id	sid	tid	token	lemma	pos
cana-1750	1	1	communications	communication	NOUN
cana-1750	1	2	on	on	ADP
cana-1750	1	3	applied	apply	VERB
cana-1750	1	4	nonlinear	nonlinear	ADJ
cana-1750	1	5	analysis	analysis	NOUN
cana-1750	1	6	issn	issn	NOUN
cana-1750	1	7	:	:	PUNCT
cana-1750	1	8	1074	1074	NUM
cana-1750	1	9	-	-	PUNCT
cana-1750	1	10	133x	133x	NUM
cana-1750	1	11	vol	vol	NOUN
cana-1750	1	12	32	32	NUM
cana-1750	1	13	no	no	NOUN
cana-1750	1	14	.	.	NOUN
cana-1750	1	15	2	2	NUM
cana-1750	1	16	(	(	PUNCT
cana-1750	1	17	2025	2025	NUM
cana-1750	1	18	)	)	PUNCT
cana-1750	1	19	383	383	NUM
cana-1750	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	1	21	toeplitz	toeplitz	NOUN
cana-1750	1	22	matrices	matrix	NOUN
cana-1750	1	23	whose	whose	DET
cana-1750	1	24	elements	element	NOUN
cana-1750	1	25	are	be	AUX
cana-1750	1	26	coefficients	coefficient	NOUN
cana-1750	1	27	of	of	ADP
cana-1750	1	28	new	new	ADJ
cana-1750	1	29	subclasses	subclass	NOUN
cana-1750	1	30	of	of	ADP
cana-1750	1	31	analytical	analytical	ADJ
cana-1750	1	32	functions	function	NOUN
cana-1750	1	33	m.	m.	NOUN
cana-1750	1	34	nandeesh1	nandeesh1	PROPN
cana-1750	1	35	,	,	PUNCT
cana-1750	1	36	m.	m.	NOUN
cana-1750	1	37	ruby	ruby	PROPN
cana-1750	1	38	salestina2	salestina2	PROPN
cana-1750	1	39	,	,	PUNCT
cana-1750	1	40	archana3	archana3	PROPN
cana-1750	1	41	,	,	PUNCT
cana-1750	1	42	g.	g.	PROPN
cana-1750	1	43	murugusundaramoorthy	murugusundaramoorthy	PROPN
cana-1750	2	1	𝟒	𝟒	NUM
cana-1750	2	2	*	*	PUNCT
cana-1750	2	3	(	(	PUNCT
cana-1750	2	4	nandeesh	nandeesh	NOUN
cana-1750	2	5	.m	.m	PROPN
cana-1750	2	6	)	)	PUNCT
cana-1750	2	7	1	1	NUM
cana-1750	2	8	,	,	PUNCT
cana-1750	2	9	department	department	NOUN
cana-1750	2	10	of	of	ADP
cana-1750	2	11	mathematics	mathematic	NOUN
cana-1750	2	12	,	,	PUNCT
cana-1750	2	13	bharathi	bharathi	PROPN
cana-1750	2	14	college	college	PROPN
cana-1750	2	15	(	(	PUNCT
cana-1750	2	16	autonomous	autonomous	ADJ
cana-1750	2	17	)	)	PUNCT
cana-1750	2	18	,	,	PUNCT
cana-1750	2	19	bharathinagara	bharathinagara	PROPN
cana-1750	2	20	,	,	PUNCT
cana-1750	2	21	maddur	maddur	PROPN
cana-1750	2	22	taluk	taluk	PROPN
cana-1750	2	23	,	,	PUNCT
cana-1750	2	24	mandya	mandya	PROPN
cana-1750	2	25	district	district	PROPN
cana-1750	2	26	,	,	PUNCT
cana-1750	2	27	karnataka	karnataka	PROPN
cana-1750	2	28	,	,	PUNCT
cana-1750	2	29	india	india	PROPN
cana-1750	2	30	571422	571422	NUM
cana-1750	2	31	.	.	PUNCT
cana-1750	3	1	e	e	X
cana-1750	3	2	-	-	NOUN
cana-1750	3	3	mail	mail	NOUN
cana-1750	3	4	address	address	NOUN
cana-1750	3	5	:	:	PUNCT
cana-1750	3	6	nandeesh02@gmail.com	nandeesh02@gmail.com	X
cana-1750	3	7	;	;	PUNCT
cana-1750	3	8	http://orcid.org/0009-0003-3389-8929	http://orcid.org/0009-0003-3389-8929	NOUN
cana-1750	3	9	.	.	PUNCT
cana-1750	4	1	(	(	PUNCT
cana-1750	4	2	ruby	ruby	PROPN
cana-1750	4	3	salestina	salestina	PROPN
cana-1750	4	4	.m	.m	PROPN
cana-1750	4	5	)	)	PUNCT
cana-1750	4	6	2	2	NUM
cana-1750	4	7	,	,	PUNCT
cana-1750	4	8	department	department	NOUN
cana-1750	4	9	of	of	ADP
cana-1750	4	10	mathematics	mathematics	PROPN
cana-1750	4	11	,	,	PUNCT
cana-1750	4	12	yuvaraja	yuvaraja	NOUN
cana-1750	4	13	's	's	PART
cana-1750	4	14	college	college	NOUN
cana-1750	4	15	,	,	PUNCT
cana-1750	4	16	university	university	NOUN
cana-1750	4	17	of	of	ADP
cana-1750	4	18	mysore	mysore	NOUN
cana-1750	4	19	,	,	PUNCT
cana-1750	4	20	mysuru	mysuru	PROPN
cana-1750	4	21	,	,	PUNCT
cana-1750	4	22	karnataka	karnataka	PROPN
cana-1750	4	23	,	,	PUNCT
cana-1750	4	24	india	india	PROPN
cana-1750	4	25	570005	570005	NUM
cana-1750	4	26	.	.	PUNCT
cana-1750	5	1	e	e	X
cana-1750	5	2	-	-	NOUN
cana-1750	5	3	mail	mail	NOUN
cana-1750	5	4	address	address	NOUN
cana-1750	5	5	:	:	PUNCT
cana-1750	5	6	ruby.salestina@gmail.com	ruby.salestina@gmail.com	X
cana-1750	5	7	;	;	PUNCT
cana-1750	5	8	http://orcid.org/0000-0002-3318-2061	http://orcid.org/0000-0002-3318-2061	NOUN
cana-1750	5	9	.	.	PUNCT
cana-1750	6	1	(	(	PUNCT
cana-1750	6	2	archana	archana	PROPN
cana-1750	6	3	)	)	PUNCT
cana-1750	6	4	3	3	NUM
cana-1750	6	5	,	,	PUNCT
cana-1750	6	6	department	department	NOUN
cana-1750	6	7	of	of	ADP
cana-1750	6	8	mathematics	mathematic	NOUN
cana-1750	6	9	,	,	PUNCT
cana-1750	6	10	bharathi	bharathi	PROPN
cana-1750	6	11	college	college	PROPN
cana-1750	6	12	(	(	PUNCT
cana-1750	6	13	autonomous	autonomous	ADJ
cana-1750	6	14	)	)	PUNCT
cana-1750	6	15	,	,	PUNCT
cana-1750	6	16	bharathinagara	bharathinagara	PROPN
cana-1750	6	17	,	,	PUNCT
cana-1750	6	18	maddur	maddur	PROPN
cana-1750	6	19	taluk	taluk	PROPN
cana-1750	6	20	,	,	PUNCT
cana-1750	6	21	mandya	mandya	PROPN
cana-1750	6	22	district	district	PROPN
cana-1750	6	23	,	,	PUNCT
cana-1750	6	24	karnataka	karnataka	PROPN
cana-1750	6	25	,	,	PUNCT
cana-1750	6	26	india	india	PROPN
cana-1750	6	27	–	–	PUNCT
cana-1750	6	28	571422	571422	NUM
cana-1750	6	29	e	e	X
cana-1750	6	30	-	-	NOUN
cana-1750	6	31	mail	mail	NOUN
cana-1750	6	32	address	address	NOUN
cana-1750	6	33	:	:	PUNCT
cana-1750	6	34	archanap6005@gmail.com	archanap6005@gmail.com	X
cana-1750	6	35	.	.	PUNCT
cana-1750	7	1	(	(	PUNCT
cana-1750	7	2	g.	g.	NOUN
cana-1750	7	3	murugusundaramoorthy	murugusundaramoorthy	PROPN
cana-1750	7	4	)	)	PUNCT
cana-1750	7	5	4	4	NUM
cana-1750	7	6	＊	＊	PROPN
cana-1750	7	7	department	department	PROPN
cana-1750	7	8	of	of	ADP
cana-1750	7	9	mathematics	mathematic	NOUN
cana-1750	7	10	,	,	PUNCT
cana-1750	7	11	school	school	NOUN
cana-1750	7	12	of	of	ADP
cana-1750	7	13	advanced	advanced	ADJ
cana-1750	7	14	science	science	NOUN
cana-1750	7	15	,	,	PUNCT
cana-1750	7	16	vellore	vellore	PROPN
cana-1750	7	17	institute	institute	PROPN
cana-1750	7	18	of	of	ADP
cana-1750	7	19	technology	technology	PROPN
cana-1750	7	20	,	,	PUNCT
cana-1750	7	21	vellore	vellore	NOUN
cana-1750	7	22	,	,	PUNCT
cana-1750	7	23	tamil	tamil	PROPN
cana-1750	7	24	nadu	nadu	PROPN
cana-1750	7	25	,	,	PUNCT
cana-1750	7	26	india	india	PROPN
cana-1750	7	27	632014	632014	NUM
cana-1750	7	28	.	.	PUNCT
cana-1750	8	1	e	e	X
cana-1750	8	2	-	-	NOUN
cana-1750	8	3	mail	mail	NOUN
cana-1750	8	4	address	address	NOUN
cana-1750	8	5	:	:	PUNCT
cana-1750	8	6	gmsmoorthy@yahoo.com	gmsmoorthy@yahoo.com	X
cana-1750	8	7	;	;	PUNCT
cana-1750	8	8	http://orcid.org/0000-0001-8285-6619	http://orcid.org/0000-0001-8285-6619	PROPN
cana-1750	8	9	.	.	PUNCT
cana-1750	9	1	article	article	NOUN
cana-1750	9	2	history	history	NOUN
cana-1750	9	3	:	:	PUNCT
cana-1750	9	4	received	receive	VERB
cana-1750	9	5	:	:	PUNCT
cana-1750	9	6	03	03	NUM
cana-1750	9	7	-	-	SYM
cana-1750	9	8	08	08	NUM
cana-1750	9	9	-	-	PUNCT
cana-1750	9	10	2024	2024	NUM
cana-1750	9	11	revised	revise	VERB
cana-1750	9	12	:	:	PUNCT
cana-1750	9	13	10	10	NUM
cana-1750	9	14	-	-	SYM
cana-1750	9	15	09	09	NUM
cana-1750	9	16	-	-	PUNCT
cana-1750	9	17	2024	2024	NUM
cana-1750	9	18	accepted	accept	VERB
cana-1750	9	19	:	:	PUNCT
cana-1750	9	20	20	20	NUM
cana-1750	9	21	-	-	SYM
cana-1750	9	22	09	09	NUM
cana-1750	9	23	-	-	PUNCT
cana-1750	9	24	2024	2024	NUM
cana-1750	9	25	abstract	abstract	NOUN
cana-1750	9	26	:	:	PUNCT
cana-1750	9	27	in	in	ADP
cana-1750	9	28	this	this	DET
cana-1750	9	29	study	study	NOUN
cana-1750	9	30	,	,	PUNCT
cana-1750	9	31	we	we	PRON
cana-1750	9	32	explore	explore	VERB
cana-1750	9	33	toeplitz	toeplitz	NOUN
cana-1750	9	34	matrices	matrix	NOUN
cana-1750	9	35	composed	compose	VERB
cana-1750	9	36	of	of	ADP
cana-1750	9	37	coefficients	coefficient	NOUN
cana-1750	9	38	from	from	ADP
cana-1750	9	39	new	new	ADJ
cana-1750	9	40	subclasses	subclass	NOUN
cana-1750	9	41	and	and	CCONJ
cana-1750	9	42	establish	establish	VERB
cana-1750	9	43	upper	upper	ADJ
cana-1750	9	44	limits	limit	NOUN
cana-1750	9	45	for	for	ADP
cana-1750	9	46	the	the	DET
cana-1750	9	47	initial	initial	ADJ
cana-1750	9	48	four	four	NUM
cana-1750	9	49	determinants	determinant	NOUN
cana-1750	9	50	like	like	ADP
cana-1750	9	51	of	of	ADP
cana-1750	9	52	these	these	DET
cana-1750	9	53	matrices	matrix	NOUN
cana-1750	9	54	.	.	PUNCT
cana-1750	10	1	our	our	PRON
cana-1750	10	2	findings	finding	NOUN
cana-1750	10	3	are	be	AUX
cana-1750	10	4	innovative	innovative	ADJ
cana-1750	10	5	and	and	CCONJ
cana-1750	10	6	unique	unique	ADJ
cana-1750	10	7	,	,	PUNCT
cana-1750	10	8	with	with	ADP
cana-1750	10	9	the	the	DET
cana-1750	10	10	only	only	ADJ
cana-1750	10	11	similar	similar	ADJ
cana-1750	10	12	results	result	NOUN
cana-1750	10	13	being	be	AUX
cana-1750	10	14	in	in	ADP
cana-1750	10	15	recent	recent	ADJ
cana-1750	10	16	works	work	NOUN
cana-1750	10	17	by	by	ADP
cana-1750	10	18	thomas	thomas	PROPN
cana-1750	10	19	and	and	CCONJ
cana-1750	10	20	halim	halim	PROPN
cana-1750	11	1	[	[	X
cana-1750	11	2	1	1	NUM
cana-1750	11	3	]	]	PUNCT
cana-1750	11	4	,	,	PUNCT
cana-1750	11	5	which	which	PRON
cana-1750	11	6	pertain	pertain	VERB
cana-1750	11	7	to	to	ADP
cana-1750	11	8	starlike	starlike	NOUN
cana-1750	11	9	and	and	CCONJ
cana-1750	11	10	close	close	ADJ
cana-1750	11	11	to	to	ADP
cana-1750	11	12	convex	convex	NOUN
cana-1750	11	13	functions	function	NOUN
cana-1750	11	14	,	,	PUNCT
cana-1750	11	15	and	and	CCONJ
cana-1750	11	16	by	by	ADP
cana-1750	11	17	radhika	radhika	PROPN
cana-1750	11	18	et	et	PROPN
cana-1750	11	19	al	al	PROPN
cana-1750	11	20	.	.	PUNCT
cana-1750	12	1	[	[	X
cana-1750	12	2	2	2	NUM
cana-1750	12	3	]	]	PUNCT
cana-1750	12	4	,	,	PUNCT
cana-1750	12	5	focusing	focus	VERB
cana-1750	12	6	on	on	ADP
cana-1750	12	7	functions	function	NOUN
cana-1750	12	8	with	with	ADP
cana-1750	12	9	bounded	bounded	ADJ
cana-1750	12	10	boundary	boundary	ADJ
cana-1750	12	11	rotation	rotation	NOUN
cana-1750	12	12	.	.	PUNCT
cana-1750	13	1	along	along	ADP
cana-1750	13	2	with	with	ADP
cana-1750	13	3	we	we	PRON
cana-1750	13	4	have	have	AUX
cana-1750	13	5	determined	determine	VERB
cana-1750	13	6	the	the	DET
cana-1750	13	7	zalcman	zalcman	PROPN
cana-1750	13	8	,	,	PUNCT
cana-1750	13	9	generalized	generalized	ADJ
cana-1750	13	10	zalcman	zalcman	NOUN
cana-1750	13	11	conjecture	conjecture	NOUN
cana-1750	13	12	and	and	CCONJ
cana-1750	13	13	krushkal	krushkal	ADJ
cana-1750	13	14	inequalities	inequality	NOUN
cana-1750	13	15	for	for	ADP
cana-1750	13	16	some	some	DET
cana-1750	13	17	parameters	parameter	NOUN
cana-1750	13	18	.	.	PUNCT
cana-1750	14	1	keywords	keyword	NOUN
cana-1750	14	2	:	:	PUNCT
cana-1750	14	3	star	star	NOUN
cana-1750	14	4	-	-	PUNCT
cana-1750	14	5	like	like	ADJ
cana-1750	14	6	function	function	NOUN
cana-1750	14	7	,	,	PUNCT
cana-1750	14	8	convex	convex	NOUN
cana-1750	14	9	function	function	NOUN
cana-1750	14	10	,	,	PUNCT
cana-1750	14	11	coefficient	coefficient	NOUN
cana-1750	14	12	bounds	bound	NOUN
cana-1750	14	13	,	,	PUNCT
cana-1750	14	14	univalent	univalent	ADJ
cana-1750	14	15	functions	function	NOUN
cana-1750	14	16	,	,	PUNCT
cana-1750	14	17	toeplitz	toeplitz	NOUN
cana-1750	14	18	matrices	matrix	NOUN
cana-1750	14	19	,	,	PUNCT
cana-1750	14	20	hankel	hankel	NOUN
cana-1750	14	21	determinants	determinant	NOUN
cana-1750	14	22	,	,	PUNCT
cana-1750	14	23	zalcman	zalcman	NOUN
cana-1750	14	24	conjecture	conjecture	NOUN
cana-1750	14	25	,	,	PUNCT
cana-1750	14	26	generalized	generalized	ADJ
cana-1750	14	27	zalcman	zalcman	NOUN
cana-1750	14	28	conjecture	conjecture	NOUN
cana-1750	14	29	and	and	CCONJ
cana-1750	14	30	krushkal	krushkal	ADJ
cana-1750	14	31	inequalities	inequality	NOUN
cana-1750	14	32	.	.	PUNCT
cana-1750	15	1	keywords	keyword	NOUN
cana-1750	15	2	:	:	PUNCT
cana-1750	15	3	star	star	NOUN
cana-1750	15	4	like	like	ADP
cana-1750	15	5	function	function	NOUN
cana-1750	15	6	,	,	PUNCT
cana-1750	15	7	convex	convex	NOUN
cana-1750	15	8	function	function	NOUN
cana-1750	15	9	,	,	PUNCT
cana-1750	15	10	coefficient	coefficient	NOUN
cana-1750	15	11	bounds	bound	NOUN
cana-1750	15	12	,	,	PUNCT
cana-1750	15	13	univalent	univalent	ADJ
cana-1750	15	14	functions	function	NOUN
cana-1750	15	15	,	,	PUNCT
cana-1750	15	16	toeplitz	toeplitz	NOUN
cana-1750	15	17	matrices	matrix	NOUN
cana-1750	15	18	,	,	PUNCT
cana-1750	15	19	hankel	hankel	NOUN
cana-1750	15	20	determinants	determinant	NOUN
cana-1750	15	21	,	,	PUNCT
cana-1750	15	22	zalcman	zalcman	NOUN
cana-1750	15	23	conjecture	conjecture	NOUN
cana-1750	15	24	,	,	PUNCT
cana-1750	15	25	generalized	generalized	ADJ
cana-1750	15	26	zalcman	zalcman	NOUN
cana-1750	15	27	conjecture	conjecture	NOUN
cana-1750	15	28	and	and	CCONJ
cana-1750	15	29	krushkal	krushkal	ADJ
cana-1750	15	30	inequalities	inequality	NOUN
cana-1750	15	31	.	.	PUNCT
cana-1750	16	1	msc	msc	PROPN
cana-1750	16	2	(	(	PUNCT
cana-1750	16	3	2010	2010	NUM
cana-1750	16	4	):	):	PUNCT
cana-1750	16	5	30c45	30c45	NUM
cana-1750	16	6	,	,	PUNCT
cana-1750	16	7	33c50	33c50	NUM
cana-1750	16	8	,	,	PUNCT
cana-1750	16	9	30c80	30c80	NUM
cana-1750	16	10	.	.	NOUN
cana-1750	17	1	1	1	X
cana-1750	17	2	.	.	X
cana-1750	17	3	introduction	introduction	NOUN
cana-1750	17	4	hankel	hankel	NOUN
cana-1750	17	5	matrices	matrix	NOUN
cana-1750	17	6	(	(	PUNCT
cana-1750	17	7	and	and	CCONJ
cana-1750	17	8	their	their	PRON
cana-1750	17	9	determinants	determinant	NOUN
cana-1750	17	10	)	)	PUNCT
cana-1750	17	11	hold	hold	VERB
cana-1750	17	12	significant	significant	ADJ
cana-1750	17	13	importance	importance	NOUN
cana-1750	17	14	in	in	ADP
cana-1750	17	15	various	various	ADJ
cana-1750	17	16	mathematical	mathematical	ADJ
cana-1750	17	17	fields	field	NOUN
cana-1750	17	18	and	and	CCONJ
cana-1750	17	19	find	find	VERB
cana-1750	17	20	numerous	numerous	ADJ
cana-1750	17	21	practical	practical	ADJ
cana-1750	17	22	uses	use	NOUN
cana-1750	17	23	.	.	PUNCT
cana-1750	18	1	a	a	DET
cana-1750	18	2	closely	closely	ADV
cana-1750	18	3	related	relate	VERB
cana-1750	18	4	concept	concept	NOUN
cana-1750	18	5	to	to	PART
cana-1750	18	6	hankel	hankel	NOUN
cana-1750	18	7	determinants	determinant	NOUN
cana-1750	18	8	is	be	AUX
cana-1750	18	9	the	the	DET
cana-1750	18	10	toeplitz	toeplitz	NOUN
cana-1750	18	11	determinants	determinant	NOUN
cana-1750	18	12	.	.	PUNCT
cana-1750	19	1	essentially	essentially	ADV
cana-1750	19	2	,	,	PUNCT
cana-1750	19	3	a	a	DET
cana-1750	19	4	toeplitz	toeplitz	NOUN
cana-1750	19	5	matrix	matrix	NOUN
cana-1750	19	6	can	can	AUX
cana-1750	19	7	be	be	AUX
cana-1750	19	8	likened	liken	VERB
cana-1750	19	9	to	to	ADP
cana-1750	19	10	an	an	DET
cana-1750	19	11	inverted	inverted	ADJ
cana-1750	19	12	hankel	hankel	NOUN
cana-1750	19	13	matrix	matrix	NOUN
cana-1750	19	14	,	,	PUNCT
cana-1750	19	15	as	as	SCONJ
cana-1750	19	16	hankel	hankel	NOUN
cana-1750	19	17	matrices	matrix	NOUN
cana-1750	19	18	have	have	VERB
cana-1750	19	19	constant	constant	ADJ
cana-1750	19	20	entries	entry	NOUN
cana-1750	19	21	along	along	ADP
cana-1750	19	22	their	their	PRON
cana-1750	19	23	reverse	reverse	ADJ
cana-1750	19	24	diagonal	diagonal	NOUN
cana-1750	19	25	,	,	PUNCT
cana-1750	19	26	while	while	SCONJ
cana-1750	19	27	toeplitz	toeplitz	NOUN
cana-1750	19	28	matrices	matrix	NOUN
cana-1750	19	29	maintain	maintain	VERB
cana-1750	19	30	constant	constant	ADJ
cana-1750	19	31	entries	entry	NOUN
cana-1750	19	32	along	along	ADP
cana-1750	19	33	their	their	PRON
cana-1750	19	34	diagonal	diagonal	NOUN
cana-1750	19	35	.	.	PUNCT
cana-1750	20	1	a	a	DET
cana-1750	20	2	comprehensive	comprehensive	ADJ
cana-1750	20	3	overview	overview	NOUN
cana-1750	20	4	of	of	ADP
cana-1750	20	5	the	the	DET
cana-1750	20	6	applications	application	NOUN
cana-1750	20	7	of	of	ADP
cana-1750	20	8	toeplitz	toeplitz	NOUN
cana-1750	20	9	matrices	matrix	NOUN
cana-1750	20	10	in	in	ADP
cana-1750	20	11	both	both	CCONJ
cana-1750	20	12	pure	pure	ADJ
cana-1750	20	13	and	and	CCONJ
cana-1750	20	14	applied	applied	ADJ
cana-1750	20	15	mathematics	mathematic	NOUN
cana-1750	20	16	can	can	AUX
cana-1750	20	17	also	also	ADV
cana-1750	20	18	be	be	AUX
cana-1750	20	19	located	locate	VERB
cana-1750	20	20	in	in	ADP
cana-1750	20	21	reference	reference	NOUN
cana-1750	20	22	[	[	X
cana-1750	20	23	7	7	NUM
cana-1750	20	24	]	]	PUNCT
cana-1750	20	25	.	.	PUNCT
cana-1750	21	1	they	they	PRON
cana-1750	21	2	possess	possess	VERB
cana-1750	21	3	excellent	excellent	ADJ
cana-1750	21	4	computational	computational	ADJ
cana-1750	21	5	properties	property	NOUN
cana-1750	21	6	and	and	CCONJ
cana-1750	21	7	are	be	AUX
cana-1750	21	8	compatible	compatible	ADJ
cana-1750	21	9	with	with	ADP
cana-1750	21	10	a	a	DET
cana-1750	21	11	wide	wide	ADJ
cana-1750	21	12	range	range	NOUN
cana-1750	21	13	of	of	ADP
cana-1750	21	14	algorithms	algorithm	NOUN
cana-1750	21	15	and	and	CCONJ
cana-1750	21	16	determinant	determinant	ADJ
cana-1750	21	17	computations	computation	NOUN
cana-1750	21	18	.	.	PUNCT
cana-1750	22	1	let	let	VERB
cana-1750	22	2	𝓐	𝓐	NOUN
cana-1750	22	3	signify	signify	VERB
cana-1750	22	4	the	the	DET
cana-1750	22	5	class	class	NOUN
cana-1750	22	6	of	of	ADP
cana-1750	22	7	functions	function	NOUN
cana-1750	22	8	of	of	ADP
cana-1750	22	9	the	the	DET
cana-1750	22	10	form	form	NOUN
cana-1750	22	11	mailto:nandeesh02@gmail.com	mailto:nandeesh02@gmail.com	NOUN
cana-1750	22	12	http://orcid.org/0009-0003-3389-8929	http://orcid.org/0009-0003-3389-8929	PROPN
cana-1750	22	13	mailto:ruby.salestina@gmail.com	mailto:ruby.salestina@gmail.com	X
cana-1750	22	14	http://orcid.org/0000-0002-3318-20619	http://orcid.org/0000-0002-3318-20619	VERB
cana-1750	22	15	mailto:archanap6005@gmail.com	mailto:archanap6005@gmail.com	X
cana-1750	22	16	mailto:gmsmoorthy@yahoo.com	mailto:gmsmoorthy@yahoo.com	PROPN
cana-1750	22	17	communications	communication	NOUN
cana-1750	22	18	on	on	ADP
cana-1750	22	19	applied	apply	VERB
cana-1750	22	20	nonlinear	nonlinear	ADJ
cana-1750	22	21	analysis	analysis	NOUN
cana-1750	22	22	issn	issn	NOUN
cana-1750	22	23	:	:	PUNCT
cana-1750	22	24	1074	1074	NUM
cana-1750	22	25	-	-	PUNCT
cana-1750	22	26	133x	133x	NUM
cana-1750	22	27	vol	vol	NOUN
cana-1750	22	28	32	32	NUM
cana-1750	22	29	no	no	NOUN
cana-1750	22	30	.	.	NOUN
cana-1750	22	31	2	2	NUM
cana-1750	22	32	(	(	PUNCT
cana-1750	22	33	2025	2025	NUM
cana-1750	22	34	)	)	PUNCT
cana-1750	22	35	384	384	NUM
cana-1750	22	36	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	22	37	𝑓(𝑧	𝑓(𝑧	PROPN
cana-1750	22	38	)	)	PUNCT
cana-1750	22	39	=	=	PUNCT
cana-1750	23	1	𝑧	𝑧	PRON
cana-1750	24	1	+	+	ADJ
cana-1750	24	2	∑	∑	PROPN
cana-1750	24	3	  	  	SPACE
cana-1750	24	4	∞	∞	PROPN
cana-1750	24	5	𝑛=2	𝑛=2	PROPN
cana-1750	24	6	 	 	SPACE
cana-1750	24	7	𝑑𝑛𝑧	𝑑𝑛𝑧	ADJ
cana-1750	24	8	𝑛.	𝑛.	NOUN
cana-1750	24	9	(	(	PUNCT
cana-1750	24	10	1.1	1.1	NUM
cana-1750	24	11	)	)	PUNCT
cana-1750	24	12	which	which	PRON
cana-1750	24	13	are	be	AUX
cana-1750	24	14	analytic	analytic	ADJ
cana-1750	24	15	in	in	ADP
cana-1750	24	16	the	the	DET
cana-1750	24	17	open	open	ADJ
cana-1750	24	18	unit	unit	NOUN
cana-1750	24	19	disk	disk	NOUN
cana-1750	24	20	𝔻	𝔻	NOUN
cana-1750	24	21	=	=	SYM
cana-1750	24	22	{	{	PUNCT
cana-1750	24	23	𝑧	𝑧	NOUN
cana-1750	24	24	:	:	PUNCT
cana-1750	24	25	𝑧	𝑧	DET
cana-1750	24	26	∈	∈	PROPN
cana-1750	24	27	ℂ	ℂ	PROPN
cana-1750	24	28	and	and	CCONJ
cana-1750	24	29	|𝑧|	|𝑧|	VERB
cana-1750	24	30	<	<	X
cana-1750	24	31	1	1	NUM
cana-1750	24	32	}	}	PUNCT
cana-1750	24	33	.	.	PUNCT
cana-1750	25	1	further	far	ADV
cana-1750	25	2	,	,	PUNCT
cana-1750	25	3	represent	represent	VERB
cana-1750	25	4	by	by	ADP
cana-1750	25	5	𝒮	𝒮	PROPN
cana-1750	25	6	the	the	DET
cana-1750	25	7	class	class	NOUN
cana-1750	25	8	of	of	ADP
cana-1750	25	9	all	all	DET
cana-1750	25	10	functions	function	NOUN
cana-1750	25	11	in	in	ADP
cana-1750	25	12	𝓐	𝓐	PRON
cana-1750	25	13	which	which	PRON
cana-1750	25	14	are	be	AUX
cana-1750	25	15	univalent	univalent	ADJ
cana-1750	25	16	in	in	ADP
cana-1750	25	17	𝔻	𝔻	PROPN
cana-1750	25	18	and	and	CCONJ
cana-1750	25	19	normalized	normalize	VERB
cana-1750	25	20	by	by	ADP
cana-1750	25	21	𝑓(0	𝑓(0	PROPN
cana-1750	25	22	)	)	PUNCT
cana-1750	25	23	=	=	SYM
cana-1750	26	1	0	0	PUNCT
cana-1750	27	1	=	=	SYM
cana-1750	27	2	𝑓′(0	𝑓′(0	PROPN
cana-1750	27	3	)	)	PUNCT
cana-1750	27	4	−	−	PROPN
cana-1750	28	1	1	1	X
cana-1750	28	2	.	.	PUNCT
cana-1750	28	3	also	also	ADV
cana-1750	28	4	,	,	PUNCT
cana-1750	28	5	an	an	DET
cana-1750	28	6	significant	significant	ADJ
cana-1750	28	7	class	class	NOUN
cana-1750	28	8	of	of	ADP
cana-1750	28	9	functions	function	NOUN
cana-1750	28	10	will	will	AUX
cana-1750	28	11	be	be	AUX
cana-1750	28	12	called	call	VERB
cana-1750	28	13	𝒫,𝒫	𝒫,𝒫	NOUN
cana-1750	28	14	defines	define	VERB
cana-1750	28	15	the	the	DET
cana-1750	28	16	family	family	NOUN
cana-1750	28	17	of	of	ADP
cana-1750	28	18	functions	function	NOUN
cana-1750	28	19	𝜙	𝜙	NOUN
cana-1750	28	20	with	with	ADP
cana-1750	28	21	the	the	DET
cana-1750	28	22	limitations	limitation	NOUN
cana-1750	28	23	that	that	SCONJ
cana-1750	28	24	the	the	DET
cana-1750	28	25	image	image	NOUN
cana-1750	28	26	domain	domain	NOUN
cana-1750	28	27	of	of	ADP
cana-1750	28	28	𝜙	𝜙	PROPN
cana-1750	28	29	(	(	PUNCT
cana-1750	28	30	𝜙	𝜙	PROPN
cana-1750	28	31	𝑖𝑠	𝑖𝑠	CCONJ
cana-1750	28	32	𝑎	𝑎	PRON
cana-1750	28	33	𝑐onvex	𝑐onvex	NOUN
cana-1750	28	34	function	function	NOUN
cana-1750	28	35	𝑤𝑖𝑡ℎ	𝑤𝑖𝑡ℎ	PROPN
cana-1750	28	36	𝑅𝑒(𝜙	𝑅𝑒(𝜙	PROPN
cana-1750	28	37	)	)	PUNCT
cana-1750	28	38	>	>	X
cana-1750	28	39	0	0	PUNCT
cana-1750	28	40	in	in	ADP
cana-1750	28	41	𝔻.	𝔻.	PROPN
cana-1750	28	42	)	)	PUNCT
cana-1750	28	43	is	be	AUX
cana-1750	28	44	symmetric	symmetric	ADJ
cana-1750	28	45	along	along	ADP
cana-1750	28	46	the	the	DET
cana-1750	28	47	real	real	ADJ
cana-1750	28	48	axis	axis	NOUN
cana-1750	28	49	and	and	CCONJ
cana-1750	28	50	star	star	NOUN
cana-1750	28	51	like	like	INTJ
cana-1750	28	52	about	about	ADP
cana-1750	28	53	𝜙(0	𝜙(0	NOUN
cana-1750	28	54	)	)	PUNCT
cana-1750	28	55	=	=	SYM
cana-1750	28	56	1	1	NUM
cana-1750	28	57	with	with	ADP
cana-1750	28	58	𝜙′(0	𝜙′(0	NOUN
cana-1750	28	59	)	)	PUNCT
cana-1750	28	60	>	>	X
cana-1750	29	1	0	0	X
cana-1750	29	2	.	.	PUNCT
cana-1750	30	1	we	we	PRON
cana-1750	30	2	say	say	VERB
cana-1750	30	3	that	that	SCONJ
cana-1750	30	4	for	for	ADP
cana-1750	30	5	𝑓1	𝑓1	ADJ
cana-1750	30	6	,	,	PUNCT
cana-1750	30	7	𝑓2	𝑓2	PROPN
cana-1750	30	8	∈	∈	PROPN
cana-1750	30	9	𝒜	𝒜	NOUN
cana-1750	30	10	,	,	PUNCT
cana-1750	30	11	an	an	DET
cana-1750	30	12	𝑓1	𝑓1	PROPN
cana-1750	30	13	is	be	AUX
cana-1750	30	14	subordinate	subordinate	ADJ
cana-1750	30	15	to	to	ADP
cana-1750	30	16	𝑓2	𝑓2	NOUN
cana-1750	30	17	and	and	CCONJ
cana-1750	30	18	write	write	VERB
cana-1750	30	19	𝑓1(𝑧	𝑓1(𝑧	NOUN
cana-1750	30	20	)	)	PUNCT
cana-1750	30	21	≺	≺	NOUN
cana-1750	30	22	𝑓2(𝑧	𝑓2(𝑧	NOUN
cana-1750	30	23	)	)	PUNCT
cana-1750	30	24	,	,	PUNCT
cana-1750	30	25	if	if	SCONJ
cana-1750	30	26	and	and	CCONJ
cana-1750	30	27	only	only	ADV
cana-1750	30	28	if	if	SCONJ
cana-1750	30	29	there	there	PRON
cana-1750	30	30	exists	exist	VERB
cana-1750	30	31	𝑤	𝑤	ADP
cana-1750	30	32	,	,	PUNCT
cana-1750	30	33	analytic	analytic	ADJ
cana-1750	30	34	in	in	ADP
cana-1750	30	35	𝔻	𝔻	PROPN
cana-1750	30	36	,	,	PUNCT
cana-1750	30	37	such	such	ADJ
cana-1750	30	38	that	that	SCONJ
cana-1750	30	39	𝑤(0	𝑤(0	NOUN
cana-1750	30	40	)	)	PUNCT
cana-1750	30	41	=	=	SYM
cana-1750	30	42	0	0	NUM
cana-1750	30	43	,	,	PUNCT
cana-1750	30	44	|𝑤(𝑧)|	|𝑤(𝑧)|	PROPN
cana-1750	30	45	<	<	X
cana-1750	30	46	1	1	NUM
cana-1750	30	47	for	for	ADP
cana-1750	30	48	|𝑧|	|𝑧|	PROPN
cana-1750	30	49	<	<	X
cana-1750	30	50	1	1	NUM
cana-1750	30	51	and	and	CCONJ
cana-1750	30	52	𝑓1(𝑧	𝑓1(𝑧	ADJ
cana-1750	30	53	)	)	PUNCT
cana-1750	30	54	=	=	SYM
cana-1750	30	55	𝑓2(𝑤(𝑧	𝑓2(𝑤(𝑧	NOUN
cana-1750	30	56	)	)	PUNCT
cana-1750	30	57	)	)	PUNCT
cana-1750	30	58	.	.	PUNCT
cana-1750	31	1	in	in	ADP
cana-1750	31	2	particular	particular	ADJ
cana-1750	31	3	,	,	PUNCT
cana-1750	31	4	if	if	SCONJ
cana-1750	31	5	𝑓2	𝑓2	NOUN
cana-1750	31	6	is	be	AUX
cana-1750	31	7	univalent	univalent	ADJ
cana-1750	31	8	in	in	ADP
cana-1750	31	9	𝔻	𝔻	PROPN
cana-1750	31	10	,	,	PUNCT
cana-1750	31	11	then	then	ADV
cana-1750	31	12	we	we	PRON
cana-1750	31	13	have	have	VERB
cana-1750	31	14	the	the	DET
cana-1750	31	15	following	follow	VERB
cana-1750	31	16	equivalence	equivalence	NOUN
cana-1750	31	17	:	:	PUNCT
cana-1750	31	18	𝑓1(𝑧	𝑓1(𝑧	ADJ
cana-1750	31	19	)	)	PUNCT
cana-1750	31	20	≺	≺	NOUN
cana-1750	31	21	𝑓2(𝑧	𝑓2(𝑧	NOUN
cana-1750	31	22	)	)	PUNCT
cana-1750	31	23	⟺	⟺	PRON
cana-1750	31	24	𝑓1(0	𝑓1(0	PROPN
cana-1750	31	25	)	)	PUNCT
cana-1750	31	26	=	=	SYM
cana-1750	31	27	𝑓2(0	𝑓2(0	NOUN
cana-1750	31	28	)	)	PUNCT
cana-1750	31	29	and	and	CCONJ
cana-1750	31	30	𝑓1(|𝑧|	𝑓1(|𝑧|	ADV
cana-1750	31	31	<	<	X
cana-1750	31	32	1	1	NUM
cana-1750	31	33	)	)	PUNCT
cana-1750	31	34	⊂	⊂	NOUN
cana-1750	31	35	𝑓2(|𝑧|	𝑓2(|𝑧|	ADV
cana-1750	31	36	<	<	X
cana-1750	31	37	1	1	NUM
cana-1750	31	38	)	)	PUNCT
cana-1750	31	39	.	.	PUNCT
cana-1750	32	1	(	(	PUNCT
cana-1750	32	2	1.2	1.2	NUM
cana-1750	32	3	)	)	PUNCT
cana-1750	32	4	two	two	NUM
cana-1750	32	5	of	of	ADP
cana-1750	32	6	the	the	DET
cana-1750	32	7	most	most	ADV
cana-1750	32	8	important	important	ADJ
cana-1750	32	9	and	and	CCONJ
cana-1750	32	10	well	well	ADV
cana-1750	32	11	investigated	investigate	VERB
cana-1750	32	12	subclass	subclass	NOUN
cana-1750	32	13	of	of	ADP
cana-1750	32	14	univalent	univalent	ADJ
cana-1750	32	15	functions	function	NOUN
cana-1750	32	16	are	be	AUX
cana-1750	32	17	the	the	DET
cana-1750	32	18	class	class	NOUN
cana-1750	32	19	𝒮∗(𝛼	𝒮∗(𝛼	NOUN
cana-1750	32	20	)	)	PUNCT
cana-1750	32	21	is	be	AUX
cana-1750	32	22	the	the	DET
cana-1750	32	23	class	class	NOUN
cana-1750	32	24	star	star	NOUN
cana-1750	32	25	like	like	ADP
cana-1750	32	26	functions	function	NOUN
cana-1750	32	27	of	of	ADP
cana-1750	32	28	order	order	NOUN
cana-1750	32	29	𝛼	𝛼	NOUN
cana-1750	32	30	,	,	PUNCT
cana-1750	32	31	(	(	PUNCT
cana-1750	32	32	0	0	NUM
cana-1750	32	33	≤	≤	NUM
cana-1750	32	34	𝛼	𝛼	X
cana-1750	32	35	<	<	X
cana-1750	32	36	1	1	NUM
cana-1750	32	37	)	)	PUNCT
cana-1750	32	38	is	be	AUX
cana-1750	32	39	defined	define	VERB
cana-1750	32	40	by	by	ADP
cana-1750	32	41	𝒮∗(𝛼	𝒮∗(𝛼	ADJ
cana-1750	32	42	)	)	PUNCT
cana-1750	32	43	=	=	PRON
cana-1750	32	44	{	{	PUNCT
cana-1750	32	45	𝑓	𝑓	PROPN
cana-1750	32	46	∈	∈	NOUN
cana-1750	32	47	𝓐:re	𝓐:re	PUNCT
cana-1750	32	48	(	(	PUNCT
cana-1750	32	49	𝑧𝑓′(𝑧	𝑧𝑓′(𝑧	PROPN
cana-1750	32	50	)	)	PUNCT
cana-1750	32	51	𝑓(𝑧	𝑓(𝑧	PROPN
cana-1750	32	52	)	)	PUNCT
cana-1750	32	53	)	)	PUNCT
cana-1750	32	54	>	>	PUNCT
cana-1750	33	1	𝛼	𝛼	X
cana-1750	33	2	,	,	PUNCT
cana-1750	33	3	(	(	PUNCT
cana-1750	33	4	𝑧	𝑧	PROPN
cana-1750	33	5	∈	∈	PROPN
cana-1750	33	6	𝔻	𝔻	NOUN
cana-1750	33	7	)	)	PUNCT
cana-1750	33	8	}	}	PUNCT
cana-1750	33	9	.	.	PUNCT
cana-1750	34	1	(	(	PUNCT
cana-1750	34	2	1.3	1.3	NUM
cana-1750	34	3	)	)	PUNCT
cana-1750	34	4	the	the	DET
cana-1750	34	5	class	class	NOUN
cana-1750	34	6	𝒦(𝛼	𝒦(𝛼	NOUN
cana-1750	34	7	)	)	PUNCT
cana-1750	34	8	⊂	⊂	PROPN
cana-1750	34	9	𝒮	𝒮	PROPN
cana-1750	34	10	of	of	ADP
cana-1750	34	11	convex	convex	NOUN
cana-1750	34	12	functions	function	NOUN
cana-1750	34	13	of	of	ADP
cana-1750	34	14	order	order	NOUN
cana-1750	34	15	𝛼	𝛼	NOUN
cana-1750	34	16	,	,	PUNCT
cana-1750	34	17	(	(	PUNCT
cana-1750	34	18	0	0	NUM
cana-1750	34	19	≤	≤	NUM
cana-1750	34	20	𝛼	𝛼	X
cana-1750	34	21	<	<	X
cana-1750	34	22	1	1	NUM
cana-1750	34	23	)	)	PUNCT
cana-1750	34	24	is	be	AUX
cana-1750	34	25	defined	define	VERB
cana-1750	34	26	by	by	ADP
cana-1750	34	27	𝒦(𝛼	𝒦(𝛼	NOUN
cana-1750	34	28	)	)	PUNCT
cana-1750	34	29	=	=	NOUN
cana-1750	34	30	{	{	PUNCT
cana-1750	34	31	𝑓	𝑓	PROPN
cana-1750	34	32	∈	∈	X
cana-1750	34	33	𝓐:re(1	𝓐:re(1	PROPN
cana-1750	34	34	+	+	NUM
cana-1750	34	35	𝑧𝑓′′(𝑧	𝑧𝑓′′(𝑧	PROPN
cana-1750	34	36	)	)	PUNCT
cana-1750	34	37	𝑓′(𝑧	𝑓′(𝑧	NOUN
cana-1750	34	38	)	)	PUNCT
cana-1750	34	39	)	)	PUNCT
cana-1750	35	1	>	>	X
cana-1750	36	1	𝛼	𝛼	X
cana-1750	36	2	,	,	PUNCT
cana-1750	36	3	(	(	PUNCT
cana-1750	36	4	𝑧	𝑧	PROPN
cana-1750	36	5	∈	∈	PROPN
cana-1750	36	6	𝔻	𝔻	NOUN
cana-1750	36	7	)	)	PUNCT
cana-1750	36	8	}	}	PUNCT
cana-1750	36	9	.	.	PUNCT
cana-1750	37	1	(	(	PUNCT
cana-1750	37	2	1.4	1.4	NUM
cana-1750	37	3	)	)	PUNCT
cana-1750	37	4	the	the	DET
cana-1750	37	5	class	class	NOUN
cana-1750	37	6	𝒱(𝛼	𝒱(𝛼	NUM
cana-1750	37	7	)	)	PUNCT
cana-1750	37	8	⊂	⊂	PROPN
cana-1750	37	9	𝒮	𝒮	PROPN
cana-1750	37	10	of	of	ADP
cana-1750	37	11	closed	close	VERB
cana-1750	37	12	to	to	PART
cana-1750	37	13	convex	convex	VERB
cana-1750	37	14	functions	function	NOUN
cana-1750	37	15	of	of	ADP
cana-1750	37	16	order	order	NOUN
cana-1750	37	17	𝛼	𝛼	NOUN
cana-1750	37	18	,	,	PUNCT
cana-1750	37	19	(	(	PUNCT
cana-1750	37	20	0	0	NUM
cana-1750	37	21	≤	≤	NUM
cana-1750	37	22	𝛼	𝛼	X
cana-1750	37	23	<	<	X
cana-1750	37	24	1	1	NUM
cana-1750	37	25	)	)	PUNCT
cana-1750	37	26	is	be	AUX
cana-1750	37	27	defined	define	VERB
cana-1750	37	28	by	by	ADP
cana-1750	37	29	𝒱(𝛼	𝒱(𝛼	NUM
cana-1750	37	30	)	)	PUNCT
cana-1750	37	31	=	=	PRON
cana-1750	37	32	{	{	PUNCT
cana-1750	37	33	𝑓	𝑓	PROPN
cana-1750	37	34	∈	∈	PROPN
cana-1750	37	35	𝓐:re	𝓐:re	NUM
cana-1750	37	36	(	(	PUNCT
cana-1750	37	37	𝑧𝑓′(𝑧	𝑧𝑓′(𝑧	PROPN
cana-1750	37	38	)	)	PUNCT
cana-1750	37	39	𝑔(𝑧	𝑔(𝑧	PROPN
cana-1750	37	40	)	)	PUNCT
cana-1750	37	41	)	)	PUNCT
cana-1750	37	42	>	>	X
cana-1750	38	1	𝛼	𝛼	X
cana-1750	38	2	,	,	PUNCT
cana-1750	38	3	(	(	PUNCT
cana-1750	38	4	𝑧	𝑧	PROPN
cana-1750	38	5	∈	∈	PROPN
cana-1750	38	6	𝔻	𝔻	NOUN
cana-1750	38	7	)	)	PUNCT
cana-1750	38	8	}	}	PUNCT
cana-1750	38	9	.	.	PUNCT
cana-1750	39	1	(	(	PUNCT
cana-1750	39	2	1.5	1.5	NUM
cana-1750	39	3	)	)	PUNCT
cana-1750	39	4	where	where	SCONJ
cana-1750	39	5	𝑔(𝑧	𝑔(𝑧	NOUN
cana-1750	39	6	)	)	PUNCT
cana-1750	39	7	=	=	SYM
cana-1750	40	1	𝑧	𝑧	PROPN
cana-1750	41	1	+	+	CCONJ
cana-1750	41	2	∑𝑛=2	∑𝑛=2	PROPN
cana-1750	41	3	∞	∞	NUM
cana-1750	41	4	 	 	SPACE
cana-1750	41	5	𝑏𝑛𝑧	𝑏𝑛𝑧	NOUN
cana-1750	41	6	𝑛	𝑛	PROPN
cana-1750	41	7	belongs	belong	VERB
cana-1750	41	8	to	to	PART
cana-1750	41	9	star	star	VERB
cana-1750	41	10	like	like	ADP
cana-1750	41	11	functions	function	NOUN
cana-1750	41	12	and	and	CCONJ
cana-1750	41	13	so	so	ADV
cana-1750	41	14	on	on	ADV
cana-1750	41	15	.	.	PUNCT
cana-1750	42	1	let	let	VERB
cana-1750	42	2	𝒫	𝒫	NOUN
cana-1750	42	3	be	be	AUX
cana-1750	42	4	an	an	DET
cana-1750	42	5	analytic	analytic	ADJ
cana-1750	42	6	and	and	CCONJ
cana-1750	42	7	univalent	univalent	ADJ
cana-1750	42	8	function	function	NOUN
cana-1750	42	9	with	with	ADP
cana-1750	42	10	positive	positive	ADJ
cana-1750	42	11	real	real	ADJ
cana-1750	42	12	part	part	NOUN
cana-1750	42	13	in	in	ADP
cana-1750	42	14	𝔻	𝔻	PROPN
cana-1750	42	15	,	,	PUNCT
cana-1750	42	16	𝑝(0	𝑝(0	PROPN
cana-1750	42	17	)	)	PUNCT
cana-1750	42	18	=	=	SYM
cana-1750	42	19	0	0	NUM
cana-1750	42	20	,	,	PUNCT
cana-1750	42	21	𝑝′(0	𝑝′(0	NOUN
cana-1750	42	22	)	)	PUNCT
cana-1750	42	23	=	=	SYM
cana-1750	42	24	1	1	NUM
cana-1750	42	25	,	,	PUNCT
cana-1750	42	26	re(𝑝(𝑧	re(𝑝(𝑧	NOUN
cana-1750	42	27	)	)	PUNCT
cana-1750	42	28	)	)	PUNCT
cana-1750	42	29	>	>	X
cana-1750	42	30	0	0	PUNCT
cana-1750	43	1	and	and	CCONJ
cana-1750	43	2	𝒫	𝒫	NOUN
cana-1750	43	3	maps	map	VERB
cana-1750	43	4	the	the	DET
cana-1750	43	5	unit	unit	NOUN
cana-1750	43	6	disk	disk	NOUN
cana-1750	43	7	𝔻	𝔻	PROPN
cana-1750	43	8	onto	onto	ADP
cana-1750	43	9	a	a	DET
cana-1750	43	10	region	region	NOUN
cana-1750	43	11	of	of	ADP
cana-1750	43	12	star	star	NOUN
cana-1750	43	13	like	like	ADP
cana-1750	43	14	function	function	NOUN
cana-1750	43	15	with	with	ADP
cana-1750	43	16	respect	respect	NOUN
cana-1750	43	17	to	to	ADP
cana-1750	43	18	symmetric	symmetric	ADJ
cana-1750	43	19	points	point	NOUN
cana-1750	43	20	of	of	ADP
cana-1750	43	21	the	the	DET
cana-1750	43	22	real	real	ADJ
cana-1750	43	23	axis	axis	NOUN
cana-1750	43	24	.	.	PUNCT
cana-1750	44	1	the	the	DET
cana-1750	44	2	taylor	taylor	PROPN
cana-1750	44	3	series	series	PROPN
cana-1750	44	4	expansion	expansion	NOUN
cana-1750	44	5	of	of	ADP
cana-1750	44	6	such	such	DET
cana-1750	44	7	that	that	DET
cana-1750	44	8	function	function	NOUN
cana-1750	44	9	.	.	PUNCT
cana-1750	45	1	𝑝(𝑧	𝑝(𝑧	NOUN
cana-1750	45	2	)	)	PUNCT
cana-1750	46	1	=	=	PUNCT
cana-1750	46	2	1	1	NUM
cana-1750	46	3	+	+	ADJ
cana-1750	46	4	∑	∑	PROPN
cana-1750	46	5	  	  	SPACE
cana-1750	46	6	∞	∞	PROPN
cana-1750	46	7	𝑛=1	𝑛=1	NOUN
cana-1750	46	8	 	 	SPACE
cana-1750	46	9	𝑝𝑛𝑧	𝑝𝑛𝑧	NOUN
cana-1750	46	10	𝑛	𝑛	PROPN
cana-1750	46	11	,	,	PUNCT
cana-1750	46	12	|𝑝𝑛|	|𝑝𝑛|	NOUN
cana-1750	46	13	≤	≤	NOUN
cana-1750	46	14	2	2	NUM
cana-1750	46	15	.	.	PUNCT
cana-1750	46	16	(	(	PUNCT
cana-1750	46	17	1.6	1.6	NUM
cana-1750	46	18	)	)	PUNCT
cana-1750	46	19	where	where	SCONJ
cana-1750	46	20	all	all	DET
cana-1750	46	21	the	the	DET
cana-1750	46	22	coefficients	coefficient	NOUN
cana-1750	46	23	are	be	AUX
cana-1750	46	24	real	real	ADJ
cana-1750	46	25	and	and	CCONJ
cana-1750	46	26	𝑝1	𝑝1	NOUN
cana-1750	46	27	>	>	X
cana-1750	46	28	0	0	X
cana-1750	46	29	.	.	PUNCT
cana-1750	47	1	throughout	throughout	ADP
cana-1750	47	2	this	this	DET
cana-1750	47	3	paper	paper	NOUN
cana-1750	47	4	we	we	PRON
cana-1750	47	5	assume	assume	VERB
cana-1750	47	6	that	that	SCONJ
cana-1750	47	7	the	the	DET
cana-1750	47	8	function	function	NOUN
cana-1750	47	9	𝑝	𝑝	PROPN
cana-1750	47	10	satisfies	satisfy	VERB
cana-1750	47	11	the	the	DET
cana-1750	47	12	above	above	ADJ
cana-1750	47	13	conditions	condition	NOUN
cana-1750	47	14	unless	unless	SCONJ
cana-1750	47	15	otherwise	otherwise	ADV
cana-1750	47	16	stated	state	VERB
cana-1750	47	17	.	.	PUNCT
cana-1750	48	1	by	by	ADP
cana-1750	48	2	𝒮∗(𝑝	𝒮∗(𝑝	NOUN
cana-1750	48	3	)	)	PUNCT
cana-1750	48	4	and	and	CCONJ
cana-1750	48	5	𝒦(𝑝	𝒦(𝑝	PUNCT
cana-1750	48	6	)	)	PUNCT
cana-1750	48	7	we	we	PRON
cana-1750	48	8	denote	denote	VERB
cana-1750	48	9	the	the	DET
cana-1750	48	10	following	follow	VERB
cana-1750	48	11	classes	class	NOUN
cana-1750	48	12	of	of	ADP
cana-1750	48	13	function	function	NOUN
cana-1750	48	14	𝒮∗(𝑝	𝒮∗(𝑝	NOUN
cana-1750	48	15	)	)	PUNCT
cana-1750	48	16	=	=	PRON
cana-1750	48	17	{	{	PUNCT
cana-1750	48	18	𝑓	𝑓	PROPN
cana-1750	48	19	∈	∈	NOUN
cana-1750	48	20	𝓐:re	𝓐:re	PUNCT
cana-1750	48	21	(	(	PUNCT
cana-1750	48	22	𝑧𝑓′(𝑧	𝑧𝑓′(𝑧	PROPN
cana-1750	48	23	)	)	PUNCT
cana-1750	48	24	𝑓(𝑧	𝑓(𝑧	PROPN
cana-1750	48	25	)	)	PUNCT
cana-1750	48	26	)	)	PUNCT
cana-1750	48	27	≺	≺	NOUN
cana-1750	48	28	𝑝(𝑧	𝑝(𝑧	PROPN
cana-1750	48	29	)	)	PUNCT
cana-1750	48	30	,	,	PUNCT
cana-1750	48	31	(	(	PUNCT
cana-1750	48	32	𝑧	𝑧	PROPN
cana-1750	48	33	∈	∈	PROPN
cana-1750	48	34	𝔻	𝔻	NOUN
cana-1750	48	35	)	)	PUNCT
cana-1750	48	36	}	}	PUNCT
cana-1750	48	37	.	.	PUNCT
cana-1750	49	1	(	(	PUNCT
cana-1750	49	2	1.7	1.7	NUM
cana-1750	49	3	)	)	PUNCT
cana-1750	49	4	𝒦(𝑝	𝒦(𝑝	PROPN
cana-1750	49	5	)	)	PUNCT
cana-1750	49	6	=	=	PRON
cana-1750	49	7	{	{	PUNCT
cana-1750	49	8	𝑓	𝑓	PROPN
cana-1750	49	9	∈	∈	NOUN
cana-1750	49	10	𝓐:re	𝓐:re	PRON
cana-1750	49	11	(	(	PUNCT
cana-1750	49	12	1	1	NUM
cana-1750	49	13	+	+	NUM
cana-1750	49	14	𝑧𝑓′′(𝑧	𝑧𝑓′′(𝑧	PROPN
cana-1750	49	15	)	)	PUNCT
cana-1750	49	16	𝑓′(𝑧	𝑓′(𝑧	NOUN
cana-1750	49	17	)	)	PUNCT
cana-1750	49	18	)	)	PUNCT
cana-1750	49	19	≺	≺	NOUN
cana-1750	49	20	𝑝(𝑧	𝑝(𝑧	PROPN
cana-1750	49	21	)	)	PUNCT
cana-1750	49	22	,	,	PUNCT
cana-1750	49	23	(	(	PUNCT
cana-1750	49	24	𝑧	𝑧	PROPN
cana-1750	49	25	∈	∈	PROPN
cana-1750	49	26	𝔻	𝔻	NOUN
cana-1750	49	27	)	)	PUNCT
cana-1750	49	28	}	}	PUNCT
cana-1750	49	29	.	.	PUNCT
cana-1750	50	1	(	(	PUNCT
cana-1750	50	2	1.8	1.8	NUM
cana-1750	50	3	)	)	PUNCT
cana-1750	50	4	communications	communication	NOUN
cana-1750	50	5	on	on	ADP
cana-1750	50	6	applied	apply	VERB
cana-1750	50	7	nonlinear	nonlinear	ADJ
cana-1750	50	8	analysis	analysis	NOUN
cana-1750	50	9	issn	issn	NOUN
cana-1750	50	10	:	:	PUNCT
cana-1750	50	11	1074	1074	NUM
cana-1750	50	12	-	-	PUNCT
cana-1750	50	13	133x	133x	NUM
cana-1750	50	14	vol	vol	NOUN
cana-1750	50	15	32	32	NUM
cana-1750	50	16	no	no	NOUN
cana-1750	50	17	.	.	NOUN
cana-1750	50	18	2	2	NUM
cana-1750	50	19	(	(	PUNCT
cana-1750	50	20	2025	2025	NUM
cana-1750	50	21	)	)	PUNCT
cana-1750	50	22	385	385	NUM
cana-1750	50	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	51	1	the	the	DET
cana-1750	51	2	classes	class	NOUN
cana-1750	51	3	𝒮∗(𝑝),𝒦(𝑝	𝒮∗(𝑝),𝒦(𝑝	ADJ
cana-1750	51	4	)	)	PUNCT
cana-1750	51	5	are	be	AUX
cana-1750	51	6	the	the	DET
cana-1750	51	7	extension	extension	NOUN
cana-1750	51	8	of	of	ADP
cana-1750	51	9	classical	classical	ADJ
cana-1750	51	10	set	set	NOUN
cana-1750	51	11	of	of	ADP
cana-1750	51	12	star	star	NOUN
cana-1750	51	13	like	like	ADP
cana-1750	51	14	and	and	CCONJ
cana-1750	51	15	convex	convex	NOUN
cana-1750	51	16	functions	function	NOUN
cana-1750	51	17	(	(	PUNCT
cana-1750	51	18	e.g.	e.g.	ADV
cana-1750	51	19	,	,	PUNCT
cana-1750	51	20	see	see	VERB
cana-1750	51	21	ma	ma	PROPN
cana-1750	51	22	and	and	CCONJ
cana-1750	51	23	minda	minda	PROPN
cana-1750	52	1	[	[	X
cana-1750	52	2	31	31	NUM
cana-1750	52	3	]	]	PUNCT
cana-1750	52	4	)	)	PUNCT
cana-1750	52	5	.	.	PUNCT
cana-1750	53	1	these	these	DET
cana-1750	53	2	functions	function	NOUN
cana-1750	53	3	serve	serve	VERB
cana-1750	53	4	as	as	ADP
cana-1750	53	5	the	the	DET
cana-1750	53	6	common	common	ADJ
cana-1750	53	7	source	source	NOUN
cana-1750	53	8	from	from	ADP
cana-1750	53	9	which	which	PRON
cana-1750	53	10	these	these	DET
cana-1750	53	11	subclasses	subclass	NOUN
cana-1750	53	12	inherit	inherit	VERB
cana-1750	53	13	their	their	PRON
cana-1750	53	14	properties	property	NOUN
cana-1750	53	15	and	and	CCONJ
cana-1750	53	16	all	all	PRON
cana-1750	53	17	took	take	VERB
cana-1750	53	18	their	their	PRON
cana-1750	53	19	sources	source	NOUN
cana-1750	53	20	from	from	ADP
cana-1750	53	21	the	the	DET
cana-1750	53	22	class	class	NOUN
cana-1750	53	23	of	of	ADP
cana-1750	53	24	caratheòdory	caratheòdory	ADJ
cana-1750	53	25	function	function	NOUN
cana-1750	53	26	𝒫.	𝒫.	NOUN
cana-1750	53	27	the	the	DET
cana-1750	53	28	work	work	NOUN
cana-1750	53	29	of	of	ADP
cana-1750	53	30	sokól	sokól	NOUN
cana-1750	53	31	and	and	CCONJ
cana-1750	53	32	stankiewicz	stankiewicz	VERB
cana-1750	53	33	[	[	X
cana-1750	53	34	19	19	NUM
cana-1750	53	35	]	]	PUNCT
cana-1750	53	36	,	,	PUNCT
cana-1750	53	37	introduced	introduce	VERB
cana-1750	53	38	a	a	DET
cana-1750	53	39	class	class	NOUN
cana-1750	53	40	denoted	denote	VERB
cana-1750	53	41	as	as	ADP
cana-1750	53	42	𝒮ℒ∗	𝒮ℒ∗	PROPN
cana-1750	53	43	,	,	PUNCT
cana-1750	53	44	which	which	PRON
cana-1750	53	45	comprises	comprise	VERB
cana-1750	53	46	normalized	normalize	VERB
cana-1750	53	47	analytic	analytic	ADJ
cana-1750	53	48	functions	function	NOUN
cana-1750	53	49	𝑓	𝑓	PRON
cana-1750	53	50	in	in	ADP
cana-1750	53	51	𝔻	𝔻	NOUN
cana-1750	53	52	satisfying	satisfy	VERB
cana-1750	53	53	the	the	DET
cana-1750	53	54	condition	condition	NOUN
cana-1750	53	55	|	|	ADP
cana-1750	53	56	[	[	PUNCT
cana-1750	53	57	𝑧𝑓′(𝑧	𝑧𝑓′(𝑧	PROPN
cana-1750	53	58	)	)	PUNCT
cana-1750	53	59	𝑓(𝑧	𝑓(𝑧	PROPN
cana-1750	53	60	)	)	PUNCT
cana-1750	53	61	]	]	PUNCT
cana-1750	53	62	2	2	NUM
cana-1750	53	63	−	−	NUM
cana-1750	53	64	1|	1|	PRON
cana-1750	53	65	<	<	X
cana-1750	53	66	1	1	NUM
cana-1750	53	67	this	this	DET
cana-1750	53	68	class	class	NOUN
cana-1750	53	69	is	be	AUX
cana-1750	53	70	referred	refer	VERB
cana-1750	53	71	to	to	ADP
cana-1750	53	72	as	as	ADP
cana-1750	53	73	sokól	sokól	PROPN
cana-1750	53	74	stankiewicz	stankiewicz	PROPN
cana-1750	53	75	star	star	NOUN
cana-1750	53	76	-	-	PUNCT
cana-1750	53	77	like	like	ADJ
cana-1750	53	78	functions	function	NOUN
cana-1750	53	79	.	.	PUNCT
cana-1750	54	1	additionally	additionally	ADV
cana-1750	54	2	,	,	PUNCT
cana-1750	54	3	raza	raza	PROPN
cana-1750	54	4	and	and	CCONJ
cana-1750	54	5	malik	malik	PROPN
cana-1750	55	1	[	[	X
cana-1750	55	2	17	17	NUM
cana-1750	55	3	]	]	PUNCT
cana-1750	55	4	,	,	PUNCT
cana-1750	55	5	have	have	AUX
cana-1750	55	6	determined	determine	VERB
cana-1750	55	7	the	the	DET
cana-1750	55	8	upper	upper	ADJ
cana-1750	55	9	bound	bound	NOUN
cana-1750	55	10	of	of	ADP
cana-1750	55	11	the	the	DET
cana-1750	55	12	third	third	ADJ
cana-1750	55	13	hankel	hankel	NOUN
cana-1750	55	14	determinant	determinant	ADJ
cana-1750	55	15	𝐻3(1	𝐻3(1	NOUN
cana-1750	55	16	)	)	PUNCT
cana-1750	55	17	for	for	ADP
cana-1750	55	18	the	the	DET
cana-1750	55	19	class	class	NOUN
cana-1750	55	20	𝒮ℒ∗.	𝒮ℒ∗.	PUNCT
cana-1750	55	21	furthermore	furthermore	ADV
cana-1750	55	22	,	,	PUNCT
cana-1750	55	23	sahoo	sahoo	PROPN
cana-1750	55	24	and	and	CCONJ
cana-1750	55	25	patel	patel	NOUN
cana-1750	56	1	[	[	X
cana-1750	56	2	18	18	NUM
cana-1750	56	3	]	]	PUNCT
cana-1750	56	4	obtained	obtain	VERB
cana-1750	56	5	some	some	DET
cana-1750	56	6	upper	upper	ADJ
cana-1750	56	7	bound	bind	VERB
cana-1750	56	8	to	to	ADP
cana-1750	56	9	the	the	DET
cana-1750	56	10	second	second	ADJ
cana-1750	56	11	hankel	hankel	NOUN
cana-1750	56	12	determinant	determinant	ADJ
cana-1750	56	13	for	for	ADP
cana-1750	56	14	the	the	DET
cana-1750	56	15	class	class	NOUN
cana-1750	56	16	ℛ̃	ℛ̃	PROPN
cana-1750	56	17	=	=	PUNCT
cana-1750	56	18	{	{	PUNCT
cana-1750	56	19	𝑓	𝑓	PROPN
cana-1750	56	20	∈	∈	PROPN
cana-1750	56	21	𝓐	𝓐	NOUN
cana-1750	56	22	:	:	PUNCT
cana-1750	56	23	|𝑓′(𝑧)2	|𝑓′(𝑧)2	PROPN
cana-1750	56	24	−	−	PROPN
cana-1750	56	25	1|	1|	NUM
cana-1750	56	26	<	<	X
cana-1750	56	27	1	1	NUM
cana-1750	56	28	,	,	PUNCT
cana-1750	56	29	(	(	PUNCT
cana-1750	56	30	𝑧	𝑧	PROPN
cana-1750	56	31	∈	∈	PROPN
cana-1750	56	32	𝔻	𝔻	NOUN
cana-1750	56	33	)	)	PUNCT
cana-1750	56	34	}	}	PUNCT
cana-1750	56	35	.	.	PUNCT
cana-1750	57	1	(	(	PUNCT
cana-1750	57	2	1.9	1.9	NUM
cana-1750	57	3	)	)	PUNCT
cana-1750	57	4	motivated	motivate	VERB
cana-1750	57	5	by	by	ADP
cana-1750	57	6	the	the	DET
cana-1750	57	7	above	above	ADV
cana-1750	57	8	-	-	PUNCT
cana-1750	57	9	mentioned	mention	VERB
cana-1750	57	10	works	work	NOUN
cana-1750	57	11	obtained	obtain	VERB
cana-1750	57	12	by	by	ADP
cana-1750	57	13	earlier	early	ADJ
cana-1750	57	14	researchers	researcher	NOUN
cana-1750	57	15	,	,	PUNCT
cana-1750	57	16	trailokya	trailokya	NOUN
cana-1750	57	17	panigrahi	panigrahi	NOUN
cana-1750	57	18	and	and	CCONJ
cana-1750	57	19	januszsokól	januszsokól	VERB
cana-1750	57	20	[	[	X
cana-1750	57	21	12	12	NUM
cana-1750	57	22	]	]	PUNCT
cana-1750	57	23	,	,	PUNCT
cana-1750	57	24	introduce	introduce	VERB
cana-1750	57	25	the	the	DET
cana-1750	57	26	following	following	ADJ
cana-1750	57	27	subclass	subclass	NOUN
cana-1750	57	28	of	of	ADP
cana-1750	57	29	analytical	analytical	ADJ
cana-1750	57	30	function	function	NOUN
cana-1750	57	31	.	.	PUNCT
cana-1750	58	1	definition	definition	NOUN
cana-1750	58	2	1.1	1.1	NUM
cana-1750	58	3	.	.	PUNCT
cana-1750	59	1	a	a	DET
cana-1750	59	2	function	function	NOUN
cana-1750	59	3	𝑓	𝑓	DET
cana-1750	59	4	∈	∈	NOUN
cana-1750	59	5	𝓐	𝓐	NOUN
cana-1750	59	6	is	be	AUX
cana-1750	59	7	said	say	VERB
cana-1750	59	8	to	to	PART
cana-1750	59	9	be	be	AUX
cana-1750	59	10	in	in	ADP
cana-1750	59	11	the	the	DET
cana-1750	59	12	class	class	NOUN
cana-1750	59	13	𝓐𝓡𝝀	𝓐𝓡𝝀	NOUN
cana-1750	59	14	∗	∗	NOUN
cana-1750	59	15	,	,	PUNCT
cana-1750	59	16	0	0	NUM
cana-1750	59	17	≤	≤	NUM
cana-1750	59	18	𝜆	𝜆	DET
cana-1750	59	19	≤	≤	NUM
cana-1750	59	20	1	1	NUM
cana-1750	59	21	,	,	PUNCT
cana-1750	59	22	if	if	SCONJ
cana-1750	59	23	it	it	PRON
cana-1750	59	24	satisfies	satisfy	VERB
cana-1750	59	25	the	the	DET
cana-1750	59	26	condition	condition	NOUN
cana-1750	59	27	|	|	ADV
cana-1750	59	28	[	[	PUNCT
cana-1750	59	29	𝑧𝑓′(𝑧	𝑧𝑓′(𝑧	PROPN
cana-1750	59	30	)	)	PUNCT
cana-1750	59	31	(	(	PUNCT
cana-1750	59	32	1	1	NUM
cana-1750	59	33	−	−	NUM
cana-1750	59	34	𝜆)𝑓(𝑧	𝜆)𝑓(𝑧	NUM
cana-1750	59	35	)	)	PUNCT
cana-1750	60	1	+	+	NUM
cana-1750	60	2	𝜆𝑧	𝜆𝑧	X
cana-1750	60	3	]	]	SYM
cana-1750	60	4	2	2	NUM
cana-1750	60	5	−	−	NOUN
cana-1750	60	6	1|	1|	NUM
cana-1750	60	7	<	<	X
cana-1750	60	8	1	1	NUM
cana-1750	60	9	,	,	PUNCT
cana-1750	60	10	(	(	PUNCT
cana-1750	60	11	𝑧	𝑧	PROPN
cana-1750	60	12	∈	∈	PROPN
cana-1750	60	13	𝔻	𝔻	PROPN
cana-1750	60	14	)	)	PUNCT
cana-1750	60	15	.	.	PUNCT
cana-1750	61	1	(	(	PUNCT
cana-1750	61	2	1.10	1.10	NUM
cana-1750	61	3	)	)	PUNCT
cana-1750	61	4	the	the	DET
cana-1750	61	5	family	family	NOUN
cana-1750	61	6	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	61	7	)	)	PUNCT
cana-1750	61	8	of	of	ADP
cana-1750	61	9	new	new	ADJ
cana-1750	61	10	subclasses	subclass	NOUN
cana-1750	61	11	in	in	ADP
cana-1750	61	12	analytical	analytical	ADJ
cana-1750	61	13	functions	function	NOUN
cana-1750	61	14	of	of	ADP
cana-1750	61	15	type	type	NOUN
cana-1750	61	16	𝜆	𝜆	ADP
cana-1750	61	17	;	;	PUNCT
cana-1750	61	18	0	0	NUM
cana-1750	61	19	≤	≤	NUM
cana-1750	61	20	𝜆	𝜆	DET
cana-1750	61	21	≤	≤	NUM
cana-1750	61	22	1	1	NUM
cana-1750	61	23	provides	provide	VERB
cana-1750	61	24	a	a	DET
cana-1750	61	25	transition	transition	NOUN
cana-1750	61	26	from	from	ADP
cana-1750	61	27	the	the	DET
cana-1750	61	28	class	class	NOUN
cana-1750	61	29	of	of	ADP
cana-1750	61	30	star	star	NOUN
cana-1750	61	31	like	like	ADP
cana-1750	61	32	functions	function	NOUN
cana-1750	61	33	to	to	ADP
cana-1750	61	34	the	the	DET
cana-1750	61	35	class	class	NOUN
cana-1750	61	36	of	of	ADP
cana-1750	61	37	functions	function	NOUN
cana-1750	61	38	of	of	ADP
cana-1750	61	39	bounded	bounded	ADJ
cana-1750	61	40	boundary	boundary	ADJ
cana-1750	61	41	rotation	rotation	NOUN
cana-1750	61	42	.	.	PUNCT
cana-1750	62	1	to	to	PART
cana-1750	62	2	see	see	VERB
cana-1750	62	3	this	this	PRON
cana-1750	62	4	,	,	PUNCT
cana-1750	62	5	we	we	PRON
cana-1750	62	6	note	note	VERB
cana-1750	62	7	that	that	SCONJ
cana-1750	62	8	for	for	ADP
cana-1750	62	9	the	the	DET
cana-1750	62	10	choice	choice	NOUN
cana-1750	62	11	of	of	ADP
cana-1750	62	12	𝜆	𝜆	NOUN
cana-1750	62	13	=	=	SYM
cana-1750	62	14	0	0	NUM
cana-1750	62	15	,	,	PUNCT
cana-1750	62	16	we	we	PRON
cana-1750	62	17	have	have	VERB
cana-1750	62	18	𝓐(𝝀	𝓐(𝝀	X
cana-1750	62	19	)	)	PUNCT
cana-1750	62	20	≡	≡	PROPN
cana-1750	62	21	𝒮∗(0	𝒮∗(0	PROPN
cana-1750	62	22	)	)	PUNCT
cana-1750	62	23	≡	≡	PROPN
cana-1750	62	24	𝒮∗	𝒮∗	VERB
cana-1750	63	1	the	the	DET
cana-1750	63	2	class	class	NOUN
cana-1750	63	3	of	of	ADP
cana-1750	63	4	star	star	NOUN
cana-1750	63	5	like	like	INTJ
cana-1750	63	6	functions	function	NOUN
cana-1750	63	7	𝑓	𝑓	PRON
cana-1750	63	8	∈	∈	PROPN
cana-1750	63	9	𝓐	𝓐	NOUN
cana-1750	63	10	,	,	PUNCT
cana-1750	63	11	so	so	SCONJ
cana-1750	63	12	that	that	SCONJ
cana-1750	63	13	ℜ	ℜ	PROPN
cana-1750	63	14	(	(	PUNCT
cana-1750	63	15	𝑧𝑓′	𝑧𝑓′	PROPN
cana-1750	63	16	𝑓	𝑓	X
cana-1750	63	17	)	)	PUNCT
cana-1750	63	18	>	>	PUNCT
cana-1750	63	19	0	0	PUNCT
cana-1750	63	20	in	in	ADP
cana-1750	63	21	𝔻	𝔻	PROPN
cana-1750	63	22	for	for	ADP
cana-1750	63	23	the	the	DET
cana-1750	63	24	choice	choice	NOUN
cana-1750	63	25	of	of	ADP
cana-1750	63	26	𝜆	𝜆	NOUN
cana-1750	63	27	=	=	SYM
cana-1750	63	28	1	1	NUM
cana-1750	63	29	,	,	PUNCT
cana-1750	63	30	we	we	PRON
cana-1750	63	31	get	get	VERB
cana-1750	63	32	the	the	DET
cana-1750	63	33	family	family	NOUN
cana-1750	63	34	of	of	ADP
cana-1750	63	35	functions	function	NOUN
cana-1750	63	36	ℛ̃	ℛ̃	PROPN
cana-1750	63	37	of	of	ADP
cana-1750	63	38	functions	function	NOUN
cana-1750	63	39	𝑓	𝑓	PRON
cana-1750	63	40	∈	∈	PROPN
cana-1750	63	41	𝓐	𝓐	NOUN
cana-1750	63	42	,	,	PUNCT
cana-1750	63	43	of	of	ADP
cana-1750	63	44	bounded	bounded	ADJ
cana-1750	63	45	boundary	boundary	ADJ
cana-1750	63	46	rotation	rotation	NOUN
cana-1750	63	47	so	so	SCONJ
cana-1750	63	48	that	that	DET
cana-1750	63	49	ℜ(𝑓′	ℜ(𝑓′	ADJ
cana-1750	63	50	)	)	PUNCT
cana-1750	63	51	>	>	X
cana-1750	63	52	0	0	PUNCT
cana-1750	64	1	in	in	ADP
cana-1750	64	2	𝔻.	𝔻.	PROPN
cana-1750	64	3	(	(	PUNCT
cana-1750	64	4	for	for	ADP
cana-1750	64	5	further	further	ADJ
cana-1750	64	6	details	detail	NOUN
cana-1750	64	7	see	see	VERB
cana-1750	64	8	[	[	X
cana-1750	64	9	3	3	NUM
cana-1750	64	10	]	]	PUNCT
cana-1750	64	11	.	.	PUNCT
cana-1750	64	12	)	)	PUNCT
cana-1750	65	1	note	note	VERB
cana-1750	65	2	that	that	SCONJ
cana-1750	65	3	for	for	ADP
cana-1750	65	4	𝜆	𝜆	PRON
cana-1750	65	5	=	=	SYM
cana-1750	65	6	0	0	NUM
cana-1750	65	7	,	,	PUNCT
cana-1750	65	8	the	the	DET
cana-1750	65	9	class	class	NOUN
cana-1750	65	10	𝓐𝓡𝟎	𝓐𝓡𝟎	PROPN
cana-1750	65	11	∗	∗	NOUN
cana-1750	65	12	,	,	PUNCT
cana-1750	65	13	reduces	reduce	VERB
cana-1750	65	14	to	to	ADP
cana-1750	65	15	the	the	DET
cana-1750	65	16	class	class	NOUN
cana-1750	65	17	𝒮ℒ∗	𝒮ℒ∗	PROPN
cana-1750	65	18	,	,	PUNCT
cana-1750	65	19	studied	study	VERB
cana-1750	65	20	by	by	ADP
cana-1750	65	21	raza	raza	PROPN
cana-1750	65	22	and	and	CCONJ
cana-1750	65	23	malik	malik	PROPN
cana-1750	66	1	[	[	X
cana-1750	66	2	17	17	NUM
cana-1750	66	3	]	]	PUNCT
cana-1750	66	4	and	and	CCONJ
cana-1750	66	5	while	while	SCONJ
cana-1750	66	6	𝜆	𝜆	PRON
cana-1750	66	7	=	=	SYM
cana-1750	66	8	1	1	NUM
cana-1750	66	9	,	,	PUNCT
cana-1750	66	10	the	the	DET
cana-1750	66	11	class	class	NOUN
cana-1750	66	12	𝓐𝓡𝟏	𝓐𝓡𝟏	PROPN
cana-1750	66	13	∗	∗	NOUN
cana-1750	66	14	,	,	PUNCT
cana-1750	66	15	reduces	reduce	VERB
cana-1750	66	16	to	to	ADP
cana-1750	66	17	ℛ̃	ℛ̃	PROPN
cana-1750	66	18	studied	study	VERB
cana-1750	66	19	by	by	ADP
cana-1750	66	20	sahoo	sahoo	PROPN
cana-1750	66	21	and	and	CCONJ
cana-1750	66	22	patel	patel	NOUN
cana-1750	66	23	[	[	X
cana-1750	66	24	18	18	NUM
cana-1750	66	25	]	]	PUNCT
cana-1750	66	26	.	.	PUNCT
cana-1750	67	1	in	in	ADP
cana-1750	67	2	terms	term	NOUN
cana-1750	67	3	of	of	ADP
cana-1750	67	4	subordination	subordination	NOUN
cana-1750	67	5	,	,	PUNCT
cana-1750	67	6	relation	relation	NOUN
cana-1750	67	7	(	(	PUNCT
cana-1750	67	8	1.10	1.10	NUM
cana-1750	67	9	)	)	PUNCT
cana-1750	67	10	,	,	PUNCT
cana-1750	67	11	can	can	AUX
cana-1750	67	12	be	be	AUX
cana-1750	67	13	written	write	VERB
cana-1750	67	14	𝓐(𝝀	𝓐(𝝀	PRON
cana-1750	67	15	)	)	PUNCT
cana-1750	67	16	=	=	SYM
cana-1750	67	17	𝑧𝑓′(𝑧	𝑧𝑓′(𝑧	PROPN
cana-1750	67	18	)	)	PUNCT
cana-1750	67	19	(	(	PUNCT
cana-1750	67	20	1	1	NUM
cana-1750	67	21	−	−	NUM
cana-1750	67	22	𝜆)𝑓(𝑧	𝜆)𝑓(𝑧	NUM
cana-1750	67	23	)	)	PUNCT
cana-1750	68	1	+	+	NUM
cana-1750	68	2	𝜆𝑧	𝜆𝑧	NOUN
cana-1750	68	3	≺	≺	NOUN
cana-1750	68	4	𝑝(𝑧	𝑝(𝑧	PROPN
cana-1750	68	5	)	)	PUNCT
cana-1750	68	6	,	,	PUNCT
cana-1750	68	7	(	(	PUNCT
cana-1750	68	8	𝑧	𝑧	PROPN
cana-1750	68	9	∈	∈	PROPN
cana-1750	68	10	𝔻	𝔻	PROPN
cana-1750	68	11	)	)	PUNCT
