id	sid	tid	token	lemma	pos
ejpam-815	1	1	15_815_goyal.dvi	15_815_goyal.dvi	NUM
ejpam-815	1	2	european	european	ADJ
ejpam-815	1	3	journal	journal	PROPN
ejpam-815	1	4	of	of	ADP
ejpam-815	1	5	pure	pure	ADJ
ejpam-815	1	6	and	and	CCONJ
ejpam-815	1	7	applied	apply	VERB
ejpam-815	1	8	mathematics	mathematic	NOUN
ejpam-815	1	9	vol	vol	NOUN
ejpam-815	1	10	.	.	PUNCT
ejpam-815	2	1	3	3	NUM
ejpam-815	2	2	,	,	PUNCT
ejpam-815	2	3	no	no	INTJ
ejpam-815	2	4	.	.	NOUN
ejpam-815	2	5	6	6	NUM
ejpam-815	2	6	,	,	PUNCT
ejpam-815	2	7	2010	2010	NUM
ejpam-815	2	8	,	,	PUNCT
ejpam-815	2	9	1118	1118	NUM
ejpam-815	2	10	-	-	SYM
ejpam-815	2	11	1123	1123	NUM
ejpam-815	2	12	issn	issn	PROPN
ejpam-815	2	13	1307	1307	NUM
ejpam-815	2	14	-	-	SYM
ejpam-815	2	15	5543	5543	NUM
ejpam-815	2	16	–	–	PUNCT
ejpam-815	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-815	2	18	special	special	ADJ
ejpam-815	2	19	issue	issue	NOUN
ejpam-815	2	20	on	on	ADP
ejpam-815	2	21	complex	complex	ADJ
ejpam-815	2	22	analysis	analysis	NOUN
ejpam-815	2	23	:	:	PUNCT
ejpam-815	2	24	theory	theory	NOUN
ejpam-815	2	25	and	and	CCONJ
ejpam-815	2	26	applications	application	NOUN
ejpam-815	2	27	dedicated	dedicate	VERB
ejpam-815	2	28	to	to	ADP
ejpam-815	2	29	professor	professor	PROPN
ejpam-815	2	30	hari	hari	PROPN
ejpam-815	2	31	m.	m.	PROPN
ejpam-815	2	32	srivastava	srivastava	PROPN
ejpam-815	2	33	,	,	PUNCT
ejpam-815	2	34	on	on	ADP
ejpam-815	2	35	the	the	DET
ejpam-815	2	36	occasion	occasion	NOUN
ejpam-815	2	37	of	of	ADP
ejpam-815	2	38	his	his	PRON
ejpam-815	2	39	70th	70th	ADJ
ejpam-815	2	40	birthday	birthday	NOUN
ejpam-815	2	41	quasi	quasi	ADJ
ejpam-815	2	42	-	-	ADJ
ejpam-815	2	43	hadamard	hadamard	ADJ
ejpam-815	2	44	product	product	NOUN
ejpam-815	2	45	of	of	ADP
ejpam-815	2	46	certain	certain	ADJ
ejpam-815	2	47	meromorphic	meromorphic	ADJ
ejpam-815	2	48	p	p	NOUN
ejpam-815	2	49	-	-	PUNCT
ejpam-815	2	50	valent	valent	NOUN
ejpam-815	2	51	analytic	analytic	ADJ
ejpam-815	2	52	functions	function	NOUN
ejpam-815	2	53	s.	s.	PROPN
ejpam-815	2	54	p.	p.	PROPN
ejpam-815	2	55	goyal1,∗	goyal1,∗	PROPN
ejpam-815	2	56	,	,	PUNCT
ejpam-815	2	57	pranay	pranay	NOUN
ejpam-815	2	58	goswami2	goswami2	PROPN
ejpam-815	2	59	1	1	NUM
ejpam-815	2	60	department	department	NOUN
ejpam-815	2	61	of	of	ADP
ejpam-815	2	62	mathematics	mathematic	NOUN
ejpam-815	2	63	,	,	PUNCT
ejpam-815	2	64	university	university	NOUN
ejpam-815	2	65	of	of	ADP
ejpam-815	2	66	rajasthan	rajasthan	PROPN
ejpam-815	2	67	,	,	PUNCT
ejpam-815	2	68	jaipur-302055	jaipur-302055	NOUN
ejpam-815	2	69	,	,	PUNCT
ejpam-815	2	70	india	india	PROPN
ejpam-815	2	71	2	2	NUM
ejpam-815	2	72	department	department	NOUN
ejpam-815	2	73	of	of	ADP
ejpam-815	2	74	mathematics	mathematic	NOUN
ejpam-815	2	75	,	,	PUNCT
ejpam-815	2	76	amity	amity	NOUN
ejpam-815	2	77	university	university	NOUN
ejpam-815	2	78	rajasthan	rajasthan	NOUN
ejpam-815	2	79	,	,	PUNCT
ejpam-815	2	80	jaipur-302002	jaipur-302002	NOUN
ejpam-815	2	81	,	,	PUNCT
ejpam-815	2	82	india	india	PROPN
ejpam-815	2	83	abstract	abstract	NOUN
ejpam-815	2	84	.	.	PUNCT
ejpam-815	3	1	in	in	ADP
ejpam-815	3	2	this	this	DET
ejpam-815	3	3	paper	paper	NOUN
ejpam-815	3	4	,	,	PUNCT
ejpam-815	3	5	we	we	PRON
ejpam-815	3	6	establish	establish	VERB
ejpam-815	3	7	certain	certain	ADJ
ejpam-815	3	8	results	result	NOUN
ejpam-815	3	9	concerning	concern	VERB
ejpam-815	3	10	the	the	DET
ejpam-815	3	11	quasi	quasi	ADJ
ejpam-815	3	12	-	-	ADJ
ejpam-815	3	13	hadamard	hadamard	ADJ
ejpam-815	3	14	product	product	NOUN
ejpam-815	3	15	for	for	ADP
ejpam-815	3	16	the	the	DET
ejpam-815	3	17	classes	class	NOUN
ejpam-815	3	18	related	relate	VERB
ejpam-815	3	19	to	to	ADP
ejpam-815	3	20	meromorphic	meromorphic	ADJ
ejpam-815	3	21	p	p	PROPN
ejpam-815	3	22	-	-	PUNCT
ejpam-815	3	23	valent	valent	NOUN
ejpam-815	3	24	analytic	analytic	ADJ
ejpam-815	3	25	functions	function	NOUN
ejpam-815	3	26	with	with	ADP
ejpam-815	3	27	positive	positive	ADJ
ejpam-815	3	28	coefficients	coefficient	NOUN
ejpam-815	3	29	.	.	PUNCT
ejpam-815	4	1	2000	2000	NUM
ejpam-815	4	2	mathematics	mathematic	NOUN
ejpam-815	4	3	subject	subject	NOUN
ejpam-815	4	4	classifications	classification	NOUN
ejpam-815	4	5	:	:	PUNCT
ejpam-815	4	6	30c45	30c45	NUM
ejpam-815	4	7	key	key	ADJ
ejpam-815	4	8	words	word	NOUN
ejpam-815	4	9	and	and	CCONJ
ejpam-815	4	10	phrases	phrase	NOUN
ejpam-815	4	11	:	:	PUNCT
ejpam-815	4	12	analytic	analytic	ADJ
ejpam-815	4	13	functions	function	NOUN
ejpam-815	4	14	,	,	PUNCT
ejpam-815	4	15	meromorphic	meromorphic	ADJ
ejpam-815	4	16	p	p	PROPN
ejpam-815	4	17	-	-	PUNCT
ejpam-815	4	18	valent	valent	NOUN
ejpam-815	4	19	functions	function	NOUN
ejpam-815	4	20	,	,	PUNCT
ejpam-815	4	21	quasi	quasi	ADJ
ejpam-815	4	22	-	-	ADJ
ejpam-815	4	23	hadamard	hadamard	ADJ
ejpam-815	4	24	product	product	NOUN
ejpam-815	4	25	1	1	NUM
ejpam-815	4	26	.	.	PUNCT
ejpam-815	5	1	introduction	introduction	NOUN
ejpam-815	5	2	throughout	throughout	ADP
ejpam-815	5	3	this	this	DET
ejpam-815	5	4	paper	paper	NOUN
ejpam-815	5	5	,	,	PUNCT
ejpam-815	5	6	let	let	VERB
ejpam-815	5	7	p	p	PRON
ejpam-815	5	8	∈	∈	PROPN
ejpam-815	5	9	n	n	NOUN
ejpam-815	5	10	=	=	PUNCT
ejpam-815	5	11	{	{	PUNCT
ejpam-815	5	12	1,2,3	1,2,3	NUM
ejpam-815	5	13	,	,	PUNCT
ejpam-815	5	14	.	.	PUNCT
ejpam-815	5	15	.	.	PUNCT
ejpam-815	6	1	.	.	PUNCT
ejpam-815	6	2	}	}	PUNCT
ejpam-815	7	1	and	and	CCONJ
ejpam-815	7	2	the	the	DET
ejpam-815	7	3	functions	function	NOUN
ejpam-815	7	4	of	of	ADP
ejpam-815	7	5	the	the	DET
ejpam-815	7	6	form	form	NOUN
ejpam-815	7	7	:	:	PUNCT
ejpam-815	7	8	ϕ(z	ϕ(z	NOUN
ejpam-815	7	9	)	)	PUNCT
ejpam-815	7	10	=	=	PUNCT
ejpam-815	8	1	apzp	apzp	ADP
ejpam-815	8	2	−	−	NUM
ejpam-815	8	3	∞	∞	PROPN
ejpam-815	8	4	∑	∑	PROPN
ejpam-815	8	5	n=1	n=1	PROPN
ejpam-815	8	6	an+pzn+p	an+pzn+p	PRON
ejpam-815	8	7	�	�	PROPN
ejpam-815	8	8	ap	ap	PROPN
ejpam-815	8	9	>	>	X
ejpam-815	8	10	0	0	NUM
ejpam-815	8	11	;	;	PUNCT
ejpam-815	8	12	ap+n	ap+n	ADJ
ejpam-815	8	13	≥	≥	X
ejpam-815	8	14	0	0	NUM
ejpam-815	8	15	�	�	PROPN
ejpam-815	8	16	,	,	PUNCT
ejpam-815	8	17	ψ(z	ψ(z	PROPN
ejpam-815	8	18	)	)	PUNCT
ejpam-815	8	19	=	=	SYM
ejpam-815	8	20	bpzp	bpzp	NOUN
ejpam-815	8	21	−	−	NOUN
ejpam-815	8	22	∞	∞	PROPN
ejpam-815	8	23	∑	∑	PROPN
ejpam-815	8	24	n=1	n=1	PROPN
ejpam-815	9	1	bn+pzn+p	bn+pzn+p	PROPN
ejpam-815	9	2	�	�	PROPN
ejpam-815	9	3	ap	ap	PROPN
ejpam-815	9	4	>	>	X
ejpam-815	9	5	0	0	NUM
ejpam-815	9	6	;	;	PUNCT
ejpam-815	9	7	bp+n	bp+n	ADJ
ejpam-815	9	8	≥	≥	X
ejpam-815	9	9	0	0	NUM
ejpam-815	9	10	�	�	PROPN
ejpam-815	9	11	,	,	PUNCT
ejpam-815	9	12	be	be	AUX
ejpam-815	9	13	analytic	analytic	ADJ
ejpam-815	9	14	and	and	CCONJ
ejpam-815	9	15	p	p	NOUN
ejpam-815	9	16	-	-	PUNCT
ejpam-815	9	17	valent	valent	NOUN
ejpam-815	9	18	in	in	ADP
ejpam-815	9	19	the	the	DET
ejpam-815	9	20	unit	unit	NOUN
ejpam-815	9	21	disc	disc	NOUN
ejpam-815	9	22	∆=	∆=	NOUN
ejpam-815	9	23	{	{	PUNCT
ejpam-815	9	24	z	z	NOUN
ejpam-815	9	25	:	:	PUNCT
ejpam-815	9	26	|z|	|z|	NOUN
ejpam-815	9	27	<	<	X
ejpam-815	9	28	1	1	NUM
ejpam-815	9	29	}	}	PUNCT
ejpam-815	9	30	.	.	PUNCT
ejpam-815	10	1	also	also	ADV
ejpam-815	10	2	,	,	PUNCT
ejpam-815	10	3	let	let	VERB
ejpam-815	10	4	f	f	PROPN
ejpam-815	10	5	(	(	PUNCT
ejpam-815	10	6	z	z	NOUN
ejpam-815	10	7	)	)	PUNCT
ejpam-815	10	8	=	=	PUNCT
ejpam-815	11	1	ap−1	ap−1	ADJ
ejpam-815	11	2	zp	zp	NOUN
ejpam-815	11	3	+	+	CCONJ
ejpam-815	11	4	∞	∞	NUM
ejpam-815	11	5	∑	∑	PUNCT
ejpam-815	11	6	n=1	n=1	PROPN
ejpam-815	11	7	an+p−1zn+p−1	an+p−1zn+p−1	PROPN
ejpam-815	11	8	�	�	PROPN
ejpam-815	11	9	ap	ap	PROPN
ejpam-815	11	10	>	>	PROPN
ejpam-815	11	11	0	0	NUM
ejpam-815	11	12	;	;	PUNCT
ejpam-815	11	13	ap+n	ap+n	ADJ
ejpam-815	11	14	≥	≥	X
ejpam-815	11	15	0	0	NUM
ejpam-815	11	16	�	�	PROPN
ejpam-815	11	17	,	,	PUNCT
ejpam-815	11	18	(	(	PUNCT
ejpam-815	11	19	1	1	X
ejpam-815	11	20	)	)	PUNCT
ejpam-815	11	21	∗corresponding	∗corresponde	VERB
ejpam-815	11	22	author	author	NOUN
ejpam-815	11	23	.	.	PUNCT
ejpam-815	12	1	email	email	NOUN
ejpam-815	12	2	addresses	address	NOUN
ejpam-815	12	3	:	:	PUNCT
ejpam-815	12	4	somprg	somprg	PROPN
ejpam-815	12	5	�	�	PROPN
ejpam-815	12	6	gmail	gmail	NOUN
ejpam-815	12	7	.	.	PUNCT
ejpam-815	13	1	om	om	PROPN
ejpam-815	13	2	(	(	PUNCT
ejpam-815	13	3	s.	s.	PROPN
ejpam-815	13	4	goyal	goyal	PROPN
ejpam-815	13	5	)	)	PUNCT
ejpam-815	13	6	,	,	PUNCT
ejpam-815	13	7	pranaygoswami83	pranaygoswami83	PROPN
ejpam-815	13	8	�	�	NOUN
ejpam-815	13	9	gmail	gmail	NOUN
ejpam-815	13	10	.	.	PUNCT
ejpam-815	14	1	om	om	PROPN
ejpam-815	14	2	(	(	PUNCT
ejpam-815	14	3	p.	p.	NOUN
ejpam-815	14	4	goswami	goswami	PROPN
ejpam-815	14	5	)	)	PUNCT
ejpam-815	14	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-815	15	1	1118	1118	NUM
ejpam-815	16	1	c	c	X
ejpam-815	16	2	©	©	PROPN
ejpam-815	16	3	2010	2010	NUM
ejpam-815	16	4	ejpam	ejpam	NOUN
ejpam-815	16	5	all	all	DET
ejpam-815	16	6	rights	right	NOUN
ejpam-815	16	7	reserved	reserve	VERB
ejpam-815	16	8	.	.	PUNCT
ejpam-815	17	1	s.	s.	PROPN
ejpam-815	17	2	goyal	goyal	PROPN
ejpam-815	17	3	,	,	PUNCT
ejpam-815	17	4	p.	p.	NOUN
ejpam-815	17	5	goswami	goswami	PROPN
ejpam-815	17	6	/	/	SYM
ejpam-815	17	7	eur	eur	PROPN
ejpam-815	17	8	.	.	PUNCT
ejpam-815	18	1	j.	j.	PROPN
ejpam-815	18	2	pure	pure	PROPN
ejpam-815	18	3	appl	appl	PROPN
ejpam-815	18	4	.	.	PROPN
ejpam-815	18	5	math	math	PROPN
ejpam-815	18	6	,	,	PUNCT
ejpam-815	18	7	3	3	NUM
ejpam-815	18	8	(	(	PUNCT
ejpam-815	18	9	2010	2010	NUM
ejpam-815	18	10	)	)	PUNCT
ejpam-815	18	11	,	,	PUNCT
ejpam-815	18	12	1118	1118	NUM
ejpam-815	18	13	-	-	SYM
ejpam-815	18	14	1123	1123	NUM
ejpam-815	18	15	1119	1119	NUM
ejpam-815	18	16	fi(z	fi(z	NOUN
ejpam-815	18	17	)	)	PUNCT
ejpam-815	18	18	=	=	SYM
ejpam-815	19	1	ap−1,i	ap−1,i	NOUN
ejpam-815	19	2	zp	zp	PROPN
ejpam-815	19	3	+	+	CCONJ
ejpam-815	19	4	∞	∞	NUM
ejpam-815	19	5	∑	∑	PUNCT
ejpam-815	19	6	n=1	n=1	PROPN
ejpam-815	19	7	an+p−1,iz	an+p−1,iz	PROPN
ejpam-815	19	8	n+p−1	n+p−1	PROPN
ejpam-815	19	9	�	�	PROPN
ejpam-815	19	10	ap	ap	PROPN
ejpam-815	19	11	,	,	PUNCT
ejpam-815	19	12	i	i	PRON
ejpam-815	19	13	>	>	X
ejpam-815	19	14	0	0	NUM
ejpam-815	19	15	;	;	PUNCT
ejpam-815	19	16	ap+n	ap+n	PROPN
