id	sid	tid	token	lemma	pos
ejpam-887	1	1	9_887_xu.dvi	9_887_xu.dvi	NUM
ejpam-887	1	2	european	european	ADJ
ejpam-887	1	3	journal	journal	NOUN
ejpam-887	1	4	of	of	ADP
ejpam-887	1	5	pure	pure	ADJ
ejpam-887	1	6	and	and	CCONJ
ejpam-887	1	7	applied	apply	VERB
ejpam-887	1	8	mathematics	mathematic	NOUN
ejpam-887	1	9	vol	vol	NOUN
ejpam-887	1	10	.	.	PUNCT
ejpam-887	2	1	3	3	NUM
ejpam-887	2	2	,	,	PUNCT
ejpam-887	2	3	no	no	INTJ
ejpam-887	2	4	.	.	NOUN
ejpam-887	2	5	6	6	NUM
ejpam-887	2	6	,	,	PUNCT
ejpam-887	2	7	2010	2010	NUM
ejpam-887	2	8	,	,	PUNCT
ejpam-887	2	9	1055	1055	NUM
ejpam-887	2	10	-	-	SYM
ejpam-887	2	11	1061	1061	NUM
ejpam-887	2	12	issn	issn	PROPN
ejpam-887	2	13	1307	1307	NUM
ejpam-887	2	14	-	-	SYM
ejpam-887	2	15	5543	5543	NUM
ejpam-887	2	16	–	–	PUNCT
ejpam-887	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-887	2	18	special	special	ADJ
ejpam-887	2	19	issue	issue	NOUN
ejpam-887	2	20	on	on	ADP
ejpam-887	2	21	complex	complex	ADJ
ejpam-887	2	22	analysis	analysis	NOUN
ejpam-887	2	23	:	:	PUNCT
ejpam-887	2	24	theory	theory	NOUN
ejpam-887	2	25	and	and	CCONJ
ejpam-887	2	26	applications	application	NOUN
ejpam-887	2	27	dedicated	dedicate	VERB
ejpam-887	2	28	to	to	ADP
ejpam-887	2	29	professor	professor	PROPN
ejpam-887	2	30	hari	hari	PROPN
ejpam-887	2	31	m.	m.	PROPN
ejpam-887	2	32	srivastava	srivastava	PROPN
ejpam-887	2	33	,	,	PUNCT
ejpam-887	2	34	on	on	ADP
ejpam-887	2	35	the	the	DET
ejpam-887	2	36	occasion	occasion	NOUN
ejpam-887	2	37	of	of	ADP
ejpam-887	2	38	his	his	PRON
ejpam-887	2	39	70th	70th	ADJ
ejpam-887	2	40	birthday	birthday	NOUN
ejpam-887	2	41	coefficient	coefficient	NOUN
ejpam-887	2	42	estimate	estimate	NOUN
ejpam-887	2	43	for	for	ADP
ejpam-887	2	44	a	a	DET
ejpam-887	2	45	subclass	subclass	NOUN
ejpam-887	2	46	of	of	ADP
ejpam-887	2	47	univalent	univalent	ADJ
ejpam-887	2	48	functions	function	NOUN
ejpam-887	2	49	with	with	ADP
ejpam-887	2	50	respect	respect	NOUN
ejpam-887	2	51	to	to	ADP
ejpam-887	2	52	symmetric	symmetric	ADJ
ejpam-887	2	53	points	point	NOUN
ejpam-887	2	54	qing	qing	NOUN
ejpam-887	2	55	-	-	PUNCT
ejpam-887	2	56	hua	hua	PROPN
ejpam-887	2	57	xu∗	xu∗	PROPN
ejpam-887	2	58	,	,	PUNCT
ejpam-887	2	59	guang	guang	PROPN
ejpam-887	2	60	-	-	PUNCT
ejpam-887	2	61	ping	ping	PROPN
ejpam-887	2	62	wu	wu	PROPN
ejpam-887	2	63	college	college	PROPN
ejpam-887	2	64	of	of	ADP
ejpam-887	2	65	mathematics	mathematics	PROPN
ejpam-887	2	66	and	and	CCONJ
ejpam-887	2	67	information	information	NOUN
ejpam-887	2	68	science	science	NOUN
ejpam-887	2	69	,	,	PUNCT
ejpam-887	2	70	jiangxi	jiangxi	PROPN
ejpam-887	2	71	normal	normal	PROPN
ejpam-887	2	72	university	university	PROPN
ejpam-887	2	73	,	,	PUNCT
ejpam-887	2	74	nanchang	nanchang	PROPN
ejpam-887	2	75	330022	330022	PROPN
ejpam-887	2	76	,	,	PUNCT
ejpam-887	2	77	china	china	PROPN
ejpam-887	2	78	abstract	abstract	NOUN
ejpam-887	2	79	.	.	PUNCT
ejpam-887	3	1	in	in	ADP
ejpam-887	3	2	this	this	DET
ejpam-887	3	3	paper	paper	NOUN
ejpam-887	3	4	,	,	PUNCT
ejpam-887	3	5	the	the	DET
ejpam-887	3	6	subclasses	subclass	NOUN
ejpam-887	3	7	s	s	PART
ejpam-887	3	8	∗	∗	NOUN
ejpam-887	3	9	s	s	PART
ejpam-887	3	10	(	(	PUNCT
ejpam-887	3	11	g	g	NOUN
ejpam-887	3	12	)	)	PUNCT
ejpam-887	3	13	and	and	CCONJ
ejpam-887	3	14	k	k	PROPN
ejpam-887	3	15	∗	∗	X
ejpam-887	3	16	s	s	PART
ejpam-887	3	17	(	(	PUNCT
ejpam-887	3	18	g	g	NOUN
ejpam-887	3	19	)	)	PUNCT
ejpam-887	3	20	of	of	ADP
ejpam-887	3	21	analytic	analytic	ADJ
ejpam-887	3	22	functions	function	NOUN
ejpam-887	3	23	.	.	PUNCT
ejpam-887	4	1	we	we	PRON
ejpam-887	4	2	obtain	obtain	VERB
ejpam-887	4	3	coefficient	coefficient	NOUN
ejpam-887	4	4	bounds	bound	NOUN
ejpam-887	4	5	for	for	ADP
ejpam-887	4	6	f	f	PROPN
ejpam-887	4	7	(	(	PUNCT
ejpam-887	4	8	z	z	NOUN
ejpam-887	4	9	)	)	PUNCT
ejpam-887	4	10	when	when	SCONJ
ejpam-887	4	11	f	f	PROPN
ejpam-887	4	12	(	(	PUNCT
ejpam-887	4	13	z	z	NOUN
ejpam-887	4	14	)	)	PUNCT
ejpam-887	4	15	is	be	AUX
ejpam-887	4	16	in	in	ADP
ejpam-887	4	17	the	the	DET
ejpam-887	4	18	class	class	NOUN
ejpam-887	4	19	s	s	PART
ejpam-887	4	20	∗	∗	NOUN
ejpam-887	4	21	g	g	NOUN
ejpam-887	4	22	or	or	CCONJ
ejpam-887	4	23	is	be	AUX
ejpam-887	4	24	in	in	ADP
ejpam-887	4	25	the	the	DET
ejpam-887	4	26	class	class	NOUN
ejpam-887	4	27	k	k	PROPN
ejpam-887	4	28	∗	∗	NOUN
ejpam-887	4	29	g	g	NOUN
ejpam-887	4	30	.	.	PUNCT
ejpam-887	5	1	these	these	DET
ejpam-887	5	2	results	result	NOUN
ejpam-887	5	3	generalize	generalize	VERB
ejpam-887	5	4	many	many	ADJ
ejpam-887	5	5	known	know	VERB
ejpam-887	5	6	results	result	NOUN
ejpam-887	5	7	.	.	PUNCT
ejpam-887	6	1	2000	2000	NUM
ejpam-887	6	2	mathematics	mathematic	NOUN
ejpam-887	6	3	subject	subject	NOUN
ejpam-887	6	4	classifications	classification	NOUN
ejpam-887	6	5	:	:	PUNCT
ejpam-887	6	6	30c45	30c45	NUM
ejpam-887	6	7	key	key	ADJ
ejpam-887	6	8	words	word	NOUN
ejpam-887	6	9	and	and	CCONJ
ejpam-887	6	10	phrases	phrase	NOUN
ejpam-887	6	11	:	:	PUNCT
ejpam-887	6	12	coefficient	coefficient	NOUN
ejpam-887	6	13	estimate	estimate	NOUN
ejpam-887	6	14	,	,	PUNCT
ejpam-887	6	15	symmetric	symmetric	ADJ
ejpam-887	6	16	points	point	NOUN
ejpam-887	6	17	,	,	PUNCT
ejpam-887	6	18	subordination	subordination	NOUN
ejpam-887	6	19	1	1	NUM
ejpam-887	6	20	.	.	PUNCT
ejpam-887	7	1	introduction	introduction	NOUN
ejpam-887	7	2	let	let	VERB
ejpam-887	7	3	c	c	NOUN
ejpam-887	7	4	be	be	AUX
ejpam-887	7	5	the	the	DET
ejpam-887	7	6	set	set	NOUN
ejpam-887	7	7	of	of	ADP
ejpam-887	7	8	complex	complex	ADJ
ejpam-887	7	9	numbers	number	NOUN
ejpam-887	7	10	,	,	PUNCT
ejpam-887	7	11	and	and	CCONJ
ejpam-887	7	12	n	n	CCONJ
ejpam-887	7	13	=	=	SYM
ejpam-887	7	14	{	{	PUNCT
ejpam-887	7	15	1,2,3	1,2,3	NUM
ejpam-887	7	16	,	,	PUNCT
ejpam-887	7	17	·	·	PUNCT
ejpam-887	7	18	·	·	PUNCT
ejpam-887	7	19	·	·	PUNCT
ejpam-887	7	20	}	}	PUNCT
ejpam-887	7	21	be	be	AUX
ejpam-887	7	22	the	the	DET
ejpam-887	7	23	set	set	NOUN
ejpam-887	7	24	of	of	ADP
ejpam-887	7	25	positive	positive	ADJ
ejpam-887	7	26	integers	integer	NOUN
ejpam-887	7	27	.	.	PUNCT
ejpam-887	8	1	we	we	PRON
ejpam-887	8	2	also	also	ADV
ejpam-887	8	3	leta	leta	PROPN
ejpam-887	8	4	denote	denote	VERB
ejpam-887	8	5	the	the	DET
ejpam-887	8	6	class	class	NOUN
ejpam-887	8	7	of	of	ADP
ejpam-887	8	8	functions	function	NOUN
ejpam-887	8	9	of	of	ADP
ejpam-887	8	10	the	the	DET
ejpam-887	8	11	form	form	NOUN
ejpam-887	8	12	f	f	X
ejpam-887	8	13	(	(	PUNCT
ejpam-887	8	14	z	z	NOUN
ejpam-887	8	15	)	)	PUNCT
ejpam-887	8	16	=	=	SYM
ejpam-887	9	1	z	z	NOUN
ejpam-887	10	1	+	+	NUM
ejpam-887	10	2	∞	∞	NUM
ejpam-887	10	3	∑	∑	CCONJ
ejpam-887	10	4	n=2	n=2	PART
ejpam-887	10	5	anzn	anzn	NOUN
ejpam-887	10	6	,	,	PUNCT
ejpam-887	10	7	(	(	PUNCT
ejpam-887	10	8	1	1	X
ejpam-887	10	9	)	)	PUNCT
ejpam-887	10	10	which	which	PRON
ejpam-887	10	11	are	be	AUX
ejpam-887	10	12	analytic	analytic	ADJ
ejpam-887	10	13	in	in	ADP
ejpam-887	10	14	the	the	DET
ejpam-887	10	15	open	open	ADJ
ejpam-887	10	16	disk	disk	NOUN
ejpam-887	10	17	u	u	NOUN
ejpam-887	10	18	=	=	PUNCT
ejpam-887	10	19	{	{	PUNCT
ejpam-887	10	20	z	z	NOUN
ejpam-887	10	21	:	:	PUNCT
ejpam-887	10	22	z	z	PROPN
ejpam-887	10	23	∈	∈	PROPN
ejpam-887	10	24	c	c	PROPN
ejpam-887	10	25	and	and	CCONJ
ejpam-887	10	26	|z|	|z|	VERB
ejpam-887	10	27	<	<	X
ejpam-887	10	28	1	1	NUM
ejpam-887	10	29	}	}	PUNCT
ejpam-887	10	30	.	.	PUNCT
ejpam-887	11	1	∗corresponding	∗corresponde	VERB
ejpam-887	11	2	author	author	NOUN
ejpam-887	11	3	.	.	PUNCT
ejpam-887	12	1	email	email	NOUN
ejpam-887	12	2	addresses	address	NOUN
ejpam-887	12	3	:	:	PUNCT
ejpam-887	12	4	xuqh�mail.ust	xuqh�mail.ust	PROPN
ejpam-887	12	5	.edu	.edu	PROPN
ejpam-887	12	6	.	.	PUNCT
ejpam-887	13	1	n	n	PROPN
ejpam-887	13	2	(	(	PUNCT
ejpam-887	13	3	q.	q.	PROPN
ejpam-887	13	4	xu	xu	PROPN
ejpam-887	13	5	)	)	PUNCT
ejpam-887	13	6	,	,	PUNCT
ejpam-887	13	7	guangpw	guangpw	PROPN
ejpam-887	13	8	�	�	PROPN
ejpam-887	13	9	sina	sina	PROPN
ejpam-887	13	10	.	.	PUNCT
ejpam-887	14	1	om	om	PROPN
ejpam-887	14	2	(	(	PUNCT
ejpam-887	14	3	g.	g.	PROPN
ejpam-887	14	4	wu	wu	PROPN
ejpam-887	14	5	)	)	PUNCT
ejpam-887	14	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-887	14	7	1055	1055	NUM
ejpam-887	14	8	c	c	X
ejpam-887	14	9	©	©	PROPN
ejpam-887	14	10	2010	2010	NUM
ejpam-887	14	11	ejpam	ejpam	NOUN
ejpam-887	14	12	all	all	DET
ejpam-887	14	13	rights	right	NOUN
ejpam-887	14	14	reserved	reserve	VERB
ejpam-887	14	15	.	.	PUNCT
ejpam-887	15	1	q.	q.	PROPN
ejpam-887	15	2	xu	xu	PROPN
ejpam-887	15	3	,	,	PUNCT
ejpam-887	15	4	g.	g.	PROPN
ejpam-887	15	5	wu	wu	PROPN
ejpam-887	15	6	/	/	SYM
ejpam-887	15	7	eur	eur	PROPN
ejpam-887	15	8	.	.	PUNCT
ejpam-887	16	1	j.	j.	PROPN
ejpam-887	16	2	pure	pure	PROPN
ejpam-887	16	3	appl	appl	PROPN
ejpam-887	16	4	.	.	PROPN
ejpam-887	16	5	math	math	PROPN
ejpam-887	16	6	,	,	PUNCT
ejpam-887	16	7	3	3	NUM
ejpam-887	16	8	(	(	PUNCT
ejpam-887	16	9	2010	2010	NUM
ejpam-887	16	10	)	)	PUNCT
ejpam-887	16	11	,	,	PUNCT
ejpam-887	16	12	1055	1055	NUM
ejpam-887	16	13	-	-	SYM
ejpam-887	16	14	1061	1061	NUM
ejpam-887	16	15	1056	1056	NUM
ejpam-887	16	16	we	we	PRON
ejpam-887	16	17	denote	denote	VERB
ejpam-887	16	18	by	by	ADP
ejpam-887	16	19	s	s	PRON
ejpam-887	16	20	the	the	DET
ejpam-887	16	21	subclass	subclass	NOUN
ejpam-887	16	22	of	of	ADP
ejpam-887	16	23	the	the	DET
ejpam-887	16	24	analytic	analytic	ADJ
ejpam-887	16	25	function	function	NOUN
ejpam-887	16	26	classa	classa	NOUN
ejpam-887	16	27	consisting	consist	VERB
ejpam-887	16	28	of	of	ADP
ejpam-887	16	29	all	all	DET
ejpam-887	16	30	functions	function	NOUN
ejpam-887	16	31	ina	ina	VERB
ejpam-887	16	32	which	which	PRON
ejpam-887	16	33	are	be	AUX
ejpam-887	16	34	also	also	ADV
ejpam-887	16	35	univalent	univalent	ADJ
ejpam-887	16	36	in	in	ADP
ejpam-887	16	37	u.	u.	NOUN
ejpam-887	16	38	for	for	ADP
ejpam-887	16	39	two	two	NUM
ejpam-887	16	40	functions	function	NOUN
ejpam-887	16	41	f	f	NOUN
ejpam-887	16	42	and	and	CCONJ
ejpam-887	16	43	g	g	NOUN
ejpam-887	16	44	,	,	PUNCT
ejpam-887	16	45	analytic	analytic	ADJ
ejpam-887	16	46	in	in	ADP
ejpam-887	16	47	u	u	NOUN
ejpam-887	16	48	,	,	PUNCT
ejpam-887	16	49	we	we	PRON
ejpam-887	16	50	say	say	VERB
ejpam-887	16	51	that	that	SCONJ
ejpam-887	16	52	f	f	PROPN
ejpam-887	16	53	(	(	PUNCT
ejpam-887	16	54	z	z	NOUN
ejpam-887	16	55	)	)	PUNCT
