id	sid	tid	token	lemma	pos
ejpam-747	1	1	13_747_sharma.dvi	13_747_sharma.dvi	NUM
ejpam-747	1	2	european	european	ADJ
ejpam-747	1	3	journal	journal	PROPN
ejpam-747	1	4	of	of	ADP
ejpam-747	1	5	pure	pure	ADJ
ejpam-747	1	6	and	and	CCONJ
ejpam-747	1	7	applied	apply	VERB
ejpam-747	1	8	mathematics	mathematic	NOUN
ejpam-747	1	9	vol	vol	NOUN
ejpam-747	1	10	.	.	PUNCT
ejpam-747	2	1	3	3	NUM
ejpam-747	2	2	,	,	PUNCT
ejpam-747	2	3	no	no	INTJ
ejpam-747	2	4	.	.	NOUN
ejpam-747	2	5	6	6	NUM
ejpam-747	2	6	,	,	PUNCT
ejpam-747	2	7	2010	2010	NUM
ejpam-747	2	8	,	,	PUNCT
ejpam-747	2	9	1093	1093	NUM
ejpam-747	2	10	-	-	SYM
ejpam-747	2	11	1112	1112	NUM
ejpam-747	2	12	issn	issn	PROPN
ejpam-747	2	13	1307	1307	NUM
ejpam-747	2	14	-	-	SYM
ejpam-747	2	15	5543	5543	NUM
ejpam-747	2	16	–	–	PUNCT
ejpam-747	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-747	2	18	special	special	ADJ
ejpam-747	2	19	issue	issue	NOUN
ejpam-747	2	20	on	on	ADP
ejpam-747	2	21	complex	complex	ADJ
ejpam-747	2	22	analysis	analysis	NOUN
ejpam-747	2	23	:	:	PUNCT
ejpam-747	2	24	theory	theory	NOUN
ejpam-747	2	25	and	and	CCONJ
ejpam-747	2	26	applications	application	NOUN
ejpam-747	2	27	dedicated	dedicate	VERB
ejpam-747	2	28	to	to	ADP
ejpam-747	2	29	professor	professor	PROPN
ejpam-747	2	30	hari	hari	PROPN
ejpam-747	2	31	m.	m.	PROPN
ejpam-747	2	32	srivastava	srivastava	PROPN
ejpam-747	2	33	,	,	PUNCT
ejpam-747	2	34	on	on	ADP
ejpam-747	2	35	the	the	DET
ejpam-747	2	36	occasion	occasion	NOUN
ejpam-747	2	37	of	of	ADP
ejpam-747	2	38	his	his	PRON
ejpam-747	2	39	70th	70th	ADJ
ejpam-747	2	40	birthday	birthday	NOUN
ejpam-747	2	41	some	some	DET
ejpam-747	2	42	properties	property	NOUN
ejpam-747	2	43	of	of	ADP
ejpam-747	2	44	a	a	DET
ejpam-747	2	45	class	class	NOUN
ejpam-747	2	46	of	of	ADP
ejpam-747	2	47	p	p	NOUN
ejpam-747	2	48	-	-	PUNCT
ejpam-747	2	49	valent	valent	NOUN
ejpam-747	2	50	analytic	analytic	ADJ
ejpam-747	2	51	functions	function	NOUN
ejpam-747	2	52	associated	associate	VERB
ejpam-747	2	53	with	with	ADP
ejpam-747	2	54	convolution	convolution	NOUN
ejpam-747	2	55	poonam	poonam	PROPN
ejpam-747	2	56	sharma	sharma	PROPN
ejpam-747	2	57	1,∗	1,∗	PROPN
ejpam-747	2	58	,	,	PUNCT
ejpam-747	2	59	prachi	prachi	PROPN
ejpam-747	2	60	srivastava	srivastava	PROPN
ejpam-747	2	61	2	2	NUM
ejpam-747	2	62	1	1	NUM
ejpam-747	2	63	department	department	NOUN
ejpam-747	2	64	of	of	ADP
ejpam-747	2	65	mathematics	mathematic	NOUN
ejpam-747	2	66	and	and	CCONJ
ejpam-747	2	67	astronomy	astronomy	NOUN
ejpam-747	2	68	,	,	PUNCT
ejpam-747	2	69	university	university	NOUN
ejpam-747	2	70	of	of	ADP
ejpam-747	2	71	lucknow	lucknow	PROPN
ejpam-747	2	72	,	,	PUNCT
ejpam-747	2	73	lucknow	lucknow	PROPN
ejpam-747	2	74	226007	226007	NUM
ejpam-747	2	75	india	india	PROPN
ejpam-747	2	76	2	2	NUM
ejpam-747	2	77	department	department	NOUN
ejpam-747	2	78	of	of	ADP
ejpam-747	2	79	mathematics	mathematic	NOUN
ejpam-747	2	80	,	,	PUNCT
ejpam-747	2	81	karamat	karamat	NOUN
ejpam-747	2	82	hussain	hussain	PROPN
ejpam-747	2	83	muslim	muslim	PROPN
ejpam-747	2	84	girls	girls	PROPN
ejpam-747	2	85	p.g	p.g	PROPN
ejpam-747	2	86	.	.	PROPN
ejpam-747	2	87	college	college	PROPN
ejpam-747	2	88	,	,	PUNCT
ejpam-747	2	89	nishatganj	nishatganj	NOUN
ejpam-747	2	90	,	,	PUNCT
ejpam-747	2	91	lucknow	lucknow	PROPN
ejpam-747	2	92	,	,	PUNCT
ejpam-747	2	93	india	india	PROPN
ejpam-747	2	94	abstract	abstract	NOUN
ejpam-747	2	95	.	.	PUNCT
ejpam-747	3	1	in	in	ADP
ejpam-747	3	2	this	this	DET
ejpam-747	3	3	paper	paper	NOUN
ejpam-747	3	4	,	,	PUNCT
ejpam-747	3	5	we	we	PRON
ejpam-747	3	6	define	define	VERB
ejpam-747	3	7	a	a	DET
ejpam-747	3	8	class	class	NOUN
ejpam-747	4	1	ℜg	ℜg	PROPN
ejpam-747	4	2	h	h	NOUN
ejpam-747	4	3	�	�	PROPN
ejpam-747	4	4	p	p	PROPN
ejpam-747	4	5	,	,	PUNCT
ejpam-747	4	6	m	m	PROPN
ejpam-747	4	7	,	,	PUNCT
ejpam-747	4	8	β	β	X
ejpam-747	4	9	�	�	PROPN
ejpam-747	4	10	associated	associate	VERB
ejpam-747	4	11	with	with	ADP
ejpam-747	4	12	convolution	convolution	NOUN
ejpam-747	4	13	of	of	ADP
ejpam-747	4	14	p	p	NOUN
ejpam-747	4	15	-	-	PUNCT
ejpam-747	4	16	valent	valent	NOUN
ejpam-747	4	17	analytic	analytic	ADJ
ejpam-747	4	18	functions	function	NOUN
ejpam-747	4	19	.	.	PUNCT
ejpam-747	5	1	some	some	DET
ejpam-747	5	2	properties	property	NOUN
ejpam-747	5	3	in	in	ADP
ejpam-747	5	4	the	the	DET
ejpam-747	5	5	form	form	NOUN
ejpam-747	5	6	of	of	ADP
ejpam-747	5	7	coefficient	coefficient	NOUN
ejpam-747	5	8	inequality	inequality	NOUN
ejpam-747	5	9	,	,	PUNCT
ejpam-747	5	10	growth	growth	NOUN
ejpam-747	5	11	and	and	CCONJ
ejpam-747	5	12	distortion	distortion	NOUN
ejpam-747	5	13	bounds	bound	NOUN
ejpam-747	5	14	,	,	PUNCT
ejpam-747	5	15	sufficient	sufficient	ADJ
ejpam-747	5	16	conditions	condition	NOUN
ejpam-747	5	17	with	with	ADP
ejpam-747	5	18	the	the	DET
ejpam-747	5	19	help	help	NOUN
ejpam-747	5	20	of	of	ADP
ejpam-747	5	21	various	various	ADJ
ejpam-747	5	22	lemmas	lemmas	ADJ
ejpam-747	5	23	,	,	PUNCT
ejpam-747	5	24	integral	integral	ADJ
ejpam-747	5	25	means	mean	NOUN
ejpam-747	5	26	inequality	inequality	NOUN
ejpam-747	5	27	for	for	ADP
ejpam-747	5	28	convolution	convolution	NOUN
ejpam-747	5	29	of	of	ADP
ejpam-747	5	30	two	two	NUM
ejpam-747	5	31	functions	function	NOUN
ejpam-747	5	32	and	and	CCONJ
ejpam-747	5	33	a	a	DET
ejpam-747	5	34	set	set	NOUN
ejpam-747	5	35	of	of	ADP
ejpam-747	5	36	class	class	NOUN
ejpam-747	5	37	preserving	preserve	VERB
ejpam-747	5	38	integral	integral	ADJ
ejpam-747	5	39	operators	operator	NOUN
ejpam-747	5	40	of	of	ADP
ejpam-747	5	41	functions	function	NOUN
ejpam-747	5	42	belonging	belong	VERB
ejpam-747	5	43	to	to	ADP
ejpam-747	5	44	this	this	DET
ejpam-747	5	45	class	class	NOUN
ejpam-747	5	46	are	be	AUX
ejpam-747	5	47	studied	study	VERB
ejpam-747	5	48	.	.	PUNCT
ejpam-747	6	1	2000	2000	NUM
ejpam-747	6	2	mathematics	mathematic	NOUN
ejpam-747	6	3	subject	subject	NOUN
ejpam-747	6	4	classifications	classification	NOUN
ejpam-747	6	5	:	:	PUNCT
ejpam-747	6	6	primary	primary	ADJ
ejpam-747	6	7	30c45	30c45	NUM
ejpam-747	6	8	,	,	PUNCT
ejpam-747	6	9	30c50	30c50	NUM
ejpam-747	6	10	,	,	PUNCT
ejpam-747	6	11	30c55	30c55	NUM
ejpam-747	6	12	key	key	ADJ
ejpam-747	6	13	words	word	NOUN
ejpam-747	6	14	and	and	CCONJ
ejpam-747	6	15	phrases	phrase	NOUN
ejpam-747	6	16	:	:	PUNCT
ejpam-747	6	17	analytic	analytic	ADJ
ejpam-747	6	18	functions	function	NOUN
ejpam-747	6	19	,	,	PUNCT
ejpam-747	6	20	convolution	convolution	NOUN
ejpam-747	6	21	,	,	PUNCT
ejpam-747	6	22	starlike	starlike	NOUN
ejpam-747	6	23	functions	function	NOUN
ejpam-747	6	24	,	,	PUNCT
ejpam-747	6	25	convex	convex	NOUN
ejpam-747	6	26	functions	function	NOUN
ejpam-747	6	27	,	,	PUNCT
ejpam-747	6	28	closeto	closeto	NOUN
ejpam-747	6	29	-	-	PUNCT
ejpam-747	6	30	convex	convex	NOUN
ejpam-747	6	31	functions	function	NOUN
ejpam-747	6	32	1	1	NUM
ejpam-747	6	33	.	.	PUNCT
ejpam-747	7	1	introduction	introduction	NOUN
ejpam-747	7	2	let	let	VERB
ejpam-747	7	3	ap	ap	PROPN
ejpam-747	7	4	denotes	denote	VERB
ejpam-747	7	5	a	a	DET
ejpam-747	7	6	class	class	NOUN
ejpam-747	7	7	of	of	ADP
ejpam-747	7	8	functions	function	NOUN
ejpam-747	7	9	of	of	ADP
ejpam-747	7	10	the	the	DET
ejpam-747	7	11	form	form	NOUN
ejpam-747	7	12	:	:	PUNCT
ejpam-747	7	13	f	f	PROPN
ejpam-747	7	14	(	(	PUNCT
ejpam-747	7	15	z	z	NOUN
ejpam-747	7	16	)	)	PUNCT
ejpam-747	7	17	=	=	SYM
ejpam-747	8	1	zp	zp	PROPN
ejpam-747	9	1	+	+	CCONJ
ejpam-747	9	2	∞	∞	NUM
ejpam-747	9	3	∑	∑	PUNCT
ejpam-747	9	4	k=1	k=1	PROPN
ejpam-747	9	5	ap+kzp+k	ap+kzp+k	PUNCT
ejpam-747	9	6	�	�	PROPN
ejpam-747	9	7	p	p	NOUN
ejpam-747	9	8	∈	∈	PROPN
ejpam-747	9	9	n	n	NOUN
ejpam-747	9	10	=	=	SYM
ejpam-747	9	11	1,2,3	1,2,3	NUM
ejpam-747	9	12	.	.	PUNCT
ejpam-747	9	13	.	.	PUNCT
ejpam-747	9	14	.	.	PUNCT
ejpam-747	10	1	�	�	PROPN
ejpam-747	10	2	,	,	PUNCT
ejpam-747	10	3	(	(	PUNCT
ejpam-747	10	4	1	1	X
ejpam-747	10	5	)	)	PUNCT
ejpam-747	10	6	which	which	PRON
ejpam-747	10	7	are	be	AUX
ejpam-747	10	8	analytic	analytic	ADJ
ejpam-747	10	9	and	and	CCONJ
ejpam-747	10	10	p	p	NOUN
ejpam-747	10	11	-	-	PUNCT
ejpam-747	10	12	valent	valent	NOUN
ejpam-747	10	13	in	in	ADP
ejpam-747	10	14	the	the	DET
ejpam-747	10	15	open	open	ADJ
ejpam-747	10	16	unit	unit	NOUN
ejpam-747	10	17	disk	disk	NOUN
ejpam-747	10	18	∆=	∆=	NOUN
ejpam-747	10	19	{	{	PUNCT
ejpam-747	10	20	z	z	NOUN
ejpam-747	10	21	∈	∈	PROPN
ejpam-747	10	22	c	c	NOUN
ejpam-747	10	23	:	:	PUNCT
ejpam-747	10	24	|z|	|z|	NOUN
ejpam-747	10	25	<	<	X
ejpam-747	10	26	1	1	NUM
ejpam-747	10	27	}	}	PUNCT
ejpam-747	10	28	.	.	PUNCT
ejpam-747	11	1	let	let	VERB
ejpam-747	11	2	g	g	NOUN
ejpam-747	11	3	,	,	PUNCT
ejpam-747	11	4	h	h	PROPN
ejpam-747	11	5	∈	∈	PROPN
ejpam-747	11	6	ap	ap	PROPN
ejpam-747	11	7	be	be	AUX
ejpam-747	11	8	of	of	ADP
ejpam-747	11	9	the	the	DET
ejpam-747	11	10	form	form	NOUN
ejpam-747	11	11	:	:	PUNCT
ejpam-747	11	12	g(z	g(z	ADJ
ejpam-747	11	13	)	)	PUNCT
ejpam-747	12	1	=	=	PUNCT
ejpam-747	12	2	zp	zp	PROPN
ejpam-747	12	3	+	+	CCONJ
ejpam-747	12	4	∞	∞	NUM
ejpam-747	12	5	∑	∑	PUNCT
ejpam-747	12	6	k=1	k=1	PROPN
ejpam-747	12	7	bp+kzp+k	bp+kzp+k	ADV
ejpam-747	12	8	,	,	PUNCT
ejpam-747	12	9	bp+k	bp+k	PROPN
ejpam-747	12	10	≥	≥	NUM
ejpam-747	12	11	0	0	NUM
ejpam-747	12	12	(	(	PUNCT
ejpam-747	12	13	2	2	X
ejpam-747	12	14	)	)	PUNCT
ejpam-747	12	15	∗corresponding	∗corresponde	VERB
ejpam-747	12	16	author	author	NOUN
ejpam-747	12	17	.	.	PUNCT
ejpam-747	13	1	email	email	NOUN
ejpam-747	13	2	addresses	address	NOUN
ejpam-747	13	3	:	:	PUNCT
ejpam-747	13	4	poonambaba	poonambaba	PROPN
ejpam-747	13	5	�	�	PROPN
ejpam-747	13	6	yahoo	yahoo	PROPN
ejpam-747	13	7	.	.	PUNCT
ejpam-747	14	1	om	om	PROPN
ejpam-747	14	2	(	(	PUNCT
ejpam-747	14	3	p.	p.	PROPN
ejpam-747	14	4	sharma	sharma	PROPN
ejpam-747	14	5	)	)	PUNCT
ejpam-747	14	6	,	,	PUNCT
ejpam-747	14	7	pra	pra	PROPN
ejpam-747	14	8	hi2384	hi2384	PROPN
ejpam-747	14	9	�	�	PROPN
ejpam-747	14	10	gmail	gmail	NOUN
ejpam-747	14	11	.	.	PUNCT
ejpam-747	15	1	om	om	PROPN
ejpam-747	15	2	(	(	PUNCT
ejpam-747	15	3	p.	p.	PROPN
ejpam-747	15	4	srivastava	srivastava	PROPN
ejpam-747	15	5	)	)	PUNCT
ejpam-747	15	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-747	16	1	1093	1093	NUM
ejpam-747	17	1	c	c	X
ejpam-747	17	2	©	©	PROPN
ejpam-747	17	3	2010	2010	NUM
ejpam-747	17	4	ejpam	ejpam	NOUN
ejpam-747	17	5	all	all	DET
ejpam-747	17	6	rights	right	NOUN
ejpam-747	17	7	reserved	reserve	VERB
ejpam-747	17	8	.	.	PUNCT
ejpam-747	18	1	p.	p.	NOUN
ejpam-747	18	2	sharma	sharma	PROPN
ejpam-747	18	3	,	,	PUNCT
ejpam-747	18	4	p.	p.	PROPN
ejpam-747	18	5	srivastava	srivastava	PROPN
ejpam-747	18	6	/	/	SYM
ejpam-747	18	7	eur	eur	PROPN
ejpam-747	18	8	.	.	PUNCT
ejpam-747	19	1	j.	j.	PROPN
ejpam-747	19	2	pure	pure	PROPN
ejpam-747	19	3	appl	appl	PROPN
ejpam-747	19	4	.	.	PROPN
ejpam-747	19	5	math	math	PROPN
ejpam-747	19	6	,	,	PUNCT
ejpam-747	19	7	3	3	NUM
ejpam-747	19	8	(	(	PUNCT
ejpam-747	19	9	2010	2010	NUM
ejpam-747	19	10	)	)	PUNCT
ejpam-747	19	11	,	,	PUNCT
ejpam-747	19	12	1093	1093	NUM
ejpam-747	19	13	-	-	SYM
ejpam-747	19	14	1112	1112	NUM
ejpam-747	19	15	1094	1094	NUM
ejpam-747	19	16	and	and	CCONJ
ejpam-747	19	17	h(z	h(z	NOUN
ejpam-747	19	18	)	)	PUNCT
ejpam-747	19	19	=	=	SYM
ejpam-747	20	1	zp	zp	NOUN
ejpam-747	21	1	+	+	CCONJ
ejpam-747	21	2	∞	∞	NUM
ejpam-747	21	3	∑	∑	PUNCT
ejpam-747	21	4	k=1	k=1	X
ejpam-747	21	5	cp+kzp+k	cp+kzp+k	X
ejpam-747	21	6	,	,	PUNCT
ejpam-747	21	7	cp+k	cp+k	X
ejpam-747	21	8	≥	≥	NOUN
ejpam-747	21	9	0	0	NUM
ejpam-747	21	10	.	.	PUNCT
ejpam-747	22	1	(	(	PUNCT
ejpam-747	22	2	3	3	X
ejpam-747	22	3	)	)	PUNCT
ejpam-747	22	4	a	a	DET
ejpam-747	22	5	function	function	NOUN
ejpam-747	22	6	f	f	PROPN
ejpam-747	22	7	∈	∈	PROPN
ejpam-747	22	8	ap	ap	PROPN
ejpam-747	22	9	is	be	AUX
ejpam-747	22	10	said	say	VERB
ejpam-747	22	11	to	to	PART
ejpam-747	22	12	be	be	AUX
ejpam-747	22	13	p	p	ADJ
ejpam-747	22	14	-	-	PUNCT
ejpam-747	22	15	valently	valently	ADV
ejpam-747	22	16	starlike	starlike	NOUN
ejpam-747	22	17	of	of	ADP
ejpam-747	22	18	order	order	NOUN
ejpam-747	22	19	α	α	PROPN
ejpam-747	22	20	in	in	ADP
ejpam-747	22	21	∆	∆	PROPN
ejpam-747	22	22	,	,	PUNCT
ejpam-747	22	23	if	if	SCONJ
ejpam-747	22	24	it	it	PRON
ejpam-747	22	25	satisfies	satisfy	VERB
ejpam-747	22	26	the	the	DET
ejpam-747	22	27	inequality	inequality	NOUN
ejpam-747	22	28	re	re	ADP
ejpam-747	22	29	(	(	PUNCT
ejpam-747	22	30	z	z	NOUN
ejpam-747	22	31	f	f	NOUN
ejpam-747	23	1	′	′	NUM
ejpam-747	24	1	(	(	PUNCT
ejpam-747	24	2	z	z	NOUN
ejpam-747	24	3	)	)	PUNCT
ejpam-747	24	4	f	f	NOUN
ejpam-747	24	5	(	(	PUNCT
ejpam-747	24	6	z	z	NOUN
ejpam-747	24	7	)	)	PUNCT
ejpam-747	24	8	)	)	PUNCT
ejpam-747	24	9	>	>	X
ejpam-747	25	1	α	α	PROPN
ejpam-747	25	2	�	�	PROPN
ejpam-747	25	3	z	z	PROPN
ejpam-747	25	4	∈∆	∈∆	NOUN
ejpam-747	25	5	;	;	PUNCT
ejpam-747	25	6	0≤	0≤	NUM
ejpam-747	25	7	α	α	NOUN
ejpam-747	25	8	<	<	X
ejpam-747	25	9	p	p	X
ejpam-747	25	10	;	;	PUNCT
ejpam-747	25	11	p	p	PROPN
ejpam-747	25	12	∈	∈	PROPN
ejpam-747	25	13	n	n	PRON
ejpam-747	25	14	�	�	PROPN
ejpam-747	25	15	.	.	PUNCT
ejpam-747	26	1	the	the	DET
ejpam-747	26	2	class	class	NOUN
ejpam-747	26	3	of	of	ADP
ejpam-747	26	4	all	all	DET
ejpam-747	26	5	p	p	ADJ
ejpam-747	26	6	-	-	PUNCT
ejpam-747	26	7	valent	valent	NOUN
ejpam-747	26	8	starlike	starlike	NOUN
ejpam-747	26	9	functions	function	NOUN
ejpam-747	26	10	of	of	ADP
ejpam-747	26	11	order	order	NOUN
ejpam-747	26	12	α	α	PRON
ejpam-747	26	13	is	be	AUX
ejpam-747	26	14	denoted	denote	VERB
ejpam-747	26	15	by	by	ADP
ejpam-747	26	16	s∗p	s∗p	NUM
ejpam-747	26	17	(	(	PUNCT
ejpam-747	26	18	α	α	NOUN
ejpam-747	26	19	)	)	PUNCT
ejpam-747	26	20	.	.	PUNCT
ejpam-747	27	1	on	on	ADP
ejpam-747	27	2	the	the	DET
ejpam-747	27	3	other	other	ADJ
ejpam-747	27	4	hand	hand	NOUN
ejpam-747	27	5	,	,	PUNCT
ejpam-747	27	6	a	a	DET
ejpam-747	27	7	function	function	NOUN
ejpam-747	27	8	f	f	PROPN
ejpam-747	27	9	∈	∈	PROPN
ejpam-747	27	10	ap	ap	PROPN
ejpam-747	27	11	is	be	AUX
ejpam-747	27	12	said	say	VERB
ejpam-747	27	13	to	to	PART
ejpam-747	27	14	be	be	AUX
ejpam-747	27	15	p	p	ADJ
ejpam-747	27	16	-	-	PUNCT
ejpam-747	27	17	valently	valently	ADV
ejpam-747	27	18	convex	convex	NOUN
ejpam-747	27	19	of	of	ADP
ejpam-747	27	20	order	order	NOUN
ejpam-747	27	21	α	α	NOUN
ejpam-747	27	22	in	in	ADP
ejpam-747	27	23	∆	∆	PROPN
ejpam-747	27	24	,	,	PUNCT
ejpam-747	27	25	if	if	SCONJ
ejpam-747	27	26	it	it	PRON
ejpam-747	27	27	satisfies	satisfy	VERB
ejpam-747	27	28	the	the	DET
ejpam-747	27	29	inequality	inequality	NOUN
ejpam-747	27	30	re	re	ADP
ejpam-747	27	31	(	(	PUNCT
ejpam-747	27	32	1	1	NUM
ejpam-747	27	33	+	+	NUM
ejpam-747	27	34	z	z	NOUN
ejpam-747	27	35	f	f	X
ejpam-747	28	1	′′	′′	PROPN
ejpam-747	28	2	(	(	PUNCT
ejpam-747	28	3	z	z	PROPN
ejpam-747	28	4	)	)	PUNCT
ejpam-747	28	5	f	f	NOUN
ejpam-747	29	1	′	′	NUM
ejpam-747	29	2	(	(	PUNCT
ejpam-747	29	3	z	z	NOUN
ejpam-747	29	4	)	)	PUNCT
ejpam-747	29	5	)	)	PUNCT
ejpam-747	29	6	>	>	X
ejpam-747	30	1	α	α	PROPN
ejpam-747	30	2	�	�	PROPN
ejpam-747	30	3	z	z	PROPN
ejpam-747	30	4	∈∆	∈∆	NOUN
ejpam-747	30	5	;	;	PUNCT
ejpam-747	30	6	0≤	0≤	NUM
ejpam-747	30	7	α	α	NOUN
ejpam-747	30	8	<	<	X
ejpam-747	30	9	p	p	X
ejpam-747	30	10	;	;	PUNCT
ejpam-747	30	11	p	p	PROPN
ejpam-747	30	12	∈	∈	PROPN
ejpam-747	30	13	n	n	PRON
ejpam-747	30	14	�	�	PROPN
ejpam-747	30	15	.	.	PUNCT
ejpam-747	31	1	the	the	DET
ejpam-747	31	2	class	class	NOUN
ejpam-747	31	3	of	of	ADP
ejpam-747	31	4	all	all	DET
ejpam-747	31	5	p	p	NOUN
ejpam-747	31	6	-	-	PUNCT
ejpam-747	31	7	valent	valent	NOUN
ejpam-747	31	8	convex	convex	NOUN
ejpam-747	31	9	functions	function	NOUN
ejpam-747	31	10	of	of	ADP
ejpam-747	31	11	order	order	NOUN
ejpam-747	31	12	α	α	PRON
ejpam-747	31	13	is	be	AUX
ejpam-747	31	14	denoted	denote	VERB
ejpam-747	31	15	by	by	ADP
ejpam-747	31	16	kp	kp	PROPN
ejpam-747	31	17	(	(	PUNCT
ejpam-747	31	18	α	α	NOUN
ejpam-747	31	19	)	)	PUNCT
ejpam-747	31	20	.	.	PUNCT
ejpam-747	32	1	furthermore	furthermore	ADV
ejpam-747	32	2	,	,	PUNCT
ejpam-747	32	3	a	a	DET
ejpam-747	32	4	function	function	NOUN
ejpam-747	32	5	f	f	PROPN
ejpam-747	32	6	∈	∈	PROPN
ejpam-747	32	7	ap	ap	PROPN
ejpam-747	32	8	is	be	AUX
ejpam-747	32	9	said	say	VERB
ejpam-747	32	10	to	to	PART
ejpam-747	32	11	be	be	AUX
ejpam-747	32	12	p	p	ADJ
ejpam-747	32	13	-	-	PUNCT
ejpam-747	32	14	valently	valently	ADV
ejpam-747	32	15	close	close	ADJ
ejpam-747	32	16	-	-	PUNCT
ejpam-747	32	17	to	to	ADP
ejpam-747	32	18	-	-	PUNCT
ejpam-747	32	19	convex	convex	NOUN
ejpam-747	32	20	of	of	ADP
ejpam-747	32	21	order	order	NOUN
ejpam-747	32	22	α	α	NOUN
ejpam-747	32	23	in	in	ADP
ejpam-747	32	24	∆	∆	PROPN
ejpam-747	32	25	,	,	PUNCT
ejpam-747	32	26	if	if	SCONJ
ejpam-747	32	27	it	it	PRON
ejpam-747	32	28	satisfies	satisfy	VERB
ejpam-747	32	29	the	the	DET
ejpam-747	32	30	inequality	inequality	NOUN
ejpam-747	32	31	re	re	ADP
ejpam-747	32	32	¦	¦	PROPN
ejpam-747	32	33	z1−p	z1−p	PROPN
ejpam-747	32	34	f	f	NOUN
ejpam-747	33	1	′	′	NUM
ejpam-747	33	2	(	(	PUNCT
ejpam-747	33	3	z	z	NOUN
ejpam-747	33	4	)	)	PUNCT
ejpam-747	34	1	©	©	NOUN
ejpam-747	34	2	>	>	X
ejpam-747	34	3	α	α	PROPN
ejpam-747	34	4	�	�	PROPN
ejpam-747	34	5	z	z	PROPN
ejpam-747	34	6	∈∆	∈∆	NOUN
ejpam-747	34	7	;	;	PUNCT
ejpam-747	34	8	0≤	0≤	NUM
ejpam-747	34	9	α	α	NOUN
ejpam-747	34	10	<	<	X
ejpam-747	34	11	p	p	X
ejpam-747	34	12	;	;	PUNCT
ejpam-747	34	13	p	p	PROPN
ejpam-747	34	14	∈	∈	PROPN
ejpam-747	34	15	n	n	PRON
ejpam-747	34	16	�	�	PROPN
ejpam-747	34	17	.	.	PUNCT
ejpam-747	35	1	the	the	DET
ejpam-747	35	2	class	class	NOUN
ejpam-747	35	3	of	of	ADP
ejpam-747	35	4	all	all	DET
ejpam-747	35	5	p	p	NOUN
ejpam-747	35	6	-	-	PUNCT
ejpam-747	35	7	valent	valent	NOUN
ejpam-747	35	8	close	close	NOUN
ejpam-747	35	9	-	-	PUNCT
ejpam-747	35	10	to	to	ADP
ejpam-747	35	11	-	-	PUNCT
ejpam-747	35	12	convex	convex	NOUN
ejpam-747	35	13	functions	function	NOUN
ejpam-747	35	14	of	of	ADP
ejpam-747	35	15	order	order	NOUN
ejpam-747	35	16	α	α	PRON
ejpam-747	35	17	is	be	AUX
ejpam-747	35	18	denoted	denote	VERB
ejpam-747	35	19	by	by	ADP
ejpam-747	35	20	ckp	ckp	PROPN
ejpam-747	35	21	(	(	PUNCT
ejpam-747	35	22	α	α	NOUN
ejpam-747	35	23	)	)	PUNCT
ejpam-747	35	24	.	.	PUNCT
ejpam-747	36	1	if	if	SCONJ
ejpam-747	36	2	f	f	PROPN
ejpam-747	36	3	∈	∈	PROPN
ejpam-747	36	4	ap	ap	PROPN
ejpam-747	36	5	satisfies	satisfy	VERB
ejpam-747	36	6	�	�	PROPN
ejpam-747	36	7	�	�	PROPN
ejpam-747	36	8	�	�	PROPN
ejpam-747	36	9	�	�	PROPN
ejpam-747	36	10	�	�	PROPN
ejpam-747	36	11	arg	arg	NOUN
ejpam-747	37	1	z	z	PROPN
ejpam-747	37	2	f	f	NOUN
ejpam-747	38	1	′	′	NUM
ejpam-747	39	1	(	(	PUNCT
ejpam-747	39	2	z	z	NOUN
ejpam-747	39	3	)	)	PUNCT
ejpam-747	39	4	f	f	NOUN
ejpam-747	39	5	(	(	PUNCT
ejpam-747	39	6	z	z	NOUN
ejpam-747	39	7	)	)	PUNCT
ejpam-747	39	8	�	�	PROPN
ejpam-747	39	9	�	�	PROPN
ejpam-747	39	10	�	�	PROPN
ejpam-747	39	11	�	�	PROPN
ejpam-747	39	12	�	�	PROPN
ejpam-747	39	13	<	<	X
ejpam-747	39	14	β	β	X
ejpam-747	39	15	p	p	X
ejpam-747	39	16	π	π	PROPN
ejpam-747	39	17	2	2	NUM
ejpam-747	39	18	(	(	PUNCT
ejpam-747	39	19	z	z	NOUN
ejpam-747	39	20	∈∆	∈∆	NOUN
ejpam-747	39	21	)	)	PUNCT
ejpam-747	39	22	,	,	PUNCT
ejpam-747	39	23	for	for	ADP
ejpam-747	39	24	some	some	PRON
ejpam-747	39	25	0	0	NUM
ejpam-747	39	26	<	<	X
ejpam-747	39	27	β	β	X
ejpam-747	39	28	≤	≤	NOUN
ejpam-747	39	29	p	p	X
ejpam-747	39	30	,	,	PUNCT
ejpam-747	39	31	then	then	ADV
ejpam-747	39	32	f	f	PROPN
ejpam-747	39	33	is	be	AUX
ejpam-747	39	34	said	say	VERB
ejpam-747	39	35	to	to	PART
ejpam-747	39	36	be	be	AUX
ejpam-747	39	37	p	p	VERB
ejpam-747	39	38	-	-	PUNCT
ejpam-747	39	39	valently	valently	ADV
ejpam-747	39	40	strongly	strongly	ADV
ejpam-747	39	41	starlike	starlike	ADJ
ejpam-747	39	42	function	function	NOUN
ejpam-747	39	43	of	of	ADP
ejpam-747	39	44	order	order	NOUN
ejpam-747	39	45	β	β	X
ejpam-747	39	46	in	in	ADP
ejpam-747	39	47	∆	∆	PROPN
ejpam-747	39	48	and	and	CCONJ
ejpam-747	39	49	this	this	DET
ejpam-747	39	50	class	class	NOUN
ejpam-747	39	51	is	be	AUX
ejpam-747	39	52	denoted	denote	VERB
ejpam-747	39	53	by	by	ADP
ejpam-747	39	54	s	s	PROPN
ejpam-747	39	55	∗	∗	NOUN
ejpam-747	39	56	p	p	X
ejpam-747	39	57	�	�	PROPN
ejpam-747	39	58	β	β	X
ejpam-747	39	59	�	�	PROPN
ejpam-747	39	60	.	.	PUNCT
ejpam-747	40	1	further	far	ADV
ejpam-747	40	2	,	,	PUNCT
ejpam-747	40	3	if	if	SCONJ
ejpam-747	40	4	f	f	PROPN
ejpam-747	40	5	∈	∈	PROPN
ejpam-747	40	6	ap	ap	PROPN
ejpam-747	40	7	satisfies	satisfy	VERB
ejpam-747	40	8	�	�	PROPN
ejpam-747	40	9	�	�	PROPN
ejpam-747	40	10	�	�	PROPN
ejpam-747	40	11	�	�	PROPN
ejpam-747	40	12	�	�	PROPN
ejpam-747	40	13	arg	arg	VERB
ejpam-747	40	14	1	1	NUM
ejpam-747	41	1	+	+	NUM
ejpam-747	41	2	z	z	NOUN
ejpam-747	41	3	f	f	X
ejpam-747	42	1	′′	′′	PROPN
ejpam-747	42	2	(	(	PUNCT
ejpam-747	42	3	z	z	PROPN
ejpam-747	42	4	)	)	PUNCT
ejpam-747	42	5	f	f	NOUN
ejpam-747	42	6	′	′	NUM
ejpam-747	42	7	(	(	PUNCT
ejpam-747	42	8	z	z	NOUN
ejpam-747	42	9	)	)	PUNCT
ejpam-747	42	10	!	!	PUNCT
ejpam-747	43	1	�	�	PROPN
ejpam-747	43	2	�	�	PROPN
ejpam-747	43	3	�	�	PROPN
ejpam-747	43	4	�	�	PROPN
ejpam-747	43	5	�	�	PROPN
ejpam-747	43	6	<	<	X
ejpam-747	43	7	β	β	X
ejpam-747	43	8	p	p	X
ejpam-747	43	9	π	π	PROPN
ejpam-747	43	10	2	2	NUM
ejpam-747	43	11	(	(	PUNCT
ejpam-747	43	12	z	z	NOUN
ejpam-747	43	13	∈∆	∈∆	NOUN
ejpam-747	43	14	)	)	PUNCT
ejpam-747	43	15	,	,	PUNCT
ejpam-747	43	16	for	for	ADP
ejpam-747	43	17	some	some	PRON
ejpam-747	43	18	0	0	NUM
ejpam-747	43	19	<	<	X
ejpam-747	43	20	β	β	X
ejpam-747	43	21	≤	≤	NOUN
ejpam-747	43	22	p	p	X
ejpam-747	43	23	,	,	PUNCT
ejpam-747	43	24	then	then	ADV
ejpam-747	43	25	f	f	PROPN
ejpam-747	43	26	is	be	AUX
ejpam-747	43	27	said	say	VERB
ejpam-747	43	28	to	to	PART
ejpam-747	43	29	be	be	AUX
ejpam-747	43	30	p	p	VERB
ejpam-747	43	31	-	-	PUNCT
ejpam-747	43	32	valently	valently	ADV
ejpam-747	43	33	strongly	strongly	ADV
ejpam-747	43	34	convex	convex	VERB
ejpam-747	43	35	function	function	NOUN
ejpam-747	43	36	of	of	ADP
ejpam-747	43	37	order	order	NOUN
ejpam-747	43	38	β	β	X
ejpam-747	43	39	in	in	ADP
ejpam-747	43	40	∆	∆	PROPN
ejpam-747	43	41	and	and	CCONJ
ejpam-747	43	42	is	be	AUX
ejpam-747	43	43	denote	denote	VERB
ejpam-747	43	44	by	by	ADP
ejpam-747	43	45	k	k	PROPN
ejpam-747	43	46	p	p	PROPN
ejpam-747	43	47	�	�	PROPN
ejpam-747	43	48	β	β	X
ejpam-747	43	49	�	�	PROPN
ejpam-747	43	50	,	,	PUNCT
ejpam-747	43	51	the	the	DET
ejpam-747	43	52	class	class	NOUN
ejpam-747	43	53	of	of	ADP
ejpam-747	43	54	all	all	DET
ejpam-747	43	55	such	such	ADJ
ejpam-747	43	56	functions	function	NOUN
ejpam-747	43	57	.	.	PUNCT
ejpam-747	44	1	also	also	ADV
ejpam-747	44	2	,	,	PUNCT
ejpam-747	44	3	if	if	SCONJ
ejpam-747	44	4	f	f	PROPN
ejpam-747	44	5	∈	∈	PROPN
ejpam-747	44	6	ap	ap	PROPN
ejpam-747	44	7	satisfies	satisfy	VERB
ejpam-747	44	8	�	�	PROPN
ejpam-747	44	9	�	�	PROPN
ejpam-747	44	10	�	�	PROPN
ejpam-747	44	11	arg	arg	NOUN
ejpam-747	44	12	¦	¦	PROPN
ejpam-747	44	13	z1−p	z1−p	PROPN
ejpam-747	44	14	f	f	NOUN
ejpam-747	45	1	′	′	NUM
ejpam-747	45	2	(	(	PUNCT
ejpam-747	45	3	z	z	NOUN
ejpam-747	45	4	)	)	PUNCT
ejpam-747	45	5	©	©	PROPN
ejpam-747	45	6	�	�	PROPN
ejpam-747	45	7	�	�	PROPN
ejpam-747	45	8	�	�	PROPN
ejpam-747	45	9	<	<	X
ejpam-747	45	10	β	β	X
ejpam-747	45	11	p	p	X
ejpam-747	45	12	π	π	PROPN
ejpam-747	45	13	2	2	NUM
ejpam-747	45	14	(	(	PUNCT
ejpam-747	45	15	z	z	NOUN
ejpam-747	45	16	∈∆	∈∆	NOUN
ejpam-747	45	17	)	)	PUNCT
ejpam-747	45	18	,	,	PUNCT
ejpam-747	45	19	for	for	ADP
ejpam-747	45	20	some	some	PRON
ejpam-747	45	21	0	0	NUM
ejpam-747	45	22	<	<	X
ejpam-747	45	23	β	β	X
ejpam-747	45	24	≤	≤	NOUN
ejpam-747	45	25	p	p	X
ejpam-747	45	26	,	,	PUNCT
ejpam-747	45	27	then	then	ADV
ejpam-747	45	28	f	f	PROPN
ejpam-747	45	29	is	be	AUX
ejpam-747	45	30	said	say	VERB
ejpam-747	45	31	to	to	PART
ejpam-747	45	32	be	be	AUX
ejpam-747	45	33	p	p	VERB
ejpam-747	45	34	-	-	PUNCT
ejpam-747	45	35	valently	valently	ADV
ejpam-747	45	36	strongly	strongly	ADV
ejpam-747	45	37	close	close	ADJ
ejpam-747	45	38	-	-	PUNCT
ejpam-747	45	39	to	to	ADP
ejpam-747	45	40	-	-	PUNCT
ejpam-747	45	41	convex	convex	NOUN
ejpam-747	45	42	function	function	NOUN
ejpam-747	45	43	of	of	ADP
ejpam-747	45	44	order	order	NOUN
ejpam-747	45	45	β	β	X
ejpam-747	45	46	in	in	ADP
ejpam-747	45	47	∆	∆	PROPN
ejpam-747	45	48	and	and	CCONJ
ejpam-747	45	49	denote	denote	VERB
ejpam-747	45	50	by	by	ADP
ejpam-747	45	51	ck	ck	PROPN
ejpam-747	45	52	p	p	PROPN
ejpam-747	45	53	�	�	PROPN
ejpam-747	45	54	β	β	X
ejpam-747	45	55	�	�	PROPN
ejpam-747	45	56	the	the	DET
ejpam-747	45	57	class	class	NOUN
ejpam-747	45	58	of	of	ADP
ejpam-747	45	59	all	all	DET
ejpam-747	45	60	such	such	ADJ
ejpam-747	45	61	functions	function	NOUN
ejpam-747	45	62	.	.	PUNCT
ejpam-747	46	1	a	a	DET
ejpam-747	46	2	convolution	convolution	NOUN
ejpam-747	46	3	(	(	PUNCT
ejpam-747	46	4	hadamard	hadamard	ADJ
ejpam-747	46	5	product	product	NOUN
ejpam-747	46	6	)	)	PUNCT
ejpam-747	46	7	of	of	ADP
ejpam-747	46	8	f	f	PROPN
ejpam-747	46	9	∈	∈	PROPN
ejpam-747	46	10	ap	ap	PROPN
ejpam-747	46	11	of	of	ADP
ejpam-747	46	12	the	the	DET
ejpam-747	46	13	form	form	NOUN
ejpam-747	46	14	(	(	PUNCT
ejpam-747	46	15	1	1	NUM
ejpam-747	46	16	)	)	PUNCT
ejpam-747	46	17	with	with	ADP
ejpam-747	46	18	g	g	PROPN
ejpam-747	46	19	∈	∈	PROPN
ejpam-747	46	20	ap	ap	PROPN
ejpam-747	46	21	of	of	ADP
ejpam-747	46	22	the	the	DET
ejpam-747	46	23	form	form	NOUN
ejpam-747	46	24	(	(	PUNCT
ejpam-747	46	25	2	2	X
ejpam-747	46	26	)	)	PUNCT
ejpam-747	46	27	is	be	AUX
ejpam-747	46	28	defined	define	VERB
ejpam-747	46	29	by	by	ADP
ejpam-747	46	30	:	:	PUNCT
ejpam-747	46	31	�	�	PROPN
ejpam-747	46	32	f	f	PROPN
ejpam-747	46	33	∗	∗	VERB
ejpam-747	46	34	g	g	PROPN
ejpam-747	46	35	�	�	PROPN
ejpam-747	46	36	(	(	PUNCT
ejpam-747	46	37	z	z	NOUN
ejpam-747	46	38	)	)	PUNCT
ejpam-747	46	39	=	=	SYM
ejpam-747	47	1	zp	zp	PROPN
ejpam-747	47	2	+	+	CCONJ
ejpam-747	47	3	∞	∞	NUM
ejpam-747	47	4	∑	∑	PUNCT
ejpam-747	48	1	k=1	k=1	ADP
ejpam-747	48	2	ap+k	ap+k	PRON
ejpam-747	48	3	bp+kzp+k	bp+kzp+k	ADV
ejpam-747	48	4	=	=	SYM
ejpam-747	48	5	�	�	PROPN
ejpam-747	48	6	g	g	PROPN
ejpam-747	48	7	∗	∗	X
ejpam-747	48	8	f	f	PROPN
ejpam-747	48	9	�	�	PROPN
ejpam-747	48	10	(	(	PUNCT
ejpam-747	48	11	z	z	NOUN
ejpam-747	48	12	)	)	PUNCT
ejpam-747	48	13	.	.	PUNCT
ejpam-747	49	1	(	(	PUNCT
ejpam-747	49	2	4	4	X
ejpam-747	49	3	)	)	PUNCT
ejpam-747	49	4	p.	p.	NOUN
ejpam-747	49	5	sharma	sharma	PROPN
ejpam-747	49	6	,	,	PUNCT
ejpam-747	49	7	p.	p.	PROPN
ejpam-747	49	8	srivastava	srivastava	PROPN
ejpam-747	49	9	/	/	SYM
ejpam-747	49	10	eur	eur	PROPN
ejpam-747	49	11	.	.	PUNCT
ejpam-747	50	1	j.	j.	PROPN
ejpam-747	50	2	pure	pure	PROPN
ejpam-747	50	3	appl	appl	PROPN
ejpam-747	50	4	.	.	PROPN
ejpam-747	50	5	math	math	PROPN
ejpam-747	50	6	,	,	PUNCT
ejpam-747	50	7	3	3	NUM
ejpam-747	50	8	(	(	PUNCT
ejpam-747	50	9	2010	2010	NUM
ejpam-747	50	10	)	)	PUNCT
ejpam-747	50	11	,	,	PUNCT
ejpam-747	50	12	1093	1093	NUM
ejpam-747	50	13	-	-	SYM
ejpam-747	50	14	1112	1112	NUM
ejpam-747	50	15	1095	1095	NUM
ejpam-747	50	16	various	various	ADJ
ejpam-747	50	17	convolution	convolution	NOUN
ejpam-747	50	18	operators	operator	NOUN
ejpam-747	50	19	have	have	AUX
ejpam-747	50	20	been	be	AUX
ejpam-747	50	21	defined	define	VERB
ejpam-747	50	22	so	so	ADV
ejpam-747	50	23	far	far	ADV
ejpam-747	50	24	,	,	PUNCT
ejpam-747	50	25	which	which	PRON
ejpam-747	50	26	can	can	AUX
ejpam-747	50	27	be	be	AUX
ejpam-747	50	28	obtained	obtain	VERB
ejpam-747	50	29	by	by	ADP
ejpam-747	50	30	taking	take	VERB
ejpam-747	50	31	suitable	suitable	ADJ
ejpam-747	50	32	g	g	NOUN
ejpam-747	50	33	in	in	ADP
ejpam-747	50	34	(	(	PUNCT
ejpam-747	50	35	4	4	NUM
ejpam-747	50	36	)	)	PUNCT
ejpam-747	50	37	.	.	PUNCT
ejpam-747	51	1	for	for	ADP
ejpam-747	51	2	example	example	NOUN
ejpam-747	51	3	the	the	DET
ejpam-747	51	4	convolution	convolution	NOUN
ejpam-747	51	5	in	in	ADP
ejpam-747	51	6	(	(	PUNCT
ejpam-747	51	7	4	4	NUM
ejpam-747	51	8	)	)	PUNCT
ejpam-747	51	9	reduces	reduce	VERB
ejpam-747	51	10	to	to	ADP
ejpam-747	51	11	the	the	DET
ejpam-747	51	12	operator	operator	NOUN
ejpam-747	51	13	w	w	ADP
ejpam-747	51	14	p	p	X
ejpam-747	51	15	q	q	PROPN
ejpam-747	51	16	,	,	PUNCT
ejpam-747	51	17	s	s	PART
ejpam-747	51	18	(	(	PUNCT
ejpam-747	51	19	�	�	PROPN
ejpam-747	51	20	α1,a1	α1,a1	PROPN
ejpam-747	51	21	�	�	PROPN
ejpam-747	51	22	)	)	PUNCT
ejpam-747	51	23	f	f	PROPN
ejpam-747	51	24	(	(	PUNCT
ejpam-747	51	25	z	z	NOUN
ejpam-747	51	26	)	)	PUNCT
ejpam-747	51	27	involving	involve	VERB
ejpam-747	51	28	a	a	DET
ejpam-747	51	29	wright	wright	PROPN
ejpam-747	51	30	’s	’s	PART
ejpam-747	51	31	generalized	generalize	VERB
ejpam-747	51	32	hypergeometric	hypergeometric	ADJ
ejpam-747	51	33	function	function	NOUN
ejpam-747	51	34	qψs	qψs	NOUN
ejpam-747	52	1	[	[	X
ejpam-747	52	2	z	z	X
ejpam-747	52	3	]	]	X
ejpam-747	52	4	≡	≡	PROPN
ejpam-747	52	5	qψs	qψs	PROPN
ejpam-747	52	6	�	�	PROPN
ejpam-747	52	7	�	�	PROPN
ejpam-747	52	8	α1,a1	α1,a1	PROPN
ejpam-747	52	9	�	�	PROPN
ejpam-747	52	10	,	,	PUNCT
ejpam-747	52	11	�	�	PROPN
ejpam-747	52	12	α2,a2	α2,a2	PROPN
ejpam-747	52	13	�	�	PROPN
ejpam-747	52	14	,	,	PUNCT
ejpam-747	52	15	.	.	PUNCT
ejpam-747	52	16	.	.	PUNCT
ejpam-747	53	1	.	.	PUNCT
ejpam-747	54	1	,	,	PUNCT
ejpam-747	54	2	�	�	PROPN
ejpam-747	54	3	αq	αq	AUX
ejpam-747	54	4	,	,	PUNCT
ejpam-747	54	5	aq	aq	PROPN
ejpam-747	54	6	�	�	PROPN
ejpam-747	54	7	�	�	PROPN
ejpam-747	54	8	β1	β1	PROPN
ejpam-747	54	9	,	,	PUNCT
ejpam-747	54	10	b1	b1	PROPN
ejpam-747	54	11	�	�	PROPN
ejpam-747	54	12	,	,	PUNCT
ejpam-747	54	13	�	�	PROPN
ejpam-747	54	14	β2	β2	PROPN
ejpam-747	54	15	,	,	PUNCT
ejpam-747	54	16	b2	b2	NOUN
ejpam-747	54	17	�	�	PROPN
ejpam-747	54	18	,	,	PUNCT
ejpam-747	54	19	.	.	PUNCT
ejpam-747	54	20	.	.	PUNCT
ejpam-747	55	1	.	.	PUNCT
ejpam-747	56	1	,	,	PUNCT
ejpam-747	56	2	�	�	PROPN
ejpam-747	56	3	βs	βs	PROPN
ejpam-747	56	4	,	,	PUNCT
ejpam-747	56	5	bs	bs	X
ejpam-747	56	6	�	�	PROPN
ejpam-747	56	7	;	;	PUNCT
ejpam-747	56	8	z	z	PROPN
ejpam-747	56	9	�	�	PROPN
ejpam-747	56	10	if	if	SCONJ
ejpam-747	56	11	g(z	g(z	ADJ
ejpam-747	56	12	)	)	PUNCT
ejpam-747	57	1	=	=	PUNCT
ejpam-747	57	2	zp	zp	PROPN
ejpam-747	57	3	s	s	PART
ejpam-747	57	4	∏	∏	PROPN
ejpam-747	57	5	i=1	i=1	PROPN
ejpam-747	57	6	γ(βi	γ(βi	NOUN
ejpam-747	57	7	)	)	PUNCT
ejpam-747	57	8	q	q	PROPN
ejpam-747	57	9	∏	∏	PROPN
ejpam-747	57	10	i=1	i=1	PROPN
ejpam-747	57	11	γ(αi	γ(αi	PROPN
ejpam-747	57	12	)	)	PUNCT
ejpam-747	58	1	qψs	qψs	NOUN
ejpam-747	59	1	[	[	X
ejpam-747	59	2	z	z	X
ejpam-747	59	3	]	]	X
ejpam-747	59	4	,	,	PUNCT
ejpam-747	59	5	where	where	SCONJ
ejpam-747	59	6	for	for	ADP
ejpam-747	59	7	αi	αi	NOUN
ejpam-747	59	8	∈	∈	PROPN
ejpam-747	60	1	c	c	X
ejpam-747	60	2	(	(	PUNCT
ejpam-747	60	3	αi	αi	INTJ
ejpam-747	60	4	ai	ai	VERB
ejpam-747	60	5	6=	6=	NOUN
ejpam-747	60	6	0,−1,−2	0,−1,−2	NUM
ejpam-747	60	7	,	,	PUNCT
ejpam-747	60	8	.	.	PUNCT
ejpam-747	60	9	.	.	PUNCT
ejpam-747	60	10	.	.	PUNCT
ejpam-747	60	11	)	)	PUNCT
ejpam-747	61	1	,	,	PUNCT
ejpam-747	61	2	i	i	PRON
ejpam-747	61	3	=	=	NOUN
ejpam-747	61	4	1,2	1,2	NUM
ejpam-747	61	5	,	,	PUNCT
ejpam-747	61	6	.	.	PUNCT
ejpam-747	61	7	.	.	PUNCT
ejpam-747	61	8	.	.	PUNCT
ejpam-747	62	1	,	,	PUNCT
ejpam-747	62	2	q	q	X
ejpam-747	62	3	,	,	PUNCT
ejpam-747	62	4	βi	βi	PROPN
ejpam-747	62	5	∈	∈	PROPN
ejpam-747	62	6	c	c	X
ejpam-747	62	7	(	(	PUNCT
ejpam-747	62	8	βi	βi	PROPN
ejpam-747	62	9	bi	bi	PROPN
ejpam-747	62	10	6=	6=	PROPN
ejpam-747	62	11	0,−1,−2	0,−1,−2	NUM
ejpam-747	62	12	,	,	PUNCT
ejpam-747	62	13	.	.	PUNCT
ejpam-747	62	14	.	.	PUNCT
ejpam-747	62	15	.	.	PUNCT
ejpam-747	62	16	)	)	PUNCT
ejpam-747	62	17	,	,	PUNCT
ejpam-747	62	18	i	i	PRON
ejpam-747	62	19	=	=	NOUN
ejpam-747	62	20	1,2	1,2	NUM
ejpam-747	62	21	,	,	PUNCT
ejpam-747	62	22	.	.	PUNCT
ejpam-747	62	23	.	.	PUNCT
ejpam-747	62	24	.	.	PUNCT
ejpam-747	63	1	,	,	PUNCT
ejpam-747	63	2	s	s	VERB
ejpam-747	63	3	and	and	CCONJ
ejpam-747	63	4	ai	ai	VERB
ejpam-747	63	5	>	>	X
ejpam-747	63	6	0	0	PROPN
ejpam-747	63	7	,	,	PUNCT
ejpam-747	63	8	i	i	PRON
ejpam-747	63	9	=	=	NOUN
ejpam-747	63	10	1,2	1,2	NUM
ejpam-747	63	11	,	,	PUNCT
ejpam-747	63	12	.	.	PUNCT
ejpam-747	63	13	.	.	PUNCT
ejpam-747	64	1	.	.	PUNCT
ejpam-747	65	1	,	,	PUNCT
ejpam-747	65	2	q	q	X
ejpam-747	65	3	,	,	PUNCT
ejpam-747	65	4	bi	bi	NOUN
ejpam-747	65	5	>	>	X
ejpam-747	65	6	0	0	PROPN
ejpam-747	65	7	,	,	PUNCT
ejpam-747	65	8	i	i	PRON
ejpam-747	65	9	=	=	NOUN
ejpam-747	65	10	1,2	1,2	NUM
ejpam-747	65	11	,	,	PUNCT
ejpam-747	65	12	.	.	PUNCT
ejpam-747	65	13	.	.	PUNCT
ejpam-747	66	1	.	.	PUNCT
ejpam-747	67	1	,	,	PUNCT
ejpam-747	67	2	s	s	VERB
ejpam-747	67	3	such	such	ADJ
ejpam-747	67	4	that	that	DET
ejpam-747	67	5	1	1	NUM
ejpam-747	67	6	+	+	SYM
ejpam-747	67	7	s	s	VERB
ejpam-747	67	8	∑	∑	PROPN
ejpam-747	67	9	i=1	i=1	PROPN
ejpam-747	67	10	bi	bi	NOUN
ejpam-747	67	11	−	−	PROPN
ejpam-747	67	12	q	q	PROPN
ejpam-747	67	13	∑	∑	PROPN
ejpam-747	67	14	i=1	i=1	PROPN
ejpam-747	67	15	ai	ai	VERB
ejpam-747	67	16	≥	≥	PROPN
ejpam-747	67	17	0	0	NUM
ejpam-747	67	18	,	,	PUNCT
ejpam-747	67	19	qψs	qψs	X
ejpam-747	68	1	[	[	X
ejpam-747	68	2	z	z	X
ejpam-747	68	3	]	]	X
ejpam-747	68	4	=	=	SYM
ejpam-747	68	5	∞	∞	NUM
ejpam-747	68	6	∑	∑	PUNCT
ejpam-747	68	7	k=0	k=0	PUNCT
ejpam-747	68	8	q	q	X
ejpam-747	68	9	∏	∏	PROPN
ejpam-747	68	10	i=1	i=1	PROPN
ejpam-747	68	11	γ(αi	γ(αi	PROPN
ejpam-747	68	12	+	+	NUM
ejpam-747	68	13	aik	aik	NOUN
ejpam-747	68	14	)	)	PUNCT
ejpam-747	68	15	s	s	PART
ejpam-747	68	16	∏	∏	PROPN
ejpam-747	68	17	i=1	i=1	PROPN
ejpam-747	68	18	γ(βi	γ(βi	PROPN
ejpam-747	68	19	+	+	CCONJ
ejpam-747	68	20	bik	bik	PROPN
ejpam-747	68	21	)	)	PUNCT
ejpam-747	69	1	k	k	X
ejpam-747	69	2	!	!	PUNCT
ejpam-747	69	3	zk	zk	PROPN
ejpam-747	69	4	,	,	PUNCT
ejpam-747	69	5	z	z	NOUN
ejpam-747	69	6	∈∆	∈∆	NOUN
ejpam-747	69	7	,	,	PUNCT
ejpam-747	69	8	(	(	PUNCT
ejpam-747	69	9	5	5	NUM
ejpam-747	69	10	)	)	PUNCT
ejpam-747	69	11	(	(	PUNCT
ejpam-747	69	12	s	s	VERB
ejpam-747	69	13	∏	∏	NUM
ejpam-747	69	14	i=1	i=1	PROPN
ejpam-747	69	15	b	b	PROPN
ejpam-747	69	16	bi	bi	NOUN
ejpam-747	70	1	i	i	PRON
ejpam-747	70	2	≥	≥	VERB
ejpam-747	70	3	q	q	PROPN
ejpam-747	70	4	∏	∏	PROPN
ejpam-747	70	5	i=1	i=1	PROPN
ejpam-747	71	1	a	a	DET
ejpam-747	71	2	ai	ai	VERB
ejpam-747	71	3	i	i	PRON
ejpam-747	71	4	in	in	ADP
ejpam-747	71	5	case	case	NOUN
ejpam-747	71	6	1	1	NUM
ejpam-747	72	1	+	+	SYM
ejpam-747	72	2	s	s	VERB
ejpam-747	72	3	∑	∑	PROPN
ejpam-747	72	4	i=1	i=1	PROPN
ejpam-747	72	5	bi−	bi−	PROPN
ejpam-747	72	6	q	q	X
ejpam-747	72	7	∑	∑	PUNCT
ejpam-747	72	8	i=1	i=1	PROPN
ejpam-747	72	9	ai	ai	VERB
ejpam-747	72	10	=	=	SYM
ejpam-747	72	11	0	0	PUNCT
ejpam-747	73	1	[	[	X
ejpam-747	73	2	15	15	NUM
ejpam-747	73	3	]	]	NUM
ejpam-747	73	4	)	)	PUNCT
ejpam-747	73	5	.	.	PUNCT
ejpam-747	74	1	the	the	DET
ejpam-747	74	2	convolution	convolution	NOUN
ejpam-747	74	3	operator	operator	NOUN
ejpam-747	74	4	w	w	PROPN
ejpam-747	74	5	p	p	X
ejpam-747	74	6	q	q	PROPN
ejpam-747	74	7	,	,	PUNCT
ejpam-747	74	8	s	s	PART
ejpam-747	74	9	(	(	PUNCT
ejpam-747	74	10	�	�	PROPN
ejpam-747	74	11	α1,a1	α1,a1	PROPN
ejpam-747	74	12	�	�	PROPN
ejpam-747	74	13	)	)	PUNCT
ejpam-747	74	14	f	f	PROPN
ejpam-747	74	15	(	(	PUNCT
ejpam-747	74	16	z	z	NOUN
ejpam-747	74	17	)	)	PUNCT
ejpam-747	74	18	,	,	PUNCT
ejpam-747	74	19	for	for	ADP
ejpam-747	74	20	which	which	PRON
ejpam-747	74	21	bp+k	bp+k	NOUN
ejpam-747	74	22	=	=	SYM
ejpam-747	74	23	q	q	X
ejpam-747	74	24	∏	∏	NUM
ejpam-747	74	25	i=1	i=1	X
ejpam-747	74	26	γ(αi+ai	γ(αi+ai	X
ejpam-747	75	1	k	k	X
ejpam-747	75	2	)	)	PUNCT
ejpam-747	75	3	γ(αi	γ(αi	NOUN
ejpam-747	75	4	)	)	PUNCT
ejpam-747	75	5	s	s	PART
ejpam-747	75	6	∏	∏	PROPN
ejpam-747	76	1	i=1	i=1	PROPN
ejpam-747	76	2	γ(βi+bi	γ(βi+bi	PROPN
ejpam-747	76	3	k	k	NOUN
ejpam-747	76	4	)	)	PUNCT
ejpam-747	76	5	γ(βi	γ(βi	NUM
ejpam-747	76	6	)	)	PUNCT
ejpam-747	77	1	k	k	X
ejpam-747	77	2	!	!	PROPN
ejpam-747	77	3	,	,	PUNCT
ejpam-747	77	4	is	be	AUX
ejpam-747	77	5	studied	study	VERB
ejpam-747	77	6	by	by	ADP
ejpam-747	77	7	aouf	aouf	PROPN
ejpam-747	77	8	and	and	CCONJ
ejpam-747	77	9	dziok	dziok	NOUN
ejpam-747	78	1	[	[	X
ejpam-747	78	2	3	3	NUM
ejpam-747	78	3	,	,	PUNCT
ejpam-747	78	4	4	4	NUM
ejpam-747	78	5	]	]	PUNCT
ejpam-747	78	6	,	,	PUNCT
ejpam-747	78	7	dziok	dziok	NOUN
ejpam-747	78	8	and	and	CCONJ
ejpam-747	78	9	raina	raina	VERB
ejpam-747	79	1	[	[	X
ejpam-747	79	2	8	8	NUM
ejpam-747	79	3	]	]	PUNCT
ejpam-747	79	4	,	,	PUNCT
ejpam-747	79	5	and	and	CCONJ
ejpam-747	79	6	dziok	dziok	NOUN
ejpam-747	79	7	et	et	PROPN
ejpam-747	79	8	al	al	PROPN
ejpam-747	79	9	.	.	PUNCT
ejpam-747	80	1	[	[	X
ejpam-747	80	2	9	9	NUM
ejpam-747	80	3	]	]	PUNCT
ejpam-747	80	4	and	and	CCONJ
ejpam-747	80	5	sharma	sharma	PROPN
ejpam-747	80	6	[	[	X
ejpam-747	80	7	25	25	NUM
ejpam-747	80	8	]	]	PUNCT
ejpam-747	80	9	in	in	ADP
ejpam-747	80	10	their	their	PRON
ejpam-747	80	11	respective	respective	ADJ
ejpam-747	80	12	work	work	NOUN
ejpam-747	80	13	and	and	CCONJ
ejpam-747	80	14	taking	take	VERB
ejpam-747	80	15	ai	ai	NOUN
ejpam-747	80	16	=	=	ADJ
ejpam-747	80	17	1	1	NUM
ejpam-747	80	18	,	,	PUNCT
ejpam-747	80	19	i	i	PRON
ejpam-747	80	20	=	=	NOUN
ejpam-747	80	21	1,2	1,2	NUM
ejpam-747	80	22	,	,	PUNCT
ejpam-747	80	23	.	.	PUNCT
ejpam-747	80	24	.	.	PUNCT
ejpam-747	80	25	.	.	PUNCT
ejpam-747	81	1	,	,	PUNCT
ejpam-747	81	2	q	q	X
ejpam-747	81	3	,	,	PUNCT
ejpam-747	81	4	bi	bi	NOUN
