id	sid	tid	token	lemma	pos
cana-4546	1	1	communications	communication	NOUN
cana-4546	1	2	on	on	ADP
cana-4546	1	3	applied	apply	VERB
cana-4546	1	4	nonlinear	nonlinear	ADJ
cana-4546	1	5	analysis	analysis	NOUN
cana-4546	1	6	issn	issn	NOUN
cana-4546	1	7	:	:	PUNCT
cana-4546	1	8	1074	1074	NUM
cana-4546	1	9	-	-	PUNCT
cana-4546	1	10	133x	133x	NUM
cana-4546	1	11	vol	vol	NOUN
cana-4546	1	12	32	32	NUM
cana-4546	1	13	no	no	NOUN
cana-4546	1	14	.	.	PUNCT
cana-4546	2	1	9s	9s	NUM
cana-4546	2	2	(	(	PUNCT
cana-4546	2	3	2025	2025	NUM
cana-4546	2	4	)	)	PUNCT
cana-4546	2	5	2650	2650	NUM
cana-4546	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4546	2	7	fekete	fekete	NOUN
cana-4546	2	8	-	-	PUNCT
cana-4546	2	9	szegö	szegö	ADJ
cana-4546	2	10	and	and	CCONJ
cana-4546	2	11	second	second	ADJ
cana-4546	2	12	hankel	hankel	NOUN
cana-4546	2	13	determinant	determinant	ADJ
cana-4546	2	14	for	for	ADP
cana-4546	2	15	a	a	DET
cana-4546	2	16	class	class	NOUN
cana-4546	2	17	of	of	ADP
cana-4546	2	18	𝖕-valent	𝖕-valent	PROPN
cana-4546	2	19	functions	function	NOUN
cana-4546	2	20	related	relate	VERB
cana-4546	2	21	to	to	ADP
cana-4546	2	22	modified	modify	VERB
cana-4546	2	23	sigmoid	sigmoid	NOUN
cana-4546	2	24	functions	function	NOUN
cana-4546	2	25	dr	dr	PROPN
cana-4546	2	26	.	.	PROPN
cana-4546	2	27	saleem	saleem	PROPN
cana-4546	2	28	ahmed1	ahmed1	PROPN
cana-4546	2	29	,	,	PUNCT
cana-4546	2	30	dr	dr	PROPN
cana-4546	2	31	.	.	PROPN
cana-4546	2	32	m.	m.	PROPN
cana-4546	2	33	musthafa	musthafa	PROPN
cana-4546	3	1	ibrahim2	ibrahim2	PROPN
cana-4546	3	2	,	,	PUNCT
cana-4546	3	3	*	*	PROPN
cana-4546	3	4	,	,	PUNCT
cana-4546	3	5	dr	dr	PROPN
cana-4546	3	6	.	.	PROPN
cana-4546	3	7	badriya	badriya	PROPN
cana-4546	3	8	nasser	nasser	PROPN
cana-4546	3	9	mohammed	mohammed	PROPN
cana-4546	3	10	al	al	PROPN
cana-4546	3	11	hashmi3	hashmi3	PROPN
cana-4546	4	1	1college	1college	PROPN
cana-4546	4	2	of	of	ADP
cana-4546	4	3	engineering	engineering	NOUN
cana-4546	4	4	,	,	PUNCT
cana-4546	4	5	university	university	PROPN
cana-4546	4	6	of	of	ADP
cana-4546	4	7	buraimi	buraimi	PROPN
cana-4546	4	8	,	,	PUNCT
cana-4546	4	9	saleem.a@uob.edu.om	saleem.a@uob.edu.om	PROPN
cana-4546	4	10	2,*college	2,*college	NUM
cana-4546	4	11	of	of	ADP
cana-4546	4	12	engineering	engineering	PROPN
cana-4546	4	13	,	,	PUNCT
cana-4546	4	14	university	university	PROPN
cana-4546	4	15	of	of	ADP
cana-4546	4	16	buraimi	buraimi	PROPN
cana-4546	4	17	,	,	PUNCT
cana-4546	4	18	musthafa.i@uob.edu.om	musthafa.i@uob.edu.om	PROPN
cana-4546	4	19	3college	3college	NUM
cana-4546	4	20	of	of	ADP
cana-4546	4	21	engineering	engineering	NOUN
cana-4546	4	22	,	,	PUNCT
cana-4546	4	23	university	university	PROPN
cana-4546	4	24	of	of	ADP
cana-4546	4	25	buraimi	buraimi	PROPN
cana-4546	4	26	,	,	PUNCT
cana-4546	4	27	badriya.n@uob.edu.om	badriya.n@uob.edu.om	PROPN
cana-4546	4	28	article	article	NOUN
cana-4546	4	29	history	history	NOUN
cana-4546	4	30	:	:	PUNCT
cana-4546	4	31	received	receive	VERB
cana-4546	4	32	:	:	PUNCT
cana-4546	4	33	12	12	NUM
cana-4546	4	34	-	-	SYM
cana-4546	4	35	01	01	NUM
cana-4546	4	36	-	-	PUNCT
cana-4546	4	37	2025	2025	NUM
cana-4546	4	38	revised	revise	VERB
cana-4546	4	39	:	:	PUNCT
cana-4546	4	40	15	15	NUM
cana-4546	4	41	-	-	NUM
cana-4546	4	42	02	02	NUM
cana-4546	4	43	-	-	PUNCT
cana-4546	4	44	2025	2025	NUM
cana-4546	4	45	accepted	accept	VERB
cana-4546	4	46	:	:	PUNCT
cana-4546	4	47	01	01	NUM
cana-4546	4	48	-	-	SYM
cana-4546	4	49	03	03	NUM
cana-4546	4	50	-	-	PUNCT
cana-4546	4	51	2025	2025	NUM
cana-4546	4	52	abstract	abstract	NOUN
cana-4546	4	53	:	:	PUNCT
cana-4546	4	54	in	in	ADP
cana-4546	4	55	this	this	DET
cana-4546	4	56	paper	paper	NOUN
cana-4546	4	57	,	,	PUNCT
cana-4546	4	58	we	we	PRON
cana-4546	4	59	study	study	VERB
cana-4546	4	60	the	the	DET
cana-4546	4	61	initial	initial	ADJ
cana-4546	4	62	coefficient	coefficient	NOUN
cana-4546	4	63	bounds	bound	VERB
cana-4546	4	64	for	for	ADP
cana-4546	4	65	a	a	DET
cana-4546	4	66	noval	noval	ADJ
cana-4546	4	67	class	class	PROPN
cana-4546	4	68	𝑀𝜆(∗)(𝜂	𝑀𝜆(∗)(𝜂	PROPN
cana-4546	4	69	,	,	PUNCT
cana-4546	4	70	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	4	71	)	)	PUNCT
cana-4546	4	72	of	of	ADP
cana-4546	4	73	𝒫-valently	𝒫-valently	ADV
cana-4546	4	74	analytic	analytic	ADJ
cana-4546	4	75	functions	function	NOUN
cana-4546	4	76	related	relate	VERB
cana-4546	4	77	to	to	ADP
cana-4546	4	78	sigmoid	sigmoid	NOUN
cana-4546	4	79	functions	function	NOUN
cana-4546	4	80	.	.	PUNCT
cana-4546	5	1	furthermore	furthermore	ADV
cana-4546	5	2	,	,	PUNCT
cana-4546	5	3	the	the	DET
cana-4546	5	4	famous	famous	ADJ
cana-4546	5	5	classical	classical	ADJ
cana-4546	5	6	fekete	fekete	NOUN
cana-4546	5	7	-	-	PUNCT
cana-4546	5	8	szegö	szegö	ADJ
cana-4546	5	9	inequality	inequality	NOUN
cana-4546	5	10	for	for	ADP
cana-4546	5	11	this	this	DET
cana-4546	5	12	class	class	NOUN
cana-4546	5	13	are	be	AUX
cana-4546	5	14	discussed	discuss	VERB
cana-4546	5	15	.	.	PUNCT
cana-4546	6	1	conclusions	conclusion	NOUN
cana-4546	6	2	:	:	PUNCT
cana-4546	6	3	in	in	ADP
cana-4546	6	4	this	this	DET
cana-4546	6	5	paper	paper	NOUN
cana-4546	6	6	,	,	PUNCT
cana-4546	6	7	we	we	PRON
cana-4546	6	8	introduced	introduce	VERB
cana-4546	6	9	and	and	CCONJ
cana-4546	6	10	investigated	investigate	VERB
cana-4546	6	11	the	the	DET
cana-4546	6	12	𝔭-univalent	𝔭-univalent	NOUN
cana-4546	6	13	function	function	NOUN
cana-4546	6	14	for	for	ADP
cana-4546	6	15	the	the	DET
cana-4546	6	16	class	class	NOUN
cana-4546	6	17	𝑀𝜆,(∗)(𝜂	𝑀𝜆,(∗)(𝜂	PROPN
cana-4546	6	18	,	,	PUNCT
cana-4546	6	19	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	6	20	)	)	PUNCT
cana-4546	6	21	related	relate	VERB
cana-4546	6	22	to	to	ADP
cana-4546	6	23	the	the	DET
cana-4546	6	24	to	to	ADP
cana-4546	6	25	modified	modify	VERB
cana-4546	6	26	sigmoid	sigmoid	NOUN
cana-4546	6	27	functions	function	NOUN
cana-4546	6	28	.	.	PUNCT
cana-4546	7	1	thus	thus	ADV
cana-4546	7	2	,	,	PUNCT
cana-4546	7	3	we	we	PRON
cana-4546	7	4	obtained	obtain	VERB
cana-4546	7	5	second	second	ADJ
cana-4546	7	6	,	,	PUNCT
cana-4546	7	7	third	third	ADJ
cana-4546	7	8	and	and	CCONJ
cana-4546	7	9	fourth	fourth	PROPN
cana-4546	7	10	taylor	taylor	PROPN
cana-4546	7	11	–	–	PUNCT
cana-4546	7	12	maclaurin	maclaurin	NOUN
cana-4546	7	13	coefficients	coefficient	NOUN
cana-4546	7	14	of	of	ADP
cana-4546	7	15	functions	function	NOUN
cana-4546	7	16	in	in	ADP
cana-4546	7	17	this	this	DET
cana-4546	7	18	class	class	NOUN
cana-4546	7	19	.	.	PUNCT
cana-4546	8	1	these	these	DET
cana-4546	8	2	results	result	NOUN
cana-4546	8	3	were	be	AUX
cana-4546	8	4	an	an	DET
cana-4546	8	5	improvement	improvement	NOUN
cana-4546	8	6	on	on	ADP
cana-4546	8	7	the	the	DET
cana-4546	8	8	estimates	estimate	NOUN
cana-4546	8	9	obtained	obtain	VERB
cana-4546	8	10	in	in	ADP
cana-4546	8	11	the	the	DET
cana-4546	8	12	recent	recent	ADJ
cana-4546	8	13	studies	study	NOUN
cana-4546	8	14	.	.	PUNCT
cana-4546	9	1	2020	2020	NUM
cana-4546	9	2	mathematics	mathematic	NOUN
cana-4546	9	3	subject	subject	ADJ
cana-4546	9	4	classification	classification	NOUN
cana-4546	9	5	.	.	PUNCT
cana-4546	10	1	primary	primary	ADJ
cana-4546	10	2	30c45	30c45	NUM
cana-4546	10	3	;	;	PUNCT
cana-4546	10	4	30c50	30c50	NUM
cana-4546	10	5	;	;	PUNCT
cana-4546	10	6	30c80	30c80	NUM
cana-4546	10	7	;	;	PUNCT
cana-4546	10	8	secondary	secondary	ADJ
cana-4546	10	9	11b65	11b65	NUM
cana-4546	10	10	,	,	PUNCT
cana-4546	10	11	47b38	47b38	NUM
cana-4546	10	12	.	.	PUNCT
cana-4546	11	1	keywords	keyword	NOUN
cana-4546	11	2	:	:	PUNCT
cana-4546	11	3	analytic	analytic	ADJ
cana-4546	11	4	functions	function	NOUN
cana-4546	11	5	,	,	PUNCT
cana-4546	11	6	modified	modify	VERB
cana-4546	11	7	hadamard	hadamard	ADJ
cana-4546	11	8	product	product	NOUN
cana-4546	11	9	,	,	PUNCT
cana-4546	11	10	sigmoid	sigmoid	NOUN
cana-4546	11	11	function	function	NOUN
cana-4546	11	12	,	,	PUNCT
cana-4546	11	13	fekete	fekete	NOUN
cana-4546	11	14	-	-	PUNCT
cana-4546	11	15	szegö	szegö	PROPN
cana-4546	11	16	inequality	inequality	NOUN
cana-4546	11	17	1	1	NUM
cana-4546	11	18	.	.	PUNCT
cana-4546	12	1	introduction	introduction	NOUN
cana-4546	12	2	and	and	CCONJ
cana-4546	12	3	motivation	motivation	NOUN
cana-4546	12	4	let	let	VERB
cana-4546	12	5	𝒜𝔭	𝒜𝔭	PROPN
cana-4546	12	6	denote	denote	VERB
cana-4546	12	7	the	the	DET
cana-4546	12	8	class	class	NOUN
cana-4546	12	9	of	of	ADP
cana-4546	12	10	functions	function	NOUN
cana-4546	12	11	of	of	ADP
cana-4546	12	12	the	the	DET
cana-4546	12	13	form	form	NOUN
cana-4546	12	14	ℑ(𝑧	ℑ(𝑧	NOUN
cana-4546	12	15	)	)	PUNCT
cana-4546	12	16	=	=	NOUN
cana-4546	12	17	𝑧𝔭	𝑧𝔭	ADP
cana-4546	12	18	+	+	NOUN
cana-4546	12	19	∑∞	∑∞	X
cana-4546	12	20	𝑘=1	𝑘=1	X
cana-4546	12	21	𝔞𝑘+𝔭	𝔞𝑘+𝔭	VERB
cana-4546	12	22	𝑧𝑘+𝔭	𝑧𝑘+𝔭	VERB
cana-4546	12	23	,	,	PUNCT
cana-4546	12	24	(	(	PUNCT
cana-4546	12	25	1.1	1.1	NUM
cana-4546	12	26	)	)	PUNCT
cana-4546	12	27	which	which	PRON
cana-4546	12	28	are	be	AUX
cana-4546	12	29	𝔭-valently	𝔭-valently	ADV
cana-4546	12	30	analytic	analytic	ADJ
cana-4546	12	31	in	in	ADP
cana-4546	12	32	the	the	DET
cana-4546	12	33	open	open	ADJ
cana-4546	12	34	unit	unit	NOUN
cana-4546	12	35	disk	disk	NOUN
cana-4546	12	36	:	:	PUNCT
cana-4546	12	37	𝕌	𝕌	PROPN
cana-4546	12	38	=	=	SYM
cana-4546	12	39	{	{	PUNCT
cana-4546	12	40	𝑧	𝑧	NOUN
cana-4546	12	41	∈	∈	PROPN
cana-4546	12	42	ℂ	ℂ	PROPN
cana-4546	12	43	:	:	PUNCT
cana-4546	12	44	0	0	NUM
cana-4546	12	45	≤	≤	NUM
cana-4546	12	46	|𝑧|	|𝑧|	NOUN
cana-4546	12	47	<	<	X
cana-4546	12	48	1	1	NUM
cana-4546	12	49	}	}	PUNCT
cana-4546	12	50	the	the	DET
cana-4546	12	51	investigation	investigation	NOUN
cana-4546	12	52	of	of	ADP
cana-4546	12	53	𝔭-valently	𝔭-valently	ADV
cana-4546	12	54	analytic	analytic	ADJ
cana-4546	12	55	functions	function	NOUN
cana-4546	12	56	regarding	regard	VERB
cana-4546	12	57	many	many	ADJ
cana-4546	12	58	aspects	aspect	NOUN
cana-4546	12	59	like	like	ADP
cana-4546	12	60	starlikeness	starlikeness	NOUN
cana-4546	12	61	,	,	PUNCT
cana-4546	12	62	subordination	subordination	NOUN
cana-4546	12	63	,	,	PUNCT
cana-4546	12	64	the	the	DET
cana-4546	12	65	introduction	introduction	NOUN
cana-4546	12	66	of	of	ADP
cana-4546	12	67	new	new	ADJ
cana-4546	12	68	subclasses	subclass	NOUN
cana-4546	12	69	are	be	AUX
cana-4546	12	70	still	still	ADV
cana-4546	12	71	inspiring	inspire	VERB
cana-4546	12	72	with	with	ADP
cana-4546	12	73	interesting	interesting	ADJ
cana-4546	12	74	outcomes	outcome	NOUN
cana-4546	12	75	.	.	PUNCT
cana-4546	13	1	special	special	ADJ
cana-4546	13	2	functions	function	NOUN
cana-4546	13	3	are	be	AUX
cana-4546	13	4	composed	compose	VERB
cana-4546	13	5	of	of	ADP
cana-4546	13	6	large	large	ADJ
cana-4546	13	7	number	number	NOUN
cana-4546	13	8	of	of	ADP
cana-4546	13	9	highly	highly	ADV
cana-4546	13	10	interconnected	interconnected	ADJ
cana-4546	13	11	processing	processing	NOUN
cana-4546	13	12	elements	element	NOUN
cana-4546	13	13	(	(	PUNCT
cana-4546	13	14	neurons	neuron	NOUN
cana-4546	13	15	)	)	PUNCT
cana-4546	13	16	working	work	VERB
cana-4546	13	17	together	together	ADV
cana-4546	13	18	to	to	PART
cana-4546	13	19	solve	solve	VERB
cana-4546	13	20	a	a	DET
cana-4546	13	21	specific	specific	ADJ
cana-4546	13	22	task	task	NOUN
cana-4546	13	23	.	.	PUNCT
cana-4546	14	1	they	they	PRON
cana-4546	14	2	play	play	VERB
cana-4546	14	3	a	a	DET
cana-4546	14	4	vital	vital	ADJ
cana-4546	14	5	role	role	NOUN
cana-4546	14	6	in	in	ADP
cana-4546	14	7	univalent	univalent	ADJ
cana-4546	14	8	function	function	NOUN
cana-4546	14	9	theory	theory	NOUN
cana-4546	14	10	.	.	PUNCT
cana-4546	15	1	these	these	DET
cana-4546	15	2	functions	function	NOUN
cana-4546	15	3	have	have	AUX
cana-4546	15	4	been	be	AUX
cana-4546	15	5	overshadowed	overshadow	VERB
cana-4546	15	6	by	by	ADP
cana-4546	15	7	other	other	ADJ
cana-4546	15	8	fields	field	NOUN
cana-4546	15	9	like	like	ADP
cana-4546	15	10	algebra	algebra	NOUN
cana-4546	15	11	,	,	PUNCT
cana-4546	15	12	differential	differential	NOUN
cana-4546	15	13	equations	equation	NOUN
cana-4546	15	14	,	,	PUNCT
cana-4546	15	15	topology	topology	NOUN
cana-4546	15	16	,	,	PUNCT
cana-4546	15	17	functional	functional	ADJ
cana-4546	15	18	analysis	analysis	NOUN
cana-4546	15	19	and	and	CCONJ
cana-4546	15	20	real	real	ADJ
cana-4546	15	21	analysis	analysis	NOUN
cana-4546	15	22	,	,	PUNCT
cana-4546	15	23	among	among	ADP
cana-4546	15	24	others	other	NOUN
cana-4546	15	25	,	,	PUNCT
cana-4546	15	26	because	because	SCONJ
cana-4546	15	27	they	they	PRON
cana-4546	15	28	work	work	VERB
cana-4546	15	29	in	in	ADP
cana-4546	15	30	the	the	DET
cana-4546	15	31	same	same	ADJ
cana-4546	15	32	way	way	NOUN
cana-4546	15	33	the	the	DET
cana-4546	15	34	brain	brain	NOUN
cana-4546	15	35	does	do	VERB
cana-4546	15	36	.	.	PUNCT
cana-4546	16	1	an	an	DET
cana-4546	16	2	example	example	NOUN
cana-4546	16	3	of	of	ADP
cana-4546	16	4	such	such	ADJ
cana-4546	16	5	functions	function	NOUN
cana-4546	16	6	is	be	AUX
cana-4546	16	7	the	the	DET
cana-4546	16	8	activation	activation	NOUN
cana-4546	16	9	function	function	NOUN
cana-4546	16	10	.	.	PUNCT
cana-4546	17	1	activation	activation	NOUN
cana-4546	17	2	function	function	NOUN
cana-4546	17	3	increases	increase	VERB
cana-4546	17	4	the	the	DET
cana-4546	17	5	size	size	NOUN
cana-4546	17	6	of	of	ADP
cana-4546	17	7	hypothesis	hypothesis	NOUN
cana-4546	17	8	space	space	NOUN
cana-4546	17	9	that	that	PRON
cana-4546	17	10	a	a	DET
cana-4546	17	11	network	network	NOUN
cana-4546	17	12	can	can	AUX
cana-4546	17	13	represent	represent	VERB
cana-4546	17	14	.	.	PUNCT
cana-4546	18	1	the	the	DET
cana-4546	18	2	most	most	ADV
cana-4546	18	3	popular	popular	ADJ
cana-4546	18	4	activation	activation	NOUN
cana-4546	18	5	function	function	NOUN
cana-4546	18	6	is	be	AUX
cana-4546	18	7	the	the	DET
cana-4546	18	8	sigmoid	sigmoid	NOUN
cana-4546	18	9	function	function	NOUN
