id	sid	tid	token	lemma	pos
ejpam-544	1	1	3_544_goyal.dvi	3_544_goyal.dvi	NUM
ejpam-544	1	2	european	european	ADJ
ejpam-544	1	3	journal	journal	PROPN
ejpam-544	1	4	of	of	ADP
ejpam-544	1	5	pure	pure	ADJ
ejpam-544	1	6	and	and	CCONJ
ejpam-544	1	7	applied	apply	VERB
ejpam-544	1	8	mathematics	mathematic	NOUN
ejpam-544	1	9	vol	vol	NOUN
ejpam-544	1	10	.	.	PROPN
ejpam-544	2	1	4	4	NUM
ejpam-544	2	2	,	,	PUNCT
ejpam-544	2	3	no	no	INTJ
ejpam-544	2	4	.	.	NOUN
ejpam-544	2	5	3	3	NUM
ejpam-544	2	6	,	,	PUNCT
ejpam-544	2	7	2011	2011	NUM
ejpam-544	2	8	,	,	PUNCT
ejpam-544	2	9	230	230	NUM
ejpam-544	2	10	-	-	SYM
ejpam-544	2	11	236	236	NUM
ejpam-544	2	12	issn	issn	PROPN
ejpam-544	2	13	1307	1307	NUM
ejpam-544	2	14	-	-	SYM
ejpam-544	2	15	5543	5543	NUM
ejpam-544	2	16	–	–	PUNCT
ejpam-544	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-544	2	18	sufficient	sufficient	ADJ
ejpam-544	2	19	conditions	condition	NOUN
ejpam-544	2	20	for	for	ADP
ejpam-544	2	21	sakaguchi	sakaguchi	ADJ
ejpam-544	2	22	type	type	NOUN
ejpam-544	2	23	functions	function	NOUN
ejpam-544	2	24	of	of	ADP
ejpam-544	2	25	order	order	NOUN
ejpam-544	2	26	β	β	X
ejpam-544	2	27	s.	s.	PROPN
ejpam-544	2	28	p.	p.	PROPN
ejpam-544	2	29	goyal1,∗	goyal1,∗	PROPN
ejpam-544	2	30	,	,	PUNCT
ejpam-544	2	31	pramila	pramila	NOUN
ejpam-544	2	32	vijaywargiya1	vijaywargiya1	NOUN
ejpam-544	2	33	,	,	PUNCT
ejpam-544	2	34	pranay	pranay	NOUN
ejpam-544	2	35	goswami2	goswami2	PROPN
ejpam-544	2	36	1	1	NUM
ejpam-544	2	37	department	department	NOUN
ejpam-544	2	38	of	of	ADP
ejpam-544	2	39	mathematics	mathematic	NOUN
ejpam-544	2	40	,	,	PUNCT
ejpam-544	2	41	university	university	NOUN
ejpam-544	2	42	of	of	ADP
ejpam-544	2	43	rajasthan	rajasthan	PROPN
ejpam-544	2	44	,	,	PUNCT
ejpam-544	2	45	jaipur-302004	jaipur-302004	NOUN
ejpam-544	2	46	,	,	PUNCT
ejpam-544	2	47	india	india	PROPN
ejpam-544	2	48	2	2	NUM
ejpam-544	2	49	department	department	NOUN
ejpam-544	2	50	of	of	ADP
ejpam-544	2	51	mathematics	mathematic	NOUN
ejpam-544	2	52	,	,	PUNCT
ejpam-544	2	53	amity	amity	NOUN
ejpam-544	2	54	university	university	NOUN
ejpam-544	2	55	rajasthan	rajasthan	NOUN
ejpam-544	2	56	,	,	PUNCT
ejpam-544	2	57	jaipur-302002	jaipur-302002	NOUN
ejpam-544	2	58	,	,	PUNCT
ejpam-544	2	59	india	india	PROPN
ejpam-544	2	60	abstract	abstract	NOUN
ejpam-544	2	61	.	.	PUNCT
ejpam-544	3	1	in	in	ADP
ejpam-544	3	2	this	this	DET
ejpam-544	3	3	paper	paper	NOUN
ejpam-544	3	4	,	,	PUNCT
ejpam-544	3	5	we	we	PRON
ejpam-544	3	6	obtain	obtain	VERB
ejpam-544	3	7	some	some	DET
ejpam-544	3	8	sufficient	sufficient	ADJ
ejpam-544	3	9	conditions	condition	NOUN
ejpam-544	3	10	for	for	ADP
ejpam-544	3	11	sakaguchi	sakaguchi	ADJ
ejpam-544	3	12	type	type	NOUN
ejpam-544	3	13	function	function	NOUN
ejpam-544	3	14	of	of	ADP
ejpam-544	3	15	order	order	NOUN
ejpam-544	3	16	β	β	X
ejpam-544	3	17	,	,	PUNCT
ejpam-544	3	18	defined	define	VERB
ejpam-544	3	19	on	on	ADP
ejpam-544	3	20	the	the	DET
ejpam-544	3	21	open	open	ADJ
ejpam-544	3	22	unit	unit	NOUN
ejpam-544	3	23	disk	disk	NOUN
ejpam-544	3	24	.	.	PUNCT
ejpam-544	4	1	several	several	ADJ
ejpam-544	4	2	interesting	interesting	ADJ
ejpam-544	4	3	consequences	consequence	NOUN
ejpam-544	4	4	of	of	ADP
ejpam-544	4	5	our	our	PRON
ejpam-544	4	6	results	result	NOUN
ejpam-544	4	7	are	be	AUX
ejpam-544	4	8	also	also	ADV
ejpam-544	4	9	pointed	point	VERB
ejpam-544	4	10	out	out	ADP
ejpam-544	4	11	.	.	PUNCT
ejpam-544	5	1	2000	2000	NUM
ejpam-544	5	2	mathematics	mathematic	NOUN
ejpam-544	5	3	subject	subject	NOUN
ejpam-544	5	4	classifications	classification	NOUN
ejpam-544	5	5	:	:	PUNCT
ejpam-544	5	6	30c45	30c45	NUM
ejpam-544	5	7	.	.	PUNCT
ejpam-544	6	1	key	key	ADJ
ejpam-544	6	2	words	word	NOUN
ejpam-544	6	3	and	and	CCONJ
ejpam-544	6	4	phrases	phrase	NOUN
ejpam-544	6	5	:	:	PUNCT
ejpam-544	6	6	sakaguchi	sakaguchi	ADJ
ejpam-544	6	7	type	type	NOUN
ejpam-544	6	8	functions	function	NOUN
ejpam-544	6	9	of	of	ADP
ejpam-544	6	10	order	order	NOUN
ejpam-544	6	11	β	β	X
ejpam-544	6	12	,	,	PUNCT
ejpam-544	6	13	univalent	univalent	ADJ
ejpam-544	6	14	functions	function	NOUN
ejpam-544	6	15	.	.	PUNCT
ejpam-544	7	1	1	1	X
ejpam-544	7	2	.	.	X
ejpam-544	7	3	introduction	introduction	NOUN
ejpam-544	7	4	let	let	VERB
ejpam-544	7	5	an	an	DET
ejpam-544	7	6	be	be	AUX
ejpam-544	7	7	the	the	DET
ejpam-544	7	8	class	class	NOUN
ejpam-544	7	9	of	of	ADP
ejpam-544	7	10	all	all	DET
ejpam-544	7	11	functions	function	NOUN
ejpam-544	7	12	f	f	X
ejpam-544	7	13	(	(	PUNCT
ejpam-544	7	14	z	z	NOUN
ejpam-544	7	15	)	)	PUNCT
ejpam-544	7	16	=	=	SYM
ejpam-544	7	17	z	z	NOUN
ejpam-544	8	1	+	+	NOUN
ejpam-544	8	2	an+1zn+1	an+1zn+1	ADJ
ejpam-544	8	3	+	+	PUNCT
ejpam-544	8	4	.	.	PUNCT
ejpam-544	8	5	.	.	PUNCT
ejpam-544	9	1	.	.	PUNCT
ejpam-544	10	1	,	,	PUNCT
ejpam-544	10	2	which	which	PRON
ejpam-544	10	3	are	be	AUX
ejpam-544	10	4	analytic	analytic	ADJ
ejpam-544	10	5	in	in	ADP
ejpam-544	10	6	the	the	DET
ejpam-544	10	7	open	open	ADJ
ejpam-544	10	8	unit	unit	NOUN
ejpam-544	10	9	disk	disk	NOUN
ejpam-544	10	10	∆=	∆=	NOUN
ejpam-544	10	11	{	{	PUNCT
ejpam-544	10	12	z	z	NOUN
ejpam-544	10	13	:	:	PUNCT
ejpam-544	10	14	z	z	PROPN
ejpam-544	10	15	∈	∈	PROPN
ejpam-544	10	16	c	c	NOUN
ejpam-544	10	17	;	;	PUNCT
ejpam-544	10	18	|z|	|z|	VERB
ejpam-544	10	19	<	<	X
ejpam-544	10	20	1	1	NUM
ejpam-544	10	21	}	}	PUNCT
ejpam-544	10	22	and	and	CCONJ
ejpam-544	10	23	let	let	VERB
ejpam-544	10	24	a1	a1	NOUN
ejpam-544	10	25	=	=	NOUN
ejpam-544	10	26	a.	a.	NOUN
ejpam-544	10	27	a	a	DET
ejpam-544	10	28	function	function	NOUN
ejpam-544	10	29	f	f	X
ejpam-544	10	30	(	(	PUNCT
ejpam-544	10	31	z	z	NOUN
ejpam-544	10	32	)	)	PUNCT
ejpam-544	10	33	∈	∈	PROPN
ejpam-544	11	1	an	an	PRON
ejpam-544	11	2	is	be	AUX
ejpam-544	11	3	said	say	VERB
ejpam-544	11	4	to	to	PART
ejpam-544	11	5	be	be	AUX
ejpam-544	11	6	in	in	ADP
ejpam-544	11	7	class	class	NOUN
ejpam-544	11	8	sn(β	sn(β	PUNCT
ejpam-544	11	9	,	,	PUNCT
ejpam-544	11	10	t	t	PROPN
ejpam-544	11	11	)	)	PUNCT
ejpam-544	11	12	,	,	PUNCT
ejpam-544	11	13	if	if	SCONJ
ejpam-544	11	14	it	it	PRON
ejpam-544	11	15	satisfies	satisfy	VERB
ejpam-544	11	16	re	re	VERB
ejpam-544	11	17	¨	¨	X
ejpam-544	11	18	(	(	PUNCT
ejpam-544	11	19	1−	1−	NUM
ejpam-544	11	20	t)z	t)z	NOUN
ejpam-544	11	21	f	f	PROPN
ejpam-544	11	22	′(z	′(z	NOUN
ejpam-544	11	23	)	)	PUNCT
ejpam-544	11	24	f	f	PROPN
ejpam-544	11	25	(	(	PUNCT
ejpam-544	11	26	z)−	z)−	PROPN
ejpam-544	11	27	f	f	X
ejpam-544	11	28	(	(	PUNCT
ejpam-544	11	29	tz	tz	PROPN
ejpam-544	11	30	)	)	PUNCT
ejpam-544	11	31	«	«	PUNCT
ejpam-544	11	32	>	>	PUNCT
ejpam-544	11	33	β	β	X
ejpam-544	11	34	,	,	PUNCT
ejpam-544	11	35	(	(	PUNCT
ejpam-544	11	36	|t|	|t|	PROPN
ejpam-544	11	37	≤	≤	NOUN
ejpam-544	11	38	1	1	NUM
ejpam-544	11	39	,	,	PUNCT
ejpam-544	11	40	t	t	PROPN
ejpam-544	11	41	6=	6=	PROPN
ejpam-544	11	42	1	1	NUM
ejpam-544	11	43	)	)	PUNCT
ejpam-544	11	44	(	(	PUNCT
ejpam-544	11	45	1	1	X
ejpam-544	11	46	)	)	PUNCT
ejpam-544	11	47	for	for	ADP
ejpam-544	11	48	some	some	DET
ejpam-544	11	49	β(0≤	β(0≤	NOUN
ejpam-544	11	50	β	β	X
ejpam-544	11	51	<	<	X
ejpam-544	11	52	1	1	NUM
ejpam-544	11	53	)	)	PUNCT
ejpam-544	11	54	and	and	CCONJ
ejpam-544	11	55	for	for	ADP
ejpam-544	11	56	all	all	DET
ejpam-544	11	57	z	z	NOUN
ejpam-544	11	58	∈∆.	∈∆.	PROPN
ejpam-544	11	59	for	for	ADP
ejpam-544	11	60	n=	n=	ADJ
ejpam-544	11	61	1	1	NUM
ejpam-544	11	62	,	,	PUNCT
ejpam-544	11	63	this	this	DET
ejpam-544	11	64	class	class	NOUN
ejpam-544	11	65	is	be	AUX
ejpam-544	11	66	reduced	reduce	VERB
ejpam-544	11	67	to	to	ADP
ejpam-544	11	68	s(β	s(β	PROPN
ejpam-544	11	69	,	,	PUNCT
ejpam-544	11	70	t	t	PROPN
ejpam-544	11	71	)	)	PUNCT
ejpam-544	11	72	(	(	PUNCT
ejpam-544	11	73	see	see	VERB
ejpam-544	11	74	,	,	PUNCT
ejpam-544	11	75	[	[	X
ejpam-544	11	76	5	5	NUM
ejpam-544	11	77	]	]	NUM
ejpam-544	11	78	)	)	PUNCT
ejpam-544	11	79	.	.	PUNCT
ejpam-544	12	1	the	the	DET
ejpam-544	12	2	class	class	NOUN
ejpam-544	12	3	s(0,−1	s(0,−1	PROPN
ejpam-544	12	4	)	)	PUNCT
ejpam-544	12	5	was	be	AUX
ejpam-544	12	6	introduced	introduce	VERB
ejpam-544	12	7	by	by	ADP
ejpam-544	12	8	sakaguchi	sakaguchi	ADJ
ejpam-544	12	9	[	[	X
ejpam-544	12	10	7	7	NUM
ejpam-544	12	11	]	]	PUNCT
ejpam-544	12	12	.	.	PUNCT
ejpam-544	13	1	therefore	therefore	ADV
ejpam-544	13	2	,	,	PUNCT
ejpam-544	13	3	a	a	DET
ejpam-544	13	4	function	function	NOUN
ejpam-544	13	5	f	f	X
ejpam-544	13	6	(	(	PUNCT
ejpam-544	13	7	z	z	NOUN
ejpam-544	13	8	)	)	PUNCT
ejpam-544	13	9	∈	∈	PROPN
ejpam-544	13	10	s(β	s(β	PROPN
ejpam-544	13	11	,	,	PUNCT
ejpam-544	13	12	−1	−1	NUM
ejpam-544	13	13	)	)	PUNCT
ejpam-544	13	14	is	be	AUX
ejpam-544	13	15	called	call	VERB
ejpam-544	13	16	sakaguchi	sakaguchi	ADJ
ejpam-544	13	17	function	function	NOUN
ejpam-544	13	18	of	of	ADP
ejpam-544	13	19	order	order	NOUN
ejpam-544	13	20	β	β	X
ejpam-544	13	21	(	(	PUNCT
ejpam-544	13	22	see	see	VERB
ejpam-544	13	23	,	,	PUNCT
ejpam-544	13	24	[	[	X
ejpam-544	13	25	1	1	NUM
ejpam-544	13	26	]	]	NUM
ejpam-544	13	27	)	)	PUNCT
ejpam-544	13	28	.	.	PUNCT
ejpam-544	14	1	recently	recently	ADV
ejpam-544	14	2	owa	owa	PROPN
ejpam-544	14	3	et	et	PROPN
ejpam-544	14	4	al	al	PROPN
ejpam-544	14	5	.	.	PUNCT
ejpam-544	15	1	[	[	X
ejpam-544	15	2	5	5	NUM
ejpam-544	15	3	]	]	PUNCT
ejpam-544	15	4	,	,	PUNCT
ejpam-544	15	5	goyal	goyal	PROPN
ejpam-544	15	6	and	and	CCONJ
ejpam-544	15	7	goswami	goswami	PROPN
ejpam-544	15	8	[	[	X
ejpam-544	15	9	2	2	X
ejpam-544	15	10	]	]	PUNCT
ejpam-544	15	11	have	have	AUX
ejpam-544	15	12	discussed	discuss	VERB
ejpam-544	15	13	some	some	DET
ejpam-544	15	14	properties	property	NOUN
ejpam-544	15	15	for	for	ADP
ejpam-544	15	16	functions	function	NOUN
ejpam-544	15	17	f	f	X
ejpam-544	15	18	(	(	PUNCT