ejpam-747	81	5	=	=	NOUN
ejpam-747	81	6	1	1	NUM
ejpam-747	81	7	,	,	PUNCT
ejpam-747	81	8	i	i	PRON
ejpam-747	81	9	=	=	NOUN
ejpam-747	81	10	1,2	1,2	NUM
ejpam-747	81	11	,	,	PUNCT
ejpam-747	81	12	.	.	PUNCT
ejpam-747	81	13	.	.	PUNCT
ejpam-747	82	1	.	.	PUNCT
ejpam-747	83	1	,	,	PUNCT
ejpam-747	83	2	s	s	X
ejpam-747	83	3	,	,	PUNCT
ejpam-747	83	4	for	for	ADP
ejpam-747	83	5	q	q	PROPN
ejpam-747	83	6	≤	≤	NUM
ejpam-747	83	7	s+	s+	PUNCT
ejpam-747	83	8	1	1	NUM
ejpam-747	83	9	,	,	PUNCT
ejpam-747	83	10	it	it	PRON
ejpam-747	83	11	reduces	reduce	VERB
ejpam-747	83	12	to	to	ADP
ejpam-747	83	13	dziok	dziok	NOUN
ejpam-747	83	14	srivastava	srivastava	PROPN
ejpam-747	83	15	operator	operator	NOUN
ejpam-747	83	16	[	[	X
ejpam-747	83	17	10	10	NUM
ejpam-747	83	18	]	]	PUNCT
ejpam-747	83	19	which	which	PRON
ejpam-747	83	20	involve	involve	VERB
ejpam-747	83	21	a	a	DET
ejpam-747	83	22	generalized	generalized	ADJ
ejpam-747	83	23	hypergeometric	hypergeometric	ADJ
ejpam-747	83	24	function	function	NOUN
ejpam-747	83	25	qfs	qfs	NOUN
ejpam-747	84	1	[	[	X
ejpam-747	84	2	z	z	X
ejpam-747	84	3	]	]	PUNCT
ejpam-747	84	4	and	and	CCONJ
ejpam-747	84	5	is	be	AUX
ejpam-747	84	6	defined	define	VERB
ejpam-747	84	7	by	by	ADP
ejpam-747	84	8	qhp	qhp	DET
ejpam-747	84	9	s	s	PART
ejpam-747	84	10	�	�	PROPN
ejpam-747	84	11	�	�	PROPN
ejpam-747	84	12	α1	α1	PROPN
ejpam-747	84	13	�	�	PROPN
ejpam-747	84	14	�	�	PROPN
ejpam-747	84	15	f	f	PROPN
ejpam-747	84	16	(	(	PUNCT
ejpam-747	84	17	z	z	NOUN
ejpam-747	84	18	)	)	PUNCT
ejpam-747	84	19	=	=	PUNCT
ejpam-747	84	20	zp	zp	NOUN
ejpam-747	84	21	qfs	qfs	NOUN
ejpam-747	85	1	[	[	X
ejpam-747	85	2	z	z	X
ejpam-747	85	3	]	]	X
ejpam-747	85	4	∗	∗	X
ejpam-747	85	5	f	f	PROPN
ejpam-747	85	6	(	(	PUNCT
ejpam-747	85	7	z	z	NOUN
ejpam-747	85	8	)	)	PUNCT
ejpam-747	85	9	(	(	PUNCT
ejpam-747	85	10	6	6	NUM
ejpam-747	85	11	)	)	PUNCT
ejpam-747	85	12	where	where	SCONJ
ejpam-747	85	13	qfs	qfs	NOUN
ejpam-747	86	1	[	[	X
ejpam-747	86	2	z	z	X
ejpam-747	86	3	]	]	X
ejpam-747	86	4	=	=	X
ejpam-747	86	5	qfs	qfs	NOUN
ejpam-747	86	6	�	�	PROPN
ejpam-747	86	7	α1,α2	α1,α2	PROPN
ejpam-747	86	8	,	,	PUNCT
ejpam-747	86	9	.	.	PUNCT
ejpam-747	86	10	.	.	PUNCT
ejpam-747	87	1	.αq;β1,β2	.αq;β1,β2	NOUN
ejpam-747	87	2	,	,	PUNCT
ejpam-747	87	3	.	.	PUNCT
ejpam-747	87	4	.	.	PUNCT
ejpam-747	88	1	.βs	.βs	PROPN
ejpam-747	88	2	;	;	PUNCT
ejpam-747	88	3	z	z	PROPN
ejpam-747	88	4	�	�	PROPN
ejpam-747	88	5	=	=	SYM
ejpam-747	89	1	∞	∞	PROPN
ejpam-747	89	2	∑	∑	PUNCT
ejpam-747	89	3	k=0	k=0	PUNCT
ejpam-747	89	4	q	q	X
ejpam-747	89	5	∏	∏	PROPN
ejpam-747	89	6	i=1	i=1	PROPN
ejpam-747	89	7	�	�	PROPN
ejpam-747	89	8	αi	αi	PART
ejpam-747	89	9	�	�	PROPN
ejpam-747	90	1	k	k	PROPN
ejpam-747	90	2	s	s	PROPN
ejpam-747	90	3	∏	∏	PROPN
ejpam-747	90	4	i=1	i=1	PROPN
ejpam-747	90	5	�	�	PROPN
ejpam-747	90	6	βi	βi	NUM
ejpam-747	90	7	�	�	PROPN
ejpam-747	90	8	k	k	PROPN
ejpam-747	90	9	k	k	PROPN
ejpam-747	90	10	!	!	PUNCT
ejpam-747	91	1	zk	zk	PROPN
ejpam-747	91	2	,	,	PUNCT
ejpam-747	91	3	z	z	NOUN
ejpam-747	91	4	∈∆	∈∆	PROPN
ejpam-747	91	5	,	,	PUNCT
ejpam-747	91	6	the	the	DET
ejpam-747	91	7	symbol	symbol	NOUN
ejpam-747	91	8	(	(	PUNCT
ejpam-747	91	9	α)k	α)k	X
ejpam-747	91	10	is	be	AUX
ejpam-747	91	11	the	the	DET
ejpam-747	91	12	familiar	familiar	ADJ
ejpam-747	91	13	pochhammer	pochhammer	NOUN
ejpam-747	91	14	symbol	symbol	NOUN
ejpam-747	91	15	defined	define	VERB
ejpam-747	91	16	by	by	ADP
ejpam-747	91	17	(	(	PUNCT
ejpam-747	91	18	α)k	α)k	NOUN
ejpam-747	91	19	=	=	SYM
ejpam-747	91	20	γ(α+	γ(α+	X
ejpam-747	91	21	k	k	X
ejpam-747	91	22	)	)	PUNCT
ejpam-747	91	23	γ(α	γ(α	PROPN
ejpam-747	91	24	)	)	PUNCT
ejpam-747	91	25	,	,	PUNCT
ejpam-747	91	26	k	k	PROPN
ejpam-747	91	27	∈	∈	PROPN
ejpam-747	91	28	n0	n0	PROPN
ejpam-747	91	29	.	.	PUNCT
ejpam-747	92	1	p.	p.	PROPN
ejpam-747	92	2	sharma	sharma	PROPN
ejpam-747	92	3	,	,	PUNCT
ejpam-747	92	4	p.	p.	PROPN
ejpam-747	92	5	srivastava	srivastava	PROPN
ejpam-747	92	6	/	/	SYM
ejpam-747	92	7	eur	eur	PROPN
ejpam-747	92	8	.	.	PUNCT
ejpam-747	93	1	j.	j.	PROPN
ejpam-747	93	2	pure	pure	PROPN
ejpam-747	93	3	appl	appl	PROPN
ejpam-747	93	4	.	.	PROPN
ejpam-747	93	5	math	math	PROPN
ejpam-747	93	6	,	,	PUNCT
ejpam-747	93	7	3	3	NUM
ejpam-747	93	8	(	(	PUNCT
ejpam-747	93	9	2010	2010	NUM
ejpam-747	93	10	)	)	PUNCT
ejpam-747	93	11	,	,	PUNCT
ejpam-747	93	12	1093	1093	NUM
ejpam-747	93	13	-	-	SYM
ejpam-747	93	14	1112	1112	NUM
ejpam-747	93	15	1096	1096	NUM
ejpam-747	93	16	the	the	DET
ejpam-747	93	17	operator	operator	NOUN
ejpam-747	93	18	qh	qh	NOUN
ejpam-747	93	19	p	p	PROPN
ejpam-747	93	20	s	s	PROPN
ejpam-747	93	21	�	�	PROPN
ejpam-747	93	22	�	�	PROPN
ejpam-747	93	23	α1	α1	PROPN
ejpam-747	93	24	�	�	PROPN
ejpam-747	93	25	�	�	PROPN
ejpam-747	93	26	f	f	PROPN
ejpam-747	93	27	(	(	PUNCT
ejpam-747	93	28	z	z	NOUN
ejpam-747	93	29	)	)	PUNCT
ejpam-747	93	30	includes	include	VERB
ejpam-747	93	31	hohlov	hohlov	NOUN
ejpam-747	93	32	operator	operator	NOUN
ejpam-747	93	33	[	[	X
ejpam-747	93	34	13	13	NUM
ejpam-747	93	35	]	]	PUNCT
ejpam-747	93	36	which	which	PRON
ejpam-747	93	37	involve	involve	VERB
ejpam-747	93	38	gaussian	gaussian	ADJ
ejpam-747	93	39	hypergeometric	hypergeometric	ADJ
ejpam-747	93	40	function	function	NOUN
ejpam-747	93	41	2f1	2f1	NUM
ejpam-747	93	42	as	as	ADV
ejpam-747	93	43	well	well	ADV
ejpam-747	93	44	as	as	ADP
ejpam-747	93	45	carlson	carlson	PROPN
ejpam-747	93	46	and	and	CCONJ
ejpam-747	93	47	shaffer	shaffer	NOUN
ejpam-747	93	48	operator	operator	NOUN
ejpam-747	94	1	[	[	X
ejpam-747	94	2	6	6	NUM
ejpam-747	94	3	]	]	PUNCT
ejpam-747	94	4	defined	define	VERB
ejpam-747	94	5	by	by	ADP
ejpam-747	94	6	saitoh	saitoh	ADJ
ejpam-747	94	7	and	and	CCONJ
ejpam-747	94	8	ruschweyh	ruschweyh	VERB
ejpam-747	94	9	derivative	derivative	ADJ
ejpam-747	94	10	operator	operator	NOUN
ejpam-747	94	11	[	[	X
ejpam-747	94	12	23	23	NUM
ejpam-747	94	13	]	]	PUNCT
ejpam-747	94	14	(	(	PUNCT
ejpam-747	94	15	for	for	ADP
ejpam-747	94	16	detail	detail	NOUN
ejpam-747	94	17	one	one	PRON
ejpam-747	94	18	may	may	AUX
ejpam-747	94	19	refer	refer	VERB
ejpam-747	94	20	to	to	ADP
ejpam-747	94	21	[	[	X
ejpam-747	94	22	8	8	NUM
ejpam-747	94	23	,	,	PUNCT
ejpam-747	94	24	9	9	NUM
ejpam-747	94	25	]	]	PUNCT
ejpam-747	94	26	)	)	PUNCT
ejpam-747	94	27	.	.	PUNCT
ejpam-747	95	1	also	also	ADV
ejpam-747	95	2	,	,	PUNCT
ejpam-747	95	3	the	the	DET
ejpam-747	95	4	convolution	convolution	NOUN
ejpam-747	95	5	(	(	PUNCT
ejpam-747	95	6	4	4	NUM
ejpam-747	95	7	)	)	PUNCT
ejpam-747	95	8	reduces	reduce	VERB
ejpam-747	95	9	to	to	ADP
ejpam-747	95	10	the	the	DET
ejpam-747	95	11	salagean	salagean	ADJ
ejpam-747	95	12	operator	operator	NOUN
ejpam-747	95	13	[	[	X
ejpam-747	95	14	24	24	NUM
ejpam-747	95	15	]	]	PUNCT
ejpam-747	95	16	if	if	SCONJ
ejpam-747	95	17	bp+k	bp+k	PROPN
ejpam-747	95	18	=	=	SYM
ejpam-747	95	19	�	�	PROPN
ejpam-747	95	20	p+	p+	PROPN
ejpam-747	95	21	k	k	PROPN
ejpam-747	95	22	p	p	X
ejpam-747	95	23	�	�	PROPN
ejpam-747	95	24	n	n	NUM
ejpam-747	95	25	,	,	PUNCT
ejpam-747	95	26	n	n	PROPN
ejpam-747	95	27	∈	∈	PROPN
ejpam-747	95	28	n0	n0	NOUN
ejpam-747	95	29	and	and	CCONJ
ejpam-747	95	30	to	to	ADP
ejpam-747	95	31	a	a	DET
ejpam-747	95	32	generalized	generalize	VERB
ejpam-747	95	33	salagean	salagean	ADJ
ejpam-747	95	34	operator	operator	NOUN
ejpam-747	95	35	[	[	X
ejpam-747	95	36	2	2	NUM
ejpam-747	95	37	]	]	PUNCT
ejpam-747	95	38	,	,	PUNCT
ejpam-747	95	39	if	if	SCONJ
ejpam-747	95	40	bp+k	bp+k	PROPN
ejpam-747	95	41	=	=	SYM
ejpam-747	95	42	�	�	PROPN
ejpam-747	95	43	p+	p+	VERB
ejpam-747	95	44	δk	δk	PROPN
ejpam-747	95	45	p	p	NOUN
ejpam-747	95	46	�	�	PROPN
ejpam-747	95	47	n	n	PROPN
ejpam-747	95	48	,	,	PUNCT
ejpam-747	95	49	δ	δ	PROPN
ejpam-747	95	50	>	>	X
ejpam-747	95	51	0	0	PROPN
ejpam-747	95	52	,	,	PUNCT
ejpam-747	95	53	n	n	PROPN
ejpam-747	95	54	∈	∈	PROPN
ejpam-747	95	55	n0	n0	PROPN
ejpam-747	95	56	.	.	PUNCT
ejpam-747	96	1	further	far	ADV
ejpam-747	96	2	,	,	PUNCT
ejpam-747	96	3	the	the	DET
ejpam-747	96	4	convolution	convolution	NOUN
ejpam-747	96	5	(	(	PUNCT
ejpam-747	96	6	4	4	NUM
ejpam-747	96	7	)	)	PUNCT
ejpam-747	96	8	reduces	reduce	VERB
ejpam-747	96	9	to	to	ADP
ejpam-747	96	10	an	an	DET
ejpam-747	96	11	integral	integral	ADJ
ejpam-747	96	12	operator	operator	NOUN
ejpam-747	96	13	involving	involve	VERB
ejpam-747	96	14	generalized	generalize	VERB
ejpam-747	96	15	fractional	fractional	ADJ
ejpam-747	96	16	integral	integral	ADJ
ejpam-747	96	17	operator	operator	NOUN
ejpam-747	96	18	i	i	PRON
ejpam-747	96	19	λ,µ,ν	λ,µ,ν	PROPN
ejpam-747	97	1	0,z	0,z	INTJ
ejpam-747	97	2	,	,	PUNCT
ejpam-747	97	3	if	if	SCONJ
ejpam-747	97	4	bp+k	bp+k	PROPN
ejpam-747	97	5	=	=	SYM
ejpam-747	97	6	�	�	PROPN
ejpam-747	97	7	p+	p+	PART
ejpam-747	97	8	1	1	NUM
ejpam-747	97	9	�	�	PROPN
ejpam-747	97	10	k	k	PROPN
ejpam-747	97	11	�	�	PROPN
ejpam-747	97	12	p−µ+	p−µ+	PROPN
ejpam-747	97	13	ν	ν	NOUN
ejpam-747	97	14	+	+	CCONJ
ejpam-747	97	15	1	1	NUM
ejpam-747	97	16	�	�	PROPN
ejpam-747	97	17	k	k	PROPN
ejpam-747	97	18	�	�	PROPN
ejpam-747	97	19	p−µ+	p−µ+	PROPN
ejpam-747	97	20	1	1	NUM
ejpam-747	97	21	�	�	PROPN
ejpam-747	97	22	k	k	PROPN
ejpam-747	97	23	�	�	PROPN
ejpam-747	97	24	p+λ+	p+λ+	NOUN
ejpam-747	97	25	ν	ν	NOUN
ejpam-747	97	26	+	+	CCONJ
ejpam-747	97	27	1	1	NUM
ejpam-747	97	28	�	�	PROPN
ejpam-747	97	29	k	k	PROPN
ejpam-747	97	30	and	and	CCONJ
ejpam-747	97	31	hence	hence	ADV
ejpam-747	97	32	�	�	PROPN
ejpam-747	97	33	f	f	PROPN
ejpam-747	97	34	∗	∗	NOUN
ejpam-747	97	35	g	g	PROPN
ejpam-747	97	36	�	�	PROPN
ejpam-747	97	37	(	(	PUNCT
ejpam-747	97	38	z	z	NOUN
ejpam-747	97	39	)	)	PUNCT
ejpam-747	97	40	=	=	PUNCT
ejpam-747	97	41	zµ	zµ	NUM
ejpam-747	97	42	γ	γ	PROPN
ejpam-747	97	43	�	�	PROPN
ejpam-747	97	44	p−µ+	p−µ+	PROPN
ejpam-747	97	45	1	1	NUM
ejpam-747	97	46	�	�	PROPN
ejpam-747	97	47	γ	γ	X
ejpam-747	97	48	�	�	PROPN
ejpam-747	97	49	p+λ+	p+λ+	NOUN
ejpam-747	97	50	ν	ν	NOUN
ejpam-747	97	51	+	+	CCONJ
ejpam-747	97	52	1	1	NUM
ejpam-747	97	53	�	�	PROPN
ejpam-747	97	54	γ	γ	PROPN
ejpam-747	97	55	�	�	PROPN
ejpam-747	97	56	p+	p+	PART
ejpam-747	97	57	1	1	NUM
ejpam-747	97	58	�	�	PROPN
ejpam-747	97	59	γ	γ	X
ejpam-747	97	60	�	�	PROPN
ejpam-747	97	61	p−µ+	p−µ+	PROPN
ejpam-747	97	62	ν	ν	NOUN
ejpam-747	97	63	+	+	CCONJ
ejpam-747	97	64	1	1	NUM
ejpam-747	97	65	�	�	NOUN
ejpam-747	97	66	i	i	PRON
ejpam-747	97	67	λ,µ,ν	λ,µ,ν	PROPN
ejpam-747	97	68	0,z	0,z	INTJ
ejpam-747	97	69	f	f	PROPN
ejpam-747	98	1	where	where	SCONJ
ejpam-747	98	2	i	i	PRON
ejpam-747	98	3	λ,µ,ν	λ,µ,ν	VERB
ejpam-747	98	4	0,z	0,z	INTJ
ejpam-747	98	5	zρ	zρ	VERB
ejpam-747	98	6	=	=	PUNCT
ejpam-747	98	7	γ	γ	X
ejpam-747	98	8	�	�	PROPN
ejpam-747	98	9	ρ+	ρ+	NUM
ejpam-747	99	1	1	1	NUM
ejpam-747	99	2	�	�	PROPN
ejpam-747	99	3	γ	γ	X
ejpam-747	99	4	�	�	PROPN
ejpam-747	99	5	ρ−µ+	ρ−µ+	PROPN
ejpam-747	100	1	ν	ν	NOUN
ejpam-747	100	2	+	+	NOUN
ejpam-747	100	3	1	1	NUM
ejpam-747	100	4	�	�	PROPN
ejpam-747	100	5	γ	γ	X
ejpam-747	100	6	�	�	PROPN
ejpam-747	100	7	ρ−µ+	ρ−µ+	PROPN
ejpam-747	100	8	1	1	NUM
ejpam-747	100	9	�	�	PROPN
ejpam-747	100	10	γ	γ	X
ejpam-747	100	11	�	�	PROPN
ejpam-747	100	12	ρ+λ+	ρ+λ+	PROPN
ejpam-747	100	13	ν	ν	NOUN
ejpam-747	100	14	+	+	CCONJ
ejpam-747	100	15	1	1	NUM
ejpam-747	100	16	�	�	PROPN
ejpam-747	100	17	zρ−µ	zρ−µ	PROPN
ejpam-747	100	18	,	,	PUNCT
ejpam-747	100	19	�	�	PROPN
ejpam-747	100	20	0≤	0≤	NUM
ejpam-747	101	1	λ	λ	X
ejpam-747	101	2	<	<	X
ejpam-747	101	3	1,ρ	1,ρ	PROPN
ejpam-747	101	4	>	>	SYM
ejpam-747	101	5	max	max	PROPN
ejpam-747	101	6	�	�	PROPN
ejpam-747	101	7	0,µ−	0,µ−	PROPN
ejpam-747	101	8	ν	ν	ADP
ejpam-747	101	9	−	−	PROPN
ejpam-747	101	10	1	1	NUM
ejpam-747	101	11	�	�	PROPN
ejpam-747	101	12	.	.	PUNCT
ejpam-747	102	1	again	again	ADV
ejpam-747	102	2	,	,	PUNCT
ejpam-747	102	3	this	this	DET
ejpam-747	102	4	convolution	convolution	NOUN
ejpam-747	102	5	(	(	PUNCT
ejpam-747	102	6	4	4	NUM
ejpam-747	102	7	)	)	PUNCT
ejpam-747	102	8	reduces	reduce	VERB
ejpam-747	102	9	to	to	ADP
ejpam-747	102	10	the	the	DET
ejpam-747	102	11	derivative	derivative	ADJ
ejpam-747	102	12	operator	operator	NOUN
ejpam-747	102	13	involving	involve	VERB
ejpam-747	102	14	generalized	generalize	VERB
ejpam-747	102	15	fractional	fractional	ADJ
ejpam-747	102	16	derivative	derivative	ADJ
ejpam-747	102	17	operator	operator	NOUN
ejpam-747	102	18	j	j	PROPN
ejpam-747	102	19	λ,µ,ν	λ,µ,ν	X
ejpam-747	103	1	0,z	0,z	INTJ
ejpam-747	103	2	,	,	PUNCT
ejpam-747	103	3	if	if	SCONJ
ejpam-747	103	4	bp+k	bp+k	PROPN
ejpam-747	103	5	=	=	SYM
ejpam-747	103	6	�	�	PROPN
ejpam-747	103	7	p+	p+	PART
ejpam-747	103	8	1	1	NUM
ejpam-747	103	9	�	�	PROPN
ejpam-747	103	10	k	k	PROPN
ejpam-747	103	11	�	�	PROPN
ejpam-747	103	12	p−µ+	p−µ+	PROPN
ejpam-747	103	13	ν	ν	NOUN
ejpam-747	103	14	+	+	CCONJ
ejpam-747	103	15	1	1	NUM
ejpam-747	103	16	�	�	PROPN
ejpam-747	103	17	k	k	PROPN
ejpam-747	103	18	�	�	PROPN
ejpam-747	103	19	p−µ+	p−µ+	PROPN
ejpam-747	103	20	1	1	NUM
ejpam-747	103	21	�	�	PROPN
ejpam-747	103	22	k	k	PROPN
ejpam-747	103	23	�	�	PROPN
ejpam-747	104	1	p−λ+	p−λ+	PROPN
ejpam-747	104	2	ν	ν	NOUN
ejpam-747	104	3	+	+	CCONJ
ejpam-747	104	4	1	1	NUM
ejpam-747	104	5	�	�	PROPN
ejpam-747	104	6	k	k	PROPN
ejpam-747	104	7	and	and	CCONJ
ejpam-747	104	8	hence	hence	ADV
ejpam-747	104	9	,	,	PUNCT
ejpam-747	104	10	�	�	PROPN
ejpam-747	104	11	f	f	PROPN
ejpam-747	104	12	∗	∗	VERB
ejpam-747	104	13	g	g	PROPN
ejpam-747	104	14	�	�	PROPN
ejpam-747	104	15	(	(	PUNCT
ejpam-747	104	16	z	z	NOUN
ejpam-747	104	17	)	)	PUNCT
ejpam-747	104	18	=	=	PUNCT
ejpam-747	104	19	zµ	zµ	NUM
ejpam-747	104	20	γ	γ	PROPN
ejpam-747	104	21	�	�	PROPN
ejpam-747	104	22	p−µ+	p−µ+	PROPN
ejpam-747	104	23	1	1	NUM
ejpam-747	104	24	�	�	PROPN
ejpam-747	104	25	γ	γ	X
ejpam-747	104	26	�	�	PROPN
ejpam-747	104	27	p−λ+	p−λ+	ADP
ejpam-747	104	28	ν	ν	NOUN
ejpam-747	104	29	+	+	NOUN
ejpam-747	104	30	1	1	NUM
ejpam-747	104	31	�	�	PROPN
ejpam-747	104	32	γ	γ	PROPN
ejpam-747	104	33	�	�	PROPN
ejpam-747	104	34	p+	p+	PART
ejpam-747	104	35	1	1	NUM
ejpam-747	104	36	�	�	PROPN
ejpam-747	104	37	γ	γ	X
ejpam-747	104	38	�	�	PROPN
ejpam-747	104	39	p−µ+	p−µ+	PROPN
ejpam-747	104	40	ν	ν	NOUN
ejpam-747	104	41	+	+	CCONJ
ejpam-747	104	42	1	1	NUM
ejpam-747	104	43	�	�	PROPN
ejpam-747	104	44	j	j	PROPN
ejpam-747	104	45	λ,µ,ν	λ,µ,ν	X
ejpam-747	105	1	0,z	0,z	PRON
ejpam-747	105	2	f	f	NOUN
ejpam-747	105	3	,	,	PUNCT
ejpam-747	105	4	where	where	SCONJ
ejpam-747	105	5	j	j	PROPN
ejpam-747	105	6	λ,µ,ν	λ,µ,ν	PROPN
ejpam-747	105	7	0,z	0,z	PROPN
ejpam-747	106	1	zρ	zρ	VERB
ejpam-747	106	2	=	=	PUNCT
ejpam-747	106	3	γ	γ	X
ejpam-747	106	4	�	�	PROPN
ejpam-747	106	5	ρ+	ρ+	NUM
ejpam-747	107	1	1	1	NUM
ejpam-747	107	2	�	�	PROPN
ejpam-747	107	3	γ	γ	X
ejpam-747	107	4	�	�	PROPN
ejpam-747	107	5	ρ−µ+	ρ−µ+	PROPN
ejpam-747	108	1	ν	ν	NOUN
ejpam-747	108	2	+	+	NOUN
ejpam-747	108	3	1	1	NUM
ejpam-747	108	4	�	�	PROPN
ejpam-747	108	5	γ	γ	X
ejpam-747	108	6	�	�	PROPN
ejpam-747	108	7	ρ−µ+	ρ−µ+	PROPN
ejpam-747	108	8	1	1	NUM
ejpam-747	108	9	�	�	PROPN
ejpam-747	108	10	γ	γ	X
ejpam-747	108	11	�	�	PROPN
ejpam-747	109	1	ρ−λ+	ρ−λ+	PROPN
ejpam-747	109	2	ν	ν	X
ejpam-747	109	3	+	+	CCONJ
ejpam-747	109	4	1	1	NUM
ejpam-747	109	5	�	�	NOUN
ejpam-747	109	6	zρ−µ.	zρ−µ.	NUM
ejpam-747	109	7	the	the	DET
ejpam-747	109	8	generalized	generalize	VERB
ejpam-747	109	9	fractional	fractional	ADJ
ejpam-747	109	10	calculus	calculus	NOUN
ejpam-747	109	11	operators	operator	NOUN
ejpam-747	110	1	i	i	PRON
ejpam-747	110	2	λ,µ,ν	λ,µ,ν	PROPN
ejpam-747	110	3	0,z	0,z	PROPN
ejpam-747	110	4	and	and	CCONJ
ejpam-747	110	5	j	j	PROPN
ejpam-747	110	6	λ,µ,ν	λ,µ,ν	PROPN
ejpam-747	110	7	0,z	0,z	PRON
ejpam-747	110	8	defined	define	VERB
ejpam-747	110	9	above	above	ADV
ejpam-747	110	10	are	be	AUX
ejpam-747	110	11	studied	study	VERB
ejpam-747	110	12	in	in	ADP
ejpam-747	110	13	[	[	X
ejpam-747	110	14	5	5	NUM
ejpam-747	110	15	]	]	PUNCT
ejpam-747	110	16	,	,	PUNCT
ejpam-747	110	17	[	[	X
ejpam-747	110	18	20	20	NUM
ejpam-747	110	19	,	,	PUNCT
ejpam-747	110	20	26	26	NUM
ejpam-747	110	21	]	]	PUNCT
ejpam-747	110	22	.	.	PUNCT
ejpam-747	111	1	these	these	DET
ejpam-747	111	2	generalized	generalize	VERB
ejpam-747	111	3	fractional	fractional	ADJ
ejpam-747	111	4	calculus	calculus	NOUN
ejpam-747	111	5	operators	operator	NOUN
ejpam-747	111	6	reduce	reduce	VERB
ejpam-747	111	7	to	to	ADP
ejpam-747	111	8	fractional	fractional	ADJ
ejpam-747	111	9	calculus	calculus	NOUN
ejpam-747	111	10	operators	operator	NOUN
ejpam-747	111	11	if	if	SCONJ
ejpam-747	111	12	we	we	PRON
ejpam-747	111	13	take	take	VERB
ejpam-747	111	14	µ	µ	NOUN
ejpam-747	111	15	=	=	SYM
ejpam-747	111	16	−λ	−λ	ADJ
ejpam-747	111	17	and	and	CCONJ
ejpam-747	111	18	µ	µ	X
ejpam-747	111	19	=	=	SYM
ejpam-747	111	20	λ	λ	NOUN
ejpam-747	111	21	respectively	respectively	ADV
ejpam-747	111	22	.	.	PUNCT
ejpam-747	112	1	let	let	VERB
ejpam-747	112	2	tp	tp	PART
ejpam-747	112	3	denotes	denote	VERB
ejpam-747	112	4	the	the	DET
ejpam-747	112	5	subclass	subclass	NOUN
ejpam-747	112	6	of	of	ADP
ejpam-747	112	7	ap	ap	PROPN
ejpam-747	112	8	consisting	consist	VERB
ejpam-747	112	9	of	of	ADP
ejpam-747	112	10	functions	function	NOUN
ejpam-747	112	11	of	of	ADP
ejpam-747	112	12	the	the	DET
ejpam-747	112	13	form	form	NOUN
ejpam-747	112	14	:	:	PUNCT
ejpam-747	112	15	f	f	PROPN
ejpam-747	112	16	(	(	PUNCT
ejpam-747	112	17	z	z	NOUN
ejpam-747	112	18	)	)	PUNCT
ejpam-747	113	1	=	=	SYM
ejpam-747	113	2	zp	zp	PROPN
ejpam-747	114	1	−	−	PROPN
ejpam-747	114	2	∞	∞	NUM
ejpam-747	114	3	∑	∑	PROPN
ejpam-747	114	4	k=1	k=1	PROPN
ejpam-747	114	5	ap+kzp+k	ap+kzp+k	ADV
ejpam-747	114	6	,	,	PUNCT
ejpam-747	114	7	ap+k	ap+k	NOUN
ejpam-747	114	8	≥	≥	NOUN
ejpam-747	114	9	0	0	NUM
ejpam-747	114	10	.	.	PUNCT
ejpam-747	115	1	(	(	PUNCT
ejpam-747	115	2	7	7	X
ejpam-747	115	3	)	)	PUNCT
ejpam-747	115	4	motivated	motivate	VERB
ejpam-747	115	5	with	with	ADP
ejpam-747	115	6	the	the	DET
ejpam-747	115	7	several	several	ADJ
ejpam-747	115	8	work	work	NOUN
ejpam-747	115	9	specially	specially	ADV
ejpam-747	115	10	the	the	DET
ejpam-747	115	11	work	work	NOUN
ejpam-747	115	12	of	of	ADP
ejpam-747	115	13	prajapat	prajapat	NOUN
ejpam-747	115	14	et	et	PROPN
ejpam-747	115	15	al	al	PROPN
ejpam-747	115	16	.	.	PUNCT
ejpam-747	116	1	[	[	X
ejpam-747	116	2	21	21	NUM
ejpam-747	116	3	]	]	PUNCT
ejpam-747	116	4	,	,	PUNCT
ejpam-747	116	5	we	we	PRON
ejpam-747	116	6	consider	consider	VERB
ejpam-747	116	7	ℜg	ℜg	PROPN
ejpam-747	116	8	h	h	PROPN
ejpam-747	116	9	�	�	PROPN
ejpam-747	116	10	p	p	PROPN
ejpam-747	116	11	,	,	PUNCT
ejpam-747	116	12	m	m	PROPN
ejpam-747	116	13	,	,	PUNCT
ejpam-747	116	14	β	β	X
ejpam-747	116	15	�	�	PROPN
ejpam-747	116	16	class	class	NOUN
ejpam-747	116	17	defined	define	VERB
ejpam-747	116	18	as	as	SCONJ
ejpam-747	116	19	follows	follow	VERB
ejpam-747	116	20	:	:	PUNCT
ejpam-747	116	21	p.	p.	PROPN
ejpam-747	116	22	sharma	sharma	PROPN
ejpam-747	116	23	,	,	PUNCT
ejpam-747	116	24	p.	p.	PROPN
ejpam-747	116	25	srivastava	srivastava	PROPN
ejpam-747	116	26	/	/	SYM
ejpam-747	116	27	eur	eur	PROPN
ejpam-747	116	28	.	.	PUNCT
ejpam-747	117	1	j.	j.	PROPN
ejpam-747	117	2	pure	pure	PROPN
ejpam-747	117	3	appl	appl	PROPN
ejpam-747	117	4	.	.	PROPN
ejpam-747	117	5	math	math	PROPN
ejpam-747	117	6	,	,	PUNCT
ejpam-747	117	7	3	3	NUM
ejpam-747	117	8	(	(	PUNCT
ejpam-747	117	9	2010	2010	NUM
ejpam-747	117	10	)	)	PUNCT
ejpam-747	117	11	,	,	PUNCT
ejpam-747	117	12	1093	1093	NUM
ejpam-747	117	13	-	-	SYM
ejpam-747	117	14	1112	1112	NUM
ejpam-747	117	15	1097	1097	NUM
ejpam-747	117	16	definition	definition	NOUN
ejpam-747	117	17	1	1	NUM
ejpam-747	117	18	.	.	PUNCT
ejpam-747	118	1	a	a	DET
ejpam-747	118	2	function	function	NOUN
ejpam-747	118	3	f	f	PROPN
ejpam-747	118	4	∈	∈	PROPN
ejpam-747	118	5	tp	tp	NOUN
ejpam-747	118	6	is	be	AUX
ejpam-747	118	7	said	say	VERB
ejpam-747	118	8	to	to	PART
ejpam-747	118	9	be	be	AUX
ejpam-747	118	10	a	a	DET
ejpam-747	118	11	member	member	NOUN
ejpam-747	118	12	of	of	ADP
ejpam-747	118	13	the	the	DET
ejpam-747	118	14	class	class	NOUN
ejpam-747	119	1	ℜg	ℜg	PROPN
ejpam-747	119	2	h	h	NOUN
ejpam-747	119	3	�	�	PROPN
ejpam-747	119	4	p	p	PROPN
ejpam-747	119	5	,	,	PUNCT
ejpam-747	119	6	m	m	PROPN
ejpam-747	119	7	,	,	PUNCT
ejpam-747	119	8	β	β	X
ejpam-747	119	9	�	�	PROPN
ejpam-747	120	1	if	if	SCONJ
ejpam-747	120	2	and	and	CCONJ
ejpam-747	120	3	only	only	ADV
ejpam-747	120	4	if	if	SCONJ
ejpam-747	120	5	for	for	ADP
ejpam-747	120	6	any	any	DET
ejpam-747	120	7	g	g	NOUN
ejpam-747	120	8	,	,	PUNCT
ejpam-747	120	9	h	h	PROPN
ejpam-747	120	10	∈	∈	PROPN
ejpam-747	120	11	ap	ap	PROPN
ejpam-747	120	12	with	with	ADP
ejpam-747	120	13	non	non	ADJ
ejpam-747	120	14	-	-	ADJ
ejpam-747	120	15	negative	negative	ADJ
ejpam-747	120	16	coefficients	coefficient	NOUN
ejpam-747	120	17	,	,	PUNCT
ejpam-747	120	18	�	�	PROPN
ejpam-747	120	19	�	�	PROPN
ejpam-747	120	20	�	�	PROPN
ejpam-747	120	21	�	�	PROPN
ejpam-747	120	22	�	�	PROPN
ejpam-747	120	23	z	z	PROPN
ejpam-747	120	24	�	�	PROPN
ejpam-747	120	25	f	f	PROPN
ejpam-747	120	26	∗	∗	VERB
ejpam-747	120	27	g	g	PROPN
ejpam-747	120	28	�	�	PROPN
ejpam-747	120	29	m+1	m+1	PRON
ejpam-747	120	30	(	(	PUNCT
ejpam-747	120	31	z	z	NOUN
ejpam-747	120	32	)	)	PUNCT
ejpam-747	120	33	�	�	PROPN
ejpam-747	120	34	f	f	PROPN
ejpam-747	120	35	∗	∗	PROPN
ejpam-747	120	36	h	h	PROPN
ejpam-747	120	37	�	�	PROPN
ejpam-747	120	38	m	m	PROPN
ejpam-747	120	39	(	(	PUNCT
ejpam-747	120	40	z	z	NOUN
ejpam-747	120	41	)	)	PUNCT
ejpam-747	120	42	−	−	PROPN
ejpam-747	120	43	�	�	PROPN
ejpam-747	120	44	p−m	p−m	PRON
ejpam-747	120	45	�	�	PROPN
ejpam-747	120	46	�	�	PROPN
ejpam-747	120	47	�	�	PROPN
ejpam-747	120	48	�	�	PROPN
ejpam-747	120	49	�	�	PROPN
ejpam-747	120	50	�	�	PROPN
ejpam-747	120	51	<	<	X
ejpam-747	120	52	β	β	X
ejpam-747	120	53	,	,	PUNCT
ejpam-747	120	54	z	z	NOUN
ejpam-747	120	55	∈∆	∈∆	ADV
ejpam-747	120	56	,	,	PUNCT
ejpam-747	120	57	p	p	PROPN
ejpam-747	120	58	∈	∈	PROPN
ejpam-747	120	59	n	n	CCONJ
ejpam-747	120	60	,	,	PUNCT
ejpam-747	120	61	p	p	X
ejpam-747	120	62	>	>	X
ejpam-747	120	63	m	m	PROPN
ejpam-747	120	64	,	,	PUNCT
ejpam-747	120	65	0	0	PUNCT
ejpam-747	120	66	<	<	X
ejpam-747	120	67	β	β	X
ejpam-747	120	68	≤	≤	NOUN
ejpam-747	121	1	p	p	X
ejpam-747	121	2	,	,	PUNCT
ejpam-747	121	3	m	m	PROPN
ejpam-747	121	4	∈	∈	PROPN
ejpam-747	121	5	n0	n0	X
ejpam-747	121	6	=	=	PUNCT
ejpam-747	121	7	n	n	PROPN
ejpam-747	121	8	⋃	⋃	NOUN
ejpam-747	121	9	{	{	PUNCT
ejpam-747	121	10	0	0	NUM
ejpam-747	121	11	}	}	PUNCT
ejpam-747	121	12	,	,	PUNCT
ejpam-747	121	13	where	where	SCONJ
ejpam-747	121	14	�	�	PROPN
ejpam-747	121	15	f	f	PROPN
ejpam-747	121	16	∗	∗	VERB
ejpam-747	121	17	g	g	PROPN
ejpam-747	121	18	�	�	PROPN
ejpam-747	121	19	r	r	NOUN
ejpam-747	121	20	(	(	PUNCT
ejpam-747	121	21	z	z	NOUN
ejpam-747	121	22	)	)	PUNCT
ejpam-747	121	23	denotes	denote	VERB
ejpam-747	121	24	the	the	DET
ejpam-747	121	25	r	r	NOUN
ejpam-747	121	26	th	th	X
ejpam-747	121	27	derivative	derivative	NOUN
ejpam-747	121	28	of	of	ADP
ejpam-747	121	29	�	�	PROPN
ejpam-747	121	30	f	f	PROPN
ejpam-747	121	31	∗	∗	NOUN
ejpam-747	121	32	g	g	PROPN
ejpam-747	121	33	�	�	PROPN
ejpam-747	121	34	and	and	CCONJ
ejpam-747	121	35	is	be	AUX
ejpam-747	121	36	given	give	VERB
ejpam-747	121	37	by	by	ADP
ejpam-747	121	38	�	�	PROPN
ejpam-747	121	39	f	f	PROPN
ejpam-747	121	40	∗	∗	VERB
ejpam-747	121	41	g	g	PROPN
ejpam-747	121	42	�	�	PROPN
ejpam-747	121	43	r	r	NOUN
ejpam-747	121	44	(	(	PUNCT
ejpam-747	121	45	z	z	NOUN
ejpam-747	121	46	)	)	PUNCT
ejpam-747	121	47	=	=	SYM
ejpam-747	122	1	p	p	X
ejpam-747	122	2	!	!	PUNCT
ejpam-747	122	3	�	�	PROPN
ejpam-747	122	4	p−	p−	NOUN
ejpam-747	122	5	r	r	NOUN
ejpam-747	122	6	�	�	PROPN
ejpam-747	122	7	!	!	PUNCT
ejpam-747	123	1	zp−r	zp−r	PROPN
ejpam-747	123	2	+	+	CCONJ
ejpam-747	123	3	∞	∞	PROPN
ejpam-747	123	4	∑	∑	PUNCT
ejpam-747	123	5	k=1	k=1	PROPN
ejpam-747	123	6	�	�	PROPN
ejpam-747	123	7	p+	p+	PROPN
ejpam-747	123	8	k	k	PROPN
ejpam-747	123	9	�	�	PROPN
ejpam-747	123	10	!	!	PUNCT
ejpam-747	124	1	�	�	PROPN
ejpam-747	124	2	p+	p+	PART
ejpam-747	124	3	k−	k−	PROPN
ejpam-747	124	4	r	r	NOUN
ejpam-747	124	5	�	�	PROPN
ejpam-747	124	6	!	!	PUNCT
ejpam-747	125	1	ap+k	ap+k	PROPN
ejpam-747	126	1	bp+kzp+k−r	bp+kzp+k−r	PROPN
ejpam-747	126	2	,	,	PUNCT
ejpam-747	126	3	r	r	PROPN
ejpam-747	126	4	∈	∈	PROPN
ejpam-747	126	5	n0	n0	PROPN
ejpam-747	126	6	.	.	PUNCT
ejpam-747	127	1	(	(	PUNCT
ejpam-747	127	2	8)	8)	NUM
ejpam-747	127	3	obviously	obviously	ADV
ejpam-747	127	4	the	the	DET
ejpam-747	127	5	class	class	NOUN
ejpam-747	127	6	ℜg	ℜg	PROPN
ejpam-747	127	7	h	h	NOUN
ejpam-747	127	8	�	�	PROPN
ejpam-747	127	9	p	p	PROPN
ejpam-747	127	10	,	,	PUNCT
ejpam-747	127	11	m	m	PROPN
ejpam-747	127	12	,	,	PUNCT
ejpam-747	127	13	β	β	X
ejpam-747	127	14	�	�	PROPN
ejpam-747	127	15	contains	contain	VERB
ejpam-747	127	16	the	the	DET
ejpam-747	127	17	class	class	NOUN
ejpam-747	127	18	s	s	PART
ejpam-747	127	19	g	g	PROPN
ejpam-747	127	20	h	h	PRON
ejpam-747	127	21	�	�	PROPN
ejpam-747	127	22	p	p	PROPN
ejpam-747	127	23	,	,	PUNCT
ejpam-747	127	24	m	m	PROPN
ejpam-747	127	25	,	,	PUNCT
ejpam-747	127	26	β	β	X
ejpam-747	127	27	�	�	PROPN
ejpam-747	127	28	,	,	PUNCT
ejpam-747	127	29	which	which	PRON
ejpam-747	127	30	is	be	AUX
ejpam-747	127	31	defined	define	VERB
ejpam-747	127	32	as	as	SCONJ
ejpam-747	127	33	follows	follow	VERB
ejpam-747	127	34	:	:	PUNCT
ejpam-747	127	35	definition	definition	NOUN
ejpam-747	127	36	2	2	NUM
ejpam-747	127	37	.	.	PUNCT
ejpam-747	127	38	a	a	DET
ejpam-747	127	39	function	function	NOUN
ejpam-747	127	40	f	f	X
ejpam-747	127	41	(	(	PUNCT
ejpam-747	127	42	z	z	NOUN
ejpam-747	127	43	)	)	PUNCT
ejpam-747	127	44	∈	∈	PROPN
ejpam-747	127	45	tp	tp	NOUN
ejpam-747	127	46	is	be	AUX
ejpam-747	127	47	said	say	VERB
ejpam-747	127	48	to	to	PART
ejpam-747	127	49	be	be	AUX
ejpam-747	127	50	a	a	DET
ejpam-747	127	51	member	member	NOUN
ejpam-747	127	52	of	of	ADP
ejpam-747	127	53	the	the	DET
ejpam-747	127	54	class	class	NOUN
ejpam-747	127	55	s	s	PART
ejpam-747	127	56	g	g	PROPN
ejpam-747	127	57	h	h	PRON
ejpam-747	127	58	�	�	PROPN
ejpam-747	127	59	p	p	PROPN
ejpam-747	127	60	,	,	PUNCT
ejpam-747	127	61	m	m	PROPN
ejpam-747	127	62	,	,	PUNCT
ejpam-747	127	63	β	β	X
ejpam-747	127	64	�	�	PROPN
ejpam-747	127	65	if	if	SCONJ
ejpam-747	127	66	and	and	CCONJ
ejpam-747	127	67	only	only	ADV
ejpam-747	127	68	if	if	SCONJ
ejpam-747	127	69	for	for	ADP
ejpam-747	127	70	any	any	DET
ejpam-747	127	71	g	g	NOUN
ejpam-747	127	72	,	,	PUNCT
ejpam-747	127	73	h	h	PROPN
ejpam-747	127	74	∈	∈	PROPN
ejpam-747	127	75	ap	ap	PROPN
ejpam-747	127	76	with	with	ADP
ejpam-747	127	77	non	non	ADJ
ejpam-747	127	78	-	-	ADJ
ejpam-747	127	79	negative	negative	ADJ
ejpam-747	127	80	coefficients	coefficient	NOUN
ejpam-747	127	81	,	,	PUNCT
ejpam-747	127	82	re	re	ADP
ejpam-747	127	83	(	(	PUNCT
ejpam-747	127	84	z	z	PROPN
ejpam-747	127	85	�	�	PROPN
ejpam-747	127	86	f	f	PROPN
ejpam-747	127	87	∗	∗	VERB
ejpam-747	127	88	g	g	PROPN
ejpam-747	127	89	�	�	PROPN
ejpam-747	127	90	m+1	m+1	PRON
ejpam-747	127	91	(	(	PUNCT
ejpam-747	127	92	z	z	NOUN
ejpam-747	127	93	)	)	PUNCT
ejpam-747	127	94	�	�	PROPN
ejpam-747	127	95	f	f	PROPN
ejpam-747	127	96	∗	∗	PROPN
ejpam-747	127	97	h	h	PROPN
ejpam-747	127	98	�	�	PROPN
ejpam-747	127	99	m	m	PROPN
ejpam-747	127	100	(	(	PUNCT
ejpam-747	127	101	z	z	NOUN
ejpam-747	127	102	)	)	PUNCT
ejpam-747	128	1	+	+	NOUN
ejpam-747	128	2	m	m	X
ejpam-747	128	3	)	)	PUNCT
ejpam-747	128	4	>	>	X
ejpam-747	129	1	p−	p−	NOUN
ejpam-747	129	2	β	β	X
ejpam-747	129	3	,	,	PUNCT
ejpam-747	129	4	z	z	NOUN
ejpam-747	129	5	∈∆	∈∆	ADV
ejpam-747	129	6	,	,	PUNCT
ejpam-747	129	7	p	p	PROPN
ejpam-747	129	8	∈	∈	PROPN
ejpam-747	129	9	n	n	CCONJ
ejpam-747	129	10	,	,	PUNCT
ejpam-747	129	11	p	p	X
ejpam-747	129	12	>	>	X
ejpam-747	129	13	m	m	PROPN
ejpam-747	129	14	,	,	PUNCT
ejpam-747	129	15	0	0	PUNCT
ejpam-747	129	16	<	<	X
ejpam-747	129	17	β	β	X
ejpam-747	129	18	≤	≤	NOUN
ejpam-747	129	19	p	p	X
ejpam-747	129	20	,	,	PUNCT
ejpam-747	129	21	m	m	PROPN
ejpam-747	129	22	∈	∈	PROPN
ejpam-747	129	23	n0	n0	PROPN
ejpam-747	129	24	.	.	PUNCT
ejpam-747	130	1	taking	take	VERB
ejpam-747	130	2	m	m	PROPN
ejpam-747	130	3	=	=	SYM
ejpam-747	130	4	0	0	NUM
ejpam-747	130	5	and	and	CCONJ
ejpam-747	130	6	1	1	NUM
ejpam-747	130	7	respectively	respectively	ADV
ejpam-747	130	8	and	and	CCONJ
ejpam-747	130	9	h(z	h(z	NOUN
ejpam-747	130	10	)	)	PUNCT
ejpam-747	131	1	=	=	SYM
ejpam-747	131	2	g	g	PROPN
ejpam-747	131	3	(	(	PUNCT
ejpam-747	131	4	z	z	NOUN
ejpam-747	131	5	)	)	PUNCT
ejpam-747	131	6	=	=	PUNCT
ejpam-747	132	1	zp	zp	PROPN
ejpam-747	132	2	1−z	1−z	NUM
ejpam-747	132	3	,	,	PUNCT
ejpam-747	132	4	the	the	DET
ejpam-747	132	5	class	class	NOUN
ejpam-747	132	6	ℜg	ℜg	PROPN
ejpam-747	132	7	h	h	NOUN
ejpam-747	132	8	�	�	PROPN
ejpam-747	132	9	p	p	PROPN
ejpam-747	132	10	,	,	PUNCT
ejpam-747	132	11	m	m	PROPN
ejpam-747	132	12	,	,	PUNCT
ejpam-747	132	13	β	β	PROPN
ejpam-747	132	14	�	�	PROPN
ejpam-747	132	15	coincides	coincide	VERB
ejpam-747	132	16	with	with	ADP
ejpam-747	132	17	the	the	DET
ejpam-747	132	18	classes	class	NOUN
ejpam-747	132	19	s	s	PART
ejpam-747	132	20	∗	∗	NOUN
ejpam-747	132	21	p	p	X
ejpam-747	132	22	�	�	PROPN
ejpam-747	132	23	β	β	X
ejpam-747	132	24	�	�	PROPN
ejpam-747	132	25	and	and	CCONJ
ejpam-747	132	26	k	k	PROPN
ejpam-747	132	27	p	p	X
ejpam-747	132	28	�	�	PROPN
ejpam-747	132	29	β	β	X
ejpam-747	132	30	�	�	PROPN
ejpam-747	132	31	respectively	respectively	ADV
ejpam-747	132	32	and	and	CCONJ
ejpam-747	132	33	the	the	DET
ejpam-747	132	34	class	class	NOUN
ejpam-747	132	35	s	s	PART
ejpam-747	132	36	g	g	PROPN
ejpam-747	132	37	h	h	PRON
ejpam-747	132	38	�	�	PROPN
ejpam-747	132	39	p	p	PROPN
ejpam-747	132	40	,	,	PUNCT
ejpam-747	132	41	m	m	PROPN
ejpam-747	132	42	,	,	PUNCT
ejpam-747	132	43	β	β	PROPN
ejpam-747	132	44	�	�	PROPN
ejpam-747	132	45	coincides	coincide	VERB
ejpam-747	132	46	with	with	ADP
ejpam-747	132	47	the	the	DET
ejpam-747	132	48	class	class	NOUN
ejpam-747	132	49	s∗p	s∗p	NUM
ejpam-747	132	50	�	�	PROPN
ejpam-747	132	51	p−	p−	PROPN
ejpam-747	132	52	β	β	X
ejpam-747	132	53	�	�	PROPN
ejpam-747	132	54	and	and	CCONJ
ejpam-747	132	55	kp	kp	PROPN
ejpam-747	132	56	�	�	PROPN
ejpam-747	132	57	p−	p−	PROPN
ejpam-747	132	58	β	β	X
ejpam-747	132	59	�	�	PROPN
ejpam-747	132	60	respectively	respectively	ADV
ejpam-747	132	61	.	.	PUNCT
ejpam-747	133	1	also	also	ADV
ejpam-747	133	2	,	,	PUNCT
ejpam-747	133	3	taking	take	VERB
ejpam-747	133	4	g	g	PRON
ejpam-747	133	5	(	(	PUNCT
ejpam-747	133	6	z	z	NOUN
ejpam-747	133	7	)	)	PUNCT
ejpam-747	133	8	=	=	PUNCT
ejpam-747	134	1	zp	zp	PROPN
ejpam-747	134	2	1−z	1−z	NUM
ejpam-747	134	3	,	,	PUNCT
ejpam-747	134	4	h(z	h(z	PROPN
ejpam-747	134	5	)	)	PUNCT
ejpam-747	134	6	=	=	SYM
ejpam-747	134	7	zp	zp	PROPN
ejpam-747	134	8	and	and	CCONJ
ejpam-747	134	9	m	m	PROPN
ejpam-747	134	10	=	=	ADJ
ejpam-747	134	11	0	0	NUM
ejpam-747	134	12	,	,	PUNCT
ejpam-747	134	13	the	the	DET
ejpam-747	134	14	class	class	NOUN
ejpam-747	134	15	ℜg	ℜg	PROPN
ejpam-747	134	16	h	h	NOUN
ejpam-747	134	17	�	�	PROPN
ejpam-747	134	18	p	p	PROPN
ejpam-747	134	19	,	,	PUNCT
ejpam-747	134	20	m	m	PROPN
ejpam-747	134	21	,	,	PUNCT
ejpam-747	134	22	β	β	X
ejpam-747	134	23	�	�	PROPN
ejpam-747	134	24	reduces	reduce	VERB
ejpam-747	134	25	to	to	ADP
ejpam-747	134	26	the	the	DET
ejpam-747	134	27	class	class	NOUN
ejpam-747	134	28	ck	ck	INTJ
ejpam-747	134	29	p	p	PROPN
ejpam-747	134	30	�	�	PROPN
ejpam-747	134	31	β	β	X
ejpam-747	134	32	�	�	PROPN
ejpam-747	134	33	and	and	CCONJ
ejpam-747	134	34	the	the	DET
ejpam-747	134	35	class	class	NOUN
ejpam-747	134	36	s	s	PART
ejpam-747	134	37	g	g	PROPN
ejpam-747	134	38	h	h	PRON
ejpam-747	134	39	�	�	PROPN
ejpam-747	134	40	p	p	PROPN
ejpam-747	134	41	,	,	PUNCT
ejpam-747	134	42	m	m	PROPN
ejpam-747	134	43	,	,	PUNCT
ejpam-747	134	44	β	β	X
ejpam-747	134	45	�	�	PROPN
ejpam-747	134	46	reduces	reduce	VERB
ejpam-747	134	47	to	to	ADP
ejpam-747	134	48	the	the	DET
ejpam-747	134	49	the	the	DET
ejpam-747	134	50	class	class	NOUN
ejpam-747	134	51	ckp	ckp	PROPN
ejpam-747	134	52	�	�	PROPN
ejpam-747	134	53	p−	p−	PROPN
ejpam-747	134	54	β	β	X
ejpam-747	134	55	�	�	PROPN
ejpam-747	134	56	.	.	PUNCT
ejpam-747	135	1	if	if	SCONJ
ejpam-747	135	2	h	h	NOUN
ejpam-747	135	3	=	=	SYM
ejpam-747	135	4	g	g	PROPN
ejpam-747	135	5	,	,	PUNCT
ejpam-747	135	6	we	we	PRON
ejpam-747	135	7	denote	denote	VERB
ejpam-747	135	8	ℜg	ℜg	PROPN
ejpam-747	135	9	h	h	NOUN
ejpam-747	135	10	�	�	PROPN
ejpam-747	135	11	p	p	PROPN
ejpam-747	135	12	,	,	PUNCT
ejpam-747	135	13	m	m	PROPN
ejpam-747	135	14	,	,	PUNCT
ejpam-747	136	1	β	β	X
ejpam-747	136	2	�	�	PROPN
ejpam-747	136	3	≡	≡	PROPN
ejpam-747	136	4	ℜg	ℜg	PROPN
ejpam-747	136	5	�	�	PROPN
ejpam-747	136	6	p	p	PROPN
ejpam-747	136	7	,	,	PUNCT
ejpam-747	136	8	m	m	PROPN
ejpam-747	136	9	,	,	PUNCT
ejpam-747	136	10	β	β	X
ejpam-747	136	11	�	�	PROPN
ejpam-747	136	12	.	.	PUNCT
ejpam-747	137	1	class	class	NOUN
ejpam-747	137	2	ℜg	ℜg	PROPN
ejpam-747	137	3	�	�	PROPN
ejpam-747	137	4	1,0,β	1,0,β	NUM
ejpam-747	137	5	�	�	PROPN
ejpam-747	137	6	for	for	ADP
ejpam-747	137	7	g	g	PROPN
ejpam-747	137	8	(	(	PUNCT
ejpam-747	137	9	z	z	NOUN
ejpam-747	137	10	)	)	PUNCT
ejpam-747	137	11	=	=	PUNCT
ejpam-747	138	1	z	z	PROPN
ejpam-747	138	2	1−z	1−z	NUM
ejpam-747	138	3	,	,	PUNCT
ejpam-747	138	4	coincides	coincide	VERB
ejpam-747	138	5	with	with	ADP
ejpam-747	138	6	the	the	DET
ejpam-747	138	7	class	class	NOUN
ejpam-747	138	8	studied	study	VERB
ejpam-747	138	9	by	by	ADP
ejpam-747	138	10	chen	chen	PROPN
ejpam-747	138	11	et	et	PROPN
ejpam-747	138	12	al	al	PROPN
ejpam-747	138	13	.	.	PUNCT
ejpam-747	139	1	[	[	X
ejpam-747	139	2	7	7	X
ejpam-747	139	3	]	]	PUNCT
ejpam-747	139	4	as	as	ADP
ejpam-747	139	5	a	a	DET
ejpam-747	139	6	particular	particular	ADJ
ejpam-747	139	7	case	case	NOUN
ejpam-747	139	8	.	.	PUNCT
ejpam-747	140	1	in	in	ADP
ejpam-747	140	2	addition	addition	NOUN
ejpam-747	140	3	,	,	PUNCT
ejpam-747	140	4	the	the	DET
ejpam-747	140	5	class	class	NOUN
ejpam-747	140	6	ℜg	ℜg	PROPN
ejpam-747	140	7	�	�	PROPN
ejpam-747	140	8	p	p	PROPN
ejpam-747	140	9	,	,	PUNCT
ejpam-747	140	10	0	0	NUM
ejpam-747	140	11	,	,	PUNCT
ejpam-747	140	12	p	p	X
ejpam-747	140	13	(	(	PUNCT
ejpam-747	140	14	1−α	1−α	NUM
ejpam-747	140	15	)	)	PUNCT
ejpam-747	140	16	�	�	PROPN
ejpam-747	140	17	reduces	reduce	VERB
ejpam-747	140	18	to	to	ADP
ejpam-747	140	19	the	the	DET
ejpam-747	140	20	class	class	NOUN
ejpam-747	140	21	studied	study	VERB
ejpam-747	140	22	by	by	ADP
ejpam-747	140	23	ali	ali	PROPN
ejpam-747	140	24	et	et	PROPN
ejpam-747	140	25	al	al	PROPN
ejpam-747	140	26	.	.	PUNCT
ejpam-747	141	1	[	[	X
ejpam-747	141	2	1	1	NUM
ejpam-747	141	3	]	]	PUNCT
ejpam-747	141	4	.	.	PUNCT
ejpam-747	142	1	taking	take	VERB
ejpam-747	142	2	,	,	PUNCT
ejpam-747	142	3	for	for	ADP
ejpam-747	142	4	n+	n+	PRON
ejpam-747	142	5	p	p	X
ejpam-747	142	6	>	>	X
ejpam-747	142	7	0	0	NUM
ejpam-747	142	8	,	,	PUNCT
ejpam-747	142	9	h(z	h(z	NOUN
ejpam-747	142	10	)	)	PUNCT
ejpam-747	142	11	=	=	SYM
ejpam-747	142	12	g	g	PROPN
ejpam-747	142	13	(	(	PUNCT
ejpam-747	142	14	z	z	NOUN
ejpam-747	142	15	)	)	PUNCT
ejpam-747	142	16	=	=	SYM
ejpam-747	142	17	zp	zp	X
ejpam-747	142	18	(	(	PUNCT
ejpam-747	142	19	1−z)n+p	1−z)n+p	NUM
ejpam-747	142	20	and	and	CCONJ
ejpam-747	142	21	g	g	PROPN
ejpam-747	142	22	(	(	PUNCT
ejpam-747	142	23	z	z	NOUN
ejpam-747	142	24	)	)	PUNCT
ejpam-747	143	1	=	=	SYM
ejpam-747	143	2	zp	zp	X
ejpam-747	143	3	(	(	PUNCT
ejpam-747	143	4	1−z)n+p	1−z)n+p	NUM
ejpam-747	143	5	,	,	PUNCT
ejpam-747	143	6	h(z	h(z	PROPN
ejpam-747	143	7	)	)	PUNCT
ejpam-747	143	8	=	=	SYM
ejpam-747	143	9	zp	zp	PROPN
ejpam-747	143	10	respectively	respectively	ADV
ejpam-747	143	11	,	,	PUNCT
ejpam-747	143	12	the	the	DET
ejpam-747	143	13	class	class	NOUN
ejpam-747	143	14	ℜg	ℜg	PROPN
ejpam-747	143	15	h	h	NOUN
ejpam-747	143	16	�	�	PROPN
ejpam-747	143	17	p	p	PROPN
ejpam-747	143	18	,	,	PUNCT
ejpam-747	143	19	m	m	PROPN
ejpam-747	143	20	,	,	PUNCT
ejpam-747	143	21	β	β	X
ejpam-747	143	22	�	�	PROPN
ejpam-747	143	23	reduces	reduce	VERB
ejpam-747	143	24	to	to	ADP
ejpam-747	143	25	the	the	DET
ejpam-747	143	26	classes	class	NOUN
ejpam-747	143	27	,	,	PUNCT
ejpam-747	143	28	which	which	PRON
ejpam-747	143	29	were	be	AUX
ejpam-747	143	30	investigated	investigate	VERB
ejpam-747	143	31	by	by	ADP
ejpam-747	143	32	raina	raina	PROPN
ejpam-747	143	33	and	and	CCONJ
ejpam-747	143	34	srivastava	srivastava	PROPN
ejpam-747	144	1	[	[	X
ejpam-747	144	2	22	22	NUM
ejpam-747	144	3	]	]	PUNCT
ejpam-747	144	4	and	and	CCONJ
ejpam-747	144	5	these	these	DET
ejpam-747	144	6	classes	class	NOUN
ejpam-747	144	7	coincide	coincide	VERB
ejpam-747	144	8	with	with	ADP
ejpam-747	144	9	the	the	DET
ejpam-747	144	10	classes	class	NOUN
ejpam-747	144	11	,	,	PUNCT
ejpam-747	144	12	studied	study	VERB
ejpam-747	144	13	by	by	ADP
ejpam-747	144	14	güney	güney	NOUN
ejpam-747	144	15	and	and	CCONJ
ejpam-747	144	16	breaz	breaz	NOUN
ejpam-747	145	1	[	[	X
ejpam-747	145	2	12	12	NUM
ejpam-747	145	3	]	]	PUNCT
ejpam-747	145	4	if	if	SCONJ
ejpam-747	145	5	n+	n+	ADP
ejpam-747	145	6	p	p	X
ejpam-747	145	7	=	=	SYM
ejpam-747	145	8	1	1	NUM
ejpam-747	146	1	and	and	CCONJ
ejpam-747	146	2	are	be	AUX
ejpam-747	146	3	the	the	DET
ejpam-747	146	4	generalization	generalization	NOUN