cana-4546	18	10	.	.	PUNCT
cana-4546	19	1	the	the	DET
cana-4546	19	2	sigmoid	sigmoid	NOUN
cana-4546	19	3	function	function	NOUN
cana-4546	19	4	of	of	ADP
cana-4546	19	5	the	the	DET
cana-4546	19	6	form	form	NOUN
cana-4546	19	7	ℵ(𝑧	ℵ(𝑧	NOUN
cana-4546	19	8	)	)	PUNCT
cana-4546	19	9	=	=	SYM
cana-4546	19	10	1	1	NUM
cana-4546	19	11	1+𝑒−𝑧	1+𝑒−𝑧	NUM
cana-4546	19	12	(	(	PUNCT
cana-4546	19	13	1.2	1.2	NUM
cana-4546	19	14	)	)	PUNCT
cana-4546	19	15	is	be	AUX
cana-4546	19	16	differentiable	differentiable	ADJ
cana-4546	19	17	and	and	CCONJ
cana-4546	19	18	has	have	VERB
cana-4546	19	19	the	the	DET
cana-4546	19	20	following	follow	VERB
cana-4546	19	21	properties	property	NOUN
cana-4546	19	22	.	.	PUNCT
cana-4546	20	1	mailto:saleem.a@uob.edu.om	mailto:saleem.a@uob.edu.om	NOUN
cana-4546	20	2	mailto:musthafa.i@uob.edu.om	mailto:musthafa.i@uob.edu.om	NOUN
cana-4546	20	3	communications	communication	NOUN
cana-4546	20	4	on	on	ADP
cana-4546	20	5	applied	apply	VERB
cana-4546	20	6	nonlinear	nonlinear	ADJ
cana-4546	20	7	analysis	analysis	NOUN
cana-4546	20	8	issn	issn	NOUN
cana-4546	20	9	:	:	PUNCT
cana-4546	20	10	1074	1074	NUM
cana-4546	20	11	-	-	PUNCT
cana-4546	20	12	133x	133x	NUM
cana-4546	20	13	vol	vol	NOUN
cana-4546	20	14	32	32	NUM
cana-4546	20	15	no	no	NOUN
cana-4546	20	16	.	.	PUNCT
cana-4546	21	1	9s	9s	NUM
cana-4546	21	2	(	(	PUNCT
cana-4546	21	3	2025	2025	NUM
cana-4546	21	4	)	)	PUNCT
cana-4546	21	5	2651	2651	NUM
cana-4546	21	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4546	21	7	•	•	NOUN
cana-4546	21	8	it	it	PRON
cana-4546	21	9	outputs	output	VERB
cana-4546	21	10	real	real	ADJ
cana-4546	21	11	numbers	number	NOUN
cana-4546	21	12	between	between	ADP
cana-4546	21	13	0	0	NUM
cana-4546	21	14	and	and	CCONJ
cana-4546	21	15	1	1	NUM
cana-4546	21	16	.	.	NUM
cana-4546	21	17	•	•	NOUN
cana-4546	21	18	it	it	PRON
cana-4546	21	19	maps	map	VERB
cana-4546	21	20	from	from	ADP
cana-4546	21	21	a	a	DET
cana-4546	21	22	very	very	ADV
cana-4546	21	23	large	large	ADJ
cana-4546	21	24	input	input	NOUN
cana-4546	21	25	domain	domain	NOUN
cana-4546	21	26	to	to	ADP
cana-4546	21	27	a	a	DET
cana-4546	21	28	small	small	ADJ
cana-4546	21	29	range	range	NOUN
cana-4546	21	30	of	of	ADP
cana-4546	21	31	outputs	output	NOUN
cana-4546	21	32	.	.	PUNCT
cana-4546	22	1	•	•	NUM
cana-4546	22	2	never	never	ADV
cana-4546	22	3	loses	lose	VERB
cana-4546	22	4	information	information	NOUN
cana-4546	22	5	because	because	SCONJ
cana-4546	22	6	it	it	PRON
cana-4546	22	7	is	be	AUX
cana-4546	22	8	a	a	DET
cana-4546	22	9	one	one	NUM
cana-4546	22	10	-	-	PUNCT
cana-4546	22	11	to	to	ADP
cana-4546	22	12	-	-	PUNCT
cana-4546	22	13	one	one	NUM
cana-4546	22	14	function	function	NOUN
cana-4546	22	15	.	.	PUNCT
cana-4546	23	1	•	•	NOUN
cana-4546	23	2	increases	increase	NOUN
cana-4546	23	3	monotonically	monotonically	ADV
cana-4546	23	4	.	.	PUNCT
cana-4546	24	1	these	these	DET
cana-4546	24	2	properties	property	NOUN
cana-4546	24	3	enable	enable	VERB
cana-4546	24	4	us	we	PRON
cana-4546	24	5	to	to	PART
cana-4546	24	6	use	use	VERB
cana-4546	24	7	sigmoid	sigmoid	NOUN
cana-4546	24	8	function	function	NOUN
cana-4546	24	9	in	in	ADP
cana-4546	24	10	univalent	univalent	ADJ
cana-4546	24	11	function	function	NOUN
cana-4546	24	12	theory	theory	NOUN
cana-4546	24	13	.	.	PUNCT
cana-4546	25	1	we	we	PRON
cana-4546	25	2	briefly	briefly	ADV
cana-4546	25	3	recall	recall	VERB
cana-4546	25	4	the	the	DET
cana-4546	25	5	following	follow	VERB
cana-4546	25	6	definitions	definition	NOUN
cana-4546	25	7	needed	need	VERB
cana-4546	25	8	our	our	PRON
cana-4546	25	9	investigation	investigation	NOUN
cana-4546	25	10	.	.	PUNCT
cana-4546	26	1	definition	definition	NOUN
cana-4546	26	2	1.1	1.1	NUM
cana-4546	26	3	(	(	PUNCT
cana-4546	26	4	[	[	X
cana-4546	26	5	14	14	NUM
cana-4546	26	6	]	]	PUNCT
cana-4546	26	7	)	)	PUNCT
cana-4546	26	8	let	let	VERB
cana-4546	26	9	ℑ(𝑧	ℑ(𝑧	PRON
cana-4546	26	10	)	)	PUNCT
cana-4546	26	11	=	=	SYM
cana-4546	26	12	𝑧𝔭	𝑧𝔭	ADP
cana-4546	26	13	+	+	NOUN
cana-4546	26	14	∑∞	∑∞	X
cana-4546	26	15	𝑘=1	𝑘=1	X
cana-4546	26	16	𝔞𝑘+𝔭	𝔞𝑘+𝔭	VERB
cana-4546	26	17	𝑧𝑘+𝔭	𝑧𝑘+𝔭	VERB
cana-4546	26	18	,	,	PUNCT
cana-4546	26	19	and	and	CCONJ
cana-4546	26	20	𝔤(𝑧	𝔤(𝑧	NUM
cana-4546	26	21	)	)	PUNCT
cana-4546	27	1	=	=	SYM
cana-4546	27	2	𝑧𝔭	𝑧𝔭	ADP
cana-4546	27	3	+	+	NOUN
cana-4546	27	4	∑∞	∑∞	X
cana-4546	27	5	𝑘=1	𝑘=1	ADJ
cana-4546	27	6	𝔟𝑘+𝔭	𝔟𝑘+𝔭	PROPN
cana-4546	27	7	𝑧𝑘+𝔭.	𝑧𝑘+𝔭.	NOUN
cana-4546	27	8	the	the	DET
cana-4546	27	9	modified	modify	VERB
cana-4546	27	10	hadamard	hadamard	ADJ
cana-4546	27	11	product	product	NOUN
cana-4546	27	12	of	of	ADP
cana-4546	27	13	two	two	NUM
cana-4546	27	14	functions	function	NOUN
cana-4546	27	15	ℑ	ℑ	PROPN
cana-4546	27	16	and	and	CCONJ
cana-4546	27	17	𝔤	𝔤	PROPN
cana-4546	27	18	which	which	PRON
cana-4546	27	19	belong	belong	VERB
cana-4546	27	20	to	to	ADP
cana-4546	27	21	𝒜𝔭	𝒜𝔭	PROPN
cana-4546	27	22	is	be	AUX
cana-4546	27	23	defined	define	VERB
cana-4546	27	24	by	by	ADP
cana-4546	27	25	ℑ(𝑧	ℑ(𝑧	PRON
cana-4546	27	26	)	)	PUNCT
cana-4546	27	27	=	=	SYM
cana-4546	27	28	(	(	PUNCT
cana-4546	27	29	ℑ	ℑ	PROPN
cana-4546	27	30	∗	∗	NOUN
cana-4546	27	31	𝔤)(𝑧	𝔤)(𝑧	NUM
cana-4546	27	32	)	)	PUNCT
cana-4546	27	33	=	=	SYM
cana-4546	27	34	𝑧𝔭	𝑧𝔭	ADP
cana-4546	27	35	+	+	NOUN
cana-4546	27	36	∑∞	∑∞	X
cana-4546	27	37	𝑘=1	𝑘=1	X
cana-4546	27	38	𝔞𝑘+𝔭𝔟𝑘+𝔭	𝔞𝑘+𝔭𝔟𝑘+𝔭	PRON
cana-4546	27	39	𝑧𝑘+𝔭	𝑧𝑘+𝔭	NOUN
cana-4546	27	40	(	(	PUNCT
cana-4546	27	41	1.3	1.3	NUM
cana-4546	27	42	)	)	PUNCT
cana-4546	27	43	definition	definition	NOUN
cana-4546	27	44	1.2	1.2	NUM
cana-4546	27	45	(	(	PUNCT
cana-4546	27	46	[	[	X
cana-4546	27	47	15	15	NUM
cana-4546	27	48	]	]	PUNCT
cana-4546	27	49	)	)	PUNCT
cana-4546	27	50	let	let	VERB
cana-4546	27	51	ℑ	ℑ	PRON
cana-4546	27	52	∈	∈	PROPN
cana-4546	27	53	𝐴.	𝐴.	NOUN
cana-4546	27	54	then	then	ADV
cana-4546	27	55	the	the	DET
cana-4546	27	56	𝔮𝑡ℎ	𝔮𝑡ℎ	NOUN
cana-4546	27	57	hankel	hankel	NOUN
cana-4546	27	58	determinant	determinant	ADJ
cana-4546	27	59	of	of	ADP
cana-4546	27	60	ℑ	ℑ	PROPN
cana-4546	27	61	is	be	AUX
cana-4546	27	62	defined	define	VERB
cana-4546	27	63	for	for	ADP
cana-4546	27	64	𝔮	𝔮	NUM
cana-4546	27	65	≥	≥	NUM
cana-4546	27	66	1	1	NUM
cana-4546	27	67	and	and	CCONJ
cana-4546	27	68	𝑛	𝑛	PRON
cana-4546	27	69	≥	≥	NOUN
cana-4546	27	70	1	1	NUM
cana-4546	27	71	by	by	ADP
cana-4546	27	72	𝐻𝔮(𝑛	𝐻𝔮(𝑛	ADJ
cana-4546	27	73	)	)	PUNCT
cana-4546	27	74	=	=	PUNCT
cana-4546	28	1	|	|	ADV
cana-4546	28	2	|	|	ADV
cana-4546	28	3	𝔞𝑛	𝔞𝑛	ADP
cana-4546	28	4	𝔞𝑛+1	𝔞𝑛+1	PROPN
cana-4546	28	5	⋯	⋯	PROPN
cana-4546	28	6	𝔞𝑛+𝑞−1	𝔞𝑛+𝑞−1	PROPN
cana-4546	28	7	𝔞𝑛+1	𝔞𝑛+1	PROPN
cana-4546	28	8	𝔞𝑛+2	𝔞𝑛+2	NUM
cana-4546	28	9	⋯	⋯	PROPN
cana-4546	28	10	𝔞𝑛+𝑞	𝔞𝑛+𝑞	PROPN
cana-4546	28	11	⋮	⋮	PROPN
cana-4546	28	12	⋮	⋮	PROPN
cana-4546	28	13	⋮	⋮	PROPN
cana-4546	28	14	⋮	⋮	NOUN
cana-4546	28	15	𝔞𝑛+𝑞−1	𝔞𝑛+𝑞−1	PROPN
cana-4546	29	1	𝔞𝑛+𝑞	𝔞𝑛+𝑞	PROPN
cana-4546	29	2	⋯	⋯	PROPN
cana-4546	29	3	𝔞𝑛+2𝑞−2	𝔞𝑛+2𝑞−2	PROPN
cana-4546	30	1	|	|	ADV
cana-4546	30	2	|	|	ADV
cana-4546	30	3	(	(	PUNCT
cana-4546	30	4	1.4	1.4	NUM
cana-4546	30	5	)	)	PUNCT
cana-4546	30	6	thus	thus	ADV
cana-4546	30	7	,	,	PUNCT
cana-4546	30	8	the	the	DET
cana-4546	30	9	second	second	ADJ
cana-4546	30	10	hankel	hankel	NOUN
cana-4546	30	11	determinant	determinant	ADJ
cana-4546	30	12	𝐻2(2	𝐻2(2	ADV
cana-4546	30	13	)	)	PUNCT
cana-4546	30	14	=	=	SYM
cana-4546	31	1	|	|	ADV
cana-4546	31	2	𝔞2	𝔞2	PROPN
cana-4546	31	3	𝔞3	𝔞3	PROPN
cana-4546	31	4	𝔞3	𝔞3	PROPN
cana-4546	31	5	𝔞4|	𝔞4|	PROPN
cana-4546	32	1	=	=	SYM
cana-4546	32	2	𝔞2𝔞4	𝔞2𝔞4	X
cana-4546	33	1	−	−	PROPN
cana-4546	33	2	𝔞3	𝔞3	PROPN
cana-4546	33	3	2	2	NUM
cana-4546	33	4	(	(	PUNCT
cana-4546	33	5	1.5	1.5	NUM
cana-4546	33	6	)	)	PUNCT
cana-4546	33	7	for	for	ADP
cana-4546	33	8	two	two	NUM
cana-4546	33	9	analytic	analytic	ADJ
cana-4546	33	10	functions	function	NOUN
cana-4546	33	11	ℑ	ℑ	PROPN
cana-4546	33	12	and	and	CCONJ
cana-4546	33	13	𝔤	𝔤	PROPN
cana-4546	33	14	,	,	PUNCT
cana-4546	33	15	the	the	DET
cana-4546	33	16	function	function	NOUN
cana-4546	33	17	ℑ	ℑ	PROPN
cana-4546	33	18	is	be	AUX
cana-4546	33	19	subordinate	subordinate	ADJ
cana-4546	33	20	to	to	ADP
cana-4546	33	21	𝔤	𝔤	PROPN
cana-4546	33	22	,	,	PUNCT
cana-4546	33	23	written	write	VERB
cana-4546	33	24	as	as	SCONJ
cana-4546	33	25	follows	follow	VERB
cana-4546	33	26	:	:	PUNCT
cana-4546	33	27	ℑ(𝑧	ℑ(𝑧	NOUN
cana-4546	33	28	)	)	PUNCT
cana-4546	33	29	≺	≺	NOUN
cana-4546	33	30	𝔤(𝑧	𝔤(𝑧	NUM
cana-4546	33	31	)	)	PUNCT
cana-4546	33	32	if	if	SCONJ
cana-4546	33	33	there	there	PRON
cana-4546	33	34	exists	exist	VERB
cana-4546	33	35	an	an	DET
cana-4546	33	36	analytic	analytic	ADJ
cana-4546	33	37	function	function	NOUN
cana-4546	33	38	𝑤	𝑤	ADP
cana-4546	33	39	,	,	PUNCT
cana-4546	33	40	with	with	ADP
cana-4546	33	41	𝑤(0	𝑤(0	NOUN
cana-4546	33	42	)	)	PUNCT
cana-4546	33	43	=	=	SYM
cana-4546	33	44	0	0	NUM
cana-4546	33	45	and	and	CCONJ
cana-4546	33	46	|𝑤(𝑧)|	|𝑤(𝑧)|	PROPN
cana-4546	33	47	<	<	X
cana-4546	33	48	1	1	NUM
cana-4546	33	49	such	such	ADJ
cana-4546	33	50	that	that	SCONJ
cana-4546	33	51	ℑ(𝑧	ℑ(𝑧	X
cana-4546	33	52	)	)	PUNCT
cana-4546	33	53	=	=	SYM
cana-4546	33	54	𝔤(𝑤(𝑧	𝔤(𝑤(𝑧	PROPN
cana-4546	33	55	)	)	PUNCT
cana-4546	33	56	)	)	PUNCT
cana-4546	33	57	.	.	PUNCT
cana-4546	34	1	in	in	ADP
cana-4546	34	2	particular	particular	ADJ
cana-4546	34	3	,	,	PUNCT
cana-4546	34	4	if	if	SCONJ
cana-4546	34	5	the	the	DET
cana-4546	34	6	function	function	NOUN
cana-4546	34	7	𝔤	𝔤	X
cana-4546	34	8	is	be	AUX
cana-4546	34	9	univalent	univalent	ADJ
cana-4546	34	10	in	in	ADP
cana-4546	34	11	𝕌	𝕌	PROPN
cana-4546	34	12	,	,	PUNCT
cana-4546	34	13	then	then	ADV
cana-4546	34	14	ℑ(𝑧	ℑ(𝑧	NOUN
cana-4546	34	15	)	)	PUNCT
cana-4546	34	16	≺	≺	NOUN
cana-4546	34	17	𝔤(𝑧	𝔤(𝑧	PROPN
cana-4546	34	18	)	)	PUNCT
cana-4546	34	19	is	be	AUX
cana-4546	34	20	equivalent	equivalent	ADJ
cana-4546	34	21	to	to	ADP
cana-4546	34	22	ℑ(0	ℑ(0	SYM
cana-4546	34	23	)	)	PUNCT
cana-4546	34	24	=	=	SYM
cana-4546	34	25	𝔤(0	𝔤(0	PROPN
cana-4546	34	26	)	)	PUNCT
cana-4546	34	27	and	and	CCONJ
cana-4546	34	28	ℑ(𝑈	ℑ(𝑈	NUM
cana-4546	34	29	)	)	PUNCT
cana-4546	34	30	⊂	⊂	ADJ
cana-4546	34	31	𝔤(𝑈	𝔤(𝑈	ADJ
cana-4546	34	32	)	)	PUNCT
cana-4546	34	33	.	.	PUNCT
cana-4546	35	1	definition	definition	NOUN
cana-4546	35	2	1.3	1.3	NUM
cana-4546	35	3	(	(	PUNCT
cana-4546	35	4	[	[	X
cana-4546	35	5	9	9	NUM
cana-4546	35	6	]	]	PUNCT
cana-4546	35	7	)	)	PUNCT
cana-4546	35	8	let	let	VERB
cana-4546	35	9	𝜂	𝜂	PRON
cana-4546	35	10	∈	∈	PROPN
cana-4546	35	11	ℂ/{0	ℂ/{0	NOUN
cana-4546	35	12	}	}	PUNCT
cana-4546	35	13	and	and	CCONJ
cana-4546	35	14	the	the	DET
cana-4546	35	15	class	class	NOUN
cana-4546	35	16	𝑀𝜆(𝜂	𝑀𝜆(𝜂	NOUN
cana-4546	35	17	,	,	PUNCT
cana-4546	35	18	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	35	19	)	)	PUNCT
cana-4546	35	20	denote	denote	VERB
cana-4546	35	21	the	the	DET
cana-4546	35	22	subclass	subclass	NOUN
cana-4546	35	23	of	of	ADP
cana-4546	35	24	𝒜𝔭	𝒜𝔭	PROPN
cana-4546	35	25	consisting	consist	VERB
cana-4546	35	26	of	of	ADP
cana-4546	35	27	functions	function	NOUN
cana-4546	35	28	ℑ	ℑ	PROPN
cana-4546	35	29	of	of	ADP
cana-4546	35	30	the	the	DET
cana-4546	35	31	form	form	NOUN
cana-4546	35	32	(	(	PUNCT
cana-4546	35	33	1.1	1.1	NUM
cana-4546	35	34	)	)	PUNCT
cana-4546	35	35	,	,	PUNCT
cana-4546	35	36	and	and	CCONJ
cana-4546	35	37	satisfying	satisfy	VERB
cana-4546	35	38	the	the	DET
cana-4546	35	39	following	follow	VERB
cana-4546	35	40	subordination	subordination	NOUN
cana-4546	35	41	condition	condition	NOUN
cana-4546	35	42	1	1	NUM
cana-4546	36	1	+	+	CCONJ
cana-4546	36	2	1	1	NUM
cana-4546	36	3	𝜂	𝜂	X
cana-4546	36	4	[	[	PUNCT
cana-4546	36	5	𝑧ℑ′(𝑧	𝑧ℑ′(𝑧	X
cana-4546	36	6	)	)	PUNCT
cana-4546	36	7	ℑ(𝑧	ℑ(𝑧	NOUN
cana-4546	36	8	)	)	PUNCT
cana-4546	36	9	+	+	CCONJ
cana-4546	36	10	𝜆	𝜆	DET
cana-4546	36	11	𝑧2ℑ′′(𝑧	𝑧2ℑ′′(𝑧	X
cana-4546	36	12	)	)	PUNCT
cana-4546	36	13	ℑ(𝑧	ℑ(𝑧	NOUN
cana-4546	36	14	)	)	PUNCT
cana-4546	36	15	−	−	PROPN
cana-4546	36	16	1	1	NUM
cana-4546	36	17	]	]	PUNCT
cana-4546	36	18	≺	≺	NOUN
cana-4546	36	19	𝜑𝑛,𝑚	𝜑𝑛,𝑚	X
cana-4546	36	20	(	(	PUNCT
cana-4546	36	21	1.6	1.6	NUM
cana-4546	36	22	)	)	PUNCT
cana-4546	36	23	for	for	ADP
cana-4546	36	24	0	0	NUM
cana-4546	36	25	≤	≤	NOUN
cana-4546	36	26	𝜆	𝜆	DET
cana-4546	36	27	≤	≤	NUM
cana-4546	36	28	1	1	NUM
cana-4546	36	29	and	and	CCONJ
cana-4546	36	30	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NOUN
cana-4546	36	31	is	be	AUX
cana-4546	36	32	a	a	DET
cana-4546	36	33	simple	simple	ADJ
cana-4546	36	34	logistic	logistic	ADJ
cana-4546	36	35	sigmoid	sigmoid	NOUN
cana-4546	36	36	activation	activation	NOUN
cana-4546	36	37	function	function	NOUN
cana-4546	36	38	.	.	PUNCT
cana-4546	37	1	in	in	ADP
cana-4546	37	2	this	this	DET
cana-4546	37	3	study	study	NOUN
cana-4546	37	4	,	,	PUNCT
cana-4546	37	5	we	we	PRON
cana-4546	37	6	solve	solve	VERB
cana-4546	37	7	the	the	DET
cana-4546	37	8	fekete	fekete	NOUN
cana-4546	37	9	-	-	PUNCT
cana-4546	37	10	szegö	szegö	ADJ
cana-4546	37	11	problem	problem	NOUN
cana-4546	37	12	for	for	ADP
cana-4546	37	13	functions	function	NOUN
cana-4546	37	14	in	in	ADP
cana-4546	37	15	the	the	DET
cana-4546	37	16	class	class	NOUN
cana-4546	37	17	𝑀𝜆(∗)(𝜂	𝑀𝜆(∗)(𝜂	PROPN
cana-4546	37	18	,	,	PUNCT
cana-4546	37	19	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	37	20	)	)	PUNCT
cana-4546	37	21	and	and	CCONJ
cana-4546	37	22	in	in	ADP
cana-4546	37	23	the	the	DET
cana-4546	37	24	special	special	ADJ
cana-4546	37	25	instances	instance	NOUN
cana-4546	37	26	,	,	PUNCT
cana-4546	37	27	as	as	ADV
cana-4546	37	28	well	well	ADV
cana-4546	37	29	as	as	ADP
cana-4546	37	30	provide	provide	VERB
cana-4546	37	31	bound	bind	VERB
cana-4546	37	32	estimates	estimate	NOUN
cana-4546	37	33	for	for	ADP
cana-4546	37	34	the	the	DET
cana-4546	37	35	coefficients	coefficient	NOUN
cana-4546	37	36	and	and	CCONJ
cana-4546	37	37	an	an	DET
cana-4546	37	38	upper	upper	ADJ
cana-4546	37	39	bound	bind	VERB
