id	sid	tid	token	lemma	pos
ejpam-856	1	1	8_856_selvakumaran.dvi	8_856_selvakumaran.dvi	NUM
ejpam-856	1	2	european	european	PROPN
ejpam-856	1	3	journal	journal	PROPN
ejpam-856	1	4	of	of	ADP
ejpam-856	1	5	pure	pure	ADJ
ejpam-856	1	6	and	and	CCONJ
ejpam-856	1	7	applied	apply	VERB
ejpam-856	1	8	mathematics	mathematic	NOUN
ejpam-856	1	9	vol	vol	NOUN
ejpam-856	1	10	.	.	PUNCT
ejpam-856	2	1	3	3	NUM
ejpam-856	2	2	,	,	PUNCT
ejpam-856	2	3	no	no	INTJ
ejpam-856	2	4	.	.	NOUN
ejpam-856	2	5	6	6	NUM
ejpam-856	2	6	,	,	PUNCT
ejpam-856	2	7	2010	2010	NUM
ejpam-856	2	8	,	,	PUNCT
ejpam-856	2	9	1048	1048	NUM
ejpam-856	2	10	-	-	SYM
ejpam-856	2	11	1054	1054	NUM
ejpam-856	2	12	issn	issn	PROPN
ejpam-856	2	13	1307	1307	NUM
ejpam-856	2	14	-	-	SYM
ejpam-856	2	15	5543	5543	NUM
ejpam-856	2	16	–	–	PUNCT
ejpam-856	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-856	2	18	special	special	ADJ
ejpam-856	2	19	issue	issue	NOUN
ejpam-856	2	20	on	on	ADP
ejpam-856	2	21	complex	complex	ADJ
ejpam-856	2	22	analysis	analysis	NOUN
ejpam-856	2	23	:	:	PUNCT
ejpam-856	2	24	theory	theory	NOUN
ejpam-856	2	25	and	and	CCONJ
ejpam-856	2	26	applications	application	NOUN
ejpam-856	2	27	dedicated	dedicate	VERB
ejpam-856	2	28	to	to	ADP
ejpam-856	2	29	professor	professor	PROPN
ejpam-856	2	30	hari	hari	PROPN
ejpam-856	2	31	m.	m.	PROPN
ejpam-856	2	32	srivastava	srivastava	PROPN
ejpam-856	2	33	,	,	PUNCT
ejpam-856	2	34	on	on	ADP
ejpam-856	2	35	the	the	DET
ejpam-856	2	36	occasion	occasion	NOUN
ejpam-856	2	37	of	of	ADP
ejpam-856	2	38	his	his	PRON
ejpam-856	2	39	70th	70th	ADJ
ejpam-856	2	40	birthday	birthday	NOUN
ejpam-856	2	41	majorization	majorization	NOUN
ejpam-856	2	42	for	for	ADP
ejpam-856	2	43	certain	certain	ADJ
ejpam-856	2	44	classes	class	NOUN
ejpam-856	2	45	of	of	ADP
ejpam-856	2	46	analytic	analytic	ADJ
ejpam-856	2	47	functions	function	NOUN
ejpam-856	2	48	defined	define	VERB
ejpam-856	2	49	by	by	ADP
ejpam-856	2	50	a	a	DET
ejpam-856	2	51	generalized	generalized	ADJ
ejpam-856	2	52	operator	operator	NOUN
ejpam-856	2	53	c.	c.	PROPN
ejpam-856	2	54	selvaraj	selvaraj	PROPN
ejpam-856	2	55	,	,	PUNCT
ejpam-856	2	56	k.a	k.a	PROPN
ejpam-856	2	57	.	.	PROPN
ejpam-856	2	58	selvakumaran∗	selvakumaran∗	PROPN
ejpam-856	2	59	dept	dept	PROPN
ejpam-856	2	60	.	.	PROPN
ejpam-856	2	61	of	of	ADP
ejpam-856	2	62	mathematics	mathematics	PROPN
ejpam-856	2	63	,	,	PUNCT
ejpam-856	2	64	presidency	presidency	NOUN
ejpam-856	2	65	college	college	NOUN
ejpam-856	2	66	(	(	PUNCT
ejpam-856	2	67	autonomous	autonomous	ADJ
ejpam-856	2	68	)	)	PUNCT
ejpam-856	2	69	,	,	PUNCT
ejpam-856	2	70	chennai-600	chennai-600	VERB
ejpam-856	2	71	005	005	NUM
ejpam-856	2	72	,	,	PUNCT
ejpam-856	2	73	india	india	PROPN
ejpam-856	2	74	abstract	abstract	NOUN
ejpam-856	2	75	.	.	PUNCT
ejpam-856	3	1	in	in	ADP
ejpam-856	3	2	this	this	DET
ejpam-856	3	3	paper	paper	NOUN
ejpam-856	3	4	,	,	PUNCT
ejpam-856	3	5	we	we	PRON
ejpam-856	3	6	investigate	investigate	VERB
ejpam-856	3	7	majorization	majorization	NOUN
ejpam-856	3	8	properties	property	NOUN
ejpam-856	3	9	for	for	ADP
ejpam-856	3	10	certain	certain	ADJ
ejpam-856	3	11	classes	class	NOUN
ejpam-856	3	12	of	of	ADP
ejpam-856	3	13	multivalent	multivalent	NOUN
ejpam-856	3	14	analytic	analytic	ADJ
ejpam-856	3	15	functions	function	NOUN
ejpam-856	3	16	defined	define	VERB
ejpam-856	3	17	by	by	ADP
ejpam-856	3	18	a	a	DET
ejpam-856	3	19	generalized	generalized	ADJ
ejpam-856	3	20	operator	operator	NOUN
ejpam-856	3	21	.	.	PUNCT
ejpam-856	4	1	also	also	ADV
ejpam-856	4	2	,	,	PUNCT
ejpam-856	4	3	we	we	PRON
ejpam-856	4	4	point	point	VERB
ejpam-856	4	5	out	out	ADP
ejpam-856	4	6	some	some	DET
ejpam-856	4	7	new	new	ADJ
ejpam-856	4	8	and	and	CCONJ
ejpam-856	4	9	known	known	ADJ
ejpam-856	4	10	consequences	consequence	NOUN
ejpam-856	4	11	of	of	ADP
ejpam-856	4	12	our	our	PRON
ejpam-856	4	13	main	main	ADJ
ejpam-856	4	14	result	result	NOUN
ejpam-856	4	15	.	.	PUNCT
ejpam-856	5	1	2000	2000	NUM
ejpam-856	5	2	mathematics	mathematic	NOUN
ejpam-856	5	3	subject	subject	NOUN
ejpam-856	5	4	classifications	classification	NOUN
ejpam-856	5	5	:	:	PUNCT
ejpam-856	5	6	30c45	30c45	NUM
ejpam-856	5	7	key	key	ADJ
ejpam-856	5	8	words	word	NOUN
ejpam-856	5	9	and	and	CCONJ
ejpam-856	5	10	phrases	phrase	NOUN
ejpam-856	5	11	:	:	PUNCT
ejpam-856	5	12	analytic	analytic	ADJ
ejpam-856	5	13	functions	function	NOUN
ejpam-856	5	14	,	,	PUNCT
ejpam-856	5	15	starlike	starlike	NOUN
ejpam-856	5	16	functions	function	NOUN
ejpam-856	5	17	,	,	PUNCT
ejpam-856	5	18	hadamard	hadamard	ADJ
ejpam-856	5	19	product	product	NOUN
ejpam-856	5	20	,	,	PUNCT
ejpam-856	5	21	subordination	subordination	NOUN
ejpam-856	5	22	,	,	PUNCT
ejpam-856	5	23	majorization	majorization	NOUN
ejpam-856	5	24	1	1	NUM
ejpam-856	5	25	.	.	PUNCT
ejpam-856	5	26	introduction	introduction	NOUN
ejpam-856	5	27	and	and	CCONJ
ejpam-856	5	28	preliminaries	preliminary	NOUN
ejpam-856	5	29	letap	letap	NOUN
ejpam-856	5	30	denote	denote	VERB
ejpam-856	5	31	the	the	DET
ejpam-856	5	32	class	class	NOUN
ejpam-856	5	33	of	of	ADP
ejpam-856	5	34	functions	function	NOUN
ejpam-856	5	35	f	f	X
ejpam-856	5	36	(	(	PUNCT
ejpam-856	5	37	z	z	NOUN
ejpam-856	5	38	)	)	PUNCT
ejpam-856	5	39	of	of	ADP
ejpam-856	5	40	the	the	DET
ejpam-856	5	41	form	form	NOUN
ejpam-856	6	1	f	f	X
ejpam-856	6	2	(	(	PUNCT
ejpam-856	6	3	z	z	NOUN
ejpam-856	6	4	)	)	PUNCT
ejpam-856	6	5	=	=	SYM
ejpam-856	6	6	zp	zp	PROPN
ejpam-856	6	7	+	+	CCONJ
ejpam-856	6	8	∞	∞	NUM
ejpam-856	6	9	∑	∑	PUNCT
ejpam-856	6	10	n=1	n=1	PROPN
ejpam-856	6	11	anzp+n	anzp+n	PROPN
ejpam-856	6	12	,	,	PUNCT
ejpam-856	6	13	(	(	PUNCT
ejpam-856	6	14	p	p	NOUN
ejpam-856	6	15	∈	∈	PROPN
ejpam-856	6	16	n	n	NOUN
ejpam-856	6	17	:	:	PUNCT
ejpam-856	6	18	=	=	PUNCT
ejpam-856	6	19	{	{	PUNCT
ejpam-856	6	20	1,2,3	1,2,3	NUM
ejpam-856	6	21	,	,	PUNCT
ejpam-856	6	22	.	.	PUNCT
ejpam-856	6	23	.	.	PUNCT
ejpam-856	6	24	.	.	PUNCT
ejpam-856	6	25	}	}	PUNCT
ejpam-856	6	26	)	)	PUNCT
ejpam-856	6	27	,	,	PUNCT
ejpam-856	6	28	(	(	PUNCT
ejpam-856	6	29	1	1	X
ejpam-856	6	30	)	)	PUNCT
ejpam-856	6	31	which	which	PRON
ejpam-856	6	32	are	be	AUX
ejpam-856	6	33	analytic	analytic	ADJ
ejpam-856	6	34	and	and	CCONJ
ejpam-856	6	35	p	p	NOUN
ejpam-856	6	36	-	-	PUNCT
ejpam-856	6	37	valent	valent	NOUN
ejpam-856	6	38	in	in	ADP
ejpam-856	6	39	the	the	DET
ejpam-856	6	40	open	open	ADJ
ejpam-856	6	41	unit	unit	NOUN
ejpam-856	6	42	disk	disk	NOUN
ejpam-856	6	43	u	u	NOUN
ejpam-856	6	44	=	=	PUNCT
ejpam-856	6	45	{	{	PUNCT
ejpam-856	6	46	z	z	NOUN
ejpam-856	6	47	:	:	PUNCT
ejpam-856	6	48	z	z	PROPN
ejpam-856	6	49	∈	∈	PROPN
ejpam-856	6	50	c	c	PROPN
ejpam-856	6	51	and	and	CCONJ
ejpam-856	6	52	|z|	|z|	VERB
ejpam-856	6	53	<	<	X
ejpam-856	6	54	1	1	NUM
ejpam-856	6	55	}	}	PUNCT
ejpam-856	6	56	.	.	PUNCT
ejpam-856	7	1	also	also	ADV
ejpam-856	7	2	let	let	VERB
ejpam-856	7	3	a1	a1	NOUN
ejpam-856	7	4	=	=	NOUN
ejpam-856	7	5	:	:	PUNCT
ejpam-856	7	6	a	a	X
ejpam-856	7	7	.	.	PUNCT
ejpam-856	8	1	for	for	ADP
ejpam-856	8	2	functions	function	NOUN
ejpam-856	8	3	f	f	X
ejpam-856	8	4	j	j	PROPN
ejpam-856	8	5	∈ap	∈ap	PROPN
ejpam-856	8	6	given	give	VERB
ejpam-856	8	7	by	by	ADP
ejpam-856	8	8	f	f	PROPN
ejpam-856	8	9	j(z	j(z	PROPN
ejpam-856	8	10	)	)	PUNCT
ejpam-856	9	1	=	=	PUNCT
ejpam-856	9	2	zp	zp	NOUN
ejpam-856	10	1	+	+	CCONJ
ejpam-856	10	2	∞	∞	NUM
ejpam-856	10	3	∑	∑	PUNCT
ejpam-856	10	4	n=1	n=1	PROPN
ejpam-856	10	5	an	an	PROPN
ejpam-856	10	6	,	,	PUNCT
ejpam-856	10	7	jz	jz	PROPN
ejpam-856	10	8	p+n	p+n	PROPN
ejpam-856	10	9	,	,	PUNCT
ejpam-856	10	10	(	(	PUNCT
ejpam-856	10	11	j	j	PROPN
ejpam-856	10	12	=	=	SYM
ejpam-856	10	13	1,2	1,2	NUM
ejpam-856	10	14	;	;	PUNCT
ejpam-856	10	15	p	p	PROPN
ejpam-856	10	16	∈	∈	PROPN
ejpam-856	10	17	n	n	CCONJ
ejpam-856	10	18	)	)	PUNCT
ejpam-856	10	19	,	,	PUNCT
ejpam-856	10	20	(	(	PUNCT
ejpam-856	10	21	2	2	X
ejpam-856	10	22	)	)	PUNCT
ejpam-856	10	23	∗corresponding	∗corresponde	VERB
ejpam-856	10	24	author	author	NOUN
ejpam-856	10	25	.	.	PUNCT
ejpam-856	11	1	email	email	NOUN
ejpam-856	11	2	addresses	address	NOUN
ejpam-856	11	3	:	:	PUNCT
ejpam-856	11	4	pam	pam	PROPN
ejpam-856	11	5	9439	9439	NUM
ejpam-856	11	6	�	�	PROPN
ejpam-856	11	7	yahoo	yahoo	PROPN
ejpam-856	11	8	.	.	PUNCT
ejpam-856	12	1	o.in	o.in	PROPN
ejpam-856	12	2	(	(	PUNCT
ejpam-856	12	3	c.	c.	PROPN
ejpam-856	12	4	selvaraj	selvaraj	PROPN
ejpam-856	12	5	)	)	PUNCT
ejpam-856	12	6	,	,	PUNCT
ejpam-856	12	7	selvaa1826	selvaa1826	PROPN
ejpam-856	12	8	�	�	PROPN
ejpam-856	12	9	gmail	gmail	NOUN
ejpam-856	12	10	.	.	PUNCT
ejpam-856	13	1	om	om	PROPN
ejpam-856	13	2	(	(	PUNCT
ejpam-856	13	3	k.	k.	PROPN
ejpam-856	13	4	selvakumaran	selvakumaran	PROPN
ejpam-856	13	5	)	)	PUNCT
ejpam-856	13	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-856	13	7	1048	1048	NUM
ejpam-856	13	8	c	c	X
ejpam-856	13	9	©	©	PROPN
ejpam-856	13	10	2010	2010	NUM
ejpam-856	13	11	ejpam	ejpam	NOUN
ejpam-856	13	12	all	all	DET
ejpam-856	13	13	rights	right	NOUN
ejpam-856	13	14	reserved	reserve	VERB
ejpam-856	13	15	.	.	PUNCT
ejpam-856	14	1	c.	c.	PROPN
ejpam-856	14	2	selvaraj	selvaraj	PROPN
ejpam-856	14	3	,	,	PUNCT
ejpam-856	14	4	k.	k.	PROPN
ejpam-856	14	5	selvakumaran	selvakumaran	PROPN
ejpam-856	14	6	/	/	SYM
ejpam-856	14	7	eur	eur	PROPN
ejpam-856	14	8	.	.	PUNCT
ejpam-856	15	1	j.	j.	PROPN
ejpam-856	15	2	pure	pure	PROPN
ejpam-856	15	3	appl	appl	PROPN
ejpam-856	15	4	.	.	PROPN
ejpam-856	15	5	math	math	PROPN
ejpam-856	15	6	,	,	PUNCT
ejpam-856	15	7	3	3	NUM
ejpam-856	15	8	(	(	PUNCT
ejpam-856	15	9	2010	2010	NUM
ejpam-856	15	10	)	)	PUNCT
ejpam-856	15	11	,	,	PUNCT
ejpam-856	15	12	1048	1048	NUM
ejpam-856	15	13	-	-	SYM
ejpam-856	15	14	1054	1054	NUM
ejpam-856	15	15	1049	1049	NUM
ejpam-856	15	16	we	we	PRON
ejpam-856	15	17	define	define	VERB
ejpam-856	15	18	the	the	DET
ejpam-856	15	19	hadamard	hadamard	ADJ
ejpam-856	15	20	product	product	NOUN
ejpam-856	15	21	(	(	PUNCT
ejpam-856	15	22	or	or	CCONJ
ejpam-856	15	23	convolution	convolution	NOUN
ejpam-856	15	24	)	)	PUNCT
ejpam-856	15	25	of	of	ADP
ejpam-856	15	26	f1	f1	NOUN
ejpam-856	15	27	and	and	CCONJ
ejpam-856	15	28	f2	f2	PRON
ejpam-856	15	29	by	by	ADP
ejpam-856	15	30	(	(	PUNCT
ejpam-856	15	31	f1	f1	PROPN
ejpam-856	15	32	∗	∗	NOUN
ejpam-856	15	33	f2)(z	f2)(z	PROPN
ejpam-856	15	34	)	)	PUNCT
ejpam-856	15	35	=	=	SYM
ejpam-856	16	1	zp	zp	NOUN
ejpam-856	16	2	+	+	CCONJ
ejpam-856	16	3	∞	∞	NUM
ejpam-856	16	4	∑	∑	PUNCT
ejpam-856	16	5	n=1	n=1	PROPN
ejpam-856	16	6	an,1an,2zp+n	an,1an,2zp+n	VERB
ejpam-856	16	7	=	=	PUNCT
ejpam-856	16	8	(	(	PUNCT
ejpam-856	16	9	f2	f2	PROPN
ejpam-856	16	10	∗	∗	NOUN
ejpam-856	16	11	f1)(z	f1)(z	NOUN
ejpam-856	16	12	)	)	PUNCT
ejpam-856	16	13	.	.	PUNCT
ejpam-856	17	1	let	let	VERB
ejpam-856	17	2	f	f	PROPN
ejpam-856	17	3	(	(	PUNCT
ejpam-856	17	4	z	z	NOUN
ejpam-856	17	5	)	)	PUNCT
ejpam-856	17	6	and	and	CCONJ
ejpam-856	17	7	g(z	g(z	PROPN
ejpam-856	17	8	)	)	PUNCT
ejpam-856	17	9	be	be	AUX
ejpam-856	17	10	analytic	analytic	ADJ
ejpam-856	17	11	in	in	ADP
ejpam-856	17	12	u	u	PROPN
ejpam-856	17	13	.	.	PUNCT
ejpam-856	18	1	then	then	ADV
ejpam-856	18	2	we	we	PRON
ejpam-856	18	3	say	say	VERB
ejpam-856	18	4	that	that	SCONJ
ejpam-856	18	5	the	the	DET
ejpam-856	18	6	function	function	NOUN
ejpam-856	18	7	f	f	X
ejpam-856	18	8	(	(	PUNCT
ejpam-856	18	9	z	z	NOUN
ejpam-856	18	10	)	)	PUNCT
ejpam-856	18	11	is	be	AUX
ejpam-856	18	12	subordinate	subordinate	ADJ
ejpam-856	18	13	to	to	ADP
ejpam-856	18	14	g(z	g(z	PROPN
ejpam-856	18	15	)	)	PUNCT
ejpam-856	18	16	in	in	ADP
ejpam-856	18	17	u	u	NOUN
ejpam-856	18	18	,	,	PUNCT
ejpam-856	18	19	if	if	SCONJ
ejpam-856	18	20	there	there	PRON
ejpam-856	18	21	exists	exist	VERB
ejpam-856	18	22	an	an	DET
ejpam-856	18	23	analytic	analytic	ADJ
ejpam-856	18	24	function	function	NOUN
ejpam-856	18	25	w(z	w(z	NOUN
ejpam-856	18	26	)	)	PUNCT
ejpam-856	18	27	in	in	ADP
ejpam-856	18	28	u	u	NOUN
ejpam-856	18	29	with	with	ADP
ejpam-856	18	30	w(0	w(0	PROPN
ejpam-856	18	31	)	)	PUNCT
ejpam-856	18	32	=	=	SYM
ejpam-856	18	33	0	0	NUM
ejpam-856	18	34	,	,	PUNCT
ejpam-856	18	35	|w(z)|	|w(z)|	VERB
ejpam-856	18	36	<	<	X
ejpam-856	18	37	1	1	NUM
ejpam-856	18	38	(	(	PUNCT
ejpam-856	18	39	z	z	NOUN
ejpam-856	18	40	∈	∈	PROPN
ejpam-856	18	41	u	u	PROPN
ejpam-856	18	42	)	)	PUNCT
ejpam-856	18	43	,	,	PUNCT
ejpam-856	18	44	such	such	ADJ
ejpam-856	18	45	that	that	SCONJ
ejpam-856	18	46	f	f	PROPN
ejpam-856	18	47	(	(	PUNCT
ejpam-856	18	48	z	z	NOUN
ejpam-856	18	49	)	)	PUNCT
ejpam-856	18	50	=	=	PUNCT
ejpam-856	18	51	g(w(z	g(w(z	PROPN
ejpam-856	18	52	)	)	PUNCT
ejpam-856	18	53	)	)	PUNCT
ejpam-856	19	1	(	(	PUNCT
ejpam-856	19	2	z	z	NOUN
ejpam-856	19	3	∈	∈	PROPN
ejpam-856	19	4	u	u	NOUN
ejpam-856	19	5	)	)	PUNCT
ejpam-856	19	6	.	.	PUNCT
ejpam-856	20	1	we	we	PRON
ejpam-856	20	2	denote	denote	VERB
ejpam-856	20	3	this	this	DET
ejpam-856	20	4	subordination	subordination	NOUN
ejpam-856	20	5	by	by	ADP
ejpam-856	20	6	f	f	PROPN
ejpam-856	20	7	(	(	PUNCT
ejpam-856	20	8	z	z	NOUN
ejpam-856	20	9	)	)	PUNCT
ejpam-856	20	10	≺	≺	NOUN
ejpam-856	20	11	g(z	g(z	PROPN
ejpam-856	20	12	)	)	PUNCT
ejpam-856	20	13	.	.	PUNCT
ejpam-856	21	1	furthermore	furthermore	ADV
ejpam-856	21	2	,	,	PUNCT
ejpam-856	21	3	if	if	SCONJ
