id	sid	tid	token	lemma	pos
ejpam-411	1	1	1_xxx_srivastava.dvi	1_xxx_srivastava.dvi	NUM
ejpam-411	1	2	european	european	ADJ
ejpam-411	1	3	journal	journal	NOUN
ejpam-411	1	4	of	of	ADP
ejpam-411	1	5	pure	pure	ADJ
ejpam-411	1	6	and	and	CCONJ
ejpam-411	1	7	applied	apply	VERB
ejpam-411	1	8	mathematics	mathematic	NOUN
ejpam-411	1	9	vol	vol	NOUN
ejpam-411	1	10	.	.	PROPN
ejpam-411	2	1	2	2	NUM
ejpam-411	2	2	,	,	PUNCT
ejpam-411	2	3	no	no	INTJ
ejpam-411	2	4	.	.	NOUN
ejpam-411	2	5	3	3	NUM
ejpam-411	2	6	,	,	PUNCT
ejpam-411	2	7	2009	2009	NUM
ejpam-411	2	8	,	,	PUNCT
ejpam-411	2	9	(	(	PUNCT
ejpam-411	2	10	302	302	NUM
ejpam-411	2	11	-	-	SYM
ejpam-411	2	12	324	324	NUM
ejpam-411	2	13	)	)	PUNCT
ejpam-411	2	14	issn	issn	PROPN
ejpam-411	2	15	1307	1307	NUM
ejpam-411	2	16	-	-	SYM
ejpam-411	2	17	5543	5543	NUM
ejpam-411	2	18	–	–	PUNCT
ejpam-411	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-411	2	20	a	a	DET
ejpam-411	2	21	unified	unified	ADJ
ejpam-411	2	22	class	class	NOUN
ejpam-411	2	23	of	of	ADP
ejpam-411	2	24	analytic	analytic	ADJ
ejpam-411	2	25	functions	function	NOUN
ejpam-411	2	26	with	with	ADP
ejpam-411	2	27	varying	vary	VERB
ejpam-411	2	28	argument	argument	NOUN
ejpam-411	2	29	of	of	ADP
ejpam-411	2	30	coefficients	coefficient	NOUN
ejpam-411	2	31	j.	j.	PROPN
ejpam-411	2	32	dziok1	dziok1	PROPN
ejpam-411	2	33	and	and	CCONJ
ejpam-411	2	34	h.m	h.m	PROPN
ejpam-411	2	35	.	.	PROPN
ejpam-411	2	36	srivastava2∗	srivastava2∗	PROPN
ejpam-411	2	37	1	1	NUM
ejpam-411	2	38	institute	institute	NOUN
ejpam-411	2	39	of	of	ADP
ejpam-411	2	40	mathematics	mathematics	PROPN
ejpam-411	2	41	,	,	PUNCT
ejpam-411	2	42	university	university	NOUN
ejpam-411	2	43	of	of	ADP
ejpam-411	2	44	rzeszów	rzeszów	PROPN
ejpam-411	2	45	,	,	PUNCT
ejpam-411	2	46	ul	ul	INTJ
ejpam-411	2	47	.	.	PUNCT
ejpam-411	2	48	rejtana	rejtana	PROPN
ejpam-411	2	49	16a	16a	NOUN
ejpam-411	2	50	,	,	PUNCT
ejpam-411	2	51	pl-35	pl-35	ADV
ejpam-411	2	52	-	-	PUNCT
ejpam-411	2	53	310	310	NUM
ejpam-411	2	54	rzeszów	rzeszów	NOUN
ejpam-411	2	55	,	,	PUNCT
ejpam-411	2	56	poland	poland	PROPN
ejpam-411	2	57	2	2	NUM
ejpam-411	2	58	department	department	NOUN
ejpam-411	2	59	of	of	ADP
ejpam-411	2	60	mathematics	mathematic	NOUN
ejpam-411	2	61	and	and	CCONJ
ejpam-411	2	62	statistics	statistic	NOUN
ejpam-411	2	63	,	,	PUNCT
ejpam-411	2	64	university	university	PROPN
ejpam-411	2	65	of	of	ADP
ejpam-411	2	66	victoria	victoria	PROPN
ejpam-411	2	67	,	,	PUNCT
ejpam-411	2	68	victoria	victoria	PROPN
ejpam-411	2	69	,	,	PUNCT
ejpam-411	2	70	british	british	PROPN
ejpam-411	2	71	columbia	columbia	PROPN
ejpam-411	2	72	v8w	v8w	ADP
ejpam-411	2	73	3r4	3r4	NUM
ejpam-411	2	74	,	,	PUNCT
ejpam-411	2	75	canada	canada	PROPN
ejpam-411	2	76	abstract	abstract	NOUN
ejpam-411	2	77	.	.	PUNCT
ejpam-411	3	1	the	the	DET
ejpam-411	3	2	object	object	NOUN
ejpam-411	3	3	of	of	ADP
ejpam-411	3	4	the	the	DET
ejpam-411	3	5	present	present	ADJ
ejpam-411	3	6	paper	paper	NOUN
ejpam-411	3	7	is	be	AUX
ejpam-411	3	8	to	to	PART
ejpam-411	3	9	investigate	investigate	VERB
ejpam-411	3	10	several	several	ADJ
ejpam-411	3	11	classes	class	NOUN
ejpam-411	3	12	of	of	ADP
ejpam-411	3	13	analytic	analytic	ADJ
ejpam-411	3	14	functions	function	NOUN
ejpam-411	3	15	with	with	ADP
ejpam-411	3	16	varying	vary	VERB
ejpam-411	3	17	argument	argument	NOUN
ejpam-411	3	18	of	of	ADP
ejpam-411	3	19	coefficients	coefficient	NOUN
ejpam-411	3	20	,	,	PUNCT
ejpam-411	3	21	which	which	PRON
ejpam-411	3	22	are	be	AUX
ejpam-411	3	23	defined	define	VERB
ejpam-411	3	24	here	here	ADV
ejpam-411	3	25	by	by	ADP
ejpam-411	3	26	means	mean	NOUN
ejpam-411	3	27	of	of	ADP
ejpam-411	3	28	the	the	DET
ejpam-411	3	29	principle	principle	NOUN
ejpam-411	3	30	of	of	ADP
ejpam-411	3	31	subordination	subordination	NOUN
ejpam-411	3	32	between	between	ADP
ejpam-411	3	33	analytic	analytic	ADJ
ejpam-411	3	34	functions	function	NOUN
ejpam-411	3	35	.	.	PUNCT
ejpam-411	4	1	such	such	ADJ
ejpam-411	4	2	properties	property	NOUN
ejpam-411	4	3	as	as	ADP
ejpam-411	4	4	the	the	DET
ejpam-411	4	5	coefficient	coefficient	NOUN
ejpam-411	4	6	estimates	estimate	NOUN
ejpam-411	4	7	,	,	PUNCT
ejpam-411	4	8	distortion	distortion	NOUN
ejpam-411	4	9	theorems	theorem	NOUN
ejpam-411	4	10	,	,	PUNCT
ejpam-411	4	11	subordination	subordination	NOUN
ejpam-411	4	12	theorems	theorem	NOUN
ejpam-411	4	13	,	,	PUNCT
ejpam-411	4	14	convolution	convolution	NOUN
ejpam-411	4	15	properties	property	NOUN
ejpam-411	4	16	,	,	PUNCT
ejpam-411	4	17	integral	integral	ADJ
ejpam-411	4	18	means	mean	NOUN
ejpam-411	4	19	inequalities	inequality	NOUN
ejpam-411	4	20	,	,	PUNCT
ejpam-411	4	21	and	and	CCONJ
ejpam-411	4	22	radii	radius	NOUN
ejpam-411	4	23	of	of	ADP
ejpam-411	4	24	conexity	conexity	NOUN
ejpam-411	4	25	and	and	CCONJ
ejpam-411	4	26	starlikenes	starlikene	NOUN
ejpam-411	4	27	are	be	AUX
ejpam-411	4	28	investigated	investigate	VERB
ejpam-411	4	29	.	.	PUNCT
ejpam-411	5	1	some	some	DET
ejpam-411	5	2	consequences	consequence	NOUN
ejpam-411	5	3	of	of	ADP
ejpam-411	5	4	our	our	PRON
ejpam-411	5	5	main	main	ADJ
ejpam-411	5	6	results	result	NOUN
ejpam-411	5	7	for	for	ADP
ejpam-411	5	8	new	new	ADJ
ejpam-411	5	9	or	or	CCONJ
ejpam-411	5	10	known	known	ADJ
ejpam-411	5	11	classes	class	NOUN
ejpam-411	5	12	of	of	ADP
ejpam-411	5	13	analytic	analytic	ADJ
ejpam-411	5	14	functions	function	NOUN
ejpam-411	5	15	are	be	AUX
ejpam-411	5	16	also	also	ADV
ejpam-411	5	17	pointed	point	VERB
ejpam-411	5	18	out	out	ADP
ejpam-411	5	19	.	.	PUNCT
ejpam-411	6	1	2000	2000	NUM
ejpam-411	6	2	mathematics	mathematic	NOUN
ejpam-411	6	3	subject	subject	NOUN
ejpam-411	6	4	classifications	classification	NOUN
ejpam-411	6	5	:	:	PUNCT
ejpam-411	6	6	primary	primary	ADJ
ejpam-411	6	7	30c45	30c45	NUM
ejpam-411	6	8	,	,	PUNCT
ejpam-411	6	9	30c50	30c50	NUM
ejpam-411	6	10	;	;	PUNCT
ejpam-411	6	11	secondary	secondary	ADJ
ejpam-411	6	12	30c55	30c55	NUM
ejpam-411	6	13	.	.	PUNCT
ejpam-411	7	1	key	key	ADJ
ejpam-411	7	2	words	word	NOUN
ejpam-411	7	3	and	and	CCONJ
ejpam-411	7	4	phrases	phrase	NOUN
ejpam-411	7	5	:	:	PUNCT
ejpam-411	7	6	analytic	analytic	ADJ
ejpam-411	7	7	functions	function	NOUN
ejpam-411	7	8	;	;	PUNCT
ejpam-411	7	9	convex	convex	NOUN
ejpam-411	7	10	functions	function	NOUN
ejpam-411	7	11	;	;	PUNCT
ejpam-411	7	12	k	k	ADJ
ejpam-411	7	13	-	-	PUNCT
ejpam-411	7	14	starlike	starlike	NOUN
ejpam-411	7	15	functions	function	NOUN
ejpam-411	7	16	;	;	PUNCT
ejpam-411	7	17	uniformly	uniformly	ADV
ejpam-411	7	18	convex	convex	NOUN
ejpam-411	7	19	functions	function	NOUN
ejpam-411	7	20	;	;	PUNCT
ejpam-411	7	21	varying	vary	VERB
ejpam-411	7	22	arguments	argument	NOUN
ejpam-411	7	23	of	of	ADP
ejpam-411	7	24	coefficients	coefficient	NOUN
ejpam-411	7	25	;	;	PUNCT
ejpam-411	7	26	subordination	subordination	NOUN
ejpam-411	7	27	between	between	ADP
ejpam-411	7	28	analytic	analytic	ADJ
ejpam-411	7	29	functions	function	NOUN
ejpam-411	7	30	;	;	PUNCT
ejpam-411	7	31	hadamard	hadamard	ADJ
ejpam-411	7	32	product	product	NOUN
ejpam-411	7	33	(	(	PUNCT
ejpam-411	7	34	or	or	CCONJ
ejpam-411	7	35	convolution	convolution	NOUN
ejpam-411	7	36	)	)	PUNCT
ejpam-411	7	37	;	;	PUNCT
ejpam-411	7	38	generalized	generalize	VERB
ejpam-411	7	39	hypergeometric	hypergeometric	ADJ
ejpam-411	7	40	function	function	NOUN
ejpam-411	7	41	;	;	PUNCT
ejpam-411	7	42	dzioksrivastava	dzioksrivastava	NOUN
ejpam-411	7	43	operator	operator	NOUN
ejpam-411	7	44	.	.	PUNCT
ejpam-411	8	1	∗corresponding	∗corresponde	VERB
ejpam-411	8	2	author	author	NOUN
ejpam-411	8	3	.	.	PUNCT
ejpam-411	9	1	email	email	NOUN
ejpam-411	9	2	addresses	address	NOUN
ejpam-411	9	3	:	:	PUNCT
ejpam-411	9	4	jdziok�univ.rzeszow.pl	jdziok�univ.rzeszow.pl	PROPN
ejpam-411	9	5	(	(	PUNCT
ejpam-411	9	6	j.	j.	PROPN
ejpam-411	9	7	dziok	dziok	PROPN
ejpam-411	9	8	)	)	PUNCT
ejpam-411	9	9	,	,	PUNCT
ejpam-411	9	10	harimsri�math.uvi	harimsri�math.uvi	X
ejpam-411	9	11	.	.	PUNCT
ejpam-411	10	1	a	a	DET
ejpam-411	10	2	(	(	PUNCT
ejpam-411	10	3	h.	h.	PROPN
ejpam-411	10	4	srivastava	srivastava	PROPN
ejpam-411	10	5	)	)	PUNCT
ejpam-411	10	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-411	11	1	302	302	NUM
ejpam-411	12	1	c	c	X
ejpam-411	12	2	©	©	PROPN
ejpam-411	12	3	2009	2009	NUM
ejpam-411	12	4	ejpam	ejpam	NOUN
ejpam-411	12	5	all	all	DET
ejpam-411	12	6	rights	right	NOUN
ejpam-411	12	7	reserved	reserve	VERB
ejpam-411	12	8	.	.	PUNCT
ejpam-411	13	1	j.	j.	PROPN
ejpam-411	13	2	dziok	dziok	PROPN
ejpam-411	13	3	and	and	CCONJ
ejpam-411	13	4	h.	h.	PROPN
ejpam-411	13	5	srivastava	srivastava	PROPN
ejpam-411	13	6	/	/	SYM
ejpam-411	13	7	eur	eur	PROPN
ejpam-411	13	8	.	.	PUNCT
ejpam-411	14	1	j.	j.	PROPN
ejpam-411	14	2	pure	pure	PROPN
ejpam-411	14	3	appl	appl	PROPN
ejpam-411	14	4	.	.	PROPN
ejpam-411	14	5	math	math	PROPN
ejpam-411	14	6	,	,	PUNCT
ejpam-411	14	7	2	2	NUM
ejpam-411	14	8	(	(	PUNCT
ejpam-411	14	9	2009	2009	NUM
ejpam-411	14	10	)	)	PUNCT
ejpam-411	14	11	,	,	PUNCT
ejpam-411	14	12	(	(	PUNCT
ejpam-411	14	13	302	302	NUM
ejpam-411	14	14	-	-	SYM
ejpam-411	14	15	324	324	NUM
ejpam-411	14	16	)	)	PUNCT
ejpam-411	14	17	303	303	NUM
ejpam-411	14	18	1	1	NUM
ejpam-411	14	19	.	.	PUNCT
ejpam-411	15	1	introduction	introduction	NOUN
ejpam-411	15	2	and	and	CCONJ
ejpam-411	15	3	definitions	definition	NOUN
ejpam-411	15	4	letb	letb	ADV
ejpam-411	15	5	denote	denote	VERB
ejpam-411	15	6	the	the	DET
ejpam-411	15	7	class	class	NOUN
ejpam-411	15	8	of	of	ADP
ejpam-411	15	9	functions	function	NOUN
ejpam-411	15	10	f	f	X
ejpam-411	15	11	:	:	PUNCT
ejpam-411	15	12	u−→	u−→	PROPN
ejpam-411	15	13	c	c	X
ejpam-411	15	14	,	,	PUNCT
ejpam-411	15	15	where	where	SCONJ
ejpam-411	15	16	u	u	NOUN
ejpam-411	15	17	:	:	PUNCT
ejpam-411	15	18	=	=	SYM
ejpam-411	15	19	u(1	u(1	PROPN
ejpam-411	15	20	)	)	PUNCT
ejpam-411	15	21	and	and	CCONJ
ejpam-411	15	22	u(r	u(r	NOUN
ejpam-411	15	23	)	)	PUNCT
ejpam-411	15	24	:	:	PUNCT
ejpam-411	16	1	=	=	PUNCT
ejpam-411	16	2	{	{	PUNCT
ejpam-411	16	3	z	z	NOUN
ejpam-411	16	4	:	:	PUNCT
ejpam-411	16	5	z	z	PROPN
ejpam-411	16	6	∈	∈	PROPN
ejpam-411	16	7	c	c	NOUN
ejpam-411	16	8	and	and	CCONJ
ejpam-411	16	9	|z|	|z|	VERB
ejpam-411	16	10	<	<	X
ejpam-411	16	11	r	r	NOUN
ejpam-411	16	12	}	}	PUNCT
ejpam-411	16	13	.	.	PUNCT
ejpam-411	17	1	we	we	PRON
ejpam-411	17	2	also	also	ADV
ejpam-411	17	3	denote	denote	VERB
ejpam-411	17	4	by	by	ADP
ejpam-411	17	5	fa	fa	PROPN
ejpam-411	17	6	the	the	DET
ejpam-411	17	7	class	class	NOUN
ejpam-411	17	8	of	of	ADP
ejpam-411	17	9	functions	function	NOUN
ejpam-411	17	10	f	f	PROPN
ejpam-411	17	11	∈	∈	PROPN
ejpam-411	17	12	b	b	PROPN
ejpam-411	17	13	which	which	PRON
ejpam-411	17	14	are	be	AUX
ejpam-411	17	15	analytic	analytic	ADJ
ejpam-411	17	16	in	in	ADP
ejpam-411	17	17	u	u	PROPN
ejpam-411	17	18	(	(	PUNCT
ejpam-411	17	19	see	see	VERB
ejpam-411	17	20	,	,	PUNCT
ejpam-411	17	21	for	for	ADP
ejpam-411	17	22	details	detail	NOUN
ejpam-411	17	23	,	,	PUNCT
ejpam-411	17	24	[	[	X
ejpam-411	17	25	32	32	NUM
ejpam-411	17	26	]	]	PUNCT
ejpam-411	17	27	)	)	PUNCT
ejpam-411	17	28	.	.	PUNCT
ejpam-411	18	1	we	we	PRON
ejpam-411	18	2	say	say	VERB
ejpam-411	18	3	that	that	SCONJ
ejpam-411	18	4	a	a	DET
ejpam-411	18	5	function	function	NOUN
ejpam-411	18	6	f	f	PROPN
ejpam-411	18	7	∈b	∈b	PROPN
ejpam-411	18	8	is	be	AUX
ejpam-411	18	9	subordinate	subordinate	ADJ
ejpam-411	18	10	to	to	ADP
ejpam-411	18	11	a	a	DET
ejpam-411	18	12	function	function	NOUN
ejpam-411	18	13	f	f	PROPN
ejpam-411	18	14	∈b	∈b	PROPN
ejpam-411	18	15	,	,	PUNCT
ejpam-411	18	16	and	and	CCONJ
ejpam-411	18	17	we	we	PRON
ejpam-411	18	18	write	write	VERB
ejpam-411	18	19	f	f	PROPN
ejpam-411	18	20	(	(	PUNCT
ejpam-411	18	21	z)≺	z)≺	PROPN
ejpam-411	18	22	f(z	f(z	PROPN
ejpam-411	18	23	)	)	PUNCT
ejpam-411	18	24	or	or	CCONJ
ejpam-411	18	25	,	,	PUNCT
ejpam-411	18	26	simply	simply	ADV
ejpam-411	18	27	,	,	PUNCT
ejpam-411	18	28	f	f	PROPN
ejpam-411	18	29	≺	≺	NOUN
ejpam-411	18	30	f	f	X
ejpam-411	18	31	,	,	PUNCT
ejpam-411	18	32	if	if	SCONJ
ejpam-411	18	33	and	and	CCONJ
ejpam-411	18	34	only	only	ADV
ejpam-411	18	35	if	if	SCONJ
ejpam-411	18	36	there	there	PRON
ejpam-411	18	37	exists	exist	VERB
ejpam-411	18	38	a	a	DET
ejpam-411	18	39	function	function	NOUN
ejpam-411	18	40	w	w	NOUN
ejpam-411	18	41	∈b	∈b	NOUN
ejpam-411	18	42	with	with	ADP
ejpam-411	18	43	|w(z)|	|w(z)|	NOUN
ejpam-411	18	44	≦	≦	ADJ
ejpam-411	18	45	|z|	|z|	NOUN
ejpam-411	18	46	(	(	PUNCT
ejpam-411	18	47	z	z	NOUN
ejpam-411	18	48	∈	∈	PROPN
ejpam-411	18	49	u	u	NOUN
ejpam-411	18	50	)	)	PUNCT
ejpam-411	18	51	,	,	PUNCT
ejpam-411	18	52	such	such	ADJ
ejpam-411	18	53	that	that	SCONJ
ejpam-411	18	54	(	(	PUNCT
ejpam-411	18	55	see	see	VERB
ejpam-411	18	56	,	,	PUNCT
ejpam-411	18	57	for	for	ADP
ejpam-411	18	58	details	detail	NOUN
ejpam-411	18	59	,	,	PUNCT
ejpam-411	18	60	[	[	X
ejpam-411	18	61	15	15	NUM
ejpam-411	18	62	]	]	SYM
ejpam-411	18	63	)	)	PUNCT
ejpam-411	18	64	f	f	PROPN
ejpam-411	18	65	(	(	PUNCT
ejpam-411	18	66	z	z	NOUN
ejpam-411	18	67	)	)	PUNCT
ejpam-411	18	68	=	=	SYM
ejpam-411	18	69	f	f	PROPN
ejpam-411	18	70	�	�	PROPN
ejpam-411	18	71	w(z	w(z	PROPN
ejpam-411	18	72	)	)	PUNCT
ejpam-411	18	73	�	�	PROPN
ejpam-411	18	74	(	(	PUNCT
ejpam-411	18	75	z	z	NOUN
ejpam-411	18	76	∈	∈	PROPN
ejpam-411	18	77	u	u	NOUN
ejpam-411	18	78	)	)	PUNCT
ejpam-411	18	79	.	.	PUNCT
ejpam-411	19	1	in	in	ADP
ejpam-411	19	2	particular	particular	ADJ
ejpam-411	19	3	,	,	PUNCT
ejpam-411	19	4	if	if	SCONJ
ejpam-411	19	5	f	f	PROPN
ejpam-411	19	6	is	be	AUX
ejpam-411	19	7	univalent	univalent	ADJ
ejpam-411	19	8	in	in	ADP
ejpam-411	19	9	u	u	NOUN
ejpam-411	19	10	,	,	PUNCT
ejpam-411	19	11	we	we	PRON
ejpam-411	19	12	have	have	VERB
ejpam-411	19	13	the	the	DET
ejpam-411	19	14	following	following	ADJ
ejpam-411	19	15	equivalence	equivalence	NOUN
ejpam-411	19	16	:	:	PUNCT
ejpam-411	19	17	f	f	PROPN
ejpam-411	19	18	(	(	PUNCT
ejpam-411	19	19	z	z	NOUN
ejpam-411	19	20	)	)	PUNCT
ejpam-411	19	21	≺	≺	NOUN
ejpam-411	19	22	f(z)	f(z)	PROPN
ejpam-411	19	23	⇐	⇐	ADJ
ejpam-411	19	24	⇒	⇒	PROPN
ejpam-411	19	25	f	f	X
ejpam-411	19	26	(	(	PUNCT
ejpam-411	19	27	0	0	NUM
ejpam-411	19	28	)	)	PUNCT
ejpam-411	19	29	=	=	SYM
ejpam-411	19	30	f(0	f(0	NOUN
ejpam-411	19	31	)	)	PUNCT
ejpam-411	19	32	and	and	CCONJ
ejpam-411	19	33	f	f	PROPN
ejpam-411	19	34	(	(	PUNCT
ejpam-411	19	35	u	u	NOUN
ejpam-411	19	36	)	)	PUNCT
ejpam-411	19	37	⊂	⊂	PROPN
ejpam-411	19	38	f(u	f(u	PROPN
ejpam-411	19	39	)	)	PUNCT
ejpam-411	19	40	.	.	PUNCT
ejpam-411	20	1	for	for	ADP
ejpam-411	20	2	functions	function	NOUN
ejpam-411	20	3	f	f	NOUN
ejpam-411	20	4	,	,	PUNCT
ejpam-411	20	5	g	g	PROPN
ejpam-411	20	6	∈	∈	PROPN
ejpam-411	20	7	fa	fa	X
ejpam-411	20	8	of	of	ADP
ejpam-411	20	9	the	the	DET
ejpam-411	20	10	forms	form	NOUN
ejpam-411	20	11	:	:	PUNCT
ejpam-411	20	12	f	f	PROPN
ejpam-411	20	13	(	(	PUNCT
ejpam-411	20	14	z	z	NOUN
ejpam-411	20	15	)	)	PUNCT
ejpam-411	20	16	=	=	PUNCT
ejpam-411	21	1	∞∑	∞∑	NUM
ejpam-411	21	2	n=0	n=0	NUM
ejpam-411	21	3	anzn	anzn	NOUN
ejpam-411	21	4	and	and	CCONJ
ejpam-411	21	5	g(z	g(z	PROPN
ejpam-411	21	6	)	)	PUNCT
ejpam-411	22	1	=	=	PUNCT
ejpam-411	23	1	∞∑	∞∑	PRON
ejpam-411	23	2	n=0	n=0	NUM
ejpam-411	23	3	bnzn	bnzn	NOUN
ejpam-411	23	4	,	,	PUNCT
ejpam-411	23	5	by	by	ADP
ejpam-411	23	6	f	f	PROPN
ejpam-411	23	7	∗	∗	NOUN
ejpam-411	23	8	g	g	PROPN
ejpam-411	23	9	we	we	PRON
ejpam-411	23	10	denote	denote	VERB
ejpam-411	23	11	the	the	DET
ejpam-411	23	12	hadamard	hadamard	ADJ
ejpam-411	23	13	product	product	NOUN
ejpam-411	23	14	(	(	PUNCT
ejpam-411	23	15	or	or	CCONJ
ejpam-411	23	16	convolution	convolution	NOUN
ejpam-411	23	17	)	)	PUNCT
ejpam-411	23	18	of	of	ADP
ejpam-411	23	19	f	f	PROPN
ejpam-411	23	20	and	and	CCONJ
ejpam-411	23	21	g	g	PROPN
ejpam-411	23	22	,	,	PUNCT
ejpam-411	23	23	defined	define	VERB
ejpam-411	23	24	by	by	ADP
ejpam-411	23	25	�	�	PROPN
ejpam-411	23	26	f	f	PROPN
ejpam-411	23	27	∗	∗	NOUN
ejpam-411	23	28	g	g	PROPN
ejpam-411	23	29	�	�	PROPN
ejpam-411	23	30	(	(	PUNCT
ejpam-411	23	31	z	z	NOUN
ejpam-411	23	32	)	)	PUNCT
ejpam-411	23	33	:	:	PUNCT
ejpam-411	24	1	=	=	NOUN
ejpam-411	24	2	∞∑	∞∑	NUM
ejpam-411	24	3	n=0	n=0	NUM
ejpam-411	24	4	an	an	DET
ejpam-411	24	5	bnzn	bnzn	NOUN
ejpam-411	24	6	=	=	NOUN
ejpam-411	24	7	:	:	PUNCT
ejpam-411	24	8	�	�	PROPN
ejpam-411	24	9	g	g	PROPN
ejpam-411	24	10	∗	∗	X
ejpam-411	24	11	f	f	PROPN
ejpam-411	24	12	�	�	PROPN
ejpam-411	24	13	(	(	PUNCT
ejpam-411	24	14	z	z	NOUN
ejpam-411	24	15	)	)	PUNCT
ejpam-411	24	16	(	(	PUNCT
ejpam-411	24	17	z	z	NOUN
ejpam-411	24	18	∈	∈	PROPN
ejpam-411	24	19	u	u	NOUN
ejpam-411	24	20	)	)	PUNCT
ejpam-411	24	21	.	.	PUNCT
ejpam-411	25	1	j.	j.	PROPN
ejpam-411	25	2	dziok	dziok	PROPN
ejpam-411	25	3	and	and	CCONJ
ejpam-411	25	4	h.	h.	PROPN
ejpam-411	25	5	srivastava	srivastava	PROPN
ejpam-411	25	6	/	/	SYM
ejpam-411	25	7	eur	eur	PROPN
ejpam-411	25	8	.	.	PUNCT
ejpam-411	26	1	j.	j.	PROPN
ejpam-411	26	2	pure	pure	PROPN
ejpam-411	26	3	appl	appl	PROPN
ejpam-411	26	4	.	.	PROPN
ejpam-411	26	5	math	math	PROPN
ejpam-411	26	6	,	,	PUNCT
ejpam-411	26	7	2	2	NUM
ejpam-411	26	8	(	(	PUNCT
ejpam-411	26	9	2009	2009	NUM
ejpam-411	26	10	)	)	PUNCT
ejpam-411	26	11	,	,	PUNCT
ejpam-411	26	12	(	(	PUNCT
ejpam-411	26	13	302	302	NUM
ejpam-411	26	14	-	-	SYM
ejpam-411	26	15	324	324	NUM
ejpam-411	26	16	)	)	PUNCT
ejpam-411	26	17	304	304	NUM
ejpam-411	27	1	we	we	PRON
ejpam-411	27	2	denote	denote	VERB
ejpam-411	27	3	bya	bya	VERB
ejpam-411	27	4	the	the	DET
ejpam-411	27	5	class	class	NOUN
ejpam-411	27	6	of	of	ADP
ejpam-411	27	7	functions	function	NOUN
ejpam-411	27	8	f	f	PROPN
ejpam-411	27	9	∈b	∈b	PROPN
ejpam-411	27	10	of	of	ADP
ejpam-411	27	11	the	the	DET
ejpam-411	27	12	form	form	NOUN
ejpam-411	27	13	:	:	PUNCT
ejpam-411	27	14	f	f	PROPN
ejpam-411	27	15	(	(	PUNCT
ejpam-411	27	16	z	z	NOUN
ejpam-411	27	17	)	)	PUNCT
ejpam-411	27	18	=	=	SYM
ejpam-411	28	1	z+	z+	NUM
ejpam-411	28	2	∞∑	∞∑	NUM
ejpam-411	28	3	n=2	n=2	PRON
ejpam-411	28	4	anzn	anzn	NOUN
ejpam-411	28	5	(	(	PUNCT
ejpam-411	28	6	z	z	NOUN
ejpam-411	28	7	∈	∈	PROPN
ejpam-411	28	8	u	u	NOUN
ejpam-411	28	9	)	)	PUNCT
ejpam-411	28	10	.	.	PUNCT
ejpam-411	29	1	(	(	PUNCT
ejpam-411	29	2	1.1	1.1	NUM
ejpam-411	29	3	)	)	PUNCT
ejpam-411	29	4	we	we	PRON
ejpam-411	29	5	also	also	ADV
ejpam-411	29	6	denote	denote	VERB
ejpam-411	29	7	by	by	ADP
ejpam-411	29	8	tη	tη	PROPN
ejpam-411	29	9	�	�	PROPN
ejpam-411	29	10	η	η	PROPN
ejpam-411	29	11	∈	∈	PROPN
ejpam-411	29	12	r	r	NOUN
ejpam-411	29	13	�	�	PROPN
ejpam-411	29	14	the	the	DET
ejpam-411	29	15	class	class	NOUN
ejpam-411	29	16	of	of	ADP
ejpam-411	29	17	functions	function	NOUN
ejpam-411	29	18	f	f	PROPN
ejpam-411	29	19	∈	∈	PROPN
ejpam-411	29	20	a	a	PRON
ejpam-411	29	21	of	of	ADP
ejpam-411	29	22	the	the	DET
ejpam-411	29	23	form	form	NOUN
ejpam-411	29	24	(	(	PUNCT
ejpam-411	29	25	1.1	1.1	NUM
ejpam-411	29	26	)	)	PUNCT
ejpam-411	29	27	for	for	ADP
ejpam-411	29	28	which	which	PRON
ejpam-411	29	29	arg(an	arg(an	NOUN
ejpam-411	29	30	)	)	PUNCT
ejpam-411	29	31	=	=	SYM
ejpam-411	30	1	π+	π+	PUNCT
ejpam-411	30	2	(	(	PUNCT
ejpam-411	30	3	1−	1−	NUM
ejpam-411	30	4	n)η	n)η	X
ejpam-411	30	5	(	(	PUNCT
ejpam-411	30	6	n	n	CCONJ
ejpam-411	30	7	∈	∈	PROPN
ejpam-411	30	8	n	n	CCONJ
ejpam-411	30	9	\	\	NOUN
ejpam-411	30	10	{	{	PUNCT
ejpam-411	30	11	1	1	NUM
ejpam-411	30	12	}	}	PUNCT
ejpam-411	30	13	;	;	PUNCT
ejpam-411	30	14	n	n	CCONJ
ejpam-411	30	15	:	:	PUNCT
ejpam-411	30	16	=	=	SYM
ejpam-411	30	17	{	{	PUNCT
ejpam-411	30	18	1	1	NUM
ejpam-411	30	19	,	,	PUNCT
ejpam-411	30	20	2	2	NUM
ejpam-411	30	21	,	,	PUNCT
ejpam-411	30	22	3	3	NUM
ejpam-411	30	23	,	,	PUNCT
ejpam-411	30	24	·	·	PUNCT
ejpam-411	30	25	·	·	PUNCT
ejpam-411	30	26	·	·	PUNCT
ejpam-411	30	27	}	}	PUNCT
ejpam-411	30	28	)	)	PUNCT
ejpam-411	30	29	.	.	PUNCT
ejpam-411	31	1	(	(	PUNCT
ejpam-411	31	2	1.2	1.2	NUM
ejpam-411	31	3	)	)	PUNCT
ejpam-411	31	4	for	for	ADP
ejpam-411	31	5	η	η	PROPN
ejpam-411	31	6	=	=	SYM
ejpam-411	31	7	0	0	PROPN
ejpam-411	31	8	,	,	PUNCT
ejpam-411	31	9	we	we	PRON
ejpam-411	31	10	obtain	obtain	VERB
ejpam-411	31	11	the	the	DET
ejpam-411	31	12	familiar	familiar	ADJ
ejpam-411	31	13	class	class	NOUN
ejpam-411	31	14	t0	t0	PROPN
ejpam-411	31	15	of	of	ADP
ejpam-411	31	16	functions	function	NOUN
ejpam-411	31	17	with	with	ADP
ejpam-411	31	18	negative	negative	ADJ
ejpam-411	31	19	coefficients	coefficient	NOUN
ejpam-411	31	20	.	.	PUNCT
ejpam-411	32	1	moreover	moreover	ADV
ejpam-411	32	2	,	,	PUNCT
ejpam-411	32	3	we	we	PRON
ejpam-411	32	4	define	define	VERB
ejpam-411	32	5	t	t	NOUN
ejpam-411	32	6	:	:	PUNCT
ejpam-411	32	7	=	=	SYM
ejpam-411	32	8	⋃	⋃	NOUN
ejpam-411	32	9	η∈r	η∈r	ADJ
ejpam-411	32	10	tη	tη	PROPN
ejpam-411	32	11	.	.	PUNCT
ejpam-411	33	1	(	(	PUNCT
ejpam-411	33	2	1.3	1.3	NUM
ejpam-411	33	3	)	)	PUNCT
ejpam-411	33	4	the	the	DET
ejpam-411	33	5	class	class	NOUN
ejpam-411	33	6	t	t	PROPN
ejpam-411	33	7	was	be	AUX
ejpam-411	33	8	introduced	introduce	VERB
ejpam-411	33	9	by	by	ADP
ejpam-411	33	10	silverman	silverman	NOUN
ejpam-411	33	11	[	[	X
ejpam-411	33	12	24	24	NUM
ejpam-411	33	13	]	]	PUNCT
ejpam-411	33	14	(	(	PUNCT
ejpam-411	33	15	see	see	VERB
ejpam-411	33	16	also	also	ADV
ejpam-411	33	17	[	[	X
ejpam-411	33	18	31	31	NUM
ejpam-411	33	19	]	]	PUNCT
ejpam-411	33	20	)	)	PUNCT
ejpam-411	33	21	.	.	PUNCT
ejpam-411	34	1	it	it	PRON
ejpam-411	34	2	is	be	AUX
ejpam-411	34	3	called	call	VERB
ejpam-411	34	4	the	the	DET
ejpam-411	34	5	class	class	NOUN
ejpam-411	34	6	of	of	ADP
ejpam-411	34	7	functions	function	NOUN
ejpam-411	34	8	with	with	ADP
ejpam-411	34	9	varying	vary	VERB
ejpam-411	34	10	argument	argument	NOUN
ejpam-411	34	11	of	of	ADP
ejpam-411	34	12	coefficients	coefficient	NOUN
ejpam-411	34	13	.	.	PUNCT
ejpam-411	35	1	let	let	VERB
ejpam-411	35	2	α	α	PRON
ejpam-411	35	3	∈	∈	PROPN
ejpam-411	36	1	[	[	X
ejpam-411	36	2	0	0	NUM
ejpam-411	36	3	,	,	PUNCT
ejpam-411	36	4	1	1	NUM
ejpam-411	36	5	)	)	PUNCT
ejpam-411	36	6	and	and	CCONJ
ejpam-411	36	7	r	r	NOUN
ejpam-411	36	8	∈	∈	PROPN
ejpam-411	36	9	(	(	PUNCT
ejpam-411	36	10	0	0	NUM
ejpam-411	36	11	,	,	PUNCT
ejpam-411	36	12	1	1	NUM
ejpam-411	36	13	]	]	PUNCT
ejpam-411	36	14	.	.	PUNCT
ejpam-411	37	1	a	a	DET
ejpam-411	37	2	function	function	NOUN
ejpam-411	37	3	f	f	PROPN
ejpam-411	37	4	∈a	∈a	PROPN
ejpam-411	37	5	is	be	AUX
ejpam-411	37	6	said	say	VERB
ejpam-411	37	7	to	to	PART
ejpam-411	37	8	be	be	AUX
ejpam-411	37	9	convex	convex	NOUN
ejpam-411	37	10	of	of	ADP
ejpam-411	37	11	order	order	NOUN
ejpam-411	37	12	α	α	NOUN
ejpam-411	37	13	in	in	ADP
ejpam-411	37	14	u(r	u(r	NOUN
ejpam-411	37	15	)	)	PUNCT
ejpam-411	37	16	if	if	SCONJ
ejpam-411	37	17	and	and	CCONJ
ejpam-411	37	18	only	only	ADV
ejpam-411	37	19	if	if	SCONJ
ejpam-411	37	20	ℜ	ℜ	ADJ
ejpam-411	37	21	�	�	PROPN
ejpam-411	37	22	1	1	NUM
ejpam-411	37	23	+	+	PROPN
ejpam-411	37	24	z	z	PROPN
ejpam-411	37	25	f	f	NOUN
ejpam-411	37	26	′′(z	′′(z	PROPN
ejpam-411	37	27	)	)	PUNCT
ejpam-411	37	28	f	f	PROPN
ejpam-411	37	29	′(z	′(z	NOUN
ejpam-411	37	30	)	)	PUNCT
ejpam-411	37	31	�	�	PROPN
ejpam-411	37	32	>	>	PUNCT
ejpam-411	37	33	α	α	PROPN
ejpam-411	37	34	�	�	PROPN
ejpam-411	37	35	z	z	PROPN
ejpam-411	37	36	∈	∈	PROPN
ejpam-411	37	37	u(r	u(r	PROPN
ejpam-411	37	38	)	)	PUNCT
ejpam-411	37	39	;	;	PUNCT
ejpam-411	37	40	0	0	NUM
ejpam-411	37	41	≦	≦	VERB
ejpam-411	37	42	α	α	NOUN
ejpam-411	37	43	<	<	X
ejpam-411	37	44	1	1	NUM
ejpam-411	37	45	;	;	PUNCT
ejpam-411	37	46	0	0	NUM
ejpam-411	37	47	<	<	X
ejpam-411	37	48	r	r	NOUN
ejpam-411	37	49	≦	≦	NUM
ejpam-411	37	50	1	1	NUM
ejpam-411	37	51	�	�	PROPN
ejpam-411	37	52	.	.	PUNCT
ejpam-411	38	1	a	a	DET
ejpam-411	38	2	function	function	NOUN
ejpam-411	38	3	f	f	PROPN
ejpam-411	38	4	∈a	∈a	PROPN
ejpam-411	38	5	is	be	AUX
ejpam-411	38	6	said	say	VERB
ejpam-411	38	7	to	to	PART
ejpam-411	38	8	be	be	AUX
ejpam-411	38	9	starlike	starlike	NOUN
ejpam-411	38	10	of	of	ADP
ejpam-411	38	11	order	order	NOUN
ejpam-411	38	12	α	α	NOUN
ejpam-411	38	13	in	in	ADP
ejpam-411	38	14	u(r	u(r	NOUN
ejpam-411	38	15	)	)	PUNCT
ejpam-411	39	1	if	if	SCONJ
ejpam-411	39	2	and	and	CCONJ
ejpam-411	39	3	only	only	ADV
ejpam-411	39	4	if	if	SCONJ
ejpam-411	39	5	ℜ	ℜ	PROPN
ejpam-411	39	6	�	�	PROPN
ejpam-411	39	7	z	z	PROPN
ejpam-411	39	8	f	f	PROPN
ejpam-411	39	9	′(z	′(z	NOUN
ejpam-411	39	10	)	)	PUNCT
ejpam-411	39	11	f	f	PROPN
ejpam-411	39	12	(	(	PUNCT
ejpam-411	39	13	z	z	NOUN
ejpam-411	39	14	)	)	PUNCT
ejpam-411	39	15	�	�	PROPN
ejpam-411	39	16	>	>	PUNCT
ejpam-411	39	17	α	α	PROPN
ejpam-411	39	18	�	�	PROPN
ejpam-411	39	19	z	z	PROPN
ejpam-411	39	20	∈	∈	PROPN
ejpam-411	39	21	u(r	u(r	PROPN
ejpam-411	39	22	)	)	PUNCT
ejpam-411	39	23	;	;	PUNCT
ejpam-411	39	24	0≦	0≦	PUNCT
ejpam-411	39	25	α	α	NOUN
ejpam-411	39	26	<	<	X
ejpam-411	39	27	1	1	NUM
ejpam-411	39	28	;	;	PUNCT
ejpam-411	39	29	0	0	NUM
ejpam-411	39	30	<	<	X
ejpam-411	39	31	r	r	NOUN
ejpam-411	39	32	≦	≦	NUM
ejpam-411	39	33	1	1	NUM
ejpam-411	39	34	�	�	NOUN
ejpam-411	39	35	.	.	PUNCT
ejpam-411	40	1	(	(	PUNCT
ejpam-411	40	2	1.4	1.4	NUM
ejpam-411	40	3	)	)	PUNCT
ejpam-411	40	4	we	we	PRON
ejpam-411	40	5	denote	denote	VERB
ejpam-411	40	6	by	by	ADP
ejpam-411	40	7	s	s	PROPN
ejpam-411	40	8	c	c	PROPN
ejpam-411	40	9	(	(	PUNCT
ejpam-411	40	10	α	α	NOUN
ejpam-411	40	11	)	)	PUNCT
ejpam-411	40	12	the	the	DET
ejpam-411	40	13	class	class	NOUN
ejpam-411	40	14	of	of	ADP
ejpam-411	40	15	all	all	DET
ejpam-411	40	16	functions	function	NOUN
ejpam-411	40	17	f	f	PROPN
ejpam-411	40	18	∈	∈	PROPN
ejpam-411	40	19	a	a	PRON
ejpam-411	40	20	,	,	PUNCT
ejpam-411	40	21	which	which	PRON
ejpam-411	40	22	are	be	AUX
ejpam-411	40	23	convex	convex	ADJ
ejpam-411	40	24	of	of	ADP
ejpam-411	40	25	order	order	NOUN
ejpam-411	40	26	α	α	PROPN
ejpam-411	40	27	in	in	ADP
ejpam-411	40	28	u	u	NOUN
ejpam-411	40	29	,	,	PUNCT
ejpam-411	40	30	and	and	CCONJ
ejpam-411	40	31	by	by	ADP
ejpam-411	40	32	s	s	PROPN
ejpam-411	40	33	∗	∗	NOUN
ejpam-411	40	34	(	(	PUNCT
ejpam-411	40	35	α	α	X
ejpam-411	40	36	)	)	PUNCT
ejpam-411	40	37	we	we	PRON
ejpam-411	40	38	denote	denote	VERB
ejpam-411	40	39	the	the	DET
ejpam-411	40	40	class	class	NOUN
ejpam-411	40	41	of	of	ADP
ejpam-411	40	42	all	all	DET
ejpam-411	40	43	functions	function	NOUN
ejpam-411	40	44	f	f	PROPN
ejpam-411	40	45	∈	∈	PROPN
ejpam-411	40	46	a	a	PRON
ejpam-411	40	47	,	,	PUNCT
ejpam-411	40	48	which	which	PRON
ejpam-411	40	49	are	be	AUX
ejpam-411	40	50	starlike	starlike	NOUN
ejpam-411	40	51	of	of	ADP
ejpam-411	40	52	order	order	NOUN
ejpam-411	40	53	α	α	PROPN
ejpam-411	40	54	in	in	ADP
ejpam-411	40	55	u.	u.	NOUN
ejpam-411	40	56	we	we	PRON
ejpam-411	40	57	also	also	ADV
ejpam-411	40	58	set	set	VERB
ejpam-411	40	59	s	s	PRON
ejpam-411	40	60	c	c	NOUN
ejpam-411	40	61	=	=	SYM
ejpam-411	40	62	s	s	PROPN
ejpam-411	40	63	c(0	c(0	PROPN
ejpam-411	40	64	)	)	PUNCT
ejpam-411	40	65	and	and	CCONJ
ejpam-411	40	66	s	s	AUX
ejpam-411	40	67	∗	∗	NOUN
ejpam-411	40	68	=	=	SYM
ejpam-411	40	69	s	s	PART
ejpam-411	40	70	∗(0	∗(0	PROPN
ejpam-411	40	71	)	)	PUNCT
ejpam-411	40	72	.	.	PUNCT
ejpam-411	41	1	j.	j.	PROPN
ejpam-411	41	2	dziok	dziok	PROPN
ejpam-411	41	3	and	and	CCONJ
ejpam-411	41	4	h.	h.	PROPN
ejpam-411	41	5	srivastava	srivastava	PROPN
ejpam-411	41	6	/	/	SYM
ejpam-411	41	7	eur	eur	PROPN
ejpam-411	41	8	.	.	PUNCT
ejpam-411	42	1	j.	j.	PROPN
ejpam-411	42	2	pure	pure	PROPN
ejpam-411	42	3	appl	appl	PROPN
ejpam-411	42	4	.	.	PROPN
ejpam-411	42	5	math	math	PROPN
ejpam-411	42	6	,	,	PUNCT
ejpam-411	42	7	2	2	NUM
ejpam-411	42	8	(	(	PUNCT
ejpam-411	42	9	2009	2009	NUM
ejpam-411	42	10	)	)	PUNCT
ejpam-411	42	11	,	,	PUNCT
ejpam-411	42	12	(	(	PUNCT
ejpam-411	42	13	302	302	NUM
ejpam-411	42	14	-	-	SYM
ejpam-411	42	15	324	324	NUM
ejpam-411	42	16	)	)	PUNCT
ejpam-411	42	17	305	305	NUM
ejpam-411	42	18	it	it	PRON
ejpam-411	42	19	is	be	AUX
ejpam-411	42	20	easy	easy	ADJ
ejpam-411	42	21	to	to	PART
ejpam-411	42	22	show	show	VERB
ejpam-411	42	23	that	that	SCONJ
ejpam-411	42	24	,	,	PUNCT
ejpam-411	42	25	for	for	ADP
ejpam-411	42	26	a	a	DET
ejpam-411	42	27	function	function	NOUN
ejpam-411	42	28	f	f	PROPN
ejpam-411	42	29	∈	∈	PROPN
ejpam-411	42	30	tη	tη	PROPN
ejpam-411	42	31	,	,	PUNCT
ejpam-411	42	32	the	the	DET
ejpam-411	42	33	condition	condition	NOUN
ejpam-411	42	34	(	(	PUNCT
ejpam-411	42	35	1.4	1.4	NUM
ejpam-411	42	36	)	)	PUNCT
ejpam-411	42	37	is	be	AUX
ejpam-411	42	38	equivalent	equivalent	ADJ
ejpam-411	42	39	to	to	ADP
ejpam-411	42	40	the	the	DET
ejpam-411	42	41	following	follow	VERB
ejpam-411	42	42	inequality	inequality	NOUN
ejpam-411	42	43	:	:	PUNCT
ejpam-411	42	44	�	�	PROPN
ejpam-411	42	45	�	�	PROPN
ejpam-411	42	46	�	�	PROPN
ejpam-411	42	47	�	�	PROPN
ejpam-411	42	48	z	z	PROPN
ejpam-411	42	49	f	f	PROPN
ejpam-411	42	50	′(z	′(z	NOUN
ejpam-411	42	51	)	)	PUNCT
ejpam-411	42	52	f	f	PROPN
ejpam-411	43	1	(	(	PUNCT
ejpam-411	43	2	z	z	NOUN
ejpam-411	43	3	)	)	PUNCT
ejpam-411	43	4	−	−	PROPN
ejpam-411	43	5	1	1	NUM
ejpam-411	43	6	�	�	PROPN
ejpam-411	43	7	�	�	PROPN
ejpam-411	43	8	�	�	PROPN
ejpam-411	43	9	�	�	PROPN
ejpam-411	43	10	<	<	X
ejpam-411	43	11	1−α	1−α	NUM
ejpam-411	43	12	�	�	PROPN
ejpam-411	43	13	z	z	PROPN
ejpam-411	43	14	∈	∈	PROPN
ejpam-411	43	15	u(r	u(r	PROPN
ejpam-411	43	16	)	)	PUNCT
ejpam-411	43	17	;	;	PUNCT
ejpam-411	43	18	0≦	0≦	PUNCT
ejpam-411	43	19	α	α	NOUN
ejpam-411	43	20	<	<	X
ejpam-411	43	21	1	1	NUM
ejpam-411	43	22	;	;	PUNCT
ejpam-411	43	23	0	0	NUM
ejpam-411	43	24	<	<	X
ejpam-411	43	25	r	r	NOUN
ejpam-411	43	26	≦	≦	NUM
ejpam-411	43	27	1	1	NUM
ejpam-411	43	28	�	�	NOUN
ejpam-411	43	29	.	.	PUNCT
ejpam-411	44	1	(	(	PUNCT
ejpam-411	44	2	1.5	1.5	NUM
ejpam-411	44	3	)	)	PUNCT
ejpam-411	44	4	letb	letb	NOUN
ejpam-411	44	5	be	be	AUX
ejpam-411	44	6	a	a	DET
ejpam-411	44	7	subclass	subclass	NOUN
ejpam-411	44	8	of	of	ADP
ejpam-411	44	9	the	the	DET
ejpam-411	44	10	class	class	NOUN
ejpam-411	44	11	a	a	PRON
ejpam-411	44	12	.	.	PUNCT
ejpam-411	45	1	we	we	PRON
ejpam-411	45	2	define	define	VERB
ejpam-411	45	3	the	the	DET
ejpam-411	45	4	radius	radius	NOUN
ejpam-411	45	5	of	of	ADP
ejpam-411	45	6	starlikeness	starlikeness	NOUN
ejpam-411	45	7	of	of	ADP
ejpam-411	45	8	order	order	NOUN
ejpam-411	45	9	α	α	NOUN
ejpam-411	45	10	and	and	CCONJ
ejpam-411	45	11	the	the	DET
ejpam-411	45	12	radius	radius	NOUN
ejpam-411	45	13	of	of	ADP
ejpam-411	45	14	convexity	convexity	NOUN
ejpam-411	45	15	of	of	ADP
ejpam-411	45	16	order	order	NOUN
ejpam-411	45	17	α	α	NOUN
ejpam-411	45	18	for	for	ADP
ejpam-411	45	19	the	the	DET
ejpam-411	45	20	classb	classb	NOUN
ejpam-411	45	21	by	by	ADP
ejpam-411	45	22	r∗	r∗	PROPN
ejpam-411	45	23	α	α	PROPN
ejpam-411	45	24	(	(	PUNCT
ejpam-411	45	25	b	b	NOUN
ejpam-411	45	26	)	)	PUNCT
ejpam-411	45	27	=	=	SYM
ejpam-411	45	28	inf	inf	PROPN
ejpam-411	45	29	f	f	PROPN
ejpam-411	45	30	∈b	∈b	PROPN
ejpam-411	45	31	�	�	PROPN
ejpam-411	45	32	sup	sup	PROPN
ejpam-411	45	33	�	�	PROPN
ejpam-411	45	34	r	r	NOUN
ejpam-411	45	35	∈	∈	PROPN
ejpam-411	45	36	(	(	PUNCT
ejpam-411	45	37	0	0	NUM
ejpam-411	45	38	,	,	PUNCT
ejpam-411	45	39	1	1	NUM
ejpam-411	45	40	]	]	PUNCT
ejpam-411	45	41	:	:	PUNCT
ejpam-411	45	42	f	f	PROPN
ejpam-411	45	43	is	be	AUX
ejpam-411	45	44	starlike	starlike	NOUN
ejpam-411	45	45	of	of	ADP
ejpam-411	45	46	order	order	NOUN
ejpam-411	45	47	α	α	NOUN
ejpam-411	45	48	in	in	ADP
ejpam-411	45	49	u(r	u(r	NOUN
ejpam-411	45	50	)	)	PUNCT
ejpam-411	45	51	�	�	PROPN
ejpam-411	45	52	and	and	CCONJ
ejpam-411	45	53	rc	rc	PROPN
ejpam-411	45	54	α	α	PROPN
ejpam-411	45	55	(	(	PUNCT
ejpam-411	45	56	b	b	NOUN
ejpam-411	45	57	)	)	PUNCT
ejpam-411	45	58	=	=	SYM
ejpam-411	45	59	inf	inf	PROPN
ejpam-411	45	60	f	f	PROPN
ejpam-411	45	61	∈b	∈b	PROPN
ejpam-411	45	62	�	�	PROPN
ejpam-411	45	63	sup	sup	PROPN
ejpam-411	45	64	�	�	PROPN
ejpam-411	45	65	r	r	NOUN
ejpam-411	45	66	∈	∈	PROPN
ejpam-411	45	67	(	(	PUNCT
ejpam-411	45	68	0	0	NUM
ejpam-411	45	69	,	,	PUNCT
ejpam-411	45	70	1	1	NUM
ejpam-411	45	71	]	]	PUNCT
ejpam-411	45	72	:	:	PUNCT
ejpam-411	45	73	f	f	PROPN
ejpam-411	45	74	is	be	AUX
ejpam-411	45	75	convex	convex	NOUN
ejpam-411	45	76	of	of	ADP
ejpam-411	45	77	order	order	NOUN
ejpam-411	45	78	α	α	NOUN
ejpam-411	45	79	in	in	ADP
ejpam-411	45	80	u(r	u(r	NOUN
ejpam-411	45	81	)	)	PUNCT
ejpam-411	45	82	�	�	PROPN
ejpam-411	45	83	,	,	PUNCT
ejpam-411	45	84	respectively	respectively	ADV
ejpam-411	45	85	.	.	PUNCT
ejpam-411	46	1	let	let	VERB
ejpam-411	46	2	k	k	NOUN
