id	sid	tid	token	lemma	pos
cana-1119	1	1	communications	communication	NOUN
cana-1119	1	2	on	on	ADP
cana-1119	1	3	applied	apply	VERB
cana-1119	1	4	nonlinear	nonlinear	ADJ
cana-1119	1	5	analysis	analysis	NOUN
cana-1119	1	6	issn	issn	NOUN
cana-1119	1	7	:	:	PUNCT
cana-1119	1	8	1074	1074	NUM
cana-1119	1	9	-	-	PUNCT
cana-1119	1	10	133x	133x	NUM
cana-1119	1	11	vol	vol	NOUN
cana-1119	1	12	31	31	NUM
cana-1119	1	13	no	no	NOUN
cana-1119	1	14	.	.	PUNCT
cana-1119	2	1	6s	6s	NUM
cana-1119	2	2	(	(	PUNCT
cana-1119	2	3	2024	2024	NUM
cana-1119	2	4	)	)	PUNCT
cana-1119	2	5	49	49	NUM
cana-1119	3	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1119	3	2	second	second	ADJ
cana-1119	3	3	hankel	hankel	NOUN
cana-1119	3	4	inequality	inequality	NOUN
cana-1119	3	5	for	for	ADP
cana-1119	3	6	certain	certain	ADJ
cana-1119	3	7	common	common	ADJ
cana-1119	3	8	subclass	subclass	NOUN
cana-1119	3	9	of	of	ADP
cana-1119	3	10	classes	class	NOUN
cana-1119	3	11	of	of	ADP
cana-1119	3	12	starlike	starlike	NOUN
cana-1119	3	13	and	and	CCONJ
cana-1119	3	14	convex	convex	NOUN
cana-1119	3	15	functions	function	NOUN
cana-1119	3	16	gurmeet	gurmeet	VERB
cana-1119	3	17	singh1	singh1	PROPN
cana-1119	3	18	,	,	PUNCT
cana-1119	3	19	gourav	gourav	PROPN
cana-1119	3	20	saini2	saini2	PROPN
cana-1119	3	21	,	,	PUNCT
cana-1119	3	22	paras	paras	ADJ
cana-1119	3	23	uchat3	uchat3	ADJ
cana-1119	3	24	,	,	PUNCT
cana-1119	3	25	dipa	dipa	PROPN
cana-1119	3	26	sharma4	sharma4	PROPN
cana-1119	3	27	,	,	PUNCT
cana-1119	3	28	chatinder	chatinder	ADJ
cana-1119	3	29	kaur5	kaur5	NOUN
cana-1119	4	1	1department	1department	NUM
cana-1119	4	2	of	of	ADP
cana-1119	4	3	mathematics	mathematic	NOUN
cana-1119	4	4	,	,	PUNCT
cana-1119	4	5	gssdgs	gssdgs	PROPN
cana-1119	4	6	khalsa	khalsa	PROPN
cana-1119	4	7	college	college	PROPN
cana-1119	4	8	patiala-14700	patiala-14700	PROPN
cana-1119	4	9	,	,	PUNCT
cana-1119	4	10	meetgur111@gmail.com	meetgur111@gmail.com	X
cana-1119	4	11	2	2	NUM
cana-1119	4	12	research	research	NOUN
cana-1119	4	13	scholar	scholar	NOUN
cana-1119	4	14	,	,	PUNCT
cana-1119	4	15	department	department	NOUN
cana-1119	4	16	of	of	ADP
cana-1119	4	17	mathematics	mathematics	PROPN
cana-1119	4	18	,	,	PUNCT
cana-1119	4	19	punjabi	punjabi	PROPN
cana-1119	4	20	university	university	NOUN
cana-1119	4	21	,	,	PUNCT
cana-1119	4	22	patiala-147002	patiala-147002	NOUN
cana-1119	4	23	,	,	PUNCT
cana-1119	5	1	sainig953@gmail.com	sainig953@gmail.com	PROPN
cana-1119	5	2	3assistant	3assistant	NUM
cana-1119	5	3	professor	professor	NOUN
cana-1119	5	4	,	,	PUNCT
cana-1119	5	5	iite	iite	NOUN
cana-1119	5	6	,	,	PUNCT
cana-1119	5	7	gandhinagar	gandhinagar	NOUN
cana-1119	5	8	,	,	PUNCT
cana-1119	5	9	gujarat	gujarat	NOUN
cana-1119	5	10	,	,	PUNCT
cana-1119	5	11	parasu@iite.ac.in	parasu@iite.ac.in	NOUN
cana-1119	5	12	4department	4department	NUM
cana-1119	5	13	of	of	ADP
cana-1119	5	14	mathematics	mathematic	NOUN
cana-1119	5	15	,	,	PUNCT
cana-1119	5	16	sri	sri	PROPN
cana-1119	5	17	dev	dev	PROPN
cana-1119	5	18	suman	suman	PROPN
cana-1119	5	19	uttarakhand	uttarakhand	PROPN
cana-1119	5	20	university	university	PROPN
cana-1119	5	21	pt.l.m.s.campus	pt.l.m.s.campus	PROPN
cana-1119	5	22	rishikesh	rishikesh	PROPN
cana-1119	5	23	,	,	PUNCT
cana-1119	5	24	dehradun	dehradun	PROPN
cana-1119	5	25	,	,	PUNCT
cana-1119	5	26	uttarakhand	uttarakhand	PROPN
cana-1119	5	27	,	,	PUNCT
cana-1119	5	28	dipa2014sharma@gmail.com	dipa2014sharma@gmail.com	X
cana-1119	5	29	5	5	NUM
cana-1119	5	30	research	research	NOUN
cana-1119	5	31	scholar	scholar	NOUN
cana-1119	5	32	,	,	PUNCT
cana-1119	5	33	department	department	NOUN
cana-1119	5	34	of	of	ADP
cana-1119	5	35	mathematics	mathematics	PROPN
cana-1119	5	36	,	,	PUNCT
cana-1119	5	37	punjabi	punjabi	PROPN
cana-1119	5	38	university	university	NOUN
cana-1119	5	39	,	,	PUNCT
cana-1119	5	40	patiala-147002	patiala-147002	NOUN
cana-1119	5	41	,	,	PUNCT
cana-1119	5	42	chatinderkaur@gmail.com	chatinderkaur@gmail.com	X
cana-1119	6	1	article	article	NOUN
cana-1119	6	2	history	history	NOUN
cana-1119	6	3	:	:	PUNCT
cana-1119	6	4	received	receive	VERB
cana-1119	6	5	:	:	PUNCT
cana-1119	6	6	25	25	NUM
cana-1119	6	7	-	-	PUNCT
cana-1119	6	8	05	05	NUM
cana-1119	6	9	-	-	PUNCT
cana-1119	6	10	2024	2024	NUM
cana-1119	6	11	revised	revise	VERB
cana-1119	6	12	:	:	PUNCT
cana-1119	6	13	28	28	NUM
cana-1119	6	14	-	-	SYM
cana-1119	6	15	06	06	NUM
cana-1119	6	16	-	-	PUNCT
cana-1119	6	17	2024	2024	NUM
cana-1119	6	18	accepted	accept	VERB
cana-1119	6	19	:	:	PUNCT
cana-1119	6	20	20	20	NUM
cana-1119	6	21	-	-	SYM
cana-1119	6	22	07	07	NUM
cana-1119	6	23	-	-	PUNCT
cana-1119	6	24	2024	2024	NUM
cana-1119	6	25	abstract	abstract	NOUN
cana-1119	6	26	:	:	PUNCT
cana-1119	6	27	in	in	ADP
cana-1119	6	28	this	this	DET
cana-1119	6	29	paper	paper	NOUN
cana-1119	6	30	we	we	PRON
cana-1119	6	31	will	will	AUX
cana-1119	6	32	define	define	VERB
cana-1119	6	33	a	a	DET
cana-1119	6	34	new	new	ADJ
cana-1119	6	35	class	class	NOUN
cana-1119	6	36	s	s	PROPN
cana-1119	6	37	*	*	X
cana-1119	6	38	csin	csin	NOUN
cana-1119	6	39	(	(	PUNCT
cana-1119	6	40	r	r	NOUN
cana-1119	6	41	)	)	PUNCT
cana-1119	6	42	which	which	PRON
cana-1119	6	43	is	be	AUX
cana-1119	6	44	subordinate	subordinate	ADJ
cana-1119	6	45	to	to	PART
cana-1119	6	46	function	function	VERB
cana-1119	6	47	1+sin	1+sin	PROPN
cana-1119	6	48	z	z	PROPN
cana-1119	6	49	,	,	PUNCT
cana-1119	6	50	we	we	PRON
cana-1119	6	51	will	will	AUX
cana-1119	6	52	find	find	VERB
cana-1119	6	53	the	the	DET
cana-1119	6	54	fekete	fekete	PROPN
cana-1119	6	55	szegö	szegö	PROPN
cana-1119	6	56	inequality	inequality	NOUN
cana-1119	6	57	for	for	ADP
cana-1119	6	58	this	this	DET
cana-1119	6	59	class	class	NOUN
cana-1119	6	60	along	along	ADP
cana-1119	6	61	with	with	ADP
cana-1119	6	62	fekete	fekete	PROPN
cana-1119	6	63	szegö	szegö	PROPN
cana-1119	6	64	inequality	inequality	NOUN
cana-1119	6	65	of	of	ADP
cana-1119	6	66	the	the	DET
cana-1119	6	67	functions	function	NOUN
cana-1119	6	68	of	of	ADP
cana-1119	6	69	this	this	DET
cana-1119	6	70	class	class	NOUN
cana-1119	6	71	defined	define	VERB
cana-1119	6	72	s	s	PROPN
cana-1119	6	73	*	*	X
cana-1119	6	74	csin	csin	NOUN
cana-1119	6	75	(	(	PUNCT
cana-1119	6	76	r	r	NOUN
cana-1119	6	77	,	,	PUNCT
cana-1119	6	78	θ	θ	NOUN
cana-1119	6	79	)	)	PUNCT
cana-1119	6	80	through	through	ADP
cana-1119	6	81	poisson	poisson	NOUN
cana-1119	6	82	distribution	distribution	NOUN
cana-1119	6	83	.	.	PUNCT
cana-1119	7	1	further	far	ADV
cana-1119	7	2	we	we	PRON
cana-1119	7	3	have	have	AUX
cana-1119	7	4	solved	solve	VERB
cana-1119	7	5	the	the	DET
cana-1119	7	6	second	second	ADJ
cana-1119	7	7	hankel	hankel	NOUN
cana-1119	7	8	determinant	determinant	ADJ
cana-1119	7	9	of	of	ADP
cana-1119	7	10	this	this	DET
cana-1119	7	11	new	new	ADJ
cana-1119	7	12	class	class	NOUN
cana-1119	7	13	.	.	PUNCT
cana-1119	8	1	keywords	keyword	NOUN
cana-1119	8	2	:	:	PUNCT
cana-1119	8	3	geometric	geometric	ADJ
cana-1119	8	4	function	function	NOUN
cana-1119	8	5	,	,	PUNCT
cana-1119	8	6	analytic	analytic	ADJ
cana-1119	8	7	univalent	univalent	ADJ
cana-1119	8	8	functions	function	NOUN
cana-1119	8	9	,	,	PUNCT
cana-1119	8	10	poisson	poisson	NOUN
cana-1119	8	11	distribution	distribution	NOUN
cana-1119	8	12	,	,	PUNCT
cana-1119	8	13	subordination	subordination	NOUN
cana-1119	8	14	,	,	PUNCT
cana-1119	8	15	fekete	fekete	PROPN
cana-1119	8	16	szegö	szegö	PROPN
cana-1119	8	17	inequality	inequality	PROPN
cana-1119	8	18	,	,	PUNCT
cana-1119	8	19	upper	upper	ADJ
cana-1119	8	20	bounds	bound	NOUN
cana-1119	8	21	,	,	PUNCT
cana-1119	8	22	hankel	hankel	NOUN
cana-1119	8	23	determinant	determinant	ADJ
cana-1119	8	24	,	,	PUNCT
cana-1119	8	25	coefficient	coefficient	NOUN
cana-1119	8	26	inequalities	inequality	NOUN
cana-1119	8	27	.	.	PUNCT
cana-1119	9	1	1	1	X
cana-1119	9	2	.	.	X
cana-1119	9	3	introduction	introduction	NOUN
cana-1119	9	4	the	the	DET
cana-1119	9	5	class	class	NOUN
cana-1119	9	6	of	of	ADP
cana-1119	9	7	all	all	DET
cana-1119	9	8	the	the	DET
cana-1119	9	9	analytic	analytic	ADJ
cana-1119	9	10	functions	function	NOUN
cana-1119	9	11	in	in	ADP
cana-1119	9	12	a	a	DET
cana-1119	9	13	unit	unit	NOUN
cana-1119	9	14	disk	disk	NOUN
cana-1119	9	15	𝔻:=	𝔻:=	ADJ
cana-1119	9	16	{	{	PUNCT
cana-1119	9	17	𝑧	𝑧	PRON
cana-1119	9	18	∈	∈	PROPN
cana-1119	9	19	ℂ	ℂ	PROPN
cana-1119	9	20	:	:	PUNCT
cana-1119	9	21	|𝑧|	|𝑧|	NOUN
cana-1119	9	22	<	<	X
cana-1119	9	23	1	1	NUM
cana-1119	9	24	}	}	PUNCT
cana-1119	9	25	,	,	PUNCT
cana-1119	9	26	whose	whose	DET
cana-1119	9	27	taylor	taylor	PROPN
cana-1119	9	28	's	's	PART
cana-1119	9	29	series	series	NOUN
cana-1119	9	30	expansion	expansion	NOUN
cana-1119	9	31	is	be	AUX
cana-1119	9	32	of	of	ADP
cana-1119	9	33	the	the	DET
cana-1119	9	34	form	form	NOUN
cana-1119	9	35	ℎ(𝑧):=	ℎ(𝑧):=	VERB
cana-1119	9	36	𝑧	𝑧	PRON
cana-1119	9	37	+	+	ADJ
cana-1119	9	38	∑	∑	ADJ
cana-1119	9	39	  	  	SPACE
cana-1119	9	40	∞	∞	NUM
cana-1119	9	41	𝑛=2	𝑛=2	PROPN
cana-1119	9	42	 	 	SPACE
cana-1119	9	43	𝑎𝑛𝑧	𝑎𝑛𝑧	PROPN
cana-1119	9	44	𝑛	𝑛	PROPN
cana-1119	9	45	=	=	PUNCT
cana-1119	9	46	𝑧	𝑧	PROPN
cana-1119	9	47	+	+	NOUN
cana-1119	9	48	𝑎2𝑧	𝑎2𝑧	NUM
cana-1119	9	49	2	2	NUM
cana-1119	9	50	+	+	CCONJ
cana-1119	9	51	𝑎3𝑧	𝑎3𝑧	ADJ
cana-1119	9	52	3	3	NUM
cana-1119	9	53	+	+	NUM
cana-1119	9	54	𝑎4𝑧	𝑎4𝑧	NUM
cana-1119	9	55	4⋯	4⋯	NOUN
cana-1119	9	56	∀𝑧	∀𝑧	X
cana-1119	9	57	∈	∈	PROPN
cana-1119	9	58	𝔻	𝔻	X
cana-1119	9	59	(	(	PUNCT
cana-1119	9	60	1	1	NUM
cana-1119	9	61	)	)	PUNCT
cana-1119	9	62	and	and	CCONJ
cana-1119	9	63	normalized	normalize	VERB
cana-1119	9	64	by	by	ADP
cana-1119	9	65	the	the	DET
cana-1119	9	66	conditions	condition	NOUN
cana-1119	9	67	:	:	PUNCT
cana-1119	9	68	ℎ(0	ℎ(0	NOUN
cana-1119	9	69	)	)	PUNCT
cana-1119	10	1	=	=	SYM
cana-1119	10	2	0	0	NUM
cana-1119	10	3	,	,	PUNCT
cana-1119	10	4	ℎ′(0	ℎ′(0	NOUN
cana-1119	10	5	)	)	PUNCT
cana-1119	10	6	=	=	SYM
cana-1119	11	1	1	1	NUM
cana-1119	11	2	,	,	PUNCT
cana-1119	11	3	is	be	AUX
cana-1119	11	4	denoted	denote	VERB
cana-1119	11	5	by	by	ADP
cana-1119	11	6	𝒜.	𝒜.	PROPN
cana-1119	11	7	let	let	VERB
cana-1119	11	8	𝒮	𝒮	PRON
cana-1119	11	9	denotes	denote	VERB
cana-1119	11	10	a	a	DET
cana-1119	11	11	subclass	subclass	NOUN
cana-1119	11	12	of	of	ADP
cana-1119	11	13	𝒜	𝒜	NOUN
cana-1119	11	14	of	of	ADP
cana-1119	11	15	all	all	DET
cana-1119	11	16	univalent	univalent	ADJ
cana-1119	11	17	analytic	analytic	ADJ
cana-1119	11	18	functions	function	NOUN
cana-1119	11	19	in	in	ADP
cana-1119	11	20	the	the	DET
cana-1119	11	21	unit	unit	NOUN
cana-1119	11	22	disk	disk	NOUN
cana-1119	11	23	𝔻.	𝔻.	NOUN
cana-1119	11	24	the	the	DET
cana-1119	11	25	class	class	NOUN
cana-1119	11	26	of	of	ADP
cana-1119	11	27	analytic	analytic	ADJ
cana-1119	11	28	-univalent	-univalent	NOUN
cana-1119	11	29	functions	function	NOUN
cana-1119	11	30	,	,	PUNCT
cana-1119	11	31	with	with	ADP
cana-1119	11	32	taylor	taylor	PROPN
cana-1119	11	33	's	's	PART
cana-1119	11	34	series	series	NOUN
cana-1119	11	35	expansion	expansion	NOUN
cana-1119	11	36	of	of	ADP
cana-1119	11	37	the	the	DET
cana-1119	11	38	form	form	NOUN
cana-1119	11	39	𝑝(𝑧	𝑝(𝑧	PROPN
cana-1119	11	40	)	)	PUNCT
cana-1119	11	41	=	=	PUNCT
cana-1119	12	1	1	1	NUM
cana-1119	12	2	+	+	ADJ
cana-1119	12	3	∑	∑	PROPN
cana-1119	12	4	  	  	SPACE
cana-1119	12	5	∞	∞	PROPN
cana-1119	12	6	𝑛=1	𝑛=1	NOUN
cana-1119	12	7	  	  	SPACE
cana-1119	12	8	𝑐𝑛𝑧	𝑐𝑛𝑧	ADP
cana-1119	12	9	𝑛	𝑛	PROPN
cana-1119	12	10	(	(	PUNCT
cana-1119	12	11	2	2	NUM
cana-1119	12	12	)	)	PUNCT
cana-1119	12	13	in	in	ADP
cana-1119	12	14	𝔻	𝔻	PROPN
cana-1119	12	15	,	,	PUNCT
cana-1119	12	16	such	such	ADJ
cana-1119	12	17	that	that	PRON
cana-1119	12	18	ℜ𝑒(𝑃(𝑧	ℜ𝑒(𝑃(𝑧	NOUN
cana-1119	12	19	)	)	PUNCT
cana-1119	12	20	)	)	PUNCT
cana-1119	13	1	>	>	X
cana-1119	13	2	0	0	PUNCT
cana-1119	13	3	is	be	AUX
cana-1119	13	4	denoted	denote	VERB
cana-1119	13	5	by	by	ADP
cana-1119	13	6	𝒫	𝒫	PROPN
cana-1119	13	7	in	in	ADP
cana-1119	13	8	1916	1916	NUM
cana-1119	13	9	a	a	DET
cana-1119	13	10	german	german	ADJ
cana-1119	13	11	mathematician	mathematician	ADJ
cana-1119	13	12	ludwig	ludwig	PROPN
cana-1119	13	13	bieberbach	bieberbach	NOUN
cana-1119	13	14	proposed	propose	VERB
cana-1119	13	15	a	a	DET
cana-1119	13	16	conjecture	conjecture	NOUN
cana-1119	13	17	on	on	ADP
cana-1119	13	18	the	the	DET
cana-1119	13	19	coefficients	coefficient	NOUN
cana-1119	13	20	of	of	ADP
cana-1119	13	21	analytic	analytic	ADJ
cana-1119	13	22	functions	function	NOUN
cana-1119	13	23	of	of	ADP
cana-1119	13	24	from	from	ADP
cana-1119	13	25	(	(	PUNCT
cana-1119	13	26	1	1	NUM
cana-1119	13	27	)	)	PUNCT
cana-1119	13	28	in	in	ADP
cana-1119	13	29	𝒮	𝒮	PROPN
cana-1119	13	30	,	,	PUNCT
cana-1119	13	31	i.e	i.e	PROPN
cana-1119	13	32	|𝑎𝑛|	|𝑎𝑛|	ADV
cana-1119	13	33	≤	≤	NUM
cana-1119	13	34	𝑛	𝑛	NOUN
cana-1119	13	35	,	,	PUNCT
cana-1119	13	36	𝑛	𝑛	DET
cana-1119	13	37	∈	∈	PROPN
cana-1119	13	38	ℕ	ℕ	PROPN
cana-1119	13	39	communications	communication	NOUN
cana-1119	13	40	on	on	ADP
cana-1119	13	41	applied	apply	VERB
cana-1119	13	42	nonlinear	nonlinear	ADJ
cana-1119	13	43	analysis	analysis	NOUN
cana-1119	13	44	issn	issn	NOUN
cana-1119	13	45	:	:	PUNCT
cana-1119	13	46	1074	1074	NUM
cana-1119	13	47	-	-	PUNCT
cana-1119	13	48	133x	133x	NUM
cana-1119	13	49	vol	vol	NOUN
cana-1119	13	50	31	31	NUM
cana-1119	13	51	no	no	NOUN
cana-1119	13	52	.	.	PUNCT
cana-1119	14	1	6s	6s	NUM
cana-1119	14	2	(	(	PUNCT
cana-1119	14	3	2024	2024	NUM
cana-1119	14	4	)	)	PUNCT
cana-1119	14	5	50	50	NUM
cana-1119	14	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1119	15	1	this	this	DET
cana-1119	15	2	conjecture	conjecture	NOUN
cana-1119	15	3	was	be	AUX
cana-1119	15	4	known	know	VERB
cana-1119	15	5	by	by	ADP
cana-1119	15	6	the	the	DET
cana-1119	15	7	name	name	NOUN
cana-1119	15	8	of	of	ADP
cana-1119	15	9	bieberbach	bieberbach	NOUN
cana-1119	15	10	conjecture	conjecture	NOUN
cana-1119	15	11	(	(	PUNCT
cana-1119	15	12	1916	1916	NUM
cana-1119	15	13	)	)	PUNCT
cana-1119	16	1	[	[	X
cana-1119	16	2	2	2	NUM
cana-1119	16	3	]	]	PUNCT
cana-1119	16	4	.	.	PUNCT
cana-1119	17	1	until	until	ADP
cana-1119	17	2	1985	1985	NUM
cana-1119	17	3	this	this	DET
cana-1119	17	4	conjecture	conjecture	NOUN
cana-1119	17	5	was	be	AUX
cana-1119	17	6	considered	consider	VERB
cana-1119	17	7	as	as	ADP
cana-1119	17	8	very	very	ADV
cana-1119	17	9	challenging	challenging	ADJ
cana-1119	17	10	problem	problem	NOUN
cana-1119	17	11	in	in	ADP
cana-1119	17	12	geometric	geometric	ADJ
cana-1119	17	13	function	function	NOUN
cana-1119	17	14	theory	theory	NOUN
cana-1119	17	15	of	of	ADP
cana-1119	17	16	complex	complex	ADJ
cana-1119	17	17	analysis	analysis	NOUN
cana-1119	17	18	.	.	PUNCT
cana-1119	18	1	after	after	ADP
cana-1119	18	2	69	69	NUM
cana-1119	18	3	years	year	NOUN
cana-1119	18	4	of	of	ADP
cana-1119	18	5	this	this	DET
cana-1119	18	6	conjecture	conjecture	NOUN
cana-1119	18	7	,	,	PUNCT
cana-1119	18	8	a	a	DET
cana-1119	18	9	french	french	ADJ
cana-1119	18	10	-	-	PUNCT
cana-1119	18	11	american	american	ADJ
cana-1119	18	12	mathematician	mathematician	NOUN
cana-1119	18	13	louis	louis	PROPN
cana-1119	18	14	de	de	X
cana-1119	18	15	branges	brange	NOUN
cana-1119	18	16	de	de	X
cana-1119	18	17	bourcia(1985	bourcia(1985	NOUN
cana-1119	18	18	)	)	PUNCT
cana-1119	18	19	solved	solve	VERB
cana-1119	18	20	this	this	DET
cana-1119	18	21	conjecture	conjecture	NOUN
cana-1119	18	22	[	[	X
cana-1119	18	23	3].before	3].before	NUM
cana-1119	18	24	de	de	PROPN
cana-1119	18	25	branges	brange	NOUN
cana-1119	18	26	's	's	PART
cana-1119	18	27	proof	proof	NOUN
cana-1119	18	28	many	many	ADJ
cana-1119	18	29	scholars	scholar	NOUN
cana-1119	18	30	around	around	ADP
cana-1119	18	31	the	the	DET
cana-1119	18	32	world	world	NOUN
cana-1119	18	33	tried	try	VERB
cana-1119	18	34	to	to	PART
cana-1119	18	35	prove	prove	VERB
cana-1119	18	36	or	or	CCONJ
cana-1119	18	37	disprove	disprove	VERB
cana-1119	18	38	this	this	DET
cana-1119	18	39	conjecture	conjecture	NOUN
cana-1119	18	40	,	,	PUNCT
cana-1119	18	41	as	as	ADP
cana-1119	18	42	a	a	DET
cana-1119	18	43	consequences	consequence	NOUN
cana-1119	18	44	of	of	ADP
cana-1119	18	45	their	their	PRON
cana-1119	18	46	these	these	DET
cana-1119	18	47	efforts	effort	NOUN
cana-1119	18	48	they	they	PRON
cana-1119	18	49	found	find	VERB
cana-1119	18	50	multiple	multiple	ADJ
cana-1119	18	51	subfamilies	subfamily	NOUN
cana-1119	18	52	of	of	ADP
cana-1119	18	53	class	class	NOUN
cana-1119	18	54	𝒮.	𝒮.	PROPN
cana-1119	18	55	the	the	DET
cana-1119	18	56	most	most	ADV
cana-1119	18	57	common	common	ADJ
cana-1119	18	58	subfamilies	subfamily	NOUN
cana-1119	18	59	of	of	ADP
cana-1119	18	60	𝒮	𝒮	NOUN
cana-1119	18	61	are	be	AUX
cana-1119	18	62	convex	convex	NOUN
cana-1119	18	63	,	,	PUNCT
cana-1119	18	64	star	star	NOUN
cana-1119	18	65	-	-	PUNCT
cana-1119	18	66	like	like	ADJ
cana-1119	18	67	and	and	CCONJ
cana-1119	18	68	close	close	ADV
cana-1119	18	69	-	-	PUNCT
cana-1119	18	70	to	to	ADP
cana-1119	18	71	-	-	PUNCT
cana-1119	18	72	convex	convex	NOUN
cana-1119	18	73	functions	function	NOUN
cana-1119	18	74	whose	whose	DET
cana-1119	18	75	set	set	VERB
cana-1119	18	76	builder	builder	NOUN
cana-1119	18	77	form	form	NOUN
cana-1119	18	78	is	be	AUX
cana-1119	18	79	given	give	VERB
cana-1119	18	80	by	by	ADP
cana-1119	18	81	𝐶:=	𝐶:=	NOUN
cana-1119	18	82	{	{	PUNCT
cana-1119	18	83	ℎ	ℎ	PROPN
cana-1119	18	84	∈	∈	PROPN
cana-1119	18	85	𝒮:ℜ𝑒	𝒮:ℜ𝑒	ADV
cana-1119	18	86	(	(	PUNCT
cana-1119	18	87	(	(	PUNCT
cana-1119	18	88	𝑧(ℎ′(𝑧))′	𝑧(ℎ′(𝑧))′	PROPN
cana-1119	18	89	ℎ′(𝑧	ℎ′(𝑧	PROPN
cana-1119	18	90	)	)	PUNCT
cana-1119	18	91	)	)	PUNCT
cana-1119	18	92	>	>	X
cana-1119	19	1	0	0	NUM
cana-1119	19	2	,	,	PUNCT
cana-1119	19	3	∀𝑧	∀𝑧	PRON
cana-1119	19	4	∈	∈	PROPN
cana-1119	19	5	𝔻	𝔻	ADJ
cana-1119	19	6	}	}	PUNCT
cana-1119	19	7	𝑆∗	𝑆∗	NUM
cana-1119	19	8	:	:	PUNCT
cana-1119	19	9	=	=	SYM
cana-1119	19	10	{	{	PUNCT
cana-1119	19	11	ℎ	ℎ	PROPN
cana-1119	19	12	∈	∈	PROPN
cana-1119	19	13	𝒮:ℜ𝑒	𝒮:ℜ𝑒	ADV
cana-1119	19	14	(	(	PUNCT
cana-1119	19	15	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	NOUN
cana-1119	19	16	)	)	PUNCT
cana-1119	19	17	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1119	19	18	)	)	PUNCT
cana-1119	19	19	)	)	PUNCT
cana-1119	19	20	>	>	X
cana-1119	19	21	0	0	NUM
cana-1119	19	22	,	,	PUNCT
cana-1119	19	23	∀𝑧	∀𝑧	PRON
cana-1119	19	24	∈	∈	PROPN
cana-1119	19	25	𝔻	𝔻	PROPN
cana-1119	19	26	}	}	PUNCT
cana-1119	19	27	𝑅:=	𝑅:=	PUNCT
cana-1119	19	28	{	{	PUNCT
cana-1119	19	29	ℎ	ℎ	PROPN
cana-1119	19	30	∈	∈	PROPN
cana-1119	19	31	𝒮:ℜ𝑒[ℎ′(𝑧	𝒮:ℜ𝑒[ℎ′(𝑧	NOUN
cana-1119	19	32	)	)	PUNCT
cana-1119	19	33	]	]	PUNCT
cana-1119	19	34	>	>	X
cana-1119	19	35	0	0	NUM
cana-1119	19	36	,	,	PUNCT
cana-1119	19	37	∀𝑧	∀𝑧	PRON
cana-1119	19	38	∈	∈	PROPN
cana-1119	19	39	𝔻	𝔻	ADJ
cana-1119	19	40	}	}	PUNCT
cana-1119	19	41	two	two	NUM
cana-1119	19	42	functions	function	NOUN
cana-1119	19	43	ℎ	ℎ	NOUN
cana-1119	19	44	and	and	CCONJ
cana-1119	19	45	𝑔	𝑔	PROPN
cana-1119	19	46	in	in	ADP
cana-1119	19	47	𝒜,ℎ	𝒜,ℎ	PRON
cana-1119	19	48	is	be	AUX
cana-1119	19	49	said	say	VERB
cana-1119	19	50	to	to	PART
cana-1119	19	51	be	be	AUX
cana-1119	19	52	subordinated	subordinate	VERB
cana-1119	19	53	to	to	ADP
cana-1119	19	54	𝑔	𝑔	VERB
cana-1119	19	55	,	,	PUNCT
cana-1119	19	56	or	or	CCONJ
cana-1119	19	57	written	write	VERB
cana-1119	19	58	as	as	ADP
cana-1119	19	59	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1119	19	60	)	)	PUNCT
cana-1119	19	61	≺	≺	NOUN
cana-1119	19	62	𝑔(𝑧	𝑔(𝑧	NOUN
cana-1119	19	63	)	)	PUNCT
cana-1119	19	64	,	,	PUNCT
cana-1119	19	65	if	if	SCONJ
cana-1119	19	66	we	we	PRON
cana-1119	19	67	have	have	VERB
cana-1119	19	68	a	a	DET
cana-1119	19	69	schwarz	schwarz	PROPN
cana-1119	19	70	functions	function	NOUN
cana-1119	19	71	𝜔(𝑧	𝜔(𝑧	VERB
cana-1119	19	72	)	)	PUNCT
cana-1119	19	73	analytic	analytic	NOUN
cana-1119	19	74	over	over	ADP
cana-1119	19	75	𝔻	𝔻	PROPN
cana-1119	19	76	with	with	ADP
cana-1119	19	77	𝜔(0	𝜔(0	PROPN
cana-1119	19	78	)	)	PUNCT
cana-1119	19	79	=	=	SYM
cana-1119	19	80	0	0	PUNCT
cana-1119	19	81	and	and	CCONJ
cana-1119	19	82	also	also	ADV
cana-1119	19	83	|𝜔(𝑧)|	|𝜔(𝑧)|	ADJ
cana-1119	19	84	<	<	X
cana-1119	19	85	1	1	NUM
cana-1119	19	86	,	,	PUNCT
cana-1119	19	87	such	such	ADJ
cana-1119	19	88	that	that	DET
cana-1119	19	89	ℎ(𝑧	ℎ(𝑧	NOUN
cana-1119	19	90	)	)	PUNCT
cana-1119	19	91	=	=	SYM
cana-1119	19	92	𝑔(𝜔(𝑧	𝑔(𝜔(𝑧	PROPN
cana-1119	19	93	)	)	PUNCT
cana-1119	19	94	)	)	PUNCT
cana-1119	20	1	∀𝑧	∀𝑧	PRON
cana-1119	20	2	∈	∈	NOUN
cana-1119	20	3	𝔻	𝔻	PROPN
cana-1119	20	4	,	,	PUNCT
cana-1119	20	5	but	but	CCONJ
cana-1119	20	6	if	if	SCONJ
cana-1119	20	7	function	function	NOUN
cana-1119	20	8	𝑔(𝑧	𝑔(𝑧	PROPN