cana-1750	68	12	.	.	PUNCT
cana-1750	69	1	(	(	PUNCT
cana-1750	69	2	1.11	1.11	NUM
cana-1750	69	3	)	)	PUNCT
cana-1750	69	4	in	in	ADP
cana-1750	69	5	this	this	DET
cana-1750	69	6	research	research	NOUN
cana-1750	69	7	paper	paper	NOUN
cana-1750	69	8	,	,	PUNCT
cana-1750	69	9	we	we	PRON
cana-1750	69	10	setout	setout	VERB
cana-1750	69	11	on	on	ADP
cana-1750	69	12	an	an	DET
cana-1750	69	13	investigation	investigation	NOUN
cana-1750	69	14	into	into	ADP
cana-1750	69	15	the	the	DET
cana-1750	69	16	determinants	determinant	NOUN
cana-1750	69	17	of	of	ADP
cana-1750	69	18	symmetric	symmetric	ADJ
cana-1750	69	19	toeplitz	toeplitz	NOUN
cana-1750	69	20	matrices	matrix	NOUN
cana-1750	69	21	,	,	PUNCT
cana-1750	69	22	where	where	SCONJ
cana-1750	69	23	their	their	PRON
cana-1750	69	24	entries	entry	NOUN
cana-1750	69	25	represent	represent	VERB
cana-1750	69	26	the	the	DET
cana-1750	69	27	coefficients	coefficient	NOUN
cana-1750	69	28	𝑎𝑛	𝑎𝑛	PROPN
cana-1750	69	29	of	of	ADP
cana-1750	69	30	star	star	NOUN
cana-1750	69	31	like	like	VERB
cana-1750	69	32	and	and	CCONJ
cana-1750	69	33	close	close	ADJ
cana-1750	69	34	to	to	ADP
cana-1750	69	35	convex	convex	NOUN
cana-1750	69	36	functions	function	NOUN
cana-1750	69	37	.	.	PUNCT
cana-1750	70	1	toeplitz	toeplitz	NOUN
cana-1750	70	2	matrices	matrix	NOUN
cana-1750	70	3	are	be	AUX
cana-1750	70	4	extensively	extensively	ADV
cana-1750	70	5	studied	study	VERB
cana-1750	70	6	structured	structured	ADJ
cana-1750	70	7	matrices	matrix	NOUN
cana-1750	70	8	with	with	ADP
cana-1750	70	9	applications	application	NOUN
cana-1750	70	10	in	in	ADP
cana-1750	70	11	various	various	ADJ
cana-1750	70	12	fields	field	NOUN
cana-1750	70	13	such	such	ADJ
cana-1750	70	14	as	as	ADP
cana-1750	70	15	mathematics	mathematic	NOUN
cana-1750	70	16	,	,	PUNCT
cana-1750	70	17	statistics	statistic	NOUN
cana-1750	70	18	,	,	PUNCT
cana-1750	70	19	image	image	NOUN
cana-1750	70	20	processing	processing	NOUN
cana-1750	70	21	,	,	PUNCT
cana-1750	70	22	quantum	quantum	NOUN
cana-1750	70	23	mechanics	mechanic	NOUN
cana-1750	70	24	and	and	CCONJ
cana-1750	70	25	more	more	ADJ
cana-1750	70	26	(	(	PUNCT
cana-1750	70	27	e.g.	e.g.	ADV
cana-1750	70	28	,	,	PUNCT
cana-1750	70	29	ye	ye	PRON
cana-1750	70	30	and	and	CCONJ
cana-1750	70	31	lim	lim	NOUN
cana-1750	71	1	[	[	X
cana-1750	71	2	4	4	NUM
cana-1750	71	3	]	]	PUNCT
cana-1750	71	4	)	)	PUNCT
cana-1750	71	5	.	.	PUNCT
cana-1750	72	1	we	we	PRON
cana-1750	72	2	recall	recall	VERB
cana-1750	72	3	the	the	DET
cana-1750	72	4	definition	definition	NOUN
cana-1750	72	5	of	of	ADP
cana-1750	72	6	the	the	DET
cana-1750	72	7	hankel	hankel	NOUN
cana-1750	72	8	determinant	determinant	ADJ
cana-1750	72	9	𝐻𝑘(𝑛	𝐻𝑘(𝑛	PROPN
cana-1750	72	10	)	)	PUNCT
cana-1750	72	11	=	=	PUNCT
cana-1750	73	1	|	|	ADV
cana-1750	73	2	𝑎𝑛	𝑎𝑛	VERB
cana-1750	73	3	𝑎𝑛+1	𝑎𝑛+1	PROPN
cana-1750	73	4	⋯	⋯	PROPN
cana-1750	73	5	𝑎𝑛+𝑘−1	𝑎𝑛+𝑘−1	PROPN
cana-1750	73	6	𝑎𝑛+1	𝑎𝑛+1	PROPN
cana-1750	73	7	𝑎𝑛+2	𝑎𝑛+2	PROPN
cana-1750	73	8	⋯	⋯	PROPN
cana-1750	73	9	𝑎𝑛+𝑘	𝑎𝑛+𝑘	PROPN
cana-1750	73	10	⋮	⋮	NOUN
cana-1750	73	11	⋮	⋮	PROPN
cana-1750	73	12	⋯	⋯	PROPN
cana-1750	73	13	⋮	⋮	NOUN
cana-1750	73	14	𝑎𝑛+𝑘−1	𝑎𝑛+𝑘−1	PROPN
cana-1750	73	15	𝑎𝑛+𝑘	𝑎𝑛+𝑘	PROPN
cana-1750	73	16	⋯	⋯	PROPN
cana-1750	73	17	𝑎𝑛+2𝑘−2	𝑎𝑛+2𝑘−2	X
cana-1750	73	18	|	|	ADV
cana-1750	73	19	.	.	PUNCT
cana-1750	74	1	(	(	PUNCT
cana-1750	74	2	1.12	1.12	NUM
cana-1750	74	3	)	)	PUNCT
cana-1750	74	4	communications	communication	NOUN
cana-1750	74	5	on	on	ADP
cana-1750	74	6	applied	apply	VERB
cana-1750	74	7	nonlinear	nonlinear	ADJ
cana-1750	74	8	analysis	analysis	NOUN
cana-1750	74	9	issn	issn	NOUN
cana-1750	74	10	:	:	PUNCT
cana-1750	74	11	1074	1074	NUM
cana-1750	74	12	-	-	PUNCT
cana-1750	74	13	133x	133x	NUM
cana-1750	74	14	vol	vol	NOUN
cana-1750	74	15	32	32	NUM
cana-1750	74	16	no	no	NOUN
cana-1750	74	17	.	.	NOUN
cana-1750	74	18	2	2	NUM
cana-1750	74	19	(	(	PUNCT
cana-1750	74	20	2025	2025	NUM
cana-1750	74	21	)	)	PUNCT
cana-1750	74	22	386	386	NUM
cana-1750	74	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	74	24	for	for	ADP
cana-1750	74	25	example	example	NOUN
cana-1750	74	26	,	,	PUNCT
cana-1750	74	27	𝐻2(1	𝐻2(1	NOUN
cana-1750	74	28	)	)	PUNCT
cana-1750	75	1	=	=	PUNCT
cana-1750	76	1	|	|	ADV
cana-1750	76	2	𝑎1	𝑎1	VERB
cana-1750	76	3	𝑎2	𝑎2	NOUN
cana-1750	76	4	𝑎2	𝑎2	PROPN
cana-1750	76	5	𝑎3	𝑎3	PROPN
cana-1750	76	6	|	|	ADV
cana-1750	76	7	,	,	PUNCT
cana-1750	76	8	𝐻2(2	𝐻2(2	ADJ
cana-1750	76	9	)	)	PUNCT
cana-1750	76	10	=	=	PUNCT
cana-1750	77	1	|	|	ADV
cana-1750	77	2	𝑎2	𝑎2	PROPN
cana-1750	77	3	𝑎3	𝑎3	PROPN
cana-1750	77	4	𝑎3	𝑎3	PROPN
cana-1750	77	5	𝑎4	𝑎4	PROPN
cana-1750	77	6	|	|	ADV
cana-1750	77	7	,	,	PUNCT
cana-1750	77	8	𝐻3(1	𝐻3(1	ADJ
cana-1750	77	9	)	)	PUNCT
cana-1750	78	1	=	=	PUNCT
cana-1750	79	1	|	|	ADV
cana-1750	79	2	𝑎1	𝑎1	INTJ
cana-1750	79	3	𝑎2	𝑎2	PROPN
cana-1750	79	4	𝑎3	𝑎3	PROPN
cana-1750	79	5	𝑎2	𝑎2	PROPN
cana-1750	79	6	𝑎3	𝑎3	PROPN
cana-1750	79	7	𝑎4	𝑎4	PROPN
cana-1750	79	8	𝑎3	𝑎3	PROPN
cana-1750	79	9	𝑎4	𝑎4	PROPN
cana-1750	79	10	𝑎5	𝑎5	PROPN
cana-1750	79	11	|	|	ADV
cana-1750	79	12	.	.	PUNCT
cana-1750	80	1	(	(	PUNCT
cana-1750	80	2	1.13	1.13	NUM
cana-1750	80	3	)	)	PUNCT
cana-1750	80	4	and	and	CCONJ
cana-1750	80	5	define	define	VERB
cana-1750	80	6	the	the	DET
cana-1750	80	7	symmetric	symmetric	ADJ
cana-1750	80	8	toeplitz	toeplitz	NOUN
cana-1750	80	9	determinant	determinant	ADJ
cana-1750	80	10	𝑇𝑘(𝑛	𝑇𝑘(𝑛	NOUN
cana-1750	80	11	)	)	PUNCT
cana-1750	80	12	=	=	SYM
cana-1750	81	1	|	|	ADV
cana-1750	81	2	𝑎𝑛	𝑎𝑛	VERB
cana-1750	81	3	𝑎𝑛+1	𝑎𝑛+1	PROPN
cana-1750	81	4	⋯	⋯	PROPN
cana-1750	81	5	𝑎𝑛+𝑘−1	𝑎𝑛+𝑘−1	PROPN
cana-1750	81	6	𝑎𝑛+1	𝑎𝑛+1	PROPN
cana-1750	81	7	𝑎𝑛	𝑎𝑛	PROPN
cana-1750	81	8	⋯	⋯	PROPN
cana-1750	81	9	𝑎𝑛+𝑘	𝑎𝑛+𝑘	PROPN
cana-1750	81	10	⋮	⋮	NOUN
cana-1750	81	11	⋮	⋮	PROPN
cana-1750	81	12	⋯	⋯	PROPN
cana-1750	81	13	⋮	⋮	NOUN
cana-1750	81	14	𝑎𝑛+𝑘−1	𝑎𝑛+𝑘−1	PROPN
cana-1750	81	15	𝑎𝑛+𝑘	𝑎𝑛+𝑘	PROPN
cana-1750	81	16	⋯	⋯	NOUN
cana-1750	81	17	𝑎𝑛	𝑎𝑛	PRON
cana-1750	81	18	|	|	ADV
cana-1750	81	19	.	.	PUNCT
cana-1750	82	1	(	(	PUNCT
cana-1750	82	2	1.14	1.14	NUM
cana-1750	82	3	)	)	PUNCT
cana-1750	82	4	for	for	ADP
cana-1750	82	5	example	example	NOUN
cana-1750	82	6	,	,	PUNCT
cana-1750	82	7	𝑇2(2	𝑇2(2	PROPN
cana-1750	82	8	)	)	PUNCT
cana-1750	82	9	=	=	PUNCT
cana-1750	83	1	|	|	ADV
cana-1750	83	2	𝑎2	𝑎2	PROPN
cana-1750	83	3	𝑎3	𝑎3	PROPN
cana-1750	83	4	𝑎3	𝑎3	PROPN
cana-1750	83	5	𝑎2	𝑎2	PROPN
cana-1750	83	6	|	|	ADV
cana-1750	83	7	,	,	PUNCT
cana-1750	83	8	𝑇2(3	𝑇2(3	X
cana-1750	83	9	)	)	PUNCT
cana-1750	83	10	=	=	SYM
cana-1750	84	1	|	|	ADV
cana-1750	84	2	𝑎3	𝑎3	PROPN
cana-1750	84	3	𝑎4	𝑎4	PROPN
cana-1750	84	4	𝑎4	𝑎4	PROPN
cana-1750	84	5	𝑎3	𝑎3	PROPN
cana-1750	84	6	|	|	ADV
cana-1750	84	7	,	,	PUNCT
cana-1750	84	8	𝑇3(2	𝑇3(2	NOUN
cana-1750	84	9	)	)	PUNCT
cana-1750	84	10	=	=	PUNCT
cana-1750	85	1	|	|	ADV
cana-1750	85	2	𝑎2	𝑎2	PROPN
cana-1750	85	3	𝑎3	𝑎3	PROPN
cana-1750	85	4	𝑎4	𝑎4	PROPN
cana-1750	85	5	𝑎3	𝑎3	PROPN
cana-1750	85	6	𝑎2	𝑎2	PROPN
cana-1750	85	7	𝑎3	𝑎3	PROPN
cana-1750	85	8	𝑎4	𝑎4	PROPN
cana-1750	85	9	𝑎3	𝑎3	PROPN
cana-1750	85	10	𝑎2	𝑎2	PROPN
cana-1750	85	11	|	|	ADV
cana-1750	85	12	,	,	PUNCT
cana-1750	85	13	𝑇3(1	𝑇3(1	ADV
cana-1750	85	14	)	)	PUNCT
cana-1750	85	15	=	=	SYM
cana-1750	86	1	|	|	ADV
cana-1750	86	2	1	1	NUM
cana-1750	86	3	𝑎2	𝑎2	NOUN
cana-1750	86	4	𝑎3	𝑎3	PROPN
cana-1750	86	5	𝑎2	𝑎2	PROPN
cana-1750	86	6	1	1	NUM
cana-1750	86	7	𝑎2	𝑎2	PROPN
cana-1750	86	8	𝑎3	𝑎3	PROPN
cana-1750	86	9	𝑎2	𝑎2	PROPN
cana-1750	86	10	1	1	NUM
cana-1750	86	11	|	|	ADV
cana-1750	86	12	(	(	PUNCT
cana-1750	86	13	1.15	1.15	NUM
cana-1750	86	14	)	)	PUNCT
cana-1750	86	15	for	for	ADP
cana-1750	86	16	𝑓	𝑓	DET
cana-1750	86	17	∈	∈	PROPN
cana-1750	86	18	𝓐	𝓐	PROPN
cana-1750	86	19	,	,	PUNCT
cana-1750	86	20	the	the	DET
cana-1750	86	21	problem	problem	NOUN
cana-1750	86	22	of	of	ADP
cana-1750	86	23	finding	find	VERB
cana-1750	86	24	the	the	DET
cana-1750	86	25	best	good	ADJ
cana-1750	86	26	possible	possible	ADJ
cana-1750	86	27	bounds	bound	NOUN
cana-1750	86	28	for	for	ADP
cana-1750	86	29	‖𝑎𝑛+1|	‖𝑎𝑛+1|	NOUN
cana-1750	86	30	−	−	PROPN
cana-1750	86	31	|𝑎𝑛‖	|𝑎𝑛‖	PROPN
cana-1750	86	32	has	have	VERB
cana-1750	86	33	a	a	DET
cana-1750	86	34	long	long	ADJ
cana-1750	86	35	history	history	NOUN
cana-1750	86	36	[	[	X
cana-1750	86	37	3	3	NUM
cana-1750	86	38	]	]	PUNCT
cana-1750	86	39	.	.	PUNCT
cana-1750	87	1	it	it	PRON
cana-1750	87	2	is	be	AUX
cana-1750	87	3	well	well	ADV
cana-1750	87	4	known	known	ADJ
cana-1750	87	5	[	[	X
cana-1750	87	6	3	3	NUM
cana-1750	87	7	]	]	PUNCT
cana-1750	87	8	,	,	PUNCT
cana-1750	87	9	that	that	SCONJ
cana-1750	87	10	||𝑎𝑛+1|	||𝑎𝑛+1|	PUNCT
cana-1750	87	11	−	−	PROPN
cana-1750	87	12	|𝑎𝑛‖	|𝑎𝑛‖	PROPN
cana-1750	87	13	≤	≤	PROPN
cana-1750	87	14	𝐶	𝐶	PROPN
cana-1750	87	15	;	;	PUNCT
cana-1750	87	16	however	however	ADV
cana-1750	87	17	,	,	PUNCT
cana-1750	87	18	finding	find	VERB
cana-1750	87	19	exact	exact	ADJ
cana-1750	87	20	values	value	NOUN
cana-1750	87	21	of	of	ADP
cana-1750	87	22	the	the	DET
cana-1750	87	23	constant	constant	ADJ
cana-1750	87	24	𝐶	𝐶	PROPN
cana-1750	87	25	for	for	ADP
cana-1750	87	26	𝓐	𝓐	PROPN
cana-1750	87	27	and	and	CCONJ
cana-1750	87	28	its	its	PRON
cana-1750	87	29	subclasses	subclass	NOUN
cana-1750	87	30	has	have	AUX
cana-1750	87	31	proved	prove	VERB
cana-1750	87	32	difficult	difficult	ADJ
cana-1750	87	33	.	.	PUNCT
cana-1750	88	1	it	it	PRON
cana-1750	88	2	is	be	AUX
cana-1750	88	3	clear	clear	ADJ
cana-1750	88	4	from	from	ADP
cana-1750	88	5	the	the	DET
cana-1750	88	6	definition	definition	NOUN
cana-1750	88	7	that	that	SCONJ
cana-1750	88	8	finding	find	VERB
cana-1750	88	9	estimates	estimate	NOUN
cana-1750	88	10	for	for	ADP
cana-1750	88	11	𝑇𝑘(𝑛	𝑇𝑘(𝑛	PROPN
cana-1750	88	12	)	)	PUNCT
cana-1750	88	13	is	be	AUX
cana-1750	88	14	related	relate	VERB
cana-1750	88	15	to	to	ADP
cana-1750	88	16	finding	find	VERB
cana-1750	88	17	bounds	bound	NOUN
cana-1750	88	18	for	for	ADP
cana-1750	88	19	|𝑎𝑛+1	|𝑎𝑛+1	X
cana-1750	88	20	−	−	PROPN
cana-1750	88	21	𝑎𝑛|	𝑎𝑛|	PROPN
cana-1750	88	22	.	.	PUNCT
cana-1750	89	1	the	the	DET
cana-1750	89	2	pivotal	pivotal	ADJ
cana-1750	89	3	moment	moment	NOUN
cana-1750	89	4	in	in	ADP
cana-1750	89	5	the	the	DET
cana-1750	89	6	exploration	exploration	NOUN
cana-1750	89	7	of	of	ADP
cana-1750	89	8	univalent	univalent	ADJ
cana-1750	89	9	functions	function	NOUN
cana-1750	89	10	occurred	occur	VERB
cana-1750	89	11	in	in	ADP
cana-1750	89	12	1985	1985	NUM
cana-1750	89	13	,	,	PUNCT
cana-1750	89	14	when	when	SCONJ
cana-1750	89	15	louis	louis	PROPN
cana-1750	89	16	de	de	X
cana-1750	89	17	branges	brange	NOUN
cana-1750	89	18	successfully	successfully	ADV
cana-1750	89	19	proved	prove	VERB
cana-1750	89	20	the	the	DET
cana-1750	89	21	renowned	renowned	ADJ
cana-1750	89	22	bieberbach	bieberbach	NOUN
cana-1750	89	23	conjecture	conjecture	NOUN
cana-1750	89	24	,	,	PUNCT
cana-1750	89	25	|𝑎𝑛|	|𝑎𝑛|	ADV
cana-1750	89	26	=	=	SYM
cana-1750	89	27	𝑛	𝑛	PROPN
cana-1750	89	28	for	for	ADP
cana-1750	89	29	𝑛	𝑛	NOUN
cana-1750	89	30	=	=	SYM
cana-1750	89	31	2	2	NUM
cana-1750	90	1	[	[	X
cana-1750	90	2	22	22	NUM
cana-1750	90	3	]	]	PUNCT
cana-1750	90	4	.	.	PUNCT
cana-1750	91	1	while	while	SCONJ
cana-1750	91	2	this	this	PRON
cana-1750	91	3	marked	mark	VERB
cana-1750	91	4	the	the	DET
cana-1750	91	5	conclusion	conclusion	NOUN
cana-1750	91	6	of	of	ADP
cana-1750	91	7	an	an	DET
cana-1750	91	8	era	era	NOUN
cana-1750	91	9	,	,	PUNCT
cana-1750	91	10	numerous	numerous	ADJ
cana-1750	91	11	unresolved	unresolved	ADJ
cana-1750	91	12	issues	issue	NOUN
cana-1750	91	13	persist	persist	VERB
cana-1750	91	14	,	,	PUNCT
cana-1750	91	15	including	include	VERB
cana-1750	91	16	the	the	DET
cana-1750	91	17	notable	notable	ADJ
cana-1750	91	18	zalcman	zalcman	PROPN
cana-1750	91	19	conjecture	conjecture	NOUN
cana-1750	91	20	,	,	PUNCT
cana-1750	91	21	which	which	PRON
cana-1750	91	22	pertains	pertain	VERB
cana-1750	91	23	to	to	ADP
cana-1750	91	24	the	the	DET
cana-1750	91	25	coefficients	coefficient	NOUN
cana-1750	91	26	𝑎𝑛.	𝑎𝑛.	X
cana-1750	91	27	one	one	NOUN
cana-1750	91	28	such	such	ADJ
cana-1750	91	29	is	be	AUX
cana-1750	91	30	the	the	DET
cana-1750	91	31	zalcman	zalcman	PROPN
cana-1750	91	32	conjecture	conjecture	NOUN
cana-1750	91	33	is	be	AUX
cana-1750	91	34	|𝑎𝑛	|𝑎𝑛	PROPN
cana-1750	91	35	−	−	PROPN
cana-1750	91	36	𝑎2𝑛−1|	𝑎2𝑛−1|	PROPN
cana-1750	91	37	≤	≤	NOUN
cana-1750	91	38	(	(	PUNCT
cana-1750	91	39	𝑛	𝑛	DET
cana-1750	91	40	−	−	PROPN
cana-1750	91	41	1)2	1)2	NUM
cana-1750	91	42	,	,	PUNCT
cana-1750	91	43	(	(	PUNCT
cana-1750	91	44	𝑛	𝑛	PROPN
cana-1750	91	45	∈	∈	PROPN
cana-1750	91	46	ℕ	ℕ	PROPN
cana-1750	91	47	,	,	PUNCT
cana-1750	91	48	𝑛	𝑛	DET
cana-1750	91	49	≥	≥	NOUN
cana-1750	91	50	2	2	NUM
cana-1750	91	51	)	)	PUNCT
cana-1750	91	52	.	.	PUNCT
cana-1750	92	1	(	(	PUNCT
cana-1750	92	2	1.16	1.16	NUM
cana-1750	92	3	)	)	PUNCT
cana-1750	92	4	formulated	formulate	VERB
cana-1750	92	5	in	in	ADP
cana-1750	92	6	the	the	DET
cana-1750	92	7	early	early	ADJ
cana-1750	92	8	1970s	1970	NOUN
cana-1750	92	9	,	,	PUNCT
cana-1750	92	10	krushkal	krushkal	ADJ
cana-1750	92	11	[	[	X
cana-1750	92	12	23	23	NUM
cana-1750	92	13	]	]	PUNCT
cana-1750	92	14	.	.	PUNCT
cana-1750	92	15	,	,	PUNCT
cana-1750	92	16	made	make	VERB
cana-1750	92	17	significant	significant	ADJ
cana-1750	92	18	strides	stride	NOUN
cana-1750	92	19	in	in	ADP
cana-1750	92	20	this	this	DET
cana-1750	92	21	direction	direction	NOUN
cana-1750	92	22	,	,	PUNCT
cana-1750	92	23	employing	employ	VERB
cana-1750	92	24	the	the	DET
cana-1750	92	25	complex	complex	ADJ
cana-1750	92	26	geometry	geometry	NOUN
cana-1750	92	27	of	of	ADP
cana-1750	92	28	the	the	DET
cana-1750	92	29	universal	universal	ADJ
cana-1750	92	30	teichm	teichm	NOUN
cana-1750	92	31	̈	̈	PUNCT
cana-1750	92	32	üller	üller	ADJ
cana-1750	92	33	space	space	NOUN
cana-1750	92	34	.	.	PUNCT
cana-1750	93	1	in	in	ADP
cana-1750	93	2	1999	1999	NUM
cana-1750	93	3	,	,	PUNCT
cana-1750	93	4	a	a	DET
cana-1750	93	5	broader	broad	ADJ
cana-1750	93	6	perspective	perspective	NOUN
cana-1750	93	7	on	on	ADP
cana-1750	93	8	the	the	DET
cana-1750	93	9	generalized	generalize	VERB
cana-1750	93	10	zalcman	zalcman	NOUN
cana-1750	93	11	conjecture	conjecture	NOUN
cana-1750	93	12	was	be	AUX
cana-1750	93	13	introduced	introduce	VERB
cana-1750	93	14	by	by	ADP
cana-1750	93	15	ma	ma	PROPN
cana-1750	94	1	[	[	X
cana-1750	94	2	24	24	NUM
cana-1750	94	3	]	]	PUNCT
cana-1750	94	4	.	.	PUNCT
cana-1750	95	1	the	the	DET
cana-1750	95	2	generalized	generalized	ADJ
cana-1750	95	3	zalcman	zalcman	NOUN
cana-1750	95	4	conjecture	conjecture	NOUN
cana-1750	95	5	is	be	AUX
cana-1750	95	6	|𝑎𝑚𝑎𝑛	|𝑎𝑚𝑎𝑛	PRON
cana-1750	95	7	−	−	NOUN
cana-1750	95	8	𝑎𝑚+𝑛−1|	𝑎𝑚+𝑛−1|	NOUN
cana-1750	95	9	≤	≤	NOUN
cana-1750	95	10	(	(	PUNCT
cana-1750	95	11	𝑚	𝑚	PROPN
cana-1750	95	12	−	−	PROPN
cana-1750	95	13	1)(𝑛	1)(𝑛	NUM
cana-1750	96	1	−	−	NOUN
cana-1750	96	2	1	1	NUM
cana-1750	96	3	)	)	PUNCT
cana-1750	96	4	,	,	PUNCT
cana-1750	96	5	(	(	PUNCT
cana-1750	96	6	𝑚	𝑚	X
cana-1750	96	7	,	,	PUNCT
cana-1750	96	8	𝑛	𝑛	PRON
cana-1750	96	9	∈	∈	NOUN
cana-1750	96	10	ℕ,𝑚	ℕ,𝑚	NOUN
cana-1750	96	11	≥	≥	NOUN
cana-1750	96	12	2	2	NUM
cana-1750	96	13	,	,	PUNCT
cana-1750	96	14	𝑛	𝑛	DET
cana-1750	96	15	≥	≥	NOUN
cana-1750	96	16	2	2	NUM
cana-1750	96	17	)	)	PUNCT
cana-1750	96	18	.	.	PUNCT
cana-1750	97	1	(	(	PUNCT
cana-1750	97	2	1.17	1.17	NUM
cana-1750	97	3	)	)	PUNCT
cana-1750	97	4	ma	ma	NOUN
cana-1750	98	1	[	[	X
cana-1750	98	2	23	23	NUM
cana-1750	98	3	]	]	PUNCT
cana-1750	98	4	successfully	successfully	ADV
cana-1750	98	5	resolved	resolve	VERB
cana-1750	98	6	the	the	DET
cana-1750	98	7	open	open	ADJ
cana-1750	98	8	problem	problem	NOUN
cana-1750	98	9	within	within	ADP
cana-1750	98	10	the	the	DET
cana-1750	98	11	realm	realm	NOUN
cana-1750	98	12	of	of	ADP
cana-1750	98	13	star	star	NOUN
cana-1750	98	14	-	-	PUNCT
cana-1750	98	15	like	like	ADJ
cana-1750	98	16	functions	function	NOUN
cana-1750	98	17	and	and	CCONJ
cana-1750	98	18	univalent	univalent	ADJ
cana-1750	98	19	functions	function	NOUN
cana-1750	98	20	with	with	ADP
cana-1750	98	21	real	real	ADJ
cana-1750	98	22	coefficients	coefficient	NOUN
cana-1750	98	23	.	.	PUNCT
cana-1750	99	1	ravichandran	ravichandran	NOUN
cana-1750	99	2	and	and	CCONJ
cana-1750	99	3	verma	verma	PROPN
cana-1750	99	4	,	,	PUNCT
cana-1750	99	5	as	as	SCONJ
cana-1750	99	6	documented	document	VERB
cana-1750	99	7	in	in	ADP
cana-1750	99	8	[	[	X
cana-1750	99	9	27	27	NUM
cana-1750	99	10	]	]	PUNCT
cana-1750	99	11	,	,	PUNCT
cana-1750	99	12	also	also	ADV
cana-1750	99	13	tackled	tackle	VERB
cana-1750	99	14	and	and	CCONJ
cana-1750	99	15	closed	close	VERB
cana-1750	99	16	the	the	DET
cana-1750	99	17	issue	issue	NOUN
cana-1750	99	18	for	for	ADP
cana-1750	99	19	star	star	NOUN
cana-1750	99	20	like	like	ADP
cana-1750	99	21	and	and	CCONJ
cana-1750	99	22	convex	convex	NOUN
cana-1750	99	23	functions	function	NOUN
cana-1750	99	24	of	of	ADP
cana-1750	99	25	specified	specified	ADJ
cana-1750	99	26	order	order	NOUN
cana-1750	99	27	,	,	PUNCT
cana-1750	99	28	as	as	ADV
cana-1750	99	29	well	well	ADV
cana-1750	99	30	as	as	ADP
cana-1750	99	31	for	for	ADP
cana-1750	99	32	functions	function	NOUN
cana-1750	99	33	characterized	characterize	VERB
cana-1750	99	34	by	by	ADP
cana-1750	99	35	bounded	bounded	ADJ
cana-1750	99	36	turning	turning	NOUN
cana-1750	99	37	.	.	PUNCT
cana-1750	100	1	ozaki	ozaki	PROPN
cana-1750	100	2	and	and	CCONJ
cana-1750	100	3	nunokawa	nunokawa	NOUN
cana-1750	100	4	,	,	PUNCT
cana-1750	100	5	as	as	SCONJ
cana-1750	100	6	outlined	outline	VERB
cana-1750	100	7	in	in	ADP
cana-1750	100	8	[	[	X
cana-1750	100	9	25	25	NUM
cana-1750	100	10	]	]	PUNCT
cana-1750	100	11	,	,	PUNCT
cana-1750	100	12	established	establish	VERB
cana-1750	100	13	the	the	DET
cana-1750	100	14	univalence	univalence	NOUN
cana-1750	100	15	of	of	ADP
cana-1750	100	16	functions	function	NOUN
cana-1750	100	17	within	within	ADP
cana-1750	100	18	this	this	DET
cana-1750	100	19	class	class	NOUN
cana-1750	100	20	,	,	PUNCT
cana-1750	100	21	deviating	deviate	VERB
cana-1750	100	22	from	from	ADP
cana-1750	100	23	the	the	DET
cana-1750	100	24	conventional	conventional	ADJ
cana-1750	100	25	characteristics	characteristic	NOUN
cana-1750	100	26	observed	observe	VERB
cana-1750	100	27	in	in	ADP
cana-1750	100	28	other	other	ADJ
cana-1750	100	29	univalent	univalent	ADJ
cana-1750	100	30	functions	function	NOUN
cana-1750	100	31	.	.	PUNCT
cana-1750	101	1	unlike	unlike	ADP
cana-1750	101	2	the	the	DET
cana-1750	101	3	broad	broad	ADJ
cana-1750	101	4	category	category	NOUN
cana-1750	101	5	of	of	ADP
cana-1750	101	6	star	star	NOUN
cana-1750	101	7	like	like	ADP
cana-1750	101	8	functions	function	NOUN
cana-1750	101	9	,	,	PUNCT
cana-1750	101	10	these	these	PRON
cana-1750	101	11	exhibit	exhibit	VERB
cana-1750	101	12	unique	unique	ADJ
cana-1750	101	13	patterns	pattern	NOUN
cana-1750	101	14	,	,	PUNCT
cana-1750	101	15	adding	add	VERB
cana-1750	101	16	intrigue	intrigue	NOUN
cana-1750	101	17	to	to	ADP
cana-1750	101	18	their	their	PRON
cana-1750	101	19	study	study	NOUN
cana-1750	101	20	.	.	PUNCT
cana-1750	102	1	the	the	DET
cana-1750	102	2	class	class	NOUN
cana-1750	102	3	𝔻	𝔻	PROPN
cana-1750	102	4	,	,	PUNCT
cana-1750	102	5	being	be	AUX
cana-1750	102	6	distinct	distinct	ADJ
cana-1750	102	7	,	,	PUNCT
cana-1750	102	8	has	have	AUX
cana-1750	102	9	garnered	garner	VERB
cana-1750	102	10	substantial	substantial	ADJ
cana-1750	102	11	interest	interest	NOUN
cana-1750	102	12	over	over	ADP
cana-1750	102	13	the	the	DET
cana-1750	102	14	previous	previous	ADJ
cana-1750	102	15	decades	decade	NOUN
cana-1750	102	16	.	.	PUNCT
cana-1750	103	1	chapter	chapter	NOUN
cana-1750	103	2	12	12	NUM
cana-1750	103	3	of	of	ADP
cana-1750	103	4	[	[	X
cana-1750	103	5	28	28	NUM
cana-1750	103	6	]	]	PUNCT
cana-1750	103	7	,	,	PUNCT
cana-1750	103	8	provides	provide	VERB
cana-1750	103	9	a	a	DET
cana-1750	103	10	comprehensive	comprehensive	ADJ
cana-1750	103	11	summary	summary	NOUN
cana-1750	103	12	of	of	ADP
cana-1750	103	13	the	the	DET
cana-1750	103	14	noteworthy	noteworthy	ADJ
cana-1750	103	15	findings	finding	NOUN
cana-1750	103	16	in	in	ADP
cana-1750	103	17	this	this	DET
cana-1750	103	18	field	field	NOUN
cana-1750	103	19	.	.	PUNCT
cana-1750	104	1	we	we	PRON
cana-1750	104	2	have	have	VERB
cana-1750	104	3	|𝑎𝑛	|𝑎𝑛	PROPN
cana-1750	104	4	𝑝	𝑝	NOUN
cana-1750	104	5	−	−	PROPN
cana-1750	104	6	𝑎2	𝑎2	PROPN
cana-1750	104	7	𝑝(𝑛−1	𝑝(𝑛−1	PROPN
cana-1750	104	8	)	)	PUNCT
cana-1750	104	9	|	|	ADV
cana-1750	104	10	≤	≤	NUM
cana-1750	104	11	2𝑝(𝑛−1	2𝑝(𝑛−1	NOUN
cana-1750	104	12	)	)	PUNCT
cana-1750	104	13	−	−	NOUN
cana-1750	104	14	2𝑝	2𝑝	NOUN
cana-1750	104	15	,	,	PUNCT
cana-1750	104	16	(	(	PUNCT
cana-1750	104	17	𝑚	𝑚	NOUN
cana-1750	104	18	,	,	PUNCT
cana-1750	104	19	𝑛	𝑛	PRON
cana-1750	104	20	∈	∈	NOUN
cana-1750	104	21	ℕ,𝑚	ℕ,𝑚	NOUN
cana-1750	104	22	≥	≥	NOUN
cana-1750	104	23	2	2	NUM
cana-1750	104	24	,	,	PUNCT
cana-1750	104	25	𝑛	𝑛	DET
cana-1750	104	26	≥	≥	NOUN
cana-1750	104	27	2	2	NUM
cana-1750	104	28	)	)	PUNCT
cana-1750	104	29	.	.	PUNCT
cana-1750	105	1	(	(	PUNCT
cana-1750	105	2	1.18	1.18	NUM
cana-1750	105	3	)	)	PUNCT
cana-1750	105	4	communications	communication	NOUN
cana-1750	105	5	on	on	ADP
cana-1750	105	6	applied	apply	VERB
cana-1750	105	7	nonlinear	nonlinear	ADJ
cana-1750	105	8	analysis	analysis	NOUN
cana-1750	105	9	issn	issn	NOUN
cana-1750	105	10	:	:	PUNCT
cana-1750	105	11	1074	1074	NUM
cana-1750	105	12	-	-	PUNCT
cana-1750	105	13	133x	133x	NUM
cana-1750	105	14	vol	vol	NOUN
cana-1750	105	15	32	32	NUM
cana-1750	105	16	no	no	NOUN
cana-1750	105	17	.	.	NOUN
cana-1750	105	18	2	2	NUM
cana-1750	105	19	(	(	PUNCT
cana-1750	105	20	2025	2025	NUM
cana-1750	105	21	)	)	PUNCT
cana-1750	105	22	387	387	NUM
cana-1750	105	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	105	24	over	over	ADP
cana-1750	105	25	the	the	DET
cana-1750	105	26	class	class	NOUN
cana-1750	105	27	𝔻	𝔻	PROPN
cana-1750	105	28	for	for	ADP
cana-1750	105	29	the	the	DET
cana-1750	105	30	cases	case	NOUN
cana-1750	105	31	𝑛	𝑛	VERB
cana-1750	105	32	=	=	SYM
cana-1750	105	33	4	4	NUM
cana-1750	105	34	,	,	PUNCT
cana-1750	105	35	𝑝	𝑝	NOUN
cana-1750	105	36	=	=	SYM
cana-1750	105	37	1	1	NUM
cana-1750	105	38	and	and	CCONJ
cana-1750	105	39	𝑛	𝑛	ADJ
cana-1750	105	40	=	=	SYM
cana-1750	105	41	5	5	NUM
cana-1750	105	42	,	,	PUNCT
cana-1750	105	43	𝑝	𝑝	NOUN
cana-1750	105	44	=	=	SYM
cana-1750	105	45	1	1	X
cana-1750	105	46	.	.	PUNCT
cana-1750	106	1	this	this	DET
cana-1750	106	2	inequality	inequality	NOUN
cana-1750	106	3	was	be	AUX
cana-1750	106	4	introduced	introduce	VERB
cana-1750	106	5	by	by	ADP
cana-1750	106	6	krushkal	krushkal	NOUN
cana-1750	106	7	and	and	CCONJ
cana-1750	106	8	proven	prove	VERB
cana-1750	106	9	for	for	ADP
cana-1750	106	10	the	the	DET
cana-1750	106	11	whole	whole	ADJ
cana-1750	106	12	class	class	NOUN
cana-1750	106	13	of	of	ADP
cana-1750	106	14	univalent	univalent	ADJ
cana-1750	106	15	functions	function	NOUN
cana-1750	106	16	[	[	X
cana-1750	106	17	23	23	NUM
cana-1750	106	18	]	]	PUNCT
cana-1750	106	19	.	.	PUNCT
cana-1750	107	1	2	2	X
cana-1750	107	2	.	.	X
cana-1750	107	3	definitions	definition	NOUN
cana-1750	107	4	and	and	CCONJ
cana-1750	107	5	preliminaries	preliminary	NOUN
cana-1750	107	6	lemma	lemma	VERB
cana-1750	107	7	2.1	2.1	NUM
cana-1750	107	8	.	.	PUNCT
cana-1750	108	1	[	[	X
cana-1750	108	2	17	17	NUM
cana-1750	108	3	]	]	PUNCT
cana-1750	108	4	let	let	VERB
cana-1750	108	5	𝑝	𝑝	PRON
cana-1750	108	6	∈	∈	PROPN
cana-1750	108	7	𝒫	𝒫	NOUN
cana-1750	108	8	,	,	PUNCT
cana-1750	108	9	be	be	AUX
cana-1750	108	10	given	give	VERB
cana-1750	108	11	by	by	ADP
cana-1750	108	12	(	(	PUNCT
cana-1750	108	13	1.6	1.6	NUM
cana-1750	108	14	)	)	PUNCT
cana-1750	108	15	,	,	PUNCT
cana-1750	108	16	then	then	ADV
cana-1750	108	17	|𝑝𝑛|	|𝑝𝑛|	VERB
cana-1750	108	18	≤	≤	NUM
cana-1750	108	19	2	2	NUM
cana-1750	108	20	,	,	PUNCT
cana-1750	108	21	∀𝑛	∀𝑛	PROPN
cana-1750	108	22	∈	∈	PROPN
cana-1750	108	23	ℕ.	ℕ.	PROPN
cana-1750	108	24	(	(	PUNCT
cana-1750	108	25	2.1	2.1	NUM
cana-1750	108	26	)	)	PUNCT
cana-1750	108	27	and	and	CCONJ
cana-1750	108	28	|𝑝2	|𝑝2	NOUN
cana-1750	108	29	−	−	NOUN
cana-1750	108	30	1	1	NUM
cana-1750	108	31	2	2	NUM
cana-1750	108	32	𝑝1	𝑝1	NOUN
cana-1750	108	33	2|	2|	NUM
cana-1750	108	34	≤	≤	ADV
cana-1750	108	35	2	2	NUM
cana-1750	108	36	−	−	NUM
cana-1750	108	37	1	1	NUM
cana-1750	108	38	2	2	NUM
cana-1750	108	39	|𝑝1|	|𝑝1|	VERB
cana-1750	108	40	2	2	NUM
cana-1750	108	41	.	.	PUNCT
cana-1750	108	42	(	(	PUNCT
cana-1750	108	43	2.2	2.2	NUM
cana-1750	108	44	)	)	PUNCT
cana-1750	108	45	lemma	lemma	PROPN
cana-1750	108	46	2.2	2.2	NUM
cana-1750	108	47	.	.	PUNCT
cana-1750	109	1	[	[	X
cana-1750	109	2	30	30	NUM
cana-1750	109	3	]	]	PUNCT
cana-1750	109	4	,	,	PUNCT
cana-1750	109	5	[	[	X
cana-1750	109	6	16	16	NUM
cana-1750	109	7	]	]	PUNCT
cana-1750	109	8	let	let	VERB
cana-1750	109	9	𝑝	𝑝	PRON
cana-1750	109	10	∈	∈	PROPN
cana-1750	109	11	𝒫	𝒫	NOUN
cana-1750	109	12	,	,	PUNCT
cana-1750	109	13	be	be	AUX
cana-1750	109	14	given	give	VERB
cana-1750	109	15	by	by	ADP
cana-1750	109	16	(	(	PUNCT
cana-1750	109	17	1.6	1.6	NUM
cana-1750	109	18	)	)	PUNCT
cana-1750	109	19	,	,	PUNCT
cana-1750	109	20	then	then	ADV
cana-1750	109	21	for	for	ADP
cana-1750	109	22	some	some	DET
cana-1750	109	23	complex	complex	NOUN
cana-1750	109	24	valued	value	VERB
cana-1750	109	25	𝑥	𝑥	NOUN
cana-1750	109	26	with	with	ADP
cana-1750	109	27	|𝑥|	|𝑥|	ADJ
cana-1750	109	28	≤	≤	NUM
cana-1750	109	29	1	1	NUM
cana-1750	109	30	,	,	PUNCT
cana-1750	109	31	some	some	DET
cana-1750	109	32	complex	complex	NOUN
cana-1750	109	33	valued	value	VERB
cana-1750	109	34	𝜚	𝜚	NOUN
cana-1750	109	35	with	with	ADP
cana-1750	109	36	|𝜚|	|𝜚|	PROPN
cana-1750	109	37	≤	≤	NUM
cana-1750	109	38	1	1	NUM
cana-1750	109	39	and	and	CCONJ
cana-1750	109	40	some	some	DET
cana-1750	109	41	complex	complex	ADJ
cana-1750	109	42	valued	value	VERB
cana-1750	109	43	𝜓	𝜓	NOUN
cana-1750	109	44	with	with	ADP
cana-1750	109	45	|𝜓|	|𝜓|	NOUN
cana-1750	109	46	≤	≤	NUM
cana-1750	109	47	1	1	NUM
cana-1750	109	48	.	.	PUNCT
cana-1750	110	1	we	we	PRON
cana-1750	110	2	have	have	VERB
cana-1750	110	3	2𝑝2	2𝑝2	NUM
cana-1750	110	4	=	=	SYM
cana-1750	110	5	𝑝1	𝑝1	NOUN
cana-1750	110	6	2	2	NUM
cana-1750	110	7	+	+	CCONJ
cana-1750	110	8	𝑥(4	𝑥(4	PROPN
cana-1750	110	9	−	−	PROPN
cana-1750	110	10	𝑝1	𝑝1	NOUN
cana-1750	110	11	2	2	NUM
cana-1750	110	12	)	)	PUNCT
cana-1750	110	13	(	(	PUNCT
cana-1750	110	14	2.3	2.3	NUM
cana-1750	110	15	)	)	PUNCT
cana-1750	110	16	4𝑝3	4𝑝3	NOUN
cana-1750	111	1	=	=	SYM
cana-1750	111	2	𝑝1	𝑝1	NOUN
cana-1750	111	3	3	3	NUM
cana-1750	111	4	+	+	CCONJ
cana-1750	111	5	2(4	2(4	NUM
cana-1750	111	6	−	−	PROPN
cana-1750	111	7	𝑝1	𝑝1	NOUN
cana-1750	111	8	2)𝑝1𝑥	2)𝑝1𝑥	NOUN
cana-1750	111	9	−	−	PROPN
cana-1750	111	10	𝑝1(4	𝑝1(4	PROPN
cana-1750	111	11	−	−	PROPN
cana-1750	111	12	𝑝1	𝑝1	NOUN
cana-1750	111	13	2)𝑥2	2)𝑥2	PROPN
cana-1750	111	14	+	+	CCONJ
cana-1750	111	15	2(4	2(4	NUM
cana-1750	111	16	−	−	PROPN
cana-1750	112	1	𝑝1	𝑝1	NOUN
cana-1750	112	2	2)(1	2)(1	NUM
cana-1750	112	3	−	−	PROPN
cana-1750	112	4	|𝑥|2)𝜚	|𝑥|2)𝜚	PROPN
cana-1750	112	5	(	(	PUNCT
cana-1750	112	6	2.4	2.4	NUM
cana-1750	112	7	)	)	PUNCT
cana-1750	112	8	8𝑝4	8𝑝4	NUM
cana-1750	113	1	=	=	SYM
cana-1750	113	2	𝑝1	𝑝1	NOUN
cana-1750	113	3	4	4	NUM
cana-1750	113	4	+	+	CCONJ
cana-1750	113	5	(	(	PUNCT
cana-1750	113	6	4	4	NUM
cana-1750	113	7	−	−	NOUN
cana-1750	113	8	𝑝1	𝑝1	NOUN
cana-1750	113	9	2)𝑥[𝑝1	2)𝑥[𝑝1	NUM
cana-1750	113	10	2(𝑥2	2(𝑥2	NUM
cana-1750	113	11	−	−	NOUN
cana-1750	113	12	3𝑥	3𝑥	NUM
cana-1750	113	13	+	+	CCONJ
cana-1750	113	14	3	3	X
cana-1750	113	15	)	)	PUNCT
cana-1750	113	16	+	+	NUM
cana-1750	113	17	4𝑥	4𝑥	NOUN
cana-1750	113	18	]	]	PUNCT
cana-1750	113	19	(	(	PUNCT
cana-1750	113	20	2.4	2.4	NUM
cana-1750	113	21	)	)	PUNCT
cana-1750	113	22	−4(4	−4(4	NOUN
cana-1750	113	23	−	−	PROPN
cana-1750	114	1	𝑝1	𝑝1	NOUN
cana-1750	114	2	2)(1	2)(1	NUM
cana-1750	114	3	−	−	NOUN
cana-1750	114	4	|𝑥|2)[𝑝(𝑥	|𝑥|2)[𝑝(𝑥	PRON
cana-1750	115	1	−	−	NOUN
cana-1750	115	2	1)𝜚	1)𝜚	NUM
cana-1750	115	3	+	+	PUNCT
cana-1750	115	4	𝑥‾𝜚2	𝑥‾𝜚2	ADJ
cana-1750	115	5	−	−	PROPN
cana-1750	115	6	1	1	NUM
cana-1750	115	7	−	−	NOUN
cana-1750	115	8	|𝜚|2𝜓	|𝜚|2𝜓	VERB
cana-1750	115	9	]	]	PUNCT
cana-1750	115	10	.	.	PUNCT
cana-1750	116	1	(	(	PUNCT
cana-1750	116	2	2.5	2.5	NUM
cana-1750	116	3	)	)	PUNCT
cana-1750	116	4	3	3	NUM
cana-1750	116	5	.	.	PUNCT
cana-1750	117	1	coefficient	coefficient	NOUN
cana-1750	117	2	estimates	estimate	NOUN
cana-1750	117	3	for	for	ADP
cana-1750	117	4	toeplitz	toeplitz	NOUN
cana-1750	117	5	determinant	determinant	ADJ
cana-1750	117	6	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	117	7	)	)	PUNCT
cana-1750	117	8	in	in	ADP
cana-1750	117	9	our	our	PRON
cana-1750	117	10	first	first	ADJ
cana-1750	117	11	theorem	theorem	NOUN
cana-1750	117	12	we	we	PRON
cana-1750	117	13	determinant	determinant	VERB
cana-1750	117	14	a	a	DET
cana-1750	117	15	sharp	sharp	ADV
cana-1750	117	16	bound	bind	VERB
cana-1750	117	17	for	for	ADP
cana-1750	117	18	the	the	DET
cana-1750	117	19	coefficient	coefficient	NOUN
cana-1750	117	20	body	body	NOUN
cana-1750	117	21	𝑇2(2	𝑇2(2	NOUN
cana-1750	117	22	)	)	PUNCT
cana-1750	117	23	.	.	PUNCT
cana-1750	118	1	theorem	theorem	VERB
cana-1750	118	2	3.1	3.1	NUM
cana-1750	118	3	.	.	PUNCT
cana-1750	119	1	let	let	VERB
cana-1750	119	2	𝑓	𝑓	PRON
cana-1750	119	3	given	give	VERB
cana-1750	119	4	by	by	ADP
cana-1750	119	5	(	(	PUNCT
cana-1750	119	6	1.1	1.1	NUM
cana-1750	119	7	)	)	PUNCT
cana-1750	119	8	,	,	PUNCT
cana-1750	119	9	be	be	AUX
cana-1750	119	10	in	in	ADP
cana-1750	119	11	the	the	DET
cana-1750	119	12	class	class	NOUN
cana-1750	119	13	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	119	14	)	)	PUNCT
cana-1750	119	15	;	;	PUNCT
cana-1750	119	16	(	(	PUNCT
cana-1750	119	17	0	0	NUM
cana-1750	119	18	≤	≤	NUM
cana-1750	119	19	𝜆	𝜆	PRON
cana-1750	119	20	≤	≤	NUM
cana-1750	119	21	1	1	NUM
cana-1750	119	22	)	)	PUNCT
cana-1750	119	23	.	.	PUNCT
cana-1750	120	1	then	then	ADV
cana-1750	120	2	we	we	PRON
cana-1750	120	3	have	have	AUX
cana-1750	120	4	sharp	sharp	ADV
cana-1750	120	5	bound	bind	VERB
cana-1750	120	6	|𝑇2(2)|	|𝑇2(2)|	PROPN
cana-1750	120	7	=	=	PRON
cana-1750	120	8	|𝑎3	|𝑎3	VERB
cana-1750	120	9	2	2	NUM
cana-1750	120	10	−	−	NOUN
cana-1750	120	11	𝑎2	𝑎2	NOUN
cana-1750	120	12	2|	2|	NUM
cana-1750	120	13	≤	≤	ADV
cana-1750	120	14	4	4	NUM
cana-1750	120	15	(	(	PUNCT
cana-1750	120	16	𝜆	𝜆	PRON
cana-1750	120	17	+	+	CCONJ
cana-1750	120	18	2)2	2)2	NUM
cana-1750	120	19	max	max	NOUN
cana-1750	120	20	{	{	PUNCT
cana-1750	120	21	1	1	NUM
cana-1750	120	22	,	,	PUNCT
cana-1750	120	23	|	|	ADV
cana-1750	120	24	−40𝜆3	−40𝜆3	NUM
cana-1750	121	1	−	−	PROPN
cana-1750	122	1	60𝜆2	60𝜆2	NUM
cana-1750	122	2	+	+	NUM
cana-1750	122	3	20	20	NUM
cana-1750	122	4	(	(	PUNCT
cana-1750	122	5	𝜆	𝜆	PROPN
cana-1750	122	6	+	+	CCONJ
cana-1750	122	7	1)4	1)4	NUM
cana-1750	122	8	|	|	NOUN
cana-1750	122	9	}	}	PUNCT
cana-1750	122	10	.	.	PUNCT
cana-1750	123	1	proof	proof	NOUN
cana-1750	123	2	.	.	PUNCT
cana-1750	124	1	first	first	ADV
cana-1750	124	2	note	note	VERB
cana-1750	124	3	that	that	SCONJ
cana-1750	124	4	by	by	ADP
cana-1750	124	5	equating	equate	VERB
cana-1750	124	6	the	the	DET
cana-1750	124	7	corresponding	corresponding	ADJ
cana-1750	124	8	coefficients	coefficient	NOUN
cana-1750	124	9	in	in	ADP
cana-1750	124	10	the	the	DET
cana-1750	124	11	equation	equation	NOUN
cana-1750	124	12	𝑧𝑓′(𝑧	𝑧𝑓′(𝑧	PROPN
cana-1750	124	13	)	)	PUNCT
cana-1750	124	14	(	(	PUNCT
cana-1750	124	15	1−𝜆)𝑓(𝑧)+𝜆𝑧	1−𝜆)𝑓(𝑧)+𝜆𝑧	X
cana-1750	124	16	=	=	SYM
cana-1750	124	17	𝑝(𝑧	𝑝(𝑧	PROPN
cana-1750	124	18	)	)	PUNCT
cana-1750	124	19	(	(	PUNCT
cana-1750	124	20	3.1	3.1	NUM
cana-1750	124	21	)	)	PUNCT
cana-1750	124	22	we	we	PRON
cana-1750	124	23	get	get	VERB
cana-1750	124	24	communications	communication	NOUN
cana-1750	124	25	on	on	ADP
cana-1750	124	26	applied	apply	VERB
cana-1750	124	27	nonlinear	nonlinear	ADJ
cana-1750	124	28	analysis	analysis	NOUN
cana-1750	124	29	issn	issn	NOUN
cana-1750	124	30	:	:	PUNCT
cana-1750	124	31	1074	1074	NUM
cana-1750	124	32	-	-	PUNCT
cana-1750	124	33	133x	133x	NUM
cana-1750	124	34	vol	vol	NOUN
cana-1750	124	35	32	32	NUM
cana-1750	124	36	no	no	NOUN
cana-1750	124	37	.	.	NOUN
cana-1750	124	38	2	2	NUM
cana-1750	124	39	(	(	PUNCT
cana-1750	124	40	2025	2025	NUM
cana-1750	124	41	)	)	PUNCT
cana-1750	125	1	388	388	NUM
cana-1750	125	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	125	3	𝑎2	𝑎2	NOUN
cana-1750	125	4	=	=	PUNCT
cana-1750	125	5	𝑝1	𝑝1	PROPN
cana-1750	125	6	𝜆	𝜆	NOUN
cana-1750	125	7	+	+	PROPN
cana-1750	125	8	1	1	NUM
cana-1750	125	9	,	,	PUNCT
cana-1750	125	10	(	(	PUNCT
cana-1750	125	11	3.2	3.2	NUM
cana-1750	125	12	)	)	PUNCT
cana-1750	125	13	𝑎3	𝑎3	PROPN
cana-1750	125	14	=	=	SYM
cana-1750	125	15	𝑝1	𝑝1	PROPN
cana-1750	125	16	2(1	2(1	NUM
cana-1750	125	17	−	−	NOUN
cana-1750	125	18	𝜆	𝜆	NOUN
cana-1750	125	19	)	)	PUNCT
cana-1750	125	20	(	(	PUNCT
cana-1750	125	21	𝜆	𝜆	PROPN
cana-1750	125	22	+	+	NOUN
cana-1750	125	23	1)(𝜆	1)(𝜆	NUM
cana-1750	125	24	+	+	CCONJ
cana-1750	125	25	2	2	NUM
cana-1750	125	26	)	)	PUNCT
cana-1750	125	27	+	+	NUM
cana-1750	125	28	𝑝2	𝑝2	PROPN
cana-1750	125	29	𝜆	𝜆	PROPN
cana-1750	125	30	+	+	ADJ
cana-1750	125	31	2	2	NUM
cana-1750	125	32	,	,	PUNCT
cana-1750	125	33	(	(	PUNCT
cana-1750	125	34	3.3	3.3	NUM
cana-1750	125	35	)	)	PUNCT
cana-1750	125	36	𝑎4	𝑎4	PROPN
cana-1750	125	37	=	=	SYM
cana-1750	125	38	𝑝1	𝑝1	PROPN
cana-1750	125	39	3(1	3(1	NUM
cana-1750	125	40	−	−	PROPN
cana-1750	125	41	𝜆)2	𝜆)2	NOUN
cana-1750	125	42	(	(	PUNCT
cana-1750	125	43	𝜆	𝜆	PROPN
cana-1750	125	44	+	+	ADJ
cana-1750	125	45	1)(𝜆	1)(𝜆	NUM
cana-1750	125	46	+	+	CCONJ
cana-1750	125	47	2)(𝜆	2)(𝜆	NUM
cana-1750	125	48	+	+	CCONJ
cana-1750	125	49	3	3	NUM
cana-1750	125	50	)	)	PUNCT
cana-1750	125	51	+	+	NUM
cana-1750	125	52	𝑝1𝑝2(1	𝑝1𝑝2(1	NOUN
cana-1750	125	53	−	−	NOUN
cana-1750	125	54	𝜆)(3	𝜆)(3	X
cana-1750	125	55	+	+	CCONJ
cana-1750	125	56	2𝜆	2𝜆	NUM
cana-1750	125	57	)	)	PUNCT
cana-1750	125	58	(	(	PUNCT
cana-1750	125	59	𝜆	𝜆	X
cana-1750	125	60	+	+	NOUN
cana-1750	125	61	1)(𝜆	1)(𝜆	NUM
cana-1750	125	62	+	+	CCONJ
cana-1750	125	63	2)(𝜆	2)(𝜆	NUM
cana-1750	125	64	+	+	CCONJ
cana-1750	125	65	3	3	NUM
cana-1750	125	66	)	)	PUNCT
cana-1750	125	67	+	+	CCONJ
cana-1750	126	1	𝑝3	𝑝3	ADV
cana-1750	126	2	𝜆	𝜆	ADP
cana-1750	126	3	+	+	NUM
cana-1750	126	4	3	3	NUM
cana-1750	126	5	,	,	PUNCT
cana-1750	126	6	(	(	PUNCT
cana-1750	126	7	3.4	3.4	NUM
cana-1750	126	8	)	)	PUNCT
cana-1750	126	9	𝑎5	𝑎5	PROPN
cana-1750	126	10	=	=	SYM
cana-1750	126	11	𝑝1	𝑝1	NOUN
cana-1750	126	12	4(1	4(1	NOUN
cana-1750	126	13	−	−	PROPN
cana-1750	126	14	𝜆)3	𝜆)3	NOUN
cana-1750	126	15	(	(	PUNCT
cana-1750	126	16	𝜆	𝜆	PROPN
cana-1750	126	17	+	+	ADJ
cana-1750	126	18	1)(𝜆	1)(𝜆	NUM
cana-1750	126	19	+	+	CCONJ
cana-1750	126	20	2)(𝜆	2)(𝜆	NUM
cana-1750	126	21	+	+	CCONJ
cana-1750	126	22	3)(𝜆	3)(𝜆	NUM
cana-1750	126	23	+	+	NUM
cana-1750	126	24	4	4	NUM
cana-1750	126	25	)	)	PUNCT
cana-1750	126	26	+	+	CCONJ
cana-1750	126	27	𝑝1	𝑝1	NOUN
cana-1750	126	28	2𝑝2(1	2𝑝2(1	NUM
cana-1750	126	29	−	−	NOUN
cana-1750	126	30	𝜆	𝜆	NOUN
cana-1750	126	31	)	)	PUNCT
cana-1750	126	32	2(3	2(3	NUM
cana-1750	126	33	+	+	CCONJ
cana-1750	126	34	2𝜆	2𝜆	NUM
cana-1750	126	35	)	)	PUNCT
cana-1750	126	36	(	(	PUNCT
cana-1750	126	37	𝜆	𝜆	X
cana-1750	126	38	+	+	NOUN
cana-1750	126	39	1)(𝜆	1)(𝜆	NUM
cana-1750	126	40	+	+	CCONJ
cana-1750	126	41	2)(𝜆	2)(𝜆	NUM
cana-1750	126	42	+	+	CCONJ
cana-1750	126	43	3)(𝜆	3)(𝜆	NUM
cana-1750	126	44	+	+	NUM
cana-1750	126	45	4	4	NUM
cana-1750	126	46	)	)	PUNCT
cana-1750	126	47	+	+	CCONJ
cana-1750	126	48	𝑝1𝑝3(1	𝑝1𝑝3(1	PROPN
cana-1750	126	49	−	−	NOUN
cana-1750	126	50	𝜆	𝜆	NOUN
cana-1750	126	51	)	)	PUNCT
cana-1750	126	52	(	(	PUNCT
cana-1750	126	53	𝜆	𝜆	ADP
cana-1750	126	54	+	+	CCONJ
cana-1750	126	55	3)(𝜆	3)(𝜆	NUM
cana-1750	126	56	+	+	NUM
cana-1750	126	57	4	4	NUM
cana-1750	126	58	)	)	PUNCT
cana-1750	126	59	+	+	CCONJ
cana-1750	126	60	𝑝1	𝑝1	NOUN
cana-1750	126	61	2𝑝2(1	2𝑝2(1	NUM
cana-1750	126	62	−	−	NOUN
cana-1750	126	63	𝜆	𝜆	NOUN
cana-1750	126	64	)	)	PUNCT
cana-1750	126	65	2	2	NUM
cana-1750	126	66	(	(	PUNCT
cana-1750	126	67	𝜆	𝜆	PROPN
cana-1750	126	68	+	+	NOUN
cana-1750	126	69	1)(𝜆	1)(𝜆	NUM
cana-1750	126	70	+	+	CCONJ
cana-1750	126	71	2)(𝜆	2)(𝜆	NUM
cana-1750	126	72	+	+	CCONJ
cana-1750	126	73	4	4	NUM
cana-1750	126	74	)	)	PUNCT
cana-1750	126	75	+	+	NUM
cana-1750	126	76	𝑝2	𝑝2	NOUN
cana-1750	126	77	2(1	2(1	NUM
cana-1750	126	78	−	−	NOUN
cana-1750	126	79	𝜆	𝜆	NOUN
cana-1750	126	80	)	)	PUNCT
cana-1750	126	81	(	(	PUNCT
cana-1750	126	82	𝜆	𝜆	X
cana-1750	126	83	+	+	ADJ
cana-1750	126	84	2)(𝜆	2)(𝜆	NUM
cana-1750	126	85	+	+	CCONJ
cana-1750	126	86	4	4	NUM
cana-1750	126	87	)	)	PUNCT
cana-1750	126	88	+	+	CCONJ
cana-1750	126	89	𝑝1𝑝3(1	𝑝1𝑝3(1	PROPN
cana-1750	126	90	−	−	NOUN
cana-1750	126	91	𝜆	𝜆	NOUN
cana-1750	126	92	)	)	PUNCT
cana-1750	126	93	(	(	PUNCT
cana-1750	126	94	𝜆	𝜆	PROPN
cana-1750	126	95	+	+	NOUN
cana-1750	126	96	1)(𝜆	1)(𝜆	NUM
cana-1750	126	97	+	+	CCONJ
cana-1750	126	98	4	4	NUM
cana-1750	126	99	)	)	PUNCT
cana-1750	126	100	+	+	CCONJ
cana-1750	126	101	𝑝4	𝑝4	PROPN
cana-1750	126	102	𝜆	𝜆	PROPN
cana-1750	126	103	+	+	PROPN
cana-1750	126	104	4	4	NUM
cana-1750	126	105	.	.	PUNCT
cana-1750	126	106	(	(	PUNCT
cana-1750	126	107	3.5	3.5	NUM
cana-1750	126	108	)	)	PUNCT
cana-1750	126	109	in	in	ADP
cana-1750	126	110	the	the	DET
cana-1750	126	111	view	view	NOUN
cana-1750	126	112	of	of	ADP
cana-1750	126	113	(	(	PUNCT
cana-1750	126	114	3.2	3.2	NUM
cana-1750	126	115	)	)	PUNCT
cana-1750	126	116	and	and	CCONJ
cana-1750	126	117	(	(	PUNCT
cana-1750	126	118	3.3	3.3	NUM
cana-1750	126	119	)	)	PUNCT
cana-1750	126	120	,	,	PUNCT
cana-1750	126	121	a	a	DET
cana-1750	126	122	simple	simple	ADJ
cana-1750	126	123	computation	computation	NOUN
cana-1750	126	124	leads	lead	VERB
cana-1750	126	125	to	to	ADP
cana-1750	126	126	𝑎3	𝑎3	PROPN
cana-1750	126	127	2	2	NUM
cana-1750	126	128	−	−	NOUN
cana-1750	126	129	𝑎2	𝑎2	NOUN
cana-1750	126	130	2	2	NUM
cana-1750	126	131	=	=	SYM
cana-1750	126	132	𝑝2	𝑝2	NOUN
cana-1750	126	133	2	2	NUM
cana-1750	126	134	(	(	PUNCT
cana-1750	126	135	𝜆	𝜆	NOUN
cana-1750	127	1	+	+	CCONJ
cana-1750	127	2	2)2	2)2	NUM
cana-1750	127	3	+	+	CCONJ
cana-1750	127	4	𝑝1	𝑝1	NOUN
cana-1750	127	5	4(1	4(1	NOUN
cana-1750	127	6	−	−	PROPN
cana-1750	127	7	𝜆)2	𝜆)2	NOUN
cana-1750	127	8	(	(	PUNCT
cana-1750	127	9	𝜆	𝜆	PROPN
cana-1750	127	10	+	+	NUM
cana-1750	127	11	2)2(𝜆	2)2(𝜆	NUM
cana-1750	127	12	+	+	CCONJ
cana-1750	127	13	1)2	1)2	NUM
cana-1750	127	14	+	+	NUM
cana-1750	127	15	2𝑝2𝑝1	2𝑝2𝑝1	NUM
cana-1750	127	16	2(1	2(1	NUM
cana-1750	127	17	−	−	NOUN
cana-1750	127	18	𝜆	𝜆	NOUN
cana-1750	127	19	)	)	PUNCT
cana-1750	127	20	(	(	PUNCT
cana-1750	127	21	𝜆	𝜆	PROPN
cana-1750	127	22	+	+	CCONJ
cana-1750	127	23	2)2(𝜆	2)2(𝜆	NUM
cana-1750	127	24	+	+	CCONJ
cana-1750	127	25	1	1	NUM
cana-1750	127	26	)	)	PUNCT
cana-1750	127	27	−	−	PROPN
cana-1750	128	1	𝑝1	𝑝1	NOUN
cana-1750	128	2	2	2	NUM
cana-1750	128	3	(	(	PUNCT
cana-1750	128	4	𝜆	𝜆	PROPN
cana-1750	128	5	+	+	X
cana-1750	128	6	1)2	1)2	NUM
cana-1750	128	7	.	.	PUNCT
cana-1750	129	1	(	(	PUNCT
cana-1750	129	2	3.6	3.6	NUM
cana-1750	129	3	)	)	PUNCT
cana-1750	129	4	note	note	VERB
cana-1750	129	5	that	that	SCONJ
cana-1750	129	6	,	,	PUNCT
cana-1750	129	7	by	by	ADP
cana-1750	129	8	lemma	lemma	PROPN
cana-1750	129	9	(	(	PUNCT
cana-1750	129	10	2.2	2.2	NUM
cana-1750	129	11	)	)	PUNCT
cana-1750	129	12	,	,	PUNCT
cana-1750	129	13	we	we	PRON
cana-1750	129	14	may	may	AUX
cana-1750	129	15	write	write	VERB
cana-1750	129	16	2𝑝2	2𝑝2	NUM
cana-1750	129	17	=	=	SYM
cana-1750	129	18	𝑝1	𝑝1	NOUN
cana-1750	129	19	2	2	NUM
cana-1750	130	1	+	+	CCONJ
cana-1750	130	2	𝑥(4	𝑥(4	PROPN
cana-1750	130	3	−	−	PROPN
cana-1750	130	4	𝑝1	𝑝1	NOUN
cana-1750	130	5	2	2	NUM
cana-1750	130	6	)	)	PUNCT
cana-1750	130	7	,	,	PUNCT
cana-1750	130	8	where	where	SCONJ
cana-1750	130	9	without	without	ADP
cana-1750	130	10	loss	loss	NOUN
cana-1750	130	11	of	of	ADP
cana-1750	130	12	generality	generality	NOUN
cana-1750	130	13	,	,	PUNCT
cana-1750	130	14	we	we	PRON
cana-1750	130	15	let	let	VERB
cana-1750	130	16	0	0	NUM
cana-1750	130	17	≤	≤	NOUN
cana-1750	130	18	𝑝1	𝑝1	NOUN
cana-1750	130	19	=	=	SYM
cana-1750	130	20	𝑝	𝑝	NOUN
cana-1750	130	21	≤	≤	NUM
cana-1750	130	22	2	2	NUM
cana-1750	130	23	.	.	PUNCT
cana-1750	130	24	substitute	substitute	VERB
cana-1750	130	25	this	this	PRON
cana-1750	130	26	into	into	ADP
cana-1750	130	27	the	the	DET
cana-1750	130	28	above	above	ADJ
cana-1750	130	29	equation	equation	NOUN
cana-1750	130	30	we	we	PRON
cana-1750	130	31	obtain	obtain	VERB
cana-1750	130	32	the	the	DET
cana-1750	130	33	following	follow	VERB
cana-1750	130	34	quadratic	quadratic	ADJ
cana-1750	130	35	equation	equation	NOUN
cana-1750	130	36	in	in	ADP
cana-1750	130	37	terms	term	NOUN
cana-1750	130	38	of	of	ADP
cana-1750	130	39	𝑥.	𝑥.	NOUN
cana-1750	130	40	𝑎3	𝑎3	PROPN
cana-1750	130	41	2	2	NUM
cana-1750	130	42	−	−	NOUN
cana-1750	130	43	𝑎2	𝑎2	NOUN
cana-1750	130	44	2	2	NUM
cana-1750	130	45	=	=	SYM
cana-1750	130	46	(	(	PUNCT
cana-1750	130	47	4−𝑝2	4−𝑝2	NUM
cana-1750	130	48	)	)	PUNCT
cana-1750	130	49	2	2	NUM
cana-1750	130	50	4(𝜆+2)2	4(𝜆+2)2	NUM
cana-1750	130	51	𝑥2	𝑥2	NOUN
cana-1750	130	52	+	+	CCONJ
cana-1750	130	53	𝑝2(4−𝑝2)(𝜆−3	𝑝2(4−𝑝2)(𝜆−3	X
cana-1750	130	54	)	)	PUNCT
cana-1750	130	55	2(𝜆+2)2(𝜆+1	2(𝜆+2)2(𝜆+1	NUM
cana-1750	130	56	)	)	PUNCT
cana-1750	131	1	𝑥	𝑥	X
cana-1750	132	1	+	+	PUNCT
cana-1750	133	1	𝑝2[𝑝2(𝜆4−4𝜆3−2𝜆2	𝑝2[𝑝2(𝜆4−4𝜆3−2𝜆2	NOUN
cana-1750	133	2	+	+	NOUN
cana-1750	133	3	12𝜆+9)−4(𝜆+2)2(𝜆+1)2	12𝜆+9)−4(𝜆+2)2(𝜆+1)2	ADJ
cana-1750	133	4	]	]	X
cana-1750	133	5	4(𝜆+2)2(𝜆+1)4	4(𝜆+2)2(𝜆+1)4	NOUN
cana-1750	133	6	.	.	PUNCT
cana-1750	134	1	.	.	PUNCT
cana-1750	135	1	(	(	PUNCT
cana-1750	135	2	3.7	3.7	NUM
cana-1750	135	3	)	)	PUNCT
cana-1750	135	4	using	use	VERB
cana-1750	135	5	the	the	DET
cana-1750	135	6	triangular	triangular	NOUN
cana-1750	135	7	inequality	inequality	NOUN
cana-1750	135	8	,	,	PUNCT
cana-1750	135	9	we	we	PRON
cana-1750	135	10	gain	gain	VERB
cana-1750	135	11	|𝑎3	|𝑎3	VERB
cana-1750	135	12	2	2	NUM
cana-1750	135	13	−	−	NOUN
cana-1750	135	14	𝑎2	𝑎2	NOUN
cana-1750	135	15	2|	2|	PROPN
cana-1750	135	16	≤	≤	NUM
cana-1750	135	17	(	(	PUNCT
cana-1750	135	18	4−𝑝2	4−𝑝2	NUM
cana-1750	135	19	)	)	PUNCT
cana-1750	135	20	2	2	NUM
cana-1750	135	21	4(𝜆+2)2	4(𝜆+2)2	NUM
cana-1750	135	22	+	+	CCONJ
cana-1750	135	23	𝑝2(4−𝑝2)(𝜆−3	𝑝2(4−𝑝2)(𝜆−3	NOUN
cana-1750	135	24	)	)	PUNCT
cana-1750	135	25	2(𝜆+2)2(𝜆+1	2(𝜆+2)2(𝜆+1	NUM
cana-1750	135	26	)	)	PUNCT
cana-1750	136	1	+	+	PUNCT
cana-1750	136	2	𝑝2[𝑝2(𝜆4−4𝜆3−2𝜆2	𝑝2[𝑝2(𝜆4−4𝜆3−2𝜆2	NOUN
cana-1750	136	3	+	+	ADJ
cana-1750	136	4	12𝜆+9)+4(𝜆+2)2(𝜆+1)2	12𝜆+9)+4(𝜆+2)2(𝜆+1)2	NUM
cana-1750	136	5	]	]	X
cana-1750	136	6	4(𝜆+2)2(𝜆+1)4	4(𝜆+2)2(𝜆+1)4	NOUN
cana-1750	136	7	=	=	SYM
cana-1750	136	8	υ(𝑝	υ(𝑝	NOUN
cana-1750	136	9	,	,	PUNCT
cana-1750	136	10	𝜆	𝜆	NOUN
cana-1750	136	11	)	)	PUNCT
cana-1750	136	12	.	.	PUNCT
cana-1750	137	1	(	(	PUNCT
cana-1750	137	2	3.8	3.8	NUM
cana-1750	137	3	)	)	PUNCT
cana-1750	137	4	differentiating	differentiate	VERB
cana-1750	137	5	υ(𝑝	υ(𝑝	NOUN
cana-1750	137	6	,	,	PUNCT
cana-1750	137	7	𝜆	𝜆	NOUN
cana-1750	137	8	)	)	PUNCT
cana-1750	137	9	with	with	ADP
cana-1750	137	10	respect	respect	NOUN
cana-1750	137	11	to	to	ADP
cana-1750	137	12	𝑝	𝑝	NOUN
cana-1750	137	13	,	,	PUNCT
cana-1750	137	14	we	we	PRON
cana-1750	137	15	obtain	obtain	VERB
cana-1750	137	16	𝜕(υ(𝑝	𝜕(υ(𝑝	PROPN
cana-1750	137	17	,	,	PUNCT
cana-1750	137	18	𝜆	𝜆	NOUN
cana-1750	137	19	)	)	PUNCT
cana-1750	137	20	)	)	PUNCT
cana-1750	138	1	𝜕𝑝	𝜕𝑝	NOUN
cana-1750	138	2	=	=	SYM
cana-1750	138	3	𝑝	𝑝	PROPN
cana-1750	138	4	[	[	PUNCT
cana-1750	138	5	16𝑝2	16𝑝2	NUM
cana-1750	138	6	+	+	CCONJ
cana-1750	138	7	(	(	PUNCT
cana-1750	138	8	2𝜆2	2𝜆2	NUM
cana-1750	138	9	−	−	PROPN
cana-1750	138	10	8𝜆	8𝜆	PROPN
cana-1750	138	11	−	−	PROPN
cana-1750	138	12	8)	8)	NUM
cana-1750	138	13	(	(	PUNCT
cana-1750	138	14	𝜆	𝜆	PROPN
cana-1750	138	15	+	+	NUM
cana-1750	138	16	2)2(𝜆	2)2(𝜆	NUM
cana-1750	139	1	+	+	CCONJ
cana-1750	139	2	1)2	1)2	NUM
cana-1750	139	3	]	]	PUNCT
cana-1750	139	4	(	(	PUNCT
cana-1750	139	5	3.9	3.9	NUM
cana-1750	139	6	)	)	PUNCT
cana-1750	139	7	setting	set	VERB
cana-1750	139	8	𝜕(υ(𝑝,𝜆	𝜕(υ(𝑝,𝜆	NOUN
cana-1750	139	9	)	)	PUNCT
cana-1750	139	10	)	)	PUNCT
cana-1750	139	11	𝜕𝑝	𝜕𝑝	NOUN
cana-1750	140	1	=	=	SYM
cana-1750	140	2	0	0	NUM
cana-1750	140	3	yields	yield	NOUN
cana-1750	140	4	either	either	CCONJ
cana-1750	140	5	𝑝	𝑝	X
cana-1750	140	6	=	=	SYM
cana-1750	140	7	0	0	NUM
cana-1750	140	8	or	or	CCONJ
cana-1750	140	9	𝑝2	𝑝2	NOUN
cana-1750	140	10	=	=	PUNCT
cana-1750	140	11	−	−	PROPN
cana-1750	140	12	2𝜆2	2𝜆2	NUM
cana-1750	140	13	−	−	PROPN
cana-1750	140	14	8𝜆	8𝜆	NOUN
cana-1750	140	15	−	−	PROPN
cana-1750	140	16	8	8	NUM
cana-1750	140	17	16	16	NUM
cana-1750	140	18	(	(	PUNCT
cana-1750	140	19	3.10	3.10	NUM
cana-1750	140	20	)	)	PUNCT
cana-1750	140	21	but	but	CCONJ
cana-1750	140	22	−[2𝜆2	−[2𝜆2	PROPN
cana-1750	140	23	−	−	PROPN
cana-1750	140	24	8𝜆	8𝜆	PROPN
cana-1750	140	25	−	−	PROPN
cana-1750	140	26	8	8	NUM
cana-1750	140	27	]	]	PUNCT
cana-1750	140	28	<	<	X
cana-1750	140	29	0	0	NUM
cana-1750	140	30	for	for	ADP
cana-1750	140	31	0	0	NUM
cana-1750	140	32	≤	≤	NOUN
cana-1750	140	33	𝜆	𝜆	DET
cana-1750	140	34	≤	≤	NUM
cana-1750	140	35	1	1	NUM
cana-1750	140	36	.	.	PUNCT
cana-1750	141	1	communications	communication	NOUN
cana-1750	141	2	on	on	ADP
cana-1750	141	3	applied	apply	VERB
cana-1750	141	4	nonlinear	nonlinear	ADJ
cana-1750	141	5	analysis	analysis	NOUN
cana-1750	141	6	issn	issn	NOUN
cana-1750	141	7	:	:	PUNCT
cana-1750	141	8	1074	1074	NUM
cana-1750	141	9	-	-	PUNCT
cana-1750	141	10	133x	133x	NUM
cana-1750	141	11	vol	vol	NOUN
cana-1750	141	12	32	32	NUM
cana-1750	141	13	no	no	NOUN
cana-1750	141	14	.	.	NOUN
cana-1750	141	15	2	2	NUM
cana-1750	141	16	(	(	PUNCT
cana-1750	141	17	2025	2025	NUM
cana-1750	141	18	)	)	PUNCT
cana-1750	141	19	389	389	NUM
cana-1750	141	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	141	21	figure	figure	NOUN
cana-1750	141	22	1	1	NUM
cana-1750	141	23	.	.	PUNCT
cana-1750	141	24	graph	graph	NOUN
cana-1750	141	25	of	of	ADP
cana-1750	141	26	the	the	DET
cana-1750	141	27	bound	bind	VERB
cana-1750	141	28	−2𝜆2	−2𝜆2	NOUN
cana-1750	141	29	+	+	CCONJ
cana-1750	141	30	8𝜆	8𝜆	NUM
cana-1750	141	31	+	+	CCONJ
cana-1750	141	32	8	8	NUM
cana-1750	141	33	in	in	ADP
cana-1750	141	34	the	the	DET
cana-1750	141	35	range	range	NOUN
cana-1750	141	36	𝜆	𝜆	PRON
cana-1750	141	37	∈	∈	PROPN
cana-1750	142	1	[	[	X
cana-1750	142	2	0,1	0,1	NUM
cana-1750	142	3	]	]	PUNCT
cana-1750	142	4	.	.	PUNCT
cana-1750	143	1	therefore	therefore	ADV
cana-1750	143	2	,	,	PUNCT
cana-1750	143	3	the	the	DET
cana-1750	143	4	maximum	maximum	ADJ
cana-1750	143	5	value	value	NOUN
cana-1750	143	6	of	of	ADP
cana-1750	143	7	|𝑎3	|𝑎3	VERB
cana-1750	143	8	2	2	NUM
cana-1750	143	9	−	−	NOUN
cana-1750	143	10	𝑎2	𝑎2	NOUN
cana-1750	143	11	2|	2|	PROPN
cana-1750	143	12	is	be	AUX
cana-1750	143	13	attained	attain	VERB
cana-1750	143	14	at	at	ADP
cana-1750	143	15	the	the	DET
cana-1750	143	16	end	end	NOUN
cana-1750	143	17	points	point	NOUN
cana-1750	143	18	𝑝1	𝑝1	NOUN
cana-1750	143	19	=	=	SYM
cana-1750	143	20	𝑝	𝑝	PROPN
cana-1750	143	21	∈	∈	PROPN
cana-1750	144	1	[	[	X
cana-1750	144	2	0,2	0,2	NUM
cana-1750	144	3	]	]	PUNCT
cana-1750	144	4	.	.	PUNCT
cana-1750	145	1	for	for	ADP
cana-1750	145	2	𝑝1	𝑝1	NOUN
cana-1750	145	3	=	=	SYM
cana-1750	145	4	0	0	NUM
cana-1750	145	5	,	,	PUNCT
cana-1750	145	6	𝑝2	𝑝2	NOUN
cana-1750	145	7	=	=	SYM
cana-1750	146	1	2𝑥.	2𝑥.	NUM
cana-1750	146	2	then	then	ADV
cana-1750	146	3	,	,	PUNCT
cana-1750	146	4	we	we	PRON
cana-1750	146	5	have	have	VERB
cana-1750	146	6	(	(	PUNCT
cana-1750	146	7	3.6	3.6	NUM
cana-1750	146	8	)	)	PUNCT
cana-1750	146	9	.	.	PUNCT
cana-1750	147	1	|𝑎3	|𝑎3	VERB
cana-1750	147	2	2	2	NUM
cana-1750	147	3	−	−	NOUN
cana-1750	147	4	𝑎2	𝑎2	NOUN
cana-1750	147	5	2|	2|	PROPN
cana-1750	147	6	=	=	PUNCT
cana-1750	147	7	4|𝑥|2	4|𝑥|2	NUM
cana-1750	147	8	(	(	PUNCT
cana-1750	147	9	𝜆	𝜆	NOUN
cana-1750	147	10	+	+	X
cana-1750	147	11	2)2	2)2	NUM
cana-1750	147	12	≤	≤	NUM
cana-1750	147	13	4	4	NUM
cana-1750	147	14	(	(	PUNCT
cana-1750	147	15	𝜆	𝜆	NOUN
cana-1750	147	16	+	+	ADJ
cana-1750	147	17	2)2	2)2	NUM
cana-1750	147	18	(	(	PUNCT
cana-1750	147	19	3.11	3.11	NUM
cana-1750	147	20	)	)	PUNCT
cana-1750	147	21	for	for	ADP
cana-1750	147	22	𝑝1	𝑝1	NOUN
cana-1750	147	23	=	=	SYM
cana-1750	147	24	𝑝2	𝑝2	NOUN
cana-1750	147	25	=	=	SYM
cana-1750	147	26	2	2	NUM
cana-1750	147	27	,	,	PUNCT
cana-1750	147	28	we	we	PRON
cana-1750	147	29	get	get	VERB
cana-1750	147	30	𝑎2	𝑎2	NOUN
cana-1750	147	31	=	=	NOUN
cana-1750	147	32	2	2	NUM
cana-1750	147	33	𝜆+2	𝜆+2	NUM
cana-1750	147	34	(	(	PUNCT
cana-1750	147	35	3.12	3.12	NUM
cana-1750	147	36	)	)	PUNCT
cana-1750	147	37	𝑎3	𝑎3	NOUN
cana-1750	147	38	=	=	SYM
cana-1750	147	39	4(1−𝜆	4(1−𝜆	PROPN
cana-1750	147	40	)	)	PUNCT
cana-1750	147	41	(	(	PUNCT
cana-1750	147	42	𝜆+2)(𝜆+1	𝜆+2)(𝜆+1	ADV
cana-1750	147	43	)	)	PUNCT
cana-1750	148	1	+	+	CCONJ
cana-1750	148	2	2	2	NUM
cana-1750	148	3	𝜆+2	𝜆+2	NUM
cana-1750	148	4	(	(	PUNCT
cana-1750	148	5	3.13	3.13	NUM
cana-1750	148	6	)	)	PUNCT
cana-1750	148	7	which	which	PRON
cana-1750	148	8	yields	yield	VERB
cana-1750	148	9	,	,	PUNCT
cana-1750	148	10	|𝑎3	|𝑎3	VERB
cana-1750	148	11	2	2	NUM
cana-1750	148	12	−	−	NOUN
cana-1750	148	13	𝑎2	𝑎2	NOUN
cana-1750	148	14	2|	2|	PROPN
cana-1750	148	15	≤	≤	PROPN
cana-1750	149	1	|	|	ADV
cana-1750	149	2	−40𝜆3	−40𝜆3	NUM
cana-1750	149	3	−	−	PROPN
cana-1750	150	1	60𝜆2	60𝜆2	NUM
cana-1750	150	2	+	+	NUM
cana-1750	150	3	20	20	NUM
cana-1750	150	4	(	(	PUNCT
cana-1750	150	5	𝜆	𝜆	PROPN
cana-1750	150	6	+	+	NUM
cana-1750	150	7	1)4(𝜆	1)4(𝜆	NUM
cana-1750	150	8	+	+	CCONJ
cana-1750	150	9	2)2	2)2	NUM
cana-1750	150	10	|	|	NOUN
cana-1750	150	11	(	(	PUNCT
cana-1750	150	12	3.14	3.14	NUM
cana-1750	150	13	)	)	PUNCT