ejpam-411	46	3	,	,	PUNCT
ejpam-411	46	4	a	a	PRON
ejpam-411	46	5	and	and	CCONJ
ejpam-411	46	6	b	b	NOUN
ejpam-411	46	7	be	be	AUX
ejpam-411	46	8	real	real	ADJ
ejpam-411	46	9	parameters	parameter	NOUN
ejpam-411	46	10	such	such	ADJ
ejpam-411	46	11	that	that	SCONJ
ejpam-411	46	12	k	k	PROPN
ejpam-411	46	13	≧	≧	PUNCT
ejpam-411	46	14	0	0	NUM
ejpam-411	46	15	,	,	PUNCT
ejpam-411	46	16	0	0	NUM
ejpam-411	46	17	≦	≦	NUM
ejpam-411	46	18	b	b	NOUN
ejpam-411	46	19	≦	≦	NUM
ejpam-411	46	20	1	1	NUM
ejpam-411	46	21	and	and	CCONJ
ejpam-411	46	22	−	−	NUM
ejpam-411	46	23	1	1	NUM
ejpam-411	46	24	≦	≦	NOUN
ejpam-411	46	25	a	a	DET
ejpam-411	46	26	<	<	X
ejpam-411	46	27	b.	b.	NOUN
ejpam-411	46	28	also	also	ADV
ejpam-411	46	29	let	let	VERB
ejpam-411	46	30	ϕ,φ	ϕ,φ	PRON
ejpam-411	46	31	∈	∈	PROPN
ejpam-411	46	32	a	a	PRON
ejpam-411	46	33	.	.	PUNCT
ejpam-411	47	1	by	by	ADP
ejpam-411	47	2	w	w	PROPN
ejpam-411	47	3	�	�	PROPN
ejpam-411	47	4	φ,ϕ	φ,ϕ	PROPN
ejpam-411	47	5	;	;	PUNCT
ejpam-411	47	6	a	a	DET
ejpam-411	47	7	,	,	PUNCT
ejpam-411	47	8	b	b	NOUN
ejpam-411	47	9	;	;	PUNCT
ejpam-411	47	10	k	k	PROPN
ejpam-411	47	11	�	�	PROPN
ejpam-411	47	12	we	we	PRON
ejpam-411	47	13	denote	denote	VERB
ejpam-411	47	14	the	the	DET
ejpam-411	47	15	class	class	NOUN
ejpam-411	47	16	of	of	ADP
ejpam-411	47	17	functions	function	NOUN
ejpam-411	47	18	f	f	PROPN
ejpam-411	47	19	∈	∈	PROPN
ejpam-411	48	1	a	a	DET
ejpam-411	48	2	such	such	ADJ
ejpam-411	48	3	that	that	DET
ejpam-411	48	4	�	�	PROPN
ejpam-411	48	5	ϕ	ϕ	PROPN
ejpam-411	48	6	∗	∗	X
ejpam-411	48	7	f	f	PROPN
ejpam-411	48	8	�	�	PROPN
ejpam-411	48	9	(	(	PUNCT
ejpam-411	48	10	z	z	NOUN
ejpam-411	48	11	)	)	PUNCT
ejpam-411	48	12	6=	6=	ADP
ejpam-411	48	13	0	0	NUM
ejpam-411	49	1	(	(	PUNCT
ejpam-411	49	2	z	z	NOUN
ejpam-411	49	3	∈	∈	PROPN
ejpam-411	49	4	u	u	NOUN
ejpam-411	49	5	\	\	X
ejpam-411	49	6	{	{	PUNCT
ejpam-411	49	7	0	0	NUM
ejpam-411	49	8	}	}	PUNCT
ejpam-411	49	9	)	)	PUNCT
ejpam-411	49	10	and	and	CCONJ
ejpam-411	49	11	�	�	PROPN
ejpam-411	49	12	φ	φ	PROPN
ejpam-411	49	13	∗	∗	PROPN
ejpam-411	49	14	f	f	PROPN
ejpam-411	49	15	�	�	PROPN
ejpam-411	49	16	(	(	PUNCT
ejpam-411	49	17	z	z	NOUN
ejpam-411	49	18	)	)	PUNCT
ejpam-411	49	19	�	�	PROPN
ejpam-411	49	20	ϕ	ϕ	PROPN
ejpam-411	49	21	∗	∗	X
ejpam-411	49	22	f	f	PROPN
ejpam-411	49	23	�	�	PROPN
ejpam-411	49	24	(	(	PUNCT
ejpam-411	49	25	z	z	NOUN
ejpam-411	49	26	)	)	PUNCT
ejpam-411	49	27	−	−	PROPN
ejpam-411	50	1	k	k	PROPN
ejpam-411	50	2	�	�	PROPN
ejpam-411	50	3	�	�	PROPN
ejpam-411	50	4	�	�	PROPN
ejpam-411	50	5	�	�	PROPN
ejpam-411	50	6	�	�	PROPN
ejpam-411	50	7	φ	φ	PROPN
ejpam-411	50	8	∗	∗	PROPN
ejpam-411	50	9	f	f	PROPN
ejpam-411	50	10	�	�	PROPN
ejpam-411	50	11	(	(	PUNCT
ejpam-411	50	12	z	z	NOUN
ejpam-411	50	13	)	)	PUNCT
ejpam-411	50	14	�	�	PROPN
ejpam-411	50	15	ϕ	ϕ	PROPN
ejpam-411	50	16	∗	∗	X
ejpam-411	50	17	f	f	PROPN
ejpam-411	50	18	�	�	PROPN
ejpam-411	50	19	(	(	PUNCT
ejpam-411	50	20	z	z	NOUN
ejpam-411	50	21	)	)	PUNCT
ejpam-411	50	22	−	−	PROPN
ejpam-411	50	23	1	1	NUM
ejpam-411	50	24	�	�	PROPN
ejpam-411	50	25	�	�	PROPN
ejpam-411	50	26	�	�	PROPN
ejpam-411	50	27	�	�	PROPN
ejpam-411	50	28	≺	≺	NOUN
ejpam-411	50	29	1	1	NUM
ejpam-411	50	30	+	+	NUM
ejpam-411	50	31	az	az	PROPN
ejpam-411	50	32	1	1	NUM
ejpam-411	50	33	+	+	CCONJ
ejpam-411	50	34	bz	bz	PROPN
ejpam-411	50	35	.	.	PUNCT
ejpam-411	51	1	(	(	PUNCT
ejpam-411	51	2	1.6	1.6	NUM
ejpam-411	51	3	)	)	PUNCT
ejpam-411	51	4	if	if	SCONJ
ejpam-411	51	5	0≦	0≦	NUM
ejpam-411	51	6	b	b	X
ejpam-411	51	7	<	<	X
ejpam-411	51	8	1	1	NUM
ejpam-411	51	9	,	,	PUNCT
ejpam-411	51	10	then	then	ADV
ejpam-411	51	11	the	the	DET
ejpam-411	51	12	condition	condition	NOUN
ejpam-411	51	13	(	(	PUNCT
ejpam-411	51	14	1.6	1.6	NUM
ejpam-411	51	15	)	)	PUNCT
ejpam-411	51	16	is	be	AUX
ejpam-411	51	17	equivalent	equivalent	ADJ
ejpam-411	51	18	to	to	ADP
ejpam-411	51	19	the	the	DET
ejpam-411	51	20	following	follow	VERB
ejpam-411	51	21	inequality	inequality	NOUN
ejpam-411	51	22	:	:	PUNCT
ejpam-411	52	1	�	�	PROPN
ejpam-411	52	2	�	�	PROPN
ejpam-411	52	3	�	�	PROPN
ejpam-411	52	4	�	�	PROPN
ejpam-411	52	5	�	�	PROPN
ejpam-411	52	6	�	�	PROPN
ejpam-411	52	7	φ	φ	PROPN
ejpam-411	52	8	∗	∗	PROPN
ejpam-411	52	9	f	f	PROPN
ejpam-411	52	10	�	�	PROPN
ejpam-411	52	11	(	(	PUNCT
ejpam-411	52	12	z	z	NOUN
ejpam-411	52	13	)	)	PUNCT
ejpam-411	52	14	�	�	PROPN
ejpam-411	52	15	ϕ	ϕ	PROPN
ejpam-411	52	16	∗	∗	X
ejpam-411	52	17	f	f	PROPN
ejpam-411	52	18	�	�	PROPN
ejpam-411	52	19	(	(	PUNCT
ejpam-411	52	20	z	z	NOUN
ejpam-411	52	21	)	)	PUNCT
ejpam-411	52	22	−	−	PROPN
ejpam-411	53	1	k	k	PROPN
ejpam-411	53	2	�	�	PROPN
ejpam-411	53	3	�	�	PROPN
ejpam-411	53	4	�	�	PROPN
ejpam-411	53	5	�	�	PROPN
ejpam-411	53	6	�	�	PROPN
ejpam-411	53	7	φ	φ	PROPN
ejpam-411	53	8	∗	∗	PROPN
ejpam-411	53	9	f	f	PROPN
ejpam-411	53	10	�	�	PROPN
ejpam-411	53	11	(	(	PUNCT
ejpam-411	53	12	z	z	NOUN
ejpam-411	53	13	)	)	PUNCT
ejpam-411	53	14	�	�	PROPN
ejpam-411	53	15	ϕ	ϕ	PROPN
ejpam-411	53	16	∗	∗	X
ejpam-411	53	17	f	f	PROPN
ejpam-411	53	18	�	�	PROPN
ejpam-411	53	19	(	(	PUNCT
ejpam-411	53	20	z	z	NOUN
ejpam-411	53	21	)	)	PUNCT
ejpam-411	53	22	−	−	PROPN
ejpam-411	53	23	1	1	NUM
ejpam-411	53	24	�	�	PROPN
ejpam-411	53	25	�	�	PROPN
ejpam-411	53	26	�	�	PROPN
ejpam-411	53	27	�	�	PROPN
ejpam-411	53	28	−	−	PROPN
ejpam-411	53	29	1−	1−	NUM
ejpam-411	53	30	ab	ab	PROPN
ejpam-411	53	31	1−	1−	NUM
ejpam-411	53	32	b2	b2	PROPN
ejpam-411	53	33	�	�	PROPN
ejpam-411	53	34	�	�	PROPN
ejpam-411	53	35	�	�	PROPN
ejpam-411	53	36	�	�	PROPN
ejpam-411	53	37	�	�	PROPN
ejpam-411	53	38	<	<	X
ejpam-411	53	39	b−	b−	PROPN
ejpam-411	53	40	a	a	DET
ejpam-411	53	41	1−	1−	NUM
ejpam-411	53	42	b2	b2	NOUN
ejpam-411	53	43	(	(	PUNCT
ejpam-411	53	44	z	z	NOUN
ejpam-411	53	45	∈	∈	PROPN
ejpam-411	53	46	u	u	NOUN
ejpam-411	53	47	)	)	PUNCT
ejpam-411	53	48	.	.	PUNCT
ejpam-411	54	1	(	(	PUNCT
ejpam-411	54	2	1.7	1.7	NUM
ejpam-411	54	3	)	)	PUNCT
ejpam-411	54	4	on	on	ADP
ejpam-411	54	5	the	the	DET
ejpam-411	54	6	other	other	ADJ
ejpam-411	54	7	hand	hand	NOUN
ejpam-411	54	8	,	,	PUNCT
ejpam-411	54	9	if	if	SCONJ
ejpam-411	54	10	b	b	NOUN
ejpam-411	54	11	=	=	SYM
ejpam-411	54	12	1	1	NUM
ejpam-411	54	13	,	,	PUNCT
ejpam-411	54	14	then	then	ADV
ejpam-411	54	15	we	we	PRON
ejpam-411	54	16	have	have	VERB
ejpam-411	54	17	ℜ	ℜ	PROPN
ejpam-411	54	18	�	�	PROPN
ejpam-411	54	19	�	�	PROPN
ejpam-411	54	20	φ	φ	PROPN
ejpam-411	54	21	∗	∗	PROPN
ejpam-411	54	22	f	f	PROPN
ejpam-411	54	23	�	�	PROPN
ejpam-411	54	24	(	(	PUNCT
ejpam-411	54	25	z	z	NOUN
ejpam-411	54	26	)	)	PUNCT
ejpam-411	54	27	�	�	PROPN
ejpam-411	54	28	ϕ	ϕ	PROPN
ejpam-411	54	29	∗	∗	X
ejpam-411	54	30	f	f	PROPN
ejpam-411	54	31	�	�	PROPN
ejpam-411	54	32	(	(	PUNCT
ejpam-411	54	33	z	z	NOUN
ejpam-411	54	34	)	)	PUNCT
ejpam-411	54	35	�	�	PROPN
ejpam-411	54	36	−	−	PROPN
ejpam-411	54	37	k	k	PROPN
ejpam-411	54	38	�	�	PROPN
ejpam-411	54	39	�	�	PROPN
ejpam-411	54	40	�	�	PROPN
ejpam-411	54	41	�	�	PROPN
ejpam-411	54	42	�	�	PROPN
ejpam-411	54	43	φ	φ	PROPN
ejpam-411	54	44	∗	∗	PROPN
ejpam-411	54	45	f	f	PROPN
ejpam-411	54	46	�	�	PROPN
ejpam-411	54	47	(	(	PUNCT
ejpam-411	54	48	z	z	NOUN
ejpam-411	54	49	)	)	PUNCT
ejpam-411	54	50	�	�	PROPN
ejpam-411	54	51	ϕ	ϕ	PROPN
ejpam-411	54	52	∗	∗	X
ejpam-411	55	1	f	f	PROPN
ejpam-411	55	2	�	�	PROPN
ejpam-411	55	3	(	(	PUNCT
ejpam-411	55	4	z	z	NOUN
ejpam-411	55	5	)	)	PUNCT
ejpam-411	55	6	−	−	PROPN
ejpam-411	55	7	1	1	NUM
ejpam-411	55	8	�	�	PROPN
ejpam-411	55	9	�	�	PROPN
ejpam-411	55	10	�	�	PROPN
ejpam-411	55	11	�	�	PROPN
ejpam-411	55	12	>	>	X
ejpam-411	55	13	1	1	NUM
ejpam-411	55	14	+	+	CCONJ
ejpam-411	55	15	a	a	DET
ejpam-411	55	16	2	2	NUM
ejpam-411	55	17	(	(	PUNCT
ejpam-411	55	18	z	z	NOUN
ejpam-411	55	19	∈	∈	PROPN
ejpam-411	55	20	u	u	NOUN
ejpam-411	55	21	)	)	PUNCT
ejpam-411	55	22	.	.	PUNCT
ejpam-411	56	1	(	(	PUNCT
ejpam-411	56	2	1.8	1.8	NUM
ejpam-411	56	3	)	)	PUNCT
ejpam-411	56	4	j.	j.	PROPN
ejpam-411	56	5	dziok	dziok	NOUN
ejpam-411	56	6	and	and	CCONJ
ejpam-411	56	7	h.	h.	PROPN
ejpam-411	56	8	srivastava	srivastava	PROPN
ejpam-411	56	9	/	/	SYM
ejpam-411	56	10	eur	eur	PROPN
ejpam-411	56	11	.	.	PUNCT
ejpam-411	57	1	j.	j.	PROPN
ejpam-411	57	2	pure	pure	PROPN
ejpam-411	57	3	appl	appl	PROPN
ejpam-411	57	4	.	.	PROPN
ejpam-411	57	5	math	math	PROPN
ejpam-411	57	6	,	,	PUNCT
ejpam-411	57	7	2	2	NUM
ejpam-411	57	8	(	(	PUNCT
ejpam-411	57	9	2009	2009	NUM
ejpam-411	57	10	)	)	PUNCT
ejpam-411	57	11	,	,	PUNCT
ejpam-411	57	12	(	(	PUNCT
ejpam-411	57	13	302	302	NUM
ejpam-411	57	14	-	-	SYM
ejpam-411	57	15	324	324	NUM
ejpam-411	57	16	)	)	PUNCT
ejpam-411	57	17	306	306	NUM
ejpam-411	57	18	related	relate	VERB
ejpam-411	57	19	to	to	ADP
ejpam-411	57	20	the	the	DET
ejpam-411	57	21	function	function	NOUN
ejpam-411	57	22	classes	class	NOUN
ejpam-411	57	23	t	t	PROPN
ejpam-411	57	24	and	and	CCONJ
ejpam-411	57	25	tη	tη	PROPN
ejpam-411	57	26	,	,	PUNCT
ejpam-411	57	27	we	we	PRON
ejpam-411	57	28	define	define	VERB
ejpam-411	57	29	the	the	DET
ejpam-411	57	30	following	follow	VERB
ejpam-411	57	31	two	two	NUM
ejpam-411	57	32	classes	class	NOUN
ejpam-411	57	33	:	:	PUNCT
ejpam-411	57	34	t	t	PROPN
ejpam-411	57	35	w	w	PROPN
ejpam-411	57	36	�	�	PROPN
ejpam-411	57	37	φ,ϕ	φ,ϕ	PROPN
ejpam-411	57	38	;	;	PUNCT
ejpam-411	57	39	a	a	DET
ejpam-411	57	40	,	,	PUNCT
ejpam-411	57	41	b	b	NOUN
ejpam-411	57	42	;	;	PUNCT
ejpam-411	57	43	k	k	PROPN
ejpam-411	57	44	�	�	PROPN
ejpam-411	57	45	:	:	PUNCT
ejpam-411	57	46	=	=	SYM
ejpam-411	57	47	t	t	X
ejpam-411	57	48	∩w	∩w	ADJ
ejpam-411	57	49	�	�	PROPN
ejpam-411	57	50	φ,ϕ	φ,ϕ	PROPN
ejpam-411	57	51	;	;	PUNCT
ejpam-411	57	52	a	a	DET
ejpam-411	57	53	,	,	PUNCT
ejpam-411	57	54	b	b	NOUN
ejpam-411	57	55	;	;	PUNCT
ejpam-411	57	56	k	k	PROPN
ejpam-411	57	57	�	�	PROPN
ejpam-411	57	58	and	and	CCONJ
ejpam-411	57	59	t	t	PROPN
ejpam-411	57	60	w	w	PROPN
ejpam-411	57	61	η	η	PROPN
ejpam-411	57	62	�	�	PROPN
ejpam-411	57	63	φ,ϕ	φ,ϕ	PROPN
ejpam-411	57	64	;	;	PUNCT
ejpam-411	57	65	a	a	DET
ejpam-411	57	66	,	,	PUNCT
ejpam-411	57	67	b	b	NOUN
ejpam-411	57	68	;	;	PUNCT
ejpam-411	57	69	k	k	PROPN
ejpam-411	57	70	�	�	PROPN
ejpam-411	57	71	:	:	PUNCT
ejpam-411	57	72	=	=	SYM
ejpam-411	57	73	tη	tη	PROPN
ejpam-411	57	74	∩w	∩w	PROPN
ejpam-411	57	75	�	�	PROPN
ejpam-411	57	76	φ,ϕ	φ,ϕ	PROPN
ejpam-411	57	77	;	;	PUNCT
ejpam-411	57	78	a	a	DET
ejpam-411	57	79	,	,	PUNCT
ejpam-411	57	80	b	b	NOUN
ejpam-411	57	81	;	;	PUNCT
ejpam-411	57	82	k	k	PROPN
ejpam-411	57	83	�	�	PROPN
ejpam-411	57	84	.	.	PUNCT
ejpam-411	58	1	for	for	ADP
ejpam-411	58	2	our	our	PRON
ejpam-411	58	3	present	present	ADJ
ejpam-411	58	4	investigation	investigation	NOUN
ejpam-411	58	5	,	,	PUNCT
ejpam-411	58	6	we	we	PRON
ejpam-411	58	7	assume	assume	VERB
ejpam-411	58	8	that	that	SCONJ
ejpam-411	58	9	ϕ	ϕ	PROPN
ejpam-411	58	10	and	and	CCONJ
ejpam-411	58	11	φ	φ	PROPN
ejpam-411	58	12	are	be	AUX
ejpam-411	58	13	the	the	DET
ejpam-411	58	14	functions	function	NOUN
ejpam-411	58	15	of	of	ADP
ejpam-411	58	16	the	the	DET
ejpam-411	58	17	following	follow	VERB
ejpam-411	58	18	forms	form	NOUN
ejpam-411	58	19	:	:	PUNCT
ejpam-411	58	20	ϕ(z	ϕ(z	NOUN
ejpam-411	58	21	)	)	PUNCT
ejpam-411	59	1	=	=	PUNCT
ejpam-411	60	1	z	z	NOUN
ejpam-411	61	1	+	+	NOUN
ejpam-411	61	2	∞∑	∞∑	NUM
ejpam-411	61	3	n=2	n=2	CCONJ
ejpam-411	61	4	αnzn	αnzn	NOUN
ejpam-411	61	5	and	and	CCONJ
ejpam-411	61	6	φ(z	φ(z	PROPN
ejpam-411	61	7	)	)	PUNCT
ejpam-411	61	8	=	=	SYM
ejpam-411	62	1	z	z	NOUN
ejpam-411	63	1	+	+	NOUN
ejpam-411	63	2	∞∑	∞∑	NUM
ejpam-411	63	3	n=2	n=2	ADV
ejpam-411	63	4	β	β	X
ejpam-411	63	5	nzn	nzn	NOUN
ejpam-411	63	6	(	(	PUNCT
ejpam-411	63	7	z	z	NOUN
ejpam-411	63	8	∈	∈	PROPN
ejpam-411	63	9	u	u	NOUN
ejpam-411	63	10	)	)	PUNCT
ejpam-411	63	11	,	,	PUNCT
ejpam-411	63	12	(	(	PUNCT
ejpam-411	63	13	1.9	1.9	NUM
ejpam-411	63	14	)	)	PUNCT
ejpam-411	63	15	where	where	SCONJ
ejpam-411	63	16	the	the	DET
ejpam-411	63	17	real	real	ADJ
ejpam-411	63	18	sequences	sequence	NOUN
ejpam-411	63	19	�	�	PROPN
ejpam-411	63	20	αn	αn	NOUN
ejpam-411	63	21	and	and	CCONJ
ejpam-411	63	22	�	�	PROPN
ejpam-411	63	23	β	β	X
ejpam-411	63	24	n	n	X
ejpam-411	63	25	are	be	AUX
ejpam-411	63	26	constrained	constrain	VERB
ejpam-411	63	27	further	far	ADV
ejpam-411	63	28	by	by	ADP
ejpam-411	63	29	0≦	0≦	NUM
ejpam-411	63	30	αn	αn	NOUN
ejpam-411	63	31	<	<	X
ejpam-411	63	32	β	β	X
ejpam-411	63	33	n	n	X
ejpam-411	63	34	(	(	PUNCT
ejpam-411	63	35	n	n	CCONJ
ejpam-411	63	36	∈	∈	PROPN
ejpam-411	63	37	n	n	CCONJ
ejpam-411	63	38	\	\	NOUN
ejpam-411	63	39	{	{	PUNCT
ejpam-411	63	40	1	1	NUM
ejpam-411	63	41	}	}	PUNCT
ejpam-411	63	42	)	)	PUNCT
ejpam-411	63	43	.	.	PUNCT
ejpam-411	64	1	moreover	moreover	ADV
ejpam-411	64	2	,	,	PUNCT
ejpam-411	64	3	let	let	VERB
ejpam-411	64	4	us	we	PRON
ejpam-411	64	5	put	put	VERB
ejpam-411	64	6	dn	dn	INTJ
ejpam-411	64	7	:	:	PUNCT
ejpam-411	64	8	=	=	SYM
ejpam-411	64	9	(	(	PUNCT
ejpam-411	64	10	k+	k+	NOUN
ejpam-411	64	11	1	1	NUM
ejpam-411	64	12	)	)	PUNCT
ejpam-411	64	13	(	(	PUNCT
ejpam-411	64	14	1	1	NUM
ejpam-411	64	15	+	+	NUM
ejpam-411	64	16	b)β	b)β	X
ejpam-411	64	17	n−	n−	NOUN
ejpam-411	64	18	(	(	PUNCT
ejpam-411	64	19	kb	kb	PROPN
ejpam-411	64	20	+	+	NUM
ejpam-411	64	21	a+	a+	PUNCT
ejpam-411	64	22	k+	k+	NOUN
ejpam-411	64	23	1)αn	1)αn	PROPN
ejpam-411	64	24	(	(	PUNCT
ejpam-411	64	25	n	n	NOUN
ejpam-411	64	26	∈	∈	PROPN
ejpam-411	64	27	n	n	CCONJ
ejpam-411	64	28	\	\	NOUN
ejpam-411	64	29	{	{	PUNCT
ejpam-411	64	30	1	1	NUM
ejpam-411	64	31	}	}	PUNCT
ejpam-411	64	32	)	)	PUNCT
ejpam-411	64	33	.	.	PUNCT
ejpam-411	65	1	(	(	PUNCT
ejpam-411	65	2	1.10	1.10	NUM
ejpam-411	65	3	)	)	PUNCT
ejpam-411	65	4	the	the	DET
ejpam-411	65	5	function	function	NOUN
ejpam-411	65	6	classesw	classesw	PROPN
ejpam-411	65	7	�	�	PROPN
ejpam-411	65	8	φ,ϕ	φ,ϕ	PROPN
ejpam-411	65	9	;	;	PUNCT
ejpam-411	65	10	a	a	DET
ejpam-411	65	11	,	,	PUNCT
ejpam-411	65	12	b	b	NOUN
ejpam-411	65	13	;	;	PUNCT
ejpam-411	65	14	k	k	PROPN
ejpam-411	65	15	�	�	PROPN
ejpam-411	65	16	andwη	andwη	VERB
ejpam-411	65	17	�	�	PROPN
ejpam-411	65	18	φ,ϕ	φ,ϕ	PROPN
ejpam-411	65	19	;	;	PUNCT
ejpam-411	65	20	a	a	DET
ejpam-411	65	21	,	,	PUNCT
ejpam-411	65	22	b	b	NOUN
ejpam-411	65	23	;	;	PUNCT
ejpam-411	65	24	k	k	PROPN
ejpam-411	65	25	�	�	PROPN
ejpam-411	65	26	unify	unify	VERB
ejpam-411	65	27	and	and	CCONJ
ejpam-411	65	28	extend	extend	VERB
ejpam-411	65	29	various	various	ADJ
ejpam-411	65	30	known	know	VERB
ejpam-411	65	31	classes	class	NOUN
ejpam-411	65	32	of	of	ADP
ejpam-411	65	33	analytic	analytic	ADJ
ejpam-411	65	34	functions	function	NOUN
ejpam-411	65	35	.	.	PUNCT
ejpam-411	66	1	we	we	PRON
ejpam-411	66	2	choose	choose	VERB
ejpam-411	66	3	to	to	PART
ejpam-411	66	4	list	list	VERB
ejpam-411	66	5	a	a	DET
ejpam-411	66	6	few	few	ADJ
ejpam-411	66	7	of	of	ADP
ejpam-411	66	8	these	these	DET
ejpam-411	66	9	associated	associated	ADJ
ejpam-411	66	10	analytic	analytic	ADJ
ejpam-411	66	11	function	function	NOUN
ejpam-411	66	12	classes	class	NOUN
ejpam-411	66	13	in	in	ADP
ejpam-411	66	14	the	the	DET
ejpam-411	66	15	last	last	ADJ
ejpam-411	66	16	section	section	NOUN
ejpam-411	66	17	(	(	PUNCT
ejpam-411	66	18	section	section	NOUN
ejpam-411	66	19	8)	8)	NUM
ejpam-411	66	20	.	.	PUNCT
ejpam-411	67	1	the	the	DET
ejpam-411	67	2	object	object	NOUN
ejpam-411	67	3	of	of	ADP
ejpam-411	67	4	the	the	DET
ejpam-411	67	5	present	present	ADJ
ejpam-411	67	6	paper	paper	NOUN
ejpam-411	67	7	is	be	AUX
ejpam-411	67	8	to	to	PART
ejpam-411	67	9	investigate	investigate	VERB
ejpam-411	67	10	coefficient	coefficient	NOUN
ejpam-411	67	11	estimates	estimate	NOUN
ejpam-411	67	12	,	,	PUNCT
ejpam-411	67	13	distortion	distortion	NOUN
ejpam-411	67	14	theorems	theorem	NOUN
ejpam-411	67	15	,	,	PUNCT
ejpam-411	67	16	subordination	subordination	NOUN
ejpam-411	67	17	theorems	theorem	NOUN
ejpam-411	67	18	,	,	PUNCT
ejpam-411	67	19	convolution	convolution	NOUN
ejpam-411	67	20	properties	property	NOUN
ejpam-411	67	21	,	,	PUNCT
ejpam-411	67	22	integral	integral	ADJ
ejpam-411	67	23	means	mean	NOUN
ejpam-411	67	24	inequalities	inequality	NOUN
ejpam-411	67	25	,	,	PUNCT
ejpam-411	67	26	and	and	CCONJ
ejpam-411	67	27	radii	radius	NOUN
ejpam-411	67	28	of	of	ADP
ejpam-411	67	29	conexity	conexity	NOUN
ejpam-411	67	30	and	and	CCONJ
ejpam-411	67	31	starlikenes	starlikene	NOUN
ejpam-411	67	32	of	of	ADP
ejpam-411	67	33	functions	function	NOUN
ejpam-411	67	34	in	in	ADP
ejpam-411	67	35	the	the	DET
ejpam-411	67	36	general	general	ADJ
ejpam-411	67	37	classes	class	NOUN
ejpam-411	67	38	t	t	PROPN
ejpam-411	67	39	w	w	PROPN
ejpam-411	67	40	η	η	PROPN
ejpam-411	67	41	�	�	PROPN
ejpam-411	67	42	φ,ϕ	φ,ϕ	PROPN
ejpam-411	67	43	;	;	PUNCT
ejpam-411	67	44	a	a	DET
ejpam-411	67	45	,	,	PUNCT
ejpam-411	67	46	b	b	NOUN
ejpam-411	67	47	;	;	PUNCT
ejpam-411	67	48	k	k	PROPN
ejpam-411	67	49	�	�	PROPN
ejpam-411	67	50	and	and	CCONJ
ejpam-411	67	51	t	t	PROPN
ejpam-411	67	52	w	w	PROPN
ejpam-411	67	53	�	�	PROPN
ejpam-411	67	54	φ,ϕ	φ,ϕ	PROPN
ejpam-411	67	55	;	;	PUNCT
ejpam-411	67	56	a	a	DET
ejpam-411	67	57	,	,	PUNCT
ejpam-411	67	58	b	b	NOUN
ejpam-411	67	59	;	;	PUNCT
ejpam-411	67	60	k	k	PROPN
ejpam-411	67	61	�	�	PROPN
ejpam-411	67	62	,	,	PUNCT
ejpam-411	67	63	which	which	PRON
ejpam-411	67	64	we	we	PRON
ejpam-411	67	65	have	have	AUX
ejpam-411	67	66	introduced	introduce	VERB
ejpam-411	67	67	here	here	ADV
ejpam-411	67	68	.	.	PUNCT
ejpam-411	68	1	j.	j.	PROPN
ejpam-411	68	2	dziok	dziok	PROPN
ejpam-411	68	3	and	and	CCONJ
ejpam-411	68	4	h.	h.	PROPN
ejpam-411	68	5	srivastava	srivastava	PROPN
ejpam-411	68	6	/	/	SYM
ejpam-411	68	7	eur	eur	PROPN
ejpam-411	68	8	.	.	PUNCT
ejpam-411	69	1	j.	j.	PROPN
ejpam-411	69	2	pure	pure	PROPN
ejpam-411	69	3	appl	appl	PROPN
ejpam-411	69	4	.	.	PROPN
ejpam-411	69	5	math	math	PROPN
ejpam-411	69	6	,	,	PUNCT
ejpam-411	69	7	2	2	NUM
ejpam-411	69	8	(	(	PUNCT
ejpam-411	69	9	2009	2009	NUM
ejpam-411	69	10	)	)	PUNCT
ejpam-411	69	11	,	,	PUNCT
ejpam-411	69	12	(	(	PUNCT
ejpam-411	69	13	302	302	NUM
ejpam-411	69	14	-	-	SYM
ejpam-411	69	15	324	324	NUM
ejpam-411	69	16	)	)	PUNCT
ejpam-411	69	17	307	307	NUM
ejpam-411	69	18	2	2	NUM
ejpam-411	69	19	.	.	PUNCT
ejpam-411	70	1	coefficient	coefficient	NOUN
ejpam-411	70	2	inequalities	inequality	NOUN
ejpam-411	70	3	and	and	CCONJ
ejpam-411	70	4	coefficient	coefficient	NOUN
ejpam-411	70	5	estimates	estimate	NOUN
ejpam-411	70	6	in	in	ADP
ejpam-411	70	7	this	this	DET
ejpam-411	70	8	section	section	NOUN
ejpam-411	71	1	,	,	PUNCT
ejpam-411	71	2	we	we	PRON
ejpam-411	71	3	first	first	ADV
ejpam-411	71	4	derive	derive	VERB
ejpam-411	71	5	a	a	DET
ejpam-411	71	6	sufficient	sufficient	ADJ
ejpam-411	71	7	condition	condition	NOUN
ejpam-411	71	8	for	for	ADP
ejpam-411	71	9	a	a	DET
ejpam-411	71	10	function	function	NOUN
ejpam-411	71	11	f	f	X
ejpam-411	71	12	to	to	PART
ejpam-411	71	13	belong	belong	VERB
ejpam-411	71	14	to	to	ADP
ejpam-411	71	15	the	the	DET
ejpam-411	71	16	class	class	NOUN
ejpam-411	71	17	w	w	PROPN
ejpam-411	71	18	�	�	PROPN
ejpam-411	71	19	φ,ϕ	φ,ϕ	PROPN
ejpam-411	71	20	;	;	PUNCT
ejpam-411	71	21	a	a	DET
ejpam-411	71	22	,	,	PUNCT
ejpam-411	71	23	b	b	NOUN
ejpam-411	71	24	;	;	PUNCT
ejpam-411	71	25	k	k	PROPN
ejpam-411	71	26	�	�	PROPN
ejpam-411	71	27	.	.	PUNCT
ejpam-411	72	1	theorem	theorem	VERB
ejpam-411	72	2	2.1	2.1	NUM
ejpam-411	72	3	.	.	PUNCT
ejpam-411	73	1	let	let	VERB
ejpam-411	73	2	�	�	PROPN
ejpam-411	73	3	dn	dn	PART
ejpam-411	73	4	be	be	AUX
ejpam-411	73	5	defined	define	VERB
ejpam-411	73	6	by	by	ADP
ejpam-411	73	7	(	(	PUNCT
ejpam-411	73	8	1.10	1.10	NUM
ejpam-411	73	9	)	)	PUNCT
ejpam-411	73	10	,	,	PUNCT
ejpam-411	73	11	0	0	NUM
ejpam-411	73	12	≦	≦	NUM
ejpam-411	73	13	b	b	NOUN
ejpam-411	73	14	≦	≦	NUM
ejpam-411	73	15	1	1	NUM
ejpam-411	73	16	,	,	PUNCT
ejpam-411	73	17	and	and	CCONJ
ejpam-411	73	18	−1	−1	NOUN
ejpam-411	73	19	≦	≦	VERB
ejpam-411	73	20	a	a	DET
ejpam-411	73	21	<	<	X
ejpam-411	73	22	b.	b.	NOUN
ejpam-411	74	1	if	if	SCONJ
ejpam-411	74	2	a	a	DET
ejpam-411	74	3	function	function	NOUN
ejpam-411	74	4	f	f	NOUN
ejpam-411	74	5	of	of	ADP
ejpam-411	74	6	the	the	DET
ejpam-411	74	7	form	form	NOUN
ejpam-411	74	8	(	(	PUNCT
ejpam-411	74	9	1.1	1.1	NUM
ejpam-411	74	10	)	)	PUNCT
ejpam-411	74	11	with	with	ADP
ejpam-411	74	12	�	�	PROPN
ejpam-411	74	13	ϕ	ϕ	PROPN
ejpam-411	74	14	∗	∗	X
ejpam-411	75	1	f	f	PROPN
ejpam-411	75	2	�	�	PROPN
ejpam-411	75	3	(	(	PUNCT
ejpam-411	75	4	z	z	NOUN
ejpam-411	75	5	)	)	PUNCT
ejpam-411	75	6	6=	6=	ADP
ejpam-411	75	7	0	0	NUM
ejpam-411	75	8	(	(	PUNCT
ejpam-411	75	9	z	z	NOUN
ejpam-411	75	10	∈	∈	PROPN
ejpam-411	75	11	u	u	NOUN
ejpam-411	75	12	\	\	X
ejpam-411	75	13	{	{	PUNCT
ejpam-411	75	14	0	0	NUM
ejpam-411	75	15	}	}	PUNCT
ejpam-411	75	16	)	)	PUNCT
ejpam-411	75	17	,	,	PUNCT
ejpam-411	75	18	satisfies	satisfy	VERB
ejpam-411	75	19	the	the	DET
ejpam-411	75	20	following	follow	VERB
ejpam-411	75	21	condition	condition	NOUN
ejpam-411	75	22	:	:	PUNCT
ejpam-411	75	23	∞∑	∞∑	NUM
ejpam-411	75	24	n=2	n=2	PRON
ejpam-411	75	25	dn	dn	PROPN
ejpam-411	75	26	�	�	PROPN
ejpam-411	75	27	�	�	PROPN
ejpam-411	75	28	an	an	DET
ejpam-411	75	29	�	�	PROPN
ejpam-411	75	30	�	�	PROPN
ejpam-411	75	31	≦	≦	PROPN
ejpam-411	75	32	b	b	PROPN
ejpam-411	75	33	−	−	PROPN
ejpam-411	75	34	a	a	NOUN
ejpam-411	75	35	,	,	PUNCT
ejpam-411	75	36	(	(	PUNCT
ejpam-411	75	37	2.1	2.1	NUM
ejpam-411	75	38	)	)	PUNCT
ejpam-411	75	39	then	then	ADV
ejpam-411	75	40	the	the	DET
ejpam-411	75	41	function	function	NOUN
ejpam-411	75	42	f	f	PROPN
ejpam-411	75	43	belongs	belong	VERB
ejpam-411	75	44	to	to	ADP
ejpam-411	75	45	the	the	DET
ejpam-411	75	46	class	class	NOUN
ejpam-411	75	47	w	w	PROPN
ejpam-411	75	48	�	�	PROPN
ejpam-411	75	49	φ,ϕ	φ,ϕ	PROPN
ejpam-411	75	50	;	;	PUNCT
ejpam-411	75	51	a	a	DET
ejpam-411	75	52	,	,	PUNCT
ejpam-411	75	53	b	b	NOUN
ejpam-411	75	54	;	;	PUNCT
ejpam-411	75	55	k	k	PROPN
ejpam-411	75	56	�	�	PROPN
ejpam-411	75	57	.	.	PUNCT
ejpam-411	76	1	proof	proof	NOUN
ejpam-411	76	2	.	.	PUNCT
ejpam-411	77	1	let	let	VERB
ejpam-411	77	2	0	0	NUM
ejpam-411	77	3	≦	≦	NOUN
ejpam-411	77	4	b	b	X
ejpam-411	77	5	<	<	X
ejpam-411	77	6	1	1	NUM
ejpam-411	77	7	.	.	PUNCT
ejpam-411	78	1	then	then	ADV
ejpam-411	78	2	,	,	PUNCT
ejpam-411	78	3	for	for	ADP
ejpam-411	78	4	a	a	DET
ejpam-411	78	5	function	function	NOUN
ejpam-411	78	6	f	f	PROPN
ejpam-411	78	7	of	of	ADP
ejpam-411	78	8	the	the	DET
ejpam-411	78	9	form	form	NOUN
ejpam-411	78	10	(	(	PUNCT
ejpam-411	78	11	1.1	1.1	NUM
ejpam-411	78	12	)	)	PUNCT
ejpam-411	78	13	,	,	PUNCT
ejpam-411	78	14	we	we	PRON
ejpam-411	78	15	have	have	VERB
ejpam-411	78	16	�	�	PROPN
ejpam-411	78	17	�	�	PROPN
ejpam-411	78	18	�	�	PROPN
ejpam-411	78	19	�	�	PROPN
ejpam-411	78	20	�	�	PROPN
ejpam-411	78	21	φ	φ	PROPN
ejpam-411	78	22	∗	∗	PROPN
ejpam-411	78	23	f	f	PROPN
ejpam-411	78	24	�	�	PROPN
ejpam-411	78	25	(	(	PUNCT
ejpam-411	78	26	z	z	NOUN
ejpam-411	78	27	)	)	PUNCT
ejpam-411	78	28	�	�	PROPN
ejpam-411	78	29	ϕ	ϕ	PROPN
ejpam-411	78	30	∗	∗	X
ejpam-411	78	31	f	f	PROPN
ejpam-411	78	32	�	�	PROPN
ejpam-411	78	33	(	(	PUNCT
ejpam-411	78	34	z	z	NOUN
ejpam-411	78	35	)	)	PUNCT
ejpam-411	78	36	−	−	PROPN
ejpam-411	79	1	k	k	PROPN
ejpam-411	79	2	�	�	PROPN
ejpam-411	79	3	�	�	PROPN
ejpam-411	79	4	�	�	PROPN
ejpam-411	79	5	�	�	PROPN
ejpam-411	79	6	�	�	PROPN
ejpam-411	79	7	φ	φ	PROPN
ejpam-411	79	8	∗	∗	PROPN
ejpam-411	79	9	f	f	PROPN
ejpam-411	79	10	�	�	PROPN
ejpam-411	79	11	(	(	PUNCT
ejpam-411	79	12	z	z	NOUN
ejpam-411	79	13	)	)	PUNCT
ejpam-411	79	14	�	�	PROPN
ejpam-411	79	15	ϕ	ϕ	PROPN
ejpam-411	79	16	∗	∗	X
ejpam-411	79	17	f	f	PROPN
ejpam-411	79	18	�	�	PROPN
ejpam-411	79	19	(	(	PUNCT
ejpam-411	79	20	z	z	NOUN
ejpam-411	79	21	)	)	PUNCT
ejpam-411	79	22	−	−	PROPN
ejpam-411	79	23	1	1	NUM
ejpam-411	79	24	�	�	PROPN
ejpam-411	79	25	�	�	PROPN
ejpam-411	79	26	�	�	PROPN
ejpam-411	79	27	�	�	PROPN
ejpam-411	79	28	−	−	PROPN
ejpam-411	79	29	1−	1−	NUM
ejpam-411	79	30	ab	ab	PROPN
ejpam-411	79	31	1−	1−	NUM
ejpam-411	79	32	b2	b2	PROPN
ejpam-411	79	33	�	�	PROPN
ejpam-411	79	34	�	�	PROPN
ejpam-411	79	35	�	�	PROPN
ejpam-411	79	36	�	�	PROPN
ejpam-411	79	37	≦	≦	PROPN
ejpam-411	79	38	(	(	PUNCT
ejpam-411	79	39	k+	k+	NOUN
ejpam-411	79	40	1	1	NUM
ejpam-411	79	41	)	)	PUNCT
ejpam-411	79	42	�	�	PROPN
ejpam-411	79	43	�	�	PROPN
ejpam-411	79	44	�	�	PROPN
ejpam-411	79	45	�	�	PROPN
ejpam-411	79	46	�	�	PROPN
ejpam-411	79	47	φ	φ	PROPN
ejpam-411	79	48	∗	∗	PROPN
ejpam-411	79	49	f	f	PROPN
ejpam-411	79	50	�	�	PROPN
ejpam-411	79	51	(	(	PUNCT
ejpam-411	79	52	z	z	NOUN
ejpam-411	79	53	)	)	PUNCT
ejpam-411	79	54	�	�	PROPN
ejpam-411	80	1	ϕ	ϕ	PROPN
ejpam-411	80	2	∗	∗	X
ejpam-411	80	3	f	f	PROPN
ejpam-411	80	4	�	�	PROPN
ejpam-411	80	5	(	(	PUNCT
ejpam-411	80	6	z	z	NOUN
ejpam-411	80	7	)	)	PUNCT
ejpam-411	80	8	−	−	PROPN
ejpam-411	80	9	1	1	NUM
ejpam-411	80	10	�	�	PROPN
ejpam-411	80	11	�	�	PROPN
ejpam-411	80	12	�	�	PROPN
ejpam-411	80	13	�	�	PROPN
ejpam-411	80	14	+	+	NOUN
ejpam-411	80	15	b	b	PROPN
ejpam-411	80	16	(	(	PUNCT
ejpam-411	80	17	b	b	NOUN
ejpam-411	80	18	−	−	NOUN
ejpam-411	80	19	a	a	X
ejpam-411	80	20	)	)	PUNCT
ejpam-411	80	21	1−	1−	NUM
ejpam-411	80	22	b2	b2	NOUN
ejpam-411	80	23	≦	≦	NUM
ejpam-411	80	24	(	(	PUNCT
ejpam-411	80	25	k+	k+	NOUN
ejpam-411	80	26	1	1	X
ejpam-411	80	27	)	)	PUNCT
ejpam-411	80	28	∞∑	∞∑	NUM
ejpam-411	80	29	n=2	n=2	X
ejpam-411	80	30	�	�	PROPN
ejpam-411	80	31	βn−αn	βn−αn	SYM
ejpam-411	80	32	�	�	PROPN
ejpam-411	80	33	|an||z|	|an||z|	VERB
ejpam-411	80	34	n−1	n−1	PROPN
ejpam-411	80	35	1−	1−	NUM
ejpam-411	80	36	∞∑	∞∑	NUM
ejpam-411	80	37	n=2	n=2	PRON
ejpam-411	80	38	αn|an||z|n−1	αn|an||z|n−1	NUM
ejpam-411	81	1	+	+	CCONJ
ejpam-411	81	2	b	b	X
ejpam-411	81	3	(	(	PUNCT
ejpam-411	81	4	b−	b−	PROPN
ejpam-411	81	5	a	a	NOUN
ejpam-411	81	6	)	)	PUNCT
ejpam-411	81	7	1−	1−	NUM
ejpam-411	81	8	b2	b2	NOUN
ejpam-411	81	9	.	.	PUNCT
ejpam-411	82	1	thus	thus	ADV
ejpam-411	82	2	,	,	PUNCT
ejpam-411	82	3	by	by	ADP
ejpam-411	82	4	(	(	PUNCT
ejpam-411	82	5	2.1	2.1	NUM
ejpam-411	82	6	)	)	PUNCT
ejpam-411	82	7	,	,	PUNCT
ejpam-411	82	8	we	we	PRON
ejpam-411	82	9	obtain	obtain	VERB
ejpam-411	82	10	(	(	PUNCT
ejpam-411	82	11	1.7	1.7	NUM
ejpam-411	82	12	)	)	PUNCT
ejpam-411	82	13	.	.	PUNCT
ejpam-411	83	1	consequently	consequently	ADV
ejpam-411	83	2	,	,	PUNCT
ejpam-411	83	3	f	f	PROPN
ejpam-411	83	4	∈	∈	PROPN
ejpam-411	83	5	w	w	PROPN
ejpam-411	83	6	�	�	PROPN
ejpam-411	83	7	φ,ϕ	φ,ϕ	PROPN
ejpam-411	83	8	;	;	PUNCT
ejpam-411	83	9	a	a	DET
ejpam-411	83	10	,	,	PUNCT
ejpam-411	83	11	b	b	NOUN
ejpam-411	83	12	;	;	PUNCT
ejpam-411	83	13	k	k	PROPN
ejpam-411	83	14	�	�	PROPN
ejpam-411	83	15	.	.	PUNCT
ejpam-411	84	1	we	we	PRON
ejpam-411	84	2	now	now	ADV
ejpam-411	84	3	suppose	suppose	VERB
ejpam-411	84	4	that	that	SCONJ
ejpam-411	84	5	b	b	X
ejpam-411	84	6	=	=	SYM
ejpam-411	84	7	1	1	X
ejpam-411	84	8	.	.	PUNCT
ejpam-411	85	1	then	then	ADV
ejpam-411	85	2	simple	simple	ADJ
ejpam-411	85	3	calculations	calculation	NOUN
ejpam-411	85	4	give	give	VERB
ejpam-411	85	5	k	k	PROPN
ejpam-411	85	6	�	�	PROPN
ejpam-411	85	7	�	�	PROPN
ejpam-411	85	8	�	�	PROPN
ejpam-411	85	9	�	�	PROPN
ejpam-411	85	10	�	�	PROPN
ejpam-411	85	11	φ	φ	PROPN
ejpam-411	85	12	∗	∗	PROPN
ejpam-411	85	13	f	f	PROPN
ejpam-411	85	14	�	�	PROPN
ejpam-411	85	15	(	(	PUNCT
ejpam-411	85	16	z	z	NOUN
ejpam-411	85	17	)	)	PUNCT
ejpam-411	85	18	�	�	PROPN
ejpam-411	85	19	ϕ	ϕ	PROPN
ejpam-411	85	20	∗	∗	X
ejpam-411	85	21	f	f	PROPN
ejpam-411	85	22	�	�	PROPN
ejpam-411	85	23	(	(	PUNCT
ejpam-411	85	24	z	z	NOUN
ejpam-411	85	25	)	)	PUNCT
ejpam-411	85	26	−	−	PROPN
ejpam-411	85	27	1	1	NUM
ejpam-411	85	28	�	�	PROPN
ejpam-411	85	29	�	�	PROPN
ejpam-411	85	30	�	�	PROPN
ejpam-411	85	31	�	�	PROPN
ejpam-411	85	32	−ℜ	−ℜ	PROPN
ejpam-411	85	33	�	�	PROPN
ejpam-411	85	34	�	�	PROPN
ejpam-411	85	35	φ	φ	PROPN
ejpam-411	85	36	∗	∗	PROPN
ejpam-411	85	37	f	f	PROPN
ejpam-411	85	38	�	�	PROPN
ejpam-411	85	39	(	(	PUNCT
ejpam-411	85	40	z	z	NOUN
ejpam-411	85	41	)	)	PUNCT
ejpam-411	85	42	�	�	PROPN
ejpam-411	85	43	ϕ	ϕ	PROPN
ejpam-411	85	44	∗	∗	X
ejpam-411	85	45	f	f	PROPN
ejpam-411	85	46	�	�	PROPN
ejpam-411	85	47	(	(	PUNCT
ejpam-411	85	48	z	z	NOUN
ejpam-411	85	49	)	)	PUNCT
ejpam-411	85	50	−	−	ADP
ejpam-411	86	1	1	1	NUM
ejpam-411	86	2	+	+	CCONJ
ejpam-411	86	3	a	a	DET
ejpam-411	86	4	2	2	NUM
ejpam-411	86	5	�	�	NOUN
ejpam-411	86	6	≦	≦	NUM
ejpam-411	86	7	(	(	PUNCT
ejpam-411	86	8	k+	k+	NOUN
ejpam-411	86	9	1	1	NUM
ejpam-411	86	10	)	)	PUNCT
ejpam-411	86	11	�	�	PROPN
ejpam-411	86	12	�	�	PROPN
ejpam-411	86	13	�	�	PROPN
ejpam-411	86	14	�	�	PROPN
ejpam-411	86	15	�	�	PROPN
ejpam-411	86	16	φ	φ	PROPN
ejpam-411	86	17	∗	∗	PROPN
ejpam-411	86	18	f	f	PROPN
ejpam-411	86	19	�	�	PROPN
ejpam-411	86	20	(	(	PUNCT
ejpam-411	86	21	z	z	NOUN
ejpam-411	86	22	)	)	PUNCT
ejpam-411	86	23	�	�	PROPN
ejpam-411	87	1	ϕ	ϕ	PROPN
ejpam-411	87	2	∗	∗	X
ejpam-411	87	3	f	f	PROPN
ejpam-411	87	4	�	�	PROPN
ejpam-411	87	5	(	(	PUNCT
ejpam-411	87	6	z	z	NOUN
ejpam-411	87	7	)	)	PUNCT
ejpam-411	87	8	−	−	PROPN
ejpam-411	87	9	1	1	NUM
ejpam-411	87	10	�	�	PROPN
ejpam-411	87	11	�	�	PROPN
ejpam-411	87	12	�	�	PROPN
ejpam-411	87	13	�	�	PROPN
ejpam-411	87	14	j.	j.	PROPN
ejpam-411	87	15	dziok	dziok	PROPN
ejpam-411	87	16	and	and	CCONJ
ejpam-411	87	17	h.	h.	PROPN
ejpam-411	87	18	srivastava	srivastava	PROPN
ejpam-411	87	19	/	/	SYM
ejpam-411	87	20	eur	eur	PROPN
ejpam-411	87	21	.	.	PUNCT
ejpam-411	88	1	j.	j.	PROPN
ejpam-411	88	2	pure	pure	PROPN
ejpam-411	88	3	appl	appl	PROPN
ejpam-411	88	4	.	.	PROPN
ejpam-411	88	5	math	math	PROPN
ejpam-411	88	6	,	,	PUNCT
ejpam-411	88	7	2	2	NUM
ejpam-411	88	8	(	(	PUNCT
ejpam-411	88	9	2009	2009	NUM
ejpam-411	88	10	)	)	PUNCT
ejpam-411	88	11	,	,	PUNCT
ejpam-411	88	12	(	(	PUNCT
ejpam-411	88	13	302	302	NUM
ejpam-411	88	14	-	-	SYM
ejpam-411	88	15	324	324	NUM
ejpam-411	88	16	)	)	PUNCT
ejpam-411	88	17	308	308	NUM
ejpam-411	88	18	≦	≦	NOUN
ejpam-411	88	19	(	(	PUNCT
ejpam-411	88	20	k+	k+	NOUN
ejpam-411	88	21	1	1	X
ejpam-411	88	22	)	)	PUNCT
ejpam-411	88	23	∞∑	∞∑	NUM
ejpam-411	88	24	n=2	n=2	ADJ
ejpam-411	88	25	�	�	PROPN
ejpam-411	88	26	β	β	PROPN
ejpam-411	88	27	n−αn	n−αn	PROPN
ejpam-411	88	28	�	�	PROPN
ejpam-411	88	29	|an||z|	|an||z|	VERB
ejpam-411	88	30	n−1	n−1	PROPN
ejpam-411	88	31	1−	1−	NUM
ejpam-411	88	32	∞∑	∞∑	NUM
ejpam-411	88	33	n=2	n=2	PRON
ejpam-411	88	34	αn|an||z|n−1	αn|an||z|n−1	NUM
ejpam-411	88	35	,	,	PUNCT
ejpam-411	88	36	which	which	PRON
ejpam-411	88	37	,	,	PUNCT
ejpam-411	88	38	by	by	ADP
ejpam-411	88	39	means	mean	NOUN
ejpam-411	88	40	of	of	ADP
ejpam-411	88	41	(	(	PUNCT
ejpam-411	88	42	2.1	2.1	NUM
ejpam-411	88	43	)	)	PUNCT
ejpam-411	88	44	,	,	PUNCT
ejpam-411	88	45	leads	lead	VERB
ejpam-411	88	46	us	we	PRON
ejpam-411	88	47	to	to	ADP
ejpam-411	88	48	(	(	PUNCT
ejpam-411	88	49	1.8	1.8	NUM
ejpam-411	88	50	)	)	PUNCT
ejpam-411	88	51	.	.	PUNCT
ejpam-411	89	1	therefore	therefore	ADV
ejpam-411	89	2	,	,	PUNCT
ejpam-411	89	3	f	f	PROPN
ejpam-411	89	4	∈	∈	PROPN
ejpam-411	89	5	w	w	PROPN
ejpam-411	89	6	�	�	PROPN
ejpam-411	89	7	φ,ϕ	φ,ϕ	PROPN
ejpam-411	89	8	;	;	PUNCT
ejpam-411	89	9	a	a	DET
ejpam-411	89	10	,	,	PUNCT
ejpam-411	89	11	b	b	NOUN
ejpam-411	89	12	;	;	PUNCT
ejpam-411	89	13	k	k	PROPN
ejpam-411	89	14	�	�	PROPN
ejpam-411	89	15	,	,	PUNCT
ejpam-411	89	16	and	and	CCONJ
ejpam-411	89	17	the	the	DET
ejpam-411	89	18	proof	proof	NOUN
ejpam-411	89	19	of	of	ADP
ejpam-411	89	20	theorem	theorem	ADJ
ejpam-411	89	21	2.1	2.1	NUM
ejpam-411	89	22	is	be	AUX
ejpam-411	89	23	completed	complete	VERB
ejpam-411	89	24	.	.	PUNCT
ejpam-411	90	1	our	our	PRON
ejpam-411	90	2	next	next	ADJ
ejpam-411	90	3	theorem	theorem	NOUN
ejpam-411	90	4	shows	show	VERB
ejpam-411	90	5	that	that	SCONJ
ejpam-411	90	6	the	the	DET
ejpam-411	90	7	condition	condition	NOUN
ejpam-411	90	8	(	(	PUNCT
ejpam-411	90	9	2.1	2.1	NUM
ejpam-411	90	10	)	)	PUNCT
ejpam-411	90	11	is	be	AUX
ejpam-411	90	12	necessary	necessary	ADJ
ejpam-411	90	13	as	as	ADV
ejpam-411	90	14	well	well	ADV
ejpam-411	90	15	for	for	ADP
ejpam-411	90	16	functions	function	NOUN
ejpam-411	90	17	of	of	ADP
ejpam-411	90	18	the	the	DET
ejpam-411	90	19	form	form	NOUN
ejpam-411	90	20	(	(	PUNCT
ejpam-411	90	21	1.1	1.1	NUM
ejpam-411	90	22	)	)	PUNCT
ejpam-411	90	23	satisfying	satisfy	VERB
ejpam-411	90	24	the	the	DET
ejpam-411	90	25	argument	argument	NOUN
ejpam-411	90	26	property	property	NOUN
ejpam-411	90	27	(	(	PUNCT
ejpam-411	90	28	1.2	1.2	NUM
ejpam-411	90	29	)	)	PUNCT