ejpam-856	21	4	the	the	DET
ejpam-856	21	5	function	function	NOUN
ejpam-856	21	6	g(z	g(z	PROPN
ejpam-856	21	7	)	)	PUNCT
ejpam-856	21	8	is	be	AUX
ejpam-856	21	9	univalent	univalent	ADJ
ejpam-856	21	10	in	in	ADP
ejpam-856	21	11	u	u	PROPN
ejpam-856	21	12	,	,	PUNCT
ejpam-856	21	13	then	then	ADV
ejpam-856	21	14	f	f	X
ejpam-856	21	15	(	(	PUNCT
ejpam-856	21	16	z)≺	z)≺	PROPN
ejpam-856	21	17	g(z	g(z	PROPN
ejpam-856	21	18	)	)	PUNCT
ejpam-856	21	19	(	(	PUNCT
ejpam-856	21	20	z	z	NOUN
ejpam-856	21	21	∈	∈	PROPN
ejpam-856	21	22	u	u	NOUN
ejpam-856	21	23	)	)	PUNCT
ejpam-856	21	24	⇐	⇐	ADJ
ejpam-856	21	25	⇒	⇒	PROPN
ejpam-856	21	26	f	f	X
ejpam-856	21	27	(	(	PUNCT
ejpam-856	21	28	0	0	NUM
ejpam-856	21	29	)	)	PUNCT
ejpam-856	21	30	=	=	SYM
ejpam-856	21	31	g(0	g(0	PROPN
ejpam-856	21	32	)	)	PUNCT
ejpam-856	21	33	and	and	CCONJ
ejpam-856	21	34	f	f	PROPN
ejpam-856	21	35	(	(	PUNCT
ejpam-856	21	36	u	u	NOUN
ejpam-856	21	37	)	)	PUNCT
ejpam-856	21	38	⊂	⊂	PROPN
ejpam-856	21	39	g(u	g(u	PROPN
ejpam-856	21	40	)	)	PUNCT
ejpam-856	21	41	.	.	PUNCT
ejpam-856	22	1	suppose	suppose	VERB
ejpam-856	22	2	that	that	SCONJ
ejpam-856	22	3	the	the	DET
ejpam-856	22	4	functions	function	NOUN
ejpam-856	22	5	f	f	X
ejpam-856	22	6	(	(	PUNCT
ejpam-856	22	7	z	z	NOUN
ejpam-856	22	8	)	)	PUNCT
ejpam-856	22	9	and	and	CCONJ
ejpam-856	22	10	g(z	g(z	PROPN
ejpam-856	22	11	)	)	PUNCT
ejpam-856	22	12	are	be	AUX
ejpam-856	22	13	analytic	analytic	ADJ
ejpam-856	22	14	in	in	ADP
ejpam-856	22	15	the	the	DET
ejpam-856	22	16	open	open	ADJ
ejpam-856	22	17	unit	unit	NOUN
ejpam-856	22	18	disk	disk	NOUN
ejpam-856	22	19	u	u	PROPN
ejpam-856	22	20	.	.	PUNCT
ejpam-856	23	1	then	then	ADV
ejpam-856	23	2	we	we	PRON
ejpam-856	23	3	say	say	VERB
ejpam-856	23	4	that	that	SCONJ
ejpam-856	23	5	the	the	DET
ejpam-856	23	6	function	function	NOUN
ejpam-856	23	7	f	f	X
ejpam-856	23	8	(	(	PUNCT
ejpam-856	23	9	z	z	NOUN
ejpam-856	23	10	)	)	PUNCT
ejpam-856	23	11	is	be	AUX
ejpam-856	23	12	majorized	majorize	VERB
ejpam-856	23	13	by	by	ADP
ejpam-856	23	14	g(z	g(z	PROPN
ejpam-856	23	15	)	)	PUNCT
ejpam-856	23	16	in	in	ADP
ejpam-856	23	17	u	u	NOUN
ejpam-856	23	18	(	(	PUNCT
ejpam-856	23	19	see	see	VERB
ejpam-856	23	20	[	[	X
ejpam-856	23	21	5	5	NUM
ejpam-856	23	22	]	]	PUNCT
ejpam-856	23	23	)	)	PUNCT
ejpam-856	23	24	and	and	CCONJ
ejpam-856	23	25	write	write	VERB
ejpam-856	23	26	f	f	PROPN
ejpam-856	23	27	(	(	PUNCT
ejpam-856	23	28	z)≪	z)≪	NOUN
ejpam-856	23	29	g(z	g(z	ADJ
ejpam-856	23	30	)	)	PUNCT
ejpam-856	23	31	(	(	PUNCT
ejpam-856	23	32	z	z	NOUN
ejpam-856	23	33	∈	∈	PROPN
ejpam-856	23	34	u	u	NOUN
ejpam-856	23	35	)	)	PUNCT
ejpam-856	23	36	,	,	PUNCT
ejpam-856	23	37	(	(	PUNCT
ejpam-856	23	38	3	3	X
ejpam-856	23	39	)	)	PUNCT
ejpam-856	23	40	if	if	SCONJ
ejpam-856	23	41	there	there	PRON
ejpam-856	23	42	exists	exist	VERB
ejpam-856	23	43	a	a	DET
ejpam-856	23	44	function	function	NOUN
ejpam-856	23	45	ϕ(z	ϕ(z	NOUN
ejpam-856	23	46	)	)	PUNCT
ejpam-856	23	47	,	,	PUNCT
ejpam-856	23	48	analytic	analytic	NOUN
ejpam-856	23	49	in	in	ADP
ejpam-856	23	50	u	u	PROPN
ejpam-856	23	51	,	,	PUNCT
ejpam-856	23	52	such	such	ADJ
ejpam-856	23	53	that	that	SCONJ
ejpam-856	23	54	|ϕ(z)|	|ϕ(z)|	ADJ
ejpam-856	23	55	≤	≤	NOUN
ejpam-856	23	56	1	1	NUM
ejpam-856	23	57	and	and	CCONJ
ejpam-856	23	58	f	f	PROPN
ejpam-856	23	59	(	(	PUNCT
ejpam-856	23	60	z	z	NOUN
ejpam-856	23	61	)	)	PUNCT
ejpam-856	23	62	=	=	SYM
ejpam-856	23	63	ϕ(z)g(z	ϕ(z)g(z	NOUN
ejpam-856	23	64	)	)	PUNCT
ejpam-856	23	65	(	(	PUNCT
ejpam-856	23	66	z	z	NOUN
ejpam-856	23	67	∈	∈	PROPN
ejpam-856	23	68	u	u	PROPN
ejpam-856	23	69	)	)	PUNCT
ejpam-856	23	70	.	.	PUNCT
ejpam-856	24	1	the	the	DET
ejpam-856	24	2	majorization	majorization	NOUN
ejpam-856	24	3	(	(	PUNCT
ejpam-856	24	4	3	3	X
ejpam-856	24	5	)	)	PUNCT
ejpam-856	24	6	is	be	AUX
ejpam-856	24	7	closely	closely	ADV
ejpam-856	24	8	related	relate	VERB
ejpam-856	24	9	to	to	ADP
ejpam-856	24	10	the	the	DET
ejpam-856	24	11	concept	concept	NOUN
ejpam-856	24	12	of	of	ADP
ejpam-856	24	13	quasi	quasi	NOUN
ejpam-856	24	14	-	-	NOUN
ejpam-856	24	15	subordination	subordination	NOUN
ejpam-856	24	16	between	between	ADP
ejpam-856	24	17	analytic	analytic	ADJ
ejpam-856	24	18	functions	function	NOUN
ejpam-856	24	19	in	in	ADP
ejpam-856	24	20	u	u	PROPN
ejpam-856	24	21	.	.	PUNCT
ejpam-856	25	1	let	let	VERB
ejpam-856	25	2	α1,α2	α1,α2	PROPN
ejpam-856	25	3	,	,	PUNCT
ejpam-856	25	4	.	.	PUNCT
ejpam-856	25	5	.	.	PUNCT
ejpam-856	26	1	.	.	PUNCT
ejpam-856	27	1	,	,	PUNCT
ejpam-856	27	2	αq	αq	INTJ
ejpam-856	27	3	and	and	CCONJ
ejpam-856	27	4	β1,β2	β1,β2	PROPN
ejpam-856	27	5	,	,	PUNCT
ejpam-856	27	6	.	.	PUNCT
ejpam-856	27	7	.	.	PUNCT
ejpam-856	28	1	.	.	PUNCT
ejpam-856	29	1	,	,	PUNCT
ejpam-856	29	2	βs	βs	X
ejpam-856	29	3	(	(	PUNCT
ejpam-856	29	4	q	q	NOUN
ejpam-856	29	5	,	,	PUNCT
ejpam-856	29	6	s	s	AUX
ejpam-856	29	7	∈	∈	PROPN
ejpam-856	29	8	n	n	NOUN
ejpam-856	29	9	∪	∪	X
ejpam-856	29	10	{	{	PUNCT
ejpam-856	29	11	0},q	0},q	PROPN
ejpam-856	29	12	≤	≤	PROPN
ejpam-856	29	13	s	s	PART
ejpam-856	29	14	+	+	NOUN
ejpam-856	29	15	1	1	NUM
ejpam-856	29	16	)	)	PUNCT
ejpam-856	29	17	be	be	AUX
ejpam-856	29	18	complex	complex	ADJ
ejpam-856	29	19	numbers	number	NOUN
ejpam-856	29	20	such	such	ADJ
ejpam-856	29	21	that	that	DET
ejpam-856	29	22	βl	βl	PROPN
ejpam-856	29	23	6=	6=	ADP
ejpam-856	29	24	0,−1,−2	0,−1,−2	NUM
ejpam-856	29	25	,	,	PUNCT
ejpam-856	29	26	.	.	PUNCT
ejpam-856	29	27	.	.	PUNCT
ejpam-856	29	28	.	.	PUNCT
ejpam-856	30	1	for	for	ADP
ejpam-856	30	2	l	l	PROPN
ejpam-856	30	3	∈	∈	PROPN
ejpam-856	30	4	{	{	PUNCT
ejpam-856	30	5	1,2	1,2	NUM
ejpam-856	30	6	,	,	PUNCT
ejpam-856	30	7	.	.	PUNCT
ejpam-856	30	8	.	.	PUNCT
ejpam-856	30	9	.	.	PUNCT
ejpam-856	31	1	,	,	PUNCT
ejpam-856	31	2	s	s	X
ejpam-856	31	3	}	}	PUNCT
ejpam-856	31	4	.	.	PUNCT
ejpam-856	32	1	the	the	DET
ejpam-856	32	2	generalized	generalized	ADJ
ejpam-856	32	3	hypergeometric	hypergeometric	ADJ
ejpam-856	32	4	function	function	NOUN
ejpam-856	32	5	qfs	qfs	NOUN
ejpam-856	32	6	is	be	AUX
ejpam-856	32	7	given	give	VERB
ejpam-856	32	8	by	by	ADP
ejpam-856	32	9	qfs(α1,α2	qfs(α1,α2	PROPN
ejpam-856	32	10	,	,	PUNCT
ejpam-856	32	11	.	.	PUNCT
ejpam-856	32	12	.	.	PUNCT
ejpam-856	32	13	.	.	PUNCT
ejpam-856	33	1	,	,	PUNCT
ejpam-856	33	2	αq;β1,β2	αq;β1,β2	NOUN
ejpam-856	33	3	,	,	PUNCT
ejpam-856	33	4	.	.	PUNCT
ejpam-856	33	5	.	.	PUNCT
ejpam-856	33	6	.	.	PUNCT
ejpam-856	34	1	,	,	PUNCT
ejpam-856	34	2	βs	βs	CCONJ
ejpam-856	34	3	;	;	PUNCT
ejpam-856	34	4	z	z	X
ejpam-856	34	5	)	)	PUNCT
ejpam-856	35	1	=	=	SYM
ejpam-856	35	2	∞	∞	PROPN
ejpam-856	35	3	∑	∑	PROPN
ejpam-856	35	4	n=0	n=0	NUM
ejpam-856	35	5	(	(	PUNCT
ejpam-856	35	6	α1)n(α2)n	α1)n(α2)n	NUM
ejpam-856	35	7	.	.	PUNCT
ejpam-856	35	8	.	.	PUNCT
ejpam-856	35	9	.	.	PUNCT
ejpam-856	36	1	(	(	PUNCT
ejpam-856	36	2	αq)n	αq)n	NOUN
ejpam-856	36	3	(	(	PUNCT
ejpam-856	36	4	β1)n(β2)n	β1)n(β2)n	PROPN
ejpam-856	36	5	.	.	PUNCT
ejpam-856	36	6	.	.	PUNCT
ejpam-856	36	7	.	.	PUNCT
ejpam-856	37	1	(	(	PUNCT
ejpam-856	37	2	βs)n	βs)n	NOUN
ejpam-856	37	3	zn	zn	NUM
ejpam-856	37	4	n	n	CCONJ
ejpam-856	37	5	!	!	PROPN
ejpam-856	37	6	,	,	PUNCT
ejpam-856	37	7	(	(	PUNCT
ejpam-856	37	8	z	z	NOUN
ejpam-856	37	9	∈	∈	PROPN
ejpam-856	37	10	u	u	PROPN
ejpam-856	37	11	)	)	PUNCT
ejpam-856	37	12	,	,	PUNCT
ejpam-856	37	13	where	where	SCONJ
ejpam-856	37	14	(	(	PUNCT
ejpam-856	37	15	x)n	x)n	PUNCT
ejpam-856	37	16	denotes	denote	VERB
ejpam-856	37	17	the	the	DET
ejpam-856	37	18	pochhammer	pochhammer	NOUN
ejpam-856	37	19	symbol	symbol	NOUN
ejpam-856	37	20	defined	define	VERB
ejpam-856	37	21	by	by	ADP
ejpam-856	37	22	(	(	PUNCT
ejpam-856	37	23	x)n	x)n	PUNCT
ejpam-856	37	24	=	=	SYM
ejpam-856	37	25	x(x	x(x	PROPN
ejpam-856	38	1	+	+	CCONJ
ejpam-856	38	2	1)(x	1)(x	NUM
ejpam-856	38	3	+	+	CCONJ
ejpam-856	38	4	2	2	NUM
ejpam-856	38	5	)	)	PUNCT
ejpam-856	38	6	·	·	PUNCT
ejpam-856	38	7	·	·	PUNCT
ejpam-856	38	8	·	·	PUNCT
ejpam-856	38	9	(	(	PUNCT
ejpam-856	38	10	x	x	X
ejpam-856	38	11	+	+	PUNCT
ejpam-856	38	12	n−	n−	NOUN
ejpam-856	38	13	1	1	NUM
ejpam-856	38	14	)	)	PUNCT
ejpam-856	38	15	for	for	ADP
ejpam-856	38	16	n	n	PRON
ejpam-856	38	17	∈	∈	PROPN
ejpam-856	38	18	n	n	NOUN
ejpam-856	38	19	and	and	CCONJ
ejpam-856	38	20	(	(	PUNCT
ejpam-856	38	21	x)0	x)0	X
ejpam-856	38	22	=	=	SYM
ejpam-856	38	23	1	1	X
ejpam-856	38	24	.	.	X
ejpam-856	38	25	corresponding	correspond	VERB
ejpam-856	38	26	to	to	ADP
ejpam-856	38	27	a	a	DET
ejpam-856	38	28	function	function	NOUN
ejpam-856	38	29	g	g	PROPN
ejpam-856	38	30	p	p	PROPN
ejpam-856	38	31	q	q	PROPN
ejpam-856	38	32	,	,	PUNCT
ejpam-856	38	33	s(α1;β1	s(α1;β1	NOUN
ejpam-856	38	34	;	;	PUNCT
ejpam-856	38	35	z	z	X
ejpam-856	38	36	)	)	PUNCT
ejpam-856	38	37	defined	define	VERB
ejpam-856	38	38	by	by	ADP
ejpam-856	38	39	gq	gq	PROPN
ejpam-856	38	40	,	,	PUNCT
ejpam-856	38	41	s(α1,β1	s(α1,β1	PROPN
ejpam-856	38	42	;	;	PUNCT
ejpam-856	38	43	z	z	X
ejpam-856	38	44	)	)	PUNCT
ejpam-856	38	45	:	:	PUNCT
ejpam-856	38	46	=	=	PUNCT
ejpam-856	38	47	zp	zp	PROPN
ejpam-856	38	48	qfs(α1,α2	qfs(α1,α2	PROPN
ejpam-856	38	49	,	,	PUNCT
ejpam-856	38	50	.	.	PUNCT
ejpam-856	38	51	.	.	PUNCT
ejpam-856	38	52	.	.	PUNCT
ejpam-856	39	1	,	,	PUNCT
ejpam-856	39	2	αq;β1,β2	αq;β1,β2	NOUN
ejpam-856	39	3	,	,	PUNCT
ejpam-856	39	4	.	.	PUNCT
ejpam-856	39	5	.	.	PUNCT
ejpam-856	39	6	.	.	PUNCT
ejpam-856	40	1	,	,	PUNCT
ejpam-856	40	2	βs	βs	CCONJ
ejpam-856	40	3	;	;	PUNCT
ejpam-856	41	1	z	z	X
ejpam-856	41	2	)	)	PUNCT
ejpam-856	41	3	,	,	PUNCT
ejpam-856	41	4	(	(	PUNCT
ejpam-856	41	5	4	4	X
ejpam-856	41	6	)	)	PUNCT
ejpam-856	41	7	c.selvaraj	c.selvaraj	VERB
ejpam-856	41	8	and	and	CCONJ
ejpam-856	41	9	k.r.karthikeyan	k.r.karthikeyan	VERB
ejpam-856	41	10	recently	recently	ADV
ejpam-856	41	11	defined	define	VERB
ejpam-856	41	12	the	the	DET
ejpam-856	41	13	following	follow	VERB
ejpam-856	41	14	generalized	generalized	ADJ
ejpam-856	41	15	differential	differential	NOUN
ejpam-856	41	16	operator	operator	NOUN
ejpam-856	41	17	d	d	PROPN
ejpam-856	41	18	p	p	PROPN
ejpam-856	41	19	,	,	PUNCT
ejpam-856	41	20	m	m	VERB
ejpam-856	41	21	λ	λ	X
ejpam-856	41	22	(	(	PUNCT
ejpam-856	41	23	α1,β1	α1,β1	PROPN
ejpam-856	41	24	)	)	PUNCT
ejpam-856	41	25	f	f	NOUN
ejpam-856	42	1	:	:	PUNCT
ejpam-856	42	2	ap	ap	PROPN
ejpam-856	43	1	−→ap	−→ap	NOUN
ejpam-856	43	2	by	by	ADP
ejpam-856	43	3	d	d	PROPN
ejpam-856	43	4	p,0	p,0	PROPN
ejpam-856	43	5	λ	λ	X
ejpam-856	43	6	(	(	PUNCT
ejpam-856	43	7	α1,β1	α1,β1	PROPN
ejpam-856	43	8	)	)	PUNCT
ejpam-856	43	9	f	f	NOUN
ejpam-856	43	10	(	(	PUNCT
ejpam-856	43	11	z	z	NOUN
ejpam-856	43	12	)	)	PUNCT
ejpam-856	43	13	=	=	SYM
ejpam-856	44	1	f	f	X
ejpam-856	44	2	(	(	PUNCT
ejpam-856	44	3	z	z	NOUN
ejpam-856	44	4	)	)	PUNCT
ejpam-856	44	5	∗	∗	NOUN
ejpam-856	44	6	g	g	PROPN
ejpam-856	44	7	p	p	PROPN
ejpam-856	44	8	q	q	PROPN
ejpam-856	44	9	,	,	PUNCT
ejpam-856	44	10	s(α1,β1	s(α1,β1	ADJ
ejpam-856	44	11	;	;	PUNCT
ejpam-856	44	12	z	z	X
ejpam-856	44	13	)	)	PUNCT
ejpam-856	44	14	,	,	PUNCT
ejpam-856	44	15	d	d	PROPN
ejpam-856	44	16	p,1	p,1	VERB
ejpam-856	44	17	λ	λ	PROPN
ejpam-856	44	18	(	(	PUNCT
ejpam-856	44	19	α1,β1	α1,β1	PROPN
ejpam-856	44	20	)	)	PUNCT
ejpam-856	44	21	f	f	NOUN
ejpam-856	44	22	(	(	PUNCT
ejpam-856	44	23	z	z	NOUN
ejpam-856	44	24	)	)	PUNCT
ejpam-856	44	25	=	=	SYM
ejpam-856	44	26	(	(	PUNCT
ejpam-856	44	27	1−λ	1−λ	NUM
ejpam-856	44	28	)	)	PUNCT
ejpam-856	44	29	(	(	PUNCT
ejpam-856	44	30	f	f	X
ejpam-856	44	31	(	(	PUNCT
ejpam-856	44	32	z	z	NOUN
ejpam-856	44	33	)	)	PUNCT
ejpam-856	44	34	∗	∗	NOUN
ejpam-856	44	35	g	g	PROPN
ejpam-856	44	36	p	p	PROPN
ejpam-856	44	37	q	q	PROPN
ejpam-856	44	38	,	,	PUNCT
ejpam-856	44	39	s(α1,β1	s(α1,β1	ADJ
ejpam-856	44	40	;	;	PUNCT
ejpam-856	44	41	z	z	NOUN
ejpam-856	44	42	)	)	PUNCT
ejpam-856	44	43	)	)	PUNCT
ejpam-856	45	1	+	+	CCONJ
ejpam-856	45	2	λ	λ	X
ejpam-856	45	3	p	p	X
ejpam-856	45	4	z	z	PROPN
ejpam-856	45	5	(	(	PUNCT
ejpam-856	45	6	f	f	PROPN
ejpam-856	45	7	(	(	PUNCT
ejpam-856	45	8	z	z	NOUN
ejpam-856	45	9	)	)	PUNCT
ejpam-856	45	10	∗	∗	NOUN
ejpam-856	45	11	g	g	PROPN
ejpam-856	45	12	p	p	PROPN
ejpam-856	45	13	q	q	PROPN
ejpam-856	45	14	,	,	PUNCT
ejpam-856	45	15	s(α1,β1	s(α1,β1	ADJ
ejpam-856	45	16	;	;	PUNCT
ejpam-856	45	17	z))′	z))′	X
ejpam-856	45	18	,	,	PUNCT
ejpam-856	45	19	d	d	PROPN
ejpam-856	45	20	p	p	X
ejpam-856	45	21	,	,	PUNCT
ejpam-856	45	22	m	m	VERB
ejpam-856	45	23	λ	λ	X
ejpam-856	45	24	(	(	PUNCT
ejpam-856	45	25	α1,β1	α1,β1	PROPN
ejpam-856	45	26	)	)	PUNCT
ejpam-856	45	27	f	f	NOUN
ejpam-856	45	28	(	(	PUNCT
ejpam-856	45	29	z	z	NOUN
ejpam-856	45	30	)	)	PUNCT
ejpam-856	45	31	=	=	SYM
ejpam-856	46	1	d	d	NOUN
ejpam-856	46	2	p,1	p,1	NOUN
ejpam-856	46	3	λ	λ	X
ejpam-856	46	4	(	(	PUNCT
ejpam-856	46	5	d	d	X
ejpam-856	46	6	p	p	X
ejpam-856	46	7	,	,	PUNCT
ejpam-856	46	8	m−1	m−1	PROPN
ejpam-856	46	9	λ	λ	PROPN
ejpam-856	46	10	(	(	PUNCT
ejpam-856	46	11	α1,β1	α1,β1	PROPN
ejpam-856	46	12	)	)	PUNCT
ejpam-856	46	13	f	f	NOUN
ejpam-856	46	14	(	(	PUNCT
ejpam-856	46	15	z	z	NOUN
ejpam-856	46	16	)	)	PUNCT
ejpam-856	46	17	)	)	PUNCT
ejpam-856	46	18	,	,	PUNCT
ejpam-856	46	19	(	(	PUNCT
ejpam-856	46	20	5	5	X
ejpam-856	46	21	)	)	PUNCT
ejpam-856	46	22	c.	c.	NOUN
ejpam-856	46	23	selvaraj	selvaraj	PROPN
ejpam-856	46	24	,	,	PUNCT
