id	sid	tid	token	lemma	pos
cana-5236	1	1	communications	communication	NOUN
cana-5236	1	2	on	on	ADP
cana-5236	1	3	applied	apply	VERB
cana-5236	1	4	nonlinear	nonlinear	ADJ
cana-5236	1	5	analysis	analysis	NOUN
cana-5236	1	6	issn	issn	NOUN
cana-5236	1	7	:	:	PUNCT
cana-5236	1	8	1074	1074	NUM
cana-5236	1	9	-	-	PUNCT
cana-5236	1	10	133x	133x	NUM
cana-5236	1	11	vol	vol	VERB
cana-5236	1	12	32	32	NUM
cana-5236	1	13	no	no	NOUN
cana-5236	1	14	.	.	PUNCT
cana-5236	2	1	10s	10	NOUN
cana-5236	2	2	(	(	PUNCT
cana-5236	2	3	2025	2025	NUM
cana-5236	2	4	)	)	PUNCT
cana-5236	2	5	1338	1338	NUM
cana-5236	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5236	2	7	on	on	ADP
cana-5236	2	8	class	class	NOUN
cana-5236	2	9	of	of	ADP
cana-5236	2	10	analytic	analytic	ADJ
cana-5236	2	11	function	function	NOUN
cana-5236	2	12	defined	define	VERB
cana-5236	2	13	by	by	ADP
cana-5236	2	14	generalized	generalized	ADJ
cana-5236	2	15	ruscheweyh	ruscheweyh	NOUN
cana-5236	2	16	derivative	derivative	ADJ
cana-5236	2	17	rashmi	rashmi	PROPN
cana-5236	2	18	b	b	PROPN
cana-5236	2	19	t.*and	t.*and	PROPN
cana-5236	2	20	dileep	dileep	PROPN
cana-5236	2	21	l.	l.	PROPN
cana-5236	2	22	*	*	PROPN
cana-5236	2	23	*	*	PUNCT
cana-5236	2	24	*	*	PUNCT
cana-5236	2	25	adichunchanagiri	adichunchanagiri	PROPN
cana-5236	2	26	institute	institute	PROPN
cana-5236	2	27	of	of	ADP
cana-5236	2	28	technology	technology	PROPN
cana-5236	2	29	,	,	PUNCT
cana-5236	2	30	chikkamagaluru	chikkamagaluru	NOUN
cana-5236	2	31	,	,	PUNCT
cana-5236	2	32	india-577101	india-577101	ADJ
cana-5236	2	33	*	*	ADJ
cana-5236	2	34	*	*	PROPN
cana-5236	2	35	vidyavardhaka	vidyavardhaka	NOUN
cana-5236	2	36	college	college	NOUN
cana-5236	2	37	of	of	ADP
cana-5236	2	38	engineering	engineering	NOUN
cana-5236	2	39	,	,	PUNCT
cana-5236	2	40	mysuru	mysuru	PROPN
cana-5236	2	41	,	,	PUNCT
cana-5236	2	42	india-570	india-570	NOUN
cana-5236	2	43	002	002	NUM
cana-5236	2	44	visvesvaraya	visvesvaraya	ADP
cana-5236	2	45	technological	technological	ADJ
cana-5236	2	46	university	university	NOUN
cana-5236	2	47	,	,	PUNCT
cana-5236	2	48	belagavi	belagavi	VERB
cana-5236	2	49	article	article	NOUN
cana-5236	2	50	history	history	NOUN
cana-5236	2	51	:	:	PUNCT
cana-5236	2	52	received	receive	VERB
cana-5236	2	53	:	:	PUNCT
cana-5236	2	54	12	12	NUM
cana-5236	2	55	-	-	SYM
cana-5236	2	56	01	01	NUM
cana-5236	2	57	-	-	PUNCT
cana-5236	2	58	2025	2025	NUM
cana-5236	2	59	revised	revise	VERB
cana-5236	2	60	:	:	PUNCT
cana-5236	2	61	15	15	NUM
cana-5236	2	62	-	-	NUM
cana-5236	2	63	02	02	NUM
cana-5236	2	64	-	-	PUNCT
cana-5236	2	65	2025	2025	NUM
cana-5236	2	66	accepted	accept	VERB
cana-5236	2	67	:	:	PUNCT
cana-5236	2	68	01	01	NUM
cana-5236	2	69	-	-	SYM
cana-5236	2	70	03	03	NUM
cana-5236	2	71	-	-	PUNCT
cana-5236	2	72	2025	2025	NUM
cana-5236	2	73	abstract	abstract	NOUN
cana-5236	2	74	:	:	PUNCT
cana-5236	2	75	the	the	DET
cana-5236	2	76	aim	aim	NOUN
cana-5236	2	77	of	of	ADP
cana-5236	2	78	this	this	DET
cana-5236	2	79	paper	paper	NOUN
cana-5236	2	80	is	be	AUX
cana-5236	2	81	to	to	PART
cana-5236	2	82	introduce	introduce	VERB
cana-5236	2	83	a	a	DET
cana-5236	2	84	class	class	NOUN
cana-5236	2	85	of	of	ADP
cana-5236	2	86	analytic	analytic	ADJ
cana-5236	2	87	functions	function	NOUN
cana-5236	2	88	defined	define	VERB
cana-5236	2	89	by	by	ADP
cana-5236	2	90	using	use	VERB
cana-5236	2	91	generalized	generalized	ADJ
cana-5236	2	92	ruscheweyh	ruscheweyh	NOUN
cana-5236	2	93	derivative	derivative	ADJ
cana-5236	2	94	.	.	PUNCT
cana-5236	3	1	the	the	DET
cana-5236	3	2	coefficient	coefficient	NOUN
cana-5236	3	3	bound	bind	VERB
cana-5236	3	4	,	,	PUNCT
cana-5236	3	5	inclusion	inclusion	NOUN
cana-5236	3	6	result	result	NOUN
cana-5236	3	7	and	and	CCONJ
cana-5236	3	8	a	a	DET
cana-5236	3	9	radius	radius	NOUN
cana-5236	3	10	problem	problem	NOUN
cana-5236	3	11	has	have	AUX
cana-5236	3	12	been	be	AUX
cana-5236	3	13	discussed	discuss	VERB
cana-5236	3	14	in	in	ADP
cana-5236	3	15	this	this	DET
cana-5236	3	16	paper	paper	NOUN
cana-5236	3	17	.	.	PUNCT
cana-5236	4	1	keywords	keyword	NOUN
cana-5236	4	2	:	:	PUNCT
cana-5236	4	3	univalent	univalent	ADJ
cana-5236	4	4	functions	function	NOUN
cana-5236	4	5	,	,	PUNCT
cana-5236	4	6	analytic	analytic	ADJ
cana-5236	4	7	function	function	NOUN
cana-5236	4	8	,	,	PUNCT
cana-5236	4	9	generalized	generalize	VERB
cana-5236	4	10	ruscheweyh	ruscheweyh	NOUN
cana-5236	4	11	operator	operator	NOUN
cana-5236	4	12	,	,	PUNCT
cana-5236	4	13	coefficient	coefficient	NOUN
cana-5236	4	14	inequalities	inequality	NOUN
cana-5236	4	15	,	,	PUNCT
cana-5236	4	16	convex	convex	NOUN
cana-5236	4	17	domain	domain	NOUN
cana-5236	4	18	.	.	PUNCT
cana-5236	5	1	ams	am	NOUN
cana-5236	5	2	classification	classification	NOUN
cana-5236	5	3	:	:	PUNCT
cana-5236	5	4	primary	primary	ADJ
cana-5236	5	5	30c45	30c45	NUM
cana-5236	5	6	;	;	PUNCT
cana-5236	5	7	secondary	secondary	ADJ
cana-5236	5	8	30c50;30c80	30c50;30c80	PROPN
cana-5236	5	9	conclusion	conclusion	NOUN
cana-5236	5	10	:	:	PUNCT
cana-5236	5	11	here	here	ADV
cana-5236	5	12	,	,	PUNCT
cana-5236	5	13	in	in	ADP
cana-5236	5	14	our	our	PRON
cana-5236	5	15	present	present	ADJ
cana-5236	5	16	investigation	investigation	NOUN
cana-5236	5	17	,	,	PUNCT
cana-5236	5	18	we	we	PRON
cana-5236	5	19	have	have	AUX
cana-5236	5	20	successfully	successfully	ADV
cana-5236	5	21	introduced	introduce	VERB
cana-5236	5	22	a	a	DET
cana-5236	5	23	new	new	ADJ
cana-5236	5	24	subclass	subclass	NOUN
cana-5236	5	25	of	of	ADP
cana-5236	5	26	analytic	analytic	ADJ
cana-5236	5	27	functions	function	NOUN
cana-5236	6	1	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	6	2	𝑚	𝑚	X
cana-5236	6	3	[	[	AUX
cana-5236	6	4	𝐴	𝐴	PROPN
cana-5236	6	5	,	,	PUNCT
cana-5236	6	6	𝐵	𝐵	PROPN
cana-5236	6	7	,	,	PUNCT
cana-5236	6	8	𝛼	𝛼	PROPN
cana-5236	6	9	,	,	PUNCT
cana-5236	6	10	𝑏	𝑏	NOUN
cana-5236	6	11	]	]	PUNCT
cana-5236	6	12	using	use	VERB
cana-5236	6	13	the	the	DET
cana-5236	6	14	generalized	generalized	ADJ
cana-5236	6	15	ruscheweyh	ruscheweyh	NOUN
cana-5236	6	16	derivative	derivative	ADJ
cana-5236	6	17	operator	operator	NOUN
cana-5236	6	18	.	.	PUNCT
cana-5236	7	1	many	many	ADJ
cana-5236	7	2	properties	property	NOUN
cana-5236	7	3	and	and	CCONJ
cana-5236	7	4	characteristics	characteristic	NOUN
cana-5236	7	5	of	of	ADP
cana-5236	7	6	this	this	DET
cana-5236	7	7	newly	newly	ADV
cana-5236	7	8	defined	define	VERB
cana-5236	7	9	function	function	NOUN
cana-5236	7	10	class	class	NOUN
cana-5236	7	11	such	such	ADJ
cana-5236	7	12	as	as	ADP
cana-5236	7	13	coefficient	coefficient	NOUN
cana-5236	7	14	estimates	estimate	NOUN
cana-5236	7	15	,	,	PUNCT
cana-5236	7	16	inclusion	inclusion	NOUN
cana-5236	7	17	bounds	bound	NOUN
cana-5236	7	18	and	and	CCONJ
cana-5236	7	19	radius	radius	NOUN
cana-5236	7	20	problem	problem	NOUN
cana-5236	7	21	have	have	AUX
cana-5236	7	22	been	be	AUX
cana-5236	7	23	studied	study	VERB
cana-5236	7	24	.	.	PUNCT
cana-5236	8	1	1	1	X
cana-5236	8	2	.	.	X
cana-5236	8	3	introduction	introduction	NOUN
cana-5236	8	4	let	let	VERB
cana-5236	8	5	𝒜	𝒜	NOUN
cana-5236	8	6	be	be	AUX
cana-5236	8	7	the	the	DET
cana-5236	8	8	class	class	NOUN
cana-5236	8	9	of	of	ADP
cana-5236	8	10	functions	function	NOUN
cana-5236	8	11	of	of	ADP
cana-5236	8	12	the	the	DET
cana-5236	8	13	form	form	NOUN
cana-5236	8	14	(	(	PUNCT
cana-5236	8	15	1.1	1.1	NUM
cana-5236	8	16	)	)	PUNCT
cana-5236	8	17	f(z)=	f(z)=	NOUN
cana-5236	8	18	z+∑	z+∑	PRON
cana-5236	8	19	𝑎𝑛𝑧𝑛∞	𝑎𝑛𝑧𝑛∞	NOUN
cana-5236	8	20	𝑛=2	𝑛=2	PROPN
cana-5236	8	21	which	which	PRON
cana-5236	8	22	are	be	AUX
cana-5236	8	23	analytic	analytic	ADJ
cana-5236	8	24	in	in	ADP
cana-5236	8	25	the	the	DET
cana-5236	8	26	open	open	ADJ
cana-5236	8	27	unit	unit	NOUN
cana-5236	8	28	disk	disk	NOUN
cana-5236	8	29	𝒰	𝒰	NOUN
cana-5236	8	30	=	=	PUNCT
cana-5236	8	31	{	{	PUNCT
cana-5236	8	32	z	z	NOUN
cana-5236	8	33	:	:	PUNCT
cana-5236	8	34	|z|	|z|	NOUN
cana-5236	8	35	<	<	X
cana-5236	8	36	1	1	NUM
cana-5236	8	37	}	}	PUNCT
cana-5236	8	38	.	.	PUNCT
cana-5236	9	1	if	if	SCONJ
cana-5236	9	2	f	f	PROPN
cana-5236	9	3	and	and	CCONJ
cana-5236	9	4	g	g	PROPN
cana-5236	9	5	are	be	AUX
cana-5236	9	6	analytic	analytic	ADJ
cana-5236	9	7	in	in	ADP
cana-5236	9	8	𝒰	𝒰	PROPN
cana-5236	9	9	,	,	PUNCT
cana-5236	9	10	we	we	PRON
cana-5236	9	11	say	say	VERB
cana-5236	9	12	that	that	SCONJ
cana-5236	9	13	f	f	PROPN
cana-5236	9	14	is	be	AUX
cana-5236	9	15	subordinate	subordinate	ADJ
cana-5236	9	16	to	to	ADP
cana-5236	9	17	g	g	NOUN
cana-5236	9	18	,	,	PUNCT
cana-5236	9	19	written	write	VERB
cana-5236	9	20	f	f	PROPN
cana-5236	9	21	≺	≺	NOUN
cana-5236	9	22	g	g	PROPN
cana-5236	9	23	or	or	CCONJ
cana-5236	9	24	f(z	f(z	NUM
cana-5236	9	25	)	)	PUNCT
cana-5236	9	26	≺	≺	NOUN
cana-5236	9	27	g(z	g(z	PROPN
cana-5236	9	28	)	)	PUNCT
cana-5236	9	29	,	,	PUNCT
cana-5236	9	30	if	if	SCONJ
cana-5236	9	31	there	there	PRON
cana-5236	9	32	exists	exist	VERB
cana-5236	9	33	a	a	DET
cana-5236	9	34	schwarz	schwarz	PROPN
cana-5236	9	35	function	function	NOUN
cana-5236	9	36	𝜔(z	𝜔(z	PROPN
cana-5236	9	37	)	)	PUNCT
cana-5236	9	38	in	in	ADP
cana-5236	9	39	𝒰	𝒰	PROPN
cana-5236	9	40	such	such	ADJ
cana-5236	9	41	that	that	DET
cana-5236	9	42	f(z	f(z	PROPN
cana-5236	9	43	)	)	PUNCT
cana-5236	9	44	=	=	SYM
cana-5236	9	45	g(𝜔	g(𝜔	X
cana-5236	9	46	(	(	PUNCT
cana-5236	9	47	z	z	NOUN
cana-5236	9	48	)	)	PUNCT
cana-5236	9	49	)	)	PUNCT
cana-5236	9	50	.	.	PUNCT
cana-5236	10	1	let	let	VERB
cana-5236	10	2	p[a	p[a	PROPN
cana-5236	10	3	,	,	PUNCT
cana-5236	10	4	b	b	AUX
cana-5236	10	5	]	]	PUNCT
cana-5236	10	6	be	be	AUX
cana-5236	10	7	the	the	DET
cana-5236	10	8	class	class	NOUN
cana-5236	10	9	of	of	ADP
cana-5236	10	10	functions	function	NOUN
cana-5236	10	11	h	h	NOUN
cana-5236	10	12	,	,	PUNCT
cana-5236	10	13	analytic	analytic	ADJ
cana-5236	10	14	in	in	ADP
cana-5236	10	15	𝒰	𝒰	PROPN
cana-5236	10	16	with	with	ADP
cana-5236	10	17	h(0	h(0	PROPN
cana-5236	10	18	)	)	PUNCT
cana-5236	10	19	=	=	SYM
cana-5236	10	20	1	1	NUM
cana-5236	10	21	and	and	CCONJ
cana-5236	10	22	ℎ(𝑧	ℎ(𝑧	PROPN
cana-5236	10	23	)	)	PUNCT
cana-5236	10	24	≺	≺	NOUN
cana-5236	10	25	1+𝐴𝑧	1+𝐴𝑧	NUM
cana-5236	10	26	1+𝐵𝑧	1+𝐵𝑧	NUM
cana-5236	10	27	,	,	PUNCT
cana-5236	11	1	−1	−1	NOUN
cana-5236	11	2	≤	≤	NOUN
cana-5236	11	3	b	b	NOUN
cana-5236	11	4	<	<	X
cana-5236	11	5	a	a	DET
cana-5236	11	6	≤	≤	NUM
cana-5236	11	7	1	1	NUM
cana-5236	11	8	.	.	PUNCT
cana-5236	12	1	this	this	DET
cana-5236	12	2	class	class	NOUN
cana-5236	12	3	was	be	AUX
cana-5236	12	4	introduced	introduce	VERB
cana-5236	12	5	by	by	ADP
cana-5236	12	6	janowski	janowski	NOUN
cana-5236	12	7	[	[	X
cana-5236	12	8	18	18	NUM
cana-5236	12	9	]	]	PUNCT
cana-5236	12	10	.	.	PUNCT
cana-5236	13	1	the	the	DET
cana-5236	13	2	class	class	NOUN
cana-5236	13	3	p	p	PROPN
cana-5236	14	1	[	[	X
cana-5236	14	2	a	a	X
cana-5236	14	3	,	,	PUNCT
cana-5236	14	4	b	b	NOUN
cana-5236	14	5	]	]	PUNCT
cana-5236	14	6	is	be	AUX
cana-5236	14	7	connected	connect	VERB
cana-5236	14	8	with	with	ADP
cana-5236	14	9	the	the	DET
cana-5236	14	10	class	class	NOUN
cana-5236	14	11	p	p	NOUN
cana-5236	14	12	of	of	ADP
cana-5236	14	13	functions	function	NOUN
cana-5236	14	14	with	with	ADP
cana-5236	14	15	positive	positive	ADJ
cana-5236	14	16	real	real	ADJ
cana-5236	14	17	parts	part	NOUN
cana-5236	14	18	by	by	ADP
cana-5236	14	19	the	the	DET
cana-5236	14	20	relation	relation	NOUN
cana-5236	14	21	(	(	PUNCT
cana-5236	14	22	1.2	1.2	NUM
cana-5236	14	23	)	)	PUNCT
cana-5236	14	24	ℎ	ℎ	PROPN
cana-5236	14	25	∈	∈	PROPN
cana-5236	14	26	p[a	p[a	PROPN
cana-5236	14	27	,	,	PUNCT
cana-5236	14	28	b	b	AUX
cana-5236	14	29	]	]	X
cana-5236	14	30	⟺	⟺	X
cana-5236	14	31	(	(	PUNCT
cana-5236	14	32	𝐵−1)ℎ−(𝐴−1	𝐵−1)ℎ−(𝐴−1	NOUN
cana-5236	14	33	)	)	PUNCT
cana-5236	14	34	(	(	PUNCT
cana-5236	14	35	𝐵+1)ℎ−(𝐴+1	𝐵+1)ℎ−(𝐴+1	NOUN
cana-5236	14	36	)	)	PUNCT
cana-5236	14	37	∈	∈	PROPN
cana-5236	14	38	𝑃.	𝑃.	PROPN
cana-5236	14	39	later	later	ADV
cana-5236	14	40	polato	polato	VERB
cana-5236	14	41	�	�	PROPN
cana-5236	14	42	̌	̌	NUM
cana-5236	14	43	�	�	NOUN
cana-5236	14	44	lu	lu	NOUN
cana-5236	15	1	[	[	X
cana-5236	15	2	19	19	NUM
cana-5236	15	3	]	]	PUNCT
cana-5236	15	4	defined	define	VERB
cana-5236	15	5	the	the	DET
cana-5236	15	6	class	class	NOUN
cana-5236	15	7	p[a	p[a	PROPN
cana-5236	15	8	,	,	PUNCT
cana-5236	15	9	b	b	PROPN
cana-5236	15	10	,	,	PUNCT
cana-5236	15	11	α	α	NOUN
cana-5236	15	12	]	]	PUNCT
cana-5236	15	13	as	as	SCONJ
cana-5236	15	14	:	:	PUNCT
cana-5236	15	15	let	let	VERB
cana-5236	15	16	p[a	p[a	PROPN
cana-5236	15	17	,	,	PUNCT
cana-5236	15	18	b	b	PROPN
cana-5236	15	19	,	,	PUNCT
cana-5236	15	20	α	α	NOUN
cana-5236	15	21	]	]	X
cana-5236	15	22	be	be	VERB
cana-5236	15	23	the	the	DET
cana-5236	15	24	class	class	NOUN
cana-5236	15	25	of	of	ADP
cana-5236	15	26	functions	function	NOUN
cana-5236	15	27	𝑝1	𝑝1	NOUN
cana-5236	15	28	,	,	PUNCT
cana-5236	15	29	analytic	analytic	ADJ
cana-5236	15	30	in	in	ADP
cana-5236	15	31	𝒰	𝒰	PROPN
cana-5236	15	32	with	with	ADP
cana-5236	15	33	𝑝1	𝑝1	NOUN
cana-5236	15	34	(	(	PUNCT
cana-5236	15	35	0	0	NUM
cana-5236	15	36	)	)	PUNCT
cana-5236	15	37	=	=	SYM
cana-5236	15	38	1	1	NUM
cana-5236	15	39	and	and	CCONJ
cana-5236	15	40	communications	communication	NOUN
cana-5236	15	41	on	on	ADP
cana-5236	15	42	applied	apply	VERB
cana-5236	15	43	nonlinear	nonlinear	ADJ
cana-5236	15	44	analysis	analysis	NOUN
cana-5236	15	45	issn	issn	NOUN
cana-5236	15	46	:	:	PUNCT
cana-5236	15	47	1074	1074	NUM
cana-5236	15	48	-	-	PUNCT
cana-5236	15	49	133x	133x	NUM
cana-5236	15	50	vol	vol	VERB
cana-5236	15	51	32	32	NUM
cana-5236	15	52	no	no	NOUN
cana-5236	15	53	.	.	PUNCT
cana-5236	16	1	10s	10	NOUN
cana-5236	16	2	(	(	PUNCT
cana-5236	16	3	2025	2025	NUM
cana-5236	16	4	)	)	PUNCT
cana-5236	16	5	1339	1339	NUM
cana-5236	16	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5236	16	7	(	(	PUNCT
cana-5236	16	8	1.3	1.3	NUM
cana-5236	16	9	)	)	PUNCT
cana-5236	16	10	𝑝1(𝑧	𝑝1(𝑧	NOUN
cana-5236	16	11	)	)	PUNCT
cana-5236	16	12	≺	≺	NOUN
cana-5236	16	13	1+{(1−𝛼)𝐴+𝛼𝐵}𝑧	1+{(1−𝛼)𝐴+𝛼𝐵}𝑧	PROPN
cana-5236	16	14	1+𝐵𝑧	1+𝐵𝑧	NUM
cana-5236	16	15	,	,	PUNCT
cana-5236	16	16	where	where	SCONJ
cana-5236	16	17	−1	−1	NOUN
cana-5236	16	18	≤	≤	X
cana-5236	17	1	b	b	ADP
cana-5236	17	2	<	<	X
cana-5236	17	3	a	a	DET
cana-5236	17	4	≤	≤	NUM
cana-5236	17	5	1	1	NUM
cana-5236	17	6	,	,	PUNCT
cana-5236	17	7	0	0	NUM
cana-5236	17	8	≤	≤	NUM
cana-5236	17	9	α	α	NOUN
cana-5236	17	10	<	<	X
cana-5236	17	11	1	1	NUM
cana-5236	17	12	.	.	PUNCT
cana-5236	17	13	from	from	ADP
cana-5236	17	14	(	(	PUNCT
cana-5236	17	15	1.3	1.3	NUM
cana-5236	17	16	)	)	PUNCT
cana-5236	17	17	,	,	PUNCT
cana-5236	17	18	it	it	PRON
cana-5236	17	19	can	can	AUX
cana-5236	17	20	easily	easily	ADV
cana-5236	17	21	be	be	AUX
cana-5236	17	22	seen	see	VERB
cana-5236	17	23	that	that	SCONJ
cana-5236	17	24	,	,	PUNCT
cana-5236	17	25	𝑝1	𝑝1	NOUN
cana-5236	17	26	∈	∈	PROPN
cana-5236	17	27	p[a	p[a	PROPN
cana-5236	17	28	,	,	PUNCT
cana-5236	17	29	b	b	PROPN
cana-5236	17	30	,	,	PUNCT
cana-5236	17	31	α	α	NOUN
cana-5236	17	32	]	]	X
cana-5236	17	33	,	,	PUNCT
cana-5236	17	34	if	if	SCONJ
cana-5236	17	35	and	and	CCONJ
cana-5236	17	36	only	only	ADV
cana-5236	17	37	if	if	SCONJ
cana-5236	17	38	,	,	PUNCT
cana-5236	17	39	there	there	PRON
cana-5236	17	40	exists	exist	VERB
cana-5236	17	41	h	h	NOUN
cana-5236	17	42	∈	∈	PROPN
cana-5236	17	43	p[a	p[a	PROPN
cana-5236	17	44	,	,	PUNCT
cana-5236	17	45	b	b	NOUN
cana-5236	17	46	]	]	X
cana-5236	17	47	such	such	ADJ
cana-5236	17	48	that	that	SCONJ
cana-5236	17	49	(	(	PUNCT
cana-5236	17	50	1.4	1.4	NUM
cana-5236	17	51	)	)	PUNCT
cana-5236	17	52	𝑝1(z	𝑝1(z	PROPN
cana-5236	17	53	)	)	PUNCT
cana-5236	17	54	=	=	PUNCT
cana-5236	17	55	(	(	PUNCT
cana-5236	17	56	1	1	NUM
cana-5236	17	57	−	−	PROPN
cana-5236	17	58	α)h(z	α)h(z	NUM
cana-5236	17	59	)	)	PUNCT
cana-5236	17	60	+	+	CCONJ
cana-5236	17	61	α	α	NOUN
cana-5236	17	62	,	,	PUNCT
cana-5236	17	63	0	0	NUM
cana-5236	17	64	≤	≤	NUM
cana-5236	17	65	α	α	NOUN
cana-5236	17	66	<	<	X
cana-5236	17	67	1	1	NUM
cana-5236	17	68	,	,	PUNCT
cana-5236	17	69	z	z	PROPN
cana-5236	17	70	∈	∈	NOUN
cana-5236	17	71	𝒰.	𝒰.	PROPN
cana-5236	17	72	it	it	PRON
cana-5236	17	73	is	be	AUX
cana-5236	17	74	also	also	ADV
cana-5236	17	75	noted	note	VERB
cana-5236	17	76	that	that	SCONJ
cana-5236	17	77	p	p	PROPN
cana-5236	17	78	[	[	X
cana-5236	17	79	1,−1,0	1,−1,0	NUM
cana-5236	17	80	]	]	X
cana-5236	17	81	≡	≡	PROPN
cana-5236	17	82	p	p	X
cana-5236	17	83	,	,	PUNCT
cana-5236	17	84	the	the	DET
cana-5236	17	85	well	well	ADV
cana-5236	17	86	-	-	PUNCT
cana-5236	17	87	known	know	VERB
cana-5236	17	88	class	class	NOUN
cana-5236	17	89	of	of	ADP
cana-5236	17	90	analytic	analytic	ADJ
cana-5236	17	91	functions	function	NOUN
cana-5236	17	92	in	in	ADP
cana-5236	17	93	𝒰	𝒰	PROPN
cana-5236	17	94	with	with	ADP
cana-5236	17	95	positive	positive	ADJ
cana-5236	17	96	real	real	ADJ
cana-5236	17	97	part	part	NOUN
cana-5236	17	98	.	.	PUNCT
cana-5236	18	1	noor	noor	PROPN
cana-5236	19	1	[	[	X
cana-5236	19	2	5	5	X
cana-5236	19	3	]	]	PUNCT
cana-5236	19	4	considered	consider	VERB
cana-5236	19	5	the	the	DET
cana-5236	19	6	generalized	generalized	ADJ
cana-5236	19	7	class	class	NOUN
cana-5236	19	8	𝑃𝑘[𝐴	𝑃𝑘[𝐴	PROPN
cana-5236	19	9	,	,	PUNCT
cana-5236	19	10	𝐵	𝐵	PROPN
cana-5236	19	11	,	,	PUNCT
cana-5236	19	12	α	α	NOUN
cana-5236	19	13	]	]	PUNCT
cana-5236	19	14	of	of	ADP
cana-5236	19	15	janowski	janowski	ADJ
cana-5236	19	16	functions	function	NOUN
cana-5236	19	17	which	which	PRON
cana-5236	19	18	is	be	AUX
cana-5236	19	19	defined	define	VERB
cana-5236	19	20	as	as	SCONJ
cana-5236	19	21	follows	follow	VERB
cana-5236	19	22	.	.	PUNCT
cana-5236	20	1	a	a	DET
cana-5236	20	2	function	function	NOUN
cana-5236	20	3	𝑝	𝑝	NOUN
cana-5236	20	4	is	be	AUX
