id	sid	tid	token	lemma	pos
ejpam-1188	1	1	european	european	PROPN
ejpam-1188	1	2	journal	journal	PROPN
ejpam-1188	1	3	of	of	ADP
ejpam-1188	1	4	pure	pure	ADJ
ejpam-1188	1	5	and	and	CCONJ
ejpam-1188	1	6	applied	apply	VERB
ejpam-1188	1	7	mathematics	mathematic	NOUN
ejpam-1188	1	8	vol	vol	NOUN
ejpam-1188	1	9	.	.	PROPN
ejpam-1188	2	1	6	6	NUM
ejpam-1188	2	2	,	,	PUNCT
ejpam-1188	2	3	no	no	INTJ
ejpam-1188	2	4	.	.	NOUN
ejpam-1188	2	5	4	4	NUM
ejpam-1188	2	6	,	,	PUNCT
ejpam-1188	2	7	2013	2013	NUM
ejpam-1188	2	8	,	,	PUNCT
ejpam-1188	2	9	460	460	NUM
ejpam-1188	2	10	-	-	SYM
ejpam-1188	2	11	468	468	NUM
ejpam-1188	2	12	issn	issn	PROPN
ejpam-1188	2	13	1307	1307	NUM
ejpam-1188	2	14	-	-	SYM
ejpam-1188	2	15	5543	5543	NUM
ejpam-1188	2	16	–	–	PUNCT
ejpam-1188	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1188	2	18	coefficient	coefficient	NOUN
ejpam-1188	2	19	estimates	estimate	NOUN
ejpam-1188	2	20	for	for	ADP
ejpam-1188	2	21	certain	certain	ADJ
ejpam-1188	2	22	subclasses	subclass	NOUN
ejpam-1188	2	23	of	of	ADP
ejpam-1188	2	24	analytic	analytic	ADJ
ejpam-1188	2	25	functions	function	NOUN
ejpam-1188	2	26	of	of	ADP
ejpam-1188	2	27	complex	complex	ADJ
ejpam-1188	2	28	order	order	NOUN
ejpam-1188	2	29	li	li	PROPN
ejpam-1188	2	30	zhou	zhou	PROPN
ejpam-1188	2	31	,	,	PUNCT
ejpam-1188	2	32	qing	qing	PROPN
ejpam-1188	2	33	-	-	PUNCT
ejpam-1188	2	34	hua	hua	PROPN
ejpam-1188	2	35	xu∗	xu∗	PROPN
ejpam-1188	2	36	college	college	PROPN
ejpam-1188	2	37	of	of	ADP
ejpam-1188	2	38	mathematics	mathematics	PROPN
ejpam-1188	2	39	and	and	CCONJ
ejpam-1188	2	40	information	information	NOUN
ejpam-1188	2	41	science	science	NOUN
ejpam-1188	2	42	,	,	PUNCT
ejpam-1188	2	43	jiangxi	jiangxi	PROPN
ejpam-1188	2	44	normal	normal	PROPN
ejpam-1188	2	45	university	university	PROPN
ejpam-1188	2	46	,	,	PUNCT
ejpam-1188	2	47	nanchang	nanchang	PROPN
ejpam-1188	2	48	330022	330022	PROPN
ejpam-1188	2	49	,	,	PUNCT
ejpam-1188	2	50	china	china	PROPN
ejpam-1188	2	51	abstract	abstract	NOUN
ejpam-1188	2	52	.	.	PUNCT
ejpam-1188	3	1	in	in	ADP
ejpam-1188	3	2	this	this	DET
ejpam-1188	3	3	paper	paper	NOUN
ejpam-1188	3	4	,	,	PUNCT
ejpam-1188	3	5	we	we	PRON
ejpam-1188	3	6	introduce	introduce	VERB
ejpam-1188	3	7	and	and	CCONJ
ejpam-1188	3	8	investigate	investigate	VERB
ejpam-1188	3	9	two	two	NUM
ejpam-1188	3	10	interesting	interesting	ADJ
ejpam-1188	3	11	subclasses	subclass	NOUN
ejpam-1188	3	12	hg(n	hg(n	ADP
ejpam-1188	3	13	,	,	PUNCT
ejpam-1188	3	14	b	b	PROPN
ejpam-1188	3	15	,	,	PUNCT
ejpam-1188	3	16	λ	λ	PROPN
ejpam-1188	3	17	,	,	PUNCT
ejpam-1188	3	18	α	α	NOUN
ejpam-1188	3	19	,	,	PUNCT
ejpam-1188	3	20	δ	δ	PROPN
ejpam-1188	3	21	)	)	PUNCT
ejpam-1188	3	22	and	and	CCONJ
ejpam-1188	3	23	hg(n	hg(n	PROPN
ejpam-1188	3	24	,	,	PUNCT
ejpam-1188	3	25	b	b	PROPN
ejpam-1188	3	26	,	,	PUNCT
ejpam-1188	3	27	λ	λ	PROPN
ejpam-1188	3	28	,	,	PUNCT
ejpam-1188	3	29	α	α	NOUN
ejpam-1188	3	30	,	,	PUNCT
ejpam-1188	3	31	δ	δ	PROPN
ejpam-1188	3	32	;	;	PUNCT
ejpam-1188	3	33	u	u	NOUN
ejpam-1188	3	34	)	)	PUNCT
ejpam-1188	3	35	of	of	ADP
ejpam-1188	3	36	analytic	analytic	ADJ
ejpam-1188	3	37	functions	function	NOUN
ejpam-1188	3	38	of	of	ADP
ejpam-1188	3	39	complex	complex	ADJ
ejpam-1188	3	40	order	order	NOUN
ejpam-1188	3	41	in	in	ADP
ejpam-1188	3	42	the	the	DET
ejpam-1188	3	43	open	open	ADJ
ejpam-1188	3	44	unit	unit	NOUN
ejpam-1188	3	45	disk	disk	NOUN
ejpam-1188	3	46	u	u	NOUN
ejpam-1188	3	47	,	,	PUNCT
ejpam-1188	3	48	which	which	PRON
ejpam-1188	3	49	are	be	AUX
ejpam-1188	3	50	defined	define	VERB
ejpam-1188	3	51	by	by	ADP
ejpam-1188	3	52	means	mean	NOUN
ejpam-1188	3	53	of	of	ADP
ejpam-1188	3	54	the	the	DET
ejpam-1188	3	55	familiar	familiar	ADJ
ejpam-1188	3	56	multiplier	multipli	ADJ
ejpam-1188	3	57	operator	operator	NOUN
ejpam-1188	3	58	.	.	PUNCT
ejpam-1188	4	1	formfunctions	formfunction	NOUN
ejpam-1188	4	2	belonging	belong	VERB
ejpam-1188	4	3	to	to	ADP
ejpam-1188	4	4	the	the	DET
ejpam-1188	4	5	each	each	PRON
ejpam-1188	4	6	of	of	ADP
ejpam-1188	4	7	these	these	DET
ejpam-1188	4	8	subclasses	subclass	NOUN
ejpam-1188	4	9	,	,	PUNCT
ejpam-1188	4	10	we	we	PRON
ejpam-1188	4	11	obtain	obtain	VERB
ejpam-1188	4	12	several	several	ADJ
ejpam-1188	4	13	results	result	NOUN
ejpam-1188	4	14	involving	involve	VERB
ejpam-1188	4	15	(	(	PUNCT
ejpam-1188	4	16	for	for	ADP
ejpam-1188	4	17	example	example	NOUN
ejpam-1188	4	18	)	)	PUNCT
ejpam-1188	4	19	coefficient	coefficient	NOUN
ejpam-1188	4	20	bounds	bound	NOUN
ejpam-1188	4	21	.	.	PUNCT
ejpam-1188	5	1	then	then	ADV
ejpam-1188	5	2	results	result	NOUN
ejpam-1188	5	3	presented	present	VERB
ejpam-1188	5	4	here	here	ADV
ejpam-1188	5	5	would	would	AUX
ejpam-1188	5	6	generalize	generalize	VERB
ejpam-1188	5	7	many	many	ADJ
ejpam-1188	5	8	known	know	VERB
ejpam-1188	5	9	results	result	NOUN
ejpam-1188	5	10	.	.	PUNCT
ejpam-1188	6	1	2010	2010	NUM
ejpam-1188	6	2	mathematics	mathematic	NOUN
ejpam-1188	6	3	subject	subject	NOUN
ejpam-1188	6	4	classifications	classification	NOUN
ejpam-1188	6	5	:	:	PUNCT
ejpam-1188	6	6	30c45	30c45	NUM
ejpam-1188	6	7	key	key	ADJ
ejpam-1188	6	8	words	word	NOUN
ejpam-1188	6	9	and	and	CCONJ
ejpam-1188	6	10	phrases	phrase	NOUN
ejpam-1188	6	11	:	:	PUNCT
ejpam-1188	6	12	aanalytic	aanalytic	ADJ
ejpam-1188	6	13	functions	function	NOUN
ejpam-1188	6	14	of	of	ADP
ejpam-1188	6	15	complex	complex	ADJ
ejpam-1188	6	16	order	order	NOUN
ejpam-1188	6	17	,	,	PUNCT
ejpam-1188	6	18	coefficient	coefficient	NOUN
ejpam-1188	6	19	bounds	bound	NOUN
ejpam-1188	6	20	,	,	PUNCT
ejpam-1188	6	21	multiplier	multipli	ADJ
ejpam-1188	6	22	operator	operator	NOUN
ejpam-1188	6	23	,	,	PUNCT
ejpam-1188	6	24	sălăgean	sălăgean	ADJ
ejpam-1188	6	25	derivative	derivative	ADJ
ejpam-1188	6	26	operator	operator	NOUN
ejpam-1188	6	27	,	,	PUNCT
ejpam-1188	6	28	cauchy	cauchy	NOUN
ejpam-1188	6	29	-	-	PUNCT
ejpam-1188	6	30	euler	euler	NOUN
ejpam-1188	6	31	differential	differential	ADJ
ejpam-1188	6	32	equation	equation	NOUN
ejpam-1188	6	33	,	,	PUNCT
ejpam-1188	6	34	principle	principle	NOUN
ejpam-1188	6	35	of	of	ADP
ejpam-1188	6	36	subordination	subordination	NOUN
ejpam-1188	6	37	1	1	NUM
ejpam-1188	6	38	.	.	X
ejpam-1188	6	39	introduce	introduce	VERB
ejpam-1188	6	40	let	let	VERB
ejpam-1188	6	41	r=	r=	ADJ
ejpam-1188	6	42	(	(	PUNCT
ejpam-1188	6	43	−∞,+∞	−∞,+∞	ADV
ejpam-1188	6	44	)	)	PUNCT
ejpam-1188	6	45	be	be	VERB
ejpam-1188	6	46	the	the	DET
ejpam-1188	6	47	set	set	NOUN
ejpam-1188	6	48	of	of	ADP
ejpam-1188	6	49	real	real	ADJ
ejpam-1188	6	50	numbers	number	NOUN
ejpam-1188	6	51	,	,	PUNCT
ejpam-1188	6	52	c	c	X
ejpam-1188	6	53	be	be	VERB
ejpam-1188	6	54	the	the	DET
ejpam-1188	6	55	set	set	NOUN
ejpam-1188	6	56	of	of	ADP
ejpam-1188	6	57	complex	complex	ADJ
ejpam-1188	6	58	numbers	number	NOUN
ejpam-1188	6	59	,	,	PUNCT
ejpam-1188	6	60	n=	n=	ADJ
ejpam-1188	6	61	{	{	PUNCT
ejpam-1188	6	62	1,2	1,2	NUM
ejpam-1188	6	63	,	,	PUNCT
ejpam-1188	6	64	3	3	NUM
ejpam-1188	6	65	,	,	PUNCT
ejpam-1188	6	66	.	.	PUNCT
ejpam-1188	6	67	.	.	PUNCT
ejpam-1188	7	1	.	.	PUNCT
ejpam-1188	7	2	}	}	PUNCT
ejpam-1188	7	3	be	be	AUX
ejpam-1188	7	4	the	the	DET
ejpam-1188	7	5	set	set	NOUN
ejpam-1188	7	6	of	of	ADP
ejpam-1188	7	7	positive	positive	ADJ
ejpam-1188	7	8	integers	integer	NOUN
ejpam-1188	7	9	,	,	PUNCT
ejpam-1188	7	10	n2	n2	NOUN
ejpam-1188	7	11	=	=	PUNCT
ejpam-1188	7	12	{	{	PUNCT
ejpam-1188	7	13	2	2	NUM
ejpam-1188	7	14	,	,	PUNCT
ejpam-1188	7	15	3,4	3,4	NUM
ejpam-1188	7	16	,	,	PUNCT
ejpam-1188	7	17	.	.	PUNCT
ejpam-1188	7	18	.	.	PUNCT
ejpam-1188	8	1	.	.	PUNCT
ejpam-1188	8	2	}	}	PUNCT
ejpam-1188	9	1	and	and	CCONJ
ejpam-1188	9	2	n0	n0	NOUN
ejpam-1188	9	3	=	=	SYM
ejpam-1188	9	4	n∪	n∪	PROPN
ejpam-1188	9	5	{	{	PUNCT
ejpam-1188	9	6	0	0	NUM
ejpam-1188	9	7	}	}	PUNCT
ejpam-1188	9	8	.	.	PUNCT
ejpam-1188	10	1	we	we	PRON
ejpam-1188	10	2	also	also	ADV
ejpam-1188	10	3	leta	leta	PROPN
ejpam-1188	10	4	denote	denote	VERB
ejpam-1188	10	5	the	the	DET
ejpam-1188	10	6	class	class	NOUN
ejpam-1188	10	7	of	of	ADP
ejpam-1188	10	8	functions	function	NOUN
ejpam-1188	10	9	f	f	PROPN
ejpam-1188	10	10	of	of	ADP
ejpam-1188	10	11	the	the	DET
ejpam-1188	10	12	form	form	NOUN
ejpam-1188	11	1	f	f	X
ejpam-1188	11	2	(	(	PUNCT
ejpam-1188	11	3	z	z	NOUN
ejpam-1188	11	4	)	)	PUNCT
ejpam-1188	11	5	=	=	SYM
ejpam-1188	11	6	z+	z+	NUM
ejpam-1188	11	7	∞	∞	PROPN
ejpam-1188	11	8	∑	∑	PROPN
ejpam-1188	11	9	j=2	j=2	PROPN
ejpam-1188	11	10	a	a	DET
ejpam-1188	11	11	jz	jz	PROPN
ejpam-1188	11	12	j	j	PROPN
ejpam-1188	11	13	,	,	PUNCT
ejpam-1188	11	14	(	(	PUNCT
ejpam-1188	11	15	1	1	X
ejpam-1188	11	16	)	)	PUNCT
ejpam-1188	11	17	∗corresponding	∗corresponde	VERB
ejpam-1188	11	18	author	author	NOUN
ejpam-1188	11	19	.	.	PUNCT
ejpam-1188	12	1	email	email	NOUN
ejpam-1188	12	2	addresses	address	NOUN
ejpam-1188	12	3	:	:	PUNCT
ejpam-1188	12	4	zlghhf@yahoo.com.cn	zlghhf@yahoo.com.cn	X
ejpam-1188	12	5	(	(	PUNCT
ejpam-1188	12	6	l.	l.	PROPN
ejpam-1188	12	7	zhou	zhou	PROPN
ejpam-1188	12	8	)	)	PUNCT
ejpam-1188	12	9	,	,	PUNCT
ejpam-1188	12	10	xuqh@mail.ustc.edu.cn	xuqh@mail.ustc.edu.cn	PROPN
ejpam-1188	12	11	(	(	PUNCT
ejpam-1188	12	12	q	q	ADJ
ejpam-1188	12	13	-	-	NOUN
ejpam-1188	12	14	h	h	NOUN
ejpam-1188	12	15	xu	xu	PROPN
ejpam-1188	12	16	)	)	PUNCT
ejpam-1188	12	17	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1188	13	1	460	460	NUM
ejpam-1188	14	1	c	c	X
ejpam-1188	14	2	©	©	PROPN
ejpam-1188	14	3	2013	2013	NUM
ejpam-1188	14	4	ejpam	ejpam	NOUN
ejpam-1188	14	5	all	all	DET
ejpam-1188	14	6	rights	right	NOUN
ejpam-1188	14	7	reserved	reserve	VERB
ejpam-1188	14	8	.	.	PUNCT
ejpam-1188	15	1	l.	l.	PROPN
ejpam-1188	15	2	zhou	zhou	PROPN
ejpam-1188	15	3	,	,	PUNCT
ejpam-1188	15	4	q	q	PROPN
ejpam-1188	15	5	-	-	NOUN
ejpam-1188	15	6	h	h	NOUN
ejpam-1188	15	7	xu	xu	PROPN
ejpam-1188	15	8	/	/	SYM
ejpam-1188	15	9	eur	eur	PROPN
ejpam-1188	15	10	.	.	PUNCT
ejpam-1188	16	1	j.	j.	PROPN
ejpam-1188	16	2	pure	pure	PROPN
ejpam-1188	16	3	appl	appl	PROPN
ejpam-1188	16	4	.	.	PROPN
ejpam-1188	16	5	math	math	PROPN
ejpam-1188	16	6	,	,	PUNCT
ejpam-1188	16	7	6	6	NUM
ejpam-1188	16	8	(	(	PUNCT
ejpam-1188	16	9	2013	2013	NUM
ejpam-1188	16	10	)	)	PUNCT
ejpam-1188	16	11	,	,	PUNCT
ejpam-1188	16	12	460	460	NUM
ejpam-1188	16	13	-	-	SYM
ejpam-1188	16	14	468	468	NUM
ejpam-1188	16	15	461	461	NUM
ejpam-1188	16	16	which	which	PRON
ejpam-1188	16	17	are	be	AUX
ejpam-1188	16	18	analytic	analytic	ADJ
ejpam-1188	16	19	in	in	ADP
ejpam-1188	16	20	the	the	DET
ejpam-1188	16	21	open	open	ADJ
ejpam-1188	16	22	unit	unit	NOUN
ejpam-1188	16	23	disc	disc	VERB
ejpam-1188	16	24	u=	u=	NOUN
ejpam-1188	16	25	{	{	PUNCT
ejpam-1188	16	26	z	z	NOUN
ejpam-1188	16	27	:	:	PUNCT
ejpam-1188	16	28	z	z	PROPN
ejpam-1188	16	29	∈	∈	PROPN
ejpam-1188	16	30	c	c	NOUN
ejpam-1188	16	31	and	and	CCONJ
ejpam-1188	16	32	|z|	|z|	VERB
ejpam-1188	16	33	<	<	X
ejpam-1188	16	34	1	1	NUM
ejpam-1188	16	35	}	}	PUNCT
ejpam-1188	16	36	.	.	PUNCT
ejpam-1188	17	1	a	a	DET
ejpam-1188	17	2	function	function	NOUN
ejpam-1188	17	3	f	f	X
ejpam-1188	17	4	(	(	PUNCT
ejpam-1188	17	5	z	z	NOUN
ejpam-1188	17	6	)	)	PUNCT
ejpam-1188	17	7	∈a	∈a	NUM
ejpam-1188	17	8	is	be	AUX
ejpam-1188	17	9	said	say	VERB
ejpam-1188	17	10	to	to	PART
ejpam-1188	17	11	belong	belong	VERB
ejpam-1188	17	12	to	to	ADP
ejpam-1188	17	13	the	the	DET
ejpam-1188	17	14	class	class	NOUN
ejpam-1188	17	15	s∗(α	s∗(α	PROPN
ejpam-1188	17	16	)	)	PUNCT
ejpam-1188	17	17	of	of	ADP
ejpam-1188	17	18	starlike	starlike	NOUN
ejpam-1188	17	19	functions	function	NOUN
ejpam-1188	17	20	of	of	ADP
ejpam-1188	17	21	order	order	NOUN
ejpam-1188	17	22	α	α	NOUN
ejpam-1188	17	23	in	in	ADP
ejpam-1188	17	24	u	u	PRON
ejpam-1188	17	25	if	if	SCONJ
ejpam-1188	17	26	it	it	PRON
ejpam-1188	17	27	satisfies	satisfy	VERB
ejpam-1188	17	28	the	the	DET
ejpam-1188	17	29	following	follow	VERB
ejpam-1188	17	30	inequality	inequality	NOUN
ejpam-1188	17	31	:	:	PUNCT
ejpam-1188	17	32	ℜ	ℜ	PROPN
ejpam-1188	17	33	�	�	PROPN
ejpam-1188	17	34	z	z	PROPN
ejpam-1188	17	35	f	f	PROPN
ejpam-1188	17	36	′(z	′(z	NOUN
ejpam-1188	18	1	)	)	PUNCT
ejpam-1188	18	2	f	f	PROPN
ejpam-1188	18	3	(	(	PUNCT
ejpam-1188	18	4	z	z	NOUN
ejpam-1188	18	5	)	)	PUNCT
ejpam-1188	18	6	�	�	PROPN
ejpam-1188	18	7	>	>	X
ejpam-1188	18	8	α	α	PROPN
ejpam-1188	18	9	(	(	PUNCT
ejpam-1188	18	10	z	z	NOUN
ejpam-1188	18	11	∈	∈	PROPN
ejpam-1188	18	12	u	u	NOUN
ejpam-1188	18	13	;	;	PUNCT
ejpam-1188	18	14	0≤	0≤	NUM
ejpam-1188	18	15	α	α	NOUN
ejpam-1188	18	16	<	<	X
ejpam-1188	18	17	1	1	NUM
ejpam-1188	18	18	)	)	PUNCT
ejpam-1188	18	19	.	.	PUNCT
ejpam-1188	19	1	for	for	ADP
ejpam-1188	19	2	functions	function	NOUN
ejpam-1188	19	3	f	f	X
ejpam-1188	19	4	(	(	PUNCT
ejpam-1188	19	5	z	z	NOUN
ejpam-1188	19	6	)	)	PUNCT
ejpam-1188	19	7	in	in	ADP
ejpam-1188	19	8	the	the	DET
ejpam-1188	19	9	class	class	NOUN
ejpam-1188	19	10	s∗(α	s∗(α	NOUN
ejpam-1188	19	11	)	)	PUNCT
ejpam-1188	19	12	given	give	VERB
ejpam-1188	19	13	by	by	ADP
ejpam-1188	19	14	(	(	PUNCT
ejpam-1188	19	15	1	1	NUM
ejpam-1188	19	16	)	)	PUNCT
ejpam-1188	19	17	,	,	PUNCT
ejpam-1188	19	18	robertson	robertson	PROPN
ejpam-1188	19	19	[	[	X
ejpam-1188	19	20	11	11	NUM
ejpam-1188	19	21	]	]	PUNCT
ejpam-1188	19	22	proved	prove	VERB
ejpam-1188	19	23	some	some	DET
ejpam-1188	19	24	coefficient	coefficient	NOUN
ejpam-1188	19	25	bounds	bound	NOUN
ejpam-1188	19	26	which	which	PRON
ejpam-1188	19	27	we	we	PRON
ejpam-1188	19	28	recall	recall	VERB
ejpam-1188	19	29	here	here	ADV
ejpam-1188	19	30	as	as	ADP
ejpam-1188	19	31	lemma	lemma	PROPN
ejpam-1188	19	32	1	1	NUM
ejpam-1188	19	33	below	below	ADV
ejpam-1188	19	34	.	.	PUNCT
ejpam-1188	20	1	lemma	lemma	PROPN
ejpam-1188	20	2	1	1	NUM
ejpam-1188	20	3	.	.	PUNCT
ejpam-1188	21	1	if	if	SCONJ
ejpam-1188	21	2	f	f	PROPN
ejpam-1188	21	3	(	(	PUNCT
ejpam-1188	21	4	z	z	NOUN
ejpam-1188	21	5	)	)	PUNCT
ejpam-1188	21	6	=	=	SYM
ejpam-1188	21	7	z+	z+	NUM
ejpam-1188	21	8	∞	∞	PROPN
ejpam-1188	21	9	∑	∑	PROPN