cana-1750	150	14	the	the	DET
cana-1750	150	15	result	result	NOUN
cana-1750	150	16	is	be	AUX
cana-1750	150	17	sharp	sharp	ADJ
cana-1750	150	18	for	for	ADP
cana-1750	150	19	the	the	DET
cana-1750	150	20	functions	function	NOUN
cana-1750	150	21	given	give	VERB
cana-1750	150	22	by	by	ADP
cana-1750	150	23	𝑧𝑓′(𝑧	𝑧𝑓′(𝑧	PROPN
cana-1750	150	24	)	)	PUNCT
cana-1750	150	25	(	(	PUNCT
cana-1750	150	26	1	1	NUM
cana-1750	150	27	−	−	NUM
cana-1750	150	28	𝜆)𝑓(𝑧	𝜆)𝑓(𝑧	NUM
cana-1750	150	29	)	)	PUNCT
cana-1750	151	1	+	+	NUM
cana-1750	151	2	𝜆𝑧	𝜆𝑧	X
cana-1750	151	3	=	=	SYM
cana-1750	151	4	1	1	NUM
cana-1750	151	5	+	+	CCONJ
cana-1750	151	6	𝑧	𝑧	PRON
cana-1750	151	7	1	1	NUM
cana-1750	151	8	−	−	NOUN
cana-1750	151	9	𝑧	𝑧	PROPN
cana-1750	151	10	(	(	PUNCT
cana-1750	151	11	3.15	3.15	NUM
cana-1750	151	12	)	)	PUNCT
cana-1750	151	13	remark	remark	NOUN
cana-1750	151	14	3.2	3.2	NUM
cana-1750	151	15	.	.	PUNCT
cana-1750	152	1	theorem	theorem	NOUN
cana-1750	152	2	(	(	PUNCT
cana-1750	152	3	3.1	3.1	NUM
cana-1750	152	4	)	)	PUNCT
cana-1750	152	5	,	,	PUNCT
cana-1750	152	6	for	for	ADP
cana-1750	152	7	𝜆	𝜆	DET
cana-1750	152	8	=	=	SYM
cana-1750	152	9	0	0	NUM
cana-1750	152	10	yields	yield	NOUN
cana-1750	152	11	the	the	DET
cana-1750	152	12	bound	bind	VERB
cana-1750	152	13	|𝑎3	|𝑎3	VERB
cana-1750	152	14	2	2	NUM
cana-1750	152	15	−	−	NOUN
cana-1750	152	16	𝑎2	𝑎2	NOUN
cana-1750	152	17	2|	2|	NUM
cana-1750	152	18	≤	≤	ADV
cana-1750	152	19	5	5	NUM
cana-1750	152	20	for	for	ADP
cana-1750	152	21	the	the	DET
cana-1750	152	22	class	class	NOUN
cana-1750	152	23	of	of	ADP
cana-1750	152	24	star	star	NOUN
cana-1750	152	25	like	like	ADP
cana-1750	152	26	function	function	NOUN
cana-1750	152	27	𝒮∗	𝒮∗	NOUN
cana-1750	152	28	conforming	conform	VERB
cana-1750	152	29	the	the	DET
cana-1750	152	30	bound	bind	VERB
cana-1750	152	31	obtained	obtain	VERB
cana-1750	152	32	by	by	ADP
cana-1750	152	33	thomous	thomous	PROPN
cana-1750	152	34	and	and	CCONJ
cana-1750	152	35	halim	halim	PROPN
cana-1750	153	1	[	[	X
cana-1750	153	2	1	1	X
cana-1750	153	3	]	]	PUNCT
cana-1750	153	4	and	and	CCONJ
cana-1750	153	5	for	for	ADP
cana-1750	153	6	𝜆	𝜆	DET
cana-1750	153	7	=	=	SYM
cana-1750	153	8	1	1	NUM
cana-1750	153	9	yields	yield	NOUN
cana-1750	153	10	the	the	DET
cana-1750	153	11	bound	bind	VERB
cana-1750	153	12	|𝑎3	|𝑎3	VERB
cana-1750	153	13	2	2	NUM
cana-1750	153	14	−	−	NOUN
cana-1750	153	15	𝑎2	𝑎2	NOUN
cana-1750	153	16	2|	2|	PROPN
cana-1750	153	17	≤	≤	ADV
cana-1750	153	18	5	5	NUM
cana-1750	153	19	9	9	NUM
cana-1750	153	20	for	for	ADP
cana-1750	153	21	the	the	DET
cana-1750	153	22	class	class	NOUN
cana-1750	153	23	of	of	ADP
cana-1750	153	24	functions	function	NOUN
cana-1750	153	25	with	with	ADP
cana-1750	153	26	bounded	bounded	ADJ
cana-1750	153	27	boundary	boundary	ADJ
cana-1750	153	28	rotation	rotation	NOUN
cana-1750	153	29	ℛ̃	ℛ̃	PROPN
cana-1750	153	30	conforming	conform	VERB
cana-1750	153	31	the	the	DET
cana-1750	153	32	bound	bind	VERB
cana-1750	153	33	obtained	obtain	VERB
cana-1750	153	34	by	by	ADP
cana-1750	153	35	radhika	radhika	PROPN
cana-1750	153	36	et	et	PROPN
cana-1750	153	37	al	al	PROPN
cana-1750	153	38	.	.	PUNCT
cana-1750	154	1	[	[	X
cana-1750	154	2	2	2	NUM
cana-1750	154	3	]	]	PUNCT
cana-1750	154	4	.	.	PUNCT
cana-1750	155	1	in	in	ADP
cana-1750	155	2	our	our	PRON
cana-1750	155	3	next	next	ADJ
cana-1750	155	4	theorem	theorem	NOUN
cana-1750	155	5	,	,	PUNCT
cana-1750	155	6	we	we	PRON
cana-1750	155	7	determine	determine	VERB
cana-1750	155	8	an	an	DET
cana-1750	155	9	upper	upper	ADJ
cana-1750	155	10	bound	bind	VERB
cana-1750	155	11	for	for	ADP
cana-1750	155	12	the	the	DET
cana-1750	155	13	coefficient	coefficient	NOUN
cana-1750	155	14	body	body	NOUN
cana-1750	155	15	𝑇2(3	𝑇2(3	NOUN
cana-1750	155	16	)	)	PUNCT
cana-1750	155	17	.	.	PUNCT
cana-1750	156	1	theorem	theorem	VERB
cana-1750	156	2	3.3	3.3	NUM
cana-1750	156	3	.	.	PUNCT
cana-1750	157	1	let	let	VERB
cana-1750	157	2	𝑓	𝑓	PRON
cana-1750	157	3	given	give	VERB
cana-1750	157	4	by	by	ADP
cana-1750	157	5	(	(	PUNCT
cana-1750	157	6	1.1	1.1	NUM
cana-1750	157	7	)	)	PUNCT
cana-1750	157	8	be	be	AUX
cana-1750	157	9	in	in	ADP
cana-1750	157	10	the	the	DET
cana-1750	157	11	class	class	NOUN
cana-1750	157	12	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	157	13	)	)	PUNCT
cana-1750	157	14	;	;	PUNCT
cana-1750	157	15	(	(	PUNCT
cana-1750	157	16	0	0	NUM
cana-1750	157	17	≤	≤	NUM
cana-1750	157	18	𝜆	𝜆	PRON
cana-1750	157	19	≤	≤	NUM
cana-1750	157	20	1	1	NUM
cana-1750	157	21	)	)	PUNCT
cana-1750	157	22	.	.	PUNCT
cana-1750	158	1	then	then	ADV
cana-1750	158	2	we	we	PRON
cana-1750	158	3	have	have	AUX
cana-1750	158	4	sharp	sharp	ADV
cana-1750	158	5	bound	bind	VERB
cana-1750	158	6	|𝑇2(3)|	|𝑇2(3)|	PROPN
cana-1750	158	7	=	=	PRON
cana-1750	158	8	|𝑎4	|𝑎4	ADP
cana-1750	158	9	2	2	NUM
cana-1750	158	10	−	−	NOUN
cana-1750	158	11	𝑎3	𝑎3	PROPN
cana-1750	158	12	2|	2|	PROPN
cana-1750	158	13	≤	≤	PROPN
cana-1750	159	1	max	max	PROPN
cana-1750	159	2	{	{	PUNCT
cana-1750	159	3	|64𝑅1(𝜆	|64𝑅1(𝜆	PROPN
cana-1750	159	4	)	)	PUNCT
cana-1750	159	5	−	−	NOUN
cana-1750	160	1	16𝑅2(𝜆)|	16𝑅2(𝜆)|	NUM
cana-1750	160	2	,	,	PUNCT
cana-1750	160	3	4	4	NUM
cana-1750	160	4	(	(	PUNCT
cana-1750	160	5	𝜆	𝜆	NOUN
cana-1750	160	6	+	+	CCONJ
cana-1750	160	7	2)2	2)2	NUM
cana-1750	160	8	}	}	PUNCT
cana-1750	160	9	𝑅1(𝜆	𝑅1(𝜆	PROPN
cana-1750	160	10	)	)	PUNCT
cana-1750	160	11	=	=	SYM
cana-1750	160	12	𝜆4	𝜆4	NOUN
cana-1750	160	13	−	−	PROPN
cana-1750	161	1	14𝜆3	14𝜆3	PROPN
cana-1750	161	2	+	+	NOUN
cana-1750	161	3	73𝜆2	73𝜆2	NUM
cana-1750	161	4	−	−	PROPN
cana-1750	161	5	168𝜆	168𝜆	NOUN
cana-1750	161	6	+	+	CCONJ
cana-1750	161	7	144	144	NUM
cana-1750	161	8	16(𝜆	16(𝜆	NUM
cana-1750	162	1	+	+	CCONJ
cana-1750	163	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	163	2	+	+	NUM
cana-1750	163	3	2)2(𝜆	2)2(𝜆	NUM
cana-1750	163	4	+	+	CCONJ
cana-1750	163	5	1)2	1)2	NUM
cana-1750	163	6	𝑅2(𝜆	𝑅2(𝜆	NOUN
cana-1750	163	7	)	)	PUNCT
cana-1750	164	1	=	=	SYM
cana-1750	164	2	𝜆2	𝜆2	NOUN
cana-1750	164	3	−	−	NOUN
cana-1750	164	4	6𝜆	6𝜆	NOUN
cana-1750	164	5	+	+	CCONJ
cana-1750	164	6	9	9	NUM
cana-1750	164	7	4(𝜆	4(𝜆	NUM
cana-1750	165	1	+	+	CCONJ
cana-1750	165	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	165	3	+	+	CCONJ
cana-1750	165	4	1)2	1)2	NUM
cana-1750	165	5	communications	communication	NOUN
cana-1750	165	6	on	on	ADP
cana-1750	165	7	applied	apply	VERB
cana-1750	165	8	nonlinear	nonlinear	ADJ
cana-1750	165	9	analysis	analysis	NOUN
cana-1750	165	10	issn	issn	NOUN
cana-1750	165	11	:	:	PUNCT
cana-1750	165	12	1074	1074	NUM
cana-1750	165	13	-	-	PUNCT
cana-1750	165	14	133x	133x	NUM
cana-1750	165	15	vol	vol	NOUN
cana-1750	165	16	32	32	NUM
cana-1750	165	17	no	no	NOUN
cana-1750	165	18	.	.	NOUN
cana-1750	165	19	2	2	NUM
cana-1750	165	20	(	(	PUNCT
cana-1750	165	21	2025	2025	NUM
cana-1750	165	22	)	)	PUNCT
cana-1750	165	23	390	390	NUM
cana-1750	165	24	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	165	25	proof	proof	NOUN
cana-1750	165	26	.	.	PUNCT
cana-1750	166	1	first	first	ADV
cana-1750	166	2	note	note	VERB
cana-1750	166	3	that	that	SCONJ
cana-1750	166	4	by	by	ADP
cana-1750	166	5	equating	equate	VERB
cana-1750	166	6	the	the	DET
cana-1750	166	7	corresponding	corresponding	ADJ
cana-1750	166	8	coefficient	coefficient	NOUN
cana-1750	166	9	in	in	ADP
cana-1750	166	10	the	the	DET
cana-1750	166	11	equation	equation	NOUN
cana-1750	166	12	(	(	PUNCT
cana-1750	166	13	3.1	3.1	NUM
cana-1750	166	14	)	)	PUNCT
cana-1750	166	15	.	.	PUNCT
cana-1750	167	1	in	in	ADP
cana-1750	167	2	the	the	DET
cana-1750	167	3	view	view	NOUN
cana-1750	167	4	of	of	ADP
cana-1750	167	5	(	(	PUNCT
cana-1750	167	6	3.3	3.3	NUM
cana-1750	167	7	)	)	PUNCT
cana-1750	167	8	,	,	PUNCT
cana-1750	167	9	(	(	PUNCT
cana-1750	167	10	3.4	3.4	NUM
cana-1750	167	11	)	)	PUNCT
cana-1750	167	12	and	and	CCONJ
cana-1750	167	13	applying	apply	VERB
cana-1750	167	14	lemma	lemma	PROPN
cana-1750	167	15	(	(	PUNCT
cana-1750	167	16	2.2	2.2	NUM
cana-1750	167	17	)	)	PUNCT
cana-1750	167	18	,	,	PUNCT
cana-1750	167	19	denoting	denote	VERB
cana-1750	167	20	𝑋	𝑋	NOUN
cana-1750	167	21	=	=	SYM
cana-1750	167	22	4	4	NUM
cana-1750	167	23	−	−	PROPN
cana-1750	167	24	𝑝2	𝑝2	NOUN
cana-1750	167	25	and	and	CCONJ
cana-1750	167	26	𝑌	𝑌	PROPN
cana-1750	167	27	=	=	PUNCT
cana-1750	167	28	(	(	PUNCT
cana-1750	167	29	1	1	NUM
cana-1750	167	30	−	−	PROPN
cana-1750	167	31	|𝑥|2)𝜚	|𝑥|2)𝜚	PROPN
cana-1750	167	32	,	,	PUNCT
cana-1750	167	33	where	where	SCONJ
cana-1750	167	34	0	0	NUM
cana-1750	167	35	≤	≤	NUM
cana-1750	167	36	𝑝	𝑝	NOUN
cana-1750	167	37	≤	≤	NUM
cana-1750	167	38	2	2	NUM
cana-1750	167	39	and	and	CCONJ
cana-1750	167	40	|𝜚|	|𝜚|	PROPN
cana-1750	167	41	<	<	X
cana-1750	167	42	1	1	NUM
cana-1750	167	43	,	,	PUNCT
cana-1750	167	44	we	we	PRON
cana-1750	167	45	get	get	VERB
cana-1750	167	46	𝑎4	𝑎4	PROPN
cana-1750	167	47	2	2	NUM
cana-1750	167	48	−	−	NOUN
cana-1750	167	49	𝑎3	𝑎3	PROPN
cana-1750	167	50	2	2	X
cana-1750	167	51	=	=	SYM
cana-1750	167	52	[	[	PUNCT
cana-1750	167	53	𝜆4	𝜆4	NOUN
cana-1750	167	54	−	−	PROPN
cana-1750	167	55	14𝜆3	14𝜆3	PROPN
cana-1750	167	56	+	+	NOUN
cana-1750	167	57	73𝜆2	73𝜆2	NUM
cana-1750	167	58	−	−	PROPN
cana-1750	167	59	168𝜆	168𝜆	NOUN
cana-1750	167	60	+	+	CCONJ
cana-1750	167	61	144	144	NUM
cana-1750	167	62	16(𝜆	16(𝜆	NUM
cana-1750	168	1	+	+	CCONJ
cana-1750	169	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	169	2	+	+	NUM
cana-1750	169	3	2)2(𝜆	2)2(𝜆	NUM
cana-1750	169	4	+	+	CCONJ
cana-1750	169	5	1)2	1)2	NUM
cana-1750	169	6	]	]	PUNCT
cana-1750	169	7	𝑝1	𝑝1	NOUN
cana-1750	169	8	6	6	NUM
cana-1750	169	9	+	+	CCONJ
cana-1750	169	10	[	[	PUNCT
cana-1750	169	11	−𝜆2	−𝜆2	X
cana-1750	169	12	+	+	NOUN
cana-1750	169	13	6𝜆	6𝜆	NUM
cana-1750	169	14	−	−	ADP
cana-1750	169	15	9	9	NUM
cana-1750	169	16	4(𝜆	4(𝜆	NUM
cana-1750	170	1	+	+	CCONJ
cana-1750	170	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	170	3	+	+	CCONJ
cana-1750	170	4	1)2	1)2	NUM
cana-1750	170	5	]	]	PUNCT
cana-1750	170	6	𝑝1	𝑝1	NOUN
cana-1750	170	7	4	4	NUM
cana-1750	170	8	+	+	NOUN
cana-1750	170	9	𝑋2𝑌2	𝑋2𝑌2	NOUN
cana-1750	170	10	4(𝜆	4(𝜆	NUM
cana-1750	171	1	+	+	CCONJ
cana-1750	172	1	3)2	3)2	NUM
cana-1750	172	2	+	+	CCONJ
cana-1750	172	3	𝑝1𝑥	𝑝1𝑥	ADP
cana-1750	172	4	2𝑋2𝑌	2𝑋2𝑌	NUM
cana-1750	172	5	4(𝜆	4(𝜆	NUM
cana-1750	173	1	+	+	CCONJ
cana-1750	174	1	3)2	3)2	NUM
cana-1750	174	2	+	+	NOUN
cana-1750	174	3	[	[	PUNCT
cana-1750	174	4	−𝜆2	−𝜆2	X
cana-1750	174	5	+	+	CCONJ
cana-1750	174	6	2𝜆	2𝜆	NUM
cana-1750	174	7	+	+	CCONJ
cana-1750	174	8	5	5	NUM
cana-1750	174	9	2(𝜆	2(𝜆	NUM
cana-1750	174	10	+	+	CCONJ
cana-1750	174	11	3)2(𝜆	3)2(𝜆	NUM
cana-1750	174	12	+	+	NUM
cana-1750	174	13	2)(𝜆	2)(𝜆	NUM
cana-1750	174	14	+	+	CCONJ
cana-1750	174	15	1	1	NUM
cana-1750	174	16	)	)	PUNCT
cana-1750	174	17	]	]	PUNCT
cana-1750	174	18	𝑝1𝑥𝑋	𝑝1𝑥𝑋	PROPN
cana-1750	174	19	2𝑌	2𝑌	NOUN
cana-1750	174	20	+	+	CCONJ
cana-1750	174	21	[	[	PUNCT
cana-1750	174	22	𝜆2	𝜆2	NOUN
cana-1750	174	23	−	−	NOUN
cana-1750	174	24	7𝜆	7𝜆	PROPN
cana-1750	174	25	+	+	CCONJ
cana-1750	174	26	12	12	NUM
cana-1750	174	27	4(𝜆	4(𝜆	NUM
cana-1750	174	28	+	+	CCONJ
cana-1750	174	29	3)2(𝜆	3)2(𝜆	NUM
cana-1750	174	30	+	+	NUM
cana-1750	174	31	2)(𝜆	2)(𝜆	NUM
cana-1750	174	32	+	+	CCONJ
cana-1750	174	33	1	1	NUM
cana-1750	174	34	)	)	PUNCT
cana-1750	174	35	]	]	PUNCT
cana-1750	174	36	𝑝1	𝑝1	NOUN
cana-1750	174	37	3𝑋𝑌	3𝑋𝑌	NUM
cana-1750	174	38	+	+	PROPN
cana-1750	174	39	𝑝1	𝑝1	NOUN
cana-1750	174	40	2𝑥4𝑋2	2𝑥4𝑋2	NUM
cana-1750	174	41	16(𝜆	16(𝜆	NUM
cana-1750	175	1	+	+	CCONJ
cana-1750	176	1	3)2	3)2	NUM
cana-1750	176	2	+	+	NOUN
cana-1750	176	3	[	[	PUNCT
cana-1750	176	4	−𝜆2	−𝜆2	X
cana-1750	176	5	+	+	CCONJ
cana-1750	176	6	2𝜆	2𝜆	NUM
cana-1750	176	7	+	+	CCONJ
cana-1750	176	8	5	5	NUM
cana-1750	176	9	4(𝜆	4(𝜆	NUM
cana-1750	176	10	+	+	CCONJ
cana-1750	176	11	3)2(𝜆	3)2(𝜆	NUM
cana-1750	176	12	+	+	NUM
cana-1750	176	13	2)(𝜆	2)(𝜆	NUM
cana-1750	176	14	+	+	CCONJ
cana-1750	176	15	1	1	NUM
cana-1750	176	16	)	)	PUNCT
cana-1750	176	17	]	]	PUNCT
cana-1750	176	18	𝑝1	𝑝1	NOUN
cana-1750	176	19	2𝑥3𝑋2	2𝑥3𝑋2	PROPN
cana-1750	177	1	+	+	CCONJ
cana-1750	177	2	[	[	PUNCT
cana-1750	177	3	𝜆4	𝜆4	NOUN
cana-1750	177	4	−	−	PROPN
cana-1750	177	5	4𝜆3	4𝜆3	NUM
cana-1750	177	6	−	−	ADP
cana-1750	178	1	6𝜆2	6𝜆2	NUM
cana-1750	179	1	+	+	CCONJ
cana-1750	179	2	20𝜆	20𝜆	NOUN
cana-1750	179	3	+	+	CCONJ
cana-1750	179	4	25	25	NUM
cana-1750	179	5	4(𝜆	4(𝜆	NUM
cana-1750	179	6	+	+	CCONJ
cana-1750	180	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	180	2	+	+	NUM
cana-1750	180	3	2)2(𝜆	2)2(𝜆	NUM
cana-1750	181	1	+	+	CCONJ
cana-1750	181	2	1)2	1)2	NUM
cana-1750	181	3	]	]	PUNCT
cana-1750	181	4	𝑝1	𝑝1	NOUN
cana-1750	181	5	2𝑥2𝑋2	2𝑥2𝑋2	PROPN
cana-1750	182	1	+	+	CCONJ
cana-1750	183	1	𝑥2𝑋2	𝑥2𝑋2	PROPN
cana-1750	183	2	4(𝜆	4(𝜆	NUM
cana-1750	184	1	+	+	CCONJ
cana-1750	184	2	2)2	2)2	NUM
cana-1750	184	3	+	+	CCONJ
cana-1750	184	4	[	[	PUNCT
cana-1750	184	5	𝜆2	𝜆2	NOUN
cana-1750	184	6	−	−	NOUN
cana-1750	184	7	7𝜆	7𝜆	PROPN
cana-1750	184	8	+	+	CCONJ
cana-1750	184	9	12	12	NUM
cana-1750	184	10	8(𝜆	8(𝜆	NUM
cana-1750	184	11	+	+	CCONJ
cana-1750	184	12	3)2(𝜆	3)2(𝜆	NUM
cana-1750	184	13	+	+	NUM
cana-1750	184	14	2)(𝜆	2)(𝜆	NUM
cana-1750	184	15	+	+	CCONJ
cana-1750	184	16	1	1	NUM
cana-1750	184	17	)	)	PUNCT
cana-1750	184	18	]	]	PUNCT
cana-1750	185	1	𝑝1	𝑝1	NOUN
cana-1750	185	2	4𝑥2𝑋	4𝑥2𝑋	NUM
cana-1750	185	3	+	+	PUNCT
cana-1750	185	4	[	[	PUNCT
cana-1750	185	5	−𝜆4	−𝜆4	NOUN
cana-1750	185	6	+	+	NOUN
cana-1750	185	7	9𝜆3	9𝜆3	NUM
cana-1750	185	8	−	−	PROPN
cana-1750	185	9	21𝜆2	21𝜆2	NUM
cana-1750	185	10	−	−	NOUN
cana-1750	185	11	11𝜆	11𝜆	NOUN
cana-1750	185	12	+	+	CCONJ
cana-1750	185	13	60	60	NUM
cana-1750	185	14	4(𝜆	4(𝜆	NUM
cana-1750	186	1	+	+	CCONJ
cana-1750	187	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	187	2	+	+	NUM
cana-1750	187	3	2)2(𝜆	2)2(𝜆	NUM
cana-1750	188	1	+	+	CCONJ
cana-1750	188	2	1)2	1)2	NUM
cana-1750	188	3	]	]	PUNCT
cana-1750	188	4	𝑝1	𝑝1	NOUN
cana-1750	188	5	4𝑥𝑋	4𝑥𝑋	PROPN
cana-1750	189	1	+	+	CCONJ
cana-1750	189	2	[	[	PUNCT
cana-1750	189	3	3	3	NUM
cana-1750	189	4	−	−	NOUN
cana-1750	189	5	𝜆	𝜆	DET
cana-1750	189	6	2(𝜆	2(𝜆	NUM
cana-1750	189	7	+	+	CCONJ
cana-1750	189	8	1)(𝜆	1)(𝜆	NUM
cana-1750	189	9	+	+	CCONJ
cana-1750	189	10	2)2	2)2	NUM
cana-1750	189	11	]	]	PUNCT
cana-1750	189	12	𝑝1	𝑝1	NOUN
cana-1750	189	13	2𝑥𝑋.	2𝑥𝑋.	PROPN
cana-1750	189	14	as	as	ADP
cana-1750	189	15	in	in	ADP
cana-1750	189	16	the	the	DET
cana-1750	189	17	proof	proof	NOUN
cana-1750	189	18	of	of	ADP
cana-1750	189	19	theorem	theorem	NOUN
cana-1750	189	20	(	(	PUNCT
cana-1750	189	21	3.1	3.1	NUM
cana-1750	189	22	)	)	PUNCT
cana-1750	189	23	.	.	PUNCT
cana-1750	190	1	note	note	VERB
cana-1750	190	2	that	that	SCONJ
cana-1750	190	3	,	,	PUNCT
cana-1750	190	4	by	by	ADP
cana-1750	190	5	lemma	lemma	PROPN
cana-1750	190	6	(	(	PUNCT
cana-1750	190	7	2.2	2.2	NUM
cana-1750	190	8	)	)	PUNCT
cana-1750	190	9	,	,	PUNCT
cana-1750	190	10	where	where	SCONJ
cana-1750	190	11	without	without	ADP
cana-1750	190	12	loss	loss	NOUN
cana-1750	190	13	of	of	ADP
cana-1750	190	14	generality	generality	NOUN
cana-1750	190	15	we	we	PRON
cana-1750	190	16	let	let	VERB
cana-1750	190	17	0	0	NUM
cana-1750	190	18	≤	≤	NOUN
cana-1750	190	19	𝑝1	𝑝1	NOUN
cana-1750	190	20	=	=	SYM
cana-1750	190	21	𝑝	𝑝	NOUN
cana-1750	190	22	≤	≤	NUM
cana-1750	190	23	2	2	NUM
cana-1750	190	24	.	.	PUNCT
cana-1750	190	25	substitute	substitute	VERB
cana-1750	190	26	this	this	PRON
cana-1750	190	27	into	into	ADP
cana-1750	190	28	the	the	DET
cana-1750	190	29	above	above	ADJ
cana-1750	190	30	equation	equation	NOUN
cana-1750	190	31	,	,	PUNCT
cana-1750	190	32	we	we	PRON
cana-1750	190	33	get	get	VERB
cana-1750	190	34	the	the	DET
cana-1750	190	35	following	follow	VERB
cana-1750	190	36	quadratic	quadratic	ADJ
cana-1750	190	37	equation	equation	NOUN
cana-1750	190	38	in	in	ADP
cana-1750	190	39	terms	term	NOUN
cana-1750	190	40	of	of	ADP
cana-1750	190	41	𝑥.	𝑥.	VERB
cana-1750	190	42	|𝑎4	|𝑎4	NOUN
cana-1750	190	43	2	2	NUM
cana-1750	190	44	−	−	NOUN
cana-1750	190	45	𝑎3	𝑎3	PROPN
cana-1750	190	46	2|	2|	NUM
cana-1750	190	47	≤	≤	NUM
cana-1750	190	48	(	(	PUNCT
cana-1750	190	49	2	2	NUM
cana-1750	190	50	−	−	NUM
cana-1750	190	51	𝑝)2(4	𝑝)2(4	NUM
cana-1750	190	52	−	−	NOUN
cana-1750	190	53	𝑝2)2	𝑝2)2	PRON
cana-1750	190	54	16(𝜆	16(𝜆	NUM
cana-1750	191	1	+	+	CCONJ
cana-1750	191	2	3)2	3)2	NUM
cana-1750	191	3	|𝑥|4	|𝑥|4	NOUN
cana-1750	191	4	+	+	CCONJ
cana-1750	191	5	(	(	PUNCT
cana-1750	191	6	−𝜆2	−𝜆2	PROPN
cana-1750	191	7	+	+	CCONJ
cana-1750	191	8	2𝜆	2𝜆	NUM
cana-1750	191	9	+	+	CCONJ
cana-1750	191	10	5)(4	5)(4	NUM
cana-1750	191	11	−	−	NOUN
cana-1750	191	12	𝑝2)(𝑝2	𝑝2)(𝑝2	NOUN
cana-1750	191	13	−	−	NOUN
cana-1750	191	14	2𝑝	2𝑝	NOUN
cana-1750	191	15	)	)	PUNCT
cana-1750	192	1	4(𝜆	4(𝜆	NUM
cana-1750	193	1	+	+	CCONJ
cana-1750	194	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	194	2	+	+	NUM
cana-1750	194	3	2)(𝜆	2)(𝜆	NUM
cana-1750	194	4	+	+	CCONJ
cana-1750	194	5	1	1	NUM
cana-1750	194	6	)	)	PUNCT
cana-1750	194	7	|𝑥|3	|𝑥|3	NOUN
cana-1750	194	8	+	+	CCONJ
cana-1750	194	9	[	[	PUNCT
cana-1750	194	10	(	(	PUNCT
cana-1750	194	11	𝜆2	𝜆2	NOUN
cana-1750	194	12	−	−	NOUN
cana-1750	194	13	7𝜆	7𝜆	PROPN
cana-1750	194	14	+	+	CCONJ
cana-1750	194	15	12)(4	12)(4	NUM
cana-1750	194	16	−	−	PROPN
cana-1750	194	17	𝑝2)(𝑝	𝑝2)(𝑝	PROPN
cana-1750	194	18	−	−	PROPN
cana-1750	194	19	2)𝑝3	2)𝑝3	NOUN
cana-1750	194	20	8(𝜆	8(𝜆	NUM
cana-1750	194	21	+	+	CCONJ
cana-1750	194	22	3)2(𝜆	3)2(𝜆	NUM
cana-1750	194	23	+	+	NUM
cana-1750	194	24	2)(𝜆	2)(𝜆	NUM
cana-1750	194	25	+	+	CCONJ
cana-1750	194	26	1	1	NUM
cana-1750	194	27	)	)	PUNCT
cana-1750	194	28	+	+	CCONJ
cana-1750	194	29	[	[	PUNCT
cana-1750	194	30	𝜆4	𝜆4	NOUN
cana-1750	194	31	−	−	PROPN
cana-1750	194	32	4𝜆3	4𝜆3	NUM
cana-1750	194	33	−	−	ADP
cana-1750	194	34	6𝜆2	6𝜆2	NUM
cana-1750	195	1	+	+	CCONJ
cana-1750	195	2	20𝜆	20𝜆	NOUN
cana-1750	195	3	+	+	CCONJ
cana-1750	195	4	25	25	NUM
cana-1750	195	5	4(𝜆	4(𝜆	NUM
cana-1750	195	6	+	+	CCONJ
cana-1750	196	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	196	2	+	+	NUM
cana-1750	196	3	2)2(𝜆	2)2(𝜆	NUM
cana-1750	197	1	+	+	CCONJ
cana-1750	197	2	1)2	1)2	NUM
cana-1750	197	3	]	]	PUNCT
cana-1750	197	4	𝑝2(4	𝑝2(4	PROPN
cana-1750	197	5	−	−	PROPN
cana-1750	197	6	𝑝2	𝑝2	NOUN
cana-1750	197	7	)	)	PUNCT
cana-1750	197	8	]	]	PUNCT
cana-1750	198	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	198	2	+	+	PUNCT
cana-1750	198	3	[	[	PUNCT
cana-1750	198	4	𝑝(4	𝑝(4	PROPN
cana-1750	198	5	−	−	NOUN
cana-1750	198	6	𝑝2)2	𝑝2)2	NUM
cana-1750	198	7	4(𝜆	4(𝜆	NUM
cana-1750	198	8	+	+	CCONJ
cana-1750	199	1	3)2	3)2	NUM
cana-1750	199	2	−	−	PROPN
cana-1750	199	3	[	[	PUNCT
cana-1750	199	4	𝜆2	𝜆2	NOUN
cana-1750	200	1	+	+	CCONJ
cana-1750	200	2	2𝜆	2𝜆	NUM
cana-1750	200	3	−	−	NUM
cana-1750	201	1	1	1	NUM
cana-1750	201	2	4(𝜆	4(𝜆	NUM
cana-1750	201	3	+	+	CCONJ
cana-1750	201	4	3)2(𝜆	3)2(𝜆	NUM
cana-1750	201	5	+	+	SYM
cana-1750	201	6	2)2	2)2	NUM
cana-1750	201	7	]	]	PUNCT
cana-1750	201	8	(	(	PUNCT
cana-1750	201	9	4	4	NUM
cana-1750	201	10	−	−	NOUN
cana-1750	201	11	𝑝2)2	𝑝2)2	NUM
cana-1750	201	12	]	]	X
cana-1750	201	13	|𝑥|2	|𝑥|2	ADJ
cana-1750	201	14	+	+	PUNCT
cana-1750	201	15	[	[	PUNCT
cana-1750	201	16	(	(	PUNCT
cana-1750	201	17	3	3	NUM
cana-1750	201	18	−	−	NOUN
cana-1750	201	19	𝜆)(4	𝜆)(4	NUM
cana-1750	202	1	−	−	PROPN
cana-1750	202	2	𝑝2)𝑝2	𝑝2)𝑝2	X
cana-1750	202	3	2(1	2(1	NUM
cana-1750	202	4	+	+	CCONJ
cana-1750	202	5	𝜆)(2	𝜆)(2	X
cana-1750	202	6	+	+	CCONJ
cana-1750	202	7	𝜆)2	𝜆)2	NOUN
cana-1750	202	8	+	+	CCONJ
cana-1750	202	9	(	(	PUNCT
cana-1750	202	10	−𝜆2	−𝜆2	PROPN
cana-1750	202	11	+	+	CCONJ
cana-1750	202	12	2𝜆	2𝜆	NUM
cana-1750	202	13	+	+	CCONJ
cana-1750	202	14	5)(4	5)(4	NUM
cana-1750	202	15	−	−	NOUN
cana-1750	202	16	𝑝2)𝑝	𝑝2)𝑝	PROPN
cana-1750	202	17	2(1	2(1	NUM
cana-1750	202	18	+	+	CCONJ
cana-1750	202	19	𝜆)(2	𝜆)(2	ADP
cana-1750	202	20	+	+	NOUN
cana-1750	202	21	𝜆)(3	𝜆)(3	X
cana-1750	202	22	+	+	CCONJ
cana-1750	202	23	𝜆)2	𝜆)2	NOUN
cana-1750	202	24	+	+	CCONJ
cana-1750	202	25	−𝜆4	−𝜆4	NOUN
cana-1750	202	26	+	+	NOUN
cana-1750	202	27	9𝜆3	9𝜆3	NUM
cana-1750	202	28	−	−	PROPN
cana-1750	202	29	21𝜆2	21𝜆2	NUM
cana-1750	202	30	−	−	NOUN
cana-1750	202	31	11𝜆	11𝜆	NOUN
cana-1750	202	32	+	+	CCONJ
cana-1750	202	33	60	60	NUM
cana-1750	202	34	4(𝜆	4(𝜆	NUM
cana-1750	203	1	+	+	CCONJ
cana-1750	204	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	204	2	+	+	CCONJ
cana-1750	204	3	2)2(𝜆	2)2(𝜆	NUM
cana-1750	205	1	+	+	CCONJ
cana-1750	205	2	1)2	1)2	NUM
cana-1750	205	3	𝑝4(4	𝑝4(4	NOUN
cana-1750	205	4	−	−	PROPN
cana-1750	205	5	𝑝2	𝑝2	NOUN
cana-1750	205	6	)	)	PUNCT
cana-1750	205	7	]	]	PUNCT
cana-1750	206	1	|𝑥|	|𝑥|	VERB
cana-1750	207	1	+	+	NOUN
cana-1750	207	2	|𝑅1(𝜆)𝑝	|𝑅1(𝜆)𝑝	NOUN
cana-1750	207	3	6	6	NUM
cana-1750	207	4	−	−	NOUN
cana-1750	207	5	𝑅2(𝜆)𝑝	𝑅2(𝜆)𝑝	NOUN
cana-1750	207	6	4|	4|	NUM
cana-1750	207	7	+	+	PUNCT
cana-1750	207	8	[	[	PUNCT
cana-1750	207	9	𝜆2	𝜆2	NOUN
cana-1750	207	10	−	−	NOUN
cana-1750	207	11	7𝜆	7𝜆	PROPN
cana-1750	207	12	+	+	CCONJ
cana-1750	207	13	12	12	NUM
cana-1750	207	14	4(𝜆	4(𝜆	NUM
cana-1750	208	1	+	+	CCONJ
cana-1750	209	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	209	2	+	+	NUM
cana-1750	209	3	2)(𝜆	2)(𝜆	NUM
cana-1750	209	4	+	+	CCONJ
cana-1750	209	5	1	1	NUM
cana-1750	209	6	)	)	PUNCT
cana-1750	209	7	]	]	PUNCT
cana-1750	209	8	𝑝3(4	𝑝3(4	NOUN
cana-1750	209	9	−	−	PROPN
cana-1750	209	10	𝑝2	𝑝2	NOUN
cana-1750	209	11	)	)	PUNCT
cana-1750	210	1	+	+	CCONJ
cana-1750	210	2	(	(	PUNCT
cana-1750	210	3	4	4	NUM
cana-1750	210	4	−	−	NOUN
cana-1750	210	5	𝑝2)2	𝑝2)2	NUM
cana-1750	210	6	4(𝜆	4(𝜆	NUM
cana-1750	210	7	+	+	CCONJ
cana-1750	210	8	3)2	3)2	NUM
cana-1750	210	9	.	.	PUNCT
cana-1750	211	1	=	=	PUNCT
cana-1750	211	2	θ(𝑝	θ(𝑝	NOUN
cana-1750	211	3	,	,	PUNCT
cana-1750	211	4	|𝑥|	|𝑥|	INTJ
cana-1750	211	5	)	)	PUNCT
cana-1750	211	6	where	where	SCONJ
cana-1750	211	7	,	,	PUNCT
cana-1750	211	8	𝑅1(𝜆	𝑅1(𝜆	PROPN
cana-1750	211	9	)	)	PUNCT
cana-1750	211	10	=	=	SYM
cana-1750	211	11	𝜆4	𝜆4	NOUN
cana-1750	211	12	−	−	PROPN
cana-1750	211	13	14𝜆3	14𝜆3	PROPN
cana-1750	211	14	+	+	NOUN
cana-1750	211	15	73𝜆2	73𝜆2	NUM
cana-1750	211	16	−	−	PROPN
cana-1750	211	17	168𝜆	168𝜆	NOUN
cana-1750	211	18	+	+	CCONJ
cana-1750	211	19	144	144	NUM
cana-1750	211	20	16(𝜆	16(𝜆	NUM
cana-1750	212	1	+	+	CCONJ
cana-1750	213	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	213	2	+	+	NUM
cana-1750	213	3	2)2(𝜆	2)2(𝜆	NUM
cana-1750	213	4	+	+	CCONJ
cana-1750	213	5	1)2	1)2	NUM
cana-1750	213	6	𝑅2(𝜆	𝑅2(𝜆	NOUN
cana-1750	213	7	)	)	PUNCT
cana-1750	214	1	=	=	SYM
cana-1750	214	2	𝜆2	𝜆2	NOUN
cana-1750	214	3	−	−	NOUN
cana-1750	214	4	6𝜆	6𝜆	NOUN
cana-1750	214	5	+	+	CCONJ
cana-1750	214	6	9	9	NUM
cana-1750	214	7	4(𝜆	4(𝜆	NUM
cana-1750	215	1	+	+	CCONJ
cana-1750	215	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	215	3	+	+	CCONJ
cana-1750	215	4	1)2	1)2	NUM
cana-1750	215	5	communications	communication	NOUN
cana-1750	215	6	on	on	ADP
cana-1750	215	7	applied	apply	VERB
cana-1750	215	8	nonlinear	nonlinear	ADJ
cana-1750	215	9	analysis	analysis	NOUN
cana-1750	215	10	issn	issn	NOUN
cana-1750	215	11	:	:	PUNCT
cana-1750	215	12	1074	1074	NUM
cana-1750	215	13	-	-	PUNCT
cana-1750	215	14	133x	133x	NUM
cana-1750	215	15	vol	vol	NOUN
cana-1750	215	16	32	32	NUM
cana-1750	215	17	no	no	NOUN
cana-1750	215	18	.	.	NOUN
cana-1750	215	19	2	2	NUM
cana-1750	215	20	(	(	PUNCT
cana-1750	215	21	2025	2025	NUM
cana-1750	215	22	)	)	PUNCT
cana-1750	215	23	391	391	NUM
cana-1750	215	24	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	216	1	it	it	PRON
cana-1750	216	2	is	be	AUX
cana-1750	216	3	necessary	necessary	ADJ
cana-1750	216	4	to	to	PART
cana-1750	216	5	prove	prove	VERB
cana-1750	216	6	that	that	SCONJ
cana-1750	216	7	the	the	DET
cana-1750	216	8	maximum	maximum	ADJ
cana-1750	216	9	value	value	NOUN
cana-1750	216	10	of	of	ADP
cana-1750	216	11	θ(𝑝	θ(𝑝	PROPN
cana-1750	216	12	,	,	PUNCT
cana-1750	216	13	|𝑥|	|𝑥|	INTJ
cana-1750	216	14	)	)	PUNCT
cana-1750	216	15	on	on	ADP
cana-1750	216	16	[	[	X
cana-1750	216	17	0,2	0,2	NUM
cana-1750	216	18	]	]	X
cana-1750	216	19	×	×	NOUN
cana-1750	217	1	[	[	X
cana-1750	217	2	0,1	0,1	NUM
cana-1750	217	3	]	]	PUNCT
cana-1750	217	4	.	.	PUNCT
cana-1750	218	1	first	first	ADV
cana-1750	218	2	,	,	PUNCT
cana-1750	218	3	assume	assume	VERB
cana-1750	218	4	that	that	SCONJ
cana-1750	218	5	there	there	PRON
cana-1750	218	6	is	be	VERB
cana-1750	218	7	a	a	DET
cana-1750	218	8	maximum	maximum	NOUN
cana-1750	218	9	at	at	ADP
cana-1750	218	10	an	an	DET
cana-1750	218	11	interior	interior	ADJ
cana-1750	218	12	point	point	NOUN
cana-1750	218	13	θ(𝑝0	θ(𝑝0	ADV
cana-1750	218	14	,	,	PUNCT
cana-1750	218	15	|𝑥0|	|𝑥0|	VERB
cana-1750	218	16	)	)	PUNCT
cana-1750	218	17	of	of	ADP
cana-1750	218	18	[	[	X
cana-1750	218	19	0,2	0,2	NUM
cana-1750	218	20	]	]	X
cana-1750	218	21	×	×	NOUN
cana-1750	219	1	[	[	X
cana-1750	219	2	0,1	0,1	NUM
cana-1750	219	3	]	]	PUNCT
cana-1750	219	4	.	.	PUNCT
cana-1750	220	1	differentiating	differentiate	VERB
cana-1750	220	2	θ(𝑝	θ(𝑝	NOUN
cana-1750	220	3	,	,	PUNCT
cana-1750	220	4	|𝑥|	|𝑥|	ADV
cana-1750	220	5	)	)	PUNCT
cana-1750	220	6	with	with	ADP
cana-1750	220	7	respect	respect	NOUN
cana-1750	220	8	to	to	ADP
cana-1750	220	9	|𝑥|	|𝑥|	VERB
cana-1750	220	10	and	and	CCONJ
cana-1750	220	11	equating	equate	VERB
cana-1750	220	12	it	it	PRON
cana-1750	220	13	to	to	ADP
cana-1750	220	14	0	0	NUM
cana-1750	220	15	implies	imply	VERB
cana-1750	220	16	that	that	SCONJ
cana-1750	220	17	𝑝	𝑝	X
cana-1750	220	18	=	=	SYM
cana-1750	220	19	𝑝0	𝑝0	NOUN
cana-1750	220	20	=	=	SYM
cana-1750	220	21	2	2	NUM
cana-1750	220	22	,	,	PUNCT
cana-1750	220	23	which	which	PRON
cana-1750	220	24	is	be	AUX
cana-1750	220	25	contradiction	contradiction	NOUN
cana-1750	220	26	.	.	PUNCT
cana-1750	221	1	thus	thus	ADV
cana-1750	221	2	,	,	PUNCT
cana-1750	221	3	for	for	ADP
cana-1750	221	4	the	the	DET
cana-1750	221	5	maximum	maximum	NOUN
cana-1750	221	6	of	of	ADP
cana-1750	221	7	θ(𝑝	θ(𝑝	NOUN
cana-1750	221	8	,	,	PUNCT
cana-1750	221	9	|𝑥|	|𝑥|	ADJ
cana-1750	221	10	)	)	PUNCT
cana-1750	221	11	,	,	PUNCT
cana-1750	221	12	we	we	PRON
cana-1750	221	13	need	need	VERB
cana-1750	221	14	only	only	ADV
cana-1750	221	15	to	to	PART
cana-1750	221	16	consider	consider	VERB
cana-1750	221	17	the	the	DET
cana-1750	221	18	end	end	NOUN
cana-1750	221	19	points	point	NOUN
cana-1750	221	20	of	of	ADP
cana-1750	221	21	[	[	X
cana-1750	221	22	0,2	0,2	NUM
cana-1750	221	23	]	]	X
cana-1750	221	24	×	×	NOUN
cana-1750	222	1	[	[	X
cana-1750	222	2	0,1	0,1	NUM
cana-1750	222	3	]	]	PUNCT
cana-1750	222	4	.	.	PUNCT
cana-1750	223	1	for	for	ADP
cana-1750	223	2	𝑝	𝑝	NOUN
cana-1750	223	3	=	=	SYM
cana-1750	223	4	0	0	NUM
cana-1750	223	5	,	,	PUNCT
cana-1750	223	6	we	we	PRON
cana-1750	223	7	obtain	obtain	VERB
cana-1750	223	8	θ(0	θ(0	PROPN
cana-1750	223	9	,	,	PUNCT
cana-1750	223	10	|𝑥|	|𝑥|	ADJ
cana-1750	223	11	)	)	PUNCT
cana-1750	224	1	=	=	PRON
cana-1750	224	2	4|𝑥|4	4|𝑥|4	NOUN
cana-1750	224	3	(	(	PUNCT
cana-1750	224	4	𝜆	𝜆	PROPN
cana-1750	225	1	+	+	CCONJ
cana-1750	225	2	3)2	3)2	NUM
cana-1750	225	3	−	−	NUM
cana-1750	225	4	4(𝜆2	4(𝜆2	NUM
cana-1750	226	1	+	+	NUM
cana-1750	226	2	2𝜆	2𝜆	NUM
cana-1750	226	3	−	−	NOUN
cana-1750	226	4	1)|𝑥|	1)|𝑥|	NUM
cana-1750	226	5	(	(	PUNCT
cana-1750	226	6	𝜆	𝜆	ADP
cana-1750	226	7	+	+	CCONJ
cana-1750	226	8	3)(𝜆	3)(𝜆	NUM
cana-1750	226	9	+	+	SYM
cana-1750	226	10	2)2	2)2	NUM
cana-1750	226	11	+	+	SYM
cana-1750	226	12	4	4	NUM
cana-1750	226	13	(	(	PUNCT
cana-1750	226	14	𝜆	𝜆	PROPN
cana-1750	226	15	+	+	CCONJ
cana-1750	226	16	3)2	3)2	NUM
cana-1750	226	17	≤	≤	NUM
cana-1750	226	18	4	4	NUM
cana-1750	226	19	(	(	PUNCT
cana-1750	226	20	𝜆	𝜆	NOUN
cana-1750	226	21	+	+	ADJ
cana-1750	226	22	2)2	2)2	NUM
cana-1750	226	23	(	(	PUNCT
cana-1750	226	24	3.16	3.16	NUM
cana-1750	226	25	)	)	PUNCT
cana-1750	226	26	for	for	ADP
cana-1750	226	27	𝑝	𝑝	NOUN
cana-1750	226	28	=	=	SYM
cana-1750	226	29	2	2	NUM
cana-1750	226	30	,	,	PUNCT
cana-1750	226	31	we	we	PRON
cana-1750	226	32	obtain	obtain	VERB
cana-1750	226	33	θ(2	θ(2	PROPN
cana-1750	226	34	,	,	PUNCT
cana-1750	226	35	|𝑥|	|𝑥|	ADJ
cana-1750	226	36	)	)	PUNCT
cana-1750	226	37	=	=	SYM
cana-1750	226	38	|64𝑅1(𝜆	|64𝑅1(𝜆	NOUN
cana-1750	226	39	)	)	PUNCT
cana-1750	227	1	−	−	PROPN
cana-1750	227	2	16𝑅2(𝜆)|	16𝑅2(𝜆)|	NUM
cana-1750	227	3	(	(	PUNCT
cana-1750	227	4	3.17	3.17	NUM
cana-1750	227	5	)	)	PUNCT
cana-1750	227	6	for	for	ADP
cana-1750	227	7	|𝑥|	|𝑥|	ADJ
cana-1750	227	8	=	=	SYM
cana-1750	227	9	0	0	NUM
cana-1750	227	10	,	,	PUNCT
cana-1750	227	11	we	we	PRON
cana-1750	227	12	get	get	VERB
cana-1750	227	13	θ(𝑝	θ(𝑝	NOUN
cana-1750	227	14	,	,	PUNCT
cana-1750	227	15	0	0	NUM
cana-1750	227	16	)	)	PUNCT
cana-1750	227	17	=	=	SYM
cana-1750	227	18	|𝑅1(𝜆)𝑝	|𝑅1(𝜆)𝑝	NOUN
cana-1750	227	19	6	6	NUM
cana-1750	227	20	−	−	NOUN
cana-1750	227	21	𝑅2(𝜆)𝑝	𝑅2(𝜆)𝑝	NOUN
cana-1750	227	22	4|	4|	NUM
cana-1750	227	23	+	+	PUNCT
cana-1750	227	24	[	[	PUNCT
cana-1750	227	25	𝜆2	𝜆2	NOUN
cana-1750	227	26	−	−	NOUN
cana-1750	227	27	7𝜆	7𝜆	PROPN
cana-1750	227	28	+	+	CCONJ
cana-1750	227	29	12	12	NUM
cana-1750	227	30	4(𝜆	4(𝜆	NUM
cana-1750	228	1	+	+	CCONJ
cana-1750	229	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	229	2	+	+	NUM
cana-1750	229	3	2)(𝜆	2)(𝜆	NUM
cana-1750	229	4	+	+	CCONJ
cana-1750	229	5	1	1	NUM
cana-1750	229	6	)	)	PUNCT
cana-1750	229	7	]	]	PUNCT
cana-1750	230	1	𝑝1	𝑝1	NOUN
cana-1750	230	2	3(4	3(4	NOUN
cana-1750	230	3	−	−	PROPN
cana-1750	230	4	𝑝2	𝑝2	PROPN
cana-1750	230	5	)	)	PUNCT
cana-1750	231	1	+	+	CCONJ
cana-1750	231	2	(	(	PUNCT
cana-1750	231	3	4	4	NUM
cana-1750	231	4	−	−	NOUN
cana-1750	231	5	𝑝2)2	𝑝2)2	NUM
cana-1750	231	6	4(𝜆	4(𝜆	NUM
cana-1750	232	1	+	+	CCONJ
cana-1750	232	2	3)2	3)2	NUM
cana-1750	232	3	(	(	PUNCT
cana-1750	232	4	3.18	3.18	NUM
cana-1750	232	5	)	)	PUNCT
cana-1750	232	6	which	which	PRON
cana-1750	232	7	has	have	VERB
cana-1750	232	8	the	the	DET
cana-1750	232	9	maximum	maximum	ADJ
cana-1750	232	10	value	value	NOUN
cana-1750	232	11	|𝑅1(𝜆)𝑝	|𝑅1(𝜆)𝑝	NOUN
cana-1750	232	12	6	6	NUM
cana-1750	232	13	−	−	NOUN
cana-1750	232	14	𝑅2(𝜆)𝑝	𝑅2(𝜆)𝑝	NOUN
cana-1750	232	15	4|	4|	NUM
cana-1750	232	16	on	on	ADP
cana-1750	232	17	[	[	X
cana-1750	232	18	0,2	0,2	NUM
cana-1750	232	19	]	]	PUNCT
cana-1750	232	20	.	.	PUNCT
cana-1750	233	1	for	for	ADP
cana-1750	233	2	|𝑥|	|𝑥|	ADJ
cana-1750	233	3	=	=	SYM
cana-1750	233	4	1	1	NUM
cana-1750	233	5	,	,	PUNCT
cana-1750	233	6	we	we	PRON
cana-1750	233	7	gain	gain	VERB
cana-1750	233	8	θ(𝑝	θ(𝑝	NOUN
cana-1750	233	9	,	,	PUNCT
cana-1750	233	10	1	1	NUM
cana-1750	233	11	)	)	PUNCT
cana-1750	233	12	=	=	NOUN
cana-1750	233	13	(	(	PUNCT
cana-1750	233	14	2	2	NUM
cana-1750	233	15	−	−	NUM
cana-1750	233	16	𝑝)2(4	𝑝)2(4	NUM
cana-1750	233	17	−	−	NOUN
cana-1750	233	18	𝑝2)2	𝑝2)2	PRON
cana-1750	233	19	16(𝜆	16(𝜆	NUM
cana-1750	234	1	+	+	CCONJ
cana-1750	235	1	3)2	3)2	NUM
cana-1750	235	2	+	+	CCONJ
cana-1750	235	3	(	(	PUNCT
cana-1750	235	4	−𝜆2	−𝜆2	PROPN
cana-1750	235	5	+	+	CCONJ
cana-1750	235	6	2𝜆	2𝜆	NUM
cana-1750	235	7	+	+	CCONJ
cana-1750	235	8	5)(4	5)(4	NUM
cana-1750	235	9	−	−	NOUN
cana-1750	235	10	𝑝2)(𝑝2	𝑝2)(𝑝2	NOUN
cana-1750	235	11	−	−	NOUN
cana-1750	235	12	2𝑝	2𝑝	NOUN
cana-1750	235	13	)	)	PUNCT
cana-1750	235	14	4(𝜆	4(𝜆	NUM
cana-1750	236	1	+	+	CCONJ
cana-1750	237	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	237	2	+	+	NUM
cana-1750	237	3	2)(𝜆	2)(𝜆	NUM
cana-1750	237	4	+	+	CCONJ
cana-1750	237	5	1	1	NUM
cana-1750	237	6	)	)	PUNCT
cana-1750	237	7	+	+	CCONJ
cana-1750	237	8	[	[	PUNCT
cana-1750	237	9	(	(	PUNCT
cana-1750	237	10	𝜆2	𝜆2	NOUN
cana-1750	237	11	−	−	NOUN
cana-1750	237	12	7𝜆	7𝜆	PROPN
cana-1750	237	13	+	+	CCONJ
cana-1750	237	14	12)(4	12)(4	NUM
cana-1750	237	15	−	−	PROPN
cana-1750	238	1	𝑝2)(𝑝	𝑝2)(𝑝	PROPN
cana-1750	238	2	−	−	PROPN
cana-1750	238	3	2)𝑝3	2)𝑝3	NOUN
cana-1750	238	4	8(𝜆	8(𝜆	NUM
cana-1750	239	1	+	+	CCONJ
cana-1750	240	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	240	2	+	+	NUM
cana-1750	240	3	2)(𝜆	2)(𝜆	NUM
cana-1750	240	4	+	+	CCONJ
cana-1750	240	5	1	1	NUM
cana-1750	240	6	)	)	PUNCT
cana-1750	240	7	+	+	CCONJ
cana-1750	240	8	[	[	PUNCT
cana-1750	240	9	𝜆4	𝜆4	NOUN
cana-1750	240	10	−	−	PROPN
cana-1750	240	11	4𝜆3	4𝜆3	NUM
cana-1750	240	12	−	−	ADP
cana-1750	240	13	6𝜆2	6𝜆2	NUM
cana-1750	241	1	+	+	CCONJ
cana-1750	241	2	20𝜆	20𝜆	NOUN
cana-1750	241	3	+	+	CCONJ
cana-1750	241	4	25	25	NUM
cana-1750	241	5	4(𝜆	4(𝜆	NUM
cana-1750	241	6	+	+	CCONJ
cana-1750	242	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	242	2	+	+	NUM
cana-1750	242	3	2)2(𝜆	2)2(𝜆	NUM
cana-1750	243	1	+	+	CCONJ
cana-1750	243	2	1)2	1)2	NUM
cana-1750	243	3	]	]	PUNCT
cana-1750	243	4	𝑝2(4	𝑝2(4	PROPN
cana-1750	243	5	−	−	PROPN
cana-1750	243	6	𝑝2	𝑝2	PROPN
cana-1750	243	7	)	)	PUNCT
cana-1750	243	8	]	]	PUNCT
cana-1750	244	1	+	+	CCONJ
cana-1750	244	2	[	[	PUNCT
cana-1750	244	3	𝑝(4	𝑝(4	PROPN
cana-1750	244	4	−	−	NOUN
cana-1750	244	5	𝑝2)2	𝑝2)2	NUM
cana-1750	244	6	4(𝜆	4(𝜆	NUM
cana-1750	245	1	+	+	CCONJ
cana-1750	245	2	3)2	3)2	NUM
cana-1750	245	3	−	−	PROPN
cana-1750	246	1	[	[	PUNCT
cana-1750	246	2	𝜆2	𝜆2	NOUN
cana-1750	246	3	+	+	CCONJ
cana-1750	246	4	2𝜆	2𝜆	NUM
cana-1750	246	5	−	−	NUM
cana-1750	246	6	1	1	NUM
cana-1750	246	7	4(𝜆	4(𝜆	NUM
cana-1750	246	8	+	+	CCONJ
cana-1750	246	9	3)2(𝜆	3)2(𝜆	NUM
cana-1750	246	10	+	+	SYM
cana-1750	246	11	2)2	2)2	NUM
cana-1750	246	12	]	]	PUNCT
cana-1750	246	13	(	(	PUNCT
cana-1750	246	14	4	4	NUM
cana-1750	246	15	−	−	NOUN
cana-1750	246	16	𝑝2)2	𝑝2)2	NUM
cana-1750	246	17	]	]	X
cana-1750	246	18	+	+	CCONJ
cana-1750	246	19	[	[	PUNCT
cana-1750	246	20	(	(	PUNCT
cana-1750	246	21	3	3	NUM
cana-1750	246	22	−	−	NOUN
cana-1750	246	23	𝜆)(4	𝜆)(4	NUM
cana-1750	247	1	−	−	PROPN
cana-1750	247	2	𝑝2)𝑝2	𝑝2)𝑝2	X
cana-1750	247	3	2(1	2(1	NUM
cana-1750	247	4	+	+	CCONJ
cana-1750	247	5	𝜆)(2	𝜆)(2	X
cana-1750	247	6	+	+	CCONJ
cana-1750	247	7	𝜆)2	𝜆)2	NOUN
cana-1750	247	8	+	+	CCONJ
cana-1750	247	9	(	(	PUNCT
cana-1750	247	10	−𝜆2	−𝜆2	PROPN
cana-1750	247	11	+	+	CCONJ
cana-1750	247	12	2𝜆	2𝜆	NUM
cana-1750	247	13	+	+	CCONJ
cana-1750	247	14	5)(4	5)(4	NUM
cana-1750	247	15	−	−	NOUN
cana-1750	247	16	𝑝2)𝑝	𝑝2)𝑝	PROPN
cana-1750	247	17	2(1	2(1	NUM
cana-1750	247	18	+	+	CCONJ
cana-1750	247	19	𝜆)(2	𝜆)(2	ADP
cana-1750	247	20	+	+	NOUN
cana-1750	247	21	𝜆)(3	𝜆)(3	X
cana-1750	247	22	+	+	CCONJ
cana-1750	247	23	𝜆)2	𝜆)2	NOUN
cana-1750	247	24	+	+	CCONJ
cana-1750	247	25	−𝜆4	−𝜆4	NOUN
cana-1750	247	26	+	+	NOUN
cana-1750	247	27	9𝜆3	9𝜆3	NUM
cana-1750	247	28	−	−	PROPN
cana-1750	247	29	21𝜆2	21𝜆2	NUM
cana-1750	247	30	−	−	NOUN
cana-1750	247	31	11𝜆	11𝜆	NOUN
cana-1750	247	32	+	+	CCONJ
cana-1750	247	33	60	60	NUM
cana-1750	247	34	4(𝜆	4(𝜆	NUM
cana-1750	248	1	+	+	CCONJ
cana-1750	249	1	3)2(𝜆	3)2(𝜆	NUM
cana-1750	249	2	+	+	CCONJ
cana-1750	249	3	2)2(𝜆	2)2(𝜆	NUM
cana-1750	250	1	+	+	CCONJ
cana-1750	250	2	1)2	1)2	NUM
cana-1750	250	3	𝑝4(4	𝑝4(4	NOUN
cana-1750	250	4	−	−	PROPN
cana-1750	250	5	𝑝2	𝑝2	NOUN
cana-1750	250	6	)	)	PUNCT
cana-1750	250	7	]	]	PUNCT
cana-1750	251	1	+	+	PUNCT
cana-1750	251	2	|𝑅1(𝜆)𝑝	|𝑅1(𝜆)𝑝	NOUN
cana-1750	251	3	6	6	NUM
cana-1750	251	4	−	−	NOUN
cana-1750	251	5	𝑅2(𝜆)𝑝	𝑅2(𝜆)𝑝	NOUN
cana-1750	251	6	4|	4|	NUM
cana-1750	251	7	+	+	PUNCT
cana-1750	251	8	[	[	PUNCT
cana-1750	251	9	𝜆2	𝜆2	NOUN
cana-1750	251	10	−	−	NOUN
cana-1750	251	11	7𝜆	7𝜆	PROPN
cana-1750	251	12	+	+	CCONJ
cana-1750	251	13	12	12	NUM
cana-1750	251	14	4(𝜆	4(𝜆	NUM
cana-1750	251	15	+	+	CCONJ
cana-1750	251	16	3)2(𝜆	3)2(𝜆	NUM
cana-1750	251	17	+	+	NUM
cana-1750	251	18	2)(𝜆	2)(𝜆	NUM
cana-1750	251	19	+	+	CCONJ
cana-1750	251	20	1	1	NUM
cana-1750	251	21	)	)	PUNCT
cana-1750	251	22	]	]	PUNCT
cana-1750	251	23	𝑝3(4	𝑝3(4	NOUN
cana-1750	251	24	−	−	PROPN
cana-1750	251	25	𝑝2	𝑝2	NOUN
cana-1750	251	26	)	)	PUNCT
cana-1750	251	27	+	+	CCONJ
cana-1750	251	28	(	(	PUNCT
cana-1750	251	29	4	4	NUM
cana-1750	251	30	−	−	NOUN
cana-1750	251	31	𝑝2)2	𝑝2)2	NUM
cana-1750	251	32	4(𝜆	4(𝜆	NUM
cana-1750	251	33	+	+	CCONJ
cana-1750	251	34	3)2	3)2	NUM
cana-1750	251	35	.	.	PUNCT
cana-1750	252	1	which	which	PRON
cana-1750	252	2	has	have	VERB
cana-1750	252	3	the	the	DET
cana-1750	252	4	maximum	maximum	ADJ
cana-1750	252	5	values	value	NOUN
cana-1750	252	6	|64𝑅1(𝜆	|64𝑅1(𝜆	NOUN
cana-1750	252	7	)	)	PUNCT
cana-1750	253	1	−	−	PROPN
cana-1750	253	2	16𝑅2(𝜆)|	16𝑅2(𝜆)|	NUM
cana-1750	253	3	for	for	ADP
cana-1750	253	4	𝑝	𝑝	NOUN
cana-1750	253	5	=	=	SYM
cana-1750	253	6	2	2	NUM
cana-1750	253	7	and	and	CCONJ
cana-1750	253	8	4	4	NUM
cana-1750	253	9	(	(	PUNCT
cana-1750	253	10	𝜆+2)2	𝜆+2)2	NOUN
cana-1750	253	11	for	for	ADP
cana-1750	253	12	𝑝	𝑝	NOUN
cana-1750	253	13	=	=	SYM
cana-1750	253	14	0	0	NUM
cana-1750	253	15	remark	remark	NOUN
cana-1750	253	16	3.4	3.4	NUM
cana-1750	253	17	.	.	PUNCT
cana-1750	254	1	theorem	theorem	NOUN
cana-1750	254	2	(	(	PUNCT
cana-1750	254	3	3.3	3.3	NUM
cana-1750	254	4	)	)	PUNCT
cana-1750	254	5	,	,	PUNCT
cana-1750	254	6	for	for	ADP
cana-1750	254	7	𝜆	𝜆	DET
cana-1750	254	8	=	=	SYM
cana-1750	254	9	0	0	NUM
cana-1750	254	10	yields	yield	NOUN
cana-1750	254	11	the	the	DET
cana-1750	254	12	bound	bind	VERB
cana-1750	254	13	|𝑎4	|𝑎4	NOUN
cana-1750	254	14	2	2	NUM
cana-1750	254	15	−	−	NOUN
cana-1750	254	16	𝑎3	𝑎3	PROPN
cana-1750	254	17	2|	2|	NUM
cana-1750	254	18	≤	≤	ADV
cana-1750	254	19	7	7	NUM
cana-1750	254	20	for	for	ADP
cana-1750	254	21	the	the	DET
cana-1750	254	22	class	class	NOUN
cana-1750	254	23	of	of	ADP
cana-1750	254	24	star	star	NOUN
cana-1750	254	25	like	like	ADP
cana-1750	254	26	function	function	NOUN
cana-1750	254	27	𝒮∗	𝒮∗	NOUN
cana-1750	254	28	conforming	conform	VERB
cana-1750	254	29	the	the	DET
cana-1750	254	30	bound	bind	VERB
cana-1750	254	31	obtained	obtain	VERB
cana-1750	254	32	by	by	ADP
cana-1750	254	33	thomous	thomous	PROPN
cana-1750	254	34	and	and	CCONJ
cana-1750	254	35	halim	halim	PROPN
cana-1750	255	1	[	[	X
cana-1750	255	2	1	1	NUM
cana-1750	255	3	]	]	PUNCT
cana-1750	255	4	.	.	PUNCT
cana-1750	256	1	and	and	CCONJ
cana-1750	256	2	for	for	ADP
cana-1750	256	3	𝜆	𝜆	DET
cana-1750	256	4	=	=	SYM
cana-1750	256	5	1	1	NUM
cana-1750	256	6	yields	yield	NOUN
cana-1750	256	7	the	the	DET
cana-1750	256	8	bound	bind	VERB
cana-1750	256	9	|𝑎4	|𝑎4	NOUN
cana-1750	256	10	2	2	NUM
cana-1750	256	11	−	−	NOUN
cana-1750	256	12	𝑎3	𝑎3	PROPN
cana-1750	256	13	2|	2|	NUM
cana-1750	256	14	≤	≤	NUM
cana-1750	256	15	4	4	NUM
cana-1750	256	16	9	9	NUM
cana-1750	256	17	for	for	ADP
cana-1750	256	18	the	the	DET
cana-1750	256	19	class	class	NOUN
cana-1750	256	20	of	of	ADP
cana-1750	256	21	functions	function	NOUN
cana-1750	256	22	with	with	ADP
cana-1750	256	23	bounded	bounded	ADJ
cana-1750	256	24	boundary	boundary	ADJ
cana-1750	256	25	rotation	rotation	NOUN
cana-1750	256	26	ℛ̃	ℛ̃	PROPN
cana-1750	256	27	conforming	conform	VERB
cana-1750	256	28	the	the	DET
cana-1750	256	29	bound	bind	VERB
cana-1750	256	30	obtained	obtain	VERB
cana-1750	256	31	by	by	ADP
cana-1750	256	32	radhika	radhika	PROPN
cana-1750	256	33	et	et	PROPN
cana-1750	256	34	al	al	PROPN
cana-1750	256	35	.	.	PUNCT
cana-1750	257	1	[	[	X
cana-1750	257	2	2	2	NUM
cana-1750	257	3	]	]	PUNCT
cana-1750	257	4	.	.	PUNCT
cana-1750	258	1	theorem	theorem	NOUN
cana-1750	258	2	3.5	3.5	NUM
cana-1750	258	3	.	.	PUNCT
cana-1750	259	1	let	let	VERB
cana-1750	259	2	𝑓	𝑓	PRON
cana-1750	259	3	given	give	VERB
cana-1750	259	4	by	by	ADP
cana-1750	259	5	(	(	PUNCT
cana-1750	259	6	1.1	1.1	NUM
cana-1750	259	7	)	)	PUNCT
cana-1750	259	8	,	,	PUNCT
cana-1750	259	9	be	be	AUX
cana-1750	259	10	in	in	ADP
cana-1750	259	11	the	the	DET
cana-1750	259	12	class	class	NOUN
cana-1750	259	13	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	259	14	)	)	PUNCT
cana-1750	259	15	;	;	PUNCT
cana-1750	259	16	(	(	PUNCT
cana-1750	259	17	0	0	NUM
cana-1750	259	18	≤	≤	NUM
cana-1750	260	1	𝜆	𝜆	DET
cana-1750	260	2	≤	≤	NUM
cana-1750	260	3	1	1	NUM
cana-1750	260	4	;	;	PUNCT
cana-1750	260	5	𝜆	𝜆	DET
cana-1750	260	6	≠	≠	PROPN
cana-1750	260	7	𝜆0	𝜆0	NOUN
cana-1750	260	8	)	)	PUNCT
cana-1750	260	9	.	.	PUNCT
cana-1750	261	1	then	then	ADV
cana-1750	261	2	we	we	PRON
cana-1750	261	3	have	have	VERB
cana-1750	261	4	sharp	sharp	ADV
cana-1750	261	5	bound	bind	VERB
cana-1750	261	6	|𝑇3(2)|	|𝑇3(2)|	PROPN
cana-1750	261	7	=	=	PUNCT
cana-1750	261	8	|(|	|(|	PROPN
cana-1750	261	9	𝑎2	𝑎2	PROPN
cana-1750	261	10	𝑎3	𝑎3	PROPN
cana-1750	261	11	𝑎4	𝑎4	PROPN
cana-1750	261	12	𝑎3	𝑎3	PROPN
cana-1750	261	13	𝑎2	𝑎2	PROPN
cana-1750	261	14	𝑎3	𝑎3	PROPN
cana-1750	261	15	𝑎4	𝑎4	PROPN
cana-1750	261	16	𝑎3	𝑎3	PROPN
cana-1750	261	17	𝑎2	𝑎2	PROPN
cana-1750	261	18	|)|	|)|	PROPN
cana-1750	261	19	≤	≤	PROPN
cana-1750	261	20	{	{	PUNCT
cana-1750	261	21	max	max	PROPN
cana-1750	261	22	{	{	PUNCT
cana-1750	261	23	|𝑅(𝜆)𝑈(𝜆)|	|𝑅(𝜆)𝑈(𝜆)|	PROPN
cana-1750	261	24	,	,	PUNCT
cana-1750	261	25	8|𝑅(𝜆)|	8|𝑅(𝜆)|	NUM
cana-1750	261	26	(	(	PUNCT
cana-1750	261	27	𝜆	𝜆	ADP
cana-1750	261	28	+	+	ADJ
cana-1750	261	29	2)2	2)2	NUM
cana-1750	261	30	}	}	PUNCT
cana-1750	261	31	;	;	PUNCT
cana-1750	261	32	if	if	SCONJ
cana-1750	261	33	𝜆	𝜆	DET
cana-1750	261	34	≠	≠	PROPN
cana-1750	261	35	𝜆0	𝜆0	NOUN
cana-1750	261	36	max	max	NOUN
cana-1750	261	37	{	{	PUNCT
cana-1750	261	38	|𝑈(𝜆)𝐵(𝜆)|	|𝑈(𝜆)𝐵(𝜆)|	PROPN
cana-1750	261	39	,	,	PUNCT
cana-1750	261	40	8|𝐵(𝜆)|	8|𝐵(𝜆)|	NUM
cana-1750	261	41	(	(	PUNCT
cana-1750	261	42	𝜆	𝜆	ADP
cana-1750	261	43	+	+	ADJ
cana-1750	261	44	2)2	2)2	NUM
cana-1750	261	45	}	}	PUNCT
cana-1750	261	46	;	;	PUNCT
cana-1750	261	47	if	if	SCONJ
cana-1750	261	48	𝜆	𝜆	PRON
cana-1750	261	49	=	=	SYM
cana-1750	261	50	𝜆0	𝜆0	NUM
cana-1750	261	51	communications	communication	NOUN
cana-1750	261	52	on	on	ADP
cana-1750	261	53	applied	apply	VERB
cana-1750	261	54	nonlinear	nonlinear	ADJ
cana-1750	261	55	analysis	analysis	NOUN
cana-1750	261	56	issn	issn	NOUN
cana-1750	261	57	:	:	PUNCT
cana-1750	261	58	1074	1074	NUM
cana-1750	261	59	-	-	PUNCT
cana-1750	261	60	133x	133x	NUM
cana-1750	261	61	vol	vol	NOUN
cana-1750	261	62	32	32	NUM
cana-1750	261	63	no	no	NOUN
cana-1750	261	64	.	.	NOUN
cana-1750	261	65	2	2	NUM
cana-1750	261	66	(	(	PUNCT
cana-1750	261	67	2025	2025	NUM
cana-1750	261	68	)	)	PUNCT
cana-1750	261	69	392	392	NUM
cana-1750	261	70	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	261	71	where	where	SCONJ
cana-1750	261	72	𝜆0	𝜆0	NOUN
cana-1750	261	73	≈	≈	PROPN
cana-1750	261	74	0.5	0.5	NUM
cana-1750	261	75	is	be	AUX
cana-1750	261	76	the	the	DET
cana-1750	261	77	positive	positive	ADJ
cana-1750	261	78	root	root	NOUN
cana-1750	261	79	of	of	ADP
cana-1750	261	80	the	the	DET
cana-1750	261	81	polynomial	polynomial	ADJ
cana-1750	261	82	24𝑥	24𝑥	PUNCT
cana-1750	261	83	−	−	PROPN
cana-1750	261	84	12	12	NUM
cana-1750	261	85	=	=	SYM
cana-1750	261	86	0	0	NUM
cana-1750	261	87	,	,	PUNCT
cana-1750	261	88	𝑅(𝜆	𝑅(𝜆	NOUN
cana-1750	261	89	)	)	PUNCT
cana-1750	261	90	=	=	NOUN
cana-1750	261	91	24𝑥	24𝑥	X
cana-1750	262	1	−	−	NOUN
cana-1750	262	2	12	12	NUM
cana-1750	262	3	(	(	PUNCT
cana-1750	262	4	𝜆	𝜆	ADP
cana-1750	262	5	+	+	CCONJ
cana-1750	262	6	3)(𝜆	3)(𝜆	NUM
cana-1750	262	7	+	+	NUM
cana-1750	262	8	2)(𝜆	2)(𝜆	NUM
cana-1750	262	9	+	+	NOUN
cana-1750	262	10	1	1	NUM
cana-1750	262	11	)	)	PUNCT
cana-1750	262	12	(	(	PUNCT
cana-1750	262	13	3.19	3.19	NUM
cana-1750	262	14	)	)	PUNCT
cana-1750	262	15	𝑈(𝜆	𝑈(𝜆	NUM
cana-1750	262	16	)	)	PUNCT
cana-1750	262	17	=	=	NOUN
cana-1750	262	18	4(8𝜆2	4(8𝜆2	X
cana-1750	262	19	+	+	ADJ
cana-1750	262	20	32𝜆	32𝜆	NOUN
cana-1750	262	21	−	−	PROPN
cana-1750	262	22	18	18	NUM
cana-1750	262	23	)	)	PUNCT
cana-1750	262	24	(	(	PUNCT
cana-1750	262	25	𝜆	𝜆	ADP
cana-1750	262	26	+	+	CCONJ
cana-1750	262	27	3)(𝜆	3)(𝜆	NUM
cana-1750	262	28	+	+	NUM
cana-1750	262	29	2)2(𝜆	2)2(𝜆	NUM
cana-1750	263	1	+	+	CCONJ
cana-1750	263	2	1)2	1)2	NUM
cana-1750	263	3	(	(	PUNCT
cana-1750	263	4	3.20	3.20	NUM
cana-1750	263	5	)	)	PUNCT
cana-1750	263	6	𝐵(𝜆	𝐵(𝜆	X
cana-1750	263	7	)	)	PUNCT
cana-1750	263	8	=	=	SYM
cana-1750	263	9	4𝜆2	4𝜆2	NUM
cana-1750	264	1	−	−	NOUN
cana-1750	264	2	4𝜆	4𝜆	NOUN
cana-1750	264	3	+	+	CCONJ
cana-1750	264	4	36	36	NUM
cana-1750	264	5	(	(	PUNCT
cana-1750	264	6	𝜆	𝜆	NOUN
cana-1750	264	7	+	+	CCONJ
cana-1750	264	8	3)(𝜆	3)(𝜆	NUM
cana-1750	264	9	+	+	NUM
cana-1750	264	10	2)(𝜆	2)(𝜆	NUM
cana-1750	264	11	+	+	NOUN
cana-1750	264	12	1	1	NUM
cana-1750	264	13	)	)	PUNCT
cana-1750	264	14	(	(	PUNCT
cana-1750	264	15	3.21	3.21	NUM
cana-1750	264	16	)	)	PUNCT
cana-1750	264	17	proof	proof	NOUN
cana-1750	264	18	.	.	PUNCT
cana-1750	265	1	write	write	VERB
cana-1750	265	2	|𝑇3(2)|	|𝑇3(2)|	PROPN
cana-1750	265	3	=	=	PUNCT
cana-1750	265	4	|𝑎2	|𝑎2	NOUN
cana-1750	265	5	3	3	NUM
cana-1750	265	6	−	−	PROPN
cana-1750	265	7	2𝑎2𝑎3	2𝑎2𝑎3	NUM
cana-1750	265	8	2	2	NUM
cana-1750	265	9	+	+	CCONJ
cana-1750	265	10	2𝑎3	2𝑎3	NUM
cana-1750	265	11	2𝑎4	2𝑎4	NUM
cana-1750	265	12	−	−	NOUN
cana-1750	266	1	𝑎2𝑎4|	𝑎2𝑎4|	PROPN
cana-1750	266	2	(	(	PUNCT
cana-1750	266	3	3.22	3.22	NUM
cana-1750	266	4	)	)	PUNCT
cana-1750	266	5	=	=	SYM
cana-1750	266	6	|(𝑎2	|(𝑎2	NOUN
cana-1750	266	7	−	−	NOUN
cana-1750	266	8	𝑎4)(𝑎2	𝑎4)(𝑎2	NOUN
cana-1750	266	9	2	2	NUM
cana-1750	266	10	−	−	NOUN
cana-1750	266	11	2𝑎3	2𝑎3	NUM
cana-1750	266	12	2	2	NUM
cana-1750	266	13	+	+	CCONJ
cana-1750	266	14	𝑎2𝑎4)|	𝑎2𝑎4)|	X
cana-1750	266	15	(	(	PUNCT
cana-1750	266	16	3.23	3.23	NUM
cana-1750	266	17	)	)	PUNCT
cana-1750	266	18	using	use	VERB
cana-1750	266	19	the	the	DET
cana-1750	266	20	same	same	ADJ
cana-1750	266	21	techniques	technique	NOUN
cana-1750	266	22	as	as	ADP
cana-1750	266	23	the	the	DET
cana-1750	266	24	theorem	theorem	NOUN
cana-1750	266	25	(	(	PUNCT
cana-1750	266	26	3.1	3.1	NUM
cana-1750	266	27	)	)	PUNCT
cana-1750	266	28	,	,	PUNCT
cana-1750	266	29	one	one	PRON
cana-1750	266	30	can	can	AUX
cana-1750	266	31	obtain	obtain	VERB
cana-1750	266	32	with	with	ADP
cana-1750	266	33	simple	simple	ADJ
cana-1750	266	34	computations	computation	NOUN
cana-1750	266	35	that	that	PRON
cana-1750	266	36	|𝑎2	|𝑎2	NOUN
cana-1750	266	37	−	−	PROPN
cana-1750	266	38	𝑎4|	𝑎4|	PROPN
cana-1750	266	39	≤	≤	ADJ
cana-1750	266	40	|𝑅(𝜆)|	|𝑅(𝜆)|	NOUN
cana-1750	266	41	for	for	ADP
cana-1750	266	42	𝜆	𝜆	DET
cana-1750	266	43	≠	≠	PROPN
cana-1750	266	44	𝜆0	𝜆0	NOUN
cana-1750	266	45	.	.	PUNCT
cana-1750	267	1	(	(	PUNCT
cana-1750	267	2	3.24	3.24	NUM
cana-1750	267	3	)	)	PUNCT
cana-1750	267	4	we	we	PRON
cana-1750	267	5	need	need	VERB
cana-1750	267	6	to	to	PART
cana-1750	267	7	show	show	VERB
cana-1750	267	8	that	that	SCONJ
cana-1750	267	9	|𝑎2	|𝑎2	NOUN
cana-1750	267	10	3	3	NUM
cana-1750	267	11	−	−	NOUN
cana-1750	267	12	2𝑎3	2𝑎3	NUM
cana-1750	267	13	2	2	NUM
cana-1750	267	14	+	+	CCONJ
cana-1750	267	15	𝑎2𝑎4|	𝑎2𝑎4|	PROPN
cana-1750	267	16	≤	≤	ADJ
cana-1750	267	17	|𝑈(∣	|𝑈(∣	PROPN
cana-1750	267	18	𝜆)|	𝜆)|	NOUN
cana-1750	267	19	.	.	PUNCT
cana-1750	268	1	(	(	PUNCT
cana-1750	268	2	3.25	3.25	NUM
cana-1750	268	3	)	)	PUNCT
cana-1750	268	4	in	in	ADP
cana-1750	268	5	the	the	DET
cana-1750	268	6	view	view	NOUN
cana-1750	268	7	of	of	ADP
cana-1750	268	8	(	(	PUNCT
cana-1750	268	9	3.2),(3.3	3.2),(3.3	NUM
cana-1750	268	10	)	)	PUNCT
cana-1750	268	11	,	,	PUNCT
cana-1750	268	12	(	(	PUNCT
cana-1750	268	13	3.5	3.5	NUM
cana-1750	268	14	)	)	PUNCT
cana-1750	268	15	and	and	CCONJ
cana-1750	268	16	lemma	lemma	PROPN
cana-1750	268	17	(	(	PUNCT
cana-1750	268	18	2.2	2.2	NUM
cana-1750	268	19	)	)	PUNCT
cana-1750	268	20	,	,	PUNCT
cana-1750	268	21	where	where	SCONJ
cana-1750	268	22	we	we	PRON
cana-1750	268	23	denote	denote	VERB
cana-1750	268	24	𝑋	𝑋	NOUN
cana-1750	268	25	=	=	SYM
cana-1750	268	26	4	4	NUM
cana-1750	268	27	−	−	PROPN
cana-1750	268	28	𝑝2	𝑝2	NOUN
cana-1750	268	29	and	and	CCONJ
cana-1750	268	30	𝑌	𝑌	PROPN
cana-1750	268	31	=	=	PUNCT
cana-1750	268	32	(	(	PUNCT
cana-1750	268	33	1	1	NUM
cana-1750	268	34	−	−	PROPN
cana-1750	268	35	|𝑥|2)𝜚	|𝑥|2)𝜚	PROPN
cana-1750	268	36	,	,	PUNCT
cana-1750	268	37	where	where	SCONJ
cana-1750	268	38	0	0	NUM
cana-1750	268	39	≤	≤	NUM
cana-1750	268	40	𝑝	𝑝	NOUN
cana-1750	268	41	≤	≤	NUM
cana-1750	268	42	2	2	NUM
cana-1750	268	43	and	and	CCONJ
cana-1750	268	44	|𝜚|	|𝜚|	PROPN
cana-1750	268	45	<	<	X
cana-1750	268	46	1	1	NUM
cana-1750	268	47	,	,	PUNCT
cana-1750	268	48	one	one	PRON
cana-1750	268	49	may	may	AUX
cana-1750	268	50	easily	easily	ADV
cana-1750	268	51	get	get	VERB
cana-1750	268	52	|𝑎2	|𝑎2	NOUN
cana-1750	268	53	2	2	NUM
cana-1750	268	54	−	−	NOUN
cana-1750	268	55	2𝑎3	2𝑎3	NUM
cana-1750	268	56	2	2	NUM
cana-1750	268	57	+	+	CCONJ
cana-1750	268	58	𝑎2𝑎4|	𝑎2𝑎4|	PROPN
cana-1750	268	59	=	=	SYM
cana-1750	268	60	|	|	NOUN
cana-1750	268	61	[	[	PUNCT
cana-1750	268	62	−𝜆3	−𝜆3	NOUN
cana-1750	268	63	+	+	NUM
cana-1750	268	64	𝜆2	𝜆2	PROPN
cana-1750	268	65	+	+	NOUN
cana-1750	268	66	16𝜆	16𝜆	NOUN
cana-1750	268	67	−	−	PROPN
cana-1750	268	68	30	30	NUM
cana-1750	268	69	4(𝜆	4(𝜆	NUM
cana-1750	269	1	+	+	CCONJ
cana-1750	269	2	3)(𝜆	3)(𝜆	NUM
cana-1750	269	3	+	+	NUM
cana-1750	269	4	2)2(𝜆	2)2(𝜆	NUM
cana-1750	269	5	+	+	CCONJ
cana-1750	269	6	1)2	1)2	NUM
cana-1750	269	7	]	]	PUNCT
cana-1750	269	8	𝑝1	𝑝1	NOUN
cana-1750	269	9	4	4	NUM
cana-1750	269	10	+	+	NOUN
cana-1750	269	11	𝑝1	𝑝1	NOUN
cana-1750	269	12	2	2	NUM
cana-1750	269	13	(	(	PUNCT
cana-1750	269	14	𝜆	𝜆	PROPN
cana-1750	269	15	+	+	PROPN
cana-1750	269	16	1)2	1)2	NUM
cana-1750	269	17	−	−	NOUN
cana-1750	269	18	𝑝1	𝑝1	NOUN
cana-1750	269	19	2𝑋𝑥2	2𝑋𝑥2	NOUN
cana-1750	269	20	4(𝜆	4(𝜆	NUM
cana-1750	270	1	+	+	CCONJ
cana-1750	270	2	3)(𝜆	3)(𝜆	NUM
cana-1750	270	3	+	+	NUM
cana-1750	270	4	1	1	NUM
cana-1750	270	5	)	)	PUNCT
cana-1750	271	1	|	|	ADV
cana-1750	272	1	+	+	CCONJ
cana-1750	272	2	|	|	ADV
cana-1750	272	3	𝑋𝑌𝑝1	𝑋𝑌𝑝1	SYM
cana-1750	272	4	2(𝜆	2(𝜆	NUM
cana-1750	272	5	+	+	CCONJ
cana-1750	272	6	3)(𝜆	3)(𝜆	NUM
cana-1750	272	7	+	+	NUM
cana-1750	272	8	1	1	NUM
cana-1750	272	9	)	)	PUNCT
cana-1750	272	10	−	−	NOUN
cana-1750	272	11	𝑋2𝑥2	𝑋2𝑥2	VERB
cana-1750	272	12	2(𝜆	2(𝜆	NUM
cana-1750	272	13	+	+	CCONJ
cana-1750	272	14	2)2	2)2	NUM
cana-1750	272	15	+	+	CCONJ
cana-1750	272	16	[	[	PUNCT
cana-1750	272	17	𝜆3	𝜆3	NOUN
cana-1750	272	18	+	+	CCONJ
cana-1750	272	19	2𝜆2	2𝜆2	NUM
cana-1750	272	20	−	−	PROPN
cana-1750	272	21	9𝜆	9𝜆	NUM
cana-1750	272	22	−	−	NUM
cana-1750	272	23	8	8	NUM
