835	199	30	;	;	PUNCT
cana-835	199	31	(	(	PUNCT
cana-835	199	32	1.1,2,2.9	1.1,2,2.9	NUM
cana-835	199	33	)	)	PUNCT
cana-835	199	34	,	,	PUNCT
cana-835	199	35	(	(	PUNCT
cana-835	199	36	1.4687,2.6875,3.9062	1.4687,2.6875,3.9062	NUM
cana-835	199	37	)	)	PUNCT
cana-835	199	38	;	;	PUNCT
cana-835	199	39	(	(	PUNCT
cana-835	199	40	1.55,2.6875,3.825	1.55,2.6875,3.825	NUM
cana-835	199	41	)	)	PUNCT
cana-835	199	42	]	]	PUNCT
cana-835	199	43	(	(	PUNCT
cana-835	199	44	�	�	PROPN
cana-835	199	45	̃	̃	NOUN
cana-835	199	46	�	�	NOUN
cana-835	199	47	2	2	NUM
cana-835	199	48	)	)	PUNCT
cana-835	199	49	=	=	NOUN
cana-835	199	50	[	[	PUNCT
cana-835	199	51	(	(	PUNCT
cana-835	199	52	1.6693,2.2708,2.8724	1.6693,2.2708,2.8724	NUM
cana-835	199	53	)	)	PUNCT
cana-835	199	54	;	;	PUNCT
cana-835	199	55	(	(	PUNCT
cana-835	199	56	1.7184,2.2708,2.8232	1.7184,2.2708,2.8232	NUM
cana-835	199	57	)	)	PUNCT
cana-835	199	58	,	,	PUNCT
cana-835	199	59	(	(	PUNCT
cana-835	199	60	1.47524,2.0333,3.1315	1.47524,2.0333,3.1315	NUM
cana-835	199	61	)	)	PUNCT
cana-835	199	62	;	;	PUNCT
cana-835	199	63	(	(	PUNCT
cana-835	199	64	1.5429,2.3033,3.0638	1.5429,2.3033,3.0638	NUM
cana-835	199	65	)	)	PUNCT
cana-835	199	66	]	]	PUNCT
cana-835	199	67	thus	thus	ADV
cana-835	199	68	,	,	PUNCT
cana-835	199	69	f(x	f(x	PROPN
cana-835	199	70	)	)	PUNCT
cana-835	199	71	is	be	AUX
cana-835	199	72	minimum	minimum	ADJ
cana-835	199	73	at	at	ADP
cana-835	199	74	𝑥	𝑥	PROPN
cana-835	199	75	=	=	SYM
cana-835	199	76	2.28675𝑖	2.28675𝑖	PROPN
cana-835	199	77	,	,	PUNCT
cana-835	199	78	instead	instead	ADV
cana-835	199	79	the	the	DET
cana-835	199	80	elementary	elementary	ADJ
cana-835	199	81	calculus	calculus	NOUN
cana-835	199	82	technique	technique	NOUN
cana-835	199	83	produces	produces	AUX
cana-835	199	84	minima	minima	VERB
cana-835	199	85	at	at	ADP
cana-835	199	86	𝑥	𝑥	PROPN
cana-835	199	87	=	=	SYM
cana-835	199	88	2.28675𝑖	2.28675𝑖	PROPN
cana-835	199	89	.	.	PUNCT
cana-835	200	1	example	example	NOUN
cana-835	200	2	2	2	NUM
cana-835	200	3	:	:	PUNCT
cana-835	200	4	communications	communication	NOUN
cana-835	200	5	on	on	ADP
cana-835	200	6	applied	apply	VERB
cana-835	200	7	nonlinear	nonlinear	ADJ
cana-835	200	8	analysis	analysis	NOUN
cana-835	200	9	issn	issn	NOUN
cana-835	200	10	:	:	PUNCT
cana-835	200	11	1074	1074	NUM
cana-835	200	12	-	-	PUNCT
cana-835	200	13	133x	133x	NUM
cana-835	200	14	vol	vol	NOUN
cana-835	200	15	31	31	NUM
cana-835	200	16	no	no	NOUN
cana-835	200	17	.	.	PUNCT
cana-835	201	1	4s	4s	NUM
cana-835	201	2	(	(	PUNCT
cana-835	201	3	2024	2024	NUM
cana-835	201	4	)	)	PUNCT
cana-835	201	5	193	193	NUM
cana-835	201	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	201	7	consider	consider	VERB
cana-835	201	8	x	x	PRON
cana-835	201	9	and	and	CCONJ
cana-835	201	10	y	y	PROPN
cana-835	201	11	as	as	ADP
cana-835	201	12	distinct	distinct	ADJ
cana-835	201	13	diagnostic	diagnostic	ADJ
cana-835	201	14	markers	marker	NOUN
cana-835	201	15	or	or	CCONJ
cana-835	201	16	criteria	criterion	NOUN
cana-835	201	17	for	for	ADP
cana-835	201	18	medical	medical	ADJ
cana-835	201	19	diagnosis	diagnosis	NOUN
cana-835	201	20	.	.	PUNCT
cana-835	202	1	these	these	DET
cana-835	202	2	signals	signal	NOUN
cana-835	202	3	could	could	AUX
cana-835	202	4	be	be	AUX
cana-835	202	5	anything	anything	PRON
cana-835	202	6	from	from	ADP
cana-835	202	7	specific	specific	ADJ
cana-835	202	8	lab	lab	NOUN
cana-835	202	9	readings	reading	NOUN
cana-835	202	10	to	to	ADP
cana-835	202	11	clinical	clinical	ADJ
cana-835	202	12	complaints	complaint	NOUN
cana-835	202	13	or	or	CCONJ
cana-835	202	14	imaging	imaging	NOUN
cana-835	202	15	results	result	NOUN
cana-835	202	16	.	.	PUNCT
cana-835	203	1	the	the	DET
cana-835	203	2	equation	equation	NOUN
cana-835	203	3	then	then	ADV
cana-835	203	4	reflects	reflect	VERB
cana-835	203	5	the	the	DET
cana-835	203	6	interaction	interaction	NOUN
cana-835	203	7	of	of	ADP
cana-835	203	8	various	various	ADJ
cana-835	203	9	diagnostic	diagnostic	ADJ
cana-835	203	10	signs	sign	NOUN
cana-835	203	11	in	in	ADP
cana-835	203	12	evaluating	evaluate	VERB
cana-835	203	13	a	a	DET
cana-835	203	14	patient	patient	NOUN
cana-835	203	15	's	's	PART
cana-835	203	16	status	status	NOUN
cana-835	203	17	.	.	PUNCT
cana-835	204	1	in	in	ADP
cana-835	204	2	a	a	DET
cana-835	204	3	medical	medical	ADJ
cana-835	204	4	context	context	NOUN
cana-835	204	5	,	,	PUNCT
cana-835	204	6	x	x	PUNCT
cana-835	204	7	and	and	CCONJ
cana-835	204	8	y	y	PROPN
cana-835	204	9	may	may	AUX
cana-835	204	10	indicate	indicate	VERB
cana-835	204	11	various	various	ADJ
cana-835	204	12	clinical	clinical	ADJ
cana-835	204	13	aspects	aspect	NOUN
cana-835	204	14	or	or	CCONJ
cana-835	204	15	biomarkers	biomarker	NOUN
cana-835	204	16	associated	associate	VERB
cana-835	204	17	with	with	ADP
cana-835	204	18	a	a	DET
cana-835	204	19	specific	specific	ADJ
cana-835	204	20	disease	disease	NOUN
cana-835	204	21	or	or	CCONJ
cana-835	204	22	condition	condition	NOUN
cana-835	204	23	.	.	PUNCT
cana-835	205	1	for	for	ADP
cana-835	205	2	example	example	NOUN
cana-835	205	3	,	,	PUNCT
cana-835	205	4	x	x	PRON
cana-835	205	5	might	might	AUX
cana-835	205	6	indicate	indicate	VERB
cana-835	205	7	blood	blood	NOUN
cana-835	205	8	pressure	pressure	NOUN
cana-835	205	9	data	datum	NOUN
cana-835	205	10	,	,	PUNCT
cana-835	205	11	and	and	CCONJ
cana-835	205	12	y	y	PROPN
cana-835	205	13	could	could	AUX
cana-835	205	14	represent	represent	VERB
cana-835	205	15	blood	blood	NOUN
cana-835	205	16	glucose	glucose	NOUN
cana-835	205	17	levels	level	NOUN
cana-835	205	18	in	in	ADP
cana-835	205	19	a	a	DET
cana-835	205	20	diabetic	diabetic	ADJ
cana-835	205	21	patient	patient	NOUN
cana-835	205	22	.	.	PUNCT
cana-835	206	1	the	the	DET
cana-835	206	2	equation	equation	NOUN
cana-835	206	3	𝑥3	𝑥3	NOUN
cana-835	206	4	−	−	PROPN
cana-835	206	5	3𝑥𝑦	3𝑥𝑦	NOUN
cana-835	207	1	+	+	CCONJ
cana-835	207	2	𝑦3	𝑦3	PROPN
cana-835	207	3	could	could	AUX
cana-835	207	4	represent	represent	VERB
cana-835	207	5	a	a	DET
cana-835	207	6	diagnostic	diagnostic	ADJ
cana-835	207	7	situation	situation	NOUN
cana-835	207	8	in	in	ADP
cana-835	207	9	which	which	PRON
cana-835	207	10	the	the	DET
cana-835	207	11	values	value	NOUN
cana-835	207	12	of	of	ADP
cana-835	207	13	certain	certain	ADJ
cana-835	207	14	indicators	indicator	NOUN
cana-835	207	15	interact	interact	VERB
cana-835	207	16	in	in	ADP
cana-835	207	17	a	a	DET
cana-835	207	18	given	give	VERB
cana-835	207	19	manner	manner	NOUN
cana-835	207	20	,	,	PUNCT