ejpam-856	46	25	k.	k.	PROPN
ejpam-856	46	26	selvakumaran	selvakumaran	PROPN
ejpam-856	46	27	/	/	SYM
ejpam-856	46	28	eur	eur	PROPN
ejpam-856	46	29	.	.	PUNCT
ejpam-856	47	1	j.	j.	PROPN
ejpam-856	47	2	pure	pure	PROPN
ejpam-856	47	3	appl	appl	PROPN
ejpam-856	47	4	.	.	PROPN
ejpam-856	47	5	math	math	PROPN
ejpam-856	47	6	,	,	PUNCT
ejpam-856	47	7	3	3	NUM
ejpam-856	47	8	(	(	PUNCT
ejpam-856	47	9	2010	2010	NUM
ejpam-856	47	10	)	)	PUNCT
ejpam-856	47	11	,	,	PUNCT
ejpam-856	47	12	1048	1048	NUM
ejpam-856	47	13	-	-	SYM
ejpam-856	47	14	1054	1054	NUM
ejpam-856	47	15	1050	1050	NUM
ejpam-856	47	16	where	where	SCONJ
ejpam-856	47	17	m	m	PROPN
ejpam-856	47	18	∈	∈	PROPN
ejpam-856	47	19	n0	n0	PROPN
ejpam-856	47	20	=	=	SYM
ejpam-856	47	21	n∪	n∪	PROPN
ejpam-856	47	22	{	{	PUNCT
ejpam-856	47	23	0	0	NUM
ejpam-856	47	24	}	}	PUNCT
ejpam-856	47	25	and	and	CCONJ
ejpam-856	47	26	λ≥	λ≥	ADP
ejpam-856	47	27	0	0	NUM
ejpam-856	47	28	.	.	PUNCT
ejpam-856	48	1	if	if	SCONJ
ejpam-856	48	2	f	f	PROPN
ejpam-856	48	3	(	(	PUNCT
ejpam-856	48	4	z	z	NOUN
ejpam-856	48	5	)	)	PUNCT
ejpam-856	48	6	∈ap	∈ap	PROPN
ejpam-856	48	7	,	,	PUNCT
ejpam-856	48	8	then	then	ADV
ejpam-856	48	9	we	we	PRON
ejpam-856	48	10	have	have	VERB
ejpam-856	48	11	d	d	PROPN
ejpam-856	48	12	p	p	PROPN
ejpam-856	48	13	,	,	PUNCT
ejpam-856	48	14	m	m	VERB
ejpam-856	48	15	λ	λ	X
ejpam-856	48	16	(	(	PUNCT
ejpam-856	48	17	α1,β1	α1,β1	PROPN
ejpam-856	48	18	)	)	PUNCT
ejpam-856	48	19	f	f	NOUN
ejpam-856	48	20	(	(	PUNCT
ejpam-856	48	21	z	z	NOUN
ejpam-856	48	22	)	)	PUNCT
ejpam-856	48	23	=	=	SYM
ejpam-856	49	1	zp	zp	PROPN
ejpam-856	50	1	+	+	CCONJ
ejpam-856	50	2	∞	∞	NUM
ejpam-856	50	3	∑	∑	SYM
ejpam-856	50	4	n=1	n=1	PROPN
ejpam-856	50	5	�	�	PROPN
ejpam-856	50	6	p+λn	p+λn	PROPN
ejpam-856	50	7	p	p	PROPN
ejpam-856	50	8	�	�	PROPN
ejpam-856	50	9	m	m	PROPN
ejpam-856	50	10	(	(	PUNCT
ejpam-856	50	11	α1)n(α2)n	α1)n(α2)n	NUM
ejpam-856	50	12	.	.	PUNCT
ejpam-856	50	13	.	.	PUNCT
ejpam-856	50	14	.	.	PUNCT
ejpam-856	51	1	(	(	PUNCT
ejpam-856	51	2	αq)n	αq)n	NOUN
ejpam-856	51	3	(	(	PUNCT
ejpam-856	51	4	β1)n(β2)n	β1)n(β2)n	PROPN
ejpam-856	51	5	.	.	PUNCT
ejpam-856	51	6	.	.	PUNCT
ejpam-856	51	7	.	.	PUNCT
ejpam-856	52	1	(	(	PUNCT
ejpam-856	52	2	βs)n	βs)n	ADV
ejpam-856	52	3	an	an	DET
ejpam-856	52	4	zp+n	zp+n	NOUN
ejpam-856	52	5	n	n	CCONJ
ejpam-856	52	6	!	!	PUNCT
ejpam-856	52	7	.	.	PUNCT
ejpam-856	53	1	(	(	PUNCT
ejpam-856	53	2	6	6	X
ejpam-856	53	3	)	)	PUNCT
ejpam-856	53	4	it	it	PRON
ejpam-856	53	5	can	can	AUX
ejpam-856	53	6	be	be	AUX
ejpam-856	53	7	seen	see	VERB
ejpam-856	53	8	that	that	SCONJ
ejpam-856	53	9	,	,	PUNCT
ejpam-856	53	10	by	by	ADP
ejpam-856	53	11	specializing	specialize	VERB
ejpam-856	53	12	the	the	DET
ejpam-856	53	13	parameters	parameter	NOUN
ejpam-856	53	14	the	the	DET
ejpam-856	53	15	operator	operator	NOUN
ejpam-856	53	16	d	d	PROPN
ejpam-856	53	17	p	p	PROPN
ejpam-856	53	18	,	,	PUNCT
ejpam-856	53	19	m	m	VERB
ejpam-856	53	20	λ	λ	X
ejpam-856	53	21	(	(	PUNCT
ejpam-856	53	22	α1,β1	α1,β1	PROPN
ejpam-856	53	23	)	)	PUNCT
ejpam-856	53	24	f	f	NOUN
ejpam-856	53	25	(	(	PUNCT
ejpam-856	53	26	z	z	NOUN
ejpam-856	53	27	)	)	PUNCT
ejpam-856	53	28	reduces	reduce	VERB
ejpam-856	53	29	to	to	ADP
ejpam-856	53	30	many	many	ADJ
ejpam-856	53	31	known	know	VERB
ejpam-856	53	32	and	and	CCONJ
ejpam-856	53	33	new	new	ADJ
ejpam-856	53	34	integral	integral	ADJ
ejpam-856	53	35	and	and	CCONJ
ejpam-856	53	36	differential	differential	ADJ
ejpam-856	53	37	operators	operator	NOUN
ejpam-856	53	38	.	.	PUNCT
ejpam-856	54	1	in	in	ADP
ejpam-856	54	2	particular	particular	ADJ
ejpam-856	54	3	,	,	PUNCT
ejpam-856	54	4	when	when	SCONJ
ejpam-856	54	5	m	m	VERB
ejpam-856	54	6	=	=	SYM
ejpam-856	54	7	0	0	NUM
ejpam-856	54	8	and	and	CCONJ
ejpam-856	54	9	p	p	X
ejpam-856	54	10	=	=	NOUN
ejpam-856	54	11	1	1	NUM
ejpam-856	54	12	the	the	DET
ejpam-856	54	13	operator	operator	NOUN
ejpam-856	54	14	d	d	PROPN
ejpam-856	54	15	p	p	PROPN
ejpam-856	54	16	,	,	PUNCT
ejpam-856	54	17	m	m	VERB
ejpam-856	54	18	λ	λ	X
ejpam-856	54	19	(	(	PUNCT
ejpam-856	54	20	α1,β1	α1,β1	PROPN
ejpam-856	54	21	)	)	PUNCT
ejpam-856	54	22	f	f	NOUN
ejpam-856	54	23	(	(	PUNCT
ejpam-856	54	24	z	z	NOUN
ejpam-856	54	25	)	)	PUNCT
ejpam-856	54	26	reduces	reduce	VERB
ejpam-856	54	27	to	to	ADP
ejpam-856	54	28	the	the	DET
ejpam-856	54	29	well	well	ADV
ejpam-856	54	30	known	know	VERB
ejpam-856	54	31	dzioksrivastava	dzioksrivastava	NOUN
ejpam-856	54	32	operator	operator	NOUN
ejpam-856	54	33	[	[	X
ejpam-856	54	34	3	3	NUM
ejpam-856	54	35	]	]	PUNCT
ejpam-856	54	36	and	and	CCONJ
ejpam-856	54	37	for	for	ADP
ejpam-856	54	38	p	p	NOUN
ejpam-856	54	39	=	=	SYM
ejpam-856	54	40	1	1	NUM
ejpam-856	54	41	,	,	PUNCT
ejpam-856	54	42	q	q	NOUN
ejpam-856	54	43	=	=	SYM
ejpam-856	54	44	2	2	NUM
ejpam-856	54	45	,	,	PUNCT
ejpam-856	54	46	s	s	PART
ejpam-856	54	47	=	=	SYM
ejpam-856	54	48	1	1	NUM
ejpam-856	54	49	,	,	PUNCT
ejpam-856	54	50	α1	α1	PROPN
ejpam-856	54	51	=	=	SYM
ejpam-856	54	52	β1	β1	PROPN
ejpam-856	54	53	,	,	PUNCT
ejpam-856	54	54	and	and	CCONJ
ejpam-856	54	55	α2	α2	NOUN
ejpam-856	54	56	=	=	SYM
ejpam-856	55	1	1	1	NUM
ejpam-856	55	2	,	,	PUNCT
ejpam-856	55	3	it	it	PRON
ejpam-856	55	4	reduces	reduce	VERB
ejpam-856	55	5	to	to	ADP
ejpam-856	55	6	the	the	DET
ejpam-856	55	7	operator	operator	NOUN
ejpam-856	55	8	introduced	introduce	VERB
ejpam-856	55	9	by	by	ADP
ejpam-856	55	10	f.	f.	PROPN
ejpam-856	55	11	al	al	PROPN
ejpam-856	55	12	-	-	PUNCT
ejpam-856	55	13	oboudi	oboudi	NOUN
ejpam-856	55	14	[	[	X
ejpam-856	55	15	1	1	NUM
ejpam-856	55	16	]	]	PUNCT
ejpam-856	55	17	.	.	PUNCT
ejpam-856	56	1	further	far	ADV
ejpam-856	56	2	we	we	PRON
ejpam-856	56	3	remark	remark	VERB
ejpam-856	56	4	that	that	SCONJ
ejpam-856	56	5	,	,	PUNCT
ejpam-856	56	6	when	when	SCONJ
ejpam-856	56	7	p	p	NOUN
ejpam-856	56	8	=	=	NOUN
ejpam-856	56	9	1	1	NUM
ejpam-856	56	10	,	,	PUNCT
ejpam-856	56	11	q	q	NOUN
ejpam-856	56	12	=	=	SYM
ejpam-856	56	13	2	2	NUM
ejpam-856	56	14	,	,	PUNCT
ejpam-856	56	15	s	s	PART
ejpam-856	56	16	=	=	SYM
ejpam-856	56	17	1	1	NUM
ejpam-856	56	18	,	,	PUNCT
ejpam-856	56	19	α1	α1	PROPN
ejpam-856	56	20	=	=	SYM
ejpam-856	56	21	β1	β1	PROPN
ejpam-856	56	22	,	,	PUNCT
ejpam-856	56	23	α2	α2	NOUN
ejpam-856	56	24	=	=	SYM
ejpam-856	56	25	1	1	NUM
ejpam-856	56	26	,	,	PUNCT
ejpam-856	56	27	and	and	CCONJ
ejpam-856	56	28	λ=	λ=	VERB
ejpam-856	56	29	1	1	NUM
ejpam-856	56	30	the	the	DET
ejpam-856	56	31	operator	operator	NOUN
ejpam-856	56	32	d	d	PROPN
ejpam-856	56	33	p	p	PROPN
ejpam-856	56	34	,	,	PUNCT
ejpam-856	56	35	m	m	VERB
ejpam-856	56	36	λ	λ	X
ejpam-856	56	37	(	(	PUNCT
ejpam-856	56	38	α1,β1	α1,β1	PROPN
ejpam-856	56	39	)	)	PUNCT
ejpam-856	56	40	f	f	NOUN
ejpam-856	56	41	(	(	PUNCT
ejpam-856	56	42	z	z	NOUN
ejpam-856	56	43	)	)	PUNCT
ejpam-856	56	44	reduces	reduce	VERB
ejpam-856	56	45	to	to	ADP
ejpam-856	56	46	the	the	DET
ejpam-856	56	47	operator	operator	NOUN
ejpam-856	56	48	introduced	introduce	VERB
ejpam-856	56	49	by	by	ADP
ejpam-856	56	50	g.	g.	PROPN
ejpam-856	56	51	s.	s.	PROPN
ejpam-856	56	52	sălăgean	sălăgean	PROPN
ejpam-856	57	1	[	[	X
ejpam-856	57	2	8	8	NUM
ejpam-856	57	3	]	]	PUNCT
ejpam-856	57	4	.	.	PUNCT
ejpam-856	58	1	it	it	PRON
ejpam-856	58	2	can	can	AUX
ejpam-856	58	3	be	be	AUX
ejpam-856	58	4	easily	easily	ADV
ejpam-856	58	5	verified	verify	VERB
ejpam-856	58	6	from	from	ADP
ejpam-856	58	7	(	(	PUNCT
ejpam-856	58	8	6	6	NUM
ejpam-856	58	9	)	)	PUNCT
ejpam-856	58	10	that	that	SCONJ
ejpam-856	58	11	λz(d	λz(d	X
ejpam-856	59	1	p	p	X
ejpam-856	59	2	,	,	PUNCT
ejpam-856	59	3	m	m	VERB
ejpam-856	59	4	λ	λ	X
ejpam-856	59	5	(	(	PUNCT
ejpam-856	59	6	α1,β1	α1,β1	PROPN
ejpam-856	59	7	)	)	PUNCT
ejpam-856	59	8	f	f	NOUN
ejpam-856	59	9	(	(	PUNCT
ejpam-856	59	10	z	z	NOUN
ejpam-856	59	11	)	)	PUNCT
ejpam-856	59	12	)	)	PUNCT
ejpam-856	60	1	′	′	NUM
ejpam-856	61	1	=	=	PUNCT
ejpam-856	61	2	pd	pd	PROPN
ejpam-856	61	3	p	p	X
ejpam-856	61	4	,	,	PUNCT
ejpam-856	61	5	m+1	m+1	PROPN
ejpam-856	61	6	λ	λ	PROPN
ejpam-856	61	7	(	(	PUNCT
ejpam-856	61	8	α1,β1	α1,β1	PROPN
ejpam-856	61	9	)	)	PUNCT
ejpam-856	61	10	f	f	NOUN
ejpam-856	61	11	(	(	PUNCT
ejpam-856	61	12	z)−	z)−	PROPN
ejpam-856	61	13	p(1−λ)dp	p(1−λ)dp	PROPN
ejpam-856	61	14	,	,	PUNCT
ejpam-856	61	15	m	m	NOUN
ejpam-856	61	16	λ	λ	X
ejpam-856	61	17	(	(	PUNCT
ejpam-856	61	18	α1,β1	α1,β1	PROPN
ejpam-856	61	19	)	)	PUNCT
ejpam-856	61	20	f	f	NOUN
ejpam-856	61	21	(	(	PUNCT
ejpam-856	61	22	z	z	NOUN
ejpam-856	61	23	)	)	PUNCT
ejpam-856	61	24	.	.	PUNCT
ejpam-856	62	1	(	(	PUNCT
ejpam-856	62	2	7	7	X
ejpam-856	62	3	)	)	PUNCT
ejpam-856	62	4	using	use	VERB
ejpam-856	62	5	the	the	DET
ejpam-856	62	6	operator	operator	NOUN
ejpam-856	62	7	d	d	PROPN
ejpam-856	62	8	p	p	PROPN
ejpam-856	62	9	,	,	PUNCT
ejpam-856	62	10	m	m	VERB
ejpam-856	62	11	λ	λ	X
ejpam-856	62	12	(	(	PUNCT
ejpam-856	62	13	α1,β1	α1,β1	PROPN
ejpam-856	62	14	)	)	PUNCT
ejpam-856	62	15	f	f	NOUN
ejpam-856	62	16	(	(	PUNCT
ejpam-856	62	17	z	z	X
ejpam-856	62	18	)	)	PUNCT
ejpam-856	62	19	we	we	PRON
ejpam-856	62	20	now	now	ADV
ejpam-856	62	21	define	define	VERB
ejpam-856	62	22	the	the	DET
ejpam-856	62	23	following	follow	VERB
ejpam-856	62	24	class	class	NOUN
ejpam-856	62	25	of	of	ADP
ejpam-856	62	26	p	p	NOUN
ejpam-856	62	27	-	-	PUNCT
ejpam-856	62	28	valent	valent	NOUN
ejpam-856	62	29	analytic	analytic	ADJ
ejpam-856	62	30	functions	function	NOUN
ejpam-856	62	31	.	.	PUNCT
ejpam-856	63	1	definition	definition	NOUN
ejpam-856	63	2	1	1	NUM
ejpam-856	63	3	.	.	PUNCT
ejpam-856	64	1	a	a	DET
ejpam-856	64	2	function	function	NOUN
ejpam-856	64	3	f	f	X
ejpam-856	64	4	(	(	PUNCT
ejpam-856	64	5	z	z	NOUN
ejpam-856	64	6	)	)	PUNCT
ejpam-856	64	7	∈	∈	PROPN
ejpam-856	64	8	ap	ap	PROPN
ejpam-856	64	9	is	be	AUX
ejpam-856	64	10	said	say	VERB
ejpam-856	64	11	to	to	PART
ejpam-856	64	12	be	be	AUX
ejpam-856	64	13	in	in	ADP
ejpam-856	64	14	the	the	DET
ejpam-856	64	15	class	class	NOUN
ejpam-856	64	16	s	s	PART
ejpam-856	64	17	p	p	X
ejpam-856	64	18	,	,	PUNCT
ejpam-856	64	19	j	j	PROPN
ejpam-856	64	20	λ	λ	PROPN
ejpam-856	64	21	,	,	PUNCT
ejpam-856	64	22	m(a	m(a	PROPN
ejpam-856	64	23	,	,	PUNCT
ejpam-856	64	24	b;γ	b;γ	NUM
ejpam-856	64	25	)	)	PUNCT
ejpam-856	64	26	of	of	ADP
ejpam-856	64	27	p	p	NOUN
ejpam-856	64	28	-	-	PUNCT
ejpam-856	64	29	valent	valent	NOUN
ejpam-856	64	30	functions	function	NOUN
ejpam-856	64	31	of	of	ADP
ejpam-856	64	32	complex	complex	ADJ
ejpam-856	64	33	order	order	NOUN
ejpam-856	64	34	γ	γ	X
ejpam-856	64	35	6=	6=	PRON
ejpam-856	64	36	0	0	NUM
ejpam-856	64	37	in	in	ADP
ejpam-856	64	38	u	u	PRON
ejpam-856	64	39	if	if	SCONJ
ejpam-856	64	40	and	and	CCONJ
ejpam-856	64	41	only	only	ADV
ejpam-856	64	42	if	if	SCONJ
ejpam-856	64	43	re	re	ADJ
ejpam-856	64	44	�	�	NOUN
ejpam-856	64	45	1	1	NUM
ejpam-856	64	46	+	+	NUM
ejpam-856	64	47	1	1	NUM
ejpam-856	64	48	γ	γ	X
ejpam-856	64	49	�	�	PROPN
ejpam-856	64	50	z	z	PROPN
ejpam-856	64	51	�	�	PROPN
ejpam-856	65	1	d	d	PROPN
ejpam-856	65	2	p	p	PROPN
ejpam-856	65	3	,	,	PUNCT
ejpam-856	65	4	m	m	VERB
ejpam-856	65	5	λ	λ	X
ejpam-856	65	6	(	(	PUNCT
ejpam-856	65	7	α1,β1	α1,β1	PROPN
ejpam-856	65	8	)	)	PUNCT
ejpam-856	65	9	f	f	NOUN
ejpam-856	65	10	(	(	PUNCT
ejpam-856	65	11	z	z	NOUN
ejpam-856	65	12	)	)	PUNCT
ejpam-856	65	13	�	�	PROPN
ejpam-856	65	14	(	(	PUNCT
ejpam-856	65	15	j+1	j+1	PROPN
ejpam-856	65	16	)	)	PUNCT
ejpam-856	65	17	�	�	PROPN
ejpam-856	66	1	d	d	X
ejpam-856	66	2	p	p	PROPN
ejpam-856	66	3	,	,	PUNCT
ejpam-856	66	4	m	m	VERB
ejpam-856	66	5	λ	λ	X
ejpam-856	66	6	(	(	PUNCT
ejpam-856	66	7	α1,β1	α1,β1	PROPN
ejpam-856	66	8	)	)	PUNCT
ejpam-856	66	9	f	f	NOUN
ejpam-856	66	10	(	(	PUNCT
ejpam-856	66	11	z	z	NOUN
ejpam-856	66	12	)	)	PUNCT
ejpam-856	66	13	�	�	PROPN
ejpam-856	66	14	(	(	PUNCT
ejpam-856	66	15	j	j	PROPN
ejpam-856	66	16	)	)	PUNCT
ejpam-856	66	17	−	−	PROPN
ejpam-856	66	18	p+	p+	VERB
ejpam-856	66	19	j	j	PROPN
ejpam-856	66	20	�	�	PROPN
ejpam-856	66	21	�	�	PROPN
ejpam-856	66	22	≺	≺	NOUN
ejpam-856	66	23	1	1	NUM
ejpam-856	66	24	+	+	NUM
ejpam-856	66	25	az	az	PROPN
ejpam-856	66	26	1	1	NUM
ejpam-856	66	27	+	+	CCONJ
ejpam-856	66	28	bz	bz	PROPN
ejpam-856	66	29	(	(	PUNCT
ejpam-856	66	30	8)	8)	NUM
ejpam-856	66	31	(	(	PUNCT
ejpam-856	66	32	z	z	NOUN
ejpam-856	66	33	∈	∈	PROPN
ejpam-856	66	34	u	u	NOUN
ejpam-856	66	35	;	;	PUNCT
ejpam-856	66	36	−1≤	−1≤	PROPN
ejpam-856	66	37	b	b	NOUN
ejpam-856	66	38	<	<	X
ejpam-856	66	39	a≤	a≤	PRON
ejpam-856	66	40	1	1	NUM
ejpam-856	66	41	;	;	PUNCT
ejpam-856	66	42	p	p	PROPN
ejpam-856	66	43	∈	∈	PROPN
ejpam-856	66	44	n	n	CCONJ
ejpam-856	66	45	;	;	PUNCT
ejpam-856	66	46	m	m	PROPN
ejpam-856	66	47	,	,	PUNCT
ejpam-856	66	48	j	j	PROPN
ejpam-856	66	49	∈	∈	PROPN
ejpam-856	66	50	n0	n0	PROPN
ejpam-856	66	51	;	;	PUNCT
ejpam-856	66	52	γ	γ	X
ejpam-856	66	53	∈	∈	NOUN
ejpam-856	66	54	c−	c−	NOUN
ejpam-856	66	55	{	{	PUNCT
ejpam-856	66	56	0	0	NUM
ejpam-856	66	57	}	}	PUNCT
ejpam-856	66	58	;	;	PUNCT
ejpam-856	66	59	|γλ(a−	|γλ(a−	PROPN
ejpam-856	66	60	b	b	X
ejpam-856	66	61	)	)	PUNCT
ejpam-856	66	62	+	+	CCONJ
ejpam-856	66	63	pb|	pb|	ADJ
ejpam-856	66	64	≤	≤	NUM
ejpam-856	66	65	p	p	NOUN
ejpam-856	66	66	)	)	PUNCT
ejpam-856	66	67	.	.	PUNCT
ejpam-856	67	1	it	it	PRON
ejpam-856	67	2	can	can	AUX
ejpam-856	67	3	be	be	AUX