ejpam-815	19	17	,	,	PUNCT
ejpam-815	19	18	i	i	PRON
ejpam-815	19	19	≥	≥	NOUN
ejpam-815	19	20	0	0	NUM
ejpam-815	19	21	�	�	PROPN
ejpam-815	19	22	,	,	PUNCT
ejpam-815	19	23	(	(	PUNCT
ejpam-815	19	24	2	2	X
ejpam-815	19	25	)	)	PUNCT
ejpam-815	19	26	g(z	g(z	ADJ
ejpam-815	19	27	)	)	PUNCT
ejpam-815	20	1	=	=	PUNCT
ejpam-815	21	1	bp−1	bp−1	PROPN
ejpam-815	21	2	zp	zp	PROPN
ejpam-815	22	1	+	+	CCONJ
ejpam-815	22	2	∞	∞	NUM
ejpam-815	22	3	∑	∑	PUNCT
ejpam-815	22	4	n=1	n=1	PROPN
ejpam-815	22	5	bn+p−1zn+p−1	bn+p−1zn+p−1	PROPN
ejpam-815	22	6	�	�	PROPN
ejpam-815	22	7	bp	bp	PROPN
ejpam-815	22	8	>	>	X
ejpam-815	22	9	0	0	NUM
ejpam-815	22	10	;	;	PUNCT
ejpam-815	22	11	bp+n	bp+n	ADJ
ejpam-815	22	12	≥	≥	X
ejpam-815	22	13	0	0	NUM
ejpam-815	22	14	�	�	PROPN
ejpam-815	22	15	,	,	PUNCT
ejpam-815	22	16	(	(	PUNCT
ejpam-815	22	17	3	3	X
ejpam-815	22	18	)	)	PUNCT
ejpam-815	22	19	and	and	CCONJ
ejpam-815	22	20	gi(z	gi(z	NOUN
ejpam-815	22	21	)	)	PUNCT
ejpam-815	22	22	=	=	PUNCT
ejpam-815	23	1	bp−1,i	bp−1,i	NOUN
ejpam-815	23	2	zp	zp	NOUN
ejpam-815	23	3	+	+	CCONJ
ejpam-815	23	4	∞	∞	NUM
ejpam-815	23	5	∑	∑	PROPN
ejpam-815	23	6	n=1	n=1	PROPN
ejpam-815	23	7	bn+p−1,iz	bn+p−1,iz	PROPN
ejpam-815	23	8	n+p−1	n+p−1	PROPN
ejpam-815	23	9	�	�	PROPN
ejpam-815	23	10	bp	bp	PROPN
ejpam-815	23	11	,	,	PUNCT
ejpam-815	23	12	i	i	PRON
ejpam-815	23	13	>	>	X
ejpam-815	23	14	0	0	NUM
ejpam-815	23	15	;	;	PUNCT
ejpam-815	23	16	bp+n	bp+n	ADJ
ejpam-815	23	17	,	,	PUNCT
ejpam-815	23	18	i	i	PRON
ejpam-815	23	19	≥	≥	VERB
ejpam-815	23	20	0	0	NUM
ejpam-815	23	21	�	�	PROPN
ejpam-815	23	22	,	,	PUNCT
ejpam-815	23	23	(	(	PUNCT
ejpam-815	23	24	4	4	X
ejpam-815	23	25	)	)	PUNCT
ejpam-815	23	26	be	be	AUX
ejpam-815	23	27	analytic	analytic	ADJ
ejpam-815	23	28	and	and	CCONJ
ejpam-815	23	29	p	p	NOUN
ejpam-815	23	30	-	-	PUNCT
ejpam-815	23	31	valent	valent	NOUN
ejpam-815	23	32	in	in	ADP
ejpam-815	23	33	the	the	DET
ejpam-815	23	34	punctured	punctured	ADJ
ejpam-815	23	35	disc	disc	NOUN
ejpam-815	23	36	∆∗	∆∗	NOUN
ejpam-815	23	37	=	=	PUNCT
ejpam-815	23	38	{	{	PUNCT
ejpam-815	23	39	z	z	NOUN
ejpam-815	23	40	:	:	PUNCT
ejpam-815	23	41	0	0	PUNCT
ejpam-815	23	42	<	<	X
ejpam-815	23	43	|z|	|z|	NOUN
ejpam-815	23	44	<	<	X
ejpam-815	23	45	1	1	NUM
ejpam-815	23	46	}	}	PUNCT
ejpam-815	23	47	.	.	PUNCT
ejpam-815	24	1	let	let	VERB
ejpam-815	24	2	∑	∑	PROPN
ejpam-815	24	3	s	s	PROPN
ejpam-815	24	4	t	t	PROPN
ejpam-815	24	5	∗0(p	∗0(p	PROPN
ejpam-815	24	6	,	,	PUNCT
ejpam-815	24	7	α	α	NUM
ejpam-815	24	8	)	)	PUNCT
ejpam-815	24	9	denote	denote	VERB
ejpam-815	24	10	the	the	DET
ejpam-815	24	11	class	class	NOUN
ejpam-815	24	12	of	of	ADP
ejpam-815	24	13	functions	function	NOUN
ejpam-815	24	14	f	f	X
ejpam-815	24	15	(	(	PUNCT
ejpam-815	24	16	z	z	NOUN
ejpam-815	24	17	)	)	PUNCT
ejpam-815	24	18	defined	define	VERB
ejpam-815	24	19	by	by	ADP
ejpam-815	24	20	(	(	PUNCT
ejpam-815	24	21	1	1	NUM
ejpam-815	24	22	)	)	PUNCT
ejpam-815	24	23	and	and	CCONJ
ejpam-815	24	24	satisfy	satisfy	VERB
ejpam-815	24	25	the	the	DET
ejpam-815	24	26	condition	condition	NOUN
ejpam-815	24	27	−re	−re	NOUN
ejpam-815	24	28	¨	¨	NOUN
ejpam-815	24	29	1	1	NUM
ejpam-815	24	30	+	+	NUM
ejpam-815	24	31	z	z	NOUN
ejpam-815	24	32	f	f	NOUN
ejpam-815	24	33	′(z	′(z	NOUN
ejpam-815	24	34	)	)	PUNCT
ejpam-815	24	35	f	f	PROPN
ejpam-815	24	36	(	(	PUNCT
ejpam-815	24	37	z	z	NOUN
ejpam-815	24	38	)	)	PUNCT
ejpam-815	24	39	«	«	PUNCT
ejpam-815	24	40	>	>	X
ejpam-815	24	41	α	α	X
ejpam-815	24	42	,	,	PUNCT
ejpam-815	24	43	(	(	PUNCT
ejpam-815	24	44	z	z	NOUN
ejpam-815	24	45	∈∆∗	∈∆∗	PRON
ejpam-815	24	46	)	)	PUNCT
ejpam-815	24	47	(	(	PUNCT
ejpam-815	24	48	5	5	NUM
ejpam-815	24	49	)	)	PUNCT
ejpam-815	24	50	and	and	CCONJ
ejpam-815	24	51	∑	∑	ADP
ejpam-815	24	52	c	c	PROPN
ejpam-815	24	53	∗0	∗0	PROPN
ejpam-815	24	54	(	(	PUNCT
ejpam-815	24	55	p	p	X
ejpam-815	24	56	,	,	PUNCT
ejpam-815	24	57	α	α	NOUN
ejpam-815	24	58	)	)	PUNCT
ejpam-815	24	59	denote	denote	VERB
ejpam-815	24	60	the	the	DET
ejpam-815	24	61	class	class	NOUN
ejpam-815	24	62	of	of	ADP
ejpam-815	24	63	functions	function	NOUN
ejpam-815	24	64	f	f	X
ejpam-815	24	65	(	(	PUNCT
ejpam-815	24	66	z	z	NOUN
ejpam-815	24	67	)	)	PUNCT
ejpam-815	24	68	defined	define	VERB
ejpam-815	24	69	by	by	ADP
ejpam-815	24	70	(	(	PUNCT
ejpam-815	24	71	1	1	NUM
ejpam-815	24	72	)	)	PUNCT
ejpam-815	24	73	and	and	CCONJ
ejpam-815	24	74	satisfy	satisfy	VERB
ejpam-815	24	75	the	the	DET
ejpam-815	24	76	condition	condition	NOUN
ejpam-815	24	77	−re	−re	PROPN
ejpam-815	24	78	¨	¨	NOUN
ejpam-815	24	79	z	z	PROPN
ejpam-815	24	80	f	f	PROPN
ejpam-815	24	81	′(z	′(z	NOUN
ejpam-815	24	82	)	)	PUNCT
ejpam-815	24	83	f	f	PROPN
ejpam-815	24	84	(	(	PUNCT
ejpam-815	24	85	z	z	NOUN
ejpam-815	24	86	)	)	PUNCT
ejpam-815	24	87	«	«	PUNCT
ejpam-815	24	88	>	>	X
ejpam-815	24	89	α	α	X
ejpam-815	24	90	,	,	PUNCT
ejpam-815	24	91	(	(	PUNCT
ejpam-815	24	92	z	z	NOUN
ejpam-815	24	93	∈∆∗	∈∆∗	PRON
ejpam-815	24	94	)	)	PUNCT
ejpam-815	24	95	(	(	PUNCT
ejpam-815	24	96	6	6	NUM
ejpam-815	24	97	)	)	PUNCT
ejpam-815	24	98	where	where	SCONJ
ejpam-815	24	99	0≤	0≤	DET
ejpam-815	24	100	α	α	NOUN
ejpam-815	24	101	<	<	X
ejpam-815	24	102	p.	p.	NOUN
ejpam-815	24	103	the	the	DET
ejpam-815	24	104	quasi	quasi	ADJ
ejpam-815	24	105	-	-	ADJ
ejpam-815	24	106	hadamard	hadamard	ADJ
ejpam-815	24	107	product	product	NOUN
ejpam-815	24	108	of	of	ADP
ejpam-815	24	109	two	two	NUM
ejpam-815	24	110	or	or	CCONJ
ejpam-815	24	111	more	more	ADJ
ejpam-815	24	112	functions	function	NOUN
ejpam-815	24	113	has	have	AUX
ejpam-815	24	114	recently	recently	ADV
ejpam-815	24	115	been	be	AUX
ejpam-815	24	116	defined	define	VERB
ejpam-815	24	117	and	and	CCONJ
ejpam-815	24	118	used	use	VERB
ejpam-815	24	119	by	by	ADP
ejpam-815	24	120	kumar	kumar	PROPN
ejpam-815	24	121	(	(	PUNCT
ejpam-815	24	122	[	[	X
ejpam-815	24	123	7],[8	7],[8	NUM
ejpam-815	24	124	]	]	PUNCT
ejpam-815	24	125	,	,	PUNCT
ejpam-815	24	126	and	and	CCONJ
ejpam-815	25	1	[	[	X
ejpam-815	25	2	9	9	NUM
ejpam-815	25	3	]	]	NUM
ejpam-815	25	4	)	)	PUNCT
ejpam-815	25	5	,	,	PUNCT
ejpam-815	25	6	aouf	aouf	PROPN
ejpam-815	25	7	et	et	PROPN
ejpam-815	25	8	al	al	PROPN
ejpam-815	25	9	.	.	PUNCT
ejpam-815	26	1	[	[	X
ejpam-815	26	2	3	3	NUM
ejpam-815	26	3	]	]	PUNCT
ejpam-815	26	4	,	,	PUNCT
ejpam-815	26	5	hossen	hossen	NOUN
ejpam-815	26	6	[	[	X
ejpam-815	26	7	6	6	NUM
ejpam-815	26	8	]	]	PUNCT
ejpam-815	26	9	,	,	PUNCT
ejpam-815	26	10	darwish	darwish	X
ejpam-815	27	1	[	[	X
ejpam-815	27	2	4	4	NUM
ejpam-815	27	3	]	]	PUNCT
ejpam-815	27	4	and	and	CCONJ
ejpam-815	27	5	sekine	sekine	ADJ
ejpam-815	28	1	[	[	X
ejpam-815	28	2	12	12	NUM
ejpam-815	28	3	]	]	PUNCT
ejpam-815	28	4	.	.	PUNCT
ejpam-815	29	1	accordingly	accordingly	ADV
ejpam-815	29	2	,	,	PUNCT
ejpam-815	29	3	the	the	DET
ejpam-815	29	4	quasi	quasi	ADJ
ejpam-815	29	5	-	-	ADJ
ejpam-815	29	6	hadamard	hadamard	ADJ
ejpam-815	29	7	product	product	NOUN
ejpam-815	29	8	of	of	ADP
ejpam-815	29	9	two	two	NUM
ejpam-815	29	10	functions	function	NOUN
ejpam-815	29	11	ϕ(z	ϕ(z	NOUN
ejpam-815	29	12	)	)	PUNCT
ejpam-815	29	13	and	and	CCONJ
ejpam-815	29	14	ψ(z	ψ(z	PROPN
ejpam-815	29	15	)	)	PUNCT
ejpam-815	29	16	is	be	AUX
ejpam-815	29	17	defined	define	VERB
ejpam-815	29	18	by	by	ADP
ejpam-815	29	19	(	(	PUNCT
ejpam-815	29	20	ϕ	ϕ	NOUN
ejpam-815	29	21	∗ψ)(z	∗ψ)(z	NOUN
ejpam-815	29	22	)	)	PUNCT
ejpam-815	29	23	=	=	SYM
ejpam-815	29	24	ap	ap	PROPN
ejpam-815	29	25	bpzp	bpzp	NOUN
ejpam-815	29	26	−	−	PROPN
ejpam-815	29	27	∞	∞	PROPN
ejpam-815	29	28	∑	∑	PROPN
ejpam-815	29	29	n=1	n=1	PROPN
ejpam-815	29	30	an+p	an+p	PROPN
ejpam-815	29	31	bn+pzn+p	bn+pzn+p	PROPN
ejpam-815	29	32	(	(	PUNCT
ejpam-815	29	33	7	7	NUM
ejpam-815	29	34	)	)	PUNCT
ejpam-815	29	35	aouf	aouf	NOUN
ejpam-815	30	1	[	[	X
ejpam-815	30	2	1	1	X
ejpam-815	30	3	]	]	PUNCT
ejpam-815	30	4	defined	define	VERB
ejpam-815	30	5	the	the	DET
ejpam-815	30	6	hadamard	hadamard	ADJ
ejpam-815	30	7	product	product	NOUN
ejpam-815	30	8	of	of	ADP
ejpam-815	30	9	two	two	NUM
ejpam-815	30	10	meromorphic	meromorphic	ADJ
ejpam-815	30	11	p	p	NOUN
ejpam-815	30	12	-	-	PUNCT
ejpam-815	30	13	valent	valent	NOUN
ejpam-815	30	14	functions	function	NOUN
ejpam-815	30	15	f	f	X
ejpam-815	30	16	(	(	PUNCT
ejpam-815	30	17	z	z	NOUN
ejpam-815	30	18	)	)	PUNCT
ejpam-815	30	19	and	and	CCONJ
ejpam-815	30	20	g(z	g(z	PROPN
ejpam-815	30	21	)	)	PUNCT
ejpam-815	30	22	by	by	ADP
ejpam-815	30	23	(	(	PUNCT
ejpam-815	30	24	f	f	PROPN
ejpam-815	30	25	∗	∗	PROPN
ejpam-815	30	26	g)(z	g)(z	PUNCT
ejpam-815	30	27	)	)	PUNCT
ejpam-815	31	1	=	=	SYM
ejpam-815	32	1	ap−1	ap−1	INTJ
ejpam-815	32	2	bp−1	bp−1	INTJ
ejpam-815	32	3	zp	zp	PROPN
ejpam-815	33	1	+	+	CCONJ
ejpam-815	33	2	∞	∞	NUM
ejpam-815	33	3	∑	∑	PUNCT
ejpam-815	33	4	n=1	n=1	PROPN
ejpam-815	33	5	an+p−1	an+p−1	PROPN
ejpam-815	33	6	bn+p−1zn+p−1	bn+p−1zn+p−1	PROPN
ejpam-815	34	1	(	(	PUNCT
ejpam-815	34	2	8)	8)	NUM
ejpam-815	34	3	similarly	similarly	ADV
ejpam-815	34	4	,	,	PUNCT
ejpam-815	34	5	we	we	PRON
ejpam-815	34	6	can	can	AUX
ejpam-815	34	7	define	define	VERB
ejpam-815	34	8	the	the	DET
ejpam-815	34	9	hadamard	hadamard	ADJ
ejpam-815	34	10	product	product	NOUN
ejpam-815	34	11	of	of	ADP
ejpam-815	34	12	more	more	ADJ
ejpam-815	34	13	than	than	ADP
ejpam-815	34	14	two	two	NUM
ejpam-815	34	15	meromorphic	meromorphic	ADJ
ejpam-815	34	16	p−valent	p−valent	NOUN
ejpam-815	34	17	functions	function	NOUN
ejpam-815	34	18	.	.	PUNCT
ejpam-815	35	1	let	let	VERB
ejpam-815	35	2	λ(z	λ(z	NOUN
ejpam-815	35	3	)	)	PUNCT
ejpam-815	35	4	be	be	AUX
ejpam-815	35	5	a	a	DET
ejpam-815	35	6	fixed	fix	VERB
ejpam-815	35	7	function	function	NOUN
ejpam-815	35	8	of	of	ADP
ejpam-815	35	9	the	the	DET
ejpam-815	35	10	form	form	NOUN
ejpam-815	35	11	λ(z	λ(z	NOUN
ejpam-815	35	12	)	)	PUNCT
ejpam-815	36	1	=	=	PUNCT
ejpam-815	36	2	cp−1	cp−1	PROPN
ejpam-815	36	3	zp	zp	PROPN
ejpam-815	37	1	+	+	CCONJ
ejpam-815	37	2	∞	∞	NUM
ejpam-815	37	3	∑	∑	PUNCT
ejpam-815	37	4	n=1	n=1	PROPN
ejpam-815	37	5	cn+p−1zn+p−1	cn+p−1zn+p−1	PROPN
ejpam-815	37	6	�	�	PROPN
ejpam-815	37	7	cp	cp	X
ejpam-815	37	8	>	>	PROPN
ejpam-815	37	9	0	0	NUM
ejpam-815	37	10	;	;	PUNCT
ejpam-815	37	11	cp+n	cp+n	VERB
ejpam-815	37	12	≥	≥	X