cana-1119	20	9	)	)	PUNCT
cana-1119	20	10	is	be	AUX
cana-1119	20	11	univalent	univalent	ADJ
cana-1119	20	12	in	in	ADP
cana-1119	20	13	𝔻	𝔻	PROPN
cana-1119	20	14	,	,	PUNCT
cana-1119	20	15	then	then	ADV
cana-1119	20	16	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1119	20	17	)	)	PUNCT
cana-1119	20	18	≺	≺	NOUN
cana-1119	20	19	𝑔(𝑧	𝑔(𝑧	NOUN
cana-1119	20	20	)	)	PUNCT
cana-1119	20	21	iff	iff	PROPN
cana-1119	20	22	ℎ(0	ℎ(0	PROPN
cana-1119	20	23	)	)	PUNCT
cana-1119	20	24	=	=	SYM
cana-1119	21	1	𝑔(0	𝑔(0	ADJ
cana-1119	21	2	)	)	PUNCT
cana-1119	21	3	and	and	CCONJ
cana-1119	21	4	ℎ(𝔻	ℎ(𝔻	NUM
cana-1119	21	5	)	)	PUNCT
cana-1119	22	1	⊂	⊂	PROPN
cana-1119	22	2	𝑔(𝔻	𝑔(𝔻	PROPN
cana-1119	22	3	)	)	PUNCT
cana-1119	22	4	ma	ma	PROPN
cana-1119	22	5	and	and	CCONJ
cana-1119	22	6	minda	minda	PROPN
cana-1119	23	1	[	[	X
cana-1119	23	2	4	4	X
cana-1119	23	3	]	]	PUNCT
cana-1119	23	4	introduced	introduce	VERB
cana-1119	23	5	two	two	NUM
cana-1119	23	6	classes	class	NOUN
cana-1119	23	7	of	of	ADP
cana-1119	23	8	analytic	analytic	ADJ
cana-1119	23	9	functions	function	NOUN
cana-1119	23	10	which	which	PRON
cana-1119	23	11	are	be	AUX
cana-1119	23	12	.	.	PUNCT
cana-1119	24	1	𝑆∗(𝜙):=	𝑆∗(𝜙):=	PUNCT
cana-1119	24	2	{	{	PUNCT
cana-1119	24	3	ℎ	ℎ	PROPN
cana-1119	24	4	∈	∈	PROPN
cana-1119	24	5	𝒜	𝒜	NOUN
cana-1119	24	6	:	:	PUNCT
cana-1119	24	7	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	PROPN
cana-1119	24	8	)	)	PUNCT
cana-1119	24	9	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1119	24	10	)	)	PUNCT
cana-1119	24	11	≺	≺	NOUN
cana-1119	24	12	𝜙(𝑧	𝜙(𝑧	NOUN
cana-1119	24	13	)	)	PUNCT
cana-1119	24	14	,	,	PUNCT
cana-1119	24	15	∀𝑧	∀𝑧	PRON
cana-1119	24	16	∈	∈	PROPN
cana-1119	24	17	𝔻	𝔻	ADJ
cana-1119	24	18	}	}	PUNCT
cana-1119	24	19	and	and	CCONJ
cana-1119	24	20	𝐶(𝜙):=	𝐶(𝜙):=	ADJ
cana-1119	24	21	{	{	PUNCT
cana-1119	24	22	ℎ	ℎ	PROPN
cana-1119	24	23	∈	∈	PROPN
cana-1119	24	24	𝒜	𝒜	NOUN
cana-1119	24	25	:	:	PUNCT
cana-1119	24	26	1	1	NUM
cana-1119	24	27	+	+	NUM
cana-1119	24	28	𝑧ℎ′′(𝑧	𝑧ℎ′′(𝑧	NOUN
cana-1119	24	29	)	)	PUNCT
cana-1119	24	30	ℎ′(𝑧	ℎ′(𝑧	NOUN
cana-1119	24	31	)	)	PUNCT
cana-1119	24	32	≺	≺	NOUN
cana-1119	24	33	𝜙(𝑧	𝜙(𝑧	NOUN
cana-1119	24	34	)	)	PUNCT
cana-1119	24	35	,	,	PUNCT
cana-1119	24	36	∀𝑧	∀𝑧	PRON
cana-1119	24	37	∈	∈	PROPN
cana-1119	24	38	𝔻	𝔻	PROPN
cana-1119	24	39	}	}	PUNCT
cana-1119	24	40	the	the	DET
cana-1119	24	41	function	function	NOUN
cana-1119	24	42	𝜙(𝑧	𝜙(𝑧	NOUN
cana-1119	24	43	)	)	PUNCT
cana-1119	24	44	is	be	AUX
cana-1119	24	45	an	an	DET
cana-1119	24	46	univalent	univalent	ADJ
cana-1119	24	47	analytic	analytic	ADJ
cana-1119	24	48	function	function	NOUN
cana-1119	24	49	with	with	ADP
cana-1119	24	50	positive	positive	ADJ
cana-1119	24	51	real	real	ADJ
cana-1119	24	52	part	part	NOUN
cana-1119	24	53	in	in	ADP
cana-1119	24	54	the	the	DET
cana-1119	24	55	unit	unit	NOUN
cana-1119	24	56	disk	disk	NOUN
cana-1119	24	57	𝔻	𝔻	PROPN
cana-1119	24	58	such	such	ADJ
cana-1119	24	59	that	that	DET
cana-1119	24	60	𝜙(0	𝜙(0	PROPN
cana-1119	24	61	)	)	PUNCT
cana-1119	25	1	=	=	SYM
cana-1119	25	2	1	1	NUM
cana-1119	25	3	,	,	PUNCT
cana-1119	25	4	𝜙′(0	𝜙′(0	NOUN
cana-1119	25	5	)	)	PUNCT
cana-1119	25	6	>	>	X
cana-1119	25	7	0	0	NUM
cana-1119	25	8	where	where	SCONJ
cana-1119	25	9	𝜙	𝜙	PROPN
cana-1119	25	10	maps	map	VERB
cana-1119	25	11	the	the	DET
cana-1119	25	12	open	open	ADJ
cana-1119	25	13	unit	unit	NOUN
cana-1119	25	14	disk	disk	NOUN
cana-1119	25	15	onto	onto	ADP
cana-1119	25	16	a	a	DET
cana-1119	25	17	region	region	NOUN
cana-1119	25	18	starlike	starlike	NOUN
cana-1119	25	19	with	with	ADP
cana-1119	25	20	respect	respect	NOUN
cana-1119	25	21	to	to	ADP
cana-1119	25	22	1	1	NUM
cana-1119	25	23	and	and	CCONJ
cana-1119	25	24	symmetric	symmetric	ADJ
cana-1119	25	25	with	with	ADP
cana-1119	25	26	respect	respect	NOUN
cana-1119	25	27	to	to	ADP
cana-1119	25	28	the	the	DET
cana-1119	25	29	real	real	ADJ
cana-1119	25	30	axis	axis	NOUN
cana-1119	25	31	,	,	PUNCT
cana-1119	25	32	several	several	ADJ
cana-1119	25	33	other	other	ADJ
cana-1119	25	34	classes	class	NOUN
cana-1119	25	35	can	can	AUX
cana-1119	25	36	be	be	AUX
cana-1119	25	37	formed	form	VERB
cana-1119	25	38	by	by	ADP
cana-1119	25	39	varying	vary	VERB
cana-1119	25	40	the	the	DET
cana-1119	25	41	function	function	NOUN
cana-1119	25	42	𝜙	𝜙	NOUN
cana-1119	25	43	,	,	PUNCT
cana-1119	25	44	some	some	PRON
cana-1119	25	45	of	of	ADP
cana-1119	25	46	the	the	DET
cana-1119	25	47	examples	example	NOUN
cana-1119	25	48	are	be	AUX
cana-1119	25	49	as	as	SCONJ
cana-1119	25	50	follows	follow	VERB
cana-1119	25	51	•	•	ADV
cana-1119	25	52	when	when	SCONJ
cana-1119	25	53	𝜙	𝜙	PROPN
cana-1119	25	54	=	=	SYM
cana-1119	25	55	𝑒𝑧	𝑒𝑧	PROPN
cana-1119	25	56	,	,	PUNCT
cana-1119	25	57	this	this	DET
cana-1119	25	58	class	class	NOUN
cana-1119	25	59	is	be	AUX
cana-1119	25	60	denoted	denote	VERB
cana-1119	25	61	by	by	ADP
cana-1119	25	62	𝑆𝑒	𝑆𝑒	NOUN
cana-1119	25	63	∗	∗	NOUN
cana-1119	25	64	,	,	PUNCT
cana-1119	25	65	check	check	VERB
cana-1119	25	66	out	out	ADP
cana-1119	25	67	[	[	X
cana-1119	25	68	5	5	NUM
cana-1119	25	69	,	,	PUNCT
cana-1119	25	70	6	6	NUM
cana-1119	25	71	]	]	PUNCT
cana-1119	25	72	for	for	ADP
cana-1119	25	73	more	more	ADJ
cana-1119	25	74	details	detail	NOUN
cana-1119	25	75	.	.	PUNCT
cana-1119	26	1	•	•	NUM
cana-1119	26	2	when	when	SCONJ
cana-1119	26	3	𝜙	𝜙	NOUN
cana-1119	26	4	=	=	SYM
cana-1119	26	5	1	1	NUM
cana-1119	26	6	+	+	SYM
cana-1119	26	7	2	2	NUM
cana-1119	26	8	𝜋2	𝜋2	NOUN
cana-1119	26	9	(	(	PUNCT
cana-1119	26	10	log	log	VERB
cana-1119	26	11	1+√𝑧	1+√𝑧	NUM
cana-1119	26	12	1−√𝑧	1−√𝑧	NUM
cana-1119	26	13	)	)	PUNCT
cana-1119	26	14	2	2	NUM
cana-1119	26	15	,	,	PUNCT
cana-1119	26	16	we	we	PRON
cana-1119	26	17	get	get	VERB
cana-1119	26	18	a	a	DET
cana-1119	26	19	new	new	ADJ
cana-1119	26	20	class	class	NOUN
cana-1119	26	21	,	,	PUNCT
cana-1119	26	22	for	for	SCONJ
cana-1119	26	23	further	further	ADJ
cana-1119	26	24	details	detail	NOUN
cana-1119	26	25	see	see	VERB
cana-1119	26	26	[	[	X
cana-1119	26	27	7	7	X
cana-1119	26	28	]	]	SYM
cana-1119	26	29	•	•	NOUN
cana-1119	26	30	when	when	SCONJ
cana-1119	26	31	𝜙	𝜙	PROPN
cana-1119	26	32	=	=	VERB
cana-1119	26	33	1+𝐶𝑧	1+𝐶𝑧	NUM
cana-1119	26	34	1+𝐷𝑧	1+𝐷𝑧	NUM
cana-1119	26	35	(	(	PUNCT
cana-1119	26	36	−1	−1	NOUN
cana-1119	26	37	≤	≤	NUM
cana-1119	26	38	𝐷	𝐷	NOUN
cana-1119	26	39	<	<	X
cana-1119	26	40	<	<	X
cana-1119	26	41	𝐶	𝐶	PROPN
cana-1119	26	42	≤	≤	NUM
cana-1119	26	43	1	1	NUM
cana-1119	26	44	)	)	PUNCT
cana-1119	26	45	,	,	PUNCT
cana-1119	26	46	we	we	PRON
cana-1119	26	47	get	get	VERB
cana-1119	26	48	the	the	DET
cana-1119	26	49	class	class	NOUN
cana-1119	26	50	𝑆∗(𝐶	𝑆∗(𝐶	PROPN
cana-1119	26	51	,	,	PUNCT
cana-1119	26	52	𝐷	𝐷	PROPN
cana-1119	26	53	)	)	PUNCT
cana-1119	26	54	.	.	PUNCT
cana-1119	27	1	see	see	VERB
cana-1119	27	2	[	[	X
cana-1119	27	3	8	8	NUM
cana-1119	27	4	]	]	PUNCT
cana-1119	27	5	for	for	ADP
cana-1119	27	6	more	more	ADJ
cana-1119	27	7	details	detail	NOUN
cana-1119	27	8	.	.	PUNCT
cana-1119	28	1	•	•	NUM
cana-1119	28	2	when	when	SCONJ
cana-1119	28	3	𝜙	𝜙	NOUN
cana-1119	28	4	=	=	VERB
cana-1119	28	5	cosh	cosh	PROPN
cana-1119	28	6	(	(	PUNCT
cana-1119	28	7	z	z	NOUN
cana-1119	28	8	)	)	PUNCT
cana-1119	28	9	,	,	PUNCT
cana-1119	28	10	this	this	DET
cana-1119	28	11	new	new	ADJ
cana-1119	28	12	class	class	NOUN
cana-1119	28	13	is	be	AUX
cana-1119	28	14	denoted	denote	VERB
cana-1119	28	15	by	by	ADP
cana-1119	28	16	𝑆cosh	𝑆cosh	PROPN
cana-1119	28	17	∗	∗	NOUN
cana-1119	28	18	see.[9	see.[9	NOUN
cana-1119	28	19	]	]	PUNCT
cana-1119	28	20	communications	communication	NOUN
cana-1119	28	21	on	on	ADP
cana-1119	28	22	applied	apply	VERB
cana-1119	28	23	nonlinear	nonlinear	ADJ
cana-1119	28	24	analysis	analysis	NOUN
cana-1119	29	1	issn	issn	NOUN
cana-1119	29	2	:	:	PUNCT
cana-1119	29	3	1074	1074	NUM
cana-1119	29	4	-	-	PUNCT
cana-1119	29	5	133x	133x	NUM
cana-1119	29	6	vol	vol	NOUN
cana-1119	29	7	31	31	NUM
cana-1119	29	8	no	no	NOUN
cana-1119	29	9	.	.	PUNCT
cana-1119	30	1	6s	6s	NUM
cana-1119	30	2	(	(	PUNCT
cana-1119	30	3	2024	2024	NUM
cana-1119	30	4	)	)	PUNCT
cana-1119	30	5	51	51	NUM
cana-1119	30	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1119	30	7	•	•	NOUN
cana-1119	30	8	when	when	SCONJ
cana-1119	30	9	𝜙	𝜙	NOUN
cana-1119	30	10	=	=	SYM
cana-1119	30	11	1	1	NUM
cana-1119	30	12	+	+	CCONJ
cana-1119	30	13	sin	sin	NOUN
cana-1119	30	14	(	(	PUNCT
cana-1119	30	15	𝑧	𝑧	NOUN
cana-1119	30	16	)	)	PUNCT
cana-1119	30	17	,	,	PUNCT
cana-1119	30	18	the	the	DET
cana-1119	30	19	class	class	NOUN
cana-1119	30	20	is	be	AUX
cana-1119	30	21	denoted	denote	VERB
cana-1119	30	22	by	by	ADP
cana-1119	30	23	𝑆sin	𝑆sin	PROPN
cana-1119	30	24	∗	∗	NOUN
cana-1119	30	25	,	,	PUNCT
cana-1119	30	26	for	for	SCONJ
cana-1119	30	27	more	more	ADJ
cana-1119	30	28	details	detail	NOUN
cana-1119	30	29	see	see	VERB
cana-1119	30	30	[	[	X
cana-1119	30	31	10	10	NUM
cana-1119	30	32	,	,	PUNCT
cana-1119	30	33	11	11	NUM
cana-1119	30	34	]	]	PUNCT
cana-1119	30	35	c.	c.	NOUN
cana-1119	30	36	pommerenke	pommerenke	NOUN
cana-1119	30	37	(	(	PUNCT
cana-1119	30	38	1966	1966	NUM
cana-1119	30	39	-	-	SYM
cana-1119	30	40	67	67	NUM
cana-1119	30	41	)	)	PUNCT
cana-1119	30	42	,	,	PUNCT
cana-1119	31	1	[	[	X
cana-1119	31	2	12	12	NUM
cana-1119	31	3	,	,	PUNCT
cana-1119	31	4	13	13	NUM
cana-1119	31	5	]	]	PUNCT
cana-1119	31	6	stated	state	VERB
cana-1119	31	7	the	the	DET
cana-1119	31	8	𝑝th	𝑝th	NOUN
cana-1119	31	9	hankel	hankel	NOUN
cana-1119	31	10	determinant	determinant	ADJ
cana-1119	31	11	for	for	ADP
cana-1119	31	12	𝑝	𝑝	PROPN
cana-1119	31	13	≥	≥	NUM
cana-1119	31	14	1	1	NUM
cana-1119	31	15	and	and	CCONJ
cana-1119	31	16	𝑛	𝑛	DET
cana-1119	31	17	≥	≥	NOUN
cana-1119	31	18	1	1	NUM
cana-1119	31	19	where	where	SCONJ
cana-1119	31	20	𝑝	𝑝	NOUN
cana-1119	31	21	,	,	PUNCT
cana-1119	31	22	𝑛	𝑛	DET
cana-1119	31	23	∈	∈	PROPN
cana-1119	31	24	ℕ	ℕ	PROPN
cana-1119	31	25	of	of	ADP
cana-1119	31	26	functions	function	NOUN
cana-1119	31	27	ℎ	ℎ	NOUN
cana-1119	31	28	of	of	ADP
cana-1119	31	29	form	form	NOUN
cana-1119	31	30	?	?	PUNCT
cana-1119	31	31	?	?	PUNCT
cana-1119	31	32	is	be	AUX
cana-1119	31	33	defined	define	VERB
cana-1119	31	34	as	as	ADP
cana-1119	31	35	ℋ(𝑝,𝑛)(ℎ	ℋ(𝑝,𝑛)(ℎ	NOUN
cana-1119	31	36	)	)	PUNCT
cana-1119	31	37	=	=	PUNCT
cana-1119	32	1	|	|	ADV
cana-1119	32	2	𝑎𝑛	𝑎𝑛	PRON
cana-1119	32	3	𝑎𝑛+1	𝑎𝑛+1	PROPN
cana-1119	32	4	⋯	⋯	PROPN
cana-1119	32	5	𝑎𝑛+𝑝−1	𝑎𝑛+𝑝−1	PROPN
cana-1119	32	6	𝑎𝑛+1	𝑎𝑛+1	PROPN
cana-1119	32	7	𝑎𝑛+2	𝑎𝑛+2	NOUN
cana-1119	32	8	⋯	⋯	VERB
cana-1119	32	9	𝑎𝑛+𝑝	𝑎𝑛+𝑝	PROPN
cana-1119	32	10	⋮	⋮	NOUN
cana-1119	32	11	⋮	⋮	ADJ
cana-1119	32	12	⋮	⋮	PROPN
cana-1119	32	13	⋮	⋮	PROPN
cana-1119	32	14	𝑎𝑛+𝑝−1	𝑎𝑛+𝑝−1	PROPN
cana-1119	33	1	𝑎𝑛+𝑝	𝑎𝑛+𝑝	PROPN
cana-1119	33	2	⋯	⋯	ADP
cana-1119	33	3	𝑎𝑛+2𝑝−2	𝑎𝑛+2𝑝−2	PROPN
cana-1119	33	4	|	|	ADV
cana-1119	33	5	in	in	ADP
cana-1119	33	6	geometric	geometric	ADJ
cana-1119	33	7	function	function	NOUN
cana-1119	33	8	theory	theory	NOUN
cana-1119	33	9	of	of	ADP
cana-1119	33	10	complex	complex	ADJ
cana-1119	33	11	analysis	analysis	NOUN
cana-1119	33	12	finding	find	VERB
cana-1119	33	13	upper	upper	ADJ
cana-1119	33	14	bounds	bound	NOUN
cana-1119	33	15	of	of	ADP
cana-1119	33	16	hankel	hankel	NOUN
cana-1119	33	17	determinant	determinant	ADJ
cana-1119	33	18	of	of	ADP
cana-1119	33	19	various	various	ADJ
cana-1119	33	20	subfamilies	subfamily	NOUN
cana-1119	33	21	of	of	ADP
cana-1119	33	22	𝒜	𝒜	NOUN
cana-1119	33	23	is	be	AUX
cana-1119	33	24	a	a	DET
cana-1119	33	25	widely	widely	ADV
cana-1119	33	26	famous	famous	ADJ
cana-1119	33	27	and	and	CCONJ
cana-1119	33	28	an	an	DET
cana-1119	33	29	interesting	interesting	ADJ
cana-1119	33	30	problem	problem	NOUN
cana-1119	33	31	.	.	PUNCT
cana-1119	34	1	noonan(1976	noonan(1976	NOUN
cana-1119	34	2	)	)	PUNCT
cana-1119	34	3	and	and	CCONJ
cana-1119	34	4	noor(1983	noor(1983	NUM
cana-1119	34	5	)	)	PUNCT
cana-1119	35	1	[	[	X
cana-1119	35	2	14	14	NUM
cana-1119	35	3	,	,	PUNCT
cana-1119	35	4	15	15	NUM
cana-1119	35	5	]	]	PUNCT
cana-1119	35	6	studied	study	VERB
cana-1119	35	7	the	the	DET
cana-1119	35	8	growth	growth	NOUN
cana-1119	35	9	rate	rate	NOUN
cana-1119	35	10	of	of	ADP
cana-1119	35	11	ℋ(𝑝,𝑛	ℋ(𝑝,𝑛	NUM
cana-1119	35	12	)	)	PUNCT
cana-1119	35	13	for	for	ADP
cana-1119	35	14	fixed	fix	VERB
cana-1119	35	15	values	value	NOUN
cana-1119	35	16	of	of	ADP
cana-1119	35	17	𝑝	𝑝	NOUN
cana-1119	35	18	and	and	CCONJ
cana-1119	35	19	𝑛	𝑛	NOUN
cana-1119	35	20	,	,	PUNCT
cana-1119	35	21	as	as	ADP
cana-1119	35	22	𝑛	𝑛	PROPN
cana-1119	35	23	→	→	SYM
cana-1119	35	24	∞	∞	NUM
cana-1119	35	25	of	of	ADP
cana-1119	35	26	different	different	ADJ
cana-1119	35	27	subfamilies	subfamily	NOUN
cana-1119	35	28	of	of	ADP
cana-1119	35	29	the	the	DET
cana-1119	35	30	univalent	univalent	ADJ
cana-1119	35	31	function	function	NOUN
cana-1119	35	32	of	of	ADP
cana-1119	35	33	class	class	NOUN
cana-1119	35	34	𝒮.	𝒮.	PROPN
cana-1119	35	35	where	where	SCONJ
cana-1119	35	36	ℋ(2,2)(𝑓	ℋ(2,2)(𝑓	VERB
cana-1119	35	37	)	)	PUNCT
cana-1119	35	38	=	=	PUNCT
cana-1119	36	1	|	|	ADV
cana-1119	36	2	𝑎2	𝑎2	PROPN
cana-1119	36	3	𝑎3	𝑎3	PROPN
cana-1119	36	4	𝑎3	𝑎3	PROPN
cana-1119	36	5	𝑎4	𝑎4	PROPN
cana-1119	36	6	|	|	ADV
cana-1119	36	7	=	=	SYM
cana-1119	36	8	𝑎2𝑎4	𝑎2𝑎4	PRON
cana-1119	36	9	−	−	PROPN
cana-1119	36	10	𝑎3	𝑎3	NOUN
cana-1119	36	11	2	2	NUM
cana-1119	36	12	from	from	ADP
cana-1119	36	13	past	past	ADJ
cana-1119	36	14	many	many	ADJ
cana-1119	36	15	years	year	NOUN
cana-1119	36	16	,	,	PUNCT
cana-1119	36	17	a	a	DET
cana-1119	36	18	huge	huge	ADJ
cana-1119	36	19	collection	collection	NOUN
cana-1119	36	20	of	of	ADP
cana-1119	36	21	research	research	NOUN
cana-1119	36	22	papers	paper	NOUN
cana-1119	36	23	have	have	AUX
cana-1119	36	24	been	be	AUX
cana-1119	36	25	dedicated	dedicate	VERB
cana-1119	36	26	for	for	ADP
cana-1119	36	27	finding	find	VERB
cana-1119	36	28	the	the	DET
cana-1119	36	29	upper	upper	ADJ
cana-1119	36	30	bounds	bound	NOUN
cana-1119	36	31	for	for	ADP
cana-1119	36	32	various	various	ADJ
cana-1119	36	33	orders	order	NOUN
cana-1119	36	34	of	of	ADP
cana-1119	36	35	hankel	hankel	NOUN
cana-1119	36	36	determinant	determinant	ADJ
cana-1119	36	37	,	,	PUNCT
cana-1119	36	38	some	some	DET
cana-1119	36	39	recent	recent	ADJ
cana-1119	36	40	work	work	NOUN
cana-1119	36	41	on	on	ADP
cana-1119	36	42	second	second	ADJ
cana-1119	36	43	,	,	PUNCT
cana-1119	36	44	third	third	ADJ
cana-1119	36	45	and	and	CCONJ
cana-1119	36	46	fourth	fourth	ADJ
cana-1119	36	47	order	order	NOUN
cana-1119	36	48	hankel	hankel	NOUN
cana-1119	36	49	determinants	determinant	NOUN
cana-1119	36	50	see	see	VERB
cana-1119	36	51	[	[	X
cana-1119	36	52	[	[	X
cana-1119	36	53	16	16	NUM
cana-1119	36	54	]	]	X
cana-1119	37	1	[	[	X
cana-1119	37	2	21	21	NUM
cana-1119	37	3	]	]	X
cana-1119	37	4	]	]	X
cana-1119	37	5	,	,	PUNCT
cana-1119	37	6	recently	recently	ADV
cana-1119	37	7	,	,	PUNCT
cana-1119	37	8	cho	cho	PROPN
cana-1119	37	9	et	et	PROPN
cana-1119	37	10	al	al	PROPN
cana-1119	37	11	.	.	PUNCT
cana-1119	38	1	[	[	X
cana-1119	38	2	10	10	NUM
cana-1119	38	3	]	]	PUNCT
cana-1119	38	4	introduced	introduce	VERB
cana-1119	38	5	the	the	DET
cana-1119	38	6	following	follow	VERB
cana-1119	38	7	function	function	NOUN
cana-1119	38	8	class	class	NOUN
cana-1119	38	9	𝑆sin	𝑆sin	PROPN
cana-1119	38	10	∗	∗	VERB
cana-1119	38	11	𝑆sin	𝑆sin	PROPN
cana-1119	38	12	∗	∗	NOUN
cana-1119	38	13	:	:	PUNCT
cana-1119	39	1	=	=	SYM
cana-1119	39	2	{	{	PUNCT
cana-1119	39	3	ℎ	ℎ	PROPN
cana-1119	39	4	∈	∈	PROPN
cana-1119	39	5	𝒜	𝒜	NOUN
cana-1119	39	6	:	:	PUNCT
cana-1119	39	7	1	1	NUM
cana-1119	39	8	+	+	NUM
cana-1119	39	9	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	NOUN
cana-1119	39	10	)	)	PUNCT
cana-1119	39	11	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1119	39	12	)	)	PUNCT
cana-1119	39	13	≺	≺	NOUN
cana-1119	39	14	1	1	NUM
cana-1119	39	15	+	+	CCONJ
cana-1119	39	16	sin	sin	NOUN
cana-1119	39	17	𝑧	𝑧	NOUN
cana-1119	39	18	,	,	PUNCT
cana-1119	39	19	∀𝑧	∀𝑧	PRON
cana-1119	39	20	∈	∈	PROPN
cana-1119	39	21	𝔻	𝔻	ADJ
cana-1119	39	22	}	}	PUNCT
cana-1119	39	23	various	various	ADJ
cana-1119	39	24	researchers	researcher	NOUN
cana-1119	39	25	established	establish	VERB
cana-1119	39	26	fekete	fekete	PROPN
cana-1119	39	27	szegö	szegö	PROPN
cana-1119	39	28	inequality	inequality	NOUN
cana-1119	39	29	for	for	ADP
cana-1119	39	30	various	various	ADJ
cana-1119	39	31	classes	class	NOUN
cana-1119	39	32	afterwards	afterwards	ADV
cana-1119	39	33	(	(	PUNCT
cana-1119	39	34	[	[	X
cana-1119	39	35	25	25	NUM
cana-1119	39	36	]	]	X
cana-1119	40	1	[	[	X
cana-1119	40	2	31	31	NUM
cana-1119	40	3	]	]	PUNCT
cana-1119	40	4	)	)	PUNCT
cana-1119	40	5	.	.	PUNCT
cana-1119	41	1	lets	lets	AUX
cana-1119	41	2	define	define	VERB
cana-1119	41	3	a	a	DET
cana-1119	41	4	new	new	ADJ
cana-1119	41	5	subclass	subclass	NOUN
cana-1119	41	6	𝑆∗𝐶sin	𝑆∗𝐶sin	NOUN
cana-1119	41	7	(	(	PUNCT
cana-1119	41	8	𝑟)of	𝑟)of	PROPN
cana-1119	41	9	𝒜.	𝒜.	PROPN
cana-1119	41	10	this	this	DET
cana-1119	41	11	subclass	subclass	NOUN
cana-1119	41	12	contains	contain	VERB
cana-1119	41	13	all	all	DET
cana-1119	41	14	those	those	DET
cana-1119	41	15	analytic	analytic	ADJ
cana-1119	41	16	univalent	univalent	ADJ
cana-1119	41	17	functions	function	NOUN
cana-1119	41	18	in	in	ADP
cana-1119	41	19	𝒜	𝒜	NOUN
cana-1119	41	20	which	which	PRON
cana-1119	41	21	satisfies	satisfy	VERB
cana-1119	41	22	,	,	PUNCT
cana-1119	41	23	(	(	PUNCT
cana-1119	41	24	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	NOUN
cana-1119	41	25	)	)	PUNCT
cana-1119	41	26	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1119	41	27	)	)	PUNCT
cana-1119	41	28	)	)	PUNCT
cana-1119	42	1	𝑟	𝑟	NOUN
cana-1119	42	2	(	(	PUNCT
cana-1119	42	3	(	(	PUNCT
cana-1119	42	4	𝑧ℎ′(𝑧))′	𝑧ℎ′(𝑧))′	PROPN
cana-1119	42	5	ℎ′(𝑧	ℎ′(𝑧	PROPN
cana-1119	42	6	)	)	PUNCT
cana-1119	42	7	)	)	PUNCT
cana-1119	42	8	1−𝑟	1−𝑟	NUM
cana-1119	42	9	,	,	PUNCT
cana-1119	42	10	𝑧	𝑧	PROPN
cana-1119	42	11	∈	∈	PROPN
cana-1119	42	12	𝔻	𝔻	ADJ
cana-1119	42	13	𝑆∗𝐶sin(𝑟):=	𝑆∗𝐶sin(𝑟):=	PROPN
cana-1119	42	14	{	{	PUNCT
cana-1119	42	15	ℎ	ℎ	PROPN
cana-1119	42	16	∈	∈	PROPN
cana-1119	42	17	𝒜	𝒜	NOUN
cana-1119	42	18	:	:	PUNCT
cana-1119	42	19	(	(	PUNCT
cana-1119	42	20	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	NOUN
cana-1119	42	21	)	)	PUNCT
cana-1119	42	22	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1119	42	23	)	)	PUNCT
cana-1119	42	24	)	)	PUNCT
cana-1119	43	1	𝑟	𝑟	NOUN
cana-1119	43	2	(	(	PUNCT
cana-1119	43	3	(	(	PUNCT
cana-1119	43	4	𝑧ℎ′(𝑧))′	𝑧ℎ′(𝑧))′	PROPN
cana-1119	43	5	ℎ′(𝑧	ℎ′(𝑧	PROPN
cana-1119	43	6	)	)	PUNCT
cana-1119	43	7	)	)	PUNCT
cana-1119	44	1	1−𝑟	1−𝑟	NUM
cana-1119	44	2	≺	≺	NOUN
cana-1119	44	3	1	1	NUM
cana-1119	44	4	+	+	CCONJ
cana-1119	44	5	sin	sin	NOUN
cana-1119	44	6	(	(	PUNCT
cana-1119	44	7	𝑧	𝑧	NOUN
cana-1119	44	8	)	)	PUNCT
cana-1119	44	9	}	}	PUNCT
cana-1119	44	10	from	from	ADP
cana-1119	44	11	above	above	ADP
cana-1119	44	12	we	we	PRON
cana-1119	44	13	have	have	VERB
cana-1119	44	14	𝑆∗𝐶sin(0):=	𝑆∗𝐶sin(0):=	PROPN
cana-1119	44	15	𝐶sin	𝐶sin	PROPN
cana-1119	44	16	=	=	SYM
cana-1119	44	17	𝐶sin	𝐶sin	PROPN
cana-1119	44	18	:	:	PUNCT
cana-1119	44	19	=	=	X
cana-1119	44	20	{	{	PUNCT
cana-1119	44	21	ℎ	ℎ	PROPN
cana-1119	44	22	∈	∈	PROPN
cana-1119	44	23	𝒜	𝒜	NOUN
cana-1119	44	24	:	:	PUNCT
cana-1119	44	25	(	(	PUNCT
cana-1119	44	26	(	(	PUNCT
cana-1119	44	27	𝑧ℎ′(𝑧))′	𝑧ℎ′(𝑧))′	PROPN
cana-1119	44	28	ℎ′(𝑧	ℎ′(𝑧	PROPN
cana-1119	44	29	)	)	PUNCT
cana-1119	44	30	)	)	PUNCT
cana-1119	44	31	≺	≺	NOUN
cana-1119	44	32	1	1	NUM
cana-1119	45	1	+	+	CCONJ
cana-1119	45	2	sin	sin	NOUN
cana-1119	45	3	(	(	PUNCT
cana-1119	45	4	𝑧	𝑧	NOUN
cana-1119	45	5	)	)	PUNCT
cana-1119	45	6	}	}	PUNCT
cana-1119	45	7	and	and	CCONJ
cana-1119	45	8	𝑆∗𝐶sin(1):=	𝑆∗𝐶sin(1):=	PROPN
cana-1119	45	9	𝑆sin	𝑆sin	PROPN
cana-1119	45	10	∗	∗	NOUN
cana-1119	45	11	:	:	PUNCT
cana-1119	46	1	=	=	SYM
cana-1119	46	2	{	{	PUNCT
cana-1119	46	3	ℎ	ℎ	PROPN
cana-1119	46	4	∈	∈	PROPN
cana-1119	46	5	𝒜	𝒜	NOUN
cana-1119	46	6	:	:	PUNCT
cana-1119	46	7	(	(	PUNCT
cana-1119	46	8	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	NOUN
cana-1119	46	9	)	)	PUNCT
cana-1119	46	10	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1119	46	11	)	)	PUNCT
cana-1119	46	12	)	)	PUNCT
cana-1119	46	13	≺	≺	NOUN
cana-1119	46	14	1	1	NUM
cana-1119	46	15	+	+	CCONJ
cana-1119	46	16	sin	sin	NOUN
cana-1119	46	17	(	(	PUNCT
cana-1119	46	18	𝑧	𝑧	NOUN
cana-1119	46	19	)	)	PUNCT
cana-1119	46	20	}	}	PUNCT
cana-1119	46	21	communications	communication	NOUN
cana-1119	46	22	on	on	ADP
cana-1119	46	23	applied	apply	VERB
cana-1119	46	24	nonlinear	nonlinear	ADJ
cana-1119	46	25	analysis	analysis	NOUN