ejpam-544	15	19	z	z	NOUN
ejpam-544	15	20	)	)	PUNCT
ejpam-544	15	21	∈	∈	PROPN
ejpam-544	15	22	s(β	s(β	PROPN
ejpam-544	15	23	,	,	PUNCT
ejpam-544	15	24	t	t	PROPN
ejpam-544	15	25	)	)	PUNCT
ejpam-544	15	26	.	.	PUNCT
ejpam-544	16	1	in	in	ADP
ejpam-544	16	2	this	this	DET
ejpam-544	16	3	paper	paper	NOUN
ejpam-544	16	4	,	,	PUNCT
ejpam-544	16	5	we	we	PRON
ejpam-544	16	6	obtain	obtain	VERB
ejpam-544	16	7	some	some	DET
ejpam-544	16	8	sufficient	sufficient	ADJ
ejpam-544	16	9	conditions	condition	NOUN
ejpam-544	16	10	for	for	ADP
ejpam-544	16	11	functions	function	NOUN
ejpam-544	16	12	f	f	X
ejpam-544	16	13	(	(	PUNCT
ejpam-544	16	14	z	z	NOUN
ejpam-544	16	15	)	)	PUNCT
ejpam-544	16	16	∈	∈	PROPN
ejpam-544	16	17	sn(β	sn(β	NUM
ejpam-544	16	18	,	,	PUNCT
ejpam-544	16	19	t	t	PROPN
ejpam-544	16	20	)	)	PUNCT
ejpam-544	16	21	.	.	PUNCT
ejpam-544	17	1	to	to	PART
ejpam-544	17	2	prove	prove	VERB
ejpam-544	17	3	our	our	PRON
ejpam-544	17	4	results	result	NOUN
ejpam-544	17	5	,	,	PUNCT
ejpam-544	17	6	we	we	PRON
ejpam-544	17	7	need	need	VERB
ejpam-544	17	8	the	the	DET
ejpam-544	17	9	following	follow	VERB
ejpam-544	17	10	:	:	PUNCT
ejpam-544	17	11	lemma	lemma	PROPN
ejpam-544	17	12	1	1	NUM
ejpam-544	17	13	(	(	PUNCT
ejpam-544	17	14	[	[	X
ejpam-544	17	15	4	4	NUM
ejpam-544	17	16	]	]	NUM
ejpam-544	17	17	)	)	PUNCT
ejpam-544	17	18	.	.	PUNCT
ejpam-544	18	1	let	let	VERB
ejpam-544	18	2	ω	ω	PRON
ejpam-544	18	3	be	be	AUX
ejpam-544	18	4	a	a	DET
ejpam-544	18	5	set	set	NOUN
ejpam-544	18	6	in	in	ADP
ejpam-544	18	7	the	the	DET
ejpam-544	18	8	complex	complex	ADJ
ejpam-544	18	9	plane	plane	NOUN
ejpam-544	18	10	c	c	NOUN
ejpam-544	18	11	and	and	CCONJ
ejpam-544	18	12	suppose	suppose	VERB
ejpam-544	18	13	that	that	SCONJ
ejpam-544	18	14	φ	φ	PROPN
ejpam-544	18	15	is	be	AUX
ejpam-544	18	16	a	a	DET
ejpam-544	18	17	mapping	mapping	NOUN
ejpam-544	18	18	from	from	ADP
ejpam-544	18	19	c	c	PROPN
ejpam-544	18	20	2	2	NUM
ejpam-544	18	21	×∆	×∆	ADV
ejpam-544	18	22	to	to	ADP
ejpam-544	18	23	c	c	NOUN
ejpam-544	18	24	which	which	PRON
ejpam-544	18	25	satisfies	satisfy	VERB
ejpam-544	18	26	φ(i	φ(i	PROPN
ejpam-544	18	27	x	x	SYM
ejpam-544	18	28	,	,	PUNCT
ejpam-544	18	29	y	y	PROPN
ejpam-544	18	30	;	;	PUNCT
ejpam-544	18	31	z	z	X
ejpam-544	18	32	)	)	PUNCT
ejpam-544	18	33	6∈	6∈	PROPN
ejpam-544	18	34	ω	ω	PROPN
ejpam-544	18	35	for	for	ADP
ejpam-544	18	36	z	z	NOUN
ejpam-544	18	37	∈∆	∈∆	NOUN
ejpam-544	18	38	,	,	PUNCT
ejpam-544	18	39	and	and	CCONJ
ejpam-544	18	40	for	for	ADP
ejpam-544	18	41	all	all	DET
ejpam-544	18	42	real	real	ADJ
ejpam-544	18	43	x	x	NOUN
ejpam-544	18	44	,	,	PUNCT
ejpam-544	18	45	y	y	PROPN
ejpam-544	18	46	such	such	ADJ
ejpam-544	18	47	that	that	SCONJ
ejpam-544	18	48	y	y	PROPN
ejpam-544	18	49	≤	≤	PROPN
ejpam-544	18	50	−n(1+x2)/2	−n(1+x2)/2	PROPN
ejpam-544	18	51	.	.	PUNCT
ejpam-544	19	1	if	if	SCONJ
ejpam-544	19	2	the	the	DET
ejpam-544	19	3	function	function	NOUN
ejpam-544	19	4	p(z	p(z	NOUN
ejpam-544	19	5	)	)	PUNCT
ejpam-544	20	1	=	=	SYM
ejpam-544	21	1	1+cnzn+	1+cnzn+	NUM
ejpam-544	21	2	.	.	PUNCT
ejpam-544	21	3	.	.	PUNCT
ejpam-544	21	4	.	.	PUNCT
ejpam-544	22	1	is	be	AUX
ejpam-544	22	2	analytic	analytic	ADJ
ejpam-544	22	3	in∆	in∆	PROPN
ejpam-544	22	4	and	and	CCONJ
ejpam-544	22	5	φ(p(z	φ(p(z	NUM
ejpam-544	22	6	)	)	PUNCT
ejpam-544	22	7	,	,	PUNCT
ejpam-544	22	8	zp′(z	zp′(z	PROPN
ejpam-544	22	9	)	)	PUNCT
ejpam-544	22	10	;	;	PUNCT
ejpam-544	22	11	z	z	X
ejpam-544	22	12	)	)	PUNCT
ejpam-544	22	13	∈	∈	PROPN
ejpam-544	22	14	ω	ω	PROPN
ejpam-544	22	15	for	for	ADP
ejpam-544	22	16	all	all	DET
ejpam-544	22	17	z	z	NOUN
ejpam-544	22	18	∈∆	∈∆	NOUN
ejpam-544	22	19	,	,	PUNCT
ejpam-544	22	20	then	then	ADV
ejpam-544	22	21	re(p(z	re(p(z	ADJ
ejpam-544	22	22	)	)	PUNCT
ejpam-544	22	23	)	)	PUNCT
ejpam-544	23	1	>	>	X
ejpam-544	23	2	0	0	X
ejpam-544	23	3	.	.	X
ejpam-544	23	4	∗corresponding	∗corresponde	VERB
ejpam-544	23	5	author	author	NOUN
ejpam-544	23	6	.	.	PUNCT
ejpam-544	24	1	email	email	NOUN
ejpam-544	24	2	addresses	address	NOUN
ejpam-544	24	3	:	:	PUNCT
ejpam-544	24	4	somprg	somprg	PROPN
ejpam-544	24	5	�	�	PROPN
ejpam-544	24	6	gmail	gmail	NOUN
ejpam-544	24	7	.	.	PUNCT
ejpam-544	25	1	om	om	PROPN
ejpam-544	25	2	(	(	PUNCT
ejpam-544	25	3	s.	s.	PROPN
ejpam-544	25	4	goyal	goyal	PROPN
ejpam-544	25	5	)	)	PUNCT
ejpam-544	25	6	,	,	PUNCT
ejpam-544	25	7	pramilavijay1979	pramilavijay1979	NOUN
ejpam-544	25	8	�	�	NOUN
ejpam-544	25	9	gmail	gmail	NOUN
ejpam-544	25	10	.	.	PUNCT
ejpam-544	26	1	om	om	PROPN
ejpam-544	26	2	(	(	PUNCT
ejpam-544	26	3	p.	p.	NOUN
ejpam-544	26	4	vijaywargiya),pranaygoswami83	vijaywargiya),pranaygoswami83	NOUN
ejpam-544	26	5	�	�	NOUN
ejpam-544	26	6	gmail	gmail	NOUN
ejpam-544	26	7	.	.	PUNCT
ejpam-544	27	1	om	om	PROPN
ejpam-544	27	2	(	(	PUNCT
ejpam-544	27	3	p.	p.	NOUN
ejpam-544	27	4	goswami	goswami	PROPN
ejpam-544	27	5	)	)	PUNCT
ejpam-544	27	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-544	28	1	230	230	NUM
ejpam-544	28	2	c	c	NOUN
ejpam-544	28	3	©	©	NOUN
ejpam-544	28	4	2011	2011	NUM
ejpam-544	28	5	ejpam	ejpam	VERB
ejpam-544	28	6	all	all	DET
ejpam-544	28	7	rights	right	NOUN
ejpam-544	28	8	reserved	reserve	VERB
ejpam-544	28	9	.	.	PUNCT
ejpam-544	29	1	s.	s.	PROPN
ejpam-544	29	2	goyal	goyal	PROPN
ejpam-544	29	3	,	,	PUNCT
ejpam-544	29	4	p.	p.	NOUN
ejpam-544	29	5	vijaywargiya	vijaywargiya	NOUN
ejpam-544	29	6	,	,	PUNCT
ejpam-544	29	7	p.	p.	NOUN
ejpam-544	29	8	goswami	goswami	PROPN
ejpam-544	29	9	/	/	SYM
ejpam-544	29	10	eur	eur	PROPN
ejpam-544	29	11	.	.	PUNCT
ejpam-544	30	1	j.	j.	PROPN
ejpam-544	30	2	pure	pure	PROPN
ejpam-544	30	3	appl	appl	PROPN
ejpam-544	30	4	.	.	PROPN
ejpam-544	30	5	math	math	PROPN
ejpam-544	30	6	,	,	PUNCT
ejpam-544	30	7	4	4	NUM
ejpam-544	30	8	(	(	PUNCT
ejpam-544	30	9	2011	2011	NUM
ejpam-544	30	10	)	)	PUNCT
ejpam-544	30	11	,	,	PUNCT
ejpam-544	30	12	230	230	NUM
ejpam-544	30	13	-	-	SYM
ejpam-544	30	14	236	236	NUM
ejpam-544	30	15	231	231	NUM
ejpam-544	30	16	2	2	NUM
ejpam-544	30	17	.	.	PUNCT
ejpam-544	31	1	main	main	ADJ
ejpam-544	31	2	results	result	NOUN
ejpam-544	31	3	theorem	theorem	VERB
ejpam-544	31	4	1	1	NUM
ejpam-544	31	5	.	.	PUNCT
ejpam-544	32	1	if	if	SCONJ
ejpam-544	32	2	f	f	PROPN
ejpam-544	32	3	(	(	PUNCT
ejpam-544	32	4	z	z	NOUN
ejpam-544	32	5	)	)	PUNCT
ejpam-544	32	6	∈	∈	PROPN
ejpam-544	32	7	an	an	DET
ejpam-544	32	8	satisfies	satisfie	NOUN
ejpam-544	32	9	re	re	VERB
ejpam-544	32	10	�	�	PROPN
ejpam-544	32	11	(	(	PUNCT
ejpam-544	32	12	1−	1−	NUM
ejpam-544	32	13	t)2z	t)2z	PRON
ejpam-544	32	14	f	f	PROPN
ejpam-544	32	15	′(z	′(z	NOUN
ejpam-544	32	16	)	)	PUNCT
ejpam-544	32	17	f	f	PROPN
ejpam-544	32	18	(	(	PUNCT
ejpam-544	32	19	z)−	z)−	PROPN
ejpam-544	32	20	f	f	X
ejpam-544	32	21	(	(	PUNCT
ejpam-544	32	22	tz	tz	PROPN
ejpam-544	32	23	)	)	PUNCT
ejpam-544	32	24	¨	¨	NOUN
ejpam-544	32	25	αz	αz	ADP
ejpam-544	32	26	f	f	PROPN
ejpam-544	32	27	′′(z	′′(z	PROPN
ejpam-544	32	28	)	)	PUNCT
ejpam-544	32	29	f	f	PROPN
ejpam-544	32	30	′(z	′(z	NOUN
ejpam-544	32	31	)	)	PUNCT
ejpam-544	33	1	+	+	CCONJ
ejpam-544	33	2	αtz	αtz	NOUN
ejpam-544	33	3	f	f	PROPN
ejpam-544	33	4	′(tz	′(tz	PROPN
ejpam-544	33	5	)	)	PUNCT
ejpam-544	34	1	f	f	PROPN
ejpam-544	34	2	(	(	PUNCT
ejpam-544	34	3	z)−	z)−	PROPN
ejpam-544	34	4	f	f	X
ejpam-544	34	5	(	(	PUNCT
ejpam-544	34	6	tz	tz	PROPN
ejpam-544	34	7	)	)	PUNCT
ejpam-544	34	8	+	+	CCONJ
ejpam-544	34	9	1	1	NUM
ejpam-544	34	10	«	«	PUNCT
ejpam-544	34	11	�	�	X
ejpam-544	34	12	>	>	X
ejpam-544	34	13	αβ	αβ	PROPN
ejpam-544	34	14	§	§	PROPN
ejpam-544	34	15	β	β	X
ejpam-544	34	16	+	+	CCONJ
ejpam-544	34	17	n	n	PRON
ejpam-544	34	18	2	2	NUM
ejpam-544	34	19	(	(	PUNCT
ejpam-544	34	20	1−	1−	NUM
ejpam-544	34	21	t)−	t)−	PROPN
ejpam-544	34	22	(	(	PUNCT
ejpam-544	34	23	1−	1−	NUM
ejpam-544	34	24	t	t	NOUN
ejpam-544	34	25	)	)	PUNCT
ejpam-544	34	26	ª	ª	PROPN
ejpam-544	35	1	+	+	PROPN
ejpam-544	35	2	§	§	PROPN
ejpam-544	35	3	β	β	X
ejpam-544	35	4	−	−	PROPN
ejpam-544	35	5	nα	nα	VERB
ejpam-544	35	6	2	2	NUM
ejpam-544	35	7	ª	ª	SYM
ejpam-544	35	8	(	(	PUNCT
ejpam-544	35	9	1−	1−	NUM
ejpam-544	35	10	t	t	NOUN
ejpam-544	35	11	)	)	PUNCT
ejpam-544	35	12	for	for	ADP
ejpam-544	35	13	(	(	PUNCT
ejpam-544	35	14	z	z	NOUN
ejpam-544	35	15	∈∆	∈∆	PROPN
ejpam-544	35	16	,	,	PUNCT
ejpam-544	35	17	0≤	0≤	NUM
ejpam-544	35	18	α	α	DET
ejpam-544	35	19	≤	≤	NUM
ejpam-544	35	20	1	1	NUM
ejpam-544	35	21	,	,	PUNCT
ejpam-544	35	22	0≤	0≤	PUNCT
ejpam-544	35	23	β	β	X
ejpam-544	35	24	<	<	X
ejpam-544	35	25	1	1	NUM
ejpam-544	35	26	,	,	PUNCT
ejpam-544	35	27	|t|	|t|	VERB
ejpam-544	35	28	≤	≤	NOUN
ejpam-544	35	29	1	1	NUM
ejpam-544	35	30	and	and	CCONJ
ejpam-544	35	31	t	t	PROPN
ejpam-544	35	32	6=	6=	NUM
ejpam-544	35	33	1	1	NUM
ejpam-544	35	34	)	)	PUNCT
ejpam-544	35	35	,	,	PUNCT
ejpam-544	35	36	then	then	ADV
ejpam-544	35	37	f	f	X
ejpam-544	35	38	(	(	PUNCT
ejpam-544	35	39	z	z	NOUN
ejpam-544	35	40	)	)	PUNCT
ejpam-544	35	41	∈	∈	PROPN
ejpam-544	35	42	sn(β	sn(β	NUM
ejpam-544	35	43	,	,	PUNCT
ejpam-544	35	44	t	t	PROPN
ejpam-544	35	45	)	)	PUNCT
ejpam-544	35	46	.	.	PUNCT
ejpam-544	36	1	proof	proof	NOUN
ejpam-544	36	2	.	.	PUNCT
ejpam-544	37	1	define	define	VERB
ejpam-544	37	2	p(z	p(z	NOUN
ejpam-544	37	3	)	)	PUNCT
ejpam-544	37	4	by	by	ADP
ejpam-544	37	5	(	(	PUNCT
ejpam-544	37	6	1−	1−	NUM
ejpam-544	37	7	t)z	t)z	NOUN
ejpam-544	37	8	f	f	PROPN
ejpam-544	37	9	′(z	′(z	NOUN
ejpam-544	37	10	)	)	PUNCT
ejpam-544	37	11	f	f	PROPN
ejpam-544	37	12	(	(	PUNCT
ejpam-544	37	13	z)−	z)−	PROPN
ejpam-544	37	14	f	f	X
ejpam-544	37	15	(	(	PUNCT
ejpam-544	37	16	tz	tz	PROPN
ejpam-544	37	17	)	)	PUNCT
ejpam-544	37	18	=	=	SYM
ejpam-544	37	19	(	(	PUNCT
ejpam-544	37	20	1−	1−	NUM
ejpam-544	37	21	β)p(z	β)p(z	NOUN
ejpam-544	37	22	)	)	PUNCT