ejpam-815	37	13	0	0	NUM
ejpam-815	37	14	�	�	PROPN
ejpam-815	37	15	,	,	PUNCT
ejpam-815	37	16	(	(	PUNCT
ejpam-815	37	17	9	9	X
ejpam-815	37	18	)	)	PUNCT
ejpam-815	37	19	using	use	VERB
ejpam-815	37	20	the	the	DET
ejpam-815	37	21	function	function	NOUN
ejpam-815	37	22	defined	define	VERB
ejpam-815	37	23	by	by	ADP
ejpam-815	37	24	(	(	PUNCT
ejpam-815	37	25	9	9	NUM
ejpam-815	37	26	)	)	PUNCT
ejpam-815	37	27	,	,	PUNCT
ejpam-815	37	28	we	we	PRON
ejpam-815	37	29	now	now	ADV
ejpam-815	37	30	define	define	VERB
ejpam-815	37	31	the	the	DET
ejpam-815	37	32	following	follow	VERB
ejpam-815	37	33	new	new	ADJ
ejpam-815	37	34	classes	class	NOUN
ejpam-815	37	35	s.	s.	PROPN
ejpam-815	37	36	goyal	goyal	PROPN
ejpam-815	37	37	,	,	PUNCT
ejpam-815	37	38	p.	p.	NOUN
ejpam-815	37	39	goswami	goswami	PROPN
ejpam-815	37	40	/	/	SYM
ejpam-815	37	41	eur	eur	PROPN
ejpam-815	37	42	.	.	PUNCT
ejpam-815	38	1	j.	j.	PROPN
ejpam-815	38	2	pure	pure	PROPN
ejpam-815	38	3	appl	appl	PROPN
ejpam-815	38	4	.	.	PROPN
ejpam-815	38	5	math	math	PROPN
ejpam-815	38	6	,	,	PUNCT
ejpam-815	38	7	3	3	NUM
ejpam-815	38	8	(	(	PUNCT
ejpam-815	38	9	2010	2010	NUM
ejpam-815	38	10	)	)	PUNCT
ejpam-815	38	11	,	,	PUNCT
ejpam-815	38	12	1118	1118	NUM
ejpam-815	38	13	-	-	SYM
ejpam-815	38	14	1123	1123	NUM
ejpam-815	38	15	1120	1120	NUM
ejpam-815	38	16	definition	definition	NOUN
ejpam-815	38	17	1	1	NUM
ejpam-815	38	18	.	.	PUNCT
ejpam-815	39	1	a	a	DET
ejpam-815	39	2	function	function	NOUN
ejpam-815	39	3	f	f	X
ejpam-815	39	4	(	(	PUNCT
ejpam-815	39	5	z	z	NOUN
ejpam-815	39	6	)	)	PUNCT
ejpam-815	39	7	∈	∈	PROPN
ejpam-815	39	8	∑	∑	PUNCT
ejpam-815	39	9	m	m	PROPN
ejpam-815	39	10	0	0	NUM
ejpam-815	39	11	λ	λ	INTJ
ejpam-815	39	12	(	(	PUNCT
ejpam-815	39	13	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	39	14	)	)	PUNCT
ejpam-815	39	15	(	(	PUNCT
ejpam-815	39	16	cn+p−1	cn+p−1	VERB
ejpam-815	39	17	≥	≥	X
ejpam-815	39	18	cp	cp	INTJ
ejpam-815	39	19	>	>	X
ejpam-815	39	20	0	0	PROPN
ejpam-815	39	21	;	;	PUNCT
ejpam-815	39	22	n≥	n≥	PROPN
ejpam-815	39	23	2	2	X
ejpam-815	39	24	)	)	PUNCT
ejpam-815	39	25	if	if	SCONJ
ejpam-815	39	26	and	and	CCONJ
ejpam-815	39	27	only	only	ADV
ejpam-815	39	28	if	if	SCONJ
ejpam-815	39	29	∞	∞	PROPN
ejpam-815	39	30	∑	∑	SYM
ejpam-815	39	31	n=1	n=1	PROPN
ejpam-815	39	32	cn+p−1an+p−1	cn+p−1an+p−1	PROPN
ejpam-815	39	33	≤	≤	PROPN
ejpam-815	40	1	δap−1	δap−1	PROPN
ejpam-815	40	2	(	(	PUNCT
ejpam-815	40	3	10	10	NUM
ejpam-815	40	4	)	)	PUNCT
ejpam-815	40	5	where	where	SCONJ
ejpam-815	40	6	δ	δ	X
ejpam-815	40	7	>	>	X
ejpam-815	40	8	0	0	PROPN
ejpam-815	40	9	.	.	PUNCT
ejpam-815	40	10	definition	definition	NOUN
ejpam-815	40	11	2	2	NUM
ejpam-815	40	12	.	.	PUNCT
ejpam-815	41	1	a	a	DET
ejpam-815	41	2	function	function	NOUN
ejpam-815	41	3	f	f	X
ejpam-815	41	4	(	(	PUNCT
ejpam-815	41	5	z	z	NOUN
ejpam-815	41	6	)	)	PUNCT
ejpam-815	41	7	∈	∈	PROPN
ejpam-815	41	8	∑	∑	PUNCT
ejpam-815	41	9	b	b	PROPN
ejpam-815	41	10	k	k	PROPN
ejpam-815	41	11	λ	λ	PROPN
ejpam-815	41	12	(	(	PUNCT
ejpam-815	41	13	cn+p−1,δ	cn+p−1,δ	PROPN
ejpam-815	41	14	)	)	PUNCT
ejpam-815	41	15	(	(	PUNCT
ejpam-815	41	16	cn+p−1	cn+p−1	VERB
ejpam-815	41	17	≥	≥	X
ejpam-815	41	18	cp	cp	INTJ
ejpam-815	41	19	>	>	X
ejpam-815	41	20	0	0	PROPN
ejpam-815	41	21	;	;	PUNCT
ejpam-815	41	22	n≥	n≥	PROPN
ejpam-815	41	23	2	2	X
ejpam-815	41	24	)	)	PUNCT
ejpam-815	41	25	if	if	SCONJ
ejpam-815	41	26	and	and	CCONJ
ejpam-815	41	27	only	only	ADV
ejpam-815	41	28	if	if	SCONJ
ejpam-815	41	29	∞	∞	PROPN
ejpam-815	41	30	∑	∑	SYM
ejpam-815	41	31	n=1	n=1	PROPN
ejpam-815	41	32	�	�	PROPN
ejpam-815	41	33	n+	n+	PUNCT
ejpam-815	41	34	p−	p−	NOUN
ejpam-815	41	35	1	1	NUM
ejpam-815	41	36	p	p	NOUN
ejpam-815	41	37	�	�	PROPN
ejpam-815	41	38	k	k	NOUN
ejpam-815	41	39	cn+p−1an+p−1	cn+p−1an+p−1	PROPN
ejpam-815	41	40	≤	≤	PROPN
ejpam-815	42	1	δap−1	δap−1	PROPN
ejpam-815	42	2	(	(	PUNCT
ejpam-815	42	3	11	11	NUM
ejpam-815	42	4	)	)	PUNCT
ejpam-815	42	5	where	where	SCONJ
ejpam-815	42	6	δ	δ	X
ejpam-815	42	7	>	>	X
ejpam-815	42	8	0	0	X
ejpam-815	42	9	.	.	PUNCT
ejpam-815	43	1	it	it	PRON
ejpam-815	43	2	is	be	AUX
ejpam-815	43	3	easy	easy	ADJ
ejpam-815	43	4	to	to	PART
ejpam-815	43	5	check	check	VERB
ejpam-815	43	6	that	that	PRON
ejpam-815	43	7	various	various	ADJ
ejpam-815	43	8	subclasses	subclass	NOUN
ejpam-815	43	9	of	of	ADP
ejpam-815	43	10	meromorphic	meromorphic	ADJ
ejpam-815	43	11	and	and	CCONJ
ejpam-815	43	12	multivalent	multivalent	NOUN
ejpam-815	43	13	functions	function	NOUN
ejpam-815	43	14	can	can	AUX
ejpam-815	43	15	be	be	AUX
ejpam-815	43	16	(	(	PUNCT
ejpam-815	43	17	studied	study	VERB
ejpam-815	43	18	by	by	ADP
ejpam-815	43	19	various	various	ADJ
ejpam-815	43	20	authors	author	NOUN
ejpam-815	43	21	)	)	PUNCT
ejpam-815	43	22	represented	represent	VERB
ejpam-815	43	23	as	as	ADP
ejpam-815	43	24	∑	∑	PROPN
ejpam-815	43	25	b	b	PROPN
ejpam-815	43	26	k	k	PROPN
ejpam-815	43	27	λ	λ	PROPN
ejpam-815	43	28	(	(	PUNCT
ejpam-815	43	29	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	43	30	)	)	PUNCT
ejpam-815	43	31	for	for	ADP
ejpam-815	43	32	suitable	suitable	ADJ
ejpam-815	43	33	choices	choice	NOUN
ejpam-815	43	34	of	of	ADP
ejpam-815	43	35	cn	cn	PROPN
ejpam-815	43	36	,	,	PUNCT
ejpam-815	43	37	δ	δ	PROPN
ejpam-815	43	38	and	and	CCONJ
ejpam-815	43	39	k.	k.	PROPN
ejpam-815	43	40	for	for	ADP
ejpam-815	43	41	example	example	NOUN
ejpam-815	43	42	:	:	PUNCT
ejpam-815	43	43	(	(	PUNCT
ejpam-815	43	44	1	1	X
ejpam-815	43	45	)	)	PUNCT
ejpam-815	43	46	∑	∑	PROPN
ejpam-815	43	47	b	b	PROPN
ejpam-815	43	48	k	k	PROPN
ejpam-815	43	49	λ	λ	PROPN
ejpam-815	43	50	(	(	PUNCT
ejpam-815	43	51	(	(	PUNCT
ejpam-815	43	52	n+	n+	NUM
ejpam-815	43	53	2p−	2p−	NOUN
ejpam-815	43	54	1	1	NUM
ejpam-815	43	55	)	)	PUNCT
ejpam-815	43	56	+	+	NUM
ejpam-815	43	57	β(n+	β(n+	PUNCT
ejpam-815	44	1	2α−	2α−	NUM
ejpam-815	44	2	1	1	NUM
ejpam-815	44	3	)	)	PUNCT
ejpam-815	44	4	,	,	PUNCT
ejpam-815	44	5	2β(p−α))≡	2β(p−α))≡	NUM
ejpam-815	44	6	∗	∗	NOUN
ejpam-815	44	7	∑	∑	PUNCT
ejpam-815	44	8	k	k	X
ejpam-815	44	9	(	(	PUNCT
ejpam-815	44	10	p	p	X
ejpam-815	44	11	,	,	PUNCT
ejpam-815	44	12	α	α	NOUN
ejpam-815	44	13	,	,	PUNCT
ejpam-815	44	14	β	β	NOUN
ejpam-815	44	15	)	)	PUNCT
ejpam-815	44	16	(	(	PUNCT
ejpam-815	44	17	2	2	X
ejpam-815	44	18	)	)	PUNCT
ejpam-815	44	19	∑	∑	PUNCT
ejpam-815	44	20	b0	b0	VERB
ejpam-815	44	21	λ	λ	PROPN
ejpam-815	44	22	(	(	PUNCT
ejpam-815	44	23	(	(	PUNCT
ejpam-815	44	24	n+	n+	NUM
ejpam-815	44	25	2p−	2p−	NUM
ejpam-815	44	26	1)+	1)+	NUM
ejpam-815	44	27	β(n+	β(n+	PUNCT
ejpam-815	45	1	2α−	2α−	NUM
ejpam-815	45	2	1	1	NUM
ejpam-815	45	3	)	)	PUNCT
ejpam-815	45	4	,	,	PUNCT
ejpam-815	45	5	2β(p−α))≡	2β(p−α))≡	NUM
ejpam-815	45	6	∑	∑	PUNCT
ejpam-815	45	7	s∗0(p	s∗0(p	PROPN
ejpam-815	45	8	,	,	PUNCT
ejpam-815	45	9	α	α	NOUN
ejpam-815	45	10	,	,	PUNCT
ejpam-815	45	11	β	β	NOUN
ejpam-815	45	12	)	)	PUNCT
ejpam-815	45	13	(	(	PUNCT
ejpam-815	45	14	3	3	X
ejpam-815	45	15	)	)	PUNCT
ejpam-815	45	16	∑	∑	PUNCT
ejpam-815	45	17	b1	b1	NOUN
ejpam-815	45	18	λ	λ	PROPN
ejpam-815	45	19	(	(	PUNCT
ejpam-815	45	20	(	(	PUNCT
ejpam-815	45	21	n+	n+	NUM
ejpam-815	45	22	2p−	2p−	NUM
ejpam-815	45	23	1)+	1)+	NUM
ejpam-815	45	24	β(n+	β(n+	PUNCT
ejpam-815	46	1	2α−	2α−	NUM
ejpam-815	46	2	1	1	NUM
ejpam-815	46	3	)	)	PUNCT
ejpam-815	46	4	,	,	PUNCT
ejpam-815	46	5	2β(p−α))≡	2β(p−α))≡	NUM
ejpam-815	46	6	∑	∑	PUNCT
ejpam-815	46	7	c∗0(p	c∗0(p	PROPN
ejpam-815	46	8	,	,	PUNCT
ejpam-815	46	9	α	α	NOUN
ejpam-815	46	10	,	,	PUNCT
ejpam-815	46	11	β	β	NOUN
ejpam-815	46	12	)	)	PUNCT
ejpam-815	46	13	(	(	PUNCT
ejpam-815	46	14	4	4	NUM
ejpam-815	46	15	)	)	PUNCT
ejpam-815	46	16	∑	∑	PROPN
ejpam-815	46	17	b	b	PROPN
ejpam-815	46	18	k	k	PROPN
ejpam-815	46	19	λ	λ	PROPN
ejpam-815	46	20	(	(	PUNCT
ejpam-815	46	21	(	(	PUNCT
ejpam-815	46	22	n(1	n(1	X
ejpam-815	46	23	+	+	NOUN
ejpam-815	46	24	β	β	NOUN
ejpam-815	46	25	)	)	PUNCT
ejpam-815	47	1	+	+	CCONJ
ejpam-815	47	2	(	(	PUNCT
ejpam-815	47	3	2α−	2α−	NUM
ejpam-815	47	4	1)β	1)β	NUM
ejpam-815	47	5	+	+	CCONJ
ejpam-815	47	6	1	1	NUM
ejpam-815	47	7	,	,	PUNCT
ejpam-815	47	8	2β(1−α))≡	2β(1−α))≡	NUM
ejpam-815	47	9	∑	∑	ADV
ejpam-815	47	10	s∗0(k	s∗0(k	PROPN
ejpam-815	47	11	,	,	PUNCT
ejpam-815	47	12	α	α	NOUN
ejpam-815	47	13	,	,	PUNCT
ejpam-815	47	14	β	β	NOUN
ejpam-815	47	15	)	)	PUNCT
ejpam-815	47	16	for	for	ADP
ejpam-815	47	17	p	p	NOUN
ejpam-815	47	18	=	=	SYM
ejpam-815	47	19	1	1	NUM
ejpam-815	47	20	(	(	PUNCT
ejpam-815	47	21	5	5	NUM
ejpam-815	47	22	)	)	PUNCT
ejpam-815	47	23	∑	∑	PROPN
ejpam-815	47	24	b	b	PROPN
ejpam-815	47	25	k	k	PROPN
ejpam-815	47	26	λ	λ	PROPN
ejpam-815	47	27	(	(	PUNCT
ejpam-815	47	28	n(n(1	n(n(1	X
ejpam-815	47	29	+	+	X
ejpam-815	47	30	β	β	NOUN
ejpam-815	47	31	)	)	PUNCT
ejpam-815	48	1	+	+	CCONJ
ejpam-815	48	2	(	(	PUNCT
ejpam-815	48	3	2α−	2α−	NUM
ejpam-815	48	4	1)β	1)β	NUM
ejpam-815	48	5	+	+	CCONJ
ejpam-815	48	6	1	1	NUM
ejpam-815	48	7	)	)	PUNCT
ejpam-815	48	8	,	,	PUNCT
ejpam-815	48	9	2β(1−α))≡	2β(1−α))≡	NUM
ejpam-815	48	10	∑	∑	ADV
ejpam-815	48	11	c∗0(k	c∗0(k	NOUN
ejpam-815	48	12	,	,	PUNCT
ejpam-815	48	13	α	α	NOUN
ejpam-815	48	14	,	,	PUNCT
ejpam-815	48	15	β	β	NOUN
ejpam-815	48	16	)	)	PUNCT
ejpam-815	48	17	for	for	ADP
ejpam-815	48	18	p=	p=	NOUN
ejpam-815	48	19	1	1	NUM
ejpam-815	48	20	the	the	DET
ejpam-815	48	21	classes	class	NOUN
ejpam-815	48	22	∗	∗	VERB
ejpam-815	48	23	∑	∑	PROPN
ejpam-815	48	24	k	k	X
ejpam-815	48	25	(	(	PUNCT
ejpam-815	48	26	p	p	X
ejpam-815	48	27	,	,	PUNCT
ejpam-815	48	28	α	α	NOUN
ejpam-815	48	29	,	,	PUNCT
ejpam-815	48	30	β	β	NOUN
ejpam-815	48	31	)	)	PUNCT
ejpam-815	48	32	,	,	PUNCT
ejpam-815	48	33	∑	∑	PROPN
ejpam-815	48	34	s∗0(p	s∗0(p	PROPN
ejpam-815	48	35	,	,	PUNCT
ejpam-815	48	36	α	α	NOUN
ejpam-815	48	37	,	,	PUNCT
ejpam-815	48	38	β	β	NOUN
ejpam-815	48	39	)	)	PUNCT
ejpam-815	48	40	and	and	CCONJ
ejpam-815	48	41	∑	∑	PROPN
ejpam-815	48	42	c∗0(p	c∗0(p	PROPN
ejpam-815	48	43	,	,	PUNCT
ejpam-815	48	44	α	α	NOUN
ejpam-815	48	45	,	,	PUNCT
ejpam-815	48	46	β	β	NOUN
ejpam-815	48	47	)	)	PUNCT
ejpam-815	48	48	have	have	AUX
ejpam-815	48	49	been	be	AUX
ejpam-815	48	50	studied	study	VERB
ejpam-815	48	51	by	by	ADP
ejpam-815	48	52	aouf	aouf	PROPN
