id	sid	tid	token	lemma	pos
cana-1649	1	1	communications	communication	NOUN
cana-1649	1	2	on	on	ADP
cana-1649	1	3	applied	apply	VERB
cana-1649	1	4	nonlinear	nonlinear	ADJ
cana-1649	1	5	analysis	analysis	NOUN
cana-1649	1	6	issn	issn	NOUN
cana-1649	1	7	:	:	PUNCT
cana-1649	1	8	1074	1074	NUM
cana-1649	1	9	-	-	PUNCT
cana-1649	1	10	133x	133x	NUM
cana-1649	1	11	vol	vol	NOUN
cana-1649	1	12	32	32	NUM
cana-1649	1	13	no	no	NOUN
cana-1649	1	14	.	.	NOUN
cana-1649	1	15	1	1	NUM
cana-1649	1	16	(	(	PUNCT
cana-1649	1	17	2025	2025	NUM
cana-1649	1	18	)	)	PUNCT
cana-1649	1	19	292	292	NUM
cana-1649	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1649	1	21	on	on	ADP
cana-1649	1	22	𝓟-stable	𝓟-stable	ADJ
cana-1649	1	23	functions	function	NOUN
cana-1649	1	24	m	m	VERB
cana-1649	1	25	p	p	ADJ
cana-1649	1	26	jeyaraman1	jeyaraman1	PROPN
cana-1649	1	27	,	,	PUNCT
cana-1649	1	28	t	t	PROPN
cana-1649	1	29	g	g	PROPN
cana-1649	1	30	bhaskar2	bhaskar2	NOUN
cana-1649	1	31	,	,	PUNCT
cana-1649	1	32	h	h	PROPN
cana-1649	1	33	aaisha	aaisha	PROPN
cana-1649	1	34	farzana3	farzana3	PROPN
cana-1649	1	35	,	,	PUNCT
cana-1649	1	36	m	m	VERB
cana-1649	1	37	p	p	ADJ
cana-1649	1	38	rajakumar4	rajakumar4	PROPN
cana-1649	2	1	1department	1department	NUM
cana-1649	2	2	of	of	ADP
cana-1649	2	3	mathematics	mathematic	NOUN
cana-1649	2	4	,	,	PUNCT
cana-1649	2	5	presidency	presidency	NOUN
cana-1649	2	6	college(autonomous	college(autonomous	ADJ
cana-1649	2	7	)	)	PUNCT
cana-1649	2	8	,	,	PUNCT
cana-1649	2	9	chennai	chennai	NOUN
cana-1649	2	10	,	,	PUNCT
cana-1649	2	11	600005	600005	NUM
cana-1649	2	12	,	,	PUNCT
cana-1649	2	13	tamil	tamil	PROPN
cana-1649	2	14	nadu	nadu	PROPN
cana-1649	2	15	,	,	PUNCT
cana-1649	2	16	india	india	PROPN
cana-1649	2	17	.	.	PUNCT
cana-1649	3	1	jeyaraman_mp@yahoo.co.in	jeyaraman_mp@yahoo.co.in	PROPN
cana-1649	4	1	2department	2department	NUM
cana-1649	4	2	of	of	ADP
cana-1649	4	3	mathematics	mathematic	NOUN
cana-1649	4	4	,	,	PUNCT
cana-1649	4	5	government	government	NOUN
cana-1649	4	6	arts	art	NOUN
cana-1649	4	7	college(autonomous	college(autonomous	PROPN
cana-1649	4	8	)	)	PUNCT
cana-1649	4	9	,	,	PUNCT
cana-1649	4	10	nandanam	nandanam	PROPN
cana-1649	4	11	,	,	PUNCT
cana-1649	4	12	chennai	chennai	NOUN
cana-1649	4	13	,	,	PUNCT
cana-1649	4	14	600035	600035	NUM
cana-1649	4	15	,	,	PUNCT
cana-1649	4	16	tamil	tamil	PROPN
cana-1649	4	17	nadu	nadu	PROPN
cana-1649	4	18	,	,	PUNCT
cana-1649	4	19	india	india	PROPN
cana-1649	4	20	.	.	PUNCT
cana-1649	5	1	tgbhas@yahoo.co.in	tgbhas@yahoo.co.in	X
cana-1649	6	1	3department	3department	NUM
cana-1649	6	2	of	of	ADP
cana-1649	6	3	mathematics	mathematic	NOUN
cana-1649	6	4	with	with	ADP
cana-1649	6	5	computer	computer	NOUN
cana-1649	6	6	applications	application	NOUN
cana-1649	6	7	,	,	PUNCT
cana-1649	6	8	a.m.	a.m.	PROPN
cana-1649	6	9	jain	jain	PROPN
cana-1649	6	10	college	college	PROPN
cana-1649	6	11	,	,	PUNCT
cana-1649	6	12	meenambakkam	meenambakkam	PROPN
cana-1649	6	13	,	,	PUNCT
cana-1649	6	14	chennai	chennai	PROPN
cana-1649	6	15	,	,	PUNCT
cana-1649	6	16	600061	600061	NUM
cana-1649	6	17	,	,	PUNCT
cana-1649	6	18	tamilnadu	tamilnadu	NOUN
cana-1649	6	19	,	,	PUNCT
cana-1649	6	20	india	india	PROPN
cana-1649	6	21	.	.	PUNCT
cana-1649	7	1	h.aaisha@gmail.com	h.aaisha@gmail.com	X
cana-1649	8	1	4department	4department	NUM
cana-1649	8	2	of	of	ADP
cana-1649	8	3	computer	computer	NOUN
cana-1649	8	4	science	science	NOUN
cana-1649	8	5	and	and	CCONJ
cana-1649	8	6	engineering	engineering	NOUN
cana-1649	8	7	,	,	PUNCT
cana-1649	8	8	st.joseph	st.joseph	X
cana-1649	8	9	’s	’s	PART
cana-1649	8	10	college	college	NOUN
cana-1649	8	11	of	of	ADP
cana-1649	8	12	engineering	engineering	PROPN
cana-1649	8	13	,	,	PUNCT
cana-1649	8	14	omr	omr	NOUN
cana-1649	8	15	,	,	PUNCT
cana-1649	8	16	chennai	chennai	NOUN
cana-1649	8	17	,	,	PUNCT
cana-1649	8	18	600119	600119	NUM
cana-1649	8	19	,	,	PUNCT
cana-1649	8	20	tamilnadu	tamilnadu	NOUN
cana-1649	8	21	,	,	PUNCT
cana-1649	8	22	india	india	PROPN
cana-1649	8	23	.	.	PUNCT
cana-1649	9	1	rajranjhu@gmail.com	rajranjhu@gmail.com	X
cana-1649	10	1	article	article	NOUN
cana-1649	10	2	history	history	NOUN
cana-1649	10	3	:	:	PUNCT
cana-1649	10	4	received	receive	VERB
cana-1649	10	5	:	:	PUNCT
cana-1649	10	6	14	14	NUM
cana-1649	10	7	-	-	SYM
cana-1649	10	8	07	07	NUM
cana-1649	10	9	-	-	PUNCT
cana-1649	10	10	2024	2024	NUM
cana-1649	10	11	revised	revise	VERB
cana-1649	10	12	:	:	PUNCT
cana-1649	10	13	29	29	NUM
cana-1649	10	14	-	-	SYM
cana-1649	10	15	08	08	NUM
cana-1649	10	16	-	-	PUNCT
cana-1649	10	17	2024	2024	NUM
cana-1649	10	18	accepted	accept	VERB
cana-1649	10	19	:	:	PUNCT
cana-1649	10	20	10	10	NUM
cana-1649	10	21	-	-	SYM
cana-1649	10	22	09	09	NUM
cana-1649	10	23	-	-	PUNCT
cana-1649	10	24	2024	2024	NUM
cana-1649	10	25	abstract	abstract	NOUN
cana-1649	10	26	let	let	VERB
cana-1649	10	27	ℎ1	ℎ1	PROPN
cana-1649	10	28	,	,	PUNCT
cana-1649	10	29	ℎ2	ℎ2	NOUN
cana-1649	10	30	be	be	VERB
cana-1649	10	31	two	two	NUM
cana-1649	10	32	analytic	analytic	ADJ
cana-1649	10	33	functions	function	NOUN
cana-1649	10	34	defined	define	VERB
cana-1649	10	35	in	in	ADP
cana-1649	10	36	the	the	DET
cana-1649	10	37	open	open	ADJ
cana-1649	10	38	unit	unit	NOUN
cana-1649	10	39	disc	disc	NOUN
cana-1649	10	40	δ:=	δ:=	NOUN
cana-1649	10	41	{	{	PUNCT
cana-1649	10	42	𝑧	𝑧	PRON
cana-1649	10	43	∈	∈	PROPN
cana-1649	10	44	ℂ	ℂ	PROPN
cana-1649	10	45	:	:	PUNCT
cana-1649	10	46	|𝑧|	|𝑧|	PROPN
cana-1649	10	47	<	<	X
cana-1649	10	48	1	1	NUM
cana-1649	10	49	}	}	PUNCT
cana-1649	10	50	which	which	PRON
cana-1649	10	51	are	be	AUX
cana-1649	10	52	normalized	normalize	VERB
cana-1649	10	53	by	by	ADP
cana-1649	10	54	the	the	DET
cana-1649	10	55	condition	condition	NOUN
cana-1649	10	56	ℎ1(0	ℎ1(0	PROPN
cana-1649	10	57	)	)	PUNCT
cana-1649	10	58	=	=	SYM
cana-1649	10	59	1	1	NUM
cana-1649	10	60	=	=	SYM
cana-1649	10	61	ℎ2(0	ℎ2(0	PROPN
cana-1649	10	62	)	)	PUNCT
cana-1649	10	63	.	.	PUNCT
cana-1649	11	1	then	then	ADV
cana-1649	11	2	ℎ1	ℎ1	PROPN
cana-1649	11	3	is	be	AUX
cana-1649	11	4	𝒫-stable	𝒫-stable	ADJ
cana-1649	11	5	with	with	ADP
cana-1649	11	6	respect	respect	NOUN
cana-1649	11	7	to	to	ADP
cana-1649	11	8	ℎ2	ℎ2	NOUN
cana-1649	11	9	,	,	PUNCT
cana-1649	11	10	whenever	whenever	SCONJ
cana-1649	11	11	𝒫𝑛(ℎ1	𝒫𝑛(ℎ1	NOUN
cana-1649	11	12	,	,	PUNCT
cana-1649	11	13	𝑧	𝑧	NOUN
cana-1649	11	14	)	)	PUNCT
cana-1649	11	15	ℎ1(𝑧	ℎ1(𝑧	NOUN
cana-1649	11	16	)	)	PUNCT
cana-1649	11	17	≺	≺	NOUN
cana-1649	11	18	1	1	NUM
cana-1649	11	19	ℎ2(𝑧	ℎ2(𝑧	NOUN
cana-1649	11	20	)	)	PUNCT
cana-1649	11	21	(	(	PUNCT
cana-1649	11	22	𝑧	𝑧	PROPN
cana-1649	11	23	∈	∈	PROPN
cana-1649	11	24	δ	δ	PROPN
cana-1649	11	25	)	)	PUNCT
cana-1649	11	26	,	,	PUNCT
cana-1649	11	27	holds	hold	VERB
cana-1649	11	28	for	for	ADP
cana-1649	11	29	all	all	DET
cana-1649	11	30	𝑛	𝑛	DET
cana-1649	11	31	∈	∈	PROPN
cana-1649	11	32	ℕ.	ℕ.	PROPN
cana-1649	11	33	here	here	ADV
cana-1649	11	34	’	'	PUNCT
cana-1649	11	35	≺	≺	NOUN
cana-1649	11	36	’	'	PUNCT
cana-1649	11	37	stands	stand	VERB
cana-1649	11	38	for	for	ADP
cana-1649	11	39	subordination	subordination	NOUN
cana-1649	11	40	and	and	CCONJ
cana-1649	11	41	𝒫𝑛(ℎ	𝒫𝑛(ℎ	ADJ
cana-1649	11	42	,	,	PUNCT
cana-1649	11	43	𝑧	𝑧	NOUN
cana-1649	11	44	)	)	PUNCT
cana-1649	11	45	=	=	SYM
cana-1649	11	46	𝒫𝑛(𝑧	𝒫𝑛(𝑧	X
cana-1649	11	47	)	)	PUNCT
cana-1649	11	48	∗	∗	NOUN
cana-1649	11	49	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1649	11	50	)	)	PUNCT
cana-1649	11	51	where	where	SCONJ
cana-1649	11	52	𝒫𝑛(𝑧	𝒫𝑛(𝑧	NOUN
cana-1649	11	53	)	)	PUNCT
cana-1649	11	54	denote	denote	VERB
cana-1649	11	55	the	the	DET
cana-1649	11	56	𝑛-degree	𝑛-degree	NOUN
cana-1649	11	57	polynomial	polynomial	NOUN
cana-1649	11	58	induced	induce	VERB
cana-1649	11	59	by	by	ADP
cana-1649	11	60	the	the	DET
cana-1649	11	61	(	(	PUNCT
cana-1649	11	62	𝑛	𝑛	PROPN
cana-1649	11	63	+	+	PROPN
cana-1649	11	64	1)th	1)th	NUM
cana-1649	11	65	row	row	NOUN
cana-1649	11	66	entities	entity	NOUN
cana-1649	11	67	in	in	ADP
cana-1649	11	68	an	an	DET
cana-1649	11	69	admissible	admissible	ADJ
cana-1649	11	70	lower	low	ADJ
cana-1649	11	71	triangular	triangular	NOUN
cana-1649	11	72	matrix	matrix	NOUN
cana-1649	11	73	.	.	PUNCT
cana-1649	12	1	the	the	DET
cana-1649	12	2	main	main	ADJ
cana-1649	12	3	purpose	purpose	NOUN
cana-1649	12	4	of	of	ADP
cana-1649	12	5	this	this	DET
cana-1649	12	6	article	article	NOUN
cana-1649	12	7	is	be	AUX
cana-1649	12	8	to	to	PART
cana-1649	12	9	prove	prove	VERB
cana-1649	12	10	that	that	SCONJ
cana-1649	12	11	the	the	DET
cana-1649	12	12	function	function	NOUN
cana-1649	12	13	(	(	PUNCT
cana-1649	12	14	(	(	PUNCT
cana-1649	12	15	𝐴𝑧	𝐴𝑧	X
cana-1649	12	16	+	+	CCONJ
cana-1649	12	17	1)/(𝐵𝑧	1)/(𝐵𝑧	NUM
cana-1649	12	18	+	+	CCONJ
cana-1649	12	19	1))𝛿	1))𝛿	NUM
cana-1649	12	20	is	be	AUX
cana-1649	12	21	𝒫-stable	𝒫-stable	ADJ
cana-1649	12	22	with	with	ADP
cana-1649	12	23	respect	respect	NOUN
cana-1649	12	24	to	to	ADP
cana-1649	12	25	(	(	PUNCT
cana-1649	12	26	𝐵𝑧	𝐵𝑧	PROPN
cana-1649	12	27	+	+	CCONJ
cana-1649	12	28	1)−𝛿	1)−𝛿	NUM
cana-1649	12	29	,	,	PUNCT
cana-1649	12	30	for	for	ADP
cana-1649	12	31	𝛿	𝛿	PROPN
cana-1649	12	32	∈	∈	PROPN
cana-1649	12	33	(	(	PUNCT
cana-1649	12	34	0,1	0,1	NOUN
cana-1649	12	35	]	]	PUNCT
cana-1649	12	36	and	and	CCONJ
cana-1649	12	37	−1	−1	NOUN
cana-1649	12	38	≤	≤	NOUN
cana-1649	12	39	𝐵	𝐵	PROPN
cana-1649	12	40	<	<	X
cana-1649	12	41	𝐴	𝐴	PROPN
cana-1649	12	42	≤	≤	NOUN
cana-1649	12	43	0	0	PUNCT
cana-1649	12	44	but	but	CCONJ
cana-1649	12	45	not	not	PART
cana-1649	12	46	𝒫-stable	𝒫-stable	ADJ
cana-1649	12	47	with	with	ADP
cana-1649	12	48	respect	respect	NOUN
cana-1649	12	49	to	to	ADP
cana-1649	12	50	itself	itself	PRON
cana-1649	12	51	,	,	PUNCT
cana-1649	12	52	when	when	SCONJ
cana-1649	12	53	−1	−1	NOUN
cana-1649	12	54	≤	≤	PUNCT
cana-1649	12	55	𝐵	𝐵	PROPN
cana-1649	12	56	<	<	X
cana-1649	12	57	𝐴	𝐴	PROPN
cana-1649	12	58	<	<	X
cana-1649	12	59	0	0	NUM
cana-1649	12	60	and	and	CCONJ
cana-1649	12	61	𝛿	𝛿	DET
cana-1649	12	62	∈	∈	PROPN
cana-1649	12	63	(	(	PUNCT
cana-1649	12	64	0,1	0,1	NOUN
cana-1649	12	65	]	]	PUNCT
cana-1649	12	66	.	.	PUNCT
cana-1649	13	1	as	as	ADP
cana-1649	13	2	an	an	DET
cana-1649	13	3	application	application	NOUN
cana-1649	13	4	,	,	PUNCT
cana-1649	13	5	considered	consider	VERB
cana-1649	13	6	different	different	ADJ
cana-1649	13	7	admissible	admissible	ADJ
cana-1649	13	8	lower	low	ADJ
cana-1649	13	9	triangular	triangular	NOUN
cana-1649	13	10	matrices	matrix	NOUN
cana-1649	13	11	to	to	PART
cana-1649	13	12	derive	derive	VERB
cana-1649	13	13	various	various	ADJ
cana-1649	13	14	results	result	NOUN
cana-1649	13	15	related	relate	VERB
cana-1649	13	16	on	on	ADP
cana-1649	13	17	stability	stability	NOUN
cana-1649	13	18	.	.	PUNCT
cana-1649	14	1	keywords	keyword	NOUN
cana-1649	14	2	:	:	PUNCT
cana-1649	14	3	stable	stable	ADJ
cana-1649	14	4	functions	function	NOUN
cana-1649	14	5	,	,	PUNCT
cana-1649	14	6	𝒫-stable	𝒫-stable	ADJ
cana-1649	14	7	functions	function	NOUN
cana-1649	14	8	,	,	PUNCT
cana-1649	14	9	generalized	generalize	VERB
cana-1649	14	10	cesàro	cesàro	PROPN
cana-1649	14	11	stable	stable	ADJ
cana-1649	14	12	functions	function	NOUN
cana-1649	14	13	,	,	PUNCT
cana-1649	14	14	subordinations	subordination	NOUN
cana-1649	14	15	,	,	PUNCT
cana-1649	14	16	cesàro	cesàro	PROPN
cana-1649	14	17	mean	mean	VERB
cana-1649	14	18	,	,	PUNCT
cana-1649	14	19	janowski	janowski	ADJ
cana-1649	14	20	function	function	NOUN
cana-1649	14	21	.	.	PUNCT
cana-1649	15	1	1	1	X
cana-1649	15	2	.	.	X
cana-1649	15	3	introduction	introduction	NOUN
cana-1649	15	4	and	and	CCONJ
cana-1649	15	5	preliminaries	preliminary	NOUN
cana-1649	15	6	let	let	VERB
cana-1649	15	7	𝒜	𝒜	NOUN
cana-1649	15	8	be	be	AUX
cana-1649	15	9	the	the	DET
cana-1649	15	10	class	class	NOUN
cana-1649	15	11	of	of	ADP
cana-1649	15	12	analytic	analytic	ADJ
cana-1649	15	13	functions	function	NOUN
cana-1649	15	14	ℎ	ℎ	NOUN
cana-1649	15	15	in	in	ADP
cana-1649	15	16	the	the	DET
cana-1649	15	17	unit	unit	NOUN
cana-1649	15	18	disc	disc	VERB
cana-1649	15	19	δ	δ	PROPN
cana-1649	15	20	=	=	PRON
cana-1649	15	21	{	{	PUNCT
cana-1649	15	22	𝑧	𝑧	NOUN
cana-1649	15	23	∈	∈	PROPN
cana-1649	15	24	ℂ	ℂ	PROPN
cana-1649	15	25	:	:	PUNCT
cana-1649	15	26	|𝑧|	|𝑧|	NOUN
cana-1649	15	27	<	<	X
cana-1649	15	28	1	1	NUM
cana-1649	15	29	}	}	PUNCT
cana-1649	15	30	.	.	PUNCT
cana-1649	16	1	let	let	VERB
cana-1649	16	2	𝒜0	𝒜0	NOUN
cana-1649	16	3	and	and	CCONJ
cana-1649	16	4	𝒜1	𝒜1	NOUN
cana-1649	16	5	be	be	AUX
cana-1649	16	6	the	the	DET
cana-1649	16	7	subclass	subclass	NOUN
cana-1649	16	8	of	of	ADP
cana-1649	16	9	𝒜	𝒜	NOUN
cana-1649	16	10	with	with	ADP
cana-1649	16	11	the	the	DET
cana-1649	16	12	normalization	normalization	NOUN
cana-1649	16	13	ℎ(0	ℎ(0	NOUN
cana-1649	16	14	)	)	PUNCT
cana-1649	16	15	=	=	SYM
cana-1649	16	16	1	1	NUM
cana-1649	16	17	and	and	CCONJ
cana-1649	16	18	ℎ(0	ℎ(0	NOUN
cana-1649	16	19	)	)	PUNCT
cana-1649	16	20	=	=	SYM
cana-1649	16	21	ℎ′(0	ℎ′(0	NOUN
cana-1649	16	22	)	)	PUNCT
cana-1649	16	23	−	−	PROPN
cana-1649	16	24	1	1	NUM
cana-1649	16	25	=	=	SYM
cana-1649	16	26	0	0	NUM
cana-1649	16	27	,	,	PUNCT
cana-1649	16	28	respectively	respectively	ADV
cana-1649	16	29	.	.	PUNCT
cana-1649	17	1	the	the	DET
cana-1649	17	2	class	class	NOUN
cana-1649	17	3	𝒮	𝒮	PROPN
cana-1649	17	4	⊂	⊂	PROPN
cana-1649	17	5	𝒜	𝒜	PROPN
cana-1649	17	6	consists	consist	VERB
cana-1649	17	7	of	of	ADP
cana-1649	17	8	all	all	DET
cana-1649	17	9	univalent	univalent	ADJ
cana-1649	17	10	functions	function	NOUN
cana-1649	17	11	in	in	ADP
cana-1649	17	12	δ	δ	PROPN
cana-1649	17	13	.	.	PUNCT
cana-1649	18	1	for	for	ADP
cana-1649	18	2	0	0	NUM
cana-1649	18	3	≤	≤	NOUN
cana-1649	18	4	𝛾	𝛾	ADP
cana-1649	18	5	<	<	X
cana-1649	18	6	1	1	NUM
cana-1649	18	7	,	,	PUNCT
cana-1649	18	8	a	a	DET
cana-1649	18	9	function	function	NOUN
cana-1649	18	10	ℎ	ℎ	ADP
cana-1649	18	11	∈	∈	PROPN
cana-1649	18	12	𝒜	𝒜	NOUN
cana-1649	18	13	belongs	belong	VERB
cana-1649	18	14	to	to	ADP
cana-1649	18	15	the	the	DET
cana-1649	18	16	class	class	NOUN
cana-1649	18	17	𝒮∗(𝛾	𝒮∗(𝛾	CCONJ
cana-1649	18	18	)	)	PUNCT
cana-1649	18	19	of	of	ADP
cana-1649	18	20	starlike	starlike	NOUN
cana-1649	18	21	of	of	ADP
cana-1649	18	22	order	order	NOUN
cana-1649	18	23	𝛾	𝛾	NOUN
cana-1649	18	24	and	and	CCONJ
cana-1649	18	25	𝒞(𝛾	𝒞(𝛾	NUM
cana-1649	18	26	)	)	PUNCT
cana-1649	18	27	of	of	ADP
cana-1649	18	28	convex	convex	NOUN
cana-1649	18	29	of	of	ADP
cana-1649	18	30	order	order	NOUN
cana-1649	18	31	𝛾	𝛾	NOUN
cana-1649	18	32	,	,	PUNCT
cana-1649	18	33	if	if	SCONJ
cana-1649	18	34	ℎ	ℎ	PROPN
cana-1649	18	35	maps	map	VERB
cana-1649	18	36	conformally	conformally	ADV
cana-1649	18	37	the	the	DET
cana-1649	18	38	unit	unit	NOUN
cana-1649	18	39	disc	disc	VERB
cana-1649	18	40	δ	δ	PROPN
cana-1649	18	41	onto	onto	ADP
cana-1649	18	42	the	the	DET
cana-1649	18	43	domains	domain	NOUN
cana-1649	18	44	that	that	PRON
cana-1649	18	45	are	be	AUX
cana-1649	18	46	starlike	starlike	NOUN
cana-1649	18	47	and	and	CCONJ
cana-1649	18	48	convex	convex	NOUN
cana-1649	18	49	while	while	SCONJ
cana-1649	18	50	the	the	DET
cana-1649	18	51	analytical	analytical	ADJ
cana-1649	18	52	characterization	characterization	NOUN
cana-1649	18	53	of	of	ADP
cana-1649	18	54	these	these	DET
cana-1649	18	55	classes	class	NOUN
cana-1649	18	56	are	be	AUX
cana-1649	18	57	given	give	VERB
cana-1649	18	58	by	by	ADP
cana-1649	18	59	𝑅𝑒	𝑅𝑒	PROPN
cana-1649	18	60	(	(	PUNCT
cana-1649	18	61	𝑧ℎ′(𝑧	𝑧ℎ′(𝑧	NOUN
cana-1649	18	62	)	)	PUNCT
cana-1649	18	63	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1649	18	64	)	)	PUNCT
cana-1649	18	65	)	)	PUNCT
cana-1649	18	66	>	>	X
cana-1649	19	1	𝛾	𝛾	PROPN
cana-1649	20	1	and	and	CCONJ
cana-1649	20	2	𝑅𝑒	𝑅𝑒	VERB
cana-1649	20	3	(	(	PUNCT
cana-1649	20	4	1	1	NUM
cana-1649	20	5	+	+	NUM
cana-1649	20	6	𝑧ℎ′′(𝑧	𝑧ℎ′′(𝑧	NOUN
cana-1649	20	7	)	)	PUNCT
cana-1649	20	8	ℎ′(𝑧	ℎ′(𝑧	PROPN
cana-1649	20	9	)	)	PUNCT
cana-1649	20	10	)	)	PUNCT
cana-1649	20	11	>	>	X
cana-1649	21	1	𝛾	𝛾	X
cana-1649	21	2	in	in	ADP
cana-1649	21	3	δ	δ	PROPN
cana-1649	21	4	,	,	PUNCT
cana-1649	21	5	respectively	respectively	ADV
cana-1649	21	6	.	.	PUNCT
cana-1649	22	1	also	also	ADV
cana-1649	22	2	,	,	PUNCT
cana-1649	22	3	we	we	PRON
cana-1649	22	4	denote	denote	VERB
cana-1649	22	5	𝒮∗(0):=	𝒮∗(0):=	NOUN
cana-1649	22	6	𝒮∗	𝒮∗	NOUN
cana-1649	23	1	and	and	CCONJ
cana-1649	23	2	𝒞(0):=	𝒞(0):=	PROPN
cana-1649	23	3	𝒞.	𝒞.	PROPN
cana-1649	23	4	these	these	DET
cana-1649	23	5	subclasses	subclass	NOUN
cana-1649	23	6	has	have	VERB
cana-1649	23	7	a	a	DET
cana-1649	23	8	proper	proper	ADJ
cana-1649	23	9	inclusion	inclusion	NOUN
cana-1649	23	10	as	as	SCONJ
cana-1649	23	11	follows	follow	VERB
cana-1649	23	12	:	:	PUNCT
cana-1649	23	13	𝒞	𝒞	PROPN
cana-1649	23	14	⊂	⊂	PROPN
cana-1649	23	15	𝒮∗	𝒮∗	NOUN
cana-1649	23	16	⊂	⊂	PROPN
cana-1649	23	17	𝒮	𝒮	PROPN
cana-1649	23	18	⊂	⊂	PROPN
cana-1649	23	19	𝒜.	𝒜.	PROPN
cana-1649	23	20	by	by	ADP
cana-1649	23	21	alexander	alexander	PROPN
cana-1649	23	22	transformation	transformation	PROPN
cana-1649	23	23	,	,	PUNCT
cana-1649	23	24	we	we	PRON
cana-1649	23	25	have	have	VERB
cana-1649	23	26	ℎ	ℎ	NOUN
cana-1649	23	27	∈	∈	VERB
cana-1649	23	28	𝒞	𝒞	PROPN
cana-1649	23	29	if	if	SCONJ
cana-1649	24	1	and	and	CCONJ
cana-1649	24	2	only	only	ADV
cana-1649	24	3	if	if	SCONJ
cana-1649	24	4	𝑧ℎ′	𝑧ℎ′	NOUN
cana-1649	24	5	∈	∈	PROPN
cana-1649	24	6	𝒮∗.	𝒮∗.	ADP
cana-1649	24	7	a	a	DET
cana-1649	24	8	function	function	NOUN
cana-1649	24	9	ℎ	ℎ	PART
cana-1649	24	10	∈	∈	NOUN
cana-1649	24	11	𝒜1	𝒜1	NOUN
cana-1649	24	12	is	be	AUX
cana-1649	24	13	pre	pre	ADJ
cana-1649	24	14	-	-	ADJ
cana-1649	24	15	starlike	starlike	NOUN
cana-1649	24	16	of	of	ADP
cana-1649	24	17	order	order	NOUN
cana-1649	24	18	𝛾	𝛾	NOUN
cana-1649	24	19	if	if	SCONJ
cana-1649	24	20	ℎ	ℎ	PROPN
cana-1649	24	21	∗	∗	VERB
cana-1649	24	22	𝒦𝛾	𝒦𝛾	PROPN
cana-1649	24	23	∈	∈	PROPN
cana-1649	24	24	𝒮	𝒮	PROPN
cana-1649	24	25	∗(𝛾	∗(𝛾	PROPN
cana-1649	24	26	)	)	PUNCT
cana-1649	24	27	,	,	PUNCT
cana-1649	24	28	where	where	SCONJ
cana-1649	24	29	𝒦𝛾(𝑧	𝒦𝛾(𝑧	NOUN
cana-1649	24	30	)	)	PUNCT
cana-1649	25	1	=	=	SYM
cana-1649	25	2	𝑧	𝑧	PROPN
cana-1649	25	3	(	(	PUNCT
cana-1649	25	4	1−𝑧)2−2𝛾	1−𝑧)2−2𝛾	NUM
cana-1649	25	5	.	.	PUNCT
cana-1649	26	1	if	if	SCONJ
cana-1649	26	2	ℎ1	ℎ1	PROPN
cana-1649	26	3	,	,	PUNCT
cana-1649	26	4	ℎ2	ℎ2	NOUN
cana-1649	26	5	are	be	AUX
cana-1649	26	6	analytic	analytic	ADJ
cana-1649	26	7	functions	function	NOUN
cana-1649	26	8	in	in	ADP
cana-1649	26	9	δ	δ	PROPN
cana-1649	26	10	,	,	PUNCT
cana-1649	26	11	we	we	PRON
cana-1649	26	12	say	say	VERB
cana-1649	26	13	ℎ1	ℎ1	PROPN
cana-1649	26	14	is	be	AUX
cana-1649	26	15	subordinate	subordinate	ADJ
cana-1649	26	16	to	to	ADP
cana-1649	26	17	ℎ2	ℎ2	NOUN
cana-1649	26	18	,	,	PUNCT
cana-1649	26	19	written	write	VERB
cana-1649	26	20	ℎ1	ℎ1	PROPN
cana-1649	26	21	≺	≺	NOUN
cana-1649	26	22	ℎ2	ℎ2	NOUN
cana-1649	26	23	,	,	PUNCT
cana-1649	26	24	if	if	SCONJ
cana-1649	26	25	ℎ1	ℎ1	PROPN
cana-1649	26	26	=	=	AUX
cana-1649	26	27	ℎ2	ℎ2	VERB
cana-1649	26	28	∘	∘	NOUN
cana-1649	26	29	𝜔	𝜔	NOUN
cana-1649	26	30	for	for	ADP
cana-1649	26	31	some	some	DET
cana-1649	26	32	analytic	analytic	ADJ
cana-1649	26	33	function	function	NOUN
cana-1649	26	34	𝜔	𝜔	NOUN
cana-1649	26	35	:	:	PUNCT
cana-1649	26	36	δ	δ	PROPN
cana-1649	26	37	→	→	SYM
cana-1649	26	38	δ	δ	PROPN
cana-1649	26	39	with	with	ADP
cana-1649	26	40	𝜔(0	𝜔(0	PROPN
cana-1649	26	41	)	)	PUNCT
cana-1649	26	42	=	=	PUNCT
cana-1649	27	1	0	0	X
cana-1649	27	2	.	.	PUNCT
cana-1649	28	1	if	if	SCONJ
cana-1649	28	2	ℎ2	ℎ2	NOUN
cana-1649	28	3	is	be	AUX
cana-1649	28	4	univalent	univalent	ADJ
cana-1649	28	5	in	in	ADP
cana-1649	28	6	δ	δ	PROPN
cana-1649	28	7	,	,	PUNCT
cana-1649	28	8	then	then	ADV
cana-1649	28	9	ℎ1	ℎ1	PROPN
cana-1649	28	10	≺	≺	VERB
cana-1649	28	11	ℎ2	ℎ2	NOUN
cana-1649	28	12	if	if	SCONJ
cana-1649	28	13	and	and	CCONJ
cana-1649	28	14	only	only	ADV
cana-1649	28	15	if	if	SCONJ
cana-1649	28	16	ℎ1(δ	ℎ1(δ	PROPN
cana-1649	28	17	)	)	PUNCT
cana-1649	28	18	⊆	⊆	NUM
cana-1649	28	19	ℎ2(δ	ℎ2(δ	NUM
cana-1649	28	20	)	)	PUNCT
cana-1649	28	21	and	and	CCONJ
cana-1649	28	22	ℎ1(0	ℎ1(0	PROPN
cana-1649	28	23	)	)	PUNCT
cana-1649	28	24	=	=	SYM
cana-1649	28	25	ℎ2(0	ℎ2(0	PROPN
cana-1649	28	26	)	)	PUNCT
cana-1649	28	27	.	.	PUNCT
cana-1649	29	1	communications	communication	NOUN
cana-1649	29	2	on	on	ADP
cana-1649	29	3	applied	apply	VERB
cana-1649	29	4	nonlinear	nonlinear	ADJ
cana-1649	29	5	analysis	analysis	NOUN
cana-1649	29	6	issn	issn	NOUN
cana-1649	29	7	:	:	PUNCT
cana-1649	29	8	1074	1074	NUM
cana-1649	29	9	-	-	PUNCT
cana-1649	29	10	133x	133x	NUM
cana-1649	29	11	vol	vol	NOUN
cana-1649	29	12	32	32	NUM
cana-1649	29	13	no	no	NOUN
cana-1649	29	14	.	.	NOUN
cana-1649	29	15	1	1	NUM
cana-1649	29	16	(	(	PUNCT
cana-1649	29	17	2025	2025	NUM
cana-1649	29	18	)	)	PUNCT
cana-1649	30	1	293	293	NUM
cana-1649	30	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1649	30	3	for	for	ADP
cana-1649	30	4	−1	−1	NOUN
cana-1649	30	5	≤	≤	NUM
cana-1649	30	6	𝐵	𝐵	PROPN
cana-1649	30	7	<	<	X
cana-1649	30	8	𝐴	𝐴	PROPN
cana-1649	30	9	≤	≤	NOUN
cana-1649	30	10	1	1	NUM
cana-1649	30	11	and	and	CCONJ
cana-1649	30	12	𝛿	𝛿	PRON
cana-1649	30	13	∈	∈	PROPN
cana-1649	30	14	(	(	PUNCT
cana-1649	30	15	0,1	0,1	NUM
cana-1649	30	16	]	]	PUNCT
cana-1649	30	17	,	,	PUNCT
cana-1649	30	18	we	we	PRON
cana-1649	30	19	define	define	VERB
cana-1649	30	20	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADV
cana-1649	30	21	𝛿	𝛿	PROPN
cana-1649	30	22	(	(	PUNCT
cana-1649	30	23	𝑧	𝑧	NOUN
cana-1649	30	24	)	)	PUNCT
cana-1649	30	25	=	=	SYM