ejpam-856	67	4	seen	see	VERB
ejpam-856	67	5	that	that	SCONJ
ejpam-856	67	6	,	,	PUNCT
ejpam-856	67	7	by	by	ADP
ejpam-856	67	8	specializing	specialize	VERB
ejpam-856	67	9	the	the	DET
ejpam-856	67	10	parameters	parameter	NOUN
ejpam-856	67	11	the	the	DET
ejpam-856	67	12	class	class	NOUN
ejpam-856	67	13	s	s	PROPN
ejpam-856	67	14	p	p	X
ejpam-856	67	15	,	,	PUNCT
ejpam-856	67	16	j	j	PROPN
ejpam-856	67	17	λ	λ	PROPN
ejpam-856	67	18	,	,	PUNCT
ejpam-856	67	19	m(a	m(a	PROPN
ejpam-856	67	20	,	,	PUNCT
ejpam-856	67	21	b;γ	b;γ	NUM
ejpam-856	67	22	)	)	PUNCT
ejpam-856	67	23	reduces	reduce	VERB
ejpam-856	67	24	to	to	ADP
ejpam-856	67	25	many	many	ADJ
ejpam-856	67	26	known	know	VERB
ejpam-856	67	27	subclasses	subclass	NOUN
ejpam-856	67	28	of	of	ADP
ejpam-856	67	29	analytic	analytic	ADJ
ejpam-856	67	30	functions	function	NOUN
ejpam-856	67	31	.	.	PUNCT
ejpam-856	68	1	in	in	ADP
ejpam-856	68	2	particular	particular	ADJ
ejpam-856	68	3	,	,	PUNCT
ejpam-856	68	4	when	when	SCONJ
ejpam-856	68	5	a=	a=	PROPN
ejpam-856	68	6	1	1	NUM
ejpam-856	68	7	and	and	CCONJ
ejpam-856	68	8	b	b	X
ejpam-856	68	9	=	=	SYM
ejpam-856	68	10	−1	−1	NOUN
ejpam-856	68	11	the	the	DET
ejpam-856	68	12	class	class	NOUN
ejpam-856	68	13	reduces	reduce	VERB
ejpam-856	68	14	to	to	ADP
ejpam-856	68	15	the	the	DET
ejpam-856	68	16	class	class	NOUN
ejpam-856	68	17	s	s	PART
ejpam-856	68	18	p	p	X
ejpam-856	68	19	,	,	PUNCT
ejpam-856	68	20	j	j	PROPN
ejpam-856	68	21	λ	λ	PROPN
ejpam-856	68	22	,	,	PUNCT
ejpam-856	68	23	m(γ	m(γ	NOUN
ejpam-856	68	24	)	)	PUNCT
ejpam-856	68	25	which	which	PRON
ejpam-856	68	26	has	have	AUX
ejpam-856	68	27	recently	recently	ADV
ejpam-856	68	28	been	be	AUX
ejpam-856	68	29	introduced	introduce	VERB
ejpam-856	68	30	by	by	ADP
ejpam-856	68	31	c.selvaraj	c.selvaraj	ADJ
ejpam-856	68	32	and	and	CCONJ
ejpam-856	68	33	k.a.selvakumaran	k.a.selvakumaran	NOUN
ejpam-856	68	34	[	[	X
ejpam-856	68	35	9	9	NUM
ejpam-856	68	36	]	]	PUNCT
ejpam-856	68	37	.	.	PUNCT
ejpam-856	69	1	further	far	ADV
ejpam-856	69	2	,	,	PUNCT
ejpam-856	69	3	when	when	SCONJ
ejpam-856	69	4	q	q	X
ejpam-856	69	5	=	=	SYM
ejpam-856	69	6	2	2	NUM
ejpam-856	69	7	,	,	PUNCT
ejpam-856	69	8	s	s	PART
ejpam-856	69	9	=	=	SYM
ejpam-856	69	10	1	1	NUM
ejpam-856	69	11	,	,	PUNCT
ejpam-856	69	12	α1	α1	PROPN
ejpam-856	69	13	=	=	SYM
ejpam-856	69	14	β1	β1	PROPN
ejpam-856	69	15	,	,	PUNCT
ejpam-856	69	16	and	and	CCONJ
ejpam-856	69	17	α2	α2	NOUN
ejpam-856	69	18	=	=	SYM
ejpam-856	69	19	1	1	NUM
ejpam-856	69	20	,	,	PUNCT
ejpam-856	69	21	we	we	PRON
ejpam-856	69	22	have	have	VERB
ejpam-856	69	23	the	the	DET
ejpam-856	69	24	following	follow	VERB
ejpam-856	69	25	relationships	relationship	NOUN
ejpam-856	69	26	:	:	PUNCT
ejpam-856	69	27	(	(	PUNCT
ejpam-856	69	28	1	1	X
ejpam-856	69	29	)	)	PUNCT
ejpam-856	69	30	s	s	PART
ejpam-856	69	31	1,0	1,0	NUM
ejpam-856	69	32	λ,0(1,−1;γ	λ,0(1,−1;γ	NOUN
ejpam-856	69	33	)	)	PUNCT
ejpam-856	70	1	=	=	SYM
ejpam-856	70	2	s	s	X
ejpam-856	70	3	(	(	PUNCT
ejpam-856	70	4	γ	γ	X
ejpam-856	70	5	)	)	PUNCT
ejpam-856	70	6	(	(	PUNCT
ejpam-856	70	7	γ	γ	X
ejpam-856	70	8	∈	∈	ADJ
ejpam-856	70	9	c−	c−	NOUN
ejpam-856	70	10	{	{	PUNCT
ejpam-856	70	11	0	0	NUM
ejpam-856	70	12	}	}	PUNCT
ejpam-856	70	13	)	)	PUNCT
ejpam-856	70	14	.	.	PUNCT
ejpam-856	71	1	(	(	PUNCT
ejpam-856	71	2	2	2	X
ejpam-856	71	3	)	)	PUNCT
ejpam-856	71	4	s	s	PART
ejpam-856	71	5	1,1	1,1	NUM
ejpam-856	71	6	λ,0(1,−1;γ	λ,0(1,−1;γ	NOUN
ejpam-856	71	7	)	)	PUNCT
ejpam-856	72	1	=	=	SYM
ejpam-856	72	2	k	k	X
ejpam-856	72	3	(	(	PUNCT
ejpam-856	72	4	γ	γ	X
ejpam-856	72	5	)	)	PUNCT
ejpam-856	72	6	(	(	PUNCT
ejpam-856	72	7	γ	γ	X
ejpam-856	72	8	∈	∈	ADJ
ejpam-856	72	9	c−	c−	NOUN
ejpam-856	72	10	{	{	PUNCT
ejpam-856	72	11	0	0	NUM
ejpam-856	72	12	}	}	PUNCT
ejpam-856	72	13	)	)	PUNCT
ejpam-856	72	14	.	.	PUNCT
ejpam-856	73	1	(	(	PUNCT
ejpam-856	73	2	3	3	X
ejpam-856	73	3	)	)	PUNCT
ejpam-856	73	4	s	s	PART
ejpam-856	73	5	1,0	1,0	NUM
ejpam-856	73	6	λ,0(1,−1	λ,0(1,−1	NOUN
ejpam-856	73	7	;	;	PUNCT
ejpam-856	73	8	1−α	1−α	NUM
ejpam-856	73	9	)	)	PUNCT
ejpam-856	74	1	=	=	PRON
ejpam-856	74	2	s	s	VERB
ejpam-856	74	3	∗(α	∗(α	PROPN
ejpam-856	74	4	)	)	PUNCT
ejpam-856	74	5	for	for	ADP
ejpam-856	74	6	0≤	0≤	NUM
ejpam-856	74	7	α	α	NOUN
ejpam-856	74	8	<	<	X
ejpam-856	74	9	1	1	NUM
ejpam-856	74	10	.	.	PUNCT
ejpam-856	75	1	the	the	DET
ejpam-856	75	2	classes	class	NOUN
ejpam-856	75	3	s	s	PART
ejpam-856	75	4	(	(	PUNCT
ejpam-856	75	5	γ	γ	NOUN
ejpam-856	75	6	)	)	PUNCT
ejpam-856	75	7	and	and	CCONJ
ejpam-856	75	8	k	k	PROPN
ejpam-856	75	9	(	(	PUNCT
ejpam-856	75	10	γ	γ	X
ejpam-856	75	11	)	)	PUNCT
ejpam-856	75	12	are	be	AUX
ejpam-856	75	13	said	say	VERB
ejpam-856	75	14	to	to	PART
ejpam-856	75	15	be	be	AUX
ejpam-856	75	16	the	the	DET
ejpam-856	75	17	classes	class	NOUN
ejpam-856	75	18	of	of	ADP
ejpam-856	75	19	starlike	starlike	NOUN
ejpam-856	75	20	and	and	CCONJ
ejpam-856	75	21	convex	convex	NOUN
ejpam-856	75	22	functions	function	NOUN
ejpam-856	75	23	of	of	ADP
ejpam-856	75	24	complex	complex	ADJ
ejpam-856	75	25	order	order	NOUN
ejpam-856	75	26	γ	γ	X
ejpam-856	75	27	6=	6=	PRON
ejpam-856	75	28	0	0	NUM
ejpam-856	75	29	in	in	ADP
ejpam-856	75	30	u	u	NOUN
ejpam-856	75	31	which	which	PRON
ejpam-856	75	32	were	be	AUX
ejpam-856	75	33	studied	study	VERB
ejpam-856	75	34	by	by	ADP
ejpam-856	75	35	m.	m.	NOUN
ejpam-856	75	36	a.	a.	PROPN
ejpam-856	75	37	nasr	nasr	PROPN
ejpam-856	75	38	and	and	CCONJ
ejpam-856	75	39	m.	m.	PROPN
ejpam-856	75	40	k.	k.	PROPN
ejpam-856	75	41	aouf	aouf	PROPN
ejpam-856	76	1	[	[	X
ejpam-856	76	2	6	6	NUM
ejpam-856	76	3	]	]	PUNCT
ejpam-856	76	4	and	and	CCONJ
ejpam-856	76	5	p.	p.	NOUN
ejpam-856	76	6	wiatrowski	wiatrowski	VERB
ejpam-856	77	1	[	[	X
ejpam-856	77	2	10	10	NUM
ejpam-856	77	3	]	]	PUNCT
ejpam-856	77	4	and	and	CCONJ
ejpam-856	77	5	s	s	VERB
ejpam-856	77	6	∗(α	∗(α	PROPN
ejpam-856	77	7	)	)	PUNCT
ejpam-856	77	8	is	be	AUX
ejpam-856	77	9	the	the	DET
ejpam-856	77	10	class	class	NOUN
ejpam-856	77	11	of	of	ADP
ejpam-856	77	12	starlike	starlike	NOUN
ejpam-856	77	13	functions	function	NOUN
ejpam-856	77	14	of	of	ADP
ejpam-856	77	15	order	order	NOUN
ejpam-856	77	16	α	α	NOUN
ejpam-856	77	17	in	in	ADP
ejpam-856	77	18	u	u	PROPN
ejpam-856	77	19	.	.	PUNCT
ejpam-856	78	1	c.	c.	PROPN
ejpam-856	78	2	selvaraj	selvaraj	PROPN
ejpam-856	78	3	,	,	PUNCT
ejpam-856	78	4	k.	k.	PROPN
ejpam-856	78	5	selvakumaran	selvakumaran	PROPN
ejpam-856	78	6	/	/	SYM
ejpam-856	78	7	eur	eur	PROPN
ejpam-856	78	8	.	.	PUNCT
ejpam-856	79	1	j.	j.	PROPN
ejpam-856	79	2	pure	pure	PROPN
ejpam-856	79	3	appl	appl	PROPN
ejpam-856	79	4	.	.	PROPN
ejpam-856	79	5	math	math	PROPN
ejpam-856	79	6	,	,	PUNCT
ejpam-856	79	7	3	3	NUM
ejpam-856	79	8	(	(	PUNCT
ejpam-856	79	9	2010	2010	NUM
ejpam-856	79	10	)	)	PUNCT
ejpam-856	79	11	,	,	PUNCT
ejpam-856	79	12	1048	1048	NUM
ejpam-856	79	13	-	-	SYM
ejpam-856	79	14	1054	1054	NUM
ejpam-856	79	15	1051	1051	NUM
ejpam-856	79	16	2	2	NUM
ejpam-856	79	17	.	.	PUNCT
ejpam-856	80	1	majorization	majorization	NOUN
ejpam-856	80	2	problem	problem	NOUN
ejpam-856	80	3	for	for	ADP
ejpam-856	80	4	the	the	DET
ejpam-856	80	5	class	class	NOUN
ejpam-856	80	6	s	s	PROPN
ejpam-856	80	7	p	p	X
ejpam-856	80	8	,	,	PUNCT
ejpam-856	80	9	j	j	PROPN
ejpam-856	80	10	λ	λ	PROPN
ejpam-856	80	11	,	,	PUNCT
ejpam-856	80	12	m(a	m(a	PROPN
ejpam-856	80	13	,	,	PUNCT
ejpam-856	80	14	b;γ	b;γ	NUM
ejpam-856	80	15	)	)	PUNCT
ejpam-856	80	16	theorem	theorem	NOUN
ejpam-856	80	17	1	1	NUM
ejpam-856	80	18	.	.	PUNCT
ejpam-856	81	1	let	let	VERB
ejpam-856	81	2	the	the	DET
ejpam-856	81	3	function	function	NOUN
ejpam-856	81	4	f	f	PROPN
ejpam-856	81	5	(	(	PUNCT
ejpam-856	81	6	z	z	NOUN
ejpam-856	81	7	)	)	PUNCT
ejpam-856	81	8	be	be	AUX
ejpam-856	81	9	in	in	ADP
ejpam-856	81	10	the	the	DET
ejpam-856	81	11	class	class	NOUN
ejpam-856	81	12	ap	ap	PROPN
ejpam-856	81	13	and	and	CCONJ
ejpam-856	81	14	suppose	suppose	VERB
ejpam-856	81	15	that	that	SCONJ
ejpam-856	81	16	g(z	g(z	PROPN
ejpam-856	81	17	)	)	PUNCT
ejpam-856	81	18	∈	∈	PROPN
ejpam-856	81	19	s	s	PART
ejpam-856	81	20	p	p	X
ejpam-856	81	21	,	,	PUNCT
ejpam-856	81	22	j	j	PROPN
ejpam-856	81	23	λ	λ	PROPN
ejpam-856	81	24	,	,	PUNCT
ejpam-856	81	25	m(a	m(a	PROPN
ejpam-856	81	26	,	,	PUNCT
ejpam-856	81	27	b;γ	b;γ	NUM
ejpam-856	81	28	)	)	PUNCT
ejpam-856	81	29	.	.	PUNCT
ejpam-856	82	1	if	if	SCONJ
ejpam-856	82	2	�	�	PROPN
ejpam-856	82	3	d	d	PROPN
ejpam-856	82	4	p	p	PROPN
ejpam-856	82	5	,	,	PUNCT
ejpam-856	82	6	m	m	VERB
ejpam-856	82	7	λ	λ	X
ejpam-856	82	8	(	(	PUNCT
ejpam-856	82	9	α1,β1	α1,β1	PROPN
ejpam-856	82	10	)	)	PUNCT
ejpam-856	82	11	f	f	NOUN
ejpam-856	82	12	(	(	PUNCT
ejpam-856	82	13	z	z	NOUN
ejpam-856	82	14	)	)	PUNCT
ejpam-856	82	15	�	�	PROPN
ejpam-856	82	16	(	(	PUNCT
ejpam-856	82	17	j	j	NOUN
ejpam-856	82	18	)	)	PUNCT
ejpam-856	82	19	is	be	AUX
ejpam-856	82	20	majorized	majorize	VERB
ejpam-856	82	21	by	by	ADP
ejpam-856	82	22	�	�	PROPN
ejpam-856	82	23	d	d	PROPN
ejpam-856	82	24	p	p	PROPN
ejpam-856	82	25	,	,	PUNCT
ejpam-856	82	26	m	m	VERB
ejpam-856	82	27	λ	λ	X
ejpam-856	82	28	(	(	PUNCT
ejpam-856	82	29	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	82	30	)	)	PUNCT
ejpam-856	82	31	�	�	PROPN
ejpam-856	82	32	(	(	PUNCT
ejpam-856	82	33	j	j	NOUN
ejpam-856	82	34	)	)	PUNCT
ejpam-856	82	35	in	in	ADP
ejpam-856	82	36	u	u	NOUN
ejpam-856	82	37	for	for	ADP
ejpam-856	82	38	j	j	PROPN
ejpam-856	82	39	∈	∈	PROPN
ejpam-856	82	40	n0	n0	PROPN
ejpam-856	82	41	,	,	PUNCT
ejpam-856	82	42	then	then	ADV
ejpam-856	82	43	�	�	PROPN
ejpam-856	82	44	�	�	PROPN
ejpam-856	82	45	�	�	PROPN
ejpam-856	82	46	d	d	PROPN
ejpam-856	82	47	p	p	PROPN
ejpam-856	82	48	,	,	PUNCT
ejpam-856	82	49	m+1	m+1	NUM
ejpam-856	82	50	λ	λ	PROPN
ejpam-856	82	51	(	(	PUNCT
ejpam-856	82	52	α1,β1	α1,β1	PROPN
ejpam-856	82	53	)	)	PUNCT
ejpam-856	82	54	f	f	NOUN
ejpam-856	82	55	(	(	PUNCT
ejpam-856	82	56	z	z	NOUN
ejpam-856	82	57	)	)	PUNCT
ejpam-856	82	58	�	�	PROPN
ejpam-856	82	59	(	(	PUNCT
ejpam-856	82	60	j	j	PROPN
ejpam-856	82	61	)	)	PUNCT
ejpam-856	82	62	�	�	PROPN
ejpam-856	82	63	�	�	PROPN
ejpam-856	82	64	≤	≤	PROPN
ejpam-856	83	1	�	�	PROPN
ejpam-856	83	2	�	�	PROPN
ejpam-856	83	3	�	�	PROPN
ejpam-856	83	4	d	d	PROPN
ejpam-856	83	5	p	p	PROPN
ejpam-856	83	6	,	,	PUNCT
ejpam-856	83	7	m+1	m+1	NUM
ejpam-856	83	8	λ	λ	PROPN
ejpam-856	83	9	(	(	PUNCT
ejpam-856	83	10	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	83	11	)	)	PUNCT
ejpam-856	83	12	�	�	PROPN
ejpam-856	83	13	(	(	PUNCT
ejpam-856	83	14	j	j	PROPN
ejpam-856	83	15	)	)	PUNCT
ejpam-856	83	16	�	�	PROPN
ejpam-856	83	17	�	�	PROPN
ejpam-856	83	18	for	for	ADP
ejpam-856	83	19	|z|	|z|	NOUN
ejpam-856	83	20	≤	≤	NUM
ejpam-856	83	21	r1	r1	NOUN
ejpam-856	83	22	,	,	PUNCT
ejpam-856	83	23	(	(	PUNCT
ejpam-856	83	24	9	9	NUM
ejpam-856	83	25	)	)	PUNCT
ejpam-856	83	26	where	where	SCONJ
ejpam-856	83	27	r1	r1	NOUN
ejpam-856	83	28	=	=	SYM
ejpam-856	83	29	r1(p	r1(p	PROPN
ejpam-856	83	30	,	,	PUNCT
ejpam-856	83	31	γ	γ	X
ejpam-856	83	32	,	,	PUNCT
ejpam-856	83	33	λ	λ	PROPN
ejpam-856	83	34	,	,	PUNCT
ejpam-856	83	35	a	a	DET
ejpam-856	83	36	,	,	PUNCT
ejpam-856	83	37	b	b	NOUN
ejpam-856	83	38	)	)	PUNCT
ejpam-856	83	39	is	be	AUX
ejpam-856	83	40	the	the	DET
ejpam-856	83	41	smallest	small	ADJ
ejpam-856	83	42	positive	positive	ADJ
ejpam-856	83	43	root	root	NOUN
ejpam-856	83	44	of	of	ADP
ejpam-856	83	45	the	the	DET
ejpam-856	83	46	equation	equation	NOUN
ejpam-856	83	47	|γλ(a−	|γλ(a−	PROPN
ejpam-856	83	48	b	b	PROPN
ejpam-856	83	49	)	)	PUNCT
ejpam-856	84	1	+	+	CCONJ
ejpam-856	84	2	pb|r3	pb|r3	ADV
ejpam-856	84	3	−	−	PROPN
ejpam-856	84	4	(	(	PUNCT
ejpam-856	84	5	p+	p+	NOUN
ejpam-856	84	6	2λ|b|)r2−	2λ|b|)r2−	NUM
ejpam-856	84	7	(	(	PUNCT
ejpam-856	84	8	|γλ(a−	|γλ(a−	PROPN
ejpam-856	84	9	b	b	PROPN
ejpam-856	84	10	)	)	PUNCT
ejpam-856	85	1	+	+	CCONJ
ejpam-856	85	2	pb|+	pb|+	PROPN
ejpam-856	85	3	2λ)r	2λ)r	NUM
ejpam-856	86	1	+	+	CCONJ
ejpam-856	86	2	p	p	X
ejpam-856	86	3	=	=	SYM
ejpam-856	86	4	0	0	NUM
ejpam-856	86	5	(	(	PUNCT
ejpam-856	86	6	10	10	NUM
ejpam-856	86	7	)	)	PUNCT
ejpam-856	86	8	(	(	PUNCT
ejpam-856	86	9	−1≤	−1≤	VERB
ejpam-856	86	10	b	b	ADP
ejpam-856	86	11	<	<	X
ejpam-856	86	12	a≤	a≤	PRON
ejpam-856	86	13	1	1	NUM
ejpam-856	86	14	;	;	PUNCT
ejpam-856	86	15	p	p	PROPN
ejpam-856	86	16	∈	∈	PROPN
ejpam-856	86	17	n	n	CCONJ
ejpam-856	86	18	;	;	PUNCT
ejpam-856	86	19	γ	γ	X
ejpam-856	86	20	∈	∈	NOUN
ejpam-856	86	21	c−	c−	NOUN
ejpam-856	86	22	{	{	PUNCT
ejpam-856	86	23	0	0	NUM
ejpam-856	86	24	}	}	PUNCT
ejpam-856	86	25	;	;	PUNCT
ejpam-856	86	26	λ≥	λ≥	PROPN
ejpam-856	86	27	0	0	NUM
ejpam-856	86	28	)	)	PUNCT
ejpam-856	86	29	.	.	PUNCT
ejpam-856	87	1	proof	proof	NOUN
ejpam-856	87	2	.	.	PUNCT
ejpam-856	88	1	let	let	VERB
ejpam-856	88	2	h(z	h(z	NOUN
ejpam-856	88	3	)	)	PUNCT
ejpam-856	88	4	=	=	PUNCT
ejpam-856	89	1	1	1	NUM
ejpam-856	89	2	+	+	SYM
ejpam-856	89	3	1	1	NUM
ejpam-856	89	4	γ	γ	X
ejpam-856	89	5	�	�	PROPN
ejpam-856	89	6	z	z	PROPN
ejpam-856	89	7	�	�	PROPN
ejpam-856	89	8	d	d	PROPN
ejpam-856	89	9	p	p	PROPN
ejpam-856	89	10	,	,	PUNCT
ejpam-856	89	11	m	m	VERB
ejpam-856	89	12	λ	λ	X
ejpam-856	89	13	(	(	PUNCT
ejpam-856	89	14	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	89	15	)	)	PUNCT