ejpam-544	38	1	+	+	CCONJ
ejpam-544	38	2	β	β	X
ejpam-544	38	3	.	.	PUNCT
ejpam-544	39	1	then	then	ADV
ejpam-544	39	2	p(z	p(z	PROPN
ejpam-544	39	3	)	)	PUNCT
ejpam-544	39	4	=	=	SYM
ejpam-544	39	5	1	1	NUM
ejpam-544	39	6	+	+	NUM
ejpam-544	39	7	cnzn	cnzn	NOUN
ejpam-544	39	8	+	+	PUNCT
ejpam-544	39	9	.	.	PUNCT
ejpam-544	39	10	.	.	PUNCT
ejpam-544	39	11	.	.	PUNCT
ejpam-544	40	1	and	and	CCONJ
ejpam-544	40	2	is	be	AUX
ejpam-544	40	3	an	an	DET
ejpam-544	40	4	analytic	analytic	NOUN
ejpam-544	40	5	in	in	ADP
ejpam-544	40	6	∆.	∆.	NOUN
ejpam-544	40	7	a	a	DET
ejpam-544	40	8	computation	computation	NOUN
ejpam-544	40	9	shows	show	VERB
ejpam-544	40	10	that	that	SCONJ
ejpam-544	40	11	z	z	NOUN
ejpam-544	40	12	f	f	PROPN
ejpam-544	40	13	′′(z	′′(z	PROPN
ejpam-544	40	14	)	)	PUNCT
ejpam-544	40	15	f	f	PROPN
ejpam-544	40	16	′(z	′(z	NOUN
ejpam-544	40	17	)	)	PUNCT
ejpam-544	41	1	+	+	CCONJ
ejpam-544	41	2	tz	tz	PROPN
ejpam-544	41	3	f	f	PROPN
ejpam-544	41	4	′(tz	′(tz	PROPN
ejpam-544	41	5	)	)	PUNCT
ejpam-544	42	1	f	f	PROPN
ejpam-544	42	2	(	(	PUNCT
ejpam-544	42	3	z)−	z)−	PROPN
ejpam-544	42	4	f	f	X
ejpam-544	42	5	(	(	PUNCT
ejpam-544	42	6	tz	tz	PROPN
ejpam-544	42	7	)	)	PUNCT
ejpam-544	42	8	=	=	SYM
ejpam-544	42	9	(	(	PUNCT
ejpam-544	42	10	1−	1−	NUM
ejpam-544	42	11	t)(1−	t)(1−	NOUN
ejpam-544	42	12	β)zp′(z	β)zp′(z	NUM
ejpam-544	42	13	)	)	PUNCT
ejpam-544	42	14	+	+	CCONJ
ejpam-544	43	1	[	[	X
ejpam-544	43	2	(	(	PUNCT
ejpam-544	43	3	1−	1−	NUM
ejpam-544	43	4	β)p(z	β)p(z	NOUN
ejpam-544	43	5	)	)	PUNCT
ejpam-544	43	6	+	+	NUM
ejpam-544	43	7	β]2	β]2	SYM
ejpam-544	43	8	−	−	PROPN
ejpam-544	43	9	(	(	PUNCT
ejpam-544	43	10	1−	1−	NUM
ejpam-544	43	11	t)[(1−	t)[(1−	NOUN
ejpam-544	43	12	β)p(z	β)p(z	NOUN
ejpam-544	43	13	)	)	PUNCT
ejpam-544	44	1	+	+	PUNCT
ejpam-544	44	2	β	β	X
ejpam-544	44	3	]	]	X
ejpam-544	44	4	(	(	PUNCT
ejpam-544	44	5	1−	1−	NUM
ejpam-544	44	6	t)[(1−	t)[(1−	NOUN
ejpam-544	44	7	β)p(z	β)p(z	NOUN
ejpam-544	44	8	)	)	PUNCT
ejpam-544	45	1	+	+	CCONJ
ejpam-544	45	2	β	β	X
ejpam-544	45	3	]	]	X
ejpam-544	45	4	and	and	CCONJ
ejpam-544	45	5	hence	hence	ADV
ejpam-544	45	6	(	(	PUNCT
ejpam-544	45	7	1−	1−	NUM
ejpam-544	45	8	t)2z	t)2z	ADV
ejpam-544	45	9	f	f	PROPN
ejpam-544	45	10	′(z	′(z	NOUN
ejpam-544	45	11	)	)	PUNCT
ejpam-544	45	12	f	f	PROPN
ejpam-544	46	1	(	(	PUNCT
ejpam-544	46	2	z)−	z)−	PROPN
ejpam-544	46	3	f	f	X
ejpam-544	46	4	(	(	PUNCT
ejpam-544	46	5	tz	tz	PROPN
ejpam-544	46	6	)	)	PUNCT
ejpam-544	46	7	�	�	PROPN
ejpam-544	46	8	αz	αz	ADP
ejpam-544	46	9	f	f	PROPN
ejpam-544	46	10	′′(z	′′(z	PROPN
ejpam-544	46	11	)	)	PUNCT
ejpam-544	46	12	f	f	PROPN
ejpam-544	46	13	′(z	′(z	NOUN
ejpam-544	46	14	)	)	PUNCT
ejpam-544	47	1	+	+	CCONJ
ejpam-544	47	2	αtz	αtz	NOUN
ejpam-544	47	3	f	f	PROPN
ejpam-544	47	4	′(tz	′(tz	PROPN
ejpam-544	47	5	)	)	PUNCT
ejpam-544	48	1	f	f	PROPN
ejpam-544	48	2	(	(	PUNCT
ejpam-544	48	3	z)−	z)−	PROPN
ejpam-544	48	4	f	f	X
ejpam-544	48	5	(	(	PUNCT
ejpam-544	48	6	tz	tz	PROPN
ejpam-544	48	7	)	)	PUNCT
ejpam-544	48	8	+	+	CCONJ
ejpam-544	48	9	1	1	NUM
ejpam-544	48	10	�	�	NOUN
ejpam-544	48	11	=	=	SYM
ejpam-544	48	12	α(1−	α(1−	PROPN
ejpam-544	48	13	t)(1−	t)(1−	PROPN
ejpam-544	48	14	β)zp′(z	β)zp′(z	PROPN
ejpam-544	48	15	)	)	PUNCT
ejpam-544	48	16	+	+	ADJ
ejpam-544	48	17	α(1−	α(1−	ADJ
ejpam-544	48	18	β)2p2(z	β)2p2(z	X
ejpam-544	48	19	)	)	PUNCT
ejpam-544	49	1	+	+	CCONJ
ejpam-544	49	2	(	(	PUNCT
ejpam-544	49	3	1−	1−	NUM
ejpam-544	49	4	β)[2αβ	β)[2αβ	NOUN
ejpam-544	49	5	+	+	CCONJ
ejpam-544	49	6	(	(	PUNCT
ejpam-544	49	7	1−α)(1−	1−α)(1−	NUM
ejpam-544	49	8	t)]p(z	t)]p(z	NUM
ejpam-544	49	9	)	)	PUNCT
ejpam-544	49	10	+	+	CCONJ
ejpam-544	50	1	β[αβ	β[αβ	PROPN
ejpam-544	50	2	+	+	CCONJ
ejpam-544	50	3	(	(	PUNCT
ejpam-544	50	4	1−α)(1−	1−α)(1−	NUM
ejpam-544	50	5	t	t	NOUN
ejpam-544	50	6	)	)	PUNCT
ejpam-544	50	7	]	]	PUNCT
ejpam-544	51	1	=	=	PUNCT
ejpam-544	51	2	φ(p(z	φ(p(z	NOUN
ejpam-544	51	3	)	)	PUNCT
ejpam-544	51	4	,	,	PUNCT
ejpam-544	51	5	zp′(z	zp′(z	PROPN
ejpam-544	51	6	)	)	PUNCT
ejpam-544	51	7	;	;	PUNCT
ejpam-544	52	1	z	z	X
ejpam-544	52	2	)	)	PUNCT
ejpam-544	52	3	(	(	PUNCT
ejpam-544	52	4	say	say	INTJ
ejpam-544	52	5	)	)	PUNCT
ejpam-544	52	6	,	,	PUNCT
ejpam-544	52	7	where	where	SCONJ
ejpam-544	52	8	φ(r	φ(r	ADJ
ejpam-544	52	9	,	,	PUNCT
ejpam-544	52	10	s	s	PART
ejpam-544	52	11	;	;	PUNCT
ejpam-544	52	12	z	z	X
ejpam-544	52	13	)	)	PUNCT
ejpam-544	52	14	=	=	PUNCT
ejpam-544	52	15	α(1−t)(1−β)s+α(1−β)2r2+(1−β)[2αβ+(1−α)(1−t)]r+β[αβ+(1−α)(1−t	α(1−t)(1−β)s+α(1−β)2r2+(1−β)[2αβ+(1−α)(1−t)]r+β[αβ+(1−α)(1−t	NOUN
ejpam-544	52	16	)	)	PUNCT
ejpam-544	52	17	]	]	PUNCT
ejpam-544	52	18	.	.	PUNCT
ejpam-544	53	1	for	for	ADP
ejpam-544	53	2	all	all	DET
ejpam-544	53	3	real	real	ADJ
ejpam-544	53	4	x	x	NOUN
ejpam-544	53	5	and	and	CCONJ
ejpam-544	53	6	y	y	PROPN
ejpam-544	53	7	satisfying	satisfy	VERB
ejpam-544	53	8	y	y	NOUN
ejpam-544	53	9	≤	≤	NOUN
ejpam-544	53	10	−n(1	−n(1	PROPN
ejpam-544	53	11	+	+	SYM
ejpam-544	53	12	x2)/2	x2)/2	ADJ
ejpam-544	53	13	,	,	PUNCT
ejpam-544	53	14	we	we	PRON
ejpam-544	53	15	have	have	VERB
ejpam-544	53	16	re[φ(i	re[φ(i	PROPN
ejpam-544	53	17	x	x	SYM
ejpam-544	53	18	,	,	PUNCT
ejpam-544	53	19	y	y	PROPN
ejpam-544	53	20	;	;	PUNCT
ejpam-544	53	21	z	z	X
ejpam-544	53	22	)	)	PUNCT
ejpam-544	53	23	]	]	PUNCT
ejpam-544	54	1	=	=	PUNCT
ejpam-544	54	2	α(1−	α(1−	PROPN
ejpam-544	54	3	t)(1−	t)(1−	X
ejpam-544	54	4	β)y	β)y	PUNCT
ejpam-544	54	5	−α(1−	−α(1−	NOUN
ejpam-544	54	6	β)2	β)2	NOUN
ejpam-544	54	7	x2	x2	PROPN
ejpam-544	54	8	+	+	CCONJ
ejpam-544	54	9	β[αβ	β[αβ	PROPN
ejpam-544	54	10	+	+	CCONJ
ejpam-544	54	11	(	(	PUNCT
ejpam-544	54	12	1−α)(1−	1−α)(1−	NUM
ejpam-544	54	13	t	t	NOUN
ejpam-544	54	14	)	)	PUNCT
ejpam-544	54	15	]	]	PUNCT
ejpam-544	55	1	≤	≤	NUM
ejpam-544	55	2	α(1−	α(1−	PROPN
ejpam-544	55	3	t)(1−	t)(1−	PROPN
ejpam-544	55	4	β	β	X
ejpam-544	55	5	)	)	PUNCT
ejpam-544	55	6	¦	¦	X
ejpam-544	55	7	−n(1	−n(1	X
ejpam-544	55	8	+	+	CCONJ
ejpam-544	55	9	x2)/2	x2)/2	NOUN
ejpam-544	55	10	©	©	PROPN
ejpam-544	55	11	−α(1−	−α(1−	PROPN
ejpam-544	55	12	β)2	β)2	NOUN
ejpam-544	55	13	x2	x2	PROPN
ejpam-544	55	14	+	+	CCONJ
ejpam-544	55	15	β[αβ	β[αβ	PROPN
ejpam-544	55	16	+	+	CCONJ
ejpam-544	55	17	(	(	PUNCT
ejpam-544	55	18	1−α)(1−	1−α)(1−	NUM
ejpam-544	55	19	t	t	NOUN
ejpam-544	55	20	)	)	PUNCT
ejpam-544	55	21	]	]	PUNCT
ejpam-544	56	1	=	=	PUNCT
ejpam-544	56	2	−αn	−αn	NOUN
ejpam-544	56	3	2	2	NUM
ejpam-544	56	4	(	(	PUNCT
ejpam-544	56	5	1−	1−	NUM
ejpam-544	56	6	t)(1−	t)(1−	PROPN
ejpam-544	56	7	β)−	β)−	PROPN
ejpam-544	56	8	§	§	NOUN
ejpam-544	56	9	αn	αn	NOUN
ejpam-544	56	10	2	2	NUM
ejpam-544	56	11	(	(	PUNCT
ejpam-544	56	12	1−	1−	NUM
ejpam-544	56	13	t)(1−	t)(1−	NOUN
ejpam-544	56	14	β	β	X
ejpam-544	56	15	)	)	PUNCT
ejpam-544	56	16	+	+	ADJ
ejpam-544	56	17	α(1−	α(1−	ADJ
ejpam-544	56	18	β)2	β)2	X
ejpam-544	56	19	ª	ª	NOUN
ejpam-544	56	20	x2	x2	PROPN
ejpam-544	56	21	+	+	CCONJ
ejpam-544	56	22	β[αβ	β[αβ	PROPN
ejpam-544	56	23	+	+	CCONJ
ejpam-544	56	24	(	(	PUNCT
ejpam-544	56	25	1−α)(1−	1−α)(1−	NUM
ejpam-544	56	26	t	t	NOUN
ejpam-544	56	27	)	)	PUNCT
ejpam-544	56	28	]	]	PUNCT
ejpam-544	56	29	≤	≤	NUM
ejpam-544	56	30	−αn	−αn	NOUN
ejpam-544	56	31	2	2	NUM
ejpam-544	56	32	(	(	PUNCT
ejpam-544	56	33	1−	1−	NUM
ejpam-544	56	34	t)(1−	t)(1−	NOUN
ejpam-544	56	35	β	β	X
ejpam-544	56	36	)	)	PUNCT
ejpam-544	56	37	+	+	CCONJ
ejpam-544	56	38	β[αβ	β[αβ	PROPN
ejpam-544	56	39	+	+	CCONJ
ejpam-544	56	40	(	(	PUNCT
ejpam-544	56	41	1−α)(1−	1−α)(1−	NUM
ejpam-544	56	42	t	t	NOUN
ejpam-544	56	43	)	)	PUNCT
ejpam-544	56	44	]	]	PUNCT
ejpam-544	57	1	=	=	SYM
ejpam-544	57	2	αβ	αβ	INTJ
ejpam-544	57	3	§	§	PROPN
ejpam-544	57	4	β	β	X
ejpam-544	57	5	+	+	CCONJ
ejpam-544	57	6	n	n	PRON
ejpam-544	57	7	2	2	NUM
ejpam-544	57	8	(	(	PUNCT
ejpam-544	57	9	1−	1−	NUM
ejpam-544	57	10	t)−	t)−	PROPN
ejpam-544	57	11	(	(	PUNCT
ejpam-544	57	12	1−	1−	NUM
ejpam-544	57	13	t	t	NOUN
ejpam-544	57	14	)	)	PUNCT
ejpam-544	57	15	ª	ª	PROPN
ejpam-544	58	1	+	+	PROPN
ejpam-544	58	2	§	§	PROPN
ejpam-544	58	3	β	β	X
ejpam-544	58	4	−	−	PROPN
ejpam-544	58	5	nα	nα	VERB
ejpam-544	58	6	2	2	NUM
ejpam-544	58	7	ª	ª	SYM
ejpam-544	58	8	(	(	PUNCT
ejpam-544	58	9	1−	1−	NUM
ejpam-544	58	10	t	t	NUM
ejpam-544	58	11	)	)	PUNCT
ejpam-544	58	12	.	.	PUNCT
ejpam-544	59	1	s.	s.	PROPN
ejpam-544	59	2	goyal	goyal	PROPN
ejpam-544	59	3	,	,	PUNCT
ejpam-544	59	4	p.	p.	NOUN
ejpam-544	59	5	vijaywargiya	vijaywargiya	NOUN
ejpam-544	59	6	,	,	PUNCT
ejpam-544	59	7	p.	p.	NOUN
ejpam-544	59	8	goswami	goswami	PROPN
ejpam-544	59	9	/	/	SYM
ejpam-544	59	10	eur	eur	PROPN
ejpam-544	59	11	.	.	PUNCT
ejpam-544	60	1	j.	j.	PROPN
ejpam-544	60	2	pure	pure	PROPN
ejpam-544	60	3	appl	appl	PROPN
ejpam-544	60	4	.	.	PROPN
ejpam-544	60	5	math	math	PROPN
ejpam-544	60	6	,	,	PUNCT
ejpam-544	60	7	4	4	NUM
ejpam-544	60	8	(	(	PUNCT
ejpam-544	60	9	2011	2011	NUM
ejpam-544	60	10	)	)	PUNCT
ejpam-544	60	11	,	,	PUNCT
ejpam-544	60	12	230	230	NUM
ejpam-544	60	13	-	-	SYM
ejpam-544	60	14	236	236	NUM
ejpam-544	60	15	232	232	NUM
ejpam-544	60	16	let	let	VERB
ejpam-544	60	17	ω	ω	NOUN
ejpam-544	60	18	=	=	SYM
ejpam-544	60	19	¦	¦	PROPN
ejpam-544	60	20	w	w	PROPN
ejpam-544	60	21	;	;	PUNCT
ejpam-544	60	22	re(w	re(w	NUM
ejpam-544	60	23	)	)	PUNCT
ejpam-544	60	24	>	>	X
ejpam-544	61	1	αβ	αβ	INTJ
ejpam-544	62	1	¦	¦	PROPN
ejpam-544	62	2	β	β	X
ejpam-544	62	3	+	+	X
ejpam-544	62	4	n	n	CCONJ
ejpam-544	62	5	2	2	NUM
ejpam-544	62	6	(	(	PUNCT
ejpam-544	62	7	1−	1−	NUM
ejpam-544	62	8	t)−	t)−	PROPN
ejpam-544	62	9	(	(	PUNCT
ejpam-544	62	10	1−	1−	NUM
ejpam-544	62	11	t	t	NOUN
ejpam-544	62	12	)	)	PUNCT
ejpam-544	62	13	©	©	PROPN
ejpam-544	62	14	+	+	CCONJ
ejpam-544	62	15	¦	¦	PROPN
ejpam-544	62	16	β	β	X
ejpam-544	62	17	−	−	PROPN
ejpam-544	62	18	nα	nα	VERB