ejpam-1188	21	10	j=2	j=2	PROPN
ejpam-1188	21	11	a	a	DET
ejpam-1188	21	12	jz	jz	PROPN
ejpam-1188	21	13	j	j	PROPN
ejpam-1188	21	14	∈	∈	PROPN
ejpam-1188	21	15	s∗(α	s∗(α	PROPN
ejpam-1188	21	16	)	)	PUNCT
ejpam-1188	21	17	,	,	PUNCT
ejpam-1188	21	18	then	then	ADV
ejpam-1188	21	19	|a	|a	VERB
ejpam-1188	21	20	j|	j|	PROPN
ejpam-1188	21	21	≤	≤	PROPN
ejpam-1188	21	22	j−2	j−2	PROPN
ejpam-1188	21	23	∏	∏	PROPN
ejpam-1188	21	24	k=0	k=0	PUNCT
ejpam-1188	22	1	[	[	X
ejpam-1188	22	2	k+	k+	NOUN
ejpam-1188	22	3	2(1−α	2(1−α	NUM
ejpam-1188	22	4	)	)	PUNCT
ejpam-1188	22	5	]	]	PUNCT
ejpam-1188	23	1	j	j	X
ejpam-1188	23	2	!	!	PUNCT
ejpam-1188	24	1	(	(	PUNCT
ejpam-1188	24	2	j	j	PROPN
ejpam-1188	24	3	∈	∈	PROPN
ejpam-1188	24	4	n2	n2	PROPN
ejpam-1188	24	5	)	)	PUNCT
ejpam-1188	24	6	.	.	PUNCT
ejpam-1188	25	1	(	(	PUNCT
ejpam-1188	25	2	2	2	X
ejpam-1188	25	3	)	)	PUNCT
ejpam-1188	25	4	nasr	nasr	PROPN
ejpam-1188	25	5	and	and	CCONJ
ejpam-1188	25	6	aouf	aouf	PROPN
ejpam-1188	26	1	[	[	X
ejpam-1188	26	2	10	10	NUM
ejpam-1188	26	3	]	]	PUNCT
ejpam-1188	26	4	and	and	CCONJ
ejpam-1188	26	5	altintaş	altintaş	PROPN
ejpam-1188	26	6	et	et	PROPN
ejpam-1188	26	7	.	.	PUNCT
ejpam-1188	27	1	al	al	PROPN
ejpam-1188	28	1	[	[	X
ejpam-1188	28	2	1–8	1–8	X
ejpam-1188	28	3	]	]	X
ejpam-1188	28	4	have	have	AUX
ejpam-1188	28	5	extended	extend	VERB
ejpam-1188	28	6	the	the	DET
ejpam-1188	28	7	coefficient	coefficient	NOUN
ejpam-1188	28	8	bounds	bound	NOUN
ejpam-1188	28	9	(	(	PUNCT
ejpam-1188	28	10	2	2	NUM
ejpam-1188	28	11	)	)	PUNCT
ejpam-1188	28	12	for	for	ADP
ejpam-1188	28	13	the	the	DET
ejpam-1188	28	14	class	class	NOUN
ejpam-1188	28	15	of	of	ADP
ejpam-1188	28	16	s∗(α	s∗(α	NOUN
ejpam-1188	28	17	)	)	PUNCT
ejpam-1188	28	18	to	to	PART
ejpam-1188	28	19	hold	hold	VERB
ejpam-1188	28	20	true	true	ADJ
ejpam-1188	28	21	for	for	ADP
ejpam-1188	28	22	various	various	ADJ
ejpam-1188	28	23	interesting	interesting	ADJ
ejpam-1188	28	24	subclasses	subclass	NOUN
ejpam-1188	28	25	of	of	ADP
ejpam-1188	28	26	analytic	analytic	ADJ
ejpam-1188	28	27	functions	function	NOUN
ejpam-1188	28	28	of	of	ADP
ejpam-1188	28	29	complex	complex	ADJ
ejpam-1188	28	30	order	order	NOUN
ejpam-1188	28	31	.	.	PUNCT
ejpam-1188	29	1	for	for	ADP
ejpam-1188	29	2	a	a	DET
ejpam-1188	29	3	function	function	NOUN
ejpam-1188	29	4	f	f	X
ejpam-1188	29	5	(	(	PUNCT
ejpam-1188	29	6	z	z	NOUN
ejpam-1188	29	7	)	)	PUNCT
ejpam-1188	29	8	in	in	ADP
ejpam-1188	29	9	a	a	PRON
ejpam-1188	29	10	,	,	PUNCT
ejpam-1188	29	11	the	the	DET
ejpam-1188	29	12	multiplier	multipli	ADJ
ejpam-1188	29	13	operator	operator	NOUN
ejpam-1188	29	14	dn	dn	PROPN
ejpam-1188	29	15	α	α	PROPN
ejpam-1188	29	16	,	,	PUNCT
ejpam-1188	29	17	δ	δ	PROPN
ejpam-1188	29	18	f	f	X
ejpam-1188	29	19	(	(	PUNCT
ejpam-1188	29	20	z	z	NOUN
ejpam-1188	29	21	)	)	PUNCT
ejpam-1188	29	22	was	be	AUX
ejpam-1188	29	23	extended	extend	VERB
ejpam-1188	29	24	by	by	ADP
ejpam-1188	29	25	deniz	deniz	PROPN
ejpam-1188	29	26	and	and	CCONJ
ejpam-1188	29	27	orhan	orhan	PROPN
ejpam-1188	29	28	in	in	ADP
ejpam-1188	29	29	[	[	X
ejpam-1188	29	30	17	17	NUM
ejpam-1188	29	31	]	]	PUNCT
ejpam-1188	29	32	as	as	SCONJ
ejpam-1188	29	33	follows	follow	VERB
ejpam-1188	29	34	:	:	PUNCT
ejpam-1188	29	35	d0	d0	PROPN
ejpam-1188	29	36	α	α	NOUN
ejpam-1188	29	37	,	,	PUNCT
ejpam-1188	29	38	δ	δ	PROPN
ejpam-1188	29	39	f	f	X
ejpam-1188	29	40	(	(	PUNCT
ejpam-1188	29	41	z	z	NOUN
ejpam-1188	29	42	)	)	PUNCT
ejpam-1188	30	1	=	=	SYM
ejpam-1188	30	2	f	f	X
ejpam-1188	30	3	(	(	PUNCT
ejpam-1188	30	4	z	z	NOUN
ejpam-1188	30	5	)	)	PUNCT
ejpam-1188	30	6	d1	d1	PROPN
ejpam-1188	30	7	α	α	NOUN
ejpam-1188	30	8	,	,	PUNCT
ejpam-1188	30	9	δ	δ	PROPN
ejpam-1188	30	10	f	f	X
ejpam-1188	30	11	(	(	PUNCT
ejpam-1188	30	12	z	z	NOUN
ejpam-1188	30	13	)	)	PUNCT
ejpam-1188	30	14	=	=	NOUN
ejpam-1188	30	15	dα	dα	NOUN
ejpam-1188	30	16	,	,	PUNCT
ejpam-1188	30	17	δ	δ	PROPN
ejpam-1188	30	18	f	f	X
ejpam-1188	30	19	(	(	PUNCT
ejpam-1188	30	20	z	z	NOUN
ejpam-1188	30	21	)	)	PUNCT
ejpam-1188	30	22	=	=	VERB
ejpam-1188	30	23	αδz2	αδz2	PROPN
ejpam-1188	30	24	f	f	PROPN
ejpam-1188	30	25	′′(z	′′(z	PROPN
ejpam-1188	30	26	)	)	PUNCT
ejpam-1188	31	1	+	+	CCONJ
ejpam-1188	31	2	(	(	PUNCT
ejpam-1188	31	3	α−δ)z	α−δ)z	PROPN
ejpam-1188	31	4	f	f	PROPN
ejpam-1188	31	5	′(z	′(z	ADV
ejpam-1188	31	6	)	)	PUNCT
ejpam-1188	32	1	+	+	CCONJ
ejpam-1188	32	2	(	(	PUNCT
ejpam-1188	32	3	1−α+δ	1−α+δ	NUM
ejpam-1188	32	4	)	)	PUNCT
ejpam-1188	32	5	f	f	NOUN
ejpam-1188	32	6	(	(	PUNCT
ejpam-1188	32	7	z	z	NOUN
ejpam-1188	32	8	)	)	PUNCT
ejpam-1188	32	9	.	.	PUNCT
ejpam-1188	32	10	.	.	PUNCT
ejpam-1188	32	11	.	.	PUNCT
ejpam-1188	33	1	dn	dn	PROPN
ejpam-1188	33	2	α	α	PROPN
ejpam-1188	33	3	,	,	PUNCT
ejpam-1188	33	4	δ	δ	PROPN
ejpam-1188	33	5	f	f	X
ejpam-1188	33	6	(	(	PUNCT
ejpam-1188	33	7	z	z	NOUN
ejpam-1188	33	8	)	)	PUNCT
ejpam-1188	34	1	=	=	NOUN
ejpam-1188	34	2	dα	dα	NOUN
ejpam-1188	34	3	,	,	PUNCT
ejpam-1188	34	4	δ(d	δ(d	PROPN
ejpam-1188	34	5	n−1	n−1	PROPN
ejpam-1188	34	6	α	α	NOUN
ejpam-1188	34	7	,	,	PUNCT
ejpam-1188	34	8	δ	δ	PROPN
ejpam-1188	34	9	f	f	X
ejpam-1188	34	10	(	(	PUNCT
ejpam-1188	34	11	z	z	NOUN
ejpam-1188	34	12	)	)	PUNCT
ejpam-1188	34	13	)	)	PUNCT
ejpam-1188	34	14	where	where	SCONJ
ejpam-1188	34	15	α≥	α≥	NOUN
ejpam-1188	34	16	δ	δ	PROPN
ejpam-1188	34	17	≥	≥	X
ejpam-1188	34	18	0	0	NUM
ejpam-1188	34	19	and	and	CCONJ
ejpam-1188	34	20	n	n	PRON
ejpam-1188	34	21	∈	∈	PROPN
ejpam-1188	34	22	n0	n0	PROPN
ejpam-1188	34	23	.	.	PUNCT
ejpam-1188	35	1	if	if	SCONJ
ejpam-1188	35	2	f	f	PROPN
ejpam-1188	35	3	∈a	∈a	PROPN
ejpam-1188	35	4	is	be	AUX
ejpam-1188	35	5	given	give	VERB
ejpam-1188	35	6	by	by	ADP
ejpam-1188	35	7	(	(	PUNCT
ejpam-1188	35	8	1	1	NUM
ejpam-1188	35	9	)	)	PUNCT
ejpam-1188	35	10	then	then	ADV
ejpam-1188	35	11	from	from	ADP
ejpam-1188	35	12	the	the	DET
ejpam-1188	35	13	definition	definition	NOUN
ejpam-1188	35	14	of	of	ADP
ejpam-1188	35	15	the	the	DET
ejpam-1188	35	16	operator	operator	NOUN
ejpam-1188	35	17	dn	dn	PROPN
ejpam-1188	35	18	α	α	PROPN
ejpam-1188	35	19	,	,	PUNCT
ejpam-1188	35	20	δ	δ	PROPN
ejpam-1188	35	21	f	f	X
ejpam-1188	35	22	(	(	PUNCT
ejpam-1188	35	23	z	z	NOUN
ejpam-1188	35	24	)	)	PUNCT
ejpam-1188	35	25	,	,	PUNCT
ejpam-1188	35	26	it	it	PRON
ejpam-1188	35	27	is	be	AUX
ejpam-1188	35	28	easy	easy	ADJ
ejpam-1188	35	29	verity	verity	NOUN
ejpam-1188	35	30	that	that	PRON
ejpam-1188	35	31	dn	dn	PROPN
ejpam-1188	35	32	α	α	PROPN
ejpam-1188	35	33	,	,	PUNCT
ejpam-1188	35	34	δ	δ	PROPN
ejpam-1188	35	35	f	f	X
ejpam-1188	35	36	(	(	PUNCT
ejpam-1188	35	37	z	z	NOUN
ejpam-1188	35	38	)	)	PUNCT
ejpam-1188	35	39	=	=	SYM
ejpam-1188	36	1	z+	z+	NUM
ejpam-1188	36	2	∞	∞	PROPN
ejpam-1188	36	3	∑	∑	PROPN
ejpam-1188	36	4	k=2	k=2	PROPN
ejpam-1188	36	5	φn	φn	PROPN
ejpam-1188	36	6	k	k	PROPN
ejpam-1188	36	7	akzk	akzk	PROPN
ejpam-1188	36	8	,	,	PUNCT
ejpam-1188	36	9	where	where	SCONJ
ejpam-1188	36	10	φk	φk	ADP
ejpam-1188	36	11	=	=	SYM
ejpam-1188	37	1	[	[	X
ejpam-1188	37	2	1	1	NUM
ejpam-1188	37	3	+	+	CCONJ
ejpam-1188	37	4	(	(	PUNCT
ejpam-1188	37	5	αδk+α−δ)(k−	αδk+α−δ)(k−	PROPN
ejpam-1188	37	6	1	1	NUM
ejpam-1188	37	7	)	)	PUNCT
ejpam-1188	37	8	]	]	PUNCT
ejpam-1188	37	9	,	,	PUNCT
ejpam-1188	37	10	(	(	PUNCT
ejpam-1188	37	11	φn	φn	ADP
ejpam-1188	37	12	k	k	NOUN
ejpam-1188	37	13	=	=	PUNCT
ejpam-1188	38	1	[	[	X
ejpam-1188	38	2	φk]n	φk]n	PROPN
ejpam-1188	38	3	)	)	PUNCT
ejpam-1188	38	4	;	;	PUNCT
ejpam-1188	38	5	α≥	α≥	VERB
ejpam-1188	38	6	δ	δ	PROPN
ejpam-1188	38	7	≥	≥	X
ejpam-1188	38	8	0	0	NUM
ejpam-1188	38	9	and	and	CCONJ
ejpam-1188	38	10	n	n	PRON
ejpam-1188	38	11	∈	∈	PROPN
ejpam-1188	38	12	n0	n0	PROPN
ejpam-1188	38	13	.	.	PROPN
ejpam-1188	39	1	remark	remark	PROPN
ejpam-1188	39	2	1	1	NUM
ejpam-1188	39	3	.	.	PUNCT
ejpam-1188	39	4	dn	dn	PROPN
ejpam-1188	39	5	α	α	PROPN
ejpam-1188	39	6	,	,	PUNCT
ejpam-1188	39	7	δ	δ	PROPN
ejpam-1188	39	8	f	f	X
ejpam-1188	39	9	(	(	PUNCT
ejpam-1188	39	10	z	z	NOUN
ejpam-1188	39	11	)	)	PUNCT
ejpam-1188	39	12	is	be	AUX
ejpam-1188	39	13	a	a	DET
ejpam-1188	39	14	generalization	generalization	NOUN
ejpam-1188	39	15	of	of	ADP
ejpam-1188	39	16	many	many	ADJ
ejpam-1188	39	17	other	other	ADJ
ejpam-1188	39	18	linear	linear	PROPN
ejpam-1188	39	19	operators	operator	NOUN
ejpam-1188	39	20	considered	consider	VERB
ejpam-1188	39	21	earlier	early	ADV
ejpam-1188	39	22	.	.	PUNCT
ejpam-1188	40	1	in	in	ADP
ejpam-1188	40	2	particular	particular	ADJ
ejpam-1188	40	3	,	,	PUNCT
ejpam-1188	40	4	for	for	ADP
ejpam-1188	40	5	f	f	PROPN
ejpam-1188	40	6	(	(	PUNCT
ejpam-1188	40	7	z	z	NOUN
ejpam-1188	40	8	)	)	PUNCT
ejpam-1188	40	9	ina	ina	PROPN
ejpam-1188	40	10	we	we	PRON
ejpam-1188	40	11	have	have	VERB
ejpam-1188	40	12	the	the	DET
ejpam-1188	40	13	following	follow	VERB
ejpam-1188	40	14	:	:	PUNCT
ejpam-1188	40	15	•	•	NUM
ejpam-1188	40	16	dn	dn	PROPN
ejpam-1188	40	17	1,0	1,0	NUM
ejpam-1188	40	18	f	f	X
ejpam-1188	40	19	(	(	PUNCT
ejpam-1188	40	20	z)≡	z)≡	PROPN
ejpam-1188	40	21	dn	dn	PROPN
ejpam-1188	40	22	f	f	PROPN
ejpam-1188	40	23	(	(	PUNCT
ejpam-1188	40	24	z	z	X
ejpam-1188	40	25	)	)	PUNCT
ejpam-1188	40	26	the	the	DET
ejpam-1188	40	27	operator	operator	NOUN
ejpam-1188	40	28	defined	define	VERB
ejpam-1188	40	29	by	by	ADP
ejpam-1188	40	30	sălăgean	sălăgean	PROPN
ejpam-1188	40	31	(	(	PUNCT
ejpam-1188	40	32	see	see	VERB
ejpam-1188	40	33	[	[	X
ejpam-1188	40	34	13	13	NUM
ejpam-1188	40	35	]	]	NUM
ejpam-1188	40	36	)	)	PUNCT
ejpam-1188	40	37	.	.	PUNCT
ejpam-1188	41	1	•	•	NUM
ejpam-1188	41	2	dn	dn	NOUN
ejpam-1188	41	3	α,0	α,0	NUM
ejpam-1188	41	4	f	f	PROPN
ejpam-1188	41	5	(	(	PUNCT
ejpam-1188	41	6	z)≡	z)≡	PROPN
ejpam-1188	41	7	dn	dn	NOUN
ejpam-1188	41	8	α	α	PROPN
ejpam-1188	41	9	f	f	X
ejpam-1188	41	10	(	(	PUNCT
ejpam-1188	41	11	z	z	NOUN
ejpam-1188	41	12	)	)	PUNCT
ejpam-1188	41	13	(	(	PUNCT
ejpam-1188	41	14	see	see	VERB
ejpam-1188	41	15	[	[	X
ejpam-1188	41	16	16	16	NUM
ejpam-1188	41	17	]	]	SYM
ejpam-1188	41	18	)	)	PUNCT
ejpam-1188	41	19	.	.	PUNCT
ejpam-1188	42	1	l.	l.	PROPN
ejpam-1188	42	2	zhou	zhou	PROPN
ejpam-1188	42	3	,	,	PUNCT
ejpam-1188	42	4	q	q	PROPN
ejpam-1188	42	5	-	-	NOUN
ejpam-1188	42	6	h	h	NOUN
ejpam-1188	42	7	xu	xu	PROPN
ejpam-1188	42	8	/	/	SYM
ejpam-1188	42	9	eur	eur	PROPN
ejpam-1188	42	10	.	.	PUNCT
ejpam-1188	43	1	j.	j.	PROPN
ejpam-1188	43	2	pure	pure	PROPN
ejpam-1188	43	3	appl	appl	PROPN
ejpam-1188	43	4	.	.	PROPN
ejpam-1188	43	5	math	math	PROPN
ejpam-1188	43	6	,	,	PUNCT
ejpam-1188	43	7	6	6	NUM
ejpam-1188	43	8	(	(	PUNCT
ejpam-1188	43	9	2013	2013	NUM
ejpam-1188	43	10	)	)	PUNCT
ejpam-1188	43	11	,	,	PUNCT
ejpam-1188	43	12	460	460	NUM
ejpam-1188	43	13	-	-	SYM
ejpam-1188	43	14	468	468	NUM
ejpam-1188	43	15	462	462	NUM
ejpam-1188	43	16	recently	recently	ADV
ejpam-1188	44	1	,	,	PUNCT
ejpam-1188	44	2	several	several	ADJ
ejpam-1188	44	3	authors	author	NOUN
ejpam-1188	44	4	have	have	AUX
ejpam-1188	44	5	obtained	obtain	VERB
ejpam-1188	44	6	many	many	ADJ
ejpam-1188	44	7	interesting	interesting	ADJ
ejpam-1188	44	8	results	result	NOUN
ejpam-1188	44	9	for	for	ADP
ejpam-1188	44	10	various	various	ADJ
ejpam-1188	44	11	subclasses	subclass	NOUN
ejpam-1188	44	12	of	of	ADP
ejpam-1188	44	13	analytic	analytic	ADJ
ejpam-1188	44	14	functions	function	NOUN
ejpam-1188	44	15	involving	involve	VERB
ejpam-1188	44	16	the	the	DET
ejpam-1188	44	17	sălăgean	sălăgean	ADJ
ejpam-1188	44	18	derivative	derivative	ADJ
ejpam-1188	44	19	operator	operator	NOUN
ejpam-1188	44	20	dn	dn	PROPN
ejpam-1188	44	21	f	f	PROPN
ejpam-1188	44	22	(	(	PUNCT
ejpam-1188	44	23	z	z	NOUN
ejpam-1188	44	24	)	)	PUNCT
ejpam-1188	44	25	.	.	PUNCT
ejpam-1188	45	1	for	for	ADP
ejpam-1188	45	2	example	example	NOUN
ejpam-1188	45	3	,	,	PUNCT
ejpam-1188	45	4	deng	deng	PROPN
ejpam-1188	46	1	[	[	X
ejpam-1188	46	2	9	9	NUM
ejpam-1188	46	3	]	]	PUNCT
ejpam-1188	46	4	defines	define	VERB
ejpam-1188	46	5	a	a	DET
ejpam-1188	46	6	function	function	NOUN
ejpam-1188	46	7	classb(n	classb(n	NOUN
ejpam-1188	46	8	,	,	PUNCT
ejpam-1188	46	9	λ	λ	PROPN
ejpam-1188	46	10	,	,	PUNCT
ejpam-1188	46	11	α	α	NOUN
ejpam-1188	46	12	,	,	PUNCT
ejpam-1188	46	13	b	b	NOUN
ejpam-1188	46	14	)	)	PUNCT
ejpam-1188	46	15	by	by	ADP
ejpam-1188	46	16	ℜ(1	ℜ(1	NOUN
ejpam-1188	46	17	+	+	SYM
ejpam-1188	46	18	1	1	NUM
ejpam-1188	46	19	b	b	X
ejpam-1188	46	20	[	[	PUNCT
ejpam-1188	46	21	z[(1−λ)dn	z[(1−λ)dn	PROPN
ejpam-1188	46	22	f	f	X
ejpam-1188	46	23	(	(	PUNCT
ejpam-1188	46	24	z	z	NOUN
ejpam-1188	46	25	)	)	PUNCT
ejpam-1188	46	26	+	+	NOUN
ejpam-1188	46	27	λdn+1	λdn+1	X
ejpam-1188	46	28	f	f	X
ejpam-1188	46	29	(	(	PUNCT
ejpam-1188	46	30	z)]′	z)]′	NUM
ejpam-1188	46	31	(	(	PUNCT
ejpam-1188	46	32	1−λ)dn	1−λ)dn	NUM
ejpam-1188	46	33	f	f	X
ejpam-1188	46	34	(	(	PUNCT
ejpam-1188	46	35	z	z	NOUN
ejpam-1188	46	36	)	)	PUNCT
ejpam-1188	47	1	+	+	NOUN
ejpam-1188	47	2	λdn+1	λdn+1	X
ejpam-1188	47	3	f	f	X
ejpam-1188	47	4	(	(	PUNCT
ejpam-1188	47	5	z	z	NOUN
ejpam-1188	47	6	)	)	PUNCT
ejpam-1188	47	7	−	−	PROPN
ejpam-1188	47	8	1	1	NUM
ejpam-1188	47	9	]	]	NUM
ejpam-1188	47	10	)	)	PUNCT
ejpam-1188	47	11	>	>	X
ejpam-1188	48	1	α	α	PROPN
ejpam-1188	48	2	(	(	PUNCT
ejpam-1188	48	3	0≤	0≤	NUM
ejpam-1188	48	4	α	α	NOUN
ejpam-1188	48	5	<	<	X
ejpam-1188	48	6	1;0≤	1;0≤	PRON
ejpam-1188	48	7	λ≤	λ≤	NOUN
ejpam-1188	48	8	1	1	NUM
ejpam-1188	48	9	;	;	PUNCT
ejpam-1188	48	10	n	n	PRON
ejpam-1188	48	11	∈	∈	PROPN
ejpam-1188	48	12	n0	n0	NUM
ejpam-1188	48	13	;	;	PUNCT
ejpam-1188	48	14	b	b	X
ejpam-1188	48	15	∈	∈	PROPN
ejpam-1188	48	16	c\{0	c\{0	NOUN
ejpam-1188	48	17	}	}	PUNCT
ejpam-1188	48	18	)	)	PUNCT
ejpam-1188	48	19	and	and	CCONJ
ejpam-1188	48	20	also	also	ADV
ejpam-1188	48	21	investigated	investigate	VERB
ejpam-1188	48	22	the	the	DET
ejpam-1188	48	23	subclass	subclass	NOUN
ejpam-1188	48	24	t	t	NOUN
ejpam-1188	48	25	(	(	PUNCT
ejpam-1188	48	26	n	n	CCONJ
ejpam-1188	48	27	,	,	PUNCT
ejpam-1188	48	28	λ	λ	PROPN
ejpam-1188	48	29	,	,	PUNCT
ejpam-1188	48	30	α	α	NOUN
ejpam-1188	48	31	,	,	PUNCT
ejpam-1188	48	32	b	b	NOUN