cana-835	207	21	resulting	result	VERB
cana-835	207	22	in	in	ADP
cana-835	207	23	a	a	DET
cana-835	207	24	particular	particular	ADJ
cana-835	207	25	diagnosis	diagnosis	NOUN
cana-835	207	26	or	or	CCONJ
cana-835	207	27	clinical	clinical	ADJ
cana-835	207	28	consequence	consequence	NOUN
cana-835	207	29	.	.	PUNCT
cana-835	208	1	the	the	DET
cana-835	208	2	equation	equation	NOUN
cana-835	208	3	may	may	AUX
cana-835	208	4	be	be	AUX
cana-835	208	5	analyzed	analyze	VERB
cana-835	208	6	to	to	PART
cana-835	208	7	determine	determine	VERB
cana-835	208	8	how	how	SCONJ
cana-835	208	9	changes	change	NOUN
cana-835	208	10	in	in	ADP
cana-835	208	11	one	one	NUM
cana-835	208	12	diagnostic	diagnostic	ADJ
cana-835	208	13	marker	marker	NOUN
cana-835	208	14	affect	affect	VERB
cana-835	208	15	the	the	DET
cana-835	208	16	interpretation	interpretation	NOUN
cana-835	208	17	of	of	ADP
cana-835	208	18	another	another	PRON
cana-835	208	19	,	,	PUNCT
cana-835	208	20	as	as	ADV
cana-835	208	21	well	well	ADV
cana-835	208	22	as	as	ADP
cana-835	208	23	how	how	SCONJ
cana-835	208	24	these	these	DET
cana-835	208	25	interactions	interaction	NOUN
cana-835	208	26	influence	influence	VERB
cana-835	208	27	the	the	DET
cana-835	208	28	diagnostic	diagnostic	ADJ
cana-835	208	29	process	process	NOUN
cana-835	208	30	.	.	PUNCT
cana-835	209	1	let	let	VERB
cana-835	209	2	us	we	PRON
cana-835	209	3	c0nsider	c0nsider	VERB
cana-835	209	4	the	the	DET
cana-835	209	5	following	follow	VERB
cana-835	209	6	unc0nstrained	unc0nstraine	VERB
cana-835	209	7	fuzzy	fuzzy	ADJ
cana-835	209	8	0ptimization	0ptimization	NOUN
cana-835	209	9	pr0blem	pr0blem	NOUN
cana-835	209	10	with	with	ADP
cana-835	209	11	intuiti0nistic	intuiti0nistic	ADJ
cana-835	209	12	triangular(0.5,1,1.5	triangular(0.5,1,1.5	NOUN
cana-835	209	13	)	)	PUNCT
cana-835	209	14	;	;	PUNCT
cana-835	209	15	(	(	PUNCT
cana-835	209	16	0.4,1,1.6)𝑥3	0.4,1,1.6)𝑥3	NUM
cana-835	209	17	−	−	PROPN
cana-835	209	18	(	(	PUNCT
cana-835	209	19	2,3,4	2,3,4	NUM
cana-835	209	20	)	)	PUNCT
cana-835	209	21	;	;	PUNCT
cana-835	209	22	(	(	PUNCT
cana-835	209	23	2.1,3,3.9)𝑥𝑦	2.1,3,3.9)𝑥𝑦	NUM
cana-835	209	24	+	+	CCONJ
cana-835	209	25	(	(	PUNCT
cana-835	209	26	0.5,1,1.5	0.5,1,1.5	ADJ
cana-835	209	27	)	)	PUNCT
cana-835	209	28	;	;	PUNCT
cana-835	209	29	(	(	PUNCT
cana-835	209	30	0.4,1,1.6)𝑦3	0.4,1,1.6)𝑦3	NOUN
cana-835	209	31	,	,	PUNCT
cana-835	209	32	initial	initial	ADJ
cana-835	209	33	interval	interval	NOUN
cana-835	209	34	intuiti0nistic	intuiti0nistic	ADJ
cana-835	209	35	value	value	NOUN
cana-835	209	36	for	for	ADP
cana-835	209	37	𝑋0	𝑋0	NOUN
cana-835	209	38	=	=	SYM
cana-835	210	1	[	[	X
cana-835	210	2	(	(	PUNCT
cana-835	210	3	0.5,1,1.5	0.5,1,1.5	ADJ
cana-835	210	4	)	)	PUNCT
cana-835	210	5	;	;	PUNCT
cana-835	210	6	(	(	PUNCT
cana-835	210	7	0.4,1,1.6	0.4,1,1.6	NOUN
cana-835	210	8	)	)	PUNCT
cana-835	210	9	,	,	PUNCT
cana-835	210	10	(	(	PUNCT
cana-835	210	11	1,2,3	1,2,3	NUM
cana-835	210	12	)	)	PUNCT
cana-835	210	13	;	;	PUNCT
cana-835	210	14	(	(	PUNCT
cana-835	210	15	0.9,2,3.1	0.9,2,3.1	ADJ
cana-835	210	16	)	)	PUNCT
cana-835	210	17	]	]	PUNCT
cana-835	210	18	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-835	210	19	𝑌0	𝑌0	NOUN
cana-835	210	20	=	=	SYM
cana-835	211	1	[	[	X
cana-835	211	2	(	(	PUNCT
cana-835	211	3	0.5,1,1.5	0.5,1,1.5	ADJ
cana-835	211	4	)	)	PUNCT
cana-835	211	5	;	;	PUNCT
cana-835	211	6	(	(	PUNCT
cana-835	211	7	0.4,1,1.6	0.4,1,1.6	NOUN
cana-835	211	8	)	)	PUNCT
cana-835	211	9	,	,	PUNCT
cana-835	211	10	(	(	PUNCT
cana-835	211	11	1,2,3	1,2,3	NUM
cana-835	211	12	)	)	PUNCT
cana-835	211	13	;	;	PUNCT
cana-835	211	14	(	(	PUNCT
cana-835	211	15	0.9,2,3.1	0.9,2,3.1	ADJ
cana-835	211	16	)	)	PUNCT
cana-835	211	17	]	]	PUNCT
cana-835	211	18	m(𝑋𝑘	m(𝑋𝑘	NOUN
cana-835	211	19	)	)	PUNCT
cana-835	211	20	=	=	SYM
cana-835	212	1	[	[	X
cana-835	212	2	(	(	PUNCT
cana-835	212	3	0.75,1.5,2.25	0.75,1.5,2.25	NOUN
cana-835	212	4	)	)	PUNCT
cana-835	212	5	;	;	PUNCT
cana-835	212	6	(	(	PUNCT
cana-835	212	7	0.65,1.5,2.35	0.65,1.5,2.35	NOUN
cana-835	212	8	)	)	PUNCT
cana-835	212	9	]	]	PUNCT
cana-835	212	10	m(𝑌𝑘	m(𝑌𝑘	NOUN
cana-835	212	11	)	)	PUNCT
cana-835	212	12	=	=	PUNCT
cana-835	213	1	[	[	X
cana-835	213	2	(	(	PUNCT
cana-835	213	3	0.75,1.5,2.25	0.75,1.5,2.25	NOUN
cana-835	213	4	)	)	PUNCT
cana-835	213	5	;	;	PUNCT
cana-835	213	6	(	(	PUNCT
cana-835	213	7	0.65,1.5,2.35	0.65,1.5,2.35	NOUN
cana-835	213	8	)	)	PUNCT
cana-835	213	9	]	]	PUNCT
cana-835	213	10	𝑓′(𝑋𝑘	𝑓′(𝑋𝑘	NOUN
cana-835	213	11	)	)	PUNCT
cana-835	213	12	=	=	SYM
cana-835	213	13	(	(	PUNCT
cana-835	213	14	(	(	PUNCT
cana-835	213	15	0.375,0.75,1.125	0.375,0.75,1.125	NUM
cana-835	213	16	)	)	PUNCT
cana-835	213	17	;	;	PUNCT
cana-835	213	18	(	(	PUNCT
cana-835	213	19	0.325,0.75,1.175	0.325,0.75,1.175	NUM
cana-835	213	20	)	)	PUNCT
cana-835	213	21	)	)	PUNCT
cana-835	213	22	and	and	CCONJ
cana-835	213	23	𝑓′(𝑌𝑘	𝑓′(𝑌𝑘	ADP
cana-835	213	24	)	)	PUNCT
cana-835	213	25	=	=	SYM
cana-835	213	26	(	(	PUNCT
cana-835	213	27	(	(	PUNCT
cana-835	213	28	0.375,0.75,1.125	0.375,0.75,1.125	NUM
cana-835	213	29	)	)	PUNCT
cana-835	213	30	;	;	PUNCT
cana-835	213	31	(	(	PUNCT
cana-835	213	32	0.325,0.75,1.175	0.325,0.75,1.175	NUM
cana-835	213	33	)	)	PUNCT
cana-835	213	34	)	)	PUNCT
cana-835	213	35	𝑓′′(𝑋𝑘	𝑓′′(𝑋𝑘	ADV
cana-835	213	36	)	)	PUNCT
cana-835	213	37	=	=	PUNCT
cana-835	214	1	[	[	X
cana-835	214	2	(	(	PUNCT
cana-835	214	3	(	(	PUNCT
cana-835	214	4	1,2,3	1,2,3	NUM
cana-835	214	5	)	)	PUNCT
cana-835	214	6	;	;	PUNCT
cana-835	214	7	(	(	PUNCT
cana-835	214	8	0.8,2,3.2	0.8,2,3.2	NOUN
cana-835	214	9	)	)	PUNCT
cana-835	214	10	)	)	PUNCT
cana-835	214	11	,	,	PUNCT
cana-835	214	12	(	(	PUNCT
cana-835	214	13	(	(	PUNCT
cana-835	214	14	2,4,6	2,4,6	NUM
cana-835	214	15	)	)	PUNCT
cana-835	214	16	;	;	PUNCT
cana-835	214	17	(	(	PUNCT
cana-835	214	18	1.8,4,6.2	1.8,4,6.2	NOUN
cana-835	214	19	)	)	PUNCT
cana-835	214	20	)	)	PUNCT
cana-835	214	21	]	]	PUNCT
cana-835	214	22	and	and	CCONJ
cana-835	214	23	𝑓′′(𝑌𝑘	𝑓′′(𝑌𝑘	NOUN
cana-835	214	24	)	)	PUNCT
cana-835	214	25	=	=	PUNCT
cana-835	215	1	[	[	X
cana-835	215	2	(	(	PUNCT
cana-835	215	3	(	(	PUNCT
cana-835	215	4	1,2,3	1,2,3	NUM
cana-835	215	5	)	)	PUNCT
cana-835	215	6	;	;	PUNCT
cana-835	215	7	(	(	PUNCT
cana-835	215	8	0.8,2,3.2	0.8,2,3.2	NOUN
cana-835	215	9	)	)	PUNCT
cana-835	215	10	)	)	PUNCT
cana-835	215	11	,	,	PUNCT
cana-835	215	12	(	(	PUNCT
cana-835	215	13	(	(	PUNCT
cana-835	215	14	2,4,6	2,4,6	NUM
cana-835	215	15	)	)	PUNCT
cana-835	215	16	;	;	PUNCT
cana-835	215	17	(	(	PUNCT