ejpam-544	62	19	2	2	NUM
ejpam-544	62	20	©	©	NOUN
ejpam-544	62	21	(	(	PUNCT
ejpam-544	62	22	1−	1−	NUM
ejpam-544	62	23	t	t	NOUN
ejpam-544	62	24	)	)	PUNCT
ejpam-544	62	25	©	©	PROPN
ejpam-544	62	26	.	.	PUNCT
ejpam-544	63	1	then	then	ADV
ejpam-544	63	2	φ(p(z	φ(p(z	ADV
ejpam-544	63	3	)	)	PUNCT
ejpam-544	63	4	,	,	PUNCT
ejpam-544	63	5	zp′(z	zp′(z	PROPN
ejpam-544	63	6	)	)	PUNCT
ejpam-544	63	7	;	;	PUNCT
ejpam-544	63	8	z	z	X
ejpam-544	63	9	)	)	PUNCT
ejpam-544	63	10	∈	∈	PROPN
ejpam-544	63	11	ω	ω	PROPN
ejpam-544	63	12	and	and	CCONJ
ejpam-544	63	13	φ(i	φ(i	PROPN
ejpam-544	63	14	x	x	SYM
ejpam-544	63	15	,	,	PUNCT
ejpam-544	63	16	y	y	PROPN
ejpam-544	63	17	;	;	PUNCT
ejpam-544	63	18	z	z	X
ejpam-544	63	19	)	)	PUNCT
ejpam-544	63	20	6∈	6∈	PROPN
ejpam-544	63	21	ω	ω	PROPN
ejpam-544	63	22	for	for	ADP
ejpam-544	63	23	all	all	DET
ejpam-544	63	24	real	real	ADJ
ejpam-544	63	25	x	x	NOUN
ejpam-544	63	26	and	and	CCONJ
ejpam-544	63	27	y	y	PROPN
ejpam-544	63	28	≤	≤	NOUN
ejpam-544	64	1	−n(1	−n(1	X
ejpam-544	64	2	+	+	SYM
ejpam-544	64	3	x2)/2	x2)/2	ADJ
ejpam-544	64	4	,	,	PUNCT
ejpam-544	64	5	z	z	PROPN
ejpam-544	64	6	∈	∈	PROPN
ejpam-544	65	1	∆.	∆.	X
ejpam-544	65	2	by	by	ADP
ejpam-544	65	3	an	an	DET
ejpam-544	65	4	application	application	NOUN
ejpam-544	65	5	of	of	ADP
ejpam-544	65	6	lemma	lemma	PROPN
ejpam-544	65	7	1	1	NUM
ejpam-544	65	8	,	,	PUNCT
ejpam-544	65	9	the	the	DET
ejpam-544	65	10	result	result	NOUN
ejpam-544	65	11	fellows	fellow	VERB
ejpam-544	65	12	.	.	PUNCT
ejpam-544	66	1	on	on	ADP
ejpam-544	66	2	taking	take	VERB
ejpam-544	66	3	t	t	PROPN
ejpam-544	66	4	=	=	SYM
ejpam-544	66	5	−1	−1	NOUN
ejpam-544	66	6	,	,	PUNCT
ejpam-544	66	7	in	in	ADP
ejpam-544	66	8	the	the	DET
ejpam-544	66	9	theorem	theorem	NOUN
ejpam-544	66	10	1	1	NUM
ejpam-544	66	11	,	,	PUNCT
ejpam-544	66	12	we	we	PRON
ejpam-544	66	13	have	have	AUX
ejpam-544	66	14	following	follow	VERB
ejpam-544	66	15	corollary	corollary	ADJ
ejpam-544	66	16	1	1	NUM
ejpam-544	66	17	.	.	PUNCT
ejpam-544	67	1	if	if	SCONJ
ejpam-544	67	2	f	f	PROPN
ejpam-544	67	3	(	(	PUNCT
ejpam-544	67	4	z	z	NOUN
ejpam-544	67	5	)	)	PUNCT
ejpam-544	67	6	∈	∈	PROPN
ejpam-544	67	7	an	an	DET
ejpam-544	67	8	satisfies	satisfie	NOUN
ejpam-544	67	9	re	re	VERB
ejpam-544	67	10	�	�	PROPN
ejpam-544	67	11	z	z	PROPN
ejpam-544	67	12	f	f	PROPN
ejpam-544	67	13	′(z	′(z	NOUN
ejpam-544	67	14	)	)	PUNCT
ejpam-544	67	15	f	f	PROPN
ejpam-544	67	16	(	(	PUNCT
ejpam-544	67	17	z)−	z)−	PROPN
ejpam-544	67	18	f	f	X
ejpam-544	67	19	(	(	PUNCT
ejpam-544	67	20	−z	−z	NOUN
ejpam-544	67	21	)	)	PUNCT
ejpam-544	67	22	¨	¨	NOUN
ejpam-544	68	1	αz	αz	ADP
ejpam-544	68	2	f	f	PROPN
ejpam-544	68	3	′′(z	′′(z	PROPN
ejpam-544	68	4	)	)	PUNCT
ejpam-544	68	5	f	f	PROPN
ejpam-544	68	6	′(z	′(z	NOUN
ejpam-544	68	7	)	)	PUNCT
ejpam-544	68	8	−	−	NOUN
ejpam-544	69	1	αz	αz	ADP
ejpam-544	69	2	f	f	PROPN
ejpam-544	69	3	′(−z	′(−z	ADV
ejpam-544	69	4	)	)	PUNCT
ejpam-544	69	5	f	f	PROPN
ejpam-544	69	6	(	(	PUNCT
ejpam-544	69	7	z)−	z)−	PROPN
ejpam-544	69	8	f	f	X
ejpam-544	69	9	(	(	PUNCT
ejpam-544	69	10	−z	−z	NOUN
ejpam-544	69	11	)	)	PUNCT
ejpam-544	69	12	+	+	CCONJ
ejpam-544	69	13	1	1	NUM
ejpam-544	69	14	«	«	PUNCT
ejpam-544	69	15	�	�	X
ejpam-544	69	16	>	>	X
ejpam-544	69	17	αβ	αβ	PROPN
ejpam-544	69	18	4	4	NUM
ejpam-544	69	19	�	�	PROPN
ejpam-544	69	20	β	β	X
ejpam-544	69	21	+	+	CCONJ
ejpam-544	69	22	n−	n−	NOUN
ejpam-544	69	23	2	2	NUM
ejpam-544	69	24	+	+	NUM
ejpam-544	69	25	�	�	PROPN
ejpam-544	69	26	2β	2β	NOUN
ejpam-544	69	27	−	−	PROPN
ejpam-544	69	28	nα	nα	PROPN
ejpam-544	69	29	4	4	NUM
ejpam-544	69	30	�	�	NOUN
ejpam-544	69	31	for	for	ADP
ejpam-544	69	32	(	(	PUNCT
ejpam-544	69	33	z	z	NOUN
ejpam-544	69	34	∈∆	∈∆	PROPN
ejpam-544	69	35	,	,	PUNCT
ejpam-544	69	36	0≤	0≤	NUM
ejpam-544	69	37	α	α	DET
ejpam-544	69	38	≤	≤	NUM
ejpam-544	69	39	1	1	NUM
ejpam-544	69	40	,	,	PUNCT
ejpam-544	69	41	0≤	0≤	PUNCT
ejpam-544	69	42	β	β	X
ejpam-544	69	43	<	<	X
ejpam-544	69	44	1	1	NUM
ejpam-544	69	45	)	)	PUNCT
ejpam-544	69	46	,	,	PUNCT
ejpam-544	69	47	then	then	ADV
ejpam-544	69	48	f	f	X
ejpam-544	69	49	(	(	PUNCT
ejpam-544	69	50	z	z	NOUN
ejpam-544	69	51	)	)	PUNCT
ejpam-544	69	52	∈	∈	PROPN
ejpam-544	69	53	sn(β	sn(β	NUM
ejpam-544	69	54	,	,	PUNCT
ejpam-544	69	55	−1	−1	NOUN
ejpam-544	69	56	)	)	PUNCT
ejpam-544	69	57	.	.	PUNCT
ejpam-544	70	1	by	by	ADP
ejpam-544	70	2	taking	take	VERB
ejpam-544	70	3	β	β	X
ejpam-544	70	4	=	=	SYM
ejpam-544	70	5	0	0	NUM
ejpam-544	70	6	in	in	ADP
ejpam-544	70	7	corollary	corollary	ADJ
ejpam-544	70	8	1	1	NUM
ejpam-544	70	9	,	,	PUNCT
ejpam-544	70	10	we	we	PRON
ejpam-544	70	11	have	have	VERB
ejpam-544	70	12	corollary	corollary	ADJ
ejpam-544	70	13	2	2	NUM
ejpam-544	70	14	.	.	PUNCT
ejpam-544	71	1	if	if	SCONJ
ejpam-544	71	2	f	f	PROPN
ejpam-544	71	3	(	(	PUNCT
ejpam-544	71	4	z	z	NOUN
ejpam-544	71	5	)	)	PUNCT
ejpam-544	71	6	∈	∈	PROPN
ejpam-544	71	7	an	an	DET
ejpam-544	71	8	satisfies	satisfie	NOUN
ejpam-544	71	9	re	re	VERB
ejpam-544	71	10	�	�	PROPN
ejpam-544	71	11	z	z	PROPN
ejpam-544	71	12	f	f	PROPN
ejpam-544	71	13	′(z	′(z	NOUN
ejpam-544	71	14	)	)	PUNCT
ejpam-544	71	15	f	f	PROPN
ejpam-544	71	16	(	(	PUNCT
ejpam-544	71	17	z)−	z)−	PROPN
ejpam-544	71	18	f	f	X
ejpam-544	71	19	(	(	PUNCT
ejpam-544	71	20	−z	−z	NOUN
ejpam-544	71	21	)	)	PUNCT
ejpam-544	71	22	¨	¨	NOUN
ejpam-544	72	1	αz	αz	ADP
ejpam-544	72	2	f	f	PROPN
ejpam-544	72	3	′′(z	′′(z	PROPN
ejpam-544	72	4	)	)	PUNCT
ejpam-544	72	5	f	f	PROPN
ejpam-544	72	6	′(z	′(z	NOUN
ejpam-544	72	7	)	)	PUNCT
ejpam-544	72	8	−	−	NOUN
ejpam-544	73	1	αz	αz	ADP
ejpam-544	73	2	f	f	PROPN
ejpam-544	73	3	′(−z	′(−z	ADV
ejpam-544	73	4	)	)	PUNCT
ejpam-544	73	5	f	f	PROPN
ejpam-544	73	6	(	(	PUNCT
ejpam-544	73	7	z)−	z)−	PROPN
ejpam-544	73	8	f	f	X
ejpam-544	73	9	(	(	PUNCT
ejpam-544	73	10	−z	−z	NOUN
ejpam-544	73	11	)	)	PUNCT
ejpam-544	73	12	+	+	CCONJ
ejpam-544	73	13	1	1	NUM
ejpam-544	73	14	«	«	PUNCT
ejpam-544	73	15	�	�	X
ejpam-544	73	16	>	>	X
ejpam-544	73	17	−nα	−nα	PROPN
ejpam-544	73	18	4	4	NUM
ejpam-544	73	19	where	where	SCONJ
ejpam-544	73	20	(	(	PUNCT
ejpam-544	73	21	z	z	NOUN
ejpam-544	73	22	∈∆	∈∆	NOUN
ejpam-544	73	23	,	,	PUNCT
ejpam-544	73	24	0≤	0≤	NUM
ejpam-544	73	25	α	α	PRON
ejpam-544	73	26	≤	≤	NUM
ejpam-544	73	27	1	1	NUM
ejpam-544	73	28	)	)	PUNCT
ejpam-544	73	29	,	,	PUNCT
ejpam-544	73	30	then	then	ADV
ejpam-544	73	31	f	f	X
ejpam-544	73	32	(	(	PUNCT
ejpam-544	73	33	z	z	NOUN
ejpam-544	73	34	)	)	PUNCT
ejpam-544	73	35	∈	∈	PROPN
ejpam-544	73	36	sn(0,−1	sn(0,−1	NOUN
ejpam-544	73	37	)	)	PUNCT
ejpam-544	73	38	.	.	PUNCT
ejpam-544	74	1	if	if	SCONJ
ejpam-544	74	2	we	we	PRON
ejpam-544	74	3	take	take	VERB
ejpam-544	74	4	t	t	NOUN
ejpam-544	74	5	=	=	SYM
ejpam-544	74	6	0	0	NUM
ejpam-544	74	7	in	in	ADP
ejpam-544	74	8	the	the	DET
ejpam-544	74	9	theorem	theorem	NOUN
ejpam-544	74	10	1	1	NUM
ejpam-544	74	11	,	,	PUNCT
ejpam-544	74	12	we	we	PRON
ejpam-544	74	13	have	have	VERB
ejpam-544	74	14	the	the	DET
ejpam-544	74	15	following	follow	VERB
ejpam-544	74	16	corollary	corollary	NOUN
ejpam-544	74	17	3	3	NUM
ejpam-544	74	18	(	(	PUNCT
ejpam-544	74	19	[	[	X
ejpam-544	74	20	6	6	NUM
ejpam-544	74	21	]	]	PUNCT
ejpam-544	74	22	)	)	PUNCT
ejpam-544	74	23	.	.	PUNCT
ejpam-544	75	1	if	if	SCONJ
ejpam-544	75	2	f	f	PROPN
ejpam-544	75	3	(	(	PUNCT
ejpam-544	75	4	z	z	NOUN
ejpam-544	75	5	)	)	PUNCT
ejpam-544	75	6	∈	∈	PROPN
ejpam-544	75	7	an	an	DET
ejpam-544	75	8	satisfies	satisfie	NOUN
ejpam-544	75	9	re	re	VERB
ejpam-544	75	10	�	�	PROPN
ejpam-544	75	11	z	z	PROPN
ejpam-544	75	12	f	f	PROPN
ejpam-544	75	13	′(z	′(z	NOUN
ejpam-544	75	14	)	)	PUNCT
ejpam-544	75	15	f	f	PROPN
ejpam-544	75	16	(	(	PUNCT
ejpam-544	75	17	z	z	NOUN
ejpam-544	75	18	)	)	PUNCT
ejpam-544	75	19	¨	¨	NOUN
ejpam-544	75	20	αz	αz	ADP
ejpam-544	75	21	f	f	PROPN
ejpam-544	75	22	′′(z	′′(z	PROPN
ejpam-544	75	23	)	)	PUNCT
ejpam-544	75	24	f	f	PROPN
ejpam-544	75	25	′(z	′(z	NOUN
ejpam-544	75	26	)	)	PUNCT
ejpam-544	76	1	+	+	CCONJ
ejpam-544	76	2	1	1	NUM
ejpam-544	76	3	«	«	PUNCT
ejpam-544	76	4	�	�	X
ejpam-544	76	5	>	>	X
ejpam-544	76	6	αβ	αβ	PROPN
ejpam-544	76	7	§	§	PROPN
ejpam-544	76	8	β	β	X
ejpam-544	76	9	+	+	NOUN
ejpam-544	76	10	n	n	CCONJ
ejpam-544	76	11	2	2	NUM
ejpam-544	76	12	−	−	NUM
ejpam-544	76	13	1	1	NUM
ejpam-544	76	14	ª	ª	PROPN
ejpam-544	76	15	+	+	X
ejpam-544	76	16	§	§	PROPN
ejpam-544	76	17	β	β	X
ejpam-544	76	18	−	−	PROPN
ejpam-544	76	19	nα	nα	VERB
ejpam-544	76	20	2	2	NUM
ejpam-544	76	21	ª	ª	NOUN
ejpam-544	76	22	for	for	ADP
ejpam-544	76	23	(	(	PUNCT
ejpam-544	76	24	z	z	NOUN
ejpam-544	76	25	∈∆	∈∆	PROPN
ejpam-544	76	26	,	,	PUNCT
ejpam-544	76	27	0≤	0≤	NUM
ejpam-544	76	28	α	α	DET
ejpam-544	76	29	≤	≤	NUM
ejpam-544	76	30	1	1	NUM
ejpam-544	76	31	,	,	PUNCT
ejpam-544	76	32	0≤	0≤	PUNCT
ejpam-544	76	33	β	β	X
ejpam-544	76	34	<	<	X
ejpam-544	76	35	1	1	NUM
ejpam-544	76	36	)	)	PUNCT
ejpam-544	76	37	,	,	PUNCT
ejpam-544	76	38	then	then	ADV
ejpam-544	76	39	f	f	X
ejpam-544	76	40	(	(	PUNCT
ejpam-544	76	41	z	z	NOUN
ejpam-544	76	42	)	)	PUNCT
ejpam-544	76	43	∈	∈	PROPN
ejpam-544	76	44	sn(β	sn(β	NUM
ejpam-544	76	45	,	,	PUNCT
ejpam-544	76	46	0	0	NUM
ejpam-544	76	47	)	)	PUNCT
ejpam-544	76	48	=	=	SYM
ejpam-544	76	49	s∗n(β	s∗n(β	PROPN
ejpam-544	76	50	)	)	PUNCT
ejpam-544	76	51	.	.	PUNCT
ejpam-544	77	1	if	if	SCONJ
ejpam-544	77	2	we	we	PRON
ejpam-544	77	3	take	take	VERB
ejpam-544	77	4	β	β	NOUN
ejpam-544	77	5	=	=	SYM
ejpam-544	77	6	0	0	NUM
ejpam-544	77	7	and	and	CCONJ
ejpam-544	77	8	n=	n=	ADJ
ejpam-544	77	9	1	1	NUM
ejpam-544	77	10	in	in	ADP
ejpam-544	77	11	corollary	corollary	ADJ
ejpam-544	77	12	3	3	NUM
ejpam-544	77	13	,	,	PUNCT
ejpam-544	77	14	we	we	PRON
ejpam-544	77	15	have	have	VERB
ejpam-544	77	16	corollary	corollary	ADJ
ejpam-544	77	17	4	4	NUM