cana-5236	20	5	said	say	VERB
cana-5236	20	6	to	to	PART
cana-5236	20	7	be	be	AUX
cana-5236	20	8	in	in	ADP
cana-5236	20	9	the	the	DET
cana-5236	20	10	class	class	NOUN
cana-5236	20	11	𝑃𝑘[𝐴	𝑃𝑘[𝐴	PROPN
cana-5236	20	12	,	,	PUNCT
cana-5236	20	13	𝐵	𝐵	PROPN
cana-5236	20	14	,	,	PUNCT
cana-5236	20	15	α	α	NOUN
cana-5236	20	16	]	]	X
cana-5236	20	17	,	,	PUNCT
cana-5236	20	18	if	if	SCONJ
cana-5236	20	19	and	and	CCONJ
cana-5236	20	20	only	only	ADV
cana-5236	20	21	if	if	SCONJ
cana-5236	20	22	,	,	PUNCT
cana-5236	20	23	(	(	PUNCT
cana-5236	20	24	1.5	1.5	NUM
cana-5236	20	25	)	)	PUNCT
cana-5236	20	26	𝑝(𝑧	𝑝(𝑧	PROPN
cana-5236	20	27	)	)	PUNCT
cana-5236	21	1	=	=	PRON
cana-5236	21	2	(	(	PUNCT
cana-5236	21	3	𝑘	𝑘	PROPN
cana-5236	21	4	4	4	NUM
cana-5236	21	5	+	+	SYM
cana-5236	21	6	1	1	NUM
cana-5236	21	7	2	2	NUM
cana-5236	21	8	)	)	PUNCT
cana-5236	21	9	𝑝1(z	𝑝1(z	PROPN
cana-5236	21	10	)	)	PUNCT
cana-5236	21	11	(	(	PUNCT
cana-5236	21	12	𝑘	𝑘	PROPN
cana-5236	21	13	4	4	NUM
cana-5236	21	14	−	−	NOUN
cana-5236	21	15	1	1	NUM
cana-5236	21	16	2	2	NUM
cana-5236	21	17	)	)	PUNCT
cana-5236	21	18	𝑝2(z	𝑝2(z	NUM
cana-5236	21	19	)	)	PUNCT
cana-5236	21	20	where	where	SCONJ
cana-5236	21	21	𝑝1	𝑝1	NOUN
cana-5236	21	22	,	,	PUNCT
cana-5236	21	23	𝑝2	𝑝2	NOUN
cana-5236	21	24	∈	∈	PROPN
cana-5236	21	25	p	p	X
cana-5236	22	1	[	[	X
cana-5236	22	2	a	a	X
cana-5236	22	3	,	,	PUNCT
cana-5236	22	4	b	b	PROPN
cana-5236	22	5	,	,	PUNCT
cana-5236	22	6	α	α	NOUN
cana-5236	22	7	]	]	X
cana-5236	22	8	,	,	PUNCT
cana-5236	23	1	−1	−1	NOUN
cana-5236	23	2	≤	≤	PROPN
cana-5236	23	3	b	b	ADP
cana-5236	23	4	<	<	X
cana-5236	23	5	a	a	DET
cana-5236	23	6	≤	≤	NUM
cana-5236	23	7	1	1	NUM
cana-5236	23	8	,	,	PUNCT
cana-5236	23	9	k	k	PROPN
cana-5236	23	10	≥	≥	NUM
cana-5236	23	11	2	2	NUM
cana-5236	23	12	and	and	CCONJ
cana-5236	23	13	0	0	NUM
cana-5236	23	14	≤	≤	NUM
cana-5236	23	15	α	α	NOUN
cana-5236	23	16	<	<	X
cana-5236	23	17	1	1	NUM
cana-5236	23	18	.	.	PUNCT
cana-5236	24	1	it	it	PRON
cana-5236	24	2	is	be	AUX
cana-5236	24	3	clear	clear	ADJ
cana-5236	24	4	that	that	SCONJ
cana-5236	24	5	𝑃2[𝐴	𝑃2[𝐴	PROPN
cana-5236	24	6	,	,	PUNCT
cana-5236	24	7	𝐵	𝐵	PROPN
cana-5236	24	8	,	,	PUNCT
cana-5236	24	9	α	α	NOUN
cana-5236	24	10	]	]	X
cana-5236	24	11	≡	≡	PROPN
cana-5236	24	12	p[a	p[a	PROPN
cana-5236	24	13	,	,	PUNCT
cana-5236	24	14	b	b	PROPN
cana-5236	24	15	,	,	PUNCT
cana-5236	24	16	α	α	NOUN
cana-5236	24	17	]	]	PUNCT
cana-5236	24	18	and	and	CCONJ
cana-5236	24	19	𝑃𝑘[1	𝑃𝑘[1	PROPN
cana-5236	24	20	,	,	PUNCT
cana-5236	24	21	−1	−1	NOUN
cana-5236	24	22	,	,	PUNCT
cana-5236	24	23	0	0	NUM
cana-5236	24	24	]	]	X
cana-5236	24	25	≡	≡	PROPN
cana-5236	24	26	𝑃𝑘	𝑃𝑘	PROPN
cana-5236	24	27	,	,	PUNCT
cana-5236	24	28	the	the	DET
cana-5236	24	29	well	well	ADV
cana-5236	24	30	-	-	PUNCT
cana-5236	24	31	known	know	VERB
cana-5236	24	32	class	class	NOUN
cana-5236	24	33	given	give	VERB
cana-5236	24	34	and	and	CCONJ
cana-5236	24	35	studied	study	VERB
cana-5236	24	36	by	by	ADP
cana-5236	24	37	pinchuk[3	pinchuk[3	PROPN
cana-5236	24	38	]	]	PUNCT
cana-5236	24	39	.	.	PUNCT
cana-5236	25	1	for	for	ADP
cana-5236	25	2	any	any	DET
cana-5236	25	3	two	two	NUM
cana-5236	25	4	analytic	analytic	ADJ
cana-5236	25	5	functions	function	NOUN
cana-5236	25	6	𝑓1(z)=	𝑓1(z)=	NOUN
cana-5236	25	7	∑	∑	ADP
cana-5236	25	8	𝑎𝑛𝑧𝑛∞	𝑎𝑛𝑧𝑛∞	VERB
cana-5236	25	9	𝑛=0	𝑛=0	NOUN
cana-5236	25	10	and	and	CCONJ
cana-5236	25	11	𝑓2(z)=	𝑓2(z)=	PRON
cana-5236	25	12	∑	∑	PUNCT
cana-5236	25	13	𝑏𝑛𝑧𝑛∞	𝑏𝑛𝑧𝑛∞	X
cana-5236	25	14	𝑛=0	𝑛=0	X
cana-5236	25	15	(	(	PUNCT
cana-5236	25	16	𝑧	𝑧	PROPN
cana-5236	25	17	∈	∈	PROPN
cana-5236	25	18	𝒰	𝒰	PROPN
cana-5236	25	19	)	)	PUNCT
cana-5236	25	20	the	the	DET
cana-5236	25	21	convolution	convolution	NOUN
cana-5236	25	22	of	of	ADP
cana-5236	25	23	𝑓1	𝑓1	PROPN
cana-5236	25	24	and	and	CCONJ
cana-5236	25	25	𝑓2	𝑓2	NOUN
cana-5236	25	26	is	be	AUX
cana-5236	25	27	defined	define	VERB
cana-5236	25	28	by	by	ADP
cana-5236	25	29	(	(	PUNCT
cana-5236	25	30	1.6	1.6	NUM
cana-5236	25	31	)	)	PUNCT
cana-5236	25	32	(	(	PUNCT
cana-5236	25	33	(	(	PUNCT
cana-5236	25	34	𝑓1	𝑓1	PROPN
cana-5236	25	35	∗	∗	NOUN
cana-5236	25	36	𝑓2)(𝑧	𝑓2)(𝑧	NOUN
cana-5236	25	37	)	)	PUNCT
cana-5236	25	38	=	=	SYM
cana-5236	26	1	∑	∑	PUNCT
cana-5236	26	2	𝑎𝑛𝑏𝑛𝑧𝑛∞	𝑎𝑛𝑏𝑛𝑧𝑛∞	PROPN
cana-5236	26	3	𝑛=1	𝑛=1	VERB
cana-5236	26	4	the	the	DET
cana-5236	26	5	generalized	generalize	VERB
cana-5236	26	6	ruscheweyh	ruscheweyh	NOUN
cana-5236	26	7	derivative	derivative	ADJ
cana-5236	26	8	𝒟𝜆	𝒟𝜆	PROPN
cana-5236	26	9	𝑚	𝑚	X
cana-5236	27	1	[	[	X
cana-5236	27	2	4	4	NUM
cana-5236	27	3	]	]	PUNCT
cana-5236	27	4	is	be	AUX
cana-5236	27	5	defined	define	VERB
cana-5236	27	6	as	as	ADP
cana-5236	27	7	follows	follow	VERB
cana-5236	27	8	,	,	PUNCT
cana-5236	27	9	for	for	ADP
cana-5236	27	10	f	f	PROPN
cana-5236	27	11	∈	∈	PROPN
cana-5236	27	12	𝒜	𝒜	PROPN
cana-5236	27	13	,	,	PUNCT
cana-5236	27	14	λ	λ	X
cana-5236	27	15	≥	≥	NOUN
cana-5236	27	16	0	0	NUM
cana-5236	27	17	and	and	CCONJ
cana-5236	27	18	m	m	PROPN
cana-5236	27	19	∈ℝ	∈ℝ	NOUN
cana-5236	27	20	,	,	PUNCT
cana-5236	27	21	m	m	VERB
cana-5236	27	22	>	>	X
cana-5236	27	23	−1	−1	NOUN
cana-5236	27	24	,	,	PUNCT
cana-5236	27	25	we	we	PRON
cana-5236	27	26	have	have	VERB
cana-5236	27	27	(	(	PUNCT
cana-5236	27	28	1.7	1.7	NUM
cana-5236	27	29	)	)	PUNCT
cana-5236	28	1	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	28	2	𝑚𝑓(𝑧	𝑚𝑓(𝑧	PUNCT
cana-5236	28	3	)	)	PUNCT
cana-5236	29	1	=	=	SYM
cana-5236	29	2	𝑧	𝑧	X
cana-5236	29	3	(	(	PUNCT
cana-5236	29	4	1−𝑧)𝑚+1*𝐷𝜆𝑓(𝑧	1−𝑧)𝑚+1*𝐷𝜆𝑓(𝑧	NUM
cana-5236	29	5	)	)	PUNCT
cana-5236	29	6	,	,	PUNCT
cana-5236	29	7	𝑧	𝑧	PROPN
cana-5236	29	8	∈	∈	PROPN
cana-5236	29	9	𝒰.	𝒰.	PROPN
cana-5236	29	10	(	(	PUNCT
cana-5236	29	11	1.8	1.8	NUM
cana-5236	29	12	)	)	PUNCT
cana-5236	29	13	(	(	PUNCT
cana-5236	29	14	𝑚	𝑚	PROPN
cana-5236	29	15	+	+	NUM
cana-5236	29	16	1)𝒟𝜆	1)𝒟𝜆	NUM
cana-5236	29	17	𝑚+1𝑓(𝑧	𝑚+1𝑓(𝑧	NUM
cana-5236	29	18	)	)	PUNCT
cana-5236	29	19	=	=	SYM
cana-5236	29	20	𝑚𝒟𝜆	𝑚𝒟𝜆	NOUN
cana-5236	29	21	𝑚𝑓(𝑧	𝑚𝑓(𝑧	NUM
cana-5236	29	22	)	)	PUNCT
cana-5236	29	23	+	+	CCONJ
cana-5236	29	24	𝑧(𝒟𝜆	𝑧(𝒟𝜆	ADJ
cana-5236	29	25	𝑚𝑓(𝑧))′	𝑚𝑓(𝑧))′	NOUN
cana-5236	29	26	for	for	ADP
cana-5236	29	27	function	function	NOUN
cana-5236	29	28	f	f	PROPN
cana-5236	29	29	∈	∈	PROPN
cana-5236	29	30	𝒜	𝒜	PROPN
cana-5236	29	31	of	of	ADP
cana-5236	29	32	the	the	DET
cana-5236	29	33	form	form	NOUN
cana-5236	29	34	(	(	PUNCT
cana-5236	29	35	1.1	1.1	NUM
cana-5236	29	36	)	)	PUNCT
cana-5236	29	37	,	,	PUNCT
cana-5236	29	38	we	we	PRON
cana-5236	29	39	obtain	obtain	VERB
cana-5236	29	40	the	the	DET
cana-5236	29	41	power	power	NOUN
cana-5236	29	42	series	series	NOUN
cana-5236	29	43	expansion	expansion	NOUN
cana-5236	29	44	of	of	ADP
cana-5236	29	45	the	the	DET
cana-5236	29	46	form	form	NOUN
cana-5236	29	47	,	,	PUNCT
cana-5236	29	48	(	(	PUNCT
cana-5236	29	49	1.9	1.9	NUM
cana-5236	29	50	)	)	PUNCT
cana-5236	29	51	𝒟𝜆	𝒟𝜆	PROPN
cana-5236	29	52	𝑚𝑓(𝑧	𝑚𝑓(𝑧	PUNCT
cana-5236	29	53	)	)	PUNCT
cana-5236	29	54	=	=	SYM
cana-5236	29	55	𝑧	𝑧	PROPN
cana-5236	30	1	+	+	NOUN
cana-5236	30	2	∑	∑	PUNCT
cana-5236	30	3	[	[	X
cana-5236	30	4	1	1	NUM
cana-5236	30	5	+	+	CCONJ
cana-5236	30	6	(	(	PUNCT
cana-5236	30	7	𝑛	𝑛	DET
cana-5236	30	8	−	−	PROPN
cana-5236	30	9	1)𝜆	1)𝜆	NUM
cana-5236	30	10	]	]	PUNCT
cana-5236	30	11	(	(	PUNCT
cana-5236	30	12	𝑚+1)(𝑛−1	𝑚+1)(𝑛−1	PROPN
cana-5236	30	13	)	)	PUNCT
cana-5236	30	14	(	(	PUNCT
cana-5236	30	15	1)(𝑛−1	1)(𝑛−1	NOUN
cana-5236	30	16	)	)	PUNCT
cana-5236	30	17	𝑎𝑛𝑧𝑛∞	𝑎𝑛𝑧𝑛∞	NOUN
cana-5236	30	18	𝑛=2	𝑛=2	NOUN
cana-5236	30	19	,	,	PUNCT
cana-5236	30	20	𝑧𝜖	𝑧𝜖	INTJ
cana-5236	30	21	𝒰	𝒰	PROPN
cana-5236	31	1	where	where	SCONJ
cana-5236	31	2	(	(	PUNCT
cana-5236	31	3	a)n	a)n	NOUN
cana-5236	31	4	=	=	SYM
cana-5236	31	5	γ(a	γ(a	PROPN
cana-5236	31	6	+	+	CCONJ
cana-5236	31	7	n	n	CCONJ
cana-5236	31	8	)	)	PUNCT
cana-5236	31	9	γ(a	γ(a	PROPN
cana-5236	31	10	)	)	PUNCT
cana-5236	31	11	=	=	PRON
cana-5236	31	12	{	{	PUNCT
cana-5236	31	13	1	1	NUM
cana-5236	31	14	,	,	PUNCT
cana-5236	31	15	for	for	ADP
cana-5236	31	16	n	n	NOUN
cana-5236	31	17	=	=	SYM
cana-5236	31	18	0	0	NUM
cana-5236	31	19	a(a	a(a	PROPN
cana-5236	31	20	+	+	CCONJ
cana-5236	31	21	1)(a	1)(a	NUM
cana-5236	31	22	+	+	CCONJ
cana-5236	31	23	2	2	NUM
cana-5236	31	24	)	)	PUNCT
cana-5236	31	25	…	…	PUNCT
cana-5236	31	26	(	(	PUNCT
cana-5236	31	27	a	a	DET
cana-5236	31	28	+	+	NOUN
cana-5236	31	29	n	n	CCONJ
cana-5236	31	30	−	−	PROPN
cana-5236	31	31	1	1	NUM
cana-5236	31	32	)	)	PUNCT
cana-5236	31	33	,	,	PUNCT
cana-5236	31	34	for	for	ADP
cana-5236	31	35	n	n	PRON
cana-5236	31	36	∈	∈	PROPN
cana-5236	31	37	ℕ	ℕ	PROPN
cana-5236	31	38	communications	communication	NOUN
cana-5236	31	39	on	on	ADP
cana-5236	31	40	applied	apply	VERB
cana-5236	31	41	nonlinear	nonlinear	ADJ
cana-5236	31	42	analysis	analysis	NOUN
cana-5236	31	43	issn	issn	NOUN
cana-5236	31	44	:	:	PUNCT
cana-5236	31	45	1074	1074	NUM
cana-5236	31	46	-	-	PUNCT
cana-5236	31	47	133x	133x	NUM
cana-5236	31	48	vol	vol	VERB
cana-5236	31	49	32	32	NUM
cana-5236	31	50	no	no	NOUN
cana-5236	31	51	.	.	PUNCT
cana-5236	32	1	10s	10	NOUN
cana-5236	32	2	(	(	PUNCT
cana-5236	32	3	2025	2025	NUM
cana-5236	32	4	)	)	PUNCT
cana-5236	32	5	1340	1340	NUM
cana-5236	32	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5236	32	7	definition	definition	NOUN
cana-5236	32	8	1.1	1.1	NUM
cana-5236	32	9	.	.	PUNCT
cana-5236	33	1	a	a	DET
cana-5236	33	2	function	function	NOUN
cana-5236	33	3	f	f	PROPN
cana-5236	33	4	∈	∈	PROPN
cana-5236	33	5	𝒜	𝒜	NOUN
cana-5236	33	6	is	be	AUX
cana-5236	33	7	in	in	ADP
cana-5236	33	8	the	the	DET
cana-5236	33	9	class	class	NOUN
cana-5236	33	10	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	33	11	𝑚	𝑚	X
cana-5236	33	12	[	[	X
cana-5236	33	13	𝐴	𝐴	PROPN
cana-5236	33	14	,	,	PUNCT
cana-5236	33	15	𝐵	𝐵	PROPN
cana-5236	33	16	,	,	PUNCT
cana-5236	33	17	𝛼	𝛼	PROPN
cana-5236	33	18	,	,	PUNCT
cana-5236	33	19	𝑏	𝑏	NOUN
cana-5236	33	20	]	]	X
cana-5236	33	21	if	if	SCONJ
cana-5236	33	22	and	and	CCONJ
cana-5236	33	23	only	only	ADV
cana-5236	33	24	if	if	SCONJ
cana-5236	33	25	,	,	PUNCT
cana-5236	33	26	(	(	PUNCT
cana-5236	33	27	1	1	NUM
cana-5236	33	28	−	−	NUM
cana-5236	33	29	2	2	NUM
cana-5236	33	30	𝑏	𝑏	NOUN
cana-5236	33	31	+	+	NOUN
cana-5236	33	32	2	2	NUM
cana-5236	33	33	𝑏	𝑏	NOUN
cana-5236	33	34	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	33	35	𝑚+1𝑓(𝑧	𝑚+1𝑓(𝑧	NUM
cana-5236	33	36	)	)	PUNCT
cana-5236	34	1	𝐷𝜆	𝐷𝜆	NOUN
cana-5236	34	2	𝑚𝑓(𝑧	𝑚𝑓(𝑧	NUM
cana-5236	34	3	)	)	PUNCT
cana-5236	34	4	)	)	PUNCT
cana-5236	35	1	∈	∈	PROPN
cana-5236	35	2	𝑃𝑘[𝐴	𝑃𝑘[𝐴	PROPN
cana-5236	35	3	,	,	PUNCT
cana-5236	35	4	𝐵	𝐵	NOUN
cana-5236	35	5	,	,	PUNCT
cana-5236	35	6	𝛼	𝛼	PROPN
cana-5236	35	7	]	]	X
cana-5236	35	8	,	,	PUNCT
cana-5236	35	9	z	z	PROPN
cana-5236	35	10	𝜖	𝜖	PROPN
cana-5236	35	11	𝒰	𝒰	PROPN
cana-5236	35	12	,	,	PUNCT
cana-5236	35	13	where	where	SCONJ
cana-5236	35	14	k≥	k≥	PROPN
cana-5236	35	15	2	2	NUM
cana-5236	35	16	,	,	PUNCT
cana-5236	35	17	m	m	VERB
cana-5236	35	18	≥0	≥0	NOUN
cana-5236	35	19	,	,	PUNCT
cana-5236	35	20	-1≤	-1≤	PUNCT
cana-5236	35	21	𝐵	𝐵	PROPN
cana-5236	35	22	<	<	X
cana-5236	35	23	𝐴	𝐴	PROPN
cana-5236	35	24	≤1	≤1	PROPN
cana-5236	35	25	,	,	PUNCT
cana-5236	35	26	0	0	NUM
cana-5236	35	27	≤	≤	NUM
cana-5236	35	28	𝛼<1	𝛼<1	NOUN
cana-5236	35	29	and	and	CCONJ
cana-5236	35	30	b	b	NOUN
cana-5236	35	31	∈	∈	PROPN
cana-5236	35	32	ℂ	ℂ	PROPN
cana-5236	35	33	−	−	PROPN
cana-5236	35	34	{	{	PUNCT
cana-5236	35	35	0	0	NUM
cana-5236	35	36	}	}	PUNCT
cana-5236	35	37	.	.	PUNCT
cana-5236	36	1	assigning	assign	VERB
cana-5236	36	2	certain	certain	ADJ
cana-5236	36	3	values	value	NOUN
cana-5236	36	4	to	to	ADP
cana-5236	36	5	different	different	ADJ
cana-5236	36	6	parameters	parameter	NOUN
cana-5236	36	7	,	,	PUNCT
cana-5236	36	8	we	we	PRON
cana-5236	36	9	have	have	VERB
cana-5236	36	10	different	different	ADJ
cana-5236	36	11	well	well	ADV
cana-5236	36	12	-	-	PUNCT
cana-5236	36	13	known	know	VERB
cana-5236	36	14	classes	class	NOUN
cana-5236	36	15	of	of	ADP
cana-5236	36	16	analytic	analytic	ADJ
cana-5236	36	17	functions	function	NOUN
cana-5236	36	18	as	as	SCONJ
cana-5236	36	19	can	can	AUX
cana-5236	36	20	be	be	AUX
cana-5236	36	21	seen	see	VERB
cana-5236	36	22	below	below	ADP
cana-5236	36	23	.	.	PUNCT
cana-5236	37	1	special	special	ADJ
cana-5236	37	2	cases	case	NOUN
cana-5236	37	3	(	(	PUNCT
cana-5236	37	4	i	i	NOUN
cana-5236	37	5	)	)	PUNCT
cana-5236	37	6	for	for	ADP
cana-5236	37	7	a	a	DET
cana-5236	37	8	parametric	parametric	ADJ
cana-5236	37	9	value	value	NOUN
cana-5236	37	10	λ	λ	NOUN
cana-5236	37	11	=	=	NOUN
cana-5236	37	12	1	1	NUM
cana-5236	37	13	;	;	PUNCT
cana-5236	37	14	we	we	PRON
cana-5236	37	15	get	get	VERB
cana-5236	37	16	the	the	DET
cana-5236	37	17	class	class	NOUN
cana-5236	37	18	studied	study	VERB
cana-5236	37	19	by	by	ADP
cana-5236	37	20	s.n	s.n	PROPN
cana-5236	37	21	.	.	PROPN
cana-5236	37	22	malik	malik	PROPN
cana-5236	37	23	,	,	PUNCT
cana-5236	37	24	m.	m.	PROPN
cana-5236	37	25	arif	arif	PROPN
cana-5236	37	26	,	,	PUNCT
cana-5236	37	27	k.i	k.i	PROPN
cana-5236	37	28	.	.	PUNCT
cana-5236	38	1	noor	noor	PROPN
cana-5236	38	2	and	and	CCONJ
cana-5236	38	3	m.	m.	PROPN
cana-5236	38	4	raza.[15	raza.[15	PROPN
cana-5236	38	5	]	]	PUNCT
cana-5236	38	6	(	(	PUNCT
cana-5236	38	7	ii	ii	NOUN
cana-5236	38	8	)	)	PUNCT
cana-5236	38	9	𝒱𝑘	𝒱𝑘	PROPN
cana-5236	38	10	λ[1	λ[1	PROPN
cana-5236	38	11	,	,	PUNCT
cana-5236	38	12	−1	−1	ADV
cana-5236	38	13	,	,	PUNCT
cana-5236	38	14	𝛼	𝛼	X
cana-5236	38	15	,	,	PUNCT
cana-5236	38	16	𝑏	𝑏	NOUN
cana-5236	38	17	]	]	X
cana-5236	38	18	≡	≡	PROPN
cana-5236	38	19	𝑉𝑘(𝑎	𝑉𝑘(𝑎	PROPN
cana-5236	38	20	,	,	PUNCT
cana-5236	38	21	𝑏	𝑏	PROPN
cana-5236	38	22	,	,	PUNCT
cana-5236	38	23	λ	λ	PROPN
cana-5236	38	24	)	)	PUNCT
cana-5236	38	25	,	,	PUNCT
cana-5236	38	26	the	the	DET
cana-5236	38	27	well	well	ADV
cana-5236	38	28	-	-	PUNCT
cana-5236	38	29	known	know	VERB
cana-5236	38	30	class	class	NOUN
cana-5236	38	31	defined	define	VERB
cana-5236	38	32	by	by	ADP
cana-5236	38	33	latha	latha	PROPN
cana-5236	38	34	and	and	CCONJ
cana-5236	38	35	nanjunda	nanjunda	ADJ
cana-5236	38	36	rao	rao	NOUN
cana-5236	38	37	in	in	ADP
cana-5236	38	38	[	[	X
cana-5236	38	39	14	14	NUM
cana-5236	38	40	]	]	PUNCT
cana-5236	38	41	.	.	PUNCT
cana-5236	39	1	(	(	PUNCT
cana-5236	39	2	iii	iii	NOUN
cana-5236	39	3	)	)	PUNCT
cana-5236	39	4	𝒱2	𝒱2	NOUN
cana-5236	39	5	1[𝐴	1[𝐴	NOUN
cana-5236	39	6	,	,	PUNCT
cana-5236	39	7	𝐵	𝐵	NOUN
cana-5236	39	8	,	,	PUNCT
cana-5236	39	9	𝛼	𝛼	PROPN
cana-5236	39	10	,	,	PUNCT
cana-5236	39	11	1	1	NUM
cana-5236	39	12	]	]	PUNCT
cana-5236	39	13	≡	≡	PROPN
cana-5236	39	14	c[a	c[a	PROPN
cana-5236	39	15	,	,	PUNCT
cana-5236	39	16	b	b	NOUN
cana-5236	39	17	,	,	PUNCT
cana-5236	39	18	𝛼	𝛼	NOUN
cana-5236	39	19	]	]	X
cana-5236	39	20	𝒱2	𝒱2	PROPN
cana-5236	39	21	0[𝐴	0[𝐴	PROPN
cana-5236	39	22	,	,	PUNCT
cana-5236	39	23	𝐵	𝐵	NOUN
cana-5236	39	24	,	,	PUNCT
cana-5236	39	25	𝛼	𝛼	PROPN
cana-5236	39	26	,	,	PUNCT
cana-5236	39	27	2	2	NUM
cana-5236	39	28	]	]	PUNCT
cana-5236	39	29	≡	≡	PROPN
cana-5236	39	30	𝑆∗[𝐴	𝑆∗[𝐴	PROPN
cana-5236	39	31	,	,	PUNCT
cana-5236	39	32	𝐵	𝐵	NOUN
cana-5236	39	33	,	,	PUNCT
cana-5236	39	34	𝛼	𝛼	PROPN
cana-5236	39	35	]	]	PUNCT
cana-5236	39	36	,	,	PUNCT
cana-5236	39	37	the	the	DET
cana-5236	39	38	well	well	ADV
cana-5236	39	39	-	-	PUNCT
cana-5236	39	40	known	know	VERB
cana-5236	39	41	class	class	NOUN
cana-5236	39	42	defined	define	VERB
cana-5236	39	43	by	by	ADP
cana-5236	39	44	polato	polato	NOUN
cana-5236	39	45	�	�	PROPN
cana-5236	39	46	̌	̌	NUM
cana-5236	39	47	�	�	NOUN
cana-5236	39	48	lu	lu	NOUN
cana-5236	39	49	[	[	X
cana-5236	39	50	19	19	NUM
cana-5236	39	51	]	]	PUNCT
cana-5236	39	52	(	(	PUNCT
cana-5236	39	53	iv	iv	X
cana-5236	39	54	)	)	PUNCT
cana-5236	40	1	𝒱𝑘	𝒱𝑘	NOUN
cana-5236	40	2	1[𝐴	1[𝐴	NUM
cana-5236	40	3	,	,	PUNCT
cana-5236	40	4	𝐵	𝐵	NOUN
cana-5236	40	5	,	,	PUNCT
cana-5236	40	6	0,1	0,1	NUM
cana-5236	40	7	]	]	PUNCT
cana-5236	40	8	≡	≡	PROPN
cana-5236	40	9	𝑉𝑘[𝐴	𝑉𝑘[𝐴	PROPN
cana-5236	40	10	,	,	PUNCT
cana-5236	40	11	𝐵	𝐵	PROPN
cana-5236	40	12	]	]	X
cana-5236	40	13	,	,	PUNCT
cana-5236	40	14	𝒱2	𝒱2	PROPN
cana-5236	40	15	0[𝐴	0[𝐴	PROPN
cana-5236	40	16	,	,	PUNCT
cana-5236	40	17	𝐵	𝐵	NOUN
cana-5236	40	18	,	,	PUNCT
cana-5236	40	19	0,2	0,2	NUM
cana-5236	40	20	]	]	PUNCT
cana-5236	40	21	≡	≡	PROPN
cana-5236	40	22	𝑅𝑘[𝐴	𝑅𝑘[𝐴	PROPN
cana-5236	40	23	,	,	PUNCT
cana-5236	40	24	𝐵	𝐵	PROPN
cana-5236	40	25	]	]	PUNCT
cana-5236	40	26	,	,	PUNCT
cana-5236	40	27	where	where	SCONJ
cana-5236	40	28	𝑉𝑘[𝐴	𝑉𝑘[𝐴	NOUN
cana-5236	40	29	,	,	PUNCT
cana-5236	40	30	𝐵	𝐵	NOUN
cana-5236	40	31	]	]	PUNCT
cana-5236	40	32	and	and	CCONJ
cana-5236	40	33	𝑅𝑘[𝐴	𝑅𝑘[𝐴	PROPN
cana-5236	40	34	,	,	PUNCT
cana-5236	40	35	𝐵	𝐵	PROPN
cana-5236	40	36	]	]	PUNCT
cana-5236	40	37	denote	denote	VERB
cana-5236	40	38	the	the	DET
cana-5236	40	39	class	class	NOUN
cana-5236	40	40	of	of	ADP
cana-5236	40	41	janowski	janowski	ADJ
cana-5236	40	42	functions	function	NOUN
cana-5236	40	43	with	with	ADP
cana-5236	40	44	bounded	bounded	ADJ
cana-5236	40	45	boundary	boundary	NOUN
cana-5236	40	46	and	and	CCONJ
cana-5236	40	47	bounded	bound	VERB
cana-5236	40	48	radius	radius	NOUN
cana-5236	40	49	rotations	rotation	NOUN
cana-5236	40	50	respectively	respectively	ADV
cana-5236	40	51	,	,	PUNCT
cana-5236	40	52	given	give	VERB
cana-5236	40	53	by	by	ADP
cana-5236	40	54	noor	noor	PROPN
cana-5236	41	1	[	[	X
cana-5236	41	2	9	9	NUM
cana-5236	41	3	]	]	SYM
cana-5236	41	4	.	.	PUNCT
cana-5236	42	1	2	2	X
cana-5236	42	2	.	.	X
cana-5236	42	3	preliminary	preliminary	ADJ
cana-5236	42	4	results	result	NOUN
cana-5236	42	5	we	we	PRON
cana-5236	42	6	need	need	VERB
cana-5236	42	7	the	the	DET
cana-5236	42	8	following	follow	VERB
cana-5236	42	9	results	result	NOUN
cana-5236	42	10	to	to	PART