cana-835	215	18	1.8,4,6.2	1.8,4,6.2	NOUN
cana-835	215	19	)	)	PUNCT
cana-835	215	20	)	)	PUNCT
cana-835	215	21	]	]	PUNCT
cana-835	216	1	𝑋1	𝑋1	NOUN
cana-835	216	2	=	=	PUNCT
cana-835	217	1	[	[	PUNCT
cana-835	217	2	[	[	X
cana-835	217	3	(	(	PUNCT
cana-835	217	4	0.75,1.5,2.25	0.75,1.5,2.25	NOUN
cana-835	217	5	)	)	PUNCT
cana-835	217	6	;	;	PUNCT
cana-835	217	7	(	(	PUNCT
cana-835	217	8	0.65,1.5,2.35	0.65,1.5,2.35	NOUN
cana-835	217	9	)	)	PUNCT
cana-835	217	10	]	]	PUNCT
cana-835	218	1	−	−	PROPN
cana-835	218	2	(	(	PUNCT
cana-835	218	3	(	(	PUNCT
cana-835	218	4	0.375,0.75,1.125	0.375,0.75,1.125	NUM
cana-835	218	5	)	)	PUNCT
cana-835	218	6	;	;	PUNCT
cana-835	218	7	(	(	PUNCT
cana-835	218	8	0.325,0.75,1.175	0.325,0.75,1.175	NUM
cana-835	218	9	)	)	PUNCT
cana-835	218	10	)	)	PUNCT
cana-835	219	1	[	[	X
cana-835	219	2	(	(	PUNCT
cana-835	219	3	(	(	PUNCT
cana-835	219	4	1,2,3	1,2,3	NUM
cana-835	219	5	)	)	PUNCT
cana-835	219	6	;	;	PUNCT
cana-835	219	7	(	(	PUNCT
cana-835	219	8	0.8,2,3.2	0.8,2,3.2	NOUN
cana-835	219	9	)	)	PUNCT
cana-835	219	10	)	)	PUNCT
cana-835	219	11	,	,	PUNCT
cana-835	219	12	(	(	PUNCT
cana-835	219	13	(	(	PUNCT
cana-835	219	14	2,4,6	2,4,6	NUM
cana-835	219	15	)	)	PUNCT
cana-835	219	16	;	;	PUNCT
cana-835	219	17	(	(	PUNCT
cana-835	219	18	1.8,4,6.2	1.8,4,6.2	NOUN
cana-835	219	19	)	)	PUNCT
cana-835	219	20	)	)	PUNCT
cana-835	219	21	]	]	PUNCT
cana-835	219	22	]	]	PUNCT
cana-835	220	1	∩	∩	NOUN
cana-835	220	2	[	[	X
cana-835	220	3	(	(	PUNCT
cana-835	220	4	0.5,1,1.5	0.5,1,1.5	ADJ
cana-835	220	5	)	)	PUNCT
cana-835	220	6	;	;	PUNCT
cana-835	220	7	(	(	PUNCT
cana-835	220	8	0.4,1,1.6	0.4,1,1.6	NOUN
cana-835	220	9	)	)	PUNCT
cana-835	220	10	,	,	PUNCT
cana-835	220	11	(	(	PUNCT
cana-835	220	12	1,2,3	1,2,3	NUM
cana-835	220	13	)	)	PUNCT
cana-835	220	14	;	;	PUNCT
cana-835	220	15	(	(	PUNCT
cana-835	220	16	0.9,2,3.1	0.9,2,3.1	ADJ
cana-835	220	17	)	)	PUNCT
cana-835	220	18	]	]	PUNCT
cana-835	220	19	𝑋1	𝑋1	NOUN
cana-835	221	1	=	=	PUNCT
cana-835	221	2	[	[	PUNCT
cana-835	221	3	(	(	PUNCT
cana-835	221	4	(	(	PUNCT
cana-835	221	5	0.5625,1.125,1.6875	0.5625,1.125,1.6875	NUM
cana-835	221	6	)	)	PUNCT
cana-835	221	7	;	;	PUNCT
cana-835	221	8	(	(	PUNCT
cana-835	221	9	0.4875,1.125,1.7625	0.4875,1.125,1.7625	NUM
cana-835	221	10	)	)	PUNCT
cana-835	221	11	)	)	PUNCT
cana-835	221	12	,	,	PUNCT
cana-835	221	13	(	(	PUNCT
cana-835	221	14	(	(	PUNCT
cana-835	221	15	0.6562,1.3125,1.9687	0.6562,1.3125,1.9687	NUM
cana-835	221	16	)	)	PUNCT
cana-835	221	17	;	;	PUNCT
cana-835	221	18	(	(	PUNCT
cana-835	221	19	0.5688,1.3125,2.0563	0.5688,1.3125,2.0563	NUM
cana-835	221	20	)	)	PUNCT
cana-835	221	21	]	]	PUNCT
cana-835	221	22	∩	∩	NOUN
cana-835	221	23	[	[	X
cana-835	221	24	(	(	PUNCT
cana-835	221	25	0.5,1,1.5	0.5,1,1.5	ADJ
cana-835	221	26	)	)	PUNCT
cana-835	221	27	;	;	PUNCT
cana-835	221	28	(	(	PUNCT
cana-835	221	29	0.4,1,1.6	0.4,1,1.6	NOUN
cana-835	221	30	)	)	PUNCT
cana-835	221	31	,	,	PUNCT
cana-835	221	32	(	(	PUNCT
cana-835	221	33	1,2,3	1,2,3	NUM
cana-835	221	34	)	)	PUNCT
cana-835	221	35	;	;	PUNCT
cana-835	221	36	(	(	PUNCT
cana-835	221	37	0.9,2,3.1	0.9,2,3.1	ADJ
cana-835	221	38	)	)	PUNCT
cana-835	221	39	]	]	PUNCT
cana-835	221	40	𝑋1	𝑋1	NOUN
cana-835	222	1	=	=	PUNCT
cana-835	222	2	[	[	PUNCT
cana-835	222	3	(	(	PUNCT
cana-835	222	4	(	(	PUNCT
cana-835	222	5	0.5625,1.125,1.6875	0.5625,1.125,1.6875	NUM
cana-835	222	6	)	)	PUNCT
cana-835	222	7	;	;	PUNCT
cana-835	222	8	(	(	PUNCT
cana-835	222	9	0.4875,1.125,1.7625	0.4875,1.125,1.7625	NUM
cana-835	222	10	)	)	PUNCT
cana-835	222	11	)	)	PUNCT
cana-835	222	12	,	,	PUNCT
cana-835	222	13	(	(	PUNCT
cana-835	222	14	(	(	PUNCT
cana-835	222	15	0.6562,1.3125,1.9687	0.6562,1.3125,1.9687	NUM
cana-835	222	16	)	)	PUNCT
cana-835	222	17	;	;	PUNCT
cana-835	222	18	(	(	PUNCT
cana-835	222	19	0.5688,1.3125,2.0563	0.5688,1.3125,2.0563	NUM
cana-835	222	20	)	)	PUNCT
cana-835	222	21	]	]	PUNCT
cana-835	222	22	and	and	CCONJ
cana-835	222	23	𝑌1	𝑌1	NOUN
cana-835	222	24	=	=	PUNCT
cana-835	223	1	[	[	PUNCT
cana-835	223	2	(	(	PUNCT
cana-835	223	3	(	(	PUNCT
cana-835	223	4	0.5625,1.125,1.6875	0.5625,1.125,1.6875	NUM
cana-835	223	5	)	)	PUNCT
cana-835	223	6	;	;	PUNCT
cana-835	223	7	(	(	PUNCT
cana-835	223	8	0.4875,1.125,1.7625	0.4875,1.125,1.7625	NUM
cana-835	223	9	)	)	PUNCT
cana-835	223	10	)	)	PUNCT
cana-835	223	11	,	,	PUNCT
cana-835	223	12	(	(	PUNCT
cana-835	223	13	(	(	PUNCT
cana-835	223	14	0.6562,1.3125,1.9687	0.6562,1.3125,1.9687	NUM
cana-835	223	15	)	)	PUNCT
cana-835	223	16	;	;	PUNCT
cana-835	223	17	(	(	PUNCT
cana-835	223	18	0.5688,1.3125,2.0563	0.5688,1.3125,2.0563	NUM
cana-835	223	19	)	)	PUNCT
cana-835	223	20	]	]	PUNCT
cana-835	224	1	𝑋2	𝑋2	VERB
cana-835	224	2	=	=	X
cana-835	224	3	[	[	PUNCT
cana-835	224	4	(	(	PUNCT
cana-835	224	5	(	(	PUNCT
cana-835	224	6	0.5625,1.125,1.6875	0.5625,1.125,1.6875	NUM
cana-835	224	7	)	)	PUNCT
cana-835	224	8	;	;	PUNCT
cana-835	224	9	(	(	PUNCT
cana-835	224	10	0.4875,1.125,1.7625	0.4875,1.125,1.7625	NUM
cana-835	224	11	)	)	PUNCT
cana-835	224	12	)	)	PUNCT
cana-835	224	13	,	,	PUNCT
cana-835	224	14	(	(	PUNCT
cana-835	224	15	(	(	PUNCT
cana-835	224	16	0.5586,1.1172,1.6758	0.5586,1.1172,1.6758	NUM
cana-835	224	17	)	)	PUNCT
cana-835	224	18	;	;	PUNCT
cana-835	224	19	(	(	PUNCT
cana-835	224	20	0.4841,1.1172,1.7503	0.4841,1.1172,1.7503	NUM
cana-835	224	21	)	)	PUNCT
cana-835	224	22	)	)	PUNCT
cana-835	224	23	]	]	PUNCT
cana-835	225	1	communications	communication	NOUN
cana-835	225	2	on	on	ADP
cana-835	225	3	applied	apply	VERB
cana-835	225	4	nonlinear	nonlinear	ADJ
cana-835	225	5	analysis	analysis	NOUN
cana-835	225	6	issn	issn	NOUN
cana-835	225	7	:	:	PUNCT
cana-835	225	8	1074	1074	NUM
cana-835	225	9	-	-	PUNCT
cana-835	225	10	133x	133x	NUM
cana-835	225	11	vol	vol	NOUN
cana-835	225	12	31	31	NUM
cana-835	225	13	no	no	NOUN
cana-835	225	14	.	.	PUNCT
cana-835	226	1	4s	4s	NUM
cana-835	226	2	(	(	PUNCT
cana-835	226	3	2024	2024	NUM
cana-835	226	4	)	)	PUNCT
cana-835	226	5	194	194	NUM
cana-835	227	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	227	2	𝑌2	𝑌2	NOUN
cana-835	227	3	=	=	PUNCT
cana-835	227	4	[	[	PUNCT
cana-835	227	5	(	(	PUNCT
cana-835	227	6	(	(	PUNCT
cana-835	227	7	0.5625,1.125,1.6875	0.5625,1.125,1.6875	NUM
cana-835	227	8	)	)	PUNCT
cana-835	227	9	;	;	PUNCT
cana-835	227	10	(	(	PUNCT
cana-835	227	11	0.4875,1.125,1.7625	0.4875,1.125,1.7625	NUM
cana-835	227	12	)	)	PUNCT
cana-835	227	13	)	)	PUNCT
cana-835	227	14	,	,	PUNCT
cana-835	227	15	(	(	PUNCT
cana-835	227	16	(	(	PUNCT