ejpam-747	146	5	of	of	ADP
ejpam-747	146	6	the	the	DET
ejpam-747	146	7	classes	class	NOUN
ejpam-747	146	8	investigated	investigate	VERB
ejpam-747	146	9	by	by	ADP
ejpam-747	146	10	murugusundaramoorthi	murugusundaramoorthi	PROPN
ejpam-747	146	11	and	and	CCONJ
ejpam-747	146	12	srivastava	srivastava	PROPN
ejpam-747	147	1	[	[	X
ejpam-747	147	2	18	18	NUM
ejpam-747	147	3	]	]	PUNCT
ejpam-747	147	4	.	.	PUNCT
ejpam-747	148	1	further	far	ADV
ejpam-747	148	2	,	,	PUNCT
ejpam-747	148	3	taking	take	VERB
ejpam-747	148	4	g	g	NOUN
ejpam-747	148	5	∈	∈	NOUN
ejpam-747	148	6	a1	a1	NOUN
ejpam-747	148	7	so	so	SCONJ
ejpam-747	148	8	that	that	SCONJ
ejpam-747	148	9	bk+1	bk+1	NOUN
ejpam-747	148	10	=	=	SYM
ejpam-747	148	11	(	(	PUNCT
ejpam-747	148	12	1	1	NUM
ejpam-747	148	13	+	+	CCONJ
ejpam-747	148	14	k)n	k)n	NOUN
ejpam-747	148	15	,	,	PUNCT
ejpam-747	148	16	n	n	PROPN
ejpam-747	148	17	∈	∈	PROPN
ejpam-747	148	18	n0	n0	PROPN
ejpam-747	148	19	,	,	PUNCT
ejpam-747	148	20	the	the	DET
ejpam-747	148	21	class	class	NOUN
ejpam-747	148	22	ℜg	ℜg	PROPN
ejpam-747	148	23	(	(	PUNCT
ejpam-747	148	24	1,0,1−α	1,0,1−α	NUM
ejpam-747	148	25	)	)	PUNCT
ejpam-747	148	26	would	would	AUX
ejpam-747	148	27	reduce	reduce	VERB
ejpam-747	148	28	to	to	ADP
ejpam-747	148	29	the	the	DET
ejpam-747	148	30	class	class	NOUN
ejpam-747	148	31	studied	study	VERB
ejpam-747	148	32	in	in	ADP
ejpam-747	148	33	[	[	X
ejpam-747	148	34	1	1	NUM
ejpam-747	148	35	]	]	PUNCT
ejpam-747	148	36	.	.	PUNCT
ejpam-747	149	1	moreover	moreover	ADV
ejpam-747	149	2	,	,	PUNCT
ejpam-747	149	3	a	a	DET
ejpam-747	149	4	class	class	NOUN
ejpam-747	149	5	similar	similar	ADJ
ejpam-747	149	6	to	to	ADP
ejpam-747	149	7	ℜg	ℜg	PROPN
ejpam-747	149	8	�	�	PROPN
ejpam-747	149	9	p	p	PROPN
ejpam-747	149	10	,	,	PUNCT
ejpam-747	149	11	m	m	PROPN
ejpam-747	149	12	,	,	PUNCT
ejpam-747	149	13	β	β	X
ejpam-747	149	14	�	�	PROPN
ejpam-747	149	15	is	be	AUX
ejpam-747	149	16	studied	study	VERB
ejpam-747	149	17	by	by	ADP
ejpam-747	149	18	prajapat	prajapat	NOUN
ejpam-747	149	19	et	et	PROPN
ejpam-747	149	20	al	al	PROPN
ejpam-747	149	21	.	.	PUNCT
ejpam-747	150	1	[	[	X
ejpam-747	150	2	21	21	NUM
ejpam-747	150	3	]	]	PUNCT
ejpam-747	150	4	.	.	PUNCT
ejpam-747	151	1	in	in	ADP
ejpam-747	151	2	this	this	DET
ejpam-747	151	3	paper	paper	NOUN
ejpam-747	151	4	,	,	PUNCT
ejpam-747	151	5	we	we	PRON
ejpam-747	151	6	study	study	VERB
ejpam-747	151	7	coefficient	coefficient	NOUN
ejpam-747	151	8	inequality	inequality	NOUN
ejpam-747	151	9	,	,	PUNCT
ejpam-747	151	10	growth	growth	NOUN
ejpam-747	151	11	and	and	CCONJ
ejpam-747	151	12	distortion	distortion	NOUN
ejpam-747	151	13	bounds	bound	NOUN
ejpam-747	151	14	,	,	PUNCT
ejpam-747	151	15	sufficient	sufficient	ADJ
ejpam-747	151	16	conditions	condition	NOUN
ejpam-747	151	17	with	with	ADP
ejpam-747	151	18	the	the	DET
ejpam-747	151	19	help	help	NOUN
ejpam-747	151	20	of	of	ADP
ejpam-747	151	21	various	various	ADJ
ejpam-747	151	22	lemmas	lemmas	ADJ
ejpam-747	151	23	,	,	PUNCT
ejpam-747	151	24	integral	integral	ADJ
ejpam-747	151	25	means	mean	NOUN
ejpam-747	151	26	inequality	inequality	NOUN
ejpam-747	151	27	for	for	ADP
ejpam-747	151	28	convolution	convolution	NOUN
ejpam-747	151	29	of	of	ADP
ejpam-747	151	30	two	two	NUM
ejpam-747	151	31	functions	function	NOUN
ejpam-747	151	32	and	and	CCONJ
ejpam-747	151	33	a	a	DET
ejpam-747	151	34	set	set	NOUN
ejpam-747	151	35	of	of	ADP
ejpam-747	151	36	class	class	NOUN
ejpam-747	151	37	preserving	preserve	VERB
ejpam-747	151	38	integral	integral	ADJ
ejpam-747	151	39	operators	operator	NOUN
ejpam-747	151	40	for	for	ADP
ejpam-747	151	41	functions	function	NOUN
ejpam-747	151	42	belonging	belong	VERB
ejpam-747	151	43	to	to	ADP
ejpam-747	151	44	the	the	DET
ejpam-747	151	45	class	class	NOUN
ejpam-747	152	1	ℜg	ℜg	PROPN
ejpam-747	152	2	h	h	NOUN
ejpam-747	152	3	�	�	PROPN
ejpam-747	152	4	p	p	PROPN
ejpam-747	152	5	,	,	PUNCT
ejpam-747	152	6	m	m	PROPN
ejpam-747	152	7	,	,	PUNCT
ejpam-747	152	8	β	β	X
ejpam-747	152	9	�	�	PROPN
ejpam-747	152	10	.	.	PUNCT
ejpam-747	153	1	p.	p.	PROPN
ejpam-747	153	2	sharma	sharma	PROPN
ejpam-747	153	3	,	,	PUNCT
ejpam-747	153	4	p.	p.	PROPN
ejpam-747	153	5	srivastava	srivastava	PROPN
ejpam-747	153	6	/	/	SYM
ejpam-747	153	7	eur	eur	PROPN
ejpam-747	153	8	.	.	PUNCT
ejpam-747	154	1	j.	j.	PROPN
ejpam-747	154	2	pure	pure	PROPN
ejpam-747	154	3	appl	appl	PROPN
ejpam-747	154	4	.	.	PROPN
ejpam-747	154	5	math	math	PROPN
ejpam-747	154	6	,	,	PUNCT
ejpam-747	154	7	3	3	NUM
ejpam-747	154	8	(	(	PUNCT
ejpam-747	154	9	2010	2010	NUM
ejpam-747	154	10	)	)	PUNCT
ejpam-747	154	11	,	,	PUNCT
ejpam-747	154	12	1093	1093	NUM
ejpam-747	154	13	-	-	SYM
ejpam-747	154	14	1112	1112	NUM
ejpam-747	154	15	1098	1098	NUM
ejpam-747	154	16	2	2	NUM
ejpam-747	154	17	.	.	PUNCT
ejpam-747	155	1	coefficient	coefficient	NOUN
ejpam-747	155	2	inequality	inequality	NOUN
ejpam-747	155	3	,	,	PUNCT
ejpam-747	155	4	growth	growth	NOUN
ejpam-747	155	5	and	and	CCONJ
ejpam-747	155	6	distortion	distortion	NOUN
ejpam-747	155	7	bounds	bound	NOUN
ejpam-747	155	8	for	for	ADP
ejpam-747	155	9	the	the	DET
ejpam-747	155	10	class	class	NOUN
ejpam-747	155	11	ℜg	ℜg	PROPN
ejpam-747	155	12	h	h	NOUN
ejpam-747	155	13	�	�	PROPN
ejpam-747	155	14	p	p	PROPN
ejpam-747	155	15	,	,	PUNCT
ejpam-747	155	16	m	m	PROPN
ejpam-747	155	17	,	,	PUNCT
ejpam-747	155	18	β	β	X
ejpam-747	155	19	�	�	PROPN
ejpam-747	155	20	a	a	DET
ejpam-747	155	21	necessary	necessary	ADJ
ejpam-747	155	22	and	and	CCONJ
ejpam-747	155	23	sufficient	sufficient	ADJ
ejpam-747	155	24	coefficient	coefficient	NOUN
ejpam-747	155	25	condition	condition	NOUN
ejpam-747	155	26	for	for	ADP
ejpam-747	155	27	a	a	DET
ejpam-747	155	28	function	function	NOUN
ejpam-747	155	29	f	f	PROPN
ejpam-747	155	30	∈	∈	PROPN
ejpam-747	155	31	tp	tp	NOUN
ejpam-747	155	32	to	to	PART
ejpam-747	155	33	be	be	AUX
ejpam-747	155	34	in	in	ADP
ejpam-747	155	35	the	the	DET
ejpam-747	155	36	class	class	NOUN
ejpam-747	156	1	ℜg	ℜg	PROPN
ejpam-747	156	2	h	h	NOUN
ejpam-747	156	3	�	�	PROPN
ejpam-747	156	4	p	p	PROPN
ejpam-747	156	5	,	,	PUNCT
ejpam-747	156	6	m	m	PROPN
ejpam-747	156	7	,	,	PUNCT
ejpam-747	156	8	β	β	X
ejpam-747	156	9	�	�	PROPN
ejpam-747	156	10	is	be	AUX
ejpam-747	156	11	derived	derive	VERB
ejpam-747	156	12	in	in	ADP
ejpam-747	156	13	the	the	DET
ejpam-747	156	14	form	form	NOUN
ejpam-747	156	15	of	of	ADP
ejpam-747	156	16	following	follow	VERB
ejpam-747	156	17	theorem	theorem	ADJ
ejpam-747	156	18	:	:	PUNCT
ejpam-747	156	19	theorem	theorem	NOUN
ejpam-747	156	20	1	1	X
ejpam-747	156	21	.	.	PUNCT
ejpam-747	157	1	let	let	VERB
ejpam-747	157	2	the	the	DET
ejpam-747	157	3	function	function	NOUN
ejpam-747	157	4	f	f	X
ejpam-747	157	5	be	be	AUX
ejpam-747	157	6	of	of	ADP
ejpam-747	157	7	the	the	DET
ejpam-747	157	8	form	form	NOUN
ejpam-747	157	9	(	(	PUNCT
ejpam-747	157	10	7	7	NUM
ejpam-747	157	11	)	)	PUNCT
ejpam-747	157	12	and	and	CCONJ
ejpam-747	157	13	g	g	NOUN
ejpam-747	158	1	,	,	PUNCT
ejpam-747	158	2	h	h	PROPN
ejpam-747	158	3	∈	∈	PROPN
ejpam-747	158	4	ap	ap	PROPN
ejpam-747	158	5	of	of	ADP
ejpam-747	158	6	the	the	DET
ejpam-747	158	7	form	form	NOUN
ejpam-747	158	8	(	(	PUNCT
ejpam-747	158	9	2	2	NUM
ejpam-747	158	10	)	)	PUNCT
ejpam-747	158	11	and	and	CCONJ
ejpam-747	158	12	(	(	PUNCT
ejpam-747	158	13	3	3	X
ejpam-747	158	14	)	)	PUNCT
ejpam-747	158	15	respectively	respectively	ADV
ejpam-747	158	16	with	with	ADP
ejpam-747	158	17	�	�	PROPN
ejpam-747	158	18	p+	p+	PART
ejpam-747	158	19	k−m	k−m	NOUN
ejpam-747	158	20	�	�	PROPN
ejpam-747	158	21	bp+k	bp+k	PROPN
ejpam-747	158	22	>	>	X
ejpam-747	158	23	�	�	PROPN
ejpam-747	158	24	p−m−	p−m−	PROPN
ejpam-747	158	25	β	β	X
ejpam-747	158	26	�	�	PROPN
ejpam-747	158	27	cp+k	cp+k	X
ejpam-747	158	28	.	.	PUNCT
ejpam-747	159	1	then	then	ADV
ejpam-747	159	2	f	f	PROPN
ejpam-747	159	3	is	be	AUX
ejpam-747	159	4	in	in	ADP
ejpam-747	159	5	the	the	DET
ejpam-747	159	6	class	class	NOUN
ejpam-747	160	1	ℜg	ℜg	PROPN
ejpam-747	160	2	h	h	NOUN
ejpam-747	160	3	�	�	PROPN
ejpam-747	160	4	p	p	PROPN
ejpam-747	160	5	,	,	PUNCT
ejpam-747	160	6	m	m	PROPN
ejpam-747	160	7	,	,	PUNCT
ejpam-747	160	8	β	β	X
ejpam-747	160	9	�	�	PROPN
ejpam-747	161	1	if	if	SCONJ
ejpam-747	161	2	and	and	CCONJ
ejpam-747	161	3	only	only	ADV
ejpam-747	161	4	if	if	SCONJ
ejpam-747	161	5	∞	∞	PROPN
ejpam-747	161	6	∑	∑	PUNCT
ejpam-747	161	7	k=1	k=1	PROPN
ejpam-747	161	8	�	�	PROPN
ejpam-747	161	9	p+	p+	PROPN
ejpam-747	161	10	k	k	PROPN
ejpam-747	161	11	�	�	PROPN
ejpam-747	161	12	!	!	PUNCT
ejpam-747	161	13	�	�	PROPN
ejpam-747	161	14	�	�	PROPN
ejpam-747	161	15	p+	p+	PART
ejpam-747	161	16	k−m	k−m	NOUN
ejpam-747	161	17	�	�	PROPN
ejpam-747	161	18	bp+k	bp+k	PROPN
ejpam-747	161	19	−	−	PROPN
ejpam-747	161	20	�	�	PROPN
ejpam-747	161	21	p−m−	p−m−	PROPN
ejpam-747	161	22	β	β	X
ejpam-747	161	23	�	�	PROPN
ejpam-747	161	24	cp+k	cp+k	PROPN
ejpam-747	161	25	�	�	PROPN
ejpam-747	161	26	�	�	PROPN
ejpam-747	161	27	p+	p+	PART
ejpam-747	161	28	k−m	k−m	PROPN
ejpam-747	161	29	�	�	PROPN
ejpam-747	161	30	!	!	PUNCT
ejpam-747	162	1	ap+k	ap+k	NOUN
ejpam-747	163	1	≤	≤	NOUN
ejpam-747	163	2	βp	βp	PROPN
ejpam-747	163	3	!	!	PUNCT
ejpam-747	163	4	�	�	PROPN
ejpam-747	163	5	p−m	p−m	PRON
ejpam-747	163	6	�	�	PROPN
ejpam-747	163	7	!	!	PUNCT
ejpam-747	164	1	,	,	PUNCT
ejpam-747	164	2	(	(	PUNCT
ejpam-747	164	3	9	9	X
ejpam-747	164	4	)	)	PUNCT
ejpam-747	164	5	p	p	NOUN
ejpam-747	164	6	∈	∈	PROPN
ejpam-747	164	7	n	n	CCONJ
ejpam-747	164	8	,	,	PUNCT
ejpam-747	164	9	p	p	X
ejpam-747	164	10	>	>	X
ejpam-747	164	11	m	m	PROPN
ejpam-747	164	12	,	,	PUNCT
ejpam-747	164	13	0	0	PUNCT
ejpam-747	164	14	<	<	X
ejpam-747	164	15	β	β	X
ejpam-747	164	16	≤	≤	PROPN
ejpam-747	165	1	p.	p.	NOUN
ejpam-747	165	2	the	the	DET
ejpam-747	165	3	result	result	NOUN
ejpam-747	165	4	is	be	AUX
ejpam-747	165	5	sharp	sharp	ADJ
ejpam-747	165	6	for	for	ADP
ejpam-747	165	7	the	the	DET
ejpam-747	165	8	function	function	NOUN
ejpam-747	165	9	f	f	NOUN
ejpam-747	165	10	given	give	VERB
ejpam-747	165	11	by	by	ADP
ejpam-747	165	12	fk	fk	INTJ
ejpam-747	165	13	(	(	PUNCT
ejpam-747	165	14	z	z	NOUN
ejpam-747	165	15	)	)	PUNCT
ejpam-747	165	16	=	=	PUNCT
ejpam-747	166	1	zp	zp	NOUN
ejpam-747	166	2	−	−	NUM
ejpam-747	166	3	βp	βp	PROPN
ejpam-747	166	4	!	!	PROPN
ejpam-747	166	5	�	�	PROPN
ejpam-747	166	6	p+	p+	PART
ejpam-747	166	7	k−m	k−m	PROPN
ejpam-747	166	8	�	�	PROPN
ejpam-747	166	9	!	!	PUNCT
ejpam-747	167	1	�	�	PROPN
ejpam-747	167	2	p+	p+	PART
ejpam-747	167	3	k	k	PROPN
ejpam-747	167	4	�	�	PROPN
ejpam-747	167	5	!	!	PUNCT
ejpam-747	167	6	�	�	PROPN
ejpam-747	167	7	p−m	p−m	PRON
ejpam-747	167	8	�	�	PROPN
ejpam-747	167	9	!	!	PUNCT
ejpam-747	168	1	�	�	PROPN
ejpam-747	168	2	�	�	PROPN
ejpam-747	168	3	p+	p+	PART
ejpam-747	168	4	k−m	k−m	NOUN
ejpam-747	168	5	�	�	PROPN
ejpam-747	168	6	bp+k	bp+k	PROPN
ejpam-747	168	7	−	−	PROPN
ejpam-747	168	8	�	�	PROPN
ejpam-747	168	9	p−m−	p−m−	PROPN
ejpam-747	168	10	β	β	X
ejpam-747	168	11	�	�	PROPN
ejpam-747	168	12	cp+k	cp+k	PROPN
ejpam-747	168	13	�	�	NOUN
ejpam-747	168	14	zp+k	zp+k	PROPN
ejpam-747	168	15	(	(	PUNCT
ejpam-747	168	16	k	k	X
ejpam-747	168	17	≥	≥	NUM
ejpam-747	168	18	1	1	NUM
ejpam-747	168	19	)	)	PUNCT
ejpam-747	168	20	.	.	PUNCT
ejpam-747	169	1	(	(	PUNCT
ejpam-747	169	2	10	10	NUM
ejpam-747	169	3	)	)	PUNCT
ejpam-747	169	4	proof	proof	NOUN
ejpam-747	169	5	.	.	PUNCT
ejpam-747	170	1	we	we	PRON
ejpam-747	170	2	assume	assume	VERB
ejpam-747	170	3	that	that	SCONJ
ejpam-747	170	4	the	the	DET
ejpam-747	170	5	inequality	inequality	NOUN
ejpam-747	170	6	(	(	PUNCT
ejpam-747	170	7	9	9	NUM
ejpam-747	170	8	)	)	PUNCT
ejpam-747	170	9	holds	hold	VERB
ejpam-747	170	10	true	true	ADJ
ejpam-747	170	11	,	,	PUNCT
ejpam-747	170	12	then	then	ADV
ejpam-747	170	13	we	we	PRON
ejpam-747	170	14	have	have	VERB
ejpam-747	170	15	to	to	PART
ejpam-747	170	16	show	show	VERB
ejpam-747	170	17	that	that	SCONJ
ejpam-747	170	18	�	�	PROPN
ejpam-747	170	19	�	�	PROPN
ejpam-747	170	20	�	�	PROPN
ejpam-747	170	21	�	�	PROPN
ejpam-747	170	22	�	�	PROPN
ejpam-747	170	23	z	z	PROPN
ejpam-747	170	24	�	�	PROPN
ejpam-747	170	25	f	f	PROPN
ejpam-747	170	26	∗	∗	VERB
ejpam-747	170	27	g	g	PROPN
ejpam-747	170	28	�	�	PROPN
ejpam-747	170	29	m+1	m+1	PRON
ejpam-747	170	30	(	(	PUNCT
ejpam-747	170	31	z	z	NOUN
ejpam-747	170	32	)	)	PUNCT
ejpam-747	170	33	�	�	PROPN
ejpam-747	170	34	f	f	PROPN
ejpam-747	170	35	∗	∗	PROPN
ejpam-747	170	36	h	h	PROPN
ejpam-747	170	37	�	�	PROPN
ejpam-747	170	38	m	m	PROPN
ejpam-747	170	39	(	(	PUNCT
ejpam-747	170	40	z	z	NOUN
ejpam-747	170	41	)	)	PUNCT
ejpam-747	170	42	−	−	PROPN
ejpam-747	170	43	�	�	PROPN
ejpam-747	170	44	p−m	p−m	PRON
ejpam-747	170	45	�	�	PROPN
ejpam-747	170	46	�	�	PROPN
ejpam-747	170	47	�	�	PROPN
ejpam-747	170	48	�	�	PROPN
ejpam-747	170	49	�	�	PROPN
ejpam-747	170	50	�	�	PROPN
ejpam-747	170	51	−	−	PROPN
ejpam-747	170	52	β	β	X
ejpam-747	170	53	<	<	X
ejpam-747	170	54	0	0	NUM
ejpam-747	170	55	or	or	CCONJ
ejpam-747	170	56	,	,	PUNCT
ejpam-747	170	57	�	�	PROPN
ejpam-747	170	58	�	�	PROPN
ejpam-747	170	59	�	�	PROPN
ejpam-747	170	60	z	z	PROPN
ejpam-747	170	61	�	�	PROPN
ejpam-747	170	62	f	f	PROPN
ejpam-747	170	63	∗	∗	VERB
ejpam-747	170	64	g	g	PROPN
ejpam-747	170	65	�	�	PROPN
ejpam-747	170	66	m+1	m+1	PRON
ejpam-747	170	67	(	(	PUNCT
ejpam-747	170	68	z)−	z)−	PROPN
ejpam-747	170	69	�	�	PROPN
ejpam-747	170	70	p−m	p−m	PROPN
ejpam-747	170	71	�	�	PROPN
ejpam-747	170	72	�	�	PROPN
ejpam-747	170	73	f	f	PROPN
ejpam-747	170	74	∗	∗	PROPN
ejpam-747	170	75	h	h	PROPN
ejpam-747	170	76	�	�	PROPN
ejpam-747	170	77	m	m	PROPN
ejpam-747	170	78	(	(	PUNCT
ejpam-747	170	79	z	z	NOUN
ejpam-747	170	80	)	)	PUNCT
ejpam-747	170	81	�	�	PROPN
ejpam-747	170	82	�	�	PROPN
ejpam-747	170	83	�	�	PROPN
ejpam-747	170	84	−	−	PROPN
ejpam-747	170	85	β	β	X
ejpam-747	170	86	�	�	PROPN
ejpam-747	170	87	�	�	PROPN
ejpam-747	170	88	�	�	PROPN
ejpam-747	170	89	f	f	PROPN
ejpam-747	170	90	∗	∗	PROPN
ejpam-747	170	91	h	h	PROPN
ejpam-747	170	92	�	�	PROPN
ejpam-747	170	93	m	m	PROPN
ejpam-747	170	94	(	(	PUNCT
ejpam-747	170	95	z	z	NOUN
ejpam-747	170	96	)	)	PUNCT
ejpam-747	170	97	�	�	PROPN
ejpam-747	170	98	�	�	PROPN
ejpam-747	170	99	<	<	X
ejpam-747	170	100	0	0	X
ejpam-747	170	101	.	.	PUNCT
ejpam-747	171	1	using	use	VERB
ejpam-747	171	2	series	series	NOUN
ejpam-747	171	3	expansion	expansion	NOUN
ejpam-747	171	4	of	of	ADP
ejpam-747	171	5	�	�	PROPN
ejpam-747	171	6	f	f	PROPN
ejpam-747	171	7	∗	∗	VERB
ejpam-747	171	8	g	g	PROPN
ejpam-747	171	9	�	�	PROPN
ejpam-747	171	10	m+1	m+1	NUM
ejpam-747	171	11	and	and	CCONJ
ejpam-747	171	12	�	�	PROPN
ejpam-747	171	13	f	f	PROPN
ejpam-747	171	14	∗	∗	VERB
ejpam-747	171	15	g	g	PROPN
ejpam-747	171	16	�	�	PROPN
ejpam-747	171	17	m	m	VERB
ejpam-747	171	18	from	from	ADP
ejpam-747	171	19	(	(	PUNCT
ejpam-747	171	20	8)	8)	NUM
ejpam-747	171	21	,	,	PUNCT
ejpam-747	171	22	we	we	PRON
ejpam-747	171	23	have	have	VERB
ejpam-747	171	24	�	�	PROPN
ejpam-747	171	25	�	�	PROPN
ejpam-747	171	26	�	�	PROPN
ejpam-747	171	27	�	�	PROPN
ejpam-747	171	28	�	�	PROPN
ejpam-747	171	29	−	−	NUM
ejpam-747	171	30	∞	∞	NUM
ejpam-747	171	31	∑	∑	PUNCT
ejpam-747	172	1	k=1	k=1	PROPN
ejpam-747	172	2	�	�	PROPN
ejpam-747	172	3	p+	p+	PROPN
ejpam-747	172	4	k	k	PROPN
ejpam-747	172	5	�	�	PROPN
ejpam-747	172	6	!	!	PUNCT
ejpam-747	173	1	ap+k	ap+k	PROPN
ejpam-747	173	2	�	�	PROPN
ejpam-747	173	3	p+	p+	PART
ejpam-747	173	4	k−m	k−m	PROPN
ejpam-747	173	5	�	�	PROPN
ejpam-747	173	6	!	!	PUNCT
ejpam-747	174	1	¦	¦	PROPN
ejpam-747	174	2	�	�	PROPN
ejpam-747	174	3	p+	p+	PART
ejpam-747	174	4	k−m	k−m	NOUN
ejpam-747	174	5	�	�	PROPN
ejpam-747	174	6	bp+k	bp+k	PROPN
ejpam-747	174	7	−	−	PROPN
ejpam-747	174	8	�	�	PROPN
ejpam-747	174	9	p−m	p−m	X
ejpam-747	174	10	�	�	PROPN
ejpam-747	174	11	cp+k	cp+k	NOUN
ejpam-747	174	12	©	©	ADP
ejpam-747	174	13	zp+k−m	zp+k−m	PROPN
ejpam-747	174	14	�	�	PROPN
ejpam-747	174	15	�	�	PROPN
ejpam-747	174	16	�	�	PROPN
ejpam-747	174	17	�	�	PROPN
ejpam-747	174	18	�	�	PROPN
ejpam-747	174	19	−β	−β	PROPN
ejpam-747	174	20	�	�	PROPN
ejpam-747	174	21	�	�	PROPN
ejpam-747	174	22	�	�	PROPN
ejpam-747	174	23	�	�	PROPN
ejpam-747	174	24	�	�	PROPN
ejpam-747	174	25	p!zp−m	p!zp−m	X
ejpam-747	174	26	�	�	PROPN
ejpam-747	174	27	p−m	p−m	X
ejpam-747	174	28	�	�	PROPN
ejpam-747	174	29	!	!	PUNCT
ejpam-747	175	1	−	−	PROPN
ejpam-747	176	1	∞	∞	NUM
ejpam-747	176	2	∑	∑	PUNCT
ejpam-747	176	3	k=1	k=1	PROPN
ejpam-747	176	4	�	�	PROPN
ejpam-747	176	5	p+	p+	PROPN
ejpam-747	176	6	k	k	PROPN
ejpam-747	176	7	�	�	PROPN
ejpam-747	176	8	!	!	PUNCT
ejpam-747	176	9	ap+kcp+k	ap+kcp+k	PROPN
ejpam-747	176	10	�	�	PROPN
ejpam-747	176	11	p+	p+	PART
ejpam-747	176	12	k−m	k−m	PROPN
ejpam-747	176	13	�	�	PROPN
ejpam-747	176	14	!	!	PUNCT
ejpam-747	177	1	zp+k−m	zp+k−m	PROPN
ejpam-747	177	2	�	�	PROPN
ejpam-747	177	3	�	�	PROPN
ejpam-747	177	4	�	�	PROPN
ejpam-747	177	5	�	�	PROPN
ejpam-747	177	6	�	�	PROPN
ejpam-747	177	7	≤	≤	NUM
ejpam-747	177	8	∞	∞	PROPN
ejpam-747	177	9	∑	∑	PUNCT
ejpam-747	178	1	k=1	k=1	PROPN
ejpam-747	178	2	�	�	PROPN
ejpam-747	178	3	p+	p+	PROPN
ejpam-747	178	4	k	k	PROPN
ejpam-747	178	5	�	�	PROPN
ejpam-747	178	6	!	!	PUNCT
ejpam-747	179	1	ap+k	ap+k	PROPN
ejpam-747	179	2	�	�	PROPN
ejpam-747	179	3	p+	p+	PART
ejpam-747	179	4	k−m	k−m	PROPN
ejpam-747	179	5	�	�	PROPN
ejpam-747	179	6	!	!	PUNCT
ejpam-747	180	1	¦	¦	PROPN
ejpam-747	180	2	�	�	PROPN
ejpam-747	180	3	p+	p+	PART
ejpam-747	180	4	k−m	k−m	NOUN
ejpam-747	180	5	�	�	PROPN
ejpam-747	180	6	bp+k	bp+k	PROPN
ejpam-747	180	7	−	−	PROPN
ejpam-747	180	8	�	�	PROPN
ejpam-747	180	9	p−m	p−m	X
ejpam-747	180	10	�	�	PROPN
ejpam-747	180	11	cp+k	cp+k	NOUN
ejpam-747	180	12	©	©	ADP
ejpam-747	180	13	−	−	PROPN
ejpam-747	180	14	β	β	X
ejpam-747	180	15	(	(	PUNCT
ejpam-747	180	16	p	p	X
ejpam-747	180	17	!	!	PUNCT
ejpam-747	180	18	�	�	PROPN
ejpam-747	180	19	p−m	p−m	PROPN
ejpam-747	180	20	�	�	PROPN
ejpam-747	180	21	!	!	PUNCT
ejpam-747	181	1	−	−	PROPN
ejpam-747	182	1	∞	∞	NUM
ejpam-747	182	2	∑	∑	PUNCT
ejpam-747	182	3	k=1	k=1	PROPN
ejpam-747	182	4	�	�	PROPN
ejpam-747	182	5	p+	p+	PROPN
ejpam-747	182	6	k	k	PROPN
ejpam-747	182	7	�	�	PROPN
ejpam-747	182	8	!	!	PUNCT
ejpam-747	182	9	ap+kcp+k	ap+kcp+k	PROPN
ejpam-747	182	10	�	�	PROPN
ejpam-747	182	11	p+	p+	PART
ejpam-747	182	12	k−m	k−m	PROPN
ejpam-747	182	13	�	�	PROPN
ejpam-747	182	14	!	!	PUNCT
ejpam-747	182	15	)	)	PUNCT
ejpam-747	183	1	=	=	PUNCT
ejpam-747	183	2	∞	∞	NUM
ejpam-747	183	3	∑	∑	PUNCT
ejpam-747	183	4	k=1	k=1	PROPN
ejpam-747	183	5	�	�	PROPN
ejpam-747	183	6	p+	p+	PROPN
ejpam-747	183	7	k	k	PROPN
ejpam-747	183	8	�	�	PROPN
ejpam-747	183	9	!	!	PUNCT
ejpam-747	184	1	ap+k	ap+k	PROPN
ejpam-747	184	2	�	�	PROPN
ejpam-747	184	3	p+	p+	PART
ejpam-747	184	4	k−m	k−m	PROPN
ejpam-747	184	5	�	�	PROPN
ejpam-747	184	6	!	!	PUNCT
ejpam-747	185	1	¦	¦	PROPN
ejpam-747	185	2	�	�	PROPN
ejpam-747	185	3	p+	p+	PART
ejpam-747	185	4	k−m	k−m	NOUN
ejpam-747	185	5	�	�	PROPN
ejpam-747	185	6	bp+k	bp+k	PROPN
ejpam-747	185	7	−	−	PROPN
ejpam-747	185	8	�	�	PROPN
ejpam-747	185	9	p−m−	p−m−	PROPN
ejpam-747	185	10	β	β	X
ejpam-747	185	11	�	�	PROPN
ejpam-747	185	12	cp+k	cp+k	VERB
ejpam-747	185	13	©	©	ADP
ejpam-747	185	14	−	−	PROPN
ejpam-747	185	15	βp	βp	PROPN
ejpam-747	185	16	!	!	PUNCT
ejpam-747	185	17	�	�	PROPN
ejpam-747	185	18	p−m	p−m	PRON
ejpam-747	185	19	�	�	PROPN
ejpam-747	185	20	!	!	PUNCT
ejpam-747	186	1	≤	≤	ADJ
ejpam-747	186	2	0	0	NUM
ejpam-747	186	3	,	,	PUNCT
ejpam-747	186	4	if	if	SCONJ
ejpam-747	186	5	(	(	PUNCT
ejpam-747	186	6	9	9	X
ejpam-747	186	7	)	)	PUNCT
ejpam-747	186	8	holds	hold	NOUN
ejpam-747	186	9	.	.	PUNCT
ejpam-747	187	1	hence	hence	ADV
ejpam-747	187	2	,	,	PUNCT
ejpam-747	187	3	f	f	PROPN
ejpam-747	187	4	∈	∈	PROPN
ejpam-747	187	5	ℜg	ℜg	PROPN
ejpam-747	187	6	h	h	NOUN
ejpam-747	187	7	�	�	PROPN
ejpam-747	187	8	p	p	PROPN
ejpam-747	187	9	,	,	PUNCT
ejpam-747	187	10	m	m	PROPN
ejpam-747	187	11	,	,	PUNCT
ejpam-747	187	12	β	β	X
ejpam-747	187	13	�	�	PROPN
ejpam-747	187	14	.	.	PUNCT
ejpam-747	188	1	to	to	PART
ejpam-747	188	2	prove	prove	VERB
ejpam-747	188	3	the	the	DET
ejpam-747	188	4	converse	converse	NOUN
ejpam-747	188	5	,	,	PUNCT
ejpam-747	188	6	we	we	PRON
ejpam-747	188	7	suppose	suppose	VERB
ejpam-747	188	8	that	that	SCONJ
ejpam-747	188	9	f	f	PROPN
ejpam-747	188	10	∈	∈	PROPN
ejpam-747	188	11	ℜg	ℜg	PROPN
ejpam-747	188	12	h	h	NOUN
ejpam-747	188	13	�	�	PROPN
ejpam-747	188	14	p	p	PROPN
ejpam-747	188	15	,	,	PUNCT
ejpam-747	188	16	m	m	PROPN
ejpam-747	188	17	,	,	PUNCT
ejpam-747	188	18	β	β	X
ejpam-747	188	19	�	�	PROPN
ejpam-747	188	20	,	,	PUNCT
ejpam-747	188	21	that	that	ADV
ejpam-747	188	22	is	is	ADV
ejpam-747	188	23	�	�	PROPN
ejpam-747	188	24	�	�	PROPN
ejpam-747	188	25	�	�	PROPN
ejpam-747	188	26	�	�	PROPN
ejpam-747	188	27	�	�	PROPN
ejpam-747	188	28	z	z	PROPN
ejpam-747	188	29	�	�	PROPN
ejpam-747	188	30	f	f	PROPN
ejpam-747	188	31	∗	∗	VERB
ejpam-747	188	32	g	g	PROPN
ejpam-747	188	33	�	�	PROPN
ejpam-747	188	34	m+1	m+1	PRON
ejpam-747	188	35	(	(	PUNCT
ejpam-747	188	36	z	z	NOUN
ejpam-747	188	37	)	)	PUNCT
ejpam-747	188	38	�	�	PROPN
ejpam-747	188	39	f	f	PROPN
ejpam-747	188	40	∗	∗	PROPN
ejpam-747	188	41	h	h	PROPN
ejpam-747	188	42	�	�	PROPN
ejpam-747	188	43	m	m	PROPN
ejpam-747	188	44	(	(	PUNCT
ejpam-747	188	45	z	z	NOUN
ejpam-747	188	46	)	)	PUNCT
ejpam-747	188	47	−	−	PROPN
ejpam-747	188	48	�	�	PROPN
ejpam-747	188	49	p−m	p−m	PRON
ejpam-747	188	50	�	�	PROPN
ejpam-747	188	51	�	�	PROPN
ejpam-747	188	52	�	�	PROPN
ejpam-747	188	53	�	�	PROPN
ejpam-747	188	54	�	�	PROPN
ejpam-747	188	55	�	�	PROPN
ejpam-747	188	56	<	<	X
ejpam-747	188	57	β	β	X
ejpam-747	188	58	,	,	PUNCT
ejpam-747	188	59	(	(	PUNCT
ejpam-747	188	60	11	11	NUM
ejpam-747	188	61	)	)	PUNCT
ejpam-747	188	62	p.	p.	NOUN
ejpam-747	188	63	sharma	sharma	PROPN
ejpam-747	188	64	,	,	PUNCT
ejpam-747	188	65	p.	p.	PROPN
ejpam-747	188	66	srivastava	srivastava	PROPN
ejpam-747	188	67	/	/	SYM
ejpam-747	188	68	eur	eur	PROPN
ejpam-747	188	69	.	.	PUNCT
ejpam-747	189	1	j.	j.	PROPN
ejpam-747	189	2	pure	pure	PROPN
ejpam-747	189	3	appl	appl	PROPN
ejpam-747	189	4	.	.	PROPN
ejpam-747	189	5	math	math	PROPN
ejpam-747	189	6	,	,	PUNCT
ejpam-747	189	7	3	3	NUM
ejpam-747	189	8	(	(	PUNCT
ejpam-747	189	9	2010	2010	NUM
ejpam-747	189	10	)	)	PUNCT
ejpam-747	189	11	,	,	PUNCT
ejpam-747	189	12	1093	1093	NUM
ejpam-747	189	13	-	-	SYM
ejpam-747	189	14	1112	1112	NUM
ejpam-747	189	15	1099	1099	NUM
ejpam-747	189	16	z	z	PROPN
ejpam-747	189	17	∈	∈	PROPN
ejpam-747	189	18	∆	∆	PROPN
ejpam-747	189	19	,	,	PUNCT
ejpam-747	189	20	p	p	PROPN
ejpam-747	189	21	∈	∈	PROPN
ejpam-747	189	22	n	n	CCONJ
ejpam-747	189	23	,	,	PUNCT
ejpam-747	189	24	p	p	X
ejpam-747	189	25	>	>	X
ejpam-747	189	26	m	m	PROPN
ejpam-747	189	27	,	,	PUNCT
ejpam-747	189	28	0	0	PUNCT
ejpam-747	189	29	<	<	X
ejpam-747	189	30	β	β	X
ejpam-747	189	31	≤	≤	NOUN
ejpam-747	189	32	p	p	X
ejpam-747	189	33	,	,	PUNCT
ejpam-747	189	34	m	m	PROPN
ejpam-747	189	35	∈	∈	PROPN
ejpam-747	189	36	n0	n0	PROPN
ejpam-747	189	37	.	.	PUNCT
ejpam-747	190	1	since	since	SCONJ
ejpam-747	190	2	|re	|re	PRON
ejpam-747	190	3	(	(	PUNCT
ejpam-747	190	4	z)|	z)|	ADP
ejpam-747	190	5	≤	≤	VERB
ejpam-747	190	6	|z|	|z|	NOUN
ejpam-747	190	7	for	for	ADP
ejpam-747	190	8	any	any	DET
ejpam-747	190	9	z.	z.	PROPN
ejpam-747	190	10	choosing	choose	VERB
ejpam-747	190	11	z	z	PROPN
ejpam-747	190	12	to	to	PART
ejpam-747	190	13	be	be	AUX
ejpam-747	190	14	real	real	ADJ
ejpam-747	190	15	and	and	CCONJ
ejpam-747	190	16	letting	let	VERB
ejpam-747	190	17	z→	z→	PROPN
ejpam-747	190	18	1−	1−	NUM
ejpam-747	190	19	through	through	ADP
ejpam-747	190	20	real	real	ADJ
ejpam-747	190	21	values	value	NOUN
ejpam-747	190	22	,	,	PUNCT
ejpam-747	190	23	(	(	PUNCT
ejpam-747	190	24	11	11	NUM
ejpam-747	190	25	)	)	PUNCT
ejpam-747	190	26	yields	yield	NOUN
ejpam-747	190	27	∞	∞	PROPN
ejpam-747	190	28	∑	∑	PUNCT
ejpam-747	190	29	k=1	k=1	PROPN
ejpam-747	190	30	�	�	PROPN
ejpam-747	190	31	p+	p+	PROPN
ejpam-747	190	32	k	k	PROPN
ejpam-747	190	33	�	�	PROPN
ejpam-747	190	34	!	!	PUNCT
ejpam-747	191	1	ap+k	ap+k	PROPN
ejpam-747	191	2	�	�	PROPN
ejpam-747	191	3	p+	p+	PART
ejpam-747	191	4	k−m	k−m	PROPN
ejpam-747	191	5	�	�	PROPN
ejpam-747	191	6	!	!	PUNCT
ejpam-747	192	1	¦	¦	PROPN
ejpam-747	192	2	�	�	PROPN
ejpam-747	192	3	p+	p+	PART
ejpam-747	192	4	k−m	k−m	NOUN
ejpam-747	192	5	�	�	PROPN
ejpam-747	192	6	bp+k	bp+k	PROPN
ejpam-747	192	7	−	−	PROPN
ejpam-747	192	8	�	�	PROPN
ejpam-747	192	9	p−m	p−m	X
ejpam-747	192	10	�	�	PROPN
ejpam-747	192	11	cp+k	cp+k	NOUN
ejpam-747	192	12	©	©	ADP
ejpam-747	192	13	−β	−β	NOUN
ejpam-747	192	14	(	(	PUNCT
ejpam-747	192	15	p	p	X
ejpam-747	192	16	!	!	PUNCT
ejpam-747	192	17	�	�	PROPN
ejpam-747	192	18	p−m	p−m	PROPN
ejpam-747	192	19	�	�	PROPN
ejpam-747	192	20	!	!	PUNCT
ejpam-747	193	1	−	−	PROPN
ejpam-747	194	1	∞	∞	NUM
ejpam-747	194	2	∑	∑	PUNCT
ejpam-747	194	3	k=1	k=1	PROPN
ejpam-747	194	4	�	�	PROPN
ejpam-747	194	5	p+	p+	PROPN
ejpam-747	194	6	k	k	PROPN
ejpam-747	194	7	�	�	PROPN
ejpam-747	194	8	!	!	PUNCT
ejpam-747	194	9	ap+kcp+k	ap+kcp+k	PROPN
ejpam-747	194	10	�	�	PROPN
ejpam-747	194	11	p+	p+	PART
ejpam-747	194	12	k−m	k−m	PROPN
ejpam-747	194	13	�	�	PROPN
ejpam-747	194	14	!	!	PUNCT
ejpam-747	194	15	)	)	PUNCT
ejpam-747	195	1	≤	≤	ADV
ejpam-747	195	2	0	0	NUM
ejpam-747	196	1	or	or	CCONJ
ejpam-747	196	2	,	,	PUNCT
ejpam-747	196	3	∞	∞	PROPN
ejpam-747	196	4	∑	∑	PUNCT
ejpam-747	197	1	k=1	k=1	PROPN
ejpam-747	197	2	�	�	PROPN
ejpam-747	197	3	p+	p+	PROPN
ejpam-747	197	4	k	k	PROPN
ejpam-747	197	5	�	�	PROPN
ejpam-747	197	6	!	!	PUNCT
ejpam-747	197	7	�	�	PROPN
ejpam-747	197	8	�	�	PROPN
ejpam-747	197	9	p+	p+	PART
ejpam-747	197	10	k−m	k−m	NOUN
ejpam-747	197	11	�	�	PROPN
ejpam-747	197	12	bp+k	bp+k	PROPN
ejpam-747	197	13	−	−	PROPN
ejpam-747	197	14	�	�	PROPN
ejpam-747	197	15	p−m−	p−m−	PROPN
ejpam-747	197	16	β	β	X
ejpam-747	197	17	�	�	PROPN
ejpam-747	197	18	cp+k	cp+k	PROPN
ejpam-747	197	19	�	�	PROPN
ejpam-747	197	20	�	�	PROPN
ejpam-747	197	21	p+	p+	PART
ejpam-747	197	22	k−m	k−m	PROPN
ejpam-747	197	23	�	�	PROPN
ejpam-747	197	24	!	!	PUNCT
ejpam-747	198	1	ap+k	ap+k	NOUN
ejpam-747	199	1	≤	≤	NOUN
ejpam-747	199	2	βp	βp	PROPN
ejpam-747	199	3	!	!	PUNCT
ejpam-747	199	4	�	�	PROPN
ejpam-747	199	5	p−m	p−m	PRON
ejpam-747	199	6	�	�	PROPN
ejpam-747	199	7	!	!	PUNCT
ejpam-747	200	1	which	which	PRON
ejpam-747	200	2	leads	lead	VERB
ejpam-747	200	3	us	we	PRON
ejpam-747	200	4	immediately	immediately	ADV
ejpam-747	200	5	to	to	ADP
ejpam-747	200	6	the	the	DET
ejpam-747	200	7	desired	desire	VERB
ejpam-747	200	8	inequality	inequality	NOUN
ejpam-747	200	9	(	(	PUNCT
ejpam-747	200	10	9	9	NUM
ejpam-747	200	11	)	)	PUNCT
ejpam-747	200	12	.	.	PUNCT
ejpam-747	201	1	sharpness	sharpness	NOUN
ejpam-747	201	2	follows	follow	VERB
ejpam-747	201	3	if	if	SCONJ
ejpam-747	201	4	we	we	PRON
ejpam-747	201	5	take	take	VERB
ejpam-747	201	6	extremal	extremal	ADJ
ejpam-747	201	7	function	function	NOUN
ejpam-747	201	8	given	give	VERB
ejpam-747	201	9	by	by	ADP
ejpam-747	201	10	(	(	PUNCT
ejpam-747	201	11	10	10	NUM
ejpam-747	201	12	)	)	PUNCT
ejpam-747	201	13	.	.	PUNCT
ejpam-747	202	1	corollary	corollary	ADJ
ejpam-747	202	2	1	1	NUM
ejpam-747	202	3	.	.	PUNCT
ejpam-747	203	1	if	if	SCONJ
ejpam-747	203	2	f	f	PROPN
ejpam-747	203	3	∈	∈	PROPN
ejpam-747	203	4	ℜg	ℜg	PROPN
ejpam-747	203	5	h	h	NOUN
ejpam-747	203	6	�	�	PROPN
ejpam-747	203	7	p	p	PROPN
ejpam-747	203	8	,	,	PUNCT
ejpam-747	203	9	m	m	PROPN
ejpam-747	203	10	,	,	PUNCT
ejpam-747	203	11	β	β	X
ejpam-747	203	12	�	�	PROPN
ejpam-747	203	13	,	,	PUNCT
ejpam-747	203	14	then	then	ADV
ejpam-747	203	15	ap+k	ap+k	VERB
ejpam-747	203	16	≤	≤	X
ejpam-747	203	17	βp	βp	PROPN
ejpam-747	203	18	!	!	PUNCT
ejpam-747	203	19	�	�	PROPN
ejpam-747	203	20	p+	p+	PART
ejpam-747	203	21	k−m	k−m	PROPN
ejpam-747	203	22	�	�	PROPN
ejpam-747	203	23	!	!	PUNCT
ejpam-747	204	1	�	�	PROPN
ejpam-747	204	2	p+	p+	PART
ejpam-747	204	3	k	k	PROPN
ejpam-747	204	4	�	�	PROPN
ejpam-747	204	5	!	!	PUNCT
ejpam-747	204	6	�	�	PROPN
ejpam-747	204	7	p−m	p−m	PRON
ejpam-747	204	8	�	�	PROPN
ejpam-747	204	9	!	!	PUNCT
ejpam-747	205	1	�	�	PROPN
ejpam-747	205	2	�	�	PROPN
ejpam-747	205	3	p+	p+	PART
ejpam-747	205	4	k−m	k−m	NOUN
ejpam-747	205	5	�	�	PROPN
ejpam-747	205	6	bp+k	bp+k	PROPN
ejpam-747	205	7	−	−	PROPN
ejpam-747	205	8	�	�	PROPN
ejpam-747	205	9	p−m−	p−m−	PROPN
ejpam-747	205	10	β	β	X
ejpam-747	205	11	�	�	PROPN
ejpam-747	205	12	cp+k	cp+k	PROPN
ejpam-747	205	13	�	�	PROPN
ejpam-747	205	14	,	,	PUNCT
ejpam-747	205	15	k	k	X
ejpam-747	205	16	≥	≥	NUM
ejpam-747	205	17	1	1	NUM
ejpam-747	205	18	.	.	PUNCT
ejpam-747	206	1	(	(	PUNCT
ejpam-747	206	2	12	12	NUM
ejpam-747	206	3	)	)	PUNCT
ejpam-747	206	4	the	the	DET
ejpam-747	206	5	equality	equality	NOUN
ejpam-747	206	6	in	in	ADP
ejpam-747	206	7	(	(	PUNCT
ejpam-747	206	8	12	12	NUM
ejpam-747	206	9	)	)	PUNCT
ejpam-747	206	10	is	be	AUX
ejpam-747	206	11	attained	attain	VERB
ejpam-747	206	12	for	for	ADP
ejpam-747	206	13	the	the	DET
ejpam-747	206	14	function	function	NOUN
ejpam-747	206	15	fk	fk	INTJ
ejpam-747	206	16	given	give	VERB
ejpam-747	206	17	by	by	ADP
ejpam-747	206	18	(	(	PUNCT
ejpam-747	206	19	10	10	NUM
ejpam-747	206	20	)	)	PUNCT
ejpam-747	206	21	.	.	PUNCT
ejpam-747	207	1	corollary	corollary	ADJ
ejpam-747	207	2	2	2	NUM
ejpam-747	207	3	.	.	PUNCT
ejpam-747	208	1	let	let	VERB
ejpam-747	208	2	f	f	PROPN
ejpam-747	208	3	∈	∈	PROPN
ejpam-747	208	4	ℜg	ℜg	PROPN
ejpam-747	208	5	h	h	NOUN
ejpam-747	208	6	�	�	PROPN
ejpam-747	208	7	p	p	PROPN
ejpam-747	208	8	,	,	PUNCT
ejpam-747	208	9	m	m	PROPN
ejpam-747	208	10	,	,	PUNCT
ejpam-747	208	11	β	β	X
ejpam-747	208	12	�	�	PROPN
ejpam-747	208	13	and	and	CCONJ
ejpam-747	208	14	dp+k	dp+k	NOUN
ejpam-747	209	1	:	:	PUNCT
ejpam-747	209	2	=	=	SYM
ejpam-747	209	3	�	�	PROPN
ejpam-747	209	4	p+	p+	PART
ejpam-747	209	5	k−m	k−m	NOUN
ejpam-747	209	6	�	�	PROPN
ejpam-747	209	7	bp+k	bp+k	PROPN
ejpam-747	209	8	−	−	PROPN
ejpam-747	209	9	�	�	PROPN
ejpam-747	209	10	p−m−	p−m−	PROPN
ejpam-747	209	11	β	β	X
ejpam-747	209	12	�	�	PROPN
ejpam-747	209	13	cp+k	cp+k	PRON
ejpam-747	209	14	be	be	AUX
ejpam-747	209	15	such	such	ADJ
ejpam-747	209	16	that	that	SCONJ
ejpam-747	209	17	dp+k	dp+k	NOUN
ejpam-747	209	18	≥	≥	NOUN
ejpam-747	209	19	dp+1,∀	dp+1,∀	VERB
ejpam-747	209	20	k	k	X
ejpam-747	209	21	≥	≥	NUM
ejpam-747	209	22	1	1	NUM
ejpam-747	209	23	,	,	PUNCT
ejpam-747	209	24	then	then	ADV
ejpam-747	209	25	∞	∞	NUM
ejpam-747	209	26	∑	∑	PUNCT
ejpam-747	209	27	k=1	k=1	VERB
ejpam-747	209	28	ap+k	ap+k	NOUN
ejpam-747	209	29	≤	≤	ADV
ejpam-747	209	30	β	β	X
ejpam-747	209	31	�	�	PROPN
ejpam-747	209	32	p−m+	p−m+	PROPN
ejpam-747	209	33	1	1	NUM
ejpam-747	209	34	�	�	PROPN
ejpam-747	209	35	�	�	PROPN
ejpam-747	209	36	p+	p+	PART
ejpam-747	209	37	1	1	NUM
ejpam-747	209	38	�	�	PROPN
ejpam-747	209	39	dp+1	dp+1	PROPN
ejpam-747	209	40	.	.	PUNCT
ejpam-747	210	1	(	(	PUNCT
ejpam-747	210	2	13	13	NUM
ejpam-747	210	3	)	)	PUNCT
ejpam-747	210	4	corollary	corollary	NOUN
ejpam-747	210	5	3	3	X
ejpam-747	210	6	.	.	PUNCT
ejpam-747	211	1	let	let	VERB
ejpam-747	211	2	f	f	PROPN
ejpam-747	211	3	∈	∈	PROPN
ejpam-747	211	4	ℜg	ℜg	PROPN
ejpam-747	211	5	h	h	NOUN
ejpam-747	211	6	�	�	PROPN
ejpam-747	211	7	p	p	PROPN
ejpam-747	211	8	,	,	PUNCT
ejpam-747	211	9	m	m	PROPN
ejpam-747	211	10	,	,	PUNCT
ejpam-747	211	11	β	β	X
ejpam-747	211	12	�	�	PROPN
ejpam-747	211	13	and	and	CCONJ
ejpam-747	211	14	dp+k	dp+k	NOUN
ejpam-747	211	15	:	:	PUNCT
ejpam-747	211	16	=	=	SYM
ejpam-747	211	17	�	�	PROPN
ejpam-747	211	18	p+	p+	PART
ejpam-747	211	19	k−m	k−m	NOUN
ejpam-747	211	20	�	�	PROPN
ejpam-747	211	21	bp+k	bp+k	PROPN
ejpam-747	211	22	−	−	PROPN
ejpam-747	211	23	�	�	PROPN
ejpam-747	211	24	p−m−	p−m−	PROPN
ejpam-747	211	25	β	β	X
ejpam-747	211	26	�	�	PROPN
ejpam-747	211	27	cp+k	cp+k	PRON
ejpam-747	211	28	be	be	AUX
ejpam-747	211	29	such	such	ADJ
ejpam-747	211	30	that	that	SCONJ
ejpam-747	211	31	dp+k	dp+k	NOUN
ejpam-747	211	32	≥	≥	NOUN
ejpam-747	211	33	dp+1,∀	dp+1,∀	VERB
ejpam-747	211	34	k	k	X
ejpam-747	211	35	≥	≥	NUM
ejpam-747	211	36	1	1	NUM
ejpam-747	211	37	,	,	PUNCT
ejpam-747	211	38	then	then	ADV
ejpam-747	211	39	∞	∞	NUM
ejpam-747	211	40	∑	∑	PUNCT
ejpam-747	212	1	k=1	k=1	PROPN
ejpam-747	212	2	�	�	PROPN
ejpam-747	212	3	p+	p+	PROPN
ejpam-747	212	4	k	k	PROPN
ejpam-747	212	5	�	�	PROPN
ejpam-747	212	6	ap+k	ap+k	PROPN
ejpam-747	212	7	≤	≤	ADV
ejpam-747	212	8	β	β	X
ejpam-747	212	9	�	�	PROPN
ejpam-747	212	10	p−m+	p−m+	PROPN
ejpam-747	212	11	1	1	NUM
ejpam-747	212	12	�	�	PROPN
ejpam-747	212	13	dp+1	dp+1	PROPN
ejpam-747	212	14	.	.	PUNCT
ejpam-747	213	1	corollary	corollary	ADJ
ejpam-747	213	2	4	4	NUM
ejpam-747	213	3	.	.	PUNCT
ejpam-747	214	1	let	let	VERB
ejpam-747	214	2	the	the	DET
ejpam-747	214	3	function	function	NOUN
ejpam-747	214	4	f	f	X
ejpam-747	214	5	be	be	AUX
ejpam-747	214	6	of	of	ADP
ejpam-747	214	7	the	the	DET
ejpam-747	214	8	form	form	NOUN
ejpam-747	214	9	(	(	PUNCT
ejpam-747	214	10	7	7	NUM
ejpam-747	214	11	)	)	PUNCT
ejpam-747	214	12	and	and	CCONJ
ejpam-747	214	13	g	g	NOUN
ejpam-747	215	1	,	,	PUNCT
ejpam-747	215	2	h	h	PROPN
ejpam-747	215	3	∈	∈	PROPN
ejpam-747	215	4	ap	ap	PROPN
ejpam-747	215	5	of	of	ADP
ejpam-747	215	6	the	the	DET
ejpam-747	215	7	form	form	NOUN
ejpam-747	215	8	(	(	PUNCT
ejpam-747	215	9	2	2	NUM
ejpam-747	215	10	)	)	PUNCT
ejpam-747	215	11	and	and	CCONJ
ejpam-747	215	12	(	(	PUNCT
ejpam-747	215	13	3	3	X
ejpam-747	215	14	)	)	PUNCT
ejpam-747	215	15	respectively	respectively	ADV
ejpam-747	215	16	with	with	ADP
ejpam-747	215	17	�	�	PROPN
ejpam-747	215	18	p+	p+	PART
ejpam-747	215	19	k−m	k−m	NOUN
ejpam-747	215	20	�	�	PROPN
ejpam-747	215	21	bp+k	bp+k	PROPN
ejpam-747	215	22	>	>	X
ejpam-747	215	23	�	�	PROPN
ejpam-747	215	24	p−m−	p−m−	PROPN
ejpam-747	215	25	β	β	X
ejpam-747	215	26	�	�	PROPN
ejpam-747	215	27	cp+k	cp+k	ADV
ejpam-747	215	28	,	,	PUNCT
ejpam-747	215	29	if	if	SCONJ
ejpam-747	215	30	∞	∞	PROPN
ejpam-747	215	31	∑	∑	PUNCT
ejpam-747	215	32	k=1	k=1	PROPN
ejpam-747	215	33	�	�	PROPN
ejpam-747	215	34	p+	p+	PROPN
ejpam-747	215	35	k	k	PROPN
ejpam-747	215	36	�	�	PROPN
ejpam-747	215	37	!	!	PUNCT
ejpam-747	215	38	�	�	PROPN
ejpam-747	216	1	�	�	PROPN
ejpam-747	216	2	p+	p+	PART
ejpam-747	216	3	k−m	k−m	NOUN
ejpam-747	216	4	�	�	PROPN
ejpam-747	216	5	bp+k	bp+k	PROPN
ejpam-747	216	6	−	−	PROPN
ejpam-747	216	7	�	�	PROPN
ejpam-747	216	8	p−m−	p−m−	PROPN
ejpam-747	216	9	β	β	X
ejpam-747	216	10	�	�	PROPN
ejpam-747	216	11	cp+k	cp+k	PROPN
ejpam-747	216	12	�	�	PROPN
ejpam-747	216	13	�	�	PROPN
ejpam-747	216	14	p+	p+	PART
ejpam-747	216	15	k−m	k−m	PROPN
ejpam-747	216	16	�	�	PROPN
ejpam-747	216	17	!	!	PUNCT
ejpam-747	217	1	ap+k	ap+k	NOUN
ejpam-747	218	1	≤	≤	NOUN
ejpam-747	218	2	βp	βp	PROPN
ejpam-747	218	3	!	!	PUNCT
ejpam-747	218	4	�	�	PROPN
ejpam-747	218	5	p−m	p−m	PRON
ejpam-747	218	6	�	�	PROPN
ejpam-747	218	7	!	!	PUNCT
ejpam-747	218	8	,	,	PUNCT
ejpam-747	218	9	p	p	PROPN
ejpam-747	218	10	∈	∈	PROPN
ejpam-747	218	11	n	n	CCONJ
ejpam-747	218	12	,	,	PUNCT
ejpam-747	218	13	p	p	X
ejpam-747	218	14	>	>	X
ejpam-747	218	15	m	m	PROPN
ejpam-747	218	16	,	,	PUNCT
ejpam-747	218	17	0	0	PUNCT
ejpam-747	218	18	<	<	X
ejpam-747	218	19	β	β	X
ejpam-747	218	20	≤	≤	NOUN
ejpam-747	218	21	p	p	NOUN
ejpam-747	218	22	holds	hold	NOUN
ejpam-747	218	23	,	,	PUNCT
ejpam-747	218	24	then	then	ADV
ejpam-747	218	25	f	f	PROPN
ejpam-747	218	26	∈	∈	PROPN
ejpam-747	218	27	s	s	PART
ejpam-747	218	28	g	g	PROPN
ejpam-747	218	29	h	h	PROPN
ejpam-747	218	30	�	�	PROPN
ejpam-747	218	31	p	p	PROPN
ejpam-747	218	32	,	,	PUNCT
ejpam-747	218	33	m	m	PROPN
ejpam-747	218	34	,	,	PUNCT
ejpam-747	218	35	β	β	X
ejpam-747	218	36	�	�	PROPN
ejpam-747	218	37	.	.	PUNCT
ejpam-747	219	1	theorem	theorem	NOUN
ejpam-747	219	2	2	2	NUM
ejpam-747	219	3	.	.	PUNCT
ejpam-747	220	1	let	let	VERB
ejpam-747	220	2	f	f	PROPN
ejpam-747	220	3	∈	∈	PROPN
ejpam-747	220	4	tp	tp	X
ejpam-747	220	5	of	of	ADP
ejpam-747	220	6	the	the	DET
ejpam-747	220	7	form	form	NOUN
ejpam-747	220	8	(	(	PUNCT
ejpam-747	220	9	7	7	X
ejpam-747	220	10	)	)	PUNCT
ejpam-747	220	11	be	be	AUX
ejpam-747	220	12	in	in	ADP
ejpam-747	220	13	the	the	DET
ejpam-747	220	14	class	class	NOUN
ejpam-747	221	1	ℜg	ℜg	PROPN
ejpam-747	221	2	h	h	NOUN
ejpam-747	221	3	�	�	PROPN
ejpam-747	221	4	p	p	PROPN
ejpam-747	221	5	,	,	PUNCT
ejpam-747	221	6	m	m	PROPN
ejpam-747	221	7	,	,	PUNCT
ejpam-747	221	8	β	β	X
ejpam-747	221	9	�	�	PROPN
ejpam-747	221	10	and	and	CCONJ
ejpam-747	221	11	g	g	PROPN
ejpam-747	221	12	,	,	PUNCT
ejpam-747	221	13	h	h	PROPN
ejpam-747	221	14	be	be	VERB
ejpam-747	221	15	of	of	ADP
ejpam-747	221	16	the	the	DET
ejpam-747	221	17	form	form	NOUN
ejpam-747	221	18	(	(	PUNCT
ejpam-747	221	19	2	2	NUM
ejpam-747	221	20	)	)	PUNCT
ejpam-747	221	21	,	,	PUNCT
ejpam-747	221	22	(	(	PUNCT
ejpam-747	221	23	3	3	X
ejpam-747	221	24	)	)	PUNCT
ejpam-747	221	25	respectively	respectively	ADV
ejpam-747	221	26	with	with	ADP
ejpam-747	221	27	dp+k	dp+k	NOUN
ejpam-747	221	28	:	:	PUNCT
ejpam-747	221	29	=	=	SYM
ejpam-747	221	30	�	�	PROPN
ejpam-747	221	31	p+	p+	PART
ejpam-747	221	32	k−m	k−m	NOUN
ejpam-747	221	33	�	�	PROPN
ejpam-747	221	34	bp+k	bp+k	PROPN
ejpam-747	221	35	−	−	PROPN
ejpam-747	221	36	�	�	PROPN
ejpam-747	221	37	p−m−	p−m−	PROPN