cana-4546	37	40	estimate	estimate	NOUN
cana-4546	37	41	for	for	ADP
cana-4546	37	42	the	the	DET
cana-4546	37	43	second	second	ADJ
cana-4546	37	44	hankel	hankel	NOUN
cana-4546	37	45	determinant	determinant	ADJ
cana-4546	37	46	.	.	PUNCT
cana-4546	38	1	communications	communication	NOUN
cana-4546	38	2	on	on	ADP
cana-4546	38	3	applied	apply	VERB
cana-4546	38	4	nonlinear	nonlinear	ADJ
cana-4546	38	5	analysis	analysis	NOUN
cana-4546	38	6	issn	issn	NOUN
cana-4546	38	7	:	:	PUNCT
cana-4546	38	8	1074	1074	NUM
cana-4546	38	9	-	-	PUNCT
cana-4546	38	10	133x	133x	NUM
cana-4546	38	11	vol	vol	NOUN
cana-4546	38	12	32	32	NUM
cana-4546	38	13	no	no	NOUN
cana-4546	38	14	.	.	PUNCT
cana-4546	39	1	9s	9s	NUM
cana-4546	39	2	(	(	PUNCT
cana-4546	39	3	2025	2025	NUM
cana-4546	39	4	)	)	PUNCT
cana-4546	39	5	2652	2652	NUM
cana-4546	40	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4546	40	2	definition	definition	NOUN
cana-4546	40	3	1.4	1.4	NUM
cana-4546	40	4	let	let	VERB
cana-4546	40	5	𝜂	𝜂	PROPN
cana-4546	40	6	∈	∈	PROPN
cana-4546	40	7	ℂ/{0	ℂ/{0	NOUN
cana-4546	40	8	}	}	PUNCT
cana-4546	40	9	and	and	CCONJ
cana-4546	40	10	the	the	DET
cana-4546	40	11	class	class	NOUN
cana-4546	40	12	𝑀𝜆(∗)(𝜂	𝑀𝜆(∗)(𝜂	PROPN
cana-4546	40	13	,	,	PUNCT
cana-4546	40	14	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	40	15	)	)	PUNCT
cana-4546	40	16	denote	denote	VERB
cana-4546	40	17	the	the	DET
cana-4546	40	18	subclass	subclass	NOUN
cana-4546	40	19	of	of	ADP
cana-4546	40	20	𝒜𝔭	𝒜𝔭	PROPN
cana-4546	40	21	consisting	consist	VERB
cana-4546	40	22	of	of	ADP
cana-4546	40	23	functions	function	NOUN
cana-4546	40	24	ℑ	ℑ	PROPN
cana-4546	40	25	of	of	ADP
cana-4546	40	26	the	the	DET
cana-4546	40	27	form	form	NOUN
cana-4546	40	28	(	(	PUNCT
cana-4546	40	29	1.1	1.1	NUM
cana-4546	40	30	)	)	PUNCT
cana-4546	40	31	,	,	PUNCT
cana-4546	40	32	and	and	CCONJ
cana-4546	40	33	satisfying	satisfy	VERB
cana-4546	40	34	the	the	DET
cana-4546	40	35	following	follow	VERB
cana-4546	40	36	subordination	subordination	NOUN
cana-4546	40	37	condition	condition	NOUN
cana-4546	40	38	1	1	NUM
cana-4546	41	1	+	+	CCONJ
cana-4546	41	2	1	1	NUM
cana-4546	41	3	𝜂	𝜂	NOUN
cana-4546	41	4	[	[	PUNCT
cana-4546	41	5	𝑧(ℑ∗𝔤)′(𝑧	𝑧(ℑ∗𝔤)′(𝑧	PROPN
cana-4546	41	6	)	)	PUNCT
cana-4546	41	7	(	(	PUNCT
cana-4546	41	8	ℑ∗𝔤)(𝑧	ℑ∗𝔤)(𝑧	NOUN
cana-4546	41	9	)	)	PUNCT
cana-4546	41	10	+	+	CCONJ
cana-4546	41	11	𝜆	𝜆	X
cana-4546	41	12	𝑧2(ℑ∗𝔤)′′(𝑧	𝑧2(ℑ∗𝔤)′′(𝑧	X
cana-4546	41	13	)	)	PUNCT
cana-4546	41	14	(	(	PUNCT
cana-4546	41	15	ℑ∗𝔤)(𝑧	ℑ∗𝔤)(𝑧	NOUN
cana-4546	41	16	)	)	PUNCT
cana-4546	41	17	−	−	NOUN
cana-4546	41	18	1	1	NUM
cana-4546	41	19	]	]	PUNCT
cana-4546	41	20	≺	≺	NOUN
cana-4546	41	21	𝜑𝑛,𝑚	𝜑𝑛,𝑚	X
cana-4546	41	22	=	=	SYM
cana-4546	41	23	1	1	NUM
cana-4546	41	24	+	+	NUM
cana-4546	41	25	∑∞	∑∞	X
cana-4546	41	26	𝑚=1	𝑚=1	X
cana-4546	41	27	(	(	PUNCT
cana-4546	41	28	−1)𝑚	−1)𝑚	NUM
cana-4546	41	29	2𝑚	2𝑚	NOUN
cana-4546	41	30	(	(	PUNCT
cana-4546	41	31	∑∞	∑∞	NOUN
cana-4546	41	32	𝑛=1	𝑛=1	NOUN
cana-4546	41	33	(	(	PUNCT
cana-4546	41	34	−1)𝑚	−1)𝑚	NOUN
cana-4546	41	35	𝑛	𝑛	PROPN
cana-4546	41	36	!	!	PROPN
cana-4546	41	37	𝑧𝑛	𝑧𝑛	PROPN
cana-4546	41	38	)	)	PUNCT
cana-4546	41	39	𝑚	𝑚	PROPN
cana-4546	41	40	(	(	PUNCT
cana-4546	41	41	1.7	1.7	NUM
cana-4546	41	42	)	)	PUNCT
cana-4546	41	43	for	for	ADP
cana-4546	41	44	0	0	NUM
cana-4546	41	45	≤	≤	NOUN
cana-4546	41	46	𝜆	𝜆	DET
cana-4546	41	47	≤	≤	NUM
cana-4546	41	48	1	1	NUM
cana-4546	41	49	and	and	CCONJ
cana-4546	41	50	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NOUN
cana-4546	41	51	is	be	AUX
cana-4546	41	52	a	a	DET
cana-4546	41	53	simple	simple	ADJ
cana-4546	41	54	logistic	logistic	ADJ
cana-4546	41	55	sigmoid	sigmoid	NOUN
cana-4546	41	56	activation	activation	NOUN
cana-4546	41	57	function	function	NOUN
cana-4546	41	58	.	.	PUNCT
cana-4546	42	1	2	2	X
cana-4546	42	2	.	.	X
cana-4546	42	3	preliminary	preliminary	ADJ
cana-4546	42	4	results	result	NOUN
cana-4546	42	5	the	the	DET
cana-4546	42	6	following	follow	VERB
cana-4546	42	7	results	result	NOUN
cana-4546	42	8	are	be	AUX
cana-4546	42	9	needed	need	VERB
cana-4546	42	10	for	for	ADP
cana-4546	42	11	our	our	PRON
cana-4546	42	12	investigation	investigation	NOUN
cana-4546	42	13	let	let	VERB
cana-4546	42	14	𝑃	𝑃	PRON
cana-4546	42	15	be	be	AUX
cana-4546	42	16	the	the	DET
cana-4546	42	17	family	family	NOUN
cana-4546	42	18	of	of	ADP
cana-4546	42	19	all	all	DET
cana-4546	42	20	functions	function	NOUN
cana-4546	42	21	𝑝	𝑝	DET
cana-4546	42	22	analytic	analytic	NOUN
cana-4546	42	23	in	in	ADP
cana-4546	42	24	𝕌	𝕌	PROPN
cana-4546	42	25	for	for	ADP
cana-4546	42	26	which	which	PRON
cana-4546	42	27	ℜ{𝛼(𝑧	ℜ{𝛼(𝑧	NUM
cana-4546	42	28	)	)	PUNCT
cana-4546	42	29	}	}	PUNCT
cana-4546	42	30	>	>	X
cana-4546	42	31	0	0	PUNCT
cana-4546	42	32	and	and	CCONJ
cana-4546	42	33	𝑝(𝑧	𝑝(𝑧	PROPN
cana-4546	42	34	)	)	PUNCT
cana-4546	42	35	=	=	PUNCT
cana-4546	43	1	1	1	NUM
cana-4546	43	2	+	+	CCONJ
cana-4546	43	3	𝑃1𝑧	𝑃1𝑧	PROPN
cana-4546	43	4	+	+	CCONJ
cana-4546	43	5	𝑃2𝑧2	𝑃2𝑧2	PROPN
cana-4546	43	6	+	+	CCONJ
cana-4546	43	7	⋯	⋯	PROPN
cana-4546	43	8	,	,	PUNCT
cana-4546	43	9	(	(	PUNCT
cana-4546	43	10	𝑓𝑜𝑟𝑧	𝑓𝑜𝑟𝑧	ADJ
cana-4546	43	11	∈	∈	PROPN
cana-4546	43	12	𝕌	𝕌	PROPN
cana-4546	43	13	)	)	PUNCT
cana-4546	43	14	lemma	lemma	PROPN
cana-4546	43	15	2.1	2.1	NUM
cana-4546	43	16	(	(	PUNCT
cana-4546	43	17	[	[	X
cana-4546	43	18	8	8	NUM
cana-4546	43	19	]	]	SYM
cana-4546	43	20	)	)	PUNCT
cana-4546	43	21	if	if	SCONJ
cana-4546	43	22	𝑝	𝑝	NOUN
cana-4546	43	23	∈	∈	PROPN
cana-4546	43	24	𝑃	𝑃	NOUN
cana-4546	43	25	,	,	PUNCT
cana-4546	43	26	then	then	ADV
cana-4546	43	27	|𝑃𝑘|	|𝑃𝑘|	PROPN
cana-4546	43	28	≤	≤	ADV
cana-4546	43	29	2	2	NUM
cana-4546	43	30	(	(	PUNCT
cana-4546	43	31	2,3,4	2,3,4	NUM
cana-4546	43	32	,	,	PUNCT
cana-4546	43	33	⋯	⋯	PROPN
cana-4546	43	34	)	)	PUNCT
cana-4546	43	35	lemma	lemma	PROPN
cana-4546	43	36	2.2	2.2	NUM
cana-4546	43	37	(	(	PUNCT
cana-4546	43	38	[	[	X
cana-4546	43	39	6	6	NUM
cana-4546	43	40	]	]	PUNCT
cana-4546	43	41	)	)	PUNCT
cana-4546	43	42	let	let	VERB
cana-4546	43	43	𝑔	𝑔	PART
cana-4546	43	44	be	be	AUX
cana-4546	43	45	a	a	DET
cana-4546	43	46	sigmoid	sigmoid	NOUN
cana-4546	43	47	function	function	NOUN
cana-4546	43	48	defined	define	VERB
cana-4546	43	49	in	in	ADP
cana-4546	43	50	(	(	PUNCT
cana-4546	43	51	1.2	1.2	NUM
cana-4546	43	52	)	)	PUNCT
cana-4546	43	53	and	and	CCONJ
cana-4546	43	54	𝜑(𝑧	𝜑(𝑧	NOUN
cana-4546	43	55	)	)	PUNCT
cana-4546	43	56	=	=	SYM
cana-4546	43	57	2𝑔(𝑧	2𝑔(𝑧	NUM
cana-4546	43	58	)	)	PUNCT
cana-4546	44	1	=	=	SYM
cana-4546	44	2	1	1	NUM
cana-4546	44	3	+	+	NUM
cana-4546	44	4	∑∞	∑∞	X
cana-4546	44	5	𝑚=1	𝑚=1	X
cana-4546	44	6	(	(	PUNCT
cana-4546	44	7	−1)𝑚	−1)𝑚	NUM
cana-4546	44	8	2𝑚	2𝑚	NOUN
cana-4546	44	9	(	(	PUNCT
cana-4546	44	10	∑∞	∑∞	NOUN
cana-4546	44	11	𝑛=1	𝑛=1	NOUN
cana-4546	44	12	(	(	PUNCT
cana-4546	44	13	−1)𝑚	−1)𝑚	NOUN
cana-4546	44	14	𝑛	𝑛	PROPN
cana-4546	44	15	!	!	PROPN
cana-4546	44	16	𝑧𝑛	𝑧𝑛	PROPN
cana-4546	44	17	)	)	PUNCT
cana-4546	44	18	𝑚	𝑚	PROPN
cana-4546	44	19	(	(	PUNCT
cana-4546	44	20	2.1	2.1	NUM
cana-4546	44	21	)	)	PUNCT
cana-4546	44	22	then	then	ADV
cana-4546	44	23	𝜑(𝑧	𝜑(𝑧	NUM
cana-4546	44	24	)	)	PUNCT
cana-4546	44	25	∈	∈	PROPN
cana-4546	44	26	𝑃	𝑃	NOUN
cana-4546	44	27	,	,	PUNCT
cana-4546	44	28	|𝑧|	|𝑧|	NOUN
cana-4546	44	29	<	<	X
cana-4546	44	30	1	1	NUM
cana-4546	44	31	where	where	SCONJ
cana-4546	44	32	𝜑(𝑧	𝜑(𝑧	NOUN
cana-4546	44	33	)	)	PUNCT
cana-4546	44	34	is	be	AUX
cana-4546	44	35	a	a	DET
cana-4546	44	36	modified	modify	VERB
cana-4546	44	37	sigmoid	sigmoid	NOUN
cana-4546	44	38	function	function	NOUN
cana-4546	44	39	.	.	PUNCT
cana-4546	45	1	lemma	lemma	PROPN
cana-4546	45	2	2.3	2.3	NUM
cana-4546	45	3	(	(	PUNCT
cana-4546	45	4	[	[	X
cana-4546	45	5	6	6	NUM
cana-4546	45	6	]	]	PUNCT
cana-4546	45	7	)	)	PUNCT
cana-4546	45	8	let	let	VERB
cana-4546	45	9	𝑔	𝑔	PART
cana-4546	45	10	be	be	AUX
cana-4546	45	11	a	a	DET
cana-4546	45	12	sigmoid	sigmoid	NOUN
cana-4546	45	13	function	function	NOUN
cana-4546	45	14	defined	define	VERB
cana-4546	45	15	in	in	ADP
cana-4546	45	16	(	(	PUNCT
cana-4546	45	17	1.1	1.1	NUM
cana-4546	45	18	)	)	PUNCT
cana-4546	45	19	and	and	CCONJ
cana-4546	45	20	𝜑𝑛,𝑚(𝑧	𝜑𝑛,𝑚(𝑧	ADJ
cana-4546	45	21	)	)	PUNCT
cana-4546	45	22	=	=	SYM
cana-4546	46	1	1	1	NUM
cana-4546	46	2	+	+	NUM
cana-4546	46	3	∑∞	∑∞	X
cana-4546	46	4	𝑚=1	𝑚=1	X
cana-4546	46	5	(	(	PUNCT
cana-4546	46	6	−1)𝑚	−1)𝑚	NUM
cana-4546	46	7	2𝑚	2𝑚	NOUN
cana-4546	46	8	(	(	PUNCT
cana-4546	46	9	∑∞	∑∞	NOUN
cana-4546	46	10	𝑛=1	𝑛=1	NOUN
cana-4546	46	11	(	(	PUNCT
cana-4546	46	12	−1)𝑚	−1)𝑚	NOUN
cana-4546	46	13	𝑛	𝑛	PROPN
cana-4546	46	14	!	!	PROPN
cana-4546	46	15	𝑧𝑛	𝑧𝑛	PROPN
cana-4546	46	16	)	)	PUNCT
cana-4546	46	17	𝑚	𝑚	PROPN
cana-4546	46	18	(	(	PUNCT
cana-4546	46	19	2.2	2.2	NUM
cana-4546	46	20	)	)	PUNCT
cana-4546	46	21	then	then	ADV
cana-4546	46	22	|𝜑𝑛,𝑚(𝑧)|	|𝜑𝑛,𝑚(𝑧)|	ADV
cana-4546	46	23	<	<	X
cana-4546	46	24	2	2	X
cana-4546	46	25	.	.	PUNCT
cana-4546	47	1	lemma	lemma	PROPN
cana-4546	47	2	2.4	2.4	NUM
cana-4546	47	3	(	(	PUNCT
cana-4546	47	4	[	[	X
cana-4546	47	5	6	6	NUM
cana-4546	47	6	]	]	PUNCT
cana-4546	47	7	)	)	PUNCT
cana-4546	47	8	let	let	VERB
cana-4546	47	9	𝜑(𝑧	𝜑(𝑧	NOUN
cana-4546	47	10	)	)	PUNCT
cana-4546	47	11	∈	∈	NOUN
cana-4546	47	12	𝑃	𝑃	NOUN
cana-4546	47	13	and	and	CCONJ
cana-4546	47	14	be	be	AUX
cana-4546	47	15	starlike	starlike	NOUN
cana-4546	47	16	,	,	PUNCT
cana-4546	47	17	then	then	ADV
cana-4546	47	18	ℑ	ℑ	PROPN
cana-4546	47	19	is	be	AUX
cana-4546	47	20	a	a	DET
cana-4546	47	21	normalized	normalize	VERB
cana-4546	47	22	univalent	univalent	ADJ
cana-4546	47	23	function	function	NOUN
cana-4546	47	24	of	of	ADP
cana-4546	47	25	the	the	DET
cana-4546	47	26	form	form	NOUN
cana-4546	47	27	(	(	PUNCT
cana-4546	47	28	1.1	1.1	NUM
cana-4546	47	29	)	)	PUNCT
cana-4546	47	30	.	.	PUNCT
cana-4546	48	1	setting	set	VERB
cana-4546	48	2	𝑚	𝑚	X
cana-4546	48	3	=	=	SYM
cana-4546	48	4	1	1	NUM
cana-4546	48	5	,	,	PUNCT
cana-4546	48	6	fadipe	fadipe	PROPN
cana-4546	48	7	et	et	PROPN
cana-4546	48	8	al	al	PROPN
cana-4546	48	9	.	.	PUNCT
cana-4546	49	1	[	[	X
cana-4546	49	2	6	6	NUM
cana-4546	49	3	]	]	PUNCT
cana-4546	49	4	remarked	remark	VERB
cana-4546	49	5	that	that	SCONJ
cana-4546	49	6	𝜑(𝑧	𝜑(𝑧	NOUN
cana-4546	49	7	)	)	PUNCT
cana-4546	49	8	=	=	SYM
cana-4546	49	9	1	1	NUM
cana-4546	49	10	+	+	NUM
cana-4546	49	11	∑∞	∑∞	NOUN
cana-4546	49	12	𝑛=1	𝑛=1	NOUN
cana-4546	49	13	𝑐𝑛𝑧𝑛	𝑐𝑛𝑧𝑛	NOUN
cana-4546	49	14	(	(	PUNCT
cana-4546	49	15	2.3	2.3	NUM
cana-4546	49	16	)	)	PUNCT
cana-4546	49	17	where	where	SCONJ
cana-4546	49	18	𝑐𝑛	𝑐𝑛	ADP
cana-4546	49	19	=	=	PRON
cana-4546	49	20	(	(	PUNCT
cana-4546	49	21	−1)𝑛+1	−1)𝑛+1	PROPN
cana-4546	49	22	2𝑛	2𝑛	NUM
cana-4546	49	23	!	!	PUNCT
cana-4546	50	1	,	,	PUNCT
cana-4546	50	2	then	then	ADV
cana-4546	50	3	|𝑐𝑛|	|𝑐𝑛|	NOUN
cana-4546	50	4	≤	≤	NOUN
cana-4546	50	5	2	2	NUM
cana-4546	50	6	for	for	ADP
cana-4546	50	7	𝑛	𝑛	NOUN
cana-4546	50	8	=	=	SYM
cana-4546	50	9	2,3,4	2,3,4	NUM
cana-4546	50	10	,	,	PUNCT
cana-4546	50	11	⋯	⋯	VERB
cana-4546	50	12	and	and	CCONJ
cana-4546	50	13	the	the	DET
cana-4546	50	14	result	result	NOUN
cana-4546	50	15	is	be	AUX
cana-4546	50	16	sharp	sharp	ADJ
cana-4546	50	17	for	for	ADP
cana-4546	50	18	each	each	DET
cana-4546	50	19	𝑛.	𝑛.	NOUN
cana-4546	50	20	3	3	NUM
cana-4546	50	21	.	.	PUNCT
cana-4546	51	1	some	some	DET
cana-4546	51	2	coefficient	coefficient	NOUN
cana-4546	51	3	estimates	estimate	NOUN
cana-4546	51	4	for	for	ADP
cana-4546	51	5	the	the	DET
cana-4546	51	6	class	class	NOUN
cana-4546	51	7	of	of	ADP
cana-4546	51	8	𝑴𝝀,(∗)(𝜼	𝑴𝝀,(∗)(𝜼	NOUN
cana-4546	51	9	,	,	PUNCT
cana-4546	51	10	𝝋𝒏,𝒎	𝝋𝒏,𝒎	ADP
cana-4546	51	11	)	)	PUNCT
cana-4546	51	12	in	in	ADP
cana-4546	51	13	this	this	DET
cana-4546	51	14	section	section	NOUN
cana-4546	51	15	,	,	PUNCT
cana-4546	51	16	we	we	PRON
cana-4546	51	17	will	will	AUX
cana-4546	51	18	find	find	VERB
cana-4546	51	19	the	the	DET
cana-4546	51	20	estimates	estimate	NOUN
cana-4546	51	21	on	on	ADP
cana-4546	51	22	the	the	DET
cana-4546	51	23	coefficients	coefficient	NOUN
cana-4546	51	24	𝔞𝔭+1𝔟𝔭+1	𝔞𝔭+1𝔟𝔭+1	ADV
cana-4546	51	25	,	,	PUNCT
cana-4546	51	26	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	NOUN
cana-4546	51	27	and	and	CCONJ
cana-4546	51	28	𝔞𝔭+3𝔟𝔭+3	𝔞𝔭+3𝔟𝔭+3	NOUN
cana-4546	51	29	for	for	ADP
cana-4546	51	30	functions	function	NOUN
cana-4546	51	31	in	in	ADP
cana-4546	51	32	the	the	DET
cana-4546	51	33	class	class	NOUN
cana-4546	51	34	𝑀𝜆,(∗)(𝜂	𝑀𝜆,(∗)(𝜂	NOUN
cana-4546	51	35	,	,	PUNCT
cana-4546	51	36	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	51	37	)	)	PUNCT
cana-4546	51	38	.	.	PUNCT
cana-4546	52	1	theorem	theorem	VERB
cana-4546	52	2	3.1	3.1	NUM
cana-4546	52	3	let	let	NOUN
cana-4546	52	4	𝜑𝑛,𝑚(𝑧	𝜑𝑛,𝑚(𝑧	ADJ
cana-4546	52	5	)	)	PUNCT
cana-4546	53	1	=	=	SYM
cana-4546	53	2	1	1	NUM
cana-4546	53	3	+	+	NUM
cana-4546	53	4	∑∞	∑∞	X
cana-4546	53	5	𝑚=1	𝑚=1	X
cana-4546	53	6	(	(	PUNCT
cana-4546	53	7	−1)𝑚	−1)𝑚	NUM
cana-4546	53	8	2𝑚	2𝑚	NOUN
cana-4546	53	9	(	(	PUNCT
cana-4546	53	10	∑∞	∑∞	NOUN
cana-4546	53	11	𝑛=1	𝑛=1	NOUN
cana-4546	53	12	(	(	PUNCT
cana-4546	53	13	−1)𝑚	−1)𝑚	NOUN
cana-4546	53	14	𝑛	𝑛	PROPN
cana-4546	53	15	!	!	PROPN
cana-4546	53	16	𝑧𝑛	𝑧𝑛	PROPN
cana-4546	53	17	)	)	PUNCT
cana-4546	53	18	𝑚	𝑚	ADP
cana-4546	53	19	where	where	SCONJ
cana-4546	53	20	𝜑𝑛,𝑚(𝑧	𝜑𝑛,𝑚(𝑧	ADJ
cana-4546	53	21	)	)	PUNCT
cana-4546	53	22	∈	∈	PROPN
cana-4546	53	23	𝐴	𝐴	PROPN
cana-4546	53	24	is	be	AUX
cana-4546	53	25	a	a	DET
cana-4546	53	26	modified	modify	VERB
cana-4546	53	27	logistic	logistic	ADJ
cana-4546	53	28	sigmoid	sigmoid	NOUN
cana-4546	53	29	activation	activation	NOUN
cana-4546	53	30	function	function	NOUN
cana-4546	53	31	and	and	CCONJ
cana-4546	53	32	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NOUN
cana-4546	53	33	′	′	NUM
cana-4546	53	34	(	(	PUNCT
cana-4546	53	35	0	0	NUM
cana-4546	53	36	)	)	PUNCT
cana-4546	53	37	>	>	X
cana-4546	54	1	0	0	X
cana-4546	54	2	.	.	PUNCT