cana-1119	46	26	issn	issn	NOUN
cana-1119	46	27	:	:	PUNCT
cana-1119	46	28	1074	1074	NUM
cana-1119	46	29	-	-	PUNCT
cana-1119	46	30	133x	133x	NUM
cana-1119	46	31	vol	vol	NOUN
cana-1119	46	32	31	31	NUM
cana-1119	46	33	no	no	NOUN
cana-1119	46	34	.	.	PUNCT
cana-1119	47	1	6s	6s	NUM
cana-1119	47	2	(	(	PUNCT
cana-1119	47	3	2024	2024	NUM
cana-1119	47	4	)	)	PUNCT
cana-1119	47	5	52	52	NUM
cana-1119	47	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1119	47	7	2	2	NUM
cana-1119	47	8	.	.	PUNCT
cana-1119	47	9	preliminary	preliminary	ADJ
cana-1119	47	10	lemmas	lemma	NOUN
cana-1119	47	11	.	.	PUNCT
cana-1119	48	1	let	let	VERB
cana-1119	48	2	𝒫	𝒫	NOUN
cana-1119	48	3	denotes	denote	VERB
cana-1119	48	4	the	the	DET
cana-1119	48	5	class	class	NOUN
cana-1119	48	6	of	of	ADP
cana-1119	48	7	analytic	analytic	ADJ
cana-1119	48	8	functions	function	NOUN
cana-1119	48	9	of	of	ADP
cana-1119	48	10	the	the	DET
cana-1119	48	11	form	form	NOUN
cana-1119	48	12	𝑝(𝑧	𝑝(𝑧	PROPN
cana-1119	48	13	)	)	PUNCT
cana-1119	49	1	=	=	PUNCT
cana-1119	49	2	1	1	NUM
cana-1119	49	3	+	+	CCONJ
cana-1119	49	4	∑	∑	NOUN
cana-1119	49	5	 	 	SPACE
cana-1119	49	6	∞	∞	PROPN
cana-1119	49	7	𝑛=1	𝑛=1	NOUN
cana-1119	49	8	  	  	SPACE
cana-1119	49	9	𝑐𝑛𝑧	𝑐𝑛𝑧	PROPN
cana-1119	49	10	𝑛	𝑛	PROPN
cana-1119	49	11	,	,	PUNCT
cana-1119	49	12	𝑧	𝑧	PRON
cana-1119	49	13	∈	∈	PROPN
cana-1119	49	14	𝔻	𝔻	PROPN
cana-1119	49	15	(	(	PUNCT
cana-1119	49	16	3	3	NUM
cana-1119	49	17	)	)	PUNCT
cana-1119	49	18	whereℜ(𝑝(𝑧	whereℜ(𝑝(𝑧	NOUN
cana-1119	49	19	)	)	PUNCT
cana-1119	49	20	)	)	PUNCT
cana-1119	49	21	>	>	X
cana-1119	49	22	0	0	PUNCT
cana-1119	50	1	in	in	ADP
cana-1119	50	2	𝔻.	𝔻.	PROPN
cana-1119	50	3	lemma	lemma	PROPN
cana-1119	50	4	2.1	2.1	NUM
cana-1119	50	5	.	.	PUNCT
cana-1119	51	1	(	(	PUNCT
cana-1119	51	2	see	see	VERB
cana-1119	51	3	[	[	X
cana-1119	51	4	13	13	NUM
cana-1119	51	5	]	]	SYM
cana-1119	51	6	)	)	PUNCT
cana-1119	51	7	if	if	SCONJ
cana-1119	51	8	𝑝(𝑧	𝑝(𝑧	NOUN
cana-1119	51	9	)	)	PUNCT
cana-1119	51	10	∈	∈	PROPN
cana-1119	51	11	𝒫	𝒫	PROPN
cana-1119	51	12	,	,	PUNCT
cana-1119	51	13	and	and	CCONJ
cana-1119	51	14	𝑐𝑛	𝑐𝑛	PROPN
cana-1119	51	15	be	be	AUX
cana-1119	51	16	the	the	DET
cana-1119	51	17	𝑛th	𝑛th	NOUN
cana-1119	51	18	cofficients	cofficient	NOUN
cana-1119	51	19	of	of	ADP
cana-1119	51	20	𝑃(𝑧	𝑃(𝑧	NOUN
cana-1119	51	21	)	)	PUNCT
cana-1119	51	22	,	,	PUNCT
cana-1119	51	23	then	then	ADV
cana-1119	51	24	|𝑐𝑛|	|𝑐𝑛|	NOUN
cana-1119	51	25	≤	≤	NOUN
cana-1119	51	26	2	2	NUM
cana-1119	51	27	for	for	ADP
cana-1119	51	28	all	all	DET
cana-1119	51	29	𝑛	𝑛	DET
cana-1119	51	30	∈	∈	PROPN
cana-1119	51	31	ℕ	ℕ	PROPN
cana-1119	51	32	(	(	PUNCT
cana-1119	51	33	4	4	NUM
cana-1119	51	34	)	)	PUNCT
cana-1119	51	35	|𝑐2	|𝑐2	NOUN
cana-1119	52	1	−	−	PROPN
cana-1119	52	2	𝛾𝑐1	𝛾𝑐1	PROPN
cana-1119	52	3	2|	2|	NUM
cana-1119	52	4	≤	≤	NOUN
cana-1119	52	5	2𝑚𝑎𝑥{1	2𝑚𝑎𝑥{1	NUM
cana-1119	52	6	,	,	PUNCT
cana-1119	52	7	|2𝛾	|2𝛾	NUM
cana-1119	52	8	−	−	PROPN
cana-1119	52	9	1|	1|	NUM
cana-1119	52	10	}	}	PUNCT
cana-1119	52	11	where	where	SCONJ
cana-1119	52	12	𝛾	𝛾	ADP
cana-1119	52	13	∈	∈	PROPN
cana-1119	52	14	ℂ	ℂ	PROPN
cana-1119	52	15	(	(	PUNCT
cana-1119	52	16	5	5	NUM
cana-1119	52	17	)	)	PUNCT
cana-1119	52	18	|𝑐𝑛+𝑚	|𝑐𝑛+𝑚	ADJ
cana-1119	52	19	−	−	PROPN
cana-1119	52	20	𝛾𝑐𝑛𝑐𝑚|	𝛾𝑐𝑛𝑐𝑚|	VERB
cana-1119	52	21	≤	≤	NUM
cana-1119	52	22	2	2	NUM
cana-1119	52	23	,	,	PUNCT
cana-1119	52	24	𝛾	𝛾	ADP
cana-1119	52	25	∈	∈	PROPN
cana-1119	53	1	[	[	X
cana-1119	53	2	0,1	0,1	NUM
cana-1119	53	3	]	]	PUNCT
cana-1119	53	4	,	,	PUNCT
cana-1119	53	5	where	where	SCONJ
cana-1119	53	6	𝑛,𝑚	𝑛,𝑚	NOUN
cana-1119	53	7	∈	∈	PROPN
cana-1119	53	8	ℕ	ℕ	PROPN
cana-1119	53	9	(	(	PUNCT
cana-1119	53	10	6	6	NUM
cana-1119	53	11	)	)	PUNCT
cana-1119	53	12	|𝑐2	|𝑐2	NOUN
cana-1119	53	13	−	−	NOUN
cana-1119	53	14	𝛿𝑐1	𝛿𝑐1	X
cana-1119	53	15	2|	2|	NUM
cana-1119	53	16	≤	≤	NOUN
cana-1119	53	17	{	{	PUNCT
cana-1119	53	18	−4𝛿	−4𝛿	PROPN
cana-1119	54	1	+	+	CCONJ
cana-1119	54	2	2	2	NUM
cana-1119	54	3	,	,	PUNCT
cana-1119	54	4	if	if	SCONJ
cana-1119	54	5	𝛿	𝛿	DET
cana-1119	54	6	≤	≤	NOUN
cana-1119	54	7	0	0	NUM
cana-1119	54	8	,	,	PUNCT
cana-1119	54	9	2	2	NUM
cana-1119	54	10	,	,	PUNCT
cana-1119	54	11	if	if	SCONJ
cana-1119	54	12	0	0	NUM
cana-1119	54	13	≤	≤	NUM
cana-1119	54	14	𝛿	𝛿	DET
cana-1119	54	15	≤	≤	NUM
cana-1119	54	16	1	1	NUM
cana-1119	54	17	,	,	PUNCT
cana-1119	54	18	4𝛿	4𝛿	NOUN
cana-1119	54	19	−	−	NOUN
cana-1119	54	20	2	2	NUM
cana-1119	54	21	,	,	PUNCT
cana-1119	54	22	if	if	SCONJ
cana-1119	54	23	1	1	NUM
cana-1119	54	24	≤	≤	NOUN
cana-1119	54	25	𝛿	𝛿	ADJ
cana-1119	54	26	,	,	PUNCT
cana-1119	54	27	(	(	PUNCT
cana-1119	54	28	7	7	X
cana-1119	54	29	)	)	PUNCT
cana-1119	54	30	lemma	lemma	PROPN
cana-1119	54	31	2.2.(see[17	2.2.(see[17	PROPN
cana-1119	54	32	]	]	PUNCT
cana-1119	54	33	)	)	PUNCT
cana-1119	54	34	if	if	SCONJ
cana-1119	54	35	𝑃(𝑧	𝑃(𝑧	NOUN
cana-1119	54	36	)	)	PUNCT
cana-1119	54	37	∈	∈	PROPN
cana-1119	54	38	𝒫	𝒫	NOUN
cana-1119	54	39	then	then	ADV
cana-1119	54	40	there	there	PRON
cana-1119	54	41	exists	exist	VERB
cana-1119	54	42	𝑥	𝑥	PRON
cana-1119	54	43	,	,	PUNCT
cana-1119	54	44	𝑧	𝑧	PROPN
cana-1119	54	45	∈	∈	PROPN
cana-1119	54	46	�	�	NOUN
cana-1119	54	47	̅	̅	NOUN
cana-1119	54	48	�	�	NOUN
cana-1119	54	49	with	with	ADP
cana-1119	54	50	|𝑥|	|𝑥|	ADJ
cana-1119	54	51	≤	≤	NUM
cana-1119	54	52	1	1	NUM
cana-1119	54	53	,	,	PUNCT
cana-1119	54	54	|𝑦|	|𝑦|	PROPN
cana-1119	54	55	≤	≤	ADV
cana-1119	54	56	1	1	NUM
cana-1119	54	57	,	,	PUNCT
cana-1119	54	58	such	such	ADJ
cana-1119	54	59	that	that	SCONJ
cana-1119	54	60	2𝑐2	2𝑐2	NUM
cana-1119	54	61	=	=	SYM
cana-1119	54	62	𝑐1	𝑐1	NOUN
cana-1119	54	63	2	2	NUM
cana-1119	55	1	+	+	CCONJ
cana-1119	55	2	𝑥(4	𝑥(4	NOUN
cana-1119	55	3	−	−	NOUN
cana-1119	55	4	𝑐1	𝑐1	NOUN
cana-1119	55	5	2	2	NUM
cana-1119	55	6	)	)	PUNCT
cana-1119	55	7	(	(	PUNCT
cana-1119	55	8	8)	8)	NUM
cana-1119	55	9	4𝑐3	4𝑐3	NUM
cana-1119	55	10	=	=	PUNCT
cana-1119	56	1	𝑐1	𝑐1	NOUN
cana-1119	56	2	3	3	NUM
cana-1119	57	1	+	+	SYM
cana-1119	57	2	2(4	2(4	NUM
cana-1119	57	3	−	−	NOUN
cana-1119	58	1	𝑐1	𝑐1	NOUN
cana-1119	58	2	2)𝑐1𝑥	2)𝑐1𝑥	NUM
cana-1119	58	3	−	−	NOUN
cana-1119	58	4	(	(	PUNCT
cana-1119	58	5	4	4	NUM
cana-1119	58	6	−	−	NOUN
cana-1119	58	7	𝑐1	𝑐1	NOUN
cana-1119	58	8	2)𝑐1𝑥	2)𝑐1𝑥	NUM
cana-1119	58	9	2	2	NUM
cana-1119	58	10	+	+	CCONJ
cana-1119	58	11	2(4	2(4	NUM
cana-1119	58	12	−	−	NOUN
cana-1119	59	1	𝑐1	𝑐1	NOUN
cana-1119	59	2	2)(1	2)(1	NUM
cana-1119	59	3	−	−	NOUN
cana-1119	59	4	|𝑥|2)𝑦	|𝑥|2)𝑦	NUM
cana-1119	59	5	(	(	PUNCT
cana-1119	59	6	9	9	NUM
cana-1119	59	7	)	)	SYM
cana-1119	59	8	3	3	NUM
cana-1119	59	9	.	.	PUNCT
cana-1119	59	10	important	important	ADJ
cana-1119	59	11	theorems	theorem	NOUN
cana-1119	59	12	.	.	PUNCT
cana-1119	60	1	theorem	theorem	VERB
cana-1119	60	2	3.1	3.1	NUM
cana-1119	60	3	.	.	PUNCT
cana-1119	61	1	if	if	SCONJ
cana-1119	61	2	the	the	DET
cana-1119	61	3	function	function	NOUN
cana-1119	61	4	ℎ(𝑧	ℎ(𝑧	NOUN
cana-1119	61	5	)	)	PUNCT
cana-1119	61	6	∈	∈	PROPN
cana-1119	61	7	𝑆∗𝐶sin	𝑆∗𝐶sin	NOUN
cana-1119	61	8	(	(	PUNCT
cana-1119	61	9	𝑟	𝑟	NOUN
cana-1119	61	10	)	)	PUNCT
cana-1119	61	11	and	and	CCONJ
cana-1119	61	12	is	be	AUX
cana-1119	61	13	of	of	ADP
cana-1119	61	14	the	the	DET
cana-1119	61	15	form	form	NOUN
cana-1119	61	16	(	(	PUNCT
cana-1119	61	17	1	1	NUM
cana-1119	61	18	)	)	PUNCT
cana-1119	61	19	,	,	PUNCT
cana-1119	61	20	then	then	ADV
cana-1119	61	21	|𝑎2|	|𝑎2|	NOUN
cana-1119	61	22	≤	≤	NOUN
cana-1119	61	23	1	1	NUM
cana-1119	61	24	(	(	PUNCT
cana-1119	61	25	2	2	NUM
cana-1119	61	26	−	−	NUM
cana-1119	61	27	𝑟	𝑟	NOUN
cana-1119	61	28	)	)	PUNCT
cana-1119	61	29	|𝑎3|	|𝑎3|	NOUN
cana-1119	61	30	≤	≤	NUM
cana-1119	61	31	1	1	NUM
cana-1119	61	32	2(3	2(3	NUM
cana-1119	61	33	−	−	PROPN
cana-1119	61	34	2𝑟	2𝑟	NUM
cana-1119	61	35	)	)	PUNCT
cana-1119	61	36	max	max	PROPN
cana-1119	61	37	{	{	PUNCT
cana-1119	61	38	1	1	NUM
cana-1119	61	39	,	,	PUNCT
cana-1119	61	40	|	|	ADV
cana-1119	61	41	𝑟2	𝑟2	NOUN
cana-1119	61	42	+	+	NOUN
cana-1119	61	43	5𝑟	5𝑟	NUM
cana-1119	61	44	−	−	NOUN
cana-1119	61	45	8	8	NUM
cana-1119	61	46	2(−2	2(−2	NUM
cana-1119	61	47	+	+	CCONJ
cana-1119	61	48	𝑟)2	𝑟)2	NOUN
cana-1119	61	49	|	|	ADV
cana-1119	61	50	}	}	PUNCT
cana-1119	61	51	and	and	CCONJ
cana-1119	61	52	|𝑎3	|𝑎3	VERB
cana-1119	61	53	−	−	PROPN
cana-1119	61	54	𝛿𝑎2	𝛿𝑎2	NOUN
cana-1119	61	55	2|	2|	NOUN
cana-1119	61	56	≤	≤	ADV
cana-1119	61	57	1	1	NUM
cana-1119	61	58	2(3	2(3	NUM
cana-1119	61	59	−	−	PROPN
cana-1119	61	60	2𝑟	2𝑟	NUM
cana-1119	61	61	)	)	PUNCT
cana-1119	61	62	max	max	PROPN
cana-1119	61	63	{	{	PUNCT
cana-1119	61	64	1	1	NUM
cana-1119	61	65	,	,	PUNCT
cana-1119	61	66	|	|	ADV
cana-1119	61	67	𝑟2	𝑟2	NOUN
cana-1119	61	68	+	+	NOUN
cana-1119	61	69	5𝑟	5𝑟	NUM
cana-1119	61	70	+	+	CCONJ
cana-1119	61	71	4𝛿(3	4𝛿(3	X
cana-1119	61	72	−	−	VERB
cana-1119	61	73	2𝑟	2𝑟	NUM
cana-1119	61	74	)	)	PUNCT
cana-1119	61	75	−	−	ADP
cana-1119	62	1	8	8	NUM
cana-1119	62	2	2(𝑟	2(𝑟	NUM
cana-1119	62	3	−	−	NOUN
cana-1119	62	4	2)2	2)2	NUM
cana-1119	62	5	|	|	NOUN
cana-1119	62	6	}	}	PUNCT
cana-1119	62	7	proof	proof	NOUN
cana-1119	62	8	.	.	PUNCT
cana-1119	63	1	from	from	ADP
cana-1119	63	2	definition	definition	NOUN
cana-1119	63	3	of	of	ADP
cana-1119	63	4	subordination	subordination	NOUN
cana-1119	63	5	we	we	PRON
cana-1119	63	6	have	have	VERB
cana-1119	63	7	𝑆∗𝐶sin(𝑟	𝑆∗𝐶sin(𝑟	VERB
cana-1119	63	8	)	)	PUNCT
cana-1119	63	9	=	=	NOUN
cana-1119	64	1	{	{	PUNCT
cana-1119	64	2	ℎ	ℎ	PROPN
cana-1119	64	3	∈	∈	PROPN
cana-1119	64	4	𝒜	𝒜	NOUN
cana-1119	64	5	:	:	PUNCT
cana-1119	64	6	(	(	PUNCT
cana-1119	64	7	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	NOUN
cana-1119	64	8	)	)	PUNCT
cana-1119	64	9	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1119	64	10	)	)	PUNCT
cana-1119	64	11	)	)	PUNCT
cana-1119	65	1	𝑟	𝑟	NOUN
cana-1119	65	2	(	(	PUNCT
cana-1119	65	3	(	(	PUNCT
cana-1119	65	4	𝑧ℎ′(𝑧))′	𝑧ℎ′(𝑧))′	PROPN
cana-1119	65	5	ℎ′(𝑧	ℎ′(𝑧	PROPN
cana-1119	65	6	)	)	PUNCT
cana-1119	65	7	)	)	PUNCT
cana-1119	66	1	1−𝑟	1−𝑟	NUM
cana-1119	66	2	≺	≺	NOUN
cana-1119	66	3	1	1	NUM
cana-1119	66	4	+	+	CCONJ
cana-1119	66	5	sin	sin	NOUN
cana-1119	66	6	(	(	PUNCT
cana-1119	66	7	𝑧	𝑧	NOUN
cana-1119	66	8	)	)	PUNCT
cana-1119	66	9	}	}	PUNCT
cana-1119	66	10	(	(	PUNCT
cana-1119	66	11	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	NOUN
cana-1119	66	12	)	)	PUNCT
cana-1119	66	13	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1119	66	14	)	)	PUNCT
cana-1119	66	15	)	)	PUNCT
cana-1119	67	1	𝑟	𝑟	NOUN
cana-1119	67	2	(	(	PUNCT
cana-1119	67	3	(	(	PUNCT
cana-1119	67	4	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	NOUN
cana-1119	67	5	)	)	PUNCT
cana-1119	67	6	)	)	PUNCT
cana-1119	68	1	′	′	NUM
cana-1119	69	1	ℎ′(𝑧	ℎ′(𝑧	NOUN
cana-1119	69	2	)	)	PUNCT
cana-1119	69	3	)	)	PUNCT
cana-1119	70	1	1−𝑟	1−𝑟	NUM
cana-1119	71	1	=	=	SYM
cana-1119	71	2	𝑧𝑟[ℎ′(𝑧	𝑧𝑟[ℎ′(𝑧	NOUN
cana-1119	71	3	)	)	PUNCT
cana-1119	71	4	]	]	PUNCT
cana-1119	72	1	2𝑟−1	2𝑟−1	NUM
cana-1119	73	1	[	[	X
cana-1119	73	2	(	(	PUNCT
cana-1119	73	3	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	NOUN
cana-1119	73	4	)	)	PUNCT
cana-1119	73	5	)	)	PUNCT
cana-1119	74	1	′	′	NUM
cana-1119	74	2	]	]	PUNCT
cana-1119	75	1	1−𝑟	1−𝑟	NUM
cana-1119	76	1	[	[	X
cana-1119	76	2	ℎ(𝑧)]𝑟	ℎ(𝑧)]𝑟	PROPN
cana-1119	76	3	(	(	PUNCT
cana-1119	76	4	10	10	NUM
cana-1119	76	5	)	)	PUNCT
cana-1119	76	6	after	after	ADP
cana-1119	76	7	expanding	expand	VERB
cana-1119	76	8	𝑧𝑟[ℎ′(𝑧	𝑧𝑟[ℎ′(𝑧	NOUN
cana-1119	76	9	)	)	PUNCT
cana-1119	76	10	]	]	PUNCT
cana-1119	77	1	2𝑟−1	2𝑟−1	NUM
cana-1119	78	1	[	[	X
cana-1119	78	2	(	(	PUNCT
cana-1119	78	3	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	NOUN
cana-1119	78	4	)	)	PUNCT
cana-1119	78	5	)	)	PUNCT
cana-1119	79	1	′	′	NUM
cana-1119	79	2	]	]	PUNCT
cana-1119	80	1	1−𝑟	1−𝑟	NUM
cana-1119	81	1	[	[	X
cana-1119	81	2	ℎ(𝑧)]𝑟	ℎ(𝑧)]𝑟	PROPN
cana-1119	81	3	,	,	PUNCT
cana-1119	81	4	in	in	ADP
cana-1119	81	5	a	a	DET
cana-1119	81	6	series	series	NOUN
cana-1119	81	7	form	form	NOUN
cana-1119	81	8	we	we	PRON
cana-1119	81	9	have	have	VERB
cana-1119	81	10	communications	communication	NOUN
cana-1119	81	11	on	on	ADP
cana-1119	81	12	applied	apply	VERB
cana-1119	81	13	nonlinear	nonlinear	ADJ
cana-1119	81	14	analysis	analysis	NOUN
cana-1119	81	15	issn	issn	NOUN
cana-1119	81	16	:	:	PUNCT
cana-1119	81	17	1074	1074	NUM
cana-1119	81	18	-	-	PUNCT
cana-1119	81	19	133x	133x	NUM
cana-1119	81	20	vol	vol	NOUN
cana-1119	81	21	31	31	NUM
cana-1119	81	22	no	no	NOUN
cana-1119	81	23	.	.	PUNCT
cana-1119	82	1	6s	6s	NUM
cana-1119	82	2	(	(	PUNCT
cana-1119	82	3	2024	2024	NUM
cana-1119	82	4	)	)	PUNCT
cana-1119	82	5	53	53	NUM
cana-1119	82	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1119	82	7	=	=	SYM
cana-1119	82	8	1	1	NUM
cana-1119	82	9	+	+	CCONJ
cana-1119	82	10	𝑎2(2	𝑎2(2	ADJ
cana-1119	82	11	−	−	NOUN
cana-1119	82	12	𝑟)𝑧	𝑟)𝑧	NOUN
cana-1119	83	1	+	+	CCONJ
cana-1119	83	2	𝑧	𝑧	X
cana-1119	83	3	2	2	NUM
cana-1119	83	4	(	(	PUNCT
cana-1119	83	5	1	1	NUM
cana-1119	83	6	2	2	NUM
cana-1119	83	7	𝑎2	𝑎2	NOUN
cana-1119	83	8	2(𝑟2	2(𝑟2	NUM
cana-1119	83	9	+	+	NUM
cana-1119	83	10	5𝑟	5𝑟	NUM
cana-1119	83	11	−	−	PROPN
cana-1119	83	12	8)	8)	NUM
cana-1119	83	13	+	+	CCONJ
cana-1119	83	14	2𝑎3(3	2𝑎3(3	NUM
cana-1119	83	15	−	−	PROPN
cana-1119	83	16	2𝑟	2𝑟	NUM
cana-1119	83	17	)	)	PUNCT
cana-1119	83	18	)	)	PUNCT
cana-1119	84	1	+	+	X
cana-1119	84	2	𝑧3	𝑧3	PROPN
cana-1119	84	3	(	(	PUNCT
cana-1119	84	4	𝑎3𝑎2(4𝑟	𝑎3𝑎2(4𝑟	PROPN
cana-1119	84	5	2	2	NUM
cana-1119	84	6	+	+	NUM
cana-1119	84	7	11𝑟	11𝑟	NOUN
cana-1119	84	8	−	−	PROPN
cana-1119	84	9	18	18	NUM
cana-1119	84	10	)	)	PUNCT
cana-1119	84	11	+	+	CCONJ
cana-1119	84	12	1	1	NUM
cana-1119	84	13	6	6	NUM
cana-1119	84	14	𝑎2	𝑎2	NOUN
cana-1119	84	15	3(−𝑟3	3(−𝑟3	ADP
cana-1119	85	1	−	−	PROPN
cana-1119	85	2	21𝑟2	21𝑟2	NUM
cana-1119	85	3	−	−	NOUN
cana-1119	85	4	20𝑟	20𝑟	X
cana-1119	85	5	+	+	CCONJ
cana-1119	85	6	48	48	NUM
cana-1119	85	7	)	)	PUNCT
cana-1119	85	8	+3𝑎4(4	+3𝑎4(4	NUM
cana-1119	85	9	−	−	PROPN
cana-1119	85	10	3𝑟	3𝑟	NUM
cana-1119	85	11	)	)	PUNCT
cana-1119	85	12	)	)	PUNCT
cana-1119	86	1	+	+	CCONJ
cana-1119	86	2	𝑧	𝑧	DET
cana-1119	86	3	4(𝑎4𝑎2(9𝑟	4(𝑎4𝑎2(9𝑟	NUM
cana-1119	86	4	2	2	NUM
cana-1119	86	5	+	+	NOUN
cana-1119	86	6	19𝑟	19𝑟	NOUN
cana-1119	86	7	−	−	ADP
cana-1119	86	8	32	32	NUM
cana-1119	86	9	)	)	PUNCT
cana-1119	86	10	+	+	CCONJ
cana-1119	86	11	2𝑎3	2𝑎3	NUM
cana-1119	86	12	2(4𝑟2	2(4𝑟2	NOUN
cana-1119	87	1	+	+	CCONJ
cana-1119	87	2	4𝑟	4𝑟	PROPN
cana-1119	87	3	−	−	NOUN
cana-1119	87	4	9	9	NUM
cana-1119	87	5	)	)	PUNCT
cana-1119	87	6	−2𝑎3𝑎2	−2𝑎3𝑎2	NOUN
cana-1119	87	7	2(𝑟3	2(𝑟3	NUM
cana-1119	87	8	+	+	CCONJ
cana-1119	87	9	16𝑟2	16𝑟2	NUM
cana-1119	87	10	+	+	NUM
cana-1119	87	11	5𝑟	5𝑟	NUM
cana-1119	87	12	−	−	NOUN
cana-1119	87	13	24	24	NUM
cana-1119	87	14	)	)	PUNCT
cana-1119	88	1	+	+	CCONJ
cana-1119	88	2	1	1	NUM
cana-1119	88	3	24	24	NUM
cana-1119	88	4	𝑎2	𝑎2	NOUN
cana-1119	88	5	4(𝑟4	4(𝑟4	NUM
cana-1119	89	1	+	+	CCONJ
cana-1119	90	1	46𝑟3	46𝑟3	NUM
cana-1119	90	2	+	+	CCONJ
cana-1119	90	3	371𝑟2	371𝑟2	NUM
cana-1119	90	4	−	−	NOUN
cana-1119	90	5	58𝑟	58𝑟	PROPN
cana-1119	90	6	−	−	PROPN
cana-1119	90	7	384	384	NUM
cana-1119	90	8	)	)	PUNCT
cana-1119	90	9	+	+	CCONJ
cana-1119	90	10	⋯	⋯	VERB
cana-1119	90	11	(	(	PUNCT
cana-1119	90	12	11	11	NUM
cana-1119	90	13	)	)	PUNCT
cana-1119	90	14	using	use	VERB
cana-1119	90	15	principal	principal	NOUN
cana-1119	90	16	of	of	ADP
cana-1119	90	17	subordination	subordination	NOUN
cana-1119	90	18	and	and	CCONJ
cana-1119	90	19	expending	expend	VERB
cana-1119	90	20	1	1	NUM
cana-1119	90	21	+	+	CCONJ
cana-1119	90	22	sin	sin	NOUN
cana-1119	90	23	(	(	PUNCT
cana-1119	90	24	𝜔(𝑧	𝜔(𝑧	PROPN
cana-1119	90	25	)	)	PUNCT
cana-1119	90	26	)	)	PUNCT
cana-1119	91	1	in	in	ADP
cana-1119	91	2	series	series	NOUN
cana-1119	91	3	form	form	VERB
cana-1119	91	4	1	1	NUM
cana-1119	91	5	+	+	CCONJ
cana-1119	91	6	sin	sin	NOUN
cana-1119	91	7	(	(	PUNCT
cana-1119	91	8	𝜔(𝑧	𝜔(𝑧	PROPN
cana-1119	91	9	)	)	PUNCT
cana-1119	91	10	)	)	PUNCT
cana-1119	92	1	=	=	SYM
cana-1119	92	2	1	1	NUM
cana-1119	92	3	+	+	NUM
cana-1119	92	4	𝑐1𝑧	𝑐1𝑧	X
cana-1119	92	5	2	2	NUM
cana-1119	92	6	+	+	CCONJ
cana-1119	92	7	(	(	PUNCT
cana-1119	92	8	𝑐2	𝑐2	NOUN
cana-1119	92	9	2	2	NUM
cana-1119	92	10	−	−	NOUN
cana-1119	92	11	𝑐1	𝑐1	NOUN
cana-1119	92	12	2	2	NUM
cana-1119	92	13	4	4	NUM
cana-1119	92	14	)	)	PUNCT
cana-1119	92	15	𝑧2	𝑧2	NOUN
cana-1119	93	1	+	+	CCONJ
cana-1119	93	2	1	1	NUM
cana-1119	93	3	48	48	NUM
cana-1119	93	4	(	(	PUNCT
cana-1119	93	5	5𝑐1	5𝑐1	NUM
cana-1119	93	6	3	3	NUM
cana-1119	93	7	−	−	NOUN
cana-1119	93	8	24𝑐2𝑐1	24𝑐2𝑐1	NOUN
cana-1119	93	9	+	+	CCONJ
cana-1119	93	10	24𝑐3)𝑧	24𝑐3)𝑧	NUM
cana-1119	93	11	3	3	NUM
cana-1119	93	12	+	+	CCONJ
cana-1119	93	13	1	1	NUM
cana-1119	93	14	32	32	NUM
cana-1119	93	15	(	(	PUNCT
cana-1119	93	16	−𝑐1	−𝑐1	NOUN
cana-1119	93	17	4	4	NUM
cana-1119	93	18	+	+	SYM
cana-1119	93	19	10𝑐2𝑐1	10𝑐2𝑐1	NUM
cana-1119	93	20	2	2	NUM
cana-1119	93	21	−	−	PROPN
cana-1119	93	22	16𝑐3𝑐1	16𝑐3𝑐1	NOUN
cana-1119	93	23	−	−	PROPN
cana-1119	93	24	8𝑐2	8𝑐2	NUM
cana-1119	93	25	2	2	NUM
cana-1119	93	26	+	+	NUM
cana-1119	93	27	16𝑐4)𝑧	16𝑐4)𝑧	NUM
cana-1119	93	28	4	4	NUM
cana-1119	93	29	(	(	PUNCT
cana-1119	93	30	12	12	NUM
cana-1119	93	31	)	)	PUNCT
cana-1119	93	32	comparing	compare	VERB
cana-1119	93	33	(	(	PUNCT
cana-1119	93	34	11	11	NUM
cana-1119	93	35	)	)	PUNCT
cana-1119	93	36	and	and	CCONJ
cana-1119	93	37	(	(	PUNCT
cana-1119	93	38	12	12	NUM
cana-1119	93	39	)	)	PUNCT
cana-1119	93	40	,	,	PUNCT
cana-1119	93	41	we	we	PRON
cana-1119	93	42	will	will	AUX
cana-1119	93	43	get	get	VERB
cana-1119	93	44	𝑎2	𝑎2	NOUN
cana-1119	93	45	=	=	PUNCT
cana-1119	94	1	−𝑐1	−𝑐1	NOUN
cana-1119	94	2	2(𝑟−2	2(𝑟−2	NUM
cana-1119	94	3	)	)	PUNCT
cana-1119	94	4	(	(	PUNCT
cana-1119	94	5	13	13	NUM
cana-1119	94	6	)	)	PUNCT
cana-1119	94	7	𝑎3	𝑎3	NOUN
cana-1119	94	8	=	=	SYM
cana-1119	95	1	3𝑐1	3𝑐1	NUM
cana-1119	95	2	2𝑟2−4𝑐2𝑟	2𝑟2−4𝑐2𝑟	NOUN
cana-1119	95	3	2−3𝑐1	2−3𝑐1	NUM
cana-1119	95	4	2𝑟+16𝑐2𝑟−16𝑐2	2𝑟+16𝑐2𝑟−16𝑐2	NUM
cana-1119	95	5	16(𝑟−2)2(2𝑟−3	16(𝑟−2)2(2𝑟−3	NUM
cana-1119	95	6	)	)	PUNCT
cana-1119	95	7	(	(	PUNCT
cana-1119	95	8	14	14	NUM
cana-1119	95	9	)	)	PUNCT
cana-1119	95	10	𝑎4	𝑎4	NOUN
cana-1119	95	11	=	=	SYM
cana-1119	95	12	1	1	NUM
cana-1119	95	13	288(𝑟−2)3(6𝑟2−17𝑟+12	288(𝑟−2)3(6𝑟2−17𝑟+12	NUM
cana-1119	95	14	)	)	PUNCT
cana-1119	96	1	[	[	X
cana-1119	96	2	−52𝑐1	−52𝑐1	X
cana-1119	96	3	3𝑟4	3𝑟4	NUM
cana-1119	96	4	+	+	CCONJ
cana-1119	96	5	144𝑐1𝑐2𝑟	144𝑐1𝑐2𝑟	NUM
cana-1119	96	6	4	4	NUM
cana-1119	96	7	−	−	NOUN
cana-1119	96	8	96𝑐3𝑟	96𝑐3𝑟	NUM
cana-1119	96	9	4	4	NUM
cana-1119	96	10	+	+	CCONJ
cana-1119	96	11	165𝑐1	165𝑐1	NUM
cana-1119	96	12	3𝑟3	3𝑟3	NUM
cana-1119	96	13	−	−	NOUN
cana-1119	97	1	780𝑐1𝑐2𝑟	780𝑐1𝑐2𝑟	NUM
cana-1119	97	2	3	3	NUM
cana-1119	97	3	+	+	CCONJ
cana-1119	97	4	720𝑐3𝑟	720𝑐3𝑟	NUM
cana-1119	97	5	3−205𝑐1	3−205𝑐1	NOUN
cana-1119	97	6	3𝑟2	3𝑟2	NUM
cana-1119	97	7	+	+	CCONJ
cana-1119	97	8	1464𝑐1𝑐2𝑟	1464𝑐1𝑐2𝑟	NUM
cana-1119	97	9	2	2	NUM
cana-1119	97	10	−	−	NOUN
cana-1119	97	11	2016𝑐3𝑟	2016𝑐3𝑟	NUM
cana-1119	97	12	2	2	NUM
cana-1119	97	13	+	+	SYM
cana-1119	97	14	46𝑐1	46𝑐1	NUM
cana-1119	97	15	3𝑟	3𝑟	NUM
cana-1119	97	16	−	−	PROPN
cana-1119	97	17	1104𝑐1𝑐2𝑟	1104𝑐1𝑐2𝑟	NUM
cana-1119	97	18	+	+	CCONJ
cana-1119	97	19	2496𝑐3𝑟	2496𝑐3𝑟	NUM
cana-1119	97	20	+	+	SYM
cana-1119	97	21	48𝑐1	48𝑐1	NUM
cana-1119	97	22	3	3	NUM
cana-1119	97	23	+	+	CCONJ
cana-1119	97	24	288𝑐1𝑐2	288𝑐1𝑐2	NUM
cana-1119	97	25	−	−	NOUN
cana-1119	97	26	1152𝑐3	1152𝑐3	NUM
cana-1119	97	27	]	]	X
cana-1119	97	28	(	(	PUNCT
cana-1119	97	29	15	15	NUM
cana-1119	97	30	)	)	PUNCT
cana-1119	97	31	from	from	ADP
cana-1119	97	32	equation	equation	NOUN
cana-1119	97	33	(	(	PUNCT
cana-1119	97	34	13	13	NUM
cana-1119	97	35	)	)	PUNCT
cana-1119	97	36	and	and	CCONJ
cana-1119	97	37	(	(	PUNCT
cana-1119	97	38	14	14	NUM
cana-1119	97	39	)	)	PUNCT
cana-1119	97	40	|𝑎2|	|𝑎2|	NOUN
cana-1119	97	41	≤	≤	NOUN
cana-1119	97	42	1	1	NUM
cana-1119	97	43	2	2	NUM
cana-1119	97	44	−	−	NOUN
cana-1119	97	45	𝑟	𝑟	NOUN
cana-1119	97	46	𝑎3	𝑎3	X
cana-1119	97	47	=	=	SYM
cana-1119	97	48	1	1	NUM
cana-1119	97	49	4(3	4(3	NUM
cana-1119	97	50	−	−	PROPN
cana-1119	97	51	2𝑟	2𝑟	NUM
cana-1119	97	52	)	)	PUNCT
cana-1119	98	1	[	[	X
cana-1119	98	2	𝑐2	𝑐2	NOUN
cana-1119	98	3	−	−	NOUN
cana-1119	98	4	𝑐1	𝑐1	NOUN
cana-1119	98	5	2(3𝑟2	2(3𝑟2	NUM
cana-1119	98	6	−	−	PROPN
cana-1119	98	7	3𝑟	3𝑟	NUM
cana-1119	98	8	)	)	PUNCT
cana-1119	98	9	4(−2	4(−2	PUNCT
cana-1119	99	1	+	+	CCONJ
cana-1119	99	2	𝑟)2	𝑟)2	NOUN
cana-1119	99	3	]	]	PUNCT
cana-1119	99	4	|𝑎3|	|𝑎3|	NOUN
cana-1119	99	5	≤	≤	NUM
cana-1119	99	6	1	1	NUM
cana-1119	99	7	4(3	4(3	NUM
cana-1119	99	8	−	−	PROPN
cana-1119	99	9	2𝑟	2𝑟	NUM
cana-1119	99	10	)	)	PUNCT
cana-1119	100	1	|𝑐2	|𝑐2	NOUN
cana-1119	101	1	−	−	NOUN
cana-1119	101	2	𝛿𝑐1	𝛿𝑐1	PRON