ejpam-747	221	38	β	β	X
ejpam-747	221	39	�	�	PROPN
ejpam-747	222	1	cp+k	cp+k	X
ejpam-747	222	2	≥	≥	AUX
ejpam-747	222	3	dp+1,∀	dp+1,∀	X
ejpam-747	222	4	k	k	PROPN
ejpam-747	222	5	≥	≥	NUM
ejpam-747	222	6	1	1	NUM
ejpam-747	222	7	,	,	PUNCT
ejpam-747	222	8	then	then	ADV
ejpam-747	222	9	|zp|	|zp|	ADP
ejpam-747	222	10	−	−	NOUN
ejpam-747	222	11	β	β	X
ejpam-747	222	12	�	�	PROPN
ejpam-747	222	13	p−m+	p−m+	PROPN
ejpam-747	222	14	1	1	NUM
ejpam-747	222	15	�	�	PROPN
ejpam-747	222	16	�	�	PROPN
ejpam-747	222	17	p+	p+	PART
ejpam-747	222	18	1	1	NUM
ejpam-747	222	19	�	�	PROPN
ejpam-747	222	20	dp+1	dp+1	PROPN
ejpam-747	222	21	�	�	PROPN
ejpam-747	222	22	�	�	PROPN
ejpam-747	222	23	zp+1	zp+1	NUM
ejpam-747	222	24	�	�	PROPN
ejpam-747	222	25	�	�	PROPN
ejpam-747	222	26	≤	≤	PROPN
ejpam-747	222	27	�	�	PROPN
ejpam-747	222	28	�	�	PROPN
ejpam-747	222	29	f	f	PROPN
ejpam-747	222	30	(	(	PUNCT
ejpam-747	222	31	z	z	PROPN
ejpam-747	222	32	)	)	PUNCT
ejpam-747	222	33	�	�	PROPN
ejpam-747	222	34	�	�	PROPN
ejpam-747	222	35	≤	≤	PROPN
ejpam-747	222	36	|zp|+	|zp|+	VERB
ejpam-747	222	37	β	β	X
ejpam-747	222	38	�	�	PROPN
ejpam-747	222	39	p−m+	p−m+	PROPN
ejpam-747	222	40	1	1	NUM
ejpam-747	222	41	�	�	PROPN
ejpam-747	222	42	�	�	PROPN
ejpam-747	222	43	p+	p+	PART
ejpam-747	222	44	1	1	NUM
ejpam-747	222	45	�	�	PROPN
ejpam-747	222	46	dp+1	dp+1	PROPN
ejpam-747	222	47	�	�	PROPN
ejpam-747	222	48	�	�	PROPN
ejpam-747	222	49	zp+1	zp+1	NUM
ejpam-747	222	50	�	�	PROPN
ejpam-747	222	51	�	�	PROPN
ejpam-747	222	52	(	(	PUNCT
ejpam-747	222	53	14	14	NUM
ejpam-747	222	54	)	)	PUNCT
ejpam-747	222	55	p.	p.	NOUN
ejpam-747	222	56	sharma	sharma	PROPN
ejpam-747	222	57	,	,	PUNCT
ejpam-747	222	58	p.	p.	PROPN
ejpam-747	222	59	srivastava	srivastava	PROPN
ejpam-747	222	60	/	/	SYM
ejpam-747	222	61	eur	eur	PROPN
ejpam-747	222	62	.	.	PUNCT
ejpam-747	223	1	j.	j.	PROPN
ejpam-747	223	2	pure	pure	PROPN
ejpam-747	223	3	appl	appl	PROPN
ejpam-747	223	4	.	.	PROPN
ejpam-747	223	5	math	math	PROPN
ejpam-747	223	6	,	,	PUNCT
ejpam-747	223	7	3	3	NUM
ejpam-747	223	8	(	(	PUNCT
ejpam-747	223	9	2010	2010	NUM
ejpam-747	223	10	)	)	PUNCT
ejpam-747	223	11	,	,	PUNCT
ejpam-747	223	12	1093	1093	NUM
ejpam-747	223	13	-	-	SYM
ejpam-747	223	14	1112	1112	NUM
ejpam-747	223	15	1100	1100	NUM
ejpam-747	223	16	and	and	CCONJ
ejpam-747	223	17	�	�	PROPN
ejpam-747	223	18	�	�	PROPN
ejpam-747	223	19	pzp−1	pzp−1	PROPN
ejpam-747	223	20	�	�	PROPN
ejpam-747	223	21	�	�	PROPN
ejpam-747	223	22	−	−	PROPN
ejpam-747	223	23	β	β	X
ejpam-747	223	24	�	�	PROPN
ejpam-747	223	25	p−m+	p−m+	PROPN
ejpam-747	223	26	1	1	NUM
ejpam-747	223	27	�	�	PROPN
ejpam-747	223	28	dp+1	dp+1	NOUN
ejpam-747	223	29	|zp|	|zp|	PROPN
ejpam-747	223	30	≤	≤	NUM
ejpam-747	223	31	�	�	PROPN
ejpam-747	223	32	�	�	PROPN
ejpam-747	223	33	�	�	PROPN
ejpam-747	223	34	f	f	PROPN
ejpam-747	224	1	′	′	NUM
ejpam-747	224	2	(	(	PUNCT
ejpam-747	224	3	z	z	NOUN
ejpam-747	224	4	)	)	PUNCT
ejpam-747	224	5	�	�	PROPN
ejpam-747	224	6	�	�	PROPN
ejpam-747	224	7	�	�	PROPN
ejpam-747	224	8	≤	≤	PROPN
ejpam-747	224	9	�	�	PROPN
ejpam-747	224	10	�	�	PROPN
ejpam-747	224	11	pzp−1	pzp−1	PROPN
ejpam-747	224	12	�	�	PROPN
ejpam-747	224	13	�	�	PROPN
ejpam-747	224	14	+	+	PROPN
ejpam-747	224	15	β	β	X
ejpam-747	224	16	�	�	NOUN
ejpam-747	224	17	p−m+	p−m+	PROPN
ejpam-747	224	18	1	1	NUM
ejpam-747	224	19	�	�	PROPN
ejpam-747	224	20	dp+1	dp+1	NOUN
ejpam-747	224	21	|zp|	|zp|	ADV
ejpam-747	224	22	.	.	PUNCT
ejpam-747	225	1	(	(	PUNCT
ejpam-747	225	2	15	15	NUM
ejpam-747	225	3	)	)	PUNCT
ejpam-747	225	4	also	also	ADV
ejpam-747	225	5	let	let	VERB
ejpam-747	225	6	g	g	NOUN
ejpam-747	225	7	(	(	PUNCT
ejpam-747	225	8	1	1	X
ejpam-747	225	9	)	)	PUNCT
ejpam-747	225	10	be	be	AUX
ejpam-747	225	11	finite	finite	ADJ
ejpam-747	225	12	and	and	CCONJ
ejpam-747	225	13	ζ	ζ	NOUN
ejpam-747	225	14	:	:	PUNCT
ejpam-747	225	15	=	=	NUM
ejpam-747	225	16	max	max	PROPN
ejpam-747	225	17	bp+k	bp+k	PROPN
ejpam-747	225	18	(	(	PUNCT
ejpam-747	225	19	k	k	X
ejpam-747	225	20	≥	≥	NUM
ejpam-747	225	21	1	1	NUM
ejpam-747	225	22	)	)	PUNCT
ejpam-747	225	23	,	,	PUNCT
ejpam-747	225	24	then	then	ADV
ejpam-747	225	25	|zp|	|zp|	ADP
ejpam-747	225	26	−	−	NOUN
ejpam-747	225	27	βζ	βζ	ADP
ejpam-747	225	28	�	�	PROPN
ejpam-747	225	29	p−m+	p−m+	PROPN
ejpam-747	225	30	1	1	NUM
ejpam-747	225	31	�	�	PROPN
ejpam-747	225	32	�	�	PROPN
ejpam-747	225	33	p+	p+	PART
ejpam-747	225	34	1	1	NUM
ejpam-747	225	35	�	�	PROPN
ejpam-747	225	36	dp+1	dp+1	PROPN
ejpam-747	225	37	�	�	PROPN
ejpam-747	225	38	�	�	PROPN
ejpam-747	225	39	zp+1	zp+1	NUM
ejpam-747	225	40	�	�	PROPN
ejpam-747	225	41	�	�	PROPN
ejpam-747	225	42	≤	≤	PROPN
ejpam-747	225	43	�	�	PROPN
ejpam-747	225	44	�	�	PROPN
ejpam-747	225	45	�	�	PROPN
ejpam-747	225	46	f	f	PROPN
ejpam-747	225	47	∗	∗	VERB
ejpam-747	225	48	g	g	PROPN
ejpam-747	225	49	�	�	PROPN
ejpam-747	225	50	(	(	PUNCT
ejpam-747	225	51	z	z	NOUN
ejpam-747	225	52	)	)	PUNCT
ejpam-747	225	53	�	�	PROPN
ejpam-747	225	54	�	�	PROPN
ejpam-747	225	55	≤	≤	PROPN
ejpam-747	225	56	|zp|+	|zp|+	VERB
ejpam-747	225	57	βζ	βζ	ADV
ejpam-747	225	58	�	�	PROPN
ejpam-747	225	59	p−m+	p−m+	PROPN
ejpam-747	225	60	1	1	NUM
ejpam-747	225	61	�	�	PROPN
ejpam-747	225	62	�	�	PROPN
ejpam-747	225	63	p+	p+	PART
ejpam-747	225	64	1	1	NUM
ejpam-747	225	65	�	�	PROPN
ejpam-747	225	66	dp+1	dp+1	PROPN
ejpam-747	225	67	�	�	PROPN
ejpam-747	225	68	�	�	PROPN
ejpam-747	225	69	zp+1	zp+1	NUM
ejpam-747	225	70	�	�	PROPN
ejpam-747	225	71	�	�	PROPN
ejpam-747	225	72	.	.	PUNCT
ejpam-747	226	1	(	(	PUNCT
ejpam-747	226	2	16	16	NUM
ejpam-747	226	3	)	)	PUNCT
ejpam-747	226	4	the	the	DET
ejpam-747	226	5	bounds	bound	NOUN
ejpam-747	226	6	are	be	AUX
ejpam-747	226	7	sharp	sharp	ADJ
ejpam-747	226	8	and	and	CCONJ
ejpam-747	226	9	extremal	extremal	ADJ
ejpam-747	226	10	function	function	NOUN
ejpam-747	226	11	may	may	AUX
ejpam-747	226	12	given	give	VERB
ejpam-747	226	13	by	by	ADP
ejpam-747	226	14	f	f	PROPN
ejpam-747	226	15	(	(	PUNCT
ejpam-747	226	16	z	z	NOUN
ejpam-747	226	17	)	)	PUNCT
ejpam-747	226	18	=	=	PUNCT
ejpam-747	227	1	zp	zp	PROPN
ejpam-747	227	2	−	−	PROPN
ejpam-747	227	3	β	β	X
ejpam-747	227	4	�	�	PROPN
ejpam-747	227	5	p−m+	p−m+	PROPN
ejpam-747	227	6	1	1	NUM
ejpam-747	227	7	�	�	PROPN
ejpam-747	227	8	�	�	PROPN
ejpam-747	227	9	p+	p+	PART
ejpam-747	227	10	1	1	NUM
ejpam-747	227	11	�	�	PROPN
ejpam-747	227	12	dp+1	dp+1	PROPN
ejpam-747	227	13	zp+1	zp+1	NOUN
ejpam-747	227	14	.	.	PUNCT
ejpam-747	228	1	(	(	PUNCT
ejpam-747	228	2	17	17	NUM
ejpam-747	228	3	)	)	PUNCT
ejpam-747	228	4	proof	proof	NOUN
ejpam-747	228	5	.	.	PUNCT
ejpam-747	229	1	taking	take	VERB
ejpam-747	229	2	absolute	absolute	ADJ
ejpam-747	229	3	value	value	NOUN
ejpam-747	229	4	of	of	ADP
ejpam-747	229	5	f	f	PROPN
ejpam-747	229	6	(	(	PUNCT
ejpam-747	229	7	z	z	NOUN
ejpam-747	229	8	)	)	PUNCT
ejpam-747	229	9	given	give	VERB
ejpam-747	229	10	in	in	ADP
ejpam-747	229	11	(	(	PUNCT
ejpam-747	229	12	7	7	NUM
ejpam-747	229	13	)	)	PUNCT
ejpam-747	229	14	and	and	CCONJ
ejpam-747	229	15	using	use	VERB
ejpam-747	229	16	corollary	corollary	ADJ
ejpam-747	229	17	2	2	NUM
ejpam-747	229	18	,	,	PUNCT
ejpam-747	229	19	we	we	PRON
ejpam-747	229	20	get	get	VERB
ejpam-747	229	21	�	�	PROPN
ejpam-747	229	22	�	�	PROPN
ejpam-747	229	23	f	f	PROPN
ejpam-747	229	24	(	(	PUNCT
ejpam-747	229	25	z	z	PROPN
ejpam-747	229	26	)	)	PUNCT
ejpam-747	229	27	�	�	PROPN
ejpam-747	229	28	�	�	PROPN
ejpam-747	229	29	≤	≤	PROPN
ejpam-747	229	30	|zp|+	|zp|+	CCONJ
ejpam-747	229	31	∞	∞	PROPN
ejpam-747	229	32	∑	∑	PUNCT
ejpam-747	229	33	k=1	k=1	ADP
ejpam-747	229	34	ap+k	ap+k	PROPN
ejpam-747	229	35	�	�	PROPN
ejpam-747	229	36	�	�	PROPN
ejpam-747	229	37	zp+k	zp+k	PROPN
ejpam-747	229	38	�	�	PROPN
ejpam-747	229	39	�	�	PROPN
ejpam-747	229	40	≤	≤	PROPN
ejpam-747	229	41	|zp|+	|zp|+	VERB
ejpam-747	229	42	β	β	X
ejpam-747	229	43	�	�	PROPN
ejpam-747	229	44	p−m+	p−m+	PROPN
ejpam-747	229	45	1	1	NUM
ejpam-747	229	46	�	�	PROPN
ejpam-747	229	47	�	�	PROPN
ejpam-747	229	48	p+	p+	PART
ejpam-747	229	49	1	1	NUM
ejpam-747	229	50	�	�	PROPN
ejpam-747	229	51	dp+1	dp+1	PROPN
ejpam-747	229	52	�	�	PROPN
ejpam-747	229	53	�	�	PROPN
ejpam-747	229	54	zp+1	zp+1	NUM
ejpam-747	229	55	�	�	PROPN
ejpam-747	229	56	�	�	PROPN
ejpam-747	229	57	and	and	CCONJ
ejpam-747	229	58	�	�	PROPN
ejpam-747	229	59	�	�	PROPN
ejpam-747	229	60	f	f	PROPN
ejpam-747	229	61	(	(	PUNCT
ejpam-747	229	62	z	z	PROPN
ejpam-747	229	63	)	)	PUNCT
ejpam-747	229	64	�	�	PROPN
ejpam-747	229	65	�	�	PROPN
ejpam-747	229	66	≥	≥	NUM
ejpam-747	229	67	|zp|	|zp|	ADV
ejpam-747	229	68	−	−	NUM
ejpam-747	229	69	∞	∞	NUM
ejpam-747	229	70	∑	∑	PUNCT
ejpam-747	229	71	k=1	k=1	ADP
ejpam-747	229	72	ap+k	ap+k	PROPN
ejpam-747	229	73	�	�	PROPN
ejpam-747	229	74	�	�	PROPN
ejpam-747	229	75	zp+k	zp+k	PROPN
ejpam-747	229	76	�	�	PROPN
ejpam-747	229	77	�	�	PROPN
ejpam-747	229	78	≥	≥	NUM
ejpam-747	229	79	|zp|	|zp|	ADP
ejpam-747	229	80	−	−	NOUN
ejpam-747	229	81	β	β	X
ejpam-747	229	82	�	�	PROPN
ejpam-747	229	83	p−m+	p−m+	PROPN
ejpam-747	229	84	1	1	NUM
ejpam-747	229	85	�	�	PROPN
ejpam-747	229	86	�	�	PROPN
ejpam-747	229	87	p+	p+	PART
ejpam-747	229	88	1	1	NUM
ejpam-747	229	89	�	�	PROPN
ejpam-747	229	90	dp+1	dp+1	PROPN
ejpam-747	229	91	�	�	PROPN
ejpam-747	229	92	�	�	PROPN
ejpam-747	229	93	zp+1	zp+1	NUM
ejpam-747	229	94	�	�	PROPN
ejpam-747	229	95	�	�	PROPN
ejpam-747	229	96	,	,	PUNCT
ejpam-747	229	97	which	which	PRON
ejpam-747	229	98	prove	prove	VERB
ejpam-747	229	99	assertion	assertion	NOUN
ejpam-747	229	100	(	(	PUNCT
ejpam-747	229	101	14	14	NUM
ejpam-747	229	102	)	)	PUNCT
ejpam-747	229	103	.	.	PUNCT
ejpam-747	230	1	again	again	ADV
ejpam-747	230	2	,	,	PUNCT
ejpam-747	230	3	taking	take	VERB
ejpam-747	230	4	absolute	absolute	ADJ
ejpam-747	230	5	value	value	NOUN
ejpam-747	230	6	of	of	ADP
ejpam-747	230	7	f	f	PROPN
ejpam-747	230	8	′	′	NUM
ejpam-747	231	1	(	(	PUNCT
ejpam-747	231	2	z	z	NOUN
ejpam-747	231	3	)	)	PUNCT
ejpam-747	231	4	and	and	CCONJ
ejpam-747	231	5	using	use	VERB
ejpam-747	231	6	corollary	corollary	ADJ
ejpam-747	231	7	3	3	NUM
ejpam-747	231	8	,	,	PUNCT
ejpam-747	231	9	we	we	PRON
ejpam-747	231	10	get	get	VERB
ejpam-747	231	11	�	�	PROPN
ejpam-747	231	12	�	�	PROPN
ejpam-747	231	13	�	�	PROPN
ejpam-747	231	14	f	f	PROPN
ejpam-747	232	1	′	′	NUM
ejpam-747	232	2	(	(	PUNCT
ejpam-747	232	3	z	z	NOUN
ejpam-747	232	4	)	)	PUNCT
ejpam-747	232	5	�	�	PROPN
ejpam-747	232	6	�	�	PROPN
ejpam-747	232	7	�	�	PROPN
ejpam-747	232	8	≤	≤	PROPN
ejpam-747	232	9	�	�	PROPN
ejpam-747	232	10	�	�	PROPN
ejpam-747	232	11	pzp−1	pzp−1	PROPN
ejpam-747	232	12	�	�	PROPN
ejpam-747	232	13	�	�	PROPN
ejpam-747	232	14	+	+	NUM
ejpam-747	232	15	∞	∞	NUM
ejpam-747	232	16	∑	∑	PUNCT
ejpam-747	232	17	k=1	k=1	PROPN
ejpam-747	232	18	�	�	PROPN
ejpam-747	232	19	p+	p+	PROPN
ejpam-747	232	20	k	k	PROPN
ejpam-747	232	21	�	�	PROPN
ejpam-747	232	22	ap+k	ap+k	PROPN
ejpam-747	232	23	�	�	PROPN
ejpam-747	232	24	�	�	PROPN
ejpam-747	232	25	zp+k−1	zp+k−1	PROPN
ejpam-747	232	26	�	�	PROPN
ejpam-747	232	27	�	�	PROPN
ejpam-747	232	28	≤	≤	PROPN
ejpam-747	232	29	�	�	PROPN
ejpam-747	232	30	�	�	PROPN
ejpam-747	232	31	pzp−1	pzp−1	PROPN
ejpam-747	232	32	�	�	PROPN
ejpam-747	232	33	�	�	PROPN
ejpam-747	232	34	+	+	PROPN
ejpam-747	232	35	β	β	X
ejpam-747	232	36	�	�	NOUN
ejpam-747	232	37	p−m+	p−m+	PROPN
ejpam-747	232	38	1	1	NUM
ejpam-747	232	39	�	�	PROPN
ejpam-747	232	40	dp+1	dp+1	NOUN
ejpam-747	232	41	|zp|	|zp|	NOUN
ejpam-747	232	42	and	and	CCONJ
ejpam-747	232	43	�	�	PROPN
ejpam-747	232	44	�	�	PROPN
ejpam-747	232	45	�	�	PROPN
ejpam-747	232	46	f	f	PROPN
ejpam-747	233	1	′	′	NUM
ejpam-747	233	2	(	(	PUNCT
ejpam-747	233	3	z	z	NOUN
ejpam-747	233	4	)	)	PUNCT
ejpam-747	233	5	�	�	PROPN
ejpam-747	233	6	�	�	PROPN
ejpam-747	233	7	�	�	PROPN
ejpam-747	233	8	≥	≥	PROPN
ejpam-747	233	9	�	�	PROPN
ejpam-747	233	10	�	�	PROPN
ejpam-747	233	11	pzp−1	pzp−1	PROPN
ejpam-747	233	12	�	�	PROPN
ejpam-747	233	13	�	�	PROPN
ejpam-747	233	14	−	−	NOUN
ejpam-747	233	15	∞	∞	NUM
ejpam-747	233	16	∑	∑	PUNCT
ejpam-747	234	1	k=1	k=1	PROPN
ejpam-747	234	2	�	�	PROPN
ejpam-747	234	3	p+	p+	PROPN
ejpam-747	234	4	k	k	PROPN
ejpam-747	234	5	�	�	PROPN
ejpam-747	234	6	ap+k	ap+k	PROPN
ejpam-747	234	7	�	�	PROPN
ejpam-747	234	8	�	�	PROPN
ejpam-747	234	9	zp+k−1	zp+k−1	PROPN
ejpam-747	234	10	�	�	PROPN
ejpam-747	234	11	�	�	PROPN
ejpam-747	234	12	≥	≥	PROPN
ejpam-747	234	13	�	�	PROPN
ejpam-747	234	14	�	�	PROPN
ejpam-747	234	15	pzp−1	pzp−1	PROPN
ejpam-747	234	16	�	�	PROPN
ejpam-747	234	17	�	�	PROPN
ejpam-747	234	18	−	−	PROPN
ejpam-747	234	19	β	β	X
ejpam-747	234	20	�	�	PROPN
ejpam-747	234	21	p−m+	p−m+	PROPN
ejpam-747	234	22	1	1	NUM
ejpam-747	234	23	�	�	PROPN
ejpam-747	234	24	dp+1	dp+1	NOUN
ejpam-747	234	25	|zp|	|zp|	NOUN
ejpam-747	234	26	,	,	PUNCT
ejpam-747	234	27	which	which	PRON
ejpam-747	234	28	prove	prove	VERB
ejpam-747	234	29	assertion	assertion	NOUN
ejpam-747	234	30	(	(	PUNCT
ejpam-747	234	31	15	15	NUM
ejpam-747	234	32	)	)	PUNCT
ejpam-747	234	33	.	.	PUNCT
ejpam-747	235	1	further	far	ADV
ejpam-747	235	2	,	,	PUNCT
ejpam-747	235	3	taking	take	VERB
ejpam-747	235	4	absolute	absolute	ADJ
ejpam-747	235	5	value	value	NOUN
ejpam-747	235	6	of	of	ADP
ejpam-747	235	7	f	f	PROPN
ejpam-747	235	8	∗	∗	NOUN
ejpam-747	235	9	g	g	PROPN
ejpam-747	235	10	,	,	PUNCT
ejpam-747	235	11	where	where	SCONJ
ejpam-747	235	12	f	f	PROPN
ejpam-747	235	13	and	and	CCONJ
ejpam-747	235	14	g	g	PROPN
ejpam-747	235	15	are	be	AUX
ejpam-747	235	16	of	of	ADP
ejpam-747	235	17	the	the	DET
ejpam-747	235	18	form	form	NOUN
ejpam-747	235	19	(	(	PUNCT
ejpam-747	235	20	7	7	NUM
ejpam-747	235	21	)	)	PUNCT
ejpam-747	235	22	and	and	CCONJ
ejpam-747	235	23	(	(	PUNCT
ejpam-747	235	24	2	2	X
ejpam-747	235	25	)	)	PUNCT
ejpam-747	235	26	respectively	respectively	ADV
ejpam-747	235	27	.	.	PUNCT
ejpam-747	236	1	if	if	SCONJ
ejpam-747	236	2	ζ	ζ	X
ejpam-747	236	3	:	:	PUNCT
ejpam-747	236	4	=	=	NUM
ejpam-747	236	5	max	max	PROPN
ejpam-747	236	6	bp+k	bp+k	PROPN
ejpam-747	236	7	,	,	PUNCT
ejpam-747	236	8	then	then	ADV
ejpam-747	236	9	using	use	VERB
ejpam-747	236	10	corollary	corollary	ADJ
ejpam-747	236	11	(	(	PUNCT
ejpam-747	236	12	2	2	NUM
ejpam-747	236	13	)	)	PUNCT
ejpam-747	236	14	,	,	PUNCT
ejpam-747	236	15	we	we	PRON
ejpam-747	236	16	get	get	VERB
ejpam-747	236	17	�	�	PROPN
ejpam-747	236	18	�	�	PROPN
ejpam-747	236	19	�	�	PROPN
ejpam-747	236	20	f	f	PROPN
ejpam-747	236	21	∗	∗	VERB
ejpam-747	236	22	g	g	PROPN
ejpam-747	236	23	�	�	PROPN
ejpam-747	236	24	(	(	PUNCT
ejpam-747	236	25	z	z	NOUN
ejpam-747	236	26	)	)	PUNCT
ejpam-747	236	27	�	�	PROPN
ejpam-747	236	28	�	�	PROPN
ejpam-747	236	29	≤	≤	PROPN
ejpam-747	236	30	|zp|+	|zp|+	CCONJ
ejpam-747	236	31	∞	∞	PROPN
ejpam-747	236	32	∑	∑	PUNCT
ejpam-747	236	33	k=1	k=1	ADP
ejpam-747	236	34	ap+k	ap+k	NOUN
ejpam-747	236	35	bp+k	bp+k	PROPN
ejpam-747	236	36	�	�	PROPN
ejpam-747	236	37	�	�	PROPN
ejpam-747	236	38	zp+k	zp+k	PROPN
ejpam-747	236	39	�	�	PROPN
ejpam-747	236	40	�	�	PROPN
ejpam-747	236	41	≤	≤	PROPN
ejpam-747	236	42	|zp|+	|zp|+	VERB
ejpam-747	236	43	βζ	βζ	ADV
ejpam-747	236	44	�	�	PROPN
ejpam-747	236	45	p−m+	p−m+	PROPN
ejpam-747	236	46	1	1	NUM
ejpam-747	236	47	�	�	PROPN
ejpam-747	236	48	�	�	PROPN
ejpam-747	236	49	p+	p+	PART
ejpam-747	236	50	1	1	NUM
ejpam-747	236	51	�	�	PROPN
ejpam-747	236	52	dp+1	dp+1	PROPN
ejpam-747	236	53	�	�	PROPN
ejpam-747	236	54	�	�	PROPN
ejpam-747	236	55	zp+1	zp+1	NUM
ejpam-747	236	56	�	�	PROPN
ejpam-747	236	57	�	�	PROPN
ejpam-747	236	58	and	and	CCONJ
ejpam-747	236	59	�	�	PROPN
ejpam-747	236	60	�	�	PROPN
ejpam-747	236	61	�	�	PROPN
ejpam-747	236	62	f	f	PROPN
ejpam-747	236	63	∗	∗	VERB
ejpam-747	236	64	g	g	PROPN
ejpam-747	236	65	�	�	PROPN
ejpam-747	236	66	(	(	PUNCT
ejpam-747	236	67	z	z	NOUN
ejpam-747	236	68	)	)	PUNCT
ejpam-747	236	69	�	�	PROPN
ejpam-747	236	70	�	�	PROPN
ejpam-747	236	71	≥	≥	NUM
ejpam-747	236	72	|zp|	|zp|	ADV
ejpam-747	236	73	−	−	NUM
ejpam-747	236	74	∞	∞	NUM
ejpam-747	236	75	∑	∑	PUNCT
ejpam-747	236	76	k=1	k=1	ADP
ejpam-747	236	77	ap+k	ap+k	NOUN
ejpam-747	236	78	bp+k	bp+k	PROPN
ejpam-747	236	79	�	�	PROPN
ejpam-747	236	80	�	�	PROPN
ejpam-747	236	81	zp+k	zp+k	PROPN
ejpam-747	236	82	�	�	PROPN
ejpam-747	236	83	�	�	PROPN
ejpam-747	236	84	≥	≥	NUM
ejpam-747	236	85	|zp|	|zp|	ADP
ejpam-747	236	86	−	−	PROPN
ejpam-747	236	87	βζ	βζ	INTJ
ejpam-747	236	88	�	�	PROPN
ejpam-747	236	89	p−m+	p−m+	PROPN
ejpam-747	236	90	1	1	NUM
ejpam-747	236	91	�	�	PROPN
ejpam-747	236	92	�	�	PROPN
ejpam-747	236	93	p+	p+	PART
ejpam-747	236	94	1	1	NUM
ejpam-747	236	95	�	�	PROPN
ejpam-747	236	96	dp+1	dp+1	PROPN
ejpam-747	236	97	�	�	PROPN
ejpam-747	236	98	�	�	PROPN
ejpam-747	236	99	zp+1	zp+1	NUM
ejpam-747	236	100	�	�	PROPN
ejpam-747	236	101	�	�	PROPN
ejpam-747	236	102	,	,	PUNCT
ejpam-747	236	103	which	which	PRON
ejpam-747	236	104	prove	prove	VERB
ejpam-747	236	105	(	(	PUNCT
ejpam-747	236	106	16	16	NUM
ejpam-747	236	107	)	)	PUNCT
ejpam-747	236	108	.	.	PUNCT
ejpam-747	237	1	the	the	DET
ejpam-747	237	2	bounds	bound	NOUN
ejpam-747	237	3	in	in	ADP
ejpam-747	237	4	(	(	PUNCT
ejpam-747	237	5	14	14	NUM
ejpam-747	237	6	)	)	PUNCT
ejpam-747	237	7	,	,	PUNCT
ejpam-747	237	8	(	(	PUNCT
ejpam-747	237	9	15	15	NUM
ejpam-747	237	10	)	)	PUNCT
ejpam-747	237	11	and	and	CCONJ
ejpam-747	237	12	(	(	PUNCT
ejpam-747	237	13	16	16	NUM
ejpam-747	237	14	)	)	PUNCT
ejpam-747	237	15	are	be	AUX
ejpam-747	237	16	sharp	sharp	ADJ
ejpam-747	237	17	,	,	PUNCT
ejpam-747	237	18	with	with	ADP
ejpam-747	237	19	extremal	extremal	ADJ
ejpam-747	237	20	function	function	NOUN
ejpam-747	237	21	given	give	VERB
ejpam-747	237	22	by	by	ADP
ejpam-747	237	23	(	(	PUNCT
ejpam-747	237	24	10	10	NUM
ejpam-747	237	25	)	)	PUNCT
ejpam-747	237	26	.	.	PUNCT
ejpam-747	238	1	p.	p.	PROPN
ejpam-747	238	2	sharma	sharma	PROPN
ejpam-747	238	3	,	,	PUNCT
ejpam-747	238	4	p.	p.	PROPN
ejpam-747	238	5	srivastava	srivastava	PROPN
ejpam-747	238	6	/	/	SYM
ejpam-747	238	7	eur	eur	PROPN
ejpam-747	238	8	.	.	PUNCT
ejpam-747	239	1	j.	j.	PROPN
ejpam-747	239	2	pure	pure	PROPN
ejpam-747	239	3	appl	appl	PROPN
ejpam-747	239	4	.	.	PROPN
ejpam-747	239	5	math	math	PROPN
ejpam-747	239	6	,	,	PUNCT
ejpam-747	239	7	3	3	NUM
ejpam-747	239	8	(	(	PUNCT
ejpam-747	239	9	2010	2010	NUM
ejpam-747	239	10	)	)	PUNCT
ejpam-747	239	11	,	,	PUNCT
ejpam-747	239	12	1093	1093	NUM
ejpam-747	239	13	-	-	SYM
ejpam-747	239	14	1112	1112	NUM
ejpam-747	239	15	1101	1101	NUM
ejpam-747	239	16	3	3	NUM
ejpam-747	239	17	.	.	PUNCT
ejpam-747	239	18	sufficient	sufficient	ADJ
ejpam-747	239	19	conditions	condition	NOUN
ejpam-747	239	20	for	for	ADP
ejpam-747	239	21	classes	class	NOUN
ejpam-747	240	1	ℜg	ℜg	ADP
ejpam-747	240	2	h	h	PROPN
ejpam-747	240	3	�	�	PROPN
ejpam-747	240	4	p	p	PROPN
ejpam-747	240	5	,	,	PUNCT
ejpam-747	240	6	m	m	PROPN
ejpam-747	240	7	,	,	PUNCT
ejpam-747	240	8	β	β	X
ejpam-747	240	9	�	�	PROPN
ejpam-747	240	10	and	and	CCONJ
ejpam-747	240	11	s	s	VERB
ejpam-747	240	12	g	g	PROPN
ejpam-747	240	13	h	h	PROPN
ejpam-747	240	14	�	�	PROPN
ejpam-747	240	15	p	p	PROPN
ejpam-747	240	16	,	,	PUNCT
ejpam-747	240	17	m	m	PROPN
ejpam-747	240	18	,	,	PUNCT
ejpam-747	240	19	β	β	X
ejpam-747	240	20	�	�	PROPN
ejpam-747	240	21	in	in	ADP
ejpam-747	240	22	this	this	DET
ejpam-747	240	23	section	section	NOUN
ejpam-747	240	24	,	,	PUNCT
ejpam-747	240	25	we	we	PRON
ejpam-747	240	26	obtain	obtain	VERB
ejpam-747	240	27	sufficient	sufficient	ADJ
ejpam-747	240	28	conditions	condition	NOUN
ejpam-747	240	29	for	for	ADP
ejpam-747	240	30	the	the	DET
ejpam-747	240	31	classesℜg	classesℜg	PROPN
ejpam-747	240	32	h	h	NOUN
ejpam-747	240	33	�	�	PROPN
ejpam-747	240	34	p	p	PROPN
ejpam-747	240	35	,	,	PUNCT
ejpam-747	240	36	m	m	PROPN
ejpam-747	240	37	,	,	PUNCT
ejpam-747	240	38	β	β	X
ejpam-747	240	39	�	�	PROPN
ejpam-747	240	40	and	and	CCONJ
ejpam-747	240	41	s	s	VERB
ejpam-747	240	42	g	g	PROPN
ejpam-747	240	43	h	h	PROPN
ejpam-747	240	44	�	�	PROPN
ejpam-747	240	45	p	p	PROPN
ejpam-747	240	46	,	,	PUNCT
ejpam-747	240	47	m	m	PROPN
ejpam-747	240	48	,	,	PUNCT
ejpam-747	240	49	β	β	X
ejpam-747	240	50	�	�	PROPN
ejpam-747	240	51	with	with	ADP
ejpam-747	240	52	the	the	DET
ejpam-747	240	53	use	use	NOUN
ejpam-747	240	54	of	of	ADP
ejpam-747	240	55	following	follow	VERB
ejpam-747	240	56	lemmas	lemmas	PROPN
ejpam-747	240	57	:	:	PUNCT
ejpam-747	240	58	lemma	lemma	PROPN
ejpam-747	240	59	1	1	NUM
ejpam-747	240	60	.	.	PUNCT
ejpam-747	241	1	[	[	X
ejpam-747	241	2	14	14	NUM
ejpam-747	241	3	]	]	X
ejpam-747	241	4	let	let	AUX
ejpam-747	241	5	w	w	PROPN
ejpam-747	241	6	(	(	PUNCT
ejpam-747	241	7	z	z	NOUN
ejpam-747	241	8	)	)	PUNCT
ejpam-747	241	9	be	be	AUX
ejpam-747	241	10	analytic	analytic	ADJ
ejpam-747	241	11	in	in	ADP
ejpam-747	241	12	∆	∆	PROPN
ejpam-747	241	13	and	and	CCONJ
ejpam-747	242	1	such	such	ADJ
ejpam-747	242	2	that	that	PRON
ejpam-747	242	3	w	w	NOUN
ejpam-747	242	4	(	(	PUNCT
ejpam-747	242	5	0	0	NUM
ejpam-747	242	6	)	)	PUNCT
ejpam-747	242	7	=	=	SYM
ejpam-747	242	8	0	0	X
ejpam-747	242	9	.	.	PUNCT
ejpam-747	243	1	then	then	ADV
ejpam-747	243	2	if	if	SCONJ
ejpam-747	243	3	|w	|w	PROPN
ejpam-747	243	4	(	(	PUNCT
ejpam-747	243	5	z)|	z)|	NOUN
ejpam-747	243	6	attains	attain	VERB
ejpam-747	243	7	its	its	PRON
ejpam-747	243	8	maximum	maximum	ADJ
ejpam-747	243	9	value	value	NOUN
ejpam-747	243	10	on	on	ADP
ejpam-747	243	11	circle	circle	NOUN
ejpam-747	243	12	|z|	|z|	NOUN
ejpam-747	243	13	=	=	SYM
ejpam-747	243	14	r	r	NOUN
ejpam-747	243	15	<	<	X
ejpam-747	243	16	1	1	NUM
ejpam-747	243	17	at	at	ADP
ejpam-747	243	18	a	a	DET
ejpam-747	243	19	point	point	NOUN
ejpam-747	243	20	z0	z0	NOUN
ejpam-747	243	21	∈∆	∈∆	NOUN
ejpam-747	243	22	,	,	PUNCT
ejpam-747	243	23	we	we	PRON
ejpam-747	243	24	have	have	VERB
ejpam-747	243	25	z0w	z0w	NUM
ejpam-747	243	26	′	′	NUM
ejpam-747	243	27	�	�	PROPN
ejpam-747	243	28	z0	z0	PROPN
ejpam-747	243	29	�	�	PROPN
ejpam-747	243	30	=	=	SYM
ejpam-747	243	31	kw	kw	PROPN
ejpam-747	243	32	�	�	PROPN
ejpam-747	243	33	z0	z0	PROPN
ejpam-747	243	34	�	�	PROPN
ejpam-747	243	35	,	,	PUNCT
ejpam-747	243	36	where	where	SCONJ
ejpam-747	243	37	k	k	PROPN
ejpam-747	243	38	≥	≥	NUM
ejpam-747	243	39	1	1	NUM
ejpam-747	243	40	is	be	AUX
ejpam-747	243	41	a	a	DET
ejpam-747	243	42	real	real	ADJ
ejpam-747	243	43	number	number	NOUN
ejpam-747	243	44	.	.	PUNCT
ejpam-747	244	1	lemma	lemma	PROPN
ejpam-747	244	2	2	2	NUM
ejpam-747	244	3	.	.	PUNCT
ejpam-747	245	1	[	[	X
ejpam-747	245	2	17	17	NUM
ejpam-747	245	3	]	]	PUNCT
ejpam-747	245	4	let	let	VERB
ejpam-747	245	5	φ	φ	PROPN
ejpam-747	245	6	(	(	PUNCT
ejpam-747	245	7	u	u	NOUN
ejpam-747	245	8	,	,	PUNCT
ejpam-747	245	9	v	v	NOUN
ejpam-747	245	10	)	)	PUNCT
ejpam-747	245	11	be	be	AUX
ejpam-747	245	12	a	a	DET
ejpam-747	245	13	complex	complex	ADJ
ejpam-747	245	14	valued	value	VERB
ejpam-747	245	15	function	function	NOUN
ejpam-747	245	16	:	:	PUNCT
ejpam-747	245	17	φ	φ	PROPN
ejpam-747	245	18	:	:	PUNCT
ejpam-747	246	1	d→	d→	VERB
ejpam-747	246	2	c	c	PROPN
ejpam-747	246	3	,	,	PUNCT
ejpam-747	246	4	�	�	PROPN
ejpam-747	246	5	d	d	PROPN
ejpam-747	246	6	⊂	⊂	PROPN
ejpam-747	246	7	c×c	c×c	PROPN
ejpam-747	246	8	;	;	PUNCT
ejpam-747	246	9	cis	cis	NOUN
ejpam-747	246	10	the	the	DET
ejpam-747	246	11	complex	complex	ADJ
ejpam-747	246	12	plane	plane	NOUN
ejpam-747	246	13	�	�	PROPN
ejpam-747	246	14	,	,	PUNCT
ejpam-747	246	15	and	and	CCONJ
ejpam-747	246	16	let	let	VERB
ejpam-747	246	17	u=	u=	ADJ
ejpam-747	246	18	u1	u1	NOUN
ejpam-747	246	19	+	+	CCONJ
ejpam-747	246	20	iu2	iu2	NOUN
ejpam-747	246	21	and	and	CCONJ
ejpam-747	246	22	v	v	NOUN
ejpam-747	246	23	=	=	SYM
ejpam-747	246	24	v1	v1	PROPN
ejpam-747	246	25	+	+	CCONJ
ejpam-747	246	26	iv2	iv2	NOUN
ejpam-747	246	27	.	.	PUNCT
ejpam-747	246	28	suppose	suppose	VERB
ejpam-747	246	29	that	that	SCONJ
ejpam-747	246	30	the	the	DET
ejpam-747	246	31	function	function	NOUN
ejpam-747	246	32	φ	φ	PROPN
ejpam-747	246	33	(	(	PUNCT
ejpam-747	246	34	u	u	NOUN
ejpam-747	246	35	,	,	PUNCT
ejpam-747	246	36	v	v	NOUN
ejpam-747	246	37	)	)	PUNCT
ejpam-747	246	38	satisfies	satisfie	NOUN
ejpam-747	246	39	(	(	PUNCT
ejpam-747	246	40	i	i	NOUN
ejpam-747	246	41	)	)	PUNCT
ejpam-747	246	42	φ	φ	PROPN
ejpam-747	246	43	(	(	PUNCT
ejpam-747	246	44	u	u	NOUN
ejpam-747	246	45	,	,	PUNCT
ejpam-747	246	46	v	v	NOUN
ejpam-747	246	47	)	)	PUNCT
ejpam-747	246	48	is	be	AUX
ejpam-747	246	49	continuous	continuous	ADJ
ejpam-747	246	50	in	in	ADP
ejpam-747	246	51	d	d	PROPN
ejpam-747	246	52	;	;	PUNCT
ejpam-747	246	53	(	(	PUNCT
ejpam-747	246	54	ii	ii	NOUN
ejpam-747	246	55	)	)	PUNCT
ejpam-747	246	56	(	(	PUNCT
ejpam-747	246	57	1,0	1,0	NUM
ejpam-747	246	58	)	)	PUNCT
ejpam-747	246	59	∈	∈	PROPN
ejpam-747	246	60	d	d	NOUN
ejpam-747	246	61	and	and	CCONJ
ejpam-747	246	62	re	re	ADP
ejpam-747	246	63	�	�	PROPN
ejpam-747	246	64	φ	φ	PROPN
ejpam-747	246	65	(	(	PUNCT
ejpam-747	246	66	1,0	1,0	NUM
ejpam-747	246	67	)	)	PUNCT
ejpam-747	246	68	�	�	PROPN
ejpam-747	246	69	>	>	X
ejpam-747	246	70	0	0	NUM
ejpam-747	246	71	;	;	PUNCT
ejpam-747	246	72	(	(	PUNCT
ejpam-747	246	73	iii	iii	X
ejpam-747	246	74	)	)	PUNCT
ejpam-747	246	75	re	re	ADP
ejpam-747	246	76	�	�	PROPN
ejpam-747	246	77	φ	φ	PROPN
ejpam-747	246	78	�	�	PROPN
ejpam-747	246	79	iu2	iu2	PROPN
ejpam-747	246	80	,	,	PUNCT
ejpam-747	246	81	v1	v1	PROPN
ejpam-747	246	82	�	�	PROPN
ejpam-747	246	83	�	�	PROPN
ejpam-747	246	84	≤	≤	NOUN
ejpam-747	246	85	0	0	NUM
ejpam-747	246	86	for	for	ADP
ejpam-747	246	87	all	all	DET
ejpam-747	246	88	�	�	PROPN
ejpam-747	246	89	iu2	iu2	NOUN
ejpam-747	246	90	,	,	PUNCT
ejpam-747	246	91	v1	v1	PROPN
ejpam-747	246	92	�	�	PROPN
ejpam-747	246	93	∈	∈	PROPN
ejpam-747	246	94	d	d	PROPN
ejpam-747	246	95	and	and	CCONJ
ejpam-747	246	96	such	such	ADJ
ejpam-747	246	97	that	that	DET
ejpam-747	246	98	v1	v1	NOUN
ejpam-747	246	99	≤	≤	PUNCT
ejpam-747	246	100	−	−	ADP
ejpam-747	246	101	�	�	PROPN
ejpam-747	246	102	1	1	NUM
ejpam-747	246	103	+	+	PROPN
ejpam-747	246	104	u2	u2	PROPN
ejpam-747	246	105	2	2	NUM
ejpam-747	246	106	�	�	PROPN
ejpam-747	246	107	/2	/2	PUNCT
ejpam-747	246	108	.	.	PUNCT
ejpam-747	247	1	let	let	VERB
ejpam-747	247	2	p	p	NOUN
ejpam-747	247	3	(	(	PUNCT
ejpam-747	247	4	z	z	NOUN
ejpam-747	247	5	)	)	PUNCT
ejpam-747	247	6	=	=	SYM
ejpam-747	248	1	1	1	NUM
ejpam-747	248	2	+	+	NUM
ejpam-747	248	3	p1z	p1z	NOUN
ejpam-747	248	4	+	+	CCONJ
ejpam-747	248	5	p2z2	p2z2	X
ejpam-747	248	6	+	+	X
ejpam-747	248	7	·	·	PUNCT
ejpam-747	248	8	·	·	PUNCT
ejpam-747	248	9	·	·	PUNCT
ejpam-747	248	10	be	be	AUX
ejpam-747	248	11	regular	regular	ADJ
ejpam-747	248	12	in	in	ADP
ejpam-747	248	13	∆	∆	PROPN
ejpam-747	248	14	such	such	ADJ
ejpam-747	248	15	that	that	PRON
ejpam-747	248	16	�	�	PROPN
ejpam-747	248	17	p	p	PROPN
ejpam-747	248	18	(	(	PUNCT
ejpam-747	248	19	z	z	NOUN
ejpam-747	248	20	)	)	PUNCT
ejpam-747	248	21	,	,	PUNCT
ejpam-747	248	22	zp	zp	NOUN
ejpam-747	248	23	′	′	NUM
ejpam-747	248	24	(	(	PUNCT
ejpam-747	248	25	z	z	X
ejpam-747	248	26	)	)	PUNCT
ejpam-747	248	27	�	�	PROPN
ejpam-747	248	28	∈	∈	PROPN
ejpam-747	248	29	d	d	PROPN
ejpam-747	248	30	for	for	ADP
ejpam-747	248	31	all	all	DET
ejpam-747	248	32	z	z	NOUN
ejpam-747	248	33	∈	∈	PROPN
ejpam-747	249	1	∆.	∆.	NOUN
ejpam-747	249	2	if	if	SCONJ
ejpam-747	249	3	re	re	ADP
ejpam-747	249	4	�	�	PROPN
ejpam-747	249	5	φ	φ	PROPN
ejpam-747	249	6	�	�	PROPN
ejpam-747	249	7	p	p	PROPN
ejpam-747	249	8	(	(	PUNCT
ejpam-747	249	9	z	z	NOUN
ejpam-747	249	10	)	)	PUNCT
ejpam-747	249	11	,	,	PUNCT
ejpam-747	249	12	zp	zp	NOUN
ejpam-747	249	13	′	′	NUM
ejpam-747	249	14	(	(	PUNCT
ejpam-747	249	15	z	z	NOUN
ejpam-747	249	16	)	)	PUNCT
ejpam-747	249	17	�	�	PROPN
ejpam-747	249	18	�	�	PROPN
ejpam-747	249	19	>	>	X
ejpam-747	249	20	0	0	PUNCT
ejpam-747	250	1	(	(	PUNCT
ejpam-747	250	2	z	z	NOUN
ejpam-747	250	3	∈∆	∈∆	NOUN
ejpam-747	250	4	)	)	PUNCT
ejpam-747	250	5	,	,	PUNCT
ejpam-747	250	6	then	then	ADV
ejpam-747	250	7	re	re	VERB
ejpam-747	250	8	�	�	PROPN
ejpam-747	250	9	p	p	PROPN
ejpam-747	250	10	(	(	PUNCT
ejpam-747	250	11	z	z	NOUN
ejpam-747	250	12	)	)	PUNCT
ejpam-747	250	13	�	�	PROPN
ejpam-747	250	14	>	>	X
ejpam-747	250	15	0	0	PUNCT
ejpam-747	251	1	(	(	PUNCT
ejpam-747	251	2	z	z	NOUN
ejpam-747	251	3	∈∆	∈∆	NOUN
ejpam-747	251	4	)	)	PUNCT
ejpam-747	251	5	.	.	PUNCT
ejpam-747	252	1	lemma	lemma	PROPN
ejpam-747	252	2	3	3	X
ejpam-747	252	3	.	.	PUNCT
ejpam-747	253	1	[	[	X
ejpam-747	253	2	19	19	NUM
ejpam-747	253	3	]	]	PUNCT
ejpam-747	253	4	let	let	VERB
ejpam-747	253	5	a	a	DET
ejpam-747	253	6	function	function	NOUN
ejpam-747	253	7	p	p	NOUN
ejpam-747	253	8	(	(	PUNCT
ejpam-747	253	9	z	z	NOUN
ejpam-747	253	10	)	)	PUNCT
ejpam-747	253	11	be	be	AUX
ejpam-747	253	12	analytic	analytic	ADJ
ejpam-747	253	13	in	in	ADP
ejpam-747	253	14	∆	∆	PROPN
ejpam-747	253	15	,	,	PUNCT
ejpam-747	253	16	p	p	X
ejpam-747	253	17	(	(	PUNCT
ejpam-747	253	18	0	0	NUM
ejpam-747	253	19	)	)	PUNCT
ejpam-747	253	20	=	=	SYM
ejpam-747	253	21	1	1	NUM
ejpam-747	253	22	,	,	PUNCT
ejpam-747	253	23	and	and	CCONJ
ejpam-747	253	24	p	p	X
ejpam-747	253	25	(	(	PUNCT
ejpam-747	253	26	z	z	NOUN
ejpam-747	253	27	)	)	PUNCT
ejpam-747	253	28	6=	6=	ADP
ejpam-747	253	29	0	0	NUM
ejpam-747	254	1	(	(	PUNCT
ejpam-747	254	2	z	z	NOUN
ejpam-747	254	3	∈∆	∈∆	NOUN
ejpam-747	254	4	)	)	PUNCT
ejpam-747	254	5	.	.	PUNCT
ejpam-747	255	1	if	if	SCONJ
ejpam-747	255	2	there	there	PRON
ejpam-747	255	3	exists	exist	VERB
ejpam-747	255	4	a	a	DET
ejpam-747	255	5	point	point	NOUN
ejpam-747	255	6	z0	z0	NOUN
ejpam-747	255	7	∈∆	∈∆	VERB
ejpam-747	255	8	such	such	ADJ
ejpam-747	255	9	that	that	SCONJ
ejpam-747	255	10	�	�	PROPN
ejpam-747	255	11	�	�	PROPN
ejpam-747	255	12	arg	arg	NOUN
ejpam-747	255	13	p	p	NOUN
ejpam-747	255	14	(	(	PUNCT
ejpam-747	255	15	z	z	NOUN
ejpam-747	255	16	)	)	PUNCT
ejpam-747	255	17	�	�	PROPN
ejpam-747	255	18	�	�	PROPN
ejpam-747	255	19	<	<	X
ejpam-747	255	20	π	π	PROPN
ejpam-747	255	21	2	2	NUM
ejpam-747	255	22	β	β	X
ejpam-747	255	23	for	for	ADP
ejpam-747	255	24	|z|	|z|	NOUN
ejpam-747	255	25	<	<	X
ejpam-747	255	26	�	�	PROPN
ejpam-747	255	27	�	�	PROPN
ejpam-747	255	28	z0	z0	PROPN
ejpam-747	255	29	�	�	PROPN
ejpam-747	255	30	�	�	PROPN
ejpam-747	255	31	and	and	CCONJ
ejpam-747	255	32	�	�	PROPN
ejpam-747	255	33	�	�	PROPN
ejpam-747	255	34	arg	arg	NOUN
ejpam-747	255	35	p	p	PROPN
ejpam-747	255	36	�	�	PROPN
ejpam-747	255	37	z0	z0	PROPN
ejpam-747	255	38	�	�	PROPN
ejpam-747	255	39	�	�	PROPN
ejpam-747	255	40	�	�	PROPN
ejpam-747	255	41	=	=	SYM
ejpam-747	255	42	π	π	PROPN
ejpam-747	255	43	2	2	NUM
ejpam-747	255	44	β	β	NOUN
ejpam-747	255	45	with	with	ADP
ejpam-747	255	46	0	0	NUM
ejpam-747	255	47	<	<	X
ejpam-747	255	48	β	β	X
ejpam-747	255	49	≤	≤	NUM
ejpam-747	255	50	1	1	NUM
ejpam-747	255	51	,	,	PUNCT
ejpam-747	255	52	then	then	ADV
ejpam-747	255	53	we	we	PRON
ejpam-747	255	54	have	have	VERB
ejpam-747	255	55	z0p	z0p	AUX
ejpam-747	255	56	′	′	NUM
ejpam-747	255	57	�	�	PROPN
ejpam-747	255	58	z0	z0	PROPN
ejpam-747	255	59	�	�	PROPN
ejpam-747	255	60	p	p	PROPN
ejpam-747	255	61	�	�	PROPN
ejpam-747	255	62	z0	z0	PROPN
ejpam-747	255	63	�	�	PROPN
ejpam-747	255	64	=	=	PRON
ejpam-747	255	65	ilβ	ilβ	VERB
ejpam-747	255	66	where	where	SCONJ
ejpam-747	255	67	l	l	NOUN
ejpam-747	255	68	≥	≥	NUM
ejpam-747	255	69	1	1	NUM
ejpam-747	255	70	when	when	SCONJ
ejpam-747	255	71	arg	arg	VERB
ejpam-747	255	72	p	p	PROPN
ejpam-747	255	73	�	�	PROPN
ejpam-747	255	74	z0	z0	PROPN
ejpam-747	255	75	�	�	PROPN
ejpam-747	255	76	=	=	PUNCT
ejpam-747	255	77	π	π	PROPN
ejpam-747	255	78	2	2	NUM
ejpam-747	255	79	β	β	X
ejpam-747	255	80	and	and	CCONJ
ejpam-747	255	81	l	l	NOUN
ejpam-747	255	82	≤	≤	NUM
ejpam-747	255	83	−1	−1	NOUN
ejpam-747	255	84	when	when	SCONJ
ejpam-747	255	85	arg	arg	VERB
ejpam-747	255	86	p	p	PROPN
ejpam-747	255	87	�	�	PROPN
ejpam-747	255	88	z0	z0	PROPN
ejpam-747	255	89	�	�	PROPN
ejpam-747	255	90	=	=	PUNCT
ejpam-747	256	1	−	−	PROPN
ejpam-747	257	1	π	π	PROPN
ejpam-747	257	2	2	2	NUM
ejpam-747	257	3	β	β	X
ejpam-747	257	4	.	.	PUNCT
ejpam-747	258	1	p.	p.	PROPN
ejpam-747	258	2	sharma	sharma	PROPN
ejpam-747	258	3	,	,	PUNCT
ejpam-747	258	4	p.	p.	PROPN
ejpam-747	258	5	srivastava	srivastava	PROPN
ejpam-747	258	6	/	/	SYM
ejpam-747	258	7	eur	eur	PROPN
ejpam-747	258	8	.	.	PUNCT
ejpam-747	259	1	j.	j.	PROPN
ejpam-747	259	2	pure	pure	PROPN
ejpam-747	259	3	appl	appl	PROPN
ejpam-747	259	4	.	.	PROPN
ejpam-747	259	5	math	math	PROPN
ejpam-747	259	6	,	,	PUNCT
ejpam-747	259	7	3	3	NUM
ejpam-747	259	8	(	(	PUNCT
ejpam-747	259	9	2010	2010	NUM
ejpam-747	259	10	)	)	PUNCT
ejpam-747	259	11	,	,	PUNCT
ejpam-747	259	12	1093	1093	NUM
ejpam-747	259	13	-	-	SYM
ejpam-747	259	14	1112	1112	NUM
ejpam-747	259	15	1102	1102	NUM
ejpam-747	259	16	theorem	theorem	VERB
ejpam-747	259	17	3	3	X
ejpam-747	259	18	.	.	PUNCT
ejpam-747	260	1	let	let	VERB
ejpam-747	260	2	the	the	DET
ejpam-747	260	3	function	function	NOUN
ejpam-747	260	4	f	f	PROPN
ejpam-747	260	5	∈	∈	PROPN
ejpam-747	260	6	ap	ap	PROPN
ejpam-747	260	7	,	,	PUNCT
ejpam-747	260	8	if	if	SCONJ
ejpam-747	260	9	for	for	ADP
ejpam-747	260	10	g	g	NOUN
ejpam-747	260	11	,	,	PUNCT
ejpam-747	260	12	h	h	PROPN
ejpam-747	260	13	∈	∈	PROPN
ejpam-747	260	14	ap	ap	PROPN
ejpam-747	260	15	,	,	PUNCT
ejpam-747	260	16	p	p	PROPN
ejpam-747	260	17	∈	∈	PROPN
ejpam-747	260	18	n	n	CCONJ
ejpam-747	260	19	,	,	PUNCT
ejpam-747	260	20	p	p	X
ejpam-747	260	21	>	>	X
ejpam-747	260	22	m	m	PROPN
ejpam-747	260	23	,	,	PUNCT
ejpam-747	260	24	0	0	PUNCT
ejpam-747	260	25	<	<	X
ejpam-747	260	26	β	β	X
ejpam-747	260	27	≤	≤	NOUN
ejpam-747	260	28	p	p	X
ejpam-747	260	29	,	,	PUNCT
ejpam-747	260	30	�	�	PROPN
ejpam-747	260	31	�	�	PROPN
ejpam-747	260	32	�	�	PROPN
ejpam-747	260	33	�	�	PROPN
ejpam-747	260	34	�	�	PROPN
ejpam-747	260	35	1	1	NUM
ejpam-747	260	36	+	+	PROPN
ejpam-747	260	37	z	z	PROPN
ejpam-747	260	38	�	�	PROPN
ejpam-747	260	39	f	f	PROPN
ejpam-747	260	40	∗	∗	VERB
ejpam-747	260	41	g	g	PROPN
ejpam-747	260	42	�	�	PROPN
ejpam-747	260	43	m+2	m+2	PROPN
ejpam-747	260	44	(	(	PUNCT
ejpam-747	260	45	z	z	NOUN
ejpam-747	260	46	)	)	PUNCT
ejpam-747	260	47	�	�	PROPN
ejpam-747	260	48	f	f	PROPN
ejpam-747	260	49	∗	∗	VERB
ejpam-747	260	50	g	g	PROPN
ejpam-747	260	51	�	�	PROPN
ejpam-747	260	52	m+1	m+1	PRON
ejpam-747	260	53	(	(	PUNCT
ejpam-747	260	54	z	z	NOUN
ejpam-747	260	55	)	)	PUNCT
ejpam-747	261	1	−	−	PROPN
ejpam-747	262	1	z	z	PROPN
ejpam-747	262	2	�	�	PROPN
ejpam-747	262	3	f	f	PROPN
ejpam-747	262	4	∗	∗	PROPN
ejpam-747	262	5	h	h	PROPN
ejpam-747	262	6	�	�	PROPN
ejpam-747	262	7	m+1	m+1	PRON
ejpam-747	262	8	(	(	PUNCT
ejpam-747	262	9	z	z	NOUN
ejpam-747	262	10	)	)	PUNCT
ejpam-747	262	11	�	�	PROPN
ejpam-747	262	12	f	f	PROPN
ejpam-747	262	13	∗	∗	PROPN
ejpam-747	262	14	h	h	PROPN
ejpam-747	262	15	�	�	PROPN
ejpam-747	262	16	m	m	PROPN
ejpam-747	262	17	(	(	PUNCT
ejpam-747	262	18	z	z	NOUN
ejpam-747	262	19	)	)	PUNCT
ejpam-747	262	20	�	�	PROPN
ejpam-747	262	21	�	�	PROPN
ejpam-747	262	22	�	�	PROPN
ejpam-747	262	23	�	�	PROPN
ejpam-747	262	24	�	�	PROPN
ejpam-747	262	25	<	<	X
ejpam-747	262	26	β	β	X
ejpam-747	262	27	�	�	PROPN
ejpam-747	262	28	p−m	p−m	PROPN
ejpam-747	262	29	�	�	PROPN
ejpam-747	262	30	+	+	NUM
ejpam-747	262	31	β	β	X
ejpam-747	262	32	,	,	PUNCT
ejpam-747	262	33	(	(	PUNCT
ejpam-747	262	34	18	18	NUM
ejpam-747	262	35	)	)	PUNCT
ejpam-747	262	36	holds	hold	VERB
ejpam-747	262	37	,	,	PUNCT
ejpam-747	262	38	then	then	ADV
ejpam-747	262	39	f	f	PROPN
ejpam-747	262	40	∈	∈	PROPN
ejpam-747	262	41	ℜg	ℜg	PROPN
ejpam-747	262	42	h	h	NOUN
ejpam-747	262	43	�	�	PROPN
ejpam-747	262	44	p	p	PROPN
ejpam-747	262	45	,	,	PUNCT
ejpam-747	262	46	m	m	PROPN
ejpam-747	262	47	,	,	PUNCT
ejpam-747	262	48	β	β	X
ejpam-747	262	49	�	�	PROPN
ejpam-747	262	50	.	.	PUNCT
ejpam-747	263	1	proof	proof	NOUN
ejpam-747	263	2	.	.	PUNCT
ejpam-747	264	1	let	let	VERB
ejpam-747	264	2	w	w	X
ejpam-747	264	3	(	(	PUNCT
ejpam-747	264	4	z	z	AUX
ejpam-747	264	5	)	)	PUNCT
ejpam-747	264	6	be	be	AUX
ejpam-747	264	7	defined	define	VERB
ejpam-747	264	8	by	by	ADP
ejpam-747	264	9	z	z	PROPN
ejpam-747	264	10	�	�	PROPN
ejpam-747	264	11	f	f	PROPN
ejpam-747	264	12	∗	∗	VERB
ejpam-747	264	13	g	g	PROPN
ejpam-747	264	14	�	�	PROPN
ejpam-747	264	15	m+1	m+1	PRON
ejpam-747	264	16	(	(	PUNCT
ejpam-747	264	17	z	z	NOUN
ejpam-747	264	18	)	)	PUNCT
ejpam-747	264	19	�	�	PROPN
ejpam-747	264	20	f	f	PROPN
ejpam-747	264	21	∗	∗	PROPN
ejpam-747	264	22	h	h	PROPN
ejpam-747	264	23	�	�	PROPN
ejpam-747	264	24	m	m	PROPN
ejpam-747	264	25	(	(	PUNCT
ejpam-747	264	26	z	z	NOUN
ejpam-747	264	27	)	)	PUNCT
ejpam-747	264	28	=	=	SYM
ejpam-747	264	29	�	�	PROPN
ejpam-747	264	30	p−m	p−m	PRON
ejpam-747	264	31	�	�	PROPN
ejpam-747	265	1	+	+	ADP
ejpam-747	265	2	βw	βw	PROPN
ejpam-747	265	3	(	(	PUNCT
ejpam-747	265	4	z	z	NOUN
ejpam-747	265	5	)	)	PUNCT
ejpam-747	265	6	.	.	PUNCT
ejpam-747	266	1	clearly	clearly	ADV
ejpam-747	266	2	w	w	PROPN
ejpam-747	266	3	(	(	PUNCT
ejpam-747	266	4	z	z	NOUN
ejpam-747	266	5	)	)	PUNCT
ejpam-747	266	6	is	be	AUX
ejpam-747	266	7	analytic	analytic	ADJ
ejpam-747	266	8	in	in	ADP
ejpam-747	266	9	∆	∆	PROPN
ejpam-747	266	10	and	and	CCONJ
ejpam-747	266	11	w	w	PROPN
ejpam-747	266	12	(	(	PUNCT
ejpam-747	266	13	0	0	NUM
ejpam-747	266	14	)	)	PUNCT
ejpam-747	266	15	=	=	SYM
ejpam-747	266	16	0	0	X
ejpam-747	266	17	.	.	X