ejpam-544	77	18	(	(	PUNCT
ejpam-544	77	19	[	[	X
ejpam-544	77	20	3	3	NUM
ejpam-544	77	21	]	]	PUNCT
ejpam-544	77	22	)	)	PUNCT
ejpam-544	77	23	.	.	PUNCT
ejpam-544	78	1	if	if	SCONJ
ejpam-544	78	2	f	f	PROPN
ejpam-544	78	3	(	(	PUNCT
ejpam-544	78	4	z	z	NOUN
ejpam-544	78	5	)	)	PUNCT
ejpam-544	78	6	∈	∈	PROPN
ejpam-544	78	7	a	a	DET
ejpam-544	78	8	satisfies	satisfie	NOUN
ejpam-544	78	9	re	re	VERB
ejpam-544	78	10	�	�	PROPN
ejpam-544	78	11	z	z	PROPN
ejpam-544	78	12	f	f	PROPN
ejpam-544	78	13	′(z	′(z	NOUN
ejpam-544	78	14	)	)	PUNCT
ejpam-544	78	15	f	f	PROPN
ejpam-544	78	16	(	(	PUNCT
ejpam-544	78	17	z	z	NOUN
ejpam-544	78	18	)	)	PUNCT
ejpam-544	78	19	¨	¨	NOUN
ejpam-544	78	20	αz	αz	ADP
ejpam-544	78	21	f	f	PROPN
ejpam-544	78	22	′′(z	′′(z	PROPN
ejpam-544	78	23	)	)	PUNCT
ejpam-544	78	24	f	f	PROPN
ejpam-544	78	25	′(z	′(z	NOUN
ejpam-544	78	26	)	)	PUNCT
ejpam-544	79	1	+	+	CCONJ
ejpam-544	79	2	1	1	NUM
ejpam-544	79	3	«	«	PUNCT
ejpam-544	79	4	�	�	X
ejpam-544	79	5	>	>	X
ejpam-544	79	6	−α	−α	PROPN
ejpam-544	79	7	2	2	NUM
ejpam-544	79	8	(	(	PUNCT
ejpam-544	79	9	z	z	NOUN
ejpam-544	79	10	∈∆	∈∆	NOUN
ejpam-544	79	11	)	)	PUNCT
ejpam-544	79	12	,	,	PUNCT
ejpam-544	79	13	for	for	ADP
ejpam-544	79	14	some	some	DET
ejpam-544	79	15	α(α≥	α(α≥	NUM
ejpam-544	79	16	0	0	NUM
ejpam-544	79	17	)	)	PUNCT
ejpam-544	79	18	,	,	PUNCT
ejpam-544	79	19	then	then	ADV
ejpam-544	79	20	f	f	X
ejpam-544	79	21	(	(	PUNCT
ejpam-544	79	22	z	z	NOUN
ejpam-544	79	23	)	)	PUNCT
ejpam-544	79	24	∈	∈	PROPN
ejpam-544	79	25	s1(0,0	s1(0,0	NOUN
ejpam-544	79	26	)	)	PUNCT
ejpam-544	79	27	=	=	PUNCT
ejpam-544	80	1	s∗.	s∗.	ADJ
ejpam-544	80	2	if	if	SCONJ
ejpam-544	80	3	we	we	PRON
ejpam-544	80	4	take	take	VERB
ejpam-544	80	5	β	β	X
ejpam-544	80	6	=	=	PUNCT
ejpam-544	80	7	α	α	PRON
ejpam-544	80	8	2	2	NUM
ejpam-544	80	9	and	and	CCONJ
ejpam-544	80	10	n=	n=	ADJ
ejpam-544	80	11	1	1	NUM
ejpam-544	80	12	,	,	PUNCT
ejpam-544	80	13	in	in	ADP
ejpam-544	80	14	corollary	corollary	ADJ
ejpam-544	80	15	3	3	NUM
ejpam-544	80	16	,	,	PUNCT
ejpam-544	80	17	we	we	PRON
ejpam-544	80	18	get	get	VERB
ejpam-544	80	19	the	the	DET
ejpam-544	80	20	following	follow	VERB
ejpam-544	80	21	s.	s.	PROPN
ejpam-544	80	22	goyal	goyal	PROPN
ejpam-544	80	23	,	,	PUNCT
ejpam-544	80	24	p.	p.	NOUN
ejpam-544	80	25	vijaywargiya	vijaywargiya	NOUN
ejpam-544	80	26	,	,	PUNCT
ejpam-544	80	27	p.	p.	NOUN
ejpam-544	80	28	goswami	goswami	PROPN
ejpam-544	80	29	/	/	SYM
ejpam-544	80	30	eur	eur	PROPN
ejpam-544	80	31	.	.	PUNCT
ejpam-544	81	1	j.	j.	PROPN
ejpam-544	81	2	pure	pure	PROPN
ejpam-544	81	3	appl	appl	PROPN
ejpam-544	81	4	.	.	PROPN
ejpam-544	81	5	math	math	PROPN
ejpam-544	81	6	,	,	PUNCT
ejpam-544	81	7	4	4	NUM
ejpam-544	81	8	(	(	PUNCT
ejpam-544	81	9	2011	2011	NUM
ejpam-544	81	10	)	)	PUNCT
ejpam-544	81	11	,	,	PUNCT
ejpam-544	81	12	230	230	NUM
ejpam-544	81	13	-	-	SYM
ejpam-544	81	14	236	236	NUM
ejpam-544	81	15	233	233	NUM
ejpam-544	81	16	corollary	corollary	ADJ
ejpam-544	81	17	5	5	NUM
ejpam-544	81	18	(	(	PUNCT
ejpam-544	81	19	[	[	X
ejpam-544	81	20	3	3	NUM
ejpam-544	81	21	]	]	PUNCT
ejpam-544	81	22	)	)	PUNCT
ejpam-544	81	23	.	.	PUNCT
ejpam-544	82	1	if	if	SCONJ
ejpam-544	82	2	f	f	PROPN
ejpam-544	82	3	(	(	PUNCT
ejpam-544	82	4	z	z	NOUN
ejpam-544	82	5	)	)	PUNCT
ejpam-544	82	6	∈	∈	PROPN
ejpam-544	82	7	a	a	DET
ejpam-544	82	8	satisfies	satisfie	NOUN
ejpam-544	82	9	re	re	VERB
ejpam-544	82	10	�	�	PROPN
ejpam-544	82	11	z	z	PROPN
ejpam-544	82	12	f	f	PROPN
ejpam-544	82	13	′(z	′(z	NOUN
ejpam-544	82	14	)	)	PUNCT
ejpam-544	82	15	f	f	PROPN
ejpam-544	82	16	(	(	PUNCT
ejpam-544	82	17	z	z	NOUN
ejpam-544	82	18	)	)	PUNCT
ejpam-544	82	19	¨	¨	NOUN
ejpam-544	82	20	αz	αz	ADP
ejpam-544	82	21	f	f	PROPN
ejpam-544	82	22	′′(z	′′(z	PROPN
ejpam-544	82	23	)	)	PUNCT
ejpam-544	82	24	f	f	PROPN
ejpam-544	82	25	′(z	′(z	NOUN
ejpam-544	82	26	)	)	PUNCT
ejpam-544	83	1	+	+	CCONJ
ejpam-544	83	2	1	1	NUM
ejpam-544	83	3	«	«	PUNCT
ejpam-544	83	4	�	�	X
ejpam-544	83	5	>	>	X
ejpam-544	83	6	−α2	−α2	PROPN
ejpam-544	83	7	4	4	NUM
ejpam-544	83	8	(	(	PUNCT
ejpam-544	83	9	1−α	1−α	NUM
ejpam-544	83	10	)	)	PUNCT
ejpam-544	83	11	(	(	PUNCT
ejpam-544	83	12	z	z	NOUN
ejpam-544	83	13	∈∆	∈∆	NOUN
ejpam-544	83	14	)	)	PUNCT
ejpam-544	83	15	,	,	PUNCT
ejpam-544	83	16	for	for	ADP
ejpam-544	83	17	some	some	DET
ejpam-544	83	18	α(0≤	α(0≤	PROPN
ejpam-544	83	19	α	α	NOUN
ejpam-544	83	20	<	<	X
ejpam-544	83	21	2	2	NUM
ejpam-544	83	22	)	)	PUNCT
ejpam-544	83	23	,	,	PUNCT
ejpam-544	83	24	then	then	ADV
ejpam-544	83	25	f	f	X
ejpam-544	83	26	(	(	PUNCT
ejpam-544	83	27	z	z	NOUN
ejpam-544	83	28	)	)	PUNCT
ejpam-544	83	29	∈	∈	PROPN
ejpam-544	83	30	s1	s1	NOUN
ejpam-544	83	31	(	(	PUNCT
ejpam-544	83	32	α	α	NOUN
ejpam-544	83	33	2	2	NUM
ejpam-544	83	34	,	,	PUNCT
ejpam-544	83	35	0	0	NUM
ejpam-544	83	36	)	)	PUNCT
ejpam-544	83	37	=	=	SYM
ejpam-544	83	38	s∗(α	s∗(α	X
ejpam-544	83	39	2	2	NUM
ejpam-544	83	40	)	)	PUNCT
ejpam-544	83	41	.	.	PUNCT
ejpam-544	84	1	theorem	theorem	NOUN
ejpam-544	84	2	2	2	NUM
ejpam-544	84	3	.	.	PUNCT
ejpam-544	85	1	let	let	VERB
ejpam-544	85	2	0≤	0≤	NUM
ejpam-544	85	3	β	β	X
ejpam-544	85	4	<	<	X
ejpam-544	85	5	1	1	NUM
ejpam-544	85	6	,	,	PUNCT
ejpam-544	85	7	|t|	|t|	VERB
ejpam-544	85	8	≤	≤	ADJ
ejpam-544	85	9	1	1	NUM
ejpam-544	85	10	,	,	PUNCT
ejpam-544	85	11	t	t	PROPN
ejpam-544	85	12	6=	6=	NUM
ejpam-544	85	13	1	1	NUM
ejpam-544	85	14	with	with	ADP
ejpam-544	85	15	−1≤	−1≤	ADJ
ejpam-544	85	16	t	t	NOUN
ejpam-544	85	17	+	+	X
ejpam-544	85	18	β	β	X
ejpam-544	85	19	<	<	X
ejpam-544	85	20	1	1	NUM
ejpam-544	85	21	,	,	PUNCT
ejpam-544	85	22	λ=	λ=	NOUN
ejpam-544	85	23	(	(	PUNCT
ejpam-544	85	24	1−	1−	NUM
ejpam-544	85	25	β)2	β)2	X
ejpam-544	85	26	§	§	PROPN
ejpam-544	85	27	1−	1−	NUM
ejpam-544	85	28	β	β	X
ejpam-544	85	29	+	+	X
ejpam-544	85	30	(	(	PUNCT
ejpam-544	85	31	1−	1−	NUM
ejpam-544	85	32	t	t	PROPN
ejpam-544	85	33	)	)	PUNCT
ejpam-544	85	34	n	n	PRON
ejpam-544	85	35	2	2	NUM
ejpam-544	85	36	ª2	ª2	NOUN
ejpam-544	85	37	,	,	PUNCT
ejpam-544	85	38	µ=	µ=	NOUN
ejpam-544	85	39	§	§	PROPN
ejpam-544	85	40	(	(	PUNCT
ejpam-544	85	41	1−β)(1−	1−β)(1−	NUM
ejpam-544	85	42	t	t	NOUN
ejpam-544	85	43	)	)	PUNCT
ejpam-544	85	44	n	n	CCONJ
ejpam-544	85	45	2	2	NUM
ejpam-544	85	46	−	−	NOUN
ejpam-544	85	47	(	(	PUNCT
ejpam-544	85	48	β2	β2	NOUN
ejpam-544	85	49	−	−	PROPN
ejpam-544	85	50	(	(	PUNCT
ejpam-544	85	51	1−	1−	NUM
ejpam-544	85	52	t)β	t)β	NOUN
ejpam-544	85	53	)	)	PUNCT
ejpam-544	85	54	ª2	ª2	NOUN
ejpam-544	85	55	,	,	PUNCT
ejpam-544	85	56	ν	ν	X
ejpam-544	85	57	=	=	SYM
ejpam-544	85	58	¦	¦	X
ejpam-544	85	59	(	(	PUNCT
ejpam-544	85	60	1−	1−	NUM
ejpam-544	85	61	β)2	β)2	X
ejpam-544	85	62	+	+	CCONJ
ejpam-544	85	63	(	(	PUNCT
ejpam-544	85	64	β2	β2	NOUN
ejpam-544	85	65	−	−	PROPN
ejpam-544	85	66	(	(	PUNCT
ejpam-544	85	67	1−	1−	NUM
ejpam-544	85	68	t)β	t)β	NOUN
ejpam-544	85	69	)	)	PUNCT
ejpam-544	86	1	©	©	PROPN
ejpam-544	86	2	2	2	NUM
ejpam-544	86	3	and	and	CCONJ
ejpam-544	86	4	σ	σ	NUM
ejpam-544	86	5	=	=	SYM
ejpam-544	86	6	(	(	PUNCT
ejpam-544	86	7	1−	1−	NUM
ejpam-544	86	8	β)2(2β	β)2(2β	NOUN
ejpam-544	86	9	−	−	PROPN
ejpam-544	86	10	1	1	NUM
ejpam-544	86	11	+	+	NUM
ejpam-544	86	12	t)2	t)2	NOUN
ejpam-544	86	13	(	(	PUNCT
ejpam-544	86	14	2	2	NUM
ejpam-544	86	15	)	)	PUNCT
ejpam-544	86	16	satisfy	satisfy	NOUN
ejpam-544	86	17	(	(	PUNCT
ejpam-544	86	18	λ+µ−	λ+µ−	PROPN
ejpam-544	86	19	ν	ν	X
ejpam-544	86	20	+	+	PROPN
ejpam-544	86	21	σ)β2	σ)β2	NOUN
ejpam-544	86	22	<	<	X
ejpam-544	86	23	(	(	PUNCT
ejpam-544	86	24	1−	1−	NUM
ejpam-544	86	25	2β)µ.	2β)µ.	NUM
ejpam-544	86	26	also	also	ADV
ejpam-544	86	27	suppose	suppose	VERB
ejpam-544	86	28	that	that	SCONJ
ejpam-544	86	29	u0	u0	PROPN
ejpam-544	86	30	be	be	AUX
ejpam-544	86	31	the	the	DET
ejpam-544	86	32	positive	positive	ADJ
ejpam-544	86	33	real	real	ADJ
ejpam-544	86	34	root	root	NOUN
ejpam-544	86	35	of	of	ADP
ejpam-544	86	36	the	the	DET
ejpam-544	86	37	equation	equation	NOUN
ejpam-544	86	38	2λ(1−	2λ(1−	NUM
ejpam-544	86	39	β)2u3	β)2u3	PUNCT
ejpam-544	86	40	+	+	CCONJ
ejpam-544	86	41	¦	¦	X
ejpam-544	86	42	(	(	PUNCT
ejpam-544	86	43	1−	1−	NUM
ejpam-544	86	44	β)2(2λ+µ−	β)2(2λ+µ−	PROPN
ejpam-544	86	45	ν	ν	X
ejpam-544	86	46	+	+	PROPN
ejpam-544	86	47	σ	σ	NOUN
ejpam-544	86	48	)	)	PUNCT
ejpam-544	87	1	+	+	NUM
ejpam-544	87	2	3λβ2	3λβ2	NUM
ejpam-544	87	3	©	©	PROPN
ejpam-544	87	4	u2	u2	NOUN
ejpam-544	87	5	+	+	CCONJ
ejpam-544	87	6	2β2(2λ+µ−	2β2(2λ+µ−	NUM
ejpam-544	87	7	ν	ν	NOUN
ejpam-544	87	8	+	+	ADJ
ejpam-544	87	9	σ)u	σ)u	ADJ
ejpam-544	87	10	+	+	ADJ
ejpam-544	87	11	(	(	PUNCT
ejpam-544	87	12	λ+	λ+	NUM
ejpam-544	87	13	2µ−	2µ−	NUM
ejpam-544	87	14	ν	ν	NOUN
ejpam-544	87	15	+	+	PROPN
ejpam-544	87	16	σ)β2	σ)β2	NOUN
ejpam-544	87	17	−	−	PROPN
ejpam-544	87	18	(	(	PUNCT
ejpam-544	87	19	1−	1−	NUM
ejpam-544	87	20	β)2µ	β)2µ	NOUN
ejpam-544	87	21	=	=	SYM
ejpam-544	87	22	0	0	NUM
ejpam-544	87	23	(	(	PUNCT
ejpam-544	87	24	3	3	NUM
ejpam-544	87	25	)	)	PUNCT
ejpam-544	87	26	and	and	CCONJ
ejpam-544	87	27	ρ2	ρ2	NOUN
ejpam-544	87	28	=	=	SYM
ejpam-544	87	29	(	(	PUNCT
ejpam-544	87	30	1−	1−	NUM
ejpam-544	87	31	β)2(1	β)2(1	NOUN
ejpam-544	87	32	+	+	CCONJ
ejpam-544	87	33	u0	u0	ADJ
ejpam-544	87	34	)	)	PUNCT
ejpam-544	87	35	(	(	PUNCT
ejpam-544	87	36	1−	1−	NUM
ejpam-544	87	37	t)2	t)2	PROPN
ejpam-544	87	38	�	�	PROPN
ejpam-544	87	39	(	(	PUNCT
ejpam-544	87	40	1−	1−	NUM
ejpam-544	87	41	β)2uo	β)2uo	NOUN
ejpam-544	88	1	+	+	X
ejpam-544	88	2	β	β	X
ejpam-544	88	3	2	2	NUM
ejpam-544	88	4	[	[	X
ejpam-544	88	5	λu2	λu2	NOUN
ejpam-544	88	6	0	0	NUM
ejpam-544	89	1	+	+	CCONJ
ejpam-544	89	2	(	(	PUNCT
ejpam-544	89	3	λ+µ−	λ+µ−	PROPN
ejpam-544	89	4	ν	ν	X
ejpam-544	89	5	+	+	ADJ
ejpam-544	89	6	σ)u0	σ)u0	PROPN
ejpam-544	89	7	+	+	NOUN
ejpam-544	89	8	µ	µ	NOUN