ejpam-815	49	1	[	[	X
ejpam-815	49	2	1	1	X
ejpam-815	49	3	]	]	PUNCT
ejpam-815	49	4	and	and	CCONJ
ejpam-815	49	5	the	the	DET
ejpam-815	49	6	classes	class	NOUN
ejpam-815	49	7	∑	∑	PUNCT
ejpam-815	49	8	s∗0(k	s∗0(k	PROPN
ejpam-815	49	9	,	,	PUNCT
ejpam-815	49	10	α	α	NOUN
ejpam-815	49	11	,	,	PUNCT
ejpam-815	49	12	β	β	NOUN
ejpam-815	49	13	)	)	PUNCT
ejpam-815	49	14	and	and	CCONJ
ejpam-815	49	15	∑	∑	ADV
ejpam-815	49	16	c∗0(k	c∗0(k	PROPN
ejpam-815	49	17	,	,	PUNCT
ejpam-815	49	18	α	α	X
ejpam-815	49	19	,	,	PUNCT
ejpam-815	49	20	β	β	NOUN
ejpam-815	49	21	)	)	PUNCT
ejpam-815	49	22	have	have	AUX
ejpam-815	49	23	been	be	AUX
ejpam-815	49	24	studied	study	VERB
ejpam-815	49	25	by	by	ADP
ejpam-815	49	26	el	el	PROPN
ejpam-815	49	27	-	-	NOUN
ejpam-815	49	28	ashwah	ashwah	NOUN
ejpam-815	49	29	and	and	CCONJ
ejpam-815	49	30	aouf	aouf	PROPN
ejpam-815	50	1	[	[	X
ejpam-815	50	2	5	5	NUM
ejpam-815	50	3	]	]	PUNCT
ejpam-815	50	4	.	.	PUNCT
ejpam-815	51	1	evidently	evidently	ADV
ejpam-815	51	2	,	,	PUNCT
ejpam-815	51	3	∑	∑	ADP
ejpam-815	51	4	b0	b0	VERB
ejpam-815	51	5	λ	λ	PROPN
ejpam-815	51	6	(	(	PUNCT
ejpam-815	51	7	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	51	8	)	)	PUNCT
ejpam-815	51	9	≡	≡	PROPN
ejpam-815	51	10	∑	∑	PROPN
ejpam-815	51	11	m	m	PROPN
ejpam-815	51	12	0	0	NUM
ejpam-815	51	13	λ	λ	INTJ
ejpam-815	51	14	(	(	PUNCT
ejpam-815	51	15	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	51	16	)	)	PUNCT
ejpam-815	51	17	.	.	PUNCT
ejpam-815	52	1	further	far	ADV
ejpam-815	52	2	,	,	PUNCT
ejpam-815	52	3	∑	∑	PROPN
ejpam-815	52	4	b	b	PROPN
ejpam-815	52	5	k	k	PROPN
ejpam-815	52	6	λ	λ	PROPN
ejpam-815	52	7	(	(	PUNCT
ejpam-815	52	8	cn+p−1,δ	cn+p−1,δ	PROPN
ejpam-815	52	9	)	)	PUNCT
ejpam-815	52	10	⊂	⊂	PROPN
ejpam-815	52	11	∑	∑	PUNCT
ejpam-815	52	12	bh	bh	PROPN
ejpam-815	52	13	λ	λ	PROPN
ejpam-815	52	14	(	(	PUNCT
ejpam-815	52	15	cn+p−1,δ	cn+p−1,δ	PROPN
ejpam-815	52	16	)	)	PUNCT
ejpam-815	52	17	if	if	SCONJ
ejpam-815	52	18	k	k	PROPN
ejpam-815	52	19	>	>	X
ejpam-815	52	20	h	h	PROPN
ejpam-815	52	21	≥	≥	PROPN
ejpam-815	52	22	0	0	NUM
ejpam-815	52	23	,	,	PUNCT
ejpam-815	52	24	the	the	DET
ejpam-815	52	25	containment	containment	NOUN
ejpam-815	52	26	being	be	AUX
ejpam-815	52	27	proper	proper	ADJ
ejpam-815	52	28	.	.	PUNCT
ejpam-815	53	1	moreover	moreover	ADV
ejpam-815	53	2	,	,	PUNCT
ejpam-815	53	3	for	for	ADP
ejpam-815	53	4	any	any	DET
ejpam-815	53	5	positive	positive	ADJ
ejpam-815	53	6	integer	integer	NOUN
ejpam-815	53	7	k	k	PROPN
ejpam-815	53	8	we	we	PRON
ejpam-815	53	9	have	have	VERB
ejpam-815	53	10	the	the	DET
ejpam-815	53	11	following	follow	VERB
ejpam-815	53	12	inclusion	inclusion	NOUN
ejpam-815	53	13	relation	relation	NOUN
ejpam-815	53	14	∑	∑	PROPN
ejpam-815	53	15	b	b	PROPN
ejpam-815	53	16	k	k	PROPN
ejpam-815	53	17	λ(cn+p−1,δ	λ(cn+p−1,δ	PROPN
ejpam-815	53	18	)	)	PUNCT
ejpam-815	54	1	⊂	⊂	PROPN
ejpam-815	54	2	∑	∑	PUNCT
ejpam-815	54	3	b	b	X
ejpam-815	54	4	k−1	k−1	PROPN
ejpam-815	54	5	λ	λ	PROPN
ejpam-815	54	6	(	(	PUNCT
ejpam-815	54	7	cn+p−1,δ)⊂	cn+p−1,δ)⊂	X
ejpam-815	54	8	.	.	PUNCT
ejpam-815	54	9	.	.	PUNCT
ejpam-815	54	10	.	.	PUNCT
ejpam-815	55	1	⊂	⊂	PROPN
ejpam-815	55	2	∑	∑	PROPN
ejpam-815	56	1	m	m	VERB
ejpam-815	56	2	0	0	NUM
ejpam-815	56	3	λ	λ	X
ejpam-815	56	4	(	(	PUNCT
ejpam-815	56	5	cn+p−1,δ)⊂	cn+p−1,δ)⊂	X
ejpam-815	56	6	∑	∑	PUNCT
ejpam-815	56	7	c	c	PROPN
ejpam-815	56	8	∗0	∗0	PROPN
ejpam-815	56	9	(	(	PUNCT
ejpam-815	56	10	p	p	X
ejpam-815	56	11	,	,	PUNCT
ejpam-815	56	12	α	α	NOUN
ejpam-815	56	13	)	)	PUNCT
ejpam-815	56	14	⊂	⊂	PROPN
ejpam-815	56	15	∑	∑	PUNCT
ejpam-815	56	16	s	s	VERB
ejpam-815	56	17	∗0	∗0	PROPN
ejpam-815	56	18	(	(	PUNCT
ejpam-815	56	19	p	p	X
ejpam-815	56	20	,	,	PUNCT
ejpam-815	56	21	α	α	NOUN
ejpam-815	56	22	)	)	PUNCT
ejpam-815	56	23	.	.	PUNCT
ejpam-815	57	1	we	we	PRON
ejpam-815	57	2	also	also	ADV
ejpam-815	57	3	note	note	VERB
ejpam-815	57	4	that	that	SCONJ
ejpam-815	57	5	for	for	ADP
ejpam-815	57	6	every	every	DET
ejpam-815	57	7	nonnegative	nonnegative	ADJ
ejpam-815	57	8	real	real	ADJ
ejpam-815	57	9	number	number	NOUN
ejpam-815	57	10	k	k	PROPN
ejpam-815	57	11	,	,	PUNCT
ejpam-815	57	12	the	the	DET
ejpam-815	57	13	class	class	NOUN
ejpam-815	57	14	∑	∑	PROPN
ejpam-815	57	15	b	b	PROPN
ejpam-815	57	16	k	k	PROPN
ejpam-815	57	17	λ	λ	PROPN
ejpam-815	57	18	(	(	PUNCT
ejpam-815	57	19	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	57	20	)	)	PUNCT
ejpam-815	57	21	is	be	AUX
ejpam-815	57	22	nonempty	nonempty	ADJ
ejpam-815	57	23	as	as	ADP
ejpam-815	57	24	the	the	DET
ejpam-815	57	25	functions	function	NOUN
ejpam-815	57	26	of	of	ADP
ejpam-815	57	27	the	the	DET
ejpam-815	57	28	form	form	NOUN
ejpam-815	58	1	f	f	X
ejpam-815	58	2	(	(	PUNCT
ejpam-815	58	3	z	z	NOUN
ejpam-815	58	4	)	)	PUNCT
ejpam-815	58	5	=	=	PUNCT
ejpam-815	59	1	ap−1	ap−1	ADJ
ejpam-815	59	2	zp	zp	NOUN
ejpam-815	59	3	+	+	CCONJ
ejpam-815	59	4	∞	∞	NUM
ejpam-815	59	5	∑	∑	PUNCT
ejpam-815	59	6	n=1	n=1	PROPN
ejpam-815	59	7	�	�	PROPN
ejpam-815	59	8	p	p	NOUN
ejpam-815	59	9	n+	n+	ADP
ejpam-815	59	10	p−	p−	PROPN
ejpam-815	59	11	1	1	NUM
ejpam-815	59	12	�	�	PROPN
ejpam-815	59	13	k	k	PROPN
ejpam-815	59	14	δap+n−1	δap+n−1	PROPN
ejpam-815	59	15	cp+n−1	cp+n−1	PROPN
ejpam-815	59	16	µn+p−1zn+p−1	µn+p−1zn+p−1	PROPN
ejpam-815	59	17	�	�	PROPN
ejpam-815	59	18	ap	ap	PROPN
ejpam-815	59	19	>	>	PROPN
ejpam-815	59	20	0	0	NUM
ejpam-815	59	21	;	;	PUNCT
ejpam-815	59	22	ap+n	ap+n	ADJ
ejpam-815	59	23	≥	≥	X
ejpam-815	59	24	0	0	NUM
ejpam-815	59	25	�	�	PROPN
ejpam-815	59	26	,	,	PUNCT
ejpam-815	59	27	where	where	SCONJ
ejpam-815	59	28	ap−1	ap−1	PROPN
ejpam-815	59	29	>	>	X
ejpam-815	59	30	0	0	PROPN
ejpam-815	59	31	,	,	PUNCT
ejpam-815	59	32	µn+p−1	µn+p−1	PROPN
ejpam-815	59	33	≥	≥	NUM
ejpam-815	59	34	0	0	NUM
ejpam-815	59	35	and	and	CCONJ
ejpam-815	59	36	∑∞	∑∞	PROPN
ejpam-815	59	37	n=1µn+p−1	n=1µn+p−1	NOUN
ejpam-815	59	38	≤	≤	ADV
ejpam-815	59	39	1	1	NUM
ejpam-815	59	40	,	,	PUNCT
ejpam-815	59	41	satisfy	satisfy	VERB
ejpam-815	59	42	the	the	DET
ejpam-815	59	43	inequality	inequality	NOUN
ejpam-815	59	44	(	(	PUNCT
ejpam-815	59	45	11	11	NUM
ejpam-815	59	46	)	)	PUNCT
ejpam-815	59	47	.	.	PUNCT
ejpam-815	60	1	in	in	ADP
ejpam-815	60	2	this	this	DET
ejpam-815	60	3	paper	paper	NOUN
ejpam-815	60	4	we	we	PRON
ejpam-815	60	5	establish	establish	VERB
ejpam-815	60	6	a	a	DET
ejpam-815	60	7	theorem	theorem	NOUN
ejpam-815	60	8	concerning	concern	VERB
ejpam-815	60	9	the	the	DET
ejpam-815	60	10	quasi	quasi	ADJ
ejpam-815	60	11	-	-	ADJ
ejpam-815	60	12	hadamard	hadamard	ADJ
ejpam-815	60	13	product	product	NOUN
ejpam-815	60	14	of	of	ADP
ejpam-815	60	15	functions	function	NOUN
ejpam-815	60	16	in	in	ADP
ejpam-815	60	17	the	the	DET
ejpam-815	60	18	classes	class	NOUN
ejpam-815	60	19	∑	∑	PROPN
ejpam-815	60	20	m	m	VERB
ejpam-815	60	21	0	0	NUM
ejpam-815	60	22	λ	λ	X
ejpam-815	60	23	(	(	PUNCT
ejpam-815	60	24	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	60	25	)	)	PUNCT
ejpam-815	60	26	and	and	CCONJ
ejpam-815	60	27	∑	∑	PUNCT
ejpam-815	60	28	b	b	PROPN
ejpam-815	60	29	k	k	PROPN
ejpam-815	60	30	λ	λ	PROPN
ejpam-815	60	31	(	(	PUNCT
ejpam-815	60	32	cn+p−1,δ	cn+p−1,δ	PROPN
ejpam-815	60	33	)	)	PUNCT
ejpam-815	60	34	.	.	PUNCT
ejpam-815	61	1	the	the	DET
ejpam-815	61	2	theorem	theorem	NOUN
ejpam-815	61	3	and	and	CCONJ
ejpam-815	61	4	its	its	PRON
ejpam-815	61	5	applications	application	NOUN
ejpam-815	61	6	generalize	generalize	VERB
ejpam-815	61	7	the	the	DET
ejpam-815	61	8	results	result	NOUN
ejpam-815	61	9	obtained	obtain	VERB
ejpam-815	61	10	by	by	ADP
ejpam-815	61	11	aouf	aouf	PROPN
ejpam-815	62	1	[	[	X
ejpam-815	62	2	1	1	NUM
ejpam-815	62	3	]	]	PUNCT
ejpam-815	62	4	,	,	PUNCT
ejpam-815	62	5	mogra	mogra	VERB
ejpam-815	62	6	[	[	X
ejpam-815	62	7	11	11	NUM
ejpam-815	62	8	]	]	PUNCT
ejpam-815	62	9	and	and	CCONJ
ejpam-815	62	10	el	el	PROPN
ejpam-815	62	11	-	-	NOUN
ejpam-815	62	12	ashwah	ashwah	NOUN
ejpam-815	62	13	and	and	CCONJ
ejpam-815	62	14	aouf	aouf	PROPN
ejpam-815	63	1	[	[	X
ejpam-815	63	2	5	5	NUM
ejpam-815	63	3	]	]	PUNCT
ejpam-815	63	4	.	.	PUNCT
ejpam-815	64	1	s.	s.	PROPN
ejpam-815	64	2	goyal	goyal	PROPN
ejpam-815	64	3	,	,	PUNCT
ejpam-815	64	4	p.	p.	NOUN
ejpam-815	64	5	goswami	goswami	PROPN
ejpam-815	64	6	/	/	SYM
ejpam-815	64	7	eur	eur	PROPN
ejpam-815	64	8	.	.	PUNCT
ejpam-815	65	1	j.	j.	PROPN
ejpam-815	65	2	pure	pure	PROPN
ejpam-815	65	3	appl	appl	PROPN
ejpam-815	65	4	.	.	PROPN
ejpam-815	65	5	math	math	PROPN
ejpam-815	65	6	,	,	PUNCT
ejpam-815	65	7	3	3	NUM
ejpam-815	65	8	(	(	PUNCT
ejpam-815	65	9	2010	2010	NUM
ejpam-815	65	10	)	)	PUNCT
ejpam-815	65	11	,	,	PUNCT
ejpam-815	65	12	1118	1118	NUM
ejpam-815	65	13	-	-	SYM
ejpam-815	65	14	1123	1123	NUM
ejpam-815	65	15	1121	1121	NUM
ejpam-815	65	16	2	2	NUM
ejpam-815	65	17	.	.	X
ejpam-815	65	18	main	main	ADJ
ejpam-815	65	19	theorem	theorem	NOUN
ejpam-815	65	20	theorem	theorem	NOUN
ejpam-815	65	21	1	1	X
ejpam-815	65	22	.	.	PUNCT
ejpam-815	66	1	let	let	VERB
ejpam-815	66	2	the	the	DET
ejpam-815	66	3	functions	function	NOUN
ejpam-815	66	4	fi(z	fi(z	ADV
ejpam-815	66	5	)	)	PUNCT
ejpam-815	66	6	defined	define	VERB
ejpam-815	66	7	by	by	ADP
ejpam-815	66	8	(	(	PUNCT
ejpam-815	66	9	2	2	X
ejpam-815	66	10	)	)	PUNCT
ejpam-815	66	11	belong	belong	VERB
ejpam-815	66	12	to	to	ADP
ejpam-815	66	13	the	the	DET
ejpam-815	66	14	class	class	NOUN
ejpam-815	66	15	∑	∑	PROPN
ejpam-815	66	16	b	b	PROPN
ejpam-815	66	17	k	k	PROPN
ejpam-815	66	18	λ	λ	PROPN
ejpam-815	66	19	(	(	PUNCT
ejpam-815	66	20	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	66	21	)	)	PUNCT
ejpam-815	66	22	for	for	ADP
ejpam-815	66	23	every	every	DET
ejpam-815	66	24	i	i	NOUN
ejpam-815	66	25	=	=	NOUN
ejpam-815	66	26	1,2	1,2	NUM
ejpam-815	66	27	,	,	PUNCT
ejpam-815	66	28	.	.	PUNCT
ejpam-815	66	29	.	.	PUNCT
ejpam-815	67	1	.	.	PUNCT
ejpam-815	68	1	,	,	PUNCT
ejpam-815	68	2	m	m	PROPN
ejpam-815	68	3	,	,	PUNCT
ejpam-815	68	4	and	and	CCONJ
ejpam-815	68	5	let	let	VERB
ejpam-815	68	6	the	the	DET
ejpam-815	68	7	functions	function	NOUN
ejpam-815	68	8	g	g	ADP
ejpam-815	68	9	j(z	j(z	PROPN
ejpam-815	68	10	)	)	PUNCT
ejpam-815	68	11	defined	define	VERB
ejpam-815	68	12	by	by	ADP