ejpam-411	90	30	to	to	PART
ejpam-411	90	31	belong	belong	VERB
ejpam-411	90	32	to	to	ADP
ejpam-411	90	33	the	the	DET
ejpam-411	90	34	class	class	NOUN
ejpam-411	90	35	t	t	PROPN
ejpam-411	90	36	w	w	PROPN
ejpam-411	90	37	η	η	PROPN
ejpam-411	90	38	�	�	PROPN
ejpam-411	90	39	φ,ϕ	φ,ϕ	PROPN
ejpam-411	90	40	;	;	PUNCT
ejpam-411	90	41	a	a	DET
ejpam-411	90	42	,	,	PUNCT
ejpam-411	90	43	b	b	NOUN
ejpam-411	90	44	;	;	PUNCT
ejpam-411	90	45	k	k	PROPN
ejpam-411	90	46	�	�	PROPN
ejpam-411	90	47	.	.	PUNCT
ejpam-411	91	1	theorem	theorem	VERB
ejpam-411	91	2	2.2	2.2	NUM
ejpam-411	91	3	.	.	PUNCT
ejpam-411	92	1	let	let	VERB
ejpam-411	92	2	f	f	PRON
ejpam-411	92	3	be	be	AUX
ejpam-411	92	4	a	a	DET
ejpam-411	92	5	function	function	NOUN
ejpam-411	92	6	of	of	ADP
ejpam-411	92	7	the	the	DET
ejpam-411	92	8	form	form	NOUN
ejpam-411	92	9	(	(	PUNCT
ejpam-411	92	10	1.1	1.1	NUM
ejpam-411	92	11	)	)	PUNCT
ejpam-411	92	12	satisfying	satisfy	VERB
ejpam-411	92	13	the	the	DET
ejpam-411	92	14	argument	argument	NOUN
ejpam-411	92	15	property	property	NOUN
ejpam-411	92	16	(	(	PUNCT
ejpam-411	92	17	1.2	1.2	NUM
ejpam-411	92	18	)	)	PUNCT
ejpam-411	92	19	.	.	PUNCT
ejpam-411	93	1	then	then	ADV
ejpam-411	93	2	f	f	PROPN
ejpam-411	93	3	belongs	belong	VERB
ejpam-411	93	4	to	to	ADP
ejpam-411	93	5	the	the	DET
ejpam-411	93	6	class	class	NOUN
ejpam-411	93	7	t	t	PROPN
ejpam-411	93	8	w	w	PROPN
ejpam-411	93	9	η	η	PROPN
ejpam-411	93	10	�	�	PROPN
ejpam-411	93	11	φ,ϕ	φ,ϕ	PROPN
ejpam-411	93	12	;	;	PUNCT
ejpam-411	93	13	a	a	DET
ejpam-411	93	14	,	,	PUNCT
ejpam-411	93	15	b	b	NOUN
ejpam-411	93	16	;	;	PUNCT
ejpam-411	93	17	k	k	PROPN
ejpam-411	93	18	�	�	PROPN
ejpam-411	94	1	if	if	SCONJ
ejpam-411	94	2	and	and	CCONJ
ejpam-411	94	3	only	only	ADV
ejpam-411	94	4	if	if	SCONJ
ejpam-411	94	5	the	the	DET
ejpam-411	94	6	condition	condition	NOUN
ejpam-411	94	7	(	(	PUNCT
ejpam-411	94	8	2.1	2.1	NUM
ejpam-411	94	9	)	)	PUNCT
ejpam-411	94	10	holds	hold	VERB
ejpam-411	94	11	true	true	ADJ
ejpam-411	94	12	.	.	PUNCT
ejpam-411	95	1	proof	proof	NOUN
ejpam-411	95	2	.	.	PUNCT
ejpam-411	96	1	in	in	ADP
ejpam-411	96	2	view	view	NOUN
ejpam-411	96	3	of	of	ADP
ejpam-411	96	4	theorem	theorem	NOUN
ejpam-411	96	5	2.1	2.1	NUM
ejpam-411	96	6	,	,	PUNCT
ejpam-411	96	7	we	we	PRON
ejpam-411	96	8	need	need	VERB
ejpam-411	96	9	only	only	ADV
ejpam-411	96	10	to	to	PART
ejpam-411	96	11	show	show	VERB
ejpam-411	96	12	that	that	SCONJ
ejpam-411	96	13	each	each	DET
ejpam-411	96	14	function	function	NOUN
ejpam-411	96	15	f	f	PROPN
ejpam-411	96	16	from	from	ADP
ejpam-411	96	17	the	the	DET
ejpam-411	96	18	class	class	NOUN
ejpam-411	96	19	t	t	PROPN
ejpam-411	96	20	w	w	PROPN
ejpam-411	96	21	η	η	PROPN
ejpam-411	96	22	�	�	PROPN
ejpam-411	96	23	φ,ϕ	φ,ϕ	PROPN
ejpam-411	96	24	;	;	PUNCT
ejpam-411	96	25	a	a	DET
ejpam-411	96	26	,	,	PUNCT
ejpam-411	96	27	b	b	NOUN
ejpam-411	96	28	;	;	PUNCT
ejpam-411	96	29	k	k	PROPN
ejpam-411	96	30	�	�	PROPN
ejpam-411	96	31	satisfies	satisfy	VERB
ejpam-411	96	32	the	the	DET
ejpam-411	96	33	coefficient	coefficient	NOUN
ejpam-411	96	34	inequality	inequality	NOUN
ejpam-411	96	35	(	(	PUNCT
ejpam-411	96	36	2.1	2.1	NUM
ejpam-411	96	37	)	)	PUNCT
ejpam-411	96	38	.	.	PUNCT
ejpam-411	97	1	let	let	VERB
ejpam-411	97	2	f	f	PRON
ejpam-411	97	3	be	be	AUX
ejpam-411	97	4	a	a	DET
ejpam-411	97	5	function	function	NOUN
ejpam-411	97	6	of	of	ADP
ejpam-411	97	7	the	the	DET
ejpam-411	97	8	form	form	NOUN
ejpam-411	97	9	(	(	PUNCT
ejpam-411	97	10	1.1	1.1	NUM
ejpam-411	97	11	)	)	PUNCT
ejpam-411	97	12	and	and	CCONJ
ejpam-411	97	13	satisfying	satisfy	VERB
ejpam-411	97	14	the	the	DET
ejpam-411	97	15	argument	argument	NOUN
ejpam-411	97	16	property	property	NOUN
ejpam-411	97	17	(	(	PUNCT
ejpam-411	97	18	1.2	1.2	NUM
ejpam-411	97	19	)	)	PUNCT
ejpam-411	97	20	belong	belong	VERB
ejpam-411	97	21	to	to	ADP
ejpam-411	97	22	the	the	DET
ejpam-411	97	23	class	class	NOUN
ejpam-411	97	24	t	t	PROPN
ejpam-411	97	25	w	w	PROPN
ejpam-411	97	26	η	η	PROPN
ejpam-411	97	27	�	�	PROPN
ejpam-411	97	28	φ,ϕ	φ,ϕ	PROPN
ejpam-411	97	29	;	;	PUNCT
ejpam-411	97	30	a	a	DET
ejpam-411	97	31	,	,	PUNCT
ejpam-411	97	32	b	b	NOUN
ejpam-411	97	33	;	;	PUNCT
ejpam-411	97	34	k	k	PROPN
ejpam-411	97	35	�	�	PROPN
ejpam-411	97	36	.	.	PUNCT
ejpam-411	98	1	then	then	ADV
ejpam-411	98	2	,	,	PUNCT
ejpam-411	98	3	putting	put	VERB
ejpam-411	98	4	z	z	NOUN
ejpam-411	98	5	=	=	PUNCT
ejpam-411	98	6	r	r	NOUN
ejpam-411	98	7	iη	iη	NOUN
ejpam-411	98	8	in	in	ADP
ejpam-411	98	9	the	the	DET
ejpam-411	98	10	conditions	condition	NOUN
ejpam-411	98	11	(	(	PUNCT
ejpam-411	98	12	1.7	1.7	NUM
ejpam-411	98	13	)	)	PUNCT
ejpam-411	98	14	and	and	CCONJ
ejpam-411	98	15	(	(	PUNCT
ejpam-411	98	16	1.8	1.8	NUM
ejpam-411	98	17	)	)	PUNCT
ejpam-411	98	18	,	,	PUNCT
ejpam-411	98	19	we	we	PRON
ejpam-411	98	20	obtain	obtain	VERB
ejpam-411	98	21	(	(	PUNCT
ejpam-411	98	22	k+	k+	NOUN
ejpam-411	98	23	1	1	X
ejpam-411	98	24	)	)	PUNCT
ejpam-411	98	25	∞∑	∞∑	NUM
ejpam-411	98	26	n=2	n=2	ADJ
ejpam-411	98	27	�	�	PROPN
ejpam-411	98	28	β	β	PROPN
ejpam-411	98	29	n−αn	n−αn	PROPN
ejpam-411	98	30	�	�	PROPN
ejpam-411	98	31	|an|r	|an|r	NUM
ejpam-411	98	32	n−1	n−1	PROPN
ejpam-411	98	33	1−	1−	NUM
ejpam-411	98	34	∞∑	∞∑	NUM
ejpam-411	98	35	n=2	n=2	PRON
ejpam-411	98	36	αn|an|rn−1	αn|an|rn−1	ADJ
ejpam-411	98	37	<	<	X
ejpam-411	98	38	b−	b−	PROPN
ejpam-411	98	39	a	a	DET
ejpam-411	98	40	1	1	NUM
ejpam-411	98	41	+	+	SYM
ejpam-411	98	42	b	b	NOUN
ejpam-411	98	43	.	.	PUNCT
ejpam-411	99	1	we	we	PRON
ejpam-411	99	2	thus	thus	ADV
ejpam-411	99	3	find	find	VERB
ejpam-411	99	4	that	that	SCONJ
ejpam-411	99	5	∞∑	∞∑	NUM
ejpam-411	99	6	n=2	n=2	X
ejpam-411	99	7	�	�	PROPN
ejpam-411	99	8	(	(	PUNCT
ejpam-411	99	9	k+	k+	NOUN
ejpam-411	99	10	1	1	NUM
ejpam-411	99	11	)	)	PUNCT
ejpam-411	99	12	(	(	PUNCT
ejpam-411	99	13	1	1	NUM
ejpam-411	99	14	+	+	NUM
ejpam-411	99	15	b)β	b)β	X
ejpam-411	99	16	n−	n−	NOUN
ejpam-411	99	17	(	(	PUNCT
ejpam-411	99	18	k	k	X
ejpam-411	99	19	(	(	PUNCT
ejpam-411	99	20	1	1	NUM
ejpam-411	99	21	+	+	NUM
ejpam-411	99	22	b	b	NOUN
ejpam-411	99	23	)	)	PUNCT
ejpam-411	100	1	+	+	CCONJ
ejpam-411	101	1	1	1	NUM
ejpam-411	101	2	+	+	CCONJ
ejpam-411	101	3	a)αn	a)αn	PROPN
ejpam-411	101	4	�	�	PROPN
ejpam-411	101	5	|an|r	|an|r	NUM
ejpam-411	101	6	n−1	n−1	PROPN
ejpam-411	101	7	<	<	X
ejpam-411	101	8	b	b	X
ejpam-411	101	9	−	−	PROPN
ejpam-411	101	10	a	a	NOUN
ejpam-411	101	11	,	,	PUNCT
ejpam-411	101	12	which	which	PRON
ejpam-411	101	13	,	,	PUNCT
ejpam-411	101	14	upon	upon	SCONJ
ejpam-411	101	15	letting	let	VERB
ejpam-411	101	16	r	r	NOUN
ejpam-411	101	17	→	→	SYM
ejpam-411	101	18	1−	1−	NUM
ejpam-411	101	19	,	,	PUNCT
ejpam-411	101	20	readily	readily	ADV
ejpam-411	101	21	yields	yield	VERB
ejpam-411	101	22	the	the	DET
ejpam-411	101	23	assertion	assertion	NOUN
ejpam-411	101	24	(	(	PUNCT
ejpam-411	101	25	2.1	2.1	NUM
ejpam-411	101	26	)	)	PUNCT
ejpam-411	101	27	.	.	PUNCT
ejpam-411	102	1	since	since	SCONJ
ejpam-411	102	2	the	the	DET
ejpam-411	102	3	condition	condition	NOUN
ejpam-411	102	4	(	(	PUNCT
ejpam-411	102	5	2.1	2.1	NUM
ejpam-411	102	6	)	)	PUNCT
ejpam-411	102	7	is	be	AUX
ejpam-411	102	8	independent	independent	ADJ
ejpam-411	102	9	of	of	ADP
ejpam-411	102	10	η	η	PROPN
ejpam-411	102	11	,	,	PUNCT
ejpam-411	102	12	theorem	theorem	VERB
ejpam-411	102	13	2.2	2.2	NUM
ejpam-411	102	14	yields	yield	NOUN
ejpam-411	102	15	the	the	DET
ejpam-411	102	16	following	following	ADJ
ejpam-411	102	17	result	result	NOUN
ejpam-411	102	18	.	.	PUNCT
ejpam-411	103	1	j.	j.	PROPN
ejpam-411	103	2	dziok	dziok	PROPN
ejpam-411	103	3	and	and	CCONJ
ejpam-411	103	4	h.	h.	PROPN
ejpam-411	103	5	srivastava	srivastava	PROPN
ejpam-411	103	6	/	/	SYM
ejpam-411	103	7	eur	eur	PROPN
ejpam-411	103	8	.	.	PUNCT
ejpam-411	104	1	j.	j.	PROPN
ejpam-411	104	2	pure	pure	PROPN
ejpam-411	104	3	appl	appl	PROPN
ejpam-411	104	4	.	.	PROPN
ejpam-411	104	5	math	math	PROPN
ejpam-411	104	6	,	,	PUNCT
ejpam-411	104	7	2	2	NUM
ejpam-411	104	8	(	(	PUNCT
ejpam-411	104	9	2009	2009	NUM
ejpam-411	104	10	)	)	PUNCT
ejpam-411	104	11	,	,	PUNCT
ejpam-411	104	12	(	(	PUNCT
ejpam-411	104	13	302	302	NUM
ejpam-411	104	14	-	-	SYM
ejpam-411	104	15	324	324	NUM
ejpam-411	104	16	)	)	PUNCT
ejpam-411	104	17	309	309	NUM
ejpam-411	104	18	theorem	theorem	VERB
ejpam-411	104	19	2.3	2.3	NUM
ejpam-411	104	20	.	.	PUNCT
ejpam-411	105	1	let	let	VERB
ejpam-411	105	2	f	f	PRON
ejpam-411	105	3	be	be	AUX
ejpam-411	105	4	a	a	DET
ejpam-411	105	5	function	function	NOUN
ejpam-411	105	6	of	of	ADP
ejpam-411	105	7	the	the	DET
ejpam-411	105	8	form	form	NOUN
ejpam-411	105	9	(	(	PUNCT
ejpam-411	105	10	1.1	1.1	NUM
ejpam-411	105	11	)	)	PUNCT
ejpam-411	105	12	satisfying	satisfy	VERB
ejpam-411	105	13	the	the	DET
ejpam-411	105	14	agument	agument	ADJ
ejpam-411	105	15	property	property	NOUN
ejpam-411	105	16	(	(	PUNCT
ejpam-411	105	17	1.2	1.2	NUM
ejpam-411	105	18	)	)	PUNCT
ejpam-411	105	19	.	.	PUNCT
ejpam-411	106	1	then	then	ADV
ejpam-411	106	2	f	f	PROPN
ejpam-411	106	3	∈	∈	PROPN
ejpam-411	106	4	t	t	PROPN
ejpam-411	106	5	w	w	PROPN
ejpam-411	106	6	�	�	PROPN
ejpam-411	106	7	φ,ϕ	φ,ϕ	PROPN
ejpam-411	106	8	;	;	PUNCT
ejpam-411	106	9	a	a	DET
ejpam-411	106	10	,	,	PUNCT
ejpam-411	106	11	b	b	NOUN
ejpam-411	106	12	;	;	PUNCT
ejpam-411	106	13	k	k	PROPN
ejpam-411	106	14	�	�	PROPN
ejpam-411	107	1	if	if	SCONJ
ejpam-411	107	2	and	and	CCONJ
ejpam-411	107	3	only	only	ADV
ejpam-411	107	4	if	if	SCONJ
ejpam-411	107	5	the	the	DET
ejpam-411	107	6	condition	condition	NOUN
ejpam-411	107	7	(	(	PUNCT
ejpam-411	107	8	2.1	2.1	NUM
ejpam-411	107	9	)	)	PUNCT
ejpam-411	107	10	holds	hold	VERB
ejpam-411	107	11	true	true	ADJ
ejpam-411	107	12	.	.	PUNCT
ejpam-411	108	1	from	from	ADP
ejpam-411	108	2	theorems	theorem	NOUN
ejpam-411	108	3	2.2	2.2	NUM
ejpam-411	108	4	and	and	CCONJ
ejpam-411	108	5	2.3	2.3	NUM
ejpam-411	108	6	we	we	PRON
ejpam-411	108	7	can	can	AUX
ejpam-411	108	8	obtain	obtain	VERB
ejpam-411	108	9	the	the	DET
ejpam-411	108	10	following	follow	VERB
ejpam-411	108	11	coefficient	coefficient	NOUN
ejpam-411	108	12	estimates	estimate	NOUN
ejpam-411	108	13	for	for	ADP
ejpam-411	108	14	functions	function	NOUN
ejpam-411	108	15	in	in	ADP
ejpam-411	108	16	the	the	DET
ejpam-411	108	17	classes	class	NOUN
ejpam-411	108	18	t	t	PROPN
ejpam-411	108	19	w	w	PROPN
ejpam-411	108	20	η	η	PROPN
ejpam-411	108	21	�	�	PROPN
ejpam-411	108	22	φ,ϕ	φ,ϕ	PROPN
ejpam-411	108	23	;	;	PUNCT
ejpam-411	108	24	a	a	DET
ejpam-411	108	25	,	,	PUNCT
ejpam-411	108	26	b	b	NOUN
ejpam-411	108	27	;	;	PUNCT
ejpam-411	108	28	k	k	PROPN
ejpam-411	108	29	�	�	PROPN
ejpam-411	108	30	and	and	CCONJ
ejpam-411	108	31	t	t	PROPN
ejpam-411	108	32	w	w	PROPN
ejpam-411	108	33	�	�	PROPN
ejpam-411	108	34	φ,ϕ	φ,ϕ	PROPN
ejpam-411	108	35	;	;	PUNCT
ejpam-411	108	36	a	a	DET
ejpam-411	108	37	,	,	PUNCT
ejpam-411	108	38	b	b	NOUN
ejpam-411	108	39	;	;	PUNCT
ejpam-411	108	40	k	k	PROPN
ejpam-411	108	41	�	�	PROPN
ejpam-411	108	42	,	,	PUNCT
ejpam-411	108	43	respectively	respectively	ADV
ejpam-411	108	44	.	.	PUNCT
ejpam-411	109	1	corollary	corollary	ADJ
ejpam-411	109	2	2.1	2.1	NUM
ejpam-411	109	3	.	.	PUNCT
ejpam-411	110	1	if	if	SCONJ
ejpam-411	110	2	a	a	DET
ejpam-411	110	3	function	function	NOUN
ejpam-411	110	4	f	f	NOUN
ejpam-411	110	5	of	of	ADP
ejpam-411	110	6	the	the	DET
ejpam-411	110	7	form	form	NOUN
ejpam-411	110	8	(	(	PUNCT
ejpam-411	110	9	1.1	1.1	NUM
ejpam-411	110	10	)	)	PUNCT
ejpam-411	110	11	belongs	belong	VERB
ejpam-411	110	12	to	to	ADP
ejpam-411	110	13	the	the	DET
ejpam-411	110	14	class	class	NOUN
ejpam-411	110	15	t	t	PROPN
ejpam-411	110	16	w	w	PROPN
ejpam-411	110	17	η	η	PROPN
ejpam-411	110	18	�	�	PROPN
ejpam-411	110	19	φ,ϕ	φ,ϕ	PROPN
ejpam-411	110	20	;	;	PUNCT
ejpam-411	110	21	a	a	DET
ejpam-411	110	22	,	,	PUNCT
ejpam-411	110	23	b	b	NOUN
ejpam-411	110	24	;	;	PUNCT
ejpam-411	110	25	k	k	PROPN
ejpam-411	110	26	�	�	PROPN
ejpam-411	110	27	,	,	PUNCT
ejpam-411	110	28	then	then	ADV
ejpam-411	110	29	�	�	PROPN
ejpam-411	110	30	�	�	PROPN
ejpam-411	110	31	an	an	DET
ejpam-411	110	32	�	�	PROPN
ejpam-411	110	33	�	�	PROPN
ejpam-411	110	34	≦	≦	NUM
ejpam-411	110	35	b−	b−	NOUN
ejpam-411	110	36	a	a	DET
ejpam-411	110	37	dn	dn	NOUN
ejpam-411	110	38	(	(	PUNCT
ejpam-411	110	39	n	n	CCONJ
ejpam-411	110	40	∈	∈	PROPN
ejpam-411	110	41	n	n	CCONJ
ejpam-411	110	42	\	\	NOUN
ejpam-411	110	43	{	{	PUNCT
ejpam-411	110	44	1	1	NUM
ejpam-411	110	45	}	}	PUNCT
ejpam-411	110	46	)	)	PUNCT
ejpam-411	110	47	,	,	PUNCT
ejpam-411	110	48	(	(	PUNCT
ejpam-411	110	49	2.2	2.2	NUM
ejpam-411	110	50	)	)	PUNCT
ejpam-411	110	51	where	where	SCONJ
ejpam-411	110	52	dn	dn	PROPN
ejpam-411	110	53	is	be	AUX
ejpam-411	110	54	defined	define	VERB
ejpam-411	110	55	by	by	ADP
ejpam-411	110	56	(	(	PUNCT
ejpam-411	110	57	1.10	1.10	NUM
ejpam-411	110	58	)	)	PUNCT
ejpam-411	110	59	.	.	PUNCT
ejpam-411	111	1	the	the	DET
ejpam-411	111	2	result	result	NOUN
ejpam-411	111	3	is	be	AUX
ejpam-411	111	4	sharp	sharp	ADJ
ejpam-411	111	5	and	and	CCONJ
ejpam-411	111	6	the	the	DET
ejpam-411	111	7	functions	function	NOUN
ejpam-411	111	8	fn	fn	PROPN
ejpam-411	111	9	,	,	PUNCT
ejpam-411	111	10	η	η	PROPN
ejpam-411	111	11	given	give	VERB
ejpam-411	111	12	by	by	ADP
ejpam-411	111	13	fn	fn	PROPN
ejpam-411	111	14	,	,	PUNCT
ejpam-411	111	15	η(z	η(z	PROPN
ejpam-411	111	16	)	)	PUNCT
ejpam-411	111	17	=	=	PUNCT
ejpam-411	112	1	z−	z−	PROPN
ejpam-411	112	2	b	b	X
ejpam-411	112	3	−	−	PROPN
ejpam-411	112	4	a	a	DET
ejpam-411	112	5	dn	dn	PROPN
ejpam-411	112	6	ei(1−n)ηzn	ei(1−n)ηzn	PROPN
ejpam-411	112	7	(	(	PUNCT
ejpam-411	112	8	z	z	NOUN
ejpam-411	112	9	∈	∈	PROPN
ejpam-411	112	10	u	u	NOUN
ejpam-411	112	11	;	;	PUNCT
ejpam-411	112	12	n	n	PRON
ejpam-411	112	13	∈	∈	PROPN
ejpam-411	112	14	n	n	CCONJ
ejpam-411	112	15	)	)	PUNCT
ejpam-411	112	16	(	(	PUNCT
ejpam-411	112	17	2.3	2.3	NUM
ejpam-411	112	18	)	)	PUNCT
ejpam-411	112	19	are	be	AUX
ejpam-411	112	20	the	the	DET
ejpam-411	112	21	extremal	extremal	ADJ
ejpam-411	112	22	functions	function	NOUN
ejpam-411	112	23	.	.	PUNCT
ejpam-411	113	1	corollary	corollary	ADJ
ejpam-411	113	2	2.2	2.2	NUM
ejpam-411	113	3	.	.	PUNCT
ejpam-411	114	1	if	if	SCONJ
ejpam-411	114	2	a	a	DET
ejpam-411	114	3	function	function	NOUN
ejpam-411	114	4	f	f	NOUN
ejpam-411	114	5	of	of	ADP
ejpam-411	114	6	the	the	DET
ejpam-411	114	7	form	form	NOUN
ejpam-411	114	8	(	(	PUNCT
ejpam-411	114	9	1.1	1.1	NUM
ejpam-411	114	10	)	)	PUNCT
ejpam-411	114	11	belongs	belong	VERB
ejpam-411	114	12	to	to	ADP
ejpam-411	114	13	the	the	DET
ejpam-411	114	14	class	class	NOUN
ejpam-411	114	15	t	t	PROPN
ejpam-411	114	16	w	w	PROPN
ejpam-411	114	17	�	�	PROPN
ejpam-411	114	18	φ,ϕ	φ,ϕ	PROPN
ejpam-411	114	19	;	;	PUNCT
ejpam-411	114	20	a	a	DET
ejpam-411	114	21	,	,	PUNCT
ejpam-411	114	22	b	b	NOUN
ejpam-411	114	23	;	;	PUNCT
ejpam-411	114	24	k	k	PROPN
ejpam-411	114	25	�	�	PROPN
ejpam-411	114	26	,	,	PUNCT
ejpam-411	114	27	then	then	ADV
ejpam-411	114	28	the	the	DET
ejpam-411	114	29	coefficient	coefficient	NOUN
ejpam-411	114	30	estimates	estimate	NOUN
ejpam-411	114	31	given	give	VERB
ejpam-411	114	32	by	by	ADP
ejpam-411	114	33	(	(	PUNCT
ejpam-411	114	34	2.2	2.2	NUM
ejpam-411	114	35	)	)	PUNCT
ejpam-411	114	36	hold	hold	VERB
ejpam-411	114	37	true	true	ADJ
ejpam-411	114	38	.	.	PUNCT
ejpam-411	115	1	the	the	DET
ejpam-411	115	2	result	result	NOUN
ejpam-411	115	3	is	be	AUX
ejpam-411	115	4	sharp	sharp	ADJ
ejpam-411	115	5	and	and	CCONJ
ejpam-411	115	6	the	the	DET
ejpam-411	115	7	functions	function	NOUN
ejpam-411	115	8	fn	fn	PROPN
ejpam-411	115	9	,	,	PUNCT
ejpam-411	115	10	η	η	PROPN
ejpam-411	115	11	�	�	PROPN
ejpam-411	115	12	η	η	PROPN
ejpam-411	115	13	∈	∈	PROPN
ejpam-411	115	14	r	r	NOUN
ejpam-411	115	15	�	�	NOUN
ejpam-411	115	16	given	give	VERB
ejpam-411	115	17	by	by	ADP
ejpam-411	115	18	(	(	PUNCT
ejpam-411	115	19	2.3	2.3	NUM
ejpam-411	115	20	)	)	PUNCT
ejpam-411	115	21	are	be	AUX
ejpam-411	115	22	the	the	DET
ejpam-411	115	23	extremal	extremal	ADJ
ejpam-411	115	24	functions	function	NOUN
ejpam-411	115	25	.	.	PUNCT
ejpam-411	116	1	3	3	X
ejpam-411	116	2	.	.	X
ejpam-411	116	3	distortion	distortion	NOUN
ejpam-411	116	4	theorems	theorem	NOUN
ejpam-411	116	5	by	by	ADP
ejpam-411	116	6	applying	apply	VERB
ejpam-411	116	7	theorem	theorem	NOUN
ejpam-411	116	8	2.2	2.2	NUM
ejpam-411	116	9	,	,	PUNCT
ejpam-411	116	10	we	we	PRON
ejpam-411	116	11	can	can	AUX
ejpam-411	116	12	deduce	deduce	VERB
ejpam-411	116	13	the	the	DET
ejpam-411	116	14	following	follow	VERB
ejpam-411	116	15	lemma	lemma	PROPN
ejpam-411	116	16	.	.	PUNCT
ejpam-411	117	1	lemma	lemma	PROPN
ejpam-411	117	2	3.1	3.1	NUM
ejpam-411	117	3	.	.	PUNCT
ejpam-411	118	1	let	let	VERB
ejpam-411	118	2	a	a	DET
ejpam-411	118	3	function	function	NOUN
ejpam-411	118	4	f	f	PROPN
ejpam-411	118	5	of	of	ADP
ejpam-411	118	6	the	the	DET
ejpam-411	118	7	form	form	NOUN
ejpam-411	118	8	(	(	PUNCT
ejpam-411	118	9	1.1	1.1	NUM
ejpam-411	118	10	)	)	PUNCT
ejpam-411	118	11	belong	belong	VERB
ejpam-411	118	12	to	to	ADP
ejpam-411	118	13	the	the	DET
ejpam-411	118	14	class	class	NOUN
ejpam-411	118	15	t	t	PROPN
ejpam-411	118	16	w	w	PROPN
ejpam-411	118	17	η	η	PROPN
ejpam-411	118	18	�	�	PROPN
ejpam-411	118	19	φ,ϕ	φ,ϕ	PROPN
ejpam-411	118	20	;	;	PUNCT
ejpam-411	118	21	a	a	DET
ejpam-411	118	22	,	,	PUNCT
ejpam-411	118	23	b	b	NOUN
ejpam-411	118	24	;	;	PUNCT
ejpam-411	118	25	k	k	PROPN
ejpam-411	118	26	�	�	PROPN
ejpam-411	118	27	.	.	PUNCT
ejpam-411	119	1	if	if	SCONJ
ejpam-411	119	2	the	the	DET
ejpam-411	119	3	sequence	sequence	NOUN
ejpam-411	119	4	�	�	PROPN
ejpam-411	119	5	dn	dn	ADP
ejpam-411	119	6	defined	define	VERB
ejpam-411	119	7	by	by	ADP
ejpam-411	119	8	(	(	PUNCT
ejpam-411	119	9	1.10	1.10	NUM
ejpam-411	119	10	)	)	PUNCT
ejpam-411	119	11	satisfies	satisfy	VERB
ejpam-411	119	12	the	the	DET
ejpam-411	119	13	following	follow	VERB
ejpam-411	119	14	inequality	inequality	NOUN
ejpam-411	119	15	:	:	PUNCT
ejpam-411	119	16	d2	d2	PROPN
ejpam-411	119	17	≦	≦	PROPN
ejpam-411	119	18	dn	dn	PROPN
ejpam-411	119	19	(	(	PUNCT
ejpam-411	119	20	n	n	CCONJ
ejpam-411	119	21	∈	∈	PROPN
ejpam-411	119	22	n	n	CCONJ
ejpam-411	119	23	\	\	NOUN
ejpam-411	119	24	{	{	PUNCT
ejpam-411	119	25	1	1	NUM
ejpam-411	119	26	}	}	PUNCT
ejpam-411	119	27	)	)	PUNCT
ejpam-411	119	28	,	,	PUNCT
ejpam-411	119	29	(	(	PUNCT
ejpam-411	119	30	3.1	3.1	NUM
ejpam-411	119	31	)	)	PUNCT
ejpam-411	119	32	j.	j.	PROPN
ejpam-411	119	33	dziok	dziok	NOUN
ejpam-411	119	34	and	and	CCONJ
ejpam-411	119	35	h.	h.	PROPN
ejpam-411	119	36	srivastava	srivastava	PROPN
ejpam-411	119	37	/	/	SYM
ejpam-411	119	38	eur	eur	PROPN
ejpam-411	119	39	.	.	PUNCT
ejpam-411	120	1	j.	j.	PROPN
ejpam-411	120	2	pure	pure	PROPN
ejpam-411	120	3	appl	appl	PROPN
ejpam-411	120	4	.	.	PROPN
ejpam-411	120	5	math	math	PROPN
ejpam-411	120	6	,	,	PUNCT
ejpam-411	120	7	2	2	NUM
ejpam-411	120	8	(	(	PUNCT
ejpam-411	120	9	2009	2009	NUM
ejpam-411	120	10	)	)	PUNCT
ejpam-411	120	11	,	,	PUNCT
ejpam-411	120	12	(	(	PUNCT
ejpam-411	120	13	302	302	NUM
ejpam-411	120	14	-	-	SYM
ejpam-411	120	15	324	324	NUM
ejpam-411	120	16	)	)	PUNCT
ejpam-411	120	17	310	310	NUM
ejpam-411	120	18	then	then	ADV
ejpam-411	120	19	∞∑	∞∑	NUM
ejpam-411	120	20	n=2	n=2	PRON
ejpam-411	120	21	an	an	DET
ejpam-411	120	22	≦	≦	NOUN
ejpam-411	120	23	b−	b−	PROPN
ejpam-411	120	24	a	a	DET
ejpam-411	120	25	d2	d2	PROPN
ejpam-411	120	26	.	.	PUNCT
ejpam-411	121	1	moreover	moreover	ADV
ejpam-411	121	2	,	,	PUNCT
ejpam-411	121	3	if	if	SCONJ
ejpam-411	121	4	nd2	nd2	NOUN
ejpam-411	121	5	≦	≦	NUM
ejpam-411	121	6	2dn	2dn	ADJ
ejpam-411	121	7	(	(	PUNCT
ejpam-411	121	8	n	n	NOUN
ejpam-411	121	9	∈	∈	PROPN
ejpam-411	121	10	n	n	CCONJ
ejpam-411	121	11	\	\	NOUN
ejpam-411	121	12	{	{	PUNCT
ejpam-411	121	13	1	1	NUM
ejpam-411	121	14	}	}	PUNCT
ejpam-411	121	15	)	)	PUNCT
ejpam-411	121	16	,	,	PUNCT
ejpam-411	121	17	(	(	PUNCT
ejpam-411	121	18	3.2	3.2	NUM
ejpam-411	121	19	)	)	PUNCT
ejpam-411	121	20	then	then	ADV
ejpam-411	121	21	∞∑	∞∑	NUM
ejpam-411	121	22	n=2	n=2	ADV
ejpam-411	121	23	nan	nan	NOUN
ejpam-411	121	24	≦	≦	NUM
ejpam-411	121	25	2	2	NUM
ejpam-411	121	26	(	(	PUNCT
ejpam-411	121	27	b−	b−	NOUN
ejpam-411	121	28	a	a	PRON
ejpam-411	121	29	)	)	PUNCT
ejpam-411	121	30	d2	d2	PROPN
ejpam-411	121	31	.	.	PUNCT
ejpam-411	121	32	theorem	theorem	VERB
ejpam-411	121	33	3.1	3.1	NUM
ejpam-411	121	34	.	.	PUNCT
ejpam-411	122	1	let	let	VERB
ejpam-411	122	2	a	a	DET
ejpam-411	122	3	function	function	NOUN
ejpam-411	122	4	f	f	PROPN
ejpam-411	122	5	belong	belong	VERB
ejpam-411	122	6	to	to	ADP
ejpam-411	122	7	the	the	DET
ejpam-411	122	8	class	class	NOUN
ejpam-411	122	9	t	t	PROPN
ejpam-411	122	10	w	w	PROPN
ejpam-411	122	11	η	η	PROPN
ejpam-411	122	12	�	�	PROPN
ejpam-411	122	13	φ,ϕ	φ,ϕ	PROPN
ejpam-411	122	14	;	;	PUNCT
ejpam-411	122	15	a	a	DET
ejpam-411	122	16	,	,	PUNCT
ejpam-411	122	17	b	b	NOUN
ejpam-411	122	18	;	;	PUNCT
ejpam-411	122	19	k	k	PROPN
ejpam-411	122	20	�	�	PROPN
ejpam-411	122	21	.	.	PUNCT
ejpam-411	123	1	if	if	SCONJ
ejpam-411	123	2	the	the	DET
ejpam-411	123	3	sequence	sequence	NOUN
ejpam-411	123	4	�	�	PROPN
ejpam-411	123	5	dn	dn	ADP
ejpam-411	123	6	defined	define	VERB
ejpam-411	123	7	by	by	ADP
ejpam-411	123	8	(	(	PUNCT
ejpam-411	123	9	1.10	1.10	NUM
ejpam-411	123	10	)	)	PUNCT
ejpam-411	123	11	satisfies	satisfie	NOUN
ejpam-411	123	12	(	(	PUNCT
ejpam-411	123	13	3.1	3.1	NUM
ejpam-411	123	14	)	)	PUNCT
ejpam-411	123	15	,	,	PUNCT
ejpam-411	123	16	then	then	ADV
ejpam-411	123	17	r	r	NOUN
ejpam-411	123	18	−	−	PROPN
ejpam-411	123	19	b−	b−	PROPN
ejpam-411	123	20	a	a	DET
ejpam-411	123	21	d2	d2	PROPN
ejpam-411	123	22	r2	r2	PROPN
ejpam-411	123	23	≦	≦	PROPN
ejpam-411	123	24	�	�	PROPN
ejpam-411	123	25	�	�	PROPN
ejpam-411	123	26	f	f	PROPN
ejpam-411	123	27	(	(	PUNCT
ejpam-411	123	28	z	z	NOUN
ejpam-411	123	29	)	)	PUNCT
ejpam-411	123	30	�	�	PROPN
ejpam-411	123	31	�	�	PROPN
ejpam-411	123	32	≦	≦	PROPN
ejpam-411	123	33	r	r	NOUN
ejpam-411	123	34	+	+	NUM
ejpam-411	123	35	b−	b−	PROPN
ejpam-411	123	36	a	a	DET
ejpam-411	123	37	d2	d2	PROPN
ejpam-411	123	38	r2	r2	PROPN
ejpam-411	123	39	(	(	PUNCT
ejpam-411	123	40	|z|=	|z|=	NOUN
ejpam-411	123	41	r	r	NOUN
ejpam-411	123	42	<	<	X
ejpam-411	123	43	1	1	NUM
ejpam-411	123	44	)	)	PUNCT
ejpam-411	123	45	.	.	PUNCT
ejpam-411	124	1	(	(	PUNCT
ejpam-411	124	2	3.3	3.3	NUM
ejpam-411	124	3	)	)	PUNCT
ejpam-411	124	4	moreover	moreover	ADV
ejpam-411	124	5	,	,	PUNCT
ejpam-411	124	6	if	if	SCONJ
ejpam-411	124	7	(	(	PUNCT
ejpam-411	124	8	3.2	3.2	NUM
ejpam-411	124	9	)	)	PUNCT
ejpam-411	124	10	holds	hold	VERB
ejpam-411	124	11	true	true	ADJ
ejpam-411	124	12	,	,	PUNCT
ejpam-411	124	13	then	then	ADV
ejpam-411	124	14	1−	1−	NUM
ejpam-411	124	15	2	2	NUM
ejpam-411	124	16	(	(	PUNCT
ejpam-411	124	17	b−	b−	NOUN
ejpam-411	124	18	a	a	PRON
ejpam-411	124	19	)	)	PUNCT
ejpam-411	124	20	d2	d2	PROPN
ejpam-411	124	21	r	r	NOUN
ejpam-411	124	22	≦	≦	PROPN
ejpam-411	124	23	�	�	PROPN
ejpam-411	124	24	�	�	PROPN
ejpam-411	124	25	f	f	PROPN
ejpam-411	124	26	′(z	′(z	NOUN
ejpam-411	124	27	)	)	PUNCT
ejpam-411	124	28	�	�	PROPN
ejpam-411	124	29	�	�	PROPN
ejpam-411	124	30	≦	≦	NOUN
ejpam-411	124	31	1	1	NUM
ejpam-411	124	32	+	+	NUM
ejpam-411	124	33	2	2	NUM
ejpam-411	124	34	(	(	PUNCT
ejpam-411	124	35	b−	b−	NOUN
ejpam-411	124	36	a	a	PRON
ejpam-411	124	37	)	)	PUNCT
ejpam-411	124	38	d2	d2	PROPN
ejpam-411	124	39	r	r	NOUN
ejpam-411	124	40	(	(	PUNCT
ejpam-411	124	41	|z|=	|z|=	NOUN
ejpam-411	124	42	r	r	NOUN
ejpam-411	124	43	<	<	X
ejpam-411	124	44	1	1	NUM
ejpam-411	124	45	)	)	PUNCT
ejpam-411	124	46	.	.	PUNCT
ejpam-411	125	1	(	(	PUNCT
ejpam-411	125	2	3.4	3.4	NUM
ejpam-411	125	3	)	)	PUNCT
ejpam-411	125	4	the	the	DET
ejpam-411	125	5	result	result	NOUN
ejpam-411	125	6	is	be	AUX
ejpam-411	125	7	sharp	sharp	ADJ
ejpam-411	125	8	and	and	CCONJ
ejpam-411	125	9	the	the	DET
ejpam-411	125	10	extremal	extremal	ADJ
ejpam-411	125	11	function	function	NOUN
ejpam-411	125	12	f2,η	f2,η	PROPN
ejpam-411	125	13	is	be	AUX
ejpam-411	125	14	given	give	VERB
ejpam-411	125	15	by	by	ADP
ejpam-411	125	16	(	(	PUNCT
ejpam-411	125	17	2.3	2.3	NUM
ejpam-411	125	18	)	)	PUNCT
ejpam-411	125	19	.	.	PUNCT
ejpam-411	126	1	proof	proof	NOUN
ejpam-411	126	2	.	.	PUNCT
ejpam-411	127	1	let	let	VERB
ejpam-411	127	2	a	a	DET
ejpam-411	127	3	function	function	NOUN
ejpam-411	127	4	f	f	PROPN
ejpam-411	127	5	of	of	ADP
ejpam-411	127	6	the	the	DET
ejpam-411	127	7	form	form	NOUN
ejpam-411	127	8	(	(	PUNCT
ejpam-411	127	9	1.1	1.1	NUM
ejpam-411	127	10	)	)	PUNCT
ejpam-411	127	11	belong	belong	VERB
ejpam-411	127	12	to	to	ADP
ejpam-411	127	13	the	the	DET
ejpam-411	127	14	class	class	NOUN
ejpam-411	127	15	t	t	PROPN
ejpam-411	127	16	w	w	PROPN
ejpam-411	127	17	η	η	PROPN
ejpam-411	127	18	�	�	PROPN
ejpam-411	127	19	φ,ϕ	φ,ϕ	PROPN
ejpam-411	127	20	;	;	PUNCT
ejpam-411	127	21	a	a	DET
ejpam-411	127	22	,	,	PUNCT
ejpam-411	127	23	b	b	NOUN
ejpam-411	127	24	;	;	PUNCT
ejpam-411	127	25	k	k	PROPN
ejpam-411	127	26	�	�	PROPN
ejpam-411	127	27	.	.	PUNCT
ejpam-411	128	1	then	then	ADV
ejpam-411	128	2	,	,	PUNCT
ejpam-411	128	3	for	for	ADP
ejpam-411	128	4	|z|=	|z|=	NOUN
ejpam-411	128	5	r	r	NOUN
ejpam-411	128	6	<	<	X
ejpam-411	128	7	1	1	NUM
ejpam-411	128	8	,	,	PUNCT
ejpam-411	128	9	�	�	PROPN
ejpam-411	128	10	�	�	PROPN
ejpam-411	128	11	f	f	PROPN
ejpam-411	128	12	(	(	PUNCT
ejpam-411	128	13	z	z	NOUN
ejpam-411	128	14	)	)	PUNCT
ejpam-411	128	15	�	�	PROPN
ejpam-411	128	16	�	�	PROPN
ejpam-411	128	17	=	=	SYM
ejpam-411	128	18	�	�	PROPN
ejpam-411	128	19	�	�	PROPN
ejpam-411	128	20	�	�	PROPN
ejpam-411	128	21	�	�	PROPN
ejpam-411	128	22	�	�	PROPN
ejpam-411	128	23	z	z	NOUN
ejpam-411	128	24	+	+	CCONJ
ejpam-411	128	25	∞∑	∞∑	PROPN
ejpam-411	128	26	n=2	n=2	PRON
ejpam-411	128	27	anzn	anzn	NOUN
ejpam-411	128	28	�	�	PROPN
ejpam-411	128	29	�	�	PROPN
ejpam-411	128	30	�	�	PROPN
ejpam-411	128	31	�	�	PROPN
ejpam-411	128	32	�	�	PROPN
ejpam-411	128	33	≦	≦	PROPN
ejpam-411	128	34	r	r	NOUN
ejpam-411	128	35	+	+	CCONJ
ejpam-411	128	36	∞∑	∞∑	PROPN
ejpam-411	128	37	n=2	n=2	X
ejpam-411	128	38	�	�	NOUN
ejpam-411	128	39	�	�	PROPN
ejpam-411	128	40	an	an	DET
ejpam-411	128	41	�	�	PROPN
ejpam-411	128	42	�	�	PROPN
ejpam-411	128	43	rn	rn	PROPN
ejpam-411	128	44	=	=	PROPN
ejpam-411	128	45	r	r	PROPN
ejpam-411	128	46	+	+	NUM
ejpam-411	128	47	r2	r2	NOUN
ejpam-411	128	48	∞∑	∞∑	PROPN
ejpam-411	128	49	n=2	n=2	X
ejpam-411	128	50	�	�	PROPN
ejpam-411	128	51	�	�	PROPN
ejpam-411	128	52	an	an	DET
ejpam-411	128	53	�	�	PROPN
ejpam-411	128	54	�	�	PROPN
ejpam-411	128	55	rn−2	rn−2	PROPN
ejpam-411	128	56	≦	≦	PROPN
ejpam-411	128	57	r	r	NOUN
ejpam-411	128	58	+	+	NUM
ejpam-411	128	59	r2	r2	NOUN
ejpam-411	128	60	∞∑	∞∑	PROPN
ejpam-411	128	61	n=2	n=2	X
ejpam-411	128	62	�	�	PROPN
ejpam-411	128	63	�	�	PROPN
ejpam-411	128	64	an	an	DET
ejpam-411	128	65	�	�	PROPN
ejpam-411	128	66	�	�	PROPN
ejpam-411	128	67	and	and	CCONJ
ejpam-411	128	68	�	�	PROPN
ejpam-411	128	69	�	�	PROPN
ejpam-411	128	70	f	f	PROPN
ejpam-411	128	71	(	(	PUNCT
ejpam-411	128	72	z	z	NOUN
ejpam-411	128	73	)	)	PUNCT
ejpam-411	128	74	�	�	PROPN
ejpam-411	128	75	�	�	PROPN
ejpam-411	128	76	=	=	SYM
ejpam-411	128	77	�	�	PROPN
ejpam-411	128	78	�	�	PROPN
ejpam-411	128	79	�	�	PROPN
ejpam-411	128	80	�	�	PROPN
ejpam-411	128	81	�	�	PROPN
ejpam-411	128	82	z	z	NOUN
ejpam-411	128	83	+	+	CCONJ
ejpam-411	128	84	∞∑	∞∑	PROPN
ejpam-411	128	85	n=2	n=2	PRON
ejpam-411	128	86	anzn	anzn	NOUN
ejpam-411	128	87	�	�	PROPN
ejpam-411	128	88	�	�	PROPN
ejpam-411	128	89	�	�	PROPN
ejpam-411	128	90	�	�	PROPN
ejpam-411	128	91	�	�	PROPN
ejpam-411	128	92	≧	≧	SYM
ejpam-411	128	93	r	r	NOUN
ejpam-411	128	94	−	−	PROPN
ejpam-411	128	95	∞∑	∞∑	PROPN
ejpam-411	128	96	n=2	n=2	X
ejpam-411	128	97	�	�	PROPN
ejpam-411	128	98	�	�	PROPN
ejpam-411	128	99	an	an	DET
ejpam-411	128	100	�	�	PROPN
ejpam-411	128	101	�	�	PROPN
ejpam-411	128	102	rn	rn	PROPN
ejpam-411	128	103	=	=	PROPN
ejpam-411	128	104	r	r	NOUN
ejpam-411	128	105	−	−	PROPN
ejpam-411	128	106	r2	r2	NOUN
ejpam-411	128	107	∞∑	∞∑	PROPN
ejpam-411	128	108	n=2	n=2	X
ejpam-411	128	109	�	�	PROPN
ejpam-411	128	110	�	�	PROPN
ejpam-411	128	111	an	an	DET
ejpam-411	128	112	�	�	PROPN
ejpam-411	128	113	�	�	PROPN
ejpam-411	128	114	rn−2	rn−2	PROPN
ejpam-411	128	115	≧	≧	NOUN
ejpam-411	128	116	r−r2	r−r2	PUNCT
ejpam-411	128	117	∞∑	∞∑	PROPN
ejpam-411	128	118	n=2	n=2	X
ejpam-411	128	119	�	�	PROPN
ejpam-411	128	120	�	�	PROPN
ejpam-411	128	121	an	an	DET
ejpam-411	128	122	�	�	PROPN
ejpam-411	128	123	�	�	PROPN
ejpam-411	128	124	,	,	PUNCT
ejpam-411	128	125	which	which	PRON
ejpam-411	128	126	,	,	PUNCT
ejpam-411	128	127	in	in	ADP
ejpam-411	128	128	light	light	NOUN
ejpam-411	128	129	of	of	ADP
ejpam-411	128	130	lemma	lemma	PROPN
ejpam-411	128	131	3.1	3.1	NUM
ejpam-411	128	132	,	,	PUNCT
ejpam-411	128	133	yields	yield	NOUN
ejpam-411	128	134	(	(	PUNCT
ejpam-411	128	135	3.3	3.3	NUM
ejpam-411	128	136	)	)	PUNCT
ejpam-411	128	137	.	.	PUNCT
ejpam-411	129	1	analogously	analogously	ADV
ejpam-411	129	2	,	,	PUNCT
ejpam-411	129	3	we	we	PRON
ejpam-411	129	4	can	can	AUX
ejpam-411	129	5	prove	prove	VERB
ejpam-411	129	6	(	(	PUNCT
ejpam-411	129	7	3.4	3.4	NUM
ejpam-411	129	8	)	)	PUNCT
ejpam-411	129	9	.	.	PUNCT
ejpam-411	130	1	theorem	theorem	VERB
ejpam-411	130	2	3.1	3.1	NUM
ejpam-411	130	3	implies	imply	VERB
ejpam-411	130	4	the	the	DET
ejpam-411	130	5	following	follow	VERB
ejpam-411	130	6	corollary	corollary	NOUN
ejpam-411	130	7	:	:	PUNCT
ejpam-411	130	8	j.	j.	PROPN
ejpam-411	130	9	dziok	dziok	PROPN
ejpam-411	130	10	and	and	CCONJ
ejpam-411	130	11	h.	h.	PROPN
ejpam-411	130	12	srivastava	srivastava	PROPN
ejpam-411	130	13	/	/	SYM
ejpam-411	130	14	eur	eur	PROPN
ejpam-411	130	15	.	.	PUNCT
ejpam-411	131	1	j.	j.	PROPN
ejpam-411	131	2	pure	pure	PROPN
ejpam-411	131	3	appl	appl	PROPN
ejpam-411	131	4	.	.	PROPN
ejpam-411	131	5	math	math	PROPN
ejpam-411	131	6	,	,	PUNCT
ejpam-411	131	7	2	2	NUM
ejpam-411	131	8	(	(	PUNCT
ejpam-411	131	9	2009	2009	NUM
ejpam-411	131	10	)	)	PUNCT
ejpam-411	131	11	,	,	PUNCT
ejpam-411	131	12	(	(	PUNCT
ejpam-411	131	13	302	302	NUM
ejpam-411	131	14	-	-	SYM
ejpam-411	131	15	324	324	NUM
ejpam-411	131	16	)	)	PUNCT
ejpam-411	131	17	311	311	NUM
ejpam-411	131	18	corollary	corollary	NOUN
ejpam-411	131	19	3.1	3.1	NUM
ejpam-411	131	20	.	.	PUNCT
ejpam-411	132	1	let	let	VERB
ejpam-411	132	2	a	a	DET
ejpam-411	132	3	function	function	NOUN
ejpam-411	132	4	f	f	PROPN
ejpam-411	132	5	belong	belong	VERB
ejpam-411	132	6	to	to	ADP
ejpam-411	132	7	the	the	DET
ejpam-411	132	8	class	class	NOUN
ejpam-411	132	9	t	t	PROPN
ejpam-411	132	10	w	w	PROPN
ejpam-411	132	11	�	�	PROPN
ejpam-411	132	12	φ,ϕ	φ,ϕ	PROPN
ejpam-411	132	13	;	;	PUNCT
ejpam-411	132	14	a	a	DET
ejpam-411	132	15	,	,	PUNCT
ejpam-411	132	16	b	b	NOUN
ejpam-411	132	17	;	;	PUNCT
ejpam-411	132	18	k	k	PROPN
ejpam-411	132	19	�	�	PROPN
ejpam-411	132	20	.	.	PUNCT
ejpam-411	133	1	if	if	SCONJ
ejpam-411	133	2	the	the	DET
ejpam-411	133	3	sequence	sequence	NOUN
ejpam-411	133	4	�	�	PROPN
ejpam-411	133	5	dn	dn	ADP
ejpam-411	133	6	defined	define	VERB
ejpam-411	133	7	by	by	ADP
ejpam-411	133	8	(	(	PUNCT
ejpam-411	133	9	1.10	1.10	NUM
ejpam-411	133	10	)	)	PUNCT
ejpam-411	133	11	satisfies	satisfie	NOUN
ejpam-411	133	12	(	(	PUNCT
ejpam-411	133	13	3.1	3.1	NUM
ejpam-411	133	14	)	)	PUNCT
ejpam-411	133	15	,	,	PUNCT
ejpam-411	133	16	then	then	ADV
ejpam-411	133	17	the	the	DET
ejpam-411	133	18	assertion	assertion	NOUN
ejpam-411	133	19	(	(	PUNCT
ejpam-411	133	20	3.3	3.3	NUM
ejpam-411	133	21	)	)	PUNCT
ejpam-411	133	22	holds	hold	VERB
ejpam-411	133	23	true	true	ADJ
ejpam-411	133	24	.	.	PUNCT
ejpam-411	134	1	moreover	moreover	ADV
ejpam-411	134	2	,	,	PUNCT
ejpam-411	134	3	if	if	SCONJ
ejpam-411	134	4	we	we	PRON
ejpam-411	134	5	assume	assume	VERB
ejpam-411	134	6	that	that	SCONJ
ejpam-411	134	7	(	(	PUNCT
ejpam-411	134	8	3.2	3.2	NUM
ejpam-411	134	9	)	)	PUNCT
ejpam-411	134	10	is	be	AUX
ejpam-411	134	11	satisfied	satisfied	ADJ
ejpam-411	134	12	,	,	PUNCT
ejpam-411	134	13	then	then	ADV
ejpam-411	134	14	the	the	DET
ejpam-411	134	15	assertion	assertion	NOUN
ejpam-411	134	16	(	(	PUNCT
ejpam-411	134	17	3.4	3.4	NUM
ejpam-411	134	18	)	)	PUNCT
ejpam-411	134	19	holds	hold	VERB
ejpam-411	134	20	true	true	ADJ
ejpam-411	134	21	.	.	PUNCT
ejpam-411	135	1	the	the	DET
ejpam-411	135	2	result	result	NOUN
ejpam-411	135	3	is	be	AUX