ejpam-747	266	18	differentiating	differentiate	VERB
ejpam-747	266	19	logarithmically	logarithmically	ADV
ejpam-747	266	20	,	,	PUNCT
ejpam-747	266	21	we	we	PRON
ejpam-747	266	22	obtain	obtain	VERB
ejpam-747	266	23	1	1	NUM
ejpam-747	266	24	+	+	NUM
ejpam-747	267	1	z	z	PROPN
ejpam-747	267	2	�	�	PROPN
ejpam-747	267	3	f	f	PROPN
ejpam-747	267	4	∗	∗	VERB
ejpam-747	267	5	g	g	PROPN
ejpam-747	267	6	�	�	PROPN
ejpam-747	267	7	m+2	m+2	PROPN
ejpam-747	267	8	(	(	PUNCT
ejpam-747	267	9	z	z	NOUN
ejpam-747	267	10	)	)	PUNCT
ejpam-747	267	11	�	�	PROPN
ejpam-747	267	12	f	f	PROPN
ejpam-747	267	13	∗	∗	VERB
ejpam-747	267	14	g	g	PROPN
ejpam-747	267	15	�	�	PROPN
ejpam-747	267	16	m+1	m+1	PRON
ejpam-747	267	17	(	(	PUNCT
ejpam-747	267	18	z	z	NOUN
ejpam-747	267	19	)	)	PUNCT
ejpam-747	267	20	−	−	PROPN
ejpam-747	268	1	z	z	PROPN
ejpam-747	268	2	�	�	PROPN
ejpam-747	268	3	f	f	PROPN
ejpam-747	268	4	∗	∗	PROPN
ejpam-747	268	5	h	h	PROPN
ejpam-747	268	6	�	�	PROPN
ejpam-747	268	7	m+1	m+1	PRON
ejpam-747	268	8	(	(	PUNCT
ejpam-747	268	9	z	z	NOUN
ejpam-747	268	10	)	)	PUNCT
ejpam-747	268	11	�	�	PROPN
ejpam-747	268	12	f	f	PROPN
ejpam-747	268	13	∗	∗	PROPN
ejpam-747	268	14	h	h	PROPN
ejpam-747	268	15	�	�	PROPN
ejpam-747	268	16	m	m	PROPN
ejpam-747	268	17	(	(	PUNCT
ejpam-747	268	18	z	z	NOUN
ejpam-747	268	19	)	)	PUNCT
ejpam-747	268	20	=	=	SYM
ejpam-747	269	1	zβw	zβw	NOUN
ejpam-747	270	1	′	′	NUM
ejpam-747	271	1	(	(	PUNCT
ejpam-747	271	2	z	z	NOUN
ejpam-747	271	3	)	)	PUNCT
ejpam-747	271	4	�	�	PROPN
ejpam-747	271	5	�	�	PROPN
ejpam-747	271	6	p−m	p−m	PRON
ejpam-747	271	7	�	�	PROPN
ejpam-747	271	8	+	+	CCONJ
ejpam-747	271	9	βw	βw	PROPN
ejpam-747	271	10	(	(	PUNCT
ejpam-747	271	11	z	z	NOUN
ejpam-747	271	12	)	)	PUNCT
ejpam-747	271	13	�	�	PROPN
ejpam-747	271	14	.	.	PUNCT
ejpam-747	272	1	suppose	suppose	VERB
ejpam-747	272	2	that	that	SCONJ
ejpam-747	272	3	there	there	PRON
ejpam-747	272	4	exists	exist	VERB
ejpam-747	272	5	a	a	DET
ejpam-747	272	6	point	point	NOUN
ejpam-747	272	7	z0	z0	NOUN
ejpam-747	272	8	∈∆	∈∆	VERB
ejpam-747	272	9	such	such	ADJ
ejpam-747	272	10	that	that	SCONJ
ejpam-747	272	11	max	max	PROPN
ejpam-747	272	12	|z|<|z0|	|z|<|z0|	PROPN
ejpam-747	272	13	|w	|w	NOUN
ejpam-747	272	14	(	(	PUNCT
ejpam-747	272	15	z)|	z)|	PROPN
ejpam-747	272	16	=	=	SYM
ejpam-747	272	17	�	�	PROPN
ejpam-747	272	18	�	�	PROPN
ejpam-747	272	19	w	w	PROPN
ejpam-747	272	20	�	�	PROPN
ejpam-747	272	21	z0	z0	PROPN
ejpam-747	272	22	�	�	PROPN
ejpam-747	272	23	�	�	PROPN
ejpam-747	272	24	�	�	PROPN
ejpam-747	272	25	=	=	SYM
ejpam-747	272	26	1	1	NUM
ejpam-747	272	27	�	�	PROPN
ejpam-747	272	28	w(z0	w(z0	NOUN
ejpam-747	272	29	)	)	PUNCT
ejpam-747	272	30	6=	6=	ADP
ejpam-747	272	31	1	1	NUM
ejpam-747	272	32	�	�	PROPN
ejpam-747	272	33	.	.	PUNCT
ejpam-747	273	1	then	then	ADV
ejpam-747	273	2	using	use	VERB
ejpam-747	273	3	jack	jack	PROPN
ejpam-747	273	4	’s	’s	PART
ejpam-747	273	5	lemma	lemma	PROPN
ejpam-747	273	6	1	1	NUM
ejpam-747	273	7	,	,	PUNCT
ejpam-747	273	8	we	we	PRON
ejpam-747	273	9	get	get	VERB
ejpam-747	273	10	z0w	z0w	NUM
ejpam-747	273	11	′	′	NUM
ejpam-747	273	12	�	�	PROPN
ejpam-747	273	13	z0	z0	PROPN
ejpam-747	273	14	�	�	PROPN
ejpam-747	273	15	=	=	SYM
ejpam-747	273	16	kw	kw	PROPN
ejpam-747	273	17	�	�	PROPN
ejpam-747	273	18	z0	z0	PROPN
ejpam-747	273	19	�	�	PROPN
ejpam-747	273	20	(	(	PUNCT
ejpam-747	273	21	k	k	X
ejpam-747	273	22	≥	≥	NUM
ejpam-747	273	23	1	1	NUM
ejpam-747	273	24	)	)	PUNCT
ejpam-747	273	25	.	.	PUNCT
ejpam-747	274	1	therefore	therefore	ADV
ejpam-747	274	2	,	,	PUNCT
ejpam-747	274	3	letting	let	VERB
ejpam-747	274	4	w	w	ADP
ejpam-747	274	5	�	�	PROPN
ejpam-747	274	6	z0	z0	PROPN
ejpam-747	274	7	�	�	PROPN
ejpam-747	274	8	=	=	SYM
ejpam-747	274	9	eiθ	eiθ	PROPN
ejpam-747	274	10	(	(	PUNCT
ejpam-747	274	11	θ	θ	PROPN
ejpam-747	274	12	6=	6=	NUM
ejpam-747	274	13	0	0	NUM
ejpam-747	274	14	)	)	PUNCT
ejpam-747	274	15	,	,	PUNCT
ejpam-747	274	16	�	�	PROPN
ejpam-747	274	17	�	�	PROPN
ejpam-747	274	18	�	�	PROPN
ejpam-747	274	19	�	�	PROPN
ejpam-747	274	20	�	�	PROPN
ejpam-747	274	21	1	1	NUM
ejpam-747	274	22	+	+	PROPN
ejpam-747	274	23	z0	z0	PROPN
ejpam-747	274	24	�	�	PROPN
ejpam-747	274	25	f	f	PROPN
ejpam-747	274	26	∗	∗	VERB
ejpam-747	274	27	g	g	PROPN
ejpam-747	274	28	�	�	PROPN
ejpam-747	274	29	m+2	m+2	PROPN
ejpam-747	274	30	�	�	PROPN
ejpam-747	274	31	z0	z0	PROPN
ejpam-747	274	32	�	�	PROPN
ejpam-747	274	33	�	�	PROPN
ejpam-747	274	34	f	f	PROPN
ejpam-747	274	35	∗	∗	VERB
ejpam-747	274	36	g	g	PROPN
ejpam-747	274	37	�	�	PROPN
ejpam-747	274	38	m+1	m+1	PROPN
ejpam-747	274	39	�	�	PROPN
ejpam-747	274	40	z0	z0	PROPN
ejpam-747	274	41	�	�	PROPN
ejpam-747	274	42	−	−	PROPN
ejpam-747	274	43	z0	z0	PROPN
ejpam-747	274	44	�	�	PROPN
ejpam-747	274	45	f	f	PROPN
ejpam-747	274	46	∗	∗	PROPN
ejpam-747	274	47	h	h	PROPN
ejpam-747	274	48	�	�	PROPN
ejpam-747	274	49	m+1	m+1	PROPN
ejpam-747	274	50	�	�	PROPN
ejpam-747	274	51	z0	z0	PROPN
ejpam-747	274	52	�	�	PROPN
ejpam-747	274	53	�	�	PROPN
ejpam-747	274	54	f	f	PROPN
ejpam-747	274	55	∗	∗	PROPN
ejpam-747	274	56	h	h	PROPN
ejpam-747	274	57	�	�	PROPN
ejpam-747	274	58	m	m	PROPN
ejpam-747	274	59	�	�	PROPN
ejpam-747	274	60	z0	z0	PROPN
ejpam-747	274	61	�	�	PROPN
ejpam-747	274	62	�	�	PROPN
ejpam-747	274	63	�	�	PROPN
ejpam-747	274	64	�	�	PROPN
ejpam-747	274	65	�	�	PROPN
ejpam-747	274	66	�	�	PROPN
ejpam-747	274	67	=	=	SYM
ejpam-747	274	68	�	�	PROPN
ejpam-747	274	69	�	�	PROPN
ejpam-747	274	70	�	�	PROPN
ejpam-747	274	71	�	�	PROPN
ejpam-747	274	72	�	�	PROPN
ejpam-747	274	73	z0βw	z0βw	NUM
ejpam-747	274	74	′	′	NUM
ejpam-747	274	75	�	�	PROPN
ejpam-747	274	76	z0	z0	PROPN
ejpam-747	274	77	�	�	PROPN
ejpam-747	274	78	�	�	PROPN
ejpam-747	274	79	p−m	p−m	PROPN
ejpam-747	274	80	�	�	PROPN
ejpam-747	274	81	+	+	CCONJ
ejpam-747	274	82	βw	βw	ADP
ejpam-747	274	83	�	�	PROPN
ejpam-747	274	84	z0	z0	PROPN
ejpam-747	274	85	�	�	PROPN
ejpam-747	274	86	�	�	PROPN
ejpam-747	274	87	�	�	PROPN
ejpam-747	274	88	�	�	PROPN
ejpam-747	274	89	�	�	PROPN
ejpam-747	274	90	�	�	PROPN
ejpam-747	274	91	=	=	PROPN
ejpam-747	274	92	βk	βk	ADP
ejpam-747	274	93	¦	¦	PROPN
ejpam-747	274	94	�	�	PROPN
ejpam-747	274	95	p−m	p−m	PROPN
ejpam-747	274	96	�	�	PROPN
ejpam-747	274	97	2	2	NUM
ejpam-747	274	98	+	+	CCONJ
ejpam-747	274	99	β2	β2	ADJ
ejpam-747	274	100	+	+	CCONJ
ejpam-747	274	101	2β	2β	NUM
ejpam-747	274	102	�	�	PROPN
ejpam-747	274	103	p−m	p−m	PRON
ejpam-747	274	104	�	�	PROPN
ejpam-747	274	105	cos	cos	ADP
ejpam-747	274	106	θ	θ	PROPN
ejpam-747	274	107	©	©	NOUN
ejpam-747	274	108	1	1	NUM
ejpam-747	274	109	2	2	NUM
ejpam-747	274	110	≥	≥	NOUN
ejpam-747	274	111	β	β	X
ejpam-747	274	112	p−m+	p−m+	VERB
ejpam-747	274	113	β	β	X
ejpam-747	274	114	,	,	PUNCT
ejpam-747	274	115	which	which	PRON
ejpam-747	274	116	contradicts	contradict	VERB
ejpam-747	274	117	the	the	DET
ejpam-747	274	118	condition	condition	NOUN
ejpam-747	274	119	(	(	PUNCT
ejpam-747	274	120	18	18	NUM
ejpam-747	274	121	)	)	PUNCT
ejpam-747	274	122	,	,	PUNCT
ejpam-747	274	123	we	we	PRON
ejpam-747	274	124	have	have	VERB
ejpam-747	274	125	|w	|w	NOUN
ejpam-747	274	126	(	(	PUNCT
ejpam-747	274	127	z)|	z)|	X
ejpam-747	274	128	<	<	X
ejpam-747	274	129	1	1	NUM
ejpam-747	274	130	for	for	ADP
ejpam-747	274	131	all	all	DET
ejpam-747	274	132	z0	z0	PROPN
ejpam-747	274	133	∈	∈	PROPN
ejpam-747	274	134	∆	∆	PROPN
ejpam-747	274	135	,	,	PUNCT
ejpam-747	274	136	consequently	consequently	ADV
ejpam-747	274	137	,	,	PUNCT
ejpam-747	274	138	we	we	PRON
ejpam-747	274	139	conclude	conclude	VERB
ejpam-747	274	140	that	that	SCONJ
ejpam-747	274	141	f	f	PROPN
ejpam-747	274	142	∈	∈	PROPN
ejpam-747	274	143	ℜg	ℜg	PROPN
ejpam-747	274	144	h	h	NOUN
ejpam-747	274	145	�	�	PROPN
ejpam-747	274	146	p	p	PROPN
ejpam-747	274	147	,	,	PUNCT
ejpam-747	274	148	m	m	PROPN
ejpam-747	274	149	,	,	PUNCT
ejpam-747	274	150	β	β	X
ejpam-747	274	151	�	�	PROPN
ejpam-747	274	152	.	.	PUNCT
ejpam-747	275	1	taking	take	VERB
ejpam-747	275	2	h=	h=	PRON
ejpam-747	275	3	g	g	NOUN
ejpam-747	275	4	,	,	PUNCT
ejpam-747	275	5	we	we	PRON
ejpam-747	275	6	get	get	AUX
ejpam-747	275	7	following	follow	VERB
ejpam-747	275	8	inclusion	inclusion	NOUN
ejpam-747	275	9	result	result	NOUN
ejpam-747	275	10	with	with	ADP
ejpam-747	275	11	the	the	DET
ejpam-747	275	12	help	help	NOUN
ejpam-747	275	13	of	of	ADP
ejpam-747	275	14	jack	jack	PROPN
ejpam-747	275	15	’s	’s	PART
ejpam-747	275	16	lemma	lemma	PROPN
ejpam-747	275	17	.	.	PUNCT
ejpam-747	276	1	theorem	theorem	VERB
ejpam-747	276	2	4	4	NUM
ejpam-747	276	3	.	.	PUNCT
ejpam-747	277	1	for	for	ADP
ejpam-747	277	2	p	p	PROPN
ejpam-747	277	3	>	>	X
ejpam-747	277	4	m	m	PROPN
ejpam-747	277	5	,	,	PUNCT
ejpam-747	277	6	ℜg	ℜg	PROPN
ejpam-747	277	7	�	�	PROPN
ejpam-747	277	8	p	p	PROPN
ejpam-747	277	9	,	,	PUNCT
ejpam-747	277	10	m+	m+	NUM
ejpam-747	277	11	1,β	1,β	NUM
ejpam-747	277	12	�	�	PROPN
ejpam-747	277	13	⊂ℜg	⊂ℜg	PROPN
ejpam-747	277	14	�	�	PROPN
ejpam-747	277	15	p	p	PROPN
ejpam-747	277	16	,	,	PUNCT
ejpam-747	277	17	m	m	PROPN
ejpam-747	277	18	,	,	PUNCT
ejpam-747	277	19	α	α	PROPN
ejpam-747	277	20	�	�	PROPN
ejpam-747	277	21	,	,	PUNCT
ejpam-747	277	22	where	where	SCONJ
ejpam-747	277	23	0	0	X
ejpam-747	277	24	<	<	X
ejpam-747	277	25	α	α	DET
ejpam-747	277	26	≤	≤	PUNCT
ejpam-747	277	27	−	−	PROPN
ejpam-747	277	28	�	�	PROPN
ejpam-747	277	29	p−m−	p−m−	PROPN
ejpam-747	277	30	β	β	X
ejpam-747	277	31	+	+	CCONJ
ejpam-747	277	32	1	1	NUM
ejpam-747	277	33	�	�	PROPN
ejpam-747	277	34	±	±	NUM
ejpam-747	277	35	2	2	NUM
ejpam-747	277	36	æ	æ	X
ejpam-747	277	37	�	�	PROPN
ejpam-747	278	1	p−m−	p−m−	PROPN
ejpam-747	278	2	β	β	PROPN
ejpam-747	278	3	+	+	ADJ
ejpam-747	278	4	1	1	NUM
ejpam-747	278	5	�	�	NOUN
ejpam-747	278	6	2	2	NUM
ejpam-747	278	7	+	+	SYM
ejpam-747	278	8	4β	4β	NUM
ejpam-747	278	9	�	�	PROPN
ejpam-747	278	10	p−m	p−m	PRON
ejpam-747	278	11	�	�	PROPN
ejpam-747	278	12	2	2	NUM
ejpam-747	278	13	≤	≤	NOUN
ejpam-747	278	14	p−m	p−m	NOUN
ejpam-747	278	15	.	.	PUNCT
ejpam-747	279	1	(	(	PUNCT
ejpam-747	279	2	19	19	NUM
ejpam-747	279	3	)	)	PUNCT
ejpam-747	279	4	p.	p.	NOUN
ejpam-747	279	5	sharma	sharma	PROPN
ejpam-747	279	6	,	,	PUNCT
ejpam-747	279	7	p.	p.	PROPN
ejpam-747	279	8	srivastava	srivastava	PROPN
ejpam-747	279	9	/	/	SYM
ejpam-747	279	10	eur	eur	PROPN
ejpam-747	279	11	.	.	PUNCT
ejpam-747	280	1	j.	j.	PROPN
ejpam-747	280	2	pure	pure	PROPN
ejpam-747	280	3	appl	appl	PROPN
ejpam-747	280	4	.	.	PROPN
ejpam-747	280	5	math	math	PROPN
ejpam-747	280	6	,	,	PUNCT
ejpam-747	280	7	3	3	NUM
ejpam-747	280	8	(	(	PUNCT
ejpam-747	280	9	2010	2010	NUM
ejpam-747	280	10	)	)	PUNCT
ejpam-747	280	11	,	,	PUNCT
ejpam-747	280	12	1093	1093	NUM
ejpam-747	280	13	-	-	SYM
ejpam-747	280	14	1112	1112	NUM
ejpam-747	280	15	1103	1103	NUM
ejpam-747	280	16	proof	proof	NOUN
ejpam-747	280	17	.	.	PUNCT
ejpam-747	281	1	let	let	VERB
ejpam-747	281	2	f	f	PROPN
ejpam-747	281	3	∈	∈	PROPN
ejpam-747	281	4	ℜg	ℜg	PROPN
ejpam-747	281	5	�	�	PROPN
ejpam-747	281	6	p	p	PROPN
ejpam-747	281	7	,	,	PUNCT
ejpam-747	281	8	m+	m+	NUM
ejpam-747	281	9	1,β	1,β	NUM
ejpam-747	281	10	�	�	PROPN
ejpam-747	281	11	.	.	PUNCT
ejpam-747	282	1	then	then	ADV
ejpam-747	282	2	�	�	PROPN
ejpam-747	282	3	�	�	PROPN
ejpam-747	282	4	�	�	PROPN
ejpam-747	282	5	�	�	PROPN
ejpam-747	282	6	�	�	PROPN
ejpam-747	282	7	z	z	PROPN
ejpam-747	282	8	�	�	PROPN
ejpam-747	283	1	f	f	PROPN
ejpam-747	283	2	∗	∗	VERB
ejpam-747	283	3	g	g	PROPN
ejpam-747	283	4	�	�	PROPN
ejpam-747	283	5	m+2	m+2	PROPN
ejpam-747	283	6	(	(	PUNCT
ejpam-747	283	7	z	z	NOUN
ejpam-747	283	8	)	)	PUNCT
ejpam-747	283	9	�	�	PROPN
ejpam-747	283	10	f	f	PROPN
ejpam-747	283	11	∗	∗	VERB
ejpam-747	283	12	g	g	PROPN
ejpam-747	283	13	�	�	PROPN
ejpam-747	283	14	m+1	m+1	PRON
ejpam-747	283	15	(	(	PUNCT
ejpam-747	283	16	z	z	NOUN
ejpam-747	283	17	)	)	PUNCT
ejpam-747	283	18	−	−	PROPN
ejpam-747	284	1	�	�	PROPN
ejpam-747	284	2	p−m−	p−m−	PROPN
ejpam-747	284	3	1	1	NUM
ejpam-747	284	4	�	�	PROPN
ejpam-747	284	5	�	�	PROPN
ejpam-747	284	6	�	�	PROPN
ejpam-747	284	7	�	�	PROPN
ejpam-747	284	8	�	�	PROPN
ejpam-747	284	9	�	�	PROPN
ejpam-747	284	10	<	<	X
ejpam-747	284	11	β	β	X
ejpam-747	284	12	(	(	PUNCT
ejpam-747	284	13	20	20	NUM
ejpam-747	284	14	)	)	PUNCT
ejpam-747	284	15	and	and	CCONJ
ejpam-747	284	16	let	let	VERB
ejpam-747	284	17	w	w	PROPN
ejpam-747	284	18	(	(	PUNCT
ejpam-747	284	19	z	z	NOUN
ejpam-747	284	20	)	)	PUNCT
ejpam-747	284	21	be	be	AUX
ejpam-747	284	22	defined	define	VERB
ejpam-747	284	23	by	by	ADP
ejpam-747	284	24	z	z	PROPN
ejpam-747	284	25	�	�	PROPN
ejpam-747	284	26	f	f	PROPN
ejpam-747	284	27	∗	∗	VERB
ejpam-747	284	28	g	g	PROPN
ejpam-747	284	29	�	�	PROPN
ejpam-747	284	30	m+1	m+1	PRON
ejpam-747	284	31	(	(	PUNCT
ejpam-747	284	32	z	z	NOUN
ejpam-747	284	33	)	)	PUNCT
ejpam-747	284	34	�	�	PROPN
ejpam-747	284	35	f	f	PROPN
ejpam-747	284	36	∗	∗	VERB
ejpam-747	284	37	g	g	PROPN
ejpam-747	284	38	�	�	PROPN
ejpam-747	284	39	m	m	PROPN
ejpam-747	284	40	(	(	PUNCT
ejpam-747	284	41	z	z	NOUN
ejpam-747	284	42	)	)	PUNCT
ejpam-747	284	43	−	−	PROPN
ejpam-747	284	44	�	�	PROPN
ejpam-747	284	45	p−m	p−m	X
ejpam-747	284	46	�	�	PROPN
ejpam-747	284	47	=	=	PUNCT
ejpam-747	284	48	αw	αw	ADP
ejpam-747	284	49	(	(	PUNCT
ejpam-747	284	50	z	z	NOUN
ejpam-747	284	51	)	)	PUNCT
ejpam-747	284	52	.	.	PUNCT
ejpam-747	285	1	(	(	PUNCT
ejpam-747	285	2	21	21	NUM
ejpam-747	285	3	)	)	PUNCT
ejpam-747	285	4	clearly	clearly	ADV
ejpam-747	285	5	w	w	PROPN
ejpam-747	285	6	(	(	PUNCT
ejpam-747	285	7	z	z	NOUN
ejpam-747	285	8	)	)	PUNCT
ejpam-747	285	9	is	be	AUX
ejpam-747	285	10	analytic	analytic	ADJ
ejpam-747	285	11	in	in	ADP
ejpam-747	285	12	∆	∆	PROPN
ejpam-747	285	13	and	and	CCONJ
ejpam-747	285	14	w	w	PROPN
ejpam-747	285	15	(	(	PUNCT
ejpam-747	285	16	0	0	NUM
ejpam-747	285	17	)	)	PUNCT
ejpam-747	285	18	=	=	SYM
ejpam-747	286	1	0	0	X
ejpam-747	286	2	.	.	X
ejpam-747	286	3	differentiating	differentiate	VERB
ejpam-747	286	4	logarithmically	logarithmically	ADV
ejpam-747	286	5	,	,	PUNCT
ejpam-747	286	6	we	we	PRON
ejpam-747	286	7	obtain	obtain	VERB
ejpam-747	286	8	z	z	PROPN
ejpam-747	286	9	�	�	PROPN
ejpam-747	286	10	f	f	PROPN
ejpam-747	286	11	∗	∗	VERB
ejpam-747	287	1	g	g	PROPN
ejpam-747	287	2	�	�	PROPN
ejpam-747	287	3	m+2	m+2	PROPN
ejpam-747	287	4	(	(	PUNCT
ejpam-747	287	5	z	z	NOUN
ejpam-747	287	6	)	)	PUNCT
ejpam-747	287	7	�	�	PROPN
ejpam-747	287	8	f	f	PROPN
ejpam-747	287	9	∗	∗	VERB
ejpam-747	287	10	g	g	PROPN
ejpam-747	287	11	�	�	PROPN
ejpam-747	287	12	m+1	m+1	PRON
ejpam-747	287	13	(	(	PUNCT
ejpam-747	287	14	z	z	NOUN
ejpam-747	287	15	)	)	PUNCT
ejpam-747	287	16	=	=	SYM
ejpam-747	288	1	�	�	PROPN
ejpam-747	288	2	p−m−	p−m−	PROPN
ejpam-747	288	3	1	1	NUM
ejpam-747	288	4	�	�	NOUN
ejpam-747	288	5	+	+	ADP
ejpam-747	288	6	αw	αw	PROPN
ejpam-747	288	7	(	(	PUNCT
ejpam-747	288	8	z	z	NOUN
ejpam-747	288	9	)	)	PUNCT
ejpam-747	288	10	+	+	CCONJ
ejpam-747	288	11	αzw	αzw	INTJ
ejpam-747	288	12	′	′	NOUN
ejpam-747	288	13	(	(	PUNCT
ejpam-747	288	14	z	z	X
ejpam-747	288	15	)	)	PUNCT
ejpam-747	288	16	�	�	PROPN
ejpam-747	288	17	p−m	p−m	PRON
ejpam-747	288	18	�	�	PROPN
ejpam-747	289	1	+	+	PROPN
ejpam-747	289	2	αw	αw	PROPN
ejpam-747	289	3	(	(	PUNCT
ejpam-747	289	4	z	z	NOUN
ejpam-747	289	5	)	)	PUNCT
ejpam-747	289	6	z	z	NOUN
ejpam-747	289	7	�	�	PROPN
ejpam-747	289	8	f	f	PROPN
ejpam-747	289	9	∗	∗	VERB
ejpam-747	290	1	g	g	PROPN
ejpam-747	290	2	�	�	PROPN
ejpam-747	290	3	m+2	m+2	PROPN
ejpam-747	290	4	(	(	PUNCT
ejpam-747	290	5	z	z	NOUN
ejpam-747	290	6	)	)	PUNCT
ejpam-747	290	7	�	�	PROPN
ejpam-747	290	8	f	f	PROPN
ejpam-747	290	9	∗	∗	VERB
ejpam-747	290	10	g	g	PROPN
ejpam-747	290	11	�	�	PROPN
ejpam-747	290	12	m+1	m+1	PRON
ejpam-747	290	13	(	(	PUNCT
ejpam-747	290	14	z	z	NOUN
ejpam-747	290	15	)	)	PUNCT
ejpam-747	290	16	−	−	PROPN
ejpam-747	291	1	�	�	PROPN
ejpam-747	291	2	p−m−	p−m−	PROPN
ejpam-747	291	3	1	1	NUM
ejpam-747	291	4	�	�	NOUN
ejpam-747	291	5	=	=	SYM
ejpam-747	291	6	αw	αw	ADP
ejpam-747	291	7	(	(	PUNCT
ejpam-747	291	8	z	z	NOUN
ejpam-747	291	9	)	)	PUNCT
ejpam-747	291	10			NOUN
ejpam-747	291	11	1	1	NOUN
ejpam-747	291	12	+	+	CCONJ
ejpam-747	291	13	αzw	αzw	NUM
ejpam-747	291	14	′	′	NOUN
ejpam-747	291	15	(	(	PUNCT
ejpam-747	291	16	z	z	NOUN
ejpam-747	291	17	)	)	PUNCT
ejpam-747	291	18	αw	αw	ADP
ejpam-747	291	19	(	(	PUNCT
ejpam-747	291	20	z	z	NOUN
ejpam-747	291	21	)	)	PUNCT
ejpam-747	291	22	1	1	NUM
ejpam-747	291	23	�	�	PROPN
ejpam-747	291	24	p−m	p−m	PRON
ejpam-747	291	25	�	�	NOUN
ejpam-747	291	26	+	+	PROPN
ejpam-747	291	27	αw	αw	PROPN
ejpam-747	291	28	(	(	PUNCT
ejpam-747	291	29	z	z	NOUN
ejpam-747	291	30	)	)	PUNCT
ejpam-747	291	31			PROPN
ejpam-747	291	32			PROPN
ejpam-747	291	33	.	.	PUNCT
ejpam-747	292	1	now	now	ADV
ejpam-747	292	2	,	,	PUNCT
ejpam-747	292	3	suppose	suppose	VERB
ejpam-747	292	4	that	that	SCONJ
ejpam-747	292	5	there	there	PRON
ejpam-747	292	6	exists	exist	VERB
ejpam-747	292	7	a	a	DET
ejpam-747	292	8	point	point	NOUN
ejpam-747	292	9	z0	z0	NOUN
ejpam-747	292	10	∈∆	∈∆	VERB
ejpam-747	292	11	such	such	ADJ
ejpam-747	292	12	that	that	SCONJ
ejpam-747	292	13	max	max	PROPN
ejpam-747	292	14	|z|<|z0|	|z|<|z0|	PROPN
ejpam-747	292	15	|w	|w	NOUN
ejpam-747	292	16	(	(	PUNCT
ejpam-747	292	17	z)|	z)|	PROPN
ejpam-747	292	18	=	=	SYM
ejpam-747	292	19	�	�	PROPN
ejpam-747	292	20	�	�	PROPN
ejpam-747	292	21	w	w	PROPN
ejpam-747	292	22	�	�	PROPN
ejpam-747	292	23	z0	z0	PROPN
ejpam-747	292	24	�	�	PROPN
ejpam-747	292	25	�	�	PROPN
ejpam-747	292	26	�	�	PROPN
ejpam-747	292	27	=	=	SYM
ejpam-747	292	28	1	1	NUM
ejpam-747	292	29	�	�	PROPN
ejpam-747	292	30	w(z0	w(z0	NOUN
ejpam-747	292	31	)	)	PUNCT
ejpam-747	292	32	6=	6=	ADP
ejpam-747	292	33	1	1	NUM
ejpam-747	292	34	�	�	PROPN
ejpam-747	292	35	.	.	PUNCT
ejpam-747	293	1	using	use	VERB
ejpam-747	293	2	jack	jack	PROPN
ejpam-747	293	3	’s	’s	PART
ejpam-747	293	4	lemma	lemma	PROPN
ejpam-747	293	5	1	1	NUM
ejpam-747	293	6	,	,	PUNCT
ejpam-747	293	7	we	we	PRON
ejpam-747	293	8	have	have	VERB
ejpam-747	293	9	z0w	z0w	NUM
ejpam-747	293	10	′	′	NUM
ejpam-747	293	11	�	�	PROPN
ejpam-747	293	12	z0	z0	PROPN
ejpam-747	293	13	�	�	PROPN
ejpam-747	293	14	=	=	SYM
ejpam-747	293	15	kw	kw	PROPN
ejpam-747	293	16	�	�	PROPN
ejpam-747	293	17	z0	z0	PROPN
ejpam-747	293	18	�	�	PROPN
ejpam-747	293	19	(	(	PUNCT
ejpam-747	293	20	k	k	X
ejpam-747	293	21	≥	≥	NUM
ejpam-747	293	22	1	1	NUM
ejpam-747	293	23	)	)	PUNCT
ejpam-747	293	24	.	.	PUNCT
ejpam-747	294	1	therefore	therefore	ADV
ejpam-747	294	2	,	,	PUNCT
ejpam-747	294	3	letting	let	VERB
ejpam-747	294	4	w	w	ADP
ejpam-747	294	5	�	�	PROPN
ejpam-747	294	6	z0	z0	PROPN
ejpam-747	294	7	�	�	PROPN
ejpam-747	294	8	=	=	SYM
ejpam-747	294	9	eiθ	eiθ	PROPN
ejpam-747	294	10	(	(	PUNCT
ejpam-747	294	11	θ	θ	PROPN
ejpam-747	294	12	6=	6=	NUM
ejpam-747	294	13	0	0	NUM
ejpam-747	294	14	)	)	PUNCT
ejpam-747	294	15	,	,	PUNCT
ejpam-747	294	16	�	�	PROPN
ejpam-747	294	17	�	�	PROPN
ejpam-747	294	18	�	�	PROPN
ejpam-747	294	19	�	�	PROPN
ejpam-747	294	20	�	�	PROPN
ejpam-747	294	21	z0	z0	PROPN
ejpam-747	294	22	�	�	PROPN
ejpam-747	294	23	f	f	PROPN
ejpam-747	294	24	∗	∗	VERB
ejpam-747	294	25	g	g	PROPN
ejpam-747	294	26	�	�	PROPN
ejpam-747	294	27	m+2	m+2	PROPN
ejpam-747	294	28	�	�	PROPN
ejpam-747	294	29	z0	z0	PROPN
ejpam-747	294	30	�	�	PROPN
ejpam-747	294	31	�	�	PROPN
ejpam-747	294	32	f	f	PROPN
ejpam-747	294	33	∗	∗	VERB
ejpam-747	294	34	g	g	PROPN
ejpam-747	294	35	�	�	PROPN
ejpam-747	294	36	m+1	m+1	PROPN
ejpam-747	294	37	�	�	PROPN
ejpam-747	294	38	z0	z0	PROPN
ejpam-747	294	39	�	�	PROPN
ejpam-747	294	40	−	−	PROPN
ejpam-747	294	41	�	�	PROPN
ejpam-747	294	42	p−m−	p−m−	PROPN
ejpam-747	294	43	1	1	NUM
ejpam-747	294	44	�	�	PROPN
ejpam-747	294	45	�	�	PROPN
ejpam-747	294	46	�	�	PROPN
ejpam-747	294	47	�	�	PROPN
ejpam-747	294	48	�	�	PROPN
ejpam-747	294	49	�	�	PROPN
ejpam-747	294	50	=	=	SYM
ejpam-747	294	51	α	α	PROPN
ejpam-747	294	52	�	�	PROPN
ejpam-747	294	53	�	�	PROPN
ejpam-747	294	54	w(z0	w(z0	NOUN
ejpam-747	294	55	)	)	PUNCT
ejpam-747	294	56	�	�	PROPN
ejpam-747	294	57	�	�	PROPN
ejpam-747	294	58	�	�	PROPN
ejpam-747	294	59	�	�	PROPN
ejpam-747	294	60	�	�	PROPN
ejpam-747	294	61	�	�	PROPN
ejpam-747	294	62	�	�	PROPN
ejpam-747	294	63	1	1	NUM
ejpam-747	294	64	+	+	CCONJ
ejpam-747	294	65	αz0w	αz0w	ADJ
ejpam-747	294	66	′	′	NUM
ejpam-747	294	67	�	�	PROPN
ejpam-747	294	68	z0	z0	PROPN
ejpam-747	294	69	�	�	PROPN
ejpam-747	294	70	αw	αw	ADP
ejpam-747	294	71	�	�	PROPN
ejpam-747	294	72	z0	z0	PROPN
ejpam-747	294	73	�	�	PROPN
ejpam-747	294	74	1	1	NUM
ejpam-747	294	75	�	�	PROPN
ejpam-747	294	76	p−m	p−m	PRON
ejpam-747	294	77	�	�	PROPN
ejpam-747	295	1	+	+	ADP
ejpam-747	295	2	αw	αw	PROPN
ejpam-747	295	3	�	�	PROPN
ejpam-747	295	4	z0	z0	PROPN
ejpam-747	295	5	�	�	PROPN
ejpam-747	295	6	�	�	PROPN
ejpam-747	295	7	�	�	PROPN
ejpam-747	295	8	�	�	PROPN
ejpam-747	295	9	�	�	PROPN
ejpam-747	295	10	�	�	PROPN
ejpam-747	295	11	=	=	SYM
ejpam-747	295	12	α	α	PROPN
ejpam-747	295	13	�	�	PROPN
ejpam-747	295	14	�	�	PROPN
ejpam-747	295	15	�	�	PROPN
ejpam-747	295	16	�	�	PROPN
ejpam-747	295	17	1	1	NUM
ejpam-747	295	18	+	+	PROPN
ejpam-747	295	19	k	k	PROPN
ejpam-747	295	20	�	�	PROPN
ejpam-747	295	21	p−m	p−m	PROPN
ejpam-747	295	22	�	�	PROPN
ejpam-747	295	23	+	+	PROPN
ejpam-747	295	24	αeiθ	αeiθ	PROPN
ejpam-747	295	25	�	�	PROPN
ejpam-747	295	26	�	�	PROPN
ejpam-747	295	27	�	�	PROPN
ejpam-747	295	28	�	�	PROPN
ejpam-747	295	29	≥	≥	PROPN
ejpam-747	295	30	α	α	PROPN
ejpam-747	295	31			NOUN
ejpam-747	295	32			ADJ
ejpam-747	295	33			ADJ
ejpam-747	295	34			ADJ
ejpam-747	295	35			NUM
ejpam-747	295	36	1	1	NUM
ejpam-747	295	37	+	+	SYM
ejpam-747	295	38	k	k	PROPN
ejpam-747	295	39	�	�	PROPN
ejpam-747	295	40	p−m	p−m	X
ejpam-747	295	41	�	�	PROPN
ejpam-747	295	42	re	re	VERB
ejpam-747	295	43			NOUN
ejpam-747	295	44			ADP
ejpam-747	295	45			ADJ
ejpam-747	295	46	1	1	NUM
ejpam-747	295	47	+	+	NUM
ejpam-747	295	48	α	α	PROPN
ejpam-747	295	49	(	(	PUNCT
ejpam-747	295	50	p−m	p−m	X
ejpam-747	295	51	)	)	PUNCT
ejpam-747	295	52	cos	cos	ADP
ejpam-747	295	53	θ	θ	PROPN
ejpam-747	295	54	−	−	PROPN
ejpam-747	296	1	i	i	PRON
ejpam-747	296	2	α	α	INTJ
ejpam-747	296	3	(	(	PUNCT
ejpam-747	296	4	p−m	p−m	X
ejpam-747	296	5	)	)	PUNCT
ejpam-747	296	6	sin	sin	NOUN
ejpam-747	296	7	θ	θ	PROPN
ejpam-747	296	8	1	1	NUM
ejpam-747	296	9	+	+	NUM
ejpam-747	296	10	�	�	PROPN
ejpam-747	296	11	α	α	PROPN
ejpam-747	296	12	(	(	PUNCT
ejpam-747	296	13	p−m	p−m	X
ejpam-747	296	14	)	)	PUNCT
ejpam-747	296	15	�	�	NOUN
ejpam-747	296	16	2	2	NUM
ejpam-747	296	17	+	+	CCONJ
ejpam-747	296	18	2α	2α	NOUN
ejpam-747	296	19	(	(	PUNCT
ejpam-747	296	20	p−m	p−m	X
ejpam-747	296	21	)	)	PUNCT
ejpam-747	296	22	cos	cos	ADP
ejpam-747	296	23	θ	θ	PROPN
ejpam-747	296	24			PROPN
ejpam-747	296	25			PROPN
ejpam-747	296	26			NOUN
ejpam-747	296	27			PROPN
ejpam-747	296	28			PROPN
ejpam-747	296	29			PROPN
ejpam-747	296	30			PROPN
ejpam-747	296	31			PROPN
ejpam-747	296	32	=	=	PUNCT
ejpam-747	296	33	α	α	PROPN
ejpam-747	296	34			NOUN
ejpam-747	296	35			ADJ
ejpam-747	296	36			ADJ
ejpam-747	296	37			ADJ
ejpam-747	296	38			ADJ
ejpam-747	296	39			ADJ
ejpam-747	296	40			NUM
ejpam-747	296	41	1	1	NUM
ejpam-747	296	42	+	+	SYM
ejpam-747	296	43	k	k	PROPN
ejpam-747	296	44	�	�	PROPN
ejpam-747	296	45	p−m	p−m	PRON
ejpam-747	296	46	�	�	PROPN
ejpam-747	296	47			PROPN
ejpam-747	296	48			PROPN
ejpam-747	296	49			PROPN
ejpam-747	296	50			NOUN
ejpam-747	296	51			PROPN
ejpam-747	296	52			PROPN
ejpam-747	296	53			NOUN
ejpam-747	296	54	1	1	NUM
ejpam-747	296	55	2	2	NUM
ejpam-747	296	56	+	+	NUM
ejpam-747	296	57	�	�	PROPN
ejpam-747	296	58	α	α	PROPN
ejpam-747	296	59	(	(	PUNCT
ejpam-747	296	60	p−m	p−m	X
ejpam-747	296	61	)	)	PUNCT
ejpam-747	296	62	�	�	NOUN
ejpam-747	296	63	2	2	NUM
ejpam-747	296	64	−1	−1	NOUN
ejpam-747	296	65	1	1	NUM
ejpam-747	296	66	+	+	SYM
ejpam-747	296	67	α	α	PROPN
ejpam-747	296	68	(	(	PUNCT
ejpam-747	296	69	p−m	p−m	X
ejpam-747	296	70	)	)	PUNCT
ejpam-747	296	71	cos	cos	ADP
ejpam-747	296	72	θ	θ	PROPN
ejpam-747	296	73			PROPN
ejpam-747	296	74			PROPN
ejpam-747	296	75			PROPN
ejpam-747	296	76			PROPN
ejpam-747	296	77			ADJ
ejpam-747	296	78			ADJ
ejpam-747	296	79			NOUN
ejpam-747	296	80			PROPN
ejpam-747	296	81			PROPN
ejpam-747	296	82			PROPN
ejpam-747	296	83			PROPN
ejpam-747	296	84			PROPN
ejpam-747	296	85			PROPN
ejpam-747	296	86			PROPN
ejpam-747	296	87	≥	≥	NOUN
ejpam-747	296	88	α	α	NOUN
ejpam-747	296	89			PROPN
ejpam-747	296	90	1	1	NOUN
ejpam-747	296	91	+	+	NUM
ejpam-747	296	92	1	1	NUM
ejpam-747	296	93	�	�	PROPN
ejpam-747	296	94	p−m	p−m	PRON
ejpam-747	296	95	�	�	PROPN
ejpam-747	296	96	(	(	PUNCT
ejpam-747	296	97	�	�	PROPN
ejpam-747	296	98	p−m+α	p−m+α	PUNCT
ejpam-747	296	99	�	�	PROPN
ejpam-747	296	100	�	�	PROPN
ejpam-747	296	101	p−m	p−m	PRON
ejpam-747	296	102	�	�	PROPN
ejpam-747	296	103	2	2	NUM
ejpam-747	296	104	�	�	PROPN
ejpam-747	296	105	p−m+α	p−m+α	PUNCT
ejpam-747	296	106	�	�	PROPN
ejpam-747	296	107	�	�	PROPN
ejpam-747	296	108	p−m	p−m	ADP
ejpam-747	296	109	�	�	PROPN
ejpam-747	296	110	+	+	ADV
ejpam-747	296	111	α2	α2	ADJ
ejpam-747	296	112	−	−	PROPN
ejpam-747	296	113	�	�	PROPN
ejpam-747	296	114	p−m	p−m	X
ejpam-747	296	115	�	�	PROPN
ejpam-747	296	116	2	2	NUM
ejpam-747	296	117	)	)	PUNCT
ejpam-747	296	118			PROPN
ejpam-747	296	119			PROPN
ejpam-747	296	120	=	=	SYM
ejpam-747	296	121	α	α	PROPN
ejpam-747	296	122	�	�	PROPN
ejpam-747	296	123	p−m+α+	p−m+α+	PROPN
ejpam-747	296	124	1	1	NUM
ejpam-747	296	125	p−m+α	p−m+α	NOUN
ejpam-747	296	126	�	�	PROPN
ejpam-747	296	127	,	,	PUNCT
ejpam-747	296	128	p.	p.	PROPN
ejpam-747	296	129	sharma	sharma	PROPN
ejpam-747	296	130	,	,	PUNCT
ejpam-747	296	131	p.	p.	PROPN
ejpam-747	296	132	srivastava	srivastava	PROPN
ejpam-747	296	133	/	/	SYM
ejpam-747	296	134	eur	eur	PROPN
ejpam-747	296	135	.	.	PUNCT
ejpam-747	297	1	j.	j.	PROPN
ejpam-747	297	2	pure	pure	PROPN
ejpam-747	297	3	appl	appl	PROPN
ejpam-747	297	4	.	.	PROPN
ejpam-747	297	5	math	math	PROPN
ejpam-747	297	6	,	,	PUNCT
ejpam-747	297	7	3	3	NUM
ejpam-747	297	8	(	(	PUNCT
ejpam-747	297	9	2010	2010	NUM
ejpam-747	297	10	)	)	PUNCT
ejpam-747	297	11	,	,	PUNCT
ejpam-747	297	12	1093	1093	NUM
ejpam-747	297	13	-	-	SYM
ejpam-747	297	14	1112	1112	NUM
ejpam-747	297	15	1104	1104	NUM
ejpam-747	297	16	on	on	ADP
ejpam-747	297	17	using	use	VERB
ejpam-747	297	18	(	(	PUNCT
ejpam-747	297	19	19	19	NUM
ejpam-747	297	20	)	)	PUNCT
ejpam-747	298	1	,	,	PUNCT
ejpam-747	298	2	it	it	PRON
ejpam-747	298	3	gives	give	VERB
ejpam-747	298	4	�	�	PROPN
ejpam-747	298	5	�	�	PROPN
ejpam-747	298	6	�	�	PROPN
ejpam-747	298	7	�	�	PROPN
ejpam-747	298	8	�	�	PROPN
ejpam-747	298	9	z	z	PROPN
ejpam-747	298	10	�	�	PROPN
ejpam-747	298	11	f	f	PROPN
ejpam-747	298	12	∗	∗	VERB
ejpam-747	298	13	g	g	PROPN
ejpam-747	298	14	�	�	PROPN
ejpam-747	298	15	m+2	m+2	PROPN
ejpam-747	298	16	(	(	PUNCT
ejpam-747	298	17	z	z	NOUN
ejpam-747	298	18	)	)	PUNCT
ejpam-747	298	19	�	�	PROPN
ejpam-747	298	20	f	f	PROPN
ejpam-747	298	21	∗	∗	VERB
ejpam-747	298	22	g	g	PROPN
ejpam-747	298	23	�	�	PROPN
ejpam-747	298	24	m+1	m+1	PRON
ejpam-747	298	25	(	(	PUNCT
ejpam-747	298	26	z	z	NOUN
ejpam-747	298	27	)	)	PUNCT
ejpam-747	299	1	−	−	PROPN
ejpam-747	299	2	�	�	PROPN
ejpam-747	299	3	p−m−	p−m−	PROPN
ejpam-747	299	4	1	1	NUM
ejpam-747	299	5	�	�	PROPN
ejpam-747	299	6	�	�	PROPN
ejpam-747	299	7	�	�	PROPN
ejpam-747	299	8	�	�	PROPN
ejpam-747	299	9	�	�	PROPN
ejpam-747	299	10	�	�	PROPN
ejpam-747	299	11	≥	≥	NUM
ejpam-747	299	12	β	β	NOUN
ejpam-747	299	13	which	which	PRON
ejpam-747	299	14	contradicts	contradict	VERB
ejpam-747	299	15	(	(	PUNCT
ejpam-747	299	16	20	20	NUM
ejpam-747	299	17	)	)	PUNCT
ejpam-747	299	18	.	.	PUNCT
ejpam-747	300	1	hence	hence	ADV
ejpam-747	300	2	|w	|w	NOUN
ejpam-747	300	3	(	(	PUNCT
ejpam-747	300	4	z)|	z)|	X
ejpam-747	300	5	<	<	X
ejpam-747	300	6	1	1	NUM
ejpam-747	300	7	and	and	CCONJ
ejpam-747	300	8	from	from	ADP
ejpam-747	300	9	(	(	PUNCT
ejpam-747	300	10	21	21	NUM
ejpam-747	300	11	)	)	PUNCT
ejpam-747	300	12	,	,	PUNCT
ejpam-747	300	13	it	it	PRON
ejpam-747	300	14	follows	follow	VERB
ejpam-747	300	15	that	that	SCONJ
ejpam-747	300	16	f	f	PROPN
ejpam-747	300	17	∈	∈	PROPN
ejpam-747	300	18	ℜg	ℜg	PROPN
ejpam-747	300	19	�	�	PROPN
ejpam-747	300	20	p	p	PROPN
ejpam-747	300	21	,	,	PUNCT
ejpam-747	300	22	m	m	PROPN
ejpam-747	300	23	,	,	PUNCT
ejpam-747	300	24	α	α	PROPN
ejpam-747	300	25	�	�	PROPN
ejpam-747	300	26	.	.	PUNCT
ejpam-747	301	1	theorem	theorem	VERB
ejpam-747	301	2	5	5	NUM
ejpam-747	301	3	.	.	PUNCT
ejpam-747	302	1	let	let	VERB
ejpam-747	302	2	f	f	PROPN
ejpam-747	302	3	∈	∈	PROPN
ejpam-747	302	4	ap	ap	PROPN
ejpam-747	302	5	if	if	SCONJ
ejpam-747	302	6	re	re	ADP
ejpam-747	302	7			PROPN
ejpam-747	302	8			ADJ
ejpam-747	302	9			ADJ
ejpam-747	302	10			NOUN
ejpam-747	302	11			PUNCT
ejpam-747	303	1	δ	δ	NOUN
ejpam-747	303	2	z	z	PROPN
ejpam-747	303	3	�	�	PROPN
ejpam-747	303	4	f	f	PROPN
ejpam-747	303	5	∗	∗	VERB
ejpam-747	303	6	g	g	PROPN
ejpam-747	303	7	�	�	PROPN
ejpam-747	303	8	m+1	m+1	PRON
ejpam-747	303	9	(	(	PUNCT
ejpam-747	303	10	z	z	NOUN
ejpam-747	303	11	)	)	PUNCT
ejpam-747	303	12	�	�	PROPN
ejpam-747	303	13	f	f	PROPN
ejpam-747	303	14	∗	∗	PROPN
ejpam-747	303	15	h	h	PROPN
ejpam-747	303	16	�	�	PROPN
ejpam-747	303	17	m	m	PROPN
ejpam-747	303	18	(	(	PUNCT
ejpam-747	303	19	z	z	NOUN
ejpam-747	303	20	)	)	PUNCT
ejpam-747	304	1	+	+	CCONJ
ejpam-747	304	2	(	(	PUNCT
ejpam-747	304	3	1−	1−	NUM
ejpam-747	304	4	δ)z	δ)z	X
ejpam-747	304	5	(	(	PUNCT
ejpam-747	304	6	z	z	NOUN
ejpam-747	304	7	�	�	PROPN
ejpam-747	304	8	f	f	PROPN
ejpam-747	304	9	∗	∗	VERB
ejpam-747	304	10	g	g	PROPN
ejpam-747	304	11	�	�	PROPN
ejpam-747	304	12	m+1	m+1	PRON
ejpam-747	304	13	(	(	PUNCT
ejpam-747	304	14	z	z	NOUN
ejpam-747	304	15	)	)	PUNCT
ejpam-747	304	16	�	�	PROPN
ejpam-747	304	17	f	f	PROPN
ejpam-747	304	18	∗	∗	PROPN
ejpam-747	304	19	h	h	PROPN
ejpam-747	304	20	�	�	PROPN
ejpam-747	304	21	m	m	PROPN
ejpam-747	304	22	(	(	PUNCT
ejpam-747	304	23	z	z	NOUN
ejpam-747	304	24	)	)	PUNCT
ejpam-747	304	25	)	)	PUNCT
ejpam-747	305	1	′	′	NUM
ejpam-747	306	1			PROPN
ejpam-747	306	2			PROPN
ejpam-747	306	3			PROPN
ejpam-747	306	4			PROPN
ejpam-747	306	5			PROPN
ejpam-747	306	6			NOUN
ejpam-747	306	7	>	>	X
ejpam-747	306	8	γ	γ	X
ejpam-747	306	9	(	(	PUNCT
ejpam-747	306	10	z	z	NOUN
ejpam-747	306	11	∈∆	∈∆	NOUN
ejpam-747	306	12	)	)	PUNCT
ejpam-747	306	13	,	,	PUNCT
ejpam-747	306	14	for	for	ADP
ejpam-747	306	15	some	some	DET
ejpam-747	306	16	γ	γ	PRON
ejpam-747	306	17	�	�	PROPN
ejpam-747	306	18	γ	γ	PROPN
ejpam-747	306	19	<	<	X
ejpam-747	306	20	δ	δ	PROPN
ejpam-747	306	21	�	�	PROPN
ejpam-747	306	22	p−m	p−m	PROPN
ejpam-747	306	23	�	�	PROPN
ejpam-747	306	24	�	�	PROPN
ejpam-747	306	25	,	,	PUNCT
ejpam-747	306	26	0≤	0≤	NUM
ejpam-747	306	27	δ	δ	NOUN
ejpam-747	306	28	≤	≤	ADV
ejpam-747	306	29	1	1	NUM
ejpam-747	306	30	,	,	PUNCT
ejpam-747	306	31	then	then	ADV
ejpam-747	306	32	f	f	PROPN
ejpam-747	306	33	∈	∈	PROPN
ejpam-747	306	34	s	s	PART
ejpam-747	306	35	g	g	PROPN
ejpam-747	306	36	h	h	PROPN
ejpam-747	306	37	�	�	PROPN
ejpam-747	306	38	p	p	PROPN
ejpam-747	306	39	,	,	PUNCT
ejpam-747	306	40	m	m	PROPN
ejpam-747	306	41	,	,	PUNCT
ejpam-747	306	42	β	β	X
ejpam-747	306	43	�	�	PROPN
ejpam-747	306	44	,	,	PUNCT
ejpam-747	306	45	where	where	SCONJ
ejpam-747	306	46	β	β	X
ejpam-747	306	47	=	=	SYM
ejpam-747	306	48	2(δ(p−m)−γ	2(δ(p−m)−γ	NUM
ejpam-747	306	49	)	)	PUNCT
ejpam-747	306	50	1+δ	1+δ	NUM
ejpam-747	306	51	≤	≤	NOUN
ejpam-747	306	52	p.	p.	NOUN
ejpam-747	306	53	proof	proof	NOUN
ejpam-747	306	54	.	.	PUNCT
ejpam-747	307	1	if	if	SCONJ
ejpam-747	307	2	δ	δ	PROPN
ejpam-747	307	3	=	=	SYM
ejpam-747	307	4	1	1	NUM
ejpam-747	307	5	,	,	PUNCT
ejpam-747	307	6	the	the	DET
ejpam-747	307	7	result	result	NOUN
ejpam-747	307	8	holds	hold	VERB
ejpam-747	307	9	.	.	PUNCT
ejpam-747	308	1	let	let	VERB
ejpam-747	308	2	0≤	0≤	NUM
ejpam-747	308	3	δ	δ	PROPN
ejpam-747	308	4	<	<	X
ejpam-747	308	5	1	1	NUM
ejpam-747	308	6	,	,	PUNCT
ejpam-747	308	7	define	define	VERB
ejpam-747	308	8	the	the	DET
ejpam-747	308	9	function	function	NOUN
ejpam-747	308	10	p	p	NOUN
ejpam-747	308	11	(	(	PUNCT
ejpam-747	308	12	z	z	NOUN
ejpam-747	308	13	)	)	PUNCT
ejpam-747	308	14	by	by	ADP
ejpam-747	308	15	z	z	PROPN
ejpam-747	308	16	�	�	PROPN
ejpam-747	308	17	f	f	PROPN
ejpam-747	308	18	∗	∗	VERB
ejpam-747	308	19	g	g	PROPN
ejpam-747	308	20	�	�	PROPN
ejpam-747	308	21	m+1	m+1	PRON
ejpam-747	308	22	(	(	PUNCT
ejpam-747	308	23	z	z	NOUN
ejpam-747	308	24	)	)	PUNCT
ejpam-747	308	25	�	�	PROPN
ejpam-747	308	26	f	f	PROPN
ejpam-747	308	27	∗	∗	PROPN
ejpam-747	308	28	h	h	PROPN
ejpam-747	308	29	�	�	PROPN
ejpam-747	308	30	m	m	PROPN
ejpam-747	308	31	(	(	PUNCT
ejpam-747	308	32	z	z	NOUN
ejpam-747	308	33	)	)	PUNCT
ejpam-747	308	34	=	=	SYM
ejpam-747	308	35	�	�	PROPN
ejpam-747	308	36	p−m−	p−m−	PROPN
ejpam-747	308	37	β	β	X
ejpam-747	308	38	�	�	PROPN
ejpam-747	309	1	+	+	CCONJ
ejpam-747	309	2	βp	βp	PROPN
ejpam-747	309	3	(	(	PUNCT
ejpam-747	309	4	z	z	NOUN
ejpam-747	309	5	)	)	PUNCT
ejpam-747	309	6	.	.	PUNCT
ejpam-747	310	1	(	(	PUNCT
ejpam-747	310	2	22	22	NUM
ejpam-747	310	3	)	)	PUNCT
ejpam-747	310	4	then	then	ADV
ejpam-747	310	5	p	p	X
ejpam-747	310	6	(	(	PUNCT
ejpam-747	310	7	z	z	NOUN
ejpam-747	310	8	)	)	PUNCT
ejpam-747	310	9	=	=	SYM
ejpam-747	310	10	1	1	NUM
ejpam-747	310	11	+	+	NUM
ejpam-747	310	12	p1z	p1z	NOUN
ejpam-747	310	13	+	+	CCONJ
ejpam-747	310	14	p2z2	p2z2	X
ejpam-747	310	15	+	+	X
ejpam-747	310	16	·	·	PUNCT
ejpam-747	310	17	·	·	PUNCT
ejpam-747	310	18	·	·	PUNCT
ejpam-747	310	19	is	be	AUX
ejpam-747	310	20	regular	regular	ADJ
ejpam-747	310	21	in	in	ADP
ejpam-747	310	22	∆.	∆.	NOUN
ejpam-747	310	23	it	it	PRON
ejpam-747	310	24	follows	follow	VERB
ejpam-747	310	25	from	from	ADP
ejpam-747	310	26	(	(	PUNCT
ejpam-747	310	27	22	22	NUM
ejpam-747	310	28	)	)	PUNCT
ejpam-747	311	1	that	that	SCONJ
ejpam-747	311	2	1	1	NUM
ejpam-747	311	3	+	+	SYM
ejpam-747	311	4	z	z	PROPN
ejpam-747	311	5	�	�	PROPN
ejpam-747	311	6	f	f	PROPN
ejpam-747	311	7	∗	∗	VERB
ejpam-747	311	8	g	g	PROPN
ejpam-747	311	9	�	�	PROPN
ejpam-747	311	10	m+2	m+2	PROPN
ejpam-747	311	11	(	(	PUNCT
ejpam-747	311	12	z	z	NOUN
ejpam-747	311	13	)	)	PUNCT
ejpam-747	311	14	�	�	PROPN
ejpam-747	311	15	f	f	PROPN
ejpam-747	311	16	∗	∗	VERB
ejpam-747	311	17	g	g	PROPN
ejpam-747	311	18	�	�	PROPN
ejpam-747	311	19	m+1	m+1	PRON
ejpam-747	311	20	(	(	PUNCT
ejpam-747	311	21	z	z	NOUN
ejpam-747	311	22	)	)	PUNCT
ejpam-747	311	23	−	−	PROPN
ejpam-747	312	1	z	z	PROPN
ejpam-747	312	2	�	�	PROPN
ejpam-747	312	3	f	f	PROPN
ejpam-747	312	4	∗	∗	PROPN
ejpam-747	312	5	h	h	PROPN
ejpam-747	312	6	�	�	PROPN
ejpam-747	312	7	m+1	m+1	PRON
ejpam-747	312	8	(	(	PUNCT
ejpam-747	312	9	z	z	NOUN
ejpam-747	312	10	)	)	PUNCT
ejpam-747	312	11	�	�	PROPN
ejpam-747	312	12	f	f	PROPN
ejpam-747	312	13	∗	∗	PROPN
ejpam-747	312	14	h	h	PROPN
ejpam-747	312	15	�	�	PROPN
ejpam-747	312	16	m	m	PROPN
ejpam-747	312	17	(	(	PUNCT
ejpam-747	312	18	z	z	NOUN
ejpam-747	312	19	)	)	PUNCT
ejpam-747	312	20	=	=	SYM
ejpam-747	313	1	βzp	βzp	NOUN
ejpam-747	314	1	′	′	INTJ
ejpam-747	314	2	(	(	PUNCT
ejpam-747	314	3	z	z	X
ejpam-747	314	4	)	)	PUNCT
ejpam-747	314	5	�	�	PROPN
ejpam-747	314	6	p−m−	p−m−	PROPN
ejpam-747	314	7	β	β	X
ejpam-747	314	8	�	�	PROPN
ejpam-747	314	9	+	+	CCONJ
ejpam-747	314	10	βp	βp	PROPN
ejpam-747	314	11	(	(	PUNCT
ejpam-747	314	12	z	z	NOUN
ejpam-747	314	13	)	)	PUNCT
ejpam-747	314	14	,	,	PUNCT
ejpam-747	314	15	or	or	CCONJ
ejpam-747	314	16	,	,	PUNCT
ejpam-747	314	17	z	z	PROPN
ejpam-747	314	18	�	�	PROPN
ejpam-747	314	19	f	f	PROPN
ejpam-747	314	20	∗	∗	PROPN
ejpam-747	314	21	h	h	PROPN
ejpam-747	314	22	�	�	PROPN
ejpam-747	314	23	m	m	PROPN
ejpam-747	314	24	(	(	PUNCT
ejpam-747	314	25	z	z	NOUN
ejpam-747	314	26	)	)	PUNCT
ejpam-747	314	27	�	�	PROPN
ejpam-747	314	28	f	f	PROPN
ejpam-747	314	29	∗	∗	VERB
ejpam-747	314	30	g	g	PROPN
ejpam-747	314	31	�	�	PROPN
ejpam-747	314	32	m+1	m+1	PRON
ejpam-747	314	33	(	(	PUNCT
ejpam-747	314	34	z	z	NOUN
ejpam-747	314	35	)	)	PUNCT
ejpam-747	314	36	(	(	PUNCT
ejpam-747	314	37	�	�	PROPN
ejpam-747	314	38	f	f	PROPN
ejpam-747	314	39	∗	∗	VERB
ejpam-747	314	40	g	g	PROPN
ejpam-747	314	41	�	�	PROPN
ejpam-747	314	42	m+1	m+1	PRON
ejpam-747	314	43	(	(	PUNCT
ejpam-747	314	44	z	z	NOUN
ejpam-747	314	45	)	)	PUNCT
ejpam-747	314	46	�	�	PROPN
ejpam-747	314	47	f	f	PROPN
ejpam-747	314	48	∗	∗	PROPN
ejpam-747	314	49	h	h	PROPN
ejpam-747	314	50	�	�	PROPN
ejpam-747	314	51	m	m	PROPN
ejpam-747	314	52	(	(	PUNCT
ejpam-747	314	53	z	z	NOUN
ejpam-747	314	54	)	)	PUNCT
ejpam-747	314	55	)	)	PUNCT
ejpam-747	314	56	′	′	NUM
ejpam-747	315	1	=	=	PUNCT
ejpam-747	315	2	βzp	βzp	NOUN
ejpam-747	316	1	′	′	INTJ
ejpam-747	316	2	(	(	PUNCT
ejpam-747	316	3	z)−	z)−	PROPN
ejpam-747	316	4	�	�	PROPN
ejpam-747	316	5	�	�	PROPN
ejpam-747	316	6	p−m−	p−m−	PROPN
ejpam-747	316	7	β	β	X
ejpam-747	316	8	�	�	PROPN
ejpam-747	316	9	+	+	CCONJ
ejpam-747	316	10	βp	βp	PROPN
ejpam-747	316	11	(	(	PUNCT
ejpam-747	316	12	z	z	NOUN
ejpam-747	316	13	)	)	PUNCT
ejpam-747	316	14	�	�	PROPN
ejpam-747	316	15	p−m−	p−m−	PROPN
ejpam-747	316	16	β	β	X
ejpam-747	316	17	�	�	PROPN
ejpam-747	316	18	+	+	CCONJ
ejpam-747	316	19	βp	βp	PROPN
ejpam-747	316	20	(	(	PUNCT
ejpam-747	316	21	z	z	NOUN
ejpam-747	316	22	)	)	PUNCT
ejpam-747	316	23	,	,	PUNCT