ejpam-1188	48	33	;	;	PUNCT
ejpam-1188	48	34	u	u	NOUN
ejpam-1188	48	35	)	)	PUNCT
ejpam-1188	48	36	of	of	ADP
ejpam-1188	48	37	the	the	DET
ejpam-1188	48	38	analytic	analytic	ADJ
ejpam-1188	48	39	function	function	NOUN
ejpam-1188	48	40	class	class	NOUN
ejpam-1188	48	41	a	a	NOUN
ejpam-1188	48	42	,	,	PUNCT
ejpam-1188	48	43	which	which	PRON
ejpam-1188	48	44	consists	consist	VERB
ejpam-1188	48	45	of	of	ADP
ejpam-1188	48	46	functions	function	NOUN
ejpam-1188	48	47	f	f	X
ejpam-1188	48	48	(	(	PUNCT
ejpam-1188	48	49	z	z	NOUN
ejpam-1188	48	50	)	)	PUNCT
ejpam-1188	48	51	∈	∈	PROPN
ejpam-1188	48	52	a	a	DET
ejpam-1188	48	53	satisfying	satisfying	NOUN
ejpam-1188	48	54	the	the	DET
ejpam-1188	48	55	following	follow	VERB
ejpam-1188	48	56	nonhomogenous	nonhomogenous	ADJ
ejpam-1188	48	57	cauchy	cauchy	PROPN
ejpam-1188	48	58	-	-	PUNCT
ejpam-1188	48	59	differential	differential	NOUN
ejpam-1188	48	60	equation	equation	NOUN
ejpam-1188	48	61	:	:	PUNCT
ejpam-1188	48	62	z2	z2	PROPN
ejpam-1188	48	63	d2w	d2w	PROPN
ejpam-1188	48	64	dz2	dz2	NOUN
ejpam-1188	48	65	+	+	CCONJ
ejpam-1188	48	66	2(1	2(1	NUM
ejpam-1188	48	67	+	+	CCONJ
ejpam-1188	48	68	u)z	u)z	X
ejpam-1188	48	69	dw	dw	NOUN
ejpam-1188	48	70	dz	dz	NOUN
ejpam-1188	48	71	+	+	PROPN
ejpam-1188	48	72	u(1	u(1	PROPN
ejpam-1188	48	73	+	+	CCONJ
ejpam-1188	48	74	u)w	u)w	ADJ
ejpam-1188	48	75	=	=	SYM
ejpam-1188	48	76	(	(	PUNCT
ejpam-1188	48	77	1	1	NUM
ejpam-1188	48	78	+	+	NOUN
ejpam-1188	48	79	u)(2	u)(2	NUM
ejpam-1188	48	80	+	+	X
ejpam-1188	48	81	u)h(z	u)h(z	NOUN
ejpam-1188	48	82	)	)	PUNCT
ejpam-1188	48	83	,	,	PUNCT
ejpam-1188	48	84	where	where	SCONJ
ejpam-1188	48	85	w	w	NOUN
ejpam-1188	48	86	=	=	SYM
ejpam-1188	48	87	f	f	X
ejpam-1188	48	88	(	(	PUNCT
ejpam-1188	48	89	z	z	NOUN
ejpam-1188	48	90	)	)	PUNCT
ejpam-1188	48	91	∈a	∈a	ADJ
ejpam-1188	48	92	,	,	PUNCT
ejpam-1188	48	93	h(z	h(z	PROPN
ejpam-1188	48	94	)	)	PUNCT
ejpam-1188	48	95	∈b(n	∈b(n	PROPN
ejpam-1188	48	96	,	,	PUNCT
ejpam-1188	48	97	λ	λ	PROPN
ejpam-1188	48	98	,	,	PUNCT
ejpam-1188	48	99	α	α	NOUN
ejpam-1188	48	100	,	,	PUNCT
ejpam-1188	48	101	b	b	NOUN
ejpam-1188	48	102	)	)	PUNCT
ejpam-1188	48	103	and	and	CCONJ
ejpam-1188	48	104	u	u	PROPN
ejpam-1188	48	105	∈	∈	PROPN
ejpam-1188	48	106	r\(−∞,−1	r\(−∞,−1	PROPN
ejpam-1188	48	107	]	]	PUNCT
ejpam-1188	48	108	.	.	PUNCT
ejpam-1188	49	1	in	in	ADP
ejpam-1188	49	2	the	the	DET
ejpam-1188	49	3	same	same	ADJ
ejpam-1188	49	4	paper	paper	NOUN
ejpam-1188	49	5	[	[	X
ejpam-1188	49	6	9	9	NUM
ejpam-1188	49	7	]	]	PUNCT
ejpam-1188	49	8	,	,	PUNCT
ejpam-1188	49	9	coefficient	coefficient	NOUN
ejpam-1188	49	10	bounds	bound	VERB
ejpam-1188	49	11	for	for	ADP
ejpam-1188	49	12	the	the	DET
ejpam-1188	49	13	subclassb(n	subclassb(n	NOUN
ejpam-1188	49	14	,	,	PUNCT
ejpam-1188	49	15	λ	λ	PROPN
ejpam-1188	49	16	,	,	PUNCT
ejpam-1188	49	17	α	α	NOUN
ejpam-1188	49	18	,	,	PUNCT
ejpam-1188	49	19	b	b	NOUN
ejpam-1188	49	20	)	)	PUNCT
ejpam-1188	49	21	and	and	CCONJ
ejpam-1188	49	22	t	t	PROPN
ejpam-1188	49	23	(	(	PUNCT
ejpam-1188	49	24	n	n	CCONJ
ejpam-1188	49	25	,	,	PUNCT
ejpam-1188	49	26	λ	λ	PROPN
ejpam-1188	49	27	,	,	PUNCT
ejpam-1188	49	28	α	α	NOUN
ejpam-1188	49	29	,	,	PUNCT
ejpam-1188	49	30	b	b	PROPN
ejpam-1188	49	31	,	,	PUNCT
ejpam-1188	49	32	u	u	NOUN
ejpam-1188	49	33	)	)	PUNCT
ejpam-1188	49	34	of	of	ADP
ejpam-1188	49	35	analytic	analytic	ADJ
ejpam-1188	49	36	functions	function	NOUN
ejpam-1188	49	37	of	of	ADP
ejpam-1188	49	38	complex	complex	ADJ
ejpam-1188	49	39	order	order	NOUN
ejpam-1188	49	40	were	be	AUX
ejpam-1188	49	41	obtained	obtain	VERB
ejpam-1188	49	42	.	.	PUNCT
ejpam-1188	50	1	by	by	ADP
ejpam-1188	50	2	using	use	VERB
ejpam-1188	50	3	the	the	DET
ejpam-1188	50	4	multiplier	multipli	ADJ
ejpam-1188	50	5	differential	differential	ADJ
ejpam-1188	50	6	operator	operator	NOUN
ejpam-1188	50	7	dn	dn	PROPN
ejpam-1188	50	8	α	α	PROPN
ejpam-1188	50	9	,	,	PUNCT
ejpam-1188	50	10	δ	δ	PROPN
ejpam-1188	50	11	,	,	PUNCT
ejpam-1188	50	12	we	we	PRON
ejpam-1188	50	13	now	now	ADV
ejpam-1188	50	14	define	define	VERB
ejpam-1188	50	15	the	the	DET
ejpam-1188	50	16	following	follow	VERB
ejpam-1188	50	17	new	new	ADJ
ejpam-1188	50	18	subclasses	subclass	NOUN
ejpam-1188	50	19	of	of	ADP
ejpam-1188	50	20	functions	function	NOUN
ejpam-1188	50	21	belonging	belong	VERB
ejpam-1188	50	22	to	to	ADP
ejpam-1188	50	23	the	the	DET
ejpam-1188	50	24	classa	classa	NOUN
ejpam-1188	50	25	.	.	PUNCT
ejpam-1188	51	1	definition	definition	NOUN
ejpam-1188	51	2	1	1	NUM
ejpam-1188	51	3	.	.	PUNCT
ejpam-1188	52	1	let	let	VERB
ejpam-1188	52	2	g	g	NOUN
ejpam-1188	52	3	:	:	PUNCT
ejpam-1188	52	4	u→	u→	PROPN
ejpam-1188	52	5	c	c	NOUN
ejpam-1188	52	6	be	be	AUX
ejpam-1188	52	7	a	a	DET
ejpam-1188	52	8	convex	convex	NOUN
ejpam-1188	52	9	function	function	NOUN
ejpam-1188	52	10	such	such	ADJ
ejpam-1188	52	11	that	that	PRON
ejpam-1188	52	12	g(0	g(0	NOUN
ejpam-1188	52	13	)	)	PUNCT
ejpam-1188	52	14	=	=	SYM
ejpam-1188	52	15	1	1	NUM
ejpam-1188	52	16	and	and	CCONJ
ejpam-1188	52	17	ℜ(g(z	ℜ(g(z	NUM
ejpam-1188	52	18	)	)	PUNCT
ejpam-1188	52	19	)	)	PUNCT
ejpam-1188	52	20	>	>	X
ejpam-1188	52	21	0	0	PUNCT
ejpam-1188	53	1	(	(	PUNCT
ejpam-1188	53	2	z	z	NOUN
ejpam-1188	53	3	∈	∈	PROPN
ejpam-1188	53	4	u	u	NOUN
ejpam-1188	53	5	)	)	PUNCT
ejpam-1188	53	6	,	,	PUNCT
ejpam-1188	53	7	and	and	CCONJ
ejpam-1188	53	8	f	f	PROPN
ejpam-1188	53	9	be	be	VERB
ejpam-1188	53	10	an	an	DET
ejpam-1188	53	11	analytic	analytic	ADJ
ejpam-1188	53	12	function	function	NOUN
ejpam-1188	53	13	in	in	ADP
ejpam-1188	53	14	u	u	NOUN
ejpam-1188	53	15	defined	define	VERB
ejpam-1188	53	16	by	by	ADP
ejpam-1188	53	17	(	(	PUNCT
ejpam-1188	53	18	1	1	NUM
ejpam-1188	53	19	)	)	PUNCT
ejpam-1188	53	20	.	.	PUNCT
ejpam-1188	54	1	we	we	PRON
ejpam-1188	54	2	say	say	VERB
ejpam-1188	54	3	that	that	SCONJ
ejpam-1188	54	4	f	f	PROPN
ejpam-1188	54	5	∈hg(n	∈hg(n	ADV
ejpam-1188	54	6	,	,	PUNCT
ejpam-1188	54	7	b	b	PROPN
ejpam-1188	54	8	,	,	PUNCT
ejpam-1188	54	9	λ	λ	PROPN
ejpam-1188	54	10	,	,	PUNCT
ejpam-1188	54	11	α	α	NOUN
ejpam-1188	54	12	,	,	PUNCT
ejpam-1188	54	13	δ	δ	PROPN
ejpam-1188	54	14	)	)	PUNCT
ejpam-1188	54	15	if	if	SCONJ
ejpam-1188	54	16	it	it	PRON
ejpam-1188	54	17	satisfies	satisfy	VERB
ejpam-1188	54	18	the	the	DET
ejpam-1188	54	19	following	follow	VERB
ejpam-1188	54	20	condition	condition	NOUN
ejpam-1188	54	21	:	:	PUNCT
ejpam-1188	54	22	1	1	NUM
ejpam-1188	54	23	+	+	SYM
ejpam-1188	54	24	1	1	NUM
ejpam-1188	54	25	b	b	X
ejpam-1188	54	26	[	[	PUNCT
ejpam-1188	54	27	z[f	z[f	PROPN
ejpam-1188	54	28	n	n	SYM
ejpam-1188	54	29	λ	λ	PROPN
ejpam-1188	54	30	,	,	PUNCT
ejpam-1188	54	31	α	α	NOUN
ejpam-1188	54	32	,	,	PUNCT
ejpam-1188	54	33	δ(z	δ(z	NOUN
ejpam-1188	54	34	)	)	PUNCT
ejpam-1188	54	35	]	]	PUNCT
ejpam-1188	54	36	′	′	NUM
ejpam-1188	55	1	f	f	PROPN
ejpam-1188	55	2	n	n	PROPN
ejpam-1188	55	3	λ	λ	PROPN
ejpam-1188	55	4	,	,	PUNCT
ejpam-1188	55	5	α	α	NOUN
ejpam-1188	55	6	,	,	PUNCT
ejpam-1188	55	7	δ(z	δ(z	NOUN
ejpam-1188	55	8	)	)	PUNCT
ejpam-1188	55	9	−	−	NOUN
ejpam-1188	55	10	1	1	NUM
ejpam-1188	55	11	]	]	X
ejpam-1188	55	12	∈	∈	PROPN
ejpam-1188	55	13	g(u	g(u	PROPN
ejpam-1188	55	14	)	)	PUNCT
ejpam-1188	55	15	(	(	PUNCT
ejpam-1188	55	16	z	z	NOUN
ejpam-1188	55	17	∈	∈	PROPN
ejpam-1188	55	18	u	u	NOUN
ejpam-1188	55	19	)	)	PUNCT
ejpam-1188	55	20	,	,	PUNCT
ejpam-1188	55	21	where	where	SCONJ
ejpam-1188	55	22	f	f	PROPN
ejpam-1188	55	23	n	n	X
ejpam-1188	55	24	λ	λ	PROPN
ejpam-1188	55	25	,	,	PUNCT
ejpam-1188	55	26	α	α	NOUN
ejpam-1188	55	27	,	,	PUNCT
ejpam-1188	55	28	δ(z	δ(z	NOUN
ejpam-1188	55	29	)	)	PUNCT
ejpam-1188	55	30	=	=	SYM
ejpam-1188	55	31	(	(	PUNCT
ejpam-1188	55	32	1−λ)d	1−λ)d	NUM
ejpam-1188	55	33	n	n	SYM
ejpam-1188	55	34	α	α	NOUN
ejpam-1188	55	35	,	,	PUNCT
ejpam-1188	55	36	δ	δ	PROPN
ejpam-1188	55	37	f	f	X
ejpam-1188	55	38	(	(	PUNCT
ejpam-1188	55	39	z	z	NOUN
ejpam-1188	55	40	)	)	PUNCT
ejpam-1188	56	1	+	+	NOUN
ejpam-1188	56	2	λdn+1	λdn+1	NOUN
ejpam-1188	56	3	α	α	NOUN
ejpam-1188	56	4	,	,	PUNCT
ejpam-1188	56	5	δ	δ	PROPN
ejpam-1188	56	6	f	f	X
ejpam-1188	56	7	(	(	PUNCT
ejpam-1188	56	8	z	z	NOUN
ejpam-1188	56	9	)	)	PUNCT
ejpam-1188	56	10	(	(	PUNCT
ejpam-1188	56	11	α≥	α≥	NOUN
ejpam-1188	56	12	δ	δ	PROPN
ejpam-1188	56	13	≥	≥	NUM
ejpam-1188	56	14	0,0≤	0,0≤	NUM
ejpam-1188	56	15	λ≤	λ≤	NUM
ejpam-1188	56	16	1	1	NUM
ejpam-1188	56	17	;	;	PUNCT
ejpam-1188	56	18	n	n	PRON
ejpam-1188	56	19	∈	∈	PROPN
ejpam-1188	56	20	n0	n0	NUM
ejpam-1188	56	21	;	;	PUNCT
ejpam-1188	56	22	b	b	X
ejpam-1188	56	23	∈	∈	PROPN
ejpam-1188	56	24	c\{0	c\{0	NOUN
ejpam-1188	56	25	}	}	PUNCT
ejpam-1188	56	26	)	)	PUNCT
ejpam-1188	56	27	.	.	PUNCT
ejpam-1188	57	1	definition	definition	NOUN
ejpam-1188	57	2	2	2	NUM
ejpam-1188	57	3	.	.	PUNCT
ejpam-1188	58	1	a	a	DET
ejpam-1188	58	2	function	function	NOUN
ejpam-1188	58	3	f	f	X
ejpam-1188	58	4	(	(	PUNCT
ejpam-1188	58	5	z	z	NOUN
ejpam-1188	58	6	)	)	PUNCT
ejpam-1188	58	7	∈a	∈a	NUM
ejpam-1188	58	8	is	be	AUX
ejpam-1188	58	9	said	say	VERB
ejpam-1188	58	10	to	to	PART
ejpam-1188	58	11	be	be	AUX
ejpam-1188	58	12	in	in	ADP
ejpam-1188	58	13	the	the	DET
ejpam-1188	58	14	classhg(n	classhg(n	PROPN
ejpam-1188	58	15	,	,	PUNCT
ejpam-1188	58	16	b	b	PROPN
ejpam-1188	58	17	,	,	PUNCT
ejpam-1188	58	18	λ	λ	PROPN
ejpam-1188	58	19	,	,	PUNCT
ejpam-1188	58	20	α	α	NOUN
ejpam-1188	58	21	,	,	PUNCT
ejpam-1188	58	22	δ	δ	PROPN
ejpam-1188	58	23	;	;	PUNCT
ejpam-1188	58	24	u	u	NOUN
ejpam-1188	58	25	)	)	PUNCT
ejpam-1188	58	26	,	,	PUNCT
ejpam-1188	58	27	if	if	SCONJ
ejpam-1188	58	28	it	it	PRON
ejpam-1188	58	29	satisfies	satisfy	VERB
ejpam-1188	58	30	the	the	DET
ejpam-1188	58	31	following	follow	VERB
ejpam-1188	58	32	nonhomogenous	nonhomogenous	ADJ
ejpam-1188	58	33	cauchy	cauchy	PROPN
ejpam-1188	58	34	-	-	PUNCT
ejpam-1188	58	35	euler	euler	NOUN
ejpam-1188	58	36	differential	differential	ADJ
ejpam-1188	58	37	equation	equation	NOUN
ejpam-1188	58	38	:	:	PUNCT
ejpam-1188	58	39	z2	z2	PROPN
ejpam-1188	58	40	d2w	d2w	PROPN
ejpam-1188	58	41	dz2	dz2	NOUN
ejpam-1188	58	42	+	+	CCONJ
ejpam-1188	58	43	2(1	2(1	NUM
ejpam-1188	58	44	+	+	CCONJ
ejpam-1188	58	45	u)z	u)z	X
ejpam-1188	58	46	dw	dw	NOUN
ejpam-1188	58	47	dz	dz	NOUN
ejpam-1188	58	48	+	+	PROPN
ejpam-1188	58	49	u(1	u(1	PROPN
ejpam-1188	58	50	+	+	CCONJ
ejpam-1188	58	51	u)w	u)w	ADJ
ejpam-1188	58	52	=	=	SYM
ejpam-1188	58	53	(	(	PUNCT
ejpam-1188	58	54	1	1	NUM
ejpam-1188	58	55	+	+	NOUN
ejpam-1188	58	56	u)(2	u)(2	NUM
ejpam-1188	58	57	+	+	X
ejpam-1188	58	58	u)h(z	u)h(z	SYM
ejpam-1188	58	59	)	)	PUNCT
ejpam-1188	58	60	(	(	PUNCT
ejpam-1188	58	61	3	3	X
ejpam-1188	58	62	)	)	PUNCT
ejpam-1188	58	63	(	(	PUNCT
ejpam-1188	58	64	w	w	NOUN
ejpam-1188	58	65	=	=	SYM
ejpam-1188	58	66	f	f	X
ejpam-1188	58	67	(	(	PUNCT
ejpam-1188	58	68	z	z	NOUN
ejpam-1188	58	69	)	)	PUNCT
ejpam-1188	58	70	∈a	∈a	ADJ
ejpam-1188	58	71	,	,	PUNCT
ejpam-1188	58	72	h(z	h(z	NOUN
ejpam-1188	58	73	)	)	PUNCT
ejpam-1188	58	74	∈hg(n	∈hg(n	NOUN
ejpam-1188	58	75	,	,	PUNCT
ejpam-1188	58	76	b	b	NOUN
ejpam-1188	58	77	,	,	PUNCT
ejpam-1188	58	78	λ	λ	PROPN
ejpam-1188	58	79	,	,	PUNCT
ejpam-1188	58	80	α	α	NOUN
ejpam-1188	58	81	,	,	PUNCT
ejpam-1188	58	82	δ	δ	PROPN
ejpam-1188	58	83	)	)	PUNCT
ejpam-1188	58	84	and	and	CCONJ
ejpam-1188	58	85	u	u	PROPN
ejpam-1188	58	86	∈	∈	PROPN
ejpam-1188	58	87	r\(−∞,−1	r\(−∞,−1	PROPN
ejpam-1188	58	88	]	]	PUNCT
ejpam-1188	58	89	)	)	PUNCT
ejpam-1188	58	90	.	.	PUNCT
ejpam-1188	59	1	remark	remark	NOUN
ejpam-1188	59	2	2	2	NUM
ejpam-1188	59	3	.	.	PUNCT
ejpam-1188	60	1	their	their	PRON
ejpam-1188	60	2	are	be	AUX
ejpam-1188	60	3	many	many	ADJ
ejpam-1188	60	4	choices	choice	NOUN
ejpam-1188	60	5	of	of	ADP
ejpam-1188	60	6	the	the	DET
ejpam-1188	60	7	function	function	NOUN
ejpam-1188	60	8	g	g	NOUN
ejpam-1188	60	9	and	and	CCONJ
ejpam-1188	60	10	the	the	DET
ejpam-1188	60	11	values	value	NOUN
ejpam-1188	60	12	of	of	ADP
ejpam-1188	60	13	α	α	NOUN
ejpam-1188	60	14	,	,	PUNCT
ejpam-1188	60	15	δ	δ	PROPN
ejpam-1188	60	16	which	which	PRON
ejpam-1188	60	17	would	would	AUX
ejpam-1188	60	18	provide	provide	VERB
ejpam-1188	60	19	interesting	interesting	ADJ
ejpam-1188	60	20	subclasses	subclass	NOUN
ejpam-1188	60	21	of	of	ADP
ejpam-1188	60	22	analytic	analytic	ADJ
ejpam-1188	60	23	functions	function	NOUN
ejpam-1188	60	24	of	of	ADP
ejpam-1188	60	25	complex	complex	ADJ
ejpam-1188	60	26	order	order	NOUN
ejpam-1188	60	27	.	.	PUNCT
ejpam-1188	61	1	in	in	ADP
ejpam-1188	61	2	particular	particular	ADJ
ejpam-1188	61	3	,	,	PUNCT
ejpam-1188	61	4	if	if	SCONJ
ejpam-1188	61	5	we	we	PRON
ejpam-1188	61	6	let	let	VERB
ejpam-1188	61	7	g(z	g(z	ADJ
ejpam-1188	61	8	)	)	PUNCT
ejpam-1188	61	9	=	=	SYM
ejpam-1188	62	1	1	1	NUM
ejpam-1188	62	2	+	+	CCONJ
ejpam-1188	62	3	(	(	PUNCT
ejpam-1188	62	4	1−	1−	NUM
ejpam-1188	62	5	2β)z	2β)z	NUM
ejpam-1188	62	6	1−	1−	NUM
ejpam-1188	62	7	z	z	NOUN
ejpam-1188	62	8	(	(	PUNCT
ejpam-1188	62	9	0≤	0≤	NUM
ejpam-1188	62	10	β	β	X
ejpam-1188	62	11	<	<	X
ejpam-1188	62	12	1	1	NUM
ejpam-1188	62	13	;	;	PUNCT
ejpam-1188	62	14	z	z	PROPN
ejpam-1188	62	15	∈	∈	PROPN
ejpam-1188	62	16	u),α=	u),α=	PRON
ejpam-1188	62	17	1	1	NUM
ejpam-1188	62	18	,	,	PUNCT
ejpam-1188	62	19	andδ	andδ	NOUN
ejpam-1188	62	20	=	=	SYM
ejpam-1188	62	21	0	0	PROPN
ejpam-1188	62	22	,	,	PUNCT
ejpam-1188	62	23	l.	l.	PROPN
ejpam-1188	62	24	zhou	zhou	PROPN
ejpam-1188	62	25	,	,	PUNCT
ejpam-1188	62	26	q	q	PROPN
ejpam-1188	62	27	-	-	NOUN
ejpam-1188	62	28	h	h	NOUN
ejpam-1188	62	29	xu	xu	PROPN
ejpam-1188	62	30	/	/	SYM
ejpam-1188	62	31	eur	eur	PROPN
ejpam-1188	62	32	.	.	PUNCT
ejpam-1188	63	1	j.	j.	PROPN
ejpam-1188	63	2	pure	pure	PROPN
ejpam-1188	63	3	appl	appl	PROPN
ejpam-1188	63	4	.	.	PROPN
ejpam-1188	63	5	math	math	PROPN
ejpam-1188	63	6	,	,	PUNCT
ejpam-1188	63	7	6	6	NUM
ejpam-1188	63	8	(	(	PUNCT
ejpam-1188	63	9	2013	2013	NUM
ejpam-1188	63	10	)	)	PUNCT
ejpam-1188	63	11	,	,	PUNCT
ejpam-1188	63	12	460	460	NUM
ejpam-1188	63	13	-	-	SYM
ejpam-1188	63	14	468	468	NUM