cana-5236	42	11	obtain	obtain	VERB
cana-5236	42	12	our	our	PRON
cana-5236	42	13	main	main	ADJ
cana-5236	42	14	results	result	NOUN
cana-5236	42	15	.	.	PUNCT
cana-5236	43	1	lemma	lemma	PROPN
cana-5236	43	2	2.1	2.1	NUM
cana-5236	43	3	.	.	PUNCT
cana-5236	44	1	let	let	VERB
cana-5236	44	2	𝑝(𝑧	𝑝(𝑧	NOUN
cana-5236	44	3	)	)	PUNCT
cana-5236	44	4	=	=	PUNCT
cana-5236	45	1	1	1	NUM
cana-5236	45	2	+	+	CCONJ
cana-5236	45	3	∑	∑	PROPN
cana-5236	45	4	𝑞𝑛𝑧𝑛∞	𝑞𝑛𝑧𝑛∞	ADJ
cana-5236	45	5	𝑛=1	𝑛=1	PRON
cana-5236	45	6	∈	∈	PROPN
cana-5236	45	7	𝑃𝑘[𝐴	𝑃𝑘[𝐴	PROPN
cana-5236	45	8	,	,	PUNCT
cana-5236	45	9	𝐵	𝐵	NOUN
cana-5236	45	10	,	,	PUNCT
cana-5236	45	11	𝛼	𝛼	NOUN
cana-5236	45	12	]	]	X
cana-5236	45	13	.	.	PUNCT
cana-5236	46	1	then	then	ADV
cana-5236	46	2	,	,	PUNCT
cana-5236	46	3	for	for	ADP
cana-5236	46	4	all	all	DET
cana-5236	46	5	n	n	PRON
cana-5236	46	6	≥	≥	NOUN
cana-5236	46	7	1	1	NUM
cana-5236	46	8	,	,	PUNCT
cana-5236	46	9	(	(	PUNCT
cana-5236	46	10	2.1	2.1	NUM
cana-5236	46	11	)	)	PUNCT
cana-5236	46	12	|𝑞𝑛|	|𝑞𝑛|	PROPN
cana-5236	46	13	≤	≤	NUM
cana-5236	46	14	𝑘(𝐴−𝐵)(1−𝛼	𝑘(𝐴−𝐵)(1−𝛼	NOUN
cana-5236	46	15	)	)	PUNCT
cana-5236	46	16	2	2	NUM
cana-5236	46	17	this	this	DET
cana-5236	46	18	inequality	inequality	NOUN
cana-5236	46	19	is	be	AUX
cana-5236	46	20	sharp	sharp	ADJ
cana-5236	46	21	.	.	PUNCT
cana-5236	47	1	the	the	DET
cana-5236	47	2	proof	proof	NOUN
cana-5236	47	3	follows	follow	VERB
cana-5236	47	4	from	from	ADP
cana-5236	47	5	(	(	PUNCT
cana-5236	47	6	1.4	1.4	NUM
cana-5236	47	7	)	)	PUNCT
cana-5236	47	8	,	,	PUNCT
cana-5236	47	9	(	(	PUNCT
cana-5236	47	10	1.5	1.5	NUM
cana-5236	47	11	)	)	PUNCT
cana-5236	47	12	and	and	CCONJ
cana-5236	47	13	the	the	DET
cana-5236	47	14	coefficient	coefficient	NOUN
cana-5236	47	15	bound	bind	VERB
cana-5236	47	16	of	of	ADP
cana-5236	47	17	h	h	NOUN
cana-5236	47	18	∈	∈	PROPN
cana-5236	47	19	p[a	p[a	PROPN
cana-5236	47	20	,	,	PUNCT
cana-5236	47	21	b	b	NOUN
cana-5236	47	22	]	]	PUNCT
cana-5236	47	23	given	give	VERB
cana-5236	47	24	by	by	ADP
cana-5236	47	25	aouf	aouf	PROPN
cana-5236	48	1	[	[	X
cana-5236	48	2	13	13	NUM
cana-5236	48	3	]	]	PUNCT
cana-5236	48	4	.	.	PUNCT
cana-5236	49	1	lemma	lemma	PROPN
cana-5236	49	2	2.2	2.2	NUM
cana-5236	49	3	.	.	PUNCT
cana-5236	50	1	[	[	X
cana-5236	50	2	17	17	NUM
cana-5236	50	3	]	]	PUNCT
cana-5236	50	4	let	let	VERB
cana-5236	50	5	𝑢	𝑢	X
cana-5236	50	6	=	=	VERB
cana-5236	50	7	𝑢1	𝑢1	PROPN
cana-5236	50	8	+	+	CCONJ
cana-5236	50	9	𝑖𝑢2	𝑖𝑢2	NOUN
cana-5236	50	10	,	,	PUNCT
cana-5236	50	11	𝑣	𝑣	X
cana-5236	50	12	=	=	PUNCT
cana-5236	50	13	𝑣1	𝑣1	PROPN
cana-5236	50	14	+	+	CCONJ
cana-5236	50	15	𝑖𝑣2	𝑖𝑣2	PROPN
cana-5236	50	16	and	and	CCONJ
cana-5236	50	17	𝜓(𝑢	𝜓(𝑢	NOUN
cana-5236	50	18	,	,	PUNCT
cana-5236	50	19	𝑣	𝑣	NOUN
cana-5236	50	20	)	)	PUNCT
cana-5236	50	21	be	be	VERB
cana-5236	50	22	a	a	DET
cana-5236	50	23	complex	complex	ADJ
cana-5236	50	24	valued	value	VERB
cana-5236	50	25	function	function	NOUN
cana-5236	50	26	satisfying	satisfy	VERB
cana-5236	50	27	the	the	DET
cana-5236	50	28	conditions	condition	NOUN
cana-5236	50	29	:	:	PUNCT
cana-5236	50	30	(	(	PUNCT
cana-5236	50	31	i	i	NOUN
cana-5236	50	32	)	)	PUNCT
cana-5236	50	33	𝜓(𝑢	𝜓(𝑢	PROPN
cana-5236	50	34	,	,	PUNCT
cana-5236	50	35	𝑣	𝑣	NOUN
cana-5236	50	36	)	)	PUNCT
cana-5236	50	37	is	be	AUX
cana-5236	50	38	continuous	continuous	ADJ
cana-5236	50	39	in	in	ADP
cana-5236	50	40	a	a	DET
cana-5236	50	41	domain	domain	NOUN
cana-5236	50	42	,	,	PUNCT
cana-5236	50	43	𝐷	𝐷	PROPN
cana-5236	50	44	⊂	⊂	PROPN
cana-5236	50	45	ℂ2	ℂ2	PROPN
cana-5236	50	46	(	(	PUNCT
cana-5236	50	47	ii	ii	NOUN
cana-5236	50	48	)	)	PUNCT
cana-5236	50	49	(	(	PUNCT
cana-5236	50	50	1,0	1,0	NUM
cana-5236	50	51	)	)	PUNCT
cana-5236	50	52	∈𝐷	∈𝐷	NOUN
cana-5236	50	53	and	and	CCONJ
cana-5236	50	54	re	re	NOUN
cana-5236	50	55	𝜓(1,0	𝜓(1,0	NOUN
cana-5236	50	56	)	)	PUNCT
cana-5236	50	57	>	>	X
cana-5236	50	58	0	0	NUM
cana-5236	50	59	,	,	PUNCT
cana-5236	50	60	(	(	PUNCT
cana-5236	50	61	iii	iii	NOUN
cana-5236	50	62	)	)	PUNCT
cana-5236	50	63	re	re	VERB
cana-5236	50	64	𝜓(𝑖𝑢2	𝜓(𝑖𝑢2	PROPN
cana-5236	50	65	,	,	PUNCT
cana-5236	50	66	𝑣1)≤	𝑣1)≤	PROPN
cana-5236	50	67	0	0	NUM
cana-5236	50	68	,	,	PUNCT
cana-5236	50	69	whenever	whenever	SCONJ
cana-5236	50	70	(	(	PUNCT
cana-5236	50	71	𝑖𝑢2	𝑖𝑢2	NOUN
cana-5236	50	72	,	,	PUNCT
cana-5236	50	73	𝑣1	𝑣1	PROPN
cana-5236	50	74	)	)	PUNCT
cana-5236	50	75	∈𝐷	∈𝐷	NOUN
cana-5236	50	76	and	and	CCONJ
cana-5236	50	77	𝑣1	𝑣1	NOUN
cana-5236	50	78	≤	≤	PROPN
cana-5236	50	79	−	−	NUM
cana-5236	50	80	1	1	NUM
cana-5236	50	81	2	2	NUM
cana-5236	50	82	(	(	PUNCT
cana-5236	50	83	1	1	NUM
cana-5236	50	84	+	+	NUM
cana-5236	50	85	𝑢2	𝑢2	NOUN
cana-5236	50	86	)	)	PUNCT
cana-5236	50	87	.	.	PUNCT
cana-5236	50	88	.	.	PUNCT
cana-5236	51	1	if	if	SCONJ
cana-5236	51	2	h(z	h(z	NOUN
cana-5236	51	3	)	)	PUNCT
cana-5236	51	4	=	=	SYM
cana-5236	52	1	1	1	NUM
cana-5236	52	2	+	+	CCONJ
cana-5236	52	3	c1z	c1z	PROPN
cana-5236	53	1	+	+	CCONJ
cana-5236	53	2	...	...	PUNCT
cana-5236	53	3	is	be	AUX
cana-5236	53	4	a	a	DET
cana-5236	53	5	function	function	NOUN
cana-5236	53	6	analytic	analytic	NOUN
cana-5236	53	7	in	in	ADP
cana-5236	53	8	𝒰	𝒰	PROPN
cana-5236	53	9	such	such	ADJ
cana-5236	53	10	that	that	SCONJ
cana-5236	53	11	(	(	PUNCT
cana-5236	53	12	h(z),zh′(z	h(z),zh′(z	NOUN
cana-5236	53	13	)	)	PUNCT
cana-5236	53	14	)	)	PUNCT
cana-5236	54	1	∈	∈	PROPN
cana-5236	54	2	d	d	NOUN
cana-5236	54	3	and	and	CCONJ
cana-5236	54	4	re	re	ADP
cana-5236	54	5	𝜓	𝜓	PROPN
cana-5236	54	6	(	(	PUNCT
cana-5236	54	7	h(z),zh′(z	h(z),zh′(z	PROPN
cana-5236	54	8	)	)	PUNCT
cana-5236	54	9	)	)	PUNCT
cana-5236	54	10	>	>	X
cana-5236	54	11	0	0	PUNCT
cana-5236	55	1	for	for	ADP
cana-5236	55	2	z	z	PROPN
cana-5236	55	3	∈	∈	PROPN
cana-5236	55	4	𝒰	𝒰	PROPN
cana-5236	55	5	,	,	PUNCT
cana-5236	55	6	then	then	ADV
cana-5236	55	7	reh(z	reh(z	PROPN
cana-5236	55	8	)	)	PUNCT
cana-5236	55	9	>	>	X
cana-5236	55	10	0	0	PUNCT
cana-5236	55	11	in	in	ADP
cana-5236	55	12	𝒰.	𝒰.	PROPN
cana-5236	55	13	lemma	lemma	PROPN
cana-5236	55	14	2.3	2.3	NUM
cana-5236	55	15	.	.	PUNCT
cana-5236	56	1	let	let	VERB
cana-5236	56	2	𝑝	𝑝	PRON
cana-5236	56	3	∈	∈	PROPN
cana-5236	56	4	𝑃𝑘[𝐴	𝑃𝑘[𝐴	PROPN
cana-5236	56	5	,	,	PUNCT
cana-5236	56	6	𝐵	𝐵	PROPN
cana-5236	56	7	,	,	PUNCT
cana-5236	56	8	0	0	NUM
cana-5236	56	9	]	]	PUNCT
cana-5236	56	10	with	with	ADP
cana-5236	56	11	k	k	PROPN
cana-5236	56	12	≥	≥	NUM
cana-5236	56	13	2	2	NUM
cana-5236	56	14	.	.	PUNCT
cana-5236	57	1	then	then	ADV
cana-5236	57	2	,	,	PUNCT
cana-5236	57	3	for	for	ADP
cana-5236	57	4	|z|	|z|	NOUN
cana-5236	57	5	=	=	SYM
cana-5236	57	6	r	r	NOUN
cana-5236	57	7	<	<	X
cana-5236	57	8	1	1	NUM
cana-5236	57	9	,	,	PUNCT
cana-5236	57	10	communications	communication	NOUN
cana-5236	57	11	on	on	ADP
cana-5236	57	12	applied	apply	VERB
cana-5236	57	13	nonlinear	nonlinear	ADJ
cana-5236	57	14	analysis	analysis	NOUN
cana-5236	57	15	issn	issn	NOUN
cana-5236	57	16	:	:	PUNCT
cana-5236	57	17	1074	1074	NUM
cana-5236	57	18	-	-	PUNCT
cana-5236	57	19	133x	133x	NUM
cana-5236	57	20	vol	vol	VERB
cana-5236	57	21	32	32	NUM
cana-5236	57	22	no	no	NOUN
cana-5236	57	23	.	.	PUNCT
cana-5236	58	1	10s	10	NOUN
cana-5236	58	2	(	(	PUNCT
cana-5236	58	3	2025	2025	NUM
cana-5236	58	4	)	)	PUNCT
cana-5236	58	5	1341	1341	NUM
cana-5236	58	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5236	58	7	(	(	PUNCT
cana-5236	58	8	2.2	2.2	NUM
cana-5236	58	9	)	)	PUNCT
cana-5236	58	10	2−(𝐴−𝐵)𝑘𝑟−2𝐴𝐵𝑟2	2−(𝐴−𝐵)𝑘𝑟−2𝐴𝐵𝑟2	NUM
cana-5236	58	11	2(1−𝐵2𝑟2	2(1−𝐵2𝑟2	NUM
cana-5236	58	12	)	)	PUNCT
cana-5236	58	13	≤	≤	PUNCT
cana-5236	59	1	𝑅𝑒	𝑅𝑒	PROPN
cana-5236	59	2	𝑝(𝑧	𝑝(𝑧	NOUN
cana-5236	59	3	)	)	PUNCT
cana-5236	59	4	≤	≤	NOUN
cana-5236	60	1	|𝑝(𝑧)|	|𝑝(𝑧)|	PROPN
cana-5236	60	2	≤	≤	ADJ
cana-5236	60	3	2+(𝐴−𝐵)𝑘𝑟−2𝐴𝐵𝑟2	2+(𝐴−𝐵)𝑘𝑟−2𝐴𝐵𝑟2	NUM
cana-5236	60	4	2(1−𝐵2𝑟2	2(1−𝐵2𝑟2	NUM
cana-5236	60	5	)	)	PUNCT
cana-5236	60	6	the	the	DET
cana-5236	60	7	proof	proof	NOUN
cana-5236	60	8	is	be	AUX
cana-5236	60	9	immediate	immediate	ADJ
cana-5236	60	10	by	by	ADP
cana-5236	60	11	using	use	VERB
cana-5236	60	12	(	(	PUNCT
cana-5236	60	13	1.5	1.5	NUM
cana-5236	60	14	)	)	PUNCT
cana-5236	60	15	and	and	CCONJ
cana-5236	60	16	the	the	DET
cana-5236	60	17	growth	growth	NOUN
cana-5236	60	18	result	result	NOUN
cana-5236	60	19	of	of	ADP
cana-5236	60	20	h	h	NOUN
cana-5236	60	21	∈	∈	PROPN
cana-5236	60	22	p	p	X
cana-5236	61	1	[	[	X
cana-5236	61	2	a	a	X
cana-5236	61	3	,	,	PUNCT
cana-5236	61	4	b	b	NOUN
cana-5236	61	5	]	]	X
cana-5236	61	6	,	,	PUNCT
cana-5236	61	7	see	see	VERB
cana-5236	61	8	[	[	X
cana-5236	61	9	13	13	NUM
cana-5236	61	10	]	]	PUNCT
cana-5236	61	11	.	.	PUNCT
cana-5236	62	1	lemma	lemma	PROPN
cana-5236	62	2	2.4	2.4	NUM
cana-5236	62	3	.	.	PUNCT
cana-5236	63	1	let	let	VERB
cana-5236	63	2	∈	∈	PROPN
cana-5236	63	3	𝑃𝑘[𝐴	𝑃𝑘[𝐴	NOUN
cana-5236	63	4	,	,	PUNCT
cana-5236	63	5	𝐵	𝐵	PROPN
cana-5236	63	6	,	,	PUNCT
cana-5236	63	7	0	0	NUM
cana-5236	63	8	]	]	PUNCT
cana-5236	63	9	with	with	ADP
cana-5236	63	10	k	k	PROPN
cana-5236	63	11	≥	≥	NUM
cana-5236	63	12	2	2	NUM
cana-5236	63	13	.	.	PUNCT
cana-5236	64	1	then	then	ADV
cana-5236	64	2	,	,	PUNCT
cana-5236	64	3	for	for	ADP
cana-5236	64	4	|z|	|z|	NOUN
cana-5236	64	5	=	=	SYM
cana-5236	64	6	r	r	NOUN
cana-5236	64	7	<	<	X
cana-5236	64	8	1	1	NUM
cana-5236	64	9	.	.	PUNCT
cana-5236	65	1	(	(	PUNCT
cana-5236	65	2	2.3	2.3	NUM
cana-5236	65	3	)	)	PUNCT
cana-5236	65	4	|𝑧𝑝′(𝑧)|	|𝑧𝑝′(𝑧)|	NOUN
cana-5236	65	5	≤	≤	NUM
cana-5236	65	6	𝑟{(𝐴−𝐵)𝑘−4𝐵(𝐴−𝐵)𝑟+𝐵2(𝐴−𝐵)𝑘𝑟2	𝑟{(𝐴−𝐵)𝑘−4𝐵(𝐴−𝐵)𝑟+𝐵2(𝐴−𝐵)𝑘𝑟2	NUM
cana-5236	65	7	}	}	PUNCT
cana-5236	65	8	𝑅𝑒	𝑅𝑒	PROPN
cana-5236	65	9	𝑝(𝑧	𝑝(𝑧	NOUN
cana-5236	65	10	)	)	PUNCT
cana-5236	65	11	(	(	PUNCT
cana-5236	65	12	1−𝐵2𝑟2)(2+(𝐴−𝐵)𝑘𝑟−2𝐴𝐵𝑟2	1−𝐵2𝑟2)(2+(𝐴−𝐵)𝑘𝑟−2𝐴𝐵𝑟2	X
cana-5236	65	13	)	)	PUNCT
cana-5236	65	14	the	the	DET
cana-5236	65	15	result	result	NOUN
cana-5236	65	16	follows	follow	VERB
cana-5236	65	17	directly	directly	ADV
cana-5236	65	18	by	by	ADP
cana-5236	65	19	using	use	VERB
cana-5236	65	20	lemma	lemma	PROPN
cana-5236	65	21	2.3	2.3	NUM
cana-5236	65	22	3	3	NUM
cana-5236	65	23	.	.	PUNCT
cana-5236	65	24	main	main	ADJ
cana-5236	65	25	results	result	NOUN
cana-5236	65	26	theorem	theorem	VERB
cana-5236	65	27	3.1	3.1	NUM
cana-5236	65	28	.	.	PUNCT
cana-5236	66	1	let	let	VERB
cana-5236	66	2	f	f	PROPN
cana-5236	66	3	∈	∈	PROPN
cana-5236	66	4	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	67	1	𝑚	𝑚	X
cana-5236	68	1	[	[	X
cana-5236	68	2	𝐴	𝐴	PROPN
cana-5236	68	3	,	,	PUNCT
cana-5236	68	4	𝐵	𝐵	PROPN
cana-5236	68	5	,	,	PUNCT
cana-5236	68	6	𝛼	𝛼	PROPN
cana-5236	68	7	,	,	PUNCT
cana-5236	68	8	𝑏	𝑏	NOUN
cana-5236	68	9	]	]	PUNCT
cana-5236	68	10	with	with	ADP
cana-5236	68	11	-1≤	-1≤	PROPN
cana-5236	68	12	𝐵	𝐵	PROPN
cana-5236	68	13	<	<	X
cana-5236	68	14	𝐴	𝐴	PROPN
cana-5236	68	15	≤1	≤1	PROPN
cana-5236	68	16	,	,	PUNCT
cana-5236	68	17	m	m	VERB
cana-5236	68	18	≥0	≥0	NOUN
cana-5236	68	19	,	,	PUNCT
cana-5236	68	20	0	0	NUM
cana-5236	68	21	≤	≤	NUM
cana-5236	68	22	𝛼<1	𝛼<1	NOUN
cana-5236	68	23	and	and	CCONJ
cana-5236	68	24	b	b	NOUN
cana-5236	68	25	∈	∈	PROPN
cana-5236	68	26	ℂ	ℂ	PROPN
cana-5236	68	27	−	−	PROPN
cana-5236	68	28	{	{	PUNCT
cana-5236	68	29	0	0	NUM
cana-5236	68	30	}	}	PUNCT
cana-5236	68	31	.	.	PUNCT
cana-5236	69	1	then	then	ADV
cana-5236	69	2	(	(	PUNCT
cana-5236	69	3	3.1	3.1	NUM
cana-5236	69	4	)	)	PUNCT
cana-5236	69	5	|𝑎𝑛|	|𝑎𝑛|	ADV
cana-5236	69	6	≤	≤	PROPN
cana-5236	69	7	(	(	PUNCT
cana-5236	69	8	𝜎)𝑛−1	𝜎)𝑛−1	PROPN
cana-5236	69	9	(	(	PUNCT
cana-5236	69	10	𝑛−1	𝑛−1	PROPN
cana-5236	69	11	)	)	PUNCT
cana-5236	69	12	!	!	PUNCT
cana-5236	70	1	𝜙𝑛(𝑚	𝜙𝑛(𝑚	PROPN
cana-5236	70	2	)	)	PUNCT
cana-5236	70	3	,	,	PUNCT
cana-5236	70	4	∀	∀	X
cana-5236	70	5	𝑛	𝑛	PRON
cana-5236	70	6	≥	≥	NOUN
cana-5236	70	7	2	2	NUM
cana-5236	70	8	,	,	PUNCT
cana-5236	70	9	where	where	SCONJ
cana-5236	70	10	𝜎	𝜎	NOUN
cana-5236	70	11	=	=	SYM
cana-5236	70	12	𝑘|𝑏|(𝐴−𝐵)(1−𝛼)(𝑚+1	𝑘|𝑏|(𝐴−𝐵)(1−𝛼)(𝑚+1	PROPN
cana-5236	70	13	)	)	PUNCT
cana-5236	70	14	4	4	NUM
cana-5236	70	15	and	and	CCONJ
cana-5236	70	16	𝜙𝑛(𝑚)=[1+(n-1)𝜆	𝜙𝑛(𝑚)=[1+(n-1)𝜆	PROPN
cana-5236	70	17	]	]	X
cana-5236	70	18	(	(	PUNCT
cana-5236	70	19	𝑚+1)𝑛−1	𝑚+1)𝑛−1	NUM
cana-5236	70	20	(	(	PUNCT
cana-5236	70	21	1)𝑛−1	1)𝑛−1	NUM
cana-5236	70	22	.	.	PUNCT
cana-5236	71	1	this	this	DET
cana-5236	71	2	result	result	NOUN
cana-5236	71	3	is	be	AUX
cana-5236	71	4	sharp	sharp	ADJ
cana-5236	71	5	proof	proof	NOUN
cana-5236	71	6	:	:	PUNCT
cana-5236	71	7	let	let	VERB
cana-5236	71	8	(	(	PUNCT
cana-5236	71	9	3.2	3.2	NUM
cana-5236	71	10	)	)	PUNCT
cana-5236	71	11	1	1	NUM
cana-5236	71	12	−	−	PROPN
cana-5236	71	13	2	2	NUM
cana-5236	71	14	𝑏	𝑏	NOUN
cana-5236	71	15	+	+	NOUN
cana-5236	71	16	2	2	NUM
cana-5236	71	17	𝑏	𝑏	NOUN
cana-5236	71	18	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	71	19	𝑚+1𝑓(𝑧	𝑚+1𝑓(𝑧	NUM
cana-5236	71	20	)	)	PUNCT
cana-5236	72	1	𝐷𝜆	𝐷𝜆	NOUN
cana-5236	72	2	𝑚𝑓(𝑧	𝑚𝑓(𝑧	NUM
cana-5236	72	3	)	)	PUNCT
cana-5236	72	4	=	=	SYM
cana-5236	72	5	𝑝(𝑧	𝑝(𝑧	NOUN
cana-5236	72	6	)	)	PUNCT
cana-5236	72	7	so	so	SCONJ
cana-5236	72	8	that	that	SCONJ
cana-5236	72	9	𝑝	𝑝	PROPN
cana-5236	72	10	∈	∈	PROPN
cana-5236	72	11	𝑃𝑘[𝐴	𝑃𝑘[𝐴	PROPN
cana-5236	72	12	,	,	PUNCT
cana-5236	72	13	𝐵	𝐵	NOUN
cana-5236	72	14	,	,	PUNCT
cana-5236	72	15	𝛼	𝛼	NOUN
cana-5236	72	16	]	]	PUNCT
cana-5236	72	17	.	.	PUNCT
cana-5236	73	1	let	let	VERB
cana-5236	73	2	𝑝(𝑧	𝑝(𝑧	NOUN
cana-5236	73	3	)	)	PUNCT
cana-5236	73	4	=	=	PUNCT
cana-5236	74	1	1	1	NUM
cana-5236	74	2	+	+	CCONJ
cana-5236	74	3	∑	∑	PROPN
cana-5236	74	4	𝑞𝑛𝑧𝑛∞	𝑞𝑛𝑧𝑛∞	ADJ
cana-5236	74	5	𝑛=1	𝑛=1	PROPN
cana-5236	74	6	.	.	PUNCT
cana-5236	75	1	then	then	ADV
cana-5236	75	2	(	(	PUNCT
cana-5236	75	3	3.2	3.2	NUM
cana-5236	75	4	)	)	PUNCT
cana-5236	75	5	can	can	AUX
cana-5236	75	6	be	be	AUX
cana-5236	75	7	written	write	VERB
cana-5236	75	8	as	as	ADP
cana-5236	75	9	2(𝐷𝜆	2(𝐷𝜆	NUM
cana-5236	75	10	𝑚+1𝑓(𝑧	𝑚+1𝑓(𝑧	NUM
cana-5236	75	11	)	)	PUNCT
cana-5236	75	12	−	−	PUNCT
cana-5236	76	1	𝐷𝜆	𝐷𝜆	VERB
cana-5236	76	2	𝑚𝑓(𝑧))=𝑏𝐷𝜆	𝑚𝑓(𝑧))=𝑏𝐷𝜆	PRON
cana-5236	76	3	𝑚𝑓(𝑧	𝑚𝑓(𝑧	NUM
cana-5236	76	4	)	)	PUNCT
cana-5236	76	5	∑	∑	PUNCT
cana-5236	76	6	𝑞𝑛𝑧𝑛∞	𝑞𝑛𝑧𝑛∞	X
cana-5236	76	7	𝑛=1	𝑛=1	NOUN
cana-5236	76	8	which	which	PRON
cana-5236	76	9	implies	imply	VERB
cana-5236	76	10	that	that	SCONJ
cana-5236	76	11	2𝜙𝑛(𝑚)(𝑛−1)𝑎𝑛	2𝜙𝑛(𝑚)(𝑛−1)𝑎𝑛	NUM
cana-5236	76	12	(	(	PUNCT
cana-5236	76	13	𝑚+1	𝑚+1	NUM
cana-5236	76	14	)	)	PUNCT
cana-5236	76	15	=	=	SYM
cana-5236	76	16	𝑏(𝑞𝑛−1	𝑏(𝑞𝑛−1	X
cana-5236	76	17	+	+	CCONJ
cana-5236	76	18	𝜙2(𝑚)𝑎2𝑞𝑛−2	𝜙2(𝑚)𝑎2𝑞𝑛−2	VERB
cana-5236	76	19	+	+	CCONJ
cana-5236	76	20	⋯	⋯	X
cana-5236	76	21	+	+	NOUN
cana-5236	76	22	𝜙𝑛−1(𝑚)𝑎𝑛−1𝑞1	𝜙𝑛−1(𝑚)𝑎𝑛−1𝑞1	ADJ
cana-5236	76	23	)	)	PUNCT
cana-5236	76	24	.	.	PUNCT
cana-5236	77	1	using	use	VERB
cana-5236	77	2	lemma	lemma	PROPN
cana-5236	77	3	2.1	2.1	NUM
cana-5236	77	4	,	,	PUNCT
cana-5236	77	5	we	we	PRON
cana-5236	77	6	obtain	obtain	VERB
cana-5236	77	7	|𝑎𝑛|	|𝑎𝑛|	DET
cana-5236	77	8	≤	≤	NUM
cana-5236	77	9	𝑘|𝑏|(𝐴	𝑘|𝑏|(𝐴	PROPN
cana-5236	78	1	−	−	NOUN
cana-5236	78	2	𝐵)(1	𝐵)(1	NOUN
cana-5236	78	3	−	−	NOUN
cana-5236	78	4	𝛼)(𝑚	𝛼)(𝑚	ADJ
cana-5236	79	1	+	+	CCONJ
cana-5236	79	2	1	1	X
cana-5236	79	3	)	)	PUNCT
cana-5236	79	4	4(𝑛	4(𝑛	NUM
cana-5236	79	5	−	−	NOUN
cana-5236	79	6	1)𝜙𝑛(𝑚	1)𝜙𝑛(𝑚	NUM
cana-5236	79	7	)	)	PUNCT
cana-5236	79	8	(	(	PUNCT
cana-5236	79	9	1	1	NUM
cana-5236	79	10	+	+	CCONJ
cana-5236	79	11	𝜙2(𝑚)|𝑎2|	𝜙2(𝑚)|𝑎2|	PROPN
cana-5236	79	12	+	+	CCONJ
cana-5236	79	13	⋯	⋯	PROPN
cana-5236	79	14	+	+	NUM
cana-5236	79	15	𝜙𝑛−1(𝑚)|𝑎𝑛−1|	𝜙𝑛−1(𝑚)|𝑎𝑛−1|	PROPN
cana-5236	79	16	)	)	PUNCT
cana-5236	80	1	=	=	SYM
cana-5236	80	2	𝜎	𝜎	PROPN
cana-5236	80	3	(	(	PUNCT
cana-5236	80	4	𝑛−1)𝜙𝑛(𝑚	𝑛−1)𝜙𝑛(𝑚	ADV
cana-5236	80	5	)	)	PUNCT
cana-5236	80	6	(	(	PUNCT
cana-5236	80	7	1	1	NUM
cana-5236	80	8	+	+	NUM
cana-5236	80	9	∑	∑	PROPN
cana-5236	80	10	𝜙𝑖(𝑚)|𝑎𝑖|	𝜙𝑖(𝑚)|𝑎𝑖|	PROPN
cana-5236	80	11	𝑛−1	𝑛−1	PROPN
cana-5236	80	12	𝑖=2	𝑖=2	PUNCT
cana-5236	80	13	)	)	PUNCT
cana-5236	80	14	.	.	PUNCT
cana-5236	81	1	for	for	ADP
cana-5236	81	2	n=2	n=2	PRON
cana-5236	81	3	,	,	PUNCT
cana-5236	81	4	|𝑎2|	|𝑎2|	NOUN
cana-5236	81	5	≤	≤	PUNCT
cana-5236	81	6	𝜎	𝜎	X
cana-5236	81	7	𝜙2(𝑚	𝜙2(𝑚	NOUN
cana-5236	81	8	)	)	PUNCT
cana-5236	81	9	=	=	SYM
cana-5236	81	10	(	(	PUNCT
cana-5236	81	11	𝜎)2−1	𝜎)2−1	NOUN
cana-5236	81	12	(	(	PUNCT
cana-5236	81	13	2−1	2−1	NUM
cana-5236	81	14	)	)	PUNCT
cana-5236	81	15	!	!	PUNCT
cana-5236	82	1	𝜙2(𝑚	𝜙2(𝑚	NOUN
cana-5236	82	2	)	)	PUNCT
cana-5236	82	3	therefore	therefore	ADV
cana-5236	82	4	(	(	PUNCT
cana-5236	82	5	3.1	3.1	NUM
cana-5236	82	6	)	)	PUNCT
cana-5236	82	7	holds	hold	VERB
cana-5236	82	8	for	for	ADP
cana-5236	82	9	n=2	n=2	X
cana-5236	82	10	.	.	PUNCT
cana-5236	83	1	assume	assume	VERB
cana-5236	83	2	that	that	SCONJ
cana-5236	83	3	(	(	PUNCT
cana-5236	83	4	3.1	3.1	NUM
cana-5236	83	5	)	)	PUNCT
cana-5236	83	6	is	be	AUX
cana-5236	83	7	true	true	ADJ
cana-5236	83	8	for	for	ADP
cana-5236	83	9	n	n	NOUN
cana-5236	83	10	=	=	SYM
cana-5236	83	11	l	l	NOUN
cana-5236	83	12	and	and	CCONJ
cana-5236	83	13	consider	consider	VERB
cana-5236	83	14	communications	communication	NOUN
cana-5236	83	15	on	on	ADP
cana-5236	83	16	applied	apply	VERB
cana-5236	83	17	nonlinear	nonlinear	ADJ
cana-5236	83	18	analysis	analysis	NOUN
cana-5236	83	19	issn	issn	NOUN
cana-5236	83	20	:	:	PUNCT
cana-5236	83	21	1074	1074	NUM
cana-5236	83	22	-	-	PUNCT
cana-5236	83	23	133x	133x	NUM
cana-5236	83	24	vol	vol	VERB
cana-5236	83	25	32	32	NUM
cana-5236	83	26	no	no	NOUN
cana-5236	83	27	.	.	PUNCT
cana-5236	84	1	10s	10	NOUN
cana-5236	84	2	(	(	PUNCT
cana-5236	84	3	2025	2025	NUM
cana-5236	84	4	)	)	PUNCT
cana-5236	84	5	1342	1342	NUM
cana-5236	84	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5236	84	7	|𝑎𝑙+1|	|𝑎𝑙+1|	ADP
cana-5236	84	8	≤	≤	NUM
cana-5236	84	9	𝜎	𝜎	PRON
cana-5236	84	10	𝑙	𝑙	X
cana-5236	84	11	𝜙𝑙+1(𝑚	𝜙𝑙+1(𝑚	NOUN
cana-5236	84	12	)	)	PUNCT