ejpam-747	316	24	or	or	CCONJ
ejpam-747	316	25	,	,	PUNCT
ejpam-747	316	26	equivalently	equivalently	ADV
ejpam-747	316	27	z2	z2	PROPN
ejpam-747	316	28	(	(	PUNCT
ejpam-747	316	29	�	�	PROPN
ejpam-747	316	30	f	f	PROPN
ejpam-747	316	31	∗	∗	VERB
ejpam-747	316	32	g	g	PROPN
ejpam-747	316	33	�	�	PROPN
ejpam-747	316	34	m+1	m+1	PRON
ejpam-747	316	35	(	(	PUNCT
ejpam-747	316	36	z	z	NOUN
ejpam-747	316	37	)	)	PUNCT
ejpam-747	316	38	�	�	PROPN
ejpam-747	316	39	f	f	PROPN
ejpam-747	316	40	∗	∗	PROPN
ejpam-747	316	41	h	h	PROPN
ejpam-747	316	42	�	�	PROPN
ejpam-747	316	43	m	m	PROPN
ejpam-747	316	44	(	(	PUNCT
ejpam-747	316	45	z	z	NOUN
ejpam-747	316	46	)	)	PUNCT
ejpam-747	316	47	)	)	PUNCT
ejpam-747	316	48	′	′	NUM
ejpam-747	317	1	=	=	PUNCT
ejpam-747	317	2	βzp	βzp	NOUN
ejpam-747	318	1	′	′	INTJ
ejpam-747	318	2	(	(	PUNCT
ejpam-747	318	3	z)−	z)−	PROPN
ejpam-747	318	4	�	�	PROPN
ejpam-747	318	5	�	�	PROPN
ejpam-747	318	6	p−m−	p−m−	PROPN
ejpam-747	318	7	β	β	X
ejpam-747	318	8	�	�	PROPN
ejpam-747	318	9	+	+	CCONJ
ejpam-747	318	10	βp	βp	PROPN
ejpam-747	318	11	(	(	PUNCT
ejpam-747	318	12	z	z	NOUN
ejpam-747	318	13	)	)	PUNCT
ejpam-747	318	14	.	.	PUNCT
ejpam-747	319	1	therefore	therefore	ADV
ejpam-747	319	2	,	,	PUNCT
ejpam-747	319	3	we	we	PRON
ejpam-747	319	4	have	have	AUX
ejpam-747	319	5	re	re	VERB
ejpam-747	319	6			VERB
ejpam-747	319	7			ADJ
ejpam-747	319	8			ADJ
ejpam-747	319	9			NOUN
ejpam-747	319	10			PUNCT
ejpam-747	320	1	δ	δ	NOUN
ejpam-747	320	2	z	z	PROPN
ejpam-747	320	3	�	�	PROPN
ejpam-747	320	4	f	f	PROPN
ejpam-747	320	5	∗	∗	VERB
ejpam-747	320	6	g	g	PROPN
ejpam-747	320	7	�	�	PROPN
ejpam-747	320	8	m+1	m+1	PRON
ejpam-747	320	9	(	(	PUNCT
ejpam-747	320	10	z	z	NOUN
ejpam-747	320	11	)	)	PUNCT
ejpam-747	320	12	�	�	PROPN
ejpam-747	320	13	f	f	PROPN
ejpam-747	320	14	∗	∗	PROPN
ejpam-747	320	15	h	h	PROPN
ejpam-747	320	16	�	�	PROPN
ejpam-747	320	17	m	m	PROPN
ejpam-747	320	18	(	(	PUNCT
ejpam-747	320	19	z	z	NOUN
ejpam-747	320	20	)	)	PUNCT
ejpam-747	320	21	+	+	CCONJ
ejpam-747	320	22	(	(	PUNCT
ejpam-747	320	23	1−	1−	NUM
ejpam-747	320	24	δ	δ	PROPN
ejpam-747	320	25	)	)	PUNCT
ejpam-747	320	26	z	z	PROPN
ejpam-747	321	1	(	(	PUNCT
ejpam-747	321	2	z	z	NOUN
ejpam-747	321	3	�	�	PROPN
ejpam-747	321	4	f	f	PROPN
ejpam-747	321	5	∗	∗	VERB
ejpam-747	321	6	g	g	PROPN
ejpam-747	321	7	�	�	PROPN
ejpam-747	321	8	m+1	m+1	PRON
ejpam-747	321	9	(	(	PUNCT
ejpam-747	321	10	z	z	NOUN
ejpam-747	321	11	)	)	PUNCT
ejpam-747	321	12	�	�	PROPN
ejpam-747	321	13	f	f	PROPN
ejpam-747	321	14	∗	∗	PROPN
ejpam-747	321	15	h	h	PROPN
ejpam-747	321	16	�	�	PROPN
ejpam-747	321	17	m	m	PROPN
ejpam-747	321	18	(	(	PUNCT
ejpam-747	321	19	z	z	NOUN
ejpam-747	321	20	)	)	PUNCT
ejpam-747	321	21	)	)	PUNCT
ejpam-747	322	1	′	′	NUM
ejpam-747	323	1			PROPN
ejpam-747	323	2			PROPN
ejpam-747	323	3	−	−	PROPN
ejpam-747	323	4	γ	γ	PROPN
ejpam-747	323	5			PROPN
ejpam-747	323	6			PROPN
ejpam-747	323	7			NOUN
ejpam-747	323	8	=	=	SYM
ejpam-747	323	9	re	re	ADP
ejpam-747	323	10			PROPN
ejpam-747	323	11			PRON
ejpam-747	323	12			ADJ
ejpam-747	323	13			NOUN
ejpam-747	323	14			NOUN
ejpam-747	323	15			NUM
ejpam-747	323	16	z	z	X
ejpam-747	323	17	�	�	PROPN
ejpam-747	323	18	f	f	PROPN
ejpam-747	323	19	∗	∗	VERB
ejpam-747	323	20	g	g	PROPN
ejpam-747	323	21	�	�	PROPN
ejpam-747	323	22	m+1	m+1	PRON
ejpam-747	323	23	(	(	PUNCT
ejpam-747	323	24	z	z	NOUN
ejpam-747	323	25	)	)	PUNCT
ejpam-747	323	26	�	�	PROPN
ejpam-747	323	27	f	f	PROPN
ejpam-747	323	28	∗	∗	PROPN
ejpam-747	323	29	h	h	PROPN
ejpam-747	323	30	�	�	PROPN
ejpam-747	323	31	m	m	PROPN
ejpam-747	323	32	(	(	PUNCT
ejpam-747	323	33	z	z	NOUN
ejpam-747	323	34	)	)	PUNCT
ejpam-747	323	35	+	+	CCONJ
ejpam-747	323	36	(	(	PUNCT
ejpam-747	323	37	1−	1−	NUM
ejpam-747	323	38	δ	δ	PROPN
ejpam-747	323	39	)	)	PUNCT
ejpam-747	323	40	z2	z2	PROPN
ejpam-747	323	41	(	(	PUNCT
ejpam-747	323	42	�	�	PROPN
ejpam-747	323	43	f	f	PROPN
ejpam-747	323	44	∗	∗	VERB
ejpam-747	323	45	g	g	PROPN
ejpam-747	323	46	�	�	PROPN
ejpam-747	323	47	m+1	m+1	PRON
ejpam-747	323	48	(	(	PUNCT
ejpam-747	323	49	z	z	NOUN
ejpam-747	323	50	)	)	PUNCT
ejpam-747	323	51	�	�	PROPN
ejpam-747	323	52	f	f	PROPN
ejpam-747	323	53	∗	∗	PROPN
ejpam-747	323	54	h	h	PROPN
ejpam-747	323	55	�	�	PROPN
ejpam-747	323	56	m	m	PROPN
ejpam-747	323	57	(	(	PUNCT
ejpam-747	323	58	z	z	NOUN
ejpam-747	323	59	)	)	PUNCT
ejpam-747	323	60	)	)	PUNCT
ejpam-747	324	1	′	′	NUM
ejpam-747	324	2			PROPN
ejpam-747	324	3			PROPN
ejpam-747	324	4	−	−	PROPN
ejpam-747	324	5	γ	γ	PROPN
ejpam-747	324	6			PROPN
ejpam-747	324	7			PROPN
ejpam-747	324	8			PROPN
ejpam-747	324	9	p.	p.	NOUN
ejpam-747	324	10	sharma	sharma	PROPN
ejpam-747	324	11	,	,	PUNCT
ejpam-747	324	12	p.	p.	PROPN
ejpam-747	324	13	srivastava	srivastava	PROPN
ejpam-747	324	14	/	/	SYM
ejpam-747	324	15	eur	eur	PROPN
ejpam-747	324	16	.	.	PUNCT
ejpam-747	325	1	j.	j.	PROPN
ejpam-747	325	2	pure	pure	PROPN
ejpam-747	325	3	appl	appl	PROPN
ejpam-747	325	4	.	.	PROPN
ejpam-747	325	5	math	math	PROPN
ejpam-747	325	6	,	,	PUNCT
ejpam-747	325	7	3	3	NUM
ejpam-747	325	8	(	(	PUNCT
ejpam-747	325	9	2010	2010	NUM
ejpam-747	325	10	)	)	PUNCT
ejpam-747	325	11	,	,	PUNCT
ejpam-747	325	12	1093	1093	NUM
ejpam-747	325	13	-	-	SYM
ejpam-747	325	14	1112	1112	NUM
ejpam-747	325	15	1105	1105	NUM
ejpam-747	325	16	=	=	SYM
ejpam-747	325	17	re	re	PROPN
ejpam-747	325	18	¦	¦	PROPN
ejpam-747	325	19	δ	δ	PROPN
ejpam-747	325	20	�	�	PROPN
ejpam-747	325	21	p−m−β	p−m−β	PROPN
ejpam-747	325	22	�	�	PROPN
ejpam-747	325	23	+	+	CCONJ
ejpam-747	325	24	βδp	βδp	ADJ
ejpam-747	325	25	(	(	PUNCT
ejpam-747	325	26	z	z	NOUN
ejpam-747	325	27	)	)	PUNCT
ejpam-747	325	28	+	+	CCONJ
ejpam-747	325	29	(	(	PUNCT
ejpam-747	325	30	1−	1−	NUM
ejpam-747	325	31	δ)βzp	δ)βzp	NOUN
ejpam-747	325	32	′	′	NUM
ejpam-747	325	33	(	(	PUNCT
ejpam-747	325	34	z)−	z)−	PROPN
ejpam-747	325	35	γ	γ	X
ejpam-747	325	36	©	©	PROPN
ejpam-747	325	37	>	>	X
ejpam-747	325	38	0	0	PUNCT
ejpam-747	326	1	if	if	SCONJ
ejpam-747	326	2	we	we	PRON
ejpam-747	326	3	define	define	VERB
ejpam-747	326	4	a	a	DET
ejpam-747	326	5	function	function	NOUN
ejpam-747	326	6	φ	φ	X
ejpam-747	326	7	(	(	PUNCT
ejpam-747	326	8	u	u	NOUN
ejpam-747	326	9	,	,	PUNCT
ejpam-747	326	10	v	v	NOUN
ejpam-747	326	11	)	)	PUNCT
ejpam-747	326	12	by	by	ADP
ejpam-747	326	13	φ	φ	PROPN
ejpam-747	326	14	(	(	PUNCT
ejpam-747	326	15	u	u	NOUN
ejpam-747	326	16	,	,	PUNCT
ejpam-747	326	17	v	v	NOUN
ejpam-747	326	18	)	)	PUNCT
ejpam-747	326	19	=	=	SYM
ejpam-747	326	20	δ	δ	PROPN
ejpam-747	326	21	�	�	PROPN
ejpam-747	326	22	p−m−	p−m−	PROPN
ejpam-747	326	23	β	β	X
ejpam-747	326	24	�	�	PROPN
ejpam-747	326	25	+	+	SYM
ejpam-747	326	26	βδu+	βδu+	PROPN
ejpam-747	326	27	(	(	PUNCT
ejpam-747	326	28	1−	1−	NUM
ejpam-747	326	29	δ)β	δ)β	NOUN
ejpam-747	326	30	v−	v−	VERB
ejpam-747	326	31	γ	γ	X
ejpam-747	326	32	(	(	PUNCT
ejpam-747	326	33	23	23	NUM
ejpam-747	326	34	)	)	PUNCT
ejpam-747	326	35	with	with	ADP
ejpam-747	326	36	u	u	NOUN
ejpam-747	326	37	=	=	NOUN
ejpam-747	326	38	u1	u1	PROPN
ejpam-747	326	39	+	+	CCONJ
ejpam-747	326	40	iu2	iu2	NOUN
ejpam-747	326	41	and	and	CCONJ
ejpam-747	326	42	v	v	NOUN
ejpam-747	326	43	=	=	SYM
ejpam-747	326	44	v1	v1	PROPN
ejpam-747	326	45	+	+	CCONJ
ejpam-747	326	46	iv2	iv2	NOUN
ejpam-747	326	47	,	,	PUNCT
ejpam-747	326	48	then	then	ADV
ejpam-747	326	49	(	(	PUNCT
ejpam-747	326	50	i	i	NOUN
ejpam-747	326	51	)	)	PUNCT
ejpam-747	326	52	φ	φ	PROPN
ejpam-747	326	53	(	(	PUNCT
ejpam-747	326	54	u	u	NOUN
ejpam-747	326	55	,	,	PUNCT
ejpam-747	326	56	v	v	NOUN
ejpam-747	326	57	)	)	PUNCT
ejpam-747	326	58	is	be	AUX
ejpam-747	326	59	continuous	continuous	ADJ
ejpam-747	326	60	in	in	ADP
ejpam-747	326	61	d	d	PROPN
ejpam-747	326	62	⊂	⊂	PROPN
ejpam-747	326	63	c×c	c×c	PROPN
ejpam-747	326	64	;	;	PUNCT
ejpam-747	326	65	(	(	PUNCT
ejpam-747	326	66	ii	ii	NOUN
ejpam-747	326	67	)	)	PUNCT
ejpam-747	326	68	(	(	PUNCT
ejpam-747	326	69	1,0	1,0	NUM
ejpam-747	326	70	)	)	PUNCT
ejpam-747	326	71	∈	∈	PROPN
ejpam-747	326	72	d	d	NOUN
ejpam-747	326	73	and	and	CCONJ
ejpam-747	326	74	re	re	ADJ
ejpam-747	326	75	φ	φ	PROPN
ejpam-747	326	76	(	(	PUNCT
ejpam-747	326	77	1,0	1,0	NUM
ejpam-747	326	78	)	)	PUNCT
ejpam-747	326	79	=	=	SYM
ejpam-747	326	80	δ	δ	PROPN
ejpam-747	326	81	�	�	PROPN
ejpam-747	326	82	p−m	p−m	ADP
ejpam-747	326	83	�	�	PROPN
ejpam-747	326	84	−	−	PROPN
ejpam-747	326	85	γ	γ	X
ejpam-747	326	86	>	>	X
ejpam-747	326	87	0	0	NUM
ejpam-747	326	88	;	;	PUNCT
ejpam-747	326	89	(	(	PUNCT
ejpam-747	326	90	iii	iii	NOUN
ejpam-747	326	91	)	)	PUNCT
ejpam-747	326	92	for	for	ADP
ejpam-747	326	93	all	all	DET
ejpam-747	326	94	�	�	PROPN
ejpam-747	326	95	iu2	iu2	NOUN
ejpam-747	326	96	,	,	PUNCT
ejpam-747	326	97	v1	v1	PROPN
ejpam-747	326	98	�	�	PROPN
ejpam-747	326	99	∈	∈	PROPN
ejpam-747	326	100	d	d	PROPN
ejpam-747	326	101	and	and	CCONJ
ejpam-747	326	102	such	such	ADJ
ejpam-747	326	103	that	that	PRON
ejpam-747	326	104	for	for	ADP
ejpam-747	326	105	v1	v1	NOUN
ejpam-747	326	106	≤	≤	NUM
ejpam-747	326	107	−	−	ADP
ejpam-747	326	108	�	�	PROPN
ejpam-747	326	109	1	1	NUM
ejpam-747	326	110	+	+	PROPN
ejpam-747	326	111	u2	u2	PROPN
ejpam-747	326	112	2	2	NUM
ejpam-747	326	113	�	�	PROPN
ejpam-747	326	114	/2	/2	PROPN
ejpam-747	326	115	,	,	PUNCT
ejpam-747	326	116	we	we	PRON
ejpam-747	326	117	get	get	VERB
ejpam-747	326	118	re	re	VERB
ejpam-747	326	119	�	�	PROPN
ejpam-747	326	120	φ	φ	PROPN
ejpam-747	326	121	�	�	PROPN
ejpam-747	326	122	iu2	iu2	PROPN
ejpam-747	326	123	,	,	PUNCT
ejpam-747	326	124	v1	v1	PROPN
ejpam-747	326	125	�	�	PROPN
ejpam-747	326	126	=	=	SYM
ejpam-747	326	127	δ	δ	PROPN
ejpam-747	326	128	�	�	PROPN
ejpam-747	326	129	p−m−	p−m−	PROPN
ejpam-747	326	130	β	β	X
ejpam-747	326	131	�	�	PROPN
ejpam-747	326	132	+	+	CCONJ
ejpam-747	326	133	(	(	PUNCT
ejpam-747	326	134	1−	1−	NUM
ejpam-747	326	135	δ)β	δ)β	X
ejpam-747	326	136	v1	v1	VERB
ejpam-747	326	137	−	−	NOUN
ejpam-747	326	138	γ	γ	PROPN
ejpam-747	326	139	≤	≤	NUM
ejpam-747	326	140	δ	δ	PROPN
ejpam-747	326	141	�	�	PROPN
ejpam-747	326	142	p−m−	p−m−	PROPN
ejpam-747	326	143	β	β	X
ejpam-747	326	144	�	�	PROPN
ejpam-747	327	1	−	−	PROPN
ejpam-747	328	1	(	(	PUNCT
ejpam-747	328	2	1−	1−	NUM
ejpam-747	328	3	δ)β	δ)β	NUM
ejpam-747	328	4	�	�	PROPN
ejpam-747	328	5	1	1	NUM
ejpam-747	328	6	+	+	PROPN
ejpam-747	328	7	u2	u2	PROPN
ejpam-747	328	8	2	2	NUM
ejpam-747	328	9	�	�	PROPN
ejpam-747	328	10	/2−	/2−	PROPN
ejpam-747	328	11	γ	γ	X
ejpam-747	328	12	=	=	SYM
ejpam-747	328	13	−	−	PROPN
ejpam-747	328	14	(	(	PUNCT
ejpam-747	328	15	1−	1−	NUM
ejpam-747	328	16	δ)βu2	δ)βu2	NOUN
ejpam-747	328	17	2/2	2/2	NUM
ejpam-747	328	18	≤	≤	NUM
ejpam-747	328	19	0	0	NUM
ejpam-747	328	20	.	.	PUNCT
ejpam-747	329	1	therefore	therefore	ADV
ejpam-747	329	2	,	,	PUNCT
ejpam-747	329	3	φ	φ	PROPN
ejpam-747	329	4	(	(	PUNCT
ejpam-747	329	5	u	u	NOUN
ejpam-747	329	6	,	,	PUNCT
ejpam-747	329	7	v	v	NOUN
ejpam-747	329	8	)	)	PUNCT
ejpam-747	329	9	satisfies	satisfy	VERB
ejpam-747	329	10	the	the	DET
ejpam-747	329	11	conditions	condition	NOUN
ejpam-747	329	12	of	of	ADP
ejpam-747	329	13	lemma	lemma	PROPN
ejpam-747	329	14	2	2	NUM
ejpam-747	329	15	.	.	PUNCT
ejpam-747	330	1	this	this	PRON
ejpam-747	330	2	show	show	VERB
ejpam-747	330	3	that	that	SCONJ
ejpam-747	330	4	re	re	VERB
ejpam-747	330	5	�	�	PROPN
ejpam-747	330	6	p	p	PROPN
ejpam-747	330	7	(	(	PUNCT
ejpam-747	330	8	z	z	NOUN
ejpam-747	330	9	)	)	PUNCT
ejpam-747	330	10	�	�	PROPN
ejpam-747	330	11	>	>	X
ejpam-747	330	12	0	0	PUNCT
ejpam-747	331	1	(	(	PUNCT
ejpam-747	331	2	z	z	NOUN
ejpam-747	331	3	∈∆	∈∆	NOUN
ejpam-747	331	4	)	)	PUNCT
ejpam-747	331	5	,	,	PUNCT
ejpam-747	331	6	i.e.	i.e.	X
ejpam-747	331	7	re	re	X
ejpam-747	331	8	(	(	PUNCT
ejpam-747	331	9	z	z	PROPN
ejpam-747	331	10	�	�	PROPN
ejpam-747	331	11	f	f	PROPN
ejpam-747	331	12	∗	∗	VERB
ejpam-747	331	13	g	g	PROPN
ejpam-747	331	14	�	�	PROPN
ejpam-747	331	15	m+1	m+1	PRON
ejpam-747	331	16	(	(	PUNCT
ejpam-747	331	17	z	z	NOUN
ejpam-747	331	18	)	)	PUNCT
ejpam-747	331	19	�	�	PROPN
ejpam-747	331	20	f	f	PROPN
ejpam-747	331	21	∗	∗	PROPN
ejpam-747	331	22	h	h	PROPN
ejpam-747	331	23	�	�	PROPN
ejpam-747	331	24	m	m	PROPN
ejpam-747	331	25	(	(	PUNCT
ejpam-747	331	26	z	z	NOUN
ejpam-747	331	27	)	)	PUNCT
ejpam-747	331	28	)	)	PUNCT
ejpam-747	331	29	>	>	X
ejpam-747	332	1	p−m−	p−m−	NUM
ejpam-747	332	2	β	β	X
ejpam-747	332	3	(	(	PUNCT
ejpam-747	332	4	z	z	NOUN
ejpam-747	332	5	∈∆	∈∆	NOUN
ejpam-747	332	6	)	)	PUNCT
ejpam-747	332	7	which	which	PRON
ejpam-747	332	8	proves	prove	VERB
ejpam-747	332	9	that	that	SCONJ
ejpam-747	332	10	f	f	PROPN
ejpam-747	332	11	(	(	PUNCT
ejpam-747	332	12	z	z	X
ejpam-747	332	13	)	)	PUNCT
ejpam-747	332	14	∈	∈	PROPN
ejpam-747	332	15	s	s	PART
ejpam-747	332	16	g	g	PROPN
ejpam-747	332	17	h	h	PROPN
ejpam-747	332	18	�	�	PROPN
ejpam-747	332	19	p	p	PROPN
ejpam-747	332	20	,	,	PUNCT
ejpam-747	332	21	m	m	PROPN
ejpam-747	332	22	,	,	PUNCT
ejpam-747	332	23	β	β	X
ejpam-747	332	24	�	�	PROPN
ejpam-747	332	25	.	.	PUNCT
ejpam-747	333	1	theorem	theorem	VERB
ejpam-747	333	2	6	6	NUM
ejpam-747	333	3	.	.	PUNCT
ejpam-747	334	1	let	let	VERB
ejpam-747	334	2	for	for	ADP
ejpam-747	334	3	p	p	PROPN
ejpam-747	334	4	∈	∈	PROPN
ejpam-747	334	5	n	n	CCONJ
ejpam-747	334	6	,	,	PUNCT
ejpam-747	334	7	p	p	X
ejpam-747	334	8	>	>	X
ejpam-747	334	9	m	m	PROPN
ejpam-747	334	10	,	,	PUNCT
ejpam-747	334	11	m	m	PROPN
ejpam-747	334	12	∈	∈	PROPN
ejpam-747	334	13	n0	n0	PROPN
ejpam-747	334	14	,	,	PUNCT
ejpam-747	334	15	0	0	NUM
ejpam-747	334	16	<	<	X
ejpam-747	334	17	β	β	X
ejpam-747	334	18	≤	≤	NOUN
ejpam-747	335	1	p	p	X
ejpam-747	335	2	,	,	PUNCT
ejpam-747	335	3	if	if	SCONJ
ejpam-747	335	4	�	�	PROPN
ejpam-747	335	5	�	�	PROPN
ejpam-747	335	6	�	�	PROPN
ejpam-747	335	7	�	�	PROPN
ejpam-747	335	8	�	�	PROPN
ejpam-747	335	9	�	�	PROPN
ejpam-747	335	10	�	�	PROPN
ejpam-747	335	11	�	�	PROPN
ejpam-747	335	12	arg	arg	VERB
ejpam-747	335	13			PROPN
ejpam-747	335	14			ADP
ejpam-747	335	15			ADJ
ejpam-747	335	16	1	1	NUM
ejpam-747	335	17	�	�	PROPN
ejpam-747	335	18	p−m	p−m	PRON
ejpam-747	335	19	�	�	PROPN
ejpam-747	335	20			PROPN
ejpam-747	335	21			PROPN
ejpam-747	335	22			PROPN
ejpam-747	335	23	z	z	PROPN
ejpam-747	335	24	�	�	PROPN
ejpam-747	336	1	f	f	PROPN
ejpam-747	336	2	∗	∗	VERB
ejpam-747	336	3	g	g	PROPN
ejpam-747	336	4	�	�	PROPN
ejpam-747	336	5	m+1	m+1	PRON
ejpam-747	336	6	(	(	PUNCT
ejpam-747	336	7	z	z	NOUN
ejpam-747	336	8	)	)	PUNCT
ejpam-747	336	9	�	�	PROPN
ejpam-747	336	10	f	f	PROPN
ejpam-747	336	11	∗	∗	PROPN
ejpam-747	336	12	h	h	PROPN
ejpam-747	336	13	�	�	PROPN
ejpam-747	336	14	m	m	PROPN
ejpam-747	336	15	(	(	PUNCT
ejpam-747	336	16	z	z	NOUN
ejpam-747	336	17	)	)	PUNCT
ejpam-747	337	1	+	+	CCONJ
ejpam-747	337	2	z	z	NOUN
ejpam-747	337	3	z	z	NOUN
ejpam-747	337	4	�	�	PROPN
ejpam-747	337	5	f	f	PROPN
ejpam-747	337	6	∗	∗	VERB
ejpam-747	337	7	g	g	PROPN
ejpam-747	337	8	�	�	PROPN
ejpam-747	337	9	m+1	m+1	PRON
ejpam-747	337	10	(	(	PUNCT
ejpam-747	337	11	z	z	NOUN
ejpam-747	337	12	)	)	PUNCT
ejpam-747	337	13	�	�	PROPN
ejpam-747	337	14	f	f	PROPN
ejpam-747	337	15	∗	∗	PROPN
ejpam-747	337	16	h	h	PROPN
ejpam-747	337	17	�	�	PROPN
ejpam-747	337	18	m	m	PROPN
ejpam-747	337	19	(	(	PUNCT
ejpam-747	337	20	z	z	NOUN
ejpam-747	337	21	)	)	PUNCT
ejpam-747	337	22	!	!	PUNCT
ejpam-747	338	1	′	′	NUM
ejpam-747	339	1			NOUN
ejpam-747	339	2			PROPN
ejpam-747	339	3			NOUN
ejpam-747	339	4			PROPN
ejpam-747	339	5			PROPN
ejpam-747	339	6			NOUN
ejpam-747	339	7	�	�	PROPN
ejpam-747	339	8	�	�	PROPN
ejpam-747	339	9	�	�	PROPN
ejpam-747	339	10	�	�	PROPN
ejpam-747	339	11	�	�	PROPN
ejpam-747	339	12	�	�	PROPN
ejpam-747	339	13	�	�	PROPN
ejpam-747	339	14	�	�	PROPN
ejpam-747	339	15	<	<	X
ejpam-747	339	16	β	β	X
ejpam-747	339	17	p	p	X
ejpam-747	339	18	π	π	PROPN
ejpam-747	339	19	2	2	X
ejpam-747	339	20	+	+	ADJ
ejpam-747	339	21	tan−1	tan−1	PROPN
ejpam-747	339	22	�	�	PROPN
ejpam-747	339	23	β	β	X
ejpam-747	339	24	p	p	X
ejpam-747	339	25	�	�	PROPN
ejpam-747	339	26	(	(	PUNCT
ejpam-747	339	27	z	z	NOUN
ejpam-747	339	28	∈∆	∈∆	NOUN
ejpam-747	339	29	)	)	PUNCT
ejpam-747	339	30	,	,	PUNCT
ejpam-747	339	31	(	(	PUNCT
ejpam-747	339	32	24	24	NUM
ejpam-747	339	33	)	)	PUNCT
ejpam-747	339	34	then	then	ADV
ejpam-747	339	35	�	�	PROPN
ejpam-747	339	36	�	�	PROPN
ejpam-747	339	37	�	�	PROPN
ejpam-747	339	38	�	�	PROPN
ejpam-747	339	39	arg	arg	PROPN
ejpam-747	339	40	�	�	PROPN
ejpam-747	340	1	z	z	PROPN
ejpam-747	340	2	(	(	PUNCT
ejpam-747	340	3	f	f	PROPN
ejpam-747	340	4	∗g	∗g	PROPN
ejpam-747	340	5	)	)	PUNCT
ejpam-747	340	6	m+1	m+1	PRON
ejpam-747	340	7	(	(	PUNCT
ejpam-747	340	8	z	z	NOUN
ejpam-747	340	9	)	)	PUNCT
ejpam-747	340	10	(	(	PUNCT
ejpam-747	340	11	f	f	NOUN
ejpam-747	340	12	∗h	∗h	NOUN
ejpam-747	340	13	)	)	PUNCT
ejpam-747	340	14	m	m	VERB
ejpam-747	340	15	(	(	PUNCT
ejpam-747	340	16	z	z	NOUN
ejpam-747	340	17	)	)	PUNCT
ejpam-747	340	18	�	�	PROPN
ejpam-747	340	19	�	�	PROPN
ejpam-747	340	20	�	�	PROPN
ejpam-747	340	21	�	�	PROPN
ejpam-747	340	22	�	�	PROPN
ejpam-747	340	23	<	<	X
ejpam-747	340	24	β	β	X
ejpam-747	340	25	p	p	X
ejpam-747	340	26	π	π	PROPN
ejpam-747	340	27	2	2	NUM
ejpam-747	340	28	(	(	PUNCT
ejpam-747	340	29	z	z	NOUN
ejpam-747	340	30	∈∆	∈∆	NOUN
ejpam-747	340	31	)	)	PUNCT
ejpam-747	340	32	.	.	PUNCT
ejpam-747	341	1	in	in	ADP
ejpam-747	341	2	particular	particular	ADJ
ejpam-747	341	3	,	,	PUNCT
ejpam-747	341	4	if	if	SCONJ
ejpam-747	341	5	�	�	PROPN
ejpam-747	341	6	�	�	PROPN
ejpam-747	341	7	�	�	PROPN
ejpam-747	341	8	�	�	PROPN
ejpam-747	341	9	�	�	PROPN
ejpam-747	341	10	arg	arg	NOUN
ejpam-747	341	11	(	(	PUNCT
ejpam-747	341	12	z	z	NOUN
ejpam-747	341	13	f	f	NOUN
ejpam-747	341	14	′	′	NUM
ejpam-747	341	15	(	(	PUNCT
ejpam-747	341	16	z	z	NOUN
ejpam-747	341	17	)	)	PUNCT
ejpam-747	341	18	p	p	NOUN
ejpam-747	341	19	f	f	X
ejpam-747	341	20	(	(	PUNCT
ejpam-747	341	21	z	z	NOUN
ejpam-747	341	22	)	)	PUNCT
ejpam-747	341	23	2	2	NUM
ejpam-747	341	24	+	+	SYM
ejpam-747	341	25	z	z	NOUN
ejpam-747	341	26	f	f	X
ejpam-747	342	1	′′	′′	PROPN
ejpam-747	342	2	(	(	PUNCT
ejpam-747	342	3	z	z	PROPN
ejpam-747	342	4	)	)	PUNCT
ejpam-747	342	5	f	f	NOUN
ejpam-747	342	6	′	′	NUM
ejpam-747	342	7	(	(	PUNCT
ejpam-747	342	8	z	z	NOUN
ejpam-747	342	9	)	)	PUNCT
ejpam-747	342	10	−	−	PROPN
ejpam-747	343	1	z	z	NOUN
ejpam-747	343	2	f	f	NOUN
ejpam-747	344	1	′	′	NUM
ejpam-747	344	2	(	(	PUNCT
ejpam-747	344	3	z	z	NOUN
ejpam-747	344	4	)	)	PUNCT
ejpam-747	344	5	f	f	NOUN
ejpam-747	344	6	(	(	PUNCT
ejpam-747	344	7	z	z	NOUN
ejpam-747	344	8	)	)	PUNCT
ejpam-747	344	9	!	!	PUNCT
ejpam-747	344	10	)	)	PUNCT
ejpam-747	345	1	�	�	PROPN
ejpam-747	345	2	�	�	PROPN
ejpam-747	345	3	�	�	PROPN
ejpam-747	345	4	�	�	PROPN
ejpam-747	345	5	�	�	PROPN
ejpam-747	345	6	<	<	X
ejpam-747	345	7	β	β	X
ejpam-747	345	8	p	p	X
ejpam-747	345	9	π	π	PROPN
ejpam-747	345	10	2	2	NUM
ejpam-747	345	11	+	+	CCONJ
ejpam-747	345	12	tan−1	tan−1	PROPN
ejpam-747	345	13	�	�	PROPN
ejpam-747	345	14	β	β	X
ejpam-747	345	15	p	p	X
ejpam-747	345	16	�	�	PROPN
ejpam-747	345	17	(	(	PUNCT
ejpam-747	345	18	z	z	NOUN
ejpam-747	345	19	∈∆	∈∆	NOUN
ejpam-747	345	20	)	)	PUNCT
ejpam-747	345	21	,	,	PUNCT
ejpam-747	345	22	then	then	ADV
ejpam-747	345	23	f	f	PROPN
ejpam-747	345	24	∈	∈	PROPN
ejpam-747	345	25	s	s	PART
ejpam-747	345	26	∗	∗	NOUN
ejpam-747	345	27	p	p	X
ejpam-747	345	28	�	�	PROPN
ejpam-747	345	29	β	β	X
ejpam-747	345	30	�	�	PROPN
ejpam-747	345	31	.	.	PUNCT
ejpam-747	346	1	proof	proof	NOUN
ejpam-747	346	2	.	.	PUNCT
ejpam-747	347	1	let	let	VERB
ejpam-747	347	2	p(z	p(z	VERB
ejpam-747	347	3	)	)	PUNCT
ejpam-747	347	4	:	:	PUNCT
ejpam-747	348	1	=	=	SYM
ejpam-747	348	2	1	1	NUM
ejpam-747	348	3	�	�	PROPN
ejpam-747	348	4	p−m	p−m	PRON
ejpam-747	348	5	�	�	PROPN
ejpam-747	348	6	(	(	PUNCT
ejpam-747	348	7	z	z	NOUN
ejpam-747	348	8	�	�	PROPN
ejpam-747	348	9	f	f	PROPN
ejpam-747	348	10	∗	∗	VERB
ejpam-747	348	11	g	g	PROPN
ejpam-747	348	12	�	�	PROPN
ejpam-747	348	13	m+1	m+1	PRON
ejpam-747	348	14	(	(	PUNCT
ejpam-747	348	15	z	z	NOUN
ejpam-747	348	16	)	)	PUNCT
ejpam-747	348	17	�	�	PROPN
ejpam-747	348	18	f	f	PROPN
ejpam-747	348	19	∗	∗	PROPN
ejpam-747	348	20	h	h	PROPN
ejpam-747	348	21	�	�	PROPN
ejpam-747	348	22	m	m	PROPN
ejpam-747	348	23	(	(	PUNCT
ejpam-747	348	24	z	z	NOUN
ejpam-747	348	25	)	)	PUNCT
ejpam-747	348	26	)	)	PUNCT
ejpam-747	348	27	.	.	PUNCT
ejpam-747	349	1	p.	p.	NOUN
ejpam-747	349	2	sharma	sharma	PROPN
ejpam-747	349	3	,	,	PUNCT
ejpam-747	349	4	p.	p.	PROPN
ejpam-747	349	5	srivastava	srivastava	PROPN
ejpam-747	349	6	/	/	SYM
ejpam-747	349	7	eur	eur	PROPN
ejpam-747	349	8	.	.	PUNCT
ejpam-747	350	1	j.	j.	PROPN
ejpam-747	350	2	pure	pure	PROPN
ejpam-747	350	3	appl	appl	PROPN
ejpam-747	350	4	.	.	PROPN
ejpam-747	350	5	math	math	PROPN
ejpam-747	350	6	,	,	PUNCT
ejpam-747	350	7	3	3	NUM
ejpam-747	350	8	(	(	PUNCT
ejpam-747	350	9	2010	2010	NUM
ejpam-747	350	10	)	)	PUNCT
ejpam-747	350	11	,	,	PUNCT
ejpam-747	350	12	1093	1093	NUM
ejpam-747	350	13	-	-	SYM
ejpam-747	350	14	1112	1112	NUM
ejpam-747	350	15	1106	1106	NUM
ejpam-747	350	16	we	we	PRON
ejpam-747	350	17	obtain	obtain	VERB
ejpam-747	350	18	zp	zp	PROPN
ejpam-747	350	19	′	′	NUM
ejpam-747	350	20	(	(	PUNCT
ejpam-747	350	21	z	z	X
ejpam-747	350	22	)	)	PUNCT
ejpam-747	350	23	=	=	SYM
ejpam-747	350	24	z	z	PART
ejpam-747	350	25	�	�	PROPN
ejpam-747	350	26	p−m	p−m	PRON
ejpam-747	350	27	�	�	PROPN
ejpam-747	350	28	(	(	PUNCT
ejpam-747	350	29	z	z	NOUN
ejpam-747	350	30	�	�	PROPN
ejpam-747	350	31	f	f	PROPN
ejpam-747	350	32	∗	∗	VERB
ejpam-747	350	33	g	g	PROPN
ejpam-747	350	34	�	�	PROPN
ejpam-747	350	35	m+1	m+1	PRON
ejpam-747	350	36	(	(	PUNCT
ejpam-747	350	37	z	z	NOUN
ejpam-747	350	38	)	)	PUNCT
ejpam-747	350	39	�	�	PROPN
ejpam-747	350	40	f	f	PROPN
ejpam-747	350	41	∗	∗	PROPN
ejpam-747	350	42	h	h	PROPN
ejpam-747	350	43	�	�	PROPN
ejpam-747	350	44	m	m	PROPN
ejpam-747	350	45	(	(	PUNCT
ejpam-747	350	46	z	z	NOUN
ejpam-747	350	47	)	)	PUNCT
ejpam-747	350	48	)	)	PUNCT
ejpam-747	351	1	′	′	X
ejpam-747	351	2	.	.	PUNCT
ejpam-747	352	1	suppose	suppose	VERB
ejpam-747	352	2	that	that	SCONJ
ejpam-747	352	3	there	there	PRON
ejpam-747	352	4	exists	exist	VERB
ejpam-747	352	5	point	point	NOUN
ejpam-747	352	6	z0	z0	PROPN
ejpam-747	352	7	∈∆	∈∆	VERB
ejpam-747	352	8	such	such	ADJ
ejpam-747	352	9	that	that	SCONJ
ejpam-747	352	10	�	�	PROPN
ejpam-747	352	11	�	�	PROPN
ejpam-747	352	12	arg	arg	NOUN
ejpam-747	352	13	p	p	NOUN
ejpam-747	352	14	(	(	PUNCT
ejpam-747	352	15	z	z	NOUN
ejpam-747	352	16	)	)	PUNCT
ejpam-747	352	17	�	�	PROPN
ejpam-747	352	18	�	�	PROPN
ejpam-747	352	19	<	<	X
ejpam-747	352	20	β	β	X
ejpam-747	352	21	p	p	X
ejpam-747	352	22	π	π	PROPN
ejpam-747	352	23	2	2	NUM
ejpam-747	352	24	for	for	ADP
ejpam-747	352	25	|z|	|z|	NOUN
ejpam-747	352	26	<	<	X
ejpam-747	352	27	�	�	PROPN
ejpam-747	352	28	�	�	PROPN
ejpam-747	352	29	z0	z0	PROPN
ejpam-747	352	30	�	�	PROPN
ejpam-747	352	31	�	�	PROPN
ejpam-747	352	32	,	,	PUNCT
ejpam-747	352	33	�	�	PROPN
ejpam-747	352	34	�	�	PROPN
ejpam-747	352	35	arg	arg	NOUN
ejpam-747	352	36	p	p	PROPN
ejpam-747	352	37	�	�	PROPN
ejpam-747	352	38	z0	z0	PROPN
ejpam-747	352	39	�	�	PROPN
ejpam-747	352	40	�	�	PROPN
ejpam-747	352	41	�	�	PROPN
ejpam-747	352	42	=	=	PUNCT
ejpam-747	352	43	β	β	X
ejpam-747	352	44	p	p	X
ejpam-747	352	45	π	π	PROPN
ejpam-747	352	46	2	2	NUM
ejpam-747	352	47	.	.	PUNCT
ejpam-747	353	1	then	then	ADV
ejpam-747	353	2	applying	apply	VERB
ejpam-747	353	3	lemma	lemma	PROPN
ejpam-747	353	4	3	3	NUM
ejpam-747	353	5	,	,	PUNCT
ejpam-747	353	6	we	we	PRON
ejpam-747	353	7	write	write	VERB
ejpam-747	353	8	that	that	PRON
ejpam-747	353	9	z0p	z0p	PROPN
ejpam-747	353	10	′	′	NUM
ejpam-747	353	11	�	�	PROPN
ejpam-747	353	12	z0	z0	PROPN
ejpam-747	353	13	�	�	PROPN
ejpam-747	353	14	p	p	PROPN
ejpam-747	353	15	�	�	PROPN
ejpam-747	353	16	z0	z0	PROPN
ejpam-747	353	17	�	�	PROPN
ejpam-747	353	18	=	=	SYM
ejpam-747	353	19	il	il	PROPN
ejpam-747	353	20	β	β	X
ejpam-747	353	21	p	p	X
ejpam-747	353	22	where	where	SCONJ
ejpam-747	353	23	l	l	NOUN
ejpam-747	353	24	≥	≥	NOUN
ejpam-747	353	25	1	1	NUM
ejpam-747	353	26	when	when	SCONJ
ejpam-747	353	27	arg	arg	VERB
ejpam-747	353	28	p	p	PROPN
ejpam-747	353	29	�	�	PROPN
ejpam-747	353	30	z0	z0	PROPN
ejpam-747	353	31	�	�	PROPN
ejpam-747	353	32	=	=	PUNCT
ejpam-747	353	33	β	β	PROPN
ejpam-747	353	34	p	p	X
ejpam-747	353	35	π	π	PROPN
ejpam-747	353	36	2	2	NUM
ejpam-747	353	37	and	and	CCONJ
ejpam-747	353	38	l	l	NOUN
ejpam-747	353	39	≤	≤	NUM
ejpam-747	353	40	−1	−1	NOUN
ejpam-747	354	1	when	when	SCONJ
ejpam-747	354	2	arg	arg	VERB
ejpam-747	354	3	p	p	PROPN
ejpam-747	354	4	�	�	PROPN
ejpam-747	354	5	z0	z0	PROPN
ejpam-747	354	6	�	�	PROPN
ejpam-747	354	7	=	=	PUNCT
ejpam-747	354	8	−	−	PROPN
ejpam-747	354	9	β	β	X
ejpam-747	354	10	p	p	X
ejpam-747	354	11	π	π	PROPN
ejpam-747	354	12	2	2	NUM
ejpam-747	354	13	.	.	PUNCT
ejpam-747	355	1	then	then	ADV
ejpam-747	355	2	it	it	PRON
ejpam-747	355	3	follows	follow	VERB
ejpam-747	355	4	that	that	PRON
ejpam-747	355	5	arg	arg	VERB
ejpam-747	355	6			PROPN
ejpam-747	355	7			ADP
ejpam-747	355	8			ADJ
ejpam-747	355	9	1	1	NUM
ejpam-747	355	10	�	�	PROPN
ejpam-747	355	11	p−m	p−m	PRON
ejpam-747	355	12	�	�	PROPN
ejpam-747	355	13			PROPN
ejpam-747	355	14			NOUN
ejpam-747	355	15			PROPN
ejpam-747	355	16	z0	z0	PROPN
ejpam-747	355	17	�	�	PROPN
ejpam-747	355	18	f	f	PROPN
ejpam-747	355	19	∗	∗	VERB
ejpam-747	355	20	g	g	PROPN
ejpam-747	355	21	�	�	PROPN
ejpam-747	355	22	m+1	m+1	PROPN
ejpam-747	355	23	�	�	PROPN
ejpam-747	355	24	z0	z0	PROPN
ejpam-747	355	25	�	�	PROPN
ejpam-747	355	26	�	�	PROPN
ejpam-747	355	27	f	f	PROPN
ejpam-747	355	28	∗	∗	PROPN
ejpam-747	355	29	h	h	PROPN
ejpam-747	355	30	�	�	PROPN
ejpam-747	355	31	m	m	PROPN
ejpam-747	355	32	�	�	PROPN
ejpam-747	355	33	z0	z0	PROPN
ejpam-747	355	34	�	�	PROPN
ejpam-747	355	35	+	+	CCONJ
ejpam-747	356	1	z0	z0	PROPN
ejpam-747	356	2			PROPN
ejpam-747	356	3			NUM
ejpam-747	356	4	z0	z0	PROPN
ejpam-747	356	5	�	�	PROPN
ejpam-747	356	6	f	f	PROPN
ejpam-747	356	7	∗	∗	VERB
ejpam-747	356	8	g	g	PROPN
ejpam-747	356	9	�	�	PROPN
ejpam-747	356	10	m+1	m+1	PROPN
ejpam-747	356	11	�	�	PROPN
ejpam-747	356	12	z0	z0	PROPN
ejpam-747	356	13	�	�	PROPN
ejpam-747	356	14	�	�	PROPN
ejpam-747	356	15	f	f	PROPN
ejpam-747	356	16	∗	∗	PROPN
ejpam-747	356	17	h	h	PROPN
ejpam-747	356	18	�	�	PROPN
ejpam-747	356	19	m	m	PROPN
ejpam-747	356	20	�	�	PROPN
ejpam-747	356	21	z0	z0	PROPN
ejpam-747	356	22	�	�	PROPN
ejpam-747	356	23			PROPN
ejpam-747	356	24			PROPN
ejpam-747	356	25	′	′	NOUN
ejpam-747	356	26			NOUN
ejpam-747	356	27			PUNCT
ejpam-747	357	1			PROPN
ejpam-747	357	2			PROPN
ejpam-747	357	3			NOUN
ejpam-747	357	4	=	=	SYM
ejpam-747	357	5	arg	arg	NOUN
ejpam-747	357	6	¦	¦	PROPN
ejpam-747	357	7	p	p	X
ejpam-747	357	8	�	�	PROPN
ejpam-747	357	9	z0	z0	PROPN
ejpam-747	357	10	�	�	PROPN
ejpam-747	357	11	+	+	CCONJ
ejpam-747	357	12	z0p	z0p	NUM
ejpam-747	357	13	′	′	NOUN
ejpam-747	357	14	�	�	PROPN
ejpam-747	357	15	z0	z0	PROPN
ejpam-747	357	16	�	�	PROPN
ejpam-747	357	17	©	©	PROPN
ejpam-747	357	18	=	=	NOUN
ejpam-747	357	19	arg	arg	NOUN
ejpam-747	357	20	(	(	PUNCT
ejpam-747	357	21	p	p	X
ejpam-747	357	22	�	�	PROPN
ejpam-747	357	23	z0	z0	PROPN
ejpam-747	357	24	�	�	PROPN
ejpam-747	357	25	1	1	NUM
ejpam-747	357	26	+	+	NUM
ejpam-747	357	27	z0p	z0p	NUM
ejpam-747	357	28	′	′	NOUN
ejpam-747	357	29	�	�	PROPN
ejpam-747	357	30	z0	z0	PROPN
ejpam-747	357	31	�	�	PROPN
ejpam-747	357	32	p	p	PROPN
ejpam-747	357	33	�	�	PROPN
ejpam-747	357	34	z0	z0	PROPN
ejpam-747	357	35	�	�	PROPN
ejpam-747	357	36	!	!	PUNCT
ejpam-747	357	37	)	)	PUNCT
ejpam-747	358	1	=	=	PUNCT
ejpam-747	358	2	arg	arg	NOUN
ejpam-747	358	3	p	p	X
ejpam-747	358	4	�	�	PROPN
ejpam-747	358	5	z0	z0	PROPN
ejpam-747	358	6	�	�	PROPN
ejpam-747	358	7	+	+	CCONJ
ejpam-747	358	8	arg	arg	NOUN
ejpam-747	358	9	�	�	PROPN
ejpam-747	358	10	1	1	NUM
ejpam-747	358	11	+	+	NUM
ejpam-747	358	12	il	il	PROPN
ejpam-747	358	13	β	β	X
ejpam-747	358	14	p	p	X
ejpam-747	358	15	�	�	PROPN
ejpam-747	358	16	=	=	PUNCT
ejpam-747	358	17	arg	arg	NOUN
ejpam-747	358	18	p	p	X
ejpam-747	358	19	�	�	PROPN
ejpam-747	358	20	z0	z0	PROPN
ejpam-747	358	21	�	�	PROPN
ejpam-747	358	22	+	+	CCONJ
ejpam-747	358	23	tan−1	tan−1	PROPN
ejpam-747	358	24	�	�	PROPN
ejpam-747	358	25	l	l	NOUN
ejpam-747	358	26	β	β	PROPN
ejpam-747	358	27	p	p	X
ejpam-747	358	28	�	�	PROPN
ejpam-747	358	29	.	.	PUNCT
ejpam-747	359	1	when	when	SCONJ
ejpam-747	359	2	arg	arg	VERB
ejpam-747	359	3	p	p	PROPN
ejpam-747	359	4	�	�	PROPN
ejpam-747	359	5	z0	z0	PROPN
ejpam-747	359	6	�	�	PROPN
ejpam-747	359	7	=	=	PUNCT
ejpam-747	359	8	β	β	PROPN
ejpam-747	359	9	p	p	X
ejpam-747	359	10	π	π	PROPN
ejpam-747	359	11	2	2	NUM
ejpam-747	359	12	,	,	PUNCT
ejpam-747	359	13	we	we	PRON
ejpam-747	359	14	have	have	AUX
ejpam-747	359	15	arg	arg	VERB
ejpam-747	359	16			NOUN
ejpam-747	359	17			ADP
ejpam-747	359	18			ADJ
ejpam-747	359	19	1	1	NUM
ejpam-747	359	20	�	�	PROPN
ejpam-747	359	21	p−m	p−m	PRON
ejpam-747	359	22	�	�	PROPN
ejpam-747	359	23			PROPN
ejpam-747	359	24			ADP
ejpam-747	359	25			NOUN
ejpam-747	359	26	z0	z0	PROPN
ejpam-747	359	27	�	�	PROPN
ejpam-747	359	28	f	f	PROPN
ejpam-747	359	29	∗	∗	VERB
ejpam-747	359	30	g	g	PROPN
ejpam-747	359	31	�	�	PROPN
ejpam-747	359	32	m+1	m+1	PROPN
ejpam-747	359	33	�	�	PROPN
ejpam-747	359	34	z0	z0	PROPN
ejpam-747	359	35	�	�	PROPN
ejpam-747	359	36	�	�	PROPN
ejpam-747	359	37	f	f	PROPN
ejpam-747	359	38	∗	∗	PROPN
ejpam-747	359	39	h	h	PROPN
ejpam-747	359	40	�	�	PROPN
ejpam-747	359	41	m	m	PROPN
ejpam-747	359	42	�	�	PROPN
ejpam-747	359	43	z0	z0	PROPN
ejpam-747	359	44	�	�	PROPN
ejpam-747	359	45	+	+	CCONJ
ejpam-747	359	46	z0	z0	PROPN
ejpam-747	359	47	z0	z0	PROPN
ejpam-747	359	48	�	�	PROPN
ejpam-747	359	49	f	f	PROPN
ejpam-747	359	50	∗	∗	VERB
ejpam-747	359	51	g	g	PROPN
ejpam-747	359	52	�	�	PROPN
ejpam-747	359	53	m+1	m+1	PROPN
ejpam-747	359	54	�	�	PROPN
ejpam-747	359	55	z0	z0	PROPN
ejpam-747	359	56	�	�	PROPN
ejpam-747	359	57	�	�	PROPN
ejpam-747	359	58	f	f	PROPN
ejpam-747	359	59	∗	∗	PROPN
ejpam-747	359	60	h	h	PROPN
ejpam-747	359	61	�	�	PROPN
ejpam-747	359	62	m	m	PROPN
ejpam-747	359	63	�	�	PROPN
ejpam-747	359	64	z0	z0	PROPN
ejpam-747	359	65	�	�	PROPN
ejpam-747	359	66	!	!	PUNCT
ejpam-747	360	1	′	′	NUM
ejpam-747	361	1			PROPN
ejpam-747	361	2			PROPN
ejpam-747	361	3			NOUN
ejpam-747	361	4			PROPN
ejpam-747	361	5			PROPN
ejpam-747	361	6			NOUN
ejpam-747	361	7	(	(	PUNCT
ejpam-747	361	8	25	25	NUM
ejpam-747	361	9	)	)	PUNCT
ejpam-747	361	10	=	=	PUNCT
ejpam-747	362	1	β	β	X
ejpam-747	362	2	p	p	X
ejpam-747	362	3	π	π	PROPN
ejpam-747	362	4	2	2	NUM
ejpam-747	362	5	+	+	CCONJ
ejpam-747	362	6	tan−1	tan−1	PROPN
ejpam-747	362	7	�	�	PROPN
ejpam-747	362	8	l	l	NOUN
ejpam-747	362	9	β	β	PROPN
ejpam-747	362	10	p	p	X
ejpam-747	362	11	�	�	PROPN
ejpam-747	362	12	≥	≥	PROPN
ejpam-747	362	13	β	β	X
ejpam-747	362	14	p	p	X
ejpam-747	362	15	π	π	PROPN
ejpam-747	362	16	2	2	NUM
ejpam-747	362	17	+	+	CCONJ
ejpam-747	362	18	tan−1	tan−1	PROPN
ejpam-747	362	19	�	�	PROPN
ejpam-747	362	20	β	β	X
ejpam-747	362	21	p	p	X
ejpam-747	362	22	�	�	PROPN
ejpam-747	362	23	.	.	PUNCT
ejpam-747	363	1	p.	p.	PROPN
ejpam-747	363	2	sharma	sharma	PROPN
ejpam-747	363	3	,	,	PUNCT
ejpam-747	363	4	p.	p.	PROPN
ejpam-747	363	5	srivastava	srivastava	PROPN
ejpam-747	363	6	/	/	SYM
ejpam-747	363	7	eur	eur	PROPN
ejpam-747	363	8	.	.	PUNCT
ejpam-747	364	1	j.	j.	PROPN
ejpam-747	364	2	pure	pure	PROPN
ejpam-747	364	3	appl	appl	PROPN
ejpam-747	364	4	.	.	PROPN
ejpam-747	364	5	math	math	PROPN
ejpam-747	364	6	,	,	PUNCT
ejpam-747	364	7	3	3	NUM
ejpam-747	364	8	(	(	PUNCT
ejpam-747	364	9	2010	2010	NUM
ejpam-747	364	10	)	)	PUNCT
ejpam-747	364	11	,	,	PUNCT
ejpam-747	364	12	1093	1093	NUM
ejpam-747	364	13	-	-	SYM
ejpam-747	364	14	1112	1112	NUM
ejpam-747	364	15	1107	1107	NUM
ejpam-747	364	16	similarly	similarly	ADV
ejpam-747	364	17	,	,	PUNCT
ejpam-747	364	18	if	if	SCONJ
ejpam-747	364	19	arg	arg	VERB
ejpam-747	364	20	p	p	PROPN
ejpam-747	364	21	�	�	PROPN
ejpam-747	364	22	z0	z0	PROPN
ejpam-747	364	23	�	�	PROPN
ejpam-747	364	24	=	=	PUNCT
ejpam-747	364	25	−β	−β	PROPN
ejpam-747	364	26	p	p	X
ejpam-747	364	27	π	π	PROPN
ejpam-747	364	28	2	2	NUM
ejpam-747	364	29	,	,	PUNCT
ejpam-747	364	30	then	then	ADV
ejpam-747	364	31	we	we	PRON
ejpam-747	364	32	obtain	obtain	VERB
ejpam-747	364	33	that	that	DET
ejpam-747	364	34	arg	arg	NOUN
ejpam-747	364	35			NOUN
ejpam-747	364	36			ADP
ejpam-747	364	37			ADJ
ejpam-747	364	38	1	1	NUM
ejpam-747	364	39	�	�	PROPN
ejpam-747	364	40	p−m	p−m	PRON
ejpam-747	364	41	�	�	PROPN
ejpam-747	364	42			PROPN
ejpam-747	364	43			NOUN
ejpam-747	365	1			PROPN
ejpam-747	365	2	z0	z0	PROPN
ejpam-747	365	3	�	�	PROPN
ejpam-747	365	4	f	f	PROPN
ejpam-747	365	5	∗	∗	VERB
ejpam-747	365	6	g	g	PROPN
ejpam-747	365	7	�	�	PROPN
ejpam-747	365	8	m+1	m+1	PROPN
ejpam-747	365	9	�	�	PROPN
ejpam-747	365	10	z0	z0	PROPN
ejpam-747	365	11	�	�	PROPN
ejpam-747	365	12	�	�	PROPN
ejpam-747	365	13	f	f	PROPN
ejpam-747	365	14	∗	∗	PROPN
ejpam-747	365	15	h	h	PROPN
ejpam-747	365	16	�	�	PROPN
ejpam-747	365	17	m	m	PROPN
ejpam-747	365	18	�	�	PROPN
ejpam-747	365	19	z0	z0	PROPN
ejpam-747	365	20	�	�	PROPN
ejpam-747	365	21	+	+	CCONJ
ejpam-747	365	22	z0	z0	PROPN
ejpam-747	365	23			PROPN
ejpam-747	365	24			NUM
ejpam-747	365	25	z0	z0	PROPN
ejpam-747	365	26	�	�	PROPN
ejpam-747	365	27	f	f	PROPN
ejpam-747	365	28	∗	∗	VERB
ejpam-747	365	29	g	g	PROPN
ejpam-747	365	30	�	�	PROPN
ejpam-747	365	31	m+1	m+1	PROPN
ejpam-747	365	32	�	�	PROPN
ejpam-747	365	33	z0	z0	PROPN
ejpam-747	365	34	�	�	PROPN
ejpam-747	365	35	�	�	PROPN
ejpam-747	365	36	f	f	PROPN
ejpam-747	365	37	∗	∗	PROPN
ejpam-747	365	38	h	h	PROPN
ejpam-747	365	39	�	�	PROPN
ejpam-747	365	40	m	m	PROPN
ejpam-747	365	41	�	�	PROPN
ejpam-747	365	42	z0	z0	PROPN
ejpam-747	365	43	�	�	PROPN
ejpam-747	365	44			PROPN
ejpam-747	365	45			PROPN
ejpam-747	365	46	′	′	NOUN
ejpam-747	365	47			NOUN
ejpam-747	365	48			PUNCT
ejpam-747	366	1			PROPN
ejpam-747	366	2			PROPN
ejpam-747	366	3			NOUN
ejpam-747	366	4	(	(	PUNCT
ejpam-747	366	5	26	26	NUM
ejpam-747	366	6	)	)	PUNCT
ejpam-747	366	7	=	=	SYM
ejpam-747	367	1	−	−	PROPN
ejpam-747	367	2	β	β	X
ejpam-747	367	3	p	p	X
ejpam-747	367	4	π	π	PROPN
ejpam-747	367	5	2	2	NUM
ejpam-747	367	6	+	+	CCONJ
ejpam-747	367	7	tan−1	tan−1	PROPN
ejpam-747	367	8	�	�	PROPN
ejpam-747	367	9	l	l	NOUN
ejpam-747	367	10	β	β	PROPN
ejpam-747	367	11	p	p	X
ejpam-747	367	12	�	�	PROPN
ejpam-747	367	13	≤	≤	PROPN
ejpam-747	367	14	−	−	PROPN
ejpam-747	367	15	�	�	PROPN
ejpam-747	367	16	β	β	X
ejpam-747	367	17	p	p	PROPN
ejpam-747	367	18	π	π	PROPN
ejpam-747	367	19	2	2	NUM
ejpam-747	367	20	+	+	CCONJ
ejpam-747	367	21	tan−1	tan−1	PROPN
ejpam-747	367	22	�	�	PROPN
ejpam-747	367	23	β	β	X
ejpam-747	367	24	p	p	PROPN
ejpam-747	367	25	�	�	PROPN
ejpam-747	367	26	�	�	PROPN
ejpam-747	367	27	.	.	PUNCT
ejpam-747	368	1	thus	thus	ADV
ejpam-747	368	2	we	we	PRON
ejpam-747	368	3	see	see	VERB
ejpam-747	368	4	that	that	SCONJ
ejpam-747	368	5	(	(	PUNCT
ejpam-747	368	6	25	25	NUM
ejpam-747	368	7	)	)	PUNCT
ejpam-747	368	8	and	and	CCONJ
ejpam-747	368	9	(	(	PUNCT
ejpam-747	368	10	26	26	NUM
ejpam-747	368	11	)	)	PUNCT
ejpam-747	368	12	contradicts	contradict	VERB
ejpam-747	368	13	the	the	DET
ejpam-747	368	14	condition	condition	NOUN
ejpam-747	368	15	(	(	PUNCT
ejpam-747	368	16	24	24	NUM
ejpam-747	368	17	)	)	PUNCT
ejpam-747	368	18	.	.	PUNCT
ejpam-747	369	1	consequently	consequently	ADV
ejpam-747	369	2	,	,	PUNCT
ejpam-747	369	3	we	we	PRON
ejpam-747	369	4	conclude	conclude	VERB
ejpam-747	369	5	that	that	SCONJ
ejpam-747	369	6	�	�	PROPN
ejpam-747	369	7	�	�	PROPN
ejpam-747	369	8	arg	arg	PROPN
ejpam-747	369	9	p(z	p(z	NOUN
ejpam-747	369	10	)	)	PUNCT
ejpam-747	369	11	�	�	PROPN
ejpam-747	369	12	�	�	PROPN
ejpam-747	369	13	<	<	X
ejpam-747	369	14	β	β	X
ejpam-747	369	15	p	p	X
ejpam-747	369	16	π	π	PROPN
ejpam-747	369	17	2	2	NUM
ejpam-747	369	18	(	(	PUNCT
ejpam-747	369	19	z	z	NOUN
ejpam-747	369	20	∈∆	∈∆	NOUN
ejpam-747	369	21	)	)	PUNCT
ejpam-747	369	22	.	.	PUNCT
ejpam-747	370	1	this	this	PRON
ejpam-747	370	2	proves	prove	VERB
ejpam-747	370	3	theorem	theorem	ADJ
ejpam-747	370	4	6	6	NUM
ejpam-747	370	5	.	.	NOUN
ejpam-747	370	6	4	4	NUM
ejpam-747	370	7	.	.	X
ejpam-747	370	8	integral	integral	ADJ
ejpam-747	370	9	means	mean	NOUN
ejpam-747	370	10	inequality	inequality	NOUN
ejpam-747	370	11	for	for	ADP
ejpam-747	370	12	the	the	DET
ejpam-747	370	13	class	class	NOUN
ejpam-747	371	1	ℜg	ℜg	PROPN
ejpam-747	371	2	h	h	NOUN
ejpam-747	371	3	�	�	PROPN
ejpam-747	371	4	p	p	PROPN
ejpam-747	371	5	,	,	PUNCT
ejpam-747	371	6	m	m	PROPN
ejpam-747	371	7	,	,	PUNCT
ejpam-747	371	8	β	β	X
ejpam-747	371	9	�	�	PROPN
ejpam-747	371	10	definition	definition	NOUN
ejpam-747	371	11	3	3	NUM
ejpam-747	371	12	.	.	PUNCT
ejpam-747	372	1	[	[	X
ejpam-747	372	2	subordination	subordination	NOUN
ejpam-747	372	3	principle	principle	NOUN
ejpam-747	372	4	]	]	X
ejpam-747	372	5	.	.	PUNCT
ejpam-747	373	1	for	for	ADP
ejpam-747	373	2	two	two	NUM
ejpam-747	373	3	functions	function	NOUN
ejpam-747	373	4	f1	f1	NOUN
ejpam-747	373	5	and	and	CCONJ
ejpam-747	373	6	f2	f2	PROPN
ejpam-747	373	7	,	,	PUNCT
ejpam-747	373	8	analytic	analytic	ADJ
ejpam-747	373	9	in	in	ADP
ejpam-747	373	10	∆	∆	PROPN
ejpam-747	373	11	,	,	PUNCT
ejpam-747	373	12	we	we	PRON