cana-1119	101	3	2|	2|	NUM
cana-1119	101	4	where	where	SCONJ
cana-1119	101	5	𝛿	𝛿	ADJ
cana-1119	101	6	=	=	SYM
cana-1119	101	7	3𝑟2−3𝑟	3𝑟2−3𝑟	NUM
cana-1119	101	8	4(−2+𝑟)2	4(−2+𝑟)2	NOUN
cana-1119	101	9	on	on	ADP
cana-1119	101	10	applying	apply	VERB
cana-1119	101	11	lemma	lemma	PROPN
cana-1119	101	12	(	(	PUNCT
cana-1119	101	13	3.1	3.1	NUM
cana-1119	101	14	)	)	PUNCT
cana-1119	101	15	|𝑎3|	|𝑎3|	NOUN
cana-1119	101	16	=	=	SYM
cana-1119	102	1	1	1	NUM
cana-1119	102	2	2(3	2(3	NUM
cana-1119	102	3	−	−	PROPN
cana-1119	102	4	2𝑟	2𝑟	NUM
cana-1119	102	5	)	)	PUNCT
cana-1119	102	6	max	max	PROPN
cana-1119	102	7	{	{	PUNCT
cana-1119	102	8	1	1	NUM
cana-1119	102	9	,	,	PUNCT
cana-1119	102	10	|	|	ADV
cana-1119	102	11	𝑟2	𝑟2	NOUN
cana-1119	102	12	+	+	NOUN
cana-1119	102	13	5𝑟	5𝑟	NUM
cana-1119	102	14	−	−	NOUN
cana-1119	102	15	8	8	NUM
cana-1119	102	16	2(−2	2(−2	NUM
cana-1119	102	17	+	+	CCONJ
cana-1119	102	18	𝑟)2	𝑟)2	NOUN
cana-1119	102	19	|	|	ADV
cana-1119	102	20	}	}	PUNCT
cana-1119	102	21	now	now	ADV
cana-1119	102	22	𝑎3	𝑎3	PROPN
cana-1119	102	23	−	−	PROPN
cana-1119	102	24	𝛿𝑎2	𝛿𝑎2	NOUN
cana-1119	102	25	2	2	NUM
cana-1119	102	26	=	=	SYM
cana-1119	102	27	1	1	NUM
cana-1119	102	28	4(3−2𝑟	4(3−2𝑟	NUM
cana-1119	102	29	)	)	PUNCT
cana-1119	103	1	[	[	X
cana-1119	103	2	𝑐2	𝑐2	NOUN
cana-1119	103	3	−	−	NOUN
cana-1119	103	4	𝑐1	𝑐1	NOUN
cana-1119	103	5	2(4𝛿(3−2𝑟)+3𝑟2−3𝑟	2(4𝛿(3−2𝑟)+3𝑟2−3𝑟	PRON
cana-1119	103	6	)	)	PUNCT
cana-1119	104	1	4(𝑟−2)2	4(𝑟−2)2	NUM
cana-1119	104	2	]	]	PUNCT
cana-1119	104	3	(	(	PUNCT
cana-1119	104	4	16	16	NUM
cana-1119	104	5	)	)	PUNCT
cana-1119	104	6	again	again	ADV
cana-1119	104	7	using	use	VERB
cana-1119	104	8	lemma	lemma	PROPN
cana-1119	104	9	we	we	PRON
cana-1119	104	10	will	will	AUX
cana-1119	104	11	have	have	AUX
cana-1119	104	12	|𝑎3	|𝑎3	VERB
cana-1119	104	13	−	−	PROPN
cana-1119	104	14	𝛿𝑎2	𝛿𝑎2	NOUN
cana-1119	104	15	2|	2|	NOUN
cana-1119	104	16	≤	≤	ADV
cana-1119	104	17	1	1	NUM
cana-1119	104	18	2(3	2(3	NUM
cana-1119	104	19	−	−	PROPN
cana-1119	104	20	2𝑟	2𝑟	NUM
cana-1119	104	21	)	)	PUNCT
cana-1119	104	22	max	max	PROPN
cana-1119	104	23	{	{	PUNCT
cana-1119	104	24	1	1	NUM
cana-1119	104	25	,	,	PUNCT
cana-1119	104	26	|	|	ADV
cana-1119	104	27	𝑟2	𝑟2	NOUN
cana-1119	104	28	+	+	NOUN
cana-1119	104	29	5𝑟	5𝑟	NUM
cana-1119	104	30	+	+	CCONJ
cana-1119	104	31	4𝛿(3	4𝛿(3	X
cana-1119	104	32	−	−	VERB
cana-1119	104	33	2𝑟	2𝑟	NUM
cana-1119	104	34	)	)	PUNCT
cana-1119	105	1	−	−	ADP
cana-1119	105	2	8	8	NUM
cana-1119	105	3	2(𝑟	2(𝑟	NUM
cana-1119	105	4	−	−	NOUN
cana-1119	105	5	2)2	2)2	NUM
cana-1119	105	6	|	|	NOUN
cana-1119	105	7	}	}	PUNCT
cana-1119	105	8	communications	communication	NOUN
cana-1119	105	9	on	on	ADP
cana-1119	105	10	applied	apply	VERB
cana-1119	105	11	nonlinear	nonlinear	ADJ
cana-1119	105	12	analysis	analysis	NOUN
cana-1119	105	13	issn	issn	NOUN
cana-1119	105	14	:	:	PUNCT
cana-1119	105	15	1074	1074	NUM
cana-1119	105	16	-	-	PUNCT
cana-1119	105	17	133x	133x	NUM
cana-1119	105	18	vol	vol	NOUN
cana-1119	105	19	31	31	NUM
cana-1119	105	20	no	no	NOUN
cana-1119	105	21	.	.	PUNCT
cana-1119	106	1	6s	6s	NUM
cana-1119	106	2	(	(	PUNCT
cana-1119	106	3	2024	2024	NUM
cana-1119	106	4	)	)	PUNCT
cana-1119	106	5	54	54	NUM
cana-1119	106	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1119	106	7	theorem	theorem	VERB
cana-1119	106	8	3.2	3.2	NUM
cana-1119	106	9	:	:	PUNCT
cana-1119	106	10	if	if	SCONJ
cana-1119	106	11	function	function	VERB
cana-1119	106	12	ℎ	ℎ	ADP
cana-1119	106	13	∈	∈	PROPN
cana-1119	106	14	𝑆∗𝐶sin	𝑆∗𝐶sin	NOUN
cana-1119	106	15	,	,	PUNCT
cana-1119	106	16	then	then	ADV
cana-1119	106	17	|𝑎3	|𝑎3	VERB
cana-1119	106	18	−	−	PROPN
cana-1119	106	19	𝛿𝑎2	𝛿𝑎2	NOUN
cana-1119	106	20	2|	2|	NOUN
cana-1119	106	21	≤	≤	PROPN
cana-1119	106	22	{	{	PUNCT
cana-1119	106	23	−1	−1	NOUN
cana-1119	106	24	4(3	4(3	NUM
cana-1119	106	25	−	−	PROPN
cana-1119	106	26	2𝑟	2𝑟	NUM
cana-1119	106	27	)	)	PUNCT
cana-1119	107	1	[	[	PUNCT
cana-1119	107	2	𝑟2	𝑟2	NOUN
cana-1119	107	3	+	+	NOUN
cana-1119	107	4	5𝑟	5𝑟	NUM
cana-1119	107	5	−	−	NOUN
cana-1119	107	6	8	8	NUM
cana-1119	107	7	(	(	PUNCT
cana-1119	107	8	−2	−2	NOUN
cana-1119	107	9	+	+	NOUN
cana-1119	107	10	𝑟)2	𝑟)2	NOUN
cana-1119	107	11	+	+	CCONJ
cana-1119	107	12	4𝛿(3	4𝛿(3	NOUN
cana-1119	107	13	−	−	PROPN
cana-1119	107	14	2𝑟	2𝑟	NUM
cana-1119	107	15	)	)	PUNCT
cana-1119	107	16	(	(	PUNCT
cana-1119	107	17	−2	−2	NOUN
cana-1119	107	18	+	+	NOUN
cana-1119	107	19	𝑟)2	𝑟)2	NOUN
cana-1119	107	20	]	]	PUNCT
cana-1119	107	21	if	if	SCONJ
cana-1119	107	22	𝛿	𝛿	DET
cana-1119	107	23	≤	≤	NOUN
cana-1119	107	24	−3𝑟2	−3𝑟2	NUM
cana-1119	107	25	+	+	PUNCT
cana-1119	107	26	3𝑟	3𝑟	NUM
cana-1119	107	27	4(3	4(3	NUM
cana-1119	107	28	−	−	NUM
cana-1119	107	29	2𝑟	2𝑟	NUM
cana-1119	107	30	)	)	PUNCT
cana-1119	107	31	1	1	NUM
cana-1119	107	32	2(3	2(3	NUM
cana-1119	107	33	−	−	NUM
cana-1119	107	34	2𝑟	2𝑟	NUM
cana-1119	107	35	)	)	PUNCT
cana-1119	107	36	if	if	SCONJ
cana-1119	107	37	−3𝑟2	−3𝑟2	NUM
cana-1119	107	38	+	+	PUNCT
cana-1119	107	39	3𝑟	3𝑟	NUM
cana-1119	107	40	4(3	4(3	NUM
cana-1119	107	41	−	−	NUM
cana-1119	107	42	2𝑟	2𝑟	NUM
cana-1119	107	43	)	)	PUNCT
cana-1119	107	44	≤	≤	PUNCT
cana-1119	107	45	𝛿	𝛿	DET
cana-1119	107	46	≤	≤	ADJ
cana-1119	107	47	𝑟2	𝑟2	NOUN
cana-1119	107	48	−	−	NOUN
cana-1119	107	49	13𝑟	13𝑟	NOUN
cana-1119	107	50	+	+	CCONJ
cana-1119	107	51	16	16	NUM
cana-1119	107	52	4(3	4(3	NUM
cana-1119	107	53	−	−	PROPN
cana-1119	107	54	2𝑟	2𝑟	NUM
cana-1119	107	55	)	)	PUNCT
cana-1119	107	56	1	1	NUM
cana-1119	107	57	4(3	4(3	NUM
cana-1119	107	58	−	−	PROPN
cana-1119	107	59	2𝑟	2𝑟	NUM
cana-1119	107	60	)	)	PUNCT
cana-1119	107	61	[	[	PUNCT
cana-1119	107	62	𝑟2	𝑟2	NOUN
cana-1119	107	63	+	+	NOUN
cana-1119	107	64	5𝑟	5𝑟	NUM
cana-1119	107	65	−	−	NOUN
cana-1119	107	66	8	8	NUM
cana-1119	107	67	(	(	PUNCT
cana-1119	107	68	−2	−2	NOUN
cana-1119	107	69	+	+	NOUN
cana-1119	107	70	𝑟)2	𝑟)2	NOUN
cana-1119	107	71	+	+	CCONJ
cana-1119	107	72	4𝛿(3	4𝛿(3	NOUN
cana-1119	107	73	−	−	PROPN
cana-1119	107	74	2𝑟	2𝑟	NUM
cana-1119	107	75	)	)	PUNCT
cana-1119	107	76	(	(	PUNCT
cana-1119	107	77	−2	−2	NOUN
cana-1119	107	78	+	+	NOUN
cana-1119	107	79	𝑟)2	𝑟)2	NOUN
cana-1119	107	80	]	]	PUNCT
cana-1119	107	81	if	if	SCONJ
cana-1119	107	82	(	(	PUNCT
cana-1119	107	83	𝑟2	𝑟2	NOUN
cana-1119	107	84	−	−	NOUN
cana-1119	107	85	13𝑟	13𝑟	NOUN
cana-1119	107	86	+	+	CCONJ
cana-1119	107	87	16	16	NUM
cana-1119	107	88	)	)	PUNCT
cana-1119	107	89	4(3	4(3	NUM
cana-1119	107	90	−	−	PROPN
cana-1119	107	91	2𝑟	2𝑟	NUM
cana-1119	107	92	)	)	PUNCT
cana-1119	107	93	≤	≤	NOUN
cana-1119	107	94	𝛿	𝛿	DET
cana-1119	107	95	proof	proof	NOUN
cana-1119	107	96	.	.	PUNCT
cana-1119	108	1	from	from	ADP
cana-1119	108	2	(	(	PUNCT
cana-1119	108	3	16	16	NUM
cana-1119	108	4	)	)	PUNCT
cana-1119	108	5	we	we	PRON
cana-1119	108	6	have	have	VERB
cana-1119	108	7	𝑎3	𝑎3	PROPN
cana-1119	108	8	−	−	PROPN
cana-1119	108	9	𝛿𝑎2	𝛿𝑎2	NOUN
cana-1119	108	10	2	2	NUM
cana-1119	108	11	=	=	SYM
cana-1119	108	12	1	1	NUM
cana-1119	108	13	4(3−2𝑟	4(3−2𝑟	NUM
cana-1119	108	14	)	)	PUNCT
cana-1119	109	1	[	[	X
cana-1119	109	2	𝑐2	𝑐2	NOUN
cana-1119	109	3	−	−	NOUN
cana-1119	109	4	𝑐1	𝑐1	NOUN
cana-1119	109	5	2(4𝛿(3−2𝑟)+3𝑟2−3𝑟	2(4𝛿(3−2𝑟)+3𝑟2−3𝑟	PRON
cana-1119	109	6	)	)	PUNCT
cana-1119	110	1	4(𝑟−2)2	4(𝑟−2)2	NUM
cana-1119	110	2	]	]	PUNCT
cana-1119	110	3	(	(	PUNCT
cana-1119	110	4	17	17	NUM
cana-1119	110	5	)	)	PUNCT
cana-1119	110	6	this	this	PRON
cana-1119	110	7	can	can	AUX
cana-1119	110	8	be	be	AUX
cana-1119	110	9	written	write	VERB
cana-1119	110	10	as	as	ADP
cana-1119	110	11	𝑎3	𝑎3	PROPN
cana-1119	110	12	−	−	PROPN
cana-1119	110	13	𝛿𝑎2	𝛿𝑎2	NOUN
cana-1119	110	14	2	2	NUM
cana-1119	110	15	=	=	SYM
cana-1119	110	16	1	1	NUM
cana-1119	110	17	4(3	4(3	NUM
cana-1119	110	18	−	−	PROPN
cana-1119	110	19	2𝑟	2𝑟	NUM
cana-1119	110	20	)	)	PUNCT
cana-1119	111	1	[	[	X
cana-1119	111	2	𝑐2	𝑐2	NOUN
cana-1119	111	3	−	−	NOUN
cana-1119	111	4	𝛿𝑐1	𝛿𝑐1	ADV
cana-1119	111	5	2	2	X
cana-1119	111	6	]	]	X
cana-1119	111	7	where𝛿:=	where𝛿:=	PROPN
cana-1119	111	8	𝑐1	𝑐1	NOUN
cana-1119	111	9	2(4𝛿(3−2𝑟)+3𝑟2−3𝑟	2(4𝛿(3−2𝑟)+3𝑟2−3𝑟	NUM
cana-1119	111	10	)	)	PUNCT
cana-1119	112	1	4(𝑟−2)2	4(𝑟−2)2	NOUN
cana-1119	112	2	using	use	VERB
cana-1119	112	3	lemma	lemma	PROPN
cana-1119	112	4	(	(	PUNCT
cana-1119	112	5	3.1	3.1	NUM
cana-1119	112	6	)	)	PUNCT
cana-1119	112	7	in	in	ADP
cana-1119	112	8	(	(	PUNCT
cana-1119	112	9	17	17	NUM
cana-1119	112	10	)	)	PUNCT
cana-1119	112	11	we	we	PRON
cana-1119	112	12	have	have	AUX
cana-1119	112	13	|𝑎3	|𝑎3	VERB
cana-1119	112	14	−	−	PROPN
cana-1119	112	15	𝛿𝑎2	𝛿𝑎2	NOUN
cana-1119	112	16	2|	2|	NOUN
cana-1119	112	17	≤	≤	PROPN
cana-1119	112	18	{	{	PUNCT
cana-1119	112	19	−1	−1	NOUN
cana-1119	112	20	4(3	4(3	NUM
cana-1119	112	21	−	−	PROPN
cana-1119	112	22	2𝑟	2𝑟	NUM
cana-1119	112	23	)	)	PUNCT
cana-1119	113	1	[	[	PUNCT
cana-1119	113	2	𝑟2	𝑟2	NOUN
cana-1119	113	3	+	+	NOUN
cana-1119	113	4	5𝑟	5𝑟	NUM
cana-1119	113	5	−	−	NOUN
cana-1119	113	6	8	8	NUM
cana-1119	113	7	(	(	PUNCT
cana-1119	113	8	−2	−2	NOUN
cana-1119	113	9	+	+	NOUN
cana-1119	113	10	𝑟)2	𝑟)2	NOUN
cana-1119	113	11	+	+	CCONJ
cana-1119	113	12	4𝛿(3	4𝛿(3	NOUN
cana-1119	113	13	−	−	PROPN
cana-1119	113	14	2𝑟	2𝑟	NUM
cana-1119	113	15	)	)	PUNCT
cana-1119	113	16	(	(	PUNCT
cana-1119	113	17	−2	−2	NOUN
cana-1119	113	18	+	+	NOUN
cana-1119	113	19	𝑟)2	𝑟)2	NOUN
cana-1119	113	20	]	]	PUNCT
cana-1119	113	21	if	if	SCONJ
cana-1119	113	22	𝛿	𝛿	DET
cana-1119	113	23	≤	≤	NOUN
cana-1119	113	24	−3𝑟2	−3𝑟2	NUM
cana-1119	113	25	+	+	PUNCT
cana-1119	113	26	3𝑟	3𝑟	NUM
cana-1119	113	27	4(3	4(3	NUM
cana-1119	113	28	−	−	NUM
cana-1119	113	29	2𝑟	2𝑟	NUM
cana-1119	113	30	)	)	PUNCT
cana-1119	113	31	1	1	NUM
cana-1119	113	32	2(3	2(3	NUM
cana-1119	113	33	−	−	NUM
cana-1119	113	34	2𝑟	2𝑟	NUM
cana-1119	113	35	)	)	PUNCT
cana-1119	113	36	if	if	SCONJ
cana-1119	113	37	−3𝑟2	−3𝑟2	NUM
cana-1119	113	38	+	+	PUNCT
cana-1119	113	39	3𝑟	3𝑟	NUM
cana-1119	113	40	4(3	4(3	NUM
cana-1119	113	41	−	−	NUM
cana-1119	113	42	2𝑟	2𝑟	NUM
cana-1119	113	43	)	)	PUNCT
cana-1119	113	44	≤	≤	PUNCT
cana-1119	113	45	𝛿	𝛿	DET
cana-1119	113	46	≤	≤	ADJ
cana-1119	113	47	𝑟2	𝑟2	NOUN
cana-1119	113	48	−	−	NOUN
cana-1119	113	49	13𝑟	13𝑟	NOUN
cana-1119	113	50	+	+	CCONJ
cana-1119	113	51	16	16	NUM
cana-1119	113	52	4(3	4(3	NUM
cana-1119	113	53	−	−	PROPN
cana-1119	113	54	2𝑟	2𝑟	NUM
cana-1119	113	55	)	)	PUNCT
cana-1119	113	56	1	1	NUM
cana-1119	113	57	4(3	4(3	NUM
cana-1119	113	58	−	−	PROPN
cana-1119	113	59	2𝑟	2𝑟	NUM
cana-1119	113	60	)	)	PUNCT
cana-1119	113	61	[	[	PUNCT
cana-1119	113	62	𝑟2	𝑟2	NOUN
cana-1119	113	63	+	+	NOUN
cana-1119	113	64	5𝑟	5𝑟	NUM
cana-1119	113	65	−	−	NOUN
cana-1119	113	66	8	8	NUM
cana-1119	113	67	(	(	PUNCT
cana-1119	113	68	−2	−2	NOUN
cana-1119	113	69	+	+	NOUN
cana-1119	113	70	𝑟)2	𝑟)2	NOUN
cana-1119	113	71	+	+	CCONJ
cana-1119	113	72	4𝛿(3	4𝛿(3	NOUN
cana-1119	113	73	−	−	PROPN
cana-1119	113	74	2𝑟	2𝑟	NUM
cana-1119	113	75	)	)	PUNCT
cana-1119	113	76	(	(	PUNCT
cana-1119	113	77	−2	−2	NOUN
cana-1119	113	78	+	+	NOUN
cana-1119	113	79	𝑟)2	𝑟)2	NOUN
cana-1119	113	80	]	]	PUNCT
cana-1119	113	81	if	if	SCONJ
cana-1119	113	82	(	(	PUNCT
cana-1119	113	83	𝑟2	𝑟2	NOUN
cana-1119	113	84	−	−	NOUN
cana-1119	113	85	13𝑟	13𝑟	NOUN
cana-1119	113	86	+	+	CCONJ
cana-1119	113	87	16	16	NUM
cana-1119	113	88	)	)	PUNCT
cana-1119	113	89	4(3	4(3	NUM
cana-1119	113	90	−	−	PROPN
cana-1119	113	91	2𝑟	2𝑟	NUM
cana-1119	113	92	)	)	PUNCT
cana-1119	113	93	≤	≤	NOUN
cana-1119	113	94	𝛿	𝛿	DET
cana-1119	113	95	function	function	NOUN
cana-1119	113	96	defined	define	VERB
cana-1119	113	97	with	with	ADP
cana-1119	113	98	poisson	poisson	NOUN
cana-1119	113	99	distribution	distribution	NOUN
cana-1119	113	100	a	a	DET
cana-1119	113	101	discrete	discrete	ADJ
cana-1119	113	102	random	random	ADJ
cana-1119	113	103	variable	variable	NOUN
cana-1119	113	104	𝜉	𝜉	NOUN
cana-1119	113	105	is	be	AUX
cana-1119	113	106	said	say	VERB
cana-1119	113	107	to	to	PART
cana-1119	113	108	be	be	AUX
cana-1119	113	109	poisson	poisson	NOUN
cana-1119	113	110	distribution	distribution	NOUN
cana-1119	113	111	it	it	PRON
cana-1119	113	112	it	it	PRON
cana-1119	113	113	takes	take	VERB
cana-1119	113	114	the	the	DET
cana-1119	113	115	values	value	NOUN
cana-1119	113	116	0,1,2,3,4,5⋯	0,1,2,3,4,5⋯	X
cana-1119	113	117	with	with	ADP
cana-1119	113	118	probabilities𝑒−𝜂	probabilities𝑒−𝜂	PROPN
cana-1119	113	119	,	,	PUNCT
cana-1119	113	120	𝜂	𝜂	NOUN
cana-1119	113	121	𝑒−𝜂	𝑒−𝜂	VERB
cana-1119	113	122	1	1	NUM
cana-1119	113	123	!	!	PUNCT
cana-1119	113	124	,	,	PUNCT
cana-1119	113	125	𝜂2	𝜂2	VERB
cana-1119	113	126	𝑒−𝜂	𝑒−𝜂	ADJ
cana-1119	113	127	2	2	NUM
cana-1119	113	128	!	!	NUM
cana-1119	113	129	,	,	PUNCT
cana-1119	113	130	𝜂3	𝜂3	NOUN
cana-1119	113	131	𝑒−𝜂	𝑒−𝜂	VERB
cana-1119	113	132	3	3	NUM
cana-1119	113	133	!	!	PUNCT
cana-1119	113	134	,	,	PUNCT
cana-1119	113	135	𝜂4	𝜂4	NOUN
cana-1119	113	136	𝑒−𝜂	𝑒−𝜂	VERB
cana-1119	113	137	4	4	NUM
cana-1119	113	138	!	!	PUNCT
cana-1119	114	1	+	+	CCONJ
cana-1119	114	2	𝜂5	𝜂5	NOUN
cana-1119	114	3	𝑒−𝜂	𝑒−𝜂	VERB
cana-1119	114	4	5	5	NUM
cana-1119	114	5	!	!	PUNCT
cana-1119	115	1	+	+	VERB
cana-1119	115	2	⋯	⋯	NOUN
cana-1119	115	3	,	,	PUNCT
cana-1119	115	4	respectively	respectively	ADV
cana-1119	115	5	,	,	PUNCT
cana-1119	115	6	where	where	SCONJ
cana-1119	115	7	𝜂	𝜂	NOUN
cana-1119	115	8	>	>	X
cana-1119	115	9	0	0	NUM
cana-1119	115	10	is	be	AUX
cana-1119	115	11	called	call	VERB
cana-1119	115	12	the	the	DET
cana-1119	115	13	parameter	parameter	NOUN
cana-1119	115	14	.	.	PUNCT
cana-1119	116	1	thus	thus	ADV
cana-1119	116	2	𝑃(𝜉	𝑃(𝜉	PROPN
cana-1119	116	3	=	=	SYM
cana-1119	116	4	𝑘	𝑘	X
cana-1119	116	5	)	)	PUNCT
cana-1119	116	6	=	=	PUNCT
cana-1119	116	7	𝜂𝑘𝑒−𝜂	𝜂𝑘𝑒−𝜂	PROPN
cana-1119	116	8	𝑘	𝑘	X
cana-1119	116	9	!	!	PUNCT
cana-1119	116	10	,	,	PUNCT
cana-1119	116	11	𝑘	𝑘	X
cana-1119	116	12	=	=	X
cana-1119	116	13	0,1,2,3,⋯	0,1,2,3,⋯	PROPN
cana-1119	117	1	a	a	DET
cana-1119	117	2	power	power	NOUN
cana-1119	117	3	series	series	NOUN
cana-1119	117	4	with	with	ADP
cana-1119	117	5	coefficients	coefficient	NOUN
cana-1119	117	6	from	from	ADP
cana-1119	117	7	probabilities	probability	NOUN
cana-1119	117	8	of	of	ADP
cana-1119	117	9	poisson	poisson	NOUN
cana-1119	117	10	distribution	distribution	NOUN
cana-1119	117	11	,	,	PUNCT
cana-1119	117	12	was	be	AUX
cana-1119	117	13	introduced	introduce	VERB
cana-1119	117	14	by	by	ADP
cana-1119	117	15	prowal	prowal	NOUN
cana-1119	117	16	,	,	PUNCT
cana-1119	117	17	[	[	X
cana-1119	117	18	17	17	NUM
cana-1119	117	19	]	]	PUNCT
cana-1119	117	20	𝑃(𝜂	𝑃(𝜂	NOUN
cana-1119	117	21	,	,	PUNCT
cana-1119	117	22	𝑧):=	𝑧):=	ADP
cana-1119	117	23	𝑧	𝑧	PRON
cana-1119	117	24	+	+	NOUN
cana-1119	117	25	∑	∑	PROPN
cana-1119	117	26	  	  	SPACE
cana-1119	117	27	∞	∞	NUM
cana-1119	117	28	𝑛=2	𝑛=2	PROPN
cana-1119	117	29	𝜂𝑛−1	𝜂𝑛−1	NOUN
cana-1119	117	30	(	(	PUNCT
cana-1119	117	31	𝑛	𝑛	PROPN
cana-1119	117	32	−	−	PROPN
cana-1119	117	33	1	1	NUM
cana-1119	117	34	)	)	PUNCT
cana-1119	117	35	!	!	PUNCT
cana-1119	118	1	𝑒−𝜂𝑧𝑛	𝑒−𝜂𝑧𝑛	PROPN
cana-1119	118	2	,	,	PUNCT
cana-1119	118	3	𝑧	𝑧	DET
cana-1119	118	4	∈	∈	NOUN
cana-1119	118	5	ℂ	ℂ	PROPN
cana-1119	118	6	where	where	SCONJ
cana-1119	118	7	𝜂	𝜂	NOUN
cana-1119	118	8	>	>	X
cana-1119	118	9	0	0	NUM
cana-1119	118	10	.	.	PUNCT
cana-1119	119	1	by	by	ADP
cana-1119	119	2	using	use	VERB
cana-1119	119	3	ratio	ratio	NOUN
cana-1119	119	4	test	test	NOUN
cana-1119	119	5	we	we	PRON
cana-1119	119	6	can	can	AUX
cana-1119	119	7	easily	easily	ADV
cana-1119	119	8	establish	establish	VERB
cana-1119	119	9	that	that	DET
cana-1119	119	10	radius	radius	NOUN
cana-1119	119	11	of	of	ADP
cana-1119	119	12	convergence	convergence	NOUN
cana-1119	119	13	of	of	ADP
cana-1119	119	14	above	above	ADJ
cana-1119	119	15	series	series	NOUN
cana-1119	119	16	is	be	AUX
cana-1119	119	17	infinity	infinity	NOUN
cana-1119	119	18	.	.	PUNCT
cana-1119	120	1	recent	recent	ADJ
cana-1119	120	2	works	work	NOUN
cana-1119	120	3	by	by	ADP
cana-1119	120	4	g.	g.	PROPN
cana-1119	120	5	murugusundaramoorthy	murugusundaramoorthy	PROPN
cana-1119	120	6	,	,	PUNCT
cana-1119	120	7	et	et	PROPN
cana-1119	120	8	al	al	PROPN
cana-1119	120	9	and	and	CCONJ
cana-1119	120	10	s.	s.	PROPN
cana-1119	120	11	porwal	porwal	PROPN
cana-1119	120	12	et	et	PROPN
cana-1119	120	13	al	al	PROPN
cana-1119	121	1	[	[	X
cana-1119	121	2	23	23	NUM
cana-1119	121	3	,	,	PUNCT
cana-1119	121	4	24	24	NUM
cana-1119	121	5	]	]	PUNCT
cana-1119	121	6	,	,	PUNCT
cana-1119	121	7	let	let	VERB
cana-1119	121	8	the	the	DET
cana-1119	121	9	linear	linear	ADJ
cana-1119	121	10	operator	operator	NOUN
cana-1119	121	11	communications	communication	NOUN
cana-1119	121	12	on	on	ADP
cana-1119	121	13	applied	apply	VERB
cana-1119	121	14	nonlinear	nonlinear	ADJ
cana-1119	121	15	analysis	analysis	NOUN
cana-1119	121	16	issn	issn	NOUN
cana-1119	121	17	:	:	PUNCT
cana-1119	121	18	1074	1074	NUM
cana-1119	121	19	-	-	PUNCT
cana-1119	121	20	133x	133x	NUM
cana-1119	121	21	vol	vol	NOUN
cana-1119	121	22	31	31	NUM
cana-1119	121	23	no	no	NOUN
cana-1119	121	24	.	.	PUNCT
cana-1119	122	1	6s	6s	NUM
cana-1119	122	2	(	(	PUNCT
cana-1119	122	3	2024	2024	NUM
cana-1119	122	4	)	)	PUNCT
cana-1119	122	5	55	55	NUM
cana-1119	122	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1119	122	7	𝑃𝜂(𝑧):𝒜	𝑃𝜂(𝑧):𝒜	PROPN
cana-1119	122	8	→	→	SYM
cana-1119	122	9	𝒜	𝒜	NOUN
cana-1119	122	10	be	be	AUX
cana-1119	122	11	given	give	VERB
cana-1119	122	12	by	by	ADP
cana-1119	122	13	𝑃𝜂ℎ(𝑧	𝑃𝜂ℎ(𝑧	NOUN
cana-1119	122	14	)	)	PUNCT
cana-1119	122	15	=	=	SYM
cana-1119	122	16	𝑃(𝜂	𝑃(𝜂	NOUN
cana-1119	122	17	,	,	PUNCT
cana-1119	122	18	𝑧	𝑧	NOUN
cana-1119	122	19	)	)	PUNCT
cana-1119	122	20	⋆	⋆	VERB
cana-1119	122	21	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1119	122	22	)	)	PUNCT
cana-1119	122	23	=	=	PUNCT
cana-1119	123	1	𝑧	𝑧	PRON
cana-1119	123	2	+	+	ADJ
cana-1119	123	3	∑	∑	PROPN
cana-1119	123	4	  	  	SPACE
cana-1119	123	5	∞	∞	NUM
cana-1119	123	6	𝑛=2	𝑛=2	NOUN
cana-1119	123	7	  	  	SPACE
cana-1119	123	8	𝜂𝑛−1	𝜂𝑛−1	PROPN
cana-1119	123	9	(	(	PUNCT
cana-1119	123	10	𝑛	𝑛	PROPN
cana-1119	123	11	−	−	PROPN
cana-1119	123	12	1	1	NUM
cana-1119	123	13	)	)	PUNCT
cana-1119	123	14	!	!	PUNCT
cana-1119	124	1	𝑒−𝜂𝑎𝑛𝑧	𝑒−𝜂𝑎𝑛𝑧	VERB
cana-1119	124	2	𝑛	𝑛	PRON
cana-1119	124	3	=	=	PUNCT
cana-1119	124	4	𝑧	𝑧	PROPN
cana-1119	124	5	+	+	ADJ
cana-1119	124	6	∑	∑	PROPN
cana-1119	124	7	  	  	SPACE
cana-1119	124	8	∞	∞	NUM
cana-1119	124	9	𝑛=2	𝑛=2	PROPN
cana-1119	124	10	 	 	SPACE
cana-1119	124	11	θ𝑛(𝜂)𝑎𝑛𝑧	θ𝑛(𝜂)𝑎𝑛𝑧	DET
cana-1119	124	12	𝑛	𝑛	PROPN
cana-1119	124	13	where	where	SCONJ
cana-1119	124	14	θ𝑛	θ𝑛	ADP
cana-1119	124	15	=	=	SYM
cana-1119	124	16	θ(𝜂	θ(𝜂	X
cana-1119	124	17	)	)	PUNCT
cana-1119	125	1	=	=	SYM
cana-1119	125	2	𝜂𝑛−1	𝜂𝑛−1	PROPN
cana-1119	125	3	(	(	PUNCT
cana-1119	125	4	𝑛−1	𝑛−1	PROPN
cana-1119	125	5	)	)	PUNCT
cana-1119	125	6	!	!	PUNCT
cana-1119	126	1	𝑒−𝜂	𝑒−𝜂	VERB
cana-1119	126	2	and	and	CCONJ
cana-1119	126	3	⋆	⋆	VERB
cana-1119	126	4	denote	denote	VERB
cana-1119	126	5	the	the	DET
cana-1119	126	6	convolution	convolution	NOUN
cana-1119	126	7	or	or	CCONJ
cana-1119	126	8	the	the	DET
cana-1119	126	9	hadmard	hadmard	ADJ
cana-1119	126	10	product	product	NOUN
cana-1119	126	11	of	of	ADP
cana-1119	126	12	the	the	DET
cana-1119	126	13	two	two	NUM
cana-1119	126	14	series	series	NOUN
cana-1119	126	15	.	.	PUNCT
cana-1119	127	1	here	here	ADV
cana-1119	127	2	we	we	PRON
cana-1119	127	3	will	will	AUX
cana-1119	127	4	define	define	VERB
cana-1119	127	5	a	a	DET
cana-1119	127	6	new	new	ADJ
cana-1119	127	7	class	class	NOUN
cana-1119	127	8	𝑆∗𝐶sin(𝑟	𝑆∗𝐶sin(𝑟	NOUN
cana-1119	127	9	,	,	PUNCT
cana-1119	127	10	θ	θ	PROPN
cana-1119	127	11	)	)	PUNCT
cana-1119	127	12	whose	whose	DET
cana-1119	127	13	functions	function	NOUN
cana-1119	127	14	having	have	VERB
cana-1119	127	15	power	power	NOUN
cana-1119	127	16	series	series	NOUN
cana-1119	127	17	whose	whose	DET
cana-1119	127	18	coefficients	coefficient	NOUN
cana-1119	127	19	are	be	AUX
cana-1119	127	20	probabilities	probability	NOUN
cana-1119	127	21	of	of	ADP
cana-1119	127	22	poisson	poisson	NOUN
cana-1119	127	23	distribution	distribution	NOUN
cana-1119	127	24	functions	function	NOUN
cana-1119	127	25	defined	define	VERB
cana-1119	127	26	by	by	ADP
cana-1119	127	27	poisson	poisson	NOUN
cana-1119	127	28	distribution	distribution	NOUN
cana-1119	127	29	𝑆∗𝐶sin(𝑟	𝑆∗𝐶sin(𝑟	NOUN
cana-1119	127	30	,	,	PUNCT
cana-1119	127	31	θ):=	θ):=	PRON
cana-1119	127	32	{	{	PUNCT
cana-1119	127	33	ℎ	ℎ	PROPN
cana-1119	127	34	∈	∈	PROPN
cana-1119	127	35	𝒜	𝒜	NOUN
cana-1119	127	36	:	:	PUNCT
cana-1119	127	37	[	[	PUNCT
cana-1119	127	38	𝑧[𝑃𝜂ℎ(𝑧)]′	𝑧[𝑃𝜂ℎ(𝑧)]′	X
cana-1119	127	39	𝑃𝜂ℎ(𝑧	𝑃𝜂ℎ(𝑧	NOUN
cana-1119	127	40	)	)	PUNCT
cana-1119	127	41	]	]	PUNCT
cana-1119	128	1	𝑟	𝑟	NOUN