cana-5236	84	13	(	(	PUNCT
cana-5236	84	14	1	1	NUM
cana-5236	84	15	+	+	NUM
cana-5236	84	16	∑	∑	PROPN
cana-5236	84	17	𝜙𝑖(𝑚)|𝑎𝑖|	𝜙𝑖(𝑚)|𝑎𝑖|	PROPN
cana-5236	84	18	𝑙	𝑙	NOUN
cana-5236	84	19	𝑖=2	𝑖=2	PUNCT
cana-5236	84	20	)	)	PUNCT
cana-5236	84	21	≤	≤	NUM
cana-5236	85	1	𝜎	𝜎	PRON
cana-5236	85	2	𝑙	𝑙	X
cana-5236	85	3	𝜙𝑙+1(𝑚	𝜙𝑙+1(𝑚	NOUN
cana-5236	85	4	)	)	PUNCT
cana-5236	85	5	(	(	PUNCT
cana-5236	85	6	1	1	NUM
cana-5236	85	7	+	+	CCONJ
cana-5236	85	8	∑	∑	PROPN
cana-5236	85	9	(	(	PUNCT
cana-5236	85	10	𝜎)𝑖−1	𝜎)𝑖−1	NOUN
cana-5236	85	11	(	(	PUNCT
cana-5236	85	12	𝑖−1	𝑖−1	PROPN
cana-5236	85	13	)	)	PUNCT
cana-5236	85	14	!	!	PUNCT
cana-5236	86	1	𝑙	𝑙	X
cana-5236	86	2	𝑖=2	𝑖=2	PUNCT
cana-5236	86	3	)	)	PUNCT
cana-5236	86	4	=	=	SYM
cana-5236	86	5	𝜎	𝜎	PROPN
cana-5236	86	6	𝑙	𝑙	X
cana-5236	86	7	𝜙𝑙+1(𝑚	𝜙𝑙+1(𝑚	NOUN
cana-5236	86	8	)	)	PUNCT
cana-5236	86	9	(	(	PUNCT
cana-5236	86	10	1	1	NUM
cana-5236	86	11	+	+	CCONJ
cana-5236	86	12	∑	∑	PROPN
cana-5236	86	13	𝜎	𝜎	PROPN
cana-5236	86	14	∏	∏	PROPN
cana-5236	86	15	(	(	PUNCT
cana-5236	86	16	1	1	NUM
cana-5236	86	17	+	+	SYM
cana-5236	86	18	𝜎	𝜎	PRON
cana-5236	86	19	𝑗	𝑗	NOUN
cana-5236	86	20	)	)	PUNCT
cana-5236	86	21	𝑖−1	𝑖−1	PROPN
cana-5236	87	1	𝑗=1	𝑗=1	PROPN
cana-5236	87	2	𝑙	𝑙	X
cana-5236	87	3	𝑖=2	𝑖=2	PUNCT
cana-5236	87	4	)	)	PUNCT
cana-5236	87	5	=	=	SYM
cana-5236	87	6	𝜎	𝜎	PROPN
cana-5236	87	7	𝑙	𝑙	X
cana-5236	87	8	𝜙𝑙+1(𝑚	𝜙𝑙+1(𝑚	PROPN
cana-5236	87	9	)	)	PUNCT
cana-5236	87	10	∏	∏	PROPN
cana-5236	87	11	(	(	PUNCT
cana-5236	87	12	1	1	NUM
cana-5236	87	13	+	+	SYM
cana-5236	87	14	𝜎	𝜎	ADJ
cana-5236	87	15	𝑗	𝑗	NOUN
cana-5236	87	16	)	)	PUNCT
cana-5236	87	17	𝑙−1	𝑙−1	NOUN
cana-5236	87	18	𝑗=1	𝑗=1	PROPN
cana-5236	87	19	=	=	PUNCT
cana-5236	87	20	(	(	PUNCT
cana-5236	87	21	𝜎)𝑙	𝜎)𝑙	NOUN
cana-5236	87	22	𝑙	𝑙	X
cana-5236	87	23	!	!	PUNCT
cana-5236	88	1	𝜙𝑙+1(𝑚	𝜙𝑙+1(𝑚	NOUN
cana-5236	88	2	)	)	PUNCT
cana-5236	88	3	.	.	PUNCT
cana-5236	89	1	therefore	therefore	ADV
cana-5236	89	2	,	,	PUNCT
cana-5236	89	3	the	the	DET
cana-5236	89	4	result	result	NOUN
cana-5236	89	5	is	be	AUX
cana-5236	89	6	true	true	ADJ
cana-5236	89	7	for	for	ADP
cana-5236	89	8	n	n	NOUN
cana-5236	89	9	=	=	SYM
cana-5236	89	10	l	l	NOUN
cana-5236	89	11	+	+	NOUN
cana-5236	89	12	1	1	X
cana-5236	89	13	.	.	X
cana-5236	89	14	using	use	VERB
cana-5236	89	15	mathematical	mathematical	ADJ
cana-5236	89	16	induction	induction	NOUN
cana-5236	89	17	,	,	PUNCT
cana-5236	89	18	(	(	PUNCT
cana-5236	89	19	3.1	3.1	NUM
cana-5236	89	20	)	)	PUNCT
cana-5236	89	21	holds	hold	VERB
cana-5236	89	22	true	true	ADJ
cana-5236	89	23	for	for	ADP
cana-5236	89	24	all	all	DET
cana-5236	89	25	n	n	PRON
cana-5236	89	26	≥	≥	NOUN
cana-5236	89	27	2	2	NUM
cana-5236	89	28	.	.	PUNCT
cana-5236	90	1	this	this	DET
cana-5236	90	2	result	result	NOUN
cana-5236	90	3	is	be	AUX
cana-5236	90	4	sharp	sharp	ADJ
cana-5236	90	5	for	for	SCONJ
cana-5236	90	6	m	m	PROPN
cana-5236	90	7	≥	≥	NOUN
cana-5236	90	8	0	0	NUM
cana-5236	90	9	,	,	PUNCT
cana-5236	90	10	0	0	NUM
cana-5236	90	11	≤	≤	NUM
cana-5236	90	12	α	α	NOUN
cana-5236	90	13	<	<	X
cana-5236	90	14	1	1	NUM
cana-5236	90	15	,	,	PUNCT
cana-5236	91	1	b	b	X
cana-5236	91	2	∈	∈	PROPN
cana-5236	91	3	ℂ−	ℂ−	X
cana-5236	91	4	{	{	PUNCT
cana-5236	91	5	0	0	NUM
cana-5236	91	6	}	}	PUNCT
cana-5236	91	7	and	and	CCONJ
cana-5236	91	8	k	k	X
cana-5236	91	9	≥	≥	NUM
cana-5236	91	10	2	2	NUM
cana-5236	91	11	as	as	SCONJ
cana-5236	91	12	can	can	AUX
cana-5236	91	13	be	be	AUX
cana-5236	91	14	seen	see	VERB
cana-5236	91	15	from	from	ADP
cana-5236	91	16	the	the	DET
cana-5236	91	17	functions	function	NOUN
cana-5236	91	18	𝑓0(𝑧	𝑓0(𝑧	NOUN
cana-5236	91	19	)	)	PUNCT
cana-5236	91	20	which	which	PRON
cana-5236	91	21	are	be	AUX
cana-5236	91	22	given	give	VERB
cana-5236	91	23	as	as	ADP
cana-5236	91	24	1	1	NUM
cana-5236	91	25	−	−	NUM
cana-5236	91	26	2	2	NUM
cana-5236	91	27	𝑏	𝑏	NOUN
cana-5236	91	28	+	+	NOUN
cana-5236	91	29	2	2	NUM
cana-5236	91	30	𝑏	𝑏	DET
cana-5236	91	31	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	91	32	𝑚+1𝑓0(𝑧	𝑚+1𝑓0(𝑧	PROPN
cana-5236	91	33	)	)	PUNCT
cana-5236	91	34	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	91	35	𝑚𝑓0(𝑧	𝑚𝑓0(𝑧	NUM
cana-5236	91	36	)	)	PUNCT
cana-5236	91	37	=	=	PUNCT
cana-5236	91	38	(	(	PUNCT
cana-5236	91	39	1	1	NUM
cana-5236	91	40	−	−	NOUN
cana-5236	91	41	𝛼	𝛼	NOUN
cana-5236	91	42	)	)	PUNCT
cana-5236	92	1	[	[	X
cana-5236	92	2	(	(	PUNCT
cana-5236	92	3	𝑘	𝑘	DET
cana-5236	92	4	4	4	NUM
cana-5236	92	5	+	+	SYM
cana-5236	92	6	1	1	NUM
cana-5236	92	7	2	2	NUM
cana-5236	92	8	)	)	PUNCT
cana-5236	92	9	1+𝐴𝑧	1+𝐴𝑧	NUM
cana-5236	92	10	1+𝐵𝑧	1+𝐵𝑧	NUM
cana-5236	92	11	−	−	PROPN
cana-5236	93	1	(	(	PUNCT
cana-5236	93	2	𝑘	𝑘	PROPN
cana-5236	93	3	4	4	NUM
cana-5236	93	4	−	−	NOUN
cana-5236	93	5	1	1	NUM
cana-5236	93	6	2	2	NUM
cana-5236	93	7	)	)	PUNCT
cana-5236	93	8	1−𝐴𝑧	1−𝐴𝑧	NUM
cana-5236	93	9	1−𝐵𝑧	1−𝐵𝑧	NUM
cana-5236	93	10	]	]	PUNCT
cana-5236	94	1	+	+	CCONJ
cana-5236	94	2	𝛼.	𝛼.	NOUN
cana-5236	94	3	for	for	ADP
cana-5236	94	4	different	different	ADJ
cana-5236	94	5	values	value	NOUN
cana-5236	94	6	of	of	ADP
cana-5236	94	7	a	a	DET
cana-5236	94	8	,	,	PUNCT
cana-5236	94	9	b	b	PROPN
cana-5236	94	10	,	,	PUNCT
cana-5236	94	11	α	α	PROPN
cana-5236	94	12	,	,	PUNCT
cana-5236	94	13	b	b	NOUN
cana-5236	94	14	and	and	CCONJ
cana-5236	94	15	λ	λ	PROPN
cana-5236	94	16	,	,	PUNCT
cana-5236	94	17	we	we	PRON
cana-5236	94	18	obtain	obtain	VERB
cana-5236	94	19	the	the	DET
cana-5236	94	20	following	follow	VERB
cana-5236	94	21	results	result	NOUN
cana-5236	94	22	[	[	X
cana-5236	94	23	16	16	NUM
cana-5236	94	24	]	]	PUNCT
cana-5236	94	25	.	.	PUNCT
cana-5236	95	1	corollary	corollary	ADJ
cana-5236	95	2	3.2	3.2	NUM
cana-5236	95	3	.	.	PUNCT
cana-5236	96	1	if	if	SCONJ
cana-5236	96	2	f	f	PROPN
cana-5236	96	3	∈	∈	PROPN
cana-5236	96	4	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	96	5	0	0	PUNCT
cana-5236	97	1	[	[	X
cana-5236	97	2	1	1	NUM
cana-5236	97	3	,	,	PUNCT
cana-5236	97	4	−1	−1	NOUN
cana-5236	97	5	,	,	PUNCT
cana-5236	97	6	𝛼	𝛼	X
cana-5236	97	7	,	,	PUNCT
cana-5236	97	8	2	2	NUM
cana-5236	97	9	]	]	PUNCT
cana-5236	97	10	=	=	PUNCT
cana-5236	97	11	𝑅𝑘(𝛼	𝑅𝑘(𝛼	NOUN
cana-5236	97	12	)	)	PUNCT
cana-5236	97	13	,	,	PUNCT
cana-5236	97	14	then	then	ADV
cana-5236	97	15	|𝑎𝑛|	|𝑎𝑛|	DET
cana-5236	97	16	≤	≤	PUNCT
cana-5236	97	17	(	(	PUNCT
cana-5236	97	18	𝑘(1	𝑘(1	INTJ
cana-5236	97	19	−	−	ADP
cana-5236	97	20	𝛼	𝛼	NOUN
cana-5236	97	21	)	)	PUNCT
cana-5236	97	22	)	)	PUNCT
cana-5236	98	1	𝑛−1	𝑛−1	PROPN
cana-5236	98	2	(	(	PUNCT
cana-5236	98	3	𝑛	𝑛	PROPN
cana-5236	98	4	−	−	PROPN
cana-5236	98	5	1	1	NUM
cana-5236	98	6	)	)	PUNCT
cana-5236	98	7	!	!	PUNCT
cana-5236	98	8	,	,	PUNCT
cana-5236	98	9	∀	∀	X
cana-5236	98	10	𝑛	𝑛	PRON
cana-5236	98	11	≥	≥	NUM
cana-5236	98	12	2	2	NUM
cana-5236	98	13	this	this	DET
cana-5236	98	14	result	result	NOUN
cana-5236	98	15	is	be	AUX
cana-5236	98	16	sharp	sharp	ADJ
cana-5236	98	17	.	.	PUNCT
cana-5236	99	1	corollary	corollary	ADJ
cana-5236	99	2	3.3	3.3	NUM
cana-5236	99	3	.	.	PUNCT
cana-5236	100	1	if	if	SCONJ
cana-5236	100	2	f	f	PROPN
cana-5236	100	3	∈	∈	PROPN
cana-5236	100	4	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	100	5	1	1	NUM
cana-5236	101	1	[	[	X
cana-5236	101	2	1	1	NUM
cana-5236	101	3	,	,	PUNCT
cana-5236	101	4	−1	−1	NOUN
cana-5236	101	5	,	,	PUNCT
cana-5236	101	6	𝛼	𝛼	X
cana-5236	101	7	,	,	PUNCT
cana-5236	101	8	1	1	NUM
cana-5236	101	9	]	]	PUNCT
cana-5236	101	10	=	=	SYM
cana-5236	101	11	𝑉𝑘(𝛼	𝑉𝑘(𝛼	NOUN
cana-5236	101	12	)	)	PUNCT
cana-5236	101	13	,	,	PUNCT
cana-5236	101	14	then	then	ADV
cana-5236	101	15	|𝑎𝑛|	|𝑎𝑛|	DET
cana-5236	101	16	≤	≤	PUNCT
cana-5236	101	17	(	(	PUNCT
cana-5236	101	18	𝑘(1	𝑘(1	INTJ
cana-5236	101	19	−	−	ADP
cana-5236	101	20	𝛼	𝛼	NOUN
cana-5236	101	21	)	)	PUNCT
cana-5236	101	22	)	)	PUNCT
cana-5236	102	1	𝑛−1	𝑛−1	PROPN
cana-5236	102	2	(	(	PUNCT
cana-5236	102	3	𝑛	𝑛	NOUN
cana-5236	102	4	)	)	PUNCT
cana-5236	102	5	!	!	PUNCT
cana-5236	102	6	,	,	PUNCT
cana-5236	102	7	∀	∀	X
cana-5236	102	8	𝑛	𝑛	PRON
cana-5236	102	9	≥	≥	NOUN
cana-5236	102	10	2	2	NUM
cana-5236	102	11	.	.	PUNCT
cana-5236	103	1	this	this	DET
cana-5236	103	2	result	result	NOUN
cana-5236	103	3	is	be	AUX
cana-5236	103	4	sharp	sharp	ADJ
cana-5236	103	5	.	.	PUNCT
cana-5236	104	1	theorem	theorem	VERB
cana-5236	104	2	3.4	3.4	NUM
cana-5236	104	3	.	.	PUNCT
cana-5236	105	1	for	for	ADP
cana-5236	105	2	real	real	ADJ
cana-5236	105	3	b	b	PROPN
cana-5236	105	4	>	>	X
cana-5236	105	5	0	0	PROPN
cana-5236	105	6	,	,	PUNCT
cana-5236	105	7	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	105	8	𝑚+1[𝐴	𝑚+1[𝐴	X
cana-5236	105	9	,	,	PUNCT
cana-5236	105	10	𝐵	𝐵	PROPN
cana-5236	105	11	,	,	PUNCT
cana-5236	105	12	𝛼	𝛼	PROPN
cana-5236	105	13	,	,	PUNCT
cana-5236	105	14	𝑏	𝑏	NOUN
cana-5236	105	15	]	]	PUNCT
cana-5236	105	16	⊆	⊆	NUM
cana-5236	105	17	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	105	18	𝑚	𝑚	X
cana-5236	105	19	[	[	X
cana-5236	105	20	1	1	NUM
cana-5236	105	21	,	,	PUNCT
cana-5236	105	22	−1	−1	NOUN
cana-5236	105	23	,	,	PUNCT
cana-5236	105	24	𝛽	𝛽	NOUN
cana-5236	105	25	,	,	PUNCT
cana-5236	105	26	𝑏	𝑏	PROPN
cana-5236	105	27	+	+	NOUN
cana-5236	105	28	1	1	NUM
cana-5236	105	29	]	]	PUNCT
cana-5236	105	30	,	,	PUNCT
cana-5236	105	31	z	z	PROPN
cana-5236	105	32	𝜖	𝜖	PROPN
cana-5236	105	33	𝒰	𝒰	PROPN
cana-5236	105	34	,	,	PUNCT
cana-5236	105	35	where	where	SCONJ
cana-5236	105	36	β	β	X
cana-5236	105	37	(	(	PUNCT
cana-5236	105	38	0	0	NUM
cana-5236	105	39	≤	≤	NOUN
cana-5236	105	40	β	β	X
cana-5236	105	41	<	<	X
cana-5236	105	42	1	1	NUM
cana-5236	105	43	)	)	PUNCT
cana-5236	105	44	is	be	AUX
cana-5236	105	45	one	one	NUM
cana-5236	105	46	of	of	ADP
cana-5236	105	47	the	the	DET
cana-5236	105	48	roots	root	NOUN
cana-5236	105	49	of	of	ADP
cana-5236	105	50	(	(	PUNCT
cana-5236	105	51	3.3	3.3	NUM
cana-5236	105	52	)	)	PUNCT
cana-5236	105	53	𝜂1𝜂2𝑏2(𝑚	𝜂1𝜂2𝑏2(𝑚	PROPN
cana-5236	105	54	+	+	CCONJ
cana-5236	105	55	2)2(1	2)2(1	NUM
cana-5236	105	56	−	−	NOUN
cana-5236	105	57	𝛼)2	𝛼)2	PROPN
cana-5236	105	58	−	−	PROPN
cana-5236	105	59	𝑏(𝑚	𝑏(𝑚	NOUN
cana-5236	105	60	+	+	CCONJ
cana-5236	105	61	2)(1	2)(1	NUM
cana-5236	105	62	−	−	NOUN
cana-5236	105	63	𝛼)[𝜂1(𝐵	𝛼)[𝜂1(𝐵	NOUN
cana-5236	105	64	+	+	NOUN
cana-5236	105	65	1	1	NUM
cana-5236	105	66	)	)	PUNCT
cana-5236	106	1	+	+	CCONJ
cana-5236	106	2	𝜂2(𝐵	𝜂2(𝐵	NOUN
cana-5236	106	3	−	−	NOUN
cana-5236	106	4	1	1	NUM
cana-5236	106	5	)	)	PUNCT
cana-5236	106	6	]	]	PUNCT
cana-5236	107	1	+	+	CCONJ
cana-5236	107	2	(	(	PUNCT
cana-5236	107	3	𝐵2	𝐵2	NOUN
cana-5236	107	4	−	−	NOUN
cana-5236	107	5	1	1	NUM
cana-5236	107	6	)	)	PUNCT
cana-5236	107	7	=	=	SYM
cana-5236	107	8	0	0	NUM
cana-5236	107	9	,	,	PUNCT
cana-5236	107	10	where	where	SCONJ
cana-5236	107	11	(	(	PUNCT
cana-5236	107	12	3.4	3.4	NUM
cana-5236	107	13	)	)	PUNCT
cana-5236	107	14	𝜂1	𝜂1	NOUN
cana-5236	107	15	=	=	SYM
cana-5236	107	16	(	(	PUNCT
cana-5236	107	17	1−𝑏)+𝛽(1+𝑏	1−𝑏)+𝛽(1+𝑏	NOUN
cana-5236	107	18	)	)	PUNCT
cana-5236	107	19	(	(	PUNCT
cana-5236	107	20	1+𝑏)(1−𝛽	1+𝑏)(1−𝛽	NUM
cana-5236	107	21	)	)	PUNCT
cana-5236	107	22	[	[	X
cana-5236	107	23	δ(b	δ(b	NOUN
cana-5236	107	24	−	−	PROPN
cana-5236	107	25	1	1	NUM
cana-5236	107	26	)	)	PUNCT
cana-5236	107	27	−	−	PROPN
cana-5236	107	28	(	(	PUNCT
cana-5236	107	29	a	a	DET
cana-5236	107	30	−	−	PROPN
cana-5236	107	31	1	1	NUM
cana-5236	107	32	)	)	PUNCT
cana-5236	107	33	]	]	PUNCT
cana-5236	107	34	(	(	PUNCT
cana-5236	107	35	3.5	3.5	NUM
cana-5236	107	36	)	)	PUNCT
cana-5236	107	37	𝜂2	𝜂2	NOUN
cana-5236	107	38	=	=	SYM
cana-5236	107	39	(	(	PUNCT
cana-5236	107	40	1−𝑏)+𝛽(1+𝑏	1−𝑏)+𝛽(1+𝑏	NOUN
cana-5236	107	41	)	)	PUNCT
cana-5236	107	42	(	(	PUNCT
cana-5236	107	43	1+𝑏)(1−𝛽	1+𝑏)(1−𝛽	NUM
cana-5236	107	44	)	)	PUNCT
cana-5236	108	1	[	[	X
cana-5236	108	2	δ(b	δ(b	NOUN
cana-5236	108	3	+	+	CCONJ
cana-5236	108	4	1	1	X
cana-5236	108	5	)	)	PUNCT
cana-5236	108	6	−	−	PROPN
cana-5236	108	7	(	(	PUNCT
cana-5236	108	8	a	a	DET
cana-5236	108	9	+	+	NOUN
cana-5236	108	10	1	1	NUM
cana-5236	108	11	)	)	PUNCT
cana-5236	108	12	]	]	PUNCT
cana-5236	108	13	and	and	CCONJ
cana-5236	108	14	communications	communication	NOUN
cana-5236	108	15	on	on	ADP
cana-5236	108	16	applied	apply	VERB
cana-5236	108	17	nonlinear	nonlinear	ADJ
cana-5236	108	18	analysis	analysis	NOUN
cana-5236	108	19	issn	issn	NOUN
cana-5236	108	20	:	:	PUNCT
cana-5236	108	21	1074	1074	NUM
cana-5236	108	22	-	-	PUNCT
cana-5236	108	23	133x	133x	NUM
cana-5236	108	24	vol	vol	VERB
cana-5236	108	25	32	32	NUM
cana-5236	108	26	no	no	NOUN
cana-5236	108	27	.	.	PUNCT
cana-5236	109	1	10s	10	NOUN
cana-5236	109	2	(	(	PUNCT
cana-5236	109	3	2025	2025	NUM
cana-5236	109	4	)	)	PUNCT
cana-5236	109	5	1343	1343	NUM
cana-5236	109	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5236	109	7	δ	δ	X
cana-5236	109	8	=	=	SYM
cana-5236	109	9	1	1	NUM
cana-5236	109	10	−	−	PROPN
cana-5236	109	11	(	(	PUNCT
cana-5236	109	12	1	1	NUM
cana-5236	109	13	+	+	CCONJ
cana-5236	109	14	𝑏)(𝑚	𝑏)(𝑚	PROPN
cana-5236	109	15	+	+	CCONJ
cana-5236	109	16	1)(1	1)(1	NUM
cana-5236	109	17	−	−	ADP
cana-5236	109	18	𝛽	𝛽	NOUN
cana-5236	109	19	)	)	PUNCT
cana-5236	109	20	𝑏(𝑚	𝑏(𝑚	PROPN
cana-5236	109	21	+	+	CCONJ
cana-5236	109	22	2)(1	2)(1	NUM
cana-5236	109	23	−	−	NUM
cana-5236	109	24	𝛼	𝛼	NOUN
cana-5236	109	25	)	)	PUNCT
cana-5236	109	26	.	.	PUNCT
cana-5236	110	1	proof	proof	NOUN
cana-5236	110	2	:	:	PUNCT
cana-5236	110	3	suppose	suppose	VERB
cana-5236	110	4	f	f	PROPN
cana-5236	110	5	∈	∈	PROPN
cana-5236	110	6	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	110	7	𝑚+1[𝐴	𝑚+1[𝐴	X
cana-5236	110	8	,	,	PUNCT
cana-5236	110	9	𝐵	𝐵	NOUN
cana-5236	110	10	,	,	PUNCT
cana-5236	110	11	𝛼	𝛼	PROPN
cana-5236	110	12	,	,	PUNCT
cana-5236	110	13	𝑏	𝑏	NOUN
cana-5236	110	14	]	]	PUNCT
cana-5236	110	15	and	and	CCONJ
cana-5236	110	16	set	set	VERB
cana-5236	110	17	(	(	PUNCT
cana-5236	110	18	3.6	3.6	NUM
cana-5236	110	19	)	)	PUNCT
cana-5236	110	20	𝑝(𝑧	𝑝(𝑧	NOUN
cana-5236	110	21	)	)	PUNCT
cana-5236	110	22	=	=	SYM
cana-5236	111	1	1	1	NUM
cana-5236	111	2	−	−	NUM
cana-5236	111	3	2	2	NUM
cana-5236	111	4	𝑏+1	𝑏+1	PROPN
cana-5236	111	5	+	+	NUM
cana-5236	111	6	2	2	NUM
cana-5236	111	7	𝑏+1	𝑏+1	X
cana-5236	111	8	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	111	9	𝑚+1𝑓(𝑧	𝑚+1𝑓(𝑧	PROPN
cana-5236	111	10	)	)	PUNCT
cana-5236	112	1	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	112	2	𝑚𝑓(𝑧	𝑚𝑓(𝑧	NOUN
cana-5236	112	3	)	)	PUNCT
cana-5236	112	4	where	where	SCONJ
cana-5236	112	5	𝑝	𝑝	NOUN
cana-5236	112	6	is	be	AUX
cana-5236	112	7	analytic	analytic	ADJ
cana-5236	112	8	in	in	ADP
cana-5236	112	9	𝒰	𝒰	PROPN
cana-5236	112	10	with	with	ADP
cana-5236	112	11	𝑝(0	𝑝(0	PROPN
cana-5236	112	12	)	)	PUNCT
cana-5236	112	13	=	=	SYM
cana-5236	113	1	1	1	X
cana-5236	113	2	.	.	PUNCT
cana-5236	113	3	then	then	ADV
cana-5236	113	4	,	,	PUNCT
cana-5236	113	5	by	by	ADP
cana-5236	113	6	simple	simple	ADJ
cana-5236	113	7	computations	computation	NOUN
cana-5236	113	8	together	together	ADV
cana-5236	113	9	with	with	ADP
cana-5236	113	10	(	(	PUNCT
cana-5236	113	11	3.6	3.6	NUM
cana-5236	113	12	)	)	PUNCT
cana-5236	113	13	and	and	CCONJ
cana-5236	113	14	(	(	PUNCT
cana-5236	113	15	1.9	1.9	NUM
cana-5236	113	16	)	)	PUNCT
cana-5236	113	17	yield	yield	NOUN
cana-5236	113	18	(	(	PUNCT
cana-5236	113	19	3.7	3.7	NUM
cana-5236	113	20	)	)	PUNCT
cana-5236	113	21	1	1	NUM
cana-5236	113	22	−	−	PROPN
cana-5236	113	23	2	2	NUM
cana-5236	113	24	𝑏	𝑏	NOUN
cana-5236	113	25	+	+	NOUN
cana-5236	113	26	2	2	NUM
cana-5236	113	27	𝑏	𝑏	NOUN
cana-5236	113	28	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	113	29	𝑚+2𝑓(𝑧	𝑚+2𝑓(𝑧	NUM
cana-5236	113	30	)	)	PUNCT
cana-5236	113	31	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	113	32	𝑚+1𝑓(𝑧	𝑚+1𝑓(𝑧	NUM
cana-5236	113	33	)	)	PUNCT
cana-5236	113	34	=	=	SYM
cana-5236	113	35	(	(	PUNCT
cana-5236	113	36	1	1	NUM
cana-5236	113	37	−	−	NOUN
cana-5236	113	38	𝜇1	𝜇1	NOUN
cana-5236	113	39	)	)	PUNCT
cana-5236	113	40	+	+	NUM
cana-5236	113	41	𝜇1	𝜇1	PROPN
cana-5236	113	42	[	[	X
cana-5236	113	43	𝑝(𝑧	𝑝(𝑧	PROPN
cana-5236	113	44	)	)	PUNCT
cana-5236	113	45	+	+	NUM
cana-5236	113	46	𝜇2𝑧𝑝′(𝑧	𝜇2𝑧𝑝′(𝑧	NOUN
cana-5236	113	47	)	)	PUNCT
cana-5236	113	48	𝑝(𝑧)+𝜇3	𝑝(𝑧)+𝜇3	NOUN
cana-5236	113	49	]	]	X
cana-5236	113	50	,	,	PUNCT
cana-5236	113	51	where	where	SCONJ
cana-5236	113	52	𝜇1	𝜇1	NOUN
cana-5236	113	53	=	=	SYM
cana-5236	113	54	𝑚+1	𝑚+1	PROPN
cana-5236	113	55	𝑚+2	𝑚+2	PROPN
cana-5236	113	56	𝑏+1	𝑏+1	PROPN
cana-5236	113	57	𝑏	𝑏	PROPN
cana-5236	113	58	,	,	PUNCT
cana-5236	113	59	𝜇2	𝜇2	NOUN
cana-5236	113	60	=	=	SYM
cana-5236	113	61	2	2	NUM
cana-5236	113	62	(	(	PUNCT
cana-5236	113	63	𝑚+1)(𝑏+1	𝑚+1)(𝑏+1	NOUN
cana-5236	113	64	)	)	PUNCT
cana-5236	113	65	,	,	PUNCT
cana-5236	113	66	𝜇3	𝜇3	NOUN
cana-5236	113	67	=	=	NOUN
cana-5236	113	68	2	2	NUM
cana-5236	113	69	𝑏+1	𝑏+1	SYM
cana-5236	113	70	−	−	NUM
cana-5236	113	71	1	1	NUM
cana-5236	113	72	.	.	PUNCT
cana-5236	114	1	since	since	SCONJ
cana-5236	114	2	f	f	PROPN
cana-5236	114	3	∈	∈	PROPN
cana-5236	114	4	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	114	5	𝑚+1[𝐴	𝑚+1[𝐴	X
cana-5236	114	6	,	,	PUNCT
cana-5236	114	7	𝐵	𝐵	NOUN
cana-5236	114	8	,	,	PUNCT
cana-5236	114	9	𝛼	𝛼	PROPN
cana-5236	114	10	,	,	PUNCT
cana-5236	114	11	𝑏	𝑏	NOUN
cana-5236	114	12	]	]	PUNCT
cana-5236	114	13	,	,	PUNCT
cana-5236	114	14	it	it	PRON
cana-5236	114	15	follows	follow	VERB
cana-5236	114	16	that	that	SCONJ
cana-5236	114	17	(	(	PUNCT
cana-5236	114	18	1	1	NUM
cana-5236	114	19	−	−	NOUN
cana-5236	114	20	𝜇1	𝜇1	NOUN
cana-5236	114	21	)	)	PUNCT
cana-5236	115	1	+	+	NUM
cana-5236	115	2	𝜇1	𝜇1	PROPN
cana-5236	115	3	[	[	X
cana-5236	115	4	𝑝(𝑧	𝑝(𝑧	PROPN
cana-5236	115	5	)	)	PUNCT
cana-5236	116	1	+	+	NUM
cana-5236	116	2	𝜇2𝑧𝑝′(𝑧	𝜇2𝑧𝑝′(𝑧	NOUN
cana-5236	116	3	)	)	PUNCT
cana-5236	116	4	𝑝(𝑧)+𝜇3	𝑝(𝑧)+𝜇3	NOUN
cana-5236	116	5	]	]	PUNCT