ejpam-747	373	13	say	say	VERB
ejpam-747	373	14	that	that	SCONJ
ejpam-747	373	15	the	the	DET
ejpam-747	373	16	function	function	NOUN
ejpam-747	373	17	f1	f1	NOUN
ejpam-747	373	18	(	(	PUNCT
ejpam-747	373	19	z	z	NOUN
ejpam-747	373	20	)	)	PUNCT
ejpam-747	373	21	is	be	AUX
ejpam-747	373	22	subordinate	subordinate	ADJ
ejpam-747	373	23	to	to	ADP
ejpam-747	373	24	f2	f2	PROPN
ejpam-747	373	25	(	(	PUNCT
ejpam-747	373	26	z	z	NOUN
ejpam-747	373	27	)	)	PUNCT
ejpam-747	373	28	in	in	ADP
ejpam-747	373	29	∆	∆	PROPN
ejpam-747	373	30	,	,	PUNCT
ejpam-747	373	31	and	and	CCONJ
ejpam-747	373	32	write	write	VERB
ejpam-747	373	33	f1	f1	PROPN
ejpam-747	373	34	(	(	PUNCT
ejpam-747	373	35	z	z	NOUN
ejpam-747	373	36	)	)	PUNCT
ejpam-747	373	37	≺	≺	NOUN
ejpam-747	373	38	f2	f2	PROPN
ejpam-747	373	39	(	(	PUNCT
ejpam-747	373	40	z	z	NOUN
ejpam-747	373	41	)	)	PUNCT
ejpam-747	373	42	(	(	PUNCT
ejpam-747	373	43	z	z	NOUN
ejpam-747	373	44	∈∆	∈∆	NOUN
ejpam-747	373	45	)	)	PUNCT
ejpam-747	373	46	,	,	PUNCT
ejpam-747	373	47	if	if	SCONJ
ejpam-747	373	48	there	there	PRON
ejpam-747	373	49	exists	exist	VERB
ejpam-747	373	50	a	a	DET
ejpam-747	373	51	schwartz	schwartz	PROPN
ejpam-747	373	52	function	function	PROPN
ejpam-747	373	53	w	w	PROPN
ejpam-747	373	54	(	(	PUNCT
ejpam-747	373	55	z	z	NOUN
ejpam-747	373	56	)	)	PUNCT
ejpam-747	373	57	,	,	PUNCT
ejpam-747	373	58	analytic	analytic	ADJ
ejpam-747	373	59	in	in	ADP
ejpam-747	373	60	∆	∆	PROPN
ejpam-747	373	61	with	with	ADP
ejpam-747	373	62	w	w	PROPN
ejpam-747	373	63	(	(	PUNCT
ejpam-747	373	64	0	0	NUM
ejpam-747	373	65	)	)	PUNCT
ejpam-747	373	66	=	=	SYM
ejpam-747	373	67	0	0	NUM
ejpam-747	373	68	and	and	CCONJ
ejpam-747	373	69	|w	|w	NOUN
ejpam-747	373	70	(	(	PUNCT
ejpam-747	373	71	z)|	z)|	X
ejpam-747	373	72	<	<	X
ejpam-747	373	73	1	1	NUM
ejpam-747	373	74	,	,	PUNCT
ejpam-747	373	75	such	such	ADJ
ejpam-747	373	76	that	that	DET
ejpam-747	373	77	f1	f1	NOUN
ejpam-747	373	78	(	(	PUNCT
ejpam-747	373	79	z	z	NOUN
ejpam-747	373	80	)	)	PUNCT
ejpam-747	373	81	=	=	PRON
ejpam-747	374	1	f2	f2	PROPN
ejpam-747	374	2	(	(	PUNCT
ejpam-747	374	3	w	w	PROPN
ejpam-747	374	4	(	(	PUNCT
ejpam-747	374	5	z	z	NOUN
ejpam-747	374	6	)	)	PUNCT
ejpam-747	374	7	)	)	PUNCT
ejpam-747	375	1	(	(	PUNCT
ejpam-747	375	2	z	z	NOUN
ejpam-747	375	3	∈∆	∈∆	NOUN
ejpam-747	375	4	)	)	PUNCT
ejpam-747	375	5	.	.	PUNCT
ejpam-747	376	1	in	in	ADP
ejpam-747	376	2	particular	particular	ADJ
ejpam-747	376	3	,	,	PUNCT
ejpam-747	376	4	if	if	SCONJ
ejpam-747	376	5	the	the	DET
ejpam-747	376	6	function	function	NOUN
ejpam-747	376	7	f2	f2	PROPN
ejpam-747	376	8	is	be	AUX
ejpam-747	376	9	univalent	univalent	ADJ
ejpam-747	376	10	in	in	ADP
ejpam-747	376	11	∆	∆	PROPN
ejpam-747	376	12	,	,	PUNCT
ejpam-747	376	13	the	the	DET
ejpam-747	376	14	subordination	subordination	NOUN
ejpam-747	376	15	is	be	AUX
ejpam-747	376	16	equivalent	equivalent	ADJ
ejpam-747	376	17	to	to	ADP
ejpam-747	376	18	f1	f1	NOUN
ejpam-747	376	19	(	(	PUNCT
ejpam-747	376	20	0	0	NUM
ejpam-747	376	21	)	)	PUNCT
ejpam-747	376	22	=	=	PRON
ejpam-747	376	23	f2	f2	PRON
ejpam-747	376	24	(	(	PUNCT
ejpam-747	376	25	0	0	NUM
ejpam-747	376	26	)	)	PUNCT
ejpam-747	376	27	and	and	CCONJ
ejpam-747	376	28	f1	f1	PROPN
ejpam-747	376	29	(	(	PUNCT
ejpam-747	376	30	∆)⊂	∆)⊂	ADP
ejpam-747	376	31	f2	f2	PROPN
ejpam-747	376	32	(	(	PUNCT
ejpam-747	376	33	∆	∆	PROPN
ejpam-747	376	34	)	)	PUNCT
ejpam-747	376	35	.	.	PUNCT
ejpam-747	377	1	littlewood	littlewood	PROPN
ejpam-747	378	1	[	[	X
ejpam-747	378	2	16	16	NUM
ejpam-747	378	3	]	]	PUNCT
ejpam-747	378	4	proved	prove	VERB
ejpam-747	378	5	the	the	DET
ejpam-747	378	6	following	follow	VERB
ejpam-747	378	7	subordination	subordination	NOUN
ejpam-747	378	8	result	result	NOUN
ejpam-747	378	9	(	(	PUNCT
ejpam-747	378	10	see	see	VERB
ejpam-747	378	11	also	also	ADV
ejpam-747	378	12	duren	duren	PROPN
ejpam-747	379	1	[	[	X
ejpam-747	379	2	11	11	NUM
ejpam-747	379	3	]	]	NUM
ejpam-747	379	4	)	)	PUNCT
ejpam-747	379	5	.	.	PUNCT
ejpam-747	380	1	lemma	lemma	PROPN
ejpam-747	380	2	4	4	NUM
ejpam-747	380	3	.	.	PUNCT
ejpam-747	381	1	[	[	X
ejpam-747	381	2	16	16	NUM
ejpam-747	381	3	]	]	PUNCT
ejpam-747	381	4	if	if	SCONJ
ejpam-747	381	5	f1	f1	PROPN
ejpam-747	381	6	and	and	CCONJ
ejpam-747	381	7	f2	f2	PROPN
ejpam-747	381	8	are	be	AUX
ejpam-747	381	9	analytic	analytic	ADJ
ejpam-747	381	10	in∆	in∆	PROPN
ejpam-747	381	11	with	with	ADP
ejpam-747	381	12	f1	f1	NOUN
ejpam-747	381	13	≺	≺	NOUN
ejpam-747	381	14	f2	f2	PROPN
ejpam-747	381	15	,	,	PUNCT
ejpam-747	381	16	then	then	ADV
ejpam-747	381	17	for	for	ADP
ejpam-747	381	18	τ	τ	PROPN
ejpam-747	381	19	>	>	X
ejpam-747	381	20	0	0	PUNCT
ejpam-747	381	21	and	and	CCONJ
ejpam-747	381	22	z	z	NOUN
ejpam-747	381	23	=	=	SYM
ejpam-747	381	24	reiθ	reiθ	PROPN
ejpam-747	381	25	(	(	PUNCT
ejpam-747	381	26	0	0	NUM
ejpam-747	381	27	<	<	X
ejpam-747	381	28	r	r	NOUN
ejpam-747	381	29	<	<	X
ejpam-747	381	30	1	1	NUM
ejpam-747	381	31	)	)	PUNCT
ejpam-747	381	32	,	,	PUNCT
ejpam-747	381	33	2π	2π	PROPN
ejpam-747	381	34	∫	∫	NOUN
ejpam-747	381	35	0	0	NUM
ejpam-747	381	36	�	�	PROPN
ejpam-747	381	37	�	�	PROPN
ejpam-747	381	38	f1	f1	PROPN
ejpam-747	381	39	(	(	PUNCT
ejpam-747	381	40	z	z	NOUN
ejpam-747	381	41	)	)	PUNCT
ejpam-747	381	42	�	�	PROPN
ejpam-747	381	43	�	�	PROPN
ejpam-747	381	44	τ	τ	PROPN
ejpam-747	381	45	dθ	dθ	PROPN
ejpam-747	381	46	≤	≤	PROPN
ejpam-747	382	1	2π	2π	PROPN
ejpam-747	382	2	∫	∫	NOUN
ejpam-747	382	3	0	0	NUM
ejpam-747	382	4	�	�	PROPN
ejpam-747	382	5	�	�	PROPN
ejpam-747	382	6	f2	f2	PROPN
ejpam-747	382	7	(	(	PUNCT
ejpam-747	382	8	z	z	NOUN
ejpam-747	382	9	)	)	PUNCT
ejpam-747	382	10	�	�	PROPN
ejpam-747	382	11	�	�	PROPN
ejpam-747	382	12	τ	τ	PROPN
ejpam-747	382	13	dθ	dθ	PROPN
ejpam-747	382	14	.	.	PUNCT
ejpam-747	383	1	p.	p.	PROPN
ejpam-747	383	2	sharma	sharma	PROPN
ejpam-747	383	3	,	,	PUNCT
ejpam-747	383	4	p.	p.	PROPN
ejpam-747	383	5	srivastava	srivastava	PROPN
ejpam-747	383	6	/	/	SYM
ejpam-747	383	7	eur	eur	PROPN
ejpam-747	383	8	.	.	PUNCT
ejpam-747	384	1	j.	j.	PROPN
ejpam-747	384	2	pure	pure	PROPN
ejpam-747	384	3	appl	appl	PROPN
ejpam-747	384	4	.	.	PROPN
ejpam-747	384	5	math	math	PROPN
ejpam-747	384	6	,	,	PUNCT
ejpam-747	384	7	3	3	NUM
ejpam-747	384	8	(	(	PUNCT
ejpam-747	384	9	2010	2010	NUM
ejpam-747	384	10	)	)	PUNCT
ejpam-747	384	11	,	,	PUNCT
ejpam-747	384	12	1093	1093	NUM
ejpam-747	384	13	-	-	SYM
ejpam-747	384	14	1112	1112	NUM
ejpam-747	384	15	1108	1108	NUM
ejpam-747	384	16	theorem	theorem	VERB
ejpam-747	384	17	7	7	NUM
ejpam-747	384	18	.	.	PUNCT
ejpam-747	385	1	let	let	VERB
ejpam-747	385	2	g	g	PROPN
ejpam-747	385	3	(	(	PUNCT
ejpam-747	385	4	z	z	NOUN
ejpam-747	385	5	)	)	PUNCT
ejpam-747	385	6	,	,	PUNCT
ejpam-747	385	7	h(z	h(z	NOUN
ejpam-747	385	8	)	)	PUNCT
ejpam-747	385	9	be	be	VERB
ejpam-747	385	10	of	of	ADP
ejpam-747	385	11	the	the	DET
ejpam-747	385	12	form	form	NOUN
ejpam-747	385	13	(	(	PUNCT
ejpam-747	385	14	2	2	NUM
ejpam-747	385	15	)	)	PUNCT
ejpam-747	385	16	,	,	PUNCT
ejpam-747	385	17	(	(	PUNCT
ejpam-747	385	18	3	3	X
ejpam-747	385	19	)	)	PUNCT
ejpam-747	385	20	respectively	respectively	ADV
ejpam-747	385	21	and	and	CCONJ
ejpam-747	385	22	f	f	PROPN
ejpam-747	385	23	∈	∈	PROPN
ejpam-747	385	24	ℜg	ℜg	PROPN
ejpam-747	385	25	h	h	NOUN
ejpam-747	385	26	�	�	PROPN
ejpam-747	385	27	p	p	PROPN
ejpam-747	385	28	,	,	PUNCT
ejpam-747	385	29	m	m	PROPN
ejpam-747	385	30	,	,	PUNCT
ejpam-747	385	31	β	β	X
ejpam-747	385	32	�	�	PROPN
ejpam-747	385	33	be	be	AUX
ejpam-747	385	34	of	of	ADP
ejpam-747	385	35	the	the	DET
ejpam-747	385	36	form	form	NOUN
ejpam-747	385	37	(	(	PUNCT
ejpam-747	385	38	7	7	NUM
ejpam-747	385	39	)	)	PUNCT
ejpam-747	385	40	and	and	CCONJ
ejpam-747	385	41	let	let	VERB
ejpam-747	385	42	for	for	ADP
ejpam-747	385	43	some	some	DET
ejpam-747	385	44	i	i	PRON
ejpam-747	385	45	∈	∈	PROPN
ejpam-747	385	46	n	n	CCONJ
ejpam-747	385	47	,	,	PUNCT
ejpam-747	385	48	ϕi	ϕi	ADP
ejpam-747	385	49	bp+i	bp+i	NOUN
ejpam-747	385	50	=	=	SYM
ejpam-747	385	51	min	min	NOUN
ejpam-747	385	52	k≥1	k≥1	NOUN
ejpam-747	385	53	ϕk	ϕk	ADP
ejpam-747	385	54	bp+k	bp+k	PROPN
ejpam-747	385	55	,	,	PUNCT
ejpam-747	385	56	where	where	SCONJ
ejpam-747	385	57	ϕk	ϕk	ADV
ejpam-747	385	58	:	:	PUNCT
ejpam-747	385	59	=	=	SYM
ejpam-747	385	60	(	(	PUNCT
ejpam-747	385	61	p+k)!dp+k	p+k)!dp+k	PROPN
ejpam-747	385	62	(	(	PUNCT
ejpam-747	385	63	p+k−m	p+k−m	PROPN
ejpam-747	385	64	)	)	PUNCT
ejpam-747	385	65	!	!	PUNCT
ejpam-747	386	1	and	and	CCONJ
ejpam-747	386	2	dp+k	dp+k	NOUN
ejpam-747	386	3	:	:	PUNCT
ejpam-747	386	4	=	=	SYM
ejpam-747	386	5	�	�	PROPN
ejpam-747	386	6	�	�	PROPN
ejpam-747	386	7	p+	p+	PART
ejpam-747	386	8	k−m	k−m	NOUN
ejpam-747	386	9	�	�	PROPN
ejpam-747	386	10	bp+k	bp+k	PROPN
ejpam-747	386	11	−	−	PROPN
ejpam-747	386	12	�	�	PROPN
ejpam-747	386	13	p−m−	p−m−	PROPN
ejpam-747	386	14	β	β	X
ejpam-747	386	15	�	�	PROPN
ejpam-747	386	16	cp+k	cp+k	PROPN
ejpam-747	386	17	�	�	PROPN
ejpam-747	386	18	>	>	X
ejpam-747	386	19	0	0	X
ejpam-747	386	20	.	.	PUNCT
ejpam-747	386	21	also	also	ADV
ejpam-747	386	22	let	let	VERB
ejpam-747	386	23	for	for	ADP
ejpam-747	386	24	such	such	ADJ
ejpam-747	386	25	i	i	PROPN
ejpam-747	386	26	∈	∈	PROPN
ejpam-747	386	27	n	n	CCONJ
ejpam-747	386	28	,	,	PUNCT
ejpam-747	386	29	functions	function	NOUN
ejpam-747	386	30	fi	fi	NOUN
ejpam-747	386	31	and	and	CCONJ
ejpam-747	386	32	gi	gi	NOUN
ejpam-747	386	33	be	be	AUX
ejpam-747	386	34	defined	define	VERB
ejpam-747	386	35	respectively	respectively	ADV
ejpam-747	386	36	by	by	ADP
ejpam-747	386	37	fi	fi	NOUN
ejpam-747	386	38	(	(	PUNCT
ejpam-747	386	39	z	z	NOUN
ejpam-747	386	40	)	)	PUNCT
ejpam-747	386	41	=	=	PUNCT
ejpam-747	387	1	zp	zp	NOUN
ejpam-747	388	1	−	−	NUM
ejpam-747	388	2	βp	βp	PROPN
ejpam-747	388	3	!	!	PROPN
ejpam-747	388	4	�	�	PROPN
ejpam-747	388	5	p+	p+	VERB
ejpam-747	388	6	i	i	PROPN
ejpam-747	388	7	−m	−m	PROPN
ejpam-747	388	8	�	�	PROPN
ejpam-747	388	9	!	!	PUNCT
ejpam-747	389	1	dp+i	dp+i	PROPN
ejpam-747	390	1	�	�	PROPN
ejpam-747	390	2	p+	p+	VERB
ejpam-747	390	3	i	i	PROPN
ejpam-747	390	4	�	�	PROPN
ejpam-747	390	5	!	!	PUNCT
ejpam-747	391	1	�	�	PROPN
ejpam-747	391	2	p−m	p−m	PRON
ejpam-747	391	3	�	�	PROPN
ejpam-747	391	4	!	!	PUNCT
ejpam-747	392	1	zp+i	zp+i	PROPN
ejpam-747	392	2	,	,	PUNCT
ejpam-747	392	3	gi	gi	NOUN
ejpam-747	392	4	=	=	PUNCT
ejpam-747	392	5	zp	zp	PROPN
ejpam-747	392	6	+	+	CCONJ
ejpam-747	392	7	bp+iz	bp+iz	PROPN
ejpam-747	392	8	p+i	p+i	NUM
ejpam-747	392	9	,	,	PUNCT
ejpam-747	392	10	(	(	PUNCT
ejpam-747	392	11	27	27	NUM
ejpam-747	392	12	)	)	PUNCT
ejpam-747	392	13	if	if	SCONJ
ejpam-747	392	14	there	there	PRON
ejpam-747	392	15	exists	exist	VERB
ejpam-747	392	16	an	an	DET
ejpam-747	392	17	analytic	analytic	ADJ
ejpam-747	392	18	function	function	NOUN
ejpam-747	393	1	w	w	ADP
ejpam-747	393	2	defined	define	VERB
ejpam-747	393	3	by	by	ADP
ejpam-747	393	4	{	{	PUNCT
ejpam-747	393	5	w	w	PROPN
ejpam-747	393	6	(	(	PUNCT
ejpam-747	393	7	z)}i	z)}i	NUM
ejpam-747	393	8	=	=	SYM
ejpam-747	393	9	dp+i	dp+i	PROPN
ejpam-747	393	10	�	�	PROPN
ejpam-747	393	11	p+	p+	VERB
ejpam-747	393	12	i	i	PROPN
ejpam-747	393	13	�	�	PROPN
ejpam-747	393	14	!	!	PUNCT
ejpam-747	393	15	�	�	PROPN
ejpam-747	393	16	p−m	p−m	PRON
ejpam-747	393	17	�	�	PROPN
ejpam-747	393	18	!	!	PUNCT
ejpam-747	394	1	bp+iβp	bp+iβp	PROPN
ejpam-747	394	2	!	!	PUNCT
ejpam-747	395	1	�	�	PROPN
ejpam-747	395	2	p+	p+	VERB
ejpam-747	395	3	i	i	PRON
ejpam-747	395	4	−m	−m	PROPN
ejpam-747	395	5	�	�	PROPN
ejpam-747	395	6	!	!	PUNCT
ejpam-747	396	1	∞	∞	PROPN
ejpam-747	396	2	∑	∑	PUNCT
ejpam-747	397	1	k=1	k=1	PROPN
ejpam-747	397	2	ap+k	ap+k	PROPN
ejpam-747	397	3	bp+kzk	bp+kzk	ADV
ejpam-747	397	4	then	then	ADV
ejpam-747	397	5	,	,	PUNCT
ejpam-747	397	6	for	for	ADP
ejpam-747	397	7	τ	τ	PROPN
ejpam-747	397	8	>	>	X
ejpam-747	397	9	0	0	PUNCT
ejpam-747	397	10	and	and	CCONJ
ejpam-747	397	11	z	z	NOUN
ejpam-747	397	12	=	=	SYM
ejpam-747	397	13	reiθ	reiθ	PROPN
ejpam-747	397	14	(	(	PUNCT
ejpam-747	397	15	0	0	NUM
ejpam-747	397	16	<	<	X
ejpam-747	397	17	r	r	NOUN
ejpam-747	397	18	<	<	X
ejpam-747	397	19	1	1	NUM
ejpam-747	397	20	)	)	PUNCT
ejpam-747	397	21	,	,	PUNCT
ejpam-747	397	22	2π	2π	PROPN
ejpam-747	397	23	∫	∫	NOUN
ejpam-747	397	24	0	0	NUM
ejpam-747	397	25	�	�	PROPN
ejpam-747	397	26	�	�	PROPN
ejpam-747	397	27	�	�	PROPN
ejpam-747	397	28	f	f	PROPN
ejpam-747	397	29	∗	∗	VERB
ejpam-747	397	30	g	g	PROPN
ejpam-747	397	31	�	�	PROPN
ejpam-747	397	32	(	(	PUNCT
ejpam-747	397	33	z	z	NOUN
ejpam-747	397	34	)	)	PUNCT
ejpam-747	397	35	�	�	PROPN
ejpam-747	397	36	�	�	PROPN
ejpam-747	397	37	τ	τ	PROPN
ejpam-747	397	38	dθ	dθ	PROPN
ejpam-747	397	39	≤	≤	PROPN
ejpam-747	398	1	2π	2π	PROPN
ejpam-747	398	2	∫	∫	NOUN
ejpam-747	398	3	0	0	NUM
ejpam-747	398	4	�	�	PROPN
ejpam-747	398	5	�	�	PROPN
ejpam-747	398	6	�	�	PROPN
ejpam-747	398	7	fi	fi	NOUN
ejpam-747	398	8	∗	∗	PROPN
ejpam-747	398	9	gi	gi	PROPN
ejpam-747	398	10	�	�	PROPN
ejpam-747	398	11	�	�	PROPN
ejpam-747	398	12	�	�	PROPN
ejpam-747	398	13	τ	τ	PROPN
ejpam-747	398	14	dθ	dθ	PROPN
ejpam-747	398	15	(	(	PUNCT
ejpam-747	398	16	τ	τ	X
ejpam-747	398	17	>	>	X
ejpam-747	398	18	0	0	NUM
ejpam-747	398	19	)	)	PUNCT
ejpam-747	398	20	.	.	PUNCT
ejpam-747	399	1	proof	proof	NOUN
ejpam-747	399	2	.	.	PUNCT
ejpam-747	400	1	convolution	convolution	NOUN
ejpam-747	400	2	of	of	ADP
ejpam-747	400	3	f	f	PROPN
ejpam-747	400	4	and	and	CCONJ
ejpam-747	400	5	g	g	PROPN
ejpam-747	400	6	is	be	AUX
ejpam-747	400	7	defined	define	VERB
ejpam-747	400	8	as	as	ADP
ejpam-747	400	9	:	:	PUNCT
ejpam-747	400	10	�	�	PROPN
ejpam-747	400	11	f	f	PROPN
ejpam-747	400	12	∗	∗	VERB
ejpam-747	400	13	g	g	PROPN
ejpam-747	400	14	�	�	PROPN
ejpam-747	400	15	(	(	PUNCT
ejpam-747	400	16	z	z	NOUN
ejpam-747	400	17	)	)	PUNCT
ejpam-747	401	1	=	=	SYM
ejpam-747	401	2	zp	zp	PROPN
ejpam-747	401	3	−	−	NOUN
ejpam-747	401	4	∞	∞	NUM
ejpam-747	401	5	∑	∑	PUNCT
ejpam-747	402	1	k=1	k=1	ADP
ejpam-747	402	2	ap+k	ap+k	NOUN
ejpam-747	402	3	bp+kzp+k	bp+kzp+k	ADV
ejpam-747	402	4	=	=	PUNCT
ejpam-747	402	5	zp	zp	NOUN
ejpam-747	402	6	1−	1−	NUM
ejpam-747	402	7	∞	∞	NUM
ejpam-747	402	8	∑	∑	PUNCT
ejpam-747	402	9	k=1	k=1	VERB
ejpam-747	402	10	ap+k	ap+k	PRON
ejpam-747	402	11	bp+kzk	bp+kzk	ADV
ejpam-747	402	12	!	!	PUNCT
ejpam-747	403	1	similarly	similarly	ADV
ejpam-747	403	2	,	,	PUNCT
ejpam-747	403	3	from	from	ADP
ejpam-747	403	4	(	(	PUNCT
ejpam-747	403	5	27	27	NUM
ejpam-747	403	6	)	)	PUNCT
ejpam-747	403	7	,	,	PUNCT
ejpam-747	403	8	we	we	PRON
ejpam-747	403	9	obtain	obtain	VERB
ejpam-747	403	10	�	�	PROPN
ejpam-747	403	11	fi	fi	NOUN
ejpam-747	403	12	∗	∗	NOUN
ejpam-747	403	13	gi	gi	NOUN
ejpam-747	403	14	�	�	PROPN
ejpam-747	403	15	(	(	PUNCT
ejpam-747	403	16	z	z	NOUN
ejpam-747	403	17	)	)	PUNCT
ejpam-747	403	18	=	=	SYM
ejpam-747	403	19	zp	zp	PROPN
ejpam-747	404	1	−	−	PROPN
ejpam-747	404	2	bp+iβp	bp+iβp	PROPN
ejpam-747	404	3	!	!	PUNCT
ejpam-747	405	1	�	�	PROPN
ejpam-747	405	2	p+	p+	VERB
ejpam-747	405	3	i	i	PROPN
ejpam-747	405	4	−m	−m	PROPN
ejpam-747	405	5	�	�	PROPN
ejpam-747	405	6	!	!	PUNCT
ejpam-747	406	1	dp+i	dp+i	PROPN
ejpam-747	407	1	�	�	PROPN
ejpam-747	407	2	p+	p+	VERB
ejpam-747	407	3	i	i	PROPN
ejpam-747	407	4	�	�	PROPN
ejpam-747	407	5	!	!	PUNCT
ejpam-747	408	1	�	�	PROPN
ejpam-747	408	2	p−m	p−m	PRON
ejpam-747	408	3	�	�	PROPN
ejpam-747	408	4	!	!	PUNCT
ejpam-747	409	1	zp+i	zp+i	X
ejpam-747	409	2	=	=	SYM
ejpam-747	409	3	zp	zp	PROPN
ejpam-747	409	4	�	�	PROPN
ejpam-747	409	5	1−	1−	NUM
ejpam-747	409	6	bp+iβp	bp+iβp	PROPN
ejpam-747	409	7	!	!	PUNCT
ejpam-747	410	1	�	�	PROPN
ejpam-747	410	2	p+	p+	VERB
ejpam-747	410	3	i	i	PROPN
ejpam-747	410	4	−m	−m	PROPN
ejpam-747	410	5	�	�	PROPN
ejpam-747	410	6	!	!	PUNCT
ejpam-747	411	1	dp+i	dp+i	PROPN
ejpam-747	412	1	�	�	PROPN
ejpam-747	412	2	p+	p+	VERB
ejpam-747	412	3	i	i	PROPN
ejpam-747	412	4	�	�	PROPN
ejpam-747	412	5	!	!	PUNCT
ejpam-747	413	1	�	�	PROPN
ejpam-747	413	2	p−m	p−m	PRON
ejpam-747	413	3	�	�	PROPN
ejpam-747	413	4	!	!	PUNCT
ejpam-747	414	1	z	z	VERB
ejpam-747	415	1	i	i	PRON
ejpam-747	415	2	�	�	PROPN
ejpam-747	415	3	.	.	PUNCT
ejpam-747	416	1	to	to	PART
ejpam-747	416	2	prove	prove	VERB
ejpam-747	416	3	the	the	DET
ejpam-747	416	4	theorem	theorem	NOUN
ejpam-747	416	5	,	,	PUNCT
ejpam-747	416	6	we	we	PRON
ejpam-747	416	7	must	must	AUX
ejpam-747	416	8	show	show	VERB
ejpam-747	416	9	that	that	SCONJ
ejpam-747	416	10	for	for	ADP
ejpam-747	416	11	τ	τ	PROPN
ejpam-747	416	12	>	>	X
ejpam-747	416	13	0	0	PUNCT
ejpam-747	416	14	and	and	CCONJ
ejpam-747	416	15	z	z	NOUN
ejpam-747	416	16	=	=	SYM
ejpam-747	416	17	reiθ	reiθ	PROPN
ejpam-747	416	18	(	(	PUNCT
ejpam-747	416	19	0	0	NUM
ejpam-747	416	20	<	<	X
ejpam-747	416	21	r	r	NOUN
ejpam-747	416	22	<	<	X
ejpam-747	416	23	1	1	NUM
ejpam-747	416	24	)	)	PUNCT
ejpam-747	416	25	,	,	PUNCT
ejpam-747	416	26	2π	2π	PROPN
ejpam-747	416	27	∫	∫	NOUN
ejpam-747	416	28	0	0	NUM
ejpam-747	416	29	�	�	PROPN
ejpam-747	416	30	�	�	PROPN
ejpam-747	416	31	�	�	PROPN
ejpam-747	416	32	�	�	PROPN
ejpam-747	416	33	�	�	PROPN
ejpam-747	416	34	1−	1−	NUM
ejpam-747	416	35	∞	∞	NUM
ejpam-747	416	36	∑	∑	PUNCT
ejpam-747	416	37	k=1	k=1	ADP
ejpam-747	416	38	ap+k	ap+k	PROPN
ejpam-747	416	39	bp+kzk	bp+kzk	PROPN
ejpam-747	416	40	�	�	PROPN
ejpam-747	416	41	�	�	PROPN
ejpam-747	416	42	�	�	PROPN
ejpam-747	416	43	�	�	PROPN
ejpam-747	416	44	�	�	PROPN
ejpam-747	416	45	τ	τ	PROPN
ejpam-747	416	46	dθ	dθ	PROPN
ejpam-747	416	47	≤	≤	PROPN
ejpam-747	416	48	2π	2π	PROPN
ejpam-747	416	49	∫	∫	NOUN
ejpam-747	416	50	0	0	NUM
ejpam-747	416	51	�	�	PROPN
ejpam-747	416	52	�	�	PROPN
ejpam-747	416	53	�	�	PROPN
ejpam-747	416	54	�	�	PROPN
ejpam-747	416	55	�	�	PROPN
ejpam-747	416	56	1−	1−	NUM
ejpam-747	416	57	bp+iβp	bp+iβp	PROPN
ejpam-747	416	58	!	!	PUNCT
ejpam-747	417	1	�	�	PROPN
ejpam-747	417	2	p+	p+	VERB
ejpam-747	417	3	i	i	PROPN
ejpam-747	417	4	−m	−m	PROPN
ejpam-747	417	5	�	�	PROPN
ejpam-747	417	6	!	!	PUNCT
ejpam-747	418	1	dp+i	dp+i	PROPN
ejpam-747	419	1	�	�	PROPN
ejpam-747	419	2	p+	p+	VERB
ejpam-747	419	3	i	i	PROPN
ejpam-747	419	4	�	�	PROPN
ejpam-747	419	5	!	!	PUNCT
ejpam-747	420	1	�	�	PROPN
ejpam-747	420	2	p−m	p−m	PRON
ejpam-747	420	3	�	�	PROPN
ejpam-747	420	4	!	!	PUNCT
ejpam-747	421	1	z	z	VERB
ejpam-747	422	1	i	i	PRON
ejpam-747	422	2	�	�	PROPN
ejpam-747	422	3	�	�	PROPN
ejpam-747	422	4	�	�	PROPN
ejpam-747	422	5	�	�	PROPN
ejpam-747	422	6	�	�	PROPN
ejpam-747	422	7	τ	τ	PROPN
ejpam-747	422	8	dθ	dθ	PROPN
ejpam-747	422	9	.	.	PUNCT
ejpam-747	423	1	thus	thus	ADV
ejpam-747	423	2	,	,	PUNCT
ejpam-747	423	3	by	by	ADP
ejpam-747	423	4	applying	apply	VERB
ejpam-747	423	5	lemma	lemma	PROPN
ejpam-747	423	6	4	4	NUM
ejpam-747	423	7	,	,	PUNCT
ejpam-747	423	8	it	it	PRON
ejpam-747	423	9	would	would	AUX
ejpam-747	423	10	suffice	suffice	VERB
ejpam-747	423	11	to	to	PART
ejpam-747	423	12	show	show	VERB
ejpam-747	423	13	that	that	SCONJ
ejpam-747	423	14	1−	1−	NUM
ejpam-747	423	15	∞	∞	NUM
ejpam-747	423	16	∑	∑	PUNCT
ejpam-747	423	17	k=1	k=1	ADP
ejpam-747	423	18	ap+k	ap+k	PROPN
ejpam-747	423	19	bp+kzk	bp+kzk	ADJ
ejpam-747	423	20	≺	≺	NOUN
ejpam-747	423	21	1−	1−	NUM
ejpam-747	423	22	bp+iβp	bp+iβp	X
ejpam-747	423	23	!	!	PUNCT
ejpam-747	424	1	�	�	PROPN
ejpam-747	424	2	p+	p+	VERB
ejpam-747	424	3	i	i	PROPN
ejpam-747	424	4	−m	−m	PROPN
ejpam-747	424	5	�	�	PROPN
ejpam-747	424	6	!	!	PUNCT
ejpam-747	425	1	dp+i	dp+i	PROPN
ejpam-747	426	1	�	�	PROPN
ejpam-747	426	2	p+	p+	VERB
ejpam-747	426	3	i	i	PROPN
ejpam-747	426	4	�	�	PROPN
ejpam-747	426	5	!	!	PUNCT
ejpam-747	427	1	�	�	PROPN
ejpam-747	427	2	p−m	p−m	PRON
ejpam-747	427	3	�	�	PROPN
ejpam-747	427	4	!	!	PUNCT
ejpam-747	428	1	z	z	NOUN
ejpam-747	429	1	i	i	PRON
ejpam-747	429	2	.	.	PUNCT
ejpam-747	430	1	(	(	PUNCT
ejpam-747	430	2	28	28	NUM
ejpam-747	430	3	)	)	PUNCT
ejpam-747	430	4	p.	p.	NOUN
ejpam-747	430	5	sharma	sharma	PROPN
ejpam-747	430	6	,	,	PUNCT
ejpam-747	430	7	p.	p.	PROPN
ejpam-747	430	8	srivastava	srivastava	PROPN
ejpam-747	430	9	/	/	SYM
ejpam-747	430	10	eur	eur	PROPN
ejpam-747	430	11	.	.	PUNCT
ejpam-747	431	1	j.	j.	PROPN
ejpam-747	431	2	pure	pure	PROPN
ejpam-747	431	3	appl	appl	PROPN
ejpam-747	431	4	.	.	PROPN
ejpam-747	431	5	math	math	PROPN
ejpam-747	431	6	,	,	PUNCT
ejpam-747	431	7	3	3	NUM
ejpam-747	431	8	(	(	PUNCT
ejpam-747	431	9	2010	2010	NUM
ejpam-747	431	10	)	)	PUNCT
ejpam-747	431	11	,	,	PUNCT
ejpam-747	431	12	1093	1093	NUM
ejpam-747	431	13	-	-	SYM
ejpam-747	431	14	1112	1112	NUM
ejpam-747	431	15	1109	1109	NUM
ejpam-747	431	16	if	if	SCONJ
ejpam-747	431	17	the	the	DET
ejpam-747	431	18	subordination	subordination	NOUN
ejpam-747	431	19	(	(	PUNCT
ejpam-747	431	20	28	28	NUM
ejpam-747	431	21	)	)	PUNCT
ejpam-747	431	22	holds	hold	VERB
ejpam-747	431	23	true	true	ADJ
ejpam-747	431	24	,	,	PUNCT
ejpam-747	431	25	then	then	ADV
ejpam-747	431	26	there	there	PRON
ejpam-747	431	27	exist	exist	VERB
ejpam-747	431	28	an	an	DET
ejpam-747	431	29	analytic	analytic	ADJ
ejpam-747	431	30	function	function	NOUN
ejpam-747	431	31	w	w	NOUN
ejpam-747	431	32	with	with	ADP
ejpam-747	431	33	w	w	PROPN
ejpam-747	431	34	(	(	PUNCT
ejpam-747	431	35	0	0	NUM
ejpam-747	431	36	)	)	PUNCT
ejpam-747	431	37	=	=	SYM
ejpam-747	431	38	0	0	NUM
ejpam-747	431	39	and	and	CCONJ
ejpam-747	431	40	|w	|w	NOUN
ejpam-747	432	1	(	(	PUNCT
ejpam-747	432	2	z)|	z)|	X
ejpam-747	432	3	<	<	X
ejpam-747	432	4	1	1	NUM
ejpam-747	432	5	such	such	ADJ
ejpam-747	432	6	that	that	DET
ejpam-747	432	7	1−	1−	NUM
ejpam-747	432	8	∞	∞	NUM
ejpam-747	432	9	∑	∑	PUNCT
ejpam-747	432	10	k=1	k=1	ADP
ejpam-747	432	11	ap+k	ap+k	PROPN
ejpam-747	432	12	bp+kzk	bp+kzk	PROPN
ejpam-747	432	13	=	=	SYM
ejpam-747	432	14	1−	1−	NUM
ejpam-747	432	15	bp+iβp	bp+iβp	X
ejpam-747	432	16	!	!	PUNCT
ejpam-747	433	1	�	�	PROPN
ejpam-747	433	2	p+	p+	VERB
ejpam-747	433	3	i	i	PROPN
ejpam-747	433	4	−m	−m	PROPN
ejpam-747	433	5	�	�	PROPN
ejpam-747	433	6	!	!	PUNCT
ejpam-747	434	1	dp+i	dp+i	PROPN
ejpam-747	435	1	�	�	PROPN
ejpam-747	435	2	p+	p+	VERB
ejpam-747	435	3	i	i	PROPN
ejpam-747	435	4	�	�	PROPN
ejpam-747	435	5	!	!	PUNCT
ejpam-747	436	1	�	�	PROPN
ejpam-747	436	2	p−m	p−m	PRON
ejpam-747	436	3	�	�	PROPN
ejpam-747	436	4	!	!	PUNCT
ejpam-747	437	1	{	{	PUNCT
ejpam-747	438	1	w	w	X
ejpam-747	438	2	(	(	PUNCT
ejpam-747	438	3	z)}i	z)}i	PROPN
ejpam-747	438	4	.	.	PUNCT
ejpam-747	439	1	from	from	ADP
ejpam-747	439	2	the	the	DET
ejpam-747	439	3	hypothesis	hypothesis	NOUN
ejpam-747	439	4	of	of	ADP
ejpam-747	439	5	the	the	DET
ejpam-747	439	6	theorem	theorem	NOUN
ejpam-747	439	7	,	,	PUNCT
ejpam-747	439	8	there	there	PRON
ejpam-747	439	9	exists	exist	VERB
ejpam-747	439	10	an	an	DET
ejpam-747	439	11	analytic	analytic	ADJ
ejpam-747	439	12	function	function	NOUN
ejpam-747	439	13	w	w	NOUN
ejpam-747	439	14	given	give	VERB
ejpam-747	439	15	by	by	ADP
ejpam-747	439	16	{	{	PUNCT
ejpam-747	439	17	w	w	PROPN
ejpam-747	439	18	(	(	PUNCT
ejpam-747	439	19	z)}i	z)}i	NUM
ejpam-747	439	20	=	=	SYM
ejpam-747	439	21	dp+i	dp+i	PROPN
ejpam-747	439	22	�	�	PROPN
ejpam-747	439	23	p+	p+	VERB
ejpam-747	439	24	i	i	PROPN
ejpam-747	439	25	�	�	PROPN
ejpam-747	439	26	!	!	PUNCT
ejpam-747	440	1	�	�	PROPN
ejpam-747	440	2	p−m	p−m	PRON
ejpam-747	440	3	�	�	PROPN
ejpam-747	440	4	!	!	PUNCT
ejpam-747	441	1	bp+iβp	bp+iβp	PROPN
ejpam-747	441	2	!	!	PUNCT
ejpam-747	442	1	�	�	PROPN
ejpam-747	442	2	p+	p+	VERB
ejpam-747	442	3	i	i	PRON
ejpam-747	442	4	−m	−m	PROPN
ejpam-747	442	5	�	�	PROPN
ejpam-747	442	6	!	!	PUNCT
ejpam-747	443	1	∞	∞	PROPN
ejpam-747	443	2	∑	∑	PUNCT
ejpam-747	444	1	k=1	k=1	PROPN
ejpam-747	444	2	ap+k	ap+k	PROPN
ejpam-747	444	3	bp+kzk	bp+kzk	X
ejpam-747	444	4	which	which	PRON
ejpam-747	444	5	readily	readily	ADV
ejpam-747	444	6	yields	yield	VERB
ejpam-747	444	7	w	w	PROPN
ejpam-747	444	8	(	(	PUNCT
ejpam-747	444	9	0	0	NUM
ejpam-747	444	10	)	)	PUNCT
ejpam-747	444	11	=	=	SYM
ejpam-747	444	12	0	0	X
ejpam-747	444	13	.	.	PUNCT
ejpam-747	444	14	thus	thus	ADV
ejpam-747	444	15	for	for	ADP
ejpam-747	444	16	such	such	ADJ
ejpam-747	444	17	function	function	NOUN
ejpam-747	444	18	w	w	PROPN
ejpam-747	444	19	,	,	PUNCT
ejpam-747	444	20	using	use	VERB
ejpam-747	444	21	the	the	DET
ejpam-747	444	22	hypothesis	hypothesis	NOUN
ejpam-747	444	23	in	in	ADP
ejpam-747	444	24	the	the	DET
ejpam-747	444	25	coefficient	coefficient	NOUN
ejpam-747	444	26	inequality	inequality	NOUN
ejpam-747	444	27	for	for	ADP
ejpam-747	444	28	the	the	DET
ejpam-747	444	29	class	class	NOUN
ejpam-747	444	30	ℜg	ℜg	PROPN
ejpam-747	444	31	h	h	NOUN
ejpam-747	444	32	�	�	PROPN
ejpam-747	444	33	p	p	PROPN
ejpam-747	444	34	,	,	PUNCT
ejpam-747	444	35	m	m	PROPN
ejpam-747	444	36	,	,	PUNCT
ejpam-747	444	37	β	β	X
ejpam-747	444	38	�	�	PROPN
ejpam-747	444	39	,	,	PUNCT
ejpam-747	444	40	we	we	PRON
ejpam-747	444	41	get	get	VERB
ejpam-747	444	42	|w	|w	NOUN
ejpam-747	444	43	(	(	PUNCT
ejpam-747	444	44	z)|r	z)|r	PROPN
ejpam-747	444	45	≤	≤	PROPN
ejpam-747	444	46	dp+i	dp+i	PROPN
ejpam-747	444	47	�	�	PROPN
ejpam-747	444	48	p+	p+	VERB
ejpam-747	444	49	i	i	PROPN
ejpam-747	444	50	�	�	PROPN
ejpam-747	444	51	!	!	PUNCT
ejpam-747	445	1	�	�	PROPN
ejpam-747	445	2	p−m	p−m	PRON
ejpam-747	445	3	�	�	PROPN
ejpam-747	445	4	!	!	PUNCT
ejpam-747	446	1	bp+iβp	bp+iβp	PROPN
ejpam-747	446	2	!	!	PUNCT
ejpam-747	447	1	�	�	PROPN
ejpam-747	447	2	p+	p+	VERB
ejpam-747	447	3	i	i	PRON
ejpam-747	447	4	−m	−m	PROPN
ejpam-747	447	5	�	�	PROPN
ejpam-747	447	6	!	!	PUNCT
ejpam-747	448	1	∞	∞	PROPN
ejpam-747	448	2	∑	∑	PUNCT
ejpam-747	449	1	k=1	k=1	ADP
ejpam-747	449	2	ap+k	ap+k	NOUN
ejpam-747	449	3	bp+k	bp+k	PROPN
ejpam-747	449	4	|z|	|z|	VERB
ejpam-747	449	5	k	k	PROPN
ejpam-747	449	6	≤	≤	PROPN
ejpam-747	449	7	|z|	|z|	NOUN
ejpam-747	449	8	dp+i	dp+i	NOUN
ejpam-747	449	9	�	�	PROPN
ejpam-747	449	10	p+	p+	VERB
ejpam-747	449	11	i	i	PROPN
ejpam-747	449	12	�	�	PROPN
ejpam-747	449	13	!	!	PUNCT
ejpam-747	450	1	�	�	PROPN
ejpam-747	450	2	p−m	p−m	PRON
ejpam-747	450	3	�	�	PROPN
ejpam-747	450	4	!	!	PUNCT
ejpam-747	451	1	bp+iβp	bp+iβp	PROPN
ejpam-747	451	2	!	!	PUNCT
ejpam-747	452	1	�	�	PROPN
ejpam-747	452	2	p+	p+	VERB
ejpam-747	452	3	i	i	PRON
ejpam-747	452	4	−m	−m	PROPN
ejpam-747	452	5	�	�	PROPN
ejpam-747	452	6	!	!	PUNCT
ejpam-747	453	1	∞	∞	PROPN
ejpam-747	453	2	∑	∑	PUNCT
ejpam-747	454	1	k=1	k=1	VERB
ejpam-747	454	2	ap+k	ap+k	NOUN
ejpam-747	454	3	bp+k	bp+k	NOUN
ejpam-747	454	4	≤	≤	NOUN
ejpam-747	454	5	|z|	|z|	VERB
ejpam-747	454	6	<	<	X
ejpam-747	454	7	1	1	NUM
ejpam-747	454	8	.	.	PUNCT
ejpam-747	455	1	therefore	therefore	ADV
ejpam-747	455	2	the	the	DET
ejpam-747	455	3	subordination	subordination	NOUN
ejpam-747	455	4	(	(	PUNCT
ejpam-747	455	5	28	28	NUM
ejpam-747	455	6	)	)	PUNCT
ejpam-747	455	7	holds	hold	VERB
ejpam-747	455	8	true	true	ADJ
ejpam-747	455	9	,	,	PUNCT
ejpam-747	455	10	thus	thus	ADV
ejpam-747	455	11	the	the	DET
ejpam-747	455	12	theorem	theorem	NOUN
ejpam-747	455	13	is	be	AUX
ejpam-747	455	14	proved	prove	VERB
ejpam-747	455	15	.	.	PUNCT
ejpam-747	456	1	5	5	X
ejpam-747	456	2	.	.	X
ejpam-747	456	3	class	class	NOUN
ejpam-747	456	4	-	-	PUNCT
ejpam-747	456	5	preserving	preserve	VERB
ejpam-747	456	6	integral	integral	ADJ
ejpam-747	456	7	-	-	PUNCT
ejpam-747	456	8	operators	operator	NOUN
ejpam-747	456	9	for	for	ADP
ejpam-747	456	10	the	the	DET
ejpam-747	456	11	class	class	NOUN
ejpam-747	456	12	ℜg	ℜg	PROPN
ejpam-747	456	13	h	h	NOUN
ejpam-747	456	14	�	�	PROPN
ejpam-747	456	15	p	p	PROPN
ejpam-747	456	16	,	,	PUNCT
ejpam-747	456	17	m	m	PROPN
ejpam-747	456	18	,	,	PUNCT
ejpam-747	456	19	β	β	X
ejpam-747	456	20	�	�	PROPN
ejpam-747	456	21	in	in	ADP
ejpam-747	456	22	this	this	DET
ejpam-747	456	23	section	section	NOUN
ejpam-747	456	24	,	,	PUNCT
ejpam-747	456	25	we	we	PRON
ejpam-747	456	26	present	present	VERB
ejpam-747	456	27	several	several	ADJ
ejpam-747	456	28	integral	integral	ADJ
ejpam-747	456	29	operators	operator	NOUN
ejpam-747	456	30	which	which	PRON
ejpam-747	456	31	preserve	preserve	VERB
ejpam-747	456	32	class	class	NOUN
ejpam-747	456	33	ℜg	ℜg	PROPN
ejpam-747	456	34	h	h	NOUN
ejpam-747	456	35	�	�	PROPN
ejpam-747	456	36	p	p	PROPN
ejpam-747	456	37	,	,	PUNCT
ejpam-747	456	38	m	m	PROPN
ejpam-747	456	39	,	,	PUNCT
ejpam-747	456	40	β	β	X
ejpam-747	456	41	�	�	PROPN
ejpam-747	456	42	.	.	PUNCT
ejpam-747	457	1	for	for	ADP
ejpam-747	457	2	f	f	PROPN
ejpam-747	457	3	∈	∈	PROPN
ejpam-747	457	4	ℜg	ℜg	PROPN
ejpam-747	457	5	h	h	NOUN
ejpam-747	457	6	�	�	PROPN
ejpam-747	457	7	p	p	PROPN
ejpam-747	457	8	,	,	PUNCT
ejpam-747	457	9	m	m	PROPN
ejpam-747	457	10	,	,	PUNCT
ejpam-747	457	11	β	β	X
ejpam-747	457	12	�	�	PROPN
ejpam-747	457	13	,	,	PUNCT
ejpam-747	457	14	we	we	PRON
ejpam-747	457	15	define	define	VERB
ejpam-747	457	16	the	the	DET
ejpam-747	457	17	integral	integral	ADJ
ejpam-747	457	18	operators	operator	NOUN
ejpam-747	457	19	by	by	ADP
ejpam-747	457	20	l1	l1	PROPN
ejpam-747	457	21	f	f	PROPN
ejpam-747	457	22	(	(	PUNCT
ejpam-747	457	23	z	z	NOUN
ejpam-747	457	24	)	)	PUNCT
ejpam-747	457	25	=	=	SYM
ejpam-747	457	26	�	�	PROPN
ejpam-747	457	27	p+	p+	PROPN
ejpam-747	457	28	c	c	PROPN
ejpam-747	457	29	�	�	PROPN
ejpam-747	457	30	zc	zc	PROPN
ejpam-747	457	31	z	z	PROPN
ejpam-747	457	32	∫	∫	PROPN
ejpam-747	457	33	0	0	PROPN
ejpam-747	458	1	t	t	PROPN
ejpam-747	458	2	c−1	c−1	PROPN
ejpam-747	458	3	f	f	PROPN
ejpam-747	458	4	(	(	PUNCT
ejpam-747	458	5	t	t	PROPN
ejpam-747	458	6	)	)	PUNCT
ejpam-747	458	7	d	d	PROPN
ejpam-747	458	8	t	t	PROPN
ejpam-747	458	9	,	,	PUNCT
ejpam-747	458	10	c	c	X
ejpam-747	458	11	>	>	X
ejpam-747	458	12	−p	−p	NOUN
ejpam-747	458	13	,	,	PUNCT
ejpam-747	458	14	l2	l2	NOUN
ejpam-747	458	15	f	f	X
ejpam-747	458	16	(	(	PUNCT
ejpam-747	458	17	z	z	NOUN
ejpam-747	458	18	)	)	PUNCT
ejpam-747	458	19	=	=	SYM
ejpam-747	458	20	�	�	PROPN
ejpam-747	458	21	p+	p+	PROPN
ejpam-747	458	22	c	c	PROPN
ejpam-747	458	23	�	�	PROPN
ejpam-747	458	24	σ	σ	PROPN
ejpam-747	458	25	zcγ(σ	zcγ(σ	PROPN
ejpam-747	458	26	)	)	PUNCT
ejpam-747	458	27	z	z	NOUN
ejpam-747	458	28	∫	∫	PROPN
ejpam-747	458	29	0	0	NUM
ejpam-747	459	1	t	t	PROPN
ejpam-747	459	2	c−1	c−1	PROPN
ejpam-747	459	3	�	�	PROPN
ejpam-747	459	4	log	log	VERB
ejpam-747	459	5	z	z	PROPN
ejpam-747	459	6	t	t	PROPN
ejpam-747	459	7	�	�	PROPN
ejpam-747	460	1	σ−1	σ−1	PROPN
ejpam-747	460	2	f	f	PROPN
ejpam-747	460	3	(	(	PUNCT
ejpam-747	460	4	t	t	PROPN
ejpam-747	460	5	)	)	PUNCT
ejpam-747	460	6	d	d	PROPN
ejpam-747	460	7	t	t	PROPN
ejpam-747	460	8	,	,	PUNCT
ejpam-747	460	9	c	c	X
ejpam-747	460	10	>	>	X
ejpam-747	460	11	−p	−p	NOUN
ejpam-747	460	12	,	,	PUNCT
ejpam-747	460	13	σ	σ	X
ejpam-747	460	14	≥	≥	NOUN
ejpam-747	460	15	0	0	NUM
ejpam-747	460	16	,	,	PUNCT
ejpam-747	460	17	l3	l3	PROPN
ejpam-747	460	18	f	f	PROPN
ejpam-747	460	19	(	(	PUNCT
ejpam-747	460	20	z	z	NOUN
ejpam-747	460	21	)	)	PUNCT
ejpam-747	460	22	=	=	SYM
ejpam-747	460	23	�	�	PROPN
ejpam-747	460	24	p+	p+	NOUN
ejpam-747	460	25	c	c	PROPN
ejpam-747	461	1	+	+	NOUN
ejpam-747	461	2	σ−	σ−	PROPN
ejpam-747	461	3	1	1	NUM
ejpam-747	461	4	p+	p+	NOUN
ejpam-747	461	5	c	c	NOUN
ejpam-747	461	6	−	−	PROPN
ejpam-747	461	7	1	1	NUM
ejpam-747	461	8	�	�	PROPN
ejpam-747	461	9	σ	σ	PROPN
ejpam-747	461	10	zc	zc	PROPN
ejpam-747	461	11	z	z	PROPN
ejpam-747	461	12	∫	∫	PROPN
ejpam-747	461	13	0	0	PROPN
ejpam-747	461	14	�	�	PROPN
ejpam-747	461	15	1−	1−	NUM
ejpam-747	461	16	t	t	PROPN
ejpam-747	461	17	z	z	NOUN
ejpam-747	461	18	�	�	PROPN
ejpam-747	462	1	σ−1	σ−1	PROPN
ejpam-747	462	2	t	t	NOUN
ejpam-747	462	3	c−1	c−1	PROPN
ejpam-747	462	4	f	f	PROPN
ejpam-747	462	5	(	(	PUNCT
ejpam-747	462	6	t	t	PROPN
ejpam-747	462	7	)	)	PUNCT
ejpam-747	462	8	d	d	PROPN
ejpam-747	462	9	t	t	PROPN
ejpam-747	462	10	,	,	PUNCT
ejpam-747	462	11	c	c	X
ejpam-747	462	12	>	>	X
ejpam-747	462	13	−p	−p	NOUN
ejpam-747	462	14	,	,	PUNCT
ejpam-747	462	15	σ	σ	X
ejpam-747	462	16	≥	≥	NOUN
ejpam-747	462	17	0	0	NUM
ejpam-747	462	18	.	.	PUNCT
ejpam-747	462	19	theorem	theorem	NOUN
ejpam-747	462	20	8	8	NUM
ejpam-747	462	21	.	.	PUNCT
ejpam-747	463	1	let	let	VERB
ejpam-747	463	2	f	f	PROPN
ejpam-747	463	3	∈	∈	PROPN
ejpam-747	463	4	ℜg	ℜg	PROPN
ejpam-747	463	5	h	h	NOUN
ejpam-747	463	6	�	�	PROPN
ejpam-747	463	7	p	p	PROPN
ejpam-747	463	8	,	,	PUNCT
ejpam-747	463	9	m	m	PROPN
ejpam-747	463	10	,	,	PUNCT
ejpam-747	463	11	β	β	X
ejpam-747	463	12	�	�	PROPN
ejpam-747	463	13	,	,	PUNCT
ejpam-747	463	14	then	then	ADV
ejpam-747	463	15	for	for	ADP
ejpam-747	463	16	p	p	PROPN
ejpam-747	463	17	>	>	X
ejpam-747	463	18	m	m	PROPN
ejpam-747	463	19	,	,	PUNCT
ejpam-747	463	20	0	0	PUNCT
ejpam-747	463	21	<	<	X
ejpam-747	463	22	β	β	X
ejpam-747	463	23	≤	≤	NOUN
ejpam-747	463	24	p	p	X
ejpam-747	463	25	,	,	PUNCT
ejpam-747	463	26	c	c	X
ejpam-747	463	27	>	>	X
ejpam-747	463	28	−p	−p	NOUN
ejpam-747	463	29	and	and	CCONJ
ejpam-747	463	30	σ	σ	PROPN
ejpam-747	463	31	≥	≥	PROPN
ejpam-747	463	32	0	0	NUM
ejpam-747	463	33	,	,	PUNCT
ejpam-747	463	34	l	l	PROPN
ejpam-747	463	35	j	j	PROPN
ejpam-747	463	36	f	f	X
ejpam-747	463	37	∈	∈	PROPN
ejpam-747	463	38	ℜg	ℜg	PROPN
ejpam-747	463	39	h	h	NOUN
ejpam-747	463	40	�	�	PROPN
ejpam-747	463	41	p	p	PROPN
ejpam-747	463	42	,	,	PUNCT
ejpam-747	463	43	m	m	PROPN
ejpam-747	463	44	,	,	PUNCT
ejpam-747	463	45	β	β	X
ejpam-747	463	46	�	�	PROPN
ejpam-747	463	47	,	,	PUNCT
ejpam-747	464	1	j	j	PROPN
ejpam-747	464	2	=	=	PROPN
ejpam-747	464	3	1,2,3	1,2,3	NUM
ejpam-747	464	4	.	.	PUNCT
ejpam-747	465	1	references	reference	NOUN
ejpam-747	465	2	1110	1110	NUM
ejpam-747	465	3	proof	proof	NOUN
ejpam-747	465	4	.	.	PUNCT
ejpam-747	466	1	let	let	VERB
ejpam-747	466	2	f	f	PROPN
ejpam-747	466	3	∈	∈	PROPN
ejpam-747	466	4	tp	tp	X
ejpam-747	466	5	of	of	ADP
ejpam-747	466	6	the	the	DET
ejpam-747	466	7	form	form	NOUN
ejpam-747	466	8	(	(	PUNCT
ejpam-747	466	9	7	7	X
ejpam-747	466	10	)	)	PUNCT
ejpam-747	466	11	be	be	AUX
ejpam-747	466	12	in	in	ADP
ejpam-747	466	13	the	the	DET
ejpam-747	466	14	class	class	NOUN
ejpam-747	467	1	ℜg	ℜg	PROPN
ejpam-747	467	2	h	h	NOUN
ejpam-747	467	3	�	�	PROPN
ejpam-747	467	4	p	p	PROPN
ejpam-747	467	5	,	,	PUNCT
ejpam-747	467	6	m	m	PROPN
ejpam-747	467	7	,	,	PUNCT
ejpam-747	467	8	β	β	X
ejpam-747	467	9	�	�	PROPN
ejpam-747	467	10	,	,	PUNCT
ejpam-747	467	11	then	then	ADV
ejpam-747	467	12	l1	l1	PROPN
ejpam-747	467	13	f	f	PROPN
ejpam-747	467	14	(	(	PUNCT
ejpam-747	467	15	z	z	NOUN
ejpam-747	467	16	)	)	PUNCT
ejpam-747	467	17	=	=	SYM
ejpam-747	468	1	zp	zp	PROPN
ejpam-747	469	1	−	−	PROPN
ejpam-747	469	2	∞	∞	NUM
ejpam-747	469	3	∑	∑	PUNCT
ejpam-747	469	4	k=1	k=1	PROPN
ejpam-747	469	5	�	�	PROPN
ejpam-747	469	6	c	c	PROPN
ejpam-747	470	1	+	+	CCONJ
ejpam-747	470	2	p	p	X
ejpam-747	470	3	c	c	PROPN
ejpam-747	470	4	+	+	X
ejpam-747	470	5	p+	p+	PROPN
ejpam-747	470	6	k	k	PROPN
ejpam-747	470	7	�	�	PROPN
ejpam-747	470	8	ap+kzp+k	ap+kzp+k	PROPN
ejpam-747	470	9	,	,	PUNCT
ejpam-747	470	10	l2	l2	NOUN
ejpam-747	470	11	f	f	X
ejpam-747	470	12	(	(	PUNCT
ejpam-747	470	13	z	z	NOUN
ejpam-747	470	14	)	)	PUNCT
ejpam-747	470	15	=	=	SYM
ejpam-747	471	1	zp	zp	PROPN
ejpam-747	472	1	−	−	PROPN
ejpam-747	472	2	∞	∞	NUM
ejpam-747	472	3	∑	∑	PUNCT
ejpam-747	472	4	k=1	k=1	PROPN
ejpam-747	472	5	�	�	PROPN
ejpam-747	472	6	c	c	PROPN
ejpam-747	473	1	+	+	CCONJ
ejpam-747	473	2	p	p	X
ejpam-747	473	3	c	c	PROPN
ejpam-747	473	4	+	+	X
ejpam-747	473	5	p+	p+	PROPN
ejpam-747	473	6	k	k	PROPN
ejpam-747	473	7	�	�	PROPN
ejpam-747	473	8	σ	σ	PROPN
ejpam-747	473	9	ap+kzp+k	ap+kzp+k	PROPN
ejpam-747	473	10	,	,	PUNCT
ejpam-747	473	11	l3	l3	PROPN
ejpam-747	473	12	f	f	PROPN
ejpam-747	473	13	(	(	PUNCT
ejpam-747	473	14	z	z	NOUN
ejpam-747	473	15	)	)	PUNCT
ejpam-747	473	16	=	=	SYM
ejpam-747	474	1	zp	zp	PROPN
ejpam-747	475	1	−	−	PROPN
ejpam-747	475	2	∞	∞	NUM
ejpam-747	475	3	∑	∑	PUNCT
ejpam-747	475	4	k=1	k=1	PROPN
ejpam-747	475	5	�	�	PROPN
ejpam-747	475	6	p+	p+	PROPN
ejpam-747	475	7	c	c	PROPN
ejpam-747	475	8	�	�	PROPN
ejpam-747	475	9	k	k	PROPN
ejpam-747	475	10	�	�	PROPN
ejpam-747	475	11	p+	p+	PROPN
ejpam-747	475	12	c	c	PROPN
ejpam-747	475	13	+	+	PROPN
ejpam-747	475	14	σ	σ	PROPN
ejpam-747	475	15	�	�	PROPN
ejpam-747	475	16	k	k	PROPN
ejpam-747	475	17	ap+kzp+k	ap+kzp+k	PROPN
ejpam-747	475	18	.	.	PUNCT
ejpam-747	476	1	since	since	SCONJ
ejpam-747	476	2	�	�	PROPN
ejpam-747	476	3	c+p	c+p	VERB
ejpam-747	476	4	c+p+k	c+p+k	X
ejpam-747	476	5	�	�	PROPN
ejpam-747	476	6	<	<	X
ejpam-747	476	7	1	1	NUM
ejpam-747	476	8	,	,	PUNCT
ejpam-747	476	9	for	for	ADP
ejpam-747	476	10	σ	σ	PROPN
ejpam-747	476	11	≥	≥	PROPN
ejpam-747	476	12	0	0	NUM
ejpam-747	476	13	,	,	PUNCT
ejpam-747	476	14	�	�	PROPN
ejpam-747	476	15	c+p	c+p	NOUN
ejpam-747	476	16	c+p+k	c+p+k	X
ejpam-747	476	17	�	�	PROPN
ejpam-747	476	18	σ	σ	NOUN
ejpam-747	476	19	≤	≤	NUM
ejpam-747	476	20	1	1	NUM
ejpam-747	476	21	and	and	CCONJ
ejpam-747	476	22	(	(	PUNCT
ejpam-747	476	23	p+c)k	p+c)k	PROPN
ejpam-747	476	24	(	(	PUNCT
ejpam-747	476	25	p+c+σ)k	p+c+σ)k	NOUN
ejpam-747	476	26	≤	≤	ADV
ejpam-747	476	27	1	1	NUM
ejpam-747	476	28	,	,	PUNCT
ejpam-747	476	29	k	k	PROPN
ejpam-747	476	30	≥	≥	NUM
ejpam-747	476	31	1	1	NUM
ejpam-747	476	32	,	,	PUNCT
ejpam-747	476	33	by	by	ADP
ejpam-747	476	34	theorem	theorem	NOUN
ejpam-747	476	35	1	1	NUM
ejpam-747	476	36	,	,	PUNCT
ejpam-747	476	37	we	we	PRON
ejpam-747	476	38	see	see	VERB
ejpam-747	476	39	that	that	SCONJ
ejpam-747	476	40	∞	∞	PROPN
ejpam-747	476	41	∑	∑	PUNCT