cana-1119	128	2	[	[	PUNCT
cana-1119	128	3	[	[	X
cana-1119	128	4	𝑧(𝑃𝜂ℎ(𝑧))′]′	𝑧(𝑃𝜂ℎ(𝑧))′]′	X
cana-1119	128	5	(	(	PUNCT
cana-1119	128	6	𝑃𝜂ℎ(𝑧))′	𝑃𝜂ℎ(𝑧))′	X
cana-1119	128	7	]	]	PUNCT
cana-1119	128	8	1−𝑟	1−𝑟	NUM
cana-1119	128	9	≺	≺	NOUN
cana-1119	128	10	1	1	NUM
cana-1119	128	11	+	+	CCONJ
cana-1119	128	12	sin	sin	NOUN
cana-1119	128	13	(	(	PUNCT
cana-1119	128	14	𝑧	𝑧	NOUN
cana-1119	128	15	)	)	PUNCT
cana-1119	128	16	}	}	PUNCT
cana-1119	128	17	theorem	theorem	VERB
cana-1119	128	18	3.3	3.3	NUM
cana-1119	128	19	.	.	PUNCT
cana-1119	129	1	let	let	VERB
cana-1119	129	2	0	0	NUM
cana-1119	129	3	≤	≤	NUM
cana-1119	129	4	𝑟	𝑟	NOUN
cana-1119	129	5	≤	≤	NUM
cana-1119	129	6	1	1	NUM
cana-1119	129	7	,	,	PUNCT
cana-1119	129	8	𝛿	𝛿	DET
cana-1119	129	9	∈	∈	NOUN
cana-1119	129	10	ℂ	ℂ	PROPN
cana-1119	129	11	if	if	SCONJ
cana-1119	129	12	ℎ	ℎ	PROPN
cana-1119	129	13	∈	∈	PROPN
cana-1119	129	14	𝑆∗𝐶sin(𝑟	𝑆∗𝐶sin(𝑟	ADP
cana-1119	129	15	,	,	PUNCT
cana-1119	129	16	θ	θ	PROPN
cana-1119	129	17	)	)	PUNCT
cana-1119	129	18	,	,	PUNCT
cana-1119	129	19	and	and	CCONJ
cana-1119	129	20	𝑃𝜂ℎ(𝑧	𝑃𝜂ℎ(𝑧	ADP
cana-1119	129	21	)	)	PUNCT
cana-1119	129	22	=	=	SYM
cana-1119	130	1	𝑧	𝑧	PROPN
cana-1119	130	2	+	+	NOUN
cana-1119	130	3	θ2𝑎2𝑧	θ2𝑎2𝑧	NUM
cana-1119	130	4	2	2	NUM
cana-1119	130	5	+	+	CCONJ
cana-1119	130	6	θ3𝑎3𝑧	θ3𝑎3𝑧	NUM
cana-1119	130	7	3	3	NUM
cana-1119	130	8	+	+	CCONJ
cana-1119	130	9	θ4𝑎4𝑧	θ4𝑎4𝑧	NUM
cana-1119	130	10	4	4	NUM
cana-1119	130	11	+	+	CCONJ
cana-1119	130	12	θ5𝑎5𝑧	θ5𝑎5𝑧	NUM
cana-1119	130	13	5	5	NUM
cana-1119	131	1	+	+	NOUN
cana-1119	131	2	⋯	⋯	PROPN
cana-1119	131	3	then	then	ADV
cana-1119	131	4	we	we	PRON
cana-1119	131	5	have	have	AUX
cana-1119	131	6	|𝑎3	|𝑎3	VERB
cana-1119	131	7	−	−	PROPN
cana-1119	131	8	𝛿𝑎2	𝛿𝑎2	NOUN
cana-1119	131	9	2|	2|	NOUN
cana-1119	131	10	≤	≤	ADV
cana-1119	131	11	1	1	NUM
cana-1119	131	12	2(3	2(3	NUM
cana-1119	131	13	−	−	NUM
cana-1119	132	1	2𝑟)θ3	2𝑟)θ3	NUM
cana-1119	133	1	max	max	PROPN
cana-1119	133	2	{	{	PUNCT
cana-1119	133	3	1	1	NUM
cana-1119	133	4	,	,	PUNCT
cana-1119	133	5	|	|	ADV
cana-1119	133	6	3𝑟2	3𝑟2	NUM
cana-1119	133	7	−	−	NOUN
cana-1119	133	8	3𝑟	3𝑟	NOUN
cana-1119	133	9	2(𝑟	2(𝑟	NUM
cana-1119	133	10	−	−	NOUN
cana-1119	133	11	2)2	2)2	NUM
cana-1119	133	12	−	−	NUM
cana-1119	133	13	4𝛿(2𝑟	4𝛿(2𝑟	NUM
cana-1119	133	14	−	−	NOUN
cana-1119	134	1	3)θ3	3)θ3	NUM
cana-1119	134	2	2(𝑟	2(𝑟	NUM
cana-1119	134	3	−	−	NOUN
cana-1119	134	4	2)2θ2	2)2θ2	NUM
cana-1119	134	5	2	2	NUM
cana-1119	134	6	|	|	NOUN
cana-1119	134	7	}	}	PUNCT
cana-1119	134	8	proof	proof	NOUN
cana-1119	134	9	.	.	PUNCT
cana-1119	135	1	we	we	PRON
cana-1119	135	2	have	have	VERB
cana-1119	135	3	ℎ	ℎ	PART
cana-1119	135	4	∈	∈	PROPN
cana-1119	135	5	𝑆∗𝐶sin(𝑟	𝑆∗𝐶sin(𝑟	PROPN
cana-1119	135	6	,	,	PUNCT
cana-1119	135	7	θ	θ	PROPN
cana-1119	135	8	)	)	PUNCT
cana-1119	135	9	which	which	PRON
cana-1119	135	10	is	be	AUX
cana-1119	135	11	defined	define	VERB
cana-1119	135	12	as	as	ADP
cana-1119	135	13	𝑃𝜂ℎ(𝑧	𝑃𝜂ℎ(𝑧	NOUN
cana-1119	135	14	)	)	PUNCT
cana-1119	135	15	=	=	SYM
cana-1119	135	16	𝑧	𝑧	PROPN
cana-1119	136	1	+	+	NOUN
cana-1119	136	2	θ2𝑎2𝑧	θ2𝑎2𝑧	NUM
cana-1119	136	3	2	2	NUM
cana-1119	136	4	+	+	CCONJ
cana-1119	136	5	θ3𝑎3𝑧	θ3𝑎3𝑧	NUM
cana-1119	136	6	3	3	NUM
cana-1119	136	7	+	+	CCONJ
cana-1119	136	8	θ4𝑎4𝑧	θ4𝑎4𝑧	NUM
cana-1119	136	9	4	4	NUM
cana-1119	136	10	+	+	CCONJ
cana-1119	136	11	θ5𝑎5𝑧	θ5𝑎5𝑧	NUM
cana-1119	136	12	5	5	NUM
cana-1119	136	13	+	+	NOUN
cana-1119	136	14	⋯.	⋯.	NOUN
cana-1119	136	15	from	from	ADP
cana-1119	136	16	the	the	DET
cana-1119	136	17	definition	definition	NOUN
cana-1119	136	18	we	we	PRON
cana-1119	136	19	have	have	VERB
cana-1119	136	20	[	[	PUNCT
cana-1119	136	21	𝑧[𝑃𝜂ℎ(𝑧)]′	𝑧[𝑃𝜂ℎ(𝑧)]′	X
cana-1119	136	22	𝑃𝜂ℎ(𝑧	𝑃𝜂ℎ(𝑧	NOUN
cana-1119	136	23	)	)	PUNCT
cana-1119	136	24	]	]	PUNCT
cana-1119	136	25	𝑟	𝑟	NOUN
cana-1119	136	26	[	[	PUNCT
cana-1119	136	27	[	[	X
cana-1119	136	28	𝑧(𝑃𝜂ℎ(𝑧))′]′	𝑧(𝑃𝜂ℎ(𝑧))′]′	X
cana-1119	136	29	(	(	PUNCT
cana-1119	136	30	𝑃𝜂ℎ(𝑧))′	𝑃𝜂ℎ(𝑧))′	X
cana-1119	136	31	]	]	PUNCT
cana-1119	136	32	1−𝑟	1−𝑟	NUM
cana-1119	136	33	=	=	SYM
cana-1119	136	34	1	1	NUM
cana-1119	136	35	+	+	CCONJ
cana-1119	136	36	sin	sin	NOUN
cana-1119	136	37	(	(	PUNCT
cana-1119	136	38	𝑤(𝑧	𝑤(𝑧	PROPN
cana-1119	136	39	)	)	PUNCT
cana-1119	136	40	)	)	PUNCT
cana-1119	136	41	expansion	expansion	NOUN
cana-1119	136	42	of	of	ADP
cana-1119	136	43	[	[	PUNCT
cana-1119	136	44	𝑧[𝑃𝜂ℎ(𝑧)]′	𝑧[𝑃𝜂ℎ(𝑧)]′	X
cana-1119	136	45	𝑃𝜂ℎ(𝑧	𝑃𝜂ℎ(𝑧	NOUN
cana-1119	136	46	)	)	PUNCT
cana-1119	136	47	]	]	PUNCT
cana-1119	137	1	𝑟	𝑟	X
cana-1119	137	2	[	[	PUNCT
cana-1119	137	3	[	[	X
cana-1119	137	4	𝑧(𝑃𝜂ℎ(𝑧))′	𝑧(𝑃𝜂ℎ(𝑧))′	X
cana-1119	137	5	]	]	X
cana-1119	137	6	′	′	NUM
cana-1119	137	7	(	(	PUNCT
cana-1119	137	8	𝑃𝜂ℎ(𝑧))′	𝑃𝜂ℎ(𝑧))′	X
cana-1119	137	9	]	]	PUNCT
cana-1119	137	10	1−𝑟	1−𝑟	NUM
cana-1119	137	11	is	be	AUX
cana-1119	137	12	1	1	NUM
cana-1119	137	13	+	+	CCONJ
cana-1119	137	14	𝑎2θ2(2	𝑎2θ2(2	ADV
cana-1119	137	15	−	−	NOUN
cana-1119	138	1	𝑟)𝑧	𝑟)𝑧	NOUN
cana-1119	139	1	+	+	CCONJ
cana-1119	139	2	𝑧	𝑧	X
cana-1119	139	3	2	2	NUM
cana-1119	139	4	(	(	PUNCT
cana-1119	139	5	1	1	NUM
cana-1119	139	6	2	2	NUM
cana-1119	139	7	𝑎2	𝑎2	NOUN
cana-1119	139	8	2θ2	2θ2	NUM
cana-1119	139	9	2(𝑟2	2(𝑟2	NUM
cana-1119	139	10	+	+	NUM
cana-1119	139	11	5𝑟	5𝑟	NUM
cana-1119	139	12	−	−	PROPN
cana-1119	139	13	8)	8)	NUM
cana-1119	139	14	+	+	CCONJ
cana-1119	139	15	2𝑎3θ3(3	2𝑎3θ3(3	NUM
cana-1119	139	16	−	−	PROPN
cana-1119	139	17	2𝑟	2𝑟	NUM
cana-1119	139	18	)	)	PUNCT
cana-1119	139	19	)	)	PUNCT
cana-1119	140	1	+	+	X
cana-1119	140	2	𝑧3	𝑧3	PROPN
cana-1119	140	3	(	(	PUNCT
cana-1119	140	4	𝑎2𝑎3θ3θ2(4𝑟	𝑎2𝑎3θ3θ2(4𝑟	X
cana-1119	140	5	2	2	NUM
cana-1119	140	6	+	+	NUM
cana-1119	140	7	11𝑟	11𝑟	NOUN
cana-1119	140	8	−	−	PROPN
cana-1119	140	9	18	18	NUM
cana-1119	140	10	)	)	PUNCT
cana-1119	140	11	+	+	CCONJ
cana-1119	140	12	1	1	NUM
cana-1119	140	13	6	6	NUM
cana-1119	140	14	𝑎2	𝑎2	NOUN
cana-1119	140	15	3θ2	3θ2	NUM
cana-1119	140	16	3(−𝑟3	3(−𝑟3	NOUN
cana-1119	141	1	−	−	NUM
cana-1119	141	2	21𝑟2	21𝑟2	NUM
cana-1119	141	3	−	−	NOUN
cana-1119	141	4	20𝑟	20𝑟	X
cana-1119	141	5	+	+	CCONJ
cana-1119	141	6	48	48	NUM
cana-1119	141	7	)	)	PUNCT
cana-1119	142	1	+	+	CCONJ
cana-1119	142	2	3𝑎4θ4(4	3𝑎4θ4(4	NUM
cana-1119	142	3	−	−	NOUN
cana-1119	142	4	3𝑟	3𝑟	NUM
cana-1119	142	5	)	)	PUNCT
cana-1119	142	6	)	)	PUNCT
cana-1119	143	1	+	+	VERB
cana-1119	143	2	𝑧4(𝑎2𝑎4θ4θ2(9𝑟	𝑧4(𝑎2𝑎4θ4θ2(9𝑟	NOUN
cana-1119	143	3	2	2	NUM
cana-1119	143	4	+	+	NOUN
cana-1119	143	5	19𝑟	19𝑟	NOUN
cana-1119	143	6	−	−	ADP
cana-1119	143	7	32	32	NUM
cana-1119	143	8	)	)	PUNCT
cana-1119	143	9	+	+	CCONJ
cana-1119	143	10	2𝑎3	2𝑎3	NUM
cana-1119	143	11	2θ3	2θ3	NUM
cana-1119	143	12	2(4𝑟2	2(4𝑟2	NOUN
cana-1119	143	13	+	+	CCONJ
cana-1119	143	14	4𝑟	4𝑟	NUM
cana-1119	143	15	−	−	NOUN
cana-1119	143	16	9	9	NUM
cana-1119	143	17	)	)	PUNCT
cana-1119	143	18	+	+	CCONJ
cana-1119	143	19	⋯	⋯	VERB
cana-1119	143	20	(	(	PUNCT
cana-1119	143	21	18	18	NUM
cana-1119	143	22	)	)	PUNCT
cana-1119	143	23	comparing	compare	VERB
cana-1119	143	24	above	above	ADV
cana-1119	143	25	with	with	ADP
cana-1119	143	26	expansion	expansion	NOUN
cana-1119	143	27	of	of	ADP
cana-1119	143	28	1	1	NUM
cana-1119	143	29	+	+	CCONJ
cana-1119	143	30	sin	sin	NOUN
cana-1119	143	31	(	(	PUNCT
cana-1119	143	32	𝑤(𝑧	𝑤(𝑧	PROPN
cana-1119	143	33	)	)	PUNCT
cana-1119	143	34	)	)	PUNCT
cana-1119	143	35	communications	communication	NOUN
cana-1119	143	36	on	on	ADP
cana-1119	143	37	applied	apply	VERB
cana-1119	143	38	nonlinear	nonlinear	ADJ
cana-1119	143	39	analysis	analysis	NOUN
cana-1119	143	40	issn	issn	NOUN
cana-1119	143	41	:	:	PUNCT
cana-1119	143	42	1074	1074	NUM
cana-1119	143	43	-	-	PUNCT
cana-1119	143	44	133x	133x	NUM
cana-1119	143	45	vol	vol	NOUN
cana-1119	143	46	31	31	NUM
cana-1119	143	47	no	no	NOUN
cana-1119	143	48	.	.	PUNCT
cana-1119	144	1	6s	6s	NUM
cana-1119	144	2	(	(	PUNCT
cana-1119	144	3	2024	2024	NUM
cana-1119	144	4	)	)	PUNCT
cana-1119	144	5	56	56	NUM
cana-1119	144	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1119	144	7	1	1	NUM
cana-1119	144	8	+	+	NUM
cana-1119	144	9	𝑐1𝑧	𝑐1𝑧	X
cana-1119	144	10	2	2	NUM
cana-1119	144	11	+	+	CCONJ
cana-1119	144	12	(	(	PUNCT
cana-1119	144	13	𝑐2	𝑐2	NOUN
cana-1119	144	14	2	2	NUM
cana-1119	144	15	−	−	NOUN
cana-1119	144	16	𝑐1	𝑐1	NOUN
cana-1119	144	17	2	2	NUM
cana-1119	144	18	4	4	NUM
cana-1119	144	19	)	)	PUNCT
cana-1119	144	20	𝑧2	𝑧2	NOUN
cana-1119	145	1	+	+	CCONJ
cana-1119	145	2	1	1	NUM
cana-1119	145	3	48	48	NUM
cana-1119	145	4	(	(	PUNCT
cana-1119	145	5	5𝑐1	5𝑐1	NUM
cana-1119	145	6	3	3	NUM
cana-1119	145	7	−	−	NOUN
cana-1119	145	8	24𝑐2𝑐1	24𝑐2𝑐1	NOUN
cana-1119	145	9	+	+	CCONJ
cana-1119	145	10	24𝑐3)𝑧	24𝑐3)𝑧	NUM
cana-1119	145	11	3	3	NUM
cana-1119	145	12	+	+	CCONJ
cana-1119	145	13	1	1	NUM
cana-1119	145	14	32	32	NUM
cana-1119	145	15	(	(	PUNCT
cana-1119	145	16	−𝑐1	−𝑐1	NOUN
cana-1119	145	17	4	4	NUM
cana-1119	145	18	+	+	SYM
cana-1119	145	19	10𝑐2𝑐1	10𝑐2𝑐1	NUM
cana-1119	145	20	2	2	NUM
cana-1119	145	21	−	−	PROPN
cana-1119	145	22	16𝑐3𝑐1	16𝑐3𝑐1	NOUN
cana-1119	145	23	−	−	PROPN
cana-1119	145	24	8𝑐2	8𝑐2	NUM
cana-1119	145	25	2	2	NUM
cana-1119	145	26	+	+	NUM
cana-1119	145	27	16𝑐4)𝑧	16𝑐4)𝑧	NUM
cana-1119	145	28	4	4	NUM
cana-1119	145	29	+	+	CCONJ
cana-1119	145	30	(	(	PUNCT
cana-1119	145	31	𝑐1	𝑐1	NOUN
cana-1119	145	32	5	5	NUM
cana-1119	145	33	−	−	NOUN
cana-1119	145	34	480𝑐2𝑐1	480𝑐2𝑐1	NUM
cana-1119	145	35	3	3	NUM
cana-1119	145	36	+	+	CCONJ
cana-1119	145	37	1200𝑐3𝑐1	1200𝑐3𝑐1	NUM
cana-1119	145	38	2	2	NUM
cana-1119	145	39	+	+	CCONJ
cana-1119	145	40	1200𝑐2	1200𝑐2	NOUN
cana-1119	145	41	2𝑐1	2𝑐1	NUM
cana-1119	146	1	−	−	PROPN
cana-1119	146	2	1920𝑐4𝑐1	1920𝑐4𝑐1	NUM
cana-1119	147	1	−	−	NOUN
cana-1119	147	2	1920𝑐2𝑐3	1920𝑐2𝑐3	NUM
cana-1119	148	1	+	+	CCONJ
cana-1119	148	2	1920𝑐5)𝑧	1920𝑐5)𝑧	NUM
cana-1119	148	3	5	5	NUM
cana-1119	148	4	3840	3840	NUM
cana-1119	148	5	+	+	PROPN
cana-1119	148	6	⋯	⋯	NOUN
cana-1119	148	7	we	we	PRON
cana-1119	148	8	will	will	AUX
cana-1119	148	9	get	get	VERB
cana-1119	148	10	𝑎2	𝑎2	NOUN
cana-1119	148	11	=	=	NOUN
cana-1119	149	1	−𝑐1	−𝑐1	NOUN
cana-1119	149	2	2θ2(𝑟	2θ2(𝑟	NUM
cana-1119	149	3	−	−	ADP
cana-1119	149	4	2	2	X
cana-1119	149	5	)	)	PUNCT
cana-1119	149	6	𝑎3	𝑎3	NOUN
cana-1119	149	7	=	=	PUNCT
cana-1119	149	8	3𝑐1	3𝑐1	NUM
cana-1119	149	9	2𝑟2	2𝑟2	NUM
cana-1119	149	10	−	−	NOUN
cana-1119	149	11	4𝑐2𝑟	4𝑐2𝑟	NOUN
cana-1119	149	12	2	2	NUM
cana-1119	149	13	−	−	PROPN
cana-1119	149	14	3𝑐1	3𝑐1	NUM
cana-1119	149	15	2𝑟	2𝑟	NUM
cana-1119	149	16	+	+	CCONJ
cana-1119	149	17	16𝑐2𝑟	16𝑐2𝑟	NUM
cana-1119	149	18	−	−	PROPN
cana-1119	149	19	16𝑐2	16𝑐2	NUM
cana-1119	149	20	16θ3(𝑟	16θ3(𝑟	NUM
cana-1119	149	21	−	−	PROPN
cana-1119	149	22	2)2(2𝑟	2)2(2𝑟	NOUN
cana-1119	149	23	−	−	NOUN
cana-1119	149	24	3	3	X
cana-1119	149	25	)	)	PUNCT
cana-1119	149	26	𝑎4	𝑎4	NOUN
cana-1119	149	27	=	=	SYM
cana-1119	149	28	1	1	NUM
cana-1119	149	29	288(𝑟	288(𝑟	NUM
cana-1119	149	30	−	−	NOUN
cana-1119	149	31	2)3θ4(6𝑟	2)3θ4(6𝑟	NUM
cana-1119	149	32	2	2	NUM
cana-1119	149	33	−	−	NOUN
cana-1119	149	34	17𝑟	17𝑟	NUM
cana-1119	149	35	+	+	CCONJ
cana-1119	149	36	12	12	NUM
cana-1119	149	37	)	)	PUNCT
cana-1119	150	1	[	[	X
cana-1119	150	2	−52𝑐1	−52𝑐1	X
cana-1119	150	3	3𝑟4	3𝑟4	NUM
cana-1119	150	4	+	+	CCONJ
cana-1119	150	5	144𝑐1𝑐2𝑟	144𝑐1𝑐2𝑟	NUM
cana-1119	150	6	4	4	NUM
cana-1119	150	7	−	−	NOUN
cana-1119	150	8	96𝑐3𝑟	96𝑐3𝑟	NUM
cana-1119	150	9	4	4	NUM
cana-1119	150	10	+	+	CCONJ
cana-1119	150	11	165𝑐1	165𝑐1	NUM
cana-1119	150	12	3𝑟3𝑧	3𝑟3𝑧	NUM
cana-1119	150	13	−780𝑐1𝑐2𝑟	−780𝑐1𝑐2𝑟	VERB
cana-1119	150	14	3	3	NUM
cana-1119	150	15	+	+	CCONJ
cana-1119	150	16	720𝑐3𝑟	720𝑐3𝑟	NUM
cana-1119	150	17	3	3	NUM
cana-1119	150	18	−	−	PROPN
cana-1119	150	19	250𝑐1	250𝑐1	NUM
cana-1119	150	20	3𝑟2	3𝑟2	NUM
cana-1119	150	21	+	+	CCONJ
cana-1119	151	1	1464𝑐1𝑐2𝑟	1464𝑐1𝑐2𝑟	NUM
cana-1119	151	2	2	2	NUM
cana-1119	151	3	−	−	NOUN
cana-1119	151	4	2016𝑐3𝑟	2016𝑐3𝑟	NUM
cana-1119	151	5	2	2	NUM
cana-1119	151	6	+	+	SYM
cana-1119	151	7	46𝑐1	46𝑐1	NUM
cana-1119	151	8	3𝑟	3𝑟	NOUN
cana-1119	151	9	−	−	PROPN
cana-1119	151	10	1104𝑐1𝑐2𝑟	1104𝑐1𝑐2𝑟	NUM
cana-1119	151	11	+	+	CCONJ
cana-1119	151	12	2496𝑐3𝑟	2496𝑐3𝑟	NUM
cana-1119	151	13	+	+	SYM
cana-1119	151	14	48𝑐1	48𝑐1	NUM
cana-1119	151	15	3	3	NUM
cana-1119	151	16	+	+	CCONJ
cana-1119	151	17	288𝑐1𝑐2	288𝑐1𝑐2	NUM
cana-1119	151	18	−	−	NOUN
cana-1119	151	19	1152𝑐3	1152𝑐3	NUM
cana-1119	151	20	]	]	X
cana-1119	151	21	(	(	PUNCT
cana-1119	151	22	19	19	NUM
cana-1119	151	23	)	)	PUNCT
cana-1119	151	24	from	from	ADP
cana-1119	151	25	above	above	ADP
cana-1119	151	26	we	we	PRON
cana-1119	151	27	will	will	AUX
cana-1119	151	28	have	have	VERB
cana-1119	151	29	[	[	PUNCT
cana-1119	151	30	𝑧[𝑃𝜂ℎ(𝑧)]′	𝑧[𝑃𝜂ℎ(𝑧)]′	X
cana-1119	151	31	𝑃𝜂ℎ(𝑧	𝑃𝜂ℎ(𝑧	NOUN
cana-1119	151	32	)	)	PUNCT
cana-1119	151	33	]	]	PUNCT
cana-1119	152	1	𝑟	𝑟	NOUN
cana-1119	152	2	[	[	PUNCT
cana-1119	152	3	[	[	X
cana-1119	152	4	𝑧(𝑃𝜂ℎ(𝑧))′]′	𝑧(𝑃𝜂ℎ(𝑧))′]′	X
cana-1119	152	5	(	(	PUNCT
cana-1119	152	6	𝑃𝜂ℎ(𝑧))′	𝑃𝜂ℎ(𝑧))′	X
cana-1119	152	7	]	]	PUNCT
cana-1119	152	8	1−𝑟	1−𝑟	NUM
cana-1119	153	1	=	=	SYM
cana-1119	153	2	1	1	NUM
cana-1119	153	3	+	+	CCONJ
cana-1119	153	4	sin	sin	NOUN
cana-1119	153	5	(	(	PUNCT
cana-1119	153	6	𝑤(𝑧	𝑤(𝑧	PROPN
cana-1119	153	7	)	)	PUNCT
cana-1119	153	8	)	)	PUNCT
cana-1119	153	9	𝑎3	𝑎3	PROPN
cana-1119	153	10	−	−	PROPN
cana-1119	153	11	𝛿𝑎2	𝛿𝑎2	NOUN
cana-1119	153	12	2	2	NUM
cana-1119	153	13	=	=	SYM
cana-1119	153	14	1	1	NUM
cana-1119	153	15	4(3−2𝑟)θ3	4(3−2𝑟)θ3	NUM
cana-1119	154	1	[	[	X
cana-1119	154	2	c2	c2	PROPN
cana-1119	154	3	−	−	PROPN
cana-1119	154	4	𝑐1	𝑐1	NOUN
cana-1119	154	5	2(4𝛿(3−2𝑟)θ3+(3𝑟	2(4𝛿(3−2𝑟)θ3+(3𝑟	NUM
cana-1119	154	6	2−3𝑟)θ2	2−3𝑟)θ2	NUM
cana-1119	154	7	2𝑟	2𝑟	NUM
cana-1119	154	8	)	)	PUNCT
cana-1119	154	9	4(𝑟−2)2θ2	4(𝑟−2)2θ2	NOUN
cana-1119	154	10	2	2	NUM
cana-1119	154	11	]	]	PUNCT
cana-1119	154	12	(	(	PUNCT
cana-1119	154	13	20	20	NUM
cana-1119	154	14	)	)	PUNCT
cana-1119	154	15	from	from	ADP
cana-1119	154	16	lemma	lemma	PROPN
cana-1119	154	17	(	(	PUNCT
cana-1119	154	18	3.1	3.1	NUM
cana-1119	154	19	)	)	PUNCT
cana-1119	154	20	we	we	PRON
cana-1119	154	21	have	have	AUX
cana-1119	154	22	|𝑎3	|𝑎3	VERB
cana-1119	154	23	−	−	PROPN
cana-1119	155	1	𝛿𝑎2	𝛿𝑎2	NOUN
cana-1119	155	2	2|	2|	NOUN
cana-1119	155	3	≤	≤	ADV
cana-1119	155	4	1	1	NUM
cana-1119	155	5	2(3	2(3	NUM
cana-1119	155	6	−	−	NUM
cana-1119	156	1	2𝑟)θ3	2𝑟)θ3	NUM
cana-1119	156	2	max	max	PROPN
cana-1119	156	3	{	{	PUNCT
cana-1119	156	4	1	1	NUM
cana-1119	156	5	,	,	PUNCT
cana-1119	156	6	|	|	ADV
cana-1119	156	7	3𝑟2	3𝑟2	NUM
cana-1119	156	8	−	−	NOUN
cana-1119	156	9	3𝑟	3𝑟	NOUN
cana-1119	156	10	2(𝑟	2(𝑟	NUM
cana-1119	156	11	−	−	NOUN
cana-1119	156	12	2)2	2)2	NUM
cana-1119	156	13	−	−	NUM
cana-1119	156	14	4𝛿(2𝑟	4𝛿(2𝑟	NUM
cana-1119	156	15	−	−	NOUN
cana-1119	156	16	3)θ3	3)θ3	NUM
cana-1119	156	17	2(𝑟	2(𝑟	NUM
cana-1119	156	18	−	−	NOUN
cana-1119	156	19	2)2θ2	2)2θ2	NUM
cana-1119	156	20	2	2	NUM
cana-1119	156	21	|	|	NOUN
cana-1119	156	22	}	}	PUNCT
cana-1119	156	23	theorem	theorem	VERB
cana-1119	156	24	3.4	3.4	NUM
cana-1119	156	25	.	.	PUNCT
cana-1119	157	1	let	let	VERB
cana-1119	157	2	0	0	NUM
cana-1119	157	3	≤	≤	NUM
cana-1119	157	4	𝑟	𝑟	PRON
cana-1119	157	5	≤	≤	NOUN
cana-1119	157	6	1and	1and	NUM
cana-1119	157	7	𝑃𝜂ℎ(𝑧	𝑃𝜂ℎ(𝑧	NOUN
cana-1119	157	8	)	)	PUNCT
cana-1119	157	9	=	=	SYM
cana-1119	158	1	𝑧	𝑧	PROPN
cana-1119	158	2	+	+	NOUN
cana-1119	158	3	θ2𝑎2𝑧	θ2𝑎2𝑧	NUM
cana-1119	158	4	2	2	NUM
cana-1119	158	5	+	+	CCONJ
cana-1119	158	6	θ3𝑎3𝑧	θ3𝑎3𝑧	NUM
cana-1119	158	7	3	3	NUM
cana-1119	158	8	+	+	CCONJ
cana-1119	158	9	θ4𝑎4𝑧	θ4𝑎4𝑧	NUM
cana-1119	158	10	4	4	NUM
cana-1119	158	11	+	+	CCONJ
cana-1119	158	12	θ5𝑎5𝑧	θ5𝑎5𝑧	NUM
cana-1119	158	13	5	5	NUM
cana-1119	158	14	+	+	ADJ
cana-1119	158	15	⋯	⋯	PROPN
cana-1119	158	16	,	,	PUNCT
cana-1119	158	17	with	with	ADP
cana-1119	158	18	𝛿	𝛿	DET
cana-1119	158	19	∈	∈	PROPN
cana-1119	158	20	ℝ	ℝ	PROPN
cana-1119	158	21	then	then	ADV
cana-1119	158	22	|𝑎3	|𝑎3	VERB
cana-1119	158	23	−	−	PROPN
cana-1119	158	24	𝛿𝑎2	𝛿𝑎2	NOUN
cana-1119	158	25	2|	2|	NOUN
cana-1119	158	26	≤	≤	PROPN
cana-1119	158	27	{	{	PUNCT
cana-1119	158	28	−1	−1	NOUN
cana-1119	158	29	4(3	4(3	NUM
cana-1119	158	30	−	−	NUM
cana-1119	158	31	2𝑟)θ3	2𝑟)θ3	NUM
cana-1119	158	32	[	[	PUNCT
cana-1119	158	33	𝑟2	𝑟2	NOUN
cana-1119	158	34	+	+	CCONJ
cana-1119	158	35	5𝑟	5𝑟	NUM
cana-1119	158	36	−	−	NOUN
cana-1119	158	37	8	8	NUM
cana-1119	158	38	(	(	PUNCT
cana-1119	158	39	−2	−2	NOUN
cana-1119	158	40	+	+	NOUN
cana-1119	158	41	𝑟)2	𝑟)2	NOUN
cana-1119	158	42	+	+	CCONJ
cana-1119	158	43	4𝛿(3	4𝛿(3	NOUN
cana-1119	158	44	−	−	PROPN
cana-1119	158	45	2𝑟)θ3	2𝑟)θ3	NUM
cana-1119	158	46	(	(	PUNCT
cana-1119	158	47	−2	−2	NOUN
cana-1119	159	1	+	+	CCONJ
cana-1119	159	2	𝑟)2θ2	𝑟)2θ2	NOUN
cana-1119	159	3	2	2	NUM
cana-1119	159	4	]	]	PUNCT
cana-1119	159	5	if	if	SCONJ
cana-1119	159	6	𝛿	𝛿	PRON
cana-1119	159	7	≤	≤	NOUN
cana-1119	159	8	(	(	PUNCT
cana-1119	159	9	−3𝑟2	−3𝑟2	X
cana-1119	159	10	+	+	CCONJ
cana-1119	159	11	3𝑟)θ2	3𝑟)θ2	NUM
cana-1119	159	12	2	2	NUM
cana-1119	159	13	4(3	4(3	NUM
cana-1119	159	14	−	−	NUM
cana-1119	159	15	2𝑟)θ3	2𝑟)θ3	NUM
cana-1119	159	16	1	1	NUM
cana-1119	159	17	2(3	2(3	NUM
cana-1119	159	18	−	−	NUM
cana-1119	159	19	2𝑟)θ3	2𝑟)θ3	NOUN
cana-1119	159	20	if	if	SCONJ
cana-1119	159	21	(	(	PUNCT
cana-1119	159	22	−3𝑟2	−3𝑟2	NUM
cana-1119	159	23	+	+	NUM
cana-1119	159	24	3𝑟)θ3	3𝑟)θ3	NUM
cana-1119	159	25	4(3	4(3	NUM
cana-1119	159	26	−	−	NOUN
cana-1119	159	27	2𝑟)θ2	2𝑟)θ2	NUM
cana-1119	159	28	2	2	NUM
cana-1119	159	29	≤	≤	NOUN
cana-1119	159	30	𝛿	𝛿	PRON
cana-1119	159	31	≤	≤	NOUN
cana-1119	159	32	(	(	PUNCT
cana-1119	159	33	𝑟2	𝑟2	NOUN
cana-1119	159	34	−	−	NOUN
cana-1119	159	35	13𝑟	13𝑟	NOUN
cana-1119	159	36	+	+	CCONJ
cana-1119	159	37	16)θ2	16)θ2	NUM
cana-1119	159	38	2	2	NUM
cana-1119	159	39	4(3	4(3	NUM
cana-1119	159	40	−	−	NUM
cana-1119	159	41	2𝑟)θ3	2𝑟)θ3	NUM
cana-1119	159	42	1	1	NUM
cana-1119	159	43	4(3	4(3	NUM
cana-1119	159	44	−	−	NUM
cana-1119	159	45	2𝑟)θ3	2𝑟)θ3	NUM
cana-1119	159	46	[	[	PUNCT
cana-1119	159	47	𝑟2	𝑟2	NOUN
cana-1119	159	48	+	+	CCONJ
cana-1119	159	49	5𝑟	5𝑟	NUM
cana-1119	159	50	−	−	NOUN
cana-1119	159	51	8	8	NUM
cana-1119	159	52	(	(	PUNCT
cana-1119	159	53	−2	−2	NOUN
cana-1119	159	54	+	+	NOUN
cana-1119	159	55	𝑟)2	𝑟)2	NOUN
cana-1119	159	56	+	+	CCONJ
cana-1119	159	57	4𝛿(3	4𝛿(3	NOUN
cana-1119	159	58	−	−	PROPN
cana-1119	159	59	2𝑟)θ3	2𝑟)θ3	NUM
cana-1119	159	60	(	(	PUNCT
cana-1119	159	61	−2	−2	NOUN
cana-1119	159	62	+	+	NOUN
cana-1119	159	63	𝑟)2	𝑟)2	NOUN
cana-1119	159	64	]	]	PUNCT
cana-1119	159	65	if	if	SCONJ
cana-1119	159	66	(	(	PUNCT
cana-1119	159	67	𝑟2	𝑟2	NOUN
cana-1119	159	68	−	−	NOUN
cana-1119	159	69	13𝑟	13𝑟	NOUN
cana-1119	159	70	+	+	CCONJ
cana-1119	159	71	16)θ2	16)θ2	NUM
cana-1119	159	72	2	2	NUM
cana-1119	159	73	4(3	4(3	NUM
cana-1119	159	74	−	−	NUM
cana-1119	159	75	2𝑟)θ3	2𝑟)θ3	NUM
cana-1119	159	76	≤	≤	NOUN
cana-1119	159	77	𝛿	𝛿	DET
cana-1119	159	78	proof	proof	NOUN
cana-1119	159	79	.	.	PUNCT
cana-1119	160	1	from	from	ADP
cana-1119	160	2	(	(	PUNCT
cana-1119	160	3	20	20	NUM
cana-1119	160	4	)	)	PUNCT
cana-1119	160	5	and	and	CCONJ
cana-1119	160	6	along	along	ADP
cana-1119	160	7	with	with	ADP
cana-1119	160	8	using	use	VERB
cana-1119	160	9	lemma	lemma	PROPN
cana-1119	160	10	(	(	PUNCT
cana-1119	160	11	3.1	3.1	NUM
cana-1119	160	12	)	)	PUNCT
cana-1119	160	13	we	we	PRON
cana-1119	160	14	will	will	AUX
cana-1119	160	15	get	get	VERB
cana-1119	160	16	the	the	DET
cana-1119	160	17	desired	desire	VERB
cana-1119	160	18	result	result	NOUN
cana-1119	160	19	.	.	PUNCT
cana-1119	161	1	second	second	ADJ
cana-1119	161	2	hankel	hankel	NOUN
cana-1119	161	3	inequality	inequality	NOUN
cana-1119	161	4	for	for	ADP
cana-1119	161	5	𝒉	𝒉	PROPN
cana-1119	161	6	∈	∈	PROPN
cana-1119	161	7	𝑺∗𝑪𝐬𝐢𝐧	𝑺∗𝑪𝐬𝐢𝐧	PROPN
cana-1119	161	8	theorem	theorem	VERB
cana-1119	161	9	3.5	3.5	NUM
cana-1119	161	10	.	.	PUNCT
cana-1119	162	1	if	if	SCONJ
cana-1119	162	2	the	the	DET
cana-1119	162	3	function	function	NOUN
cana-1119	162	4	ℎ	ℎ	X
cana-1119	162	5	∈	∈	PROPN
cana-1119	162	6	𝑆∗𝐶sin(𝑟	𝑆∗𝐶sin(𝑟	PROPN
cana-1119	162	7	)	)	PUNCT
cana-1119	162	8	then	then	ADV
cana-1119	162	9	|𝑎2𝑎4	|𝑎2𝑎4	VERB
cana-1119	162	10	−	−	PROPN
cana-1119	162	11	𝑎3	𝑎3	NOUN
cana-1119	162	12	2|	2|	NUM
cana-1119	162	13	≤	≤	NOUN
cana-1119	162	14	1	1	NUM
cana-1119	162	15	4(3	4(3	NUM
cana-1119	162	16	−	−	NUM
cana-1119	162	17	2𝑟)2	2𝑟)2	NUM
cana-1119	162	18	communications	communication	NOUN
cana-1119	162	19	on	on	ADP
cana-1119	162	20	applied	apply	VERB
cana-1119	162	21	nonlinear	nonlinear	ADJ
cana-1119	162	22	analysis	analysis	NOUN
cana-1119	162	23	issn	issn	NOUN
cana-1119	162	24	:	:	PUNCT
cana-1119	162	25	1074	1074	NUM
cana-1119	162	26	-	-	PUNCT
cana-1119	162	27	133x	133x	NUM
cana-1119	162	28	vol	vol	NOUN
cana-1119	162	29	31	31	NUM