cana-5236	116	6	∈	∈	PROPN
cana-5236	116	7	𝑃𝑘[𝐴	𝑃𝑘[𝐴	PROPN
cana-5236	116	8	,	,	PUNCT
cana-5236	116	9	𝐵	𝐵	NOUN
cana-5236	116	10	,	,	PUNCT
cana-5236	116	11	𝛼	𝛼	PROPN
cana-5236	116	12	]	]	X
cana-5236	116	13	,	,	PUNCT
cana-5236	116	14	or	or	CCONJ
cana-5236	116	15	,	,	PUNCT
cana-5236	116	16	equivalently	equivalently	ADV
cana-5236	116	17	(	(	PUNCT
cana-5236	116	18	3.8	3.8	NUM
cana-5236	116	19	)	)	PUNCT
cana-5236	116	20	(	(	PUNCT
cana-5236	116	21	1−𝛼−𝜇1	1−𝛼−𝜇1	NUM
cana-5236	116	22	)	)	PUNCT
cana-5236	116	23	(	(	PUNCT
cana-5236	116	24	1−𝛼	1−𝛼	NUM
cana-5236	116	25	)	)	PUNCT
cana-5236	117	1	+	+	X
cana-5236	117	2	𝜇1	𝜇1	PROPN
cana-5236	117	3	1−𝛼	1−𝛼	X
cana-5236	118	1	[	[	X
cana-5236	118	2	𝑝(𝑧	𝑝(𝑧	NOUN
cana-5236	118	3	)	)	PUNCT
cana-5236	118	4	+	+	NUM
cana-5236	118	5	𝜇2𝑧𝑝′(𝑧	𝜇2𝑧𝑝′(𝑧	NOUN
cana-5236	118	6	)	)	PUNCT
cana-5236	118	7	𝑝(𝑧)+𝜇3	𝑝(𝑧)+𝜇3	NOUN
cana-5236	118	8	]	]	PUNCT
cana-5236	118	9	∈	∈	PROPN
cana-5236	118	10	𝑃𝑘[𝐴	𝑃𝑘[𝐴	PROPN
cana-5236	118	11	,	,	PUNCT
cana-5236	118	12	𝐵	𝐵	PROPN
cana-5236	118	13	]	]	PUNCT
cana-5236	118	14	.	.	PUNCT
cana-5236	119	1	define	define	VERB
cana-5236	119	2	𝜙(𝑧	𝜙(𝑧	NOUN
cana-5236	119	3	)	)	PUNCT
cana-5236	119	4	=	=	SYM
cana-5236	119	5	1	1	NUM
cana-5236	119	6	(	(	PUNCT
cana-5236	119	7	1	1	NUM
cana-5236	119	8	+	+	NUM
cana-5236	119	9	𝜇3	𝜇3	NOUN
cana-5236	119	10	)	)	PUNCT
cana-5236	119	11	𝑧	𝑧	PROPN
cana-5236	119	12	(	(	PUNCT
cana-5236	119	13	1	1	NUM
cana-5236	119	14	−	−	PROPN
cana-5236	119	15	𝑧)𝜇2	𝑧)𝜇2	PROPN
cana-5236	119	16	+	+	CCONJ
cana-5236	119	17	𝜇3	𝜇3	PROPN
cana-5236	119	18	(	(	PUNCT
cana-5236	119	19	1	1	NUM
cana-5236	119	20	+	+	NUM
cana-5236	119	21	𝜇3	𝜇3	NOUN
cana-5236	119	22	)	)	PUNCT
cana-5236	119	23	𝑧	𝑧	PROPN
cana-5236	119	24	(	(	PUNCT
cana-5236	119	25	1	1	NUM
cana-5236	119	26	−	−	ADP
cana-5236	119	27	𝑧)𝜇2	𝑧)𝜇2	PROPN
cana-5236	119	28	+	+	PROPN
cana-5236	119	29	1	1	NUM
cana-5236	119	30	,	,	PUNCT
cana-5236	119	31	and	and	CCONJ
cana-5236	119	32	by	by	ADP
cana-5236	119	33	using	use	VERB
cana-5236	119	34	convolution	convolution	NOUN
cana-5236	119	35	techniques	technique	NOUN
cana-5236	119	36	given	give	VERB
cana-5236	119	37	by	by	ADP
cana-5236	119	38	noor[3	noor[3	PROPN
cana-5236	119	39	]	]	PUNCT
cana-5236	119	40	,	,	PUNCT
cana-5236	119	41	we	we	PRON
cana-5236	119	42	have	have	VERB
cana-5236	119	43	𝑝(𝑧	𝑝(𝑧	PROPN
cana-5236	119	44	)	)	PUNCT
cana-5236	120	1	+	+	CCONJ
cana-5236	120	2	𝜇2𝑧𝑝′(𝑧	𝜇2𝑧𝑝′(𝑧	NOUN
cana-5236	120	3	)	)	PUNCT
cana-5236	120	4	𝑝(𝑧	𝑝(𝑧	PROPN
cana-5236	120	5	)	)	PUNCT
cana-5236	121	1	+	+	CCONJ
cana-5236	121	2	𝜇3	𝜇3	NOUN
cana-5236	121	3	=	=	SYM
cana-5236	121	4	(	(	PUNCT
cana-5236	121	5	𝑘	𝑘	PROPN
cana-5236	121	6	4	4	NUM
cana-5236	121	7	+	+	SYM
cana-5236	121	8	1	1	NUM
cana-5236	121	9	2	2	NUM
cana-5236	121	10	)	)	PUNCT
cana-5236	121	11	(	(	PUNCT
cana-5236	121	12	𝑝1(𝑧	𝑝1(𝑧	PROPN
cana-5236	121	13	)	)	PUNCT
cana-5236	121	14	+	+	CCONJ
cana-5236	121	15	𝜇2𝑧𝑝1	𝜇2𝑧𝑝1	VERB
cana-5236	121	16	′(𝑧	′(𝑧	NOUN
cana-5236	121	17	)	)	PUNCT
cana-5236	121	18	𝑝1(𝑧	𝑝1(𝑧	PROPN
cana-5236	121	19	)	)	PUNCT
cana-5236	121	20	+	+	NUM
cana-5236	121	21	𝜇3	𝜇3	NOUN
cana-5236	121	22	)	)	PUNCT
cana-5236	121	23	−	−	PROPN
cana-5236	122	1	(	(	PUNCT
cana-5236	122	2	𝑘	𝑘	PROPN
cana-5236	122	3	4	4	NUM
cana-5236	122	4	−	−	NOUN
cana-5236	122	5	1	1	NUM
cana-5236	122	6	2	2	NUM
cana-5236	122	7	)	)	PUNCT
cana-5236	122	8	(	(	PUNCT
cana-5236	122	9	𝑝2(𝑧	𝑝2(𝑧	NOUN
cana-5236	122	10	)	)	PUNCT
cana-5236	123	1	+	+	CCONJ
cana-5236	123	2	𝜇2𝑧𝑝2	𝜇2𝑧𝑝2	PROPN
cana-5236	123	3	′(𝑧	′(𝑧	SYM
cana-5236	123	4	)	)	PUNCT
cana-5236	123	5	𝑝2(𝑧	𝑝2(𝑧	PROPN
cana-5236	123	6	)	)	PUNCT
cana-5236	123	7	+	+	CCONJ
cana-5236	123	8	𝜇3	𝜇3	NOUN
cana-5236	123	9	)	)	PUNCT
cana-5236	123	10	by	by	ADP
cana-5236	123	11	using	use	VERB
cana-5236	123	12	(	(	PUNCT
cana-5236	123	13	3.8	3.8	NUM
cana-5236	123	14	)	)	PUNCT
cana-5236	123	15	,	,	PUNCT
cana-5236	123	16	we	we	PRON
cana-5236	123	17	see	see	VERB
cana-5236	123	18	that	that	SCONJ
cana-5236	123	19	(	(	PUNCT
cana-5236	123	20	1	1	NUM
cana-5236	123	21	−	−	PROPN
cana-5236	123	22	𝛼	𝛼	PRON
cana-5236	123	23	−	−	PROPN
cana-5236	123	24	𝜇1	𝜇1	NOUN
cana-5236	123	25	)	)	PUNCT
cana-5236	123	26	(	(	PUNCT
cana-5236	123	27	1	1	NUM
cana-5236	123	28	−	−	NOUN
cana-5236	123	29	𝛼	𝛼	NOUN
cana-5236	123	30	)	)	PUNCT
cana-5236	123	31	+	+	SYM
cana-5236	123	32	𝜇1	𝜇1	ADJ
cana-5236	123	33	1	1	NUM
cana-5236	123	34	−	−	PROPN
cana-5236	123	35	𝛼	𝛼	PRON
cana-5236	123	36	[	[	X
cana-5236	123	37	𝑝𝑖(𝑧	𝑝𝑖(𝑧	X
cana-5236	123	38	)	)	PUNCT
cana-5236	124	1	+	+	CCONJ
cana-5236	124	2	𝜇2𝑧𝑝𝑖	𝜇2𝑧𝑝𝑖	PROPN
cana-5236	124	3	′(𝑧	′(𝑧	NOUN
cana-5236	124	4	)	)	PUNCT
cana-5236	124	5	𝑝𝑖(𝑧	𝑝𝑖(𝑧	VERB
cana-5236	124	6	)	)	PUNCT
cana-5236	125	1	+	+	CCONJ
cana-5236	125	2	𝜇3	𝜇3	NOUN
cana-5236	125	3	]	]	PUNCT
cana-5236	125	4	∈	∈	PROPN
cana-5236	125	5	𝑃[𝐴	𝑃[𝐴	NOUN
cana-5236	125	6	,	,	PUNCT
cana-5236	125	7	𝐵	𝐵	NOUN
cana-5236	125	8	]	]	X
cana-5236	125	9	,	,	PUNCT
cana-5236	125	10	where	where	SCONJ
cana-5236	125	11	z	z	PROPN
cana-5236	125	12	𝜖	𝜖	PROPN
cana-5236	125	13	𝒰	𝒰	PROPN
cana-5236	125	14	,	,	PUNCT
cana-5236	125	15	i=1,2	i=1,2	NOUN
cana-5236	125	16	.	.	PUNCT
cana-5236	126	1	now	now	ADV
cana-5236	126	2	,	,	PUNCT
cana-5236	126	3	want	want	VERB
cana-5236	126	4	to	to	PART
cana-5236	126	5	show	show	VERB
cana-5236	126	6	that	that	SCONJ
cana-5236	126	7	𝑝𝑖	𝑝𝑖	PROPN
cana-5236	126	8	∈	∈	PROPN
cana-5236	126	9	𝑃[𝐴	𝑃[𝐴	NOUN
cana-5236	126	10	,	,	PUNCT
cana-5236	126	11	𝐵	𝐵	PROPN
cana-5236	126	12	,	,	PUNCT
cana-5236	126	13	𝛽	𝛽	NOUN
cana-5236	126	14	]	]	X
cana-5236	126	15	,	,	PUNCT
cana-5236	126	16	where	where	SCONJ
cana-5236	126	17	𝛽(0	𝛽(0	PROPN
cana-5236	126	18	≤	≤	PROPN
cana-5236	126	19	𝛽	𝛽	NOUN
cana-5236	126	20	<	<	X
cana-5236	126	21	1	1	NUM
cana-5236	126	22	)	)	PUNCT
cana-5236	126	23	is	be	AUX
cana-5236	126	24	one	one	NUM
cana-5236	126	25	of	of	ADP
cana-5236	126	26	the	the	DET
cana-5236	126	27	root	root	NOUN
cana-5236	126	28	of	of	ADP
cana-5236	126	29	(	(	PUNCT
cana-5236	126	30	3.3	3.3	NUM
cana-5236	126	31	)	)	PUNCT
cana-5236	126	32	.	.	PUNCT
cana-5236	127	1	let	let	VERB
cana-5236	127	2	𝑝𝑖(𝑧	𝑝𝑖(𝑧	NOUN
cana-5236	127	3	)	)	PUNCT
cana-5236	127	4	=	=	PUNCT
cana-5236	127	5	(	(	PUNCT
cana-5236	127	6	1	1	NUM
cana-5236	127	7	−	−	PROPN
cana-5236	127	8	𝛽)ℎ𝑖(𝑧	𝛽)ℎ𝑖(𝑧	NUM
cana-5236	127	9	)	)	PUNCT
cana-5236	128	1	+	+	SYM
cana-5236	128	2	𝛽	𝛽	NOUN
cana-5236	128	3	,	,	PUNCT
cana-5236	128	4	i=1,2	i=1,2	ADJ
cana-5236	128	5	.	.	PUNCT
cana-5236	129	1	then	then	ADV
cana-5236	129	2	,	,	PUNCT
cana-5236	129	3	(	(	PUNCT
cana-5236	129	4	1	1	NUM
cana-5236	129	5	−	−	NOUN
cana-5236	129	6	𝛼	𝛼	NOUN
cana-5236	129	7	−	−	PROPN
cana-5236	129	8	𝜇1)(1	𝜇1)(1	NOUN
cana-5236	129	9	−	−	NOUN
cana-5236	129	10	𝛽	𝛽	NOUN
cana-5236	129	11	)	)	PUNCT
cana-5236	129	12	(	(	PUNCT
cana-5236	129	13	1	1	NUM
cana-5236	129	14	−	−	NOUN
cana-5236	129	15	𝛼	𝛼	NOUN
cana-5236	129	16	)	)	PUNCT
cana-5236	129	17	+	+	CCONJ
cana-5236	129	18	𝜇1(1	𝜇1(1	ADJ
cana-5236	129	19	−	−	PROPN
cana-5236	129	20	𝛽	𝛽	NOUN
cana-5236	129	21	)	)	PUNCT
cana-5236	129	22	1	1	NUM
cana-5236	129	23	−	−	NOUN
cana-5236	129	24	𝛼	𝛼	PRON
cana-5236	129	25	[	[	NOUN
cana-5236	129	26	ℎ𝑖(𝑧	ℎ𝑖(𝑧	NOUN
cana-5236	129	27	)	)	PUNCT
cana-5236	130	1	+	+	SYM
cana-5236	130	2	𝜇2	𝜇2	NOUN
cana-5236	130	3	(	(	PUNCT
cana-5236	130	4	1	1	NUM
cana-5236	130	5	−	−	PROPN
cana-5236	130	6	𝛽	𝛽	NOUN
cana-5236	130	7	)	)	PUNCT
cana-5236	130	8	𝑧ℎ𝑖	𝑧ℎ𝑖	PROPN
cana-5236	130	9	′(𝑧	′(𝑧	NOUN
cana-5236	130	10	)	)	PUNCT
cana-5236	130	11	ℎ𝑖(𝑧	ℎ𝑖(𝑧	NOUN
cana-5236	130	12	)	)	PUNCT
cana-5236	131	1	+	+	CCONJ
cana-5236	131	2	𝜇3	𝜇3	NOUN
cana-5236	131	3	+	+	CCONJ
cana-5236	131	4	𝛽	𝛽	PROPN
cana-5236	131	5	(	(	PUNCT
cana-5236	131	6	1	1	NUM
cana-5236	131	7	−	−	PROPN
cana-5236	131	8	𝛽	𝛽	NOUN
cana-5236	131	9	)	)	PUNCT
cana-5236	131	10	]	]	PUNCT
cana-5236	131	11	∈	∈	PROPN
cana-5236	131	12	𝑃[𝐴	𝑃[𝐴	NOUN
cana-5236	131	13	,	,	PUNCT
cana-5236	131	14	𝐵	𝐵	NOUN
cana-5236	131	15	]	]	PUNCT
cana-5236	131	16	using	use	VERB
cana-5236	131	17	the	the	DET
cana-5236	131	18	fact	fact	NOUN
cana-5236	131	19	illustrated	illustrate	VERB
cana-5236	131	20	in	in	ADP
cana-5236	131	21	(	(	PUNCT
cana-5236	131	22	1.2	1.2	NUM
cana-5236	131	23	)	)	PUNCT
cana-5236	131	24	,	,	PUNCT
cana-5236	131	25	we	we	PRON
cana-5236	131	26	have	have	VERB
cana-5236	131	27	communications	communication	NOUN
cana-5236	131	28	on	on	ADP
cana-5236	131	29	applied	apply	VERB
cana-5236	131	30	nonlinear	nonlinear	ADJ
cana-5236	131	31	analysis	analysis	NOUN
cana-5236	131	32	issn	issn	NOUN
cana-5236	131	33	:	:	PUNCT
cana-5236	131	34	1074	1074	NUM
cana-5236	131	35	-	-	PUNCT
cana-5236	131	36	133x	133x	NUM
cana-5236	131	37	vol	vol	VERB
cana-5236	131	38	32	32	NUM
cana-5236	131	39	no	no	NOUN
cana-5236	131	40	.	.	PUNCT
cana-5236	132	1	10s	10	NOUN
cana-5236	132	2	(	(	PUNCT
cana-5236	132	3	2025	2025	NUM
cana-5236	132	4	)	)	PUNCT
cana-5236	132	5	1344	1344	NUM
cana-5236	133	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-5236	133	2	{	{	PUNCT
cana-5236	133	3	(	(	PUNCT
cana-5236	133	4	𝐵	𝐵	NOUN
cana-5236	133	5	−	−	PROPN
cana-5236	133	6	1)[(𝜂	1)[(𝜂	NUM
cana-5236	133	7	+	+	CCONJ
cana-5236	133	8	𝜇ℎ𝑖(𝑧))(ℎ𝑖(𝑧	𝜇ℎ𝑖(𝑧))(ℎ𝑖(𝑧	PROPN
cana-5236	133	9	)	)	PUNCT
cana-5236	133	10	+	+	SYM
cana-5236	133	11	𝜔2	𝜔2	PROPN
cana-5236	133	12	)	)	PUNCT
cana-5236	133	13	+	+	CCONJ
cana-5236	133	14	𝜔1𝜇𝑧ℎ𝑖	𝜔1𝜇𝑧ℎ𝑖	NUM
cana-5236	133	15	′(𝑧	′(𝑧	NOUN
cana-5236	133	16	)	)	PUNCT
cana-5236	133	17	]	]	PUNCT
cana-5236	134	1	−	−	PROPN
cana-5236	134	2	(	(	PUNCT
cana-5236	134	3	𝐴	𝐴	PROPN
cana-5236	134	4	−	−	PROPN
cana-5236	134	5	1)(ℎ𝑖(𝑧	1)(ℎ𝑖(𝑧	NUM
cana-5236	134	6	)	)	PUNCT
cana-5236	134	7	+	+	CCONJ
cana-5236	134	8	𝜔2	𝜔2	PROPN
cana-5236	134	9	)	)	PUNCT
cana-5236	134	10	(	(	PUNCT
cana-5236	134	11	𝐵	𝐵	NOUN
cana-5236	134	12	+	+	CCONJ
cana-5236	134	13	1)[(𝜂	1)[(𝜂	NUM
cana-5236	134	14	+	+	CCONJ
cana-5236	134	15	𝜇ℎ𝑖(𝑧))(ℎ𝑖(𝑧	𝜇ℎ𝑖(𝑧))(ℎ𝑖(𝑧	PROPN
cana-5236	134	16	)	)	PUNCT
cana-5236	134	17	+	+	SYM
cana-5236	134	18	𝜔2	𝜔2	PROPN
cana-5236	134	19	)	)	PUNCT
cana-5236	134	20	+	+	CCONJ
cana-5236	134	21	𝜔1𝜇𝑧ℎ𝑖	𝜔1𝜇𝑧ℎ𝑖	NUM
cana-5236	134	22	′(𝑧	′(𝑧	NOUN
cana-5236	134	23	)	)	PUNCT
cana-5236	134	24	]	]	PUNCT
cana-5236	135	1	−	−	PROPN
cana-5236	135	2	(	(	PUNCT
cana-5236	135	3	𝐴	𝐴	PROPN
cana-5236	135	4	+	+	CCONJ
cana-5236	135	5	1)(ℎ𝑖(𝑧	1)(ℎ𝑖(𝑧	NUM
cana-5236	135	6	)	)	PUNCT
cana-5236	135	7	+	+	CCONJ
cana-5236	135	8	𝜔2	𝜔2	PROPN
cana-5236	135	9	)	)	PUNCT
cana-5236	135	10	}	}	PUNCT
cana-5236	135	11	∈	∈	PROPN
cana-5236	135	12	𝑃	𝑃	NOUN
cana-5236	135	13	,	,	PUNCT
cana-5236	135	14	where	where	SCONJ
cana-5236	135	15	𝜔1	𝜔1	ADJ
cana-5236	135	16	=	=	SYM
cana-5236	135	17	𝜇2	𝜇2	PROPN
cana-5236	135	18	1−𝛽	1−𝛽	NUM
cana-5236	135	19	,	,	PUNCT
cana-5236	135	20	𝜔2	𝜔2	PROPN
cana-5236	135	21	=	=	SYM
cana-5236	135	22	𝜇3+𝛽	𝜇3+𝛽	NOUN
cana-5236	135	23	1−𝛽	1−𝛽	NUM
cana-5236	135	24	,	,	PUNCT
cana-5236	135	25	𝜂	𝜂	NOUN
cana-5236	135	26	=	=	SYM
cana-5236	135	27	1−𝛼−𝜇1(1−𝛽	1−𝛼−𝜇1(1−𝛽	NUM
cana-5236	135	28	)	)	PUNCT
cana-5236	135	29	1−𝛼	1−𝛼	NUM
cana-5236	135	30	and	and	CCONJ
cana-5236	135	31	𝜇	𝜇	X
cana-5236	135	32	=	=	X
cana-5236	135	33	𝜇1(1−𝛽	𝜇1(1−𝛽	X
cana-5236	135	34	)	)	PUNCT
cana-5236	135	35	1−𝛼	1−𝛼	NUM
cana-5236	135	36	.	.	PUNCT
cana-5236	136	1	we	we	PRON
cana-5236	136	2	now	now	ADV
cana-5236	136	3	form	form	VERB
cana-5236	136	4	the	the	DET
cana-5236	136	5	functional	functional	ADJ
cana-5236	136	6	𝜓(𝑢	𝜓(𝑢	NOUN
cana-5236	136	7	,	,	PUNCT
cana-5236	136	8	𝑣	𝑣	NOUN
cana-5236	136	9	)	)	PUNCT
cana-5236	136	10	by	by	ADP
cana-5236	136	11	choosing	choose	VERB
cana-5236	136	12	𝑢	𝑢	NOUN
cana-5236	136	13	=	=	NOUN
cana-5236	136	14	ℎ𝑖(𝑧	ℎ𝑖(𝑧	NOUN
cana-5236	136	15	)	)	PUNCT
cana-5236	136	16	,	,	PUNCT
cana-5236	136	17	𝑣	𝑣	X
cana-5236	136	18	=	=	PUNCT
cana-5236	136	19	𝑧ℎ𝑖	𝑧ℎ𝑖	PROPN
cana-5236	136	20	′(𝑧	′(𝑧	INTJ
cana-5236	136	21	)	)	PUNCT
cana-5236	136	22	and	and	CCONJ
cana-5236	136	23	note	note	VERB
cana-5236	136	24	that	that	SCONJ
cana-5236	136	25	the	the	DET
cana-5236	136	26	first	first	ADJ
cana-5236	136	27	two	two	NUM
cana-5236	136	28	conditions	condition	NOUN
cana-5236	136	29	of	of	ADP
cana-5236	136	30	lemma	lemma	PROPN
cana-5236	136	31	2.2	2.2	NUM
cana-5236	136	32	are	be	AUX
cana-5236	136	33	clearly	clearly	ADV
cana-5236	136	34	satisfied	satisfied	ADJ
cana-5236	136	35	.	.	PUNCT
cana-5236	137	1	we	we	PRON
cana-5236	137	2	check	check	VERB
cana-5236	137	3	condition	condition	NOUN
cana-5236	137	4	(	(	PUNCT
cana-5236	137	5	iii	iii	NOUN
cana-5236	137	6	)	)	PUNCT
cana-5236	137	7	as	as	SCONJ
cana-5236	137	8	follows	follow	VERB
cana-5236	137	9	.	.	PUNCT
cana-5236	138	1	𝜓(𝑢	𝜓(𝑢	NOUN
cana-5236	138	2	,	,	PUNCT
cana-5236	138	3	𝑣	𝑣	NOUN
cana-5236	138	4	)	)	PUNCT
cana-5236	138	5	=	=	SYM
cana-5236	138	6	{	{	PUNCT
cana-5236	138	7	(	(	PUNCT
cana-5236	138	8	𝐵	𝐵	NOUN
cana-5236	138	9	−	−	NOUN
cana-5236	138	10	1)[(𝜂	1)[(𝜂	NUM
cana-5236	138	11	+	+	PUNCT
cana-5236	138	12	𝜇𝑢)(𝑢	𝜇𝑢)(𝑢	PROPN
cana-5236	138	13	+	+	X
cana-5236	138	14	𝜔2	𝜔2	PROPN
cana-5236	138	15	)	)	PUNCT
cana-5236	138	16	+	+	CCONJ
cana-5236	138	17	𝜔1𝜇𝑣	𝜔1𝜇𝑣	PUNCT
cana-5236	138	18	]	]	X
cana-5236	138	19	−	−	PROPN
cana-5236	138	20	(	(	PUNCT
cana-5236	138	21	𝐴	𝐴	PROPN
cana-5236	138	22	−	−	PROPN
cana-5236	138	23	1)(𝑢	1)(𝑢	NUM
cana-5236	138	24	+	+	SYM
cana-5236	138	25	𝜔2	𝜔2	PROPN
cana-5236	138	26	)	)	PUNCT
cana-5236	138	27	}	}	PUNCT
cana-5236	138	28	{	{	PUNCT
cana-5236	138	29	(	(	PUNCT
cana-5236	138	30	𝐵	𝐵	NOUN
cana-5236	138	31	+	+	CCONJ
cana-5236	138	32	1)[(𝜂	1)[(𝜂	NUM
cana-5236	138	33	+	+	CCONJ
cana-5236	138	34	𝜇𝑢)(𝑢	𝜇𝑢)(𝑢	PROPN
cana-5236	138	35	+	+	X
cana-5236	138	36	𝜔2	𝜔2	PROPN
cana-5236	138	37	)	)	PUNCT
cana-5236	138	38	+	+	CCONJ
cana-5236	138	39	𝜔1𝜇𝑣	𝜔1𝜇𝑣	PUNCT
cana-5236	138	40	]	]	X
cana-5236	138	41	−	−	PROPN
cana-5236	138	42	(	(	PUNCT
cana-5236	138	43	𝐴	𝐴	PROPN
cana-5236	138	44	+	+	CCONJ
cana-5236	138	45	1)(𝑢	1)(𝑢	NUM
cana-5236	138	46	+	+	SYM
cana-5236	138	47	𝜔2	𝜔2	PROPN
cana-5236	138	48	)	)	PUNCT
cana-5236	138	49	}	}	PUNCT
cana-5236	138	50	=	=	PRON
cana-5236	138	51	{	{	PUNCT
cana-5236	138	52	𝜂1+𝜔1𝜇(𝐵−1)𝑣+[𝜂+𝜇(𝑢+𝜔2))(𝐵−1)−(𝐴−1)]𝑢	𝜂1+𝜔1𝜇(𝐵−1)𝑣+[𝜂+𝜇(𝑢+𝜔2))(𝐵−1)−(𝐴−1)]𝑢	NOUN
cana-5236	138	53	}	}	PUNCT
cana-5236	138	54	{	{	PUNCT
cana-5236	138	55	𝜂2+𝜔1𝜇(𝐵+1)𝑣+[(𝜂+𝜇(𝑢+𝜔2))(𝐵+1)−(𝐴+1)]𝑢	𝜂2+𝜔1𝜇(𝐵+1)𝑣+[(𝜂+𝜇(𝑢+𝜔2))(𝐵+1)−(𝐴+1)]𝑢	NOUN
cana-5236	138	56	}	}	PUNCT
cana-5236	138	57	where	where	SCONJ
cana-5236	138	58	𝜂1	𝜂1	PROPN
cana-5236	138	59	=	=	SYM
cana-5236	138	60	𝜔2[𝜂(𝐵	𝜔2[𝜂(𝐵	VERB
cana-5236	138	61	−	−	PROPN
cana-5236	138	62	1	1	NUM
cana-5236	138	63	)	)	PUNCT
cana-5236	138	64	−	−	PROPN
cana-5236	138	65	(	(	PUNCT
cana-5236	138	66	𝐴	𝐴	PROPN
cana-5236	138	67	−	−	PROPN
cana-5236	138	68	1	1	NUM
cana-5236	138	69	)	)	PUNCT
cana-5236	138	70	]	]	PUNCT
cana-5236	138	71	and	and	CCONJ
cana-5236	138	72	𝜂2	𝜂2	NOUN
cana-5236	138	73	=	=	SYM
cana-5236	138	74	𝜔2[𝜂(𝐵	𝜔2[𝜂(𝐵	NOUN
cana-5236	138	75	+	+	NOUN
cana-5236	138	76	1	1	X
cana-5236	138	77	)	)	PUNCT
cana-5236	138	78	−	−	PROPN
cana-5236	138	79	(	(	PUNCT
cana-5236	138	80	𝐴	𝐴	NOUN
cana-5236	138	81	+	+	CCONJ
cana-5236	138	82	1	1	NUM
cana-5236	138	83	)	)	PUNCT
cana-5236	138	84	]	]	PUNCT
cana-5236	138	85	.	.	PUNCT
cana-5236	139	1	now	now	ADV
cana-5236	139	2	,	,	PUNCT
cana-5236	139	3	𝜓(𝑖𝑢2	𝜓(𝑖𝑢2	NOUN
cana-5236	139	4	,	,	PUNCT
cana-5236	139	5	𝑣1	𝑣1	PROPN
cana-5236	139	6	)	)	PUNCT
cana-5236	139	7	=	=	PUNCT
cana-5236	139	8	{	{	PUNCT
cana-5236	139	9	𝜂1	𝜂1	PROPN
cana-5236	139	10	+	+	CCONJ
cana-5236	139	11	𝜇(𝜔1𝑣1	𝜇(𝜔1𝑣1	PROPN
cana-5236	139	12	−	−	PROPN
cana-5236	139	13	𝑢2	𝑢2	PROPN
cana-5236	139	14	2)(𝐵	2)(𝐵	PROPN
cana-5236	140	1	−	−	PROPN
cana-5236	140	2	1	1	NUM
cana-5236	140	3	)	)	PUNCT
cana-5236	140	4	+	+	CCONJ
cana-5236	141	1	[	[	X
cana-5236	141	2	(	(	PUNCT
cana-5236	141	3	𝜂	𝜂	NOUN
cana-5236	141	4	+	+	NUM
cana-5236	141	5	𝜇𝜔2)(𝐵	𝜇𝜔2)(𝐵	NUM
cana-5236	141	6	−	−	NOUN
cana-5236	141	7	1	1	NUM
cana-5236	141	8	)	)	PUNCT
cana-5236	141	9	−	−	PROPN
cana-5236	141	10	(	(	PUNCT
cana-5236	141	11	𝐴	𝐴	PROPN
cana-5236	141	12	−	−	PROPN
cana-5236	141	13	1)]𝑖𝑢2	1)]𝑖𝑢2	NOUN
cana-5236	141	14	}	}	PUNCT
cana-5236	141	15	{	{	PUNCT
cana-5236	141	16	𝜂2	𝜂2	VERB
cana-5236	141	17	+	+	CCONJ
cana-5236	141	18	𝜇(𝜔1𝑣1	𝜇(𝜔1𝑣1	PROPN
cana-5236	141	19	−	−	PROPN
cana-5236	141	20	𝑢2	𝑢2	PROPN
cana-5236	141	21	2)(𝐵	2)(𝐵	PROPN
cana-5236	141	22	+	+	CCONJ
cana-5236	141	23	1	1	NUM
cana-5236	141	24	)	)	PUNCT
cana-5236	141	25	+	+	CCONJ
cana-5236	141	26	[	[	X
cana-5236	141	27	(	(	PUNCT
cana-5236	141	28	𝜂	𝜂	NOUN
cana-5236	141	29	+	+	NUM
cana-5236	141	30	𝜇𝑢2)(𝐵	𝜇𝑢2)(𝐵	NUM
cana-5236	141	31	+	+	NOUN
cana-5236	141	32	1	1	X
cana-5236	141	33	)	)	PUNCT
cana-5236	141	34	−	−	PROPN
cana-5236	142	1	(	(	PUNCT
cana-5236	142	2	𝐴	𝐴	PROPN
cana-5236	142	3	+	+	CCONJ
cana-5236	142	4	1)]𝑖𝑢2	1)]𝑖𝑢2	NOUN
cana-5236	142	5	}	}	PUNCT
cana-5236	142	6	taking	take	VERB
cana-5236	142	7	real	real	ADJ
cana-5236	142	8	part	part	NOUN
cana-5236	142	9	of	of	ADP
cana-5236	142	10	𝜓(𝑖𝑢2	𝜓(𝑖𝑢2	NOUN
cana-5236	142	11	,	,	PUNCT
cana-5236	142	12	𝑣1	𝑣1	PROPN
cana-5236	142	13	)	)	PUNCT
cana-5236	142	14	,	,	PUNCT
cana-5236	142	15	we	we	PRON
cana-5236	142	16	have	have	AUX
cana-5236	142	17	re	re	VERB
cana-5236	142	18	ψ(iu2	ψ(iu2	ADJ
cana-5236	142	19	,	,	PUNCT
cana-5236	142	20	v1	v1	NOUN
cana-5236	142	21	)	)	PUNCT
cana-5236	142	22	=	=	PUNCT
cana-5236	143	1	[	[	X
cana-5236	143	2	−η1	−η1	X
cana-5236	143	3	+	+	CCONJ
cana-5236	143	4	μ(ω1v1	μ(ω1v1	ADJ
cana-5236	143	5	−	−	PROPN
cana-5236	143	6	u2	u2	PROPN
cana-5236	143	7	2)(1	2)(1	PROPN
cana-5236	143	8	−	−	NOUN
cana-5236	143	9	b)][η2	b)][η2	NOUN
cana-5236	143	10	+	+	CCONJ
cana-5236	143	11	μ(ω1v1	μ(ω1v1	ADJ
cana-5236	143	12	−	−	NOUN
cana-5236	143	13	u2	u2	NOUN
cana-5236	143	14	2)(b	2)(b	NUM
cana-5236	143	15	+	+	NOUN
cana-5236	143	16	1	1	NUM
cana-5236	143	17	)	)	PUNCT
cana-5236	143	18	]	]	PUNCT