cana-835	227	17	0.5586,1.1172,1.6758	0.5586,1.1172,1.6758	NUM
cana-835	227	18	)	)	PUNCT
cana-835	227	19	;	;	PUNCT
cana-835	227	20	(	(	PUNCT
cana-835	227	21	0.4841,1.1172,1.7503	0.4841,1.1172,1.7503	NUM
cana-835	227	22	)	)	PUNCT
cana-835	227	23	)	)	PUNCT
cana-835	227	24	]	]	PUNCT
cana-835	228	1	in	in	ADP
cana-835	228	2	a	a	DET
cana-835	228	3	hypothetical	hypothetical	ADJ
cana-835	228	4	scenario	scenario	NOUN
cana-835	228	5	where	where	SCONJ
cana-835	228	6	x	x	PRON
cana-835	228	7	denotes	denote	VERB
cana-835	228	8	blood	blood	NOUN
cana-835	228	9	pressure	pressure	NOUN
cana-835	228	10	and	and	CCONJ
cana-835	228	11	y	y	PRON
cana-835	228	12	represents	represent	VERB
cana-835	228	13	blood	blood	NOUN
cana-835	228	14	glucose	glucose	NOUN
cana-835	228	15	levels	level	NOUN
cana-835	228	16	,	,	PUNCT
cana-835	228	17	a	a	DET
cana-835	228	18	negative	negative	ADJ
cana-835	228	19	coefficient	coefficient	NOUN
cana-835	228	20	like	like	ADP
cana-835	228	21	-3	-3	PUNCT
cana-835	228	22	implies	imply	VERB
cana-835	228	23	that	that	SCONJ
cana-835	228	24	an	an	DET
cana-835	228	25	increase	increase	NOUN
cana-835	228	26	in	in	ADP
cana-835	228	27	blood	blood	NOUN
cana-835	228	28	pressure	pressure	NOUN
cana-835	228	29	is	be	AUX
cana-835	228	30	associated	associate	VERB
cana-835	228	31	with	with	ADP
cana-835	228	32	a	a	DET
cana-835	228	33	decrease	decrease	NOUN
cana-835	228	34	in	in	ADP
cana-835	228	35	blood	blood	NOUN
cana-835	228	36	glucose	glucose	NOUN
cana-835	228	37	levels	level	NOUN
cana-835	228	38	.	.	PUNCT
cana-835	229	1	this	this	DET
cana-835	229	2	relationship	relationship	NOUN
cana-835	229	3	could	could	AUX
cana-835	229	4	potentially	potentially	ADV
cana-835	229	5	indicate	indicate	VERB
cana-835	229	6	the	the	DET
cana-835	229	7	presence	presence	NOUN
cana-835	229	8	of	of	ADP
cana-835	229	9	a	a	DET
cana-835	229	10	specific	specific	ADJ
cana-835	229	11	medical	medical	ADJ
cana-835	229	12	condition	condition	NOUN
cana-835	229	13	or	or	CCONJ
cana-835	229	14	risk	risk	NOUN
cana-835	229	15	factor	factor	NOUN
cana-835	229	16	that	that	PRON
cana-835	229	17	influences	influence	VERB
cana-835	229	18	both	both	DET
cana-835	229	19	blood	blood	NOUN
cana-835	229	20	pressure	pressure	NOUN
cana-835	229	21	and	and	CCONJ
cana-835	229	22	glucose	glucose	NOUN
cana-835	229	23	levels	level	NOUN
cana-835	229	24	in	in	ADP
cana-835	229	25	this	this	DET
cana-835	229	26	manner	manner	NOUN
cana-835	229	27	.	.	PUNCT
cana-835	230	1	however	however	ADV
cana-835	230	2	,	,	PUNCT
cana-835	230	3	to	to	PART
cana-835	230	4	confirm	confirm	VERB
cana-835	230	5	such	such	DET
cana-835	230	6	a	a	DET
cana-835	230	7	connection	connection	NOUN
cana-835	230	8	,	,	PUNCT
cana-835	230	9	further	further	ADJ
cana-835	230	10	research	research	NOUN
cana-835	230	11	and	and	CCONJ
cana-835	230	12	analysis	analysis	NOUN
cana-835	230	13	involving	involve	VERB
cana-835	230	14	larger	large	ADJ
cana-835	230	15	datasets	dataset	NOUN
cana-835	230	16	and	and	CCONJ
cana-835	230	17	expert	expert	NOUN
cana-835	230	18	input	input	NOUN
cana-835	230	19	would	would	AUX
cana-835	230	20	be	be	AUX
cana-835	230	21	necessary	necessary	ADJ
cana-835	230	22	.	.	PUNCT
cana-835	231	1	5	5	X
cana-835	231	2	.	.	X
cana-835	231	3	conclusion	conclusion	NOUN
cana-835	231	4	the	the	DET
cana-835	231	5	proposed	propose	VERB
cana-835	231	6	paper	paper	NOUN
cana-835	231	7	introduces	introduce	VERB
cana-835	231	8	an	an	DET
cana-835	231	9	innovative	innovative	ADJ
cana-835	231	10	approach	approach	NOUN
cana-835	231	11	to	to	PART
cana-835	231	12	tackle	tackle	VERB
cana-835	231	13	interval	interval	NOUN
cana-835	231	14	-	-	PUNCT
cana-835	231	15	based	base	VERB
cana-835	231	16	intuiti0nistic	intuiti0nistic	ADJ
cana-835	231	17	fuzzy	fuzzy	ADJ
cana-835	231	18	optimization	optimization	NOUN
cana-835	231	19	problems	problem	NOUN
cana-835	231	20	.	.	PUNCT
cana-835	232	1	by	by	ADP
cana-835	232	2	employing	employ	VERB
cana-835	232	3	triangular	triangular	NOUN
cana-835	232	4	interval	interval	NOUN
cana-835	232	5	-	-	PUNCT
cana-835	232	6	valued	value	VERB
cana-835	232	7	fuzzy	fuzzy	ADJ
cana-835	232	8	numbers	number	NOUN
cana-835	232	9	and	and	CCONJ
cana-835	232	10	the	the	DET
cana-835	232	11	interval	interval	NOUN
cana-835	232	12	newt0n	newt0n	PROPN
cana-835	232	13	's	's	PART
cana-835	232	14	meth0d	meth0d	PROPN
cana-835	232	15	,	,	PUNCT
cana-835	232	16	it	it	PRON
cana-835	232	17	aἰm	aἰm	VERB
cana-835	232	18	to	to	PART
cana-835	232	19	provide	provide	VERB
cana-835	232	20	a	a	DET
cana-835	232	21	reliable	reliable	ADJ
cana-835	232	22	solution	solution	NOUN
cana-835	232	23	for	for	ADP
cana-835	232	24	these	these	DET
cana-835	232	25	complex	complex	ADJ
cana-835	232	26	issues	issue	NOUN
cana-835	232	27	.	.	PUNCT
cana-835	233	1	the	the	DET
cana-835	233	2	effectiveness	effectiveness	NOUN
cana-835	233	3	of	of	ADP
cana-835	233	4	this	this	DET
cana-835	233	5	meth0d	meth0d	PROPN
cana-835	233	6	is	be	AUX
cana-835	233	7	demonstrated	demonstrate	VERB
cana-835	233	8	through	through	ADP
cana-835	233	9	the	the	DET
cana-835	233	10	presentation	presentation	NOUN
cana-835	233	11	of	of	ADP
cana-835	233	12	relevant	relevant	ADJ
cana-835	233	13	numerical	numerical	ADJ
cana-835	233	14	examples	example	NOUN
cana-835	233	15	.	.	PUNCT
cana-835	234	1	acknowledgement	acknowledgement	NOUN
cana-835	234	2	the	the	DET
cana-835	234	3	authors	author	NOUN
cana-835	234	4	express	express	VERB
cana-835	234	5	their	their	PRON
cana-835	234	6	gratitude	gratitude	NOUN
cana-835	234	7	to	to	ADP
cana-835	234	8	the	the	DET
cana-835	234	9	unanim0us	unanim0us	PROPN
cana-835	234	10	referees	referee	NOUN
cana-835	234	11	f0r	f0r	VERB
cana-835	235	1	theἰr	theἰr	VERB
cana-835	235	2	valuable	valuable	ADJ
cana-835	235	3	suggestions	suggestion	NOUN
cana-835	235	4	,	,	PUNCT
cana-835	235	5	which	which	PRON
cana-835	235	6	significantly	significantly	ADV
cana-835	235	7	contributed	contribute	VERB
cana-835	235	8	to	to	ADP
cana-835	235	9	enhancing	enhance	VERB
cana-835	235	10	the	the	DET
cana-835	235	11	quality	quality	NOUN
cana-835	235	12	0f	0f	NOUN
cana-835	235	13	their	their	PRON
cana-835	235	14	research	research	NOUN
cana-835	235	15	paper	paper	NOUN
cana-835	235	16	.	.	PUNCT
cana-835	236	1	references	reference	NOUN
cana-835	236	2	[	[	X
cana-835	236	3	1	1	NUM
cana-835	236	4	]	]	X
cana-835	236	5	ben	ben	PROPN
cana-835	236	6	aicha.f	aicha.f	PROPN
cana-835	236	7	.	.	PUNCT
cana-835	236	8	,	,	PUNCT