ejpam-887	16	56	is	be	AUX
ejpam-887	16	57	subordinate	subordinate	ADJ
ejpam-887	16	58	to	to	ADP
ejpam-887	16	59	g(z	g(z	PROPN
ejpam-887	16	60	)	)	PUNCT
ejpam-887	16	61	in	in	ADP
ejpam-887	16	62	u(written	u(written	ADJ
ejpam-887	16	63	f	f	PROPN
ejpam-887	16	64	≺	≺	PROPN
ejpam-887	16	65	g)if	g)if	PROPN
ejpam-887	16	66	there	there	PRON
ejpam-887	16	67	exists	exist	VERB
ejpam-887	16	68	a	a	DET
ejpam-887	16	69	schwarz	schwarz	NOUN
ejpam-887	16	70	function	function	NOUN
ejpam-887	16	71	w(z	w(z	NOUN
ejpam-887	16	72	)	)	PUNCT
ejpam-887	16	73	,	,	PUNCT
ejpam-887	16	74	analytic	analytic	ADJ
ejpam-887	16	75	in	in	ADP
ejpam-887	16	76	u	u	NOUN
ejpam-887	16	77	with	with	ADP
ejpam-887	16	78	w(0	w(0	PROPN
ejpam-887	16	79	)	)	PUNCT
ejpam-887	16	80	=	=	SYM
ejpam-887	16	81	0	0	NUM
ejpam-887	17	1	and	and	CCONJ
ejpam-887	17	2	|w(z)|	|w(z)|	VERB
ejpam-887	17	3	<	<	X
ejpam-887	17	4	1	1	NUM
ejpam-887	17	5	(	(	PUNCT
ejpam-887	17	6	z	z	NOUN
ejpam-887	17	7	∈	∈	PROPN
ejpam-887	17	8	u	u	NOUN
ejpam-887	17	9	)	)	PUNCT
ejpam-887	17	10	,	,	PUNCT
ejpam-887	17	11	such	such	ADJ
ejpam-887	17	12	that	that	SCONJ
ejpam-887	17	13	f	f	PROPN
ejpam-887	17	14	(	(	PUNCT
ejpam-887	17	15	z	z	NOUN
ejpam-887	17	16	)	)	PUNCT
ejpam-887	17	17	=	=	PUNCT
ejpam-887	17	18	g(w(z	g(w(z	PROPN
ejpam-887	17	19	)	)	PUNCT
ejpam-887	17	20	)	)	PUNCT
ejpam-887	18	1	(	(	PUNCT
ejpam-887	18	2	z	z	NOUN
ejpam-887	18	3	∈	∈	PROPN
ejpam-887	18	4	u	u	NOUN
ejpam-887	18	5	)	)	PUNCT
ejpam-887	18	6	.	.	PUNCT
ejpam-887	19	1	in	in	ADP
ejpam-887	19	2	particular	particular	ADJ
ejpam-887	19	3	,	,	PUNCT
ejpam-887	19	4	if	if	SCONJ
ejpam-887	19	5	the	the	DET
ejpam-887	19	6	function	function	NOUN
ejpam-887	19	7	g	g	PROPN
ejpam-887	19	8	is	be	AUX
ejpam-887	19	9	univalent	univalent	ADJ
ejpam-887	19	10	in	in	ADP
ejpam-887	19	11	u	u	PROPN
ejpam-887	19	12	,	,	PUNCT
ejpam-887	19	13	the	the	DET
ejpam-887	19	14	above	above	ADJ
ejpam-887	19	15	subordination	subordination	NOUN
ejpam-887	19	16	is	be	AUX
ejpam-887	19	17	equivalent	equivalent	ADJ
ejpam-887	19	18	to	to	ADP
ejpam-887	19	19	f	f	PROPN
ejpam-887	19	20	(	(	PUNCT
ejpam-887	19	21	0	0	NUM
ejpam-887	19	22	)	)	PUNCT
ejpam-887	19	23	=	=	SYM
ejpam-887	19	24	g(0	g(0	PROPN
ejpam-887	19	25	)	)	PUNCT
ejpam-887	19	26	and	and	CCONJ
ejpam-887	19	27	f	f	PROPN
ejpam-887	19	28	(	(	PUNCT
ejpam-887	19	29	u)⊂	u)⊂	CCONJ
ejpam-887	19	30	g(u	g(u	PROPN
ejpam-887	19	31	)	)	PUNCT
ejpam-887	19	32	.	.	PUNCT
ejpam-887	20	1	in	in	ADP
ejpam-887	20	2	many	many	ADJ
ejpam-887	20	3	earlier	early	ADJ
ejpam-887	20	4	investigations	investigation	NOUN
ejpam-887	20	5	various	various	ADJ
ejpam-887	20	6	interesting	interesting	ADJ
ejpam-887	20	7	subclasses	subclass	NOUN
ejpam-887	20	8	of	of	ADP
ejpam-887	20	9	the	the	DET
ejpam-887	20	10	analytic	analytic	ADJ
ejpam-887	20	11	function	function	NOUN
ejpam-887	20	12	class	class	NOUN
ejpam-887	20	13	a	a	NOUN
ejpam-887	20	14	and	and	CCONJ
ejpam-887	20	15	the	the	DET
ejpam-887	20	16	univalent	univalent	ADJ
ejpam-887	20	17	function	function	NOUN
ejpam-887	20	18	class	class	NOUN
ejpam-887	20	19	s	s	VERB
ejpam-887	20	20	have	have	AUX
ejpam-887	20	21	been	be	AUX
ejpam-887	20	22	studied	study	VERB
ejpam-887	20	23	from	from	ADP
ejpam-887	20	24	a	a	DET
ejpam-887	20	25	number	number	NOUN
ejpam-887	20	26	of	of	ADP
ejpam-887	20	27	different	different	ADJ
ejpam-887	20	28	viewpoints	viewpoint	NOUN
ejpam-887	20	29	.	.	PUNCT
ejpam-887	21	1	we	we	PRON
ejpam-887	21	2	choose	choose	VERB
ejpam-887	21	3	to	to	PART
ejpam-887	21	4	recall	recall	VERB
ejpam-887	21	5	here	here	ADV
ejpam-887	21	6	the	the	DET
ejpam-887	21	7	investigations	investigation	NOUN
ejpam-887	21	8	by	by	ADP
ejpam-887	21	9	(	(	PUNCT
ejpam-887	21	10	for	for	ADP
ejpam-887	21	11	example	example	NOUN
ejpam-887	21	12	)	)	PUNCT
ejpam-887	21	13	srivastava	srivastava	PROPN
ejpam-887	21	14	et	et	PROPN
ejpam-887	21	15	al	al	PROPN
ejpam-887	21	16	(	(	PUNCT
ejpam-887	21	17	[	[	X
ejpam-887	21	18	1	1	NUM
ejpam-887	21	19	]	]	PUNCT
ejpam-887	21	20	,	,	PUNCT
ejpam-887	21	21	[	[	X
ejpam-887	21	22	2	2	NUM
ejpam-887	21	23	]	]	PUNCT
ejpam-887	21	24	and	and	CCONJ
ejpam-887	21	25	[	[	X
ejpam-887	21	26	3	3	NUM
ejpam-887	21	27	]	]	NUM
ejpam-887	21	28	)	)	PUNCT
ejpam-887	21	29	,	,	PUNCT
ejpam-887	21	30	breaz	breaz	VERB
ejpam-887	21	31	et	et	PROPN
ejpam-887	21	32	al.[4	al.[4	PROPN
ejpam-887	21	33	]	]	PUNCT
ejpam-887	21	34	,	,	PUNCT
ejpam-887	21	35	owa	owa	PROPN
ejpam-887	21	36	et	et	PROPN
ejpam-887	21	37	al	al	PROPN
ejpam-887	21	38	.	.	PUNCT
ejpam-887	22	1	[	[	X
ejpam-887	22	2	5	5	NUM
ejpam-887	22	3	]	]	PUNCT
ejpam-887	22	4	,	,	PUNCT
ejpam-887	22	5	in	in	ADP
ejpam-887	22	6	particular	particular	ADJ
ejpam-887	22	7	,	,	PUNCT
ejpam-887	22	8	sakaguchi	sakaguchi	ADJ
ejpam-887	22	9	[	[	X
ejpam-887	22	10	6	6	NUM
ejpam-887	22	11	]	]	PUNCT
ejpam-887	22	12	introduced	introduce	VERB
ejpam-887	22	13	a	a	DET
ejpam-887	22	14	subclass	subclass	NOUN
ejpam-887	22	15	s	s	PART
ejpam-887	22	16	∗s	∗s	NOUN
ejpam-887	22	17	of	of	ADP
ejpam-887	22	18	analytic	analytic	ADJ
ejpam-887	22	19	functions	function	NOUN
ejpam-887	22	20	.	.	PUNCT
ejpam-887	23	1	definition	definition	NOUN
ejpam-887	23	2	1	1	NUM
ejpam-887	23	3	.	.	PUNCT
ejpam-887	24	1	(	(	PUNCT
ejpam-887	24	2	[	[	X
ejpam-887	24	3	6	6	NUM
ejpam-887	24	4	]	]	NUM
ejpam-887	24	5	)	)	PUNCT
ejpam-887	24	6	.	.	PUNCT
ejpam-887	25	1	a	a	DET
ejpam-887	25	2	function	function	NOUN
ejpam-887	25	3	f	f	X
ejpam-887	25	4	(	(	PUNCT
ejpam-887	25	5	z	z	NOUN
ejpam-887	25	6	)	)	PUNCT
ejpam-887	25	7	∈	∈	PROPN
ejpam-887	25	8	a	a	PRON
ejpam-887	25	9	is	be	AUX
ejpam-887	25	10	said	say	VERB
ejpam-887	25	11	to	to	PART
ejpam-887	25	12	belong	belong	VERB
ejpam-887	25	13	to	to	ADP
ejpam-887	25	14	the	the	DET
ejpam-887	25	15	class	class	NOUN
ejpam-887	25	16	s	s	PART
ejpam-887	25	17	∗s	∗s	NOUN
ejpam-887	25	18	of	of	ADP
ejpam-887	25	19	starlike	starlike	NOUN
ejpam-887	25	20	with	with	ADP
ejpam-887	25	21	respect	respect	NOUN
ejpam-887	25	22	to	to	ADP
ejpam-887	25	23	symmetric	symmetric	ADJ
ejpam-887	25	24	points	point	NOUN
ejpam-887	25	25	in	in	ADP
ejpam-887	25	26	u	u	NOUN
ejpam-887	25	27	if	if	SCONJ
ejpam-887	25	28	it	it	PRON
ejpam-887	25	29	satisfies	satisfy	VERB
ejpam-887	25	30	the	the	DET
ejpam-887	25	31	following	follow	VERB
ejpam-887	25	32	inequality	inequality	NOUN
ejpam-887	25	33	:	:	PUNCT
ejpam-887	26	1	ℜ	ℜ	ADJ
ejpam-887	26	2	¨	¨	NOUN
ejpam-887	26	3	2z	2z	NUM
ejpam-887	26	4	f	f	NOUN
ejpam-887	26	5	′(z	′(z	NOUN
ejpam-887	26	6	)	)	PUNCT
ejpam-887	26	7	f	f	PROPN
ejpam-887	26	8	(	(	PUNCT
ejpam-887	26	9	z)−	z)−	PROPN
ejpam-887	26	10	f	f	X
ejpam-887	26	11	(	(	PUNCT
ejpam-887	26	12	−z	−z	NOUN
ejpam-887	26	13	)	)	PUNCT
ejpam-887	26	14	«	«	PUNCT
ejpam-887	26	15	>	>	X
ejpam-887	26	16	0	0	PUNCT
ejpam-887	26	17	(	(	PUNCT
ejpam-887	26	18	z	z	NOUN
ejpam-887	26	19	∈	∈	PROPN
ejpam-887	26	20	u	u	NOUN
ejpam-887	26	21	)	)	PUNCT
ejpam-887	26	22	.	.	PUNCT
ejpam-887	27	1	then	then	ADV
ejpam-887	27	2	,	,	PUNCT
ejpam-887	27	3	goel	goel	PROPN
ejpam-887	27	4	and	and	CCONJ
ejpam-887	27	5	mehrok	mehrok	NOUN
ejpam-887	27	6	in	in	ADP
ejpam-887	27	7	1982	1982	NUM
ejpam-887	27	8	introduced	introduce	VERB
ejpam-887	27	9	a	a	DET
ejpam-887	27	10	subclass	subclass	NOUN
ejpam-887	27	11	of	of	ADP
ejpam-887	27	12	s	s	NOUN
ejpam-887	27	13	∗s	∗s	ADP
ejpam-887	27	14	which	which	PRON
ejpam-887	27	15	were	be	AUX
ejpam-887	27	16	denoted	denote	VERB
ejpam-887	27	17	by	by	ADP
ejpam-887	27	18	s	s	PROPN
ejpam-887	27	19	∗s	∗s	PROPN
ejpam-887	27	20	(	(	PUNCT
ejpam-887	27	21	a	a	DET
ejpam-887	27	22	,	,	PUNCT
ejpam-887	27	23	b	b	NOUN
ejpam-887	27	24	)	)	PUNCT
ejpam-887	27	25	.	.	PUNCT
ejpam-887	28	1	definition	definition	NOUN
ejpam-887	28	2	2	2	NUM
ejpam-887	28	3	.	.	PUNCT
ejpam-887	29	1	(	(	PUNCT
ejpam-887	29	2	see	see	VERB
ejpam-887	29	3	[	[	X
ejpam-887	29	4	7	7	NUM
ejpam-887	29	5	]	]	PUNCT
ejpam-887	29	6	)	)	PUNCT
ejpam-887	29	7	a	a	DET
ejpam-887	29	8	function	function	NOUN
ejpam-887	29	9	f	f	X
ejpam-887	29	10	(	(	PUNCT
ejpam-887	29	11	z	z	NOUN
ejpam-887	29	12	)	)	PUNCT
ejpam-887	29	13	∈a	∈a	NUM
ejpam-887	29	14	is	be	AUX
ejpam-887	29	15	said	say	VERB
ejpam-887	29	16	to	to	PART
ejpam-887	29	17	belong	belong	VERB
ejpam-887	29	18	to	to	ADP
ejpam-887	29	19	the	the	DET
ejpam-887	29	20	class	class	NOUN
ejpam-887	29	21	s	s	PART
ejpam-887	29	22	∗s	∗s	NOUN
ejpam-887	29	23	(	(	PUNCT
ejpam-887	29	24	a	a	DET
ejpam-887	29	25	,	,	PUNCT
ejpam-887	29	26	b	b	NOUN
ejpam-887	29	27	)	)	PUNCT
ejpam-887	29	28	if	if	SCONJ
ejpam-887	29	29	it	it	PRON
ejpam-887	29	30	satisfies	satisfy	VERB
ejpam-887	29	31	the	the	DET
ejpam-887	29	32	following	follow	VERB
ejpam-887	29	33	condition	condition	NOUN
ejpam-887	29	34	:	:	PUNCT
ejpam-887	29	35	2z	2z	NUM
ejpam-887	29	36	f	f	NOUN
ejpam-887	29	37	′(z	′(z	NOUN
ejpam-887	29	38	)	)	PUNCT
ejpam-887	29	39	f	f	PROPN
ejpam-887	29	40	(	(	PUNCT
ejpam-887	29	41	z)−	z)−	PROPN
ejpam-887	29	42	f	f	X
ejpam-887	29	43	(	(	PUNCT
ejpam-887	29	44	−z	−z	NOUN
ejpam-887	29	45	)	)	PUNCT
ejpam-887	29	46	≺	≺	NOUN
ejpam-887	29	47	1	1	NUM
ejpam-887	29	48	+	+	NUM
ejpam-887	29	49	az	az	PROPN
ejpam-887	29	50	1	1	NUM
ejpam-887	29	51	+	+	CCONJ
ejpam-887	29	52	bz	bz	PROPN
ejpam-887	29	53	(	(	PUNCT
ejpam-887	29	54	z	z	NOUN
ejpam-887	29	55	∈	∈	PROPN
ejpam-887	29	56	u	u	NOUN
ejpam-887	29	57	;	;	PUNCT
ejpam-887	29	58	−1≤	−1≤	PROPN
ejpam-887	29	59	b	b	NOUN
ejpam-887	29	60	<	<	X
ejpam-887	29	61	a≤	a≤	ADP
ejpam-887	29	62	1	1	NUM
ejpam-887	29	63	)	)	PUNCT
ejpam-887	29	64	.	.	PUNCT
ejpam-887	30	1	recently	recently	ADV
ejpam-887	30	2	,	,	PUNCT
ejpam-887	30	3	aini	aini	PROPN
ejpam-887	30	4	janteng	janteng	PROPN
ejpam-887	30	5	and	and	CCONJ
ejpam-887	30	6	suzeini	suzeini	PROPN
ejpam-887	30	7	abdul	abdul	PROPN
ejpam-887	30	8	[	[	X
ejpam-887	30	9	8	8	NUM
ejpam-887	30	10	]	]	X
ejpam-887	30	11	extended	extended	ADJ
ejpam-887	30	12	definition	definition	NOUN
ejpam-887	30	13	2	2	NUM
ejpam-887	30	14	by	by	ADP
ejpam-887	30	15	introducing	introduce	VERB
ejpam-887	30	16	the	the	DET
ejpam-887	30	17	following	follow	VERB
ejpam-887	30	18	subclass	subclass	NOUN
ejpam-887	30	19	of	of	ADP
ejpam-887	30	20	analytic	analytic	ADJ
ejpam-887	30	21	functions	function	NOUN
ejpam-887	30	22	.	.	PUNCT