cana-5236	144	1	−	−	PROPN
cana-5236	145	1	[	[	X
cana-5236	145	2	(	(	PUNCT
cana-5236	145	3	η	η	PROPN
cana-5236	145	4	+	+	PROPN
cana-5236	145	5	μω2)(b	μω2)(b	ADJ
cana-5236	145	6	−	−	NUM
cana-5236	145	7	1	1	NUM
cana-5236	145	8	)	)	PUNCT
cana-5236	145	9	−	−	PROPN
cana-5236	146	1	(	(	PUNCT
cana-5236	146	2	a	a	DET
cana-5236	146	3	−	−	PROPN
cana-5236	146	4	1)][(η	1)][(η	NOUN
cana-5236	147	1	+	+	CCONJ
cana-5236	147	2	μω2)(b	μω2)(b	ADJ
cana-5236	147	3	+	+	CCONJ
cana-5236	147	4	1	1	NUM
cana-5236	147	5	)	)	PUNCT
cana-5236	147	6	−	−	PROPN
cana-5236	147	7	(	(	PUNCT
cana-5236	147	8	a	a	DET
cana-5236	147	9	+	+	NOUN
cana-5236	147	10	1)]𝑢2	1)]𝑢2	NUM
cana-5236	147	11	2	2	NUM
cana-5236	147	12	−[η2	−[η2	NOUN
cana-5236	147	13	+	+	CCONJ
cana-5236	147	14	μ(ω1v1	μ(ω1v1	PROPN
cana-5236	147	15	+	+	CCONJ
cana-5236	147	16	u2)(b	u2)(b	ADJ
cana-5236	147	17	+	+	CCONJ
cana-5236	147	18	1)]2	1)]2	NUM
cana-5236	147	19	−	−	PUNCT
cana-5236	148	1	[	[	X
cana-5236	148	2	(	(	PUNCT
cana-5236	148	3	η	η	PROPN
cana-5236	148	4	+	+	PROPN
cana-5236	148	5	μω2)(b	μω2)(b	PROPN
cana-5236	148	6	+	+	CCONJ
cana-5236	148	7	1	1	NUM
cana-5236	148	8	)	)	PUNCT
cana-5236	148	9	−	−	PROPN
cana-5236	148	10	(	(	PUNCT
cana-5236	148	11	a	a	DET
cana-5236	148	12	+	+	X
cana-5236	148	13	1)]2𝑢2	1)]2𝑢2	NUM
cana-5236	148	14	2	2	NUM
cana-5236	148	15	as	as	ADP
cana-5236	148	16	𝜔1	𝜔1	PROPN
cana-5236	148	17	>	>	X
cana-5236	148	18	0	0	NUM
cana-5236	148	19	,	,	PUNCT
cana-5236	148	20	𝜇	𝜇	X
cana-5236	148	21	>	>	X
cana-5236	148	22	0	0	NUM
cana-5236	148	23	,	,	PUNCT
cana-5236	148	24	so	so	ADV
cana-5236	148	25	applying	apply	VERB
cana-5236	148	26	𝑣1	𝑣1	NOUN
cana-5236	148	27	≤	≤	NOUN
cana-5236	148	28	−	−	ADP
cana-5236	148	29	1	1	NUM
cana-5236	148	30	2	2	NUM
cana-5236	148	31	(	(	PUNCT
cana-5236	148	32	1	1	NUM
cana-5236	148	33	+	+	NUM
cana-5236	148	34	𝑢2	𝑢2	PROPN
cana-5236	148	35	2	2	NUM
cana-5236	148	36	)	)	PUNCT
cana-5236	148	37	and	and	CCONJ
cana-5236	148	38	after	after	ADP
cana-5236	148	39	a	a	DET
cana-5236	148	40	little	little	ADJ
cana-5236	148	41	simplification	simplification	NOUN
cana-5236	148	42	,	,	PUNCT
cana-5236	148	43	we	we	PRON
cana-5236	148	44	have	have	VERB
cana-5236	148	45	(	(	PUNCT
cana-5236	148	46	3.9	3.9	NUM
cana-5236	148	47	)	)	PUNCT
cana-5236	148	48	re	re	VERB
cana-5236	148	49	ψ(iu2	ψ(iu2	PROPN
cana-5236	148	50	,	,	PUNCT
cana-5236	148	51	v1	v1	NOUN
cana-5236	148	52	)	)	PUNCT
cana-5236	148	53	≤	≤	NUM
cana-5236	148	54	a1+b1u2	a1+b1u2	VERB
cana-5236	148	55	2+c1u2	2+c1u2	NUM
cana-5236	148	56	4	4	NUM
cana-5236	148	57	d1	d1	NOUN
cana-5236	148	58	where	where	SCONJ
cana-5236	148	59	𝐴1	𝐴1	PROPN
cana-5236	148	60	=	=	NOUN
cana-5236	148	61	1	1	NUM
cana-5236	148	62	4	4	NUM
cana-5236	149	1	[	[	SYM
cana-5236	149	2	2𝜂1	2𝜂1	NUM
cana-5236	149	3	−	−	NOUN
cana-5236	149	4	𝜔1𝜇(𝐵	𝜔1𝜇(𝐵	ADV
cana-5236	149	5	−	−	PROPN
cana-5236	149	6	1)][2𝜂2	1)][2𝜂2	NUM
cana-5236	149	7	−	−	NOUN
cana-5236	149	8	𝜔1𝜇(𝐵	𝜔1𝜇(𝐵	ADV
cana-5236	150	1	+	+	CCONJ
cana-5236	150	2	1	1	NUM
cana-5236	150	3	]	]	PUNCT
cana-5236	150	4	,	,	PUNCT
cana-5236	150	5	𝐵1	𝐵1	NOUN
cana-5236	150	6	=	=	SYM
cana-5236	150	7	−	−	PROPN
cana-5236	150	8	1	1	NUM
cana-5236	150	9	2	2	NUM
cana-5236	150	10	𝜇(𝜔1	𝜇(𝜔1	NOUN
cana-5236	150	11	+	+	NOUN
cana-5236	150	12	2)[𝜂1(𝐵	2)[𝜂1(𝐵	NOUN
cana-5236	150	13	+	+	CCONJ
cana-5236	150	14	1	1	NUM
cana-5236	150	15	)	)	PUNCT
cana-5236	150	16	−	−	NOUN
cana-5236	151	1	𝜔1𝜇(𝐵2	𝜔1𝜇(𝐵2	NOUN
cana-5236	151	2	−	−	NOUN
cana-5236	151	3	1	1	NUM
cana-5236	151	4	)	)	PUNCT
cana-5236	151	5	+	+	CCONJ
cana-5236	151	6	𝜂2(𝐵	𝜂2(𝐵	NOUN
cana-5236	151	7	−	−	NOUN
cana-5236	151	8	1	1	NUM
cana-5236	151	9	)	)	PUNCT
cana-5236	151	10	]	]	PUNCT
cana-5236	152	1	+	+	CCONJ
cana-5236	152	2	(	(	PUNCT
cana-5236	152	3	𝜂	𝜂	X
cana-5236	152	4	+	+	NUM
cana-5236	152	5	𝜇𝜔2)2(𝐵2	𝜇𝜔2)2(𝐵2	NOUN
cana-5236	152	6	−	−	NOUN
cana-5236	152	7	1	1	NUM
cana-5236	152	8	)	)	PUNCT
cana-5236	152	9	−	−	NOUN
cana-5236	152	10	2(𝜂	2(𝜂	NUM
cana-5236	153	1	+	+	CCONJ
cana-5236	153	2	𝜇𝜔2)(𝐴𝐵	𝜇𝜔2)(𝐴𝐵	ADJ
cana-5236	153	3	−	−	NOUN
cana-5236	153	4	1	1	NUM
cana-5236	153	5	)	)	PUNCT
cana-5236	153	6	+	+	CCONJ
cana-5236	153	7	(	(	PUNCT
cana-5236	153	8	𝐴2	𝐴2	PROPN
cana-5236	153	9	−	−	PROPN
cana-5236	153	10	1	1	NUM
cana-5236	153	11	)	)	PUNCT
cana-5236	153	12	,	,	PUNCT
cana-5236	153	13	𝐶1	𝐶1	X
cana-5236	153	14	=	=	SYM
cana-5236	154	1	−	−	NOUN
cana-5236	154	2	1	1	NUM
cana-5236	154	3	4	4	NUM
cana-5236	154	4	𝜇2(1	𝜇2(1	NOUN
cana-5236	154	5	−	−	PROPN
cana-5236	154	6	𝐵2)(𝜔1	𝐵2)(𝜔1	PROPN
cana-5236	154	7	+	+	CCONJ
cana-5236	154	8	2)2	2)2	NUM
cana-5236	154	9	,	,	PUNCT
cana-5236	154	10	and	and	CCONJ
cana-5236	154	11	𝐷1	𝐷1	NOUN
cana-5236	155	1	=	=	PUNCT
cana-5236	156	1	[	[	X
cana-5236	156	2	𝜂2	𝜂2	X
cana-5236	156	3	+	+	X
cana-5236	156	4	𝜇(𝜔1𝑣1	𝜇(𝜔1𝑣1	PROPN
cana-5236	156	5	+	+	CCONJ
cana-5236	156	6	𝑢2)(𝐵	𝑢2)(𝐵	PROPN
cana-5236	156	7	+	+	CCONJ
cana-5236	156	8	1)]2	1)]2	NUM
cana-5236	156	9	+	+	CCONJ
cana-5236	157	1	[	[	X
cana-5236	157	2	(	(	PUNCT
cana-5236	157	3	𝜂	𝜂	NOUN
cana-5236	157	4	+	+	NUM
cana-5236	157	5	𝜇𝜔2)(𝐵	𝜇𝜔2)(𝐵	NUM
cana-5236	157	6	+	+	NOUN
cana-5236	157	7	1	1	NUM
cana-5236	157	8	)	)	PUNCT
cana-5236	157	9	−	−	PROPN
cana-5236	157	10	(	(	PUNCT
cana-5236	157	11	𝐴	𝐴	PROPN
cana-5236	157	12	+	+	CCONJ
cana-5236	157	13	1)]2𝑢2	1)]2𝑢2	NUM
cana-5236	157	14	2	2	NUM
cana-5236	157	15	.	.	PUNCT
cana-5236	158	1	the	the	DET
cana-5236	158	2	right	right	ADJ
cana-5236	158	3	hand	hand	NOUN
cana-5236	158	4	side	side	NOUN
cana-5236	158	5	of	of	ADP
cana-5236	158	6	(	(	PUNCT
cana-5236	158	7	3.9	3.9	NUM
cana-5236	158	8	)	)	PUNCT
cana-5236	158	9	is	be	AUX
cana-5236	158	10	negative	negative	ADJ
cana-5236	158	11	if	if	SCONJ
cana-5236	158	12	𝐴1	𝐴1	PROPN
cana-5236	158	13	≤	≤	X
cana-5236	158	14	0	0	NUM
cana-5236	158	15	and	and	CCONJ
cana-5236	158	16	𝐵1	𝐵1	NOUN
cana-5236	158	17	≤	≤	NUM
cana-5236	158	18	0	0	NUM
cana-5236	158	19	.	.	PUNCT
cana-5236	159	1	from	from	ADP
cana-5236	159	2	𝐴1	𝐴1	PROPN
cana-5236	159	3	≤	≤	NUM
cana-5236	159	4	0	0	NUM
cana-5236	159	5	,	,	PUNCT
cana-5236	159	6	we	we	PRON
cana-5236	159	7	have	have	VERB
cana-5236	159	8	𝛽	𝛽	NOUN
cana-5236	159	9	to	to	PART
cana-5236	159	10	be	be	AUX
cana-5236	159	11	one	one	NUM
cana-5236	159	12	of	of	ADP
cana-5236	159	13	the	the	DET
cana-5236	159	14	roots	root	NOUN
cana-5236	159	15	of	of	ADP
cana-5236	159	16	𝜂1𝜂2𝑏2(𝑚	𝜂1𝜂2𝑏2(𝑚	PROPN
cana-5236	159	17	+	+	CCONJ
cana-5236	159	18	2)2(1	2)2(1	NUM
cana-5236	159	19	−	−	NOUN
cana-5236	159	20	𝛼)2	𝛼)2	PROPN
cana-5236	159	21	−	−	PROPN
cana-5236	159	22	𝑏(𝑚	𝑏(𝑚	NOUN
cana-5236	159	23	+	+	CCONJ
cana-5236	160	1	2)(1	2)(1	NUM
cana-5236	160	2	−	−	NOUN
cana-5236	160	3	𝛼)[𝜂1(𝐵	𝛼)[𝜂1(𝐵	NOUN
cana-5236	160	4	+	+	NOUN
cana-5236	160	5	1	1	NUM
cana-5236	160	6	)	)	PUNCT
cana-5236	160	7	+	+	CCONJ
cana-5236	160	8	𝜂2(𝐵	𝜂2(𝐵	NOUN
cana-5236	160	9	−	−	NOUN
cana-5236	160	10	1	1	NUM
cana-5236	160	11	)	)	PUNCT
cana-5236	160	12	]	]	PUNCT
cana-5236	161	1	+	+	CCONJ
cana-5236	161	2	(	(	PUNCT
cana-5236	161	3	𝐵2	𝐵2	NOUN
cana-5236	161	4	−	−	NOUN
cana-5236	161	5	1	1	NUM
cana-5236	161	6	)	)	PUNCT
cana-5236	161	7	=	=	SYM
cana-5236	161	8	0	0	NUM
cana-5236	161	9	communications	communication	NOUN
cana-5236	161	10	on	on	ADP
cana-5236	161	11	applied	apply	VERB
cana-5236	161	12	nonlinear	nonlinear	ADJ
cana-5236	161	13	analysis	analysis	NOUN
cana-5236	161	14	issn	issn	NOUN
cana-5236	161	15	:	:	PUNCT
cana-5236	161	16	1074	1074	NUM
cana-5236	161	17	-	-	PUNCT
cana-5236	161	18	133x	133x	NUM
cana-5236	161	19	vol	vol	VERB
cana-5236	161	20	32	32	NUM
cana-5236	161	21	no	no	NOUN
cana-5236	161	22	.	.	PUNCT
cana-5236	162	1	10s	10	NOUN
cana-5236	162	2	(	(	PUNCT
cana-5236	162	3	2025	2025	NUM
cana-5236	162	4	)	)	PUNCT
cana-5236	162	5	1345	1345	NUM
cana-5236	162	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5236	162	7	with	with	ADP
cana-5236	162	8	0	0	NUM
cana-5236	162	9	≤	≤	NOUN
cana-5236	162	10	β	β	X
cana-5236	162	11	<	<	X
cana-5236	162	12	1	1	NUM
cana-5236	162	13	and	and	CCONJ
cana-5236	162	14	also	also	ADV
cana-5236	162	15	for	for	ADP
cana-5236	162	16	0	0	NUM
cana-5236	162	17	≤	≤	NOUN
cana-5236	162	18	β	β	X
cana-5236	162	19	<	<	X
cana-5236	162	20	1	1	NUM
cana-5236	162	21	,	,	PUNCT
cana-5236	162	22	we	we	PRON
cana-5236	162	23	have	have	VERB
cana-5236	162	24	𝐵1≤	𝐵1≤	SYM
cana-5236	162	25	0	0	NUM
cana-5236	162	26	.	.	PUNCT
cana-5236	163	1	since	since	SCONJ
cana-5236	163	2	all	all	DET
cana-5236	163	3	the	the	DET
cana-5236	163	4	conditions	condition	NOUN
cana-5236	163	5	of	of	ADP
cana-5236	163	6	lemma	lemma	PROPN
cana-5236	163	7	2.2	2.2	NUM
cana-5236	163	8	are	be	AUX
cana-5236	163	9	satisfied	satisfied	ADJ
cana-5236	163	10	,	,	PUNCT
cana-5236	163	11	it	it	PRON
cana-5236	163	12	follows	follow	VERB
cana-5236	163	13	that	that	SCONJ
cana-5236	163	14	ℎ𝑖	ℎ𝑖	NOUN
cana-5236	163	15	∈	∈	PROPN
cana-5236	163	16	𝑃	𝑃	NOUN
cana-5236	163	17	,	,	PUNCT
cana-5236	163	18	i=1,2	i=1,2	ADJ
cana-5236	163	19	and	and	CCONJ
cana-5236	163	20	consequently	consequently	ADV
cana-5236	163	21	𝑝	𝑝	PROPN
cana-5236	163	22	∈	∈	PROPN
cana-5236	163	23	𝑃𝑘[1	𝑃𝑘[1	PROPN
cana-5236	163	24	,	,	PUNCT
cana-5236	163	25	−1	−1	NOUN
cana-5236	163	26	,	,	PUNCT
cana-5236	163	27	𝛽	𝛽	NOUN
cana-5236	163	28	]	]	PUNCT
cana-5236	163	29	.	.	PUNCT
cana-5236	164	1	hence	hence	ADV
cana-5236	164	2	from	from	ADP
cana-5236	164	3	(	(	PUNCT
cana-5236	164	4	3.6	3.6	NUM
cana-5236	164	5	)	)	PUNCT
cana-5236	164	6	,	,	PUNCT
cana-5236	164	7	𝑓	𝑓	PRON
cana-5236	164	8	∈	∈	NOUN
cana-5236	164	9	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	164	10	𝑚	𝑚	X
cana-5236	165	1	[	[	X
cana-5236	165	2	1	1	NUM
cana-5236	165	3	,	,	PUNCT
cana-5236	165	4	−1	−1	NOUN
cana-5236	165	5	,	,	PUNCT
cana-5236	165	6	𝛽	𝛽	NOUN
cana-5236	165	7	,	,	PUNCT
cana-5236	165	8	𝑏	𝑏	PROPN
cana-5236	165	9	+	+	NOUN
cana-5236	165	10	1	1	NUM
cana-5236	165	11	]	]	PUNCT
cana-5236	165	12	.	.	PUNCT
cana-5236	166	1	by	by	ADP
cana-5236	166	2	choosing	choose	VERB
cana-5236	166	3	the	the	DET
cana-5236	166	4	parameters	parameter	NOUN
cana-5236	166	5	a	a	DET
cana-5236	166	6	=	=	SYM
cana-5236	166	7	1	1	NUM
cana-5236	166	8	,	,	PUNCT
cana-5236	166	9	b	b	NOUN
cana-5236	166	10	=	=	SYM
cana-5236	166	11	−1	−1	NOUN
cana-5236	166	12	,	,	PUNCT
cana-5236	166	13	b	b	NOUN
cana-5236	166	14	=	=	SYM
cana-5236	166	15	1	1	NUM
cana-5236	166	16	,	,	PUNCT
cana-5236	166	17	m	m	VERB
cana-5236	166	18	=	=	NOUN
cana-5236	166	19	0	0	NUM
cana-5236	166	20	,	,	PUNCT
cana-5236	166	21	we	we	PRON
cana-5236	166	22	obtain	obtain	VERB
cana-5236	166	23	the	the	DET
cana-5236	166	24	following	follow	VERB
cana-5236	166	25	known	know	VERB
cana-5236	166	26	result	result	NOUN
cana-5236	166	27	,	,	PUNCT
cana-5236	166	28	proved	prove	VERB
cana-5236	166	29	in	in	ADP
cana-5236	166	30	[	[	X
cana-5236	166	31	11	11	NUM
cana-5236	166	32	]	]	PUNCT
cana-5236	166	33	.	.	PUNCT
cana-5236	167	1	corollary	corollary	ADJ
cana-5236	167	2	3.5	3.5	NUM
cana-5236	167	3	.	.	PUNCT
cana-5236	168	1	let	let	VERB
cana-5236	168	2	𝑓	𝑓	PRON
cana-5236	168	3	∈	∈	NOUN
cana-5236	168	4	𝑉𝑘,𝜆(𝛼	𝑉𝑘,𝜆(𝛼	NOUN
cana-5236	168	5	)	)	PUNCT
cana-5236	168	6	.	.	PUNCT
cana-5236	169	1	then	then	ADV
cana-5236	169	2	𝑓	𝑓	DET
cana-5236	169	3	∈	∈	NOUN
cana-5236	169	4	𝑅𝑘,𝜆(𝛽	𝑅𝑘,𝜆(𝛽	NOUN
cana-5236	169	5	)	)	PUNCT
cana-5236	169	6	,	,	PUNCT
cana-5236	169	7	where	where	SCONJ
cana-5236	169	8	𝛽	𝛽	NOUN
cana-5236	169	9	is	be	AUX
cana-5236	169	10	a	a	DET
cana-5236	169	11	root	root	NOUN
cana-5236	169	12	of	of	ADP
cana-5236	169	13	2𝛽2	2𝛽2	NUM
cana-5236	169	14	−	−	PROPN
cana-5236	169	15	(	(	PUNCT
cana-5236	169	16	2𝛼	2𝛼	PROPN
cana-5236	169	17	−	−	PROPN
cana-5236	169	18	1)𝛽	1)𝛽	NUM
cana-5236	169	19	−	−	PROPN
cana-5236	169	20	1	1	NUM
cana-5236	169	21	=	=	SYM
cana-5236	169	22	0	0	NUM
cana-5236	169	23	with	with	ADP
cana-5236	169	24	0	0	NUM
cana-5236	169	25	≤	≤	NOUN
cana-5236	169	26	β	β	X
cana-5236	169	27	<	<	X
cana-5236	169	28	1	1	NUM
cana-5236	169	29	,	,	PUNCT
cana-5236	169	30	which	which	PRON
cana-5236	169	31	is	be	AUX
cana-5236	169	32	β	β	NOUN
cana-5236	169	33	=	=	NOUN
cana-5236	169	34	1	1	NUM
cana-5236	169	35	4	4	NUM
cana-5236	169	36	[	[	X
cana-5236	169	37	(	(	PUNCT
cana-5236	169	38	2𝛼	2𝛼	NUM
cana-5236	169	39	−	−	NOUN
cana-5236	169	40	1	1	NUM
cana-5236	169	41	)	)	PUNCT
cana-5236	169	42	+	+	CCONJ
cana-5236	169	43	√4𝛼2	√4𝛼2	PROPN
cana-5236	169	44	−	−	PROPN
cana-5236	169	45	4𝛼	4𝛼	NOUN
cana-5236	169	46	+	+	CCONJ
cana-5236	169	47	9	9	NUM
cana-5236	169	48	]	]	PUNCT
cana-5236	169	49	.	.	PUNCT
cana-5236	170	1	for	for	ADP
cana-5236	170	2	𝛼	𝛼	NOUN
cana-5236	170	3	=	=	SYM
cana-5236	170	4	0	0	NUM
cana-5236	170	5	,	,	PUNCT
cana-5236	170	6	𝑘	𝑘	X
cana-5236	170	7	=	=	SYM
cana-5236	170	8	2	2	NUM
cana-5236	170	9	in	in	ADP
cana-5236	170	10	corollary	corollary	ADJ
cana-5236	170	11	3.5	3.5	NUM
cana-5236	170	12	,	,	PUNCT
cana-5236	170	13	we	we	PRON
cana-5236	170	14	have	have	VERB
cana-5236	170	15	the	the	DET
cana-5236	170	16	following	follow	VERB
cana-5236	170	17	well	well	ADV
cana-5236	170	18	known	know	VERB
cana-5236	170	19	results	result	NOUN
cana-5236	170	20	[	[	X
cana-5236	170	21	2	2	NUM
cana-5236	170	22	]	]	PUNCT
cana-5236	170	23	.	.	PUNCT
cana-5236	171	1	𝑉2,𝜆(0	𝑉2,𝜆(0	NOUN
cana-5236	171	2	)	)	PUNCT
cana-5236	171	3	=	=	SYM
cana-5236	171	4	𝐶	𝐶	PROPN
cana-5236	171	5	⊆	⊆	NUM
cana-5236	171	6	𝑅2,𝜆	𝑅2,𝜆	NUM
cana-5236	171	7	(	(	PUNCT
cana-5236	171	8	1	1	NUM
cana-5236	171	9	2	2	NUM
cana-5236	171	10	)	)	PUNCT
cana-5236	171	11	=	=	SYM
cana-5236	171	12	𝑆∗	𝑆∗	X
cana-5236	171	13	(	(	PUNCT
cana-5236	171	14	1	1	NUM
cana-5236	171	15	2	2	NUM
cana-5236	171	16	)	)	PUNCT
cana-5236	171	17	,	,	PUNCT
cana-5236	171	18	for	for	ADP
cana-5236	171	19	z	z	PROPN
cana-5236	171	20	∈	∈	PROPN
cana-5236	171	21	𝒰.	𝒰.	PROPN
cana-5236	171	22	theorem	theorem	VERB
cana-5236	171	23	3.6	3.6	NUM
cana-5236	171	24	.	.	PUNCT
cana-5236	172	1	let	let	VERB
cana-5236	172	2	f	f	PROPN
cana-5236	172	3	∈	∈	PROPN
cana-5236	172	4	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	173	1	𝑚	𝑚	X
cana-5236	174	1	[	[	X
cana-5236	174	2	𝐴	𝐴	PROPN
cana-5236	174	3	,	,	PUNCT
cana-5236	174	4	𝐵	𝐵	PROPN
cana-5236	174	5	,	,	PUNCT
cana-5236	174	6	0	0	NUM
cana-5236	174	7	,	,	PUNCT
cana-5236	174	8	𝑏	𝑏	NOUN
cana-5236	174	9	]	]	X
cana-5236	174	10	,	,	PUNCT
cana-5236	174	11	𝑚	𝑚	X
cana-5236	174	12	≥	≥	NUM
cana-5236	174	13	0	0	NUM
cana-5236	174	14	,	,	PUNCT
cana-5236	174	15	b>0(real	b>0(real	NOUN
cana-5236	174	16	)	)	PUNCT
cana-5236	174	17	,	,	PUNCT
cana-5236	174	18	k≥	k≥	PROPN
cana-5236	174	19	2	2	NUM
cana-5236	174	20	and	and	CCONJ
cana-5236	174	21	0	0	NUM
cana-5236	174	22	<	<	X
cana-5236	174	23	𝑎	𝑎	X
cana-5236	174	24	=	=	PUNCT
cana-5236	174	25	𝑏(𝑚+1	𝑏(𝑚+1	NUM
cana-5236	174	26	)	)	PUNCT
cana-5236	174	27	2	2	NUM
cana-5236	174	28	≤	≤	NUM
cana-5236	174	29	1	1	NUM
cana-5236	174	30	.	.	PUNCT
cana-5236	174	31	then	then	ADV
cana-5236	174	32	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	174	33	𝑚𝑓(𝑧	𝑚𝑓(𝑧	PUNCT
cana-5236	174	34	)	)	PUNCT
cana-5236	174	35	maps	map	VERB
cana-5236	174	36	|𝑧|	|𝑧|	PROPN
cana-5236	174	37	<	<	X
cana-5236	174	38	𝑟0	𝑟0	NOUN
cana-5236	174	39	onto	onto	ADP
cana-5236	174	40	a	a	DET
cana-5236	174	41	convex	convex	ADJ
cana-5236	174	42	domain	domain	NOUN
cana-5236	174	43	,	,	PUNCT
cana-5236	174	44	where	where	SCONJ
cana-5236	174	45	𝑟0	𝑟0	PROPN
cana-5236	174	46	is	be	AUX
cana-5236	174	47	the	the	DET
cana-5236	174	48	least	least	ADV
cana-5236	174	49	positive	positive	ADJ
cana-5236	174	50	root	root	NOUN
cana-5236	174	51	of	of	ADP
cana-5236	174	52	the	the	DET
cana-5236	174	53	equation	equation	NOUN
cana-5236	174	54	(	(	PUNCT
cana-5236	174	55	3.10	3.10	NUM
cana-5236	174	56	)	)	PUNCT
cana-5236	174	57	𝑎1𝑟4	𝑎1𝑟4	NOUN
cana-5236	174	58	+	+	NUM
cana-5236	174	59	𝑎2𝑟3	𝑎2𝑟3	NOUN
cana-5236	174	60	+	+	CCONJ
cana-5236	174	61	𝑎3𝑟2	𝑎3𝑟2	X
cana-5236	174	62	+	+	CCONJ
cana-5236	174	63	𝑎4𝑟	𝑎4𝑟	NOUN
cana-5236	174	64	+	+	NUM
cana-5236	174	65	4(2𝑎	4(2𝑎	NUM
cana-5236	174	66	−	−	NOUN
cana-5236	174	67	1	1	NUM
cana-5236	174	68	)	)	PUNCT
cana-5236	174	69	=	=	SYM
cana-5236	174	70	0	0	NUM
cana-5236	174	71	with	with	ADP
cana-5236	174	72	0≤	0≤	NUM
cana-5236	174	73	𝑟	𝑟	NOUN
cana-5236	174	74	<	<	X
cana-5236	174	75	1	1	NUM
cana-5236	174	76	,	,	PUNCT
cana-5236	174	77	where	where	SCONJ
cana-5236	174	78	𝑎1	𝑎1	NOUN
cana-5236	174	79	=	=	PUNCT
cana-5236	174	80	4𝑎2𝐴2𝐵2	4𝑎2𝐴2𝐵2	NUM
cana-5236	174	81	−	−	NOUN
cana-5236	175	1	4(𝑎	4(𝑎	NUM
cana-5236	175	2	−	−	PROPN
cana-5236	175	3	1)2𝐵4	1)2𝐵4	NUM
cana-5236	175	4	𝑎2	𝑎2	NOUN
cana-5236	175	5	=	=	SYM
cana-5236	175	6	2a(2a	2a(2a	NUM
cana-5236	175	7	−	−	NUM
cana-5236	176	1	1)(b	1)(b	NUM
cana-5236	176	2	−	−	ADP
cana-5236	176	3	a)𝐵2𝑘	a)𝐵2𝑘	DET
cana-5236	176	4	𝑎3	𝑎3	NOUN
cana-5236	176	5	=	=	PUNCT
cana-5236	176	6	8𝑎2(𝑎	8𝑎2(𝑎	NUM
cana-5236	177	1	−	−	NUM
cana-5236	177	2	2	2	NUM
cana-5236	177	3	)	)	PUNCT
cana-5236	177	4	+	+	NUM
cana-5236	177	5	8𝑎(1	8𝑎(1	NUM
cana-5236	177	6	−	−	NOUN
cana-5236	177	7	𝑎)𝐴𝐵	𝑎)𝐴𝐵	NUM
cana-5236	177	8	−	−	PROPN
cana-5236	177	9	𝑎2(𝐴	𝑎2(𝐴	PROPN
cana-5236	177	10	−	−	PROPN
cana-5236	177	11	𝐵)2𝑘2	𝐵)2𝑘2	NOUN
cana-5236	177	12	𝑎4	𝑎4	PROPN
cana-5236	177	13	=	=	PUNCT
cana-5236	177	14	2𝑎(2𝑎	2𝑎(2𝑎	NUM
cana-5236	177	15	−	−	NOUN
cana-5236	178	1	3)(𝐴	3)(𝐴	PROPN
cana-5236	178	2	−	−	PROPN
cana-5236	179	1	𝐵)𝑘.	𝐵)𝑘.	NOUN
cana-5236	179	2	this	this	DET
cana-5236	179	3	result	result	NOUN
cana-5236	179	4	is	be	AUX
cana-5236	179	5	sharp	sharp	ADJ
cana-5236	179	6	.	.	PUNCT
cana-5236	180	1	proof	proof	NOUN
cana-5236	180	2	:	:	PUNCT
cana-5236	181	1	since	since	SCONJ
cana-5236	181	2	f	f	PROPN
cana-5236	181	3	∈	∈	PROPN
cana-5236	181	4	𝒱𝑘,𝜆	𝒱𝑘,𝜆	PROPN
cana-5236	181	5	𝑚	𝑚	X
cana-5236	181	6	[	[	X
cana-5236	181	7	𝐴	𝐴	PROPN
cana-5236	181	8	,	,	PUNCT
cana-5236	181	9	𝐵	𝐵	PROPN