cana-1119	162	30	no	no	NOUN
cana-1119	162	31	.	.	PUNCT
cana-1119	163	1	6s	6s	NUM
cana-1119	163	2	(	(	PUNCT
cana-1119	163	3	2024	2024	NUM
cana-1119	163	4	)	)	PUNCT
cana-1119	163	5	57	57	NUM
cana-1119	163	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1119	163	7	proof	proof	NOUN
cana-1119	163	8	.	.	PUNCT
cana-1119	164	1	from	from	ADP
cana-1119	164	2	(	(	PUNCT
cana-1119	164	3	15	15	NUM
cana-1119	164	4	)	)	PUNCT
cana-1119	164	5	,	,	PUNCT
cana-1119	164	6	we	we	PRON
cana-1119	164	7	have	have	VERB
cana-1119	164	8	𝑎4	𝑎4	NOUN
cana-1119	164	9	=	=	SYM
cana-1119	164	10	1	1	NUM
cana-1119	164	11	288(𝑟	288(𝑟	NUM
cana-1119	164	12	−	−	NOUN
cana-1119	164	13	2)3(6𝑟2	2)3(6𝑟2	NUM
cana-1119	164	14	−	−	NOUN
cana-1119	164	15	17𝑟	17𝑟	NUM
cana-1119	165	1	+	+	CCONJ
cana-1119	166	1	12	12	NUM
cana-1119	166	2	)	)	PUNCT
cana-1119	167	1	[	[	X
cana-1119	167	2	−52𝑐1	−52𝑐1	X
cana-1119	167	3	3𝑟4	3𝑟4	NUM
cana-1119	167	4	+	+	CCONJ
cana-1119	167	5	144𝑐1𝑐2𝑟	144𝑐1𝑐2𝑟	NUM
cana-1119	167	6	4	4	NUM
cana-1119	167	7	−	−	NOUN
cana-1119	167	8	96𝑐3𝑟	96𝑐3𝑟	NUM
cana-1119	167	9	4	4	NUM
cana-1119	167	10	+	+	CCONJ
cana-1119	167	11	165𝑐1	165𝑐1	NUM
cana-1119	167	12	3𝑟3	3𝑟3	NUM
cana-1119	167	13	−	−	NOUN
cana-1119	167	14	780𝑐1𝑐2𝑟	780𝑐1𝑐2𝑟	NUM
cana-1119	167	15	3	3	NUM
cana-1119	167	16	+	+	CCONJ
cana-1119	167	17	720𝑐3𝑟	720𝑐3𝑟	NUM
cana-1119	167	18	3	3	NUM
cana-1119	167	19	−205𝑐1	−205𝑐1	NOUN
cana-1119	167	20	3𝑟2	3𝑟2	NUM
cana-1119	167	21	+	+	CCONJ
cana-1119	167	22	1464𝑐1𝑐2𝑟	1464𝑐1𝑐2𝑟	NUM
cana-1119	167	23	2	2	NUM
cana-1119	167	24	−	−	NOUN
cana-1119	167	25	2016𝑐3𝑟	2016𝑐3𝑟	NUM
cana-1119	167	26	2	2	NUM
cana-1119	167	27	+	+	SYM
cana-1119	167	28	46𝑐1	46𝑐1	NUM
cana-1119	167	29	3𝑟	3𝑟	NUM
cana-1119	167	30	−	−	PROPN
cana-1119	167	31	1104𝑐1𝑐2	1104𝑐1𝑐2	NUM
cana-1119	167	32	𝑟	𝑟	NOUN
cana-1119	167	33	+	+	NUM
cana-1119	167	34	2496𝑐3	2496𝑐3	NOUN
cana-1119	167	35	𝑟	𝑟	NOUN
cana-1119	167	36	+	+	CCONJ
cana-1119	167	37	48𝑐1	48𝑐1	NUM
cana-1119	167	38	3	3	NUM
cana-1119	167	39	+	+	CCONJ
cana-1119	167	40	288𝑐1𝑐2	288𝑐1𝑐2	NUM
cana-1119	167	41	−	−	NOUN
cana-1119	167	42	1152𝑐3	1152𝑐3	NUM
cana-1119	167	43	(	(	PUNCT
cana-1119	167	44	21	21	NUM
cana-1119	167	45	)	)	PUNCT
cana-1119	167	46	using	use	VERB
cana-1119	167	47	(	(	PUNCT
cana-1119	167	48	13	13	NUM
cana-1119	167	49	)	)	PUNCT
cana-1119	167	50	,	,	PUNCT
cana-1119	167	51	(	(	PUNCT
cana-1119	167	52	14	14	NUM
cana-1119	167	53	)	)	PUNCT
cana-1119	167	54	and	and	CCONJ
cana-1119	167	55	(	(	PUNCT
cana-1119	167	56	15	15	X
cana-1119	167	57	)	)	PUNCT
cana-1119	167	58	we	we	PRON
cana-1119	167	59	will	will	AUX
cana-1119	167	60	have	have	VERB
cana-1119	167	61	𝑎2𝑎4	𝑎2𝑎4	SYM
cana-1119	167	62	−	−	NUM
cana-1119	167	63	𝑎3	𝑎3	NOUN
cana-1119	167	64	2	2	NUM
cana-1119	167	65	=	=	SYM
cana-1119	167	66	1	1	NUM
cana-1119	167	67	2304	2304	NUM
cana-1119	167	68	[	[	X
cana-1119	167	69	−	−	NOUN
cana-1119	167	70	24𝑐2𝑐1	24𝑐2𝑐1	VERB
cana-1119	167	71	2(21𝑟3	2(21𝑟3	NUM
cana-1119	168	1	−	−	PROPN
cana-1119	168	2	77𝑟2	77𝑟2	NUM
cana-1119	169	1	+	+	CCONJ
cana-1119	169	2	90𝑟	90𝑟	NUM
cana-1119	169	3	−	−	ADP
cana-1119	169	4	36	36	NUM
cana-1119	169	5	)	)	PUNCT
cana-1119	169	6	(	(	PUNCT
cana-1119	169	7	3	3	NUM
cana-1119	169	8	−	−	PROPN
cana-1119	169	9	2𝑟)2(𝑟	2𝑟)2(𝑟	NUM
cana-1119	169	10	−	−	NOUN
cana-1119	169	11	2)2(3𝑟	2)2(3𝑟	NUM
cana-1119	170	1	−	−	PROPN
cana-1119	170	2	4	4	NUM
cana-1119	170	3	)	)	PUNCT
cana-1119	171	1	+	+	CCONJ
cana-1119	171	2	𝑐1	𝑐1	NOUN
cana-1119	171	3	4(173𝑟5	4(173𝑟5	NUM
cana-1119	171	4	−	−	PROPN
cana-1119	171	5	1134𝑟4	1134𝑟4	PROPN
cana-1119	172	1	+	+	CCONJ
cana-1119	172	2	2729𝑟3	2729𝑟3	NUM
cana-1119	173	1	−	−	X
cana-1119	173	2	2504𝑟2	2504𝑟2	PROPN
cana-1119	174	1	+	+	CCONJ
cana-1119	174	2	168𝑟	168𝑟	NUM
cana-1119	174	3	+	+	CCONJ
cana-1119	174	4	576	576	NUM
cana-1119	174	5	)	)	PUNCT
cana-1119	174	6	(	(	PUNCT
cana-1119	174	7	3	3	NUM
cana-1119	174	8	−	−	PROPN
cana-1119	174	9	2𝑟)2(𝑟	2𝑟)2(𝑟	NUM
cana-1119	174	10	−	−	PROPN
cana-1119	174	11	2)4(3𝑟	2)4(3𝑟	NUM
cana-1119	175	1	−	−	NOUN
cana-1119	175	2	4	4	NUM
cana-1119	175	3	)	)	PUNCT
cana-1119	175	4	+	+	NUM
cana-1119	175	5	192𝑐3𝑐1	192𝑐3𝑐1	NUM
cana-1119	175	6	(	(	PUNCT
cana-1119	175	7	𝑟	𝑟	X
cana-1119	175	8	−	−	ADP
cana-1119	175	9	2)(3𝑟	2)(3𝑟	NUM
cana-1119	175	10	−	−	NOUN
cana-1119	175	11	4	4	NUM
cana-1119	175	12	)	)	PUNCT
cana-1119	175	13	−	−	PROPN
cana-1119	175	14	144𝑐2	144𝑐2	NUM
cana-1119	175	15	2	2	NUM
cana-1119	175	16	(	(	PUNCT
cana-1119	175	17	3	3	NUM
cana-1119	175	18	−	−	NUM
cana-1119	175	19	2𝑟)2	2𝑟)2	NUM
cana-1119	175	20	]	]	PUNCT
cana-1119	175	21	without	without	ADP
cana-1119	175	22	loss	loss	NOUN
cana-1119	175	23	of	of	ADP
cana-1119	175	24	generality	generality	NOUN
cana-1119	175	25	we	we	PRON
cana-1119	175	26	can	can	AUX
cana-1119	175	27	say	say	VERB
cana-1119	175	28	that	that	PRON
cana-1119	175	29	𝑐:=	𝑐:=	PROPN
cana-1119	175	30	𝑐1	𝑐1	NOUN
cana-1119	175	31	,	,	PUNCT
cana-1119	175	32	where	where	SCONJ
cana-1119	175	33	|𝑐1|	|𝑐1|	NOUN
cana-1119	175	34	≤	≤	ADV
cana-1119	175	35	2	2	NUM
cana-1119	175	36	and	and	CCONJ
cana-1119	175	37	substituting	substitute	VERB
cana-1119	175	38	the	the	DET
cana-1119	175	39	values	value	NOUN
cana-1119	175	40	of	of	ADP
cana-1119	175	41	𝑐2	𝑐2	NOUN
cana-1119	175	42	and	and	CCONJ
cana-1119	175	43	𝑐3	𝑐3	NOUN
cana-1119	175	44	we	we	PRON
cana-1119	175	45	have	have	VERB
cana-1119	175	46	(	(	PUNCT
cana-1119	175	47	𝑎2𝑎4	𝑎2𝑎4	PRON
cana-1119	175	48	−	−	PROPN
cana-1119	175	49	𝑎3	𝑎3	NOUN
cana-1119	175	50	2	2	NUM
cana-1119	175	51	)	)	PUNCT
cana-1119	175	52	=	=	SYM
cana-1119	175	53	1	1	NUM
cana-1119	175	54	2304	2304	NUM
cana-1119	175	55	[	[	PUNCT
cana-1119	175	56	96(1	96(1	NOUN
cana-1119	176	1	−	−	PROPN
cana-1119	176	2	|𝑥|2)(4	|𝑥|2)(4	PROPN
cana-1119	176	3	−	−	PROPN
cana-1119	177	1	𝑐2)𝑐𝑦	𝑐2)𝑐𝑦	PROPN
cana-1119	177	2	(	(	PUNCT
cana-1119	177	3	𝑟	𝑟	X
cana-1119	177	4	−	−	ADP
cana-1119	177	5	2)(3𝑟	2)(3𝑟	NUM
cana-1119	177	6	−	−	NOUN
cana-1119	177	7	4	4	NUM
cana-1119	177	8	)	)	PUNCT
cana-1119	177	9	−	−	NOUN
cana-1119	178	1	𝑥2(4	𝑥2(4	VERB
cana-1119	178	2	−	−	PROPN
cana-1119	178	3	𝑐2	𝑐2	NOUN
cana-1119	178	4	)	)	PUNCT
cana-1119	179	1	(	(	PUNCT
cana-1119	179	2	48𝑐2	48𝑐2	NUM
cana-1119	179	3	(	(	PUNCT
cana-1119	179	4	𝑟	𝑟	NOUN
cana-1119	179	5	−	−	PROPN
cana-1119	179	6	2)(3𝑟	2)(3𝑟	NUM
cana-1119	179	7	−	−	NOUN
cana-1119	179	8	4	4	NUM
cana-1119	179	9	)	)	PUNCT
cana-1119	179	10	+	+	CCONJ
cana-1119	179	11	36(4	36(4	NUM
cana-1119	179	12	−	−	NOUN
cana-1119	179	13	𝑐2	𝑐2	NOUN
cana-1119	179	14	)	)	PUNCT
cana-1119	179	15	(	(	PUNCT
cana-1119	179	16	3	3	NUM
cana-1119	179	17	−	−	NUM
cana-1119	179	18	2𝑟)2	2𝑟)2	NUM
cana-1119	179	19	)	)	PUNCT
cana-1119	180	1	−	−	PROPN
cana-1119	181	1	12𝑥(4	12𝑥(4	NUM
cana-1119	181	2	−	−	NOUN
cana-1119	182	1	𝑐2)𝑐2(12	𝑐2)𝑐2(12	ADV
cana-1119	182	2	−	−	PROPN
cana-1119	182	3	6𝑟	6𝑟	NOUN
cana-1119	182	4	−	−	PROPN
cana-1119	182	5	13𝑟27𝑟3	13𝑟27𝑟3	NUM
cana-1119	182	6	)	)	PUNCT
cana-1119	182	7	(	(	PUNCT
cana-1119	182	8	3	3	NUM
cana-1119	182	9	−	−	PROPN
cana-1119	182	10	2𝑟)2(𝑟	2𝑟)2(𝑟	NUM
cana-1119	182	11	−	−	NOUN
cana-1119	182	12	2)2(3𝑟	2)2(3𝑟	NUM
cana-1119	182	13	−	−	PROPN
cana-1119	182	14	4	4	NUM
cana-1119	182	15	)	)	PUNCT
cana-1119	183	1	+	+	CCONJ
cana-1119	183	2	𝑐4(5𝑟5	𝑐4(5𝑟5	NOUN
cana-1119	184	1	+	+	X
cana-1119	185	1	78𝑟4	78𝑟4	NUM
cana-1119	185	2	−	−	NUM
cana-1119	186	1	607𝑟3	607𝑟3	NUM
cana-1119	187	1	+	+	CCONJ
cana-1119	187	2	1816𝑟2	1816𝑟2	NUM
cana-1119	187	3	−	−	PROPN
cana-1119	187	4	2424𝑟	2424𝑟	NUM
cana-1119	187	5	+	+	CCONJ
cana-1119	187	6	1152	1152	NUM
cana-1119	187	7	)	)	PUNCT
cana-1119	188	1	(	(	PUNCT
cana-1119	188	2	3	3	NUM
cana-1119	188	3	−	−	PROPN
cana-1119	188	4	2𝑟)2(𝑟	2𝑟)2(𝑟	NUM
cana-1119	188	5	−	−	PROPN
cana-1119	188	6	2)4(3𝑟	2)4(3𝑟	NUM
cana-1119	188	7	−	−	NOUN
cana-1119	188	8	4	4	NUM
cana-1119	188	9	)	)	PUNCT
cana-1119	188	10	]	]	PUNCT
cana-1119	188	11	replacing	replace	VERB
cana-1119	188	12	|𝑥|	|𝑥|	ADV
cana-1119	188	13	by	by	ADP
cana-1119	188	14	𝑏	𝑏	PRON
cana-1119	188	15	and	and	CCONJ
cana-1119	188	16	using	use	VERB
cana-1119	188	17	triangular	triangular	NOUN
cana-1119	188	18	inequality	inequality	NOUN
cana-1119	188	19	and	and	CCONJ
cana-1119	188	20	the	the	DET
cana-1119	188	21	inequality	inequality	NOUN
cana-1119	188	22	|𝑦|	|𝑦|	PROPN
cana-1119	188	23	≤	≤	ADV
cana-1119	188	24	1	1	NUM
cana-1119	188	25	in	in	ADP
cana-1119	188	26	above	above	ADP
cana-1119	188	27	we	we	PRON
cana-1119	188	28	will	will	AUX
cana-1119	188	29	get	get	VERB
cana-1119	188	30	|𝑎2𝑎4	|𝑎2𝑎4	NOUN
cana-1119	188	31	−	−	PROPN
cana-1119	188	32	𝑎3	𝑎3	NOUN
cana-1119	188	33	2|	2|	NUM
cana-1119	188	34	≤	≤	NUM
cana-1119	188	35	1	1	NUM
cana-1119	188	36	2304	2304	NUM
cana-1119	188	37	[	[	PUNCT
cana-1119	188	38	96(1	96(1	NOUN
cana-1119	188	39	−	−	NOUN
cana-1119	188	40	𝑏2)(4	𝑏2)(4	NOUN
cana-1119	188	41	−	−	PROPN
cana-1119	188	42	𝑐2)𝑐	𝑐2)𝑐	NOUN
cana-1119	188	43	(	(	PUNCT
cana-1119	188	44	𝑟	𝑟	NOUN
cana-1119	188	45	−	−	ADP
cana-1119	188	46	2)(3𝑟	2)(3𝑟	NUM
cana-1119	188	47	−	−	NOUN
cana-1119	188	48	4	4	NUM
cana-1119	188	49	)	)	PUNCT
cana-1119	188	50	+	+	CCONJ
cana-1119	188	51	𝑏2(4	𝑏2(4	PROPN
cana-1119	188	52	−	−	PROPN
cana-1119	188	53	𝑐2	𝑐2	PROPN
cana-1119	188	54	)	)	PUNCT
cana-1119	188	55	(	(	PUNCT
cana-1119	188	56	48𝑐2	48𝑐2	NUM
cana-1119	188	57	(	(	PUNCT
cana-1119	188	58	𝑟	𝑟	NOUN
cana-1119	188	59	−	−	PROPN
cana-1119	188	60	2)(3𝑟	2)(3𝑟	NUM
cana-1119	188	61	−	−	NOUN
cana-1119	188	62	4	4	NUM
cana-1119	188	63	)	)	PUNCT
cana-1119	188	64	+	+	CCONJ
cana-1119	188	65	36(4	36(4	NUM
cana-1119	188	66	−	−	NOUN
cana-1119	188	67	𝑐2	𝑐2	NOUN
cana-1119	188	68	)	)	PUNCT
cana-1119	188	69	(	(	PUNCT
cana-1119	188	70	3	3	NUM
cana-1119	188	71	−	−	NOUN
cana-1119	188	72	2𝑟)2	2𝑟)2	NUM
cana-1119	188	73	)	)	PUNCT
cana-1119	189	1	+	+	CCONJ
cana-1119	190	1	12𝑏(4	12𝑏(4	NUM
cana-1119	190	2	−	−	NOUN
cana-1119	190	3	𝑐2)𝑐2(12	𝑐2)𝑐2(12	ADV
cana-1119	190	4	−	−	PROPN
cana-1119	190	5	6𝑟	6𝑟	NOUN
cana-1119	190	6	−	−	NOUN
cana-1119	190	7	3𝑟2	3𝑟2	NUM
cana-1119	190	8	+	+	CCONJ
cana-1119	190	9	7𝑟3	7𝑟3	NUM
cana-1119	190	10	)	)	PUNCT
cana-1119	190	11	(	(	PUNCT
cana-1119	190	12	3	3	NUM
cana-1119	190	13	−	−	PROPN
cana-1119	190	14	2𝑟)2(𝑟	2𝑟)2(𝑟	NUM
cana-1119	190	15	−	−	NOUN
cana-1119	190	16	2)2(3𝑟	2)2(3𝑟	NUM
cana-1119	190	17	−	−	PROPN
cana-1119	190	18	4	4	NUM
cana-1119	190	19	)	)	PUNCT
cana-1119	190	20	+	+	CCONJ
cana-1119	190	21	𝑐4(5𝑟5	𝑐4(5𝑟5	NOUN
cana-1119	191	1	+	+	X
cana-1119	192	1	78𝑟4	78𝑟4	NUM
cana-1119	192	2	−	−	NUM
cana-1119	193	1	607𝑟3	607𝑟3	NUM
cana-1119	194	1	+	+	CCONJ
cana-1119	194	2	1816𝑟2	1816𝑟2	NUM
cana-1119	194	3	−	−	PROPN
cana-1119	194	4	2424𝑟	2424𝑟	NUM
cana-1119	194	5	+	+	CCONJ
cana-1119	194	6	1152	1152	NUM
cana-1119	194	7	)	)	PUNCT
cana-1119	195	1	(	(	PUNCT
cana-1119	195	2	3	3	NUM
cana-1119	195	3	−	−	PROPN
cana-1119	195	4	2𝑟)2(𝑟	2𝑟)2(𝑟	ADJ
cana-1119	195	5	−	−	PROPN
cana-1119	195	6	2)4(4	2)4(4	NUM
cana-1119	195	7	−	−	NOUN
cana-1119	195	8	3𝑟	3𝑟	NOUN
cana-1119	195	9	)	)	PUNCT
cana-1119	195	10	]	]	PUNCT
cana-1119	196	1	let	let	VERB
cana-1119	196	2	us	we	PRON
cana-1119	196	3	assume	assume	VERB
cana-1119	196	4	that	that	SCONJ
cana-1119	196	5	above	above	ADV
cana-1119	196	6	is	be	AUX
cana-1119	196	7	𝐼(𝑐	𝐼(𝑐	NOUN
cana-1119	196	8	,	,	PUNCT
cana-1119	196	9	𝑏	𝑏	NOUN
cana-1119	196	10	)	)	PUNCT
cana-1119	196	11	=	=	SYM
cana-1119	196	12	1	1	NUM
cana-1119	196	13	2304	2304	NUM
cana-1119	196	14	[	[	PUNCT
cana-1119	196	15	96(1	96(1	NOUN
cana-1119	196	16	−	−	NOUN
cana-1119	196	17	𝑏2)(4	𝑏2)(4	NOUN
cana-1119	196	18	−	−	PROPN
cana-1119	196	19	𝑐2)𝑐	𝑐2)𝑐	NOUN
cana-1119	196	20	(	(	PUNCT
cana-1119	196	21	𝑟	𝑟	NOUN
cana-1119	196	22	−	−	ADP
cana-1119	196	23	2)(3𝑟	2)(3𝑟	NUM
cana-1119	196	24	−	−	NOUN
cana-1119	196	25	4	4	NUM
cana-1119	196	26	)	)	PUNCT
cana-1119	196	27	+	+	CCONJ
cana-1119	196	28	𝑏2(4	𝑏2(4	PROPN
cana-1119	196	29	−	−	PROPN
cana-1119	196	30	𝑐2	𝑐2	PROPN
cana-1119	196	31	)	)	PUNCT
cana-1119	196	32	(	(	PUNCT
cana-1119	196	33	48𝑐2	48𝑐2	NUM
cana-1119	196	34	(	(	PUNCT
cana-1119	196	35	𝑟	𝑟	NOUN
cana-1119	196	36	−	−	PROPN
cana-1119	196	37	2)(3𝑟	2)(3𝑟	NUM
cana-1119	196	38	−	−	NOUN
cana-1119	196	39	4	4	NUM
cana-1119	196	40	)	)	PUNCT
cana-1119	196	41	+	+	CCONJ
cana-1119	196	42	36(4	36(4	NUM
cana-1119	196	43	−	−	NOUN
cana-1119	196	44	𝑐2	𝑐2	NOUN
cana-1119	196	45	)	)	PUNCT
cana-1119	196	46	(	(	PUNCT
cana-1119	196	47	3	3	NUM
cana-1119	196	48	−	−	NOUN
cana-1119	196	49	2𝑟)2	2𝑟)2	NUM
cana-1119	196	50	)	)	PUNCT
cana-1119	197	1	+	+	CCONJ
cana-1119	198	1	12𝑏(4	12𝑏(4	NUM
cana-1119	198	2	−	−	NOUN
cana-1119	198	3	𝑐2)𝑐2(12	𝑐2)𝑐2(12	ADV
cana-1119	198	4	−	−	PROPN
cana-1119	198	5	6𝑟	6𝑟	NOUN
cana-1119	198	6	−	−	PROPN
cana-1119	198	7	13𝑟2	13𝑟2	NUM
cana-1119	198	8	+	+	CCONJ
cana-1119	198	9	7𝑟3	7𝑟3	NUM
cana-1119	198	10	)	)	PUNCT
cana-1119	198	11	(	(	PUNCT
cana-1119	198	12	3	3	NUM
cana-1119	198	13	−	−	PROPN
cana-1119	198	14	2𝑟)2(𝑟	2𝑟)2(𝑟	NUM
cana-1119	198	15	−	−	NOUN
cana-1119	198	16	2)2(3𝑟	2)2(3𝑟	NUM
cana-1119	198	17	−	−	PROPN
cana-1119	198	18	4	4	NUM
cana-1119	198	19	)	)	PUNCT
cana-1119	198	20	+	+	CCONJ
cana-1119	198	21	𝑐4(5𝑟5	𝑐4(5𝑟5	NOUN
cana-1119	199	1	+	+	X
cana-1119	200	1	78𝑟4	78𝑟4	NUM
cana-1119	200	2	−	−	NUM
cana-1119	201	1	607𝑟3	607𝑟3	NUM
cana-1119	202	1	+	+	CCONJ
cana-1119	202	2	1816𝑟2	1816𝑟2	NUM
cana-1119	202	3	−	−	PROPN
cana-1119	202	4	2424𝑟	2424𝑟	NUM
cana-1119	202	5	+	+	CCONJ
cana-1119	202	6	1152	1152	NUM
cana-1119	202	7	)	)	PUNCT
cana-1119	203	1	(	(	PUNCT
cana-1119	203	2	3	3	NUM
cana-1119	203	3	−	−	PROPN
cana-1119	203	4	2𝑟)2(𝑟	2𝑟)2(𝑟	NUM
cana-1119	203	5	−	−	PROPN
cana-1119	203	6	2)4(3𝑟	2)4(3𝑟	NUM
cana-1119	203	7	−	−	NOUN
cana-1119	203	8	4	4	NUM
cana-1119	203	9	)	)	PUNCT
cana-1119	203	10	]	]	PUNCT
cana-1119	204	1	we	we	PRON
cana-1119	204	2	have	have	VERB
cana-1119	204	3	to	to	PART
cana-1119	204	4	maximize	maximize	VERB
cana-1119	204	5	the	the	DET
cana-1119	204	6	function	function	NOUN
cana-1119	204	7	𝐼(𝑐	𝐼(𝑐	NOUN
cana-1119	204	8	,	,	PUNCT
cana-1119	204	9	𝑏)for	𝑏)for	PROPN
cana-1119	204	10	(	(	PUNCT
cana-1119	204	11	𝑐	𝑐	PROPN
cana-1119	204	12	,	,	PUNCT
cana-1119	204	13	𝑏	𝑏	NOUN
cana-1119	204	14	)	)	PUNCT
cana-1119	204	15	∈	∈	NOUN
cana-1119	205	1	[	[	X
cana-1119	205	2	0,2	0,2	NUM
cana-1119	205	3	]	]	X
cana-1119	205	4	×	×	NOUN
cana-1119	205	5	[	[	X
cana-1119	205	6	0,1	0,1	NUM
cana-1119	205	7	]	]	PUNCT
cana-1119	205	8	,	,	PUNCT
cana-1119	205	9	now	now	ADV
cana-1119	205	10	differentiation	differentiation	VERB
cana-1119	205	11	the	the	DET
cana-1119	205	12	above	above	ADJ
cana-1119	205	13	functions	function	NOUN
cana-1119	205	14	partially	partially	ADV
cana-1119	205	15	with	with	ADP
cana-1119	205	16	respect	respect	NOUN
cana-1119	205	17	to	to	ADP
cana-1119	205	18	𝑏	𝑏	NOUN
cana-1119	205	19	we	we	PRON
cana-1119	205	20	will	will	AUX
cana-1119	205	21	have	have	VERB
cana-1119	205	22	∂𝐼	∂𝐼	NOUN
cana-1119	206	1	∂𝑏	∂𝑏	NOUN
cana-1119	206	2	=	=	SYM
cana-1119	206	3	1	1	NUM
cana-1119	206	4	2304	2304	NUM
cana-1119	206	5	[	[	PUNCT
cana-1119	206	6	−192(4	−192(4	PROPN
cana-1119	206	7	−	−	PROPN
cana-1119	206	8	𝑐2)𝑐	𝑐2)𝑐	NOUN
cana-1119	206	9	(	(	PUNCT
cana-1119	206	10	𝑟	𝑟	NOUN
cana-1119	206	11	−	−	ADP
cana-1119	206	12	2)(3𝑟	2)(3𝑟	NUM
cana-1119	206	13	−	−	NOUN
cana-1119	206	14	4	4	NUM
cana-1119	206	15	)	)	PUNCT
cana-1119	206	16	+2𝑏(4	+2𝑏(4	NOUN
cana-1119	206	17	−	−	PROPN
cana-1119	206	18	𝑐2	𝑐2	NOUN
cana-1119	206	19	)	)	PUNCT
cana-1119	206	20	(	(	PUNCT
cana-1119	206	21	48𝑐2	48𝑐2	NUM
cana-1119	206	22	(	(	PUNCT
cana-1119	206	23	𝑟	𝑟	NOUN
cana-1119	206	24	−	−	PROPN
cana-1119	206	25	2)(3𝑟	2)(3𝑟	NUM
cana-1119	206	26	−	−	NOUN
cana-1119	206	27	4	4	NUM
cana-1119	206	28	)	)	PUNCT
cana-1119	206	29	+	+	CCONJ
cana-1119	206	30	36(4	36(4	NUM
cana-1119	206	31	−	−	NOUN
cana-1119	206	32	𝑐2	𝑐2	NOUN
cana-1119	206	33	)	)	PUNCT
cana-1119	206	34	(	(	PUNCT
cana-1119	206	35	3	3	NUM
cana-1119	206	36	−	−	NOUN
cana-1119	206	37	2𝑟)2	2𝑟)2	NUM
cana-1119	206	38	)	)	PUNCT
cana-1119	207	1	+	+	CCONJ
cana-1119	208	1	12(4	12(4	NUM
cana-1119	208	2	−	−	NOUN
cana-1119	208	3	𝑐2)𝑐2(12	𝑐2)𝑐2(12	ADP
cana-1119	208	4	−	−	PROPN
cana-1119	209	1	6𝑟	6𝑟	NOUN
cana-1119	209	2	−	−	PROPN
cana-1119	209	3	13𝑟2	13𝑟2	NUM
cana-1119	209	4	+	+	CCONJ
cana-1119	209	5	7𝑟3	7𝑟3	NUM
cana-1119	209	6	)	)	PUNCT
cana-1119	209	7	(	(	PUNCT
cana-1119	209	8	3	3	NUM
cana-1119	209	9	−	−	PROPN
cana-1119	209	10	2𝑟)2(𝑟	2𝑟)2(𝑟	NUM
cana-1119	209	11	−	−	NOUN
cana-1119	209	12	2)2(3𝑟	2)2(3𝑟	NUM
cana-1119	209	13	−	−	PROPN
cana-1119	209	14	4	4	NUM
cana-1119	209	15	)	)	PUNCT
cana-1119	209	16	]	]	PUNCT
cana-1119	209	17	for	for	ADP
cana-1119	209	18	0	0	NUM
cana-1119	209	19	≤	≤	NUM
cana-1119	209	20	𝑏	𝑏	DET
cana-1119	209	21	≤	≤	NUM
cana-1119	209	22	1	1	NUM
cana-1119	209	23	and	and	CCONJ
cana-1119	209	24	for	for	ADP
cana-1119	209	25	any	any	DET
cana-1119	209	26	𝑐	𝑐	PROPN
cana-1119	209	27	∈	∈	PROPN
cana-1119	210	1	[	[	X
cana-1119	210	2	0,2	0,2	NUM
cana-1119	210	3	]	]	PUNCT
cana-1119	210	4	,	,	PUNCT
cana-1119	210	5	we	we	PRON
cana-1119	210	6	can	can	AUX
cana-1119	210	7	easily	easily	ADV
cana-1119	210	8	check	check	VERB
cana-1119	210	9	that	that	PRON
cana-1119	210	10	∂𝐼	∂𝐼	PUNCT
cana-1119	211	1	∂𝑏	∂𝑏	X
cana-1119	211	2	>	>	X
cana-1119	211	3	0	0	NUM
cana-1119	211	4	,	,	PUNCT
cana-1119	211	5	from	from	ADP
cana-1119	211	6	this	this	PRON
cana-1119	211	7	we	we	PRON
cana-1119	211	8	can	can	AUX
cana-1119	211	9	conclude	conclude	VERB
cana-1119	211	10	that	that	SCONJ
cana-1119	211	11	𝐼(𝑐	𝐼(𝑐	PROPN
cana-1119	211	12	,	,	PUNCT
cana-1119	211	13	𝑏	𝑏	NOUN
cana-1119	211	14	)	)	PUNCT
cana-1119	211	15	is	be	AUX
cana-1119	211	16	an	an	DET
cana-1119	211	17	increasing	increase	VERB
cana-1119	211	18	function	function	NOUN
cana-1119	211	19	of	of	ADP
cana-1119	211	20	𝑐	𝑐	NOUN
cana-1119	211	21	,	,	PUNCT
cana-1119	211	22	and	and	CCONJ
cana-1119	211	23	it	it	PRON
cana-1119	211	24	will	will	AUX
cana-1119	211	25	attain	attain	VERB
cana-1119	211	26	maximum	maximum	ADJ
cana-1119	211	27	value	value	NOUN
cana-1119	211	28	at	at	ADP
cana-1119	211	29	𝑏	𝑏	NOUN
cana-1119	211	30	=	=	SYM
cana-1119	211	31	1	1	NUM
cana-1119	211	32	.	.	PUNCT
cana-1119	211	33	by	by	ADP
cana-1119	211	34	putting	put	VERB
cana-1119	211	35	𝑏	𝑏	NOUN
cana-1119	211	36	=	=	SYM
cana-1119	211	37	1	1	NUM
cana-1119	211	38	in	in	ADP
cana-1119	211	39	above	above	ADP
cana-1119	211	40	we	we	PRON
cana-1119	211	41	will	will	AUX
cana-1119	211	42	have	have	VERB
cana-1119	211	43	communications	communication	NOUN
cana-1119	211	44	on	on	ADP
cana-1119	211	45	applied	apply	VERB
cana-1119	211	46	nonlinear	nonlinear	ADJ
cana-1119	211	47	analysis	analysis	NOUN
cana-1119	211	48	issn	issn	NOUN
cana-1119	211	49	:	:	PUNCT
cana-1119	211	50	1074	1074	NUM
cana-1119	211	51	-	-	PUNCT
cana-1119	211	52	133x	133x	NUM
cana-1119	211	53	vol	vol	NOUN
cana-1119	211	54	31	31	NUM
cana-1119	211	55	no	no	NOUN
cana-1119	211	56	.	.	PUNCT
cana-1119	212	1	6s	6s	NUM
cana-1119	212	2	(	(	PUNCT
cana-1119	212	3	2024	2024	NUM
cana-1119	212	4	)	)	PUNCT
cana-1119	212	5	58	58	NUM
cana-1119	212	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1119	212	7	𝐼(𝑐	𝐼(𝑐	PROPN
cana-1119	212	8	,	,	PUNCT
cana-1119	212	9	1	1	NUM
cana-1119	212	10	)	)	PUNCT
cana-1119	212	11	=	=	SYM
cana-1119	212	12	𝐸(𝑐	𝐸(𝑐	NUM
cana-1119	212	13	)	)	PUNCT
cana-1119	212	14	=	=	SYM
cana-1119	212	15	1	1	NUM
cana-1119	212	16	2304	2304	NUM
cana-1119	212	17	[	[	X
cana-1119	212	18	(	(	PUNCT
cana-1119	212	19	4	4	NUM
cana-1119	212	20	−	−	NOUN
cana-1119	212	21	𝑐2	𝑐2	NOUN
cana-1119	212	22	)	)	PUNCT
cana-1119	212	23	(	(	PUNCT
cana-1119	212	24	48𝑐2	48𝑐2	NUM
cana-1119	212	25	(	(	PUNCT
cana-1119	212	26	𝑟	𝑟	NOUN
cana-1119	212	27	−	−	PROPN
cana-1119	212	28	2)(3𝑟	2)(3𝑟	NUM
cana-1119	212	29	−	−	NOUN
cana-1119	212	30	4	4	NUM
cana-1119	212	31	)	)	PUNCT
cana-1119	212	32	+	+	CCONJ
cana-1119	212	33	36(4	36(4	NUM
cana-1119	212	34	−	−	NOUN
cana-1119	212	35	𝑐2	𝑐2	NOUN
cana-1119	212	36	)	)	PUNCT
cana-1119	212	37	(	(	PUNCT
cana-1119	212	38	3	3	NUM
cana-1119	212	39	−	−	NOUN
cana-1119	212	40	2𝑟)2	2𝑟)2	NUM
cana-1119	212	41	)	)	PUNCT
cana-1119	213	1	+	+	CCONJ
cana-1119	214	1	12(4	12(4	NUM
cana-1119	214	2	−	−	NOUN
cana-1119	214	3	𝑐2)𝑐2(12	𝑐2)𝑐2(12	ADP
cana-1119	214	4	−	−	PROPN
cana-1119	215	1	6𝑟	6𝑟	NOUN
cana-1119	215	2	−	−	PROPN
cana-1119	215	3	13𝑟2	13𝑟2	NUM
cana-1119	215	4	+	+	CCONJ
cana-1119	215	5	7𝑟3	7𝑟3	NUM
cana-1119	215	6	)	)	PUNCT
cana-1119	215	7	(	(	PUNCT
cana-1119	215	8	3	3	NUM
cana-1119	215	9	−	−	PROPN
cana-1119	215	10	2𝑟)2(𝑟	2𝑟)2(𝑟	NUM
cana-1119	215	11	−	−	NOUN
cana-1119	215	12	2)2(3𝑟	2)2(3𝑟	NUM
cana-1119	215	13	−	−	PROPN
cana-1119	215	14	4	4	NUM
cana-1119	215	15	)	)	PUNCT
cana-1119	215	16	+	+	CCONJ
cana-1119	215	17	𝑐4(5𝑟5	𝑐4(5𝑟5	NOUN
