id	sid	tid	token	lemma	pos
cana-763	1	1	communications	communication	NOUN
cana-763	1	2	on	on	ADP
cana-763	1	3	applied	apply	VERB
cana-763	1	4	nonlinear	nonlinear	ADJ
cana-763	1	5	analysis	analysis	NOUN
cana-763	1	6	issn	issn	NOUN
cana-763	1	7	:	:	PUNCT
cana-763	1	8	1074	1074	NUM
cana-763	1	9	-	-	PUNCT
cana-763	1	10	133x	133x	NUM
cana-763	1	11	vol	vol	NOUN
cana-763	1	12	31	31	NUM
cana-763	1	13	no	no	NOUN
cana-763	1	14	.	.	PUNCT
cana-763	2	1	3s	3s	NUM
cana-763	2	2	(	(	PUNCT
cana-763	2	3	2024	2024	NUM
cana-763	2	4	)	)	PUNCT
cana-763	2	5	254	254	NUM
cana-763	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-763	2	7	subclass	subclass	NOUN
cana-763	2	8	of	of	ADP
cana-763	2	9	analytic	analytic	ADJ
cana-763	2	10	functions	function	NOUN
cana-763	2	11	associated	associate	VERB
cana-763	2	12	with	with	ADP
cana-763	2	13	differential	differential	ADJ
cana-763	2	14	operator	operator	NOUN
cana-763	2	15	katterapalle	katterapalle	PROPN
cana-763	2	16	sridevi𝟏	sridevi𝟏	PROPN
cana-763	2	17	,	,	PUNCT
cana-763	2	18	n.	n.	PROPN
cana-763	2	19	sri	sri	PROPN
cana-763	2	20	lakshmi	lakshmi	PROPN
cana-763	2	21	sudha	sudha	PROPN
cana-763	2	22	rani𝟐	rani𝟐	PROPN
cana-763	2	23	1	1	NUM
cana-763	2	24	department	department	NOUN
cana-763	2	25	of	of	ADP
cana-763	2	26	mathematics	mathematic	NOUN
cana-763	2	27	,	,	PUNCT
cana-763	2	28	dr.b.r.ambedkar	dr.b.r.ambedkar	PROPN
cana-763	2	29	open	open	PROPN
cana-763	2	30	university	university	PROPN
cana-763	2	31	,	,	PUNCT
cana-763	2	32	hyderabad	hyderabad	PROPN
cana-763	2	33	500	500	NUM
cana-763	2	34	033	033	NUM
cana-763	2	35	,	,	PUNCT
cana-763	2	36	t.s	t.s	PROPN
cana-763	2	37	,	,	PUNCT
cana-763	2	38	india	india	PROPN
cana-763	2	39	.	.	PUNCT
cana-763	3	1	sridevidrk18@gmail.com	sridevidrk18@gmail.com	X
cana-763	3	2	2	2	NUM
cana-763	3	3	department	department	NOUN
cana-763	3	4	of	of	ADP
cana-763	3	5	mathematics	mathematic	NOUN
cana-763	3	6	,	,	PUNCT
cana-763	3	7	dr.b.r.ambedkar	dr.b.r.ambedkar	PROPN
cana-763	3	8	open	open	PROPN
cana-763	3	9	university	university	PROPN
cana-763	3	10	,	,	PUNCT
cana-763	3	11	hyderabad	hyderabad	PROPN
cana-763	3	12	500	500	NUM
cana-763	3	13	033	033	NUM
cana-763	3	14	,	,	PUNCT
cana-763	3	15	t.s	t.s	PROPN
cana-763	3	16	,	,	PUNCT
cana-763	3	17	india	india	PROPN
cana-763	3	18	.	.	PUNCT
cana-763	3	19	lakshmisudha1848@gmail.com	lakshmisudha1848@gmail.com	X
cana-763	4	1	article	article	NOUN
cana-763	4	2	history	history	NOUN
cana-763	4	3	:	:	PUNCT
cana-763	4	4	received	receive	VERB
cana-763	4	5	:	:	PUNCT
cana-763	4	6	16	16	NUM
cana-763	4	7	-	-	PUNCT
cana-763	4	8	04	04	NUM
cana-763	4	9	-	-	PUNCT
cana-763	4	10	2024	2024	NUM
cana-763	4	11	revised	revise	VERB
cana-763	4	12	:	:	PUNCT
cana-763	4	13	28	28	NUM
cana-763	4	14	-	-	SYM
cana-763	4	15	05	05	NUM
cana-763	4	16	-	-	PUNCT
cana-763	4	17	2024	2024	NUM
cana-763	4	18	accepted	accept	VERB
cana-763	4	19	:	:	PUNCT
cana-763	4	20	13	13	NUM
cana-763	4	21	-	-	SYM
cana-763	4	22	06	06	NUM
cana-763	4	23	-	-	PUNCT
cana-763	4	24	2024	2024	NUM
cana-763	4	25	abstract	abstract	NOUN
cana-763	4	26	:	:	PUNCT
cana-763	4	27	introduction	introduction	NOUN
cana-763	4	28	:	:	PUNCT
cana-763	4	29	:	:	PUNCT
cana-763	4	30	in	in	ADP
cana-763	4	31	this	this	DET
cana-763	4	32	work	work	NOUN
cana-763	4	33	,	,	PUNCT
cana-763	4	34	we	we	PRON
cana-763	4	35	introduce	introduce	VERB
cana-763	4	36	and	and	CCONJ
cana-763	4	37	investigate	investigate	VERB
cana-763	4	38	a	a	DET
cana-763	4	39	new	new	ADJ
cana-763	4	40	class	class	NOUN
cana-763	4	41	�	�	PROPN
cana-763	4	42	̃	̃	PROPN
cana-763	4	43	�	�	PROPN
cana-763	4	44	𝑆𝑠	𝑆𝑠	PROPN
cana-763	4	45	𝑚(ς	𝑚(ς	NOUN
cana-763	4	46	,	,	PUNCT
cana-763	4	47	ℏ	ℏ	PROPN
cana-763	4	48	,	,	PUNCT
cana-763	4	49	℘	℘	PROPN
cana-763	4	50	,	,	PUNCT
cana-763	4	51	ϱ	ϱ	NOUN
cana-763	4	52	,	,	PUNCT
cana-763	4	53	𝑡	𝑡	NOUN
cana-763	4	54	)	)	PUNCT
cana-763	4	55	of	of	ADP
cana-763	4	56	analytic	analytic	ADJ
cana-763	4	57	functions	function	NOUN
cana-763	4	58	in	in	ADP
cana-763	4	59	the	the	DET
cana-763	4	60	open	open	ADJ
cana-763	4	61	unit	unit	NOUN
cana-763	4	62	disc	disc	VERB
cana-763	4	63	𝑈	𝑈	PROPN
cana-763	4	64	with	with	ADP
cana-763	4	65	negative	negative	ADJ
cana-763	4	66	coefficients	coefficient	NOUN
cana-763	4	67	.	.	PUNCT
cana-763	5	1	the	the	DET
cana-763	5	2	object	object	NOUN
cana-763	5	3	of	of	ADP
cana-763	5	4	the	the	DET
cana-763	5	5	present	present	ADJ
cana-763	5	6	paper	paper	NOUN
cana-763	5	7	is	be	AUX
cana-763	5	8	to	to	PART
cana-763	5	9	determine	determine	VERB
cana-763	5	10	coefficient	coefficient	NOUN
cana-763	5	11	estimates	estimate	NOUN
cana-763	5	12	,	,	PUNCT
cana-763	5	13	neighborhoods	neighborhood	NOUN
cana-763	5	14	and	and	CCONJ
cana-763	5	15	partial	partial	ADJ
cana-763	5	16	sums	sum	NOUN
cana-763	5	17	for	for	ADP
cana-763	5	18	functions	function	NOUN
cana-763	5	19	𝑓	𝑓	PRON
cana-763	5	20	belonging	belong	VERB
cana-763	5	21	to	to	ADP
cana-763	5	22	this	this	DET
cana-763	5	23	class	class	NOUN
cana-763	5	24	.	.	PUNCT
cana-763	6	1	keywords	keyword	NOUN
cana-763	6	2	:	:	PUNCT
cana-763	6	3	:	:	PUNCT
cana-763	6	4	analytic	analytic	ADJ
cana-763	6	5	function	function	NOUN
cana-763	6	6	,	,	PUNCT
cana-763	6	7	uniformly	uniformly	ADV
cana-763	6	8	starlike	starlike	NOUN
cana-763	6	9	function	function	NOUN
cana-763	6	10	,	,	PUNCT
cana-763	6	11	coefficient	coefficient	NOUN
cana-763	6	12	estimate	estimate	NOUN
cana-763	6	13	,	,	PUNCT
cana-763	6	14	neighborhood	neighborhood	NOUN
cana-763	6	15	,	,	PUNCT
cana-763	6	16	partial	partial	ADJ
cana-763	6	17	sums	sum	NOUN
cana-763	6	18	.	.	PUNCT
cana-763	7	1	ams	am	NOUN
cana-763	7	2	subject	subject	ADJ
cana-763	7	3	classification	classification	NOUN
cana-763	7	4	:	:	PUNCT
cana-763	7	5	30c45	30c45	NUM
cana-763	7	6	.	.	PUNCT
cana-763	8	1	1	1	X
cana-763	8	2	.	.	X
cana-763	8	3	introduction	introduction	NOUN
cana-763	8	4	let	let	VERB
cana-763	8	5	𝐴	𝐴	PROPN
cana-763	8	6	denote	denote	VERB
cana-763	8	7	the	the	DET
cana-763	8	8	class	class	NOUN
cana-763	8	9	of	of	ADP
cana-763	8	10	analytic	analytic	ADJ
cana-763	8	11	functions	function	NOUN
cana-763	8	12	𝑓	𝑓	PRON
cana-763	8	13	defined	define	VERB
cana-763	8	14	on	on	ADP
cana-763	8	15	the	the	DET
cana-763	8	16	unit	unit	NOUN
cana-763	8	17	disk	disk	NOUN
cana-763	8	18	𝑈	𝑈	PROPN
cana-763	8	19	=	=	PUNCT
cana-763	8	20	{	{	PUNCT
cana-763	8	21	𝑧	𝑧	X
cana-763	8	22	:	:	PUNCT
cana-763	8	23	|𝑧|	|𝑧|	PROPN
cana-763	8	24	<	<	X
cana-763	8	25	1	1	NUM
cana-763	8	26	}	}	PUNCT
cana-763	8	27	with	with	ADP
cana-763	8	28	normalization	normalization	NOUN
cana-763	8	29	𝑓(0	𝑓(0	PROPN
cana-763	8	30	)	)	PUNCT
cana-763	8	31	=	=	SYM
cana-763	8	32	0	0	NUM
cana-763	8	33	and	and	CCONJ
cana-763	8	34	𝑓′(0	𝑓′(0	PROPN
cana-763	8	35	)	)	PUNCT
cana-763	8	36	=	=	SYM
cana-763	8	37	1	1	X
cana-763	8	38	.	.	X
cana-763	8	39	such	such	DET
cana-763	8	40	a	a	DET
cana-763	8	41	function	function	NOUN
cana-763	8	42	has	have	VERB
cana-763	8	43	the	the	DET
cana-763	8	44	taylor	taylor	PROPN
cana-763	8	45	series	series	PROPN
cana-763	8	46	expansion	expansion	NOUN
cana-763	8	47	about	about	ADP
cana-763	8	48	the	the	DET
cana-763	8	49	origin	origin	NOUN
cana-763	8	50	in	in	ADP
cana-763	8	51	the	the	DET
cana-763	8	52	form	form	NOUN
cana-763	8	53	𝑓(𝑧	𝑓(𝑧	NUM
cana-763	8	54	)	)	PUNCT
cana-763	8	55	=	=	PUNCT
cana-763	9	1	𝑧	𝑧	PROPN
cana-763	10	1	+	+	CCONJ
cana-763	10	2	∑	∑	PROPN
cana-763	10	3	𝑎𝑛	𝑎𝑛	PROPN
cana-763	10	4	∞	∞	NUM
cana-763	10	5	𝑛=2	𝑛=2	NOUN
cana-763	10	6	𝑧𝑛	𝑧𝑛	INTJ
cana-763	10	7	(	(	PUNCT
cana-763	10	8	1.1	1.1	NUM
cana-763	10	9	)	)	PUNCT
cana-763	10	10	,	,	PUNCT
cana-763	10	11	denoted	denote	VERB
cana-763	10	12	by	by	ADP
cana-763	10	13	𝑆	𝑆	PROPN
cana-763	10	14	,	,	PUNCT
cana-763	10	15	the	the	DET
cana-763	10	16	subclass	subclass	NOUN
cana-763	10	17	of	of	ADP
cana-763	10	18	𝐴	𝐴	PROPN
cana-763	10	19	consisting	consist	VERB
cana-763	10	20	of	of	ADP
cana-763	10	21	functions	function	NOUN
cana-763	10	22	that	that	PRON
cana-763	10	23	are	be	AUX
cana-763	10	24	univalent	univalent	ADJ
cana-763	10	25	in	in	ADP
cana-763	10	26	𝑈.	𝑈.	PROPN
cana-763	10	27	for	for	ADP
cana-763	10	28	𝑓	𝑓	DET
cana-763	10	29	∈	∈	PROPN
cana-763	10	30	𝐴	𝐴	PROPN
cana-763	10	31	given	give	VERB
cana-763	10	32	by	by	ADP
cana-763	10	33	(	(	PUNCT
cana-763	10	34	1.1	1.1	NUM
cana-763	10	35	)	)	PUNCT
cana-763	10	36	and	and	CCONJ
cana-763	10	37	𝑔(𝑧	𝑔(𝑧	NOUN
cana-763	10	38	)	)	PUNCT
cana-763	10	39	given	give	VERB
cana-763	10	40	by	by	ADP
cana-763	10	41	𝑔(𝑧	𝑔(𝑧	NOUN
cana-763	10	42	)	)	PUNCT
cana-763	10	43	=	=	PUNCT
cana-763	11	1	𝑧	𝑧	PROPN
cana-763	12	1	+	+	CCONJ
cana-763	12	2	∑	∑	PROPN
cana-763	12	3	𝑏𝑛	𝑏𝑛	ADP
cana-763	12	4	∞	∞	PROPN
cana-763	12	5	𝑛=2	𝑛=2	PROPN
cana-763	12	6	𝑧𝑛	𝑧𝑛	INTJ
cana-763	12	7	(	(	PUNCT
cana-763	12	8	1.2	1.2	NUM
cana-763	12	9	)	)	PUNCT
cana-763	12	10	their	their	PRON
cana-763	12	11	convolution	convolution	NOUN
cana-763	12	12	(	(	PUNCT
cana-763	12	13	or	or	CCONJ
cana-763	12	14	hadamard	hadamard	ADJ
cana-763	12	15	product	product	NOUN
cana-763	12	16	)	)	PUNCT
cana-763	12	17	,	,	PUNCT
cana-763	12	18	denoted	denote	VERB
cana-763	12	19	by	by	ADP
cana-763	12	20	(	(	PUNCT
cana-763	12	21	𝑓	𝑓	DET
cana-763	12	22	∗	∗	NOUN
cana-763	12	23	𝑔	𝑔	NOUN
cana-763	12	24	)	)	PUNCT
cana-763	12	25	,	,	PUNCT
cana-763	12	26	is	be	AUX
cana-763	12	27	defined	define	VERB
cana-763	12	28	as	as	ADP
cana-763	12	29	(	(	PUNCT
cana-763	12	30	𝑓	𝑓	DET
cana-763	12	31	∗	∗	NOUN
cana-763	12	32	𝑔)(𝑧	𝑔)(𝑧	NOUN
cana-763	12	33	)	)	PUNCT
cana-763	12	34	=	=	SYM
cana-763	13	1	𝑧	𝑧	PROPN
cana-763	14	1	+	+	CCONJ
cana-763	14	2	∑	∑	PROPN
cana-763	14	3	𝑎𝑛	𝑎𝑛	PROPN
cana-763	14	4	∞	∞	NUM
cana-763	14	5	𝑛=2	𝑛=2	NOUN
cana-763	14	6	𝑏𝑛𝑧𝑛	𝑏𝑛𝑧𝑛	NOUN
cana-763	14	7	=	=	PUNCT
cana-763	14	8	(	(	PUNCT
cana-763	14	9	𝑔	𝑔	NOUN
cana-763	14	10	∗	∗	NOUN
cana-763	14	11	𝑓)(𝑧	𝑓)(𝑧	NOUN
cana-763	14	12	)	)	PUNCT
cana-763	14	13	(	(	PUNCT
cana-763	14	14	𝑧	𝑧	PROPN
cana-763	14	15	∈	∈	PROPN
cana-763	14	16	𝑈	𝑈	PROPN
cana-763	14	17	)	)	PUNCT
cana-763	14	18	.	.	PUNCT
cana-763	15	1	(	(	PUNCT
cana-763	15	2	1.3	1.3	NUM
cana-763	15	3	)	)	PUNCT
cana-763	15	4	note	note	VERB
cana-763	15	5	that	that	SCONJ
cana-763	15	6	𝑓	𝑓	DET
cana-763	15	7	∗	∗	NOUN
cana-763	15	8	𝑔	𝑔	PROPN
cana-763	15	9	∈	∈	PROPN
cana-763	15	10	𝐴.	𝐴.	PROPN
cana-763	15	11	a	a	DET
cana-763	15	12	function	function	NOUN
cana-763	15	13	𝑓	𝑓	DET
cana-763	15	14	∈	∈	PROPN
cana-763	15	15	𝐴	𝐴	PROPN
cana-763	15	16	is	be	AUX
cana-763	15	17	said	say	VERB
cana-763	15	18	to	to	PART
cana-763	15	19	be	be	AUX
cana-763	15	20	in	in	ADP
cana-763	15	21	𝑈𝑆(ϱ	𝑈𝑆(ϱ	NOUN
cana-763	15	22	)	)	PUNCT
cana-763	15	23	,	,	PUNCT
cana-763	15	24	the	the	DET
cana-763	15	25	class	class	NOUN
cana-763	15	26	of	of	ADP
cana-763	15	27	uniformly	uniformly	ADJ
cana-763	15	28	starlike	starlike	NOUN
cana-763	15	29	functions	function	NOUN
cana-763	15	30	of	of	ADP
cana-763	15	31	order	order	NOUN
cana-763	15	32	ϱ	ϱ	VERB
cana-763	15	33	,	,	PUNCT
cana-763	15	34	0	0	NUM
cana-763	15	35	≤	≤	NUM
cana-763	15	36	ϱ	ϱ	ADP
cana-763	15	37	<	<	X
cana-763	15	38	1	1	NUM
cana-763	15	39	,	,	PUNCT
cana-763	15	40	if	if	SCONJ
cana-763	15	41	satisfies	satisfy	VERB
cana-763	15	42	the	the	DET
cana-763	15	43	condition	condition	NOUN
cana-763	15	44	communications	communication	NOUN
cana-763	15	45	on	on	ADP
cana-763	15	46	applied	apply	VERB
cana-763	15	47	nonlinear	nonlinear	ADJ
cana-763	15	48	analysis	analysis	NOUN
cana-763	15	49	issn	issn	NOUN
cana-763	15	50	:	:	PUNCT
cana-763	15	51	1074	1074	NUM
cana-763	15	52	-	-	PUNCT
cana-763	15	53	133x	133x	NUM
cana-763	15	54	vol	vol	NOUN
cana-763	15	55	31	31	NUM
cana-763	15	56	no	no	NOUN
cana-763	15	57	.	.	PUNCT
cana-763	16	1	3s	3s	NUM
cana-763	16	2	(	(	PUNCT
cana-763	16	3	2024	2024	NUM
cana-763	16	4	)	)	PUNCT
cana-763	16	5	255	255	NUM
cana-763	16	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-763	16	7	ℜ	ℜ	PROPN
cana-763	16	8	{	{	PUNCT
cana-763	16	9	𝑧𝑓′(𝑧	𝑧𝑓′(𝑧	PROPN
cana-763	16	10	)	)	PUNCT
cana-763	16	11	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	16	12	)	)	PUNCT
cana-763	16	13	}	}	PUNCT
cana-763	16	14	>	>	PUNCT
cana-763	17	1	|	|	ADV
cana-763	17	2	𝑧𝑓′(𝑧	𝑧𝑓′(𝑧	PROPN
cana-763	17	3	)	)	PUNCT
cana-763	17	4	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	17	5	)	)	PUNCT
cana-763	17	6	−	−	NOUN
cana-763	17	7	1|	1|	NUM
cana-763	18	1	+	+	CCONJ
cana-763	18	2	ϱ	ϱ	PROPN
cana-763	18	3	,	,	PUNCT
cana-763	18	4	(	(	PUNCT
cana-763	18	5	1.4	1.4	NUM
cana-763	18	6	)	)	PUNCT
cana-763	18	7	and	and	CCONJ
cana-763	18	8	a	a	DET
cana-763	18	9	function	function	NOUN
cana-763	18	10	𝑓	𝑓	DET
cana-763	18	11	∈	∈	PROPN
cana-763	18	12	𝐴	𝐴	PROPN
cana-763	18	13	is	be	AUX
cana-763	18	14	said	say	VERB
cana-763	18	15	to	to	PART
cana-763	18	16	be	be	AUX
cana-763	18	17	in	in	ADP
cana-763	18	18	𝑈𝐶(ϱ	𝑈𝐶(ϱ	ADJ
cana-763	18	19	)	)	PUNCT
cana-763	18	20	,	,	PUNCT
cana-763	18	21	the	the	DET
cana-763	18	22	class	class	NOUN
cana-763	18	23	of	of	ADP
cana-763	18	24	uniformly	uniformly	ADV
cana-763	18	25	convex	convex	NOUN
cana-763	18	26	functions	function	NOUN
cana-763	18	27	of	of	ADP
cana-763	18	28	order	order	NOUN
cana-763	18	29	ϱ	ϱ	VERB
cana-763	18	30	,	,	PUNCT
cana-763	18	31	0	0	NUM
cana-763	18	32	≤	≤	NUM
cana-763	18	33	ϱ	ϱ	ADP
cana-763	18	34	<	<	X
cana-763	18	35	1	1	NUM
cana-763	18	36	,	,	PUNCT
cana-763	18	37	if	if	SCONJ
cana-763	18	38	satisfies	satisfy	VERB
cana-763	18	39	the	the	DET
cana-763	18	40	condition	condition	NOUN
cana-763	18	41	ℜ	ℜ	X
cana-763	18	42	{	{	PUNCT
cana-763	18	43	1	1	NUM
cana-763	18	44	+	+	NUM
cana-763	18	45	𝑧𝑓″(𝑧	𝑧𝑓″(𝑧	NOUN
cana-763	18	46	)	)	PUNCT
cana-763	18	47	𝑓′(𝑧	𝑓′(𝑧	NOUN
cana-763	18	48	)	)	PUNCT
cana-763	18	49	}	}	PUNCT
cana-763	18	50	>	>	X
cana-763	18	51	|	|	ADV
cana-763	18	52	𝑧𝑓″(𝑧	𝑧𝑓″(𝑧	NOUN
cana-763	18	53	)	)	PUNCT
cana-763	18	54	𝑓′(𝑧	𝑓′(𝑧	NOUN
cana-763	18	55	)	)	PUNCT
cana-763	19	1	|	|	ADV
cana-763	19	2	+	+	NUM
cana-763	19	3	ϱ.	ϱ.	NOUN
cana-763	19	4	(	(	PUNCT
cana-763	19	5	1.5	1.5	NUM
cana-763	19	6	)	)	PUNCT
cana-763	19	7	uniformly	uniformly	ADV
cana-763	19	8	starlike	starlike	NOUN
cana-763	19	9	and	and	CCONJ
cana-763	19	10	uniformly	uniformly	ADV
cana-763	19	11	convex	convex	NOUN
cana-763	19	12	functions	function	NOUN
cana-763	19	13	were	be	AUX
cana-763	19	14	first	first	ADV
cana-763	19	15	introduced	introduce	VERB
cana-763	19	16	by	by	ADP
cana-763	19	17	goodman	goodman	PROPN
cana-763	19	18	[	[	X
cana-763	19	19	8	8	NUM
cana-763	19	20	]	]	PUNCT
cana-763	19	21	and	and	CCONJ
cana-763	19	22	then	then	ADV
cana-763	19	23	studied	study	VERB
cana-763	19	24	by	by	ADP
cana-763	19	25	various	various	ADJ
cana-763	19	26	authors	author	NOUN
cana-763	19	27	.	.	PUNCT
cana-763	20	1	in	in	ADP
cana-763	20	2	,	,	PUNCT
cana-763	20	3	sakaguchi	sakaguchi	ADJ
cana-763	20	4	[	[	X
cana-763	20	5	11	11	NUM
cana-763	20	6	]	]	PUNCT
cana-763	20	7	defined	define	VERB
cana-763	20	8	the	the	DET
cana-763	20	9	class	class	NOUN
cana-763	20	10	𝑆𝑠	𝑆𝑠	PROPN
cana-763	20	11	of	of	ADP
cana-763	20	12	starlike	starlike	NOUN
cana-763	20	13	functions	function	NOUN
cana-763	20	14	with	with	ADP
cana-763	20	15	respect	respect	NOUN
cana-763	20	16	to	to	ADP
cana-763	20	17	symmetric	symmetric	ADJ
cana-763	20	18	points	point	NOUN
cana-763	20	19	as	as	SCONJ
cana-763	20	20	follows	follow	VERB
cana-763	20	21	:	:	PUNCT
cana-763	20	22	let	let	VERB
cana-763	21	1	𝑓	𝑓	DET
cana-763	21	2	∈	∈	NOUN
cana-763	21	3	𝐴.	𝐴.	NOUN
cana-763	21	4	then	then	ADV
cana-763	21	5	𝑓	𝑓	PRON
cana-763	21	6	is	be	AUX
cana-763	21	7	said	say	VERB
cana-763	21	8	to	to	PART
cana-763	21	9	be	be	AUX
cana-763	21	10	starlike	starlike	NOUN
cana-763	21	11	with	with	ADP
cana-763	21	12	respect	respect	NOUN
cana-763	21	13	to	to	ADP
cana-763	21	14	symmetric	symmetric	ADJ
cana-763	21	15	points	point	NOUN
cana-763	21	16	in	in	ADP
cana-763	21	17	𝑈	𝑈	PROPN
cana-763	21	18	if	if	SCONJ
cana-763	22	1	and	and	CCONJ
cana-763	22	2	only	only	ADV
cana-763	22	3	if	if	SCONJ
cana-763	22	4	ℜ	ℜ	X
cana-763	22	5	{	{	PUNCT
cana-763	22	6	2𝑧𝑓′(𝑧	2𝑧𝑓′(𝑧	NUM
cana-763	22	7	)	)	PUNCT
cana-763	22	8	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	22	9	)	)	PUNCT
cana-763	22	10	−	−	NUM
cana-763	22	11	𝑓(−𝑧	𝑓(−𝑧	NOUN
cana-763	22	12	)	)	PUNCT
cana-763	22	13	}	}	PUNCT
cana-763	22	14	>	>	X
cana-763	22	15	0	0	NUM
cana-763	22	16	,	,	PUNCT
cana-763	22	17	(	(	PUNCT
cana-763	22	18	𝑧	𝑧	PROPN
cana-763	22	19	∈	∈	PROPN
cana-763	22	20	𝑈	𝑈	PROPN
cana-763	22	21	)	)	PUNCT
cana-763	22	22	.	.	PUNCT
cana-763	23	1	recently	recently	ADV
cana-763	23	2	,	,	PUNCT
cana-763	23	3	owa	owa	PROPN
cana-763	23	4	et	et	PROPN
cana-763	23	5	al	al	PROPN
cana-763	23	6	.	.	PUNCT
cana-763	24	1	[	[	X
cana-763	24	2	10	10	NUM
cana-763	24	3	]	]	PUNCT
cana-763	24	4	defined	define	VERB
cana-763	24	5	the	the	DET
cana-763	24	6	class	class	NOUN
cana-763	24	7	𝑆𝑠(ς	𝑆𝑠(ς	NOUN
cana-763	24	8	,	,	PUNCT
cana-763	24	9	𝑡	𝑡	NOUN
cana-763	24	10	)	)	PUNCT
cana-763	24	11	as	as	SCONJ
cana-763	24	12	follows	follow	VERB
cana-763	24	13	:	:	PUNCT
cana-763	24	14	ℜ	ℜ	ADJ
cana-763	24	15	{	{	PUNCT
cana-763	24	16	(	(	PUNCT
cana-763	24	17	1	1	NUM
cana-763	24	18	−	−	PROPN
cana-763	24	19	𝑡)𝑧𝑓′(𝑧	𝑡)𝑧𝑓′(𝑧	X
cana-763	24	20	)	)	PUNCT
cana-763	24	21	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	24	22	)	)	PUNCT