cana-1649	30	26	(	(	PUNCT
cana-1649	30	27	𝐴𝑧+1	𝐴𝑧+1	NOUN
cana-1649	30	28	𝐵𝑧+1	𝐵𝑧+1	NOUN
cana-1649	30	29	)	)	PUNCT
cana-1649	31	1	𝛿	𝛿	PRON
cana-1649	31	2	=	=	SYM
cana-1649	31	3	1	1	NUM
cana-1649	31	4	+	+	NUM
cana-1649	31	5	∑∞𝑗=1	∑∞𝑗=1	NOUN
cana-1649	31	6	𝑏𝑗	𝑏𝑗	NOUN
cana-1649	31	7	𝐴,𝐵(𝛿)𝑧𝑗	𝐴,𝐵(𝛿)𝑧𝑗	NOUN
cana-1649	31	8	(	(	PUNCT
cana-1649	31	9	𝑧	𝑧	PROPN
cana-1649	31	10	∈	∈	PROPN
cana-1649	31	11	δ	δ	PROPN
cana-1649	31	12	)	)	PUNCT
cana-1649	31	13	,	,	PUNCT
cana-1649	31	14	(	(	PUNCT
cana-1649	31	15	1.1	1.1	NUM
cana-1649	31	16	)	)	PUNCT
cana-1649	31	17	where	where	SCONJ
cana-1649	31	18	𝑏𝑗	𝑏𝑗	VERB
cana-1649	31	19	:	:	PUNCT
cana-1649	31	20	=	=	PUNCT
cana-1649	31	21	𝑏𝑗	𝑏𝑗	NOUN
cana-1649	31	22	𝐴,𝐵(𝛿	𝐴,𝐵(𝛿	NOUN
cana-1649	31	23	)	)	PUNCT
cana-1649	31	24	=	=	PUNCT
cana-1649	31	25	∑𝑗𝑖=0	∑𝑗𝑖=0	PROPN
cana-1649	32	1	[	[	X
cana-1649	32	2	𝛿]𝑖	𝛿]𝑖	NOUN
cana-1649	32	3	𝑖	𝑖	X
cana-1649	32	4	!	!	PUNCT
cana-1649	32	5	(	(	PUNCT
cana-1649	32	6	𝛿)𝑗−𝑖	𝛿)𝑗−𝑖	PROPN
cana-1649	32	7	(	(	PUNCT
cana-1649	32	8	𝑗−𝑖	𝑗−𝑖	PROPN
cana-1649	32	9	)	)	PUNCT
cana-1649	32	10	!	!	PUNCT
cana-1649	33	1	𝐴𝑖(−𝐵)𝑗−𝑖.	𝐴𝑖(−𝐵)𝑗−𝑖.	PROPN
cana-1649	34	1	also	also	ADV
cana-1649	34	2	,	,	PUNCT
cana-1649	35	1	[	[	X
cana-1649	35	2	𝛿]𝑗	𝛿]𝑗	NOUN
cana-1649	35	3	=	=	X
cana-1649	35	4	{	{	PUNCT
cana-1649	35	5	1	1	NUM
cana-1649	35	6	,	,	PUNCT
cana-1649	35	7	𝑗	𝑗	NOUN
cana-1649	35	8	=	=	SYM
cana-1649	35	9	0	0	NUM
cana-1649	35	10	𝛿[𝛿	𝛿[𝛿	NUM
cana-1649	35	11	−	−	PROPN
cana-1649	36	1	1]𝑗−1	1]𝑗−1	NUM
cana-1649	36	2	,	,	PUNCT
cana-1649	36	3	𝑗	𝑗	PROPN
cana-1649	36	4	≥	≥	NUM
cana-1649	36	5	1	1	NUM
cana-1649	36	6	and	and	CCONJ
cana-1649	36	7	(	(	PUNCT
cana-1649	36	8	𝛿)𝑗	𝛿)𝑗	NOUN
cana-1649	36	9	=	=	SYM
cana-1649	36	10	{	{	PUNCT
cana-1649	36	11	1	1	NUM
cana-1649	36	12	,	,	PUNCT
cana-1649	36	13	𝑗	𝑗	NOUN
cana-1649	36	14	=	=	SYM
cana-1649	36	15	0	0	NUM
cana-1649	36	16	𝛿(𝛿	𝛿(𝛿	NOUN
cana-1649	36	17	+	+	CCONJ
cana-1649	36	18	1)𝑗−1	1)𝑗−1	NUM
cana-1649	36	19	,	,	PUNCT
cana-1649	36	20	𝑗	𝑗	DET
cana-1649	36	21	≥	≥	NUM
cana-1649	36	22	1	1	NUM
cana-1649	36	23	are	be	AUX
cana-1649	36	24	the	the	DET
cana-1649	36	25	factorial	factorial	ADJ
cana-1649	36	26	polynomials	polynomial	NOUN
cana-1649	36	27	.	.	PUNCT
cana-1649	37	1	moreover	moreover	ADV
cana-1649	37	2	,	,	PUNCT
cana-1649	37	3	we	we	PRON
cana-1649	37	4	have	have	VERB
cana-1649	37	5	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADJ
cana-1649	37	6	𝛿	𝛿	PROPN
cana-1649	37	7	(	(	PUNCT
cana-1649	37	8	𝑧)′	𝑧)′	PROPN
cana-1649	37	9	+	+	CCONJ
cana-1649	37	10	(	(	PUNCT
cana-1649	37	11	(	(	PUNCT
cana-1649	37	12	𝐵−𝐴)𝛿	𝐵−𝐴)𝛿	PROPN
cana-1649	37	13	1+(𝐵+𝐴)𝑧+𝐵𝐴𝑧2	1+(𝐵+𝐴)𝑧+𝐵𝐴𝑧2	NOUN
cana-1649	37	14	)	)	PUNCT
cana-1649	37	15	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADP
cana-1649	37	16	𝛿	𝛿	PRON
cana-1649	37	17	(	(	PUNCT
cana-1649	37	18	𝑧	𝑧	NOUN
cana-1649	37	19	)	)	PUNCT
cana-1649	37	20	=	=	SYM
cana-1649	37	21	0	0	X
cana-1649	37	22	.	.	PUNCT
cana-1649	38	1	(	(	PUNCT
cana-1649	38	2	1.2	1.2	NUM
cana-1649	38	3	)	)	PUNCT
cana-1649	38	4	note	note	VERB
cana-1649	38	5	that	that	SCONJ
cana-1649	38	6	,	,	PUNCT
cana-1649	38	7	from	from	ADP
cana-1649	38	8	(	(	PUNCT
cana-1649	38	9	1.1	1.1	NUM
cana-1649	38	10	)	)	PUNCT
cana-1649	38	11	for	for	ADP
cana-1649	38	12	𝐴	𝐴	PROPN
cana-1649	38	13	=	=	SYM
cana-1649	38	14	0	0	NUM
cana-1649	38	15	and	and	CCONJ
cana-1649	38	16	−1	−1	NOUN
cana-1649	38	17	≤	≤	NOUN
cana-1649	38	18	𝐵	𝐵	NOUN
cana-1649	38	19	<	<	X
cana-1649	38	20	0	0	NUM
cana-1649	38	21	,	,	PUNCT
cana-1649	38	22	we	we	PRON
cana-1649	38	23	have	have	VERB
cana-1649	38	24	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	38	25	𝛿	𝛿	ADJ
cana-1649	38	26	(	(	PUNCT
cana-1649	38	27	𝑧	𝑧	NOUN
cana-1649	38	28	)	)	PUNCT
cana-1649	38	29	=	=	SYM
cana-1649	39	1	(	(	PUNCT
cana-1649	39	2	𝐵𝑧	𝐵𝑧	PROPN
cana-1649	39	3	+	+	CCONJ
cana-1649	39	4	1)−𝛿	1)−𝛿	NUM
cana-1649	39	5	=	=	SYM
cana-1649	39	6	1	1	NUM
cana-1649	39	7	+	+	NUM
cana-1649	39	8	∑∞𝑗=1	∑∞𝑗=1	PROPN
cana-1649	39	9	(	(	PUNCT
cana-1649	39	10	𝛿)𝑗	𝛿)𝑗	NOUN
cana-1649	39	11	𝑗	𝑗	X
cana-1649	39	12	!	!	PUNCT
cana-1649	39	13	(	(	PUNCT
cana-1649	39	14	−𝐵)𝑗𝑧𝑗	−𝐵)𝑗𝑧𝑗	PROPN
cana-1649	39	15	=	=	SYM
cana-1649	39	16	1	1	NUM
cana-1649	39	17	+	+	NUM
cana-1649	39	18	∑∞𝑗=1	∑∞𝑗=1	NOUN
cana-1649	39	19	𝑐𝑗𝑧	𝑐𝑗𝑧	NOUN
cana-1649	39	20	𝑗	𝑗	PROPN
cana-1649	39	21	(	(	PUNCT
cana-1649	39	22	𝑧	𝑧	PROPN
cana-1649	39	23	∈	∈	PROPN
cana-1649	39	24	δ	δ	PROPN
cana-1649	39	25	)	)	PUNCT
cana-1649	39	26	.	.	PUNCT
cana-1649	40	1	(	(	PUNCT
cana-1649	40	2	1.3	1.3	NUM
cana-1649	40	3	)	)	PUNCT
cana-1649	40	4	definition	definition	NOUN
cana-1649	40	5	1.1	1.1	NUM
cana-1649	40	6	.	.	PUNCT
cana-1649	41	1	[	[	X
cana-1649	41	2	11	11	NUM
cana-1649	41	3	]	]	PUNCT
cana-1649	41	4	for	for	ADP
cana-1649	41	5	ℎ	ℎ	PROPN
cana-1649	41	6	∈	∈	NOUN
cana-1649	41	7	𝒜0	𝒜0	NOUN
cana-1649	41	8	and	and	CCONJ
cana-1649	41	9	0	0	NUM
cana-1649	41	10	<	<	X
cana-1649	41	11	𝑐	𝑐	X
cana-1649	41	12	<	<	X
cana-1649	41	13	1	1	NUM
cana-1649	41	14	+	+	SYM
cana-1649	41	15	𝑏	𝑏	NOUN
cana-1649	41	16	,	,	PUNCT
cana-1649	41	17	the	the	DET
cana-1649	41	18	𝑛th	𝑛th	NOUN
cana-1649	41	19	cesàro	cesàro	PROPN
cana-1649	41	20	mean	mean	VERB
cana-1649	41	21	of	of	ADP
cana-1649	41	22	type	type	NOUN
cana-1649	41	23	(	(	PUNCT
cana-1649	41	24	𝑏	𝑏	PROPN
cana-1649	41	25	−	−	PROPN
cana-1649	41	26	1	1	NUM
cana-1649	41	27	,	,	PUNCT
cana-1649	41	28	𝑐	𝑐	NOUN
cana-1649	41	29	)	)	PUNCT
cana-1649	41	30	of	of	ADP
cana-1649	41	31	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1649	41	32	)	)	PUNCT
cana-1649	41	33	=	=	SYM
cana-1649	42	1	∑𝑛𝑗=0	∑𝑛𝑗=0	ADJ
cana-1649	42	2	𝑎𝑘𝑧	𝑎𝑘𝑧	INTJ
cana-1649	42	3	𝑘	𝑘	NOUN
cana-1649	42	4	is	be	AUX
cana-1649	42	5	defined	define	VERB
cana-1649	42	6	as	as	ADP
cana-1649	42	7	𝜎𝑛	𝜎𝑛	DET
cana-1649	42	8	𝑏−1,𝑐(ℎ	𝑏−1,𝑐(ℎ	PROPN
cana-1649	42	9	,	,	PUNCT
cana-1649	42	10	𝑧	𝑧	NOUN
cana-1649	42	11	)	)	PUNCT
cana-1649	42	12	=	=	SYM
cana-1649	43	1	1	1	NUM
cana-1649	43	2	𝐵𝑛	𝐵𝑛	PROPN
cana-1649	43	3	∑𝑛𝑗=0	∑𝑛𝑗=0	PROPN
cana-1649	43	4	𝐵𝑛−𝑗𝑏𝑗𝑧	𝐵𝑛−𝑗𝑏𝑗𝑧	VERB
cana-1649	43	5	𝑗	𝑗	PROPN
cana-1649	43	6	=	=	NOUN
cana-1649	43	7	𝜎𝑛	𝜎𝑛	PRON
cana-1649	43	8	𝑏−1,𝑐(𝑧	𝑏−1,𝑐(𝑧	PROPN
cana-1649	43	9	)	)	PUNCT
cana-1649	43	10	∗	∗	NOUN
cana-1649	43	11	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1649	43	12	)	)	PUNCT
cana-1649	43	13	,	,	PUNCT
cana-1649	43	14	𝑛	𝑛	DET
cana-1649	43	15	∈	∈	PROPN
cana-1649	43	16	ℕ	ℕ	PROPN
cana-1649	43	17	∪	∪	X
cana-1649	43	18	{	{	PUNCT
cana-1649	43	19	0	0	NUM
cana-1649	43	20	}	}	PUNCT
cana-1649	43	21	(	(	PUNCT
cana-1649	43	22	1.4	1.4	NUM
cana-1649	43	23	)	)	PUNCT
cana-1649	43	24	where	where	SCONJ
cana-1649	43	25	𝐵𝑗	𝐵𝑗	PROPN
cana-1649	43	26	=	=	SYM
cana-1649	43	27	(	(	PUNCT
cana-1649	43	28	𝑏)𝑗	𝑏)𝑗	X
cana-1649	43	29	(	(	PUNCT
cana-1649	43	30	𝑐)𝑗	𝑐)𝑗	NOUN
cana-1649	43	31	𝑏−𝑐+1	𝑏−𝑐+1	NOUN
cana-1649	43	32	𝑏	𝑏	NOUN
cana-1649	43	33	and	and	CCONJ
cana-1649	43	34	𝐵0	𝐵0	NOUN
cana-1649	43	35	=	=	SYM
cana-1649	44	1	1	1	X
cana-1649	44	2	.	.	X
cana-1649	44	3	note	note	VERB
cana-1649	44	4	that	that	SCONJ
cana-1649	44	5	,	,	PUNCT
cana-1649	44	6	for	for	ADP
cana-1649	44	7	𝑏	𝑏	NOUN
cana-1649	44	8	=	=	SYM
cana-1649	44	9	1	1	NUM
cana-1649	44	10	+	+	SYM
cana-1649	44	11	𝛽	𝛽	NOUN
cana-1649	44	12	and	and	CCONJ
cana-1649	44	13	𝑐	𝑐	NOUN
cana-1649	44	14	=	=	SYM
cana-1649	44	15	1	1	NUM
cana-1649	44	16	,	,	PUNCT
cana-1649	44	17	(	(	PUNCT
cana-1649	44	18	1.4	1.4	NUM
cana-1649	44	19	)	)	PUNCT
cana-1649	44	20	represents	represents	AUX
cana-1649	44	21	𝑛th	𝑛th	VERB
cana-1649	44	22	cesàro	cesàro	PROPN
cana-1649	44	23	mean	mean	VERB
cana-1649	44	24	of	of	ADP
cana-1649	44	25	order	order	NOUN
cana-1649	44	26	𝛽	𝛽	NOUN
cana-1649	44	27	≥	≥	NOUN
cana-1649	44	28	0	0	NUM
cana-1649	44	29	which	which	PRON
cana-1649	44	30	was	be	AUX
cana-1649	44	31	studied	study	VERB
cana-1649	44	32	by	by	ADP
cana-1649	44	33	mondal	mondal	NOUN
cana-1649	44	34	and	and	CCONJ
cana-1649	44	35	swaminathan	swaminathan	ADV
cana-1649	44	36	in	in	ADP
cana-1649	44	37	[	[	X
cana-1649	44	38	6	6	NUM
cana-1649	44	39	]	]	PUNCT
cana-1649	44	40	.	.	PUNCT
cana-1649	45	1	also	also	ADV
cana-1649	45	2	note	note	VERB
cana-1649	45	3	that	that	SCONJ
cana-1649	45	4	for	for	ADP
cana-1649	45	5	𝑏	𝑏	NOUN
cana-1649	45	6	=	=	SYM
cana-1649	45	7	1	1	NUM
cana-1649	45	8	and	and	CCONJ
cana-1649	45	9	𝑐	𝑐	NOUN
cana-1649	45	10	=	=	SYM
cana-1649	45	11	1	1	NUM
cana-1649	45	12	in	in	ADP
cana-1649	45	13	(	(	PUNCT
cana-1649	45	14	1.4	1.4	NUM
cana-1649	45	15	)	)	PUNCT
cana-1649	45	16	,	,	PUNCT
cana-1649	45	17	then	then	ADV
cana-1649	45	18	we	we	PRON
cana-1649	45	19	get	get	VERB
cana-1649	45	20	𝑛th	𝑛th	VERB
cana-1649	45	21	partial	partial	ADJ
cana-1649	45	22	sum	sum	NOUN
cana-1649	45	23	of	of	ADP
cana-1649	45	24	ℎ	ℎ	PROPN
cana-1649	45	25	∈	∈	PROPN
cana-1649	45	26	𝒜0	𝒜0	NOUN
cana-1649	45	27	.	.	PUNCT
cana-1649	46	1	definition	definition	NOUN
cana-1649	46	2	1.2	1.2	NUM
cana-1649	46	3	.	.	PUNCT
cana-1649	47	1	[	[	X
cana-1649	47	2	11	11	NUM
cana-1649	47	3	]	]	PUNCT
cana-1649	47	4	let	let	VERB
cana-1649	47	5	ℋ𝑛(𝑛	ℋ𝑛(𝑛	PROPN
cana-1649	47	6	∈	∈	PROPN
cana-1649	47	7	ℕ	ℕ	PROPN
cana-1649	47	8	)	)	PUNCT
cana-1649	47	9	be	be	VERB
cana-1649	47	10	a	a	DET
cana-1649	47	11	non	non	ADJ
cana-1649	47	12	-	-	ADJ
cana-1649	47	13	empty	empty	ADJ
cana-1649	47	14	set	set	NOUN
cana-1649	47	15	consisting	consist	VERB
cana-1649	47	16	of	of	ADP
cana-1649	47	17	lower	low	ADJ
cana-1649	47	18	triangular	triangular	NOUN
cana-1649	47	19	matrices	matrix	NOUN
cana-1649	47	20	𝐻	𝐻	NOUN
cana-1649	47	21	=	=	SYM
cana-1649	47	22	(	(	PUNCT
cana-1649	47	23	ℎ𝑖𝑗	ℎ𝑖𝑗	NOUN
cana-1649	47	24	)	)	PUNCT
cana-1649	47	25	of	of	ADP
cana-1649	47	26	order	order	NOUN
cana-1649	47	27	(	(	PUNCT
cana-1649	47	28	𝑛	𝑛	PROPN
cana-1649	47	29	+	+	NOUN
cana-1649	47	30	1	1	NUM
cana-1649	47	31	)	)	PUNCT
cana-1649	47	32	with	with	ADP
cana-1649	47	33	ℎ𝑖𝑗	ℎ𝑖𝑗	PROPN
cana-1649	47	34	≥	≥	NUM
cana-1649	47	35	0	0	NUM
cana-1649	47	36	,	,	PUNCT
cana-1649	47	37	for	for	ADP
cana-1649	47	38	all	all	DET
cana-1649	47	39	𝑖	𝑖	ADP
cana-1649	47	40	,	,	PUNCT
cana-1649	47	41	𝑗	𝑗	NOUN
cana-1649	47	42	=	=	NOUN
cana-1649	47	43	0,1,2	0,1,2	NUM
cana-1649	47	44	,	,	PUNCT
cana-1649	47	45	.	.	PUNCT
cana-1649	47	46	.	.	PUNCT
cana-1649	48	1	.	.	PUNCT
cana-1649	49	1	,	,	PUNCT
cana-1649	49	2	𝑛	𝑛	PROPN
cana-1649	49	3	is	be	AUX
cana-1649	49	4	called	call	VERB
cana-1649	49	5	admissible	admissible	ADJ
cana-1649	49	6	lower	low	ADJ
cana-1649	49	7	triangular	triangular	NOUN
cana-1649	49	8	matrix	matrix	NOUN
cana-1649	49	9	set	set	VERB
cana-1649	49	10	if	if	SCONJ
cana-1649	49	11	each	each	DET
cana-1649	49	12	matrix	matrix	NOUN
cana-1649	49	13	satisfies	satisfy	VERB
cana-1649	49	14	the	the	DET
cana-1649	49	15	following	follow	VERB
cana-1649	49	16	admissible	admissible	ADJ
cana-1649	49	17	conditions	condition	NOUN
cana-1649	49	18	:	:	PUNCT
cana-1649	49	19	(	(	PUNCT
cana-1649	49	20	𝑖	𝑖	X
cana-1649	49	21	)	)	PUNCT
cana-1649	49	22	ℎ𝑖0	ℎ𝑖0	NOUN
cana-1649	50	1	=	=	SYM
cana-1649	50	2	1	1	NUM
cana-1649	50	3	,	,	PUNCT
cana-1649	50	4	∀	∀	X
cana-1649	50	5	0	0	NUM
cana-1649	50	6	≤	≤	NUM
cana-1649	50	7	𝑖	𝑖	SYM
cana-1649	50	8	≤	≤	NUM
cana-1649	50	9	𝑛	𝑛	NOUN
cana-1649	50	10	,	,	PUNCT
cana-1649	50	11	(	(	PUNCT
cana-1649	50	12	𝑖𝑖	𝑖𝑖	X
cana-1649	50	13	)	)	PUNCT
cana-1649	50	14	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
cana-1649	50	15	𝑒𝑎𝑐ℎ	𝑒𝑎𝑐ℎ	PROPN
cana-1649	50	16	𝑓𝑖𝑥𝑒𝑑	𝑓𝑖𝑥𝑒𝑑	NOUN
cana-1649	50	17	𝑖	𝑖	SYM
cana-1649	50	18	≥	≥	NUM
cana-1649	50	19	1	1	NUM
cana-1649	50	20	,	,	PUNCT
cana-1649	50	21	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	50	22	=	=	SYM
cana-1649	50	23	ℎ𝑖1ℎ𝑖−1,𝑗−1	ℎ𝑖1ℎ𝑖−1,𝑗−1	NOUN
cana-1649	50	24	,	,	PUNCT
cana-1649	50	25	∀	∀	X
cana-1649	50	26	1	1	NUM
cana-1649	50	27	≤	≤	NUM
cana-1649	50	28	𝑗	𝑗	PRON
cana-1649	50	29	≤	≤	NUM
cana-1649	50	30	𝑛	𝑛	NOUN
cana-1649	50	31	,	,	PUNCT
cana-1649	50	32	(	(	PUNCT
cana-1649	50	33	𝑖𝑖𝑖	𝑖𝑖𝑖	NOUN
cana-1649	50	34	)	)	PUNCT
cana-1649	50	35	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
cana-1649	50	36	𝑒𝑎𝑐ℎ	𝑒𝑎𝑐ℎ	PROPN
cana-1649	50	37	𝑓𝑖𝑥𝑒𝑑	𝑓𝑖𝑥𝑒𝑑	NOUN
cana-1649	50	38	𝑖	𝑖	SYM
cana-1649	50	39	≥	≥	NUM
cana-1649	50	40	1	1	NUM
cana-1649	50	41	,	,	PUNCT
cana-1649	50	42	{	{	PUNCT
cana-1649	50	43	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	50	44	}	}	PUNCT
cana-1649	50	45	𝑖𝑠	𝑖𝑠	NOUN
cana-1649	50	46	𝑎	𝑎	DET
cana-1649	50	47	𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔	𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑖𝑛𝑔	NOUN
cana-1649	50	48	𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒.	𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒.	NOUN
cana-1649	50	49	then	then	ADV
cana-1649	50	50	(	(	PUNCT
cana-1649	50	51	𝑛	𝑛	PROPN
cana-1649	50	52	+	+	NUM
cana-1649	50	53	1)th	1)th	NUM
cana-1649	50	54	row	row	NOUN
cana-1649	50	55	of	of	ADP
cana-1649	50	56	each	each	DET
cana-1649	50	57	(	(	PUNCT
cana-1649	50	58	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	50	59	)	)	PUNCT
cana-1649	50	60	∈	∈	PROPN
cana-1649	51	1	ℋ𝑛	ℋ𝑛	NOUN
cana-1649	51	2	induces	induce	VERB
cana-1649	51	3	a	a	DET
cana-1649	51	4	𝑛-degree	𝑛-degree	NUM
cana-1649	51	5	polynomial	polynomial	ADJ
cana-1649	51	6	𝒫𝑛	𝒫𝑛	PROPN
cana-1649	51	7	defined	define	VERB
cana-1649	51	8	as	as	ADP
cana-1649	51	9	𝒫𝑛(𝑧	𝒫𝑛(𝑧	NOUN
cana-1649	51	10	)	)	PUNCT
cana-1649	51	11	=	=	SYM
cana-1649	52	1	1	1	NUM
cana-1649	52	2	+	+	CCONJ
cana-1649	52	3	∑𝑛𝑗=1	∑𝑛𝑗=1	NUM
cana-1649	52	4	ℎ𝑛𝑗𝑧	ℎ𝑛𝑗𝑧	VERB
cana-1649	52	5	𝑗	𝑗	INTJ
cana-1649	52	6	.	.	PUNCT
cana-1649	53	1	(	(	PUNCT
cana-1649	53	2	1.5	1.5	NUM
cana-1649	53	3	)	)	PUNCT
cana-1649	53	4	the	the	DET
cana-1649	53	5	convolution	convolution	NOUN
cana-1649	53	6	of	of	ADP
cana-1649	53	7	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1649	53	8	)	)	PUNCT
cana-1649	53	9	=	=	SYM
cana-1649	54	1	∑𝑛𝑗=0	∑𝑛𝑗=0	PROPN
cana-1649	54	2	𝑎𝑘𝑧	𝑎𝑘𝑧	VERB
cana-1649	54	3	𝑘	𝑘	PRON
cana-1649	54	4	∈	∈	PROPN
cana-1649	54	5	𝒜0	𝒜0	NOUN
cana-1649	54	6	with	with	ADP
cana-1649	54	7	𝑛-degree	𝑛-degree	NOUN
cana-1649	54	8	polynomial	polynomial	ADJ
cana-1649	54	9	𝒫𝑛	𝒫𝑛	PROPN
cana-1649	54	10	is	be	AUX
cana-1649	54	11	given	give	VERB
cana-1649	54	12	by	by	ADP
cana-1649	54	13	𝒫𝑛(ℎ	𝒫𝑛(ℎ	ADJ
cana-1649	54	14	,	,	PUNCT
cana-1649	54	15	𝑧	𝑧	NOUN
cana-1649	54	16	)	)	PUNCT
cana-1649	54	17	=	=	SYM
cana-1649	54	18	𝒫𝑛(𝑧	𝒫𝑛(𝑧	X
cana-1649	54	19	)	)	PUNCT
cana-1649	54	20	∗	∗	NOUN
cana-1649	54	21	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1649	54	22	)	)	PUNCT
cana-1649	54	23	=	=	SYM
cana-1649	54	24	1	1	NUM
cana-1649	54	25	+	+	CCONJ
cana-1649	54	26	∑	∑	PROPN
cana-1649	54	27	𝑛	𝑛	DET
cana-1649	54	28	𝑗=1	𝑗=1	PROPN
cana-1649	54	29	ℎ𝑛𝑗𝑏𝑗𝑧	ℎ𝑛𝑗𝑏𝑗𝑧	X
cana-1649	54	30	𝑗	𝑗	NOUN
cana-1649	54	31	,	,	PUNCT
cana-1649	54	32	𝑛	𝑛	DET
cana-1649	54	33	∈	∈	PROPN
cana-1649	54	34	ℕ.	ℕ.	PROPN
cana-1649	54	35	(	(	PUNCT
cana-1649	54	36	1.6	1.6	NUM
cana-1649	54	37	)	)	PUNCT
cana-1649	54	38	communications	communication	NOUN
cana-1649	54	39	on	on	ADP
cana-1649	54	40	applied	apply	VERB
cana-1649	54	41	nonlinear	nonlinear	ADJ
cana-1649	54	42	analysis	analysis	NOUN
cana-1649	54	43	issn	issn	NOUN
cana-1649	54	44	:	:	PUNCT
cana-1649	54	45	1074	1074	NUM
cana-1649	54	46	-	-	PUNCT
cana-1649	54	47	133x	133x	NUM
cana-1649	54	48	vol	vol	NOUN
cana-1649	54	49	32	32	NUM
cana-1649	54	50	no	no	NOUN
cana-1649	54	51	.	.	NOUN
cana-1649	54	52	1	1	NUM
cana-1649	54	53	(	(	PUNCT
cana-1649	54	54	2025	2025	NUM
cana-1649	54	55	)	)	PUNCT
cana-1649	54	56	294	294	NUM
cana-1649	54	57	https://internationalpubls.com	https://internationalpubls.com	X
cana-1649	54	58	also	also	ADV
cana-1649	54	59	we	we	PRON
cana-1649	54	60	have	have	VERB
cana-1649	54	61	,	,	PUNCT
cana-1649	54	62	𝒫𝑛(ℎ	𝒫𝑛(ℎ	ADJ
cana-1649	54	63	,	,	PUNCT
cana-1649	54	64	𝑧	𝑧	NOUN
cana-1649	54	65	)	)	PUNCT
cana-1649	54	66	=	=	SYM
cana-1649	54	67	ℎ𝑛1𝒫𝑛−1(ℎ	ℎ𝑛1𝒫𝑛−1(ℎ	PROPN
cana-1649	54	68	,	,	PUNCT
cana-1649	54	69	𝑧	𝑧	PROPN
cana-1649	54	70	)	)	PUNCT
cana-1649	55	1	+	+	CCONJ
cana-1649	55	2	∑	∑	PROPN
cana-1649	55	3	𝑛−1	𝑛−1	PROPN
cana-1649	55	4	𝑗=0	𝑗=0	PROPN
cana-1649	55	5	(	(	PUNCT
cana-1649	55	6	ℎ𝑛𝑗	ℎ𝑛𝑗	NOUN
cana-1649	55	7	−	−	PROPN
cana-1649	55	8	ℎ𝑛1ℎ𝑛−1,𝑗)𝑏𝑗𝑧	ℎ𝑛1ℎ𝑛−1,𝑗)𝑏𝑗𝑧	PROPN
cana-1649	55	9	𝑗	𝑗	NOUN
cana-1649	55	10	+	+	X
cana-1649	55	11	ℎ𝑛𝑛𝑏𝑛𝑧	ℎ𝑛𝑛𝑏𝑛𝑧	ADJ
cana-1649	55	12	𝑛.	𝑛.	NOUN
cana-1649	55	13	(	(	PUNCT
cana-1649	55	14	1.7	1.7	NUM
cana-1649	55	15	)	)	PUNCT
cana-1649	55	16	here	here	ADV
cana-1649	55	17	we	we	PRON
cana-1649	55	18	provide	provide	VERB
cana-1649	55	19	some	some	DET
cana-1649	55	20	examples	example	NOUN
cana-1649	55	21	of	of	ADP
cana-1649	55	22	admissible	admissible	ADJ
cana-1649	55	23	lower	low	ADJ
cana-1649	55	24	triangular	triangular	NOUN
cana-1649	55	25	matrix	matrix	NOUN
cana-1649	55	26	which	which	PRON
cana-1649	55	27	will	will	AUX
cana-1649	55	28	be	be	AUX
cana-1649	55	29	useful	useful	ADJ
cana-1649	55	30	in	in	ADP
cana-1649	55	31	deriving	derive	VERB
cana-1649	55	32	new	new	ADJ
cana-1649	55	33	and	and	CCONJ
cana-1649	55	34	existing	exist	VERB
cana-1649	55	35	results	result	NOUN
cana-1649	55	36	from	from	ADP
cana-1649	55	37	our	our	PRON
cana-1649	55	38	main	main	ADJ
cana-1649	55	39	results	result	NOUN
cana-1649	55	40	.	.	PUNCT
cana-1649	56	1	example	example	NOUN
cana-1649	56	2	1.1	1.1	NUM
cana-1649	56	3	.	.	PUNCT
cana-1649	57	1	if	if	SCONJ
cana-1649	57	2	we	we	PRON
cana-1649	57	3	choose	choose	VERB
cana-1649	57	4	the	the	DET
cana-1649	57	5	admissible	admissible	ADJ
cana-1649	57	6	matrix	matrix	NOUN
cana-1649	57	7	as	as	ADP
cana-1649	57	8	𝐻	𝐻	PROPN
cana-1649	57	9	=	=	SYM
cana-1649	57	10	(	(	PUNCT
cana-1649	57	11	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	57	12	)	)	PUNCT
cana-1649	57	13	=	=	PRON
cana-1649	57	14	{	{	PUNCT
cana-1649	57	15	1	1	NUM
cana-1649	57	16	0	0	NUM
cana-1649	57	17	≤	≤	NOUN
cana-1649	58	1	𝑗	𝑗	PRON
cana-1649	58	2	≤	≤	NUM
cana-1649	58	3	𝑖	𝑖	SYM
cana-1649	58	4	0	0	PUNCT
cana-1649	59	1	𝑗	𝑗	VERB
cana-1649	59	2	≥	≥	NOUN
cana-1649	59	3	𝑖	𝑖	SYM
cana-1649	59	4	+	+	NOUN
cana-1649	59	5	1	1	NUM
cana-1649	59	6	,	,	PUNCT
cana-1649	59	7	then	then	ADV
cana-1649	59	8	(	(	PUNCT
cana-1649	59	9	1.5	1.5	NUM
cana-1649	59	10	)	)	PUNCT
cana-1649	59	11	represents	represent	VERB
cana-1649	59	12	the	the	DET
cana-1649	59	13	𝑛th	𝑛th	VERB
cana-1649	59	14	partial	partial	ADJ
cana-1649	59	15	sum	sum	NOUN
cana-1649	59	16	of	of	ADP
cana-1649	59	17	ℎ	ℎ	PROPN
cana-1649	59	18	∈	∈	PROPN
cana-1649	59	19	𝒜0	𝒜0	NOUN
cana-1649	59	20	.	.	PUNCT
cana-1649	59	21	example	example	NOUN
cana-1649	60	1	1.2	1.2	NUM
cana-1649	60	2	.	.	PUNCT
cana-1649	61	1	for	for	ADP
cana-1649	61	2	the	the	DET
cana-1649	61	3	choice	choice	NOUN
cana-1649	61	4	of	of	ADP
cana-1649	61	5	the	the	DET
cana-1649	61	6	admissible	admissible	ADJ
cana-1649	61	7	matrix	matrix	NOUN
cana-1649	61	8	𝐻	𝐻	NOUN
cana-1649	61	9	=	=	SYM
cana-1649	61	10	(	(	PUNCT
cana-1649	61	11	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	61	12	)	)	PUNCT
cana-1649	61	13	=	=	PRON
cana-1649	61	14	{	{	PUNCT
cana-1649	61	15	1	1	NUM
cana-1649	61	16	𝑗	𝑗	NOUN
cana-1649	61	17	=	=	SYM
cana-1649	61	18	0	0	NUM
cana-1649	61	19	(	(	PUNCT
cana-1649	61	20	1+𝛽)𝑖−𝑗	1+𝛽)𝑖−𝑗	PROPN
cana-1649	61	21	(	(	PUNCT
cana-1649	61	22	𝑖−𝑗	𝑖−𝑗	NOUN
cana-1649	61	23	)	)	PUNCT
cana-1649	61	24	!	!	PUNCT
cana-1649	62	1	𝑖	𝑖	X
cana-1649	62	2	!	!	PUNCT
cana-1649	63	1	(	(	PUNCT
cana-1649	63	2	1+𝛽)𝑖	1+𝛽)𝑖	NUM
cana-1649	63	3	1	1	NUM
cana-1649	63	4	≤	≤	NOUN
cana-1649	63	5	𝑗	𝑗	PRON
cana-1649	63	6	≤	≤	NUM
cana-1649	63	7	𝑖	𝑖	SYM
cana-1649	63	8	0	0	PUNCT
cana-1649	63	9	𝑗	𝑗	VERB
cana-1649	63	10	≥	≥	NOUN
cana-1649	63	11	𝑖	𝑖	SYM
cana-1649	64	1	+	+	NOUN
cana-1649	64	2	1	1	NUM
cana-1649	64	3	,	,	PUNCT
cana-1649	64	4	then	then	ADV
cana-1649	64	5	(	(	PUNCT
cana-1649	64	6	1.5	1.5	NUM
cana-1649	64	7	)	)	PUNCT
cana-1649	64	8	represents	represent	VERB
cana-1649	64	9	the	the	DET
cana-1649	64	10	𝑛th	𝑛th	NOUN
cana-1649	64	11	cesàro	cesàro	PROPN
cana-1649	64	12	mean	mean	VERB
cana-1649	64	13	of	of	ADP
cana-1649	64	14	order	order	NOUN
cana-1649	64	15	𝛽	𝛽	NOUN
cana-1649	64	16	≥	≥	NOUN
cana-1649	64	17	0	0	NUM
cana-1649	64	18	.	.	PUNCT
cana-1649	64	19	example	example	NOUN
cana-1649	64	20	1.3	1.3	NUM
cana-1649	64	21	.	.	PUNCT
cana-1649	65	1	if	if	SCONJ
cana-1649	65	2	the	the	DET
cana-1649	65	3	admissible	admissible	ADJ
cana-1649	65	4	matrix	matrix	NOUN
cana-1649	65	5	is	be	AUX
cana-1649	65	6	𝐻	𝐻	PROPN
cana-1649	65	7	=	=	SYM
cana-1649	65	8	(	(	PUNCT
cana-1649	65	9	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	65	10	)	)	PUNCT
cana-1649	65	11	=	=	PRON
cana-1649	65	12	{	{	PUNCT
cana-1649	65	13	1	1	NUM
cana-1649	65	14	𝑗	𝑗	NOUN
cana-1649	65	15	=	=	SYM
cana-1649	65	16	0	0	NUM
cana-1649	65	17	𝐵𝑖−𝑗	𝐵𝑖−𝑗	PUNCT
cana-1649	65	18	𝐵𝑖	𝐵𝑖	PROPN
cana-1649	65	19	1	1	NUM
cana-1649	65	20	≤	≤	NUM
cana-1649	65	21	𝑗	𝑗	PRON
cana-1649	65	22	≤	≤	NUM
cana-1649	65	23	𝑖	𝑖	SYM
cana-1649	65	24	0	0	PUNCT
cana-1649	66	1	𝑗	𝑗	VERB
cana-1649	66	2	≥	≥	NOUN
cana-1649	66	3	𝑖	𝑖	SYM
cana-1649	66	4	+	+	NOUN
cana-1649	66	5	1	1	NUM
cana-1649	66	6	,	,	PUNCT
cana-1649	66	7	then	then	ADV
cana-1649	66	8	(	(	PUNCT
cana-1649	66	9	1.5	1.5	NUM
cana-1649	66	10	)	)	PUNCT
cana-1649	66	11	represents	represents	AUX
cana-1649	66	12	𝑛th	𝑛th	VERB
cana-1649	66	13	cesàro	cesàro	PROPN
cana-1649	66	14	mean	mean	VERB
cana-1649	66	15	of	of	ADP
cana-1649	66	16	type	type	NOUN
cana-1649	66	17	(	(	PUNCT
cana-1649	66	18	𝑏	𝑏	PROPN
cana-1649	66	19	−	−	PROPN
cana-1649	66	20	1	1	NUM
cana-1649	66	21	,	,	PUNCT
cana-1649	66	22	𝑐	𝑐	NOUN
cana-1649	66	23	)	)	PUNCT
cana-1649	66	24	.	.	PUNCT