cana-5236	181	10	,	,	PUNCT
cana-5236	181	11	0	0	NUM
cana-5236	181	12	,	,	PUNCT
cana-5236	181	13	𝑏	𝑏	NOUN
cana-5236	181	14	]	]	PUNCT
cana-5236	181	15	then	then	ADV
cana-5236	181	16	(	(	PUNCT
cana-5236	181	17	3.11	3.11	NUM
cana-5236	181	18	)	)	PUNCT
cana-5236	181	19	dλ	dλ	NOUN
cana-5236	181	20	m+1f(z	m+1f(z	PROPN
cana-5236	181	21	)	)	PUNCT
cana-5236	181	22	dλ	dλ	NOUN
cana-5236	181	23	mf(z	mf(z	NUM
cana-5236	181	24	)	)	PUNCT
cana-5236	182	1	=	=	SYM
cana-5236	182	2	b(p(z)−1)+2	b(p(z)−1)+2	NOUN
cana-5236	182	3	2	2	NUM
cana-5236	182	4	where	where	SCONJ
cana-5236	182	5	p	p	PROPN
cana-5236	182	6	∈	∈	PROPN
cana-5236	182	7	𝑃𝑘[𝐴	𝑃𝑘[𝐴	PROPN
cana-5236	182	8	,	,	PUNCT
cana-5236	182	9	𝐵	𝐵	PROPN
cana-5236	182	10	,	,	PUNCT
cana-5236	182	11	0	0	NUM
cana-5236	182	12	]	]	PUNCT
cana-5236	182	13	.	.	PUNCT
cana-5236	183	1	using	use	VERB
cana-5236	183	2	the	the	DET
cana-5236	183	3	identity	identity	NOUN
cana-5236	183	4	(	(	PUNCT
cana-5236	183	5	1.9	1.9	NUM
cana-5236	183	6	)	)	PUNCT
cana-5236	183	7	,	,	PUNCT
cana-5236	183	8	we	we	PRON
cana-5236	183	9	have	have	AUX
cana-5236	183	10	from	from	ADP
cana-5236	183	11	(	(	PUNCT
cana-5236	183	12	3.11	3.11	NUM
cana-5236	183	13	)	)	PUNCT
cana-5236	183	14	,	,	PUNCT
cana-5236	183	15	(	(	PUNCT
cana-5236	183	16	3.12	3.12	NUM
cana-5236	183	17	)	)	PUNCT
cana-5236	183	18	𝑧(𝐷𝜆	𝑧(𝐷𝜆	VERB
cana-5236	183	19	𝑚𝑓(𝑧))′	𝑚𝑓(𝑧))′	X
cana-5236	184	1	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	184	2	𝑚𝑓(𝑧	𝑚𝑓(𝑧	PUNCT
cana-5236	184	3	)	)	PUNCT
cana-5236	184	4	=	=	PUNCT
cana-5236	185	1	𝑏(𝑝(𝑧)−1)(𝑚+1)+2	𝑏(𝑝(𝑧)−1)(𝑚+1)+2	NOUN
cana-5236	185	2	2	2	NUM
cana-5236	185	3	logarithmic	logarithmic	ADJ
cana-5236	185	4	differentiation	differentiation	NOUN
cana-5236	185	5	of	of	ADP
cana-5236	185	6	(	(	PUNCT
cana-5236	185	7	3.12	3.12	NUM
cana-5236	185	8	)	)	PUNCT
cana-5236	185	9	yields	yield	NOUN
cana-5236	185	10	(	(	PUNCT
cana-5236	185	11	𝒛(𝐷𝜆	𝒛(𝐷𝜆	NOUN
cana-5236	185	12	𝑚𝑓(𝑧))′)′	𝑚𝑓(𝑧))′)′	NOUN
cana-5236	185	13	(	(	PUNCT
cana-5236	185	14	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	185	15	𝑚𝑓(𝑧))′	𝑚𝑓(𝑧))′	NOUN
cana-5236	185	16	=	=	SYM
cana-5236	185	17	𝑎𝑝(𝑧	𝑎𝑝(𝑧	NOUN
cana-5236	185	18	)	)	PUNCT
cana-5236	185	19	−	−	PROPN
cana-5236	186	1	𝑎	𝑎	X
cana-5236	186	2	+	+	NUM
cana-5236	186	3	1	1	NUM
cana-5236	186	4	+	+	CCONJ
cana-5236	186	5	𝑧𝑝′(𝑧	𝑧𝑝′(𝑧	PROPN
cana-5236	186	6	)	)	PUNCT
cana-5236	186	7	𝑝(𝑧	𝑝(𝑧	PROPN
cana-5236	186	8	)	)	PUNCT
cana-5236	186	9	−	−	PROPN
cana-5236	187	1	1	1	NUM
cana-5236	187	2	+	+	NUM
cana-5236	187	3	1	1	NUM
cana-5236	187	4	𝑎	𝑎	NOUN
cana-5236	187	5	communications	communication	NOUN
cana-5236	187	6	on	on	ADP
cana-5236	187	7	applied	apply	VERB
cana-5236	187	8	nonlinear	nonlinear	ADJ
cana-5236	187	9	analysis	analysis	NOUN
cana-5236	187	10	issn	issn	NOUN
cana-5236	187	11	:	:	PUNCT
cana-5236	187	12	1074	1074	NUM
cana-5236	187	13	-	-	PUNCT
cana-5236	187	14	133x	133x	NUM
cana-5236	187	15	vol	vol	VERB
cana-5236	187	16	32	32	NUM
cana-5236	187	17	no	no	NOUN
cana-5236	187	18	.	.	PUNCT
cana-5236	188	1	10s	10	NOUN
cana-5236	188	2	(	(	PUNCT
cana-5236	188	3	2025	2025	NUM
cana-5236	188	4	)	)	PUNCT
cana-5236	188	5	1346	1346	NUM
cana-5236	188	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5236	188	7	where	where	SCONJ
cana-5236	188	8	𝑎	𝑎	X
cana-5236	188	9	=	=	SYM
cana-5236	188	10	𝑏(𝑚+1	𝑏(𝑚+1	NUM
cana-5236	188	11	)	)	PUNCT
cana-5236	188	12	2	2	NUM
cana-5236	188	13	.	.	PUNCT
cana-5236	189	1	then	then	ADV
cana-5236	189	2	we	we	PRON
cana-5236	189	3	have	have	AUX
cana-5236	189	4	re	re	VERB
cana-5236	189	5	(	(	PUNCT
cana-5236	189	6	1	1	NUM
cana-5236	189	7	+	+	CCONJ
cana-5236	189	8	z(𝐷𝜆	z(𝐷𝜆	NOUN
cana-5236	189	9	𝑚𝑓(𝑧	𝑚𝑓(𝑧	NOUN
cana-5236	189	10	)	)	PUNCT
cana-5236	189	11	)	)	PUNCT
cana-5236	189	12	"	"	PUNCT
cana-5236	190	1	(	(	PUNCT
cana-5236	190	2	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	190	3	𝑚𝑓(𝑧))′	𝑚𝑓(𝑧))′	NUM
cana-5236	190	4	)	)	PUNCT
cana-5236	190	5	≥	≥	NOUN
cana-5236	190	6	a	a	DET
cana-5236	190	7	re	re	NOUN
cana-5236	190	8	p(z	p(z	NOUN
cana-5236	190	9	)	)	PUNCT
cana-5236	191	1	+	+	CCONJ
cana-5236	191	2	(	(	PUNCT
cana-5236	191	3	1	1	NUM
cana-5236	191	4	−	−	NOUN
cana-5236	191	5	a	a	X
cana-5236	191	6	)	)	PUNCT
cana-5236	191	7	−	−	PROPN
cana-5236	191	8	|𝑧𝑝′(𝑧)|	|𝑧𝑝′(𝑧)|	NOUN
cana-5236	191	9	|𝑝(𝑧	|𝑝(𝑧	PROPN
cana-5236	191	10	)	)	PUNCT
cana-5236	191	11	−	−	PROPN
cana-5236	192	1	1	1	NUM
cana-5236	192	2	+	+	SYM
cana-5236	192	3	1	1	NUM
cana-5236	192	4	𝑎|	𝑎|	ADJ
cana-5236	192	5	,	,	PUNCT
cana-5236	192	6	and	and	CCONJ
cana-5236	192	7	hence	hence	ADV
cana-5236	192	8	,	,	PUNCT
cana-5236	192	9	by	by	ADP
cana-5236	192	10	using	use	VERB
cana-5236	192	11	lemma	lemma	PROPN
cana-5236	192	12	2.3	2.3	NUM
cana-5236	192	13	and	and	CCONJ
cana-5236	192	14	lemma	lemma	PROPN
cana-5236	192	15	2.4	2.4	NUM
cana-5236	192	16	,	,	PUNCT
cana-5236	192	17	re	re	ADP
cana-5236	192	18	(	(	PUNCT
cana-5236	192	19	1	1	NUM
cana-5236	192	20	+	+	CCONJ
cana-5236	192	21	z(𝐷𝜆	z(𝐷𝜆	NOUN
cana-5236	192	22	𝑚𝑓(𝑧	𝑚𝑓(𝑧	NOUN
cana-5236	192	23	)	)	PUNCT
cana-5236	192	24	)	)	PUNCT
cana-5236	192	25	"	"	PUNCT
cana-5236	193	1	(	(	PUNCT
cana-5236	193	2	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	193	3	𝑚𝑓(𝑧))′	𝑚𝑓(𝑧))′	NUM
cana-5236	193	4	)	)	PUNCT
cana-5236	193	5	≥	≥	NOUN
cana-5236	194	1	𝑅𝑒	𝑅𝑒	VERB
cana-5236	194	2	𝑝(𝑧	𝑝(𝑧	NOUN
cana-5236	194	3	)	)	PUNCT
cana-5236	194	4	{	{	PUNCT
cana-5236	194	5	𝑎	𝑎	X
cana-5236	194	6	+	+	NUM
cana-5236	194	7	2(1	2(1	NUM
cana-5236	194	8	−	−	NOUN
cana-5236	194	9	𝑎)(1	𝑎)(1	NOUN
cana-5236	194	10	−	−	PROPN
cana-5236	194	11	𝐵2𝑟2	𝐵2𝑟2	PROPN
cana-5236	194	12	)	)	PUNCT
cana-5236	194	13	2	2	NUM
cana-5236	195	1	+	+	CCONJ
cana-5236	195	2	(	(	PUNCT
cana-5236	195	3	𝐴	𝐴	PROPN
cana-5236	195	4	−	−	PROPN
cana-5236	195	5	𝐵)𝑘𝑟	𝐵)𝑘𝑟	PROPN
cana-5236	195	6	−	−	PROPN
cana-5236	195	7	2𝐴𝐵𝑟2	2𝐴𝐵𝑟2	NUM
cana-5236	195	8	−	−	PROPN
cana-5236	195	9	2𝑎𝑟{(𝐴	2𝑎𝑟{(𝐴	NUM
cana-5236	195	10	−	−	NOUN
cana-5236	195	11	𝐵)𝑘	𝐵)𝑘	PUNCT
cana-5236	195	12	−	−	PROPN
cana-5236	195	13	4𝐵(𝐴	4𝐵(𝐴	NUM
cana-5236	195	14	−	−	NOUN
cana-5236	195	15	𝐵)𝑟	𝐵)𝑟	NOUN
cana-5236	196	1	+	+	CCONJ
cana-5236	196	2	𝐵2(𝐴	𝐵2(𝐴	ADJ
cana-5236	196	3	−	−	NOUN
cana-5236	196	4	𝐵)𝑘𝑟2	𝐵)𝑘𝑟2	NOUN
cana-5236	196	5	}	}	PUNCT
cana-5236	196	6	(	(	PUNCT
cana-5236	196	7	2	2	NUM
cana-5236	196	8	+	+	CCONJ
cana-5236	196	9	(	(	PUNCT
cana-5236	196	10	𝐴	𝐴	PROPN
cana-5236	196	11	−	−	PROPN
cana-5236	196	12	𝐵)𝑘𝑟	𝐵)𝑘𝑟	PROPN
cana-5236	196	13	−	−	PROPN
cana-5236	196	14	2𝐴𝐵𝑟2)𝜉	2𝐴𝐵𝑟2)𝜉	INTJ
cana-5236	196	15	}	}	PUNCT
cana-5236	196	16	=	=	SYM
cana-5236	196	17	𝑅𝑒	𝑅𝑒	PROPN
cana-5236	196	18	𝑝(𝑧	𝑝(𝑧	NOUN
cana-5236	196	19	)	)	PUNCT
cana-5236	196	20	{	{	PUNCT
cana-5236	196	21	𝑎1𝑟4	𝑎1𝑟4	PROPN
cana-5236	196	22	+	+	NUM
cana-5236	196	23	𝑎2𝑟3	𝑎2𝑟3	NOUN
cana-5236	196	24	+	+	CCONJ
cana-5236	196	25	𝑎3𝑟2	𝑎3𝑟2	X
cana-5236	196	26	+	+	CCONJ
cana-5236	196	27	𝑎4𝑟	𝑎4𝑟	NOUN
cana-5236	196	28	+	+	NUM
cana-5236	196	29	4(2𝑎	4(2𝑎	NUM
cana-5236	196	30	−	−	NOUN
cana-5236	196	31	1	1	NUM
cana-5236	196	32	)	)	PUNCT
cana-5236	196	33	(	(	PUNCT
cana-5236	196	34	2	2	NUM
cana-5236	196	35	+	+	CCONJ
cana-5236	196	36	(	(	PUNCT
cana-5236	196	37	𝐴	𝐴	PROPN
cana-5236	196	38	−	−	PROPN
cana-5236	196	39	𝐵)𝑘𝑟	𝐵)𝑘𝑟	PROPN
cana-5236	196	40	−	−	PROPN
cana-5236	196	41	2𝐴𝐵𝑟2)𝜉	2𝐴𝐵𝑟2)𝜉	INTJ
cana-5236	196	42	}	}	PUNCT
cana-5236	196	43	>	>	X
cana-5236	196	44	0	0	NUM
cana-5236	196	45	,	,	PUNCT
cana-5236	196	46	provided	provide	VERB
cana-5236	196	47	𝑇(𝑟	𝑇(𝑟	NUM
cana-5236	196	48	)	)	PUNCT
cana-5236	196	49	=	=	PUNCT
cana-5236	196	50	𝑎1𝑟4	𝑎1𝑟4	NOUN
cana-5236	196	51	+	+	NUM
cana-5236	196	52	𝑎2𝑟3	𝑎2𝑟3	NOUN
cana-5236	196	53	+	+	CCONJ
cana-5236	196	54	𝑎3𝑟2	𝑎3𝑟2	X
cana-5236	196	55	+	+	CCONJ
cana-5236	196	56	𝑎4𝑟	𝑎4𝑟	NOUN
cana-5236	196	57	+	+	NUM
cana-5236	196	58	4(2𝑎	4(2𝑎	NUM
cana-5236	196	59	−	−	NOUN
cana-5236	196	60	1	1	NUM
cana-5236	196	61	)	)	PUNCT
cana-5236	196	62	>	>	X
cana-5236	196	63	0	0	NUM
cana-5236	196	64	,	,	PUNCT
cana-5236	196	65	where	where	SCONJ
cana-5236	196	66	𝑎1	𝑎1	ADV
cana-5236	196	67	=	=	PUNCT
cana-5236	196	68	4𝑎2𝐴2𝐵2	4𝑎2𝐴2𝐵2	NUM
cana-5236	196	69	−	−	NOUN
cana-5236	196	70	4(𝑎	4(𝑎	NUM
cana-5236	196	71	−	−	PROPN
cana-5236	196	72	1)2𝐵4	1)2𝐵4	NUM
cana-5236	196	73	𝑎2	𝑎2	NOUN
cana-5236	196	74	=	=	SYM
cana-5236	196	75	2a(2a	2a(2a	NUM
cana-5236	196	76	−	−	NUM
cana-5236	197	1	1)(b	1)(b	NUM
cana-5236	197	2	−	−	ADP
cana-5236	197	3	a)𝐵2𝑘	a)𝐵2𝑘	DET
cana-5236	197	4	𝑎3	𝑎3	NOUN
cana-5236	197	5	=	=	PUNCT
cana-5236	197	6	8𝑎2(𝑎	8𝑎2(𝑎	NUM
cana-5236	198	1	−	−	NUM
cana-5236	198	2	2	2	NUM
cana-5236	198	3	)	)	PUNCT
cana-5236	198	4	+	+	NUM
cana-5236	198	5	8𝑎(1	8𝑎(1	NUM
cana-5236	198	6	−	−	NOUN
cana-5236	198	7	𝑎)𝐴𝐵	𝑎)𝐴𝐵	NUM
cana-5236	198	8	−	−	PROPN
cana-5236	198	9	𝑎2(𝐴	𝑎2(𝐴	PROPN
cana-5236	198	10	−	−	PROPN
cana-5236	198	11	𝐵)2𝑘2	𝐵)2𝑘2	NOUN
cana-5236	198	12	𝑎4	𝑎4	PROPN
cana-5236	198	13	=	=	PUNCT
cana-5236	198	14	2𝑎(2𝑎	2𝑎(2𝑎	NUM
cana-5236	198	15	−	−	PROPN
cana-5236	199	1	3)(𝐴	3)(𝐴	PROPN
cana-5236	199	2	−	−	NOUN
cana-5236	199	3	𝐵)𝑘	𝐵)𝑘	NOUN
cana-5236	199	4	and	and	CCONJ
cana-5236	199	5	𝜉	𝜉	X
cana-5236	199	6	=	=	SYM
cana-5236	199	7	2(2𝑎	2(2𝑎	NUM
cana-5236	199	8	−	−	NOUN
cana-5236	199	9	1	1	NUM
cana-5236	199	10	)	)	PUNCT
cana-5236	199	11	−	−	PROPN
cana-5236	199	12	𝑎(𝐴	𝑎(𝐴	PROPN
cana-5236	199	13	−	−	PROPN
cana-5236	199	14	𝐵)𝑘𝑟	𝐵)𝑘𝑟	NOUN
cana-5236	199	15	+	+	CCONJ
cana-5236	199	16	2(𝐵2	2(𝐵2	NUM
cana-5236	200	1	−	−	ADP
cana-5236	200	2	𝑎(𝐴	𝑎(𝐴	PROPN
cana-5236	200	3	+	+	X
cana-5236	200	4	𝐵)𝐵)𝑟2	𝐵)𝐵)𝑟2	NOUN
cana-5236	200	5	.	.	PUNCT
cana-5236	201	1	we	we	PRON
cana-5236	201	2	have	have	VERB
cana-5236	201	3	𝑇(0	𝑇(0	NUM
cana-5236	201	4	)	)	PUNCT
cana-5236	201	5	>	>	X
cana-5236	201	6	0	0	NUM
cana-5236	201	7	𝑎𝑛𝑑	𝑎𝑛𝑑	X
cana-5236	201	8	𝑇(1	𝑇(1	PUNCT
cana-5236	201	9	)	)	PUNCT
cana-5236	201	10	<	<	X
cana-5236	201	11	0	0	X
cana-5236	201	12	.	.	PUNCT
cana-5236	202	1	therefore	therefore	ADV
cana-5236	202	2	,	,	PUNCT
cana-5236	202	3	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	202	4	𝑚𝑓(𝑧	𝑚𝑓(𝑧	NUM
cana-5236	202	5	)	)	PUNCT
cana-5236	202	6	maps	map	VERB
cana-5236	202	7	|𝑧|	|𝑧|	PROPN
cana-5236	202	8	<	<	X
cana-5236	202	9	𝑟0	𝑟0	NOUN
cana-5236	202	10	onto	onto	ADP
cana-5236	202	11	a	a	DET
cana-5236	202	12	convex	convex	ADJ
cana-5236	202	13	domain	domain	NOUN
cana-5236	202	14	,	,	PUNCT
cana-5236	202	15	where	where	SCONJ
cana-5236	202	16	𝑟0	𝑟0	PROPN
cana-5236	202	17	is	be	AUX
cana-5236	202	18	the	the	DET
cana-5236	202	19	least	least	ADV
cana-5236	202	20	positive	positive	ADJ
cana-5236	202	21	root	root	NOUN
cana-5236	202	22	of	of	ADP
cana-5236	202	23	the	the	DET
cana-5236	202	24	equation	equation	NOUN
cana-5236	202	25	𝑇(𝑟	𝑇(𝑟	NOUN
cana-5236	202	26	)	)	PUNCT
cana-5236	202	27	=	=	SYM
cana-5236	202	28	0	0	NUM
cana-5236	202	29	,	,	PUNCT
cana-5236	202	30	lying	lie	VERB
cana-5236	202	31	in	in	ADP
cana-5236	202	32	(	(	PUNCT
cana-5236	202	33	0,1	0,1	NUM
cana-5236	202	34	)	)	PUNCT
cana-5236	202	35	.	.	PUNCT
cana-5236	203	1	for	for	ADP
cana-5236	203	2	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	203	3	𝑚𝑓1(𝑧	𝑚𝑓1(𝑧	PROPN
cana-5236	203	4	)	)	PUNCT
cana-5236	203	5	such	such	ADJ
cana-5236	203	6	that	that	SCONJ
cana-5236	203	7	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	203	8	𝑚+1𝑓1(𝑧	𝑚+1𝑓1(𝑧	PROPN
cana-5236	203	9	)	)	PUNCT
cana-5236	203	10	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	203	11	𝑚𝑓1(𝑧	𝑚𝑓1(𝑧	PROPN
cana-5236	203	12	)	)	PUNCT
cana-5236	203	13	=	=	SYM
cana-5236	203	14	𝑏(𝑝𝑘(𝑧	𝑏(𝑝𝑘(𝑧	PROPN
cana-5236	203	15	)	)	PUNCT
cana-5236	203	16	−	−	PROPN
cana-5236	203	17	1	1	NUM
cana-5236	203	18	)	)	PUNCT
cana-5236	203	19	+	+	CCONJ
cana-5236	203	20	2	2	NUM
cana-5236	203	21	2	2	NUM
cana-5236	203	22	where	where	SCONJ
cana-5236	203	23	𝑝𝑘(𝑧	𝑝𝑘(𝑧	PUNCT
cana-5236	203	24	)	)	PUNCT
cana-5236	203	25	=	=	SYM
cana-5236	204	1	2+(𝐴−𝐵)𝑘𝑧−2𝐴𝐵𝑧2	2+(𝐴−𝐵)𝑘𝑧−2𝐴𝐵𝑧2	NUM
cana-5236	204	2	2(1−𝐵2𝑧2	2(1−𝐵2𝑧2	NUM
cana-5236	204	3	)	)	PUNCT
cana-5236	204	4	,	,	PUNCT
cana-5236	204	5	we	we	PRON
cana-5236	204	6	have	have	VERB
cana-5236	204	7	(	(	PUNCT
cana-5236	204	8	𝒛(𝐷𝜆	𝒛(𝐷𝜆	NOUN
cana-5236	204	9	𝑚𝑓1(𝑧))′)′	𝑚𝑓1(𝑧))′)′	NOUN
cana-5236	204	10	(	(	PUNCT
cana-5236	204	11	𝐷𝜆	𝐷𝜆	PROPN
cana-5236	204	12	𝑚𝑓1(𝑧))′	𝑚𝑓1(𝑧))′	NOUN
cana-5236	204	13	=	=	PUNCT
cana-5236	204	14	𝑎1𝑟4	𝑎1𝑟4	NOUN
cana-5236	204	15	+	+	NUM
cana-5236	204	16	𝑎2𝑟3	𝑎2𝑟3	NOUN
cana-5236	204	17	+	+	CCONJ
cana-5236	204	18	𝑎3𝑟2	𝑎3𝑟2	X
cana-5236	204	19	+	+	CCONJ
cana-5236	204	20	𝑎4𝑟	𝑎4𝑟	NOUN
cana-5236	204	21	+	+	NUM
cana-5236	204	22	4(2𝑎	4(2𝑎	NUM
cana-5236	204	23	−	−	NOUN
cana-5236	204	24	1	1	NUM
cana-5236	204	25	)	)	PUNCT
cana-5236	204	26	(	(	PUNCT
cana-5236	204	27	2	2	NUM
cana-5236	204	28	+	+	CCONJ
cana-5236	204	29	(	(	PUNCT
cana-5236	204	30	𝐴	𝐴	PROPN
cana-5236	204	31	−	−	PROPN
cana-5236	204	32	𝐵)𝑘𝑟	𝐵)𝑘𝑟	PROPN
cana-5236	204	33	−	−	PROPN
cana-5236	204	34	2𝐴𝐵𝑟2)𝜉	2𝐴𝐵𝑟2)𝜉	NOUN
cana-5236	204	35	=	=	SYM
cana-5236	204	36	0	0	NUM
cana-5236	204	37	for	for	ADP
cana-5236	204	38	𝑧	𝑧	PRON
cana-5236	204	39	=	=	ADJ
cana-5236	204	40	𝑟0	𝑟0	NOUN
cana-5236	204	41	.	.	PUNCT
cana-5236	205	1	hence	hence	ADV
cana-5236	205	2	this	this	DET
cana-5236	205	3	radius	radius	NOUN
cana-5236	205	4	𝑟0	𝑟0	NOUN
cana-5236	205	5	is	be	AUX
cana-5236	205	6	sharp	sharp	ADJ
cana-5236	205	7	.	.	PUNCT
cana-5236	206	1	by	by	ADP
cana-5236	206	2	choosing	choose	VERB
cana-5236	206	3	the	the	DET
cana-5236	206	4	parameters	parameter	NOUN
cana-5236	206	5	𝐴	𝐴	NOUN
cana-5236	206	6	=	=	SYM
cana-5236	206	7	1	1	NUM
cana-5236	206	8	,	,	PUNCT
cana-5236	206	9	𝐵	𝐵	NOUN
cana-5236	206	10	=	=	SYM
cana-5236	206	11	−1	−1	NOUN
cana-5236	206	12	,	,	PUNCT
cana-5236	206	13	𝑘	𝑘	X
cana-5236	206	14	=	=	ADJ
cana-5236	206	15	2	2	NUM
cana-5236	206	16	,	,	PUNCT
cana-5236	206	17	𝑏	𝑏	NOUN
cana-5236	206	18	=	=	SYM
cana-5236	206	19	2	2	NUM
cana-5236	206	20	𝑎𝑛𝑑	𝑎𝑛𝑑	NOUN
cana-5236	206	21	𝑚	𝑚	NOUN
cana-5236	206	22	=	=	SYM
cana-5236	206	23	0	0	NUM
cana-5236	206	24	,	,	PUNCT
cana-5236	206	25	we	we	PRON
cana-5236	206	26	obtain	obtain	VERB
cana-5236	206	27	the	the	DET
cana-5236	206	28	following	follow	VERB
cana-5236	206	29	known	know	VERB
cana-5236	206	30	result	result	NOUN
cana-5236	206	31	,	,	PUNCT
cana-5236	206	32	see[2	see[2	NUM
cana-5236	206	33	]	]	PUNCT
cana-5236	206	34	.	.	PUNCT
cana-5236	207	1	communications	communication	NOUN
cana-5236	207	2	on	on	ADP
cana-5236	207	3	applied	apply	VERB
cana-5236	207	4	nonlinear	nonlinear	ADJ
cana-5236	207	5	analysis	analysis	NOUN
cana-5236	207	6	issn	issn	NOUN
cana-5236	207	7	:	:	PUNCT
cana-5236	207	8	1074	1074	NUM
cana-5236	207	9	-	-	PUNCT
cana-5236	207	10	133x	133x	NUM
cana-5236	207	11	vol	vol	VERB
cana-5236	207	12	32	32	NUM
cana-5236	207	13	no	no	NOUN
cana-5236	207	14	.	.	PUNCT
cana-5236	208	1	10s	10	NOUN
cana-5236	208	2	(	(	PUNCT
cana-5236	208	3	2025	2025	NUM
cana-5236	208	4	)	)	PUNCT
cana-5236	208	5	1347	1347	NUM
cana-5236	208	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5236	208	7	corollary	corollary	NOUN
cana-5236	208	8	3.7	3.7	NUM
cana-5236	208	9	:	:	PUNCT
cana-5236	208	10	let	let	VERB
cana-5236	208	11	𝑓	𝑓	DET
cana-5236	208	12	∈	∈	PROPN
cana-5236	208	13	𝑆′.	𝑆′.	NOUN
cana-5236	208	14	then	then	ADV
cana-5236	208	15	𝑓	𝑓	DET
cana-5236	208	16	maps	map	NOUN
cana-5236	208	17	|𝑧|	|𝑧|	PROPN
cana-5236	208	18	<	<	X
cana-5236	208	19	𝑟0	𝑟0	NOUN
cana-5236	208	20	onto	onto	ADP
cana-5236	208	21	a	a	DET
cana-5236	208	22	convex	convex	ADJ
cana-5236	208	23	domain	domain	NOUN
cana-5236	208	24	,	,	PUNCT
cana-5236	208	25	where	where	SCONJ
cana-5236	208	26	𝑟0	𝑟0	PROPN
cana-5236	208	27	is	be	AUX
cana-5236	208	28	the	the	DET
cana-5236	208	29	least	least	ADV
cana-5236	208	30	positive	positive	ADJ
cana-5236	208	31	root	root	NOUN
cana-5236	208	32	of	of	ADP
cana-5236	208	33	the	the	DET
cana-5236	208	34	equation	equation	NOUN
cana-5236	208	35	𝑟4	𝑟4	PROPN
cana-5236	208	36	−	−	PROPN
cana-5236	208	37	2𝑟3	2𝑟3	NUM
cana-5236	208	38	−	−	NUM
cana-5236	208	39	6𝑟2	6𝑟2	NUM
cana-5236	208	40	−	−	PROPN
cana-5236	208	41	2𝑟	2𝑟	NUM
cana-5236	208	42	+	+	CCONJ
cana-5236	208	43	1	1	NUM
cana-5236	208	44	=	=	SYM
cana-5236	208	45	0	0	NUM
cana-5236	208	46	with	with	ADP
cana-5236	208	47	0	0	NUM
cana-5236	208	48	≤	≤	NUM
cana-5236	208	49	𝑟	𝑟	NOUN
cana-5236	208	50	<	<	X
cana-5236	208	51	1	1	NUM
cana-5236	208	52	,	,	PUNCT
cana-5236	208	53	which	which	PRON
cana-5236	208	54	is	be	AUX
cana-5236	208	55	𝑟0	𝑟0	NOUN
cana-5236	208	56	=	=	SYM
cana-5236	209	1	2	2	NUM
cana-5236	209	2	−	−	PROPN
cana-5236	209	3	√3	√3	PROPN
cana-5236	209	4	.	.	PUNCT
cana-5236	210	1	this	this	PRON
cana-5236	210	2	is	be	AUX
cana-5236	210	3	also	also	ADV
cana-5236	210	4	sharp	sharp	ADJ
cana-5236	210	5	.	.	PUNCT
cana-5236	211	1	4	4	X
cana-5236	211	2	.	.	NUM
cana-5236	211	3	references	reference	NOUN
cana-5236	211	4	[	[	X
cana-5236	211	5	1	1	NUM
cana-5236	211	6	]	]	PUNCT
cana-5236	211	7	m.arif	m.arif	NOUN
cana-5236	211	8	,	,	PUNCT
cana-5236	211	9	k.i	k.i	PROPN
cana-5236	211	10	.	.	PUNCT
cana-5236	212	1	noor	noor	PROPN
cana-5236	212	2	,	,	PUNCT
cana-5236	212	3	m.	m.	NOUN
cana-5236	212	4	raza	raza	PROPN
cana-5236	212	5	,	,	PUNCT
cana-5236	212	6	w.	w.	PROPN
cana-5236	212	7	hag	hag	PROPN
cana-5236	212	8	,	,	PUNCT
cana-5236	212	9	some	some	DET
cana-5236	212	10	properties	property	NOUN
cana-5236	212	11	of	of	ADP
cana-5236	212	12	a	a	DET
cana-5236	212	13	generalized	generalized	ADJ
cana-5236	212	14	class	class	NOUN
cana-5236	212	15	of	of	ADP
cana-5236	212	16	analytic	analytic	ADJ
cana-5236	212	17	functions	function	NOUN
cana-5236	212	18	related	relate	VERB
cana-5236	212	19	with	with	ADP
cana-5236	212	20	janowski	janowski	ADJ
cana-5236	212	21	functions	function	NOUN
cana-5236	212	22	,	,	PUNCT
cana-5236	212	23	abst	abst	PROPN
cana-5236	212	24	.	.	PUNCT
cana-5236	212	25	appl	appl	PROPN