cana-835	236	9	bouani	bouani	PROPN
cana-835	236	10	,	,	PUNCT
cana-835	236	11	f.and	f.and	NOUN
cana-835	236	12	ksouri	ksouri	NOUN
cana-835	236	13	,	,	PUNCT
cana-835	236	14	m(2013	m(2013	NOUN
cana-835	236	15	)	)	PUNCT
cana-835	236	16	,	,	PUNCT
cana-835	236	17	a	a	DET
cana-835	236	18	multivariable	multivariable	ADJ
cana-835	236	19	multiobjective	multiobjective	ADJ
cana-835	236	20	predictive	predictive	ADJ
cana-835	236	21	controller	controller	NOUN
cana-835	236	22	,	,	PUNCT
cana-835	236	23	international	international	ADJ
cana-835	236	24	journal	journal	NOUN
cana-835	236	25	of	of	ADP
cana-835	236	26	applied	apply	VERB
cana-835	236	27	mathematics	mathematic	NOUN
cana-835	236	28	and	and	CCONJ
cana-835	236	29	computer	computer	NOUN
cana-835	236	30	science,23(1):35	science,23(1):35	NOUN
cana-835	236	31	-	-	SYM
cana-835	236	32	45	45	NUM
cana-835	236	33	,	,	PUNCT
cana-835	236	34	doi:10.2478	doi:10.2478	X
cana-835	236	35	/	/	SYM
cana-835	236	36	amcs-2013	amcs-2013	NOUN
cana-835	236	37	-	-	NOUN
cana-835	236	38	004	004	NOUN
cana-835	236	39	.	.	PUNCT
cana-835	237	1	[	[	X
cana-835	237	2	2	2	NUM
cana-835	237	3	]	]	X
cana-835	237	4	debski	debski	NOUN
cana-835	237	5	,	,	PUNCT
cana-835	237	6	r.(2016	r.(2016	PROPN
cana-835	237	7	)	)	PUNCT
cana-835	237	8	.	.	PUNCT
cana-835	238	1	an	an	DET
cana-835	238	2	adaptive	adaptive	ADJ
cana-835	238	3	multi	multi	ADJ
cana-835	238	4	-	-	ADJ
cana-835	238	5	spline	spline	ADJ
cana-835	238	6	refinement	refinement	NOUN
cana-835	238	7	algorithm	algorithm	NOUN
cana-835	238	8	in	in	ADP
cana-835	238	9	simulation	simulation	NOUN
cana-835	238	10	based	base	VERB
cana-835	238	11	sailboat	sailboat	NOUN
cana-835	238	12	trajectory	trajectory	NOUN
cana-835	238	13	optimization	optimization	NOUN
cana-835	238	14	using	use	VERB
cana-835	238	15	onboard	onboard	ADP
cana-835	238	16	multi	multi	ADJ
cana-835	238	17	-	-	ADJ
cana-835	238	18	core	core	ADJ
cana-835	238	19	computer	computer	NOUN
cana-835	238	20	systems	system	NOUN
cana-835	238	21	,	,	PUNCT
cana-835	238	22	international	international	ADJ
cana-835	238	23	journal	journal	NOUN
cana-835	238	24	of	of	ADP
cana-835	238	25	applied	apply	VERB
cana-835	238	26	mathematics	mathematic	NOUN
cana-835	238	27	and	and	CCONJ
cana-835	238	28	computer	computer	NOUN
cana-835	238	29	science	science	NOUN
cana-835	238	30	.26(2	.26(2	PROPN
cana-835	238	31	):	):	PUNCT
cana-835	238	32	351	351	NUM
cana-835	238	33	-	-	SYM
cana-835	238	34	36	36	NUM
cana-835	238	35	,	,	PUNCT
cana-835	238	36	doi:10.1515	doi:10.1515	NOUN
cana-835	238	37	/	/	SYM
cana-835	238	38	amcs-2016	amcs-2016	NOUN
cana-835	238	39	-	-	PUNCT
cana-835	238	40	0025	0025	NUM
cana-835	238	41	[	[	X
cana-835	238	42	3	3	X
cana-835	238	43	]	]	X
cana-835	238	44	dennis	dennis	PROPN
cana-835	238	45	j.e	j.e	PROPN
cana-835	238	46	,	,	PUNCT
cana-835	238	47	shanable	shanable	ADJ
cana-835	238	48	r.b	r.b	PROPN
cana-835	238	49	.	.	PROPN
cana-835	238	50	,	,	PUNCT
cana-835	238	51	numerical	numerical	ADJ
cana-835	238	52	methods	method	NOUN
cana-835	238	53	for	for	ADP
cana-835	238	54	unconstrained	unconstrained	ADJ
cana-835	238	55	optimization	optimization	NOUN
cana-835	238	56	and	and	CCONJ
cana-835	238	57	non	non	ADJ
cana-835	238	58	linear	linear	PROPN
cana-835	238	59	equations	equation	NOUN
cana-835	238	60	,	,	PUNCT
cana-835	238	61	prentice	prentice	NOUN
cana-835	238	62	hall	hall	PROPN
cana-835	238	63	,	,	PUNCT
cana-835	238	64	newyork	newyork	PROPN
cana-835	238	65	1983	1983	NUM
cana-835	238	66	.	.	PUNCT
cana-835	239	1	[	[	X
cana-835	239	2	4	4	NUM
cana-835	239	3	]	]	X
cana-835	239	4	helmut	helmut	PROPN
cana-835	239	5	ratschek	ratschek	NOUN
cana-835	239	6	,	,	PUNCT
cana-835	239	7	jonr	jonr	ADJ
cana-835	239	8	,	,	PUNCT
cana-835	239	9	“	"	PUNCT
cana-835	239	10	handbook	handbook	NOUN
cana-835	239	11	of	of	ADP
cana-835	239	12	global	global	ADJ
cana-835	239	13	optimization	optimization	NOUN
cana-835	239	14	”	"	PUNCT
cana-835	239	15	,	,	PUNCT
cana-835	239	16	springer	springer	NOUN
cana-835	239	17	science	science	PROPN
cana-835	239	18	business	business	NOUN
cana-835	239	19	media	medium	NOUN
cana-835	239	20	dordreecht	dordreecht	NOUN
cana-835	239	21	,	,	PUNCT
cana-835	239	22	1995	1995	NUM
cana-835	239	23	,	,	PUNCT
cana-835	239	24	pp	pp	ADP
cana-835	239	25	751	751	NUM
cana-835	239	26	-	-	SYM
cana-835	239	27	828	828	NUM
cana-835	239	28	.	.	PUNCT
cana-835	240	1	[	[	X
cana-835	240	2	5	5	NUM
cana-835	240	3	]	]	SYM
cana-835	240	4	irene	irene	PROPN
cana-835	240	5	hepzibah	hepzibah	PROPN
cana-835	240	6	.	.	PUNCT
cana-835	240	7	,r	,r	PUNCT
cana-835	240	8	.	.	PUNCT
cana-835	240	9	,shilpa	,shilpa	PUNCT
cana-835	240	10	ivin	ivin	PROPN
cana-835	240	11	emimal(2022	emimal(2022	PROPN
cana-835	240	12	)	)	PUNCT
cana-835	240	13	,	,	PUNCT
cana-835	240	14	”	"	PUNCT
cana-835	240	15	solving	solve	VERB
cana-835	240	16	fuzzy	fuzzy	ADJ
cana-835	240	17	unconstrained	unconstraine	VERB
cana-835	240	18	optimization	optimization	NOUN
cana-835	240	19	problems	problem	NOUN
cana-835	240	20	using	use	VERB
cana-835	240	21	interval	interval	PROPN
cana-835	240	22	newton	newton	PROPN
cana-835	240	23	’s	’s	PART
cana-835	240	24	method	method	PROPN
cana-835	240	25	”	"	PUNCT
cana-835	240	26	,	,	PUNCT
cana-835	240	27	advances	advance	NOUN
cana-835	240	28	and	and	CCONJ
cana-835	240	29	applications	application	NOUN
cana-835	240	30	in	in	ADP
cana-835	240	31	mathematical	mathematical	ADJ
cana-835	240	32	sciences	science	NOUN
cana-835	240	33	,	,	PUNCT
cana-835	240	34	volume	volume	NOUN
cana-835	240	35	21	21	NUM
cana-835	240	36	,	,	PUNCT
cana-835	240	37	issue	issue	NOUN
cana-835	240	38	3	3	NUM
cana-835	240	39	,	,	PUNCT
cana-835	240	40	january	january	PROPN
cana-835	240	41	2022	2022	NUM
cana-835	240	42	,	,	PUNCT
cana-835	240	43	pages	page	NOUN
cana-835	240	44	1463	1463	NUM
cana-835	240	45	-	-	SYM
cana-835	240	46	1477	1477	NUM
cana-835	240	47	©	©	PROPN
cana-835	240	48	2022	2022	NUM
cana-835	240	49	mili	mili	PROPN
cana-835	240	50	publications	publication	NOUN
cana-835	240	51	,	,	PUNCT
cana-835	240	52	india	india	PROPN
cana-835	240	53	.	.	PUNCT
cana-835	241	1	[	[	X
cana-835	241	2	6	6	NUM
cana-835	241	3	]	]	PUNCT
cana-835	241	4	karl	karl	PROPN
cana-835	241	5	nickel	nickel	PROPN
cana-835	241	6	,	,	PUNCT
cana-835	241	7	“	"	PUNCT
cana-835	241	8	on	on	ADP
cana-835	241	9	the	the	DET
cana-835	241	10	newton	newton	PROPN
cana-835	241	11	method	method	NOUN
cana-835	241	12	in	in	ADP
cana-835	241	13	interval	interval	NOUN