ejpam-411	135	4	sharp	sharp	ADJ
ejpam-411	135	5	and	and	CCONJ
ejpam-411	135	6	the	the	DET
ejpam-411	135	7	extremal	extremal	ADJ
ejpam-411	135	8	functions	function	NOUN
ejpam-411	135	9	f2,η	f2,η	PROPN
ejpam-411	135	10	�	�	PROPN
ejpam-411	135	11	η	η	PROPN
ejpam-411	135	12	∈	∈	PROPN
ejpam-411	135	13	r	r	NOUN
ejpam-411	135	14	�	�	PROPN
ejpam-411	135	15	are	be	AUX
ejpam-411	135	16	given	give	VERB
ejpam-411	135	17	by	by	ADP
ejpam-411	135	18	(	(	PUNCT
ejpam-411	135	19	2.3	2.3	NUM
ejpam-411	135	20	)	)	PUNCT
ejpam-411	135	21	.	.	PUNCT
ejpam-411	136	1	4	4	X
ejpam-411	136	2	.	.	X
ejpam-411	136	3	results	result	NOUN
ejpam-411	136	4	involving	involve	VERB
ejpam-411	136	5	subordination	subordination	NOUN
ejpam-411	136	6	between	between	ADP
ejpam-411	136	7	analytic	analytic	ADJ
ejpam-411	136	8	functions	function	NOUN
ejpam-411	136	9	before	before	ADP
ejpam-411	136	10	stating	state	VERB
ejpam-411	136	11	and	and	CCONJ
ejpam-411	136	12	proving	prove	VERB
ejpam-411	136	13	our	our	PRON
ejpam-411	136	14	subordination	subordination	NOUN
ejpam-411	136	15	theorems	theorem	NOUN
ejpam-411	136	16	for	for	ADP
ejpam-411	136	17	the	the	DET
ejpam-411	136	18	function	function	NOUN
ejpam-411	136	19	classes	class	NOUN
ejpam-411	136	20	t	t	PROPN
ejpam-411	136	21	w	w	PROPN
ejpam-411	136	22	η	η	PROPN
ejpam-411	136	23	�	�	PROPN
ejpam-411	136	24	φ,ϕ	φ,ϕ	PROPN
ejpam-411	136	25	;	;	PUNCT
ejpam-411	136	26	a	a	DET
ejpam-411	136	27	,	,	PUNCT
ejpam-411	136	28	b	b	NOUN
ejpam-411	136	29	;	;	PUNCT
ejpam-411	136	30	k	k	PROPN
ejpam-411	136	31	�	�	PROPN
ejpam-411	136	32	and	and	CCONJ
ejpam-411	136	33	t	t	PROPN
ejpam-411	136	34	w	w	PROPN
ejpam-411	136	35	�	�	PROPN
ejpam-411	136	36	φ,ϕ	φ,ϕ	PROPN
ejpam-411	136	37	;	;	PUNCT
ejpam-411	136	38	a	a	DET
ejpam-411	136	39	,	,	PUNCT
ejpam-411	136	40	b	b	NOUN
ejpam-411	136	41	;	;	PUNCT
ejpam-411	136	42	k	k	PROPN
ejpam-411	136	43	�	�	PROPN
ejpam-411	136	44	,	,	PUNCT
ejpam-411	136	45	we	we	PRON
ejpam-411	136	46	need	need	VERB
ejpam-411	136	47	the	the	DET
ejpam-411	136	48	following	follow	VERB
ejpam-411	136	49	definition	definition	NOUN
ejpam-411	136	50	as	as	ADV
ejpam-411	136	51	well	well	ADV
ejpam-411	136	52	as	as	ADP
ejpam-411	136	53	lemma	lemma	PROPN
ejpam-411	136	54	4.1	4.1	NUM
ejpam-411	136	55	.	.	PUNCT
ejpam-411	137	1	definition	definition	NOUN
ejpam-411	137	2	4.1	4.1	NUM
ejpam-411	137	3	.	.	PUNCT
ejpam-411	138	1	a	a	DET
ejpam-411	138	2	sequence	sequence	NOUN
ejpam-411	138	3	{	{	PUNCT
ejpam-411	138	4	bn	bn	NOUN
ejpam-411	138	5	}	}	PUNCT
ejpam-411	138	6	of	of	ADP
ejpam-411	138	7	complex	complex	ADJ
ejpam-411	138	8	numbers	number	NOUN
ejpam-411	138	9	is	be	AUX
ejpam-411	138	10	said	say	VERB
ejpam-411	138	11	to	to	PART
ejpam-411	138	12	be	be	AUX
ejpam-411	138	13	a	a	DET
ejpam-411	138	14	subordinating	subordinate	VERB
ejpam-411	138	15	factor	factor	NOUN
ejpam-411	138	16	sequence	sequence	NOUN
ejpam-411	138	17	if	if	SCONJ
ejpam-411	138	18	,	,	PUNCT
ejpam-411	138	19	for	for	ADP
ejpam-411	138	20	each	each	DET
ejpam-411	138	21	function	function	NOUN
ejpam-411	138	22	f	f	PROPN
ejpam-411	138	23	of	of	ADP
ejpam-411	138	24	the	the	DET
ejpam-411	138	25	form	form	NOUN
ejpam-411	138	26	(	(	PUNCT
ejpam-411	138	27	1.1	1.1	NUM
ejpam-411	138	28	)	)	PUNCT
ejpam-411	138	29	from	from	ADP
ejpam-411	138	30	the	the	DET
ejpam-411	138	31	class	class	NOUN
ejpam-411	138	32	s	s	PART
ejpam-411	138	33	c	c	NOUN
ejpam-411	138	34	,	,	PUNCT
ejpam-411	138	35	we	we	PRON
ejpam-411	138	36	have	have	VERB
ejpam-411	138	37	∞∑	∞∑	NUM
ejpam-411	138	38	n=1	n=1	PROPN
ejpam-411	138	39	bnanzn	bnanzn	NOUN
ejpam-411	138	40	≺	≺	NOUN
ejpam-411	138	41	f	f	X
ejpam-411	138	42	(	(	PUNCT
ejpam-411	138	43	z	z	NOUN
ejpam-411	138	44	)	)	PUNCT
ejpam-411	138	45	�	�	PROPN
ejpam-411	138	46	a1	a1	NOUN
ejpam-411	138	47	=	=	SYM
ejpam-411	138	48	1	1	NUM
ejpam-411	138	49	�	�	PROPN
ejpam-411	138	50	.	.	PUNCT
ejpam-411	139	1	(	(	PUNCT
ejpam-411	139	2	4.1	4.1	NUM
ejpam-411	139	3	)	)	PUNCT
ejpam-411	139	4	lemma	lemma	PROPN
ejpam-411	139	5	4.1	4.1	NUM
ejpam-411	139	6	.	.	PUNCT
ejpam-411	140	1	(	(	PUNCT
ejpam-411	140	2	see	see	VERB
ejpam-411	140	3	[	[	X
ejpam-411	140	4	36	36	NUM
ejpam-411	140	5	]	]	PUNCT
ejpam-411	140	6	)	)	PUNCT
ejpam-411	140	7	the	the	DET
ejpam-411	140	8	sequence	sequence	NOUN
ejpam-411	140	9	{	{	PUNCT
ejpam-411	140	10	bn	bn	NUM
ejpam-411	140	11	}	}	PUNCT
ejpam-411	140	12	is	be	AUX
ejpam-411	140	13	a	a	DET
ejpam-411	140	14	subordinating	subordinate	VERB
ejpam-411	140	15	factor	factor	NOUN
ejpam-411	140	16	sequence	sequence	NOUN
ejpam-411	140	17	if	if	SCONJ
ejpam-411	140	18	and	and	CCONJ
ejpam-411	140	19	only	only	ADV
ejpam-411	140	20	if	if	SCONJ
ejpam-411	140	21	ℜ	ℜ	ADJ
ejpam-411	140	22	1	1	NUM
ejpam-411	140	23	+	+	SYM
ejpam-411	140	24	2	2	NUM
ejpam-411	140	25	∞∑	∞∑	NUM
ejpam-411	140	26	n=1	n=1	PROPN
ejpam-411	140	27	bnzn	bnzn	NOUN
ejpam-411	140	28	!	!	PUNCT
ejpam-411	141	1	>	>	X
ejpam-411	141	2	0	0	PUNCT
ejpam-411	142	1	(	(	PUNCT
ejpam-411	142	2	z	z	NOUN
ejpam-411	142	3	∈	∈	PROPN
ejpam-411	142	4	u	u	NOUN
ejpam-411	142	5	)	)	PUNCT
ejpam-411	142	6	.	.	PUNCT
ejpam-411	143	1	(	(	PUNCT
ejpam-411	143	2	4.2	4.2	NUM
ejpam-411	143	3	)	)	PUNCT
ejpam-411	143	4	theorem	theorem	VERB
ejpam-411	143	5	4.1	4.1	NUM
ejpam-411	143	6	.	.	PUNCT
ejpam-411	144	1	let	let	VERB
ejpam-411	144	2	the	the	DET
ejpam-411	144	3	sequence	sequence	NOUN
ejpam-411	144	4	�	�	PROPN
ejpam-411	144	5	dn	dn	PROPN
ejpam-411	144	6	,	,	PUNCT
ejpam-411	144	7	defined	define	VERB
ejpam-411	144	8	by	by	ADP
ejpam-411	144	9	(	(	PUNCT
ejpam-411	144	10	1.10	1.10	NUM
ejpam-411	144	11	)	)	PUNCT
ejpam-411	144	12	,	,	PUNCT
ejpam-411	144	13	satisfy	satisfy	VERB
ejpam-411	144	14	the	the	DET
ejpam-411	144	15	inequality	inequality	NOUN
ejpam-411	144	16	(	(	PUNCT
ejpam-411	144	17	3.1	3.1	NUM
ejpam-411	144	18	)	)	PUNCT
ejpam-411	144	19	.	.	PUNCT
ejpam-411	145	1	if	if	SCONJ
ejpam-411	145	2	g	g	PROPN
ejpam-411	145	3	∈	∈	PROPN
ejpam-411	145	4	s	s	PART
ejpam-411	145	5	c	c	NOUN
ejpam-411	145	6	and	and	CCONJ
ejpam-411	145	7	f	f	PROPN
ejpam-411	145	8	∈	∈	PROPN
ejpam-411	145	9	t	t	PROPN
ejpam-411	145	10	w	w	PROPN
ejpam-411	145	11	η	η	PROPN
ejpam-411	145	12	�	�	PROPN
ejpam-411	145	13	φ,ϕ	φ,ϕ	PROPN
ejpam-411	145	14	;	;	PUNCT
ejpam-411	145	15	a	a	DET
ejpam-411	145	16	,	,	PUNCT
ejpam-411	145	17	b	b	NOUN
ejpam-411	145	18	;	;	PUNCT
ejpam-411	145	19	k	k	PROPN
ejpam-411	145	20	�	�	PROPN
ejpam-411	145	21	,	,	PUNCT
ejpam-411	145	22	then	then	ADV
ejpam-411	145	23	ǫ	ǫ	X
ejpam-411	145	24	(	(	PUNCT
ejpam-411	145	25	f	f	PROPN
ejpam-411	145	26	∗	∗	X
ejpam-411	145	27	g)(z)≺	g)(z)≺	PROPN
ejpam-411	145	28	g(z	g(z	PROPN
ejpam-411	145	29	)	)	PUNCT
ejpam-411	145	30	(	(	PUNCT
ejpam-411	145	31	4.3	4.3	NUM
ejpam-411	145	32	)	)	PUNCT
ejpam-411	145	33	and	and	CCONJ
ejpam-411	145	34	ℜ	ℜ	PROPN
ejpam-411	145	35	�	�	PROPN
ejpam-411	145	36	f	f	PROPN
ejpam-411	145	37	(	(	PUNCT
ejpam-411	145	38	z	z	PROPN
ejpam-411	145	39	)	)	PUNCT
ejpam-411	145	40	�	�	PROPN
ejpam-411	145	41	>	>	PUNCT
ejpam-411	145	42	−	−	PROPN
ejpam-411	145	43	1	1	NUM
ejpam-411	145	44	2ǫ	2ǫ	NOUN
ejpam-411	145	45	(	(	PUNCT
ejpam-411	145	46	z	z	NOUN
ejpam-411	145	47	∈	∈	PROPN
ejpam-411	145	48	u	u	NOUN
ejpam-411	145	49	)	)	PUNCT
ejpam-411	145	50	,	,	PUNCT
ejpam-411	145	51	(	(	PUNCT
ejpam-411	145	52	4.4	4.4	NUM
ejpam-411	145	53	)	)	PUNCT
ejpam-411	145	54	where	where	SCONJ
ejpam-411	145	55	ǫ	ǫ	NOUN
ejpam-411	145	56	=	=	SYM
ejpam-411	145	57	d2	d2	PROPN
ejpam-411	145	58	2	2	NUM
ejpam-411	145	59	�	�	PROPN
ejpam-411	145	60	b−	b−	PROPN
ejpam-411	145	61	a+	a+	PUNCT
ejpam-411	145	62	d2	d2	PROPN
ejpam-411	145	63	�	�	PROPN
ejpam-411	145	64	.	.	PUNCT
ejpam-411	146	1	(	(	PUNCT
ejpam-411	146	2	4.5	4.5	NUM
ejpam-411	146	3	)	)	PUNCT
ejpam-411	146	4	the	the	DET
ejpam-411	146	5	constant	constant	ADJ
ejpam-411	146	6	factor	factor	NOUN
ejpam-411	146	7	ǫ	ǫ	PRON
ejpam-411	146	8	can	can	AUX
ejpam-411	146	9	not	not	PART
ejpam-411	146	10	be	be	AUX
ejpam-411	146	11	replaced	replace	VERB
ejpam-411	146	12	by	by	ADP
ejpam-411	146	13	a	a	DET
ejpam-411	146	14	larger	large	ADJ
ejpam-411	146	15	number	number	NOUN
ejpam-411	146	16	.	.	PUNCT
ejpam-411	147	1	j.	j.	PROPN
ejpam-411	147	2	dziok	dziok	PROPN
ejpam-411	147	3	and	and	CCONJ
ejpam-411	147	4	h.	h.	PROPN
ejpam-411	147	5	srivastava	srivastava	PROPN
ejpam-411	147	6	/	/	SYM
ejpam-411	147	7	eur	eur	PROPN
ejpam-411	147	8	.	.	PUNCT
ejpam-411	148	1	j.	j.	PROPN
ejpam-411	148	2	pure	pure	PROPN
ejpam-411	148	3	appl	appl	PROPN
ejpam-411	148	4	.	.	PROPN
ejpam-411	148	5	math	math	PROPN
ejpam-411	148	6	,	,	PUNCT
ejpam-411	148	7	2	2	NUM
ejpam-411	148	8	(	(	PUNCT
ejpam-411	148	9	2009	2009	NUM
ejpam-411	148	10	)	)	PUNCT
ejpam-411	148	11	,	,	PUNCT
ejpam-411	148	12	(	(	PUNCT
ejpam-411	148	13	302	302	NUM
ejpam-411	148	14	-	-	SYM
ejpam-411	148	15	324	324	NUM
ejpam-411	148	16	)	)	PUNCT
ejpam-411	148	17	312	312	NUM
ejpam-411	148	18	proof	proof	NOUN
ejpam-411	148	19	.	.	PUNCT
ejpam-411	149	1	let	let	VERB
ejpam-411	149	2	a	a	DET
ejpam-411	149	3	function	function	NOUN
ejpam-411	149	4	f	f	PROPN
ejpam-411	149	5	of	of	ADP
ejpam-411	149	6	the	the	DET
ejpam-411	149	7	form	form	NOUN
ejpam-411	149	8	(	(	PUNCT
ejpam-411	149	9	1.1	1.1	NUM
ejpam-411	149	10	)	)	PUNCT
ejpam-411	149	11	belong	belong	VERB
ejpam-411	149	12	to	to	ADP
ejpam-411	149	13	the	the	DET
ejpam-411	149	14	class	class	NOUN
ejpam-411	149	15	t	t	PROPN
ejpam-411	149	16	w	w	PROPN
ejpam-411	149	17	η	η	PROPN
ejpam-411	149	18	�	�	PROPN
ejpam-411	149	19	φ,ϕ	φ,ϕ	PROPN
ejpam-411	149	20	;	;	PUNCT
ejpam-411	149	21	a	a	DET
ejpam-411	149	22	,	,	PUNCT
ejpam-411	149	23	b	b	NOUN
ejpam-411	149	24	;	;	PUNCT
ejpam-411	149	25	k	k	PROPN
ejpam-411	149	26	�	�	PROPN
ejpam-411	149	27	and	and	CCONJ
ejpam-411	149	28	suppose	suppose	VERB
ejpam-411	149	29	that	that	SCONJ
ejpam-411	149	30	g(z	g(z	ADJ
ejpam-411	149	31	)	)	PUNCT
ejpam-411	149	32	=	=	SYM
ejpam-411	149	33	z+	z+	NUM
ejpam-411	149	34	∞∑	∞∑	NUM
ejpam-411	149	35	n=2	n=2	PRON
ejpam-411	149	36	cnzn	cnzn	NOUN
ejpam-411	149	37	(	(	PUNCT
ejpam-411	149	38	z	z	NOUN
ejpam-411	149	39	∈	∈	PROPN
ejpam-411	149	40	u	u	NOUN
ejpam-411	149	41	)	)	PUNCT
ejpam-411	149	42	belongs	belong	VERB
ejpam-411	149	43	to	to	ADP
ejpam-411	149	44	the	the	DET
ejpam-411	149	45	class	class	NOUN
ejpam-411	149	46	s	s	PART
ejpam-411	149	47	c.	c.	NOUN
ejpam-411	150	1	then	then	ADV
ejpam-411	150	2	ǫ	ǫ	X
ejpam-411	150	3	(	(	PUNCT
ejpam-411	150	4	f	f	PROPN
ejpam-411	150	5	∗	∗	NOUN
ejpam-411	150	6	g)(z	g)(z	PUNCT
ejpam-411	150	7	)	)	PUNCT
ejpam-411	151	1	=	=	SYM
ejpam-411	152	1	ǫz	ǫz	PROPN
ejpam-411	152	2	+	+	CCONJ
ejpam-411	152	3	∞∑	∞∑	PROPN
ejpam-411	152	4	n=2	n=2	ADJ
ejpam-411	152	5	�	�	PROPN
ejpam-411	152	6	ǫan	ǫan	NOUN
ejpam-411	152	7	�	�	PROPN
ejpam-411	152	8	cnzn	cnzn	NOUN
ejpam-411	152	9	.	.	PUNCT
ejpam-411	153	1	thus	thus	ADV
ejpam-411	153	2	,	,	PUNCT
ejpam-411	153	3	by	by	ADP
ejpam-411	153	4	the	the	DET
ejpam-411	153	5	above	above	ADJ
ejpam-411	153	6	definition	definition	NOUN
ejpam-411	153	7	,	,	PUNCT
ejpam-411	153	8	the	the	DET
ejpam-411	153	9	subordination	subordination	NOUN
ejpam-411	153	10	result	result	VERB
ejpam-411	153	11	(	(	PUNCT
ejpam-411	153	12	4.3	4.3	NUM
ejpam-411	153	13	)	)	PUNCT
ejpam-411	153	14	holds	hold	VERB
ejpam-411	153	15	true	true	ADJ
ejpam-411	153	16	if	if	SCONJ
ejpam-411	153	17	�	�	PROPN
ejpam-411	153	18	ǫan	ǫan	NOUN
ejpam-411	153	19	∞	∞	PROPN
ejpam-411	153	20	n=1	n=1	PUNCT
ejpam-411	153	21	�	�	PROPN
ejpam-411	153	22	a1	a1	NOUN
ejpam-411	153	23	=	=	SYM
ejpam-411	153	24	1	1	NUM
ejpam-411	153	25	�	�	PROPN
ejpam-411	153	26	is	be	AUX
ejpam-411	153	27	a	a	DET
ejpam-411	153	28	subordinating	subordinate	VERB
ejpam-411	153	29	factor	factor	NOUN
ejpam-411	153	30	sequence	sequence	NOUN
ejpam-411	153	31	.	.	PUNCT
ejpam-411	154	1	in	in	ADP
ejpam-411	154	2	view	view	NOUN
ejpam-411	154	3	of	of	ADP
ejpam-411	154	4	lemma	lemma	PROPN
ejpam-411	154	5	4.1	4.1	NUM
ejpam-411	154	6	,	,	PUNCT
ejpam-411	154	7	this	this	PRON
ejpam-411	154	8	is	be	AUX
ejpam-411	154	9	equivalent	equivalent	ADJ
ejpam-411	154	10	to	to	ADP
ejpam-411	154	11	the	the	DET
ejpam-411	154	12	following	follow	VERB
ejpam-411	154	13	inequality	inequality	NOUN
ejpam-411	154	14	:	:	PUNCT
ejpam-411	154	15	ℜ	ℜ	PROPN
ejpam-411	154	16	1	1	NUM
ejpam-411	154	17	+	+	SYM
ejpam-411	154	18	2	2	NUM
ejpam-411	154	19	∞∑	∞∑	NUM
ejpam-411	154	20	n=1	n=1	PROPN
ejpam-411	154	21	ǫanzn	ǫanzn	NOUN
ejpam-411	154	22	!	!	PUNCT
ejpam-411	155	1	>	>	X
ejpam-411	155	2	0	0	PUNCT
ejpam-411	156	1	(	(	PUNCT
ejpam-411	156	2	z	z	NOUN
ejpam-411	156	3	∈	∈	PROPN
ejpam-411	156	4	u	u	NOUN
ejpam-411	156	5	)	)	PUNCT
ejpam-411	156	6	.	.	PUNCT
ejpam-411	157	1	(	(	PUNCT
ejpam-411	157	2	4.6	4.6	NUM
ejpam-411	157	3	)	)	PUNCT
ejpam-411	157	4	by	by	ADP
ejpam-411	157	5	(	(	PUNCT
ejpam-411	157	6	3.1	3.1	NUM
ejpam-411	157	7	)	)	PUNCT
ejpam-411	157	8	for	for	ADP
ejpam-411	157	9	|z|=	|z|=	NOUN
ejpam-411	157	10	r	r	NOUN
ejpam-411	157	11	<	<	X
ejpam-411	157	12	1	1	NUM
ejpam-411	157	13	,	,	PUNCT
ejpam-411	157	14	we	we	PRON
ejpam-411	157	15	have	have	VERB
ejpam-411	157	16	ℜ	ℜ	ADV
ejpam-411	157	17	1	1	NUM
ejpam-411	157	18	+	+	NUM
ejpam-411	157	19	2	2	NUM
ejpam-411	157	20	∞∑	∞∑	NUM
ejpam-411	157	21	n=1	n=1	ADP
ejpam-411	157	22	ǫanzn	ǫanzn	NOUN
ejpam-411	157	23	!	!	PUNCT
ejpam-411	158	1	=	=	PUNCT
ejpam-411	158	2	ℜ	ℜ	ADJ
ejpam-411	158	3	1	1	NUM
ejpam-411	158	4	+	+	NUM
ejpam-411	158	5	2ǫz	2ǫz	NOUN
ejpam-411	158	6	+	+	CCONJ
ejpam-411	158	7	∞∑	∞∑	PROPN
ejpam-411	159	1	n=2	n=2	X
ejpam-411	159	2	d2	d2	PROPN
ejpam-411	159	3	b	b	PROPN
ejpam-411	159	4	−	−	PROPN
ejpam-411	159	5	a+	a+	PUNCT
ejpam-411	159	6	d2	d2	PROPN
ejpam-411	159	7	anzn	anzn	NOUN
ejpam-411	159	8	!	!	PUNCT
ejpam-411	160	1	≧	≧	X
ejpam-411	161	1	1−	1−	NUM
ejpam-411	161	2	2ǫr	2ǫr	ADJ
ejpam-411	161	3	−	−	NOUN
ejpam-411	161	4	r	r	NOUN
ejpam-411	161	5	b−	b−	NOUN
ejpam-411	161	6	a+	a+	PUNCT
ejpam-411	161	7	d2	d2	PROPN
ejpam-411	161	8	∞∑	∞∑	PROPN
ejpam-411	161	9	n=2	n=2	ADV
ejpam-411	161	10	dn	dn	PROPN
ejpam-411	161	11	�	�	PROPN
ejpam-411	161	12	�	�	PROPN
ejpam-411	161	13	an	an	DET
ejpam-411	161	14	�	�	PROPN
ejpam-411	161	15	�	�	PROPN
ejpam-411	161	16	rn−1	rn−1	PROPN
ejpam-411	161	17	.	.	PUNCT
ejpam-411	162	1	consequently	consequently	ADV
ejpam-411	162	2	,	,	PUNCT
ejpam-411	162	3	by	by	ADP
ejpam-411	162	4	using	use	VERB
ejpam-411	162	5	theorem	theorem	NOUN
ejpam-411	162	6	2.2	2.2	NUM
ejpam-411	162	7	,	,	PUNCT
ejpam-411	162	8	we	we	PRON
ejpam-411	162	9	obtain	obtain	VERB
ejpam-411	162	10	ℜ	ℜ	SYM
ejpam-411	162	11	1	1	NUM
ejpam-411	162	12	+	+	NUM
ejpam-411	162	13	2	2	NUM
ejpam-411	162	14	∞∑	∞∑	NUM
ejpam-411	162	15	n=1	n=1	PROPN
ejpam-411	162	16	ǫanzn	ǫanzn	NOUN
ejpam-411	162	17	!	!	PUNCT
ejpam-411	163	1	≧	≧	X
ejpam-411	164	1	1−	1−	NUM
ejpam-411	164	2	d2	d2	PROPN
ejpam-411	164	3	b−	b−	PROPN
ejpam-411	164	4	a+	a+	PUNCT
ejpam-411	164	5	d2	d2	PROPN
ejpam-411	164	6	r	r	NOUN
ejpam-411	164	7	−	−	PROPN
ejpam-411	164	8	b−	b−	PROPN
ejpam-411	164	9	a	a	DET
ejpam-411	164	10	b	b	NOUN
ejpam-411	164	11	−	−	PROPN
ejpam-411	164	12	a+	a+	PUNCT
ejpam-411	164	13	d2	d2	PROPN
ejpam-411	164	14	r	r	NOUN
ejpam-411	164	15	>	>	X
ejpam-411	164	16	0	0	NUM
ejpam-411	164	17	.	.	PUNCT
ejpam-411	165	1	this	this	PRON
ejpam-411	165	2	evidently	evidently	ADV
ejpam-411	165	3	proves	prove	VERB
ejpam-411	165	4	the	the	DET
ejpam-411	165	5	inequality	inequality	NOUN
ejpam-411	165	6	(	(	PUNCT
ejpam-411	165	7	4.6	4.6	NUM
ejpam-411	165	8	)	)	PUNCT
ejpam-411	165	9	and	and	CCONJ
ejpam-411	165	10	hence	hence	ADV
ejpam-411	165	11	the	the	DET
ejpam-411	165	12	subordination	subordination	NOUN
ejpam-411	165	13	result	result	NOUN
ejpam-411	165	14	(	(	PUNCT
ejpam-411	165	15	4.3	4.3	NUM
ejpam-411	165	16	)	)	PUNCT
ejpam-411	165	17	.	.	PUNCT
ejpam-411	166	1	the	the	DET
ejpam-411	166	2	inequality	inequality	NOUN
ejpam-411	166	3	(	(	PUNCT
ejpam-411	166	4	4.4	4.4	NUM
ejpam-411	166	5	)	)	PUNCT
ejpam-411	166	6	follows	follow	VERB
ejpam-411	166	7	from	from	ADP
ejpam-411	166	8	(	(	PUNCT
ejpam-411	166	9	4.3	4.3	NUM
ejpam-411	166	10	)	)	PUNCT
ejpam-411	166	11	by	by	ADP
ejpam-411	166	12	taking	take	VERB
ejpam-411	166	13	g(z	g(z	PROPN
ejpam-411	166	14	)	)	PUNCT
ejpam-411	167	1	=	=	PUNCT
ejpam-411	167	2	z	z	NOUN
ejpam-411	167	3	1−	1−	NUM
ejpam-411	167	4	z	z	NOUN
ejpam-411	167	5	=	=	SYM
ejpam-411	168	1	z+	z+	NUM
ejpam-411	168	2	∞∑	∞∑	NUM
ejpam-411	168	3	n=2	n=2	X
ejpam-411	168	4	zn	zn	NOUN
ejpam-411	168	5	(	(	PUNCT
ejpam-411	168	6	z	z	NOUN
ejpam-411	168	7	∈	∈	PROPN
ejpam-411	168	8	u	u	NOUN
ejpam-411	168	9	)	)	PUNCT
ejpam-411	168	10	.	.	PUNCT
ejpam-411	169	1	j.	j.	PROPN
ejpam-411	169	2	dziok	dziok	PROPN
ejpam-411	169	3	and	and	CCONJ
ejpam-411	169	4	h.	h.	PROPN
ejpam-411	169	5	srivastava	srivastava	PROPN
ejpam-411	169	6	/	/	SYM
ejpam-411	169	7	eur	eur	PROPN
ejpam-411	169	8	.	.	PUNCT
ejpam-411	170	1	j.	j.	PROPN
ejpam-411	170	2	pure	pure	PROPN
ejpam-411	170	3	appl	appl	PROPN
ejpam-411	170	4	.	.	PROPN
ejpam-411	170	5	math	math	PROPN
ejpam-411	170	6	,	,	PUNCT
ejpam-411	170	7	2	2	NUM
ejpam-411	170	8	(	(	PUNCT
ejpam-411	170	9	2009	2009	NUM
ejpam-411	170	10	)	)	PUNCT
ejpam-411	170	11	,	,	PUNCT
ejpam-411	170	12	(	(	PUNCT
ejpam-411	170	13	302	302	NUM
ejpam-411	170	14	-	-	SYM
ejpam-411	170	15	324	324	NUM
ejpam-411	170	16	)	)	PUNCT
ejpam-411	170	17	313	313	NUM
ejpam-411	170	18	we	we	PRON
ejpam-411	170	19	next	next	ADV
ejpam-411	170	20	observe	observe	VERB
ejpam-411	170	21	that	that	SCONJ
ejpam-411	170	22	the	the	DET
ejpam-411	170	23	function	function	NOUN
ejpam-411	170	24	f2,η	f2,η	PROPN
ejpam-411	170	25	of	of	ADP
ejpam-411	170	26	the	the	DET
ejpam-411	170	27	form	form	NOUN
ejpam-411	170	28	(	(	PUNCT
ejpam-411	170	29	2.3	2.3	NUM
ejpam-411	170	30	)	)	PUNCT
ejpam-411	170	31	belongs	belong	VERB
ejpam-411	170	32	to	to	ADP
ejpam-411	170	33	the	the	DET
ejpam-411	170	34	class	class	NOUN
ejpam-411	170	35	t	t	PROPN
ejpam-411	170	36	w	w	PROPN
ejpam-411	170	37	η	η	PROPN
ejpam-411	170	38	�	�	PROPN
ejpam-411	170	39	φ,ϕ	φ,ϕ	PROPN
ejpam-411	170	40	;	;	PUNCT
ejpam-411	170	41	a	a	DET
ejpam-411	170	42	,	,	PUNCT
ejpam-411	170	43	b	b	NOUN
ejpam-411	170	44	;	;	PUNCT
ejpam-411	170	45	k	k	PROPN
ejpam-411	170	46	�	�	PROPN
ejpam-411	170	47	.	.	PUNCT
ejpam-411	171	1	it	it	PRON
ejpam-411	171	2	is	be	AUX
ejpam-411	171	3	easily	easily	ADV
ejpam-411	171	4	verified	verify	VERB
ejpam-411	171	5	that	that	SCONJ
ejpam-411	171	6	min	min	PROPN
ejpam-411	171	7	�	�	PROPN
ejpam-411	171	8	ℜ	ℜ	PROPN
ejpam-411	171	9	�	�	PROPN
ejpam-411	171	10	ǫ	ǫ	PRON
ejpam-411	171	11	f2,η	f2,η	PROPN
ejpam-411	171	12	(	(	PUNCT
ejpam-411	171	13	z	z	NOUN
ejpam-411	171	14	)	)	PUNCT
ejpam-411	171	15	�	�	PROPN
ejpam-411	172	1	=	=	SYM
ejpam-411	172	2	−	−	PROPN
ejpam-411	172	3	1	1	NUM
ejpam-411	172	4	2	2	NUM
ejpam-411	172	5	(	(	PUNCT
ejpam-411	172	6	z	z	NOUN
ejpam-411	172	7	∈	∈	PROPN
ejpam-411	172	8	u	u	NOUN
ejpam-411	172	9	)	)	PUNCT
ejpam-411	172	10	.	.	PUNCT
ejpam-411	173	1	this	this	PRON
ejpam-411	173	2	shows	show	VERB
ejpam-411	173	3	that	that	SCONJ
ejpam-411	173	4	the	the	DET
ejpam-411	173	5	constant	constant	ADJ
ejpam-411	173	6	(	(	PUNCT
ejpam-411	173	7	4.5	4.5	NUM
ejpam-411	173	8	)	)	PUNCT
ejpam-411	173	9	can	can	AUX
ejpam-411	173	10	not	not	PART
ejpam-411	173	11	be	be	AUX
ejpam-411	173	12	replaced	replace	VERB
ejpam-411	173	13	by	by	ADP
ejpam-411	173	14	any	any	DET
ejpam-411	173	15	larger	large	ADJ
ejpam-411	173	16	number	number	NOUN
ejpam-411	173	17	.	.	PUNCT
ejpam-411	174	1	directly	directly	ADV
ejpam-411	174	2	from	from	ADP
ejpam-411	174	3	theorem	theorem	ADJ
ejpam-411	174	4	4.1	4.1	NUM
ejpam-411	174	5	,	,	PUNCT
ejpam-411	174	6	we	we	PRON
ejpam-411	174	7	can	can	AUX
ejpam-411	174	8	obtain	obtain	AUX
ejpam-411	174	9	theorem	theorem	VERB
ejpam-411	174	10	4.2	4.2	NUM
ejpam-411	174	11	below	below	ADV
ejpam-411	174	12	.	.	PUNCT
ejpam-411	175	1	theorem	theorem	VERB
ejpam-411	175	2	4.2	4.2	NUM
ejpam-411	175	3	.	.	PUNCT
ejpam-411	176	1	let	let	VERB
ejpam-411	176	2	the	the	DET
ejpam-411	176	3	sequence	sequence	NOUN
ejpam-411	176	4	�	�	PROPN
ejpam-411	176	5	dn	dn	PROPN
ejpam-411	176	6	,	,	PUNCT
ejpam-411	176	7	defined	define	VERB
ejpam-411	176	8	by	by	ADP
ejpam-411	176	9	(	(	PUNCT
ejpam-411	176	10	1.10	1.10	NUM
ejpam-411	176	11	)	)	PUNCT
ejpam-411	176	12	,	,	PUNCT
ejpam-411	176	13	satisfy	satisfy	VERB
ejpam-411	176	14	the	the	DET
ejpam-411	176	15	inequality	inequality	NOUN
ejpam-411	176	16	(	(	PUNCT
ejpam-411	176	17	3.1	3.1	NUM
ejpam-411	176	18	)	)	PUNCT
ejpam-411	176	19	.	.	PUNCT
ejpam-411	177	1	if	if	SCONJ
ejpam-411	177	2	g	g	PROPN
ejpam-411	177	3	∈	∈	PROPN
ejpam-411	177	4	s	s	PART
ejpam-411	177	5	c	c	NOUN
ejpam-411	177	6	and	and	CCONJ
ejpam-411	177	7	f	f	PROPN
ejpam-411	177	8	∈	∈	PROPN
ejpam-411	177	9	t	t	PROPN
ejpam-411	177	10	w	w	PROPN
ejpam-411	177	11	�	�	PROPN
ejpam-411	177	12	φ,ϕ	φ,ϕ	PROPN
ejpam-411	177	13	;	;	PUNCT
ejpam-411	177	14	a	a	DET
ejpam-411	177	15	,	,	PUNCT
ejpam-411	177	16	b	b	NOUN
ejpam-411	177	17	;	;	PUNCT
ejpam-411	177	18	k	k	PROPN
ejpam-411	177	19	�	�	PROPN
ejpam-411	177	20	,	,	PUNCT
ejpam-411	177	21	then	then	ADV
ejpam-411	177	22	the	the	DET
ejpam-411	177	23	conditions	condition	NOUN
ejpam-411	177	24	(	(	PUNCT
ejpam-411	177	25	4.3	4.3	NUM
ejpam-411	177	26	)	)	PUNCT
ejpam-411	177	27	and	and	CCONJ
ejpam-411	177	28	(	(	PUNCT
ejpam-411	177	29	4.4	4.4	NUM
ejpam-411	177	30	)	)	PUNCT
ejpam-411	177	31	hold	hold	VERB
ejpam-411	177	32	true	true	ADJ
ejpam-411	177	33	.	.	PUNCT
ejpam-411	178	1	the	the	DET
ejpam-411	178	2	constant	constant	ADJ
ejpam-411	178	3	factor	factor	NOUN
ejpam-411	178	4	ǫ	ǫ	PRON
ejpam-411	178	5	in	in	ADP
ejpam-411	178	6	(	(	PUNCT
ejpam-411	178	7	4.3	4.3	NUM
ejpam-411	178	8	)	)	PUNCT
ejpam-411	178	9	can	can	AUX
ejpam-411	178	10	not	not	PART
ejpam-411	178	11	be	be	AUX
ejpam-411	178	12	replaced	replace	VERB
ejpam-411	178	13	by	by	ADP
ejpam-411	178	14	a	a	DET
ejpam-411	178	15	larger	large	ADJ
ejpam-411	178	16	number	number	NOUN
ejpam-411	178	17	.	.	PUNCT
ejpam-411	179	1	5	5	X
ejpam-411	179	2	.	.	X
ejpam-411	179	3	integral	integral	ADJ
ejpam-411	179	4	means	mean	NOUN
ejpam-411	179	5	inequalities	inequality	NOUN
ejpam-411	179	6	following	follow	VERB
ejpam-411	179	7	the	the	DET
ejpam-411	179	8	work	work	NOUN
ejpam-411	179	9	of	of	ADP
ejpam-411	179	10	littlewood	littlewood	PROPN
ejpam-411	180	1	[	[	X
ejpam-411	180	2	11	11	NUM
ejpam-411	180	3	]	]	PUNCT
ejpam-411	180	4	,	,	PUNCT
ejpam-411	180	5	we	we	PRON
ejpam-411	180	6	obtain	obtain	VERB
ejpam-411	180	7	here	here	ADV
ejpam-411	180	8	some	some	DET
ejpam-411	180	9	integral	integral	ADJ
ejpam-411	180	10	means	mean	NOUN
ejpam-411	180	11	inequalities	inequality	NOUN
ejpam-411	180	12	for	for	ADP
ejpam-411	180	13	functions	function	NOUN
ejpam-411	180	14	belonging	belong	VERB
ejpam-411	180	15	to	to	ADP
ejpam-411	180	16	the	the	DET
ejpam-411	180	17	class	class	NOUN
ejpam-411	180	18	t	t	PROPN
ejpam-411	180	19	w	w	PROPN
ejpam-411	180	20	η	η	PROPN
ejpam-411	180	21	�	�	PROPN
ejpam-411	180	22	φ,ϕ	φ,ϕ	PROPN
ejpam-411	180	23	;	;	PUNCT
ejpam-411	180	24	a	a	DET
ejpam-411	180	25	,	,	PUNCT
ejpam-411	180	26	b	b	NOUN
ejpam-411	180	27	;	;	PUNCT
ejpam-411	180	28	k	k	PROPN
ejpam-411	180	29	�	�	PROPN
ejpam-411	180	30	.	.	PUNCT
ejpam-411	181	1	lemma	lemma	PROPN
ejpam-411	181	2	5.1	5.1	NUM
ejpam-411	181	3	.	.	PUNCT
ejpam-411	182	1	(	(	PUNCT
ejpam-411	182	2	see	see	VERB
ejpam-411	182	3	[	[	X
ejpam-411	182	4	11	11	NUM
ejpam-411	182	5	]	]	PUNCT
ejpam-411	182	6	)	)	PUNCT
ejpam-411	182	7	let	let	VERB
ejpam-411	182	8	f	f	PRON
ejpam-411	182	9	,	,	PUNCT
ejpam-411	182	10	g	g	PROPN
ejpam-411	182	11	∈	∈	PROPN
ejpam-411	182	12	fa	fa	INTJ
ejpam-411	182	13	.	.	PUNCT
ejpam-411	183	1	if	if	SCONJ
ejpam-411	183	2	f	f	PROPN
ejpam-411	183	3	≺	≺	VERB
ejpam-411	183	4	g	g	NOUN
ejpam-411	183	5	,	,	PUNCT
ejpam-411	183	6	then	then	ADV
ejpam-411	183	7	∫	∫	PROPN
ejpam-411	183	8	2π	2π	PROPN
ejpam-411	183	9	0	0	NUM
ejpam-411	183	10	�	�	PROPN
ejpam-411	183	11	�	�	PROPN
ejpam-411	183	12	f	f	PROPN
ejpam-411	183	13	(	(	PUNCT
ejpam-411	183	14	reiθ	reiθ	PROPN
ejpam-411	183	15	)	)	PUNCT
ejpam-411	183	16	�	�	PROPN
ejpam-411	183	17	�	�	PROPN
ejpam-411	183	18	η	η	PROPN
ejpam-411	183	19	dθ	dθ	PROPN
ejpam-411	183	20	≦	≦	PROPN
ejpam-411	183	21	∫	∫	PROPN
ejpam-411	183	22	2π	2π	PROPN
ejpam-411	183	23	0	0	NUM
ejpam-411	183	24	�	�	PROPN
ejpam-411	183	25	�	�	PROPN
ejpam-411	183	26	g(reiθ	g(reiθ	NOUN
ejpam-411	183	27	)	)	PUNCT
ejpam-411	183	28	�	�	PROPN
ejpam-411	183	29	�	�	PROPN
ejpam-411	183	30	η	η	PROPN
ejpam-411	183	31	dθ	dθ	PROPN
ejpam-411	183	32	�	�	PROPN
ejpam-411	183	33	0	0	NUM
ejpam-411	183	34	<	<	X
ejpam-411	183	35	r	r	X
ejpam-411	183	36	<	<	X
ejpam-411	183	37	1	1	NUM
ejpam-411	183	38	;	;	PUNCT
ejpam-411	183	39	η	η	PROPN
ejpam-411	183	40	>	>	X
ejpam-411	183	41	0	0	NUM
ejpam-411	183	42	�	�	PROPN
ejpam-411	183	43	.	.	PUNCT
ejpam-411	184	1	(	(	PUNCT
ejpam-411	184	2	5.1	5.1	NUM
ejpam-411	184	3	)	)	PUNCT
ejpam-411	184	4	silverman	silverman	NOUN
ejpam-411	185	1	[	[	X
ejpam-411	185	2	23	23	NUM
ejpam-411	185	3	]	]	PUNCT
ejpam-411	185	4	found	find	VERB
ejpam-411	185	5	that	that	SCONJ
ejpam-411	185	6	the	the	DET
ejpam-411	185	7	following	follow	VERB
ejpam-411	185	8	function	function	NOUN
ejpam-411	185	9	:	:	PUNCT
ejpam-411	185	10	g(z	g(z	ADJ
ejpam-411	185	11	)	)	PUNCT
ejpam-411	185	12	=	=	SYM
ejpam-411	185	13	z	z	NOUN
ejpam-411	185	14	−	−	PROPN
ejpam-411	185	15	z2	z2	NOUN
ejpam-411	185	16	2	2	NUM
ejpam-411	185	17	(	(	PUNCT
ejpam-411	185	18	z	z	NOUN
ejpam-411	185	19	∈	∈	PROPN
ejpam-411	185	20	u	u	NOUN
ejpam-411	185	21	)	)	PUNCT
ejpam-411	185	22	,	,	PUNCT
ejpam-411	185	23	is	be	AUX
ejpam-411	185	24	often	often	ADV
ejpam-411	185	25	extremal	extremal	ADJ
ejpam-411	185	26	over	over	ADP
ejpam-411	185	27	the	the	DET
ejpam-411	185	28	family	family	NOUN
ejpam-411	185	29	of	of	ADP
ejpam-411	185	30	functions	function	NOUN
ejpam-411	185	31	with	with	ADP
ejpam-411	185	32	negative	negative	ADJ
ejpam-411	185	33	coefficients	coefficient	NOUN
ejpam-411	185	34	.	.	PUNCT
ejpam-411	186	1	he	he	PRON
ejpam-411	186	2	applied	apply	VERB
ejpam-411	186	3	this	this	DET
ejpam-411	186	4	function	function	NOUN
ejpam-411	186	5	to	to	PART
ejpam-411	186	6	resolve	resolve	VERB
ejpam-411	186	7	a	a	DET
ejpam-411	186	8	certain	certain	ADJ
ejpam-411	186	9	integral	integral	ADJ
ejpam-411	186	10	means	mean	NOUN
ejpam-411	186	11	inequality	inequality	NOUN
ejpam-411	186	12	,	,	PUNCT
ejpam-411	186	13	which	which	PRON
ejpam-411	186	14	was	be	AUX
ejpam-411	186	15	conjectured	conjecture	VERB
ejpam-411	186	16	in	in	ADP
ejpam-411	186	17	[	[	X
ejpam-411	186	18	25	25	NUM
ejpam-411	186	19	]	]	PUNCT
ejpam-411	186	20	and	and	CCONJ
ejpam-411	186	21	settled	settle	VERB
ejpam-411	186	22	in	in	ADP
ejpam-411	186	23	[	[	X
ejpam-411	186	24	26	26	NUM
ejpam-411	186	25	]	]	PUNCT
ejpam-411	186	26	,	,	PUNCT
ejpam-411	186	27	that	that	SCONJ
ejpam-411	186	28	(	(	PUNCT
ejpam-411	186	29	5.1	5.1	NUM
ejpam-411	186	30	)	)	PUNCT
ejpam-411	186	31	holds	hold	VERB
ejpam-411	186	32	true	true	ADJ
ejpam-411	186	33	for	for	ADP
ejpam-411	186	34	all	all	DET
ejpam-411	186	35	functions	function	NOUN
ejpam-411	186	36	f	f	PROPN
ejpam-411	186	37	with	with	ADP
ejpam-411	186	38	negative	negative	ADJ
ejpam-411	186	39	coefficients	coefficient	NOUN
ejpam-411	186	40	.	.	PUNCT
ejpam-411	187	1	silverman	silverman	NOUN
ejpam-411	188	1	[	[	X
ejpam-411	188	2	26	26	NUM
ejpam-411	188	3	]	]	PUNCT
ejpam-411	188	4	also	also	ADV
ejpam-411	188	5	proved	prove	VERB
ejpam-411	188	6	his	his	PRON
ejpam-411	188	7	conjecture	conjecture	NOUN
ejpam-411	188	8	for	for	ADP
ejpam-411	188	9	some	some	DET
ejpam-411	188	10	subclasses	subclass	NOUN
ejpam-411	188	11	of	of	ADP
ejpam-411	188	12	t	t	PROPN
ejpam-411	188	13	.	.	PUNCT
ejpam-411	189	1	applying	apply	VERB
ejpam-411	189	2	lemma	lemma	PROPN
ejpam-411	189	3	5.1	5.1	NUM
ejpam-411	189	4	and	and	CCONJ
ejpam-411	189	5	theorem	theorem	VERB
ejpam-411	189	6	2.2	2.2	NUM
ejpam-411	189	7	,	,	PUNCT
ejpam-411	189	8	we	we	PRON
ejpam-411	189	9	now	now	ADV
ejpam-411	189	10	prove	prove	VERB
ejpam-411	189	11	the	the	DET
ejpam-411	189	12	following	follow	VERB
ejpam-411	189	13	result	result	NOUN
ejpam-411	189	14	.	.	PUNCT
ejpam-411	190	1	j.	j.	PROPN
ejpam-411	190	2	dziok	dziok	PROPN
ejpam-411	190	3	and	and	CCONJ
ejpam-411	190	4	h.	h.	PROPN
ejpam-411	190	5	srivastava	srivastava	PROPN
ejpam-411	190	6	/	/	SYM
ejpam-411	190	7	eur	eur	PROPN
ejpam-411	190	8	.	.	PUNCT
ejpam-411	191	1	j.	j.	PROPN
ejpam-411	191	2	pure	pure	PROPN
ejpam-411	191	3	appl	appl	PROPN
ejpam-411	191	4	.	.	PROPN
ejpam-411	191	5	math	math	PROPN
ejpam-411	191	6	,	,	PUNCT
ejpam-411	191	7	2	2	NUM
ejpam-411	191	8	(	(	PUNCT
ejpam-411	191	9	2009	2009	NUM
ejpam-411	191	10	)	)	PUNCT
ejpam-411	191	11	,	,	PUNCT
ejpam-411	191	12	(	(	PUNCT
ejpam-411	191	13	302	302	NUM
ejpam-411	191	14	-	-	SYM
ejpam-411	191	15	324	324	NUM
ejpam-411	191	16	)	)	PUNCT
ejpam-411	191	17	314	314	NUM
ejpam-411	191	18	theorem	theorem	VERB
ejpam-411	191	19	5.1	5.1	NUM
ejpam-411	191	20	.	.	PUNCT
ejpam-411	192	1	let	let	VERB
ejpam-411	192	2	the	the	DET
ejpam-411	192	3	sequence	sequence	NOUN
ejpam-411	192	4	�	�	PROPN
ejpam-411	192	5	dn	dn	ADP
ejpam-411	192	6	defined	define	VERB
ejpam-411	192	7	by	by	ADP
ejpam-411	192	8	(	(	PUNCT
ejpam-411	192	9	1.10	1.10	NUM
ejpam-411	192	10	)	)	PUNCT
ejpam-411	192	11	satisfy	satisfy	VERB
ejpam-411	192	12	the	the	DET
ejpam-411	192	13	inequality	inequality	NOUN
ejpam-411	192	14	(	(	PUNCT
ejpam-411	192	15	3.1	3.1	NUM
ejpam-411	192	16	)	)	PUNCT
ejpam-411	192	17	.	.	PUNCT
ejpam-411	193	1	if	if	SCONJ
ejpam-411	193	2	f	f	PROPN
ejpam-411	193	3	∈	∈	PROPN
ejpam-411	193	4	t	t	PROPN
ejpam-411	193	5	w	w	PROPN
ejpam-411	193	6	η	η	PROPN
ejpam-411	193	7	�	�	PROPN
ejpam-411	193	8	φ,ϕ	φ,ϕ	PROPN
ejpam-411	193	9	;	;	PUNCT
ejpam-411	193	10	a	a	DET
ejpam-411	193	11	,	,	PUNCT
ejpam-411	193	12	b	b	NOUN
ejpam-411	193	13	;	;	PUNCT
ejpam-411	193	14	k	k	PROPN
ejpam-411	193	15	�	�	PROPN
ejpam-411	193	16	,	,	PUNCT
ejpam-411	193	17	then	then	ADV
ejpam-411	193	18	∫	∫	PROPN
ejpam-411	193	19	2π	2π	PROPN
ejpam-411	193	20	0	0	NUM
ejpam-411	193	21	�	�	PROPN
ejpam-411	193	22	�	�	PROPN
ejpam-411	193	23	f	f	PROPN
ejpam-411	193	24	(	(	PUNCT
ejpam-411	193	25	reiθ	reiθ	PROPN
ejpam-411	193	26	)	)	PUNCT
ejpam-411	193	27	�	�	PROPN
ejpam-411	193	28	�	�	PROPN
ejpam-411	193	29	λ	λ	PROPN
ejpam-411	193	30	dθ	dθ	PROPN
ejpam-411	193	31	≦	≦	PROPN
ejpam-411	193	32	∫	∫	PROPN
ejpam-411	193	33	2π	2π	PROPN
ejpam-411	193	34	0	0	NUM
ejpam-411	193	35	�	�	PROPN
ejpam-411	193	36	�	�	PROPN
ejpam-411	193	37	f2,η(reiθ	f2,η(reiθ	PROPN
ejpam-411	193	38	)	)	PUNCT
ejpam-411	193	39	�	�	PROPN
ejpam-411	193	40	�	�	PROPN
ejpam-411	193	41	λ	λ	PROPN
ejpam-411	193	42	dθ	dθ	NOUN
ejpam-411	193	43	(	(	PUNCT
ejpam-411	193	44	0	0	PUNCT
ejpam-411	193	45	<	<	X
ejpam-411	193	46	r	r	X
ejpam-411	193	47	<	<	X
ejpam-411	193	48	1	1	NUM
ejpam-411	193	49	;	;	PUNCT
ejpam-411	193	50	λ	λ	X
ejpam-411	193	51	>	>	X
ejpam-411	193	52	0	0	NUM
ejpam-411	193	53	)	)	PUNCT
ejpam-411	193	54	,	,	PUNCT
ejpam-411	193	55	(	(	PUNCT
ejpam-411	193	56	5.2	5.2	NUM
ejpam-411	193	57	)	)	PUNCT
ejpam-411	193	58	where	where	SCONJ
ejpam-411	193	59	f2,η(z	f2,η(z	X
ejpam-411	193	60	)	)	PUNCT
ejpam-411	193	61	is	be	AUX
ejpam-411	193	62	defined	define	VERB
ejpam-411	193	63	by	by	ADP
ejpam-411	193	64	(	(	PUNCT
ejpam-411	193	65	2.3	2.3	NUM
ejpam-411	193	66	)	)	PUNCT
ejpam-411	193	67	.	.	PUNCT
ejpam-411	194	1	proof	proof	NOUN
ejpam-411	194	2	.	.	PUNCT
ejpam-411	195	1	for	for	ADP
ejpam-411	195	2	a	a	DET
ejpam-411	195	3	function	function	NOUN
ejpam-411	195	4	f	f	PROPN
ejpam-411	195	5	of	of	ADP
ejpam-411	195	6	the	the	DET
ejpam-411	195	7	form	form	NOUN
ejpam-411	195	8	(	(	PUNCT
ejpam-411	195	9	1.1	1.1	NUM
ejpam-411	195	10	)	)	PUNCT
ejpam-411	195	11	,	,	PUNCT
ejpam-411	195	12	the	the	DET
ejpam-411	195	13	inequality	inequality	NOUN
ejpam-411	195	14	(	(	PUNCT
ejpam-411	195	15	5.2	5.2	NUM
ejpam-411	195	16	)	)	PUNCT
ejpam-411	195	17	is	be	AUX
ejpam-411	195	18	equivalent	equivalent	ADJ
ejpam-411	195	19	to	to	ADP
ejpam-411	195	20	the	the	DET