cana-4546	55	1	if	if	SCONJ
cana-4546	55	2	𝐹(𝑧	𝐹(𝑧	ADP
cana-4546	55	3	)	)	PUNCT
cana-4546	55	4	=	=	SYM
cana-4546	55	5	(	(	PUNCT
cana-4546	55	6	ℑ	ℑ	PROPN
cana-4546	55	7	∗	∗	NOUN
cana-4546	55	8	𝔤)(𝑧	𝔤)(𝑧	NOUN
cana-4546	55	9	)	)	PUNCT
cana-4546	55	10	given	give	VERB
cana-4546	55	11	by	by	ADP
cana-4546	55	12	(	(	PUNCT
cana-4546	55	13	1.1	1.1	NUM
cana-4546	55	14	)	)	PUNCT
cana-4546	55	15	belongs	belong	VERB
cana-4546	55	16	to	to	ADP
cana-4546	55	17	the	the	DET
cana-4546	55	18	class	class	NOUN
cana-4546	55	19	𝑀𝜆,(∗)(𝜂	𝑀𝜆,(∗)(𝜂	PROPN
cana-4546	55	20	,	,	PUNCT
cana-4546	55	21	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	55	22	)	)	PUNCT
cana-4546	55	23	then	then	ADV
cana-4546	55	24	,	,	PUNCT
cana-4546	55	25	𝔞𝔭+1𝔟𝔭+1	𝔞𝔭+1𝔟𝔭+1	X
cana-4546	55	26	=	=	SYM
cana-4546	55	27	𝜂	𝜂	NOUN
cana-4546	55	28	2𝔭(1+𝜆(𝔭+1	2𝔭(1+𝜆(𝔭+1	NUM
cana-4546	55	29	)	)	PUNCT
cana-4546	55	30	)	)	PUNCT
cana-4546	55	31	(	(	PUNCT
cana-4546	55	32	3.1	3.1	NUM
cana-4546	55	33	)	)	PUNCT
cana-4546	55	34	communications	communication	NOUN
cana-4546	55	35	on	on	ADP
cana-4546	55	36	applied	apply	VERB
cana-4546	55	37	nonlinear	nonlinear	ADJ
cana-4546	55	38	analysis	analysis	NOUN
cana-4546	55	39	issn	issn	NOUN
cana-4546	55	40	:	:	PUNCT
cana-4546	55	41	1074	1074	NUM
cana-4546	55	42	-	-	PUNCT
cana-4546	55	43	133x	133x	NUM
cana-4546	55	44	vol	vol	NOUN
cana-4546	55	45	32	32	NUM
cana-4546	56	1	no	no	NOUN
cana-4546	56	2	.	.	PUNCT
cana-4546	57	1	9s	9s	NUM
cana-4546	57	2	(	(	PUNCT
cana-4546	57	3	2025	2025	NUM
cana-4546	57	4	)	)	PUNCT
cana-4546	57	5	2653	2653	NUM
cana-4546	57	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4546	57	7	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	X
cana-4546	57	8	=	=	SYM
cana-4546	57	9	𝜂2	𝜂2	PROPN
cana-4546	57	10	4𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	4𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	NUM
cana-4546	57	11	)	)	PUNCT
cana-4546	57	12	)	)	PUNCT
cana-4546	57	13	(	(	PUNCT
cana-4546	57	14	3.2	3.2	NUM
cana-4546	57	15	)	)	PUNCT
cana-4546	57	16	𝔞𝔭+3𝔟𝔭+3	𝔞𝔭+3𝔟𝔭+3	NOUN
cana-4546	57	17	=	=	SYM
cana-4546	57	18	𝜂(3𝜂2−𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	𝜂(3𝜂2−𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	NOUN
cana-4546	57	19	)	)	PUNCT
cana-4546	57	20	)	)	PUNCT
cana-4546	57	21	)	)	PUNCT
cana-4546	58	1	24𝔭(𝔭+1)(𝔭+2)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	24𝔭(𝔭+1)(𝔭+2)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	NUM
cana-4546	58	2	)	)	PUNCT
cana-4546	58	3	)	)	PUNCT
cana-4546	58	4	(	(	PUNCT
cana-4546	58	5	3.3	3.3	NUM
cana-4546	58	6	)	)	PUNCT
cana-4546	58	7	proof	proof	NOUN
cana-4546	58	8	.	.	PUNCT
cana-4546	59	1	let	let	VERB
cana-4546	59	2	ℑ(𝑧	ℑ(𝑧	PRON
cana-4546	59	3	)	)	PUNCT
cana-4546	59	4	=	=	SYM
cana-4546	59	5	𝑧𝔭	𝑧𝔭	ADP
cana-4546	59	6	+	+	NOUN
cana-4546	59	7	∑∞	∑∞	X
cana-4546	59	8	𝑘=1	𝑘=1	X
cana-4546	59	9	𝔞𝑘+𝔭	𝔞𝑘+𝔭	VERB
cana-4546	59	10	𝑧𝑘+𝔭	𝑧𝑘+𝔭	VERB
cana-4546	59	11	,	,	PUNCT
cana-4546	59	12	and	and	CCONJ
cana-4546	59	13	𝔤(𝑧	𝔤(𝑧	NUM
cana-4546	59	14	)	)	PUNCT
cana-4546	60	1	=	=	SYM
cana-4546	60	2	𝑧𝔭	𝑧𝔭	ADP
cana-4546	60	3	+	+	NOUN
cana-4546	60	4	∑∞	∑∞	X
cana-4546	60	5	𝑘=1	𝑘=1	ADJ
cana-4546	60	6	𝔟𝑘+𝔭	𝔟𝑘+𝔭	PROPN
cana-4546	60	7	𝑧𝑘+𝔭.	𝑧𝑘+𝔭.	NOUN
cana-4546	60	8	then	then	ADV
cana-4546	60	9	we	we	PRON
cana-4546	60	10	can	can	AUX
cana-4546	60	11	write	write	VERB
cana-4546	60	12	the	the	DET
cana-4546	60	13	following	follow	VERB
cana-4546	60	14	equalities	equality	NOUN
cana-4546	60	15	:	:	PUNCT
cana-4546	60	16	ℑ(𝑧	ℑ(𝑧	X
cana-4546	60	17	)	)	PUNCT
cana-4546	60	18	=	=	SYM
cana-4546	60	19	(	(	PUNCT
cana-4546	60	20	ℑ	ℑ	PROPN
cana-4546	60	21	∗	∗	NOUN
cana-4546	60	22	𝔤)(𝑧	𝔤)(𝑧	NUM
cana-4546	60	23	)	)	PUNCT
cana-4546	60	24	=	=	SYM
cana-4546	60	25	𝑧𝔭	𝑧𝔭	ADP
cana-4546	60	26	+	+	NOUN
cana-4546	60	27	∑∞	∑∞	X
cana-4546	60	28	𝑘=1	𝑘=1	X
cana-4546	60	29	𝔞𝑘+𝔭𝔟𝑘+𝔭	𝔞𝑘+𝔭𝔟𝑘+𝔭	NOUN
cana-4546	60	30	𝑧𝑘+𝔭	𝑧𝑘+𝔭	PROPN
cana-4546	60	31	⇒	⇒	NOUN
cana-4546	60	32	(	(	PUNCT
cana-4546	60	33	ℑ	ℑ	PROPN
cana-4546	60	34	∗	∗	NOUN
cana-4546	60	35	𝔤)′(𝑧	𝔤)′(𝑧	NOUN
cana-4546	60	36	)	)	PUNCT
cana-4546	60	37	=	=	PUNCT
cana-4546	61	1	𝔭𝑧𝑝−1	𝔭𝑧𝑝−1	PROPN
cana-4546	61	2	+	+	NUM
cana-4546	61	3	∑∞	∑∞	NOUN
cana-4546	62	1	𝑘=1	𝑘=1	X
cana-4546	62	2	(	(	PUNCT
cana-4546	62	3	𝑘	𝑘	X
cana-4546	62	4	+	+	NOUN
cana-4546	62	5	𝔭)𝔞𝑘+𝔭𝔟𝑘+𝔭	𝔭)𝔞𝑘+𝔭𝔟𝑘+𝔭	PROPN
cana-4546	62	6	𝑧𝑘+𝔭−1	𝑧𝑘+𝔭−1	ADJ
cana-4546	62	7	⇒	⇒	NOUN
cana-4546	62	8	(	(	PUNCT
cana-4546	62	9	ℑ	ℑ	PROPN
cana-4546	62	10	∗	∗	NOUN
cana-4546	62	11	𝔤)′′(𝑧	𝔤)′′(𝑧	X
cana-4546	62	12	)	)	PUNCT
cana-4546	63	1	=	=	PUNCT
cana-4546	63	2	𝔭(𝔭	𝔭(𝔭	NOUN
cana-4546	63	3	−	−	PROPN
cana-4546	63	4	1)𝑧𝑝−2	1)𝑧𝑝−2	NUM
cana-4546	63	5	+	+	NUM
cana-4546	63	6	∑∞	∑∞	NOUN
cana-4546	63	7	𝑘=1	𝑘=1	X
cana-4546	63	8	(	(	PUNCT
cana-4546	63	9	𝑘	𝑘	X
cana-4546	63	10	+	+	ADJ
cana-4546	63	11	𝔭)(𝑘	𝔭)(𝑘	NOUN
cana-4546	64	1	+	+	CCONJ
cana-4546	64	2	𝔭	𝔭	X
cana-4546	64	3	−	−	PROPN
cana-4546	64	4	1)𝔞𝑘+𝔭𝔟𝑘+𝔭	1)𝔞𝑘+𝔭𝔟𝑘+𝔭	NUM
cana-4546	64	5	𝑧𝑘+𝔭−2	𝑧𝑘+𝔭−2	NOUN
cana-4546	64	6	thus	thus	ADV
cana-4546	64	7	,	,	PUNCT
cana-4546	64	8	we	we	PRON
cana-4546	64	9	obtain	obtain	VERB
cana-4546	64	10	𝑧(ℑ	𝑧(ℑ	NOUN
cana-4546	64	11	∗	∗	NOUN
cana-4546	64	12	𝔤)′(𝑧	𝔤)′(𝑧	NUM
cana-4546	64	13	)	)	PUNCT
cana-4546	65	1	+	+	CCONJ
cana-4546	65	2	𝜆𝑧2(ℑ	𝜆𝑧2(ℑ	NOUN
cana-4546	65	3	∗	∗	NOUN
cana-4546	65	4	𝔤)′′(𝑧	𝔤)′′(𝑧	NUM
cana-4546	65	5	)	)	PUNCT
cana-4546	66	1	=	=	PUNCT
cana-4546	67	1	𝔭(1	𝔭(1	NOUN
cana-4546	67	2	−	−	NOUN
cana-4546	68	1	𝜆	𝜆	PRON
cana-4546	69	1	+	+	CCONJ
cana-4546	69	2	𝜆𝔭)𝑧𝔭	𝜆𝔭)𝑧𝔭	SYM
cana-4546	69	3	+	+	NUM
cana-4546	69	4	∑∞	∑∞	NOUN
cana-4546	69	5	𝑘=1	𝑘=1	X
cana-4546	69	6	(	(	PUNCT
cana-4546	69	7	𝑘	𝑘	X
cana-4546	69	8	+	+	ADJ
cana-4546	69	9	𝔭)(1	𝔭)(1	X
cana-4546	70	1	+	+	CCONJ
cana-4546	70	2	(	(	PUNCT
cana-4546	70	3	𝑘	𝑘	X
cana-4546	70	4	+	+	NOUN
cana-4546	70	5	𝔭	𝔭	NOUN
cana-4546	70	6	−	−	NUM
cana-4546	70	7	1)𝜆)𝔞𝑘+𝔭𝔟𝑘+𝔭	1)𝜆)𝔞𝑘+𝔭𝔟𝑘+𝔭	NUM
cana-4546	70	8	𝑧𝑘+𝔭	𝑧𝑘+𝔭	NOUN
cana-4546	70	9	and	and	CCONJ
cana-4546	70	10	𝑧(ℑ	𝑧(ℑ	PROPN
cana-4546	70	11	∗	∗	NOUN
cana-4546	70	12	𝔤)′(𝑧	𝔤)′(𝑧	PROPN
cana-4546	70	13	)	)	PUNCT
cana-4546	70	14	+	+	CCONJ
cana-4546	70	15	𝜆𝑧2(ℑ	𝜆𝑧2(ℑ	NOUN
cana-4546	70	16	∗	∗	NOUN
cana-4546	70	17	𝔤)′′(𝑧	𝔤)′′(𝑧	NUM
cana-4546	70	18	)	)	PUNCT
cana-4546	70	19	−	−	PROPN
cana-4546	71	1	(	(	PUNCT
cana-4546	71	2	ℑ	ℑ	PROPN
cana-4546	71	3	∗	∗	NOUN
cana-4546	71	4	𝔤)(𝑧	𝔤)(𝑧	NUM
cana-4546	71	5	)	)	PUNCT
cana-4546	71	6	=	=	PUNCT
cana-4546	71	7	(	(	PUNCT
cana-4546	71	8	𝔭	𝔭	X
cana-4546	71	9	−	−	NUM
cana-4546	71	10	1)(1	1)(1	NUM
cana-4546	71	11	+	+	CCONJ
cana-4546	71	12	𝜆𝔭)𝑧𝔭	𝜆𝔭)𝑧𝔭	PUNCT
cana-4546	71	13	+	+	NUM
cana-4546	71	14	∑∞	∑∞	NOUN
cana-4546	71	15	𝑘=1	𝑘=1	X
cana-4546	71	16	(	(	PUNCT
cana-4546	71	17	𝑘	𝑘	X
cana-4546	71	18	+	+	NOUN
cana-4546	71	19	𝔭	𝔭	ADP
cana-4546	71	20	−	−	NUM
cana-4546	71	21	1)(1	1)(1	NUM
cana-4546	71	22	+	+	CCONJ
cana-4546	71	23	(	(	PUNCT
cana-4546	71	24	𝑘	𝑘	X
cana-4546	71	25	+	+	NOUN
cana-4546	71	26	𝔭)𝜆)𝔞𝑘+𝔭𝔟𝑘+𝔭	𝔭)𝜆)𝔞𝑘+𝔭𝔟𝑘+𝔭	NOUN
cana-4546	71	27	𝑧𝑘+𝔭	𝑧𝑘+𝔭	VERB
cana-4546	71	28	if	if	SCONJ
cana-4546	71	29	𝐹	𝐹	PROPN
cana-4546	71	30	∈	∈	PROPN
cana-4546	71	31	𝑀𝜆(∗)(𝜂	𝑀𝜆(∗)(𝜂	PROPN
cana-4546	71	32	,	,	PUNCT
cana-4546	71	33	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	71	34	)	)	PUNCT
cana-4546	71	35	,	,	PUNCT
cana-4546	71	36	then	then	ADV
cana-4546	71	37	we	we	PRON
cana-4546	71	38	have	have	VERB
cana-4546	71	39	1	1	NUM
cana-4546	71	40	𝜂	𝜂	NOUN
cana-4546	71	41	[	[	PUNCT
cana-4546	71	42	𝑧(ℑ∗𝔤)′(𝑧)+𝜆𝑧2(ℑ∗𝔤)′′(𝑧)−(ℑ∗𝔤)(𝑧	𝑧(ℑ∗𝔤)′(𝑧)+𝜆𝑧2(ℑ∗𝔤)′′(𝑧)−(ℑ∗𝔤)(𝑧	NOUN
cana-4546	71	43	)	)	PUNCT
cana-4546	71	44	(	(	PUNCT
cana-4546	71	45	ℑ∗𝔤)(𝑧	ℑ∗𝔤)(𝑧	NOUN
cana-4546	71	46	)	)	PUNCT
cana-4546	71	47	]	]	PUNCT
cana-4546	72	1	=	=	SYM
cana-4546	72	2	𝜑𝑛,𝑚	𝜑𝑛,𝑚	X
cana-4546	72	3	−	−	PROPN
cana-4546	72	4	1	1	NUM
cana-4546	72	5	(	(	PUNCT
cana-4546	72	6	3.4	3.4	NUM
cana-4546	72	7	)	)	PUNCT
cana-4546	72	8	where	where	SCONJ
cana-4546	72	9	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NOUN
cana-4546	72	10	is	be	AUX
cana-4546	72	11	a	a	DET
cana-4546	72	12	modified	modify	VERB
cana-4546	72	13	sigmoid	sigmoid	NOUN
cana-4546	72	14	function	function	NOUN
cana-4546	72	15	given	give	VERB
cana-4546	72	16	by	by	ADP
cana-4546	72	17	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NOUN
cana-4546	72	18	=	=	SYM
cana-4546	72	19	1	1	NUM
cana-4546	72	20	+	+	NUM
cana-4546	72	21	1	1	NUM
cana-4546	72	22	2	2	NUM
cana-4546	72	23	𝑧	𝑧	DET
cana-4546	72	24	−	−	NUM
cana-4546	72	25	1	1	NUM
cana-4546	72	26	24	24	NUM
cana-4546	72	27	𝑧3	𝑧3	ADJ
cana-4546	72	28	+	+	CCONJ
cana-4546	72	29	1	1	NUM
cana-4546	72	30	240	240	NUM
cana-4546	72	31	𝑧5	𝑧5	PROPN
cana-4546	72	32	−	−	PROPN
cana-4546	72	33	17	17	NUM
cana-4546	72	34	40320	40320	NUM
cana-4546	72	35	𝑧7	𝑧7	NOUN
cana-4546	72	36	+	+	X
cana-4546	72	37	⋯	⋯	PROPN
cana-4546	72	38	(	(	PUNCT
cana-4546	72	39	3.5	3.5	NUM
cana-4546	72	40	)	)	PUNCT
cana-4546	72	41	in	in	ADP
cana-4546	72	42	view	view	NOUN
cana-4546	72	43	of	of	ADP
cana-4546	72	44	(	(	PUNCT
cana-4546	72	45	3.4	3.4	NUM
cana-4546	72	46	)	)	PUNCT
cana-4546	72	47	and	and	CCONJ
cana-4546	72	48	(	(	PUNCT
cana-4546	72	49	3.5	3.5	NUM
cana-4546	72	50	)	)	PUNCT
cana-4546	72	51	,	,	PUNCT
cana-4546	72	52	expanding	expand	VERB
cana-4546	72	53	in	in	ADP
cana-4546	72	54	series	series	NOUN
cana-4546	72	55	forms	form	NOUN
cana-4546	72	56	we	we	PRON
cana-4546	72	57	have	have	VERB
cana-4546	72	58	1	1	NUM
cana-4546	72	59	𝜂	𝜂	NOUN
cana-4546	72	60	[	[	X
cana-4546	72	61	(	(	PUNCT
cana-4546	72	62	𝔭	𝔭	NOUN
cana-4546	72	63	−	−	NUM
cana-4546	72	64	1)(1	1)(1	NUM
cana-4546	72	65	+	+	CCONJ
cana-4546	72	66	𝜆𝔭)𝑧𝔭	𝜆𝔭)𝑧𝔭	PUNCT
cana-4546	73	1	+	+	NUM
cana-4546	73	2	∑∞	∑∞	NOUN
cana-4546	73	3	𝑘=1	𝑘=1	X
cana-4546	73	4	(	(	PUNCT
cana-4546	73	5	𝑘	𝑘	X
cana-4546	73	6	+	+	NOUN
cana-4546	73	7	𝔭	𝔭	ADP
cana-4546	73	8	−	−	NUM
cana-4546	73	9	1)(1	1)(1	NUM
cana-4546	73	10	+	+	CCONJ
cana-4546	73	11	(	(	PUNCT
cana-4546	73	12	𝑘	𝑘	X
cana-4546	73	13	+	+	NOUN
cana-4546	73	14	𝔭)𝜆)𝔞𝑘+𝔭𝔟𝑘+𝔭	𝔭)𝜆)𝔞𝑘+𝔭𝔟𝑘+𝔭	NOUN
cana-4546	73	15	𝑧𝑘+𝔭	𝑧𝑘+𝔭	ADV
cana-4546	73	16	]	]	PUNCT
cana-4546	73	17	=	=	PUNCT
cana-4546	74	1	[	[	X
cana-4546	74	2	𝑧𝔭	𝑧𝔭	ADP
cana-4546	74	3	+	+	NOUN
cana-4546	74	4	∑∞	∑∞	X
cana-4546	74	5	𝑘=1	𝑘=1	X
cana-4546	74	6	𝔞𝑘+𝔭𝔟𝑘+𝔭	𝔞𝑘+𝔭𝔟𝑘+𝔭	NOUN
cana-4546	74	7	𝑧𝑘+𝔭	𝑧𝑘+𝔭	NOUN
cana-4546	74	8	]	]	X
cana-4546	74	9	[	[	PUNCT
cana-4546	74	10	1	1	NUM
cana-4546	74	11	2	2	NUM
cana-4546	74	12	𝑧	𝑧	DET
cana-4546	74	13	−	−	NUM
cana-4546	74	14	1	1	NUM
cana-4546	74	15	24	24	NUM
cana-4546	74	16	𝑧3	𝑧3	ADJ
cana-4546	74	17	+	+	CCONJ
cana-4546	74	18	1	1	NUM
cana-4546	74	19	240	240	NUM
cana-4546	74	20	𝑧5	𝑧5	PROPN
cana-4546	74	21	−	−	PROPN
cana-4546	74	22	17	17	NUM
cana-4546	74	23	40320	40320	NUM
cana-4546	74	24	𝑧7	𝑧7	NOUN
cana-4546	74	25	+	+	PROPN
cana-4546	74	26	⋯	⋯	ADP
cana-4546	74	27	]	]	PUNCT
cana-4546	74	28	(	(	PUNCT
cana-4546	74	29	3.6	3.6	NUM
cana-4546	74	30	)	)	PUNCT
cana-4546	74	31	comparing	compare	VERB
cana-4546	74	32	the	the	DET
cana-4546	74	33	coefficients	coefficient	NOUN
cana-4546	74	34	of	of	ADP
cana-4546	74	35	𝑧𝔭+1	𝑧𝔭+1	NOUN
cana-4546	74	36	,	,	PUNCT
cana-4546	74	37	𝑧𝔭+2	𝑧𝔭+2	X
cana-4546	74	38	and	and	CCONJ
cana-4546	74	39	𝑧𝔭+3	𝑧𝔭+3	VERB
cana-4546	74	40	in(3.6	in(3.6	PROPN
cana-4546	74	41	)	)	PUNCT
cana-4546	74	42	,	,	PUNCT
cana-4546	74	43	we	we	PRON
cana-4546	74	44	obtain	obtain	VERB
cana-4546	74	45	𝔞𝔭+1𝔟𝔭+1	𝔞𝔭+1𝔟𝔭+1	NOUN
cana-4546	74	46	=	=	SYM
cana-4546	74	47	𝜂	𝜂	NOUN
cana-4546	74	48	2𝔭(1+𝜆(𝔭+1	2𝔭(1+𝜆(𝔭+1	NUM
cana-4546	74	49	)	)	PUNCT
cana-4546	74	50	)	)	PUNCT
cana-4546	74	51	(	(	PUNCT
cana-4546	74	52	3.7	3.7	NUM
cana-4546	74	53	)	)	PUNCT
cana-4546	74	54	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	NOUN
cana-4546	74	55	=	=	SYM
cana-4546	74	56	𝜂2	𝜂2	PROPN
cana-4546	74	57	4𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	4𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	NUM
cana-4546	74	58	)	)	PUNCT
cana-4546	74	59	)	)	PUNCT
cana-4546	74	60	(	(	PUNCT
cana-4546	74	61	3.8	3.8	NUM
cana-4546	74	62	)	)	PUNCT
cana-4546	74	63	𝔞𝔭+3𝔟𝔭+3	𝔞𝔭+3𝔟𝔭+3	NOUN
cana-4546	74	64	=	=	SYM
cana-4546	74	65	𝜂(3𝜂2−𝑝(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	𝜂(3𝜂2−𝑝(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	PROPN
cana-4546	74	66	)	)	PUNCT
cana-4546	74	67	)	)	PUNCT
cana-4546	74	68	)	)	PUNCT
cana-4546	75	1	24𝑝(𝔭+1)(𝔭+2)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	24𝑝(𝔭+1)(𝔭+2)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	NUM
cana-4546	75	2	)	)	PUNCT
cana-4546	75	3	)	)	PUNCT
cana-4546	75	4	(	(	PUNCT
cana-4546	75	5	3.9	3.9	NUM
cana-4546	75	6	)	)	PUNCT
cana-4546	75	7	communications	communication	NOUN
cana-4546	75	8	on	on	ADP
cana-4546	75	9	applied	apply	VERB
cana-4546	75	10	nonlinear	nonlinear	ADJ
cana-4546	75	11	analysis	analysis	NOUN
cana-4546	75	12	issn	issn	NOUN
cana-4546	75	13	:	:	PUNCT
cana-4546	75	14	1074	1074	NUM
cana-4546	75	15	-	-	PUNCT
cana-4546	75	16	133x	133x	NUM
cana-4546	75	17	vol	vol	NOUN
cana-4546	75	18	32	32	NUM
cana-4546	75	19	no	no	NOUN
cana-4546	75	20	.	.	PUNCT
cana-4546	76	1	9s	9s	NUM
cana-4546	76	2	(	(	PUNCT
cana-4546	76	3	2025	2025	NUM
cana-4546	76	4	)	)	PUNCT
cana-4546	76	5	2654	2654	NUM
cana-4546	76	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4546	76	7	corollary	corollary	ADJ
cana-4546	76	8	3.2	3.2	NUM
cana-4546	76	9	for	for	ADP
cana-4546	76	10	coefficient	coefficient	NOUN
cana-4546	76	11	𝔞𝔭+1𝔟𝔭+1	𝔞𝔭+1𝔟𝔭+1	NOUN
cana-4546	76	12	,	,	PUNCT
cana-4546	76	13	|𝔞𝔭+1𝔟𝔭+1|	|𝔞𝔭+1𝔟𝔭+1|	PROPN
cana-4546	76	14	=	=	SYM
cana-4546	76	15	|𝜂|	|𝜂|	NOUN
cana-4546	76	16	2𝔭(1+𝜆(𝔭+1	2𝔭(1+𝜆(𝔭+1	NUM
cana-4546	76	17	)	)	PUNCT
cana-4546	76	18	)	)	PUNCT
cana-4546	76	19	is	be	AUX
cana-4546	76	20	written	write	VERB
cana-4546	76	21	and	and	CCONJ
cana-4546	76	22	since	since	SCONJ
cana-4546	76	23	𝜑(𝜆	𝜑(𝜆	PROPN
cana-4546	76	24	)	)	PUNCT
cana-4546	76	25	=	=	SYM
cana-4546	76	26	1	1	NUM
cana-4546	76	27	(	(	PUNCT