cana-763	25	1	−	−	ADP
cana-763	25	2	𝑓(𝑡𝑧	𝑓(𝑡𝑧	NOUN
cana-763	25	3	)	)	PUNCT
cana-763	25	4	}	}	PUNCT
cana-763	25	5	>	>	PUNCT
cana-763	26	1	ς	ς	PROPN
cana-763	26	2	,	,	PUNCT
cana-763	26	3	(	(	PUNCT
cana-763	26	4	𝑧	𝑧	PROPN
cana-763	26	5	∈	∈	PROPN
cana-763	26	6	𝑈	𝑈	PROPN
cana-763	26	7	)	)	PUNCT
cana-763	26	8	,	,	PUNCT
cana-763	26	9	where	where	SCONJ
cana-763	26	10	0	0	NUM
cana-763	26	11	≤	≤	NUM
cana-763	26	12	ς	ς	X
cana-763	26	13	<	<	X
cana-763	26	14	1	1	NUM
cana-763	26	15	,	,	PUNCT
cana-763	26	16	|𝑡|	|𝑡|	ADP
cana-763	26	17	≤	≤	NOUN
cana-763	26	18	1	1	NUM
cana-763	26	19	,	,	PUNCT
cana-763	26	20	𝑡	𝑡	ADP
cana-763	26	21	≠	≠	PROPN
cana-763	26	22	1	1	NUM
cana-763	26	23	.	.	PUNCT
cana-763	26	24	note	note	VERB
cana-763	26	25	that	that	SCONJ
cana-763	26	26	𝑆𝑠(0	𝑆𝑠(0	PROPN
cana-763	26	27	,	,	PUNCT
cana-763	26	28	−1	−1	NOUN
cana-763	26	29	)	)	PUNCT
cana-763	26	30	=	=	SYM
cana-763	27	1	𝑆𝑠	𝑆𝑠	PROPN
cana-763	27	2	and	and	CCONJ
cana-763	27	3	𝑆𝑠(ς	𝑆𝑠(ς	NOUN
cana-763	27	4	,	,	PUNCT
cana-763	27	5	−1	−1	NOUN
cana-763	27	6	)	)	PUNCT
cana-763	27	7	=	=	SYM
cana-763	27	8	𝑆𝑠(ς	𝑆𝑠(ς	VERB
cana-763	27	9	)	)	PUNCT
cana-763	27	10	is	be	AUX
cana-763	27	11	called	call	VERB
cana-763	27	12	sakaguchi	sakaguchi	ADJ
cana-763	27	13	function	function	NOUN
cana-763	27	14	of	of	ADP
cana-763	27	15	order	order	NOUN
cana-763	27	16	ς	ς	NOUN
cana-763	27	17	.	.	PUNCT
cana-763	28	1	in	in	ADP
cana-763	28	2	,	,	PUNCT
cana-763	28	3	darus	darus	NOUN
cana-763	28	4	and	and	CCONJ
cana-763	28	5	faisal	faisal	NOUN
cana-763	28	6	[	[	X
cana-763	28	7	5	5	NUM
cana-763	28	8	]	]	PUNCT
cana-763	28	9	introduced	introduce	VERB
cana-763	28	10	the	the	DET
cana-763	28	11	following	following	ADJ
cana-763	28	12	differential	differential	ADJ
cana-763	28	13	operator	operator	NOUN
cana-763	28	14	.	.	PUNCT
cana-763	29	1	for	for	ADP
cana-763	29	2	a	a	DET
cana-763	29	3	function	function	NOUN
cana-763	29	4	𝑓	𝑓	DET
cana-763	29	5	∈	∈	PROPN
cana-763	29	6	𝐴	𝐴	PROPN
cana-763	29	7	,	,	PUNCT
cana-763	29	8	𝒟℘	𝒟℘	NUM
cana-763	29	9	0	0	PUNCT
cana-763	30	1	(	(	PUNCT
cana-763	30	2	ς	ς	NOUN
cana-763	30	3	,	,	PUNCT
cana-763	30	4	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	30	5	)	)	PUNCT
cana-763	30	6	=	=	SYM
cana-763	30	7	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	30	8	)	)	PUNCT
cana-763	30	9	𝒟℘	𝒟℘	VERB
cana-763	30	10	1	1	NUM
cana-763	30	11	(	(	PUNCT
cana-763	30	12	ς	ς	NOUN
cana-763	30	13	,	,	PUNCT
cana-763	30	14	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	30	15	)	)	PUNCT
cana-763	30	16	=	=	SYM
cana-763	31	1	(	(	PUNCT
cana-763	31	2	ς	ς	PROPN
cana-763	31	3	−	−	PROPN
cana-763	31	4	ℏ	ℏ	PROPN
cana-763	31	5	−	−	PROPN
cana-763	31	6	℘	℘	PROPN
cana-763	31	7	ς	ς	PROPN
cana-763	31	8	)	)	PUNCT
cana-763	31	9	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	31	10	)	)	PUNCT
cana-763	32	1	+	+	CCONJ
cana-763	32	2	(	(	PUNCT
cana-763	32	3	ℏ	ℏ	X
cana-763	32	4	+	+	CCONJ
cana-763	32	5	℘	℘	PROPN
cana-763	32	6	ς	ς	PROPN
cana-763	32	7	)	)	PUNCT
cana-763	32	8	𝑧𝑓′(𝑧	𝑧𝑓′(𝑧	PROPN
cana-763	32	9	)	)	PUNCT
cana-763	32	10	𝒟℘	𝒟℘	VERB
cana-763	32	11	2	2	NUM
cana-763	32	12	(	(	PUNCT
cana-763	32	13	ς	ς	NOUN
cana-763	32	14	,	,	PUNCT
cana-763	32	15	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	33	1	)	)	PUNCT
cana-763	33	2	=	=	SYM
cana-763	33	3	𝒟	𝒟	NOUN
cana-763	33	4	(	(	PUNCT
cana-763	33	5	𝒟℘	𝒟℘	NUM
cana-763	33	6	1	1	NUM
cana-763	33	7	(	(	PUNCT
cana-763	33	8	ς	ς	NOUN
cana-763	33	9	,	,	PUNCT
cana-763	33	10	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	33	11	)	)	PUNCT
cana-763	33	12	)	)	PUNCT
cana-763	33	13	⋮	⋮	NOUN
cana-763	33	14	𝒟℘	𝒟℘	NUM
cana-763	34	1	𝑚(ς	𝑚(ς	NOUN
cana-763	34	2	,	,	PUNCT
cana-763	34	3	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	34	4	)	)	PUNCT
cana-763	34	5	=	=	PUNCT
cana-763	34	6	𝒟℘	𝒟℘	NOUN
cana-763	34	7	(	(	PUNCT
cana-763	34	8	𝒟℘	𝒟℘	NUM
cana-763	34	9	𝑚−1(ς	𝑚−1(ς	PROPN
cana-763	34	10	,	,	PUNCT
cana-763	34	11	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	34	12	)	)	PUNCT
cana-763	34	13	)	)	PUNCT
cana-763	34	14	where	where	SCONJ
cana-763	34	15	ς	ς	NOUN
cana-763	34	16	,	,	PUNCT
cana-763	34	17	ℏ	ℏ	PROPN
cana-763	34	18	,	,	PUNCT
cana-763	34	19	℘	℘	NOUN
cana-763	34	20	≥	≥	NOUN
cana-763	34	21	0	0	NUM
cana-763	34	22	,	,	PUNCT
cana-763	34	23	ς	ς	PROPN
cana-763	34	24	≠	≠	PROPN
cana-763	34	25	0	0	NUM
cana-763	34	26	and	and	CCONJ
cana-763	34	27	𝑚	𝑚	ADP
cana-763	34	28	∈	∈	PROPN
cana-763	34	29	ℕ0	ℕ0	NOUN
cana-763	34	30	=	=	SYM
cana-763	34	31	ℕ	ℕ	PROPN
cana-763	34	32	∪	∪	X
cana-763	34	33	{	{	PUNCT
cana-763	34	34	0	0	NUM
cana-763	34	35	}	}	PUNCT
cana-763	34	36	.	.	PUNCT
cana-763	35	1	if	if	SCONJ
cana-763	35	2	𝑓	𝑓	PRON
cana-763	35	3	is	be	AUX
cana-763	35	4	given	give	VERB
cana-763	35	5	by	by	ADP
cana-763	35	6	(	(	PUNCT
cana-763	35	7	1.1	1.1	NUM
cana-763	35	8	)	)	PUNCT
cana-763	35	9	then	then	ADV
cana-763	35	10	from	from	ADP
cana-763	35	11	the	the	DET
cana-763	35	12	definition	definition	NOUN
cana-763	35	13	of	of	ADP
cana-763	35	14	the	the	DET
cana-763	35	15	operator	operator	NOUN
cana-763	35	16	𝒟℘	𝒟℘	X
cana-763	35	17	𝑚(ς	𝑚(ς	NOUN
cana-763	35	18	,	,	PUNCT
cana-763	35	19	ℏ)𝑓	ℏ)𝑓	PUNCT
cana-763	35	20	it	it	PRON
cana-763	35	21	is	be	AUX
cana-763	35	22	easy	easy	ADJ
cana-763	35	23	to	to	PART
cana-763	35	24	see	see	VERB
cana-763	35	25	that	that	SCONJ
cana-763	35	26	𝒟℘	𝒟℘	ADJ
cana-763	35	27	𝑚(ς	𝑚(ς	NOUN
cana-763	35	28	,	,	PUNCT
cana-763	35	29	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	35	30	)	)	PUNCT
cana-763	35	31	=	=	SYM
cana-763	35	32	𝑧	𝑧	PROPN
cana-763	36	1	+	+	CCONJ
cana-763	36	2	∑	∑	PROPN
cana-763	36	3	𝜙𝑛	𝜙𝑛	PROPN
cana-763	36	4	∞	∞	PROPN
cana-763	36	5	𝑛=2	𝑛=2	PROPN
cana-763	36	6	(	(	PUNCT
cana-763	36	7	ς	ς	PROPN
cana-763	36	8	,	,	PUNCT
cana-763	36	9	ℏ	ℏ	PROPN
cana-763	36	10	,	,	PUNCT
cana-763	36	11	℘	℘	PROPN
cana-763	36	12	,	,	PUNCT
cana-763	36	13	𝑚)𝑎𝑛𝑧𝑛	𝑚)𝑎𝑛𝑧𝑛	NUM
cana-763	36	14	(	(	PUNCT
cana-763	36	15	1.6	1.6	NUM
cana-763	36	16	)	)	PUNCT
cana-763	37	1	where	where	SCONJ
cana-763	37	2	𝜙𝑛(ς	𝜙𝑛(ς	NOUN
cana-763	37	3	,	,	PUNCT
cana-763	37	4	ℏ	ℏ	PROPN
cana-763	37	5	,	,	PUNCT
cana-763	37	6	℘	℘	PROPN
cana-763	37	7	,	,	PUNCT
cana-763	37	8	𝑚	𝑚	NOUN
cana-763	37	9	)	)	PUNCT
cana-763	37	10	=	=	SYM
cana-763	37	11	(	(	PUNCT
cana-763	37	12	ς+(ℏ+℘)(𝑛−1	ς+(ℏ+℘)(𝑛−1	NOUN
cana-763	37	13	)	)	PUNCT
cana-763	37	14	ς	ς	PROPN
cana-763	37	15	)	)	PUNCT
cana-763	37	16	𝑚	𝑚	PROPN
cana-763	37	17	(	(	PUNCT
cana-763	37	18	1.7	1.7	NUM
cana-763	37	19	)	)	PUNCT
cana-763	37	20	communications	communication	NOUN
cana-763	37	21	on	on	ADP
cana-763	37	22	applied	apply	VERB
cana-763	37	23	nonlinear	nonlinear	ADJ
cana-763	37	24	analysis	analysis	NOUN
cana-763	37	25	issn	issn	NOUN
cana-763	37	26	:	:	PUNCT
cana-763	37	27	1074	1074	NUM
cana-763	37	28	-	-	PUNCT
cana-763	37	29	133x	133x	NUM
cana-763	37	30	vol	vol	NOUN
cana-763	37	31	31	31	NUM
cana-763	37	32	no	no	NOUN
cana-763	38	1	.	.	PUNCT
cana-763	39	1	3s	3s	NUM
cana-763	39	2	(	(	PUNCT
cana-763	39	3	2024	2024	NUM
cana-763	39	4	)	)	PUNCT
cana-763	39	5	256	256	NUM
cana-763	39	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-763	39	7	by	by	ADP
cana-763	39	8	specializing	specialize	VERB
cana-763	39	9	the	the	DET
cana-763	39	10	parameters	parameter	NOUN
cana-763	39	11	of	of	ADP
cana-763	39	12	𝒟℘	𝒟℘	X
cana-763	39	13	𝑚(ς	𝑚(ς	NOUN
cana-763	39	14	,	,	PUNCT
cana-763	39	15	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	39	16	)	)	PUNCT
cana-763	39	17	,	,	PUNCT
cana-763	39	18	we	we	PRON
cana-763	39	19	get	get	VERB
cana-763	39	20	the	the	DET
cana-763	39	21	following	follow	VERB
cana-763	39	22	differential	differential	ADJ
cana-763	39	23	operators	operator	NOUN
cana-763	39	24	.	.	PUNCT
cana-763	40	1	if	if	SCONJ
cana-763	40	2	we	we	PRON
cana-763	40	3	substitute	substitute	VERB
cana-763	40	4	(	(	PUNCT
cana-763	40	5	i	i	NOUN
cana-763	40	6	)	)	PUNCT
cana-763	40	7	ς	ς	PROPN
cana-763	40	8	=	=	SYM
cana-763	40	9	1and	1and	NUM
cana-763	40	10	ℏ	ℏ	PROPN
cana-763	40	11	=	=	SYM
cana-763	40	12	0	0	NUM
cana-763	40	13	,	,	PUNCT
cana-763	40	14	we	we	PRON
cana-763	40	15	get	get	VERB
cana-763	40	16	𝒟𝑚𝑓(𝑧	𝒟𝑚𝑓(𝑧	PUNCT
cana-763	40	17	)	)	PUNCT
cana-763	40	18	=	=	SYM
cana-763	41	1	𝑧	𝑧	PROPN
cana-763	42	1	+	+	NOUN
cana-763	42	2	∑	∑	PUNCT
cana-763	42	3	(	(	PUNCT
cana-763	42	4	1	1	NUM
cana-763	42	5	+	+	NUM
cana-763	42	6	℘(𝑛	℘(𝑛	NOUN
cana-763	42	7	−	−	NOUN
cana-763	42	8	1	1	NUM
cana-763	42	9	)	)	PUNCT
cana-763	42	10	)	)	PUNCT
cana-763	42	11	𝑚∞	𝑚∞	PROPN
cana-763	43	1	𝑛=2	𝑛=2	PROPN
cana-763	43	2	𝑎𝑛𝑧𝑛	𝑎𝑛𝑧𝑛	ADJ
cana-763	43	3	oof	oof	PROPN
cana-763	43	4	differential	differential	NOUN
cana-763	43	5	operator	operator	NOUN
cana-763	43	6	given	give	VERB
cana-763	43	7	by	by	ADP
cana-763	43	8	al	al	PROPN
cana-763	43	9	-	-	PUNCT
cana-763	43	10	oboudi	oboudi	NOUN
cana-763	43	11	[	[	X
cana-763	43	12	1	1	NUM
cana-763	43	13	]	]	PUNCT
cana-763	43	14	.	.	PUNCT
cana-763	44	1	(	(	PUNCT
cana-763	44	2	ii	ii	NOUN
cana-763	44	3	)	)	PUNCT
cana-763	44	4	ς	ς	PROPN
cana-763	44	5	=	=	SYM
cana-763	44	6	1	1	NUM
cana-763	44	7	,	,	PUNCT
cana-763	44	8	ℏ	ℏ	PROPN
cana-763	44	9	=	=	SYM
cana-763	44	10	0	0	NUM
cana-763	44	11	and	and	CCONJ
cana-763	44	12	℘	℘	NUM
cana-763	44	13	=	=	SYM
cana-763	44	14	1	1	NUM
cana-763	44	15	,	,	PUNCT
cana-763	44	16	we	we	PRON
cana-763	44	17	get	get	VERB
cana-763	44	18	𝒟𝑚𝑓(𝑧	𝒟𝑚𝑓(𝑧	PUNCT
cana-763	44	19	)	)	PUNCT
cana-763	45	1	=	=	SYM
cana-763	45	2	𝑧	𝑧	PROPN
cana-763	46	1	+	+	X
cana-763	46	2	∑	∑	PROPN
cana-763	46	3	(	(	PUNCT
cana-763	46	4	𝑛)𝑚∞	𝑛)𝑚∞	PROPN
cana-763	46	5	𝑛=2	𝑛=2	PROPN
cana-763	46	6	𝑎𝑛𝑧𝑛	𝑎𝑛𝑧𝑛	NOUN
cana-763	46	7	of	of	ADP
cana-763	46	8	salagean	salagean	ADJ
cana-763	46	9	differential	differential	NOUN
cana-763	46	10	operator[12	operator[12	PROPN
cana-763	46	11	]	]	PUNCT
cana-763	46	12	.	.	PUNCT
cana-763	47	1	now	now	ADV
cana-763	47	2	,	,	PUNCT
cana-763	47	3	by	by	ADP
cana-763	47	4	making	make	VERB
cana-763	47	5	use	use	NOUN
cana-763	47	6	of	of	ADP
cana-763	47	7	the	the	DET
cana-763	47	8	differential	differential	ADJ
cana-763	47	9	operator	operator	NOUN
cana-763	47	10	𝒟℘	𝒟℘	X
cana-763	47	11	𝑚(ς	𝑚(ς	NOUN
cana-763	47	12	,	,	PUNCT
cana-763	47	13	ℏ)𝑓	ℏ)𝑓	PUNCT
cana-763	47	14	,	,	PUNCT
cana-763	47	15	we	we	PRON
cana-763	47	16	define	define	VERB
cana-763	47	17	a	a	DET
cana-763	47	18	new	new	ADJ
cana-763	47	19	subclass	subclass	NOUN
cana-763	47	20	of	of	ADP
cana-763	47	21	functions	function	NOUN
cana-763	47	22	belonging	belong	VERB
cana-763	47	23	to	to	ADP
cana-763	47	24	the	the	DET
cana-763	47	25	class	class	NOUN
cana-763	47	26	𝐴.	𝐴.	PROPN
cana-763	47	27	definition	definition	NOUN
cana-763	47	28	1	1	NUM
cana-763	47	29	.	.	PUNCT
cana-763	48	1	a	a	DET
cana-763	48	2	function	function	NOUN
cana-763	48	3	𝑓	𝑓	DET
cana-763	48	4	∈	∈	PROPN
cana-763	48	5	𝐴	𝐴	PROPN
cana-763	48	6	is	be	AUX
cana-763	48	7	said	say	VERB
cana-763	48	8	to	to	PART
cana-763	48	9	be	be	AUX
cana-763	48	10	in	in	ADP
cana-763	48	11	the	the	DET
cana-763	48	12	class	class	NOUN
cana-763	48	13	𝛩𝑆𝑠	𝛩𝑆𝑠	X
cana-763	48	14	𝑚(ς	𝑚(ς	NOUN
cana-763	48	15	,	,	PUNCT
cana-763	48	16	ℏ	ℏ	PROPN
cana-763	48	17	,	,	PUNCT
cana-763	48	18	℘	℘	PROPN
cana-763	48	19	,	,	PUNCT
cana-763	48	20	ϱ	ϱ	NOUN
cana-763	48	21	,	,	PUNCT
cana-763	48	22	𝑡	𝑡	NOUN
cana-763	48	23	)	)	PUNCT
cana-763	48	24	if	if	SCONJ
cana-763	48	25	for	for	ADP
cana-763	48	26	all	all	DET
cana-763	48	27	𝑧	𝑧	DET
cana-763	48	28	∈	∈	PROPN
cana-763	48	29	𝑈	𝑈	PROPN
cana-763	48	30	ℜ	ℜ	PROPN
cana-763	48	31	{	{	PUNCT
cana-763	48	32	(	(	PUNCT
cana-763	48	33	1	1	NUM
cana-763	48	34	−	−	NOUN
cana-763	48	35	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	48	36	(	(	PUNCT
cana-763	48	37	𝒟℘	𝒟℘	X
cana-763	48	38	𝑚(ς	𝑚(ς	NOUN
cana-763	48	39	,	,	PUNCT
cana-763	48	40	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	48	41	)	)	PUNCT
cana-763	48	42	)	)	PUNCT
cana-763	48	43	′	′	NUM
cana-763	49	1	𝒟℘	𝒟℘	NUM
cana-763	49	2	𝑚(ς	𝑚(ς	NOUN
cana-763	49	3	,	,	PUNCT
cana-763	49	4	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	49	5	)	)	PUNCT
cana-763	49	6	−	−	NOUN
cana-763	49	7	𝒟℘	𝒟℘	NUM
cana-763	49	8	𝑚(ς	𝑚(ς	NOUN
cana-763	49	9	,	,	PUNCT
cana-763	49	10	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	49	11	)	)	PUNCT
cana-763	49	12	}	}	PUNCT
cana-763	49	13	≥	≥	NUM
cana-763	50	1	|	|	ADV
cana-763	50	2	(	(	PUNCT
cana-763	50	3	1	1	NUM
cana-763	50	4	−	−	PROPN
cana-763	50	5	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	50	6	(	(	PUNCT
cana-763	50	7	𝒟℘	𝒟℘	X
cana-763	50	8	𝑚(ς	𝑚(ς	NOUN
cana-763	50	9	,	,	PUNCT
cana-763	50	10	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	50	11	)	)	PUNCT
cana-763	50	12	)	)	PUNCT
cana-763	50	13	′	′	NUM
cana-763	50	14	𝒟℘	𝒟℘	NUM
cana-763	51	1	𝑚(ς	𝑚(ς	NOUN
cana-763	51	2	,	,	PUNCT
cana-763	51	3	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	51	4	)	)	PUNCT
cana-763	51	5	−	−	NOUN
cana-763	51	6	𝒟℘	𝒟℘	NUM
cana-763	51	7	𝑚(ς	𝑚(ς	NOUN
cana-763	51	8	,	,	PUNCT
cana-763	51	9	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	51	10	)	)	PUNCT
cana-763	51	11	−	−	ADP
cana-763	51	12	1|	1|	NUM
cana-763	52	1	+	+	CCONJ
cana-763	52	2	ϱ	ϱ	VERB
cana-763	52	3	,	,	PUNCT
cana-763	52	4	for	for	ADP
cana-763	52	5	℘	℘	NUM
cana-763	52	6	≥	≥	NOUN
cana-763	52	7	0	0	NUM
cana-763	52	8	,	,	PUNCT
cana-763	52	9	𝑚	𝑚	PROPN
cana-763	52	10	,	,	PUNCT
cana-763	52	11	|𝑡|	|𝑡|	ADP
cana-763	52	12	≤	≤	NOUN
cana-763	52	13	1	1	NUM
cana-763	52	14	,	,	PUNCT
cana-763	52	15	𝑡	𝑡	ADP
cana-763	52	16	≠	≠	PROPN
cana-763	52	17	1,0	1,0	NUM
cana-763	52	18	≤	≤	NUM
cana-763	52	19	ϱ	ϱ	ADP
cana-763	52	20	<	<	X
cana-763	52	21	1	1	NUM
cana-763	52	22	.	.	PUNCT
cana-763	53	1	furthermore	furthermore	ADV
cana-763	53	2	,	,	PUNCT
cana-763	53	3	we	we	PRON
cana-763	53	4	say	say	VERB
cana-763	53	5	that	that	SCONJ
cana-763	53	6	a	a	DET
cana-763	53	7	function	function	NOUN
cana-763	53	8	𝑓	𝑓	DET
cana-763	53	9	∈	∈	PROPN
cana-763	53	10	𝑈𝑆𝑠	𝑈𝑆𝑠	NOUN
cana-763	53	11	𝑚(ς	𝑚(ς	NOUN
cana-763	53	12	,	,	PUNCT
cana-763	53	13	ℏ	ℏ	PROPN
cana-763	53	14	,	,	PUNCT
cana-763	53	15	℘	℘	PROPN
cana-763	53	16	,	,	PUNCT
cana-763	53	17	ϱ	ϱ	NOUN
cana-763	53	18	,	,	PUNCT
cana-763	53	19	𝑡	𝑡	NOUN
cana-763	53	20	)	)	PUNCT
cana-763	53	21	is	be	AUX
cana-763	53	22	in	in	ADP
cana-763	53	23	the	the	DET
cana-763	53	24	subclass	subclass	PROPN
cana-763	53	25	�	�	PROPN
cana-763	53	26	̃	̃	PROPN
cana-763	53	27	�	�	PROPN
cana-763	53	28	𝑆𝑠	𝑆𝑠	PROPN
cana-763	53	29	𝑚(ς	𝑚(ς	NOUN
cana-763	53	30	,	,	PUNCT
cana-763	53	31	ℏ	ℏ	PROPN
cana-763	53	32	,	,	PUNCT
cana-763	53	33	℘	℘	PROPN
cana-763	53	34	,	,	PUNCT
cana-763	53	35	ϱ	ϱ	NOUN
cana-763	53	36	,	,	PUNCT
cana-763	53	37	𝑡	𝑡	NOUN
cana-763	53	38	)	)	PUNCT
cana-763	53	39	if	if	SCONJ
cana-763	53	40	𝑓(𝑧	𝑓(𝑧	NOUN
cana-763	53	41	)	)	PUNCT
cana-763	53	42	is	be	AUX
cana-763	53	43	of	of	ADP
cana-763	53	44	the	the	DET
cana-763	53	45	following	follow	VERB
cana-763	53	46	form	form	NOUN
cana-763	53	47	𝑓(𝑧	𝑓(𝑧	NUM
cana-763	53	48	)	)	PUNCT
cana-763	53	49	=	=	SYM
cana-763	53	50	𝑧	𝑧	PRON
cana-763	53	51	−	−	NOUN
cana-763	53	52	∑	∑	PROPN
cana-763	53	53	𝑎𝑛	𝑎𝑛	PROPN
cana-763	53	54	∞	∞	PROPN
cana-763	53	55	𝑛=2	𝑛=2	PROPN
cana-763	53	56	𝑧𝑛	𝑧𝑛	NOUN
cana-763	53	57	,	,	PUNCT
cana-763	53	58	𝑎𝑛	𝑎𝑛	PROPN
cana-763	53	59	≥	≥	NOUN
cana-763	53	60	0	0	NUM
cana-763	53	61	,	,	PUNCT
cana-763	53	62	𝑛	𝑛	DET
cana-763	53	63	∈	∈	PROPN
cana-763	53	64	ℕ	ℕ	PROPN
cana-763	53	65	,	,	PUNCT
cana-763	53	66	𝑧	𝑧	PRON
cana-763	53	67	∈	∈	PROPN
cana-763	53	68	𝑈.	𝑈.	NOUN
cana-763	53	69	(	(	PUNCT
cana-763	53	70	1.8	1.8	NUM
cana-763	53	71	)	)	PUNCT
cana-763	53	72	the	the	DET
cana-763	53	73	aim	aim	NOUN
cana-763	53	74	of	of	ADP
cana-763	53	75	the	the	DET
cana-763	53	76	present	present	ADJ
cana-763	53	77	paper	paper	NOUN
cana-763	53	78	is	be	AUX
cana-763	53	79	to	to	PART
cana-763	53	80	study	study	VERB
cana-763	53	81	the	the	DET
cana-763	53	82	coefficient	coefficient	NOUN
cana-763	53	83	bounds	bound	NOUN
cana-763	53	84	,	,	PUNCT
cana-763	53	85	partial	partial	ADJ
cana-763	53	86	sums	sum	NOUN
cana-763	53	87	and	and	CCONJ
cana-763	53	88	certain	certain	ADJ
cana-763	53	89	neighborhood	neighborhood	NOUN
cana-763	53	90	results	result	NOUN
cana-763	53	91	of	of	ADP
cana-763	53	92	the	the	DET
cana-763	53	93	class	class	NOUN
cana-763	53	94	�	�	PROPN
cana-763	53	95	̃	̃	PROPN
cana-763	53	96	�	�	PROPN
cana-763	53	97	𝑆𝑠	𝑆𝑠	PROPN
cana-763	53	98	𝑚(ς	𝑚(ς	NOUN
cana-763	53	99	,	,	PUNCT
cana-763	53	100	ℏ	ℏ	PROPN
cana-763	53	101	,	,	PUNCT
cana-763	53	102	℘	℘	PROPN
cana-763	53	103	,	,	PUNCT
cana-763	53	104	ϱ	ϱ	NOUN
cana-763	53	105	,	,	PUNCT
cana-763	53	106	𝑡	𝑡	NOUN
cana-763	53	107	)	)	PUNCT
cana-763	53	108	.	.	PUNCT
cana-763	54	1	firstly	firstly	ADV
cana-763	54	2	,	,	PUNCT
cana-763	54	3	we	we	PRON
cana-763	54	4	shall	shall	AUX
cana-763	54	5	need	need	VERB
cana-763	54	6	the	the	DET
cana-763	54	7	following	follow	VERB
cana-763	54	8	lemmas	lemmas	NOUN
cana-763	54	9	.	.	PUNCT
cana-763	55	1	lemma	lemma	PROPN
cana-763	55	2	2	2	X
cana-763	55	3	.	.	PUNCT
cana-763	56	1	let	let	VERB
cana-763	56	2	𝑤	𝑤	ADP
cana-763	56	3	=	=	SYM
cana-763	56	4	𝑢	𝑢	X
cana-763	56	5	+	+	X
cana-763	56	6	𝑖𝑣.	𝑖𝑣.	NOUN
cana-763	56	7	then	then	ADV
cana-763	56	8	ℜ	ℜ	PROPN
cana-763	56	9	(	(	PUNCT
cana-763	56	10	𝑤	𝑤	NOUN
cana-763	56	11	)	)	PUNCT
cana-763	56	12	≥	≥	NOUN