ejpam-856	89	16	�	�	PROPN
ejpam-856	89	17	(	(	PUNCT
ejpam-856	89	18	j+1	j+1	PROPN
ejpam-856	89	19	)	)	PUNCT
ejpam-856	89	20	�	�	PROPN
ejpam-856	90	1	d	d	X
ejpam-856	90	2	p	p	PROPN
ejpam-856	90	3	,	,	PUNCT
ejpam-856	90	4	m	m	VERB
ejpam-856	90	5	λ	λ	X
ejpam-856	90	6	(	(	PUNCT
ejpam-856	90	7	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	90	8	)	)	PUNCT
ejpam-856	90	9	�	�	PROPN
ejpam-856	90	10	(	(	PUNCT
ejpam-856	90	11	j	j	PROPN
ejpam-856	90	12	)	)	PUNCT
ejpam-856	90	13	−	−	PROPN
ejpam-856	90	14	p+	p+	PROPN
ejpam-856	90	15	j	j	PROPN
ejpam-856	90	16	�	�	PROPN
ejpam-856	90	17	(	(	PUNCT
ejpam-856	90	18	11	11	NUM
ejpam-856	90	19	)	)	PUNCT
ejpam-856	90	20	(	(	PUNCT
ejpam-856	90	21	p	p	NOUN
ejpam-856	90	22	∈	∈	PROPN
ejpam-856	90	23	n	n	CCONJ
ejpam-856	90	24	;	;	PUNCT
ejpam-856	90	25	m	m	PROPN
ejpam-856	90	26	,	,	PUNCT
ejpam-856	90	27	j	j	PROPN
ejpam-856	90	28	∈	∈	PROPN
ejpam-856	90	29	n0	n0	PROPN
ejpam-856	90	30	;	;	PUNCT
ejpam-856	90	31	γ	γ	X
ejpam-856	90	32	∈	∈	NOUN
ejpam-856	90	33	c−	c−	NOUN
ejpam-856	90	34	{	{	PUNCT
ejpam-856	90	35	0	0	NUM
ejpam-856	90	36	}	}	PUNCT
ejpam-856	90	37	;	;	PUNCT
ejpam-856	90	38	p	p	PROPN
ejpam-856	90	39	>	>	X
ejpam-856	90	40	j	j	PROPN
ejpam-856	90	41	)	)	PUNCT
ejpam-856	90	42	.	.	PUNCT
ejpam-856	91	1	since	since	SCONJ
ejpam-856	91	2	g(z	g(z	PROPN
ejpam-856	91	3	)	)	PUNCT
ejpam-856	91	4	∈	∈	PROPN
ejpam-856	91	5	s	s	PART
ejpam-856	91	6	p	p	X
ejpam-856	91	7	,	,	PUNCT
ejpam-856	91	8	j	j	PROPN
ejpam-856	91	9	λ	λ	PROPN
ejpam-856	91	10	,	,	PUNCT
ejpam-856	91	11	m(γ	m(γ	PROPN
ejpam-856	91	12	)	)	PUNCT
ejpam-856	91	13	,	,	PUNCT
ejpam-856	91	14	we	we	PRON
ejpam-856	91	15	find	find	VERB
ejpam-856	91	16	from	from	ADP
ejpam-856	91	17	(	(	PUNCT
ejpam-856	91	18	8)	8)	NUM
ejpam-856	91	19	that	that	DET
ejpam-856	91	20	h(z	h(z	NOUN
ejpam-856	91	21	)	)	PUNCT
ejpam-856	91	22	=	=	PUNCT
ejpam-856	92	1	1	1	NUM
ejpam-856	92	2	+	+	CCONJ
ejpam-856	92	3	aw(z	aw(z	VERB
ejpam-856	92	4	)	)	PUNCT
ejpam-856	92	5	1	1	NUM
ejpam-856	93	1	+	+	NUM
ejpam-856	93	2	bw(z	bw(z	NOUN
ejpam-856	93	3	)	)	PUNCT
ejpam-856	94	1	,	,	PUNCT
ejpam-856	94	2	(	(	PUNCT
ejpam-856	94	3	12	12	NUM
ejpam-856	94	4	)	)	PUNCT
ejpam-856	94	5	where	where	SCONJ
ejpam-856	94	6	w(z	w(z	NOUN
ejpam-856	94	7	)	)	PUNCT
ejpam-856	94	8	is	be	AUX
ejpam-856	94	9	analytic	analytic	ADJ
ejpam-856	94	10	in	in	ADP
ejpam-856	94	11	u	u	PROPN
ejpam-856	94	12	,	,	PUNCT
ejpam-856	94	13	which	which	PRON
ejpam-856	94	14	satisfies	satisfy	VERB
ejpam-856	94	15	the	the	DET
ejpam-856	94	16	conditions	condition	NOUN
ejpam-856	94	17	w(0	w(0	PROPN
ejpam-856	94	18	)	)	PUNCT
ejpam-856	95	1	=	=	SYM
ejpam-856	95	2	0	0	NUM
ejpam-856	96	1	and	and	CCONJ
ejpam-856	96	2	|w(z)|	|w(z)|	VERB
ejpam-856	96	3	<	<	X
ejpam-856	96	4	1	1	NUM
ejpam-856	96	5	(	(	PUNCT
ejpam-856	96	6	z	z	NOUN
ejpam-856	96	7	∈	∈	PROPN
ejpam-856	96	8	u	u	NOUN
ejpam-856	96	9	)	)	PUNCT
ejpam-856	96	10	.	.	PUNCT
ejpam-856	97	1	it	it	PRON
ejpam-856	97	2	follows	follow	VERB
ejpam-856	97	3	from	from	ADP
ejpam-856	97	4	(	(	PUNCT
ejpam-856	97	5	11	11	NUM
ejpam-856	97	6	)	)	PUNCT
ejpam-856	97	7	and	and	CCONJ
ejpam-856	97	8	(	(	PUNCT
ejpam-856	97	9	12)that	12)that	NOUN
ejpam-856	97	10	z	z	NOUN
ejpam-856	97	11	�	�	PROPN
ejpam-856	98	1	d	d	X
ejpam-856	98	2	p	p	PROPN
ejpam-856	98	3	,	,	PUNCT
ejpam-856	98	4	m	m	VERB
ejpam-856	98	5	λ	λ	X
ejpam-856	98	6	(	(	PUNCT
ejpam-856	98	7	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	98	8	)	)	PUNCT
ejpam-856	98	9	�	�	PROPN
ejpam-856	98	10	(	(	PUNCT
ejpam-856	98	11	j+1	j+1	PROPN
ejpam-856	98	12	)	)	PUNCT
ejpam-856	98	13	�	�	PROPN
ejpam-856	99	1	d	d	X
ejpam-856	99	2	p	p	PROPN
ejpam-856	99	3	,	,	PUNCT
ejpam-856	99	4	m	m	VERB
ejpam-856	99	5	λ	λ	X
ejpam-856	99	6	(	(	PUNCT
ejpam-856	99	7	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	99	8	)	)	PUNCT
ejpam-856	99	9	�	�	PROPN
ejpam-856	99	10	(	(	PUNCT
ejpam-856	99	11	j	j	PROPN
ejpam-856	99	12	)	)	PUNCT
ejpam-856	99	13	=	=	PUNCT
ejpam-856	100	1	(	(	PUNCT
ejpam-856	100	2	p−	p−	NOUN
ejpam-856	100	3	j)+	j)+	NOUN
ejpam-856	101	1	[	[	PUNCT
ejpam-856	101	2	γ(a−	γ(a−	PROPN
ejpam-856	101	3	b	b	NOUN
ejpam-856	101	4	)	)	PUNCT
ejpam-856	101	5	+	+	CCONJ
ejpam-856	101	6	(	(	PUNCT
ejpam-856	101	7	p−	p−	NOUN
ejpam-856	101	8	j)b]w(z	j)b]w(z	NOUN
ejpam-856	101	9	)	)	PUNCT
ejpam-856	101	10	1	1	NUM
ejpam-856	101	11	+	+	NUM
ejpam-856	101	12	bw(z	bw(z	NOUN
ejpam-856	101	13	)	)	PUNCT
ejpam-856	101	14	(	(	PUNCT
ejpam-856	101	15	13	13	NUM
ejpam-856	101	16	)	)	PUNCT
ejpam-856	101	17	in	in	ADP
ejpam-856	101	18	view	view	NOUN
ejpam-856	101	19	of	of	ADP
ejpam-856	101	20	λz(d	λz(d	PRON
ejpam-856	101	21	p	p	X
ejpam-856	101	22	,	,	PUNCT
ejpam-856	101	23	m	m	VERB
ejpam-856	101	24	λ	λ	X
ejpam-856	101	25	(	(	PUNCT
ejpam-856	101	26	α1,β1	α1,β1	PROPN
ejpam-856	101	27	)	)	PUNCT
ejpam-856	101	28	f	f	NOUN
ejpam-856	101	29	(	(	PUNCT
ejpam-856	101	30	z	z	NOUN
ejpam-856	101	31	)	)	PUNCT
ejpam-856	101	32	)	)	PUNCT
ejpam-856	101	33	(	(	PUNCT
ejpam-856	101	34	j+1	j+1	X
ejpam-856	101	35	)	)	PUNCT
ejpam-856	101	36	=	=	PUNCT
ejpam-856	102	1	p(d	p(d	NOUN
ejpam-856	102	2	p	p	X
ejpam-856	102	3	,	,	PUNCT
ejpam-856	102	4	m+1	m+1	NUM
ejpam-856	102	5	λ	λ	PROPN
ejpam-856	102	6	(	(	PUNCT
ejpam-856	102	7	α1,β1	α1,β1	PROPN
ejpam-856	102	8	)	)	PUNCT
ejpam-856	102	9	f	f	NOUN
ejpam-856	102	10	(	(	PUNCT
ejpam-856	102	11	z	z	NOUN
ejpam-856	102	12	)	)	PUNCT
ejpam-856	102	13	)	)	PUNCT
ejpam-856	103	1	(	(	PUNCT
ejpam-856	103	2	j	j	NOUN
ejpam-856	103	3	)	)	PUNCT
ejpam-856	103	4	−	−	PROPN
ejpam-856	104	1	(	(	PUNCT
ejpam-856	104	2	p−	p−	NOUN
ejpam-856	104	3	pλ+λ	pλ+λ	ADJ
ejpam-856	104	4	j)(d	j)(d	NOUN
ejpam-856	104	5	p	p	NOUN
ejpam-856	104	6	,	,	PUNCT
ejpam-856	104	7	m	m	VERB
ejpam-856	104	8	λ	λ	X
ejpam-856	104	9	(	(	PUNCT
ejpam-856	104	10	α1,β1	α1,β1	PROPN
ejpam-856	104	11	)	)	PUNCT
ejpam-856	104	12	f	f	NOUN
ejpam-856	104	13	(	(	PUNCT
ejpam-856	104	14	z	z	NOUN
ejpam-856	104	15	)	)	PUNCT
ejpam-856	104	16	)	)	PUNCT
ejpam-856	105	1	(	(	PUNCT
ejpam-856	105	2	j	j	NOUN
ejpam-856	105	3	)	)	PUNCT
ejpam-856	105	4	,	,	PUNCT
ejpam-856	105	5	(	(	PUNCT
ejpam-856	105	6	14	14	NUM
ejpam-856	105	7	)	)	PUNCT
ejpam-856	105	8	(	(	PUNCT
ejpam-856	105	9	13	13	NUM
ejpam-856	105	10	)	)	PUNCT
ejpam-856	105	11	immediately	immediately	ADV
ejpam-856	105	12	yields	yield	VERB
ejpam-856	105	13	the	the	DET
ejpam-856	105	14	following	follow	VERB
ejpam-856	105	15	inequality	inequality	NOUN
ejpam-856	105	16	:	:	PUNCT
ejpam-856	105	17	�	�	PROPN
ejpam-856	105	18	�	�	PROPN
ejpam-856	105	19	�	�	PROPN
ejpam-856	105	20	�	�	PROPN
ejpam-856	105	21	�	�	PROPN
ejpam-856	105	22	d	d	PROPN
ejpam-856	105	23	p	p	PROPN
ejpam-856	105	24	,	,	PUNCT
ejpam-856	105	25	m	m	VERB
ejpam-856	105	26	λ	λ	X
ejpam-856	105	27	(	(	PUNCT
ejpam-856	105	28	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	105	29	)	)	PUNCT
ejpam-856	105	30	�	�	PROPN
ejpam-856	105	31	(	(	PUNCT
ejpam-856	105	32	j	j	PROPN
ejpam-856	105	33	)	)	PUNCT
ejpam-856	105	34	�	�	PROPN
ejpam-856	105	35	�	�	PROPN
ejpam-856	105	36	�	�	PROPN
ejpam-856	105	37	�	�	PROPN
ejpam-856	105	38	≤	≤	PROPN
ejpam-856	105	39	p(1	p(1	PROPN
ejpam-856	105	40	+	+	NOUN
ejpam-856	105	41	|b||z|	|b||z|	NOUN
ejpam-856	105	42	)	)	PUNCT
ejpam-856	105	43	p−	p−	NOUN
ejpam-856	105	44	|γλ(a−	|γλ(a−	PROPN
ejpam-856	105	45	b	b	PROPN
ejpam-856	105	46	)	)	PUNCT
ejpam-856	105	47	+	+	CCONJ
ejpam-856	105	48	pb||z|	pb||z|	PROPN
ejpam-856	105	49	�	�	PROPN
ejpam-856	105	50	�	�	PROPN
ejpam-856	105	51	�	�	PROPN
ejpam-856	105	52	�	�	PROPN
ejpam-856	105	53	�	�	PROPN
ejpam-856	105	54	d	d	PROPN
ejpam-856	105	55	p	p	PROPN
ejpam-856	105	56	,	,	PUNCT
ejpam-856	105	57	m+1	m+1	NUM
ejpam-856	105	58	λ	λ	PROPN
ejpam-856	105	59	(	(	PUNCT
ejpam-856	105	60	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	105	61	)	)	PUNCT
ejpam-856	105	62	�	�	PROPN
ejpam-856	105	63	(	(	PUNCT
ejpam-856	105	64	j	j	PROPN
ejpam-856	105	65	)	)	PUNCT
ejpam-856	105	66	�	�	PROPN
ejpam-856	105	67	�	�	PROPN
ejpam-856	105	68	�	�	PROPN
ejpam-856	105	69	�	�	PROPN
ejpam-856	105	70	.	.	PUNCT
ejpam-856	106	1	(	(	PUNCT
ejpam-856	106	2	15	15	NUM
ejpam-856	106	3	)	)	PUNCT
ejpam-856	106	4	since	since	SCONJ
ejpam-856	106	5	�	�	PROPN
ejpam-856	106	6	d	d	PROPN
ejpam-856	106	7	p	p	PROPN
ejpam-856	106	8	,	,	PUNCT
ejpam-856	106	9	m	m	VERB
ejpam-856	106	10	λ	λ	X
ejpam-856	106	11	(	(	PUNCT
ejpam-856	106	12	α1,β1	α1,β1	PROPN
ejpam-856	106	13	)	)	PUNCT
ejpam-856	106	14	f	f	NOUN
ejpam-856	106	15	(	(	PUNCT
ejpam-856	106	16	z	z	NOUN
ejpam-856	106	17	)	)	PUNCT
ejpam-856	106	18	�	�	PROPN
ejpam-856	106	19	(	(	PUNCT
ejpam-856	106	20	j	j	NOUN
ejpam-856	106	21	)	)	PUNCT
ejpam-856	106	22	is	be	AUX
ejpam-856	106	23	majorized	majorize	VERB
ejpam-856	106	24	by	by	ADP
ejpam-856	106	25	�	�	PROPN
ejpam-856	106	26	d	d	PROPN
ejpam-856	106	27	p	p	PROPN
ejpam-856	106	28	,	,	PUNCT
ejpam-856	106	29	m	m	VERB
ejpam-856	106	30	λ	λ	X
ejpam-856	106	31	(	(	PUNCT
ejpam-856	106	32	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	106	33	)	)	PUNCT
ejpam-856	106	34	�	�	PROPN
ejpam-856	106	35	(	(	PUNCT
ejpam-856	106	36	j	j	PROPN
ejpam-856	106	37	)	)	PUNCT
ejpam-856	106	38	inu	inu	NOUN
ejpam-856	106	39	,	,	PUNCT
ejpam-856	106	40	there	there	PRON
ejpam-856	106	41	exist	exist	VERB
ejpam-856	106	42	an	an	DET
ejpam-856	106	43	analytic	analytic	ADJ
ejpam-856	106	44	function	function	NOUN
ejpam-856	106	45	ϕ(z	ϕ(z	NOUN
ejpam-856	106	46	)	)	PUNCT
ejpam-856	107	1	such	such	ADJ
ejpam-856	107	2	that	that	PRON
ejpam-856	107	3	�	�	PROPN
ejpam-856	108	1	d	d	X
ejpam-856	108	2	p	p	PROPN
ejpam-856	108	3	,	,	PUNCT
ejpam-856	108	4	m	m	VERB
ejpam-856	108	5	λ	λ	X
ejpam-856	108	6	(	(	PUNCT
ejpam-856	108	7	α1,β1	α1,β1	PROPN
ejpam-856	108	8	)	)	PUNCT
ejpam-856	108	9	f	f	NOUN
ejpam-856	108	10	(	(	PUNCT
ejpam-856	108	11	z	z	NOUN
ejpam-856	108	12	)	)	PUNCT
ejpam-856	108	13	�	�	PROPN
ejpam-856	108	14	(	(	PUNCT
ejpam-856	108	15	j	j	NOUN
ejpam-856	108	16	)	)	PUNCT
ejpam-856	108	17	=	=	SYM
ejpam-856	108	18	ϕ(z	ϕ(z	PROPN
ejpam-856	108	19	)	)	PUNCT
ejpam-856	108	20	�	�	PROPN
ejpam-856	109	1	d	d	X
ejpam-856	109	2	p	p	PROPN
ejpam-856	109	3	,	,	PUNCT
ejpam-856	109	4	m	m	VERB
ejpam-856	109	5	λ	λ	X
ejpam-856	109	6	(	(	PUNCT
ejpam-856	109	7	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	109	8	)	)	PUNCT
ejpam-856	109	9	�	�	PROPN
ejpam-856	109	10	(	(	PUNCT
ejpam-856	109	11	j	j	NOUN
ejpam-856	109	12	)	)	PUNCT
ejpam-856	109	13	(	(	PUNCT
ejpam-856	109	14	16	16	NUM
ejpam-856	109	15	)	)	PUNCT
ejpam-856	109	16	c.	c.	PROPN
ejpam-856	109	17	selvaraj	selvaraj	PROPN
ejpam-856	109	18	,	,	PUNCT
ejpam-856	109	19	k.	k.	PROPN
ejpam-856	109	20	selvakumaran	selvakumaran	PROPN
ejpam-856	109	21	/	/	SYM
ejpam-856	109	22	eur	eur	PROPN
ejpam-856	109	23	.	.	PUNCT
ejpam-856	110	1	j.	j.	PROPN
ejpam-856	110	2	pure	pure	PROPN
ejpam-856	110	3	appl	appl	PROPN
ejpam-856	110	4	.	.	PROPN
ejpam-856	110	5	math	math	PROPN
ejpam-856	110	6	,	,	PUNCT
ejpam-856	110	7	3	3	NUM
ejpam-856	110	8	(	(	PUNCT
ejpam-856	110	9	2010	2010	NUM
ejpam-856	110	10	)	)	PUNCT
ejpam-856	110	11	,	,	PUNCT
ejpam-856	110	12	1048	1048	NUM
ejpam-856	110	13	-	-	SYM
ejpam-856	110	14	1054	1054	NUM
ejpam-856	110	15	1052	1052	NUM
ejpam-856	110	16	and	and	CCONJ
ejpam-856	110	17	|ϕ(z)|	|ϕ(z)|	ADJ
ejpam-856	110	18	≤	≤	ADJ
ejpam-856	110	19	1	1	NUM
ejpam-856	110	20	(	(	PUNCT
ejpam-856	110	21	z	z	NOUN
ejpam-856	110	22	∈	∈	PROPN
ejpam-856	110	23	u	u	NOUN
ejpam-856	110	24	)	)	PUNCT
ejpam-856	110	25	.	.	PUNCT
ejpam-856	111	1	thus	thus	ADV
ejpam-856	111	2	we	we	PRON
ejpam-856	111	3	have	have	VERB
ejpam-856	111	4	z	z	NOUN
ejpam-856	111	5	�	�	PROPN
ejpam-856	112	1	d	d	PROPN
ejpam-856	112	2	p	p	PROPN
ejpam-856	112	3	,	,	PUNCT
ejpam-856	112	4	m	m	VERB
ejpam-856	112	5	λ	λ	X
ejpam-856	112	6	(	(	PUNCT
ejpam-856	112	7	α1,β1	α1,β1	PROPN
ejpam-856	112	8	)	)	PUNCT
ejpam-856	112	9	f	f	NOUN
ejpam-856	112	10	(	(	PUNCT
ejpam-856	112	11	z	z	NOUN
ejpam-856	112	12	)	)	PUNCT
ejpam-856	112	13	�	�	PROPN
ejpam-856	112	14	(	(	PUNCT
ejpam-856	112	15	j+1	j+1	PROPN
ejpam-856	112	16	)	)	PUNCT
ejpam-856	112	17	=	=	SYM
ejpam-856	112	18	zϕ′(z	zϕ′(z	PROPN
ejpam-856	112	19	)	)	PUNCT
ejpam-856	112	20	�	�	PROPN
ejpam-856	113	1	d	d	X
ejpam-856	113	2	p	p	PROPN
ejpam-856	113	3	,	,	PUNCT
ejpam-856	113	4	m	m	VERB
ejpam-856	113	5	λ	λ	X
ejpam-856	113	6	(	(	PUNCT
ejpam-856	113	7	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	113	8	)	)	PUNCT
ejpam-856	113	9	�	�	PROPN
ejpam-856	113	10	(	(	PUNCT
ejpam-856	113	11	j	j	PROPN
ejpam-856	113	12	)	)	PUNCT
ejpam-856	113	13	+	+	NOUN
ejpam-856	113	14	zϕ(z	zϕ(z	SYM
ejpam-856	113	15	)	)	PUNCT
ejpam-856	113	16	�	�	PROPN
ejpam-856	114	1	d	d	X
ejpam-856	114	2	p	p	PROPN
ejpam-856	114	3	,	,	PUNCT
ejpam-856	114	4	m	m	VERB
ejpam-856	114	5	λ	λ	X
ejpam-856	114	6	(	(	PUNCT
ejpam-856	114	7	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	114	8	)	)	PUNCT
ejpam-856	114	9	�	�	PROPN
ejpam-856	114	10	(	(	PUNCT
ejpam-856	114	11	j+1	j+1	PROPN
ejpam-856	114	12	)	)	PUNCT
ejpam-856	114	13	.	.	PUNCT
ejpam-856	115	1	(	(	PUNCT
ejpam-856	115	2	17	17	NUM
ejpam-856	115	3	)	)	PUNCT
ejpam-856	115	4	using	use	VERB