cana-1119	215	18	+	+	X
cana-1119	215	19	78𝑟4	78𝑟4	NUM
cana-1119	215	20	−	−	NUM
cana-1119	215	21	607𝑟3	607𝑟3	NUM
cana-1119	216	1	+	+	CCONJ
cana-1119	216	2	1816𝑟2	1816𝑟2	NUM
cana-1119	216	3	−	−	PROPN
cana-1119	216	4	2424𝑟	2424𝑟	NUM
cana-1119	216	5	+	+	CCONJ
cana-1119	216	6	1152	1152	NUM
cana-1119	216	7	)	)	PUNCT
cana-1119	217	1	(	(	PUNCT
cana-1119	217	2	3	3	NUM
cana-1119	217	3	−	−	PROPN
cana-1119	217	4	2𝑟)2(𝑟	2𝑟)2(𝑟	NUM
cana-1119	217	5	−	−	PROPN
cana-1119	217	6	2)4(3𝑟	2)4(3𝑟	NUM
cana-1119	217	7	−	−	NOUN
cana-1119	217	8	4	4	NUM
cana-1119	217	9	)	)	PUNCT
cana-1119	217	10	]	]	PUNCT
cana-1119	218	1	we	we	PRON
cana-1119	218	2	have	have	VERB
cana-1119	218	3	𝐸′(𝑐	𝐸′(𝑐	NOUN
cana-1119	218	4	)	)	PUNCT
cana-1119	219	1	=	=	NOUN
cana-1119	219	2	𝑐3(−5𝑟5	𝑐3(−5𝑟5	NOUN
cana-1119	219	3	+	+	CCONJ
cana-1119	219	4	150𝑟4	150𝑟4	NUM
cana-1119	219	5	−	−	NUM
cana-1119	219	6	953𝑟3	953𝑟3	NUM
cana-1119	220	1	+	+	CCONJ
cana-1119	221	1	2120𝑟2	2120𝑟2	NUM
cana-1119	221	2	−	−	PROPN
cana-1119	221	3	1896𝑟	1896𝑟	NUM
cana-1119	221	4	+	+	CCONJ
cana-1119	221	5	576	576	NUM
cana-1119	221	6	)	)	PUNCT
cana-1119	221	7	−	−	PROPN
cana-1119	222	1	24𝑐(𝑟	24𝑐(𝑟	NUM
cana-1119	222	2	−	−	NOUN
cana-1119	222	3	2)2(9𝑟3	2)2(9𝑟3	NUM
cana-1119	222	4	−	−	NUM
cana-1119	222	5	29𝑟2	29𝑟2	NUM
cana-1119	222	6	+	+	NUM
cana-1119	222	7	30𝑟	30𝑟	NOUN
cana-1119	222	8	−	−	PROPN
cana-1119	222	9	12	12	NUM
cana-1119	222	10	)	)	PUNCT
cana-1119	222	11	576(3	576(3	NUM
cana-1119	222	12	−	−	PROPN
cana-1119	222	13	2𝑟)2(𝑟	2𝑟)2(𝑟	NUM
cana-1119	222	14	−	−	PROPN
cana-1119	222	15	2)4(3𝑟	2)4(3𝑟	NUM
cana-1119	222	16	−	−	NOUN
cana-1119	222	17	4	4	NUM
cana-1119	222	18	)	)	PUNCT
cana-1119	222	19	from	from	ADP
cana-1119	222	20	𝐸′(𝑐	𝐸′(𝑐	PROPN
cana-1119	222	21	)	)	PUNCT
cana-1119	223	1	=	=	SYM
cana-1119	223	2	0	0	NUM
cana-1119	224	1	we	we	PRON
cana-1119	224	2	will	will	AUX
cana-1119	224	3	have	have	VERB
cana-1119	224	4	𝑐	𝑐	NOUN
cana-1119	224	5	=	=	SYM
cana-1119	224	6	0	0	NUM
cana-1119	224	7	𝐸′′(0	𝐸′′(0	NOUN
cana-1119	224	8	)	)	PUNCT
cana-1119	225	1	=	=	SYM
cana-1119	225	2	−	−	PROPN
cana-1119	225	3	9𝑟3	9𝑟3	NUM
cana-1119	226	1	−	−	NOUN
cana-1119	226	2	29𝑟2	29𝑟2	NUM
cana-1119	226	3	+	+	NUM
cana-1119	226	4	30𝑟	30𝑟	NOUN
cana-1119	226	5	−	−	PROPN
cana-1119	226	6	12	12	NUM
cana-1119	226	7	24(3	24(3	NUM
cana-1119	226	8	−	−	PROPN
cana-1119	226	9	2𝑟)2(𝑟	2𝑟)2(𝑟	ADJ
cana-1119	226	10	−	−	NOUN
cana-1119	226	11	2)2(3𝑟	2)2(3𝑟	NUM
cana-1119	226	12	−	−	PROPN
cana-1119	226	13	4	4	NUM
cana-1119	226	14	)	)	PUNCT
cana-1119	226	15	that	that	SCONJ
cana-1119	226	16	we	we	PRON
cana-1119	226	17	can	can	AUX
cana-1119	226	18	easily	easily	ADV
cana-1119	226	19	conclude	conclude	VERB
cana-1119	226	20	that	that	PRON
cana-1119	226	21	𝐸′′(0	𝐸′′(0	NOUN
cana-1119	226	22	)	)	PUNCT
cana-1119	226	23	is	be	AUX
cana-1119	226	24	negative	negative	ADJ
cana-1119	226	25	,	,	PUNCT
cana-1119	226	26	which	which	PRON
cana-1119	226	27	implies	imply	VERB
cana-1119	226	28	that	that	SCONJ
cana-1119	226	29	at	at	ADP
cana-1119	226	30	𝑐	𝑐	NOUN
cana-1119	226	31	=	=	SYM
cana-1119	226	32	0	0	NOUN
cana-1119	226	33	the	the	DET
cana-1119	226	34	function	function	NOUN
cana-1119	226	35	will	will	AUX
cana-1119	226	36	attain	attain	VERB
cana-1119	226	37	its	its	PRON
cana-1119	226	38	maxima	maxima	NOUN
cana-1119	226	39	.	.	PUNCT
cana-1119	226	40	|𝑎2𝑎4	|𝑎2𝑎4	PROPN
cana-1119	227	1	−	−	PROPN
cana-1119	227	2	𝑎3	𝑎3	NOUN
cana-1119	227	3	2|	2|	NUM
cana-1119	227	4	≤	≤	NOUN
cana-1119	227	5	1	1	NUM
cana-1119	227	6	4(3	4(3	NUM
cana-1119	227	7	−	−	NUM
cana-1119	227	8	2𝑟)2	2𝑟)2	NUM
cana-1119	227	9	corollary	corollary	NOUN
cana-1119	227	10	when	when	SCONJ
cana-1119	227	11	𝑟	𝑟	X
cana-1119	227	12	=	=	SYM
cana-1119	227	13	0	0	NUM
cana-1119	227	14	,	,	PUNCT
cana-1119	227	15	we	we	PRON
cana-1119	227	16	have	have	VERB
cana-1119	227	17	ℎ	ℎ	PART
cana-1119	227	18	∈	∈	NOUN
cana-1119	227	19	𝑆∗𝐶sin	𝑆∗𝐶sin	NOUN
cana-1119	227	20	(	(	PUNCT
cana-1119	227	21	0):=	0):=	NUM
cana-1119	227	22	𝐶sin	𝐶sin	NOUN
cana-1119	227	23	and	and	CCONJ
cana-1119	227	24	we	we	PRON
cana-1119	227	25	get	get	VERB
cana-1119	227	26	|𝑎2𝑎4	|𝑎2𝑎4	NOUN
cana-1119	227	27	−	−	PROPN
cana-1119	227	28	𝑎3	𝑎3	NOUN
cana-1119	227	29	2|	2|	NUM
cana-1119	227	30	≤	≤	NUM
cana-1119	227	31	1	1	NUM
cana-1119	227	32	36	36	NUM
cana-1119	227	33	when	when	SCONJ
cana-1119	227	34	𝑟	𝑟	NOUN
cana-1119	227	35	=	=	SYM
cana-1119	227	36	1	1	NUM
cana-1119	227	37	we	we	PRON
cana-1119	227	38	have	have	VERB
cana-1119	227	39	ℎ	ℎ	X
cana-1119	227	40	∈	∈	PROPN
cana-1119	227	41	𝑆∗𝐶sin(1):=	𝑆∗𝐶sin(1):=	PROPN
cana-1119	227	42	𝑆sin	𝑆sin	PROPN
cana-1119	227	43	∗	∗	NOUN
cana-1119	227	44	,	,	PUNCT
cana-1119	227	45	and	and	CCONJ
cana-1119	227	46	we	we	PRON
cana-1119	227	47	get	get	VERB
cana-1119	227	48	|𝑎2𝑎4	|𝑎2𝑎4	NOUN
cana-1119	227	49	−	−	PROPN
cana-1119	227	50	𝑎3	𝑎3	NOUN
cana-1119	227	51	2|	2|	NUM
cana-1119	227	52	≤	≤	NUM
cana-1119	227	53	1	1	NUM
cana-1119	227	54	4	4	NUM
cana-1119	227	55	4	4	NUM
cana-1119	227	56	.	.	PUNCT
cana-1119	228	1	conclusions	conclusion	NOUN
cana-1119	228	2	in	in	ADP
cana-1119	228	3	this	this	DET
cana-1119	228	4	paper	paper	NOUN
cana-1119	228	5	we	we	PRON
cana-1119	228	6	have	have	AUX
cana-1119	228	7	introduced	introduce	VERB
cana-1119	228	8	a	a	DET
cana-1119	228	9	new	new	ADJ
cana-1119	228	10	class	class	NOUN
cana-1119	228	11	𝑆∗𝐶sin(𝑟	𝑆∗𝐶sin(𝑟	NOUN
cana-1119	228	12	)	)	PUNCT
cana-1119	228	13	,	,	PUNCT
cana-1119	228	14	where	where	SCONJ
cana-1119	228	15	(	(	PUNCT
cana-1119	228	16	0	0	NUM
cana-1119	228	17	≤	≤	NUM
cana-1119	228	18	𝑟	𝑟	NOUN
cana-1119	228	19	≤	≤	NUM
cana-1119	228	20	1	1	NUM
cana-1119	228	21	)	)	PUNCT
cana-1119	228	22	,	,	PUNCT
cana-1119	228	23	and	and	CCONJ
cana-1119	228	24	have	have	AUX
cana-1119	228	25	worked	work	VERB
cana-1119	228	26	on	on	ADP
cana-1119	228	27	the	the	DET
cana-1119	228	28	fekete	fekete	NOUN
cana-1119	228	29	-	-	PUNCT
cana-1119	228	30	szegö	szegö	PROPN
cana-1119	228	31	inequality	inequality	NOUN
cana-1119	228	32	along	along	ADP
cana-1119	228	33	with	with	ADP
cana-1119	228	34	upper	upper	ADJ
cana-1119	228	35	bound	bind	VERB
cana-1119	228	36	of	of	ADP
cana-1119	228	37	second	second	ADJ
cana-1119	228	38	hankel	hankel	NOUN
cana-1119	228	39	determinant	determinant	ADJ
cana-1119	228	40	.	.	PUNCT
cana-1119	229	1	we	we	PRON
cana-1119	229	2	have	have	AUX
cana-1119	229	3	stated	state	VERB
cana-1119	229	4	the	the	DET
cana-1119	229	5	fekete	fekete	PROPN
cana-1119	229	6	-	-	PUNCT
cana-1119	229	7	szegö	szegö	PROPN
cana-1119	229	8	inequality	inequality	NOUN
cana-1119	229	9	related	relate	VERB
cana-1119	229	10	to	to	ADP
cana-1119	229	11	poisson	poisson	NOUN
cana-1119	229	12	distribution	distribution	NOUN
cana-1119	229	13	of	of	ADP
cana-1119	229	14	this	this	DET
cana-1119	229	15	new	new	ADJ
cana-1119	229	16	class	class	NOUN
cana-1119	229	17	.	.	PUNCT
cana-1119	230	1	as	as	SCONJ
cana-1119	230	2	ℎ	ℎ	PROPN
cana-1119	230	3	∈	∈	PROPN
cana-1119	230	4	𝑆∗𝐶sin(𝑟	𝑆∗𝐶sin(𝑟	PROPN
cana-1119	230	5	)	)	PUNCT
cana-1119	230	6	by	by	ADP
cana-1119	230	7	fixing	fix	VERB
cana-1119	230	8	parameter	parameter	NOUN
cana-1119	230	9	𝑟	𝑟	NOUN
cana-1119	231	1	=	=	SYM
cana-1119	231	2	0function	0function	NUM
cana-1119	231	3	ℎ	ℎ	PROPN
cana-1119	231	4	∈	∈	PROPN
cana-1119	231	5	𝐶sin	𝐶sin	PROPN
cana-1119	231	6	,	,	PUNCT
cana-1119	231	7	and	and	CCONJ
cana-1119	231	8	when	when	SCONJ
cana-1119	231	9	we	we	PRON
cana-1119	231	10	fix	fix	VERB
cana-1119	231	11	𝑟	𝑟	NOUN
cana-1119	231	12	=	=	SYM
cana-1119	231	13	1	1	NUM
cana-1119	231	14	then	then	ADV
cana-1119	231	15	we	we	PRON
cana-1119	231	16	have	have	VERB
cana-1119	231	17	ℎ	ℎ	PROPN
cana-1119	231	18	∈	∈	PROPN
cana-1119	231	19	𝑆sin	𝑆sin	PROPN
cana-1119	231	20	∗	∗	NOUN
cana-1119	231	21	.	.	PUNCT
cana-1119	232	1	our	our	PRON
cana-1119	232	2	this	this	DET
cana-1119	232	3	research	research	NOUN
cana-1119	232	4	paper	paper	NOUN
cana-1119	232	5	is	be	AUX
cana-1119	232	6	an	an	DET
cana-1119	232	7	extended	extended	ADJ
cana-1119	232	8	work	work	NOUN
cana-1119	232	9	of	of	ADP
cana-1119	232	10	research	research	NOUN
cana-1119	232	11	article	article	NOUN
cana-1119	232	12	[	[	X
cana-1119	232	13	32	32	NUM
cana-1119	232	14	]	]	PUNCT
cana-1119	232	15	,	,	PUNCT
cana-1119	232	16	readers	reader	NOUN
cana-1119	232	17	and	and	CCONJ
cana-1119	232	18	interested	interested	ADJ
cana-1119	232	19	scholars	scholar	NOUN
cana-1119	232	20	can	can	AUX
cana-1119	232	21	extend	extend	VERB
cana-1119	232	22	our	our	PRON
cana-1119	232	23	work	work	NOUN
cana-1119	232	24	further	far	ADV
cana-1119	232	25	by	by	ADP
cana-1119	232	26	working	work	VERB
cana-1119	232	27	on	on	ADP
cana-1119	232	28	higher	high	ADJ
cana-1119	232	29	order	order	NOUN
cana-1119	232	30	of	of	ADP
cana-1119	232	31	hankel	hankel	NOUN
cana-1119	232	32	determinant	determinant	ADJ
cana-1119	232	33	and	and	CCONJ
cana-1119	232	34	coefficients	coefficient	NOUN
cana-1119	232	35	inequalities	inequality	NOUN
cana-1119	232	36	on	on	ADP
cana-1119	232	37	this	this	DET
cana-1119	232	38	newly	newly	ADV
cana-1119	232	39	introduced	introduce	VERB
cana-1119	232	40	class	class	NOUN
cana-1119	232	41	.	.	PUNCT
cana-1119	233	1	5	5	X
cana-1119	233	2	.	.	X
cana-1119	233	3	acknowledgment	acknowledgment	NOUN
cana-1119	233	4	the	the	DET
cana-1119	233	5	authors	author	NOUN
cana-1119	233	6	are	be	AUX
cana-1119	233	7	very	very	ADV
cana-1119	233	8	much	much	ADV
cana-1119	233	9	thankful	thankful	ADJ
cana-1119	233	10	to	to	ADP
cana-1119	233	11	the	the	DET
cana-1119	233	12	anonymous	anonymous	ADJ
cana-1119	233	13	editor	editor	NOUN
cana-1119	233	14	and	and	CCONJ
cana-1119	233	15	referees	referee	NOUN
cana-1119	233	16	for	for	ADP
cana-1119	233	17	their	their	PRON
cana-1119	233	18	valuable	valuable	ADJ
cana-1119	233	19	suggestions	suggestion	NOUN
cana-1119	233	20	to	to	PART
cana-1119	233	21	improve	improve	VERB
cana-1119	233	22	the	the	DET
cana-1119	233	23	paper	paper	NOUN
cana-1119	233	24	.	.	PUNCT
cana-1119	234	1	funding	funding	NOUN
cana-1119	234	2	:	:	PUNCT
cana-1119	234	3	not	not	PART
cana-1119	234	4	applicable	applicable	ADJ
cana-1119	234	5	conflict	conflict	NOUN
cana-1119	234	6	of	of	ADP
cana-1119	234	7	interest	interest	NOUN
cana-1119	234	8	:	:	PUNCT
cana-1119	234	9	not	not	PART
cana-1119	234	10	applicable	applicable	ADJ
cana-1119	234	11	communications	communication	NOUN
cana-1119	234	12	on	on	ADP
cana-1119	234	13	applied	apply	VERB
cana-1119	234	14	nonlinear	nonlinear	ADJ
cana-1119	234	15	analysis	analysis	NOUN
cana-1119	234	16	issn	issn	NOUN
cana-1119	234	17	:	:	PUNCT
cana-1119	234	18	1074	1074	NUM
cana-1119	234	19	-	-	PUNCT
cana-1119	234	20	133x	133x	NUM
cana-1119	234	21	vol	vol	NOUN
cana-1119	234	22	31	31	NUM
cana-1119	234	23	no	no	NOUN
cana-1119	234	24	.	.	PUNCT
cana-1119	235	1	6s	6s	NUM
cana-1119	235	2	(	(	PUNCT
cana-1119	235	3	2024	2024	NUM
cana-1119	235	4	)	)	PUNCT
cana-1119	235	5	59	59	NUM
cana-1119	235	6	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1119	235	7	references	reference	NOUN
cana-1119	235	8	[	[	X
cana-1119	235	9	1	1	NUM
cana-1119	235	10	]	]	PUNCT
cana-1119	235	11	k.	k.	PROPN
cana-1119	235	12	o.	o.	PROPN
cana-1119	235	13	babalola	babalola	PROPN
cana-1119	235	14	,	,	PUNCT
cana-1119	235	15	on	on	ADP
cana-1119	235	16	hankel	hankel	NOUN
cana-1119	235	17	determinant	determinant	ADJ
cana-1119	235	18	for	for	ADP
cana-1119	235	19	some	some	DET
cana-1119	235	20	classes	class	NOUN
cana-1119	235	21	of	of	ADP
cana-1119	235	22	univalent	univalent	ADJ
cana-1119	235	23	functions	function	NOUN
cana-1119	235	24	,	,	PUNCT
cana-1119	235	25	arxiv	arxiv	PROPN
cana-1119	235	26	complex	complex	PROPN
cana-1119	235	27	variables	variable	NOUN
cana-1119	235	28	,	,	PUNCT
cana-1119	235	29	6	6	NUM
cana-1119	235	30	,	,	PUNCT
cana-1119	235	31	(	(	PUNCT
cana-1119	235	32	2009	2009	NUM
cana-1119	235	33	)	)	PUNCT
cana-1119	235	34	,	,	PUNCT
cana-1119	235	35	1	1	NUM
cana-1119	235	36	-	-	SYM
cana-1119	235	37	7	7	NUM
cana-1119	235	38	[	[	X
cana-1119	235	39	2	2	NUM
cana-1119	235	40	]	]	PUNCT
cana-1119	235	41	ludwig	ludwig	PROPN
cana-1119	235	42	bieberbach	bieberbach	NOUN
cana-1119	235	43	,	,	PUNCT
cana-1119	235	44	uber	uber	ADJ
cana-1119	235	45	die	die	NOUN
cana-1119	235	46	koeffizienten	koeffizienten	NOUN
cana-1119	235	47	derjenigen	derjenigen	PROPN
cana-1119	235	48	potenzreihen	potenzreihen	ADV
cana-1119	235	49	,	,	PUNCT
cana-1119	235	50	welche	welche	PROPN
cana-1119	235	51	eine	eine	PROPN
cana-1119	235	52	schlichte	schlichte	PROPN
cana-1119	235	53	abbildungdes	abbildungdes	PROPN
cana-1119	235	54	einheitskreises	einheitskreise	VERB
cana-1119	235	55	vermitteln	vermitteln	NOUN
cana-1119	235	56	,	,	PUNCT
cana-1119	235	57	sitzungsberichte	sitzungsberichte	PROPN
cana-1119	235	58	preussische	preussische	PROPN
cana-1119	235	59	akademie	akademie	PROPN
cana-1119	235	60	der	der	PROPN
cana-1119	235	61	wissenschaften	wissenschaften	NOUN
cana-1119	235	62	,	,	PUNCT
cana-1119	235	63	138	138	NUM
cana-1119	235	64	,	,	PUNCT
cana-1119	235	65	(	(	PUNCT
cana-1119	235	66	1916	1916	NUM
cana-1119	235	67	)	)	PUNCT
cana-1119	235	68	,	,	PUNCT
cana-1119	235	69	940	940	NUM
cana-1119	235	70	-	-	SYM
cana-1119	235	71	955	955	NUM
cana-1119	235	72	.	.	PUNCT
cana-1119	236	1	[	[	X
cana-1119	236	2	3	3	X
cana-1119	236	3	]	]	X
cana-1119	236	4	l.	l.	PROPN
cana-1119	236	5	de	de	PROPN
cana-1119	236	6	branges	brange	NOUN
cana-1119	236	7	,	,	PUNCT
cana-1119	236	8	a	a	DET
cana-1119	236	9	proof	proof	NOUN
cana-1119	236	10	of	of	ADP
cana-1119	236	11	the	the	DET
cana-1119	236	12	bieberbach	bieberbach	NOUN
cana-1119	236	13	conjecture	conjecture	NOUN
cana-1119	236	14	,	,	PUNCT
cana-1119	236	15	acta	acta	PROPN
cana-1119	236	16	mathematica	mathematica	PROPN
cana-1119	236	17	,	,	PUNCT
cana-1119	236	18	154	154	NUM
cana-1119	236	19	,	,	PUNCT
cana-1119	236	20	(	(	PUNCT
cana-1119	236	21	1985	1985	NUM
cana-1119	236	22	)	)	PUNCT
cana-1119	236	23	,	,	PUNCT
cana-1119	236	24	.	.	PUNCT
cana-1119	237	1	[	[	X
cana-1119	237	2	4	4	X
cana-1119	237	3	]	]	PUNCT
cana-1119	237	4	w.	w.	PROPN
cana-1119	237	5	ma	ma	PROPN
cana-1119	237	6	,	,	PUNCT
cana-1119	237	7	d.	d.	PROPN
cana-1119	237	8	minda	minda	PROPN
cana-1119	237	9	,	,	PUNCT
cana-1119	237	10	a	a	DET
cana-1119	237	11	unified	unified	ADJ
cana-1119	237	12	treatment	treatment	NOUN
cana-1119	237	13	of	of	ADP
cana-1119	237	14	some	some	DET
cana-1119	237	15	special	special	ADJ
cana-1119	237	16	classes	class	NOUN
cana-1119	237	17	of	of	ADP
cana-1119	237	18	univalent	univalent	ADJ
cana-1119	237	19	functions	function	NOUN
cana-1119	237	20	,	,	PUNCT
cana-1119	237	21	in	in	ADP
cana-1119	237	22	:	:	PUNCT
cana-1119	237	23	proceeding	proceeding	NOUN
cana-1119	237	24	of	of	ADP
cana-1119	237	25	the	the	DET
cana-1119	237	26	international	international	ADJ
cana-1119	237	27	conference	conference	NOUN
cana-1119	237	28	on	on	ADP
cana-1119	237	29	complex	complex	ADJ
cana-1119	237	30	analysis	analysis	NOUN
cana-1119	237	31	at	at	ADP
cana-1119	237	32	the	the	DET
cana-1119	237	33	nankai	nankai	PROPN
cana-1119	237	34	institute	institute	PROPN
cana-1119	237	35	of	of	ADP
cana-1119	237	36	mathematics	mathematics	PROPN
cana-1119	237	37	,	,	PUNCT
cana-1119	237	38	international	international	ADJ
cana-1119	237	39	press	press	NOUN
cana-1119	237	40	,	,	PUNCT
cana-1119	237	41	(	(	PUNCT
cana-1119	237	42	1992	1992	NUM
cana-1119	237	43	)	)	PUNCT
cana-1119	237	44	,	,	PUNCT
cana-1119	237	45	157	157	NUM
cana-1119	237	46	-	-	SYM
cana-1119	237	47	169	169	NUM
cana-1119	237	48	.	.	PUNCT
cana-1119	238	1	[	[	X
cana-1119	238	2	5	5	NUM
cana-1119	238	3	]	]	X
cana-1119	238	4	r.	r.	PROPN
cana-1119	238	5	mendiratta	mendiratta	PROPN
cana-1119	238	6	,	,	PUNCT
cana-1119	238	7	s.	s.	PROPN
cana-1119	238	8	nagpal	nagpal	PROPN
cana-1119	238	9	,	,	PUNCT
cana-1119	238	10	v.	v.	ADP
cana-1119	238	11	ravichandran	ravichandran	NOUN
cana-1119	238	12	,	,	PUNCT
cana-1119	238	13	on	on	ADP
cana-1119	238	14	a	a	DET
cana-1119	238	15	subclass	subclass	NOUN
cana-1119	238	16	of	of	ADP
cana-1119	238	17	strongly	strongly	ADV
cana-1119	238	18	starlike	starlike	NOUN
cana-1119	238	19	functions	function	NOUN
cana-1119	238	20	associated	associate	VERB
cana-1119	238	21	with	with	ADP
cana-1119	238	22	exponential	exponential	ADJ
cana-1119	238	23	function	function	NOUN
cana-1119	238	24	,	,	PUNCT
cana-1119	238	25	bulletin	bulletin	NOUN
cana-1119	238	26	of	of	ADP
cana-1119	238	27	the	the	DET
cana-1119	238	28	malaysian	malaysian	PROPN
cana-1119	238	29	mathematical	mathematical	PROPN
cana-1119	238	30	sciences	sciences	PROPN
cana-1119	238	31	society	society	NOUN
cana-1119	238	32	,	,	PUNCT
cana-1119	238	33	38(2	38(2	NOUN
cana-1119	238	34	)	)	PUNCT
cana-1119	238	35	,	,	PUNCT
cana-1119	238	36	(	(	PUNCT
cana-1119	238	37	2015	2015	NUM
cana-1119	238	38	)	)	PUNCT
cana-1119	238	39	,	,	PUNCT
cana-1119	238	40	365	365	NUM
cana-1119	238	41	-	-	SYM
cana-1119	238	42	386	386	NUM
cana-1119	238	43	.	.	PUNCT
cana-1119	239	1	[	[	X
cana-1119	239	2	6	6	NUM
cana-1119	239	3	]	]	PUNCT
cana-1119	239	4	l.	l.	PROPN
cana-1119	239	5	shi	shi	PROPN
cana-1119	239	6	,	,	PUNCT
cana-1119	239	7	h.	h.	PROPN
cana-1119	239	8	m.	m.	PROPN
cana-1119	239	9	srivastava	srivastava	PROPN
cana-1119	239	10	,	,	PUNCT
cana-1119	239	11	m.	m.	PROPN
cana-1119	239	12	arif	arif	PROPN
cana-1119	239	13	,	,	PUNCT
cana-1119	239	14	s.	s.	PROPN
cana-1119	239	15	hussain	hussain	PROPN
cana-1119	239	16	,	,	PUNCT
cana-1119	239	17	h.	h.	PROPN
cana-1119	239	18	khan	khan	PROPN
cana-1119	239	19	,	,	PUNCT
cana-1119	239	20	an	an	DET
cana-1119	239	21	investigation	investigation	NOUN
cana-1119	239	22	of	of	ADP
cana-1119	239	23	the	the	DET
cana-1119	239	24	third	third	ADJ
cana-1119	239	25	hankel	hankel	NOUN
cana-1119	239	26	determinant	determinant	ADJ
cana-1119	239	27	problem	problem	NOUN
cana-1119	239	28	for	for	ADP
cana-1119	239	29	certain	certain	ADJ
cana-1119	239	30	subfamilies	subfamily	NOUN
cana-1119	239	31	of	of	ADP
cana-1119	239	32	univalent	univalent	ADJ
cana-1119	239	33	functions	function	NOUN
cana-1119	239	34	involving	involve	VERB
cana-1119	239	35	the	the	DET
cana-1119	239	36	exponential	exponential	ADJ
cana-1119	239	37	function	function	NOUN
cana-1119	239	38	,	,	PUNCT
cana-1119	239	39	symmetry	symmetry	NOUN
cana-1119	239	40	,	,	PUNCT
cana-1119	239	41	11(5	11(5	NUM
cana-1119	239	42	)	)	PUNCT
cana-1119	239	43	,	,	PUNCT
cana-1119	239	44	(	(	PUNCT
cana-1119	239	45	2019	2019	NUM
cana-1119	239	46	)	)	PUNCT
cana-1119	239	47	,	,	PUNCT
cana-1119	239	48	598	598	NUM
cana-1119	239	49	.	.	PUNCT
cana-1119	240	1	[	[	X
cana-1119	240	2	7	7	X
cana-1119	240	3	]	]	X
cana-1119	240	4	f.	f.	PROPN
cana-1119	240	5	ronning	ronning	PROPN
cana-1119	240	6	,	,	PUNCT
cana-1119	240	7	uniformly	uniformly	ADV
cana-1119	240	8	convex	convex	NOUN
cana-1119	240	9	functions	function	NOUN
cana-1119	240	10	and	and	CCONJ
cana-1119	240	11	a	a	DET
cana-1119	240	12	corresponding	corresponding	ADJ
cana-1119	240	13	class	class	NOUN
cana-1119	240	14	of	of	ADP
cana-1119	240	15	starlike	starlike	NOUN
cana-1119	240	16	functions	function	NOUN
cana-1119	240	17	,	,	PUNCT
cana-1119	240	18	proceedings	proceeding	NOUN
cana-1119	240	19	of	of	ADP
cana-1119	240	20	the	the	DET
cana-1119	240	21	american	american	PROPN
cana-1119	240	22	mathematical	mathematical	PROPN
cana-1119	240	23	society	society	NOUN
cana-1119	240	24	,	,	PUNCT
cana-1119	240	25	118,(1993	118,(1993	NUM
cana-1119	240	26	)	)	PUNCT
cana-1119	240	27	189	189	NUM
cana-1119	240	28	-	-	SYM
cana-1119	240	29	196	196	NUM
cana-1119	240	30	.	.	PUNCT
cana-1119	241	1	[	[	X
cana-1119	241	2	8	8	NUM
cana-1119	241	3	]	]	X
cana-1119	241	4	w.	w.	PROPN
cana-1119	241	5	janowski	janowski	PROPN
cana-1119	241	6	,	,	PUNCT
cana-1119	241	7	extremal	extremal	ADJ
cana-1119	241	8	problems	problem	NOUN
cana-1119	241	9	for	for	ADP
cana-1119	241	10	a	a	DET
cana-1119	241	11	family	family	NOUN
cana-1119	241	12	of	of	ADP
cana-1119	241	13	functions	function	NOUN
cana-1119	241	14	with	with	ADP
cana-1119	241	15	positive	positive	ADJ
cana-1119	241	16	real	real	ADJ
cana-1119	241	17	part	part	NOUN
cana-1119	241	18	and	and	CCONJ
cana-1119	241	19	for	for	ADP
cana-1119	241	20	some	some	DET
cana-1119	241	21	related	relate	VERB
cana-1119	241	22	families	family	NOUN
cana-1119	241	23	,	,	PUNCT
cana-1119	241	24	annales	annale	VERB
cana-1119	241	25	polonici	polonici	ADJ
cana-1119	241	26	mathematici	mathematici	NOUN
cana-1119	241	27	,	,	PUNCT
cana-1119	241	28	23,(1970	23,(1970	NUM
cana-1119	241	29	)	)	PUNCT
cana-1119	241	30	,	,	PUNCT