cana-1750	272	24	2(𝜆	2(𝜆	NUM
cana-1750	272	25	+	+	CCONJ
cana-1750	273	1	3)(𝜆	3)(𝜆	NUM
cana-1750	273	2	+	+	NUM
cana-1750	273	3	2)2(𝜆	2)2(𝜆	NUM
cana-1750	273	4	+	+	CCONJ
cana-1750	273	5	1)2	1)2	NUM
cana-1750	273	6	]	]	PUNCT
cana-1750	273	7	𝑝1	𝑝1	NOUN
cana-1750	273	8	2𝑋𝑥|	2𝑋𝑥|	NUM
cana-1750	273	9	applying	apply	VERB
cana-1750	273	10	the	the	DET
cana-1750	273	11	triangle	triangle	NOUN
cana-1750	273	12	inequality	inequality	NOUN
cana-1750	273	13	and	and	CCONJ
cana-1750	273	14	assuming	assume	VERB
cana-1750	273	15	that	that	SCONJ
cana-1750	273	16	𝑝1	𝑝1	NOUN
cana-1750	273	17	=	=	SYM
cana-1750	273	18	𝑝	𝑝	PROPN
cana-1750	273	19	,	,	PUNCT
cana-1750	273	20	where	where	SCONJ
cana-1750	273	21	0	0	NUM
cana-1750	273	22	≤	≤	NOUN
cana-1750	273	23	𝑝	𝑝	NOUN
cana-1750	273	24	≤	≤	NOUN
cana-1750	273	25	2	2	NUM
cana-1750	273	26	,	,	PUNCT
cana-1750	273	27	we	we	PRON
cana-1750	273	28	obtain	obtain	VERB
cana-1750	273	29	|𝑎2	|𝑎2	NOUN
cana-1750	273	30	2	2	NUM
cana-1750	273	31	−	−	NOUN
cana-1750	273	32	2𝑎3	2𝑎3	NUM
cana-1750	273	33	2	2	NUM
cana-1750	273	34	+	+	CCONJ
cana-1750	273	35	𝑎2𝑎4|	𝑎2𝑎4|	PROPN
cana-1750	273	36	≤	≤	X
cana-1750	273	37	[	[	PUNCT
cana-1750	273	38	𝑝2(4	𝑝2(4	PROPN
cana-1750	273	39	−	−	PROPN
cana-1750	273	40	𝑝2	𝑝2	NOUN
cana-1750	273	41	)	)	PUNCT
cana-1750	273	42	4(𝜆	4(𝜆	NUM
cana-1750	274	1	+	+	CCONJ
cana-1750	274	2	3)(𝜆	3)(𝜆	NUM
cana-1750	274	3	+	+	NUM
cana-1750	274	4	1	1	NUM
cana-1750	274	5	)	)	PUNCT
cana-1750	274	6	+	+	CCONJ
cana-1750	274	7	𝑝2(4	𝑝2(4	PROPN
cana-1750	274	8	−	−	PROPN
cana-1750	274	9	𝑝2	𝑝2	NOUN
cana-1750	274	10	)	)	PUNCT
cana-1750	274	11	2(𝜆	2(𝜆	NUM
cana-1750	275	1	+	+	CCONJ
cana-1750	275	2	3)(𝜆	3)(𝜆	NUM
cana-1750	275	3	+	+	NUM
cana-1750	275	4	1	1	NUM
cana-1750	275	5	)	)	PUNCT
cana-1750	276	1	+	+	CCONJ
cana-1750	276	2	(	(	PUNCT
cana-1750	276	3	4	4	NUM
cana-1750	276	4	−	−	NOUN
cana-1750	276	5	𝑝2)2	𝑝2)2	NUM
cana-1750	276	6	2(𝜆	2(𝜆	NUM
cana-1750	276	7	+	+	CCONJ
cana-1750	276	8	2)2	2)2	NUM
cana-1750	276	9	]	]	PUNCT
cana-1750	276	10	|𝑥|2	|𝑥|2	ADJ
cana-1750	276	11	+	+	PUNCT
cana-1750	277	1	[	[	X
cana-1750	277	2	[	[	PUNCT
cana-1750	277	3	𝜆3	𝜆3	NOUN
cana-1750	277	4	+	+	NOUN
cana-1750	277	5	2𝜆2	2𝜆2	NUM
cana-1750	277	6	−	−	PROPN
cana-1750	277	7	9𝜆	9𝜆	NUM
cana-1750	277	8	−	−	NUM
cana-1750	277	9	8	8	NUM
cana-1750	277	10	2(𝜆	2(𝜆	NUM
cana-1750	277	11	+	+	CCONJ
cana-1750	277	12	3)(𝜆	3)(𝜆	NUM
cana-1750	277	13	+	+	NUM
cana-1750	277	14	2)(𝜆	2)(𝜆	NUM
cana-1750	277	15	+	+	CCONJ
cana-1750	277	16	1)2	1)2	NUM
cana-1750	277	17	]	]	PUNCT
cana-1750	277	18	𝑝(4	𝑝(4	PROPN
cana-1750	277	19	−	−	PROPN
cana-1750	277	20	𝑝2	𝑝2	NOUN
cana-1750	277	21	)	)	PUNCT
cana-1750	277	22	]	]	PUNCT
cana-1750	278	1	|𝑥|	|𝑥|	PROPN
cana-1750	279	1	+	+	CCONJ
cana-1750	279	2	𝑝(4	𝑝(4	PROPN
cana-1750	279	3	−	−	PROPN
cana-1750	279	4	𝑝2	𝑝2	NOUN
cana-1750	279	5	)	)	PUNCT
cana-1750	279	6	2(𝜆	2(𝜆	NUM
cana-1750	280	1	+	+	CCONJ
cana-1750	281	1	3)(𝜆	3)(𝜆	NUM
cana-1750	281	2	+	+	NUM
cana-1750	281	3	1	1	NUM
cana-1750	281	4	)	)	PUNCT
cana-1750	281	5	+	+	NUM
cana-1750	281	6	𝑝2	𝑝2	NOUN
cana-1750	281	7	(	(	PUNCT
cana-1750	281	8	𝜆	𝜆	PROPN
cana-1750	281	9	+	+	X
cana-1750	281	10	1)2	1)2	NUM
cana-1750	281	11	+	+	CCONJ
cana-1750	281	12	[	[	PUNCT
cana-1750	281	13	−𝜆3	−𝜆3	NOUN
cana-1750	281	14	+	+	NUM
cana-1750	281	15	𝜆2	𝜆2	NOUN
cana-1750	281	16	+	+	NOUN
cana-1750	281	17	16𝜆	16𝜆	NOUN
cana-1750	281	18	−	−	PROPN
cana-1750	281	19	30	30	NUM
cana-1750	281	20	4(𝜆	4(𝜆	NUM
cana-1750	282	1	+	+	CCONJ
cana-1750	282	2	3)(𝜆	3)(𝜆	NUM
cana-1750	282	3	+	+	NUM
cana-1750	282	4	2)2(𝜆	2)2(𝜆	NUM
cana-1750	282	5	+	+	CCONJ
cana-1750	282	6	1)2	1)2	NUM
cana-1750	282	7	]	]	PUNCT
cana-1750	282	8	𝑝4	𝑝4	NOUN
cana-1750	282	9	=	=	SYM
cana-1750	282	10	ψ(𝑝	ψ(𝑝	PROPN
cana-1750	282	11	,	,	PUNCT
cana-1750	282	12	|𝑥|	|𝑥|	INTJ
cana-1750	282	13	)	)	PUNCT
cana-1750	282	14	we	we	PRON
cana-1750	282	15	have	have	VERB
cana-1750	282	16	to	to	PART
cana-1750	282	17	prove	prove	VERB
cana-1750	282	18	that	that	SCONJ
cana-1750	282	19	the	the	DET
cana-1750	282	20	maximum	maximum	ADJ
cana-1750	282	21	value	value	NOUN
cana-1750	282	22	of	of	ADP
cana-1750	282	23	ψ(𝑝	ψ(𝑝	PROPN
cana-1750	282	24	,	,	PUNCT
cana-1750	282	25	|𝑥|	|𝑥|	INTJ
cana-1750	282	26	)	)	PUNCT
cana-1750	282	27	on	on	ADP
cana-1750	282	28	[	[	X
cana-1750	282	29	0,2	0,2	NUM
cana-1750	282	30	]	]	X
cana-1750	282	31	×	×	NOUN
cana-1750	283	1	[	[	X
cana-1750	283	2	0,1	0,1	NUM
cana-1750	283	3	]	]	PUNCT
cana-1750	283	4	.	.	PUNCT
cana-1750	284	1	first	first	ADV
cana-1750	284	2	,	,	PUNCT
cana-1750	284	3	assume	assume	VERB
cana-1750	284	4	that	that	SCONJ
cana-1750	284	5	there	there	PRON
cana-1750	284	6	is	be	VERB
cana-1750	284	7	a	a	DET
cana-1750	284	8	maximum	maximum	NOUN
cana-1750	284	9	at	at	ADP
cana-1750	284	10	an	an	DET
cana-1750	284	11	interior	interior	ADJ
cana-1750	284	12	point	point	NOUN
cana-1750	284	13	ψ(𝑝0	ψ(𝑝0	NOUN
cana-1750	284	14	,	,	PUNCT
cana-1750	284	15	|𝑥0|	|𝑥0|	VERB
cana-1750	284	16	)	)	PUNCT
cana-1750	284	17	of	of	ADP
cana-1750	284	18	[	[	X
cana-1750	284	19	0,2	0,2	NUM
cana-1750	284	20	]	]	X
cana-1750	284	21	×	×	NOUN
cana-1750	285	1	[	[	X
cana-1750	285	2	0,1	0,1	NUM
cana-1750	285	3	]	]	PUNCT
cana-1750	285	4	.	.	PUNCT
cana-1750	286	1	differentiating	differentiate	VERB
cana-1750	286	2	ψ(𝑝	ψ(𝑝	PROPN
cana-1750	286	3	,	,	PUNCT
cana-1750	286	4	|𝑥|	|𝑥|	PROPN
cana-1750	286	5	)	)	PUNCT
cana-1750	286	6	with	with	ADP
cana-1750	286	7	respect	respect	NOUN
cana-1750	286	8	to	to	ADP
cana-1750	286	9	|𝑥|	|𝑥|	VERB
cana-1750	286	10	and	and	CCONJ
cana-1750	286	11	equating	equate	VERB
cana-1750	286	12	it	it	PRON
cana-1750	286	13	to	to	ADP
cana-1750	286	14	0	0	NUM
cana-1750	286	15	implies	imply	VERB
cana-1750	286	16	that	that	SCONJ
cana-1750	286	17	𝑝	𝑝	X
cana-1750	286	18	=	=	SYM
cana-1750	286	19	𝑝0	𝑝0	NOUN
cana-1750	286	20	=	=	SYM
cana-1750	286	21	2	2	NUM
cana-1750	286	22	which	which	PRON
cana-1750	286	23	is	be	AUX
cana-1750	286	24	contradiction	contradiction	NOUN
cana-1750	286	25	.	.	PUNCT
cana-1750	287	1	thus	thus	ADV
cana-1750	287	2	,	,	PUNCT
cana-1750	287	3	for	for	ADP
cana-1750	287	4	the	the	DET
cana-1750	287	5	maximum	maximum	NOUN
cana-1750	287	6	of	of	ADP
cana-1750	287	7	ψ(𝑝	ψ(𝑝	PROPN
cana-1750	287	8	,	,	PUNCT
cana-1750	287	9	|𝑥|	|𝑥|	PROPN
cana-1750	287	10	)	)	PUNCT
cana-1750	287	11	,	,	PUNCT
cana-1750	287	12	we	we	PRON
cana-1750	287	13	need	need	VERB
cana-1750	287	14	only	only	ADV
cana-1750	287	15	to	to	PART
cana-1750	287	16	consider	consider	VERB
cana-1750	287	17	the	the	DET
cana-1750	287	18	end	end	NOUN
cana-1750	287	19	points	point	NOUN
cana-1750	287	20	of	of	ADP
cana-1750	287	21	[	[	X
cana-1750	287	22	0,2	0,2	NUM
cana-1750	287	23	]	]	X
cana-1750	287	24	×	×	NOUN
cana-1750	288	1	[	[	X
cana-1750	288	2	0,1	0,1	NUM
cana-1750	288	3	]	]	PUNCT
cana-1750	288	4	.	.	PUNCT
cana-1750	289	1	for	for	ADP
cana-1750	289	2	𝑝	𝑝	NOUN
cana-1750	289	3	=	=	SYM
cana-1750	289	4	0	0	NUM
cana-1750	289	5	,	,	PUNCT
cana-1750	289	6	we	we	PRON
cana-1750	289	7	obtain	obtain	VERB
cana-1750	289	8	ψ(0	ψ(0	PROPN
cana-1750	289	9	,	,	PUNCT
cana-1750	289	10	|𝑥|	|𝑥|	ADJ
cana-1750	289	11	)	)	PUNCT
cana-1750	290	1	=	=	SYM
cana-1750	290	2	8|𝑥|2	8|𝑥|2	NUM
cana-1750	290	3	(	(	PUNCT
cana-1750	290	4	𝜆	𝜆	ADP
cana-1750	290	5	+	+	X
cana-1750	290	6	2)2	2)2	NUM
cana-1750	290	7	≤	≤	NUM
cana-1750	290	8	8	8	NUM
cana-1750	290	9	(	(	PUNCT
cana-1750	290	10	𝜆	𝜆	NOUN
cana-1750	290	11	+	+	ADJ
cana-1750	290	12	2)2	2)2	NUM
cana-1750	290	13	(	(	PUNCT
cana-1750	290	14	3.26	3.26	NUM
cana-1750	290	15	)	)	PUNCT
cana-1750	290	16	communications	communication	NOUN
cana-1750	290	17	on	on	ADP
cana-1750	290	18	applied	apply	VERB
cana-1750	290	19	nonlinear	nonlinear	ADJ
cana-1750	290	20	analysis	analysis	NOUN
cana-1750	290	21	issn	issn	NOUN
cana-1750	290	22	:	:	PUNCT
cana-1750	290	23	1074	1074	NUM
cana-1750	290	24	-	-	PUNCT
cana-1750	290	25	133x	133x	NUM
cana-1750	290	26	vol	vol	NOUN
cana-1750	290	27	32	32	NUM
cana-1750	290	28	no	no	NOUN
cana-1750	290	29	.	.	NOUN
cana-1750	290	30	2	2	NUM
cana-1750	290	31	(	(	PUNCT
cana-1750	290	32	2025	2025	NUM
cana-1750	290	33	)	)	PUNCT
cana-1750	290	34	393	393	NUM
cana-1750	290	35	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	290	36	for	for	ADP
cana-1750	290	37	𝑝	𝑝	NOUN
cana-1750	290	38	=	=	SYM
cana-1750	290	39	2	2	NUM
cana-1750	290	40	,	,	PUNCT
cana-1750	290	41	we	we	PRON
cana-1750	290	42	have	have	VERB
cana-1750	290	43	ψ(2	ψ(2	NOUN
cana-1750	290	44	,	,	PUNCT
cana-1750	290	45	|𝑥|	|𝑥|	ADJ
cana-1750	290	46	)	)	PUNCT
cana-1750	291	1	=	=	SYM
cana-1750	291	2	4(8𝜆2	4(8𝜆2	X
cana-1750	292	1	+	+	ADJ
cana-1750	292	2	32𝜆	32𝜆	NOUN
cana-1750	292	3	−	−	PROPN
cana-1750	292	4	18	18	NUM
cana-1750	292	5	)	)	PUNCT
cana-1750	292	6	(	(	PUNCT
cana-1750	292	7	𝜆	𝜆	PROPN
cana-1750	292	8	+	+	ADJ
cana-1750	292	9	1)(𝜆	1)(𝜆	NUM
cana-1750	292	10	+	+	X
cana-1750	292	11	2)2(3	2)2(3	NUM
cana-1750	292	12	+	+	CCONJ
cana-1750	292	13	𝜆	𝜆	X
cana-1750	292	14	)	)	PUNCT
cana-1750	292	15	=	=	SYM
cana-1750	292	16	𝑈(𝜆	𝑈(𝜆	NUM
cana-1750	292	17	)	)	PUNCT
cana-1750	292	18	(	(	PUNCT
cana-1750	292	19	3.27	3.27	NUM
cana-1750	292	20	)	)	PUNCT
cana-1750	292	21	for	for	ADP
cana-1750	292	22	𝑥	𝑥	NOUN
cana-1750	292	23	=	=	SYM
cana-1750	292	24	0	0	NUM
cana-1750	292	25	,	,	PUNCT
cana-1750	292	26	we	we	PRON
cana-1750	292	27	brought	bring	VERB
cana-1750	292	28	ψ(𝑝	ψ(𝑝	PROPN
cana-1750	292	29	,	,	PUNCT
cana-1750	292	30	0	0	NUM
cana-1750	292	31	)	)	PUNCT
cana-1750	292	32	=	=	PUNCT
cana-1750	293	1	|	|	NOUN
cana-1750	293	2	𝑝2	𝑝2	NOUN
cana-1750	293	3	(	(	PUNCT
cana-1750	293	4	𝜆	𝜆	PROPN
cana-1750	293	5	+	+	X
cana-1750	293	6	1)2	1)2	NUM
cana-1750	293	7	+	+	CCONJ
cana-1750	293	8	𝑝(4	𝑝(4	PROPN
cana-1750	293	9	−	−	PROPN
cana-1750	293	10	𝑝2	𝑝2	NOUN
cana-1750	293	11	)	)	PUNCT
cana-1750	293	12	2(𝜆	2(𝜆	NUM
cana-1750	294	1	+	+	CCONJ
cana-1750	294	2	3)(𝜆	3)(𝜆	NUM
cana-1750	294	3	+	+	NUM
cana-1750	294	4	1	1	NUM
cana-1750	294	5	)	)	PUNCT
cana-1750	294	6	+	+	CCONJ
cana-1750	295	1	−𝜆3	−𝜆3	ADJ
cana-1750	295	2	+	+	NUM
cana-1750	295	3	𝜆2	𝜆2	NOUN
cana-1750	295	4	+	+	NOUN
cana-1750	295	5	16𝜆	16𝜆	NOUN
cana-1750	295	6	−	−	PROPN
cana-1750	295	7	30	30	NUM
cana-1750	295	8	4(𝜆	4(𝜆	NUM
cana-1750	296	1	+	+	CCONJ
cana-1750	296	2	3)(𝜆	3)(𝜆	NUM
cana-1750	296	3	+	+	NUM
cana-1750	296	4	2)2(𝜆	2)2(𝜆	NUM
cana-1750	296	5	+	+	CCONJ
cana-1750	296	6	1)2	1)2	NUM
cana-1750	296	7	𝑝4|	𝑝4|	PROPN
cana-1750	296	8	(	(	PUNCT
cana-1750	296	9	3.28	3.28	NUM
cana-1750	296	10	)	)	PUNCT
cana-1750	296	11	which	which	PRON
cana-1750	296	12	has	have	VERB
cana-1750	296	13	the	the	DET
cana-1750	296	14	maximum	maximum	ADJ
cana-1750	296	15	value	value	NOUN
cana-1750	296	16	ψ(𝑝	ψ(𝑝	PROPN
cana-1750	296	17	,	,	PUNCT
cana-1750	296	18	0	0	NUM
cana-1750	296	19	)	)	PUNCT
cana-1750	296	20	=	=	SYM
cana-1750	296	21	𝑈(𝜆	𝑈(𝜆	NUM
cana-1750	296	22	)	)	PUNCT
cana-1750	296	23	attained	attain	VERB
cana-1750	296	24	at	at	ADP
cana-1750	296	25	the	the	DET
cana-1750	296	26	end	end	NOUN
cana-1750	296	27	point	point	NOUN
cana-1750	296	28	𝑝	𝑝	NOUN
cana-1750	296	29	=	=	SYM
cana-1750	296	30	2	2	NUM
cana-1750	296	31	.	.	PUNCT
cana-1750	296	32	hence	hence	ADV
cana-1750	296	33	,	,	PUNCT
cana-1750	296	34	for	for	ADP
cana-1750	296	35	|𝑥|	|𝑥|	ADJ
cana-1750	296	36	=	=	SYM
cana-1750	296	37	1	1	NUM
cana-1750	296	38	,	,	PUNCT
cana-1750	296	39	we	we	PRON
cana-1750	296	40	obtain	obtain	VERB
cana-1750	296	41	ψ(𝑝	ψ(𝑝	PROPN
cana-1750	296	42	,	,	PUNCT
cana-1750	296	43	1	1	NUM
cana-1750	296	44	)	)	PUNCT
cana-1750	296	45	=	=	NOUN
cana-1750	297	1	[	[	PUNCT
cana-1750	297	2	𝑝2(4	𝑝2(4	PROPN
cana-1750	297	3	−	−	PROPN
cana-1750	297	4	𝑝2	𝑝2	NOUN
cana-1750	297	5	)	)	PUNCT
cana-1750	297	6	4(𝜆	4(𝜆	NUM
cana-1750	298	1	+	+	CCONJ
cana-1750	298	2	3)(𝜆	3)(𝜆	NUM
cana-1750	298	3	+	+	NUM
cana-1750	298	4	1	1	NUM
cana-1750	298	5	)	)	PUNCT
cana-1750	298	6	+	+	CCONJ
cana-1750	298	7	𝑝2(4	𝑝2(4	PROPN
cana-1750	298	8	−	−	PROPN
cana-1750	298	9	𝑝2	𝑝2	NOUN
cana-1750	298	10	)	)	PUNCT
cana-1750	298	11	2(𝜆	2(𝜆	NUM
cana-1750	299	1	+	+	CCONJ
cana-1750	299	2	3)(𝜆	3)(𝜆	NUM
cana-1750	299	3	+	+	NUM
cana-1750	299	4	1	1	NUM
cana-1750	299	5	)	)	PUNCT
cana-1750	300	1	+	+	CCONJ
cana-1750	300	2	(	(	PUNCT
cana-1750	300	3	4	4	NUM
cana-1750	300	4	−	−	NOUN
cana-1750	300	5	𝑝2)2	𝑝2)2	NUM
cana-1750	300	6	2(𝜆	2(𝜆	NUM
cana-1750	300	7	+	+	CCONJ
cana-1750	300	8	2)2	2)2	NUM
cana-1750	300	9	]	]	PUNCT
cana-1750	301	1	+	+	CCONJ
cana-1750	301	2	[	[	PUNCT
cana-1750	301	3	𝜆3	𝜆3	NOUN
cana-1750	301	4	+	+	CCONJ
cana-1750	301	5	2𝜆2	2𝜆2	NUM
cana-1750	301	6	−	−	PROPN
cana-1750	301	7	9𝜆	9𝜆	NUM
cana-1750	301	8	−	−	NUM
cana-1750	301	9	8	8	NUM
cana-1750	301	10	2(𝜆	2(𝜆	NUM
cana-1750	301	11	+	+	CCONJ
cana-1750	301	12	3)(𝜆	3)(𝜆	NUM
cana-1750	301	13	+	+	NUM
cana-1750	301	14	2)2(𝜆	2)2(𝜆	NUM
cana-1750	302	1	+	+	X
cana-1750	302	2	1)2	1)2	NUM
cana-1750	302	3	]	]	PUNCT
cana-1750	302	4	𝑝(4	𝑝(4	PROPN
cana-1750	302	5	−	−	PROPN
cana-1750	302	6	𝑝2	𝑝2	NOUN
cana-1750	302	7	)	)	PUNCT
cana-1750	303	1	+	+	CCONJ
cana-1750	303	2	𝑝(4	𝑝(4	PROPN
cana-1750	303	3	−	−	PROPN
cana-1750	303	4	𝑝2	𝑝2	NOUN
cana-1750	303	5	)	)	PUNCT
cana-1750	303	6	2(𝜆	2(𝜆	NUM
cana-1750	304	1	+	+	CCONJ
cana-1750	305	1	3)(𝜆	3)(𝜆	NUM
cana-1750	305	2	+	+	NUM
cana-1750	305	3	1	1	NUM
cana-1750	305	4	)	)	PUNCT
cana-1750	305	5	+	+	NUM
cana-1750	305	6	𝑝2	𝑝2	NOUN
cana-1750	305	7	(	(	PUNCT
cana-1750	305	8	𝜆	𝜆	PROPN
cana-1750	305	9	+	+	X
cana-1750	305	10	1)2	1)2	NUM
cana-1750	305	11	+	+	CCONJ
cana-1750	305	12	[	[	PUNCT
cana-1750	305	13	−𝜆3	−𝜆3	NOUN
cana-1750	305	14	+	+	NUM
cana-1750	305	15	𝜆2	𝜆2	NOUN
cana-1750	305	16	+	+	NOUN
cana-1750	305	17	16𝜆	16𝜆	NOUN
cana-1750	305	18	−	−	PROPN
cana-1750	305	19	30	30	NUM
cana-1750	305	20	4(𝜆	4(𝜆	NUM
cana-1750	306	1	+	+	CCONJ
cana-1750	306	2	3)(𝜆	3)(𝜆	NUM
cana-1750	306	3	+	+	NUM
cana-1750	306	4	2)2(𝜆	2)2(𝜆	NUM
cana-1750	306	5	+	+	CCONJ
cana-1750	306	6	1)2	1)2	NUM
cana-1750	306	7	]	]	PUNCT
cana-1750	306	8	𝑝4	𝑝4	PROPN
cana-1750	306	9	.	.	PUNCT
cana-1750	307	1	which	which	PRON
cana-1750	307	2	has	have	VERB
cana-1750	307	3	maximum	maximum	ADJ
cana-1750	307	4	ψ(𝑝	ψ(𝑝	NOUN
cana-1750	307	5	,	,	PUNCT
cana-1750	307	6	1	1	NUM
cana-1750	307	7	)	)	PUNCT
cana-1750	307	8	=	=	SYM
cana-1750	307	9	8	8	NUM
cana-1750	307	10	(	(	PUNCT
cana-1750	307	11	𝜆+2)2	𝜆+2)2	PROPN
cana-1750	307	12	at	at	ADP
cana-1750	307	13	𝑝	𝑝	NOUN
cana-1750	307	14	=	=	SYM
cana-1750	307	15	0	0	PROPN
cana-1750	307	16	and	and	CCONJ
cana-1750	307	17	ψ(𝑝	ψ(𝑝	PROPN
cana-1750	307	18	,	,	PUNCT
cana-1750	307	19	1	1	NUM
cana-1750	307	20	)	)	PUNCT
cana-1750	307	21	=	=	SYM
cana-1750	307	22	𝑈(𝜆	𝑈(𝜆	NUM
cana-1750	307	23	)	)	PUNCT
cana-1750	307	24	at	at	ADP
cana-1750	307	25	𝑝	𝑝	NOUN
cana-1750	307	26	=	=	SYM
cana-1750	307	27	2	2	NUM
cana-1750	307	28	.	.	X
cana-1750	307	29	|𝑎2	|𝑎2	NOUN
cana-1750	307	30	2	2	NUM
cana-1750	307	31	−	−	PROPN
cana-1750	307	32	2𝑎3	2𝑎3	NUM
cana-1750	307	33	2	2	NUM
cana-1750	307	34	+	+	CCONJ
cana-1750	307	35	𝑎2𝑎4|	𝑎2𝑎4|	PROPN
cana-1750	307	36	≤	≤	ADJ
cana-1750	307	37	max	max	PROPN
cana-1750	307	38	{	{	PUNCT
cana-1750	307	39	|𝑈(𝜆)|	|𝑈(𝜆)|	PROPN
cana-1750	307	40	,	,	PUNCT
cana-1750	307	41	8	8	NUM
cana-1750	307	42	(	(	PUNCT
cana-1750	307	43	𝜆	𝜆	NOUN
cana-1750	307	44	+	+	ADJ
cana-1750	307	45	2)2	2)2	NUM
cana-1750	307	46	}	}	PUNCT
cana-1750	307	47	.	.	PUNCT
cana-1750	308	1	(	(	PUNCT
cana-1750	308	2	3.29	3.29	NUM
cana-1750	308	3	)	)	PUNCT
cana-1750	308	4	thus	thus	ADV
cana-1750	308	5	|𝑇3(2)|	|𝑇3(2)|	PROPN
cana-1750	308	6	=	=	PUNCT
cana-1750	308	7	|(𝑎2	|(𝑎2	PROPN
cana-1750	308	8	−	−	NOUN
cana-1750	308	9	𝑎4)(𝑎2	𝑎4)(𝑎2	NOUN
cana-1750	308	10	2	2	NUM
cana-1750	308	11	−	−	NOUN
cana-1750	308	12	2𝑎3	2𝑎3	NUM
cana-1750	308	13	2	2	NUM
cana-1750	308	14	+	+	CCONJ
cana-1750	308	15	𝑎2𝑎4)|	𝑎2𝑎4)|	VERB
cana-1750	308	16	≤	≤	NUM
cana-1750	308	17	max	max	PROPN
cana-1750	308	18	{	{	PUNCT
cana-1750	308	19	|𝑅(𝜆)𝑈(𝜆)|	|𝑅(𝜆)𝑈(𝜆)|	PROPN
cana-1750	308	20	,	,	PUNCT
cana-1750	308	21	8|𝑅(𝜆)|	8|𝑅(𝜆)|	NUM
cana-1750	308	22	(	(	PUNCT
cana-1750	308	23	𝜆	𝜆	ADP
cana-1750	308	24	+	+	ADJ
cana-1750	308	25	2)2	2)2	NUM
cana-1750	308	26	}	}	PUNCT
cana-1750	308	27	.	.	PUNCT
cana-1750	309	1	(	(	PUNCT
cana-1750	309	2	3.30	3.30	NUM
cana-1750	309	3	)	)	PUNCT
cana-1750	309	4	for	for	ADP
cana-1750	309	5	the	the	DET
cana-1750	309	6	case	case	NOUN
cana-1750	309	7	𝜆	𝜆	ADP
cana-1750	309	8	=	=	SYM
cana-1750	309	9	𝜆0	𝜆0	NOUN
cana-1750	309	10	,	,	PUNCT
cana-1750	309	11	we	we	PRON
cana-1750	309	12	compute	compute	VERB
cana-1750	309	13	|𝑎2	|𝑎2	NOUN
cana-1750	309	14	−	−	PROPN
cana-1750	309	15	𝑎4|	𝑎4|	PROPN
cana-1750	309	16	as	as	SCONJ
cana-1750	309	17	follows	follow	VERB
cana-1750	309	18	|𝑎2	|𝑎2	NOUN
cana-1750	309	19	−	−	PROPN
cana-1750	309	20	𝑎4|	𝑎4|	PROPN
cana-1750	309	21	=	=	PUNCT
cana-1750	310	1	|	|	ADV
cana-1750	310	2	𝑝1	𝑝1	NOUN
cana-1750	310	3	𝜆	𝜆	PROPN
cana-1750	311	1	+	+	NOUN
cana-1750	311	2	1	1	NUM
cana-1750	311	3	−	−	NOUN
cana-1750	311	4	[	[	PUNCT
cana-1750	311	5	𝑝1	𝑝1	NOUN
cana-1750	311	6	3(1	3(1	PROPN
cana-1750	311	7	−	−	PROPN
cana-1750	311	8	𝜆)2	𝜆)2	NOUN
cana-1750	311	9	(	(	PUNCT
cana-1750	311	10	𝜆	𝜆	ADP
cana-1750	311	11	+	+	CCONJ
cana-1750	311	12	3)(𝜆	3)(𝜆	NUM
cana-1750	311	13	+	+	NUM
cana-1750	311	14	2)(𝜆	2)(𝜆	NUM
cana-1750	311	15	+	+	CCONJ
cana-1750	311	16	1	1	NUM
cana-1750	311	17	)	)	PUNCT
cana-1750	311	18	+	+	NUM
cana-1750	311	19	𝑝1𝑝2(1	𝑝1𝑝2(1	NOUN
cana-1750	311	20	−	−	NOUN
cana-1750	311	21	𝜆)(3	𝜆)(3	X
cana-1750	311	22	+	+	CCONJ
cana-1750	311	23	2𝜆	2𝜆	NUM
cana-1750	311	24	)	)	PUNCT
cana-1750	311	25	(	(	PUNCT
cana-1750	311	26	𝜆	𝜆	ADP
cana-1750	311	27	+	+	CCONJ
cana-1750	311	28	3)(𝜆	3)(𝜆	NUM
cana-1750	311	29	+	+	NUM
cana-1750	311	30	2)(𝜆	2)(𝜆	NUM
cana-1750	311	31	+	+	CCONJ
cana-1750	311	32	1	1	NUM
cana-1750	311	33	)	)	PUNCT
cana-1750	311	34	+	+	CCONJ
cana-1750	311	35	𝑝3	𝑝3	ADV
cana-1750	311	36	𝜆	𝜆	ADP
cana-1750	311	37	+	+	ADJ
cana-1750	311	38	3	3	NUM
cana-1750	311	39	]	]	X
cana-1750	311	40	|	|	INTJ
cana-1750	311	41	(	(	PUNCT
cana-1750	311	42	3.31	3.31	NUM
cana-1750	311	43	)	)	PUNCT
cana-1750	311	44	since	since	SCONJ
cana-1750	311	45	each	each	DET
cana-1750	311	46	|𝑝𝑛|	|𝑝𝑛|	NOUN
cana-1750	311	47	≤	≤	ADV
cana-1750	311	48	2	2	NUM
cana-1750	311	49	,	,	PUNCT
cana-1750	311	50	an	an	DET
cana-1750	311	51	application	application	NOUN
cana-1750	311	52	of	of	ADP
cana-1750	311	53	triangle	triangle	NOUN
cana-1750	311	54	inequality	inequality	NOUN
cana-1750	311	55	shows	show	VERB
cana-1750	311	56	that	that	SCONJ
cana-1750	311	57	|𝑎2	|𝑎2	NOUN
cana-1750	311	58	−	−	PROPN
cana-1750	311	59	𝑎4|	𝑎4|	PROPN
cana-1750	311	60	≤	≤	PUNCT
cana-1750	312	1	|𝐵(𝜆)|	|𝐵(𝜆)|	ADP
cana-1750	312	2	=	=	SYM
cana-1750	312	3	4𝜆2	4𝜆2	NUM
cana-1750	312	4	−	−	NOUN
cana-1750	312	5	4𝜆	4𝜆	NOUN
cana-1750	312	6	+	+	CCONJ
cana-1750	312	7	36	36	NUM
cana-1750	312	8	(	(	PUNCT
cana-1750	312	9	𝜆	𝜆	NOUN
cana-1750	312	10	+	+	CCONJ
cana-1750	312	11	3)(𝜆	3)(𝜆	NUM
cana-1750	312	12	+	+	NUM
cana-1750	312	13	2)(𝜆	2)(𝜆	NUM
cana-1750	312	14	+	+	NOUN
cana-1750	312	15	1	1	NUM
cana-1750	312	16	)	)	PUNCT
cana-1750	312	17	.	.	PUNCT
cana-1750	313	1	(	(	PUNCT
cana-1750	313	2	3.32	3.32	NUM
cana-1750	313	3	)	)	PUNCT
cana-1750	313	4	therefore	therefore	ADV
cana-1750	313	5	,	,	PUNCT
cana-1750	313	6	|𝑇3(2)|	|𝑇3(2)|	PROPN
cana-1750	313	7	=	=	PUNCT
cana-1750	313	8	|(𝑎2	|(𝑎2	PROPN
cana-1750	313	9	−	−	NOUN
cana-1750	313	10	𝑎4)(𝑎2	𝑎4)(𝑎2	NOUN
cana-1750	313	11	2	2	NUM
cana-1750	313	12	−	−	NOUN
cana-1750	313	13	2𝑎3	2𝑎3	NUM
cana-1750	313	14	2	2	NUM
cana-1750	313	15	+	+	CCONJ
cana-1750	313	16	𝑎2𝑎4)|	𝑎2𝑎4)|	VERB
cana-1750	313	17	≤	≤	NUM
cana-1750	313	18	max	max	PROPN
cana-1750	313	19	{	{	PUNCT
cana-1750	313	20	|𝑈(𝜆)𝐵(𝜆)|	|𝑈(𝜆)𝐵(𝜆)|	PROPN
cana-1750	313	21	,	,	PUNCT
cana-1750	313	22	8|𝐵(𝜆)|	8|𝐵(𝜆)|	NUM
cana-1750	313	23	(	(	PUNCT
cana-1750	313	24	𝜆	𝜆	ADP
cana-1750	313	25	+	+	ADJ
cana-1750	313	26	2)2	2)2	NUM
cana-1750	313	27	}	}	PUNCT
cana-1750	313	28	.	.	PUNCT
cana-1750	314	1	(	(	PUNCT
cana-1750	314	2	3.33	3.33	NUM
cana-1750	314	3	)	)	PUNCT
cana-1750	314	4	this	this	PRON
cana-1750	314	5	completes	complete	VERB
cana-1750	314	6	the	the	DET
cana-1750	314	7	proof	proof	NOUN
cana-1750	314	8	the	the	DET
cana-1750	314	9	theorem	theorem	NOUN
cana-1750	314	10	(	(	PUNCT
cana-1750	314	11	3.5	3.5	NUM
cana-1750	314	12	)	)	PUNCT
cana-1750	314	13	.	.	PUNCT
cana-1750	315	1	remark	remark	PROPN
cana-1750	315	2	3.6	3.6	NUM
cana-1750	315	3	.	.	PUNCT
cana-1750	316	1	theorem	theorem	NOUN
cana-1750	316	2	(	(	PUNCT
cana-1750	316	3	3.5	3.5	NUM
cana-1750	316	4	)	)	PUNCT
cana-1750	316	5	,	,	PUNCT
cana-1750	316	6	for	for	ADP
cana-1750	316	7	𝜆	𝜆	DET
cana-1750	316	8	=	=	SYM
cana-1750	316	9	0	0	NUM
cana-1750	316	10	yields	yield	NOUN
cana-1750	316	11	the	the	DET
cana-1750	316	12	bound	bind	VERB
cana-1750	316	13	|𝑇3(2)|	|𝑇3(2)|	PROPN
cana-1750	316	14	≤	≤	NUM
cana-1750	316	15	12	12	NUM
cana-1750	316	16	for	for	ADP
cana-1750	316	17	the	the	DET
cana-1750	316	18	class	class	NOUN
cana-1750	316	19	of	of	ADP
cana-1750	316	20	star	star	NOUN
cana-1750	316	21	like	like	ADP
cana-1750	316	22	function	function	NOUN
cana-1750	316	23	𝒮∗	𝒮∗	NOUN
cana-1750	316	24	conforming	conform	VERB
cana-1750	316	25	the	the	DET
cana-1750	316	26	bound	bind	VERB
cana-1750	316	27	obtained	obtain	VERB
cana-1750	316	28	by	by	ADP
cana-1750	316	29	thomous	thomous	PROPN
cana-1750	316	30	and	and	CCONJ
cana-1750	316	31	halim	halim	PROPN
cana-1750	317	1	[	[	X
cana-1750	317	2	1	1	NUM
cana-1750	317	3	]	]	PUNCT
cana-1750	317	4	.	.	PUNCT
cana-1750	318	1	and	and	CCONJ
cana-1750	318	2	for	for	ADP
cana-1750	318	3	𝜆	𝜆	DET
cana-1750	318	4	=	=	SYM
cana-1750	318	5	1	1	NUM
cana-1750	318	6	yields	yield	NOUN
cana-1750	318	7	the	the	DET
cana-1750	318	8	bound	bind	VERB
cana-1750	318	9	communications	communication	NOUN
cana-1750	318	10	on	on	ADP
cana-1750	318	11	applied	apply	VERB
cana-1750	318	12	nonlinear	nonlinear	ADJ
cana-1750	318	13	analysis	analysis	NOUN
cana-1750	318	14	issn	issn	NOUN
cana-1750	318	15	:	:	PUNCT
cana-1750	318	16	1074	1074	NUM
cana-1750	318	17	-	-	PUNCT
cana-1750	318	18	133x	133x	NUM
cana-1750	318	19	vol	vol	NOUN
cana-1750	318	20	32	32	NUM
cana-1750	318	21	no	no	NOUN
cana-1750	318	22	.	.	NOUN
cana-1750	318	23	2	2	NUM
cana-1750	318	24	(	(	PUNCT
cana-1750	318	25	2025	2025	NUM
cana-1750	318	26	)	)	PUNCT
cana-1750	319	1	394	394	NUM
cana-1750	319	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	319	3	|𝑇3(2)|	|𝑇3(2)|	PROPN
cana-1750	319	4	≤	≤	NUM
cana-1750	319	5	8	8	NUM
cana-1750	319	6	9	9	NUM
cana-1750	319	7	for	for	ADP
cana-1750	319	8	the	the	DET
cana-1750	319	9	class	class	NOUN
cana-1750	319	10	of	of	ADP
cana-1750	319	11	functions	function	NOUN
cana-1750	319	12	with	with	ADP
cana-1750	319	13	bounded	bounded	ADJ
cana-1750	319	14	boundary	boundary	ADJ
cana-1750	319	15	rotation	rotation	NOUN
cana-1750	319	16	ℛ̃	ℛ̃	PROPN
cana-1750	319	17	conforming	conform	VERB
cana-1750	319	18	the	the	DET
cana-1750	319	19	bound	bind	VERB
cana-1750	319	20	obtained	obtain	VERB
cana-1750	319	21	by	by	ADP
cana-1750	319	22	radhika	radhika	PROPN
cana-1750	319	23	et	et	PROPN
cana-1750	319	24	al	al	PROPN
cana-1750	319	25	.	.	PUNCT
cana-1750	320	1	[	[	X
cana-1750	320	2	2	2	NUM
cana-1750	320	3	]	]	PUNCT
cana-1750	320	4	.	.	PUNCT
cana-1750	320	5	theorem	theorem	VERB
cana-1750	320	6	3.7	3.7	NUM
cana-1750	320	7	.	.	PUNCT
cana-1750	321	1	let	let	VERB
cana-1750	321	2	𝑓	𝑓	PRON
cana-1750	321	3	given	give	VERB
cana-1750	321	4	by	by	ADP
cana-1750	321	5	(	(	PUNCT
cana-1750	321	6	1.1	1.1	NUM
cana-1750	321	7	)	)	PUNCT
cana-1750	321	8	,	,	PUNCT
cana-1750	321	9	be	be	AUX
cana-1750	321	10	in	in	ADP
cana-1750	321	11	the	the	DET
cana-1750	321	12	class	class	NOUN
cana-1750	321	13	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	321	14	)	)	PUNCT
cana-1750	321	15	;	;	PUNCT
cana-1750	321	16	0	0	NUM
cana-1750	321	17	≤	≤	NUM
cana-1750	321	18	𝜆	𝜆	DET
cana-1750	321	19	≤	≤	NUM
cana-1750	321	20	1	1	NUM
cana-1750	321	21	.	.	PUNCT
cana-1750	322	1	then	then	ADV
cana-1750	322	2	we	we	PRON
cana-1750	322	3	have	have	VERB
cana-1750	322	4	sharp	sharp	ADV
cana-1750	322	5	bound	bind	VERB
cana-1750	322	6	|𝑇3(1)|	|𝑇3(1)|	PROPN
cana-1750	322	7	=	=	SYM
cana-1750	322	8	|(|	|(|	SYM
cana-1750	322	9	1	1	NUM
cana-1750	322	10	𝑎2	𝑎2	NOUN
cana-1750	322	11	𝑎3	𝑎3	PROPN
cana-1750	322	12	𝑎2	𝑎2	PROPN
cana-1750	322	13	1	1	NUM
cana-1750	322	14	𝑎2	𝑎2	PROPN
cana-1750	322	15	𝑎3	𝑎3	PROPN
cana-1750	322	16	𝑎2	𝑎2	PROPN
cana-1750	322	17	1	1	NUM
cana-1750	322	18	|)|	|)|	PROPN
cana-1750	322	19	≤	≤	PROPN
cana-1750	322	20	max	max	PROPN
cana-1750	322	21	{	{	PUNCT
cana-1750	322	22	1	1	NUM
cana-1750	322	23	+	+	NUM
cana-1750	322	24	1	1	NUM
cana-1750	322	25	4(𝜆	4(𝜆	NUM
cana-1750	322	26	+	+	CCONJ
cana-1750	322	27	2)2	2)2	NUM
cana-1750	322	28	,	,	PUNCT
cana-1750	322	29	|𝑁(𝜆)|	|𝑁(𝜆)|	NOUN
cana-1750	322	30	}	}	PUNCT
cana-1750	322	31	where	where	SCONJ
cana-1750	322	32	,	,	PUNCT
cana-1750	322	33	𝑁(𝜆	𝑁(𝜆	NOUN
cana-1750	322	34	)	)	PUNCT
cana-1750	322	35	=	=	SYM
cana-1750	323	1	𝜆5	𝜆5	NOUN
cana-1750	324	1	+	+	X
cana-1750	324	2	7𝜆4	7𝜆4	NUM
cana-1750	325	1	+	+	NUM
cana-1750	325	2	7𝜆3	7𝜆3	NUM
cana-1750	326	1	−	−	NUM
cana-1750	326	2	11𝜆2	11𝜆2	NUM
cana-1750	326	3	−	−	PROPN
cana-1750	326	4	44𝜆	44𝜆	NOUN
cana-1750	326	5	+	+	CCONJ
cana-1750	326	6	32	32	NUM
cana-1750	326	7	(	(	PUNCT
cana-1750	326	8	𝜆	𝜆	PROPN
cana-1750	326	9	+	+	NUM
cana-1750	326	10	2)2(𝜆	2)2(𝜆	NUM
cana-1750	326	11	+	+	CCONJ
cana-1750	326	12	1)3	1)3	PROPN
cana-1750	326	13	proof	proof	NOUN
cana-1750	326	14	.	.	PUNCT
cana-1750	327	1	expanding	expand	VERB
cana-1750	327	2	the	the	DET
cana-1750	327	3	determinant	determinant	ADJ
cana-1750	327	4	by	by	ADP
cana-1750	327	5	using	use	VERB
cana-1750	327	6	equation	equation	NOUN
cana-1750	327	7	(	(	PUNCT
cana-1750	327	8	3.1	3.1	NUM
cana-1750	327	9	)	)	PUNCT
cana-1750	327	10	,	,	PUNCT
cana-1750	327	11	we	we	PRON
cana-1750	327	12	get	get	VERB
cana-1750	327	13	(	(	PUNCT
cana-1750	327	14	3.2	3.2	NUM
cana-1750	327	15	)	)	PUNCT
cana-1750	327	16	and	and	CCONJ
cana-1750	327	17	(	(	PUNCT
cana-1750	327	18	3.3	3.3	NUM
cana-1750	327	19	)	)	PUNCT
cana-1750	327	20	,	,	PUNCT
cana-1750	327	21	we	we	PRON
cana-1750	327	22	have	have	VERB
cana-1750	327	23	𝑇3(1	𝑇3(1	ADV
cana-1750	327	24	)	)	PUNCT
cana-1750	327	25	=	=	SYM
cana-1750	328	1	1	1	NUM
cana-1750	328	2	+	+	NUM
cana-1750	328	3	2𝑎2	2𝑎2	NUM
cana-1750	328	4	2(𝑎3	2(𝑎3	NUM
cana-1750	328	5	−	−	NOUN
cana-1750	328	6	1	1	NUM
cana-1750	328	7	)	)	PUNCT
cana-1750	328	8	−	−	NOUN
cana-1750	328	9	𝑎3	𝑎3	NOUN
cana-1750	328	10	2	2	NUM
cana-1750	328	11	=	=	SYM
cana-1750	328	12	1	1	NUM
cana-1750	328	13	+	+	NUM
cana-1750	328	14	2𝑝1	2𝑝1	NUM
cana-1750	328	15	2	2	NUM
cana-1750	328	16	(	(	PUNCT
cana-1750	328	17	𝜆	𝜆	PROPN
cana-1750	328	18	+	+	X
cana-1750	328	19	1)2	1)2	NUM
cana-1750	328	20	(	(	PUNCT
cana-1750	328	21	𝑝1	𝑝1	NOUN
cana-1750	328	22	2(1	2(1	NUM
cana-1750	328	23	−	−	NOUN
cana-1750	328	24	𝜆	𝜆	NOUN
cana-1750	328	25	)	)	PUNCT
cana-1750	328	26	(	(	PUNCT
cana-1750	328	27	𝜆	𝜆	X
cana-1750	328	28	+	+	ADJ
cana-1750	328	29	2)(𝜆	2)(𝜆	NUM
cana-1750	328	30	+	+	CCONJ
cana-1750	328	31	1	1	NUM
cana-1750	328	32	)	)	PUNCT
cana-1750	328	33	+	+	NUM
cana-1750	328	34	𝑝2	𝑝2	PROPN
cana-1750	328	35	𝜆	𝜆	PROPN
cana-1750	328	36	+	+	NOUN
cana-1750	328	37	2	2	NUM
cana-1750	328	38	−	−	NUM
cana-1750	328	39	1	1	NUM
cana-1750	328	40	)	)	PUNCT
cana-1750	328	41	−	−	PROPN
cana-1750	329	1	[	[	PUNCT
cana-1750	329	2	𝑝1	𝑝1	NOUN
cana-1750	329	3	4(1	4(1	X
cana-1750	329	4	−	−	NOUN
cana-1750	329	5	𝜆	𝜆	NOUN
cana-1750	329	6	)	)	PUNCT
cana-1750	329	7	(	(	PUNCT
cana-1750	329	8	𝜆	𝜆	PROPN
cana-1750	330	1	+	+	NUM
cana-1750	330	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	330	3	+	+	CCONJ
cana-1750	330	4	1)2	1)2	NUM
cana-1750	330	5	+	+	CCONJ
cana-1750	330	6	𝑝2	𝑝2	NOUN
cana-1750	330	7	2	2	NUM
cana-1750	330	8	(	(	PUNCT
cana-1750	330	9	𝜆	𝜆	NOUN
cana-1750	330	10	+	+	CCONJ
cana-1750	330	11	2)2	2)2	NUM
cana-1750	330	12	+	+	SYM
cana-1750	330	13	2(1	2(1	NUM
cana-1750	330	14	−	−	NOUN
cana-1750	330	15	𝜆)𝑝1	𝜆)𝑝1	PROPN
cana-1750	330	16	2𝑝2	2𝑝2	NUM
cana-1750	330	17	(	(	PUNCT
cana-1750	330	18	𝜆	𝜆	PROPN
cana-1750	330	19	+	+	ADJ
cana-1750	330	20	2)2(𝜆	2)2(𝜆	NUM
cana-1750	330	21	+	+	CCONJ
cana-1750	330	22	1	1	NUM
cana-1750	330	23	)	)	PUNCT
cana-1750	330	24	]	]	PUNCT
cana-1750	330	25	.	.	PUNCT
cana-1750	331	1	=	=	SYM
cana-1750	331	2	1	1	NUM
cana-1750	332	1	+	+	CCONJ
cana-1750	332	2	[	[	PUNCT
cana-1750	332	3	−𝜆3	−𝜆3	NOUN
cana-1750	332	4	+	+	NUM
cana-1750	332	5	𝜆2	𝜆2	NOUN
cana-1750	332	6	+	+	CCONJ
cana-1750	332	7	𝜆	𝜆	ADP
cana-1750	332	8	+	+	CCONJ
cana-1750	332	9	15	15	NUM
cana-1750	332	10	4(𝜆	4(𝜆	NUM
cana-1750	333	1	+	+	CCONJ
cana-1750	333	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	333	3	+	+	CCONJ
cana-1750	333	4	1)3	1)3	PROPN
cana-1750	333	5	]	]	PUNCT
cana-1750	333	6	𝑝1	𝑝1	NOUN
cana-1750	333	7	4	4	NUM
cana-1750	333	8	+	+	CCONJ
cana-1750	333	9	[	[	PUNCT
cana-1750	333	10	𝜆2	𝜆2	NOUN
cana-1750	333	11	+	+	CCONJ
cana-1750	333	12	1	1	NUM
cana-1750	333	13	2(𝜆	2(𝜆	NUM
cana-1750	333	14	+	+	CCONJ
cana-1750	333	15	2)2(𝜆	2)2(𝜆	NUM
cana-1750	334	1	+	+	CCONJ
cana-1750	334	2	1)2	1)2	NUM
cana-1750	334	3	]	]	PUNCT
cana-1750	334	4	𝑝1	𝑝1	NOUN
cana-1750	334	5	2𝑥𝑋	2𝑥𝑋	NOUN
cana-1750	334	6	−	−	PROPN
cana-1750	334	7	2𝑝1	2𝑝1	NUM
cana-1750	334	8	2	2	NUM
cana-1750	334	9	(	(	PUNCT
cana-1750	334	10	𝜆	𝜆	PROPN
cana-1750	334	11	+	+	ADJ
cana-1750	334	12	1)2	1)2	NUM
cana-1750	334	13	−	−	NOUN
cana-1750	335	1	𝑥2𝑋2	𝑥2𝑋2	NOUN
cana-1750	335	2	4(𝜆	4(𝜆	NUM
cana-1750	335	3	+	+	CCONJ
cana-1750	335	4	2)2	2)2	NUM
cana-1750	335	5	.	.	PUNCT
cana-1750	336	1	note	note	VERB
cana-1750	336	2	that	that	SCONJ
cana-1750	336	3	,	,	PUNCT
cana-1750	336	4	by	by	ADP
cana-1750	336	5	lemma	lemma	PROPN
cana-1750	336	6	(	(	PUNCT
cana-1750	336	7	2.2	2.2	NUM
cana-1750	336	8	)	)	PUNCT
cana-1750	336	9	,	,	PUNCT
cana-1750	336	10	without	without	ADP
cana-1750	336	11	loss	loss	NOUN
cana-1750	336	12	of	of	ADP
cana-1750	336	13	generality	generality	NOUN
cana-1750	336	14	we	we	PRON
cana-1750	336	15	let	let	VERB
cana-1750	336	16	0	0	NUM
cana-1750	336	17	≤	≤	NOUN
cana-1750	336	18	𝑝1	𝑝1	NOUN
cana-1750	336	19	=	=	SYM
cana-1750	336	20	𝑝	𝑝	NOUN
cana-1750	336	21	≤	≤	NUM
cana-1750	336	22	2	2	NUM
cana-1750	336	23	.	.	PUNCT
cana-1750	336	24	substitute	substitute	VERB
cana-1750	336	25	this	this	PRON
cana-1750	336	26	into	into	ADP
cana-1750	336	27	the	the	DET
cana-1750	336	28	above	above	ADJ
cana-1750	336	29	equation	equation	NOUN
cana-1750	336	30	and	and	CCONJ
cana-1750	336	31	applying	apply	VERB
cana-1750	336	32	the	the	DET
cana-1750	336	33	triangle	triangle	NOUN
cana-1750	336	34	inequality	inequality	NOUN
cana-1750	336	35	,	,	PUNCT
cana-1750	336	36	we	we	PRON
cana-1750	336	37	obtain	obtain	VERB
cana-1750	336	38	the	the	DET
cana-1750	336	39	following	follow	VERB
cana-1750	336	40	quadratic	quadratic	ADJ
cana-1750	336	41	equation	equation	NOUN
cana-1750	336	42	in	in	ADP
cana-1750	336	43	terms	term	NOUN
cana-1750	336	44	of	of	ADP
cana-1750	336	45	𝑥.	𝑥.	NOUN
cana-1750	336	46	𝑇3(1	𝑇3(1	NOUN
cana-1750	336	47	)	)	PUNCT
cana-1750	336	48	≤	≤	NOUN
cana-1750	336	49	[	[	PUNCT
cana-1750	336	50	(	(	PUNCT
cana-1750	336	51	4	4	NUM
cana-1750	336	52	−	−	NOUN
cana-1750	336	53	𝑝2)2	𝑝2)2	NUM
cana-1750	336	54	4(𝜆	4(𝜆	NUM
cana-1750	336	55	+	+	CCONJ
cana-1750	336	56	2)2	2)2	NUM
cana-1750	336	57	]	]	PUNCT
cana-1750	337	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	338	1	+	+	PUNCT
cana-1750	339	1	[	[	PUNCT
cana-1750	339	2	𝑝2(4	𝑝2(4	PROPN
cana-1750	339	3	−	−	PROPN
cana-1750	339	4	𝑝2)(𝜆2	𝑝2)(𝜆2	VERB
cana-1750	339	5	+	+	CCONJ
cana-1750	339	6	1	1	X
cana-1750	339	7	)	)	PUNCT
cana-1750	339	8	2(𝜆	2(𝜆	NUM
cana-1750	340	1	+	+	CCONJ
cana-1750	340	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	341	1	+	+	CCONJ
cana-1750	341	2	1)2	1)2	NUM
cana-1750	341	3	]	]	PUNCT
cana-1750	341	4	|𝑥|	|𝑥|	INTJ
cana-1750	342	1	+	+	PUNCT
cana-1750	342	2	[	[	X
cana-1750	342	3	1	1	NUM
cana-1750	342	4	+	+	NUM
cana-1750	342	5	8(𝜆	8(𝜆	NUM
cana-1750	342	6	+	+	CCONJ
cana-1750	342	7	2)2(𝜆	2)2(𝜆	NUM
cana-1750	342	8	+	+	CCONJ
cana-1750	342	9	1	1	NUM
cana-1750	342	10	)	)	PUNCT
cana-1750	342	11	+	+	CCONJ
cana-1750	342	12	(	(	PUNCT
cana-1750	342	13	−𝜆3	−𝜆3	NOUN
cana-1750	342	14	+	+	NOUN
cana-1750	342	15	𝜆2	𝜆2	NOUN
cana-1750	342	16	+	+	CCONJ
cana-1750	342	17	𝜆	𝜆	NOUN
cana-1750	343	1	+	+	CCONJ
cana-1750	343	2	15)𝑝2	15)𝑝2	NUM
cana-1750	343	3	4(𝜆	4(𝜆	NUM
cana-1750	344	1	+	+	CCONJ
cana-1750	344	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	344	3	+	+	CCONJ
cana-1750	344	4	1)3	1)3	PROPN
cana-1750	344	5	𝑝2	𝑝2	NOUN
cana-1750	344	6	]	]	PUNCT
cana-1750	344	7	.	.	PUNCT
cana-1750	345	1	𝑇3(1	𝑇3(1	ADV
cana-1750	345	2	)	)	PUNCT
cana-1750	345	3	≤	≤	NOUN
cana-1750	345	4	[	[	PUNCT
cana-1750	345	5	(	(	PUNCT
cana-1750	345	6	4	4	NUM
cana-1750	345	7	−	−	PROPN
cana-1750	345	8	𝑝2	𝑝2	NOUN
cana-1750	345	9	)	)	PUNCT
cana-1750	345	10	4(𝜆	4(𝜆	NUM
cana-1750	346	1	+	+	CCONJ
cana-1750	346	2	2)2	2)2	NUM
cana-1750	346	3	]	]	PUNCT
cana-1750	347	1	+	+	CCONJ
cana-1750	347	2	[	[	PUNCT
cana-1750	347	3	𝑝2(4	𝑝2(4	PROPN
cana-1750	347	4	−	−	PROPN
cana-1750	347	5	𝑝2)(𝜆2	𝑝2)(𝜆2	VERB
cana-1750	347	6	+	+	CCONJ
cana-1750	347	7	1	1	X
cana-1750	347	8	)	)	PUNCT
cana-1750	347	9	2(𝜆	2(𝜆	NUM
cana-1750	348	1	+	+	CCONJ
cana-1750	348	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	349	1	+	+	CCONJ
cana-1750	349	2	1)2	1)2	NUM
cana-1750	349	3	]	]	PUNCT
cana-1750	350	1	+	+	CCONJ
cana-1750	350	2	[	[	X
cana-1750	350	3	1	1	NUM
cana-1750	350	4	+	+	NUM
cana-1750	350	5	8(𝜆	8(𝜆	NUM
cana-1750	350	6	+	+	CCONJ
cana-1750	350	7	2)2(𝜆	2)2(𝜆	NUM
cana-1750	350	8	+	+	CCONJ
cana-1750	350	9	1	1	NUM
cana-1750	350	10	)	)	PUNCT
cana-1750	350	11	+	+	CCONJ
cana-1750	350	12	(	(	PUNCT
cana-1750	350	13	−𝜆3	−𝜆3	NOUN
cana-1750	350	14	+	+	NOUN
cana-1750	350	15	𝜆2	𝜆2	NOUN
cana-1750	350	16	+	+	CCONJ
cana-1750	350	17	𝜆	𝜆	NOUN
cana-1750	351	1	+	+	CCONJ
cana-1750	351	2	15)𝑝2	15)𝑝2	NUM
cana-1750	351	3	4(𝜆	4(𝜆	NUM
cana-1750	352	1	+	+	CCONJ
cana-1750	352	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	352	3	+	+	CCONJ
cana-1750	352	4	1)3	1)3	PROPN
cana-1750	352	5	𝑝2	𝑝2	NOUN
cana-1750	352	6	]	]	PUNCT
cana-1750	352	7	.	.	PUNCT
cana-1750	353	1	=	=	PUNCT
cana-1750	353	2	ξ(𝑝	ξ(𝑝	PROPN
cana-1750	353	3	,	,	PUNCT
cana-1750	353	4	𝜆	𝜆	NOUN
cana-1750	353	5	)	)	PUNCT
cana-1750	353	6	.	.	PUNCT
cana-1750	354	1	differentiating	differentiate	VERB
cana-1750	354	2	ξ(𝑝	ξ(𝑝	PROPN
cana-1750	354	3	,	,	PUNCT
cana-1750	354	4	𝜆	𝜆	NOUN
cana-1750	354	5	)	)	PUNCT
cana-1750	354	6	with	with	ADP
cana-1750	354	7	respect	respect	NOUN
cana-1750	354	8	to	to	ADP
cana-1750	354	9	𝑝	𝑝	NOUN
cana-1750	354	10	,	,	PUNCT
cana-1750	354	11	we	we	PRON
cana-1750	354	12	obtain	obtain	VERB
cana-1750	354	13	𝜕(ξ(𝑝	𝜕(ξ(𝑝	PROPN
cana-1750	354	14	,	,	PUNCT
cana-1750	354	15	𝜆	𝜆	NOUN
cana-1750	354	16	)	)	PUNCT
cana-1750	354	17	)	)	PUNCT
cana-1750	354	18	𝜕𝑝	𝜕𝑝	NOUN
cana-1750	354	19	=	=	SYM
cana-1750	354	20	𝑝	𝑝	PROPN
cana-1750	354	21	[	[	PUNCT
cana-1750	354	22	𝑝2(−2𝜆3	𝑝2(−2𝜆3	NOUN
cana-1750	354	23	+	+	CCONJ
cana-1750	354	24	2𝜆2	2𝜆2	NUM
cana-1750	355	1	+	+	CCONJ
cana-1750	355	2	2𝜆	2𝜆	NUM
cana-1750	355	3	+	+	CCONJ
cana-1750	355	4	14	14	NUM
cana-1750	355	5	)	)	PUNCT
cana-1750	356	1	+	+	CCONJ
cana-1750	356	2	(	(	PUNCT
cana-1750	356	3	4𝜆3	4𝜆3	NUM
cana-1750	356	4	+	+	SYM
cana-1750	356	5	12𝜆2	12𝜆2	NUM
cana-1750	356	6	+	+	NOUN
cana-1750	356	7	24𝜆	24𝜆	NOUN
cana-1750	356	8	+	+	CCONJ
cana-1750	356	9	16	16	NUM
cana-1750	356	10	)	)	PUNCT
cana-1750	356	11	(	(	PUNCT
cana-1750	356	12	𝜆	𝜆	X
cana-1750	356	13	+	+	NUM
cana-1750	356	14	2)2(𝜆	2)2(𝜆	NUM
cana-1750	356	15	+	+	CCONJ
cana-1750	356	16	1)3	1)3	PROPN
cana-1750	356	17	]	]	PUNCT
cana-1750	356	18	.	.	PUNCT
cana-1750	357	1	(	(	PUNCT
cana-1750	357	2	3.34	3.34	NUM
cana-1750	357	3	)	)	PUNCT
cana-1750	357	4	setting	set	VERB
cana-1750	357	5	𝜕(ξ(𝑝,𝜆	𝜕(ξ(𝑝,𝜆	NOUN
cana-1750	357	6	)	)	PUNCT
cana-1750	357	7	)	)	PUNCT
cana-1750	357	8	𝜕𝑝	𝜕𝑝	NOUN
cana-1750	358	1	=	=	SYM
cana-1750	358	2	0	0	NUM
cana-1750	358	3	yields	yield	NOUN
cana-1750	358	4	either	either	CCONJ
cana-1750	358	5	𝑝	𝑝	X
cana-1750	358	6	=	=	SYM
cana-1750	358	7	0	0	NUM
cana-1750	358	8	or	or	CCONJ
cana-1750	358	9	communications	communication	NOUN
cana-1750	358	10	on	on	ADP
cana-1750	358	11	applied	apply	VERB
cana-1750	358	12	nonlinear	nonlinear	ADJ
cana-1750	358	13	analysis	analysis	NOUN
cana-1750	358	14	issn	issn	NOUN
cana-1750	358	15	:	:	PUNCT
cana-1750	358	16	1074	1074	NUM
cana-1750	358	17	-	-	PUNCT
cana-1750	358	18	133x	133x	NUM
cana-1750	358	19	vol	vol	NOUN
cana-1750	358	20	32	32	NUM
cana-1750	358	21	no	no	NOUN
cana-1750	358	22	.	.	NOUN
cana-1750	358	23	2	2	NUM
cana-1750	358	24	(	(	PUNCT
cana-1750	358	25	2025	2025	NUM
cana-1750	358	26	)	)	PUNCT
cana-1750	358	27	395	395	NUM
cana-1750	358	28	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	358	29	𝑝2	𝑝2	NOUN
cana-1750	358	30	=	=	PUNCT
cana-1750	359	1	−4𝜆3	−4𝜆3	NUM
cana-1750	359	2	−	−	PROPN
cana-1750	359	3	12𝜆2	12𝜆2	NUM
cana-1750	359	4	−	−	NOUN
cana-1750	359	5	24𝜆	24𝜆	NOUN
cana-1750	359	6	−	−	PROPN
cana-1750	359	7	16	16	NUM
cana-1750	359	8	−2𝜆3	−2𝜆3	NUM
cana-1750	359	9	+	+	SYM
cana-1750	359	10	2𝜆2	2𝜆2	NUM
cana-1750	360	1	+	+	CCONJ
cana-1750	360	2	2𝜆	2𝜆	NUM
cana-1750	360	3	+	+	CCONJ
cana-1750	360	4	14	14	NUM
cana-1750	360	5	.	.	PUNCT
cana-1750	361	1	(	(	PUNCT
cana-1750	361	2	3.35	3.35	NUM
cana-1750	361	3	)	)	PUNCT
cana-1750	361	4	but	but	CCONJ
cana-1750	361	5	−4𝜆3	−4𝜆3	NUM
cana-1750	361	6	−	−	NOUN
cana-1750	361	7	12𝜆2	12𝜆2	NUM
cana-1750	361	8	−	−	NOUN
cana-1750	361	9	24𝜆	24𝜆	NOUN
cana-1750	361	10	−	−	PROPN
cana-1750	361	11	16	16	NUM
cana-1750	361	12	<	<	X
cana-1750	361	13	0	0	NUM
cana-1750	361	14	for	for	ADP
cana-1750	361	15	0	0	NUM
cana-1750	361	16	≤	≤	NOUN
cana-1750	361	17	𝜆	𝜆	DET
cana-1750	361	18	≤	≤	NUM
cana-1750	361	19	1	1	NUM
cana-1750	361	20	and	and	CCONJ
cana-1750	361	21	therefore	therefore	ADV
cana-1750	361	22	the	the	DET
cana-1750	361	23	maximum	maximum	ADJ
cana-1750	361	24	value	value	NOUN
cana-1750	361	25	of	of	ADP
cana-1750	361	26	𝑇3(1	𝑇3(1	ADV
cana-1750	361	27	)	)	PUNCT
cana-1750	361	28	is	be	AUX
cana-1750	361	29	attained	attain	VERB
cana-1750	361	30	at	at	ADP
cana-1750	361	31	the	the	DET
cana-1750	361	32	end	end	NOUN
cana-1750	361	33	points	point	NOUN
cana-1750	361	34	𝑝1	𝑝1	NOUN
cana-1750	361	35	=	=	SYM
cana-1750	361	36	𝑝	𝑝	PROPN
cana-1750	361	37	∈	∈	PROPN
cana-1750	362	1	[	[	X
cana-1750	362	2	0,2	0,2	NUM
cana-1750	362	3	]	]	PUNCT
cana-1750	362	4	.	.	PUNCT
cana-1750	363	1	figure	figure	NOUN
cana-1750	363	2	2	2	NUM
cana-1750	363	3	.	.	PUNCT
cana-1750	363	4	graph	graph	NOUN
cana-1750	363	5	of	of	ADP
cana-1750	363	6	the	the	DET
cana-1750	363	7	bound	bound	ADJ
cana-1750	363	8	−4𝜆3	−4𝜆3	NOUN
cana-1750	363	9	−	−	PROPN
cana-1750	363	10	12𝜆2	12𝜆2	NUM
cana-1750	363	11	−	−	NOUN
cana-1750	363	12	24𝜆	24𝜆	NOUN
cana-1750	363	13	−	−	PROPN
cana-1750	363	14	16	16	NUM
cana-1750	363	15	in	in	ADP
cana-1750	363	16	the	the	DET
cana-1750	363	17	range	range	NOUN
cana-1750	363	18	𝜆	𝜆	PRON
cana-1750	363	19	∈	∈	PROPN
cana-1750	364	1	[	[	X
cana-1750	364	2	0,1	0,1	NUM
cana-1750	364	3	]	]	PUNCT
cana-1750	364	4	.	.	PUNCT
cana-1750	365	1	for	for	ADP
cana-1750	365	2	𝑝1	𝑝1	NOUN
cana-1750	365	3	=	=	SYM
cana-1750	365	4	0	0	NUM
cana-1750	365	5	and	and	CCONJ
cana-1750	365	6	𝑝2	𝑝2	NOUN
cana-1750	365	7	=	=	SYM
cana-1750	366	1	2𝑥.	2𝑥.	NUM
cana-1750	366	2	then	then	ADV
cana-1750	366	3	,	,	PUNCT
cana-1750	366	4	we	we	PRON
cana-1750	366	5	have	have	VERB
cana-1750	366	6	|1	|1	PRON
cana-1750	367	1	+	+	NUM
cana-1750	367	2	2𝑎2	2𝑎2	NUM
cana-1750	367	3	2(𝑎3	2(𝑎3	NUM
cana-1750	367	4	−	−	NOUN
cana-1750	367	5	1	1	NUM
cana-1750	367	6	)	)	PUNCT
cana-1750	367	7	−	−	NOUN
cana-1750	367	8	𝑎3	𝑎3	PROPN
cana-1750	367	9	2|	2|	NUM
cana-1750	367	10	=	=	SYM
cana-1750	368	1	1	1	NUM
cana-1750	368	2	−	−	NUM
cana-1750	368	3	4|𝑥|2	4|𝑥|2	NUM
cana-1750	368	4	(	(	PUNCT
cana-1750	368	5	𝜆	𝜆	ADP
cana-1750	368	6	+	+	X
cana-1750	368	7	2)2	2)2	NUM
cana-1750	368	8	≤	≤	NUM
cana-1750	368	9	1	1	NUM
cana-1750	368	10	+	+	NUM
cana-1750	368	11	4	4	NUM
cana-1750	368	12	(	(	PUNCT
cana-1750	368	13	𝜆	𝜆	NOUN
cana-1750	368	14	+	+	ADJ
cana-1750	368	15	2)2	2)2	NUM
cana-1750	368	16	.	.	PUNCT
cana-1750	369	1	(	(	PUNCT
cana-1750	369	2	3.36	3.36	NUM
cana-1750	369	3	)	)	PUNCT
cana-1750	369	4	in	in	ADP
cana-1750	369	5	the	the	DET
cana-1750	369	6	view	view	NOUN
cana-1750	369	7	of	of	ADP
cana-1750	369	8	(	(	PUNCT
cana-1750	369	9	3.2	3.2	NUM
cana-1750	369	10	)	)	PUNCT
cana-1750	369	11	,	,	PUNCT
cana-1750	369	12	(	(	PUNCT
cana-1750	369	13	3.3	3.3	NUM
cana-1750	369	14	)	)	PUNCT
cana-1750	369	15	and	and	CCONJ
cana-1750	369	16	𝑝1	𝑝1	NOUN
cana-1750	369	17	=	=	PROPN
cana-1750	369	18	𝑝2	𝑝2	NOUN
cana-1750	369	19	=	=	SYM
cana-1750	369	20	2	2	NUM
cana-1750	369	21	,	,	PUNCT
cana-1750	369	22	we	we	PRON
cana-1750	369	23	get	get	VERB
cana-1750	369	24	2𝑎2	2𝑎2	NOUN
cana-1750	369	25	2𝑎3	2𝑎3	NUM
cana-1750	369	26	=	=	SYM
cana-1750	369	27	32(1	32(1	NOUN
cana-1750	370	1	−	−	NOUN
cana-1750	370	2	𝜆	𝜆	NOUN
cana-1750	370	3	)	)	PUNCT
cana-1750	370	4	(	(	PUNCT
cana-1750	370	5	𝜆	𝜆	X
cana-1750	370	6	+	+	ADJ
cana-1750	370	7	2)(𝜆	2)(𝜆	NUM
cana-1750	370	8	+	+	CCONJ
cana-1750	370	9	1)3	1)3	PROPN
cana-1750	371	1	+	+	NUM
cana-1750	371	2	16	16	NUM
cana-1750	371	3	(	(	PUNCT
cana-1750	371	4	𝜆	𝜆	PROPN
cana-1750	371	5	+	+	ADJ
cana-1750	371	6	2)(𝜆	2)(𝜆	NUM
cana-1750	371	7	+	+	CCONJ
cana-1750	371	8	1)2	1)2	NUM
cana-1750	371	9	.	.	PUNCT
cana-1750	372	1	(	(	PUNCT
cana-1750	372	2	3.37	3.37	NUM
cana-1750	372	3	)	)	PUNCT
cana-1750	372	4	−2𝑎2	−2𝑎2	PUNCT
cana-1750	372	5	2	2	NUM
cana-1750	372	6	=	=	SYM
cana-1750	372	7	−8	−8	X
cana-1750	372	8	(	(	PUNCT
cana-1750	372	9	𝜆	𝜆	PROPN
cana-1750	372	10	+	+	X
cana-1750	372	11	1)2	1)2	NUM
cana-1750	372	12	.	.	PUNCT
cana-1750	373	1	(	(	PUNCT
cana-1750	373	2	3.38	3.38	NUM
cana-1750	373	3	)	)	PUNCT
cana-1750	373	4	−𝑎3	−𝑎3	PROPN
cana-1750	373	5	2	2	NUM
cana-1750	373	6	=	=	SYM
cana-1750	373	7	−	−	PROPN
cana-1750	373	8	16(1	16(1	NUM
cana-1750	373	9	−	−	PROPN
cana-1750	373	10	𝜆)2	𝜆)2	NOUN
cana-1750	373	11	(	(	PUNCT
cana-1750	373	12	𝜆	𝜆	ADP
cana-1750	373	13	+	+	ADJ
cana-1750	373	14	2)(𝜆	2)(𝜆	NUM
cana-1750	373	15	+	+	CCONJ
cana-1750	374	1	1)2	1)2	NUM
cana-1750	374	2	−	−	NOUN
cana-1750	374	3	4	4	NUM
cana-1750	374	4	(	(	PUNCT
cana-1750	374	5	2	2	NUM
cana-1750	374	6	+	+	NUM
cana-1750	374	7	𝜆)2	𝜆)2	NOUN
cana-1750	374	8	−	−	NOUN
cana-1750	375	1	16(1	16(1	NUM
cana-1750	375	2	−	−	NOUN
cana-1750	375	3	𝜆	𝜆	X
cana-1750	375	4	)	)	PUNCT
cana-1750	375	5	(	(	PUNCT
cana-1750	375	6	𝜆	𝜆	PROPN
cana-1750	375	7	+	+	CCONJ
cana-1750	375	8	2)2(𝜆	2)2(𝜆	NUM
cana-1750	375	9	+	+	CCONJ
cana-1750	375	10	1	1	NUM
cana-1750	375	11	)	)	PUNCT
cana-1750	375	12	.	.	PUNCT
cana-1750	376	1	(	(	PUNCT
cana-1750	376	2	3.39	3.39	NUM
cana-1750	376	3	)	)	PUNCT
cana-1750	376	4	substitute	substitute	NOUN
cana-1750	376	5	the	the	DET
cana-1750	376	6	values	value	NOUN
cana-1750	376	7	of	of	ADP
cana-1750	376	8	(	(	PUNCT
cana-1750	376	9	3.37	3.37	NUM
cana-1750	376	10	)	)	PUNCT
cana-1750	376	11	,	,	PUNCT
cana-1750	376	12	(	(	PUNCT
cana-1750	376	13	3.38	3.38	NUM
cana-1750	376	14	)	)	PUNCT
cana-1750	376	15	and	and	CCONJ
cana-1750	376	16	(	(	PUNCT
cana-1750	376	17	3.39	3.39	NUM
cana-1750	376	18	)	)	PUNCT
cana-1750	376	19	in	in	ADP
cana-1750	376	20	(	(	PUNCT
cana-1750	376	21	3.22	3.22	NUM
cana-1750	376	22	)	)	PUNCT
cana-1750	376	23	,	,	PUNCT
cana-1750	376	24	we	we	PRON
cana-1750	376	25	may	may	AUX
cana-1750	376	26	get	get	VERB
cana-1750	376	27	|1	|1	PRON
cana-1750	376	28	+	+	NUM
cana-1750	376	29	2𝑎2	2𝑎2	NUM
cana-1750	376	30	2(𝑎3	2(𝑎3	NUM
cana-1750	376	31	−	−	NOUN
cana-1750	377	1	1	1	NUM
cana-1750	377	2	)	)	PUNCT
cana-1750	377	3	−	−	NOUN
cana-1750	377	4	𝑎3	𝑎3	PROPN
cana-1750	377	5	2|	2|	PROPN
cana-1750	377	6	≤	≤	PUNCT
cana-1750	378	1	|	|	ADV
cana-1750	378	2	𝜆5	𝜆5	CCONJ
cana-1750	378	3	+	+	CCONJ
cana-1750	378	4	7𝜆4	7𝜆4	NUM
cana-1750	379	1	+	+	NUM
cana-1750	379	2	7𝜆3	7𝜆3	NUM
cana-1750	380	1	−	−	NUM
cana-1750	380	2	11𝜆2	11𝜆2	NUM
cana-1750	380	3	−	−	PROPN
cana-1750	380	4	44𝜆	44𝜆	NOUN
cana-1750	380	5	+	+	CCONJ
cana-1750	380	6	32	32	NUM
cana-1750	380	7	(	(	PUNCT
cana-1750	380	8	𝜆	𝜆	PROPN
cana-1750	380	9	+	+	NUM
cana-1750	380	10	2)2(𝜆	2)2(𝜆	NUM
cana-1750	381	1	+	+	SYM
cana-1750	381	2	1)3	1)3	PROPN
cana-1750	381	3	|	|	CCONJ
cana-1750	381	4	≤	≤	PROPN
cana-1750	381	5	𝑁(𝜆	𝑁(𝜆	NOUN
cana-1750	381	6	)	)	PUNCT
cana-1750	381	7	.	.	PUNCT
cana-1750	382	1	(	(	PUNCT
cana-1750	382	2	3.40	3.40	NUM
cana-1750	382	3	)	)	PUNCT
cana-1750	382	4	where	where	SCONJ
cana-1750	382	5	,	,	PUNCT
cana-1750	382	6	𝑁(𝜆	𝑁(𝜆	NOUN
cana-1750	382	7	)	)	PUNCT
cana-1750	382	8	=	=	PUNCT
cana-1750	383	1	|	|	ADV
cana-1750	383	2	𝜆5	𝜆5	X
cana-1750	383	3	+	+	CCONJ
cana-1750	383	4	7𝜆4	7𝜆4	NUM
cana-1750	383	5	+	+	NUM
cana-1750	383	6	7𝜆3	7𝜆3	NUM
cana-1750	384	1	−	−	NUM
cana-1750	384	2	11𝜆2	11𝜆2	NUM
cana-1750	384	3	−	−	PROPN
cana-1750	384	4	44𝜆	44𝜆	NOUN
cana-1750	384	5	+	+	CCONJ
cana-1750	384	6	32	32	NUM
cana-1750	384	7	(	(	PUNCT
cana-1750	384	8	𝜆	𝜆	PROPN
cana-1750	384	9	+	+	NUM
cana-1750	384	10	2)2(𝜆	2)2(𝜆	NUM
cana-1750	385	1	+	+	SYM
cana-1750	385	2	1)3	1)3	PROPN
cana-1750	386	1	|	|	INTJ
cana-1750	386	2	.	.	PUNCT
cana-1750	387	1	(	(	PUNCT
cana-1750	387	2	3.41	3.41	NUM
cana-1750	387	3	)	)	PUNCT
cana-1750	387	4	this	this	PRON
cana-1750	387	5	completes	complete	VERB
cana-1750	387	6	the	the	DET
cana-1750	387	7	proof	proof	NOUN
cana-1750	387	8	of	of	ADP
cana-1750	387	9	the	the	DET
cana-1750	387	10	theorem	theorem	NOUN
cana-1750	387	11	(	(	PUNCT
cana-1750	387	12	3.7	3.7	NUM
cana-1750	387	13	)	)	PUNCT
cana-1750	387	14	.	.	PUNCT
cana-1750	388	1	remark	remark	VERB
cana-1750	388	2	3.8	3.8	NUM
cana-1750	388	3	.	.	PUNCT
cana-1750	389	1	theorem	theorem	NOUN
cana-1750	389	2	(	(	PUNCT
cana-1750	389	3	3.7	3.7	NUM
cana-1750	389	4	)	)	PUNCT
cana-1750	389	5	,	,	PUNCT
cana-1750	389	6	for	for	ADP
cana-1750	389	7	𝜆	𝜆	PRON
cana-1750	389	8	=	=	SYM
cana-1750	389	9	0	0	NUM
cana-1750	389	10	yields	yield	NOUN
cana-1750	389	11	the	the	DET
cana-1750	389	12	bound	bind	VERB
cana-1750	389	13	|1	|1	PRON
cana-1750	390	1	+	+	NUM
cana-1750	390	2	2𝑎2	2𝑎2	NUM
cana-1750	390	3	2(𝑎3	2(𝑎3	NUM
cana-1750	390	4	−	−	NOUN
cana-1750	390	5	1	1	NUM
cana-1750	390	6	)	)	PUNCT
cana-1750	390	7	−	−	NOUN
cana-1750	390	8	𝑎3	𝑎3	PROPN
cana-1750	390	9	2|	2|	NUM
cana-1750	390	10	≤	≤	NUM
cana-1750	390	11	8	8	NUM
cana-1750	390	12	for	for	ADP
cana-1750	390	13	the	the	DET
cana-1750	390	14	class	class	NOUN
cana-1750	390	15	of	of	ADP
cana-1750	390	16	star	star	NOUN
cana-1750	390	17	like	like	ADP
cana-1750	390	18	function	function	NOUN
cana-1750	390	19	𝒮∗	𝒮∗	NOUN
cana-1750	390	20	conforming	conform	VERB
cana-1750	390	21	the	the	DET
cana-1750	390	22	bound	bind	VERB
cana-1750	390	23	obtained	obtain	VERB
cana-1750	390	24	by	by	ADP
cana-1750	390	25	thomous	thomous	PROPN
cana-1750	390	26	and	and	CCONJ
cana-1750	390	27	halim	halim	PROPN
cana-1750	391	1	[	[	X
cana-1750	391	2	1	1	NUM
cana-1750	391	3	]	]	PUNCT
cana-1750	391	4	.	.	PUNCT
cana-1750	392	1	and	and	CCONJ
cana-1750	392	2	for	for	ADP
cana-1750	392	3	𝜆	𝜆	DET
cana-1750	392	4	=	=	SYM
cana-1750	392	5	1	1	NUM
cana-1750	392	6	yields	yield	NOUN
cana-1750	392	7	the	the	DET
cana-1750	392	8	bound	bind	VERB
cana-1750	392	9	|1	|1	PRON
cana-1750	393	1	+	+	NUM
cana-1750	393	2	2𝑎2	2𝑎2	NUM
cana-1750	393	3	2(𝑎3	2(𝑎3	NUM
cana-1750	393	4	−	−	NOUN
cana-1750	393	5	1	1	NUM
cana-1750	393	6	)	)	PUNCT
cana-1750	393	7	−	−	NOUN
cana-1750	393	8	𝑎3	𝑎3	PROPN
cana-1750	393	9	2|	2|	NUM
cana-1750	393	10	≤	≤	ADV
cana-1750	393	11	13	13	NUM
cana-1750	393	12	9	9	NUM
cana-1750	393	13	for	for	ADP
cana-1750	393	14	the	the	DET
cana-1750	393	15	class	class	NOUN
cana-1750	393	16	of	of	ADP
cana-1750	393	17	functions	function	NOUN
cana-1750	393	18	with	with	ADP
cana-1750	393	19	bounded	bounded	ADJ
cana-1750	393	20	boundary	boundary	ADJ
cana-1750	393	21	rotation	rotation	NOUN
cana-1750	393	22	ℛ̃	ℛ̃	PROPN
cana-1750	393	23	conforming	conform	VERB
cana-1750	393	24	the	the	DET
cana-1750	393	25	bound	bind	VERB
cana-1750	393	26	obtained	obtain	VERB
cana-1750	393	27	by	by	ADP
cana-1750	393	28	radhika	radhika	PROPN
cana-1750	393	29	et	et	PROPN
cana-1750	393	30	al	al	PROPN
cana-1750	393	31	.	.	PUNCT
cana-1750	394	1	[	[	X
cana-1750	394	2	2	2	NUM
cana-1750	394	3	]	]	PUNCT
cana-1750	394	4	.	.	PUNCT
cana-1750	395	1	communications	communication	NOUN
cana-1750	395	2	on	on	ADP
cana-1750	395	3	applied	apply	VERB
cana-1750	395	4	nonlinear	nonlinear	ADJ
cana-1750	395	5	analysis	analysis	NOUN
cana-1750	395	6	issn	issn	NOUN
cana-1750	395	7	:	:	PUNCT
cana-1750	395	8	1074	1074	NUM
cana-1750	395	9	-	-	PUNCT
cana-1750	395	10	133x	133x	NUM
cana-1750	395	11	vol	vol	NOUN
cana-1750	395	12	32	32	NUM
cana-1750	395	13	no	no	NOUN
cana-1750	395	14	.	.	NOUN
cana-1750	395	15	2	2	NUM
cana-1750	395	16	(	(	PUNCT
cana-1750	395	17	2025	2025	NUM
cana-1750	395	18	)	)	PUNCT
cana-1750	395	19	396	396	NUM
cana-1750	395	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	395	21	4	4	X
cana-1750	395	22	.	.	X
cana-1750	395	23	zalcman	zalcman	NOUN
cana-1750	395	24	conjecture	conjecture	VERB
cana-1750	395	25	for	for	ADP
cana-1750	395	26	the	the	DET
cana-1750	395	27	class	class	NOUN
cana-1750	395	28	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	395	29	)	)	PUNCT
cana-1750	395	30	theorem	theorem	VERB
cana-1750	395	31	4.1	4.1	NUM
cana-1750	395	32	.	.	PUNCT
cana-1750	396	1	let	let	VERB
cana-1750	396	2	𝑓	𝑓	PRON
cana-1750	396	3	given	give	VERB
cana-1750	396	4	by	by	ADP
cana-1750	396	5	(	(	PUNCT
cana-1750	396	6	1.1	1.1	NUM
cana-1750	396	7	)	)	PUNCT
cana-1750	396	8	,	,	PUNCT
cana-1750	396	9	be	be	AUX
cana-1750	396	10	in	in	ADP
cana-1750	396	11	the	the	DET