ejpam-856	115	5	(	(	PUNCT
ejpam-856	115	6	14	14	NUM
ejpam-856	115	7	)	)	PUNCT
ejpam-856	115	8	,	,	PUNCT
ejpam-856	115	9	in	in	ADP
ejpam-856	115	10	the	the	DET
ejpam-856	115	11	above	above	ADJ
ejpam-856	115	12	equation	equation	NOUN
ejpam-856	115	13	,	,	PUNCT
ejpam-856	115	14	we	we	PRON
ejpam-856	115	15	get	get	VERB
ejpam-856	115	16	�	�	PROPN
ejpam-856	115	17	d	d	PROPN
ejpam-856	115	18	p	p	PROPN
ejpam-856	115	19	,	,	PUNCT
ejpam-856	115	20	m+1	m+1	NUM
ejpam-856	115	21	λ	λ	PROPN
ejpam-856	115	22	(	(	PUNCT
ejpam-856	115	23	α1,β1	α1,β1	PROPN
ejpam-856	115	24	)	)	PUNCT
ejpam-856	115	25	f	f	NOUN
ejpam-856	115	26	(	(	PUNCT
ejpam-856	115	27	z	z	NOUN
ejpam-856	115	28	)	)	PUNCT
ejpam-856	115	29	�	�	PROPN
ejpam-856	115	30	(	(	PUNCT
ejpam-856	115	31	j	j	PROPN
ejpam-856	115	32	)	)	PUNCT
ejpam-856	115	33	=	=	PUNCT
ejpam-856	116	1	λz	λz	X
ejpam-856	116	2	p	p	NOUN
ejpam-856	116	3	ϕ′(z	ϕ′(z	NOUN
ejpam-856	116	4	)	)	PUNCT
ejpam-856	116	5	�	�	PROPN
ejpam-856	117	1	d	d	X
ejpam-856	117	2	p	p	PROPN
ejpam-856	117	3	,	,	PUNCT
ejpam-856	117	4	m	m	VERB
ejpam-856	117	5	λ	λ	X
ejpam-856	117	6	(	(	PUNCT
ejpam-856	117	7	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	117	8	)	)	PUNCT
ejpam-856	117	9	�	�	PROPN
ejpam-856	117	10	(	(	PUNCT
ejpam-856	117	11	j	j	PROPN
ejpam-856	117	12	)	)	PUNCT
ejpam-856	118	1	+	+	NOUN
ejpam-856	118	2	ϕ(z	ϕ(z	PROPN
ejpam-856	118	3	)	)	PUNCT
ejpam-856	118	4	�	�	PROPN
ejpam-856	119	1	d	d	PROPN
ejpam-856	119	2	p	p	PROPN
ejpam-856	119	3	,	,	PUNCT
ejpam-856	119	4	m+1	m+1	NUM
ejpam-856	119	5	λ	λ	PROPN
ejpam-856	119	6	(	(	PUNCT
ejpam-856	119	7	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	119	8	)	)	PUNCT
ejpam-856	119	9	�	�	PROPN
ejpam-856	119	10	(	(	PUNCT
ejpam-856	119	11	j	j	PROPN
ejpam-856	119	12	)	)	PUNCT
ejpam-856	119	13	.	.	PUNCT
ejpam-856	120	1	(	(	PUNCT
ejpam-856	120	2	18	18	NUM
ejpam-856	120	3	)	)	PUNCT
ejpam-856	120	4	noting	note	VERB
ejpam-856	120	5	that	that	SCONJ
ejpam-856	120	6	ϕ(z	ϕ(z	NOUN
ejpam-856	120	7	)	)	PUNCT
ejpam-856	120	8	satisfies	satisfie	NOUN
ejpam-856	120	9	(	(	PUNCT
ejpam-856	120	10	cf	cf	NOUN
ejpam-856	120	11	.	.	PUNCT
ejpam-856	121	1	[	[	X
ejpam-856	121	2	4	4	NUM
ejpam-856	121	3	,	,	PUNCT
ejpam-856	121	4	7	7	NUM
ejpam-856	121	5	]	]	PUNCT
ejpam-856	121	6	)	)	PUNCT
ejpam-856	121	7	|ϕ′(z)|	|ϕ′(z)|	PRON
ejpam-856	121	8	≤	≤	PROPN
ejpam-856	121	9	1−	1−	NUM
ejpam-856	121	10	|ϕ(z)|2	|ϕ(z)|2	PROPN
ejpam-856	121	11	1−	1−	NUM
ejpam-856	121	12	|z|2	|z|2	PROPN
ejpam-856	121	13	(	(	PUNCT
ejpam-856	121	14	z	z	NOUN
ejpam-856	121	15	∈	∈	PROPN
ejpam-856	121	16	u	u	NOUN
ejpam-856	121	17	)	)	PUNCT
ejpam-856	121	18	,	,	PUNCT
ejpam-856	121	19	(	(	PUNCT
ejpam-856	121	20	19	19	NUM
ejpam-856	121	21	)	)	PUNCT
ejpam-856	121	22	we	we	PRON
ejpam-856	121	23	see	see	VERB
ejpam-856	121	24	that	that	SCONJ
ejpam-856	121	25	�	�	PROPN
ejpam-856	121	26	�	�	PROPN
ejpam-856	121	27	�	�	PROPN
ejpam-856	121	28	�	�	PROPN
ejpam-856	121	29	�	�	PROPN
ejpam-856	121	30	d	d	PROPN
ejpam-856	121	31	p	p	PROPN
ejpam-856	121	32	,	,	PUNCT
ejpam-856	121	33	m+1	m+1	NUM
ejpam-856	121	34	λ	λ	PROPN
ejpam-856	121	35	(	(	PUNCT
ejpam-856	121	36	α1,β1	α1,β1	PROPN
ejpam-856	121	37	)	)	PUNCT
ejpam-856	121	38	f	f	NOUN
ejpam-856	121	39	(	(	PUNCT
ejpam-856	121	40	z	z	NOUN
ejpam-856	121	41	)	)	PUNCT
ejpam-856	121	42	�	�	PROPN
ejpam-856	121	43	(	(	PUNCT
ejpam-856	121	44	j	j	PROPN
ejpam-856	121	45	)	)	PUNCT
ejpam-856	121	46	�	�	PROPN
ejpam-856	121	47	�	�	PROPN
ejpam-856	121	48	�	�	PROPN
ejpam-856	121	49	�	�	PROPN
ejpam-856	121	50	≤	≤	PROPN
ejpam-856	121	51	�	�	PROPN
ejpam-856	121	52	ϕ(z	ϕ(z	PROPN
ejpam-856	121	53	)	)	PUNCT
ejpam-856	122	1	+	+	CCONJ
ejpam-856	122	2	1−	1−	NUM
ejpam-856	122	3	|ϕ(z)|2	|ϕ(z)|2	NUM
ejpam-856	122	4	1−	1−	NUM
ejpam-856	122	5	|z|2	|z|2	NOUN
ejpam-856	122	6	λ|z|(1	λ|z|(1	NOUN
ejpam-856	122	7	+	+	NUM
ejpam-856	122	8	|b||z|	|b||z|	NOUN
ejpam-856	122	9	)	)	PUNCT
ejpam-856	122	10	p−	p−	NOUN
ejpam-856	122	11	|γλ(a−	|γλ(a−	PROPN
ejpam-856	122	12	b	b	PROPN
ejpam-856	122	13	)	)	PUNCT
ejpam-856	123	1	+	+	CCONJ
ejpam-856	123	2	pb||z|	pb||z|	PROPN
ejpam-856	123	3	�	�	PROPN
ejpam-856	123	4	�	�	PROPN
ejpam-856	123	5	�	�	PROPN
ejpam-856	123	6	�	�	PROPN
ejpam-856	123	7	�	�	PROPN
ejpam-856	123	8	�	�	PROPN
ejpam-856	123	9	d	d	PROPN
ejpam-856	123	10	p	p	PROPN
ejpam-856	123	11	,	,	PUNCT
ejpam-856	123	12	m+1	m+1	NUM
ejpam-856	123	13	λ	λ	PROPN
ejpam-856	123	14	(	(	PUNCT
ejpam-856	123	15	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	123	16	)	)	PUNCT
ejpam-856	123	17	�	�	PROPN
ejpam-856	123	18	(	(	PUNCT
ejpam-856	123	19	j	j	PROPN
ejpam-856	123	20	)	)	PUNCT
ejpam-856	123	21	�	�	PROPN
ejpam-856	123	22	�	�	PROPN
ejpam-856	123	23	�	�	PROPN
ejpam-856	123	24	�	�	PROPN
ejpam-856	123	25	(	(	PUNCT
ejpam-856	123	26	20	20	NUM
ejpam-856	123	27	)	)	PUNCT
ejpam-856	123	28	which	which	PRON
ejpam-856	123	29	,	,	PUNCT
ejpam-856	123	30	upon	upon	SCONJ
ejpam-856	123	31	setting	set	VERB
ejpam-856	123	32	|z|	|z|	NOUN
ejpam-856	123	33	=	=	SYM
ejpam-856	123	34	r	r	NOUN
ejpam-856	123	35	,	,	PUNCT
ejpam-856	123	36	and	and	CCONJ
ejpam-856	123	37	|ϕ(z)|	|ϕ(z)|	PROPN
ejpam-856	123	38	=	=	SYM
ejpam-856	123	39	ρ	ρ	PROPN
ejpam-856	123	40	(	(	PUNCT
ejpam-856	123	41	0≤	0≤	PROPN
ejpam-856	123	42	ρ	ρ	PROPN
ejpam-856	123	43	≤	≤	NUM
ejpam-856	123	44	1	1	NUM
ejpam-856	123	45	)	)	PUNCT
ejpam-856	123	46	leads	lead	VERB
ejpam-856	123	47	us	we	PRON
ejpam-856	123	48	to	to	ADP
ejpam-856	123	49	the	the	DET
ejpam-856	123	50	following	follow	VERB
ejpam-856	123	51	inequality	inequality	NOUN
ejpam-856	123	52	:	:	PUNCT
ejpam-856	123	53	�	�	PROPN
ejpam-856	123	54	�	�	PROPN
ejpam-856	123	55	�	�	PROPN
ejpam-856	123	56	�	�	PROPN
ejpam-856	123	57	�	�	PROPN
ejpam-856	123	58	d	d	PROPN
ejpam-856	123	59	p	p	PROPN
ejpam-856	123	60	,	,	PUNCT
ejpam-856	123	61	m+1	m+1	NUM
ejpam-856	123	62	λ	λ	PROPN
ejpam-856	123	63	(	(	PUNCT
ejpam-856	123	64	α1,β1	α1,β1	PROPN
ejpam-856	123	65	)	)	PUNCT
ejpam-856	123	66	f	f	NOUN
ejpam-856	123	67	(	(	PUNCT
ejpam-856	123	68	z	z	NOUN
ejpam-856	123	69	)	)	PUNCT
ejpam-856	123	70	�	�	PROPN
ejpam-856	123	71	(	(	PUNCT
ejpam-856	123	72	j	j	PROPN
ejpam-856	123	73	)	)	PUNCT
ejpam-856	123	74	�	�	PROPN
ejpam-856	123	75	�	�	PROPN
ejpam-856	123	76	�	�	PROPN
ejpam-856	123	77	�	�	PROPN
ejpam-856	123	78	≤	≤	PROPN
ejpam-856	123	79	θ(ρ	θ(ρ	PROPN
ejpam-856	123	80	)	)	PUNCT
ejpam-856	123	81	(	(	PUNCT
ejpam-856	123	82	1−	1−	NUM
ejpam-856	123	83	r2)(p−	r2)(p−	VERB
ejpam-856	123	84	|γλ(a−	|γλ(a−	PROPN
ejpam-856	123	85	b	b	PROPN
ejpam-856	123	86	)	)	PUNCT
ejpam-856	123	87	+	+	CCONJ
ejpam-856	123	88	pb|r	pb|r	X
ejpam-856	123	89	)	)	PUNCT
ejpam-856	123	90	�	�	PROPN
ejpam-856	123	91	�	�	PROPN
ejpam-856	123	92	�	�	PROPN
ejpam-856	123	93	�	�	PROPN
ejpam-856	123	94	�	�	PROPN
ejpam-856	123	95	d	d	PROPN
ejpam-856	123	96	p	p	PROPN
ejpam-856	123	97	,	,	PUNCT
ejpam-856	123	98	m+1	m+1	NUM
ejpam-856	123	99	λ	λ	PROPN
ejpam-856	123	100	(	(	PUNCT
ejpam-856	123	101	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	123	102	)	)	PUNCT
ejpam-856	123	103	�	�	PROPN
ejpam-856	123	104	(	(	PUNCT
ejpam-856	123	105	j	j	PROPN
ejpam-856	123	106	)	)	PUNCT
ejpam-856	123	107	�	�	PROPN
ejpam-856	123	108	�	�	PROPN
ejpam-856	123	109	�	�	PROPN
ejpam-856	123	110	�	�	PROPN
ejpam-856	123	111	,	,	PUNCT
ejpam-856	123	112	(	(	PUNCT
ejpam-856	123	113	21	21	NUM
ejpam-856	123	114	)	)	PUNCT
ejpam-856	123	115	where	where	SCONJ
ejpam-856	123	116	the	the	DET
ejpam-856	123	117	function	function	NOUN
ejpam-856	123	118	θ(ρ	θ(ρ	PROPN
ejpam-856	123	119	)	)	PUNCT
ejpam-856	123	120	defined	define	VERB
ejpam-856	123	121	by	by	ADP
ejpam-856	123	122	θ(ρ	θ(ρ	PROPN
ejpam-856	123	123	)	)	PUNCT
ejpam-856	123	124	:	:	PUNCT
ejpam-856	123	125	=	=	PUNCT
ejpam-856	123	126	−λr(1	−λr(1	PROPN
ejpam-856	123	127	+	+	NOUN
ejpam-856	123	128	|b|r)ρ2	|b|r)ρ2	NUM
ejpam-856	123	129	+	+	SYM
ejpam-856	123	130	(	(	PUNCT
ejpam-856	123	131	1−	1−	NUM
ejpam-856	123	132	r2)(p−	r2)(p−	VERB
ejpam-856	123	133	|γλ(a−	|γλ(a−	PROPN
ejpam-856	123	134	b	b	NOUN
ejpam-856	123	135	)	)	PUNCT
ejpam-856	123	136	+	+	CCONJ
ejpam-856	123	137	pb|r)ρ	pb|r)ρ	NOUN
ejpam-856	123	138	+	+	NOUN
ejpam-856	123	139	λr(1	λr(1	PROPN
ejpam-856	123	140	+	+	NOUN
ejpam-856	123	141	|b|r	|b|r	NOUN
ejpam-856	123	142	)	)	PUNCT
ejpam-856	123	143	(	(	PUNCT
ejpam-856	123	144	0≤	0≤	NUM
ejpam-856	123	145	ρ	ρ	NUM
ejpam-856	123	146	≤	≤	NUM
ejpam-856	123	147	1	1	NUM
ejpam-856	123	148	)	)	PUNCT
ejpam-856	123	149	takes	take	VERB
ejpam-856	123	150	its	its	PRON
ejpam-856	123	151	maximum	maximum	ADJ
ejpam-856	123	152	value	value	NOUN
ejpam-856	123	153	at	at	ADP
ejpam-856	123	154	ρ	ρ	PROPN
ejpam-856	123	155	=	=	SYM
ejpam-856	123	156	1	1	NUM
ejpam-856	123	157	with	with	ADP
ejpam-856	123	158	r	r	NOUN
ejpam-856	123	159	=	=	SYM
ejpam-856	123	160	r1(p	r1(p	PROPN
ejpam-856	123	161	,	,	PUNCT
ejpam-856	123	162	γ	γ	X
ejpam-856	123	163	,	,	PUNCT
ejpam-856	123	164	λ	λ	PROPN
ejpam-856	123	165	,	,	PUNCT
ejpam-856	123	166	a	a	DET
ejpam-856	123	167	,	,	PUNCT
ejpam-856	123	168	b	b	NOUN
ejpam-856	123	169	)	)	PUNCT
ejpam-856	123	170	,	,	PUNCT
ejpam-856	123	171	the	the	DET
ejpam-856	123	172	smallest	small	ADJ
ejpam-856	123	173	positive	positive	ADJ
ejpam-856	123	174	root	root	NOUN
ejpam-856	123	175	of	of	ADP
ejpam-856	123	176	the	the	DET
ejpam-856	123	177	equation	equation	NOUN
ejpam-856	123	178	(	(	PUNCT
ejpam-856	123	179	10	10	NUM
ejpam-856	123	180	)	)	PUNCT
ejpam-856	123	181	.	.	PUNCT
ejpam-856	124	1	furthermore	furthermore	ADV
ejpam-856	124	2	,	,	PUNCT
ejpam-856	124	3	if	if	SCONJ
ejpam-856	124	4	0≤	0≤	ADJ
ejpam-856	124	5	σ	σ	VERB
ejpam-856	124	6	≤	≤	NOUN
ejpam-856	124	7	r1(p	r1(p	SYM
ejpam-856	124	8	,	,	PUNCT
ejpam-856	124	9	γ	γ	X
ejpam-856	124	10	,	,	PUNCT
ejpam-856	124	11	λ	λ	PROPN
ejpam-856	124	12	,	,	PUNCT
ejpam-856	124	13	a	a	PRON
ejpam-856	124	14	,	,	PUNCT
ejpam-856	124	15	b	b	NOUN
ejpam-856	124	16	)	)	PUNCT
ejpam-856	124	17	,	,	PUNCT
ejpam-856	124	18	then	then	ADV
ejpam-856	124	19	the	the	DET
ejpam-856	124	20	function	function	NOUN
ejpam-856	124	21	φ(ρ	φ(ρ	NUM
ejpam-856	124	22	)	)	PUNCT
ejpam-856	124	23	:	:	PUNCT
ejpam-856	124	24	=	=	PUNCT
ejpam-856	124	25	−λσ(1	−λσ(1	PUNCT
ejpam-856	124	26	+	+	NUM
ejpam-856	124	27	|b|σ)ρ2	|b|σ)ρ2	NUM
ejpam-856	124	28	+	+	CCONJ
ejpam-856	124	29	(	(	PUNCT
ejpam-856	124	30	1−σ2)(p−	1−σ2)(p−	NUM
ejpam-856	124	31	|γλ(a−	|γλ(a−	PROPN
ejpam-856	124	32	b	b	PROPN
ejpam-856	124	33	)	)	PUNCT
ejpam-856	124	34	+	+	CCONJ
ejpam-856	124	35	pb|σ)ρ	pb|σ)ρ	VERB
ejpam-856	124	36	+	+	PROPN
ejpam-856	124	37	λσ(1	λσ(1	PROPN
ejpam-856	124	38	+	+	ADJ
ejpam-856	124	39	|b|σ	|b|σ	PROPN
ejpam-856	124	40	)	)	PUNCT
ejpam-856	124	41	increases	increase	NOUN
ejpam-856	124	42	in	in	ADP
ejpam-856	124	43	the	the	DET
ejpam-856	124	44	interval	interval	NOUN
ejpam-856	124	45	0≤	0≤	NUM
ejpam-856	124	46	ρ	ρ	PROPN
ejpam-856	124	47	≤	≤	NUM
ejpam-856	124	48	1	1	NUM
ejpam-856	124	49	,	,	PUNCT
ejpam-856	124	50	so	so	SCONJ
ejpam-856	124	51	that	that	SCONJ
ejpam-856	124	52	φ(ρ	φ(ρ	NUM
ejpam-856	124	53	)	)	PUNCT
ejpam-856	124	54	does	do	AUX
ejpam-856	124	55	not	not	PART
ejpam-856	124	56	exceed	exceed	VERB
ejpam-856	124	57	φ(1	φ(1	PROPN
ejpam-856	124	58	)	)	PUNCT
ejpam-856	124	59	=	=	PUNCT
ejpam-856	125	1	(	(	PUNCT
ejpam-856	125	2	1−σ2)(p−	1−σ2)(p−	NUM
ejpam-856	125	3	|γλ(a−	|γλ(a−	PROPN
ejpam-856	125	4	b	b	PROPN
ejpam-856	125	5	)	)	PUNCT
ejpam-856	125	6	+	+	NUM
ejpam-856	125	7	pb|σ	pb|σ	NOUN
ejpam-856	125	8	)	)	PUNCT
ejpam-856	125	9	(	(	PUNCT
ejpam-856	125	10	0≤	0≤	PROPN
ejpam-856	125	11	σ	σ	VERB
ejpam-856	125	12	≤	≤	NUM
ejpam-856	125	13	r1(p	r1(p	SYM
ejpam-856	125	14	,	,	PUNCT
ejpam-856	125	15	γ	γ	X
ejpam-856	125	16	,	,	PUNCT
ejpam-856	125	17	λ	λ	PROPN
ejpam-856	125	18	,	,	PUNCT
ejpam-856	125	19	a	a	PRON
ejpam-856	125	20	,	,	PUNCT
ejpam-856	125	21	b	b	NOUN
ejpam-856	125	22	)	)	PUNCT
ejpam-856	125	23	)	)	PUNCT
ejpam-856	125	24	.	.	PUNCT
ejpam-856	126	1	therefore	therefore	ADV
ejpam-856	126	2	,	,	PUNCT
ejpam-856	126	3	from	from	ADP
ejpam-856	126	4	this	this	DET
ejpam-856	126	5	fact	fact	NOUN
ejpam-856	126	6	,	,	PUNCT
ejpam-856	126	7	(	(	PUNCT
ejpam-856	126	8	21	21	NUM
ejpam-856	126	9	)	)	PUNCT
ejpam-856	126	10	gives	give	VERB
ejpam-856	126	11	the	the	DET
ejpam-856	126	12	inequality	inequality	NOUN
ejpam-856	126	13	(	(	PUNCT
ejpam-856	126	14	9	9	NUM
ejpam-856	126	15	)	)	PUNCT
ejpam-856	126	16	.	.	PUNCT
ejpam-856	127	1	as	as	ADP
ejpam-856	127	2	a	a	DET
ejpam-856	127	3	special	special	ADJ
ejpam-856	127	4	case	case	NOUN
ejpam-856	127	5	of	of	ADP
ejpam-856	127	6	theorem	theorem	NOUN
ejpam-856	127	7	1	1	NUM
ejpam-856	127	8	,	,	PUNCT
ejpam-856	127	9	when	when	SCONJ
ejpam-856	127	10	a=	a=	PROPN
ejpam-856	127	11	1	1	NUM
ejpam-856	127	12	and	and	CCONJ
ejpam-856	127	13	b	b	X
ejpam-856	127	14	=	=	SYM
ejpam-856	127	15	−1	−1	NOUN
ejpam-856	127	16	,	,	PUNCT
ejpam-856	127	17	we	we	PRON
ejpam-856	127	18	have	have	VERB
ejpam-856	127	19	c.	c.	PROPN
ejpam-856	127	20	selvaraj	selvaraj	PROPN
ejpam-856	127	21	,	,	PUNCT
ejpam-856	127	22	k.	k.	PROPN
ejpam-856	127	23	selvakumaran	selvakumaran	PROPN
ejpam-856	127	24	/	/	SYM
ejpam-856	127	25	eur	eur	PROPN