cana-1649	67	1	definition	definition	NOUN
cana-1649	67	2	1.3	1.3	NUM
cana-1649	67	3	.	.	PUNCT
cana-1649	68	1	[	[	X
cana-1649	68	2	5	5	NUM
cana-1649	68	3	]	]	PUNCT
cana-1649	68	4	for	for	ADP
cana-1649	68	5	fixed	fix	VERB
cana-1649	68	6	𝑛	𝑛	DET
cana-1649	68	7	∈	∈	PROPN
cana-1649	68	8	ℕ	ℕ	PROPN
cana-1649	68	9	and	and	CCONJ
cana-1649	68	10	ℎ1	ℎ1	PROPN
cana-1649	68	11	,	,	PUNCT
cana-1649	68	12	ℎ2	ℎ2	ADJ
cana-1649	68	13	∈	∈	PROPN
cana-1649	68	14	𝒜0	𝒜0	NOUN
cana-1649	68	15	we	we	PRON
cana-1649	68	16	say	say	VERB
cana-1649	68	17	that	that	SCONJ
cana-1649	68	18	ℎ1	ℎ1	PROPN
cana-1649	68	19	is	be	AUX
cana-1649	68	20	𝒫𝑛-stable	𝒫𝑛-stable	ADJ
cana-1649	68	21	with	with	ADP
cana-1649	68	22	respect	respect	NOUN
cana-1649	68	23	to	to	ADP
cana-1649	68	24	ℎ2	ℎ2	NOUN
cana-1649	68	25	,	,	PUNCT
cana-1649	68	26	if	if	SCONJ
cana-1649	68	27	𝒫𝑛(ℎ1,𝑧	𝒫𝑛(ℎ1,𝑧	NOUN
cana-1649	68	28	)	)	PUNCT
cana-1649	68	29	ℎ1(𝑧	ℎ1(𝑧	VERB
cana-1649	68	30	)	)	PUNCT
cana-1649	68	31	≺	≺	NOUN
cana-1649	68	32	1	1	NUM
cana-1649	68	33	ℎ2(𝑧	ℎ2(𝑧	NOUN
cana-1649	68	34	)	)	PUNCT
cana-1649	68	35	.	.	PUNCT
cana-1649	69	1	(	(	PUNCT
cana-1649	69	2	1.8	1.8	NUM
cana-1649	69	3	)	)	PUNCT
cana-1649	69	4	in	in	ADP
cana-1649	69	5	particular	particular	ADJ
cana-1649	69	6	,	,	PUNCT
cana-1649	69	7	ℎ1	ℎ1	PROPN
cana-1649	69	8	is	be	AUX
cana-1649	69	9	𝒫𝑛-stable	𝒫𝑛-stable	ADJ
cana-1649	69	10	with	with	ADP
cana-1649	69	11	respect	respect	NOUN
cana-1649	69	12	to	to	ADP
cana-1649	69	13	itself	itself	PRON
cana-1649	69	14	then	then	ADV
cana-1649	69	15	it	it	PRON
cana-1649	69	16	is	be	AUX
cana-1649	69	17	just	just	ADV
cana-1649	69	18	𝒫𝑛-stable	𝒫𝑛-stable	ADJ
cana-1649	69	19	.	.	PUNCT
cana-1649	70	1	suppose	suppose	VERB
cana-1649	70	2	the	the	DET
cana-1649	70	3	above	above	ADJ
cana-1649	70	4	condition	condition	NOUN
cana-1649	70	5	holds	hold	VERB
cana-1649	70	6	for	for	ADP
cana-1649	70	7	every	every	DET
cana-1649	70	8	𝑛	𝑛	NOUN
cana-1649	70	9	,	,	PUNCT
cana-1649	70	10	then	then	ADV
cana-1649	70	11	ℎ1	ℎ1	PROPN
cana-1649	70	12	is	be	AUX
cana-1649	70	13	called	call	VERB
cana-1649	70	14	as	as	ADP
cana-1649	70	15	𝒫-stable	𝒫-stable	PROPN
cana-1649	70	16	(	(	PUNCT
cana-1649	70	17	with	with	ADP
cana-1649	70	18	respect	respect	NOUN
cana-1649	70	19	to	to	ADP
cana-1649	70	20	ℎ2	ℎ2	NOUN
cana-1649	70	21	)	)	PUNCT
cana-1649	70	22	.	.	PUNCT
cana-1649	71	1	note	note	VERB
cana-1649	71	2	that	that	SCONJ
cana-1649	71	3	,	,	PUNCT
cana-1649	71	4	for	for	ADP
cana-1649	71	5	the	the	DET
cana-1649	71	6	choices	choice	NOUN
cana-1649	71	7	of	of	ADP
cana-1649	71	8	matrix	matrix	NOUN
cana-1649	71	9	𝐻	𝐻	NOUN
cana-1649	71	10	=	=	SYM
cana-1649	71	11	(	(	PUNCT
cana-1649	71	12	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	71	13	)	)	PUNCT
cana-1649	71	14	given	give	VERB
cana-1649	71	15	in	in	ADP
cana-1649	71	16	example	example	NOUN
cana-1649	71	17	1.1	1.1	NUM
cana-1649	71	18	,	,	PUNCT
cana-1649	71	19	example	example	NOUN
cana-1649	71	20	1.2	1.2	NUM
cana-1649	71	21	and	and	CCONJ
cana-1649	71	22	example	example	NOUN
cana-1649	71	23	1.3	1.3	NUM
cana-1649	71	24	,	,	PUNCT
cana-1649	71	25	the	the	DET
cana-1649	71	26	equation	equation	NOUN
cana-1649	71	27	(	(	PUNCT
cana-1649	71	28	1.8	1.8	NUM
cana-1649	71	29	)	)	PUNCT
cana-1649	71	30	represents	represent	VERB
cana-1649	71	31	the	the	DET
cana-1649	71	32	definition	definition	NOUN
cana-1649	71	33	of	of	ADP
cana-1649	71	34	stable[9	stable[9	NOUN
cana-1649	71	35	]	]	PUNCT
cana-1649	71	36	,	,	PUNCT
cana-1649	71	37	cesàro	cesàro	PROPN
cana-1649	71	38	stable[6	stable[6	PUNCT
cana-1649	71	39	]	]	PUNCT
cana-1649	71	40	and	and	CCONJ
cana-1649	71	41	generalized	generalize	VERB
cana-1649	71	42	cesàro	cesàro	PROPN
cana-1649	71	43	stable[11	stable[11	PROPN
cana-1649	71	44	]	]	PUNCT
cana-1649	71	45	,	,	PUNCT
cana-1649	71	46	respectively	respectively	ADV
cana-1649	71	47	.	.	PUNCT
cana-1649	72	1	the	the	DET
cana-1649	72	2	concept	concept	NOUN
cana-1649	72	3	of	of	ADP
cana-1649	72	4	stable	stable	ADJ
cana-1649	72	5	functions	function	NOUN
cana-1649	72	6	was	be	AUX
cana-1649	72	7	first	first	ADV
cana-1649	72	8	introduced	introduce	VERB
cana-1649	72	9	by	by	ADP
cana-1649	72	10	ruscheweyh	ruscheweyh	NOUN
cana-1649	72	11	and	and	CCONJ
cana-1649	72	12	salinas[9	salinas[9	ADP
cana-1649	72	13	]	]	PUNCT
cana-1649	72	14	and	and	CCONJ
cana-1649	72	15	they	they	PRON
cana-1649	72	16	proved	prove	VERB
cana-1649	72	17	that	that	SCONJ
cana-1649	72	18	𝒥0,−1	𝒥0,−1	ADV
cana-1649	72	19	𝛿	𝛿	ADJ
cana-1649	72	20	(	(	PUNCT
cana-1649	72	21	𝑧	𝑧	NOUN
cana-1649	72	22	)	)	PUNCT
cana-1649	72	23	is	be	AUX
cana-1649	72	24	stable	stable	ADJ
cana-1649	72	25	with	with	ADP
cana-1649	72	26	respect	respect	NOUN
cana-1649	72	27	to	to	ADP
cana-1649	72	28	itself	itself	PRON
cana-1649	72	29	,	,	PUNCT
cana-1649	72	30	for	for	ADP
cana-1649	72	31	0	0	NUM
cana-1649	72	32	<	<	X
cana-1649	72	33	𝛿	𝛿	PROPN
cana-1649	72	34	≤	≤	ADJ
cana-1649	72	35	1	1	NUM
cana-1649	72	36	.	.	PUNCT
cana-1649	73	1	for	for	ADP
cana-1649	73	2	related	related	ADJ
cana-1649	73	3	works	work	NOUN
cana-1649	73	4	on	on	ADP
cana-1649	73	5	stable	stable	ADJ
cana-1649	73	6	functions	function	NOUN
cana-1649	73	7	and	and	CCONJ
cana-1649	73	8	its	its	PRON
cana-1649	73	9	application	application	NOUN
cana-1649	73	10	on	on	ADP
cana-1649	73	11	various	various	ADJ
cana-1649	73	12	subclasses	subclass	NOUN
cana-1649	73	13	,	,	PUNCT
cana-1649	73	14	we	we	PRON
cana-1649	73	15	refer	refer	VERB
cana-1649	73	16	(	(	PUNCT
cana-1649	73	17	[	[	X
cana-1649	73	18	1	1	NUM
cana-1649	73	19	]	]	PUNCT
cana-1649	73	20	,	,	PUNCT
cana-1649	73	21	[	[	X
cana-1649	73	22	2	2	NUM
cana-1649	73	23	]	]	PUNCT
cana-1649	73	24	,	,	PUNCT
cana-1649	73	25	[	[	X
cana-1649	73	26	8	8	NUM
cana-1649	73	27	]	]	PUNCT
cana-1649	73	28	,	,	PUNCT
cana-1649	73	29	[	[	X
cana-1649	73	30	10	10	NUM
cana-1649	73	31	]	]	PUNCT
cana-1649	73	32	,	,	PUNCT
cana-1649	74	1	[	[	X
cana-1649	74	2	12	12	NUM
cana-1649	74	3	]	]	PUNCT
cana-1649	74	4	)	)	PUNCT
cana-1649	74	5	.	.	PUNCT
cana-1649	75	1	sangal	sangal	PROPN
cana-1649	75	2	and	and	CCONJ
cana-1649	75	3	swaminathan[11	swaminathan[11	ADJ
cana-1649	75	4	]	]	PUNCT
cana-1649	75	5	developed	develop	VERB
cana-1649	75	6	𝑛th	𝑛th	VERB
cana-1649	75	7	cesàro	cesàro	PROPN
cana-1649	75	8	mean	mean	VERB
cana-1649	75	9	of	of	ADP
cana-1649	75	10	type	type	NOUN
cana-1649	75	11	(	(	PUNCT
cana-1649	75	12	𝑏	𝑏	PROPN
cana-1649	75	13	−	−	PROPN
cana-1649	75	14	1	1	NUM
cana-1649	75	15	,	,	PUNCT
cana-1649	75	16	𝑐	𝑐	NOUN
cana-1649	75	17	)	)	PUNCT
cana-1649	75	18	,	,	PUNCT
cana-1649	75	19	for	for	ADP
cana-1649	75	20	𝑏	𝑏	PROPN
cana-1649	75	21	+	+	ADP
cana-1649	75	22	1	1	NUM
cana-1649	75	23	>	>	SYM
cana-1649	75	24	𝑐	𝑐	X
cana-1649	75	25	>	>	X
cana-1649	75	26	0	0	NUM
cana-1649	75	27	which	which	PRON
cana-1649	75	28	give	give	VERB
cana-1649	75	29	rise	rise	NOUN
cana-1649	75	30	to	to	ADP
cana-1649	75	31	generalized	generalize	VERB
cana-1649	75	32	cesàro	cesàro	PROPN
cana-1649	75	33	stable	stable	ADJ
cana-1649	75	34	function	function	NOUN
cana-1649	75	35	and	and	CCONJ
cana-1649	75	36	as	as	ADP
cana-1649	75	37	an	an	DET
cana-1649	75	38	application	application	NOUN
cana-1649	75	39	they	they	PRON
cana-1649	75	40	proved	prove	VERB
cana-1649	75	41	that	that	SCONJ
cana-1649	75	42	𝒥0,−1	𝒥0,−1	NOUN
cana-1649	75	43	𝛿	𝛿	ADJ
cana-1649	75	44	(	(	PUNCT
cana-1649	75	45	𝑧	𝑧	NOUN
cana-1649	75	46	)	)	PUNCT
cana-1649	75	47	,	,	PUNCT
cana-1649	75	48	(	(	PUNCT
cana-1649	75	49	−1	−1	NOUN
cana-1649	75	50	≤	≤	X
cana-1649	75	51	𝛿	𝛿	DET
cana-1649	75	52	≤	≤	NUM
cana-1649	75	53	1	1	NUM
cana-1649	75	54	)	)	PUNCT
cana-1649	75	55	is	be	AUX
cana-1649	75	56	generalized	generalize	VERB
cana-1649	75	57	cesàro	cesàro	PROPN
cana-1649	75	58	stable	stable	ADJ
cana-1649	75	59	with	with	ADP
cana-1649	75	60	respect	respect	NOUN
cana-1649	75	61	to	to	ADP
cana-1649	75	62	itself	itself	PRON
cana-1649	75	63	.	.	PUNCT
cana-1649	76	1	recently	recently	ADV
cana-1649	76	2	,	,	PUNCT
cana-1649	76	3	jeyaraman	jeyaraman	NOUN
cana-1649	76	4	and	and	CCONJ
cana-1649	76	5	bhaskar[3	bhaskar[3	NOUN
cana-1649	76	6	]	]	PUNCT
cana-1649	76	7	proved	prove	VERB
cana-1649	76	8	that	that	SCONJ
cana-1649	76	9	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADP
cana-1649	76	10	𝛿	𝛿	PROPN
cana-1649	76	11	(	(	PUNCT
cana-1649	76	12	𝑧	𝑧	NOUN
cana-1649	76	13	)	)	PUNCT
cana-1649	76	14	is	be	AUX
cana-1649	76	15	generalized	generalize	VERB
cana-1649	76	16	cesàro	cesàro	PROPN
cana-1649	76	17	stable	stable	ADJ
cana-1649	76	18	with	with	ADP
cana-1649	76	19	respect	respect	NOUN
cana-1649	76	20	to	to	ADP
cana-1649	76	21	𝒥0,−1	𝒥0,−1	ADV
cana-1649	76	22	𝛿	𝛿	ADJ
cana-1649	76	23	(	(	PUNCT
cana-1649	76	24	𝑧	𝑧	NOUN
cana-1649	76	25	)	)	PUNCT
cana-1649	76	26	,	,	PUNCT
cana-1649	76	27	for	for	ADP
cana-1649	76	28	𝛿	𝛿	PROPN
cana-1649	76	29	∈	∈	PROPN
cana-1649	76	30	(	(	PUNCT
cana-1649	76	31	0,1	0,1	NOUN
cana-1649	76	32	]	]	PUNCT
cana-1649	76	33	and	and	CCONJ
cana-1649	76	34	−1	−1	NOUN
cana-1649	76	35	≤	≤	NOUN
cana-1649	76	36	𝐵	𝐵	PROPN
cana-1649	76	37	<	<	X
cana-1649	76	38	𝐴	𝐴	PROPN
cana-1649	76	39	≤	≤	ADV
cana-1649	76	40	0	0	NUM
cana-1649	76	41	.	.	PUNCT
cana-1649	77	1	communications	communication	NOUN
cana-1649	77	2	on	on	ADP
cana-1649	77	3	applied	apply	VERB
cana-1649	77	4	nonlinear	nonlinear	ADJ
cana-1649	77	5	analysis	analysis	NOUN
cana-1649	77	6	issn	issn	NOUN
cana-1649	77	7	:	:	PUNCT
cana-1649	77	8	1074	1074	NUM
cana-1649	77	9	-	-	PUNCT
cana-1649	77	10	133x	133x	NUM
cana-1649	77	11	vol	vol	NOUN
cana-1649	77	12	32	32	NUM
cana-1649	77	13	no	no	NOUN
cana-1649	77	14	.	.	NOUN
cana-1649	77	15	1	1	NUM
cana-1649	77	16	(	(	PUNCT
cana-1649	77	17	2025	2025	NUM
cana-1649	77	18	)	)	PUNCT
cana-1649	77	19	295	295	NUM
cana-1649	78	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1649	78	2	mondal	mondal	NOUN
cana-1649	78	3	𝑒𝑡	𝑒𝑡	PROPN
cana-1649	78	4	𝑎𝑙.[5	𝑎𝑙.[5	PROPN
cana-1649	78	5	]	]	PUNCT
cana-1649	78	6	introduced	introduce	VERB
cana-1649	78	7	the	the	DET
cana-1649	78	8	concept	concept	NOUN
cana-1649	78	9	of	of	ADP
cana-1649	78	10	𝒫-stable	𝒫-stable	ADJ
cana-1649	78	11	function	function	NOUN
cana-1649	78	12	and	and	CCONJ
cana-1649	78	13	proved	prove	VERB
cana-1649	78	14	that	that	SCONJ
cana-1649	78	15	𝒥1−2𝛼,−1	𝒥1−2𝛼,−1	PROPN
cana-1649	78	16	𝛿	𝛿	ADJ
cana-1649	78	17	is	be	AUX
cana-1649	78	18	𝒫-stable	𝒫-stable	ADJ
cana-1649	78	19	with	with	ADP
cana-1649	78	20	respect	respect	NOUN
cana-1649	78	21	to	to	ADP
cana-1649	78	22	𝒥0,−1	𝒥0,−1	ADV
cana-1649	78	23	𝛿	𝛿	ADJ
cana-1649	78	24	,	,	PUNCT
cana-1649	78	25	for	for	ADP
cana-1649	78	26	0	0	NUM
cana-1649	78	27	<	<	X
cana-1649	78	28	𝛿	𝛿	PROPN
cana-1649	78	29	≤	≤	NUM
cana-1649	78	30	1	1	NUM
cana-1649	78	31	and	and	CCONJ
cana-1649	78	32	1/2	1/2	NUM
cana-1649	78	33	≤	≤	NUM
cana-1649	78	34	𝛼	𝛼	X
cana-1649	78	35	<	<	X
cana-1649	78	36	1	1	NUM
cana-1649	78	37	.	.	PUNCT
cana-1649	79	1	it	it	PRON
cana-1649	79	2	is	be	AUX
cana-1649	79	3	worth	worth	ADJ
cana-1649	79	4	mentioning	mention	VERB
cana-1649	79	5	that	that	SCONJ
cana-1649	79	6	the	the	DET
cana-1649	79	7	authors	author	NOUN
cana-1649	79	8	in	in	ADP
cana-1649	79	9	[	[	X
cana-1649	79	10	5	5	NUM
cana-1649	79	11	]	]	PUNCT
cana-1649	79	12	considered	consider	VERB
cana-1649	79	13	different	different	ADJ
cana-1649	79	14	admissible	admissible	ADJ
cana-1649	79	15	lower	low	ADJ
cana-1649	79	16	triangular	triangular	NOUN
cana-1649	79	17	matrices	matrix	NOUN
cana-1649	79	18	to	to	PART
cana-1649	79	19	derive	derive	VERB
cana-1649	79	20	various	various	ADJ
cana-1649	79	21	results	result	NOUN
cana-1649	79	22	on	on	ADP
cana-1649	79	23	stability	stability	NOUN
cana-1649	79	24	.	.	PUNCT
cana-1649	80	1	in	in	ADP
cana-1649	80	2	this	this	DET
cana-1649	80	3	paper	paper	NOUN
cana-1649	80	4	,	,	PUNCT
cana-1649	80	5	motivated	motivate	VERB
cana-1649	80	6	by	by	ADP
cana-1649	80	7	the	the	DET
cana-1649	80	8	aforesaid	aforesaid	NOUN
cana-1649	80	9	works	work	NOUN
cana-1649	80	10	,	,	PUNCT
cana-1649	80	11	our	our	PRON
cana-1649	80	12	aim	aim	NOUN
cana-1649	80	13	is	be	AUX
cana-1649	80	14	to	to	PART
cana-1649	80	15	prove	prove	VERB
cana-1649	80	16	that	that	SCONJ
cana-1649	80	17	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADP
cana-1649	80	18	𝛿	𝛿	PROPN
cana-1649	80	19	(	(	PUNCT
cana-1649	80	20	𝑧	𝑧	NOUN
cana-1649	80	21	)	)	PUNCT
cana-1649	80	22	is	be	AUX
cana-1649	80	23	𝒫-stable	𝒫-stable	ADJ
cana-1649	80	24	with	with	ADP
cana-1649	80	25	respect	respect	NOUN
cana-1649	80	26	to	to	ADP
cana-1649	80	27	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	80	28	𝛿	𝛿	ADJ
cana-1649	80	29	(	(	PUNCT
cana-1649	80	30	𝑧	𝑧	NOUN
cana-1649	80	31	)	)	PUNCT
cana-1649	80	32	,	,	PUNCT
cana-1649	80	33	for	for	ADP
cana-1649	80	34	−1	−1	NOUN
cana-1649	80	35	≤	≤	NUM
cana-1649	80	36	𝐵	𝐵	PROPN
cana-1649	80	37	<	<	X
cana-1649	80	38	𝐴	𝐴	PROPN
cana-1649	80	39	≤	≤	NOUN
cana-1649	80	40	0	0	NUM
cana-1649	80	41	and	and	CCONJ
cana-1649	80	42	𝛿	𝛿	PRON
cana-1649	80	43	∈	∈	PROPN
cana-1649	80	44	(	(	PUNCT
cana-1649	80	45	0,1	0,1	NOUN
cana-1649	80	46	]	]	PUNCT
cana-1649	80	47	but	but	CCONJ
cana-1649	80	48	not	not	PART
cana-1649	80	49	𝒫-stable	𝒫-stable	ADJ
cana-1649	80	50	with	with	ADP
cana-1649	80	51	respect	respect	NOUN
cana-1649	80	52	to	to	ADP
cana-1649	80	53	itself	itself	PRON
cana-1649	80	54	,	,	PUNCT
cana-1649	80	55	when	when	SCONJ
cana-1649	80	56	−1	−1	NOUN
cana-1649	80	57	≤	≤	PUNCT
cana-1649	80	58	𝐵	𝐵	PROPN
cana-1649	80	59	<	<	X
cana-1649	80	60	𝐴	𝐴	PROPN
cana-1649	80	61	<	<	X
cana-1649	80	62	0	0	NUM
cana-1649	80	63	and	and	CCONJ
cana-1649	80	64	𝛿	𝛿	DET
cana-1649	80	65	∈	∈	PROPN
cana-1649	80	66	(	(	PUNCT
cana-1649	80	67	0,1	0,1	NOUN
cana-1649	80	68	]	]	PUNCT
cana-1649	80	69	.	.	PUNCT
cana-1649	81	1	as	as	ADP
cana-1649	81	2	an	an	DET
cana-1649	81	3	application	application	NOUN
cana-1649	81	4	,	,	PUNCT
cana-1649	81	5	for	for	ADP
cana-1649	81	6	various	various	ADJ
cana-1649	81	7	choices	choice	NOUN
cana-1649	81	8	of	of	ADP
cana-1649	81	9	admissible	admissible	ADJ
cana-1649	81	10	lower	low	ADJ
cana-1649	81	11	triangular	triangular	NOUN
cana-1649	81	12	matrices	matrix	NOUN
cana-1649	81	13	we	we	PRON
cana-1649	81	14	obtain	obtain	VERB
cana-1649	81	15	existing	exist	VERB
cana-1649	81	16	results	result	NOUN
cana-1649	81	17	on	on	ADP
cana-1649	81	18	stability	stability	NOUN
cana-1649	81	19	,	,	PUNCT
cana-1649	81	20	cesàro	cesàro	PROPN
cana-1649	81	21	stability	stability	NOUN
cana-1649	81	22	and	and	CCONJ
cana-1649	81	23	generalized	generalize	VERB
cana-1649	81	24	cesàro	cesàro	PROPN
cana-1649	81	25	stability	stability	NOUN
cana-1649	81	26	.	.	PUNCT
cana-1649	82	1	we	we	PRON
cana-1649	82	2	need	need	VERB
cana-1649	82	3	the	the	DET
cana-1649	82	4	following	follow	VERB
cana-1649	82	5	lemmas	lemmas	ADJ
cana-1649	82	6	,	,	PUNCT
cana-1649	82	7	in	in	ADP
cana-1649	82	8	order	order	NOUN
cana-1649	82	9	to	to	PART
cana-1649	82	10	prove	prove	VERB
cana-1649	82	11	our	our	PRON
cana-1649	82	12	main	main	ADJ
cana-1649	82	13	results	result	NOUN
cana-1649	82	14	.	.	PUNCT
cana-1649	83	1	lemma	lemma	PROPN
cana-1649	83	2	1.1	1.1	NUM
cana-1649	83	3	.	.	PUNCT
cana-1649	84	1	[	[	X
cana-1649	84	2	2	2	NUM
cana-1649	84	3	,	,	PUNCT
cana-1649	84	4	p.3	p.3	NOUN
cana-1649	84	5	]	]	PUNCT
cana-1649	84	6	suppose	suppose	VERB
cana-1649	84	7	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADV
cana-1649	84	8	𝛿	𝛿	PROPN
cana-1649	84	9	(	(	PUNCT
cana-1649	84	10	𝑧	𝑧	NOUN
cana-1649	84	11	)	)	PUNCT
cana-1649	84	12	is	be	AUX
cana-1649	84	13	the	the	DET
cana-1649	84	14	function	function	NOUN
cana-1649	84	15	defined	define	VERB
cana-1649	84	16	in	in	ADP
cana-1649	84	17	(	(	PUNCT
cana-1649	84	18	1.1	1.1	NUM
cana-1649	84	19	)	)	PUNCT
cana-1649	84	20	,	,	PUNCT
cana-1649	84	21	then	then	ADV
cana-1649	84	22	for	for	ADP
cana-1649	84	23	𝛿	𝛿	PROPN
cana-1649	84	24	∈	∈	PROPN
cana-1649	84	25	(	(	PUNCT
cana-1649	84	26	0,1	0,1	NOUN
cana-1649	84	27	]	]	PUNCT
cana-1649	84	28	and	and	CCONJ
cana-1649	84	29	−1	−1	NOUN
cana-1649	84	30	≤	≤	NOUN
cana-1649	84	31	𝐵	𝐵	PROPN
cana-1649	84	32	<	<	X
cana-1649	84	33	𝐴	𝐴	PROPN
cana-1649	84	34	≤	≤	ADV
cana-1649	84	35	0	0	NUM
cana-1649	84	36	,	,	PUNCT
cana-1649	84	37	we	we	PRON
cana-1649	84	38	have	have	AUX
cana-1649	84	39	(	(	PUNCT
cana-1649	84	40	𝑖	𝑖	X
cana-1649	84	41	)	)	PUNCT
cana-1649	84	42	𝑏𝑚1	𝑏𝑚1	NOUN
cana-1649	84	43	≥	≥	NUM
cana-1649	84	44	0	0	NUM
cana-1649	84	45	,	,	PUNCT
cana-1649	84	46	(	(	PUNCT
cana-1649	84	47	𝑖𝑖	𝑖𝑖	X
cana-1649	84	48	)	)	PUNCT
cana-1649	84	49	(	(	PUNCT
cana-1649	84	50	𝑚1	𝑚1	NOUN
cana-1649	84	51	+	+	CCONJ
cana-1649	84	52	1)(𝑚2	1)(𝑚2	NUM
cana-1649	84	53	+	+	CCONJ
cana-1649	84	54	1)𝑏𝑚1	1)𝑏𝑚1	NUM
cana-1649	84	55	+	+	SYM
cana-1649	84	56	1	1	NUM
cana-1649	84	57	+	+	ADP
cana-1649	84	58	𝑚1𝑚2𝐵𝑏𝑚1	𝑚1𝑚2𝐵𝑏𝑚1	PROPN
cana-1649	84	59	≥	≥	NOUN
cana-1649	84	60	0	0	NUM
cana-1649	84	61	,	,	PUNCT
cana-1649	84	62	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
cana-1649	84	63	𝑎𝑙𝑙	𝑎𝑙𝑙	PROPN
cana-1649	84	64	𝑚1	𝑚1	PROPN
cana-1649	84	65	,	,	PUNCT
cana-1649	84	66	𝑚2	𝑚2	PROPN
cana-1649	84	67	∈	∈	PROPN
cana-1649	84	68	ℕ.	ℕ.	PROPN
cana-1649	84	69	lemma	lemma	PROPN
cana-1649	84	70	1.2	1.2	NUM
cana-1649	84	71	.	.	PUNCT
cana-1649	85	1	[	[	X
cana-1649	85	2	7	7	NUM
cana-1649	85	3	,	,	PUNCT
cana-1649	85	4	p.54	p.54	PROPN
cana-1649	85	5	]	]	X
cana-1649	85	6	let	let	VERB
cana-1649	85	7	𝜐	𝜐	PROPN
cana-1649	85	8	and	and	CCONJ
cana-1649	85	9	𝜈	𝜈	PROPN
cana-1649	85	10	are	be	AUX
cana-1649	85	11	prestarlike	prestarlike	ADP
cana-1649	85	12	function	function	NOUN
cana-1649	85	13	and	and	CCONJ
cana-1649	85	14	starlike	starlike	NOUN
cana-1649	85	15	function	function	NOUN
cana-1649	85	16	,	,	PUNCT
cana-1649	85	17	respectively	respectively	ADV
cana-1649	85	18	of	of	ADP
cana-1649	85	19	order	order	NOUN
cana-1649	85	20	𝛾	𝛾	AUX
cana-1649	85	21	∈	∈	PROPN
cana-1649	86	1	[	[	X
cana-1649	86	2	0,1	0,1	NUM
cana-1649	86	3	)	)	PUNCT
cana-1649	86	4	.	.	PUNCT
cana-1649	87	1	then	then	ADV
cana-1649	87	2	for	for	ADP
cana-1649	87	3	any	any	DET
cana-1649	87	4	analytic	analytic	ADJ
cana-1649	87	5	function	function	NOUN
cana-1649	87	6	𝜔	𝜔	X
cana-1649	87	7	in	in	ADP
cana-1649	87	8	δ	δ	PROPN
cana-1649	87	9	,	,	PUNCT
cana-1649	87	10	we	we	PRON
cana-1649	87	11	have	have	AUX
cana-1649	87	12	𝜐∗(𝜈𝜔	𝜐∗(𝜈𝜔	NOUN
cana-1649	87	13	)	)	PUNCT
cana-1649	87	14	𝜐∗𝜈	𝜐∗𝜈	PUNCT
cana-1649	87	15	(	(	PUNCT
cana-1649	87	16	δ	δ	NOUN
cana-1649	87	17	)	)	PUNCT
cana-1649	87	18	⊂	⊂	PROPN
cana-1649	87	19	𝑐𝑜(𝜔(δ	𝑐𝑜(𝜔(δ	NOUN
cana-1649	87	20	)	)	PUNCT
cana-1649	87	21	)	)	PUNCT
cana-1649	87	22	,	,	PUNCT
cana-1649	87	23	where	where	SCONJ
cana-1649	87	24	𝑐𝑜(⋅	𝑐𝑜(⋅	NOUN
cana-1649	87	25	)	)	PUNCT
cana-1649	87	26	is	be	AUX
cana-1649	87	27	the	the	DET
cana-1649	87	28	closed	close	VERB
cana-1649	87	29	convex	convex	NOUN
cana-1649	87	30	hull	hull	NOUN
cana-1649	87	31	of	of	ADP
cana-1649	87	32	a	a	DET
cana-1649	87	33	set	set	NOUN
cana-1649	87	34	.	.	PUNCT
cana-1649	88	1	lemma	lemma	PROPN
cana-1649	88	2	1.3	1.3	NUM
cana-1649	88	3	.	.	PUNCT
cana-1649	89	1	[	[	X
cana-1649	89	2	4	4	NUM
cana-1649	89	3	,	,	PUNCT
cana-1649	89	4	p.57	p.57	X
cana-1649	89	5	]	]	X
cana-1649	89	6	let	let	VERB
cana-1649	89	7	−1	−1	NOUN
cana-1649	89	8	≤	≤	VERB
cana-1649	89	9	𝐵	𝐵	NOUN
cana-1649	89	10	<	<	X
cana-1649	89	11	0	0	NUM
cana-1649	89	12	and	and	CCONJ
cana-1649	89	13	𝛿1	𝛿1	NOUN
cana-1649	89	14	,	,	PUNCT
cana-1649	89	15	𝛿2	𝛿2	NOUN
cana-1649	89	16	>	>	X
cana-1649	89	17	0	0	PROPN
cana-1649	89	18	.	.	PUNCT
cana-1649	90	1	if	if	SCONJ
cana-1649	90	2	𝐻1	𝐻1	NOUN
cana-1649	90	3	≺	≺	NOUN
cana-1649	90	4	[	[	X
cana-1649	90	5	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	90	6	𝛿1	𝛿1	NOUN
cana-1649	90	7	(	(	PUNCT
cana-1649	90	8	𝑧)]−1	𝑧)]−1	ADJ
cana-1649	90	9	and	and	CCONJ
cana-1649	90	10	𝐻2	𝐻2	ADJ
cana-1649	90	11	≺	≺	NOUN
cana-1649	90	12	[	[	X
cana-1649	90	13	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	90	14	𝛿2	𝛿2	NOUN
cana-1649	90	15	(	(	PUNCT
cana-1649	90	16	𝑧)]−1	𝑧)]−1	X
cana-1649	90	17	,	,	PUNCT
cana-1649	90	18	then	then	ADV
cana-1649	90	19	𝐻1𝐻2	𝐻1𝐻2	NOUN
cana-1649	90	20	≺	≺	NOUN
cana-1649	90	21	[	[	X
cana-1649	90	22	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	90	23	𝛿1+𝛿2(𝑧)]−1	𝛿1+𝛿2(𝑧)]−1	PROPN
cana-1649	90	24	,	,	PUNCT
cana-1649	90	25	for	for	ADP
cana-1649	90	26	𝑧	𝑧	DET
cana-1649	90	27	∈	∈	PROPN
cana-1649	90	28	δ	δ	PROPN
cana-1649	90	29	.	.	PROPN
cana-1649	90	30	2	2	NUM
cana-1649	90	31	.	.	X
cana-1649	91	1	𝓟-stability	𝓟-stability	PROPN
cana-1649	91	2	of	of	ADP
cana-1649	91	3	𝓙𝑨,𝑩	𝓙𝑨,𝑩	PROPN
cana-1649	91	4	𝜹	𝜹	X
cana-1649	91	5	(	(	PUNCT
cana-1649	91	6	𝒛	𝒛	NOUN
cana-1649	91	7	)	)	PUNCT
cana-1649	91	8	for	for	ADP
cana-1649	91	9	a	a	DET
cana-1649	91	10	constant	constant	ADJ
cana-1649	91	11	𝑎	𝑎	PRON
cana-1649	91	12	∈	∈	NOUN
cana-1649	91	13	ℝ	ℝ	NOUN
cana-1649	91	14	and	and	CCONJ
cana-1649	91	15	−1	−1	NOUN
cana-1649	91	16	≤	≤	NOUN
cana-1649	91	17	𝐵	𝐵	PROPN
cana-1649	91	18	<	<	X
cana-1649	91	19	𝐴	𝐴	PROPN
cana-1649	91	20	≤	≤	NOUN
cana-1649	91	21	0	0	NUM
cana-1649	91	22	,	,	PUNCT
cana-1649	91	23	using	use	VERB
cana-1649	91	24	(	(	PUNCT
cana-1649	91	25	1.1	1.1	NUM
cana-1649	91	26	)	)	PUNCT
cana-1649	91	27	,	,	PUNCT
cana-1649	91	28	(	(	PUNCT
cana-1649	91	29	1.6	1.6	NUM
cana-1649	91	30	)	)	PUNCT
cana-1649	91	31	and	and	CCONJ
cana-1649	91	32	(	(	PUNCT
cana-1649	91	33	1.7	1.7	NUM
cana-1649	91	34	)	)	PUNCT
cana-1649	91	35	we	we	PRON
cana-1649	91	36	have	have	VERB
cana-1649	91	37	the	the	DET
cana-1649	91	38	following	follow	VERB