cana-1750	396	12	class	class	NOUN
cana-1750	396	13	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	396	14	)	)	PUNCT
cana-1750	396	15	;	;	PUNCT
cana-1750	396	16	(	(	PUNCT
cana-1750	396	17	0	0	NUM
cana-1750	396	18	≤	≤	NUM
cana-1750	396	19	𝜆	𝜆	PRON
cana-1750	396	20	≤	≤	NUM
cana-1750	396	21	1	1	NUM
cana-1750	396	22	)	)	PUNCT
cana-1750	396	23	.	.	PUNCT
cana-1750	397	1	then	then	ADV
cana-1750	397	2	we	we	PRON
cana-1750	397	3	have	have	VERB
cana-1750	397	4	sharp	sharp	ADV
cana-1750	397	5	bound	bind	VERB
cana-1750	397	6	|𝑎2	|𝑎2	NOUN
cana-1750	397	7	2	2	NUM
cana-1750	397	8	−	−	PROPN
cana-1750	397	9	𝑎3|	𝑎3|	NOUN
cana-1750	397	10	≤	≤	NUM
cana-1750	397	11	max	max	PROPN
cana-1750	397	12	{	{	PUNCT
cana-1750	397	13	2	2	NUM
cana-1750	397	14	(	(	PUNCT
cana-1750	397	15	𝜆	𝜆	NOUN
cana-1750	397	16	+	+	ADJ
cana-1750	397	17	2	2	NUM
cana-1750	397	18	)	)	PUNCT
cana-1750	397	19	,	,	PUNCT
cana-1750	397	20	𝒯(𝜆	𝒯(𝜆	PROPN
cana-1750	397	21	)	)	PUNCT
cana-1750	397	22	(	(	PUNCT
cana-1750	397	23	𝜆	𝜆	X
cana-1750	397	24	+	+	CCONJ
cana-1750	397	25	1)2(𝜆	1)2(𝜆	NUM
cana-1750	397	26	+	+	CCONJ
cana-1750	397	27	2	2	NUM
cana-1750	397	28	)	)	PUNCT
cana-1750	397	29	}	}	PUNCT
cana-1750	397	30	(	(	PUNCT
cana-1750	397	31	4.1	4.1	NUM
cana-1750	397	32	)	)	PUNCT
cana-1750	397	33	where	where	SCONJ
cana-1750	397	34	𝒯(𝜆	𝒯(𝜆	X
cana-1750	397	35	)	)	PUNCT
cana-1750	397	36	=	=	SYM
cana-1750	398	1	2(𝜆2	2(𝜆2	NUM
cana-1750	398	2	+	+	CCONJ
cana-1750	398	3	1	1	NUM
cana-1750	398	4	)	)	PUNCT
cana-1750	398	5	(	(	PUNCT
cana-1750	398	6	4.2	4.2	NUM
cana-1750	398	7	)	)	PUNCT
cana-1750	398	8	proof	proof	NOUN
cana-1750	398	9	.	.	PUNCT
cana-1750	399	1	first	first	ADV
cana-1750	399	2	note	note	VERB
cana-1750	399	3	that	that	SCONJ
cana-1750	399	4	by	by	ADP
cana-1750	399	5	equating	equate	VERB
cana-1750	399	6	the	the	DET
cana-1750	399	7	corresponding	corresponding	ADJ
cana-1750	399	8	coefficients	coefficient	NOUN
cana-1750	399	9	in	in	ADP
cana-1750	399	10	the	the	DET
cana-1750	399	11	equation	equation	NOUN
cana-1750	399	12	(	(	PUNCT
cana-1750	399	13	3.1	3.1	NUM
cana-1750	399	14	)	)	PUNCT
cana-1750	399	15	.	.	PUNCT
cana-1750	400	1	we	we	PRON
cana-1750	400	2	get	get	VERB
cana-1750	400	3	,	,	PUNCT
cana-1750	400	4	in	in	ADP
cana-1750	400	5	the	the	DET
cana-1750	400	6	view	view	NOUN
cana-1750	400	7	of	of	ADP
cana-1750	400	8	(	(	PUNCT
cana-1750	400	9	3.2	3.2	NUM
cana-1750	400	10	)	)	PUNCT
cana-1750	400	11	and	and	CCONJ
cana-1750	400	12	(	(	PUNCT
cana-1750	400	13	3.3	3.3	NUM
cana-1750	400	14	)	)	PUNCT
cana-1750	400	15	,	,	PUNCT
cana-1750	400	16	a	a	DET
cana-1750	400	17	simple	simple	ADJ
cana-1750	400	18	computation	computation	NOUN
cana-1750	400	19	leads	lead	VERB
cana-1750	400	20	to	to	ADP
cana-1750	400	21	𝑎2	𝑎2	NOUN
cana-1750	400	22	2	2	NUM
cana-1750	400	23	−	−	NOUN
cana-1750	400	24	𝑎3	𝑎3	NOUN
cana-1750	400	25	=	=	PUNCT
cana-1750	400	26	[	[	PUNCT
cana-1750	400	27	𝑝1	𝑝1	NOUN
cana-1750	400	28	𝜆	𝜆	NOUN
cana-1750	400	29	+	+	PROPN
cana-1750	400	30	1	1	NUM
cana-1750	400	31	]	]	SYM
cana-1750	400	32	2	2	NUM
cana-1750	400	33	−	−	NOUN
cana-1750	400	34	[	[	PUNCT
cana-1750	400	35	𝑝1	𝑝1	NOUN
cana-1750	400	36	2(1	2(1	NUM
cana-1750	400	37	−	−	NOUN
cana-1750	400	38	𝜆	𝜆	NOUN
cana-1750	400	39	)	)	PUNCT
cana-1750	400	40	(	(	PUNCT
cana-1750	400	41	𝜆	𝜆	PROPN
cana-1750	400	42	+	+	NOUN
cana-1750	400	43	1)(𝜆	1)(𝜆	NUM
cana-1750	400	44	+	+	CCONJ
cana-1750	400	45	2	2	NUM
cana-1750	400	46	)	)	PUNCT
cana-1750	400	47	+	+	NUM
cana-1750	401	1	𝑝2	𝑝2	PROPN
cana-1750	401	2	𝜆	𝜆	PROPN
cana-1750	402	1	+	+	NOUN
cana-1750	402	2	2	2	NUM
cana-1750	402	3	]	]	PUNCT
cana-1750	402	4	=	=	SYM
cana-1750	402	5	𝑝2	𝑝2	NOUN
cana-1750	402	6	1	1	NUM
cana-1750	402	7	(	(	PUNCT
cana-1750	402	8	𝜆	𝜆	PROPN
cana-1750	402	9	+	+	PROPN
cana-1750	402	10	1)2	1)2	NUM
cana-1750	402	11	−	−	NOUN
cana-1750	402	12	𝑝1	𝑝1	NOUN
cana-1750	402	13	2(1	2(1	NUM
cana-1750	402	14	−	−	NOUN
cana-1750	402	15	𝜆	𝜆	NOUN
cana-1750	402	16	)	)	PUNCT
cana-1750	402	17	(	(	PUNCT
cana-1750	402	18	𝜆	𝜆	PROPN
cana-1750	402	19	+	+	NOUN
cana-1750	402	20	1)(𝜆	1)(𝜆	NUM
cana-1750	402	21	+	+	CCONJ
cana-1750	402	22	2	2	NUM
cana-1750	402	23	)	)	PUNCT
cana-1750	402	24	−	−	PROPN
cana-1750	402	25	𝑝2	𝑝2	PROPN
cana-1750	402	26	𝜆	𝜆	PROPN
cana-1750	402	27	+	+	NOUN
cana-1750	402	28	2	2	NUM
cana-1750	402	29	.	.	PUNCT
cana-1750	403	1	(	(	PUNCT
cana-1750	403	2	4.3	4.3	NUM
cana-1750	403	3	)	)	PUNCT
cana-1750	403	4	note	note	VERB
cana-1750	403	5	that	that	SCONJ
cana-1750	403	6	,	,	PUNCT
cana-1750	403	7	by	by	ADP
cana-1750	403	8	lemma	lemma	PROPN
cana-1750	403	9	(	(	PUNCT
cana-1750	403	10	2.2	2.2	NUM
cana-1750	403	11	)	)	PUNCT
cana-1750	403	12	,	,	PUNCT
cana-1750	403	13	we	we	PRON
cana-1750	403	14	may	may	AUX
cana-1750	403	15	write	write	VERB
cana-1750	403	16	2𝑝2	2𝑝2	NUM
cana-1750	403	17	=	=	SYM
cana-1750	403	18	𝑝1	𝑝1	NOUN
cana-1750	403	19	2	2	NUM
cana-1750	404	1	+	+	CCONJ
cana-1750	404	2	𝑥(4	𝑥(4	PROPN
cana-1750	404	3	−	−	PROPN
cana-1750	404	4	𝑝1	𝑝1	NOUN
cana-1750	404	5	2	2	NUM
cana-1750	404	6	)	)	PUNCT
cana-1750	404	7	,	,	PUNCT
cana-1750	404	8	we	we	PRON
cana-1750	404	9	can	can	AUX
cana-1750	404	10	easily	easily	ADV
cana-1750	404	11	get	get	VERB
cana-1750	404	12	=	=	PUNCT
cana-1750	404	13	[	[	PUNCT
cana-1750	404	14	𝜆2	𝜆2	NOUN
cana-1750	404	15	+	+	CCONJ
cana-1750	404	16	1	1	NUM
cana-1750	404	17	2(𝜆	2(𝜆	NUM
cana-1750	404	18	+	+	CCONJ
cana-1750	404	19	1)(𝜆	1)(𝜆	NUM
cana-1750	404	20	+	+	CCONJ
cana-1750	404	21	2	2	NUM
cana-1750	404	22	)	)	PUNCT
cana-1750	404	23	]	]	PUNCT
cana-1750	404	24	𝑝1	𝑝1	NOUN
cana-1750	404	25	2	2	NUM
cana-1750	404	26	−	−	NOUN
cana-1750	405	1	𝑋𝑥	𝑋𝑥	PROPN
cana-1750	405	2	2(𝜆	2(𝜆	NUM
cana-1750	405	3	+	+	CCONJ
cana-1750	405	4	2	2	NUM
cana-1750	405	5	)	)	PUNCT
cana-1750	405	6	.	.	PUNCT
cana-1750	406	1	(	(	PUNCT
cana-1750	406	2	4.4	4.4	NUM
cana-1750	406	3	)	)	PUNCT
cana-1750	406	4	without	without	ADP
cana-1750	406	5	loss	loss	NOUN
cana-1750	406	6	of	of	ADP
cana-1750	406	7	generality	generality	NOUN
cana-1750	406	8	,	,	PUNCT
cana-1750	406	9	we	we	PRON
cana-1750	406	10	let	let	VERB
cana-1750	406	11	0	0	NUM
cana-1750	406	12	≤	≤	NOUN
cana-1750	406	13	𝑝1	𝑝1	NOUN
cana-1750	406	14	=	=	SYM
cana-1750	406	15	𝑝	𝑝	NOUN
cana-1750	406	16	≤	≤	NUM
cana-1750	406	17	2	2	NUM
cana-1750	406	18	.	.	PUNCT
cana-1750	406	19	substitute	substitute	VERB
cana-1750	406	20	this	this	PRON
cana-1750	406	21	into	into	ADP
cana-1750	406	22	the	the	DET
cana-1750	406	23	above	above	ADJ
cana-1750	406	24	equation	equation	NOUN
cana-1750	406	25	,	,	PUNCT
cana-1750	406	26	we	we	PRON
cana-1750	406	27	obtain	obtain	VERB
cana-1750	406	28	the	the	DET
cana-1750	406	29	following	follow	VERB
cana-1750	406	30	quadratic	quadratic	ADJ
cana-1750	406	31	equation	equation	NOUN
cana-1750	406	32	in	in	ADP
cana-1750	406	33	terms	term	NOUN
cana-1750	406	34	of	of	ADP
cana-1750	406	35	𝑥.	𝑥.	NOUN
cana-1750	406	36	|𝑎2	|𝑎2	NOUN
cana-1750	406	37	2	2	NUM
cana-1750	406	38	−	−	PROPN
cana-1750	406	39	𝑎3|	𝑎3|	NOUN
cana-1750	406	40	=	=	NOUN
cana-1750	406	41	4	4	NUM
cana-1750	406	42	−	−	PROPN
cana-1750	406	43	𝑝2	𝑝2	NOUN
cana-1750	406	44	2(𝜆	2(𝜆	NUM
cana-1750	406	45	+	+	CCONJ
cana-1750	406	46	2	2	X
cana-1750	406	47	)	)	PUNCT
cana-1750	406	48	|𝑥|	|𝑥|	NOUN
cana-1750	407	1	+	+	PUNCT
cana-1750	407	2	[	[	PUNCT
cana-1750	407	3	𝜆2	𝜆2	NOUN
cana-1750	407	4	+	+	CCONJ
cana-1750	407	5	1	1	NUM
cana-1750	407	6	2(𝜆	2(𝜆	NUM
cana-1750	407	7	+	+	CCONJ
cana-1750	407	8	1)2(𝜆	1)2(𝜆	NUM
cana-1750	407	9	+	+	CCONJ
cana-1750	407	10	2	2	NUM
cana-1750	407	11	)	)	PUNCT
cana-1750	407	12	]	]	PUNCT
cana-1750	407	13	𝑝1	𝑝1	NOUN
cana-1750	407	14	2	2	NUM
cana-1750	407	15	.	.	PUNCT
cana-1750	407	16	(	(	PUNCT
cana-1750	407	17	4.5	4.5	NUM
cana-1750	407	18	)	)	PUNCT
cana-1750	407	19	=	=	SYM
cana-1750	407	20	¥	¥	PROPN
cana-1750	407	21	(	(	PUNCT
cana-1750	407	22	𝑝	𝑝	NOUN
cana-1750	407	23	,	,	PUNCT
cana-1750	407	24	|𝑥|	|𝑥|	ADJ
cana-1750	407	25	)	)	PUNCT
cana-1750	407	26	.	.	PUNCT
cana-1750	408	1	(	(	PUNCT
cana-1750	408	2	4.6	4.6	X
cana-1750	408	3	)	)	PUNCT
cana-1750	408	4	we	we	PRON
cana-1750	408	5	required	require	VERB
cana-1750	408	6	to	to	PART
cana-1750	408	7	prove	prove	VERB
cana-1750	408	8	that	that	SCONJ
cana-1750	408	9	the	the	DET
cana-1750	408	10	maximum	maximum	ADJ
cana-1750	408	11	value	value	NOUN
cana-1750	408	12	of	of	ADP
cana-1750	408	13	¥	¥	PROPN
cana-1750	408	14	(	(	PUNCT
cana-1750	408	15	𝑝	𝑝	PROPN
cana-1750	408	16	,	,	PUNCT
cana-1750	408	17	|𝑥|	|𝑥|	ADJ
cana-1750	408	18	)	)	PUNCT
cana-1750	408	19	on	on	ADP
cana-1750	408	20	[	[	X
cana-1750	408	21	0,2	0,2	NUM
cana-1750	408	22	]	]	X
cana-1750	408	23	×	×	NOUN
cana-1750	409	1	[	[	X
cana-1750	409	2	0,1	0,1	NUM
cana-1750	409	3	]	]	PUNCT
cana-1750	409	4	.	.	PUNCT
cana-1750	410	1	first	first	ADV
cana-1750	410	2	,	,	PUNCT
cana-1750	410	3	assume	assume	VERB
cana-1750	410	4	that	that	SCONJ
cana-1750	410	5	there	there	PRON
cana-1750	410	6	is	be	VERB
cana-1750	410	7	a	a	DET
cana-1750	410	8	maximum	maximum	NOUN
cana-1750	410	9	at	at	ADP
cana-1750	410	10	an	an	DET
cana-1750	410	11	interior	interior	ADJ
cana-1750	410	12	point	point	NOUN
cana-1750	410	13	¥	¥	NOUN
cana-1750	410	14	(	(	PUNCT
cana-1750	410	15	𝑝0	𝑝0	PROPN
cana-1750	410	16	,	,	PUNCT
cana-1750	410	17	|𝑥0|	|𝑥0|	VERB
cana-1750	410	18	)	)	PUNCT
cana-1750	410	19	of	of	ADP
cana-1750	410	20	[	[	X
cana-1750	410	21	0,2	0,2	NUM
cana-1750	410	22	]	]	X
cana-1750	410	23	×	×	NOUN
cana-1750	411	1	[	[	X
cana-1750	411	2	0,1	0,1	NUM
cana-1750	411	3	]	]	PUNCT
cana-1750	411	4	.	.	PUNCT
cana-1750	412	1	differentiating	differentiate	VERB
cana-1750	412	2	¥	¥	PROPN
cana-1750	412	3	(	(	PUNCT
cana-1750	412	4	𝑝	𝑝	PROPN
cana-1750	412	5	,	,	PUNCT
cana-1750	412	6	|𝑥|	|𝑥|	ADJ
cana-1750	412	7	)	)	PUNCT
cana-1750	412	8	with	with	ADP
cana-1750	412	9	respect	respect	NOUN
cana-1750	412	10	to	to	ADP
cana-1750	412	11	|𝑥|	|𝑥|	VERB
cana-1750	412	12	and	and	CCONJ
cana-1750	412	13	equating	equate	VERB
cana-1750	412	14	it	it	PRON
cana-1750	412	15	to	to	ADP
cana-1750	412	16	0	0	NUM
cana-1750	412	17	implies	imply	VERB
cana-1750	412	18	that	that	SCONJ
cana-1750	412	19	𝑝	𝑝	X
cana-1750	412	20	=	=	SYM
cana-1750	412	21	𝑝0	𝑝0	NOUN
cana-1750	412	22	=	=	SYM
cana-1750	412	23	2	2	NUM
cana-1750	412	24	which	which	PRON
cana-1750	412	25	is	be	AUX
cana-1750	412	26	contradiction	contradiction	NOUN
cana-1750	412	27	.	.	PUNCT
cana-1750	413	1	thus	thus	ADV
cana-1750	413	2	,	,	PUNCT
cana-1750	413	3	for	for	ADP
cana-1750	413	4	the	the	DET
cana-1750	413	5	maximum	maximum	ADJ
cana-1750	413	6	¥	¥	PROPN
cana-1750	413	7	(	(	PUNCT
cana-1750	413	8	𝑝	𝑝	NOUN
cana-1750	413	9	,	,	PUNCT
cana-1750	413	10	|𝑥|	|𝑥|	ADJ
cana-1750	413	11	)	)	PUNCT
cana-1750	413	12	,	,	PUNCT
cana-1750	413	13	we	we	PRON
cana-1750	413	14	must	must	AUX
cana-1750	413	15	consider	consider	VERB
cana-1750	413	16	the	the	DET
cana-1750	413	17	end	end	NOUN
cana-1750	413	18	points	point	NOUN
cana-1750	413	19	of	of	ADP
cana-1750	413	20	[	[	X
cana-1750	413	21	0,2	0,2	NUM
cana-1750	413	22	]	]	X
cana-1750	413	23	×	×	NOUN
cana-1750	414	1	[	[	X
cana-1750	414	2	0,1	0,1	NUM
cana-1750	414	3	]	]	PUNCT
cana-1750	414	4	.	.	PUNCT
cana-1750	415	1	for	for	ADP
cana-1750	415	2	𝑝	𝑝	NOUN
cana-1750	415	3	=	=	SYM
cana-1750	415	4	0	0	NUM
cana-1750	415	5	,	,	PUNCT
cana-1750	415	6	we	we	PRON
cana-1750	415	7	obtain	obtain	VERB
cana-1750	415	8	¥	¥	NUM
cana-1750	415	9	(	(	PUNCT
cana-1750	415	10	0	0	NUM
cana-1750	415	11	,	,	PUNCT
cana-1750	415	12	|𝑥|	|𝑥|	ADJ
cana-1750	415	13	)	)	PUNCT
cana-1750	415	14	=	=	SYM
cana-1750	415	15	4	4	NUM
cana-1750	415	16	2(𝜆	2(𝜆	NUM
cana-1750	415	17	+	+	CCONJ
cana-1750	415	18	2	2	NUM
cana-1750	415	19	)	)	PUNCT
cana-1750	415	20	|𝑥|2	|𝑥|2	ADJ
cana-1750	415	21	≤	≤	ADV
cana-1750	415	22	2	2	NUM
cana-1750	415	23	𝜆	𝜆	NOUN
cana-1750	415	24	+	+	ADJ
cana-1750	415	25	2	2	NUM
cana-1750	415	26	.	.	PUNCT
cana-1750	416	1	(	(	PUNCT
cana-1750	416	2	4.7	4.7	NUM
cana-1750	416	3	)	)	PUNCT
cana-1750	416	4	for	for	ADP
cana-1750	416	5	𝑝	𝑝	NOUN
cana-1750	416	6	=	=	SYM
cana-1750	416	7	2	2	NUM
cana-1750	416	8	,	,	PUNCT
cana-1750	416	9	we	we	PRON
cana-1750	416	10	owe	owe	VERB
cana-1750	416	11	¥	¥	NUM
cana-1750	416	12	(	(	PUNCT
cana-1750	416	13	2	2	NUM
cana-1750	416	14	,	,	PUNCT
cana-1750	416	15	|𝑥|	|𝑥|	ADJ
cana-1750	416	16	)	)	PUNCT
cana-1750	417	1	=	=	PUNCT
cana-1750	418	1	[	[	PUNCT
cana-1750	418	2	2(𝜆2	2(𝜆2	NUM
cana-1750	418	3	+	+	NOUN
cana-1750	418	4	1	1	NUM
cana-1750	418	5	)	)	PUNCT
cana-1750	418	6	(	(	PUNCT
cana-1750	418	7	𝜆	𝜆	PROPN
cana-1750	418	8	+	+	CCONJ
cana-1750	418	9	1)2(𝜆	1)2(𝜆	NUM
cana-1750	418	10	+	+	CCONJ
cana-1750	418	11	2	2	NUM
cana-1750	418	12	)	)	PUNCT
cana-1750	418	13	]	]	PUNCT
cana-1750	418	14	.	.	PUNCT
cana-1750	419	1	(	(	PUNCT
cana-1750	419	2	4.8	4.8	NUM
cana-1750	419	3	)	)	PUNCT
cana-1750	419	4	for	for	ADP
cana-1750	419	5	|𝑥|	|𝑥|	ADJ
cana-1750	419	6	=	=	SYM
cana-1750	419	7	0	0	NUM
cana-1750	419	8	,	,	PUNCT
cana-1750	419	9	we	we	PRON
cana-1750	419	10	receive	receive	VERB
cana-1750	419	11	¥	¥	PROPN
cana-1750	419	12	(	(	PUNCT
cana-1750	419	13	𝑝	𝑝	NOUN
cana-1750	419	14	,	,	PUNCT
cana-1750	419	15	0	0	NUM
cana-1750	419	16	)	)	PUNCT
cana-1750	419	17	=	=	NOUN
cana-1750	420	1	[	[	PUNCT
cana-1750	420	2	𝜆2	𝜆2	NOUN
cana-1750	420	3	+	+	CCONJ
cana-1750	420	4	1	1	NUM
cana-1750	420	5	2(𝜆	2(𝜆	NUM
cana-1750	420	6	+	+	CCONJ
cana-1750	420	7	1)2(𝜆	1)2(𝜆	NUM
cana-1750	420	8	+	+	CCONJ
cana-1750	420	9	2	2	NUM
cana-1750	420	10	)	)	PUNCT
cana-1750	420	11	]	]	PUNCT
cana-1750	420	12	𝑝2	𝑝2	NOUN
cana-1750	420	13	.	.	PUNCT
cana-1750	421	1	(	(	PUNCT
cana-1750	421	2	4.9	4.9	NUM
cana-1750	421	3	)	)	PUNCT
cana-1750	421	4	communications	communication	NOUN
cana-1750	421	5	on	on	ADP
cana-1750	421	6	applied	apply	VERB
cana-1750	421	7	nonlinear	nonlinear	ADJ
cana-1750	421	8	analysis	analysis	NOUN
cana-1750	421	9	issn	issn	NOUN
cana-1750	421	10	:	:	PUNCT
cana-1750	421	11	1074	1074	NUM
cana-1750	421	12	-	-	PUNCT
cana-1750	421	13	133x	133x	NUM
cana-1750	421	14	vol	vol	NOUN
cana-1750	421	15	32	32	NUM
cana-1750	421	16	no	no	NOUN
cana-1750	421	17	.	.	NOUN
cana-1750	421	18	2	2	NUM
cana-1750	421	19	(	(	PUNCT
cana-1750	421	20	2025	2025	NUM
cana-1750	421	21	)	)	PUNCT
cana-1750	421	22	397	397	NUM
cana-1750	421	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	421	24	which	which	PRON
cana-1750	421	25	has	have	VERB
cana-1750	421	26	maximum	maximum	ADJ
cana-1750	421	27	value	value	NOUN
cana-1750	421	28	|𝒯(𝜆)|	|𝒯(𝜆)|	ADP
cana-1750	421	29	(	(	PUNCT
cana-1750	421	30	𝜆+1)2(𝜆+2	𝜆+1)2(𝜆+2	PROPN
cana-1750	421	31	)	)	PUNCT
cana-1750	421	32	attained	attain	VERB
cana-1750	421	33	at	at	ADP
cana-1750	421	34	the	the	DET
cana-1750	421	35	end	end	NOUN
cana-1750	421	36	point	point	NOUN
cana-1750	421	37	𝑝	𝑝	NOUN
cana-1750	421	38	=	=	SYM
cana-1750	421	39	2	2	X
cana-1750	421	40	.	.	X
cana-1750	422	1	for	for	ADP
cana-1750	422	2	|𝑥|	|𝑥|	ADJ
cana-1750	422	3	=	=	SYM
cana-1750	422	4	1	1	NUM
cana-1750	422	5	,	,	PUNCT
cana-1750	422	6	we	we	PRON
cana-1750	422	7	obtained	obtain	VERB
cana-1750	422	8	¥	¥	PROPN
cana-1750	422	9	(	(	PUNCT
cana-1750	422	10	𝑝	𝑝	NOUN
cana-1750	422	11	,	,	PUNCT
cana-1750	422	12	1	1	NUM
cana-1750	422	13	)	)	PUNCT
cana-1750	422	14	=	=	NOUN
cana-1750	423	1	[	[	PUNCT
cana-1750	423	2	𝜆2	𝜆2	NOUN
cana-1750	423	3	+	+	CCONJ
cana-1750	423	4	1	1	NUM
cana-1750	423	5	2(𝜆	2(𝜆	NUM
cana-1750	423	6	+	+	CCONJ
cana-1750	423	7	1)2(𝜆	1)2(𝜆	NUM
cana-1750	423	8	+	+	CCONJ
cana-1750	423	9	2	2	NUM
cana-1750	423	10	)	)	PUNCT
cana-1750	423	11	]	]	PUNCT
cana-1750	423	12	𝑝2	𝑝2	NOUN
cana-1750	423	13	+	+	CCONJ
cana-1750	423	14	4	4	NUM
cana-1750	423	15	−	−	PROPN
cana-1750	423	16	𝑝2	𝑝2	NOUN
cana-1750	423	17	2(𝜆	2(𝜆	NUM
cana-1750	423	18	+	+	CCONJ
cana-1750	423	19	1	1	NUM
cana-1750	423	20	)	)	PUNCT
cana-1750	423	21	.	.	PUNCT
cana-1750	424	1	(	(	PUNCT
cana-1750	424	2	4.10	4.10	NUM
cana-1750	424	3	)	)	PUNCT
cana-1750	424	4	which	which	PRON
cana-1750	424	5	is	be	AUX
cana-1750	424	6	maximum	maximum	ADJ
cana-1750	424	7	value	value	NOUN
cana-1750	424	8	of	of	ADP
cana-1750	424	9	¥	¥	PROPN
cana-1750	424	10	(	(	PUNCT
cana-1750	424	11	𝑝	𝑝	NOUN
cana-1750	424	12	,	,	PUNCT
cana-1750	424	13	1	1	NUM
cana-1750	424	14	)	)	PUNCT
cana-1750	424	15	=	=	SYM
cana-1750	425	1	2	2	X
cana-1750	425	2	𝜆+1	𝜆+1	X
cana-1750	425	3	at	at	ADP
cana-1750	425	4	𝑝	𝑝	NOUN
cana-1750	425	5	=	=	SYM
cana-1750	425	6	0	0	NUM
cana-1750	425	7	and	and	CCONJ
cana-1750	425	8	|𝒯(𝜆)|	|𝒯(𝜆)|	ADV
cana-1750	425	9	(	(	PUNCT
cana-1750	425	10	𝜆+1)2(𝜆+2	𝜆+1)2(𝜆+2	NOUN
cana-1750	425	11	)	)	PUNCT
cana-1750	425	12	at	at	ADP
cana-1750	425	13	𝑝	𝑝	NOUN
cana-1750	425	14	=	=	SYM
cana-1750	425	15	2	2	NUM
cana-1750	425	16	.	.	PUNCT
cana-1750	425	17	hence	hence	ADV
cana-1750	425	18	|𝑎2	|𝑎2	NOUN
cana-1750	425	19	2	2	NUM
cana-1750	425	20	−	−	PROPN
cana-1750	425	21	𝑎3|	𝑎3|	NOUN
cana-1750	425	22	≤	≤	NUM
cana-1750	425	23	max	max	NOUN
cana-1750	425	24	{	{	PUNCT
cana-1750	425	25	2	2	NUM
cana-1750	425	26	4(𝜆	4(𝜆	NUM
cana-1750	425	27	+	+	CCONJ
cana-1750	425	28	2	2	NUM
cana-1750	425	29	)	)	PUNCT
cana-1750	425	30	,	,	PUNCT
cana-1750	425	31	|𝒯(𝜆)|	|𝒯(𝜆)|	PROPN
cana-1750	425	32	(	(	PUNCT
cana-1750	425	33	𝜆	𝜆	PROPN
cana-1750	425	34	+	+	CCONJ
cana-1750	425	35	1)2(𝜆	1)2(𝜆	NUM
cana-1750	425	36	+	+	CCONJ
cana-1750	425	37	2	2	NUM
cana-1750	425	38	)	)	PUNCT
cana-1750	425	39	}	}	PUNCT
cana-1750	425	40	(	(	PUNCT
cana-1750	425	41	4.11	4.11	NUM
cana-1750	425	42	)	)	PUNCT
cana-1750	425	43	where	where	SCONJ
cana-1750	425	44	𝒯(𝜆	𝒯(𝜆	X
cana-1750	425	45	)	)	PUNCT
cana-1750	425	46	=	=	SYM
cana-1750	426	1	2(𝜆2	2(𝜆2	NUM
cana-1750	426	2	+	+	CCONJ
cana-1750	426	3	1	1	NUM
cana-1750	426	4	)	)	PUNCT
cana-1750	426	5	(	(	PUNCT
cana-1750	426	6	4.12	4.12	NUM
cana-1750	426	7	)	)	PUNCT
cana-1750	426	8	theorem	theorem	VERB
cana-1750	426	9	4.2	4.2	NUM
cana-1750	426	10	.	.	PUNCT
cana-1750	427	1	let	let	VERB
cana-1750	427	2	𝑓	𝑓	PRON
cana-1750	427	3	given	give	VERB
cana-1750	427	4	by	by	ADP
cana-1750	427	5	(	(	PUNCT
cana-1750	427	6	1.1	1.1	NUM
cana-1750	427	7	)	)	PUNCT
cana-1750	427	8	,	,	PUNCT
cana-1750	427	9	be	be	AUX
cana-1750	427	10	in	in	ADP
cana-1750	427	11	the	the	DET
cana-1750	427	12	class	class	NOUN
cana-1750	427	13	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	427	14	)	)	PUNCT
cana-1750	427	15	;	;	PUNCT
cana-1750	427	16	(	(	PUNCT
cana-1750	427	17	0	0	NUM
cana-1750	427	18	≤	≤	NUM
cana-1750	427	19	𝜆	𝜆	PRON
cana-1750	427	20	≤	≤	NUM
cana-1750	427	21	1	1	NUM
cana-1750	427	22	)	)	PUNCT
cana-1750	427	23	.	.	PUNCT
cana-1750	428	1	then	then	ADV
cana-1750	428	2	we	we	PRON
cana-1750	428	3	have	have	AUX
cana-1750	428	4	sharp	sharp	ADV
cana-1750	428	5	bound	bind	VERB
cana-1750	428	6	|𝑎3	|𝑎3	VERB
cana-1750	428	7	2	2	NUM
cana-1750	428	8	−	−	NOUN
cana-1750	428	9	𝑎5|	𝑎5|	PROPN
cana-1750	428	10	≤	≤	NUM
cana-1750	428	11	max	max	NOUN
cana-1750	428	12	{	{	PUNCT
cana-1750	428	13	(	(	PUNCT
cana-1750	428	14	3	3	NUM
cana-1750	428	15	+	+	NUM
cana-1750	428	16	2𝜆)4	2𝜆)4	NUM
cana-1750	428	17	(	(	PUNCT
cana-1750	428	18	𝜆	𝜆	PROPN
cana-1750	428	19	+	+	ADJ
cana-1750	428	20	2)(𝜆	2)(𝜆	NUM
cana-1750	428	21	+	+	CCONJ
cana-1750	428	22	4	4	NUM
cana-1750	428	23	)	)	PUNCT
cana-1750	428	24	+	+	CCONJ
cana-1750	428	25	6	6	NUM
cana-1750	428	26	𝜆	𝜆	NOUN
cana-1750	428	27	+	+	NUM
cana-1750	428	28	4	4	NUM
cana-1750	428	29	,	,	PUNCT
cana-1750	428	30	|𝒢(𝜆)|	|𝒢(𝜆)|	PROPN
cana-1750	428	31	(	(	PUNCT
cana-1750	428	32	𝜆	𝜆	PROPN
cana-1750	428	33	+	+	CCONJ
cana-1750	428	34	1)2(𝜆	1)2(𝜆	NUM
cana-1750	428	35	+	+	CCONJ
cana-1750	428	36	2)2(𝜆	2)2(𝜆	NUM
cana-1750	428	37	+	+	CCONJ
cana-1750	428	38	3)(𝜆	3)(𝜆	NUM
cana-1750	428	39	+	+	NUM
cana-1750	428	40	4	4	NUM
cana-1750	428	41	)	)	PUNCT
cana-1750	428	42	}	}	PUNCT
cana-1750	428	43	where	where	SCONJ
cana-1750	428	44	,	,	PUNCT
cana-1750	428	45	𝒢(𝜆	𝒢(𝜆	PRON
cana-1750	428	46	)	)	PUNCT
cana-1750	428	47	=	=	SYM
cana-1750	428	48	2(𝜆5	2(𝜆5	NUM
cana-1750	429	1	−	−	NOUN
cana-1750	429	2	7𝜆4	7𝜆4	NUM
cana-1750	430	1	+	+	CCONJ
cana-1750	430	2	15𝜆3	15𝜆3	NUM
cana-1750	430	3	+	+	SYM
cana-1750	430	4	12𝜆2	12𝜆2	NUM
cana-1750	430	5	−	−	PROPN
cana-1750	430	6	104𝜆	104𝜆	NOUN
cana-1750	430	7	+	+	CCONJ
cana-1750	430	8	96	96	NUM
cana-1750	430	9	)	)	PUNCT
cana-1750	430	10	(	(	PUNCT
cana-1750	430	11	4.13	4.13	X
cana-1750	430	12	)	)	PUNCT
cana-1750	430	13	proof	proof	NOUN
cana-1750	430	14	.	.	PUNCT
cana-1750	431	1	first	first	ADV
cana-1750	431	2	note	note	VERB
cana-1750	431	3	that	that	SCONJ
cana-1750	431	4	by	by	ADP
cana-1750	431	5	equating	equate	VERB
cana-1750	431	6	the	the	DET
cana-1750	431	7	corresponding	corresponding	ADJ
cana-1750	431	8	coefficients	coefficient	NOUN
cana-1750	431	9	in	in	ADP
cana-1750	431	10	the	the	DET
cana-1750	431	11	equation	equation	NOUN
cana-1750	431	12	(	(	PUNCT
cana-1750	431	13	3.1	3.1	NUM
cana-1750	431	14	)	)	PUNCT
cana-1750	431	15	.	.	PUNCT
cana-1750	432	1	we	we	PRON
cana-1750	432	2	get	get	VERB
cana-1750	432	3	,	,	PUNCT
cana-1750	432	4	in	in	ADP
cana-1750	432	5	the	the	DET
cana-1750	432	6	view	view	NOUN
cana-1750	432	7	of	of	ADP
cana-1750	432	8	(	(	PUNCT
cana-1750	432	9	3.3	3.3	NUM
cana-1750	432	10	)	)	PUNCT
cana-1750	432	11	,	,	PUNCT
cana-1750	432	12	(	(	PUNCT
cana-1750	432	13	3.5	3.5	NUM
cana-1750	432	14	)	)	PUNCT
cana-1750	432	15	and	and	CCONJ
cana-1750	432	16	lemma	lemma	PROPN
cana-1750	432	17	(	(	PUNCT
cana-1750	432	18	2.2	2.2	NUM
cana-1750	432	19	)	)	PUNCT
cana-1750	432	20	,	,	PUNCT
cana-1750	432	21	we	we	PRON
cana-1750	432	22	may	may	AUX
cana-1750	432	23	write	write	VERB
cana-1750	432	24	2𝑝2	2𝑝2	NUM
cana-1750	432	25	=	=	SYM
cana-1750	432	26	𝑝1	𝑝1	NOUN
cana-1750	432	27	2	2	NUM
cana-1750	433	1	+	+	CCONJ
cana-1750	433	2	𝑥(4	𝑥(4	PROPN
cana-1750	433	3	−	−	PROPN
cana-1750	433	4	𝑝1	𝑝1	NOUN
cana-1750	433	5	2	2	NUM
cana-1750	433	6	)	)	PUNCT
cana-1750	433	7	,	,	PUNCT
cana-1750	433	8	𝑌	𝑌	PROPN
cana-1750	433	9	=	=	PUNCT
cana-1750	433	10	(	(	PUNCT
cana-1750	433	11	1	1	NUM
cana-1750	433	12	−	−	PROPN
cana-1750	433	13	|𝑥|2)𝜚	|𝑥|2)𝜚	PROPN
cana-1750	433	14	,	,	PUNCT
cana-1750	433	15	a	a	DET
cana-1750	433	16	simple	simple	ADJ
cana-1750	433	17	computation	computation	NOUN
cana-1750	433	18	leads	lead	VERB
cana-1750	433	19	to	to	ADP
cana-1750	433	20	𝑎3	𝑎3	PROPN
cana-1750	433	21	2	2	NUM
cana-1750	433	22	−	−	NOUN
cana-1750	433	23	𝑎5	𝑎5	PROPN
cana-1750	433	24	=	=	SYM
cana-1750	433	25	[	[	PUNCT
cana-1750	433	26	𝜆5	𝜆5	ADV
cana-1750	433	27	−	−	PROPN
cana-1750	433	28	7𝜆4	7𝜆4	NUM
cana-1750	434	1	+	+	CCONJ
cana-1750	434	2	15𝜆3	15𝜆3	NUM
cana-1750	434	3	+	+	SYM
cana-1750	434	4	12𝜆2	12𝜆2	NUM
cana-1750	434	5	−	−	PROPN
cana-1750	434	6	104𝜆	104𝜆	NOUN
cana-1750	434	7	+	+	CCONJ
cana-1750	434	8	96	96	NUM
cana-1750	434	9	8(𝜆	8(𝜆	NUM
cana-1750	434	10	+	+	CCONJ
cana-1750	434	11	1)2(𝜆	1)2(𝜆	NUM
cana-1750	435	1	+	+	NUM
cana-1750	435	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	436	1	+	+	CCONJ
cana-1750	436	2	3)(𝜆	3)(𝜆	NUM
cana-1750	436	3	+	+	NUM
cana-1750	436	4	4	4	NUM
cana-1750	436	5	)	)	PUNCT
cana-1750	436	6	]	]	PUNCT
cana-1750	436	7	𝑝1	𝑝1	NOUN
cana-1750	436	8	4	4	NUM
cana-1750	436	9	+	+	CCONJ
cana-1750	436	10	[	[	PUNCT
cana-1750	436	11	3	3	NUM
cana-1750	436	12	+	+	CCONJ
cana-1750	436	13	2𝜆	2𝜆	NUM
cana-1750	436	14	4(2	4(2	NUM
cana-1750	437	1	+	+	CCONJ
cana-1750	437	2	𝜆)(4	𝜆)(4	NUM
cana-1750	438	1	+	+	CCONJ
cana-1750	438	2	𝜆	𝜆	X
cana-1750	438	3	)	)	PUNCT
cana-1750	438	4	]	]	PUNCT
cana-1750	439	1	𝑥2𝑋2	𝑥2𝑋2	PUNCT
cana-1750	439	2	+	+	PUNCT
cana-1750	439	3	[	[	PUNCT
cana-1750	439	4	−𝜆2	−𝜆2	X
cana-1750	439	5	+	+	CCONJ
cana-1750	439	6	8𝜆	8𝜆	NUM
cana-1750	439	7	+	+	CCONJ
cana-1750	439	8	17	17	NUM
cana-1750	439	9	8(1	8(1	NOUN
cana-1750	439	10	+	+	CCONJ
cana-1750	439	11	𝜆)(3	𝜆)(3	X
cana-1750	439	12	+	+	CCONJ
cana-1750	439	13	𝜆)(4	𝜆)(4	PUNCT
cana-1750	440	1	+	+	CCONJ
cana-1750	440	2	𝜆	𝜆	X
cana-1750	440	3	)	)	PUNCT
cana-1750	440	4	]	]	PUNCT
cana-1750	440	5	𝑝1	𝑝1	NOUN
cana-1750	440	6	2𝑥2𝑋	2𝑥2𝑋	NUM
cana-1750	441	1	+	+	PUNCT
cana-1750	441	2	[	[	PUNCT
cana-1750	441	3	−7𝜆3	−7𝜆3	X
cana-1750	441	4	+	+	CCONJ
cana-1750	441	5	2𝜆2	2𝜆2	NUM
cana-1750	441	6	+	+	CCONJ
cana-1750	441	7	35𝜆	35𝜆	NOUN
cana-1750	441	8	+	+	CCONJ
cana-1750	441	9	58	58	NUM
cana-1750	441	10	8(1	8(1	NOUN
cana-1750	441	11	+	+	CCONJ
cana-1750	441	12	𝜆)(2	𝜆)(2	ADP
cana-1750	441	13	+	+	NOUN
cana-1750	441	14	𝜆)(3	𝜆)(3	NOUN
cana-1750	441	15	+	+	CCONJ
cana-1750	441	16	𝜆)(4	𝜆)(4	PUNCT
cana-1750	442	1	+	+	CCONJ
cana-1750	442	2	𝜆	𝜆	X
cana-1750	442	3	)	)	PUNCT
cana-1750	442	4	]	]	PUNCT
cana-1750	443	1	𝑝1	𝑝1	NOUN
cana-1750	443	2	2𝑥𝑋	2𝑥𝑋	PROPN
cana-1750	443	3	+	+	X
cana-1750	443	4	[	[	PUNCT
cana-1750	443	5	𝜆2	𝜆2	NOUN
cana-1750	443	6	−	−	PROPN
cana-1750	443	7	2𝜆	2𝜆	NUM
cana-1750	443	8	−	−	PROPN
cana-1750	443	9	7	7	NUM
cana-1750	443	10	2(𝜆	2(𝜆	NUM
cana-1750	443	11	+	+	CCONJ
cana-1750	443	12	1)(𝜆	1)(𝜆	NUM
cana-1750	444	1	+	+	CCONJ
cana-1750	444	2	3)(𝜆	3)(𝜆	NUM
cana-1750	444	3	+	+	NUM
cana-1750	444	4	4	4	NUM
cana-1750	444	5	)	)	PUNCT
cana-1750	444	6	]	]	PUNCT
cana-1750	444	7	𝑝1𝑋𝑌	𝑝1𝑋𝑌	VERB
cana-1750	444	8	−	−	PROPN
cana-1750	444	9	𝑝1	𝑝1	NOUN
cana-1750	444	10	2𝑥3𝑋	2𝑥3𝑋	PROPN
cana-1750	444	11	8(𝜆	8(𝜆	NUM
cana-1750	444	12	+	+	CCONJ
cana-1750	444	13	4	4	NUM
cana-1750	444	14	)	)	PUNCT
cana-1750	444	15	−	−	PROPN
cana-1750	444	16	𝑥2𝑋	𝑥2𝑋	SYM
cana-1750	444	17	2(𝜆	2(𝜆	NUM
cana-1750	444	18	+	+	CCONJ
cana-1750	444	19	4	4	NUM
cana-1750	444	20	)	)	PUNCT
cana-1750	444	21	+	+	CCONJ
cana-1750	444	22	𝑥𝑋𝑌𝑝1	𝑥𝑋𝑌𝑝1	ADP
cana-1750	444	23	2(𝜆	2(𝜆	NUM
cana-1750	444	24	+	+	CCONJ
cana-1750	444	25	4	4	NUM
cana-1750	444	26	)	)	PUNCT
cana-1750	444	27	+	+	CCONJ
cana-1750	444	28	𝑋𝑌𝑥‾	𝑋𝑌𝑥‾	NOUN
cana-1750	444	29	2(𝜆	2(𝜆	NUM
cana-1750	444	30	+	+	CCONJ
cana-1750	444	31	4	4	NUM
cana-1750	444	32	)	)	PUNCT
cana-1750	444	33	.	.	PUNCT
cana-1750	445	1	without	without	ADP
cana-1750	445	2	loss	loss	NOUN
cana-1750	445	3	of	of	ADP
cana-1750	445	4	generality	generality	NOUN
cana-1750	445	5	,	,	PUNCT
cana-1750	445	6	we	we	PRON
cana-1750	445	7	let	let	VERB
cana-1750	445	8	0	0	NUM
cana-1750	445	9	≤	≤	NOUN
cana-1750	445	10	𝑝1	𝑝1	NOUN
cana-1750	445	11	=	=	SYM
cana-1750	445	12	𝑝	𝑝	NOUN
cana-1750	445	13	≤	≤	NUM
cana-1750	445	14	2	2	NUM
cana-1750	445	15	.	.	PUNCT
cana-1750	445	16	substitute	substitute	VERB
cana-1750	445	17	this	this	PRON
cana-1750	445	18	into	into	ADP
cana-1750	445	19	the	the	DET
cana-1750	445	20	above	above	ADJ
cana-1750	445	21	equation	equation	NOUN
cana-1750	445	22	,	,	PUNCT
cana-1750	445	23	we	we	PRON
cana-1750	445	24	obtain	obtain	VERB
cana-1750	445	25	the	the	DET
cana-1750	445	26	following	follow	VERB
cana-1750	445	27	quadratic	quadratic	ADJ
cana-1750	445	28	equation	equation	NOUN
cana-1750	445	29	in	in	ADP
cana-1750	445	30	terms	term	NOUN
cana-1750	445	31	of	of	ADP
cana-1750	445	32	𝑥.	𝑥.	ADJ
cana-1750	445	33	communications	communication	NOUN
cana-1750	445	34	on	on	ADP
cana-1750	445	35	applied	apply	VERB
cana-1750	445	36	nonlinear	nonlinear	ADJ
cana-1750	445	37	analysis	analysis	NOUN
cana-1750	445	38	issn	issn	NOUN
cana-1750	445	39	:	:	PUNCT
cana-1750	445	40	1074	1074	NUM
cana-1750	445	41	-	-	PUNCT
cana-1750	445	42	133x	133x	NUM
cana-1750	445	43	vol	vol	NOUN
cana-1750	445	44	32	32	NUM
cana-1750	445	45	no	no	NOUN
cana-1750	445	46	.	.	NOUN
cana-1750	445	47	2	2	NUM
cana-1750	445	48	(	(	PUNCT
cana-1750	445	49	2025	2025	NUM
cana-1750	445	50	)	)	PUNCT
cana-1750	445	51	398	398	NUM
cana-1750	445	52	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	445	53	|𝑎3	|𝑎3	VERB
cana-1750	445	54	2	2	NUM
cana-1750	445	55	−	−	NOUN
cana-1750	445	56	𝑎5|	𝑎5|	PROPN
cana-1750	445	57	≤	≤	NOUN
cana-1750	445	58	[	[	PUNCT
cana-1750	445	59	𝑝2(4	𝑝2(4	NOUN
cana-1750	445	60	−	−	PROPN
cana-1750	445	61	𝑝2	𝑝2	NOUN
cana-1750	445	62	)	)	PUNCT
cana-1750	445	63	8(𝜆	8(𝜆	NUM
cana-1750	446	1	+	+	CCONJ
cana-1750	446	2	4	4	NUM
cana-1750	446	3	)	)	PUNCT
cana-1750	446	4	−	−	PROPN
cana-1750	446	5	𝑝(4	𝑝(4	PROPN
cana-1750	446	6	−	−	PROPN
cana-1750	446	7	𝑝2	𝑝2	NOUN
cana-1750	446	8	)	)	PUNCT
cana-1750	446	9	2(𝜆	2(𝜆	NUM
cana-1750	447	1	+	+	CCONJ
cana-1750	447	2	4	4	NUM
cana-1750	447	3	)	)	PUNCT
cana-1750	447	4	]	]	PUNCT
cana-1750	448	1	|𝑥|3	|𝑥|3	PROPN
cana-1750	448	2	+	+	CCONJ
cana-1750	448	3	[	[	PUNCT
cana-1750	448	4	(	(	PUNCT
cana-1750	448	5	3	3	NUM
cana-1750	448	6	+	+	SYM
cana-1750	448	7	2𝜆)(4	2𝜆)(4	NUM
cana-1750	448	8	−	−	NOUN
cana-1750	448	9	𝑝2)2	𝑝2)2	NUM
cana-1750	448	10	4(2	4(2	NUM
cana-1750	448	11	+	+	CCONJ
cana-1750	448	12	𝜆)(4	𝜆)(4	NUM
cana-1750	449	1	+	+	CCONJ
cana-1750	449	2	𝜆	𝜆	X
cana-1750	449	3	)	)	PUNCT
cana-1750	449	4	+	+	CCONJ
cana-1750	449	5	(	(	PUNCT
cana-1750	449	6	−𝜆2	−𝜆2	X
cana-1750	449	7	+	+	CCONJ
cana-1750	449	8	8𝜆	8𝜆	NUM
cana-1750	449	9	+	+	CCONJ
cana-1750	449	10	17)(4	17)(4	NUM
cana-1750	449	11	−	−	NOUN
cana-1750	449	12	𝑝2)𝑝2	𝑝2)𝑝2	PROPN
cana-1750	449	13	8(1	8(1	NOUN
cana-1750	449	14	+	+	CCONJ
cana-1750	449	15	𝜆)(𝜆	𝜆)(𝜆	NOUN
cana-1750	450	1	+	+	CCONJ
cana-1750	450	2	3)(𝜆	3)(𝜆	NUM
cana-1750	450	3	+	+	NUM
cana-1750	450	4	4	4	NUM
cana-1750	450	5	)	)	PUNCT
cana-1750	450	6	−	−	PROPN
cana-1750	450	7	(	(	PUNCT
cana-1750	450	8	4	4	NUM
cana-1750	450	9	−	−	NOUN
cana-1750	450	10	𝑝2)𝑥‾	𝑝2)𝑥‾	PROPN
cana-1750	450	11	2(𝜆	2(𝜆	NUM
cana-1750	450	12	+	+	CCONJ
cana-1750	450	13	4	4	NUM
cana-1750	450	14	)	)	PUNCT
cana-1750	450	15	]	]	PUNCT
cana-1750	451	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	451	2	+	+	PUNCT
cana-1750	451	3	[	[	PUNCT
cana-1750	451	4	(	(	PUNCT
cana-1750	451	5	4	4	NUM
cana-1750	451	6	−	−	PROPN
cana-1750	451	7	𝑝2	𝑝2	NOUN
cana-1750	451	8	)	)	PUNCT
cana-1750	451	9	2(𝜆	2(𝜆	NUM
cana-1750	451	10	+	+	CCONJ
cana-1750	451	11	4	4	NUM
cana-1750	451	12	)	)	PUNCT
cana-1750	451	13	−	−	PROPN
cana-1750	451	14	(	(	PUNCT
cana-1750	451	15	𝜆2	𝜆2	NOUN
cana-1750	451	16	−	−	PROPN
cana-1750	451	17	2𝜆	2𝜆	NUM
cana-1750	451	18	−	−	PROPN
cana-1750	451	19	7)𝑝(4	7)𝑝(4	CCONJ
cana-1750	451	20	−	−	PROPN
cana-1750	451	21	𝑝2	𝑝2	NOUN
cana-1750	451	22	)	)	PUNCT
cana-1750	451	23	2(𝜆	2(𝜆	NUM
cana-1750	452	1	+	+	CCONJ
cana-1750	452	2	1)(𝜆	1)(𝜆	NUM
cana-1750	453	1	+	+	CCONJ
cana-1750	453	2	3)(𝜆	3)(𝜆	NUM
cana-1750	453	3	+	+	NUM
cana-1750	453	4	4	4	NUM
cana-1750	453	5	)	)	PUNCT
cana-1750	453	6	]	]	PUNCT
cana-1750	454	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	454	2	+	+	PUNCT
cana-1750	455	1	[	[	X
cana-1750	455	2	[	[	PUNCT
cana-1750	455	3	−7𝜆3	−7𝜆3	X
cana-1750	455	4	+	+	CCONJ
cana-1750	455	5	2𝜆2	2𝜆2	NUM
cana-1750	455	6	+	+	CCONJ
cana-1750	455	7	35𝜆	35𝜆	NOUN
cana-1750	455	8	+	+	CCONJ
cana-1750	455	9	58	58	NUM
cana-1750	455	10	8(𝜆	8(𝜆	NUM
cana-1750	455	11	+	+	SYM
cana-1750	455	12	1)(𝜆	1)(𝜆	NUM
cana-1750	455	13	+	+	NUM
cana-1750	455	14	2)(𝜆	2)(𝜆	NUM
cana-1750	455	15	+	+	CCONJ
cana-1750	455	16	3)(𝜆	3)(𝜆	NUM
cana-1750	455	17	+	+	NUM
cana-1750	455	18	4	4	NUM
cana-1750	455	19	)	)	PUNCT
cana-1750	455	20	]	]	PUNCT
cana-1750	456	1	𝑝2(4	𝑝2(4	PROPN
cana-1750	456	2	−	−	PROPN
cana-1750	456	3	𝑝2	𝑝2	PROPN
cana-1750	456	4	)	)	PUNCT
cana-1750	457	1	+	+	CCONJ
cana-1750	457	2	𝑝(4	𝑝(4	PROPN
cana-1750	457	3	−	−	PROPN
cana-1750	457	4	𝑝2	𝑝2	NOUN
cana-1750	457	5	)	)	PUNCT
cana-1750	457	6	2(𝜆	2(𝜆	NUM
cana-1750	458	1	+	+	CCONJ
cana-1750	459	1	4	4	NUM
cana-1750	459	2	)	)	PUNCT
cana-1750	459	3	]	]	PUNCT
cana-1750	460	1	|𝑥|	|𝑥|	INTJ
cana-1750	461	1	+	+	PUNCT
cana-1750	461	2	[	[	PUNCT
cana-1750	461	3	𝜆5	𝜆5	ADV
cana-1750	461	4	−	−	NOUN
cana-1750	461	5	7𝜆4	7𝜆4	NUM
cana-1750	462	1	+	+	CCONJ
cana-1750	462	2	15𝜆3	15𝜆3	NUM
cana-1750	462	3	+	+	SYM
cana-1750	462	4	12𝜆2	12𝜆2	NUM
cana-1750	462	5	−	−	PROPN
cana-1750	462	6	104𝜆	104𝜆	NOUN
cana-1750	462	7	+	+	CCONJ
cana-1750	462	8	96	96	NUM
cana-1750	462	9	8(𝜆	8(𝜆	NUM
cana-1750	462	10	+	+	CCONJ
cana-1750	462	11	1)2(𝜆	1)2(𝜆	NUM
cana-1750	463	1	+	+	NUM
cana-1750	463	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	464	1	+	+	CCONJ
cana-1750	464	2	3)(𝜆	3)(𝜆	NUM
cana-1750	464	3	+	+	NUM
cana-1750	464	4	4	4	NUM
cana-1750	464	5	)	)	PUNCT
cana-1750	464	6	]	]	PUNCT
cana-1750	465	1	𝑝4	𝑝4	NOUN
cana-1750	465	2	+	+	CCONJ
cana-1750	465	3	[	[	PUNCT
cana-1750	465	4	𝜆2	𝜆2	NOUN
cana-1750	465	5	−	−	PROPN
cana-1750	465	6	2𝜆	2𝜆	NUM
cana-1750	465	7	−	−	PROPN
cana-1750	465	8	7	7	NUM
cana-1750	465	9	2(𝜆	2(𝜆	NUM
cana-1750	465	10	+	+	CCONJ
cana-1750	465	11	1)(𝜆	1)(𝜆	NUM
cana-1750	465	12	+	+	CCONJ
cana-1750	465	13	3)(𝜆	3)(𝜆	NUM
cana-1750	465	14	+	+	NUM
cana-1750	465	15	4	4	NUM
cana-1750	465	16	)	)	PUNCT
cana-1750	465	17	]	]	PUNCT
cana-1750	466	1	𝑝(4	𝑝(4	PROPN
cana-1750	466	2	−	−	PROPN
cana-1750	466	3	𝑝2	𝑝2	NOUN
cana-1750	466	4	)	)	PUNCT
cana-1750	467	1	+	+	CCONJ
cana-1750	467	2	(	(	PUNCT
cana-1750	467	3	4	4	NUM
cana-1750	467	4	−	−	NOUN
cana-1750	467	5	𝑝2)𝑥‾	𝑝2)𝑥‾	PROPN
cana-1750	467	6	2(𝜆	2(𝜆	NUM
cana-1750	467	7	+	+	CCONJ
cana-1750	467	8	4	4	NUM
cana-1750	467	9	)	)	PUNCT
cana-1750	467	10	.	.	PUNCT
cana-1750	468	1	=	=	PUNCT
cana-1750	468	2	𝐶(𝑝	𝐶(𝑝	PRON
cana-1750	468	3	,	,	PUNCT
cana-1750	468	4	|𝑥|	|𝑥|	NUM
cana-1750	468	5	)	)	PUNCT
cana-1750	468	6	.	.	PUNCT
cana-1750	469	1	we	we	PRON
cana-1750	469	2	want	want	VERB
cana-1750	469	3	to	to	PART
cana-1750	469	4	prove	prove	VERB
cana-1750	469	5	that	that	SCONJ
cana-1750	469	6	the	the	DET
cana-1750	469	7	maximum	maximum	ADJ
cana-1750	469	8	value	value	NOUN
cana-1750	469	9	of	of	ADP
cana-1750	469	10	𝐶(𝑝	𝐶(𝑝	PRON
cana-1750	469	11	,	,	PUNCT
cana-1750	469	12	|𝑥|	|𝑥|	ADJ
cana-1750	469	13	)	)	PUNCT
cana-1750	469	14	on	on	ADP
cana-1750	469	15	[	[	X
cana-1750	469	16	0,2	0,2	NUM
cana-1750	469	17	]	]	X
cana-1750	469	18	×	×	NOUN
cana-1750	470	1	[	[	X
cana-1750	470	2	0,1	0,1	NUM
cana-1750	470	3	]	]	PUNCT
cana-1750	470	4	.	.	PUNCT
cana-1750	471	1	first	first	ADV
cana-1750	471	2	,	,	PUNCT
cana-1750	471	3	assume	assume	VERB
cana-1750	471	4	that	that	SCONJ
cana-1750	471	5	there	there	PRON
cana-1750	471	6	is	be	VERB
cana-1750	471	7	a	a	DET
cana-1750	471	8	maximum	maximum	NOUN
cana-1750	471	9	at	at	ADP
cana-1750	471	10	an	an	DET
cana-1750	471	11	interior	interior	ADJ
cana-1750	471	12	point	point	NOUN
cana-1750	471	13	𝐶(𝑝0	𝐶(𝑝0	PROPN
cana-1750	471	14	,	,	PUNCT
cana-1750	471	15	|𝑥0|	|𝑥0|	X
cana-1750	471	16	)	)	PUNCT
cana-1750	471	17	of	of	ADP
cana-1750	471	18	[	[	X
cana-1750	471	19	0,2	0,2	NUM
cana-1750	471	20	]	]	X
cana-1750	471	21	×	×	NOUN
cana-1750	472	1	[	[	X
cana-1750	472	2	0,1	0,1	NUM
cana-1750	472	3	]	]	PUNCT
cana-1750	472	4	.	.	PUNCT
cana-1750	473	1	differentiating	differentiate	VERB
cana-1750	473	2	𝐶(𝑝	𝐶(𝑝	NOUN
cana-1750	473	3	,	,	PUNCT
cana-1750	473	4	|𝑥|	|𝑥|	PROPN
cana-1750	473	5	)	)	PUNCT
cana-1750	473	6	with	with	ADP
cana-1750	473	7	respect	respect	NOUN
cana-1750	473	8	to	to	ADP
cana-1750	473	9	|𝑥|	|𝑥|	VERB
cana-1750	473	10	and	and	CCONJ
cana-1750	473	11	equating	equate	VERB
cana-1750	473	12	it	it	PRON
cana-1750	473	13	to	to	ADP
cana-1750	473	14	0	0	NUM
cana-1750	473	15	implies	imply	VERB
cana-1750	473	16	that	that	SCONJ
cana-1750	473	17	𝑝	𝑝	X
cana-1750	473	18	=	=	SYM
cana-1750	473	19	𝑝0	𝑝0	NOUN
cana-1750	473	20	=	=	SYM
cana-1750	473	21	2	2	NUM
cana-1750	473	22	which	which	PRON
cana-1750	473	23	is	be	AUX
cana-1750	473	24	contradiction	contradiction	NOUN
cana-1750	473	25	.	.	PUNCT
cana-1750	474	1	thus	thus	ADV
cana-1750	474	2	for	for	ADP
cana-1750	474	3	the	the	DET
cana-1750	474	4	maximum	maximum	NOUN
cana-1750	474	5	of	of	ADP
cana-1750	474	6	𝐶(𝑝	𝐶(𝑝	PRON
cana-1750	474	7	,	,	PUNCT
cana-1750	474	8	|𝑥|	|𝑥|	ADJ
cana-1750	474	9	)	)	PUNCT
cana-1750	474	10	,	,	PUNCT
cana-1750	474	11	we	we	PRON
cana-1750	474	12	need	need	VERB
cana-1750	474	13	to	to	PART
cana-1750	474	14	consider	consider	VERB
cana-1750	474	15	the	the	DET
cana-1750	474	16	end	end	NOUN
cana-1750	474	17	points	point	NOUN
cana-1750	474	18	of	of	ADP
cana-1750	474	19	[	[	X
cana-1750	474	20	0,2	0,2	NUM
cana-1750	474	21	]	]	X
cana-1750	474	22	×	×	NOUN
cana-1750	475	1	[	[	X
cana-1750	475	2	0,1	0,1	NUM
cana-1750	475	3	]	]	PUNCT
cana-1750	475	4	.	.	PUNCT
cana-1750	476	1	for	for	ADP
cana-1750	476	2	𝑝	𝑝	NOUN
cana-1750	476	3	=	=	SYM
cana-1750	476	4	0	0	NUM
cana-1750	476	5	,	,	PUNCT
cana-1750	476	6	we	we	PRON
cana-1750	476	7	obtain	obtain	VERB
cana-1750	476	8	𝐶(0	𝐶(0	ADP
cana-1750	476	9	,	,	PUNCT
cana-1750	476	10	|𝑥|	|𝑥|	ADJ
cana-1750	476	11	)	)	PUNCT
cana-1750	477	1	=	=	PUNCT
cana-1750	477	2	[	[	PUNCT
cana-1750	477	3	(	(	PUNCT
cana-1750	477	4	3	3	NUM
cana-1750	477	5	+	+	NUM
cana-1750	477	6	2𝜆)4	2𝜆)4	NUM
cana-1750	477	7	(	(	PUNCT
cana-1750	477	8	𝜆	𝜆	PROPN
cana-1750	477	9	+	+	ADJ
cana-1750	477	10	2)(𝜆	2)(𝜆	NUM
cana-1750	477	11	+	+	CCONJ
cana-1750	477	12	4	4	NUM
cana-1750	477	13	)	)	PUNCT
cana-1750	477	14	−	−	PROPN
cana-1750	477	15	2	2	NUM
cana-1750	477	16	(	(	PUNCT
cana-1750	477	17	𝜆	𝜆	NOUN
cana-1750	477	18	+	+	NOUN
cana-1750	477	19	4	4	NUM
cana-1750	477	20	)	)	PUNCT
cana-1750	477	21	𝑥‾	𝑥‾	X
cana-1750	477	22	]	]	X
cana-1750	477	23	|𝑥|2	|𝑥|2	ADJ
cana-1750	477	24	+	+	PUNCT
cana-1750	477	25	[	[	PUNCT
cana-1750	477	26	4	4	NUM
cana-1750	477	27	2(𝜆	2(𝜆	NUM
cana-1750	477	28	+	+	CCONJ
cana-1750	477	29	4	4	NUM
cana-1750	477	30	)	)	PUNCT
cana-1750	477	31	]	]	PUNCT
cana-1750	478	1	|	|	X
cana-1750	478	2	𝑥|2	𝑥|2	PROPN
cana-1750	478	3	+	+	NUM
cana-1750	478	4	4	4	NUM
cana-1750	478	5	2(4	2(4	NUM
cana-1750	478	6	+	+	CCONJ
cana-1750	478	7	𝑥	𝑥	X
cana-1750	478	8	)	)	PUNCT
cana-1750	478	9	𝑥‾	𝑥‾	DET
cana-1750	478	10	≤	≤	NOUN
cana-1750	478	11	(	(	PUNCT
cana-1750	478	12	3	3	NUM
cana-1750	478	13	+	+	NUM
cana-1750	478	14	2𝜆)4	2𝜆)4	NUM
cana-1750	478	15	(	(	PUNCT
cana-1750	478	16	𝜆	𝜆	PROPN
cana-1750	478	17	+	+	ADJ
cana-1750	478	18	2)(𝜆	2)(𝜆	NUM
cana-1750	478	19	+	+	CCONJ
cana-1750	478	20	4	4	NUM
cana-1750	478	21	)	)	PUNCT
cana-1750	478	22	+	+	CCONJ
cana-1750	478	23	6	6	NUM
cana-1750	478	24	(	(	PUNCT
cana-1750	478	25	𝜆	𝜆	NOUN
cana-1750	478	26	+	+	NOUN
cana-1750	478	27	4	4	NUM
cana-1750	478	28	)	)	PUNCT
cana-1750	478	29	(	(	PUNCT
cana-1750	478	30	4.14	4.14	NUM
cana-1750	478	31	)	)	PUNCT
cana-1750	478	32	for	for	ADP
cana-1750	478	33	𝑝	𝑝	NOUN
cana-1750	478	34	=	=	SYM
cana-1750	478	35	2	2	NUM
cana-1750	478	36	,	,	PUNCT
cana-1750	478	37	we	we	PRON
cana-1750	478	38	acquire	acquire	VERB
cana-1750	478	39	𝐶(2	𝐶(2	VERB
cana-1750	478	40	,	,	PUNCT
cana-1750	478	41	|𝑥|	|𝑥|	ADJ
cana-1750	478	42	)	)	PUNCT
cana-1750	479	1	=	=	SYM
cana-1750	480	1	|𝒢(𝜆)|	|𝒢(𝜆)|	PROPN
cana-1750	480	2	(	(	PUNCT
cana-1750	480	3	𝜆	𝜆	PROPN
cana-1750	480	4	+	+	CCONJ
cana-1750	480	5	1)2(𝜆	1)2(𝜆	NUM
cana-1750	480	6	+	+	CCONJ
cana-1750	480	7	2)2(𝜆	2)2(𝜆	NUM
cana-1750	481	1	+	+	CCONJ
cana-1750	481	2	3)(𝜆	3)(𝜆	NUM
cana-1750	481	3	+	+	NUM
cana-1750	481	4	4	4	NUM
cana-1750	481	5	)	)	PUNCT
cana-1750	481	6	(	(	PUNCT
cana-1750	481	7	4.15	4.15	NUM
cana-1750	481	8	)	)	PUNCT
cana-1750	482	1	where	where	SCONJ
cana-1750	482	2	,	,	PUNCT
cana-1750	482	3	𝒢(𝜆	𝒢(𝜆	PRON
cana-1750	482	4	)	)	PUNCT
cana-1750	482	5	=	=	SYM
cana-1750	482	6	2(𝜆5	2(𝜆5	NUM
cana-1750	482	7	−	−	NOUN
cana-1750	482	8	7𝜆4	7𝜆4	NUM
cana-1750	483	1	+	+	CCONJ
cana-1750	483	2	15𝜆3	15𝜆3	NUM
cana-1750	483	3	+	+	SYM
cana-1750	483	4	12𝜆2	12𝜆2	NUM
cana-1750	483	5	−	−	PROPN
cana-1750	483	6	104𝜆	104𝜆	NOUN
cana-1750	483	7	+	+	CCONJ
cana-1750	483	8	96	96	NUM
cana-1750	483	9	)	)	PUNCT
cana-1750	483	10	(	(	PUNCT
cana-1750	483	11	4.16	4.16	NUM
cana-1750	483	12	)	)	PUNCT
cana-1750	483	13	for	for	ADP
cana-1750	483	14	|𝑥|	|𝑥|	ADJ
cana-1750	483	15	=	=	SYM
cana-1750	483	16	0	0	NUM
cana-1750	483	17	,	,	PUNCT
cana-1750	483	18	we	we	PRON
cana-1750	483	19	attained	attain	VERB
cana-1750	483	20	𝐶(𝑝	𝐶(𝑝	NOUN
cana-1750	483	21	,	,	PUNCT
cana-1750	483	22	0	0	NUM
cana-1750	483	23	)	)	PUNCT
cana-1750	483	24	=	=	NOUN
cana-1750	484	1	[	[	PUNCT
cana-1750	484	2	𝜆5−7𝜆4	𝜆5−7𝜆4	ADJ
cana-1750	484	3	+	+	ADJ
cana-1750	484	4	15𝜆3	15𝜆3	NUM
cana-1750	484	5	+	+	SYM
cana-1750	484	6	12𝜆2−104𝜆+96	12𝜆2−104𝜆+96	ADJ
cana-1750	484	7	(	(	PUNCT
cana-1750	484	8	𝜆+1)2(𝜆+2)2(𝜆+3)(𝜆+4	𝜆+1)2(𝜆+2)2(𝜆+3)(𝜆+4	NOUN
cana-1750	484	9	)	)	PUNCT
cana-1750	484	10	]	]	PUNCT
cana-1750	485	1	𝑝4	𝑝4	NOUN
cana-1750	486	1	+	+	PROPN
cana-1750	486	2	[	[	X
cana-1750	486	3	−𝜆2−2𝜆−7	−𝜆2−2𝜆−7	NOUN
cana-1750	486	4	2(𝜆+1)(𝜆+3)(𝜆+4	2(𝜆+1)(𝜆+3)(𝜆+4	NUM
cana-1750	486	5	)	)	PUNCT
cana-1750	486	6	]	]	PUNCT
cana-1750	487	1	𝑝(4	𝑝(4	PROPN
cana-1750	487	2	−	−	PROPN
cana-1750	487	3	𝑝2	𝑝2	NOUN
cana-1750	487	4	)	)	PUNCT
cana-1750	487	5	.	.	PUNCT
cana-1750	488	1	(	(	PUNCT
cana-1750	488	2	4.17	4.17	NUM
cana-1750	488	3	)	)	PUNCT
cana-1750	488	4	for	for	ADP
cana-1750	488	5	|𝑥|	|𝑥|	ADJ
cana-1750	488	6	=	=	SYM
cana-1750	488	7	1	1	NUM
cana-1750	488	8	,	,	PUNCT
cana-1750	488	9	we	we	PRON
cana-1750	488	10	have	have	VERB
cana-1750	488	11	communications	communication	NOUN
cana-1750	488	12	on	on	ADP
cana-1750	488	13	applied	apply	VERB
cana-1750	488	14	nonlinear	nonlinear	ADJ
cana-1750	488	15	analysis	analysis	NOUN
cana-1750	488	16	issn	issn	NOUN
cana-1750	488	17	:	:	PUNCT
cana-1750	488	18	1074	1074	NUM
cana-1750	488	19	-	-	PUNCT
cana-1750	488	20	133x	133x	NUM
cana-1750	488	21	vol	vol	NOUN
cana-1750	488	22	32	32	NUM
cana-1750	489	1	no	no	NOUN
cana-1750	489	2	.	.	NOUN
cana-1750	489	3	2	2	NUM
cana-1750	489	4	(	(	PUNCT
cana-1750	489	5	2025	2025	NUM
cana-1750	489	6	)	)	PUNCT
cana-1750	489	7	399	399	NUM
cana-1750	489	8	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	489	9	𝐶(𝑝	𝐶(𝑝	NOUN
cana-1750	489	10	,	,	PUNCT
cana-1750	489	11	1	1	NUM
cana-1750	489	12	)	)	PUNCT
cana-1750	489	13	=	=	NOUN
cana-1750	490	1	[	[	PUNCT
cana-1750	490	2	𝑝2(4	𝑝2(4	PROPN
cana-1750	490	3	−	−	PROPN
cana-1750	490	4	𝑝2	𝑝2	NOUN
cana-1750	490	5	)	)	PUNCT
cana-1750	490	6	8(𝜆	8(𝜆	NUM
cana-1750	491	1	+	+	CCONJ
cana-1750	491	2	4	4	NUM
cana-1750	491	3	)	)	PUNCT
cana-1750	491	4	−	−	PROPN
cana-1750	491	5	𝑝(4	𝑝(4	PROPN
cana-1750	491	6	−	−	PROPN
cana-1750	491	7	𝑝2	𝑝2	NOUN
cana-1750	491	8	)	)	PUNCT
cana-1750	491	9	2(𝜆	2(𝜆	NUM
cana-1750	492	1	+	+	CCONJ
cana-1750	493	1	4	4	NUM
cana-1750	493	2	)	)	PUNCT
cana-1750	493	3	]	]	PUNCT
cana-1750	494	1	+	+	CCONJ
cana-1750	494	2	[	[	PUNCT
cana-1750	494	3	(	(	PUNCT
cana-1750	494	4	3	3	NUM
cana-1750	494	5	+	+	SYM
cana-1750	494	6	2𝜆)(4	2𝜆)(4	NUM
cana-1750	494	7	−	−	NOUN
cana-1750	494	8	𝑝2)2	𝑝2)2	NUM
cana-1750	494	9	4(2	4(2	NUM
cana-1750	494	10	+	+	CCONJ
cana-1750	494	11	𝜆)(4	𝜆)(4	NUM
cana-1750	495	1	+	+	CCONJ
cana-1750	495	2	𝜆	𝜆	X
cana-1750	495	3	)	)	PUNCT
cana-1750	495	4	+	+	CCONJ
cana-1750	495	5	(	(	PUNCT
cana-1750	495	6	−𝜆2	−𝜆2	X
cana-1750	495	7	+	+	CCONJ
cana-1750	495	8	8𝜆	8𝜆	NUM
cana-1750	495	9	+	+	CCONJ
cana-1750	495	10	17)(4	17)(4	NUM
cana-1750	495	11	−	−	NOUN
cana-1750	495	12	𝑝2)𝑝2	𝑝2)𝑝2	PROPN
cana-1750	495	13	8(1	8(1	NOUN
cana-1750	495	14	+	+	CCONJ
cana-1750	495	15	𝜆)(𝜆	𝜆)(𝜆	NOUN
cana-1750	496	1	+	+	CCONJ
cana-1750	496	2	3)(𝜆	3)(𝜆	NUM
cana-1750	496	3	+	+	NUM
cana-1750	496	4	4	4	NUM
cana-1750	496	5	)	)	PUNCT
cana-1750	496	6	−	−	PROPN
cana-1750	496	7	(	(	PUNCT
cana-1750	496	8	4	4	NUM
cana-1750	496	9	−	−	NOUN
cana-1750	496	10	𝑝2)𝑥‾	𝑝2)𝑥‾	PROPN
cana-1750	496	11	2(𝜆	2(𝜆	NUM
cana-1750	496	12	+	+	CCONJ
cana-1750	496	13	4	4	NUM
cana-1750	496	14	)	)	PUNCT
cana-1750	496	15	]	]	PUNCT
cana-1750	497	1	+	+	CCONJ
cana-1750	497	2	[	[	PUNCT
cana-1750	497	3	(	(	PUNCT
cana-1750	497	4	4	4	NUM
cana-1750	497	5	−	−	PROPN
cana-1750	497	6	𝑝2	𝑝2	NOUN
cana-1750	497	7	)	)	PUNCT
cana-1750	497	8	2(𝜆	2(𝜆	NUM
cana-1750	498	1	+	+	CCONJ
cana-1750	498	2	4	4	NUM
cana-1750	498	3	)	)	PUNCT
cana-1750	498	4	−	−	PROPN
cana-1750	499	1	(	(	PUNCT
cana-1750	499	2	𝜆2	𝜆2	NOUN
cana-1750	499	3	−	−	PROPN
cana-1750	499	4	2𝜆	2𝜆	NUM
cana-1750	499	5	−	−	PROPN
cana-1750	499	6	7)𝑝(4	7)𝑝(4	CCONJ
cana-1750	499	7	−	−	PROPN
cana-1750	499	8	𝑝2	𝑝2	NOUN
cana-1750	499	9	)	)	PUNCT
cana-1750	499	10	2(𝜆	2(𝜆	NUM
cana-1750	500	1	+	+	CCONJ
cana-1750	500	2	1)(𝜆	1)(𝜆	NUM
cana-1750	501	1	+	+	CCONJ
cana-1750	501	2	3)(𝜆	3)(𝜆	NUM
cana-1750	501	3	+	+	NUM
cana-1750	501	4	4	4	NUM
cana-1750	501	5	)	)	PUNCT
cana-1750	501	6	]	]	PUNCT
cana-1750	502	1	+	+	CCONJ
cana-1750	502	2	[	[	PUNCT
cana-1750	502	3	−7𝜆3	−7𝜆3	X
cana-1750	502	4	+	+	CCONJ
cana-1750	502	5	2𝜆2	2𝜆2	NUM
cana-1750	502	6	+	+	CCONJ
cana-1750	502	7	35𝜆	35𝜆	NOUN
cana-1750	502	8	+	+	CCONJ
cana-1750	502	9	58	58	NUM
cana-1750	502	10	8(𝜆	8(𝜆	NUM
cana-1750	502	11	+	+	SYM
cana-1750	502	12	1)(𝜆	1)(𝜆	NUM
cana-1750	502	13	+	+	NUM
cana-1750	502	14	2)(𝜆	2)(𝜆	NUM
cana-1750	502	15	+	+	CCONJ
cana-1750	502	16	3)(𝜆	3)(𝜆	NUM
cana-1750	502	17	+	+	SYM
cana-1750	502	18	4	4	NUM
cana-1750	502	19	)	)	PUNCT
cana-1750	502	20	𝑝2(4	𝑝2(4	NOUN
cana-1750	502	21	−	−	PROPN
cana-1750	502	22	𝑝2	𝑝2	PROPN
cana-1750	502	23	)	)	PUNCT
cana-1750	503	1	+	+	CCONJ
cana-1750	503	2	𝑝(4	𝑝(4	PROPN
cana-1750	503	3	−	−	PROPN
cana-1750	503	4	𝑝2	𝑝2	NOUN
cana-1750	503	5	)	)	PUNCT
cana-1750	503	6	2(𝜆	2(𝜆	NUM
cana-1750	504	1	+	+	CCONJ
cana-1750	504	2	2	2	NUM
cana-1750	504	3	)	)	PUNCT
cana-1750	504	4	]	]	PUNCT
cana-1750	505	1	+	+	CCONJ
cana-1750	505	2	[	[	PUNCT
cana-1750	505	3	𝜆5	𝜆5	ADV
cana-1750	505	4	−	−	NOUN
cana-1750	505	5	7𝜆4	7𝜆4	NUM
cana-1750	506	1	+	+	CCONJ
cana-1750	506	2	15𝜆3	15𝜆3	NUM
cana-1750	506	3	+	+	SYM
cana-1750	506	4	12𝜆2	12𝜆2	NUM
cana-1750	506	5	−	−	PROPN
cana-1750	506	6	104𝜆	104𝜆	NOUN
cana-1750	506	7	+	+	CCONJ
cana-1750	506	8	96	96	NUM
cana-1750	506	9	8(𝜆	8(𝜆	NUM
cana-1750	506	10	+	+	CCONJ
cana-1750	506	11	1)2(𝜆	1)2(𝜆	NUM
cana-1750	507	1	+	+	NUM
cana-1750	507	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	508	1	+	+	CCONJ
cana-1750	508	2	3)(𝜆	3)(𝜆	NUM
cana-1750	508	3	+	+	NUM
cana-1750	508	4	4	4	NUM
cana-1750	508	5	)	)	PUNCT
cana-1750	508	6	]	]	PUNCT
cana-1750	508	7	𝑝4	𝑝4	NOUN
cana-1750	508	8	+	+	CCONJ
cana-1750	508	9	[	[	PUNCT
cana-1750	508	10	−𝜆2	−𝜆2	PROPN
cana-1750	508	11	−	−	PROPN
cana-1750	508	12	2𝜆	2𝜆	NUM
cana-1750	508	13	−	−	NUM
cana-1750	508	14	7	7	NUM
cana-1750	508	15	2(𝜆	2(𝜆	NUM
cana-1750	508	16	+	+	CCONJ
cana-1750	508	17	1)(𝜆	1)(𝜆	NUM
cana-1750	508	18	+	+	CCONJ
cana-1750	508	19	3)(𝜆	3)(𝜆	NUM
cana-1750	508	20	+	+	NUM
cana-1750	508	21	4	4	NUM
cana-1750	508	22	)	)	PUNCT
cana-1750	508	23	]	]	PUNCT
cana-1750	509	1	𝑝(4	𝑝(4	PROPN
cana-1750	509	2	−	−	PROPN
cana-1750	509	3	𝑝2	𝑝2	NOUN
cana-1750	509	4	)	)	PUNCT
cana-1750	510	1	+	+	CCONJ
cana-1750	510	2	4	4	NUM
cana-1750	510	3	−	−	NOUN
cana-1750	510	4	𝑝2	𝑝2	NOUN
cana-1750	510	5	2(𝜆	2(𝜆	NUM
cana-1750	510	6	+	+	CCONJ
cana-1750	510	7	4	4	NUM
cana-1750	510	8	)	)	PUNCT
cana-1750	510	9	.	.	PUNCT
cana-1750	511	1	(	(	PUNCT
cana-1750	511	2	4.18	4.18	NUM
cana-1750	511	3	)	)	PUNCT
cana-1750	511	4	which	which	PRON
cana-1750	511	5	has	have	VERB
cana-1750	511	6	maximum	maximum	ADJ
cana-1750	511	7	value	value	NOUN
cana-1750	511	8	|𝒢(𝜆)|	|𝒢(𝜆)|	PROPN
cana-1750	511	9	(	(	PUNCT
cana-1750	511	10	𝜆+1)2(𝜆+2)2(𝜆+3)(𝜆+4	𝜆+1)2(𝜆+2)2(𝜆+3)(𝜆+4	PROPN
cana-1750	511	11	)	)	PUNCT
cana-1750	511	12	attained	attain	VERB
cana-1750	511	13	at	at	ADP
cana-1750	511	14	the	the	DET
cana-1750	511	15	end	end	NOUN
cana-1750	511	16	point	point	NOUN
cana-1750	511	17	𝑝	𝑝	NOUN
cana-1750	511	18	=	=	SYM
cana-1750	511	19	2	2	NUM
cana-1750	511	20	and	and	CCONJ
cana-1750	511	21	(	(	PUNCT
cana-1750	511	22	3	3	NUM
cana-1750	511	23	+	+	NOUN
cana-1750	511	24	2𝜆)4	2𝜆)4	NUM
cana-1750	511	25	(	(	PUNCT
cana-1750	511	26	𝜆+2)(𝜆+4	𝜆+2)(𝜆+4	NUM
cana-1750	511	27	)	)	PUNCT
cana-1750	512	1	+	+	CCONJ
cana-1750	512	2	6	6	NUM
cana-1750	512	3	(	(	PUNCT
cana-1750	512	4	𝜆+4	𝜆+4	NUM
cana-1750	512	5	)	)	PUNCT
cana-1750	512	6	at	at	ADP
cana-1750	512	7	𝑝	𝑝	NOUN
cana-1750	512	8	=	=	SYM
cana-1750	512	9	0	0	NUM
cana-1750	512	10	.	.	NOUN
cana-1750	513	1	5	5	NUM
cana-1750	513	2	.	.	NUM
cana-1750	513	3	generalized	generalize	VERB
cana-1750	513	4	zalcman	zalcman	PROPN
cana-1750	513	5	conjecture	conjecture	NOUN
cana-1750	513	6	for	for	ADP
cana-1750	513	7	the	the	DET
cana-1750	513	8	class	class	NOUN
cana-1750	513	9	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	513	10	)	)	PUNCT
cana-1750	513	11	theorem	theorem	VERB
cana-1750	513	12	5.1	5.1	NUM
cana-1750	513	13	.	.	PUNCT
cana-1750	514	1	let	let	VERB
cana-1750	514	2	𝑓	𝑓	PRON
cana-1750	514	3	given	give	VERB
cana-1750	514	4	by	by	ADP
cana-1750	514	5	(	(	PUNCT
cana-1750	514	6	1.1	1.1	NUM
cana-1750	514	7	)	)	PUNCT
cana-1750	514	8	,	,	PUNCT
cana-1750	514	9	be	be	AUX
cana-1750	514	10	in	in	ADP
cana-1750	514	11	the	the	DET
cana-1750	514	12	class	class	NOUN
cana-1750	514	13	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	514	14	)	)	PUNCT
cana-1750	514	15	;	;	PUNCT
cana-1750	514	16	(	(	PUNCT
cana-1750	514	17	0	0	NUM
cana-1750	514	18	≤	≤	NUM
cana-1750	514	19	𝜆	𝜆	PRON
cana-1750	514	20	≤	≤	NUM
cana-1750	514	21	1	1	NUM
cana-1750	514	22	)	)	PUNCT
cana-1750	514	23	.	.	PUNCT
cana-1750	515	1	then	then	ADV
cana-1750	515	2	we	we	PRON
cana-1750	515	3	have	have	VERB
cana-1750	515	4	sharp	sharp	ADJ
cana-1750	515	5	bound	bind	VERB
cana-1750	515	6	|𝑎2𝑎3	|𝑎2𝑎3	NOUN
cana-1750	515	7	−	−	PROPN
cana-1750	515	8	𝑎4|	𝑎4|	PROPN
cana-1750	515	9	≤	≤	PROPN
cana-1750	515	10	max	max	PROPN
cana-1750	515	11	{	{	PUNCT
cana-1750	515	12	4	4	NUM
cana-1750	515	13	(	(	PUNCT
cana-1750	515	14	𝜆	𝜆	NOUN
cana-1750	515	15	+	+	ADJ
cana-1750	515	16	3	3	NUM
cana-1750	515	17	)	)	PUNCT
cana-1750	515	18	,	,	PUNCT
cana-1750	515	19	|ℋ(𝜆)|	|ℋ(𝜆)|	PROPN
cana-1750	515	20	(	(	PUNCT
cana-1750	515	21	𝜆	𝜆	PROPN
cana-1750	515	22	+	+	CCONJ
cana-1750	515	23	1)2(𝜆	1)2(𝜆	NUM
cana-1750	515	24	+	+	CCONJ
cana-1750	515	25	2)(𝜆	2)(𝜆	NUM
cana-1750	515	26	+	+	CCONJ
cana-1750	515	27	3	3	NUM
cana-1750	515	28	)	)	PUNCT
cana-1750	515	29	}	}	PUNCT
cana-1750	515	30	where	where	SCONJ
cana-1750	515	31	ℋ(𝜆	ℋ(𝜆	X
cana-1750	515	32	)	)	PUNCT
cana-1750	515	33	=	=	SYM
cana-1750	516	1	2(−𝜆3	2(−𝜆3	NUM
cana-1750	517	1	+	+	NOUN
cana-1750	517	2	4𝜆2	4𝜆2	NUM
cana-1750	517	3	−	−	NOUN
cana-1750	517	4	5𝜆	5𝜆	NOUN
cana-1750	517	5	+	+	CCONJ
cana-1750	517	6	6	6	NUM
cana-1750	517	7	)	)	PUNCT
cana-1750	517	8	(	(	PUNCT
cana-1750	517	9	5.1	5.1	NUM
cana-1750	517	10	)	)	PUNCT
cana-1750	517	11	proof	proof	NOUN