ejpam-1188	63	15	463	463	NUM
ejpam-1188	63	16	it	it	PRON
ejpam-1188	63	17	is	be	AUX
ejpam-1188	63	18	easy	easy	ADJ
ejpam-1188	63	19	to	to	PART
ejpam-1188	63	20	see	see	VERB
ejpam-1188	63	21	g	g	PROPN
ejpam-1188	63	22	is	be	AUX
ejpam-1188	63	23	a	a	DET
ejpam-1188	63	24	convex	convex	ADJ
ejpam-1188	63	25	function	function	NOUN
ejpam-1188	63	26	in	in	ADP
ejpam-1188	63	27	u	u	NOUN
ejpam-1188	63	28	and	and	CCONJ
ejpam-1188	63	29	satisfies	satisfy	VERB
ejpam-1188	63	30	the	the	DET
ejpam-1188	63	31	hypotheses	hypothesis	NOUN
ejpam-1188	63	32	of	of	ADP
ejpam-1188	63	33	definition	definition	NOUN
ejpam-1188	63	34	1	1	NUM
ejpam-1188	63	35	.	.	PUNCT
ejpam-1188	64	1	if	if	SCONJ
ejpam-1188	64	2	f	f	PROPN
ejpam-1188	64	3	∈hg(n	∈hg(n	NOUN
ejpam-1188	64	4	,	,	PUNCT
ejpam-1188	64	5	b	b	PROPN
ejpam-1188	64	6	,	,	PUNCT
ejpam-1188	64	7	λ	λ	PROPN
ejpam-1188	64	8	,	,	PUNCT
ejpam-1188	64	9	α	α	NOUN
ejpam-1188	64	10	,	,	PUNCT
ejpam-1188	64	11	δ	δ	PROPN
ejpam-1188	64	12	)	)	PUNCT
ejpam-1188	64	13	,	,	PUNCT
ejpam-1188	64	14	then	then	ADV
ejpam-1188	64	15	ℜ(1	ℜ(1	X
ejpam-1188	64	16	+	+	SYM
ejpam-1188	64	17	1	1	NUM
ejpam-1188	64	18	b	b	X
ejpam-1188	64	19	[	[	PUNCT
ejpam-1188	64	20	z[(1−λ)dn	z[(1−λ)dn	PROPN
ejpam-1188	64	21	f	f	X
ejpam-1188	64	22	(	(	PUNCT
ejpam-1188	64	23	z	z	NOUN
ejpam-1188	64	24	)	)	PUNCT
ejpam-1188	65	1	+	+	NOUN
ejpam-1188	65	2	λdn+1	λdn+1	X
ejpam-1188	65	3	f	f	X
ejpam-1188	65	4	(	(	PUNCT
ejpam-1188	65	5	z)]′	z)]′	NUM
ejpam-1188	65	6	(	(	PUNCT
ejpam-1188	65	7	1−λ)dn	1−λ)dn	NUM
ejpam-1188	65	8	f	f	X
ejpam-1188	65	9	(	(	PUNCT
ejpam-1188	65	10	z	z	NOUN
ejpam-1188	65	11	)	)	PUNCT
ejpam-1188	65	12	+	+	NOUN
ejpam-1188	65	13	λdn+1	λdn+1	X
ejpam-1188	65	14	f	f	X
ejpam-1188	65	15	(	(	PUNCT
ejpam-1188	65	16	z	z	NOUN
ejpam-1188	65	17	)	)	PUNCT
ejpam-1188	65	18	−	−	PROPN
ejpam-1188	65	19	1	1	NUM
ejpam-1188	65	20	]	]	NUM
ejpam-1188	65	21	)	)	PUNCT
ejpam-1188	65	22	>	>	X
ejpam-1188	65	23	β(z	β(z	PROPN
ejpam-1188	65	24	∈	∈	PROPN
ejpam-1188	65	25	u	u	PROPN
ejpam-1188	65	26	)	)	PUNCT
ejpam-1188	65	27	,	,	PUNCT
ejpam-1188	65	28	that	that	PRON
ejpam-1188	65	29	is	be	AUX
ejpam-1188	65	30	f	f	PROPN
ejpam-1188	65	31	∈b(n	∈b(n	PROPN
ejpam-1188	65	32	,	,	PUNCT
ejpam-1188	65	33	λ	λ	PROPN
ejpam-1188	65	34	,	,	PUNCT
ejpam-1188	65	35	β	β	X
ejpam-1188	65	36	,	,	PUNCT
ejpam-1188	65	37	b	b	NOUN
ejpam-1188	65	38	)	)	PUNCT
ejpam-1188	65	39	.	.	PUNCT
ejpam-1188	66	1	remark	remark	PROPN
ejpam-1188	66	2	3	3	NUM
ejpam-1188	66	3	.	.	PUNCT
ejpam-1188	67	1	in	in	ADP
ejpam-1188	67	2	view	view	NOUN
ejpam-1188	67	3	of	of	ADP
ejpam-1188	67	4	remark	remark	NOUN
ejpam-1188	67	5	2	2	NUM
ejpam-1188	67	6	,	,	PUNCT
ejpam-1188	67	7	ifwe	ifwe	NOUN
ejpam-1188	67	8	take	take	VERB
ejpam-1188	67	9	g(z	g(z	NOUN
ejpam-1188	67	10	)	)	PUNCT
ejpam-1188	67	11	=	=	SYM
ejpam-1188	68	1	1	1	NUM
ejpam-1188	68	2	+	+	CCONJ
ejpam-1188	68	3	(	(	PUNCT
ejpam-1188	68	4	1−	1−	NUM
ejpam-1188	68	5	2β)z	2β)z	NUM
ejpam-1188	68	6	1−	1−	NUM
ejpam-1188	68	7	z	z	NOUN
ejpam-1188	68	8	(	(	PUNCT
ejpam-1188	68	9	0≤	0≤	NUM
ejpam-1188	68	10	β	β	X
ejpam-1188	68	11	<	<	X
ejpam-1188	68	12	1	1	NUM
ejpam-1188	68	13	;	;	PUNCT
ejpam-1188	68	14	z	z	PROPN
ejpam-1188	68	15	∈	∈	PROPN
ejpam-1188	68	16	u),α=	u),α=	ADJ
ejpam-1188	68	17	1	1	NUM
ejpam-1188	68	18	,	,	PUNCT
ejpam-1188	68	19	and	and	CCONJ
ejpam-1188	68	20	δ	δ	PROPN
ejpam-1188	68	21	=	=	NOUN
ejpam-1188	68	22	0	0	NUM
ejpam-1188	68	23	in	in	ADP
ejpam-1188	68	24	definitions	definition	NOUN
ejpam-1188	68	25	1	1	NUM
ejpam-1188	68	26	and	and	CCONJ
ejpam-1188	68	27	2	2	NUM
ejpam-1188	68	28	,	,	PUNCT
ejpam-1188	68	29	it	it	PRON
ejpam-1188	68	30	is	be	AUX
ejpam-1188	68	31	easy	easy	ADJ
ejpam-1188	68	32	to	to	PART
ejpam-1188	68	33	observe	observe	VERB
ejpam-1188	68	34	that	that	SCONJ
ejpam-1188	68	35	the	the	DET
ejpam-1188	68	36	function	function	NOUN
ejpam-1188	68	37	classes	class	NOUN
ejpam-1188	68	38	hg(n	hg(n	ADP
ejpam-1188	68	39	,	,	PUNCT
ejpam-1188	68	40	b	b	PROPN
ejpam-1188	68	41	,	,	PUNCT
ejpam-1188	68	42	λ	λ	PROPN
ejpam-1188	68	43	,	,	PUNCT
ejpam-1188	68	44	α	α	NOUN
ejpam-1188	68	45	,	,	PUNCT
ejpam-1188	68	46	δ	δ	PROPN
ejpam-1188	68	47	)	)	PUNCT
ejpam-1188	68	48	andhg(n	andhg(n	PROPN
ejpam-1188	68	49	,	,	PUNCT
ejpam-1188	68	50	b	b	PROPN
ejpam-1188	68	51	,	,	PUNCT
ejpam-1188	68	52	λ	λ	PROPN
ejpam-1188	68	53	,	,	PUNCT
ejpam-1188	68	54	α	α	NOUN
ejpam-1188	68	55	,	,	PUNCT
ejpam-1188	68	56	δ	δ	PROPN
ejpam-1188	68	57	;	;	PUNCT
ejpam-1188	68	58	u	u	X
ejpam-1188	68	59	)	)	PUNCT
ejpam-1188	68	60	become	become	VERB
ejpam-1188	68	61	the	the	DET
ejpam-1188	68	62	aforementioned	aforementioned	ADJ
ejpam-1188	68	63	function	function	NOUN
ejpam-1188	68	64	classes	class	NOUN
ejpam-1188	68	65	b(n	b(n	PROPN
ejpam-1188	68	66	,	,	PUNCT
ejpam-1188	68	67	λ	λ	PROPN
ejpam-1188	68	68	,	,	PUNCT
ejpam-1188	68	69	α	α	NOUN
ejpam-1188	68	70	,	,	PUNCT
ejpam-1188	68	71	b	b	NOUN
ejpam-1188	68	72	)	)	PUNCT
ejpam-1188	68	73	and	and	CCONJ
ejpam-1188	68	74	t	t	PROPN
ejpam-1188	68	75	(	(	PUNCT
ejpam-1188	68	76	n	n	CCONJ
ejpam-1188	68	77	,	,	PUNCT
ejpam-1188	68	78	λ	λ	PROPN
ejpam-1188	68	79	,	,	PUNCT
ejpam-1188	68	80	α	α	NOUN
ejpam-1188	68	81	,	,	PUNCT
ejpam-1188	68	82	b	b	NOUN
ejpam-1188	68	83	;	;	PUNCT
ejpam-1188	68	84	u	u	NOUN
ejpam-1188	68	85	)	)	PUNCT
ejpam-1188	68	86	,	,	PUNCT
ejpam-1188	68	87	respectively	respectively	ADV
ejpam-1188	68	88	.	.	PUNCT
ejpam-1188	69	1	in	in	ADP
ejpam-1188	69	2	our	our	PRON
ejpam-1188	69	3	investigation	investigation	NOUN
ejpam-1188	69	4	,	,	PUNCT
ejpam-1188	69	5	we	we	PRON
ejpam-1188	69	6	shall	shall	AUX
ejpam-1188	69	7	use	use	VERB
ejpam-1188	69	8	the	the	DET
ejpam-1188	69	9	principle	principle	NOUN
ejpam-1188	69	10	of	of	ADP
ejpam-1188	69	11	subordination	subordination	NOUN
ejpam-1188	69	12	between	between	ADP
ejpam-1188	69	13	analytic	analytic	ADJ
ejpam-1188	69	14	functions	function	NOUN
ejpam-1188	69	15	,	,	PUNCT
ejpam-1188	69	16	which	which	PRON
ejpam-1188	69	17	is	be	AUX
ejpam-1188	69	18	explained	explain	VERB
ejpam-1188	69	19	in	in	ADP
ejpam-1188	69	20	definition	definition	NOUN
ejpam-1188	69	21	3	3	NUM
ejpam-1188	69	22	below	below	ADV
ejpam-1188	69	23	(	(	PUNCT
ejpam-1188	69	24	see	see	VERB
ejpam-1188	69	25	also	also	ADV
ejpam-1188	69	26	[	[	X
ejpam-1188	69	27	14	14	NUM
ejpam-1188	69	28	,	,	PUNCT
ejpam-1188	69	29	15	15	NUM
ejpam-1188	69	30	]	]	NUM
ejpam-1188	69	31	)	)	PUNCT
ejpam-1188	69	32	.	.	PUNCT
ejpam-1188	70	1	definition	definition	NOUN
ejpam-1188	70	2	3	3	NUM
ejpam-1188	70	3	.	.	PUNCT
ejpam-1188	71	1	for	for	ADP
ejpam-1188	71	2	two	two	NUM
ejpam-1188	71	3	functions	function	NOUN
ejpam-1188	71	4	f	f	NOUN
ejpam-1188	71	5	and	and	CCONJ
ejpam-1188	71	6	g	g	PROPN
ejpam-1188	71	7	analytic	analytic	NOUN
ejpam-1188	71	8	in	in	ADP
ejpam-1188	71	9	u	u	NOUN
ejpam-1188	71	10	,	,	PUNCT
ejpam-1188	71	11	we	we	PRON
ejpam-1188	71	12	say	say	VERB
ejpam-1188	71	13	that	that	SCONJ
ejpam-1188	71	14	the	the	DET
ejpam-1188	71	15	function	function	NOUN
ejpam-1188	71	16	f	f	X
ejpam-1188	71	17	(	(	PUNCT
ejpam-1188	71	18	z	z	NOUN
ejpam-1188	71	19	)	)	PUNCT
ejpam-1188	71	20	is	be	AUX
ejpam-1188	71	21	subordinate	subordinate	ADJ
ejpam-1188	71	22	to	to	ADP
ejpam-1188	71	23	g(z	g(z	PROPN
ejpam-1188	71	24	)	)	PUNCT
ejpam-1188	71	25	in	in	ADP
ejpam-1188	71	26	u	u	NOUN
ejpam-1188	71	27	(	(	PUNCT
ejpam-1188	71	28	written	write	VERB
ejpam-1188	71	29	f	f	PROPN
ejpam-1188	71	30	≺	≺	NOUN
ejpam-1188	71	31	g	g	PROPN
ejpam-1188	71	32	(	(	PUNCT
ejpam-1188	71	33	z	z	NOUN
ejpam-1188	71	34	∈	∈	PROPN
ejpam-1188	71	35	u	u	NOUN
ejpam-1188	71	36	)	)	PUNCT
ejpam-1188	71	37	)	)	PUNCT
ejpam-1188	71	38	,	,	PUNCT
ejpam-1188	71	39	if	if	SCONJ
ejpam-1188	71	40	there	there	PRON
ejpam-1188	71	41	exists	exist	VERB
ejpam-1188	71	42	a	a	DET
ejpam-1188	71	43	schwarz	schwarz	PROPN
ejpam-1188	71	44	function	function	NOUN
ejpam-1188	71	45	ω(z	ω(z	PROPN
ejpam-1188	71	46	)	)	PUNCT
ejpam-1188	71	47	analytic	analytic	NOUN
ejpam-1188	71	48	in	in	ADP
ejpam-1188	71	49	u	u	NOUN
ejpam-1188	71	50	with	with	ADP
ejpam-1188	71	51	ω(0	ω(0	PROPN
ejpam-1188	71	52	)	)	PUNCT
ejpam-1188	71	53	=	=	SYM
ejpam-1188	71	54	0	0	NUM
ejpam-1188	71	55	and	and	CCONJ
ejpam-1188	71	56	|ω(z)|	|ω(z)|	ADP
ejpam-1188	71	57	<	<	X
ejpam-1188	71	58	1(z	1(z	NUM
ejpam-1188	71	59	∈	∈	PROPN
ejpam-1188	71	60	u	u	NOUN
ejpam-1188	71	61	)	)	PUNCT
ejpam-1188	71	62	,	,	PUNCT
ejpam-1188	71	63	such	such	ADJ
ejpam-1188	71	64	that	that	SCONJ
ejpam-1188	71	65	f	f	PROPN
ejpam-1188	71	66	(	(	PUNCT
ejpam-1188	71	67	z	z	NOUN
ejpam-1188	71	68	)	)	PUNCT
ejpam-1188	71	69	=	=	SYM
ejpam-1188	71	70	g(ω(z	g(ω(z	ADJ
ejpam-1188	71	71	)	)	PUNCT
ejpam-1188	71	72	)	)	PUNCT
ejpam-1188	72	1	(	(	PUNCT
ejpam-1188	72	2	z	z	NOUN
ejpam-1188	72	3	∈	∈	PROPN
ejpam-1188	72	4	u	u	NOUN
ejpam-1188	72	5	)	)	PUNCT
ejpam-1188	72	6	.	.	PUNCT
ejpam-1188	73	1	in	in	ADP
ejpam-1188	73	2	particular	particular	ADJ
ejpam-1188	73	3	,	,	PUNCT
ejpam-1188	73	4	if	if	SCONJ
ejpam-1188	73	5	the	the	DET
ejpam-1188	73	6	function	function	NOUN
ejpam-1188	73	7	g	g	PROPN
ejpam-1188	73	8	is	be	AUX
ejpam-1188	73	9	univalent	univalent	ADJ
ejpam-1188	73	10	in	in	ADP
ejpam-1188	73	11	u	u	PROPN
ejpam-1188	73	12	,	,	PUNCT
ejpam-1188	73	13	the	the	DET
ejpam-1188	73	14	above	above	ADJ
ejpam-1188	73	15	subordination	subordination	NOUN
ejpam-1188	73	16	is	be	AUX
ejpam-1188	73	17	equivalent	equivalent	ADJ
ejpam-1188	73	18	to	to	ADP
ejpam-1188	73	19	f	f	PROPN
ejpam-1188	73	20	(	(	PUNCT
ejpam-1188	73	21	0	0	NUM
ejpam-1188	73	22	)	)	PUNCT
ejpam-1188	73	23	=	=	SYM
ejpam-1188	73	24	g(0	g(0	PROPN
ejpam-1188	73	25	)	)	PUNCT
ejpam-1188	73	26	and	and	CCONJ
ejpam-1188	73	27	f	f	PROPN
ejpam-1188	73	28	(	(	PUNCT
ejpam-1188	73	29	u)⊂	u)⊂	CCONJ
ejpam-1188	73	30	g(u	g(u	PROPN
ejpam-1188	73	31	)	)	PUNCT
ejpam-1188	73	32	.	.	PUNCT
ejpam-1188	74	1	in	in	ADP
ejpam-1188	74	2	this	this	DET
ejpam-1188	74	3	paper	paper	NOUN
ejpam-1188	74	4	,	,	PUNCT
ejpam-1188	74	5	by	by	ADP
ejpam-1188	74	6	use	use	NOUN
ejpam-1188	74	7	of	of	ADP
ejpam-1188	74	8	the	the	DET
ejpam-1188	74	9	principle	principle	NOUN
ejpam-1188	74	10	of	of	ADP
ejpam-1188	74	11	subordination	subordination	NOUN
ejpam-1188	74	12	,	,	PUNCT
ejpam-1188	74	13	we	we	PRON
ejpam-1188	74	14	obtain	obtain	VERB
ejpam-1188	74	15	coefficient	coefficient	NOUN
ejpam-1188	74	16	bounds	bound	NOUN
ejpam-1188	74	17	for	for	ADP
ejpam-1188	74	18	functions	function	NOUN
ejpam-1188	74	19	in	in	ADP
ejpam-1188	74	20	the	the	DET
ejpam-1188	74	21	subclasses	subclass	NOUN
ejpam-1188	74	22	hg(n	hg(n	NOUN
ejpam-1188	74	23	,	,	PUNCT
ejpam-1188	74	24	b	b	PROPN
ejpam-1188	74	25	,	,	PUNCT
ejpam-1188	74	26	λ	λ	PROPN
ejpam-1188	74	27	,	,	PUNCT
ejpam-1188	74	28	α	α	NOUN
ejpam-1188	74	29	,	,	PUNCT
ejpam-1188	74	30	δ	δ	PROPN
ejpam-1188	74	31	)	)	PUNCT
ejpam-1188	74	32	andhg(n	andhg(n	PROPN
ejpam-1188	74	33	,	,	PUNCT
ejpam-1188	74	34	b	b	PROPN
ejpam-1188	74	35	,	,	PUNCT
ejpam-1188	74	36	λ	λ	PROPN
ejpam-1188	74	37	,	,	PUNCT
ejpam-1188	74	38	α	α	NOUN
ejpam-1188	74	39	,	,	PUNCT
ejpam-1188	74	40	δ	δ	PROPN
ejpam-1188	74	41	;	;	PUNCT
ejpam-1188	74	42	u	u	NOUN
ejpam-1188	74	43	)	)	PUNCT
ejpam-1188	74	44	of	of	ADP
ejpam-1188	74	45	analytic	analytic	ADJ
ejpam-1188	74	46	functions	function	NOUN
ejpam-1188	74	47	of	of	ADP
ejpam-1188	74	48	complex	complex	ADJ
ejpam-1188	74	49	order	order	NOUN
ejpam-1188	74	50	,	,	PUNCT
ejpam-1188	74	51	which	which	PRON
ejpam-1188	74	52	we	we	PRON
ejpam-1188	74	53	have	have	AUX
ejpam-1188	74	54	introduce	introduce	NOUN
ejpam-1188	74	55	here	here	ADV
ejpam-1188	74	56	.	.	PUNCT
ejpam-1188	75	1	our	our	PRON
ejpam-1188	75	2	results	result	NOUN
ejpam-1188	75	3	would	would	AUX
ejpam-1188	75	4	unify	unify	VERB
ejpam-1188	75	5	and	and	CCONJ
ejpam-1188	75	6	extend	extend	VERB
ejpam-1188	75	7	the	the	DET
ejpam-1188	75	8	corresponding	corresponding	ADJ
ejpam-1188	75	9	results	result	NOUN
ejpam-1188	75	10	obtained	obtain	VERB
ejpam-1188	75	11	earlier	early	ADV
ejpam-1188	75	12	by	by	ADP
ejpam-1188	75	13	nasr	nasr	PROPN
ejpam-1188	75	14	and	and	CCONJ
ejpam-1188	75	15	aouf	aouf	PROPN
ejpam-1188	76	1	[	[	X
ejpam-1188	76	2	10	10	NUM
ejpam-1188	76	3	]	]	PUNCT
ejpam-1188	76	4	,	,	PUNCT
ejpam-1188	76	5	altintaş	altintaş	PROPN
ejpam-1188	76	6	et	et	X
ejpam-1188	76	7	.	.	PUNCT
ejpam-1188	77	1	al	al	PROPN
ejpam-1188	78	1	[	[	X
ejpam-1188	78	2	1–8	1–8	X
ejpam-1188	78	3	]	]	PUNCT
ejpam-1188	78	4	and	and	CCONJ
ejpam-1188	78	5	deng	deng	PROPN
ejpam-1188	79	1	[	[	X
ejpam-1188	79	2	9	9	NUM
ejpam-1188	79	3	]	]	PUNCT
ejpam-1188	79	4	.	.	PUNCT
ejpam-1188	80	1	l.	l.	PROPN
ejpam-1188	80	2	zhou	zhou	PROPN
ejpam-1188	80	3	,	,	PUNCT
ejpam-1188	80	4	q	q	PROPN
ejpam-1188	80	5	-	-	NOUN
ejpam-1188	80	6	h	h	NOUN
ejpam-1188	80	7	xu	xu	PROPN
ejpam-1188	80	8	/	/	SYM
ejpam-1188	80	9	eur	eur	PROPN
ejpam-1188	80	10	.	.	PUNCT
ejpam-1188	81	1	j.	j.	PROPN
ejpam-1188	81	2	pure	pure	PROPN
ejpam-1188	81	3	appl	appl	PROPN
ejpam-1188	81	4	.	.	PROPN
ejpam-1188	81	5	math	math	PROPN
ejpam-1188	81	6	,	,	PUNCT
ejpam-1188	81	7	6	6	NUM
ejpam-1188	81	8	(	(	PUNCT
ejpam-1188	81	9	2013	2013	NUM
ejpam-1188	81	10	)	)	PUNCT
ejpam-1188	81	11	,	,	PUNCT
ejpam-1188	81	12	460	460	NUM
ejpam-1188	81	13	-	-	SYM
ejpam-1188	81	14	468	468	NUM
ejpam-1188	81	15	464	464	NUM
ejpam-1188	81	16	2	2	NUM
ejpam-1188	81	17	.	.	PUNCT
ejpam-1188	81	18	main	main	ADJ
ejpam-1188	81	19	results	result	NOUN
ejpam-1188	81	20	and	and	CCONJ
ejpam-1188	81	21	their	their	PRON
ejpam-1188	81	22	proofs	proof	NOUN
ejpam-1188	81	23	in	in	ADP
ejpam-1188	81	24	order	order	NOUN
ejpam-1188	81	25	to	to	PART
ejpam-1188	81	26	prove	prove	VERB
ejpam-1188	81	27	our	our	PRON
ejpam-1188	81	28	main	main	ADJ
ejpam-1188	81	29	results(theorems	results(theorem	NOUN
ejpam-1188	81	30	1	1	NUM
ejpam-1188	81	31	and	and	CCONJ
ejpam-1188	81	32	2	2	NUM
ejpam-1188	81	33	below	below	ADV