cana-763	56	13	𝛽	𝛽	NOUN
cana-763	56	14	if	if	SCONJ
cana-763	57	1	and	and	CCONJ
cana-763	57	2	only	only	ADV
cana-763	57	3	if	if	SCONJ
cana-763	57	4	|𝑤	|𝑤	PRON
cana-763	57	5	−	−	PROPN
cana-763	57	6	(	(	PUNCT
cana-763	57	7	1	1	NUM
cana-763	57	8	+	+	CCONJ
cana-763	57	9	𝛽)|	𝛽)|	NOUN
cana-763	57	10	≤	≤	NUM
cana-763	57	11	|𝑤	|𝑤	X
cana-763	58	1	+	+	CCONJ
cana-763	59	1	(	(	PUNCT
cana-763	59	2	1	1	NUM
cana-763	59	3	−	−	PROPN
cana-763	59	4	ς)|	ς)|	NOUN
cana-763	59	5	.	.	PUNCT
cana-763	60	1	lemma	lemma	PROPN
cana-763	60	2	3	3	X
cana-763	60	3	.	.	PUNCT
cana-763	61	1	let	let	VERB
cana-763	61	2	𝑤	𝑤	ADP
cana-763	61	3	=	=	SYM
cana-763	61	4	𝑢	𝑢	NOUN
cana-763	62	1	+	+	X
cana-763	62	2	𝑖𝑣	𝑖𝑣	ADJ
cana-763	62	3	and	and	CCONJ
cana-763	62	4	ς	ς	PROPN
cana-763	62	5	,	,	PUNCT
cana-763	62	6	ϱ	ϱ	NOUN
cana-763	62	7	be	be	VERB
cana-763	62	8	real	real	ADJ
cana-763	62	9	numbers	number	NOUN
cana-763	62	10	.	.	PUNCT
cana-763	63	1	then	then	ADV
cana-763	63	2	ℜ	ℜ	PROPN
cana-763	63	3	(	(	PUNCT
cana-763	63	4	𝑤	𝑤	ADP
cana-763	63	5	)	)	PUNCT
cana-763	63	6	>	>	X
cana-763	63	7	𝛽|𝑤	𝛽|𝑤	PUNCT
cana-763	64	1	−	−	X
cana-763	64	2	1|	1|	NUM
cana-763	65	1	+	+	CCONJ
cana-763	65	2	ϱ	ϱ	VERB
cana-763	65	3	if	if	SCONJ
cana-763	65	4	and	and	CCONJ
cana-763	65	5	only	only	ADV
cana-763	65	6	if	if	SCONJ
cana-763	65	7	ℜ{𝑤(1	ℜ{𝑤(1	NOUN
cana-763	65	8	+	+	SYM
cana-763	65	9	𝛽𝑒𝑖𝜃	𝛽𝑒𝑖𝜃	NOUN
cana-763	65	10	)	)	PUNCT
cana-763	65	11	−	−	PROPN
cana-763	65	12	𝛽𝑒𝑖𝜃	𝛽𝑒𝑖𝜃	PROPN
cana-763	65	13	}	}	PUNCT
cana-763	65	14	>	>	PUNCT
cana-763	65	15	ϱ	ϱ	ADP
cana-763	65	16	2	2	NUM
cana-763	65	17	coefficient	coefficient	NOUN
cana-763	65	18	bounds	bound	NOUN
cana-763	65	19	theorem	theorem	VERB
cana-763	65	20	4	4	NUM
cana-763	65	21	.	.	PUNCT
cana-763	66	1	the	the	DET
cana-763	66	2	function	function	NOUN
cana-763	66	3	𝑓	𝑓	PRON
cana-763	66	4	defined	define	VERB
cana-763	66	5	by	by	ADP
cana-763	66	6	(	(	PUNCT
cana-763	66	7	1.8	1.8	NUM
cana-763	66	8	)	)	PUNCT
cana-763	66	9	is	be	AUX
cana-763	66	10	in	in	ADP
cana-763	66	11	the	the	DET
cana-763	66	12	class	class	NOUN
cana-763	66	13	�	�	PROPN
cana-763	66	14	̃	̃	PROPN
cana-763	66	15	�	�	PROPN
cana-763	66	16	𝑆𝑠	𝑆𝑠	PROPN
cana-763	66	17	𝑚(ς	𝑚(ς	NOUN
cana-763	66	18	,	,	PUNCT
cana-763	66	19	ℏ	ℏ	PROPN
cana-763	66	20	,	,	PUNCT
cana-763	66	21	℘	℘	PROPN
cana-763	66	22	,	,	PUNCT
cana-763	66	23	ϱ	ϱ	NOUN
cana-763	66	24	,	,	PUNCT
cana-763	66	25	𝑡	𝑡	NOUN
cana-763	66	26	)	)	PUNCT
cana-763	66	27	if	if	SCONJ
cana-763	66	28	and	and	CCONJ
cana-763	66	29	only	only	ADV
cana-763	66	30	if	if	SCONJ
cana-763	66	31	∑	∑	PROPN
cana-763	66	32	𝜙𝑛	𝜙𝑛	PROPN
cana-763	66	33	∞	∞	PROPN
cana-763	66	34	𝑛=2	𝑛=2	PROPN
cana-763	66	35	(	(	PUNCT
cana-763	66	36	ς	ς	PROPN
cana-763	66	37	,	,	PUNCT
cana-763	66	38	ℏ	ℏ	PROPN
cana-763	66	39	,	,	PUNCT
cana-763	66	40	℘	℘	NOUN
cana-763	66	41	,	,	PUNCT
cana-763	66	42	𝑚)|2𝑛	𝑚)|2𝑛	NOUN
cana-763	66	43	−	−	NOUN
cana-763	66	44	𝑢𝑛(1	𝑢𝑛(1	NOUN
cana-763	66	45	+	+	CCONJ
cana-763	66	46	ϱ)|𝑎𝑛	ϱ)|𝑎𝑛	VERB
cana-763	66	47	≤	≤	NOUN
cana-763	66	48	1	1	NUM
cana-763	66	49	−	−	NOUN
cana-763	66	50	ϱ	ϱ	PROPN
cana-763	66	51	,	,	PUNCT
cana-763	66	52	(	(	PUNCT
cana-763	66	53	2.1	2.1	NUM
cana-763	66	54	)	)	PUNCT
cana-763	66	55	where	where	SCONJ
cana-763	66	56	℘	℘	PROPN
cana-763	66	57	≥	≥	NOUN
cana-763	66	58	0	0	NUM
cana-763	66	59	,	,	PUNCT
cana-763	66	60	𝑚	𝑚	PROPN
cana-763	66	61	,	,	PUNCT
cana-763	66	62	𝑘	𝑘	PRON
cana-763	66	63	≥	≥	NOUN
cana-763	66	64	0	0	NUM
cana-763	66	65	,	,	PUNCT
cana-763	66	66	|𝑡|	|𝑡|	ADP
cana-763	66	67	≤	≤	NOUN
cana-763	66	68	1	1	NUM
cana-763	66	69	,	,	PUNCT
cana-763	66	70	𝑡	𝑡	ADP
cana-763	66	71	≠	≠	PROPN
cana-763	66	72	1,0	1,0	NUM
cana-763	66	73	≤	≤	NUM
cana-763	66	74	ϱ	ϱ	ADP
cana-763	66	75	<	<	X
cana-763	66	76	1	1	NUM
cana-763	66	77	and	and	CCONJ
cana-763	66	78	𝑢𝑛	𝑢𝑛	NOUN
cana-763	66	79	=	=	SYM
cana-763	66	80	1	1	NUM
cana-763	66	81	+	+	NUM
cana-763	66	82	𝑡	𝑡	PROPN
cana-763	66	83	+	+	PROPN
cana-763	66	84	⋯	⋯	PROPN
cana-763	66	85	+	+	CCONJ
cana-763	66	86	𝑡𝑛−1	𝑡𝑛−1	NOUN
cana-763	66	87	.	.	PUNCT
cana-763	67	1	the	the	DET
cana-763	67	2	result	result	NOUN
cana-763	67	3	is	be	AUX
cana-763	67	4	sharp	sharp	ADJ
cana-763	67	5	for	for	ADP
cana-763	67	6	the	the	DET
cana-763	67	7	function	function	NOUN
cana-763	67	8	𝑓(𝑧	𝑓(𝑧	ADV
cana-763	67	9	)	)	PUNCT
cana-763	67	10	given	give	VERB
cana-763	67	11	by	by	ADP
cana-763	67	12	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	67	13	)	)	PUNCT
cana-763	67	14	=	=	PUNCT
cana-763	68	1	𝑧	𝑧	PRON
cana-763	68	2	−	−	PROPN
cana-763	68	3	1−ϱ	1−ϱ	NUM
cana-763	68	4	𝜙𝑛(ς,ℏ,℘,𝑚)|2𝑛−𝑢𝑛(1+ϱ)|	𝜙𝑛(ς,ℏ,℘,𝑚)|2𝑛−𝑢𝑛(1+ϱ)|	PRON
cana-763	68	5	𝑧𝑛.	𝑧𝑛.	ADJ
cana-763	68	6	proof	proof	NOUN
cana-763	68	7	.	.	PUNCT
cana-763	69	1	by	by	ADP
cana-763	69	2	definition	definition	NOUN
cana-763	69	3	1	1	NUM
cana-763	69	4	,	,	PUNCT
cana-763	69	5	we	we	PRON
cana-763	69	6	get	get	VERB
cana-763	69	7	ℜ	ℜ	PROPN
cana-763	69	8	{	{	PUNCT
cana-763	69	9	(	(	PUNCT
cana-763	69	10	1	1	NUM
cana-763	69	11	−	−	NOUN
cana-763	69	12	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	69	13	(	(	PUNCT
cana-763	69	14	𝒟℘	𝒟℘	X
cana-763	69	15	𝑚(ς	𝑚(ς	NOUN
cana-763	69	16	,	,	PUNCT
cana-763	69	17	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	69	18	)	)	PUNCT
cana-763	69	19	)	)	PUNCT
cana-763	70	1	′	′	NUM
cana-763	70	2	𝒟℘	𝒟℘	NUM
cana-763	71	1	𝑚(ς	𝑚(ς	NOUN
cana-763	71	2	,	,	PUNCT
cana-763	71	3	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	71	4	)	)	PUNCT
cana-763	71	5	−	−	NOUN
cana-763	71	6	𝒟℘	𝒟℘	NUM
cana-763	71	7	𝑚(ς	𝑚(ς	NOUN
cana-763	71	8	,	,	PUNCT
cana-763	71	9	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	71	10	)	)	PUNCT
cana-763	71	11	}	}	PUNCT
cana-763	71	12	≥	≥	NUM
cana-763	72	1	|	|	ADV
cana-763	72	2	(	(	PUNCT
cana-763	72	3	1	1	NUM
cana-763	72	4	−	−	PROPN
cana-763	72	5	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	72	6	(	(	PUNCT
cana-763	72	7	𝒟℘	𝒟℘	X
cana-763	72	8	𝑚(ς	𝑚(ς	NOUN
cana-763	72	9	,	,	PUNCT
cana-763	72	10	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	72	11	)	)	PUNCT
cana-763	72	12	)	)	PUNCT
cana-763	72	13	′	′	NUM
cana-763	72	14	𝒟℘	𝒟℘	NUM
cana-763	73	1	𝑚(ς	𝑚(ς	NOUN
cana-763	73	2	,	,	PUNCT
cana-763	73	3	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	73	4	)	)	PUNCT
cana-763	73	5	−	−	NOUN
cana-763	73	6	𝒟℘	𝒟℘	NUM
cana-763	73	7	𝑚(ς	𝑚(ς	NOUN
cana-763	73	8	,	,	PUNCT
cana-763	73	9	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	73	10	)	)	PUNCT
cana-763	73	11	−	−	ADP
cana-763	74	1	1|	1|	NUM
cana-763	75	1	+	+	NUM
cana-763	75	2	ϱ.	ϱ.	NOUN
cana-763	75	3	communications	communication	NOUN
cana-763	75	4	on	on	ADP
cana-763	75	5	applied	apply	VERB
cana-763	75	6	nonlinear	nonlinear	ADJ
cana-763	75	7	analysis	analysis	NOUN
cana-763	75	8	issn	issn	NOUN
cana-763	75	9	:	:	PUNCT
cana-763	75	10	1074	1074	NUM
cana-763	75	11	-	-	PUNCT
cana-763	75	12	133x	133x	NUM
cana-763	75	13	vol	vol	NOUN
cana-763	75	14	31	31	NUM
cana-763	75	15	no	no	NOUN
cana-763	75	16	.	.	PUNCT
cana-763	76	1	3s	3s	NUM
cana-763	76	2	(	(	PUNCT
cana-763	76	3	2024	2024	NUM
cana-763	76	4	)	)	PUNCT
cana-763	76	5	257	257	NUM
cana-763	76	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-763	76	7	then	then	ADV
cana-763	76	8	by	by	ADP
cana-763	76	9	lemma	lemma	PROPN
cana-763	76	10	3	3	NUM
cana-763	76	11	,	,	PUNCT
cana-763	76	12	we	we	PRON
cana-763	76	13	have	have	VERB
cana-763	76	14	ℜ	ℜ	PROPN
cana-763	76	15	{	{	PUNCT
cana-763	76	16	(	(	PUNCT
cana-763	76	17	1	1	NUM
cana-763	76	18	−	−	NOUN
cana-763	76	19	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	76	20	(	(	PUNCT
cana-763	76	21	𝒟℘	𝒟℘	X
cana-763	76	22	𝑚(ς	𝑚(ς	NOUN
cana-763	76	23	,	,	PUNCT
cana-763	76	24	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	76	25	)	)	PUNCT
cana-763	76	26	)	)	PUNCT
cana-763	76	27	′	′	NUM
cana-763	77	1	𝒟℘	𝒟℘	NUM
cana-763	77	2	𝑚(ς	𝑚(ς	NOUN
cana-763	77	3	,	,	PUNCT
cana-763	77	4	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	77	5	)	)	PUNCT
cana-763	77	6	−	−	NOUN
cana-763	77	7	𝒟℘	𝒟℘	NUM
cana-763	77	8	𝑚(ς	𝑚(ς	NOUN
cana-763	77	9	,	,	PUNCT
cana-763	77	10	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	77	11	)	)	PUNCT
cana-763	77	12	(	(	PUNCT
cana-763	77	13	1	1	NUM
cana-763	77	14	+	+	NUM
cana-763	77	15	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	77	16	)	)	PUNCT
cana-763	77	17	−	−	PROPN
cana-763	77	18	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	77	19	}	}	PUNCT
cana-763	77	20	≥	≥	X
cana-763	77	21	ϱ	ϱ	PROPN
cana-763	77	22	,	,	PUNCT
cana-763	77	23	−𝜋	−𝜋	ADJ
cana-763	77	24	<	<	X
cana-763	77	25	𝜃	𝜃	X
cana-763	77	26	≤	≤	NUM
cana-763	77	27	𝜋	𝜋	NOUN
cana-763	77	28	or	or	CCONJ
cana-763	77	29	equivalently	equivalently	ADV
cana-763	77	30	ℜ	ℜ	PROPN
cana-763	77	31	{	{	PUNCT
cana-763	77	32	(	(	PUNCT
cana-763	77	33	1	1	NUM
cana-763	77	34	−	−	NOUN
cana-763	77	35	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	77	36	(	(	PUNCT
cana-763	77	37	𝒟℘	𝒟℘	X
cana-763	77	38	𝑚(ς	𝑚(ς	NOUN
cana-763	77	39	,	,	PUNCT
cana-763	77	40	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	77	41	)	)	PUNCT
cana-763	77	42	)	)	PUNCT
cana-763	78	1	′(1	′(1	PROPN
cana-763	78	2	+	+	CCONJ
cana-763	78	3	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	78	4	)	)	PUNCT
cana-763	78	5	𝒟℘	𝒟℘	PART
cana-763	78	6	𝑚(ς	𝑚(ς	NOUN
cana-763	78	7	,	,	PUNCT
cana-763	78	8	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	78	9	)	)	PUNCT
cana-763	79	1	−	−	NOUN
cana-763	79	2	𝒟℘	𝒟℘	NUM
cana-763	79	3	𝑚(ς	𝑚(ς	NOUN
cana-763	79	4	,	,	PUNCT
cana-763	79	5	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	79	6	)	)	PUNCT
cana-763	79	7	−	−	ADP
cana-763	80	1	𝑒𝑖𝜃[𝒟℘	𝑒𝑖𝜃[𝒟℘	PROPN
cana-763	80	2	𝑚(ς	𝑚(ς	NOUN
cana-763	80	3	,	,	PUNCT
cana-763	80	4	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	80	5	)	)	PUNCT
cana-763	80	6	−	−	NOUN
cana-763	80	7	𝒟℘	𝒟℘	NUM
cana-763	80	8	𝑚(ς	𝑚(ς	NOUN
cana-763	80	9	,	,	PUNCT
cana-763	80	10	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	80	11	)	)	PUNCT
cana-763	80	12	]	]	PUNCT
cana-763	80	13	𝒟℘	𝒟℘	X
cana-763	80	14	𝑚(ς	𝑚(ς	NOUN
cana-763	80	15	,	,	PUNCT
cana-763	80	16	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	80	17	)	)	PUNCT
cana-763	80	18	−	−	NOUN
cana-763	80	19	𝒟℘	𝒟℘	NUM
cana-763	80	20	𝑚(ς	𝑚(ς	NOUN
cana-763	80	21	,	,	PUNCT
cana-763	80	22	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	80	23	)	)	PUNCT
cana-763	80	24	}	}	PUNCT
cana-763	80	25	≥	≥	X
cana-763	80	26	ϱ.	ϱ.	NOUN
cana-763	80	27	(	(	PUNCT
cana-763	80	28	2.2	2.2	NUM
cana-763	80	29	)	)	PUNCT
cana-763	80	30	let	let	VERB
cana-763	80	31	𝐹(𝑧	𝐹(𝑧	PRON
cana-763	80	32	)	)	PUNCT
cana-763	80	33	=	=	SYM
cana-763	80	34	(	(	PUNCT
cana-763	80	35	1	1	NUM
cana-763	80	36	−	−	PROPN
cana-763	81	1	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	81	2	(	(	PUNCT
cana-763	81	3	𝒟℘	𝒟℘	X
cana-763	81	4	𝑚(ς	𝑚(ς	NOUN
cana-763	81	5	,	,	PUNCT
cana-763	81	6	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	81	7	)	)	PUNCT
cana-763	81	8	)	)	PUNCT
cana-763	82	1	′(1	′(1	PROPN
cana-763	82	2	+	+	NUM
cana-763	82	3	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	82	4	)	)	PUNCT
cana-763	83	1	−	−	PROPN
cana-763	83	2	𝑒𝑖𝜃[𝒟℘	𝑒𝑖𝜃[𝒟℘	PROPN
cana-763	84	1	𝑚(ς	𝑚(ς	NOUN
cana-763	84	2	,	,	PUNCT
cana-763	84	3	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	84	4	)	)	PUNCT
cana-763	84	5	−	−	NOUN
cana-763	84	6	𝒟℘	𝒟℘	NUM
cana-763	84	7	𝑚(ς	𝑚(ς	NOUN
cana-763	84	8	,	,	PUNCT
cana-763	84	9	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	84	10	)	)	PUNCT
cana-763	84	11	]	]	PUNCT
cana-763	84	12	and	and	CCONJ
cana-763	84	13	𝐸(𝑧	𝐸(𝑧	NOUN
cana-763	84	14	)	)	PUNCT
cana-763	84	15	=	=	PUNCT
cana-763	84	16	𝒟℘	𝒟℘	NUM
cana-763	84	17	𝑚(ς	𝑚(ς	NOUN
cana-763	84	18	,	,	PUNCT
cana-763	84	19	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	84	20	)	)	PUNCT
cana-763	84	21	−	−	NOUN
cana-763	84	22	𝒟℘	𝒟℘	NUM
cana-763	84	23	𝑚(ς	𝑚(ς	NOUN
cana-763	84	24	,	,	PUNCT
cana-763	84	25	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	84	26	)	)	PUNCT
cana-763	84	27	.	.	PUNCT
cana-763	85	1	by	by	ADP
cana-763	85	2	lemma	lemma	PROPN
cana-763	85	3	2	2	PROPN
cana-763	85	4	,	,	PUNCT
cana-763	85	5	(	(	PUNCT
cana-763	85	6	2.2	2.2	NUM
cana-763	85	7	)	)	PUNCT
cana-763	85	8	is	be	AUX
cana-763	85	9	equivalent	equivalent	ADJ
cana-763	85	10	to	to	ADP
cana-763	85	11	|𝐹(𝑧	|𝐹(𝑧	ADP
cana-763	85	12	)	)	PUNCT
cana-763	86	1	+	+	CCONJ
cana-763	86	2	(	(	PUNCT
cana-763	86	3	1	1	NUM
cana-763	86	4	−	−	NOUN
cana-763	86	5	ϱ)𝐸(𝑧)|	ϱ)𝐸(𝑧)|	PROPN
cana-763	86	6	≥	≥	NUM
cana-763	86	7	|𝐹(𝑧	|𝐹(𝑧	NOUN
cana-763	86	8	)	)	PUNCT
cana-763	86	9	−	−	PROPN
cana-763	87	1	(	(	PUNCT
cana-763	87	2	1	1	NUM
cana-763	87	3	+	+	CCONJ
cana-763	87	4	ϱ)𝐸(𝑧)|	ϱ)𝐸(𝑧)|	ADJ
cana-763	87	5	,	,	PUNCT
cana-763	87	6	for	for	ADP
cana-763	87	7	0	0	NUM
cana-763	87	8	≤	≤	NUM
cana-763	87	9	ϱ	ϱ	ADP
cana-763	87	10	<	<	X
cana-763	87	11	1	1	NUM
cana-763	87	12	.	.	PUNCT
cana-763	87	13	but	but	CCONJ
cana-763	87	14	|𝐹(𝑧	|𝐹(𝑧	ADP
cana-763	87	15	)	)	PUNCT
cana-763	88	1	+	+	CCONJ
cana-763	88	2	(	(	PUNCT
cana-763	88	3	1	1	NUM
cana-763	88	4	−	−	NOUN
cana-763	88	5	ϱ)𝐸(𝑧)|	ϱ)𝐸(𝑧)|	PROPN
cana-763	88	6	=	=	SYM
cana-763	88	7	|(1	|(1	PROPN
cana-763	88	8	−	−	NOUN
cana-763	88	9	𝑡){(2	𝑡){(2	NOUN
cana-763	88	10	−	−	NOUN
cana-763	88	11	ϱ)𝑧	ϱ)𝑧	PUNCT
cana-763	88	12	−	−	PROPN
cana-763	88	13	∑	∑	PUNCT
cana-763	88	14	𝜙𝑛	𝜙𝑛	PROPN
cana-763	88	15	∞	∞	PROPN
cana-763	88	16	𝑛=2	𝑛=2	PROPN
cana-763	88	17	(	(	PUNCT
cana-763	88	18	ς	ς	PROPN
cana-763	88	19	,	,	PUNCT
cana-763	88	20	ℏ	ℏ	PROPN
cana-763	88	21	,	,	PUNCT
cana-763	88	22	℘	℘	NOUN
cana-763	88	23	,	,	PUNCT
cana-763	88	24	𝑚)(𝑛	𝑚)(𝑛	NOUN
cana-763	88	25	+	+	CCONJ
cana-763	88	26	𝑢𝑛(1	𝑢𝑛(1	PROPN
cana-763	88	27	−	−	PROPN
cana-763	88	28	ϱ))𝑎𝑛𝑧𝑛	ϱ))𝑎𝑛𝑧𝑛	PROPN
cana-763	88	29	−𝑒𝑖𝜃	−𝑒𝑖𝜃	PROPN
cana-763	88	30	∑	∑	PROPN
cana-763	88	31	𝜙𝑛	𝜙𝑛	PROPN
cana-763	88	32	∞	∞	PROPN
cana-763	89	1	𝑛=2	𝑛=2	PROPN
cana-763	89	2	(	(	PUNCT
cana-763	89	3	ς	ς	PROPN
cana-763	89	4	,	,	PUNCT
cana-763	89	5	ℏ	ℏ	PROPN
cana-763	89	6	,	,	PUNCT
cana-763	89	7	℘	℘	NOUN
cana-763	89	8	,	,	PUNCT
cana-763	89	9	𝑚)(𝑛	𝑚)(𝑛	NOUN
cana-763	89	10	−	−	PROPN
cana-763	89	11	𝑢𝑛)𝑎𝑛𝑧𝑛}|	𝑢𝑛)𝑎𝑛𝑧𝑛}|	PROPN
cana-763	89	12	≥	≥	PRON
cana-763	89	13	|1	|1	PRON
cana-763	89	14	−	−	PROPN
cana-763	89	15	𝑡|{(2	𝑡|{(2	NOUN
cana-763	90	1	−	−	PROPN
cana-763	90	2	ϱ)|𝑧|	ϱ)|𝑧|	PROPN
cana-763	90	3	−	−	PROPN
cana-763	90	4	∑	∑	PROPN
cana-763	90	5	𝜙𝑛	𝜙𝑛	PROPN
cana-763	90	6	∞	∞	PROPN
cana-763	90	7	𝑛=2	𝑛=2	PROPN
cana-763	90	8	(	(	PUNCT
cana-763	90	9	ς	ς	PROPN
cana-763	90	10	,	,	PUNCT
cana-763	90	11	ℏ	ℏ	PROPN
cana-763	90	12	,	,	PUNCT
cana-763	90	13	℘	℘	NOUN
cana-763	90	14	,	,	PUNCT
cana-763	90	15	𝑚)|𝑛	𝑚)|𝑛	NOUN
cana-763	90	16	+	+	CCONJ
cana-763	90	17	𝑢𝑛(1	𝑢𝑛(1	PROPN
cana-763	90	18	−	−	PROPN
cana-763	90	19	ϱ)|𝑎𝑛|𝑧𝑛|	ϱ)|𝑎𝑛|𝑧𝑛|	VERB
cana-763	90	20	−	−	PROPN
cana-763	90	21	∑	∑	PROPN
cana-763	90	22	𝜙𝑛	𝜙𝑛	PROPN
cana-763	90	23	∞	∞	PROPN
cana-763	90	24	𝑛=2	𝑛=2	PROPN
cana-763	90	25	(	(	PUNCT
cana-763	90	26	ς	ς	PROPN
cana-763	90	27	,	,	PUNCT
cana-763	90	28	ℏ	ℏ	PROPN
cana-763	90	29	,	,	PUNCT
cana-763	90	30	℘	℘	NOUN
cana-763	90	31	,	,	PUNCT
cana-763	90	32	𝑚)|𝑛	𝑚)|𝑛	NOUN
cana-763	90	33	−	−	PRON
cana-763	90	34	𝑢𝑛|𝑎𝑛|𝑧𝑛|	𝑢𝑛|𝑎𝑛|𝑧𝑛|	ADJ
cana-763	90	35	}	}	PUNCT
cana-763	90	36	.	.	PUNCT
cana-763	91	1	also	also	ADV
cana-763	91	2	|𝐹(𝑧	|𝐹(𝑧	ADP
cana-763	91	3	)	)	PUNCT
cana-763	92	1	−	−	PROPN
cana-763	92	2	(	(	PUNCT
cana-763	92	3	1	1	NUM
cana-763	92	4	+	+	CCONJ
cana-763	92	5	ϱ)𝐸(𝑧)|	ϱ)𝐸(𝑧)|	PROPN
cana-763	92	6	=	=	SYM
cana-763	92	7	|(1	|(1	PROPN
cana-763	92	8	−	−	NOUN
cana-763	92	9	𝑡){−ϱ𝑧	𝑡){−ϱ𝑧	PUNCT
cana-763	92	10	−	−	NOUN
cana-763	92	11	∑	∑	PUNCT
cana-763	92	12	𝜙𝑛	𝜙𝑛	PROPN
cana-763	92	13	∞	∞	PROPN
cana-763	92	14	𝑛=2	𝑛=2	PROPN
cana-763	92	15	(	(	PUNCT
cana-763	92	16	ς	ς	PROPN
cana-763	92	17	,	,	PUNCT
cana-763	92	18	ℏ	ℏ	PROPN
cana-763	92	19	,	,	PUNCT
cana-763	92	20	℘	℘	NOUN
cana-763	92	21	,	,	PUNCT
cana-763	92	22	𝑚)(𝑛	𝑚)(𝑛	NOUN
cana-763	92	23	−	−	ADP
cana-763	92	24	𝑢𝑛(1	𝑢𝑛(1	PROPN
cana-763	92	25	+	+	CCONJ
cana-763	92	26	ϱ))𝑎𝑛𝑧𝑛	ϱ))𝑎𝑛𝑧𝑛	X
cana-763	92	27	−𝑒𝑖𝜃	−𝑒𝑖𝜃	X
cana-763	92	28	∑	∑	PUNCT
cana-763	92	29	𝜙𝑛	𝜙𝑛	PROPN
cana-763	92	30	∞	∞	PROPN
cana-763	92	31	𝑛=2	𝑛=2	PROPN
cana-763	92	32	(	(	PUNCT
cana-763	92	33	ς	ς	PROPN
cana-763	92	34	,	,	PUNCT
cana-763	92	35	ℏ	ℏ	PROPN
cana-763	92	36	,	,	PUNCT
cana-763	92	37	℘	℘	NOUN
cana-763	92	38	,	,	PUNCT
cana-763	92	39	𝑚)(𝑛	𝑚)(𝑛	NOUN
cana-763	92	40	−	−	PROPN
cana-763	92	41	𝑢𝑛)𝑎𝑛𝑧𝑛}|	𝑢𝑛)𝑎𝑛𝑧𝑛}|	PROPN
cana-763	92	42	≤	≤	NOUN
cana-763	92	43	|1	|1	NUM
cana-763	93	1	−	−	NOUN
cana-763	93	2	𝑡|{ϱ|𝑧|	𝑡|{ϱ|𝑧|	PROPN
cana-763	93	3	+	+	CCONJ
cana-763	93	4	∑	∑	PROPN
cana-763	93	5	𝜙𝑛	𝜙𝑛	PROPN
cana-763	93	6	∞	∞	PROPN
cana-763	93	7	𝑛=2	𝑛=2	PROPN
cana-763	93	8	(	(	PUNCT
cana-763	93	9	ς	ς	PROPN
cana-763	93	10	,	,	PUNCT
cana-763	93	11	ℏ	ℏ	PROPN
cana-763	93	12	,	,	PUNCT
cana-763	93	13	℘	℘	NOUN
cana-763	93	14	,	,	PUNCT
cana-763	93	15	𝑚)|𝑛	𝑚)|𝑛	NOUN
cana-763	93	16	−	−	PROPN
cana-763	93	17	𝑢𝑛(1	𝑢𝑛(1	PROPN
cana-763	93	18	+	+	CCONJ
cana-763	93	19	ϱ)|𝑎𝑛|𝑧𝑛|	ϱ)|𝑎𝑛|𝑧𝑛|	VERB
cana-763	93	20	+	+	CCONJ
cana-763	93	21	∑	∑	PROPN
cana-763	93	22	𝜙𝑛	𝜙𝑛	PRON
cana-763	93	23	∞	∞	PROPN
cana-763	93	24	𝑛=2	𝑛=2	PROPN
cana-763	93	25	(	(	PUNCT
cana-763	93	26	ς	ς	PROPN
cana-763	93	27	,	,	PUNCT
cana-763	93	28	ℏ	ℏ	PROPN
cana-763	93	29	,	,	PUNCT