ejpam-887	31	1	definition	definition	NOUN
ejpam-887	31	2	3	3	NUM
ejpam-887	31	3	.	.	PUNCT
ejpam-887	32	1	(	(	PUNCT
ejpam-887	32	2	see	see	VERB
ejpam-887	32	3	[	[	X
ejpam-887	32	4	8	8	NUM
ejpam-887	32	5	]	]	PUNCT
ejpam-887	32	6	)	)	PUNCT
ejpam-887	32	7	let	let	VERB
ejpam-887	32	8	the	the	DET
ejpam-887	32	9	function	function	NOUN
ejpam-887	32	10	f	f	PROPN
ejpam-887	32	11	(	(	PUNCT
ejpam-887	32	12	z	z	NOUN
ejpam-887	32	13	)	)	PUNCT
ejpam-887	32	14	be	be	AUX
ejpam-887	32	15	analytic	analytic	ADJ
ejpam-887	32	16	in	in	ADP
ejpam-887	32	17	u	u	NOUN
ejpam-887	32	18	and	and	CCONJ
ejpam-887	32	19	defined	define	VERB
ejpam-887	32	20	by	by	ADP
ejpam-887	32	21	(	(	PUNCT
ejpam-887	32	22	1	1	NUM
ejpam-887	32	23	)	)	PUNCT
ejpam-887	32	24	.	.	PUNCT
ejpam-887	33	1	we	we	PRON
ejpam-887	33	2	say	say	VERB
ejpam-887	33	3	that	that	SCONJ
ejpam-887	33	4	f	f	PROPN
ejpam-887	33	5	∈k	∈k	ADP
ejpam-887	33	6	∗s	∗s	PROPN
ejpam-887	33	7	(	(	PUNCT
ejpam-887	33	8	a	a	DET
ejpam-887	33	9	,	,	PUNCT
ejpam-887	33	10	b	b	NOUN
ejpam-887	33	11	)	)	PUNCT
ejpam-887	33	12	if	if	SCONJ
ejpam-887	33	13	there	there	PRON
ejpam-887	33	14	exists	exist	VERB
ejpam-887	33	15	a	a	DET
ejpam-887	33	16	function	function	NOUN
ejpam-887	33	17	h(z	h(z	NOUN
ejpam-887	33	18	)	)	PUNCT
ejpam-887	33	19	∈	∈	PROPN
ejpam-887	33	20	s	s	PART
ejpam-887	33	21	∗s	∗s	NOUN
ejpam-887	33	22	(	(	PUNCT
ejpam-887	33	23	a	a	DET
ejpam-887	33	24	,	,	PUNCT
ejpam-887	33	25	b	b	NOUN
ejpam-887	33	26	)	)	PUNCT
ejpam-887	33	27	such	such	ADJ
ejpam-887	33	28	that	that	SCONJ
ejpam-887	33	29	2z	2z	NUM
ejpam-887	33	30	f	f	NOUN
ejpam-887	33	31	′(z	′(z	NOUN
ejpam-887	33	32	)	)	PUNCT
ejpam-887	33	33	h(z)−	h(z)−	PROPN
ejpam-887	33	34	h(−z	h(−z	NOUN
ejpam-887	33	35	)	)	PUNCT
ejpam-887	33	36	≺	≺	NOUN
ejpam-887	33	37	1	1	NUM
ejpam-887	33	38	+	+	NUM
ejpam-887	33	39	az	az	PROPN
ejpam-887	33	40	1	1	NUM
ejpam-887	33	41	+	+	CCONJ
ejpam-887	33	42	bz	bz	PROPN
ejpam-887	33	43	(	(	PUNCT
ejpam-887	33	44	z	z	NOUN
ejpam-887	33	45	∈	∈	PROPN
ejpam-887	33	46	u	u	NOUN
ejpam-887	33	47	;	;	PUNCT
ejpam-887	33	48	−1≤	−1≤	PROPN
ejpam-887	33	49	b	b	NOUN
ejpam-887	33	50	<	<	X
ejpam-887	33	51	a≤	a≤	ADP
ejpam-887	33	52	1	1	NUM
ejpam-887	33	53	)	)	PUNCT
ejpam-887	33	54	.	.	PUNCT
ejpam-887	34	1	here	here	ADV
ejpam-887	34	2	,	,	PUNCT
ejpam-887	34	3	in	in	ADP
ejpam-887	34	4	our	our	PRON
ejpam-887	34	5	present	present	ADJ
ejpam-887	34	6	sequel	sequel	NOUN
ejpam-887	34	7	to	to	ADP
ejpam-887	34	8	some	some	PRON
ejpam-887	34	9	of	of	ADP
ejpam-887	34	10	the	the	DET
ejpam-887	34	11	aforecited	aforecite	VERB
ejpam-887	34	12	works	work	NOUN
ejpam-887	34	13	(	(	PUNCT
ejpam-887	34	14	especially	especially	ADV
ejpam-887	34	15	[	[	X
ejpam-887	34	16	7	7	NUM
ejpam-887	34	17	]	]	PUNCT
ejpam-887	34	18	and	and	CCONJ
ejpam-887	34	19	[	[	X
ejpam-887	34	20	8	8	NUM
ejpam-887	34	21	]	]	NUM
ejpam-887	34	22	)	)	PUNCT
ejpam-887	34	23	,	,	PUNCT
ejpam-887	34	24	we	we	PRON
ejpam-887	34	25	introduce	introduce	VERB
ejpam-887	34	26	the	the	DET
ejpam-887	34	27	following	following	ADJ
ejpam-887	34	28	subclass	subclass	NOUN
ejpam-887	34	29	of	of	ADP
ejpam-887	34	30	analytic	analytic	ADJ
ejpam-887	34	31	functions	function	NOUN
ejpam-887	34	32	.	.	PUNCT
ejpam-887	35	1	q.	q.	PROPN
ejpam-887	35	2	xu	xu	PROPN
ejpam-887	35	3	,	,	PUNCT
ejpam-887	35	4	g.	g.	PROPN
ejpam-887	35	5	wu	wu	PROPN
ejpam-887	35	6	/	/	SYM
ejpam-887	35	7	eur	eur	PROPN
ejpam-887	35	8	.	.	PUNCT
ejpam-887	36	1	j.	j.	PROPN
ejpam-887	36	2	pure	pure	PROPN
ejpam-887	36	3	appl	appl	PROPN
ejpam-887	36	4	.	.	PROPN
ejpam-887	36	5	math	math	PROPN
ejpam-887	36	6	,	,	PUNCT
ejpam-887	36	7	3	3	NUM
ejpam-887	36	8	(	(	PUNCT
ejpam-887	36	9	2010	2010	NUM
ejpam-887	36	10	)	)	PUNCT
ejpam-887	36	11	,	,	PUNCT
ejpam-887	36	12	1055	1055	NUM
ejpam-887	36	13	-	-	SYM
ejpam-887	36	14	1061	1061	NUM
ejpam-887	36	15	1057	1057	NUM
ejpam-887	36	16	definition	definition	NOUN
ejpam-887	36	17	4	4	NUM
ejpam-887	36	18	.	.	PUNCT
ejpam-887	37	1	let	let	VERB
ejpam-887	37	2	g	g	NOUN
ejpam-887	37	3	:	:	PUNCT
ejpam-887	37	4	u→	u→	PROPN
ejpam-887	37	5	c	c	NOUN
ejpam-887	37	6	be	be	AUX
ejpam-887	37	7	a	a	DET
ejpam-887	37	8	convex	convex	NOUN
ejpam-887	37	9	function	function	NOUN
ejpam-887	37	10	such	such	ADJ
ejpam-887	37	11	that	that	PRON
ejpam-887	37	12	g(0	g(0	NOUN
ejpam-887	37	13	)	)	PUNCT
ejpam-887	37	14	=	=	SYM
ejpam-887	37	15	1	1	NUM
ejpam-887	37	16	,	,	PUNCT
ejpam-887	37	17	g(z̄	g(z̄	NOUN
ejpam-887	37	18	)	)	PUNCT
ejpam-887	37	19	=	=	PUNCT
ejpam-887	38	1	g(z	g(z	PROPN
ejpam-887	38	2	)	)	PUNCT
ejpam-887	38	3	,	,	PUNCT
ejpam-887	38	4	for	for	ADP
ejpam-887	38	5	z	z	PROPN
ejpam-887	38	6	∈	∈	PROPN
ejpam-887	38	7	u	u	PROPN
ejpam-887	38	8	,	,	PUNCT
ejpam-887	38	9	ℜ(g(z	ℜ(g(z	PROPN
ejpam-887	38	10	)	)	PUNCT
ejpam-887	38	11	)	)	PUNCT
ejpam-887	38	12	>	>	X
ejpam-887	38	13	0	0	PUNCT
ejpam-887	39	1	on	on	ADP
ejpam-887	39	2	z	z	PROPN
ejpam-887	39	3	∈	∈	PROPN
ejpam-887	39	4	u.	u.	NOUN
ejpam-887	39	5	let	let	VERB
ejpam-887	39	6	f	f	PRON
ejpam-887	39	7	be	be	AUX
ejpam-887	39	8	an	an	DET
ejpam-887	39	9	analytic	analytic	ADJ
ejpam-887	39	10	function	function	NOUN
ejpam-887	39	11	in	in	ADP
ejpam-887	39	12	u	u	NOUN
ejpam-887	39	13	defined	define	VERB
ejpam-887	39	14	by	by	ADP
ejpam-887	39	15	(	(	PUNCT
ejpam-887	39	16	1	1	NUM
ejpam-887	39	17	)	)	PUNCT
ejpam-887	39	18	.	.	PUNCT
ejpam-887	40	1	we	we	PRON
ejpam-887	40	2	say	say	VERB
ejpam-887	40	3	that	that	SCONJ
ejpam-887	40	4	f	f	PROPN
ejpam-887	40	5	∈	∈	PROPN
ejpam-887	40	6	s	s	PART
ejpam-887	40	7	∗s	∗s	NOUN
ejpam-887	40	8	(	(	PUNCT
ejpam-887	40	9	g	g	NOUN
ejpam-887	40	10	)	)	PUNCT
ejpam-887	40	11	,	,	PUNCT
ejpam-887	40	12	if	if	SCONJ
ejpam-887	40	13	it	it	PRON
ejpam-887	40	14	satisfies	satisfy	VERB
ejpam-887	40	15	the	the	DET
ejpam-887	40	16	following	follow	VERB
ejpam-887	40	17	condition	condition	NOUN
ejpam-887	40	18	:	:	PUNCT
ejpam-887	40	19	2z	2z	NUM
ejpam-887	40	20	f	f	NOUN
ejpam-887	40	21	′(z	′(z	NOUN
ejpam-887	40	22	)	)	PUNCT
ejpam-887	40	23	f	f	PROPN
ejpam-887	40	24	(	(	PUNCT
ejpam-887	40	25	z)−	z)−	PROPN
ejpam-887	40	26	f	f	X
ejpam-887	40	27	(	(	PUNCT
ejpam-887	40	28	−z	−z	NOUN
ejpam-887	40	29	)	)	PUNCT
ejpam-887	40	30	∈	∈	PROPN
ejpam-887	40	31	g(u	g(u	PROPN
ejpam-887	40	32	)	)	PUNCT
ejpam-887	40	33	(	(	PUNCT
ejpam-887	40	34	z	z	NOUN
ejpam-887	40	35	∈	∈	PROPN
ejpam-887	40	36	u	u	NOUN
ejpam-887	40	37	)	)	PUNCT
ejpam-887	40	38	.	.	PUNCT
ejpam-887	41	1	definition	definition	NOUN
ejpam-887	41	2	5	5	NUM
ejpam-887	41	3	.	.	PUNCT
ejpam-887	42	1	let	let	VERB
ejpam-887	42	2	g	g	PRON
ejpam-887	42	3	satisfy	satisfy	VERB
ejpam-887	42	4	the	the	DET
ejpam-887	42	5	conditions	condition	NOUN
ejpam-887	42	6	of	of	ADP
ejpam-887	42	7	definition	definition	NOUN
ejpam-887	42	8	4	4	NUM
ejpam-887	42	9	and	and	CCONJ
ejpam-887	42	10	f	f	PROPN
ejpam-887	42	11	be	be	AUX
ejpam-887	42	12	an	an	DET
ejpam-887	42	13	analytic	analytic	ADJ
ejpam-887	42	14	function	function	NOUN
ejpam-887	42	15	in	in	ADP
ejpam-887	42	16	u	u	NOUN
ejpam-887	42	17	defined	define	VERB
ejpam-887	42	18	by	by	ADP
ejpam-887	42	19	(	(	PUNCT
ejpam-887	42	20	1	1	NUM
ejpam-887	42	21	)	)	PUNCT
ejpam-887	42	22	.	.	PUNCT
ejpam-887	43	1	we	we	PRON
ejpam-887	43	2	say	say	VERB
ejpam-887	43	3	that	that	SCONJ
ejpam-887	43	4	f	f	PROPN
ejpam-887	43	5	∈k	∈k	ADP
ejpam-887	43	6	∗s	∗s	PROPN
ejpam-887	43	7	(	(	PUNCT
ejpam-887	43	8	g	g	NOUN
ejpam-887	43	9	)	)	PUNCT
ejpam-887	43	10	if	if	SCONJ
ejpam-887	43	11	there	there	PRON
ejpam-887	43	12	exists	exist	VERB
ejpam-887	43	13	a	a	DET
ejpam-887	43	14	function	function	NOUN
ejpam-887	43	15	h(z	h(z	NOUN
ejpam-887	43	16	)	)	PUNCT
ejpam-887	43	17	∈	∈	PROPN
ejpam-887	43	18	s	s	PART
ejpam-887	43	19	∗s	∗s	NOUN
ejpam-887	43	20	(	(	PUNCT
ejpam-887	43	21	g	g	NOUN
ejpam-887	43	22	)	)	PUNCT
ejpam-887	43	23	such	such	ADJ
ejpam-887	43	24	that	that	SCONJ
ejpam-887	43	25	2z	2z	NUM
ejpam-887	43	26	f	f	NOUN
ejpam-887	43	27	′(z	′(z	NOUN
ejpam-887	43	28	)	)	PUNCT
ejpam-887	43	29	h(z)−	h(z)−	PROPN
ejpam-887	43	30	h(−z	h(−z	NOUN
ejpam-887	43	31	)	)	PUNCT
ejpam-887	43	32	∈	∈	PROPN
ejpam-887	43	33	g(u	g(u	PROPN
ejpam-887	43	34	)	)	PUNCT
ejpam-887	43	35	(	(	PUNCT
ejpam-887	43	36	z	z	NOUN
ejpam-887	43	37	∈	∈	PROPN
ejpam-887	43	38	u	u	NOUN
ejpam-887	43	39	)	)	PUNCT
ejpam-887	43	40	.	.	PUNCT
ejpam-887	44	1	remark	remark	PROPN
ejpam-887	44	2	1	1	NUM
ejpam-887	44	3	.	.	PUNCT
ejpam-887	45	1	there	there	PRON
ejpam-887	45	2	are	be	VERB
ejpam-887	45	3	many	many	ADJ
ejpam-887	45	4	choices	choice	NOUN
ejpam-887	45	5	of	of	ADP
ejpam-887	45	6	the	the	DET
ejpam-887	45	7	function	function	NOUN
ejpam-887	45	8	g	g	NOUN
ejpam-887	45	9	which	which	PRON
ejpam-887	45	10	would	would	AUX
ejpam-887	45	11	provide	provide	VERB
ejpam-887	45	12	interesting	interesting	ADJ
ejpam-887	45	13	subclasses	subclass	NOUN
ejpam-887	45	14	of	of	ADP
ejpam-887	45	15	analytic	analytic	ADJ
ejpam-887	45	16	functions	function	NOUN
ejpam-887	45	17	.	.	PUNCT
ejpam-887	46	1	for	for	ADP
ejpam-887	46	2	example	example	NOUN
ejpam-887	46	3	,	,	PUNCT
ejpam-887	46	4	if	if	SCONJ
ejpam-887	46	5	we	we	PRON
ejpam-887	46	6	let	let	VERB
ejpam-887	46	7	g(z	g(z	ADJ
ejpam-887	46	8	)	)	PUNCT
ejpam-887	46	9	=	=	SYM
ejpam-887	47	1	1	1	NUM
ejpam-887	47	2	+	+	NUM
ejpam-887	47	3	az	az	PROPN
ejpam-887	47	4	1	1	NUM
ejpam-887	47	5	+	+	CCONJ
ejpam-887	47	6	bz	bz	PROPN
ejpam-887	47	7	(	(	PUNCT
ejpam-887	47	8	z	z	NOUN
ejpam-887	47	9	∈	∈	PROPN
ejpam-887	47	10	u	u	NOUN
ejpam-887	47	11	;	;	PUNCT
ejpam-887	47	12	−1≤	−1≤	PROPN
ejpam-887	47	13	b	b	NOUN
ejpam-887	47	14	<	<	X
ejpam-887	47	15	a≤	a≤	ADP
ejpam-887	47	16	1	1	NUM
ejpam-887	47	17	)	)	PUNCT
ejpam-887	47	18	,	,	PUNCT
ejpam-887	47	19	then	then	ADV
ejpam-887	47	20	it	it	PRON
ejpam-887	47	21	is	be	AUX
ejpam-887	47	22	easy	easy	ADJ
ejpam-887	47	23	to	to	PART
ejpam-887	47	24	verify	verify	VERB
ejpam-887	47	25	that	that	SCONJ
ejpam-887	47	26	g	g	PROPN
ejpam-887	47	27	satisfies	satisfy	VERB
ejpam-887	47	28	the	the	DET
ejpam-887	47	29	hypotheses	hypothesis	NOUN
ejpam-887	47	30	of	of	ADP
ejpam-887	47	31	definition	definition	NOUN
ejpam-887	47	32	4	4	NUM
ejpam-887	47	33	.	.	PUNCT
ejpam-887	48	1	so	so	ADV
ejpam-887	48	2	,	,	PUNCT
ejpam-887	48	3	by	by	ADP