ejpam-544	89	9	]	]	X
ejpam-544	89	10	.	.	PUNCT
ejpam-544	90	1	(	(	PUNCT
ejpam-544	90	2	4	4	X
ejpam-544	90	3	)	)	PUNCT
ejpam-544	90	4	now	now	ADV
ejpam-544	90	5	if	if	SCONJ
ejpam-544	90	6	f	f	PROPN
ejpam-544	90	7	(	(	PUNCT
ejpam-544	90	8	z	z	NOUN
ejpam-544	90	9	)	)	PUNCT
ejpam-544	90	10	∈	∈	PROPN
ejpam-544	90	11	an	an	DET
ejpam-544	90	12	satisfies	satisfie	NOUN
ejpam-544	90	13	�	�	PROPN
ejpam-544	90	14	�	�	PROPN
ejpam-544	90	15	�	�	PROPN
ejpam-544	90	16	�	�	PROPN
ejpam-544	90	17	�	�	PROPN
ejpam-544	90	18	�	�	PROPN
ejpam-544	90	19	(	(	PUNCT
ejpam-544	90	20	1−	1−	NUM
ejpam-544	90	21	t)z	t)z	NOUN
ejpam-544	90	22	f	f	PROPN
ejpam-544	90	23	′(z	′(z	NOUN
ejpam-544	90	24	)	)	PUNCT
ejpam-544	90	25	f	f	PROPN
ejpam-544	90	26	(	(	PUNCT
ejpam-544	90	27	z)−	z)−	PROPN
ejpam-544	90	28	f	f	X
ejpam-544	90	29	(	(	PUNCT
ejpam-544	90	30	tz	tz	PROPN
ejpam-544	90	31	)	)	PUNCT
ejpam-544	90	32	−	−	PROPN
ejpam-544	90	33	1	1	NUM
ejpam-544	90	34	�	�	PROPN
ejpam-544	90	35	�	�	PROPN
ejpam-544	90	36	z	z	PROPN
ejpam-544	90	37	f	f	PROPN
ejpam-544	90	38	′′(z	′′(z	PROPN
ejpam-544	90	39	)	)	PUNCT
ejpam-544	90	40	f	f	PROPN
ejpam-544	90	41	′(z	′(z	NOUN
ejpam-544	90	42	)	)	PUNCT
ejpam-544	91	1	+	+	CCONJ
ejpam-544	91	2	tz	tz	PROPN
ejpam-544	91	3	f	f	PROPN
ejpam-544	91	4	′(tz	′(tz	PROPN
ejpam-544	91	5	)	)	PUNCT
ejpam-544	92	1	f	f	PROPN
ejpam-544	92	2	(	(	PUNCT
ejpam-544	92	3	z)−	z)−	PROPN
ejpam-544	92	4	f	f	X
ejpam-544	92	5	(	(	PUNCT
ejpam-544	92	6	tz	tz	PROPN
ejpam-544	92	7	)	)	PUNCT
ejpam-544	92	8	�	�	PROPN
ejpam-544	92	9	�	�	PROPN
ejpam-544	92	10	�	�	PROPN
ejpam-544	92	11	�	�	PROPN
ejpam-544	92	12	�	�	PROPN
ejpam-544	92	13	�	�	PROPN
ejpam-544	92	14	≤	≤	PROPN
ejpam-544	92	15	ρ	ρ	PROPN
ejpam-544	92	16	(	(	PUNCT
ejpam-544	92	17	z	z	NOUN
ejpam-544	92	18	∈∆	∈∆	NOUN
ejpam-544	92	19	)	)	PUNCT
ejpam-544	92	20	,	,	PUNCT
ejpam-544	92	21	then	then	ADV
ejpam-544	92	22	f	f	X
ejpam-544	92	23	(	(	PUNCT
ejpam-544	92	24	z	z	NOUN
ejpam-544	92	25	)	)	PUNCT
ejpam-544	92	26	∈	∈	PROPN
ejpam-544	92	27	sn(β	sn(β	NUM
ejpam-544	92	28	,	,	PUNCT
ejpam-544	92	29	t	t	PROPN
ejpam-544	92	30	)	)	PUNCT
ejpam-544	92	31	.	.	PUNCT
ejpam-544	93	1	proof	proof	NOUN
ejpam-544	93	2	.	.	PUNCT
ejpam-544	94	1	define	define	VERB
ejpam-544	94	2	p(z	p(z	NOUN
ejpam-544	94	3	)	)	PUNCT
ejpam-544	94	4	by	by	ADP
ejpam-544	94	5	(	(	PUNCT
ejpam-544	94	6	1−	1−	NUM
ejpam-544	94	7	t)z	t)z	NOUN
ejpam-544	94	8	f	f	PROPN
ejpam-544	94	9	′(z	′(z	NOUN
ejpam-544	94	10	)	)	PUNCT
ejpam-544	94	11	f	f	PROPN
ejpam-544	94	12	(	(	PUNCT
ejpam-544	94	13	z)−	z)−	PROPN
ejpam-544	94	14	f	f	X
ejpam-544	94	15	(	(	PUNCT
ejpam-544	94	16	tz	tz	PROPN
ejpam-544	94	17	)	)	PUNCT
ejpam-544	94	18	=	=	SYM
ejpam-544	94	19	(	(	PUNCT
ejpam-544	94	20	1−	1−	NUM
ejpam-544	94	21	β)p(z	β)p(z	NOUN
ejpam-544	94	22	)	)	PUNCT
ejpam-544	95	1	+	+	CCONJ
ejpam-544	95	2	β	β	X
ejpam-544	95	3	.	.	PUNCT
ejpam-544	96	1	then	then	ADV
ejpam-544	96	2	p(z	p(z	PROPN
ejpam-544	96	3	)	)	PUNCT
ejpam-544	96	4	=	=	SYM
ejpam-544	96	5	1	1	NUM
ejpam-544	96	6	+	+	NUM
ejpam-544	96	7	cnzn	cnzn	NOUN
ejpam-544	96	8	+	+	PUNCT
ejpam-544	96	9	.	.	PUNCT
ejpam-544	96	10	.	.	PUNCT
ejpam-544	96	11	.	.	PUNCT
ejpam-544	97	1	and	and	CCONJ
ejpam-544	97	2	is	be	AUX
ejpam-544	97	3	an	an	DET
ejpam-544	97	4	analytic	analytic	NOUN
ejpam-544	97	5	in	in	ADP
ejpam-544	97	6	∆.	∆.	NOUN
ejpam-544	97	7	a	a	DET
ejpam-544	97	8	computation	computation	NOUN
ejpam-544	97	9	shows	show	VERB
ejpam-544	97	10	that	that	SCONJ
ejpam-544	97	11	z	z	NOUN
ejpam-544	97	12	f	f	PROPN
ejpam-544	97	13	′′(z	′′(z	PROPN
ejpam-544	97	14	)	)	PUNCT
ejpam-544	97	15	f	f	PROPN
ejpam-544	97	16	′(z	′(z	NOUN
ejpam-544	97	17	)	)	PUNCT
ejpam-544	98	1	+	+	CCONJ
ejpam-544	98	2	tz	tz	PROPN
ejpam-544	98	3	f	f	PROPN
ejpam-544	98	4	′(tz	′(tz	PROPN
ejpam-544	98	5	)	)	PUNCT
ejpam-544	99	1	f	f	PROPN
ejpam-544	99	2	(	(	PUNCT
ejpam-544	99	3	z)−	z)−	PROPN
ejpam-544	99	4	f	f	X
ejpam-544	99	5	(	(	PUNCT
ejpam-544	99	6	tz	tz	PROPN
ejpam-544	99	7	)	)	PUNCT
ejpam-544	99	8	=	=	SYM
ejpam-544	99	9	(	(	PUNCT
ejpam-544	99	10	1−	1−	NUM
ejpam-544	99	11	t)(1−	t)(1−	NOUN
ejpam-544	99	12	β)zp′(z	β)zp′(z	NUM
ejpam-544	99	13	)	)	PUNCT
ejpam-544	99	14	+	+	CCONJ
ejpam-544	100	1	[	[	X
ejpam-544	100	2	(	(	PUNCT
ejpam-544	100	3	1−	1−	NUM
ejpam-544	100	4	β)p(z	β)p(z	NOUN
ejpam-544	100	5	)	)	PUNCT
ejpam-544	100	6	+	+	NUM
ejpam-544	100	7	β]2	β]2	SYM
ejpam-544	100	8	−	−	PROPN
ejpam-544	100	9	(	(	PUNCT
ejpam-544	100	10	1−	1−	NUM
ejpam-544	100	11	t)[(1−	t)[(1−	NOUN
ejpam-544	100	12	β)p(z	β)p(z	NOUN
ejpam-544	100	13	)	)	PUNCT
ejpam-544	101	1	+	+	PUNCT
ejpam-544	101	2	β	β	X
ejpam-544	101	3	]	]	X
ejpam-544	101	4	(	(	PUNCT
ejpam-544	101	5	1−	1−	NUM
ejpam-544	101	6	t)[(1−	t)[(1−	NOUN
ejpam-544	101	7	β)p(z	β)p(z	NOUN
ejpam-544	101	8	)	)	PUNCT
ejpam-544	102	1	+	+	CCONJ
ejpam-544	102	2	β	β	X
ejpam-544	102	3	]	]	X
ejpam-544	102	4	and	and	CCONJ
ejpam-544	102	5	hence	hence	ADV
ejpam-544	102	6	�	�	PROPN
ejpam-544	102	7	(	(	PUNCT
ejpam-544	102	8	1−	1−	NUM
ejpam-544	102	9	t)z	t)z	NOUN
ejpam-544	102	10	f	f	PROPN
ejpam-544	102	11	′(z	′(z	NOUN
ejpam-544	102	12	)	)	PUNCT
ejpam-544	102	13	f	f	PROPN
ejpam-544	102	14	(	(	PUNCT
ejpam-544	102	15	z)−	z)−	PROPN
ejpam-544	102	16	f	f	X
ejpam-544	102	17	(	(	PUNCT
ejpam-544	102	18	tz	tz	PROPN
ejpam-544	102	19	)	)	PUNCT
ejpam-544	102	20	−	−	PROPN
ejpam-544	102	21	1	1	NUM
ejpam-544	102	22	�	�	PROPN
ejpam-544	102	23	�	�	PROPN
ejpam-544	102	24	z	z	PROPN
ejpam-544	102	25	f	f	PROPN
ejpam-544	102	26	′′(z	′′(z	PROPN
ejpam-544	102	27	)	)	PUNCT
ejpam-544	102	28	f	f	PROPN
ejpam-544	102	29	′(z	′(z	NOUN
ejpam-544	102	30	)	)	PUNCT
ejpam-544	103	1	+	+	CCONJ
ejpam-544	103	2	tz	tz	PROPN
ejpam-544	103	3	f	f	PROPN
ejpam-544	103	4	′(tz	′(tz	PROPN
ejpam-544	103	5	)	)	PUNCT
ejpam-544	104	1	f	f	PROPN
ejpam-544	104	2	(	(	PUNCT
ejpam-544	104	3	z)−	z)−	PROPN
ejpam-544	104	4	f	f	X
ejpam-544	104	5	(	(	PUNCT
ejpam-544	104	6	tz	tz	PROPN
ejpam-544	104	7	)	)	PUNCT
ejpam-544	104	8	�	�	PROPN
ejpam-544	104	9	=	=	SYM
ejpam-544	104	10	(	(	PUNCT
ejpam-544	104	11	1−	1−	NUM
ejpam-544	104	12	β)(p(z)−	β)(p(z)−	NUM
ejpam-544	104	13	1	1	NUM
ejpam-544	104	14	)	)	PUNCT
ejpam-544	104	15	(	(	PUNCT
ejpam-544	104	16	1−	1−	NUM
ejpam-544	104	17	t)[(1−	t)[(1−	NOUN
ejpam-544	104	18	β)p(z	β)p(z	NOUN
ejpam-544	104	19	)	)	PUNCT
ejpam-544	105	1	+	+	CCONJ
ejpam-544	105	2	β	β	X
ejpam-544	105	3	]	]	X
ejpam-544	105	4	�	�	PROPN
ejpam-544	105	5	(	(	PUNCT
ejpam-544	105	6	1−	1−	NUM
ejpam-544	105	7	t)(1−	t)(1−	NOUN
ejpam-544	105	8	β)zp′(z	β)zp′(z	NUM
ejpam-544	105	9	)	)	PUNCT
ejpam-544	105	10	+	+	CCONJ
ejpam-544	106	1	[	[	X
ejpam-544	106	2	(	(	PUNCT
ejpam-544	106	3	1−	1−	NUM
ejpam-544	106	4	β)p(z	β)p(z	NOUN
ejpam-544	106	5	)	)	PUNCT
ejpam-544	106	6	+	+	SYM
ejpam-544	106	7	β]2	β]2	SYM
ejpam-544	106	8	−(1−	−(1−	ADP
ejpam-544	106	9	t)[(1−β)p(z	t)[(1−β)p(z	PROPN
ejpam-544	106	10	)	)	PUNCT
ejpam-544	106	11	+	+	CCONJ
ejpam-544	106	12	β	β	X
ejpam-544	106	13	]	]	X
ejpam-544	106	14	s.	s.	PROPN
ejpam-544	106	15	goyal	goyal	PROPN
ejpam-544	106	16	,	,	PUNCT
ejpam-544	106	17	p.	p.	NOUN
ejpam-544	106	18	vijaywargiya	vijaywargiya	NOUN
ejpam-544	106	19	,	,	PUNCT
ejpam-544	106	20	p.	p.	NOUN
ejpam-544	106	21	goswami	goswami	PROPN
ejpam-544	106	22	/	/	SYM
ejpam-544	106	23	eur	eur	PROPN
ejpam-544	106	24	.	.	PUNCT
ejpam-544	107	1	j.	j.	PROPN
ejpam-544	107	2	pure	pure	PROPN
ejpam-544	107	3	appl	appl	PROPN
ejpam-544	107	4	.	.	PROPN
ejpam-544	107	5	math	math	PROPN
ejpam-544	107	6	,	,	PUNCT
ejpam-544	107	7	4	4	NUM
ejpam-544	107	8	(	(	PUNCT
ejpam-544	107	9	2011	2011	NUM
ejpam-544	107	10	)	)	PUNCT
ejpam-544	107	11	,	,	PUNCT
ejpam-544	107	12	230	230	NUM
ejpam-544	107	13	-	-	SYM
ejpam-544	107	14	236	236	NUM
ejpam-544	107	15	234	234	NUM
ejpam-544	107	16	=	=	SYM
ejpam-544	107	17	φ(p(z	φ(p(z	NOUN
ejpam-544	107	18	)	)	PUNCT
ejpam-544	107	19	,	,	PUNCT
ejpam-544	107	20	zp′(z	zp′(z	PROPN
ejpam-544	107	21	)	)	PUNCT
ejpam-544	107	22	;	;	PUNCT
ejpam-544	108	1	z	z	X
ejpam-544	108	2	)	)	PUNCT
ejpam-544	108	3	.	.	PUNCT
ejpam-544	109	1	then	then	ADV
ejpam-544	109	2	,	,	PUNCT
ejpam-544	109	3	for	for	ADP
ejpam-544	109	4	all	all	DET
ejpam-544	109	5	real	real	ADJ
ejpam-544	109	6	x	x	NOUN
ejpam-544	109	7	and	and	CCONJ
ejpam-544	109	8	y	y	PROPN
ejpam-544	109	9	satisfying	satisfy	VERB
ejpam-544	109	10	y	y	NOUN
ejpam-544	109	11	≤	≤	NOUN
ejpam-544	110	1	−n(1	−n(1	PROPN
ejpam-544	110	2	+	+	SYM
ejpam-544	110	3	x2)/2	x2)/2	ADJ
ejpam-544	110	4	,	,	PUNCT
ejpam-544	110	5	we	we	PRON
ejpam-544	110	6	have	have	VERB
ejpam-544	110	7	|φ(i	|φ(i	PROPN
ejpam-544	110	8	x	x	SYM
ejpam-544	110	9	,	,	PUNCT
ejpam-544	110	10	y	y	PROPN
ejpam-544	110	11	;	;	PUNCT
ejpam-544	110	12	z)|2	z)|2	NUM
ejpam-544	110	13	=	=	PUNCT
ejpam-544	110	14	(	(	PUNCT
ejpam-544	110	15	1−	1−	NUM
ejpam-544	110	16	β)2(1	β)2(1	NOUN
ejpam-544	110	17	+	+	CCONJ
ejpam-544	110	18	x2	x2	NOUN
ejpam-544	110	19	)	)	PUNCT
ejpam-544	110	20	(	(	PUNCT
ejpam-544	110	21	1−	1−	NUM
ejpam-544	110	22	t)2[(1−β)2	t)2[(1−β)2	PROPN
ejpam-544	110	23	x2	x2	PROPN
ejpam-544	110	24	+	+	PROPN
ejpam-544	110	25	β2	β2	VERB
ejpam-544	110	26	]	]	PUNCT
ejpam-544	110	27	×	×	NOUN
ejpam-544	110	28	h	h	NOUN
ejpam-544	110	29	¦	¦	PROPN
ejpam-544	110	30	(	(	PUNCT
ejpam-544	110	31	1−	1−	NUM
ejpam-544	110	32	t)(1−β)y	t)(1−β)y	NOUN
ejpam-544	111	1	−	−	PROPN
ejpam-544	111	2	β(1−	β(1−	NOUN
ejpam-544	111	3	t	t	NOUN
ejpam-544	111	4	−β)−	−β)−	NOUN
ejpam-544	111	5	(	(	PUNCT
ejpam-544	111	6	1−	1−	NUM
ejpam-544	111	7	β)2	β)2	X
ejpam-544	111	8	x2	x2	PROPN
ejpam-544	112	1	©	©	PROPN
ejpam-544	112	2	2	2	NUM
ejpam-544	112	3	+	+	CCONJ
ejpam-544	112	4	(	(	PUNCT
ejpam-544	112	5	1−	1−	NUM