cana-1649	91	39	relations	relation	NOUN
cana-1649	91	40	:	:	PUNCT
cana-1649	91	41	𝑎𝒫′𝑛(𝒥𝐴,𝐵	𝑎𝒫′𝑛(𝒥𝐴,𝐵	NOUN
cana-1649	91	42	𝛿	𝛿	ADJ
cana-1649	91	43	(	(	PUNCT
cana-1649	91	44	𝑧	𝑧	NOUN
cana-1649	91	45	)	)	PUNCT
cana-1649	91	46	,	,	PUNCT
cana-1649	91	47	𝑧	𝑧	X
cana-1649	91	48	)	)	PUNCT
cana-1649	91	49	=	=	SYM
cana-1649	91	50	𝒫𝑛(𝑎𝒥𝐴,𝐵	𝒫𝑛(𝑎𝒥𝐴,𝐵	PROPN
cana-1649	91	51	𝛿	𝛿	PROPN
cana-1649	91	52	(	(	PUNCT
cana-1649	91	53	𝑧)′	𝑧)′	PROPN
cana-1649	91	54	,	,	PUNCT
cana-1649	91	55	𝑧	𝑧	NOUN
cana-1649	91	56	)	)	PUNCT
cana-1649	91	57	−𝑎(𝑛	−𝑎(𝑛	NOUN
cana-1649	91	58	+	+	CCONJ
cana-1649	91	59	1)ℎ𝑛𝑛𝑏𝑛+1𝑧	1)ℎ𝑛𝑛𝑏𝑛+1𝑧	NUM
cana-1649	91	60	𝑛	𝑛	VERB
cana-1649	92	1	+	+	ADJ
cana-1649	92	2	𝑎	𝑎	X
cana-1649	92	3	∑𝑛−1𝑗=0	∑𝑛−1𝑗=0	ADJ
cana-1649	92	4	(	(	PUNCT
cana-1649	92	5	ℎ𝑛,𝑗+1	ℎ𝑛,𝑗+1	NOUN
cana-1649	92	6	−	−	NOUN
cana-1649	92	7	ℎ𝑛𝑗)(𝑗	ℎ𝑛𝑗)(𝑗	NOUN
cana-1649	93	1	+	+	X
cana-1649	93	2	1)𝑏𝑗+1𝑧	1)𝑏𝑗+1𝑧	NUM
cana-1649	93	3	𝑗	𝑗	INTJ
cana-1649	93	4	𝑎𝑧𝒫′𝑛(𝒥𝐴,𝐵	𝑎𝑧𝒫′𝑛(𝒥𝐴,𝐵	NOUN
cana-1649	93	5	𝛿	𝛿	ADJ
cana-1649	93	6	(	(	PUNCT
cana-1649	93	7	𝑧	𝑧	NOUN
cana-1649	93	8	)	)	PUNCT
cana-1649	93	9	,	,	PUNCT
cana-1649	93	10	𝑧	𝑧	X
cana-1649	93	11	)	)	PUNCT
cana-1649	93	12	=	=	SYM
cana-1649	93	13	𝒫𝑛(𝑎𝑧𝒥𝐴,𝐵	𝒫𝑛(𝑎𝑧𝒥𝐴,𝐵	PROPN
cana-1649	93	14	𝛿	𝛿	PROPN
cana-1649	93	15	(	(	PUNCT
cana-1649	93	16	𝑧)′	𝑧)′	PROPN
cana-1649	93	17	,	,	PUNCT
cana-1649	93	18	𝑧	𝑧	PART
cana-1649	93	19	)	)	PUNCT
cana-1649	93	20	𝑎𝑧2𝒫′𝑛(𝒥𝐴,𝐵	𝑎𝑧2𝒫′𝑛(𝒥𝐴,𝐵	PROPN
cana-1649	93	21	𝛿	𝛿	ADJ
cana-1649	93	22	(	(	PUNCT
cana-1649	93	23	𝑧	𝑧	NOUN
cana-1649	93	24	)	)	PUNCT
cana-1649	93	25	,	,	PUNCT
cana-1649	93	26	𝑧	𝑧	X
cana-1649	93	27	)	)	PUNCT
cana-1649	93	28	=	=	SYM
cana-1649	93	29	𝒫𝑛(𝑎𝑧	𝒫𝑛(𝑎𝑧	PROPN
cana-1649	93	30	2𝒥𝐴,𝐵	2𝒥𝐴,𝐵	NUM
cana-1649	93	31	𝛿	𝛿	ADJ
cana-1649	93	32	(	(	PUNCT
cana-1649	93	33	𝑧)′	𝑧)′	PROPN
cana-1649	93	34	,	,	PUNCT
cana-1649	93	35	𝑧	𝑧	NOUN
cana-1649	93	36	)	)	PUNCT
cana-1649	94	1	+	+	ADJ
cana-1649	94	2	𝑎𝑛ℎ𝑛𝑛𝑏𝑛𝑧	𝑎𝑛ℎ𝑛𝑛𝑏𝑛𝑧	ADJ
cana-1649	94	3	𝑛+1	𝑛+1	ADP
cana-1649	94	4	+	+	PROPN
cana-1649	94	5	𝑎	𝑎	PRON
cana-1649	94	6	∑𝑛𝑗=2	∑𝑛𝑗=2	PROPN
cana-1649	94	7	(	(	PUNCT
cana-1649	94	8	ℎ𝑛,𝑗−1	ℎ𝑛,𝑗−1	NOUN
cana-1649	94	9	−	−	PROPN
cana-1649	94	10	ℎ𝑛𝑗)(𝑗	ℎ𝑛𝑗)(𝑗	NOUN
cana-1649	94	11	−	−	PROPN
cana-1649	94	12	1)𝑏𝑗−1𝑧	1)𝑏𝑗−1𝑧	NUM
cana-1649	94	13	𝑗.	𝑗.	PROPN
cana-1649	94	14	}	}	PUNCT
cana-1649	94	15	(	(	PUNCT
cana-1649	94	16	2.1	2.1	NUM
cana-1649	94	17	)	)	PUNCT
cana-1649	94	18	similarly	similarly	ADV
cana-1649	94	19	,	,	PUNCT
cana-1649	94	20	for	for	ADP
cana-1649	94	21	a	a	DET
cana-1649	94	22	constant	constant	ADJ
cana-1649	94	23	𝑎	𝑎	PRON
cana-1649	94	24	∈	∈	NOUN
cana-1649	94	25	ℝ	ℝ	NOUN
cana-1649	94	26	and	and	CCONJ
cana-1649	94	27	−1	−1	NOUN
cana-1649	94	28	≤	≤	NOUN
cana-1649	94	29	𝐵	𝐵	NOUN
cana-1649	94	30	<	<	X
cana-1649	94	31	0	0	NUM
cana-1649	94	32	,	,	PUNCT
cana-1649	94	33	using	use	VERB
cana-1649	94	34	(	(	PUNCT
cana-1649	94	35	1.3	1.3	NUM
cana-1649	94	36	)	)	PUNCT
cana-1649	94	37	and	and	CCONJ
cana-1649	94	38	(	(	PUNCT
cana-1649	94	39	1.6	1.6	NUM
cana-1649	94	40	)	)	PUNCT
cana-1649	94	41	the	the	DET
cana-1649	94	42	following	follow	VERB
cana-1649	94	43	relations	relation	NOUN
cana-1649	94	44	hold	hold	VERB
cana-1649	94	45	.	.	PUNCT
cana-1649	95	1	communications	communication	NOUN
cana-1649	95	2	on	on	ADP
cana-1649	95	3	applied	apply	VERB
cana-1649	95	4	nonlinear	nonlinear	ADJ
cana-1649	95	5	analysis	analysis	NOUN
cana-1649	95	6	issn	issn	NOUN
cana-1649	95	7	:	:	PUNCT
cana-1649	95	8	1074	1074	NUM
cana-1649	95	9	-	-	PUNCT
cana-1649	95	10	133x	133x	NUM
cana-1649	95	11	vol	vol	NOUN
cana-1649	95	12	32	32	NUM
cana-1649	95	13	no	no	NOUN
cana-1649	95	14	.	.	NOUN
cana-1649	95	15	1	1	NUM
cana-1649	95	16	(	(	PUNCT
cana-1649	95	17	2025	2025	NUM
cana-1649	95	18	)	)	PUNCT
cana-1649	95	19	296	296	NUM
cana-1649	95	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1649	95	21	𝑎𝒫′𝑛(𝒥0,𝐵	𝑎𝒫′𝑛(𝒥0,𝐵	PROPN
cana-1649	95	22	𝛿	𝛿	ADJ
cana-1649	95	23	(	(	PUNCT
cana-1649	95	24	𝑧	𝑧	NOUN
cana-1649	95	25	)	)	PUNCT
cana-1649	95	26	,	,	PUNCT
cana-1649	95	27	𝑧	𝑧	X
cana-1649	95	28	)	)	PUNCT
cana-1649	95	29	=	=	SYM
cana-1649	96	1	ℎ𝑛1𝒫𝑛−1(𝑎𝒥0,𝐵	ℎ𝑛1𝒫𝑛−1(𝑎𝒥0,𝐵	ADV
cana-1649	96	2	𝛿	𝛿	ADJ
cana-1649	96	3	(	(	PUNCT
cana-1649	96	4	𝑧)′	𝑧)′	PROPN
cana-1649	96	5	,	,	PUNCT
cana-1649	96	6	𝑧	𝑧	NOUN
cana-1649	96	7	)	)	PUNCT
cana-1649	96	8	𝑎𝑧𝒫′𝑛(𝒥0,𝐵	𝑎𝑧𝒫′𝑛(𝒥0,𝐵	NOUN
cana-1649	96	9	𝛿	𝛿	ADJ
cana-1649	96	10	(	(	PUNCT
cana-1649	96	11	𝑧	𝑧	NOUN
cana-1649	96	12	)	)	PUNCT
cana-1649	96	13	,	,	PUNCT
cana-1649	96	14	𝑧	𝑧	X
cana-1649	96	15	)	)	PUNCT
cana-1649	96	16	=	=	SYM
cana-1649	97	1	𝒫𝑛(𝑎𝑧𝒥0,𝐵	𝒫𝑛(𝑎𝑧𝒥0,𝐵	PROPN
cana-1649	97	2	𝛿	𝛿	PROPN
cana-1649	97	3	(	(	PUNCT
cana-1649	97	4	𝑧)′	𝑧)′	PROPN
cana-1649	97	5	,	,	PUNCT
cana-1649	97	6	𝑧	𝑧	NOUN
cana-1649	97	7	)	)	PUNCT
cana-1649	97	8	𝒫𝑛(𝑎𝑧𝒥0,𝐵	𝒫𝑛(𝑎𝑧𝒥0,𝐵	PROPN
cana-1649	97	9	𝛿	𝛿	PROPN
cana-1649	97	10	(	(	PUNCT
cana-1649	97	11	𝑧)′	𝑧)′	PROPN
cana-1649	97	12	,	,	PUNCT
cana-1649	97	13	𝑧	𝑧	PROPN
cana-1649	97	14	)	)	PUNCT
cana-1649	97	15	=	=	SYM
cana-1649	97	16	ℎ𝑛1𝒫𝑛−1(𝑎𝑧𝒥0,𝐵	ℎ𝑛1𝒫𝑛−1(𝑎𝑧𝒥0,𝐵	PROPN
cana-1649	97	17	𝛿	𝛿	ADJ
cana-1649	97	18	(	(	PUNCT
cana-1649	97	19	𝑧)′	𝑧)′	PROPN
cana-1649	97	20	,	,	PUNCT
cana-1649	97	21	𝑧	𝑧	PROPN
cana-1649	97	22	)	)	PUNCT
cana-1649	98	1	+	+	CCONJ
cana-1649	99	1	𝑎∑𝑛−1𝑗=0	𝑎∑𝑛−1𝑗=0	NUM
cana-1649	99	2	(	(	PUNCT
cana-1649	99	3	ℎ𝑛𝑗	ℎ𝑛𝑗	NOUN
cana-1649	99	4	−	−	PROPN
cana-1649	99	5	ℎ𝑛1ℎ𝑛−1,𝑗)𝑗𝑐𝑗𝑧	ℎ𝑛1ℎ𝑛−1,𝑗)𝑗𝑐𝑗𝑧	NOUN
cana-1649	99	6	𝑗	𝑗	PROPN
cana-1649	99	7	+	+	NUM
cana-1649	99	8	𝑎ℎ𝑛𝑛𝑛𝑐𝑛𝑧	𝑎ℎ𝑛𝑛𝑛𝑐𝑛𝑧	NOUN
cana-1649	99	9	𝑛.	𝑛.	NOUN
cana-1649	99	10	}	}	PUNCT
cana-1649	99	11	(	(	PUNCT
cana-1649	99	12	2.2	2.2	NUM
cana-1649	99	13	)	)	PUNCT
cana-1649	99	14	theorem	theorem	VERB
cana-1649	99	15	2.1	2.1	NUM
cana-1649	99	16	.	.	PUNCT
cana-1649	100	1	let	let	VERB
cana-1649	100	2	𝐻	𝐻	PROPN
cana-1649	100	3	=	=	SYM
cana-1649	100	4	(	(	PUNCT
cana-1649	100	5	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	100	6	)	)	PUNCT
cana-1649	100	7	be	be	VERB
cana-1649	100	8	admissible	admissible	ADJ
cana-1649	100	9	lower	low	ADJ
cana-1649	100	10	triangular	triangular	NOUN
cana-1649	100	11	matrix	matrix	NOUN
cana-1649	100	12	with	with	ADP
cana-1649	100	13	ℎ𝑖1	ℎ𝑖1	NOUN
cana-1649	100	14	≤	≤	NUM
cana-1649	100	15	1	1	NUM
cana-1649	100	16	,	,	PUNCT
cana-1649	100	17	∀	∀	NOUN
cana-1649	100	18	𝑖	𝑖	PRON
cana-1649	100	19	≥	≥	NOUN
cana-1649	100	20	1	1	NUM
cana-1649	100	21	.	.	PUNCT
cana-1649	101	1	then	then	ADV
cana-1649	101	2	for	for	ADP
cana-1649	101	3	−1	−1	NOUN
cana-1649	101	4	≤	≤	NUM
cana-1649	101	5	𝐵	𝐵	PROPN
cana-1649	101	6	<	<	X
cana-1649	101	7	𝐴	𝐴	PROPN
cana-1649	101	8	≤	≤	NOUN
cana-1649	101	9	0	0	NUM
cana-1649	101	10	and	and	CCONJ
cana-1649	101	11	𝛿	𝛿	DET
cana-1649	101	12	∈	∈	PROPN
cana-1649	101	13	(	(	PUNCT
cana-1649	101	14	0,1	0,1	NOUN
cana-1649	101	15	]	]	PUNCT
cana-1649	101	16	,	,	PUNCT
cana-1649	101	17	the	the	DET
cana-1649	101	18	function	function	NOUN
cana-1649	102	1	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADV
cana-1649	102	2	𝛿	𝛿	PROPN
cana-1649	102	3	(	(	PUNCT
cana-1649	102	4	𝑧	𝑧	NOUN
cana-1649	102	5	)	)	PUNCT
cana-1649	102	6	is	be	AUX
cana-1649	102	7	𝒫-stable	𝒫-stable	ADJ
cana-1649	102	8	with	with	ADP
cana-1649	102	9	respect	respect	NOUN
cana-1649	102	10	to	to	ADP
cana-1649	102	11	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	102	12	𝛿	𝛿	ADJ
cana-1649	102	13	(	(	PUNCT
cana-1649	102	14	𝑧	𝑧	NOUN
cana-1649	102	15	)	)	PUNCT
cana-1649	102	16	.	.	PUNCT
cana-1649	103	1	proof	proof	NOUN
cana-1649	103	2	.	.	PUNCT
cana-1649	104	1	to	to	PART
cana-1649	104	2	prove	prove	VERB
cana-1649	104	3	that	that	SCONJ
cana-1649	104	4	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADP
cana-1649	104	5	𝛿	𝛿	PROPN
cana-1649	104	6	(	(	PUNCT
cana-1649	104	7	𝑧	𝑧	NOUN
cana-1649	104	8	)	)	PUNCT
cana-1649	104	9	is	be	AUX
cana-1649	104	10	𝒫-stable	𝒫-stable	ADJ
cana-1649	104	11	with	with	ADP
cana-1649	104	12	respect	respect	NOUN
cana-1649	104	13	to	to	ADP
cana-1649	104	14	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	104	15	𝛿	𝛿	ADJ
cana-1649	104	16	(	(	PUNCT
cana-1649	104	17	𝑧	𝑧	PROPN
cana-1649	104	18	)	)	PUNCT
cana-1649	104	19	,	,	PUNCT
cana-1649	104	20	we	we	PRON
cana-1649	104	21	must	must	AUX
cana-1649	104	22	show	show	VERB
cana-1649	104	23	that	that	SCONJ
cana-1649	104	24	𝒫𝑛(𝒥𝐴,𝐵	𝒫𝑛(𝒥𝐴,𝐵	NOUN
cana-1649	104	25	𝛿	𝛿	PROPN
cana-1649	104	26	(	(	PUNCT
cana-1649	104	27	𝑧),𝑧	𝑧),𝑧	NOUN
cana-1649	104	28	)	)	PUNCT
cana-1649	104	29	𝒥𝐴,𝐵	𝒥𝐴,𝐵	NOUN
cana-1649	104	30	𝛿	𝛿	PRON
cana-1649	104	31	(	(	PUNCT
cana-1649	104	32	𝑧	𝑧	NOUN
cana-1649	104	33	)	)	PUNCT
cana-1649	104	34	≺	≺	NOUN
cana-1649	104	35	1	1	NUM
cana-1649	105	1	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	105	2	𝛿	𝛿	ADJ
cana-1649	105	3	(	(	PUNCT
cana-1649	105	4	𝑧	𝑧	NOUN
cana-1649	105	5	)	)	PUNCT
cana-1649	105	6	(	(	PUNCT
cana-1649	105	7	𝑧	𝑧	PROPN
cana-1649	105	8	∈	∈	PROPN
cana-1649	105	9	δ	δ	PROPN
cana-1649	105	10	)	)	PUNCT
cana-1649	105	11	.	.	PUNCT
cana-1649	106	1	therefore	therefore	ADV
cana-1649	106	2	,	,	PUNCT
cana-1649	106	3	it	it	PRON
cana-1649	106	4	is	be	AUX
cana-1649	106	5	enough	enough	ADJ
cana-1649	106	6	to	to	PART
cana-1649	106	7	prove	prove	VERB
cana-1649	106	8	that	that	SCONJ
cana-1649	107	1	|	|	INTJ
cana-1649	107	2	(	(	PUNCT
cana-1649	107	3	𝐵𝑧+1)[𝒫𝑛(𝒥𝐴,𝐵	𝐵𝑧+1)[𝒫𝑛(𝒥𝐴,𝐵	ADP
cana-1649	107	4	𝛿	𝛿	X
cana-1649	107	5	(	(	PUNCT
cana-1649	107	6	𝑧),𝑧	𝑧),𝑧	PROPN
cana-1649	107	7	)	)	PUNCT
cana-1649	107	8	]	]	PUNCT
cana-1649	108	1	1	1	NUM
cana-1649	108	2	𝛿	𝛿	ADJ
cana-1649	108	3	(	(	PUNCT
cana-1649	108	4	𝐴𝑧+1	𝐴𝑧+1	NOUN
cana-1649	108	5	)	)	PUNCT
cana-1649	108	6	−	−	ADP
cana-1649	108	7	1|	1|	NUM
cana-1649	108	8	≤	≤	NUM
cana-1649	108	9	1	1	NUM
cana-1649	108	10	.	.	PUNCT
cana-1649	108	11	for	for	ADP
cana-1649	108	12	fixed	fix	VERB
cana-1649	108	13	𝑛	𝑛	PRON
cana-1649	108	14	and	and	CCONJ
cana-1649	108	15	𝛿	𝛿	ADJ
cana-1649	108	16	,	,	PUNCT
cana-1649	108	17	let	let	VERB
cana-1649	108	18	us	we	PRON
cana-1649	108	19	consider	consider	VERB
cana-1649	108	20	𝑄(𝑧	𝑄(𝑧	NOUN
cana-1649	108	21	)	)	PUNCT
cana-1649	108	22	=	=	SYM
cana-1649	108	23	1	1	NUM
cana-1649	108	24	−	−	PROPN
cana-1649	108	25	(	(	PUNCT
cana-1649	108	26	𝐵𝑧+1)[𝒫𝑛(𝒥𝐴,𝐵	𝐵𝑧+1)[𝒫𝑛(𝒥𝐴,𝐵	PROPN
cana-1649	108	27	𝛿	𝛿	X
cana-1649	108	28	(	(	PUNCT
cana-1649	108	29	𝑧),𝑧	𝑧),𝑧	PROPN
cana-1649	108	30	)	)	PUNCT
cana-1649	108	31	]	]	PUNCT
cana-1649	108	32	1	1	NUM
cana-1649	108	33	𝛿	𝛿	ADJ
cana-1649	108	34	(	(	PUNCT
cana-1649	108	35	𝐴𝑧+1	𝐴𝑧+1	NOUN
cana-1649	108	36	)	)	PUNCT
cana-1649	108	37	.	.	PUNCT
cana-1649	109	1	a	a	DET
cana-1649	109	2	simple	simple	ADJ
cana-1649	109	3	computation	computation	NOUN
cana-1649	109	4	yields	yield	NOUN
cana-1649	109	5	𝑄′(𝑧	𝑄′(𝑧	PROPN
cana-1649	109	6	)	)	PUNCT
cana-1649	109	7	=	=	PUNCT
cana-1649	109	8	(	(	PUNCT
cana-1649	109	9	𝐴−𝐵)[𝒫𝑛(𝒥𝐴,𝐵	𝐴−𝐵)[𝒫𝑛(𝒥𝐴,𝐵	VERB
cana-1649	109	10	𝛿	𝛿	X
cana-1649	109	11	(	(	PUNCT
cana-1649	109	12	𝑧),𝑧	𝑧),𝑧	PROPN
cana-1649	109	13	)	)	PUNCT
cana-1649	109	14	]	]	PUNCT
cana-1649	110	1	1	1	NUM
cana-1649	110	2	𝛿	𝛿	PRON
cana-1649	110	3	−1	−1	NOUN
cana-1649	110	4	(	(	PUNCT
cana-1649	110	5	𝐴𝑧+1)2	𝐴𝑧+1)2	VERB
cana-1649	110	6	[	[	PUNCT
cana-1649	110	7	𝒫𝑛(𝒥𝐴,𝐵	𝒫𝑛(𝒥𝐴,𝐵	NOUN
cana-1649	110	8	𝛿	𝛿	PROPN
cana-1649	110	9	(	(	PUNCT
cana-1649	110	10	𝑧	𝑧	NOUN
cana-1649	110	11	)	)	PUNCT
cana-1649	110	12	,	,	PUNCT
cana-1649	110	13	𝑧	𝑧	NOUN
cana-1649	110	14	)	)	PUNCT
cana-1649	110	15	−	−	PROPN
cana-1649	111	1	(	(	PUNCT
cana-1649	111	2	1+(𝐴+𝐵)𝑧+𝐴𝐵𝑧2	1+(𝐴+𝐵)𝑧+𝐴𝐵𝑧2	NUM
cana-1649	111	3	𝛿(𝐴−𝐵	𝛿(𝐴−𝐵	NOUN
cana-1649	111	4	)	)	PUNCT
cana-1649	111	5	)	)	PUNCT
cana-1649	112	1	𝒫′𝑛(𝒥𝐴,𝐵	𝒫′𝑛(𝒥𝐴,𝐵	ADP
cana-1649	112	2	𝛿	𝛿	PROPN
cana-1649	112	3	(	(	PUNCT
cana-1649	112	4	𝑧	𝑧	NOUN
cana-1649	112	5	)	)	PUNCT
cana-1649	112	6	,	,	PUNCT
cana-1649	112	7	𝑧	𝑧	NOUN
cana-1649	112	8	)	)	PUNCT
cana-1649	112	9	]	]	PUNCT
cana-1649	112	10	.	.	PUNCT
cana-1649	113	1	(	(	PUNCT
cana-1649	113	2	2.3	2.3	NUM
cana-1649	113	3	)	)	PUNCT
cana-1649	113	4	using	use	VERB
cana-1649	113	5	(	(	PUNCT
cana-1649	113	6	2.1	2.1	NUM
cana-1649	113	7	)	)	PUNCT
cana-1649	113	8	and	and	CCONJ
cana-1649	113	9	(	(	PUNCT
cana-1649	113	10	1.2	1.2	NUM
cana-1649	113	11	)	)	PUNCT
cana-1649	113	12	in	in	ADP
cana-1649	113	13	(	(	PUNCT
cana-1649	113	14	2.3	2.3	NUM
cana-1649	113	15	)	)	PUNCT
cana-1649	113	16	,	,	PUNCT
cana-1649	113	17	we	we	PRON
cana-1649	113	18	have	have	VERB
cana-1649	113	19	𝑄′(𝑧	𝑄′(𝑧	PRON
cana-1649	113	20	)	)	PUNCT
cana-1649	114	1	=	=	PRON
cana-1649	114	2	(	(	PUNCT
cana-1649	114	3	𝐴	𝐴	PROPN
cana-1649	114	4	−	−	PROPN
cana-1649	114	5	𝐵)[𝒫𝑛(𝒥𝐴,𝐵	𝐵)[𝒫𝑛(𝒥𝐴,𝐵	X
cana-1649	114	6	𝛿	𝛿	PROPN
cana-1649	114	7	(	(	PUNCT
cana-1649	114	8	𝑧	𝑧	NOUN
cana-1649	114	9	)	)	PUNCT
cana-1649	114	10	,	,	PUNCT
cana-1649	114	11	𝑧	𝑧	NOUN
cana-1649	114	12	)	)	PUNCT
cana-1649	114	13	]	]	PUNCT
cana-1649	114	14	1	1	NUM
cana-1649	114	15	𝛿	𝛿	PRON
cana-1649	114	16	−1	−1	NOUN
cana-1649	114	17	(	(	PUNCT
cana-1649	114	18	𝐴𝑧	𝐴𝑧	PROPN
cana-1649	114	19	+	+	CCONJ
cana-1649	114	20	1)2	1)2	NUM
cana-1649	115	1	[	[	X
cana-1649	115	2	𝒫𝑛(𝒥𝐴,𝐵	𝒫𝑛(𝒥𝐴,𝐵	NOUN
cana-1649	115	3	𝛿	𝛿	PROPN
cana-1649	115	4	(	(	PUNCT
cana-1649	115	5	𝑧	𝑧	NOUN
cana-1649	115	6	)	)	PUNCT
cana-1649	115	7	−	−	PROPN
cana-1649	115	8	(	(	PUNCT
cana-1649	115	9	1	1	NUM
cana-1649	115	10	+	+	CCONJ
cana-1649	115	11	(	(	PUNCT
cana-1649	115	12	𝐴	𝐴	PROPN
cana-1649	115	13	+	+	X
cana-1649	115	14	𝐵)𝑧	𝐵)𝑧	PUNCT
cana-1649	116	1	+	+	CCONJ
cana-1649	116	2	𝐴𝐵𝑧2	𝐴𝐵𝑧2	NUM
cana-1649	116	3	𝛿(𝐴	𝛿(𝐴	NOUN
cana-1649	116	4	−	−	PROPN
cana-1649	116	5	𝐵	𝐵	NOUN
cana-1649	116	6	)	)	PUNCT
cana-1649	116	7	)	)	PUNCT
cana-1649	116	8	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADV
cana-1649	116	9	𝛿	𝛿	PROPN
cana-1649	116	10	(	(	PUNCT
cana-1649	116	11	𝑧)′	𝑧)′	PROPN
cana-1649	116	12	,	,	PUNCT
cana-1649	116	13	𝑧	𝑧	PROPN
cana-1649	116	14	)	)	PUNCT
cana-1649	116	15	+	+	CCONJ
cana-1649	116	16	1	1	NUM
cana-1649	116	17	𝛿(𝐴	𝛿(𝐴	NOUN
cana-1649	116	18	−	−	PROPN
cana-1649	116	19	𝐵	𝐵	NOUN
cana-1649	116	20	)	)	PUNCT
cana-1649	116	21	(	(	PUNCT
cana-1649	116	22	(	(	PUNCT
cana-1649	116	23	𝑛	𝑛	ADP
cana-1649	116	24	+	+	NUM
cana-1649	116	25	1)ℎ𝑛𝑛𝑏𝑛+1𝑧	1)ℎ𝑛𝑛𝑏𝑛+1𝑧	NUM
cana-1649	116	26	𝑛	𝑛	PRON
cana-1649	116	27	−∑	−∑	PROPN
cana-1649	116	28	𝑛−1	𝑛−1	PROPN
cana-1649	116	29	𝑗=0	𝑗=0	PROPN
cana-1649	116	30	(	(	PUNCT
cana-1649	116	31	ℎ𝑛,𝑗+1	ℎ𝑛,𝑗+1	NOUN
cana-1649	116	32	−	−	NOUN
cana-1649	116	33	ℎ𝑛𝑗)(𝑗	ℎ𝑛𝑗)(𝑗	NOUN
cana-1649	117	1	+	+	X
cana-1649	117	2	1)𝑏𝑗+1𝑧	1)𝑏𝑗+1𝑧	NUM
cana-1649	117	3	𝑗	𝑗	NOUN
cana-1649	117	4	)	)	PUNCT
cana-1649	117	5	−	−	PROPN
cana-1649	117	6	𝐴𝐵	𝐴𝐵	NOUN
cana-1649	117	7	𝛿(𝐴	𝛿(𝐴	VERB
cana-1649	117	8	−	−	PROPN
cana-1649	117	9	𝐵	𝐵	NOUN
cana-1649	117	10	)	)	PUNCT
cana-1649	117	11	(	(	PUNCT
cana-1649	117	12	𝑛ℎ𝑛𝑛𝑏𝑛	𝑛ℎ𝑛𝑛𝑏𝑛	NOUN
cana-1649	117	13	𝑧	𝑧	PRON
cana-1649	117	14	𝑛+1	𝑛+1	PROPN
cana-1649	117	15	+	+	PROPN
cana-1649	117	16	∑	∑	PROPN
cana-1649	117	17	𝑛	𝑛	PRON
cana-1649	117	18	𝑗=2	𝑗=2	PROPN
cana-1649	117	19	(	(	PUNCT
cana-1649	117	20	ℎ𝑛,𝑗−1	ℎ𝑛,𝑗−1	NOUN
cana-1649	117	21	−	−	PROPN
cana-1649	117	22	ℎ𝑛𝑗)(𝑗	ℎ𝑛𝑗)(𝑗	NOUN
cana-1649	117	23	−	−	PROPN
cana-1649	117	24	1)𝑏𝑗−1𝑧	1)𝑏𝑗−1𝑧	NUM
cana-1649	117	25	𝑗	𝑗	PROPN
cana-1649	117	26	)	)	PUNCT
cana-1649	117	27	]	]	PUNCT
cana-1649	117	28	.	.	PUNCT
cana-1649	118	1	communications	communication	NOUN
cana-1649	118	2	on	on	ADP
cana-1649	118	3	applied	apply	VERB
cana-1649	118	4	nonlinear	nonlinear	ADJ
cana-1649	118	5	analysis	analysis	NOUN
cana-1649	118	6	issn	issn	NOUN
cana-1649	118	7	:	:	PUNCT
cana-1649	118	8	1074	1074	NUM
cana-1649	118	9	-	-	PUNCT
cana-1649	118	10	133x	133x	NUM
cana-1649	118	11	vol	vol	NOUN
cana-1649	118	12	32	32	NUM
cana-1649	118	13	no	no	NOUN
cana-1649	118	14	.	.	NOUN
cana-1649	118	15	1	1	NUM
cana-1649	118	16	(	(	PUNCT
cana-1649	118	17	2025	2025	NUM
cana-1649	118	18	)	)	PUNCT
cana-1649	118	19	297	297	NUM
cana-1649	118	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1649	118	21	=	=	PUNCT
cana-1649	119	1	[	[	X
cana-1649	119	2	𝒫𝑛(𝒥𝐴,𝐵	𝒫𝑛(𝒥𝐴,𝐵	NOUN
cana-1649	119	3	𝛿	𝛿	PROPN
cana-1649	119	4	(	(	PUNCT
cana-1649	119	5	𝑧),𝑧	𝑧),𝑧	NOUN
cana-1649	119	6	)	)	PUNCT
cana-1649	119	7	]	]	PUNCT
cana-1649	119	8	1	1	NUM
cana-1649	119	9	𝛿	𝛿	PRON
cana-1649	119	10	−1	−1	NOUN
cana-1649	119	11	𝛿	𝛿	NOUN
cana-1649	119	12	[	[	X
cana-1649	119	13	(	(	PUNCT
cana-1649	119	14	(	(	PUNCT
cana-1649	119	15	𝑛	𝑛	PROPN
cana-1649	119	16	+	+	X
cana-1649	119	17	1)𝑏𝑛+1	1)𝑏𝑛+1	ADJ
cana-1649	119	18	+	+	CCONJ
cana-1649	119	19	∑	∑	PROPN
cana-1649	119	20	∞	∞	PROPN
cana-1649	119	21	𝑛1=1	𝑛1=1	PROPN
cana-1649	119	22	(	(	PUNCT
cana-1649	119	23	(	(	PUNCT
cana-1649	119	24	𝑛1	𝑛1	NOUN
cana-1649	119	25	+	+	NOUN
cana-1649	119	26	1)(𝑛	1)(𝑛	NUM
cana-1649	119	27	+	+	CCONJ
cana-1649	119	28	1)𝑏𝑛+1	1)𝑏𝑛+1	ADJ
cana-1649	119	29	+	+	CCONJ
cana-1649	119	30	𝑛1𝑛𝐵𝑏𝑛)(−𝐴	𝑛1𝑛𝐵𝑏𝑛)(−𝐴	NOUN
cana-1649	119	31	)	)	PUNCT
cana-1649	119	32	𝑛1𝑧𝑛1)ℎ𝑛𝑛𝑧	𝑛1𝑧𝑛1)ℎ𝑛𝑛𝑧	PROPN
cana-1649	119	33	𝑛	𝑛	PRON
cana-1649	119	34	+	+	ADJ
cana-1649	119	35	(	(	PUNCT
cana-1649	119	36	(	(	PUNCT
cana-1649	119	37	ℎ𝑛0	ℎ𝑛0	X
cana-1649	119	38	−	−	PROPN
cana-1649	119	39	ℎ𝑛1)𝑏1)(∑	ℎ𝑛1)𝑏1)(∑	PROPN
cana-1649	119	40	∞	∞	NUM
cana-1649	119	41	𝑛1=0	𝑛1=0	PROPN
cana-1649	119	42	(	(	PUNCT
cana-1649	119	43	𝑛1	𝑛1	ADJ
cana-1649	119	44	+	+	NOUN
cana-1649	119	45	1)(−𝐴	1)(−𝐴	NUM
cana-1649	119	46	)	)	PUNCT
cana-1649	119	47	𝑛1𝑧𝑛1	𝑛1𝑧𝑛1	NOUN
cana-1649	119	48	)	)	PUNCT
cana-1649	120	1	+	+	PROPN
cana-1649	120	2	∑𝑛−1𝑗=1	∑𝑛−1𝑗=1	PROPN
cana-1649	120	3	(	(	PUNCT
cana-1649	120	4	ℎ𝑛𝑗	ℎ𝑛𝑗	PROPN
cana-1649	120	5	−	−	PROPN
cana-1649	120	6	ℎ𝑛,𝑗+1)𝑧	ℎ𝑛,𝑗+1)𝑧	PROPN
cana-1649	120	7	𝑗((𝑗	𝑗((𝑗	PROPN
cana-1649	121	1	+	+	CCONJ
cana-1649	121	2	1)𝑏𝑗+1	1)𝑏𝑗+1	NUM
cana-1649	121	3	−	−	NOUN
cana-1649	121	4	𝐴𝐵𝑗𝑏𝑗𝑧)(∑	𝐴𝐵𝑗𝑏𝑗𝑧)(∑	VERB
cana-1649	121	5	∞	∞	PROPN
cana-1649	121	6	𝑛1=0	𝑛1=0	PROPN
cana-1649	121	7	(	(	PUNCT
cana-1649	121	8	𝑛1	𝑛1	ADJ
cana-1649	121	9	+	+	NOUN
cana-1649	121	10	1)(−𝐴	1)(−𝐴	NUM
cana-1649	121	11	)	)	PUNCT
cana-1649	121	12	𝑛1𝑧𝑛1	𝑛1𝑧𝑛1	NOUN
cana-1649	121	13	)	)	PUNCT
cana-1649	121	14	]	]	PUNCT
cana-1649	122	1	=	=	PUNCT
cana-1649	123	1	[	[	X
cana-1649	123	2	𝒫𝑛(𝒥𝐴,𝐵	𝒫𝑛(𝒥𝐴,𝐵	NOUN
cana-1649	123	3	𝛿	𝛿	PROPN
cana-1649	123	4	(	(	PUNCT
cana-1649	123	5	𝑧),𝑧	𝑧),𝑧	NOUN
cana-1649	123	6	)	)	PUNCT
cana-1649	123	7	]	]	PUNCT
cana-1649	123	8	1	1	NUM
cana-1649	123	9	𝛿	𝛿	PRON
cana-1649	123	10	−1	−1	NOUN
cana-1649	123	11	𝛿	𝛿	NOUN
cana-1649	123	12	[	[	X
cana-1649	123	13	(	(	PUNCT
cana-1649	123	14	(	(	PUNCT
cana-1649	123	15	𝑛	𝑛	PROPN
cana-1649	123	16	+	+	X
cana-1649	123	17	1)𝑏𝑛+1	1)𝑏𝑛+1	ADJ
cana-1649	123	18	+	+	CCONJ
cana-1649	123	19	∑	∑	PROPN
cana-1649	123	20	∞	∞	PROPN
cana-1649	123	21	𝑛1=1	𝑛1=1	PROPN
cana-1649	123	22	(	(	PUNCT
cana-1649	123	23	(	(	PUNCT
cana-1649	123	24	𝑛1	𝑛1	NOUN
cana-1649	123	25	+	+	NOUN
cana-1649	123	26	1)(𝑛	1)(𝑛	NUM
cana-1649	123	27	+	+	CCONJ
cana-1649	123	28	1)𝑏𝑛+1	1)𝑏𝑛+1	ADJ
cana-1649	123	29	+	+	CCONJ
cana-1649	123	30	𝑛1𝑛𝐵𝑏𝑛)(−𝐴	𝑛1𝑛𝐵𝑏𝑛)(−𝐴	NOUN
cana-1649	123	31	)	)	PUNCT
cana-1649	123	32	𝑛1𝑧𝑛1)ℎ𝑛𝑛𝑧	𝑛1𝑧𝑛1)ℎ𝑛𝑛𝑧	PROPN
cana-1649	123	33	𝑛	𝑛	PRON
cana-1649	123	34	+	+	ADJ
cana-1649	123	35	(	(	PUNCT
cana-1649	123	36	(	(	PUNCT
cana-1649	123	37	ℎ𝑛0	ℎ𝑛0	X
cana-1649	123	38	−	−	PROPN
cana-1649	123	39	ℎ𝑛1)𝑏1)(∑	ℎ𝑛1)𝑏1)(∑	PROPN
cana-1649	123	40	∞	∞	NUM
cana-1649	123	41	𝑛1=0	𝑛1=0	PROPN
cana-1649	123	42	(	(	PUNCT
cana-1649	123	43	𝑛1	𝑛1	ADJ
cana-1649	123	44	+	+	NOUN
cana-1649	123	45	1)(−𝐴	1)(−𝐴	NUM
cana-1649	123	46	)	)	PUNCT
cana-1649	123	47	𝑛1𝑧𝑛1	𝑛1𝑧𝑛1	NOUN
cana-1649	123	48	)	)	PUNCT
cana-1649	124	1	+	+	PROPN
cana-1649	124	2	∑𝑛−1𝑗=1	∑𝑛−1𝑗=1	PROPN
cana-1649	124	3	(	(	PUNCT
cana-1649	124	4	ℎ𝑛𝑗	ℎ𝑛𝑗	PROPN
cana-1649	124	5	−	−	PROPN
cana-1649	124	6	ℎ𝑛,𝑗+1)𝑧	ℎ𝑛,𝑗+1)𝑧	PROPN
cana-1649	124	7	𝑗((𝑗	𝑗((𝑗	PROPN
cana-1649	125	1	+	+	CCONJ
cana-1649	125	2	1)𝑏𝑗+1	1)𝑏𝑗+1	NUM
cana-1649	125	3	+	+	CCONJ
cana-1649	125	4	∑	∑	PROPN
cana-1649	125	5	∞	∞	PROPN
cana-1649	125	6	𝑛1=1	𝑛1=1	PROPN
cana-1649	125	7	(	(	PUNCT
cana-1649	125	8	(	(	PUNCT
cana-1649	125	9	𝑛1	𝑛1	NOUN
cana-1649	126	1	+	+	NOUN
cana-1649	126	2	1)(𝑗	1)(𝑗	NUM
cana-1649	126	3	+	+	CCONJ
cana-1649	126	4	1)𝑏𝑗+1	1)𝑏𝑗+1	NUM
cana-1649	126	5	+	+	CCONJ
cana-1649	126	6	𝐵𝑛1𝑗𝑏𝑗)(−𝐴	𝐵𝑛1𝑗𝑏𝑗)(−𝐴	NOUN
cana-1649	126	7	)	)	PUNCT
cana-1649	126	8	𝑛1𝑧𝑛1	𝑛1𝑧𝑛1	NOUN
cana-1649	126	9	)	)	PUNCT
cana-1649	126	10	]	]	PUNCT
cana-1649	126	11	.	.	PUNCT
cana-1649	127	1	(	(	PUNCT
cana-1649	127	2	2.4	2.4	NUM
cana-1649	127	3	)	)	PUNCT
cana-1649	127	4	using	use	VERB
cana-1649	127	5	lemma	lemma	PROPN
cana-1649	127	6	1.1	1.1	NUM
cana-1649	127	7	and	and	CCONJ
cana-1649	127	8	definition	definition	NOUN
cana-1649	127	9	1.2	1.2	NUM
cana-1649	127	10	,	,	PUNCT
cana-1649	127	11	from	from	ADP
cana-1649	127	12	(	(	PUNCT
cana-1649	127	13	2.4	2.4	NUM
cana-1649	127	14	)	)	PUNCT
cana-1649	127	15	it	it	PRON
cana-1649	127	16	follows	follow	VERB
cana-1649	127	17	that	that	SCONJ
cana-1649	127	18	the	the	DET
cana-1649	127	19	expression	expression	NOUN
cana-1649	127	20	[	[	X
cana-1649	127	21	(	(	PUNCT
cana-1649	127	22	(	(	PUNCT
cana-1649	127	23	𝑛	𝑛	PROPN
cana-1649	127	24	+	+	X
cana-1649	127	25	1)𝑏𝑛+1	1)𝑏𝑛+1	ADJ
cana-1649	127	26	+	+	CCONJ
cana-1649	127	27	∑	∑	PROPN
cana-1649	127	28	∞	∞	PROPN
cana-1649	127	29	𝑛1=1	𝑛1=1	PROPN
cana-1649	127	30	(	(	PUNCT
cana-1649	127	31	(	(	PUNCT
cana-1649	127	32	𝑛1	𝑛1	NOUN
cana-1649	127	33	+	+	NOUN
cana-1649	127	34	1)(𝑛	1)(𝑛	NUM
cana-1649	127	35	+	+	CCONJ
cana-1649	127	36	1)𝑏𝑛+1	1)𝑏𝑛+1	ADJ
cana-1649	127	37	+	+	CCONJ
cana-1649	127	38	𝑛1𝑛𝐵𝑏𝑛)(−𝐴	𝑛1𝑛𝐵𝑏𝑛)(−𝐴	NOUN
cana-1649	127	39	)	)	PUNCT
cana-1649	127	40	𝑛1𝑧𝑛1)ℎ𝑛𝑛𝑧	𝑛1𝑧𝑛1)ℎ𝑛𝑛𝑧	PROPN
cana-1649	127	41	𝑛	𝑛	PRON
cana-1649	127	42	+	+	ADJ
cana-1649	127	43	(	(	PUNCT
cana-1649	127	44	(	(	PUNCT
cana-1649	127	45	ℎ𝑛0	ℎ𝑛0	X