cana-4546	76	28	1+𝜆(𝔭+1	1+𝜆(𝔭+1	NUM
cana-4546	76	29	)	)	PUNCT
cana-4546	76	30	)	)	PUNCT
cana-4546	76	31	,	,	PUNCT
cana-4546	77	1	𝜑′(𝜆	𝜑′(𝜆	PUNCT
cana-4546	77	2	)	)	PUNCT
cana-4546	77	3	<	<	X
cana-4546	77	4	0	0	PUNCT
cana-4546	77	5	in	in	ADP
cana-4546	77	6	the	the	DET
cana-4546	77	7	interval	interval	NOUN
cana-4546	77	8	0	0	NUM
cana-4546	77	9	≤	≤	NUM
cana-4546	77	10	𝜆	𝜆	DET
cana-4546	77	11	≤	≤	NUM
cana-4546	77	12	1	1	NUM
cana-4546	77	13	and	and	CCONJ
cana-4546	77	14	𝜑(𝜆	𝜑(𝜆	PROPN
cana-4546	77	15	)	)	PUNCT
cana-4546	77	16	is	be	AUX
cana-4546	77	17	decreasing	decrease	VERB
cana-4546	77	18	,	,	PUNCT
cana-4546	77	19	it	it	PRON
cana-4546	77	20	will	will	AUX
cana-4546	77	21	be	be	AUX
cana-4546	77	22	|𝜂|	|𝜂|	NOUN
cana-4546	77	23	2𝔭(𝔭+2	2𝔭(𝔭+2	NUM
cana-4546	77	24	)	)	PUNCT
cana-4546	77	25	≤	≤	NOUN
cana-4546	78	1	|𝔞𝔭+1𝔟𝔭+1|	|𝔞𝔭+1𝔟𝔭+1|	PROPN
cana-4546	78	2	≤	≤	NUM
cana-4546	78	3	|𝜂|	|𝜂|	NUM
cana-4546	78	4	2𝔭	2𝔭	PROPN
cana-4546	78	5	(	(	PUNCT
cana-4546	78	6	3.10	3.10	NUM
cana-4546	78	7	)	)	PUNCT
cana-4546	78	8	for	for	ADP
cana-4546	78	9	1	1	NUM
cana-4546	78	10	2	2	NUM
cana-4546	78	11	≤	≤	NUM
cana-4546	78	12	1	1	NUM
cana-4546	78	13	(	(	PUNCT
cana-4546	78	14	1+𝜆(𝔭+1	1+𝜆(𝔭+1	NUM
cana-4546	78	15	)	)	PUNCT
cana-4546	78	16	)	)	PUNCT
cana-4546	78	17	≤	≤	NUM
cana-4546	79	1	1	1	NUM
cana-4546	79	2	.	.	PUNCT
cana-4546	79	3	similarly	similarly	ADV
cana-4546	79	4	,	,	PUNCT
cana-4546	79	5	since	since	SCONJ
cana-4546	79	6	the	the	DET
cana-4546	79	7	coefficients	coefficient	NOUN
cana-4546	79	8	𝔞𝔭+1𝔟𝔭+1	𝔞𝔭+1𝔟𝔭+1	ADV
cana-4546	79	9	,	,	PUNCT
cana-4546	79	10	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	NOUN
cana-4546	79	11	and	and	CCONJ
cana-4546	79	12	𝔞𝔭+3𝔟𝔭+3	𝔞𝔭+3𝔟𝔭+3	NOUN
cana-4546	79	13	depend	depend	VERB
cana-4546	79	14	on	on	ADP
cana-4546	79	15	𝜆	𝜆	PRON
cana-4546	79	16	and	and	CCONJ
cana-4546	79	17	are	be	AUX
cana-4546	79	18	decreasing	decrease	VERB
cana-4546	79	19	with	with	ADP
cana-4546	79	20	respect	respect	NOUN
cana-4546	79	21	to	to	ADP
cana-4546	79	22	𝜆	𝜆	PRON
cana-4546	79	23	,	,	PUNCT
cana-4546	79	24	the	the	DET
cana-4546	79	25	following	follow	VERB
cana-4546	79	26	inequalities	inequality	NOUN
cana-4546	79	27	can	can	AUX
cana-4546	79	28	be	be	AUX
cana-4546	79	29	written	write	VERB
cana-4546	79	30	easily	easily	ADV
cana-4546	79	31	:	:	PUNCT
cana-4546	79	32	|𝜂2|	|𝜂2|	NOUN
cana-4546	79	33	4(𝔭+1)(𝔭+2)(𝔭+3	4(𝔭+1)(𝔭+2)(𝔭+3	NUM
cana-4546	79	34	)	)	PUNCT
cana-4546	79	35	≤	≤	NUM
cana-4546	80	1	|𝔞𝔭+2𝔟𝔭+2|	|𝔞𝔭+2𝔟𝔭+2|	NOUN
cana-4546	80	2	≤	≤	ADJ
cana-4546	80	3	|𝜂|2	|𝜂|2	PROPN
cana-4546	80	4	4𝑝(𝔭+1	4𝑝(𝔭+1	NOUN
cana-4546	80	5	)	)	PUNCT
cana-4546	80	6	(	(	PUNCT
cana-4546	80	7	3.11	3.11	NUM
cana-4546	80	8	)	)	PUNCT
cana-4546	80	9	|(3𝜂3−𝑝(𝔭+1)(𝔭+2)(𝔭+3)𝜂)|	|(3𝜂3−𝑝(𝔭+1)(𝔭+2)(𝔭+3)𝜂)|	ADJ
cana-4546	80	10	24(𝔭+1)(𝔭+2)2(𝔭+3)(𝔭+4	24(𝔭+1)(𝔭+2)2(𝔭+3)(𝔭+4	NOUN
cana-4546	80	11	)	)	PUNCT
cana-4546	80	12	≤	≤	NUM
cana-4546	81	1	|𝔞𝔭+3𝔟𝔭+3|	|𝔞𝔭+3𝔟𝔭+3|	NOUN
cana-4546	81	2	≤	≤	NUM
cana-4546	81	3	|(𝜂3−𝑝(𝔭+1)𝜂)|	|(𝜂3−𝑝(𝔭+1)𝜂)|	NUM
cana-4546	81	4	24𝑝(𝔭+1)(𝔭+2	24𝑝(𝔭+1)(𝔭+2	NUM
cana-4546	81	5	)	)	PUNCT
cana-4546	81	6	(	(	PUNCT
cana-4546	81	7	3.12	3.12	NUM
cana-4546	81	8	)	)	PUNCT
cana-4546	81	9	4	4	NUM
cana-4546	81	10	.	.	PUNCT
cana-4546	82	1	some	some	DET
cana-4546	82	2	results	result	NOUN
cana-4546	82	3	connected	connect	VERB
cana-4546	82	4	with	with	ADP
cana-4546	82	5	the	the	DET
cana-4546	82	6	fekete	fekete	NOUN
cana-4546	82	7	-	-	PUNCT
cana-4546	82	8	szegö	szegö	NOUN
cana-4546	82	9	inequality	inequality	NOUN
cana-4546	82	10	and	and	CCONJ
cana-4546	82	11	hankel	hankel	NOUN
cana-4546	82	12	coefficient	coefficient	NOUN
cana-4546	82	13	for	for	ADP
cana-4546	82	14	the	the	DET
cana-4546	82	15	class	class	NOUN
cana-4546	82	16	of	of	ADP
cana-4546	82	17	𝑴𝝀,(∗)(𝜼	𝑴𝝀,(∗)(𝜼	NOUN
cana-4546	82	18	,	,	PUNCT
cana-4546	82	19	𝝋𝒏,𝒎	𝝋𝒏,𝒎	ADP
cana-4546	82	20	)	)	PUNCT
cana-4546	82	21	the	the	DET
cana-4546	82	22	fekete	fekete	PROPN
cana-4546	82	23	-	-	PUNCT
cana-4546	82	24	szegö	szegö	ADJ
cana-4546	82	25	problem	problem	NOUN
cana-4546	82	26	may	may	AUX
cana-4546	82	27	be	be	AUX
cana-4546	82	28	considered	consider	VERB
cana-4546	82	29	one	one	NUM
cana-4546	82	30	of	of	ADP
cana-4546	82	31	the	the	DET
cana-4546	82	32	most	most	ADV
cana-4546	82	33	important	important	ADJ
cana-4546	82	34	results	result	NOUN
cana-4546	82	35	about	about	ADP
cana-4546	82	36	univalent	univalent	ADJ
cana-4546	82	37	functions	function	NOUN
cana-4546	82	38	,	,	PUNCT
cana-4546	82	39	which	which	PRON
cana-4546	82	40	is	be	AUX
cana-4546	82	41	related	relate	VERB
cana-4546	82	42	to	to	ADP
cana-4546	82	43	coefficients	coefficient	NOUN
cana-4546	82	44	an	an	PRON
cana-4546	82	45	of	of	ADP
cana-4546	82	46	a	a	DET
cana-4546	82	47	function	function	NOUN
cana-4546	82	48	’s	’s	PART
cana-4546	82	49	taylor	taylor	PROPN
cana-4546	82	50	series	series	PROPN
cana-4546	82	51	and	and	CCONJ
cana-4546	82	52	was	be	AUX
cana-4546	82	53	introduced	introduce	VERB
cana-4546	82	54	by	by	ADP
cana-4546	82	55	fekete	fekete	NOUN
cana-4546	82	56	-	-	PUNCT
cana-4546	82	57	szegö	szegö	NOUN
cana-4546	83	1	[	[	X
cana-4546	83	2	1	1	NUM
cana-4546	83	3	]	]	PUNCT
cana-4546	83	4	.	.	PUNCT
cana-4546	84	1	the	the	DET
cana-4546	84	2	problem	problem	NOUN
cana-4546	84	3	of	of	ADP
cana-4546	84	4	maximizing	maximize	VERB
cana-4546	84	5	the	the	DET
cana-4546	84	6	absolute	absolute	ADJ
cana-4546	84	7	value	value	NOUN
cana-4546	84	8	of	of	ADP
cana-4546	84	9	functional	functional	ADJ
cana-4546	84	10	𝑎3	𝑎3	PROPN
cana-4546	84	11	−	−	PROPN
cana-4546	84	12	𝜇𝑎2	𝜇𝑎2	NOUN
cana-4546	84	13	2	2	NUM
cana-4546	84	14	is	be	AUX
cana-4546	84	15	called	call	VERB
cana-4546	84	16	the	the	DET
cana-4546	84	17	fekete	fekete	PROPN
cana-4546	84	18	-	-	PUNCT
cana-4546	84	19	szegö	szegö	ADJ
cana-4546	84	20	problem	problem	NOUN
cana-4546	84	21	.	.	PUNCT
cana-4546	85	1	this	this	DET
cana-4546	85	2	result	result	NOUN
cana-4546	85	3	is	be	AUX
cana-4546	85	4	sharp	sharp	ADJ
cana-4546	85	5	and	and	CCONJ
cana-4546	85	6	is	be	AUX
cana-4546	85	7	studied	study	VERB
cana-4546	85	8	thoroughly	thoroughly	ADV
cana-4546	85	9	by	by	ADP
cana-4546	85	10	many	many	ADJ
cana-4546	85	11	researchers	researcher	NOUN
cana-4546	85	12	.	.	PUNCT
cana-4546	86	1	the	the	DET
cana-4546	86	2	equality	equality	NOUN
cana-4546	86	3	holds	hold	VERB
cana-4546	86	4	true	true	ADJ
cana-4546	86	5	for	for	ADP
cana-4546	86	6	the	the	DET
cana-4546	86	7	koebe	koebe	NOUN
cana-4546	86	8	function	function	NOUN
cana-4546	86	9	.	.	PUNCT
cana-4546	87	1	in	in	ADP
cana-4546	87	2	1969	1969	NUM
cana-4546	87	3	,	,	PUNCT
cana-4546	87	4	keogh	keogh	PROPN
cana-4546	87	5	and	and	CCONJ
cana-4546	87	6	merkes	merke	NOUN
cana-4546	88	1	[	[	X
cana-4546	88	2	2	2	NUM
cana-4546	88	3	]	]	PUNCT
cana-4546	88	4	obtained	obtain	VERB
cana-4546	88	5	the	the	DET
cana-4546	88	6	sharp	sharp	ADJ
cana-4546	88	7	upper	upper	ADJ
cana-4546	88	8	bound	bind	VERB
cana-4546	88	9	of	of	ADP
cana-4546	88	10	the	the	DET
cana-4546	88	11	fekete	fekete	PROPN
cana-4546	88	12	-	-	PUNCT
cana-4546	88	13	szegö	szegö	ADJ
cana-4546	88	14	functional	functional	NOUN
cana-4546	88	15	|𝑎3	|𝑎3	VERB
cana-4546	88	16	−	−	PROPN
cana-4546	88	17	𝜇𝑎2	𝜇𝑎2	NOUN
cana-4546	88	18	2|	2|	NUM
cana-4546	88	19	for	for	ADP
cana-4546	88	20	some	some	DET
cana-4546	88	21	subclasses	subclass	NOUN
cana-4546	88	22	of	of	ADP
cana-4546	88	23	univalent	univalent	ADJ
cana-4546	88	24	function	function	NOUN
cana-4546	88	25	.	.	PUNCT
cana-4546	89	1	recently	recently	ADV
cana-4546	89	2	,	,	PUNCT
cana-4546	89	3	murugusundarmoorthy	murugusundarmoorthy	ADJ
cana-4546	89	4	and	and	CCONJ
cana-4546	89	5	janani	janani	NOUN
cana-4546	90	1	[	[	X
cana-4546	90	2	3	3	NUM
cana-4546	90	3	]	]	PUNCT
cana-4546	90	4	,	,	PUNCT
cana-4546	90	5	olantunji	olantunji	ADV
cana-4546	90	6	et	et	PROPN
cana-4546	90	7	al	al	PROPN
cana-4546	90	8	.	.	PUNCT
cana-4546	91	1	[	[	X
cana-4546	91	2	5	5	NUM
cana-4546	91	3	]	]	PUNCT
cana-4546	91	4	,	,	PUNCT
cana-4546	91	5	olantunji	olantunji	ADV
cana-4546	91	6	[	[	X
cana-4546	91	7	4	4	NUM
cana-4546	91	8	]	]	PUNCT
cana-4546	91	9	,	,	PUNCT
cana-4546	91	10	and	and	CCONJ
cana-4546	91	11	orhan	orhan	PROPN
cana-4546	91	12	and	and	CCONJ
cana-4546	91	13	çağlar	çağlar	ADJ
cana-4546	91	14	[	[	X
cana-4546	91	15	7]have	7]have	NUM
cana-4546	91	16	studied	study	VERB
cana-4546	91	17	sigmoid	sigmoid	NOUN
cana-4546	91	18	function	function	NOUN
cana-4546	91	19	for	for	ADP
cana-4546	91	20	various	various	ADJ
cana-4546	91	21	classes	class	NOUN
cana-4546	91	22	of	of	ADP
cana-4546	91	23	analytic	analytic	ADJ
cana-4546	91	24	and	and	CCONJ
cana-4546	91	25	univalent	univalent	ADJ
cana-4546	91	26	functions	function	NOUN
cana-4546	91	27	.	.	PUNCT
cana-4546	92	1	in	in	ADP
cana-4546	92	2	this	this	DET
cana-4546	92	3	section	section	NOUN
cana-4546	92	4	,	,	PUNCT
cana-4546	92	5	we	we	PRON
cana-4546	92	6	first	first	ADV
cana-4546	92	7	prove	prove	VERB
cana-4546	92	8	the	the	DET
cana-4546	92	9	following	follow	VERB
cana-4546	92	10	fekete	fekete	NOUN
cana-4546	92	11	-	-	PUNCT
cana-4546	92	12	szegö	szegö	PROPN
cana-4546	92	13	result	result	NOUN
cana-4546	92	14	for	for	ADP
cana-4546	92	15	the	the	DET
cana-4546	92	16	function	function	NOUN
cana-4546	92	17	in	in	ADP
cana-4546	92	18	the	the	DET
cana-4546	92	19	classes	class	NOUN
cana-4546	92	20	𝑀𝜆,(∗)(𝜂	𝑀𝜆,(∗)(𝜂	PROPN
cana-4546	92	21	,	,	PUNCT
cana-4546	92	22	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	92	23	)	)	PUNCT
cana-4546	92	24	with	with	ADP
cana-4546	92	25	the	the	DET
cana-4546	92	26	values	value	NOUN
cana-4546	92	27	of	of	ADP
cana-4546	92	28	𝔞𝔭+1𝔟𝔭+1	𝔞𝔭+1𝔟𝔭+1	NOUN
cana-4546	92	29	and	and	CCONJ
cana-4546	92	30	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	NOUN
cana-4546	92	31	.	.	PUNCT
cana-4546	93	1	theorem	theorem	VERB
cana-4546	93	2	4.1	4.1	NUM
cana-4546	93	3	if	if	SCONJ
cana-4546	93	4	𝐹(𝑧	𝐹(𝑧	ADP
cana-4546	93	5	)	)	PUNCT
cana-4546	93	6	∈	∈	NOUN
cana-4546	94	1	𝒜𝒫	𝒜𝒫	ADV
cana-4546	94	2	given	give	VERB
cana-4546	94	3	by	by	ADP
cana-4546	94	4	(	(	PUNCT
cana-4546	94	5	1.1	1.1	NUM
cana-4546	94	6	)	)	PUNCT
cana-4546	94	7	belongs	belong	VERB
cana-4546	94	8	to	to	ADP
cana-4546	94	9	the	the	DET
cana-4546	94	10	class	class	NOUN
cana-4546	94	11	𝑀𝜆,(∗)(𝜂	𝑀𝜆,(∗)(𝜂	PROPN
cana-4546	94	12	,	,	PUNCT
cana-4546	94	13	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	94	14	)	)	PUNCT
cana-4546	94	15	then	then	ADV
cana-4546	94	16	,	,	PUNCT
cana-4546	94	17	|𝔞𝔭+2𝔟𝔭+2	|𝔞𝔭+2𝔟𝔭+2	X
cana-4546	94	18	−	−	NOUN
cana-4546	94	19	𝜇(𝔞𝔭+1𝔟𝔭+1	𝜇(𝔞𝔭+1𝔟𝔭+1	NOUN
cana-4546	94	20	)	)	PUNCT
cana-4546	94	21	2	2	NUM
cana-4546	95	1	|	|	NOUN
cana-4546	95	2	=	=	PUNCT
cana-4546	95	3	|𝜂|2	|𝜂|2	PROPN
cana-4546	95	4	4𝔭(𝔭+1	4𝔭(𝔭+1	NUM
cana-4546	95	5	)	)	PUNCT
cana-4546	95	6	(	(	PUNCT
cana-4546	95	7	1	1	NUM
cana-4546	95	8	+	+	NUM
cana-4546	95	9	|𝜇|	|𝜇|	X
cana-4546	95	10	(	(	PUNCT
cana-4546	95	11	𝔭+1	𝔭+1	NUM
cana-4546	95	12	)	)	PUNCT
cana-4546	95	13	𝔭	𝔭	NOUN
cana-4546	95	14	)	)	PUNCT
cana-4546	95	15	(	(	PUNCT
cana-4546	95	16	4.1	4.1	NUM
cana-4546	95	17	)	)	PUNCT
cana-4546	95	18	proof	proof	NOUN
cana-4546	95	19	.	.	PUNCT
cana-4546	96	1	if	if	SCONJ
cana-4546	96	2	the	the	DET
cana-4546	96	3	values	value	NOUN
cana-4546	96	4	of	of	ADP
cana-4546	96	5	𝔞𝔭+1𝔟𝔭+1	𝔞𝔭+1𝔟𝔭+1	NOUN
cana-4546	96	6	and	and	CCONJ
cana-4546	96	7	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	NOUN
cana-4546	96	8	determined	determine	VERB
cana-4546	96	9	by	by	ADP
cana-4546	96	10	(	(	PUNCT
cana-4546	96	11	3.7	3.7	NUM
cana-4546	96	12	)	)	PUNCT
cana-4546	96	13	and	and	CCONJ
cana-4546	96	14	(	(	PUNCT
cana-4546	96	15	3.8	3.8	NUM
cana-4546	96	16	)	)	PUNCT
cana-4546	96	17	are	be	AUX
cana-4546	96	18	written	write	VERB
cana-4546	96	19	instead	instead	ADV
cana-4546	96	20	of	of	ADP
cana-4546	96	21	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	NOUN
cana-4546	96	22	−	−	PROPN
cana-4546	96	23	𝜇(𝔞𝔭+1𝔟𝔭+1	𝜇(𝔞𝔭+1𝔟𝔭+1	NOUN
cana-4546	96	24	)	)	PUNCT
cana-4546	96	25	2	2	NUM
cana-4546	96	26	,	,	PUNCT
cana-4546	96	27	we	we	PRON
cana-4546	96	28	get	get	VERB
cana-4546	96	29	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	VERB
cana-4546	96	30	−	−	ADP
cana-4546	96	31	𝜇(𝔞𝔭+1𝔟𝔭+1	𝜇(𝔞𝔭+1𝔟𝔭+1	NOUN
cana-4546	96	32	)	)	PUNCT
cana-4546	96	33	2	2	NUM
cana-4546	96	34	=	=	SYM
cana-4546	96	35	𝜂2	𝜂2	X
cana-4546	96	36	4𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	4𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	NUM
cana-4546	96	37	)	)	PUNCT
cana-4546	96	38	)	)	PUNCT
cana-4546	97	1	−	−	PROPN
cana-4546	97	2	𝜇	𝜇	ADP
cana-4546	97	3	(	(	PUNCT
cana-4546	97	4	𝜂	𝜂	NOUN
cana-4546	97	5	2𝔭(1+𝜆(𝔭+1	2𝔭(1+𝜆(𝔭+1	NUM
cana-4546	97	6	)	)	PUNCT
cana-4546	97	7	)	)	PUNCT
cana-4546	97	8	)	)	PUNCT
cana-4546	97	9	2	2	NUM
cana-4546	97	10	=	=	SYM
cana-4546	97	11	𝜂2	𝜂2	X
cana-4546	97	12	4𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	4𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	NUM
cana-4546	97	13	)	)	PUNCT
cana-4546	97	14	)	)	PUNCT
cana-4546	97	15	−	−	ADP
cana-4546	98	1	𝜇	𝜇	X
cana-4546	98	2	(	(	PUNCT
cana-4546	98	3	𝜂)2	𝜂)2	NOUN
cana-4546	98	4	4𝑝2(1+𝜆(𝔭+1))2	4𝑝2(1+𝜆(𝔭+1))2	NUM
cana-4546	98	5	.	.	PUNCT
cana-4546	99	1	communications	communication	NOUN
cana-4546	99	2	on	on	ADP
cana-4546	99	3	applied	apply	VERB
cana-4546	99	4	nonlinear	nonlinear	ADJ
cana-4546	99	5	analysis	analysis	NOUN
cana-4546	99	6	issn	issn	NOUN
cana-4546	99	7	:	:	PUNCT
cana-4546	99	8	1074	1074	NUM
cana-4546	99	9	-	-	PUNCT
cana-4546	99	10	133x	133x	NUM
cana-4546	99	11	vol	vol	NOUN
cana-4546	99	12	32	32	NUM
cana-4546	99	13	no	no	NOUN
cana-4546	99	14	.	.	PUNCT
cana-4546	100	1	9s	9s	NUM
cana-4546	100	2	(	(	PUNCT
cana-4546	100	3	2025	2025	NUM
cana-4546	100	4	)	)	PUNCT
cana-4546	100	5	2655	2655	NUM
cana-4546	101	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4546	101	2	taking	take	VERB
cana-4546	101	3	absolute	absolute	ADJ