ejpam-856	127	26	.	.	PUNCT
ejpam-856	128	1	j.	j.	PROPN
ejpam-856	128	2	pure	pure	PROPN
ejpam-856	128	3	appl	appl	PROPN
ejpam-856	128	4	.	.	PROPN
ejpam-856	128	5	math	math	PROPN
ejpam-856	128	6	,	,	PUNCT
ejpam-856	128	7	3	3	NUM
ejpam-856	128	8	(	(	PUNCT
ejpam-856	128	9	2010	2010	NUM
ejpam-856	128	10	)	)	PUNCT
ejpam-856	128	11	,	,	PUNCT
ejpam-856	128	12	1048	1048	NUM
ejpam-856	128	13	-	-	SYM
ejpam-856	128	14	1054	1054	NUM
ejpam-856	128	15	1053	1053	NUM
ejpam-856	128	16	corollary	corollary	NOUN
ejpam-856	128	17	1	1	NUM
ejpam-856	128	18	.	.	PUNCT
ejpam-856	129	1	[	[	X
ejpam-856	129	2	9	9	NUM
ejpam-856	129	3	]	]	PUNCT
ejpam-856	129	4	let	let	VERB
ejpam-856	129	5	the	the	DET
ejpam-856	129	6	function	function	NOUN
ejpam-856	129	7	f	f	PROPN
ejpam-856	129	8	(	(	PUNCT
ejpam-856	129	9	z	z	NOUN
ejpam-856	129	10	)	)	PUNCT
ejpam-856	129	11	be	be	AUX
ejpam-856	129	12	in	in	ADP
ejpam-856	129	13	the	the	DET
ejpam-856	129	14	class	class	NOUN
ejpam-856	129	15	ap	ap	PROPN
ejpam-856	129	16	and	and	CCONJ
ejpam-856	129	17	suppose	suppose	VERB
ejpam-856	129	18	that	that	SCONJ
ejpam-856	129	19	g(z	g(z	PROPN
ejpam-856	129	20	)	)	PUNCT
ejpam-856	129	21	∈	∈	PROPN
ejpam-856	129	22	s	s	PART
ejpam-856	129	23	p	p	X
ejpam-856	129	24	,	,	PUNCT
ejpam-856	129	25	j	j	PROPN
ejpam-856	129	26	λ	λ	PROPN
ejpam-856	129	27	,	,	PUNCT
ejpam-856	129	28	m(γ	m(γ	NOUN
ejpam-856	129	29	)	)	PUNCT
ejpam-856	129	30	.	.	PUNCT
ejpam-856	130	1	if	if	SCONJ
ejpam-856	130	2	�	�	PROPN
ejpam-856	130	3	d	d	PROPN
ejpam-856	130	4	p	p	PROPN
ejpam-856	130	5	,	,	PUNCT
ejpam-856	130	6	m	m	VERB
ejpam-856	130	7	λ	λ	X
ejpam-856	130	8	(	(	PUNCT
ejpam-856	130	9	α1,β1	α1,β1	PROPN
ejpam-856	130	10	)	)	PUNCT
ejpam-856	130	11	f	f	NOUN
ejpam-856	130	12	(	(	PUNCT
ejpam-856	130	13	z	z	NOUN
ejpam-856	130	14	)	)	PUNCT
ejpam-856	130	15	�	�	PROPN
ejpam-856	130	16	(	(	PUNCT
ejpam-856	130	17	j	j	NOUN
ejpam-856	130	18	)	)	PUNCT
ejpam-856	130	19	is	be	AUX
ejpam-856	130	20	majorized	majorize	VERB
ejpam-856	130	21	by	by	ADP
ejpam-856	130	22	�	�	PROPN
ejpam-856	130	23	d	d	PROPN
ejpam-856	130	24	p	p	PROPN
ejpam-856	130	25	,	,	PUNCT
ejpam-856	130	26	m	m	VERB
ejpam-856	130	27	λ	λ	X
ejpam-856	130	28	(	(	PUNCT
ejpam-856	130	29	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	130	30	)	)	PUNCT
ejpam-856	130	31	�	�	PROPN
ejpam-856	130	32	(	(	PUNCT
ejpam-856	130	33	j	j	NOUN
ejpam-856	130	34	)	)	PUNCT
ejpam-856	130	35	in	in	ADP
ejpam-856	130	36	u	u	NOUN
ejpam-856	130	37	for	for	ADP
ejpam-856	130	38	j	j	PROPN
ejpam-856	130	39	∈	∈	PROPN
ejpam-856	130	40	n0	n0	PROPN
ejpam-856	130	41	,	,	PUNCT
ejpam-856	130	42	then	then	ADV
ejpam-856	130	43	�	�	PROPN
ejpam-856	130	44	�	�	PROPN
ejpam-856	130	45	�	�	PROPN
ejpam-856	130	46	d	d	PROPN
ejpam-856	130	47	p	p	PROPN
ejpam-856	130	48	,	,	PUNCT
ejpam-856	130	49	m+1	m+1	NUM
ejpam-856	130	50	λ	λ	PROPN
ejpam-856	130	51	(	(	PUNCT
ejpam-856	130	52	α1,β1	α1,β1	PROPN
ejpam-856	130	53	)	)	PUNCT
ejpam-856	130	54	f	f	NOUN
ejpam-856	130	55	(	(	PUNCT
ejpam-856	130	56	z	z	NOUN
ejpam-856	130	57	)	)	PUNCT
ejpam-856	130	58	�	�	PROPN
ejpam-856	130	59	(	(	PUNCT
ejpam-856	130	60	j	j	PROPN
ejpam-856	130	61	)	)	PUNCT
ejpam-856	130	62	�	�	PROPN
ejpam-856	130	63	�	�	PROPN
ejpam-856	130	64	≤	≤	PROPN
ejpam-856	131	1	�	�	PROPN
ejpam-856	131	2	�	�	PROPN
ejpam-856	131	3	�	�	PROPN
ejpam-856	131	4	d	d	PROPN
ejpam-856	131	5	p	p	PROPN
ejpam-856	131	6	,	,	PUNCT
ejpam-856	131	7	m+1	m+1	NUM
ejpam-856	131	8	λ	λ	PROPN
ejpam-856	131	9	(	(	PUNCT
ejpam-856	131	10	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	131	11	)	)	PUNCT
ejpam-856	131	12	�	�	PROPN
ejpam-856	131	13	(	(	PUNCT
ejpam-856	131	14	j	j	PROPN
ejpam-856	131	15	)	)	PUNCT
ejpam-856	131	16	�	�	PROPN
ejpam-856	131	17	�	�	PROPN
ejpam-856	131	18	for	for	ADP
ejpam-856	131	19	|z|	|z|	NOUN
ejpam-856	131	20	≤	≤	NUM
ejpam-856	131	21	r1	r1	NOUN
ejpam-856	131	22	,	,	PUNCT
ejpam-856	131	23	(	(	PUNCT
ejpam-856	131	24	22	22	NUM
ejpam-856	131	25	)	)	PUNCT
ejpam-856	131	26	where	where	SCONJ
ejpam-856	131	27	r1	r1	NOUN
ejpam-856	131	28	=	=	SYM
ejpam-856	131	29	r1(p	r1(p	PROPN
ejpam-856	131	30	,	,	PUNCT
ejpam-856	131	31	γ	γ	X
ejpam-856	131	32	,	,	PUNCT
ejpam-856	131	33	λ	λ	NOUN
ejpam-856	131	34	)	)	PUNCT
ejpam-856	131	35	:	:	PUNCT
ejpam-856	131	36	=	=	SYM
ejpam-856	131	37	k−	k−	PROPN
ejpam-856	131	38	p	p	PROPN
ejpam-856	131	39	k2	k2	PROPN
ejpam-856	131	40	−	−	PROPN
ejpam-856	131	41	4p|2γλ−	4p|2γλ−	NUM
ejpam-856	131	42	p|	p|	NOUN
ejpam-856	131	43	2|2γλ−	2|2γλ−	NUM
ejpam-856	131	44	p|	p|	NOUN
ejpam-856	131	45	(	(	PUNCT
ejpam-856	131	46	23	23	NUM
ejpam-856	131	47	)	)	PUNCT
ejpam-856	131	48	(	(	PUNCT
ejpam-856	131	49	k	k	X
ejpam-856	131	50	:	:	PUNCT
ejpam-856	131	51	=	=	SYM
ejpam-856	131	52	2λ+	2λ+	NUM
ejpam-856	131	53	p+	p+	VERB
ejpam-856	131	54	|2γλ−	|2γλ−	ADJ
ejpam-856	131	55	p|	p|	PROPN
ejpam-856	131	56	;	;	PUNCT
ejpam-856	131	57	p	p	PROPN
ejpam-856	131	58	∈	∈	PROPN
ejpam-856	131	59	n	n	CCONJ
ejpam-856	131	60	;	;	PUNCT
ejpam-856	131	61	γ	γ	X
ejpam-856	131	62	∈	∈	NOUN
ejpam-856	131	63	c−	c−	NOUN
ejpam-856	131	64	{	{	PUNCT
ejpam-856	131	65	0	0	NUM
ejpam-856	131	66	}	}	PUNCT
ejpam-856	131	67	;	;	PUNCT
ejpam-856	131	68	λ≥	λ≥	PROPN
ejpam-856	131	69	0	0	NUM
ejpam-856	131	70	)	)	PUNCT
ejpam-856	131	71	.	.	PUNCT
ejpam-856	132	1	setting	set	VERB
ejpam-856	132	2	a=	a=	NOUN
ejpam-856	132	3	1	1	NUM
ejpam-856	132	4	,	,	PUNCT
ejpam-856	132	5	b	b	NOUN
ejpam-856	132	6	=	=	SYM
ejpam-856	132	7	−1	−1	NOUN
ejpam-856	132	8	,	,	PUNCT
ejpam-856	132	9	p	p	NOUN
ejpam-856	132	10	=	=	NOUN
ejpam-856	132	11	1	1	NUM
ejpam-856	132	12	and	and	CCONJ
ejpam-856	132	13	j	j	PROPN
ejpam-856	133	1	=	=	SYM
ejpam-856	133	2	0	0	PROPN
ejpam-856	133	3	in	in	ADP
ejpam-856	133	4	theorem	theorem	NOUN
ejpam-856	133	5	1	1	NUM
ejpam-856	133	6	,	,	PUNCT
ejpam-856	133	7	we	we	PRON
ejpam-856	133	8	have	have	VERB
ejpam-856	133	9	corollary	corollary	ADJ
ejpam-856	133	10	2	2	NUM
ejpam-856	133	11	.	.	PUNCT
ejpam-856	134	1	let	let	VERB
ejpam-856	134	2	the	the	DET
ejpam-856	134	3	function	function	NOUN
ejpam-856	134	4	f	f	PROPN
ejpam-856	134	5	(	(	PUNCT
ejpam-856	134	6	z	z	NOUN
ejpam-856	134	7	)	)	PUNCT
ejpam-856	134	8	∈	∈	PROPN
ejpam-856	134	9	a	a	DET
ejpam-856	134	10	be	be	NOUN
ejpam-856	134	11	analytic	analytic	ADJ
ejpam-856	134	12	and	and	CCONJ
ejpam-856	134	13	univalent	univalent	ADJ
ejpam-856	134	14	in	in	ADP
ejpam-856	134	15	the	the	DET
ejpam-856	134	16	open	open	ADJ
ejpam-856	134	17	unit	unit	NOUN
ejpam-856	134	18	disk	disk	NOUN
ejpam-856	134	19	u	u	NOUN
ejpam-856	134	20	and	and	CCONJ
ejpam-856	134	21	suppose	suppose	VERB
ejpam-856	134	22	that	that	SCONJ
ejpam-856	134	23	g(z	g(z	PROPN
ejpam-856	134	24	)	)	PUNCT
ejpam-856	134	25	∈	∈	PROPN
ejpam-856	134	26	s	s	PART
ejpam-856	134	27	1,0	1,0	NUM
ejpam-856	134	28	λ	λ	NOUN
ejpam-856	134	29	,	,	PUNCT
ejpam-856	134	30	m(γ	m(γ	NOUN
ejpam-856	134	31	)	)	PUNCT
ejpam-856	134	32	.	.	PUNCT
ejpam-856	135	1	if	if	SCONJ
ejpam-856	135	2	�	�	PROPN
ejpam-856	135	3	d	d	PROPN
ejpam-856	135	4	1,m	1,m	PROPN
ejpam-856	135	5	λ	λ	X
ejpam-856	135	6	(	(	PUNCT
ejpam-856	135	7	α1,β1	α1,β1	PROPN
ejpam-856	135	8	)	)	PUNCT
ejpam-856	135	9	f	f	NOUN
ejpam-856	135	10	(	(	PUNCT
ejpam-856	135	11	z	z	NOUN
ejpam-856	135	12	)	)	PUNCT
ejpam-856	135	13	�	�	PROPN
ejpam-856	135	14	is	be	AUX
ejpam-856	135	15	majorized	majorize	VERB
ejpam-856	135	16	by	by	ADP
ejpam-856	135	17	�	�	PROPN
ejpam-856	135	18	d	d	PROPN
ejpam-856	135	19	1,m	1,m	PROPN
ejpam-856	135	20	λ	λ	X
ejpam-856	135	21	(	(	PUNCT
ejpam-856	135	22	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	135	23	)	)	PUNCT
ejpam-856	135	24	�	�	PROPN
ejpam-856	135	25	in	in	ADP
ejpam-856	135	26	u	u	PROPN
ejpam-856	135	27	,	,	PUNCT
ejpam-856	135	28	then	then	ADV
ejpam-856	135	29	�	�	PROPN
ejpam-856	135	30	�	�	PROPN
ejpam-856	135	31	�	�	PROPN
ejpam-856	135	32	d	d	PROPN
ejpam-856	135	33	1,m+1	1,m+1	PROPN
ejpam-856	135	34	λ	λ	X
ejpam-856	135	35	(	(	PUNCT
ejpam-856	135	36	α1,β1	α1,β1	PROPN
ejpam-856	135	37	)	)	PUNCT
ejpam-856	135	38	f	f	NOUN
ejpam-856	135	39	(	(	PUNCT
ejpam-856	135	40	z	z	NOUN
ejpam-856	135	41	)	)	PUNCT
ejpam-856	135	42	�	�	PROPN
ejpam-856	135	43	�	�	PROPN
ejpam-856	135	44	�	�	PROPN
ejpam-856	135	45	≤	≤	PROPN
ejpam-856	135	46	�	�	PROPN
ejpam-856	135	47	�	�	PROPN
ejpam-856	135	48	�	�	PROPN
ejpam-856	135	49	d	d	PROPN
ejpam-856	135	50	1,m+1	1,m+1	PROPN
ejpam-856	135	51	λ	λ	X
ejpam-856	135	52	(	(	PUNCT
ejpam-856	135	53	α1,β1)g(z	α1,β1)g(z	PROPN
ejpam-856	135	54	)	)	PUNCT
ejpam-856	135	55	�	�	PROPN
ejpam-856	135	56	�	�	PROPN
ejpam-856	135	57	�	�	PROPN
ejpam-856	135	58	for	for	ADP
ejpam-856	135	59	|z|	|z|	NOUN
ejpam-856	135	60	≤	≤	NUM
ejpam-856	135	61	r2	r2	NOUN
ejpam-856	135	62	,	,	PUNCT
ejpam-856	135	63	(	(	PUNCT
ejpam-856	135	64	24	24	NUM
ejpam-856	135	65	)	)	PUNCT
ejpam-856	135	66	where	where	SCONJ
ejpam-856	135	67	r2	r2	NOUN
ejpam-856	135	68	:	:	PUNCT
ejpam-856	135	69	=	=	SYM
ejpam-856	135	70	k−	k−	PROPN
ejpam-856	135	71	p	p	PROPN
ejpam-856	135	72	k2	k2	PROPN
ejpam-856	135	73	−	−	PROPN
ejpam-856	135	74	4|2γλ−	4|2γλ−	NUM
ejpam-856	135	75	1|	1|	NUM
ejpam-856	135	76	2|2γλ−	2|2γλ−	NUM
ejpam-856	135	77	1|	1|	NUM
ejpam-856	135	78	(	(	PUNCT
ejpam-856	135	79	25	25	NUM
ejpam-856	135	80	)	)	PUNCT
ejpam-856	135	81	(	(	PUNCT
ejpam-856	135	82	k	k	X
ejpam-856	135	83	:	:	PUNCT
ejpam-856	136	1	=	=	NOUN
ejpam-856	136	2	2λ+	2λ+	NUM
ejpam-856	136	3	1	1	NUM
ejpam-856	136	4	+	+	NUM
ejpam-856	136	5	|2γλ−	|2γλ−	ADJ
ejpam-856	136	6	1|	1|	NUM
ejpam-856	136	7	;	;	PUNCT
ejpam-856	136	8	γ	γ	X
ejpam-856	136	9	∈	∈	NOUN
ejpam-856	136	10	c−	c−	NOUN
ejpam-856	136	11	{	{	PUNCT
ejpam-856	136	12	0	0	NUM
ejpam-856	136	13	}	}	PUNCT
ejpam-856	136	14	;	;	PUNCT
ejpam-856	136	15	λ	λ	X
ejpam-856	136	16	≥	≥	NOUN
ejpam-856	136	17	0	0	NUM
ejpam-856	136	18	)	)	PUNCT
ejpam-856	136	19	.	.	PUNCT
ejpam-856	137	1	further	far	ADV
ejpam-856	137	2	putting	put	VERB
ejpam-856	137	3	λ=	λ=	ADJ
ejpam-856	137	4	1	1	NUM
ejpam-856	137	5	,	,	PUNCT
ejpam-856	137	6	m	m	VERB
ejpam-856	137	7	=	=	NOUN
ejpam-856	137	8	0	0	NUM
ejpam-856	137	9	,	,	PUNCT
ejpam-856	137	10	q	q	NOUN
ejpam-856	137	11	=	=	SYM
ejpam-856	137	12	2	2	NUM
ejpam-856	137	13	,	,	PUNCT
ejpam-856	137	14	s	s	PART
ejpam-856	137	15	=	=	SYM
ejpam-856	137	16	1	1	NUM
ejpam-856	137	17	,	,	PUNCT
ejpam-856	137	18	α1	α1	PROPN
ejpam-856	137	19	=	=	SYM
ejpam-856	137	20	β1	β1	PROPN
ejpam-856	137	21	,	,	PUNCT
ejpam-856	137	22	and	and	CCONJ
ejpam-856	137	23	α2	α2	NOUN
ejpam-856	137	24	=	=	SYM
ejpam-856	137	25	1	1	NUM
ejpam-856	137	26	in	in	ADP
ejpam-856	137	27	corollary	corollary	ADJ
ejpam-856	137	28	2	2	NUM
ejpam-856	137	29	,	,	PUNCT
ejpam-856	137	30	we	we	PRON
ejpam-856	137	31	get	get	VERB
ejpam-856	137	32	corollary	corollary	ADJ
ejpam-856	137	33	3	3	NUM
ejpam-856	137	34	.	.	PUNCT
ejpam-856	138	1	[	[	X
ejpam-856	138	2	2	2	X
ejpam-856	138	3	]	]	PUNCT
ejpam-856	138	4	let	let	VERB
ejpam-856	138	5	the	the	DET
ejpam-856	138	6	function	function	NOUN
ejpam-856	138	7	f	f	PROPN
ejpam-856	138	8	(	(	PUNCT
ejpam-856	138	9	z	z	NOUN
ejpam-856	138	10	)	)	PUNCT
ejpam-856	138	11	∈	∈	PROPN
ejpam-856	138	12	a	a	DET
ejpam-856	138	13	be	be	NOUN
ejpam-856	138	14	analytic	analytic	ADJ
ejpam-856	138	15	and	and	CCONJ
ejpam-856	138	16	univalent	univalent	ADJ
ejpam-856	138	17	in	in	ADP
ejpam-856	138	18	the	the	DET
ejpam-856	138	19	open	open	ADJ
ejpam-856	138	20	unit	unit	NOUN
ejpam-856	138	21	disk	disk	NOUN
ejpam-856	138	22	u	u	NOUN
ejpam-856	138	23	and	and	CCONJ
ejpam-856	138	24	suppose	suppose	VERB
ejpam-856	138	25	that	that	SCONJ
ejpam-856	138	26	g(z	g(z	PROPN
ejpam-856	138	27	)	)	PUNCT
ejpam-856	138	28	∈	∈	PROPN
ejpam-856	138	29	s	s	PART
ejpam-856	138	30	(	(	PUNCT
ejpam-856	138	31	γ	γ	NOUN
ejpam-856	138	32	)	)	PUNCT
ejpam-856	138	33	.	.	PUNCT
ejpam-856	139	1	if	if	SCONJ
ejpam-856	139	2	f	f	PROPN
ejpam-856	139	3	(	(	PUNCT
ejpam-856	139	4	z	z	NOUN
ejpam-856	139	5	)	)	PUNCT
ejpam-856	139	6	is	be	AUX
ejpam-856	139	7	majorized	majorize	VERB
ejpam-856	139	8	by	by	ADP
ejpam-856	139	9	g(z	g(z	PROPN
ejpam-856	139	10	)	)	PUNCT
ejpam-856	139	11	in	in	ADP
ejpam-856	139	12	u	u	NOUN
ejpam-856	139	13	,	,	PUNCT
ejpam-856	139	14	then	then	ADV
ejpam-856	139	15	�	�	PROPN
ejpam-856	139	16	�	�	PROPN
ejpam-856	139	17	f	f	PROPN
ejpam-856	139	18	′(z	′(z	NOUN
ejpam-856	139	19	)	)	PUNCT
ejpam-856	139	20	�	�	PROPN
ejpam-856	139	21	�	�	PROPN
ejpam-856	139	22	≤	≤	PROPN
ejpam-856	139	23	�	�	PROPN
ejpam-856	139	24	�	�	PROPN
ejpam-856	139	25	g′(z	g′(z	NOUN
ejpam-856	139	26	)	)	PUNCT
ejpam-856	139	27	�	�	PROPN
ejpam-856	139	28	�	�	PROPN
ejpam-856	139	29	for	for	ADP
ejpam-856	139	30	|z|	|z|	NOUN
ejpam-856	139	31	≤	≤	NUM
ejpam-856	139	32	r3	r3	NOUN
ejpam-856	139	33	,	,	PUNCT
ejpam-856	139	34	(	(	PUNCT
ejpam-856	139	35	26	26	NUM
ejpam-856	139	36	)	)	PUNCT
ejpam-856	139	37	where	where	SCONJ
ejpam-856	139	38	r3	r3	PROPN
ejpam-856	139	39	:	:	PUNCT
ejpam-856	139	40	=	=	SYM
ejpam-856	140	1	3	3	NUM
ejpam-856	140	2	+	+	NUM
ejpam-856	140	3	|2γ−	|2γ−	X
ejpam-856	140	4	1|	1|	NUM
ejpam-856	140	5	−	−	PROPN
ejpam-856	140	6	p	p	NOUN
ejpam-856	140	7	9	9	NUM
ejpam-856	140	8	+	+	NUM