cana-1750	517	12	.	.	PUNCT
cana-1750	518	1	first	first	ADV
cana-1750	518	2	note	note	VERB
cana-1750	518	3	that	that	SCONJ
cana-1750	518	4	by	by	ADP
cana-1750	518	5	equating	equate	VERB
cana-1750	518	6	the	the	DET
cana-1750	518	7	corresponding	corresponding	ADJ
cana-1750	518	8	coefficients	coefficient	NOUN
cana-1750	518	9	in	in	ADP
cana-1750	518	10	the	the	DET
cana-1750	518	11	equation	equation	NOUN
cana-1750	518	12	(	(	PUNCT
cana-1750	518	13	3.1	3.1	NUM
cana-1750	518	14	)	)	PUNCT
cana-1750	518	15	,	,	PUNCT
cana-1750	518	16	we	we	PRON
cana-1750	518	17	bring	bring	VERB
cana-1750	518	18	,	,	PUNCT
cana-1750	518	19	in	in	ADP
cana-1750	518	20	the	the	DET
cana-1750	518	21	view	view	NOUN
cana-1750	518	22	of	of	ADP
cana-1750	518	23	(	(	PUNCT
cana-1750	518	24	3.2	3.2	NUM
cana-1750	518	25	)	)	PUNCT
cana-1750	518	26	,	,	PUNCT
cana-1750	518	27	(	(	PUNCT
cana-1750	518	28	3.3	3.3	NUM
cana-1750	518	29	)	)	PUNCT
cana-1750	518	30	and	and	CCONJ
cana-1750	518	31	(	(	PUNCT
cana-1750	518	32	3.4	3.4	NUM
cana-1750	518	33	)	)	PUNCT
cana-1750	518	34	,	,	PUNCT
cana-1750	518	35	a	a	DET
cana-1750	518	36	simple	simple	ADJ
cana-1750	518	37	computation	computation	NOUN
cana-1750	518	38	leads	lead	VERB
cana-1750	518	39	to	to	ADP
cana-1750	518	40	𝑎2𝑎3	𝑎2𝑎3	PROPN
cana-1750	518	41	−	−	PROPN
cana-1750	518	42	𝑎4	𝑎4	PROPN
cana-1750	518	43	=	=	PUNCT
cana-1750	518	44	[	[	PUNCT
cana-1750	518	45	𝑝1	𝑝1	NOUN
cana-1750	518	46	𝜆	𝜆	NOUN
cana-1750	518	47	+	+	PROPN
cana-1750	518	48	1	1	NUM
cana-1750	518	49	]	]	PUNCT
cana-1750	518	50	[	[	PUNCT
cana-1750	518	51	𝑝1	𝑝1	NOUN
cana-1750	518	52	2(1	2(1	NUM
cana-1750	518	53	−	−	NOUN
cana-1750	518	54	𝜆	𝜆	NOUN
cana-1750	518	55	)	)	PUNCT
cana-1750	518	56	(	(	PUNCT
cana-1750	518	57	𝜆	𝜆	PROPN
cana-1750	518	58	+	+	NOUN
cana-1750	518	59	1)(𝜆	1)(𝜆	NUM
cana-1750	518	60	+	+	CCONJ
cana-1750	518	61	2	2	NUM
cana-1750	518	62	)	)	PUNCT
cana-1750	518	63	+	+	NUM
cana-1750	518	64	𝑝2	𝑝2	PROPN
cana-1750	518	65	𝜆	𝜆	PROPN
cana-1750	519	1	+	+	ADJ
cana-1750	519	2	2	2	NUM
cana-1750	519	3	]	]	PUNCT
cana-1750	519	4	.	.	PUNCT
cana-1750	520	1	−	−	NOUN
cana-1750	521	1	[	[	PUNCT
cana-1750	521	2	𝑝1	𝑝1	NOUN
cana-1750	521	3	3(1	3(1	PROPN
cana-1750	521	4	−	−	PROPN
cana-1750	521	5	𝜆)2	𝜆)2	NOUN
cana-1750	521	6	(	(	PUNCT
cana-1750	521	7	𝜆	𝜆	PROPN
cana-1750	521	8	+	+	ADJ
cana-1750	521	9	1)(𝜆	1)(𝜆	NUM
cana-1750	521	10	+	+	CCONJ
cana-1750	521	11	2)(𝜆	2)(𝜆	NUM
cana-1750	521	12	+	+	CCONJ
cana-1750	521	13	3	3	NUM
cana-1750	521	14	)	)	PUNCT
cana-1750	521	15	+	+	NUM
cana-1750	521	16	𝑝1𝑝2(1	𝑝1𝑝2(1	NOUN
cana-1750	521	17	−	−	NOUN
cana-1750	521	18	𝜆)(3	𝜆)(3	X
cana-1750	521	19	+	+	CCONJ
cana-1750	521	20	2𝜆	2𝜆	NUM
cana-1750	521	21	)	)	PUNCT
cana-1750	521	22	(	(	PUNCT
cana-1750	521	23	𝜆	𝜆	X
cana-1750	521	24	+	+	NOUN
cana-1750	521	25	1)(𝜆	1)(𝜆	NUM
cana-1750	521	26	+	+	CCONJ
cana-1750	521	27	2)(𝜆	2)(𝜆	NUM
cana-1750	521	28	+	+	CCONJ
cana-1750	521	29	3	3	NUM
cana-1750	521	30	)	)	PUNCT
cana-1750	521	31	+	+	CCONJ
cana-1750	521	32	𝑝3	𝑝3	ADV
cana-1750	521	33	𝜆	𝜆	ADP
cana-1750	521	34	+	+	ADJ
cana-1750	521	35	3	3	NUM
cana-1750	521	36	]	]	PUNCT
cana-1750	521	37	.	.	PUNCT
cana-1750	522	1	(	(	PUNCT
cana-1750	522	2	5.2	5.2	NUM
cana-1750	522	3	)	)	PUNCT
cana-1750	522	4	note	note	VERB
cana-1750	522	5	that	that	SCONJ
cana-1750	522	6	,	,	PUNCT
cana-1750	522	7	by	by	ADP
cana-1750	522	8	lemma	lemma	PROPN
cana-1750	522	9	(	(	PUNCT
cana-1750	522	10	2.2	2.2	NUM
cana-1750	522	11	)	)	PUNCT
cana-1750	522	12	,	,	PUNCT
cana-1750	522	13	we	we	PRON
cana-1750	522	14	may	may	AUX
cana-1750	522	15	write	write	VERB
cana-1750	522	16	𝑎2𝑎3	𝑎2𝑎3	ADP
cana-1750	522	17	−	−	PROPN
cana-1750	522	18	𝑎4	𝑎4	PROPN
cana-1750	522	19	=	=	SYM
cana-1750	522	20	𝑝1𝑋𝑥	𝑝1𝑋𝑥	PROPN
cana-1750	522	21	2	2	NUM
cana-1750	522	22	4(𝜆+3	4(𝜆+3	NUM
cana-1750	522	23	)	)	PUNCT
cana-1750	523	1	+	+	CCONJ
cana-1750	523	2	𝑋𝑌	𝑋𝑌	PROPN
cana-1750	523	3	2(𝜆+3	2(𝜆+3	NUM
cana-1750	523	4	)	)	PUNCT
cana-1750	524	1	+	+	CCONJ
cana-1750	524	2	[	[	PUNCT
cana-1750	524	3	𝜆2−𝜆−2	𝜆2−𝜆−2	NOUN
cana-1750	524	4	2(𝜆+1)(𝜆+2)(𝜆+3	2(𝜆+1)(𝜆+2)(𝜆+3	NUM
cana-1750	524	5	)	)	PUNCT
cana-1750	524	6	]	]	PUNCT
cana-1750	525	1	𝑝1𝑥𝑋	𝑝1𝑥𝑋	PROPN
cana-1750	525	2	+	+	X
cana-1750	525	3	[	[	PUNCT
cana-1750	525	4	−𝜆3	−𝜆3	ADJ
cana-1750	525	5	+	+	NOUN
cana-1750	525	6	4𝜆2−5𝜆+6	4𝜆2−5𝜆+6	NUM
cana-1750	525	7	4(𝜆+1)2(𝜆+2)(𝜆+3	4(𝜆+1)2(𝜆+2)(𝜆+3	NUM
cana-1750	525	8	)	)	PUNCT
cana-1750	525	9	]	]	PUNCT
cana-1750	525	10	𝑝1	𝑝1	NOUN
cana-1750	525	11	3	3	NUM
cana-1750	525	12	.	.	PUNCT
cana-1750	525	13	without	without	ADP
cana-1750	525	14	loss	loss	NOUN
cana-1750	525	15	of	of	ADP
cana-1750	525	16	generality	generality	NOUN
cana-1750	525	17	,	,	PUNCT
cana-1750	525	18	we	we	PRON
cana-1750	525	19	let	let	VERB
cana-1750	525	20	0	0	NUM
cana-1750	525	21	≤	≤	NOUN
cana-1750	525	22	𝑝1	𝑝1	NOUN
cana-1750	525	23	=	=	SYM
cana-1750	525	24	𝑝	𝑝	NOUN
cana-1750	525	25	≤	≤	NUM
cana-1750	525	26	2	2	NUM
cana-1750	525	27	.	.	PUNCT
cana-1750	525	28	substitute	substitute	VERB
cana-1750	525	29	this	this	PRON
cana-1750	525	30	into	into	ADP
cana-1750	525	31	the	the	DET
cana-1750	525	32	above	above	ADJ
cana-1750	525	33	equation	equation	NOUN
cana-1750	525	34	,	,	PUNCT
cana-1750	525	35	we	we	PRON
cana-1750	525	36	obtain	obtain	VERB
cana-1750	525	37	the	the	DET
cana-1750	525	38	following	follow	VERB
cana-1750	525	39	quadratic	quadratic	ADJ
cana-1750	525	40	equation	equation	NOUN
cana-1750	525	41	in	in	ADP
cana-1750	525	42	terms	term	NOUN
cana-1750	525	43	of	of	ADP
cana-1750	525	44	𝑥.	𝑥.	NOUN
cana-1750	525	45	|𝑎2𝑎3	|𝑎2𝑎3	PROPN
cana-1750	525	46	−	−	PROPN
cana-1750	525	47	𝑎4|	𝑎4|	PROPN
cana-1750	525	48	≤	≤	NOUN
cana-1750	525	49	[	[	PUNCT
cana-1750	525	50	𝑝(4	𝑝(4	PROPN
cana-1750	525	51	−	−	PROPN
cana-1750	525	52	𝑝2	𝑝2	NOUN
cana-1750	525	53	)	)	PUNCT
cana-1750	525	54	4(𝜆	4(𝜆	NUM
cana-1750	526	1	+	+	CCONJ
cana-1750	526	2	3	3	X
cana-1750	526	3	)	)	PUNCT
cana-1750	526	4	−	−	PROPN
cana-1750	526	5	(	(	PUNCT
cana-1750	526	6	4	4	NUM
cana-1750	526	7	−	−	PROPN
cana-1750	526	8	𝑝2	𝑝2	NOUN
cana-1750	526	9	)	)	PUNCT
cana-1750	526	10	2(𝜆	2(𝜆	NUM
cana-1750	527	1	+	+	CCONJ
cana-1750	528	1	3	3	NUM
cana-1750	528	2	)	)	PUNCT
cana-1750	528	3	]	]	PUNCT
cana-1750	529	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	529	2	+	+	PUNCT
cana-1750	529	3	[	[	PUNCT
cana-1750	529	4	𝜆2	𝜆2	NOUN
cana-1750	529	5	−	−	PROPN
cana-1750	529	6	𝜆	𝜆	PRON
cana-1750	529	7	−	−	PROPN
cana-1750	529	8	2	2	NUM
cana-1750	529	9	2(𝜆	2(𝜆	NUM
cana-1750	529	10	+	+	CCONJ
cana-1750	529	11	1)(𝜆	1)(𝜆	NUM
cana-1750	529	12	+	+	CCONJ
cana-1750	529	13	2)(𝜆	2)(𝜆	NUM
cana-1750	529	14	+	+	CCONJ
cana-1750	529	15	3	3	NUM
cana-1750	529	16	)	)	PUNCT
cana-1750	529	17	]	]	PUNCT
cana-1750	529	18	(	(	PUNCT
cana-1750	529	19	4	4	NUM
cana-1750	529	20	−	−	NOUN
cana-1750	529	21	𝑝2)𝑥𝑝	𝑝2)𝑥𝑝	X
cana-1750	529	22	+	+	CCONJ
cana-1750	529	23	[	[	PUNCT
cana-1750	529	24	−𝜆3	−𝜆3	NOUN
cana-1750	529	25	+	+	NOUN
cana-1750	529	26	4𝜆2	4𝜆2	NUM
cana-1750	529	27	−	−	NOUN
cana-1750	529	28	5𝜆	5𝜆	NOUN
cana-1750	529	29	+	+	CCONJ
cana-1750	529	30	6	6	NUM
cana-1750	529	31	4(𝜆	4(𝜆	NUM
cana-1750	529	32	+	+	CCONJ
cana-1750	529	33	1)2(𝜆	1)2(𝜆	NUM
cana-1750	529	34	+	+	CCONJ
cana-1750	529	35	2)(𝜆	2)(𝜆	NUM
cana-1750	529	36	+	+	CCONJ
cana-1750	529	37	3	3	NUM
cana-1750	529	38	)	)	PUNCT
cana-1750	529	39	]	]	PUNCT
cana-1750	530	1	𝑝3	𝑝3	ADV
cana-1750	530	2	+	+	NUM
cana-1750	530	3	4	4	NUM
cana-1750	530	4	−	−	NOUN
cana-1750	530	5	𝑝2	𝑝2	NOUN
cana-1750	530	6	2(𝜆	2(𝜆	NUM
cana-1750	530	7	+	+	CCONJ
cana-1750	530	8	3	3	X
cana-1750	530	9	)	)	PUNCT
cana-1750	530	10	=	=	SYM
cana-1750	530	11	£	£	SYM
cana-1750	530	12	(	(	PUNCT
cana-1750	530	13	𝑝	𝑝	NOUN
cana-1750	530	14	,	,	PUNCT
cana-1750	530	15	|𝑥|	|𝑥|	ADJ
cana-1750	530	16	)	)	PUNCT
cana-1750	530	17	(	(	PUNCT
cana-1750	530	18	5.3	5.3	NUM
cana-1750	530	19	)	)	PUNCT
cana-1750	530	20	communications	communication	NOUN
cana-1750	530	21	on	on	ADP
cana-1750	530	22	applied	apply	VERB
cana-1750	530	23	nonlinear	nonlinear	ADJ
cana-1750	530	24	analysis	analysis	NOUN
cana-1750	530	25	issn	issn	NOUN
cana-1750	530	26	:	:	PUNCT
cana-1750	530	27	1074	1074	NUM
cana-1750	530	28	-	-	PUNCT
cana-1750	530	29	133x	133x	NUM
cana-1750	530	30	vol	vol	NOUN
cana-1750	530	31	32	32	NUM
cana-1750	530	32	no	no	NOUN
cana-1750	530	33	.	.	NOUN
cana-1750	530	34	2	2	NUM
cana-1750	530	35	(	(	PUNCT
cana-1750	530	36	2025	2025	NUM
cana-1750	530	37	)	)	PUNCT
cana-1750	530	38	400	400	NUM
cana-1750	530	39	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	530	40	we	we	PRON
cana-1750	530	41	prove	prove	VERB
cana-1750	530	42	that	that	SCONJ
cana-1750	530	43	the	the	DET
cana-1750	530	44	maximum	maximum	ADJ
cana-1750	530	45	value	value	NOUN
cana-1750	530	46	of	of	ADP
cana-1750	530	47	£	£	SYM
cana-1750	530	48	(	(	PUNCT
cana-1750	530	49	𝑝	𝑝	NOUN
cana-1750	530	50	,	,	PUNCT
cana-1750	530	51	|𝑥|	|𝑥|	ADJ
cana-1750	530	52	)	)	PUNCT
cana-1750	530	53	on	on	ADP
cana-1750	530	54	[	[	X
cana-1750	530	55	0,2	0,2	NUM
cana-1750	530	56	]	]	X
cana-1750	530	57	×	×	NOUN
cana-1750	530	58	[	[	X
cana-1750	530	59	0,1	0,1	NUM
cana-1750	530	60	]	]	PUNCT
cana-1750	530	61	.	.	PUNCT
cana-1750	531	1	first	first	ADV
cana-1750	531	2	,	,	PUNCT
cana-1750	531	3	assume	assume	VERB
cana-1750	531	4	that	that	SCONJ
cana-1750	531	5	there	there	PRON
cana-1750	531	6	is	be	VERB
cana-1750	531	7	a	a	DET
cana-1750	531	8	maximum	maximum	NOUN
cana-1750	531	9	at	at	ADP
cana-1750	531	10	an	an	DET
cana-1750	531	11	interior	interior	ADJ
cana-1750	531	12	point	point	NOUN
cana-1750	531	13	£	£	SYM
cana-1750	531	14	(	(	PUNCT
cana-1750	531	15	𝑝0	𝑝0	PROPN
cana-1750	531	16	,	,	PUNCT
cana-1750	531	17	|𝑥0|	|𝑥0|	VERB
cana-1750	531	18	)	)	PUNCT
cana-1750	531	19	of	of	ADP
cana-1750	531	20	[	[	X
cana-1750	531	21	0,2	0,2	NUM
cana-1750	531	22	]	]	X
cana-1750	531	23	×	×	NOUN
cana-1750	531	24	[	[	X
cana-1750	531	25	0,1	0,1	NUM
cana-1750	531	26	]	]	PUNCT
cana-1750	531	27	.	.	PUNCT
cana-1750	532	1	differentiating	differentiate	VERB
cana-1750	532	2	£	£	SYM
cana-1750	532	3	(	(	PUNCT
cana-1750	532	4	𝑝	𝑝	NOUN
cana-1750	532	5	,	,	PUNCT
cana-1750	532	6	|𝑥|	|𝑥|	ADJ
cana-1750	532	7	)	)	PUNCT
cana-1750	532	8	with	with	ADP
cana-1750	532	9	respect	respect	NOUN
cana-1750	532	10	to	to	ADP
cana-1750	532	11	|𝑥|	|𝑥|	VERB
cana-1750	532	12	and	and	CCONJ
cana-1750	532	13	equating	equate	VERB
cana-1750	532	14	it	it	PRON
cana-1750	532	15	to	to	ADP
cana-1750	532	16	0	0	NUM
cana-1750	532	17	implies	imply	VERB
cana-1750	532	18	that	that	SCONJ
cana-1750	532	19	𝑝	𝑝	X
cana-1750	532	20	=	=	SYM
cana-1750	532	21	𝑝0	𝑝0	NOUN
cana-1750	532	22	=	=	SYM
cana-1750	532	23	2	2	NUM
cana-1750	532	24	which	which	PRON
cana-1750	532	25	is	be	AUX
cana-1750	532	26	contradiction	contradiction	NOUN
cana-1750	532	27	.	.	PUNCT
cana-1750	533	1	thus	thus	ADV
cana-1750	533	2	,	,	PUNCT
cana-1750	533	3	for	for	ADP
cana-1750	533	4	the	the	DET
cana-1750	533	5	maximum	maximum	NOUN
cana-1750	533	6	of	of	ADP
cana-1750	533	7	£	£	SYM
cana-1750	533	8	(	(	PUNCT
cana-1750	533	9	𝑝	𝑝	NOUN
cana-1750	533	10	,	,	PUNCT
cana-1750	533	11	|𝑥|	|𝑥|	ADJ
cana-1750	533	12	)	)	PUNCT
cana-1750	533	13	,	,	PUNCT
cana-1750	533	14	we	we	PRON
cana-1750	533	15	need	need	VERB
cana-1750	533	16	to	to	PART
cana-1750	533	17	consider	consider	VERB
cana-1750	533	18	the	the	DET
cana-1750	533	19	end	end	NOUN
cana-1750	533	20	points	point	NOUN
cana-1750	533	21	of	of	ADP
cana-1750	533	22	[	[	X
cana-1750	533	23	0,2	0,2	NUM
cana-1750	533	24	]	]	X
cana-1750	533	25	×	×	NOUN
cana-1750	534	1	[	[	X
cana-1750	534	2	0,1	0,1	NUM
cana-1750	534	3	]	]	PUNCT
cana-1750	534	4	.	.	PUNCT
cana-1750	535	1	for	for	ADP
cana-1750	535	2	𝑝	𝑝	NOUN
cana-1750	535	3	=	=	SYM
cana-1750	535	4	0	0	NUM
cana-1750	535	5	,	,	PUNCT
cana-1750	535	6	we	we	PRON
cana-1750	535	7	obtain	obtain	VERB
cana-1750	535	8	£	£	SYM
cana-1750	535	9	(	(	PUNCT
cana-1750	535	10	0	0	NUM
cana-1750	535	11	,	,	PUNCT
cana-1750	535	12	|𝑥|	|𝑥|	ADJ
cana-1750	535	13	)	)	PUNCT
cana-1750	536	1	=	=	PRON
cana-1750	536	2	−4	−4	X
cana-1750	536	3	2(𝜆	2(𝜆	NUM
cana-1750	537	1	+	+	CCONJ
cana-1750	537	2	3	3	X
cana-1750	537	3	)	)	PUNCT
cana-1750	537	4	|𝑥|2	|𝑥|2	NOUN
cana-1750	537	5	+	+	CCONJ
cana-1750	537	6	4	4	NUM
cana-1750	537	7	2(𝜆	2(𝜆	NUM
cana-1750	537	8	+	+	CCONJ
cana-1750	537	9	3	3	X
cana-1750	537	10	)	)	PUNCT
cana-1750	537	11	≤	≤	NOUN
cana-1750	537	12	4	4	NUM
cana-1750	537	13	𝜆	𝜆	NOUN
cana-1750	537	14	+	+	NUM
cana-1750	537	15	3	3	NUM
cana-1750	537	16	(	(	PUNCT
cana-1750	537	17	5.4	5.4	NUM
cana-1750	537	18	)	)	PUNCT
cana-1750	537	19	for	for	ADP
cana-1750	537	20	𝑝	𝑝	NOUN
cana-1750	537	21	=	=	SYM
cana-1750	537	22	2	2	NUM
cana-1750	537	23	,	,	PUNCT
cana-1750	537	24	we	we	PRON
cana-1750	537	25	obtain	obtain	VERB
cana-1750	537	26	£	£	SYM
cana-1750	537	27	(	(	PUNCT
cana-1750	537	28	2	2	NUM
cana-1750	537	29	,	,	PUNCT
cana-1750	537	30	|𝑥|	|𝑥|	ADJ
cana-1750	537	31	)	)	PUNCT
cana-1750	538	1	=	=	SYM
cana-1750	539	1	2(−𝜆3	2(−𝜆3	NUM
cana-1750	540	1	+	+	NOUN
cana-1750	540	2	4𝜆2	4𝜆2	NUM
cana-1750	540	3	−	−	NOUN
cana-1750	540	4	5𝜆	5𝜆	NOUN
cana-1750	540	5	+	+	CCONJ
cana-1750	540	6	6	6	NUM
cana-1750	540	7	)	)	PUNCT
cana-1750	540	8	(	(	PUNCT
cana-1750	540	9	𝜆	𝜆	PROPN
cana-1750	540	10	+	+	CCONJ
cana-1750	540	11	1)2(𝜆	1)2(𝜆	NUM
cana-1750	540	12	+	+	CCONJ
cana-1750	540	13	2)(𝜆	2)(𝜆	NUM
cana-1750	540	14	+	+	CCONJ
cana-1750	540	15	3	3	NUM
cana-1750	540	16	)	)	PUNCT
cana-1750	540	17	(	(	PUNCT
cana-1750	540	18	5.5	5.5	NUM
cana-1750	540	19	)	)	PUNCT
cana-1750	540	20	for	for	ADP
cana-1750	540	21	|𝑥|	|𝑥|	ADJ
cana-1750	540	22	=	=	SYM
cana-1750	540	23	0	0	NUM
cana-1750	540	24	,	,	PUNCT
cana-1750	540	25	we	we	PRON
cana-1750	540	26	get	get	VERB
cana-1750	540	27	£	£	SYM
cana-1750	540	28	(	(	PUNCT
cana-1750	540	29	𝑝	𝑝	NOUN
cana-1750	540	30	,	,	PUNCT
cana-1750	540	31	0	0	NUM
cana-1750	540	32	)	)	PUNCT
cana-1750	540	33	=	=	NOUN
cana-1750	541	1	[	[	PUNCT
cana-1750	541	2	−𝜆3	−𝜆3	NOUN
cana-1750	541	3	+	+	NUM
cana-1750	541	4	4𝜆2	4𝜆2	NUM
cana-1750	541	5	−	−	NOUN
cana-1750	541	6	5𝜆	5𝜆	NOUN
cana-1750	541	7	+	+	CCONJ
cana-1750	541	8	6	6	NUM
cana-1750	541	9	4(𝜆	4(𝜆	NUM
cana-1750	541	10	+	+	CCONJ
cana-1750	541	11	1)2(𝜆	1)2(𝜆	NUM
cana-1750	541	12	+	+	CCONJ
cana-1750	541	13	2)(𝜆	2)(𝜆	NUM
cana-1750	541	14	+	+	CCONJ
cana-1750	541	15	3	3	NUM
cana-1750	541	16	)	)	PUNCT
cana-1750	541	17	]	]	PUNCT
cana-1750	541	18	𝑝3	𝑝3	ADV
cana-1750	541	19	+	+	NUM
cana-1750	541	20	4	4	NUM
cana-1750	541	21	−	−	NOUN
cana-1750	541	22	𝑝2	𝑝2	NOUN
cana-1750	541	23	2(𝜆	2(𝜆	NUM
cana-1750	541	24	+	+	CCONJ
cana-1750	541	25	3	3	NUM
cana-1750	541	26	)	)	PUNCT
cana-1750	541	27	(	(	PUNCT
cana-1750	541	28	5.6	5.6	NUM
cana-1750	541	29	)	)	PUNCT
cana-1750	541	30	which	which	PRON
cana-1750	541	31	has	have	VERB
cana-1750	541	32	maximum	maximum	ADJ
cana-1750	541	33	value	value	NOUN
cana-1750	541	34	|ℋ(𝜆)|	|ℋ(𝜆)|	NOUN
cana-1750	541	35	(	(	PUNCT
cana-1750	541	36	𝜆+1)2(𝜆+2)(𝜆+3	𝜆+1)2(𝜆+2)(𝜆+3	NOUN
cana-1750	541	37	)	)	PUNCT
cana-1750	541	38	attained	attain	VERB
cana-1750	541	39	at	at	ADP
cana-1750	541	40	the	the	DET
cana-1750	541	41	end	end	NOUN
cana-1750	541	42	point	point	NOUN
cana-1750	541	43	𝑝	𝑝	NOUN
cana-1750	541	44	=	=	SYM
cana-1750	541	45	2	2	X
cana-1750	541	46	.	.	X
cana-1750	542	1	for	for	ADP
cana-1750	542	2	|𝑥|	|𝑥|	ADJ
cana-1750	542	3	=	=	SYM
cana-1750	542	4	1	1	NUM
cana-1750	542	5	,	,	PUNCT
cana-1750	542	6	we	we	PRON
cana-1750	542	7	obtain	obtain	VERB
cana-1750	542	8	£	£	SYM
cana-1750	542	9	(	(	PUNCT
cana-1750	542	10	𝑝	𝑝	NOUN
cana-1750	542	11	,	,	PUNCT
cana-1750	542	12	1	1	NUM
cana-1750	542	13	)	)	PUNCT
cana-1750	542	14	=	=	NOUN
cana-1750	542	15	[	[	PUNCT
cana-1750	542	16	𝑝(4	𝑝(4	PROPN
cana-1750	542	17	−	−	PROPN
cana-1750	542	18	𝑝2	𝑝2	NOUN
cana-1750	542	19	)	)	PUNCT
cana-1750	542	20	4(𝜆	4(𝜆	NUM
cana-1750	543	1	+	+	CCONJ
cana-1750	543	2	3	3	X
cana-1750	543	3	)	)	PUNCT
cana-1750	543	4	−	−	PROPN
cana-1750	543	5	(	(	PUNCT
cana-1750	543	6	4	4	NUM
cana-1750	543	7	−	−	PROPN
cana-1750	543	8	𝑝2	𝑝2	NOUN
cana-1750	543	9	)	)	PUNCT
cana-1750	543	10	2(𝜆	2(𝜆	NUM
cana-1750	544	1	+	+	CCONJ
cana-1750	545	1	3	3	NUM
cana-1750	545	2	)	)	PUNCT
cana-1750	545	3	]	]	PUNCT
cana-1750	546	1	+	+	CCONJ
cana-1750	546	2	[	[	PUNCT
cana-1750	546	3	𝜆2	𝜆2	NOUN
cana-1750	546	4	−	−	PROPN
cana-1750	546	5	𝜆	𝜆	PRON
cana-1750	546	6	−	−	PROPN
cana-1750	546	7	2	2	NUM
cana-1750	546	8	2(𝜆	2(𝜆	NUM
cana-1750	546	9	+	+	CCONJ
cana-1750	546	10	3)(𝜆	3)(𝜆	NUM
cana-1750	546	11	+	+	NUM
cana-1750	546	12	1	1	NUM
cana-1750	546	13	)	)	PUNCT
cana-1750	546	14	]	]	PUNCT
cana-1750	547	1	(	(	PUNCT
cana-1750	547	2	4	4	NUM
cana-1750	547	3	−	−	NOUN
cana-1750	547	4	𝑝2)𝑝	𝑝2)𝑝	ADJ
cana-1750	547	5	+	+	CCONJ
cana-1750	547	6	[	[	PUNCT
cana-1750	547	7	−𝜆3	−𝜆3	NOUN
cana-1750	547	8	+	+	NOUN
cana-1750	547	9	4𝜆2	4𝜆2	NUM
cana-1750	547	10	−	−	NOUN
cana-1750	547	11	5𝜆	5𝜆	NOUN
cana-1750	547	12	+	+	CCONJ
cana-1750	547	13	6	6	NUM
cana-1750	547	14	4(𝜆	4(𝜆	NUM
cana-1750	548	1	+	+	CCONJ
cana-1750	548	2	1)2(𝜆	1)2(𝜆	NUM
cana-1750	548	3	+	+	CCONJ
cana-1750	548	4	𝜆)(𝜆	𝜆)(𝜆	X
cana-1750	549	1	+	+	CCONJ
cana-1750	549	2	3	3	NUM
cana-1750	549	3	)	)	PUNCT
cana-1750	549	4	]	]	PUNCT
cana-1750	550	1	𝑝3	𝑝3	ADV
cana-1750	550	2	+	+	NUM
cana-1750	550	3	4	4	NUM
cana-1750	550	4	−	−	NOUN
cana-1750	550	5	𝑝2	𝑝2	NOUN
cana-1750	550	6	2(𝜆	2(𝜆	NUM
cana-1750	550	7	+	+	CCONJ
cana-1750	550	8	3	3	NUM
cana-1750	550	9	)	)	PUNCT
cana-1750	550	10	.	.	PUNCT
cana-1750	551	1	(	(	PUNCT
cana-1750	551	2	5.7	5.7	NUM
cana-1750	551	3	)	)	PUNCT
cana-1750	551	4	which	which	PRON
cana-1750	551	5	is	be	AUX
cana-1750	551	6	maximum	maximum	ADJ
cana-1750	551	7	value	value	NOUN
cana-1750	551	8	of	of	ADP
cana-1750	551	9	£	£	SYM
cana-1750	551	10	(	(	PUNCT
cana-1750	551	11	𝑝	𝑝	NOUN
cana-1750	551	12	,	,	PUNCT
cana-1750	551	13	1	1	NUM
cana-1750	551	14	)	)	PUNCT
cana-1750	551	15	=	=	SYM
cana-1750	552	1	4	4	NUM
cana-1750	552	2	𝜆+1	𝜆+1	X
cana-1750	552	3	at	at	ADP
cana-1750	552	4	𝑝	𝑝	NOUN
cana-1750	552	5	=	=	SYM
cana-1750	552	6	0	0	NUM
cana-1750	552	7	and	and	CCONJ
cana-1750	552	8	£	£	SYM
cana-1750	552	9	(	(	PUNCT
cana-1750	552	10	𝑝	𝑝	NOUN
cana-1750	552	11	,	,	PUNCT
cana-1750	552	12	1	1	NUM
cana-1750	552	13	)	)	PUNCT
cana-1750	552	14	=	=	SYM
cana-1750	552	15	|ℋ(𝜆)|	|ℋ(𝜆)|	NOUN
cana-1750	552	16	(	(	PUNCT
cana-1750	552	17	𝜆+1)2(𝜆+2)(𝜆+3	𝜆+1)2(𝜆+2)(𝜆+3	NOUN
cana-1750	552	18	)	)	PUNCT
cana-1750	552	19	at	at	ADP
cana-1750	552	20	𝑝	𝑝	NOUN
cana-1750	552	21	=	=	SYM
cana-1750	552	22	2	2	NUM
cana-1750	552	23	.	.	PUNCT
cana-1750	552	24	hence	hence	ADV
cana-1750	552	25	|𝑎2𝑎3	|𝑎2𝑎3	PROPN
cana-1750	552	26	−	−	PROPN
cana-1750	552	27	𝑎4|	𝑎4|	PROPN
cana-1750	552	28	≤	≤	PROPN
cana-1750	552	29	max	max	PROPN
cana-1750	552	30	{	{	PUNCT
cana-1750	552	31	4	4	NUM
cana-1750	552	32	(	(	PUNCT
cana-1750	552	33	𝜆	𝜆	NOUN
cana-1750	552	34	+	+	ADJ
cana-1750	552	35	3	3	NUM
cana-1750	552	36	)	)	PUNCT
cana-1750	552	37	,	,	PUNCT
cana-1750	552	38	|ℋ(𝜆)|	|ℋ(𝜆)|	PROPN
cana-1750	552	39	(	(	PUNCT
cana-1750	552	40	𝜆	𝜆	PROPN
cana-1750	552	41	+	+	CCONJ
cana-1750	552	42	1)2(𝜆	1)2(𝜆	NUM
cana-1750	552	43	+	+	CCONJ
cana-1750	552	44	2)(𝜆	2)(𝜆	NUM
cana-1750	552	45	+	+	CCONJ
cana-1750	552	46	3	3	NUM
cana-1750	552	47	)	)	PUNCT
cana-1750	552	48	}	}	PUNCT
cana-1750	552	49	.	.	PUNCT
cana-1750	553	1	(	(	PUNCT
cana-1750	553	2	5.8	5.8	NUM
cana-1750	553	3	)	)	PUNCT
cana-1750	553	4	ℋ(𝜆	ℋ(𝜆	NUM
cana-1750	553	5	)	)	PUNCT
cana-1750	553	6	=	=	SYM
cana-1750	553	7	2(−𝜆3	2(−𝜆3	NUM
cana-1750	554	1	+	+	NOUN
cana-1750	554	2	4𝜆2	4𝜆2	NUM
cana-1750	554	3	−	−	NOUN
cana-1750	554	4	5𝜆	5𝜆	NOUN
cana-1750	554	5	+	+	CCONJ
cana-1750	554	6	6	6	NUM
cana-1750	554	7	)	)	PUNCT
cana-1750	554	8	.	.	PUNCT
cana-1750	555	1	(	(	PUNCT
cana-1750	555	2	5.9	5.9	NUM
cana-1750	555	3	)	)	PUNCT
cana-1750	555	4	theorem	theorem	VERB
cana-1750	555	5	5.2	5.2	NUM
cana-1750	555	6	.	.	PUNCT
cana-1750	556	1	let	let	VERB
cana-1750	556	2	𝑓	𝑓	PRON
cana-1750	556	3	given	give	VERB
cana-1750	556	4	by	by	ADP
cana-1750	556	5	(	(	PUNCT
cana-1750	556	6	1.1	1.1	NUM
cana-1750	556	7	)	)	PUNCT
cana-1750	556	8	,	,	PUNCT
cana-1750	556	9	be	be	AUX
cana-1750	556	10	in	in	ADP
cana-1750	556	11	the	the	DET
cana-1750	556	12	class	class	NOUN
cana-1750	556	13	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	556	14	)	)	PUNCT
cana-1750	556	15	;	;	PUNCT
cana-1750	556	16	(	(	PUNCT
cana-1750	556	17	0	0	NUM
cana-1750	556	18	≤	≤	NUM
cana-1750	556	19	𝜆	𝜆	PRON
cana-1750	556	20	≤	≤	NUM
cana-1750	556	21	1	1	NUM
cana-1750	556	22	)	)	PUNCT
cana-1750	556	23	.	.	PUNCT
cana-1750	557	1	then	then	ADV
cana-1750	557	2	we	we	PRON
cana-1750	557	3	have	have	VERB
cana-1750	557	4	sharp	sharp	ADJ
cana-1750	557	5	bound	bind	VERB
cana-1750	557	6	|𝑎2𝑎4	|𝑎2𝑎4	NOUN
cana-1750	557	7	−	−	ADP
cana-1750	557	8	𝑎5|	𝑎5|	PROPN
cana-1750	557	9	≤	≤	NUM
cana-1750	557	10	max	max	NOUN
cana-1750	557	11	{	{	PUNCT
cana-1750	557	12	4	4	NUM
cana-1750	557	13	(	(	PUNCT
cana-1750	557	14	𝜆	𝜆	NOUN
cana-1750	557	15	+	+	ADJ
cana-1750	557	16	2	2	NUM
cana-1750	557	17	)	)	PUNCT
cana-1750	557	18	,	,	PUNCT
cana-1750	557	19	|𝜕(𝜆)|	|𝜕(𝜆)|	CCONJ
cana-1750	557	20	(	(	PUNCT
cana-1750	557	21	𝜆	𝜆	PROPN
cana-1750	557	22	+	+	CCONJ
cana-1750	557	23	1)2(𝜆	1)2(𝜆	NUM
cana-1750	557	24	+	+	NUM
cana-1750	557	25	2)(𝜆	2)(𝜆	NUM
cana-1750	557	26	+	+	CCONJ
cana-1750	557	27	3)(𝜆	3)(𝜆	NUM
cana-1750	557	28	+	+	NUM
cana-1750	557	29	4	4	NUM
cana-1750	557	30	)	)	PUNCT
cana-1750	557	31	}	}	PUNCT
cana-1750	557	32	.	.	PUNCT
cana-1750	558	1	where	where	SCONJ
cana-1750	558	2	,	,	PUNCT
cana-1750	558	3	𝒥(𝜆	𝒥(𝜆	NOUN
cana-1750	558	4	)	)	PUNCT
cana-1750	558	5	=	=	SYM
cana-1750	558	6	2(𝜆4	2(𝜆4	NUM
cana-1750	558	7	−	−	NOUN
cana-1750	558	8	9𝜆3	9𝜆3	NUM
cana-1750	558	9	+	+	CCONJ
cana-1750	558	10	29𝜆2	29𝜆2	NUM
cana-1750	558	11	−	−	NOUN
cana-1750	558	12	45𝜆	45𝜆	NOUN
cana-1750	558	13	+	+	PUNCT
cana-1750	558	14	36	36	NUM
cana-1750	558	15	)	)	PUNCT
cana-1750	558	16	.	.	PUNCT
cana-1750	559	1	(	(	PUNCT
cana-1750	559	2	5.10	5.10	NUM
cana-1750	559	3	)	)	PUNCT
cana-1750	559	4	proof	proof	NOUN
cana-1750	559	5	.	.	PUNCT
cana-1750	560	1	first	first	ADV
cana-1750	560	2	note	note	VERB
cana-1750	560	3	that	that	SCONJ
cana-1750	560	4	by	by	ADP
cana-1750	560	5	equating	equate	VERB
cana-1750	560	6	the	the	DET
cana-1750	560	7	corresponding	corresponding	ADJ
cana-1750	560	8	coefficients	coefficient	NOUN
cana-1750	560	9	in	in	ADP
cana-1750	560	10	the	the	DET
cana-1750	560	11	equation	equation	NOUN
cana-1750	560	12	(	(	PUNCT
cana-1750	560	13	3.1	3.1	NUM
cana-1750	560	14	)	)	PUNCT
cana-1750	560	15	.	.	PUNCT
cana-1750	561	1	in	in	ADP
cana-1750	561	2	view	view	NOUN
cana-1750	561	3	of	of	ADP
cana-1750	561	4	(	(	PUNCT
cana-1750	561	5	3.2	3.2	NUM
cana-1750	561	6	)	)	PUNCT
cana-1750	561	7	,	,	PUNCT
cana-1750	561	8	(	(	PUNCT
cana-1750	561	9	3.4	3.4	NUM
cana-1750	561	10	)	)	PUNCT
cana-1750	561	11	and	and	CCONJ
cana-1750	561	12	(	(	PUNCT
cana-1750	561	13	3.5	3.5	NUM
cana-1750	561	14	)	)	PUNCT
cana-1750	561	15	,	,	PUNCT
cana-1750	561	16	we	we	PRON
cana-1750	561	17	may	may	AUX
cana-1750	561	18	write	write	VERB
cana-1750	561	19	2𝑝2	2𝑝2	NUM
cana-1750	561	20	=	=	SYM
cana-1750	561	21	𝑝1	𝑝1	NOUN
cana-1750	561	22	2	2	NUM
cana-1750	562	1	+	+	CCONJ
cana-1750	562	2	𝑥(4	𝑥(4	PROPN
cana-1750	562	3	−	−	PROPN
cana-1750	562	4	𝑝1	𝑝1	NOUN
cana-1750	562	5	2	2	NUM
cana-1750	562	6	)	)	PUNCT
cana-1750	562	7	,	,	PUNCT
cana-1750	562	8	𝑌	𝑌	PROPN
cana-1750	562	9	=	=	PUNCT
cana-1750	562	10	(	(	PUNCT
cana-1750	562	11	1	1	NUM
cana-1750	562	12	−	−	PROPN
cana-1750	562	13	|𝑥|2)𝜚	|𝑥|2)𝜚	NOUN
cana-1750	562	14	and	and	CCONJ
cana-1750	562	15	applying	apply	VERB
cana-1750	562	16	lemma	lemma	PROPN
cana-1750	562	17	(	(	PUNCT
cana-1750	562	18	2.2	2.2	NUM
cana-1750	562	19	)	)	PUNCT
cana-1750	562	20	,	,	PUNCT
cana-1750	562	21	a	a	DET
cana-1750	562	22	simple	simple	ADJ
cana-1750	562	23	computation	computation	NOUN
cana-1750	562	24	leads	lead	VERB
cana-1750	562	25	to	to	ADP
cana-1750	562	26	communications	communication	NOUN
cana-1750	562	27	on	on	ADP
cana-1750	562	28	applied	apply	VERB
cana-1750	562	29	nonlinear	nonlinear	ADJ
cana-1750	562	30	analysis	analysis	NOUN
cana-1750	562	31	issn	issn	NOUN
cana-1750	562	32	:	:	PUNCT
cana-1750	562	33	1074	1074	NUM
cana-1750	562	34	-	-	PUNCT
cana-1750	562	35	133x	133x	NUM
cana-1750	562	36	vol	vol	NOUN
cana-1750	562	37	32	32	NUM
cana-1750	562	38	no	no	NOUN
cana-1750	562	39	.	.	NOUN
cana-1750	562	40	2	2	NUM
cana-1750	562	41	(	(	PUNCT
cana-1750	562	42	2025	2025	NUM
cana-1750	562	43	)	)	PUNCT
cana-1750	563	1	401	401	NUM
cana-1750	563	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	563	3	𝑎2𝑎4	𝑎2𝑎4	PRON
cana-1750	563	4	−	−	PROPN
cana-1750	563	5	𝑎5	𝑎5	PROPN
cana-1750	563	6	=	=	SYM
cana-1750	563	7	[	[	PUNCT
cana-1750	563	8	𝜆4−9𝜆3	𝜆4−9𝜆3	PROPN
cana-1750	563	9	+	+	PROPN
cana-1750	563	10	29𝜆2−45𝜆+36	29𝜆2−45𝜆+36	NUM
cana-1750	563	11	8(𝜆+1)2(𝜆+2)(𝜆+3)(𝜆+4	8(𝜆+1)2(𝜆+2)(𝜆+3)(𝜆+4	NUM
cana-1750	563	12	)	)	PUNCT
cana-1750	563	13	]	]	PUNCT
cana-1750	564	1	𝑝1	𝑝1	NOUN
cana-1750	564	2	4	4	NUM
cana-1750	564	3	+	+	CCONJ
cana-1750	564	4	[	[	PUNCT
cana-1750	564	5	−3𝜆4	−3𝜆4	NUM
cana-1750	564	6	+	+	NOUN
cana-1750	564	7	11𝜆3	11𝜆3	NUM
cana-1750	564	8	+	+	ADJ
cana-1750	564	9	9𝜆2−35𝜆−6	9𝜆2−35𝜆−6	NOUN
cana-1750	564	10	8(𝜆+1)2(𝜆+2)(𝜆+3)(𝜆+4	8(𝜆+1)2(𝜆+2)(𝜆+3)(𝜆+4	NUM
cana-1750	564	11	)	)	PUNCT
cana-1750	564	12	]	]	PUNCT
cana-1750	565	1	𝑝1	𝑝1	NOUN
cana-1750	565	2	2𝑥𝑋	2𝑥𝑋	PROPN
cana-1750	565	3	+	+	X
cana-1750	565	4	[	[	PUNCT
cana-1750	565	5	−𝜆2	−𝜆2	X
cana-1750	565	6	+	+	PROPN
cana-1750	565	7	6𝜆+9	6𝜆+9	PROPN
cana-1750	565	8	8(𝜆+1)(𝜆+3)(𝜆+4	8(𝜆+1)(𝜆+3)(𝜆+4	NUM
cana-1750	565	9	)	)	PUNCT
cana-1750	565	10	]	]	PUNCT
cana-1750	566	1	𝑝1	𝑝1	NOUN
cana-1750	566	2	2𝑥2𝑋	2𝑥2𝑋	NUM
cana-1750	567	1	+	+	CCONJ
cana-1750	567	2	[	[	PUNCT
cana-1750	567	3	3𝜆2	3𝜆2	NUM
cana-1750	567	4	+	+	PROPN
cana-1750	567	5	7𝜆+3	7𝜆+3	NOUN
cana-1750	567	6	2(𝜆+1)(𝜆+3)(𝜆+4	2(𝜆+1)(𝜆+3)(𝜆+4	NUM
cana-1750	567	7	)	)	PUNCT
cana-1750	567	8	]	]	PUNCT
cana-1750	567	9	𝑝1𝑋𝑌	𝑝1𝑋𝑌	VERB
cana-1750	567	10	+	+	CCONJ
cana-1750	567	11	[	[	PUNCT
cana-1750	567	12	1−𝜆	1−𝜆	NUM
cana-1750	567	13	4(𝜆+2)(𝜆+4	4(𝜆+2)(𝜆+4	NUM
cana-1750	567	14	)	)	PUNCT
cana-1750	567	15	]	]	PUNCT
cana-1750	568	1	𝑥2𝑋2	𝑥2𝑋2	PUNCT
cana-1750	568	2	−	−	PROPN
cana-1750	568	3	𝑝1	𝑝1	NOUN
cana-1750	568	4	2𝑥3𝑋	2𝑥3𝑋	PROPN
cana-1750	568	5	8(𝜆+4	8(𝜆+4	NUM
cana-1750	568	6	)	)	PUNCT
cana-1750	568	7	−	−	PROPN
cana-1750	568	8	𝑥2𝑋	𝑥2𝑋	NOUN
cana-1750	568	9	2(𝜆+4	2(𝜆+4	NUM
cana-1750	568	10	)	)	PUNCT
cana-1750	568	11	−	−	PROPN
cana-1750	568	12	𝑥𝑋𝑝1	𝑥𝑋𝑝1	PROPN
cana-1750	568	13	2(𝜆+4	2(𝜆+4	NUM
cana-1750	568	14	)	)	PUNCT
cana-1750	569	1	+	+	CCONJ
cana-1750	569	2	𝑋𝑌	𝑋𝑌	PROPN
cana-1750	569	3	�	�	NOUN
cana-1750	569	4	̅	̅	NOUN
cana-1750	569	5	�	�	NOUN
cana-1750	569	6	2(𝜆+4	2(𝜆+4	NUM
cana-1750	569	7	)	)	PUNCT
cana-1750	569	8	(	(	PUNCT
cana-1750	569	9	5.11	5.11	NUM
cana-1750	569	10	)	)	PUNCT
cana-1750	569	11	without	without	ADP
cana-1750	569	12	loss	loss	NOUN
cana-1750	569	13	of	of	ADP
cana-1750	569	14	generality	generality	NOUN
cana-1750	569	15	,	,	PUNCT
cana-1750	569	16	we	we	PRON
cana-1750	569	17	let	let	VERB
cana-1750	569	18	0	0	NUM
cana-1750	569	19	≤	≤	NOUN
cana-1750	569	20	𝑝1	𝑝1	NOUN
cana-1750	569	21	=	=	SYM
cana-1750	569	22	𝑝	𝑝	NOUN
cana-1750	569	23	≤	≤	NUM
cana-1750	569	24	2	2	NUM
cana-1750	569	25	.	.	PUNCT
cana-1750	569	26	substitute	substitute	VERB
cana-1750	569	27	this	this	PRON
cana-1750	569	28	into	into	ADP
cana-1750	569	29	the	the	DET
cana-1750	569	30	above	above	ADJ
cana-1750	569	31	equation	equation	NOUN
cana-1750	569	32	,	,	PUNCT
cana-1750	569	33	we	we	PRON
cana-1750	569	34	obtain	obtain	VERB
cana-1750	569	35	the	the	DET
cana-1750	569	36	following	follow	VERB
cana-1750	569	37	quadratic	quadratic	ADJ
cana-1750	569	38	equation	equation	NOUN
cana-1750	569	39	in	in	ADP
cana-1750	569	40	terms	term	NOUN
cana-1750	569	41	of	of	ADP
cana-1750	569	42	𝑥.	𝑥.	ADJ
cana-1750	569	43	|𝑎2𝑎4	|𝑎2𝑎4	NOUN
cana-1750	569	44	−	−	PROPN
cana-1750	569	45	𝑎5|	𝑎5|	NOUN
cana-1750	569	46	≤	≤	NOUN
cana-1750	569	47	[	[	PUNCT
cana-1750	569	48	𝑝2(4	𝑝2(4	NOUN
cana-1750	569	49	−	−	PROPN
cana-1750	569	50	𝑝2	𝑝2	NOUN
cana-1750	569	51	)	)	PUNCT
cana-1750	569	52	8(𝜆	8(𝜆	NUM
cana-1750	570	1	+	+	CCONJ
cana-1750	570	2	4	4	NUM
cana-1750	570	3	)	)	PUNCT
cana-1750	570	4	−	−	PROPN
cana-1750	570	5	𝑝(4	𝑝(4	PROPN
cana-1750	570	6	−	−	PROPN
cana-1750	570	7	𝑝2	𝑝2	NOUN
cana-1750	570	8	)	)	PUNCT
cana-1750	570	9	2(𝜆	2(𝜆	NUM
cana-1750	571	1	+	+	CCONJ
cana-1750	571	2	4	4	NUM
cana-1750	571	3	)	)	PUNCT
cana-1750	571	4	]	]	PUNCT
cana-1750	572	1	|𝑥|3	|𝑥|3	PROPN
cana-1750	572	2	+	+	CCONJ
cana-1750	572	3	[	[	PUNCT
cana-1750	572	4	(	(	PUNCT
cana-1750	572	5	−𝜆2	−𝜆2	PROPN
cana-1750	572	6	+	+	VERB
cana-1750	572	7	6𝜆	6𝜆	NUM
cana-1750	572	8	+	+	CCONJ
cana-1750	572	9	9)(4	9)(4	NUM
cana-1750	572	10	−	−	NOUN
cana-1750	572	11	𝑝2)𝑝2	𝑝2)𝑝2	PROPN
cana-1750	572	12	8(𝜆	8(𝜆	NUM
cana-1750	572	13	+	+	NUM
cana-1750	572	14	1)(𝜆	1)(𝜆	NUM
cana-1750	572	15	+	+	CCONJ
cana-1750	572	16	3)(𝜆	3)(𝜆	NUM
cana-1750	572	17	+	+	NUM
cana-1750	572	18	4	4	NUM
cana-1750	572	19	)	)	PUNCT
cana-1750	572	20	+	+	CCONJ
cana-1750	572	21	4	4	NUM
cana-1750	572	22	−	−	NOUN
cana-1750	572	23	𝑝2	𝑝2	NOUN
cana-1750	572	24	2(𝜆	2(𝜆	NUM
cana-1750	572	25	+	+	CCONJ
cana-1750	572	26	4	4	NUM
cana-1750	572	27	)	)	PUNCT
cana-1750	572	28	]	]	PUNCT
cana-1750	573	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	573	2	+	+	PUNCT
cana-1750	573	3	[	[	PUNCT
cana-1750	573	4	(	(	PUNCT
cana-1750	573	5	4	4	NUM
cana-1750	573	6	−	−	NOUN
cana-1750	573	7	𝑝2)2	𝑝2)2	NUM
cana-1750	573	8	4(2	4(2	NUM
cana-1750	574	1	+	+	PUNCT
cana-1750	574	2	𝜆)(𝜆	𝜆)(𝜆	PUNCT
cana-1750	575	1	+	+	CCONJ
cana-1750	575	2	4	4	X
cana-1750	575	3	)	)	PUNCT
cana-1750	575	4	−	−	PROPN
cana-1750	575	5	(	(	PUNCT
cana-1750	575	6	3𝜆2	3𝜆2	NUM
cana-1750	576	1	+	+	NUM
cana-1750	576	2	7𝜆	7𝜆	NUM
cana-1750	576	3	+	+	CCONJ
cana-1750	576	4	3)(4	3)(4	NUM
cana-1750	576	5	−	−	NOUN
cana-1750	576	6	𝑝2)𝑝	𝑝2)𝑝	VERB
cana-1750	576	7	2(𝜆	2(𝜆	NUM
cana-1750	577	1	+	+	CCONJ
cana-1750	577	2	1)(𝜆	1)(𝜆	NUM
cana-1750	578	1	+	+	CCONJ
cana-1750	578	2	3)(𝜆	3)(𝜆	NUM
cana-1750	578	3	+	+	NUM
cana-1750	578	4	4	4	NUM
cana-1750	578	5	)	)	PUNCT
cana-1750	578	6	−	−	PROPN
cana-1750	578	7	(	(	PUNCT
cana-1750	578	8	4	4	NUM
cana-1750	578	9	−	−	NOUN
cana-1750	578	10	𝑝2)𝑥‾	𝑝2)𝑥‾	PROPN
cana-1750	578	11	2(𝜆	2(𝜆	NUM
cana-1750	578	12	+	+	CCONJ
cana-1750	578	13	4	4	NUM
cana-1750	578	14	)	)	PUNCT
cana-1750	578	15	]	]	PUNCT
cana-1750	579	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	579	2	+	+	PUNCT
cana-1750	579	3	[	[	PUNCT
cana-1750	579	4	−3𝜆4	−3𝜆4	X
cana-1750	579	5	+	+	NUM
cana-1750	579	6	11𝜆3	11𝜆3	NUM
cana-1750	579	7	+	+	CCONJ
cana-1750	579	8	9𝜆2	9𝜆2	NUM
cana-1750	579	9	−	−	NUM
cana-1750	579	10	35𝜆	35𝜆	NOUN
cana-1750	579	11	−	−	PROPN
cana-1750	579	12	6	6	NUM
cana-1750	579	13	8(𝜆	8(𝜆	NUM
cana-1750	579	14	+	+	CCONJ
cana-1750	579	15	1)2(𝜆	1)2(𝜆	NUM
cana-1750	579	16	+	+	NUM
cana-1750	579	17	2)(𝜆	2)(𝜆	NUM
cana-1750	579	18	+	+	CCONJ
cana-1750	579	19	3)(𝜆	3)(𝜆	NUM
cana-1750	579	20	+	+	SYM
cana-1750	579	21	4	4	NUM
cana-1750	579	22	)	)	PUNCT
cana-1750	579	23	𝑝2(4	𝑝2(4	NOUN
cana-1750	579	24	−	−	PROPN
cana-1750	579	25	𝑝2	𝑝2	PROPN
cana-1750	579	26	)	)	PUNCT
cana-1750	580	1	+	+	CCONJ
cana-1750	580	2	𝑝(4	𝑝(4	PROPN
cana-1750	580	3	−	−	PROPN
cana-1750	580	4	𝑝2	𝑝2	NOUN
cana-1750	580	5	)	)	PUNCT
cana-1750	580	6	2(𝜆	2(𝜆	NUM
cana-1750	581	1	+	+	CCONJ
cana-1750	582	1	2	2	NUM
cana-1750	582	2	)	)	PUNCT
cana-1750	582	3	]	]	PUNCT
cana-1750	583	1	|𝑥|	|𝑥|	INTJ
cana-1750	584	1	+	+	PUNCT
cana-1750	584	2	[	[	PUNCT
cana-1750	584	3	3𝜆2	3𝜆2	NUM
cana-1750	584	4	+	+	NUM
cana-1750	584	5	7𝜆	7𝜆	NUM
cana-1750	584	6	+	+	CCONJ
cana-1750	584	7	3	3	NUM
cana-1750	584	8	2(𝜆	2(𝜆	NUM
cana-1750	584	9	+	+	CCONJ
cana-1750	584	10	1)(𝜆	1)(𝜆	NUM
cana-1750	584	11	+	+	CCONJ
cana-1750	584	12	3)(𝜆	3)(𝜆	NUM
cana-1750	584	13	+	+	NUM
cana-1750	584	14	4	4	NUM
cana-1750	584	15	)	)	PUNCT
cana-1750	584	16	]	]	PUNCT
cana-1750	584	17	𝑝(4	𝑝(4	PROPN
cana-1750	584	18	−	−	PROPN
cana-1750	584	19	𝑝2	𝑝2	NOUN
cana-1750	584	20	)	)	PUNCT
cana-1750	584	21	+	+	CCONJ
cana-1750	584	22	(	(	PUNCT
cana-1750	584	23	4	4	NUM
cana-1750	584	24	−	−	NOUN
cana-1750	584	25	𝑝2)𝑥‾	𝑝2)𝑥‾	PROPN
cana-1750	584	26	2(𝜆	2(𝜆	NUM
cana-1750	584	27	+	+	CCONJ
cana-1750	584	28	4	4	NUM
cana-1750	584	29	)	)	PUNCT
cana-1750	584	30	+	+	CCONJ
cana-1750	584	31	[	[	PUNCT
cana-1750	584	32	𝜆4	𝜆4	NOUN
cana-1750	584	33	−	−	NOUN
cana-1750	584	34	9𝜆3	9𝜆3	NUM
cana-1750	585	1	+	+	CCONJ
cana-1750	585	2	29𝜆2	29𝜆2	NUM
cana-1750	585	3	−	−	NOUN
cana-1750	585	4	45𝜆	45𝜆	NOUN
cana-1750	585	5	+	+	CCONJ
cana-1750	586	1	36	36	NUM
cana-1750	586	2	8(𝜆	8(𝜆	NUM
cana-1750	586	3	+	+	CCONJ
cana-1750	586	4	1)2(𝜆	1)2(𝜆	NUM
cana-1750	586	5	+	+	NUM
cana-1750	586	6	2)(𝜆	2)(𝜆	NUM
cana-1750	586	7	+	+	CCONJ
cana-1750	586	8	3)(𝜆	3)(𝜆	NUM
cana-1750	586	9	+	+	NUM
cana-1750	586	10	4	4	NUM
cana-1750	586	11	)	)	PUNCT
cana-1750	586	12	]	]	PUNCT
cana-1750	586	13	𝑝4	𝑝4	NOUN
cana-1750	586	14	.	.	PUNCT
cana-1750	587	1	=	=	PUNCT
cana-1750	587	2	δ(𝑝	δ(𝑝	X
cana-1750	587	3	,	,	PUNCT
cana-1750	587	4	|𝑥|	|𝑥|	NUM
cana-1750	587	5	)	)	PUNCT
cana-1750	587	6	.	.	PUNCT
cana-1750	588	1	(	(	PUNCT
cana-1750	588	2	5.12	5.12	NUM
cana-1750	588	3	)	)	PUNCT
cana-1750	588	4	we	we	PRON
cana-1750	588	5	need	need	VERB
cana-1750	588	6	to	to	PART
cana-1750	588	7	prove	prove	VERB
cana-1750	588	8	that	that	SCONJ
cana-1750	588	9	the	the	DET
cana-1750	588	10	maximum	maximum	ADJ
cana-1750	588	11	value	value	NOUN
cana-1750	588	12	of	of	ADP
cana-1750	588	13	δ(𝑝	δ(𝑝	NOUN
cana-1750	588	14	,	,	PUNCT
cana-1750	588	15	|𝑥|	|𝑥|	NUM
cana-1750	588	16	)	)	PUNCT
cana-1750	588	17	on	on	ADP
cana-1750	588	18	[	[	X
cana-1750	588	19	0,2	0,2	NUM
cana-1750	588	20	]	]	X
cana-1750	588	21	×	×	NOUN
cana-1750	589	1	[	[	X
cana-1750	589	2	0,1	0,1	NUM
cana-1750	589	3	]	]	PUNCT
cana-1750	589	4	.	.	PUNCT
cana-1750	590	1	first	first	ADV
cana-1750	590	2	,	,	PUNCT
cana-1750	590	3	assume	assume	VERB
cana-1750	590	4	that	that	SCONJ
cana-1750	590	5	there	there	PRON
cana-1750	590	6	is	be	VERB
cana-1750	590	7	a	a	DET
cana-1750	590	8	maximum	maximum	NOUN
cana-1750	590	9	at	at	ADP
cana-1750	590	10	an	an	DET
cana-1750	590	11	interior	interior	ADJ
cana-1750	590	12	point	point	NOUN
cana-1750	590	13	δ(𝑝0	δ(𝑝0	NOUN
cana-1750	590	14	,	,	PUNCT
cana-1750	590	15	|𝑥0|	|𝑥0|	VERB
cana-1750	590	16	)	)	PUNCT
cana-1750	590	17	of	of	ADP
cana-1750	590	18	[	[	X
cana-1750	590	19	0,2	0,2	NUM
cana-1750	590	20	]	]	X
cana-1750	590	21	×	×	NOUN
cana-1750	591	1	[	[	X
cana-1750	591	2	0,1	0,1	NUM
cana-1750	591	3	]	]	PUNCT
cana-1750	591	4	.	.	PUNCT
cana-1750	592	1	differentiating	differentiate	VERB
cana-1750	592	2	δ(𝑝	δ(𝑝	NOUN
cana-1750	592	3	,	,	PUNCT
cana-1750	592	4	|𝑥|	|𝑥|	PROPN
cana-1750	592	5	)	)	PUNCT
cana-1750	592	6	with	with	ADP
cana-1750	592	7	respect	respect	NOUN
cana-1750	592	8	to	to	ADP
cana-1750	592	9	|𝑥|	|𝑥|	VERB
cana-1750	592	10	and	and	CCONJ
cana-1750	592	11	equating	equate	VERB
cana-1750	592	12	it	it	PRON
cana-1750	592	13	to	to	ADP
cana-1750	592	14	0	0	NUM
cana-1750	592	15	implies	imply	VERB
cana-1750	592	16	that	that	SCONJ
cana-1750	592	17	𝑝	𝑝	X
cana-1750	592	18	=	=	SYM
cana-1750	592	19	𝑝0	𝑝0	NOUN
cana-1750	592	20	=	=	SYM
cana-1750	592	21	2	2	NUM
cana-1750	592	22	which	which	PRON
cana-1750	592	23	is	be	AUX
cana-1750	592	24	contradiction	contradiction	NOUN
cana-1750	592	25	.	.	PUNCT
cana-1750	593	1	thus	thus	ADV
cana-1750	593	2	,	,	PUNCT
cana-1750	593	3	for	for	ADP
cana-1750	593	4	the	the	DET
cana-1750	593	5	maximum	maximum	NOUN
cana-1750	593	6	of	of	ADP
cana-1750	593	7	δ(𝑝	δ(𝑝	NOUN
cana-1750	593	8	,	,	PUNCT
cana-1750	593	9	|𝑥|	|𝑥|	PROPN
cana-1750	593	10	)	)	PUNCT
cana-1750	593	11	,	,	PUNCT
cana-1750	593	12	we	we	PRON
cana-1750	593	13	should	should	AUX
cana-1750	593	14	consider	consider	VERB
cana-1750	593	15	the	the	DET
cana-1750	593	16	end	end	NOUN
cana-1750	593	17	points	point	NOUN
cana-1750	593	18	of	of	ADP
cana-1750	593	19	[	[	X
cana-1750	593	20	0,2	0,2	NUM
cana-1750	593	21	]	]	X
cana-1750	593	22	×	×	NOUN
cana-1750	594	1	[	[	X
cana-1750	594	2	0,1	0,1	NUM
cana-1750	594	3	]	]	PUNCT
cana-1750	594	4	.	.	PUNCT
cana-1750	595	1	for	for	ADP
cana-1750	595	2	𝑝	𝑝	NOUN
cana-1750	595	3	=	=	SYM
cana-1750	595	4	0	0	NUM
cana-1750	595	5	,	,	PUNCT
cana-1750	595	6	we	we	PRON
cana-1750	595	7	obtain	obtain	VERB
cana-1750	595	8	δ(0	δ(0	NOUN
cana-1750	595	9	,	,	PUNCT
cana-1750	595	10	|𝑥|	|𝑥|	ADJ
cana-1750	595	11	)	)	PUNCT
cana-1750	596	1	=	=	PUNCT
cana-1750	596	2	[	[	PUNCT
cana-1750	596	3	2	2	NUM
cana-1750	596	4	(	(	PUNCT
cana-1750	596	5	4	4	NUM
cana-1750	596	6	+	+	CCONJ
cana-1750	596	7	𝜆	𝜆	X
cana-1750	596	8	)	)	PUNCT
cana-1750	596	9	+	+	NUM
cana-1750	596	10	4	4	NUM
cana-1750	596	11	(	(	PUNCT
cana-1750	596	12	𝜆	𝜆	PROPN
cana-1750	596	13	+	+	CCONJ
cana-1750	596	14	2)(4	2)(4	NUM
cana-1750	596	15	+	+	SYM
cana-1750	596	16	𝜆	𝜆	X
cana-1750	596	17	)	)	PUNCT
cana-1750	596	18	−	−	PROPN
cana-1750	596	19	2𝑥‾	2𝑥‾	NUM
cana-1750	596	20	(	(	PUNCT
cana-1750	596	21	4	4	NUM
cana-1750	596	22	+	+	SYM
cana-1750	596	23	𝜆	𝜆	X
cana-1750	596	24	)	)	PUNCT
cana-1750	596	25	]	]	PUNCT
cana-1750	597	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	597	2	+	+	PUNCT
cana-1750	597	3	2𝑥‾	2𝑥‾	NUM
cana-1750	597	4	(	(	PUNCT
cana-1750	597	5	4	4	NUM
cana-1750	597	6	+	+	SYM
cana-1750	597	7	𝜆	𝜆	X
cana-1750	597	8	)	)	PUNCT
cana-1750	597	9	.	.	PUNCT
cana-1750	598	1	(	(	PUNCT
cana-1750	598	2	5.13	5.13	NUM
cana-1750	598	3	)	)	PUNCT
cana-1750	598	4	for	for	ADP
cana-1750	598	5	𝑝	𝑝	NOUN
cana-1750	598	6	=	=	SYM
cana-1750	598	7	2	2	NUM
cana-1750	598	8	,	,	PUNCT
cana-1750	598	9	we	we	PRON
cana-1750	598	10	have	have	VERB
cana-1750	598	11	δ(2	δ(2	PROPN
cana-1750	598	12	,	,	PUNCT
cana-1750	598	13	|𝑥|	|𝑥|	ADJ
cana-1750	598	14	)	)	PUNCT
cana-1750	599	1	=	=	SYM
cana-1750	599	2	|𝒥(𝜆)|	|𝒥(𝜆)|	NOUN
cana-1750	599	3	(	(	PUNCT
cana-1750	599	4	𝜆	𝜆	PROPN
cana-1750	599	5	+	+	CCONJ
cana-1750	599	6	1)2(𝜆	1)2(𝜆	NUM
cana-1750	599	7	+	+	NUM
cana-1750	599	8	2)(𝜆	2)(𝜆	NUM
cana-1750	599	9	+	+	CCONJ
cana-1750	599	10	3)(𝜆	3)(𝜆	NUM
cana-1750	599	11	+	+	NUM
cana-1750	599	12	4	4	NUM
cana-1750	599	13	)	)	PUNCT
cana-1750	599	14	.	.	PUNCT
cana-1750	600	1	(	(	PUNCT
cana-1750	600	2	5.14	5.14	NUM
cana-1750	600	3	)	)	PUNCT
cana-1750	600	4	for	for	ADP
cana-1750	600	5	|𝑥|	|𝑥|	ADJ
cana-1750	600	6	=	=	SYM
cana-1750	600	7	0	0	NUM
cana-1750	600	8	,	,	PUNCT
cana-1750	600	9	we	we	PRON
cana-1750	600	10	gain	gain	VERB
cana-1750	600	11	δ(𝑝	δ(𝑝	NOUN
cana-1750	600	12	,	,	PUNCT
cana-1750	600	13	0	0	NUM
cana-1750	600	14	)	)	PUNCT
cana-1750	601	1	=	=	NOUN
cana-1750	602	1	[	[	PUNCT
cana-1750	602	2	3𝜆3	3𝜆3	NUM
cana-1750	603	1	+	+	CCONJ
cana-1750	603	2	7𝜆	7𝜆	NUM
cana-1750	603	3	+	+	CCONJ
cana-1750	603	4	3	3	NUM
cana-1750	603	5	2(𝜆	2(𝜆	NUM
cana-1750	603	6	+	+	CCONJ
cana-1750	603	7	1)(𝜆	1)(𝜆	NUM
cana-1750	603	8	+	+	CCONJ
cana-1750	603	9	3)(𝜆	3)(𝜆	NUM
cana-1750	603	10	+	+	NUM
cana-1750	603	11	4	4	NUM
cana-1750	603	12	)	)	PUNCT
cana-1750	603	13	]	]	PUNCT
cana-1750	603	14	𝑝(4	𝑝(4	PROPN
cana-1750	603	15	−	−	PROPN
cana-1750	603	16	𝑝2	𝑝2	NOUN
cana-1750	603	17	)	)	PUNCT
cana-1750	604	1	+	+	CCONJ
cana-1750	604	2	[	[	PUNCT
cana-1750	604	3	𝜆4	𝜆4	NOUN
cana-1750	604	4	−	−	NOUN
cana-1750	604	5	9𝜆3	9𝜆3	NUM
cana-1750	605	1	+	+	CCONJ
cana-1750	605	2	29𝜆2	29𝜆2	NUM
cana-1750	605	3	−	−	NOUN
cana-1750	605	4	45𝜆	45𝜆	NOUN
cana-1750	605	5	+	+	CCONJ
cana-1750	606	1	36	36	NUM
cana-1750	606	2	8(𝜆	8(𝜆	NUM
cana-1750	606	3	+	+	CCONJ
cana-1750	606	4	1)2(𝜆	1)2(𝜆	NUM
cana-1750	606	5	+	+	NUM
cana-1750	606	6	2)2(𝜆	2)2(𝜆	NUM
cana-1750	606	7	+	+	CCONJ
cana-1750	606	8	3)(𝜆	3)(𝜆	NUM
cana-1750	606	9	+	+	NUM
cana-1750	606	10	4	4	NUM
cana-1750	606	11	)	)	PUNCT
cana-1750	606	12	]	]	PUNCT
cana-1750	606	13	𝑝4	𝑝4	NOUN
cana-1750	606	14	.	.	PUNCT
cana-1750	607	1	(	(	PUNCT
cana-1750	607	2	5.15	5.15	NUM
cana-1750	607	3	)	)	PUNCT
cana-1750	607	4	communications	communication	NOUN
cana-1750	607	5	on	on	ADP
cana-1750	607	6	applied	apply	VERB
cana-1750	607	7	nonlinear	nonlinear	ADJ
cana-1750	607	8	analysis	analysis	NOUN
cana-1750	607	9	issn	issn	NOUN
cana-1750	607	10	:	:	PUNCT
cana-1750	607	11	1074	1074	NUM
cana-1750	607	12	-	-	PUNCT
cana-1750	607	13	133x	133x	NUM
cana-1750	607	14	vol	vol	NOUN
cana-1750	607	15	32	32	NUM
cana-1750	607	16	no	no	NOUN
cana-1750	607	17	.	.	NOUN
cana-1750	607	18	2	2	NUM
cana-1750	607	19	(	(	PUNCT
cana-1750	607	20	2025	2025	NUM
cana-1750	607	21	)	)	PUNCT
cana-1750	607	22	402	402	NUM
cana-1750	607	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	607	24	for	for	ADP
cana-1750	607	25	|𝑥|	|𝑥|	ADJ
cana-1750	607	26	=	=	SYM
cana-1750	607	27	1	1	NUM
cana-1750	607	28	,	,	PUNCT
cana-1750	607	29	we	we	PRON
cana-1750	607	30	obtain	obtain	VERB
cana-1750	607	31	δ(𝑝	δ(𝑝	NOUN
cana-1750	607	32	,	,	PUNCT
cana-1750	607	33	1	1	NUM
cana-1750	607	34	)	)	PUNCT
cana-1750	607	35	=	=	NOUN
cana-1750	608	1	[	[	PUNCT
cana-1750	608	2	𝑝2(4	𝑝2(4	PROPN
cana-1750	608	3	−	−	PROPN
cana-1750	608	4	𝑝2	𝑝2	NOUN
cana-1750	608	5	)	)	PUNCT
cana-1750	608	6	8(𝜆	8(𝜆	NUM
cana-1750	609	1	+	+	CCONJ
cana-1750	609	2	4	4	NUM
cana-1750	609	3	)	)	PUNCT
cana-1750	609	4	−	−	PROPN
cana-1750	609	5	𝑝(4	𝑝(4	PROPN
cana-1750	609	6	−	−	PROPN
cana-1750	609	7	𝑝2	𝑝2	NOUN
cana-1750	609	8	)	)	PUNCT
cana-1750	609	9	2(𝜆	2(𝜆	NUM
cana-1750	610	1	+	+	CCONJ
cana-1750	611	1	4	4	NUM
cana-1750	611	2	)	)	PUNCT
cana-1750	611	3	]	]	PUNCT
cana-1750	612	1	+	+	CCONJ
cana-1750	612	2	[	[	PUNCT
cana-1750	612	3	(	(	PUNCT
cana-1750	612	4	−𝜆2	−𝜆2	PROPN
cana-1750	612	5	+	+	VERB
cana-1750	612	6	6𝜆	6𝜆	NUM
cana-1750	612	7	+	+	CCONJ
cana-1750	612	8	9)(4	9)(4	NUM
cana-1750	612	9	−	−	NOUN
cana-1750	612	10	𝑝2)𝑝2	𝑝2)𝑝2	PROPN
cana-1750	612	11	8(𝜆	8(𝜆	NUM
cana-1750	612	12	+	+	NUM
cana-1750	612	13	1)(𝜆	1)(𝜆	NUM
cana-1750	612	14	+	+	CCONJ
cana-1750	612	15	3)(𝜆	3)(𝜆	NUM
cana-1750	612	16	+	+	NUM
cana-1750	612	17	4	4	NUM
cana-1750	612	18	)	)	PUNCT
cana-1750	612	19	+	+	CCONJ
cana-1750	612	20	4	4	NUM
cana-1750	612	21	−	−	NOUN
cana-1750	612	22	𝑝2	𝑝2	NOUN
cana-1750	612	23	2(𝜆	2(𝜆	NUM
cana-1750	612	24	+	+	CCONJ
cana-1750	612	25	4	4	NUM
cana-1750	612	26	)	)	PUNCT
cana-1750	612	27	]	]	PUNCT
cana-1750	613	1	+	+	CCONJ
cana-1750	613	2	[	[	PUNCT
cana-1750	613	3	(	(	PUNCT
cana-1750	613	4	4	4	NUM
cana-1750	613	5	−	−	NOUN
cana-1750	613	6	𝑝2)2	𝑝2)2	NUM
cana-1750	613	7	4(2	4(2	NUM
cana-1750	614	1	+	+	PUNCT
cana-1750	614	2	𝜆)(𝜆	𝜆)(𝜆	PUNCT
cana-1750	615	1	+	+	CCONJ
cana-1750	615	2	4	4	X
cana-1750	615	3	)	)	PUNCT
cana-1750	615	4	−	−	PROPN
cana-1750	615	5	(	(	PUNCT
cana-1750	615	6	3𝜆2	3𝜆2	NUM
cana-1750	616	1	+	+	NUM
cana-1750	616	2	7𝜆	7𝜆	NUM
cana-1750	616	3	+	+	CCONJ
cana-1750	616	4	3)(4	3)(4	NUM
cana-1750	616	5	−	−	NOUN
cana-1750	616	6	𝑝2)𝑝	𝑝2)𝑝	VERB
cana-1750	616	7	2(𝜆	2(𝜆	NUM
cana-1750	617	1	+	+	CCONJ
cana-1750	617	2	1)(𝜆	1)(𝜆	NUM
cana-1750	618	1	+	+	CCONJ
cana-1750	618	2	3)(𝜆	3)(𝜆	NUM
cana-1750	618	3	+	+	NUM
cana-1750	618	4	4	4	NUM
cana-1750	618	5	)	)	PUNCT
cana-1750	618	6	−	−	PROPN
cana-1750	618	7	(	(	PUNCT
cana-1750	618	8	4	4	NUM
cana-1750	618	9	−	−	PROPN
cana-1750	618	10	𝑝2	𝑝2	NOUN
cana-1750	618	11	)	)	PUNCT
cana-1750	618	12	2(𝜆	2(𝜆	NUM
cana-1750	619	1	+	+	CCONJ
cana-1750	620	1	4	4	NUM
cana-1750	620	2	)	)	PUNCT
cana-1750	620	3	]	]	PUNCT
cana-1750	621	1	+	+	CCONJ
cana-1750	621	2	[	[	PUNCT
cana-1750	621	3	−3𝜆4	−3𝜆4	X
cana-1750	621	4	+	+	NUM
cana-1750	621	5	11𝜆3	11𝜆3	NUM
cana-1750	621	6	+	+	CCONJ
cana-1750	621	7	9𝜆2	9𝜆2	NUM
cana-1750	622	1	−	−	NUM
cana-1750	622	2	35𝜆	35𝜆	NOUN
cana-1750	622	3	−	−	PROPN
cana-1750	622	4	6	6	NUM
cana-1750	622	5	8(𝜆	8(𝜆	NUM
cana-1750	622	6	+	+	CCONJ
cana-1750	622	7	1)2(𝜆	1)2(𝜆	NUM
cana-1750	622	8	+	+	NUM
cana-1750	622	9	2)(𝜆	2)(𝜆	NUM
cana-1750	622	10	+	+	CCONJ
cana-1750	622	11	3)(𝜆	3)(𝜆	NUM
cana-1750	622	12	+	+	SYM
cana-1750	622	13	4	4	NUM
cana-1750	622	14	)	)	PUNCT
cana-1750	622	15	𝑝2(4	𝑝2(4	NOUN
cana-1750	622	16	−	−	PROPN
cana-1750	622	17	𝑝2	𝑝2	PROPN
cana-1750	622	18	)	)	PUNCT
cana-1750	623	1	+	+	CCONJ
cana-1750	623	2	𝑝(4	𝑝(4	PROPN
cana-1750	623	3	−	−	PROPN
cana-1750	623	4	𝑝2	𝑝2	NOUN
cana-1750	623	5	)	)	PUNCT
cana-1750	623	6	2(𝜆	2(𝜆	NUM
cana-1750	624	1	+	+	CCONJ
cana-1750	624	2	2	2	NUM
cana-1750	624	3	)	)	PUNCT
cana-1750	624	4	]	]	PUNCT
cana-1750	625	1	+	+	CCONJ
cana-1750	625	2	[	[	PUNCT
cana-1750	625	3	3𝜆2	3𝜆2	NUM
cana-1750	625	4	+	+	NUM
cana-1750	625	5	7𝜆	7𝜆	NUM
cana-1750	625	6	+	+	CCONJ
cana-1750	625	7	3	3	NUM
cana-1750	625	8	2(𝜆	2(𝜆	NUM
cana-1750	625	9	+	+	CCONJ
cana-1750	625	10	1)(𝜆	1)(𝜆	NUM
cana-1750	625	11	+	+	CCONJ
cana-1750	625	12	3)(𝜆	3)(𝜆	NUM
cana-1750	625	13	+	+	NUM
cana-1750	625	14	4	4	NUM
cana-1750	625	15	)	)	PUNCT
cana-1750	625	16	]	]	PUNCT
cana-1750	625	17	𝑝(4	𝑝(4	PROPN
cana-1750	625	18	−	−	PROPN
cana-1750	625	19	𝑝2	𝑝2	NOUN
cana-1750	625	20	)	)	PUNCT
cana-1750	625	21	+	+	CCONJ
cana-1750	625	22	4	4	NUM
cana-1750	625	23	−	−	NOUN
cana-1750	625	24	𝑝2	𝑝2	NOUN
cana-1750	625	25	2(𝜆	2(𝜆	NUM
cana-1750	625	26	+	+	CCONJ
cana-1750	625	27	4	4	NUM
cana-1750	625	28	)	)	PUNCT
cana-1750	625	29	+	+	CCONJ
cana-1750	625	30	[	[	PUNCT
cana-1750	625	31	𝜆4	𝜆4	NOUN
cana-1750	625	32	−	−	NOUN
cana-1750	625	33	9𝜆3	9𝜆3	NUM
cana-1750	625	34	+	+	CCONJ
cana-1750	625	35	29𝜆2	29𝜆2	NUM
cana-1750	625	36	−	−	NOUN
cana-1750	625	37	45𝜆	45𝜆	NOUN
cana-1750	625	38	+	+	CCONJ
cana-1750	625	39	36	36	NUM
cana-1750	625	40	8(𝜆	8(𝜆	NUM
cana-1750	625	41	+	+	CCONJ
cana-1750	625	42	1)2(𝜆	1)2(𝜆	NUM
cana-1750	626	1	+	+	NUM
cana-1750	626	2	2)2(𝜆	2)2(𝜆	NUM
cana-1750	627	1	+	+	CCONJ
cana-1750	627	2	3)(𝜆	3)(𝜆	NUM
cana-1750	627	3	+	+	NUM
cana-1750	627	4	4	4	NUM
cana-1750	627	5	)	)	PUNCT
cana-1750	627	6	]	]	PUNCT
cana-1750	627	7	𝑝4	𝑝4	NOUN
cana-1750	627	8	.	.	PUNCT
cana-1750	628	1	(	(	PUNCT
cana-1750	628	2	5.16	5.16	NUM
cana-1750	628	3	)	)	PUNCT
cana-1750	628	4	which	which	PRON
cana-1750	628	5	has	have	VERB
cana-1750	628	6	maximum	maximum	ADJ
cana-1750	628	7	value	value	NOUN
cana-1750	628	8	|𝜕(𝜆)|	|𝜕(𝜆)|	CCONJ
cana-1750	628	9	(	(	PUNCT
cana-1750	628	10	𝜆+1)2(𝜆+2)(𝜆+3)(𝜆+4	𝜆+1)2(𝜆+2)(𝜆+3)(𝜆+4	PROPN
cana-1750	628	11	)	)	PUNCT
cana-1750	628	12	attained	attain	VERB
cana-1750	628	13	at	at	ADP
cana-1750	628	14	the	the	DET
cana-1750	628	15	end	end	NOUN
cana-1750	628	16	point	point	NOUN
cana-1750	628	17	𝑝	𝑝	NOUN
cana-1750	628	18	=	=	SYM
cana-1750	628	19	2	2	NUM
cana-1750	628	20	and	and	CCONJ
cana-1750	628	21	4	4	NUM
cana-1750	628	22	𝜆+2	𝜆+2	NOUN
cana-1750	628	23	at	at	ADP
cana-1750	628	24	𝑝	𝑝	NOUN
cana-1750	628	25	=	=	SYM
cana-1750	628	26	0	0	PROPN
cana-1750	628	27	.	.	PUNCT
cana-1750	629	1	where	where	SCONJ
cana-1750	629	2	,	,	PUNCT
cana-1750	629	3	𝒥(𝜆	𝒥(𝜆	NOUN
cana-1750	629	4	)	)	PUNCT
cana-1750	629	5	=	=	SYM
cana-1750	629	6	2(𝜆4	2(𝜆4	NUM
cana-1750	629	7	−	−	NOUN
cana-1750	629	8	9𝜆3	9𝜆3	NUM
cana-1750	629	9	+	+	CCONJ
cana-1750	629	10	29𝜆2	29𝜆2	NUM
cana-1750	629	11	−	−	NOUN
cana-1750	629	12	45𝜆	45𝜆	NOUN
cana-1750	629	13	+	+	PUNCT
cana-1750	629	14	36	36	NUM
cana-1750	629	15	)	)	PUNCT
cana-1750	629	16	.	.	PUNCT
cana-1750	630	1	(	(	PUNCT
cana-1750	630	2	5.17	5.17	NUM
cana-1750	630	3	)	)	PUNCT
cana-1750	630	4	6	6	NUM
cana-1750	630	5	.	.	PUNCT
cana-1750	630	6	krushkal	krushkal	ADJ
cana-1750	630	7	inequality	inequality	NOUN
cana-1750	630	8	for	for	ADP
cana-1750	630	9	the	the	DET
cana-1750	630	10	class	class	NOUN
cana-1750	630	11	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	630	12	)	)	PUNCT
cana-1750	630	13	theorem	theorem	VERB
cana-1750	630	14	6.1	6.1	NUM
cana-1750	630	15	.	.	PUNCT
cana-1750	631	1	let	let	VERB
cana-1750	631	2	𝑓	𝑓	PRON
cana-1750	631	3	given	give	VERB
cana-1750	631	4	by	by	ADP
cana-1750	631	5	(	(	PUNCT
cana-1750	631	6	1.1	1.1	NUM
cana-1750	631	7	)	)	PUNCT
cana-1750	631	8	,	,	PUNCT
cana-1750	631	9	be	be	AUX
cana-1750	631	10	in	in	ADP
cana-1750	631	11	the	the	DET
cana-1750	631	12	class	class	NOUN
cana-1750	631	13	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	631	14	)	)	PUNCT
cana-1750	631	15	;	;	PUNCT
cana-1750	631	16	(	(	PUNCT
cana-1750	631	17	0	0	NUM
cana-1750	631	18	≤	≤	NUM
cana-1750	631	19	𝜆	𝜆	PRON
cana-1750	631	20	≤	≤	NUM
cana-1750	631	21	1	1	NUM
cana-1750	631	22	)	)	PUNCT
cana-1750	631	23	.	.	PUNCT
cana-1750	632	1	then	then	ADV
cana-1750	632	2	we	we	PRON
cana-1750	632	3	have	have	VERB
cana-1750	632	4	sharp	sharp	ADV
cana-1750	632	5	bound	bind	VERB
cana-1750	632	6	|𝑎4	|𝑎4	ADP
cana-1750	632	7	−	−	PROPN
cana-1750	632	8	𝑎2	𝑎2	PROPN
cana-1750	632	9	3|	3|	NUM
cana-1750	632	10	=	=	SYM
cana-1750	632	11	max	max	PROPN
cana-1750	632	12	{	{	PUNCT
cana-1750	632	13	4	4	NUM
cana-1750	632	14	𝜆	𝜆	NOUN
cana-1750	632	15	+	+	NUM
cana-1750	632	16	3	3	NUM
cana-1750	632	17	,	,	PUNCT
cana-1750	632	18	|ℒ(𝜆)|	|ℒ(𝜆)|	PROPN
cana-1750	632	19	(	(	PUNCT
cana-1750	632	20	𝜆	𝜆	PROPN
cana-1750	632	21	+	+	ADJ
cana-1750	632	22	1)3(𝜆	1)3(𝜆	NUM
cana-1750	632	23	+	+	CCONJ
cana-1750	632	24	2)(𝜆	2)(𝜆	NUM
cana-1750	632	25	+	+	CCONJ
cana-1750	632	26	3	3	NUM
cana-1750	632	27	)	)	PUNCT
cana-1750	632	28	}	}	PUNCT
cana-1750	632	29	.	.	PUNCT
cana-1750	633	1	where	where	SCONJ
cana-1750	633	2	,	,	PUNCT
cana-1750	633	3	ℒ(𝜆	ℒ(𝜆	NUM
cana-1750	633	4	)	)	PUNCT
cana-1750	633	5	=	=	SYM
cana-1750	633	6	𝜆4	𝜆4	NOUN
cana-1750	633	7	−	−	PROPN
cana-1750	633	8	5𝜆3	5𝜆3	NUM
cana-1750	633	9	−	−	NOUN
cana-1750	633	10	5𝜆2	5𝜆2	NUM
cana-1750	633	11	−	−	NOUN
cana-1750	633	12	3𝜆	3𝜆	ADJ
cana-1750	633	13	−	−	PROPN
cana-1750	633	14	12	12	NUM
cana-1750	633	15	.	.	PUNCT
cana-1750	634	1	(	(	PUNCT
cana-1750	634	2	6.1	6.1	NUM
cana-1750	634	3	)	)	PUNCT
cana-1750	634	4	proof	proof	NOUN
cana-1750	634	5	.	.	PUNCT
cana-1750	635	1	first	first	ADV
cana-1750	635	2	note	note	VERB
cana-1750	635	3	that	that	SCONJ
cana-1750	635	4	by	by	ADP
cana-1750	635	5	equating	equate	VERB
cana-1750	635	6	the	the	DET
cana-1750	635	7	corresponding	corresponding	ADJ