ejpam-815	68	13	(	(	PUNCT
ejpam-815	68	14	4	4	X
ejpam-815	68	15	)	)	PUNCT
ejpam-815	68	16	belong	belong	VERB
ejpam-815	68	17	to	to	ADP
ejpam-815	68	18	the	the	DET
ejpam-815	68	19	class	class	NOUN
ejpam-815	68	20	∑	∑	PROPN
ejpam-815	69	1	m	m	PROPN
ejpam-815	69	2	0	0	NUM
ejpam-815	69	3	λ	λ	INTJ
ejpam-815	69	4	(	(	PUNCT
ejpam-815	69	5	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	69	6	)	)	PUNCT
ejpam-815	69	7	for	for	ADP
ejpam-815	69	8	every	every	DET
ejpam-815	69	9	j	j	PROPN
ejpam-815	69	10	=	=	SYM
ejpam-815	69	11	1,2	1,2	NUM
ejpam-815	69	12	,	,	PUNCT
ejpam-815	69	13	.	.	PUNCT
ejpam-815	69	14	.	.	PUNCT
ejpam-815	69	15	.	.	PUNCT
ejpam-815	70	1	,	,	PUNCT
ejpam-815	70	2	q.	q.	PROPN
ejpam-815	70	3	if	if	SCONJ
ejpam-815	70	4	cn+p−1	cn+p−1	PROPN
ejpam-815	70	5	≥	≥	X
ejpam-815	70	6	�	�	PROPN
ejpam-815	70	7	n+p−1	n+p−1	PROPN
ejpam-815	70	8	p	p	PROPN
ejpam-815	70	9	�	�	PROPN
ejpam-815	70	10	δ	δ	PROPN
ejpam-815	70	11	,	,	PUNCT
ejpam-815	70	12	then	then	ADV
ejpam-815	70	13	the	the	DET
ejpam-815	70	14	quasi	quasi	ADJ
ejpam-815	70	15	-	-	ADJ
ejpam-815	70	16	hadamard	hadamard	ADJ
ejpam-815	70	17	product	product	NOUN
ejpam-815	70	18	f1	f1	NOUN
ejpam-815	70	19	∗	∗	NOUN
ejpam-815	70	20	f2	f2	PROPN
ejpam-815	70	21	∗	∗	NOUN
ejpam-815	70	22	.	.	PUNCT
ejpam-815	70	23	.	.	PUNCT
ejpam-815	70	24	.	.	PUNCT
ejpam-815	71	1	∗	∗	NOUN
ejpam-815	71	2	fm	fm	PROPN
ejpam-815	71	3	∗	∗	PROPN
ejpam-815	71	4	g1	g1	PROPN
ejpam-815	71	5	∗	∗	PROPN
ejpam-815	71	6	g2	g2	PROPN
ejpam-815	71	7	∗	∗	NOUN
ejpam-815	71	8	.	.	PUNCT
ejpam-815	71	9	.	.	PUNCT
ejpam-815	71	10	.	.	PUNCT
ejpam-815	72	1	∗	∗	NOUN
ejpam-815	72	2	gq(z	gq(z	PUNCT
ejpam-815	72	3	)	)	PUNCT
ejpam-815	72	4	belongs	belong	VERB
ejpam-815	72	5	to	to	ADP
ejpam-815	72	6	the	the	DET
ejpam-815	72	7	class	class	NOUN
ejpam-815	72	8	∑	∑	PROPN
ejpam-815	72	9	b	b	PROPN
ejpam-815	72	10	(	(	PUNCT
ejpam-815	72	11	k+1)m+q−1	k+1)m+q−1	X
ejpam-815	72	12	λ	λ	X
ejpam-815	72	13	(	(	PUNCT
ejpam-815	72	14	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	72	15	)	)	PUNCT
ejpam-815	72	16	.	.	PUNCT
ejpam-815	73	1	proof	proof	NOUN
ejpam-815	73	2	.	.	PUNCT
ejpam-815	74	1	let	let	VERB
ejpam-815	74	2	h(z	h(z	NOUN
ejpam-815	74	3	)	)	PUNCT
ejpam-815	74	4	:	:	PUNCT
ejpam-815	74	5	=	=	SYM
ejpam-815	74	6	f1	f1	PROPN
ejpam-815	74	7	∗	∗	NOUN
ejpam-815	74	8	f2	f2	PROPN
ejpam-815	74	9	∗	∗	NOUN
ejpam-815	74	10	.	.	PUNCT
ejpam-815	74	11	.	.	PUNCT
ejpam-815	74	12	.	.	PUNCT
ejpam-815	75	1	∗	∗	NOUN
ejpam-815	75	2	fm	fm	PROPN
ejpam-815	75	3	∗	∗	PROPN
ejpam-815	75	4	g1	g1	PROPN
ejpam-815	75	5	∗	∗	PROPN
ejpam-815	75	6	g2	g2	PROPN
ejpam-815	75	7	∗	∗	NOUN
ejpam-815	75	8	.	.	PUNCT
ejpam-815	75	9	.	.	PUNCT
ejpam-815	75	10	.	.	PUNCT
ejpam-815	76	1	∗	∗	NOUN
ejpam-815	76	2	gq(z	gq(z	PUNCT
ejpam-815	76	3	)	)	PUNCT
ejpam-815	76	4	,	,	PUNCT
ejpam-815	76	5	then	then	ADV
ejpam-815	76	6	h(z	h(z	NOUN
ejpam-815	76	7	)	)	PUNCT
ejpam-815	76	8	=	=	PRON
ejpam-815	76	9	(	(	PUNCT
ejpam-815	76	10	m	m	VERB
ejpam-815	76	11	∏	∏	PROPN
ejpam-815	76	12	i=1	i=1	PROPN
ejpam-815	76	13	ap−1,i	ap−1,i	NOUN
ejpam-815	76	14	q	q	X
ejpam-815	76	15	∏	∏	PROPN
ejpam-815	76	16	j=1	j=1	PROPN
ejpam-815	76	17	bp−1	bp−1	PROPN
ejpam-815	76	18	,	,	PUNCT
ejpam-815	76	19	j	j	PROPN
ejpam-815	76	20	)	)	PUNCT
ejpam-815	77	1	zp	zp	PROPN
ejpam-815	78	1	+	+	CCONJ
ejpam-815	78	2	∞	∞	NUM
ejpam-815	78	3	∑	∑	PUNCT
ejpam-815	78	4	n=1	n=1	PROPN
ejpam-815	78	5			PROPN
ejpam-815	78	6			PROPN
ejpam-815	78	7			PROPN
ejpam-815	78	8	m	m	PROPN
ejpam-815	78	9	∏	∏	PROPN
ejpam-815	78	10	i=1	i=1	PROPN
ejpam-815	79	1	an+p−1,i	an+p−1,i	PROPN
ejpam-815	79	2	q	q	X
ejpam-815	79	3	∏	∏	PROPN
ejpam-815	79	4	j=1	j=1	PROPN
ejpam-815	79	5	bn+p−1	bn+p−1	PROPN
ejpam-815	79	6	,	,	PUNCT
ejpam-815	79	7	j	j	PROPN
ejpam-815	79	8			PROPN
ejpam-815	79	9			PROPN
ejpam-815	79	10			PROPN
ejpam-815	79	11	zn+p−1	zn+p−1	PROPN
ejpam-815	79	12	.	.	PUNCT
ejpam-815	80	1	(	(	PUNCT
ejpam-815	80	2	12	12	NUM
ejpam-815	80	3	)	)	PUNCT
ejpam-815	80	4	it	it	PRON
ejpam-815	80	5	is	be	AUX
ejpam-815	80	6	sufficient	sufficient	ADJ
ejpam-815	80	7	to	to	PART
ejpam-815	80	8	show	show	VERB
ejpam-815	80	9	that	that	SCONJ
ejpam-815	80	10	∞	∞	PROPN
ejpam-815	80	11	∑	∑	PROPN
ejpam-815	80	12	n=1	n=1	PROPN
ejpam-815	80	13	�	�	PROPN
ejpam-815	80	14	n+	n+	PUNCT
ejpam-815	80	15	p−	p−	NOUN
ejpam-815	80	16	1	1	NUM
ejpam-815	80	17	p	p	NOUN
ejpam-815	80	18	�	�	NOUN
ejpam-815	80	19	m(k+1)+q−1	m(k+1)+q−1	NOUN
ejpam-815	80	20	m	m	VERB
ejpam-815	80	21	∏	∏	NOUN
ejpam-815	80	22	i=1	i=1	PROPN
ejpam-815	81	1	an+p−1,i	an+p−1,i	PROPN
ejpam-815	81	2	q	q	X
ejpam-815	81	3	∏	∏	PROPN
ejpam-815	81	4	j=1	j=1	PROPN
ejpam-815	81	5	bn+p−1	bn+p−1	PROPN
ejpam-815	81	6	,	,	PUNCT
ejpam-815	81	7	j	j	PROPN
ejpam-815	81	8	≤	≤	PROPN
ejpam-815	81	9	δ	δ	PROPN
ejpam-815	81	10	m	m	VERB
ejpam-815	81	11	∏	∏	PROPN
ejpam-815	81	12	i=1	i=1	PROPN
ejpam-815	81	13	ap−1,i	ap−1,i	NOUN
ejpam-815	81	14	q	q	X
ejpam-815	81	15	∏	∏	PROPN
ejpam-815	81	16	j=1	j=1	PROPN
ejpam-815	81	17	bp−1	bp−1	PROPN
ejpam-815	81	18	,	,	PUNCT
ejpam-815	81	19	j	j	PROPN
ejpam-815	81	20	(	(	PUNCT
ejpam-815	81	21	13	13	NUM
ejpam-815	81	22	)	)	PUNCT
ejpam-815	81	23	since	since	SCONJ
ejpam-815	81	24	fi(z	fi(z	NOUN
ejpam-815	81	25	)	)	PUNCT
ejpam-815	81	26	∈	∈	PROPN
ejpam-815	81	27	∑	∑	PUNCT
ejpam-815	81	28	b	b	PROPN
ejpam-815	81	29	k	k	PROPN
ejpam-815	81	30	λ	λ	PROPN
ejpam-815	81	31	(	(	PUNCT
ejpam-815	81	32	cn+p−1,δ	cn+p−1,δ	PROPN
ejpam-815	81	33	)	)	PUNCT
ejpam-815	81	34	,	,	PUNCT
ejpam-815	81	35	we	we	PRON
ejpam-815	81	36	have	have	VERB
ejpam-815	81	37	∞	∞	PROPN
ejpam-815	81	38	∑	∑	PROPN
ejpam-815	81	39	n=1	n=1	PROPN
ejpam-815	81	40	�	�	PROPN
ejpam-815	81	41	n+	n+	PUNCT
ejpam-815	81	42	p−	p−	NOUN
ejpam-815	81	43	1	1	NUM
ejpam-815	81	44	p	p	NOUN
ejpam-815	81	45	�	�	PROPN
ejpam-815	81	46	k	k	PROPN
ejpam-815	81	47	cn+p−1an+p−1,i	cn+p−1an+p−1,i	PROPN
ejpam-815	81	48	≤	≤	PROPN
ejpam-815	81	49	δap−1,i	δap−1,i	NUM
ejpam-815	81	50	(	(	PUNCT
ejpam-815	81	51	14	14	NUM
ejpam-815	81	52	)	)	PUNCT
ejpam-815	81	53	for	for	ADP
ejpam-815	81	54	every	every	DET
ejpam-815	81	55	i	i	NOUN
ejpam-815	81	56	=	=	NOUN
ejpam-815	81	57	1,2	1,2	NUM
ejpam-815	81	58	,	,	PUNCT
ejpam-815	81	59	.	.	PUNCT
ejpam-815	81	60	.	.	PUNCT
ejpam-815	81	61	.	.	PUNCT
ejpam-815	82	1	,	,	PUNCT
ejpam-815	82	2	m.	m.	NOUN
ejpam-815	82	3	therefore	therefore	ADV
ejpam-815	82	4	,	,	PUNCT
ejpam-815	82	5	an+p−1,i	an+p−1,i	PROPN
ejpam-815	82	6	≤	≤	ADJ
ejpam-815	82	7	�	�	PROPN
ejpam-815	82	8	n+	n+	PUNCT
ejpam-815	82	9	p−	p−	NOUN
ejpam-815	82	10	1	1	NUM
ejpam-815	82	11	p	p	PRON
ejpam-815	82	12	�	�	NOUN
ejpam-815	82	13	−k	−k	PROPN
ejpam-815	82	14	�	�	PROPN
ejpam-815	82	15	δ	δ	PROPN
ejpam-815	82	16	cn+p−1	cn+p−1	PROPN
ejpam-815	82	17	�	�	PROPN
ejpam-815	82	18	ap−1,i	ap−1,i	PROPN
ejpam-815	82	19	(	(	PUNCT
ejpam-815	82	20	15	15	NUM
ejpam-815	82	21	)	)	PUNCT
ejpam-815	82	22	which	which	PRON
ejpam-815	82	23	by	by	ADP
ejpam-815	82	24	virtue	virtue	NOUN
ejpam-815	82	25	of	of	ADP
ejpam-815	82	26	the	the	DET
ejpam-815	82	27	condition	condition	NOUN
ejpam-815	82	28	(	(	PUNCT
ejpam-815	82	29	given	give	VERB
ejpam-815	82	30	with	with	ADP
ejpam-815	82	31	the	the	DET
ejpam-815	82	32	theorem	theorem	NOUN
ejpam-815	82	33	)	)	PUNCT
ejpam-815	82	34	implies	imply	VERB
ejpam-815	82	35	that	that	SCONJ
ejpam-815	82	36	an+p−1,i	an+p−1,i	PROPN
ejpam-815	82	37	≤	≤	PROPN
ejpam-815	82	38	�	�	PROPN
ejpam-815	82	39	n+	n+	PUNCT
ejpam-815	82	40	p−	p−	NOUN
ejpam-815	82	41	1	1	NUM
ejpam-815	82	42	p	p	NOUN
ejpam-815	82	43	�	�	PROPN
ejpam-815	82	44	−k−1	−k−1	NUM
ejpam-815	82	45	ap−1,i	ap−1,i	NOUN
ejpam-815	82	46	(	(	PUNCT
ejpam-815	82	47	16	16	NUM
ejpam-815	82	48	)	)	PUNCT
ejpam-815	82	49	for	for	ADP
ejpam-815	82	50	every	every	DET
ejpam-815	82	51	i	i	NOUN
ejpam-815	82	52	=	=	NOUN
ejpam-815	82	53	1,2	1,2	NUM
ejpam-815	82	54	,	,	PUNCT
ejpam-815	82	55	.	.	PUNCT
ejpam-815	82	56	.	.	PUNCT
ejpam-815	83	1	.	.	PUNCT
ejpam-815	84	1	,	,	PUNCT
ejpam-815	84	2	m.	m.	NOUN
ejpam-815	84	3	further	far	ADV
ejpam-815	84	4	,	,	PUNCT
ejpam-815	84	5	since	since	SCONJ
ejpam-815	84	6	g	g	PROPN
ejpam-815	84	7	j(z	j(z	PROPN
ejpam-815	84	8	)	)	PUNCT
ejpam-815	84	9	∈	∈	PROPN
ejpam-815	84	10	∑	∑	PROPN
ejpam-815	84	11	m	m	PROPN
ejpam-815	84	12	0	0	NUM
ejpam-815	84	13	λ	λ	INTJ
ejpam-815	84	14	(	(	PUNCT
ejpam-815	84	15	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	84	16	)	)	PUNCT
ejpam-815	84	17	,	,	PUNCT
ejpam-815	84	18	we	we	PRON
ejpam-815	84	19	have	have	VERB
ejpam-815	84	20	∞	∞	PROPN
ejpam-815	84	21	∑	∑	PUNCT
ejpam-815	84	22	n=1	n=1	PROPN
ejpam-815	84	23	cn+p−1	cn+p−1	PROPN
ejpam-815	84	24	bn+p−1	bn+p−1	PROPN
ejpam-815	84	25	,	,	PUNCT
ejpam-815	84	26	j	j	PROPN
ejpam-815	84	27	≤	≤	PROPN
ejpam-815	84	28	δbp−1	δbp−1	PROPN
ejpam-815	84	29	,	,	PUNCT
ejpam-815	84	30	j	j	PROPN
ejpam-815	84	31	(	(	PUNCT
ejpam-815	84	32	17	17	NUM
ejpam-815	84	33	)	)	PUNCT
ejpam-815	84	34	for	for	ADP
ejpam-815	84	35	every	every	DET
ejpam-815	84	36	j	j	PROPN
ejpam-815	84	37	=	=	SYM
ejpam-815	84	38	1,2	1,2	NUM
ejpam-815	84	39	,	,	PUNCT
ejpam-815	84	40	.	.	PUNCT
ejpam-815	84	41	.	.	PUNCT
ejpam-815	85	1	.	.	PUNCT
ejpam-815	86	1	,	,	PUNCT
ejpam-815	86	2	q.	q.	PROPN
ejpam-815	86	3	hence	hence	ADV
ejpam-815	86	4	we	we	PRON
ejpam-815	86	5	obtain	obtain	VERB
ejpam-815	86	6	bn+p−1	bn+p−1	PROPN
ejpam-815	86	7	,	,	PUNCT
ejpam-815	86	8	j	j	PROPN
ejpam-815	86	9	≤	≤	PROPN
ejpam-815	86	10	�	�	PROPN
ejpam-815	86	11	n+	n+	PUNCT
ejpam-815	86	12	p−	p−	NOUN
ejpam-815	86	13	1	1	NUM
ejpam-815	86	14	p	p	NOUN
ejpam-815	86	15	�	�	PROPN
ejpam-815	86	16	−1	−1	NOUN
ejpam-815	86	17	bp−1	bp−1	PROPN
ejpam-815	86	18	,	,	PUNCT
ejpam-815	86	19	j	j	PROPN
ejpam-815	86	20	(	(	PUNCT
ejpam-815	86	21	18	18	NUM
ejpam-815	86	22	)	)	PUNCT
ejpam-815	86	23	s.	s.	PROPN
ejpam-815	86	24	goyal	goyal	PROPN
ejpam-815	86	25	,	,	PUNCT
ejpam-815	86	26	p.	p.	NOUN
ejpam-815	86	27	goswami	goswami	PROPN
ejpam-815	86	28	/	/	SYM
ejpam-815	86	29	eur	eur	PROPN
ejpam-815	86	30	.	.	PUNCT
ejpam-815	87	1	j.	j.	PROPN
ejpam-815	87	2	pure	pure	PROPN
ejpam-815	87	3	appl	appl	PROPN
ejpam-815	87	4	.	.	PROPN