cana-1649	127	46	−	−	PROPN
cana-1649	127	47	ℎ𝑛1)𝑏1)(∑	ℎ𝑛1)𝑏1)(∑	PROPN
cana-1649	127	48	∞	∞	NUM
cana-1649	127	49	𝑛1=0	𝑛1=0	PROPN
cana-1649	127	50	(	(	PUNCT
cana-1649	127	51	𝑛1	𝑛1	ADJ
cana-1649	127	52	+	+	NOUN
cana-1649	127	53	1)(−𝐴	1)(−𝐴	NUM
cana-1649	127	54	)	)	PUNCT
cana-1649	127	55	𝑛1𝑧𝑛1	𝑛1𝑧𝑛1	NOUN
cana-1649	127	56	)	)	PUNCT
cana-1649	128	1	+	+	CCONJ
cana-1649	129	1	∑𝑛−1𝑗=1	∑𝑛−1𝑗=1	PROPN
cana-1649	129	2	(	(	PUNCT
cana-1649	129	3	ℎ𝑛𝑗	ℎ𝑛𝑗	PROPN
cana-1649	129	4	−	−	PROPN
cana-1649	130	1	ℎ𝑛,𝑗+1)𝑧	ℎ𝑛,𝑗+1)𝑧	PROPN
cana-1649	130	2	𝑗	𝑗	PROPN
cana-1649	130	3	(	(	PUNCT
cana-1649	130	4	(	(	PUNCT
cana-1649	130	5	𝑗	𝑗	PROPN
cana-1649	130	6	+	+	X
cana-1649	130	7	1)𝑏𝑗+1	1)𝑏𝑗+1	NUM
cana-1649	130	8	+	+	CCONJ
cana-1649	130	9	∑	∑	PROPN
cana-1649	130	10	∞	∞	PROPN
cana-1649	130	11	𝑛1=1	𝑛1=1	PROPN
cana-1649	130	12	(	(	PUNCT
cana-1649	130	13	(	(	PUNCT
cana-1649	130	14	𝑛1	𝑛1	NOUN
cana-1649	130	15	+	+	NOUN
cana-1649	130	16	1)(𝑗	1)(𝑗	NUM
cana-1649	130	17	+	+	CCONJ
cana-1649	130	18	1)𝑏𝑗+1	1)𝑏𝑗+1	NUM
cana-1649	130	19	+	+	CCONJ
cana-1649	130	20	𝐵𝑛1𝑗𝑏𝑗)(−𝐴	𝐵𝑛1𝑗𝑏𝑗)(−𝐴	NOUN
cana-1649	130	21	)	)	PUNCT
cana-1649	130	22	𝑛1𝑧𝑛1	𝑛1𝑧𝑛1	NOUN
cana-1649	130	23	)	)	PUNCT
cana-1649	130	24	]	]	PUNCT
cana-1649	130	25	,	,	PUNCT
cana-1649	130	26	represents	represent	VERB
cana-1649	130	27	a	a	DET
cana-1649	130	28	series	series	NOUN
cana-1649	130	29	of	of	ADP
cana-1649	130	30	positive	positive	PROPN
cana-1649	130	31	taylor	taylor	PROPN
cana-1649	130	32	’s	’s	PART
cana-1649	130	33	coefficients	coefficient	NOUN
cana-1649	130	34	about	about	ADP
cana-1649	130	35	𝑧	𝑧	NOUN
cana-1649	130	36	=	=	NOUN
cana-1649	130	37	0	0	X
cana-1649	130	38	.	.	PUNCT
cana-1649	130	39	again	again	ADV
cana-1649	130	40	by	by	ADP
cana-1649	130	41	lemma	lemma	PROPN
cana-1649	130	42	1.1	1.1	NUM
cana-1649	130	43	,	,	PUNCT
cana-1649	130	44	we	we	PRON
cana-1649	130	45	have	have	VERB
cana-1649	130	46	𝑏𝑗	𝑏𝑗	X
cana-1649	130	47	>	>	X
cana-1649	130	48	0	0	PUNCT
cana-1649	131	1	for	for	ADP
cana-1649	131	2	all	all	DET
cana-1649	131	3	𝑗	𝑗	PRON
cana-1649	131	4	∈	∈	PROPN
cana-1649	131	5	ℕ	ℕ	PROPN
cana-1649	131	6	,	,	PUNCT
cana-1649	131	7	it	it	PRON
cana-1649	131	8	follows	follow	VERB
cana-1649	131	9	that	that	SCONJ
cana-1649	131	10	𝒫𝑛(𝒥𝐴,𝐵	𝒫𝑛(𝒥𝐴,𝐵	NOUN
cana-1649	131	11	𝛿	𝛿	PROPN
cana-1649	131	12	(	(	PUNCT
cana-1649	131	13	𝑧	𝑧	NOUN
cana-1649	131	14	)	)	PUNCT
cana-1649	131	15	,	,	PUNCT
cana-1649	131	16	𝑧	𝑧	X
cana-1649	131	17	)	)	PUNCT
cana-1649	131	18	has	have	VERB
cana-1649	131	19	a	a	DET
cana-1649	131	20	series	series	NOUN
cana-1649	131	21	representation	representation	NOUN
cana-1649	131	22	with	with	ADP
cana-1649	131	23	positive	positive	ADJ
cana-1649	131	24	taylor	taylor	PROPN
cana-1649	131	25	’s	’s	PART
cana-1649	131	26	coefficients	coefficient	NOUN
cana-1649	131	27	about	about	ADP
cana-1649	131	28	𝑧	𝑧	NOUN
cana-1649	131	29	=	=	SYM
cana-1649	131	30	0	0	NUM
cana-1649	131	31	which	which	PRON
cana-1649	131	32	implies	imply	VERB
cana-1649	131	33	that	that	PRON
cana-1649	131	34	|𝒫𝑛(𝒥𝐴,𝐵	|𝒫𝑛(𝒥𝐴,𝐵	VERB
cana-1649	131	35	𝛿	𝛿	ADJ
cana-1649	131	36	(	(	PUNCT
cana-1649	131	37	𝑧	𝑧	NOUN
cana-1649	131	38	)	)	PUNCT
cana-1649	131	39	,	,	PUNCT
cana-1649	131	40	𝑧)|	𝑧)|	PROPN
cana-1649	131	41	≤	≤	PUNCT
cana-1649	131	42	𝒫𝑛(𝒥𝐴,𝐵	𝒫𝑛(𝒥𝐴,𝐵	NOUN
cana-1649	131	43	𝛿	𝛿	X
cana-1649	131	44	(	(	PUNCT
cana-1649	131	45	𝑧	𝑧	NOUN
cana-1649	131	46	)	)	PUNCT
cana-1649	131	47	,	,	PUNCT
cana-1649	131	48	|𝑧|	|𝑧|	PROPN
cana-1649	131	49	)	)	PUNCT
cana-1649	131	50	.	.	PUNCT
cana-1649	132	1	applying	apply	VERB
cana-1649	132	2	these	these	DET
cana-1649	132	3	results	result	NOUN
cana-1649	132	4	in	in	ADP
cana-1649	132	5	(	(	PUNCT
cana-1649	132	6	2.3	2.3	NUM
cana-1649	132	7	)	)	PUNCT
cana-1649	132	8	,	,	PUNCT
cana-1649	132	9	we	we	PRON
cana-1649	132	10	conclude	conclude	VERB
cana-1649	132	11	that	that	SCONJ
cana-1649	132	12	𝑄′(𝑧	𝑄′(𝑧	PROPN
cana-1649	132	13	)	)	PUNCT
cana-1649	132	14	is	be	AUX
cana-1649	132	15	a	a	DET
cana-1649	132	16	series	series	NOUN
cana-1649	132	17	with	with	ADP
cana-1649	132	18	positive	positive	PROPN
cana-1649	132	19	taylor	taylor	PROPN
cana-1649	132	20	’s	’s	PART
cana-1649	132	21	coefficients	coefficient	NOUN
cana-1649	132	22	about	about	ADP
cana-1649	132	23	𝑧	𝑧	NOUN
cana-1649	132	24	=	=	NOUN
cana-1649	132	25	0	0	NUM
cana-1649	132	26	.	.	PUNCT
cana-1649	133	1	hence	hence	ADV
cana-1649	133	2	,	,	PUNCT
cana-1649	133	3	|𝑄′(𝑧)|	|𝑄′(𝑧)|	ADJ
cana-1649	133	4	≤	≤	ADJ
cana-1649	133	5	𝑄′(|𝑧|	𝑄′(|𝑧|	PROPN
cana-1649	133	6	)	)	PUNCT
cana-1649	133	7	.	.	PUNCT
cana-1649	134	1	since	since	SCONJ
cana-1649	134	2	𝑄(0	𝑄(0	NUM
cana-1649	134	3	)	)	PUNCT
cana-1649	134	4	=	=	SYM
cana-1649	134	5	0	0	NUM
cana-1649	134	6	and	and	CCONJ
cana-1649	134	7	𝑄(−𝐵	𝑄(−𝐵	ADJ
cana-1649	134	8	)	)	PUNCT
cana-1649	134	9	=	=	SYM
cana-1649	134	10	1	1	X
cana-1649	134	11	,	,	PUNCT
cana-1649	134	12	it	it	PRON
cana-1649	134	13	follows	follow	VERB
cana-1649	134	14	that	that	SCONJ
cana-1649	134	15	|𝑄(𝑧)|	|𝑄(𝑧)|	PROPN
cana-1649	134	16	=	=	SYM
cana-1649	134	17	|∫	|∫	NOUN
cana-1649	134	18	𝑧	𝑧	NOUN
cana-1649	134	19	0	0	NUM
cana-1649	134	20	𝑄′(𝑡	𝑄′(𝑡	NUM
cana-1649	134	21	)	)	PUNCT
cana-1649	135	1	𝑑𝑡|	𝑑𝑡|	NOUN
cana-1649	135	2	≤	≤	NUM
cana-1649	135	3	∫	∫	NOUN
cana-1649	136	1	−𝐵	−𝐵	PROPN
cana-1649	136	2	0	0	PUNCT
cana-1649	136	3	|𝑄′	|𝑄′	PROPN
cana-1649	136	4	(	(	PUNCT
cana-1649	136	5	−	−	PROPN
cana-1649	136	6	𝑡𝑧	𝑡𝑧	NOUN
cana-1649	136	7	𝐵	𝐵	NOUN
cana-1649	136	8	)	)	PUNCT
cana-1649	136	9	|	|	ADV
cana-1649	136	10	𝑑𝑡	𝑑𝑡	ADP
cana-1649	136	11	≤	≤	NUM
cana-1649	136	12	∫	∫	NOUN
cana-1649	136	13	−𝐵	−𝐵	PROPN
cana-1649	136	14	0	0	SYM
cana-1649	136	15	𝑄′(𝑡	𝑄′(𝑡	NUM
cana-1649	136	16	)	)	PUNCT
cana-1649	136	17	𝑑𝑡	𝑑𝑡	ADP
cana-1649	136	18	=	=	SYM
cana-1649	136	19	1	1	X
cana-1649	136	20	.	.	PUNCT
cana-1649	136	21	therefore	therefore	ADV
cana-1649	136	22	,	,	PUNCT
cana-1649	136	23	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADP
cana-1649	136	24	𝛿	𝛿	PRON
cana-1649	136	25	(	(	PUNCT
cana-1649	136	26	𝑧	𝑧	NOUN
cana-1649	136	27	)	)	PUNCT
cana-1649	136	28	is	be	AUX
cana-1649	136	29	𝒫𝑛-stable	𝒫𝑛-stable	ADJ
cana-1649	136	30	with	with	ADP
cana-1649	136	31	respect	respect	NOUN
cana-1649	136	32	to	to	ADP
cana-1649	136	33	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	136	34	𝛿	𝛿	ADJ
cana-1649	136	35	(	(	PUNCT
cana-1649	136	36	𝑧	𝑧	NOUN
cana-1649	136	37	)	)	PUNCT
cana-1649	136	38	for	for	ADP
cana-1649	136	39	all	all	DET
cana-1649	136	40	𝑛	𝑛	DET
cana-1649	136	41	∈	∈	NOUN
cana-1649	136	42	ℕ.	ℕ.	PROPN
cana-1649	136	43	hence	hence	ADV
cana-1649	136	44	the	the	DET
cana-1649	136	45	proof	proof	NOUN
cana-1649	136	46	.	.	PUNCT
cana-1649	137	1	remark	remark	VERB
cana-1649	137	2	2.1	2.1	NUM
cana-1649	137	3	.	.	PUNCT
cana-1649	138	1	(	(	PUNCT
cana-1649	138	2	i	i	NOUN
cana-1649	138	3	)	)	PUNCT
cana-1649	138	4	for	for	ADP
cana-1649	138	5	𝐴	𝐴	NOUN
cana-1649	138	6	=	=	NOUN
cana-1649	139	1	1	1	NUM
cana-1649	139	2	−	−	PROPN
cana-1649	139	3	2𝛼	2𝛼	PROPN
cana-1649	139	4	and	and	CCONJ
cana-1649	139	5	𝐵	𝐵	NOUN
cana-1649	139	6	=	=	SYM
cana-1649	139	7	−1	−1	NOUN
cana-1649	139	8	,	,	PUNCT
cana-1649	139	9	theorem	theorem	VERB
cana-1649	139	10	2.1	2.1	NUM
cana-1649	139	11	reduces	reduce	NOUN
cana-1649	139	12	to	to	ADP
cana-1649	139	13	[	[	X
cana-1649	139	14	5	5	NUM
cana-1649	139	15	,	,	PUNCT
cana-1649	139	16	theorem	theorem	VERB
cana-1649	139	17	2.2	2.2	NUM
cana-1649	139	18	]	]	PUNCT
cana-1649	139	19	.	.	PUNCT
cana-1649	140	1	(	(	PUNCT
cana-1649	140	2	ii	ii	NOUN
cana-1649	140	3	)	)	PUNCT
cana-1649	140	4	for	for	ADP
cana-1649	140	5	the	the	DET
cana-1649	140	6	choices	choice	NOUN
cana-1649	140	7	of	of	ADP
cana-1649	140	8	matrix	matrix	NOUN
cana-1649	140	9	𝐻	𝐻	NOUN
cana-1649	140	10	=	=	SYM
cana-1649	140	11	(	(	PUNCT
cana-1649	140	12	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	140	13	)	)	PUNCT
cana-1649	140	14	as	as	SCONJ
cana-1649	140	15	given	give	VERB
cana-1649	140	16	in	in	ADP
cana-1649	140	17	example	example	NOUN
cana-1649	140	18	1.1	1.1	NUM
cana-1649	140	19	,	,	PUNCT
cana-1649	140	20	example	example	NOUN
cana-1649	140	21	1.2	1.2	NUM
cana-1649	140	22	and	and	CCONJ
cana-1649	140	23	example	example	NOUN
cana-1649	140	24	1.3	1.3	NUM
cana-1649	140	25	in	in	ADP
cana-1649	140	26	theorem	theorem	NOUN
cana-1649	140	27	2.1	2.1	NUM
cana-1649	140	28	,	,	PUNCT
cana-1649	140	29	we	we	PRON
cana-1649	140	30	have	have	VERB
cana-1649	140	31	the	the	DET
cana-1649	140	32	result	result	NOUN
cana-1649	140	33	of	of	ADP
cana-1649	140	34	stability[2	stability[2	PROPN
cana-1649	140	35	,	,	PUNCT
cana-1649	140	36	theorem	theorem	VERB
cana-1649	140	37	3	3	NUM
cana-1649	140	38	]	]	PUNCT
cana-1649	140	39	,	,	PUNCT
cana-1649	140	40	cesàro	cesàro	PROPN
cana-1649	140	41	stability[3	stability[3	PROPN
cana-1649	140	42	,	,	PUNCT
cana-1649	140	43	corollary	corollary	ADJ
cana-1649	140	44	2.3	2.3	NUM
cana-1649	140	45	]	]	PUNCT
cana-1649	140	46	and	and	CCONJ
cana-1649	140	47	generalized	generalize	VERB
cana-1649	140	48	cesàro	cesàro	PROPN
cana-1649	140	49	stability[3	stability[3	PROPN
cana-1649	140	50	,	,	PUNCT
cana-1649	140	51	theorem	theorem	VERB
cana-1649	140	52	2.1	2.1	NUM
cana-1649	140	53	]	]	PUNCT
cana-1649	140	54	,	,	PUNCT
cana-1649	140	55	respectively	respectively	ADV
cana-1649	140	56	.	.	PUNCT
cana-1649	141	1	(	(	PUNCT
cana-1649	141	2	iii	iii	X
cana-1649	141	3	)	)	PUNCT
cana-1649	141	4	if	if	SCONJ
cana-1649	141	5	we	we	PRON
cana-1649	141	6	take	take	VERB
cana-1649	141	7	𝐴	𝐴	NOUN
cana-1649	141	8	=	=	NOUN
cana-1649	141	9	1	1	NUM
cana-1649	141	10	−	−	NOUN
cana-1649	141	11	2𝛼	2𝛼	NOUN
cana-1649	141	12	,	,	PUNCT
cana-1649	141	13	𝐵	𝐵	NOUN
cana-1649	141	14	=	=	SYM
cana-1649	141	15	−1	−1	NOUN
cana-1649	141	16	with	with	ADP
cana-1649	141	17	the	the	DET
cana-1649	141	18	choice	choice	NOUN
cana-1649	141	19	of	of	ADP
cana-1649	141	20	matrix	matrix	NOUN
cana-1649	141	21	𝐻	𝐻	NOUN
cana-1649	141	22	=	=	SYM
cana-1649	141	23	(	(	PUNCT
cana-1649	141	24	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	141	25	)	)	PUNCT
cana-1649	141	26	as	as	ADP
cana-1649	141	27	per	per	ADP
cana-1649	141	28	example	example	NOUN
cana-1649	141	29	1.1	1.1	NUM
cana-1649	141	30	,	,	PUNCT
cana-1649	141	31	example	example	NOUN
cana-1649	141	32	1.2	1.2	NUM
cana-1649	141	33	and	and	CCONJ
cana-1649	141	34	example	example	NOUN
cana-1649	141	35	1.3	1.3	NUM
cana-1649	141	36	in	in	ADP
cana-1649	141	37	theorem	theorem	ADJ
cana-1649	141	38	2.1	2.1	NUM
cana-1649	141	39	,	,	PUNCT
cana-1649	141	40	then	then	ADV
cana-1649	141	41	we	we	PRON
cana-1649	141	42	have	have	VERB
cana-1649	141	43	the	the	DET
cana-1649	141	44	result	result	NOUN
cana-1649	141	45	obtained	obtain	VERB
cana-1649	141	46	in	in	ADP
cana-1649	141	47	[	[	X
cana-1649	141	48	1	1	NUM
cana-1649	141	49	,	,	PUNCT
cana-1649	141	50	theorem	theorem	VERB
cana-1649	141	51	2.1	2.1	NUM
cana-1649	141	52	]	]	PUNCT
cana-1649	141	53	,	,	PUNCT
cana-1649	142	1	[	[	X
cana-1649	142	2	5	5	NUM
cana-1649	142	3	,	,	PUNCT
cana-1649	142	4	theorem	theorem	VERB
cana-1649	142	5	2.3	2.3	NUM
cana-1649	142	6	]	]	PUNCT
cana-1649	142	7	and	and	CCONJ
cana-1649	142	8	[	[	X
cana-1649	142	9	5	5	NUM
cana-1649	142	10	,	,	PUNCT
cana-1649	142	11	theorem	theorem	VERB
cana-1649	142	12	2.4	2.4	NUM
cana-1649	142	13	]	]	PUNCT
cana-1649	142	14	,	,	PUNCT
cana-1649	142	15	respectively	respectively	ADV
cana-1649	142	16	.	.	PUNCT
cana-1649	143	1	now	now	ADV
cana-1649	143	2	,	,	PUNCT
cana-1649	143	3	by	by	ADP
cana-1649	143	4	extending	extend	VERB
cana-1649	143	5	the	the	DET
cana-1649	143	6	range	range	NOUN
cana-1649	143	7	of	of	ADP
cana-1649	143	8	the	the	DET
cana-1649	143	9	parameter	parameter	NOUN
cana-1649	143	10	𝛿	𝛿	PROPN
cana-1649	143	11	from	from	ADP
cana-1649	143	12	(	(	PUNCT
cana-1649	143	13	0,1	0,1	NUM
cana-1649	143	14	]	]	PUNCT
cana-1649	143	15	to	to	ADP
cana-1649	143	16	[	[	X
cana-1649	143	17	−1,1	−1,1	X
cana-1649	143	18	]	]	PUNCT
cana-1649	143	19	and	and	CCONJ
cana-1649	143	20	letting	let	VERB
cana-1649	143	21	𝐴	𝐴	PROPN
cana-1649	143	22	=	=	SYM
cana-1649	143	23	0	0	NUM
cana-1649	143	24	in	in	ADP
cana-1649	143	25	theorem	theorem	NOUN
cana-1649	143	26	2.1	2.1	NUM
cana-1649	143	27	,	,	PUNCT
cana-1649	143	28	we	we	PRON
cana-1649	143	29	have	have	VERB
cana-1649	143	30	the	the	DET
cana-1649	143	31	following	following	NOUN
cana-1649	143	32	:	:	PUNCT
cana-1649	143	33	theorem	theorem	VERB
cana-1649	143	34	2.2	2.2	NUM
cana-1649	143	35	.	.	PUNCT
cana-1649	144	1	let	let	VERB
cana-1649	144	2	𝐻	𝐻	PROPN
cana-1649	144	3	=	=	SYM
cana-1649	144	4	(	(	PUNCT
cana-1649	144	5	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	144	6	)	)	PUNCT
cana-1649	144	7	be	be	VERB
cana-1649	144	8	admissible	admissible	ADJ
cana-1649	144	9	lower	low	ADJ
cana-1649	144	10	triangular	triangular	NOUN
cana-1649	144	11	matrix	matrix	NOUN
cana-1649	144	12	with	with	ADP
cana-1649	144	13	ℎ𝑖1	ℎ𝑖1	NOUN
cana-1649	144	14	≤	≤	NUM
cana-1649	144	15	1	1	NUM
cana-1649	144	16	,	,	PUNCT
cana-1649	144	17	∀	∀	NOUN
cana-1649	144	18	𝑖	𝑖	PRON
cana-1649	144	19	≥	≥	NOUN
cana-1649	144	20	1	1	NUM
cana-1649	144	21	.	.	PUNCT
cana-1649	145	1	then	then	ADV
cana-1649	145	2	for	for	ADP
cana-1649	145	3	−1	−1	NOUN
cana-1649	145	4	≤	≤	NUM
cana-1649	145	5	𝐵	𝐵	NOUN
cana-1649	145	6	<	<	X
cana-1649	145	7	0	0	NUM
cana-1649	145	8	and	and	CCONJ
cana-1649	145	9	𝛿	𝛿	PRON
cana-1649	145	10	∈	∈	PROPN
cana-1649	146	1	[	[	X
cana-1649	146	2	−1,1	−1,1	NOUN
cana-1649	146	3	]	]	X
cana-1649	146	4	,	,	PUNCT
cana-1649	146	5	the	the	DET
cana-1649	146	6	function	function	NOUN
cana-1649	146	7	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	146	8	𝛿	𝛿	ADJ
cana-1649	146	9	(	(	PUNCT
cana-1649	146	10	𝑧	𝑧	NOUN
cana-1649	146	11	)	)	PUNCT
cana-1649	146	12	is	be	AUX
cana-1649	146	13	𝒫-stable	𝒫-stable	ADJ
cana-1649	146	14	.	.	PUNCT
cana-1649	147	1	proof	proof	NOUN
cana-1649	147	2	.	.	PUNCT
cana-1649	148	1	to	to	PART
cana-1649	148	2	prove	prove	VERB
cana-1649	148	3	that	that	SCONJ
cana-1649	148	4	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	148	5	𝛿	𝛿	ADJ
cana-1649	148	6	(	(	PUNCT
cana-1649	148	7	𝑧	𝑧	NOUN
cana-1649	148	8	)	)	PUNCT
cana-1649	148	9	is	be	AUX
cana-1649	148	10	𝒫-stable	𝒫-stable	PROPN
cana-1649	148	11	,	,	PUNCT
cana-1649	148	12	we	we	PRON
cana-1649	148	13	must	must	AUX
cana-1649	148	14	show	show	VERB
cana-1649	148	15	that	that	SCONJ
cana-1649	148	16	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	PROPN
cana-1649	148	17	𝛿	𝛿	ADJ
cana-1649	148	18	(	(	PUNCT
cana-1649	148	19	𝑧),𝑧	𝑧),𝑧	PROPN
cana-1649	148	20	)	)	PUNCT
cana-1649	148	21	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	148	22	𝛿	𝛿	ADJ
cana-1649	148	23	(	(	PUNCT
cana-1649	148	24	𝑧	𝑧	NOUN
cana-1649	148	25	)	)	PUNCT
cana-1649	148	26	≺	≺	NOUN
cana-1649	148	27	1	1	NUM
cana-1649	148	28	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	148	29	𝛿	𝛿	ADJ
cana-1649	148	30	(	(	PUNCT
cana-1649	148	31	𝑧	𝑧	NOUN
cana-1649	148	32	)	)	PUNCT
cana-1649	148	33	(	(	PUNCT
cana-1649	148	34	𝑧	𝑧	PROPN
cana-1649	148	35	∈	∈	PROPN
cana-1649	148	36	δ	δ	PROPN
cana-1649	148	37	)	)	PUNCT
cana-1649	148	38	.	.	PUNCT
cana-1649	149	1	communications	communication	NOUN
cana-1649	149	2	on	on	ADP
cana-1649	149	3	applied	apply	VERB
cana-1649	149	4	nonlinear	nonlinear	ADJ
cana-1649	149	5	analysis	analysis	NOUN
cana-1649	149	6	issn	issn	NOUN
cana-1649	149	7	:	:	PUNCT
cana-1649	149	8	1074	1074	NUM
cana-1649	149	9	-	-	PUNCT
cana-1649	149	10	133x	133x	NUM
cana-1649	149	11	vol	vol	NOUN
cana-1649	149	12	32	32	NUM
cana-1649	149	13	no	no	NOUN
cana-1649	149	14	.	.	NOUN
cana-1649	149	15	1	1	NUM
cana-1649	149	16	(	(	PUNCT
cana-1649	149	17	2025	2025	NUM
cana-1649	149	18	)	)	PUNCT
cana-1649	150	1	298	298	NUM
cana-1649	150	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1649	150	3	therefore	therefore	ADV
cana-1649	150	4	,	,	PUNCT
cana-1649	150	5	it	it	PRON
cana-1649	150	6	is	be	AUX
cana-1649	150	7	enough	enough	ADJ
cana-1649	150	8	to	to	PART
cana-1649	150	9	prove	prove	VERB
cana-1649	150	10	that	that	PRON
cana-1649	150	11	|(𝐵𝑧	|(𝐵𝑧	PUNCT
cana-1649	151	1	+	+	CCONJ
cana-1649	151	2	1)[𝒫𝑛(𝒥0,𝐵	1)[𝒫𝑛(𝒥0,𝐵	NUM
cana-1649	151	3	𝛿	𝛿	ADJ
cana-1649	151	4	(	(	PUNCT
cana-1649	151	5	𝑧	𝑧	NOUN
cana-1649	151	6	)	)	PUNCT
cana-1649	151	7	,	,	PUNCT
cana-1649	151	8	𝑧	𝑧	NOUN
cana-1649	151	9	)	)	PUNCT
cana-1649	151	10	]	]	PUNCT
cana-1649	151	11	1	1	NUM
cana-1649	151	12	𝛿	𝛿	PRON
cana-1649	151	13	−	−	PROPN
cana-1649	151	14	1|	1|	NUM
cana-1649	151	15	≤	≤	NUM
cana-1649	151	16	1	1	NUM
cana-1649	151	17	.	.	PUNCT
cana-1649	151	18	for	for	ADP
cana-1649	151	19	fixed	fix	VERB
cana-1649	151	20	𝑛	𝑛	PRON
cana-1649	151	21	and	and	CCONJ
cana-1649	151	22	𝛿	𝛿	ADJ
cana-1649	151	23	,	,	PUNCT
cana-1649	151	24	let	let	VERB
cana-1649	151	25	us	we	PRON
cana-1649	151	26	consider	consider	VERB
cana-1649	151	27	𝑅(𝑧	𝑅(𝑧	PRON
cana-1649	151	28	)	)	PUNCT
cana-1649	151	29	=	=	SYM
cana-1649	151	30	1	1	NUM
cana-1649	151	31	−	−	NOUN
cana-1649	151	32	(	(	PUNCT
cana-1649	151	33	𝐵𝑧	𝐵𝑧	PROPN
cana-1649	151	34	+	+	CCONJ
cana-1649	151	35	1)[𝒫𝑛(𝒥0,𝐵	1)[𝒫𝑛(𝒥0,𝐵	NUM
cana-1649	151	36	𝛿	𝛿	ADJ
cana-1649	151	37	(	(	PUNCT
cana-1649	151	38	𝑧	𝑧	NOUN
cana-1649	151	39	)	)	PUNCT
cana-1649	151	40	,	,	PUNCT
cana-1649	151	41	𝑧	𝑧	NOUN
cana-1649	151	42	)	)	PUNCT
cana-1649	151	43	]	]	PUNCT
cana-1649	151	44	1	1	NUM
cana-1649	151	45	𝛿.	𝛿.	NOUN
cana-1649	151	46	(	(	PUNCT
cana-1649	151	47	2.5	2.5	NUM
cana-1649	151	48	)	)	PUNCT
cana-1649	151	49	we	we	PRON
cana-1649	151	50	note	note	VERB
cana-1649	151	51	that	that	SCONJ
cana-1649	151	52	for	for	ADP
cana-1649	151	53	𝐴	𝐴	PROPN
cana-1649	151	54	=	=	SYM
cana-1649	151	55	0	0	NUM
cana-1649	152	1	in	in	ADP
cana-1649	152	2	(	(	PUNCT
cana-1649	152	3	1.2	1.2	NUM
cana-1649	152	4	)	)	PUNCT
cana-1649	152	5	,	,	PUNCT
cana-1649	152	6	we	we	PRON
cana-1649	152	7	get	get	VERB
cana-1649	152	8	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	152	9	𝛿	𝛿	ADJ
cana-1649	152	10	(	(	PUNCT
cana-1649	152	11	𝑧)′	𝑧)′	PROPN
cana-1649	152	12	+	+	CCONJ
cana-1649	152	13	(	(	PUNCT
cana-1649	152	14	𝐵𝛿	𝐵𝛿	PROPN
cana-1649	152	15	1+𝐵𝑧	1+𝐵𝑧	NUM
cana-1649	152	16	)	)	PUNCT
cana-1649	152	17	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	152	18	𝛿	𝛿	ADJ
cana-1649	152	19	(	(	PUNCT
cana-1649	152	20	𝑧	𝑧	NOUN
cana-1649	152	21	)	)	PUNCT
cana-1649	152	22	=	=	SYM
cana-1649	152	23	0	0	X
cana-1649	152	24	.	.	PUNCT
cana-1649	153	1	(	(	PUNCT
cana-1649	153	2	2.6	2.6	NUM
cana-1649	153	3	)	)	PUNCT
cana-1649	153	4	clearly	clearly	ADV
cana-1649	153	5	for	for	ADP
cana-1649	153	6	𝛿	𝛿	PROPN
cana-1649	153	7	=	=	SYM
cana-1649	153	8	0	0	NUM
cana-1649	153	9	,	,	PUNCT
cana-1649	153	10	we	we	PRON
cana-1649	153	11	have	have	VERB
cana-1649	153	12	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	153	13	𝛿	𝛿	ADJ
cana-1649	153	14	(	(	PUNCT
cana-1649	153	15	𝑧	𝑧	NOUN
cana-1649	153	16	)	)	PUNCT
cana-1649	153	17	=	=	SYM
cana-1649	153	18	1	1	NUM
cana-1649	153	19	and	and	CCONJ
cana-1649	153	20	hence	hence	ADV
cana-1649	153	21	|𝑅(𝑧)|	|𝑅(𝑧)|	ADJ
cana-1649	153	22	≤	≤	NUM
cana-1649	153	23	1	1	NUM
cana-1649	153	24	.	.	PUNCT
cana-1649	154	1	for	for	ADP
cana-1649	154	2	𝛿	𝛿	DET
cana-1649	154	3	≠	≠	PROPN
cana-1649	154	4	0	0	NUM
cana-1649	154	5	,	,	PUNCT
cana-1649	154	6	a	a	DET
cana-1649	154	7	simple	simple	ADJ
cana-1649	154	8	calculation	calculation	NOUN
cana-1649	154	9	using	use	VERB
cana-1649	154	10	(	(	PUNCT
cana-1649	154	11	2.5	2.5	NUM
cana-1649	154	12	)	)	PUNCT
cana-1649	154	13	yields	yield	NOUN
cana-1649	154	14	𝑅′(𝑧	𝑅′(𝑧	NUM
cana-1649	154	15	)	)	PUNCT
cana-1649	155	1	=	=	SYM
cana-1649	155	2	(	(	PUNCT
cana-1649	155	3	−𝐵)[𝒫𝑛(𝒥0,𝐵	−𝐵)[𝒫𝑛(𝒥0,𝐵	NOUN
cana-1649	155	4	𝛿	𝛿	ADJ
cana-1649	155	5	(	(	PUNCT
cana-1649	155	6	𝑧	𝑧	NOUN
cana-1649	155	7	)	)	PUNCT
cana-1649	155	8	,	,	PUNCT
cana-1649	155	9	𝑧	𝑧	NOUN
cana-1649	155	10	)	)	PUNCT
cana-1649	155	11	]	]	PUNCT
cana-1649	155	12	1	1	NUM
cana-1649	155	13	𝛿	𝛿	PRON
cana-1649	155	14	−1	−1	NOUN
cana-1649	156	1	[	[	X
cana-1649	156	2	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	PROPN
cana-1649	156	3	𝛿	𝛿	ADJ
cana-1649	156	4	(	(	PUNCT
cana-1649	156	5	𝑧	𝑧	NOUN
cana-1649	156	6	)	)	PUNCT
cana-1649	156	7	,	,	PUNCT
cana-1649	156	8	𝑧	𝑧	X
cana-1649	156	9	)	)	PUNCT
cana-1649	156	10	+	+	CCONJ
cana-1649	156	11	(	(	PUNCT
cana-1649	156	12	𝐵𝑧+1	𝐵𝑧+1	ADJ
cana-1649	156	13	𝐵𝛿	𝐵𝛿	PROPN
cana-1649	156	14	)	)	PUNCT
cana-1649	156	15	𝑃′𝑛(𝒥0,𝐵	𝑃′𝑛(𝒥0,𝐵	NOUN
cana-1649	156	16	𝛿	𝛿	PROPN
cana-1649	156	17	(	(	PUNCT
cana-1649	156	18	𝑧	𝑧	NOUN
cana-1649	156	19	)	)	PUNCT
cana-1649	156	20	,	,	PUNCT
cana-1649	156	21	𝑧	𝑧	NOUN
cana-1649	156	22	)	)	PUNCT
cana-1649	156	23	]	]	PUNCT
cana-1649	156	24	.	.	PUNCT
cana-1649	157	1	(	(	PUNCT
cana-1649	157	2	2.7	2.7	NUM
cana-1649	157	3	)	)	PUNCT
cana-1649	157	4	using	use	VERB
cana-1649	157	5	(	(	PUNCT
cana-1649	157	6	2.2	2.2	NUM
cana-1649	157	7	)	)	PUNCT
cana-1649	157	8	and	and	CCONJ
cana-1649	157	9	(	(	PUNCT
cana-1649	157	10	2.6	2.6	NUM
cana-1649	157	11	)	)	PUNCT
cana-1649	157	12	in	in	ADP
cana-1649	157	13	(	(	PUNCT
cana-1649	157	14	2.7	2.7	NUM
cana-1649	157	15	)	)	PUNCT
cana-1649	157	16	,	,	PUNCT
cana-1649	157	17	we	we	PRON
cana-1649	157	18	have	have	VERB
cana-1649	157	19	𝑅′(𝑧	𝑅′(𝑧	PUNCT
cana-1649	157	20	)	)	PUNCT
cana-1649	158	1	=	=	SYM
cana-1649	158	2	(	(	PUNCT
cana-1649	158	3	−𝐵)[𝒫𝑛(𝒥0,𝐵	−𝐵)[𝒫𝑛(𝒥0,𝐵	NOUN
cana-1649	158	4	𝛿	𝛿	ADJ
cana-1649	158	5	(	(	PUNCT
cana-1649	158	6	𝑧	𝑧	NOUN
cana-1649	158	7	)	)	PUNCT
cana-1649	158	8	,	,	PUNCT
cana-1649	158	9	𝑧	𝑧	NOUN
cana-1649	158	10	)	)	PUNCT
cana-1649	158	11	]	]	PUNCT