cana-5236	212	26	.	.	PUNCT
cana-5236	213	1	analy	analy	PROPN
cana-5236	213	2	.	.	PROPN
cana-5236	213	3	,vol(2012	,vol(2012	PUNCT
cana-5236	213	4	)	)	PUNCT
cana-5236	214	1	article	article	NOUN
cana-5236	214	2	i	i	PROPN
cana-5236	214	3	d	d	PROPN
cana-5236	214	4	279843	279843	NUM
cana-5236	214	5	,	,	PUNCT
cana-5236	214	6	pp.11	pp.11	VERB
cana-5236	214	7	[	[	X
cana-5236	214	8	2	2	NUM
cana-5236	214	9	]	]	X
cana-5236	214	10	dileep	dileep	PROPN
cana-5236	214	11	l	l	PROPN
cana-5236	214	12	and	and	CCONJ
cana-5236	214	13	latha	latha	PROPN
cana-5236	214	14	s	s	PROPN
cana-5236	214	15	,	,	PUNCT
cana-5236	214	16	neighborhood	neighborhood	NOUN
cana-5236	214	17	properties	property	NOUN
cana-5236	214	18	of	of	ADP
cana-5236	214	19	generalized	generalized	ADJ
cana-5236	214	20	ruscheweyh	ruscheweyh	NOUN
cana-5236	214	21	type	type	VERB
cana-5236	214	22	analytic	analytic	ADJ
cana-5236	214	23	functions	function	NOUN
cana-5236	214	24	.	.	PUNCT
cana-5236	215	1	[	[	X
cana-5236	215	2	3	3	NUM
cana-5236	215	3	]	]	X
cana-5236	215	4	a.w.goodman	a.w.goodman	ADJ
cana-5236	215	5	,	,	PUNCT
cana-5236	215	6	univalent	univalent	ADJ
cana-5236	215	7	functions	function	NOUN
cana-5236	215	8	,	,	PUNCT
cana-5236	215	9	vol	vol	NOUN
cana-5236	215	10	.	.	PUNCT
cana-5236	216	1	i	i	PRON
cana-5236	216	2	,	,	PUNCT
cana-5236	216	3	ii	ii	PROPN
cana-5236	216	4	,	,	PUNCT
cana-5236	216	5	mariner	mariner	NOUN
cana-5236	216	6	publishing	publishing	NOUN
cana-5236	216	7	company	company	NOUN
cana-5236	216	8	,	,	PUNCT
cana-5236	216	9	tempa	tempa	PROPN
cana-5236	216	10	florida	florida	PROPN
cana-5236	216	11	,	,	PUNCT
cana-5236	216	12	u.s.a	u.s.a	PROPN
cana-5236	216	13	,	,	PUNCT
cana-5236	216	14	1983	1983	NUM
cana-5236	216	15	.	.	PUNCT
cana-5236	217	1	[	[	X
cana-5236	217	2	4	4	X
cana-5236	217	3	]	]	PUNCT
cana-5236	217	4	s.	s.	PROPN
cana-5236	217	5	latha	latha	PROPN
cana-5236	217	6	,	,	PUNCT
cana-5236	217	7	s.	s.	PROPN
cana-5236	217	8	nanjunda	nanjunda	PROPN
cana-5236	217	9	rao	rao	PROPN
cana-5236	217	10	,	,	PUNCT
cana-5236	217	11	convex	convex	ADJ
cana-5236	217	12	combinations	combination	NOUN
cana-5236	217	13	of	of	ADP
cana-5236	217	14	n	n	DET
cana-5236	217	15	analytic	analytic	ADJ
cana-5236	217	16	functions	function	NOUN
cana-5236	217	17	in	in	ADP
cana-5236	217	18	generalized	generalized	ADJ
cana-5236	217	19	ruscheweyh	ruscheweyh	NOUN
cana-5236	217	20	class	class	NOUN
cana-5236	217	21	,	,	PUNCT
cana-5236	217	22	int	int	NOUN
cana-5236	217	23	.	.	PUNCT
cana-5236	218	1	j.	j.	PROPN
cana-5236	218	2	math	math	PROPN
cana-5236	218	3	.	.	PUNCT
cana-5236	219	1	educ	educ	PROPN
cana-5236	219	2	.	.	PUNCT
cana-5236	220	1	sci	sci	PROPN
cana-5236	220	2	.	.	PUNCT
cana-5236	220	3	technology	technology	PROPN
cana-5236	220	4	,	,	PUNCT
cana-5236	220	5	25(6)(1994	25(6)(1994	NUM
cana-5236	220	6	)	)	PUNCT
cana-5236	220	7	,	,	PUNCT
cana-5236	220	8	791	791	NUM
cana-5236	220	9	-	-	SYM
cana-5236	220	10	795	795	NUM
cana-5236	220	11	.	.	PUNCT
cana-5236	221	1	[	[	X
cana-5236	221	2	5	5	NUM
cana-5236	221	3	]	]	SYM
cana-5236	221	4	a.a	a.a	PROPN
cana-5236	221	5	.	.	PROPN
cana-5236	221	6	lupas	lupas	PROPN
cana-5236	221	7	,	,	PUNCT
cana-5236	221	8	on	on	ADP
cana-5236	221	9	special	special	ADJ
cana-5236	221	10	differential	differential	NOUN
cana-5236	221	11	superordinations	superordination	NOUN
cana-5236	221	12	using	use	VERB
cana-5236	221	13	a	a	DET
cana-5236	221	14	generalized	generalize	VERB
cana-5236	221	15	salagean	salagean	ADJ
cana-5236	221	16	operator	operator	NOUN
cana-5236	221	17	and	and	CCONJ
cana-5236	221	18	ruscheweyh	ruscheweyh	NOUN
cana-5236	221	19	derivative	derivative	ADJ
cana-5236	221	20	,	,	PUNCT
cana-5236	221	21	comput	comput	ADJ
cana-5236	221	22	math	math	NOUN
cana-5236	221	23	.	.	PUNCT
cana-5236	222	1	appl	appl	PROPN
cana-5236	222	2	.	.	PROPN
cana-5236	222	3	,	,	PUNCT
cana-5236	222	4	61(4)(2011	61(4)(2011	NUM
cana-5236	222	5	)	)	PUNCT
cana-5236	222	6	,	,	PUNCT
cana-5236	222	7	1048	1048	NUM
cana-5236	222	8	-	-	SYM
cana-5236	222	9	1058	1058	NUM
cana-5236	222	10	..	..	PUNCT
cana-5236	223	1	[	[	X
cana-5236	223	2	6	6	NUM
cana-5236	223	3	]	]	SYM
cana-5236	223	4	s.n	s.n	PROPN
cana-5236	223	5	.	.	PROPN
cana-5236	223	6	malik	malik	PROPN
cana-5236	223	7	,	,	PUNCT
cana-5236	223	8	m.	m.	PROPN
cana-5236	223	9	arif	arif	PROPN
cana-5236	223	10	,	,	PUNCT
cana-5236	223	11	k.i	k.i	PROPN
cana-5236	223	12	.	.	PUNCT
cana-5236	224	1	noor	noor	PROPN
cana-5236	224	2	and	and	CCONJ
cana-5236	224	3	m.	m.	PROPN
cana-5236	224	4	raza	raza	PROPN
cana-5236	224	5	,	,	PUNCT
cana-5236	224	6	on	on	ADP
cana-5236	224	7	a	a	DET
cana-5236	224	8	class	class	NOUN
cana-5236	224	9	of	of	ADP
cana-5236	224	10	analytic	analytic	ADJ
cana-5236	224	11	functions	function	NOUN
cana-5236	224	12	defined	define	VERB
cana-5236	224	13	by	by	ADP
cana-5236	224	14	ruscheweyh	ruscheweyh	NOUN
cana-5236	224	15	derivative.life	derivative.life	PROPN
cana-5236	224	16	science	science	PROPN
cana-5236	224	17	journal	journal	PROPN
cana-5236	224	18	,	,	PUNCT
cana-5236	224	19	9(2012	9(2012	NUM
cana-5236	224	20	)	)	PUNCT
cana-5236	224	21	,	,	PUNCT
cana-5236	224	22	3829	3829	NUM
cana-5236	224	23	-	-	SYM
cana-5236	224	24	3835	3835	NUM
cana-5236	224	25	.	.	PUNCT
cana-5236	225	1	[	[	X
cana-5236	225	2	7	7	X
cana-5236	225	3	]	]	X
cana-5236	225	4	s.s	s.s	PROPN
cana-5236	225	5	miller	miller	PROPN
cana-5236	225	6	,	,	PUNCT
cana-5236	225	7	differential	differential	ADJ
cana-5236	225	8	inequalities	inequality	NOUN
cana-5236	225	9	and	and	CCONJ
cana-5236	225	10	cartheodory	cartheodory	ADJ
cana-5236	225	11	functions	function	NOUN
cana-5236	225	12	,	,	PUNCT
cana-5236	225	13	bull	bull	NOUN
cana-5236	225	14	.	.	PUNCT
cana-5236	225	15	amer	amer	PROPN
cana-5236	225	16	.	.	PUNCT
cana-5236	225	17	math	math	PROPN
cana-5236	225	18	.	.	PUNCT
cana-5236	226	1	soc	soc	PROPN
cana-5236	226	2	.	.	PUNCT
cana-5236	226	3	,	,	PUNCT
cana-5236	226	4	81(1975	81(1975	NUM
cana-5236	226	5	)	)	PUNCT
cana-5236	226	6	,	,	PUNCT
cana-5236	226	7	79	79	NUM
cana-5236	226	8	-	-	SYM
cana-5236	226	9	82	82	NUM
cana-5236	226	10	.	.	PUNCT
cana-5236	227	1	[	[	X
cana-5236	227	2	8	8	NUM
cana-5236	227	3	]	]	X
cana-5236	227	4	k.i	k.i	PROPN
cana-5236	227	5	.	.	PUNCT
cana-5236	227	6	noor	noor	PROPN
cana-5236	227	7	,	,	PUNCT
cana-5236	227	8	applications	application	NOUN
cana-5236	227	9	of	of	ADP
cana-5236	227	10	certain	certain	ADJ
cana-5236	227	11	operators	operator	NOUN
cana-5236	227	12	to	to	ADP
cana-5236	227	13	the	the	DET
cana-5236	227	14	classes	class	NOUN
cana-5236	227	15	related	relate	VERB
cana-5236	227	16	with	with	ADP
cana-5236	227	17	generalized	generalized	ADJ
cana-5236	227	18	janowski	janowski	ADJ
cana-5236	227	19	functions	function	NOUN
cana-5236	227	20	,	,	PUNCT
cana-5236	227	21	integral	integral	ADJ
cana-5236	227	22	transform	transform	NOUN
cana-5236	227	23	spec	spec	NOUN
cana-5236	227	24	.	.	PUNCT
cana-5236	228	1	funct	funct	PROPN
cana-5236	228	2	.	.	PUNCT
cana-5236	228	3	,21(8)(2010	,21(8)(2010	PUNCT
cana-5236	228	4	)	)	PUNCT
cana-5236	228	5	,	,	PUNCT
cana-5236	228	6	557	557	NUM
cana-5236	228	7	-	-	SYM
cana-5236	228	8	567	567	NUM
cana-5236	228	9	[	[	PUNCT
cana-5236	228	10	9	9	NUM
cana-5236	228	11	]	]	X
cana-5236	228	12	k.i	k.i	PROPN
cana-5236	228	13	.	.	PUNCT
cana-5236	229	1	noor	noor	PROPN
cana-5236	229	2	,	,	PUNCT
cana-5236	229	3	higher	high	ADJ
cana-5236	229	4	order	order	NOUN
cana-5236	229	5	close	close	VERB
cana-5236	229	6	-	-	PUNCT
cana-5236	229	7	to	to	ADP
cana-5236	229	8	-	-	PUNCT
cana-5236	229	9	convex	convex	NOUN
cana-5236	229	10	functions	function	NOUN
cana-5236	229	11	,	,	PUNCT
cana-5236	229	12	math	math	NOUN
cana-5236	229	13	.	.	PUNCT
cana-5236	230	1	japonica	japonica	PROPN
cana-5236	230	2	,	,	PUNCT
cana-5236	230	3	37(1)(1992	37(1)(1992	NUM
cana-5236	230	4	)	)	PUNCT
cana-5236	230	5	,	,	PUNCT
cana-5236	230	6	1	1	NUM
cana-5236	230	7	-	-	SYM
cana-5236	230	8	8	8	NUM
cana-5236	230	9	.	.	PUNCT
cana-5236	231	1	[	[	X
cana-5236	231	2	10	10	NUM
cana-5236	231	3	]	]	X
cana-5236	231	4	k.i	k.i	PROPN
cana-5236	231	5	.	.	PUNCT
cana-5236	232	1	noor	noor	PROPN
cana-5236	232	2	,	,	PUNCT
cana-5236	232	3	m.	m.	PROPN
cana-5236	232	4	arif	arif	PROPN
cana-5236	232	5	,	,	PUNCT
cana-5236	232	6	mapping	mapping	NOUN
cana-5236	232	7	properties	property	NOUN
cana-5236	232	8	of	of	ADP
cana-5236	232	9	an	an	DET
cana-5236	232	10	integral	integral	ADJ
cana-5236	232	11	operator	operator	NOUN
cana-5236	232	12	,	,	PUNCT
cana-5236	232	13	applied	apply	VERB
cana-5236	232	14	math	math	NOUN
cana-5236	232	15	.	.	PUNCT
cana-5236	233	1	lett	lett	PROPN
cana-5236	233	2	.	.	PROPN
cana-5236	233	3	,25(2012	,25(2012	PROPN
cana-5236	233	4	)	)	PUNCT
cana-5236	233	5	,	,	PUNCT
cana-5236	233	6	1826	1826	NUM
cana-5236	233	7	-	-	SYM
cana-5236	233	8	1829	1829	NUM
cana-5236	233	9	.	.	PUNCT
cana-5236	234	1	[	[	X
cana-5236	234	2	11	11	NUM
cana-5236	234	3	]	]	X
cana-5236	234	4	k.i.noor	k.i.noor	NOUN
cana-5236	234	5	,	,	PUNCT
cana-5236	234	6	m.arif	m.arif	X
cana-5236	234	7	,	,	PUNCT
cana-5236	234	8	on	on	ADP
cana-5236	234	9	some	some	DET
cana-5236	234	10	application	application	NOUN
cana-5236	234	11	of	of	ADP
cana-5236	234	12	ruscheweyh	ruscheweyh	NOUN
cana-5236	234	13	derivative	derivative	ADJ
cana-5236	234	14	,	,	PUNCT
cana-5236	234	15	comp	comp	NOUN
cana-5236	234	16	.	.	PUNCT
cana-5236	235	1	math	math	PROPN
cana-5236	235	2	appl	appl	PROPN
cana-5236	235	3	.	.	PUNCT
cana-5236	235	4	,62(2011	,62(2011	PUNCT
cana-5236	235	5	)	)	PUNCT
cana-5236	235	6	,	,	PUNCT
cana-5236	235	7	4726	4726	NUM
cana-5236	235	8	-	-	SYM
cana-5236	235	9	4732	4732	NUM
cana-5236	235	10	.	.	PUNCT
cana-5236	236	1	[	[	X
cana-5236	236	2	12	12	NUM
cana-5236	236	3	]	]	X
cana-5236	236	4	k.i	k.i	PROPN
cana-5236	236	5	.	.	PUNCT
cana-5236	237	1	noor	noor	PROPN
cana-5236	237	2	,	,	PUNCT
cana-5236	237	3	on	on	ADP
cana-5236	237	4	some	some	DET
cana-5236	237	5	integral	integral	ADJ
cana-5236	237	6	operators	operator	NOUN
cana-5236	237	7	for	for	ADP
cana-5236	237	8	certain	certain	ADJ
cana-5236	237	9	families	family	NOUN
cana-5236	237	10	of	of	ADP
cana-5236	237	11	analytic	analytic	ADJ
cana-5236	237	12	function	function	NOUN
cana-5236	237	13	,	,	PUNCT
cana-5236	237	14	tamkang	tamkang	PROPN
cana-5236	237	15	j.	j.	PROPN
cana-5236	237	16	math	math	PROPN
cana-5236	237	17	.	.	PROPN
cana-5236	237	18	,	,	PUNCT
cana-5236	237	19	22(1991	22(1991	NUM
cana-5236	237	20	)	)	PUNCT
cana-5236	237	21	,	,	PUNCT
cana-5236	237	22	113	113	NUM
cana-5236	237	23	-	-	SYM
cana-5236	237	24	117	117	NUM
cana-5236	237	25	.	.	PUNCT
cana-5236	238	1	[	[	X
cana-5236	238	2	13	13	NUM
cana-5236	238	3	]	]	X
cana-5236	238	4	k.i	k.i	PROPN
cana-5236	238	5	.	.	PUNCT
cana-5236	238	6	noor	noor	PROPN
cana-5236	238	7	,	,	PUNCT
cana-5236	238	8	s.n	s.n	PROPN
cana-5236	238	9	.	.	PROPN
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cana-5236	238	11	,	,	PUNCT
cana-5236	238	12	on	on	ADP
cana-5236	238	13	a	a	DET
cana-5236	238	14	subclass	subclass	NOUN
cana-5236	238	15	of	of	ADP
cana-5236	238	16	quasi	quasi	ADJ
cana-5236	238	17	-	-	ADJ
cana-5236	238	18	convex	convex	ADJ
cana-5236	238	19	univalent	univalent	ADJ
cana-5236	238	20	functions	function	NOUN
cana-5236	238	21	,	,	PUNCT
cana-5236	238	22	world	world	NOUN
cana-5236	238	23	appl	appl	NOUN
cana-5236	238	24	.	.	PUNCT
cana-5236	239	1	sci	sci	PROPN
cana-5236	239	2	.	.	PUNCT
cana-5236	239	3	j.	j.	PROPN
cana-5236	239	4	,12(12)(2011	,12(12)(2011	PUNCT
cana-5236	239	5	)	)	PUNCT
cana-5236	239	6	,	,	PUNCT
cana-5236	239	7	2202	2202	NUM
cana-5236	239	8	-	-	SYM
cana-5236	239	9	2209	2209	NUM
cana-5236	239	10	.	.	PUNCT
cana-5236	240	1	[	[	X
cana-5236	240	2	14	14	NUM
cana-5236	240	3	]	]	X
cana-5236	240	4	k.i.noor	k.i.noor	NOUN
cana-5236	240	5	,	,	PUNCT
cana-5236	240	6	w.haq	w.haq	PROPN
cana-5236	240	7	,	,	PUNCT
cana-5236	240	8	m.arif	m.arif	ADJ
cana-5236	240	9	and	and	CCONJ
cana-5236	240	10	s.mustafa	s.mustafa	ADJ
cana-5236	240	11	,	,	PUNCT
cana-5236	240	12	on	on	ADP
cana-5236	240	13	bounded	bound	VERB
cana-5236	240	14	boundary	boundary	NOUN
cana-5236	240	15	and	and	CCONJ
cana-5236	240	16	bounded	bound	VERB
cana-5236	240	17	radius	radius	NOUN
cana-5236	240	18	rotations	rotation	NOUN
cana-5236	240	19	,	,	PUNCT
cana-5236	240	20	j.inequ	j.inequ	NOUN
cana-5236	240	21	.	.	PUNCT
cana-5236	241	1	appl	appl	PROPN
cana-5236	241	2	.	.	PROPN
cana-5236	241	3	,	,	PUNCT
cana-5236	241	4	vol.(2009	vol.(2009	VERB
cana-5236	241	5	)	)	PUNCT
cana-5236	241	6	art	art	NOUN
cana-5236	241	7	.	.	PUNCT
cana-5236	242	1	i	i	PRON
cana-5236	242	2	d	d	PROPN
cana-5236	242	3	813687	813687	NUM
cana-5236	242	4	,	,	PUNCT
cana-5236	242	5	pp	pp	ADP
cana-5236	242	6	12	12	NUM
cana-5236	242	7	.	.	PUNCT
cana-5236	243	1	[	[	X
cana-5236	243	2	15	15	NUM
cana-5236	243	3	]	]	X
cana-5236	243	4	r.	r.	PROPN
cana-5236	243	5	parvatham	parvatham	PROPN
cana-5236	243	6	,	,	PUNCT
cana-5236	243	7	t.n.shanmugan	t.n.shanmugan	NOUN
cana-5236	243	8	,	,	PUNCT
cana-5236	243	9	on	on	ADP
cana-5236	243	10	analytic	analytic	ADJ
cana-5236	243	11	functions	function	NOUN
cana-5236	243	12	with	with	ADP
cana-5236	243	13	reference	reference	NOUN
cana-5236	243	14	to	to	ADP
cana-5236	243	15	an	an	DET
cana-5236	243	16	integral	integral	ADJ
cana-5236	243	17	operator	operator	NOUN
cana-5236	243	18	,	,	PUNCT
cana-5236	243	19	bull	bull	NOUN
cana-5236	243	20	.	.	PUNCT
cana-5236	244	1	austral	austral	PROPN
cana-5236	244	2	.	.	PUNCT
cana-5236	245	1	math	math	NOUN
cana-5236	245	2	.	.	PUNCT
cana-5236	246	1	soc	soc	PROPN
cana-5236	246	2	.	.	PUNCT
cana-5236	246	3	,	,	PUNCT
cana-5236	246	4	28(1983	28(1983	PROPN
cana-5236	246	5	)	)	PUNCT
cana-5236	246	6	,	,	PUNCT
cana-5236	246	7	207	207	NUM
cana-5236	246	8	-	-	SYM
cana-5236	246	9	215	215	NUM
cana-5236	246	10	.	.	PUNCT
cana-5236	247	1	[	[	X
cana-5236	247	2	16	16	NUM
cana-5236	247	3	]	]	X
cana-5236	247	4	b.	b.	PROPN
cana-5236	247	5	pinchuk	pinchuk	PROPN
cana-5236	247	6	,	,	PUNCT
cana-5236	247	7	function	function	VERB
cana-5236	247	8	with	with	ADP
cana-5236	247	9	bounded	bounded	ADJ
cana-5236	247	10	boundary	boundary	ADJ
cana-5236	247	11	rotation	rotation	NOUN
cana-5236	247	12	,	,	PUNCT
cana-5236	247	13	israel	israel	PROPN
cana-5236	247	14	j.	j.	PROPN
cana-5236	247	15	math	math	PROPN
cana-5236	247	16	.	.	PUNCT
cana-5236	248	1	10(1971	10(1971	NUM
cana-5236	248	2	)	)	PUNCT
cana-5236	248	3	,	,	PUNCT
cana-5236	248	4	7	7	NUM
cana-5236	248	5	-	-	SYM
cana-5236	248	6	16	16	NUM
cana-5236	248	7	.	.	PUNCT
cana-5236	249	1	[	[	X
cana-5236	249	2	17	17	NUM
cana-5236	249	3	]	]	X
cana-5236	249	4	y.	y.	PROPN
cana-5236	249	5	polatoglu	polatoglu	PROPN
cana-5236	249	6	,	,	PUNCT
cana-5236	249	7	m.	m.	NOUN
cana-5236	249	8	bolcal	bolcal	PROPN
cana-5236	249	9	,	,	PUNCT
cana-5236	249	10	a.	a.	PROPN
cana-5236	249	11	sen	sen	PROPN
cana-5236	249	12	and	and	CCONJ
cana-5236	249	13	e.	e.	PROPN
cana-5236	249	14	yavuz	yavuz	PROPN
cana-5236	249	15	,	,	PUNCT
cana-5236	249	16	a	a	DET
cana-5236	249	17	study	study	NOUN
cana-5236	249	18	on	on	ADP
cana-5236	249	19	the	the	DET
cana-5236	249	20	generalization	generalization	NOUN
cana-5236	249	21	of	of	ADP
cana-5236	249	22	janowski	janowski	ADJ
cana-5236	249	23	function	function	NOUN
cana-5236	249	24	in	in	ADP
cana-5236	249	25	the	the	DET
cana-5236	249	26	unit	unit	NOUN
cana-5236	249	27	disc	disc	NOUN
cana-5236	249	28	,	,	PUNCT
cana-5236	249	29	acta	acta	PROPN
cana-5236	249	30	mathematica	mathematica	PROPN
cana-5236	249	31	academiae	academiae	PROPN
cana-5236	249	32	paedagogicae	paedagogicae	ADJ
cana-5236	249	33	nyiregyhaziensis	nyiregyhaziensis	NOUN
cana-5236	249	34	,	,	PUNCT
cana-5236	249	35	22(2006	22(2006	NUM
cana-5236	249	36	)	)	PUNCT
cana-5236	249	37	,	,	PUNCT
cana-5236	249	38	27	27	NUM
cana-5236	249	39	-	-	SYM
cana-5236	249	40	31	31	NUM
cana-5236	249	41	.	.	PUNCT
cana-5236	250	1	[	[	X
cana-5236	250	2	18	18	NUM
cana-5236	250	3	]	]	X
cana-5236	250	4	s.	s.	PROPN
cana-5236	250	5	ruscheweyh	ruscheweyh	PROPN
cana-5236	250	6	,	,	PUNCT
cana-5236	250	7	a	a	DET
cana-5236	250	8	new	new	ADJ
cana-5236	250	9	criteria	criterion	NOUN
cana-5236	250	10	for	for	ADP
cana-5236	250	11	univalent	univalent	ADJ
cana-5236	250	12	function	function	NOUN
cana-5236	250	13	,	,	PUNCT
cana-5236	250	14	proc	proc	PROPN
cana-5236	250	15	.	.	PUNCT
cana-5236	251	1	amer	amer	PROPN
cana-5236	251	2	.	.	PUNCT
cana-5236	251	3	math	math	PROPN
cana-5236	251	4	.	.	PUNCT
cana-5236	252	1	soc	soc	PROPN
cana-5236	252	2	.	.	PUNCT
cana-5236	252	3	,	,	PUNCT
cana-5236	252	4	49(1)(1975	49(1)(1975	NUM
cana-5236	252	5	)	)	PUNCT
cana-5236	252	6	,	,	PUNCT
cana-5236	252	7	109	109	NUM
cana-5236	252	8	-	-	SYM
cana-5236	252	9	115	115	NUM
cana-5236	252	10	.	.	PUNCT
cana-5236	253	1	[	[	X
cana-5236	253	2	19	19	NUM
cana-5236	253	3	]	]	X
cana-5236	253	4	w.	w.	PROPN
cana-5236	253	5	janowski	janowski	PROPN
cana-5236	253	6	,	,	PUNCT
cana-5236	253	7	some	some	DET
cana-5236	253	8	extremal	extremal	ADJ
cana-5236	253	9	problems	problem	NOUN
cana-5236	253	10	for	for	ADP
cana-5236	253	11	certain	certain	ADJ
cana-5236	253	12	families	family	NOUN
cana-5236	253	13	of	of	ADP
cana-5236	253	14	analytic	analytic	ADJ
cana-5236	253	15	functions	function	NOUN
cana-5236	253	16	,	,	PUNCT
cana-5236	253	17	ann	ann	PROPN
cana-5236	253	18	.	.	PROPN
cana-5236	253	19	polon	polon	PROPN
cana-5236	253	20	.	.	PUNCT
cana-5236	253	21	math	math	NOUN
cana-5236	253	22	.	.	PUNCT
cana-5236	253	23	,	,	PUNCT
cana-5236	253	24	28(1973	28(1973	NUM
cana-5236	253	25	)	)	PUNCT
cana-5236	253	26	,	,	PUNCT
cana-5236	253	27	297	297	NUM
cana-5236	253	28	-	-	SYM
cana-5236	253	29	326	326	NUM
cana-5236	253	30	.	.	PUNCT