ejpam-815	87	5	math	math	PROPN
ejpam-815	87	6	,	,	PUNCT
ejpam-815	87	7	3	3	NUM
ejpam-815	87	8	(	(	PUNCT
ejpam-815	87	9	2010	2010	NUM
ejpam-815	87	10	)	)	PUNCT
ejpam-815	87	11	,	,	PUNCT
ejpam-815	87	12	1118	1118	NUM
ejpam-815	87	13	-	-	SYM
ejpam-815	87	14	1123	1123	NUM
ejpam-815	87	15	1122	1122	NUM
ejpam-815	87	16	using	use	VERB
ejpam-815	87	17	(	(	PUNCT
ejpam-815	87	18	16	16	NUM
ejpam-815	87	19	)	)	PUNCT
ejpam-815	87	20	for	for	ADP
ejpam-815	87	21	i	i	X
ejpam-815	87	22	=	=	SYM
ejpam-815	87	23	1,2	1,2	NUM
ejpam-815	87	24	,	,	PUNCT
ejpam-815	87	25	.	.	PUNCT
ejpam-815	87	26	.	.	PUNCT
ejpam-815	88	1	.	.	PUNCT
ejpam-815	89	1	,	,	PUNCT
ejpam-815	89	2	m	m	PROPN
ejpam-815	89	3	,	,	PUNCT
ejpam-815	89	4	and	and	CCONJ
ejpam-815	89	5	(	(	PUNCT
ejpam-815	89	6	18	18	NUM
ejpam-815	89	7	)	)	PUNCT
ejpam-815	89	8	for	for	ADP
ejpam-815	89	9	j	j	PROPN
ejpam-815	89	10	=	=	SYM
ejpam-815	89	11	1,2	1,2	NUM
ejpam-815	89	12	,	,	PUNCT
ejpam-815	89	13	.	.	PUNCT
ejpam-815	89	14	.	.	PUNCT
ejpam-815	90	1	.	.	PUNCT
ejpam-815	91	1	,	,	PUNCT
ejpam-815	91	2	q−	q−	PROPN
ejpam-815	91	3	1	1	NUM
ejpam-815	91	4	,	,	PUNCT
ejpam-815	91	5	and	and	CCONJ
ejpam-815	91	6	(	(	PUNCT
ejpam-815	91	7	17	17	NUM
ejpam-815	91	8	)	)	PUNCT
ejpam-815	91	9	for	for	ADP
ejpam-815	91	10	j	j	PROPN
ejpam-815	91	11	=	=	SYM
ejpam-815	91	12	q	q	PROPN
ejpam-815	91	13	,	,	PUNCT
ejpam-815	91	14	we	we	PRON
ejpam-815	91	15	get	get	VERB
ejpam-815	91	16	∞	∞	PROPN
ejpam-815	91	17	∑	∑	PUNCT
ejpam-815	91	18	n=1	n=1	PROPN
ejpam-815	92	1			NOUN
ejpam-815	92	2			ADJ
ejpam-815	92	3			ADJ
ejpam-815	92	4			ADJ
ejpam-815	92	5			NUM
ejpam-815	92	6	�	�	NOUN
ejpam-815	92	7	n+	n+	NUM
ejpam-815	92	8	p−	p−	NOUN
ejpam-815	92	9	1	1	NUM
ejpam-815	92	10	p	p	NOUN
ejpam-815	92	11	�	�	NOUN
ejpam-815	92	12	m(k+1)+q−1	m(k+1)+q−1	NOUN
ejpam-815	92	13	cn+p−1	cn+p−1	VERB
ejpam-815	92	14			PROPN
ejpam-815	92	15			PRON
ejpam-815	92	16			PROPN
ejpam-815	92	17	m	m	PROPN
ejpam-815	92	18	∏	∏	PROPN
ejpam-815	92	19	i=1	i=1	PROPN
ejpam-815	93	1	an+p−1,i	an+p−1,i	PROPN
ejpam-815	93	2	q	q	X
ejpam-815	93	3	∏	∏	PROPN
ejpam-815	93	4	j=1	j=1	PROPN
ejpam-815	93	5	bn+p−1	bn+p−1	PROPN
ejpam-815	93	6	,	,	PUNCT
ejpam-815	93	7	j	j	PROPN
ejpam-815	93	8			PROPN
ejpam-815	93	9			PROPN
ejpam-815	93	10			NOUN
ejpam-815	93	11			PROPN
ejpam-815	93	12			PROPN
ejpam-815	93	13			PROPN
ejpam-815	93	14			PROPN
ejpam-815	93	15			PROPN
ejpam-815	93	16	≤	≤	NOUN
ejpam-815	93	17	∞	∞	NUM
ejpam-815	93	18	∑	∑	PROPN
ejpam-815	93	19	n=1	n=1	PROPN
ejpam-815	93	20	�	�	PROPN
ejpam-815	93	21	�	�	PROPN
ejpam-815	93	22	n+	n+	PUNCT
ejpam-815	93	23	p−	p−	NOUN
ejpam-815	93	24	1	1	NUM
ejpam-815	93	25	p	p	NOUN
ejpam-815	93	26	�	�	PROPN
ejpam-815	93	27	m(k+1)+q−1	m(k+1)+q−1	PROPN
ejpam-815	93	28	�	�	PROPN
ejpam-815	93	29	n+	n+	PART
ejpam-815	93	30	p−	p−	NOUN
ejpam-815	93	31	1	1	NUM
ejpam-815	93	32	p	p	NOUN
ejpam-815	93	33	�	�	PROPN
ejpam-815	93	34	−m(k+1)	−m(k+1)	NOUN
ejpam-815	93	35	�	�	PROPN
ejpam-815	93	36	n+	n+	NOUN
ejpam-815	93	37	p−	p−	NOUN
ejpam-815	93	38	1	1	NUM
ejpam-815	93	39	p	p	NOUN
ejpam-815	93	40	�	�	NOUN
ejpam-815	93	41	−(q−1	−(q−1	PROPN
ejpam-815	93	42	)	)	PUNCT
ejpam-815	93	43			PROPN
ejpam-815	93	44			PRON
ejpam-815	93	45			PROPN
ejpam-815	93	46	m	m	PROPN
ejpam-815	93	47	∏	∏	PROPN
ejpam-815	93	48	i=1	i=1	PROPN
ejpam-815	93	49	ap−1,i	ap−1,i	NOUN
ejpam-815	93	50	q−1	q−1	PROPN
ejpam-815	93	51	∏	∏	NUM
ejpam-815	93	52	j=1	j=1	PROPN
ejpam-815	93	53	bn+p−1	bn+p−1	PROPN
ejpam-815	93	54	,	,	PUNCT
ejpam-815	93	55	j	j	PROPN
ejpam-815	93	56			PROPN
ejpam-815	93	57			PROPN
ejpam-815	93	58			NOUN
ejpam-815	93	59	cn+p−1	cn+p−1	PROPN
ejpam-815	94	1	bn+p−1,q	bn+p−1,q	X
ejpam-815	94	2			NUM
ejpam-815	94	3			PROPN
ejpam-815	94	4			PROPN
ejpam-815	94	5			PROPN
ejpam-815	94	6			PROPN
ejpam-815	94	7	=	=	PUNCT
ejpam-815	94	8			PROPN
ejpam-815	94	9			NOUN
ejpam-815	94	10			PROPN
ejpam-815	94	11	m	m	VERB
ejpam-815	94	12	∏	∏	NUM
ejpam-815	94	13	i=1	i=1	PROPN
ejpam-815	94	14	ap−1,i	ap−1,i	NOUN
ejpam-815	94	15	q−1	q−1	PROPN
ejpam-815	94	16	∏	∏	NUM
ejpam-815	94	17	j=1	j=1	PROPN
ejpam-815	94	18	bp−1	bp−1	PROPN
ejpam-815	94	19	,	,	PUNCT
ejpam-815	94	20	j	j	PROPN
ejpam-815	94	21			PROPN
ejpam-815	94	22			VERB
ejpam-815	94	23			PUNCT
ejpam-815	95	1	∞	∞	NUM
ejpam-815	95	2	∑	∑	PUNCT
ejpam-815	95	3	n=1	n=1	PROPN
ejpam-815	95	4	cn+p−1	cn+p−1	PROPN
ejpam-815	95	5	bn+p−1,q	bn+p−1,q	NOUN
ejpam-815	95	6	!	!	PUNCT
ejpam-815	96	1	≤	≤	NUM
ejpam-815	97	1	δ	δ	PROPN
ejpam-815	97	2	m	m	VERB
ejpam-815	97	3	∏	∏	NUM
ejpam-815	97	4	i=1	i=1	PROPN
ejpam-815	97	5	ap−1,i	ap−1,i	NOUN
ejpam-815	97	6	q	q	X
ejpam-815	97	7	∏	∏	PROPN
ejpam-815	97	8	j=1	j=1	PROPN
ejpam-815	97	9	bp−1	bp−1	PROPN
ejpam-815	97	10	,	,	PUNCT
ejpam-815	97	11	j	j	PROPN
ejpam-815	97	12	(	(	PUNCT
ejpam-815	97	13	by	by	ADP
ejpam-815	97	14	(	(	PUNCT
ejpam-815	97	15	17	17	NUM
ejpam-815	97	16	)	)	PUNCT
ejpam-815	97	17	)	)	PUNCT
ejpam-815	97	18	hence	hence	ADV
ejpam-815	97	19	h(z	h(z	NOUN
ejpam-815	97	20	)	)	PUNCT
ejpam-815	97	21	∈	∈	PROPN
ejpam-815	97	22	∑	∑	PROPN
ejpam-815	97	23	b	b	PROPN
ejpam-815	97	24	(	(	PUNCT
ejpam-815	97	25	k+1)m+q−1	k+1)m+q−1	X
ejpam-815	97	26	λ	λ	X
ejpam-815	97	27	(	(	PUNCT
ejpam-815	97	28	cn+p−1,δ	cn+p−1,δ	PROPN
ejpam-815	97	29	)	)	PUNCT
ejpam-815	97	30	.	.	PUNCT
ejpam-815	98	1	this	this	PRON
ejpam-815	98	2	completes	complete	VERB
ejpam-815	98	3	the	the	DET
ejpam-815	98	4	proof	proof	NOUN
ejpam-815	98	5	of	of	ADP
ejpam-815	98	6	the	the	DET
ejpam-815	98	7	theorem	theorem	NOUN
ejpam-815	98	8	1	1	X
ejpam-815	98	9	.	.	PUNCT
ejpam-815	98	10	taking	take	VERB
ejpam-815	98	11	k	k	NOUN
ejpam-815	98	12	=	=	PUNCT
ejpam-815	98	13	0	0	NUM
ejpam-815	98	14	in	in	ADP
ejpam-815	98	15	the	the	DET
ejpam-815	98	16	proof	proof	NOUN
ejpam-815	98	17	of	of	ADP
ejpam-815	98	18	the	the	DET
ejpam-815	98	19	above	above	ADJ
ejpam-815	98	20	theorem	theorem	NOUN
ejpam-815	98	21	,	,	PUNCT
ejpam-815	98	22	we	we	PRON
ejpam-815	98	23	obtain	obtain	VERB
ejpam-815	98	24	corollary	corollary	ADJ
ejpam-815	98	25	1	1	NUM
ejpam-815	98	26	.	.	PUNCT
ejpam-815	99	1	let	let	VERB
ejpam-815	99	2	the	the	DET
ejpam-815	99	3	functions	function	NOUN
ejpam-815	99	4	fi(z	fi(z	ADV
ejpam-815	99	5	)	)	PUNCT
ejpam-815	99	6	defined	define	VERB
ejpam-815	99	7	by	by	ADP
ejpam-815	99	8	(	(	PUNCT
ejpam-815	99	9	2	2	NUM
ejpam-815	99	10	)	)	PUNCT
ejpam-815	99	11	and	and	CCONJ
ejpam-815	99	12	the	the	DET
ejpam-815	99	13	functions	function	NOUN
ejpam-815	99	14	g	g	ADP
ejpam-815	99	15	j(z	j(z	PROPN
ejpam-815	99	16	)	)	PUNCT
ejpam-815	99	17	defined	define	VERB
ejpam-815	99	18	by	by	ADP
ejpam-815	99	19	(	(	PUNCT
ejpam-815	99	20	4	4	X
ejpam-815	99	21	)	)	PUNCT
ejpam-815	99	22	belong	belong	VERB
ejpam-815	99	23	to	to	ADP
ejpam-815	99	24	the	the	DET
ejpam-815	99	25	class	class	NOUN
ejpam-815	99	26	∑	∑	PROPN
ejpam-815	100	1	m	m	PROPN
ejpam-815	100	2	0	0	NUM
ejpam-815	100	3	λ	λ	INTJ
ejpam-815	100	4	(	(	PUNCT
ejpam-815	100	5	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	100	6	)	)	PUNCT
ejpam-815	100	7	for	for	ADP
ejpam-815	100	8	every	every	DET
ejpam-815	100	9	i	i	NOUN
ejpam-815	100	10	=	=	NOUN
ejpam-815	100	11	1,2	1,2	NUM
ejpam-815	100	12	,	,	PUNCT
ejpam-815	100	13	.	.	PUNCT
ejpam-815	100	14	.	.	PUNCT
ejpam-815	100	15	.	.	PUNCT
ejpam-815	101	1	,	,	PUNCT
ejpam-815	101	2	m	m	PROPN
ejpam-815	101	3	,	,	PUNCT
ejpam-815	101	4	and	and	CCONJ
ejpam-815	101	5	j	j	PROPN
ejpam-815	101	6	=	=	SYM
ejpam-815	101	7	1,2	1,2	NUM
ejpam-815	101	8	,	,	PUNCT
ejpam-815	101	9	.	.	PUNCT
ejpam-815	101	10	.	.	PUNCT
ejpam-815	101	11	.	.	PUNCT
ejpam-815	102	1	,	,	PUNCT
ejpam-815	102	2	q.	q.	PROPN
ejpam-815	102	3	if	if	SCONJ
ejpam-815	102	4	cn+p−1	cn+p−1	PROPN
ejpam-815	102	5	≥	≥	X
ejpam-815	102	6	�	�	PROPN
ejpam-815	102	7	n+p−1	n+p−1	PROPN
ejpam-815	102	8	p	p	PROPN
ejpam-815	102	9	�	�	PROPN
ejpam-815	102	10	δ	δ	PROPN
ejpam-815	102	11	,	,	PUNCT
ejpam-815	102	12	then	then	ADV
ejpam-815	102	13	the	the	DET
ejpam-815	102	14	quasi	quasi	ADJ
ejpam-815	102	15	-	-	ADJ
ejpam-815	102	16	hadamard	hadamard	ADJ
ejpam-815	102	17	product	product	NOUN
ejpam-815	102	18	f1	f1	NOUN
ejpam-815	102	19	∗	∗	NOUN
ejpam-815	102	20	f2	f2	PROPN
ejpam-815	102	21	∗	∗	NOUN
ejpam-815	102	22	.	.	PUNCT
ejpam-815	102	23	.	.	PUNCT
ejpam-815	102	24	.	.	PUNCT
ejpam-815	103	1	∗	∗	NOUN
ejpam-815	103	2	fm	fm	PROPN
ejpam-815	103	3	∗	∗	PROPN
ejpam-815	103	4	g1	g1	PROPN
ejpam-815	103	5	∗	∗	PROPN
ejpam-815	103	6	g2	g2	PROPN
ejpam-815	103	7	∗	∗	NOUN
ejpam-815	103	8	.	.	PUNCT
ejpam-815	103	9	.	.	PUNCT
ejpam-815	103	10	.	.	PUNCT
ejpam-815	104	1	∗	∗	NOUN
ejpam-815	104	2	gq(z	gq(z	PUNCT
ejpam-815	104	3	)	)	PUNCT
ejpam-815	104	4	belongs	belong	VERB
ejpam-815	104	5	to	to	ADP
ejpam-815	104	6	the	the	DET
ejpam-815	104	7	class	class	NOUN
ejpam-815	104	8	∑	∑	PROPN
ejpam-815	104	9	bm+q−1	bm+q−1	PROPN
ejpam-815	104	10	λ	λ	PROPN
ejpam-815	104	11	(	(	PUNCT
ejpam-815	104	12	cn+p−1,δ	cn+p−1,δ	PROPN
ejpam-815	104	13	)	)	PUNCT
ejpam-815	104	14	.	.	PUNCT
ejpam-815	105	1	now	now	ADV
ejpam-815	105	2	taking	take	VERB
ejpam-815	105	3	into	into	ADP
ejpam-815	105	4	account	account	NOUN
ejpam-815	105	5	the	the	DET
ejpam-815	105	6	quasi	quasi	ADJ
ejpam-815	105	7	-	-	ADJ
ejpam-815	105	8	hadamard	hadamard	ADJ
ejpam-815	105	9	product	product	NOUN
ejpam-815	105	10	functions	function	NOUN
ejpam-815	105	11	g1(z	g1(z	NOUN
ejpam-815	105	12	)	)	PUNCT
ejpam-815	105	13	∗	∗	NOUN
ejpam-815	105	14	g2(z	g2(z	NOUN
ejpam-815	105	15	)	)	PUNCT
ejpam-815	105	16	∗	∗	NOUN
ejpam-815	105	17	.	.	PUNCT
ejpam-815	105	18	.	.	PUNCT
ejpam-815	105	19	.	.	PUNCT
ejpam-815	106	1	∗	∗	NOUN
ejpam-815	106	2	gq(z	gq(z	PUNCT
ejpam-815	106	3	)	)	PUNCT
ejpam-815	106	4	only	only	ADV
ejpam-815	106	5	,	,	PUNCT
ejpam-815	106	6	in	in	ADP
ejpam-815	106	7	the	the	DET
ejpam-815	106	8	proof	proof	NOUN
ejpam-815	106	9	of	of	ADP
ejpam-815	106	10	the	the	DET
ejpam-815	106	11	above	above	ADJ
ejpam-815	106	12	theorem	theorem	NOUN
ejpam-815	106	13	,	,	PUNCT
ejpam-815	106	14	and	and	CCONJ
ejpam-815	106	15	using	use	VERB
ejpam-815	106	16	(	(	PUNCT
ejpam-815	106	17	18	18	NUM