ejpam-887	48	4	taking	take	VERB
ejpam-887	48	5	g(z	g(z	PROPN
ejpam-887	48	6	)	)	PUNCT
ejpam-887	48	7	=	=	SYM
ejpam-887	49	1	1	1	NUM
ejpam-887	49	2	+	+	NUM
ejpam-887	49	3	az	az	PROPN
ejpam-887	49	4	1	1	NUM
ejpam-887	49	5	+	+	CCONJ
ejpam-887	49	6	bz	bz	PROPN
ejpam-887	49	7	(	(	PUNCT
ejpam-887	49	8	z	z	NOUN
ejpam-887	49	9	∈	∈	PROPN
ejpam-887	49	10	u	u	NOUN
ejpam-887	49	11	;	;	PUNCT
ejpam-887	49	12	−1≤	−1≤	PROPN
ejpam-887	49	13	b	b	NOUN
ejpam-887	49	14	<	<	X
ejpam-887	49	15	a≤	a≤	ADP
ejpam-887	49	16	1	1	NUM
ejpam-887	49	17	)	)	PUNCT
ejpam-887	49	18	in	in	ADP
ejpam-887	49	19	definitions	definition	NOUN
ejpam-887	49	20	4	4	NUM
ejpam-887	49	21	and	and	CCONJ
ejpam-887	49	22	5	5	NUM
ejpam-887	49	23	,	,	PUNCT
ejpam-887	49	24	we	we	PRON
ejpam-887	49	25	easily	easily	ADV
ejpam-887	49	26	observe	observe	VERB
ejpam-887	49	27	that	that	SCONJ
ejpam-887	49	28	the	the	DET
ejpam-887	49	29	function	function	NOUN
ejpam-887	49	30	classes	class	NOUN
ejpam-887	49	31	s	s	PART
ejpam-887	49	32	∗s	∗s	NOUN
ejpam-887	49	33	(	(	PUNCT
ejpam-887	49	34	g	g	NOUN
ejpam-887	49	35	)	)	PUNCT
ejpam-887	49	36	and	and	CCONJ
ejpam-887	49	37	k	k	PROPN
ejpam-887	49	38	∗s	∗s	PROPN
ejpam-887	49	39	(	(	PUNCT
ejpam-887	49	40	g	g	NOUN
ejpam-887	49	41	)	)	PUNCT
ejpam-887	49	42	become	become	VERB
ejpam-887	49	43	the	the	DET
ejpam-887	49	44	aforementioned	aforementioned	ADJ
ejpam-887	49	45	function	function	NOUN
ejpam-887	49	46	classes	class	NOUN
ejpam-887	49	47	s	s	PART
ejpam-887	49	48	∗s	∗s	NOUN
ejpam-887	49	49	(	(	PUNCT
ejpam-887	49	50	a	a	DET
ejpam-887	49	51	,	,	PUNCT
ejpam-887	49	52	b	b	NOUN
ejpam-887	49	53	)	)	PUNCT
ejpam-887	49	54	and	and	CCONJ
ejpam-887	49	55	k	k	PROPN
ejpam-887	49	56	∗s	∗s	PROPN
ejpam-887	49	57	(	(	PUNCT
ejpam-887	49	58	a	a	DET
ejpam-887	49	59	,	,	PUNCT
ejpam-887	49	60	b	b	NOUN
ejpam-887	49	61	)	)	PUNCT
ejpam-887	49	62	,	,	PUNCT
ejpam-887	49	63	respectively	respectively	ADV
ejpam-887	49	64	.	.	PUNCT
ejpam-887	50	1	in	in	ADP
ejpam-887	50	2	this	this	DET
ejpam-887	50	3	paper	paper	NOUN
ejpam-887	50	4	,	,	PUNCT
ejpam-887	50	5	by	by	ADP
ejpam-887	50	6	using	use	VERB
ejpam-887	50	7	the	the	DET
ejpam-887	50	8	principle	principle	NOUN
ejpam-887	50	9	of	of	ADP
ejpam-887	50	10	subordination	subordination	NOUN
ejpam-887	50	11	,	,	PUNCT
ejpam-887	50	12	we	we	PRON
ejpam-887	50	13	obtain	obtain	VERB
ejpam-887	50	14	coefficient	coefficient	NOUN
ejpam-887	50	15	bounds	bound	NOUN
ejpam-887	50	16	for	for	ADP
ejpam-887	50	17	functions	function	NOUN
ejpam-887	50	18	in	in	ADP
ejpam-887	50	19	the	the	DET
ejpam-887	50	20	subclasses	subclass	NOUN
ejpam-887	50	21	s	s	X
ejpam-887	50	22	∗s	∗s	NOUN
ejpam-887	50	23	(	(	PUNCT
ejpam-887	50	24	g	g	NOUN
ejpam-887	50	25	)	)	PUNCT
ejpam-887	50	26	and	and	CCONJ
ejpam-887	50	27	k	k	PROPN
ejpam-887	50	28	∗s	∗s	PROPN
ejpam-887	50	29	(	(	PUNCT
ejpam-887	50	30	g	g	NOUN
ejpam-887	50	31	)	)	PUNCT
ejpam-887	50	32	.	.	PUNCT
ejpam-887	51	1	our	our	PRON
ejpam-887	51	2	results	result	NOUN
ejpam-887	51	3	would	would	AUX
ejpam-887	51	4	unify	unify	VERB
ejpam-887	51	5	and	and	CCONJ
ejpam-887	51	6	extend	extend	VERB
ejpam-887	51	7	the	the	DET
ejpam-887	51	8	corresponding	corresponding	ADJ
ejpam-887	51	9	works	work	NOUN
ejpam-887	51	10	of	of	ADP
ejpam-887	51	11	some	some	DET
ejpam-887	51	12	authors	author	NOUN
ejpam-887	51	13	.	.	PUNCT
ejpam-887	52	1	2	2	X
ejpam-887	52	2	.	.	X
ejpam-887	52	3	main	main	ADJ
ejpam-887	52	4	results	result	NOUN
ejpam-887	52	5	and	and	CCONJ
ejpam-887	52	6	their	their	PRON
ejpam-887	52	7	proofs	proof	NOUN
ejpam-887	52	8	in	in	ADP
ejpam-887	52	9	order	order	NOUN
ejpam-887	52	10	to	to	PART
ejpam-887	52	11	prove	prove	VERB
ejpam-887	52	12	our	our	PRON
ejpam-887	52	13	main	main	ADJ
ejpam-887	52	14	results	result	NOUN
ejpam-887	52	15	,	,	PUNCT
ejpam-887	52	16	we	we	PRON
ejpam-887	52	17	first	first	ADV
ejpam-887	52	18	recall	recall	VERB
ejpam-887	52	19	the	the	DET
ejpam-887	52	20	following	follow	VERB
ejpam-887	52	21	lemma	lemma	PROPN
ejpam-887	52	22	due	due	ADP
ejpam-887	52	23	to	to	PART
ejpam-887	52	24	rogosinski	rogosinski	VERB
ejpam-887	52	25	.	.	PUNCT
ejpam-887	53	1	lemma	lemma	PROPN
ejpam-887	53	2	1	1	X
ejpam-887	53	3	.	.	PUNCT
ejpam-887	54	1	let	let	VERB
ejpam-887	54	2	the	the	DET
ejpam-887	54	3	function	function	NOUN
ejpam-887	54	4	g	g	NOUN
ejpam-887	54	5	given	give	VERB
ejpam-887	54	6	by	by	ADP
ejpam-887	54	7	g(z	g(z	PROPN
ejpam-887	54	8	)	)	PUNCT
ejpam-887	55	1	=	=	SYM
ejpam-887	55	2	∞	∞	NUM
ejpam-887	55	3	∑	∑	PUNCT
ejpam-887	55	4	k=1	k=1	PROPN
ejpam-887	55	5	gkzk	gkzk	VERB
ejpam-887	55	6	(	(	PUNCT
ejpam-887	55	7	z	z	NOUN
ejpam-887	55	8	∈	∈	PROPN
ejpam-887	55	9	u	u	NOUN
ejpam-887	55	10	)	)	PUNCT
ejpam-887	55	11	q.	q.	PROPN
ejpam-887	55	12	xu	xu	PROPN
ejpam-887	55	13	,	,	PUNCT
ejpam-887	55	14	g.	g.	PROPN
ejpam-887	55	15	wu	wu	PROPN
ejpam-887	55	16	/	/	SYM
ejpam-887	55	17	eur	eur	PROPN
ejpam-887	55	18	.	.	PUNCT
ejpam-887	56	1	j.	j.	PROPN
ejpam-887	56	2	pure	pure	PROPN
ejpam-887	56	3	appl	appl	PROPN
ejpam-887	56	4	.	.	PROPN
ejpam-887	56	5	math	math	PROPN
ejpam-887	56	6	,	,	PUNCT
ejpam-887	56	7	3	3	NUM
ejpam-887	56	8	(	(	PUNCT
ejpam-887	56	9	2010	2010	NUM
ejpam-887	56	10	)	)	PUNCT
ejpam-887	56	11	,	,	PUNCT
ejpam-887	56	12	1055	1055	NUM
ejpam-887	56	13	-	-	SYM
ejpam-887	56	14	1061	1061	NUM
ejpam-887	56	15	1058	1058	NUM
ejpam-887	56	16	be	be	AUX
ejpam-887	56	17	convex	convex	ADJ
ejpam-887	56	18	in	in	ADP
ejpam-887	56	19	u.	u.	PROPN
ejpam-887	56	20	suppose	suppose	VERB
ejpam-887	56	21	also	also	ADV
ejpam-887	56	22	that	that	SCONJ
ejpam-887	56	23	the	the	DET
ejpam-887	56	24	function	function	NOUN
ejpam-887	56	25	f	f	X
ejpam-887	56	26	(	(	PUNCT
ejpam-887	56	27	z	z	NOUN
ejpam-887	56	28	)	)	PUNCT
ejpam-887	56	29	given	give	VERB
ejpam-887	56	30	by	by	ADP
ejpam-887	56	31	f	f	PROPN
ejpam-887	56	32	(	(	PUNCT
ejpam-887	56	33	z	z	NOUN
ejpam-887	56	34	)	)	PUNCT
ejpam-887	56	35	=	=	SYM
ejpam-887	57	1	∞	∞	NUM
ejpam-887	57	2	∑	∑	PUNCT
ejpam-887	57	3	k=1	k=1	PROPN
ejpam-887	57	4	akzk	akzk	PROPN
ejpam-887	57	5	(	(	PUNCT
ejpam-887	57	6	z	z	NOUN
ejpam-887	57	7	∈	∈	PROPN
ejpam-887	57	8	u	u	NOUN
ejpam-887	57	9	)	)	PUNCT
ejpam-887	57	10	be	be	AUX
ejpam-887	57	11	holomorphic	holomorphic	ADJ
ejpam-887	57	12	in	in	ADP
ejpam-887	57	13	u.	u.	PROPN
ejpam-887	57	14	if	if	SCONJ
ejpam-887	57	15	f	f	PROPN
ejpam-887	57	16	(	(	PUNCT
ejpam-887	57	17	z	z	NOUN
ejpam-887	57	18	)	)	PUNCT
ejpam-887	57	19	≺	≺	NOUN
ejpam-887	57	20	g(z	g(z	PROPN
ejpam-887	57	21	)	)	PUNCT
ejpam-887	57	22	(	(	PUNCT
ejpam-887	57	23	z	z	NOUN
ejpam-887	57	24	∈	∈	PROPN
ejpam-887	57	25	u	u	NOUN
ejpam-887	57	26	)	)	PUNCT
ejpam-887	57	27	,	,	PUNCT
ejpam-887	57	28	then	then	ADV
ejpam-887	57	29	|ak|	|ak|	PROPN
ejpam-887	57	30	≤	≤	NUM
ejpam-887	57	31	|g1|	|g1|	NOUN
ejpam-887	57	32	(	(	PUNCT
ejpam-887	57	33	k	k	PROPN
ejpam-887	57	34	∈	∈	PROPN
ejpam-887	57	35	n	n	CCONJ
ejpam-887	57	36	)	)	PUNCT
ejpam-887	57	37	.	.	PUNCT
ejpam-887	58	1	we	we	PRON
ejpam-887	58	2	now	now	ADV
ejpam-887	58	3	state	state	VERB
ejpam-887	58	4	and	and	CCONJ
ejpam-887	58	5	prove	prove	VERB
ejpam-887	58	6	the	the	DET
ejpam-887	58	7	main	main	ADJ
ejpam-887	58	8	results	result	NOUN
ejpam-887	58	9	of	of	ADP
ejpam-887	58	10	our	our	PRON
ejpam-887	58	11	present	present	ADJ
ejpam-887	58	12	investigation	investigation	NOUN
ejpam-887	58	13	.	.	PUNCT
ejpam-887	59	1	theorem	theorem	NOUN
ejpam-887	59	2	1	1	NUM
ejpam-887	59	3	.	.	PUNCT
ejpam-887	60	1	let	let	VERB
ejpam-887	60	2	the	the	DET
ejpam-887	60	3	function	function	NOUN
ejpam-887	60	4	f	f	PROPN
ejpam-887	60	5	(	(	PUNCT
ejpam-887	60	6	z	z	NOUN
ejpam-887	60	7	)	)	PUNCT
ejpam-887	60	8	∈	∈	PROPN
ejpam-887	60	9	a	a	PRON
ejpam-887	60	10	be	be	AUX
ejpam-887	60	11	given	give	VERB
ejpam-887	60	12	by	by	ADP
ejpam-887	60	13	(	(	PUNCT
ejpam-887	60	14	1	1	NUM
ejpam-887	60	15	)	)	PUNCT
ejpam-887	60	16	.	.	PUNCT
ejpam-887	61	1	if	if	SCONJ
ejpam-887	61	2	f	f	PROPN
ejpam-887	61	3	∈	∈	PROPN
ejpam-887	61	4	s	s	X
ejpam-887	61	5	∗s	∗s	NOUN
ejpam-887	61	6	(	(	PUNCT
ejpam-887	61	7	g	g	NOUN
ejpam-887	61	8	)	)	PUNCT
ejpam-887	61	9	,	,	PUNCT
ejpam-887	61	10	then	then	ADV
ejpam-887	61	11	|a2n+1|	|a2n+1|	PROPN
ejpam-887	61	12	≤	≤	PROPN
ejpam-887	61	13	|g′(0)|	|g′(0)|	NOUN
ejpam-887	61	14	n!2n	n!2n	PROPN
ejpam-887	61	15	n−1	n−1	PROPN
ejpam-887	61	16	∏	∏	PROPN
ejpam-887	61	17	j=1	j=1	NOUN
ejpam-887	61	18	(	(	PUNCT
ejpam-887	61	19	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	61	20	2	2	NUM
ejpam-887	61	21	j	j	NOUN
ejpam-887	61	22	)	)	PUNCT
ejpam-887	61	23	(	(	PUNCT
ejpam-887	61	24	n	n	CCONJ
ejpam-887	61	25	∈	∈	PROPN
ejpam-887	61	26	n	n	CCONJ
ejpam-887	61	27	)	)	PUNCT
ejpam-887	61	28	,	,	PUNCT
ejpam-887	61	29	(	(	PUNCT
ejpam-887	61	30	2	2	X
ejpam-887	61	31	)	)	PUNCT
ejpam-887	61	32	and	and	CCONJ
ejpam-887	61	33	|a2n|	|a2n|	NUM
ejpam-887	61	34	≤	≤	NUM
ejpam-887	61	35	|g′(0)|	|g′(0)|	NOUN
ejpam-887	61	36	n!2n	n!2n	PROPN
ejpam-887	61	37	n−1	n−1	PROPN
ejpam-887	61	38	∏	∏	PROPN
ejpam-887	61	39	j=1	j=1	NOUN
ejpam-887	61	40	(	(	PUNCT
ejpam-887	61	41	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	61	42	2	2	NUM
ejpam-887	61	43	j	j	NOUN
ejpam-887	61	44	)	)	PUNCT
ejpam-887	61	45	(	(	PUNCT
ejpam-887	61	46	n	n	CCONJ
ejpam-887	61	47	∈	∈	PROPN
ejpam-887	61	48	n	n	CCONJ
ejpam-887	61	49	)	)	PUNCT
ejpam-887	61	50	.	.	PUNCT
ejpam-887	62	1	(	(	PUNCT
ejpam-887	62	2	3	3	X
ejpam-887	62	3	)	)	PUNCT
ejpam-887	62	4	proof	proof	NOUN
ejpam-887	62	5	.	.	PUNCT
ejpam-887	63	1	first	first	ADV
ejpam-887	63	2	we	we	PRON
ejpam-887	63	3	prove	prove	VERB
ejpam-887	63	4	(	(	PUNCT
ejpam-887	63	5	2	2	X
ejpam-887	63	6	)	)	PUNCT
ejpam-887	63	7	using	use	VERB
ejpam-887	63	8	the	the	DET
ejpam-887	63	9	principle	principle	NOUN
ejpam-887	63	10	of	of	ADP
ejpam-887	63	11	mathematical	mathematical	ADJ
ejpam-887	63	12	induction	induction	NOUN
ejpam-887	63	13	.	.	PUNCT
ejpam-887	64	1	let	let	VERB
ejpam-887	64	2	p(z	p(z	VERB
ejpam-887	64	3	)	)	PUNCT
ejpam-887	65	1	=	=	PUNCT
ejpam-887	66	1	2z	2z	NUM
ejpam-887	66	2	f	f	NOUN
ejpam-887	66	3	′(z	′(z	NOUN
ejpam-887	66	4	)	)	PUNCT
ejpam-887	66	5	f	f	PROPN
ejpam-887	67	1	(	(	PUNCT
ejpam-887	67	2	z)−	z)−	PROPN
ejpam-887	67	3	f	f	X
ejpam-887	67	4	(	(	PUNCT