cana-1649	158	12	1	1	NUM
cana-1649	158	13	𝛿	𝛿	PRON
cana-1649	158	14	−1	−1	NOUN
cana-1649	159	1	[	[	X
cana-1649	159	2	ℎ𝑛1𝑃𝑛−1	ℎ𝑛1𝑃𝑛−1	X
cana-1649	159	3	(	(	PUNCT
cana-1649	159	4	𝒥0,𝐵	𝒥0,𝐵	ADV
cana-1649	159	5	𝛿	𝛿	ADJ
cana-1649	159	6	(	(	PUNCT
cana-1649	159	7	𝑧	𝑧	NOUN
cana-1649	159	8	)	)	PUNCT
cana-1649	159	9	+	+	CCONJ
cana-1649	159	10	𝐵𝑧	𝐵𝑧	PROPN
cana-1649	159	11	+	+	CCONJ
cana-1649	159	12	1	1	NUM
cana-1649	159	13	𝐵𝛿	𝐵𝛿	PROPN
cana-1649	159	14	𝒥0,𝐵	𝒥0,𝐵	ADJ
cana-1649	159	15	𝛿	𝛿	PROPN
cana-1649	159	16	(	(	PUNCT
cana-1649	159	17	𝑧)′	𝑧)′	PROPN
cana-1649	159	18	,	,	PUNCT
cana-1649	159	19	𝑧	𝑧	NOUN
cana-1649	159	20	)	)	PUNCT
cana-1649	159	21	+	+	ADJ
cana-1649	159	22	∑𝑛−1𝑗=0	∑𝑛−1𝑗=0	PROPN
cana-1649	159	23	(	(	PUNCT
cana-1649	159	24	ℎ𝑛𝑗	ℎ𝑛𝑗	NOUN
cana-1649	159	25	−	−	PROPN
cana-1649	159	26	ℎ𝑛1ℎ𝑛−1,𝑗	ℎ𝑛1ℎ𝑛−1,𝑗	NOUN
cana-1649	159	27	)	)	PUNCT
cana-1649	159	28	(	(	PUNCT
cana-1649	159	29	𝑐𝑗	𝑐𝑗	CCONJ
cana-1649	159	30	+	+	NUM
cana-1649	159	31	𝑗𝑐𝑗	𝑗𝑐𝑗	NOUN
cana-1649	159	32	𝛿	𝛿	NOUN
cana-1649	159	33	)	)	PUNCT
cana-1649	159	34	𝑧𝑗	𝑧𝑗	PROPN
cana-1649	159	35	+	+	NUM
cana-1649	159	36	ℎ𝑛𝑛	ℎ𝑛𝑛	ADJ
cana-1649	159	37	(	(	PUNCT
cana-1649	159	38	𝑐𝑛	𝑐𝑛	NOUN
cana-1649	159	39	+	+	SYM
cana-1649	159	40	𝑛𝑐𝑛	𝑛𝑐𝑛	NUM
cana-1649	159	41	𝛿	𝛿	NOUN
cana-1649	159	42	)	)	PUNCT
cana-1649	159	43	𝑧𝑛	𝑧𝑛	ADP
cana-1649	159	44	]	]	X
cana-1649	159	45	.	.	PUNCT
cana-1649	160	1	therefore	therefore	ADV
cana-1649	160	2	,	,	PUNCT
cana-1649	160	3	𝑅′(𝑧	𝑅′(𝑧	PUNCT
cana-1649	160	4	)	)	PUNCT
cana-1649	160	5	=	=	SYM
cana-1649	160	6	(	(	PUNCT
cana-1649	160	7	−𝐵)[𝒫𝑛(𝒥0,𝐵	−𝐵)[𝒫𝑛(𝒥0,𝐵	NOUN
cana-1649	160	8	𝛿	𝛿	ADJ
cana-1649	160	9	(	(	PUNCT
cana-1649	160	10	𝑧	𝑧	NOUN
cana-1649	160	11	)	)	PUNCT
cana-1649	160	12	,	,	PUNCT
cana-1649	160	13	𝑧	𝑧	NOUN
cana-1649	160	14	)	)	PUNCT
cana-1649	160	15	]	]	PUNCT
cana-1649	161	1	1	1	NUM
cana-1649	161	2	𝛿	𝛿	PRON
cana-1649	161	3	−1	−1	NOUN
cana-1649	161	4	[	[	X
cana-1649	161	5	ℎ𝑛𝑛	ℎ𝑛𝑛	X
cana-1649	161	6	(	(	PUNCT
cana-1649	161	7	(	(	PUNCT
cana-1649	161	8	−1)𝑛𝐵𝑛(𝛿	−1)𝑛𝐵𝑛(𝛿	X
cana-1649	161	9	+	+	CCONJ
cana-1649	161	10	1)𝑛	1)𝑛	NUM
cana-1649	161	11	𝑛	𝑛	PROPN
cana-1649	161	12	!	!	PUNCT
cana-1649	161	13	)	)	PUNCT
cana-1649	162	1	𝑧𝑛	𝑧𝑛	ADP
cana-1649	162	2	+	+	ADJ
cana-1649	162	3	∑𝑛−1𝑗=0	∑𝑛−1𝑗=0	PROPN
cana-1649	162	4	ℎ𝑛1(ℎ𝑛−1,𝑗−1	ℎ𝑛1(ℎ𝑛−1,𝑗−1	PROPN
cana-1649	162	5	−	−	PROPN
cana-1649	162	6	ℎ𝑛−1,𝑗	ℎ𝑛−1,𝑗	PROPN
cana-1649	162	7	)	)	PUNCT
cana-1649	162	8	(	(	PUNCT
cana-1649	162	9	(	(	PUNCT
cana-1649	162	10	−1)𝑗𝐵𝑗(𝛿+1)𝑗	−1)𝑗𝐵𝑗(𝛿+1)𝑗	PUNCT
cana-1649	162	11	𝑗	𝑗	NOUN
cana-1649	162	12	!	!	PUNCT
cana-1649	162	13	)	)	PUNCT
cana-1649	163	1	𝑧𝑗	𝑧𝑗	VERB
cana-1649	163	2	]	]	PUNCT
cana-1649	163	3	.	.	PUNCT
cana-1649	164	1	(	(	PUNCT
cana-1649	164	2	2.8	2.8	NUM
cana-1649	164	3	)	)	PUNCT
cana-1649	164	4	using	use	VERB
cana-1649	164	5	the	the	DET
cana-1649	164	6	definition	definition	NOUN
cana-1649	164	7	1.2	1.2	NUM
cana-1649	164	8	in	in	ADP
cana-1649	164	9	(	(	PUNCT
cana-1649	164	10	2.8	2.8	NUM
cana-1649	164	11	)	)	PUNCT
cana-1649	164	12	,	,	PUNCT
cana-1649	164	13	it	it	PRON
cana-1649	164	14	follows	follow	VERB
cana-1649	164	15	that	that	SCONJ
cana-1649	164	16	the	the	DET
cana-1649	164	17	expression	expression	NOUN
cana-1649	164	18	[	[	X
cana-1649	164	19	ℎ𝑛𝑛	ℎ𝑛𝑛	X
cana-1649	164	20	(	(	PUNCT
cana-1649	164	21	(	(	PUNCT
cana-1649	164	22	−1)𝑛𝐵𝑛(𝛿+1)𝑛	−1)𝑛𝐵𝑛(𝛿+1)𝑛	NOUN
cana-1649	164	23	𝑛	𝑛	PROPN
cana-1649	164	24	!	!	PUNCT
cana-1649	164	25	)	)	PUNCT
cana-1649	165	1	𝑧𝑛	𝑧𝑛	ADP
cana-1649	165	2	+	+	CCONJ
cana-1649	165	3	∑𝑛−1𝑗=0	∑𝑛−1𝑗=0	ADJ
cana-1649	165	4	ℎ𝑛1(ℎ𝑛−1,𝑗−1	ℎ𝑛1(ℎ𝑛−1,𝑗−1	PROPN
cana-1649	165	5	−	−	PROPN
cana-1649	165	6	ℎ𝑛−1,𝑗	ℎ𝑛−1,𝑗	PROPN
cana-1649	165	7	)	)	PUNCT
cana-1649	165	8	(	(	PUNCT
cana-1649	165	9	(	(	PUNCT
cana-1649	165	10	−1)𝑗𝐵𝑗(𝛿+1)𝑗	−1)𝑗𝐵𝑗(𝛿+1)𝑗	PUNCT
cana-1649	165	11	𝑗	𝑗	NOUN
cana-1649	165	12	!	!	PUNCT
cana-1649	165	13	)	)	PUNCT
cana-1649	166	1	𝑧𝑗	𝑧𝑗	ADP
cana-1649	166	2	]	]	PUNCT
cana-1649	166	3	,	,	PUNCT
cana-1649	166	4	represents	represent	VERB
cana-1649	166	5	a	a	DET
cana-1649	166	6	series	series	NOUN
cana-1649	166	7	of	of	ADP
cana-1649	166	8	positive	positive	PROPN
cana-1649	166	9	taylor	taylor	PROPN
cana-1649	166	10	’s	’s	PART
cana-1649	166	11	coefficients	coefficient	NOUN
cana-1649	166	12	about	about	ADP
cana-1649	166	13	𝑧	𝑧	NOUN
cana-1649	166	14	=	=	ADJ
cana-1649	166	15	0	0	PROPN
cana-1649	166	16	.	.	PUNCT
cana-1649	166	17	case	case	NOUN
cana-1649	166	18	(	(	PUNCT
cana-1649	166	19	i	i	NOUN
cana-1649	166	20	):	):	PUNCT
cana-1649	166	21	for	for	ADP
cana-1649	166	22	𝛿	𝛿	PROPN
cana-1649	166	23	∈	∈	PROPN
cana-1649	166	24	(	(	PUNCT
cana-1649	166	25	0,1	0,1	NOUN
cana-1649	166	26	]	]	PUNCT
cana-1649	166	27	,	,	PUNCT
cana-1649	166	28	since	since	SCONJ
cana-1649	166	29	𝑐𝑗	𝑐𝑗	ADV
cana-1649	166	30	>	>	X
cana-1649	166	31	0	0	PUNCT
cana-1649	166	32	for	for	ADP
cana-1649	166	33	all	all	DET
cana-1649	166	34	𝑗	𝑗	PRON
cana-1649	166	35	∈	∈	PROPN
cana-1649	166	36	ℕ	ℕ	PROPN
cana-1649	166	37	,	,	PUNCT
cana-1649	166	38	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	PROPN
cana-1649	166	39	𝛿	𝛿	ADJ
cana-1649	166	40	(	(	PUNCT
cana-1649	166	41	𝑧	𝑧	NOUN
cana-1649	166	42	)	)	PUNCT
cana-1649	166	43	,	,	PUNCT
cana-1649	166	44	𝑧	𝑧	X
cana-1649	166	45	)	)	PUNCT
cana-1649	166	46	has	have	VERB
cana-1649	166	47	a	a	DET
cana-1649	166	48	series	series	NOUN
cana-1649	166	49	representation	representation	NOUN
cana-1649	166	50	with	with	ADP
cana-1649	166	51	positive	positive	ADJ
cana-1649	166	52	taylor	taylor	PROPN
cana-1649	166	53	’s	’s	PART
cana-1649	166	54	coefficients	coefficient	NOUN
cana-1649	166	55	about	about	ADP
cana-1649	166	56	𝑧	𝑧	NOUN
cana-1649	166	57	=	=	NOUN
cana-1649	166	58	0	0	NUM
cana-1649	166	59	.	.	PUNCT
cana-1649	167	1	hence	hence	ADV
cana-1649	167	2	,	,	PUNCT
cana-1649	167	3	|𝒫𝑛(𝒥0,𝐵	|𝒫𝑛(𝒥0,𝐵	PROPN
cana-1649	167	4	𝛿	𝛿	PROPN
cana-1649	167	5	(	(	PUNCT
cana-1649	167	6	𝑧	𝑧	NOUN
cana-1649	167	7	)	)	PUNCT
cana-1649	167	8	,	,	PUNCT
cana-1649	167	9	𝑧)|	𝑧)|	PROPN
cana-1649	167	10	≤	≤	PUNCT
cana-1649	168	1	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	PROPN
cana-1649	168	2	𝛿	𝛿	ADJ
cana-1649	168	3	(	(	PUNCT
cana-1649	168	4	𝑧	𝑧	NOUN
cana-1649	168	5	)	)	PUNCT
cana-1649	168	6	,	,	PUNCT
cana-1649	168	7	|𝑧|	|𝑧|	PROPN
cana-1649	168	8	)	)	PUNCT
cana-1649	168	9	.	.	PUNCT
cana-1649	169	1	case	case	NOUN
cana-1649	169	2	(	(	PUNCT
cana-1649	169	3	ii	ii	NUM
cana-1649	169	4	):	):	PUNCT
cana-1649	169	5	for	for	ADP
cana-1649	169	6	𝛿	𝛿	PROPN
cana-1649	169	7	∈	∈	PROPN
cana-1649	169	8	[	[	X
cana-1649	169	9	−1,0	−1,0	NOUN
cana-1649	169	10	)	)	PUNCT
cana-1649	169	11	,	,	PUNCT
cana-1649	169	12	the	the	DET
cana-1649	169	13	series	series	NOUN
cana-1649	169	14	(	(	PUNCT
cana-1649	169	15	1.3	1.3	NUM
cana-1649	169	16	)	)	PUNCT
cana-1649	169	17	has	have	VERB
cana-1649	169	18	coefficients	coefficient	NOUN
cana-1649	169	19	𝑐𝑗	𝑐𝑗	ADP
cana-1649	169	20	<	<	X
cana-1649	169	21	0	0	PUNCT
cana-1649	169	22	for	for	ADP
cana-1649	169	23	all	all	DET
cana-1649	169	24	𝑗	𝑗	PRON
cana-1649	169	25	∈	∈	NOUN
cana-1649	169	26	ℕ.	ℕ.	PROPN
cana-1649	169	27	thus	thus	ADV
cana-1649	169	28	,	,	PUNCT
cana-1649	169	29	we	we	PRON
cana-1649	169	30	can	can	AUX
cana-1649	169	31	write	write	VERB
cana-1649	169	32	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	PROPN
cana-1649	169	33	𝛿	𝛿	ADJ
cana-1649	169	34	(	(	PUNCT
cana-1649	169	35	𝑧	𝑧	NOUN
cana-1649	169	36	)	)	PUNCT
cana-1649	169	37	,	,	PUNCT
cana-1649	169	38	𝑧	𝑧	X
cana-1649	169	39	)	)	PUNCT
cana-1649	169	40	=	=	SYM
cana-1649	170	1	1	1	NUM
cana-1649	170	2	+	+	CCONJ
cana-1649	170	3	∑𝑛𝑗=1	∑𝑛𝑗=1	NUM
cana-1649	170	4	ℎ𝑛𝑗𝑐𝑗𝑧	ℎ𝑛𝑗𝑐𝑗𝑧	NOUN
cana-1649	170	5	𝑗	𝑗	NOUN
cana-1649	170	6	=	=	NOUN
cana-1649	170	7	1	1	NUM
cana-1649	170	8	−	−	PROPN
cana-1649	170	9	𝜏(𝑧	𝜏(𝑧	NUM
cana-1649	170	10	)	)	PUNCT
cana-1649	170	11	,	,	PUNCT
cana-1649	170	12	where	where	SCONJ
cana-1649	170	13	𝜏(𝑧	𝜏(𝑧	NUM
cana-1649	170	14	)	)	PUNCT
cana-1649	170	15	is	be	AUX
cana-1649	170	16	series	series	NOUN
cana-1649	170	17	with	with	ADP
cana-1649	170	18	positive	positive	PROPN
cana-1649	170	19	taylor	taylor	PROPN
cana-1649	170	20	’s	’s	PART
cana-1649	170	21	coefficients	coefficient	NOUN
cana-1649	170	22	about	about	ADP
cana-1649	170	23	𝑧	𝑧	NOUN
cana-1649	170	24	=	=	NOUN
cana-1649	170	25	0	0	NUM
cana-1649	170	26	.	.	PUNCT
cana-1649	171	1	therefore	therefore	ADV
cana-1649	171	2	,	,	PUNCT
cana-1649	171	3	[	[	X
cana-1649	171	4	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	ADJ
cana-1649	171	5	𝛿	𝛿	ADJ
cana-1649	171	6	(	(	PUNCT
cana-1649	171	7	𝑧	𝑧	NOUN
cana-1649	171	8	)	)	PUNCT
cana-1649	171	9	,	,	PUNCT
cana-1649	171	10	𝑧	𝑧	NOUN
cana-1649	171	11	)	)	PUNCT
cana-1649	171	12	]	]	PUNCT
cana-1649	171	13	1	1	NUM
cana-1649	171	14	𝛿	𝛿	PRON
cana-1649	171	15	−1	−1	NOUN
cana-1649	171	16	=	=	PUNCT
cana-1649	172	1	[	[	X
cana-1649	172	2	1	1	NUM
cana-1649	172	3	−	−	PROPN
cana-1649	172	4	𝜏(𝑧	𝜏(𝑧	NUM
cana-1649	172	5	)	)	PUNCT
cana-1649	172	6	]	]	PUNCT
cana-1649	172	7	1	1	NUM
cana-1649	172	8	𝛿	𝛿	PRON
cana-1649	172	9	−1	−1	NOUN
cana-1649	172	10	=	=	SYM
cana-1649	172	11	1	1	NUM
cana-1649	172	12	+	+	NUM
cana-1649	172	13	∑∞𝑗=1	∑∞𝑗=1	NOUN
cana-1649	172	14	(	(	PUNCT
cana-1649	172	15	1−	1−	NUM
cana-1649	172	16	1	1	NUM
cana-1649	172	17	𝛿	𝛿	NOUN
cana-1649	172	18	)	)	PUNCT
cana-1649	172	19	𝑗	𝑗	PROPN
cana-1649	172	20	𝑗	𝑗	NOUN
cana-1649	172	21	!	!	PUNCT
cana-1649	172	22	(	(	PUNCT
cana-1649	172	23	𝜏(𝑧))𝑗.	𝜏(𝑧))𝑗.	ADJ
cana-1649	172	24	communications	communication	NOUN
cana-1649	172	25	on	on	ADP
cana-1649	172	26	applied	apply	VERB
cana-1649	172	27	nonlinear	nonlinear	ADJ
cana-1649	172	28	analysis	analysis	NOUN
cana-1649	172	29	issn	issn	NOUN
cana-1649	172	30	:	:	PUNCT
cana-1649	172	31	1074	1074	NUM
cana-1649	172	32	-	-	PUNCT
cana-1649	172	33	133x	133x	NUM
cana-1649	172	34	vol	vol	NOUN
cana-1649	172	35	32	32	NUM
cana-1649	172	36	no	no	NOUN
cana-1649	172	37	.	.	NOUN
cana-1649	172	38	1	1	NUM
cana-1649	172	39	(	(	PUNCT
cana-1649	172	40	2025	2025	NUM
cana-1649	172	41	)	)	PUNCT
cana-1649	172	42	299	299	NUM
cana-1649	172	43	https://internationalpubls.com	https://internationalpubls.com	X
cana-1649	172	44	thus	thus	ADV
cana-1649	172	45	,	,	PUNCT
cana-1649	173	1	[	[	X
cana-1649	173	2	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	ADJ
cana-1649	173	3	𝛿	𝛿	ADJ
cana-1649	173	4	(	(	PUNCT
cana-1649	173	5	𝑧	𝑧	NOUN
cana-1649	173	6	)	)	PUNCT
cana-1649	173	7	,	,	PUNCT
cana-1649	173	8	𝑧	𝑧	NOUN
cana-1649	173	9	)	)	PUNCT
cana-1649	173	10	]	]	PUNCT
cana-1649	173	11	1	1	NUM
cana-1649	173	12	𝛿	𝛿	PRON
cana-1649	173	13	−1	−1	NOUN
cana-1649	173	14	is	be	AUX
cana-1649	173	15	a	a	DET
cana-1649	173	16	series	series	NOUN
cana-1649	173	17	with	with	ADP
cana-1649	173	18	positive	positive	PROPN
cana-1649	173	19	taylor	taylor	PROPN
cana-1649	173	20	’s	’s	PART
cana-1649	173	21	coefficients	coefficient	NOUN
cana-1649	173	22	about	about	ADP
cana-1649	173	23	𝑧	𝑧	NOUN
cana-1649	173	24	=	=	NOUN
cana-1649	173	25	0	0	NUM
cana-1649	173	26	.	.	PUNCT
cana-1649	174	1	hence	hence	ADV
cana-1649	174	2	,	,	PUNCT
cana-1649	174	3	|[𝒫𝑛(𝒥0,𝐵	|[𝒫𝑛(𝒥0,𝐵	ADJ
cana-1649	174	4	𝛿	𝛿	ADJ
cana-1649	174	5	(	(	PUNCT
cana-1649	174	6	𝑧	𝑧	NOUN
cana-1649	174	7	)	)	PUNCT
cana-1649	174	8	,	,	PUNCT
cana-1649	174	9	𝑧	𝑧	NOUN
cana-1649	174	10	)	)	PUNCT
cana-1649	174	11	]	]	PUNCT
cana-1649	174	12	1	1	NUM
cana-1649	174	13	𝛿	𝛿	NOUN
cana-1649	174	14	−1|	−1|	NOUN
cana-1649	174	15	≤	≤	NOUN
cana-1649	175	1	[	[	X
cana-1649	175	2	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	ADJ
cana-1649	175	3	𝛿	𝛿	ADJ
cana-1649	175	4	(	(	PUNCT
cana-1649	175	5	𝑧	𝑧	NOUN
cana-1649	175	6	)	)	PUNCT
cana-1649	175	7	,	,	PUNCT
cana-1649	175	8	|𝑧|	|𝑧|	PROPN
cana-1649	175	9	)	)	PUNCT
cana-1649	175	10	]	]	PUNCT
cana-1649	175	11	1	1	NUM
cana-1649	175	12	𝛿	𝛿	PRON
cana-1649	175	13	−1	−1	NOUN
cana-1649	175	14	.	.	PUNCT
cana-1649	176	1	from	from	ADP
cana-1649	176	2	the	the	DET
cana-1649	176	3	case	case	NOUN
cana-1649	176	4	(	(	PUNCT
cana-1649	176	5	i	i	NOUN
cana-1649	176	6	)	)	PUNCT
cana-1649	176	7	and	and	CCONJ
cana-1649	176	8	case	case	NOUN
cana-1649	176	9	(	(	PUNCT
cana-1649	176	10	ii	ii	NOUN
cana-1649	176	11	)	)	PUNCT
cana-1649	176	12	,	,	PUNCT
cana-1649	176	13	we	we	PRON
cana-1649	176	14	observe	observe	VERB
cana-1649	176	15	that	that	SCONJ
cana-1649	176	16	𝑅′(𝑧	𝑅′(𝑧	PUNCT
cana-1649	176	17	)	)	PUNCT
cana-1649	176	18	is	be	AUX
cana-1649	176	19	a	a	DET
cana-1649	176	20	series	series	NOUN
cana-1649	176	21	with	with	ADP
cana-1649	176	22	positive	positive	PROPN
cana-1649	176	23	taylor	taylor	PROPN
cana-1649	176	24	’s	’s	PART
cana-1649	176	25	coefficients	coefficient	NOUN
cana-1649	176	26	about	about	ADP
cana-1649	176	27	𝑧	𝑧	NOUN
cana-1649	176	28	=	=	NOUN
cana-1649	176	29	0	0	NUM
cana-1649	176	30	.	.	PUNCT
cana-1649	177	1	hence	hence	ADV
cana-1649	177	2	,	,	PUNCT
cana-1649	177	3	|𝑅′(𝑧)|	|𝑅′(𝑧)|	PRON
cana-1649	177	4	≤	≤	NUM
cana-1649	177	5	𝑅′(|𝑧|	𝑅′(|𝑧|	NOUN
cana-1649	177	6	)	)	PUNCT
cana-1649	177	7	.	.	PUNCT
cana-1649	178	1	since	since	SCONJ
cana-1649	178	2	𝑅(0	𝑅(0	NUM
cana-1649	178	3	)	)	PUNCT
cana-1649	178	4	=	=	SYM
cana-1649	178	5	0	0	NUM
cana-1649	178	6	and	and	CCONJ
cana-1649	178	7	𝑅(−𝐵	𝑅(−𝐵	PRON
cana-1649	178	8	)	)	PUNCT
cana-1649	178	9	=	=	SYM
cana-1649	178	10	1	1	X
cana-1649	178	11	,	,	PUNCT
cana-1649	178	12	it	it	PRON
cana-1649	178	13	follows	follow	VERB
cana-1649	178	14	that	that	SCONJ
cana-1649	178	15	|𝑅(𝑧)|	|𝑅(𝑧)|	PROPN
cana-1649	178	16	=	=	SYM
cana-1649	178	17	|∫	|∫	NOUN
cana-1649	178	18	𝑧	𝑧	PRON
cana-1649	178	19	0	0	NUM
cana-1649	178	20	𝑅′(𝑡	𝑅′(𝑡	NOUN
cana-1649	178	21	)	)	PUNCT
cana-1649	178	22	𝑑𝑡|	𝑑𝑡|	NOUN
cana-1649	178	23	≤	≤	NUM
cana-1649	178	24	∫	∫	NOUN
cana-1649	178	25	−𝐵	−𝐵	PROPN
cana-1649	178	26	0	0	NUM
cana-1649	178	27	|𝑅′	|𝑅′	NOUN
cana-1649	178	28	(	(	PUNCT
cana-1649	178	29	−	−	NOUN
cana-1649	178	30	𝑡𝑧	𝑡𝑧	NOUN
cana-1649	178	31	𝐵	𝐵	NOUN
cana-1649	178	32	)	)	PUNCT
cana-1649	178	33	|	|	ADV
cana-1649	178	34	𝑑𝑡	𝑑𝑡	ADP
cana-1649	178	35	≤	≤	NUM
cana-1649	178	36	∫	∫	NOUN
cana-1649	178	37	−𝐵	−𝐵	PROPN
cana-1649	178	38	0	0	NUM
cana-1649	178	39	𝑅′(𝑡	𝑅′(𝑡	PROPN
cana-1649	178	40	)	)	PUNCT
cana-1649	178	41	𝑑𝑡	𝑑𝑡	ADP
cana-1649	178	42	=	=	SYM
cana-1649	178	43	1	1	X
cana-1649	178	44	.	.	PUNCT
cana-1649	179	1	therefore	therefore	ADV
cana-1649	179	2	,	,	PUNCT
cana-1649	179	3	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	179	4	𝛿	𝛿	ADJ
cana-1649	179	5	(	(	PUNCT
cana-1649	179	6	𝑧	𝑧	NOUN
cana-1649	179	7	)	)	PUNCT
cana-1649	179	8	is	be	AUX
cana-1649	179	9	𝒫𝑛-stable	𝒫𝑛-stable	ADJ
cana-1649	179	10	for	for	ADP
cana-1649	179	11	all	all	DET
cana-1649	179	12	𝑛	𝑛	DET
cana-1649	179	13	∈	∈	NOUN
cana-1649	179	14	ℕ.	ℕ.	PROPN
cana-1649	179	15	hence	hence	ADV
cana-1649	179	16	the	the	DET
cana-1649	179	17	proof	proof	NOUN
cana-1649	179	18	.	.	PUNCT
cana-1649	180	1	remark	remark	VERB
cana-1649	180	2	2.2	2.2	NUM
cana-1649	180	3	.	.	PUNCT
cana-1649	181	1	(	(	PUNCT
cana-1649	181	2	i	i	NOUN
cana-1649	181	3	)	)	PUNCT
cana-1649	181	4	for	for	ADP
cana-1649	181	5	the	the	DET
cana-1649	181	6	choice	choice	NOUN
cana-1649	181	7	of	of	ADP
cana-1649	181	8	matrix	matrix	NOUN
cana-1649	181	9	𝐻	𝐻	NOUN
cana-1649	181	10	=	=	SYM
cana-1649	181	11	(	(	PUNCT
cana-1649	181	12	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	181	13	)	)	PUNCT
cana-1649	181	14	given	give	VERB
cana-1649	181	15	in	in	ADP
cana-1649	181	16	example	example	NOUN
cana-1649	181	17	1.3	1.3	NUM
cana-1649	181	18	,	,	PUNCT
cana-1649	181	19	theorem	theorem	VERB
cana-1649	181	20	2.2	2.2	NUM
cana-1649	181	21	reduces	reduce	NOUN
cana-1649	181	22	to	to	ADP
cana-1649	181	23	[	[	X
cana-1649	181	24	3	3	NUM
cana-1649	181	25	,	,	PUNCT
cana-1649	181	26	theorem	theorem	VERB
cana-1649	181	27	2.2	2.2	NUM
cana-1649	181	28	]	]	PUNCT
cana-1649	181	29	.	.	PUNCT
cana-1649	182	1	(	(	PUNCT
cana-1649	182	2	ii	ii	NOUN
cana-1649	182	3	)	)	PUNCT
cana-1649	182	4	for	for	ADP
cana-1649	182	5	the	the	DET
cana-1649	182	6	choice	choice	NOUN
cana-1649	182	7	𝐵	𝐵	NOUN
cana-1649	182	8	=	=	PUNCT
cana-1649	182	9	−1	−1	NOUN
cana-1649	182	10	and	and	CCONJ
cana-1649	182	11	matrix	matrix	NOUN
cana-1649	182	12	𝐻	𝐻	NOUN
cana-1649	182	13	=	=	SYM
cana-1649	182	14	(	(	PUNCT
cana-1649	182	15	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	182	16	)	)	PUNCT
cana-1649	182	17	given	give	VERB
cana-1649	182	18	in	in	ADP
cana-1649	182	19	example	example	NOUN
cana-1649	182	20	1.1	1.1	NUM
cana-1649	182	21	,	,	PUNCT
cana-1649	182	22	example	example	NOUN
cana-1649	182	23	1.2	1.2	NUM
cana-1649	182	24	and	and	CCONJ
cana-1649	182	25	example	example	NOUN
cana-1649	182	26	1.3	1.3	NUM
cana-1649	182	27	,	,	PUNCT
cana-1649	182	28	we	we	PRON
cana-1649	182	29	have	have	VERB
cana-1649	182	30	the	the	DET
cana-1649	182	31	results	result	NOUN
cana-1649	182	32	of	of	ADP
cana-1649	182	33	[	[	X
cana-1649	182	34	10	10	NUM
cana-1649	182	35	,	,	PUNCT
cana-1649	182	36	theorem	theorem	VERB
cana-1649	182	37	1.1	1.1	NUM
cana-1649	182	38	]	]	PUNCT
cana-1649	182	39	,	,	PUNCT
cana-1649	183	1	[	[	X
cana-1649	183	2	6	6	NUM
cana-1649	183	3	,	,	PUNCT
cana-1649	183	4	theorem	theorem	VERB
cana-1649	183	5	2.2	2.2	NUM
cana-1649	183	6	]	]	PUNCT
cana-1649	183	7	and	and	CCONJ
cana-1649	183	8	[	[	X
cana-1649	183	9	11	11	NUM
cana-1649	183	10	,	,	PUNCT
cana-1649	183	11	theorem	theorem	VERB
cana-1649	183	12	2.1	2.1	NUM
cana-1649	183	13	]	]	PUNCT
cana-1649	183	14	,	,	PUNCT
cana-1649	183	15	respectively	respectively	ADV
cana-1649	183	16	.	.	PUNCT
cana-1649	184	1	theorem	theorem	VERB
cana-1649	184	2	2.3	2.3	NUM
cana-1649	184	3	.	.	PUNCT
cana-1649	185	1	let	let	VERB
cana-1649	185	2	𝐻	𝐻	PROPN
cana-1649	185	3	=	=	SYM
cana-1649	185	4	(	(	PUNCT
cana-1649	185	5	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	185	6	)	)	PUNCT
cana-1649	185	7	be	be	VERB
cana-1649	185	8	admissible	admissible	ADJ
cana-1649	185	9	lower	low	ADJ
cana-1649	185	10	triangular	triangular	NOUN
cana-1649	185	11	matrix	matrix	NOUN
cana-1649	185	12	with	with	ADP
cana-1649	185	13	ℎ𝑖1	ℎ𝑖1	NOUN
cana-1649	185	14	≤	≤	NUM
cana-1649	185	15	1	1	NUM
cana-1649	185	16	,	,	PUNCT
cana-1649	185	17	∀	∀	NOUN
cana-1649	185	18	𝑖	𝑖	PRON
cana-1649	185	19	≥	≥	NOUN
cana-1649	185	20	1	1	NUM
cana-1649	185	21	.	.	PUNCT
cana-1649	186	1	then	then	ADV
cana-1649	186	2	for	for	ADP
cana-1649	186	3	−1	−1	NOUN
cana-1649	186	4	≤	≤	NUM
cana-1649	186	5	𝐵	𝐵	PROPN
cana-1649	186	6	<	<	X
cana-1649	186	7	𝐴	𝐴	PROPN
cana-1649	186	8	<	<	X
cana-1649	186	9	0	0	NUM
cana-1649	186	10	and	and	CCONJ
cana-1649	186	11	𝛿	𝛿	PRON
cana-1649	186	12	∈	∈	PROPN
cana-1649	186	13	(	(	PUNCT
cana-1649	186	14	0,1	0,1	NOUN
cana-1649	186	15	]	]	PUNCT
cana-1649	186	16	,	,	PUNCT
cana-1649	186	17	the	the	DET
cana-1649	186	18	function	function	NOUN
cana-1649	186	19	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADV
cana-1649	186	20	𝛿	𝛿	PROPN
cana-1649	186	21	(	(	PUNCT
cana-1649	186	22	𝑧	𝑧	NOUN
cana-1649	186	23	)	)	PUNCT
cana-1649	186	24	is	be	AUX
cana-1649	186	25	not	not	PART
cana-1649	186	26	𝒫-stable	𝒫-stable	ADJ
cana-1649	186	27	with	with	ADP
cana-1649	186	28	respect	respect	NOUN
cana-1649	186	29	to	to	ADP
cana-1649	186	30	itself	itself	PRON
cana-1649	186	31	.	.	PUNCT
cana-1649	187	1	proof	proof	NOUN
cana-1649	187	2	.	.	PUNCT
cana-1649	188	1	to	to	PART
cana-1649	188	2	prove	prove	VERB
cana-1649	188	3	the	the	DET
cana-1649	188	4	result	result	NOUN
cana-1649	188	5	,	,	PUNCT
cana-1649	188	6	it	it	PRON
cana-1649	188	7	is	be	AUX
cana-1649	188	8	enough	enough	ADJ
cana-1649	188	9	to	to	PART
cana-1649	188	10	show	show	VERB
cana-1649	188	11	that	that	SCONJ
cana-1649	188	12	𝒫𝑛(𝒥𝐴,𝐵	𝒫𝑛(𝒥𝐴,𝐵	NOUN
cana-1649	188	13	𝛿	𝛿	PROPN
cana-1649	188	14	(	(	PUNCT
cana-1649	188	15	𝑧),𝑧	𝑧),𝑧	NOUN
cana-1649	188	16	)	)	PUNCT
cana-1649	188	17	𝒥𝐴,𝐵	𝒥𝐴,𝐵	NOUN
cana-1649	188	18	𝛿	𝛿	PRON
cana-1649	188	19	(	(	PUNCT
cana-1649	188	20	𝑧	𝑧	NOUN
cana-1649	188	21	)	)	PUNCT
cana-1649	188	22	⊀	⊀	PROPN
cana-1649	188	23	1	1	NUM
cana-1649	188	24	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADP
cana-1649	188	25	𝛿	𝛿	PROPN
cana-1649	188	26	(	(	PUNCT
cana-1649	188	27	𝑧	𝑧	NOUN
cana-1649	188	28	)	)	PUNCT
cana-1649	188	29	(	(	PUNCT
cana-1649	188	30	𝑧	𝑧	PROPN
cana-1649	188	31	∈	∈	PROPN
cana-1649	188	32	δ	δ	PROPN
cana-1649	188	33	)	)	PUNCT
cana-1649	188	34	,	,	PUNCT
cana-1649	188	35	or	or	CCONJ
cana-1649	188	36	equivalently	equivalently	ADV
cana-1649	188	37	,	,	PUNCT
cana-1649	188	38	𝑆(𝑧	𝑆(𝑧	NOUN
cana-1649	188	39	)	)	PUNCT
cana-1649	188	40	=	=	SYM
cana-1649	188	41	(	(	PUNCT
cana-1649	188	42	𝐵𝑧+1)[𝒫𝑛(𝒥𝐴,𝐵	𝐵𝑧+1)[𝒫𝑛(𝒥𝐴,𝐵	PROPN
cana-1649	188	43	𝛿	𝛿	X
cana-1649	188	44	(	(	PUNCT
cana-1649	188	45	𝑧),𝑧	𝑧),𝑧	PROPN
cana-1649	188	46	)	)	PUNCT
cana-1649	188	47	]	]	PUNCT
cana-1649	188	48	1	1	NUM
cana-1649	188	49	𝛿	𝛿	ADJ
cana-1649	188	50	(	(	PUNCT
cana-1649	188	51	𝐴𝑧+1	𝐴𝑧+1	NOUN
cana-1649	188	52	)	)	PUNCT
cana-1649	188	53	is	be	AUX
cana-1649	188	54	not	not	PART
cana-1649	188	55	subordinate	subordinate	ADJ
cana-1649	188	56	to	to	ADP
cana-1649	188	57	𝑇(𝑧	𝑇(𝑧	NUM
cana-1649	188	58	)	)	PUNCT
cana-1649	188	59	=	=	SYM
cana-1649	188	60	𝐵𝑧+1	𝐵𝑧+1	NOUN
cana-1649	188	61	𝐴𝑧+1	𝐴𝑧+1	NOUN
cana-1649	188	62	.	.	PUNCT
cana-1649	189	1	if	if	SCONJ
cana-1649	189	2	𝑆(𝑧	𝑆(𝑧	NUM
cana-1649	189	3	)	)	PUNCT
cana-1649	189	4	≺	≺	NOUN
cana-1649	189	5	𝑇(𝑧	𝑇(𝑧	ADP
cana-1649	189	6	)	)	PUNCT
cana-1649	189	7	,	,	PUNCT
cana-1649	189	8	then	then	ADV
cana-1649	189	9	by	by	ADP
cana-1649	189	10	definition	definition	NOUN
cana-1649	189	11	of	of	ADP
cana-1649	189	12	subordination	subordination	NOUN