cana-835	241	14	analysis	analysis	NOUN
cana-835	241	15	”	"	PUNCT
cana-835	241	16	,	,	PUNCT
cana-835	241	17	the	the	DET
cana-835	241	18	university	university	NOUN
cana-835	241	19	of	of	ADP
cana-835	241	20	wiscosin	wiscosin	NOUN
cana-835	241	21	mathematics	mathematics	PROPN
cana-835	241	22	research	research	NOUN
cana-835	241	23	centre	centre	NOUN
cana-835	241	24	,	,	PUNCT
cana-835	241	25	1970	1970	NUM
cana-835	241	26	[	[	X
cana-835	241	27	7	7	X
cana-835	241	28	]	]	X
cana-835	241	29	nagoor	nagoor	PROPN
cana-835	241	30	gani.a	gani.a	PROPN
cana-835	241	31	and	and	CCONJ
cana-835	241	32	s.n.mohamed	s.n.mohame	VERB
cana-835	241	33	assarudeen	assarudeen	VERB
cana-835	241	34	,	,	PUNCT
cana-835	241	35	“	"	PUNCT
cana-835	241	36	a	a	DET
cana-835	241	37	new	new	ADJ
cana-835	241	38	operation	operation	NOUN
cana-835	241	39	on	on	ADP
cana-835	241	40	triangular	triangular	NOUN
cana-835	241	41	fuzzy	fuzzy	ADJ
cana-835	241	42	number	number	NOUN
cana-835	241	43	for	for	ADP
cana-835	241	44	solving	solve	VERB
cana-835	241	45	fuzzy	fuzzy	ADJ
cana-835	241	46	linear	linear	ADJ
cana-835	241	47	programming	programming	NOUN
cana-835	241	48	problem	problem	NOUN
cana-835	241	49	”	"	PUNCT
cana-835	241	50	,	,	PUNCT
cana-835	241	51	applied	apply	VERB
cana-835	241	52	mathematics	mathematic	NOUN
cana-835	241	53	and	and	CCONJ
cana-835	241	54	sciences	science	NOUN
cana-835	241	55	,	,	PUNCT
cana-835	241	56	vol.6,2012	vol.6,2012	PROPN
cana-835	241	57	,	,	PUNCT
cana-835	241	58	no.11,525	no.11,525	PROPN
cana-835	241	59	-	-	SYM
cana-835	241	60	532	532	NUM
cana-835	241	61	.	.	PUNCT
cana-835	242	1	[	[	X
cana-835	242	2	8	8	NUM
cana-835	242	3	]	]	X
cana-835	242	4	sophia	sophia	PROPN
cana-835	242	5	porchelvi	porchelvi	PROPN
cana-835	242	6	.	.	PUNCT
cana-835	243	1	r	r	NOUN
cana-835	243	2	,	,	PUNCT
cana-835	243	3	sathya	sathya	PROPN
cana-835	243	4	.s	.s	PROPN
cana-835	243	5	,	,	PUNCT
cana-835	243	6	on	on	ADP
cana-835	243	7	solving	solve	VERB
cana-835	243	8	bivariate	bivariate	ADJ
cana-835	243	9	unconstrained	unconstrained	ADJ
cana-835	243	10	optimization	optimization	NOUN
cana-835	243	11	problems	problem	NOUN
cana-835	243	12	using	use	VERB
cana-835	243	13	interval	interval	NOUN
cana-835	243	14	analysis	analysis	NOUN
cana-835	243	15	,	,	PUNCT
cana-835	243	16	international	international	ADJ
cana-835	243	17	journal	journal	NOUN
cana-835	243	18	of	of	ADP
cana-835	243	19	science	science	NOUN
cana-835	243	20	and	and	CCONJ
cana-835	243	21	research	research	NOUN
cana-835	243	22	(	(	PUNCT
cana-835	243	23	ijsr	ijsr	PROPN
cana-835	243	24	)	)	PUNCT
cana-835	243	25	india	india	PROPN
cana-835	243	26	online	online	PROPN
cana-835	243	27	,	,	PUNCT
cana-835	243	28	issn	issn	PROPN
cana-835	243	29	:	:	PUNCT
cana-835	243	30	2319	2319	NUM
cana-835	243	31	-7064	-7064	PROPN
cana-835	243	32	,	,	PUNCT
cana-835	243	33	volume	volume	NOUN
cana-835	243	34	2	2	NUM
cana-835	243	35	,	,	PUNCT
cana-835	243	36	issue	issue	NOUN
cana-835	243	37	1	1	NUM
cana-835	243	38	,	,	PUNCT
cana-835	243	39	2013	2013	NUM
cana-835	243	40	page	page	NOUN
cana-835	244	1	no	no	DET
cana-835	244	2	:	:	PUNCT
cana-835	244	3	726	726	NUM
cana-835	244	4	–	–	PUNCT
cana-835	244	5	729	729	NUM
cana-835	244	6	.	.	PUNCT
cana-835	245	1	[	[	X
cana-835	245	2	9	9	NUM
cana-835	245	3	]	]	X
cana-835	245	4	shashi	shashi	PROPN
cana-835	245	5	kant	kant	PROPN
cana-835	245	6	mishra	mishra	PROPN
cana-835	245	7	,	,	PUNCT
cana-835	245	8	bhagwat	bhagwat	NOUN
cana-835	245	9	ram	ram	NOUN
cana-835	245	10	,	,	PUNCT
cana-835	245	11	introduction	introduction	NOUN
cana-835	245	12	to	to	ADP
cana-835	245	13	unconstrained	unconstrained	ADJ
cana-835	245	14	optimization	optimization	NOUN
cana-835	245	15	in	in	ADP
cana-835	245	16	r	r	NOUN
cana-835	245	17	,	,	PUNCT
cana-835	245	18	springer	springer	NOUN
cana-835	245	19	2019	2019	NUM
cana-835	245	20	.	.	PUNCT
cana-835	246	1	[	[	X
cana-835	246	2	10	10	NUM
cana-835	246	3	]	]	X
cana-835	246	4	t.c.e	t.c.e	PROPN
cana-835	246	5	cheng	cheng	PROPN
cana-835	246	6	,	,	PUNCT
cana-835	246	7	mikhail	mikhail	PROPN
cana-835	246	8	y.kovalyov	y.kovalyov	NOUN
cana-835	246	9	(	(	PUNCT
cana-835	246	10	2002	2002	NUM
cana-835	246	11	)	)	PUNCT
cana-835	246	12	,	,	PUNCT
cana-835	246	13	an	an	DET
cana-835	246	14	unconstrained	unconstrained	ADJ
cana-835	246	15	optimization	optimization	NOUN
cana-835	246	16	problem	problem	NOUN
cana-835	246	17	is	be	AUX
cana-835	246	18	np	np	INTJ
cana-835	246	19	-	-	PUNCT
cana-835	246	20	hard	hard	ADV
cana-835	246	21	given	give	VERB
cana-835	246	22	an	an	DET
cana-835	246	23	oracle	oracle	NOUN
cana-835	246	24	representation	representation	NOUN
cana-835	246	25	of	of	ADP
cana-835	246	26	its	its	PRON
cana-835	246	27	objective	objective	ADJ
cana-835	246	28	function	function	NOUN
cana-835	246	29	:	:	PUNCT
cana-835	246	30	a	a	DET
cana-835	246	31	technical	technical	ADJ
cana-835	246	32	note	note	NOUN
cana-835	246	33	,	,	PUNCT
cana-835	246	34	computer	computer	NOUN
cana-835	246	35	&	&	CCONJ
cana-835	246	36	operations	operations	PROPN
cana-835	246	37	research	research	NOUN
cana-835	246	38	,	,	PUNCT
cana-835	246	39	volume	volume	NOUN
cana-835	246	40	29,issue	29,issue	NUM
cana-835	246	41	14	14	NUM
cana-835	246	42	,	,	PUNCT
cana-835	246	43	pages-2087	pages-2087	NOUN
cana-835	246	44	-	-	PUNCT
cana-835	246	45	2091	2091	NUM
cana-835	246	46	.	.	PUNCT
cana-835	247	1	[	[	X
cana-835	247	2	11	11	NUM
cana-835	247	3	]	]	X
cana-835	247	4	timothy	timothy	PROPN
cana-835	247	5	,	,	PUNCT
cana-835	247	6	j.r.(2010	j.r.(2010	PROPN
cana-835	247	7	)	)	PUNCT
cana-835	247	8	,	,	PUNCT
cana-835	247	9	fuzzy	fuzzy	ADJ
cana-835	247	10	logic	logic	NOUN
cana-835	247	11	with	with	ADP
cana-835	247	12	engineering	engineering	NOUN
cana-835	247	13	applications	application	NOUN
cana-835	247	14	,	,	PUNCT
cana-835	247	15	3rd	3rd	ADJ
cana-835	247	16	edition	edition	NOUN
cana-835	247	17	.	.	PUNCT
cana-835	247	18	,	,	PUNCT
cana-835	247	19	wiley	wiley	PROPN
cana-835	247	20	,	,	PUNCT
cana-835	247	21	new	new	PROPN
cana-835	247	22	york	york	PROPN
cana-835	247	23	,	,	PUNCT
cana-835	247	24	ny	ny	PROPN
cana-835	247	25	.	.	PUNCT
cana-835	248	1	[	[	X
cana-835	248	2	12	12	NUM
cana-835	248	3	]	]	SYM
cana-835	248	4	tyrrell.r	tyrrell.r	NUM
cana-835	248	5	,	,	PUNCT
cana-835	248	6	“	"	PUNCT
cana-835	248	7	a	a	DET
cana-835	248	8	dual	dual	ADJ
cana-835	248	9	approach	approach	NOUN
cana-835	248	10	to	to	ADP
cana-835	248	11	solving	solve	VERB
cana-835	248	12	nonlinear	nonlinear	ADJ