ejpam-411	195	21	following	follow	VERB
ejpam-411	195	22	inequality	inequality	NOUN
ejpam-411	195	23	:	:	PUNCT
ejpam-411	196	1	∫	∫	PROPN
ejpam-411	196	2	2π	2π	PROPN
ejpam-411	196	3	0	0	NUM
ejpam-411	196	4	�	�	PROPN
ejpam-411	196	5	�	�	PROPN
ejpam-411	196	6	�	�	PROPN
ejpam-411	196	7	�	�	PROPN
ejpam-411	196	8	�	�	PROPN
ejpam-411	196	9	1	1	NUM
ejpam-411	196	10	+	+	NOUN
ejpam-411	196	11	∞∑	∞∑	NUM
ejpam-411	196	12	n=2	n=2	PRON
ejpam-411	196	13	anzn−1	anzn−1	PROPN
ejpam-411	196	14	�	�	PROPN
ejpam-411	196	15	�	�	PROPN
ejpam-411	196	16	�	�	PROPN
ejpam-411	196	17	�	�	PROPN
ejpam-411	196	18	�	�	PROPN
ejpam-411	196	19	λ	λ	PROPN
ejpam-411	197	1	dθ	dθ	PROPN
ejpam-411	197	2	≦	≦	PROPN
ejpam-411	197	3	∫	∫	PROPN
ejpam-411	197	4	2π	2π	PROPN
ejpam-411	197	5	0	0	NUM
ejpam-411	197	6	�	�	PROPN
ejpam-411	197	7	�	�	PROPN
ejpam-411	197	8	�	�	PROPN
ejpam-411	197	9	�	�	PROPN
ejpam-411	197	10	1−	1−	NUM
ejpam-411	197	11	b−	b−	PROPN
ejpam-411	197	12	a	a	DET
ejpam-411	197	13	d2	d2	PROPN
ejpam-411	197	14	e−iη	e−iη	PROPN
ejpam-411	197	15	z	z	PROPN
ejpam-411	197	16	�	�	PROPN
ejpam-411	197	17	�	�	PROPN
ejpam-411	197	18	�	�	PROPN
ejpam-411	197	19	�	�	PROPN
ejpam-411	197	20	λ	λ	PROPN
ejpam-411	197	21	dθ	dθ	PROPN
ejpam-411	197	22	�	�	PROPN
ejpam-411	197	23	z	z	PROPN
ejpam-411	197	24	=	=	SYM
ejpam-411	197	25	reiθ	reiθ	PROPN
ejpam-411	197	26	�	�	PROPN
ejpam-411	197	27	.	.	PUNCT
ejpam-411	198	1	thus	thus	ADV
ejpam-411	198	2	,	,	PUNCT
ejpam-411	198	3	by	by	ADP
ejpam-411	198	4	lemma	lemma	PROPN
ejpam-411	198	5	5.1	5.1	NUM
ejpam-411	198	6	,	,	PUNCT
ejpam-411	198	7	it	it	PRON
ejpam-411	198	8	suffices	suffice	VERB
ejpam-411	198	9	to	to	PART
ejpam-411	198	10	show	show	VERB
ejpam-411	198	11	that	that	SCONJ
ejpam-411	198	12	∞∑	∞∑	NUM
ejpam-411	198	13	n=2	n=2	ADV
ejpam-411	198	14	anzn−1	anzn−1	VERB
ejpam-411	198	15	≺−	≺−	PUNCT
ejpam-411	198	16	b	b	X
ejpam-411	198	17	−	−	PROPN
ejpam-411	198	18	a	a	DET
ejpam-411	198	19	d2	d2	PROPN
ejpam-411	198	20	e−iηz	e−iηz	NOUN
ejpam-411	198	21	.	.	PUNCT
ejpam-411	199	1	(	(	PUNCT
ejpam-411	199	2	5.3	5.3	NUM
ejpam-411	199	3	)	)	PUNCT
ejpam-411	199	4	upon	upon	SCONJ
ejpam-411	199	5	setting	set	VERB
ejpam-411	199	6	w(z	w(z	NOUN
ejpam-411	199	7	)	)	PUNCT
ejpam-411	199	8	=	=	PUNCT
ejpam-411	200	1	∞∑	∞∑	NUM
ejpam-411	200	2	n=2	n=2	PRON
ejpam-411	200	3	d2eiη	d2eiη	VERB
ejpam-411	200	4	a−	a−	PROPN
ejpam-411	200	5	b	b	PROPN
ejpam-411	200	6	an	an	DET
ejpam-411	200	7	zn−1	zn−1	PROPN
ejpam-411	200	8	(	(	PUNCT
ejpam-411	200	9	z	z	NOUN
ejpam-411	200	10	∈	∈	PROPN
ejpam-411	200	11	u	u	NOUN
ejpam-411	200	12	)	)	PUNCT
ejpam-411	200	13	,	,	PUNCT
ejpam-411	200	14	and	and	CCONJ
ejpam-411	200	15	using	use	VERB
ejpam-411	200	16	(	(	PUNCT
ejpam-411	200	17	3.1	3.1	NUM
ejpam-411	200	18	)	)	PUNCT
ejpam-411	200	19	and	and	CCONJ
ejpam-411	200	20	theorem	theorem	VERB
ejpam-411	200	21	2.2	2.2	NUM
ejpam-411	200	22	,	,	PUNCT
ejpam-411	200	23	we	we	PRON
ejpam-411	200	24	obtain	obtain	VERB
ejpam-411	200	25	|w(z)|	|w(z)|	PROPN
ejpam-411	200	26	=	=	SYM
ejpam-411	200	27	�	�	PROPN
ejpam-411	200	28	�	�	PROPN
ejpam-411	200	29	�	�	PROPN
ejpam-411	200	30	�	�	PROPN
ejpam-411	200	31	�	�	PROPN
ejpam-411	200	32	∞∑	∞∑	PROPN
ejpam-411	200	33	n=2	n=2	X
ejpam-411	200	34	d2	d2	PROPN
ejpam-411	200	35	a−	a−	PROPN
ejpam-411	200	36	b	b	PROPN
ejpam-411	200	37	an	an	DET
ejpam-411	200	38	zn−1	zn−1	PROPN
ejpam-411	200	39	�	�	PROPN
ejpam-411	200	40	�	�	PROPN
ejpam-411	200	41	�	�	PROPN
ejpam-411	200	42	�	�	PROPN
ejpam-411	200	43	�	�	PROPN
ejpam-411	200	44	≦	≦	PART
ejpam-411	200	45	|z|	|z|	VERB
ejpam-411	200	46	∞∑	∞∑	NUM
ejpam-411	200	47	n=2	n=2	ADV
ejpam-411	200	48	dn	dn	ADP
ejpam-411	200	49	b−	b−	PROPN
ejpam-411	200	50	a	a	DET
ejpam-411	200	51	�	�	PROPN
ejpam-411	200	52	�	�	PROPN
ejpam-411	200	53	an	an	DET
ejpam-411	200	54	�	�	PROPN
ejpam-411	200	55	�	�	NOUN
ejpam-411	200	56	≦	≦	PART
ejpam-411	200	57	|z|	|z|	NOUN
ejpam-411	200	58	(	(	PUNCT
ejpam-411	200	59	z	z	NOUN
ejpam-411	200	60	∈	∈	PROPN
ejpam-411	200	61	u	u	NOUN
ejpam-411	200	62	)	)	PUNCT
ejpam-411	200	63	.	.	PUNCT
ejpam-411	201	1	since	since	SCONJ
ejpam-411	201	2	∞∑	∞∑	NUM
ejpam-411	201	3	n=2	n=2	ADV
ejpam-411	201	4	anzn−1	anzn−1	ADV
ejpam-411	201	5	=	=	SYM
ejpam-411	201	6	−	−	NOUN
ejpam-411	201	7	b	b	NOUN
ejpam-411	201	8	−	−	PROPN
ejpam-411	201	9	a	a	DET
ejpam-411	201	10	d2	d2	PROPN
ejpam-411	201	11	e−iηw(z	e−iηw(z	NUM
ejpam-411	201	12	)	)	PUNCT
ejpam-411	201	13	(	(	PUNCT
ejpam-411	201	14	z	z	NOUN
ejpam-411	201	15	∈	∈	PROPN
ejpam-411	201	16	u	u	NOUN
ejpam-411	201	17	)	)	PUNCT
ejpam-411	201	18	,	,	PUNCT
ejpam-411	201	19	by	by	ADP
ejpam-411	201	20	the	the	DET
ejpam-411	201	21	definition	definition	NOUN
ejpam-411	201	22	of	of	ADP
ejpam-411	201	23	subordination	subordination	NOUN
ejpam-411	201	24	,	,	PUNCT
ejpam-411	201	25	we	we	PRON
ejpam-411	201	26	have	have	VERB
ejpam-411	201	27	(	(	PUNCT
ejpam-411	201	28	5.3	5.3	NUM
ejpam-411	201	29	)	)	PUNCT
ejpam-411	201	30	.	.	PUNCT
ejpam-411	202	1	this	this	PRON
ejpam-411	202	2	completes	complete	VERB
ejpam-411	202	3	the	the	DET
ejpam-411	202	4	proof	proof	NOUN
ejpam-411	202	5	of	of	ADP
ejpam-411	202	6	theorem	theorem	NOUN
ejpam-411	202	7	5.1	5.1	NUM
ejpam-411	202	8	.	.	PUNCT
ejpam-411	203	1	we	we	PRON
ejpam-411	203	2	can	can	AUX
ejpam-411	203	3	restate	restate	VERB
ejpam-411	203	4	theorem	theorem	ADJ
ejpam-411	203	5	5.1	5.1	NUM
ejpam-411	203	6	as	as	SCONJ
ejpam-411	203	7	theorem	theorem	VERB
ejpam-411	203	8	5.2	5.2	NUM
ejpam-411	203	9	below	below	ADV
ejpam-411	203	10	.	.	PUNCT
ejpam-411	204	1	theorem	theorem	VERB
ejpam-411	204	2	5.2	5.2	NUM
ejpam-411	204	3	.	.	PUNCT
ejpam-411	205	1	let	let	VERB
ejpam-411	205	2	the	the	DET
ejpam-411	205	3	sequence	sequence	NOUN
ejpam-411	205	4	�	�	PROPN
ejpam-411	205	5	dn	dn	ADP
ejpam-411	205	6	defined	define	VERB
ejpam-411	205	7	by	by	ADP
ejpam-411	205	8	(	(	PUNCT
ejpam-411	205	9	1.10	1.10	NUM
ejpam-411	205	10	)	)	PUNCT
ejpam-411	205	11	satisfy	satisfy	VERB
ejpam-411	205	12	the	the	DET
ejpam-411	205	13	inequality	inequality	NOUN
ejpam-411	205	14	(	(	PUNCT
ejpam-411	205	15	3.1	3.1	NUM
ejpam-411	205	16	)	)	PUNCT
ejpam-411	205	17	.	.	PUNCT
ejpam-411	206	1	if	if	SCONJ
ejpam-411	206	2	a	a	DET
ejpam-411	206	3	function	function	NOUN
ejpam-411	206	4	f	f	NOUN
ejpam-411	206	5	of	of	ADP
ejpam-411	206	6	the	the	DET
ejpam-411	206	7	form	form	NOUN
ejpam-411	206	8	(	(	PUNCT
ejpam-411	206	9	1.1	1.1	NUM
ejpam-411	206	10	)	)	PUNCT
ejpam-411	206	11	satisfying	satisfy	VERB
ejpam-411	206	12	the	the	DET
ejpam-411	206	13	argument	argument	NOUN
ejpam-411	206	14	property	property	NOUN
ejpam-411	206	15	(	(	PUNCT
ejpam-411	206	16	1.2	1.2	NUM
ejpam-411	206	17	)	)	PUNCT
ejpam-411	206	18	belongs	belong	VERB
ejpam-411	206	19	to	to	ADP
ejpam-411	206	20	the	the	DET
ejpam-411	206	21	class	class	NOUN
ejpam-411	206	22	t	t	PROPN
ejpam-411	206	23	w	w	PROPN
ejpam-411	206	24	�	�	PROPN
ejpam-411	206	25	φ,ϕ	φ,ϕ	PROPN
ejpam-411	206	26	;	;	PUNCT
ejpam-411	206	27	a	a	DET
ejpam-411	206	28	,	,	PUNCT
ejpam-411	206	29	b	b	NOUN
ejpam-411	206	30	;	;	PUNCT
ejpam-411	206	31	k	k	PROPN
ejpam-411	206	32	�	�	PROPN
ejpam-411	206	33	,	,	PUNCT
ejpam-411	206	34	then	then	ADV
ejpam-411	206	35	the	the	DET
ejpam-411	206	36	integral	integral	ADJ
ejpam-411	206	37	means	mean	NOUN
ejpam-411	206	38	inequality	inequality	NOUN
ejpam-411	206	39	(	(	PUNCT
ejpam-411	206	40	5.2	5.2	NUM
ejpam-411	206	41	)	)	PUNCT
ejpam-411	206	42	holds	hold	VERB
ejpam-411	206	43	true	true	ADJ
ejpam-411	206	44	.	.	PUNCT
ejpam-411	207	1	j.	j.	PROPN
ejpam-411	207	2	dziok	dziok	PROPN
ejpam-411	207	3	and	and	CCONJ
ejpam-411	207	4	h.	h.	PROPN
ejpam-411	207	5	srivastava	srivastava	PROPN
ejpam-411	207	6	/	/	SYM
ejpam-411	207	7	eur	eur	PROPN
ejpam-411	207	8	.	.	PUNCT
ejpam-411	208	1	j.	j.	PROPN
ejpam-411	208	2	pure	pure	PROPN
ejpam-411	208	3	appl	appl	PROPN
ejpam-411	208	4	.	.	PROPN
ejpam-411	208	5	math	math	PROPN
ejpam-411	208	6	,	,	PUNCT
ejpam-411	208	7	2	2	NUM
ejpam-411	208	8	(	(	PUNCT
ejpam-411	208	9	2009	2009	NUM
ejpam-411	208	10	)	)	PUNCT
ejpam-411	208	11	,	,	PUNCT
ejpam-411	208	12	(	(	PUNCT
ejpam-411	208	13	302	302	NUM
ejpam-411	208	14	-	-	SYM
ejpam-411	208	15	324	324	NUM
ejpam-411	208	16	)	)	PUNCT
ejpam-411	208	17	315	315	NUM
ejpam-411	208	18	6	6	NUM
ejpam-411	208	19	.	.	PUNCT
ejpam-411	209	1	the	the	DET
ejpam-411	209	2	radii	radius	NOUN
ejpam-411	209	3	of	of	ADP
ejpam-411	209	4	convexity	convexity	NOUN
ejpam-411	209	5	and	and	CCONJ
ejpam-411	209	6	starlikeness	starlikeness	NOUN
ejpam-411	209	7	we	we	PRON
ejpam-411	209	8	begin	begin	VERB
ejpam-411	209	9	this	this	DET
ejpam-411	209	10	section	section	NOUN
ejpam-411	209	11	by	by	ADP
ejpam-411	209	12	proving	prove	VERB
ejpam-411	209	13	the	the	DET
ejpam-411	209	14	following	follow	VERB
ejpam-411	209	15	result	result	NOUN
ejpam-411	209	16	.	.	PUNCT
ejpam-411	210	1	theorem	theorem	VERB
ejpam-411	210	2	6.1	6.1	NUM
ejpam-411	210	3	.	.	PUNCT
ejpam-411	211	1	the	the	DET
ejpam-411	211	2	radius	radius	NOUN
ejpam-411	211	3	of	of	ADP
ejpam-411	211	4	starlikeness	starlikeness	NOUN
ejpam-411	211	5	of	of	ADP
ejpam-411	211	6	order	order	NOUN
ejpam-411	211	7	α	α	NOUN
ejpam-411	211	8	for	for	ADP
ejpam-411	211	9	the	the	DET
ejpam-411	211	10	class	class	NOUN
ejpam-411	211	11	t	t	PROPN
ejpam-411	211	12	w	w	PROPN
ejpam-411	211	13	η	η	PROPN
ejpam-411	211	14	�	�	PROPN
ejpam-411	211	15	φ,ϕ	φ,ϕ	PROPN
ejpam-411	211	16	;	;	PUNCT
ejpam-411	211	17	a	a	DET
ejpam-411	211	18	,	,	PUNCT
ejpam-411	211	19	b	b	NOUN
ejpam-411	211	20	;	;	PUNCT
ejpam-411	211	21	k	k	PROPN
ejpam-411	211	22	�	�	PROPN
ejpam-411	211	23	is	be	AUX
ejpam-411	211	24	given	give	VERB
ejpam-411	211	25	by	by	ADP
ejpam-411	211	26	r∗	r∗	PROPN
ejpam-411	211	27	α	α	PROPN
ejpam-411	211	28	�	�	PROPN
ejpam-411	211	29	t	t	PROPN
ejpam-411	211	30	w	w	PROPN
ejpam-411	211	31	η	η	PROPN
ejpam-411	211	32	�	�	PROPN
ejpam-411	211	33	φ,ϕ	φ,ϕ	PROPN
ejpam-411	211	34	;	;	PUNCT
ejpam-411	211	35	a	a	DET
ejpam-411	211	36	,	,	PUNCT
ejpam-411	211	37	b	b	NOUN
ejpam-411	211	38	;	;	PUNCT
ejpam-411	211	39	k	k	PROPN
ejpam-411	211	40	�	�	PROPN
ejpam-411	211	41	�	�	PROPN
ejpam-411	211	42	=	=	PUNCT
ejpam-411	211	43	inf	inf	PROPN
ejpam-411	211	44	n∈n\{1	n∈n\{1	PROPN
ejpam-411	211	45	}	}	PUNCT
ejpam-411	211	46	�	�	PROPN
ejpam-411	211	47	(	(	PUNCT
ejpam-411	211	48	1−α	1−α	NUM
ejpam-411	211	49	)	)	PUNCT
ejpam-411	211	50	dn	dn	NOUN
ejpam-411	211	51	(	(	PUNCT
ejpam-411	211	52	n−α	n−α	NUM
ejpam-411	211	53	)	)	PUNCT
ejpam-411	211	54	(	(	PUNCT
ejpam-411	211	55	b	b	X
ejpam-411	211	56	−	−	PROPN
ejpam-411	211	57	a	a	PRON
ejpam-411	211	58	)	)	PUNCT
ejpam-411	211	59	�	�	PROPN
ejpam-411	211	60	1	1	NUM
ejpam-411	211	61	n−1	n−1	PROPN
ejpam-411	211	62	,	,	PUNCT
ejpam-411	211	63	(	(	PUNCT
ejpam-411	211	64	6.1	6.1	NUM
ejpam-411	211	65	)	)	PUNCT
ejpam-411	211	66	where	where	SCONJ
ejpam-411	211	67	dn	dn	PROPN
ejpam-411	211	68	is	be	AUX
ejpam-411	211	69	defined	define	VERB
ejpam-411	211	70	by	by	ADP
ejpam-411	211	71	(	(	PUNCT
ejpam-411	211	72	1.10	1.10	NUM
ejpam-411	211	73	)	)	PUNCT
ejpam-411	211	74	.	.	PUNCT
ejpam-411	212	1	proof	proof	NOUN
ejpam-411	212	2	.	.	PUNCT
ejpam-411	213	1	a	a	DET
ejpam-411	213	2	function	function	NOUN
ejpam-411	213	3	f	f	PROPN
ejpam-411	213	4	∈	∈	PROPN
ejpam-411	213	5	tη	tη	PROPN
ejpam-411	213	6	of	of	ADP
ejpam-411	213	7	the	the	DET
ejpam-411	213	8	form	form	NOUN
ejpam-411	213	9	(	(	PUNCT
ejpam-411	213	10	1.1	1.1	NUM
ejpam-411	213	11	)	)	PUNCT
ejpam-411	213	12	is	be	AUX
ejpam-411	213	13	starlike	starlike	NOUN
ejpam-411	213	14	of	of	ADP
ejpam-411	213	15	order	order	NOUN
ejpam-411	213	16	α	α	NOUN
ejpam-411	213	17	in	in	ADP
ejpam-411	213	18	the	the	DET
ejpam-411	213	19	disk	disk	NOUN
ejpam-411	213	20	u(r	u(r	NOUN
ejpam-411	213	21	)	)	PUNCT
ejpam-411	214	1	(	(	PUNCT
ejpam-411	214	2	0	0	NUM
ejpam-411	214	3	<	<	X
ejpam-411	214	4	r	r	NOUN
ejpam-411	214	5	≦	≦	NUM
ejpam-411	214	6	1	1	NUM
ejpam-411	214	7	)	)	PUNCT
ejpam-411	214	8	if	if	SCONJ
ejpam-411	214	9	and	and	CCONJ
ejpam-411	214	10	only	only	ADV
ejpam-411	214	11	if	if	SCONJ
ejpam-411	214	12	it	it	PRON
ejpam-411	214	13	satisfies	satisfy	VERB
ejpam-411	214	14	the	the	DET
ejpam-411	214	15	condition	condition	NOUN
ejpam-411	214	16	(	(	PUNCT
ejpam-411	214	17	1.5	1.5	NUM
ejpam-411	214	18	)	)	PUNCT
ejpam-411	214	19	.	.	PUNCT
ejpam-411	215	1	since	since	SCONJ
ejpam-411	215	2	�	�	PROPN
ejpam-411	215	3	�	�	PROPN
ejpam-411	215	4	�	�	PROPN
ejpam-411	215	5	�	�	PROPN
ejpam-411	215	6	z	z	PROPN
ejpam-411	215	7	f	f	PROPN
ejpam-411	215	8	′(z	′(z	NOUN
ejpam-411	215	9	)	)	PUNCT
ejpam-411	215	10	f	f	PROPN
ejpam-411	215	11	(	(	PUNCT
ejpam-411	215	12	z	z	NOUN
ejpam-411	215	13	)	)	PUNCT
ejpam-411	215	14	−	−	PROPN
ejpam-411	215	15	1	1	NUM
ejpam-411	215	16	�	�	PROPN
ejpam-411	215	17	�	�	PROPN
ejpam-411	215	18	�	�	PROPN
ejpam-411	215	19	�	�	PROPN
ejpam-411	215	20	=	=	SYM
ejpam-411	215	21	�	�	PROPN
ejpam-411	215	22	�	�	PROPN
ejpam-411	215	23	�	�	PROPN
ejpam-411	215	24	�	�	PROPN
ejpam-411	215	25	�	�	PROPN
ejpam-411	215	26	�	�	PROPN
ejpam-411	215	27	�	�	PROPN
ejpam-411	215	28	�	�	PROPN
ejpam-411	215	29	∞∑	∞∑	PROPN
ejpam-411	215	30	n=2	n=2	PRON
ejpam-411	215	31	(	(	PUNCT
ejpam-411	215	32	n−	n−	NOUN
ejpam-411	215	33	1	1	NUM
ejpam-411	215	34	)	)	PUNCT
ejpam-411	215	35	anzn	anzn	NOUN
ejpam-411	215	36	z	z	NOUN
ejpam-411	215	37	+	+	CCONJ
ejpam-411	215	38	∞∑	∞∑	NUM
ejpam-411	215	39	n=2	n=2	PRON
ejpam-411	215	40	anzn	anzn	NOUN
ejpam-411	215	41	�	�	PROPN
ejpam-411	215	42	�	�	PROPN
ejpam-411	215	43	�	�	PROPN
ejpam-411	215	44	�	�	PROPN
ejpam-411	215	45	�	�	PROPN
ejpam-411	215	46	�	�	PROPN
ejpam-411	215	47	�	�	PROPN
ejpam-411	215	48	�	�	PROPN
ejpam-411	215	49	≦	≦	NUM
ejpam-411	215	50	∞∑	∞∑	PROPN
ejpam-411	215	51	n=2	n=2	PRON
ejpam-411	215	52	(	(	PUNCT
ejpam-411	215	53	n−	n−	NOUN
ejpam-411	215	54	1	1	NUM
ejpam-411	215	55	)	)	PUNCT
ejpam-411	215	56	�	�	PROPN
ejpam-411	215	57	�	�	PROPN
ejpam-411	215	58	an	an	PRON
ejpam-411	215	59	�	�	PROPN
ejpam-411	215	60	�	�	PROPN
ejpam-411	215	61	|z|n−1	|z|n−1	NUM
ejpam-411	215	62	1−	1−	NUM
ejpam-411	215	63	∞∑	∞∑	PROPN
ejpam-411	215	64	n=2	n=2	X
ejpam-411	215	65	�	�	PROPN
ejpam-411	215	66	�	�	PROPN
ejpam-411	215	67	an	an	DET
ejpam-411	215	68	�	�	PROPN
ejpam-411	215	69	�	�	PROPN
ejpam-411	215	70	|z|n−1	|z|n−1	NUM
ejpam-411	215	71	,	,	PUNCT
ejpam-411	215	72	by	by	ADP
ejpam-411	215	73	putting	put	VERB
ejpam-411	215	74	|z|=	|z|=	NOUN
ejpam-411	215	75	r	r	NOUN
ejpam-411	215	76	,	,	PUNCT
ejpam-411	215	77	the	the	DET
ejpam-411	215	78	condition	condition	NOUN
ejpam-411	215	79	(	(	PUNCT
ejpam-411	215	80	1.5	1.5	NUM
ejpam-411	215	81	)	)	PUNCT
ejpam-411	215	82	is	be	AUX
ejpam-411	215	83	true	true	ADJ
ejpam-411	215	84	if	if	SCONJ
ejpam-411	215	85	∞∑	∞∑	NUM
ejpam-411	215	86	n=2	n=2	ADV
ejpam-411	215	87	n−α	n−α	ADJ
ejpam-411	215	88	1−α	1−α	NUM
ejpam-411	215	89	�	�	PROPN
ejpam-411	215	90	�	�	PROPN
ejpam-411	215	91	an	an	DET
ejpam-411	215	92	�	�	PROPN
ejpam-411	215	93	�	�	PROPN
ejpam-411	215	94	rn−1	rn−1	PROPN
ejpam-411	215	95	≦	≦	PROPN
ejpam-411	215	96	1	1	NUM
ejpam-411	215	97	.	.	PUNCT
ejpam-411	216	1	(	(	PUNCT
ejpam-411	216	2	6.2	6.2	NUM
ejpam-411	216	3	)	)	PUNCT
ejpam-411	216	4	by	by	ADP
ejpam-411	216	5	theorem	theorem	NOUN
ejpam-411	216	6	2.2	2.2	NUM
ejpam-411	216	7	,	,	PUNCT
ejpam-411	216	8	we	we	PRON
ejpam-411	216	9	have	have	VERB
ejpam-411	216	10	∞∑	∞∑	NUM
ejpam-411	216	11	n=2	n=2	ADV
ejpam-411	216	12	dn	dn	ADP
ejpam-411	216	13	b−	b−	PROPN
ejpam-411	216	14	a	a	DET
ejpam-411	216	15	�	�	PROPN
ejpam-411	216	16	�	�	PROPN
ejpam-411	216	17	an	an	DET
ejpam-411	216	18	�	�	PROPN
ejpam-411	216	19	�	�	PROPN
ejpam-411	216	20	≦	≦	NUM
ejpam-411	216	21	1	1	NUM
ejpam-411	216	22	,	,	PUNCT
ejpam-411	216	23	so	so	SCONJ
ejpam-411	216	24	that	that	SCONJ
ejpam-411	216	25	the	the	DET
ejpam-411	216	26	condition	condition	NOUN
ejpam-411	216	27	(	(	PUNCT
ejpam-411	216	28	6.2	6.2	NUM
ejpam-411	216	29	)	)	PUNCT
ejpam-411	216	30	is	be	AUX
ejpam-411	216	31	true	true	ADJ
ejpam-411	216	32	if	if	SCONJ
ejpam-411	216	33	n−α	n−α	NOUN
ejpam-411	216	34	1−α	1−α	NUM
ejpam-411	216	35	rn−1	rn−1	PROPN
ejpam-411	216	36	≦	≦	NUM
ejpam-411	216	37	dn	dn	ADP
ejpam-411	216	38	b−	b−	PROPN
ejpam-411	216	39	a	a	PRON
ejpam-411	216	40	(	(	PUNCT
ejpam-411	216	41	n	n	CCONJ
ejpam-411	216	42	∈	∈	PROPN
ejpam-411	216	43	n	n	CCONJ
ejpam-411	216	44	\	\	NOUN
ejpam-411	216	45	{	{	PUNCT
ejpam-411	216	46	1	1	NUM
ejpam-411	216	47	}	}	PUNCT
ejpam-411	216	48	)	)	PUNCT
ejpam-411	216	49	,	,	PUNCT
ejpam-411	216	50	that	that	ADV
ejpam-411	216	51	is	is	ADV
ejpam-411	216	52	,	,	PUNCT
ejpam-411	216	53	if	if	SCONJ
ejpam-411	216	54	r	r	NOUN
ejpam-411	216	55	≦	≦	PROPN
ejpam-411	216	56	�	�	PROPN
ejpam-411	216	57	(	(	PUNCT
ejpam-411	216	58	1−α	1−α	NUM
ejpam-411	216	59	)	)	PUNCT
ejpam-411	216	60	dn	dn	NOUN
ejpam-411	216	61	(	(	PUNCT
ejpam-411	216	62	n−α	n−α	NUM
ejpam-411	216	63	)	)	PUNCT
ejpam-411	216	64	(	(	PUNCT
ejpam-411	216	65	b−	b−	PROPN
ejpam-411	216	66	a	a	PRON
ejpam-411	216	67	)	)	PUNCT
ejpam-411	216	68	�	�	PROPN
ejpam-411	216	69	1	1	NUM
ejpam-411	216	70	n−1	n−1	PROPN
ejpam-411	216	71	(	(	PUNCT
ejpam-411	216	72	n	n	NOUN
ejpam-411	216	73	∈	∈	PROPN
ejpam-411	216	74	n	n	CCONJ
ejpam-411	216	75	\	\	NOUN
ejpam-411	216	76	{	{	PUNCT
ejpam-411	216	77	1	1	NUM
ejpam-411	216	78	}	}	PUNCT
ejpam-411	216	79	)	)	PUNCT
ejpam-411	216	80	.	.	PUNCT
ejpam-411	217	1	it	it	PRON
ejpam-411	217	2	follows	follow	VERB
ejpam-411	217	3	that	that	SCONJ
ejpam-411	217	4	each	each	DET
ejpam-411	217	5	function	function	NOUN
ejpam-411	217	6	f	f	PROPN
ejpam-411	217	7	∈	∈	PROPN
ejpam-411	217	8	t	t	PROPN
ejpam-411	217	9	w	w	PROPN
ejpam-411	217	10	η	η	PROPN
ejpam-411	217	11	�	�	PROPN
ejpam-411	217	12	φ,ϕ	φ,ϕ	PROPN
ejpam-411	217	13	;	;	PUNCT
ejpam-411	217	14	a	a	DET
ejpam-411	217	15	,	,	PUNCT
ejpam-411	217	16	b	b	NOUN
ejpam-411	217	17	;	;	PUNCT
ejpam-411	217	18	k	k	PROPN
ejpam-411	217	19	�	�	PROPN
ejpam-411	217	20	is	be	AUX
ejpam-411	217	21	starlike	starlike	NOUN
ejpam-411	217	22	of	of	ADP
ejpam-411	217	23	order	order	NOUN
ejpam-411	217	24	α	α	NOUN
ejpam-411	217	25	in	in	ADP
ejpam-411	217	26	the	the	DET
ejpam-411	217	27	disk	disk	NOUN
ejpam-411	217	28	u(r	u(r	NOUN
ejpam-411	217	29	)	)	PUNCT
ejpam-411	217	30	,	,	PUNCT
ejpam-411	217	31	where	where	SCONJ
ejpam-411	217	32	r	r	NOUN
ejpam-411	217	33	=	=	SYM
ejpam-411	217	34	r∗	r∗	VERB
ejpam-411	217	35	α	α	PROPN
ejpam-411	217	36	�	�	PROPN
ejpam-411	217	37	t	t	PROPN
ejpam-411	217	38	w	w	PROPN
ejpam-411	217	39	η	η	PROPN
ejpam-411	217	40	�	�	PROPN
ejpam-411	217	41	φ,ϕ	φ,ϕ	PROPN
ejpam-411	217	42	;	;	PUNCT
ejpam-411	217	43	a	a	DET
ejpam-411	217	44	,	,	PUNCT
ejpam-411	217	45	b	b	NOUN
ejpam-411	217	46	;	;	PUNCT
ejpam-411	217	47	k	k	PROPN
ejpam-411	217	48	�	�	PROPN
ejpam-411	217	49	�	�	PROPN
ejpam-411	217	50	is	be	AUX
ejpam-411	217	51	defined	define	VERB
ejpam-411	217	52	by	by	ADP
ejpam-411	217	53	(	(	PUNCT
ejpam-411	217	54	6.1	6.1	NUM
ejpam-411	217	55	)	)	PUNCT
ejpam-411	217	56	.	.	PUNCT
ejpam-411	218	1	j.	j.	PROPN
ejpam-411	218	2	dziok	dziok	PROPN
ejpam-411	218	3	and	and	CCONJ
ejpam-411	218	4	h.	h.	PROPN
ejpam-411	218	5	srivastava	srivastava	PROPN
ejpam-411	218	6	/	/	SYM
ejpam-411	218	7	eur	eur	PROPN
ejpam-411	218	8	.	.	PUNCT
ejpam-411	219	1	j.	j.	PROPN
ejpam-411	219	2	pure	pure	PROPN
ejpam-411	219	3	appl	appl	PROPN
ejpam-411	219	4	.	.	PROPN
ejpam-411	219	5	math	math	PROPN
ejpam-411	219	6	,	,	PUNCT
ejpam-411	219	7	2	2	NUM
ejpam-411	219	8	(	(	PUNCT
ejpam-411	219	9	2009	2009	NUM
ejpam-411	219	10	)	)	PUNCT
ejpam-411	219	11	,	,	PUNCT
ejpam-411	219	12	(	(	PUNCT
ejpam-411	219	13	302	302	NUM
ejpam-411	219	14	-	-	SYM
ejpam-411	219	15	324	324	NUM
ejpam-411	219	16	)	)	PUNCT
ejpam-411	219	17	316	316	NUM
ejpam-411	219	18	theorem	theorem	VERB
ejpam-411	219	19	6.2	6.2	NUM
ejpam-411	219	20	.	.	PUNCT
ejpam-411	220	1	the	the	DET
ejpam-411	220	2	radius	radius	NOUN
ejpam-411	220	3	of	of	ADP
ejpam-411	220	4	convexity	convexity	NOUN
ejpam-411	220	5	of	of	ADP
ejpam-411	220	6	order	order	NOUN
ejpam-411	220	7	α	α	NOUN
ejpam-411	220	8	for	for	ADP
ejpam-411	220	9	the	the	DET
ejpam-411	220	10	class	class	NOUN
ejpam-411	220	11	t	t	PROPN
ejpam-411	220	12	w	w	PROPN
ejpam-411	220	13	η	η	PROPN
ejpam-411	220	14	�	�	PROPN
ejpam-411	220	15	φ,ϕ	φ,ϕ	PROPN
ejpam-411	220	16	;	;	PUNCT
ejpam-411	220	17	a	a	DET
ejpam-411	220	18	,	,	PUNCT
ejpam-411	220	19	b	b	NOUN
ejpam-411	220	20	;	;	PUNCT
ejpam-411	220	21	k	k	PROPN
ejpam-411	220	22	�	�	PROPN
ejpam-411	220	23	is	be	AUX
ejpam-411	220	24	given	give	VERB
ejpam-411	220	25	by	by	ADP
ejpam-411	220	26	rc	rc	PROPN
ejpam-411	220	27	α	α	PROPN
ejpam-411	220	28	�	�	PROPN
ejpam-411	220	29	t	t	PROPN
ejpam-411	220	30	w	w	PROPN
ejpam-411	220	31	η	η	PROPN
ejpam-411	220	32	�	�	PROPN
ejpam-411	220	33	φ,ϕ	φ,ϕ	PROPN
ejpam-411	220	34	;	;	PUNCT
ejpam-411	220	35	a	a	DET
ejpam-411	220	36	,	,	PUNCT
ejpam-411	220	37	b	b	NOUN
ejpam-411	220	38	;	;	PUNCT
ejpam-411	220	39	k	k	PROPN
ejpam-411	220	40	�	�	PROPN
ejpam-411	220	41	�	�	PROPN
ejpam-411	220	42	=	=	PUNCT
ejpam-411	220	43	inf	inf	PROPN
ejpam-411	220	44	n∈n\{1	n∈n\{1	PROPN
ejpam-411	220	45	}	}	PUNCT
ejpam-411	220	46	�	�	PROPN
ejpam-411	220	47	(	(	PUNCT
ejpam-411	220	48	1−α	1−α	NUM
ejpam-411	220	49	)	)	PUNCT
ejpam-411	220	50	dn	dn	NOUN
ejpam-411	220	51	n	n	PROPN
ejpam-411	220	52	(	(	PUNCT
ejpam-411	220	53	n−α	n−α	NOUN
ejpam-411	220	54	)	)	PUNCT
ejpam-411	220	55	(	(	PUNCT
ejpam-411	220	56	b−	b−	PROPN
ejpam-411	220	57	a	a	PRON
ejpam-411	220	58	)	)	PUNCT
ejpam-411	220	59	�	�	PROPN
ejpam-411	220	60	1	1	NUM
ejpam-411	220	61	n−1	n−1	PROPN
ejpam-411	220	62	,	,	PUNCT
ejpam-411	220	63	where	where	SCONJ
ejpam-411	220	64	dn	dn	PROPN
ejpam-411	220	65	is	be	AUX
ejpam-411	220	66	defined	define	VERB
ejpam-411	220	67	by	by	ADP
ejpam-411	220	68	(	(	PUNCT
ejpam-411	220	69	1.10	1.10	NUM
ejpam-411	220	70	)	)	PUNCT
ejpam-411	220	71	.	.	PUNCT
ejpam-411	221	1	proof	proof	NOUN
ejpam-411	221	2	.	.	PUNCT
ejpam-411	222	1	the	the	DET
ejpam-411	222	2	proof	proof	NOUN
ejpam-411	222	3	of	of	ADP
ejpam-411	222	4	theorem	theorem	ADJ
ejpam-411	222	5	6.2	6.2	NUM
ejpam-411	222	6	is	be	AUX
ejpam-411	222	7	analogous	analogous	ADJ
ejpam-411	222	8	to	to	ADP
ejpam-411	222	9	that	that	PRON
ejpam-411	222	10	of	of	ADP
ejpam-411	222	11	theorem	theorem	NOUN
ejpam-411	222	12	6.1	6.1	NUM
ejpam-411	222	13	,	,	PUNCT
ejpam-411	222	14	and	and	CCONJ
ejpam-411	222	15	we	we	PRON
ejpam-411	222	16	omit	omit	VERB
ejpam-411	222	17	the	the	DET
ejpam-411	222	18	details	detail	NOUN
ejpam-411	222	19	involved	involve	VERB
ejpam-411	222	20	.	.	PUNCT
ejpam-411	223	1	by	by	ADP
ejpam-411	223	2	applying	apply	VERB
ejpam-411	223	3	theorems	theorem	NOUN
ejpam-411	223	4	6.1	6.1	NUM
ejpam-411	223	5	and	and	CCONJ
ejpam-411	223	6	6.2	6.2	NUM
ejpam-411	223	7	,	,	PUNCT
ejpam-411	223	8	we	we	PRON
ejpam-411	223	9	obtain	obtain	VERB
ejpam-411	223	10	the	the	DET
ejpam-411	223	11	following	follow	VERB
ejpam-411	223	12	two	two	NUM
ejpam-411	223	13	corollaries	corollary	NOUN
ejpam-411	223	14	.	.	PUNCT
ejpam-411	224	1	corollary	corollary	ADJ
ejpam-411	224	2	6.1	6.1	NUM
ejpam-411	224	3	.	.	PUNCT
ejpam-411	225	1	the	the	DET
ejpam-411	225	2	radius	radius	NOUN
ejpam-411	225	3	of	of	ADP
ejpam-411	225	4	starlikeness	starlikeness	NOUN
ejpam-411	225	5	of	of	ADP
ejpam-411	225	6	order	order	NOUN
ejpam-411	225	7	α	α	NOUN
ejpam-411	225	8	for	for	ADP
ejpam-411	225	9	the	the	DET
ejpam-411	225	10	class	class	NOUN
ejpam-411	225	11	t	t	PROPN
ejpam-411	225	12	w	w	PROPN
ejpam-411	225	13	�	�	PROPN
ejpam-411	225	14	φ,ϕ	φ,ϕ	PROPN
ejpam-411	225	15	;	;	PUNCT
ejpam-411	225	16	a	a	DET
ejpam-411	225	17	,	,	PUNCT
ejpam-411	225	18	b	b	NOUN
ejpam-411	225	19	;	;	PUNCT
ejpam-411	225	20	k	k	PROPN
ejpam-411	225	21	�	�	PROPN
ejpam-411	225	22	is	be	AUX
ejpam-411	225	23	given	give	VERB
ejpam-411	225	24	by	by	ADP
ejpam-411	225	25	r∗	r∗	PROPN
ejpam-411	225	26	α	α	PROPN
ejpam-411	225	27	�	�	PROPN
ejpam-411	225	28	t	t	PROPN
ejpam-411	225	29	w	w	PROPN
ejpam-411	225	30	�	�	PROPN
ejpam-411	225	31	φ,ϕ	φ,ϕ	PROPN
ejpam-411	225	32	;	;	PUNCT
ejpam-411	225	33	a	a	DET
ejpam-411	225	34	,	,	PUNCT
ejpam-411	225	35	b	b	NOUN
ejpam-411	225	36	;	;	PUNCT
ejpam-411	225	37	k	k	PROPN
ejpam-411	225	38	�	�	PROPN
ejpam-411	225	39	�	�	PROPN
ejpam-411	225	40	=	=	PUNCT
ejpam-411	225	41	inf	inf	PROPN
ejpam-411	225	42	n∈n\{1	n∈n\{1	PROPN
ejpam-411	225	43	}	}	PUNCT
ejpam-411	225	44	�	�	PROPN
ejpam-411	225	45	(	(	PUNCT
ejpam-411	225	46	1−α	1−α	NUM
ejpam-411	225	47	)	)	PUNCT
ejpam-411	225	48	dn	dn	NOUN
ejpam-411	225	49	(	(	PUNCT
ejpam-411	225	50	n−α	n−α	NUM
ejpam-411	225	51	)	)	PUNCT
ejpam-411	225	52	(	(	PUNCT
ejpam-411	225	53	b	b	X
ejpam-411	225	54	−	−	PROPN
ejpam-411	225	55	a	a	PRON
ejpam-411	225	56	)	)	PUNCT
ejpam-411	225	57	�	�	PROPN
ejpam-411	225	58	1	1	NUM
ejpam-411	225	59	n−1	n−1	PROPN
ejpam-411	225	60	,	,	PUNCT
ejpam-411	225	61	where	where	SCONJ
ejpam-411	225	62	dn	dn	PROPN
ejpam-411	225	63	is	be	AUX
ejpam-411	225	64	defined	define	VERB
ejpam-411	225	65	by	by	ADP
ejpam-411	225	66	(	(	PUNCT
ejpam-411	225	67	1.10	1.10	NUM
ejpam-411	225	68	)	)	PUNCT
ejpam-411	225	69	.	.	PUNCT
ejpam-411	226	1	corollary	corollary	ADJ
ejpam-411	226	2	6.2	6.2	NUM
ejpam-411	226	3	.	.	PUNCT
ejpam-411	227	1	the	the	DET
ejpam-411	227	2	radius	radius	NOUN
ejpam-411	227	3	of	of	ADP
ejpam-411	227	4	convexity	convexity	NOUN
ejpam-411	227	5	of	of	ADP
ejpam-411	227	6	order	order	NOUN
ejpam-411	227	7	α	α	NOUN
ejpam-411	227	8	for	for	ADP
ejpam-411	227	9	the	the	DET
ejpam-411	227	10	class	class	NOUN
ejpam-411	227	11	t	t	PROPN
ejpam-411	227	12	w	w	PROPN
ejpam-411	227	13	�	�	PROPN
ejpam-411	227	14	φ,ϕ	φ,ϕ	PROPN
ejpam-411	227	15	;	;	PUNCT
ejpam-411	227	16	a	a	DET
ejpam-411	227	17	,	,	PUNCT
ejpam-411	227	18	b	b	NOUN
ejpam-411	227	19	;	;	PUNCT
ejpam-411	227	20	k	k	PROPN
ejpam-411	227	21	�	�	PROPN
ejpam-411	227	22	is	be	AUX
ejpam-411	227	23	given	give	VERB
ejpam-411	227	24	by	by	ADP
ejpam-411	227	25	rc	rc	PROPN
ejpam-411	227	26	α	α	PROPN
ejpam-411	227	27	�	�	PROPN
ejpam-411	227	28	t	t	PROPN
ejpam-411	227	29	w	w	PROPN
ejpam-411	227	30	�	�	PROPN
ejpam-411	227	31	φ,ϕ	φ,ϕ	PROPN
ejpam-411	227	32	;	;	PUNCT
ejpam-411	227	33	a	a	DET
ejpam-411	227	34	,	,	PUNCT
ejpam-411	227	35	b	b	NOUN
ejpam-411	227	36	;	;	PUNCT
ejpam-411	227	37	k	k	PROPN
ejpam-411	227	38	�	�	PROPN
ejpam-411	227	39	�	�	PROPN
ejpam-411	227	40	=	=	PUNCT
ejpam-411	227	41	inf	inf	PROPN
ejpam-411	227	42	n∈n\{1	n∈n\{1	PROPN
ejpam-411	227	43	}	}	PUNCT
ejpam-411	227	44	�	�	PROPN
ejpam-411	227	45	(	(	PUNCT
ejpam-411	227	46	1−α	1−α	NUM
ejpam-411	227	47	)	)	PUNCT
ejpam-411	227	48	dn	dn	NOUN
ejpam-411	227	49	n	n	PROPN
ejpam-411	227	50	(	(	PUNCT
ejpam-411	227	51	n−α	n−α	NOUN
ejpam-411	227	52	)	)	PUNCT
ejpam-411	227	53	(	(	PUNCT
ejpam-411	227	54	b−	b−	PROPN
ejpam-411	227	55	a	a	PRON
ejpam-411	227	56	)	)	PUNCT
ejpam-411	227	57	�	�	PROPN
ejpam-411	227	58	1	1	NUM
ejpam-411	227	59	n−1	n−1	PROPN
ejpam-411	227	60	,	,	PUNCT
ejpam-411	227	61	where	where	SCONJ
ejpam-411	227	62	dn	dn	PROPN
ejpam-411	227	63	is	be	AUX
ejpam-411	227	64	defined	define	VERB
ejpam-411	227	65	by	by	ADP
ejpam-411	227	66	(	(	PUNCT
ejpam-411	227	67	1.10	1.10	NUM
ejpam-411	227	68	)	)	PUNCT
ejpam-411	227	69	.	.	PUNCT
ejpam-411	228	1	7	7	X
ejpam-411	228	2	.	.	X
ejpam-411	228	3	convolution	convolution	NOUN
ejpam-411	228	4	properties	property	NOUN
ejpam-411	228	5	theorem	theorem	VERB
ejpam-411	228	6	7.1	7.1	NUM
ejpam-411	228	7	.	.	PUNCT
ejpam-411	229	1	let	let	VERB
ejpam-411	229	2	the	the	DET
ejpam-411	229	3	sequence	sequence	NOUN
ejpam-411	229	4	�	�	PROPN
ejpam-411	229	5	dn	dn	ADP
ejpam-411	229	6	defined	define	VERB
ejpam-411	229	7	by	by	ADP
ejpam-411	229	8	(	(	PUNCT
ejpam-411	229	9	1.10	1.10	NUM
ejpam-411	229	10	)	)	PUNCT
ejpam-411	229	11	satisfy	satisfy	VERB
ejpam-411	229	12	the	the	DET
ejpam-411	229	13	inequality	inequality	NOUN
ejpam-411	229	14	(	(	PUNCT
ejpam-411	229	15	3.1	3.1	NUM
ejpam-411	229	16	)	)	PUNCT
ejpam-411	229	17	with	with	ADP
ejpam-411	229	18	d2	d2	PROPN
ejpam-411	229	19	≧	≧	X
ejpam-411	229	20	b−	b−	PROPN
ejpam-411	229	21	a.	a.	NOUN
ejpam-411	229	22	if	if	SCONJ
ejpam-411	229	23	f	f	PROPN
ejpam-411	229	24	∈	∈	PROPN
ejpam-411	229	25	t	t	PROPN
ejpam-411	229	26	w	w	PROPN
ejpam-411	229	27	η	η	PROPN
ejpam-411	229	28	�	�	PROPN
ejpam-411	229	29	φ,ϕ	φ,ϕ	PROPN
ejpam-411	229	30	;	;	PUNCT
ejpam-411	229	31	a	a	DET
ejpam-411	229	32	,	,	PUNCT
ejpam-411	229	33	b	b	NOUN
ejpam-411	229	34	;	;	PUNCT
ejpam-411	229	35	k	k	PROPN
ejpam-411	229	36	�	�	PROPN
ejpam-411	229	37	and	and	CCONJ
ejpam-411	229	38	g	g	PROPN
ejpam-411	229	39	∈	∈	PROPN
ejpam-411	229	40	t	t	PROPN
ejpam-411	229	41	w	w	PROPN
ejpam-411	229	42	µ	µ	PRON
ejpam-411	229	43	�	�	PROPN
ejpam-411	229	44	φ,ϕ	φ,ϕ	PROPN
ejpam-411	229	45	;	;	PUNCT
ejpam-411	229	46	a	a	DET
ejpam-411	229	47	,	,	PUNCT
ejpam-411	229	48	b	b	NOUN
ejpam-411	229	49	;	;	PUNCT
ejpam-411	229	50	k	k	PROPN
ejpam-411	229	51	�	�	PROPN
ejpam-411	229	52	,	,	PUNCT
ejpam-411	229	53	then	then	ADV
ejpam-411	229	54	f	f	PROPN
ejpam-411	229	55	∗	∗	VERB
ejpam-411	229	56	g	g	PROPN
ejpam-411	229	57	∈	∈	PROPN
ejpam-411	229	58	t	t	PROPN
ejpam-411	229	59	w	w	PROPN
ejpam-411	229	60	η+µ	η+µ	PROPN
ejpam-411	229	61	�	�	PROPN
ejpam-411	229	62	φ,ϕ	φ,ϕ	PROPN
ejpam-411	229	63	;	;	PUNCT
ejpam-411	229	64	a	a	DET
ejpam-411	229	65	,	,	PUNCT
ejpam-411	229	66	b	b	NOUN
ejpam-411	229	67	;	;	PUNCT
ejpam-411	229	68	k	k	PROPN
ejpam-411	229	69	�	�	PROPN
ejpam-411	229	70	.	.	PUNCT
ejpam-411	230	1	j.	j.	PROPN
ejpam-411	230	2	dziok	dziok	PROPN
ejpam-411	230	3	and	and	CCONJ
ejpam-411	230	4	h.	h.	PROPN
ejpam-411	230	5	srivastava	srivastava	PROPN
ejpam-411	230	6	/	/	SYM
ejpam-411	230	7	eur	eur	PROPN
ejpam-411	230	8	.	.	PUNCT
ejpam-411	231	1	j.	j.	PROPN
ejpam-411	231	2	pure	pure	PROPN
ejpam-411	231	3	appl	appl	PROPN
ejpam-411	231	4	.	.	PROPN
ejpam-411	231	5	math	math	PROPN
ejpam-411	231	6	,	,	PUNCT
ejpam-411	231	7	2	2	NUM
ejpam-411	231	8	(	(	PUNCT
ejpam-411	231	9	2009	2009	NUM
ejpam-411	231	10	)	)	PUNCT
ejpam-411	231	11	,	,	PUNCT
ejpam-411	231	12	(	(	PUNCT
ejpam-411	231	13	302	302	NUM
ejpam-411	231	14	-	-	SYM
ejpam-411	231	15	324	324	NUM
ejpam-411	231	16	)	)	PUNCT
ejpam-411	231	17	317	317	NUM
ejpam-411	231	18	proof	proof	NOUN
ejpam-411	231	19	.	.	PUNCT
ejpam-411	232	1	let	let	VERB
ejpam-411	232	2	the	the	DET
ejpam-411	232	3	functions	function	NOUN
ejpam-411	232	4	f	f	PROPN
ejpam-411	232	5	and	and	CCONJ
ejpam-411	232	6	g	g	PROPN
ejpam-411	232	7	of	of	ADP
ejpam-411	232	8	the	the	DET
ejpam-411	232	9	forms	form	NOUN
ejpam-411	232	10	:	:	PUNCT
ejpam-411	232	11	f	f	PROPN
ejpam-411	232	12	(	(	PUNCT
ejpam-411	232	13	z	z	NOUN
ejpam-411	232	14	)	)	PUNCT
ejpam-411	232	15	=	=	SYM
ejpam-411	233	1	z	z	NOUN
ejpam-411	233	2	+	+	NOUN
ejpam-411	234	1	∞∑	∞∑	NUM
ejpam-411	234	2	n=2	n=2	CCONJ
ejpam-411	234	3	anzn	anzn	NOUN
ejpam-411	234	4	and	and	CCONJ
ejpam-411	234	5	g(z	g(z	ADJ
ejpam-411	234	6	)	)	PUNCT
ejpam-411	234	7	=	=	SYM
ejpam-411	235	1	z+	z+	NUM
ejpam-411	235	2	∞∑	∞∑	NUM
ejpam-411	235	3	n=2	n=2	PRON
ejpam-411	235	4	bnzn	bnzn	NOUN
ejpam-411	235	5	(	(	PUNCT
ejpam-411	235	6	z	z	NOUN
ejpam-411	235	7	∈	∈	PROPN
ejpam-411	235	8	u	u	NOUN
ejpam-411	235	9	)	)	PUNCT
ejpam-411	235	10	.	.	PUNCT
ejpam-411	236	1	(	(	PUNCT
ejpam-411	236	2	7.1	7.1	X
ejpam-411	236	3	)	)	PUNCT
ejpam-411	236	4	belong	belong	VERB
ejpam-411	236	5	to	to	ADP
ejpam-411	236	6	the	the	DET
ejpam-411	236	7	classes	class	NOUN
ejpam-411	236	8	t	t	PROPN
ejpam-411	236	9	w	w	PROPN
ejpam-411	236	10	η	η	PROPN
ejpam-411	236	11	�	�	PROPN
ejpam-411	236	12	φ,ϕ	φ,ϕ	PROPN
ejpam-411	236	13	;	;	PUNCT
ejpam-411	236	14	a	a	DET
ejpam-411	236	15	,	,	PUNCT
ejpam-411	236	16	b	b	NOUN
ejpam-411	236	17	;	;	PUNCT
ejpam-411	236	18	k	k	PROPN
ejpam-411	236	19	�	�	PROPN
ejpam-411	236	20	and	and	CCONJ
ejpam-411	236	21	t	t	PROPN
ejpam-411	236	22	w	w	PROPN
ejpam-411	236	23	µ	µ	PROPN
ejpam-411	236	24	�	�	PROPN
ejpam-411	236	25	φ,ϕ	φ,ϕ	PROPN
ejpam-411	236	26	;	;	PUNCT
ejpam-411	236	27	a	a	DET
ejpam-411	236	28	,	,	PUNCT
ejpam-411	236	29	b	b	NOUN
ejpam-411	236	30	;	;	PUNCT
ejpam-411	236	31	k	k	PROPN
ejpam-411	236	32	�	�	PROPN
ejpam-411	236	33	,	,	PUNCT