cana-1649	189	13	and	and	CCONJ
cana-1649	189	14	schwarz	schwarz	PROPN
cana-1649	189	15	lemma	lemma	PROPN
cana-1649	189	16	,	,	PUNCT
cana-1649	189	17	we	we	PRON
cana-1649	189	18	have	have	VERB
cana-1649	189	19	|𝑆′(0)|	|𝑆′(0)|	NUM
cana-1649	189	20	≤	≤	NOUN
cana-1649	189	21	|𝑇′(0)|	|𝑇′(0)|	NUM
cana-1649	189	22	and	and	CCONJ
cana-1649	189	23	𝑆(|𝑧|	𝑆(|𝑧|	ADJ
cana-1649	189	24	≤	≤	ADJ
cana-1649	190	1	𝑟	𝑟	NOUN
cana-1649	190	2	)	)	PUNCT
cana-1649	190	3	⊆	⊆	NUM
cana-1649	190	4	𝑇(|𝑧|	𝑇(|𝑧|	NOUN
cana-1649	190	5	≤	≤	NUM
cana-1649	190	6	𝑟	𝑟	NOUN
cana-1649	190	7	)	)	PUNCT
cana-1649	190	8	,	,	PUNCT
cana-1649	190	9	where	where	SCONJ
cana-1649	190	10	0	0	NUM
cana-1649	190	11	≤	≤	NUM
cana-1649	190	12	𝑟	𝑟	X
cana-1649	190	13	<	<	X
cana-1649	190	14	1	1	NUM
cana-1649	190	15	.	.	PUNCT
cana-1649	190	16	to	to	PART
cana-1649	190	17	prove	prove	VERB
cana-1649	190	18	𝑆(𝑧	𝑆(𝑧	NUM
cana-1649	190	19	)	)	PUNCT
cana-1649	190	20	≺	≺	NOUN
cana-1649	190	21	𝑇(𝑧	𝑇(𝑧	ADP
cana-1649	190	22	)	)	PUNCT
cana-1649	190	23	,	,	PUNCT
cana-1649	190	24	for	for	ADP
cana-1649	190	25	𝑧	𝑧	PRON
cana-1649	190	26	=	=	VERB
cana-1649	190	27	𝐵𝑤+1	𝐵𝑤+1	PRON
cana-1649	190	28	𝐴𝑤+1	𝐴𝑤+1	NOUN
cana-1649	190	29	,	,	PUNCT
cana-1649	190	30	we	we	PRON
cana-1649	190	31	have	have	VERB
cana-1649	190	32	to	to	PART
cana-1649	190	33	show	show	VERB
cana-1649	190	34	that	that	SCONJ
cana-1649	190	35	there	there	PRON
cana-1649	190	36	exist	exist	VERB
cana-1649	190	37	atleast	atleast	ADP
cana-1649	190	38	a	a	DET
cana-1649	190	39	point	point	NOUN
cana-1649	190	40	𝑧0	𝑧0	PROPN
cana-1649	190	41	∈	∈	PROPN
cana-1649	190	42	δ	δ	PROPN
cana-1649	190	43	with	with	ADP
cana-1649	190	44	|𝑧0|	|𝑧0|	NOUN
cana-1649	190	45	≤	≤	NUM
cana-1649	190	46	𝑟0	𝑟0	NOUN
cana-1649	190	47	,	,	PUNCT
cana-1649	190	48	for	for	ADP
cana-1649	190	49	which	which	PRON
cana-1649	190	50	𝑆(𝑧0	𝑆(𝑧0	PROPN
cana-1649	190	51	)	)	PUNCT
cana-1649	190	52	lies	lie	VERB
cana-1649	190	53	outside	outside	ADP
cana-1649	190	54	the	the	DET
cana-1649	190	55	disc	disc	NOUN
cana-1649	190	56	,	,	PUNCT
cana-1649	190	57	|𝑤	|𝑤	PRON
cana-1649	190	58	−	−	PROPN
cana-1649	191	1	𝑟2𝐴−𝐵	𝑟2𝐴−𝐵	ADP
cana-1649	191	2	𝐵2−𝑟2𝐴2	𝐵2−𝑟2𝐴2	PUNCT
cana-1649	191	3	|	|	ADV
cana-1649	191	4	≤	≤	NUM
cana-1649	191	5	𝑟(𝐴−𝐵	𝑟(𝐴−𝐵	PROPN
cana-1649	191	6	)	)	PUNCT
cana-1649	191	7	𝐵2−𝑟2𝐴2	𝐵2−𝑟2𝐴2	PUNCT
cana-1649	191	8	,	,	PUNCT
cana-1649	191	9	for	for	ADP
cana-1649	191	10	−1	−1	NOUN
cana-1649	191	11	≤	≤	NUM
cana-1649	191	12	𝐵	𝐵	PROPN
cana-1649	191	13	<	<	X
cana-1649	191	14	𝐴	𝐴	PROPN
cana-1649	191	15	≤	≤	NOUN
cana-1649	191	16	0	0	NUM
cana-1649	191	17	.	.	PUNCT
cana-1649	192	1	on	on	ADP
cana-1649	192	2	choosing	choose	VERB
cana-1649	192	3	𝑧0	𝑧0	NOUN
cana-1649	192	4	=	=	PUNCT
cana-1649	192	5	0.907512	0.907512	NUM
cana-1649	192	6	+	+	CCONJ
cana-1649	192	7	0.395628𝑖	0.395628𝑖	NUM
cana-1649	192	8	,	,	PUNCT
cana-1649	192	9	𝑟0	𝑟0	NOUN
cana-1649	192	10	=	=	SYM
cana-1649	192	11	0.99	0.99	NUM
cana-1649	192	12	,	,	PUNCT
cana-1649	192	13	𝐴0	𝐴0	PROPN
cana-1649	192	14	=	=	SYM
cana-1649	192	15	−0.4	−0.4	PROPN
cana-1649	192	16	,	,	PUNCT
cana-1649	192	17	𝐵0	𝐵0	NOUN
cana-1649	192	18	=	=	SYM
cana-1649	192	19	−1	−1	NOUN
cana-1649	192	20	,	,	PUNCT
cana-1649	192	21	𝛿0	𝛿0	NOUN
cana-1649	192	22	=	=	SYM
cana-1649	192	23	0.4	0.4	NUM
cana-1649	192	24	and	and	CCONJ
cana-1649	192	25	𝑛	𝑛	ADJ
cana-1649	192	26	=	=	SYM
cana-1649	192	27	1	1	NUM
cana-1649	192	28	,	,	PUNCT
cana-1649	192	29	we	we	PRON
cana-1649	192	30	obtain	obtain	VERB
cana-1649	192	31	𝑟0	𝑟0	NOUN
cana-1649	192	32	2𝐴0−𝐵0	2𝐴0−𝐵0	NUM
cana-1649	192	33	𝐵0	𝐵0	NOUN
cana-1649	192	34	2−𝑟0	2−𝑟0	NUM
cana-1649	192	35	2𝐴0	2𝐴0	NUM
cana-1649	192	36	2	2	NUM
cana-1649	192	37	=	=	SYM
cana-1649	192	38	0.721028862	0.721028862	NUM
cana-1649	192	39	and	and	CCONJ
cana-1649	192	40	𝑟0(𝐴0−𝐵0	𝑟0(𝐴0−𝐵0	NOUN
cana-1649	192	41	)	)	PUNCT
cana-1649	192	42	𝐵0	𝐵0	NOUN
cana-1649	192	43	2−𝑟0	2−𝑟0	NUM
cana-1649	192	44	2𝐴0	2𝐴0	NUM
cana-1649	192	45	2	2	NUM
cana-1649	192	46	=	=	SYM
cana-1649	192	47	0.70447257	0.70447257	NUM
cana-1649	192	48	.	.	PUNCT
cana-1649	193	1	to	to	PART
cana-1649	193	2	complete	complete	VERB
cana-1649	193	3	the	the	DET
cana-1649	193	4	proof	proof	NOUN
cana-1649	193	5	,	,	PUNCT
cana-1649	193	6	we	we	PRON
cana-1649	193	7	need	need	VERB
cana-1649	193	8	to	to	PART
cana-1649	193	9	show	show	VERB
cana-1649	193	10	that	that	SCONJ
cana-1649	193	11	𝑆(|𝑧|	𝑆(|𝑧|	ADJ
cana-1649	193	12	≤	≤	ADJ
cana-1649	193	13	𝑟	𝑟	NOUN
cana-1649	193	14	)	)	PUNCT
cana-1649	193	15	⊈	⊈	PUNCT
cana-1649	194	1	𝑇(|𝑧|	𝑇(|𝑧|	ADJ
cana-1649	194	2	≤	≤	NUM
cana-1649	194	3	𝑟	𝑟	NOUN
cana-1649	194	4	)	)	PUNCT
cana-1649	194	5	for	for	ADP
cana-1649	194	6	the	the	DET
cana-1649	194	7	values	value	NOUN
cana-1649	194	8	of	of	ADP
cana-1649	194	9	ℎ11	ℎ11	ADV
cana-1649	194	10	≥	≥	NOUN
cana-1649	194	11	0	0	NUM
cana-1649	194	12	,	,	PUNCT
cana-1649	194	13	which	which	PRON
cana-1649	194	14	is	be	AUX
cana-1649	194	15	possible	possible	ADJ
cana-1649	194	16	for	for	ADP
cana-1649	194	17	various	various	ADJ
cana-1649	194	18	choices	choice	NOUN
cana-1649	194	19	of	of	ADP
cana-1649	194	20	admissible	admissible	ADJ
cana-1649	194	21	lower	low	ADJ
cana-1649	194	22	triangular	triangular	NOUN
cana-1649	194	23	matrices	matrix	NOUN
cana-1649	194	24	.	.	PUNCT
cana-1649	195	1	here	here	ADV
cana-1649	195	2	,	,	PUNCT
cana-1649	195	3	we	we	PRON
cana-1649	195	4	provide	provide	VERB
cana-1649	195	5	the	the	DET
cana-1649	195	6	table	table	NOUN
cana-1649	195	7	for	for	ADP
cana-1649	195	8	some	some	DET
cana-1649	195	9	values	value	NOUN
cana-1649	195	10	of	of	ADP
cana-1649	195	11	ℎ11	ℎ11	NOUN
cana-1649	195	12	.	.	PUNCT
cana-1649	196	1	it	it	PRON
cana-1649	196	2	is	be	AUX
cana-1649	196	3	clear	clear	ADJ
cana-1649	196	4	from	from	ADP
cana-1649	196	5	the	the	DET
cana-1649	196	6	table	table	NOUN
cana-1649	196	7	1	1	NUM
cana-1649	196	8	that	that	SCONJ
cana-1649	196	9	𝑆(𝑧0	𝑆(𝑧0	PROPN
cana-1649	196	10	)	)	PUNCT
cana-1649	196	11	lies	lie	VERB
cana-1649	196	12	outside	outside	ADP
cana-1649	196	13	the	the	DET
cana-1649	196	14	disc	disc	NOUN
cana-1649	196	15	|𝑤	|𝑤	PUNCT
cana-1649	196	16	−	−	PROPN
cana-1649	196	17	0.721028862|	0.721028862|	NOUN
cana-1649	196	18	≤	≤	NOUN
cana-1649	196	19	0.70447257	0.70447257	NUM
cana-1649	196	20	for	for	ADP
cana-1649	196	21	the	the	DET
cana-1649	196	22	values	value	NOUN
cana-1649	196	23	of	of	ADP
cana-1649	196	24	ℎ11	ℎ11	NOUN
cana-1649	196	25	in	in	ADP
cana-1649	196	26	the	the	DET
cana-1649	196	27	interval	interval	NOUN
cana-1649	196	28	[	[	X
cana-1649	196	29	0,1	0,1	NUM
cana-1649	196	30	]	]	PUNCT
cana-1649	196	31	.	.	PUNCT
cana-1649	197	1	also	also	ADV
cana-1649	197	2	from	from	ADP
cana-1649	197	3	the	the	DET
cana-1649	197	4	figure	figure	NOUN
cana-1649	197	5	1(a	1(a	NUM
cana-1649	197	6	)	)	PUNCT
cana-1649	197	7	and	and	CCONJ
cana-1649	197	8	figure	figure	VERB
cana-1649	197	9	1(b	1(b	NUM
cana-1649	197	10	)	)	PUNCT
cana-1649	197	11	,	,	PUNCT
cana-1649	197	12	we	we	PRON
cana-1649	197	13	observe	observe	VERB
cana-1649	197	14	that	that	SCONJ
cana-1649	197	15	the	the	DET
cana-1649	197	16	𝑆(𝑧	𝑆(𝑧	NOUN
cana-1649	197	17	)	)	PUNCT
cana-1649	197	18	is	be	AUX
cana-1649	197	19	not	not	PART
cana-1649	197	20	subordinate	subordinate	ADJ
cana-1649	197	21	to	to	ADP
cana-1649	197	22	𝑇(𝑧	𝑇(𝑧	NUM
cana-1649	197	23	)	)	PUNCT
cana-1649	197	24	for	for	ADP
cana-1649	197	25	the	the	DET
cana-1649	197	26	values	value	NOUN
cana-1649	197	27	of	of	ADP
cana-1649	197	28	ℎ11	ℎ11	NOUN
cana-1649	197	29	=	=	NOUN
cana-1649	197	30	0.3	0.3	NUM
cana-1649	197	31	and	and	CCONJ
cana-1649	197	32	ℎ11	ℎ11	NOUN
cana-1649	197	33	=	=	NOUN
cana-1649	197	34	0.5	0.5	NUM
cana-1649	197	35	respectively	respectively	ADV
cana-1649	197	36	.	.	PUNCT
cana-1649	198	1	therefore	therefore	ADV
cana-1649	198	2	,	,	PUNCT
cana-1649	198	3	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADP
cana-1649	198	4	𝛿	𝛿	PRON
cana-1649	198	5	(	(	PUNCT
cana-1649	198	6	𝑧	𝑧	NOUN
cana-1649	198	7	)	)	PUNCT
cana-1649	198	8	is	be	AUX
cana-1649	198	9	not	not	PART
cana-1649	198	10	𝒫1	𝒫1	NOUN
cana-1649	198	11	-	-	PUNCT
cana-1649	198	12	stable	stable	ADJ
cana-1649	198	13	.	.	PUNCT
cana-1649	199	1	hence	hence	ADV
cana-1649	199	2	,	,	PUNCT
cana-1649	199	3	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADP
cana-1649	199	4	𝛿	𝛿	PRON
cana-1649	199	5	(	(	PUNCT
cana-1649	199	6	𝑧	𝑧	NOUN
cana-1649	199	7	)	)	PUNCT
cana-1649	199	8	is	be	AUX
cana-1649	199	9	not	not	PART
cana-1649	199	10	𝒫-stable	𝒫-stable	PROPN
cana-1649	199	11	,	,	PUNCT
cana-1649	199	12	which	which	PRON
cana-1649	199	13	completes	complete	VERB
cana-1649	199	14	the	the	DET
cana-1649	199	15	proof	proof	NOUN
cana-1649	199	16	.	.	PUNCT
cana-1649	200	1	communications	communication	NOUN
cana-1649	200	2	on	on	ADP
cana-1649	200	3	applied	apply	VERB
cana-1649	200	4	nonlinear	nonlinear	ADJ
cana-1649	200	5	analysis	analysis	NOUN
cana-1649	200	6	issn	issn	NOUN
cana-1649	200	7	:	:	PUNCT
cana-1649	200	8	1074	1074	NUM
cana-1649	200	9	-	-	PUNCT
cana-1649	200	10	133x	133x	NUM
cana-1649	200	11	vol	vol	NOUN
cana-1649	200	12	32	32	NUM
cana-1649	200	13	no	no	NOUN
cana-1649	200	14	.	.	NOUN
cana-1649	200	15	1	1	NUM
cana-1649	200	16	(	(	PUNCT
cana-1649	200	17	2025	2025	NUM
cana-1649	200	18	)	)	PUNCT
cana-1649	201	1	300	300	NUM
cana-1649	201	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1649	201	3	sl	sl	NOUN
cana-1649	201	4	.	.	PUNCT
cana-1649	201	5	no	no	INTJ
cana-1649	201	6	.	.	PUNCT
cana-1649	202	1	values	value	NOUN
cana-1649	202	2	of	of	ADP
cana-1649	202	3	ℎ11	ℎ11	NOUN
cana-1649	202	4	𝑆(𝑧0	𝑆(𝑧0	PROPN
cana-1649	202	5	)	)	PUNCT
cana-1649	202	6	|𝑆(𝑧0	|𝑆(𝑧0	PROPN
cana-1649	202	7	)	)	PUNCT
cana-1649	202	8	−	−	PROPN
cana-1649	202	9	r0	r0	NOUN
cana-1649	202	10	2𝐴0	2𝐴0	NUM
cana-1649	202	11	−	−	PROPN
cana-1649	203	1	𝐵0	𝐵0	PROPN
cana-1649	203	2	𝐵0	𝐵0	VERB
cana-1649	203	3	2	2	NUM
cana-1649	203	4	−	−	NOUN
cana-1649	203	5	r0	r0	NOUN
cana-1649	203	6	2a0	2a0	NUM
cana-1649	203	7	2	2	NUM
cana-1649	204	1	|	|	ADV
cana-1649	204	2	1	1	NUM
cana-1649	204	3	0.1	0.1	NUM
cana-1649	204	4	0.311155	0.311155	NUM
cana-1649	204	5	-	-	PUNCT
cana-1649	204	6	0.5744904i	0.5744904i	ADJ
cana-1649	204	7	0.7057165	0.7057165	NUM
cana-1649	204	8	2	2	NUM
cana-1649	204	9	0.3	0.3	NUM
cana-1649	204	10	0.373144	0.373144	NUM
cana-1649	204	11	-	-	PUNCT
cana-1649	204	12	0.6225204i	0.6225204i	VERB
cana-1649	204	13	0.7131308	0.7131308	NUM
cana-1649	204	14	3	3	NUM
cana-1649	204	15	0.5	0.5	NUM
cana-1649	204	16	0.4403595	0.4403595	NUM
cana-1649	204	17	-	-	PUNCT
cana-1649	204	18	0.6719527i	0.6719527i	NUM
cana-1649	204	19	0.7282141	0.7282141	NUM
cana-1649	204	20	4	4	NUM
cana-1649	204	21	0.8	0.8	NUM
cana-1649	204	22	0.5512408	0.5512408	NUM
cana-1649	204	23	-	-	SYM
cana-1649	204	24	0.748699i	0.748699i	NUM
cana-1649	204	25	0.7677097	0.7677097	NUM
cana-1649	204	26	5	5	NUM
cana-1649	204	27	1	1	NUM
cana-1649	204	28	0.6320364	0.6320364	NUM
cana-1649	204	29	-	-	PUNCT
cana-1649	204	30	0.8015772i	0.8015772i	NOUN
cana-1649	204	31	0.8065021	0.8065021	NUM
cana-1649	204	32	table	table	NOUN
cana-1649	204	33	1	1	NUM
cana-1649	204	34	figure	figure	NOUN
cana-1649	204	35	1	1	NUM
cana-1649	204	36	(	(	PUNCT
cana-1649	204	37	a	a	NOUN
cana-1649	204	38	)	)	PUNCT
cana-1649	204	39	boundary	boundary	ADJ
cana-1649	204	40	curves	curve	NOUN
cana-1649	204	41	for	for	ADP
cana-1649	204	42	h11	h11	NOUN
cana-1649	204	43	=	=	NOUN
cana-1649	204	44	0.3	0.3	NUM
cana-1649	204	45	figure	figure	NOUN
cana-1649	204	46	1	1	NUM
cana-1649	204	47	(	(	PUNCT
cana-1649	204	48	b	b	NOUN
cana-1649	204	49	)	)	PUNCT
cana-1649	204	50	boundary	boundary	ADJ
cana-1649	204	51	curves	curve	NOUN
cana-1649	204	52	for	for	ADP
cana-1649	204	53	h11	h11	NOUN
cana-1649	204	54	=	=	SYM
cana-1649	204	55	0.5	0.5	NUM
cana-1649	204	56	remark	remark	NOUN
cana-1649	204	57	2.3	2.3	NUM
cana-1649	204	58	.	.	PUNCT
cana-1649	205	1	it	it	PRON
cana-1649	205	2	is	be	AUX
cana-1649	205	3	clear	clear	ADJ
cana-1649	205	4	that	that	SCONJ
cana-1649	205	5	for	for	ADP
cana-1649	205	6	𝛽	𝛽	PROPN
cana-1649	205	7	≥	≥	NOUN
cana-1649	205	8	0	0	NUM
cana-1649	205	9	,	,	PUNCT
cana-1649	205	10	𝛿	𝛿	PRON
cana-1649	205	11	∈	∈	PROPN
cana-1649	205	12	(	(	PUNCT
cana-1649	205	13	0,1	0,1	NOUN
cana-1649	205	14	]	]	PUNCT
cana-1649	205	15	and	and	CCONJ
cana-1649	205	16	−1	−1	NOUN
cana-1649	205	17	≤	≤	NOUN
cana-1649	205	18	𝐵	𝐵	PROPN
cana-1649	205	19	<	<	X
cana-1649	205	20	𝐴	𝐴	PROPN
cana-1649	205	21	<	<	X
cana-1649	205	22	0	0	PROPN
cana-1649	205	23	,	,	PUNCT
cana-1649	205	24	𝒥𝐴,𝐵	𝒥𝐴,𝐵	ADV
cana-1649	205	25	𝛿	𝛿	PRON
cana-1649	205	26	(	(	PUNCT
cana-1649	205	27	𝑧	𝑧	NOUN
cana-1649	205	28	)	)	PUNCT
cana-1649	205	29	is	be	AUX
cana-1649	205	30	not	not	PART
cana-1649	205	31	a	a	DET
cana-1649	205	32	cesàro	cesàro	NOUN
cana-1649	205	33	stable	stable	ADJ
cana-1649	205	34	with	with	ADP
cana-1649	205	35	respect	respect	NOUN
cana-1649	205	36	to	to	ADP
cana-1649	205	37	itself	itself	PRON
cana-1649	205	38	.	.	PUNCT
cana-1649	206	1	3	3	X
cana-1649	206	2	.	.	X
cana-1649	206	3	on	on	ADP
cana-1649	206	4	𝓟-stability	𝓟-stability	PROPN
cana-1649	206	5	of	of	ADP
cana-1649	206	6	𝒉	𝒉	PROPN
cana-1649	206	7	∈	∈	PROPN
cana-1649	206	8	𝑺∗(𝜹	𝑺∗(𝜹	NOUN
cana-1649	206	9	)	)	PUNCT
cana-1649	206	10	also	also	ADV
cana-1649	206	11	𝑧ℎ𝛿(𝑧	𝑧ℎ𝛿(𝑧	X
cana-1649	206	12	)	)	PUNCT
cana-1649	206	13	=	=	SYM
cana-1649	206	14	𝑧	𝑧	PROPN
cana-1649	206	15	(	(	PUNCT
cana-1649	206	16	1−𝑧)𝛿	1−𝑧)𝛿	NUM
cana-1649	206	17	∈	∈	PROPN
cana-1649	206	18	𝑆∗(1	𝑆∗(1	PUNCT
cana-1649	206	19	−	−	PROPN
cana-1649	206	20	𝛿/2	𝛿/2	NUM
cana-1649	206	21	)	)	PUNCT
cana-1649	206	22	,	,	PUNCT
cana-1649	206	23	𝛿	𝛿	PROPN
cana-1649	206	24	∈	∈	PROPN
cana-1649	206	25	(	(	PUNCT
cana-1649	206	26	0,1	0,1	NUM
cana-1649	206	27	]	]	PUNCT
cana-1649	206	28	is	be	AUX
cana-1649	206	29	an	an	DET
cana-1649	206	30	extremal	extremal	ADJ
cana-1649	206	31	function	function	NOUN
cana-1649	206	32	which	which	PRON
cana-1649	206	33	plays	play	VERB
cana-1649	206	34	an	an	DET
cana-1649	206	35	important	important	ADJ
cana-1649	206	36	role	role	NOUN
cana-1649	206	37	in	in	ADP
cana-1649	206	38	studying	study	VERB
cana-1649	206	39	several	several	ADJ
cana-1649	206	40	properties	property	NOUN
cana-1649	206	41	like	like	ADP
cana-1649	206	42	growth	growth	NOUN
cana-1649	206	43	,	,	PUNCT
cana-1649	206	44	distortion	distortion	NOUN
cana-1649	206	45	,	,	PUNCT
cana-1649	206	46	etc	etc	X
cana-1649	206	47	.	.	X
cana-1649	206	48	,	,	PUNCT
cana-1649	206	49	it	it	PRON
cana-1649	206	50	is	be	AUX
cana-1649	206	51	observed	observe	VERB
cana-1649	206	52	that	that	SCONJ
cana-1649	206	53	for	for	ADP
cana-1649	206	54	𝛿	𝛿	PROPN
cana-1649	206	55	∈	∈	PROPN
cana-1649	206	56	(	(	PUNCT
cana-1649	206	57	0,1	0,1	NUM
cana-1649	206	58	]	]	PUNCT
cana-1649	206	59	and	and	CCONJ
cana-1649	206	60	𝐵	𝐵	NOUN
cana-1649	206	61	=	=	SYM
cana-1649	206	62	−1	−1	NOUN
cana-1649	206	63	in	in	ADP
cana-1649	206	64	theorem	theorem	NOUN
cana-1649	206	65	2.2	2.2	NUM
cana-1649	206	66	,	,	PUNCT
cana-1649	206	67	we	we	PRON
cana-1649	206	68	have	have	VERB
cana-1649	206	69	communications	communication	NOUN
cana-1649	206	70	on	on	ADP
cana-1649	206	71	applied	apply	VERB
cana-1649	206	72	nonlinear	nonlinear	ADJ
cana-1649	206	73	analysis	analysis	NOUN
cana-1649	206	74	issn	issn	NOUN
cana-1649	206	75	:	:	PUNCT
cana-1649	206	76	1074	1074	NUM
cana-1649	206	77	-	-	PUNCT
cana-1649	206	78	133x	133x	NUM
cana-1649	206	79	vol	vol	NOUN
cana-1649	206	80	32	32	NUM
cana-1649	206	81	no	no	NOUN
cana-1649	206	82	.	.	NOUN
cana-1649	206	83	1	1	NUM
cana-1649	206	84	(	(	PUNCT
cana-1649	206	85	2025	2025	NUM
cana-1649	206	86	)	)	PUNCT
cana-1649	206	87	301	301	NUM
cana-1649	206	88	https://internationalpubls.com	https://internationalpubls.com	X
cana-1649	206	89	𝒫𝑛(ℎ𝛿,𝑧	𝒫𝑛(ℎ𝛿,𝑧	PROPN
cana-1649	206	90	)	)	PUNCT
cana-1649	207	1	ℎ𝛿	ℎ𝛿	PROPN
cana-1649	207	2	≺	≺	NOUN
cana-1649	207	3	1	1	NUM
cana-1649	207	4	ℎ𝛿	ℎ𝛿	X
cana-1649	207	5	.	.	PUNCT
cana-1649	208	1	(	(	PUNCT
cana-1649	208	2	3.1	3.1	NUM
cana-1649	208	3	)	)	PUNCT
cana-1649	208	4	theorem	theorem	VERB
cana-1649	208	5	3.1	3.1	NUM
cana-1649	208	6	.	.	PUNCT
cana-1649	209	1	let	let	VERB
cana-1649	209	2	ℎ	ℎ	PROPN
cana-1649	209	3	∈	∈	PROPN
cana-1649	209	4	𝑆∗(1	𝑆∗(1	PROPN
cana-1649	209	5	−	−	PROPN
cana-1649	209	6	𝛿/2	𝛿/2	NUM
cana-1649	209	7	)	)	PUNCT
cana-1649	209	8	,	,	PUNCT
cana-1649	209	9	for	for	ADP
cana-1649	209	10	𝛿	𝛿	PROPN
cana-1649	209	11	∈	∈	PROPN
cana-1649	209	12	(	(	PUNCT
cana-1649	209	13	0,1	0,1	NOUN
cana-1649	209	14	]	]	PUNCT
cana-1649	209	15	.	.	PUNCT
cana-1649	210	1	then	then	ADV
cana-1649	210	2	𝒫𝑛(ℎ/𝑧,𝑧	𝒫𝑛(ℎ/𝑧,𝑧	NOUN
cana-1649	210	3	)	)	PUNCT
cana-1649	210	4	ℎ(𝑧)/𝑧	ℎ(𝑧)/𝑧	PROPN
cana-1649	210	5	≺	≺	NOUN
cana-1649	210	6	(	(	PUNCT
cana-1649	210	7	1	1	NUM
cana-1649	210	8	−	−	NOUN
cana-1649	210	9	𝑧)𝛿	𝑧)𝛿	NOUN
cana-1649	210	10	(	(	PUNCT
cana-1649	210	11	𝑧	𝑧	PROPN
cana-1649	210	12	∈	∈	PROPN
cana-1649	210	13	δ	δ	PROPN
cana-1649	210	14	)	)	PUNCT
cana-1649	210	15	.	.	PUNCT
cana-1649	211	1	proof	proof	NOUN
cana-1649	211	2	.	.	PUNCT
cana-1649	212	1	if	if	SCONJ
cana-1649	212	2	ℎ	ℎ	PROPN
cana-1649	212	3	∈	∈	PROPN
cana-1649	212	4	𝑆∗(1	𝑆∗(1	X
cana-1649	212	5	−	−	PROPN
cana-1649	212	6	𝛿/2	𝛿/2	NUM
cana-1649	212	7	)	)	PUNCT
cana-1649	212	8	,	,	PUNCT
cana-1649	212	9	then	then	ADV
cana-1649	212	10	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1649	212	11	)	)	PUNCT
cana-1649	212	12	=	=	SYM
cana-1649	212	13	𝑧ℎ𝛿	𝑧ℎ𝛿	NOUN
cana-1649	212	14	∗	∗	NOUN
cana-1649	212	15	𝐻(𝑧	𝐻(𝑧	NUM
cana-1649	212	16	)	)	PUNCT
cana-1649	212	17	,	,	PUNCT
cana-1649	212	18	where	where	SCONJ
cana-1649	212	19	𝐻(𝑧	𝐻(𝑧	NUM
cana-1649	212	20	)	)	PUNCT
cana-1649	212	21	is	be	AUX
cana-1649	212	22	an	an	DET
cana-1649	212	23	unique	unique	ADJ
cana-1649	212	24	prestarlike	prestarlike	ADJ
cana-1649	212	25	function	function	NOUN
cana-1649	212	26	of	of	ADP
cana-1649	212	27	order	order	NOUN
cana-1649	212	28	(	(	PUNCT
cana-1649	212	29	1	1	NUM
cana-1649	212	30	−	−	PROPN
cana-1649	212	31	𝛿/2	𝛿/2	NUM
cana-1649	212	32	)	)	PUNCT
cana-1649	212	33	.	.	PUNCT
cana-1649	213	1	using	use	VERB
cana-1649	213	2	ℎ(𝑧	ℎ(𝑧	NOUN
cana-1649	213	3	)	)	PUNCT
cana-1649	213	4	=	=	SYM
cana-1649	213	5	𝑧ℎ𝛿	𝑧ℎ𝛿	NOUN
cana-1649	213	6	∗	∗	NOUN
cana-1649	213	7	𝐻(𝑧	𝐻(𝑧	NUM
cana-1649	213	8	)	)	PUNCT
cana-1649	213	9	,	,	PUNCT
cana-1649	213	10	we	we	PRON
cana-1649	213	11	have	have	AUX
cana-1649	213	12	𝒫𝑛(ℎ/𝑧,𝑧	𝒫𝑛(ℎ/𝑧,𝑧	NOUN
cana-1649	213	13	)	)	PUNCT
cana-1649	213	14	ℎ(𝑧)/𝑧	ℎ(𝑧)/𝑧	PROPN
cana-1649	213	15	=	=	SYM
cana-1649	214	1	𝑧𝒫𝑛(𝑧)∗ℎ(𝑧	𝑧𝒫𝑛(𝑧)∗ℎ(𝑧	PROPN
cana-1649	214	2	)	)	PUNCT
cana-1649	214	3	ℎ(𝑧	ℎ(𝑧	PROPN
cana-1649	214	4	)	)	PUNCT
cana-1649	214	5	=	=	SYM
cana-1649	214	6	𝐻(𝑧)∗[(𝑧ℎ𝛿	𝐻(𝑧)∗[(𝑧ℎ𝛿	NOUN
cana-1649	214	7	)	)	PUNCT
cana-1649	214	8	𝒫𝑛(ℎ𝛿,𝑧	𝒫𝑛(ℎ𝛿,𝑧	PROPN
cana-1649	214	9	)	)	PUNCT
cana-1649	214	10	ℎ𝛿	ℎ𝛿	PROPN
cana-1649	214	11	]	]	PUNCT
cana-1649	214	12	𝐻(𝑧)∗𝑧ℎ𝛿	𝐻(𝑧)∗𝑧ℎ𝛿	ADJ
cana-1649	214	13	∈	∈	PROPN
cana-1649	214	14	𝑐𝑜	𝑐𝑜	INTJ
cana-1649	214	15	(	(	PUNCT
cana-1649	214	16	𝒫𝑛(ℎ𝛿,𝑧	𝒫𝑛(ℎ𝛿,𝑧	PROPN
cana-1649	214	17	)	)	PUNCT
cana-1649	214	18	ℎ𝛿	ℎ𝛿	PROPN
cana-1649	214	19	(	(	PUNCT
cana-1649	214	20	δ	δ	PROPN
cana-1649	214	21	)	)	PUNCT
cana-1649	214	22	)	)	PUNCT
cana-1649	214	23	.	.	PUNCT
cana-1649	215	1	by	by	ADP
cana-1649	215	2	lemma	lemma	PROPN
cana-1649	215	3	1.2	1.2	NUM
cana-1649	215	4	,	,	PUNCT
cana-1649	215	5	we	we	PRON
cana-1649	215	6	see	see	VERB
cana-1649	215	7	that	that	SCONJ
cana-1649	215	8	the	the	DET
cana-1649	215	9	range	range	NOUN
cana-1649	215	10	of	of	ADP
cana-1649	215	11	𝒫𝑛(ℎ/𝑧,𝑧	𝒫𝑛(ℎ/𝑧,𝑧	NOUN
cana-1649	215	12	)	)	PUNCT
cana-1649	215	13	ℎ(𝑧)/𝑧	ℎ(𝑧)/𝑧	PROPN
cana-1649	215	14	lies	lie	VERB
cana-1649	215	15	in	in	ADP
cana-1649	215	16	the	the	DET
cana-1649	215	17	closed	closed	ADJ
cana-1649	215	18	convex	convex	NOUN
cana-1649	215	19	hull	hull	NOUN
cana-1649	215	20	of	of	ADP
cana-1649	215	21	image	image	NOUN
cana-1649	215	22	of	of	ADP
cana-1649	215	23	𝒫𝑛(ℎ𝛿,𝑧	𝒫𝑛(ℎ𝛿,𝑧	PROPN
cana-1649	215	24	)	)	PUNCT
cana-1649	215	25	ℎ𝛿	ℎ𝛿	VERB
cana-1649	215	26	under	under	ADP
cana-1649	215	27	δ	δ	PROPN
cana-1649	215	28	.	.	PUNCT
cana-1649	216	1	now	now	ADV
cana-1649	216	2	applying	apply	VERB
cana-1649	216	3	(	(	PUNCT
cana-1649	216	4	3.1	3.1	NUM
cana-1649	216	5	)	)	PUNCT
cana-1649	216	6	,	,	PUNCT
cana-1649	216	7	for	for	ADP
cana-1649	216	8	𝛿	𝛿	PROPN
cana-1649	216	9	∈	∈	PROPN
cana-1649	216	10	(	(	PUNCT
cana-1649	216	11	0,1	0,1	NUM
cana-1649	216	12	]	]	PUNCT
cana-1649	216	13	,	,	PUNCT
cana-1649	216	14	we	we	PRON
cana-1649	216	15	have	have	AUX
cana-1649	216	16	𝒫𝑛(ℎ/𝑧,𝑧	𝒫𝑛(ℎ/𝑧,𝑧	NOUN
cana-1649	216	17	)	)	PUNCT
cana-1649	216	18	ℎ(𝑧)/𝑧	ℎ(𝑧)/𝑧	PROPN
cana-1649	216	19	≺	≺	NOUN
cana-1649	216	20	(	(	PUNCT
cana-1649	216	21	1	1	NUM
cana-1649	216	22	−	−	NOUN
cana-1649	216	23	𝑧)𝛿	𝑧)𝛿	NOUN
cana-1649	216	24	(	(	PUNCT
cana-1649	216	25	𝑧	𝑧	PROPN
cana-1649	216	26	∈	∈	PROPN
cana-1649	216	27	δ	δ	PROPN
cana-1649	216	28	)	)	PUNCT
cana-1649	216	29	.	.	PUNCT
cana-1649	217	1	hence	hence	ADV
cana-1649	217	2	,	,	PUNCT
cana-1649	217	3	the	the	DET
cana-1649	217	4	proof	proof	NOUN
cana-1649	217	5	.	.	PUNCT
cana-1649	218	1	remark	remark	PROPN
cana-1649	218	2	3.1	3.1	NUM
cana-1649	218	3	.	.	PUNCT
cana-1649	219	1	for	for	ADP
cana-1649	219	2	the	the	DET
cana-1649	219	3	choice	choice	NOUN
cana-1649	219	4	of	of	ADP
cana-1649	219	5	matrix	matrix	NOUN
cana-1649	219	6	𝐻	𝐻	NOUN
cana-1649	219	7	=	=	SYM
cana-1649	219	8	(	(	PUNCT
cana-1649	219	9	ℎ𝑖𝑗	ℎ𝑖𝑗	ADJ
cana-1649	219	10	)	)	PUNCT
cana-1649	219	11	as	as	SCONJ
cana-1649	219	12	given	give	VERB