cana-763	93	30	℘	℘	NOUN
cana-763	93	31	,	,	PUNCT
cana-763	93	32	𝑚)|𝑛	𝑚)|𝑛	NOUN
cana-763	93	33	−	−	PRON
cana-763	93	34	𝑢𝑛|𝑎𝑛|𝑧𝑛|	𝑢𝑛|𝑎𝑛|𝑧𝑛|	ADJ
cana-763	93	35	}	}	PUNCT
cana-763	93	36	.	.	PUNCT
cana-763	94	1	communications	communication	NOUN
cana-763	94	2	on	on	ADP
cana-763	94	3	applied	apply	VERB
cana-763	94	4	nonlinear	nonlinear	ADJ
cana-763	94	5	analysis	analysis	NOUN
cana-763	94	6	issn	issn	NOUN
cana-763	94	7	:	:	PUNCT
cana-763	94	8	1074	1074	NUM
cana-763	94	9	-	-	PUNCT
cana-763	94	10	133x	133x	NUM
cana-763	94	11	vol	vol	NOUN
cana-763	94	12	31	31	NUM
cana-763	94	13	no	no	NOUN
cana-763	94	14	.	.	PUNCT
cana-763	95	1	3s	3s	NUM
cana-763	95	2	(	(	PUNCT
cana-763	95	3	2024	2024	NUM
cana-763	95	4	)	)	PUNCT
cana-763	95	5	258	258	NUM
cana-763	95	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-763	95	7	so	so	ADV
cana-763	95	8	|𝐹(𝑧	|𝐹(𝑧	ADP
cana-763	95	9	)	)	PUNCT
cana-763	96	1	+	+	CCONJ
cana-763	96	2	(	(	PUNCT
cana-763	96	3	1	1	NUM
cana-763	96	4	−	−	PROPN
cana-763	96	5	ϱ)𝐸(𝑧)|	ϱ)𝐸(𝑧)|	PROPN
cana-763	96	6	−	−	PROPN
cana-763	96	7	|𝐹(𝑧	|𝐹(𝑧	NOUN
cana-763	96	8	)	)	PUNCT
cana-763	96	9	−	−	PROPN
cana-763	97	1	(	(	PUNCT
cana-763	97	2	1	1	NUM
cana-763	97	3	+	+	X
cana-763	97	4	ϱ)𝐸(𝑧)|	ϱ)𝐸(𝑧)|	PROPN
cana-763	97	5	≥	≥	NUM
cana-763	97	6	|1	|1	PRON
cana-763	97	7	−	−	PROPN
cana-763	97	8	𝑡|{2(1	𝑡|{2(1	NOUN
cana-763	97	9	−	−	PROPN
cana-763	97	10	ϱ)|𝑧|	ϱ)|𝑧|	PROPN
cana-763	97	11	−	−	PROPN
cana-763	97	12	∑	∑	PROPN
cana-763	97	13	𝜙𝑛	𝜙𝑛	PROPN
cana-763	97	14	∞	∞	PROPN
cana-763	97	15	𝑛=2	𝑛=2	PROPN
cana-763	97	16	(	(	PUNCT
cana-763	97	17	ς	ς	PROPN
cana-763	97	18	,	,	PUNCT
cana-763	97	19	ℏ	ℏ	PROPN
cana-763	97	20	,	,	PUNCT
cana-763	97	21	℘	℘	NOUN
cana-763	97	22	,	,	PUNCT
cana-763	97	23	𝑚)[|𝑛	𝑚)[|𝑛	NOUN
cana-763	97	24	+	+	CCONJ
cana-763	97	25	𝑢𝑛(1	𝑢𝑛(1	VERB
cana-763	97	26	−	−	PROPN
cana-763	97	27	ϱ)|	ϱ)|	NOUN
cana-763	97	28	+	+	CCONJ
cana-763	97	29	|𝑛	|𝑛	X
cana-763	97	30	−	−	NOUN
cana-763	97	31	𝑢𝑛(1	𝑢𝑛(1	NOUN
cana-763	97	32	+	+	CCONJ
cana-763	97	33	ϱ)|	ϱ)|	PROPN
cana-763	97	34	+	+	CCONJ
cana-763	97	35	2|𝑛	2|𝑛	NUM
cana-763	97	36	−	−	PROPN
cana-763	97	37	𝑢𝑛|	𝑢𝑛|	NOUN
cana-763	97	38	]	]	PUNCT
cana-763	97	39	𝑎𝑛|𝑧𝑛|	𝑎𝑛|𝑧𝑛|	ADJ
cana-763	97	40	}	}	PUNCT
cana-763	97	41	≥	≥	X
cana-763	97	42	2(1	2(1	NUM
cana-763	97	43	−	−	PROPN
cana-763	98	1	ϱ)|𝑧|	ϱ)|𝑧|	PROPN
cana-763	98	2	−	−	PROPN
cana-763	98	3	∑	∑	PROPN
cana-763	98	4	2	2	NUM
cana-763	98	5	∞	∞	NUM
cana-763	98	6	𝑛=2	𝑛=2	NOUN
cana-763	98	7	𝜙𝑛(ς	𝜙𝑛(ς	NOUN
cana-763	98	8	,	,	PUNCT
cana-763	98	9	ℏ	ℏ	PROPN
cana-763	98	10	,	,	PUNCT
cana-763	98	11	℘	℘	NOUN
cana-763	98	12	,	,	PUNCT
cana-763	98	13	𝑚)|2𝑛	𝑚)|2𝑛	NOUN
cana-763	98	14	−	−	NOUN
cana-763	98	15	𝑢𝑛(1	𝑢𝑛(1	PROPN
cana-763	98	16	+	+	CCONJ
cana-763	98	17	ϱ)|𝑎𝑛|𝑧𝑛|	ϱ)|𝑎𝑛|𝑧𝑛|	VERB
cana-763	98	18	≥	≥	NOUN
cana-763	98	19	0	0	NUM
cana-763	98	20	or	or	CCONJ
cana-763	98	21	∑	∑	ADP
cana-763	98	22	𝜙𝑛	𝜙𝑛	PROPN
cana-763	98	23	∞	∞	PROPN
cana-763	98	24	𝑛=2	𝑛=2	PROPN
cana-763	98	25	(	(	PUNCT
cana-763	98	26	ς	ς	PROPN
cana-763	98	27	,	,	PUNCT
cana-763	98	28	ℏ	ℏ	PROPN
cana-763	98	29	,	,	PUNCT
cana-763	98	30	℘	℘	NOUN
cana-763	98	31	,	,	PUNCT
cana-763	98	32	𝑚)|2𝑛	𝑚)|2𝑛	NOUN
cana-763	98	33	−	−	NOUN
cana-763	98	34	𝑢𝑛(1	𝑢𝑛(1	NOUN
cana-763	98	35	+	+	CCONJ
cana-763	98	36	ϱ)|𝑎𝑛	ϱ)|𝑎𝑛	VERB
cana-763	98	37	≤	≤	NOUN
cana-763	98	38	1	1	NUM
cana-763	98	39	−	−	NOUN
cana-763	98	40	ϱ.	ϱ.	NOUN
cana-763	98	41	conversely	conversely	ADV
cana-763	98	42	,	,	PUNCT
cana-763	98	43	suppose	suppose	VERB
cana-763	98	44	that	that	SCONJ
cana-763	98	45	(	(	PUNCT
cana-763	98	46	2.1	2.1	NUM
cana-763	98	47	)	)	PUNCT
cana-763	98	48	holds	hold	VERB
cana-763	98	49	.	.	PUNCT
cana-763	99	1	then	then	ADV
cana-763	99	2	we	we	PRON
cana-763	99	3	must	must	AUX
cana-763	99	4	show	show	VERB
cana-763	99	5	ℜ	ℜ	PROPN
cana-763	99	6	{	{	PUNCT
cana-763	99	7	(	(	PUNCT
cana-763	99	8	1	1	NUM
cana-763	99	9	−	−	NOUN
cana-763	99	10	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	99	11	(	(	PUNCT
cana-763	99	12	𝒟℘	𝒟℘	X
cana-763	99	13	𝑚(ς	𝑚(ς	NOUN
cana-763	99	14	,	,	PUNCT
cana-763	99	15	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	99	16	)	)	PUNCT
cana-763	99	17	)	)	PUNCT
cana-763	100	1	′(1	′(1	PROPN
cana-763	100	2	+	+	NUM
cana-763	100	3	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	100	4	)	)	PUNCT
cana-763	101	1	−	−	PROPN
cana-763	101	2	𝑒𝑖𝜃[𝒟℘	𝑒𝑖𝜃[𝒟℘	PROPN
cana-763	102	1	𝑚(ς	𝑚(ς	NOUN
cana-763	102	2	,	,	PUNCT
cana-763	102	3	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	102	4	)	)	PUNCT
cana-763	102	5	−	−	NOUN
cana-763	102	6	𝒟℘	𝒟℘	NUM
cana-763	102	7	𝑚(ς	𝑚(ς	NOUN
cana-763	102	8	,	,	PUNCT
cana-763	102	9	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	102	10	)	)	PUNCT
cana-763	102	11	]	]	PUNCT
cana-763	103	1	𝒟℘	𝒟℘	X
cana-763	103	2	𝑚(ς	𝑚(ς	NOUN
cana-763	103	3	,	,	PUNCT
cana-763	103	4	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	103	5	)	)	PUNCT
cana-763	103	6	−	−	NOUN
cana-763	103	7	𝒟℘	𝒟℘	NUM
cana-763	103	8	𝑚(ς	𝑚(ς	NOUN
cana-763	103	9	,	,	PUNCT
cana-763	103	10	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	103	11	)	)	PUNCT
cana-763	103	12	}	}	PUNCT
cana-763	103	13	≥	≥	X
cana-763	103	14	ϱ.	ϱ.	ADV
cana-763	103	15	upon	upon	SCONJ
cana-763	103	16	choosing	choose	VERB
cana-763	103	17	the	the	DET
cana-763	103	18	values	value	NOUN
cana-763	103	19	of	of	ADP
cana-763	103	20	𝑧	𝑧	PRON
cana-763	103	21	on	on	ADP
cana-763	103	22	the	the	DET
cana-763	103	23	positive	positive	ADJ
cana-763	103	24	real	real	ADJ
cana-763	103	25	axis	axis	NOUN
cana-763	103	26	where	where	SCONJ
cana-763	103	27	0	0	NUM
cana-763	103	28	≤	≤	NUM
cana-763	103	29	|𝑧|	|𝑧|	NOUN
cana-763	103	30	=	=	SYM
cana-763	103	31	𝑟	𝑟	X
cana-763	103	32	<	<	X
cana-763	103	33	1	1	NUM
cana-763	103	34	,	,	PUNCT
cana-763	103	35	the	the	DET
cana-763	103	36	above	above	ADJ
cana-763	103	37	inequality	inequality	NOUN
cana-763	103	38	reduces	reduce	VERB
cana-763	103	39	to	to	ADP
cana-763	103	40	ℜ	ℜ	PROPN
cana-763	103	41	{	{	PUNCT
cana-763	103	42	(	(	PUNCT
cana-763	103	43	1	1	NUM
cana-763	103	44	−	−	NUM
cana-763	103	45	ϱ	ϱ	NOUN
cana-763	103	46	)	)	PUNCT
cana-763	103	47	−	−	PROPN
cana-763	103	48	∑	∑	PROPN
cana-763	103	49	𝜙𝑛	𝜙𝑛	PROPN
cana-763	103	50	∞	∞	PROPN
cana-763	103	51	𝑛=2	𝑛=2	PROPN
cana-763	103	52	(	(	PUNCT
cana-763	103	53	ς	ς	PROPN
cana-763	103	54	,	,	PUNCT
cana-763	103	55	ℏ	ℏ	PROPN
cana-763	103	56	,	,	PUNCT
cana-763	103	57	℘	℘	NOUN
cana-763	103	58	,	,	PUNCT
cana-763	103	59	𝑚)[𝑛(1	𝑚)[𝑛(1	NOUN
cana-763	104	1	+	+	CCONJ
cana-763	104	2	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	104	3	)	)	PUNCT
cana-763	104	4	−	−	NOUN
cana-763	104	5	𝑢𝑛(ϱ	𝑢𝑛(ϱ	X
cana-763	105	1	+	+	CCONJ
cana-763	105	2	𝑒𝑖𝜃)]𝑎𝑛𝑧𝑛−1	𝑒𝑖𝜃)]𝑎𝑛𝑧𝑛−1	NOUN
cana-763	105	3	1	1	NUM
cana-763	105	4	−	−	PROPN
cana-763	105	5	∑	∑	PUNCT
cana-763	105	6	𝜙𝑛	𝜙𝑛	PROPN
cana-763	105	7	∞	∞	PROPN
cana-763	105	8	𝑛=2	𝑛=2	PROPN
cana-763	105	9	(	(	PUNCT
cana-763	105	10	ς	ς	PROPN
cana-763	105	11	,	,	PUNCT
cana-763	105	12	ℏ	ℏ	PROPN
cana-763	105	13	,	,	PUNCT
cana-763	105	14	℘	℘	PROPN
cana-763	105	15	,	,	PUNCT
cana-763	105	16	𝑚)𝑢𝑛𝑎𝑛𝑧𝑛−1	𝑚)𝑢𝑛𝑎𝑛𝑧𝑛−1	PROPN
cana-763	105	17	}	}	PUNCT
cana-763	105	18	≥	≥	NOUN
cana-763	105	19	0	0	NUM
cana-763	105	20	.	.	PUNCT
cana-763	106	1	since	since	SCONJ
cana-763	106	2	ℜ(−𝑒𝑖𝜃	ℜ(−𝑒𝑖𝜃	PROPN
cana-763	106	3	)	)	PUNCT
cana-763	106	4	≥	≥	X
cana-763	106	5	−|𝑒𝑖𝜃|	−|𝑒𝑖𝜃|	NOUN
cana-763	106	6	=	=	SYM
cana-763	106	7	−1	−1	NOUN
cana-763	106	8	,	,	PUNCT
cana-763	106	9	the	the	DET
cana-763	106	10	above	above	ADJ
cana-763	106	11	inequality	inequality	NOUN
cana-763	106	12	reduces	reduce	VERB
cana-763	106	13	to	to	ADP
cana-763	106	14	ℜ	ℜ	PROPN
cana-763	106	15	{	{	PUNCT
cana-763	106	16	(	(	PUNCT
cana-763	106	17	1	1	NUM
cana-763	106	18	−	−	NUM
cana-763	106	19	ϱ	ϱ	NOUN
cana-763	106	20	)	)	PUNCT
cana-763	106	21	−	−	PROPN
cana-763	106	22	∑	∑	PROPN
cana-763	106	23	𝜙𝑛	𝜙𝑛	PROPN
cana-763	106	24	∞	∞	PROPN
cana-763	106	25	𝑛=2	𝑛=2	PROPN
cana-763	106	26	(	(	PUNCT
cana-763	106	27	ς	ς	PROPN
cana-763	106	28	,	,	PUNCT
cana-763	106	29	ℏ	ℏ	PROPN
cana-763	106	30	,	,	PUNCT
cana-763	106	31	℘	℘	PROPN
cana-763	106	32	,	,	PUNCT
cana-763	106	33	𝑚)[2𝑛	𝑚)[2𝑛	PROPN
cana-763	106	34	−	−	NOUN
cana-763	106	35	𝑢𝑛(1	𝑢𝑛(1	PROPN
cana-763	106	36	+	+	CCONJ
cana-763	106	37	ϱ]𝑎𝑛𝑟𝑛−1	ϱ]𝑎𝑛𝑟𝑛−1	PROPN
cana-763	106	38	1	1	NUM
cana-763	106	39	−	−	NOUN
cana-763	106	40	∑	∑	PUNCT
cana-763	106	41	𝜙𝑛	𝜙𝑛	PROPN
cana-763	106	42	∞	∞	PROPN
cana-763	106	43	𝑛=2	𝑛=2	PROPN
cana-763	106	44	(	(	PUNCT
cana-763	106	45	ς	ς	PROPN
cana-763	106	46	,	,	PUNCT
cana-763	106	47	ℏ	ℏ	PROPN
cana-763	106	48	,	,	PUNCT
cana-763	106	49	℘	℘	PROPN
cana-763	106	50	,	,	PUNCT
cana-763	106	51	𝑚)𝑢𝑛𝑎𝑛𝑟𝑛−1	𝑚)𝑢𝑛𝑎𝑛𝑟𝑛−1	PROPN
cana-763	106	52	}	}	PUNCT
cana-763	106	53	≥	≥	NOUN
cana-763	106	54	0	0	NUM
cana-763	106	55	.	.	PUNCT
cana-763	107	1	letting	let	VERB
cana-763	107	2	𝑟	𝑟	NOUN
cana-763	107	3	→	→	SYM
cana-763	107	4	1−	1−	NUM
cana-763	107	5	,	,	PUNCT
cana-763	107	6	we	we	PRON
cana-763	107	7	have	have	AUX
cana-763	107	8	desired	desire	VERB
cana-763	107	9	conclusion	conclusion	NOUN
cana-763	107	10	.	.	PUNCT
cana-763	108	1	corollary	corollary	ADJ
cana-763	108	2	5	5	NUM
cana-763	108	3	.	.	PUNCT
cana-763	109	1	if	if	SCONJ
cana-763	109	2	𝑓(𝑧	𝑓(𝑧	NUM
cana-763	109	3	)	)	PUNCT
cana-763	109	4	∈	∈	PROPN
cana-763	109	5	�	�	PROPN
cana-763	109	6	̃	̃	PROPN
cana-763	109	7	�	�	PROPN
cana-763	109	8	𝑆𝑠	𝑆𝑠	PROPN
cana-763	109	9	𝑚(ς	𝑚(ς	NOUN
cana-763	109	10	,	,	PUNCT
cana-763	109	11	ℏ	ℏ	PROPN
cana-763	109	12	,	,	PUNCT
cana-763	109	13	℘	℘	PROPN
cana-763	109	14	,	,	PUNCT
cana-763	109	15	ϱ	ϱ	NOUN
cana-763	109	16	,	,	PUNCT
cana-763	109	17	𝑡	𝑡	NOUN
cana-763	109	18	)	)	PUNCT
cana-763	109	19	then	then	ADV
cana-763	109	20	𝑎𝑛	𝑎𝑛	VERB
cana-763	109	21	≤	≤	PROPN
cana-763	109	22	1−ϱ	1−ϱ	PROPN
cana-763	109	23	𝜙𝑛(ς,ℏ,℘,𝑚)|2𝑛−𝑢𝑛(1+ϱ)|	𝜙𝑛(ς,ℏ,℘,𝑚)|2𝑛−𝑢𝑛(1+ϱ)|	NUM
cana-763	109	24	where	where	SCONJ
cana-763	109	25	℘	℘	PROPN
cana-763	109	26	≥	≥	NOUN
cana-763	109	27	0	0	NUM
cana-763	109	28	,	,	PUNCT
cana-763	109	29	𝑚	𝑚	PROPN
cana-763	109	30	,	,	PUNCT
cana-763	109	31	|𝑡|	|𝑡|	ADP
cana-763	109	32	≤	≤	NOUN
cana-763	109	33	1	1	NUM
cana-763	109	34	,	,	PUNCT
cana-763	109	35	𝑡	𝑡	ADP
cana-763	109	36	≠	≠	PROPN
cana-763	109	37	1,0	1,0	NUM
cana-763	109	38	≤	≤	NUM
cana-763	109	39	ϱ	ϱ	ADP
cana-763	109	40	<	<	X
cana-763	109	41	1	1	NUM
cana-763	109	42	and	and	CCONJ
cana-763	109	43	𝑢𝑛	𝑢𝑛	NOUN
cana-763	109	44	=	=	SYM
cana-763	109	45	1	1	NUM
cana-763	109	46	+	+	NUM
cana-763	109	47	𝑡	𝑡	PROPN
cana-763	109	48	+	+	PROPN
cana-763	109	49	⋯	⋯	PROPN
cana-763	109	50	+	+	CCONJ
cana-763	109	51	𝑡𝑛−1	𝑡𝑛−1	ADJ
cana-763	109	52	.	.	NOUN
cana-763	109	53	3	3	NUM
cana-763	109	54	neighborhood	neighborhood	NOUN
cana-763	109	55	property	property	NOUN
cana-763	109	56	following	follow	VERB
cana-763	109	57	the	the	DET
cana-763	109	58	earlier	early	ADJ
cana-763	109	59	investigations	investigation	NOUN
cana-763	109	60	(	(	PUNCT
cana-763	109	61	based	base	VERB
cana-763	109	62	upon	upon	SCONJ
cana-763	109	63	the	the	DET
cana-763	109	64	familiar	familiar	ADJ
cana-763	109	65	concept	concept	NOUN
cana-763	109	66	of	of	ADP
cana-763	109	67	neighborhoods	neighborhood	NOUN
cana-763	109	68	of	of	ADP
cana-763	109	69	analytic	analytic	ADJ
cana-763	109	70	functions	function	NOUN
cana-763	109	71	)	)	PUNCT
cana-763	109	72	by	by	ADP
cana-763	109	73	goodman	goodman	PROPN
cana-763	110	1	[	[	X
cana-763	110	2	7	7	NUM
cana-763	110	3	]	]	PUNCT
cana-763	110	4	,	,	PUNCT
cana-763	110	5	srinivas	srinivas	PROPN
cana-763	110	6	et	et	PROPN
cana-763	110	7	al	al	PROPN
cana-763	111	1	[	[	X
cana-763	111	2	16	16	NUM
cana-763	111	3	]	]	PUNCT
cana-763	111	4	,	,	PUNCT
cana-763	111	5	altintas	altinta	NOUN
cana-763	111	6	et	et	PROPN
cana-763	111	7	al	al	PROPN
cana-763	112	1	[	[	X
cana-763	112	2	2	2	NUM
cana-763	112	3	,	,	PUNCT
cana-763	112	4	3	3	NUM
cana-763	112	5	]	]	PUNCT
cana-763	112	6	.	.	PUNCT
cana-763	113	1	and	and	CCONJ
cana-763	113	2	others	other	NOUN
cana-763	113	3	including	include	VERB
cana-763	113	4	srivastava	srivastava	PROPN
cana-763	113	5	et	et	PROPN
cana-763	113	6	al.[15	al.[15	PROPN
cana-763	113	7	]	]	PUNCT
cana-763	113	8	,	,	PUNCT
cana-763	113	9	orhan	orhan	PROPN
cana-763	113	10	[	[	X
cana-763	113	11	9	9	NUM
cana-763	113	12	]	]	PUNCT
cana-763	113	13	,	,	PUNCT
cana-763	113	14	deniz	deniz	PROPN
cana-763	113	15	et	et	PROPN
cana-763	113	16	al	al	PROPN
cana-763	113	17	.	.	PUNCT
cana-763	114	1	[	[	X
cana-763	114	2	6	6	NUM
cana-763	114	3	]	]	PUNCT
cana-763	114	4	,	,	PUNCT
cana-763	114	5	catas	cata	NOUN
cana-763	114	6	[	[	X
cana-763	114	7	4	4	NUM
cana-763	114	8	]	]	PUNCT
cana-763	114	9	.	.	PUNCT
cana-763	115	1	definition	definition	NOUN
cana-763	115	2	6	6	NUM
cana-763	115	3	.	.	PUNCT
cana-763	116	1	let	let	VERB
cana-763	116	2	℘	℘	PROPN
cana-763	116	3	≥	≥	NOUN
cana-763	116	4	0	0	NUM
cana-763	116	5	,	,	PUNCT
cana-763	116	6	𝑚	𝑚	PROPN
cana-763	116	7	,	,	PUNCT
cana-763	116	8	|𝑡|	|𝑡|	ADP
cana-763	116	9	≤	≤	NOUN
cana-763	116	10	1	1	NUM
cana-763	116	11	,	,	PUNCT
cana-763	116	12	𝑡	𝑡	ADP
cana-763	116	13	≠	≠	PROPN
cana-763	116	14	1,0	1,0	NUM
cana-763	116	15	≤	≤	NUM
cana-763	116	16	ϱ	ϱ	ADP
cana-763	116	17	<	<	X
cana-763	116	18	1	1	NUM
cana-763	116	19	,	,	PUNCT
cana-763	116	20	ς	ς	PROPN
cana-763	116	21	≥	≥	NOUN
cana-763	116	22	0	0	NUM
cana-763	116	23	and	and	CCONJ
cana-763	116	24	𝑢𝑛	𝑢𝑛	NOUN
cana-763	116	25	=	=	SYM
cana-763	116	26	1	1	NUM
cana-763	116	27	+	+	NUM
cana-763	116	28	𝑡	𝑡	PROPN
cana-763	116	29	+	+	PROPN
cana-763	116	30	⋯	⋯	PROPN
cana-763	116	31	+	+	CCONJ
cana-763	116	32	𝑡𝑛−1	𝑡𝑛−1	NOUN
cana-763	116	33	.	.	PUNCT
cana-763	117	1	we	we	PRON
cana-763	117	2	define	define	VERB
cana-763	117	3	the	the	DET
cana-763	117	4	ς	ς	PROPN
cana-763	117	5	−neighborhood	−neighborhood	NOUN
cana-763	117	6	of	of	ADP
cana-763	117	7	a	a	DET
cana-763	117	8	function	function	NOUN
cana-763	117	9	𝑓	𝑓	DET
cana-763	117	10	∈	∈	PROPN
cana-763	117	11	𝐴	𝐴	PROPN
cana-763	117	12	and	and	CCONJ
cana-763	117	13	denote	denote	VERB
cana-763	117	14	by	by	ADP
cana-763	117	15	𝑁ς(𝑓	𝑁ς(𝑓	NOUN
cana-763	117	16	)	)	PUNCT
cana-763	117	17	consisting	consist	VERB
cana-763	117	18	of	of	ADP
cana-763	117	19	all	all	DET
cana-763	117	20	functions	function	NOUN
cana-763	117	21	𝑔(𝑧	𝑔(𝑧	NOUN
cana-763	117	22	)	)	PUNCT
cana-763	117	23	=	=	SYM
cana-763	117	24	𝑧	𝑧	DET
cana-763	117	25	−	−	NOUN
cana-763	117	26	∑	∑	PROPN
cana-763	117	27	𝑏𝑛	𝑏𝑛	ADP
cana-763	117	28	∞	∞	PROPN
cana-763	117	29	𝑛=2	𝑛=2	VERB
cana-763	117	30	𝑧𝑛	𝑧𝑛	ADP
cana-763	117	31	∈	∈	PROPN
cana-763	117	32	𝑆(𝑏𝑛	𝑆(𝑏𝑛	NOUN
cana-763	117	33	≥	≥	NOUN
cana-763	117	34	0	0	NUM
cana-763	117	35	,	,	PUNCT
cana-763	117	36	𝑛	𝑛	DET
cana-763	117	37	∈	∈	PROPN
cana-763	117	38	ℕ	ℕ	PROPN
cana-763	117	39	)	)	PUNCT
cana-763	117	40	satisfying	satisfy	VERB
cana-763	117	41	∑	∑	ADP
cana-763	117	42	𝜙𝑛(ς	𝜙𝑛(ς	NUM
cana-763	117	43	,	,	PUNCT
cana-763	117	44	ℏ	ℏ	PROPN
cana-763	117	45	,	,	PUNCT
cana-763	117	46	℘	℘	NOUN
cana-763	117	47	,	,	PUNCT
cana-763	117	48	𝑚)|2𝑛	𝑚)|2𝑛	NOUN
cana-763	117	49	−	−	NOUN
cana-763	118	1	𝑢𝑛(1	𝑢𝑛(1	NOUN
cana-763	119	1	+	+	CCONJ
cana-763	119	2	ϱ)|	ϱ)|	PROPN
cana-763	119	3	1	1	NUM
cana-763	119	4	−	−	NOUN
cana-763	119	5	ϱ	ϱ	ADP
cana-763	119	6	∞	∞	PROPN
cana-763	119	7	𝑛=2	𝑛=2	X
cana-763	119	8	|𝑎𝑛	|𝑎𝑛	NUM
cana-763	119	9	−	−	PROPN
cana-763	119	10	𝑏𝑛|	𝑏𝑛|	PROPN
cana-763	119	11	≤	≤	NUM
cana-763	120	1	1	1	NUM
cana-763	120	2	−	−	PROPN
cana-763	120	3	ς	ς	PROPN
cana-763	120	4	.	.	PUNCT
cana-763	120	5	communications	communication	NOUN
cana-763	120	6	on	on	ADP
cana-763	120	7	applied	apply	VERB
cana-763	120	8	nonlinear	nonlinear	ADJ
cana-763	120	9	analysis	analysis	NOUN
cana-763	120	10	issn	issn	NOUN
cana-763	120	11	:	:	PUNCT
cana-763	120	12	1074	1074	NUM
cana-763	120	13	-	-	PUNCT
cana-763	120	14	133x	133x	NUM
cana-763	120	15	vol	vol	NOUN
cana-763	120	16	31	31	NUM
cana-763	120	17	no	no	NOUN
cana-763	120	18	.	.	PUNCT
cana-763	121	1	3s	3s	NUM
cana-763	121	2	(	(	PUNCT
cana-763	121	3	2024	2024	NUM
cana-763	121	4	)	)	PUNCT
cana-763	121	5	259	259	NUM
cana-763	121	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-763	121	7	theorem	theorem	VERB
cana-763	121	8	7	7	NUM
cana-763	121	9	.	.	PUNCT
cana-763	122	1	let	let	VERB
cana-763	122	2	𝑓(𝑧	𝑓(𝑧	NUM
cana-763	122	3	)	)	PUNCT
cana-763	122	4	∈	∈	PROPN
cana-763	122	5	�	�	PROPN
cana-763	122	6	̃	̃	PROPN
cana-763	122	7	�	�	PROPN
cana-763	122	8	𝑆𝑠	𝑆𝑠	PROPN
cana-763	122	9	𝑚(ς	𝑚(ς	NOUN
cana-763	122	10	,	,	PUNCT
cana-763	122	11	ℏ	ℏ	PROPN
cana-763	122	12	,	,	PUNCT
cana-763	122	13	℘	℘	PROPN
cana-763	122	14	,	,	PUNCT
cana-763	122	15	ϱ	ϱ	NOUN
cana-763	122	16	,	,	PUNCT
cana-763	122	17	𝑡	𝑡	NOUN
cana-763	122	18	)	)	PUNCT
cana-763	122	19	and	and	CCONJ
cana-763	122	20	for	for	ADP
cana-763	122	21	all	all	DET
cana-763	122	22	real	real	ADJ
cana-763	122	23	𝜃	𝜃	NOUN
cana-763	122	24	we	we	PRON
cana-763	122	25	have	have	VERB
cana-763	122	26	ϱ(𝑒𝑖𝜃	ϱ(𝑒𝑖𝜃	PROPN
cana-763	123	1	−	−	NOUN
cana-763	123	2	1	1	NUM
cana-763	123	3	)	)	PUNCT
cana-763	123	4	−	−	PROPN
cana-763	123	5	2𝑒𝑖𝜃	2𝑒𝑖𝜃	PROPN
cana-763	123	6	≠	≠	PROPN
cana-763	123	7	0	0	NUM
cana-763	123	8	.	.	PUNCT
cana-763	124	1	for	for	ADP
cana-763	124	2	any	any	DET
cana-763	124	3	complex	complex	ADJ
cana-763	124	4	number	number	NOUN
cana-763	124	5	𝜖	𝜖	X
cana-763	124	6	with	with	ADP
cana-763	124	7	|𝜖|	|𝜖|	PROPN