ejpam-747	476	42	k=1	k=1	PROPN
ejpam-747	476	43	�	�	PROPN
ejpam-747	476	44	p+	p+	PROPN
ejpam-747	476	45	k	k	PROPN
ejpam-747	476	46	�	�	PROPN
ejpam-747	476	47	!	!	PUNCT
ejpam-747	477	1	�	�	PROPN
ejpam-747	477	2	�	�	PROPN
ejpam-747	477	3	p+	p+	PART
ejpam-747	477	4	k−m	k−m	NOUN
ejpam-747	477	5	�	�	PROPN
ejpam-747	477	6	bp+k	bp+k	PROPN
ejpam-747	477	7	−	−	PROPN
ejpam-747	477	8	�	�	PROPN
ejpam-747	477	9	p−m−	p−m−	PROPN
ejpam-747	477	10	β	β	X
ejpam-747	477	11	�	�	PROPN
ejpam-747	477	12	cp+k	cp+k	PROPN
ejpam-747	477	13	�	�	PROPN
ejpam-747	477	14	�	�	PROPN
ejpam-747	477	15	p+	p+	PART
ejpam-747	477	16	k−m	k−m	PROPN
ejpam-747	477	17	�	�	PROPN
ejpam-747	477	18	!	!	PUNCT
ejpam-747	477	19	�	�	PROPN
ejpam-747	478	1	c	c	PROPN
ejpam-747	479	1	+	+	CCONJ
ejpam-747	479	2	p	p	X
ejpam-747	479	3	c	c	PROPN
ejpam-747	479	4	+	+	X
ejpam-747	479	5	p+	p+	VERB
ejpam-747	479	6	k	k	PROPN
ejpam-747	479	7	�	�	PROPN
ejpam-747	479	8	ap+k	ap+k	PROPN
ejpam-747	479	9	≤	≤	NOUN
ejpam-747	479	10	∞	∞	NUM
ejpam-747	479	11	∑	∑	PUNCT
ejpam-747	479	12	k=1	k=1	PROPN
ejpam-747	479	13	�	�	PROPN
ejpam-747	479	14	p+	p+	PROPN
ejpam-747	479	15	k	k	PROPN
ejpam-747	479	16	�	�	PROPN
ejpam-747	479	17	!	!	PUNCT
ejpam-747	480	1	�	�	PROPN
ejpam-747	480	2	�	�	PROPN
ejpam-747	480	3	p+	p+	PART
ejpam-747	480	4	k−m	k−m	NOUN
ejpam-747	480	5	�	�	PROPN
ejpam-747	480	6	bp+k	bp+k	PROPN
ejpam-747	480	7	−	−	PROPN
ejpam-747	480	8	�	�	PROPN
ejpam-747	480	9	p−m−	p−m−	PROPN
ejpam-747	480	10	β	β	X
ejpam-747	480	11	�	�	PROPN
ejpam-747	480	12	cp+k	cp+k	PROPN
ejpam-747	480	13	�	�	PROPN
ejpam-747	480	14	�	�	PROPN
ejpam-747	480	15	p+	p+	PART
ejpam-747	480	16	k−m	k−m	PROPN
ejpam-747	480	17	�	�	PROPN
ejpam-747	480	18	!	!	PUNCT
ejpam-747	481	1	ap+k	ap+k	NOUN
ejpam-747	482	1	≤	≤	NOUN
ejpam-747	482	2	βp	βp	PROPN
ejpam-747	482	3	!	!	PUNCT
ejpam-747	482	4	�	�	PROPN
ejpam-747	482	5	p−m	p−m	PRON
ejpam-747	482	6	�	�	PROPN
ejpam-747	482	7	!	!	PUNCT
ejpam-747	482	8	.	.	PUNCT
ejpam-747	483	1	hence	hence	ADV
ejpam-747	483	2	,	,	PUNCT
ejpam-747	483	3	by	by	ADP
ejpam-747	483	4	theorem	theorem	NOUN
ejpam-747	483	5	1	1	NUM
ejpam-747	483	6	,	,	PUNCT
ejpam-747	483	7	l1	l1	PROPN
ejpam-747	483	8	f	f	PROPN
ejpam-747	483	9	(	(	PUNCT
ejpam-747	483	10	z	z	NOUN
ejpam-747	483	11	)	)	PUNCT
ejpam-747	483	12	∈	∈	PROPN
ejpam-747	484	1	ℜg	ℜg	PROPN
ejpam-747	484	2	h	h	NOUN
ejpam-747	484	3	�	�	PROPN
ejpam-747	484	4	p	p	PROPN
ejpam-747	484	5	,	,	PUNCT
ejpam-747	484	6	m	m	PROPN
ejpam-747	484	7	,	,	PUNCT
ejpam-747	484	8	β	β	X
ejpam-747	484	9	�	�	PROPN
ejpam-747	484	10	.	.	PUNCT
ejpam-747	485	1	also	also	ADV
ejpam-747	485	2	∞	∞	NUM
ejpam-747	485	3	∑	∑	PROPN
ejpam-747	485	4	k=1	k=1	PROPN
ejpam-747	485	5	�	�	PROPN
ejpam-747	485	6	p+	p+	PROPN
ejpam-747	485	7	k	k	PROPN
ejpam-747	485	8	�	�	PROPN
ejpam-747	485	9	!	!	PUNCT
ejpam-747	486	1	�	�	PROPN
ejpam-747	486	2	�	�	PROPN
ejpam-747	486	3	p+	p+	PART
ejpam-747	486	4	k−m	k−m	NOUN
ejpam-747	486	5	�	�	PROPN
ejpam-747	486	6	bp+k	bp+k	PROPN
ejpam-747	486	7	−	−	PROPN
ejpam-747	486	8	�	�	PROPN
ejpam-747	486	9	p−m−	p−m−	PROPN
ejpam-747	486	10	β	β	X
ejpam-747	486	11	�	�	PROPN
ejpam-747	486	12	cp+k	cp+k	PROPN
ejpam-747	486	13	�	�	PROPN
ejpam-747	486	14	�	�	PROPN
ejpam-747	486	15	p+	p+	PART
ejpam-747	486	16	k−m	k−m	PROPN
ejpam-747	486	17	�	�	PROPN
ejpam-747	486	18	!	!	PUNCT
ejpam-747	486	19	�	�	PROPN
ejpam-747	487	1	c	c	PROPN
ejpam-747	488	1	+	+	CCONJ
ejpam-747	488	2	p	p	X
ejpam-747	488	3	c	c	PROPN
ejpam-747	488	4	+	+	X
ejpam-747	488	5	p+	p+	PROPN
ejpam-747	488	6	k	k	PROPN
ejpam-747	488	7	�	�	PROPN
ejpam-747	488	8	σ	σ	PROPN
ejpam-747	488	9	ap+k	ap+k	NOUN
ejpam-747	488	10	≤	≤	NOUN
ejpam-747	488	11	∞	∞	NUM
ejpam-747	488	12	∑	∑	PUNCT
ejpam-747	489	1	k=1	k=1	PROPN
ejpam-747	489	2	�	�	PROPN
ejpam-747	489	3	p+	p+	PROPN
ejpam-747	489	4	k	k	PROPN
ejpam-747	489	5	�	�	PROPN
ejpam-747	489	6	!	!	PUNCT
ejpam-747	489	7	�	�	PROPN
ejpam-747	489	8	�	�	PROPN
ejpam-747	489	9	p+	p+	PART
ejpam-747	489	10	k−m	k−m	NOUN
ejpam-747	489	11	�	�	PROPN
ejpam-747	489	12	bp+k	bp+k	PROPN
ejpam-747	489	13	−	−	PROPN
ejpam-747	489	14	�	�	PROPN
ejpam-747	489	15	p−m−	p−m−	PROPN
ejpam-747	489	16	β	β	X
ejpam-747	489	17	�	�	PROPN
ejpam-747	489	18	cp+k	cp+k	PROPN
ejpam-747	489	19	�	�	PROPN
ejpam-747	489	20	�	�	PROPN
ejpam-747	489	21	p+	p+	PART
ejpam-747	489	22	k−m	k−m	PROPN
ejpam-747	489	23	�	�	PROPN
ejpam-747	489	24	!	!	PUNCT
ejpam-747	490	1	ap+k	ap+k	NOUN
ejpam-747	491	1	≤	≤	NOUN
ejpam-747	491	2	βp	βp	PROPN
ejpam-747	491	3	!	!	PUNCT
ejpam-747	491	4	�	�	PROPN
ejpam-747	491	5	p−m	p−m	PRON
ejpam-747	491	6	�	�	PROPN
ejpam-747	491	7	!	!	PUNCT
ejpam-747	491	8	.	.	PUNCT
ejpam-747	492	1	hence	hence	ADV
ejpam-747	492	2	,	,	PUNCT
ejpam-747	492	3	l2	l2	PROPN
ejpam-747	492	4	f	f	X
ejpam-747	492	5	(	(	PUNCT
ejpam-747	492	6	z	z	NOUN
ejpam-747	492	7	)	)	PUNCT
ejpam-747	492	8	∈	∈	PROPN
ejpam-747	492	9	ℜg	ℜg	PROPN
ejpam-747	492	10	h	h	NOUN
ejpam-747	492	11	�	�	PROPN
ejpam-747	492	12	p	p	PROPN
ejpam-747	492	13	,	,	PUNCT
ejpam-747	492	14	m	m	PROPN
ejpam-747	492	15	,	,	PUNCT
ejpam-747	492	16	β	β	X
ejpam-747	492	17	�	�	PROPN
ejpam-747	492	18	.	.	PUNCT
ejpam-747	493	1	similarly	similarly	ADV
ejpam-747	493	2	,	,	PUNCT
ejpam-747	493	3	we	we	PRON
ejpam-747	493	4	obtain	obtain	VERB
ejpam-747	493	5	that	that	SCONJ
ejpam-747	493	6	l3	l3	PROPN
ejpam-747	493	7	f	f	PROPN
ejpam-747	493	8	(	(	PUNCT
ejpam-747	493	9	z	z	NOUN
ejpam-747	493	10	)	)	PUNCT
ejpam-747	493	11	∈	∈	PROPN
ejpam-747	493	12	ℜg	ℜg	PROPN
ejpam-747	493	13	h	h	NOUN
ejpam-747	493	14	�	�	PROPN
ejpam-747	493	15	p	p	PROPN
ejpam-747	493	16	,	,	PUNCT
ejpam-747	493	17	m	m	PROPN
ejpam-747	493	18	,	,	PUNCT
ejpam-747	493	19	β	β	X
ejpam-747	493	20	�	�	PROPN
ejpam-747	493	21	.	.	PUNCT
ejpam-747	494	1	references	reference	NOUN
ejpam-747	494	2	[	[	X
ejpam-747	494	3	1	1	NUM
ejpam-747	494	4	]	]	X
ejpam-747	494	5	r.m	r.m	PROPN
ejpam-747	494	6	.	.	PROPN
ejpam-747	494	7	ali	ali	PROPN
ejpam-747	494	8	and	and	CCONJ
ejpam-747	494	9	m.h	m.h	PROPN
ejpam-747	494	10	.	.	PROPN
ejpam-747	494	11	hussain	hussain	PROPN
ejpam-747	494	12	,	,	PUNCT
ejpam-747	494	13	v.	v.	ADP
ejpam-747	494	14	ravichandran	ravichandran	NOUN
ejpam-747	494	15	and	and	CCONJ
ejpam-747	494	16	k.g	k.g	PROPN
ejpam-747	494	17	.	.	PROPN
ejpam-747	494	18	subramanian	subramanian	PROPN
ejpam-747	494	19	,	,	PUNCT
ejpam-747	494	20	a	a	DET
ejpam-747	494	21	class	class	NOUN
ejpam-747	494	22	of	of	ADP
ejpam-747	494	23	multivalent	multivalent	NOUN
ejpam-747	494	24	functions	function	NOUN
ejpam-747	494	25	with	with	ADP
ejpam-747	494	26	negative	negative	ADJ
ejpam-747	494	27	coefficients	coefficient	NOUN
ejpam-747	494	28	defined	define	VERB
ejpam-747	494	29	by	by	ADP
ejpam-747	494	30	convolution	convolution	NOUN
ejpam-747	494	31	,	,	PUNCT
ejpam-747	494	32	bull	bull	NOUN
ejpam-747	494	33	.	.	PUNCT
ejpam-747	495	1	korean	korean	ADJ
ejpam-747	495	2	math	math	PROPN
ejpam-747	495	3	.	.	PUNCT
ejpam-747	496	1	soc	soc	PROPN
ejpam-747	496	2	.	.	PUNCT
ejpam-747	496	3	,	,	PUNCT
ejpam-747	496	4	43	43	NUM
ejpam-747	496	5	,	,	PUNCT
ejpam-747	496	6	179	179	NUM
ejpam-747	496	7	-	-	SYM
ejpam-747	496	8	188	188	NUM
ejpam-747	496	9	.	.	PUNCT
ejpam-747	497	1	2006	2006	NUM
ejpam-747	497	2	.	.	PUNCT
ejpam-747	498	1	[	[	X
ejpam-747	498	2	2	2	NUM
ejpam-747	498	3	]	]	X
ejpam-747	498	4	al	al	PROPN
ejpam-747	498	5	-	-	PUNCT
ejpam-747	498	6	oboudi	oboudi	NOUN
ejpam-747	498	7	,	,	PUNCT
ejpam-747	498	8	on	on	ADP
ejpam-747	498	9	univalent	univalent	ADJ
ejpam-747	498	10	functions	function	NOUN
ejpam-747	498	11	defined	define	VERB
ejpam-747	498	12	by	by	ADP
ejpam-747	498	13	a	a	DET
ejpam-747	498	14	generalized	generalize	VERB
ejpam-747	498	15	salagean	salagean	ADJ
ejpam-747	498	16	operator	operator	NOUN
ejpam-747	498	17	.	.	PUNCT
ejpam-747	499	1	int	int	NOUN
ejpam-747	499	2	.	.	PUNCT
ejpam-747	500	1	j.	j.	PROPN
ejpam-747	500	2	math	math	PROPN
ejpam-747	500	3	.	.	PUNCT
ejpam-747	501	1	sci	sci	PROPN
ejpam-747	501	2	.	.	PROPN
ejpam-747	501	3	,	,	PUNCT
ejpam-747	501	4	27	27	NUM
ejpam-747	501	5	,	,	PUNCT
ejpam-747	501	6	1429	1429	NUM
ejpam-747	501	7	-	-	SYM
ejpam-747	501	8	1436	1436	NUM
ejpam-747	501	9	.	.	PUNCT
ejpam-747	502	1	2004	2004	NUM
ejpam-747	502	2	.	.	PUNCT
ejpam-747	503	1	[	[	X
ejpam-747	503	2	3	3	X
ejpam-747	503	3	]	]	X
ejpam-747	503	4	m.k	m.k	PROPN
ejpam-747	503	5	.	.	PROPN
ejpam-747	503	6	aouf	aouf	PROPN
ejpam-747	503	7	and	and	CCONJ
ejpam-747	503	8	j.	j.	PROPN
ejpam-747	503	9	dziok	dziok	PROPN
ejpam-747	503	10	,	,	PUNCT
ejpam-747	503	11	distortion	distortion	NOUN
ejpam-747	503	12	and	and	CCONJ
ejpam-747	503	13	convolutional	convolutional	ADJ
ejpam-747	503	14	theorems	theorem	NOUN
ejpam-747	503	15	for	for	ADP
ejpam-747	503	16	operators	operator	NOUN
ejpam-747	503	17	of	of	ADP
ejpam-747	503	18	generalized	generalized	ADJ
ejpam-747	503	19	fractional	fractional	ADJ
ejpam-747	503	20	calculus	calculus	NOUN
ejpam-747	503	21	involving	involve	VERB
ejpam-747	503	22	wright	wright	PROPN
ejpam-747	503	23	function	function	PROPN
ejpam-747	503	24	,	,	PUNCT
ejpam-747	503	25	journal	journal	NOUN
ejpam-747	503	26	of	of	ADP
ejpam-747	503	27	appl	appl	PROPN
ejpam-747	503	28	.	.	PUNCT
ejpam-747	504	1	anal	anal	PROPN
ejpam-747	504	2	.	.	PROPN
ejpam-747	504	3	,	,	PUNCT
ejpam-747	504	4	14	14	NUM
ejpam-747	504	5	,	,	PUNCT
ejpam-747	504	6	no	no	INTJ
ejpam-747	504	7	.	.	NOUN
ejpam-747	504	8	2	2	NUM
ejpam-747	504	9	,	,	PUNCT
ejpam-747	504	10	183	183	NUM
ejpam-747	504	11	-	-	SYM
ejpam-747	504	12	192	192	NUM
ejpam-747	504	13	.	.	PUNCT
ejpam-747	504	14	2008	2008	NUM
ejpam-747	504	15	.	.	PUNCT
ejpam-747	505	1	references	reference	NOUN
ejpam-747	505	2	1111	1111	NUM
ejpam-747	506	1	[	[	X
ejpam-747	506	2	4	4	NUM
ejpam-747	506	3	]	]	X
ejpam-747	506	4	m.k	m.k	PROPN
ejpam-747	506	5	.	.	PROPN
ejpam-747	506	6	aouf	aouf	PROPN
ejpam-747	506	7	and	and	CCONJ
ejpam-747	506	8	j.	j.	PROPN
ejpam-747	506	9	dziok	dziok	PROPN
ejpam-747	506	10	,	,	PUNCT
ejpam-747	506	11	certain	certain	ADJ
ejpam-747	506	12	class	class	NOUN
ejpam-747	506	13	of	of	ADP
ejpam-747	506	14	analytic	analytic	ADJ
ejpam-747	506	15	functions	function	NOUN
ejpam-747	506	16	associated	associate	VERB
ejpam-747	506	17	with	with	ADP
ejpam-747	506	18	the	the	DET
ejpam-747	506	19	wright	wright	PROPN
ejpam-747	506	20	generalized	generalize	VERB
ejpam-747	506	21	hypergeometric	hypergeometric	ADJ
ejpam-747	506	22	function	function	NOUN
ejpam-747	506	23	,	,	PUNCT
ejpam-747	506	24	j.	j.	PROPN
ejpam-747	506	25	math	math	PROPN
ejpam-747	506	26	.	.	PUNCT
ejpam-747	507	1	appl	appl	PROPN
ejpam-747	507	2	.	.	PROPN
ejpam-747	507	3	,	,	PUNCT
ejpam-747	507	4	30	30	NUM
ejpam-747	507	5	,	,	PUNCT
ejpam-747	507	6	23	23	NUM
ejpam-747	507	7	-	-	SYM
ejpam-747	507	8	32	32	NUM
ejpam-747	507	9	.	.	PUNCT
ejpam-747	507	10	2008	2008	NUM
ejpam-747	507	11	.	.	PUNCT
ejpam-747	508	1	[	[	X
ejpam-747	508	2	5	5	NUM
ejpam-747	508	3	]	]	X
ejpam-747	508	4	m.k	m.k	PROPN
ejpam-747	508	5	.	.	PROPN
ejpam-747	508	6	aouf	aouf	PROPN
ejpam-747	508	7	,	,	PUNCT
ejpam-747	508	8	a.o	a.o	PROPN
ejpam-747	508	9	.	.	PROPN
ejpam-747	508	10	mostafa	mostafa	PROPN
ejpam-747	508	11	,	,	PUNCT
ejpam-747	508	12	some	some	DET
ejpam-747	508	13	properties	property	NOUN
ejpam-747	508	14	of	of	ADP
ejpam-747	508	15	a	a	DET
ejpam-747	508	16	subclass	subclass	NOUN
ejpam-747	508	17	of	of	ADP
ejpam-747	508	18	uniformly	uniformly	ADJ
ejpam-747	508	19	convex	convex	NOUN
ejpam-747	508	20	functions	function	NOUN
ejpam-747	508	21	with	with	ADP
ejpam-747	508	22	negative	negative	ADJ
ejpam-747	508	23	coefficients	coefficient	NOUN
ejpam-747	508	24	,	,	PUNCT
ejpam-747	508	25	demonstratio	demonstratio	PROPN
ejpam-747	508	26	math	math	PROPN
ejpam-747	508	27	.	.	PUNCT
ejpam-747	508	28	,	,	PUNCT
ejpam-747	508	29	61	61	NUM
ejpam-747	508	30	,	,	PUNCT
ejpam-747	508	31	no	no	INTJ
ejpam-747	508	32	.	.	NOUN
ejpam-747	508	33	2	2	NUM
ejpam-747	508	34	,	,	PUNCT
ejpam-747	508	35	253	253	NUM
ejpam-747	508	36	-	-	SYM
ejpam-747	508	37	270	270	NUM
ejpam-747	508	38	.	.	PUNCT
ejpam-747	508	39	2008	2008	NUM
ejpam-747	508	40	.	.	PUNCT
ejpam-747	509	1	[	[	X
ejpam-747	509	2	6	6	NUM
ejpam-747	509	3	]	]	SYM
ejpam-747	509	4	b.c	b.c	PROPN
ejpam-747	509	5	.	.	PROPN
ejpam-747	509	6	carlson	carlson	PROPN
ejpam-747	509	7	and	and	CCONJ
ejpam-747	509	8	d.b	d.b	PROPN
ejpam-747	509	9	.	.	PROPN
ejpam-747	509	10	shaffer	shaffer	PROPN
ejpam-747	509	11	,	,	PUNCT
ejpam-747	509	12	starlike	starlike	NOUN
ejpam-747	509	13	and	and	CCONJ
ejpam-747	509	14	prestarlike	prestarlike	ADJ
ejpam-747	509	15	hypergeometric	hypergeometric	ADJ
ejpam-747	509	16	functions	function	NOUN
ejpam-747	509	17	.	.	PUNCT
ejpam-747	510	1	siam	siam	PROPN
ejpam-747	510	2	j.	j.	PROPN
ejpam-747	510	3	math	math	PROPN
ejpam-747	510	4	.	.	PUNCT
ejpam-747	511	1	anal	anal	PROPN
ejpam-747	511	2	.	.	PROPN
ejpam-747	511	3	,	,	PUNCT
ejpam-747	511	4	15	15	NUM
ejpam-747	511	5	(	(	PUNCT
ejpam-747	511	6	4	4	NUM
ejpam-747	511	7	)	)	PUNCT
ejpam-747	511	8	,	,	PUNCT
ejpam-747	511	9	737	737	NUM
ejpam-747	511	10	-	-	SYM
ejpam-747	511	11	745	745	NUM
ejpam-747	511	12	.	.	NOUN
ejpam-747	511	13	1984	1984	NUM
ejpam-747	512	1	[	[	X
ejpam-747	512	2	7	7	NUM
ejpam-747	512	3	]	]	PUNCT
ejpam-747	512	4	m.	m.	NOUN
ejpam-747	512	5	chen	chen	PROPN
ejpam-747	512	6	,	,	PUNCT
ejpam-747	512	7	h.	h.	PROPN
ejpam-747	512	8	irmak	irmak	PROPN
ejpam-747	512	9	and	and	CCONJ
ejpam-747	512	10	h.m	h.m	PROPN
ejpam-747	512	11	.	.	PROPN
ejpam-747	512	12	srivastava	srivastava	PROPN
ejpam-747	512	13	,	,	PUNCT
ejpam-747	512	14	some	some	DET
ejpam-747	512	15	families	family	NOUN
ejpam-747	512	16	of	of	ADP
ejpam-747	512	17	multivalently	multivalently	ADJ
ejpam-747	512	18	analytic	analytic	ADJ
ejpam-747	512	19	functions	function	NOUN
ejpam-747	512	20	with	with	ADP
ejpam-747	512	21	negative	negative	ADJ
ejpam-747	512	22	coefficients	coefficient	NOUN
ejpam-747	512	23	.	.	PUNCT
ejpam-747	513	1	j.	j.	PROPN
ejpam-747	513	2	math	math	PROPN
ejpam-747	513	3	.	.	PUNCT
ejpam-747	514	1	anal	anal	PROPN
ejpam-747	514	2	.	.	PUNCT
ejpam-747	515	1	appl	appl	PROPN
ejpam-747	515	2	.	.	PROPN
ejpam-747	515	3	,	,	PUNCT
ejpam-747	515	4	214	214	NUM
ejpam-747	515	5	,	,	PUNCT
ejpam-747	515	6	art.no	art.no	PROPN
ejpam-747	515	7	.	.	PUNCT
ejpam-747	516	1	ay975615	ay975615	NOUN
ejpam-747	516	2	,	,	PUNCT
ejpam-747	516	3	674	674	NUM
ejpam-747	516	4	-	-	SYM
ejpam-747	516	5	690	690	NUM
ejpam-747	516	6	.	.	PUNCT
ejpam-747	516	7	1997	1997	NUM
ejpam-747	516	8	.	.	PUNCT
ejpam-747	517	1	[	[	X
ejpam-747	517	2	8	8	X
ejpam-747	517	3	]	]	X
ejpam-747	517	4	j.	j.	PROPN
ejpam-747	517	5	dziok	dziok	PROPN
ejpam-747	517	6	and	and	CCONJ
ejpam-747	517	7	r.k	r.k	PROPN
ejpam-747	517	8	.	.	PROPN
ejpam-747	517	9	raina	raina	PROPN
ejpam-747	517	10	,	,	PUNCT
ejpam-747	517	11	families	family	NOUN
ejpam-747	517	12	of	of	ADP
ejpam-747	517	13	analytic	analytic	ADJ
ejpam-747	517	14	functions	function	NOUN
ejpam-747	517	15	associated	associate	VERB
ejpam-747	517	16	with	with	ADP
ejpam-747	517	17	the	the	DET
ejpam-747	517	18	wright	wright	PROPN
ejpam-747	517	19	generalized	generalize	VERB
ejpam-747	517	20	hypergeometric	hypergeometric	ADJ
ejpam-747	517	21	function	function	NOUN
ejpam-747	517	22	,	,	PUNCT
ejpam-747	517	23	demonstratio	demonstratio	PROPN
ejpam-747	517	24	math	math	PROPN
ejpam-747	517	25	.	.	PUNCT
ejpam-747	518	1	,	,	PUNCT
ejpam-747	518	2	37	37	NUM
ejpam-747	518	3	,	,	PUNCT
ejpam-747	518	4	no	no	INTJ
ejpam-747	518	5	.	.	NOUN
ejpam-747	518	6	3	3	NUM
ejpam-747	518	7	,	,	PUNCT
ejpam-747	518	8	533	533	NUM
ejpam-747	518	9	-	-	SYM
ejpam-747	518	10	542	542	NUM
ejpam-747	518	11	.	.	PUNCT
ejpam-747	519	1	2004	2004	NUM
ejpam-747	519	2	.	.	PUNCT
ejpam-747	520	1	[	[	X
ejpam-747	520	2	9	9	X
ejpam-747	520	3	]	]	PUNCT
ejpam-747	520	4	j.	j.	PROPN
ejpam-747	520	5	dziok	dziok	PROPN
ejpam-747	520	6	,	,	PUNCT
ejpam-747	520	7	r.k	r.k	PROPN
ejpam-747	520	8	.	.	PROPN
ejpam-747	520	9	raina	raina	PROPN
ejpam-747	520	10	and	and	CCONJ
ejpam-747	520	11	h.m	h.m	PROPN
ejpam-747	520	12	.	.	PROPN
ejpam-747	520	13	srivastava	srivastava	PROPN
ejpam-747	520	14	,	,	PUNCT
ejpam-747	520	15	some	some	DET
ejpam-747	520	16	classes	class	NOUN
ejpam-747	520	17	of	of	ADP
ejpam-747	520	18	analytic	analytic	ADJ
ejpam-747	520	19	functions	function	NOUN
ejpam-747	520	20	associated	associate	VERB
ejpam-747	520	21	with	with	ADP
ejpam-747	520	22	operators	operator	NOUN
ejpam-747	520	23	on	on	ADP
ejpam-747	520	24	hilbert	hilbert	NOUN
ejpam-747	520	25	space	space	NOUN
ejpam-747	520	26	involving	involve	VERB
ejpam-747	520	27	wright	wright	PROPN
ejpam-747	520	28	’s	’s	PART
ejpam-747	520	29	generalized	generalize	VERB
ejpam-747	520	30	hypergeometric	hypergeometric	ADJ
ejpam-747	520	31	function	function	NOUN
ejpam-747	520	32	,	,	PUNCT
ejpam-747	520	33	proc	proc	NOUN
ejpam-747	520	34	.	.	PUNCT
ejpam-747	521	1	jangjeon	jangjeon	PROPN
ejpam-747	521	2	math	math	PROPN
ejpam-747	521	3	.	.	PUNCT
ejpam-747	522	1	soc	soc	PROPN
ejpam-747	522	2	.	.	PUNCT
ejpam-747	522	3	,	,	PUNCT
ejpam-747	522	4	7	7	NUM
ejpam-747	522	5	,	,	PUNCT
ejpam-747	522	6	43	43	NUM
ejpam-747	522	7	-	-	SYM
ejpam-747	522	8	55	55	NUM
ejpam-747	522	9	.	.	PUNCT
ejpam-747	523	1	2004	2004	NUM
ejpam-747	523	2	.	.	PUNCT
ejpam-747	524	1	[	[	X
ejpam-747	524	2	10	10	NUM
ejpam-747	524	3	]	]	X
ejpam-747	524	4	j.	j.	PROPN
ejpam-747	524	5	dziok	dziok	PROPN
ejpam-747	524	6	and	and	CCONJ
ejpam-747	524	7	h.m	h.m	PROPN
ejpam-747	524	8	.	.	PROPN
ejpam-747	524	9	srivastava	srivastava	PROPN
ejpam-747	524	10	,	,	PUNCT
ejpam-747	524	11	classes	class	NOUN
ejpam-747	524	12	of	of	ADP
ejpam-747	524	13	analytic	analytic	ADJ
ejpam-747	524	14	functions	function	NOUN
ejpam-747	524	15	associated	associate	VERB
ejpam-747	524	16	with	with	ADP
ejpam-747	524	17	the	the	DET
ejpam-747	524	18	generalized	generalized	ADJ
ejpam-747	524	19	hypergeometric	hypergeometric	ADJ
ejpam-747	524	20	functions	function	NOUN
ejpam-747	524	21	.	.	PUNCT
ejpam-747	525	1	appl	appl	PROPN
ejpam-747	525	2	.	.	PROPN
ejpam-747	525	3	math	math	PROPN
ejpam-747	525	4	.	.	PUNCT
ejpam-747	526	1	comput	comput	NOUN
ejpam-747	526	2	.	.	PUNCT
ejpam-747	526	3	,	,	PUNCT
ejpam-747	526	4	103	103	NUM
ejpam-747	526	5	,	,	PUNCT
ejpam-747	526	6	1	1	NUM
ejpam-747	526	7	-	-	SYM
ejpam-747	526	8	13	13	NUM
ejpam-747	526	9	.	.	PUNCT
ejpam-747	526	10	1999	1999	NUM
ejpam-747	526	11	.	.	PUNCT
ejpam-747	527	1	[	[	X
ejpam-747	527	2	11	11	NUM
ejpam-747	527	3	]	]	X
ejpam-747	527	4	p.l	p.l	PROPN
ejpam-747	527	5	.	.	PUNCT
ejpam-747	527	6	duren	duren	PROPN
ejpam-747	527	7	,	,	PUNCT
ejpam-747	527	8	univalent	univalent	ADJ
ejpam-747	527	9	functions	function	NOUN
ejpam-747	527	10	,	,	PUNCT
ejpam-747	527	11	springer	springer	NOUN
ejpam-747	527	12	-	-	PUNCT
ejpam-747	527	13	verlag	verlag	PROPN
ejpam-747	527	14	,	,	PUNCT
ejpam-747	527	15	new	new	PROPN
ejpam-747	527	16	york	york	PROPN
ejpam-747	527	17	,	,	PUNCT
ejpam-747	527	18	1983	1983	NUM
ejpam-747	527	19	.	.	PUNCT
ejpam-747	528	1	[	[	X
ejpam-747	528	2	12	12	NUM
ejpam-747	528	3	]	]	X
ejpam-747	528	4	h.ö	h.ö	PROPN
ejpam-747	528	5	.	.	PROPN
ejpam-747	528	6	güney	güney	PROPN
ejpam-747	528	7	and	and	CCONJ
ejpam-747	528	8	d.	d.	PROPN
ejpam-747	528	9	breaz	breaz	PROPN
ejpam-747	528	10	,	,	PUNCT
ejpam-747	528	11	integral	integral	ADJ
ejpam-747	528	12	properties	property	NOUN
ejpam-747	528	13	of	of	ADP
ejpam-747	528	14	some	some	DET
ejpam-747	528	15	families	family	NOUN
ejpam-747	528	16	of	of	ADP
ejpam-747	528	17	multivalent	multivalent	NOUN
ejpam-747	528	18	functions	function	NOUN
ejpam-747	528	19	with	with	ADP
ejpam-747	528	20	complex	complex	ADJ
ejpam-747	528	21	order	order	NOUN
ejpam-747	528	22	,	,	PUNCT
ejpam-747	528	23	studia	studia	PROPN
ejpam-747	528	24	univ	univ	PROPN
ejpam-747	528	25	.	.	PUNCT
ejpam-747	529	1	"	"	PUNCT
ejpam-747	529	2	babes	babe	NOUN
ejpam-747	529	3	-	-	PUNCT
ejpam-747	529	4	bolyai	bolyai	NOUN
ejpam-747	529	5	"	"	PUNCT
ejpam-747	529	6	,	,	PUNCT
ejpam-747	529	7	mathematica	mathematica	PROPN
ejpam-747	529	8	,	,	PUNCT
ejpam-747	529	9	vol	vol	NOUN
ejpam-747	529	10	.	.	PUNCT
ejpam-747	530	1	liv	liv	PROPN
ejpam-747	530	2	,	,	PUNCT
ejpam-747	530	3	no	no	INTJ
ejpam-747	530	4	.	.	NOUN
ejpam-747	530	5	1	1	NUM
ejpam-747	530	6	,	,	PUNCT
ejpam-747	530	7	march	march	PROPN
ejpam-747	530	8	(	(	PUNCT
ejpam-747	530	9	2009	2009	NUM
ejpam-747	530	10	)	)	PUNCT
ejpam-747	530	11	6	6	NUM
ejpam-747	530	12	pp	pp	NOUN
ejpam-747	530	13	.	.	PUNCT
ejpam-747	531	1	[	[	X
ejpam-747	531	2	13	13	NUM
ejpam-747	531	3	]	]	SYM
ejpam-747	531	4	yu	yu	PROPN
ejpam-747	531	5	.	.	PUNCT
ejpam-747	531	6	e.	e.	PROPN
ejpam-747	531	7	hohlov	hohlov	PROPN
ejpam-747	531	8	,	,	PUNCT
ejpam-747	531	9	operators	operator	NOUN
ejpam-747	531	10	and	and	CCONJ
ejpam-747	531	11	operations	operation	NOUN
ejpam-747	531	12	on	on	ADP
ejpam-747	531	13	the	the	DET
ejpam-747	531	14	class	class	NOUN
ejpam-747	531	15	of	of	ADP
ejpam-747	531	16	univalent	univalent	ADJ
ejpam-747	531	17	functions	function	NOUN
ejpam-747	531	18	,	,	PUNCT
ejpam-747	531	19	izv	izv	PROPN
ejpam-747	531	20	.	.	PROPN
ejpam-747	531	21	vyssh	vyssh	PROPN
ejpam-747	531	22	.	.	PUNCT
ejpam-747	532	1	uchebn	uchebn	NOUN
ejpam-747	532	2	.	.	PUNCT
ejpam-747	533	1	zaved	zave	VERB
ejpam-747	533	2	.	.	PUNCT
ejpam-747	534	1	mat	mat	PROPN
ejpam-747	534	2	.	.	PROPN
ejpam-747	534	3	,	,	PUNCT
ejpam-747	534	4	10	10	NUM
ejpam-747	534	5	,	,	PUNCT
ejpam-747	534	6	83–89	83–89	NUM
ejpam-747	534	7	.	.	NOUN
ejpam-747	534	8	1978	1978	NUM
ejpam-747	534	9	.	.	PUNCT
ejpam-747	535	1	[	[	X
ejpam-747	535	2	14	14	NUM
ejpam-747	535	3	]	]	X
ejpam-747	535	4	i.s	i.s	PROPN
ejpam-747	535	5	.	.	PROPN
ejpam-747	535	6	jack	jack	PROPN
ejpam-747	535	7	,	,	PUNCT
ejpam-747	535	8	functions	function	NOUN
ejpam-747	535	9	starlike	starlike	NOUN
ejpam-747	535	10	and	and	CCONJ
ejpam-747	535	11	convex	convex	NOUN
ejpam-747	535	12	of	of	ADP
ejpam-747	535	13	order	order	NOUN
ejpam-747	535	14	α	α	PROPN
ejpam-747	535	15	j.	j.	PROPN
ejpam-747	535	16	london	london	PROPN
ejpam-747	535	17	.	.	PUNCT
ejpam-747	536	1	math	math	PROPN
ejpam-747	536	2	.	.	PUNCT
ejpam-747	537	1	soc	soc	PROPN
ejpam-747	537	2	.	.	PUNCT
ejpam-747	537	3	,	,	PUNCT
ejpam-747	537	4	3	3	NUM
ejpam-747	537	5	,	,	PUNCT
ejpam-747	537	6	469	469	NUM
ejpam-747	537	7	-	-	NUM
ejpam-747	537	8	474	474	NUM
ejpam-747	537	9	.	.	PUNCT
ejpam-747	537	10	1971	1971	NUM
ejpam-747	537	11	.	.	PUNCT
ejpam-747	538	1	[	[	X
ejpam-747	538	2	15	15	NUM
ejpam-747	538	3	]	]	X
ejpam-747	538	4	a.a	a.a	PROPN
ejpam-747	538	5	.	.	PROPN
ejpam-747	538	6	kilbas	kilbas	PROPN
ejpam-747	538	7	,	,	PUNCT
ejpam-747	538	8	m.	m.	NOUN
ejpam-747	538	9	saigo	saigo	PROPN
ejpam-747	538	10	,	,	PUNCT
ejpam-747	538	11	and	and	CCONJ
ejpam-747	538	12	j.j	j.j	PROPN
ejpam-747	538	13	.	.	PROPN
ejpam-747	538	14	trujillo	trujillo	PROPN
ejpam-747	538	15	,	,	PUNCT
ejpam-747	538	16	on	on	ADP
ejpam-747	538	17	the	the	DET
ejpam-747	538	18	generalized	generalized	ADJ
ejpam-747	538	19	wright	wright	PROPN
ejpam-747	538	20	function	function	PROPN
ejpam-747	538	21	,	,	PUNCT
ejpam-747	538	22	fract	fract	PROPN
ejpam-747	538	23	.	.	PUNCT
ejpam-747	539	1	calc	calc	PROPN
ejpam-747	539	2	.	.	PUNCT
ejpam-747	540	1	appl	appl	PROPN
ejpam-747	540	2	.	.	PUNCT
ejpam-747	541	1	anal	anal	PROPN
ejpam-747	541	2	.	.	PROPN
ejpam-747	541	3	,	,	PUNCT
ejpam-747	541	4	5	5	NUM
ejpam-747	541	5	(	(	PUNCT
ejpam-747	541	6	4	4	NUM
ejpam-747	541	7	)	)	PUNCT
ejpam-747	541	8	,	,	PUNCT
ejpam-747	541	9	437	437	NUM
ejpam-747	541	10	-	-	SYM
ejpam-747	541	11	460	460	NUM
ejpam-747	541	12	.	.	PUNCT
ejpam-747	541	13	2002	2002	NUM
ejpam-747	541	14	.	.	PUNCT
ejpam-747	542	1	[	[	X
ejpam-747	542	2	16	16	NUM
ejpam-747	542	3	]	]	X
ejpam-747	542	4	j.e	j.e	PROPN
ejpam-747	542	5	.	.	PROPN
ejpam-747	542	6	littlewood	littlewood	PROPN
ejpam-747	542	7	,	,	PUNCT
ejpam-747	542	8	on	on	ADP
ejpam-747	542	9	inequalities	inequality	NOUN
ejpam-747	542	10	in	in	ADP
ejpam-747	542	11	the	the	DET
ejpam-747	542	12	theory	theory	NOUN
ejpam-747	542	13	of	of	ADP
ejpam-747	542	14	functions	function	NOUN
ejpam-747	542	15	,	,	PUNCT
ejpam-747	542	16	proc	proc	NOUN
ejpam-747	542	17	.	.	PUNCT
ejpam-747	543	1	london	london	PROPN
ejpam-747	543	2	math	math	PROPN
ejpam-747	543	3	.	.	PUNCT
ejpam-747	544	1	soc	soc	PROPN
ejpam-747	544	2	.	.	PUNCT
ejpam-747	545	1	,	,	PUNCT
ejpam-747	545	2	23	23	NUM
ejpam-747	545	3	,	,	PUNCT
ejpam-747	545	4	481	481	NUM
ejpam-747	545	5	-	-	SYM
ejpam-747	545	6	519	519	NUM
ejpam-747	545	7	.	.	NUM
ejpam-747	545	8	1925	1925	NUM
ejpam-747	545	9	.	.	PUNCT
ejpam-747	546	1	[	[	X
ejpam-747	546	2	17	17	NUM
ejpam-747	546	3	]	]	X
ejpam-747	546	4	s.s	s.s	PROPN
ejpam-747	546	5	.	.	PROPN
ejpam-747	546	6	miller	miller	PROPN
ejpam-747	546	7	and	and	CCONJ
ejpam-747	546	8	p.t	p.t	PROPN
ejpam-747	546	9	.	.	PROPN
ejpam-747	546	10	mocanu	mocanu	PROPN
ejpam-747	546	11	,	,	PUNCT
ejpam-747	546	12	second	second	ADJ
ejpam-747	546	13	order	order	NOUN
ejpam-747	546	14	differential	differential	ADJ
ejpam-747	546	15	inequalities	inequality	NOUN
ejpam-747	546	16	in	in	ADP
ejpam-747	546	17	the	the	DET
ejpam-747	546	18	complex	complex	ADJ
ejpam-747	546	19	plane	plane	NOUN
ejpam-747	546	20	,	,	PUNCT
ejpam-747	546	21	j.	j.	PROPN
ejpam-747	546	22	math	math	PROPN
ejpam-747	546	23	.	.	PUNCT
ejpam-747	547	1	ana	ana	PROPN
ejpam-747	547	2	.	.	PUNCT
ejpam-747	547	3	appl	appl	PROPN
ejpam-747	547	4	.	.	PROPN
ejpam-747	547	5	,	,	PUNCT
ejpam-747	547	6	65	65	NUM
ejpam-747	547	7	,	,	PUNCT
ejpam-747	547	8	289	289	NUM
ejpam-747	547	9	-	-	SYM
ejpam-747	547	10	305	305	NUM
ejpam-747	547	11	.	.	PUNCT
ejpam-747	548	1	1978	1978	NUM
ejpam-747	548	2	.	.	PUNCT
ejpam-747	549	1	[	[	X
ejpam-747	549	2	18	18	NUM
ejpam-747	549	3	]	]	X
ejpam-747	549	4	g.	g.	PROPN
ejpam-747	549	5	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-747	549	6	and	and	CCONJ
ejpam-747	549	7	h.m	h.m	PROPN
ejpam-747	549	8	.	.	PROPN
ejpam-747	549	9	srivastava	srivastava	PROPN
ejpam-747	549	10	,	,	PUNCT
ejpam-747	549	11	neighborhoods	neighborhood	NOUN
ejpam-747	549	12	of	of	ADP
ejpam-747	549	13	certain	certain	ADJ
ejpam-747	549	14	classes	class	NOUN
ejpam-747	549	15	of	of	ADP
ejpam-747	549	16	analytic	analytic	ADJ
ejpam-747	549	17	functions	function	NOUN
ejpam-747	549	18	of	of	ADP
ejpam-747	549	19	complex	complex	ADJ
ejpam-747	549	20	order	order	NOUN
ejpam-747	549	21	,	,	PUNCT
ejpam-747	549	22	j.	j.	PROPN
ejpam-747	549	23	inequal	inequal	PROPN
ejpam-747	549	24	.	.	PUNCT
ejpam-747	550	1	pure	pure	ADJ
ejpam-747	550	2	.	.	PUNCT
ejpam-747	551	1	and	and	CCONJ
ejpam-747	551	2	appl	appl	PROPN
ejpam-747	551	3	.	.	PROPN
ejpam-747	551	4	math	math	PROPN
ejpam-747	551	5	.	.	PUNCT
ejpam-747	552	1	,	,	PUNCT
ejpam-747	552	2	5	5	NUM
ejpam-747	552	3	(	(	PUNCT
ejpam-747	552	4	2	2	NUM
ejpam-747	552	5	)	)	PUNCT
ejpam-747	552	6	art	art	NOUN
ejpam-747	552	7	.	.	PUNCT
ejpam-747	553	1	24	24	NUM
ejpam-747	553	2	,	,	PUNCT
ejpam-747	553	3	7	7	NUM
ejpam-747	553	4	pp	pp	NOUN
ejpam-747	553	5	.	.	PUNCT
ejpam-747	554	1	2004	2004	NUM
ejpam-747	554	2	.	.	PUNCT
ejpam-747	555	1	references	reference	NOUN
ejpam-747	555	2	1112	1112	NUM
ejpam-747	555	3	[	[	X
ejpam-747	555	4	19	19	NUM
ejpam-747	555	5	]	]	PUNCT
ejpam-747	555	6	m.	m.	NOUN
ejpam-747	555	7	nunokawa	nunokawa	NOUN
ejpam-747	555	8	,	,	PUNCT
ejpam-747	555	9	on	on	ADP
ejpam-747	555	10	some	some	DET
ejpam-747	555	11	angular	angular	ADJ
ejpam-747	555	12	estimates	estimate	NOUN
ejpam-747	555	13	of	of	ADP
ejpam-747	555	14	analytic	analytic	ADJ
ejpam-747	555	15	functions	function	NOUN
ejpam-747	555	16	,	,	PUNCT
ejpam-747	555	17	math	math	NOUN
ejpam-747	555	18	.	.	PUNCT
ejpam-747	556	1	japonica	japonica	PROPN
ejpam-747	556	2	,	,	PUNCT
ejpam-747	556	3	41	41	NUM
ejpam-747	556	4	,	,	PUNCT
ejpam-747	556	5	447	447	NUM
ejpam-747	556	6	-	-	SYM
ejpam-747	556	7	452	452	NUM
ejpam-747	556	8	.	.	NOUN
ejpam-747	556	9	1995	1995	NUM
ejpam-747	556	10	.	.	PUNCT
ejpam-747	557	1	[	[	X
ejpam-747	557	2	20	20	NUM
ejpam-747	557	3	]	]	PUNCT
ejpam-747	557	4	s.	s.	PROPN
ejpam-747	557	5	owa	owa	PROPN
ejpam-747	557	6	,	,	PUNCT
ejpam-747	557	7	m.	m.	NOUN
ejpam-747	557	8	saigo	saigo	PROPN
ejpam-747	557	9	and	and	CCONJ
ejpam-747	557	10	h.m	h.m	PROPN
ejpam-747	557	11	.	.	PROPN
ejpam-747	557	12	srivastava	srivastava	PROPN
ejpam-747	557	13	,	,	PUNCT
ejpam-747	557	14	some	some	DET
ejpam-747	557	15	characterization	characterization	NOUN
ejpam-747	557	16	theorem	theorem	VERB
ejpam-747	557	17	for	for	ADP
ejpam-747	557	18	starlike	starlike	NOUN
ejpam-747	557	19	and	and	CCONJ
ejpam-747	557	20	convex	convex	NOUN
ejpam-747	557	21	functions	function	NOUN
ejpam-747	557	22	involving	involve	VERB
ejpam-747	557	23	a	a	DET
ejpam-747	557	24	certain	certain	ADJ
ejpam-747	557	25	fractional	fractional	ADJ
ejpam-747	557	26	integral	integral	ADJ
ejpam-747	557	27	operator	operator	NOUN
ejpam-747	557	28	,	,	PUNCT
ejpam-747	557	29	j.	j.	PROPN
ejpam-747	557	30	math	math	PROPN
ejpam-747	557	31	.	.	PUNCT
ejpam-747	558	1	anal	anal	PROPN
ejpam-747	558	2	.	.	PUNCT
ejpam-747	559	1	appl	appl	PROPN
ejpam-747	559	2	.	.	PROPN
ejpam-747	559	3	,	,	PUNCT
ejpam-747	559	4	140	140	NUM
ejpam-747	559	5	,	,	PUNCT
ejpam-747	559	6	419	419	NUM
ejpam-747	559	7	-	-	SYM
ejpam-747	559	8	426	426	NUM
ejpam-747	559	9	.	.	NUM
ejpam-747	559	10	1981	1981	NUM
ejpam-747	559	11	.	.	PUNCT
ejpam-747	560	1	[	[	X
ejpam-747	560	2	21	21	NUM
ejpam-747	560	3	]	]	X
ejpam-747	560	4	j.k	j.k	PROPN
ejpam-747	560	5	.	.	PROPN
ejpam-747	560	6	prajapat	prajapat	PROPN
ejpam-747	560	7	,	,	PUNCT
ejpam-747	560	8	r.	r.	PROPN
ejpam-747	560	9	k.	k.	PROPN
ejpam-747	560	10	raina	raina	PROPN
ejpam-747	560	11	and	and	CCONJ
ejpam-747	560	12	h.m	h.m	PROPN
ejpam-747	560	13	.	.	PROPN
ejpam-747	560	14	srivastava	srivastava	PROPN
ejpam-747	560	15	,	,	PUNCT
ejpam-747	560	16	inclusion	inclusion	NOUN
ejpam-747	560	17	and	and	CCONJ
ejpam-747	560	18	neighborhood	neighborhood	NOUN
ejpam-747	560	19	properties	property	NOUN
ejpam-747	560	20	for	for	ADP
ejpam-747	560	21	certain	certain	ADJ
ejpam-747	560	22	classes	class	NOUN
ejpam-747	560	23	of	of	ADP
ejpam-747	560	24	multivalently	multivalently	ADJ
ejpam-747	560	25	analytic	analytic	ADJ
ejpam-747	560	26	functions	function	NOUN
ejpam-747	560	27	associated	associate	VERB
ejpam-747	560	28	with	with	ADP
ejpam-747	560	29	the	the	DET
ejpam-747	560	30	convolution	convolution	NOUN
ejpam-747	560	31	structure	structure	NOUN
ejpam-747	560	32	,	,	PUNCT
ejpam-747	560	33	j.	j.	PROPN
ejpam-747	560	34	inequal	inequal	PROPN
ejpam-747	560	35	.	.	PUNCT
ejpam-747	561	1	pure	pure	ADJ
ejpam-747	561	2	.	.	PUNCT
ejpam-747	562	1	and	and	CCONJ
ejpam-747	562	2	appl	appl	PROPN
ejpam-747	562	3	.	.	PROPN
ejpam-747	562	4	math	math	PROPN
ejpam-747	562	5	.	.	PUNCT
ejpam-747	563	1	,	,	PUNCT
ejpam-747	563	2	8	8	NUM
ejpam-747	563	3	(	(	PUNCT
ejpam-747	563	4	1	1	NUM
ejpam-747	563	5	)	)	PUNCT
ejpam-747	563	6	,	,	PUNCT
ejpam-747	563	7	8	8	NUM
ejpam-747	563	8	pp	pp	NOUN
ejpam-747	563	9	.	.	PUNCT
ejpam-747	564	1	2007	2007	NUM
ejpam-747	564	2	.	.	PUNCT
ejpam-747	565	1	[	[	X
ejpam-747	565	2	22	22	NUM
ejpam-747	565	3	]	]	X
ejpam-747	565	4	r.k	r.k	PROPN
ejpam-747	565	5	.	.	PROPN
ejpam-747	565	6	raina	raina	PROPN
ejpam-747	565	7	and	and	CCONJ
ejpam-747	565	8	h.m	h.m	PROPN
ejpam-747	565	9	.	.	PROPN
ejpam-747	565	10	srivastava	srivastava	PROPN
ejpam-747	565	11	,	,	PUNCT
ejpam-747	565	12	inclusion	inclusion	NOUN
ejpam-747	565	13	and	and	CCONJ
ejpam-747	565	14	neighborhood	neighborhood	NOUN
ejpam-747	565	15	properties	property	NOUN
ejpam-747	565	16	of	of	ADP
ejpam-747	565	17	some	some	DET
ejpam-747	565	18	analytic	analytic	ADJ
ejpam-747	565	19	and	and	CCONJ
ejpam-747	565	20	multivalent	multivalent	NOUN
ejpam-747	565	21	functions	function	NOUN
ejpam-747	565	22	,	,	PUNCT
ejpam-747	565	23	j.	j.	PROPN
ejpam-747	565	24	inequal	inequal	PROPN
ejpam-747	565	25	.	.	PUNCT
ejpam-747	566	1	pure	pure	ADJ
ejpam-747	566	2	.	.	PUNCT
ejpam-747	567	1	and	and	CCONJ
ejpam-747	567	2	appl	appl	PROPN
ejpam-747	567	3	.	.	PROPN
ejpam-747	567	4	math	math	PROPN
ejpam-747	567	5	.	.	PUNCT
ejpam-747	568	1	,	,	PUNCT
ejpam-747	568	2	7	7	NUM
ejpam-747	568	3	(	(	PUNCT
ejpam-747	568	4	1	1	NUM
ejpam-747	568	5	)	)	PUNCT
ejpam-747	568	6	,	,	PUNCT
ejpam-747	568	7	art	art	NOUN
ejpam-747	568	8	.	.	PUNCT
ejpam-747	569	1	5	5	NUM
ejpam-747	569	2	,	,	PUNCT
ejpam-747	569	3	1	1	NUM
ejpam-747	569	4	-	-	SYM
ejpam-747	569	5	6	6	NUM
ejpam-747	569	6	.	.	NOUN
ejpam-747	569	7	2006	2006	NUM
ejpam-747	569	8	.	.	PUNCT
ejpam-747	570	1	[	[	X
ejpam-747	570	2	23	23	NUM
ejpam-747	570	3	]	]	X
ejpam-747	570	4	s.	s.	PROPN
ejpam-747	570	5	ruscheweyh	ruscheweyh	PROPN
ejpam-747	570	6	,	,	PUNCT
ejpam-747	570	7	new	new	ADJ
ejpam-747	570	8	criteria	criterion	NOUN
ejpam-747	570	9	for	for	ADP
ejpam-747	570	10	univalent	univalent	ADJ
ejpam-747	570	11	functions	function	NOUN
ejpam-747	570	12	,	,	PUNCT
ejpam-747	570	13	proc	proc	NOUN
ejpam-747	570	14	.	.	PUNCT
ejpam-747	570	15	amer	amer	PROPN
ejpam-747	570	16	.	.	PUNCT
ejpam-747	570	17	math	math	PROPN
ejpam-747	570	18	.	.	PUNCT
ejpam-747	571	1	soc	soc	PROPN
ejpam-747	571	2	.	.	PROPN
ejpam-747	571	3	,	,	PUNCT
ejpam-747	571	4	49	49	NUM
ejpam-747	571	5	,	,	PUNCT
ejpam-747	571	6	109115	109115	NUM
ejpam-747	571	7	.	.	PUNCT
ejpam-747	572	1	1975	1975	NUM
ejpam-747	572	2	.	.	PUNCT
ejpam-747	573	1	[	[	X
ejpam-747	573	2	24	24	NUM
ejpam-747	573	3	]	]	X
ejpam-747	573	4	g.	g.	PROPN
ejpam-747	573	5	salagean	salagean	PROPN
ejpam-747	573	6	,	,	PUNCT
ejpam-747	573	7	subclasses	subclass	NOUN
ejpam-747	573	8	of	of	ADP
ejpam-747	573	9	univalent	univalent	ADJ
ejpam-747	573	10	functions	function	NOUN
ejpam-747	573	11	,	,	PUNCT
ejpam-747	573	12	lect	lect	PROPN
ejpam-747	573	13	.	.	PUNCT
ejpam-747	574	1	notes	note	NOUN
ejpam-747	574	2	in	in	ADP
ejpam-747	574	3	math	math	NOUN
ejpam-747	574	4	.	.	PUNCT
ejpam-747	575	1	(	(	PUNCT
ejpam-747	575	2	springer	springer	NOUN
ejpam-747	575	3	verlag	verlag	PROPN
ejpam-747	575	4	)	)	PUNCT
ejpam-747	575	5	,	,	PUNCT
ejpam-747	575	6	10	10	NUM
ejpam-747	575	7	(	(	PUNCT
ejpam-747	575	8	13	13	NUM
ejpam-747	575	9	)	)	PUNCT
ejpam-747	575	10	,	,	PUNCT
ejpam-747	575	11	362	362	NUM
ejpam-747	575	12	-	-	SYM
ejpam-747	575	13	372	372	NUM
ejpam-747	575	14	.	.	NOUN
ejpam-747	575	15	1983	1983	NUM
ejpam-747	575	16	.	.	PUNCT
ejpam-747	576	1	[	[	X
ejpam-747	576	2	25	25	NUM
ejpam-747	576	3	]	]	X
ejpam-747	576	4	p.	p.	PROPN
ejpam-747	576	5	sharma	sharma	PROPN
ejpam-747	576	6	,	,	PUNCT
ejpam-747	576	7	a	a	DET
ejpam-747	576	8	class	class	NOUN
ejpam-747	576	9	of	of	ADP
ejpam-747	576	10	multivalent	multivalent	NOUN
ejpam-747	576	11	analytic	analytic	ADJ
ejpam-747	576	12	functions	function	NOUN
ejpam-747	576	13	with	with	ADP
ejpam-747	576	14	fixed	fix	VERB
ejpam-747	576	15	argument	argument	NOUN
ejpam-747	576	16	of	of	ADP
ejpam-747	576	17	coefficients	coefficient	NOUN
ejpam-747	576	18	involving	involve	VERB
ejpam-747	576	19	wright	wright	PROPN
ejpam-747	576	20	’s	’s	PART
ejpam-747	576	21	generalized	generalize	VERB
ejpam-747	576	22	hypergeometric	hypergeometric	ADJ
ejpam-747	576	23	functions	function	NOUN
ejpam-747	576	24	,	,	PUNCT
ejpam-747	576	25	bull	bull	NOUN
ejpam-747	576	26	.	.	PUNCT
ejpam-747	577	1	math	math	NOUN
ejpam-747	577	2	.	.	PUNCT
ejpam-747	578	1	anal	anal	PROPN
ejpam-747	578	2	.	.	PUNCT
ejpam-747	578	3	appl	appl	PROPN
ejpam-747	578	4	.	.	PROPN
ejpam-747	579	1	,	,	PUNCT
ejpam-747	579	2	2	2	NUM
ejpam-747	579	3	(	(	PUNCT
ejpam-747	579	4	1	1	NUM
ejpam-747	579	5	)	)	PUNCT
ejpam-747	579	6	,	,	PUNCT
ejpam-747	579	7	56	56	NUM
ejpam-747	579	8	-	-	SYM
ejpam-747	579	9	65	65	NUM
ejpam-747	579	10	.	.	PUNCT
ejpam-747	579	11	2010	2010	NUM
ejpam-747	579	12	.	.	PUNCT
ejpam-747	580	1	[	[	X
ejpam-747	580	2	26	26	NUM
ejpam-747	580	3	]	]	X
ejpam-747	580	4	h.m	h.m	PROPN
ejpam-747	580	5	.	.	PROPN
ejpam-747	580	6	srivastava	srivastava	PROPN
ejpam-747	580	7	,	,	PUNCT
ejpam-747	580	8	m.	m.	NOUN
ejpam-747	580	9	saigo	saigo	PROPN
ejpam-747	580	10	and	and	CCONJ
ejpam-747	580	11	s.	s.	PROPN
ejpam-747	580	12	owa	owa	PROPN
ejpam-747	580	13	,	,	PUNCT
ejpam-747	580	14	a	a	DET
ejpam-747	580	15	class	class	NOUN
ejpam-747	580	16	of	of	ADP
ejpam-747	580	17	distortion	distortion	NOUN
ejpam-747	580	18	theorems	theorem	NOUN
ejpam-747	580	19	involving	involve	VERB
ejpam-747	580	20	certain	certain	ADJ
ejpam-747	580	21	operators	operator	NOUN
ejpam-747	580	22	of	of	ADP
ejpam-747	580	23	fractional	fractional	ADJ
ejpam-747	580	24	calculus	calculus	NOUN
ejpam-747	580	25	,	,	PUNCT
ejpam-747	580	26	j.	j.	PROPN
ejpam-747	580	27	math	math	PROPN
ejpam-747	580	28	.	.	PUNCT
ejpam-747	581	1	ana	ana	PROPN
ejpam-747	581	2	.	.	PUNCT
ejpam-747	581	3	appl	appl	PROPN
ejpam-747	581	4	.	.	PROPN
ejpam-747	582	1	,	,	PUNCT
ejpam-747	582	2	131	131	NUM
ejpam-747	582	3	,	,	PUNCT
ejpam-747	582	4	412	412	NUM
ejpam-747	582	5	-	-	SYM
ejpam-747	582	6	420	420	NUM
ejpam-747	582	7	.	.	PUNCT
ejpam-747	583	1	1988	1988	NUM
ejpam-747	583	2	.	.	PUNCT