cana-1649	219	13	in	in	ADP
cana-1649	219	14	example	example	NOUN
cana-1649	219	15	1.1	1.1	NUM
cana-1649	219	16	,	,	PUNCT
cana-1649	219	17	example	example	NOUN
cana-1649	219	18	1.2	1.2	NUM
cana-1649	219	19	and	and	CCONJ
cana-1649	219	20	example	example	NOUN
cana-1649	219	21	1.3	1.3	NUM
cana-1649	219	22	,	,	PUNCT
cana-1649	219	23	theorem	theorem	VERB
cana-1649	219	24	3.1	3.1	NUM
cana-1649	219	25	reduces	reduce	NOUN
cana-1649	219	26	to	to	ADP
cana-1649	219	27	[	[	X
cana-1649	219	28	9	9	NUM
cana-1649	219	29	,	,	PUNCT
cana-1649	219	30	theorem	theorem	VERB
cana-1649	219	31	1.1	1.1	NUM
cana-1649	219	32	]	]	PUNCT
cana-1649	219	33	,	,	PUNCT
cana-1649	220	1	[	[	X
cana-1649	220	2	6	6	NUM
cana-1649	220	3	,	,	PUNCT
cana-1649	220	4	theorem	theorem	VERB
cana-1649	220	5	2.3	2.3	NUM
cana-1649	220	6	]	]	PUNCT
cana-1649	220	7	and	and	CCONJ
cana-1649	220	8	[	[	X
cana-1649	220	9	11	11	NUM
cana-1649	220	10	,	,	PUNCT
cana-1649	220	11	theorem	theorem	VERB
cana-1649	220	12	2.2	2.2	NUM
cana-1649	220	13	]	]	PUNCT
cana-1649	220	14	,	,	PUNCT
cana-1649	220	15	respectively	respectively	ADV
cana-1649	220	16	.	.	PUNCT
cana-1649	221	1	now	now	ADV
cana-1649	221	2	if	if	SCONJ
cana-1649	221	3	we	we	PRON
cana-1649	221	4	consider	consider	VERB
cana-1649	221	5	0	0	NUM
cana-1649	221	6	<	<	X
cana-1649	221	7	𝛿	𝛿	PROPN
cana-1649	221	8	≤	≤	X
cana-1649	221	9	𝜇	𝜇	ADP
cana-1649	221	10	≤	≤	NUM
cana-1649	221	11	1	1	NUM
cana-1649	221	12	in	in	ADP
cana-1649	221	13	theorem	theorem	ADJ
cana-1649	221	14	2.2	2.2	NUM
cana-1649	221	15	,	,	PUNCT
cana-1649	221	16	then	then	ADV
cana-1649	221	17	we	we	PRON
cana-1649	221	18	have	have	VERB
cana-1649	221	19	the	the	DET
cana-1649	221	20	following	follow	VERB
cana-1649	221	21	result	result	NOUN
cana-1649	221	22	.	.	PUNCT
cana-1649	222	1	theorem	theorem	ADJ
cana-1649	222	2	3.2	3.2	NUM
cana-1649	222	3	.	.	PUNCT
cana-1649	223	1	let	let	VERB
cana-1649	223	2	−1	−1	NOUN
cana-1649	223	3	≤	≤	VERB
cana-1649	223	4	𝐵	𝐵	NOUN
cana-1649	223	5	<	<	X
cana-1649	223	6	0	0	NUM
cana-1649	223	7	and	and	CCONJ
cana-1649	223	8	0	0	NUM
cana-1649	223	9	<	<	X
cana-1649	223	10	𝛿	𝛿	PROPN
cana-1649	223	11	≤	≤	X
cana-1649	223	12	𝜇	𝜇	ADP
cana-1649	223	13	≤	≤	NUM
cana-1649	223	14	1	1	NUM
cana-1649	223	15	.	.	PUNCT
cana-1649	224	1	then	then	ADV
cana-1649	224	2	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	PROPN
cana-1649	224	3	𝛿	𝛿	PROPN
cana-1649	224	4	(	(	PUNCT
cana-1649	224	5	𝑧),𝑧	𝑧),𝑧	PROPN
cana-1649	224	6	)	)	PUNCT
cana-1649	224	7	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	224	8	𝜇	𝜇	ADP
cana-1649	224	9	(	(	PUNCT
cana-1649	224	10	𝑧	𝑧	NOUN
cana-1649	224	11	)	)	PUNCT
cana-1649	224	12	≺	≺	NOUN
cana-1649	224	13	1	1	NUM
cana-1649	224	14	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	224	15	𝜇	𝜇	X
cana-1649	224	16	(	(	PUNCT
cana-1649	224	17	𝑧	𝑧	NOUN
cana-1649	224	18	)	)	PUNCT
cana-1649	224	19	(	(	PUNCT
cana-1649	224	20	𝑧	𝑧	PROPN
cana-1649	224	21	∈	∈	PROPN
cana-1649	224	22	δ	δ	PROPN
cana-1649	224	23	)	)	PUNCT
cana-1649	224	24	.	.	PUNCT
cana-1649	225	1	proof	proof	NOUN
cana-1649	225	2	.	.	PUNCT
cana-1649	226	1	using	use	VERB
cana-1649	226	2	theorem	theorem	ADJ
cana-1649	226	3	2.2	2.2	NUM
cana-1649	226	4	and	and	CCONJ
cana-1649	226	5	lemma	lemma	PROPN
cana-1649	226	6	1.3	1.3	NUM
cana-1649	226	7	,	,	PUNCT
cana-1649	226	8	we	we	PRON
cana-1649	226	9	have	have	VERB
cana-1649	226	10	𝑙𝑜𝑔	𝑙𝑜𝑔	ADJ
cana-1649	226	11	[	[	PUNCT
cana-1649	226	12	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	PROPN
cana-1649	226	13	𝛿	𝛿	ADJ
cana-1649	226	14	(	(	PUNCT
cana-1649	226	15	𝑧	𝑧	NOUN
cana-1649	226	16	)	)	PUNCT
cana-1649	226	17	,	,	PUNCT
cana-1649	226	18	𝑧	𝑧	NOUN
cana-1649	226	19	)	)	PUNCT
cana-1649	226	20	𝒥0,𝐵	𝒥0,𝐵	ADV
cana-1649	226	21	𝜇	𝜇	ADP
cana-1649	226	22	(	(	PUNCT
cana-1649	226	23	𝑧	𝑧	NOUN
cana-1649	226	24	)	)	PUNCT
cana-1649	226	25	]	]	PUNCT
cana-1649	226	26	1	1	NUM
cana-1649	226	27	𝜇	𝜇	ADP
cana-1649	226	28	=	=	X
cana-1649	226	29	𝑙𝑜𝑔	𝑙𝑜𝑔	PROPN
cana-1649	227	1	[	[	PUNCT
cana-1649	227	2	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	PROPN
cana-1649	227	3	𝛿	𝛿	ADJ
cana-1649	227	4	(	(	PUNCT
cana-1649	227	5	𝑧	𝑧	NOUN
cana-1649	227	6	)	)	PUNCT
cana-1649	227	7	,	,	PUNCT
cana-1649	227	8	𝑧	𝑧	NOUN
cana-1649	227	9	)	)	PUNCT
cana-1649	227	10	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	227	11	𝜇−𝛿	𝜇−𝛿	PROPN
cana-1649	227	12	(	(	PUNCT
cana-1649	227	13	𝑧)𝒥0,𝐵	𝑧)𝒥0,𝐵	NUM
cana-1649	227	14	𝛿	𝛿	ADJ
cana-1649	227	15	(	(	PUNCT
cana-1649	227	16	𝑧	𝑧	PROPN
cana-1649	227	17	)	)	PUNCT
cana-1649	227	18	]	]	PUNCT
cana-1649	227	19	1	1	NUM
cana-1649	227	20	𝜇	𝜇	X
cana-1649	227	21	=	=	X
cana-1649	227	22	𝑙𝑜𝑔	𝑙𝑜𝑔	X
cana-1649	227	23	[	[	PUNCT
cana-1649	227	24	1	1	NUM
cana-1649	227	25	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	227	26	𝜇−𝛿	𝜇−𝛿	PROPN
cana-1649	227	27	(	(	PUNCT
cana-1649	227	28	𝑧	𝑧	PROPN
cana-1649	227	29	)	)	PUNCT
cana-1649	227	30	]	]	PUNCT
cana-1649	227	31	1	1	NUM
cana-1649	227	32	𝜇	𝜇	ADP
cana-1649	227	33	+	+	X
cana-1649	227	34	𝑙𝑜𝑔	𝑙𝑜𝑔	NOUN
cana-1649	227	35	[	[	PUNCT
cana-1649	227	36	𝒫𝑛(𝒥0,𝐵	𝒫𝑛(𝒥0,𝐵	PROPN
cana-1649	227	37	𝛿	𝛿	ADJ
cana-1649	227	38	(	(	PUNCT
cana-1649	227	39	𝑧	𝑧	NOUN
cana-1649	227	40	)	)	PUNCT
cana-1649	227	41	,	,	PUNCT
cana-1649	227	42	𝑧	𝑧	NOUN
cana-1649	227	43	)	)	PUNCT
cana-1649	227	44	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	227	45	𝛿	𝛿	ADJ
cana-1649	227	46	(	(	PUNCT
cana-1649	227	47	𝑧	𝑧	PROPN
cana-1649	227	48	)	)	PUNCT
cana-1649	227	49	]	]	PUNCT
cana-1649	227	50	1	1	NUM
cana-1649	227	51	𝜇	𝜇	X
cana-1649	227	52	=	=	PUNCT
cana-1649	227	53	𝑙𝑜𝑔[(𝐵𝜔1(𝑧	𝑙𝑜𝑔[(𝐵𝜔1(𝑧	PROPN
cana-1649	227	54	)	)	PUNCT
cana-1649	227	55	+	+	CCONJ
cana-1649	227	56	1	1	X
cana-1649	227	57	)	)	PUNCT
cana-1649	227	58	𝜇−𝛿	𝜇−𝛿	PROPN
cana-1649	227	59	]	]	PUNCT
cana-1649	227	60	1	1	NUM
cana-1649	227	61	𝜇	𝜇	ADP
cana-1649	227	62	+	+	X
cana-1649	227	63	𝑙𝑜𝑔[(𝐵𝜔2(𝑧	𝑙𝑜𝑔[(𝐵𝜔2(𝑧	NOUN
cana-1649	227	64	)	)	PUNCT
cana-1649	227	65	+	+	CCONJ
cana-1649	227	66	1	1	X
cana-1649	227	67	)	)	PUNCT
cana-1649	227	68	𝛿	𝛿	ADJ
cana-1649	227	69	]	]	X
cana-1649	227	70	1	1	NUM
cana-1649	227	71	𝜇	𝜇	ADP
cana-1649	227	72	≺	≺	NOUN
cana-1649	227	73	𝑙𝑜𝑔	𝑙𝑜𝑔	X
cana-1649	227	74	[	[	PUNCT
cana-1649	227	75	1	1	NUM
cana-1649	227	76	𝒥0,𝐵	𝒥0,𝐵	PROPN
cana-1649	227	77	𝜇	𝜇	X
cana-1649	227	78	(	(	PUNCT
cana-1649	227	79	𝑧	𝑧	NOUN
cana-1649	227	80	)	)	PUNCT
cana-1649	227	81	]	]	PUNCT
cana-1649	227	82	1	1	NUM
cana-1649	227	83	𝜇	𝜇	ADP
cana-1649	227	84	,	,	PUNCT
cana-1649	227	85	for	for	ADP
cana-1649	227	86	some	some	DET
cana-1649	227	87	analytic	analytic	ADJ
cana-1649	227	88	functions	function	NOUN
cana-1649	227	89	|𝜔1(𝑧)|	|𝜔1(𝑧)|	NOUN
cana-1649	227	90	≤	≤	NUM
cana-1649	227	91	|𝑧|	|𝑧|	PROPN
cana-1649	227	92	and	and	CCONJ
cana-1649	227	93	|𝜔2(𝑧)|	|𝜔2(𝑧)|	PUNCT
cana-1649	227	94	≤	≤	NUM
cana-1649	227	95	|𝑧|	|𝑧|	PROPN
cana-1649	227	96	in	in	ADP
cana-1649	227	97	δ	δ	PROPN
cana-1649	227	98	.	.	PUNCT
cana-1649	228	1	hence	hence	ADV
cana-1649	228	2	the	the	DET
cana-1649	228	3	proof	proof	NOUN
cana-1649	228	4	.	.	PUNCT
cana-1649	229	1	acknowledgements	acknowledgement	NOUN
cana-1649	229	2	.	.	PUNCT
cana-1649	230	1	the	the	DET
cana-1649	230	2	authors	author	NOUN
cana-1649	230	3	are	be	AUX
cana-1649	230	4	thankful	thankful	ADJ
cana-1649	230	5	to	to	ADP
cana-1649	230	6	the	the	DET
cana-1649	230	7	referees	referee	NOUN
cana-1649	230	8	for	for	ADP
cana-1649	230	9	their	their	PRON
cana-1649	230	10	insightful	insightful	ADJ
cana-1649	230	11	suggestions	suggestion	NOUN
cana-1649	230	12	.	.	PUNCT
cana-1649	231	1	references	reference	NOUN
cana-1649	231	2	[	[	X
cana-1649	231	3	1	1	X
cana-1649	231	4	]	]	PUNCT
cana-1649	231	5	s.	s.	PROPN
cana-1649	231	6	chakraborty	chakraborty	PROPN
cana-1649	231	7	and	and	CCONJ
cana-1649	231	8	a.	a.	NOUN
cana-1649	231	9	vasudevarao	vasudevarao	PROPN
cana-1649	231	10	,	,	PUNCT
cana-1649	231	11	on	on	ADP
cana-1649	231	12	stable	stable	ADJ
cana-1649	231	13	functions	function	NOUN
cana-1649	231	14	,	,	PUNCT
cana-1649	231	15	comput	comput	NOUN
cana-1649	231	16	.	.	PUNCT
cana-1649	232	1	methods	method	NOUN
cana-1649	232	2	funct	funct	VERB
cana-1649	232	3	.	.	PUNCT
cana-1649	233	1	theory	theory	NOUN
cana-1649	233	2	18	18	NUM
cana-1649	233	3	(	(	PUNCT
cana-1649	233	4	4	4	NUM
cana-1649	233	5	)	)	PUNCT
cana-1649	233	6	,	,	PUNCT
cana-1649	233	7	(	(	PUNCT
cana-1649	233	8	2018	2018	NUM
cana-1649	233	9	)	)	PUNCT
cana-1649	233	10	,	,	PUNCT
cana-1649	233	11	677	677	NUM
cana-1649	233	12	-	-	SYM
cana-1649	233	13	688	688	NUM
cana-1649	233	14	.	.	PUNCT
cana-1649	234	1	[	[	X
cana-1649	234	2	2	2	NUM
cana-1649	234	3	]	]	PUNCT
cana-1649	234	4	k.	k.	PROPN
cana-1649	234	5	chandrasekaran	chandrasekaran	PROPN
cana-1649	234	6	,	,	PUNCT
cana-1649	234	7	d.	d.	PROPN
cana-1649	234	8	j.	j.	PROPN
cana-1649	234	9	prabhakaran	prabhakaran	PROPN
cana-1649	234	10	and	and	CCONJ
cana-1649	234	11	p.	p.	PROPN
cana-1649	234	12	sangal	sangal	ADJ
cana-1649	234	13	,	,	PUNCT
cana-1649	234	14	stable	stable	ADJ
cana-1649	234	15	functions	function	NOUN
cana-1649	234	16	of	of	ADP
cana-1649	234	17	janowski	janowski	ADJ
cana-1649	234	18	type	type	NOUN
cana-1649	234	19	,	,	PUNCT
cana-1649	234	20	j.	j.	PROPN
cana-1649	234	21	math	math	PROPN
cana-1649	234	22	.	.	PUNCT
cana-1649	235	1	inequal	inequal	ADJ
cana-1649	235	2	.	.	PUNCT
cana-1649	236	1	15	15	NUM
cana-1649	236	2	,	,	PUNCT
cana-1649	236	3	(	(	PUNCT
cana-1649	236	4	2021	2021	NUM
cana-1649	236	5	)	)	PUNCT
cana-1649	236	6	,	,	PUNCT
cana-1649	236	7	969	969	NUM
cana-1649	236	8	-	-	SYM
cana-1649	236	9	979	979	NUM
cana-1649	236	10	.	.	PUNCT
cana-1649	237	1	[	[	X
cana-1649	237	2	3	3	X
cana-1649	237	3	]	]	PUNCT
cana-1649	237	4	m.	m.	NOUN
cana-1649	237	5	p.	p.	NOUN
cana-1649	237	6	jeyaraman	jeyaraman	PROPN
cana-1649	237	7	and	and	CCONJ
cana-1649	237	8	t.	t.	PROPN
cana-1649	237	9	g.	g.	PROPN
cana-1649	237	10	bhaskar	bhaskar	PROPN
cana-1649	237	11	,	,	PUNCT
cana-1649	237	12	some	some	PRON
cana-1649	237	13	results	result	NOUN
cana-1649	237	14	on	on	ADP
cana-1649	237	15	generalized	generalize	VERB
cana-1649	237	16	cesàro	cesàro	PROPN
cana-1649	237	17	stable	stable	ADJ
cana-1649	237	18	of	of	ADP
cana-1649	237	19	janowski	janowski	PROPN
cana-1649	237	20	function	function	NOUN
cana-1649	237	21	,	,	PUNCT
cana-1649	237	22	afr	afr	PROPN
cana-1649	237	23	.	.	PUNCT
cana-1649	238	1	mat	mat	PROPN
cana-1649	238	2	.	.	PROPN
cana-1649	238	3	35	35	NUM
cana-1649	238	4	(	(	PUNCT
cana-1649	238	5	39	39	NUM
cana-1649	238	6	)	)	PUNCT
cana-1649	238	7	,	,	PUNCT
cana-1649	238	8	(	(	PUNCT
cana-1649	238	9	2024	2024	NUM
cana-1649	238	10	)	)	PUNCT
cana-1649	238	11	,	,	PUNCT
cana-1649	238	12	1	1	NUM
cana-1649	238	13	-	-	SYM
cana-1649	238	14	9	9	NUM
cana-1649	238	15	.	.	PUNCT
cana-1649	238	16	communications	communication	NOUN
cana-1649	238	17	on	on	ADP
cana-1649	238	18	applied	apply	VERB
cana-1649	238	19	nonlinear	nonlinear	ADJ
cana-1649	238	20	analysis	analysis	NOUN
cana-1649	238	21	issn	issn	NOUN
cana-1649	238	22	:	:	PUNCT
cana-1649	238	23	1074	1074	NUM
cana-1649	238	24	-	-	PUNCT
cana-1649	238	25	133x	133x	NUM
cana-1649	238	26	vol	vol	NOUN
cana-1649	238	27	32	32	NUM
cana-1649	238	28	no	no	NOUN
cana-1649	238	29	.	.	NOUN
cana-1649	238	30	1	1	NUM
cana-1649	238	31	(	(	PUNCT
cana-1649	238	32	2025	2025	NUM
cana-1649	238	33	)	)	PUNCT
cana-1649	238	34	302	302	NUM
cana-1649	238	35	https://internationalpubls.com	https://internationalpubls.com	X
cana-1649	239	1	[	[	X
cana-1649	239	2	4	4	X
cana-1649	239	3	]	]	PUNCT
cana-1649	239	4	s.	s.	PROPN
cana-1649	239	5	koumandos	koumandos	PROPN
cana-1649	239	6	and	and	CCONJ
cana-1649	239	7	s.	s.	PROPN
cana-1649	239	8	ruscheweyh	ruscheweyh	PROPN
cana-1649	239	9	,	,	PUNCT
cana-1649	239	10	on	on	ADP
cana-1649	239	11	a	a	DET
cana-1649	239	12	conjecture	conjecture	NOUN
cana-1649	239	13	for	for	ADP
cana-1649	239	14	trigonometric	trigonometric	ADJ
cana-1649	239	15	sums	sum	NOUN
cana-1649	239	16	and	and	CCONJ
cana-1649	239	17	starlike	starlike	NOUN
cana-1649	239	18	functions	function	NOUN
cana-1649	239	19	,	,	PUNCT
cana-1649	239	20	j.	j.	PROPN
cana-1649	239	21	approx	approx	PROPN
cana-1649	239	22	.	.	PUNCT
cana-1649	240	1	theory	theory	NOUN
cana-1649	240	2	149	149	NUM
cana-1649	240	3	(	(	PUNCT
cana-1649	240	4	1	1	NUM
cana-1649	240	5	)	)	PUNCT
cana-1649	240	6	,	,	PUNCT
cana-1649	240	7	(	(	PUNCT
cana-1649	240	8	2007	2007	NUM
cana-1649	240	9	)	)	PUNCT
cana-1649	240	10	,	,	PUNCT
cana-1649	240	11	42	42	NUM
cana-1649	240	12	-	-	SYM
cana-1649	240	13	58	58	NUM
cana-1649	240	14	.	.	PUNCT
cana-1649	241	1	[	[	X
cana-1649	241	2	5	5	X
cana-1649	241	3	]	]	PUNCT
cana-1649	241	4	s.	s.	PROPN
cana-1649	241	5	r.	r.	PROPN
cana-1649	241	6	mondal	mondal	PROPN
cana-1649	241	7	,	,	PUNCT
cana-1649	241	8	k.	k.	PROPN
cana-1649	241	9	s.	s.	PROPN
cana-1649	241	10	nisar	nisar	PROPN
cana-1649	241	11	and	and	CCONJ
cana-1649	241	12	t.	t.	PROPN
cana-1649	241	13	abdeljawad	abdeljawad	NOUN
cana-1649	241	14	,	,	PUNCT
cana-1649	241	15	some	some	DET
cana-1649	241	16	subordination	subordination	NOUN
cana-1649	241	17	involving	involve	VERB
cana-1649	241	18	polynomials	polynomial	NOUN
cana-1649	241	19	induced	induce	VERB
cana-1649	241	20	by	by	ADP
cana-1649	241	21	lower	low	ADJ
cana-1649	241	22	triangular	triangular	NOUN
cana-1649	241	23	matrices	matrix	NOUN
cana-1649	241	24	,	,	PUNCT
cana-1649	241	25	adv	adv	PROPN
cana-1649	241	26	.	.	PUNCT
cana-1649	241	27	differ	differ	VERB
cana-1649	241	28	.	.	PUNCT
cana-1649	242	1	equ	equ	PROPN
cana-1649	242	2	.	.	PROPN
cana-1649	242	3	,	,	PUNCT
cana-1649	242	4	springer	springer	NOUN
cana-1649	242	5	,	,	PUNCT
cana-1649	242	6	538	538	NUM
cana-1649	242	7	,	,	PUNCT
cana-1649	242	8	(	(	PUNCT
cana-1649	242	9	2020	2020	NUM
cana-1649	242	10	)	)	PUNCT
cana-1649	242	11	.	.	PUNCT
cana-1649	243	1	[	[	X
cana-1649	243	2	6	6	X
cana-1649	243	3	]	]	PUNCT
cana-1649	243	4	s.	s.	PROPN
cana-1649	243	5	r.	r.	PROPN
cana-1649	243	6	mondal	mondal	PROPN
cana-1649	243	7	and	and	CCONJ
cana-1649	243	8	a.	a.	NOUN
cana-1649	243	9	swaminathan	swaminathan	PROPN
cana-1649	243	10	,	,	PUNCT
cana-1649	243	11	stable	stable	ADJ
cana-1649	243	12	functions	function	NOUN
cana-1649	243	13	and	and	CCONJ
cana-1649	243	14	extension	extension	NOUN
cana-1649	243	15	of	of	ADP
cana-1649	243	16	vietoris	vietoris	NOUN
cana-1649	243	17	’	'	PUNCT
cana-1649	243	18	theorem	theorem	PROPN
cana-1649	243	19	,	,	PUNCT
cana-1649	243	20	results	result	VERB
cana-1649	243	21	math	math	NOUN
cana-1649	243	22	.	.	PUNCT
cana-1649	244	1	62	62	NUM
cana-1649	244	2	(	(	PUNCT
cana-1649	244	3	1	1	NUM
cana-1649	244	4	-	-	SYM
cana-1649	244	5	2	2	NUM
cana-1649	244	6	)	)	PUNCT
cana-1649	244	7	,	,	PUNCT
cana-1649	244	8	(	(	PUNCT
cana-1649	244	9	2012	2012	NUM
cana-1649	244	10	)	)	PUNCT
cana-1649	244	11	,	,	PUNCT
cana-1649	244	12	33	33	NUM
cana-1649	244	13	-	-	SYM
cana-1649	244	14	51	51	NUM
cana-1649	244	15	.	.	PUNCT
cana-1649	245	1	[	[	X
cana-1649	245	2	7	7	X
cana-1649	245	3	]	]	X
cana-1649	245	4	s.	s.	PROPN
cana-1649	245	5	ruscheweyh	ruscheweyh	PROPN
cana-1649	245	6	,	,	PUNCT
cana-1649	245	7	linear	linear	PROPN
cana-1649	245	8	operators	operator	NOUN
cana-1649	245	9	between	between	ADP
cana-1649	245	10	classes	class	NOUN
cana-1649	245	11	of	of	ADP
cana-1649	245	12	prestarlike	prestarlike	ADJ
cana-1649	245	13	functions	function	NOUN
cana-1649	245	14	,	,	PUNCT
cana-1649	245	15	comment	comment	NOUN
cana-1649	245	16	.	.	PUNCT
cana-1649	246	1	math	math	NOUN
cana-1649	246	2	.	.	PUNCT
cana-1649	247	1	helv	helv	PROPN
cana-1649	247	2	.	.	PROPN
cana-1649	248	1	52	52	NUM
cana-1649	248	2	(	(	PUNCT
cana-1649	248	3	4	4	NUM
cana-1649	248	4	)	)	PUNCT
cana-1649	248	5	,	,	PUNCT
cana-1649	248	6	(	(	PUNCT
cana-1649	248	7	1977	1977	NUM
cana-1649	248	8	)	)	PUNCT
cana-1649	248	9	,	,	PUNCT
cana-1649	248	10	497	497	NUM
cana-1649	248	11	-	-	SYM
cana-1649	248	12	509	509	NUM
cana-1649	248	13	.	.	PUNCT
cana-1649	249	1	[	[	X
cana-1649	249	2	8	8	NUM
cana-1649	249	3	]	]	PUNCT
cana-1649	249	4	s.	s.	PROPN
cana-1649	249	5	ruscheweyh	ruscheweyh	PROPN
cana-1649	249	6	,	,	PUNCT
cana-1649	249	7	on	on	ADP
cana-1649	249	8	the	the	DET
cana-1649	249	9	kakeya	kakeya	NOUN
cana-1649	249	10	-	-	PUNCT
cana-1649	249	11	enestrom	enestrom	NOUN
cana-1649	249	12	theorem	theorem	NOUN
cana-1649	249	13	and	and	CCONJ
cana-1649	249	14	gegenbauer	gegenbauer	NOUN
cana-1649	249	15	polynomial	polynomial	ADJ
cana-1649	249	16	sums	sum	NOUN
cana-1649	249	17	,	,	PUNCT
cana-1649	249	18	siam	siam	NOUN
cana-1649	249	19	,	,	PUNCT
cana-1649	249	20	oest	oest	NOUN
cana-1649	249	21	.	.	PUNCT
cana-1649	250	1	j.	j.	PROPN
cana-1649	250	2	math	math	PROPN
cana-1649	250	3	.	.	PUNCT
cana-1649	251	1	anal	anal	ADJ
cana-1649	251	2	.	.	PUNCT
cana-1649	252	1	9	9	NUM
cana-1649	252	2	(	(	PUNCT
cana-1649	252	3	4	4	NUM
cana-1649	252	4	)	)	PUNCT
cana-1649	252	5	,	,	PUNCT
cana-1649	252	6	(	(	PUNCT
cana-1649	252	7	1978	1978	NUM
cana-1649	252	8	)	)	PUNCT
cana-1649	252	9	,	,	PUNCT
cana-1649	252	10	682	682	NUM
cana-1649	252	11	-	-	SYM
cana-1649	252	12	686	686	NUM
cana-1649	252	13	.	.	PUNCT
cana-1649	253	1	[	[	X
cana-1649	253	2	9	9	NUM
cana-1649	253	3	]	]	PUNCT
cana-1649	253	4	s.	s.	PROPN
cana-1649	253	5	ruscheweyh	ruscheweyh	PROPN
cana-1649	253	6	and	and	CCONJ
cana-1649	253	7	l.	l.	PROPN
cana-1649	253	8	salinas	salinas	PROPN
cana-1649	253	9	,	,	PUNCT
cana-1649	253	10	on	on	ADP
cana-1649	253	11	starlike	starlike	NOUN
cana-1649	253	12	functions	function	NOUN
cana-1649	253	13	of	of	ADP
cana-1649	253	14	order	order	NOUN
cana-1649	253	15	𝜆	𝜆	PRON
cana-1649	253	16	∈	∈	PROPN
cana-1649	253	17	[	[	PUNCT
cana-1649	253	18	1	1	NUM
cana-1649	253	19	2	2	NUM
cana-1649	253	20	,	,	PUNCT
cana-1649	253	21	1	1	NUM
cana-1649	253	22	)	)	PUNCT
cana-1649	253	23	,	,	PUNCT
cana-1649	253	24	ann	ann	PROPN
cana-1649	253	25	.	.	PROPN
cana-1649	253	26	univ	univ	PROPN
cana-1649	253	27	.	.	PUNCT
cana-1649	254	1	mariae	mariae	PROPN
cana-1649	254	2	curie	curie	PROPN
cana-1649	254	3	-	-	PUNCT
cana-1649	254	4	sklodowska	sklodowska	PROPN
cana-1649	254	5	,	,	PUNCT
cana-1649	254	6	sec	sec	PROPN
cana-1649	254	7	.	.	PROPN
cana-1649	255	1	a	a	DET
cana-1649	255	2	(	(	PUNCT
cana-1649	255	3	54	54	NUM
cana-1649	255	4	)	)	PUNCT
cana-1649	255	5	,	,	PUNCT
cana-1649	255	6	(	(	PUNCT
cana-1649	255	7	2000	2000	NUM
cana-1649	255	8	)	)	PUNCT
cana-1649	255	9	,	,	PUNCT
cana-1649	255	10	117	117	NUM
cana-1649	255	11	-	-	SYM
cana-1649	255	12	123	123	NUM
cana-1649	255	13	.	.	PUNCT
cana-1649	256	1	[	[	X
cana-1649	256	2	10	10	NUM
cana-1649	256	3	]	]	X
cana-1649	256	4	s.	s.	PROPN
cana-1649	256	5	ruscheweyh	ruscheweyh	PROPN
cana-1649	256	6	and	and	CCONJ
cana-1649	256	7	l.	l.	PROPN
cana-1649	256	8	salinas	salinas	PROPN
cana-1649	256	9	,	,	PUNCT
cana-1649	256	10	stable	stable	ADJ
cana-1649	256	11	functions	function	NOUN
cana-1649	256	12	and	and	CCONJ
cana-1649	256	13	vietoris	vietoris	NOUN
cana-1649	256	14	’	'	PUNCT
cana-1649	256	15	theorem	theorem	PROPN
cana-1649	256	16	,	,	PUNCT
cana-1649	256	17	j.	j.	PROPN
cana-1649	256	18	math	math	PROPN
cana-1649	256	19	.	.	PUNCT
cana-1649	257	1	anal	anal	PROPN
cana-1649	257	2	.	.	PUNCT
cana-1649	258	1	appl	appl	PROPN
cana-1649	258	2	.	.	PROPN
cana-1649	259	1	291	291	NUM
cana-1649	259	2	(	(	PUNCT
cana-1649	259	3	2	2	NUM
cana-1649	259	4	)	)	PUNCT
cana-1649	259	5	,	,	PUNCT
cana-1649	259	6	(	(	PUNCT
cana-1649	259	7	2004	2004	NUM
cana-1649	259	8	)	)	PUNCT
cana-1649	259	9	,	,	PUNCT
cana-1649	259	10	596604	596604	NUM
cana-1649	259	11	.	.	PUNCT
cana-1649	260	1	[	[	X
cana-1649	260	2	11	11	NUM
cana-1649	260	3	]	]	PUNCT
cana-1649	260	4	p.	p.	NOUN
cana-1649	260	5	sangal	sangal	PROPN
cana-1649	260	6	and	and	CCONJ
cana-1649	260	7	a.	a.	NOUN
cana-1649	260	8	swaminathan	swaminathan	ADV
cana-1649	260	9	,	,	PUNCT
cana-1649	260	10	on	on	ADP
cana-1649	260	11	generalised	generalise	VERB
cana-1649	260	12	cesàro	cesàro	PROPN
cana-1649	260	13	stable	stable	ADJ
cana-1649	260	14	functions	function	NOUN
cana-1649	260	15	,	,	PUNCT
cana-1649	260	16	math	math	NOUN
cana-1649	260	17	.	.	PUNCT
cana-1649	261	1	inequal	inequal	PROPN
cana-1649	261	2	.	.	PUNCT
cana-1649	262	1	appl	appl	PROPN
cana-1649	262	2	.	.	PUNCT
cana-1649	263	1	22	22	NUM
cana-1649	263	2	(	(	PUNCT
cana-1649	263	3	1	1	NUM
cana-1649	263	4	)	)	PUNCT
cana-1649	263	5	,	,	PUNCT
cana-1649	263	6	(	(	PUNCT
cana-1649	263	7	2019	2019	NUM
cana-1649	263	8	)	)	PUNCT
cana-1649	263	9	,	,	PUNCT
cana-1649	263	10	227247	227247	NUM
cana-1649	263	11	.	.	PUNCT
cana-1649	264	1	[	[	X
cana-1649	264	2	12	12	NUM
cana-1649	264	3	]	]	X
cana-1649	264	4	l.	l.	PROPN
cana-1649	264	5	vietoris	vietoris	PROPN
cana-1649	264	6	,	,	PUNCT
cana-1649	264	7	uber	uber	PROPN
cana-1649	264	8	das	das	PROPN
cana-1649	264	9	vorzeichen	vorzeichen	PROPN
cana-1649	264	10	geiwisser	geiwisser	NOUN
cana-1649	264	11	trigonometrishcher	trigonometrishcher	PROPN
cana-1649	264	12	summen	summen	PROPN
cana-1649	264	13	,	,	PUNCT
cana-1649	264	14	sitzungsber	sitzungsber	NOUN
cana-1649	264	15	,	,	PUNCT
cana-1649	264	16	oest	o	ADJ
cana-1649	264	17	.	.	PUNCT
cana-1649	265	1	akad	akad	PROPN
cana-1649	265	2	.	.	PUNCT
cana-1649	266	1	wiss	wiss	PROPN
cana-1649	266	2	.	.	PUNCT
cana-1649	267	1	167	167	NUM
cana-1649	267	2	,	,	PUNCT
cana-1649	267	3	(	(	PUNCT
cana-1649	267	4	1958	1958	NUM
cana-1649	267	5	)	)	PUNCT
cana-1649	267	6	,	,	PUNCT
cana-1649	267	7	125	125	NUM
cana-1649	267	8	-	-	SYM
cana-1649	267	9	135	135	NUM
cana-1649	267	10	.	.	PUNCT