ejpam-411	236	34	respectively	respectively	ADV
ejpam-411	236	35	.	.	PUNCT
ejpam-411	237	1	then	then	ADV
ejpam-411	237	2	,	,	PUNCT
ejpam-411	237	3	by	by	ADP
ejpam-411	237	4	appealing	appeal	VERB
ejpam-411	237	5	to	to	PART
ejpam-411	237	6	theorem	theorem	VERB
ejpam-411	237	7	2.2	2.2	NUM
ejpam-411	237	8	,	,	PUNCT
ejpam-411	237	9	we	we	PRON
ejpam-411	237	10	have	have	VERB
ejpam-411	237	11	∞∑	∞∑	NUM
ejpam-411	237	12	n=2	n=2	ADV
ejpam-411	237	13	dn	dn	ADP
ejpam-411	237	14	b	b	NOUN
ejpam-411	237	15	−	−	PROPN
ejpam-411	237	16	a	a	DET
ejpam-411	237	17	�	�	PROPN
ejpam-411	237	18	�	�	PROPN
ejpam-411	237	19	an	an	DET
ejpam-411	237	20	�	�	PROPN
ejpam-411	237	21	�	�	PROPN
ejpam-411	237	22	≦	≦	NUM
ejpam-411	237	23	1	1	NUM
ejpam-411	237	24	and	and	CCONJ
ejpam-411	237	25	∞∑	∞∑	NUM
ejpam-411	237	26	n=2	n=2	ADV
ejpam-411	237	27	dn	dn	ADP
ejpam-411	237	28	b−	b−	PROPN
ejpam-411	237	29	a	a	DET
ejpam-411	237	30	�	�	PROPN
ejpam-411	237	31	�	�	PROPN
ejpam-411	237	32	bn	bn	PROPN
ejpam-411	237	33	�	�	PROPN
ejpam-411	237	34	�	�	PROPN
ejpam-411	237	35	≦	≦	NOUN
ejpam-411	237	36	1	1	NUM
ejpam-411	237	37	.	.	PUNCT
ejpam-411	238	1	thus	thus	ADV
ejpam-411	238	2	,	,	PUNCT
ejpam-411	238	3	by	by	ADP
ejpam-411	238	4	the	the	DET
ejpam-411	238	5	cauchy	cauchy	PROPN
ejpam-411	238	6	-	-	PUNCT
ejpam-411	238	7	schwarz	schwarz	PROPN
ejpam-411	238	8	inequality	inequality	NOUN
ejpam-411	238	9	,	,	PUNCT
ejpam-411	238	10	we	we	PRON
ejpam-411	238	11	obtain	obtain	VERB
ejpam-411	238	12	∞∑	∞∑	NUM
ejpam-411	238	13	n=2	n=2	ADV
ejpam-411	238	14	dn	dn	ADP
ejpam-411	238	15	b−	b−	PROPN
ejpam-411	238	16	a	a	DET
ejpam-411	238	17	æ	æ	PROPN
ejpam-411	238	18	�	�	PROPN
ejpam-411	238	19	�	�	PROPN
ejpam-411	238	20	an	an	DET
ejpam-411	238	21	bn	bn	PROPN
ejpam-411	238	22	�	�	PROPN
ejpam-411	238	23	�	�	PROPN
ejpam-411	238	24	≦	≦	NOUN
ejpam-411	238	25	1	1	NUM
ejpam-411	238	26	.	.	PUNCT
ejpam-411	239	1	(	(	PUNCT
ejpam-411	239	2	7.2	7.2	NUM
ejpam-411	239	3	)	)	PUNCT
ejpam-411	239	4	in	in	ADP
ejpam-411	239	5	order	order	NOUN
ejpam-411	239	6	to	to	PART
ejpam-411	239	7	prove	prove	VERB
ejpam-411	239	8	that	that	SCONJ
ejpam-411	239	9	∞∑	∞∑	NUM
ejpam-411	239	10	k=2	k=2	PROPN
ejpam-411	239	11	dn	dn	PROPN
ejpam-411	239	12	b−	b−	PROPN
ejpam-411	239	13	a	a	DET
ejpam-411	239	14	�	�	PROPN
ejpam-411	239	15	�	�	PROPN
ejpam-411	239	16	an	an	DET
ejpam-411	239	17	bn	bn	PROPN
ejpam-411	239	18	�	�	PROPN
ejpam-411	239	19	�	�	PROPN
ejpam-411	239	20	≦	≦	NUM
ejpam-411	239	21	1	1	NUM
ejpam-411	239	22	,	,	PUNCT
ejpam-411	239	23	by	by	ADP
ejpam-411	239	24	virtue	virtue	NOUN
ejpam-411	239	25	of	of	ADP
ejpam-411	239	26	(	(	PUNCT
ejpam-411	239	27	7.2	7.2	NUM
ejpam-411	239	28	)	)	PUNCT
ejpam-411	239	29	,	,	PUNCT
ejpam-411	239	30	it	it	PRON
ejpam-411	239	31	is	be	AUX
ejpam-411	239	32	sufficient	sufficient	ADJ
ejpam-411	239	33	to	to	PART
ejpam-411	239	34	show	show	VERB
ejpam-411	239	35	that	that	SCONJ
ejpam-411	239	36	�	�	PROPN
ejpam-411	239	37	�	�	PROPN
ejpam-411	239	38	an	an	DET
ejpam-411	239	39	bn	bn	PROPN
ejpam-411	239	40	�	�	PROPN
ejpam-411	239	41	�	�	PROPN
ejpam-411	239	42	≦	≦	PROPN
ejpam-411	239	43	æ	æ	NOUN
ejpam-411	239	44	�	�	PROPN
ejpam-411	239	45	�	�	PROPN
ejpam-411	239	46	anbn	anbn	PROPN
ejpam-411	239	47	�	�	PROPN
ejpam-411	239	48	�	�	PROPN
ejpam-411	239	49	(	(	PUNCT
ejpam-411	239	50	n	n	NOUN
ejpam-411	239	51	∈	∈	PROPN
ejpam-411	239	52	n	n	CCONJ
ejpam-411	239	53	\	\	NOUN
ejpam-411	239	54	{	{	PUNCT
ejpam-411	239	55	1	1	NUM
ejpam-411	239	56	}	}	PUNCT
ejpam-411	239	57	)	)	PUNCT
ejpam-411	239	58	or	or	CCONJ
ejpam-411	239	59	,	,	PUNCT
ejpam-411	239	60	equivalently	equivalently	ADV
ejpam-411	239	61	,	,	PUNCT
ejpam-411	239	62	that	that	SCONJ
ejpam-411	239	63	æ	æ	X
ejpam-411	239	64	�	�	PROPN
ejpam-411	239	65	�	�	PROPN
ejpam-411	239	66	an	an	DET
ejpam-411	239	67	bn	bn	PROPN
ejpam-411	239	68	�	�	PROPN
ejpam-411	239	69	�	�	PROPN
ejpam-411	239	70	≦	≦	PROPN
ejpam-411	239	71	1	1	NUM
ejpam-411	239	72	(	(	PUNCT
ejpam-411	239	73	n	n	NOUN
ejpam-411	239	74	∈	∈	PROPN
ejpam-411	239	75	n	n	CCONJ
ejpam-411	239	76	\	\	NOUN
ejpam-411	239	77	{	{	PUNCT
ejpam-411	239	78	1	1	NUM
ejpam-411	239	79	}	}	PUNCT
ejpam-411	239	80	)	)	PUNCT
ejpam-411	239	81	.	.	PUNCT
ejpam-411	240	1	we	we	PRON
ejpam-411	240	2	note	note	VERB
ejpam-411	240	3	from	from	ADP
ejpam-411	240	4	(	(	PUNCT
ejpam-411	240	5	7.2	7.2	NUM
ejpam-411	240	6	)	)	PUNCT
ejpam-411	240	7	that	that	PRON
ejpam-411	240	8	æ	æ	X
ejpam-411	240	9	�	�	PROPN
ejpam-411	240	10	�	�	PROPN
ejpam-411	240	11	an	an	DET
ejpam-411	240	12	bn	bn	PROPN
ejpam-411	240	13	�	�	PROPN
ejpam-411	240	14	�	�	PROPN
ejpam-411	240	15	≦	≦	PROPN
ejpam-411	240	16	b	b	PROPN
ejpam-411	240	17	−	−	PROPN
ejpam-411	240	18	a	a	DET
ejpam-411	240	19	dn	dn	NOUN
ejpam-411	240	20	(	(	PUNCT
ejpam-411	240	21	n	n	CCONJ
ejpam-411	240	22	∈	∈	PROPN
ejpam-411	240	23	n	n	CCONJ
ejpam-411	240	24	\	\	NOUN
ejpam-411	240	25	{	{	PUNCT
ejpam-411	240	26	1	1	NUM
ejpam-411	240	27	}	}	PUNCT
ejpam-411	240	28	)	)	PUNCT
ejpam-411	240	29	.	.	PUNCT
ejpam-411	241	1	consequently	consequently	ADV
ejpam-411	241	2	,	,	PUNCT
ejpam-411	241	3	we	we	PRON
ejpam-411	241	4	need	need	VERB
ejpam-411	241	5	only	only	ADV
ejpam-411	241	6	to	to	PART
ejpam-411	241	7	prove	prove	VERB
ejpam-411	241	8	that	that	SCONJ
ejpam-411	241	9	b−	b−	PROPN
ejpam-411	241	10	a	a	DET
ejpam-411	241	11	dn	dn	NOUN
ejpam-411	241	12	≦	≦	NUM
ejpam-411	241	13	1	1	NUM
ejpam-411	241	14	(	(	PUNCT
ejpam-411	241	15	n	n	NOUN
ejpam-411	241	16	∈	∈	PROPN
ejpam-411	241	17	n	n	CCONJ
ejpam-411	241	18	\	\	NOUN
ejpam-411	241	19	{	{	PUNCT
ejpam-411	241	20	1	1	NUM
ejpam-411	241	21	}	}	PUNCT
ejpam-411	241	22	)	)	PUNCT
ejpam-411	241	23	.	.	PUNCT
ejpam-411	242	1	since	since	SCONJ
ejpam-411	242	2	d2	d2	PROPN
ejpam-411	242	3	≧	≧	PROPN
ejpam-411	242	4	b	b	ADP
ejpam-411	243	1	−	−	NOUN
ejpam-411	243	2	a	a	X
ejpam-411	243	3	,	,	PUNCT
ejpam-411	243	4	by	by	ADP
ejpam-411	243	5	hypothesis	hypothesis	NOUN
ejpam-411	243	6	,	,	PUNCT
ejpam-411	243	7	so	so	CCONJ
ejpam-411	243	8	the	the	DET
ejpam-411	243	9	last	last	ADJ
ejpam-411	243	10	inequality	inequality	NOUN
ejpam-411	243	11	follows	follow	VERB
ejpam-411	243	12	from	from	ADP
ejpam-411	243	13	(	(	PUNCT
ejpam-411	243	14	3.1	3.1	NUM
ejpam-411	243	15	)	)	PUNCT
ejpam-411	243	16	.	.	PUNCT
ejpam-411	244	1	by	by	ADP
ejpam-411	244	2	applying	apply	VERB
ejpam-411	244	3	theorem	theorem	NOUN
ejpam-411	244	4	7.1	7.1	NUM
ejpam-411	244	5	,	,	PUNCT
ejpam-411	244	6	we	we	PRON
ejpam-411	244	7	obtain	obtain	VERB
ejpam-411	244	8	the	the	DET
ejpam-411	244	9	following	follow	VERB
ejpam-411	244	10	corollary	corollary	NOUN
ejpam-411	244	11	.	.	PUNCT
ejpam-411	245	1	j.	j.	PROPN
ejpam-411	245	2	dziok	dziok	PROPN
ejpam-411	245	3	and	and	CCONJ
ejpam-411	245	4	h.	h.	PROPN
ejpam-411	245	5	srivastava	srivastava	PROPN
ejpam-411	245	6	/	/	SYM
ejpam-411	245	7	eur	eur	PROPN
ejpam-411	245	8	.	.	PUNCT
ejpam-411	246	1	j.	j.	PROPN
ejpam-411	246	2	pure	pure	PROPN
ejpam-411	246	3	appl	appl	PROPN
ejpam-411	246	4	.	.	PROPN
ejpam-411	246	5	math	math	PROPN
ejpam-411	246	6	,	,	PUNCT
ejpam-411	246	7	2	2	NUM
ejpam-411	246	8	(	(	PUNCT
ejpam-411	246	9	2009	2009	NUM
ejpam-411	246	10	)	)	PUNCT
ejpam-411	246	11	,	,	PUNCT
ejpam-411	246	12	(	(	PUNCT
ejpam-411	246	13	302	302	NUM
ejpam-411	246	14	-	-	SYM
ejpam-411	246	15	324	324	NUM
ejpam-411	246	16	)	)	PUNCT
ejpam-411	246	17	318	318	NUM
ejpam-411	246	18	corollary	corollary	NOUN
ejpam-411	246	19	7.1	7.1	NUM
ejpam-411	246	20	.	.	PUNCT
ejpam-411	247	1	let	let	VERB
ejpam-411	247	2	the	the	DET
ejpam-411	247	3	sequence	sequence	NOUN
ejpam-411	247	4	�	�	PROPN
ejpam-411	247	5	dn	dn	ADP
ejpam-411	247	6	defined	define	VERB
ejpam-411	247	7	by	by	ADP
ejpam-411	247	8	(	(	PUNCT
ejpam-411	247	9	1.10	1.10	NUM
ejpam-411	247	10	)	)	PUNCT
ejpam-411	247	11	satisfy	satisfy	VERB
ejpam-411	247	12	the	the	DET
ejpam-411	247	13	inequality	inequality	NOUN
ejpam-411	247	14	(	(	PUNCT
ejpam-411	247	15	3.1	3.1	NUM
ejpam-411	247	16	)	)	PUNCT
ejpam-411	247	17	with	with	ADP
ejpam-411	247	18	d2	d2	PROPN
ejpam-411	247	19	≧	≧	X
ejpam-411	247	20	b−	b−	PROPN
ejpam-411	247	21	a.	a.	NOUN
ejpam-411	247	22	if	if	SCONJ
ejpam-411	247	23	f	f	PROPN
ejpam-411	247	24	,	,	PUNCT
ejpam-411	247	25	g	g	PROPN
ejpam-411	247	26	∈	∈	PROPN
ejpam-411	247	27	t	t	PROPN
ejpam-411	247	28	w	w	PROPN
ejpam-411	247	29	�	�	PROPN
ejpam-411	247	30	φ,ϕ	φ,ϕ	PROPN
ejpam-411	247	31	;	;	PUNCT
ejpam-411	247	32	a	a	DET
ejpam-411	247	33	,	,	PUNCT
ejpam-411	247	34	b	b	NOUN
ejpam-411	247	35	;	;	PUNCT
ejpam-411	247	36	k	k	PROPN
ejpam-411	247	37	�	�	PROPN
ejpam-411	247	38	,	,	PUNCT
ejpam-411	247	39	then	then	ADV
ejpam-411	247	40	f	f	PROPN
ejpam-411	247	41	∗	∗	VERB
ejpam-411	247	42	g	g	PROPN
ejpam-411	247	43	∈	∈	PROPN
ejpam-411	247	44	t	t	PROPN
ejpam-411	247	45	w	w	PROPN
ejpam-411	247	46	�	�	PROPN
ejpam-411	247	47	φ,ϕ	φ,ϕ	PROPN
ejpam-411	247	48	;	;	PUNCT
ejpam-411	247	49	a	a	DET
ejpam-411	247	50	,	,	PUNCT
ejpam-411	247	51	b	b	NOUN
ejpam-411	247	52	;	;	PUNCT
ejpam-411	247	53	k	k	PROPN
ejpam-411	247	54	�	�	PROPN
ejpam-411	247	55	.	.	PUNCT
ejpam-411	248	1	theorem	theorem	VERB
ejpam-411	248	2	7.2	7.2	NUM
ejpam-411	248	3	.	.	PUNCT
ejpam-411	249	1	let	let	VERB
ejpam-411	249	2	the	the	DET
ejpam-411	249	3	sequence	sequence	NOUN
ejpam-411	249	4	�	�	PROPN
ejpam-411	249	5	dn	dn	ADP
ejpam-411	249	6	defined	define	VERB
ejpam-411	249	7	by	by	ADP
ejpam-411	249	8	(	(	PUNCT
ejpam-411	249	9	1.10	1.10	NUM
ejpam-411	249	10	)	)	PUNCT
ejpam-411	249	11	satisfy	satisfy	VERB
ejpam-411	249	12	the	the	DET
ejpam-411	249	13	inequality	inequality	NOUN
ejpam-411	249	14	(	(	PUNCT
ejpam-411	249	15	3.1	3.1	NUM
ejpam-411	249	16	)	)	PUNCT
ejpam-411	249	17	with	with	ADP
ejpam-411	249	18	d2	d2	PROPN
ejpam-411	249	19	≧	≧	PUNCT
ejpam-411	249	20	2	2	NUM
ejpam-411	249	21	(	(	PUNCT
ejpam-411	249	22	b−	b−	NOUN
ejpam-411	249	23	a	a	PRON
ejpam-411	249	24	)	)	PUNCT
ejpam-411	249	25	.	.	PUNCT
ejpam-411	250	1	if	if	SCONJ
ejpam-411	250	2	the	the	DET
ejpam-411	250	3	functions	function	NOUN
ejpam-411	250	4	f	f	PROPN
ejpam-411	250	5	and	and	CCONJ
ejpam-411	250	6	g	g	PROPN
ejpam-411	250	7	of	of	ADP
ejpam-411	250	8	the	the	DET
ejpam-411	250	9	form	form	NOUN
ejpam-411	250	10	(	(	PUNCT
ejpam-411	250	11	7.1	7.1	NUM
ejpam-411	250	12	)	)	PUNCT
ejpam-411	250	13	belong	belong	VERB
ejpam-411	250	14	to	to	ADP
ejpam-411	250	15	the	the	DET
ejpam-411	250	16	class	class	NOUN
ejpam-411	250	17	t	t	PROPN
ejpam-411	250	18	w	w	PROPN
ejpam-411	250	19	η	η	PROPN
ejpam-411	250	20	�	�	PROPN
ejpam-411	250	21	φ,ϕ	φ,ϕ	PROPN
ejpam-411	250	22	;	;	PUNCT
ejpam-411	250	23	a	a	DET
ejpam-411	250	24	,	,	PUNCT
ejpam-411	250	25	b	b	NOUN
ejpam-411	250	26	;	;	PUNCT
ejpam-411	250	27	k	k	PROPN
ejpam-411	250	28	�	�	PROPN
ejpam-411	250	29	,	,	PUNCT
ejpam-411	250	30	then	then	ADV
ejpam-411	250	31	the	the	DET
ejpam-411	250	32	function	function	NOUN
ejpam-411	250	33	h(z	h(z	NOUN
ejpam-411	250	34	)	)	PUNCT
ejpam-411	250	35	given	give	VERB
ejpam-411	250	36	by	by	ADP
ejpam-411	250	37	h(z	h(z	NOUN
ejpam-411	250	38	)	)	PUNCT
ejpam-411	250	39	=	=	PUNCT
ejpam-411	250	40	z−	z−	NOUN
ejpam-411	251	1	∞∑	∞∑	ADJ
ejpam-411	251	2	n=2	n=2	PRON
ejpam-411	251	3	(	(	PUNCT
ejpam-411	251	4	�	�	PROPN
ejpam-411	251	5	�	�	PROPN
ejpam-411	251	6	an	an	DET
ejpam-411	251	7	�	�	NOUN
ejpam-411	251	8	�	�	NOUN
ejpam-411	251	9	2	2	NUM
ejpam-411	251	10	+	+	NUM
ejpam-411	251	11	�	�	PROPN
ejpam-411	251	12	�	�	PROPN
ejpam-411	251	13	bn	bn	PROPN
ejpam-411	251	14	�	�	PROPN
ejpam-411	251	15	�	�	PROPN
ejpam-411	251	16	2	2	NUM
ejpam-411	251	17	)	)	PUNCT
ejpam-411	251	18	zn	zn	PROPN
ejpam-411	251	19	(	(	PUNCT
ejpam-411	251	20	7.3	7.3	NUM
ejpam-411	251	21	)	)	PUNCT
ejpam-411	251	22	belongs	belong	VERB
ejpam-411	251	23	to	to	ADP
ejpam-411	251	24	the	the	DET
ejpam-411	251	25	class	class	NOUN
ejpam-411	251	26	t	t	PROPN
ejpam-411	251	27	w	w	PROPN
ejpam-411	251	28	0	0	PROPN
ejpam-411	251	29	�	�	PROPN
ejpam-411	251	30	φ,ϕ	φ,ϕ	PROPN
ejpam-411	251	31	;	;	PUNCT
ejpam-411	251	32	a	a	DET
ejpam-411	251	33	,	,	PUNCT
ejpam-411	251	34	b	b	NOUN
ejpam-411	251	35	;	;	PUNCT
ejpam-411	251	36	k	k	PROPN
ejpam-411	251	37	�	�	PROPN
ejpam-411	251	38	.	.	PUNCT
ejpam-411	252	1	proof	proof	NOUN
ejpam-411	252	2	.	.	PUNCT
ejpam-411	253	1	suppose	suppose	VERB
ejpam-411	253	2	that	that	SCONJ
ejpam-411	253	3	each	each	PRON
ejpam-411	253	4	of	of	ADP
ejpam-411	253	5	the	the	DET
ejpam-411	253	6	functions	function	NOUN
ejpam-411	253	7	f	f	PROPN
ejpam-411	253	8	and	and	CCONJ
ejpam-411	253	9	g	g	PROPN
ejpam-411	253	10	of	of	ADP
ejpam-411	253	11	the	the	DET
ejpam-411	253	12	form	form	NOUN
ejpam-411	253	13	(	(	PUNCT
ejpam-411	253	14	7.1	7.1	NUM
ejpam-411	253	15	)	)	PUNCT
ejpam-411	253	16	belongs	belong	VERB
ejpam-411	253	17	to	to	ADP
ejpam-411	253	18	the	the	DET
ejpam-411	253	19	class	class	NOUN
ejpam-411	253	20	t	t	PROPN
ejpam-411	253	21	w	w	PROPN
ejpam-411	253	22	η	η	PROPN
ejpam-411	253	23	�	�	PROPN
ejpam-411	253	24	φ,ϕ	φ,ϕ	PROPN
ejpam-411	253	25	;	;	PUNCT
ejpam-411	253	26	a	a	DET
ejpam-411	253	27	,	,	PUNCT
ejpam-411	253	28	b	b	NOUN
ejpam-411	253	29	;	;	PUNCT
ejpam-411	253	30	k	k	PROPN
ejpam-411	253	31	�	�	PROPN
ejpam-411	253	32	.	.	PUNCT
ejpam-411	254	1	then	then	ADV
ejpam-411	254	2	,	,	PUNCT
ejpam-411	254	3	by	by	ADP
ejpam-411	254	4	theorem	theorem	NOUN
ejpam-411	254	5	2.2	2.2	NUM
ejpam-411	254	6	,	,	PUNCT
ejpam-411	254	7	we	we	PRON
ejpam-411	254	8	have	have	VERB
ejpam-411	254	9	∞∑	∞∑	NUM
ejpam-411	254	10	n=2	n=2	X
ejpam-411	254	11	�	�	NOUN
ejpam-411	254	12	dn	dn	NOUN
ejpam-411	254	13	b	b	PROPN
ejpam-411	255	1	−	−	PROPN
ejpam-411	256	1	a	a	DET
ejpam-411	256	2	�	�	PROPN
ejpam-411	256	3	�	�	PROPN
ejpam-411	256	4	an	an	DET
ejpam-411	256	5	�	�	PROPN
ejpam-411	256	6	�	�	PROPN
ejpam-411	256	7	�	�	PROPN
ejpam-411	256	8	2	2	NUM
ejpam-411	256	9	≦	≦	NUM
ejpam-411	256	10	1	1	NUM
ejpam-411	256	11	and	and	CCONJ
ejpam-411	256	12	∞∑	∞∑	NUM
ejpam-411	256	13	n=2	n=2	PRON
ejpam-411	256	14	�	�	PROPN
ejpam-411	256	15	dn	dn	ADP
ejpam-411	256	16	b−	b−	PROPN
ejpam-411	256	17	a	a	DET
ejpam-411	256	18	�	�	PROPN
ejpam-411	256	19	�	�	PROPN
ejpam-411	256	20	bn	bn	PROPN
ejpam-411	256	21	�	�	PROPN
ejpam-411	256	22	�	�	PROPN
ejpam-411	256	23	�	�	PROPN
ejpam-411	256	24	2	2	NUM
ejpam-411	256	25	≦	≦	NUM
ejpam-411	256	26	1	1	NUM
ejpam-411	256	27	.	.	PUNCT
ejpam-411	257	1	we	we	PRON
ejpam-411	257	2	thus	thus	ADV
ejpam-411	257	3	obtain	obtain	VERB
ejpam-411	257	4	∞∑	∞∑	NUM
ejpam-411	257	5	n=2	n=2	PRON
ejpam-411	257	6	1	1	NUM
ejpam-411	257	7	2	2	NUM
ejpam-411	257	8	�	�	PROPN
ejpam-411	257	9	dn	dn	ADP
ejpam-411	257	10	b−	b−	PROPN
ejpam-411	257	11	a	a	DET
ejpam-411	257	12	�	�	PROPN
ejpam-411	257	13	2	2	NUM
ejpam-411	257	14	�	�	PROPN
ejpam-411	257	15	�	�	PROPN
ejpam-411	257	16	�	�	PROPN
ejpam-411	257	17	an	an	DET
ejpam-411	257	18	�	�	NOUN
ejpam-411	257	19	�	�	NOUN
ejpam-411	257	20	2	2	NUM
ejpam-411	257	21	+	+	NUM
ejpam-411	257	22	�	�	PROPN
ejpam-411	257	23	�	�	PROPN
ejpam-411	257	24	bn	bn	PROPN
ejpam-411	257	25	�	�	PROPN
ejpam-411	257	26	�	�	PROPN
ejpam-411	257	27	2	2	NUM
ejpam-411	257	28	�	�	PROPN
ejpam-411	257	29	≦	≦	NUM
ejpam-411	257	30	1	1	NUM
ejpam-411	257	31	.	.	PUNCT
ejpam-411	258	1	(	(	PUNCT
ejpam-411	258	2	7.4	7.4	NUM
ejpam-411	258	3	)	)	PUNCT
ejpam-411	258	4	in	in	ADP
ejpam-411	258	5	order	order	NOUN
ejpam-411	258	6	to	to	PART
ejpam-411	258	7	prove	prove	VERB
ejpam-411	258	8	that	that	SCONJ
ejpam-411	258	9	∞∑	∞∑	NUM
ejpam-411	258	10	k=2	k=2	PROPN
ejpam-411	258	11	dn	dn	PROPN
ejpam-411	258	12	b	b	PROPN
ejpam-411	258	13	−	−	PROPN
ejpam-411	258	14	a	a	DET
ejpam-411	258	15	�	�	PROPN
ejpam-411	258	16	�	�	PROPN
ejpam-411	258	17	�	�	PROPN
ejpam-411	258	18	an	an	DET
ejpam-411	258	19	�	�	NOUN
ejpam-411	258	20	�	�	NOUN
ejpam-411	258	21	2	2	NUM
ejpam-411	258	22	+	+	NUM
ejpam-411	258	23	�	�	PROPN
ejpam-411	258	24	�	�	PROPN
ejpam-411	258	25	bn	bn	PROPN
ejpam-411	258	26	�	�	PROPN
ejpam-411	258	27	�	�	PROPN
ejpam-411	258	28	2	2	NUM
ejpam-411	258	29	�	�	PROPN
ejpam-411	258	30	≦	≦	NUM
ejpam-411	258	31	1	1	NUM
ejpam-411	258	32	,	,	PUNCT
ejpam-411	258	33	by	by	ADP
ejpam-411	258	34	means	mean	NOUN
ejpam-411	258	35	of	of	ADP
ejpam-411	258	36	(	(	PUNCT
ejpam-411	258	37	7.4	7.4	NUM
ejpam-411	258	38	)	)	PUNCT
ejpam-411	258	39	,	,	PUNCT
ejpam-411	258	40	it	it	PRON
ejpam-411	258	41	is	be	AUX
ejpam-411	258	42	sufficient	sufficient	ADJ
ejpam-411	258	43	to	to	PART
ejpam-411	258	44	show	show	VERB
ejpam-411	258	45	that	that	SCONJ
ejpam-411	258	46	dn	dn	NOUN
ejpam-411	258	47	b−	b−	PROPN
ejpam-411	258	48	a	a	DET
ejpam-411	258	49	≧	≧	NUM
ejpam-411	258	50	2	2	NUM
ejpam-411	258	51	(	(	PUNCT
ejpam-411	258	52	n	n	NOUN
ejpam-411	258	53	∈	∈	PROPN
ejpam-411	258	54	n	n	CCONJ
ejpam-411	258	55	\	\	NOUN
ejpam-411	258	56	{	{	PUNCT
ejpam-411	258	57	1	1	NUM
ejpam-411	258	58	}	}	PUNCT
ejpam-411	258	59	)	)	PUNCT
ejpam-411	258	60	.	.	PUNCT
ejpam-411	259	1	since	since	SCONJ
ejpam-411	259	2	d2	d2	PROPN
ejpam-411	259	3	≧	≧	X
ejpam-411	259	4	2	2	NUM
ejpam-411	259	5	(	(	PUNCT
ejpam-411	259	6	b−	b−	NOUN
ejpam-411	259	7	a	a	PRON
ejpam-411	259	8	)	)	PUNCT
ejpam-411	259	9	,	,	PUNCT
ejpam-411	259	10	by	by	ADP
ejpam-411	259	11	hypothesis	hypothesis	NOUN
ejpam-411	259	12	,	,	PUNCT
ejpam-411	259	13	so	so	CCONJ
ejpam-411	259	14	the	the	DET
ejpam-411	259	15	last	last	ADJ
ejpam-411	259	16	inequality	inequality	NOUN
ejpam-411	259	17	follows	follow	VERB
ejpam-411	259	18	from	from	ADP
ejpam-411	259	19	(	(	PUNCT
ejpam-411	259	20	3.1	3.1	NUM
ejpam-411	259	21	)	)	PUNCT
ejpam-411	259	22	.	.	PUNCT
ejpam-411	260	1	j.	j.	PROPN
ejpam-411	260	2	dziok	dziok	PROPN
ejpam-411	260	3	and	and	CCONJ
ejpam-411	260	4	h.	h.	PROPN
ejpam-411	260	5	srivastava	srivastava	PROPN
ejpam-411	260	6	/	/	SYM
ejpam-411	260	7	eur	eur	PROPN
ejpam-411	260	8	.	.	PUNCT
ejpam-411	261	1	j.	j.	PROPN
ejpam-411	261	2	pure	pure	PROPN
ejpam-411	261	3	appl	appl	PROPN
ejpam-411	261	4	.	.	PROPN
ejpam-411	261	5	math	math	PROPN
ejpam-411	261	6	,	,	PUNCT
ejpam-411	261	7	2	2	NUM
ejpam-411	261	8	(	(	PUNCT
ejpam-411	261	9	2009	2009	NUM
ejpam-411	261	10	)	)	PUNCT
ejpam-411	261	11	,	,	PUNCT
ejpam-411	261	12	(	(	PUNCT
ejpam-411	261	13	302	302	NUM
ejpam-411	261	14	-	-	SYM
ejpam-411	261	15	324	324	NUM
ejpam-411	261	16	)	)	PUNCT
ejpam-411	261	17	319	319	NUM
ejpam-411	261	18	8	8	NUM
ejpam-411	261	19	.	.	PUNCT
ejpam-411	261	20	concluding	conclude	VERB
ejpam-411	261	21	remarks	remark	NOUN
ejpam-411	261	22	and	and	CCONJ
ejpam-411	261	23	observations	observation	NOUN
ejpam-411	261	24	we	we	PRON
ejpam-411	261	25	conclude	conclude	VERB
ejpam-411	261	26	this	this	DET
ejpam-411	261	27	paper	paper	NOUN
ejpam-411	261	28	by	by	ADP
ejpam-411	261	29	observing	observe	VERB
ejpam-411	261	30	that	that	SCONJ
ejpam-411	261	31	,	,	PUNCT
ejpam-411	261	32	in	in	ADP
ejpam-411	261	33	view	view	NOUN
ejpam-411	261	34	of	of	ADP
ejpam-411	261	35	the	the	DET
ejpam-411	261	36	subordination	subordination	NOUN
ejpam-411	261	37	relation	relation	NOUN
ejpam-411	261	38	(	(	PUNCT
ejpam-411	261	39	1.6	1.6	NUM
ejpam-411	261	40	)	)	PUNCT
ejpam-411	261	41	,	,	PUNCT
ejpam-411	261	42	by	by	ADP
ejpam-411	261	43	suitably	suitably	ADV
ejpam-411	261	44	choosing	choose	VERB
ejpam-411	261	45	the	the	DET
ejpam-411	261	46	functions	function	NOUN
ejpam-411	261	47	φ	φ	PROPN
ejpam-411	261	48	and	and	CCONJ
ejpam-411	261	49	ϕ	ϕ	PROPN
ejpam-411	261	50	,	,	PUNCT
ejpam-411	261	51	we	we	PRON
ejpam-411	261	52	can	can	AUX
ejpam-411	261	53	consider	consider	VERB
ejpam-411	261	54	various	various	ADJ
ejpam-411	261	55	new	new	ADJ
ejpam-411	261	56	or	or	CCONJ
ejpam-411	261	57	known	known	ADJ
ejpam-411	261	58	classes	class	NOUN
ejpam-411	261	59	of	of	ADP
ejpam-411	261	60	functions	function	NOUN
ejpam-411	261	61	.	.	PUNCT
ejpam-411	262	1	let	let	VERB
ejpam-411	262	2	wn	wn	PROPN
ejpam-411	262	3	�	�	PROPN
ejpam-411	262	4	ϕ	ϕ	PROPN
ejpam-411	262	5	;	;	PUNCT
ejpam-411	262	6	a	a	DET
ejpam-411	262	7	,	,	PUNCT
ejpam-411	262	8	b	b	NOUN
ejpam-411	262	9	;	;	PUNCT
ejpam-411	262	10	k	k	PROPN
ejpam-411	262	11	�	�	PROPN
ejpam-411	262	12	:	:	PUNCT
ejpam-411	263	1	=	=	X
ejpam-411	263	2	w	w	NOUN
ejpam-411	263	3	zϕ′	zϕ′	X
ejpam-411	263	4	(	(	PUNCT
ejpam-411	263	5	z	z	NOUN
ejpam-411	263	6	)	)	PUNCT
ejpam-411	263	7	,	,	PUNCT
ejpam-411	263	8	n−1∑	n−1∑	PROPN
ejpam-411	263	9	k=0	k=0	PROPN
ejpam-411	263	10	ϕ	ϕ	PROPN
ejpam-411	263	11	�	�	PROPN
ejpam-411	263	12	x	x	SYM
ejpam-411	263	13	kz	kz	PROPN
ejpam-411	263	14	�	�	PROPN
ejpam-411	263	15	;	;	PUNCT
ejpam-411	263	16	a	a	DET
ejpam-411	263	17	,	,	PUNCT
ejpam-411	263	18	b	b	NOUN
ejpam-411	263	19	;	;	PUNCT
ejpam-411	263	20	k	k	X
ejpam-411	263	21	!	!	PUNCT
ejpam-411	264	1	(	(	PUNCT
ejpam-411	264	2	n	n	X
ejpam-411	264	3	∈	∈	PROPN
ejpam-411	264	4	n	n	CCONJ
ejpam-411	264	5	;	;	PUNCT
ejpam-411	264	6	x	x	SYM
ejpam-411	264	7	=	=	PUNCT
ejpam-411	264	8	e	e	NOUN
ejpam-411	264	9	2πi	2πi	NOUN
ejpam-411	264	10	n	n	CCONJ
ejpam-411	264	11	)	)	PUNCT
ejpam-411	264	12	.	.	PUNCT
ejpam-411	265	1	in	in	ADP
ejpam-411	265	2	particular	particular	ADJ
ejpam-411	265	3	,	,	PUNCT
ejpam-411	265	4	the	the	DET
ejpam-411	265	5	class	class	NOUN
ejpam-411	265	6	wn	wn	PROPN
ejpam-411	265	7	�	�	PROPN
ejpam-411	265	8	ϕ	ϕ	PROPN
ejpam-411	265	9	;	;	PUNCT
ejpam-411	265	10	a	a	DET
ejpam-411	265	11	,	,	PUNCT
ejpam-411	265	12	b	b	PROPN
ejpam-411	265	13	�	�	PROPN
ejpam-411	265	14	:	:	PUNCT
ejpam-411	265	15	=	=	NUM
ejpam-411	265	16	wn	wn	PROPN
ejpam-411	265	17	�	�	PROPN
ejpam-411	265	18	ϕ	ϕ	PROPN
ejpam-411	265	19	;	;	PUNCT
ejpam-411	265	20	a	a	DET
ejpam-411	265	21	,	,	PUNCT
ejpam-411	265	22	b	b	NOUN
ejpam-411	265	23	;	;	PUNCT
ejpam-411	265	24	0	0	NUM
ejpam-411	265	25	�	�	PROPN
ejpam-411	265	26	consists	consist	VERB
ejpam-411	265	27	of	of	ADP
ejpam-411	265	28	functions	function	NOUN
ejpam-411	265	29	f	f	PROPN
ejpam-411	265	30	∈a	∈a	PROPN
ejpam-411	265	31	,	,	PUNCT
ejpam-411	265	32	which	which	PRON
ejpam-411	265	33	satisfy	satisfy	VERB
ejpam-411	265	34	the	the	DET
ejpam-411	265	35	following	follow	VERB
ejpam-411	265	36	subordination	subordination	NOUN
ejpam-411	265	37	condition	condition	NOUN
ejpam-411	265	38	:	:	PUNCT
ejpam-411	266	1	z	z	PROPN
ejpam-411	266	2	�	�	PROPN
ejpam-411	266	3	ϕ	ϕ	PROPN
ejpam-411	266	4	∗	∗	X
ejpam-411	266	5	f	f	PROPN
ejpam-411	266	6	�	�	PROPN
ejpam-411	266	7	′	′	PROPN
ejpam-411	266	8	(	(	PUNCT
ejpam-411	266	9	z	z	NOUN
ejpam-411	266	10	)	)	PUNCT
ejpam-411	266	11	n−1∑	n−1∑	PROPN
ejpam-411	266	12	k=0	k=0	PROPN
ejpam-411	266	13	�	�	PROPN
ejpam-411	266	14	ϕ	ϕ	PROPN
ejpam-411	266	15	∗	∗	X
ejpam-411	266	16	f	f	PROPN
ejpam-411	266	17	�	�	PROPN
ejpam-411	266	18	�	�	PROPN
ejpam-411	266	19	x	x	SYM
ejpam-411	266	20	kz	kz	PROPN
ejpam-411	266	21	�	�	PROPN
ejpam-411	266	22	≺	≺	VERB
ejpam-411	266	23	1	1	NUM
ejpam-411	266	24	+	+	NUM
ejpam-411	266	25	az	az	PROPN
ejpam-411	266	26	1	1	NUM
ejpam-411	266	27	+	+	CCONJ
ejpam-411	266	28	bz	bz	PROPN
ejpam-411	266	29	.	.	PUNCT
ejpam-411	267	1	it	it	PRON
ejpam-411	267	2	is	be	AUX
ejpam-411	267	3	related	relate	VERB
ejpam-411	267	4	to	to	ADP
ejpam-411	267	5	the	the	DET
ejpam-411	267	6	class	class	NOUN
ejpam-411	267	7	of	of	ADP
ejpam-411	267	8	starlike	starlike	NOUN
ejpam-411	267	9	functions	function	NOUN
ejpam-411	267	10	with	with	ADP
ejpam-411	267	11	respect	respect	NOUN
ejpam-411	267	12	to	to	ADP
ejpam-411	267	13	n	n	CCONJ
ejpam-411	267	14	-	-	PUNCT
ejpam-411	267	15	symmetric	symmetric	ADJ
ejpam-411	267	16	points	point	NOUN
ejpam-411	267	17	.	.	PUNCT
ejpam-411	268	1	moreover	moreover	ADV
ejpam-411	268	2	,	,	PUNCT
ejpam-411	268	3	by	by	ADP
ejpam-411	268	4	putting	put	VERB
ejpam-411	268	5	n	n	X
ejpam-411	268	6	=	=	SYM
ejpam-411	268	7	1	1	NUM
ejpam-411	268	8	,	,	PUNCT
ejpam-411	268	9	we	we	PRON
ejpam-411	268	10	obtain	obtain	VERB
ejpam-411	268	11	the	the	DET
ejpam-411	268	12	class	class	NOUN
ejpam-411	268	13	w	w	PROPN
ejpam-411	268	14	�	�	PROPN
ejpam-411	268	15	ϕ	ϕ	PROPN
ejpam-411	268	16	;	;	PUNCT
ejpam-411	268	17	a	a	DET
ejpam-411	268	18	,	,	PUNCT
ejpam-411	268	19	b	b	PROPN
ejpam-411	268	20	�	�	PROPN
ejpam-411	268	21	:	:	PUNCT
ejpam-411	268	22	=	=	NOUN
ejpam-411	268	23	w1	w1	PROPN
ejpam-411	268	24	�	�	PROPN
ejpam-411	268	25	ϕ	ϕ	PROPN
ejpam-411	268	26	;	;	PUNCT
ejpam-411	268	27	a	a	DET
ejpam-411	268	28	,	,	PUNCT
ejpam-411	268	29	b	b	X
ejpam-411	268	30	�	�	PROPN
ejpam-411	268	31	defined	define	VERB
ejpam-411	268	32	by	by	ADP
ejpam-411	268	33	the	the	DET
ejpam-411	268	34	following	follow	VERB
ejpam-411	268	35	subordination	subordination	NOUN
ejpam-411	268	36	condition	condition	NOUN
ejpam-411	268	37	:	:	PUNCT
ejpam-411	268	38	z	z	PROPN
ejpam-411	268	39	�	�	PROPN
ejpam-411	269	1	ϕ	ϕ	PROPN
ejpam-411	269	2	∗	∗	X
ejpam-411	269	3	f	f	PROPN
ejpam-411	269	4	�	�	PROPN
ejpam-411	269	5	′	′	PROPN
ejpam-411	269	6	(	(	PUNCT
ejpam-411	269	7	z	z	NOUN
ejpam-411	269	8	)	)	PUNCT
ejpam-411	269	9	�	�	PROPN
ejpam-411	269	10	ϕ	ϕ	PROPN
ejpam-411	269	11	∗	∗	X
ejpam-411	269	12	f	f	PROPN
ejpam-411	269	13	�	�	PROPN
ejpam-411	269	14	(	(	PUNCT
ejpam-411	269	15	z	z	NOUN
ejpam-411	269	16	)	)	PUNCT
ejpam-411	269	17	≺	≺	NOUN
ejpam-411	269	18	1	1	NUM
ejpam-411	269	19	+	+	NUM
ejpam-411	269	20	az	az	PROPN
ejpam-411	269	21	1	1	NUM
ejpam-411	269	22	+	+	CCONJ
ejpam-411	269	23	bz	bz	PROPN
ejpam-411	269	24	.	.	PUNCT
ejpam-411	270	1	this	this	DET
ejpam-411	270	2	class	class	NOUN
ejpam-411	270	3	is	be	AUX
ejpam-411	270	4	related	relate	VERB
ejpam-411	270	5	to	to	ADP
ejpam-411	270	6	the	the	DET
ejpam-411	270	7	familiar	familiar	ADJ
ejpam-411	270	8	class	class	NOUN
ejpam-411	270	9	of	of	ADP
ejpam-411	270	10	starlike	starlike	NOUN
ejpam-411	270	11	functions	function	NOUN
ejpam-411	270	12	.	.	PUNCT
ejpam-411	271	1	analogously	analogously	ADV
ejpam-411	271	2	,	,	PUNCT
ejpam-411	271	3	the	the	DET
ejpam-411	271	4	class	class	NOUN
ejpam-411	271	5	defined	define	VERB
ejpam-411	271	6	by	by	ADP
ejpam-411	271	7	hn	hn	PROPN
ejpam-411	271	8	�	�	PROPN
ejpam-411	271	9	ϕ;γ	ϕ;γ	PROPN
ejpam-411	271	10	,	,	PUNCT
ejpam-411	271	11	k	k	PROPN
ejpam-411	271	12	�	�	PROPN
ejpam-411	271	13	:	:	PUNCT
ejpam-411	271	14	=	=	NUM
ejpam-411	271	15	wn	wn	PROPN
ejpam-411	271	16	�	�	PROPN
ejpam-411	271	17	ϕ	ϕ	PROPN
ejpam-411	271	18	;	;	PUNCT
ejpam-411	271	19	2γ−	2γ−	NUM
ejpam-411	271	20	1	1	NUM
ejpam-411	271	21	,	,	PUNCT
ejpam-411	271	22	1	1	NUM
ejpam-411	271	23	;	;	PUNCT
ejpam-411	271	24	k	k	PROPN
ejpam-411	271	25	�	�	PROPN
ejpam-411	271	26	�	�	PROPN
ejpam-411	271	27	0	0	NUM
ejpam-411	271	28	≦	≦	VERB
ejpam-411	271	29	γ	γ	X
ejpam-411	271	30	<	<	X
ejpam-411	271	31	1	1	NUM
ejpam-411	271	32	�	�	PROPN
ejpam-411	271	33	consists	consist	VERB
ejpam-411	271	34	of	of	ADP
ejpam-411	271	35	functions	function	NOUN
ejpam-411	271	36	f	f	PROPN
ejpam-411	271	37	∈a	∈a	PROPN
ejpam-411	271	38	,	,	PUNCT
ejpam-411	271	39	which	which	PRON
ejpam-411	271	40	satisfy	satisfy	VERB
ejpam-411	271	41	the	the	DET
ejpam-411	271	42	following	follow	VERB
ejpam-411	271	43	condition	condition	NOUN
ejpam-411	271	44	:	:	PUNCT
ejpam-411	271	45	ℜ	ℜ	ADJ
ejpam-411	271	46			NOUN
ejpam-411	272	1			PROPN
ejpam-411	272	2	z	z	PROPN
ejpam-411	272	3	�	�	PROPN
ejpam-411	272	4	ϕ	ϕ	PROPN
ejpam-411	272	5	∗	∗	X
ejpam-411	272	6	f	f	PROPN
ejpam-411	272	7	�	�	PROPN
ejpam-411	272	8	′	′	PROPN
ejpam-411	272	9	(	(	PUNCT
ejpam-411	272	10	z	z	NOUN
ejpam-411	272	11	)	)	PUNCT
ejpam-411	272	12	n−1∑	n−1∑	PROPN
ejpam-411	272	13	k=0	k=0	PROPN
ejpam-411	272	14	�	�	PROPN
ejpam-411	272	15	ϕ	ϕ	PROPN
ejpam-411	272	16	∗	∗	X
ejpam-411	272	17	f	f	PROPN
ejpam-411	272	18	�	�	PROPN
ejpam-411	272	19	�	�	PROPN
ejpam-411	272	20	x	x	SYM
ejpam-411	272	21	kz	kz	PROPN
ejpam-411	272	22	�	�	PROPN
ejpam-411	273	1	−	−	PROPN
ejpam-411	273	2	γ	γ	X
ejpam-411	273	3			NOUN
ejpam-411	274	1			NUM
ejpam-411	274	2	>	>	X
ejpam-411	274	3	k	k	PROPN
ejpam-411	274	4	�	�	PROPN
ejpam-411	274	5	�	�	PROPN
ejpam-411	274	6	�	�	PROPN
ejpam-411	274	7	�	�	PROPN
ejpam-411	274	8	�	�	PROPN
ejpam-411	274	9	�	�	PROPN
ejpam-411	274	10	�	�	PROPN
ejpam-411	274	11	�	�	PROPN
ejpam-411	274	12	�	�	PROPN
ejpam-411	274	13	z	z	PROPN
ejpam-411	274	14	�	�	PROPN
ejpam-411	274	15	ϕ	ϕ	PROPN
ejpam-411	274	16	∗	∗	X
ejpam-411	274	17	f	f	PROPN
ejpam-411	274	18	�	�	PROPN
ejpam-411	274	19	′	′	PROPN
ejpam-411	274	20	(	(	PUNCT
ejpam-411	274	21	z	z	NOUN
ejpam-411	274	22	)	)	PUNCT
ejpam-411	274	23	n−1∑	n−1∑	PROPN
ejpam-411	274	24	k=0	k=0	PROPN
ejpam-411	274	25	�	�	PROPN
ejpam-411	274	26	ϕ	ϕ	PROPN
ejpam-411	274	27	∗	∗	X
ejpam-411	274	28	f	f	PROPN
ejpam-411	274	29	�	�	PROPN
ejpam-411	274	30	�	�	PROPN
ejpam-411	274	31	x	x	SYM
ejpam-411	274	32	kz	kz	PROPN
ejpam-411	274	33	�	�	PROPN
ejpam-411	274	34	−	−	PROPN
ejpam-411	274	35	1	1	NUM
ejpam-411	274	36	�	�	PROPN
ejpam-411	274	37	�	�	PROPN
ejpam-411	274	38	�	�	PROPN
ejpam-411	274	39	�	�	PROPN
ejpam-411	274	40	�	�	PROPN
ejpam-411	274	41	�	�	PROPN
ejpam-411	274	42	�	�	PROPN
ejpam-411	274	43	�	�	PROPN
ejpam-411	274	44	�	�	PROPN
ejpam-411	274	45	(	(	PUNCT
ejpam-411	274	46	z	z	NOUN
ejpam-411	274	47	∈	∈	PROPN
ejpam-411	274	48	u	u	NOUN
ejpam-411	274	49	)	)	PUNCT
ejpam-411	274	50	.	.	PUNCT
ejpam-411	275	1	j.	j.	PROPN
ejpam-411	275	2	dziok	dziok	PROPN
ejpam-411	275	3	and	and	CCONJ
ejpam-411	275	4	h.	h.	PROPN
ejpam-411	275	5	srivastava	srivastava	PROPN
ejpam-411	275	6	/	/	SYM
ejpam-411	275	7	eur	eur	PROPN
ejpam-411	275	8	.	.	PUNCT
ejpam-411	276	1	j.	j.	PROPN
ejpam-411	276	2	pure	pure	PROPN
ejpam-411	276	3	appl	appl	PROPN
ejpam-411	276	4	.	.	PROPN
ejpam-411	276	5	math	math	PROPN
ejpam-411	276	6	,	,	PUNCT
ejpam-411	276	7	2	2	NUM
ejpam-411	276	8	(	(	PUNCT
ejpam-411	276	9	2009	2009	NUM
ejpam-411	276	10	)	)	PUNCT
ejpam-411	276	11	,	,	PUNCT
ejpam-411	276	12	(	(	PUNCT
ejpam-411	276	13	302	302	NUM
ejpam-411	276	14	-	-	SYM
ejpam-411	276	15	324	324	NUM
ejpam-411	276	16	)	)	PUNCT
ejpam-411	276	17	320	320	NUM
ejpam-411	276	18	it	it	PRON
ejpam-411	276	19	is	be	AUX
ejpam-411	276	20	related	relate	VERB
ejpam-411	276	21	to	to	ADP
ejpam-411	276	22	the	the	DET
ejpam-411	276	23	class	class	NOUN
ejpam-411	276	24	of	of	ADP
ejpam-411	276	25	k	k	NOUN
ejpam-411	276	26	-	-	ADJ
ejpam-411	276	27	uniformly	uniformly	ADJ
ejpam-411	276	28	convex	convex	NOUN
ejpam-411	276	29	functions	function	NOUN
ejpam-411	276	30	of	of	ADP
ejpam-411	276	31	order	order	NOUN
ejpam-411	276	32	γ	γ	NOUN
ejpam-411	276	33	with	with	ADP
ejpam-411	276	34	respect	respect	NOUN
ejpam-411	276	35	to	to	ADP
ejpam-411	276	36	n	n	CCONJ
ejpam-411	276	37	-	-	PUNCT
ejpam-411	276	38	symmetric	symmetric	ADJ
ejpam-411	276	39	points	point	NOUN
ejpam-411	276	40	.	.	PUNCT
ejpam-411	277	1	moreover	moreover	ADV
ejpam-411	277	2	,	,	PUNCT
ejpam-411	277	3	by	by	ADP
ejpam-411	277	4	setting	set	VERB
ejpam-411	277	5	n	n	X
ejpam-411	277	6	=	=	SYM
ejpam-411	277	7	1	1	NUM
ejpam-411	277	8	,	,	PUNCT
ejpam-411	277	9	we	we	PRON
ejpam-411	277	10	obtain	obtain	VERB
ejpam-411	277	11	the	the	DET
ejpam-411	277	12	function	function	NOUN
ejpam-411	277	13	class	class	NOUN
ejpam-411	277	14	h	h	PROPN
ejpam-411	277	15	�	�	PROPN
ejpam-411	278	1	ϕ;γ	ϕ;γ	PROPN
ejpam-411	278	2	,	,	PUNCT
ejpam-411	278	3	k	k	PROPN
ejpam-411	278	4	�	�	PROPN
ejpam-411	278	5	:	:	PUNCT
ejpam-411	278	6	=	=	SYM
ejpam-411	278	7	h1	h1	PROPN
ejpam-411	278	8	�	�	PROPN
ejpam-411	278	9	ϕ;γ	ϕ;γ	PROPN
ejpam-411	278	10	,	,	PUNCT
ejpam-411	278	11	k	k	PROPN
ejpam-411	278	12	�	�	PROPN
ejpam-411	278	13	,	,	PUNCT
ejpam-411	278	14	which	which	PRON
ejpam-411	278	15	is	be	AUX
ejpam-411	278	16	defined	define	VERB
ejpam-411	278	17	by	by	ADP
ejpam-411	278	18	the	the	DET
ejpam-411	278	19	following	follow	VERB
ejpam-411	278	20	condition	condition	NOUN
ejpam-411	278	21	:	:	PUNCT
ejpam-411	278	22	ℜ	ℜ	PROPN
ejpam-411	278	23	�	�	PROPN
ejpam-411	278	24	z	z	PROPN
ejpam-411	278	25	�	�	PROPN
ejpam-411	278	26	ϕ	ϕ	PROPN
ejpam-411	278	27	∗	∗	X
ejpam-411	278	28	f	f	PROPN
ejpam-411	278	29	�	�	PROPN
ejpam-411	278	30	′	′	PROPN
ejpam-411	278	31	(	(	PUNCT
ejpam-411	278	32	z	z	NOUN
ejpam-411	278	33	)	)	PUNCT
ejpam-411	278	34	�	�	PROPN
ejpam-411	278	35	ϕ	ϕ	PROPN
ejpam-411	278	36	∗	∗	X
ejpam-411	278	37	f	f	PROPN
ejpam-411	278	38	�	�	PROPN
ejpam-411	278	39	(	(	PUNCT
ejpam-411	278	40	z	z	NOUN
ejpam-411	278	41	)	)	PUNCT
ejpam-411	278	42	−	−	PROPN