cana-4546	101	4	value	value	NOUN
cana-4546	101	5	on	on	ADP
cana-4546	101	6	both	both	DET
cana-4546	101	7	sides	side	NOUN
cana-4546	101	8	of	of	ADP
cana-4546	101	9	the	the	DET
cana-4546	101	10	above	above	ADJ
cana-4546	101	11	equation	equation	NOUN
cana-4546	101	12	and	and	CCONJ
cana-4546	101	13	applying	apply	VERB
cana-4546	101	14	triangle	triangle	NOUN
cana-4546	101	15	inequality	inequality	NOUN
cana-4546	101	16	,	,	PUNCT
cana-4546	101	17	we	we	PRON
cana-4546	101	18	get	get	VERB
cana-4546	101	19	|𝔞𝔭+2𝔟𝔭+2	|𝔞𝔭+2𝔟𝔭+2	VERB
cana-4546	101	20	−	−	NOUN
cana-4546	101	21	𝜇(𝔞𝔭+1𝔟𝔭+1	𝜇(𝔞𝔭+1𝔟𝔭+1	NOUN
cana-4546	101	22	)	)	PUNCT
cana-4546	101	23	2	2	NUM
cana-4546	102	1	|	|	ADV
cana-4546	102	2	≤	≤	X
cana-4546	102	3	|𝜂|2	|𝜂|2	PROPN
cana-4546	102	4	4𝑝(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	4𝑝(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	NUM
cana-4546	102	5	)	)	PUNCT
cana-4546	102	6	)	)	PUNCT
cana-4546	103	1	+	+	CCONJ
cana-4546	103	2	|𝜇|	|𝜇|	NOUN
cana-4546	103	3	|(𝜂)|2	|(𝜂)|2	ADJ
cana-4546	103	4	4𝔭2(1+𝜆(𝔭+1))2	4𝔭2(1+𝜆(𝔭+1))2	NOUN
cana-4546	103	5	.	.	PUNCT
cana-4546	104	1	here	here	ADV
cana-4546	104	2	𝜁1	𝜁1	PROPN
cana-4546	104	3	=	=	SYM
cana-4546	104	4	1	1	NUM
cana-4546	104	5	(	(	PUNCT
cana-4546	104	6	1+𝜆(𝔭+1))(1+𝜆(𝔭+2	1+𝜆(𝔭+1))(1+𝜆(𝔭+2	NUM
cana-4546	104	7	)	)	PUNCT
cana-4546	104	8	)	)	PUNCT
cana-4546	104	9	and	and	CCONJ
cana-4546	104	10	𝜁2	𝜁2	NOUN
cana-4546	104	11	=	=	SYM
cana-4546	104	12	1	1	NUM
cana-4546	104	13	(	(	PUNCT
cana-4546	104	14	1+𝜆(𝔭+1))2	1+𝜆(𝔭+1))2	NOUN
cana-4546	104	15	are	be	AUX
cana-4546	104	16	taken	take	VERB
cana-4546	104	17	and	and	CCONJ
cana-4546	104	18	these	these	DET
cana-4546	104	19	functions	function	NOUN
cana-4546	104	20	depending	depend	VERB
cana-4546	104	21	on	on	ADP
cana-4546	104	22	𝜆	𝜆	NUM
cana-4546	104	23	are	be	AUX
cana-4546	104	24	considered	consider	VERB
cana-4546	104	25	to	to	PART
cana-4546	104	26	be	be	AUX
cana-4546	104	27	decreasing	decrease	VERB
cana-4546	104	28	in	in	ADP
cana-4546	104	29	the	the	DET
cana-4546	104	30	interval	interval	NOUN
cana-4546	104	31	0	0	NUM
cana-4546	104	32	≤	≤	NUM
cana-4546	104	33	𝜆	𝜆	DET
cana-4546	104	34	≤	≤	NUM
cana-4546	104	35	1	1	NUM
cana-4546	104	36	,	,	PUNCT
cana-4546	104	37	since	since	SCONJ
cana-4546	104	38	max	max	PROPN
cana-4546	104	39	0≤𝜆≤1	0≤𝜆≤1	PROPN
cana-4546	104	40	1	1	NUM
cana-4546	104	41	(	(	PUNCT
cana-4546	104	42	1+𝜆(𝔭+1))(1+𝜆(𝔭+2	1+𝜆(𝔭+1))(1+𝜆(𝔭+2	NUM
cana-4546	104	43	)	)	PUNCT
cana-4546	104	44	)	)	PUNCT
cana-4546	105	1	=	=	SYM
cana-4546	105	2	1	1	NUM
cana-4546	105	3	and	and	CCONJ
cana-4546	105	4	max	max	PROPN
cana-4546	105	5	0≤𝜆≤1	0≤𝜆≤1	NOUN
cana-4546	105	6	1	1	NUM
cana-4546	105	7	(	(	PUNCT
cana-4546	105	8	1+𝜆(𝔭+1))2	1+𝜆(𝔭+1))2	NUM
cana-4546	105	9	=	=	SYM
cana-4546	105	10	1	1	NUM
cana-4546	105	11	we	we	PRON
cana-4546	105	12	get	get	VERB
cana-4546	105	13	|𝔞𝔭+2𝔟𝔭+2	|𝔞𝔭+2𝔟𝔭+2	VERB
cana-4546	105	14	−	−	NOUN
cana-4546	105	15	𝜇(𝔞𝔭+1𝔟𝔭+1	𝜇(𝔞𝔭+1𝔟𝔭+1	NOUN
cana-4546	105	16	)	)	PUNCT
cana-4546	105	17	2	2	NUM
cana-4546	105	18	|	|	ADV
cana-4546	105	19	≤	≤	X
cana-4546	105	20	|𝜂|2	|𝜂|2	PROPN
cana-4546	105	21	4𝔭(𝔭+1	4𝔭(𝔭+1	NUM
cana-4546	105	22	)	)	PUNCT
cana-4546	106	1	+	+	CCONJ
cana-4546	106	2	|𝜇|	|𝜇|	NUM
cana-4546	106	3	|𝜂|2	|𝜂|2	PROPN
cana-4546	106	4	4𝑝2	4𝑝2	NUM
cana-4546	106	5	.	.	PUNCT
cana-4546	107	1	thus	thus	ADV
cana-4546	107	2	we	we	PRON
cana-4546	107	3	obtain	obtain	VERB
cana-4546	107	4	|𝔞𝔭+2𝔟𝔭+2	|𝔞𝔭+2𝔟𝔭+2	NOUN
cana-4546	107	5	−	−	NOUN
cana-4546	107	6	𝜇(𝔞𝔭+1𝔟𝔭+1	𝜇(𝔞𝔭+1𝔟𝔭+1	NOUN
cana-4546	107	7	)	)	PUNCT
cana-4546	107	8	2	2	NUM
cana-4546	108	1	|	|	ADV
cana-4546	108	2	≤	≤	X
cana-4546	108	3	|𝜂|2	|𝜂|2	PROPN
cana-4546	108	4	4𝔭(𝔭+1	4𝔭(𝔭+1	NUM
cana-4546	108	5	)	)	PUNCT
cana-4546	108	6	(	(	PUNCT
cana-4546	108	7	1	1	NUM
cana-4546	108	8	+	+	NUM
cana-4546	108	9	|𝜇|	|𝜇|	X
cana-4546	108	10	(	(	PUNCT
cana-4546	108	11	𝔭+1	𝔭+1	NUM
cana-4546	108	12	)	)	PUNCT
cana-4546	108	13	𝑝	𝑝	NOUN
cana-4546	108	14	)	)	PUNCT
cana-4546	108	15	hence	hence	ADV
cana-4546	108	16	,	,	PUNCT
cana-4546	108	17	we	we	PRON
cana-4546	108	18	have	have	AUX
cana-4546	108	19	reached	reach	VERB
cana-4546	108	20	the	the	DET
cana-4546	108	21	desired	desire	VERB
cana-4546	108	22	assertion	assertion	NOUN
cana-4546	108	23	of	of	ADP
cana-4546	108	24	the	the	DET
cana-4546	108	25	theorem(4.1	theorem(4.1	NOUN
cana-4546	108	26	)	)	PUNCT
cana-4546	108	27	,	,	PUNCT
cana-4546	108	28	|𝔞𝔭+2𝔟𝔭+2	|𝔞𝔭+2𝔟𝔭+2	X
cana-4546	108	29	−	−	NOUN
cana-4546	108	30	𝜇(𝔞𝔭+1𝔟𝔭+1	𝜇(𝔞𝔭+1𝔟𝔭+1	NOUN
cana-4546	108	31	)	)	PUNCT
cana-4546	108	32	2	2	NUM
cana-4546	109	1	|	|	ADV
cana-4546	109	2	≤	≤	NUM
cana-4546	109	3	{	{	PUNCT
cana-4546	109	4	|𝜂|2	|𝜂|2	PROPN
cana-4546	109	5	4𝔭(𝔭+1	4𝔭(𝔭+1	NUM
cana-4546	109	6	)	)	PUNCT
cana-4546	109	7	(	(	PUNCT
cana-4546	109	8	1	1	NUM
cana-4546	109	9	+	+	NUM
cana-4546	109	10	|𝜇|	|𝜇|	X
cana-4546	109	11	(	(	PUNCT
cana-4546	109	12	𝔭+1	𝔭+1	NUM
cana-4546	109	13	)	)	PUNCT
cana-4546	109	14	𝑝	𝑝	NOUN
cana-4546	109	15	)	)	PUNCT
cana-4546	109	16	,	,	PUNCT
cana-4546	109	17	𝜇	𝜇	ADP
cana-4546	109	18	≥	≥	NOUN
cana-4546	109	19	0	0	NUM
cana-4546	109	20	|𝜂|2	|𝜂|2	PROPN
cana-4546	109	21	4𝔭(𝔭+1	4𝔭(𝔭+1	NUM
cana-4546	109	22	)	)	PUNCT
cana-4546	109	23	(	(	PUNCT
cana-4546	109	24	1	1	NUM
cana-4546	109	25	−	−	PROPN
cana-4546	109	26	|𝜇|	|𝜇|	X
cana-4546	109	27	(	(	PUNCT
cana-4546	109	28	𝔭+1	𝔭+1	NUM
cana-4546	109	29	)	)	PUNCT
cana-4546	109	30	𝑝	𝑝	NOUN
cana-4546	109	31	)	)	PUNCT
cana-4546	109	32	,	,	PUNCT
cana-4546	109	33	𝜇	𝜇	ADP
cana-4546	109	34	≤	≤	X
cana-4546	109	35	0	0	NUM
cana-4546	110	1	this	this	PRON
cana-4546	110	2	completes	complete	VERB
cana-4546	110	3	the	the	DET
cana-4546	110	4	proof	proof	NOUN
cana-4546	110	5	of	of	ADP
cana-4546	110	6	the	the	DET
cana-4546	110	7	theorem	theorem	NOUN
cana-4546	110	8	.	.	PROPN
cana-4546	111	1	in	in	ADP
cana-4546	111	2	the	the	DET
cana-4546	111	3	theory	theory	NOUN
cana-4546	111	4	of	of	ADP
cana-4546	111	5	singularities	singularity	NOUN
cana-4546	111	6	[	[	X
cana-4546	111	7	10	10	NUM
cana-4546	111	8	]	]	PUNCT
cana-4546	111	9	and	and	CCONJ
cana-4546	111	10	the	the	DET
cana-4546	111	11	investigation	investigation	NOUN
cana-4546	111	12	of	of	ADP
cana-4546	111	13	power	power	NOUN
cana-4546	111	14	series	series	NOUN
cana-4546	111	15	with	with	ADP
cana-4546	111	16	integral	integral	ADJ
cana-4546	111	17	coefficients	coefficient	NOUN
cana-4546	111	18	,	,	PUNCT
cana-4546	111	19	the	the	DET
cana-4546	111	20	hankel	hankel	NOUN
cana-4546	111	21	determinant	determinant	ADJ
cana-4546	111	22	is	be	AUX
cana-4546	111	23	very	very	ADV
cana-4546	111	24	important	important	ADJ
cana-4546	111	25	.	.	PUNCT
cana-4546	112	1	the	the	DET
cana-4546	112	2	reader	reader	NOUN
cana-4546	112	3	is	be	AUX
cana-4546	112	4	encouraged	encourage	VERB
cana-4546	112	5	to	to	PART
cana-4546	112	6	read	read	VERB
cana-4546	112	7	[	[	X
cana-4546	112	8	15	15	NUM
cana-4546	112	9	]	]	PUNCT
cana-4546	112	10	for	for	ADP
cana-4546	112	11	more	more	ADJ
cana-4546	112	12	information	information	NOUN
cana-4546	112	13	.	.	PUNCT
cana-4546	113	1	for	for	ADP
cana-4546	113	2	several	several	ADJ
cana-4546	113	3	subfamilies	subfamily	NOUN
cana-4546	113	4	of	of	ADP
cana-4546	113	5	univalent	univalent	ADJ
cana-4546	113	6	functions	function	NOUN
cana-4546	113	7	,	,	PUNCT
cana-4546	113	8	the	the	DET
cana-4546	113	9	growth	growth	NOUN
cana-4546	113	10	of	of	ADP
cana-4546	113	11	𝐻𝑞(𝑛	𝐻𝑞(𝑛	NOUN
cana-4546	113	12	)	)	PUNCT
cana-4546	113	13	has	have	AUX
cana-4546	113	14	been	be	AUX
cana-4546	113	15	explored	explore	VERB
cana-4546	113	16	.	.	PUNCT
cana-4546	114	1	we	we	PRON
cana-4546	114	2	know	know	VERB
cana-4546	114	3	that	that	SCONJ
cana-4546	114	4	the	the	DET
cana-4546	114	5	function	function	NOUN
cana-4546	114	6	𝐻2(1	𝐻2(1	NOUN
cana-4546	114	7	)	)	PUNCT
cana-4546	115	1	=	=	SYM
cana-4546	115	2	𝑎3	𝑎3	PROPN
cana-4546	115	3	−	−	PROPN
cana-4546	115	4	𝑎2	𝑎2	PROPN
cana-4546	115	5	2	2	NUM
cana-4546	115	6	for	for	ADP
cana-4546	115	7	𝑞	𝑞	NOUN
cana-4546	115	8	=	=	SYM
cana-4546	115	9	2	2	NUM
cana-4546	115	10	and	and	CCONJ
cana-4546	115	11	𝑛	𝑛	NOUN
cana-4546	115	12	=	=	SYM
cana-4546	115	13	1	1	NUM
cana-4546	115	14	is	be	AUX
cana-4546	115	15	a	a	DET
cana-4546	115	16	well	well	ADV
cana-4546	115	17	recognized	recognize	VERB
cana-4546	115	18	fekete	fekete	NOUN
cana-4546	115	19	-	-	PUNCT
cana-4546	115	20	szegö	szegö	ADJ
cana-4546	115	21	functional	functional	ADJ
cana-4546	115	22	.	.	PUNCT
cana-4546	116	1	for	for	ADP
cana-4546	116	2	the	the	DET
cana-4546	116	3	bi	bi	NOUN
cana-4546	116	4	-	-	ADJ
cana-4546	116	5	convex	convex	ADJ
cana-4546	116	6	and	and	CCONJ
cana-4546	116	7	bi	bi	ADJ
cana-4546	116	8	-	-	ADJ
cana-4546	116	9	starlike	starlike	ADJ
cana-4546	116	10	classes	class	NOUN
cana-4546	116	11	,	,	PUNCT
cana-4546	116	12	the	the	DET
cana-4546	116	13	second	second	ADJ
cana-4546	116	14	hankel	hankel	NOUN
cana-4546	116	15	determinant	determinant	ADJ
cana-4546	116	16	𝐻2(2	𝐻2(2	ADV
cana-4546	116	17	)	)	PUNCT
cana-4546	116	18	is	be	AUX
cana-4546	116	19	given	give	VERB
cana-4546	116	20	by	by	ADP
cana-4546	116	21	𝐻2(2	𝐻2(2	ADJ
cana-4546	116	22	)	)	PUNCT
cana-4546	116	23	=	=	SYM
cana-4546	117	1	𝑎2𝑎4	𝑎2𝑎4	DET
cana-4546	117	2	−	−	NOUN
cana-4546	117	3	𝑎3	𝑎3	NOUN
cana-4546	117	4	2	2	NUM
cana-4546	117	5	[	[	X
cana-4546	117	6	12	12	NUM
cana-4546	117	7	]	]	PUNCT
cana-4546	117	8	.	.	PUNCT
cana-4546	118	1	the	the	DET
cana-4546	118	2	following	follow	VERB
cana-4546	118	3	theorem	theorem	NOUN
cana-4546	118	4	will	will	AUX
cana-4546	118	5	give	give	VERB
cana-4546	118	6	some	some	DET
cana-4546	118	7	results	result	NOUN
cana-4546	118	8	related	relate	VERB
cana-4546	118	9	to	to	PART
cana-4546	118	10	hankel	hankel	VERB
cana-4546	118	11	determinant	determinant	ADJ
cana-4546	118	12	for	for	ADP
cana-4546	118	13	the	the	DET
cana-4546	118	14	functions	function	NOUN
cana-4546	118	15	belonging	belong	VERB
cana-4546	118	16	to	to	ADP
cana-4546	118	17	classes	class	NOUN
cana-4546	118	18	𝑀𝜆,(∗)(𝜂	𝑀𝜆,(∗)(𝜂	PROPN
cana-4546	118	19	,	,	PUNCT
cana-4546	118	20	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	118	21	)	)	PUNCT
cana-4546	118	22	.	.	PUNCT
cana-4546	119	1	theorem	theorem	VERB
cana-4546	119	2	4.2	4.2	NUM
cana-4546	119	3	if	if	SCONJ
cana-4546	119	4	𝐹(𝑧	𝐹(𝑧	ADP
cana-4546	119	5	)	)	PUNCT
cana-4546	119	6	∈	∈	NOUN
cana-4546	120	1	𝒜𝒫	𝒜𝒫	ADV
cana-4546	120	2	given	give	VERB
cana-4546	120	3	by	by	ADP
cana-4546	120	4	(	(	PUNCT
cana-4546	120	5	1.1	1.1	NUM
cana-4546	120	6	)	)	PUNCT
cana-4546	120	7	belongs	belong	VERB
cana-4546	120	8	to	to	ADP
cana-4546	120	9	the	the	DET
cana-4546	120	10	class	class	NOUN
cana-4546	120	11	𝑀𝜆,(∗)(𝜂	𝑀𝜆,(∗)(𝜂	PROPN
cana-4546	120	12	,	,	PUNCT
cana-4546	120	13	𝜑𝑛,𝑚	𝜑𝑛,𝑚	NUM
cana-4546	120	14	)	)	PUNCT
cana-4546	120	15	then	then	ADV
cana-4546	120	16	,	,	PUNCT
cana-4546	120	17	|(𝔞𝔭+1𝔟𝔭+1)(𝔞𝔭+3𝔟𝔭+3	|(𝔞𝔭+1𝔟𝔭+1)(𝔞𝔭+3𝔟𝔭+3	NUM
cana-4546	120	18	)	)	PUNCT
cana-4546	121	1	−	−	PROPN
cana-4546	121	2	(	(	PUNCT
cana-4546	121	3	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	NOUN
cana-4546	121	4	)	)	PUNCT
cana-4546	121	5	2	2	NUM
cana-4546	121	6	|	|	ADV
cana-4546	121	7	≤	≤	X
cana-4546	121	8	|𝜂|2	|𝜂|2	PROPN
cana-4546	121	9	48𝔭2(𝔭+1)2(𝔭+2	48𝔭2(𝔭+1)2(𝔭+2	NUM
cana-4546	121	10	)	)	PUNCT
cana-4546	121	11	(	(	PUNCT
cana-4546	121	12	(	(	PUNCT
cana-4546	121	13	𝔭	𝔭	X
cana-4546	121	14	+	+	NOUN
cana-4546	121	15	1)|3𝜂2	1)|3𝜂2	NUM
cana-4546	121	16	−	−	PROPN
cana-4546	121	17	𝑝(𝔭	𝑝(𝔭	PROPN
cana-4546	121	18	+	+	CCONJ
cana-4546	121	19	1)|	1)|	NUM
cana-4546	122	1	+	+	CCONJ
cana-4546	122	2	3(𝔭	3(𝔭	NUM
cana-4546	122	3	+	+	CCONJ
cana-4546	122	4	2)|𝜂|2	2)|𝜂|2	NUM
cana-4546	122	5	)	)	PUNCT
cana-4546	122	6	(	(	PUNCT
cana-4546	122	7	4.2	4.2	NUM
cana-4546	122	8	)	)	PUNCT
cana-4546	122	9	proof	proof	NOUN
cana-4546	122	10	.	.	PUNCT
cana-4546	123	1	from	from	ADP
cana-4546	123	2	(	(	PUNCT
cana-4546	123	3	3.7	3.7	NUM
cana-4546	123	4	)	)	PUNCT
cana-4546	123	5	,	,	PUNCT
cana-4546	123	6	(	(	PUNCT
cana-4546	123	7	3.8)and	3.8)and	NUM
cana-4546	123	8	(	(	PUNCT
cana-4546	123	9	3.9	3.9	NUM
cana-4546	123	10	)	)	PUNCT
cana-4546	123	11	,	,	PUNCT
cana-4546	123	12	we	we	PRON
cana-4546	123	13	get	get	VERB
cana-4546	123	14	communications	communication	NOUN
cana-4546	123	15	on	on	ADP
cana-4546	123	16	applied	apply	VERB
cana-4546	123	17	nonlinear	nonlinear	ADJ
cana-4546	123	18	analysis	analysis	NOUN
cana-4546	123	19	issn	issn	NOUN
cana-4546	123	20	:	:	PUNCT
cana-4546	123	21	1074	1074	NUM
cana-4546	123	22	-	-	PUNCT
cana-4546	123	23	133x	133x	NUM
cana-4546	123	24	vol	vol	NOUN
cana-4546	123	25	32	32	NUM
cana-4546	123	26	no	no	NOUN
cana-4546	123	27	.	.	PUNCT
cana-4546	124	1	9s	9s	NUM
cana-4546	124	2	(	(	PUNCT
cana-4546	124	3	2025	2025	NUM
cana-4546	124	4	)	)	PUNCT
cana-4546	124	5	2656	2656	NUM
cana-4546	124	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4546	124	7	𝐻2(2	𝐻2(2	ADJ
cana-4546	124	8	)	)	PUNCT
cana-4546	124	9	=	=	SYM
cana-4546	125	1	|	|	ADV
cana-4546	125	2	𝔞2	𝔞2	PROPN
cana-4546	125	3	𝔞3	𝔞3	PROPN
cana-4546	125	4	𝔞3	𝔞3	PROPN
cana-4546	125	5	𝔞4|	𝔞4|	PROPN
cana-4546	126	1	=	=	SYM
cana-4546	126	2	𝔞2𝔞4	𝔞2𝔞4	X
cana-4546	126	3	−	−	PROPN
cana-4546	126	4	𝔞3	𝔞3	PROPN
cana-4546	126	5	2	2	NUM
cana-4546	126	6	(	(	PUNCT
cana-4546	126	7	4.3	4.3	NUM
cana-4546	126	8	)	)	PUNCT
cana-4546	126	9	(	(	PUNCT
cana-4546	126	10	𝔞𝔭+1𝔟𝔭+1)(𝔞𝔭+3𝔟𝔭+3	𝔞𝔭+1𝔟𝔭+1)(𝔞𝔭+3𝔟𝔭+3	NOUN
cana-4546	126	11	)	)	PUNCT
cana-4546	126	12	−	−	PROPN
cana-4546	126	13	(	(	PUNCT
cana-4546	126	14	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	NOUN
cana-4546	126	15	)	)	PUNCT
cana-4546	126	16	2	2	NUM
cana-4546	126	17	=	=	SYM
cana-4546	126	18	(	(	PUNCT
cana-4546	126	19	𝜂	𝜂	NOUN
cana-4546	126	20	2𝔭(1+𝜆(𝔭+1	2𝔭(1+𝜆(𝔭+1	NUM
cana-4546	126	21	)	)	PUNCT
cana-4546	126	22	)	)	PUNCT
cana-4546	126	23	)	)	PUNCT
cana-4546	126	24	(	(	PUNCT