ejpam-887	67	5	−z	−z	NOUN
ejpam-887	67	6	)	)	PUNCT
ejpam-887	67	7	.	.	PUNCT
ejpam-887	68	1	(	(	PUNCT
ejpam-887	68	2	4	4	X
ejpam-887	68	3	)	)	PUNCT
ejpam-887	68	4	since	since	SCONJ
ejpam-887	68	5	f	f	PROPN
ejpam-887	68	6	∈	∈	PROPN
ejpam-887	68	7	s	s	PART
ejpam-887	68	8	∗s	∗s	NOUN
ejpam-887	68	9	(	(	PUNCT
ejpam-887	68	10	g	g	NOUN
ejpam-887	68	11	)	)	PUNCT
ejpam-887	68	12	,	,	PUNCT
ejpam-887	68	13	it	it	PRON
ejpam-887	68	14	follows	follow	VERB
ejpam-887	68	15	that	that	SCONJ
ejpam-887	68	16	p(0	p(0	NOUN
ejpam-887	68	17	)	)	PUNCT
ejpam-887	68	18	=	=	SYM
ejpam-887	68	19	g(0	g(0	PROPN
ejpam-887	68	20	)	)	PUNCT
ejpam-887	68	21	=	=	SYM
ejpam-887	68	22	1	1	NUM
ejpam-887	68	23	and	and	CCONJ
ejpam-887	68	24	p(z	p(z	NOUN
ejpam-887	68	25	)	)	PUNCT
ejpam-887	68	26	∈	∈	PROPN
ejpam-887	68	27	g(u	g(u	PROPN
ejpam-887	68	28	)	)	PUNCT
ejpam-887	68	29	(	(	PUNCT
ejpam-887	68	30	z	z	NOUN
ejpam-887	68	31	∈	∈	PROPN
ejpam-887	68	32	u	u	NOUN
ejpam-887	68	33	)	)	PUNCT
ejpam-887	68	34	.	.	PUNCT
ejpam-887	69	1	therefore	therefore	ADV
ejpam-887	69	2	,	,	PUNCT
ejpam-887	69	3	we	we	PRON
ejpam-887	69	4	have	have	AUX
ejpam-887	69	5	p(z	p(z	NOUN
ejpam-887	69	6	)	)	PUNCT
ejpam-887	69	7	≺	≺	NOUN
ejpam-887	69	8	g(z	g(z	PROPN
ejpam-887	69	9	)	)	PUNCT
ejpam-887	69	10	(	(	PUNCT
ejpam-887	69	11	z	z	NOUN
ejpam-887	69	12	∈	∈	PROPN
ejpam-887	69	13	u	u	NOUN
ejpam-887	69	14	)	)	PUNCT
ejpam-887	69	15	,	,	PUNCT
ejpam-887	69	16	where	where	SCONJ
ejpam-887	69	17	p(z	p(z	NOUN
ejpam-887	69	18	)	)	PUNCT
ejpam-887	69	19	=	=	SYM
ejpam-887	70	1	1	1	NUM
ejpam-887	70	2	+	+	NUM
ejpam-887	70	3	p1z	p1z	NOUN
ejpam-887	70	4	+	+	CCONJ
ejpam-887	70	5	p2z2	p2z2	X
ejpam-887	70	6	+	+	PUNCT
ejpam-887	70	7	.	.	PUNCT
ejpam-887	70	8	.	.	PUNCT
ejpam-887	70	9	.	.	PUNCT
ejpam-887	71	1	according	accord	VERB
ejpam-887	71	2	to	to	ADP
ejpam-887	71	3	lemma	lemma	PROPN
ejpam-887	71	4	1	1	NUM
ejpam-887	71	5	,	,	PUNCT
ejpam-887	71	6	we	we	PRON
ejpam-887	71	7	obtain	obtain	VERB
ejpam-887	71	8	|pi|	|pi|	NUM
ejpam-887	71	9	≤	≤	NOUN
ejpam-887	71	10	|g	|g	VERB
ejpam-887	71	11	′(0)|	′(0)|	NOUN
ejpam-887	71	12	(	(	PUNCT
ejpam-887	71	13	i	i	NOUN
ejpam-887	71	14	∈	∈	PROPN
ejpam-887	71	15	n	n	CCONJ
ejpam-887	71	16	)	)	PUNCT
ejpam-887	71	17	.	.	PUNCT
ejpam-887	72	1	(	(	PUNCT
ejpam-887	72	2	5	5	NUM
ejpam-887	72	3	)	)	PUNCT
ejpam-887	72	4	from	from	ADP
ejpam-887	72	5	(	(	PUNCT
ejpam-887	72	6	4	4	NUM
ejpam-887	72	7	)	)	PUNCT
ejpam-887	72	8	,	,	PUNCT
ejpam-887	72	9	we	we	PRON
ejpam-887	72	10	deduce	deduce	VERB
ejpam-887	72	11	that	that	SCONJ
ejpam-887	72	12	z	z	PROPN
ejpam-887	73	1	+	+	X
ejpam-887	73	2	2a2z2	2a2z2	NUM
ejpam-887	73	3	+	+	CCONJ
ejpam-887	73	4	3a3z3	3a3z3	NUM
ejpam-887	73	5	+	+	CCONJ
ejpam-887	73	6	.	.	PUNCT
ejpam-887	73	7	.	.	PUNCT
ejpam-887	74	1	.+	.+	NOUN
ejpam-887	75	1	2na2nz2n	2na2nz2n	NUM
ejpam-887	75	2	+	+	CCONJ
ejpam-887	75	3	(	(	PUNCT
ejpam-887	75	4	2n+	2n+	NUM
ejpam-887	75	5	1)a2n+1z2n+1	1)a2n+1z2n+1	NUM
ejpam-887	75	6	+	+	PUNCT
ejpam-887	75	7	.	.	PUNCT
ejpam-887	75	8	.	.	PUNCT
ejpam-887	75	9	.	.	PUNCT
ejpam-887	76	1	=	=	PUNCT
ejpam-887	77	1	[	[	X
ejpam-887	77	2	z	z	X
ejpam-887	77	3	+	+	X
ejpam-887	77	4	a3z3	a3z3	VERB
ejpam-887	77	5	+	+	CCONJ
ejpam-887	77	6	a5z5	a5z5	X
ejpam-887	77	7	+	+	X
ejpam-887	77	8	.	.	PUNCT
ejpam-887	77	9	.	.	PUNCT
ejpam-887	78	1	.+	.+	NOUN
ejpam-887	78	2	a2n−1z2n−1	a2n−1z2n−1	PROPN
ejpam-887	78	3	+	+	CCONJ
ejpam-887	78	4	a2n+1z2n+1	a2n+1z2n+1	PROPN
ejpam-887	78	5	+	+	PUNCT
ejpam-887	78	6	.	.	PUNCT
ejpam-887	78	7	.	.	PUNCT
ejpam-887	79	1	.](1	.](1	PUNCT
ejpam-887	79	2	+	+	NUM
ejpam-887	79	3	p1z	p1z	NOUN
ejpam-887	79	4	+	+	CCONJ
ejpam-887	79	5	p2z2	p2z2	X
ejpam-887	79	6	+	+	PUNCT
ejpam-887	79	7	.	.	PUNCT
ejpam-887	79	8	.	.	PUNCT
ejpam-887	79	9	.	.	PUNCT
ejpam-887	79	10	)	)	PUNCT
ejpam-887	79	11	.	.	PUNCT
ejpam-887	80	1	equating	equate	VERB
ejpam-887	80	2	the	the	DET
ejpam-887	80	3	coefficients	coefficient	NOUN
ejpam-887	80	4	of	of	ADP
ejpam-887	80	5	the	the	DET
ejpam-887	80	6	same	same	ADJ
ejpam-887	80	7	powers	power	NOUN
ejpam-887	80	8	of	of	ADP
ejpam-887	80	9	z	z	NOUN
ejpam-887	80	10	,	,	PUNCT
ejpam-887	80	11	we	we	PRON
ejpam-887	80	12	obtain	obtain	VERB
ejpam-887	80	13	that	that	DET
ejpam-887	80	14	2na2n+1	2na2n+1	NUM
ejpam-887	80	15	=	=	PRON
ejpam-887	80	16	p2n	p2n	PUNCT
ejpam-887	81	1	+	+	CCONJ
ejpam-887	81	2	p2n−2a3	p2n−2a3	ADJ
ejpam-887	81	3	+	+	NOUN
ejpam-887	81	4	.	.	PUNCT
ejpam-887	81	5	.	.	PUNCT
ejpam-887	82	1	.+	.+	NOUN
ejpam-887	82	2	p2a2n−1	p2a2n−1	X
ejpam-887	82	3	(	(	PUNCT
ejpam-887	82	4	n	n	NOUN
ejpam-887	82	5	∈	∈	NOUN
ejpam-887	82	6	n∗	n∗	NOUN
ejpam-887	82	7	:	:	PUNCT
ejpam-887	82	8	=	=	SYM
ejpam-887	82	9	n	n	CCONJ
ejpam-887	82	10	\	\	NOUN
ejpam-887	82	11	{	{	PUNCT
ejpam-887	82	12	1}=	1}=	NUM
ejpam-887	82	13	{	{	PUNCT
ejpam-887	82	14	2,3,4	2,3,4	NUM
ejpam-887	82	15	,	,	PUNCT
ejpam-887	82	16	.	.	PUNCT
ejpam-887	82	17	.	.	PUNCT
ejpam-887	82	18	.	.	PUNCT
ejpam-887	82	19	}	}	PUNCT
ejpam-887	82	20	)	)	PUNCT
ejpam-887	82	21	(	(	PUNCT
ejpam-887	82	22	6	6	X
ejpam-887	82	23	)	)	PUNCT
ejpam-887	82	24	q.	q.	NOUN
ejpam-887	82	25	xu	xu	PROPN
ejpam-887	82	26	,	,	PUNCT
ejpam-887	82	27	g.	g.	PROPN
ejpam-887	82	28	wu	wu	PROPN
ejpam-887	82	29	/	/	SYM
ejpam-887	82	30	eur	eur	PROPN
ejpam-887	82	31	.	.	PUNCT
ejpam-887	83	1	j.	j.	PROPN
ejpam-887	83	2	pure	pure	PROPN
ejpam-887	83	3	appl	appl	PROPN
ejpam-887	83	4	.	.	PROPN
ejpam-887	83	5	math	math	PROPN
ejpam-887	83	6	,	,	PUNCT
ejpam-887	83	7	3	3	NUM
ejpam-887	83	8	(	(	PUNCT
ejpam-887	83	9	2010	2010	NUM
ejpam-887	83	10	)	)	PUNCT
ejpam-887	83	11	,	,	PUNCT
ejpam-887	83	12	1055	1055	NUM
ejpam-887	83	13	-	-	SYM
ejpam-887	83	14	1061	1061	NUM
ejpam-887	83	15	1059	1059	NUM
ejpam-887	83	16	and	and	CCONJ
ejpam-887	83	17	2na2n	2na2n	NUM
ejpam-887	83	18	=	=	SYM
ejpam-887	83	19	p2n−1	p2n−1	PROPN
ejpam-887	83	20	+	+	CCONJ
ejpam-887	83	21	p2n−3a3	p2n−3a3	PROPN
ejpam-887	83	22	+	+	NUM
ejpam-887	83	23	.	.	PUNCT
ejpam-887	83	24	.	.	PUNCT
ejpam-887	84	1	.+	.+	PRON
ejpam-887	84	2	p1a2n−1	p1a2n−1	NOUN
ejpam-887	84	3	(	(	PUNCT
ejpam-887	84	4	n	n	NOUN
ejpam-887	84	5	∈	∈	PROPN
ejpam-887	84	6	n∗	n∗	PROPN
ejpam-887	84	7	)	)	PUNCT
ejpam-887	84	8	.	.	PUNCT
ejpam-887	85	1	(	(	PUNCT
ejpam-887	85	2	7	7	X
ejpam-887	85	3	)	)	PUNCT
ejpam-887	85	4	combining(3	combining(3	PROPN
ejpam-887	85	5	)	)	PUNCT
ejpam-887	85	6	,	,	PUNCT
ejpam-887	85	7	(	(	PUNCT
ejpam-887	85	8	4	4	X
ejpam-887	85	9	)	)	PUNCT
ejpam-887	85	10	and	and	CCONJ
ejpam-887	85	11	(	(	PUNCT
ejpam-887	85	12	5	5	NUM
ejpam-887	85	13	)	)	PUNCT
ejpam-887	85	14	,	,	PUNCT
ejpam-887	85	15	for	for	ADP
ejpam-887	85	16	n=	n=	ADJ
ejpam-887	85	17	1,2	1,2	NUM
ejpam-887	85	18	,	,	PUNCT
ejpam-887	85	19	we	we	PRON
ejpam-887	85	20	obtain	obtain	AUX
ejpam-887	85	21	|a2|	|a2|	NOUN
ejpam-887	85	22	≤	≤	ADJ
ejpam-887	85	23	|g′(0)|	|g′(0)|	NOUN
ejpam-887	85	24	2	2	NUM
ejpam-887	85	25	,	,	PUNCT
ejpam-887	85	26	|a3|	|a3|	VERB
ejpam-887	85	27	≤	≤	ADJ
ejpam-887	85	28	|g′(0)|	|g′(0)|	NOUN
ejpam-887	85	29	2	2	NUM
ejpam-887	85	30	,	,	PUNCT
ejpam-887	85	31	|a4|	|a4|	ADJ
ejpam-887	85	32	≤	≤	NOUN
ejpam-887	85	33	|g′(0)|	|g′(0)|	NOUN
ejpam-887	85	34	·	·	PUNCT
ejpam-887	85	35	(	(	PUNCT
ejpam-887	85	36	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	85	37	2	2	NUM
ejpam-887	85	38	)	)	PUNCT
ejpam-887	85	39	2×	2×	NUM
ejpam-887	85	40	4	4	NUM
ejpam-887	85	41	(	(	PUNCT
ejpam-887	85	42	8)	8)	NUM
ejpam-887	85	43	and	and	CCONJ
ejpam-887	85	44	|a5|	|a5|	VERB
ejpam-887	85	45	≤	≤	ADJ
ejpam-887	85	46	|g′(0)|	|g′(0)|	NOUN
ejpam-887	85	47	·	·	PUNCT
ejpam-887	85	48	(	(	PUNCT
ejpam-887	85	49	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	85	50	2	2	NUM
ejpam-887	85	51	)	)	PUNCT
ejpam-887	85	52	2×	2×	NUM
ejpam-887	85	53	4	4	NUM
ejpam-887	85	54	,	,	PUNCT
ejpam-887	85	55	(	(	PUNCT
ejpam-887	85	56	9	9	X
ejpam-887	85	57	)	)	PUNCT
ejpam-887	85	58	respectively	respectively	ADV
ejpam-887	85	59	.	.	PUNCT
ejpam-887	86	1	according	accord	VERB
ejpam-887	86	2	to	to	ADP
ejpam-887	86	3	lemma	lemma	PROPN
ejpam-887	86	4	1	1	NUM
ejpam-887	86	5	and	and	CCONJ
ejpam-887	86	6	(	(	PUNCT
ejpam-887	86	7	5	5	NUM
ejpam-887	86	8	)	)	PUNCT
ejpam-887	86	9	,	,	PUNCT
ejpam-887	86	10	we	we	PRON
ejpam-887	86	11	obtain	obtain	VERB
ejpam-887	86	12	that	that	DET
ejpam-887	86	13	|a2n+1|	|a2n+1|	PROPN
ejpam-887	86	14	≤	≤	ADJ
ejpam-887	86	15	|g′(0)|	|g′(0)|	NOUN
ejpam-887	86	16	2n	2n	NUM
ejpam-887	86	17			PROPN
ejpam-887	86	18	1	1	NOUN
ejpam-887	86	19	+	+	PROPN
ejpam-887	87	1	n−1	n−1	PROPN
ejpam-887	88	1	∑	∑	PUNCT
ejpam-887	88	2	k=1	k=1	PROPN
ejpam-887	88	3	|a2k+1|	|a2k+1|	PROPN
ejpam-887	88	4			PROPN
ejpam-887	88	5			PROPN
ejpam-887	88	6	(	(	PUNCT
ejpam-887	88	7	n	n	NOUN
ejpam-887	88	8	∈	∈	NOUN
ejpam-887	88	9	n∗	n∗	NOUN
ejpam-887	88	10	:	:	PUNCT
ejpam-887	88	11	=	=	SYM
ejpam-887	88	12	n	n	CCONJ
ejpam-887	88	13	\	\	NOUN
ejpam-887	88	14	{	{	PUNCT
ejpam-887	88	15	1	1	NUM
ejpam-887	88	16	}	}	PUNCT
ejpam-887	88	17	=	=	PUNCT
ejpam-887	88	18	{	{	PUNCT
ejpam-887	88	19	2,3,4	2,3,4	NUM
ejpam-887	88	20	,	,	PUNCT
ejpam-887	88	21	.	.	PUNCT
ejpam-887	88	22	.	.	PUNCT
ejpam-887	89	1	.	.	PUNCT
ejpam-887	89	2	}	}	PUNCT
ejpam-887	89	3	)	)	PUNCT
ejpam-887	89	4	.	.	PUNCT
ejpam-887	90	1	(	(	PUNCT
ejpam-887	90	2	10	10	NUM
ejpam-887	90	3	)	)	PUNCT
ejpam-887	90	4	we	we	PRON
ejpam-887	90	5	assume	assume	VERB
ejpam-887	90	6	that	that	SCONJ
ejpam-887	90	7	(	(	PUNCT
ejpam-887	90	8	2	2	X
ejpam-887	90	9	)	)	PUNCT
ejpam-887	90	10	holds	hold	VERB
ejpam-887	90	11	for	for	ADP
ejpam-887	90	12	k	k	NOUN
ejpam-887	90	13	=	=	SYM
ejpam-887	90	14	3,4	3,4	NUM
ejpam-887	90	15	,	,	PUNCT
ejpam-887	90	16	.	.	PUNCT
ejpam-887	90	17	.	.	PUNCT
ejpam-887	90	18	.	.	PUNCT
ejpam-887	91	1	(	(	PUNCT
ejpam-887	91	2	n−	n−	NOUN
ejpam-887	91	3	1	1	NUM
ejpam-887	91	4	)	)	PUNCT
ejpam-887	91	5	.	.	PUNCT
ejpam-887	92	1	then	then	ADV
ejpam-887	92	2	from	from	ADP
ejpam-887	92	3	(	(	PUNCT
ejpam-887	92	4	8)	8)	NUM
ejpam-887	92	5	,	,	PUNCT
ejpam-887	92	6	we	we	PRON
ejpam-887	92	7	obtain	obtain	VERB
ejpam-887	92	8	|a2n+1|	|a2n+1|	PROPN
ejpam-887	92	9	≤	≤	ADJ
ejpam-887	92	10	|g′(0)|	|g′(0)|	NOUN
ejpam-887	92	11	2n	2n	NUM
ejpam-887	92	12			PROPN
ejpam-887	92	13			ADJ
ejpam-887	92	14	1	1	NOUN
ejpam-887	93	1	+	+	CCONJ