ejpam-1188	81	34	)	)	PUNCT
ejpam-1188	82	1	,	,	PUNCT
ejpam-1188	82	2	we	we	PRON
ejpam-1188	82	3	first	first	ADV
ejpam-1188	82	4	recall	recall	VERB
ejpam-1188	82	5	the	the	DET
ejpam-1188	82	6	following	follow	VERB
ejpam-1188	82	7	lemma	lemma	PROPN
ejpam-1188	82	8	due	due	ADP
ejpam-1188	82	9	to	to	PART
ejpam-1188	82	10	rogosinski	rogosinski	VERB
ejpam-1188	82	11	[	[	PUNCT
ejpam-1188	82	12	12	12	NUM
ejpam-1188	82	13	]	]	PUNCT
ejpam-1188	82	14	.	.	PUNCT
ejpam-1188	83	1	lemma	lemma	PROPN
ejpam-1188	83	2	2	2	X
ejpam-1188	83	3	.	.	PUNCT
ejpam-1188	84	1	let	let	VERB
ejpam-1188	84	2	the	the	DET
ejpam-1188	84	3	function	function	NOUN
ejpam-1188	84	4	g	g	NOUN
ejpam-1188	84	5	given	give	VERB
ejpam-1188	84	6	by	by	ADP
ejpam-1188	84	7	g(z	g(z	PROPN
ejpam-1188	84	8	)	)	PUNCT
ejpam-1188	85	1	=	=	PUNCT
ejpam-1188	85	2	z+	z+	NUM
ejpam-1188	85	3	∞	∞	NUM
ejpam-1188	85	4	∑	∑	PROPN
ejpam-1188	86	1	k=1	k=1	PROPN
ejpam-1188	86	2	gkzk	gkzk	VERB
ejpam-1188	86	3	be	be	AUX
ejpam-1188	86	4	convex	convex	PROPN
ejpam-1188	86	5	u.	u.	PROPN
ejpam-1188	86	6	also	also	ADV
ejpam-1188	86	7	let	let	VERB
ejpam-1188	86	8	the	the	DET
ejpam-1188	86	9	function	function	NOUN
ejpam-1188	86	10	f	f	NOUN
ejpam-1188	86	11	given	give	VERB
ejpam-1188	86	12	by	by	ADP
ejpam-1188	86	13	f	f	PROPN
ejpam-1188	86	14	(	(	PUNCT
ejpam-1188	86	15	z	z	NOUN
ejpam-1188	86	16	)	)	PUNCT
ejpam-1188	86	17	=	=	SYM
ejpam-1188	87	1	z+	z+	NUM
ejpam-1188	87	2	∞	∞	NUM
ejpam-1188	87	3	∑	∑	PROPN
ejpam-1188	87	4	k=1	k=1	PROPN
ejpam-1188	87	5	akzk	akzk	PROPN
ejpam-1188	87	6	be	be	AUX
ejpam-1188	87	7	holomorphic	holomorphic	ADJ
ejpam-1188	87	8	in	in	ADP
ejpam-1188	87	9	u.	u.	PROPN
ejpam-1188	87	10	if	if	SCONJ
ejpam-1188	87	11	f	f	PROPN
ejpam-1188	87	12	(	(	PUNCT
ejpam-1188	87	13	z)≺	z)≺	PROPN
ejpam-1188	87	14	g(z	g(z	PROPN
ejpam-1188	87	15	)	)	PUNCT
ejpam-1188	87	16	(	(	PUNCT
ejpam-1188	87	17	z	z	NOUN
ejpam-1188	87	18	∈	∈	PROPN
ejpam-1188	87	19	u	u	NOUN
ejpam-1188	87	20	)	)	PUNCT
ejpam-1188	87	21	,	,	PUNCT
ejpam-1188	87	22	then	then	ADV
ejpam-1188	87	23	|ak|	|ak|	PROPN
ejpam-1188	87	24	≤	≤	NUM
ejpam-1188	87	25	|g1|	|g1|	NOUN
ejpam-1188	87	26	(	(	PUNCT
ejpam-1188	87	27	k	k	PROPN
ejpam-1188	87	28	∈	∈	PROPN
ejpam-1188	87	29	n	n	CCONJ
ejpam-1188	87	30	)	)	PUNCT
ejpam-1188	87	31	.	.	PUNCT
ejpam-1188	88	1	we	we	PRON
ejpam-1188	88	2	now	now	ADV
ejpam-1188	88	3	state	state	VERB
ejpam-1188	88	4	and	and	CCONJ
ejpam-1188	88	5	prove	prove	VERB
ejpam-1188	88	6	each	each	PRON
ejpam-1188	88	7	of	of	ADP
ejpam-1188	88	8	our	our	PRON
ejpam-1188	88	9	main	main	ADJ
ejpam-1188	88	10	results	result	NOUN
ejpam-1188	88	11	given	give	VERB
ejpam-1188	88	12	by	by	ADP
ejpam-1188	88	13	theorems	theorem	NOUN
ejpam-1188	88	14	1	1	NUM
ejpam-1188	88	15	and	and	CCONJ
ejpam-1188	88	16	2	2	NUM
ejpam-1188	88	17	below	below	ADV
ejpam-1188	88	18	.	.	PUNCT
ejpam-1188	89	1	theorem	theorem	NOUN
ejpam-1188	89	2	1	1	NUM
ejpam-1188	89	3	.	.	PUNCT
ejpam-1188	90	1	let	let	VERB
ejpam-1188	90	2	the	the	DET
ejpam-1188	90	3	function	function	NOUN
ejpam-1188	90	4	f	f	PROPN
ejpam-1188	90	5	∈a	∈a	PROPN
ejpam-1188	90	6	be	be	AUX
ejpam-1188	90	7	given	give	VERB
ejpam-1188	90	8	by	by	ADP
ejpam-1188	90	9	(	(	PUNCT
ejpam-1188	90	10	1	1	NUM
ejpam-1188	90	11	)	)	PUNCT
ejpam-1188	90	12	.	.	PUNCT
ejpam-1188	91	1	if	if	SCONJ
ejpam-1188	91	2	f	f	PROPN
ejpam-1188	91	3	∈hg(n	∈hg(n	NOUN
ejpam-1188	91	4	,	,	PUNCT
ejpam-1188	91	5	b	b	PROPN
ejpam-1188	91	6	,	,	PUNCT
ejpam-1188	91	7	λ	λ	PROPN
ejpam-1188	91	8	,	,	PUNCT
ejpam-1188	91	9	α	α	NOUN
ejpam-1188	91	10	,	,	PUNCT
ejpam-1188	91	11	δ	δ	PROPN
ejpam-1188	91	12	)	)	PUNCT
ejpam-1188	91	13	,	,	PUNCT
ejpam-1188	91	14	then	then	ADV
ejpam-1188	91	15	|a	|a	VERB
ejpam-1188	91	16	j|	j|	PROPN
ejpam-1188	91	17	≤	≤	PROPN
ejpam-1188	91	18	j−2	j−2	PROPN
ejpam-1188	91	19	∏	∏	PROPN
ejpam-1188	91	20	k=0	k=0	PROPN
ejpam-1188	91	21	(	(	PUNCT
ejpam-1188	91	22	k+	k+	PROPN
ejpam-1188	91	23	|g	|g	PROPN
ejpam-1188	91	24	′(0)||b|	′(0)||b|	NOUN
ejpam-1188	91	25	)	)	PUNCT
ejpam-1188	91	26	φn	φn	ADP
ejpam-1188	91	27	j	j	PROPN
ejpam-1188	92	1	[	[	X
ejpam-1188	92	2	1−λ+λφ	1−λ+λφ	NUM
ejpam-1188	92	3	j	j	X
ejpam-1188	92	4	]	]	X
ejpam-1188	92	5	(	(	PUNCT
ejpam-1188	92	6	j−	j−	PROPN
ejpam-1188	92	7	1	1	NUM
ejpam-1188	92	8	)	)	PUNCT
ejpam-1188	92	9	!	!	PUNCT
ejpam-1188	93	1	(	(	PUNCT
ejpam-1188	93	2	j	j	PROPN
ejpam-1188	93	3	∈	∈	PROPN
ejpam-1188	93	4	n2	n2	NOUN
ejpam-1188	93	5	)	)	PUNCT
ejpam-1188	93	6	.	.	PUNCT
ejpam-1188	94	1	proof	proof	NOUN
ejpam-1188	94	2	.	.	PUNCT
ejpam-1188	95	1	by	by	ADP
ejpam-1188	95	2	definition	definition	NOUN
ejpam-1188	95	3	of	of	ADP
ejpam-1188	95	4	dn	dn	PROPN
ejpam-1188	95	5	α	α	PROPN
ejpam-1188	95	6	,	,	PUNCT
ejpam-1188	95	7	δ	δ	PROPN
ejpam-1188	95	8	f	f	X
ejpam-1188	95	9	(	(	PUNCT
ejpam-1188	95	10	z	z	NOUN
ejpam-1188	95	11	)	)	PUNCT
ejpam-1188	95	12	and	and	CCONJ
ejpam-1188	95	13	f	f	PROPN
ejpam-1188	95	14	n	n	PROPN
ejpam-1188	95	15	λ	λ	PROPN
ejpam-1188	95	16	,	,	PUNCT
ejpam-1188	95	17	α	α	NOUN
ejpam-1188	95	18	,	,	PUNCT
ejpam-1188	95	19	δ(z	δ(z	PROPN
ejpam-1188	95	20	)	)	PUNCT
ejpam-1188	95	21	,	,	PUNCT
ejpam-1188	95	22	we	we	PRON
ejpam-1188	95	23	can	can	AUX
ejpam-1188	95	24	write	write	VERB
ejpam-1188	95	25	f	f	PROPN
ejpam-1188	95	26	n	n	PRON
ejpam-1188	95	27	λ	λ	PROPN
ejpam-1188	95	28	,	,	PUNCT
ejpam-1188	95	29	α	α	NOUN
ejpam-1188	95	30	,	,	PUNCT
ejpam-1188	95	31	δ(z	δ(z	NOUN
ejpam-1188	95	32	)	)	PUNCT
ejpam-1188	95	33	=	=	SYM
ejpam-1188	96	1	z+	z+	NUM
ejpam-1188	96	2	∞	∞	PROPN
ejpam-1188	96	3	∑	∑	PROPN
ejpam-1188	96	4	j=2	j=2	PROPN
ejpam-1188	96	5	a	a	DET
ejpam-1188	96	6	jz	jz	PROPN
ejpam-1188	96	7	j	j	PROPN
ejpam-1188	96	8	(	(	PUNCT
ejpam-1188	96	9	z	z	PROPN
ejpam-1188	96	10	∈	∈	PROPN
ejpam-1188	96	11	u	u	NOUN
ejpam-1188	96	12	)	)	PUNCT
ejpam-1188	96	13	,	,	PUNCT
ejpam-1188	96	14	(	(	PUNCT
ejpam-1188	96	15	4	4	X
ejpam-1188	96	16	)	)	PUNCT
ejpam-1188	96	17	where	where	SCONJ
ejpam-1188	96	18	a	a	DET
ejpam-1188	96	19	j	j	PROPN
ejpam-1188	96	20	=	=	SYM
ejpam-1188	96	21	φ	φ	PROPN
ejpam-1188	96	22	n	n	PROPN
ejpam-1188	96	23	j	j	PROPN
ejpam-1188	96	24	(	(	PUNCT
ejpam-1188	96	25	1−λ+λφ	1−λ+λφ	NUM
ejpam-1188	96	26	j	j	NOUN
ejpam-1188	96	27	)	)	PUNCT
ejpam-1188	96	28	(	(	PUNCT
ejpam-1188	96	29	j	j	PROPN
ejpam-1188	96	30	∈	∈	PROPN
ejpam-1188	96	31	n2	n2	PROPN
ejpam-1188	96	32	)	)	PUNCT
ejpam-1188	96	33	.	.	PUNCT
ejpam-1188	97	1	(	(	PUNCT
ejpam-1188	97	2	5	5	NUM
ejpam-1188	97	3	)	)	PUNCT
ejpam-1188	97	4	from	from	ADP
ejpam-1188	97	5	definition	definition	NOUN
ejpam-1188	97	6	1	1	NUM
ejpam-1188	97	7	,	,	PUNCT
ejpam-1188	97	8	we	we	PRON
ejpam-1188	97	9	thus	thus	ADV
ejpam-1188	97	10	have	have	VERB
ejpam-1188	97	11	1	1	NUM
ejpam-1188	97	12	+	+	SYM
ejpam-1188	97	13	1	1	NUM
ejpam-1188	97	14	b	b	NOUN
ejpam-1188	97	15			NOUN
ejpam-1188	97	16			X
ejpam-1188	97	17	z[f	z[f	X
ejpam-1188	97	18	n	n	PRON
ejpam-1188	97	19	λ	λ	PROPN
ejpam-1188	97	20	,	,	PUNCT
ejpam-1188	97	21	α	α	NOUN
ejpam-1188	97	22	,	,	PUNCT
ejpam-1188	97	23	δ(z	δ(z	NOUN
ejpam-1188	97	24	)	)	PUNCT
ejpam-1188	97	25	]	]	PUNCT
ejpam-1188	98	1	′	′	NUM
ejpam-1188	98	2	f	f	PROPN
ejpam-1188	98	3	n	n	PROPN
ejpam-1188	98	4	λ	λ	PROPN
ejpam-1188	98	5	,	,	PUNCT
ejpam-1188	98	6	α	α	NOUN
ejpam-1188	98	7	,	,	PUNCT
ejpam-1188	98	8	δ(z	δ(z	NOUN
ejpam-1188	98	9	)	)	PUNCT
ejpam-1188	98	10	−	−	NOUN
ejpam-1188	98	11	1	1	NUM
ejpam-1188	98	12			PROPN
ejpam-1188	98	13			PROPN
ejpam-1188	98	14	∈	∈	NOUN
ejpam-1188	98	15	g(u	g(u	NOUN
ejpam-1188	98	16	)	)	PUNCT
ejpam-1188	98	17	.	.	PUNCT
ejpam-1188	99	1	by	by	ADP
ejpam-1188	99	2	setting	set	VERB
ejpam-1188	99	3	p(z	p(z	NOUN
ejpam-1188	99	4	)	)	PUNCT
ejpam-1188	99	5	=	=	PUNCT
ejpam-1188	99	6	1	1	NUM
ejpam-1188	99	7	+	+	SYM
ejpam-1188	99	8	1	1	NUM
ejpam-1188	99	9	b	b	NOUN
ejpam-1188	99	10			NOUN
ejpam-1188	99	11			X
ejpam-1188	99	12	z[f	z[f	X
ejpam-1188	99	13	n	n	PRON
ejpam-1188	99	14	λ	λ	PROPN
ejpam-1188	99	15	,	,	PUNCT
ejpam-1188	99	16	α	α	NOUN
ejpam-1188	99	17	,	,	PUNCT
ejpam-1188	99	18	δ(z	δ(z	NOUN
ejpam-1188	99	19	)	)	PUNCT
ejpam-1188	99	20	]	]	PUNCT
ejpam-1188	99	21	′	′	NUM
ejpam-1188	99	22	f	f	PROPN
ejpam-1188	99	23	n	n	PROPN
ejpam-1188	99	24	λ	λ	PROPN
ejpam-1188	99	25	,	,	PUNCT
ejpam-1188	99	26	α	α	NOUN
ejpam-1188	99	27	,	,	PUNCT
ejpam-1188	99	28	δ(z	δ(z	NOUN
ejpam-1188	99	29	)	)	PUNCT
ejpam-1188	99	30	−	−	NOUN
ejpam-1188	99	31	1	1	NUM
ejpam-1188	99	32			PROPN
ejpam-1188	99	33			PROPN
ejpam-1188	99	34	,	,	PUNCT
ejpam-1188	99	35	(	(	PUNCT
ejpam-1188	99	36	6	6	NUM
ejpam-1188	99	37	)	)	PUNCT
ejpam-1188	99	38	l.	l.	PROPN
ejpam-1188	99	39	zhou	zhou	PROPN
ejpam-1188	99	40	,	,	PUNCT
ejpam-1188	99	41	q	q	PROPN
ejpam-1188	99	42	-	-	NOUN
ejpam-1188	99	43	h	h	NOUN
ejpam-1188	99	44	xu	xu	PROPN
ejpam-1188	99	45	/	/	SYM
ejpam-1188	99	46	eur	eur	PROPN
ejpam-1188	99	47	.	.	PUNCT
ejpam-1188	100	1	j.	j.	PROPN
ejpam-1188	100	2	pure	pure	PROPN
ejpam-1188	100	3	appl	appl	PROPN
ejpam-1188	100	4	.	.	PROPN
ejpam-1188	100	5	math	math	PROPN
ejpam-1188	100	6	,	,	PUNCT
ejpam-1188	100	7	6	6	NUM
ejpam-1188	100	8	(	(	PUNCT
ejpam-1188	100	9	2013	2013	NUM
ejpam-1188	100	10	)	)	PUNCT
ejpam-1188	100	11	,	,	PUNCT
ejpam-1188	100	12	460	460	NUM
ejpam-1188	100	13	-	-	SYM
ejpam-1188	100	14	468	468	NUM
ejpam-1188	100	15	465	465	NUM
ejpam-1188	100	16	we	we	PRON
ejpam-1188	100	17	also	also	ADV
ejpam-1188	100	18	deduce	deduce	VERB
ejpam-1188	100	19	that	that	PRON
ejpam-1188	100	20	p(0	p(0	NOUN
ejpam-1188	100	21	)	)	PUNCT
ejpam-1188	100	22	=	=	SYM
ejpam-1188	100	23	g(0	g(0	PROPN
ejpam-1188	100	24	)	)	PUNCT
ejpam-1188	100	25	=	=	SYM
ejpam-1188	100	26	1andp(z	1andp(z	NUM
ejpam-1188	100	27	)	)	PUNCT
ejpam-1188	100	28	∈	∈	PROPN
ejpam-1188	100	29	g(u	g(u	PROPN
ejpam-1188	100	30	)	)	PUNCT
ejpam-1188	100	31	(	(	PUNCT
ejpam-1188	100	32	z	z	NOUN
ejpam-1188	100	33	∈	∈	PROPN
ejpam-1188	100	34	u	u	NOUN
ejpam-1188	100	35	)	)	PUNCT
ejpam-1188	100	36	.	.	PUNCT
ejpam-1188	101	1	therefore	therefore	ADV
ejpam-1188	101	2	,	,	PUNCT
ejpam-1188	101	3	we	we	PRON
ejpam-1188	101	4	have	have	VERB
ejpam-1188	101	5	p(z)≺	p(z)≺	VERB
ejpam-1188	101	6	g(z	g(z	PROPN
ejpam-1188	101	7	)	)	PUNCT
ejpam-1188	101	8	(	(	PUNCT
ejpam-1188	101	9	z	z	NOUN
ejpam-1188	101	10	∈	∈	PROPN
ejpam-1188	101	11	u	u	NOUN
ejpam-1188	101	12	)	)	PUNCT
ejpam-1188	101	13	.	.	PUNCT
ejpam-1188	102	1	according	accord	VERB
ejpam-1188	102	2	to	to	ADP
ejpam-1188	102	3	lemma	lemma	PROPN
ejpam-1188	102	4	2	2	NUM
ejpam-1188	102	5	,	,	PUNCT
ejpam-1188	102	6	we	we	PRON
ejpam-1188	102	7	obtain	obtain	VERB
ejpam-1188	102	8	|pm|=	|pm|=	ADP
ejpam-1188	102	9	�	�	PROPN
ejpam-1188	102	10	�	�	PROPN
ejpam-1188	102	11	�	�	PROPN
ejpam-1188	102	12	�	�	PROPN
ejpam-1188	102	13	�	�	PROPN
ejpam-1188	102	14	p(m)(0	p(m)(0	NUM
ejpam-1188	102	15	)	)	PUNCT
ejpam-1188	102	16	m	m	PROPN
ejpam-1188	102	17	!	!	PUNCT
ejpam-1188	102	18	�	�	PROPN
ejpam-1188	102	19	�	�	PROPN
ejpam-1188	102	20	�	�	PROPN
ejpam-1188	102	21	�	�	PROPN
ejpam-1188	102	22	�	�	PROPN
ejpam-1188	102	23	≤	≤	PROPN
ejpam-1188	102	24	|g	|g	VERB
ejpam-1188	102	25	′(0)|=	′(0)|=	PROPN
ejpam-1188	102	26	|g1|	|g1|	PROPN
ejpam-1188	102	27	.	.	PUNCT
ejpam-1188	103	1	(	(	PUNCT
ejpam-1188	103	2	7	7	X
ejpam-1188	103	3	)	)	PUNCT
ejpam-1188	103	4	on	on	ADP
ejpam-1188	103	5	the	the	DET
ejpam-1188	103	6	other	other	ADJ
ejpam-1188	103	7	hand	hand	NOUN
ejpam-1188	103	8	,	,	PUNCT
ejpam-1188	103	9	we	we	PRON
ejpam-1188	103	10	find	find	VERB
ejpam-1188	103	11	from	from	ADP
ejpam-1188	103	12	(	(	PUNCT
ejpam-1188	103	13	6	6	NUM
ejpam-1188	103	14	)	)	PUNCT
ejpam-1188	103	15	that	that	SCONJ
ejpam-1188	103	16	z[f	z[f	PROPN
ejpam-1188	103	17	n	n	PRON
ejpam-1188	103	18	λ	λ	PROPN
ejpam-1188	103	19	,	,	PUNCT
ejpam-1188	103	20	α	α	NOUN
ejpam-1188	103	21	,	,	PUNCT
ejpam-1188	103	22	δ(z	δ(z	NOUN
ejpam-1188	103	23	)	)	PUNCT
ejpam-1188	103	24	]	]	PUNCT
ejpam-1188	103	25	′	′	NOUN
ejpam-1188	104	1	=	=	PUNCT
ejpam-1188	105	1	[	[	X
ejpam-1188	105	2	1	1	NUM
ejpam-1188	105	3	+	+	NUM
ejpam-1188	105	4	b(p(z)−	b(p(z)−	NOUN
ejpam-1188	105	5	1)]f	1)]f	NUM
ejpam-1188	105	6	n	n	PROPN
ejpam-1188	105	7	λ	λ	PROPN
ejpam-1188	105	8	,	,	PUNCT
ejpam-1188	105	9	α	α	NOUN
ejpam-1188	105	10	,	,	PUNCT
ejpam-1188	105	11	δ(z	δ(z	PROPN
ejpam-1188	105	12	)	)	PUNCT
ejpam-1188	105	13	(	(	PUNCT
ejpam-1188	105	14	z	z	NOUN
ejpam-1188	105	15	∈	∈	PROPN
ejpam-1188	105	16	u	u	NOUN
ejpam-1188	105	17	)	)	PUNCT
ejpam-1188	105	18	.	.	PUNCT
ejpam-1188	106	1	(	(	PUNCT
ejpam-1188	106	2	8)	8)	NUM
ejpam-1188	106	3	next	next	ADV
ejpam-1188	106	4	,	,	PUNCT
ejpam-1188	106	5	we	we	PRON
ejpam-1188	106	6	suppose	suppose	VERB
ejpam-1188	106	7	that	that	SCONJ
ejpam-1188	106	8	p(z	p(z	NOUN
ejpam-1188	106	9	)	)	PUNCT
ejpam-1188	106	10	=	=	SYM
ejpam-1188	107	1	1	1	NUM
ejpam-1188	107	2	+	+	CCONJ
ejpam-1188	107	3	p1z+	p1z+	PROPN
ejpam-1188	107	4	p2z2	p2z2	PROPN
ejpam-1188	107	5	+	+	NUM
ejpam-1188	107	6	.	.	PUNCT
ejpam-1188	107	7	.	.	PUNCT
ejpam-1188	107	8	.	.	PUNCT
ejpam-1188	108	1	(	(	PUNCT
ejpam-1188	108	2	z	z	NOUN
ejpam-1188	108	3	∈	∈	PROPN
ejpam-1188	108	4	u	u	NOUN
ejpam-1188	108	5	)	)	PUNCT
ejpam-1188	108	6	.	.	PUNCT
ejpam-1188	109	1	(	(	PUNCT
ejpam-1188	109	2	9	9	X
ejpam-1188	109	3	)	)	PUNCT
ejpam-1188	109	4	since	since	SCONJ
ejpam-1188	109	5	a1	a1	NOUN
ejpam-1188	109	6	=	=	SYM
ejpam-1188	109	7	1	1	NUM
ejpam-1188	109	8	,	,	PUNCT
ejpam-1188	109	9	in	in	ADP
ejpam-1188	109	10	view	view	NOUN
ejpam-1188	109	11	of	of	ADP
ejpam-1188	109	12	(	(	PUNCT
ejpam-1188	109	13	4	4	NUM
ejpam-1188	109	14	)	)	PUNCT
ejpam-1188	109	15	,	,	PUNCT
ejpam-1188	109	16	(	(	PUNCT
ejpam-1188	109	17	8)	8)	NUM
ejpam-1188	109	18	,	,	PUNCT
ejpam-1188	109	19	(	(	PUNCT
ejpam-1188	109	20	9	9	NUM
ejpam-1188	109	21	)	)	PUNCT
ejpam-1188	109	22	,	,	PUNCT
ejpam-1188	109	23	we	we	PRON
ejpam-1188	109	24	deduce	deduce	VERB
ejpam-1188	109	25	that	that	PRON
ejpam-1188	109	26	(	(	PUNCT