ejpam-856	140	9	2|2γ−	2|2γ−	NUM
ejpam-856	140	10	1|+	1|+	NUM
ejpam-856	140	11	|2γ−	|2γ−	PROPN
ejpam-856	140	12	1|2	1|2	NUM
ejpam-856	140	13	2|2γ−	2|2γ−	NUM
ejpam-856	140	14	1|	1|	NUM
ejpam-856	140	15	.	.	PUNCT
ejpam-856	141	1	(	(	PUNCT
ejpam-856	141	2	27	27	NUM
ejpam-856	141	3	)	)	PUNCT
ejpam-856	141	4	for	for	ADP
ejpam-856	141	5	γ=	γ=	PROPN
ejpam-856	141	6	1	1	NUM
ejpam-856	141	7	,	,	PUNCT
ejpam-856	141	8	corollary	corollary	ADJ
ejpam-856	141	9	3	3	NUM
ejpam-856	141	10	reduces	reduce	VERB
ejpam-856	141	11	to	to	ADP
ejpam-856	141	12	the	the	DET
ejpam-856	141	13	following	following	ADJ
ejpam-856	141	14	result	result	NOUN
ejpam-856	141	15	:	:	PUNCT
ejpam-856	141	16	corollary	corollary	ADJ
ejpam-856	141	17	4	4	NUM
ejpam-856	141	18	.	.	PUNCT
ejpam-856	142	1	[	[	X
ejpam-856	142	2	5	5	NUM
ejpam-856	142	3	]	]	PUNCT
ejpam-856	142	4	let	let	VERB
ejpam-856	142	5	the	the	DET
ejpam-856	142	6	function	function	NOUN
ejpam-856	142	7	f	f	PROPN
ejpam-856	142	8	(	(	PUNCT
ejpam-856	142	9	z	z	NOUN
ejpam-856	142	10	)	)	PUNCT
ejpam-856	142	11	∈	∈	PROPN
ejpam-856	142	12	a	a	DET
ejpam-856	142	13	be	be	NOUN
ejpam-856	142	14	analytic	analytic	ADJ
ejpam-856	142	15	and	and	CCONJ
ejpam-856	142	16	univalent	univalent	ADJ
ejpam-856	142	17	in	in	ADP
ejpam-856	142	18	the	the	DET
ejpam-856	142	19	open	open	ADJ
ejpam-856	142	20	unit	unit	NOUN
ejpam-856	142	21	disk	disk	NOUN
ejpam-856	142	22	u	u	NOUN
ejpam-856	142	23	and	and	CCONJ
ejpam-856	142	24	suppose	suppose	VERB
ejpam-856	142	25	that	that	SCONJ
ejpam-856	142	26	g(z	g(z	ADJ
ejpam-856	142	27	)	)	PUNCT
ejpam-856	142	28	∈	∈	PROPN
ejpam-856	142	29	s	s	PART
ejpam-856	142	30	∗	∗	NOUN
ejpam-856	142	31	=	=	SYM
ejpam-856	142	32	s	s	PART
ejpam-856	142	33	∗(0	∗(0	NOUN
ejpam-856	142	34	)	)	PUNCT
ejpam-856	142	35	.	.	PUNCT
ejpam-856	143	1	if	if	SCONJ
ejpam-856	143	2	f	f	PROPN
ejpam-856	143	3	(	(	PUNCT
ejpam-856	143	4	z	z	NOUN
ejpam-856	143	5	)	)	PUNCT
ejpam-856	143	6	is	be	AUX
ejpam-856	143	7	majorized	majorize	VERB
ejpam-856	143	8	by	by	ADP
ejpam-856	143	9	g(z	g(z	PROPN
ejpam-856	143	10	)	)	PUNCT
ejpam-856	143	11	in	in	ADP
ejpam-856	143	12	u	u	NOUN
ejpam-856	143	13	,	,	PUNCT
ejpam-856	143	14	then	then	ADV
ejpam-856	143	15	�	�	PROPN
ejpam-856	143	16	�	�	PROPN
ejpam-856	143	17	f	f	PROPN
ejpam-856	143	18	′(z	′(z	NOUN
ejpam-856	143	19	)	)	PUNCT
ejpam-856	143	20	�	�	PROPN
ejpam-856	143	21	�	�	PROPN
ejpam-856	143	22	≤	≤	PROPN
ejpam-856	143	23	�	�	PROPN
ejpam-856	143	24	�	�	PROPN
ejpam-856	143	25	g′(z	g′(z	NOUN
ejpam-856	143	26	)	)	PUNCT
ejpam-856	143	27	�	�	PROPN
ejpam-856	143	28	�	�	PROPN
ejpam-856	143	29	for	for	ADP
ejpam-856	143	30	|z|	|z|	NOUN
ejpam-856	143	31	≤	≤	NOUN
ejpam-856	143	32	2−p3	2−p3	NUM
ejpam-856	143	33	.	.	PUNCT
ejpam-856	144	1	(	(	PUNCT
ejpam-856	144	2	28	28	NUM
ejpam-856	144	3	)	)	PUNCT
ejpam-856	144	4	references	reference	NOUN
ejpam-856	144	5	1054	1054	NUM
ejpam-856	144	6	references	reference	NOUN
ejpam-856	144	7	[	[	X
ejpam-856	144	8	1	1	NUM
ejpam-856	144	9	]	]	PUNCT
ejpam-856	144	10	f.	f.	PROPN
ejpam-856	144	11	m.	m.	PROPN
ejpam-856	144	12	al	al	PROPN
ejpam-856	144	13	-	-	PUNCT
ejpam-856	144	14	oboudi	oboudi	NOUN
ejpam-856	144	15	,	,	PUNCT
ejpam-856	144	16	on	on	ADP
ejpam-856	144	17	univalent	univalent	ADJ
ejpam-856	144	18	functions	function	NOUN
ejpam-856	144	19	defined	define	VERB
ejpam-856	144	20	by	by	ADP
ejpam-856	144	21	a	a	DET
ejpam-856	144	22	generalized	generalized	ADJ
ejpam-856	144	23	sălăgean	sălăgean	ADJ
ejpam-856	144	24	operator	operator	NOUN
ejpam-856	144	25	,	,	PUNCT
ejpam-856	144	26	int	int	NOUN
ejpam-856	144	27	.	.	PUNCT
ejpam-856	145	1	j.	j.	PROPN
ejpam-856	145	2	math	math	PROPN
ejpam-856	145	3	.	.	PUNCT
ejpam-856	146	1	math	math	NOUN
ejpam-856	146	2	.	.	PUNCT
ejpam-856	147	1	sci	sci	PROPN
ejpam-856	147	2	.	.	PROPN
ejpam-856	147	3	,	,	PUNCT
ejpam-856	147	4	no	no	INTJ
ejpam-856	147	5	.	.	NOUN
ejpam-856	147	6	25	25	NUM
ejpam-856	147	7	-	-	SYM
ejpam-856	147	8	28	28	NUM
ejpam-856	147	9	,	,	PUNCT
ejpam-856	147	10	1429–1436	1429–1436	NUM
ejpam-856	147	11	.	.	PUNCT
ejpam-856	147	12	2004	2004	NUM
ejpam-856	147	13	.	.	PUNCT
ejpam-856	148	1	[	[	X
ejpam-856	148	2	2	2	X
ejpam-856	148	3	]	]	PUNCT
ejpam-856	148	4	o.	o.	PROPN
ejpam-856	148	5	altintaş	altintaş	PROPN
ejpam-856	148	6	,	,	PUNCT
ejpam-856	148	7	ö.	ö.	VERB
ejpam-856	148	8	özkan	özkan	PROPN
ejpam-856	148	9	and	and	CCONJ
ejpam-856	148	10	h.	h.	PROPN
ejpam-856	148	11	m.	m.	PROPN
ejpam-856	148	12	srivastava	srivastava	PROPN
ejpam-856	148	13	,	,	PUNCT
ejpam-856	148	14	majorization	majorization	NOUN
ejpam-856	148	15	by	by	ADP
ejpam-856	148	16	starlike	starlike	NOUN
ejpam-856	148	17	functions	function	NOUN
ejpam-856	148	18	of	of	ADP
ejpam-856	148	19	complex	complex	ADJ
ejpam-856	148	20	order	order	NOUN
ejpam-856	148	21	,	,	PUNCT
ejpam-856	148	22	complex	complex	ADJ
ejpam-856	148	23	variables	variable	NOUN
ejpam-856	148	24	theory	theory	NOUN
ejpam-856	148	25	appl	appl	PROPN
ejpam-856	148	26	.	.	PROPN
ejpam-856	149	1	46	46	NUM
ejpam-856	149	2	,	,	PUNCT
ejpam-856	149	3	no	no	INTJ
ejpam-856	149	4	.	.	NOUN
ejpam-856	149	5	3	3	NUM
ejpam-856	149	6	,	,	PUNCT
ejpam-856	149	7	207–218	207–218	NUM
ejpam-856	149	8	.	.	NOUN
ejpam-856	149	9	2001	2001	NUM
ejpam-856	149	10	.	.	PUNCT
ejpam-856	150	1	[	[	X
ejpam-856	150	2	3	3	X
ejpam-856	150	3	]	]	X
ejpam-856	150	4	j.	j.	PROPN
ejpam-856	150	5	dziok	dziok	PROPN
ejpam-856	150	6	and	and	CCONJ
ejpam-856	150	7	h.	h.	PROPN
ejpam-856	150	8	m.	m.	PROPN
ejpam-856	150	9	srivastava	srivastava	PROPN
ejpam-856	150	10	,	,	PUNCT
ejpam-856	150	11	classes	class	NOUN
ejpam-856	150	12	of	of	ADP
ejpam-856	150	13	analytic	analytic	ADJ
ejpam-856	150	14	functions	function	NOUN
ejpam-856	150	15	associated	associate	VERB
ejpam-856	150	16	with	with	ADP
ejpam-856	150	17	the	the	DET
ejpam-856	150	18	generalized	generalize	VERB
ejpam-856	150	19	hypergeometric	hypergeometric	ADJ
ejpam-856	150	20	function	function	NOUN
ejpam-856	150	21	,	,	PUNCT
ejpam-856	150	22	appl	appl	PROPN
ejpam-856	150	23	.	.	PROPN
ejpam-856	150	24	math	math	PROPN
ejpam-856	150	25	.	.	PUNCT
ejpam-856	151	1	comput	comput	NOUN
ejpam-856	151	2	.	.	PUNCT
ejpam-856	152	1	103	103	NUM
ejpam-856	152	2	,	,	PUNCT
ejpam-856	152	3	no	no	INTJ
ejpam-856	152	4	.	.	NOUN
ejpam-856	152	5	1	1	NUM
ejpam-856	152	6	,	,	PUNCT
ejpam-856	152	7	1–13	1–13	NOUN
ejpam-856	152	8	.	.	PUNCT
ejpam-856	152	9	1999	1999	NUM
ejpam-856	152	10	.	.	PUNCT
ejpam-856	153	1	[	[	X
ejpam-856	153	2	4	4	NUM
ejpam-856	153	3	]	]	PUNCT
ejpam-856	153	4	a.	a.	PROPN
ejpam-856	153	5	w.	w.	PROPN
ejpam-856	153	6	goodman	goodman	PROPN
ejpam-856	153	7	,	,	PUNCT
ejpam-856	153	8	univalent	univalent	ADJ
ejpam-856	153	9	functions	function	NOUN
ejpam-856	153	10	.	.	PUNCT
ejpam-856	154	1	vol	vol	NOUN
ejpam-856	154	2	.	.	PUNCT
ejpam-856	155	1	i	i	PRON
ejpam-856	155	2	,	,	PUNCT
ejpam-856	155	3	mariner	mariner	NOUN
ejpam-856	155	4	,	,	PUNCT
ejpam-856	155	5	tampa	tampa	PROPN
ejpam-856	155	6	,	,	PUNCT
ejpam-856	155	7	fl	fl	PROPN
ejpam-856	155	8	,	,	PUNCT
ejpam-856	155	9	1983	1983	NUM
ejpam-856	155	10	.	.	PUNCT
ejpam-856	156	1	[	[	X
ejpam-856	156	2	5	5	X
ejpam-856	156	3	]	]	PUNCT
ejpam-856	156	4	t.	t.	PROPN
ejpam-856	156	5	h.	h.	PROPN
ejpam-856	156	6	macgregor	macgregor	PROPN
ejpam-856	156	7	,	,	PUNCT
ejpam-856	156	8	majorization	majorization	NOUN
ejpam-856	156	9	by	by	ADP
ejpam-856	156	10	univalent	univalent	ADJ
ejpam-856	156	11	functions	function	NOUN
ejpam-856	156	12	,	,	PUNCT
ejpam-856	156	13	duke	duke	PROPN
ejpam-856	156	14	math	math	PROPN
ejpam-856	156	15	.	.	PUNCT
ejpam-856	157	1	j.	j.	PROPN
ejpam-856	157	2	34	34	PROPN
ejpam-856	157	3	,	,	PUNCT
ejpam-856	157	4	95–102	95–102	NUM
ejpam-856	157	5	.	.	NOUN
ejpam-856	157	6	1967	1967	NUM
ejpam-856	157	7	.	.	PUNCT
ejpam-856	158	1	[	[	X
ejpam-856	158	2	6	6	NUM
ejpam-856	158	3	]	]	PUNCT
ejpam-856	158	4	m.	m.	NOUN
ejpam-856	158	5	a.	a.	PROPN
ejpam-856	158	6	nasr	nasr	PROPN
ejpam-856	158	7	and	and	CCONJ
ejpam-856	158	8	m.	m.	PROPN
ejpam-856	158	9	k.	k.	PROPN
ejpam-856	158	10	aouf	aouf	PROPN
ejpam-856	158	11	,	,	PUNCT
ejpam-856	158	12	starlike	starlike	NOUN
ejpam-856	158	13	function	function	NOUN
ejpam-856	158	14	of	of	ADP
ejpam-856	158	15	complex	complex	ADJ
ejpam-856	158	16	order	order	NOUN
ejpam-856	158	17	,	,	PUNCT
ejpam-856	158	18	j.	j.	PROPN
ejpam-856	158	19	natur	natur	PROPN
ejpam-856	158	20	.	.	PUNCT
ejpam-856	159	1	sci	sci	PROPN
ejpam-856	159	2	.	.	PUNCT
ejpam-856	159	3	math	math	PROPN
ejpam-856	159	4	.	.	PUNCT
ejpam-856	160	1	25	25	NUM
ejpam-856	160	2	,	,	PUNCT
ejpam-856	160	3	no	no	INTJ
ejpam-856	160	4	.	.	NOUN
ejpam-856	160	5	1	1	NUM
ejpam-856	160	6	,	,	PUNCT
ejpam-856	160	7	1–12	1–12	NOUN
ejpam-856	160	8	.	.	PUNCT
ejpam-856	161	1	1985	1985	NUM
ejpam-856	161	2	.	.	PUNCT
ejpam-856	162	1	[	[	X
ejpam-856	162	2	7	7	X
ejpam-856	162	3	]	]	PUNCT
ejpam-856	162	4	z.	z.	PROPN
ejpam-856	162	5	nehari	nehari	PROPN
ejpam-856	162	6	,	,	PUNCT
ejpam-856	162	7	conformal	conformal	NOUN
ejpam-856	162	8	mapping	mapping	NOUN
ejpam-856	162	9	,	,	PUNCT
ejpam-856	162	10	mcgraw	mcgraw	PROPN
ejpam-856	162	11	-	-	PUNCT
ejpam-856	162	12	hill	hill	PROPN
ejpam-856	162	13	,	,	PUNCT
ejpam-856	162	14	inc	inc	PROPN
ejpam-856	162	15	.	.	PROPN
ejpam-856	162	16	,	,	PUNCT
ejpam-856	162	17	new	new	PROPN
ejpam-856	162	18	york	york	PROPN
ejpam-856	162	19	,	,	PUNCT
ejpam-856	162	20	toronto	toronto	PROPN
ejpam-856	162	21	,	,	PUNCT
ejpam-856	162	22	london	london	PROPN
ejpam-856	162	23	,	,	PUNCT
ejpam-856	162	24	1952	1952	NUM
ejpam-856	162	25	.	.	PUNCT
ejpam-856	163	1	[	[	X
ejpam-856	163	2	8	8	NUM
ejpam-856	163	3	]	]	PUNCT
ejpam-856	163	4	g.	g.	PROPN
ejpam-856	163	5	ş.	ş.	PROPN
ejpam-856	163	6	sălăgean	sălăgean	PROPN
ejpam-856	163	7	,	,	PUNCT
ejpam-856	163	8	subclasses	subclass	NOUN
ejpam-856	163	9	of	of	ADP
ejpam-856	163	10	univalent	univalent	ADJ
ejpam-856	163	11	functions	function	NOUN
ejpam-856	163	12	,	,	PUNCT
ejpam-856	163	13	in	in	ADP
ejpam-856	163	14	complex	complex	ADJ
ejpam-856	163	15	analysis	analysis	NOUN
ejpam-856	163	16	—	—	PUNCT
ejpam-856	163	17	fifth	fifth	ADJ
ejpam-856	163	18	romanianfinnish	romanianfinnish	ADJ
ejpam-856	163	19	seminar	seminar	NOUN
ejpam-856	163	20	,	,	PUNCT
ejpam-856	163	21	part	part	NOUN
ejpam-856	163	22	1	1	NUM
ejpam-856	163	23	(	(	PUNCT
ejpam-856	163	24	bucharest	bucharest	PROPN
ejpam-856	163	25	)	)	PUNCT
ejpam-856	163	26	,	,	PUNCT
ejpam-856	163	27	362–372	362–372	NUM
ejpam-856	163	28	lecture	lecture	NOUN
ejpam-856	163	29	notes	note	NOUN
ejpam-856	163	30	in	in	ADP
ejpam-856	163	31	math	math	NOUN
ejpam-856	163	32	.	.	PUNCT
ejpam-856	163	33	,	,	PUNCT
ejpam-856	163	34	1013	1013	NUM
ejpam-856	163	35	,	,	PUNCT
ejpam-856	163	36	springer	springer	NOUN
ejpam-856	163	37	,	,	PUNCT
ejpam-856	163	38	berlin	berlin	PROPN
ejpam-856	163	39	.	.	PUNCT
ejpam-856	163	40	1981	1981	NUM
ejpam-856	163	41	.	.	PUNCT
ejpam-856	164	1	[	[	X
ejpam-856	164	2	9	9	NUM
ejpam-856	164	3	]	]	X
ejpam-856	164	4	c.	c.	PROPN
ejpam-856	164	5	selvaraj	selvaraj	PROPN
ejpam-856	164	6	and	and	CCONJ
ejpam-856	164	7	k.	k.	PROPN
ejpam-856	164	8	a.	a.	PROPN
ejpam-856	164	9	selvakumarn	selvakumarn	PROPN
ejpam-856	164	10	,	,	PUNCT
ejpam-856	164	11	majorization	majorization	NOUN
ejpam-856	164	12	problems	problem	NOUN
ejpam-856	164	13	for	for	ADP
ejpam-856	164	14	certain	certain	ADJ
ejpam-856	164	15	classes	class	NOUN
ejpam-856	164	16	of	of	ADP
ejpam-856	164	17	analytic	analytic	ADJ
ejpam-856	164	18	functions	function	NOUN
ejpam-856	164	19	,	,	PUNCT
ejpam-856	164	20	int	int	NOUN
ejpam-856	164	21	.	.	PUNCT
ejpam-856	164	22	math	math	PROPN
ejpam-856	164	23	.	.	PUNCT
ejpam-856	165	1	forum	forum	PROPN
ejpam-856	165	2	,	,	PUNCT
ejpam-856	165	3	accepted	accept	VERB
ejpam-856	165	4	article	article	NOUN
ejpam-856	165	5	in	in	ADP
ejpam-856	165	6	press	press	NOUN
ejpam-856	165	7	.	.	PUNCT
ejpam-856	166	1	[	[	X
ejpam-856	166	2	10	10	NUM
ejpam-856	166	3	]	]	X
ejpam-856	166	4	p.	p.	NOUN
ejpam-856	166	5	wiatrowski	wiatrowski	PROPN
ejpam-856	166	6	,	,	PUNCT
ejpam-856	166	7	the	the	DET
ejpam-856	166	8	coefficients	coefficient	NOUN
ejpam-856	166	9	of	of	ADP
ejpam-856	166	10	a	a	DET
ejpam-856	166	11	certain	certain	ADJ
ejpam-856	166	12	family	family	NOUN
ejpam-856	166	13	of	of	ADP
ejpam-856	166	14	holomorphic	holomorphic	ADJ
ejpam-856	166	15	functions	function	NOUN
ejpam-856	166	16	,	,	PUNCT
ejpam-856	166	17	zeszyty	zeszyty	PROPN
ejpam-856	166	18	nauk	nauk	PROPN
ejpam-856	166	19	.	.	PUNCT
ejpam-856	167	1	uniw	uniw	PROPN
ejpam-856	167	2	.	.	PUNCT
ejpam-856	168	1	łódz	łódz	PROPN
ejpam-856	168	2	.	.	PUNCT
ejpam-856	169	1	nauki	nauki	PROPN
ejpam-856	169	2	mat	mat	PROPN
ejpam-856	169	3	.	.	PUNCT
ejpam-856	169	4	przyrod	przyrod	PROPN
ejpam-856	169	5	.	.	PUNCT
ejpam-856	170	1	ser	ser	PROPN
ejpam-856	170	2	.	.	PUNCT
ejpam-856	170	3	ii	ii	PROPN
ejpam-856	171	1	no	no	INTJ
ejpam-856	171	2	.	.	PROPN
ejpam-856	171	3	39	39	NUM
ejpam-856	172	1	mat	mat	NOUN
ejpam-856	172	2	.	.	PROPN
ejpam-856	172	3	,	,	PUNCT
ejpam-856	172	4	75–85	75–85	NUM
ejpam-856	172	5	.	.	PUNCT
ejpam-856	172	6	1971	1971	NUM
ejpam-856	172	7	.	.	PUNCT