ejpam-544	112	6	β)2(2β	β)2(2β	NOUN
ejpam-544	112	7	−	−	PROPN
ejpam-544	112	8	1	1	NUM
ejpam-544	112	9	+	+	NUM
ejpam-544	112	10	t)2	t)2	NOUN
ejpam-544	113	1	x2	x2	NOUN
ejpam-544	113	2	i	i	NOUN
ejpam-544	113	3	=	=	PUNCT
ejpam-544	113	4	(	(	PUNCT
ejpam-544	113	5	1−	1−	NUM
ejpam-544	113	6	β)2(1	β)2(1	NOUN
ejpam-544	113	7	+	+	CCONJ
ejpam-544	113	8	u	u	NOUN
ejpam-544	113	9	)	)	PUNCT
ejpam-544	113	10	(	(	PUNCT
ejpam-544	113	11	1−	1−	NUM
ejpam-544	113	12	t)2[(1−β)2u+	t)2[(1−β)2u+	NUM
ejpam-544	114	1	β2	β2	NOUN
ejpam-544	114	2	]	]	PUNCT
ejpam-544	115	1	×	×	NOUN
ejpam-544	115	2	h	h	NOUN
ejpam-544	115	3	¦	¦	PROPN
ejpam-544	115	4	(	(	PUNCT
ejpam-544	115	5	1−	1−	NUM
ejpam-544	115	6	t)(1−β)y	t)(1−β)y	NOUN
ejpam-544	115	7	−	−	PROPN
ejpam-544	115	8	β(1−	β(1−	NOUN
ejpam-544	115	9	t	t	NOUN
ejpam-544	115	10	−β)−	−β)−	NOUN
ejpam-544	115	11	(	(	PUNCT
ejpam-544	115	12	1−	1−	NUM
ejpam-544	115	13	β)2u	β)2u	NOUN
ejpam-544	115	14	©	©	ADJ
ejpam-544	115	15	2	2	NUM
ejpam-544	115	16	+	+	CCONJ
ejpam-544	115	17	(	(	PUNCT
ejpam-544	115	18	1−β)2(2β	1−β)2(2β	NUM
ejpam-544	115	19	−	−	NUM
ejpam-544	115	20	1	1	NUM
ejpam-544	115	21	+	+	NUM
ejpam-544	115	22	t)2u	t)2u	NOUN
ejpam-544	115	23	i	i	NOUN
ejpam-544	115	24	=	=	PUNCT
ejpam-544	115	25	g(u	g(u	PROPN
ejpam-544	115	26	,	,	PUNCT
ejpam-544	115	27	y	y	NOUN
ejpam-544	115	28	)	)	PUNCT
ejpam-544	115	29	where	where	SCONJ
ejpam-544	115	30	u=	u=	ADV
ejpam-544	115	31	x2	x2	PROPN
ejpam-544	115	32	>	>	X
ejpam-544	115	33	0	0	PUNCT
ejpam-544	115	34	and	and	CCONJ
ejpam-544	115	35	y	y	PROPN
ejpam-544	115	36	≤	≤	NOUN
ejpam-544	115	37	−n(1	−n(1	X
ejpam-544	115	38	+	+	CCONJ
ejpam-544	115	39	x2)/2	x2)/2	ADJ
ejpam-544	115	40	.	.	PUNCT
ejpam-544	116	1	since	since	SCONJ
ejpam-544	116	2	∂	∂	NUM
ejpam-544	116	3	g	g	PROPN
ejpam-544	116	4	∂	∂	NOUN
ejpam-544	116	5	y	y	PROPN
ejpam-544	116	6	=	=	PUNCT
ejpam-544	116	7	2(1−	2(1−	PUNCT
ejpam-544	116	8	β)3(1	β)3(1	NOUN
ejpam-544	116	9	+	+	NUM
ejpam-544	116	10	u	u	NOUN
ejpam-544	116	11	)	)	PUNCT
ejpam-544	116	12	(	(	PUNCT
ejpam-544	116	13	1−	1−	NUM
ejpam-544	116	14	t)[(1−	t)[(1−	NOUN
ejpam-544	116	15	β)2u+	β)2u+	ADP
ejpam-544	116	16	β2	β2	PROPN
ejpam-544	116	17	]	]	X
ejpam-544	116	18	¦	¦	X
ejpam-544	116	19	(	(	PUNCT
ejpam-544	116	20	1−	1−	NUM
ejpam-544	116	21	t)(1−	t)(1−	NOUN
ejpam-544	116	22	β)y	β)y	PUNCT
ejpam-544	117	1	−	−	NUM
ejpam-544	117	2	β(1−	β(1−	NOUN
ejpam-544	118	1	t	t	NOUN
ejpam-544	119	1	−	−	PROPN
ejpam-544	119	2	β)−	β)−	PROPN
ejpam-544	119	3	(	(	PUNCT
ejpam-544	119	4	1−β)2u	1−β)2u	NUM
ejpam-544	119	5	©	©	NOUN
ejpam-544	119	6	<	<	X
ejpam-544	119	7	0	0	NUM
ejpam-544	119	8	,	,	PUNCT
ejpam-544	119	9	therefore	therefore	ADV
ejpam-544	119	10	we	we	PRON
ejpam-544	119	11	have	have	AUX
ejpam-544	119	12	h(u	h(u	X
ejpam-544	119	13	)	)	PUNCT
ejpam-544	120	1	=	=	SYM
ejpam-544	120	2	g[u,−n(1	g[u,−n(1	PROPN
ejpam-544	120	3	+	+	X
ejpam-544	120	4	u)/2]≤	u)/2]≤	PROPN
ejpam-544	120	5	g(u	g(u	PROPN
ejpam-544	120	6	,	,	PUNCT
ejpam-544	120	7	y	y	PROPN
ejpam-544	120	8	)	)	PUNCT
ejpam-544	120	9	,	,	PUNCT
ejpam-544	120	10	where	where	SCONJ
ejpam-544	120	11	h(u	h(u	NOUN
ejpam-544	120	12	)	)	PUNCT
ejpam-544	120	13	=	=	PUNCT
ejpam-544	120	14	(	(	PUNCT
ejpam-544	120	15	1−	1−	NUM
ejpam-544	120	16	β)2(1	β)2(1	NOUN
ejpam-544	120	17	+	+	CCONJ
ejpam-544	120	18	u	u	NOUN
ejpam-544	120	19	)	)	PUNCT
ejpam-544	120	20	(	(	PUNCT
ejpam-544	120	21	1−	1−	NUM
ejpam-544	120	22	t)2	t)2	PROPN
ejpam-544	120	23	�	�	PROPN
ejpam-544	120	24	(	(	PUNCT
ejpam-544	120	25	1−	1−	NUM
ejpam-544	120	26	β)2u+	β)2u+	ADP
ejpam-544	120	27	β2	β2	NOUN
ejpam-544	120	28	[	[	X
ejpam-544	120	29	λu2	λu2	X
ejpam-544	120	30	+	+	X
ejpam-544	120	31	(	(	PUNCT
ejpam-544	120	32	λ+µ−	λ+µ−	PROPN
ejpam-544	120	33	ν	ν	X
ejpam-544	120	34	+	+	NOUN
ejpam-544	120	35	σ)u+µ	σ)u+µ	PROPN
ejpam-544	120	36	]	]	PUNCT
ejpam-544	120	37	,	,	PUNCT
ejpam-544	120	38	(	(	PUNCT
ejpam-544	120	39	5	5	NUM
ejpam-544	120	40	)	)	PUNCT
ejpam-544	120	41	where	where	SCONJ
ejpam-544	120	42	λ	λ	PROPN
ejpam-544	120	43	,	,	PUNCT
ejpam-544	120	44	µ	µ	NOUN
ejpam-544	120	45	,	,	PUNCT
ejpam-544	120	46	ν	ν	NOUN
ejpam-544	120	47	and	and	CCONJ
ejpam-544	120	48	σ	σ	PROPN
ejpam-544	120	49	are	be	AUX
ejpam-544	120	50	given	give	VERB
ejpam-544	120	51	in	in	ADP
ejpam-544	120	52	(	(	PUNCT
ejpam-544	120	53	2	2	NUM
ejpam-544	120	54	)	)	PUNCT
ejpam-544	120	55	.	.	PUNCT
ejpam-544	121	1	now	now	ADV
ejpam-544	121	2	differentaiting	differentaite	VERB
ejpam-544	121	3	(	(	PUNCT
ejpam-544	121	4	5	5	NUM
ejpam-544	121	5	)	)	PUNCT
ejpam-544	121	6	and	and	CCONJ
ejpam-544	121	7	using	use	VERB
ejpam-544	121	8	h′(u	h′(u	PROPN
ejpam-544	121	9	)	)	PUNCT
ejpam-544	121	10	=	=	SYM
ejpam-544	121	11	0	0	NUM
ejpam-544	121	12	,	,	PUNCT
ejpam-544	121	13	we	we	PRON
ejpam-544	121	14	get	get	VERB
ejpam-544	121	15	2λ(1−	2λ(1−	NUM
ejpam-544	121	16	β)2u3	β)2u3	PUNCT
ejpam-544	122	1	+	+	CCONJ
ejpam-544	122	2	¦	¦	X
ejpam-544	122	3	(	(	PUNCT
ejpam-544	122	4	1−	1−	NUM
ejpam-544	122	5	β)2(2λ+µ−	β)2(2λ+µ−	PROPN
ejpam-544	122	6	ν	ν	X
ejpam-544	122	7	+	+	PROPN
ejpam-544	122	8	σ	σ	NOUN
ejpam-544	122	9	)	)	PUNCT
ejpam-544	122	10	+	+	NUM
ejpam-544	122	11	3λβ2	3λβ2	NUM
ejpam-544	122	12	©	©	PROPN
ejpam-544	122	13	u2	u2	NOUN
ejpam-544	122	14	+	+	X
ejpam-544	122	15	2β2(2λ+µ−	2β2(2λ+µ−	NUM
ejpam-544	122	16	ν	ν	NOUN
ejpam-544	122	17	+	+	PUNCT
ejpam-544	122	18	σ)u+	σ)u+	X
ejpam-544	122	19	(	(	PUNCT
ejpam-544	122	20	λ+	λ+	NUM
ejpam-544	122	21	2µ−	2µ−	NUM
ejpam-544	122	22	ν	ν	NOUN
ejpam-544	122	23	+	+	PROPN
ejpam-544	122	24	σ)β2	σ)β2	NOUN
ejpam-544	122	25	−	−	PROPN
ejpam-544	123	1	(	(	PUNCT
ejpam-544	123	2	1−	1−	NUM
ejpam-544	123	3	β)2µ	β)2µ	NOUN
ejpam-544	123	4	=	=	SYM
ejpam-544	123	5	0	0	NUM
ejpam-544	123	6	which	which	PRON
ejpam-544	123	7	is	be	AUX
ejpam-544	123	8	a	a	DET
ejpam-544	123	9	cubic	cubic	ADJ
ejpam-544	123	10	equation	equation	NOUN
ejpam-544	123	11	in	in	ADP
ejpam-544	123	12	u.	u.	NOUN
ejpam-544	123	13	since	since	SCONJ
ejpam-544	123	14	u0	u0	ADJ
ejpam-544	123	15	is	be	AUX
ejpam-544	123	16	the	the	DET
ejpam-544	123	17	positive	positive	ADJ
ejpam-544	123	18	real	real	ADJ
ejpam-544	123	19	root	root	NOUN
ejpam-544	123	20	of	of	ADP
ejpam-544	123	21	this	this	DET
ejpam-544	123	22	equation	equation	NOUN
ejpam-544	123	23	we	we	PRON
ejpam-544	123	24	have	have	VERB
ejpam-544	123	25	h(u)≥	h(u)≥	NOUN
ejpam-544	123	26	h(u0	h(u0	PROPN
ejpam-544	123	27	)	)	PUNCT
ejpam-544	123	28	and	and	CCONJ
ejpam-544	123	29	hence	hence	ADV
ejpam-544	123	30	|φ(i	|φ(i	PROPN
ejpam-544	123	31	x	x	SYM
ejpam-544	123	32	,	,	PUNCT
ejpam-544	123	33	y	y	PROPN
ejpam-544	123	34	;	;	PUNCT
ejpam-544	123	35	z)|2	z)|2	PROPN
ejpam-544	123	36	≥	≥	PROPN
ejpam-544	123	37	h(u0	h(u0	NOUN
ejpam-544	123	38	)	)	PUNCT
ejpam-544	124	1	=	=	PUNCT
ejpam-544	124	2	ρ	ρ	PROPN
ejpam-544	124	3	2	2	NUM
ejpam-544	124	4	.	.	PUNCT
ejpam-544	124	5	define	define	VERB
ejpam-544	124	6	ω	ω	PROPN
ejpam-544	124	7	=	=	SYM
ejpam-544	124	8	�	�	PROPN
ejpam-544	124	9	w	w	PROPN
ejpam-544	124	10	;	;	PUNCT
ejpam-544	124	11	|w|	|w|	VERB
ejpam-544	124	12	<	<	X
ejpam-544	124	13	ρ	ρ	PROPN
ejpam-544	124	14	,	,	PUNCT
ejpam-544	124	15	then	then	ADV
ejpam-544	124	16	φ(p(z	φ(p(z	ADJ
ejpam-544	124	17	)	)	PUNCT
ejpam-544	124	18	,	,	PUNCT
ejpam-544	124	19	zp′(z	zp′(z	PROPN
ejpam-544	124	20	)	)	PUNCT
ejpam-544	124	21	;	;	PUNCT
ejpam-544	125	1	z	z	X
ejpam-544	125	2	)	)	PUNCT
ejpam-544	125	3	∈	∈	PROPN
ejpam-544	125	4	ω	ω	PROPN
ejpam-544	125	5	and	and	CCONJ
ejpam-544	125	6	φ(i	φ(i	PROPN
ejpam-544	125	7	x	x	SYM
ejpam-544	125	8	,	,	PUNCT
ejpam-544	125	9	y	y	PROPN
ejpam-544	125	10	;	;	PUNCT
ejpam-544	125	11	z	z	X
ejpam-544	125	12	)	)	PUNCT
ejpam-544	125	13	6∈	6∈	PROPN
ejpam-544	125	14	ω	ω	PROPN
ejpam-544	125	15	for	for	ADP
ejpam-544	125	16	all	all	DET
ejpam-544	125	17	real	real	ADJ
ejpam-544	125	18	x	x	NOUN
ejpam-544	125	19	and	and	CCONJ
ejpam-544	125	20	y	y	PROPN
ejpam-544	125	21	≤	≤	NOUN
ejpam-544	126	1	−n(1	−n(1	X
ejpam-544	126	2	+	+	SYM
ejpam-544	126	3	x2)/2	x2)/2	ADJ
ejpam-544	126	4	,	,	PUNCT
ejpam-544	126	5	z	z	PROPN
ejpam-544	126	6	∈∆.	∈∆.	PROPN
ejpam-544	126	7	therefore	therefore	ADV
ejpam-544	126	8	by	by	ADP
ejpam-544	126	9	an	an	DET
ejpam-544	126	10	application	application	NOUN
ejpam-544	126	11	of	of	ADP
ejpam-544	126	12	lemma	lemma	PROPN
ejpam-544	126	13	1	1	NUM
ejpam-544	126	14	.	.	PUNCT
ejpam-544	127	1	the	the	DET
ejpam-544	127	2	result	result	NOUN
ejpam-544	127	3	follows	follow	VERB
ejpam-544	127	4	.	.	PUNCT
ejpam-544	128	1	by	by	ADP
ejpam-544	128	2	taking	take	VERB
ejpam-544	128	3	t	t	NOUN
ejpam-544	128	4	=	=	SYM
ejpam-544	128	5	−1	−1	NOUN
ejpam-544	128	6	,	,	PUNCT
ejpam-544	128	7	in	in	ADP
ejpam-544	128	8	theorem	theorem	NOUN
ejpam-544	128	9	2	2	NUM
ejpam-544	128	10	,	,	PUNCT
ejpam-544	128	11	we	we	PRON
ejpam-544	128	12	have	have	VERB
ejpam-544	128	13	the	the	DET
ejpam-544	128	14	following	follow	VERB
ejpam-544	128	15	corollary	corollary	NOUN
ejpam-544	128	16	6	6	NUM
ejpam-544	128	17	.	.	PUNCT
ejpam-544	129	1	let	let	VERB
ejpam-544	129	2	0	0	NUM
ejpam-544	129	3	≤	≤	NOUN
ejpam-544	129	4	β	β	X
ejpam-544	129	5	<	<	X
ejpam-544	129	6	1	1	NUM
ejpam-544	129	7	,	,	PUNCT
ejpam-544	129	8	λ1	λ1	NOUN
ejpam-544	129	9	=	=	PUNCT
ejpam-544	129	10	(	(	PUNCT
ejpam-544	129	11	1	1	NUM
ejpam-544	129	12	−	−	NOUN
ejpam-544	129	13	β	β	NOUN
ejpam-544	129	14	)	)	PUNCT
ejpam-544	129	15	2	2	NUM
ejpam-544	129	16	�	�	PROPN
ejpam-544	129	17	1−	1−	NUM
ejpam-544	129	18	β	β	X
ejpam-544	129	19	+	+	CCONJ
ejpam-544	129	20	n	n	CCONJ
ejpam-544	129	21	2	2	NUM
ejpam-544	129	22	,	,	PUNCT
ejpam-544	129	23	µ1	µ1	PROPN
ejpam-544	129	24	=	=	SYM
ejpam-544	129	25	¦	¦	X
ejpam-544	129	26	(	(	PUNCT