ejpam-1188	109	27	j−	j−	VERB
ejpam-1188	109	28	1)a	1)a	NUM
ejpam-1188	109	29	j	j	PROPN
ejpam-1188	110	1	=	=	PRON
ejpam-1188	110	2	(	(	PUNCT
ejpam-1188	110	3	p1a	p1a	VERB
ejpam-1188	110	4	j−1	j−1	PROPN
ejpam-1188	110	5	+	+	CCONJ
ejpam-1188	110	6	p2a	p2a	ADJ
ejpam-1188	110	7	j−2	j−2	PROPN
ejpam-1188	110	8	+	+	NUM
ejpam-1188	110	9	.	.	PUNCT
ejpam-1188	110	10	.	.	PUNCT
ejpam-1188	111	1	.+	.+	NOUN
ejpam-1188	112	1	p	p	PRON
ejpam-1188	112	2	j−1)b	j−1)b	PROPN
ejpam-1188	113	1	(	(	PUNCT
ejpam-1188	113	2	j	j	PROPN
ejpam-1188	113	3	∈	∈	PROPN
ejpam-1188	113	4	n2	n2	PROPN
ejpam-1188	113	5	)	)	PUNCT
ejpam-1188	113	6	.	.	PUNCT
ejpam-1188	114	1	(	(	PUNCT
ejpam-1188	114	2	10	10	NUM
ejpam-1188	114	3	)	)	PUNCT
ejpam-1188	114	4	in	in	ADP
ejpam-1188	114	5	view	view	NOUN
ejpam-1188	114	6	of	of	ADP
ejpam-1188	114	7	(	(	PUNCT
ejpam-1188	114	8	7	7	NUM
ejpam-1188	114	9	)	)	PUNCT
ejpam-1188	114	10	and	and	CCONJ
ejpam-1188	114	11	(	(	PUNCT
ejpam-1188	114	12	10	10	NUM
ejpam-1188	114	13	)	)	PUNCT
ejpam-1188	114	14	,	,	PUNCT
ejpam-1188	114	15	for	for	ADP
ejpam-1188	114	16	j	j	PROPN
ejpam-1188	114	17	=	=	SYM
ejpam-1188	114	18	2	2	NUM
ejpam-1188	114	19	,	,	PUNCT
ejpam-1188	114	20	3,4	3,4	NUM
ejpam-1188	114	21	,	,	PUNCT
ejpam-1188	114	22	we	we	PRON
ejpam-1188	114	23	obtain	obtain	VERB
ejpam-1188	114	24	|a2|	|a2|	NOUN
ejpam-1188	114	25	≤|g	≤|g	PROPN
ejpam-1188	114	26	′(0)||b|	′(0)||b|	NOUN
ejpam-1188	114	27	,	,	PUNCT
ejpam-1188	114	28	|a3|	|a3|	VERB
ejpam-1188	114	29	≤	≤	PROPN
ejpam-1188	114	30	|g	|g	VERB
ejpam-1188	114	31	′(0)||b|(1	′(0)||b|(1	PROPN
ejpam-1188	114	32	+	+	CCONJ
ejpam-1188	114	33	|g	|g	PROPN
ejpam-1188	114	34	′(0)||b|	′(0)||b|	NOUN
ejpam-1188	114	35	)	)	PUNCT
ejpam-1188	114	36	2	2	NUM
ejpam-1188	114	37	!	!	PUNCT
ejpam-1188	114	38	|a4|	|a4|	ADJ
ejpam-1188	114	39	≤	≤	PROPN
ejpam-1188	114	40	|g	|g	VERB
ejpam-1188	114	41	′(0)||b|(1	′(0)||b|(1	PROPN
ejpam-1188	114	42	+	+	CCONJ
ejpam-1188	114	43	|g	|g	PROPN
ejpam-1188	114	44	′(0)||b|)(2	′(0)||b|)(2	NOUN
ejpam-1188	114	45	+	+	NUM
ejpam-1188	114	46	|g	|g	NOUN
ejpam-1188	114	47	′(0)||b|	′(0)||b|	NOUN
ejpam-1188	114	48	)	)	PUNCT
ejpam-1188	114	49	3	3	NUM
ejpam-1188	114	50	!	!	NUM
ejpam-1188	114	51	,	,	PUNCT
ejpam-1188	114	52	respectively	respectively	ADV
ejpam-1188	114	53	.	.	PUNCT
ejpam-1188	115	1	also	also	ADV
ejpam-1188	115	2	,	,	PUNCT
ejpam-1188	115	3	making	make	VERB
ejpam-1188	115	4	use	use	NOUN
ejpam-1188	115	5	of	of	ADP
ejpam-1188	115	6	the	the	DET
ejpam-1188	115	7	principle	principle	NOUN
ejpam-1188	115	8	of	of	ADP
ejpam-1188	115	9	mathematical	mathematical	ADJ
ejpam-1188	115	10	induction	induction	NOUN
ejpam-1188	115	11	,	,	PUNCT
ejpam-1188	115	12	we	we	PRON
ejpam-1188	115	13	can	can	AUX
ejpam-1188	115	14	obtain	obtain	VERB
ejpam-1188	115	15	|a	|a	PRON
ejpam-1188	115	16	j|	j|	PROPN
ejpam-1188	115	17	≤	≤	PROPN
ejpam-1188	115	18	j−2	j−2	PROPN
ejpam-1188	115	19	∏	∏	PROPN
ejpam-1188	115	20	k=0	k=0	PROPN
ejpam-1188	115	21	(	(	PUNCT
ejpam-1188	115	22	k+	k+	PUNCT
ejpam-1188	115	23	|g	|g	PROPN
ejpam-1188	115	24	′(0)||b|	′(0)||b|	NOUN
ejpam-1188	115	25	)	)	PUNCT
ejpam-1188	115	26	)	)	PUNCT
ejpam-1188	116	1	(	(	PUNCT
ejpam-1188	116	2	j−	j−	PROPN
ejpam-1188	116	3	1	1	NUM
ejpam-1188	116	4	)	)	PUNCT
ejpam-1188	116	5	!	!	PUNCT
ejpam-1188	117	1	(	(	PUNCT
ejpam-1188	117	2	j	j	PROPN
ejpam-1188	117	3	∈	∈	PROPN
ejpam-1188	117	4	n2	n2	PROPN
ejpam-1188	117	5	)	)	PUNCT
ejpam-1188	117	6	.	.	PUNCT
ejpam-1188	118	1	from	from	ADP
ejpam-1188	118	2	(	(	PUNCT
ejpam-1188	118	3	5	5	NUM
ejpam-1188	118	4	)	)	PUNCT
ejpam-1188	118	5	,	,	PUNCT
ejpam-1188	118	6	we	we	PRON
ejpam-1188	118	7	can	can	AUX
ejpam-1188	118	8	easily	easily	ADV
ejpam-1188	118	9	obtain	obtain	VERB
ejpam-1188	118	10	|a	|a	PRON
ejpam-1188	118	11	j|	j|	PROPN
ejpam-1188	118	12	≤	≤	PROPN
ejpam-1188	118	13	j−2	j−2	PROPN
ejpam-1188	118	14	∏	∏	PROPN
ejpam-1188	118	15	k=0	k=0	PROPN
ejpam-1188	118	16	(	(	PUNCT
ejpam-1188	118	17	k+	k+	PROPN
ejpam-1188	118	18	|g	|g	PROPN
ejpam-1188	118	19	′(0)||b|	′(0)||b|	NOUN
ejpam-1188	118	20	)	)	PUNCT
ejpam-1188	118	21	φn	φn	ADP
ejpam-1188	118	22	j	j	PROPN
ejpam-1188	119	1	[	[	X
ejpam-1188	119	2	1−λ+λφ	1−λ+λφ	NUM
ejpam-1188	119	3	j	j	X
ejpam-1188	119	4	]	]	X
ejpam-1188	119	5	(	(	PUNCT
ejpam-1188	119	6	j−	j−	PROPN
ejpam-1188	119	7	1	1	NUM
ejpam-1188	119	8	)	)	PUNCT
ejpam-1188	119	9	!	!	PUNCT
ejpam-1188	120	1	(	(	PUNCT
ejpam-1188	120	2	j	j	PROPN
ejpam-1188	120	3	∈	∈	PROPN
ejpam-1188	120	4	n2	n2	NOUN
ejpam-1188	120	5	)	)	PUNCT
ejpam-1188	120	6	,	,	PUNCT
ejpam-1188	120	7	as	as	SCONJ
ejpam-1188	120	8	asserted	assert	VERB
ejpam-1188	120	9	by	by	ADP
ejpam-1188	120	10	theorem	theorem	NOUN
ejpam-1188	120	11	1	1	NUM
ejpam-1188	120	12	.	.	PUNCT
ejpam-1188	121	1	this	this	PRON
ejpam-1188	121	2	completes	complete	VERB
ejpam-1188	121	3	the	the	DET
ejpam-1188	121	4	proof	proof	NOUN
ejpam-1188	121	5	of	of	ADP
ejpam-1188	121	6	theorem	theorem	NOUN
ejpam-1188	121	7	1	1	NUM
ejpam-1188	121	8	.	.	PUNCT
ejpam-1188	121	9	l.	l.	PROPN
ejpam-1188	121	10	zhou	zhou	PROPN
ejpam-1188	121	11	,	,	PUNCT
ejpam-1188	121	12	q	q	PROPN
ejpam-1188	121	13	-	-	NOUN
ejpam-1188	121	14	h	h	NOUN
ejpam-1188	121	15	xu	xu	PROPN
ejpam-1188	121	16	/	/	SYM
ejpam-1188	121	17	eur	eur	PROPN
ejpam-1188	121	18	.	.	PUNCT
ejpam-1188	122	1	j.	j.	PROPN
ejpam-1188	122	2	pure	pure	PROPN
ejpam-1188	122	3	appl	appl	PROPN
ejpam-1188	122	4	.	.	PROPN
ejpam-1188	122	5	math	math	PROPN
ejpam-1188	122	6	,	,	PUNCT
ejpam-1188	122	7	6	6	NUM
ejpam-1188	122	8	(	(	PUNCT
ejpam-1188	122	9	2013	2013	NUM
ejpam-1188	122	10	)	)	PUNCT
ejpam-1188	122	11	,	,	PUNCT
ejpam-1188	122	12	460	460	NUM
ejpam-1188	122	13	-	-	SYM
ejpam-1188	122	14	468	468	NUM
ejpam-1188	122	15	466	466	NUM
ejpam-1188	122	16	theorem	theorem	NOUN
ejpam-1188	122	17	2	2	NUM
ejpam-1188	122	18	.	.	PUNCT
ejpam-1188	123	1	let	let	VERB
ejpam-1188	123	2	the	the	DET
ejpam-1188	123	3	function	function	NOUN
ejpam-1188	123	4	f	f	PROPN
ejpam-1188	123	5	∈a	∈a	PROPN
ejpam-1188	123	6	be	be	AUX
ejpam-1188	123	7	given	give	VERB
ejpam-1188	123	8	by	by	ADP
ejpam-1188	123	9	(	(	PUNCT
ejpam-1188	123	10	1	1	NUM
ejpam-1188	123	11	)	)	PUNCT
ejpam-1188	123	12	.	.	PUNCT
ejpam-1188	124	1	if	if	SCONJ
ejpam-1188	124	2	f	f	PROPN
ejpam-1188	124	3	∈hg(n	∈hg(n	NOUN
ejpam-1188	124	4	,	,	PUNCT
ejpam-1188	124	5	b	b	PROPN
ejpam-1188	124	6	,	,	PUNCT
ejpam-1188	124	7	λ	λ	PROPN
ejpam-1188	124	8	,	,	PUNCT
ejpam-1188	124	9	α	α	NOUN
ejpam-1188	124	10	,	,	PUNCT
ejpam-1188	124	11	δ	δ	PROPN
ejpam-1188	124	12	;	;	PUNCT
ejpam-1188	124	13	u	u	NOUN
ejpam-1188	124	14	)	)	PUNCT
ejpam-1188	124	15	,	,	PUNCT
ejpam-1188	124	16	then	then	ADV
ejpam-1188	124	17	|a	|a	VERB
ejpam-1188	124	18	j|	j|	PROPN
ejpam-1188	124	19	≤	≤	PROPN
ejpam-1188	124	20	(	(	PUNCT
ejpam-1188	124	21	1	1	NUM
ejpam-1188	124	22	+	+	NOUN
ejpam-1188	124	23	u)(2	u)(2	NUM
ejpam-1188	124	24	+	+	SYM
ejpam-1188	124	25	u	u	NOUN
ejpam-1188	124	26	)	)	PUNCT
ejpam-1188	124	27	j−2	j−2	PROPN
ejpam-1188	124	28	∏	∏	PROPN
ejpam-1188	124	29	k=0	k=0	PROPN
ejpam-1188	124	30	(	(	PUNCT
ejpam-1188	124	31	k+	k+	PUNCT
ejpam-1188	124	32	|g	|g	PROPN
ejpam-1188	124	33	′(0)||b|	′(0)||b|	PROPN
ejpam-1188	124	34	)	)	PUNCT
ejpam-1188	124	35	(	(	PUNCT
ejpam-1188	124	36	j+	j+	NUM
ejpam-1188	124	37	u	u	NOUN
ejpam-1188	124	38	)	)	PUNCT
ejpam-1188	124	39	(	(	PUNCT
ejpam-1188	124	40	j+	j+	NUM
ejpam-1188	124	41	u+	u+	NUM
ejpam-1188	125	1	1)φn	1)φn	NUM
ejpam-1188	125	2	j	j	PROPN
ejpam-1188	126	1	[	[	X
ejpam-1188	126	2	1−λ+λφ	1−λ+λφ	NUM
ejpam-1188	126	3	j	j	X
ejpam-1188	126	4	]	]	X
ejpam-1188	126	5	(	(	PUNCT
ejpam-1188	126	6	j−	j−	PROPN
ejpam-1188	126	7	1	1	NUM
ejpam-1188	126	8	)	)	PUNCT
ejpam-1188	126	9	!	!	PUNCT
ejpam-1188	127	1	(	(	PUNCT
ejpam-1188	127	2	j	j	PROPN
ejpam-1188	127	3	∈	∈	PROPN
ejpam-1188	127	4	n2	n2	NOUN
ejpam-1188	127	5	;	;	PUNCT
ejpam-1188	127	6	u	u	PROPN
ejpam-1188	127	7	∈	∈	PROPN
ejpam-1188	127	8	r\(−∞,−1	r\(−∞,−1	PROPN
ejpam-1188	127	9	]	]	PUNCT
ejpam-1188	127	10	)	)	PUNCT
ejpam-1188	127	11	.	.	PUNCT
ejpam-1188	128	1	proof	proof	NOUN
ejpam-1188	128	2	.	.	PUNCT
ejpam-1188	129	1	let	let	VERB
ejpam-1188	129	2	the	the	DET
ejpam-1188	129	3	function	function	NOUN
ejpam-1188	129	4	f	f	PROPN
ejpam-1188	129	5	∈a	∈a	PROPN
ejpam-1188	129	6	be	be	AUX
ejpam-1188	129	7	given	give	VERB
ejpam-1188	129	8	by	by	ADP
ejpam-1188	129	9	(	(	PUNCT
ejpam-1188	129	10	1	1	NUM
ejpam-1188	129	11	)	)	PUNCT
ejpam-1188	129	12	.	.	PUNCT
ejpam-1188	130	1	also	also	ADV
ejpam-1188	130	2	let	let	VERB
ejpam-1188	130	3	h(z	h(z	NOUN
ejpam-1188	130	4	)	)	PUNCT
ejpam-1188	130	5	=	=	PUNCT
ejpam-1188	131	1	z+	z+	NUM
ejpam-1188	131	2	∞	∞	PROPN
ejpam-1188	131	3	∑	∑	PROPN
ejpam-1188	131	4	j=2	j=2	PROPN
ejpam-1188	131	5	h	h	NOUN
ejpam-1188	131	6	jz	jz	PROPN
ejpam-1188	131	7	j	j	PROPN
ejpam-1188	131	8	∈hg(n	∈hg(n	PROPN
ejpam-1188	131	9	,	,	PUNCT
ejpam-1188	131	10	b	b	PROPN
ejpam-1188	131	11	,	,	PUNCT
ejpam-1188	131	12	λ	λ	PROPN
ejpam-1188	131	13	,	,	PUNCT
ejpam-1188	131	14	α	α	NOUN
ejpam-1188	131	15	,	,	PUNCT
ejpam-1188	131	16	δ	δ	PROPN
ejpam-1188	131	17	)	)	PUNCT
ejpam-1188	131	18	.	.	PUNCT
ejpam-1188	132	1	thus	thus	ADV
ejpam-1188	132	2	,	,	PUNCT
ejpam-1188	132	3	from	from	ADP
ejpam-1188	132	4	(	(	PUNCT
ejpam-1188	132	5	3	3	NUM
ejpam-1188	132	6	)	)	PUNCT
ejpam-1188	132	7	,	,	PUNCT
ejpam-1188	132	8	we	we	PRON
ejpam-1188	132	9	deduce	deduce	VERB
ejpam-1188	132	10	that	that	SCONJ
ejpam-1188	132	11	a	a	DET
ejpam-1188	132	12	j	j	NOUN
ejpam-1188	132	13	=	=	PUNCT
ejpam-1188	132	14	(	(	PUNCT
ejpam-1188	132	15	1	1	NUM
ejpam-1188	132	16	+	+	NOUN
ejpam-1188	132	17	u)(2	u)(2	NUM
ejpam-1188	132	18	+	+	NOUN
ejpam-1188	132	19	u)h	u)h	ADJ
ejpam-1188	132	20	j	j	PROPN
ejpam-1188	132	21	(	(	PUNCT
ejpam-1188	132	22	j+	j+	PROPN
ejpam-1188	132	23	u	u	NOUN
ejpam-1188	132	24	)	)	PUNCT
ejpam-1188	132	25	(	(	PUNCT
ejpam-1188	132	26	j+	j+	X
ejpam-1188	132	27	u+	u+	NUM
ejpam-1188	132	28	1	1	NUM
ejpam-1188	132	29	)	)	PUNCT
ejpam-1188	132	30	(	(	PUNCT
ejpam-1188	132	31	j	j	PROPN
ejpam-1188	132	32	∈	∈	PROPN
ejpam-1188	132	33	n2	n2	NOUN
ejpam-1188	132	34	;	;	PUNCT
ejpam-1188	132	35	u	u	PROPN
ejpam-1188	132	36	∈	∈	PROPN
ejpam-1188	132	37	r\(−∞,−1	r\(−∞,−1	PROPN
ejpam-1188	132	38	]	]	PUNCT
ejpam-1188	132	39	)	)	PUNCT
ejpam-1188	132	40	.	.	PUNCT
ejpam-1188	133	1	using	use	VERB
ejpam-1188	133	2	theorem	theorem	NOUN
ejpam-1188	133	3	1	1	NUM
ejpam-1188	133	4	,	,	PUNCT
ejpam-1188	133	5	we	we	PRON
ejpam-1188	133	6	obtain	obtain	VERB
ejpam-1188	133	7	|a	|a	VERB
ejpam-1188	133	8	j|	j|	PROPN
ejpam-1188	133	9	≤	≤	PROPN
ejpam-1188	133	10	(	(	PUNCT
ejpam-1188	133	11	1	1	NUM
ejpam-1188	133	12	+	+	NOUN
ejpam-1188	133	13	u)(2	u)(2	NUM
ejpam-1188	133	14	+	+	SYM
ejpam-1188	133	15	u	u	NOUN
ejpam-1188	133	16	)	)	PUNCT
ejpam-1188	133	17	j−2	j−2	PROPN
ejpam-1188	133	18	∏	∏	PROPN
ejpam-1188	133	19	k=0	k=0	PROPN
ejpam-1188	133	20	(	(	PUNCT
ejpam-1188	133	21	k+	k+	PUNCT
ejpam-1188	133	22	|g	|g	PROPN
ejpam-1188	133	23	′(0)||b|	′(0)||b|	PROPN
ejpam-1188	133	24	)	)	PUNCT
ejpam-1188	133	25	(	(	PUNCT
ejpam-1188	133	26	j+	j+	NUM
ejpam-1188	133	27	u	u	NOUN
ejpam-1188	133	28	)	)	PUNCT
ejpam-1188	133	29	(	(	PUNCT
ejpam-1188	133	30	j+	j+	NUM
ejpam-1188	133	31	u+	u+	NUM
ejpam-1188	134	1	1)φn	1)φn	NUM
ejpam-1188	134	2	j	j	PROPN
ejpam-1188	135	1	[	[	X
ejpam-1188	135	2	1−λ+λφ	1−λ+λφ	NUM
ejpam-1188	135	3	j	j	X
ejpam-1188	135	4	]	]	X
ejpam-1188	135	5	(	(	PUNCT
ejpam-1188	135	6	j−	j−	PROPN
ejpam-1188	135	7	1	1	NUM
ejpam-1188	135	8	)	)	PUNCT
ejpam-1188	135	9	!	!	PUNCT
ejpam-1188	136	1	(	(	PUNCT
ejpam-1188	136	2	j	j	PROPN
ejpam-1188	136	3	∈	∈	PROPN
ejpam-1188	136	4	n2	n2	NOUN
ejpam-1188	136	5	;	;	PUNCT
ejpam-1188	136	6	u	u	PROPN
ejpam-1188	136	7	∈	∈	PROPN
ejpam-1188	136	8	r\(−∞,−1	r\(−∞,−1	PROPN
ejpam-1188	136	9	]	]	PUNCT
ejpam-1188	136	10	)	)	PUNCT
ejpam-1188	136	11	,	,	PUNCT
ejpam-1188	136	12	as	as	SCONJ
ejpam-1188	136	13	claimed	claim	VERB
ejpam-1188	136	14	in	in	ADP
ejpam-1188	136	15	theorem	theorem	NOUN
ejpam-1188	136	16	2	2	NUM
ejpam-1188	136	17	.	.	PUNCT
ejpam-1188	137	1	this	this	PRON
ejpam-1188	137	2	completes	complete	VERB
ejpam-1188	137	3	the	the	DET
ejpam-1188	137	4	proof	proof	NOUN
ejpam-1188	137	5	of	of	ADP
ejpam-1188	137	6	theorem	theorem	NOUN
ejpam-1188	137	7	2	2	NUM
ejpam-1188	137	8	.	.	NOUN
ejpam-1188	137	9	3	3	NUM
ejpam-1188	137	10	.	.	NOUN
ejpam-1188	137	11	corollaries	corollary	NOUN
ejpam-1188	137	12	and	and	CCONJ
ejpam-1188	137	13	consequences	consequence	NOUN
ejpam-1188	137	14	in	in	ADP
ejpam-1188	137	15	view	view	NOUN
ejpam-1188	137	16	of	of	ADP
ejpam-1188	137	17	remark	remark	NOUN
ejpam-1188	137	18	2	2	NUM
ejpam-1188	137	19	,	,	PUNCT
ejpam-1188	137	20	if	if	SCONJ
ejpam-1188	137	21	we	we	PRON
ejpam-1188	137	22	set	set	VERB
ejpam-1188	137	23	g(z	g(z	PROPN
ejpam-1188	137	24	)	)	PUNCT
ejpam-1188	137	25	=	=	SYM
ejpam-1188	138	1	1	1	NUM
ejpam-1188	138	2	+	+	CCONJ
ejpam-1188	138	3	(	(	PUNCT
ejpam-1188	138	4	1−	1−	NUM
ejpam-1188	138	5	2β)z	2β)z	NUM
ejpam-1188	138	6	1−	1−	NUM
ejpam-1188	138	7	z	z	NOUN
ejpam-1188	138	8	(	(	PUNCT
ejpam-1188	138	9	0≤	0≤	NUM
ejpam-1188	138	10	β	β	X
ejpam-1188	138	11	<	<	X
ejpam-1188	138	12	1	1	NUM
ejpam-1188	138	13	;	;	PUNCT
ejpam-1188	138	14	z	z	PROPN
ejpam-1188	138	15	∈	∈	PROPN
ejpam-1188	138	16	u	u	NOUN
ejpam-1188	138	17	)	)	PUNCT
ejpam-1188	138	18	,	,	PUNCT
ejpam-1188	138	19	α=	α=	NOUN
ejpam-1188	138	20	1	1	NUM
ejpam-1188	138	21	,	,	PUNCT
ejpam-1188	138	22	and	and	CCONJ
ejpam-1188	138	23	δ	δ	PROPN
ejpam-1188	138	24	=	=	NOUN
ejpam-1188	138	25	0	0	NUM
ejpam-1188	138	26	in	in	ADP
ejpam-1188	138	27	theorems	theorem	NOUN
ejpam-1188	138	28	1	1	NUM
ejpam-1188	138	29	and	and	CCONJ
ejpam-1188	138	30	2	2	NUM
ejpam-1188	138	31	,	,	PUNCT
ejpam-1188	138	32	respectively	respectively	ADV
ejpam-1188	138	33	,	,	PUNCT
ejpam-1188	138	34	we	we	PRON
ejpam-1188	138	35	can	can	AUX