ejpam-815	106	18	)	)	PUNCT
ejpam-815	106	19	for	for	ADP
ejpam-815	106	20	j	j	PROPN
ejpam-815	106	21	=	=	SYM
ejpam-815	106	22	1,2,3	1,2,3	NUM
ejpam-815	106	23	.	.	PUNCT
ejpam-815	106	24	.	.	PUNCT
ejpam-815	107	1	.	.	PUNCT
ejpam-815	108	1	,	,	PUNCT
ejpam-815	108	2	q−	q−	PROPN
ejpam-815	108	3	1	1	NUM
ejpam-815	108	4	,	,	PUNCT
ejpam-815	108	5	and	and	CCONJ
ejpam-815	108	6	(	(	PUNCT
ejpam-815	108	7	17	17	NUM
ejpam-815	108	8	)	)	PUNCT
ejpam-815	108	9	for	for	ADP
ejpam-815	108	10	j	j	PROPN
ejpam-815	108	11	=	=	SYM
ejpam-815	108	12	m	m	PROPN
ejpam-815	108	13	,	,	PUNCT
ejpam-815	108	14	we	we	PRON
ejpam-815	108	15	obtain	obtain	VERB
ejpam-815	108	16	corollary	corollary	ADJ
ejpam-815	108	17	2	2	NUM
ejpam-815	108	18	.	.	PUNCT
ejpam-815	109	1	let	let	VERB
ejpam-815	109	2	the	the	DET
ejpam-815	109	3	functions	function	NOUN
ejpam-815	109	4	g	g	ADP
ejpam-815	109	5	j(z	j(z	PROPN
ejpam-815	109	6	)	)	PUNCT
ejpam-815	109	7	defined	define	VERB
ejpam-815	109	8	by	by	ADP
ejpam-815	109	9	(	(	PUNCT
ejpam-815	109	10	4	4	X
ejpam-815	109	11	)	)	PUNCT
ejpam-815	109	12	belong	belong	VERB
ejpam-815	109	13	to	to	ADP
ejpam-815	109	14	the	the	DET
ejpam-815	109	15	class	class	NOUN
ejpam-815	109	16	∑	∑	PROPN
ejpam-815	109	17	m	m	PROPN
ejpam-815	109	18	0	0	NUM
ejpam-815	109	19	λ	λ	INTJ
ejpam-815	109	20	(	(	PUNCT
ejpam-815	109	21	cn+p−1,δ	cn+p−1,δ	NOUN
ejpam-815	109	22	)	)	PUNCT
ejpam-815	109	23	for	for	ADP
ejpam-815	109	24	j	j	PROPN
ejpam-815	109	25	=	=	SYM
ejpam-815	109	26	1,2	1,2	NUM
ejpam-815	109	27	,	,	PUNCT
ejpam-815	109	28	.	.	PUNCT
ejpam-815	109	29	.	.	PUNCT
ejpam-815	110	1	.	.	PUNCT
ejpam-815	111	1	,	,	PUNCT
ejpam-815	111	2	q.	q.	PROPN
ejpam-815	112	1	if	if	SCONJ
ejpam-815	112	2	cn+p−1	cn+p−1	PROPN
ejpam-815	112	3	≥	≥	X
ejpam-815	112	4	�	�	PROPN
ejpam-815	112	5	n+p−1	n+p−1	PROPN
ejpam-815	112	6	p	p	PROPN
ejpam-815	112	7	�	�	PROPN
ejpam-815	112	8	δ	δ	PROPN
ejpam-815	112	9	,	,	PUNCT
ejpam-815	112	10	then	then	ADV
ejpam-815	112	11	hadamard	hadamard	ADJ
ejpam-815	112	12	product	product	NOUN
ejpam-815	112	13	g1	g1	PROPN
ejpam-815	112	14	∗	∗	PROPN
ejpam-815	112	15	g2	g2	PROPN
ejpam-815	112	16	∗	∗	NOUN
ejpam-815	112	17	.	.	PUNCT
ejpam-815	112	18	.	.	PUNCT
ejpam-815	112	19	.	.	PUNCT
ejpam-815	113	1	∗	∗	NOUN
ejpam-815	113	2	gq(z	gq(z	PUNCT
ejpam-815	113	3	)	)	PUNCT
ejpam-815	113	4	belongs	belong	VERB
ejpam-815	113	5	to	to	ADP
ejpam-815	113	6	the	the	DET
ejpam-815	113	7	class	class	NOUN
ejpam-815	113	8	∑	∑	PUNCT
ejpam-815	113	9	bq−1	bq−1	PROPN
ejpam-815	113	10	λ	λ	PROPN
ejpam-815	113	11	(	(	PUNCT
ejpam-815	113	12	cn+p−1,δ	cn+p−1,δ	PROPN
ejpam-815	113	13	)	)	PUNCT
ejpam-815	113	14	.	.	PUNCT
ejpam-815	114	1	remark	remark	PROPN
ejpam-815	114	2	1	1	NUM
ejpam-815	114	3	.	.	PUNCT
ejpam-815	115	1	(	(	PUNCT
ejpam-815	115	2	i	i	NOUN
ejpam-815	115	3	)	)	PUNCT
ejpam-815	115	4	putting	put	VERB
ejpam-815	115	5	cn+p−1	cn+p−1	NOUN
ejpam-815	115	6	=	=	PUNCT
ejpam-815	115	7	(	(	PUNCT
ejpam-815	115	8	n+	n+	NUM
ejpam-815	115	9	2p−	2p−	NUM
ejpam-815	115	10	1)+β(n+	1)+β(n+	NUM
ejpam-815	115	11	2α−	2α−	NUM
ejpam-815	115	12	1	1	NUM
ejpam-815	115	13	)	)	PUNCT
ejpam-815	115	14	and	and	CCONJ
ejpam-815	116	1	δ	δ	X
ejpam-815	116	2	=	=	SYM
ejpam-815	116	3	2β(p−α	2β(p−α	NUM
ejpam-815	116	4	)	)	PUNCT
ejpam-815	116	5	in	in	ADP
ejpam-815	116	6	the	the	DET
ejpam-815	116	7	above	above	ADJ
ejpam-815	116	8	theorem	theorem	NOUN
ejpam-815	116	9	,	,	PUNCT
ejpam-815	116	10	we	we	PRON
ejpam-815	116	11	obtain	obtain	VERB
ejpam-815	116	12	the	the	DET
ejpam-815	116	13	results	result	NOUN
ejpam-815	116	14	obtained	obtain	VERB
ejpam-815	116	15	by	by	ADP
ejpam-815	116	16	aouf	aouf	PROPN
ejpam-815	117	1	[	[	X
ejpam-815	117	2	1	1	NUM
ejpam-815	117	3	]	]	PUNCT
ejpam-815	117	4	.	.	PUNCT
ejpam-815	118	1	(	(	PUNCT
ejpam-815	118	2	ii	ii	NOUN
ejpam-815	118	3	)	)	PUNCT
ejpam-815	118	4	putting	put	VERB
ejpam-815	118	5	p	p	NOUN
ejpam-815	118	6	=	=	NOUN
ejpam-815	118	7	1	1	NUM
ejpam-815	118	8	,	,	PUNCT
ejpam-815	118	9	cn	cn	X
ejpam-815	118	10	=	=	PUNCT
ejpam-815	118	11	n((n+	n((n+	PROPN
ejpam-815	118	12	1)+β(n+	1)+β(n+	PROPN
ejpam-815	118	13	2α−	2α−	NUM
ejpam-815	118	14	1	1	NUM
ejpam-815	118	15	)	)	PUNCT
ejpam-815	118	16	)	)	PUNCT
ejpam-815	118	17	and	and	CCONJ
ejpam-815	118	18	δ	δ	PROPN
ejpam-815	118	19	=	=	SYM
ejpam-815	118	20	2β(1−α	2β(1−α	PROPN
ejpam-815	118	21	)	)	PUNCT
ejpam-815	118	22	in	in	ADP
ejpam-815	118	23	the	the	DET
ejpam-815	118	24	above	above	ADJ
ejpam-815	118	25	theorem	theorem	NOUN
ejpam-815	118	26	,	,	PUNCT
ejpam-815	118	27	we	we	PRON
ejpam-815	118	28	obtain	obtain	VERB
ejpam-815	118	29	the	the	DET
ejpam-815	118	30	results	result	NOUN
ejpam-815	118	31	obtained	obtain	VERB
ejpam-815	118	32	by	by	ADP
ejpam-815	118	33	mogra	mogra	NOUN
ejpam-815	118	34	[	[	X
ejpam-815	118	35	11	11	NUM
ejpam-815	118	36	]	]	PUNCT
ejpam-815	118	37	.	.	PUNCT
ejpam-815	119	1	(	(	PUNCT
ejpam-815	119	2	iii	iii	X
ejpam-815	119	3	)	)	PUNCT
ejpam-815	119	4	putting	put	VERB
ejpam-815	119	5	p	p	NOUN
ejpam-815	119	6	=	=	NOUN
ejpam-815	119	7	1	1	NUM
ejpam-815	119	8	,	,	PUNCT
ejpam-815	119	9	in	in	ADP
ejpam-815	119	10	corollary	corollary	ADJ
ejpam-815	119	11	2	2	NUM
ejpam-815	119	12	,	,	PUNCT
ejpam-815	119	13	we	we	PRON
ejpam-815	119	14	obtain	obtain	VERB
ejpam-815	119	15	the	the	DET
ejpam-815	119	16	results	result	NOUN
ejpam-815	119	17	obtained	obtain	VERB
ejpam-815	119	18	by	by	ADP
ejpam-815	119	19	el	el	PROPN
ejpam-815	119	20	-	-	NOUN
ejpam-815	119	21	ashwah	ashwah	NOUN
ejpam-815	119	22	and	and	CCONJ
ejpam-815	119	23	aouf	aouf	PROPN
ejpam-815	120	1	[	[	X
ejpam-815	120	2	5	5	NUM
ejpam-815	120	3	]	]	PUNCT
ejpam-815	120	4	.	.	PUNCT
ejpam-815	121	1	references	reference	NOUN
ejpam-815	121	2	1123	1123	NUM
ejpam-815	121	3	acknowledgements	acknowledgement	NOUN
ejpam-815	121	4	the	the	DET
ejpam-815	121	5	first	first	ADJ
ejpam-815	121	6	author	author	NOUN
ejpam-815	121	7	(	(	PUNCT
ejpam-815	121	8	s	s	PROPN
ejpam-815	121	9	p	p	NOUN
ejpam-815	121	10	g	g	NOUN
ejpam-815	121	11	)	)	PUNCT
ejpam-815	121	12	is	be	AUX
ejpam-815	121	13	thankful	thankful	ADJ
ejpam-815	121	14	to	to	ADP
ejpam-815	121	15	csir	csir	PROPN
ejpam-815	121	16	,	,	PUNCT
ejpam-815	121	17	new	new	ADJ
ejpam-815	121	18	delhi	delhi	PROPN
ejpam-815	121	19	,	,	PUNCT
ejpam-815	121	20	india	india	PROPN
ejpam-815	121	21	for	for	ADP
ejpam-815	121	22	awarding	award	VERB
ejpam-815	121	23	emeritius	emeritius	NOUN
ejpam-815	121	24	scientist	scientist	NOUN
ejpam-815	121	25	under	under	ADP
ejpam-815	121	26	scheme	scheme	PROPN
ejpam-815	121	27	no	no	NOUN
ejpam-815	121	28	.	.	NOUN
ejpam-815	121	29	21(084)/10	21(084)/10	NUM
ejpam-815	121	30	/	/	SYM
ejpam-815	121	31	emr	emr	PROPN
ejpam-815	121	32	-	-	PUNCT
ejpam-815	121	33	ii	ii	PROPN
ejpam-815	121	34	.	.	PUNCT
ejpam-815	122	1	references	reference	NOUN
ejpam-815	122	2	[	[	X
ejpam-815	122	3	1	1	X
ejpam-815	122	4	]	]	X
ejpam-815	122	5	m.k	m.k	PROPN
ejpam-815	122	6	.	.	PROPN
ejpam-815	122	7	aouf	aouf	PROPN
ejpam-815	122	8	,	,	PUNCT
ejpam-815	122	9	hadamard	hadamard	ADJ
ejpam-815	122	10	product	product	NOUN
ejpam-815	122	11	of	of	ADP
ejpam-815	122	12	certain	certain	ADJ
ejpam-815	122	13	meromorphic	meromorphic	ADJ
ejpam-815	122	14	p	p	NOUN
ejpam-815	122	15	-	-	PUNCT
ejpam-815	122	16	valent	valent	NOUN
ejpam-815	122	17	starlike	starlike	NOUN
ejpam-815	122	18	functions	function	NOUN
ejpam-815	122	19	and	and	CCONJ
ejpam-815	122	20	meromorphic	meromorphic	ADJ
ejpam-815	122	21	p	p	NOUN
ejpam-815	122	22	-	-	PUNCT
ejpam-815	122	23	valent	valent	NOUN
ejpam-815	122	24	convex	convex	NOUN
ejpam-815	122	25	functions	function	NOUN
ejpam-815	122	26	,	,	PUNCT
ejpam-815	122	27	j.	j.	PROPN
ejpam-815	122	28	inq	inq	PROPN
ejpam-815	122	29	.	.	PUNCT
ejpam-815	123	1	pure	pure	ADJ
ejpam-815	123	2	appl	appl	PROPN
ejpam-815	123	3	.	.	PUNCT
ejpam-815	124	1	math	math	PROPN
ejpam-815	124	2	(	(	PUNCT
ejpam-815	124	3	jipam	jipam	PROPN
ejpam-815	124	4	)	)	PUNCT
ejpam-815	124	5	,	,	PUNCT
ejpam-815	124	6	10(2	10(2	NUM
ejpam-815	124	7	)	)	PUNCT
ejpam-815	124	8	,	,	PUNCT
ejpam-815	124	9	article	article	NOUN
ejpam-815	124	10	43	43	NUM
ejpam-815	124	11	,	,	PUNCT
ejpam-815	124	12	7	7	NUM
ejpam-815	124	13	pp	pp	NOUN
ejpam-815	124	14	.	.	PUNCT
ejpam-815	125	1	2009	2009	NUM
ejpam-815	125	2	.	.	PUNCT
ejpam-815	126	1	[	[	X
ejpam-815	126	2	2	2	NUM
ejpam-815	126	3	]	]	X
ejpam-815	126	4	m.k	m.k	PROPN
ejpam-815	126	5	.	.	PROPN
ejpam-815	126	6	aouf	aouf	PROPN
ejpam-815	126	7	and	and	CCONJ
ejpam-815	126	8	h.e	h.e	PROPN
ejpam-815	126	9	.	.	PROPN
ejpam-815	126	10	darwish	darwish	PROPN
ejpam-815	126	11	,	,	PUNCT
ejpam-815	126	12	hadamard	hadamard	ADJ
ejpam-815	126	13	product	product	NOUN
ejpam-815	126	14	of	of	ADP
ejpam-815	126	15	certain	certain	ADJ
ejpam-815	126	16	meromorphic	meromorphic	ADJ
ejpam-815	126	17	univalent	univalent	ADJ
ejpam-815	126	18	functions	function	NOUN
ejpam-815	126	19	with	with	ADP
ejpam-815	126	20	positive	positive	ADJ
ejpam-815	126	21	coefficients	coefficient	NOUN
ejpam-815	126	22	,	,	PUNCT
ejpam-815	126	23	south	south	NOUN
ejpam-815	126	24	.	.	PUNCT
ejpam-815	127	1	asian	asian	ADJ
ejpam-815	127	2	bull	bull	PROPN
ejpam-815	127	3	.	.	PUNCT
ejpam-815	128	1	math	math	NOUN
ejpam-815	128	2	.	.	PUNCT
ejpam-815	128	3	,	,	PUNCT
ejpam-815	128	4	30	30	NUM
ejpam-815	128	5	,	,	PUNCT
ejpam-815	128	6	23–28	23–28	NUM
ejpam-815	128	7	.	.	PUNCT
ejpam-815	129	1	2006	2006	NUM
ejpam-815	129	2	.	.	PUNCT
ejpam-815	130	1	[	[	X
ejpam-815	130	2	3	3	X
ejpam-815	130	3	]	]	X
ejpam-815	130	4	m.k	m.k	PROPN
ejpam-815	130	5	.	.	PROPN
ejpam-815	130	6	aouf	aouf	PROPN
ejpam-815	130	7	,	,	PUNCT
ejpam-815	130	8	a.	a.	NOUN
ejpam-815	130	9	shamandy	shamandy	NOUN
ejpam-815	130	10	and	and	CCONJ
ejpam-815	130	11	m.f	m.f	PROPN
ejpam-815	130	12	.	.	PROPN
ejpam-815	130	13	yassen	yassen	PROPN
ejpam-815	130	14	,	,	PUNCT
ejpam-815	130	15	quasi	quasi	ADJ
ejpam-815	130	16	-	-	ADJ
ejpam-815	130	17	hadamard	hadamard	ADJ
ejpam-815	130	18	product	product	NOUN
ejpam-815	130	19	of	of	ADP
ejpam-815	130	20	p	p	NOUN
ejpam-815	130	21	-	-	PUNCT
ejpam-815	130	22	valent	valent	NOUN