cana-4546	126	25	𝜂(3𝜂2−𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	𝜂(3𝜂2−𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	NOUN
cana-4546	126	26	)	)	PUNCT
cana-4546	126	27	)	)	PUNCT
cana-4546	126	28	)	)	PUNCT
cana-4546	126	29	24𝔭(𝔭+1)(𝔭+2)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	24𝔭(𝔭+1)(𝔭+2)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	NUM
cana-4546	126	30	)	)	PUNCT
cana-4546	126	31	)	)	PUNCT
cana-4546	126	32	)	)	PUNCT
cana-4546	127	1	−	−	PROPN
cana-4546	127	2	(	(	PUNCT
cana-4546	127	3	𝜂2	𝜂2	PROPN
cana-4546	127	4	4𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	4𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2	NUM
cana-4546	127	5	)	)	PUNCT
cana-4546	127	6	)	)	PUNCT
cana-4546	127	7	)	)	PUNCT
cana-4546	127	8	2	2	NUM
cana-4546	127	9	(	(	PUNCT
cana-4546	127	10	4.4	4.4	NUM
cana-4546	127	11	)	)	PUNCT
cana-4546	127	12	=	=	SYM
cana-4546	127	13	(	(	PUNCT
cana-4546	127	14	3𝜂4−𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2))𝜂2	3𝜂4−𝔭(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2))𝜂2	NUM
cana-4546	127	15	)	)	PUNCT
cana-4546	127	16	48𝔭2(𝔭+1)(𝔭+2)(1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	48𝔭2(𝔭+1)(𝔭+2)(1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	NUM
cana-4546	127	17	)	)	PUNCT
cana-4546	127	18	)	)	PUNCT
cana-4546	128	1	−	−	PROPN
cana-4546	128	2	𝜂4	𝜂4	NOUN
cana-4546	128	3	16𝔭2(𝔭+1)2(1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))2	16𝔭2(𝔭+1)2(1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))2	NUM
cana-4546	128	4	(	(	PUNCT
cana-4546	128	5	4.5	4.5	NUM
cana-4546	128	6	)	)	PUNCT
cana-4546	128	7	and	and	CCONJ
cana-4546	128	8	thus	thus	ADV
cana-4546	128	9	|(𝔞𝔭+1𝔟𝔭+1)(𝔞𝔭+3𝔟𝔭+3	|(𝔞𝔭+1𝔟𝔭+1)(𝔞𝔭+3𝔟𝔭+3	NUM
cana-4546	128	10	)	)	PUNCT
cana-4546	128	11	−	−	PROPN
cana-4546	128	12	(	(	PUNCT
cana-4546	128	13	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	NOUN
cana-4546	128	14	)	)	PUNCT
cana-4546	128	15	2	2	NUM
cana-4546	128	16	|	|	CCONJ
cana-4546	128	17	≤	≤	NUM
cana-4546	128	18	|(3𝜂4−𝑝(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2))𝜂2)|	|(3𝜂4−𝑝(𝔭+1)(1+𝜆(𝔭+1))(1+𝜆(𝔭+2))𝜂2)|	X
cana-4546	128	19	48𝔭2(𝔭+1)(𝔭+2)(1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	48𝔭2(𝔭+1)(𝔭+2)(1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	NUM
cana-4546	128	20	)	)	PUNCT
cana-4546	128	21	)	)	PUNCT
cana-4546	129	1	+	+	CCONJ
cana-4546	129	2	|𝜂|4	|𝜂|4	PROPN
cana-4546	129	3	16𝔭2(𝔭+1)2(1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))2	16𝔭2(𝔭+1)2(1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))2	NUM
cana-4546	129	4	(	(	PUNCT
cana-4546	129	5	4.6	4.6	NUM
cana-4546	129	6	)	)	PUNCT
cana-4546	129	7	here	here	ADV
cana-4546	129	8	𝜁3	𝜁3	NOUN
cana-4546	129	9	=	=	SYM
cana-4546	129	10	1	1	NUM
cana-4546	129	11	(	(	PUNCT
cana-4546	129	12	1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	NUM
cana-4546	129	13	)	)	PUNCT
cana-4546	129	14	)	)	PUNCT
cana-4546	129	15	,	,	PUNCT
cana-4546	129	16	𝜁4	𝜁4	PROPN
cana-4546	129	17	=	=	SYM
cana-4546	129	18	1	1	NUM
cana-4546	129	19	(	(	PUNCT
cana-4546	129	20	1+𝜆(𝔭+1))(1+𝜆(𝔭+3	1+𝜆(𝔭+1))(1+𝜆(𝔭+3	NUM
cana-4546	129	21	)	)	PUNCT
cana-4546	129	22	)	)	PUNCT
cana-4546	129	23	and	and	CCONJ
cana-4546	129	24	𝜁5	𝜁5	NOUN
cana-4546	129	25	=	=	SYM
cana-4546	129	26	1	1	NUM
cana-4546	129	27	(	(	PUNCT
cana-4546	129	28	1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))2	1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))2	NOUN
cana-4546	129	29	are	be	AUX
cana-4546	129	30	taken	take	VERB
cana-4546	129	31	and	and	CCONJ
cana-4546	129	32	these	these	DET
cana-4546	129	33	functions	function	NOUN
cana-4546	129	34	depending	depend	VERB
cana-4546	129	35	on	on	ADP
cana-4546	129	36	𝜆	𝜆	NUM
cana-4546	129	37	are	be	AUX
cana-4546	129	38	considered	consider	VERB
cana-4546	129	39	to	to	PART
cana-4546	129	40	be	be	AUX
cana-4546	129	41	decreasing	decrease	VERB
cana-4546	129	42	in	in	ADP
cana-4546	129	43	the	the	DET
cana-4546	129	44	interval	interval	NOUN
cana-4546	129	45	0	0	NUM
cana-4546	129	46	≤	≤	NUM
cana-4546	129	47	𝜆	𝜆	DET
cana-4546	129	48	≤	≤	NUM
cana-4546	129	49	1	1	NUM
cana-4546	129	50	,	,	PUNCT
cana-4546	129	51	since	since	SCONJ
cana-4546	129	52	max	max	PROPN
cana-4546	129	53	0≤𝜆≤1	0≤𝜆≤1	PROPN
cana-4546	129	54	1	1	NUM
cana-4546	129	55	(	(	PUNCT
cana-4546	129	56	1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))(1+𝜆(𝔭+3	NUM
cana-4546	129	57	)	)	PUNCT
cana-4546	129	58	)	)	PUNCT
cana-4546	130	1	=	=	SYM
cana-4546	130	2	1	1	NUM
cana-4546	130	3	,	,	PUNCT
cana-4546	130	4	max	max	PROPN
cana-4546	130	5	0≤𝜆≤1	0≤𝜆≤1	NOUN
cana-4546	130	6	1	1	NUM
cana-4546	130	7	(	(	PUNCT
cana-4546	130	8	1+𝜆(𝔭+1))(1+𝜆(𝔭+3	1+𝜆(𝔭+1))(1+𝜆(𝔭+3	NUM
cana-4546	130	9	)	)	PUNCT
cana-4546	130	10	)	)	PUNCT
cana-4546	130	11	=	=	SYM
cana-4546	131	1	1	1	NUM
cana-4546	131	2	and	and	CCONJ
cana-4546	131	3	max	max	PROPN
cana-4546	131	4	0≤𝜆≤1	0≤𝜆≤1	NOUN
cana-4546	131	5	1	1	NUM
cana-4546	131	6	(	(	PUNCT
cana-4546	131	7	1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))2	1+𝜆(𝔭+1))2(1+𝜆(𝔭+2))2	NOUN
cana-4546	131	8	=	=	SYM
cana-4546	131	9	1	1	NUM
cana-4546	131	10	thus	thus	ADV
cana-4546	131	11	we	we	PRON
cana-4546	131	12	obtain	obtain	VERB
cana-4546	131	13	|(𝔞𝔭+1𝔟𝔭+1)(𝔞𝔭+3𝔟𝔭+3	|(𝔞𝔭+1𝔟𝔭+1)(𝔞𝔭+3𝔟𝔭+3	NUM
cana-4546	131	14	)	)	PUNCT
cana-4546	132	1	−	−	PROPN
cana-4546	132	2	(	(	PUNCT
cana-4546	132	3	𝔞𝔭+2𝔟𝔭+2	𝔞𝔭+2𝔟𝔭+2	NOUN
cana-4546	132	4	)	)	PUNCT
cana-4546	132	5	2	2	NUM
cana-4546	132	6	|	|	ADV
cana-4546	132	7	≤	≤	X
cana-4546	132	8	|𝜂|2	|𝜂|2	NOUN
cana-4546	132	9	48𝔭2(𝔭+1)(𝔭+2	48𝔭2(𝔭+1)(𝔭+2	NUM
cana-4546	132	10	)	)	PUNCT
cana-4546	132	11	(	(	PUNCT
cana-4546	132	12	(	(	PUNCT
cana-4546	132	13	𝔭	𝔭	X
cana-4546	132	14	+	+	NOUN
cana-4546	132	15	1)|3𝜂2	1)|3𝜂2	NUM
cana-4546	132	16	−	−	PROPN
cana-4546	132	17	𝔭(𝔭	𝔭(𝔭	PROPN
cana-4546	132	18	+	+	SYM
cana-4546	132	19	1)|	1)|	NUM
cana-4546	132	20	+	+	CCONJ
cana-4546	132	21	3(𝔭	3(𝔭	NUM
cana-4546	132	22	+	+	CCONJ
cana-4546	132	23	2)|𝜂|2	2)|𝜂|2	NUM
cana-4546	132	24	)	)	PUNCT
cana-4546	132	25	(	(	PUNCT
cana-4546	132	26	4.7	4.7	NUM
cana-4546	132	27	)	)	PUNCT
cana-4546	132	28	this	this	PRON
cana-4546	132	29	completes	complete	VERB
cana-4546	132	30	the	the	DET
cana-4546	132	31	proof	proof	NOUN
cana-4546	132	32	of	of	ADP
cana-4546	132	33	the	the	DET
cana-4546	132	34	theorem	theorem	PROPN
cana-4546	132	35	.	.	PUNCT
cana-4546	133	1	references	reference	NOUN
cana-4546	133	2	[	[	X
cana-4546	133	3	1	1	NUM
cana-4546	133	4	]	]	X
cana-4546	133	5	fekete	fekete	PROPN
cana-4546	133	6	m	m	PROPN
cana-4546	133	7	,	,	PUNCT
cana-4546	133	8	szegö	szegö	PROPN
cana-4546	133	9	g.	g.	PROPN
cana-4546	133	10	eine	eine	PROPN
cana-4546	133	11	bemerkung	bemerkung	PROPN
cana-4546	133	12	uber	uber	PROPN
cana-4546	133	13	ungerade	ungerade	PROPN
cana-4546	133	14	schlichte	schlichte	PROPN
cana-4546	133	15	funktionen	funktionen	PROPN
cana-4546	133	16	.	.	PROPN
cana-4546	134	1	journal	journal	PROPN
cana-4546	134	2	of	of	ADP
cana-4546	134	3	the	the	DET
cana-4546	134	4	london	london	PROPN
cana-4546	134	5	mathematical	mathematical	ADJ
cana-4546	134	6	society	society	NOUN
cana-4546	134	7	1993	1993	NUM
cana-4546	134	8	;	;	PUNCT
cana-4546	134	9	8	8	NUM
cana-4546	134	10	:	:	SYM
cana-4546	134	11	85	85	NUM
cana-4546	134	12	-	-	SYM
cana-4546	134	13	89	89	NUM
cana-4546	134	14	.	.	PUNCT
cana-4546	135	1	[	[	X
cana-4546	135	2	2	2	NUM
cana-4546	135	3	]	]	PUNCT
cana-4546	135	4	keogh	keogh	PROPN
cana-4546	135	5	fr	fr	PROPN
cana-4546	135	6	,	,	PUNCT
cana-4546	135	7	merkes	merke	VERB
cana-4546	135	8	ep	ep	PROPN
cana-4546	135	9	.	.	PUNCT
cana-4546	136	1	a	a	DET
cana-4546	136	2	coefficient	coefficient	NOUN
cana-4546	136	3	inequality	inequality	NOUN
cana-4546	136	4	for	for	ADP
cana-4546	136	5	certain	certain	ADJ
cana-4546	136	6	classes	class	NOUN
cana-4546	136	7	of	of	ADP
cana-4546	136	8	analytic	analytic	ADJ
cana-4546	136	9	functions	function	NOUN
cana-4546	136	10	.	.	PUNCT
cana-4546	137	1	proceedings	proceeding	NOUN
cana-4546	137	2	american	american	PROPN
cana-4546	137	3	mathematical	mathematical	ADJ
cana-4546	137	4	society	society	NOUN
cana-4546	137	5	1969	1969	NUM
cana-4546	137	6	;	;	PUNCT
cana-4546	137	7	20	20	NUM
cana-4546	137	8	:	:	SYM
cana-4546	137	9	8	8	NUM
cana-4546	137	10	-	-	SYM
cana-4546	137	11	12	12	NUM
cana-4546	137	12	.	.	PUNCT
cana-4546	138	1	communications	communication	NOUN
cana-4546	138	2	on	on	ADP
cana-4546	138	3	applied	apply	VERB
cana-4546	138	4	nonlinear	nonlinear	ADJ
cana-4546	138	5	analysis	analysis	NOUN
cana-4546	138	6	issn	issn	NOUN
cana-4546	138	7	:	:	PUNCT
cana-4546	138	8	1074	1074	NUM
cana-4546	138	9	-	-	PUNCT
cana-4546	138	10	133x	133x	NUM
cana-4546	138	11	vol	vol	NOUN
cana-4546	138	12	32	32	NUM
cana-4546	138	13	no	no	NOUN
cana-4546	138	14	.	.	PUNCT
cana-4546	139	1	9s	9s	NUM
cana-4546	139	2	(	(	PUNCT
cana-4546	139	3	2025	2025	NUM
cana-4546	139	4	)	)	PUNCT
cana-4546	139	5	2657	2657	NUM
cana-4546	139	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4546	140	1	[	[	X
cana-4546	140	2	3	3	X
cana-4546	140	3	]	]	X
cana-4546	140	4	murugusundaramoorthy	murugusundaramoorthy	ADJ
cana-4546	140	5	g	g	PROPN
cana-4546	140	6	,	,	PUNCT
cana-4546	140	7	janani	janani	ADJ
cana-4546	140	8	t.	t.	PROPN
cana-4546	140	9	sigmoid	sigmoid	NOUN
cana-4546	140	10	function	function	NOUN
cana-4546	140	11	in	in	ADP
cana-4546	140	12	the	the	DET
cana-4546	140	13	space	space	NOUN
cana-4546	140	14	of	of	ADP
cana-4546	140	15	univalent	univalent	ADJ
cana-4546	140	16	𝜆-pseudo	𝜆-pseudo	NOUN
cana-4546	140	17	starlike	starlike	NOUN
cana-4546	140	18	functions	function	NOUN
cana-4546	140	19	.	.	PUNCT
cana-4546	141	1	international	international	ADJ
cana-4546	141	2	journal	journal	NOUN
cana-4546	141	3	of	of	ADP
cana-4546	141	4	pure	pure	ADJ
cana-4546	141	5	and	and	CCONJ
cana-4546	141	6	applied	applied	ADJ
cana-4546	141	7	mathematics	mathematic	NOUN
cana-4546	141	8	2015	2015	NUM
cana-4546	141	9	;	;	PUNCT
cana-4546	141	10	101	101	NUM
cana-4546	141	11	:	:	PUNCT
cana-4546	141	12	33	33	NUM
cana-4546	141	13	-	-	SYM
cana-4546	141	14	41	41	NUM
cana-4546	141	15	.	.	PUNCT
cana-4546	142	1	[	[	X
cana-4546	142	2	4	4	NUM
cana-4546	142	3	]	]	SYM
cana-4546	142	4	olatunji	olatunji	NOUN
cana-4546	142	5	s.	s.	PROPN
cana-4546	142	6	sigmoid	sigmoid	NOUN
cana-4546	142	7	function	function	NOUN
cana-4546	142	8	in	in	ADP
cana-4546	142	9	the	the	DET
cana-4546	142	10	space	space	NOUN
cana-4546	142	11	of	of	ADP
cana-4546	142	12	univalent	univalent	ADJ
cana-4546	142	13	𝜆-pseudo	𝜆-pseudo	NOUN
cana-4546	142	14	starlike	starlike	NOUN
cana-4546	142	15	functions	function	NOUN
cana-4546	142	16	with	with	ADP
cana-4546	142	17	sakaguchi	sakaguchi	ADJ
cana-4546	142	18	type	type	NOUN
cana-4546	142	19	functions	function	NOUN
cana-4546	142	20	.	.	PUNCT
cana-4546	143	1	journal	journal	NOUN
cana-4546	143	2	of	of	ADP
cana-4546	143	3	progressive	progressive	ADJ
cana-4546	143	4	research	research	NOUN
cana-4546	143	5	in	in	ADP
cana-4546	143	6	mathematics	mathematics	PROPN
cana-4546	143	7	2016	2016	NUM
cana-4546	143	8	;	;	PUNCT
cana-4546	143	9	7	7	NUM
cana-4546	143	10	:	:	SYM
cana-4546	143	11	1164	1164	NUM
cana-4546	143	12	-	-	SYM
cana-4546	143	13	1172	1172	NUM
cana-4546	143	14	.	.	PUNCT
cana-4546	144	1	[	[	X
cana-4546	144	2	5	5	NUM
cana-4546	144	3	]	]	PUNCT
cana-4546	144	4	olatunji	olatunji	X
cana-4546	144	5	s	s	NOUN
cana-4546	144	6	,	,	PUNCT
cana-4546	144	7	dansu	dansu	NOUN
cana-4546	144	8	e	e	NOUN
cana-4546	144	9	,	,	PUNCT
cana-4546	144	10	abidemi	abidemi	NOUN
cana-4546	144	11	a.	a.	NOUN
cana-4546	144	12	on	on	ADP
cana-4546	144	13	a	a	DET
cana-4546	144	14	sakaguchi	sakaguchi	ADJ
cana-4546	144	15	type	type	NOUN
cana-4546	144	16	class	class	NOUN
cana-4546	144	17	of	of	ADP
cana-4546	144	18	analytic	analytic	ADJ
cana-4546	144	19	functions	function	NOUN
cana-4546	144	20	associated	associate	VERB
cana-4546	144	21	with	with	ADP
cana-4546	144	22	quasi	quasi	NOUN
cana-4546	144	23	-	-	NOUN
cana-4546	144	24	subordination	subordination	NOUN
cana-4546	144	25	in	in	ADP
cana-4546	144	26	the	the	DET
cana-4546	144	27	space	space	NOUN
cana-4546	144	28	of	of	ADP
cana-4546	144	29	modified	modify	VERB
cana-4546	144	30	sigmoid	sigmoid	NOUN
cana-4546	144	31	functions	function	NOUN
cana-4546	144	32	.	.	PUNCT
cana-4546	145	1	electronic	electronic	ADJ
cana-4546	145	2	journal	journal	NOUN
cana-4546	145	3	of	of	ADP
cana-4546	145	4	mathematical	mathematical	ADJ
cana-4546	145	5	analysis	analysis	NOUN
cana-4546	145	6	and	and	CCONJ
cana-4546	145	7	applications	application	NOUN
cana-4546	145	8	2017	2017	NUM
cana-4546	145	9	;	;	PUNCT
cana-4546	145	10	5	5	NUM
cana-4546	145	11	(	(	PUNCT
cana-4546	145	12	1	1	NUM
cana-4546	145	13	):	):	PUNCT
cana-4546	145	14	97	97	NUM
cana-4546	145	15	-	-	SYM
cana-4546	145	16	105	105	NUM
cana-4546	145	17	.	.	PUNCT
cana-4546	146	1	[	[	X
cana-4546	146	2	6	6	NUM
cana-4546	146	3	]	]	PUNCT
cana-4546	146	4	olubunmi	olubunmi	NOUN
cana-4546	146	5	fj	fj	PROPN
cana-4546	146	6	,	,	PUNCT
cana-4546	146	7	oladipo	oladipo	VERB
cana-4546	146	8	a	a	DET
cana-4546	146	9	,	,	PUNCT
cana-4546	146	10	ezeafulukwe	ezeafulukwe	ADJ
cana-4546	146	11	ua	ua	PROPN
cana-4546	146	12	.	.	PROPN
cana-4546	146	13	modified	modify	VERB
cana-4546	146	14	sigmoid	sigmoid	NOUN
cana-4546	146	15	function	function	NOUN
cana-4546	146	16	in	in	ADP
cana-4546	146	17	univalent	univalent	ADJ
cana-4546	146	18	function	function	NOUN
cana-4546	146	19	theory	theory	NOUN
cana-4546	146	20	.	.	PUNCT
cana-4546	147	1	international	international	ADJ
cana-4546	147	2	journal	journal	PROPN
cana-4546	147	3	of	of	ADP
cana-4546	147	4	mathematical	mathematical	ADJ
cana-4546	147	5	sciences	sciences	PROPN
cana-4546	147	6	and	and	CCONJ
cana-4546	147	7	engineering	engineering	NOUN
cana-4546	147	8	applications	application	NOUN
cana-4546	147	9	2013	2013	NUM