cana-835	248	13	programming	programming	NOUN
cana-835	248	14	problems	problem	NOUN
cana-835	248	15	by	by	ADP
cana-835	248	16	unconstrained	unconstrained	ADJ
cana-835	248	17	optimization”,mathematical	optimization”,mathematical	ADJ
cana-835	248	18	programming	programming	PROPN
cana-835	248	19	series	series	PROPN
cana-835	248	20	b	b	PROPN
cana-835	248	21	,	,	PUNCT
cana-835	248	22	springer	springer	NOUN
cana-835	248	23	volume	volume	NOUN
cana-835	248	24	5	5	NUM
cana-835	248	25	,	,	PUNCT
cana-835	248	26	page	page	NOUN
cana-835	248	27	no;354	no;354	NOUN
cana-835	248	28	-	-	PUNCT
cana-835	248	29	3733	3733	NUM
cana-835	248	30	,	,	PUNCT
cana-835	248	31	1973	1973	NUM
cana-835	248	32	.	.	PUNCT
cana-835	249	1	https://link.springer.com/chapter/10.1007/978-1-4615-2025-2_14#auth-helmut-ratschek	https://link.springer.com/chapter/10.1007/978-1-4615-2025-2_14#auth-helmut-ratschek	PROPN
cana-835	249	2	communications	communication	NOUN
cana-835	249	3	on	on	ADP
cana-835	249	4	applied	apply	VERB
cana-835	249	5	nonlinear	nonlinear	ADJ
cana-835	249	6	analysis	analysis	NOUN
cana-835	249	7	issn	issn	NOUN
cana-835	249	8	:	:	PUNCT
cana-835	249	9	1074	1074	NUM
cana-835	249	10	-	-	PUNCT
cana-835	249	11	133x	133x	NUM
cana-835	249	12	vol	vol	NOUN
cana-835	249	13	31	31	NUM
cana-835	249	14	no	no	NOUN
cana-835	249	15	.	.	PUNCT
cana-835	250	1	4s	4s	NUM
cana-835	250	2	(	(	PUNCT
cana-835	250	3	2024	2024	NUM
cana-835	250	4	)	)	PUNCT
cana-835	250	5	195	195	NUM
cana-835	250	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-835	251	1	[	[	X
cana-835	251	2	13	13	NUM
cana-835	251	3	]	]	SYM
cana-835	251	4	umamaheshwari.p	umamaheshwari.p	NOUN
cana-835	251	5	,	,	PUNCT
cana-835	251	6	ganesan.k	ganesan.k	PROPN
cana-835	251	7	,	,	PUNCT
cana-835	251	8	a	a	DET
cana-835	251	9	comparative	comparative	ADJ
cana-835	251	10	solution	solution	NOUN
cana-835	251	11	of	of	ADP
cana-835	251	12	fuzzy	fuzzy	ADJ
cana-835	251	13	unconstrained	unconstraine	VERB
cana-835	251	14	optimization	optimization	NOUN
cana-835	251	15	problems	problem	NOUN
cana-835	251	16	with	with	ADP
cana-835	251	17	triangular	triangular	NOUN
cana-835	251	18	fuzzy	fuzzy	ADJ
cana-835	251	19	number	number	NOUN
cana-835	251	20	,	,	PUNCT
cana-835	251	21	journal	journal	NOUN
cana-835	251	22	xidian	xidian	PROPN
cana-835	251	23	university	university	PROPN
cana-835	251	24	,	,	PUNCT
cana-835	251	25	issn	issn	PROPN
cana-835	251	26	no	no	PRON
cana-835	251	27	:	:	PUNCT
cana-835	251	28	1001	1001	NUM
cana-835	251	29	-	-	SYM
cana-835	251	30	2400,volume	2400,volume	NUM
cana-835	251	31	14	14	NUM
cana-835	251	32	,	,	PUNCT
cana-835	251	33	issue	issue	NOUN
cana-835	251	34	6	6	NUM
cana-835	251	35	,	,	PUNCT
cana-835	251	36	2020	2020	NUM
cana-835	251	37	-	-	SYM
cana-835	251	38	1443	1443	NUM
cana-835	251	39	-	-	PUNCT
cana-835	251	40	1455	1455	NUM
cana-835	251	41	.	.	PUNCT
cana-835	252	1	[	[	X
cana-835	252	2	14	14	NUM
cana-835	252	3	]	]	PUNCT
cana-835	252	4	umamaheshwari.p	umamaheshwari.p	NOUN
cana-835	252	5	,	,	PUNCT
cana-835	252	6	ganesan.k	ganesan.k	PROPN
cana-835	252	7	,	,	PUNCT
cana-835	252	8	a	a	DET
cana-835	252	9	solution	solution	NOUN
cana-835	252	10	approach	approach	NOUN
cana-835	252	11	to	to	ADP
cana-835	252	12	fuzzy	fuzzy	ADJ
cana-835	252	13	nonlinear	nonlinear	ADJ
cana-835	252	14	programming	programming	NOUN
cana-835	252	15	problems	problem	NOUN
cana-835	252	16	,	,	PUNCT
cana-835	252	17	international	international	ADJ
cana-835	252	18	journal	journal	NOUN
cana-835	252	19	of	of	ADP
cana-835	252	20	pure	pure	ADJ
cana-835	252	21	and	and	CCONJ
cana-835	252	22	applied	applied	ADJ
cana-835	252	23	mathematics	mathematic	NOUN
cana-835	252	24	,	,	PUNCT
cana-835	252	25	volume	volume	NOUN
cana-835	252	26	113	113	NUM
cana-835	252	27	no.13,2017,pg.no.291	no.13,2017,pg.no.291	PROPN
cana-835	252	28	-	-	PUNCT
cana-835	252	29	300,issn	300,issn	NUM
cana-835	252	30	1311	1311	NUM
cana-835	252	31	-	-	SYM
cana-835	252	32	8080	8080	NUM
cana-835	252	33	.	.	PUNCT
cana-835	253	1	[	[	X
cana-835	253	2	15	15	NUM
cana-835	253	3	]	]	PUNCT
cana-835	253	4	ved	ve	VERB
cana-835	253	5	p.	p.	PROPN
cana-835	253	6	madan	madan	PROPN
cana-835	253	7	,	,	PUNCT
cana-835	253	8	“	"	PUNCT
cana-835	253	9	interval	interval	NOUN
cana-835	253	10	newton	newton	PROPN
cana-835	253	11	method	method	PROPN
cana-835	253	12	:	:	PUNCT
cana-835	253	13	hansen	hansen	PROPN
cana-835	253	14	-	-	PUNCT
cana-835	253	15	greenberg	greenberg	PROPN
cana-835	253	16	approach	approach	NOUN
cana-835	253	17	—	—	PUNCT
cana-835	253	18	some	some	DET
cana-835	253	19	procedural	procedural	ADJ
cana-835	253	20	improvements	improvement	NOUN
cana-835	253	21	”	"	PUNCT
cana-835	253	22	,	,	PUNCT
cana-835	253	23	applied	apply	VERB
cana-835	253	24	mathematics	mathematic	NOUN
cana-835	253	25	and	and	CCONJ
cana-835	253	26	computation	computation	NOUN
cana-835	253	27	,	,	PUNCT
cana-835	253	28	volume	volume	NOUN
cana-835	253	29	35	35	NUM
cana-835	253	30	,	,	PUNCT
cana-835	253	31	issue	issue	NOUN
cana-835	253	32	3	3	NUM
cana-835	253	33	,	,	PUNCT
cana-835	253	34	february	february	PROPN
cana-835	253	35	1990	1990	NUM
cana-835	253	36	,	,	PUNCT
cana-835	253	37	pages	page	NOUN
cana-835	253	38	263	263	NUM
cana-835	253	39	-	-	SYM
cana-835	253	40	276	276	NUM
cana-835	253	41	,	,	PUNCT
cana-835	253	42	https://doi.org/10.1016/00963003(90)90046-6,1990	https://doi.org/10.1016/00963003(90)90046-6,1990	X
cana-835	254	1	[	[	X
cana-835	254	2	16	16	NUM
cana-835	254	3	]	]	PUNCT
cana-835	254	4	veermalai.g	veermalai.g	PUNCT
cana-835	254	5	,	,	PUNCT
cana-835	254	6	sundarraj	sundarraj	VERB
cana-835	254	7	.	.	PUNCT
cana-835	255	1	r.j	r.j	NOUN
cana-835	255	2	,	,	PUNCT
cana-835	255	3	single	single	ADJ
cana-835	255	4	variable	variable	ADJ
cana-835	255	5	unconstrained	unconstraine	VERB
cana-835	255	6	optimization	optimization	NOUN
cana-835	255	7	techniques	technique	NOUN
cana-835	255	8	using	use	VERB
cana-835	255	9	interval	interval	NOUN
cana-835	255	10	analysis	analysis	NOUN
cana-835	255	11	,	,	PUNCT
cana-835	255	12	iosr	iosr	ADJ
cana-835	255	13	journal	journal	NOUN
cana-835	255	14	of	of	ADP
cana-835	255	15	mathematics	mathematics	PROPN
cana-835	255	16	issn	issn	PROPN
cana-835	255	17	:	:	PUNCT
cana-835	255	18	2278	2278	NUM
cana-835	255	19	-	-	SYM
cana-835	255	20	5728,volume	5728,volume	NUM
cana-835	255	21	3	3	NUM
cana-835	255	22	,	,	PUNCT
cana-835	255	23	issue	issue	NOUN
cana-835	255	24	3	3	NUM
cana-835	255	25	,	,	PUNCT
cana-835	255	26	2012	2012	NUM