cana-1119	241	31	159	159	NUM
cana-1119	241	32	-	-	SYM
cana-1119	241	33	177	177	NUM
cana-1119	241	34	.	.	PUNCT
cana-1119	242	1	[	[	X
cana-1119	242	2	9	9	NUM
cana-1119	242	3	]	]	PUNCT
cana-1119	242	4	a.	a.	NOUN
cana-1119	242	5	alotaibi	alotaibi	NOUN
cana-1119	242	6	,	,	PUNCT
cana-1119	242	7	m.	m.	PROPN
cana-1119	242	8	arif	arif	PROPN
cana-1119	242	9	,	,	PUNCT
cana-1119	242	10	m.	m.	NOUN
cana-1119	242	11	a.	a.	NOUN
cana-1119	242	12	alghamdi	alghamdi	PROPN
cana-1119	242	13	,	,	PUNCT
cana-1119	242	14	s.	s.	PROPN
cana-1119	242	15	hussain	hussain	PROPN
cana-1119	242	16	,	,	PUNCT
cana-1119	242	17	starlikeness	starlikeness	PROPN
cana-1119	242	18	associated	associate	VERB
cana-1119	242	19	with	with	ADP
cana-1119	242	20	cosine	cosine	NOUN
cana-1119	242	21	hyperbolic	hyperbolic	ADJ
cana-1119	242	22	function	function	NOUN
cana-1119	242	23	,	,	PUNCT
cana-1119	242	24	mathematics	mathematic	NOUN
cana-1119	242	25	,	,	PUNCT
cana-1119	242	26	8	8	NUM
cana-1119	242	27	,	,	PUNCT
cana-1119	242	28	(	(	PUNCT
cana-1119	242	29	2020	2020	NUM
cana-1119	242	30	)	)	PUNCT
cana-1119	242	31	,	,	PUNCT
cana-1119	242	32	1118	1118	NUM
cana-1119	243	1	[	[	X
cana-1119	243	2	10	10	NUM
cana-1119	243	3	]	]	X
cana-1119	243	4	n.	n.	PROPN
cana-1119	243	5	e.	e.	PROPN
cana-1119	243	6	cho	cho	PROPN
cana-1119	243	7	,	,	PUNCT
cana-1119	243	8	v.	v.	PROPN
cana-1119	243	9	kumar	kumar	PROPN
cana-1119	243	10	,	,	PUNCT
cana-1119	243	11	s.	s.	PROPN
cana-1119	243	12	s.	s.	PROPN
cana-1119	243	13	kumar	kumar	PROPN
cana-1119	243	14	,	,	PUNCT
cana-1119	243	15	v.	v.	ADP
cana-1119	243	16	ravichandran	ravichandran	NOUN
cana-1119	243	17	,	,	PUNCT
cana-1119	243	18	radius	radius	NOUN
cana-1119	243	19	problems	problem	NOUN
cana-1119	243	20	for	for	ADP
cana-1119	243	21	starlike	starlike	NOUN
cana-1119	243	22	functions	function	NOUN
cana-1119	243	23	associated	associate	VERB
cana-1119	243	24	with	with	ADP
cana-1119	243	25	the	the	DET
cana-1119	243	26	sine	sine	ADJ
cana-1119	243	27	function	function	NOUN
cana-1119	243	28	,	,	PUNCT
cana-1119	243	29	bulletin	bulletin	NOUN
cana-1119	243	30	of	of	ADP
cana-1119	243	31	the	the	DET
cana-1119	243	32	iranian	iranian	PROPN
cana-1119	243	33	mathematical	mathematical	PROPN
cana-1119	243	34	society	society	NOUN
cana-1119	243	35	,	,	PUNCT
cana-1119	243	36	45	45	NUM
cana-1119	243	37	,	,	PUNCT
cana-1119	243	38	(	(	PUNCT
cana-1119	243	39	2019	2019	NUM
cana-1119	243	40	)	)	PUNCT
cana-1119	243	41	,	,	PUNCT
cana-1119	243	42	213	213	NUM
cana-1119	243	43	-	-	SYM
cana-1119	243	44	232	232	NUM
cana-1119	243	45	,	,	PUNCT
cana-1119	243	46	.	.	PUNCT
cana-1119	244	1	[	[	X
cana-1119	244	2	11	11	NUM
cana-1119	244	3	]	]	PUNCT
cana-1119	244	4	m.	m.	NOUN
cana-1119	244	5	arif	arif	PROPN
cana-1119	244	6	,	,	PUNCT
cana-1119	244	7	m.	m.	NOUN
cana-1119	244	8	raza	raza	PROPN
cana-1119	244	9	,	,	PUNCT
cana-1119	244	10	h.	h.	PROPN
cana-1119	244	11	tang	tang	PROPN
cana-1119	244	12	,	,	PUNCT
cana-1119	244	13	s.	s.	PROPN
cana-1119	244	14	hussain	hussain	PROPN
cana-1119	244	15	,	,	PUNCT
cana-1119	244	16	h.	h.	PROPN
cana-1119	244	17	khan	khan	PROPN
cana-1119	244	18	,	,	PUNCT
cana-1119	244	19	hankel	hankel	NOUN
cana-1119	244	20	determinant	determinant	ADJ
cana-1119	244	21	of	of	ADP
cana-1119	244	22	order	order	NOUN
cana-1119	244	23	three	three	NUM
cana-1119	244	24	for	for	ADP
cana-1119	244	25	familiar	familiar	ADJ
cana-1119	244	26	subsets	subset	NOUN
cana-1119	244	27	of	of	ADP
cana-1119	244	28	analytic	analytic	ADJ
cana-1119	244	29	functions	function	NOUN
cana-1119	244	30	related	relate	VERB
cana-1119	244	31	with	with	ADP
cana-1119	244	32	sine	sine	ADJ
cana-1119	244	33	function	function	NOUN
cana-1119	244	34	,	,	PUNCT
cana-1119	244	35	open	open	ADJ
cana-1119	244	36	mathematics	mathematic	NOUN
cana-1119	244	37	,	,	PUNCT
cana-1119	244	38	17	17	NUM
cana-1119	244	39	,	,	PUNCT
cana-1119	244	40	,	,	PUNCT
cana-1119	244	41	(	(	PUNCT
cana-1119	244	42	2019	2019	NUM
cana-1119	244	43	)	)	PUNCT
cana-1119	244	44	,	,	PUNCT
cana-1119	244	45	1615	1615	NUM
cana-1119	244	46	-	-	SYM
cana-1119	244	47	1630	1630	NUM
cana-1119	244	48	.	.	PUNCT
cana-1119	245	1	[	[	X
cana-1119	245	2	12	12	NUM
cana-1119	245	3	]	]	X
cana-1119	245	4	c.	c.	NOUN
cana-1119	245	5	pommerenke	pommerenke	PROPN
cana-1119	245	6	,	,	PUNCT
cana-1119	245	7	univalent	univalent	ADJ
cana-1119	245	8	functions	function	NOUN
cana-1119	245	9	,	,	PUNCT
cana-1119	245	10	studia	studia	PROPN
cana-1119	245	11	mathematica	mathematica	PROPN
cana-1119	245	12	mathematische	mathematische	PROPN
cana-1119	245	13	lehrbucher	lehrbucher	PROPN
cana-1119	245	14	,	,	PUNCT
cana-1119	245	15	vandenhoeck	vandenhoeck	NOUN
cana-1119	245	16	and	and	CCONJ
cana-1119	245	17	ruprecht	ruprecht	NOUN
cana-1119	245	18	,	,	PUNCT
cana-1119	245	19	(	(	PUNCT
cana-1119	245	20	1975	1975	NUM
cana-1119	245	21	)	)	PUNCT
cana-1119	245	22	.	.	PUNCT
cana-1119	246	1	[	[	X
cana-1119	246	2	13	13	NUM
cana-1119	246	3	]	]	X
cana-1119	246	4	ch	ch	NOUN
cana-1119	246	5	.	.	PUNCT
cana-1119	246	6	pommerenke	pommerenke	PROPN
cana-1119	246	7	,	,	PUNCT
cana-1119	246	8	on	on	ADP
cana-1119	246	9	the	the	DET
cana-1119	246	10	coefficients	coefficient	NOUN
cana-1119	246	11	and	and	CCONJ
cana-1119	246	12	hankel	hankel	NOUN
cana-1119	246	13	determinants	determinant	NOUN
cana-1119	246	14	of	of	ADP
cana-1119	246	15	univalent	univalent	ADJ
cana-1119	246	16	functions	function	NOUN
cana-1119	246	17	,	,	PUNCT
cana-1119	246	18	.	.	PUNCT
cana-1119	247	1	london	london	PROPN
cana-1119	247	2	math	math	PROPN
cana-1119	247	3	.	.	PUNCT
cana-1119	248	1	soc	soc	PROPN
cana-1119	248	2	.	.	PROPN
cana-1119	248	3	,	,	PUNCT
cana-1119	248	4	41	41	NUM
cana-1119	248	5	,	,	PUNCT
cana-1119	248	6	(	(	PUNCT
cana-1119	248	7	1966	1966	NUM
cana-1119	248	8	)	)	PUNCT
cana-1119	248	9	,	,	PUNCT
cana-1119	248	10	111	111	NUM
cana-1119	248	11	-	-	SYM
cana-1119	248	12	122	122	NUM
cana-1119	248	13	.	.	PUNCT
cana-1119	249	1	[	[	X
cana-1119	249	2	14	14	NUM
cana-1119	249	3	]	]	X
cana-1119	249	4	j.	j.	PROPN
cana-1119	249	5	noonan	noonan	PROPN
cana-1119	249	6	and	and	CCONJ
cana-1119	249	7	d.k	d.k	PROPN
cana-1119	249	8	.	.	PROPN
cana-1119	249	9	thomas	thomas	PROPN
cana-1119	249	10	,	,	PUNCT
cana-1119	249	11	on	on	ADP
cana-1119	249	12	the	the	DET
cana-1119	249	13	second	second	ADJ
cana-1119	249	14	hankel	hankel	NOUN
cana-1119	249	15	determinant	determinant	ADJ
cana-1119	249	16	of	of	ADP
cana-1119	249	17	a	a	DET
cana-1119	249	18	really	really	ADV
cana-1119	249	19	mean	mean	VERB
cana-1119	249	20	p	p	ADJ
cana-1119	249	21	-	-	PUNCT
cana-1119	249	22	valent	valent	NOUN
cana-1119	249	23	functions	function	NOUN
cana-1119	249	24	,	,	PUNCT
cana-1119	249	25	transactions	transaction	NOUN
cana-1119	249	26	of	of	ADP
cana-1119	249	27	the	the	DET
cana-1119	249	28	american	american	PROPN
cana-1119	249	29	mathematical	mathematical	PROPN
cana-1119	249	30	society	society	NOUN
cana-1119	249	31	trans	trans	PROPN
cana-1119	249	32	amer	amer	PROPN
cana-1119	249	33	math	math	PROPN
cana-1119	249	34	soc	soc	PROPN
cana-1119	249	35	,	,	PUNCT
cana-1119	249	36	223(2	223(2	NUM
cana-1119	249	37	)	)	PUNCT
cana-1119	249	38	,	,	PUNCT
cana-1119	249	39	(	(	PUNCT
cana-1119	249	40	1976	1976	NUM
cana-1119	249	41	)	)	PUNCT
cana-1119	249	42	,	,	PUNCT
cana-1119	249	43	337	337	NUM
cana-1119	249	44	-	-	SYM
cana-1119	249	45	346	346	NUM
cana-1119	249	46	.	.	PUNCT
cana-1119	250	1	[	[	X
cana-1119	250	2	15	15	NUM
cana-1119	250	3	]	]	X
cana-1119	250	4	k.	k.	PROPN
cana-1119	250	5	i.	i.	PROPN
cana-1119	250	6	noor	noor	PROPN
cana-1119	250	7	,	,	PUNCT
cana-1119	250	8	hankel	hankel	NOUN
cana-1119	250	9	determinant	determinant	ADJ
cana-1119	250	10	problem	problem	NOUN
cana-1119	250	11	for	for	ADP
cana-1119	250	12	the	the	DET
cana-1119	250	13	class	class	NOUN
cana-1119	250	14	of	of	ADP
cana-1119	250	15	functions	function	NOUN
cana-1119	250	16	with	with	ADP
cana-1119	250	17	bounded	bounded	ADJ
cana-1119	250	18	boundary	boundary	ADJ
cana-1119	250	19	rotation	rotation	NOUN
cana-1119	250	20	,	,	PUNCT
cana-1119	250	21	rev	rev	PROPN
cana-1119	250	22	.	.	PROPN
cana-1119	250	23	roum	roum	PROPN
cana-1119	250	24	.	.	PUNCT
cana-1119	251	1	math	math	NOUN
cana-1119	251	2	.	.	PUNCT
cana-1119	252	1	pures	pure	NOUN
cana-1119	252	2	appl	appl	PROPN
cana-1119	252	3	.	.	PROPN
cana-1119	252	4	,	,	PUNCT
cana-1119	252	5	28	28	NUM
cana-1119	252	6	,	,	PUNCT
cana-1119	252	7	(	(	PUNCT
cana-1119	252	8	1983	1983	NUM
cana-1119	252	9	)	)	PUNCT
cana-1119	252	10	,	,	PUNCT
cana-1119	252	11	731	731	NUM
cana-1119	252	12	-	-	SYM
cana-1119	252	13	739	739	NUM
cana-1119	252	14	.	.	PUNCT
cana-1119	253	1	[	[	X
cana-1119	253	2	16	16	NUM
cana-1119	253	3	]	]	PUNCT
cana-1119	253	4	gaganpreet	gaganpreet	NOUN
cana-1119	253	5	kaur	kaur	PROPN
cana-1119	253	6	,	,	PUNCT
cana-1119	253	7	gurmeet	gurmeet	VERB
cana-1119	253	8	singh	singh	PROPN
cana-1119	253	9	,	,	PUNCT
cana-1119	253	10	muhammad	muhammad	PROPN
cana-1119	253	11	arif	arif	PROPN
cana-1119	253	12	,	,	PUNCT
cana-1119	253	13	ronnason	ronnason	PROPN
cana-1119	253	14	chinram	chinram	PROPN
cana-1119	253	15	,	,	PUNCT
cana-1119	253	16	and	and	CCONJ
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cana-1119	253	20	a	a	DET
cana-1119	253	21	study	study	NOUN
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cana-1119	253	26	hankel	hankel	NOUN
cana-1119	253	27	determinant	determinant	ADJ
cana-1119	253	28	problem	problem	NOUN
cana-1119	253	29	for	for	ADP
cana-1119	253	30	a	a	DET
cana-1119	253	31	particular	particular	ADJ
cana-1119	253	32	class	class	NOUN
cana-1119	253	33	of	of	ADP
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cana-1119	253	35	turning	turning	NOUN
cana-1119	253	36	functions	function	NOUN
cana-1119	253	37	,	,	PUNCT
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cana-1119	253	39	problems	problem	NOUN
cana-1119	253	40	in	in	ADP
cana-1119	253	41	engineering	engineering	NOUN
cana-1119	253	42	,	,	PUNCT
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cana-1119	253	44	,	,	PUNCT
cana-1119	253	45	(	(	PUNCT
cana-1119	253	46	2021	2021	NUM
cana-1119	253	47	)	)	PUNCT
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cana-1119	254	2	17	17	NUM
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cana-1119	254	4	richard	richard	PROPN
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cana-1119	254	7	and	and	CCONJ
cana-1119	254	8	eligiusz	eligiusz	PROPN
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cana-1119	254	12	early	early	ADJ
cana-1119	254	13	coefficients	coefficient	NOUN
cana-1119	254	14	of	of	ADP
cana-1119	254	15	the	the	DET
cana-1119	254	16	inverse	inverse	NOUN
cana-1119	254	17	of	of	ADP
cana-1119	254	18	a	a	DET
cana-1119	254	19	regular	regular	ADJ
cana-1119	254	20	convex	convex	NOUN
cana-1119	254	21	function	function	NOUN
cana-1119	254	22	,	,	PUNCT
cana-1119	254	23	proc	proc	PROPN
cana-1119	254	24	.	.	PUNCT
cana-1119	255	1	amer	amer	PROPN
cana-1119	255	2	.	.	PUNCT
cana-1119	255	3	math	math	PROPN
cana-1119	255	4	.	.	PUNCT
cana-1119	256	1	soc	soc	PROPN
cana-1119	256	2	,	,	PUNCT
cana-1119	256	3	85	85	NUM
cana-1119	256	4	,	,	PUNCT
cana-1119	256	5	(	(	PUNCT
cana-1119	256	6	1982	1982	NUM
cana-1119	256	7	)	)	PUNCT
cana-1119	256	8	,	,	PUNCT
cana-1119	256	9	225	225	NUM
cana-1119	256	10	-	-	SYM
cana-1119	256	11	230	230	NUM
cana-1119	256	12	.	.	PUNCT
cana-1119	257	1	[	[	X
cana-1119	257	2	18	18	NUM
cana-1119	257	3	]	]	PUNCT
cana-1119	257	4	ch	ch	NOUN
cana-1119	257	5	pommerenke	pommerenke	NOUN
cana-1119	257	6	,	,	PUNCT
cana-1119	257	7	on	on	ADP
cana-1119	257	8	the	the	DET
cana-1119	257	9	hankel	hankel	NOUN
cana-1119	257	10	determinants	determinant	NOUN
cana-1119	257	11	of	of	ADP
cana-1119	257	12	univalent	univalent	ADJ
cana-1119	257	13	functions	function	NOUN
cana-1119	257	14	,	,	PUNCT
cana-1119	257	15	mathematika	mathematika	NOUN
cana-1119	257	16	,	,	PUNCT
cana-1119	257	17	14	14	NUM
cana-1119	257	18	,	,	PUNCT
cana-1119	257	19	(	(	PUNCT
cana-1119	257	20	1967	1967	NUM
cana-1119	257	21	)	)	PUNCT
cana-1119	257	22	,	,	PUNCT
cana-1119	257	23	108	108	NUM
cana-1119	257	24	-	-	SYM
cana-1119	257	25	112	112	NUM
cana-1119	257	26	.	.	PUNCT
cana-1119	258	1	[	[	X
cana-1119	258	2	19	19	NUM
cana-1119	258	3	]	]	PUNCT
cana-1119	258	4	luigi	luigi	PROPN
cana-1119	258	5	rodino	rodino	PROPN
cana-1119	258	6	,	,	PUNCT
cana-1119	258	7	muhammad	muhammad	PROPN
cana-1119	258	8	arif	arif	PROPN
cana-1119	258	9	,	,	PUNCT
cana-1119	258	10	lubna	lubna	PROPN
cana-1119	258	11	rani	rani	PROPN
cana-1119	258	12	,	,	PUNCT
cana-1119	258	13	mohsan	mohsan	PROPN
cana-1119	258	14	raza	raza	PROPN
cana-1119	258	15	,	,	PUNCT
cana-1119	258	16	and	and	CCONJ
cana-1119	258	17	pawel	pawel	PROPN
cana-1119	258	18	zaprawa	zaprawa	PROPN
cana-1119	258	19	,	,	PUNCT
cana-1119	258	20	fourth	fourth	ADJ
cana-1119	258	21	hankel	hankel	NOUN
cana-1119	258	22	determinant	determinant	ADJ
cana-1119	258	23	for	for	ADP
cana-1119	258	24	the	the	DET
cana-1119	258	25	set	set	NOUN
cana-1119	258	26	of	of	ADP
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cana-1119	258	28	-	-	PUNCT
cana-1119	258	29	like	like	ADJ
cana-1119	258	30	functions	function	NOUN
cana-1119	258	31	,	,	PUNCT
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cana-1119	258	33	problems	problem	NOUN
cana-1119	258	34	in	in	ADP
cana-1119	258	35	engineering	engineering	NOUN
cana-1119	258	36	,	,	PUNCT
cana-1119	258	37	(	(	PUNCT
cana-1119	258	38	2021	2021	NUM
cana-1119	258	39	)	)	PUNCT
cana-1119	258	40	,	,	PUNCT
cana-1119	258	41	1	1	NUM
cana-1119	258	42	-	-	SYM
cana-1119	258	43	8	8	NUM
cana-1119	258	44	.	.	PUNCT
cana-1119	259	1	[	[	X
cana-1119	259	2	20	20	NUM
cana-1119	259	3	]	]	X
cana-1119	259	4	hari	hari	PROPN
cana-1119	259	5	srivastava	srivastava	PROPN
cana-1119	259	6	,	,	PUNCT
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cana-1119	259	9	and	and	CCONJ
cana-1119	259	10	gurmeet	gurmeet	PROPN
cana-1119	259	11	singh	singh	PROPN
cana-1119	259	12	,	,	PUNCT
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cana-1119	259	18	determinant	determinant	ADJ
cana-1119	259	19	for	for	ADP
cana-1119	259	20	a	a	DET
cana-1119	259	21	class	class	NOUN
cana-1119	259	22	of	of	ADP
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cana-1119	259	24	functions	function	NOUN
cana-1119	259	25	with	with	ADP
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cana-1119	259	27	turnings	turning	NOUN
cana-1119	259	28	involving	involve	VERB
cana-1119	259	29	cardioid	cardioid	ADJ
cana-1119	259	30	domains	domain	NOUN
cana-1119	259	31	.	.	PUNCT
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cana-1119	259	36	and	and	CCONJ
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cana-1119	259	38	analysis	analysis	NOUN
cana-1119	259	39	,	,	PUNCT
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cana-1119	259	41	,	,	PUNCT
cana-1119	259	42	(	(	PUNCT
cana-1119	259	43	2021	2021	NUM
cana-1119	259	44	)	)	PUNCT
cana-1119	259	45	,	,	PUNCT
cana-1119	259	46	511	511	NUM
cana-1119	259	47	-	-	SYM
cana-1119	259	48	526	526	NUM
cana-1119	259	49	.	.	PUNCT
cana-1119	260	1	[	[	X
cana-1119	260	2	21	21	NUM
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cana-1119	260	8	hankel	hankel	NOUN
cana-1119	260	9	determinants	determinant	NOUN
cana-1119	260	10	for	for	ADP
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cana-1119	260	14	functions	function	NOUN
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cana-1119	261	1	,	,	PUNCT
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cana-1119	262	6	,	,	PUNCT
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cana-1119	262	10	a	a	DET
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cana-1119	262	12	distribution	distribution	NOUN
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cana-1119	262	14	on	on	ADP
cana-1119	262	15	certain	certain	ADJ
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cana-1119	262	22	analysis	analysis	NOUN
cana-1119	262	23	,	,	PUNCT
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cana-1119	263	1	https://books.google.co.in/books/about/%c3%9cber_die_koeffizienten_derjenigen_poten.html?id=7ounpgaacaaj&redir_esc=y	https://books.google.co.in/books/about/%c3%9cber_die_koeffizienten_derjenigen_poten.html?id=7ounpgaacaaj&redir_esc=y	ADV
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cana-1119	263	3	https://www.researchgate.net/profile/c-minda/publication/245129813_a_unified_treatment_of_some_special_classes_of_functions/links/543693bf0cf2bf1f1f2be1b2/a-unified-treatment-of-some-special-classes-of-functions.pdf	https://www.researchgate.net/profile/c-minda/publication/245129813_a_unified_treatment_of_some_special_classes_of_functions/links/543693bf0cf2bf1f1f2be1b2/a-unified-treatment-of-some-special-classes-of-functions.pdf	NOUN
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cana-1119	281	23	analytic	analytic	ADJ
cana-1119	281	24	functions	function	NOUN
cana-1119	281	25	with	with	ADP
cana-1119	281	26	bounded	bounded	ADJ
cana-1119	281	27	turnings	turning	NOUN
cana-1119	281	28	involving	involve	VERB
cana-1119	281	29	cardioid	cardioid	ADJ
cana-1119	281	30	domains	domain	NOUN
cana-1119	281	31	,	,	PUNCT
cana-1119	281	32	journal	journal	NOUN
cana-1119	281	33	of	of	ADP
cana-1119	281	34	nonlinear	nonlinear	ADJ
cana-1119	281	35	and	and	CCONJ
cana-1119	281	36	convex	convex	ADJ
cana-1119	281	37	analysis	analysis	NOUN
cana-1119	281	38	,	,	PUNCT
cana-1119	281	39	22(3	22(3	NUM
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cana-1119	281	45	,	,	PUNCT
cana-1119	281	46	511	511	NUM
cana-1119	281	47	-	-	SYM
cana-1119	281	48	526	526	NUM
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cana-1119	282	11	-	-	PUNCT
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cana-1119	282	24	and	and	CCONJ
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cana-1119	282	30	of	of	ADP
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cana-1119	282	34	to	to	ADP
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cana-1119	284	2	https://www.ijrat.org/downloads/vol-5/nov-2017/paper%20id-511201710.pdf	https://www.ijrat.org/downloads/vol-5/nov-2017/paper%20id-511201710.pdf	ADJ
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cana-1119	284	4	https://www.researchgate.net/publication/331741498_a_subclass_of_bi-univalent_functions_defined_by_generalized_salagean_operator_related_to_shell-like_curves_connected_with_fibonacci_numbers	https://www.researchgate.net/publication/331741498_a_subclass_of_bi-univalent_functions_defined_by_generalized_salagean_operator_related_to_shell-like_curves_connected_with_fibonacci_number	NOUN
cana-1119	284	5	https://www.researchgate.net/publication/331741498_a_subclass_of_bi-univalent_functions_defined_by_generalized_salagean_operator_related_to_shell-like_curves_connected_with_fibonacci_numbers	https://www.researchgate.net/publication/331741498_a_subclass_of_bi-univalent_functions_defined_by_generalized_salagean_operator_related_to_shell-like_curves_connected_with_fibonacci_number	NOUN
cana-1119	284	6	https://www.vijnanaparishadofindia.org/jnanabha/volume-50-no1-2020/p8	https://www.vijnanaparishadofindia.org/jnanabha/volume-50-no1-2020/p8	PRON
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cana-1119	284	11	https://www.researchgate.net/publication/350513965_estimates_of_the_fourth_hankel_determinant_for_a_class_of_analytic_functions_with_bounded_turnings_involving_cardioid_domains	https://www.researchgate.net/publication/350513965_estimates_of_the_fourth_hankel_determinant_for_a_class_of_analytic_functions_with_bounded_turnings_involving_cardioid_domain	NOUN
cana-1119	284	12	https://www.researchgate.net/publication/350513965_estimates_of_the_fourth_hankel_determinant_for_a_class_of_analytic_functions_with_bounded_turnings_involving_cardioid_domains	https://www.researchgate.net/publication/350513965_estimates_of_the_fourth_hankel_determinant_for_a_class_of_analytic_functions_with_bounded_turnings_involving_cardioid_domain	NOUN
cana-1119	284	13	https://www.researchgate.net/publication/350513965_estimates_of_the_fourth_hankel_determinant_for_a_class_of_analytic_functions_with_bounded_turnings_involving_cardioid_domains	https://www.researchgate.net/publication/350513965_estimates_of_the_fourth_hankel_determinant_for_a_class_of_analytic_functions_with_bounded_turnings_involving_cardioid_domain	VERB
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