ejpam-411	278	43	γ	γ	PROPN
ejpam-411	278	44	�	�	PROPN
ejpam-411	278	45	>	>	X
ejpam-411	278	46	k	k	PROPN
ejpam-411	278	47	�	�	PROPN
ejpam-411	278	48	�	�	PROPN
ejpam-411	278	49	�	�	PROPN
ejpam-411	278	50	�	�	PROPN
ejpam-411	278	51	�	�	PROPN
ejpam-411	278	52	z	z	PROPN
ejpam-411	278	53	�	�	PROPN
ejpam-411	278	54	ϕ	ϕ	PROPN
ejpam-411	278	55	∗	∗	X
ejpam-411	278	56	f	f	PROPN
ejpam-411	278	57	�	�	PROPN
ejpam-411	278	58	′	′	PROPN
ejpam-411	278	59	(	(	PUNCT
ejpam-411	278	60	z	z	NOUN
ejpam-411	278	61	)	)	PUNCT
ejpam-411	278	62	�	�	PROPN
ejpam-411	278	63	ϕ	ϕ	PROPN
ejpam-411	278	64	∗	∗	X
ejpam-411	278	65	f	f	PROPN
ejpam-411	278	66	�	�	PROPN
ejpam-411	278	67	(	(	PUNCT
ejpam-411	278	68	z	z	NOUN
ejpam-411	278	69	)	)	PUNCT
ejpam-411	278	70	−	−	PROPN
ejpam-411	278	71	1	1	NUM
ejpam-411	278	72	�	�	PROPN
ejpam-411	278	73	�	�	PROPN
ejpam-411	278	74	�	�	PROPN
ejpam-411	278	75	�	�	PROPN
ejpam-411	278	76	�	�	PROPN
ejpam-411	278	77	(	(	PUNCT
ejpam-411	278	78	z	z	NOUN
ejpam-411	278	79	∈	∈	PROPN
ejpam-411	278	80	u	u	NOUN
ejpam-411	278	81	)	)	PUNCT
ejpam-411	278	82	.	.	PUNCT
ejpam-411	279	1	this	this	DET
ejpam-411	279	2	class	class	NOUN
ejpam-411	279	3	is	be	AUX
ejpam-411	279	4	related	relate	VERB
ejpam-411	279	5	to	to	ADP
ejpam-411	279	6	the	the	DET
ejpam-411	279	7	class	class	NOUN
ejpam-411	279	8	of	of	ADP
ejpam-411	279	9	k	k	NOUN
ejpam-411	279	10	-	-	ADJ
ejpam-411	279	11	uniformly	uniformly	ADJ
ejpam-411	279	12	convex	convex	NOUN
ejpam-411	279	13	functions	function	NOUN
ejpam-411	279	14	of	of	ADP
ejpam-411	279	15	order	order	NOUN
ejpam-411	279	16	γ	γ	X
ejpam-411	279	17	.	.	PUNCT
ejpam-411	280	1	the	the	DET
ejpam-411	280	2	function	function	NOUN
ejpam-411	280	3	classes	class	NOUN
ejpam-411	280	4	ust	ust	PROPN
ejpam-411	280	5	�	�	PROPN
ejpam-411	280	6	γ	γ	PROPN
ejpam-411	280	7	,	,	PUNCT
ejpam-411	280	8	k	k	PROPN
ejpam-411	280	9	�	�	PROPN
ejpam-411	280	10	:	:	PUNCT
ejpam-411	280	11	=	=	NUM
ejpam-411	280	12	h	h	NOUN
ejpam-411	280	13	�	�	PROPN
ejpam-411	280	14	z	z	PROPN
ejpam-411	280	15	1−	1−	NUM
ejpam-411	280	16	z	z	NOUN
ejpam-411	280	17	;	;	PUNCT
ejpam-411	280	18	γ	γ	X
ejpam-411	280	19	,	,	PUNCT
ejpam-411	280	20	k	k	PROPN
ejpam-411	280	21	�	�	PROPN
ejpam-411	280	22	and	and	CCONJ
ejpam-411	280	23	ucv	ucv	PROPN
ejpam-411	280	24	�	�	PROPN
ejpam-411	280	25	γ	γ	PROPN
ejpam-411	280	26	,	,	PUNCT
ejpam-411	280	27	k	k	PROPN
ejpam-411	280	28	�	�	PROPN
ejpam-411	280	29	:	:	PUNCT
ejpam-411	280	30	=	=	NUM
ejpam-411	280	31	h	h	NOUN
ejpam-411	280	32	�	�	PROPN
ejpam-411	280	33	z	z	PROPN
ejpam-411	280	34	(	(	PUNCT
ejpam-411	280	35	1−	1−	NUM
ejpam-411	280	36	z	z	NOUN
ejpam-411	280	37	)	)	PUNCT
ejpam-411	280	38	2	2	NUM
ejpam-411	280	39	;	;	PUNCT
ejpam-411	280	40	γ	γ	X
ejpam-411	280	41	,	,	PUNCT
ejpam-411	280	42	k	k	PROPN
ejpam-411	280	43	�	�	PROPN
ejpam-411	280	44	are	be	AUX
ejpam-411	280	45	the	the	DET
ejpam-411	280	46	well	well	ADV
ejpam-411	280	47	-	-	PUNCT
ejpam-411	280	48	known	know	VERB
ejpam-411	280	49	classes	class	NOUN
ejpam-411	280	50	of	of	ADP
ejpam-411	280	51	of	of	ADP
ejpam-411	280	52	k	k	ADJ
ejpam-411	280	53	-	-	ADJ
ejpam-411	280	54	starlike	starlike	ADJ
ejpam-411	280	55	functions	function	NOUN
ejpam-411	280	56	of	of	ADP
ejpam-411	280	57	order	order	NOUN
ejpam-411	280	58	γ	γ	X
ejpam-411	280	59	and	and	CCONJ
ejpam-411	280	60	k	k	ADV
ejpam-411	280	61	-	-	ADJ
ejpam-411	280	62	uniformly	uniformly	ADJ
ejpam-411	280	63	convex	convex	NOUN
ejpam-411	280	64	functions	function	NOUN
ejpam-411	280	65	of	of	ADP
ejpam-411	280	66	order	order	NOUN
ejpam-411	280	67	γ	γ	NOUN
ejpam-411	280	68	,	,	PUNCT
ejpam-411	280	69	respectively	respectively	ADV
ejpam-411	280	70	.	.	PUNCT
ejpam-411	281	1	in	in	ADP
ejpam-411	281	2	particular	particular	ADJ
ejpam-411	281	3	,	,	PUNCT
ejpam-411	281	4	the	the	DET
ejpam-411	281	5	function	function	NOUN
ejpam-411	281	6	classes	class	NOUN
ejpam-411	281	7	ucv	ucv	NOUN
ejpam-411	281	8	:	:	PUNCT
ejpam-411	281	9	=	=	PROPN
ejpam-411	281	10	ucv	ucv	PROPN
ejpam-411	281	11	(	(	PUNCT
ejpam-411	281	12	1	1	NUM
ejpam-411	281	13	,	,	PUNCT
ejpam-411	281	14	0	0	NUM
ejpam-411	281	15	)	)	PUNCT
ejpam-411	281	16	and	and	CCONJ
ejpam-411	281	17	k−	k−	PROPN
ejpam-411	281	18	ucv	ucv	PROPN
ejpam-411	281	19	:	:	PUNCT
ejpam-411	281	20	=	=	PROPN
ejpam-411	281	21	ucv	ucv	PROPN
ejpam-411	281	22	(	(	PUNCT
ejpam-411	281	23	k	k	PROPN
ejpam-411	281	24	,	,	PUNCT
ejpam-411	281	25	0	0	NUM
ejpam-411	281	26	)	)	PUNCT
ejpam-411	281	27	were	be	AUX
ejpam-411	281	28	introduced	introduce	VERB
ejpam-411	281	29	by	by	ADP
ejpam-411	281	30	goodman	goodman	PROPN
ejpam-411	281	31	[	[	X
ejpam-411	281	32	8	8	NUM
ejpam-411	281	33	]	]	PUNCT
ejpam-411	281	34	(	(	PUNCT
ejpam-411	281	35	see	see	VERB
ejpam-411	281	36	also	also	ADV
ejpam-411	281	37	[	[	X
ejpam-411	281	38	14	14	NUM
ejpam-411	281	39	]	]	PUNCT
ejpam-411	281	40	and	and	CCONJ
ejpam-411	281	41	[	[	X
ejpam-411	281	42	22	22	NUM
ejpam-411	281	43	]	]	PUNCT
ejpam-411	281	44	)	)	PUNCT
ejpam-411	281	45	and	and	CCONJ
ejpam-411	281	46	kanas	kanas	PROPN
ejpam-411	281	47	et	et	PROPN
ejpam-411	281	48	al	al	PROPN
ejpam-411	281	49	.	.	PUNCT
ejpam-411	282	1	(	(	PUNCT
ejpam-411	282	2	[	[	X
ejpam-411	282	3	10	10	NUM
ejpam-411	282	4	]	]	PUNCT
ejpam-411	282	5	and	and	CCONJ
ejpam-411	282	6	[	[	X
ejpam-411	282	7	9	9	NUM
ejpam-411	282	8	]	]	NUM
ejpam-411	282	9	)	)	PUNCT
ejpam-411	282	10	,	,	PUNCT
ejpam-411	282	11	respectively	respectively	ADV
ejpam-411	282	12	(	(	PUNCT
ejpam-411	282	13	see	see	VERB
ejpam-411	282	14	also	also	ADV
ejpam-411	282	15	[	[	X
ejpam-411	282	16	7	7	NUM
ejpam-411	282	17	]	]	PUNCT
ejpam-411	282	18	,	,	PUNCT
ejpam-411	282	19	[	[	X
ejpam-411	282	20	20	20	NUM
ejpam-411	282	21	]	]	PUNCT
ejpam-411	282	22	,	,	PUNCT
ejpam-411	282	23	[	[	X
ejpam-411	282	24	21	21	NUM
ejpam-411	282	25	]	]	PUNCT
ejpam-411	282	26	,	,	PUNCT
ejpam-411	282	27	[	[	X
ejpam-411	282	28	33	33	NUM
ejpam-411	282	29	]	]	PUNCT
ejpam-411	282	30	,	,	PUNCT
ejpam-411	282	31	[	[	X
ejpam-411	282	32	34	34	NUM
ejpam-411	282	33	]	]	PUNCT
ejpam-411	282	34	and	and	CCONJ
ejpam-411	282	35	[	[	X
ejpam-411	282	36	35	35	NUM
ejpam-411	282	37	]	]	PUNCT
ejpam-411	282	38	)	)	PUNCT
ejpam-411	282	39	.	.	PUNCT
ejpam-411	283	1	we	we	PRON
ejpam-411	283	2	note	note	VERB
ejpam-411	283	3	that	that	SCONJ
ejpam-411	283	4	the	the	DET
ejpam-411	283	5	following	follow	VERB
ejpam-411	283	6	function	function	NOUN
ejpam-411	283	7	class	class	NOUN
ejpam-411	283	8	:	:	PUNCT
ejpam-411	283	9	ht	ht	PROPN
ejpam-411	283	10	�	�	PROPN
ejpam-411	283	11	ϕ;γ	ϕ;γ	PROPN
ejpam-411	283	12	,	,	PUNCT
ejpam-411	283	13	k	k	PROPN
ejpam-411	283	14	�	�	PROPN
ejpam-411	283	15	:	:	PUNCT
ejpam-411	283	16	=	=	SYM
ejpam-411	283	17	t0	t0	PROPN
ejpam-411	283	18	∩h	∩h	PROPN
ejpam-411	283	19	�	�	PROPN
ejpam-411	283	20	ϕ;γ	ϕ;γ	PROPN
ejpam-411	283	21	,	,	PUNCT
ejpam-411	283	22	k	k	PROPN
ejpam-411	283	23	�	�	PROPN
ejpam-411	283	24	was	be	AUX
ejpam-411	283	25	investigated	investigate	VERB
ejpam-411	283	26	recently	recently	ADV
ejpam-411	283	27	by	by	ADP
ejpam-411	283	28	raina	raina	PROPN
ejpam-411	283	29	and	and	CCONJ
ejpam-411	283	30	bansal	bansal	NOUN
ejpam-411	283	31	[	[	X
ejpam-411	283	32	19	19	NUM
ejpam-411	283	33	]	]	PUNCT
ejpam-411	283	34	.	.	PUNCT
ejpam-411	284	1	if	if	SCONJ
ejpam-411	284	2	we	we	PRON
ejpam-411	284	3	set	set	VERB
ejpam-411	284	4	h(α1	h(α1	NOUN
ejpam-411	284	5	,	,	PUNCT
ejpam-411	284	6	z	z	NOUN
ejpam-411	284	7	)	)	PUNCT
ejpam-411	284	8	:	:	PUNCT
ejpam-411	285	1	=	=	PUNCT
ejpam-411	285	2	z	z	NOUN
ejpam-411	285	3	q	q	NOUN
ejpam-411	285	4	fs(α1	fs(α1	NOUN
ejpam-411	285	5	,	,	PUNCT
ejpam-411	285	6	·	·	PUNCT
ejpam-411	285	7	·	·	PUNCT
ejpam-411	285	8	·	·	PUNCT
ejpam-411	285	9	,	,	PUNCT
ejpam-411	285	10	αq;β1	αq;β1	NOUN
ejpam-411	285	11	,	,	PUNCT
ejpam-411	285	12	·	·	PUNCT
ejpam-411	285	13	·	·	PUNCT
ejpam-411	285	14	·	·	PUNCT
ejpam-411	285	15	,	,	PUNCT
ejpam-411	285	16	β	β	X
ejpam-411	285	17	s	s	X
ejpam-411	285	18	;	;	PUNCT
ejpam-411	285	19	z	z	X
ejpam-411	285	20	)	)	PUNCT
ejpam-411	285	21	,	,	PUNCT
ejpam-411	285	22	where	where	SCONJ
ejpam-411	285	23	qfs	qfs	NOUN
ejpam-411	285	24	is	be	AUX
ejpam-411	285	25	the	the	DET
ejpam-411	285	26	generalized	generalized	ADJ
ejpam-411	285	27	hypergeometric	hypergeometric	ADJ
ejpam-411	285	28	function	function	NOUN
ejpam-411	285	29	(	(	PUNCT
ejpam-411	285	30	see	see	VERB
ejpam-411	285	31	,	,	PUNCT
ejpam-411	285	32	for	for	ADP
ejpam-411	285	33	details	detail	NOUN
ejpam-411	285	34	,	,	PUNCT
ejpam-411	285	35	[	[	X
ejpam-411	285	36	29	29	NUM
ejpam-411	285	37	]	]	NUM
ejpam-411	285	38	)	)	PUNCT
ejpam-411	285	39	,	,	PUNCT
ejpam-411	285	40	then	then	ADV
ejpam-411	285	41	we	we	PRON
ejpam-411	285	42	obtain	obtain	VERB
ejpam-411	285	43	the	the	DET
ejpam-411	285	44	following	follow	VERB
ejpam-411	285	45	function	function	NOUN
ejpam-411	285	46	class	class	NOUN
ejpam-411	285	47	:	:	PUNCT
ejpam-411	285	48	uh	uh	INTJ
ejpam-411	285	49	�	�	PROPN
ejpam-411	285	50	q	q	PROPN
ejpam-411	285	51	,	,	PUNCT
ejpam-411	285	52	s	s	PROPN
ejpam-411	285	53	,	,	PUNCT
ejpam-411	285	54	λ	λ	PROPN
ejpam-411	285	55	,	,	PUNCT
ejpam-411	285	56	γ	γ	X
ejpam-411	285	57	,	,	PUNCT
ejpam-411	285	58	k	k	PROPN
ejpam-411	285	59	�	�	PROPN
ejpam-411	285	60	:	:	PUNCT
ejpam-411	285	61	=	=	ADJ
ejpam-411	285	62	ht	ht	PROPN
ejpam-411	285	63	�	�	PROPN
ejpam-411	285	64	λh(α1	λh(α1	PROPN
ejpam-411	285	65	+	+	PROPN
ejpam-411	285	66	1	1	NUM
ejpam-411	285	67	,	,	PUNCT
ejpam-411	285	68	z	z	NOUN
ejpam-411	285	69	)	)	PUNCT
ejpam-411	286	1	+	+	CCONJ
ejpam-411	286	2	(	(	PUNCT
ejpam-411	286	3	1−λ)h(α1	1−λ)h(α1	PROPN
ejpam-411	286	4	,	,	PUNCT
ejpam-411	286	5	z);γ	z);γ	PROPN
ejpam-411	286	6	,	,	PUNCT
ejpam-411	286	7	k	k	PROPN
ejpam-411	286	8	�	�	PROPN
ejpam-411	286	9	(	(	PUNCT
ejpam-411	286	10	0≦	0≦	NUM
ejpam-411	286	11	λ	λ	X
ejpam-411	286	12	≦	≦	NUM
ejpam-411	286	13	1	1	NUM
ejpam-411	286	14	)	)	PUNCT
ejpam-411	286	15	references	reference	NOUN
ejpam-411	286	16	321	321	NUM
ejpam-411	286	17	which	which	PRON
ejpam-411	286	18	was	be	AUX
ejpam-411	286	19	introduced	introduce	VERB
ejpam-411	286	20	and	and	CCONJ
ejpam-411	286	21	studied	study	VERB
ejpam-411	286	22	by	by	ADP
ejpam-411	286	23	ramachandran	ramachandran	PROPN
ejpam-411	286	24	et	et	PROPN
ejpam-411	286	25	al	al	PROPN
ejpam-411	286	26	.	.	PUNCT
ejpam-411	287	1	[	[	X
ejpam-411	287	2	20	20	NUM
ejpam-411	287	3	]	]	PUNCT
ejpam-411	287	4	(	(	PUNCT
ejpam-411	287	5	see	see	VERB
ejpam-411	287	6	also	also	ADV
ejpam-411	287	7	several	several	ADJ
ejpam-411	287	8	recent	recent	ADJ
ejpam-411	287	9	works	work	NOUN
ejpam-411	287	10	including	include	VERB
ejpam-411	287	11	,	,	PUNCT
ejpam-411	287	12	for	for	ADP
ejpam-411	287	13	example	example	NOUN
ejpam-411	287	14	,	,	PUNCT
ejpam-411	287	15	[	[	X
ejpam-411	287	16	4	4	NUM
ejpam-411	287	17	]	]	PUNCT
ejpam-411	287	18	,	,	PUNCT
ejpam-411	287	19	[	[	X
ejpam-411	287	20	5	5	NUM
ejpam-411	287	21	]	]	PUNCT
ejpam-411	287	22	,	,	PUNCT
ejpam-411	287	23	[	[	X
ejpam-411	287	24	6	6	NUM
ejpam-411	287	25	]	]	PUNCT
ejpam-411	287	26	,	,	PUNCT
ejpam-411	287	27	[	[	X
ejpam-411	287	28	12	12	NUM
ejpam-411	287	29	]	]	PUNCT
ejpam-411	287	30	,	,	PUNCT
ejpam-411	287	31	[	[	X
ejpam-411	287	32	13	13	NUM
ejpam-411	287	33	]	]	PUNCT
ejpam-411	287	34	,	,	PUNCT
ejpam-411	287	35	[	[	X
ejpam-411	287	36	18	18	NUM
ejpam-411	287	37	]	]	PUNCT
ejpam-411	287	38	,	,	PUNCT
ejpam-411	287	39	[	[	X
ejpam-411	287	40	27	27	NUM
ejpam-411	287	41	]	]	PUNCT
ejpam-411	287	42	,	,	PUNCT
ejpam-411	287	43	[	[	X
ejpam-411	287	44	34	34	NUM
ejpam-411	287	45	]	]	PUNCT
ejpam-411	287	46	and	and	CCONJ
ejpam-411	287	47	[	[	X
ejpam-411	287	48	35	35	NUM
ejpam-411	287	49	]	]	PUNCT
ejpam-411	287	50	,	,	PUNCT
ejpam-411	287	51	which	which	PRON
ejpam-411	287	52	investigate	investigate	VERB
ejpam-411	287	53	various	various	ADJ
ejpam-411	287	54	properties	property	NOUN
ejpam-411	287	55	and	and	CCONJ
ejpam-411	287	56	applications	application	NOUN
ejpam-411	287	57	of	of	ADP
ejpam-411	287	58	the	the	DET
ejpam-411	287	59	dziok	dziok	NOUN
ejpam-411	287	60	-	-	PUNCT
ejpam-411	287	61	srivastava	srivastava	PROPN
ejpam-411	287	62	operator	operator	NOUN
ejpam-411	287	63	defined	define	VERB
ejpam-411	287	64	by	by	ADP
ejpam-411	287	65	means	mean	NOUN
ejpam-411	287	66	of	of	ADP
ejpam-411	287	67	the	the	DET
ejpam-411	287	68	hadamard	hadamard	ADJ
ejpam-411	287	69	product	product	NOUN
ejpam-411	287	70	involving	involve	VERB
ejpam-411	287	71	the	the	DET
ejpam-411	287	72	generalized	generalize	VERB
ejpam-411	287	73	hypergeometric	hypergeometric	ADJ
ejpam-411	287	74	function	function	NOUN
ejpam-411	287	75	q	q	NOUN
ejpam-411	287	76	fs	fs	PROPN
ejpam-411	287	77	)	)	PUNCT
ejpam-411	287	78	.	.	PUNCT
ejpam-411	288	1	let	let	VERB
ejpam-411	288	2	λ	λ	PRON
ejpam-411	288	3	be	be	AUX
ejpam-411	288	4	a	a	DET
ejpam-411	288	5	convex	convex	ADJ
ejpam-411	288	6	parameter	parameter	NOUN
ejpam-411	288	7	.	.	PUNCT
ejpam-411	289	1	a	a	DET
ejpam-411	289	2	function	function	NOUN
ejpam-411	289	3	f	f	PROPN
ejpam-411	289	4	∈a	∈a	PROPN
ejpam-411	289	5	is	be	AUX
ejpam-411	289	6	said	say	VERB
ejpam-411	289	7	to	to	PART
ejpam-411	289	8	belong	belong	VERB
ejpam-411	289	9	to	to	ADP
ejpam-411	289	10	the	the	DET
ejpam-411	289	11	class	class	NOUN
ejpam-411	289	12	vλ	vλ	ADP
ejpam-411	289	13	�	�	PROPN
ejpam-411	289	14	ϕ	ϕ	PROPN
ejpam-411	289	15	;	;	PUNCT
ejpam-411	289	16	a	a	DET
ejpam-411	289	17	,	,	PUNCT
ejpam-411	289	18	b	b	PROPN
ejpam-411	289	19	�	�	PROPN
ejpam-411	289	20	:	:	PUNCT
ejpam-411	289	21	=	=	NUM
ejpam-411	289	22	w	w	PROPN
ejpam-411	289	23	�	�	PROPN
ejpam-411	289	24	λ	λ	PROPN
ejpam-411	289	25	ϕ	ϕ	X
ejpam-411	289	26	(	(	PUNCT
ejpam-411	289	27	z	z	NOUN
ejpam-411	289	28	)	)	PUNCT
ejpam-411	289	29	z	z	NOUN
ejpam-411	290	1	+	+	CCONJ
ejpam-411	290	2	(	(	PUNCT
ejpam-411	290	3	1−λ)ϕ′	1−λ)ϕ′	NUM
ejpam-411	290	4	(	(	PUNCT
ejpam-411	290	5	z	z	NOUN
ejpam-411	290	6	)	)	PUNCT
ejpam-411	290	7	,	,	PUNCT
ejpam-411	291	1	z	z	X
ejpam-411	291	2	;	;	PUNCT
ejpam-411	291	3	a	a	DET
ejpam-411	291	4	,	,	PUNCT
ejpam-411	291	5	b	b	NOUN
ejpam-411	291	6	;	;	PUNCT
ejpam-411	291	7	0	0	NUM
ejpam-411	291	8	�	�	PROPN
ejpam-411	291	9	if	if	SCONJ
ejpam-411	291	10	it	it	PRON
ejpam-411	291	11	satisfies	satisfy	VERB
ejpam-411	291	12	the	the	DET
ejpam-411	291	13	following	follow	VERB
ejpam-411	291	14	condition	condition	NOUN
ejpam-411	291	15	:	:	PUNCT
ejpam-411	291	16	λ	λ	X
ejpam-411	291	17	�	�	PROPN
ejpam-411	291	18	ϕ	ϕ	PROPN
ejpam-411	291	19	∗	∗	X
ejpam-411	291	20	f	f	PROPN
ejpam-411	291	21	�	�	PROPN
ejpam-411	291	22	(	(	PUNCT
ejpam-411	291	23	z	z	NOUN
ejpam-411	291	24	)	)	PUNCT
ejpam-411	291	25	z	z	NOUN
ejpam-411	292	1	+	+	CCONJ
ejpam-411	292	2	(	(	PUNCT
ejpam-411	292	3	1−λ	1−λ	NUM
ejpam-411	292	4	)	)	PUNCT
ejpam-411	292	5	�	�	PROPN
ejpam-411	292	6	ϕ	ϕ	PROPN
ejpam-411	292	7	∗	∗	X
ejpam-411	292	8	f	f	PROPN
ejpam-411	292	9	�	�	PROPN
ejpam-411	292	10	′	′	NUM
ejpam-411	292	11	(	(	PUNCT
ejpam-411	292	12	z)≺	z)≺	PROPN
ejpam-411	292	13	1	1	NUM
ejpam-411	292	14	+	+	NUM
ejpam-411	292	15	az	az	PROPN
ejpam-411	292	16	1	1	NUM
ejpam-411	292	17	+	+	CCONJ
ejpam-411	292	18	bz	bz	PROPN
ejpam-411	292	19	.	.	PUNCT
ejpam-411	293	1	moreover	moreover	ADV
ejpam-411	293	2	,	,	PUNCT
ejpam-411	293	3	a	a	DET
ejpam-411	293	4	function	function	NOUN
ejpam-411	293	5	f	f	PROPN
ejpam-411	293	6	∈a	∈a	PROPN
ejpam-411	293	7	is	be	AUX
ejpam-411	293	8	said	say	VERB
ejpam-411	293	9	to	to	PART
ejpam-411	293	10	belong	belong	VERB
ejpam-411	293	11	to	to	ADP
ejpam-411	293	12	the	the	DET
ejpam-411	293	13	class	class	NOUN
ejpam-411	293	14	uλ	uλ	PRON
ejpam-411	293	15	�	�	PROPN
ejpam-411	293	16	ϕ	ϕ	PROPN
ejpam-411	293	17	;	;	PUNCT
ejpam-411	293	18	a	a	DET
ejpam-411	293	19	,	,	PUNCT
ejpam-411	293	20	b	b	PROPN
ejpam-411	293	21	�	�	PROPN
ejpam-411	293	22	:	:	PUNCT
ejpam-411	293	23	=	=	NUM
ejpam-411	293	24	w	w	PROPN
ejpam-411	293	25	�	�	PROPN
ejpam-411	293	26	λ	λ	PROPN
ejpam-411	293	27	ϕ	ϕ	X
ejpam-411	293	28	(	(	PUNCT
ejpam-411	293	29	z	z	NOUN
ejpam-411	293	30	)	)	PUNCT
ejpam-411	293	31	z	z	NOUN
ejpam-411	294	1	+	+	CCONJ
ejpam-411	294	2	(	(	PUNCT
ejpam-411	294	3	1−λ)ϕ′	1−λ)ϕ′	NUM
ejpam-411	294	4	(	(	PUNCT
ejpam-411	294	5	z	z	NOUN
ejpam-411	294	6	)	)	PUNCT
ejpam-411	294	7	;	;	PUNCT
ejpam-411	294	8	a	a	DET
ejpam-411	294	9	,	,	PUNCT
ejpam-411	294	10	b	b	NOUN
ejpam-411	294	11	;	;	PUNCT
ejpam-411	294	12	0	0	NUM
ejpam-411	294	13	�	�	PROPN
ejpam-411	294	14	if	if	SCONJ
ejpam-411	294	15	it	it	PRON
ejpam-411	294	16	satisfies	satisfy	VERB
ejpam-411	294	17	the	the	DET
ejpam-411	294	18	following	follow	VERB
ejpam-411	294	19	condition	condition	NOUN
ejpam-411	294	20	:	:	PUNCT
ejpam-411	294	21	z	z	PROPN
ejpam-411	294	22	�	�	PROPN
ejpam-411	294	23	ϕ	ϕ	PROPN
ejpam-411	294	24	∗	∗	X
ejpam-411	294	25	f	f	PROPN
ejpam-411	294	26	�	�	PROPN
ejpam-411	294	27	′	′	PROPN
ejpam-411	294	28	(	(	PUNCT
ejpam-411	294	29	z	z	NOUN
ejpam-411	294	30	)	)	PUNCT
ejpam-411	295	1	+	+	CCONJ
ejpam-411	295	2	(	(	PUNCT
ejpam-411	295	3	1−λ	1−λ	NUM
ejpam-411	295	4	)	)	PUNCT
ejpam-411	295	5	z2	z2	PROPN
ejpam-411	295	6	�	�	PROPN
ejpam-411	295	7	ϕ	ϕ	PROPN
ejpam-411	295	8	∗	∗	X
ejpam-411	295	9	f	f	PROPN
ejpam-411	295	10	�	�	PROPN
ejpam-411	295	11	′′	′′	PROPN
ejpam-411	295	12	(	(	PUNCT
ejpam-411	295	13	z	z	NOUN
ejpam-411	295	14	)	)	PUNCT
ejpam-411	295	15	λ	λ	PROPN
ejpam-411	295	16	�	�	PROPN
ejpam-411	295	17	ϕ	ϕ	PROPN
ejpam-411	295	18	∗	∗	X
ejpam-411	295	19	f	f	PROPN
ejpam-411	295	20	�	�	PROPN
ejpam-411	295	21	(	(	PUNCT
ejpam-411	295	22	z	z	NOUN
ejpam-411	295	23	)	)	PUNCT
ejpam-411	295	24	+	+	CCONJ
ejpam-411	295	25	(	(	PUNCT
ejpam-411	295	26	1−	1−	NUM
ejpam-411	295	27	λ	λ	NOUN
ejpam-411	295	28	)	)	PUNCT
ejpam-411	295	29	z	z	PROPN
ejpam-411	295	30	�	�	PROPN
ejpam-411	295	31	ϕ	ϕ	PROPN
ejpam-411	295	32	∗	∗	X
ejpam-411	295	33	f	f	PROPN
ejpam-411	295	34	�	�	PROPN
ejpam-411	295	35	′	′	NUM
ejpam-411	295	36	(	(	PUNCT
ejpam-411	295	37	z	z	NOUN
ejpam-411	295	38	)	)	PUNCT
ejpam-411	295	39	≺	≺	NOUN
ejpam-411	295	40	1	1	NUM
ejpam-411	295	41	+	+	NUM
ejpam-411	295	42	az	az	PROPN
ejpam-411	295	43	1	1	NUM
ejpam-411	295	44	+	+	CCONJ
ejpam-411	295	45	bz	bz	PROPN
ejpam-411	295	46	.	.	PUNCT
ejpam-411	296	1	(	(	PUNCT
ejpam-411	296	2	8.1	8.1	NUM
ejpam-411	296	3	)	)	PUNCT
ejpam-411	296	4	the	the	DET
ejpam-411	296	5	above	above	ADV
ejpam-411	296	6	-	-	PUNCT
ejpam-411	296	7	defined	define	VERB
ejpam-411	296	8	function	function	NOUN
ejpam-411	296	9	classes	class	NOUN
ejpam-411	296	10	wn	wn	PROPN
ejpam-411	296	11	�	�	PROPN
ejpam-411	296	12	ϕ	ϕ	PROPN
ejpam-411	296	13	;	;	PUNCT
ejpam-411	296	14	a	a	DET
ejpam-411	296	15	,	,	PUNCT
ejpam-411	296	16	b	b	PROPN
ejpam-411	296	17	�	�	PROPN
ejpam-411	296	18	,	,	PUNCT
ejpam-411	296	19	hn	hn	PROPN
ejpam-411	296	20	�	�	PROPN
ejpam-411	296	21	ϕ;γ	ϕ;γ	PROPN
ejpam-411	296	22	,	,	PUNCT
ejpam-411	296	23	k	k	PROPN
ejpam-411	296	24	�	�	PROPN
ejpam-411	296	25	,	,	PUNCT
ejpam-411	296	26	uλ	uλ	PRON
ejpam-411	296	27	�	�	PROPN
ejpam-411	296	28	ϕ	ϕ	PROPN
ejpam-411	296	29	;	;	PUNCT
ejpam-411	296	30	a	a	DET
ejpam-411	296	31	,	,	PUNCT
ejpam-411	296	32	b	b	PROPN
ejpam-411	296	33	�	�	PROPN
ejpam-411	296	34	and	and	CCONJ
ejpam-411	296	35	vλ	vλ	PROPN
ejpam-411	296	36	�	�	PROPN
ejpam-411	296	37	ϕ	ϕ	PROPN
ejpam-411	296	38	;	;	PUNCT
ejpam-411	296	39	a	a	PRON
ejpam-411	296	40	,	,	PUNCT
ejpam-411	296	41	b	b	X
ejpam-411	296	42	�	�	PROPN
ejpam-411	296	43	generalize	generalize	VERB
ejpam-411	296	44	several	several	ADJ
ejpam-411	296	45	important	important	ADJ
ejpam-411	296	46	classes	class	NOUN
ejpam-411	296	47	,	,	PUNCT
ejpam-411	296	48	many	many	ADJ
ejpam-411	296	49	of	of	ADP
ejpam-411	296	50	which	which	PRON
ejpam-411	296	51	were	be	AUX
ejpam-411	296	52	investigated	investigate	VERB
ejpam-411	296	53	systematically	systematically	ADV
ejpam-411	296	54	in	in	ADP
ejpam-411	296	55	earlier	early	ADJ
ejpam-411	296	56	works	work	NOUN
ejpam-411	296	57	(	(	PUNCT
ejpam-411	296	58	see	see	VERB
ejpam-411	296	59	,	,	PUNCT
ejpam-411	296	60	for	for	ADP
ejpam-411	296	61	example	example	NOUN
ejpam-411	296	62	,	,	PUNCT
ejpam-411	296	63	[	[	X
ejpam-411	296	64	1	1	NUM
ejpam-411	296	65	]	]	PUNCT
ejpam-411	296	66	,	,	PUNCT
ejpam-411	296	67	[	[	X
ejpam-411	296	68	2	2	NUM
ejpam-411	296	69	]	]	PUNCT
ejpam-411	296	70	,	,	PUNCT
ejpam-411	296	71	[	[	X
ejpam-411	296	72	3	3	NUM
ejpam-411	296	73	]	]	PUNCT
ejpam-411	296	74	,	,	PUNCT
ejpam-411	296	75	[	[	X
ejpam-411	296	76	16	16	NUM
ejpam-411	296	77	]	]	PUNCT
ejpam-411	296	78	,	,	PUNCT
ejpam-411	296	79	[	[	X
ejpam-411	296	80	17	17	NUM
ejpam-411	296	81	]	]	PUNCT
ejpam-411	296	82	,	,	PUNCT
ejpam-411	296	83	[	[	X
ejpam-411	296	84	28	28	NUM
ejpam-411	296	85	]	]	PUNCT
ejpam-411	296	86	and	and	CCONJ
ejpam-411	296	87	[	[	X
ejpam-411	296	88	30	30	NUM
ejpam-411	296	89	]	]	PUNCT
ejpam-411	296	90	)	)	PUNCT
ejpam-411	296	91	.	.	PUNCT
ejpam-411	297	1	if	if	SCONJ
ejpam-411	297	2	we	we	PRON
ejpam-411	297	3	apply	apply	VERB
ejpam-411	297	4	the	the	DET
ejpam-411	297	5	results	result	NOUN
ejpam-411	297	6	presented	present	VERB
ejpam-411	297	7	in	in	ADP
ejpam-411	297	8	this	this	DET
ejpam-411	297	9	paper	paper	NOUN
ejpam-411	297	10	to	to	ADP
ejpam-411	297	11	the	the	DET
ejpam-411	297	12	classes	class	NOUN
ejpam-411	297	13	discussed	discuss	VERB
ejpam-411	297	14	above	above	ADV
ejpam-411	297	15	,	,	PUNCT
ejpam-411	297	16	we	we	PRON
ejpam-411	297	17	can	can	AUX
ejpam-411	297	18	easily	easily	ADV
ejpam-411	297	19	be	be	AUX
ejpam-411	297	20	led	lead	VERB
ejpam-411	297	21	to	to	ADP
ejpam-411	297	22	a	a	DET
ejpam-411	297	23	remarkably	remarkably	ADV
ejpam-411	297	24	large	large	ADJ
ejpam-411	297	25	number	number	NOUN
ejpam-411	297	26	of	of	ADP
ejpam-411	297	27	additional	additional	ADJ
ejpam-411	297	28	new	new	ADJ
ejpam-411	297	29	or	or	CCONJ
ejpam-411	297	30	known	known	ADJ
ejpam-411	297	31	results	result	NOUN
ejpam-411	297	32	.	.	PUNCT
ejpam-411	298	1	references	reference	NOUN
ejpam-411	298	2	[	[	X
ejpam-411	298	3	1	1	NUM
ejpam-411	298	4	]	]	PUNCT
ejpam-411	298	5	m.	m.	NOUN
ejpam-411	298	6	k.	k.	PROPN
ejpam-411	298	7	aouf	aouf	PROPN
ejpam-411	298	8	and	and	CCONJ
ejpam-411	298	9	h.	h.	PROPN
ejpam-411	298	10	m	m	PROPN
ejpam-411	298	11	srivastava	srivastava	PROPN
ejpam-411	298	12	,	,	PUNCT
ejpam-411	298	13	some	some	DET
ejpam-411	298	14	families	family	NOUN
ejpam-411	298	15	of	of	ADP
ejpam-411	298	16	starlike	starlike	NOUN
ejpam-411	298	17	functions	function	NOUN
ejpam-411	298	18	with	with	ADP
ejpam-411	298	19	negative	negative	ADJ
ejpam-411	298	20	coefficients	coefficient	NOUN
ejpam-411	298	21	,	,	PUNCT
ejpam-411	298	22	j.	j.	PROPN
ejpam-411	298	23	math	math	PROPN
ejpam-411	298	24	.	.	PUNCT
ejpam-411	299	1	anal	anal	PROPN
ejpam-411	299	2	.	.	PUNCT
ejpam-411	300	1	appl	appl	PROPN
ejpam-411	300	2	.	.	PROPN
ejpam-411	301	1	203	203	NUM
ejpam-411	301	2	(	(	PUNCT
ejpam-411	301	3	1996	1996	NUM
ejpam-411	301	4	)	)	PUNCT
ejpam-411	301	5	,	,	PUNCT
ejpam-411	302	1	762–790	762–790	NUM
ejpam-411	302	2	.	.	PUNCT
ejpam-411	302	3	references	reference	NOUN
ejpam-411	302	4	322	322	NUM
ejpam-411	302	5	[	[	X
ejpam-411	302	6	2	2	NUM
ejpam-411	302	7	]	]	X
ejpam-411	302	8	n.	n.	PROPN
ejpam-411	302	9	e.	e.	PROPN
ejpam-411	302	10	cho	cho	PROPN
ejpam-411	302	11	and	and	CCONJ
ejpam-411	302	12	h.	h.	PROPN
ejpam-411	302	13	m.	m.	PROPN
ejpam-411	302	14	srivastava	srivastava	PROPN
ejpam-411	302	15	,	,	PUNCT
ejpam-411	302	16	argument	argument	NOUN
ejpam-411	302	17	estimates	estimate	NOUN
ejpam-411	302	18	of	of	ADP
ejpam-411	302	19	certain	certain	ADJ
ejpam-411	302	20	analytic	analytic	ADJ
ejpam-411	302	21	functions	function	NOUN
ejpam-411	302	22	defined	define	VERB
ejpam-411	302	23	by	by	ADP
ejpam-411	302	24	a	a	DET
ejpam-411	302	25	class	class	NOUN
ejpam-411	302	26	of	of	ADP
ejpam-411	302	27	multiplier	multipli	ADJ
ejpam-411	302	28	transformations	transformation	NOUN
ejpam-411	302	29	,	,	PUNCT
ejpam-411	302	30	math	math	NOUN
ejpam-411	302	31	.	.	PUNCT
ejpam-411	303	1	comput	comput	NOUN
ejpam-411	303	2	.	.	PUNCT
ejpam-411	304	1	modelling	model	VERB
ejpam-411	304	2	37	37	NUM
ejpam-411	304	3	(	(	PUNCT
ejpam-411	304	4	2003	2003	NUM
ejpam-411	304	5	)	)	PUNCT
ejpam-411	304	6	,	,	PUNCT
ejpam-411	304	7	39	39	NUM
ejpam-411	304	8	–	–	PUNCT
ejpam-411	304	9	49	49	NUM
ejpam-411	304	10	.	.	PUNCT
ejpam-411	305	1	[	[	X
ejpam-411	305	2	3	3	X
ejpam-411	305	3	]	]	PUNCT
ejpam-411	305	4	j.	j.	PROPN
ejpam-411	305	5	dziok	dziok	PROPN
ejpam-411	305	6	,	,	PUNCT
ejpam-411	305	7	on	on	ADP
ejpam-411	305	8	some	some	DET
ejpam-411	305	9	applications	application	NOUN
ejpam-411	305	10	of	of	ADP
ejpam-411	305	11	the	the	DET
ejpam-411	305	12	briot	briot	NOUN
ejpam-411	305	13	-	-	PUNCT
ejpam-411	305	14	bouquet	bouquet	NOUN
ejpam-411	305	15	differential	differential	NOUN
ejpam-411	305	16	subordination	subordination	NOUN
ejpam-411	305	17	,	,	PUNCT
ejpam-411	305	18	j.	j.	PROPN
ejpam-411	305	19	math	math	PROPN
ejpam-411	305	20	.	.	PUNCT
ejpam-411	306	1	anal	anal	PROPN
ejpam-411	306	2	.	.	PUNCT
ejpam-411	306	3	appl	appl	PROPN
ejpam-411	306	4	.	.	PUNCT
ejpam-411	307	1	328	328	NUM
ejpam-411	307	2	(	(	PUNCT
ejpam-411	307	3	2007	2007	NUM
ejpam-411	307	4	)	)	PUNCT
ejpam-411	307	5	,	,	PUNCT
ejpam-411	307	6	295–301	295–301	NUM
ejpam-411	307	7	.	.	PUNCT
ejpam-411	308	1	[	[	X
ejpam-411	308	2	4	4	X
ejpam-411	308	3	]	]	PUNCT
ejpam-411	308	4	j.	j.	PROPN
ejpam-411	308	5	dziok	dziok	PROPN
ejpam-411	308	6	and	and	CCONJ
ejpam-411	308	7	h.	h.	PROPN
ejpam-411	308	8	m.	m.	PROPN
ejpam-411	308	9	srivastava	srivastava	PROPN
ejpam-411	308	10	,	,	PUNCT
ejpam-411	308	11	classes	class	NOUN
ejpam-411	308	12	of	of	ADP
ejpam-411	308	13	analytic	analytic	ADJ
ejpam-411	308	14	functions	function	NOUN
ejpam-411	308	15	associated	associate	VERB
ejpam-411	308	16	with	with	ADP
ejpam-411	308	17	the	the	DET
ejpam-411	308	18	generalized	generalize	VERB
ejpam-411	308	19	hypergeometric	hypergeometric	ADJ
ejpam-411	308	20	function	function	NOUN
ejpam-411	308	21	,	,	PUNCT
ejpam-411	308	22	appl	appl	PROPN
ejpam-411	308	23	.	.	PROPN
ejpam-411	308	24	math	math	PROPN
ejpam-411	308	25	.	.	PUNCT
ejpam-411	309	1	comput	comput	NOUN
ejpam-411	309	2	.	.	PUNCT
ejpam-411	310	1	103	103	NUM
ejpam-411	310	2	(	(	PUNCT
ejpam-411	310	3	1999	1999	NUM
ejpam-411	310	4	)	)	PUNCT
ejpam-411	310	5	,	,	PUNCT
ejpam-411	310	6	1–13	1–13	NOUN
ejpam-411	310	7	.	.	PUNCT
ejpam-411	311	1	[	[	X
ejpam-411	311	2	5	5	X
ejpam-411	311	3	]	]	PUNCT
ejpam-411	311	4	j.	j.	PROPN
ejpam-411	311	5	dziok	dziok	PROPN
ejpam-411	311	6	and	and	CCONJ
ejpam-411	311	7	h.	h.	PROPN
ejpam-411	311	8	m.	m.	PROPN
ejpam-411	311	9	srivastava	srivastava	PROPN
ejpam-411	311	10	,	,	PUNCT
ejpam-411	311	11	certain	certain	ADJ
ejpam-411	311	12	subclasses	subclass	NOUN
ejpam-411	311	13	of	of	ADP
ejpam-411	311	14	analytic	analytic	ADJ
ejpam-411	311	15	functions	function	NOUN
ejpam-411	311	16	associated	associate	VERB
ejpam-411	311	17	with	with	ADP
ejpam-411	311	18	the	the	DET
ejpam-411	311	19	generalized	generalize	VERB
ejpam-411	311	20	hypergeometric	hypergeometric	ADJ
ejpam-411	311	21	function	function	NOUN
ejpam-411	311	22	,	,	PUNCT
ejpam-411	311	23	integral	integral	ADJ
ejpam-411	311	24	transform	transform	NOUN
ejpam-411	311	25	.	.	PUNCT
ejpam-411	312	1	spec	spec	PROPN
ejpam-411	312	2	.	.	PUNCT
ejpam-411	313	1	funct	funct	PROPN
ejpam-411	313	2	.	.	PUNCT
ejpam-411	314	1	14	14	NUM
ejpam-411	314	2	(	(	PUNCT
ejpam-411	314	3	2003	2003	NUM
ejpam-411	314	4	)	)	PUNCT
ejpam-411	314	5	,	,	PUNCT
ejpam-411	314	6	7–18	7–18	NOUN
ejpam-411	314	7	.	.	PUNCT
ejpam-411	315	1	[	[	X
ejpam-411	315	2	6	6	NUM
ejpam-411	315	3	]	]	PUNCT
ejpam-411	315	4	j.	j.	PROPN
ejpam-411	315	5	dziok	dziok	PROPN
ejpam-411	315	6	and	and	CCONJ
ejpam-411	315	7	h.	h.	PROPN
ejpam-411	315	8	m.	m.	PROPN
ejpam-411	315	9	srivastava	srivastava	PROPN
ejpam-411	315	10	,	,	PUNCT
ejpam-411	315	11	some	some	DET
ejpam-411	315	12	subclasses	subclass	NOUN
ejpam-411	315	13	of	of	ADP
ejpam-411	315	14	analytic	analytic	ADJ
ejpam-411	315	15	functions	function	NOUN
ejpam-411	315	16	with	with	ADP
ejpam-411	315	17	fixed	fix	VERB
ejpam-411	315	18	argument	argument	NOUN
ejpam-411	315	19	of	of	ADP
ejpam-411	315	20	coefficients	coefficient	NOUN
ejpam-411	315	21	associated	associate	VERB
ejpam-411	315	22	with	with	ADP
ejpam-411	315	23	the	the	DET
ejpam-411	315	24	generalized	generalize	VERB
ejpam-411	315	25	hypergeometric	hypergeometric	ADJ
ejpam-411	315	26	function	function	NOUN
ejpam-411	315	27	,	,	PUNCT
ejpam-411	315	28	adv	adv	PROPN
ejpam-411	315	29	.	.	PUNCT
ejpam-411	315	30	stud	stud	PROPN
ejpam-411	315	31	.	.	PUNCT
ejpam-411	316	1	contemp	contemp	NOUN
ejpam-411	316	2	.	.	PUNCT
ejpam-411	317	1	math	math	NOUN
ejpam-411	317	2	.	.	PUNCT
ejpam-411	318	1	5	5	NUM
ejpam-411	318	2	(	(	PUNCT
ejpam-411	318	3	2002	2002	NUM
ejpam-411	318	4	)	)	PUNCT
ejpam-411	318	5	,	,	PUNCT
ejpam-411	318	6	115–125	115–125	NUM
ejpam-411	318	7	.	.	PUNCT
ejpam-411	319	1	[	[	X
ejpam-411	319	2	7	7	NUM
ejpam-411	319	3	]	]	PUNCT
ejpam-411	319	4	a.	a.	NOUN
ejpam-411	319	5	gangadharan	gangadharan	NOUN
ejpam-411	319	6	,	,	PUNCT
ejpam-411	319	7	t.	t.	PROPN
ejpam-411	319	8	n.	n.	PROPN
ejpam-411	319	9	shanmugam	shanmugam	PROPN
ejpam-411	319	10	and	and	CCONJ
ejpam-411	319	11	h.	h.	PROPN
ejpam-411	319	12	m.	m.	PROPN
ejpam-411	319	13	srivastava	srivastava	PROPN
ejpam-411	319	14	,	,	PUNCT
ejpam-411	319	15	generalized	generalize	VERB
ejpam-411	319	16	hypergeometric	hypergeometric	ADJ
ejpam-411	319	17	functions	function	NOUN
ejpam-411	319	18	associated	associate	VERB
ejpam-411	319	19	with	with	ADP
ejpam-411	319	20	k	k	ADJ
ejpam-411	319	21	-	-	ADJ
ejpam-411	319	22	uniformly	uniformly	ADJ
ejpam-411	319	23	convex	convex	NOUN
ejpam-411	319	24	functions	function	NOUN
ejpam-411	319	25	,	,	PUNCT
ejpam-411	319	26	comput	comput	NOUN
ejpam-411	319	27	.	.	PUNCT
ejpam-411	320	1	math	math	NOUN
ejpam-411	320	2	.	.	PUNCT
ejpam-411	321	1	appl	appl	PROPN
ejpam-411	321	2	.	.	PROPN
ejpam-411	322	1	44	44	NUM
ejpam-411	322	2	(	(	PUNCT
ejpam-411	322	3	2002	2002	NUM
ejpam-411	322	4	)	)	PUNCT
ejpam-411	322	5	,	,	PUNCT
ejpam-411	322	6	1515–1526	1515–1526	NUM
ejpam-411	322	7	.	.	PUNCT
ejpam-411	323	1	[	[	X
ejpam-411	323	2	8	8	NUM
ejpam-411	323	3	]	]	PUNCT
ejpam-411	323	4	a.	a.	PROPN
ejpam-411	323	5	w.	w.	PROPN
ejpam-411	323	6	goodman	goodman	PROPN
ejpam-411	323	7	,	,	PUNCT
ejpam-411	323	8	on	on	ADP
ejpam-411	323	9	uniformly	uniformly	ADV
ejpam-411	323	10	convex	convex	NOUN
ejpam-411	323	11	functions	function	NOUN
ejpam-411	323	12	,	,	PUNCT
ejpam-411	323	13	ann	ann	PROPN
ejpam-411	323	14	.	.	PROPN
ejpam-411	323	15	polon	polon	PROPN
ejpam-411	323	16	.	.	PUNCT
ejpam-411	324	1	math	math	NOUN
ejpam-411	324	2	.	.	PUNCT
ejpam-411	325	1	56	56	NUM
ejpam-411	325	2	(	(	PUNCT
ejpam-411	325	3	1991	1991	NUM
ejpam-411	325	4	)	)	PUNCT
ejpam-411	325	5	,	,	PUNCT
ejpam-411	325	6	87–92	87–92	NUM
ejpam-411	325	7	.	.	PUNCT
ejpam-411	326	1	[	[	X
ejpam-411	326	2	9	9	NUM
ejpam-411	326	3	]	]	PUNCT
ejpam-411	326	4	s.	s.	PROPN
ejpam-411	326	5	kanas	kanas	PROPN
ejpam-411	326	6	and	and	CCONJ
ejpam-411	326	7	h.	h.	PROPN
ejpam-411	326	8	m.	m.	PROPN
ejpam-411	326	9	srivastava	srivastava	PROPN
ejpam-411	326	10	,	,	PUNCT
ejpam-411	326	11	linear	linear	PROPN
ejpam-411	326	12	operators	operator	NOUN
ejpam-411	326	13	associated	associate	VERB
ejpam-411	326	14	with	with	ADP
ejpam-411	326	15	k	k	ADJ
ejpam-411	326	16	-	-	ADJ
ejpam-411	326	17	uniformaly	uniformaly	ADJ
ejpam-411	326	18	convex	convex	NOUN
ejpam-411	326	19	functions	function	NOUN
ejpam-411	326	20	,	,	PUNCT
ejpam-411	326	21	intergral	intergral	ADJ
ejpam-411	326	22	transform	transform	NOUN
ejpam-411	326	23	.	.	PUNCT
ejpam-411	327	1	spec	spec	PROPN
ejpam-411	327	2	.	.	PUNCT
ejpam-411	328	1	funct	funct	PROPN
ejpam-411	328	2	.	.	PUNCT
ejpam-411	329	1	9	9	NUM
ejpam-411	329	2	(	(	PUNCT
ejpam-411	329	3	2000	2000	NUM
ejpam-411	329	4	)	)	PUNCT
ejpam-411	329	5	,	,	PUNCT
ejpam-411	329	6	121–132	121–132	NUM
ejpam-411	329	7	.	.	PUNCT
ejpam-411	330	1	[	[	X
ejpam-411	330	2	10	10	NUM
ejpam-411	330	3	]	]	X
ejpam-411	330	4	s.	s.	PROPN
ejpam-411	330	5	kanas	kanas	PROPN
ejpam-411	330	6	and	and	CCONJ