cana-835	255	27	page	page	NOUN
cana-835	255	28	no	no	DET
cana-835	255	29	30	30	NUM
cana-835	255	30	–	–	PUNCT
cana-835	255	31	34	34	NUM
cana-835	255	32	.	.	PUNCT
cana-835	256	1	[	[	X
cana-835	256	2	17	17	NUM
cana-835	256	3	]	]	PUNCT
cana-835	256	4	veeramalai	veeramalai	PROPN
cana-835	256	5	g	g	PROPN
cana-835	256	6	,	,	PUNCT
cana-835	256	7	gajendran.p	gajendran.p	PROPN
cana-835	256	8	,	,	PUNCT
cana-835	256	9	a	a	DET
cana-835	256	10	new	new	ADJ
cana-835	256	11	approach	approach	NOUN
cana-835	256	12	to	to	ADP
cana-835	256	13	solving	solve	VERB
cana-835	256	14	fuzzy	fuzzy	ADJ
cana-835	256	15	linear	linear	ADJ
cana-835	256	16	system	system	NOUN
cana-835	256	17	with	with	ADP
cana-835	256	18	interval	interval	NOUN
cana-835	256	19	valued	value	VERB
cana-835	256	20	triangular	triangular	NOUN
cana-835	256	21	fuzzy	fuzzy	ADJ
cana-835	256	22	number	number	NOUN
cana-835	256	23	,	,	PUNCT
cana-835	256	24	indian	indian	ADJ
cana-835	256	25	scholar	scholar	NOUN
cana-835	256	26	an	an	DET
cana-835	256	27	international	international	ADJ
cana-835	256	28	multidisciplinary	multidisciplinary	ADJ
cana-835	256	29	research	research	NOUN
cana-835	256	30	e	e	NOUN
cana-835	256	31	-	-	NOUN
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cana-835	256	33	,	,	PUNCT
cana-835	256	34	issn	issn	PROPN
cana-835	256	35	:	:	PUNCT
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cana-835	256	37	-	-	PUNCT
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cana-835	256	40	-2	-2	PROPN
cana-835	256	41	,	,	PUNCT
cana-835	256	42	issue	issue	NOUN
cana-835	256	43	iii	iii	NOUN
cana-835	256	44	,	,	PUNCT
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cana-835	256	46	-	-	SYM
cana-835	256	47	38	38	NUM
cana-835	256	48	.	.	PUNCT
cana-835	257	1	[	[	X
cana-835	257	2	18	18	NUM
cana-835	257	3	]	]	PUNCT
cana-835	257	4	vidhya	vidhya	PROPN
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cana-835	257	9	,	,	PUNCT
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cana-835	257	11	comparative	comparative	ADJ
cana-835	257	12	study	study	NOUN
cana-835	257	13	on	on	ADP
cana-835	257	14	interval	interval	NOUN
cana-835	257	15	arithmetic	arithmetic	ADJ
cana-835	257	16	operations	operation	NOUN
cana-835	257	17	with	with	ADP
cana-835	257	18	intuitionistic	intuitionistic	ADJ
cana-835	257	19	fuzzy	fuzzy	ADJ
cana-835	257	20	numbers	number	NOUN
cana-835	257	21	for	for	ADP
cana-835	257	22	solving	solve	VERB
cana-835	257	23	an	an	DET
cana-835	257	24	intuitionistic	intuitionistic	ADJ
cana-835	257	25	fuzzy	fuzzy	ADJ
cana-835	257	26	multi	multi	ADJ
cana-835	257	27	-	-	ADJ
cana-835	257	28	objective	objective	ADJ
cana-835	257	29	linear	linear	ADJ
cana-835	257	30	programming	programming	NOUN
cana-835	257	31	problems	problem	NOUN
cana-835	257	32	,	,	PUNCT
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cana-835	257	34	journal	journal	NOUN
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cana-835	257	39	computer	computer	NOUN
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cana-835	257	41	,	,	PUNCT
cana-835	257	42	volume	volume	NOUN
cana-835	257	43	27	27	NUM
cana-835	257	44	,	,	PUNCT
cana-835	257	45	no	no	DET
cana-835	257	46	3	3	NUM
cana-835	257	47	,	,	PUNCT
cana-835	257	48	563	563	NUM
cana-835	257	49	-	-	SYM
cana-835	257	50	573.doi:10.1515	573.doi:10.1515	NUM
cana-835	257	51	/	/	SYM
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cana-835	257	53	-	-	PUNCT
cana-835	257	54	0040	0040	NUM
cana-835	257	55	.	.	PUNCT
cana-835	258	1	[	[	X
cana-835	258	2	19	19	NUM
cana-835	258	3	]	]	X
cana-835	258	4	zadeh	zadeh	PROPN
cana-835	258	5	,	,	PUNCT
cana-835	258	6	l.a	l.a	PROPN
cana-835	258	7	,	,	PUNCT
cana-835	258	8	1965.fuzzy	1965.fuzzy	NUM
cana-835	258	9	sets	set	NOUN
cana-835	258	10	,	,	PUNCT
cana-835	258	11	information	information	NOUN
cana-835	258	12	and	and	CCONJ
cana-835	258	13	control	control	NOUN
cana-835	258	14	8:338	8:338	NUM
cana-835	258	15	-	-	SYM
cana-835	258	16	353	353	NUM
cana-835	258	17	.	.	PUNCT
cana-835	259	1	[	[	X
cana-835	259	2	20	20	NUM
cana-835	259	3	]	]	X
cana-835	259	4	zadeh	zadeh	PROPN
cana-835	259	5	l.a	l.a	PROPN
cana-835	259	6	,	,	PUNCT
cana-835	259	7	1975	1975	NUM
cana-835	259	8	.	.	PUNCT
cana-835	260	1	the	the	DET
cana-835	260	2	concept	concept	NOUN
cana-835	260	3	of	of	ADP
cana-835	260	4	a	a	DET
cana-835	260	5	linguistic	linguistic	ADJ
cana-835	260	6	variable	variable	NOUN
cana-835	260	7	and	and	CCONJ
cana-835	260	8	its	its	PRON
cana-835	260	9	application	application	NOUN
cana-835	260	10	to	to	PART
cana-835	260	11	approximate	approximate	ADJ
cana-835	260	12	reasoning	reasoning	NOUN
cana-835	260	13	–	–	PUNCT
cana-835	260	14	1	1	NUM
cana-835	260	15	,	,	PUNCT
cana-835	260	16	information	information	NOUN
cana-835	260	17	sciences	sciences	PROPN
cana-835	260	18	8:199	8:199	NUM
cana-835	260	19	-	-	SYM
cana-835	260	20	249	249	NUM
cana-835	260	21	.	.	PUNCT
cana-835	261	1	[	[	X
cana-835	261	2	21	21	NUM
cana-835	261	3	]	]	X
cana-835	261	4	zhen	zhen	PROPN
cana-835	261	5	-	-	PUNCT
cana-835	261	6	jue	jue	PROPN
cana-835	261	7	shi,(2004	shi,(2004	PROPN
cana-835	261	8	)	)	PUNCT
cana-835	261	9	.	.	PUNCT
cana-835	262	1	convergence	convergence	NOUN
cana-835	262	2	of	of	ADP
cana-835	262	3	line	line	NOUN
cana-835	262	4	search	search	NOUN
cana-835	262	5	methods	method	NOUN
cana-835	262	6	for	for	ADP
cana-835	262	7	unconstrained	unconstrained	ADJ
cana-835	262	8	optimization	optimization	NOUN
cana-835	262	9	,	,	PUNCT
cana-835	262	10	applied	apply	VERB
cana-835	262	11	mathematics	mathematic	NOUN
cana-835	262	12	and	and	CCONJ
cana-835	262	13	computation	computation	NOUN
cana-835	262	14	,	,	PUNCT
cana-835	262	15	volume	volume	NOUN
cana-835	262	16	157	157	NUM
cana-835	262	17	,	,	PUNCT
cana-835	262	18	issue	issue	VERB
cana-835	262	19	2,pages	2,page	NOUN
cana-835	262	20	393	393	NUM
cana-835	262	21	-	-	SYM
cana-835	262	22	405	405	NUM
cana-835	262	23	.	.	PUNCT
cana-835	263	1	https://www.sciencedirect.com/journal/applied-mathematics-and-computation	https://www.sciencedirect.com/journal/applied-mathematics-and-computation	NOUN
cana-835	263	2	https://www.sciencedirect.com/journal/applied-mathematics-and-computation	https://www.sciencedirect.com/journal/applied-mathematics-and-computation	NOUN
cana-835	263	3	https://www.sciencedirect.com/journal/applied-mathematics-and-computation/vol/35/issue/3	https://www.sciencedirect.com/journal/applied-mathematics-and-computation/vol/35/issue/3	NOUN