cana-4546	147	10	;	;	PUNCT
cana-4546	147	11	7	7	NUM
cana-4546	147	12	(	(	PUNCT
cana-4546	147	13	5	5	NUM
cana-4546	147	14	):	):	PUNCT
cana-4546	147	15	313	313	NUM
cana-4546	147	16	-	-	SYM
cana-4546	147	17	317	317	NUM
cana-4546	147	18	.	.	PUNCT
cana-4546	148	1	[	[	X
cana-4546	148	2	7	7	X
cana-4546	148	3	]	]	X
cana-4546	148	4	orhan	orhan	PROPN
cana-4546	148	5	h	h	PROPN
cana-4546	148	6	,	,	PUNCT
cana-4546	148	7	çağlar	çağlar	ADJ
cana-4546	148	8	m.	m.	NOUN
cana-4546	148	9	(	(	PUNCT
cana-4546	148	10	𝜃	𝜃	NOUN
cana-4546	148	11	,	,	PUNCT
cana-4546	148	12	𝜇	𝜇	ADP
cana-4546	148	13	,	,	PUNCT
cana-4546	148	14	𝑇)-neighborhood	𝑇)-neighborhood	NUM
cana-4546	148	15	for	for	ADP
cana-4546	148	16	analytic	analytic	ADJ
cana-4546	148	17	functions	function	NOUN
cana-4546	148	18	involving	involve	VERB
cana-4546	148	19	modified	modify	VERB
cana-4546	148	20	sigmoid	sigmoid	NOUN
cana-4546	148	21	function	function	NOUN
cana-4546	148	22	.	.	PUNCT
cana-4546	149	1	communications	communication	NOUN
cana-4546	149	2	faculty	faculty	NOUN
cana-4546	149	3	of	of	ADP
cana-4546	149	4	sciences	sciences	PROPN
cana-4546	149	5	university	university	PROPN
cana-4546	149	6	of	of	ADP
cana-4546	149	7	ankara	ankara	PROPN
cana-4546	149	8	series	series	PROPN
cana-4546	149	9	a1	a1	PROPN
cana-4546	149	10	-	-	PUNCT
cana-4546	149	11	mathematics	mathematic	NOUN
cana-4546	149	12	and	and	CCONJ
cana-4546	149	13	statistics	statistic	NOUN
cana-4546	149	14	2019	2019	NUM
cana-4546	149	15	;	;	PUNCT
cana-4546	149	16	68	68	NUM
cana-4546	149	17	(	(	PUNCT
cana-4546	149	18	2	2	NUM
cana-4546	149	19	):	):	PUNCT
cana-4546	149	20	2161	2161	NUM
cana-4546	149	21	-	-	SYM
cana-4546	149	22	2169	2169	NUM
cana-4546	149	23	.	.	PUNCT
cana-4546	150	1	[	[	X
cana-4546	150	2	8	8	NUM
cana-4546	150	3	]	]	PUNCT
cana-4546	150	4	pommerenke	pommerenke	NOUN
cana-4546	150	5	c.	c.	PROPN
cana-4546	150	6	univalent	univalent	ADJ
cana-4546	150	7	functions	function	NOUN
cana-4546	150	8	.	.	PUNCT
cana-4546	151	1	studia	studia	PROPN
cana-4546	151	2	mathematica	mathematica	PROPN
cana-4546	151	3	mathematische	mathematische	PROPN
cana-4546	151	4	lehrbucher	lehrbucher	PROPN
cana-4546	151	5	,	,	PUNCT
cana-4546	151	6	vandenhoeck	vandenhoeck	NOUN
cana-4546	151	7	and	and	CCONJ
cana-4546	151	8	ruprecht	ruprecht	NOUN
cana-4546	151	9	,	,	PUNCT
cana-4546	151	10	göttingen	göttingen	NOUN
cana-4546	151	11	,	,	PUNCT
cana-4546	151	12	1975	1975	NUM
cana-4546	151	13	.	.	PUNCT
cana-4546	152	1	[	[	X
cana-4546	152	2	9	9	NUM
cana-4546	152	3	]	]	PUNCT
cana-4546	152	4	ramachandran	ramachandran	PROPN
cana-4546	152	5	c	c	PROPN
cana-4546	152	6	,	,	PUNCT
cana-4546	152	7	dhanalakshmi	dhanalakshmi	PROPN
cana-4546	152	8	k.	k.	PROPN
cana-4546	152	9	the	the	DET
cana-4546	152	10	fekete	fekete	PROPN
cana-4546	152	11	-	-	PUNCT
cana-4546	152	12	szegö	szegö	ADJ
cana-4546	152	13	problem	problem	NOUN
cana-4546	152	14	for	for	ADP
cana-4546	152	15	a	a	DET
cana-4546	152	16	subclass	subclass	NOUN
cana-4546	152	17	of	of	ADP
cana-4546	152	18	analytic	analytic	ADJ
cana-4546	152	19	functions	function	NOUN
cana-4546	152	20	related	relate	VERB
cana-4546	152	21	to	to	ADP
cana-4546	152	22	sigmoid	sigmoid	NOUN
cana-4546	152	23	function	function	NOUN
cana-4546	152	24	.	.	PUNCT
cana-4546	153	1	international	international	ADJ
cana-4546	153	2	journal	journal	NOUN
cana-4546	153	3	of	of	ADP
cana-4546	153	4	pure	pure	ADJ
cana-4546	153	5	and	and	CCONJ
cana-4546	153	6	applied	applied	ADJ
cana-4546	153	7	mathematics	mathematic	NOUN
cana-4546	153	8	2017	2017	NUM
cana-4546	153	9	;	;	PUNCT
cana-4546	153	10	113	113	NUM
cana-4546	153	11	(	(	PUNCT
cana-4546	153	12	3	3	NUM
cana-4546	153	13	):	):	PUNCT
cana-4546	153	14	389	389	NUM
cana-4546	153	15	-	-	SYM
cana-4546	153	16	398	398	NUM
cana-4546	153	17	.	.	PUNCT
cana-4546	154	1	[	[	X
cana-4546	154	2	10	10	NUM
cana-4546	154	3	]	]	X
cana-4546	154	4	s.a	s.a	PROPN
cana-4546	154	5	.	.	PROPN
cana-4546	154	6	al	al	PROPN
cana-4546	154	7	-	-	PUNCT
cana-4546	154	8	ameedee	ameedee	PROPN
cana-4546	154	9	,	,	PUNCT
cana-4546	154	10	w.g	w.g	PROPN
cana-4546	154	11	.	.	PROPN
cana-4546	154	12	atshan	atshan	PROPN
cana-4546	154	13	and	and	CCONJ
cana-4546	154	14	f.a	f.a	PROPN
cana-4546	154	15	.	.	PROPN
cana-4546	154	16	al	al	PROPN
cana-4546	154	17	-	-	PUNCT
cana-4546	154	18	maamori	maamori	PROPN
cana-4546	154	19	,	,	PUNCT
cana-4546	154	20	second	second	ADJ
cana-4546	154	21	hankel	hankel	NOUN
cana-4546	154	22	determinant	determinant	ADJ
cana-4546	154	23	for	for	ADP
cana-4546	154	24	certain	certain	ADJ
cana-4546	154	25	subclasses	subclass	NOUN
cana-4546	154	26	of	of	ADP
cana-4546	154	27	biunivalent	biunivalent	NOUN
cana-4546	154	28	functions	function	NOUN
cana-4546	154	29	,	,	PUNCT
cana-4546	154	30	j.	j.	PROPN
cana-4546	154	31	phys	phys	PROPN
cana-4546	154	32	.	.	PUNCT
cana-4546	154	33	conf	conf	PROPN
cana-4546	154	34	.	.	PUNCT
cana-4546	155	1	ser	ser	PROPN
cana-4546	155	2	.	.	PUNCT
cana-4546	156	1	1664	1664	NUM
cana-4546	156	2	(	(	PUNCT
cana-4546	156	3	2020	2020	NUM
cana-4546	156	4	)	)	PUNCT
cana-4546	156	5	012044	012044	NUM
cana-4546	156	6	.	.	PUNCT
cana-4546	157	1	[	[	X
cana-4546	157	2	11	11	NUM
cana-4546	157	3	]	]	PUNCT
cana-4546	157	4	m.	m.	NOUN
cana-4546	157	5	musthafa	musthafa	PROPN
cana-4546	157	6	ibrahim	ibrahim	PROPN
cana-4546	157	7	,	,	PUNCT
cana-4546	157	8	k.r	k.r	PROPN
cana-4546	157	9	karthikeyan	karthikeyan	PROPN
cana-4546	157	10	unified	unified	ADJ
cana-4546	157	11	solution	solution	NOUN
cana-4546	157	12	of	of	ADP
cana-4546	157	13	some	some	DET
cana-4546	157	14	properties	property	NOUN
cana-4546	157	15	related	relate	VERB
cana-4546	157	16	to	to	ADP
cana-4546	157	17	𝜆pseudo	𝜆pseudo	ADJ
cana-4546	157	18	starlike	starlike	NOUN
cana-4546	157	19	functions	function	NOUN
cana-4546	157	20	,	,	PUNCT
cana-4546	157	21	contemporary	contemporary	ADJ
cana-4546	157	22	mathematics	mathematic	NOUN
cana-4546	157	23	,	,	PUNCT
cana-4546	157	24	2023;volume	2023;volume	NUM
cana-4546	157	25	4	4	NUM
cana-4546	157	26	issue	issue	NOUN
cana-4546	157	27	4	4	NUM
cana-4546	157	28	:	:	SYM
cana-4546	157	29	926	926	NUM
cana-4546	157	30	-	-	SYM
cana-4546	157	31	936	936	NUM
cana-4546	157	32	[	[	X
cana-4546	157	33	12	12	NUM
cana-4546	157	34	]	]	PUNCT
cana-4546	157	35	m.	m.	NOUN
cana-4546	157	36	musthafa	musthafa	PROPN
cana-4546	157	37	ibrahim	ibrahim	PROPN
cana-4546	157	38	,	,	PUNCT
cana-4546	157	39	a.	a.	PROPN
cana-4546	157	40	senguttuvan	senguttuvan	PROPN
cana-4546	157	41	,	,	PUNCT
cana-4546	157	42	d.	d.	PROPN
cana-4546	157	43	mohankumar	mohankumar	PROPN
cana-4546	157	44	,	,	PUNCT
cana-4546	157	45	r.	r.	PROPN
cana-4546	157	46	ganapathy	ganapathy	PROPN
cana-4546	157	47	raman	raman	PROPN
cana-4546	157	48	.	.	PUNCT
cana-4546	158	1	on	on	ADP
cana-4546	158	2	classes	class	NOUN
cana-4546	158	3	of	of	ADP
cana-4546	158	4	janowski	janowski	ADJ
cana-4546	158	5	functions	function	NOUN
cana-4546	158	6	of	of	ADP
cana-4546	158	7	complex	complex	ADJ
cana-4546	158	8	order	order	NOUN
cana-4546	158	9	involving	involve	VERB
cana-4546	158	10	a	a	DET
cana-4546	158	11	q	q	ADJ
cana-4546	158	12	-	-	ADJ
cana-4546	158	13	derivative	derivative	ADJ
cana-4546	158	14	operator	operator	NOUN
cana-4546	158	15	,	,	PUNCT
cana-4546	158	16	international	international	ADJ
cana-4546	158	17	journal	journal	NOUN
cana-4546	158	18	of	of	ADP
cana-4546	158	19	mathematics	mathematic	NOUN
cana-4546	158	20	and	and	CCONJ
cana-4546	158	21	computer	computer	NOUN
cana-4546	158	22	science	science	NOUN
cana-4546	158	23	,	,	PUNCT
cana-4546	158	24	2020	2020	NUM
cana-4546	158	25	;	;	PUNCT
cana-4546	158	26	15	15	NUM
cana-4546	158	27	,	,	PUNCT
cana-4546	158	28	no	no	INTJ
cana-4546	158	29	.	.	NOUN
cana-4546	158	30	4	4	NUM
cana-4546	158	31	,	,	PUNCT
cana-4546	158	32	1161–1172	1161–1172	NUM
cana-4546	158	33	.	.	PUNCT
cana-4546	159	1	[	[	X
cana-4546	159	2	13	13	NUM
cana-4546	159	3	]	]	PUNCT
cana-4546	159	4	k.	k.	PROPN
cana-4546	159	5	r.	r.	PROPN
cana-4546	159	6	karthikeyan	karthikeyan	PROPN
cana-4546	159	7	,	,	PUNCT
cana-4546	159	8	m.	m.	NOUN
cana-4546	159	9	musthafa	musthafa	PROPN
cana-4546	159	10	ibrahim	ibrahim	PROPN
cana-4546	159	11	and	and	CCONJ
cana-4546	159	12	k.	k.	PROPN
cana-4546	159	13	srinevasan	srinevasan	PROPN
cana-4546	159	14	,	,	PUNCT
cana-4546	159	15	coefficient	coefficient	NOUN
cana-4546	159	16	inequalities	inequality	NOUN
cana-4546	159	17	of	of	ADP
cana-4546	159	18	a	a	DET
cana-4546	159	19	subclass	subclass	NOUN
cana-4546	159	20	of	of	ADP
cana-4546	159	21	analytic	analytic	ADJ
cana-4546	159	22	functions	function	NOUN
cana-4546	159	23	defined	define	VERB
cana-4546	159	24	using	use	VERB
cana-4546	159	25	q	q	ADJ
cana-4546	159	26	-	-	PUNCT
cana-4546	159	27	differential	differential	ADJ
cana-4546	159	28	operator	operator	NOUN
cana-4546	159	29	”	"	PUNCT
cana-4546	159	30	with	with	ADP
cana-4546	159	31	.	.	PUNCT
cana-4546	160	1	international	international	ADJ
cana-4546	160	2	journal	journal	NOUN
cana-4546	160	3	of	of	ADP
cana-4546	160	4	innovative	innovative	ADJ
cana-4546	160	5	technology	technology	NOUN
cana-4546	160	6	and	and	CCONJ
cana-4546	160	7	exploring	explore	VERB
cana-4546	160	8	engineering	engineering	NOUN
cana-4546	160	9	,	,	PUNCT
cana-4546	160	10	volume-8	volume-8	NUM
cana-4546	160	11	,	,	PUNCT
cana-4546	160	12	issue-7(may	issue-7(may	PROPN
cana-4546	160	13	2019	2019	NUM
cana-4546	160	14	)	)	PUNCT
cana-4546	160	15	,	,	PUNCT
cana-4546	160	16	1098	1098	NUM
cana-4546	160	17	-	-	SYM
cana-4546	160	18	1101	1101	NUM
cana-4546	160	19	.	.	PUNCT
cana-4546	161	1	[	[	X
cana-4546	161	2	14	14	NUM
cana-4546	161	3	]	]	PUNCT
cana-4546	161	4	k.	k.	PROPN
cana-4546	161	5	r.	r.	PROPN
cana-4546	161	6	karthikeyan	karthikeyan	PROPN
cana-4546	161	7	,	,	PUNCT
cana-4546	161	8	m.	m.	NOUN
cana-4546	161	9	musthafa	musthafa	PROPN
cana-4546	161	10	ibrahim	ibrahim	PROPN
cana-4546	161	11	and	and	CCONJ
cana-4546	161	12	k.	k.	PROPN
cana-4546	161	13	srinevasan	srinevasan	PROPN
cana-4546	161	14	.	.	PUNCT
cana-4546	162	1	convolution	convolution	NOUN
cana-4546	162	2	properties	property	NOUN
cana-4546	162	3	of	of	ADP
cana-4546	162	4	multivalent	multivalent	NOUN
cana-4546	162	5	functions	function	NOUN
cana-4546	162	6	with	with	ADP
cana-4546	162	7	coefficients	coefficient	NOUN
cana-4546	162	8	of	of	ADP
cana-4546	162	9	alternating	alternate	VERB
cana-4546	162	10	type	type	NOUN
cana-4546	162	11	defined	define	VERB
cana-4546	162	12	using	use	VERB
cana-4546	162	13	q	q	ADJ
cana-4546	162	14	-	-	PUNCT
cana-4546	162	15	differential	differential	ADJ
cana-4546	162	16	operator	operator	NOUN
cana-4546	162	17	"	"	PUNCT
cana-4546	162	18	.	.	PUNCT
cana-4546	163	1	international	international	ADJ
cana-4546	163	2	journal	journal	NOUN
cana-4546	163	3	of	of	ADP
cana-4546	163	4	pure	pure	ADJ
cana-4546	163	5	and	and	CCONJ
cana-4546	163	6	applied	applied	ADJ
cana-4546	163	7	mathematics	mathematic	NOUN
cana-4546	163	8	,	,	PUNCT
cana-4546	163	9	volume	volume	NOUN
cana-4546	163	10	118	118	NUM
cana-4546	163	11	,	,	PUNCT
cana-4546	163	12	no.10	no.10	PROPN
cana-4546	163	13	(	(	PUNCT
cana-4546	163	14	2018	2018	NUM
cana-4546	163	15	)	)	PUNCT
cana-4546	163	16	,	,	PUNCT
cana-4546	163	17	page	page	NOUN
cana-4546	163	18	281	281	NUM
cana-4546	163	19	-	-	SYM
cana-4546	163	20	292	292	NUM
cana-4546	163	21	.	.	PUNCT
cana-4546	164	1	[	[	X
cana-4546	164	2	15	15	NUM
cana-4546	164	3	]	]	X
cana-4546	164	4	sadia	sadia	PROPN
cana-4546	164	5	riaz	riaz	PROPN
cana-4546	164	6	,	,	PUNCT
cana-4546	164	7	timilehin	timilehin	PROPN
cana-4546	164	8	gideon	gideon	PROPN
cana-4546	164	9	shaba	shaba	PROPN
cana-4546	164	10	,	,	PUNCT
cana-4546	164	11	qin	qin	PROPN
cana-4546	164	12	xin	xin	PROPN
cana-4546	164	13	,	,	PUNCT
cana-4546	164	14	fairouz	fairouz	ADJ
cana-4546	164	15	tchier	tchier	NOUN
cana-4546	164	16	,	,	PUNCT
cana-4546	164	17	bilal	bilal	PROPN
cana-4546	164	18	khan	khan	PROPN
cana-4546	164	19	,	,	PUNCT
cana-4546	164	20	sarfraz	sarfraz	PROPN
cana-4546	164	21	nawaz	nawaz	PROPN
cana-4546	164	22	malik	malik	PROPN
cana-4546	164	23	.	.	PUNCT
cana-4546	165	1	fekete	fekete	NOUN
cana-4546	165	2	-	-	PUNCT
cana-4546	165	3	szegö	szegö	PROPN
cana-4546	165	4	problem	problem	NOUN
cana-4546	165	5	and	and	CCONJ
cana-4546	165	6	second	second	ADJ
cana-4546	165	7	hankel	hankel	NOUN
cana-4546	165	8	determinant	determinant	ADJ
cana-4546	165	9	for	for	ADP
cana-4546	165	10	a	a	DET
cana-4546	165	11	class	class	NOUN
cana-4546	165	12	of	of	ADP
cana-4546	165	13	bi	bi	ADJ
cana-4546	165	14	-	-	ADJ
cana-4546	165	15	univalent	univalent	ADJ
cana-4546	165	16	functions	function	NOUN
cana-4546	165	17	involving	involve	VERB
cana-4546	165	18	euler	euler	NOUN
cana-4546	165	19	polynomials	polynomial	NOUN
cana-4546	166	1	.	.	PUNCT
cana-4546	167	1	[	[	X
cana-4546	167	2	16	16	NUM
cana-4546	167	3	]	]	PUNCT
cana-4546	167	4	m.	m.	NOUN
cana-4546	167	5	musthafa	musthafa	PROPN
cana-4546	167	6	ibrahim	ibrahim	PROPN
cana-4546	167	7	.	.	PUNCT
cana-4546	168	1	coefficient	coefficient	NOUN
cana-4546	168	2	estimates	estimate	NOUN
cana-4546	168	3	for	for	ADP
cana-4546	168	4	functions	function	NOUN
cana-4546	168	5	with	with	ADP
cana-4546	168	6	respect	respect	NOUN
cana-4546	168	7	to	to	ADP
cana-4546	168	8	symmetric	symmetric	ADJ
cana-4546	168	9	points	point	NOUN
cana-4546	168	10	based	base	VERB
cana-4546	168	11	on	on	ADP
cana-4546	168	12	shell	shell	NOUN
cana-4546	168	13	-	-	PUNCT
cana-4546	168	14	like	like	ADJ
cana-4546	168	15	curves	curve	NOUN
cana-4546	168	16	defined	define	VERB
cana-4546	168	17	by	by	ADP
cana-4546	168	18	convolution	convolution	NOUN
cana-4546	168	19	,	,	PUNCT
cana-4546	168	20	volume14	volume14	ADJ
cana-4546	168	21	,	,	PUNCT
cana-4546	168	22	no	no	DET
cana-4546	168	23	1	1	NUM
cana-4546	168	24	,	,	PUNCT
cana-4546	168	25	2024	2024	NUM
cana-4546	168	26	.	.	PUNCT