cana-763	124	8	<	<	X
cana-763	124	9	ς(ς	ς(ς	PROPN
cana-763	124	10	≥	≥	NOUN
cana-763	124	11	0	0	NUM
cana-763	124	12	)	)	PUNCT
cana-763	124	13	,	,	PUNCT
cana-763	124	14	if	if	SCONJ
cana-763	124	15	f	f	PROPN
cana-763	124	16	satisfies	satisfy	VERB
cana-763	124	17	the	the	DET
cana-763	124	18	following	follow	VERB
cana-763	124	19	condition	condition	NOUN
cana-763	124	20	:	:	PUNCT
cana-763	124	21	𝑓(𝑧)+𝜖𝑧	𝑓(𝑧)+𝜖𝑧	NOUN
cana-763	124	22	1+𝜖	1+𝜖	NUM
cana-763	124	23	∈	∈	PROPN
cana-763	124	24	�	�	PROPN
cana-763	124	25	̃	̃	PROPN
cana-763	124	26	�	�	PROPN
cana-763	124	27	𝑆𝑠	𝑆𝑠	PROPN
cana-763	124	28	𝑚(ς	𝑚(ς	NOUN
cana-763	124	29	,	,	PUNCT
cana-763	124	30	ℏ	ℏ	PROPN
cana-763	124	31	,	,	PUNCT
cana-763	124	32	℘	℘	PROPN
cana-763	124	33	,	,	PUNCT
cana-763	124	34	ϱ	ϱ	NOUN
cana-763	124	35	,	,	PUNCT
cana-763	124	36	𝑡	𝑡	NOUN
cana-763	124	37	)	)	PUNCT
cana-763	124	38	then	then	ADV
cana-763	124	39	𝑁ς(𝑓	𝑁ς(𝑓	NOUN
cana-763	124	40	)	)	PUNCT
cana-763	124	41	⊂	⊂	PROPN
cana-763	124	42	�	�	PROPN
cana-763	124	43	̃	̃	PROPN
cana-763	124	44	�	�	PROPN
cana-763	124	45	𝑆𝑠	𝑆𝑠	PROPN
cana-763	124	46	𝑚(ς	𝑚(ς	NOUN
cana-763	124	47	,	,	PUNCT
cana-763	124	48	ℏ	ℏ	PROPN
cana-763	124	49	,	,	PUNCT
cana-763	124	50	℘	℘	PROPN
cana-763	124	51	,	,	PUNCT
cana-763	124	52	ϱ	ϱ	NOUN
cana-763	124	53	,	,	PUNCT
cana-763	124	54	𝑡	𝑡	NOUN
cana-763	124	55	)	)	PUNCT
cana-763	124	56	.	.	PUNCT
cana-763	125	1	proof	proof	NOUN
cana-763	125	2	.	.	PUNCT
cana-763	126	1	it	it	PRON
cana-763	126	2	is	be	AUX
cana-763	126	3	obvious	obvious	ADJ
cana-763	126	4	that	that	SCONJ
cana-763	126	5	𝑓	𝑓	DET
cana-763	126	6	∈	∈	PROPN
cana-763	126	7	�	�	PROPN
cana-763	126	8	̃	̃	PROPN
cana-763	126	9	�	�	PROPN
cana-763	126	10	𝑆𝑠	𝑆𝑠	PROPN
cana-763	126	11	𝑚(ς	𝑚(ς	NOUN
cana-763	126	12	,	,	PUNCT
cana-763	126	13	ℏ	ℏ	PROPN
cana-763	126	14	,	,	PUNCT
cana-763	126	15	℘	℘	PROPN
cana-763	126	16	,	,	PUNCT
cana-763	126	17	ϱ	ϱ	NOUN
cana-763	126	18	,	,	PUNCT
cana-763	126	19	𝑡	𝑡	NOUN
cana-763	126	20	)	)	PUNCT
cana-763	126	21	if	if	SCONJ
cana-763	126	22	and	and	CCONJ
cana-763	126	23	only	only	ADV
cana-763	126	24	if	if	SCONJ
cana-763	126	25	|	|	NOUN
cana-763	126	26	(	(	PUNCT
cana-763	126	27	1	1	NUM
cana-763	126	28	−	−	PROPN
cana-763	126	29	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	126	30	(	(	PUNCT
cana-763	126	31	𝒟℘	𝒟℘	X
cana-763	126	32	𝑚(ς	𝑚(ς	NOUN
cana-763	126	33	,	,	PUNCT
cana-763	126	34	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	126	35	)	)	PUNCT
cana-763	126	36	)	)	PUNCT
cana-763	127	1	′(1	′(1	PROPN
cana-763	127	2	+	+	CCONJ
cana-763	127	3	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	127	4	)	)	PUNCT
cana-763	127	5	−	−	PROPN
cana-763	128	1	(	(	PUNCT
cana-763	128	2	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	128	3	+	+	CCONJ
cana-763	128	4	1	1	NUM
cana-763	128	5	+	+	CCONJ
cana-763	128	6	ϱ	ϱ	NOUN
cana-763	128	7	)	)	PUNCT
cana-763	128	8	(	(	PUNCT
cana-763	128	9	𝒟℘	𝒟℘	X
cana-763	128	10	𝑚(ς	𝑚(ς	NOUN
cana-763	128	11	,	,	PUNCT
cana-763	128	12	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	128	13	)	)	PUNCT
cana-763	128	14	−	−	NOUN
cana-763	128	15	𝒟℘	𝒟℘	NUM
cana-763	128	16	𝑚(ς	𝑚(ς	NOUN
cana-763	128	17	,	,	PUNCT
cana-763	128	18	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	128	19	)	)	PUNCT
cana-763	128	20	)	)	PUNCT
cana-763	128	21	(	(	PUNCT
cana-763	128	22	1	1	NUM
cana-763	128	23	−	−	PROPN
cana-763	128	24	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	128	25	(	(	PUNCT
cana-763	128	26	𝒟℘	𝒟℘	X
cana-763	128	27	𝑚(ς	𝑚(ς	NOUN
cana-763	128	28	,	,	PUNCT
cana-763	128	29	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	128	30	)	)	PUNCT
cana-763	128	31	)	)	PUNCT
cana-763	129	1	′(1	′(1	PROPN
cana-763	129	2	+	+	NUM
cana-763	129	3	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	129	4	)	)	PUNCT
cana-763	130	1	+	+	CCONJ
cana-763	130	2	(	(	PUNCT
cana-763	130	3	1	1	NUM
cana-763	130	4	−	−	PROPN
cana-763	130	5	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	130	6	−	−	ADP
cana-763	130	7	ϱ	ϱ	NOUN
cana-763	130	8	)	)	PUNCT
cana-763	130	9	(	(	PUNCT
cana-763	130	10	𝒟℘	𝒟℘	X
cana-763	130	11	𝑚(ς	𝑚(ς	NOUN
cana-763	130	12	,	,	PUNCT
cana-763	130	13	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	130	14	)	)	PUNCT
cana-763	130	15	−	−	NOUN
cana-763	130	16	𝒟℘	𝒟℘	NUM
cana-763	130	17	𝑚(ς	𝑚(ς	NOUN
cana-763	130	18	,	,	PUNCT
cana-763	130	19	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	130	20	)	)	PUNCT
cana-763	130	21	)	)	PUNCT
cana-763	131	1	|	|	ADV
cana-763	131	2	<	<	X
cana-763	131	3	1	1	NUM
cana-763	131	4	,	,	PUNCT
cana-763	131	5	(	(	PUNCT
cana-763	131	6	−𝜋	−𝜋	ADJ
cana-763	131	7	<	<	X
cana-763	131	8	𝜃	𝜃	X
cana-763	131	9	≤	≤	NUM
cana-763	131	10	𝜋	𝜋	NOUN
cana-763	131	11	)	)	PUNCT
cana-763	131	12	,	,	PUNCT
cana-763	131	13	for	for	ADP
cana-763	131	14	any	any	DET
cana-763	131	15	complex	complex	ADJ
cana-763	131	16	number	number	NOUN
cana-763	131	17	𝑠	𝑠	NOUN
cana-763	131	18	with	with	ADP
cana-763	131	19	|𝑠|	|𝑠|	PROPN
cana-763	131	20	=	=	SYM
cana-763	131	21	1	1	NUM
cana-763	131	22	,	,	PUNCT
cana-763	131	23	we	we	PRON
cana-763	131	24	have	have	VERB
cana-763	131	25	(	(	PUNCT
cana-763	131	26	1	1	NUM
cana-763	131	27	−	−	PROPN
cana-763	131	28	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	131	29	(	(	PUNCT
cana-763	131	30	𝒟℘	𝒟℘	X
cana-763	131	31	𝑚(ς	𝑚(ς	NOUN
cana-763	131	32	,	,	PUNCT
cana-763	131	33	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	131	34	)	)	PUNCT
cana-763	131	35	)	)	PUNCT
cana-763	132	1	′(1	′(1	PROPN
cana-763	132	2	+	+	CCONJ
cana-763	132	3	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	132	4	)	)	PUNCT
cana-763	132	5	−	−	PROPN
cana-763	133	1	(	(	PUNCT
cana-763	133	2	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	133	3	+	+	CCONJ
cana-763	133	4	1	1	NUM
cana-763	133	5	+	+	CCONJ
cana-763	133	6	ϱ	ϱ	NOUN
cana-763	133	7	)	)	PUNCT
cana-763	133	8	(	(	PUNCT
cana-763	133	9	𝒟℘	𝒟℘	X
cana-763	133	10	𝑚(ς	𝑚(ς	NOUN
cana-763	133	11	,	,	PUNCT
cana-763	133	12	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	133	13	)	)	PUNCT
cana-763	133	14	−	−	NOUN
cana-763	133	15	𝒟℘	𝒟℘	NUM
cana-763	133	16	𝑚(ς	𝑚(ς	NOUN
cana-763	133	17	,	,	PUNCT
cana-763	133	18	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	133	19	)	)	PUNCT
cana-763	133	20	)	)	PUNCT
cana-763	133	21	(	(	PUNCT
cana-763	133	22	1	1	NUM
cana-763	133	23	−	−	PROPN
cana-763	133	24	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	133	25	(	(	PUNCT
cana-763	133	26	𝒟℘	𝒟℘	X
cana-763	133	27	𝑚(ς	𝑚(ς	NOUN
cana-763	133	28	,	,	PUNCT
cana-763	133	29	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	133	30	)	)	PUNCT
cana-763	133	31	)	)	PUNCT
cana-763	134	1	′(1	′(1	PROPN
cana-763	134	2	+	+	NUM
cana-763	134	3	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	134	4	)	)	PUNCT
cana-763	135	1	+	+	CCONJ
cana-763	135	2	(	(	PUNCT
cana-763	135	3	1	1	NUM
cana-763	135	4	−	−	PROPN
cana-763	135	5	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	135	6	−	−	ADP
cana-763	135	7	ϱ	ϱ	NOUN
cana-763	135	8	)	)	PUNCT
cana-763	135	9	(	(	PUNCT
cana-763	135	10	𝒟℘	𝒟℘	X
cana-763	135	11	𝑚(ς	𝑚(ς	NOUN
cana-763	135	12	,	,	PUNCT
cana-763	135	13	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	135	14	)	)	PUNCT
cana-763	135	15	−	−	NOUN
cana-763	135	16	𝒟℘	𝒟℘	NUM
cana-763	135	17	𝑚(ς	𝑚(ς	NOUN
cana-763	135	18	,	,	PUNCT
cana-763	135	19	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	135	20	)	)	PUNCT
cana-763	135	21	)	)	PUNCT
cana-763	135	22	≠	≠	PROPN
cana-763	135	23	𝑠.	𝑠.	NOUN
cana-763	135	24	in	in	ADP
cana-763	135	25	other	other	ADJ
cana-763	135	26	words	word	NOUN
cana-763	135	27	,	,	PUNCT
cana-763	135	28	we	we	PRON
cana-763	135	29	must	must	AUX
cana-763	135	30	have	have	AUX
cana-763	135	31	(	(	PUNCT
cana-763	135	32	1	1	NUM
cana-763	135	33	−	−	NOUN
cana-763	135	34	𝑠)(1	𝑠)(1	NUM
cana-763	135	35	−	−	PROPN
cana-763	135	36	𝑡)𝑧	𝑡)𝑧	PROPN
cana-763	135	37	(	(	PUNCT
cana-763	135	38	𝒟℘	𝒟℘	X
cana-763	135	39	𝑚(ς	𝑚(ς	NOUN
cana-763	135	40	,	,	PUNCT
cana-763	135	41	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	135	42	)	)	PUNCT
cana-763	135	43	)	)	PUNCT
cana-763	135	44	′(1	′(1	PROPN
cana-763	135	45	+	+	CCONJ
cana-763	135	46	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	135	47	)	)	PUNCT
cana-763	135	48	−	−	PROPN
cana-763	135	49	(	(	PUNCT
cana-763	135	50	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	135	51	+	+	NOUN
cana-763	135	52	1	1	NUM
cana-763	135	53	+	+	CCONJ
cana-763	135	54	ϱ	ϱ	ADP
cana-763	135	55	+	+	X
cana-763	135	56	𝑠(−1	𝑠(−1	NOUN
cana-763	135	57	+	+	CCONJ
cana-763	135	58	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	135	59	+	+	CCONJ
cana-763	135	60	ϱ	ϱ	NOUN
cana-763	135	61	)	)	PUNCT
cana-763	135	62	)	)	PUNCT
cana-763	135	63	×	×	NOUN
cana-763	135	64	(	(	PUNCT
cana-763	135	65	𝒟℘	𝒟℘	X
cana-763	135	66	𝑚(ς	𝑚(ς	NOUN
cana-763	135	67	,	,	PUNCT
cana-763	135	68	ℏ)𝑓(𝑧	ℏ)𝑓(𝑧	NOUN
cana-763	135	69	)	)	PUNCT
cana-763	135	70	−	−	NOUN
cana-763	135	71	𝒟℘	𝒟℘	NUM
cana-763	135	72	𝑚(ς	𝑚(ς	NOUN
cana-763	135	73	,	,	PUNCT
cana-763	135	74	ℏ)𝑓(𝑡𝑧	ℏ)𝑓(𝑡𝑧	NOUN
cana-763	135	75	)	)	PUNCT
cana-763	135	76	)	)	PUNCT
cana-763	136	1	≠	≠	PROPN
cana-763	136	2	0	0	X
cana-763	136	3	.	.	PUNCT
cana-763	136	4	which	which	PRON
cana-763	136	5	is	be	AUX
cana-763	136	6	equivalent	equivalent	ADJ
cana-763	136	7	to	to	ADP
cana-763	136	8	𝑧	𝑧	PROPN
cana-763	136	9	−	−	PROPN
cana-763	136	10	∑	∑	PUNCT
cana-763	136	11	𝜙𝑛(ς	𝜙𝑛(ς	NUM
cana-763	136	12	,	,	PUNCT
cana-763	136	13	ℏ	ℏ	PROPN
cana-763	136	14	,	,	PUNCT
cana-763	136	15	℘	℘	PROPN
cana-763	136	16	,	,	PUNCT
cana-763	136	17	𝑚	𝑚	NOUN
cana-763	136	18	)	)	PUNCT
cana-763	136	19	(	(	PUNCT
cana-763	136	20	(	(	PUNCT
cana-763	136	21	𝑛	𝑛	PRON
cana-763	136	22	−	−	PROPN
cana-763	136	23	𝑢𝑛)(1	𝑢𝑛)(1	NOUN
cana-763	136	24	+	+	CCONJ
cana-763	136	25	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	136	26	−	−	PROPN
cana-763	136	27	𝑠𝑘𝑒𝑖𝜃	𝑠𝑘𝑒𝑖𝜃	PROPN
cana-763	136	28	)	)	PUNCT
cana-763	136	29	−	−	PROPN
cana-763	137	1	𝑠(𝑛	𝑠(𝑛	PROPN
cana-763	137	2	+	+	CCONJ
cana-763	137	3	𝑢𝑛	𝑢𝑛	NOUN
cana-763	137	4	)	)	PUNCT
cana-763	137	5	−	−	PROPN
cana-763	137	6	𝑢𝑛ϱ(1	𝑢𝑛ϱ(1	NOUN
cana-763	137	7	−	−	PROPN
cana-763	137	8	𝑠	𝑠	NOUN
cana-763	137	9	)	)	PUNCT
cana-763	137	10	)	)	PUNCT
cana-763	138	1	ϱ(𝑠	ϱ(𝑠	PROPN
cana-763	139	1	−	−	NOUN
cana-763	139	2	1	1	NUM
cana-763	139	3	)	)	PUNCT
cana-763	139	4	−	−	NOUN
cana-763	139	5	2𝑠	2𝑠	NOUN
cana-763	139	6	∞	∞	PROPN
cana-763	139	7	𝑛=2	𝑛=2	PROPN
cana-763	139	8	𝑧𝑛	𝑧𝑛	ADP
cana-763	139	9	≠	≠	PROPN
cana-763	139	10	0	0	X
cana-763	139	11	.	.	PUNCT
cana-763	140	1	however	however	ADV
cana-763	140	2	,	,	PUNCT
cana-763	140	3	𝑓	𝑓	PROPN
cana-763	140	4	∈	∈	PROPN
cana-763	140	5	�	�	PROPN
cana-763	140	6	̃	̃	PROPN
cana-763	140	7	�	�	PROPN
cana-763	140	8	𝑆𝑠	𝑆𝑠	PROPN
cana-763	140	9	𝑚(ς	𝑚(ς	NOUN
cana-763	140	10	,	,	PUNCT
cana-763	140	11	ℏ	ℏ	PROPN
cana-763	140	12	,	,	PUNCT
cana-763	140	13	℘	℘	PROPN
cana-763	140	14	,	,	PUNCT
cana-763	140	15	ϱ	ϱ	NOUN
cana-763	140	16	,	,	PUNCT
cana-763	140	17	𝑡	𝑡	NOUN
cana-763	140	18	)	)	PUNCT
cana-763	140	19	if	if	SCONJ
cana-763	140	20	and	and	CCONJ
cana-763	140	21	only	only	ADV
cana-763	140	22	(	(	PUNCT
cana-763	140	23	𝑓∗ℎ	𝑓∗ℎ	NUM
cana-763	140	24	)	)	PUNCT
cana-763	140	25	𝑧	𝑧	DET
cana-763	140	26	≠	≠	PROPN
cana-763	140	27	0	0	NUM
cana-763	140	28	,	,	PUNCT
cana-763	140	29	𝑧	𝑧	DET
cana-763	140	30	∈	∈	PROPN
cana-763	140	31	𝑈	𝑈	PROPN
cana-763	140	32	−	−	PROPN
cana-763	140	33	{	{	PUNCT
cana-763	140	34	0	0	NUM
cana-763	140	35	}	}	PUNCT
cana-763	140	36	,	,	PUNCT
cana-763	140	37	where	where	SCONJ
cana-763	140	38	ℎ(𝑧	ℎ(𝑧	VERB
cana-763	140	39	)	)	PUNCT
cana-763	140	40	=	=	SYM
cana-763	140	41	𝑧	𝑧	PRON
cana-763	140	42	−	−	PROPN
cana-763	140	43	∑	∑	SYM
cana-763	140	44	𝑐𝑛	𝑐𝑛	PROPN
cana-763	140	45	∞	∞	PROPN
cana-763	140	46	𝑛=2	𝑛=2	PROPN
cana-763	140	47	𝑧𝑛	𝑧𝑛	NOUN
cana-763	140	48	and	and	CCONJ
cana-763	140	49	𝑐𝑛	𝑐𝑛	PROPN
cana-763	140	50	=	=	NOUN
cana-763	140	51	𝜙𝑛(ς	𝜙𝑛(ς	PROPN
cana-763	140	52	,	,	PUNCT
cana-763	140	53	ℏ	ℏ	PROPN
cana-763	140	54	,	,	PUNCT
cana-763	140	55	℘	℘	PROPN
cana-763	140	56	,	,	PUNCT
cana-763	140	57	𝑚	𝑚	NOUN
cana-763	140	58	)	)	PUNCT
cana-763	140	59	(	(	PUNCT
cana-763	140	60	(	(	PUNCT
cana-763	140	61	𝑛	𝑛	PRON
cana-763	140	62	−	−	PROPN
cana-763	140	63	𝑢𝑛)(1	𝑢𝑛)(1	NOUN
cana-763	140	64	+	+	CCONJ
cana-763	140	65	𝑒𝑖𝜃	𝑒𝑖𝜃	PROPN
cana-763	140	66	−	−	PROPN
cana-763	140	67	𝑠𝑒𝑖𝜃	𝑠𝑒𝑖𝜃	NOUN
cana-763	140	68	)	)	PUNCT
cana-763	140	69	−	−	PROPN
cana-763	141	1	𝑠(𝑛	𝑠(𝑛	PROPN
cana-763	141	2	+	+	CCONJ
cana-763	141	3	𝑢𝑛	𝑢𝑛	NOUN
cana-763	141	4	)	)	PUNCT
cana-763	141	5	−	−	PROPN
cana-763	141	6	𝑢𝑛ϱ(1	𝑢𝑛ϱ(1	NOUN
cana-763	141	7	−	−	PROPN
cana-763	141	8	𝑠	𝑠	NOUN
cana-763	141	9	)	)	PUNCT
cana-763	141	10	)	)	PUNCT
cana-763	142	1	ϱ(𝑠	ϱ(𝑠	PROPN
cana-763	143	1	−	−	NOUN
cana-763	143	2	1	1	NUM
cana-763	143	3	)	)	PUNCT
cana-763	143	4	−	−	NOUN
cana-763	143	5	2𝑠	2𝑠	NOUN
cana-763	143	6	we	we	PRON
cana-763	143	7	note	note	VERB
cana-763	143	8	that	that	SCONJ
cana-763	143	9	|𝑐𝑛|	|𝑐𝑛|	NOUN
cana-763	143	10	≤	≤	NOUN
cana-763	143	11	𝜙𝑛(ς	𝜙𝑛(ς	NOUN
cana-763	143	12	,	,	PUNCT
cana-763	143	13	ℏ	ℏ	PROPN
cana-763	143	14	,	,	PUNCT
cana-763	143	15	℘	℘	NOUN
cana-763	143	16	,	,	PUNCT
cana-763	143	17	𝑚)|2𝑛	𝑚)|2𝑛	NOUN
cana-763	143	18	−	−	NOUN
cana-763	143	19	𝑢𝑛(1	𝑢𝑛(1	NOUN
cana-763	143	20	+	+	CCONJ
cana-763	143	21	ϱ)|	ϱ)|	PROPN
cana-763	143	22	1	1	NUM
cana-763	143	23	−	−	NOUN
cana-763	143	24	ϱ	ϱ	PROPN
cana-763	143	25	since	since	SCONJ
cana-763	143	26	𝑓(𝑧)+𝜖𝑧	𝑓(𝑧)+𝜖𝑧	NOUN
cana-763	143	27	1+𝜖	1+𝜖	NUM
cana-763	143	28	∈	∈	PROPN
cana-763	143	29	�	�	PROPN
cana-763	143	30	̃	̃	PROPN
cana-763	143	31	�	�	PROPN
cana-763	143	32	𝑆𝑠	𝑆𝑠	PROPN
cana-763	143	33	𝑚(ς	𝑚(ς	NOUN
cana-763	143	34	,	,	PUNCT
cana-763	143	35	ℏ	ℏ	PROPN
cana-763	143	36	,	,	PUNCT
cana-763	143	37	℘	℘	PROPN
cana-763	143	38	,	,	PUNCT
cana-763	143	39	ϱ	ϱ	NOUN
cana-763	143	40	,	,	PUNCT
cana-763	143	41	𝑡	𝑡	NOUN
cana-763	143	42	)	)	PUNCT
cana-763	143	43	,	,	PUNCT
cana-763	143	44	therefore	therefore	ADV
cana-763	143	45	𝑧−1	𝑧−1	PROPN
cana-763	143	46	(	(	PUNCT
cana-763	143	47	𝑓(𝑧)+𝜖𝑧	𝑓(𝑧)+𝜖𝑧	NOUN
cana-763	143	48	1+𝜖	1+𝜖	NUM
cana-763	143	49	∗	∗	NOUN
cana-763	143	50	ℎ(𝑧	ℎ(𝑧	NOUN
cana-763	143	51	)	)	PUNCT
cana-763	143	52	)	)	PUNCT
cana-763	143	53	≠	≠	PROPN
cana-763	143	54	0	0	NUM
cana-763	143	55	,	,	PUNCT
cana-763	143	56	which	which	PRON
cana-763	143	57	is	be	AUX
cana-763	143	58	equivalent	equivalent	ADJ
cana-763	143	59	to	to	ADP
cana-763	143	60	(	(	PUNCT
cana-763	143	61	𝑓	𝑓	DET
cana-763	143	62	∗	∗	NOUN
cana-763	143	63	ℎ)(𝑧	ℎ)(𝑧	NOUN
cana-763	143	64	)	)	PUNCT
cana-763	143	65	(	(	PUNCT
cana-763	143	66	1	1	NUM
cana-763	143	67	+	+	NOUN
cana-763	143	68	𝜖)𝑧	𝜖)𝑧	NOUN
cana-763	144	1	+	+	CCONJ
cana-763	144	2	𝜖	𝜖	X
cana-763	144	3	1	1	NUM
cana-763	144	4	+	+	CCONJ
cana-763	144	5	𝜖	𝜖	X
cana-763	144	6	≠	≠	PROPN
cana-763	144	7	0	0	NUM
cana-763	144	8	.	.	PUNCT
cana-763	144	9	(	(	PUNCT
cana-763	144	10	3.1	3.1	NUM
cana-763	144	11	)	)	PUNCT
cana-763	144	12	now	now	ADV
cana-763	144	13	suppose	suppose	VERB
cana-763	144	14	that	that	SCONJ
cana-763	144	15	|	|	INTJ
cana-763	144	16	(	(	PUNCT
cana-763	144	17	𝑓∗ℎ)(𝑧	𝑓∗ℎ)(𝑧	NOUN
cana-763	144	18	)	)	PUNCT
cana-763	144	19	𝑧	𝑧	PROPN
cana-763	145	1	|	|	ADV
cana-763	145	2	<	<	X
cana-763	145	3	ς	ς	PROPN
cana-763	145	4	.	.	PUNCT
cana-763	145	5	then	then	ADV
cana-763	145	6	by	by	ADP
cana-763	145	7	(	(	PUNCT
cana-763	145	8	3.1	3.1	NUM
cana-763	145	9	)	)	PUNCT
cana-763	145	10	,	,	PUNCT
cana-763	145	11	we	we	PRON
cana-763	145	12	must	must	AUX
cana-763	145	13	have	have	VERB
cana-763	145	14	communications	communication	NOUN
cana-763	145	15	on	on	ADP
cana-763	145	16	applied	apply	VERB
cana-763	145	17	nonlinear	nonlinear	ADJ
cana-763	145	18	analysis	analysis	NOUN
cana-763	145	19	issn	issn	NOUN
cana-763	145	20	:	:	PUNCT
cana-763	145	21	1074	1074	NUM
cana-763	145	22	-	-	PUNCT
cana-763	145	23	133x	133x	NUM
cana-763	145	24	vol	vol	NOUN
cana-763	145	25	31	31	NUM
cana-763	145	26	no	no	NOUN
cana-763	145	27	.	.	PUNCT
cana-763	146	1	3s	3s	NUM
cana-763	146	2	(	(	PUNCT
cana-763	146	3	2024	2024	NUM
cana-763	146	4	)	)	PUNCT
cana-763	146	5	260	260	NUM
cana-763	146	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-763	147	1	|	|	ADV
cana-763	147	2	(	(	PUNCT
cana-763	147	3	𝑓	𝑓	DET
cana-763	147	4	∗	∗	NOUN
cana-763	147	5	ℎ)(𝑧	ℎ)(𝑧	NOUN
cana-763	147	6	)	)	PUNCT
cana-763	147	7	(	(	PUNCT
cana-763	147	8	1	1	NUM
cana-763	147	9	+	+	NOUN
cana-763	147	10	𝜖)𝑧	𝜖)𝑧	NOUN
cana-763	148	1	+	+	CCONJ
cana-763	148	2	𝜖	𝜖	X
cana-763	148	3	1	1	NUM
cana-763	148	4	+	+	NUM
cana-763	148	5	𝜖	𝜖	X
cana-763	148	6	|	|	PRON
cana-763	148	7	≥	≥	NOUN
cana-763	148	8	|𝜖|	|𝜖|	PROPN
cana-763	148	9	|1	|1	PRON
cana-763	148	10	+	+	NUM
cana-763	148	11	𝜖|	𝜖|	NOUN
cana-763	148	12	−	−	NUM
cana-763	148	13	1	1	NUM
cana-763	148	14	|1	|1	PRON
cana-763	148	15	+	+	NUM
cana-763	148	16	𝜖|	𝜖|	NOUN
cana-763	148	17	|	|	ADV
cana-763	148	18	(	(	PUNCT
cana-763	148	19	𝑓	𝑓	PRON
cana-763	148	20	∗	∗	NOUN
cana-763	148	21	ℎ)(𝑧	ℎ)(𝑧	NOUN
cana-763	148	22	)	)	PUNCT
cana-763	148	23	𝑧	𝑧	PRON
cana-763	148	24	|	|	ADV
cana-763	148	25	>	>	X
cana-763	148	26	|𝜖|	|𝜖|	PROPN
cana-763	148	27	−	−	PROPN
cana-763	148	28	ς	ς	PROPN
cana-763	148	29	|1	|1	PRON
cana-763	148	30	+	+	CCONJ
cana-763	148	31	𝜖|	𝜖|	PROPN