ejpam-815	130	23	functions	function	NOUN
ejpam-815	130	24	,	,	PUNCT
ejpam-815	130	25	commun	commun	PROPN
ejpam-815	130	26	.	.	PUNCT
ejpam-815	131	1	fac	fac	PROPN
ejpam-815	131	2	.	.	PUNCT
ejpam-815	131	3	sci	sci	PROPN
ejpam-815	131	4	.	.	PROPN
ejpam-815	131	5	univ	univ	PROPN
ejpam-815	131	6	.	.	PUNCT
ejpam-815	132	1	ank	ank	PROPN
ejpam-815	132	2	.	.	PROPN
ejpam-815	132	3	series	series	PROPN
ejpam-815	132	4	a1	a1	PROPN
ejpam-815	132	5	,	,	PUNCT
ejpam-815	132	6	44	44	NUM
ejpam-815	132	7	,	,	PUNCT
ejpam-815	132	8	35–40	35–40	NUM
ejpam-815	132	9	.	.	PUNCT
ejpam-815	132	10	1995	1995	NUM
ejpam-815	133	1	[	[	X
ejpam-815	133	2	4	4	NUM
ejpam-815	133	3	]	]	X
ejpam-815	133	4	h.e	h.e	PROPN
ejpam-815	133	5	.	.	PROPN
ejpam-815	133	6	darwish	darwish	PROPN
ejpam-815	133	7	,	,	PUNCT
ejpam-815	133	8	the	the	DET
ejpam-815	133	9	quasi	quasi	ADJ
ejpam-815	133	10	-	-	ADJ
ejpam-815	133	11	hadamard	hadamard	ADJ
ejpam-815	133	12	product	product	NOUN
ejpam-815	133	13	of	of	ADP
ejpam-815	133	14	certain	certain	ADJ
ejpam-815	133	15	starlike	starlike	NOUN
ejpam-815	133	16	and	and	CCONJ
ejpam-815	133	17	convex	convex	NOUN
ejpam-815	133	18	functions	function	NOUN
ejpam-815	133	19	,	,	PUNCT
ejpam-815	133	20	appl	appl	PROPN
ejpam-815	133	21	.	.	PROPN
ejpam-815	133	22	math	math	NOUN
ejpam-815	133	23	.	.	PUNCT
ejpam-815	134	1	letters	letter	NOUN
ejpam-815	134	2	,	,	PUNCT
ejpam-815	134	3	20	20	NUM
ejpam-815	134	4	,	,	PUNCT
ejpam-815	134	5	692–695	692–695	NUM
ejpam-815	134	6	.	.	NOUN
ejpam-815	134	7	2007	2007	NUM
ejpam-815	134	8	.	.	PUNCT
ejpam-815	135	1	[	[	X
ejpam-815	135	2	5	5	NUM
ejpam-815	135	3	]	]	X
ejpam-815	135	4	r.m	r.m	PROPN
ejpam-815	135	5	.	.	PROPN
ejpam-815	135	6	el	el	PROPN
ejpam-815	135	7	-	-	NOUN
ejpam-815	135	8	ashwah	ashwah	NOUN
ejpam-815	135	9	and	and	CCONJ
ejpam-815	135	10	m.k	m.k	PROPN
ejpam-815	135	11	.	.	PROPN
ejpam-815	135	12	aouf	aouf	PROPN
ejpam-815	135	13	,	,	PUNCT
ejpam-815	135	14	hadamard	hadamard	ADJ
ejpam-815	135	15	product	product	NOUN
ejpam-815	135	16	of	of	ADP
ejpam-815	135	17	certain	certain	ADJ
ejpam-815	135	18	meromorphic	meromorphic	ADJ
ejpam-815	135	19	starlike	starlike	NOUN
ejpam-815	135	20	and	and	CCONJ
ejpam-815	135	21	convex	convex	NOUN
ejpam-815	135	22	functions	function	NOUN
ejpam-815	135	23	,	,	PUNCT
ejpam-815	135	24	computers	computer	NOUN
ejpam-815	135	25	math	math	NOUN
ejpam-815	135	26	.	.	PUNCT
ejpam-815	136	1	appl	appl	PROPN
ejpam-815	136	2	.	.	PROPN
ejpam-815	136	3	,	,	PUNCT
ejpam-815	136	4	57	57	NUM
ejpam-815	136	5	,	,	PUNCT
ejpam-815	136	6	1102–1106	1102–1106	NUM
ejpam-815	136	7	.	.	PUNCT
ejpam-815	136	8	2009	2009	NUM
ejpam-815	136	9	.	.	PUNCT
ejpam-815	137	1	[	[	X
ejpam-815	137	2	6	6	NUM
ejpam-815	137	3	]	]	X
ejpam-815	137	4	h.m	h.m	PROPN
ejpam-815	137	5	.	.	PROPN
ejpam-815	137	6	hossen	hossen	PROPN
ejpam-815	137	7	,	,	PUNCT
ejpam-815	137	8	quasi	quasi	ADJ
ejpam-815	137	9	-	-	ADJ
ejpam-815	137	10	hadamard	hadamard	ADJ
ejpam-815	137	11	product	product	NOUN
ejpam-815	137	12	of	of	ADP
ejpam-815	137	13	certain	certain	ADJ
ejpam-815	137	14	p	p	ADJ
ejpam-815	137	15	-	-	PUNCT
ejpam-815	137	16	valent	valent	NOUN
ejpam-815	137	17	functions	function	NOUN
ejpam-815	137	18	,	,	PUNCT
ejpam-815	137	19	demonstratio	demonstratio	PROPN
ejpam-815	137	20	math	math	PROPN
ejpam-815	137	21	.	.	PUNCT
ejpam-815	137	22	,	,	PUNCT
ejpam-815	137	23	33(2	33(2	NUM
ejpam-815	137	24	)	)	PUNCT
ejpam-815	137	25	,	,	PUNCT
ejpam-815	137	26	277–281	277–281	NUM
ejpam-815	137	27	.	.	PUNCT
ejpam-815	137	28	2000	2000	NUM
ejpam-815	138	1	[	[	X
ejpam-815	138	2	7	7	X
ejpam-815	138	3	]	]	X
ejpam-815	138	4	v.	v.	CCONJ
ejpam-815	138	5	kumar	kumar	PROPN
ejpam-815	138	6	,	,	PUNCT
ejpam-815	138	7	hadamard	hadamard	ADJ
ejpam-815	138	8	product	product	NOUN
ejpam-815	138	9	of	of	ADP
ejpam-815	138	10	certain	certain	ADJ
ejpam-815	138	11	starlike	starlike	NOUN
ejpam-815	138	12	functions	function	NOUN
ejpam-815	138	13	,	,	PUNCT
ejpam-815	138	14	j.	j.	PROPN
ejpam-815	138	15	math	math	PROPN
ejpam-815	138	16	.	.	PUNCT
ejpam-815	139	1	anal	anal	PROPN
ejpam-815	139	2	.	.	PUNCT
ejpam-815	140	1	appl	appl	PROPN
ejpam-815	140	2	.	.	PROPN
ejpam-815	140	3	,	,	PUNCT
ejpam-815	140	4	110	110	NUM
ejpam-815	140	5	,	,	PUNCT
ejpam-815	140	6	425–428	425–428	NUM
ejpam-815	140	7	.	.	PUNCT
ejpam-815	141	1	1985	1985	NUM
ejpam-815	141	2	[	[	X
ejpam-815	141	3	8	8	NUM
ejpam-815	141	4	]	]	X
ejpam-815	141	5	v.	v.	CCONJ
ejpam-815	141	6	kumar	kumar	PROPN
ejpam-815	141	7	,	,	PUNCT
ejpam-815	141	8	hadamard	hadamard	ADJ
ejpam-815	141	9	product	product	NOUN
ejpam-815	141	10	of	of	ADP
ejpam-815	141	11	certain	certain	ADJ
ejpam-815	141	12	starlike	starlike	PROPN
ejpam-815	141	13	functions	functions	PROPN
ejpam-815	141	14	ii	ii	PROPN
ejpam-815	141	15	,	,	PUNCT
ejpam-815	141	16	j.	j.	PROPN
ejpam-815	141	17	math	math	PROPN
ejpam-815	141	18	.	.	PUNCT
ejpam-815	142	1	anal	anal	PROPN
ejpam-815	142	2	.	.	PUNCT
ejpam-815	143	1	appl	appl	PROPN
ejpam-815	143	2	.	.	PROPN
ejpam-815	143	3	,	,	PUNCT
ejpam-815	143	4	113	113	NUM
ejpam-815	143	5	,	,	PUNCT
ejpam-815	143	6	230–234	230–234	NUM
ejpam-815	143	7	.	.	PUNCT
ejpam-815	144	1	1986	1986	NUM
ejpam-815	145	1	[	[	X
ejpam-815	145	2	9	9	NUM
ejpam-815	145	3	]	]	X
ejpam-815	145	4	v.	v.	X
ejpam-815	145	5	kumar	kumar	PROPN
ejpam-815	145	6	,	,	PUNCT
ejpam-815	145	7	quasi	quasi	ADJ
ejpam-815	145	8	-	-	ADJ
ejpam-815	145	9	hadamard	hadamard	ADJ
ejpam-815	145	10	product	product	NOUN
ejpam-815	145	11	of	of	ADP
ejpam-815	145	12	certain	certain	ADJ
ejpam-815	145	13	univalent	univalent	ADJ
ejpam-815	145	14	functions	function	NOUN
ejpam-815	145	15	,	,	PUNCT
ejpam-815	145	16	j.	j.	PROPN
ejpam-815	145	17	math	math	PROPN
ejpam-815	145	18	.	.	PUNCT
ejpam-815	146	1	anal	anal	PROPN
ejpam-815	146	2	.	.	PUNCT
ejpam-815	147	1	appl	appl	PROPN
ejpam-815	147	2	.	.	PROPN
ejpam-815	147	3	,	,	PUNCT
ejpam-815	147	4	126	126	NUM
ejpam-815	147	5	,	,	PUNCT
ejpam-815	147	6	70–77	70–77	NUM
ejpam-815	147	7	.	.	PUNCT
ejpam-815	147	8	1987	1987	NUM
ejpam-815	147	9	.	.	PUNCT
ejpam-815	148	1	[	[	X
ejpam-815	148	2	10	10	NUM
ejpam-815	148	3	]	]	X
ejpam-815	148	4	m.l	m.l	PROPN
ejpam-815	148	5	.	.	PROPN
ejpam-815	148	6	mogra	mogra	PROPN
ejpam-815	148	7	,	,	PUNCT
ejpam-815	148	8	meromorphic	meromorphic	ADJ
ejpam-815	148	9	multivalent	multivalent	NOUN
ejpam-815	148	10	functions	function	NOUN
ejpam-815	148	11	with	with	ADP
ejpam-815	148	12	positive	positive	ADJ
ejpam-815	148	13	coefficients	coefficient	NOUN
ejpam-815	148	14	.	.	PUNCT
ejpam-815	149	1	i	i	PRON
ejpam-815	149	2	,	,	PUNCT
ejpam-815	149	3	math	math	NOUN
ejpam-815	149	4	.	.	PUNCT
ejpam-815	150	1	japon	japon	PROPN
ejpam-815	150	2	.	.	PUNCT
ejpam-815	151	1	35(1	35(1	NUM
ejpam-815	151	2	)	)	PUNCT
ejpam-815	151	3	,	,	PUNCT
ejpam-815	151	4	1–11	1–11	PROPN
ejpam-815	151	5	.	.	PUNCT
ejpam-815	151	6	1990	1990	NUM
ejpam-815	151	7	.	.	PUNCT
ejpam-815	152	1	[	[	X
ejpam-815	152	2	11	11	NUM
ejpam-815	152	3	]	]	X
ejpam-815	152	4	m.l	m.l	PROPN
ejpam-815	152	5	.	.	PROPN
ejpam-815	152	6	mogra	mogra	PROPN
ejpam-815	152	7	,	,	PUNCT
ejpam-815	152	8	hadamard	hadamard	ADJ
ejpam-815	152	9	product	product	NOUN
ejpam-815	152	10	of	of	ADP
ejpam-815	152	11	certain	certain	ADJ
ejpam-815	152	12	meromorphic	meromorphic	ADJ
ejpam-815	152	13	starlike	starlike	NOUN
ejpam-815	152	14	and	and	CCONJ
ejpam-815	152	15	convex	convex	NOUN
ejpam-815	152	16	functions	function	NOUN
ejpam-815	152	17	,	,	PUNCT
ejpam-815	152	18	tamkang	tamkang	PROPN
ejpam-815	152	19	j.	j.	PROPN
ejpam-815	152	20	math	math	PROPN
ejpam-815	152	21	.	.	PUNCT
ejpam-815	152	22	,	,	PUNCT
ejpam-815	152	23	25(2	25(2	NUM
ejpam-815	152	24	)	)	PUNCT
ejpam-815	152	25	,	,	PUNCT
ejpam-815	152	26	157–162	157–162	NUM
ejpam-815	152	27	.	.	PUNCT
ejpam-815	152	28	1994	1994	NUM
ejpam-815	152	29	.	.	PUNCT
ejpam-815	153	1	[	[	X
ejpam-815	153	2	12	12	NUM
ejpam-815	153	3	]	]	PUNCT
ejpam-815	153	4	t.	t.	PROPN
ejpam-815	153	5	sekine	sekine	PROPN
ejpam-815	153	6	,	,	PUNCT
ejpam-815	153	7	on	on	ADP
ejpam-815	153	8	quasi	quasi	ADJ
ejpam-815	153	9	-	-	ADJ
ejpam-815	153	10	hadamard	hadamard	ADJ
ejpam-815	153	11	products	product	NOUN
ejpam-815	153	12	of	of	ADP
ejpam-815	153	13	p	p	NOUN
ejpam-815	153	14	-	-	PUNCT
ejpam-815	153	15	valent	valent	NOUN
ejpam-815	153	16	functions	function	NOUN
ejpam-815	153	17	with	with	ADP
ejpam-815	153	18	negative	negative	ADJ
ejpam-815	153	19	coefficients	coefficient	NOUN
ejpam-815	153	20	in	in	ADP
ejpam-815	153	21	:	:	PUNCT
ejpam-815	153	22	h.	h.	PROPN
ejpam-815	153	23	m.	m.	PROPN
ejpam-815	153	24	srivastava	srivastava	PROPN
ejpam-815	153	25	and	and	CCONJ
ejpam-815	153	26	s.	s.	PROPN
ejpam-815	153	27	owa	owa	PROPN
ejpam-815	153	28	(	(	PUNCT
ejpam-815	153	29	editors	editor	NOUN
ejpam-815	153	30	)	)	PUNCT
ejpam-815	153	31	,	,	PUNCT
ejpam-815	153	32	univalent	univalent	ADJ
ejpam-815	153	33	functions	function	NOUN
ejpam-815	153	34	,	,	PUNCT
ejpam-815	153	35	fractional	fractional	ADJ
ejpam-815	153	36	calculus	calculus	NOUN
ejpam-815	153	37	,	,	PUNCT
ejpam-815	153	38	and	and	CCONJ
ejpam-815	153	39	their	their	PRON
ejpam-815	153	40	applications	application	NOUN
ejpam-815	153	41	,	,	PUNCT
ejpam-815	153	42	halsted	halsted	ADJ
ejpam-815	153	43	press	press	NOUN
ejpam-815	153	44	(	(	PUNCT
ejpam-815	153	45	ellis	ellis	PROPN
ejpam-815	153	46	horwood	horwood	PROPN
ejpam-815	153	47	limited	limited	PROPN
ejpam-815	153	48	,	,	PUNCT
ejpam-815	153	49	chichester	chichester	PROPN
ejpam-815	153	50	)	)	PUNCT
ejpam-815	153	51	,	,	PUNCT
ejpam-815	153	52	john	john	PROPN
ejpam-815	153	53	wiley	wiley	PROPN
ejpam-815	153	54	and	and	CCONJ
ejpam-815	153	55	sons	son	NOUN
ejpam-815	153	56	,	,	PUNCT
ejpam-815	153	57	new	new	PROPN
ejpam-815	153	58	york	york	PROPN
ejpam-815	153	59	,	,	PUNCT
ejpam-815	153	60	chichester	chichester	PROPN
ejpam-815	153	61	,	,	PUNCT
ejpam-815	153	62	brisbane	brisbane	PROPN
ejpam-815	153	63	and	and	CCONJ
ejpam-815	153	64	toronto	toronto	PROPN
ejpam-815	153	65	,	,	PUNCT
ejpam-815	153	66	317–328	317–328	NUM
ejpam-815	153	67	.	.	PUNCT
ejpam-815	153	68	1989	1989	NUM
ejpam-815	153	69	.	.	PUNCT