ejpam-1188	138	36	easily	easily	ADV
ejpam-1188	138	37	deduce	deduce	VERB
ejpam-1188	138	38	the	the	DET
ejpam-1188	138	39	following	follow	VERB
ejpam-1188	138	40	two	two	NUM
ejpam-1188	138	41	corollaries	corollary	NOUN
ejpam-1188	138	42	,	,	PUNCT
ejpam-1188	138	43	which	which	PRON
ejpam-1188	138	44	we	we	PRON
ejpam-1188	138	45	merely	merely	ADV
ejpam-1188	138	46	state	state	VERB
ejpam-1188	138	47	here	here	ADV
ejpam-1188	138	48	without	without	ADP
ejpam-1188	138	49	proofs	proof	NOUN
ejpam-1188	138	50	.	.	PUNCT
ejpam-1188	139	1	corollary	corollary	ADJ
ejpam-1188	139	2	1	1	NUM
ejpam-1188	139	3	.	.	PUNCT
ejpam-1188	140	1	let	let	VERB
ejpam-1188	140	2	the	the	DET
ejpam-1188	140	3	function	function	NOUN
ejpam-1188	140	4	∈a	∈a	NOUN
ejpam-1188	140	5	be	be	AUX
ejpam-1188	140	6	given	give	VERB
ejpam-1188	140	7	by	by	ADP
ejpam-1188	140	8	(	(	PUNCT
ejpam-1188	140	9	1	1	NUM
ejpam-1188	140	10	)	)	PUNCT
ejpam-1188	140	11	.	.	PUNCT
ejpam-1188	141	1	if	if	SCONJ
ejpam-1188	141	2	f	f	PROPN
ejpam-1188	141	3	∈b(n	∈b(n	PROPN
ejpam-1188	141	4	,	,	PUNCT
ejpam-1188	141	5	λ	λ	PROPN
ejpam-1188	141	6	,	,	PUNCT
ejpam-1188	141	7	β	β	X
ejpam-1188	141	8	,	,	PUNCT
ejpam-1188	141	9	b	b	NOUN
ejpam-1188	141	10	)	)	PUNCT
ejpam-1188	141	11	,	,	PUNCT
ejpam-1188	141	12	then	then	ADV
ejpam-1188	141	13	|a	|a	VERB
ejpam-1188	141	14	j|	j|	PROPN
ejpam-1188	141	15	≤	≤	PROPN
ejpam-1188	141	16	j−2	j−2	PROPN
ejpam-1188	141	17	∏	∏	PROPN
ejpam-1188	141	18	k=0	k=0	PROPN
ejpam-1188	142	1	[	[	X
ejpam-1188	142	2	k+	k+	NOUN
ejpam-1188	142	3	2|b|(1−	2|b|(1−	NUM
ejpam-1188	142	4	β	β	NOUN
ejpam-1188	142	5	)	)	PUNCT
ejpam-1188	142	6	]	]	PUNCT
ejpam-1188	142	7	jn(1−λ+λ	jn(1−λ+λ	PROPN
ejpam-1188	142	8	j	j	PROPN
ejpam-1188	142	9	)	)	PUNCT
ejpam-1188	142	10	(	(	PUNCT
ejpam-1188	142	11	j−	j−	PROPN
ejpam-1188	142	12	1	1	NUM
ejpam-1188	142	13	)	)	PUNCT
ejpam-1188	142	14	!	!	PUNCT
ejpam-1188	143	1	(	(	PUNCT
ejpam-1188	143	2	j	j	PROPN
ejpam-1188	143	3	∈	∈	PROPN
ejpam-1188	143	4	n2	n2	NOUN
ejpam-1188	143	5	)	)	PUNCT
ejpam-1188	143	6	.	.	PUNCT
ejpam-1188	144	1	corollary	corollary	ADJ
ejpam-1188	144	2	2	2	NUM
ejpam-1188	144	3	.	.	PUNCT
ejpam-1188	145	1	let	let	VERB
ejpam-1188	145	2	the	the	DET
ejpam-1188	145	3	function	function	NOUN
ejpam-1188	145	4	f	f	PROPN
ejpam-1188	145	5	∈a	∈a	PROPN
ejpam-1188	145	6	be	be	AUX
ejpam-1188	145	7	given	give	VERB
ejpam-1188	145	8	by	by	ADP
ejpam-1188	145	9	(	(	PUNCT
ejpam-1188	145	10	1	1	NUM
ejpam-1188	145	11	)	)	PUNCT
ejpam-1188	145	12	.	.	PUNCT
ejpam-1188	146	1	if	if	SCONJ
ejpam-1188	146	2	f	f	PROPN
ejpam-1188	146	3	∈	∈	PROPN
ejpam-1188	146	4	t	t	PROPN
ejpam-1188	146	5	(	(	PUNCT
ejpam-1188	146	6	n	n	CCONJ
ejpam-1188	146	7	,	,	PUNCT
ejpam-1188	146	8	λ	λ	PROPN
ejpam-1188	146	9	,	,	PUNCT
ejpam-1188	146	10	β	β	X
ejpam-1188	146	11	,	,	PUNCT
ejpam-1188	146	12	b	b	X
ejpam-1188	146	13	;	;	PUNCT
ejpam-1188	146	14	u	u	NOUN
ejpam-1188	146	15	)	)	PUNCT
ejpam-1188	146	16	,	,	PUNCT
ejpam-1188	146	17	then	then	ADV
ejpam-1188	146	18	|a	|a	VERB
ejpam-1188	146	19	j|	j|	PROPN
ejpam-1188	146	20	≤	≤	PROPN
ejpam-1188	146	21	(	(	PUNCT
ejpam-1188	146	22	1	1	NUM
ejpam-1188	146	23	+	+	NOUN
ejpam-1188	146	24	u)(2	u)(2	NUM
ejpam-1188	146	25	+	+	SYM
ejpam-1188	146	26	u	u	NOUN
ejpam-1188	146	27	)	)	PUNCT
ejpam-1188	146	28	j−2	j−2	PROPN
ejpam-1188	146	29	∏	∏	PROPN
ejpam-1188	146	30	k=0	k=0	PROPN
ejpam-1188	147	1	[	[	X
ejpam-1188	147	2	k+	k+	X
ejpam-1188	147	3	2|b|(1−	2|b|(1−	NUM
ejpam-1188	147	4	βπ	βπ	NOUN
ejpam-1188	147	5	)	)	PUNCT
ejpam-1188	147	6	]	]	PUNCT
ejpam-1188	147	7	jn(1−λ+λ	jn(1−λ+λ	PROPN
ejpam-1188	147	8	j	j	PROPN
ejpam-1188	147	9	)	)	PUNCT
ejpam-1188	147	10	(	(	PUNCT
ejpam-1188	147	11	j−	j−	PROPN
ejpam-1188	147	12	1	1	NUM
ejpam-1188	147	13	)	)	PUNCT
ejpam-1188	147	14	!	!	PUNCT
ejpam-1188	148	1	(	(	PUNCT
ejpam-1188	148	2	j+	j+	NUM
ejpam-1188	148	3	u	u	NOUN
ejpam-1188	148	4	)	)	PUNCT
ejpam-1188	148	5	(	(	PUNCT
ejpam-1188	148	6	j+	j+	NUM
ejpam-1188	148	7	1	1	NUM
ejpam-1188	148	8	+	+	NUM
ejpam-1188	148	9	u	u	NOUN
ejpam-1188	148	10	)	)	PUNCT
ejpam-1188	148	11	(	(	PUNCT
ejpam-1188	148	12	j	j	PROPN
ejpam-1188	148	13	∈	∈	PROPN
ejpam-1188	148	14	n2	n2	NOUN
ejpam-1188	148	15	;	;	PUNCT
ejpam-1188	148	16	u	u	PROPN
ejpam-1188	148	17	∈	∈	PROPN
ejpam-1188	148	18	r\(−∞,−1	r\(−∞,−1	PROPN
ejpam-1188	148	19	]	]	PUNCT
ejpam-1188	148	20	)	)	PUNCT
ejpam-1188	148	21	.	.	PUNCT
ejpam-1188	149	1	remark	remark	PROPN
ejpam-1188	149	2	4	4	NUM
ejpam-1188	149	3	.	.	PUNCT
ejpam-1188	149	4	corollaries	corollary	NOUN
ejpam-1188	149	5	1	1	NUM
ejpam-1188	149	6	and	and	CCONJ
ejpam-1188	149	7	2	2	NUM
ejpam-1188	149	8	were	be	AUX
ejpam-1188	149	9	obtained	obtain	VERB
ejpam-1188	149	10	by	by	ADP
ejpam-1188	149	11	deng	deng	PROPN
ejpam-1188	150	1	[	[	X
ejpam-1188	150	2	9	9	NUM
ejpam-1188	150	3	]	]	PUNCT
ejpam-1188	150	4	.	.	PUNCT
ejpam-1188	151	1	however	however	ADV
ejpam-1188	151	2	,	,	PUNCT
ejpam-1188	151	3	by	by	ADP
ejpam-1188	151	4	use	use	NOUN
ejpam-1188	151	5	of	of	ADP
ejpam-1188	151	6	theorems	theorem	NOUN
ejpam-1188	151	7	1	1	NUM
ejpam-1188	151	8	and	and	CCONJ
ejpam-1188	151	9	2	2	NUM
ejpam-1188	151	10	,	,	PUNCT
ejpam-1188	151	11	we	we	PRON
ejpam-1188	151	12	are	be	AUX
ejpam-1188	151	13	able	able	ADJ
ejpam-1188	151	14	to	to	PART
ejpam-1188	151	15	derive	derive	VERB
ejpam-1188	151	16	these	these	DET
ejpam-1188	151	17	results	result	NOUN
ejpam-1188	151	18	much	much	ADV
ejpam-1188	151	19	more	more	ADV
ejpam-1188	151	20	easily	easily	ADV
ejpam-1188	151	21	.	.	PUNCT
ejpam-1188	152	1	references	reference	NOUN
ejpam-1188	152	2	467	467	NUM
ejpam-1188	152	3	acknowledgements	acknowledgement	NOUN
ejpam-1188	152	4	this	this	DET
ejpam-1188	152	5	work	work	NOUN
ejpam-1188	152	6	was	be	AUX
ejpam-1188	152	7	supported	support	VERB
ejpam-1188	152	8	by	by	ADP
ejpam-1188	152	9	nnsf	nnsf	PROPN
ejpam-1188	152	10	of	of	ADP
ejpam-1188	152	11	china	china	PROPN
ejpam-1188	152	12	(	(	PUNCT
ejpam-1188	152	13	grant	grant	PROPN
ejpam-1188	152	14	nos	nos	PROPN
ejpam-1188	152	15	.	.	PROPN
ejpam-1188	152	16	11261022	11261022	NUM
ejpam-1188	152	17	,	,	PUNCT
ejpam-1188	152	18	11061015	11061015	NUM
ejpam-1188	152	19	)	)	PUNCT
ejpam-1188	152	20	,	,	PUNCT
ejpam-1188	152	21	the	the	DET
ejpam-1188	152	22	jiangxi	jiangxi	PROPN
ejpam-1188	152	23	provincial	provincial	ADJ
ejpam-1188	152	24	natural	natural	ADJ
ejpam-1188	152	25	science	science	PROPN
ejpam-1188	152	26	foundation	foundation	PROPN
ejpam-1188	152	27	of	of	ADP
ejpam-1188	152	28	china	china	PROPN
ejpam-1188	152	29	(	(	PUNCT
ejpam-1188	152	30	grant	grant	VERB
ejpam-1188	152	31	no	no	INTJ
ejpam-1188	152	32	.	.	NOUN
ejpam-1188	152	33	20132bab201004	20132bab201004	NUM
ejpam-1188	152	34	)	)	PUNCT
ejpam-1188	152	35	,	,	PUNCT
ejpam-1188	152	36	and	and	CCONJ
ejpam-1188	152	37	the	the	DET
ejpam-1188	152	38	natural	natural	ADJ
ejpam-1188	152	39	science	science	NOUN
ejpam-1188	152	40	foundation	foundation	NOUN
ejpam-1188	152	41	of	of	ADP
ejpam-1188	152	42	department	department	PROPN
ejpam-1188	152	43	of	of	ADP
ejpam-1188	152	44	education	education	NOUN
ejpam-1188	152	45	of	of	ADP
ejpam-1188	152	46	jiangxi	jiangxi	PROPN
ejpam-1188	152	47	province	province	PROPN
ejpam-1188	152	48	,	,	PUNCT
ejpam-1188	152	49	china	china	PROPN
ejpam-1188	152	50	(	(	PUNCT
ejpam-1188	152	51	grant	grant	VERB
ejpam-1188	152	52	no	no	PROPN
ejpam-1188	152	53	.	.	PROPN
ejpam-1188	152	54	gjj12177	gjj12177	PROPN
ejpam-1188	152	55	)	)	PUNCT
ejpam-1188	152	56	.	.	PUNCT
ejpam-1188	153	1	references	reference	NOUN
ejpam-1188	153	2	[	[	X
ejpam-1188	153	3	1	1	NUM
ejpam-1188	153	4	]	]	PUNCT
ejpam-1188	153	5	o	o	X
ejpam-1188	153	6	altintaş	altintaş	PROPN
ejpam-1188	153	7	,	,	PUNCT
ejpam-1188	153	8	h	h	PROPN
ejpam-1188	153	9	irmak	irmak	PROPN
ejpam-1188	153	10	,	,	PUNCT
ejpam-1188	153	11	s	s	VERB
ejpam-1188	153	12	owa	owa	PROPN
ejpam-1188	153	13	,	,	PUNCT
ejpam-1188	153	14	and	and	CCONJ
ejpam-1188	153	15	h	h	PROPN
ejpam-1188	153	16	m	m	PROPN
ejpam-1188	153	17	srivastava	srivastava	PROPN
ejpam-1188	153	18	.	.	PUNCT
ejpam-1188	154	1	coefficients	coefficient	NOUN
ejpam-1188	154	2	bounds	bound	VERB
ejpam-1188	154	3	for	for	ADP
ejpam-1188	154	4	some	some	DET
ejpam-1188	154	5	families	family	NOUN
ejpam-1188	154	6	of	of	ADP
ejpam-1188	154	7	starlike	starlike	NOUN
ejpam-1188	154	8	and	and	CCONJ
ejpam-1188	154	9	convex	convex	NOUN
ejpam-1188	154	10	functions	function	NOUN
ejpam-1188	154	11	of	of	ADP
ejpam-1188	154	12	complex	complex	ADJ
ejpam-1188	154	13	order	order	NOUN
ejpam-1188	154	14	.	.	PUNCT
ejpam-1188	155	1	applied	apply	VERB
ejpam-1188	155	2	mathematics	mathematics	NOUN
ejpam-1188	155	3	letters	letter	NOUN
ejpam-1188	155	4	.	.	PUNCT
ejpam-1188	156	1	20	20	NUM
ejpam-1188	156	2	:	:	SYM
ejpam-1188	156	3	12181222	12181222	NUM
ejpam-1188	156	4	,	,	PUNCT
ejpam-1188	156	5	2007	2007	NUM
ejpam-1188	156	6	.	.	PUNCT
ejpam-1188	157	1	[	[	X
ejpam-1188	157	2	2	2	X
ejpam-1188	157	3	]	]	PUNCT
ejpam-1188	157	4	o	o	X
ejpam-1188	157	5	altintaş	altintaş	PROPN
ejpam-1188	157	6	,	,	PUNCT
ejpam-1188	157	7	h	h	PROPN
ejpam-1188	157	8	irmak	irmak	PROPN
ejpam-1188	157	9	,	,	PUNCT
ejpam-1188	157	10	and	and	CCONJ
ejpam-1188	157	11	h	h	PROPN
ejpam-1188	157	12	m	m	PROPN
ejpam-1188	157	13	srivastava	srivastava	PROPN
ejpam-1188	157	14	.	.	PUNCT
ejpam-1188	158	1	fractional	fractional	ADJ
ejpam-1188	158	2	calculus	calculus	NOUN
ejpam-1188	158	3	and	and	CCONJ
ejpam-1188	158	4	certain	certain	ADJ
ejpam-1188	158	5	starlike	starlike	NOUN
ejpam-1188	158	6	functions	function	NOUN
ejpam-1188	158	7	with	with	ADP
ejpam-1188	158	8	negative	negative	ADJ
ejpam-1188	158	9	coefficients	coefficient	NOUN
ejpam-1188	158	10	.	.	PUNCT
ejpam-1188	159	1	computers	computer	NOUN
ejpam-1188	159	2	&	&	CCONJ
ejpam-1188	159	3	mathematics	mathematics	PROPN
ejpam-1188	159	4	with	with	ADP
ejpam-1188	159	5	applications	application	NOUN
ejpam-1188	159	6	.	.	PUNCT
ejpam-1188	160	1	30(2	30(2	NUM
ejpam-1188	160	2	):	):	PUNCT
ejpam-1188	160	3	915	915	NUM
ejpam-1188	160	4	,	,	PUNCT
ejpam-1188	160	5	1995	1995	NUM
ejpam-1188	160	6	.	.	PUNCT
ejpam-1188	161	1	[	[	X
ejpam-1188	161	2	3	3	X
ejpam-1188	161	3	]	]	X
ejpam-1188	161	4	o	o	X
ejpam-1188	161	5	altintaş	altintaş	PROPN
ejpam-1188	161	6	and	and	CCONJ
ejpam-1188	161	7	ö	ö	PROPN
ejpam-1188	161	8	özkan	özkan	PROPN
ejpam-1188	161	9	.	.	PUNCT
ejpam-1188	162	1	starlike	starlike	PROPN
ejpam-1188	162	2	,	,	PUNCT
ejpam-1188	162	3	convex	convex	ADJ
ejpam-1188	162	4	and	and	CCONJ
ejpam-1188	162	5	close	close	ADJ
ejpam-1188	162	6	-	-	PUNCT
ejpam-1188	162	7	to	to	ADP
ejpam-1188	162	8	-	-	PUNCT
ejpam-1188	162	9	convex	convex	NOUN
ejpam-1188	162	10	functions	function	NOUN
ejpam-1188	162	11	of	of	ADP
ejpam-1188	162	12	complex	complex	ADJ
ejpam-1188	162	13	order	order	NOUN
ejpam-1188	162	14	.	.	PUNCT
ejpam-1188	163	1	hacettepe	hacettepe	ADJ
ejpam-1188	163	2	bulletin	bulletin	NOUN
ejpam-1188	163	3	of	of	ADP
ejpam-1188	163	4	natural	natural	ADJ
ejpam-1188	163	5	sciences	science	NOUN
ejpam-1188	163	6	and	and	CCONJ
ejpam-1188	163	7	engineering	engineering	NOUN
ejpam-1188	163	8	.	.	PUNCT
ejpam-1188	164	1	series	series	PROPN
ejpam-1188	164	2	b.	b.	PROPN
ejpam-1188	164	3	28	28	NUM
ejpam-1188	164	4	:	:	PUNCT
ejpam-1188	164	5	37	37	NUM
ejpam-1188	164	6	-	-	SYM
ejpam-1188	164	7	46	46	NUM
ejpam-1188	164	8	,	,	PUNCT
ejpam-1188	164	9	1991	1991	NUM
ejpam-1188	164	10	.	.	PUNCT
ejpam-1188	165	1	[	[	X
ejpam-1188	165	2	4	4	X
ejpam-1188	165	3	]	]	X
ejpam-1188	165	4	o	o	X
ejpam-1188	165	5	altintaş	altintaş	PROPN
ejpam-1188	165	6	and	and	CCONJ
ejpam-1188	165	7	ö	ö	PROPN
ejpam-1188	165	8	özkan	özkan	ADJ
ejpam-1188	165	9	.	.	PUNCT
ejpam-1188	166	1	on	on	ADP
ejpam-1188	166	2	the	the	DET
ejpam-1188	166	3	classes	class	NOUN
ejpam-1188	166	4	of	of	ADP
ejpam-1188	166	5	starlike	starlike	NOUN
ejpam-1188	166	6	and	and	CCONJ
ejpam-1188	166	7	convex	convex	NOUN
ejpam-1188	166	8	functions	function	NOUN
ejpam-1188	166	9	of	of	ADP
ejpam-1188	166	10	complex	complex	NOUN
ejpam-1188	166	11	.	.	PUNCT
ejpam-1188	167	1	hacettepe	hacettepe	ADJ
ejpam-1188	167	2	bulletin	bulletin	NOUN
ejpam-1188	167	3	of	of	ADP
ejpam-1188	167	4	natural	natural	ADJ
ejpam-1188	167	5	sciences	science	NOUN
ejpam-1188	167	6	and	and	CCONJ
ejpam-1188	167	7	engineering	engineering	NOUN
ejpam-1188	167	8	.	.	PUNCT
ejpam-1188	168	1	series	series	PROPN
ejpam-1188	168	2	b.	b.	PROPN
ejpam-1188	168	3	30	30	NUM
ejpam-1188	168	4	:	:	PUNCT
ejpam-1188	168	5	63	63	NUM
ejpam-1188	168	6	-	-	SYM
ejpam-1188	168	7	68	68	NUM
ejpam-1188	168	8	,	,	PUNCT
ejpam-1188	168	9	2001	2001	NUM
ejpam-1188	168	10	.	.	PUNCT
ejpam-1188	169	1	[	[	X
ejpam-1188	169	2	5	5	X
ejpam-1188	169	3	]	]	PUNCT
ejpam-1188	169	4	o	o	X
ejpam-1188	169	5	altintaş	altintaş	PROPN
ejpam-1188	169	6	,	,	PUNCT
ejpam-1188	169	7	ö	ö	NOUN
ejpam-1188	169	8	özkan	özkan	VERB
ejpam-1188	169	9	,	,	PUNCT
ejpam-1188	169	10	and	and	CCONJ
ejpam-1188	169	11	h	h	PROPN
ejpam-1188	169	12	m	m	PROPN
ejpam-1188	169	13	srivastava	srivastava	PROPN
ejpam-1188	169	14	.	.	PUNCT
ejpam-1188	170	1	neighborhoods	neighborhood	NOUN
ejpam-1188	170	2	of	of	ADP
ejpam-1188	170	3	a	a	DET
ejpam-1188	170	4	class	class	NOUN
ejpam-1188	170	5	of	of	ADP
ejpam-1188	170	6	analytic	analytic	ADJ
ejpam-1188	170	7	functions	function	NOUN
ejpam-1188	170	8	with	with	ADP
ejpam-1188	170	9	negative	negative	ADJ
ejpam-1188	170	10	coefficients	coefficient	NOUN
ejpam-1188	170	11	.	.	PUNCT
ejpam-1188	171	1	applied	apply	VERB
ejpam-1188	171	2	mathematics	mathematics	NOUN
ejpam-1188	171	3	letters	letter	NOUN
ejpam-1188	171	4	.	.	PUNCT
ejpam-1188	172	1	13(3	13(3	NUM
ejpam-1188	172	2	):	):	PUNCT
ejpam-1188	172	3	63	63	NUM
ejpam-1188	172	4	-	-	SYM
ejpam-1188	172	5	67	67	NUM
ejpam-1188	172	6	,	,	PUNCT
ejpam-1188	172	7	1995	1995	NUM
ejpam-1188	172	8	.	.	PUNCT
ejpam-1188	173	1	[	[	X