cana-763	148	32	≥	≥	NOUN
cana-763	148	33	0	0	NUM
cana-763	148	34	,	,	PUNCT
cana-763	148	35	this	this	PRON
cana-763	148	36	is	be	AUX
cana-763	148	37	a	a	DET
cana-763	148	38	contradiction	contradiction	NOUN
cana-763	148	39	by	by	ADP
cana-763	148	40	|𝜖|	|𝜖|	PROPN
cana-763	148	41	<	<	X
cana-763	148	42	ς	ς	PROPN
cana-763	148	43	and	and	CCONJ
cana-763	148	44	however	however	ADV
cana-763	148	45	,	,	PUNCT
cana-763	148	46	we	we	PRON
cana-763	148	47	have	have	VERB
cana-763	148	48	|	|	ADV
cana-763	148	49	(	(	PUNCT
cana-763	148	50	𝑓∗ℎ)(𝑧	𝑓∗ℎ)(𝑧	NOUN
cana-763	148	51	)	)	PUNCT
cana-763	149	1	𝑧	𝑧	PROPN
cana-763	150	1	|	|	ADV
cana-763	150	2	≥	≥	NOUN
cana-763	150	3	ς	ς	NOUN
cana-763	150	4	.	.	PUNCT
cana-763	151	1	if	if	SCONJ
cana-763	151	2	𝑔(𝑧	𝑔(𝑧	NUM
cana-763	151	3	)	)	PUNCT
cana-763	152	1	=	=	SYM
cana-763	152	2	𝑧	𝑧	DET
cana-763	152	3	−	−	NOUN
cana-763	152	4	∑	∑	PROPN
cana-763	152	5	𝑏𝑛	𝑏𝑛	ADP
cana-763	152	6	∞	∞	PROPN
cana-763	152	7	𝑛=2	𝑛=2	VERB
cana-763	152	8	𝑧𝑛	𝑧𝑛	ADP
cana-763	152	9	∈	∈	PROPN
cana-763	152	10	𝑁ς(𝑓	𝑁ς(𝑓	PROPN
cana-763	152	11	)	)	PUNCT
cana-763	152	12	,	,	PUNCT
cana-763	152	13	then	then	ADV
cana-763	152	14	ς	ς	PROPN
cana-763	152	15	−	−	PROPN
cana-763	153	1	|	|	INTJ
cana-763	153	2	(	(	PUNCT
cana-763	153	3	𝑔	𝑔	PROPN
cana-763	153	4	∗	∗	NOUN
cana-763	153	5	ℎ)(𝑧	ℎ)(𝑧	NOUN
cana-763	153	6	)	)	PUNCT
cana-763	154	1	𝑧	𝑧	PRON
cana-763	154	2	|	|	ADV
cana-763	154	3	≤	≤	PUNCT
cana-763	155	1	|	|	ADV
cana-763	155	2	(	(	PUNCT
cana-763	155	3	(	(	PUNCT
cana-763	155	4	𝑓	𝑓	DET
cana-763	155	5	−	−	PROPN
cana-763	155	6	𝑔	𝑔	NOUN
cana-763	155	7	)	)	PUNCT
cana-763	155	8	∗	∗	NOUN
cana-763	155	9	ℎ)(𝑧	ℎ)(𝑧	NOUN
cana-763	155	10	)	)	PUNCT
cana-763	155	11	𝑧	𝑧	PRON
cana-763	155	12	|	|	ADV
cana-763	155	13	≤	≤	VERB
cana-763	156	1	∑|𝑎𝑛	∑|𝑎𝑛	NOUN
cana-763	156	2	−	−	PROPN
cana-763	157	1	𝑏𝑛|	𝑏𝑛|	PROPN
cana-763	157	2	∞	∞	PROPN
cana-763	157	3	𝑛=2	𝑛=2	PROPN
cana-763	157	4	|𝑐𝑛||𝑧𝑛|	|𝑐𝑛||𝑧𝑛|	VERB
cana-763	157	5	<	<	X
cana-763	157	6	∑	∑	X
cana-763	157	7	𝜙𝑛(ς	𝜙𝑛(ς	ADJ
cana-763	157	8	,	,	PUNCT
cana-763	157	9	ℏ	ℏ	PROPN
cana-763	157	10	,	,	PUNCT
cana-763	157	11	℘	℘	NOUN
cana-763	157	12	,	,	PUNCT
cana-763	157	13	𝑚)|2𝑛	𝑚)|2𝑛	NOUN
cana-763	157	14	−	−	NOUN
cana-763	157	15	𝑢𝑛(1	𝑢𝑛(1	NOUN
cana-763	157	16	+	+	CCONJ
cana-763	157	17	ϱ)|	ϱ)|	PROPN
cana-763	157	18	1	1	NUM
cana-763	157	19	−	−	NOUN
cana-763	157	20	ϱ	ϱ	ADP
cana-763	157	21	∞	∞	PROPN
cana-763	157	22	𝑛=2	𝑛=2	X
cana-763	157	23	|𝑎𝑛	|𝑎𝑛	NUM
cana-763	157	24	−	−	PROPN
cana-763	157	25	𝑏𝑛|	𝑏𝑛|	PROPN
cana-763	157	26	≤	≤	NUM
cana-763	157	27	ς	ς	PROPN
cana-763	157	28	.	.	NOUN
cana-763	157	29	4	4	NUM
cana-763	157	30	partial	partial	ADJ
cana-763	157	31	sums	sum	NOUN
cana-763	157	32	in	in	ADP
cana-763	157	33	this	this	DET
cana-763	157	34	section	section	NOUN
cana-763	157	35	,	,	PUNCT
cana-763	157	36	applying	apply	VERB
cana-763	157	37	methods	method	NOUN
cana-763	157	38	used	use	VERB
cana-763	157	39	by	by	ADP
cana-763	157	40	silverman	silverman	NOUN
cana-763	157	41	[	[	X
cana-763	157	42	13	13	NUM
cana-763	157	43	]	]	PUNCT
cana-763	157	44	and	and	CCONJ
cana-763	157	45	silvia	silvia	PROPN
cana-763	157	46	[	[	X
cana-763	157	47	14	14	NUM
cana-763	157	48	]	]	PUNCT
cana-763	157	49	,	,	PUNCT
cana-763	157	50	we	we	PRON
cana-763	157	51	investigate	investigate	VERB
cana-763	157	52	the	the	DET
cana-763	157	53	ratio	ratio	NOUN
cana-763	157	54	of	of	ADP
cana-763	157	55	a	a	DET
cana-763	157	56	function	function	NOUN
cana-763	157	57	of	of	ADP
cana-763	157	58	the	the	DET
cana-763	157	59	form	form	NOUN
cana-763	157	60	(	(	PUNCT
cana-763	157	61	1.8	1.8	NUM
cana-763	157	62	)	)	PUNCT
cana-763	157	63	to	to	ADP
cana-763	157	64	its	its	PRON
cana-763	157	65	sequence	sequence	NOUN
cana-763	157	66	of	of	ADP
cana-763	157	67	partial	partial	ADJ
cana-763	157	68	sums	sum	NOUN
cana-763	157	69	𝑓𝑚(𝑧	𝑓𝑚(𝑧	PROPN
cana-763	157	70	)	)	PUNCT
cana-763	157	71	=	=	PUNCT
cana-763	158	1	𝑧	𝑧	PROPN
cana-763	159	1	+	+	CCONJ
cana-763	159	2	∑	∑	PROPN
cana-763	159	3	𝑎𝑛	𝑎𝑛	PROPN
cana-763	159	4	𝑚	𝑚	NOUN
cana-763	159	5	𝑛=2	𝑛=2	VERB
cana-763	159	6	𝑧𝑛.	𝑧𝑛.	NOUN
cana-763	159	7	theorem	theorem	NOUN
cana-763	159	8	8	8	NUM
cana-763	159	9	.	.	PUNCT
cana-763	160	1	if	if	SCONJ
cana-763	160	2	𝑓	𝑓	PROPN
cana-763	160	3	of	of	ADP
cana-763	160	4	the	the	DET
cana-763	160	5	form	form	NOUN
cana-763	160	6	(	(	PUNCT
cana-763	160	7	1.1	1.1	NUM
cana-763	160	8	)	)	PUNCT
cana-763	160	9	satisfies	satisfy	VERB
cana-763	160	10	the	the	DET
cana-763	160	11	condition	condition	NOUN
cana-763	160	12	(	(	PUNCT
cana-763	160	13	2.1	2.1	NUM
cana-763	160	14	)	)	PUNCT
cana-763	160	15	then	then	ADV
cana-763	160	16	ℜ	ℜ	X
cana-763	160	17	{	{	PUNCT
cana-763	160	18	𝑓(𝑧	𝑓(𝑧	NUM
cana-763	160	19	)	)	PUNCT
cana-763	160	20	𝑓𝑚(𝑧	𝑓𝑚(𝑧	PROPN
cana-763	160	21	)	)	PUNCT
cana-763	160	22	}	}	PUNCT
cana-763	160	23	≥	≥	VERB
cana-763	160	24	1	1	NUM
cana-763	160	25	−	−	PROPN
cana-763	160	26	1	1	NUM
cana-763	160	27	𝛿𝑚+1	𝛿𝑚+1	PROPN
cana-763	160	28	(	(	PUNCT
cana-763	160	29	4.1	4.1	NUM
cana-763	160	30	)	)	PUNCT
cana-763	160	31	and	and	CCONJ
cana-763	160	32	𝛿𝑛	𝛿𝑛	VERB
cana-763	160	33	=	=	PUNCT
cana-763	160	34	{	{	PUNCT
cana-763	160	35	1	1	NUM
cana-763	160	36	,	,	PUNCT
cana-763	160	37	𝑖𝑓	𝑖𝑓	ADP
cana-763	160	38	𝑛	𝑛	PRON
cana-763	160	39	=	=	SYM
cana-763	160	40	2,3	2,3	NUM
cana-763	160	41	⋯	⋯	ADP
cana-763	160	42	𝑚	𝑚	SYM
cana-763	160	43	𝛿𝑚+1	𝛿𝑚+1	PROPN
cana-763	160	44	,	,	PUNCT
cana-763	160	45	𝑖𝑓	𝑖𝑓	ADP
cana-763	160	46	𝑛	𝑛	PRON
cana-763	160	47	=	=	PUNCT
cana-763	160	48	𝑚	𝑚	PROPN
cana-763	160	49	+	+	NOUN
cana-763	160	50	1	1	NUM
cana-763	160	51	,	,	PUNCT
cana-763	160	52	𝑚	𝑚	PROPN
cana-763	160	53	∗	∗	NOUN
cana-763	160	54	2	2	NUM
cana-763	160	55	,	,	PUNCT
cana-763	160	56	⋯	⋯	VERB
cana-763	160	57	(	(	PUNCT
cana-763	160	58	4.2	4.2	NUM
cana-763	160	59	)	)	PUNCT
cana-763	160	60	where	where	SCONJ
cana-763	160	61	𝛿𝑛	𝛿𝑛	ADP
cana-763	160	62	=	=	PUNCT
cana-763	160	63	𝜙𝑛(ς,ℏ,℘,𝑚)|2𝑛−𝑢𝑛(1+ϱ)|	𝜙𝑛(ς,ℏ,℘,𝑚)|2𝑛−𝑢𝑛(1+ϱ)|	X
cana-763	160	64	1−ϱ	1−ϱ	NUM
cana-763	160	65	.	.	PUNCT
cana-763	161	1	(	(	PUNCT
cana-763	161	2	4.3	4.3	NUM
cana-763	161	3	)	)	PUNCT
cana-763	161	4	the	the	DET
cana-763	161	5	result	result	NOUN
cana-763	161	6	in	in	ADP
cana-763	161	7	(	(	PUNCT
cana-763	161	8	4.1	4.1	NUM
cana-763	161	9	)	)	PUNCT
cana-763	161	10	is	be	AUX
cana-763	161	11	sharp	sharp	ADJ
cana-763	161	12	for	for	ADP
cana-763	161	13	every	every	DET
cana-763	161	14	m	m	NOUN
cana-763	161	15	,	,	PUNCT
cana-763	161	16	with	with	ADP
cana-763	161	17	the	the	DET
cana-763	161	18	extremal	extremal	ADJ
cana-763	161	19	function	function	NOUN
cana-763	161	20	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	161	21	)	)	PUNCT
cana-763	161	22	=	=	SYM
cana-763	161	23	𝑧	𝑧	PROPN
cana-763	162	1	+	+	CCONJ
cana-763	162	2	𝑧𝑚+1	𝑧𝑚+1	NUM
cana-763	162	3	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	162	4	.	.	PUNCT
cana-763	163	1	(	(	PUNCT
cana-763	163	2	4.4	4.4	NUM
cana-763	163	3	)	)	PUNCT
cana-763	163	4	proof	proof	NOUN
cana-763	163	5	.	.	PUNCT
cana-763	164	1	define	define	VERB
cana-763	164	2	the	the	DET
cana-763	164	3	function	function	NOUN
cana-763	164	4	𝑤	𝑤	ADP
cana-763	164	5	,	,	PUNCT
cana-763	164	6	we	we	PRON
cana-763	164	7	may	may	AUX
cana-763	164	8	write	write	VERB
cana-763	164	9	1	1	NUM
cana-763	164	10	+	+	CCONJ
cana-763	164	11	𝑤(𝑧	𝑤(𝑧	NOUN
cana-763	164	12	)	)	PUNCT
cana-763	164	13	1	1	NUM
cana-763	164	14	−	−	NOUN
cana-763	164	15	𝑤(𝑧	𝑤(𝑧	NOUN
cana-763	164	16	)	)	PUNCT
cana-763	165	1	=	=	SYM
cana-763	165	2	𝛿𝑚+1	𝛿𝑚+1	PROPN
cana-763	165	3	{	{	PUNCT
cana-763	165	4	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	165	5	)	)	PUNCT
cana-763	165	6	𝑓𝑚(𝑧	𝑓𝑚(𝑧	ADJ
cana-763	165	7	)	)	PUNCT
cana-763	165	8	−	−	PROPN
cana-763	166	1	(	(	PUNCT
cana-763	166	2	1	1	NUM
cana-763	166	3	−	−	PROPN
cana-763	166	4	1	1	NUM
cana-763	166	5	𝛿𝑚+1	𝛿𝑚+1	PROPN
cana-763	166	6	)	)	PUNCT
cana-763	166	7	}	}	PUNCT
cana-763	166	8	(	(	PUNCT
cana-763	166	9	4.5	4.5	NUM
cana-763	166	10	)	)	PUNCT
cana-763	166	11	=	=	PRON
cana-763	166	12	{	{	PUNCT
cana-763	167	1	1	1	NUM
cana-763	167	2	+	+	CCONJ
cana-763	167	3	∑	∑	PROPN
cana-763	167	4	𝑎𝑛	𝑎𝑛	PROPN
cana-763	167	5	𝑚	𝑚	ADP
cana-763	167	6	𝑛=2	𝑛=2	X
cana-763	167	7	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	167	8	+	+	CCONJ
cana-763	167	9	𝛿𝑚+1	𝛿𝑚+1	VERB
cana-763	167	10	∑	∑	PROPN
cana-763	167	11	𝑎𝑛	𝑎𝑛	PROPN
cana-763	167	12	∞	∞	NUM
cana-763	167	13	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	167	14	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	167	15	1	1	NUM
cana-763	167	16	+	+	CCONJ
cana-763	167	17	∑	∑	PROPN
cana-763	167	18	𝑎𝑛	𝑎𝑛	PROPN
cana-763	167	19	𝑚	𝑚	ADP
cana-763	167	20	𝑛=2	𝑛=2	X
cana-763	167	21	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	167	22	}	}	PUNCT
cana-763	167	23	.	.	PUNCT
cana-763	168	1	then	then	ADV
cana-763	168	2	,	,	PUNCT
cana-763	168	3	from	from	ADP
cana-763	168	4	(	(	PUNCT
cana-763	168	5	4.5	4.5	NUM
cana-763	168	6	)	)	PUNCT
cana-763	168	7	,	,	PUNCT
cana-763	168	8	we	we	PRON
cana-763	168	9	can	can	AUX
cana-763	168	10	obtain	obtain	VERB
cana-763	168	11	𝑤(𝑧	𝑤(𝑧	NOUN
cana-763	168	12	)	)	PUNCT
cana-763	168	13	=	=	PUNCT
cana-763	168	14	𝛿𝑚+1	𝛿𝑚+1	VERB
cana-763	168	15	∑	∑	PUNCT
cana-763	168	16	𝑎𝑛	𝑎𝑛	PROPN
cana-763	168	17	∞	∞	NUM
cana-763	168	18	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	168	19	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	168	20	2	2	NUM
cana-763	168	21	+	+	CCONJ
cana-763	168	22	2	2	NUM
cana-763	168	23	∑	∑	PUNCT
cana-763	168	24	𝑎𝑛	𝑎𝑛	VERB
cana-763	168	25	𝑚	𝑚	ADP
cana-763	168	26	𝑛=2	𝑛=2	X
cana-763	168	27	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	168	28	+	+	CCONJ
cana-763	168	29	𝛿𝑚+1	𝛿𝑚+1	VERB
cana-763	168	30	∑	∑	PROPN
cana-763	168	31	𝑎𝑛	𝑎𝑛	PROPN
cana-763	168	32	∞	∞	NUM
cana-763	168	33	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	168	34	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	168	35	communications	communication	NOUN
cana-763	168	36	on	on	ADP
cana-763	168	37	applied	apply	VERB
cana-763	168	38	nonlinear	nonlinear	ADJ
cana-763	168	39	analysis	analysis	NOUN
cana-763	168	40	issn	issn	NOUN
cana-763	168	41	:	:	PUNCT
cana-763	168	42	1074	1074	NUM
cana-763	168	43	-	-	PUNCT
cana-763	168	44	133x	133x	NUM
cana-763	168	45	vol	vol	NOUN
cana-763	168	46	31	31	NUM
cana-763	168	47	no	no	NOUN
cana-763	168	48	.	.	PUNCT
cana-763	169	1	3s	3s	NUM
cana-763	169	2	(	(	PUNCT
cana-763	169	3	2024	2024	NUM
cana-763	169	4	)	)	PUNCT
cana-763	169	5	261	261	NUM
cana-763	169	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-763	169	7	and	and	CCONJ
cana-763	169	8	|𝑤(𝑧)|	|𝑤(𝑧)|	PROPN
cana-763	169	9	≤	≤	NUM
cana-763	169	10	𝛿𝑚+1	𝛿𝑚+1	VERB
cana-763	169	11	∑	∑	PROPN
cana-763	169	12	𝑎𝑛	𝑎𝑛	PROPN
cana-763	169	13	∞	∞	NUM
cana-763	169	14	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	169	15	2	2	NUM
cana-763	169	16	−	−	NOUN
cana-763	169	17	2	2	NUM
cana-763	169	18	∑	∑	PROPN
cana-763	169	19	𝑎𝑛	𝑎𝑛	VERB
cana-763	169	20	𝑚	𝑚	ADP
cana-763	169	21	𝑛=2	𝑛=2	X
cana-763	169	22	−	−	ADP
cana-763	169	23	𝛿𝑚+1	𝛿𝑚+1	NOUN
cana-763	169	24	∑	∑	PROPN
cana-763	169	25	𝑎𝑛	𝑎𝑛	PROPN
cana-763	169	26	∞	∞	NUM
cana-763	169	27	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	169	28	.	.	PUNCT
cana-763	170	1	now	now	ADV
cana-763	170	2	|𝑤(𝑧)|	|𝑤(𝑧)|	ADJ
cana-763	170	3	≤	≤	ADV
cana-763	170	4	1	1	NUM
cana-763	170	5	if	if	SCONJ
cana-763	170	6	2𝛿𝑚+1	2𝛿𝑚+1	VERB
cana-763	170	7	∑	∑	PROPN
cana-763	170	8	𝑎𝑛	𝑎𝑛	PROPN
cana-763	170	9	∞	∞	NUM
cana-763	170	10	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	170	11	≤	≤	ADV
cana-763	170	12	2	2	NUM
cana-763	170	13	−	−	NOUN
cana-763	170	14	2	2	NUM
cana-763	170	15	∑	∑	PROPN
cana-763	170	16	𝑎𝑛	𝑎𝑛	VERB
cana-763	170	17	𝑚	𝑚	ADP
cana-763	170	18	𝑛=2	𝑛=2	X
cana-763	170	19	,	,	PUNCT
cana-763	170	20	which	which	PRON
cana-763	170	21	is	be	AUX
cana-763	170	22	equivalent	equivalent	ADJ
cana-763	170	23	to	to	PART
cana-763	170	24	∑	∑	VERB
cana-763	170	25	𝑎𝑛	𝑎𝑛	VERB
cana-763	170	26	𝑚	𝑚	ADP
cana-763	170	27	𝑛=2	𝑛=2	X
cana-763	170	28	+	+	CCONJ
cana-763	170	29	𝛿𝑚+1	𝛿𝑚+1	VERB
cana-763	170	30	∑	∑	PROPN
cana-763	170	31	𝑎𝑛	𝑎𝑛	PROPN
cana-763	170	32	∞	∞	NUM
cana-763	170	33	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	170	34	≤	≤	ADV
cana-763	170	35	1	1	NUM
cana-763	170	36	.	.	PUNCT
cana-763	171	1	(	(	PUNCT
cana-763	171	2	4.6	4.6	NUM
cana-763	171	3	)	)	PUNCT
cana-763	171	4	it	it	PRON
cana-763	171	5	is	be	AUX
cana-763	171	6	suffices	suffice	NOUN
cana-763	171	7	to	to	PART
cana-763	171	8	show	show	VERB
cana-763	171	9	that	that	SCONJ
cana-763	171	10	the	the	DET
cana-763	171	11	left	left	ADJ
cana-763	171	12	hand	hand	NOUN
cana-763	171	13	side	side	NOUN
cana-763	171	14	of	of	ADP
cana-763	171	15	(	(	PUNCT
cana-763	171	16	4.6	4.6	NUM
cana-763	171	17	)	)	PUNCT
cana-763	171	18	is	be	AUX
cana-763	171	19	bounded	bound	VERB
cana-763	171	20	above	above	ADV
cana-763	171	21	by	by	ADP
cana-763	171	22	∑	∑	PROPN
cana-763	171	23	𝛿𝑛	𝛿𝑛	PROPN
cana-763	171	24	∞	∞	PROPN
cana-763	171	25	𝑛=2	𝑛=2	PROPN
cana-763	171	26	𝑎𝑛	𝑎𝑛	PROPN
cana-763	171	27	,	,	PUNCT
cana-763	171	28	which	which	PRON
cana-763	171	29	is	be	AUX
cana-763	171	30	equivalent	equivalent	ADJ
cana-763	171	31	to	to	ADP
cana-763	171	32	∑(𝛿𝑛	∑(𝛿𝑛	PROPN
cana-763	171	33	−	−	PROPN
cana-763	171	34	1	1	NUM
cana-763	171	35	)	)	PUNCT
cana-763	171	36	𝑚	𝑚	ADP
cana-763	171	37	𝑛=2	𝑛=2	PROPN
cana-763	171	38	𝑎𝑛	𝑎𝑛	NOUN
cana-763	171	39	+	+	NOUN
cana-763	172	1	∑	∑	PUNCT
cana-763	172	2	(	(	PUNCT
cana-763	172	3	𝛿𝑛	𝛿𝑛	ADP
cana-763	172	4	−	−	PROPN
cana-763	172	5	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	172	6	)	)	PUNCT
cana-763	172	7	∞	∞	NUM
cana-763	172	8	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	172	9	𝑎𝑛	𝑎𝑛	PRON
cana-763	172	10	≥	≥	NOUN
cana-763	172	11	0	0	NUM
cana-763	172	12	.	.	PUNCT
cana-763	173	1	to	to	PART
cana-763	173	2	see	see	VERB
cana-763	173	3	that	that	SCONJ
cana-763	173	4	the	the	DET
cana-763	173	5	function	function	NOUN
cana-763	173	6	given	give	VERB
cana-763	173	7	by	by	ADP
cana-763	173	8	(	(	PUNCT
cana-763	173	9	4.4	4.4	NUM
cana-763	173	10	)	)	PUNCT
cana-763	173	11	gives	give	VERB
cana-763	173	12	the	the	DET
cana-763	173	13	sharp	sharp	ADJ
cana-763	173	14	result	result	NOUN
cana-763	173	15	,	,	PUNCT
cana-763	173	16	we	we	PRON
cana-763	173	17	observe	observe	VERB
cana-763	173	18	that	that	SCONJ
cana-763	173	19	for	for	ADP
cana-763	173	20	𝑧	𝑧	X
cana-763	173	21	=	=	PUNCT
cana-763	173	22	𝑟𝑒𝑖𝜋/𝑛	𝑟𝑒𝑖𝜋/𝑛	NOUN
cana-763	173	23	,	,	PUNCT
cana-763	173	24	𝑓(𝑧	𝑓(𝑧	NUM
cana-763	173	25	)	)	PUNCT
cana-763	173	26	𝑓𝑚(𝑧	𝑓𝑚(𝑧	ADJ
cana-763	173	27	)	)	PUNCT
cana-763	173	28	=	=	SYM
cana-763	174	1	1	1	NUM
cana-763	174	2	+	+	CCONJ
cana-763	174	3	𝑧𝑚	𝑧𝑚	ADP
cana-763	174	4	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	174	5	(	(	PUNCT
cana-763	174	6	4.7	4.7	NUM
cana-763	174	7	)	)	PUNCT
cana-763	174	8	.	.	PUNCT
cana-763	175	1	taking	take	VERB
cana-763	175	2	𝑧	𝑧	PRON
cana-763	175	3	→	→	X
cana-763	175	4	1−	1−	NUM
cana-763	175	5	,	,	PUNCT
cana-763	175	6	we	we	PRON
cana-763	175	7	have	have	VERB
cana-763	175	8	𝑓(𝑧	𝑓(𝑧	NUM
cana-763	175	9	)	)	PUNCT
cana-763	175	10	𝑓𝑚(𝑧	𝑓𝑚(𝑧	ADJ
cana-763	175	11	)	)	PUNCT
cana-763	175	12	=	=	SYM
cana-763	176	1	1	1	NUM
cana-763	176	2	−	−	PROPN
cana-763	176	3	1	1	NUM
cana-763	176	4	𝛿𝑚+1	𝛿𝑚+1	PROPN
cana-763	176	5	.	.	PUNCT
cana-763	177	1	this	this	PRON
cana-763	177	2	completes	complete	VERB
cana-763	177	3	the	the	DET
cana-763	177	4	proof	proof	NOUN
cana-763	177	5	of	of	ADP
cana-763	177	6	theorem	theorem	NOUN
cana-763	177	7	8	8	NUM
cana-763	177	8	.	.	PUNCT
cana-763	178	1	we	we	PRON
cana-763	178	2	next	next	ADJ
cana-763	178	3	determine	determine	VERB
cana-763	178	4	bounds	bound	NOUN
cana-763	178	5	for	for	ADP
cana-763	178	6	𝑓𝑚(𝑧	𝑓𝑚(𝑧	PROPN
cana-763	178	7	)	)	PUNCT
cana-763	178	8	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	178	9	)	)	PUNCT
cana-763	178	10	.	.	PUNCT
cana-763	179	1	theorem	theorem	VERB
cana-763	179	2	9	9	NUM
cana-763	179	3	.	.	PUNCT
cana-763	180	1	if	if	SCONJ
cana-763	180	2	𝑓	𝑓	PROPN
cana-763	180	3	of	of	ADP
cana-763	180	4	the	the	DET
cana-763	180	5	form	form	NOUN
cana-763	180	6	(	(	PUNCT
cana-763	180	7	1.1	1.1	NUM
cana-763	180	8	)	)	PUNCT
cana-763	180	9	satisfies	satisfy	VERB
cana-763	180	10	the	the	DET
cana-763	180	11	condition	condition	NOUN
cana-763	180	12	(	(	PUNCT
cana-763	180	13	2.1	2.1	NUM
cana-763	180	14	)	)	PUNCT
cana-763	180	15	then	then	ADV
cana-763	180	16	ℜ	ℜ	PROPN
cana-763	180	17	{	{	PUNCT
cana-763	180	18	𝑓𝑚(𝑧	𝑓𝑚(𝑧	PROPN
cana-763	180	19	)	)	PUNCT
cana-763	180	20	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	180	21	)	)	PUNCT
cana-763	180	22	}	}	PUNCT
cana-763	180	23	≥	≥	X
cana-763	180	24	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	181	1	1+𝛿𝑚+1	1+𝛿𝑚+1	NUM
cana-763	181	2	.	.	PUNCT
cana-763	182	1	(	(	PUNCT
cana-763	182	2	4.8	4.8	NUM
cana-763	182	3	)	)	PUNCT
cana-763	182	4	the	the	DET
cana-763	182	5	result	result	NOUN
cana-763	182	6	is	be	AUX
cana-763	182	7	sharp	sharp	ADJ
cana-763	182	8	with	with	ADP
cana-763	182	9	the	the	DET
cana-763	182	10	function	function	NOUN
cana-763	182	11	given	give	VERB
cana-763	182	12	by	by	ADP
cana-763	182	13	(	(	PUNCT
cana-763	182	14	4.4	4.4	NUM
cana-763	182	15	)	)	PUNCT
cana-763	182	16	.	.	PUNCT