cana-1750	635	8	coefficients	coefficient	NOUN
cana-1750	635	9	in	in	ADP
cana-1750	635	10	the	the	DET
cana-1750	635	11	equation	equation	NOUN
cana-1750	635	12	(	(	PUNCT
cana-1750	635	13	3.1	3.1	NUM
cana-1750	635	14	)	)	PUNCT
cana-1750	635	15	.	.	PUNCT
cana-1750	636	1	we	we	PRON
cana-1750	636	2	get	get	VERB
cana-1750	636	3	,	,	PUNCT
cana-1750	636	4	in	in	ADP
cana-1750	636	5	the	the	DET
cana-1750	636	6	view	view	NOUN
cana-1750	636	7	of	of	ADP
cana-1750	636	8	(	(	PUNCT
cana-1750	636	9	3.2	3.2	NUM
cana-1750	636	10	)	)	PUNCT
cana-1750	636	11	and	and	CCONJ
cana-1750	636	12	(	(	PUNCT
cana-1750	636	13	3.4	3.4	NUM
cana-1750	636	14	)	)	PUNCT
cana-1750	636	15	,	,	PUNCT
cana-1750	636	16	we	we	PRON
cana-1750	636	17	may	may	AUX
cana-1750	636	18	write	write	VERB
cana-1750	636	19	2𝑝2	2𝑝2	NUM
cana-1750	636	20	=	=	SYM
cana-1750	636	21	𝑝1	𝑝1	NOUN
cana-1750	636	22	2	2	NUM
cana-1750	637	1	+	+	CCONJ
cana-1750	637	2	𝑥(4	𝑥(4	PROPN
cana-1750	637	3	−	−	PROPN
cana-1750	637	4	𝑝1	𝑝1	NOUN
cana-1750	637	5	2	2	NUM
cana-1750	637	6	)	)	PUNCT
cana-1750	637	7	,	,	PUNCT
cana-1750	637	8	𝑌	𝑌	PROPN
cana-1750	637	9	=	=	PUNCT
cana-1750	637	10	(	(	PUNCT
cana-1750	637	11	1	1	NUM
cana-1750	637	12	−	−	PROPN
cana-1750	637	13	|𝑥|2)𝜚	|𝑥|2)𝜚	NOUN
cana-1750	637	14	and	and	CCONJ
cana-1750	637	15	applying	apply	VERB
cana-1750	637	16	lemma	lemma	PROPN
cana-1750	637	17	(	(	PUNCT
cana-1750	637	18	2.2	2.2	NUM
cana-1750	637	19	)	)	PUNCT
cana-1750	637	20	,	,	PUNCT
cana-1750	637	21	a	a	DET
cana-1750	637	22	simple	simple	ADJ
cana-1750	637	23	computation	computation	NOUN
cana-1750	637	24	leads	lead	VERB
cana-1750	637	25	to	to	ADP
cana-1750	637	26	𝑎4	𝑎4	PROPN
cana-1750	637	27	−	−	PROPN
cana-1750	637	28	𝑎2	𝑎2	NOUN
cana-1750	637	29	3	3	NUM
cana-1750	637	30	=	=	SYM
cana-1750	637	31	[	[	PUNCT
cana-1750	637	32	𝑝1	𝑝1	NOUN
cana-1750	637	33	3(1	3(1	NUM
cana-1750	637	34	−	−	PROPN
cana-1750	637	35	𝜆)2	𝜆)2	NOUN
cana-1750	637	36	(	(	PUNCT
cana-1750	637	37	𝜆	𝜆	PROPN
cana-1750	637	38	+	+	ADJ
cana-1750	637	39	1)(𝜆	1)(𝜆	NUM
cana-1750	637	40	+	+	CCONJ
cana-1750	637	41	2)(𝜆	2)(𝜆	NUM
cana-1750	637	42	+	+	CCONJ
cana-1750	637	43	3	3	NUM
cana-1750	637	44	)	)	PUNCT
cana-1750	637	45	+	+	NUM
cana-1750	637	46	𝑝1𝑝2(1	𝑝1𝑝2(1	NOUN
cana-1750	637	47	−	−	NOUN
cana-1750	637	48	𝜆)(3	𝜆)(3	X
cana-1750	637	49	+	+	CCONJ
cana-1750	637	50	2𝜆	2𝜆	NUM
cana-1750	637	51	)	)	PUNCT
cana-1750	637	52	(	(	PUNCT
cana-1750	637	53	𝜆	𝜆	X
cana-1750	637	54	+	+	NOUN
cana-1750	637	55	1)(𝜆	1)(𝜆	NUM
cana-1750	637	56	+	+	CCONJ
cana-1750	637	57	2)(𝜆	2)(𝜆	NUM
cana-1750	637	58	+	+	CCONJ
cana-1750	637	59	3	3	NUM
cana-1750	637	60	)	)	PUNCT
cana-1750	638	1	+	+	CCONJ
cana-1750	638	2	𝑝3	𝑝3	ADV
cana-1750	638	3	𝜆	𝜆	ADP
cana-1750	639	1	+	+	ADP
cana-1750	639	2	3	3	NUM
cana-1750	639	3	]	]	PUNCT
cana-1750	639	4	−	−	PROPN
cana-1750	639	5	[	[	PUNCT
cana-1750	639	6	𝑝1	𝑝1	NOUN
cana-1750	639	7	𝜆	𝜆	NOUN
cana-1750	639	8	+	+	PROPN
cana-1750	639	9	1	1	NUM
cana-1750	639	10	]	]	SYM
cana-1750	639	11	3	3	NUM
cana-1750	639	12	.	.	PUNCT
cana-1750	640	1	(	(	PUNCT
cana-1750	640	2	6.2	6.2	NUM
cana-1750	640	3	)	)	PUNCT
cana-1750	640	4	note	note	VERB
cana-1750	640	5	that	that	SCONJ
cana-1750	640	6	,	,	PUNCT
cana-1750	640	7	by	by	ADP
cana-1750	640	8	lemma	lemma	PROPN
cana-1750	640	9	(	(	PUNCT
cana-1750	640	10	2.2	2.2	NUM
cana-1750	640	11	)	)	PUNCT
cana-1750	640	12	,	,	PUNCT
cana-1750	640	13	we	we	PRON
cana-1750	640	14	have	have	VERB
cana-1750	640	15	𝑎4	𝑎4	PROPN
cana-1750	641	1	−	−	PROPN
cana-1750	641	2	𝑎2	𝑎2	NOUN
cana-1750	641	3	3	3	NUM
cana-1750	641	4	=	=	SYM
cana-1750	641	5	[	[	PUNCT
cana-1750	641	6	(	(	PUNCT
cana-1750	641	7	1	1	NUM
cana-1750	641	8	−	−	NOUN
cana-1750	641	9	𝜆)2	𝜆)2	NOUN
cana-1750	641	10	(	(	PUNCT
cana-1750	641	11	𝜆	𝜆	PROPN
cana-1750	641	12	+	+	ADJ
cana-1750	641	13	1)(𝜆	1)(𝜆	NUM
cana-1750	642	1	+	+	CCONJ
cana-1750	642	2	2)(𝜆	2)(𝜆	NUM
cana-1750	642	3	+	+	CCONJ
cana-1750	642	4	3	3	NUM
cana-1750	642	5	)	)	PUNCT
cana-1750	642	6	+	+	CCONJ
cana-1750	642	7	(	(	PUNCT
cana-1750	642	8	1	1	NUM
cana-1750	642	9	−	−	NOUN
cana-1750	642	10	𝜆)(3	𝜆)(3	NOUN
cana-1750	642	11	+	+	CCONJ
cana-1750	642	12	2𝜆	2𝜆	NUM
cana-1750	642	13	)	)	PUNCT
cana-1750	642	14	2(𝜆	2(𝜆	NUM
cana-1750	643	1	+	+	CCONJ
cana-1750	643	2	1)(𝜆	1)(𝜆	NUM
cana-1750	644	1	+	+	CCONJ
cana-1750	644	2	2)(𝜆	2)(𝜆	NUM
cana-1750	644	3	+	+	CCONJ
cana-1750	644	4	3	3	NUM
cana-1750	644	5	)	)	PUNCT
cana-1750	644	6	+	+	CCONJ
cana-1750	644	7	1	1	NUM
cana-1750	644	8	4(𝜆	4(𝜆	NUM
cana-1750	644	9	+	+	CCONJ
cana-1750	644	10	3	3	X
cana-1750	644	11	)	)	PUNCT
cana-1750	644	12	−	−	NOUN
cana-1750	644	13	1	1	NUM
cana-1750	644	14	(	(	PUNCT
cana-1750	644	15	𝜆	𝜆	PROPN
cana-1750	644	16	+	+	X
cana-1750	644	17	1)3	1)3	PROPN
cana-1750	644	18	]	]	PUNCT
cana-1750	644	19	𝑝1	𝑝1	NOUN
cana-1750	644	20	3	3	NUM
cana-1750	645	1	+	+	CCONJ
cana-1750	645	2	[	[	PUNCT
cana-1750	645	3	(	(	PUNCT
cana-1750	645	4	1	1	NUM
cana-1750	645	5	−	−	NOUN
cana-1750	645	6	𝜆)(3	𝜆)(3	NOUN
cana-1750	645	7	+	+	CCONJ
cana-1750	645	8	2𝜆	2𝜆	NUM
cana-1750	645	9	)	)	PUNCT
cana-1750	645	10	2(𝜆	2(𝜆	NUM
cana-1750	646	1	+	+	CCONJ
cana-1750	646	2	1)(𝜆	1)(𝜆	NUM
cana-1750	647	1	+	+	CCONJ
cana-1750	647	2	2)(𝜆	2)(𝜆	NUM
cana-1750	647	3	+	+	CCONJ
cana-1750	647	4	3	3	NUM
cana-1750	647	5	)	)	PUNCT
cana-1750	647	6	+	+	CCONJ
cana-1750	647	7	1	1	NUM
cana-1750	647	8	2(𝜆	2(𝜆	NUM
cana-1750	647	9	+	+	CCONJ
cana-1750	647	10	3	3	NUM
cana-1750	647	11	)	)	PUNCT
cana-1750	647	12	]	]	PUNCT
cana-1750	648	1	𝑝1𝑋𝑥	𝑝1𝑋𝑥	PRON
cana-1750	648	2	−	−	PROPN
cana-1750	649	1	𝑝1𝑋𝑥	𝑝1𝑋𝑥	NOUN
cana-1750	649	2	4(𝜆	4(𝜆	NUM
cana-1750	650	1	+	+	CCONJ
cana-1750	650	2	3	3	X
cana-1750	650	3	)	)	PUNCT
cana-1750	650	4	+	+	CCONJ
cana-1750	650	5	𝑋𝑌	𝑋𝑌	PROPN
cana-1750	650	6	2(𝜆	2(𝜆	NUM
cana-1750	650	7	+	+	CCONJ
cana-1750	650	8	3	3	NUM
cana-1750	650	9	)	)	PUNCT
cana-1750	650	10	.	.	PUNCT
cana-1750	651	1	(	(	PUNCT
cana-1750	651	2	6.3	6.3	NUM
cana-1750	651	3	)	)	PUNCT
cana-1750	651	4	without	without	ADP
cana-1750	651	5	loss	loss	NOUN
cana-1750	651	6	of	of	ADP
cana-1750	651	7	generality	generality	NOUN
cana-1750	651	8	,	,	PUNCT
cana-1750	651	9	we	we	PRON
cana-1750	651	10	let	let	VERB
cana-1750	651	11	0	0	NUM
cana-1750	651	12	≤	≤	NOUN
cana-1750	651	13	𝑝1	𝑝1	NOUN
cana-1750	651	14	=	=	SYM
cana-1750	651	15	𝑝	𝑝	NOUN
cana-1750	651	16	≤	≤	NUM
cana-1750	651	17	2	2	NUM
cana-1750	651	18	.	.	PUNCT
cana-1750	651	19	substitute	substitute	VERB
cana-1750	651	20	this	this	PRON
cana-1750	651	21	into	into	ADP
cana-1750	651	22	the	the	DET
cana-1750	651	23	above	above	ADJ
cana-1750	651	24	equation	equation	NOUN
cana-1750	651	25	,	,	PUNCT
cana-1750	651	26	we	we	PRON
cana-1750	651	27	obtain	obtain	VERB
cana-1750	651	28	the	the	DET
cana-1750	651	29	following	follow	VERB
cana-1750	651	30	quadratic	quadratic	ADJ
cana-1750	651	31	equation	equation	NOUN
cana-1750	651	32	in	in	ADP
cana-1750	651	33	terms	term	NOUN
cana-1750	651	34	of	of	ADP
cana-1750	651	35	𝑥.	𝑥.	ADJ
cana-1750	651	36	communications	communication	NOUN
cana-1750	651	37	on	on	ADP
cana-1750	651	38	applied	apply	VERB
cana-1750	651	39	nonlinear	nonlinear	ADJ
cana-1750	651	40	analysis	analysis	NOUN
cana-1750	651	41	issn	issn	NOUN
cana-1750	651	42	:	:	PUNCT
cana-1750	651	43	1074	1074	NUM
cana-1750	651	44	-	-	PUNCT
cana-1750	651	45	133x	133x	NUM
cana-1750	651	46	vol	vol	NOUN
cana-1750	651	47	32	32	NUM
cana-1750	651	48	no	no	NOUN
cana-1750	651	49	.	.	NOUN
cana-1750	651	50	2	2	NUM
cana-1750	651	51	(	(	PUNCT
cana-1750	651	52	2025	2025	NUM
cana-1750	651	53	)	)	PUNCT
cana-1750	651	54	403	403	NUM
cana-1750	651	55	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	651	56	|𝑎4	|𝑎4	ADP
cana-1750	651	57	−	−	PROPN
cana-1750	651	58	𝑎2	𝑎2	PROPN
cana-1750	651	59	3|	3|	NUM
cana-1750	651	60	≤	≤	NOUN
cana-1750	651	61	[	[	PUNCT
cana-1750	651	62	𝑝(4	𝑝(4	PROPN
cana-1750	651	63	−	−	PROPN
cana-1750	651	64	𝑝2	𝑝2	NOUN
cana-1750	651	65	)	)	PUNCT
cana-1750	651	66	4(𝜆	4(𝜆	NUM
cana-1750	652	1	+	+	CCONJ
cana-1750	652	2	3	3	X
cana-1750	652	3	)	)	PUNCT
cana-1750	652	4	−	−	PROPN
cana-1750	652	5	4	4	NUM
cana-1750	652	6	−	−	PROPN
cana-1750	652	7	𝑝2	𝑝2	NOUN
cana-1750	652	8	2(𝜆	2(𝜆	NUM
cana-1750	652	9	+	+	CCONJ
cana-1750	652	10	3	3	NUM
cana-1750	652	11	)	)	PUNCT
cana-1750	652	12	]	]	PUNCT
cana-1750	653	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	653	2	+	+	PUNCT
cana-1750	654	1	[	[	X
cana-1750	654	2	[	[	PUNCT
cana-1750	654	3	−𝜆2	−𝜆2	X
cana-1750	654	4	+	+	CCONJ
cana-1750	654	5	2𝜆	2𝜆	NUM
cana-1750	654	6	+	+	CCONJ
cana-1750	654	7	5	5	NUM
cana-1750	654	8	2(1	2(1	NUM
cana-1750	654	9	+	+	CCONJ
cana-1750	654	10	𝜆)(2	𝜆)(2	ADP
cana-1750	654	11	+	+	NOUN
cana-1750	654	12	𝜆)(3	𝜆)(3	NOUN
cana-1750	654	13	+	+	CCONJ
cana-1750	654	14	𝜆	𝜆	X
cana-1750	654	15	)	)	PUNCT
cana-1750	654	16	]	]	PUNCT
cana-1750	654	17	𝑝(4	𝑝(4	PROPN
cana-1750	654	18	−	−	PROPN
cana-1750	654	19	𝑝2	𝑝2	NOUN
cana-1750	654	20	)	)	PUNCT
cana-1750	654	21	]	]	PUNCT
cana-1750	655	1	|𝑥|	|𝑥|	INTJ
cana-1750	656	1	+	+	PUNCT
cana-1750	656	2	[	[	PUNCT
cana-1750	656	3	𝜆4	𝜆4	NOUN
cana-1750	656	4	−	−	PROPN
cana-1750	656	5	5𝜆3	5𝜆3	NUM
cana-1750	656	6	−	−	NOUN
cana-1750	657	1	5𝜆2	5𝜆2	NUM
cana-1750	657	2	−	−	NOUN
cana-1750	657	3	3𝜆	3𝜆	ADJ
cana-1750	657	4	−	−	NOUN
cana-1750	657	5	12	12	NUM
cana-1750	658	1	4(𝜆	4(𝜆	NUM
cana-1750	659	1	+	+	CCONJ
cana-1750	660	1	1)3(𝜆	1)3(𝜆	NUM
cana-1750	660	2	+	+	CCONJ
cana-1750	660	3	2)(𝜆	2)(𝜆	NUM
cana-1750	660	4	+	+	CCONJ
cana-1750	660	5	3	3	NUM
cana-1750	660	6	)	)	PUNCT
cana-1750	660	7	]	]	PUNCT
cana-1750	661	1	𝑝3	𝑝3	ADV
cana-1750	661	2	+	+	NUM
cana-1750	661	3	4	4	NUM
cana-1750	661	4	−	−	NOUN
cana-1750	661	5	𝑝2	𝑝2	NOUN
cana-1750	661	6	2(𝜆	2(𝜆	NUM
cana-1750	661	7	+	+	CCONJ
cana-1750	661	8	3	3	NUM
cana-1750	661	9	)	)	PUNCT
cana-1750	661	10	.	.	PUNCT
cana-1750	662	1	=	=	PUNCT
cana-1750	662	2	γ(𝑝	γ(𝑝	NOUN
cana-1750	662	3	,	,	PUNCT
cana-1750	662	4	|𝑥|	|𝑥|	NUM
cana-1750	662	5	)	)	PUNCT
cana-1750	662	6	.	.	PUNCT
cana-1750	663	1	(	(	PUNCT
cana-1750	663	2	6.4	6.4	NUM
cana-1750	663	3	)	)	PUNCT
cana-1750	663	4	so	so	ADV
cana-1750	663	5	,	,	PUNCT
cana-1750	663	6	the	the	DET
cana-1750	663	7	maximum	maximum	ADJ
cana-1750	663	8	value	value	NOUN
cana-1750	663	9	of	of	ADP
cana-1750	663	10	γ(𝑝	γ(𝑝	NOUN
cana-1750	663	11	,	,	PUNCT
cana-1750	663	12	|𝑥|	|𝑥|	NUM
cana-1750	663	13	)	)	PUNCT
cana-1750	663	14	on	on	ADP
cana-1750	663	15	[	[	X
cana-1750	663	16	0,2	0,2	NUM
cana-1750	663	17	]	]	X
cana-1750	663	18	×	×	NOUN
cana-1750	663	19	[	[	X
cana-1750	663	20	0,1	0,1	NUM
cana-1750	663	21	]	]	PUNCT
cana-1750	663	22	.	.	PUNCT
cana-1750	664	1	first	first	ADV
cana-1750	664	2	,	,	PUNCT
cana-1750	664	3	assume	assume	VERB
cana-1750	664	4	that	that	SCONJ
cana-1750	664	5	there	there	PRON
cana-1750	664	6	is	be	VERB
cana-1750	664	7	a	a	DET
cana-1750	664	8	maximum	maximum	NOUN
cana-1750	664	9	at	at	ADP
cana-1750	664	10	an	an	DET
cana-1750	664	11	interior	interior	ADJ
cana-1750	664	12	point	point	NOUN
cana-1750	664	13	γ(𝑝0	γ(𝑝0	NOUN
cana-1750	664	14	,	,	PUNCT
cana-1750	664	15	|𝑥0|	|𝑥0|	VERB
cana-1750	664	16	)	)	PUNCT
cana-1750	664	17	of	of	ADP
cana-1750	664	18	[	[	X
cana-1750	664	19	0,2	0,2	NUM
cana-1750	664	20	]	]	X
cana-1750	664	21	×	×	NOUN
cana-1750	665	1	[	[	X
cana-1750	665	2	0,1	0,1	NUM
cana-1750	665	3	]	]	PUNCT
cana-1750	665	4	.	.	PUNCT
cana-1750	666	1	differentiating	differentiate	VERB
cana-1750	666	2	γ(𝑝	γ(𝑝	PROPN
cana-1750	666	3	,	,	PUNCT
cana-1750	666	4	|𝑥|	|𝑥|	PROPN
cana-1750	666	5	)	)	PUNCT
cana-1750	666	6	with	with	ADP
cana-1750	666	7	respect	respect	NOUN
cana-1750	666	8	to	to	ADP
cana-1750	666	9	|𝑥|	|𝑥|	VERB
cana-1750	666	10	and	and	CCONJ
cana-1750	666	11	equating	equate	VERB
cana-1750	666	12	it	it	PRON
cana-1750	666	13	to	to	ADP
cana-1750	666	14	0	0	NUM
cana-1750	666	15	implies	imply	VERB
cana-1750	666	16	that	that	SCONJ
cana-1750	666	17	𝑝	𝑝	X
cana-1750	666	18	=	=	SYM
cana-1750	666	19	𝑝0	𝑝0	NOUN
cana-1750	666	20	=	=	SYM
cana-1750	666	21	2	2	NUM
cana-1750	666	22	which	which	PRON
cana-1750	666	23	is	be	AUX
cana-1750	666	24	contradiction	contradiction	NOUN
cana-1750	666	25	.	.	PUNCT
cana-1750	667	1	thus	thus	ADV
cana-1750	667	2	,	,	PUNCT
cana-1750	667	3	for	for	ADP
cana-1750	667	4	the	the	DET
cana-1750	667	5	maximum	maximum	ADJ
cana-1750	667	6	value	value	NOUN
cana-1750	667	7	of	of	ADP
cana-1750	667	8	γ(𝑝	γ(𝑝	NOUN
cana-1750	667	9	,	,	PUNCT
cana-1750	667	10	|𝑥|	|𝑥|	PROPN
cana-1750	667	11	)	)	PUNCT
cana-1750	667	12	,	,	PUNCT
cana-1750	667	13	we	we	PRON
cana-1750	667	14	need	need	VERB
cana-1750	667	15	to	to	PART
cana-1750	667	16	consider	consider	VERB
cana-1750	667	17	the	the	DET
cana-1750	667	18	end	end	NOUN
cana-1750	667	19	points	point	NOUN
cana-1750	667	20	of	of	ADP
cana-1750	667	21	[	[	X
cana-1750	667	22	0,2	0,2	NUM
cana-1750	667	23	]	]	X
cana-1750	667	24	×	×	NOUN
cana-1750	668	1	[	[	X
cana-1750	668	2	0,1	0,1	NUM
cana-1750	668	3	]	]	PUNCT
cana-1750	668	4	.	.	PUNCT
cana-1750	669	1	for	for	ADP
cana-1750	669	2	𝑝	𝑝	NOUN
cana-1750	669	3	=	=	SYM
cana-1750	669	4	0	0	NUM
cana-1750	669	5	,	,	PUNCT
cana-1750	669	6	we	we	PRON
cana-1750	669	7	obtain	obtain	VERB
cana-1750	669	8	γ(0	γ(0	NOUN
cana-1750	669	9	,	,	PUNCT
cana-1750	669	10	|𝑥|	|𝑥|	ADJ
cana-1750	669	11	)	)	PUNCT
cana-1750	670	1	=	=	PUNCT
cana-1750	671	1	[	[	PUNCT
cana-1750	671	2	−4	−4	NUM
cana-1750	671	3	2(𝜆	2(𝜆	NUM
cana-1750	671	4	+	+	CCONJ
cana-1750	671	5	3	3	NUM
cana-1750	671	6	)	)	PUNCT
cana-1750	671	7	]	]	PUNCT
cana-1750	672	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	672	2	+	+	CCONJ
cana-1750	672	3	4	4	NUM
cana-1750	672	4	2(𝜆	2(𝜆	NUM
cana-1750	672	5	+	+	CCONJ
cana-1750	672	6	3	3	X
cana-1750	672	7	)	)	PUNCT
cana-1750	672	8	≤	≤	NOUN
cana-1750	672	9	4	4	NUM
cana-1750	672	10	𝜆	𝜆	NOUN
cana-1750	672	11	+	+	ADJ
cana-1750	672	12	3	3	NUM
cana-1750	672	13	.	.	PUNCT
cana-1750	673	1	(	(	PUNCT
cana-1750	673	2	6.5	6.5	NUM
cana-1750	673	3	)	)	PUNCT
cana-1750	673	4	for	for	ADP
cana-1750	673	5	𝑝	𝑝	NOUN
cana-1750	673	6	=	=	SYM
cana-1750	673	7	2	2	NUM
cana-1750	673	8	,	,	PUNCT
cana-1750	673	9	we	we	PRON
cana-1750	673	10	get	get	VERB
cana-1750	673	11	γ(2	γ(2	PROPN
cana-1750	673	12	,	,	PUNCT
cana-1750	673	13	|𝑥|	|𝑥|	ADJ
cana-1750	673	14	)	)	PUNCT
cana-1750	674	1	=	=	SYM
cana-1750	674	2	|ℒ(𝜆)|	|ℒ(𝜆)|	NOUN
cana-1750	674	3	(	(	PUNCT
cana-1750	674	4	𝜆	𝜆	PROPN
cana-1750	674	5	+	+	ADJ
cana-1750	674	6	1)3(𝜆	1)3(𝜆	NUM
cana-1750	674	7	+	+	CCONJ
cana-1750	674	8	2)(𝜆	2)(𝜆	NUM
cana-1750	674	9	+	+	CCONJ
cana-1750	674	10	3	3	NUM
cana-1750	674	11	)	)	PUNCT
cana-1750	674	12	.	.	PUNCT
cana-1750	675	1	(	(	PUNCT
cana-1750	675	2	6.6	6.6	NUM
cana-1750	675	3	)	)	PUNCT
cana-1750	675	4	for	for	ADP
cana-1750	675	5	|𝑥|	|𝑥|	ADJ
cana-1750	675	6	=	=	SYM
cana-1750	675	7	0	0	NUM
cana-1750	675	8	,	,	PUNCT
cana-1750	675	9	we	we	PRON
cana-1750	675	10	gain	gain	VERB
cana-1750	675	11	γ(𝑝	γ(𝑝	NOUN
cana-1750	675	12	,	,	PUNCT
cana-1750	675	13	0	0	NUM
cana-1750	675	14	)	)	PUNCT
cana-1750	675	15	=	=	NOUN
cana-1750	676	1	[	[	PUNCT
cana-1750	676	2	𝜆4	𝜆4	NOUN
cana-1750	676	3	−	−	PROPN
cana-1750	676	4	5𝜆3	5𝜆3	NUM
cana-1750	676	5	−	−	NOUN
cana-1750	677	1	5𝜆2	5𝜆2	NUM
cana-1750	677	2	−	−	NOUN
cana-1750	677	3	3𝜆	3𝜆	ADJ
cana-1750	677	4	−	−	NOUN
cana-1750	677	5	12	12	NUM
cana-1750	678	1	4(𝜆	4(𝜆	NUM
cana-1750	679	1	+	+	CCONJ
cana-1750	680	1	1)3(𝜆	1)3(𝜆	NUM
cana-1750	680	2	+	+	CCONJ
cana-1750	680	3	2)(𝜆	2)(𝜆	NUM
cana-1750	680	4	+	+	CCONJ
cana-1750	680	5	3	3	NUM
cana-1750	680	6	)	)	PUNCT
cana-1750	680	7	]	]	PUNCT
cana-1750	681	1	𝑝3	𝑝3	ADV
cana-1750	681	2	+	+	NUM
cana-1750	681	3	4	4	NUM
cana-1750	681	4	−	−	NOUN
cana-1750	681	5	𝑝2	𝑝2	NOUN
cana-1750	681	6	2(𝜆	2(𝜆	NUM
cana-1750	681	7	+	+	CCONJ
cana-1750	681	8	3	3	NUM
cana-1750	681	9	)	)	PUNCT
cana-1750	681	10	.	.	PUNCT
cana-1750	682	1	(	(	PUNCT
cana-1750	682	2	6.7	6.7	NUM
cana-1750	682	3	)	)	PUNCT
cana-1750	682	4	for	for	ADP
cana-1750	682	5	|𝑥|	|𝑥|	ADJ
cana-1750	682	6	=	=	SYM
cana-1750	682	7	1	1	NUM
cana-1750	682	8	,	,	PUNCT
cana-1750	682	9	we	we	PRON
cana-1750	682	10	have	have	VERB
cana-1750	682	11	γ(𝑝	γ(𝑝	NOUN
cana-1750	682	12	,	,	PUNCT
cana-1750	682	13	1	1	NUM
cana-1750	682	14	)	)	PUNCT
cana-1750	682	15	=	=	NOUN
cana-1750	682	16	[	[	PUNCT
cana-1750	682	17	𝑝(4	𝑝(4	PROPN
cana-1750	682	18	−	−	PROPN
cana-1750	682	19	𝑝2	𝑝2	NOUN
cana-1750	682	20	)	)	PUNCT
cana-1750	683	1	4(𝜆	4(𝜆	NUM
cana-1750	684	1	+	+	CCONJ
cana-1750	684	2	3	3	X
cana-1750	684	3	)	)	PUNCT
cana-1750	684	4	−	−	PROPN
cana-1750	684	5	4	4	NUM
cana-1750	684	6	−	−	PROPN
cana-1750	684	7	𝑝2	𝑝2	NOUN
cana-1750	684	8	2(𝜆	2(𝜆	NUM
cana-1750	684	9	+	+	CCONJ
cana-1750	684	10	3	3	NUM
cana-1750	684	11	)	)	PUNCT
cana-1750	684	12	]	]	PUNCT
cana-1750	685	1	+	+	CCONJ
cana-1750	685	2	[	[	PUNCT
cana-1750	685	3	−𝜆2	−𝜆2	X
cana-1750	685	4	+	+	CCONJ
cana-1750	685	5	2𝜆	2𝜆	NUM
cana-1750	685	6	+	+	CCONJ
cana-1750	685	7	5	5	NUM
cana-1750	685	8	2(1	2(1	NUM
cana-1750	685	9	+	+	CCONJ
cana-1750	685	10	𝜆)(2	𝜆)(2	ADP
cana-1750	685	11	+	+	NOUN
cana-1750	685	12	𝜆)(3	𝜆)(3	NOUN
cana-1750	685	13	+	+	CCONJ
cana-1750	685	14	𝜆	𝜆	X
cana-1750	685	15	)	)	PUNCT
cana-1750	685	16	]	]	PUNCT
cana-1750	685	17	𝑝(4	𝑝(4	PROPN
cana-1750	685	18	−	−	PROPN
cana-1750	685	19	𝑝2	𝑝2	NOUN
cana-1750	685	20	)	)	PUNCT
cana-1750	685	21	+	+	CCONJ
cana-1750	685	22	[	[	PUNCT
cana-1750	685	23	𝜆4	𝜆4	NOUN
cana-1750	685	24	−	−	PROPN
cana-1750	685	25	5𝜆3	5𝜆3	NUM
cana-1750	685	26	−	−	NOUN
cana-1750	686	1	5𝜆2	5𝜆2	NUM
cana-1750	686	2	−	−	NOUN
cana-1750	686	3	3𝜆	3𝜆	ADJ
cana-1750	686	4	−	−	NOUN
cana-1750	686	5	12	12	NUM
cana-1750	687	1	4(𝜆	4(𝜆	NUM
cana-1750	688	1	+	+	CCONJ
cana-1750	689	1	1)3(𝜆	1)3(𝜆	NUM
cana-1750	689	2	+	+	CCONJ
cana-1750	689	3	2)(𝜆	2)(𝜆	NUM
cana-1750	689	4	+	+	CCONJ
cana-1750	689	5	3	3	NUM
cana-1750	689	6	)	)	PUNCT
cana-1750	689	7	]	]	PUNCT
cana-1750	690	1	𝑝3	𝑝3	ADV
cana-1750	690	2	+	+	NUM
cana-1750	690	3	4	4	NUM
cana-1750	690	4	−	−	NOUN
cana-1750	690	5	𝑝2	𝑝2	NOUN
cana-1750	690	6	2(𝜆	2(𝜆	NUM
cana-1750	690	7	+	+	CCONJ
cana-1750	690	8	3	3	NUM
cana-1750	690	9	)	)	PUNCT
cana-1750	690	10	.	.	PUNCT
cana-1750	691	1	(	(	PUNCT
cana-1750	691	2	6.8	6.8	NUM
cana-1750	691	3	)	)	PUNCT
cana-1750	691	4	which	which	PRON
cana-1750	691	5	has	have	VERB
cana-1750	691	6	maximum	maximum	ADJ
cana-1750	691	7	value	value	NOUN
cana-1750	691	8	|ℒ(𝜆)|	|ℒ(𝜆)|	NOUN
cana-1750	691	9	(	(	PUNCT
cana-1750	691	10	𝜆+1)3(𝜆+2)(𝜆+3	𝜆+1)3(𝜆+2)(𝜆+3	NOUN
cana-1750	691	11	)	)	PUNCT
cana-1750	691	12	attained	attain	VERB
cana-1750	691	13	at	at	ADP
cana-1750	691	14	the	the	DET
cana-1750	691	15	end	end	NOUN
cana-1750	691	16	point	point	NOUN
cana-1750	691	17	𝑝	𝑝	NOUN
cana-1750	691	18	=	=	SYM
cana-1750	691	19	2	2	NUM
cana-1750	691	20	and	and	CCONJ
cana-1750	691	21	4	4	NUM
cana-1750	691	22	𝜆+3	𝜆+3	NOUN
cana-1750	691	23	at	at	ADP
cana-1750	691	24	𝑝	𝑝	PROPN
cana-1750	691	25	=	=	SYM
cana-1750	691	26	0	0	PROPN
cana-1750	691	27	.	.	PUNCT
cana-1750	692	1	where	where	SCONJ
cana-1750	692	2	,	,	PUNCT
cana-1750	692	3	ℒ(𝜆	ℒ(𝜆	NUM
cana-1750	692	4	)	)	PUNCT
cana-1750	692	5	=	=	SYM
cana-1750	692	6	𝜆4	𝜆4	NOUN
cana-1750	692	7	−	−	PROPN
cana-1750	692	8	5𝜆3	5𝜆3	NUM
cana-1750	692	9	−	−	NOUN
cana-1750	693	1	5𝜆2	5𝜆2	NUM
cana-1750	693	2	−	−	NOUN
cana-1750	693	3	3𝜆	3𝜆	ADJ
cana-1750	693	4	−	−	PROPN
cana-1750	693	5	12	12	NUM
cana-1750	693	6	.	.	PUNCT
cana-1750	694	1	(	(	PUNCT
cana-1750	694	2	6.9	6.9	NUM
cana-1750	694	3	)	)	PUNCT
cana-1750	694	4	theorem	theorem	VERB
cana-1750	694	5	6.2	6.2	NUM
cana-1750	694	6	.	.	PUNCT
cana-1750	695	1	let	let	VERB
cana-1750	695	2	𝑓	𝑓	PRON
cana-1750	695	3	given	give	VERB
cana-1750	695	4	by	by	ADP
cana-1750	695	5	(	(	PUNCT
cana-1750	695	6	1.1	1.1	NUM
cana-1750	695	7	)	)	PUNCT
cana-1750	695	8	,	,	PUNCT
cana-1750	695	9	be	be	AUX
cana-1750	695	10	in	in	ADP
cana-1750	695	11	the	the	DET
cana-1750	695	12	class	class	NOUN
cana-1750	695	13	𝓐(𝝀	𝓐(𝝀	NOUN
cana-1750	695	14	)	)	PUNCT
cana-1750	695	15	;	;	PUNCT
cana-1750	695	16	(	(	PUNCT
cana-1750	695	17	0	0	NUM
cana-1750	695	18	≤	≤	NUM
cana-1750	695	19	𝜆	𝜆	PRON
cana-1750	695	20	≤	≤	NUM
cana-1750	695	21	1	1	NUM
cana-1750	695	22	)	)	PUNCT
cana-1750	695	23	.	.	PUNCT
cana-1750	696	1	then	then	ADV
cana-1750	696	2	we	we	PRON
cana-1750	696	3	have	have	AUX
cana-1750	696	4	sharp	sharp	ADV
cana-1750	696	5	bound	bind	VERB
cana-1750	696	6	|𝑎5	|𝑎5	VERB
cana-1750	696	7	−	−	PROPN
cana-1750	696	8	𝑎2	𝑎2	NOUN
cana-1750	696	9	4|	4|	NUM
cana-1750	696	10	≤	≤	NUM
cana-1750	696	11	max	max	PROPN
cana-1750	696	12	{	{	PUNCT
cana-1750	696	13	4(1	4(1	NUM
cana-1750	696	14	+	+	CCONJ
cana-1750	696	15	𝜆	𝜆	X
cana-1750	696	16	)	)	PUNCT
cana-1750	696	17	(	(	PUNCT
cana-1750	696	18	𝜆	𝜆	X
cana-1750	697	1	+	+	ADJ
cana-1750	697	2	2)(𝜆	2)(𝜆	NUM
cana-1750	697	3	+	+	CCONJ
cana-1750	697	4	4	4	NUM
cana-1750	697	5	)	)	PUNCT
cana-1750	697	6	+	+	CCONJ
cana-1750	697	7	6	6	NUM
cana-1750	697	8	𝜆	𝜆	NOUN
cana-1750	697	9	+	+	ADP
cana-1750	697	10	4	4	NUM
cana-1750	697	11	,	,	PUNCT
cana-1750	697	12	|𝑄(𝜆)|	|𝑄(𝜆)|	NOUN
cana-1750	697	13	(	(	PUNCT
cana-1750	697	14	𝜆	𝜆	PROPN
cana-1750	697	15	+	+	ADJ
cana-1750	697	16	1)4(𝜆	1)4(𝜆	NUM
cana-1750	697	17	+	+	SYM
cana-1750	697	18	2)(𝜆	2)(𝜆	NUM
cana-1750	697	19	+	+	CCONJ
cana-1750	697	20	3)(𝜆	3)(𝜆	NUM
cana-1750	697	21	+	+	NUM
cana-1750	697	22	4	4	NUM
cana-1750	697	23	)	)	PUNCT
cana-1750	697	24	}	}	PUNCT
cana-1750	697	25	.	.	PUNCT
cana-1750	698	1	(	(	PUNCT
cana-1750	698	2	6.10	6.10	NUM
cana-1750	698	3	)	)	PUNCT
cana-1750	698	4	where	where	SCONJ
cana-1750	698	5	communications	communication	NOUN
cana-1750	698	6	on	on	ADP
cana-1750	698	7	applied	apply	VERB
cana-1750	698	8	nonlinear	nonlinear	ADJ
cana-1750	698	9	analysis	analysis	NOUN
cana-1750	698	10	issn	issn	NOUN
cana-1750	698	11	:	:	PUNCT
cana-1750	698	12	1074	1074	NUM
cana-1750	698	13	-	-	PUNCT
cana-1750	698	14	133x	133x	NUM
cana-1750	698	15	vol	vol	NOUN
cana-1750	698	16	32	32	NUM
cana-1750	698	17	no	no	NOUN
cana-1750	698	18	.	.	NOUN
cana-1750	698	19	2	2	NUM
cana-1750	698	20	(	(	PUNCT
cana-1750	698	21	2025	2025	NUM
cana-1750	698	22	)	)	PUNCT
cana-1750	698	23	404	404	NUM
cana-1750	698	24	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	698	25	𝒬(𝜆	𝒬(𝜆	NOUN
cana-1750	698	26	)	)	PUNCT
cana-1750	698	27	=	=	SYM
cana-1750	699	1	2(𝜆6	2(𝜆6	NUM
cana-1750	700	1	+	+	CCONJ
cana-1750	701	1	21𝜆5	21𝜆5	NUM
cana-1750	701	2	+	+	SYM
cana-1750	701	3	6𝜆4	6𝜆4	NUM
cana-1750	701	4	−	−	NUM
cana-1750	702	1	54𝜆3	54𝜆3	NUM
cana-1750	702	2	−	−	PROPN
cana-1750	702	3	43𝜆2	43𝜆2	NUM
cana-1750	702	4	−	−	NOUN
cana-1750	702	5	87𝜆	87𝜆	NUM
cana-1750	702	6	−	−	PROPN
cana-1750	702	7	132	132	NUM
cana-1750	702	8	)	)	PUNCT
cana-1750	702	9	.	.	PUNCT
cana-1750	703	1	(	(	PUNCT
cana-1750	703	2	6.11	6.11	NUM
cana-1750	703	3	)	)	PUNCT
cana-1750	703	4	proof	proof	NOUN
cana-1750	703	5	.	.	PUNCT
cana-1750	704	1	first	first	ADV
cana-1750	704	2	note	note	VERB
cana-1750	704	3	that	that	SCONJ
cana-1750	704	4	by	by	ADP
cana-1750	704	5	equating	equate	VERB
cana-1750	704	6	the	the	DET
cana-1750	704	7	corresponding	corresponding	ADJ
cana-1750	704	8	coefficients	coefficient	NOUN
cana-1750	704	9	in	in	ADP
cana-1750	704	10	the	the	DET
cana-1750	704	11	equation	equation	NOUN
cana-1750	704	12	(	(	PUNCT
cana-1750	704	13	3.1	3.1	NUM
cana-1750	704	14	)	)	PUNCT
cana-1750	704	15	we	we	PRON
cana-1750	704	16	get	get	VERB
cana-1750	704	17	,	,	PUNCT
cana-1750	704	18	in	in	ADP
cana-1750	704	19	the	the	DET
cana-1750	704	20	view	view	NOUN
cana-1750	704	21	of	of	ADP
cana-1750	704	22	(	(	PUNCT
cana-1750	704	23	3.2	3.2	NUM
cana-1750	704	24	)	)	PUNCT
cana-1750	704	25	and	and	CCONJ
cana-1750	704	26	(	(	PUNCT
cana-1750	704	27	3.5	3.5	NUM
cana-1750	704	28	)	)	PUNCT
cana-1750	704	29	,	,	PUNCT
cana-1750	704	30	we	we	PRON
cana-1750	704	31	may	may	AUX
cana-1750	704	32	write	write	VERB
cana-1750	704	33	𝑎5	𝑎5	PROPN
cana-1750	705	1	−	−	PROPN
cana-1750	705	2	𝑎2	𝑎2	NOUN
cana-1750	705	3	4	4	NUM
cana-1750	705	4	=	=	SYM
cana-1750	705	5	𝑝1	𝑝1	PROPN
cana-1750	705	6	4(1	4(1	NOUN
cana-1750	705	7	−	−	PROPN
cana-1750	705	8	𝜆)3	𝜆)3	NOUN
cana-1750	705	9	(	(	PUNCT
cana-1750	705	10	𝜆	𝜆	PROPN
cana-1750	705	11	+	+	ADJ
cana-1750	705	12	1)(𝜆	1)(𝜆	NUM
cana-1750	705	13	+	+	CCONJ
cana-1750	705	14	2)(𝜆	2)(𝜆	NUM
cana-1750	705	15	+	+	CCONJ
cana-1750	705	16	3)(𝜆	3)(𝜆	NUM
cana-1750	705	17	+	+	NUM
cana-1750	705	18	4	4	NUM
cana-1750	705	19	)	)	PUNCT
cana-1750	705	20	+	+	CCONJ
cana-1750	705	21	𝑝1	𝑝1	NOUN
cana-1750	705	22	2𝑝2(1	2𝑝2(1	NUM
cana-1750	705	23	−	−	NOUN
cana-1750	705	24	𝜆	𝜆	NOUN
cana-1750	705	25	)	)	PUNCT
cana-1750	705	26	2(3	2(3	NUM
cana-1750	705	27	+	+	CCONJ
cana-1750	705	28	2𝜆	2𝜆	NUM
cana-1750	705	29	)	)	PUNCT
cana-1750	705	30	(	(	PUNCT
cana-1750	705	31	𝜆	𝜆	X
cana-1750	705	32	+	+	NOUN
cana-1750	705	33	1)(𝜆	1)(𝜆	NUM
cana-1750	705	34	+	+	CCONJ
cana-1750	705	35	2)(𝜆	2)(𝜆	NUM
cana-1750	705	36	+	+	CCONJ
cana-1750	705	37	3)(𝜆	3)(𝜆	NUM
cana-1750	705	38	+	+	NUM
cana-1750	705	39	4	4	NUM
cana-1750	705	40	)	)	PUNCT
cana-1750	705	41	(	(	PUNCT
cana-1750	705	42	6.12	6.12	NUM
cana-1750	705	43	)	)	PUNCT
cana-1750	705	44	+	+	CCONJ
cana-1750	706	1	𝑝1𝑝3(1	𝑝1𝑝3(1	ADV
cana-1750	706	2	−	−	NOUN
cana-1750	706	3	𝜆	𝜆	NOUN
cana-1750	706	4	)	)	PUNCT
cana-1750	706	5	(	(	PUNCT
cana-1750	706	6	𝜆	𝜆	ADP
cana-1750	706	7	+	+	CCONJ
cana-1750	706	8	3)(𝜆	3)(𝜆	NUM
cana-1750	706	9	+	+	NUM
cana-1750	706	10	4	4	NUM
cana-1750	706	11	)	)	PUNCT
cana-1750	706	12	+	+	CCONJ
cana-1750	706	13	𝑝1	𝑝1	NOUN
cana-1750	706	14	2𝑝2(1	2𝑝2(1	NUM
cana-1750	706	15	−	−	NOUN
cana-1750	706	16	𝜆	𝜆	NOUN
cana-1750	706	17	)	)	PUNCT
cana-1750	706	18	2	2	NUM
cana-1750	706	19	(	(	PUNCT
cana-1750	706	20	𝜆	𝜆	PROPN
cana-1750	706	21	+	+	NOUN
cana-1750	706	22	1)(𝜆	1)(𝜆	NUM
cana-1750	706	23	+	+	CCONJ
cana-1750	706	24	2)(𝜆	2)(𝜆	NUM
cana-1750	706	25	+	+	CCONJ
cana-1750	706	26	4	4	NUM
cana-1750	706	27	)	)	PUNCT
cana-1750	706	28	+	+	NUM
cana-1750	706	29	𝑝2	𝑝2	NOUN
cana-1750	706	30	2(1	2(1	NUM
cana-1750	706	31	−	−	NOUN
cana-1750	706	32	𝜆	𝜆	NOUN
cana-1750	706	33	)	)	PUNCT
cana-1750	706	34	(	(	PUNCT
cana-1750	706	35	𝜆	𝜆	X
cana-1750	706	36	+	+	ADJ
cana-1750	706	37	2)(𝜆	2)(𝜆	NUM
cana-1750	706	38	+	+	CCONJ
cana-1750	706	39	4	4	NUM
cana-1750	706	40	)	)	PUNCT
cana-1750	706	41	+	+	CCONJ
cana-1750	706	42	𝑝1𝑝3(1	𝑝1𝑝3(1	PROPN
cana-1750	706	43	−	−	NOUN
cana-1750	706	44	𝜆	𝜆	NOUN
cana-1750	706	45	)	)	PUNCT
cana-1750	706	46	(	(	PUNCT
cana-1750	706	47	𝜆	𝜆	PROPN
cana-1750	706	48	+	+	NOUN
cana-1750	706	49	1)(𝜆	1)(𝜆	NUM
cana-1750	706	50	+	+	CCONJ
cana-1750	706	51	4	4	NUM
cana-1750	706	52	)	)	PUNCT
cana-1750	706	53	+	+	CCONJ
cana-1750	706	54	𝑝4	𝑝4	PROPN
cana-1750	706	55	𝜆	𝜆	PROPN
cana-1750	706	56	+	+	CCONJ
cana-1750	706	57	4	4	NUM
cana-1750	706	58	−	−	NOUN
cana-1750	706	59	(	(	PUNCT
cana-1750	706	60	𝑝1	𝑝1	NOUN
cana-1750	706	61	𝜆	𝜆	NOUN
cana-1750	706	62	+	+	PROPN
cana-1750	706	63	1	1	NUM
cana-1750	706	64	)	)	PUNCT
cana-1750	706	65	4	4	NUM
cana-1750	706	66	.	.	PUNCT
cana-1750	707	1	(	(	PUNCT
cana-1750	707	2	6.13	6.13	NUM
cana-1750	707	3	)	)	PUNCT
cana-1750	707	4	note	note	VERB
cana-1750	707	5	that	that	SCONJ
cana-1750	707	6	,	,	PUNCT
cana-1750	707	7	by	by	ADP
cana-1750	707	8	lemma	lemma	PROPN
cana-1750	707	9	(	(	PUNCT
cana-1750	707	10	2.2	2.2	NUM
cana-1750	707	11	)	)	PUNCT
cana-1750	707	12	and	and	CCONJ
cana-1750	707	13	we	we	PRON
cana-1750	707	14	have	have	VERB
cana-1750	707	15	2𝑝2	2𝑝2	NUM
cana-1750	707	16	=	=	SYM
cana-1750	707	17	𝑝1	𝑝1	NOUN
cana-1750	707	18	2	2	NUM
cana-1750	708	1	+	+	CCONJ
cana-1750	708	2	𝑥(4	𝑥(4	PROPN
cana-1750	708	3	−	−	PROPN
cana-1750	708	4	𝑝1	𝑝1	NOUN
cana-1750	708	5	2	2	NUM
cana-1750	708	6	)	)	PUNCT
cana-1750	708	7	,	,	PUNCT
cana-1750	708	8	𝑌	𝑌	PROPN
cana-1750	708	9	=	=	PUNCT
cana-1750	708	10	(	(	PUNCT
cana-1750	708	11	1	1	NUM
cana-1750	708	12	−	−	PROPN
cana-1750	708	13	|𝑥|2)𝜚	|𝑥|2)𝜚	PROPN
cana-1750	708	14	,	,	PUNCT
cana-1750	708	15	a	a	DET
cana-1750	708	16	simple	simple	ADJ
cana-1750	708	17	computation	computation	NOUN
cana-1750	708	18	leads	lead	VERB
cana-1750	708	19	to	to	ADP
cana-1750	708	20	𝑎5	𝑎5	PROPN
cana-1750	708	21	−	−	PROPN
cana-1750	708	22	𝑎2	𝑎2	NOUN
cana-1750	708	23	4	4	NUM
cana-1750	708	24	=	=	SYM
cana-1750	708	25	[	[	PUNCT
cana-1750	708	26	𝜆6	𝜆6	PROPN
cana-1750	708	27	+	+	PROPN
cana-1750	708	28	21𝜆5	21𝜆5	NUM
cana-1750	708	29	+	+	ADJ
cana-1750	708	30	6𝜆4−54𝜆3−43𝜆2−87𝜆−132	6𝜆4−54𝜆3−43𝜆2−87𝜆−132	NUM
cana-1750	708	31	8(𝜆+1)4(𝜆+2)(𝜆+3)(𝜆+4	8(𝜆+1)4(𝜆+2)(𝜆+3)(𝜆+4	NOUN
cana-1750	708	32	)	)	PUNCT
cana-1750	708	33	]	]	PUNCT
cana-1750	709	1	𝑝1	𝑝1	NOUN
cana-1750	709	2	4	4	NUM
cana-1750	709	3	+	+	CCONJ
cana-1750	709	4	[	[	PUNCT
cana-1750	709	5	3𝜆3−14𝜆2−7𝜆+90	3𝜆3−14𝜆2−7𝜆+90	NUM
cana-1750	709	6	8(𝜆+1)(𝜆+2)(𝜆+3)(𝜆+4	8(𝜆+1)(𝜆+2)(𝜆+3)(𝜆+4	NUM
cana-1750	709	7	)	)	PUNCT
cana-1750	709	8	]	]	PUNCT
cana-1750	710	1	𝑝2𝑥𝑋	𝑝2𝑥𝑋	PROPN
cana-1750	710	2	+	+	PUNCT
cana-1750	710	3	[	[	PUNCT
cana-1750	710	4	−𝜆2	−𝜆2	X
cana-1750	710	5	+	+	NOUN
cana-1750	710	6	2𝜆+7	2𝜆+7	PROPN
cana-1750	710	7	2(𝜆+1)(𝜆+3)(𝜆+4	2(𝜆+1)(𝜆+3)(𝜆+4	NUM
cana-1750	710	8	)	)	PUNCT
cana-1750	710	9	]	]	PUNCT
cana-1750	710	10	𝑝1𝑋𝑌	𝑝1𝑋𝑌	VERB
cana-1750	710	11	−	−	PROPN
cana-1750	711	1	[	[	PUNCT
cana-1750	711	2	−𝜆2	−𝜆2	X
cana-1750	711	3	+	+	ADJ
cana-1750	711	4	8𝜆+17	8𝜆+17	NUM
cana-1750	711	5	8(𝜆+1)(𝜆+3)(𝜆+4	8(𝜆+1)(𝜆+3)(𝜆+4	NUM
cana-1750	711	6	]	]	PUNCT
cana-1750	711	7	𝑝1	𝑝1	NOUN
cana-1750	711	8	2𝑋𝑥2	2𝑋𝑥2	NOUN
cana-1750	711	9	+	+	CCONJ
cana-1750	711	10	[	[	PUNCT
cana-1750	711	11	(	(	PUNCT
cana-1750	711	12	1−𝜆	1−𝜆	NUM
cana-1750	711	13	)	)	PUNCT
cana-1750	711	14	4(𝜆+2)(𝜆+4	4(𝜆+2)(𝜆+4	NUM
cana-1750	711	15	)	)	PUNCT
cana-1750	711	16	]	]	PUNCT
cana-1750	711	17	𝑋2𝑥2	𝑋2𝑥2	PROPN
cana-1750	711	18	+	+	CCONJ
cana-1750	711	19	𝑝1	𝑝1	PROPN
cana-1750	711	20	2𝑋𝑥3	2𝑋𝑥3	NOUN
cana-1750	711	21	8(𝜆+4	8(𝜆+4	NUM
cana-1750	711	22	)	)	PUNCT
cana-1750	711	23	+	+	NUM
cana-1750	711	24	𝑋𝑥2	𝑋𝑥2	NOUN
cana-1750	711	25	2(𝜆+4	2(𝜆+4	NUM
cana-1750	711	26	)	)	PUNCT
cana-1750	711	27	−	−	PROPN
cana-1750	711	28	𝑋𝑌𝑝1𝑥	𝑋𝑌𝑝1𝑥	ADJ
cana-1750	711	29	2(𝜆+4	2(𝜆+4	NUM
cana-1750	711	30	)	)	PUNCT
cana-1750	711	31	−	−	ADP
cana-1750	711	32	𝑋𝑌	𝑋𝑌	PROPN
cana-1750	711	33	�	�	NOUN
cana-1750	711	34	̅	̅	NOUN
cana-1750	711	35	�	�	NOUN
cana-1750	711	36	2(𝜆+4	2(𝜆+4	NUM
cana-1750	711	37	)	)	PUNCT
cana-1750	711	38	(	(	PUNCT
cana-1750	711	39	6.14	6.14	NUM
cana-1750	711	40	)	)	PUNCT
cana-1750	711	41	without	without	ADP
cana-1750	711	42	loss	loss	NOUN
cana-1750	711	43	of	of	ADP
cana-1750	711	44	generality	generality	NOUN
cana-1750	711	45	,	,	PUNCT
cana-1750	711	46	we	we	PRON
cana-1750	711	47	let	let	VERB
cana-1750	711	48	0	0	NUM
cana-1750	711	49	≤	≤	NOUN
cana-1750	711	50	𝑝1	𝑝1	NOUN
cana-1750	711	51	=	=	SYM
cana-1750	711	52	𝑝	𝑝	NOUN
cana-1750	711	53	≤	≤	NUM
cana-1750	711	54	2	2	NUM
cana-1750	711	55	.	.	PUNCT
cana-1750	711	56	substitute	substitute	VERB
cana-1750	711	57	this	this	PRON
cana-1750	711	58	into	into	ADP
cana-1750	711	59	the	the	DET
cana-1750	711	60	above	above	ADJ
cana-1750	711	61	equation	equation	NOUN
cana-1750	711	62	,	,	PUNCT
cana-1750	711	63	we	we	PRON
cana-1750	711	64	obtain	obtain	VERB
cana-1750	711	65	the	the	DET
cana-1750	711	66	following	follow	VERB
cana-1750	711	67	quadratic	quadratic	ADJ
cana-1750	711	68	equation	equation	NOUN
cana-1750	711	69	in	in	ADP
cana-1750	711	70	terms	term	NOUN
cana-1750	711	71	of	of	ADP
cana-1750	711	72	𝑥.	𝑥.	PROPN
cana-1750	711	73	|𝑎5	|𝑎5	VERB
cana-1750	711	74	−	−	PROPN
cana-1750	711	75	𝑎2	𝑎2	NOUN
cana-1750	711	76	4|	4|	NUM
cana-1750	711	77	≤	≤	NUM
cana-1750	712	1	[	[	PUNCT
cana-1750	712	2	𝑝2(4	𝑝2(4	PROPN
cana-1750	712	3	−	−	PROPN
cana-1750	712	4	𝑝2	𝑝2	NOUN
cana-1750	712	5	)	)	PUNCT
cana-1750	712	6	8(𝜆	8(𝜆	NUM
cana-1750	712	7	+	+	CCONJ
cana-1750	712	8	4	4	NUM
cana-1750	712	9	)	)	PUNCT
cana-1750	712	10	−	−	PROPN
cana-1750	712	11	𝑝(4	𝑝(4	PROPN
cana-1750	712	12	−	−	PROPN
cana-1750	712	13	𝑝2	𝑝2	NOUN
cana-1750	712	14	)	)	PUNCT
cana-1750	712	15	2(𝜆	2(𝜆	NUM
cana-1750	712	16	+	+	CCONJ
cana-1750	712	17	4	4	NUM
cana-1750	712	18	)	)	PUNCT
cana-1750	712	19	]	]	PUNCT
cana-1750	713	1	|𝑥|3	|𝑥|3	PROPN
cana-1750	713	2	+	+	CCONJ
cana-1750	713	3	[	[	PUNCT
cana-1750	713	4	(	(	PUNCT
cana-1750	713	5	−𝜆2	−𝜆2	PROPN
cana-1750	713	6	+	+	CCONJ
cana-1750	713	7	2𝜆	2𝜆	NUM
cana-1750	713	8	+	+	CCONJ
cana-1750	713	9	7)𝑝(4	7)𝑝(4	ADJ
cana-1750	713	10	−	−	PROPN
cana-1750	713	11	𝑝2	𝑝2	NOUN
cana-1750	713	12	)	)	PUNCT
cana-1750	713	13	2(𝜆	2(𝜆	NUM
cana-1750	714	1	+	+	CCONJ
cana-1750	714	2	1)(𝜆	1)(𝜆	NUM
cana-1750	715	1	+	+	CCONJ
cana-1750	715	2	3)(𝜆	3)(𝜆	NUM
cana-1750	715	3	+	+	NUM
cana-1750	715	4	4	4	NUM
cana-1750	715	5	)	)	PUNCT
cana-1750	716	1	+	+	CCONJ
cana-1750	716	2	(	(	PUNCT
cana-1750	716	3	−𝜆2	−𝜆2	X
cana-1750	716	4	+	+	CCONJ
cana-1750	716	5	8𝜆	8𝜆	NUM
cana-1750	716	6	+	+	CCONJ
cana-1750	716	7	17)𝑝2(4	17)𝑝2(4	NUM
cana-1750	716	8	−	−	PROPN
cana-1750	716	9	𝑝2	𝑝2	NOUN
cana-1750	716	10	)	)	PUNCT
cana-1750	716	11	8(𝜆	8(𝜆	NUM
cana-1750	717	1	+	+	CCONJ
cana-1750	717	2	1)(𝜆	1)(𝜆	NUM
cana-1750	717	3	+	+	CCONJ
cana-1750	717	4	3)(𝜆	3)(𝜆	NUM
cana-1750	717	5	+	+	NUM
cana-1750	717	6	4	4	NUM
cana-1750	717	7	)	)	PUNCT
cana-1750	717	8	]	]	PUNCT
cana-1750	718	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	718	2	+	+	PUNCT
cana-1750	718	3	[	[	PUNCT
cana-1750	718	4	(	(	PUNCT
cana-1750	718	5	4	4	NUM
cana-1750	718	6	−	−	NOUN
cana-1750	718	7	𝑝2)2(1	𝑝2)2(1	NOUN
cana-1750	718	8	−	−	NOUN
cana-1750	718	9	𝜆	𝜆	NOUN
cana-1750	718	10	)	)	PUNCT
cana-1750	718	11	4(𝜆	4(𝜆	NUM
cana-1750	719	1	+	+	CCONJ
cana-1750	719	2	2)(𝜆	2)(𝜆	NUM
cana-1750	719	3	+	+	CCONJ
cana-1750	719	4	4	4	NUM
cana-1750	719	5	)	)	PUNCT
cana-1750	719	6	+	+	CCONJ
cana-1750	719	7	(	(	PUNCT
cana-1750	719	8	4	4	NUM
cana-1750	719	9	−	−	PROPN
cana-1750	719	10	𝑝2	𝑝2	NOUN
cana-1750	719	11	)	)	PUNCT
cana-1750	719	12	2(𝜆	2(𝜆	NUM
cana-1750	720	1	+	+	CCONJ
cana-1750	720	2	4	4	NUM
cana-1750	720	3	)	)	PUNCT
cana-1750	720	4	−	−	PROPN
cana-1750	720	5	(	(	PUNCT
cana-1750	720	6	4	4	NUM
cana-1750	720	7	−	−	NOUN
cana-1750	720	8	𝑝2)𝑥‾	𝑝2)𝑥‾	PROPN
cana-1750	720	9	2(𝜆	2(𝜆	NUM
cana-1750	720	10	+	+	CCONJ
cana-1750	720	11	4	4	NUM
cana-1750	720	12	)	)	PUNCT
cana-1750	720	13	]	]	PUNCT
cana-1750	721	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	721	2	+	+	PUNCT
cana-1750	722	1	[	[	X
cana-1750	722	2	[	[	PUNCT
cana-1750	722	3	(	(	PUNCT
cana-1750	722	4	3𝜆3	3𝜆3	NUM
cana-1750	722	5	−	−	NOUN
cana-1750	722	6	14𝜆2	14𝜆2	NUM
cana-1750	722	7	−	−	NOUN
cana-1750	722	8	7𝜆	7𝜆	PROPN
cana-1750	722	9	+	+	CCONJ
cana-1750	722	10	90)𝑝2	90)𝑝2	NUM
cana-1750	722	11	8(𝜆	8(𝜆	NUM
cana-1750	722	12	+	+	NUM
cana-1750	722	13	1)(𝜆	1)(𝜆	NUM
cana-1750	722	14	+	+	CCONJ
cana-1750	722	15	3)(𝜆	3)(𝜆	NUM
cana-1750	722	16	+	+	SYM
cana-1750	722	17	4)(𝜆	4)(𝜆	NUM
cana-1750	722	18	+	+	CCONJ
cana-1750	722	19	2	2	NUM
cana-1750	722	20	)	)	PUNCT
cana-1750	722	21	+	+	SYM
cana-1750	722	22	𝑝	𝑝	SYM
cana-1750	722	23	2	2	NUM
cana-1750	722	24	+	+	CCONJ
cana-1750	722	25	𝜆	𝜆	SYM
cana-1750	722	26	]	]	X
cana-1750	722	27	(	(	PUNCT
cana-1750	722	28	4	4	NUM
cana-1750	722	29	−	−	PROPN
cana-1750	722	30	𝑝2	𝑝2	NOUN
cana-1750	722	31	)	)	PUNCT
cana-1750	722	32	]	]	PUNCT
cana-1750	723	1	|𝑥|	|𝑥|	PROPN
cana-1750	724	1	+	+	PUNCT
cana-1750	724	2	[	[	X
cana-1750	724	3	[	[	PUNCT
cana-1750	724	4	−𝜆2	−𝜆2	X
cana-1750	724	5	+	+	CCONJ
cana-1750	724	6	2𝜆	2𝜆	NUM
cana-1750	724	7	+	+	CCONJ
cana-1750	724	8	7	7	NUM
cana-1750	724	9	2(𝜆	2(𝜆	NUM
cana-1750	724	10	+	+	CCONJ
cana-1750	724	11	1)(𝜆	1)(𝜆	NUM
cana-1750	724	12	+	+	CCONJ
cana-1750	724	13	3)(𝜆	3)(𝜆	NUM
cana-1750	724	14	+	+	NUM
cana-1750	724	15	4	4	NUM
cana-1750	724	16	)	)	PUNCT
cana-1750	724	17	]	]	PUNCT
cana-1750	724	18	𝑝	𝑝	PROPN
cana-1750	725	1	+	+	CCONJ
cana-1750	725	2	𝑥‾	𝑥‾	PROPN
cana-1750	725	3	2(𝜆	2(𝜆	NUM
cana-1750	725	4	+	+	CCONJ
cana-1750	725	5	4	4	NUM
cana-1750	725	6	)	)	PUNCT
cana-1750	725	7	]	]	PUNCT
cana-1750	726	1	(	(	PUNCT
cana-1750	726	2	4	4	NUM
cana-1750	726	3	−	−	PROPN
cana-1750	726	4	𝑝2	𝑝2	NOUN
cana-1750	726	5	)	)	PUNCT
cana-1750	727	1	+	+	CCONJ
cana-1750	727	2	[	[	PUNCT
cana-1750	727	3	𝜆6	𝜆6	X
cana-1750	727	4	+	+	CCONJ
cana-1750	727	5	21𝜆5	21𝜆5	NUM
cana-1750	727	6	+	+	SYM
cana-1750	727	7	6𝜆4	6𝜆4	NUM
cana-1750	727	8	−	−	NUM
cana-1750	727	9	54𝜆3	54𝜆3	NUM
cana-1750	727	10	−	−	PROPN
cana-1750	727	11	43𝜆2	43𝜆2	NUM
cana-1750	727	12	−	−	NOUN
cana-1750	727	13	87𝜆	87𝜆	NUM
cana-1750	727	14	−	−	PROPN
cana-1750	727	15	132	132	NUM
cana-1750	727	16	8(𝜆	8(𝜆	NUM
cana-1750	727	17	+	+	CCONJ
cana-1750	727	18	1)4(𝜆	1)4(𝜆	NUM
cana-1750	728	1	+	+	SYM
cana-1750	728	2	2)(𝜆	2)(𝜆	NUM
cana-1750	728	3	+	+	CCONJ
cana-1750	728	4	3)(𝜆	3)(𝜆	NUM
cana-1750	728	5	+	+	NUM
cana-1750	728	6	4	4	NUM
cana-1750	728	7	)	)	PUNCT
cana-1750	728	8	]	]	PUNCT
cana-1750	728	9	𝑝4	𝑝4	NOUN
cana-1750	728	10	=	=	SYM
cana-1750	728	11	λ(𝑝	λ(𝑝	PROPN
cana-1750	728	12	,	,	PUNCT
cana-1750	728	13	|𝑥|	|𝑥|	INTJ
cana-1750	728	14	)	)	PUNCT
cana-1750	728	15	we	we	PRON
cana-1750	728	16	need	need	VERB
cana-1750	728	17	to	to	PART
cana-1750	728	18	prove	prove	VERB
cana-1750	728	19	that	that	SCONJ
cana-1750	728	20	the	the	DET
cana-1750	728	21	maximum	maximum	ADJ
cana-1750	728	22	value	value	NOUN
cana-1750	728	23	of	of	ADP
cana-1750	728	24	λ(𝑝	λ(𝑝	NOUN
cana-1750	728	25	,	,	PUNCT
cana-1750	728	26	|𝑥|	|𝑥|	INTJ
cana-1750	728	27	)	)	PUNCT
cana-1750	728	28	on	on	ADP
cana-1750	728	29	[	[	X
cana-1750	728	30	0,2	0,2	NUM
cana-1750	728	31	]	]	X
cana-1750	728	32	×	×	NOUN
cana-1750	729	1	[	[	X
cana-1750	729	2	0,1	0,1	NUM
cana-1750	729	3	]	]	PUNCT
cana-1750	729	4	.	.	PUNCT
cana-1750	730	1	first	first	ADV
cana-1750	730	2	assume	assume	VERB
cana-1750	730	3	,	,	PUNCT
cana-1750	730	4	that	that	SCONJ
cana-1750	730	5	there	there	PRON
cana-1750	730	6	is	be	VERB
cana-1750	730	7	a	a	DET
cana-1750	730	8	maximum	maximum	NOUN
cana-1750	730	9	at	at	ADP
cana-1750	730	10	an	an	DET
cana-1750	730	11	interior	interior	ADJ
cana-1750	730	12	point	point	NOUN
cana-1750	730	13	λ(𝑝0	λ(𝑝0	NOUN
cana-1750	730	14	,	,	PUNCT
cana-1750	730	15	|𝑥0|	|𝑥0|	VERB
cana-1750	730	16	)	)	PUNCT
cana-1750	730	17	of	of	ADP
cana-1750	730	18	[	[	X
cana-1750	730	19	0,2	0,2	NUM
cana-1750	730	20	]	]	X
cana-1750	730	21	×	×	NOUN
cana-1750	731	1	[	[	X
cana-1750	731	2	0,1	0,1	NUM
cana-1750	731	3	]	]	PUNCT
cana-1750	731	4	.	.	PUNCT
cana-1750	732	1	differentiating	differentiate	VERB
cana-1750	732	2	λ(𝑝	λ(𝑝	NOUN
cana-1750	732	3	,	,	PUNCT
cana-1750	732	4	|𝑥|	|𝑥|	INTJ
cana-1750	732	5	)	)	PUNCT
cana-1750	732	6	with	with	ADP
cana-1750	732	7	respect	respect	NOUN
cana-1750	732	8	to	to	ADP
cana-1750	732	9	|𝑥|	|𝑥|	VERB
cana-1750	732	10	and	and	CCONJ
cana-1750	732	11	equating	equate	VERB
cana-1750	732	12	it	it	PRON
cana-1750	732	13	to	to	ADP
cana-1750	732	14	0	0	NUM
cana-1750	732	15	implies	imply	VERB
cana-1750	732	16	that	that	SCONJ
cana-1750	732	17	𝑝	𝑝	X
cana-1750	732	18	=	=	SYM
cana-1750	732	19	𝑝0	𝑝0	NOUN
cana-1750	732	20	=	=	SYM
cana-1750	732	21	2	2	NUM
cana-1750	732	22	which	which	PRON
cana-1750	732	23	is	be	AUX
cana-1750	732	24	contradiction	contradiction	NOUN
cana-1750	732	25	.	.	PUNCT
cana-1750	733	1	thus	thus	ADV
cana-1750	733	2	,	,	PUNCT
cana-1750	733	3	for	for	ADP
cana-1750	733	4	the	the	DET
cana-1750	733	5	maximum	maximum	NOUN
cana-1750	733	6	of	of	ADP
cana-1750	733	7	λ(𝑝	λ(𝑝	NOUN
cana-1750	733	8	,	,	PUNCT
cana-1750	733	9	|𝑥|	|𝑥|	ADJ
cana-1750	733	10	)	)	PUNCT
cana-1750	733	11	,	,	PUNCT
cana-1750	733	12	we	we	PRON
cana-1750	733	13	have	have	VERB
cana-1750	733	14	to	to	PART
cana-1750	733	15	consider	consider	VERB
cana-1750	733	16	the	the	DET
cana-1750	733	17	end	end	NOUN
cana-1750	733	18	points	point	NOUN
cana-1750	733	19	of	of	ADP
cana-1750	733	20	[	[	X
cana-1750	733	21	0,2	0,2	NUM
cana-1750	733	22	]	]	X
cana-1750	733	23	×	×	NOUN
cana-1750	734	1	[	[	X
cana-1750	734	2	0,1	0,1	NUM
cana-1750	734	3	]	]	PUNCT
cana-1750	734	4	.	.	PUNCT
cana-1750	735	1	for	for	ADP
cana-1750	735	2	𝑝	𝑝	NOUN
cana-1750	735	3	=	=	SYM
cana-1750	735	4	0	0	NUM
cana-1750	735	5	we	we	PRON
cana-1750	735	6	obtain	obtain	VERB
cana-1750	735	7	communications	communication	NOUN
cana-1750	735	8	on	on	ADP
cana-1750	735	9	applied	apply	VERB
cana-1750	735	10	nonlinear	nonlinear	ADJ
cana-1750	735	11	analysis	analysis	NOUN
cana-1750	735	12	issn	issn	NOUN
cana-1750	735	13	:	:	PUNCT
cana-1750	735	14	1074	1074	NUM
cana-1750	735	15	-	-	PUNCT
cana-1750	735	16	133x	133x	NUM
cana-1750	735	17	vol	vol	NOUN
cana-1750	735	18	32	32	NUM
cana-1750	735	19	no	no	NOUN
cana-1750	735	20	.	.	NOUN
cana-1750	735	21	2	2	NUM
cana-1750	735	22	(	(	PUNCT
cana-1750	735	23	2025	2025	NUM
cana-1750	735	24	)	)	PUNCT
cana-1750	736	1	405	405	NUM
cana-1750	736	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	736	3	λ(0	λ(0	NOUN
cana-1750	736	4	,	,	PUNCT
cana-1750	736	5	|𝑥|	|𝑥|	ADJ
cana-1750	736	6	)	)	PUNCT
cana-1750	736	7	=	=	PUNCT
cana-1750	737	1	[	[	PUNCT
cana-1750	737	2	4(1	4(1	NUM
cana-1750	737	3	−	−	NOUN
cana-1750	737	4	𝜆	𝜆	NOUN
cana-1750	737	5	)	)	PUNCT
cana-1750	737	6	(	(	PUNCT
cana-1750	737	7	𝜆	𝜆	X
cana-1750	738	1	+	+	ADJ
cana-1750	738	2	2)(𝜆	2)(𝜆	NUM
cana-1750	738	3	+	+	CCONJ
cana-1750	738	4	4	4	NUM
cana-1750	738	5	)	)	PUNCT
cana-1750	738	6	+	+	CCONJ
cana-1750	738	7	2	2	NUM
cana-1750	738	8	(	(	PUNCT
cana-1750	738	9	𝜆	𝜆	NOUN
cana-1750	738	10	+	+	NOUN
cana-1750	738	11	4	4	NUM
cana-1750	738	12	)	)	PUNCT
cana-1750	738	13	−	−	PROPN
cana-1750	739	1	2𝑥‾	2𝑥‾	NUM
cana-1750	739	2	(	(	PUNCT
cana-1750	739	3	𝜆	𝜆	PROPN
cana-1750	739	4	+	+	NOUN
cana-1750	739	5	4	4	NUM
cana-1750	739	6	)	)	PUNCT
cana-1750	739	7	]	]	PUNCT
cana-1750	740	1	|𝑥|2	|𝑥|2	ADJ
cana-1750	740	2	+	+	PUNCT
cana-1750	740	3	2𝑥‾	2𝑥‾	NUM
cana-1750	740	4	(	(	PUNCT
cana-1750	740	5	𝜆	𝜆	NOUN
cana-1750	740	6	+	+	NOUN
cana-1750	740	7	4	4	NUM
cana-1750	740	8	)	)	PUNCT
cana-1750	740	9	.	.	PUNCT
cana-1750	741	1	(	(	PUNCT
cana-1750	741	2	6.15	6.15	NUM
cana-1750	741	3	)	)	PUNCT
cana-1750	741	4	≤	≤	NOUN
cana-1750	741	5	4(1	4(1	NUM
cana-1750	742	1	−	−	NOUN
cana-1750	742	2	𝜆	𝜆	NOUN
cana-1750	742	3	)	)	PUNCT
cana-1750	742	4	(	(	PUNCT
cana-1750	742	5	𝜆	𝜆	X
cana-1750	742	6	+	+	ADJ
cana-1750	742	7	2)(𝜆	2)(𝜆	NUM
cana-1750	742	8	+	+	CCONJ
cana-1750	742	9	4	4	NUM
cana-1750	742	10	)	)	PUNCT
cana-1750	742	11	+	+	CCONJ
cana-1750	742	12	6	6	NUM
cana-1750	742	13	𝜆	𝜆	NOUN
cana-1750	742	14	+	+	ADP
cana-1750	742	15	4	4	NUM
cana-1750	742	16	.	.	PUNCT
cana-1750	743	1	(	(	PUNCT
cana-1750	743	2	6.16	6.16	NUM
cana-1750	743	3	)	)	PUNCT
cana-1750	743	4	for	for	ADP
cana-1750	743	5	𝑝	𝑝	NOUN
cana-1750	743	6	=	=	SYM
cana-1750	743	7	2	2	NUM
cana-1750	743	8	,	,	PUNCT
cana-1750	743	9	we	we	PRON
cana-1750	743	10	obtain	obtain	VERB
cana-1750	743	11	λ(2	λ(2	PROPN
cana-1750	743	12	,	,	PUNCT
cana-1750	743	13	|𝑥|	|𝑥|	ADJ
cana-1750	743	14	)	)	PUNCT
cana-1750	744	1	=	=	SYM
cana-1750	744	2	|𝒬(𝜆)|	|𝒬(𝜆)|	NOUN
cana-1750	744	3	(	(	PUNCT
cana-1750	744	4	𝜆	𝜆	PROPN
cana-1750	744	5	+	+	ADJ
cana-1750	744	6	1)4(𝜆	1)4(𝜆	NUM
cana-1750	744	7	+	+	SYM
cana-1750	744	8	2)(𝜆	2)(𝜆	NUM
cana-1750	744	9	+	+	CCONJ
cana-1750	744	10	3)(𝜆	3)(𝜆	NUM
cana-1750	744	11	+	+	NUM
cana-1750	744	12	4	4	NUM
cana-1750	744	13	)	)	PUNCT
cana-1750	744	14	.	.	PUNCT
cana-1750	745	1	(	(	PUNCT
cana-1750	745	2	6.17	6.17	NUM
cana-1750	745	3	)	)	PUNCT
cana-1750	745	4	for	for	ADP
cana-1750	745	5	|𝑥|	|𝑥|	ADJ
cana-1750	745	6	=	=	SYM
cana-1750	745	7	0	0	NUM
cana-1750	745	8	,	,	PUNCT
cana-1750	745	9	we	we	PRON
cana-1750	745	10	have	have	VERB
cana-1750	745	11	λ(𝑝	λ(𝑝	NOUN
cana-1750	745	12	,	,	PUNCT
cana-1750	745	13	0	0	NUM
cana-1750	745	14	)	)	PUNCT
cana-1750	746	1	=	=	NOUN
cana-1750	747	1	[	[	PUNCT
cana-1750	747	2	𝜆6	𝜆6	PROPN
cana-1750	747	3	+	+	CCONJ
cana-1750	747	4	21𝜆5	21𝜆5	NUM
cana-1750	747	5	+	+	SYM
cana-1750	747	6	6𝜆4	6𝜆4	NUM
cana-1750	747	7	−	−	NUM
cana-1750	747	8	54𝜆3	54𝜆3	NUM
cana-1750	747	9	−	−	PROPN
cana-1750	747	10	43𝜆2	43𝜆2	NUM
cana-1750	747	11	−	−	NOUN
cana-1750	747	12	87𝜆	87𝜆	NUM
cana-1750	747	13	−	−	PROPN
cana-1750	747	14	132	132	NUM
cana-1750	747	15	8(𝜆	8(𝜆	NUM
cana-1750	747	16	+	+	CCONJ
cana-1750	747	17	1)4(𝜆	1)4(𝜆	NUM
cana-1750	748	1	+	+	SYM
cana-1750	748	2	2)(𝜆	2)(𝜆	NUM
cana-1750	748	3	+	+	CCONJ
cana-1750	748	4	3)(𝜆	3)(𝜆	NUM
cana-1750	748	5	+	+	NUM
cana-1750	748	6	4	4	NUM
cana-1750	748	7	)	)	PUNCT
cana-1750	748	8	]	]	PUNCT
cana-1750	749	1	𝑝4	𝑝4	NOUN
cana-1750	749	2	+	+	PROPN
cana-1750	749	3	[	[	PUNCT
cana-1750	749	4	−𝜆2	−𝜆2	X
cana-1750	749	5	+	+	CCONJ
cana-1750	749	6	2𝜆	2𝜆	NUM
cana-1750	749	7	+	+	CCONJ
cana-1750	749	8	7	7	NUM
cana-1750	749	9	2(𝜆	2(𝜆	NUM
cana-1750	749	10	+	+	CCONJ
cana-1750	749	11	1)(𝜆	1)(𝜆	NUM
cana-1750	749	12	+	+	CCONJ
cana-1750	749	13	3)(𝜆	3)(𝜆	NUM
cana-1750	749	14	+	+	NUM
cana-1750	749	15	4	4	NUM
cana-1750	749	16	)	)	PUNCT
cana-1750	749	17	]	]	PUNCT
cana-1750	749	18	𝑝(4	𝑝(4	PROPN
cana-1750	749	19	−	−	PROPN
cana-1750	749	20	𝑝2	𝑝2	NOUN
cana-1750	749	21	)	)	PUNCT
cana-1750	749	22	.	.	PUNCT
cana-1750	750	1	(	(	PUNCT
cana-1750	750	2	6.18	6.18	NUM
cana-1750	750	3	)	)	PUNCT
cana-1750	750	4	for	for	ADP
cana-1750	750	5	|𝑥|	|𝑥|	ADJ
cana-1750	750	6	=	=	SYM
cana-1750	750	7	1	1	NUM
cana-1750	750	8	,	,	PUNCT
cana-1750	750	9	we	we	PRON
cana-1750	750	10	get	get	VERB
cana-1750	750	11	λ(𝑝	λ(𝑝	NOUN
cana-1750	750	12	,	,	PUNCT
cana-1750	750	13	1	1	X
cana-1750	750	14	)	)	PUNCT
cana-1750	750	15	=	=	NOUN
cana-1750	751	1	[	[	PUNCT
cana-1750	751	2	𝑝2(4	𝑝2(4	PROPN
cana-1750	751	3	−	−	PROPN
cana-1750	751	4	𝑝2	𝑝2	NOUN
cana-1750	751	5	)	)	PUNCT
cana-1750	751	6	8(𝜆	8(𝜆	NUM
cana-1750	752	1	+	+	CCONJ
cana-1750	752	2	4	4	NUM
cana-1750	752	3	)	)	PUNCT
cana-1750	752	4	−	−	PROPN
cana-1750	752	5	𝑝(4	𝑝(4	PROPN
cana-1750	752	6	−	−	PROPN
cana-1750	752	7	𝑝2	𝑝2	NOUN
cana-1750	752	8	)	)	PUNCT
cana-1750	752	9	2(𝜆	2(𝜆	NUM
cana-1750	753	1	+	+	CCONJ
cana-1750	754	1	4	4	NUM
cana-1750	754	2	)	)	PUNCT
cana-1750	754	3	]	]	PUNCT
cana-1750	755	1	+	+	CCONJ
cana-1750	755	2	[	[	PUNCT
cana-1750	755	3	(	(	PUNCT
cana-1750	755	4	−𝜆2	−𝜆2	PROPN
cana-1750	755	5	+	+	CCONJ
cana-1750	755	6	2𝜆	2𝜆	NUM
cana-1750	755	7	+	+	CCONJ
cana-1750	755	8	7)𝑝(4	7)𝑝(4	ADJ
cana-1750	755	9	−	−	PROPN
cana-1750	755	10	𝑝2	𝑝2	NOUN
cana-1750	755	11	)	)	PUNCT
cana-1750	755	12	2(𝜆	2(𝜆	NUM
cana-1750	756	1	+	+	CCONJ
cana-1750	756	2	1)(𝜆	1)(𝜆	NUM
cana-1750	757	1	+	+	CCONJ
cana-1750	757	2	3)(𝜆	3)(𝜆	NUM
cana-1750	757	3	+	+	NUM
cana-1750	757	4	4	4	NUM
cana-1750	757	5	)	)	PUNCT
cana-1750	758	1	+	+	CCONJ
cana-1750	758	2	(	(	PUNCT
cana-1750	758	3	−𝜆2	−𝜆2	X
cana-1750	758	4	+	+	CCONJ
cana-1750	758	5	8𝜆	8𝜆	NUM
cana-1750	758	6	+	+	CCONJ
cana-1750	758	7	17)𝑝2(4	17)𝑝2(4	NUM
cana-1750	758	8	−	−	PROPN
cana-1750	758	9	𝑝2	𝑝2	NOUN
cana-1750	758	10	)	)	PUNCT
cana-1750	758	11	8(𝜆	8(𝜆	NUM
cana-1750	759	1	+	+	CCONJ
cana-1750	759	2	1)(𝜆	1)(𝜆	NUM
cana-1750	759	3	+	+	CCONJ
cana-1750	759	4	3)(𝜆	3)(𝜆	NUM
cana-1750	759	5	+	+	NUM
cana-1750	759	6	4	4	NUM
cana-1750	759	7	)	)	PUNCT
cana-1750	759	8	]	]	PUNCT
cana-1750	760	1	+	+	CCONJ
cana-1750	760	2	[	[	PUNCT
cana-1750	760	3	(	(	PUNCT
cana-1750	760	4	4	4	NUM
cana-1750	760	5	−	−	NOUN
cana-1750	760	6	𝑝2)2(1	𝑝2)2(1	NOUN
cana-1750	760	7	−	−	NOUN
cana-1750	760	8	𝜆	𝜆	NOUN
cana-1750	760	9	)	)	PUNCT
cana-1750	760	10	4(𝜆	4(𝜆	NUM
cana-1750	761	1	+	+	CCONJ
cana-1750	761	2	2)(𝜆	2)(𝜆	NUM
cana-1750	761	3	+	+	CCONJ
cana-1750	761	4	4	4	NUM
cana-1750	761	5	)	)	PUNCT
cana-1750	761	6	+	+	CCONJ
cana-1750	761	7	(	(	PUNCT
cana-1750	761	8	4	4	NUM
cana-1750	761	9	−	−	PROPN
cana-1750	761	10	𝑝2	𝑝2	NOUN
cana-1750	761	11	)	)	PUNCT
cana-1750	761	12	2(𝜆	2(𝜆	NUM
cana-1750	762	1	+	+	CCONJ
cana-1750	762	2	4	4	NUM
cana-1750	762	3	)	)	PUNCT
cana-1750	762	4	−	−	PROPN
cana-1750	762	5	(	(	PUNCT
cana-1750	762	6	4	4	NUM
cana-1750	762	7	−	−	PROPN
cana-1750	762	8	𝑝2	𝑝2	NOUN
cana-1750	762	9	)	)	PUNCT
cana-1750	762	10	2(𝜆	2(𝜆	NUM
cana-1750	763	1	+	+	CCONJ
cana-1750	764	1	4	4	NUM
cana-1750	764	2	)	)	PUNCT
cana-1750	764	3	]	]	PUNCT
cana-1750	765	1	+	+	CCONJ
cana-1750	766	1	[	[	X
cana-1750	766	2	[	[	PUNCT
cana-1750	766	3	(	(	PUNCT
cana-1750	766	4	3𝜆3	3𝜆3	NUM
cana-1750	766	5	−	−	NOUN
cana-1750	766	6	14𝜆2	14𝜆2	NUM
cana-1750	766	7	−	−	NOUN
cana-1750	766	8	7𝜆	7𝜆	PROPN
cana-1750	766	9	+	+	CCONJ
cana-1750	766	10	90)𝑝2	90)𝑝2	NUM
cana-1750	766	11	8(𝜆	8(𝜆	NUM
cana-1750	766	12	+	+	NUM
cana-1750	766	13	1)(𝜆	1)(𝜆	NUM
cana-1750	766	14	+	+	CCONJ
cana-1750	766	15	3)(𝜆	3)(𝜆	NUM
cana-1750	766	16	+	+	SYM
cana-1750	766	17	4)(𝜆	4)(𝜆	NUM
cana-1750	766	18	+	+	CCONJ
cana-1750	766	19	2	2	NUM
cana-1750	766	20	)	)	PUNCT
cana-1750	766	21	+	+	SYM
cana-1750	766	22	𝑝	𝑝	SYM
cana-1750	766	23	2	2	NUM
cana-1750	766	24	+	+	CCONJ
cana-1750	766	25	𝜆	𝜆	SYM
cana-1750	766	26	]	]	X
cana-1750	766	27	(	(	PUNCT
cana-1750	766	28	4	4	NUM
cana-1750	766	29	−	−	PROPN
cana-1750	766	30	𝑝2	𝑝2	NOUN
cana-1750	766	31	)	)	PUNCT
cana-1750	766	32	]	]	PUNCT
cana-1750	767	1	+	+	CCONJ
cana-1750	768	1	[	[	X
cana-1750	768	2	[	[	PUNCT
cana-1750	768	3	−𝜆2	−𝜆2	X
cana-1750	768	4	+	+	CCONJ
cana-1750	768	5	2𝜆	2𝜆	NUM
cana-1750	768	6	+	+	CCONJ
cana-1750	768	7	7	7	NUM
cana-1750	768	8	2(𝜆	2(𝜆	NUM
cana-1750	768	9	+	+	CCONJ
cana-1750	768	10	1)(𝜆	1)(𝜆	NUM
cana-1750	768	11	+	+	CCONJ
cana-1750	768	12	3)(𝜆	3)(𝜆	NUM
cana-1750	768	13	+	+	SYM
cana-1750	768	14	4	4	NUM
cana-1750	768	15	]	]	SYM
cana-1750	768	16	𝑝	𝑝	NOUN
cana-1750	768	17	+	+	CCONJ
cana-1750	768	18	1	1	NUM
cana-1750	768	19	2(𝜆	2(𝜆	NUM
cana-1750	768	20	+	+	CCONJ
cana-1750	768	21	4	4	NUM
cana-1750	768	22	)	)	PUNCT
cana-1750	768	23	]	]	PUNCT
cana-1750	768	24	(	(	PUNCT
cana-1750	768	25	4	4	NUM
cana-1750	768	26	−	−	PROPN
cana-1750	768	27	𝑝2	𝑝2	NOUN
cana-1750	768	28	)	)	PUNCT
cana-1750	768	29	+	+	CCONJ
cana-1750	768	30	[	[	PUNCT
cana-1750	768	31	𝜆6	𝜆6	X
cana-1750	768	32	+	+	CCONJ
cana-1750	768	33	21𝜆5	21𝜆5	NUM
cana-1750	768	34	+	+	SYM
cana-1750	768	35	6𝜆4	6𝜆4	NUM
cana-1750	768	36	−	−	NUM
cana-1750	768	37	54𝜆3	54𝜆3	NUM
cana-1750	768	38	−	−	PROPN
cana-1750	768	39	43𝜆2	43𝜆2	NUM
cana-1750	768	40	−	−	NOUN
cana-1750	768	41	87𝜆	87𝜆	NUM
cana-1750	768	42	−	−	PROPN
cana-1750	768	43	132	132	NUM
cana-1750	768	44	8(𝜆	8(𝜆	NUM