ejpam-887	93	2	n−1	n−1	PROPN
ejpam-887	93	3	∑	∑	PUNCT
ejpam-887	93	4	k=1	k=1	PROPN
ejpam-887	93	5	|g′(0)|	|g′(0)|	PROPN
ejpam-887	93	6	k!2k	k!2k	VERB
ejpam-887	93	7	k−1	k−1	PROPN
ejpam-887	93	8	∏	∏	PROPN
ejpam-887	93	9	j=1	j=1	NOUN
ejpam-887	93	10	(	(	PUNCT
ejpam-887	93	11	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	93	12	2	2	NUM
ejpam-887	93	13	j	j	NOUN
ejpam-887	93	14	)	)	PUNCT
ejpam-887	93	15			PROPN
ejpam-887	94	1			PROPN
ejpam-887	94	2			PROPN
ejpam-887	94	3	.	.	PUNCT
ejpam-887	95	1	to	to	ADP
ejpam-887	95	2	this	this	DET
ejpam-887	95	3	end	end	NOUN
ejpam-887	95	4	,	,	PUNCT
ejpam-887	95	5	it	it	PRON
ejpam-887	95	6	is	be	AUX
ejpam-887	95	7	sufficient	sufficient	ADJ
ejpam-887	95	8	to	to	PART
ejpam-887	95	9	show	show	VERB
ejpam-887	95	10	that	that	SCONJ
ejpam-887	95	11	|g′(0)|	|g′(0)|	NOUN
ejpam-887	95	12	2	2	NUM
ejpam-887	95	13	m	m	NOUN
ejpam-887	95	14			NOUN
ejpam-887	95	15			ADJ
ejpam-887	95	16	1	1	NOUN
ejpam-887	96	1	+	+	CCONJ
ejpam-887	96	2	m−1	m−1	PROPN
ejpam-887	96	3	∑	∑	PUNCT
ejpam-887	96	4	k=1	k=1	PROPN
ejpam-887	96	5	|g′(0)|	|g′(0)|	NOUN
ejpam-887	96	6	k!2k	k!2k	VERB
ejpam-887	96	7	k−1	k−1	PROPN
ejpam-887	96	8	∏	∏	PROPN
ejpam-887	96	9	j=1	j=1	NOUN
ejpam-887	96	10	(	(	PUNCT
ejpam-887	96	11	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	96	12	2	2	NUM
ejpam-887	96	13	j	j	NOUN
ejpam-887	96	14	)	)	PUNCT
ejpam-887	96	15			PROPN
ejpam-887	96	16			PROPN
ejpam-887	96	17	=	=	PUNCT
ejpam-887	96	18	|g′(0)|	|g′(0)|	NOUN
ejpam-887	96	19	m!2	m!2	NOUN
ejpam-887	96	20	m	m	NOUN
ejpam-887	96	21	m−1	m−1	PROPN
ejpam-887	96	22	∏	∏	NUM
ejpam-887	96	23	j=1	j=1	NOUN
ejpam-887	96	24	(	(	PUNCT
ejpam-887	96	25	|g′(0)|+2	|g′(0)|+2	PROPN
ejpam-887	96	26	j	j	NOUN
ejpam-887	96	27	)	)	PUNCT
ejpam-887	96	28	(	(	PUNCT
ejpam-887	96	29	m	m	NOUN
ejpam-887	96	30	=	=	SYM
ejpam-887	96	31	3,4	3,4	NUM
ejpam-887	96	32	,	,	PUNCT
ejpam-887	96	33	.	.	PUNCT
ejpam-887	96	34	.	.	PUNCT
ejpam-887	97	1	.	.	PUNCT
ejpam-887	97	2	,	,	PUNCT
ejpam-887	97	3	n	n	CCONJ
ejpam-887	97	4	)	)	PUNCT
ejpam-887	97	5	.	.	PUNCT
ejpam-887	98	1	(	(	PUNCT
ejpam-887	98	2	11	11	X
ejpam-887	98	3	)	)	PUNCT
ejpam-887	98	4	it	it	PRON
ejpam-887	98	5	is	be	AUX
ejpam-887	98	6	elementary	elementary	ADJ
ejpam-887	98	7	to	to	PART
ejpam-887	98	8	verify	verify	VERB
ejpam-887	98	9	that	that	SCONJ
ejpam-887	98	10	(	(	PUNCT
ejpam-887	98	11	2	2	X
ejpam-887	98	12	)	)	PUNCT
ejpam-887	98	13	is	be	AUX
ejpam-887	98	14	valid	valid	ADJ
ejpam-887	98	15	for	for	ADP
ejpam-887	98	16	m	m	PROPN
ejpam-887	98	17	=	=	SYM
ejpam-887	98	18	3	3	X
ejpam-887	98	19	.	.	PUNCT
ejpam-887	99	1	let	let	VERB
ejpam-887	99	2	us	we	PRON
ejpam-887	99	3	suppose	suppose	VERB
ejpam-887	99	4	that	that	SCONJ
ejpam-887	99	5	(	(	PUNCT
ejpam-887	99	6	2	2	X
ejpam-887	99	7	)	)	PUNCT
ejpam-887	99	8	is	be	AUX
ejpam-887	99	9	true	true	ADJ
ejpam-887	99	10	for	for	ADP
ejpam-887	99	11	all	all	DET
ejpam-887	99	12	m	m	NOUN
ejpam-887	99	13	,	,	PUNCT
ejpam-887	99	14	3	3	NUM
ejpam-887	99	15	<	<	X
ejpam-887	99	16	m	m	VERB
ejpam-887	99	17	≤	≤	NOUN
ejpam-887	99	18	(	(	PUNCT
ejpam-887	99	19	n−	n−	NOUN
ejpam-887	99	20	1	1	NUM
ejpam-887	99	21	)	)	PUNCT
ejpam-887	99	22	.	.	PUNCT
ejpam-887	100	1	then	then	ADV
ejpam-887	100	2	form	form	NOUN
ejpam-887	100	3	(	(	PUNCT
ejpam-887	100	4	9	9	NUM
ejpam-887	100	5	)	)	PUNCT
ejpam-887	100	6	|g′(0)|	|g′(0)|	NOUN
ejpam-887	100	7	2n	2n	NUM
ejpam-887	100	8			PROPN
ejpam-887	100	9			ADJ
ejpam-887	100	10	1	1	NOUN
ejpam-887	100	11	+	+	CCONJ
ejpam-887	100	12	n−1	n−1	PROPN
ejpam-887	100	13	∑	∑	PUNCT
ejpam-887	100	14	k=1	k=1	PROPN
ejpam-887	100	15	|g′(0)|	|g′(0)|	PROPN
ejpam-887	100	16	k!2k	k!2k	VERB
ejpam-887	100	17	k−1	k−1	PROPN
ejpam-887	100	18	∏	∏	PROPN
ejpam-887	100	19	j=1	j=1	NOUN
ejpam-887	100	20	(	(	PUNCT
ejpam-887	100	21	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	100	22	2	2	NUM
ejpam-887	100	23	j	j	NOUN
ejpam-887	100	24	)	)	PUNCT
ejpam-887	100	25			PROPN
ejpam-887	101	1			PROPN
ejpam-887	101	2			PROPN
ejpam-887	101	3	=	=	SYM
ejpam-887	101	4	2(n−	2(n−	NUM
ejpam-887	101	5	1	1	NUM
ejpam-887	101	6	)	)	PUNCT
ejpam-887	101	7	2n	2n	NUM
ejpam-887	101	8	|g′(0)|	|g′(0)|	NOUN
ejpam-887	101	9	2(n−	2(n−	NUM
ejpam-887	101	10	1	1	NUM
ejpam-887	101	11	)	)	PUNCT
ejpam-887	101	12			NOUN
ejpam-887	101	13			ADJ
ejpam-887	101	14	1	1	NOUN
ejpam-887	101	15	+	+	CCONJ
ejpam-887	101	16	n−2	n−2	PROPN
ejpam-887	101	17	∑	∑	PUNCT
ejpam-887	101	18	k=1	k=1	PROPN
ejpam-887	101	19	|g′(0)|	|g′(0)|	NOUN
ejpam-887	101	20	k!2k	k!2k	VERB
ejpam-887	101	21	k−1	k−1	PROPN
ejpam-887	101	22	∏	∏	PROPN
ejpam-887	101	23	j=1	j=1	NOUN
ejpam-887	101	24	(	(	PUNCT
ejpam-887	101	25	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	101	26	2	2	NUM
ejpam-887	101	27	j	j	NOUN
ejpam-887	101	28	)	)	PUNCT
ejpam-887	101	29			PROPN
ejpam-887	101	30			PROPN
ejpam-887	101	31	+	+	NUM
ejpam-887	101	32	|g′(0)|	|g′(0)|	NOUN
ejpam-887	101	33	2n	2n	NUM
ejpam-887	101	34	|g′(0)|	|g′(0)|	NOUN
ejpam-887	101	35	(	(	PUNCT
ejpam-887	101	36	n−	n−	NOUN
ejpam-887	101	37	1)!2n−1	1)!2n−1	NUM
ejpam-887	101	38	n−2	n−2	PROPN
ejpam-887	101	39	∏	∏	X
ejpam-887	101	40	j=1	j=1	NOUN
ejpam-887	101	41	(	(	PUNCT
ejpam-887	101	42	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	101	43	2	2	NUM
ejpam-887	101	44	j	j	NOUN
ejpam-887	101	45	)	)	PUNCT
ejpam-887	101	46	=	=	PUNCT
ejpam-887	102	1	2(n−	2(n−	NUM
ejpam-887	102	2	1	1	NUM
ejpam-887	102	3	)	)	PUNCT
ejpam-887	102	4	2n	2n	NUM
ejpam-887	102	5	|g′(0)|	|g′(0)|	NOUN
ejpam-887	102	6	(	(	PUNCT
ejpam-887	102	7	n−	n−	NOUN
ejpam-887	102	8	1)!2n−1	1)!2n−1	NUM
ejpam-887	102	9	n−2	n−2	PROPN
ejpam-887	102	10	∏	∏	X
ejpam-887	102	11	j=1	j=1	NOUN
ejpam-887	102	12	(	(	PUNCT
ejpam-887	102	13	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	102	14	2	2	NUM
ejpam-887	102	15	j)+	j)+	PROPN
ejpam-887	102	16	|g′(0)|	|g′(0)|	NOUN
ejpam-887	102	17	2n	2n	NUM
ejpam-887	102	18	|g′(0)|	|g′(0)|	NOUN
ejpam-887	102	19	(	(	PUNCT
ejpam-887	102	20	n−	n−	NOUN
ejpam-887	102	21	1)!2n−1	1)!2n−1	NUM
ejpam-887	102	22	n−2	n−2	PROPN
ejpam-887	102	23	∏	∏	X
ejpam-887	102	24	j=1	j=1	NOUN
ejpam-887	102	25	(	(	PUNCT
ejpam-887	102	26	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	102	27	2	2	NUM
ejpam-887	102	28	j	j	NOUN
ejpam-887	102	29	)	)	PUNCT
ejpam-887	102	30	=	=	SYM
ejpam-887	102	31	|g′(0)|	|g′(0)|	NOUN
ejpam-887	102	32	(	(	PUNCT
ejpam-887	102	33	2n)(n−	2n)(n−	NUM
ejpam-887	102	34	1)!2n−1	1)!2n−1	NUM
ejpam-887	102	35	n−2	n−2	PROPN
ejpam-887	102	36	∏	∏	PROPN
ejpam-887	102	37	j=1	j=1	NOUN
ejpam-887	102	38	(	(	PUNCT
ejpam-887	102	39	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	102	40	2	2	NUM
ejpam-887	102	41	j)(|g′(0)|+	j)(|g′(0)|+	PROPN
ejpam-887	102	42	2(n−	2(n−	NUM
ejpam-887	102	43	1	1	NUM
ejpam-887	102	44	)	)	PUNCT
ejpam-887	102	45	)	)	PUNCT
ejpam-887	103	1	q.	q.	PROPN
ejpam-887	103	2	xu	xu	PROPN
ejpam-887	103	3	,	,	PUNCT
ejpam-887	103	4	g.	g.	PROPN
ejpam-887	103	5	wu	wu	PROPN
ejpam-887	103	6	/	/	SYM
ejpam-887	103	7	eur	eur	PROPN
ejpam-887	103	8	.	.	PUNCT
ejpam-887	104	1	j.	j.	PROPN
ejpam-887	104	2	pure	pure	PROPN
ejpam-887	104	3	appl	appl	PROPN
ejpam-887	104	4	.	.	PROPN
ejpam-887	104	5	math	math	PROPN
ejpam-887	104	6	,	,	PUNCT
ejpam-887	104	7	3	3	NUM
ejpam-887	104	8	(	(	PUNCT
ejpam-887	104	9	2010	2010	NUM
ejpam-887	104	10	)	)	PUNCT
ejpam-887	104	11	,	,	PUNCT
ejpam-887	104	12	1055	1055	NUM
ejpam-887	104	13	-	-	SYM
ejpam-887	104	14	1061	1061	NUM
ejpam-887	104	15	1060	1060	NUM
ejpam-887	104	16	=	=	SYM
ejpam-887	104	17	|g′(0)|	|g′(0)|	NOUN
ejpam-887	104	18	n!2n	n!2n	PROPN
ejpam-887	104	19	n−1	n−1	PROPN
ejpam-887	104	20	∏	∏	PROPN
ejpam-887	104	21	j=1	j=1	NOUN
ejpam-887	104	22	(	(	PUNCT
ejpam-887	104	23	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	104	24	2	2	NUM
ejpam-887	104	25	j	j	NOUN
ejpam-887	104	26	)	)	PUNCT
ejpam-887	104	27	.	.	PUNCT
ejpam-887	105	1	thus	thus	ADV
ejpam-887	105	2	,	,	PUNCT
ejpam-887	105	3	(	(	PUNCT
ejpam-887	105	4	9	9	X
ejpam-887	105	5	)	)	PUNCT
ejpam-887	105	6	holds	hold	VERB
ejpam-887	105	7	for	for	ADP
ejpam-887	105	8	m	m	PROPN
ejpam-887	105	9	=	=	SYM
ejpam-887	105	10	n	n	PROPN
ejpam-887	105	11	and	and	CCONJ
ejpam-887	105	12	hence	hence	ADV
ejpam-887	105	13	(	(	PUNCT
ejpam-887	105	14	2	2	X
ejpam-887	105	15	)	)	PUNCT
ejpam-887	105	16	follows	follow	VERB
ejpam-887	105	17	.	.	PUNCT
ejpam-887	106	1	with	with	ADP
ejpam-887	106	2	the	the	DET
ejpam-887	106	3	similar	similar	ADJ
ejpam-887	106	4	method	method	NOUN
ejpam-887	106	5	and	and	CCONJ
ejpam-887	106	6	reasoning	reasoning	NOUN
ejpam-887	106	7	as	as	ADP
ejpam-887	106	8	in	in	ADP
ejpam-887	106	9	the	the	DET
ejpam-887	106	10	proof	proof	NOUN
ejpam-887	106	11	of	of	ADP
ejpam-887	106	12	(	(	PUNCT
ejpam-887	106	13	2	2	NUM
ejpam-887	106	14	)	)	PUNCT
ejpam-887	106	15	,	,	PUNCT
ejpam-887	106	16	we	we	PRON
ejpam-887	106	17	also	also	ADV
ejpam-887	106	18	prove	prove	VERB
ejpam-887	106	19	that	that	SCONJ
ejpam-887	106	20	(	(	PUNCT
ejpam-887	106	21	3	3	X
ejpam-887	106	22	)	)	PUNCT
ejpam-887	106	23	holds	hold	NOUN
ejpam-887	106	24	.	.	PUNCT
ejpam-887	107	1	this	this	PRON
ejpam-887	107	2	completes	complete	VERB
ejpam-887	107	3	the	the	DET
ejpam-887	107	4	proof	proof	NOUN
ejpam-887	107	5	of	of	ADP
ejpam-887	107	6	theorem	theorem	ADJ
ejpam-887	107	7	1	1	NUM
ejpam-887	107	8	.	.	PUNCT
ejpam-887	108	1	theorem	theorem	NOUN
ejpam-887	108	2	2	2	NUM
ejpam-887	108	3	.	.	PUNCT
ejpam-887	109	1	let	let	VERB
ejpam-887	109	2	the	the	DET
ejpam-887	109	3	function	function	NOUN
ejpam-887	109	4	f	f	PROPN
ejpam-887	109	5	(	(	PUNCT
ejpam-887	109	6	z	z	NOUN
ejpam-887	109	7	)	)	PUNCT
ejpam-887	109	8	∈	∈	PROPN
ejpam-887	109	9	a	a	PRON
ejpam-887	109	10	be	be	AUX
ejpam-887	109	11	given	give	VERB
ejpam-887	109	12	by	by	ADP
ejpam-887	109	13	(	(	PUNCT
ejpam-887	109	14	1	1	NUM
ejpam-887	109	15	)	)	PUNCT
ejpam-887	109	16	.	.	PUNCT
ejpam-887	110	1	if	if	SCONJ
ejpam-887	110	2	f	f	PROPN
ejpam-887	110	3	∈k	∈k	VERB
ejpam-887	110	4	∗s	∗s	PROPN
ejpam-887	110	5	(	(	PUNCT
ejpam-887	110	6	g	g	NOUN
ejpam-887	110	7	)	)	PUNCT
ejpam-887	110	8	,	,	PUNCT
ejpam-887	110	9	then	then	ADV
ejpam-887	110	10	|a2n|	|a2n|	NUM
ejpam-887	110	11	≤	≤	NUM
ejpam-887	110	12	|g′(0)|	|g′(0)|	NOUN
ejpam-887	110	13	n!2n	n!2n	PROPN