cana-763	183	1	proof	proof	NOUN
cana-763	183	2	.	.	PUNCT
cana-763	184	1	we	we	PRON
cana-763	184	2	may	may	AUX
cana-763	184	3	write	write	VERB
cana-763	184	4	1	1	NUM
cana-763	184	5	+	+	CCONJ
cana-763	184	6	𝑤(𝑧	𝑤(𝑧	NOUN
cana-763	184	7	)	)	PUNCT
cana-763	184	8	1	1	NUM
cana-763	184	9	−	−	PROPN
cana-763	184	10	𝑤(𝑧	𝑤(𝑧	NOUN
cana-763	184	11	)	)	PUNCT
cana-763	184	12	=	=	PUNCT
cana-763	185	1	(	(	PUNCT
cana-763	185	2	1	1	NUM
cana-763	185	3	+	+	CCONJ
cana-763	185	4	𝛿𝑚+1	𝛿𝑚+1	X
cana-763	185	5	)	)	PUNCT
cana-763	185	6	{	{	PUNCT
cana-763	185	7	𝑓𝑚(𝑧	𝑓𝑚(𝑧	PROPN
cana-763	185	8	)	)	PUNCT
cana-763	185	9	𝑓(𝑧	𝑓(𝑧	PROPN
cana-763	185	10	)	)	PUNCT
cana-763	185	11	−	−	NOUN
cana-763	185	12	𝛿𝑚+1	𝛿𝑚+1	NOUN
cana-763	185	13	1	1	NUM
cana-763	185	14	+	+	CCONJ
cana-763	185	15	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	185	16	}	}	PUNCT
cana-763	185	17	=	=	PUNCT
cana-763	185	18	{	{	PUNCT
cana-763	185	19	1	1	NUM
cana-763	185	20	+	+	CCONJ
cana-763	185	21	∑	∑	PROPN
cana-763	185	22	𝑎𝑛	𝑎𝑛	PROPN
cana-763	185	23	𝑚	𝑚	ADP
cana-763	185	24	𝑛=2	𝑛=2	X
cana-763	185	25	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	185	26	−	−	NOUN
cana-763	185	27	𝛿𝑚+1	𝛿𝑚+1	ADV
cana-763	185	28	∑	∑	PROPN
cana-763	185	29	𝑎𝑛	𝑎𝑛	PROPN
cana-763	185	30	∞	∞	NUM
cana-763	185	31	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	185	32	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	185	33	1	1	NUM
cana-763	185	34	+	+	CCONJ
cana-763	185	35	∑	∑	ADP
cana-763	185	36	𝑎𝑛	𝑎𝑛	PROPN
cana-763	185	37	∞	∞	NUM
cana-763	185	38	𝑛=2	𝑛=2	PROPN
cana-763	185	39	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	185	40	}	}	PUNCT
cana-763	185	41	,	,	PUNCT
cana-763	185	42	communications	communication	NOUN
cana-763	185	43	on	on	ADP
cana-763	185	44	applied	apply	VERB
cana-763	185	45	nonlinear	nonlinear	ADJ
cana-763	185	46	analysis	analysis	NOUN
cana-763	185	47	issn	issn	NOUN
cana-763	185	48	:	:	PUNCT
cana-763	185	49	1074	1074	NUM
cana-763	185	50	-	-	PUNCT
cana-763	185	51	133x	133x	NUM
cana-763	185	52	vol	vol	NOUN
cana-763	185	53	31	31	NUM
cana-763	185	54	no	no	NOUN
cana-763	185	55	.	.	PUNCT
cana-763	186	1	3s	3s	NUM
cana-763	186	2	(	(	PUNCT
cana-763	186	3	2024	2024	NUM
cana-763	186	4	)	)	PUNCT
cana-763	186	5	262	262	NUM
cana-763	186	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-763	186	7	where	where	SCONJ
cana-763	186	8	𝑤(𝑧	𝑤(𝑧	NOUN
cana-763	186	9	)	)	PUNCT
cana-763	186	10	=	=	PUNCT
cana-763	186	11	(	(	PUNCT
cana-763	186	12	1	1	NUM
cana-763	186	13	+	+	CCONJ
cana-763	186	14	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	186	15	)	)	PUNCT
cana-763	186	16	∑	∑	PUNCT
cana-763	186	17	𝑎𝑛	𝑎𝑛	PROPN
cana-763	186	18	∞	∞	NUM
cana-763	186	19	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	186	20	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	186	21	−(2	−(2	PROPN
cana-763	186	22	+	+	CCONJ
cana-763	186	23	2	2	NUM
cana-763	186	24	∑	∑	PUNCT
cana-763	186	25	𝑎𝑛	𝑎𝑛	VERB
cana-763	186	26	𝑚	𝑚	ADP
cana-763	186	27	𝑛=2	𝑛=2	X
cana-763	186	28	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	186	29	−	−	PROPN
cana-763	186	30	(	(	PUNCT
cana-763	186	31	1	1	NUM
cana-763	186	32	−	−	NUM
cana-763	186	33	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	186	34	)	)	PUNCT
cana-763	186	35	∑	∑	PROPN
cana-763	186	36	𝑎𝑛	𝑎𝑛	PROPN
cana-763	186	37	∞	∞	NUM
cana-763	186	38	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	186	39	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	186	40	)	)	PUNCT
cana-763	186	41	and	and	CCONJ
cana-763	186	42	|𝑤(𝑧)|	|𝑤(𝑧)|	PROPN
cana-763	186	43	≤	≤	NOUN
cana-763	186	44	(	(	PUNCT
cana-763	186	45	1	1	NUM
cana-763	186	46	+	+	CCONJ
cana-763	186	47	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	186	48	)	)	PUNCT
cana-763	186	49	∑	∑	PUNCT
cana-763	186	50	𝑎𝑛	𝑎𝑛	PROPN
cana-763	186	51	∞	∞	NUM
cana-763	186	52	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	186	53	2	2	NUM
cana-763	186	54	−	−	NOUN
cana-763	186	55	2	2	NUM
cana-763	186	56	∑	∑	PUNCT
cana-763	186	57	𝑎𝑛	𝑎𝑛	VERB
cana-763	186	58	𝑚	𝑚	ADP
cana-763	186	59	𝑛=2	𝑛=2	X
cana-763	187	1	+	+	CCONJ
cana-763	188	1	(	(	PUNCT
cana-763	188	2	1	1	NUM
cana-763	188	3	−	−	NUM
cana-763	188	4	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	188	5	)	)	PUNCT
cana-763	188	6	∑	∑	PROPN
cana-763	188	7	𝑎𝑛	𝑎𝑛	PROPN
cana-763	188	8	∞	∞	NUM
cana-763	188	9	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	188	10	≤	≤	ADV
cana-763	188	11	1	1	NUM
cana-763	188	12	.	.	PUNCT
cana-763	189	1	this	this	DET
cana-763	189	2	last	last	ADJ
cana-763	189	3	inequality	inequality	NOUN
cana-763	189	4	is	be	AUX
cana-763	189	5	equivalent	equivalent	ADJ
cana-763	189	6	to	to	PART
cana-763	189	7	∑	∑	VERB
cana-763	189	8	𝑎𝑛	𝑎𝑛	VERB
cana-763	189	9	𝑚	𝑚	ADP
cana-763	189	10	𝑛=2	𝑛=2	X
cana-763	189	11	+	+	CCONJ
cana-763	189	12	𝛿𝑚+1	𝛿𝑚+1	VERB
cana-763	189	13	∑	∑	PROPN
cana-763	189	14	𝑎𝑛	𝑎𝑛	PROPN
cana-763	189	15	∞	∞	NUM
cana-763	189	16	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	189	17	≤	≤	ADV
cana-763	189	18	1	1	NUM
cana-763	189	19	.	.	PUNCT
cana-763	190	1	(	(	PUNCT
cana-763	190	2	4.9	4.9	NUM
cana-763	190	3	)	)	PUNCT
cana-763	190	4	it	it	PRON
cana-763	190	5	is	be	AUX
cana-763	190	6	suffices	suffice	NOUN
cana-763	190	7	to	to	PART
cana-763	190	8	show	show	VERB
cana-763	190	9	that	that	SCONJ
cana-763	190	10	the	the	DET
cana-763	190	11	left	left	ADJ
cana-763	190	12	hand	hand	NOUN
cana-763	190	13	side	side	NOUN
cana-763	190	14	of	of	ADP
cana-763	190	15	(	(	PUNCT
cana-763	190	16	4.9	4.9	NUM
cana-763	190	17	)	)	PUNCT
cana-763	190	18	is	be	AUX
cana-763	190	19	bounded	bound	VERB
cana-763	190	20	above	above	ADV
cana-763	190	21	by	by	ADP
cana-763	190	22	∑	∑	PROPN
cana-763	190	23	𝛿𝑛	𝛿𝑛	PROPN
cana-763	190	24	∞	∞	PROPN
cana-763	190	25	𝑛=2	𝑛=2	PROPN
cana-763	190	26	𝑎𝑛	𝑎𝑛	PROPN
cana-763	190	27	,	,	PUNCT
cana-763	190	28	which	which	PRON
cana-763	190	29	is	be	AUX
cana-763	190	30	equivalent	equivalent	ADJ
cana-763	190	31	to	to	ADP
cana-763	190	32	∑(𝛿𝑛	∑(𝛿𝑛	PROPN
cana-763	190	33	−	−	PROPN
cana-763	190	34	1	1	NUM
cana-763	190	35	)	)	PUNCT
cana-763	190	36	𝑚	𝑚	ADP
cana-763	190	37	𝑛=2	𝑛=2	PROPN
cana-763	190	38	𝑎𝑛	𝑎𝑛	NOUN
cana-763	190	39	+	+	NOUN
cana-763	191	1	∑	∑	PUNCT
cana-763	191	2	(	(	PUNCT
cana-763	191	3	𝛿𝑛	𝛿𝑛	ADP
cana-763	191	4	−	−	PROPN
cana-763	191	5	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	191	6	)	)	PUNCT
cana-763	191	7	∞	∞	NUM
cana-763	191	8	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	191	9	𝑎𝑛	𝑎𝑛	PRON
cana-763	191	10	≥	≥	NOUN
cana-763	191	11	0	0	NUM
cana-763	191	12	.	.	PUNCT
cana-763	192	1	this	this	PRON
cana-763	192	2	completes	complete	VERB
cana-763	192	3	the	the	DET
cana-763	192	4	proof	proof	NOUN
cana-763	192	5	of	of	ADP
cana-763	192	6	theorem	theorem	NOUN
cana-763	192	7	.	.	PUNCT
cana-763	193	1	we	we	PRON
cana-763	193	2	next	next	ADJ
cana-763	193	3	turn	turn	VERB
cana-763	193	4	to	to	ADP
cana-763	193	5	ratios	ratio	NOUN
cana-763	193	6	involving	involve	VERB
cana-763	193	7	derivatives	derivative	NOUN
cana-763	193	8	.	.	PUNCT
cana-763	194	1	theorem	theorem	VERB
cana-763	194	2	10	10	NUM
cana-763	194	3	.	.	PUNCT
cana-763	195	1	if	if	SCONJ
cana-763	195	2	𝑓	𝑓	PROPN
cana-763	195	3	of	of	ADP
cana-763	195	4	the	the	DET
cana-763	195	5	form	form	NOUN
cana-763	195	6	(	(	PUNCT
cana-763	195	7	1.1	1.1	NUM
cana-763	195	8	)	)	PUNCT
cana-763	195	9	satisfies	satisfy	VERB
cana-763	195	10	the	the	DET
cana-763	195	11	condition	condition	NOUN
cana-763	195	12	(	(	PUNCT
cana-763	195	13	2.1	2.1	NUM
cana-763	195	14	)	)	PUNCT
cana-763	195	15	then	then	ADV
cana-763	195	16	ℜ	ℜ	PROPN
cana-763	195	17	{	{	PUNCT
cana-763	195	18	𝑓′(𝑧	𝑓′(𝑧	NOUN
cana-763	195	19	)	)	PUNCT
cana-763	195	20	𝑓𝑚′(𝑧	𝑓𝑚′(𝑧	NOUN
cana-763	195	21	)	)	PUNCT
cana-763	195	22	}	}	PUNCT
cana-763	195	23	≥	≥	VERB
cana-763	195	24	1	1	NUM
cana-763	195	25	−	−	NOUN
cana-763	195	26	𝑚	𝑚	PROPN
cana-763	196	1	+	+	PROPN
cana-763	196	2	1	1	NUM
cana-763	196	3	𝛿𝑚+1	𝛿𝑚+1	PROPN
cana-763	196	4	(	(	PUNCT
cana-763	196	5	4.10	4.10	NUM
cana-763	196	6	)	)	PUNCT
cana-763	196	7	ℜ	ℜ	PROPN
cana-763	196	8	{	{	PUNCT
cana-763	196	9	𝑓𝑚′(𝑧	𝑓𝑚′(𝑧	NOUN
cana-763	196	10	)	)	PUNCT
cana-763	196	11	𝑓′(𝑧	𝑓′(𝑧	NOUN
cana-763	196	12	)	)	PUNCT
cana-763	196	13	}	}	PUNCT
cana-763	196	14	≥	≥	VERB
cana-763	196	15	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	196	16	1	1	NUM
cana-763	196	17	+	+	CCONJ
cana-763	196	18	𝑚	𝑚	X
cana-763	196	19	+	+	X
cana-763	196	20	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	196	21	(	(	PUNCT
cana-763	196	22	4.11	4.11	NUM
cana-763	196	23	)	)	PUNCT
cana-763	196	24	where	where	SCONJ
cana-763	196	25	𝛿𝑛	𝛿𝑛	ADP
cana-763	196	26	≥	≥	X
cana-763	196	27	{	{	PUNCT
cana-763	196	28	1	1	NUM
cana-763	196	29	,	,	PUNCT
cana-763	196	30	𝑖𝑓	𝑖𝑓	ADP
cana-763	196	31	𝑛	𝑛	PRON
cana-763	196	32	=	=	SYM
cana-763	196	33	2,3	2,3	NUM
cana-763	196	34	⋯	⋯	ADP
cana-763	196	35	𝑚	𝑚	X
cana-763	196	36	𝑛	𝑛	PRON
cana-763	196	37	𝛿𝑚+1	𝛿𝑚+1	NOUN
cana-763	196	38	𝑚	𝑚	NOUN
cana-763	196	39	+	+	PROPN
cana-763	196	40	1	1	NUM
cana-763	196	41	,	,	PUNCT
cana-763	196	42	𝑖𝑓𝑛	𝑖𝑓𝑛	NOUN
cana-763	197	1	=	=	PUNCT
cana-763	197	2	𝑚	𝑚	PROPN
cana-763	198	1	+	+	NOUN
cana-763	198	2	1	1	NUM
cana-763	198	3	,	,	PUNCT
cana-763	198	4	𝑚	𝑚	PROPN
cana-763	198	5	∗	∗	NOUN
cana-763	198	6	2	2	NUM
cana-763	198	7	,	,	PUNCT
cana-763	198	8	⋯	⋯	VERB
cana-763	198	9	and	and	CCONJ
cana-763	198	10	𝛿𝑛	𝛿𝑛	NOUN
cana-763	198	11	is	be	AUX
cana-763	198	12	defined	define	VERB
cana-763	198	13	by	by	ADP
cana-763	198	14	[	[	PUNCT
cana-763	198	15	4.3	4.3	NUM
cana-763	198	16	]	]	PUNCT
cana-763	198	17	.	.	PUNCT
cana-763	199	1	the	the	DET
cana-763	199	2	estimates	estimate	NOUN
cana-763	199	3	in	in	ADP
cana-763	199	4	(	(	PUNCT
cana-763	199	5	4.10	4.10	NUM
cana-763	199	6	)	)	PUNCT
cana-763	199	7	and	and	CCONJ
cana-763	199	8	(	(	PUNCT
cana-763	199	9	4.11	4.11	NUM
cana-763	199	10	)	)	PUNCT
cana-763	199	11	are	be	AUX
cana-763	199	12	sharp	sharp	ADJ
cana-763	199	13	with	with	ADP
cana-763	199	14	the	the	DET
cana-763	199	15	extremal	extremal	ADJ
cana-763	199	16	function	function	NOUN
cana-763	199	17	given	give	VERB
cana-763	199	18	by(4.4	by(4.4	PROPN
cana-763	199	19	)	)	PUNCT
cana-763	199	20	.	.	PUNCT
cana-763	200	1	proof	proof	NOUN
cana-763	200	2	.	.	PUNCT
cana-763	201	1	firstly	firstly	ADV
cana-763	201	2	,	,	PUNCT
cana-763	201	3	we	we	PRON
cana-763	201	4	will	will	AUX
cana-763	201	5	give	give	VERB
cana-763	201	6	proof	proof	NOUN
cana-763	201	7	of	of	ADP
cana-763	201	8	(	(	PUNCT
cana-763	201	9	4.10	4.10	NUM
cana-763	201	10	)	)	PUNCT
cana-763	201	11	.	.	PUNCT
cana-763	202	1	we	we	PRON
cana-763	202	2	write	write	VERB
cana-763	202	3	1	1	NUM
cana-763	202	4	+	+	CCONJ
cana-763	202	5	𝑤(𝑧	𝑤(𝑧	NOUN
cana-763	202	6	)	)	PUNCT
cana-763	202	7	1	1	NUM
cana-763	202	8	−	−	NOUN
cana-763	202	9	𝑤(𝑧	𝑤(𝑧	NOUN
cana-763	202	10	)	)	PUNCT
cana-763	202	11	=	=	SYM
cana-763	202	12	𝛿𝑚+1	𝛿𝑚+1	PROPN
cana-763	202	13	{	{	PUNCT
cana-763	202	14	𝑓′(𝑧	𝑓′(𝑧	NOUN
cana-763	202	15	)	)	PUNCT
cana-763	202	16	𝑓𝑚′(𝑧	𝑓𝑚′(𝑧	PROPN
cana-763	202	17	)	)	PUNCT
cana-763	202	18	−	−	PROPN
cana-763	203	1	(	(	PUNCT
cana-763	203	2	1	1	NUM
cana-763	203	3	−	−	NOUN
cana-763	203	4	𝑚	𝑚	NOUN
cana-763	203	5	+	+	PROPN
cana-763	203	6	1	1	NUM
cana-763	203	7	𝛿𝑚+1	𝛿𝑚+1	NOUN
cana-763	203	8	)	)	PUNCT
cana-763	203	9	}	}	PUNCT
cana-763	203	10	=	=	PRON
cana-763	203	11	{	{	PUNCT
cana-763	204	1	1	1	NUM
cana-763	204	2	+	+	NOUN
cana-763	204	3	∑	∑	ADP
cana-763	204	4	𝑛𝑚	𝑛𝑚	ADP
cana-763	204	5	𝑛=2	𝑛=2	PUNCT
cana-763	204	6	𝑎𝑛𝑧𝑛−1	𝑎𝑛𝑧𝑛−1	PROPN
cana-763	204	7	+	+	CCONJ
cana-763	204	8	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	204	9	𝑚	𝑚	NOUN
cana-763	204	10	+	+	NOUN
cana-763	204	11	1	1	NUM
cana-763	204	12	∑	∑	ADP
cana-763	204	13	𝑛∞	𝑛∞	NOUN
cana-763	204	14	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	204	15	𝑎𝑛𝑧𝑛−1	𝑎𝑛𝑧𝑛−1	PROPN
cana-763	204	16	1	1	NUM
cana-763	204	17	+	+	CCONJ
cana-763	204	18	∑	∑	PROPN
cana-763	204	19	𝑎𝑛	𝑎𝑛	PROPN
cana-763	204	20	𝑚	𝑚	ADP
cana-763	204	21	𝑛=2	𝑛=2	X
cana-763	204	22	𝑧𝑛−1	𝑧𝑛−1	NOUN
cana-763	204	23	}	}	PUNCT
cana-763	204	24	,	,	PUNCT
cana-763	204	25	communications	communication	NOUN
cana-763	204	26	on	on	ADP
cana-763	204	27	applied	apply	VERB
cana-763	204	28	nonlinear	nonlinear	ADJ
cana-763	204	29	analysis	analysis	NOUN
cana-763	204	30	issn	issn	NOUN
cana-763	204	31	:	:	PUNCT
cana-763	204	32	1074	1074	NUM
cana-763	204	33	-	-	PUNCT
cana-763	204	34	133x	133x	NUM
cana-763	204	35	vol	vol	NOUN
cana-763	204	36	31	31	NUM
cana-763	204	37	no	no	NOUN
cana-763	204	38	.	.	PUNCT
cana-763	205	1	3s	3s	NUM
cana-763	205	2	(	(	PUNCT
cana-763	205	3	2024	2024	NUM
cana-763	205	4	)	)	PUNCT
cana-763	205	5	263	263	NUM
cana-763	205	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-763	205	7	where	where	SCONJ
cana-763	205	8	𝑤(𝑧	𝑤(𝑧	NOUN
cana-763	205	9	)	)	PUNCT
cana-763	205	10	=	=	PUNCT
cana-763	205	11	𝛿𝑚+1	𝛿𝑚+1	VERB
cana-763	205	12	𝑚	𝑚	NOUN
cana-763	205	13	+	+	PROPN
cana-763	205	14	1	1	NUM
cana-763	205	15	∑	∑	ADP
cana-763	205	16	𝑛∞	𝑛∞	NOUN
cana-763	205	17	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	205	18	𝑎𝑛𝑧𝑛−1	𝑎𝑛𝑧𝑛−1	PROPN
cana-763	205	19	2	2	NUM
cana-763	205	20	+	+	CCONJ
cana-763	205	21	2	2	NUM
cana-763	205	22	∑	∑	PUNCT
cana-763	205	23	𝑛𝑚	𝑛𝑚	ADP
cana-763	205	24	𝑛=2	𝑛=2	PUNCT
cana-763	205	25	𝑎𝑛𝑧𝑛−1	𝑎𝑛𝑧𝑛−1	PROPN
cana-763	205	26	+	+	CCONJ
cana-763	205	27	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	205	28	𝑚	𝑚	NOUN
cana-763	205	29	+	+	NOUN
cana-763	205	30	1	1	NUM
cana-763	205	31	∑	∑	NOUN
cana-763	205	32	𝑛∞	𝑛∞	NOUN
cana-763	205	33	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	205	34	𝑎𝑛𝑧𝑛−1	𝑎𝑛𝑧𝑛−1	PROPN
cana-763	205	35	and	and	CCONJ
cana-763	205	36	|𝑤(𝑧)|	|𝑤(𝑧)|	PROPN
cana-763	205	37	≤	≤	NUM
cana-763	205	38	𝛿𝑚+1	𝛿𝑚+1	VERB
cana-763	205	39	𝑚	𝑚	NOUN
cana-763	205	40	+	+	PROPN
cana-763	205	41	1	1	NUM
cana-763	205	42	∑	∑	NOUN
cana-763	205	43	𝑛∞	𝑛∞	NOUN
cana-763	205	44	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	205	45	𝑎𝑛	𝑎𝑛	ADP
cana-763	205	46	2	2	NUM
cana-763	205	47	−	−	NUM
cana-763	205	48	2	2	NUM
cana-763	205	49	∑	∑	PUNCT
cana-763	205	50	𝑛𝑚	𝑛𝑚	ADP
cana-763	205	51	𝑛=2	𝑛=2	PROPN
cana-763	205	52	𝑎𝑛	𝑎𝑛	PROPN
cana-763	205	53	+	+	CCONJ
cana-763	205	54	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	205	55	𝑚	𝑚	NOUN
cana-763	205	56	+	+	NOUN
cana-763	205	57	1	1	NUM
cana-763	205	58	∑	∑	NOUN
cana-763	205	59	𝑛∞	𝑛∞	NOUN
cana-763	205	60	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	205	61	𝑎𝑛	𝑎𝑛	PRON
cana-763	205	62	.	.	PUNCT
cana-763	206	1	now	now	ADV
cana-763	206	2	|𝑤(𝑧)|	|𝑤(𝑧)|	ADJ
cana-763	206	3	≤	≤	ADJ
cana-763	206	4	1	1	NUM
cana-763	206	5	if	if	SCONJ
cana-763	206	6	and	and	CCONJ
cana-763	206	7	only	only	ADV
cana-763	206	8	if	if	SCONJ
cana-763	206	9	∑	∑	PROPN
cana-763	206	10	𝑛	𝑛	PRON
cana-763	206	11	𝑚	𝑚	X
cana-763	206	12	𝑛=2	𝑛=2	X
cana-763	206	13	𝑎𝑛	𝑎𝑛	NOUN
cana-763	206	14	+	+	CCONJ
cana-763	206	15	𝛿𝑚+1	𝛿𝑚+1	NUM
cana-763	206	16	𝑚	𝑚	NOUN
cana-763	206	17	+	+	PROPN
cana-763	206	18	1	1	NUM
cana-763	206	19	∑	∑	ADP
cana-763	206	20	𝑛	𝑛	DET
cana-763	206	21	∞	∞	NUM
cana-763	206	22	𝑛=𝑚+1	𝑛=𝑚+1	ADJ
cana-763	206	23	𝑎𝑛	𝑎𝑛	PROPN
cana-763	206	24	≤	≤	NUM
cana-763	206	25	1	1	NUM
cana-763	206	26	,	,	PUNCT
cana-763	206	27	(	(	PUNCT
cana-763	206	28	4.12	4.12	NUM
cana-763	206	29	)	)	PUNCT
cana-763	206	30	since	since	SCONJ
cana-763	206	31	the	the	DET
cana-763	206	32	left	left	ADJ
cana-763	206	33	hand	hand	NOUN
cana-763	206	34	side	side	NOUN
cana-763	206	35	of	of	ADP
cana-763	206	36	(	(	PUNCT
cana-763	206	37	4.12)is	4.12)is	NUM
cana-763	206	38	bounded	bound	VERB
cana-763	206	39	above	above	ADV
cana-763	206	40	by	by	ADP
cana-763	206	41	∑	∑	PROPN
cana-763	206	42	𝛿𝑛	𝛿𝑛	PROPN
cana-763	206	43	∞	∞	PROPN
cana-763	206	44	𝑛=2	𝑛=2	X
cana-763	206	45	𝑎𝑛.	𝑎𝑛.	CCONJ
cana-763	206	46	the	the	DET
cana-763	206	47	proof	proof	NOUN
cana-763	206	48	of	of	ADP
cana-763	206	49	(	(	PUNCT
cana-763	206	50	4.11	4.11	NUM
cana-763	206	51	)	)	PUNCT
cana-763	206	52	follows	follow	VERB
cana-763	206	53	the	the	DET
cana-763	206	54	pattern	pattern	NOUN
cana-763	206	55	of	of	ADP
cana-763	206	56	that	that	PRON
cana-763	206	57	in	in	ADP
cana-763	206	58	theorem	theorem	NOUN
cana-763	206	59	9	9	NUM
cana-763	206	60	.	.	PUNCT
cana-763	207	1	this	this	PRON
cana-763	207	2	completes	complete	VERB
cana-763	207	3	the	the	DET
cana-763	207	4	proof	proof	NOUN
cana-763	207	5	of	of	ADP
cana-763	207	6	theorem	theorem	NOUN
cana-763	207	7	.	.	PUNCT
cana-763	208	1	refrences	refrence	VERB
cana-763	209	1	[	[	X
cana-763	209	2	1	1	X
cana-763	209	3	]	]	X
cana-763	209	4	al	al	PROPN
cana-763	209	5	-	-	PUNCT
cana-763	209	6	oboudi	oboudi	NOUN
cana-763	209	7	,	,	PUNCT
cana-763	209	8	f.m	f.m	PROPN
cana-763	209	9	.	.	PROPN
cana-763	209	10	,	,	PUNCT
cana-763	209	11	on	on	ADP
cana-763	209	12	univalent	univalent	ADJ
cana-763	209	13	functions	function	NOUN
cana-763	209	14	defined	define	VERB
cana-763	209	15	by	by	ADP
cana-763	209	16	a	a	DET
cana-763	209	17	generalized	generalize	VERB
cana-763	209	18	salagean	salagean	ADJ
cana-763	209	19	operator	operator	NOUN
cana-763	209	20	,	,	PUNCT
cana-763	209	21	int	int	NOUN
cana-763	209	22	.	.	PUNCT
cana-763	210	1	j.	j.	PROPN
cana-763	210	2	math	math	PROPN
cana-763	210	3	.	.	PUNCT