cana-1750	768	45	+	+	CCONJ
cana-1750	768	46	1)4(𝜆	1)4(𝜆	NUM
cana-1750	768	47	+	+	SYM
cana-1750	768	48	2)(𝜆	2)(𝜆	NUM
cana-1750	768	49	+	+	CCONJ
cana-1750	768	50	3)(𝜆	3)(𝜆	NUM
cana-1750	768	51	+	+	NUM
cana-1750	768	52	4	4	NUM
cana-1750	768	53	)	)	PUNCT
cana-1750	768	54	]	]	PUNCT
cana-1750	768	55	𝑝4	𝑝4	PROPN
cana-1750	768	56	.	.	PUNCT
cana-1750	769	1	which	which	PRON
cana-1750	769	2	has	have	VERB
cana-1750	769	3	maximum	maximum	ADJ
cana-1750	769	4	value	value	NOUN
cana-1750	769	5	|𝑄(𝜆)|	|𝑄(𝜆)|	NOUN
cana-1750	769	6	(	(	PUNCT
cana-1750	769	7	𝜆+1)4(𝜆+2)(𝜆+3)(𝜆+4	𝜆+1)4(𝜆+2)(𝜆+3)(𝜆+4	PROPN
cana-1750	769	8	)	)	PUNCT
cana-1750	769	9	attained	attain	VERB
cana-1750	769	10	at	at	ADP
cana-1750	769	11	the	the	DET
cana-1750	769	12	end	end	NOUN
cana-1750	769	13	point	point	NOUN
cana-1750	769	14	𝑝	𝑝	NOUN
cana-1750	769	15	=	=	SYM
cana-1750	769	16	2	2	NUM
cana-1750	769	17	and	and	CCONJ
cana-1750	769	18	4(1−𝜆	4(1−𝜆	NUM
cana-1750	769	19	)	)	PUNCT
cana-1750	769	20	(	(	PUNCT
cana-1750	769	21	𝜆+2)(𝜆+4	𝜆+2)(𝜆+4	NUM
cana-1750	769	22	)	)	PUNCT
cana-1750	770	1	+	+	CCONJ
cana-1750	770	2	6	6	NUM
cana-1750	770	3	𝜆+4	𝜆+4	NUM
cana-1750	770	4	at	at	ADP
cana-1750	770	5	𝑝	𝑝	NOUN
cana-1750	770	6	=	=	SYM
cana-1750	770	7	0	0	PROPN
cana-1750	770	8	.	.	PUNCT
cana-1750	771	1	where	where	SCONJ
cana-1750	771	2	,	,	PUNCT
cana-1750	771	3	𝑄(𝜆	𝑄(𝜆	NOUN
cana-1750	771	4	)	)	PUNCT
cana-1750	771	5	=	=	SYM
cana-1750	771	6	2(𝜆6	2(𝜆6	NUM
cana-1750	772	1	+	+	CCONJ
cana-1750	773	1	21𝜆5	21𝜆5	NUM
cana-1750	773	2	+	+	SYM
cana-1750	773	3	6𝜆4	6𝜆4	NUM
cana-1750	773	4	−	−	NUM
cana-1750	774	1	54𝜆3	54𝜆3	NUM
cana-1750	774	2	−	−	PROPN
cana-1750	774	3	43𝜆2	43𝜆2	NUM
cana-1750	774	4	−	−	NOUN
cana-1750	774	5	87𝜆	87𝜆	NUM
cana-1750	774	6	−	−	PROPN
cana-1750	774	7	132	132	NUM
cana-1750	774	8	)	)	PUNCT
cana-1750	774	9	.	.	PUNCT
cana-1750	775	1	(	(	PUNCT
cana-1750	775	2	6.19	6.19	NUM
cana-1750	775	3	)	)	PUNCT
cana-1750	775	4	conclusion	conclusion	NOUN
cana-1750	775	5	in	in	ADP
cana-1750	775	6	this	this	DET
cana-1750	775	7	present	present	ADJ
cana-1750	775	8	paper	paper	NOUN
cana-1750	775	9	toeplitz	toeplitz	NOUN
cana-1750	775	10	matrices	matrix	NOUN
cana-1750	775	11	characterized	characterize	VERB
cana-1750	775	12	by	by	ADP
cana-1750	775	13	coefficients	coefficient	NOUN
cana-1750	775	14	from	from	ADP
cana-1750	775	15	novel	novel	ADJ
cana-1750	775	16	subclasses	subclass	NOUN
cana-1750	775	17	.	.	PUNCT
cana-1750	776	1	the	the	DET
cana-1750	776	2	investigation	investigation	NOUN
cana-1750	776	3	establishes	establish	VERB
cana-1750	776	4	upper	upper	ADJ
cana-1750	776	5	limits	limit	NOUN
cana-1750	776	6	for	for	ADP
cana-1750	776	7	the	the	DET
cana-1750	776	8	initial	initial	ADJ
cana-1750	776	9	four	four	NUM
cana-1750	776	10	determinants	determinant	NOUN
cana-1750	776	11	of	of	ADP
cana-1750	776	12	these	these	DET
cana-1750	776	13	matrices	matrix	NOUN
cana-1750	776	14	,	,	PUNCT
cana-1750	776	15	presenting	present	VERB
cana-1750	776	16	innovative	innovative	ADJ
cana-1750	776	17	and	and	CCONJ
cana-1750	776	18	unique	unique	ADJ
cana-1750	776	19	findings	finding	NOUN
cana-1750	776	20	.	.	PUNCT
cana-1750	777	1	notably	notably	ADV
cana-1750	777	2	,	,	PUNCT
cana-1750	777	3	our	our	PRON
cana-1750	777	4	results	result	NOUN
cana-1750	777	5	parallel	parallel	VERB
cana-1750	777	6	recent	recent	ADJ
cana-1750	777	7	works	work	NOUN
cana-1750	777	8	by	by	ADP
cana-1750	777	9	thomas	thomas	PROPN
cana-1750	777	10	and	and	CCONJ
cana-1750	777	11	halim	halim	PROPN
cana-1750	778	1	[	[	X
cana-1750	778	2	1	1	NUM
cana-1750	778	3	]	]	PUNCT
cana-1750	778	4	,	,	PUNCT
cana-1750	778	5	communications	communication	NOUN
cana-1750	778	6	on	on	ADP
cana-1750	778	7	applied	apply	VERB
cana-1750	778	8	nonlinear	nonlinear	ADJ
cana-1750	778	9	analysis	analysis	NOUN
cana-1750	778	10	issn	issn	NOUN
cana-1750	778	11	:	:	PUNCT
cana-1750	778	12	1074	1074	NUM
cana-1750	778	13	-	-	PUNCT
cana-1750	778	14	133x	133x	NUM
cana-1750	778	15	vol	vol	NOUN
cana-1750	778	16	32	32	NUM
cana-1750	778	17	no	no	NOUN
cana-1750	778	18	.	.	NOUN
cana-1750	778	19	2	2	NUM
cana-1750	778	20	(	(	PUNCT
cana-1750	778	21	2025	2025	NUM
cana-1750	778	22	)	)	PUNCT
cana-1750	778	23	406	406	NUM
cana-1750	778	24	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	778	25	specifically	specifically	ADV
cana-1750	778	26	in	in	ADP
cana-1750	778	27	the	the	DET
cana-1750	778	28	context	context	NOUN
cana-1750	778	29	of	of	ADP
cana-1750	778	30	star	star	NOUN
cana-1750	778	31	-	-	PUNCT
cana-1750	778	32	like	like	ADJ
cana-1750	778	33	and	and	CCONJ
cana-1750	778	34	close	close	ADJ
cana-1750	778	35	to	to	ADP
cana-1750	778	36	convex	convex	NOUN
cana-1750	778	37	functions	function	NOUN
cana-1750	778	38	,	,	PUNCT
cana-1750	778	39	as	as	ADV
cana-1750	778	40	well	well	ADV
cana-1750	778	41	as	as	ADP
cana-1750	778	42	by	by	ADP
cana-1750	778	43	radhika	radhika	PROPN
cana-1750	778	44	et	et	PROPN
cana-1750	778	45	al	al	PROPN
cana-1750	778	46	.	.	PUNCT
cana-1750	779	1	[	[	X
cana-1750	779	2	2	2	NUM
cana-1750	779	3	]	]	PUNCT
cana-1750	779	4	,	,	PUNCT
cana-1750	779	5	which	which	PRON
cana-1750	779	6	concentrate	concentrate	VERB
cana-1750	779	7	on	on	ADP
cana-1750	779	8	functions	function	NOUN
cana-1750	779	9	with	with	ADP
cana-1750	779	10	bounded	bounded	ADJ
cana-1750	779	11	boundary	boundary	ADJ
cana-1750	779	12	rotation	rotation	NOUN
cana-1750	779	13	.	.	PUNCT
cana-1750	780	1	additionally	additionally	ADV
cana-1750	780	2	,	,	PUNCT
cana-1750	780	3	we	we	PRON
cana-1750	780	4	have	have	AUX
cana-1750	780	5	determined	determine	VERB
cana-1750	780	6	the	the	DET
cana-1750	780	7	zalcman	zalcman	NOUN
cana-1750	780	8	and	and	CCONJ
cana-1750	780	9	generalized	generalize	VERB
cana-1750	780	10	zalcman	zalcman	NOUN
cana-1750	780	11	conjecture	conjecture	NOUN
cana-1750	780	12	,	,	PUNCT
cana-1750	780	13	along	along	ADP
cana-1750	780	14	with	with	ADP
cana-1750	780	15	krushkal	krushkal	ADJ
cana-1750	780	16	inequalities	inequality	NOUN
cana-1750	780	17	for	for	ADP
cana-1750	780	18	certain	certain	ADJ
cana-1750	780	19	parameters	parameter	NOUN
cana-1750	780	20	.	.	PUNCT
cana-1750	781	1	this	this	PRON
cana-1750	781	2	contributes	contribute	VERB
cana-1750	781	3	to	to	ADP
cana-1750	781	4	the	the	DET
cana-1750	781	5	existing	exist	VERB
cana-1750	781	6	body	body	NOUN
cana-1750	781	7	of	of	ADP
cana-1750	781	8	knowledge	knowledge	NOUN
cana-1750	781	9	in	in	ADP
cana-1750	781	10	the	the	DET
cana-1750	781	11	field	field	NOUN
cana-1750	781	12	and	and	CCONJ
cana-1750	781	13	demonstrates	demonstrate	VERB
cana-1750	781	14	the	the	DET
cana-1750	781	15	novelty	novelty	NOUN
cana-1750	781	16	of	of	ADP
cana-1750	781	17	our	our	PRON
cana-1750	781	18	results	result	NOUN
cana-1750	781	19	in	in	ADP
cana-1750	781	20	comparison	comparison	NOUN
cana-1750	781	21	to	to	ADP
cana-1750	781	22	recent	recent	ADJ
cana-1750	781	23	literature	literature	NOUN
cana-1750	781	24	.	.	PUNCT
cana-1750	782	1	the	the	DET
cana-1750	782	2	result	result	NOUN
cana-1750	782	3	obtained	obtain	VERB
cana-1750	782	4	perhaps	perhaps	ADV
cana-1750	782	5	give	give	VERB
cana-1750	782	6	an	an	DET
cana-1750	782	7	opportunity	opportunity	NOUN
cana-1750	782	8	for	for	SCONJ
cana-1750	782	9	researchers	researcher	NOUN
cana-1750	782	10	to	to	PART
cana-1750	782	11	further	far	ADV
cana-1750	782	12	investigate	investigate	VERB
cana-1750	782	13	inequalities	inequality	NOUN
cana-1750	782	14	problems	problem	NOUN
cana-1750	782	15	for	for	ADP
cana-1750	782	16	functions	function	NOUN
cana-1750	782	17	of	of	ADP
cana-1750	782	18	the	the	DET
cana-1750	782	19	class	class	NOUN
cana-1750	782	20	𝒜	𝒜	NOUN
cana-1750	782	21	as	as	ADV
cana-1750	782	22	well	well	ADV
cana-1750	782	23	as	as	ADP
cana-1750	782	24	other	other	ADJ
cana-1750	782	25	subclasses	subclass	NOUN
cana-1750	782	26	𝒮.	𝒮.	NOUN
cana-1750	782	27	data	datum	NOUN
cana-1750	782	28	availability	availability	NOUN
cana-1750	782	29	:	:	PUNCT
cana-1750	782	30	no	no	DET
cana-1750	782	31	data	datum	NOUN
cana-1750	782	32	were	be	AUX
cana-1750	782	33	used	use	VERB
cana-1750	782	34	in	in	ADP
cana-1750	782	35	this	this	DET
cana-1750	782	36	paper	paper	NOUN
cana-1750	782	37	.	.	PUNCT
cana-1750	783	1	ethical	ethical	ADJ
cana-1750	783	2	approval	approval	NOUN
cana-1750	783	3	:	:	PUNCT
cana-1750	783	4	this	this	DET
cana-1750	783	5	article	article	NOUN
cana-1750	783	6	does	do	AUX
cana-1750	783	7	not	not	PART
cana-1750	783	8	contain	contain	VERB
cana-1750	783	9	any	any	DET
cana-1750	783	10	studies	study	NOUN
cana-1750	783	11	with	with	ADP
cana-1750	783	12	human	human	ADJ
cana-1750	783	13	participants	participant	NOUN
cana-1750	783	14	or	or	CCONJ
cana-1750	783	15	animals	animal	NOUN
cana-1750	783	16	performed	perform	VERB
cana-1750	783	17	by	by	ADP
cana-1750	783	18	any	any	PRON
cana-1750	783	19	of	of	ADP
cana-1750	783	20	the	the	DET
cana-1750	783	21	authors	author	NOUN
cana-1750	783	22	.	.	PUNCT
cana-1750	784	1	conflicts	conflict	NOUN
cana-1750	784	2	of	of	ADP
cana-1750	784	3	interest	interest	NOUN
cana-1750	784	4	:	:	PUNCT
cana-1750	784	5	the	the	DET
cana-1750	784	6	authors	author	NOUN
cana-1750	784	7	confirm	confirm	VERB
cana-1750	784	8	no	no	DET
cana-1750	784	9	competing	compete	VERB
cana-1750	784	10	interests	interest	NOUN
cana-1750	784	11	.	.	PUNCT
cana-1750	785	1	funding	funding	NOUN
cana-1750	785	2	statement	statement	NOUN
cana-1750	785	3	:	:	PUNCT
cana-1750	785	4	the	the	DET
cana-1750	785	5	research	research	NOUN
cana-1750	785	6	did	do	AUX
cana-1750	785	7	not	not	PART
cana-1750	785	8	receive	receive	VERB
cana-1750	785	9	any	any	DET
cana-1750	785	10	funding	funding	NOUN
cana-1750	785	11	.	.	PUNCT
cana-1750	786	1	author	author	NOUN
cana-1750	786	2	's	's	PART
cana-1750	786	3	contributions	contribution	NOUN
cana-1750	786	4	:	:	PUNCT
cana-1750	786	5	the	the	DET
cana-1750	786	6	authors	author	NOUN
cana-1750	786	7	read	read	VERB
cana-1750	786	8	and	and	CCONJ
cana-1750	786	9	approved	approve	VERB
cana-1750	786	10	the	the	DET
cana-1750	786	11	final	final	ADJ
cana-1750	786	12	manuscript	manuscript	NOUN
cana-1750	786	13	.	.	PUNCT
cana-1750	787	1	references	reference	NOUN
cana-1750	787	2	[	[	X
cana-1750	787	3	1	1	X
cana-1750	787	4	]	]	PUNCT
cana-1750	787	5	d.	d.	PROPN
cana-1750	787	6	k.	k.	PROPN
cana-1750	787	7	thomas	thomas	PROPN
cana-1750	787	8	,	,	PUNCT
cana-1750	787	9	s.	s.	PROPN
cana-1750	787	10	a.	a.	PROPN
cana-1750	787	11	halim	halim	PROPN
cana-1750	787	12	,	,	PUNCT
cana-1750	787	13	:	:	PUNCT
cana-1750	787	14	toeplitz	toeplitz	NOUN
cana-1750	787	15	matrices	matrix	NOUN
cana-1750	787	16	whose	whose	DET
cana-1750	787	17	elements	element	NOUN
cana-1750	787	18	are	be	AUX
cana-1750	787	19	the	the	DET
cana-1750	787	20	coefficients	coefficient	NOUN
cana-1750	787	21	of	of	ADP
cana-1750	787	22	star	star	NOUN
cana-1750	787	23	-	-	PUNCT
cana-1750	787	24	like	like	ADJ
cana-1750	787	25	and	and	CCONJ
cana-1750	787	26	close	close	ADJ
cana-1750	787	27	to	to	ADP
cana-1750	787	28	convex	convex	NOUN
cana-1750	787	29	functions	function	NOUN
cana-1750	787	30	,	,	PUNCT
cana-1750	787	31	bull	bull	NOUN
cana-1750	787	32	.	.	PUNCT
cana-1750	788	1	malays	malays	PROPN
cana-1750	788	2	.	.	PUNCT
cana-1750	789	1	math	math	NOUN
cana-1750	789	2	.	.	PUNCT
cana-1750	790	1	sci	sci	PROPN
cana-1750	790	2	.	.	PROPN
cana-1750	790	3	soc	soc	PROPN
cana-1750	790	4	.	.	PUNCT
cana-1750	790	5	,	,	PUNCT
cana-1750	790	6	2016	2016	NUM
cana-1750	790	7	.	.	PUNCT
cana-1750	791	1	https://dx.doi.org/10.1007/s40840-016-0385-4	https://dx.doi.org/10.1007/s40840-016-0385-4	X
cana-1750	791	2	,	,	PUNCT
cana-1750	791	3	(	(	PUNCT
cana-1750	791	4	published	publish	VERB
cana-1750	791	5	online	online	ADV
cana-1750	791	6	)	)	PUNCT
cana-1750	791	7	.	.	PUNCT
cana-1750	792	1	[	[	X
cana-1750	792	2	2	2	X
cana-1750	792	3	]	]	X
cana-1750	792	4	v.	v.	X
cana-1750	792	5	radhika	radhika	PROPN
cana-1750	792	6	,	,	PUNCT
cana-1750	792	7	s.	s.	PROPN
cana-1750	792	8	sivasubramanian	sivasubramanian	PROPN
cana-1750	792	9	,	,	PUNCT
cana-1750	792	10	g.	g.	PROPN
cana-1750	792	11	murugusundaramoorthy	murugusundaramoorthy	PROPN
cana-1750	792	12	,	,	PUNCT
cana-1750	792	13	j.	j.	PROPN
cana-1750	792	14	m.	m.	PROPN
cana-1750	792	15	jahangiri	jahangiri	PROPN
cana-1750	792	16	,	,	PUNCT
cana-1750	792	17	:	:	PUNCT
cana-1750	792	18	toeplitz	toeplitz	NOUN
cana-1750	792	19	matrices	matrix	NOUN
cana-1750	792	20	whose	whose	DET
cana-1750	792	21	elements	element	NOUN
cana-1750	792	22	are	be	AUX
cana-1750	792	23	the	the	DET
cana-1750	792	24	co	co	NOUN
cana-1750	792	25	efficient	efficient	ADJ
cana-1750	792	26	of	of	ADP
cana-1750	792	27	functions	function	NOUN
cana-1750	792	28	with	with	ADP
cana-1750	792	29	bounded	bounded	ADJ
cana-1750	792	30	boundary	boundary	ADJ
cana-1750	792	31	rotation	rotation	NOUN
cana-1750	792	32	,	,	PUNCT
cana-1750	792	33	j.	j.	PROPN
cana-1750	792	34	complex	complex	PROPN
cana-1750	792	35	analysis	analysis	NOUN
cana-1750	792	36	,	,	PUNCT
cana-1750	792	37	2016	2016	NUM
cana-1750	792	38	.	.	PUNCT
cana-1750	793	1	https://dx.doi.org/10.1155/2016/4960704	https://dx.doi.org/10.1155/2016/4960704	X
cana-1750	793	2	.	.	PUNCT
cana-1750	794	1	[	[	X
cana-1750	794	2	3	3	X
cana-1750	794	3	]	]	X
cana-1750	794	4	p.	p.	NOUN
cana-1750	794	5	l.	l.	PROPN
cana-1750	794	6	duren	duren	PROPN
cana-1750	794	7	,	,	PUNCT
cana-1750	794	8	:	:	PUNCT
cana-1750	794	9	univalent	univalent	ADJ
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cana-1750	794	11	,	,	PUNCT
cana-1750	794	12	grundlehren	grundlehren	PROPN
cana-1750	794	13	der	der	PROPN
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cana-1750	794	15	wissenschaften	wissenschaften	NOUN
cana-1750	794	16	,	,	PUNCT
cana-1750	794	17	springer	springer	NOUN
cana-1750	794	18	,	,	PUNCT
cana-1750	794	19	new	new	PROPN
cana-1750	794	20	york	york	PROPN
cana-1750	794	21	,	,	PUNCT
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cana-1750	794	23	.	.	PUNCT
cana-1750	795	1	[	[	X
cana-1750	795	2	4	4	X
cana-1750	795	3	]	]	X
cana-1750	795	4	al	al	PROPN
cana-1750	795	5	oboudi	oboudi	PROPN
cana-1750	795	6	f.m	f.m	PROPN
cana-1750	795	7	.	.	PROPN
cana-1750	795	8	,	,	PUNCT
cana-1750	795	9	𝑛	𝑛	PROPN
cana-1750	795	10	bazilevič	bazilevič	NOUN
cana-1750	795	11	functions	function	NOUN
cana-1750	795	12	,	,	PUNCT
cana-1750	795	13	abstr	abstr	PROPN
cana-1750	795	14	.	.	PUNCT
cana-1750	795	15	appl	appl	PROPN
cana-1750	795	16	.	.	PUNCT
cana-1750	796	1	anal	anal	PROPN
cana-1750	796	2	.	.	PROPN
cana-1750	796	3	,	,	PUNCT
cana-1750	796	4	2012	2012	NUM
cana-1750	796	5	,	,	PUNCT
cana-1750	796	6	1	1	NUM
cana-1750	796	7	10	10	NUM
cana-1750	796	8	.	.	PUNCT
cana-1750	797	1	https://dx.doi.org/10.1155/2012/383592	https://dx.doi.org/10.1155/2012/383592	INTJ
cana-1750	797	2	.	.	PUNCT
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cana-1750	798	2	5	5	NUM
cana-1750	798	3	]	]	PUNCT
cana-1750	798	4	a.	a.	NOUN
cana-1750	798	5	a.	a.	PROPN
cana-1750	798	6	amer	amer	PROPN
cana-1750	798	7	,	,	PUNCT
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cana-1750	798	10	,	,	PUNCT
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cana-1750	798	12	theorem	theorem	NOUN
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cana-1750	798	19	,	,	PUNCT
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cana-1750	799	1	j.	j.	PROPN
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cana-1750	799	3	.	.	PUNCT
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cana-1750	800	2	.	.	PUNCT
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cana-1750	801	2	,	,	PUNCT
cana-1750	802	1	volume	volume	NOUN
cana-1750	802	2	6(9	6(9	NUM
cana-1750	803	1	−	−	NOUN
cana-1750	803	2	12	12	NUM
cana-1750	803	3	)	)	PUNCT
cana-1750	803	4	,	,	PUNCT
cana-1750	803	5	591	591	NUM
cana-1750	803	6	−	−	NUM
cana-1750	803	7	597	597	NUM
cana-1750	803	8	.	.	PUNCT
cana-1750	804	1	[	[	X
cana-1750	804	2	6	6	NUM
cana-1750	804	3	]	]	X
cana-1750	804	4	y.	y.	PROPN
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cana-1750	804	18	subclass	subclass	NOUN
cana-1750	804	19	of	of	ADP
cana-1750	804	20	bazilevič	bazilevič	NOUN
cana-1750	804	21	functions	function	NOUN
cana-1750	804	22	,	,	PUNCT
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cana-1750	804	24	.	.	PROPN
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cana-1750	804	26	.	.	PUNCT
cana-1750	805	1	comput	comput	NOUN
cana-1750	805	2	,	,	PUNCT
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cana-1750	805	4	,	,	PUNCT
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cana-1750	805	7	)	)	PUNCT
cana-1750	805	8	,	,	PUNCT
cana-1750	805	9	1201	1201	NUM
cana-1750	805	10	–	–	PUNCT
cana-1750	805	11	1207	1207	NUM
cana-1750	805	12	https://dx.doi.org/10.1016/j.amc.2006.06.044	https://dx.doi.org/10.1016/j.amc.2006.06.044	PROPN
cana-1750	805	13	.	.	PUNCT
cana-1750	806	1	[	[	X
cana-1750	806	2	7	7	X
cana-1750	806	3	]	]	X
cana-1750	806	4	y.	y.	PROPN
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cana-1750	806	7	,	,	PUNCT
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cana-1750	806	10	,	,	PUNCT
cana-1750	806	11	:	:	PUNCT
cana-1750	806	12	a	a	DET
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cana-1750	806	14	on	on	ADP
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cana-1750	806	16	functions	function	NOUN
cana-1750	806	17	,	,	PUNCT
cana-1750	806	18	taiwanese	taiwanese	PROPN
cana-1750	806	19	j.	j.	PROPN
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cana-1750	806	21	.	.	PUNCT
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cana-1750	806	24	,	,	PUNCT
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cana-1750	806	26	13(5	13(5	NUM
cana-1750	806	27	)	)	PUNCT
cana-1750	806	28	,	,	PUNCT
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cana-1750	806	30	–	–	PUNCT
cana-1750	806	31	1495	1495	NUM
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cana-1750	806	33	.	.	PUNCT
cana-1750	807	1	[	[	X
cana-1750	807	2	8	8	NUM
cana-1750	807	3	]	]	X
cana-1750	807	4	r.	r.	PROPN
cana-1750	807	5	singh	singh	PROPN
cana-1750	807	6	,	,	PUNCT
cana-1750	807	7	on	on	ADP
cana-1750	807	8	bazilevič	bazilevič	NOUN
cana-1750	807	9	functions	function	NOUN
cana-1750	807	10	,	,	PUNCT
cana-1750	807	11	proc	proc	NOUN
cana-1750	807	12	.	.	PUNCT
cana-1750	808	1	amer	amer	PROPN
cana-1750	808	2	.	.	PUNCT
cana-1750	808	3	math	math	PROPN
cana-1750	808	4	.	.	PUNCT
cana-1750	809	1	soc	soc	PROPN
cana-1750	809	2	.	.	PUNCT
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cana-1750	810	2	,	,	PUNCT
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cana-1750	810	4	,	,	PUNCT
cana-1750	810	5	261	261	NUM
cana-1750	810	6	271	271	NUM
cana-1750	810	7	.	.	PUNCT
cana-1750	811	1	[	[	X
cana-1750	811	2	9	9	NUM
cana-1750	811	3	]	]	PUNCT
cana-1750	811	4	s.	s.	PROPN
cana-1750	811	5	l.	l.	PROPN
cana-1750	811	6	krushkal	krushkal	PROPN
cana-1750	811	7	,	,	PUNCT
cana-1750	811	8	:	:	PUNCT
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cana-1750	811	10	functions	function	NOUN
cana-1750	811	11	and	and	CCONJ
cana-1750	811	12	holomorphic	holomorphic	ADJ
cana-1750	811	13	motions	motion	NOUN
cana-1750	811	14	,	,	PUNCT
cana-1750	811	15	j.	j.	PROPN
cana-1750	811	16	anal	anal	PROPN
cana-1750	811	17	.	.	PUNCT
cana-1750	811	18	math	math	PROPN
cana-1750	811	19	,	,	PUNCT
cana-1750	811	20	1995	1995	NUM
cana-1750	811	21	,	,	PUNCT
cana-1750	811	22	volume	volume	NOUN
cana-1750	811	23	66(1	66(1	NOUN
cana-1750	811	24	)	)	PUNCT
cana-1750	811	25	,	,	PUNCT
cana-1750	811	26	253	253	NUM
cana-1750	811	27	−	−	NUM
cana-1750	811	28	275	275	NUM
cana-1750	811	29	.	.	PUNCT
cana-1750	812	1	[	[	X
cana-1750	812	2	10	10	NUM
cana-1750	812	3	]	]	X
cana-1750	812	4	r.	r.	PROPN
cana-1750	812	5	j.	j.	PROPN
cana-1750	812	6	libera	libera	PROPN
cana-1750	812	7	,	,	PUNCT
cana-1750	812	8	e.	e.	PROPN
cana-1750	812	9	j.	j.	PROPN
cana-1750	812	10	zloktiewicz	zloktiewicz	PROPN
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cana-1750	812	12	:	:	PUNCT
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cana-1750	812	14	bounds	bound	VERB
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cana-1750	812	17	inverse	inverse	NOUN
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cana-1750	812	19	a	a	DET
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cana-1750	812	21	with	with	ADP
cana-1750	812	22	derivative	derivative	NOUN
cana-1750	812	23	in	in	ADP
cana-1750	812	24	q	q	NOUN
cana-1750	812	25	,	,	PUNCT
cana-1750	812	26	proc	proc	PROPN
cana-1750	812	27	.	.	PUNCT
cana-1750	813	1	amer	amer	PROPN
cana-1750	813	2	.	.	PUNCT
cana-1750	813	3	math	math	PROPN
cana-1750	813	4	.	.	PUNCT
cana-1750	814	1	soc	soc	PROPN
cana-1750	814	2	.	.	PROPN
cana-1750	814	3	,	,	PUNCT
cana-1750	814	4	1983	1983	NUM
cana-1750	814	5	,	,	PUNCT
cana-1750	814	6	volume	volume	NOUN
cana-1750	814	7	87(2	87(2	NUM
cana-1750	814	8	)	)	PUNCT
cana-1750	814	9	,	,	PUNCT
cana-1750	814	10	251	251	NUM
cana-1750	814	11	257	257	NUM
cana-1750	814	12	.	.	PUNCT
cana-1750	815	1	https://dx.doi.org/10.1090/s0002-9939-1983-0681830-8	https://dx.doi.org/10.1090/s0002-9939-1983-0681830-8	X
cana-1750	815	2	.	.	PUNCT
cana-1750	816	1	[	[	X
cana-1750	816	2	11	11	NUM
cana-1750	816	3	]	]	X
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cana-1750	816	7	,	,	PUNCT
cana-1750	816	8	:	:	PUNCT
cana-1750	816	9	on	on	ADP
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cana-1750	816	12	bounded	bounded	ADJ
cana-1750	816	13	boundary	boundary	ADJ
cana-1750	816	14	rotation	rotation	NOUN
cana-1750	816	15	,	,	PUNCT
cana-1750	816	16	proceedings	proceeding	NOUN
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cana-1750	816	18	the	the	DET
cana-1750	816	19	edinburgh	edinburgh	PROPN
cana-1750	816	20	mathematical	mathematical	PROPN
cana-1750	816	21	society	society	NOUN
cana-1750	816	22	,	,	PUNCT
cana-1750	816	23	1968	1968	NUM
cana-1750	816	24	,	,	PUNCT
cana-1750	816	25	volume	volume	NOUN
cana-1750	816	26	16(2	16(2	NUM
cana-1750	816	27	)	)	PUNCT
cana-1750	816	28	,	,	PUNCT
cana-1750	816	29	339	339	NUM
cana-1750	816	30	347	347	NUM
cana-1750	816	31	.	.	PUNCT
cana-1750	817	1	https://dx.doi.org/10.2307/2039289	https://dx.doi.org/10.2307/2039289	ADJ
cana-1750	817	2	.	.	PUNCT
cana-1750	818	1	[	[	X
cana-1750	818	2	12	12	NUM
cana-1750	818	3	]	]	X
cana-1750	818	4	b.	b.	PROPN
cana-1750	818	5	pinchuk	pinchuk	PROPN
cana-1750	818	6	,	,	PUNCT
cana-1750	818	7	a	a	DET
cana-1750	818	8	variational	variational	ADJ
cana-1750	818	9	method	method	NOUN
cana-1750	818	10	for	for	ADP
cana-1750	818	11	functions	function	NOUN
cana-1750	818	12	of	of	ADP
cana-1750	818	13	bounded	bounded	ADJ
cana-1750	818	14	boundary	boundary	ADJ
cana-1750	818	15	rotation	rotation	NOUN
cana-1750	818	16	,	,	PUNCT
cana-1750	818	17	transactions	transaction	NOUN
cana-1750	818	18	of	of	ADP
cana-1750	818	19	the	the	DET
cana-1750	818	20	american	american	PROPN
cana-1750	818	21	mathematical	mathematical	PROPN
cana-1750	818	22	society	society	NOUN
cana-1750	818	23	,	,	PUNCT
cana-1750	818	24	1969	1969	NUM
cana-1750	818	25	,	,	PUNCT
cana-1750	818	26	volume	volume	NOUN
cana-1750	818	27	138	138	NUM
cana-1750	818	28	,	,	PUNCT
cana-1750	818	29	107	107	NUM
cana-1750	818	30	113	113	NUM
cana-1750	818	31	.	.	PUNCT
cana-1750	819	1	https://dx.doi.org/10.1090/s0002-9947-1969-0237761-8	https://dx.doi.org/10.1090/s0002-9947-1969-0237761-8	NOUN
cana-1750	819	2	.	.	PUNCT
cana-1750	820	1	[	[	X
cana-1750	820	2	13	13	NUM
cana-1750	820	3	]	]	PUNCT
cana-1750	820	4	m.	m.	NOUN
cana-1750	820	5	obradović	obradović	NOUN
cana-1750	820	6	,	,	PUNCT
cana-1750	820	7	n.	n.	PROPN
cana-1750	820	8	tuneski	tuneski	PROPN
cana-1750	820	9	,	,	PUNCT
cana-1750	820	10	:	:	PUNCT
cana-1750	820	11	zalcman	zalcman	NOUN
cana-1750	820	12	and	and	CCONJ
cana-1750	820	13	generalized	generalize	VERB
cana-1750	820	14	zalcman	zalcman	NOUN
cana-1750	820	15	conjecture	conjecture	NOUN
cana-1750	820	16	for	for	ADP
cana-1750	820	17	a	a	DET
cana-1750	820	18	subclass	subclass	NOUN
cana-1750	820	19	of	of	ADP
cana-1750	820	20	univalent	univalent	ADJ
cana-1750	820	21	functions	function	NOUN
cana-1750	820	22	,	,	PUNCT
cana-1750	820	23	novi	novi	PROPN
cana-1750	820	24	sad	sad	PROPN
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cana-1750	820	29	,	,	PUNCT
cana-1750	820	30	volume	volume	NOUN
cana-1750	820	31	52(1	52(1	NOUN
cana-1750	820	32	)	)	PUNCT
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cana-1750	820	34	185	185	NUM
cana-1750	820	35	190	190	NUM
cana-1750	820	36	.	.	PUNCT
cana-1750	821	1	https://dx.doi.org/10.30755/nsjom.12436	https://dx.doi.org/10.30755/nsjom.12436	X
cana-1750	821	2	.	.	PUNCT
cana-1750	822	1	[	[	X
cana-1750	822	2	14	14	NUM
cana-1750	822	3	]	]	PUNCT
cana-1750	822	4	k.	k.	PROPN
cana-1750	822	5	ye	ye	PROPN
cana-1750	822	6	and	and	CCONJ
cana-1750	822	7	l	l	PROPN
cana-1750	822	8	h.	h.	PROPN
cana-1750	822	9	lim	lim	PROPN
cana-1750	822	10	,	,	PUNCT
cana-1750	822	11	:	:	PUNCT
cana-1750	822	12	every	every	DET
cana-1750	822	13	matrix	matrix	NOUN
cana-1750	822	14	is	be	AUX
cana-1750	822	15	a	a	DET
cana-1750	822	16	product	product	NOUN
cana-1750	822	17	of	of	ADP
cana-1750	822	18	toeplitz	toeplitz	NOUN
cana-1750	822	19	matrices	matrix	NOUN
cana-1750	822	20	,	,	PUNCT
cana-1750	822	21	foundations	foundation	NOUN
cana-1750	822	22	of	of	ADP
cana-1750	822	23	computational	computational	ADJ
cana-1750	822	24	mathematics	mathematic	NOUN
cana-1750	822	25	,	,	PUNCT
cana-1750	822	26	2016	2016	NUM
cana-1750	822	27	,	,	PUNCT
cana-1750	822	28	volume	volume	NOUN
cana-1750	822	29	16(3	16(3	PROPN
cana-1750	822	30	)	)	PUNCT
cana-1750	822	31	,	,	PUNCT
cana-1750	822	32	577	577	NUM
cana-1750	822	33	598	598	NUM
cana-1750	822	34	.	.	PUNCT
cana-1750	823	1	https://dx.doi.org/10.48550/arxiv.1307.5132	https://dx.doi.org/10.48550/arxiv.1307.5132	NOUN
cana-1750	823	2	.	.	PUNCT
cana-1750	824	1	[	[	X
cana-1750	824	2	15	15	NUM
cana-1750	824	3	]	]	X
cana-1750	824	4	v.	v.	X
cana-1750	824	5	radhika	radhika	PROPN
cana-1750	824	6	,	,	PUNCT
cana-1750	824	7	j.	j.	PROPN
cana-1750	824	8	m.jahangiri	m.jahangiri	PROPN
cana-1750	824	9	,	,	PUNCT
cana-1750	824	10	s.	s.	PROPN
cana-1750	824	11	sivasubramanian	sivasubramanian	PROPN
cana-1750	824	12	,	,	PUNCT
cana-1750	824	13	g.	g.	PROPN
cana-1750	824	14	murugusundaramoorthy	murugusundaramoorthy	PROPN
cana-1750	824	15	,	,	PUNCT
cana-1750	824	16	:	:	PUNCT
cana-1750	824	17	toeplitz	toeplitz	NOUN
cana-1750	824	18	matrices	matrix	NOUN
cana-1750	824	19	whose	whose	DET
cana-1750	824	20	elements	element	NOUN
cana-1750	824	21	are	be	AUX
cana-1750	824	22	co	co	X
cana-1750	824	23	efficient	efficient	ADJ
cana-1750	824	24	of	of	ADP
cana-1750	824	25	bazilevič	bazilevič	PROPN
cana-1750	824	26	functions	function	NOUN
cana-1750	824	27	de	de	X
cana-1750	824	28	gruyter	gruyter	NOUN
cana-1750	824	29	open	open	ADJ
cana-1750	824	30	access	access	NOUN
cana-1750	824	31	,	,	PUNCT
cana-1750	824	32	2018	2018	NUM
cana-1750	824	33	.	.	PUNCT
cana-1750	825	1	https://dx.doi.org/10.1515/math-2018-0093	https://dx.doi.org/10.1515/math-2018-0093	INTJ
cana-1750	825	2	.	.	PUNCT
cana-1750	826	1	https://dx.doi.org/10.1090/s0002-9939-1983-0681830-8	https://dx.doi.org/10.1090/s0002-9939-1983-0681830-8	X
cana-1750	826	2	https://dx.doi.org/10.2307/2039289	https://dx.doi.org/10.2307/2039289	ADJ
cana-1750	826	3	https://dx.doi.org/10.1090/s0002-9947-1969-0237761-8	https://dx.doi.org/10.1090/s0002-9947-1969-0237761-8	PROPN
cana-1750	826	4	https://dx.doi.org/10.30755/nsjom	https://dx.doi.org/10.30755/nsjom	PROPN
cana-1750	826	5	https://dx.doi.org/10.48550/arxiv.1307.5132	https://dx.doi.org/10.48550/arxiv.1307.5132	PROPN
cana-1750	826	6	https://dx.doi.org/10.1515/math-2018-0093	https://dx.doi.org/10.1515/math-2018-0093	NOUN
cana-1750	826	7	communications	communication	NOUN
cana-1750	826	8	on	on	ADP
cana-1750	826	9	applied	apply	VERB
cana-1750	826	10	nonlinear	nonlinear	ADJ
cana-1750	826	11	analysis	analysis	NOUN
cana-1750	826	12	issn	issn	NOUN
cana-1750	826	13	:	:	PUNCT
cana-1750	826	14	1074	1074	NUM
cana-1750	826	15	-	-	PUNCT
cana-1750	826	16	133x	133x	NUM
cana-1750	826	17	vol	vol	NOUN
cana-1750	826	18	32	32	NUM
cana-1750	826	19	no	no	NOUN
cana-1750	826	20	.	.	NOUN
cana-1750	826	21	2	2	NUM
cana-1750	826	22	(	(	PUNCT
cana-1750	826	23	2025	2025	NUM
cana-1750	826	24	)	)	PUNCT
cana-1750	826	25	407	407	NUM
cana-1750	826	26	https://internationalpubls.com	https://internationalpubls.com	X
cana-1750	827	1	[	[	X
cana-1750	827	2	16	16	NUM
cana-1750	827	3	]	]	PUNCT
cana-1750	827	4	r.	r.	PROPN
cana-1750	827	5	j.	j.	PROPN
cana-1750	827	6	libera	libera	PROPN
cana-1750	827	7	,	,	PUNCT
cana-1750	827	8	e.	e.	PROPN
cana-1750	827	9	j.	j.	PROPN
cana-1750	827	10	zloktiewicz	zloktiewicz	PROPN
cana-1750	827	11	,	,	PUNCT
cana-1750	827	12	:	:	PUNCT
cana-1750	827	13	coefficient	coefficient	NOUN
cana-1750	827	14	bounds	bound	VERB
cana-1750	827	15	for	for	ADP
cana-1750	827	16	the	the	DET
cana-1750	827	17	inverse	inverse	NOUN
cana-1750	827	18	of	of	ADP
cana-1750	827	19	a	a	DET
cana-1750	827	20	function	function	NOUN
cana-1750	827	21	with	with	ADP
cana-1750	827	22	derivative	derivative	NOUN
cana-1750	827	23	in	in	ADP
cana-1750	827	24	𝒫	𝒫	NOUN
cana-1750	827	25	,	,	PUNCT
cana-1750	827	26	proceedings	proceeding	NOUN
cana-1750	827	27	of	of	ADP
cana-1750	827	28	the	the	DET
cana-1750	827	29	american	american	PROPN
cana-1750	827	30	mathematical	mathematical	PROPN
cana-1750	827	31	society	society	NOUN
cana-1750	827	32	.	.	PUNCT
cana-1750	828	1	https://dx.doi.org/10.1090/s0002-9939-1983-0681830-8	https://dx.doi.org/10.1090/s0002-9939-1983-0681830-8	X
cana-1750	828	2	.	.	PUNCT
cana-1750	829	1	[	[	X
cana-1750	829	2	17	17	NUM
cana-1750	829	3	]	]	PUNCT
cana-1750	829	4	m.	m.	NOUN
cana-1750	829	5	raza	raza	PROPN
cana-1750	829	6	,	,	PUNCT
cana-1750	829	7	s.	s.	PROPN
cana-1750	829	8	n.	n.	PROPN
cana-1750	829	9	malik	malik	PROPN
cana-1750	829	10	,	,	PUNCT
cana-1750	829	11	upper	upper	ADJ
cana-1750	829	12	bound	bind	VERB
cana-1750	829	13	of	of	ADP
cana-1750	829	14	the	the	DET
cana-1750	829	15	third	third	ADJ
cana-1750	829	16	hankel	hankel	NOUN
cana-1750	829	17	determinant	determinant	ADJ
cana-1750	829	18	for	for	ADP
cana-1750	829	19	a	a	DET
cana-1750	829	20	class	class	NOUN
cana-1750	829	21	of	of	ADP
cana-1750	829	22	analytic	analytic	ADJ
cana-1750	829	23	functions	function	NOUN
cana-1750	829	24	related	relate	VERB
cana-1750	829	25	with	with	ADP
cana-1750	829	26	lemniscate	lemniscate	PROPN
cana-1750	829	27	of	of	ADP
cana-1750	829	28	bernoulli	bernoulli	PROPN
cana-1750	829	29	,	,	PUNCT
cana-1750	829	30	j.	j.	PROPN
cana-1750	829	31	inequal	inequal	PROPN
cana-1750	829	32	.	.	PUNCT
cana-1750	830	1	appl	appl	PROPN
cana-1750	830	2	,	,	PUNCT
cana-1750	830	3	2013	2013	NUM
cana-1750	830	4	.	.	PUNCT
cana-1750	830	5	https://dx.doi.org/10.1186/1029-242x-2013-412	https://dx.doi.org/10.1186/1029-242x-2013-412	X
cana-1750	830	6	.	.	PUNCT
cana-1750	831	1	[	[	X
cana-1750	831	2	18	18	NUM
cana-1750	831	3	]	]	PUNCT
cana-1750	831	4	a.	a.	NOUN
cana-1750	831	5	k.	k.	PROPN
cana-1750	831	6	sahoo	sahoo	PROPN
cana-1750	831	7	and	and	CCONJ
cana-1750	831	8	j.	j.	PROPN
cana-1750	831	9	patel	patel	PROPN
cana-1750	831	10	,	,	PUNCT
cana-1750	831	11	:	:	PUNCT
cana-1750	831	12	hankel	hankel	NOUN
cana-1750	831	13	determinant	determinant	ADJ
cana-1750	831	14	for	for	ADP
cana-1750	831	15	a	a	DET
cana-1750	831	16	class	class	NOUN
cana-1750	831	17	of	of	ADP
cana-1750	831	18	analytic	analytic	ADJ
cana-1750	831	19	functions	function	NOUN
cana-1750	831	20	related	relate	VERB
cana-1750	831	21	with	with	ADP
cana-1750	831	22	lemniscate	lemniscate	PROPN
cana-1750	831	23	of	of	ADP
cana-1750	831	24	bernoulli	bernoulli	PROPN
cana-1750	831	25	,	,	PUNCT
cana-1750	831	26	int	int	PROPN
cana-1750	831	27	.	.	PUNCT
cana-1750	832	1	j.	j.	PROPN
cana-1750	832	2	anal	anal	PROPN
cana-1750	832	3	.	.	PUNCT
cana-1750	833	1	appl	appl	PROPN
cana-1750	833	2	.	.	PROPN
cana-1750	833	3	,	,	PUNCT
cana-1750	833	4	2014	2014	NUM
cana-1750	833	5	,	,	PUNCT
cana-1750	833	6	volume	volume	NOUN
cana-1750	833	7	6(2	6(2	NUM
cana-1750	833	8	)	)	PUNCT
cana-1750	833	9	,	,	PUNCT
cana-1750	833	10	170	170	NUM
cana-1750	833	11	177	177	NUM
cana-1750	833	12	.	.	PUNCT
cana-1750	834	1	[	[	X
cana-1750	834	2	19	19	NUM
cana-1750	834	3	]	]	PUNCT
cana-1750	834	4	j.	j.	PROPN
cana-1750	834	5	sokí	sokí	PROPN
cana-1750	834	6	,	,	PUNCT
cana-1750	834	7	j.	j.	PROPN
cana-1750	834	8	stankiewicz	stankiewicz	PROPN
cana-1750	834	9	,	,	PUNCT
cana-1750	834	10	radius	radius	NOUN
cana-1750	834	11	of	of	ADP
cana-1750	834	12	convexity	convexity	NOUN
cana-1750	834	13	of	of	ADP
cana-1750	834	14	some	some	DET
cana-1750	834	15	subclasses	subclass	NOUN
cana-1750	834	16	of	of	ADP
cana-1750	834	17	strongly	strongly	ADV
cana-1750	834	18	star	star	ADJ
cana-1750	834	19	like	like	ADP
cana-1750	834	20	functions	function	NOUN
cana-1750	834	21	,	,	PUNCT
cana-1750	834	22	folia	folia	PROPN
cana-1750	834	23	scient	scient	PROPN
cana-1750	834	24	.	.	PUNCT
cana-1750	835	1	univ	univ	PROPN
cana-1750	835	2	.	.	PUNCT
cana-1750	836	1	tech	tech	NOUN
cana-1750	836	2	.	.	PUNCT
cana-1750	837	1	resoviensis	resoviensis	NOUN
cana-1750	837	2	,	,	PUNCT
cana-1750	837	3	matematykaz.19	matematykaz.19	PROPN
cana-1750	837	4	,	,	PUNCT
cana-1750	837	5	1996	1996	NUM
cana-1750	837	6	,	,	PUNCT
cana-1750	837	7	101	101	NUM
cana-1750	837	8	105	105	NUM
cana-1750	837	9	.	.	PUNCT
cana-1750	838	1	[	[	X
cana-1750	838	2	20	20	NUM
cana-1750	838	3	]	]	PUNCT
cana-1750	838	4	c.	c.	NOUN
cana-1750	838	5	pommerenke	pommerenke	PROPN
cana-1750	838	6	,	,	PUNCT
cana-1750	838	7	on	on	ADP
cana-1750	838	8	the	the	DET
cana-1750	838	9	coefficients	coefficient	NOUN
cana-1750	838	10	and	and	CCONJ
cana-1750	838	11	hankel	hankel	NOUN
cana-1750	838	12	determinants	determinant	NOUN
cana-1750	838	13	of	of	ADP
cana-1750	838	14	univalent	univalent	ADJ
cana-1750	838	15	functions	function	NOUN
cana-1750	838	16	,	,	PUNCT
cana-1750	838	17	j.	j.	PROPN
cana-1750	838	18	london	london	PROPN
cana-1750	838	19	math	math	PROPN
cana-1750	838	20	.	.	PUNCT
cana-1750	839	1	soc	soc	PROPN
cana-1750	839	2	,	,	PUNCT
cana-1750	839	3	1966	1966	NUM
cana-1750	839	4	,	,	PUNCT
cana-1750	839	5	volume	volume	NOUN
cana-1750	839	6	41	41	NUM
cana-1750	839	7	,	,	PUNCT
cana-1750	839	8	111	111	NUM
cana-1750	839	9	122	122	NUM
cana-1750	839	10	.	.	PUNCT
cana-1750	840	1	https://dx.doi.org/10.1112/jlms/s1-41.1.111	https://dx.doi.org/10.1112/jlms/s1-41.1.111	ADJ
cana-1750	840	2	.	.	PUNCT
cana-1750	841	1	[	[	X
cana-1750	841	2	21	21	NUM
cana-1750	841	3	]	]	PUNCT
cana-1750	841	4	t.panigrahi	t.panigrahi	NOUN
cana-1750	841	5	,	,	PUNCT
cana-1750	841	6	j	j	PROPN
cana-1750	841	7	sokól	sokól	PROPN
cana-1750	841	8	,	,	PUNCT
cana-1750	841	9	:	:	PUNCT
cana-1750	841	10	coefficient	coefficient	NOUN
cana-1750	841	11	inequalities	inequality	NOUN
cana-1750	841	12	for	for	ADP
cana-1750	841	13	a	a	DET
cana-1750	841	14	class	class	NOUN
cana-1750	841	15	of	of	ADP
cana-1750	841	16	analytic	analytic	ADJ
cana-1750	841	17	functions	function	NOUN
cana-1750	841	18	associated	associate	VERB
cana-1750	841	19	with	with	ADP
cana-1750	841	20	the	the	DET
cana-1750	841	21	lemniscate	lemniscate	PROPN
cana-1750	841	22	af	af	PROPN
cana-1750	841	23	bernoulli	bernoulli	PROPN
cana-1750	841	24	,	,	PUNCT
cana-1750	841	25	bol	bol	NOUN
cana-1750	841	26	.	.	PUNCT
cana-1750	842	1	soc	soc	PROPN
cana-1750	842	2	.	.	PUNCT
cana-1750	843	1	paran	paran	PROPN
cana-1750	843	2	.	.	PUNCT
cana-1750	844	1	mat	mat	PROPN
cana-1750	844	2	,	,	PUNCT
cana-1750	844	3	2019	2019	NUM
cana-1750	844	4	,	,	PUNCT
cana-1750	844	5	volume	volume	NOUN
cana-1750	844	6	37(4	37(4	PROPN
cana-1750	844	7	)	)	PUNCT
cana-1750	844	8	,	,	PUNCT
cana-1750	844	9	83	83	NUM
cana-1750	844	10	95	95	NUM
cana-1750	844	11	.	.	PUNCT
cana-1750	845	1	https://dx.doi.org/10.5269/bspm.v37i4.32701	https://dx.doi.org/10.5269/bspm.v37i4.32701	X
cana-1750	845	2	.	.	PUNCT
cana-1750	846	1	[	[	X
cana-1750	846	2	22	22	NUM
cana-1750	846	3	]	]	X
cana-1750	846	4	l.	l.	PROPN
cana-1750	846	5	de	de	X
cana-1750	846	6	branges	brange	NOUN
cana-1750	846	7	,	,	PUNCT
cana-1750	846	8	:	:	PUNCT
cana-1750	846	9	a	a	DET
cana-1750	846	10	proof	proof	NOUN
cana-1750	846	11	of	of	ADP
cana-1750	846	12	the	the	DET
cana-1750	846	13	bieberbach	bieberbach	NOUN
cana-1750	846	14	conjecture	conjecture	NOUN
cana-1750	846	15	,	,	PUNCT
cana-1750	846	16	acta	acta	PROPN
cana-1750	846	17	math	math	PROPN
cana-1750	846	18	,	,	PUNCT
cana-1750	846	19	1985	1985	NUM
cana-1750	846	20	,	,	PUNCT
cana-1750	846	21	volume	volume	NOUN
cana-1750	846	22	154(1	154(1	NUM
cana-1750	846	23	-	-	SYM
cana-1750	846	24	2),137	2),137	NUM
cana-1750	846	25	152	152	NUM
cana-1750	846	26	.	.	PUNCT
cana-1750	847	1	https://dx.doi.org/10.1007/bf02392821	https://dx.doi.org/10.1007/bf02392821	NOUN
cana-1750	847	2	.	.	PUNCT
cana-1750	848	1	[	[	X
cana-1750	848	2	23	23	NUM
cana-1750	848	3	]	]	PUNCT
cana-1750	848	4	s.	s.	PROPN
cana-1750	848	5	l.	l.	PROPN
cana-1750	848	6	krushkal	krushkal	PROPN
cana-1750	848	7	,	,	PUNCT
cana-1750	848	8	:	:	PUNCT
cana-1750	848	9	a	a	DET
cana-1750	848	10	short	short	ADJ
cana-1750	848	11	geometric	geometric	ADJ
cana-1750	848	12	proof	proof	NOUN
cana-1750	848	13	of	of	ADP
cana-1750	848	14	the	the	DET
cana-1750	848	15	zalcman	zalcman	NOUN
cana-1750	848	16	and	and	CCONJ
cana-1750	848	17	bieberbach	bieberbach	NOUN
cana-1750	848	18	conjectures	conjecture	VERB
cana-1750	848	19	,	,	PUNCT
cana-1750	848	20	2014	2014	NUM
cana-1750	848	21	.	.	PUNCT
cana-1750	849	1	https://dx.doi.org/10.48550/arxiv.1408.1948	https://dx.doi.org/10.48550/arxiv.1408.1948	PROPN
cana-1750	849	2	.	.	PUNCT
cana-1750	850	1	[	[	X
cana-1750	850	2	24	24	NUM
cana-1750	850	3	]	]	X
cana-1750	850	4	w.	w.	PROPN
cana-1750	850	5	ma	ma	PROPN
cana-1750	850	6	,	,	PUNCT
cana-1750	850	7	:	:	PUNCT
cana-1750	850	8	generalized	generalized	ADJ
cana-1750	850	9	zalcman	zalcman	NOUN
cana-1750	850	10	conjecture	conjecture	NOUN
cana-1750	850	11	for	for	ADP
cana-1750	850	12	star	star	NOUN
cana-1750	850	13	like	like	ADP
cana-1750	850	14	and	and	CCONJ
cana-1750	850	15	typically	typically	ADV
cana-1750	850	16	real	real	ADJ
cana-1750	850	17	functions	function	NOUN
cana-1750	850	18	,	,	PUNCT
cana-1750	850	19	j.	j.	PROPN
cana-1750	850	20	math	math	PROPN
cana-1750	850	21	.	.	PUNCT
cana-1750	851	1	anal	anal	PROPN
cana-1750	851	2	.	.	PUNCT
cana-1750	852	1	appl	appl	PROPN
cana-1750	852	2	,	,	PUNCT
cana-1750	852	3	1999	1999	NUM
cana-1750	852	4	,	,	PUNCT
cana-1750	852	5	volume	volume	NOUN
cana-1750	852	6	234(1	234(1	NUM
cana-1750	852	7	)	)	PUNCT
cana-1750	852	8	,	,	PUNCT
cana-1750	852	9	328	328	NUM
cana-1750	852	10	339	339	NUM
cana-1750	852	11	.	.	PUNCT
cana-1750	853	1	https://dx.doi.org/10.1006/jmaa.1999.6378	https://dx.doi.org/10.1006/jmaa.1999.6378	NOUN
cana-1750	854	1	[	[	X
cana-1750	854	2	25	25	NUM
cana-1750	854	3	]	]	PUNCT
cana-1750	854	4	m.	m.	NOUN
cana-1750	854	5	obradovic	obradovic	NOUN
cana-1750	854	6	,	,	PUNCT
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cana-1750	854	9	,	,	PUNCT
cana-1750	854	10	:	:	PUNCT
cana-1750	854	11	some	some	DET
cana-1750	854	12	properties	property	NOUN
cana-1750	854	13	of	of	ADP
cana-1750	854	14	the	the	DET
cana-1750	854	15	class	class	NOUN
cana-1750	854	16	u	u	PROPN
cana-1750	854	17	,	,	PUNCT
cana-1750	854	18	ann	ann	PROPN
cana-1750	854	19	.	.	PUNCT
cana-1750	855	1	univ.mariae	univ.mariae	PROPN
cana-1750	855	2	curie	curie	NOUN
cana-1750	855	3	-	-	PUNCT
cana-1750	855	4	sk	sk	ADJ
cana-1750	855	5	lodowska	lodowska	ADJ
cana-1750	855	6	sect	sect	NOUN
cana-1750	855	7	.	.	PUNCT
cana-1750	856	1	2019	2019	NUM
cana-1750	856	2	,	,	PUNCT
cana-1750	856	3	volume	volume	NOUN
cana-1750	856	4	73(1	73(1	NUM
cana-1750	856	5	)	)	PUNCT
cana-1750	856	6	,	,	PUNCT
cana-1750	856	7	49	49	NUM
cana-1750	856	8	56	56	NUM
cana-1750	856	9	.	.	PUNCT
cana-1750	857	1	https://dx.doi.org/10.48550/arxiv	https://dx.doi.org/10.48550/arxiv	X
cana-1750	857	2	.	.	PUNCT
cana-1750	858	1	1812.08503	1812.08503	NUM
cana-1750	858	2	.	.	PUNCT
cana-1750	859	1	[	[	X
cana-1750	859	2	26	26	NUM
cana-1750	859	3	]	]	PUNCT
cana-1750	859	4	s.	s.	PROPN
cana-1750	859	5	ozaki	ozaki	PROPN
cana-1750	859	6	,	,	PUNCT
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cana-1750	859	8	nunokawa	nunokawa	PROPN
cana-1750	859	9	,	,	PUNCT
cana-1750	859	10	:	:	PUNCT
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cana-1750	859	12	schwarzian	schwarzian	PROPN
cana-1750	859	13	derivative	derivative	ADJ
cana-1750	859	14	and	and	CCONJ
cana-1750	859	15	univalent	univalent	ADJ
cana-1750	859	16	functions	function	NOUN
cana-1750	859	17	,	,	PUNCT
cana-1750	859	18	proc	proc	NOUN
cana-1750	859	19	.	.	PUNCT
cana-1750	859	20	amer	amer	PROPN
cana-1750	859	21	.	.	PUNCT
cana-1750	859	22	math	math	PROPN
cana-1750	859	23	.	.	PUNCT
cana-1750	860	1	soc	soc	PROPN
cana-1750	860	2	,	,	PUNCT
cana-1750	860	3	1972	1972	NUM
cana-1750	860	4	,	,	PUNCT
cana-1750	860	5	volume	volume	NOUN
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cana-1750	860	7	)	)	PUNCT
cana-1750	860	8	,	,	PUNCT
cana-1750	860	9	392	392	NUM
cana-1750	860	10	394	394	NUM
cana-1750	860	11	.	.	PUNCT
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cana-1750	861	2	.	.	PUNCT
cana-1750	862	1	[	[	X
cana-1750	862	2	27	27	NUM
cana-1750	862	3	]	]	X
cana-1750	862	4	v.	v.	CCONJ
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cana-1750	862	6	,	,	PUNCT
cana-1750	862	7	s.	s.	PROPN
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cana-1750	862	9	,	,	PUNCT
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cana-1750	862	17	of	of	ADP
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cana-1750	862	19	functions	function	NOUN
cana-1750	862	20	,	,	PUNCT
cana-1750	862	21	j.	j.	PROPN
cana-1750	862	22	math	math	PROPN
cana-1750	862	23	.	.	PUNCT
cana-1750	863	1	anal	anal	PROPN
cana-1750	863	2	.	.	PUNCT
cana-1750	863	3	appl	appl	PROPN
cana-1750	863	4	,	,	PUNCT
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cana-1750	863	6	,	,	PUNCT
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cana-1750	863	9	)	)	PUNCT
cana-1750	863	10	,	,	PUNCT
cana-1750	863	11	592	592	NUM
cana-1750	863	12	605	605	NUM
cana-1750	863	13	.	.	PUNCT
cana-1750	864	1	https://dx.doi.org/10.1016/j.jmaa.2017.01.053	https://dx.doi.org/10.1016/j.jmaa.2017.01.053	VERB
cana-1750	864	2	.	.	PUNCT
cana-1750	865	1	[	[	X
cana-1750	865	2	28	28	NUM
cana-1750	865	3	]	]	X
cana-1750	865	4	d.	d.	PROPN
cana-1750	865	5	k.	k.	PROPN
cana-1750	865	6	thomas	thomas	PROPN
cana-1750	865	7	,	,	PUNCT
cana-1750	865	8	n.	n.	PROPN
cana-1750	865	9	tuneski	tuneski	PROPN
cana-1750	865	10	,	,	PUNCT
cana-1750	865	11	a.	a.	NOUN
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cana-1750	865	13	,	,	PUNCT
cana-1750	865	14	:	:	PUNCT
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cana-1750	865	16	functions	function	NOUN
cana-1750	865	17	,	,	PUNCT
cana-1750	865	18	a	a	DET
cana-1750	865	19	primer	primer	NOUN
cana-1750	865	20	,	,	PUNCT
cana-1750	865	21	de	de	X
cana-1750	865	22	gruyter	gruyter	NOUN
cana-1750	865	23	studies	study	NOUN
cana-1750	865	24	in	in	ADP
cana-1750	865	25	mathematics	mathematic	NOUN
cana-1750	865	26	.	.	PUNCT
cana-1750	866	1	de	de	X
cana-1750	866	2	gruyter	gruyter	NOUN
cana-1750	866	3	,	,	PUNCT
cana-1750	866	4	berlin	berlin	PROPN
cana-1750	866	5	,	,	PUNCT
cana-1750	866	6	2018	2018	NUM
cana-1750	866	7	,	,	PUNCT
cana-1750	866	8	volume	volume	NOUN
cana-1750	866	9	69	69	NUM
cana-1750	866	10	.	.	PUNCT
cana-1750	867	1	https://dx.doi.org/10.1515/9783110560961	https://dx.doi.org/10.1515/9783110560961	NOUN
cana-1750	867	2	.	.	PUNCT
cana-1750	868	1	[	[	X
cana-1750	868	2	29	29	NUM
cana-1750	868	3	]	]	X
cana-1750	868	4	s.l	s.l	PROPN
cana-1750	868	5	.	.	PROPN
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cana-1750	868	7	,	,	PUNCT
cana-1750	868	8	:	:	PUNCT
cana-1750	868	9	proof	proof	NOUN
cana-1750	868	10	of	of	ADP
cana-1750	868	11	the	the	DET
cana-1750	868	12	zalcman	zalcman	PROPN
cana-1750	868	13	conjecture	conjecture	VERB
cana-1750	868	14	for	for	ADP
cana-1750	868	15	initial	initial	ADJ
cana-1750	868	16	coefficients	coefficient	NOUN
cana-1750	868	17	,	,	PUNCT
cana-1750	868	18	georgian	georgian	ADJ
cana-1750	868	19	math	math	NOUN
cana-1750	868	20	.	.	PUNCT
cana-1750	869	1	j.	j.	PROPN
cana-1750	869	2	,	,	PUNCT
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cana-1750	869	4	,	,	PUNCT
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cana-1750	869	6	17	17	NUM
cana-1750	869	7	,	,	PUNCT
cana-1750	869	8	663	663	NUM
cana-1750	869	9	681	681	NUM
cana-1750	869	10	.	.	PUNCT
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cana-1750	869	12	.	.	PUNCT
cana-1750	870	1	[	[	X
cana-1750	870	2	30	30	NUM
cana-1750	870	3	]	]	X
cana-1750	870	4	r.	r.	PROPN
cana-1750	870	5	j.	j.	PROPN
cana-1750	870	6	libera	libera	PROPN
cana-1750	870	7	,	,	PUNCT
cana-1750	870	8	e.	e.	PROPN
cana-1750	870	9	j.	j.	PROPN
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cana-1750	870	11	,	,	PUNCT
cana-1750	870	12	:	:	PUNCT
cana-1750	870	13	early	early	ADJ
cana-1750	870	14	coefficients	coefficient	NOUN
cana-1750	870	15	of	of	ADP
cana-1750	870	16	the	the	DET
cana-1750	870	17	inverse	inverse	NOUN
cana-1750	870	18	of	of	ADP
cana-1750	870	19	a	a	DET
cana-1750	870	20	regular	regular	ADJ
cana-1750	870	21	convex	convex	NOUN
cana-1750	870	22	function	function	NOUN
cana-1750	870	23	,	,	PUNCT
cana-1750	870	24	proc	proc	PROPN
cana-1750	870	25	.	.	PUNCT
cana-1750	871	1	amer	amer	PROPN
cana-1750	871	2	.	.	PUNCT
cana-1750	871	3	math	math	PROPN
cana-1750	871	4	.	.	PUNCT
cana-1750	872	1	soc	soc	PROPN
cana-1750	872	2	.	.	PROPN
cana-1750	872	3	,	,	PUNCT
cana-1750	872	4	1982	1982	NUM
cana-1750	872	5	,	,	PUNCT
cana-1750	872	6	volume	volume	NOUN
cana-1750	872	7	85(2	85(2	NUM
cana-1750	872	8	)	)	PUNCT
cana-1750	872	9	,	,	PUNCT
cana-1750	872	10	225	225	NUM
cana-1750	872	11	230	230	NUM
cana-1750	872	12	.	.	PUNCT
cana-1750	873	1	https://dx.doi.org/10.2307/2044286	https://dx.doi.org/10.2307/2044286	PROPN
cana-1750	873	2	.	.	PUNCT
cana-1750	874	1	[	[	X
cana-1750	874	2	31	31	NUM
cana-1750	874	3	]	]	PUNCT
cana-1750	874	4	w.	w.	PROPN
cana-1750	874	5	ma	ma	PROPN
cana-1750	874	6	and	and	CCONJ
cana-1750	874	7	d.	d.	PROPN
cana-1750	874	8	minda	minda	PROPN
cana-1750	874	9	,	,	PUNCT
cana-1750	874	10	:	:	PUNCT
cana-1750	874	11	a	a	DET
cana-1750	874	12	unified	unified	ADJ
cana-1750	874	13	treatment	treatment	NOUN
cana-1750	874	14	of	of	ADP
cana-1750	874	15	some	some	DET
cana-1750	874	16	special	special	ADJ
cana-1750	874	17	classes	class	NOUN
cana-1750	874	18	of	of	ADP
cana-1750	874	19	univalent	univalent	ADJ
cana-1750	874	20	functions	function	NOUN
cana-1750	874	21	.	.	PUNCT
cana-1750	875	1	in	in	ADP
cana-1750	875	2	proceedings	proceeding	NOUN
cana-1750	875	3	of	of	ADP
cana-1750	875	4	the	the	DET
cana-1750	875	5	conference	conference	NOUN
cana-1750	875	6	on	on	ADP
cana-1750	875	7	complex	complex	ADJ
cana-1750	875	8	analysis	analysis	NOUN
cana-1750	875	9	,	,	PUNCT
cana-1750	875	10	tianjin	tianjin	PROPN
cana-1750	875	11	,	,	PUNCT
cana-1750	875	12	china	china	PROPN
cana-1750	875	13	,	,	PUNCT
cana-1750	875	14	19	19	NUM
cana-1750	875	15	-	-	SYM
cana-1750	875	16	23	23	NUM
cana-1750	875	17	,	,	PUNCT
cana-1750	875	18	june	june	PROPN
cana-1750	875	19	,	,	PUNCT
cana-1750	875	20	1992	1992	NUM
cana-1750	875	21	,	,	PUNCT
cana-1750	875	22	conference	conference	NOUN
cana-1750	875	23	on	on	ADP
cana-1750	875	24	proceedings	proceeding	NOUN
cana-1750	875	25	lecture	lecture	VERB
cana-1750	875	26	notes	note	NOUN
cana-1750	875	27	for	for	ADP
cana-1750	875	28	analysis	analysis	NOUN
cana-1750	875	29	.	.	PUNCT
cana-1750	876	1	international	international	ADJ
cana-1750	876	2	press	press	NOUN
cana-1750	876	3	;	;	PUNCT
cana-1750	876	4	cambridge	cambridge	PROPN
cana-1750	876	5	,	,	PUNCT
cana-1750	876	6	ma	ma	PROPN
cana-1750	876	7	,	,	PUNCT
cana-1750	876	8	usa	usa	PROPN
cana-1750	876	9	,	,	PUNCT
cana-1750	876	10	1994	1994	NUM
cana-1750	876	11	,	,	PUNCT
cana-1750	876	12	157	157	NUM
cana-1750	876	13	169	169	NUM
cana-1750	876	14	.	.	PUNCT
cana-1750	877	1	https://dx.doi.org/10.1090/s0002-9939-1983-0681830-8	https://dx.doi.org/10.1090/s0002-9939-1983-0681830-8	PRON
cana-1750	877	2	https://dx.doi.org/10.1186/1029-242x-2013-412	https://dx.doi.org/10.1186/1029-242x-2013-412	ADJ
cana-1750	877	3	https://dx.doi.org/10.1112/jlms/s1-41.1.111	https://dx.doi.org/10.1112/jlms/s1-41.1.111	ADJ
cana-1750	877	4	https://dx.doi.org/10.5269/bspm.v37i4.32701	https://dx.doi.org/10.5269/bspm.v37i4.32701	NUM
cana-1750	877	5	https://dx.doi.org/10.1007/bf02392821	https://dx.doi.org/10.1007/bf02392821	NOUN
cana-1750	877	6	https://dx.doi.org/10.48550/arxiv.1408.1948	https://dx.doi.org/10.48550/arxiv.1408.1948	NOUN
cana-1750	877	7	https://dx.doi.org/10.1006/jmaa	https://dx.doi.org/10.1006/jmaa	ADJ
cana-1750	877	8	https://dx.doi.org/10.48550/arxiv.%201812.08503	https://dx.doi.org/10.48550/arxiv.%201812.08503	PROPN
cana-1750	877	9	https://dx.doi.org/10.2307/2038067	https://dx.doi.org/10.2307/2038067	NOUN
cana-1750	877	10	https://dx.doi.org/10.1016/j.jmaa.2017.01.053	https://dx.doi.org/10.1016/j.jmaa.2017.01.053	PROPN
cana-1750	877	11	https://dx.doi.org/10.1515/9783110560961	https://dx.doi.org/10.1515/9783110560961	PROPN
cana-1750	877	12	https://dx.doi.org/10.2307/2044286	https://dx.doi.org/10.2307/2044286	NOUN