ejpam-887	110	14	n−1	n−1	PROPN
ejpam-887	110	15	∏	∏	PROPN
ejpam-887	110	16	j=1	j=1	NOUN
ejpam-887	110	17	(	(	PUNCT
ejpam-887	110	18	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	110	19	2	2	NUM
ejpam-887	110	20	j	j	NOUN
ejpam-887	110	21	)	)	PUNCT
ejpam-887	110	22	(	(	PUNCT
ejpam-887	110	23	n	n	CCONJ
ejpam-887	110	24	∈	∈	PROPN
ejpam-887	110	25	n	n	CCONJ
ejpam-887	110	26	)	)	PUNCT
ejpam-887	110	27	and	and	CCONJ
ejpam-887	110	28	|a2n+1|	|a2n+1|	PROPN
ejpam-887	110	29	≤	≤	NUM
ejpam-887	110	30	|g′(0)|	|g′(0)|	NOUN
ejpam-887	110	31	n!2n	n!2n	PROPN
ejpam-887	110	32	n−1	n−1	PROPN
ejpam-887	110	33	∏	∏	PROPN
ejpam-887	110	34	j=1	j=1	NOUN
ejpam-887	110	35	(	(	PUNCT
ejpam-887	110	36	|g′(0)|+	|g′(0)|+	PROPN
ejpam-887	110	37	2	2	NUM
ejpam-887	110	38	j	j	NOUN
ejpam-887	110	39	)	)	PUNCT
ejpam-887	110	40	(	(	PUNCT
ejpam-887	110	41	n	n	CCONJ
ejpam-887	110	42	∈	∈	PROPN
ejpam-887	110	43	n	n	CCONJ
ejpam-887	110	44	)	)	PUNCT
ejpam-887	110	45	.	.	PUNCT
ejpam-887	111	1	proof	proof	NOUN
ejpam-887	111	2	.	.	PUNCT
ejpam-887	112	1	theorem	theorem	NOUN
ejpam-887	112	2	2	2	NUM
ejpam-887	112	3	can	can	AUX
ejpam-887	112	4	be	be	AUX
ejpam-887	112	5	proven	prove	VERB
ejpam-887	112	6	by	by	ADP
ejpam-887	112	7	using	use	VERB
ejpam-887	112	8	similar	similar	ADJ
ejpam-887	112	9	arguments	argument	NOUN
ejpam-887	112	10	as	as	ADP
ejpam-887	112	11	in	in	ADP
ejpam-887	112	12	the	the	DET
ejpam-887	112	13	proof	proof	NOUN
ejpam-887	112	14	of	of	ADP
ejpam-887	112	15	theorem	theorem	NOUN
ejpam-887	112	16	1	1	NUM
ejpam-887	112	17	,	,	PUNCT
ejpam-887	112	18	so	so	SCONJ
ejpam-887	112	19	we	we	PRON
ejpam-887	112	20	choose	choose	VERB
ejpam-887	112	21	to	to	PART
ejpam-887	112	22	omit	omit	VERB
ejpam-887	112	23	the	the	DET
ejpam-887	112	24	details	detail	NOUN
ejpam-887	112	25	involved	involve	VERB
ejpam-887	112	26	.	.	PUNCT
ejpam-887	113	1	3	3	X
ejpam-887	113	2	.	.	X
ejpam-887	113	3	corollaries	corollary	NOUN
ejpam-887	113	4	and	and	CCONJ
ejpam-887	113	5	consequences	consequence	NOUN
ejpam-887	113	6	in	in	ADP
ejpam-887	113	7	view	view	NOUN
ejpam-887	113	8	of	of	ADP
ejpam-887	113	9	remark	remark	NOUN
ejpam-887	113	10	1	1	NUM
ejpam-887	113	11	,	,	PUNCT
ejpam-887	113	12	if	if	SCONJ
ejpam-887	113	13	we	we	PRON
ejpam-887	113	14	set	set	VERB
ejpam-887	113	15	g(z	g(z	PROPN
ejpam-887	113	16	)	)	PUNCT
ejpam-887	113	17	=	=	SYM
ejpam-887	114	1	1	1	NUM
ejpam-887	114	2	+	+	NUM
ejpam-887	114	3	az	az	PROPN
ejpam-887	114	4	1	1	NUM
ejpam-887	114	5	+	+	CCONJ
ejpam-887	114	6	bz	bz	PROPN
ejpam-887	114	7	(	(	PUNCT
ejpam-887	114	8	z	z	NOUN
ejpam-887	114	9	∈	∈	PROPN
ejpam-887	114	10	u	u	NOUN
ejpam-887	114	11	;	;	PUNCT
ejpam-887	114	12	−1≤	−1≤	PROPN
ejpam-887	114	13	b	b	NOUN
ejpam-887	114	14	<	<	X
ejpam-887	114	15	a≤	a≤	ADP
ejpam-887	114	16	1	1	NUM
ejpam-887	114	17	)	)	PUNCT
ejpam-887	114	18	in	in	ADP
ejpam-887	114	19	theorems	theorem	NOUN
ejpam-887	114	20	1	1	NUM
ejpam-887	114	21	and	and	CCONJ
ejpam-887	114	22	2	2	NUM
ejpam-887	114	23	,	,	PUNCT
ejpam-887	114	24	we	we	PRON
ejpam-887	114	25	obtain	obtain	VERB
ejpam-887	114	26	easily	easily	ADV
ejpam-887	114	27	to	to	ADP
ejpam-887	114	28	corollaries	corollary	NOUN
ejpam-887	114	29	1	1	NUM
ejpam-887	114	30	and	and	CCONJ
ejpam-887	114	31	2	2	NUM
ejpam-887	114	32	,	,	PUNCT
ejpam-887	114	33	respectively	respectively	ADV
ejpam-887	114	34	.	.	PUNCT
ejpam-887	115	1	corollary	corollary	ADJ
ejpam-887	115	2	1	1	NUM
ejpam-887	115	3	.	.	PUNCT
ejpam-887	116	1	let	let	VERB
ejpam-887	116	2	the	the	DET
ejpam-887	116	3	function	function	NOUN
ejpam-887	116	4	f	f	PROPN
ejpam-887	116	5	(	(	PUNCT
ejpam-887	116	6	z	z	NOUN
ejpam-887	116	7	)	)	PUNCT
ejpam-887	116	8	∈a	∈a	NUM
ejpam-887	116	9	be	be	AUX
ejpam-887	116	10	given	give	VERB
ejpam-887	116	11	by	by	ADP
ejpam-887	116	12	(	(	PUNCT
ejpam-887	116	13	1	1	NUM
ejpam-887	116	14	)	)	PUNCT
ejpam-887	116	15	.	.	PUNCT
ejpam-887	117	1	if	if	SCONJ
ejpam-887	117	2	f	f	PROPN
ejpam-887	117	3	∈	∈	PROPN
ejpam-887	117	4	s	s	PART
ejpam-887	117	5	∗s	∗s	NOUN
ejpam-887	117	6	(	(	PUNCT
ejpam-887	117	7	a	a	DET
ejpam-887	117	8	,	,	PUNCT
ejpam-887	117	9	b	b	NOUN
ejpam-887	117	10	)	)	PUNCT
ejpam-887	117	11	,	,	PUNCT
ejpam-887	117	12	then	then	ADV
ejpam-887	117	13	|a2n|	|a2n|	NUM
ejpam-887	117	14	≤	≤	NOUN
ejpam-887	117	15	(	(	PUNCT
ejpam-887	117	16	a−	a−	PROPN
ejpam-887	117	17	b	b	PROPN
ejpam-887	117	18	)	)	PUNCT
ejpam-887	117	19	n!2n	n!2n	NOUN
ejpam-887	117	20	n−1	n−1	PROPN
ejpam-887	117	21	∏	∏	PROPN
ejpam-887	117	22	j=1	j=1	NOUN
ejpam-887	117	23	(	(	PUNCT
ejpam-887	117	24	a−	a−	PROPN
ejpam-887	117	25	b+	b+	ADJ
ejpam-887	117	26	2	2	NUM
ejpam-887	117	27	j	j	NOUN
ejpam-887	117	28	)	)	PUNCT
ejpam-887	117	29	(	(	PUNCT
ejpam-887	117	30	n	n	CCONJ
ejpam-887	117	31	∈	∈	PROPN
ejpam-887	117	32	n	n	CCONJ
ejpam-887	117	33	)	)	PUNCT
ejpam-887	117	34	and	and	CCONJ
ejpam-887	117	35	|a2n+1|	|a2n+1|	PROPN
ejpam-887	117	36	≤	≤	NOUN
ejpam-887	117	37	(	(	PUNCT
ejpam-887	117	38	a−	a−	PROPN
ejpam-887	117	39	b	b	PROPN
ejpam-887	117	40	)	)	PUNCT
ejpam-887	117	41	n!2n	n!2n	NOUN
ejpam-887	117	42	n−1	n−1	PROPN
ejpam-887	117	43	∏	∏	PROPN
ejpam-887	117	44	j=1	j=1	NOUN
ejpam-887	117	45	(	(	PUNCT
ejpam-887	117	46	a−	a−	PROPN
ejpam-887	117	47	b	b	PROPN
ejpam-887	117	48	+	+	CCONJ
ejpam-887	117	49	2	2	NUM
ejpam-887	117	50	j	j	NOUN
ejpam-887	117	51	)	)	PUNCT
ejpam-887	117	52	(	(	PUNCT
ejpam-887	117	53	n	n	CCONJ
ejpam-887	117	54	∈	∈	PROPN
ejpam-887	117	55	n	n	CCONJ
ejpam-887	117	56	)	)	PUNCT
ejpam-887	117	57	.	.	PUNCT
ejpam-887	118	1	corollary	corollary	ADJ
ejpam-887	118	2	2	2	NUM
ejpam-887	118	3	.	.	PUNCT
ejpam-887	119	1	let	let	VERB
ejpam-887	119	2	the	the	DET
ejpam-887	119	3	function	function	NOUN
ejpam-887	119	4	f	f	PROPN
ejpam-887	119	5	(	(	PUNCT
ejpam-887	119	6	z	z	NOUN
ejpam-887	119	7	)	)	PUNCT
ejpam-887	119	8	∈a	∈a	NUM
ejpam-887	119	9	be	be	AUX
ejpam-887	119	10	given	give	VERB
ejpam-887	119	11	by	by	ADP
ejpam-887	119	12	(	(	PUNCT
ejpam-887	119	13	1	1	NUM
ejpam-887	119	14	)	)	PUNCT
ejpam-887	119	15	.	.	PUNCT
ejpam-887	120	1	if	if	SCONJ
ejpam-887	120	2	f	f	PROPN
ejpam-887	120	3	∈k	∈k	VERB
ejpam-887	120	4	∗s	∗s	PROPN
ejpam-887	120	5	(	(	PUNCT
ejpam-887	120	6	a	a	DET
ejpam-887	120	7	,	,	PUNCT
ejpam-887	120	8	b	b	NOUN
ejpam-887	120	9	)	)	PUNCT
ejpam-887	120	10	,	,	PUNCT
ejpam-887	120	11	then	then	ADV
ejpam-887	120	12	|a2n|	|a2n|	NUM
ejpam-887	120	13	≤	≤	NOUN
ejpam-887	120	14	(	(	PUNCT
ejpam-887	120	15	a−	a−	PROPN
ejpam-887	120	16	b	b	PROPN
ejpam-887	120	17	)	)	PUNCT
ejpam-887	120	18	n!2n	n!2n	NOUN
ejpam-887	120	19	n−1	n−1	PROPN
ejpam-887	120	20	∏	∏	PROPN
ejpam-887	120	21	j=1	j=1	NOUN
ejpam-887	120	22	(	(	PUNCT
ejpam-887	120	23	a−	a−	PROPN
ejpam-887	120	24	b+	b+	ADJ
ejpam-887	120	25	2	2	NUM
ejpam-887	120	26	j	j	NOUN
ejpam-887	120	27	)	)	PUNCT
ejpam-887	120	28	(	(	PUNCT
ejpam-887	120	29	n	n	CCONJ
ejpam-887	120	30	∈	∈	PROPN
ejpam-887	120	31	n	n	CCONJ
ejpam-887	120	32	)	)	PUNCT
ejpam-887	120	33	and	and	CCONJ
ejpam-887	120	34	|a2n+1|	|a2n+1|	PROPN
ejpam-887	120	35	≤	≤	NOUN
ejpam-887	120	36	(	(	PUNCT
ejpam-887	120	37	a−	a−	PROPN
ejpam-887	120	38	b	b	PROPN
ejpam-887	120	39	)	)	PUNCT
ejpam-887	120	40	n!2n	n!2n	NOUN
ejpam-887	120	41	n−1	n−1	PROPN
ejpam-887	120	42	∏	∏	PROPN
ejpam-887	120	43	j=1	j=1	NOUN
ejpam-887	120	44	(	(	PUNCT
ejpam-887	120	45	a−	a−	PROPN
ejpam-887	120	46	b	b	PROPN
ejpam-887	120	47	+	+	CCONJ
ejpam-887	120	48	2	2	NUM
ejpam-887	120	49	j	j	NOUN
ejpam-887	120	50	)	)	PUNCT
ejpam-887	120	51	(	(	PUNCT
ejpam-887	120	52	n	n	CCONJ
ejpam-887	120	53	∈	∈	PROPN
ejpam-887	120	54	n	n	CCONJ
ejpam-887	120	55	)	)	PUNCT
ejpam-887	120	56	.	.	PUNCT
ejpam-887	121	1	remark	remark	PROPN
ejpam-887	121	2	2	2	NUM
ejpam-887	121	3	.	.	PUNCT
ejpam-887	121	4	corollaries	corollary	NOUN
ejpam-887	121	5	1	1	NUM
ejpam-887	121	6	and	and	CCONJ
ejpam-887	121	7	2	2	NUM
ejpam-887	121	8	were	be	AUX
ejpam-887	121	9	proven	prove	VERB
ejpam-887	121	10	earlier	early	ADV
ejpam-887	121	11	by	by	ADP
ejpam-887	121	12	goel	goel	PROPN
ejpam-887	121	13	and	and	CCONJ
ejpam-887	121	14	mehrok	mehrok	ADJ
ejpam-887	122	1	[	[	X
ejpam-887	122	2	7	7	X
ejpam-887	122	3	]	]	PUNCT
ejpam-887	122	4	and	and	CCONJ
ejpam-887	122	5	aini	aini	PROPN
ejpam-887	122	6	janteng	janteng	PROPN
ejpam-887	122	7	and	and	CCONJ
ejpam-887	122	8	suzeini	suzeini	PROPN
ejpam-887	122	9	abdul	abdul	PROPN
ejpam-887	123	1	[	[	X
ejpam-887	123	2	8	8	NUM
ejpam-887	123	3	]	]	PUNCT
ejpam-887	123	4	,	,	PUNCT
ejpam-887	123	5	respectively	respectively	ADV
ejpam-887	123	6	.	.	PUNCT
ejpam-887	124	1	however	however	ADV
ejpam-887	124	2	,	,	PUNCT
ejpam-887	124	3	we	we	PRON
ejpam-887	124	4	are	be	AUX
ejpam-887	124	5	able	able	ADJ
ejpam-887	124	6	to	to	PART
ejpam-887	124	7	derive	derive	VERB
ejpam-887	124	8	these	these	DET
ejpam-887	124	9	results	result	NOUN
ejpam-887	124	10	easily	easily	ADV
ejpam-887	124	11	as	as	ADP
ejpam-887	124	12	consequences	consequence	NOUN
ejpam-887	124	13	of	of	ADP
ejpam-887	124	14	theorems	theorem	NOUN
ejpam-887	124	15	1	1	NUM
ejpam-887	124	16	and	and	CCONJ
ejpam-887	124	17	2	2	NUM
ejpam-887	125	1	.	.	NUM
ejpam-887	125	2	references	reference	NOUN
ejpam-887	125	3	1061	1061	NUM
ejpam-887	125	4	references	reference	NOUN
ejpam-887	125	5	[	[	X
ejpam-887	125	6	1	1	NUM
ejpam-887	125	7	]	]	X
ejpam-887	125	8	o	o	X
ejpam-887	125	9	altinataş	altinataş	PROPN
ejpam-887	125	10	,	,	PUNCT
ejpam-887	125	11	ö	ö	PROPN
ejpam-887	125	12	özkan	özkan	NOUN
ejpam-887	125	13	and	and	CCONJ
ejpam-887	125	14	h	h	NOUN
ejpam-887	125	15	m	m	PROPN
ejpam-887	125	16	srivastava	srivastava	PROPN
ejpam-887	125	17	.	.	PUNCT
ejpam-887	126	1	neighborhoods	neighborhood	NOUN
ejpam-887	126	2	of	of	ADP
ejpam-887	126	3	a	a	DET
ejpam-887	126	4	class	class	NOUN
ejpam-887	126	5	of	of	ADP
ejpam-887	126	6	analytic	analytic	ADJ
ejpam-887	126	7	functions	function	NOUN
ejpam-887	126	8	with	with	ADP
ejpam-887	126	9	negative	negative	ADJ
ejpam-887	126	10	coefficients	coefficient	NOUN
ejpam-887	126	11	.	.	PUNCT
ejpam-887	127	1	appl	appl	PROPN
ejpam-887	127	2	.	.	PROPN
ejpam-887	127	3	math	math	PROPN
ejpam-887	127	4	.	.	PUNCT
ejpam-887	128	1	lett	lett	PROPN
ejpam-887	128	2	.	.	PROPN
ejpam-887	129	1	13	13	NUM
ejpam-887	129	2	(	(	PUNCT