cana-763	211	1	math	math	NOUN
cana-763	211	2	.	.	PUNCT
cana-763	212	1	sci	sci	PROPN
cana-763	212	2	.	.	PROPN
cana-763	212	3	,	,	PUNCT
cana-763	212	4	(	(	PUNCT
cana-763	212	5	2004	2004	NUM
cana-763	212	6	)	)	PUNCT
cana-763	212	7	article	article	NOUN
cana-763	212	8	i	i	PROPN
cana-763	212	9	d	d	PROPN
cana-763	212	10	172525	172525	NUM
cana-763	212	11	,	,	PUNCT
cana-763	212	12	1429–436	1429–436	NUM
cana-763	212	13	,	,	PUNCT
cana-763	212	14	2004	2004	NUM
cana-763	212	15	.	.	PUNCT
cana-763	213	1	[	[	X
cana-763	213	2	2	2	NUM
cana-763	213	3	]	]	X
cana-763	213	4	altinta	altinta	NOUN
cana-763	213	5	,	,	PUNCT
cana-763	213	6	s.	s.	PROPN
cana-763	213	7	o.	o.	PROPN
cana-763	213	8	and	and	CCONJ
cana-763	213	9	owa	owa	PROPN
cana-763	213	10	,	,	PUNCT
cana-763	213	11	s.	s.	PROPN
cana-763	213	12	,	,	PUNCT
cana-763	213	13	neighborhoods	neighborhood	NOUN
cana-763	213	14	of	of	ADP
cana-763	213	15	certain	certain	ADJ
cana-763	213	16	analytic	analytic	ADJ
cana-763	213	17	functions	function	NOUN
cana-763	213	18	with	with	ADP
cana-763	213	19	negative	negative	ADJ
cana-763	213	20	coefficients	coefficient	NOUN
cana-763	213	21	,	,	PUNCT
cana-763	213	22	int	int	NOUN
cana-763	213	23	.	.	PUNCT
cana-763	214	1	j.	j.	PROPN
cana-763	214	2	math	math	PROPN
cana-763	214	3	.	.	PUNCT
cana-763	215	1	and	and	CCONJ
cana-763	215	2	math	math	NOUN
cana-763	215	3	.	.	PUNCT
cana-763	216	1	sci	sci	PROPN
cana-763	216	2	.	.	PROPN
cana-763	216	3	,	,	PUNCT
cana-763	216	4	19	19	NUM
cana-763	216	5	,	,	PUNCT
cana-763	216	6	797–800	797–800	NUM
cana-763	216	7	,	,	PUNCT
cana-763	216	8	1996	1996	NUM
cana-763	216	9	.	.	PUNCT
cana-763	217	1	[	[	X
cana-763	217	2	3	3	NUM
cana-763	217	3	]	]	X
cana-763	217	4	altinta	altinta	ADJ
cana-763	217	5	,	,	PUNCT
cana-763	217	6	s.	s.	PROPN
cana-763	217	7	o.	o.	PROPN
cana-763	217	8	,	,	PUNCT
cana-763	217	9	ozkan	ozkan	PROPN
cana-763	217	10	,	,	PUNCT
cana-763	217	11	e.	e.	PROPN
cana-763	217	12	and	and	CCONJ
cana-763	217	13	srivastava	srivastava	PROPN
cana-763	217	14	,	,	PUNCT
cana-763	217	15	h.	h.	PROPN
cana-763	217	16	m.	m.	PROPN
cana-763	217	17	,	,	PUNCT
cana-763	217	18	neighborhoods	neighborhood	NOUN
cana-763	217	19	of	of	ADP
cana-763	217	20	a	a	DET
cana-763	217	21	class	class	NOUN
cana-763	217	22	of	of	ADP
cana-763	217	23	analytic	analytic	ADJ
cana-763	217	24	functions	function	NOUN
cana-763	217	25	with	with	ADP
cana-763	217	26	negative	negative	ADJ
cana-763	217	27	coefficients	coefficient	NOUN
cana-763	217	28	,	,	PUNCT
cana-763	217	29	appl	appl	PROPN
cana-763	217	30	.	.	PROPN
cana-763	217	31	math	math	PROPN
cana-763	217	32	.	.	PUNCT
cana-763	218	1	let	let	VERB
cana-763	218	2	.	.	PUNCT
cana-763	218	3	,	,	PUNCT
cana-763	218	4	13	13	NUM
cana-763	218	5	,	,	PUNCT
cana-763	218	6	63–67	63–67	NUM
cana-763	218	7	,	,	PUNCT
cana-763	218	8	2000	2000	NUM
cana-763	218	9	.	.	PUNCT
cana-763	219	1	[	[	X
cana-763	219	2	4	4	NUM
cana-763	219	3	]	]	X
cana-763	219	4	cata	cata	NOUN
cana-763	219	5	,	,	PUNCT
cana-763	219	6	s.	s.	PROPN
cana-763	219	7	a.	a.	PROPN
cana-763	219	8	,	,	PUNCT
cana-763	219	9	neighborhoods	neighborhood	NOUN
cana-763	219	10	of	of	ADP
cana-763	219	11	a	a	DET
cana-763	219	12	certain	certain	ADJ
cana-763	219	13	class	class	NOUN
cana-763	219	14	of	of	ADP
cana-763	219	15	analytic	analytic	ADJ
cana-763	219	16	functions	function	NOUN
cana-763	219	17	with	with	ADP
cana-763	219	18	negative	negative	ADJ
cana-763	219	19	coefficients	coefficient	NOUN
cana-763	219	20	,	,	PUNCT
cana-763	219	21	banach	banach	NOUN
cana-763	219	22	j.	j.	PROPN
cana-763	219	23	math	math	PROPN
cana-763	219	24	.	.	PUNCT
cana-763	220	1	anal	anal	PROPN
cana-763	220	2	.	.	PROPN
cana-763	220	3	,	,	PUNCT
cana-763	220	4	3	3	NUM
cana-763	220	5	(	(	PUNCT
cana-763	220	6	1	1	NUM
cana-763	220	7	)	)	PUNCT
cana-763	220	8	,	,	PUNCT
cana-763	220	9	111–121	111–121	NUM
cana-763	220	10	,	,	PUNCT
cana-763	220	11	2009	2009	NUM
cana-763	220	12	.	.	PUNCT
cana-763	221	1	[	[	X
cana-763	221	2	5	5	NUM
cana-763	221	3	]	]	PUNCT
cana-763	221	4	darus	darus	NOUN
cana-763	221	5	,	,	PUNCT
cana-763	221	6	m.	m.	NOUN
cana-763	221	7	,	,	PUNCT
cana-763	221	8	and	and	CCONJ
cana-763	221	9	faisal	faisal	PROPN
cana-763	221	10	,	,	PUNCT
cana-763	221	11	i.	i.	PROPN
cana-763	221	12	,	,	PUNCT
cana-763	221	13	characrerization	characrerization	NOUN
cana-763	221	14	properties	property	NOUN
cana-763	221	15	for	for	ADP
cana-763	221	16	a	a	DET
cana-763	221	17	class	class	NOUN
cana-763	221	18	of	of	ADP
cana-763	221	19	analytic	analytic	ADJ
cana-763	221	20	aunctions	aunction	NOUN
cana-763	221	21	defined	define	VERB
cana-763	221	22	by	by	ADP
cana-763	221	23	generalized	generalized	ADJ
cana-763	221	24	cho	cho	PROPN
cana-763	221	25	and	and	CCONJ
cana-763	221	26	srivastava	srivastava	PROPN
cana-763	221	27	operator	operator	NOUN
cana-763	221	28	,	,	PUNCT
cana-763	221	29	in	in	ADP
cana-763	221	30	proc	proc	NOUN
cana-763	221	31	.	.	PUNCT
cana-763	222	1	2nd	2nd	ADJ
cana-763	222	2	inter	inter	PROPN
cana-763	222	3	.	.	PUNCT
cana-763	222	4	conf	conf	PROPN
cana-763	222	5	.	.	PUNCT
cana-763	223	1	math	math	NOUN
cana-763	223	2	.	.	PUNCT
cana-763	224	1	sci	sci	PROPN
cana-763	224	2	.	.	PROPN
cana-763	224	3	,	,	PUNCT
cana-763	224	4	kuala	kuala	PROPN
cana-763	224	5	lumpur	lumpur	PROPN
cana-763	224	6	,	,	PUNCT
cana-763	224	7	malaysia	malaysia	PROPN
cana-763	224	8	,	,	PUNCT
cana-763	224	9	(	(	PUNCT
cana-763	224	10	2010	2010	NUM
cana-763	224	11	)	)	PUNCT
cana-763	224	12	,	,	PUNCT
cana-763	224	13	1106–1113	1106–1113	NUM
cana-763	224	14	.	.	PUNCT
cana-763	225	1	[	[	X
cana-763	225	2	6	6	NUM
cana-763	225	3	]	]	X
cana-763	225	4	deniz	deniz	PROPN
cana-763	225	5	,	,	PUNCT
cana-763	225	6	e.	e.	PROPN
cana-763	225	7	and	and	CCONJ
cana-763	225	8	orhan	orhan	PROPN
cana-763	225	9	.	.	PUNCT
cana-763	226	1	h.	h.	PROPN
cana-763	226	2	,	,	PUNCT
cana-763	226	3	some	some	DET
cana-763	226	4	properties	property	NOUN
cana-763	226	5	of	of	ADP
cana-763	226	6	certain	certain	ADJ
cana-763	226	7	subclasses	subclass	NOUN
cana-763	226	8	of	of	ADP
cana-763	226	9	analytic	analytic	ADJ
cana-763	226	10	functions	function	NOUN
cana-763	226	11	with	with	ADP
cana-763	226	12	negative	negative	ADJ
cana-763	226	13	coefficients	coefficient	NOUN
cana-763	226	14	by	by	ADP
cana-763	226	15	using	use	VERB
cana-763	226	16	generalized	generalized	ADJ
cana-763	226	17	ruscheweyh	ruscheweyh	NOUN
cana-763	226	18	derivative	derivative	ADJ
cana-763	226	19	operator	operator	NOUN
cana-763	226	20	,	,	PUNCT
cana-763	226	21	czechoslovak	czechoslovak	ADJ
cana-763	226	22	math	math	NOUN
cana-763	226	23	.	.	PUNCT
cana-763	227	1	j.	j.	PROPN
cana-763	227	2	,	,	PUNCT
cana-763	227	3	60	60	NUM
cana-763	227	4	(	(	PUNCT
cana-763	227	5	135	135	NUM
cana-763	227	6	)	)	PUNCT
cana-763	227	7	,	,	PUNCT
cana-763	227	8	699	699	NUM
cana-763	227	9	–	–	PUNCT
cana-763	227	10	713	713	NUM
cana-763	227	11	,	,	PUNCT
cana-763	227	12	2010	2010	NUM
cana-763	227	13	.	.	PUNCT
cana-763	228	1	[	[	X
cana-763	228	2	7	7	NUM
cana-763	228	3	]	]	X
cana-763	228	4	goodman	goodman	PROPN
cana-763	228	5	,	,	PUNCT
cana-763	228	6	a.	a.	PROPN
cana-763	228	7	w.	w.	PROPN
cana-763	228	8	,	,	PUNCT
cana-763	228	9	univalent	univalent	ADJ
cana-763	228	10	functions	function	NOUN
cana-763	228	11	and	and	CCONJ
cana-763	228	12	nonanalytic	nonanalytic	ADJ
cana-763	228	13	curves	curve	NOUN
cana-763	228	14	,	,	PUNCT
cana-763	228	15	proc	proc	NOUN
cana-763	228	16	.	.	PUNCT
cana-763	228	17	amer	amer	PROPN
cana-763	228	18	.	.	PUNCT
cana-763	228	19	math	math	PROPN
cana-763	228	20	.	.	PUNCT
cana-763	229	1	soc	soc	PROPN
cana-763	229	2	.	.	PUNCT
cana-763	229	3	,	,	PUNCT
cana-763	229	4	8	8	NUM
cana-763	229	5	,	,	PUNCT
cana-763	229	6	598–601	598–601	NUM
cana-763	229	7	,	,	PUNCT
cana-763	229	8	1957	1957	NUM
cana-763	229	9	[	[	X
cana-763	229	10	8	8	NUM
cana-763	229	11	]	]	X
cana-763	229	12	goodman	goodman	PROPN
cana-763	229	13	,	,	PUNCT
cana-763	229	14	a.	a.	PROPN
cana-763	229	15	w.	w.	PROPN
cana-763	229	16	,	,	PUNCT
cana-763	229	17	on	on	ADP
cana-763	229	18	uniformly	uniformly	ADJ
cana-763	229	19	starlike	starlike	NOUN
cana-763	229	20	functions	function	NOUN
cana-763	229	21	,	,	PUNCT
cana-763	229	22	j.	j.	PROPN
cana-763	229	23	math	math	PROPN
cana-763	229	24	.	.	PUNCT
cana-763	230	1	anal	anal	PROPN
cana-763	230	2	.	.	PUNCT
cana-763	231	1	appl	appl	PROPN
cana-763	231	2	.	.	PROPN
cana-763	231	3	,	,	PUNCT
cana-763	231	4	155	155	NUM
cana-763	231	5	,	,	PUNCT
cana-763	231	6	364–370	364–370	NUM
cana-763	231	7	,	,	PUNCT
cana-763	231	8	1991	1991	NUM
cana-763	231	9	.	.	PUNCT
cana-763	232	1	[	[	X
cana-763	232	2	9	9	NUM
cana-763	232	3	]	]	X
cana-763	232	4	orhan	orhan	PROPN
cana-763	232	5	,	,	PUNCT
cana-763	232	6	h.	h.	PROPN
cana-763	232	7	,	,	PUNCT
cana-763	232	8	on	on	ADP
cana-763	232	9	neighborhoods	neighborhood	NOUN
cana-763	232	10	of	of	ADP
cana-763	232	11	analytic	analytic	ADJ
cana-763	232	12	functions	function	NOUN
cana-763	232	13	defined	define	VERB
cana-763	232	14	by	by	ADP
cana-763	232	15	using	use	VERB
cana-763	232	16	hadamard	hadamard	ADJ
cana-763	232	17	product	product	NOUN
cana-763	232	18	,	,	PUNCT
cana-763	232	19	novi	novi	PROPN
cana-763	232	20	sad	sad	PROPN
cana-763	232	21	j.	j.	PROPN
cana-763	232	22	math	math	PROPN
cana-763	232	23	.	.	PUNCT
cana-763	232	24	,	,	PUNCT
cana-763	232	25	37(1	37(1	NUM
cana-763	232	26	)	)	PUNCT
cana-763	232	27	,	,	PUNCT
cana-763	232	28	17–25	17–25	NUM
cana-763	232	29	,	,	PUNCT
cana-763	232	30	2007	2007	NUM
cana-763	232	31	.	.	PUNCT
cana-763	233	1	[	[	X
cana-763	233	2	10	10	NUM
cana-763	233	3	]	]	X
cana-763	233	4	owa	owa	PROPN
cana-763	233	5	,	,	PUNCT
cana-763	233	6	s.	s.	PROPN
cana-763	233	7	,	,	PUNCT
cana-763	233	8	sekine	sekine	NOUN
cana-763	233	9	,	,	PUNCT
cana-763	233	10	t.	t.	PROPN
cana-763	233	11	and	and	CCONJ
cana-763	233	12	yamakawa	yamakawa	PROPN
cana-763	233	13	.	.	PUNCT
cana-763	234	1	r.	r.	PROPN
cana-763	234	2	,	,	PUNCT
cana-763	234	3	on	on	ADP
cana-763	234	4	sakaguchi	sakaguchi	ADJ
cana-763	234	5	type	type	NOUN
cana-763	234	6	functions	function	NOUN
cana-763	234	7	,	,	PUNCT
cana-763	234	8	appl	appl	PROPN
cana-763	234	9	.	.	PROPN
cana-763	234	10	math	math	PROPN
cana-763	234	11	.	.	PUNCT
cana-763	235	1	comput	comput	NOUN
cana-763	235	2	.	.	PUNCT
cana-763	235	3	,	,	PUNCT
cana-763	235	4	187	187	NUM
cana-763	235	5	,	,	PUNCT
cana-763	235	6	356–361	356–361	NUM
cana-763	235	7	,	,	PUNCT
cana-763	235	8	2007	2007	NUM
cana-763	235	9	.	.	PUNCT
cana-763	236	1	[	[	X
cana-763	236	2	11	11	NUM
cana-763	236	3	]	]	X
cana-763	236	4	sakaguchi	sakaguchi	ADJ
cana-763	236	5	,	,	PUNCT
cana-763	236	6	k.	k.	PROPN
cana-763	236	7	,	,	PUNCT
cana-763	236	8	on	on	ADP
cana-763	236	9	a	a	DET
cana-763	236	10	certain	certain	ADJ
cana-763	236	11	univalent	univalent	ADJ
cana-763	236	12	mapping	mapping	NOUN
cana-763	236	13	,	,	PUNCT
cana-763	236	14	j.	j.	PROPN
cana-763	236	15	math	math	PROPN
cana-763	236	16	.	.	PUNCT
cana-763	237	1	soc	soc	PROPN
cana-763	237	2	.	.	PUNCT
cana-763	238	1	japan	japan	PROPN
cana-763	238	2	,	,	PUNCT
cana-763	238	3	11	11	NUM
cana-763	238	4	,	,	PUNCT
cana-763	238	5	72	72	NUM
cana-763	238	6	–	–	SYM
cana-763	238	7	75	75	NUM
cana-763	238	8	,	,	PUNCT
cana-763	238	9	1959	1959	NUM
cana-763	238	10	.	.	PUNCT
cana-763	239	1	[	[	X
cana-763	239	2	12	12	NUM
cana-763	239	3	]	]	X
cana-763	239	4	salagean	salagean	PROPN
cana-763	239	5	,	,	PUNCT
cana-763	239	6	g.s	g.s	PROPN
cana-763	239	7	.	.	PROPN
cana-763	239	8	,	,	PUNCT
cana-763	239	9	subclasses	subclass	NOUN
cana-763	239	10	of	of	ADP
cana-763	239	11	univalent	univalent	ADJ
cana-763	239	12	functions	function	NOUN
cana-763	239	13	,	,	PUNCT
cana-763	239	14	lecture	lecture	NOUN
cana-763	239	15	notes	note	NOUN
cana-763	239	16	in	in	ADP
cana-763	239	17	math	math	NOUN
cana-763	239	18	.	.	PUNCT
cana-763	240	1	,	,	PUNCT
cana-763	241	1	1013	1013	NUM
cana-763	241	2	,	,	PUNCT
cana-763	241	3	springer	springer	NOUN
cana-763	241	4	-	-	PUNCT
cana-763	241	5	verlag	verlag	PROPN
cana-763	241	6	(	(	PUNCT
cana-763	241	7	1983	1983	NUM
cana-763	241	8	)	)	PUNCT
cana-763	241	9	,	,	PUNCT
cana-763	241	10	362–372	362–372	NUM
cana-763	241	11	.	.	PUNCT
cana-763	242	1	[	[	X
cana-763	242	2	13	13	NUM
cana-763	242	3	]	]	SYM
cana-763	242	4	silverman	silverman	NOUN
cana-763	242	5	,	,	PUNCT
cana-763	242	6	h.	h.	PROPN
cana-763	242	7	,	,	PUNCT
cana-763	242	8	partial	partial	ADJ
cana-763	242	9	sums	sum	NOUN
cana-763	242	10	of	of	ADP
cana-763	242	11	starlike	starlike	NOUN
cana-763	242	12	and	and	CCONJ
cana-763	242	13	convex	convex	NOUN
cana-763	242	14	functions	function	NOUN
cana-763	242	15	,	,	PUNCT
cana-763	242	16	j.	j.	PROPN
cana-763	242	17	anal	anal	PROPN
cana-763	242	18	.	.	PUNCT
cana-763	243	1	appl	appl	PROPN
cana-763	243	2	.	.	PROPN
cana-763	243	3	,	,	PUNCT
cana-763	243	4	209	209	NUM
cana-763	243	5	,	,	PUNCT
cana-763	243	6	221–227	221–227	NUM
cana-763	243	7	,	,	PUNCT
cana-763	243	8	1997	1997	NUM
cana-763	243	9	.	.	PUNCT
cana-763	244	1	[	[	X
cana-763	244	2	14	14	NUM
cana-763	244	3	]	]	X
cana-763	244	4	silvia	silvia	PROPN
cana-763	244	5	,	,	PUNCT
cana-763	244	6	e.	e.	PROPN
cana-763	244	7	m.	m.	PROPN
cana-763	244	8	,	,	PUNCT
cana-763	244	9	partial	partial	ADJ
cana-763	244	10	sums	sum	NOUN
cana-763	244	11	of	of	ADP
cana-763	244	12	convex	convex	NOUN
cana-763	244	13	functions	function	NOUN
cana-763	244	14	of	of	ADP
cana-763	244	15	order	order	NOUN
cana-763	244	16	α	α	NOUN
cana-763	244	17	,	,	PUNCT
cana-763	244	18	houston	houston	PROPN
cana-763	244	19	j.	j.	PROPN
cana-763	244	20	math	math	PROPN
cana-763	244	21	.	.	PUNCT
cana-763	244	22	,	,	PUNCT
cana-763	244	23	11	11	NUM
cana-763	244	24	(	(	PUNCT
cana-763	244	25	3	3	NUM
cana-763	244	26	)	)	PUNCT
cana-763	244	27	,	,	PUNCT
cana-763	244	28	397–404	397–404	NUM
cana-763	244	29	,	,	PUNCT
cana-763	244	30	1985	1985	NUM
cana-763	244	31	.	.	PUNCT
cana-763	245	1	[	[	X
cana-763	245	2	15	15	NUM
cana-763	245	3	]	]	X
cana-763	245	4	srivastava	srivastava	PROPN
cana-763	245	5	,	,	PUNCT
cana-763	245	6	h.	h.	PROPN
cana-763	245	7	m.	m.	PROPN
cana-763	245	8	and	and	CCONJ
cana-763	245	9	aouf	aouf	PROPN
cana-763	245	10	,	,	PUNCT
cana-763	245	11	m.	m.	PROPN
cana-763	245	12	k.	k.	PROPN
cana-763	245	13	,	,	PUNCT
cana-763	245	14	a	a	DET
cana-763	245	15	certain	certain	ADJ
cana-763	245	16	fractional	fractional	ADJ
cana-763	245	17	derivative	derivative	ADJ
cana-763	245	18	operator	operator	NOUN
cana-763	245	19	and	and	CCONJ
cana-763	245	20	its	its	PRON
cana-763	245	21	applications	application	NOUN
cana-763	245	22	to	to	ADP
cana-763	245	23	a	a	DET
cana-763	245	24	new	new	ADJ
cana-763	245	25	class	class	NOUN
cana-763	245	26	of	of	ADP
cana-763	245	27	analytic	analytic	ADJ
cana-763	245	28	and	and	CCONJ
cana-763	245	29	multivalent	multivalent	NOUN
cana-763	245	30	functions	function	NOUN
cana-763	245	31	with	with	ADP
cana-763	245	32	negative	negative	ADJ
cana-763	245	33	coefficientsi	coefficientsi	NOUN
cana-763	245	34	,	,	PUNCT
cana-763	245	35	j.	j.	PROPN
cana-763	245	36	math	math	PROPN
cana-763	245	37	.	.	PUNCT
cana-763	246	1	anal	anal	PROPN
cana-763	246	2	.	.	PUNCT
cana-763	247	1	appl	appl	PROPN
cana-763	247	2	.	.	PROPN
cana-763	247	3	,	,	PUNCT
cana-763	247	4	171	171	NUM
cana-763	247	5	,	,	PUNCT
cana-763	247	6	11	11	NUM
cana-763	247	7	-	-	SYM
cana-763	247	8	13	13	NUM
cana-763	247	9	,	,	PUNCT
cana-763	247	10	1992	1992	NUM
cana-763	247	11	.	.	PUNCT
cana-763	248	1	communications	communication	NOUN
cana-763	248	2	on	on	ADP
cana-763	248	3	applied	apply	VERB
cana-763	248	4	nonlinear	nonlinear	ADJ
cana-763	248	5	analysis	analysis	NOUN
cana-763	248	6	issn	issn	NOUN
cana-763	248	7	:	:	PUNCT
cana-763	248	8	1074	1074	NUM
cana-763	248	9	-	-	PUNCT
cana-763	248	10	133x	133x	NUM
cana-763	248	11	vol	vol	NOUN
cana-763	248	12	31	31	NUM
cana-763	248	13	no	no	NOUN
cana-763	248	14	.	.	PUNCT
cana-763	249	1	3s	3s	NUM
cana-763	249	2	(	(	PUNCT
cana-763	249	3	2024	2024	NUM
cana-763	249	4	)	)	PUNCT
cana-763	249	5	264	264	NUM
cana-763	249	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-763	250	1	[	[	X
cana-763	250	2	16	16	NUM
cana-763	250	3	]	]	X
cana-763	250	4	srinivas	srinivas	PROPN
cana-763	250	5	,	,	PUNCT
cana-763	250	6	t.	t.	PROPN
cana-763	250	7	,	,	PUNCT
cana-763	250	8	reddy	reddy	PROPN
cana-763	250	9	,	,	PUNCT
cana-763	250	10	p.t.and	p.t.and	NOUN
cana-763	250	11	madhavi.b	madhavi.b	PROPN
cana-763	250	12	.	.	PUNCT
cana-763	251	1	,neighbourhoods	,neighbourhoods	PUNCT
cana-763	251	2	of	of	ADP
cana-763	251	3	a	a	DET
cana-763	251	4	certain	certain	ADJ
cana-763	251	5	subclass	subclass	NOUN
cana-763	251	6	of	of	ADP
cana-763	251	7	uniformly	uniformly	ADJ
cana-763	251	8	starlike	starlike	NOUN
cana-763	251	9	functions	function	NOUN
cana-763	251	10	,	,	PUNCT
cana-763	251	11	tamkang	tamkang	PROPN
cana-763	251	12	journal	journal	PROPN
cana-763	251	13	of	of	ADP
cana-763	251	14	mathematics	mathematic	NOUN
cana-763	251	15	,	,	PUNCT
cana-763	251	16	43(4	43(4	NOUN
cana-763	251	17	)	)	PUNCT
cana-763	251	18	,	,	PUNCT
cana-763	251	19	587	587	NUM
cana-763	251	20	-	-	SYM
cana-763	251	21	594	594	NUM
cana-763	251	22	,	,	PUNCT
cana-763	251	23	2012	2012	NUM
cana-763	251	24	.	.	PUNCT