ejpam-1188	173	2	6	6	NUM
ejpam-1188	173	3	]	]	PUNCT
ejpam-1188	173	4	o	o	X
ejpam-1188	173	5	altintaş	altintaş	PROPN
ejpam-1188	173	6	,	,	PUNCT
ejpam-1188	173	7	ö	ö	NOUN
ejpam-1188	173	8	özkan	özkan	VERB
ejpam-1188	173	9	,	,	PUNCT
ejpam-1188	173	10	and	and	CCONJ
ejpam-1188	173	11	h	h	PROPN
ejpam-1188	173	12	m	m	PROPN
ejpam-1188	173	13	srivastava	srivastava	PROPN
ejpam-1188	173	14	.	.	PUNCT
ejpam-1188	174	1	majorization	majorization	NOUN
ejpam-1188	174	2	by	by	ADP
ejpam-1188	174	3	starlike	starlike	NOUN
ejpam-1188	174	4	functions	function	NOUN
ejpam-1188	174	5	of	of	ADP
ejpam-1188	174	6	complex	complex	ADJ
ejpam-1188	174	7	order	order	NOUN
ejpam-1188	174	8	.	.	PUNCT
ejpam-1188	175	1	complex	complex	ADJ
ejpam-1188	175	2	variables	variable	NOUN
ejpam-1188	175	3	,	,	PUNCT
ejpam-1188	175	4	theory	theory	NOUN
ejpam-1188	175	5	and	and	CCONJ
ejpam-1188	175	6	application	application	NOUN
ejpam-1188	175	7	.	.	PUNCT
ejpam-1188	176	1	46	46	NUM
ejpam-1188	176	2	:	:	PUNCT
ejpam-1188	176	3	207	207	NUM
ejpam-1188	176	4	-	-	SYM
ejpam-1188	176	5	218	218	NUM
ejpam-1188	176	6	,	,	PUNCT
ejpam-1188	176	7	2001	2001	NUM
ejpam-1188	176	8	.	.	PUNCT
ejpam-1188	177	1	[	[	X
ejpam-1188	177	2	7	7	X
ejpam-1188	177	3	]	]	X
ejpam-1188	177	4	o	o	X
ejpam-1188	177	5	altintaş	altintaş	PROPN
ejpam-1188	177	6	,	,	PUNCT
ejpam-1188	177	7	ö	ö	NOUN
ejpam-1188	177	8	özkan	özkan	VERB
ejpam-1188	177	9	,	,	PUNCT
ejpam-1188	177	10	and	and	CCONJ
ejpam-1188	177	11	h	h	PROPN
ejpam-1188	177	12	m	m	PROPN
ejpam-1188	177	13	srivastava	srivastava	PROPN
ejpam-1188	177	14	.	.	PUNCT
ejpam-1188	178	1	neighborhoods	neighborhood	NOUN
ejpam-1188	178	2	of	of	ADP
ejpam-1188	178	3	a	a	DET
ejpam-1188	178	4	certain	certain	ADJ
ejpam-1188	178	5	family	family	NOUN
ejpam-1188	178	6	of	of	ADP
ejpam-1188	178	7	multivalent	multivalent	NOUN
ejpam-1188	178	8	functions	function	NOUN
ejpam-1188	178	9	with	with	ADP
ejpam-1188	178	10	negative	negative	ADJ
ejpam-1188	178	11	coefficient	coefficient	NOUN
ejpam-1188	178	12	.	.	PUNCT
ejpam-1188	179	1	computers	computer	NOUN
ejpam-1188	179	2	&	&	CCONJ
ejpam-1188	179	3	mathematics	mathematics	PROPN
ejpam-1188	179	4	with	with	ADP
ejpam-1188	179	5	applications	application	NOUN
ejpam-1188	179	6	.	.	PUNCT
ejpam-1188	180	1	47:1667	47:1667	NOUN
ejpam-1188	180	2	-	-	PUNCT
ejpam-1188	180	3	1672	1672	NUM
ejpam-1188	180	4	,	,	PUNCT
ejpam-1188	180	5	2004	2004	NUM
ejpam-1188	180	6	.	.	PUNCT
ejpam-1188	181	1	[	[	X
ejpam-1188	181	2	8	8	NUM
ejpam-1188	181	3	]	]	X
ejpam-1188	181	4	o	o	X
ejpam-1188	181	5	altintaş	altintaş	PROPN
ejpam-1188	181	6	and	and	CCONJ
ejpam-1188	181	7	h	h	NOUN
ejpam-1188	181	8	m	m	PROPN
ejpam-1188	181	9	srivastava	srivastava	PROPN
ejpam-1188	181	10	.	.	PUNCT
ejpam-1188	182	1	some	some	DET
ejpam-1188	182	2	majorization	majorization	NOUN
ejpam-1188	182	3	problems	problem	NOUN
ejpam-1188	182	4	associated	associate	VERB
ejpam-1188	182	5	with	with	ADP
ejpam-1188	182	6	p	p	NOUN
ejpam-1188	182	7	-	-	PUNCT
ejpam-1188	182	8	valently	valently	ADV
ejpam-1188	182	9	starlike	starlike	NOUN
ejpam-1188	182	10	and	and	CCONJ
ejpam-1188	182	11	convex	convex	NOUN
ejpam-1188	182	12	functions	function	NOUN
ejpam-1188	182	13	of	of	ADP
ejpam-1188	182	14	complex	complex	ADJ
ejpam-1188	182	15	order	order	NOUN
ejpam-1188	182	16	.	.	PUNCT
ejpam-1188	183	1	east	east	ADJ
ejpam-1188	183	2	asian	asian	PROPN
ejpam-1188	183	3	mathematical	mathematical	ADJ
ejpam-1188	183	4	journal	journal	NOUN
ejpam-1188	183	5	.	.	PUNCT
ejpam-1188	184	1	17	17	NUM
ejpam-1188	184	2	:	:	PUNCT
ejpam-1188	184	3	175	175	NUM
ejpam-1188	184	4	-	-	SYM
ejpam-1188	184	5	183	183	NUM
ejpam-1188	184	6	,	,	PUNCT
ejpam-1188	184	7	2001	2001	NUM
ejpam-1188	184	8	.	.	PUNCT
ejpam-1188	185	1	[	[	X
ejpam-1188	185	2	9	9	NUM
ejpam-1188	185	3	]	]	X
ejpam-1188	185	4	q	q	X
ejpam-1188	185	5	deng	deng	PROPN
ejpam-1188	185	6	.	.	PUNCT
ejpam-1188	186	1	certain	certain	ADJ
ejpam-1188	186	2	subclass	subclass	NOUN
ejpam-1188	186	3	of	of	ADP
ejpam-1188	186	4	analytic	analytic	ADJ
ejpam-1188	186	5	functions	function	NOUN
ejpam-1188	186	6	with	with	ADP
ejpam-1188	186	7	complex	complex	ADJ
ejpam-1188	186	8	order	order	NOUN
ejpam-1188	186	9	.	.	PUNCT
ejpam-1188	187	1	applied	apply	VERB
ejpam-1188	187	2	mathematics	mathematic	NOUN
ejpam-1188	187	3	and	and	CCONJ
ejpam-1188	187	4	computation	computation	NOUN
ejpam-1188	187	5	.	.	PUNCT
ejpam-1188	188	1	208	208	NUM
ejpam-1188	188	2	:	:	PUNCT
ejpam-1188	188	3	359	359	NUM
ejpam-1188	188	4	-	-	SYM
ejpam-1188	188	5	362	362	NUM
ejpam-1188	188	6	,	,	PUNCT
ejpam-1188	188	7	2009	2009	NUM
ejpam-1188	188	8	.	.	PUNCT
ejpam-1188	189	1	[	[	X
ejpam-1188	189	2	10	10	NUM
ejpam-1188	189	3	]	]	X
ejpam-1188	189	4	m	m	VERB
ejpam-1188	189	5	a	a	DET
ejpam-1188	189	6	nasr	nasr	PROPN
ejpam-1188	189	7	and	and	CCONJ
ejpam-1188	189	8	m	m	PROPN
ejpam-1188	189	9	k	k	PROPN
ejpam-1188	189	10	aouf	aouf	PROPN
ejpam-1188	189	11	.	.	PUNCT
ejpam-1188	190	1	radius	radius	NOUN
ejpam-1188	190	2	of	of	ADP
ejpam-1188	190	3	convexity	convexity	NOUN
ejpam-1188	190	4	for	for	ADP
ejpam-1188	190	5	the	the	DET
ejpam-1188	190	6	class	class	NOUN
ejpam-1188	190	7	of	of	ADP
ejpam-1188	190	8	starlike	starlike	NOUN
ejpam-1188	190	9	functions	function	NOUN
ejpam-1188	190	10	of	of	ADP
ejpam-1188	190	11	complex	complex	ADJ
ejpam-1188	190	12	order	order	NOUN
ejpam-1188	190	13	.	.	PUNCT
ejpam-1188	191	1	bulletin	bulletin	NOUN
ejpam-1188	191	2	of	of	ADP
ejpam-1188	191	3	the	the	DET
ejpam-1188	191	4	faculty	faculty	NOUN
ejpam-1188	191	5	of	of	ADP
ejpam-1188	191	6	science	science	NOUN
ejpam-1188	191	7	.	.	PUNCT
ejpam-1188	192	1	a.	a.	NOUN
ejpam-1188	192	2	physics	physics	PROPN
ejpam-1188	192	3	and	and	CCONJ
ejpam-1188	192	4	mathematics	mathematic	NOUN
ejpam-1188	192	5	.	.	PUNCT
ejpam-1188	193	1	12	12	NUM
ejpam-1188	193	2	:	:	SYM
ejpam-1188	193	3	153	153	NUM
ejpam-1188	193	4	-	-	SYM
ejpam-1188	193	5	159	159	NUM
ejpam-1188	193	6	,	,	PUNCT
ejpam-1188	193	7	1983	1983	NUM
ejpam-1188	193	8	.	.	PUNCT
ejpam-1188	194	1	[	[	X
ejpam-1188	194	2	11	11	NUM
ejpam-1188	194	3	]	]	X
ejpam-1188	194	4	m	m	PROPN
ejpam-1188	194	5	s	s	PROPN
ejpam-1188	194	6	robertson	robertson	PROPN
ejpam-1188	194	7	.	.	PUNCT
ejpam-1188	195	1	on	on	ADP
ejpam-1188	195	2	the	the	DET
ejpam-1188	195	3	theory	theory	NOUN
ejpam-1188	195	4	of	of	ADP
ejpam-1188	195	5	univalent	univalent	ADJ
ejpam-1188	195	6	functions	function	NOUN
ejpam-1188	195	7	.	.	PUNCT
ejpam-1188	196	1	annals	annal	NOUN
ejpam-1188	196	2	of	of	ADP
ejpam-1188	196	3	mathematics	mathematic	NOUN
ejpam-1188	196	4	(	(	PUNCT
ejpam-1188	196	5	series	series	NOUN
ejpam-1188	196	6	1	1	NUM
ejpam-1188	196	7	)	)	PUNCT
ejpam-1188	196	8	.	.	PUNCT
ejpam-1188	197	1	37	37	NUM
ejpam-1188	197	2	:	:	PUNCT
ejpam-1188	197	3	374	374	NUM
ejpam-1188	197	4	-	-	SYM
ejpam-1188	197	5	408	408	NUM
ejpam-1188	197	6	,	,	PUNCT
ejpam-1188	197	7	1936	1936	NUM
ejpam-1188	197	8	.	.	PUNCT
ejpam-1188	198	1	[	[	X
ejpam-1188	198	2	12	12	NUM
ejpam-1188	198	3	]	]	X
ejpam-1188	198	4	w	w	NOUN
ejpam-1188	198	5	rogosinski	rogosinski	NOUN
ejpam-1188	198	6	.	.	PUNCT
ejpam-1188	199	1	on	on	ADP
ejpam-1188	199	2	the	the	DET
ejpam-1188	199	3	coefficients	coefficient	NOUN
ejpam-1188	199	4	of	of	ADP
ejpam-1188	199	5	subordinate	subordinate	ADJ
ejpam-1188	199	6	functions	function	NOUN
ejpam-1188	199	7	.	.	PUNCT
ejpam-1188	200	1	proceedings	proceeding	NOUN
ejpam-1188	200	2	of	of	ADP
ejpam-1188	200	3	the	the	DET
ejpam-1188	200	4	london	london	PROPN
ejpam-1188	200	5	mathematical	mathematical	ADJ
ejpam-1188	200	6	society	society	NOUN
ejpam-1188	200	7	(	(	PUNCT
ejpam-1188	200	8	series	series	NOUN
ejpam-1188	200	9	1	1	NUM
ejpam-1188	200	10	)	)	PUNCT
ejpam-1188	200	11	.	.	PUNCT
ejpam-1188	201	1	48	48	NUM
ejpam-1188	201	2	:	:	PUNCT
ejpam-1188	201	3	48	48	NUM
ejpam-1188	201	4	-	-	SYM
ejpam-1188	201	5	82	82	NUM
ejpam-1188	201	6	,	,	PUNCT
ejpam-1188	201	7	1943	1943	NUM
ejpam-1188	201	8	.	.	PUNCT
ejpam-1188	202	1	references	reference	NOUN
ejpam-1188	202	2	468	468	NUM
ejpam-1188	203	1	[	[	X
ejpam-1188	203	2	13	13	NUM
ejpam-1188	203	3	]	]	SYM
ejpam-1188	203	4	g	g	NOUN
ejpam-1188	203	5	.	.	PUNCT
ejpam-1188	204	1	sălăgean	sălăgean	NOUN
ejpam-1188	204	2	.	.	PUNCT
ejpam-1188	205	1	subclass	subclass	NOUN
ejpam-1188	205	2	of	of	ADP
ejpam-1188	205	3	univalent	univalent	ADJ
ejpam-1188	205	4	functions	function	NOUN
ejpam-1188	205	5	.	.	PUNCT
ejpam-1188	206	1	complex	complex	ADJ
ejpam-1188	206	2	analysis	analysis	NOUN
ejpam-1188	206	3	.	.	PUNCT
ejpam-1188	207	1	37	37	NUM
ejpam-1188	207	2	:	:	PUNCT
ejpam-1188	207	3	374	374	NUM
ejpam-1188	207	4	-	-	SYM
ejpam-1188	207	5	408	408	NUM
ejpam-1188	207	6	,	,	PUNCT
ejpam-1188	207	7	1936	1936	NUM
ejpam-1188	207	8	.	.	PUNCT
ejpam-1188	208	1	[	[	X
ejpam-1188	208	2	14	14	NUM
ejpam-1188	208	3	]	]	X
ejpam-1188	208	4	h	h	PROPN
ejpam-1188	208	5	m	m	PROPN
ejpam-1188	208	6	srivastava	srivastava	PROPN
ejpam-1188	208	7	,	,	PUNCT
ejpam-1188	208	8	s	s	PART
ejpam-1188	208	9	s	s	NOUN
ejpam-1188	208	10	eker	eker	ADJ
ejpam-1188	208	11	,	,	PUNCT
ejpam-1188	208	12	and	and	CCONJ
ejpam-1188	208	13	b	b	PROPN
ejpam-1188	208	14	seker	seker	NOUN
ejpam-1188	208	15	.	.	PUNCT
ejpam-1188	209	1	a	a	DET
ejpam-1188	209	2	certain	certain	ADJ
ejpam-1188	209	3	convolution	convolution	NOUN
ejpam-1188	209	4	approach	approach	NOUN
ejpam-1188	209	5	for	for	ADP
ejpam-1188	209	6	subclasses	subclass	NOUN
ejpam-1188	209	7	of	of	ADP
ejpam-1188	209	8	analytic	analytic	ADJ
ejpam-1188	209	9	functions	function	NOUN
ejpam-1188	209	10	with	with	ADP
ejpam-1188	209	11	negative	negative	ADJ
ejpam-1188	209	12	coefficients	coefficient	NOUN
ejpam-1188	209	13	.	.	PUNCT
ejpam-1188	210	1	integral	integral	ADJ
ejpam-1188	210	2	transforms	transform	NOUN
ejpam-1188	210	3	and	and	CCONJ
ejpam-1188	210	4	special	special	ADJ
ejpam-1188	210	5	functions	function	NOUN
ejpam-1188	210	6	.	.	PUNCT
ejpam-1188	211	1	20	20	NUM
ejpam-1188	211	2	:	:	PUNCT
ejpam-1188	211	3	687	687	NUM
ejpam-1188	211	4	-	-	SYM
ejpam-1188	211	5	699	699	NUM
ejpam-1188	211	6	,	,	PUNCT
ejpam-1188	211	7	2009	2009	NUM
ejpam-1188	211	8	.	.	PUNCT
ejpam-1188	212	1	[	[	X
ejpam-1188	212	2	15	15	NUM
ejpam-1188	212	3	]	]	X
ejpam-1188	212	4	h	h	PROPN
ejpam-1188	212	5	m	m	PROPN
ejpam-1188	212	6	srivastava	srivastava	PROPN
ejpam-1188	212	7	,	,	PUNCT
ejpam-1188	212	8	d	d	PROPN
ejpam-1188	212	9	-	-	PUNCT
ejpam-1188	212	10	g	g	PROPN
ejpam-1188	212	11	yang	yang	PROPN
ejpam-1188	212	12	,	,	PUNCT
ejpam-1188	212	13	and	and	CCONJ
ejpam-1188	212	14	n	n	CCONJ
ejpam-1188	212	15	-	-	PUNCT
ejpam-1188	212	16	e	e	NOUN
ejpam-1188	212	17	xu	xu	PROPN
ejpam-1188	212	18	.	.	PUNCT
ejpam-1188	213	1	subordinations	subordination	NOUN
ejpam-1188	213	2	for	for	ADP
ejpam-1188	213	3	multivalent	multivalent	NOUN
ejpam-1188	213	4	analytic	analytic	ADJ
ejpam-1188	213	5	functions	function	NOUN
ejpam-1188	213	6	associated	associate	VERB
ejpam-1188	213	7	with	with	ADP
ejpam-1188	213	8	the	the	DET
ejpam-1188	213	9	dziok	dziok	NOUN
ejpam-1188	213	10	-	-	PUNCT
ejpam-1188	213	11	srivastava	srivastava	PROPN
ejpam-1188	213	12	operator	operator	NOUN
ejpam-1188	213	13	.	.	PUNCT
ejpam-1188	214	1	integral	integral	ADJ
ejpam-1188	214	2	transforms	transform	NOUN
ejpam-1188	214	3	and	and	CCONJ
ejpam-1188	214	4	special	special	ADJ
ejpam-1188	214	5	functions	function	NOUN
ejpam-1188	214	6	.	.	PUNCT
ejpam-1188	215	1	20	20	NUM
ejpam-1188	215	2	:	:	PUNCT
ejpam-1188	215	3	581	581	NUM
ejpam-1188	215	4	-	-	SYM
ejpam-1188	215	5	606	606	NUM
ejpam-1188	215	6	,	,	PUNCT
ejpam-1188	215	7	2009	2009	NUM
ejpam-1188	215	8	.	.	PUNCT
ejpam-1188	216	1	[	[	X
ejpam-1188	216	2	16	16	NUM
ejpam-1188	216	3	]	]	X
ejpam-1188	216	4	f	f	PROPN
ejpam-1188	216	5	m	m	VERB
ejpam-1188	216	6	al	al	PROPN
ejpam-1188	216	7	-	-	PUNCT
ejpam-1188	216	8	oboudi	oboudi	NOUN
ejpam-1188	216	9	.	.	PUNCT
ejpam-1188	217	1	on	on	ADP
ejpam-1188	217	2	univalent	univalent	ADJ
ejpam-1188	217	3	functions	function	NOUN
ejpam-1188	217	4	defined	define	VERB
ejpam-1188	217	5	by	by	ADP
ejpam-1188	217	6	a	a	DET
ejpam-1188	217	7	generalized	generalized	ADJ
ejpam-1188	217	8	sălăgean	sălăgean	ADJ
ejpam-1188	217	9	operator	operator	NOUN
ejpam-1188	217	10	.	.	PUNCT
ejpam-1188	218	1	international	international	ADJ
ejpam-1188	218	2	journal	journal	PROPN
ejpam-1188	218	3	of	of	ADP
ejpam-1188	218	4	mathematics	mathematics	PROPN
ejpam-1188	218	5	and	and	CCONJ
ejpam-1188	218	6	mathematical	mathematical	ADJ
ejpam-1188	218	7	sciences	science	NOUN
ejpam-1188	218	8	.	.	PUNCT
ejpam-1188	219	1	27	27	NUM
ejpam-1188	219	2	:	:	PUNCT
ejpam-1188	219	3	1429	1429	NUM
ejpam-1188	219	4	-	-	SYM
ejpam-1188	219	5	1436	1436	NUM
ejpam-1188	219	6	,	,	PUNCT
ejpam-1188	219	7	2004	2004	NUM
ejpam-1188	219	8	.	.	PUNCT
ejpam-1188	220	1	[	[	X
ejpam-1188	220	2	17	17	NUM
ejpam-1188	220	3	]	]	X
ejpam-1188	220	4	e	e	X
ejpam-1188	220	5	deniz	deniz	PROPN
ejpam-1188	220	6	and	and	CCONJ
ejpam-1188	220	7	h	h	PROPN
ejpam-1188	220	8	orhan	orhan	PROPN
ejpam-1188	220	9	.	.	PUNCT
ejpam-1188	221	1	the	the	DET
ejpam-1188	221	2	fekete	fekete	NOUN
ejpam-1188	221	3	-	-	PUNCT
ejpam-1188	221	4	szegö	szegö	ADJ
ejpam-1188	221	5	problem	problem	NOUN
ejpam-1188	221	6	for	for	ADP
ejpam-1188	221	7	a	a	DET
ejpam-1188	221	8	generalized	generalized	ADJ
ejpam-1188	221	9	subclass	subclass	NOUN
ejpam-1188	221	10	of	of	ADP
ejpam-1188	221	11	analytic	analytic	ADJ
ejpam-1188	221	12	functions	function	NOUN
ejpam-1188	221	13	.	.	PUNCT
ejpam-1188	222	1	kyungpook	kyungpook	PROPN
ejpam-1188	222	2	mathematical	mathematical	PROPN
ejpam-1188	222	3	journal	journal	NOUN
ejpam-1188	222	4	.	.	PUNCT
ejpam-1188	223	1	50	50	NUM
ejpam-1188	223	2	:	:	PUNCT
ejpam-1188	223	3	37	37	NUM
ejpam-1188	223	4	-	-	SYM
ejpam-1188	223	5	47	47	NUM
ejpam-1188	223	6	,	,	PUNCT
ejpam-1188	223	7	2010	2010	NUM
ejpam-1188	223	8	.	.	PUNCT