ejpam-887	129	3	3	3	NUM
ejpam-887	129	4	):	):	PUNCT
ejpam-887	129	5	63	63	NUM
ejpam-887	129	6	-	-	SYM
ejpam-887	129	7	67	67	NUM
ejpam-887	129	8	,	,	PUNCT
ejpam-887	129	9	1995	1995	NUM
ejpam-887	129	10	.	.	PUNCT
ejpam-887	130	1	[	[	X
ejpam-887	130	2	2	2	NUM
ejpam-887	130	3	]	]	PUNCT
ejpam-887	130	4	o	o	X
ejpam-887	130	5	altinataş	altinataş	PROPN
ejpam-887	130	6	,	,	PUNCT
ejpam-887	130	7	h	h	PROPN
ejpam-887	130	8	irmak	irmak	PROPN
ejpam-887	130	9	,	,	PUNCT
ejpam-887	130	10	s	s	VERB
ejpam-887	130	11	owa	owa	NOUN
ejpam-887	130	12	and	and	CCONJ
ejpam-887	130	13	h	h	NOUN
ejpam-887	130	14	m	m	PROPN
ejpam-887	130	15	srivastava	srivastava	PROPN
ejpam-887	130	16	.	.	PUNCT
ejpam-887	131	1	coefficients	coefficient	NOUN
ejpam-887	131	2	bounds	bound	VERB
ejpam-887	131	3	for	for	ADP
ejpam-887	131	4	some	some	DET
ejpam-887	131	5	families	family	NOUN
ejpam-887	131	6	of	of	ADP
ejpam-887	131	7	starlike	starlike	NOUN
ejpam-887	131	8	and	and	CCONJ
ejpam-887	131	9	convex	convex	NOUN
ejpam-887	131	10	functions	function	NOUN
ejpam-887	131	11	with	with	ADP
ejpam-887	131	12	complex	complex	ADJ
ejpam-887	131	13	order	order	NOUN
ejpam-887	131	14	.	.	PUNCT
ejpam-887	132	1	appl	appl	PROPN
ejpam-887	132	2	.	.	PROPN
ejpam-887	132	3	math	math	PROPN
ejpam-887	132	4	.	.	PUNCT
ejpam-887	133	1	lett	lett	PROPN
ejpam-887	133	2	.	.	PUNCT
ejpam-887	134	1	20	20	NUM
ejpam-887	134	2	:	:	PUNCT
ejpam-887	134	3	1218	1218	NUM
ejpam-887	134	4	-	-	NOUN
ejpam-887	134	5	1222	1222	NUM
ejpam-887	134	6	,	,	PUNCT
ejpam-887	134	7	2007	2007	NUM
ejpam-887	134	8	.	.	PUNCT
ejpam-887	135	1	[	[	X
ejpam-887	135	2	3	3	NUM
ejpam-887	135	3	]	]	X
ejpam-887	135	4	d	d	X
ejpam-887	135	5	breaz	breaz	NOUN
ejpam-887	135	6	,	,	PUNCT
ejpam-887	135	7	n	n	CCONJ
ejpam-887	135	8	breaz	breaz	NOUN
ejpam-887	135	9	and	and	CCONJ
ejpam-887	135	10	h	h	NOUN
ejpam-887	135	11	m	m	PROPN
ejpam-887	135	12	srivastava	srivastava	PROPN
ejpam-887	135	13	.	.	PUNCT
ejpam-887	136	1	an	an	DET
ejpam-887	136	2	extension	extension	NOUN
ejpam-887	136	3	of	of	ADP
ejpam-887	136	4	the	the	DET
ejpam-887	136	5	univalent	univalent	ADJ
ejpam-887	136	6	condition	condition	NOUN
ejpam-887	136	7	for	for	ADP
ejpam-887	136	8	a	a	DET
ejpam-887	136	9	family	family	NOUN
ejpam-887	136	10	of	of	ADP
ejpam-887	136	11	integral	integral	ADJ
ejpam-887	136	12	operators	operator	NOUN
ejpam-887	136	13	.	.	PUNCT
ejpam-887	137	1	appl	appl	PROPN
ejpam-887	137	2	.	.	PROPN
ejpam-887	137	3	math	math	PROPN
ejpam-887	137	4	.	.	PUNCT
ejpam-887	138	1	lett	lett	PROPN
ejpam-887	138	2	.	.	PUNCT
ejpam-887	139	1	22	22	NUM
ejpam-887	139	2	:	:	PUNCT
ejpam-887	139	3	41	41	NUM
ejpam-887	139	4	-	-	SYM
ejpam-887	139	5	44	44	NUM
ejpam-887	139	6	,	,	PUNCT
ejpam-887	139	7	2009	2009	NUM
ejpam-887	139	8	.	.	PUNCT
ejpam-887	140	1	[	[	X
ejpam-887	140	2	4	4	NUM
ejpam-887	140	3	]	]	X
ejpam-887	140	4	r	r	NOUN
ejpam-887	140	5	m	m	NOUN
ejpam-887	140	6	goel	goel	NOUN
ejpam-887	140	7	and	and	CCONJ
ejpam-887	140	8	b	b	NOUN
ejpam-887	140	9	c	c	NOUN
ejpam-887	140	10	mehrok	mehrok	NOUN
ejpam-887	140	11	.	.	PUNCT
ejpam-887	141	1	a	a	DET
ejpam-887	141	2	subclass	subclass	NOUN
ejpam-887	141	3	of	of	ADP
ejpam-887	141	4	starlike	starlike	NOUN
ejpam-887	141	5	functions	function	NOUN
ejpam-887	141	6	with	with	ADP
ejpam-887	141	7	respect	respect	NOUN
ejpam-887	141	8	to	to	ADP
ejpam-887	141	9	symmetric	symmetric	ADJ
ejpam-887	141	10	points	point	NOUN
ejpam-887	141	11	.	.	PUNCT
ejpam-887	142	1	tamkang	tamkang	PROPN
ejpam-887	142	2	j.	j.	PROPN
ejpam-887	142	3	math	math	PROPN
ejpam-887	142	4	.	.	PUNCT
ejpam-887	143	1	13(1	13(1	X
ejpam-887	143	2	):	):	PUNCT
ejpam-887	143	3	11	11	NUM
ejpam-887	143	4	-	-	SYM
ejpam-887	143	5	24	24	NUM
ejpam-887	143	6	,	,	PUNCT
ejpam-887	143	7	1982	1982	NUM
ejpam-887	143	8	.	.	PUNCT
ejpam-887	144	1	[	[	X
ejpam-887	144	2	5	5	NUM
ejpam-887	144	3	]	]	PUNCT
ejpam-887	144	4	a	a	DET
ejpam-887	144	5	janteng	janteng	NOUN
ejpam-887	144	6	and	and	CCONJ
ejpam-887	144	7	s	s	VERB
ejpam-887	144	8	a	a	DET
ejpam-887	144	9	halim	halim	PROPN
ejpam-887	144	10	.	.	PUNCT
ejpam-887	145	1	coefficient	coefficient	ADJ
ejpam-887	145	2	estimate	estimate	NOUN
ejpam-887	145	3	for	for	ADP
ejpam-887	145	4	a	a	DET
ejpam-887	145	5	subclass	subclass	NOUN
ejpam-887	145	6	of	of	ADP
ejpam-887	145	7	close	close	NOUN
ejpam-887	145	8	-	-	PUNCT
ejpam-887	145	9	to	to	ADP
ejpam-887	145	10	-	-	PUNCT
ejpam-887	145	11	convex	convex	NOUN
ejpam-887	145	12	functions	function	NOUN
ejpam-887	145	13	with	with	ADP
ejpam-887	145	14	respect	respect	NOUN
ejpam-887	145	15	to	to	ADP
ejpam-887	145	16	symmetric	symmetric	ADJ
ejpam-887	145	17	points	point	NOUN
ejpam-887	145	18	,	,	PUNCT
ejpam-887	145	19	int	int	NOUN
ejpam-887	145	20	.	.	PUNCT
ejpam-887	146	1	journal	journal	PROPN
ejpam-887	146	2	of	of	ADP
ejpam-887	146	3	math	math	NOUN
ejpam-887	146	4	.	.	PUNCT
ejpam-887	147	1	analysis	analysis	NOUN
ejpam-887	147	2	.	.	PUNCT
ejpam-887	148	1	3(7	3(7	NUM
ejpam-887	148	2	):	):	PUNCT
ejpam-887	148	3	309	309	NUM
ejpam-887	148	4	-	-	SYM
ejpam-887	148	5	313	313	NUM
ejpam-887	148	6	,	,	PUNCT
ejpam-887	148	7	2009	2009	NUM
ejpam-887	148	8	.	.	PUNCT
ejpam-887	149	1	[	[	X
ejpam-887	149	2	6	6	NUM
ejpam-887	149	3	]	]	X
ejpam-887	149	4	s	s	VERB
ejpam-887	149	5	owa	owa	PROPN
ejpam-887	149	6	,	,	PUNCT
ejpam-887	149	7	m	m	VERB
ejpam-887	149	8	nunokawa	nunokawa	NOUN
ejpam-887	149	9	,	,	PUNCT
ejpam-887	149	10	h	h	NOUN
ejpam-887	149	11	saitoh	saitoh	ADJ
ejpam-887	149	12	and	and	CCONJ
ejpam-887	149	13	h	h	PROPN
ejpam-887	149	14	m	m	PROPN
ejpam-887	149	15	srivastava	srivastava	PROPN
ejpam-887	149	16	.	.	PUNCT
ejpam-887	150	1	close	close	VERB
ejpam-887	150	2	-	-	PUNCT
ejpam-887	150	3	to	to	ADP
ejpam-887	150	4	-	-	PUNCT
ejpam-887	150	5	convexity	convexity	NOUN
ejpam-887	150	6	,	,	PUNCT
ejpam-887	150	7	starlikeness	starlikeness	NOUN
ejpam-887	150	8	,	,	PUNCT
ejpam-887	150	9	and	and	CCONJ
ejpam-887	150	10	convexity	convexity	NOUN
ejpam-887	150	11	of	of	ADP
ejpam-887	150	12	certain	certain	ADJ
ejpam-887	150	13	analytic	analytic	ADJ
ejpam-887	150	14	function	function	NOUN
ejpam-887	150	15	.	.	PUNCT
ejpam-887	151	1	apple	apple	NOUN
ejpam-887	151	2	.	.	PUNCT
ejpam-887	152	1	math	math	NOUN
ejpam-887	152	2	.	.	PUNCT
ejpam-887	153	1	lett	lett	PROPN
ejpam-887	153	2	.	.	PUNCT
ejpam-887	154	1	15	15	NUM
ejpam-887	154	2	:	:	PUNCT
ejpam-887	154	3	63	63	NUM
ejpam-887	154	4	-	-	SYM
ejpam-887	154	5	69	69	NUM
ejpam-887	154	6	,	,	PUNCT
ejpam-887	154	7	2002	2002	NUM
ejpam-887	154	8	.	.	PUNCT
ejpam-887	155	1	[	[	X
ejpam-887	155	2	7	7	X
ejpam-887	155	3	]	]	X
ejpam-887	155	4	m	m	PROPN
ejpam-887	155	5	s	s	PROPN
ejpam-887	155	6	robertson	robertson	PROPN
ejpam-887	155	7	.	.	PUNCT
ejpam-887	156	1	on	on	ADP
ejpam-887	156	2	the	the	DET
ejpam-887	156	3	theory	theory	NOUN
ejpam-887	156	4	of	of	ADP
ejpam-887	156	5	univalent	univalent	ADJ
ejpam-887	156	6	functions	function	NOUN
ejpam-887	156	7	.	.	PUNCT
ejpam-887	157	1	ann	ann	PROPN
ejpam-887	157	2	.	.	PUNCT
ejpam-887	157	3	math	math	PROPN
ejpam-887	157	4	.	.	PUNCT
ejpam-887	158	1	37	37	NUM
ejpam-887	158	2	:	:	PUNCT
ejpam-887	158	3	374	374	NUM
ejpam-887	158	4	-	-	SYM
ejpam-887	158	5	408	408	NUM
ejpam-887	158	6	,	,	PUNCT
ejpam-887	158	7	1936	1936	NUM
ejpam-887	158	8	.	.	PUNCT
ejpam-887	159	1	[	[	X
ejpam-887	159	2	8	8	NUM
ejpam-887	159	3	]	]	PUNCT
ejpam-887	159	4	w	w	NOUN
ejpam-887	159	5	rogosinski	rogosinski	NOUN
ejpam-887	159	6	.	.	PUNCT
ejpam-887	160	1	on	on	ADP
ejpam-887	160	2	the	the	DET
ejpam-887	160	3	coefficients	coefficient	NOUN
ejpam-887	160	4	of	of	ADP
ejpam-887	160	5	subordinate	subordinate	ADJ
ejpam-887	160	6	functions.proc	functions.proc	PROPN
ejpam-887	160	7	.	.	PUNCT
ejpam-887	161	1	london	london	PROPN
ejpam-887	161	2	math	math	PROPN
ejpam-887	161	3	.	.	PUNCT
ejpam-887	162	1	soc	soc	PROPN
ejpam-887	162	2	.	.	PUNCT
ejpam-887	163	1	48	48	NUM
ejpam-887	163	2	:	:	PUNCT
ejpam-887	163	3	48	48	NUM
ejpam-887	163	4	-	-	SYM
ejpam-887	163	5	82	82	NUM
ejpam-887	163	6	,	,	PUNCT
ejpam-887	163	7	1943	1943	NUM
ejpam-887	163	8	.	.	PUNCT
ejpam-887	164	1	[	[	X
ejpam-887	164	2	9	9	NUM
ejpam-887	164	3	]	]	X
ejpam-887	164	4	k	k	PROPN
ejpam-887	164	5	sakaguchi	sakaguchi	PROPN
ejpam-887	164	6	.	.	PUNCT
ejpam-887	165	1	on	on	ADP
ejpam-887	165	2	a	a	DET
ejpam-887	165	3	certain	certain	ADJ
ejpam-887	165	4	univalent	univalent	ADJ
ejpam-887	165	5	mapping	mapping	NOUN
ejpam-887	165	6	.	.	PUNCT
ejpam-887	166	1	j.	j.	PROPN
ejpam-887	166	2	math	math	PROPN
ejpam-887	166	3	.	.	PUNCT
ejpam-887	167	1	soc	soc	PROPN
ejpam-887	167	2	.	.	PUNCT
ejpam-887	168	1	japan	japan	PROPN
ejpam-887	168	2	.	.	PUNCT
ejpam-887	169	1	11	11	NUM
ejpam-887	169	2	:	:	SYM
ejpam-887	169	3	72	72	NUM
ejpam-887	169	4	-	-	SYM
ejpam-887	169	5	75	75	NUM
ejpam-887	169	6	,	,	PUNCT
ejpam-887	169	7	1959	1959	NUM
ejpam-887	169	8	.	.	PUNCT
ejpam-887	170	1	[	[	X
ejpam-887	170	2	10	10	NUM
ejpam-887	170	3	]	]	X
ejpam-887	170	4	h	h	PROPN
ejpam-887	170	5	m	m	PROPN
ejpam-887	170	6	srivastava	srivastava	PROPN
ejpam-887	170	7	,	,	PUNCT
ejpam-887	170	8	qing	qing	PROPN
ejpam-887	170	9	-	-	PUNCT
ejpam-887	170	10	hua	hua	PROPN
ejpam-887	170	11	xu	xu	PROPN
ejpam-887	170	12	and	and	CCONJ
ejpam-887	170	13	guang	guang	PROPN
ejpam-887	170	14	-	-	PUNCT
ejpam-887	170	15	ping	ping	PROPN
ejpam-887	170	16	wu	wu	PROPN
ejpam-887	170	17	.	.	PUNCT
ejpam-887	171	1	coefficient	coefficient	NOUN
ejpam-887	171	2	estimates	estimate	NOUN
ejpam-887	171	3	for	for	ADP
ejpam-887	171	4	certain	certain	ADJ
ejpam-887	171	5	subclasses	subclass	NOUN
ejpam-887	171	6	of	of	ADP
ejpam-887	171	7	spiral	spiral	ADJ
ejpam-887	171	8	-	-	PUNCT
ejpam-887	171	9	like	like	ADJ
ejpam-887	171	10	functions	function	NOUN
ejpam-887	171	11	of	of	ADP
ejpam-887	171	12	complex	complex	ADJ
ejpam-887	171	13	order	order	NOUN
ejpam-887	171	14	.	.	PUNCT
ejpam-887	172	1	appl	appl	PROPN
ejpam-887	172	2	.	.	PROPN
ejpam-887	172	3	math	math	PROPN
ejpam-887	172	4	.	.	PUNCT
ejpam-887	173	1	lett	lett	PROPN
ejpam-887	173	2	.	.	PUNCT
ejpam-887	174	1	23	23	NUM
ejpam-887	174	2	:	:	PUNCT
ejpam-887	174	3	763	763	NUM
ejpam-887	174	4	-	-	SYM
ejpam-887	174	5	768	768	NUM
ejpam-887	174	6	,	,	PUNCT
ejpam-887	174	7	2010	2010	NUM
ejpam-887	174	8	.	.	PUNCT