ejpam-411	330	7	a.	a.	NOUN
ejpam-411	330	8	wisniowska	wisniowska	PROPN
ejpam-411	330	9	,	,	PUNCT
ejpam-411	330	10	conic	conic	ADJ
ejpam-411	330	11	regions	region	NOUN
ejpam-411	330	12	and	and	CCONJ
ejpam-411	330	13	k	k	ADJ
ejpam-411	330	14	-	-	PUNCT
ejpam-411	330	15	uniform	uniform	ADJ
ejpam-411	330	16	convexity	convexity	NOUN
ejpam-411	330	17	,	,	PUNCT
ejpam-411	330	18	j.	j.	PROPN
ejpam-411	330	19	comput	comput	PROPN
ejpam-411	330	20	.	.	PUNCT
ejpam-411	331	1	appl	appl	PROPN
ejpam-411	331	2	.	.	PROPN
ejpam-411	331	3	math	math	NOUN
ejpam-411	331	4	.	.	PUNCT
ejpam-411	332	1	105	105	NUM
ejpam-411	332	2	(	(	PUNCT
ejpam-411	332	3	1999	1999	NUM
ejpam-411	332	4	)	)	PUNCT
ejpam-411	332	5	,	,	PUNCT
ejpam-411	333	1	327–336	327–336	NUM
ejpam-411	333	2	.	.	PUNCT
ejpam-411	334	1	[	[	X
ejpam-411	334	2	11	11	NUM
ejpam-411	334	3	]	]	PUNCT
ejpam-411	334	4	j.	j.	PROPN
ejpam-411	334	5	e.	e.	PROPN
ejpam-411	334	6	littlewood	littlewood	PROPN
ejpam-411	334	7	,	,	PUNCT
ejpam-411	334	8	on	on	ADP
ejpam-411	334	9	inequalities	inequality	NOUN
ejpam-411	334	10	in	in	ADP
ejpam-411	334	11	theory	theory	NOUN
ejpam-411	334	12	of	of	ADP
ejpam-411	334	13	functions	function	NOUN
ejpam-411	334	14	,	,	PUNCT
ejpam-411	334	15	proc	proc	NOUN
ejpam-411	334	16	.	.	PUNCT
ejpam-411	335	1	london	london	PROPN
ejpam-411	335	2	math	math	PROPN
ejpam-411	335	3	.	.	PUNCT
ejpam-411	336	1	soc	soc	PROPN
ejpam-411	336	2	.	.	PUNCT
ejpam-411	337	1	(	(	PUNCT
ejpam-411	337	2	ser	ser	NOUN
ejpam-411	337	3	.	.	PROPN
ejpam-411	337	4	2	2	NUM
ejpam-411	337	5	)	)	PUNCT
ejpam-411	337	6	23	23	NUM
ejpam-411	337	7	(	(	PUNCT
ejpam-411	337	8	1925	1925	NUM
ejpam-411	337	9	)	)	PUNCT
ejpam-411	337	10	,	,	PUNCT
ejpam-411	337	11	481–519	481–519	NUM
ejpam-411	337	12	.	.	PUNCT
ejpam-411	338	1	[	[	X
ejpam-411	338	2	12	12	NUM
ejpam-411	338	3	]	]	X
ejpam-411	338	4	j.-l	j.-l	PROPN
ejpam-411	338	5	.	.	PUNCT
ejpam-411	339	1	liu	liu	PROPN
ejpam-411	339	2	and	and	CCONJ
ejpam-411	339	3	h.	h.	PROPN
ejpam-411	339	4	m.	m.	PROPN
ejpam-411	339	5	srivastava	srivastava	PROPN
ejpam-411	339	6	,	,	PUNCT
ejpam-411	339	7	certain	certain	ADJ
ejpam-411	339	8	properties	property	NOUN
ejpam-411	339	9	of	of	ADP
ejpam-411	339	10	the	the	DET
ejpam-411	339	11	dziok	dziok	NOUN
ejpam-411	339	12	-	-	PUNCT
ejpam-411	339	13	srivastava	srivastava	PROPN
ejpam-411	339	14	operator	operator	NOUN
ejpam-411	339	15	,	,	PUNCT
ejpam-411	339	16	appl	appl	PROPN
ejpam-411	339	17	.	.	PROPN
ejpam-411	339	18	math	math	PROPN
ejpam-411	339	19	.	.	PUNCT
ejpam-411	340	1	comput	comput	NOUN
ejpam-411	340	2	.	.	PUNCT
ejpam-411	341	1	159	159	NUM
ejpam-411	341	2	(	(	PUNCT
ejpam-411	341	3	2004	2004	NUM
ejpam-411	341	4	)	)	PUNCT
ejpam-411	341	5	,	,	PUNCT
ejpam-411	342	1	485–493	485–493	NUM
ejpam-411	342	2	.	.	PUNCT
ejpam-411	343	1	[	[	X
ejpam-411	343	2	13	13	NUM
ejpam-411	343	3	]	]	PUNCT
ejpam-411	343	4	j.-l	j.-l	PROPN
ejpam-411	343	5	.	.	PUNCT
ejpam-411	344	1	liu	liu	PROPN
ejpam-411	344	2	and	and	CCONJ
ejpam-411	344	3	h.	h.	PROPN
ejpam-411	344	4	m.	m.	PROPN
ejpam-411	344	5	srivastava	srivastava	PROPN
ejpam-411	344	6	,	,	PUNCT
ejpam-411	344	7	a	a	DET
ejpam-411	344	8	class	class	NOUN
ejpam-411	344	9	of	of	ADP
ejpam-411	344	10	multivalently	multivalently	ADJ
ejpam-411	344	11	analytic	analytic	ADJ
ejpam-411	344	12	functions	function	NOUN
ejpam-411	344	13	associated	associate	VERB
ejpam-411	344	14	with	with	ADP
ejpam-411	344	15	the	the	DET
ejpam-411	344	16	dziok	dziok	NOUN
ejpam-411	344	17	-	-	PUNCT
ejpam-411	344	18	srivastava	srivastava	PROPN
ejpam-411	344	19	operator	operator	NOUN
ejpam-411	344	20	,	,	PUNCT
ejpam-411	344	21	integral	integral	ADJ
ejpam-411	344	22	transform	transform	NOUN
ejpam-411	344	23	.	.	PUNCT
ejpam-411	345	1	spec	spec	PROPN
ejpam-411	345	2	.	.	PUNCT
ejpam-411	346	1	funct	funct	PROPN
ejpam-411	346	2	.	.	PUNCT
ejpam-411	347	1	20	20	NUM
ejpam-411	347	2	(	(	PUNCT
ejpam-411	347	3	2009	2009	NUM
ejpam-411	347	4	)	)	PUNCT
ejpam-411	347	5	,	,	PUNCT
ejpam-411	347	6	401–417	401–417	NUM
ejpam-411	347	7	.	.	PUNCT
ejpam-411	348	1	[	[	X
ejpam-411	348	2	14	14	NUM
ejpam-411	348	3	]	]	X
ejpam-411	348	4	w.	w.	PROPN
ejpam-411	348	5	ma	ma	PROPN
ejpam-411	348	6	and	and	CCONJ
ejpam-411	348	7	d.	d.	PROPN
ejpam-411	348	8	minda	minda	PROPN
ejpam-411	348	9	,	,	PUNCT
ejpam-411	348	10	uniformly	uniformly	ADV
ejpam-411	348	11	convex	convex	NOUN
ejpam-411	348	12	functions	function	NOUN
ejpam-411	348	13	,	,	PUNCT
ejpam-411	348	14	ann	ann	PROPN
ejpam-411	348	15	.	.	PROPN
ejpam-411	348	16	polon	polon	PROPN
ejpam-411	348	17	.	.	PUNCT
ejpam-411	348	18	math	math	NOUN
ejpam-411	348	19	.	.	PUNCT
ejpam-411	349	1	57	57	NUM
ejpam-411	349	2	(	(	PUNCT
ejpam-411	349	3	1992	1992	NUM
ejpam-411	349	4	)	)	PUNCT
ejpam-411	349	5	,	,	PUNCT
ejpam-411	349	6	165	165	NUM
ejpam-411	349	7	–	–	SYM
ejpam-411	349	8	175	175	NUM
ejpam-411	349	9	.	.	PUNCT
ejpam-411	349	10	references	reference	NOUN
ejpam-411	349	11	323	323	NUM
ejpam-411	350	1	[	[	X
ejpam-411	350	2	15	15	NUM
ejpam-411	350	3	]	]	X
ejpam-411	350	4	s.	s.	PROPN
ejpam-411	350	5	s.	s.	PROPN
ejpam-411	350	6	miller	miller	PROPN
ejpam-411	350	7	and	and	CCONJ
ejpam-411	350	8	p.	p.	PROPN
ejpam-411	350	9	t.	t.	PROPN
ejpam-411	350	10	mocanu	mocanu	PROPN
ejpam-411	350	11	,	,	PUNCT
ejpam-411	350	12	differential	differential	ADJ
ejpam-411	350	13	subordination	subordination	NOUN
ejpam-411	350	14	:	:	PUNCT
ejpam-411	350	15	theory	theory	NOUN
ejpam-411	350	16	and	and	CCONJ
ejpam-411	350	17	applications	application	NOUN
ejpam-411	350	18	,	,	PUNCT
ejpam-411	350	19	series	series	NOUN
ejpam-411	350	20	on	on	ADP
ejpam-411	350	21	monographs	monograph	NOUN
ejpam-411	350	22	and	and	CCONJ
ejpam-411	350	23	textbooks	textbook	NOUN
ejpam-411	350	24	in	in	ADP
ejpam-411	350	25	pure	pure	ADJ
ejpam-411	350	26	and	and	CCONJ
ejpam-411	350	27	applied	applied	ADJ
ejpam-411	350	28	mathematics	mathematic	NOUN
ejpam-411	350	29	,	,	PUNCT
ejpam-411	350	30	no	no	INTJ
ejpam-411	350	31	.	.	NOUN
ejpam-411	350	32	225	225	NUM
ejpam-411	350	33	,	,	PUNCT
ejpam-411	350	34	marcel	marcel	PROPN
ejpam-411	350	35	dekker	dekker	PROPN
ejpam-411	350	36	incorporated	incorporate	VERB
ejpam-411	350	37	,	,	PUNCT
ejpam-411	350	38	new	new	PROPN
ejpam-411	350	39	york	york	PROPN
ejpam-411	350	40	and	and	CCONJ
ejpam-411	350	41	basel	basel	PROPN
ejpam-411	350	42	,	,	PUNCT
ejpam-411	350	43	2000	2000	NUM
ejpam-411	350	44	.	.	PUNCT
ejpam-411	351	1	[	[	X
ejpam-411	351	2	16	16	NUM
ejpam-411	351	3	]	]	X
ejpam-411	351	4	j.	j.	PROPN
ejpam-411	351	5	patel	patel	PROPN
ejpam-411	351	6	and	and	CCONJ
ejpam-411	351	7	a.	a.	PROPN
ejpam-411	351	8	k.	k.	PROPN
ejpam-411	351	9	mishra	mishra	PROPN
ejpam-411	351	10	,	,	PUNCT
ejpam-411	351	11	on	on	ADP
ejpam-411	351	12	certain	certain	ADJ
ejpam-411	351	13	subclasses	subclass	NOUN
ejpam-411	351	14	of	of	ADP
ejpam-411	351	15	multivalent	multivalent	NOUN
ejpam-411	351	16	functions	function	NOUN
ejpam-411	351	17	associated	associate	VERB
ejpam-411	351	18	with	with	ADP
ejpam-411	351	19	an	an	DET
ejpam-411	351	20	extended	extended	ADJ
ejpam-411	351	21	fractional	fractional	ADJ
ejpam-411	351	22	differintegral	differintegral	ADJ
ejpam-411	351	23	operator	operator	NOUN
ejpam-411	351	24	,	,	PUNCT
ejpam-411	351	25	j.	j.	PROPN
ejpam-411	351	26	math	math	PROPN
ejpam-411	351	27	.	.	PUNCT
ejpam-411	352	1	anal	anal	PROPN
ejpam-411	352	2	.	.	PUNCT
ejpam-411	352	3	appl	appl	PROPN
ejpam-411	352	4	.	.	PUNCT
ejpam-411	353	1	332	332	NUM
ejpam-411	353	2	(	(	PUNCT
ejpam-411	353	3	2007	2007	NUM
ejpam-411	353	4	)	)	PUNCT
ejpam-411	353	5	,	,	PUNCT
ejpam-411	353	6	109	109	NUM
ejpam-411	353	7	–	–	PUNCT
ejpam-411	353	8	122	122	NUM
ejpam-411	353	9	.	.	PUNCT
ejpam-411	354	1	[	[	X
ejpam-411	354	2	17	17	NUM
ejpam-411	354	3	]	]	PUNCT
ejpam-411	354	4	j.	j.	PROPN
ejpam-411	354	5	patel	patel	PROPN
ejpam-411	354	6	,	,	PUNCT
ejpam-411	354	7	a.	a.	PROPN
ejpam-411	354	8	k.	k.	PROPN
ejpam-411	354	9	mishra	mishra	PROPN
ejpam-411	354	10	and	and	CCONJ
ejpam-411	354	11	h.	h.	PROPN
ejpam-411	354	12	m.	m.	PROPN
ejpam-411	354	13	srivastava	srivastava	PROPN
ejpam-411	354	14	,	,	PUNCT
ejpam-411	354	15	classes	class	NOUN
ejpam-411	354	16	of	of	ADP
ejpam-411	354	17	multivalent	multivalent	NOUN
ejpam-411	354	18	analytic	analytic	ADJ
ejpam-411	354	19	functions	function	NOUN
ejpam-411	354	20	involving	involve	VERB
ejpam-411	354	21	the	the	DET
ejpam-411	354	22	dziok	dziok	NOUN
ejpam-411	354	23	–	–	PUNCT
ejpam-411	354	24	srivastava	srivastava	PROPN
ejpam-411	354	25	operator	operator	NOUN
ejpam-411	354	26	,	,	PUNCT
ejpam-411	354	27	comput	comput	NOUN
ejpam-411	354	28	.	.	PUNCT
ejpam-411	354	29	math	math	NOUN
ejpam-411	354	30	.	.	PUNCT
ejpam-411	355	1	appl	appl	PROPN
ejpam-411	355	2	.	.	PUNCT
ejpam-411	356	1	54	54	NUM
ejpam-411	356	2	(	(	PUNCT
ejpam-411	356	3	2007	2007	NUM
ejpam-411	356	4	)	)	PUNCT
ejpam-411	356	5	,	,	PUNCT
ejpam-411	356	6	599–616	599–616	NUM
ejpam-411	356	7	.	.	PUNCT
ejpam-411	357	1	[	[	X
ejpam-411	357	2	18	18	NUM
ejpam-411	357	3	]	]	PUNCT
ejpam-411	357	4	k.	k.	NOUN
ejpam-411	357	5	piejko	piejko	PROPN
ejpam-411	357	6	and	and	CCONJ
ejpam-411	357	7	j.	j.	PROPN
ejpam-411	357	8	sokól	sokól	PROPN
ejpam-411	357	9	,	,	PUNCT
ejpam-411	357	10	on	on	ADP
ejpam-411	357	11	the	the	DET
ejpam-411	357	12	dziok	dziok	NOUN
ejpam-411	357	13	-	-	PUNCT
ejpam-411	357	14	srivastava	srivastava	PROPN
ejpam-411	357	15	operator	operator	NOUN
ejpam-411	357	16	under	under	ADP
ejpam-411	357	17	multivalent	multivalent	NOUN
ejpam-411	357	18	analytic	analytic	ADJ
ejpam-411	357	19	functions	function	NOUN
ejpam-411	357	20	,	,	PUNCT
ejpam-411	357	21	appl	appl	PROPN
ejpam-411	357	22	.	.	PROPN
ejpam-411	357	23	math	math	NOUN
ejpam-411	357	24	.	.	PUNCT
ejpam-411	358	1	comput	comput	NOUN
ejpam-411	358	2	.	.	PUNCT
ejpam-411	359	1	177	177	NUM
ejpam-411	359	2	(	(	PUNCT
ejpam-411	359	3	2006	2006	NUM
ejpam-411	359	4	)	)	PUNCT
ejpam-411	359	5	,	,	PUNCT
ejpam-411	359	6	839–843	839–843	NUM
ejpam-411	359	7	.	.	PUNCT
ejpam-411	360	1	[	[	X
ejpam-411	360	2	19	19	NUM
ejpam-411	360	3	]	]	PUNCT
ejpam-411	360	4	r.	r.	PROPN
ejpam-411	360	5	k.	k.	PROPN
ejpam-411	360	6	raina	raina	PROPN
ejpam-411	360	7	and	and	CCONJ
ejpam-411	360	8	d.	d.	PROPN
ejpam-411	360	9	bansal	bansal	PROPN
ejpam-411	360	10	,	,	PUNCT
ejpam-411	360	11	some	some	DET
ejpam-411	360	12	properties	property	NOUN
ejpam-411	360	13	of	of	ADP
ejpam-411	360	14	a	a	DET
ejpam-411	360	15	new	new	ADJ
ejpam-411	360	16	class	class	NOUN
ejpam-411	360	17	of	of	ADP
ejpam-411	360	18	analytic	analytic	ADJ
ejpam-411	360	19	functions	function	NOUN
ejpam-411	360	20	defined	define	VERB
ejpam-411	360	21	in	in	ADP
ejpam-411	360	22	terms	term	NOUN
ejpam-411	360	23	of	of	ADP
ejpam-411	360	24	a	a	DET
ejpam-411	360	25	hadamard	hadamard	ADJ
ejpam-411	360	26	product	product	NOUN
ejpam-411	360	27	,	,	PUNCT
ejpam-411	360	28	j.	j.	PROPN
ejpam-411	360	29	inequal	inequal	PROPN
ejpam-411	360	30	.	.	PUNCT
ejpam-411	361	1	pure	pure	ADJ
ejpam-411	361	2	appl	appl	PROPN
ejpam-411	361	3	.	.	PUNCT
ejpam-411	361	4	math	math	NOUN
ejpam-411	361	5	.	.	PUNCT
ejpam-411	362	1	9	9	NUM
ejpam-411	362	2	(	(	PUNCT
ejpam-411	362	3	1	1	NUM
ejpam-411	362	4	)	)	PUNCT
ejpam-411	362	5	(	(	PUNCT
ejpam-411	362	6	2008	2008	NUM
ejpam-411	362	7	)	)	PUNCT
ejpam-411	362	8	,	,	PUNCT
ejpam-411	362	9	article	article	NOUN
ejpam-411	362	10	22	22	NUM
ejpam-411	362	11	,	,	PUNCT
ejpam-411	362	12	1–9	1–9	NUM
ejpam-411	362	13	(	(	PUNCT
ejpam-411	362	14	electronic	electronic	ADJ
ejpam-411	362	15	)	)	PUNCT
ejpam-411	362	16	.	.	PUNCT
ejpam-411	363	1	[	[	X
ejpam-411	363	2	20	20	NUM
ejpam-411	363	3	]	]	X
ejpam-411	363	4	c.	c.	PROPN
ejpam-411	363	5	ramachandran	ramachandran	PROPN
ejpam-411	363	6	,	,	PUNCT
ejpam-411	363	7	t.	t.	PROPN
ejpam-411	363	8	n.	n.	PROPN
ejpam-411	363	9	shanmugam	shanmugam	PROPN
ejpam-411	363	10	,	,	PUNCT
ejpam-411	363	11	h.	h.	PROPN
ejpam-411	363	12	m.	m.	PROPN
ejpam-411	363	13	srivastava	srivastava	PROPN
ejpam-411	363	14	and	and	CCONJ
ejpam-411	363	15	a.	a.	NOUN
ejpam-411	363	16	swaminathan	swaminathan	PROPN
ejpam-411	363	17	,	,	PUNCT
ejpam-411	363	18	a	a	DET
ejpam-411	363	19	unified	unified	ADJ
ejpam-411	363	20	class	class	NOUN
ejpam-411	363	21	of	of	ADP
ejpam-411	363	22	k	k	NOUN
ejpam-411	363	23	-	-	ADJ
ejpam-411	363	24	uniformly	uniformly	ADJ
ejpam-411	363	25	convex	convex	NOUN
ejpam-411	363	26	functions	function	NOUN
ejpam-411	363	27	defined	define	VERB
ejpam-411	363	28	by	by	ADP
ejpam-411	363	29	the	the	DET
ejpam-411	363	30	dziok	dziok	NOUN
ejpam-411	363	31	-	-	PUNCT
ejpam-411	363	32	srivastava	srivastava	PROPN
ejpam-411	363	33	linear	linear	PROPN
ejpam-411	363	34	operator	operator	NOUN
ejpam-411	363	35	,	,	PUNCT
ejpam-411	363	36	appl	appl	PROPN
ejpam-411	363	37	.	.	PROPN
ejpam-411	363	38	math	math	PROPN
ejpam-411	363	39	.	.	PUNCT
ejpam-411	364	1	comput	comput	NOUN
ejpam-411	364	2	.	.	PUNCT
ejpam-411	365	1	190	190	NUM
ejpam-411	365	2	(	(	PUNCT
ejpam-411	365	3	2007	2007	NUM
ejpam-411	365	4	)	)	PUNCT
ejpam-411	365	5	,	,	PUNCT
ejpam-411	365	6	1627–1636	1627–1636	NUM
ejpam-411	365	7	.	.	PUNCT
ejpam-411	366	1	[	[	X
ejpam-411	366	2	21	21	NUM
ejpam-411	366	3	]	]	X
ejpam-411	366	4	c.	c.	PROPN
ejpam-411	366	5	ramachandran	ramachandran	PROPN
ejpam-411	366	6	,	,	PUNCT
ejpam-411	366	7	h.	h.	PROPN
ejpam-411	366	8	m.	m.	PROPN
ejpam-411	366	9	srivastava	srivastava	PROPN
ejpam-411	366	10	and	and	CCONJ
ejpam-411	366	11	a.	a.	NOUN
ejpam-411	366	12	swaminathan	swaminathan	PROPN
ejpam-411	366	13	,	,	PUNCT
ejpam-411	366	14	a	a	DET
ejpam-411	366	15	unified	unified	ADJ
ejpam-411	366	16	class	class	NOUN
ejpam-411	366	17	of	of	ADP
ejpam-411	366	18	k	k	NOUN
ejpam-411	366	19	-	-	ADJ
ejpam-411	366	20	uniformly	uniformly	ADJ
ejpam-411	366	21	convex	convex	NOUN
ejpam-411	366	22	functions	function	NOUN
ejpam-411	366	23	defined	define	VERB
ejpam-411	366	24	by	by	ADP
ejpam-411	366	25	the	the	DET
ejpam-411	366	26	sălăjean	sălăjean	ADJ
ejpam-411	366	27	derivative	derivative	ADJ
ejpam-411	366	28	operator	operator	NOUN
ejpam-411	366	29	,	,	PUNCT
ejpam-411	366	30	atti	atti	PROPN
ejpam-411	366	31	.	.	PROPN
ejpam-411	366	32	sem	sem	PROPN
ejpam-411	366	33	.	.	PUNCT
ejpam-411	366	34	mat	mat	PROPN
ejpam-411	366	35	.	.	PROPN
ejpam-411	366	36	fis	fis	PROPN
ejpam-411	366	37	.	.	PUNCT
ejpam-411	367	1	modena	modena	PROPN
ejpam-411	367	2	reggio	reggio	PROPN
ejpam-411	367	3	emilia	emilia	PROPN
ejpam-411	367	4	55	55	NUM
ejpam-411	367	5	(	(	PUNCT
ejpam-411	367	6	2007	2007	NUM
ejpam-411	367	7	)	)	PUNCT
ejpam-411	367	8	,	,	PUNCT
ejpam-411	367	9	47–59	47–59	NOUN
ejpam-411	367	10	.	.	PUNCT
ejpam-411	368	1	[	[	X
ejpam-411	368	2	22	22	NUM
ejpam-411	368	3	]	]	X
ejpam-411	368	4	f.	f.	PROPN
ejpam-411	368	5	rnning	rnning	PROPN
ejpam-411	368	6	,	,	PUNCT
ejpam-411	368	7	uniformly	uniformly	ADV
ejpam-411	368	8	convex	convex	NOUN
ejpam-411	368	9	functions	function	NOUN
ejpam-411	368	10	and	and	CCONJ
ejpam-411	368	11	a	a	DET
ejpam-411	368	12	corresponding	corresponding	ADJ
ejpam-411	368	13	class	class	NOUN
ejpam-411	368	14	of	of	ADP
ejpam-411	368	15	starlike	starlike	NOUN
ejpam-411	368	16	functions	function	NOUN
ejpam-411	368	17	,	,	PUNCT
ejpam-411	368	18	proc	proc	NOUN
ejpam-411	368	19	.	.	PUNCT
ejpam-411	369	1	amer	amer	PROPN
ejpam-411	369	2	.	.	PUNCT
ejpam-411	369	3	math	math	PROPN
ejpam-411	369	4	.	.	PUNCT
ejpam-411	370	1	soc	soc	PROPN
ejpam-411	370	2	.	.	PUNCT
ejpam-411	371	1	118	118	NUM
ejpam-411	371	2	(	(	PUNCT
ejpam-411	371	3	1993	1993	NUM
ejpam-411	371	4	)	)	PUNCT
ejpam-411	371	5	,	,	PUNCT
ejpam-411	371	6	189–196	189–196	NUM
ejpam-411	371	7	.	.	PUNCT
ejpam-411	372	1	[	[	X
ejpam-411	372	2	23	23	NUM
ejpam-411	372	3	]	]	PUNCT
ejpam-411	372	4	h.	h.	PROPN
ejpam-411	372	5	silverman	silverman	PROPN
ejpam-411	372	6	,	,	PUNCT
ejpam-411	372	7	univalent	univalent	ADJ
ejpam-411	372	8	functions	function	NOUN
ejpam-411	372	9	with	with	ADP
ejpam-411	372	10	negative	negative	ADJ
ejpam-411	372	11	coefficients	coefficient	NOUN
ejpam-411	372	12	,	,	PUNCT
ejpam-411	372	13	proc	proc	NOUN
ejpam-411	372	14	.	.	PUNCT
ejpam-411	373	1	amer	amer	PROPN
ejpam-411	373	2	.	.	PUNCT
ejpam-411	373	3	math	math	PROPN
ejpam-411	373	4	.	.	PUNCT
ejpam-411	374	1	soc	soc	PROPN
ejpam-411	374	2	.	.	PUNCT
ejpam-411	375	1	51	51	NUM
ejpam-411	375	2	(	(	PUNCT
ejpam-411	375	3	1975	1975	NUM
ejpam-411	375	4	)	)	PUNCT
ejpam-411	375	5	,	,	PUNCT
ejpam-411	375	6	109–116	109–116	NUM
ejpam-411	375	7	.	.	PUNCT
ejpam-411	376	1	[	[	X
ejpam-411	376	2	24	24	NUM
ejpam-411	376	3	]	]	X
ejpam-411	376	4	h.	h.	PROPN
ejpam-411	376	5	silverman	silverman	PROPN
ejpam-411	376	6	,	,	PUNCT
ejpam-411	376	7	univalent	univalent	ADJ
ejpam-411	376	8	functions	function	NOUN
ejpam-411	376	9	with	with	ADP
ejpam-411	376	10	varying	vary	VERB
ejpam-411	376	11	arguments	argument	NOUN
ejpam-411	376	12	,	,	PUNCT
ejpam-411	376	13	houston	houston	PROPN
ejpam-411	376	14	j.	j.	PROPN
ejpam-411	376	15	math	math	PROPN
ejpam-411	376	16	.	.	PUNCT
ejpam-411	377	1	7	7	NUM
ejpam-411	377	2	(	(	PUNCT
ejpam-411	377	3	1981	1981	NUM
ejpam-411	377	4	)	)	PUNCT
ejpam-411	377	5	,	,	PUNCT
ejpam-411	377	6	283–287	283–287	NUM
ejpam-411	377	7	.	.	PUNCT
ejpam-411	378	1	[	[	X
ejpam-411	378	2	25	25	NUM
ejpam-411	378	3	]	]	PUNCT
ejpam-411	378	4	h.	h.	PROPN
ejpam-411	378	5	silverman	silverman	PROPN
ejpam-411	378	6	,	,	PUNCT
ejpam-411	378	7	a	a	DET
ejpam-411	378	8	survey	survey	NOUN
ejpam-411	378	9	with	with	ADP
ejpam-411	378	10	open	open	ADJ
ejpam-411	378	11	problems	problem	NOUN
ejpam-411	378	12	on	on	ADP
ejpam-411	378	13	univalent	univalent	ADJ
ejpam-411	378	14	functions	function	NOUN
ejpam-411	378	15	whose	whose	DET
ejpam-411	378	16	coefficients	coefficient	NOUN
ejpam-411	378	17	are	be	AUX
ejpam-411	378	18	negative	negative	ADJ
ejpam-411	378	19	,	,	PUNCT
ejpam-411	378	20	rocky	rocky	ADJ
ejpam-411	378	21	mountain	mountain	NOUN
ejpam-411	378	22	j.	j.	PROPN
ejpam-411	378	23	math	math	PROPN
ejpam-411	378	24	.	.	PUNCT
ejpam-411	379	1	21	21	NUM
ejpam-411	379	2	(	(	PUNCT
ejpam-411	379	3	1991	1991	NUM
ejpam-411	379	4	)	)	PUNCT
ejpam-411	379	5	,	,	PUNCT
ejpam-411	379	6	1099–1125	1099–1125	NUM
ejpam-411	379	7	.	.	PUNCT
ejpam-411	380	1	[	[	X
ejpam-411	380	2	26	26	NUM
ejpam-411	380	3	]	]	PUNCT
ejpam-411	380	4	h.	h.	PROPN
ejpam-411	380	5	silverman	silverman	PROPN
ejpam-411	380	6	,	,	PUNCT
ejpam-411	380	7	integral	integral	ADJ
ejpam-411	380	8	means	mean	NOUN
ejpam-411	380	9	for	for	ADP
ejpam-411	380	10	univalent	univalent	ADJ
ejpam-411	380	11	functions	function	NOUN
ejpam-411	380	12	with	with	ADP
ejpam-411	380	13	negative	negative	ADJ
ejpam-411	380	14	coefficients	coefficient	NOUN
ejpam-411	380	15	,	,	PUNCT
ejpam-411	380	16	houston	houston	PROPN
ejpam-411	380	17	j.	j.	PROPN
ejpam-411	380	18	math	math	PROPN
ejpam-411	380	19	.	.	PUNCT
ejpam-411	381	1	23	23	NUM
ejpam-411	381	2	(	(	PUNCT
ejpam-411	381	3	1997	1997	NUM
ejpam-411	381	4	)	)	PUNCT
ejpam-411	381	5	,	,	PUNCT
ejpam-411	382	1	169–174	169–174	NUM
ejpam-411	382	2	.	.	PUNCT
ejpam-411	383	1	references	reference	NOUN
ejpam-411	383	2	324	324	NUM
ejpam-411	384	1	[	[	X
ejpam-411	384	2	27	27	NUM
ejpam-411	384	3	]	]	PUNCT
ejpam-411	384	4	j.	j.	PROPN
ejpam-411	384	5	sokół	sokół	PROPN
ejpam-411	384	6	,	,	PUNCT
ejpam-411	384	7	on	on	ADP
ejpam-411	384	8	some	some	DET
ejpam-411	384	9	applications	application	NOUN
ejpam-411	384	10	of	of	ADP
ejpam-411	384	11	the	the	DET
ejpam-411	384	12	dziok	dziok	NOUN
ejpam-411	384	13	-	-	PUNCT
ejpam-411	384	14	srivastava	srivastava	PROPN
ejpam-411	384	15	operator	operator	NOUN
ejpam-411	384	16	,	,	PUNCT
ejpam-411	384	17	appl	appl	PROPN
ejpam-411	384	18	.	.	PROPN
ejpam-411	384	19	math	math	PROPN
ejpam-411	384	20	.	.	PUNCT
ejpam-411	385	1	comput	comput	NOUN
ejpam-411	385	2	.	.	PUNCT
ejpam-411	386	1	201	201	NUM
ejpam-411	386	2	(	(	PUNCT
ejpam-411	386	3	2008	2008	NUM
ejpam-411	386	4	)	)	PUNCT
ejpam-411	386	5	,	,	PUNCT
ejpam-411	386	6	774–780	774–780	NUM
ejpam-411	386	7	.	.	PUNCT
ejpam-411	387	1	[	[	X
ejpam-411	387	2	28	28	NUM
ejpam-411	387	3	]	]	X
ejpam-411	387	4	h.	h.	PROPN
ejpam-411	387	5	m.	m.	PROPN
ejpam-411	387	6	srivastava	srivastava	PROPN
ejpam-411	387	7	and	and	CCONJ
ejpam-411	387	8	m.	m.	PROPN
ejpam-411	387	9	k.	k.	PROPN
ejpam-411	387	10	aouf	aouf	PROPN
ejpam-411	387	11	,	,	PUNCT
ejpam-411	387	12	a	a	DET
ejpam-411	387	13	certain	certain	ADJ
ejpam-411	387	14	fractional	fractional	ADJ
ejpam-411	387	15	derivative	derivative	ADJ
ejpam-411	387	16	operator	operator	NOUN
ejpam-411	387	17	and	and	CCONJ
ejpam-411	387	18	its	its	PRON
ejpam-411	387	19	applications	application	NOUN
ejpam-411	387	20	to	to	ADP
ejpam-411	387	21	a	a	DET
ejpam-411	387	22	new	new	ADJ
ejpam-411	387	23	class	class	NOUN
ejpam-411	387	24	of	of	ADP
ejpam-411	387	25	analytic	analytic	ADJ
ejpam-411	387	26	and	and	CCONJ
ejpam-411	387	27	multivalent	multivalent	NOUN
ejpam-411	387	28	functions	function	NOUN
ejpam-411	387	29	with	with	ADP
ejpam-411	387	30	negative	negative	ADJ
ejpam-411	387	31	coefficients	coefficient	NOUN
ejpam-411	387	32	.	.	PUNCT
ejpam-411	388	1	i	i	PRON
ejpam-411	388	2	and	and	CCONJ
ejpam-411	388	3	ii	ii	PROPN
ejpam-411	388	4	,	,	PUNCT
ejpam-411	388	5	j.	j.	PROPN
ejpam-411	388	6	math	math	PROPN
ejpam-411	388	7	.	.	PUNCT
ejpam-411	389	1	anal	anal	PROPN
ejpam-411	389	2	.	.	PUNCT
ejpam-411	390	1	appl	appl	PROPN
ejpam-411	390	2	.	.	PUNCT
ejpam-411	391	1	171	171	NUM
ejpam-411	391	2	(	(	PUNCT
ejpam-411	391	3	1992	1992	NUM
ejpam-411	391	4	)	)	PUNCT
ejpam-411	391	5	,	,	PUNCT
ejpam-411	391	6	1–13	1–13	NOUN
ejpam-411	391	7	;	;	PUNCT
ejpam-411	391	8	ibid	ibid	NOUN
ejpam-411	391	9	.	.	PUNCT
ejpam-411	392	1	192	192	NUM
ejpam-411	392	2	(	(	PUNCT
ejpam-411	392	3	1995	1995	NUM
ejpam-411	392	4	)	)	PUNCT
ejpam-411	392	5	,	,	PUNCT
ejpam-411	392	6	673–688	673–688	NUM
ejpam-411	392	7	.	.	PUNCT
ejpam-411	393	1	[	[	X
ejpam-411	393	2	29	29	NUM
ejpam-411	393	3	]	]	X
ejpam-411	393	4	h.	h.	PROPN
ejpam-411	393	5	m.	m.	PROPN
ejpam-411	393	6	srivastava	srivastava	PROPN
ejpam-411	393	7	and	and	CCONJ
ejpam-411	393	8	p.	p.	PROPN
ejpam-411	393	9	w.	w.	PROPN
ejpam-411	393	10	karlsson	karlsson	PROPN
ejpam-411	393	11	,	,	PUNCT
ejpam-411	393	12	multiple	multiple	ADJ
ejpam-411	393	13	gaussian	gaussian	ADJ
ejpam-411	393	14	hypergeometric	hypergeometric	ADJ
ejpam-411	393	15	series	series	NOUN
ejpam-411	393	16	,	,	PUNCT
ejpam-411	393	17	halsted	halsted	ADJ
ejpam-411	393	18	press	press	PROPN
ejpam-411	393	19	(	(	PUNCT
ejpam-411	393	20	ellis	ellis	PROPN
ejpam-411	393	21	horwood	horwood	PROPN
ejpam-411	393	22	limited	limited	PROPN
ejpam-411	393	23	,	,	PUNCT
ejpam-411	393	24	chichester	chichester	PROPN
ejpam-411	393	25	)	)	PUNCT
ejpam-411	393	26	,	,	PUNCT
ejpam-411	393	27	john	john	PROPN
ejpam-411	393	28	wiley	wiley	PROPN
ejpam-411	393	29	and	and	CCONJ
ejpam-411	393	30	sons	son	NOUN
ejpam-411	393	31	,	,	PUNCT
ejpam-411	393	32	new	new	PROPN
ejpam-411	393	33	york	york	PROPN
ejpam-411	393	34	,	,	PUNCT
ejpam-411	393	35	chichester	chichester	PROPN
ejpam-411	393	36	,	,	PUNCT
ejpam-411	393	37	brisbane	brisbane	NOUN
ejpam-411	393	38	and	and	CCONJ
ejpam-411	393	39	toronto	toronto	PROPN
ejpam-411	393	40	,	,	PUNCT
ejpam-411	393	41	1985	1985	NUM
ejpam-411	393	42	.	.	PUNCT
ejpam-411	394	1	[	[	X
ejpam-411	394	2	30	30	NUM
ejpam-411	394	3	]	]	X
ejpam-411	394	4	h.	h.	PROPN
ejpam-411	394	5	m.	m.	PROPN
ejpam-411	394	6	srivastava	srivastava	PROPN
ejpam-411	394	7	and	and	CCONJ
ejpam-411	394	8	a.	a.	PROPN
ejpam-411	394	9	k.	k.	PROPN
ejpam-411	394	10	mishra	mishra	PROPN
ejpam-411	394	11	,	,	PUNCT
ejpam-411	394	12	applications	application	NOUN
ejpam-411	394	13	of	of	ADP
ejpam-411	394	14	fractional	fractional	ADJ
ejpam-411	394	15	calculus	calculus	NOUN
ejpam-411	394	16	to	to	PART
ejpam-411	394	17	parabolic	parabolic	VERB
ejpam-411	394	18	starlike	starlike	NOUN
ejpam-411	394	19	and	and	CCONJ
ejpam-411	394	20	uniformly	uniformly	ADV
ejpam-411	394	21	convex	convex	NOUN
ejpam-411	394	22	functions	function	NOUN
ejpam-411	394	23	,	,	PUNCT
ejpam-411	394	24	comput	comput	NOUN
ejpam-411	394	25	.	.	PUNCT
ejpam-411	395	1	math	math	NOUN
ejpam-411	395	2	.	.	PUNCT
ejpam-411	396	1	appl	appl	PROPN
ejpam-411	396	2	.	.	PROPN
ejpam-411	397	1	39	39	NUM
ejpam-411	397	2	(	(	PUNCT
ejpam-411	397	3	2000	2000	NUM
ejpam-411	397	4	)	)	PUNCT
ejpam-411	397	5	,	,	PUNCT
ejpam-411	397	6	57–69	57–69	X
ejpam-411	397	7	.	.	PUNCT
ejpam-411	398	1	[	[	X
ejpam-411	398	2	31	31	NUM
ejpam-411	398	3	]	]	PUNCT
ejpam-411	398	4	h.	h.	PROPN
ejpam-411	398	5	m.	m.	PROPN
ejpam-411	398	6	srivastava	srivastava	PROPN
ejpam-411	398	7	and	and	CCONJ
ejpam-411	398	8	s	s	VERB
ejpam-411	398	9	owa	owa	PROPN
ejpam-411	398	10	,	,	PUNCT
ejpam-411	398	11	certain	certain	ADJ
ejpam-411	398	12	classes	class	NOUN
ejpam-411	398	13	of	of	ADP
ejpam-411	398	14	analytic	analytic	ADJ
ejpam-411	398	15	functions	function	NOUN
ejpam-411	398	16	with	with	ADP
ejpam-411	398	17	varying	vary	VERB
ejpam-411	398	18	arguments	argument	NOUN
ejpam-411	398	19	,	,	PUNCT
ejpam-411	398	20	j.	j.	PROPN
ejpam-411	398	21	math	math	PROPN
ejpam-411	398	22	.	.	PUNCT
ejpam-411	399	1	anal	anal	PROPN
ejpam-411	399	2	.	.	PUNCT
ejpam-411	399	3	appl	appl	PROPN
ejpam-411	399	4	.	.	PROPN
ejpam-411	400	1	136	136	NUM
ejpam-411	400	2	(	(	PUNCT
ejpam-411	400	3	1988	1988	NUM
ejpam-411	400	4	)	)	PUNCT
ejpam-411	400	5	,	,	PUNCT
ejpam-411	400	6	217–228	217–228	NUM
ejpam-411	400	7	.	.	PUNCT
ejpam-411	401	1	[	[	X
ejpam-411	401	2	32	32	NUM
ejpam-411	401	3	]	]	PUNCT
ejpam-411	401	4	h.	h.	PROPN
ejpam-411	401	5	m.	m.	PROPN
ejpam-411	401	6	srivastava	srivastava	PROPN
ejpam-411	401	7	and	and	CCONJ
ejpam-411	401	8	s.	s.	PROPN
ejpam-411	401	9	owa	owa	PROPN
ejpam-411	401	10	(	(	PUNCT
ejpam-411	401	11	editors	editor	NOUN
ejpam-411	401	12	)	)	PUNCT
ejpam-411	401	13	,	,	PUNCT
ejpam-411	401	14	current	current	ADJ
ejpam-411	401	15	topics	topic	NOUN
ejpam-411	401	16	in	in	ADP
ejpam-411	401	17	analytic	analytic	ADJ
ejpam-411	401	18	function	function	NOUN
ejpam-411	401	19	theory	theory	NOUN
ejpam-411	401	20	,	,	PUNCT
ejpam-411	401	21	world	world	NOUN
ejpam-411	401	22	scientific	scientific	ADJ
ejpam-411	401	23	publishing	publishing	NOUN
ejpam-411	401	24	company	company	NOUN
ejpam-411	401	25	,	,	PUNCT
ejpam-411	401	26	singapore	singapore	PROPN
ejpam-411	401	27	,	,	PUNCT
ejpam-411	401	28	new	new	PROPN
ejpam-411	401	29	jersey	jersey	PROPN
ejpam-411	401	30	,	,	PUNCT
ejpam-411	401	31	london	london	PROPN
ejpam-411	401	32	and	and	CCONJ
ejpam-411	401	33	hong	hong	PROPN
ejpam-411	401	34	kong	kong	PROPN
ejpam-411	401	35	,	,	PUNCT
ejpam-411	401	36	1992	1992	NUM
ejpam-411	401	37	.	.	PUNCT
ejpam-411	402	1	[	[	X
ejpam-411	402	2	33	33	NUM
ejpam-411	402	3	]	]	PUNCT
ejpam-411	402	4	h.	h.	PROPN
ejpam-411	402	5	m.	m.	PROPN
ejpam-411	402	6	srivastava	srivastava	PROPN
ejpam-411	402	7	,	,	PUNCT
ejpam-411	402	8	t.	t.	PROPN
ejpam-411	402	9	n.	n.	PROPN
ejpam-411	402	10	shanmugam	shanmugam	PROPN
ejpam-411	402	11	,	,	PUNCT
ejpam-411	402	12	c.	c.	PROPN
ejpam-411	402	13	ramachandran	ramachandran	PROPN
ejpam-411	402	14	and	and	CCONJ
ejpam-411	402	15	s.	s.	PROPN
ejpam-411	402	16	sivasubramanian	sivasubramanian	PROPN
ejpam-411	402	17	,	,	PUNCT
ejpam-411	402	18	a	a	DET
ejpam-411	402	19	new	new	ADJ
ejpam-411	402	20	subclass	subclass	NOUN
ejpam-411	402	21	of	of	ADP
ejpam-411	402	22	k	k	NOUN
ejpam-411	402	23	-	-	ADJ
ejpam-411	402	24	uniformly	uniformly	ADJ
ejpam-411	402	25	convex	convex	NOUN
ejpam-411	402	26	functions	function	NOUN
ejpam-411	402	27	with	with	ADP
ejpam-411	402	28	negative	negative	ADJ
ejpam-411	402	29	coefficients	coefficient	NOUN
ejpam-411	402	30	,	,	PUNCT
ejpam-411	402	31	j.	j.	PROPN
ejpam-411	402	32	inequal	inequal	PROPN
ejpam-411	402	33	.	.	PUNCT
ejpam-411	403	1	pure	pure	ADJ
ejpam-411	403	2	appl	appl	PROPN
ejpam-411	403	3	.	.	PUNCT
ejpam-411	403	4	math	math	NOUN
ejpam-411	403	5	.	.	PUNCT
ejpam-411	404	1	8	8	NUM
ejpam-411	404	2	(	(	PUNCT
ejpam-411	404	3	2	2	NUM
ejpam-411	404	4	)	)	PUNCT
ejpam-411	404	5	(	(	PUNCT
ejpam-411	404	6	2007	2007	NUM
ejpam-411	404	7	)	)	PUNCT
ejpam-411	404	8	,	,	PUNCT
ejpam-411	404	9	article	article	NOUN
ejpam-411	404	10	43	43	NUM
ejpam-411	404	11	,	,	PUNCT
ejpam-411	404	12	1–14	1–14	PROPN
ejpam-411	404	13	(	(	PUNCT
ejpam-411	404	14	electronic	electronic	ADJ
ejpam-411	404	15	)	)	PUNCT
ejpam-411	404	16	.	.	PUNCT
ejpam-411	405	1	[	[	X
ejpam-411	405	2	34	34	NUM
ejpam-411	405	3	]	]	PUNCT
ejpam-411	405	4	z.-g	z.-g	PROPN
ejpam-411	405	5	.	.	PUNCT
ejpam-411	406	1	wang	wang	PROPN
ejpam-411	406	2	,	,	PUNCT
ejpam-411	406	3	y.-p	y.-p	PROPN
ejpam-411	406	4	.	.	PUNCT
ejpam-411	407	1	jiang	jiang	PROPN
ejpam-411	407	2	and	and	CCONJ
ejpam-411	407	3	h.	h.	PROPN
ejpam-411	407	4	m.	m.	PROPN
ejpam-411	407	5	srivastava	srivastava	PROPN
ejpam-411	407	6	,	,	PUNCT
ejpam-411	407	7	some	some	DET
ejpam-411	407	8	subclasses	subclass	NOUN
ejpam-411	407	9	of	of	ADP
ejpam-411	407	10	multivalent	multivalent	NOUN
ejpam-411	407	11	analytic	analytic	ADJ
ejpam-411	407	12	functions	function	NOUN
ejpam-411	407	13	involving	involve	VERB
ejpam-411	407	14	the	the	DET
ejpam-411	407	15	dziok	dziok	NOUN
ejpam-411	407	16	-	-	PUNCT
ejpam-411	407	17	srivastava	srivastava	PROPN
ejpam-411	407	18	operator	operator	NOUN
ejpam-411	407	19	,	,	PUNCT
ejpam-411	407	20	integral	integral	ADJ
ejpam-411	407	21	transform	transform	NOUN
ejpam-411	407	22	.	.	PUNCT
ejpam-411	408	1	spec	spec	PROPN
ejpam-411	408	2	.	.	PUNCT
ejpam-411	409	1	funct	funct	PROPN
ejpam-411	409	2	.	.	PUNCT
ejpam-411	410	1	19	19	NUM
ejpam-411	410	2	(	(	PUNCT
ejpam-411	410	3	2008	2008	NUM
ejpam-411	410	4	)	)	PUNCT
ejpam-411	410	5	,	,	PUNCT
ejpam-411	410	6	129–146	129–146	NUM
ejpam-411	410	7	.	.	PUNCT
ejpam-411	411	1	[	[	X
ejpam-411	411	2	35	35	NUM
ejpam-411	411	3	]	]	X
ejpam-411	411	4	h.	h.	PROPN
ejpam-411	411	5	m.	m.	PROPN
ejpam-411	411	6	srivastava	srivastava	PROPN
ejpam-411	411	7	,	,	PUNCT
ejpam-411	411	8	d.-g	d.-g	PROPN
ejpam-411	411	9	.	.	PUNCT
ejpam-411	412	1	yang	yang	PROPN
ejpam-411	412	2	and	and	CCONJ
ejpam-411	412	3	n	n	CCONJ
ejpam-411	412	4	-	-	PROPN
ejpam-411	412	5	e.	e.	PROPN
ejpam-411	412	6	xu	xu	PROPN
ejpam-411	412	7	,	,	PUNCT
ejpam-411	412	8	subordinations	subordination	NOUN
ejpam-411	412	9	for	for	ADP
ejpam-411	412	10	multivalent	multivalent	NOUN
ejpam-411	412	11	analytic	analytic	ADJ
ejpam-411	412	12	functions	function	NOUN
ejpam-411	412	13	associated	associate	VERB
ejpam-411	412	14	with	with	ADP
ejpam-411	412	15	the	the	DET
ejpam-411	412	16	dziok	dziok	NOUN
ejpam-411	412	17	-	-	PUNCT
ejpam-411	412	18	srivastava	srivastava	PROPN
ejpam-411	412	19	operator	operator	NOUN
ejpam-411	412	20	,	,	PUNCT
ejpam-411	412	21	integral	integral	ADJ
ejpam-411	412	22	transform	transform	NOUN
ejpam-411	412	23	.	.	PUNCT
ejpam-411	413	1	spec	spec	PROPN
ejpam-411	413	2	.	.	PUNCT
ejpam-411	414	1	funct	funct	PROPN
ejpam-411	414	2	.	.	PUNCT
ejpam-411	415	1	20	20	NUM
ejpam-411	415	2	(	(	PUNCT
ejpam-411	415	3	2009	2009	NUM
ejpam-411	415	4	)	)	PUNCT
ejpam-411	415	5	,	,	PUNCT
ejpam-411	416	1	581–606	581–606	NUM
ejpam-411	416	2	.	.	PUNCT
ejpam-411	417	1	[	[	X
ejpam-411	417	2	36	36	NUM
ejpam-411	417	3	]	]	PUNCT
ejpam-411	417	4	h.	h.	PROPN
ejpam-411	417	5	s.	s.	PROPN
ejpam-411	417	6	wilf	wilf	PROPN
ejpam-411	417	7	,	,	PUNCT
ejpam-411	417	8	subordinating	subordinating	NOUN
ejpam-411	417	9	factor	factor	NOUN
ejpam-411	417	10	sequence	sequence	NOUN
ejpam-411	417	11	for	for	ADP
ejpam-411	417	12	convex	convex	NOUN
ejpam-411	417	13	maps	map	NOUN
ejpam-411	417	14	of	of	ADP
ejpam-411	417	15	the	the	DET
ejpam-411	417	16	unit	unit	NOUN
ejpam-411	417	17	circle	circle	NOUN
ejpam-411	417	18	,	,	PUNCT
ejpam-411	417	19	proc	proc	PROPN
ejpam-411	417	20	.	.	PUNCT
ejpam-411	418	1	amer	amer	PROPN
ejpam-411	418	2	.	.	PUNCT
ejpam-411	418	3	math	math	PROPN
ejpam-411	418	4	.	.	PUNCT
ejpam-411	419	1	soc	soc	PROPN
ejpam-411	419	2	.	.	PUNCT
ejpam-411	420	1	12	12	NUM
ejpam-411	420	2	(	(	PUNCT
ejpam-411	420	3	1961	1961	NUM
ejpam-411	420	4	)	)	PUNCT
ejpam-411	420	5	,	,	PUNCT
ejpam-411	420	6	689–693	689–693	NUM
ejpam-411	420	7	.	.	PUNCT