ejpam-544	129	27	1−	1−	NUM
ejpam-544	129	28	β)n−	β)n−	NOUN
ejpam-544	129	29	(	(	PUNCT
ejpam-544	129	30	β2−	β2−	NOUN
ejpam-544	129	31	2β	2β	NOUN
ejpam-544	129	32	)	)	PUNCT
ejpam-544	130	1	©	©	PROPN
ejpam-544	130	2	2	2	NUM
ejpam-544	130	3	,	,	PUNCT
ejpam-544	130	4	ν1	ν1	NOUN
ejpam-544	130	5	=	=	SYM
ejpam-544	130	6	¦	¦	X
ejpam-544	130	7	(	(	PUNCT
ejpam-544	130	8	1−	1−	NUM
ejpam-544	130	9	β)2	β)2	X
ejpam-544	130	10	+	+	CCONJ
ejpam-544	130	11	(	(	PUNCT
ejpam-544	130	12	β2	β2	NOUN
ejpam-544	130	13	−	−	NOUN
ejpam-544	130	14	2β	2β	NOUN
ejpam-544	130	15	)	)	PUNCT
ejpam-544	131	1	©	©	PROPN
ejpam-544	131	2	2	2	NUM
ejpam-544	131	3	and	and	CCONJ
ejpam-544	131	4	σ1	σ1	NOUN
ejpam-544	131	5	=	=	SYM
ejpam-544	131	6	4(1−β)4	4(1−β)4	NUM
ejpam-544	131	7	,	,	PUNCT
ejpam-544	131	8	satisfy	satisfy	NOUN
ejpam-544	131	9	(	(	PUNCT
ejpam-544	131	10	λ1+µ1−ν1+σ1)β	λ1+µ1−ν1+σ1)β	ADP
ejpam-544	131	11	2	2	NUM
ejpam-544	131	12	<	<	X
ejpam-544	131	13	(	(	PUNCT
ejpam-544	131	14	1−2β)µ1	1−2β)µ1	NUM
ejpam-544	131	15	.	.	PUNCT
ejpam-544	131	16	also	also	ADV
ejpam-544	131	17	suppose	suppose	VERB
ejpam-544	131	18	that	that	SCONJ
ejpam-544	131	19	u1	u1	NOUN
ejpam-544	131	20	be	be	AUX
ejpam-544	131	21	the	the	DET
ejpam-544	131	22	positive	positive	ADJ
ejpam-544	131	23	real	real	ADJ
ejpam-544	131	24	root	root	NOUN
ejpam-544	131	25	of	of	ADP
ejpam-544	131	26	the	the	DET
ejpam-544	131	27	equation	equation	NOUN
ejpam-544	131	28	2λ1(1−	2λ1(1−	NUM
ejpam-544	131	29	β	β	NOUN
ejpam-544	131	30	)	)	PUNCT
ejpam-544	131	31	2u3	2u3	NUM
ejpam-544	132	1	+	+	CCONJ
ejpam-544	132	2	¦	¦	X
ejpam-544	132	3	(	(	PUNCT
ejpam-544	132	4	1−	1−	NUM
ejpam-544	132	5	β)2(2λ1+µ1−	β)2(2λ1+µ1−	NUM
ejpam-544	132	6	ν1	ν1	NOUN
ejpam-544	132	7	+	+	PROPN
ejpam-544	132	8	σ1	σ1	PROPN
ejpam-544	132	9	)	)	PUNCT
ejpam-544	133	1	+	+	CCONJ
ejpam-544	133	2	3λ1β	3λ1β	NUM
ejpam-544	133	3	2	2	NUM
ejpam-544	133	4	©	©	PROPN
ejpam-544	133	5	u2	u2	PROPN
ejpam-544	133	6	s.	s.	PROPN
ejpam-544	133	7	goyal	goyal	PROPN
ejpam-544	133	8	,	,	PUNCT
ejpam-544	133	9	p.	p.	NOUN
ejpam-544	133	10	vijaywargiya	vijaywargiya	NOUN
ejpam-544	133	11	,	,	PUNCT
ejpam-544	133	12	p.	p.	NOUN
ejpam-544	133	13	goswami	goswami	PROPN
ejpam-544	133	14	/	/	SYM
ejpam-544	133	15	eur	eur	PROPN
ejpam-544	133	16	.	.	PUNCT
ejpam-544	134	1	j.	j.	PROPN
ejpam-544	134	2	pure	pure	PROPN
ejpam-544	134	3	appl	appl	PROPN
ejpam-544	134	4	.	.	PROPN
ejpam-544	134	5	math	math	PROPN
ejpam-544	134	6	,	,	PUNCT
ejpam-544	134	7	4	4	NUM
ejpam-544	134	8	(	(	PUNCT
ejpam-544	134	9	2011	2011	NUM
ejpam-544	134	10	)	)	PUNCT
ejpam-544	134	11	,	,	PUNCT
ejpam-544	134	12	230	230	NUM
ejpam-544	134	13	-	-	SYM
ejpam-544	134	14	236	236	NUM
ejpam-544	134	15	235	235	NUM
ejpam-544	134	16	+2β2(2λ1+µ1−	+2β2(2λ1+µ1−	NOUN
ejpam-544	134	17	ν1	ν1	NOUN
ejpam-544	134	18	+	+	NOUN
ejpam-544	134	19	σ1)u+	σ1)u+	PROPN
ejpam-544	134	20	(	(	PUNCT
ejpam-544	134	21	λ1	λ1	ADJ
ejpam-544	134	22	+	+	SYM
ejpam-544	134	23	2µ1−	2µ1−	NUM
ejpam-544	134	24	ν1	ν1	NOUN
ejpam-544	134	25	+	+	NOUN
ejpam-544	134	26	σ1)β	σ1)β	ADJ
ejpam-544	134	27	2	2	NUM
ejpam-544	134	28	−	−	NOUN
ejpam-544	134	29	(	(	PUNCT
ejpam-544	134	30	1−	1−	NUM
ejpam-544	134	31	β)2µ1	β)2µ1	NUM
ejpam-544	134	32	=	=	SYM
ejpam-544	134	33	0	0	NUM
ejpam-544	134	34	(	(	PUNCT
ejpam-544	134	35	6	6	NUM
ejpam-544	134	36	)	)	PUNCT
ejpam-544	134	37	and	and	CCONJ
ejpam-544	134	38	ρ2	ρ2	NOUN
ejpam-544	134	39	1	1	NUM
ejpam-544	134	40	=	=	SYM
ejpam-544	134	41	(	(	PUNCT
ejpam-544	134	42	1−	1−	NUM
ejpam-544	134	43	β)2(1	β)2(1	NOUN
ejpam-544	134	44	+	+	SYM
ejpam-544	134	45	u1	u1	NOUN
ejpam-544	134	46	)	)	PUNCT
ejpam-544	134	47	4	4	NUM
ejpam-544	134	48	�	�	PROPN
ejpam-544	134	49	(	(	PUNCT
ejpam-544	134	50	1−	1−	NUM
ejpam-544	134	51	β)2u1	β)2u1	PUNCT
ejpam-544	135	1	+	+	NUM
ejpam-544	135	2	β	β	X
ejpam-544	135	3	2	2	NUM
ejpam-544	135	4	[	[	X
ejpam-544	135	5	λ1u2	λ1u2	X
ejpam-544	135	6	1	1	NUM
ejpam-544	135	7	+	+	CCONJ
ejpam-544	135	8	(	(	PUNCT
ejpam-544	135	9	λ1	λ1	ADJ
ejpam-544	135	10	+	+	PROPN
ejpam-544	135	11	µ1−	µ1−	NOUN
ejpam-544	135	12	ν1	ν1	NOUN
ejpam-544	135	13	+	+	NOUN
ejpam-544	135	14	σ1)u1	σ1)u1	NOUN
ejpam-544	135	15	+	+	SYM
ejpam-544	135	16	µ1	µ1	NOUN
ejpam-544	135	17	]	]	PUNCT
ejpam-544	135	18	.	.	PUNCT
ejpam-544	136	1	(	(	PUNCT
ejpam-544	136	2	7	7	X
ejpam-544	136	3	)	)	PUNCT
ejpam-544	136	4	now	now	ADV
ejpam-544	136	5	if	if	SCONJ
ejpam-544	136	6	f	f	PROPN
ejpam-544	136	7	(	(	PUNCT
ejpam-544	136	8	z	z	NOUN
ejpam-544	136	9	)	)	PUNCT
ejpam-544	136	10	∈	∈	PROPN
ejpam-544	136	11	an	an	DET
ejpam-544	136	12	satisfies	satisfie	NOUN
ejpam-544	136	13	�	�	PROPN
ejpam-544	136	14	�	�	PROPN
ejpam-544	136	15	�	�	PROPN
ejpam-544	136	16	�	�	PROPN
ejpam-544	136	17	�	�	PROPN
ejpam-544	136	18	�	�	PROPN
ejpam-544	136	19	2z	2z	PROPN
ejpam-544	136	20	f	f	PROPN
ejpam-544	136	21	′(z	′(z	NOUN
ejpam-544	136	22	)	)	PUNCT
ejpam-544	136	23	f	f	PROPN
ejpam-544	136	24	(	(	PUNCT
ejpam-544	136	25	z)−	z)−	PROPN
ejpam-544	136	26	f	f	X
ejpam-544	136	27	(	(	PUNCT
ejpam-544	136	28	−z	−z	NOUN
ejpam-544	136	29	)	)	PUNCT
ejpam-544	136	30	−	−	PROPN
ejpam-544	136	31	1	1	NUM
ejpam-544	136	32	�	�	PROPN
ejpam-544	136	33	�	�	PROPN
ejpam-544	136	34	z	z	PROPN
ejpam-544	136	35	f	f	PROPN
ejpam-544	136	36	′′(z	′′(z	PROPN
ejpam-544	136	37	)	)	PUNCT
ejpam-544	136	38	f	f	PROPN
ejpam-544	136	39	′(z	′(z	NOUN
ejpam-544	136	40	)	)	PUNCT
ejpam-544	137	1	−	−	PROPN
ejpam-544	137	2	z	z	PROPN
ejpam-544	137	3	f	f	PROPN
ejpam-544	137	4	′(−z	′(−z	ADV
ejpam-544	137	5	)	)	PUNCT
ejpam-544	138	1	f	f	PROPN
ejpam-544	138	2	(	(	PUNCT
ejpam-544	138	3	z)−	z)−	PROPN
ejpam-544	138	4	f	f	X
ejpam-544	138	5	(	(	PUNCT
ejpam-544	138	6	−z	−z	NOUN
ejpam-544	138	7	)	)	PUNCT
ejpam-544	138	8	�	�	PROPN
ejpam-544	138	9	�	�	PROPN
ejpam-544	138	10	�	�	PROPN
ejpam-544	138	11	�	�	PROPN
ejpam-544	138	12	�	�	PROPN
ejpam-544	138	13	�	�	PROPN
ejpam-544	138	14	≤	≤	PROPN
ejpam-544	138	15	ρ1	ρ1	NOUN
ejpam-544	138	16	(	(	PUNCT
ejpam-544	138	17	z	z	NOUN
ejpam-544	138	18	∈∆	∈∆	NOUN
ejpam-544	138	19	)	)	PUNCT
ejpam-544	138	20	,	,	PUNCT
ejpam-544	138	21	then	then	ADV
ejpam-544	138	22	f	f	X
ejpam-544	138	23	(	(	PUNCT
ejpam-544	138	24	z	z	NOUN
ejpam-544	138	25	)	)	PUNCT
ejpam-544	138	26	∈	∈	PROPN
ejpam-544	138	27	sn(β	sn(β	NUM
ejpam-544	138	28	,	,	PUNCT
ejpam-544	138	29	−1	−1	NOUN
ejpam-544	138	30	)	)	PUNCT
ejpam-544	138	31	.	.	PUNCT
ejpam-544	139	1	by	by	ADP
ejpam-544	139	2	taking	take	VERB
ejpam-544	139	3	β	β	X
ejpam-544	139	4	=	=	SYM
ejpam-544	139	5	0	0	NUM
ejpam-544	139	6	in	in	ADP
ejpam-544	139	7	corollary	corollary	ADJ
ejpam-544	139	8	6	6	NUM
ejpam-544	139	9	,	,	PUNCT
ejpam-544	139	10	we	we	PRON
ejpam-544	139	11	get	get	VERB
ejpam-544	139	12	the	the	DET
ejpam-544	139	13	following	follow	VERB
ejpam-544	139	14	corollary	corollary	NOUN
ejpam-544	139	15	7	7	NUM
ejpam-544	139	16	.	.	PUNCT
ejpam-544	140	1	let	let	VERB
ejpam-544	140	2	u2	u2	NOUN
ejpam-544	140	3	be	be	AUX
ejpam-544	140	4	the	the	DET
ejpam-544	140	5	positive	positive	ADJ
ejpam-544	140	6	real	real	ADJ
ejpam-544	140	7	root	root	NOUN
ejpam-544	140	8	of	of	ADP
ejpam-544	140	9	the	the	DET
ejpam-544	140	10	equation	equation	NOUN
ejpam-544	140	11	2(n+	2(n+	NOUN
ejpam-544	141	1	1)2u3	1)2u3	NUM
ejpam-544	141	2	+	+	CCONJ
ejpam-544	141	3	(	(	PUNCT
ejpam-544	141	4	3n2	3n2	NUM
ejpam-544	141	5	+	+	NUM
ejpam-544	141	6	4n+	4n+	NUM
ejpam-544	141	7	5)u2−	5)u2−	NUM
ejpam-544	141	8	n2	n2	NOUN
ejpam-544	141	9	=	=	SYM
ejpam-544	141	10	0	0	PUNCT
ejpam-544	141	11	(	(	PUNCT
ejpam-544	141	12	8)	8)	NUM
ejpam-544	141	13	and	and	CCONJ
ejpam-544	141	14	ρ2	ρ2	NOUN
ejpam-544	141	15	2	2	NUM
ejpam-544	141	16	=	=	SYM
ejpam-544	141	17	(	(	PUNCT
ejpam-544	141	18	1	1	NUM
ejpam-544	141	19	+	+	NUM
ejpam-544	141	20	u2	u2	NOUN
ejpam-544	141	21	)	)	PUNCT
ejpam-544	141	22	4u2	4u2	PUNCT
ejpam-544	142	1	[	[	X
ejpam-544	142	2	(	(	PUNCT
ejpam-544	142	3	n+	n+	NUM
ejpam-544	142	4	1)2u2	1)2u2	PROPN
ejpam-544	142	5	2	2	NUM
ejpam-544	142	6	+	+	CCONJ
ejpam-544	142	7	2(n2	2(n2	NUM
ejpam-544	142	8	+	+	SYM
ejpam-544	142	9	n+	n+	NUM
ejpam-544	142	10	2)u2	2)u2	NUM
ejpam-544	142	11	+	+	CCONJ
ejpam-544	142	12	n2	n2	NOUN
ejpam-544	142	13	]	]	X
ejpam-544	142	14	.	.	PUNCT
ejpam-544	143	1	(	(	PUNCT
ejpam-544	143	2	9	9	X
ejpam-544	143	3	)	)	PUNCT
ejpam-544	143	4	now	now	ADV
ejpam-544	143	5	if	if	SCONJ
ejpam-544	143	6	f	f	PROPN
ejpam-544	143	7	(	(	PUNCT
ejpam-544	143	8	z	z	NOUN
ejpam-544	143	9	)	)	PUNCT
ejpam-544	143	10	∈	∈	PROPN
ejpam-544	143	11	an	an	DET
ejpam-544	143	12	satisfies	satisfie	NOUN
ejpam-544	143	13	�	�	PROPN
ejpam-544	143	14	�	�	PROPN
ejpam-544	143	15	�	�	PROPN
ejpam-544	143	16	�	�	PROPN
ejpam-544	143	17	�	�	PROPN
ejpam-544	143	18	�	�	PROPN
ejpam-544	143	19	2z	2z	PROPN
ejpam-544	143	20	f	f	PROPN
ejpam-544	143	21	′(z	′(z	NOUN
ejpam-544	143	22	)	)	PUNCT
ejpam-544	143	23	f	f	PROPN
ejpam-544	143	24	(	(	PUNCT
ejpam-544	143	25	z)−	z)−	PROPN
ejpam-544	143	26	f	f	X
ejpam-544	143	27	(	(	PUNCT
ejpam-544	143	28	−z	−z	NOUN
ejpam-544	143	29	)	)	PUNCT
ejpam-544	143	30	−	−	PROPN
ejpam-544	143	31	1	1	NUM
ejpam-544	143	32	�	�	PROPN
ejpam-544	143	33	�	�	PROPN
ejpam-544	143	34	z	z	PROPN
ejpam-544	143	35	f	f	PROPN
ejpam-544	143	36	′′(z	′′(z	PROPN
ejpam-544	143	37	)	)	PUNCT
ejpam-544	143	38	f	f	PROPN
ejpam-544	143	39	′(z	′(z	NOUN
ejpam-544	143	40	)	)	PUNCT
ejpam-544	144	1	−	−	PROPN
ejpam-544	144	2	z	z	PROPN
ejpam-544	144	3	f	f	PROPN
ejpam-544	144	4	′(−z	′(−z	ADV
ejpam-544	144	5	)	)	PUNCT
ejpam-544	145	1	f	f	PROPN
ejpam-544	145	2	(	(	PUNCT
ejpam-544	145	3	z)−	z)−	PROPN
ejpam-544	145	4	f	f	X
ejpam-544	145	5	(	(	PUNCT
ejpam-544	145	6	−z	−z	NOUN
ejpam-544	145	7	)	)	PUNCT
ejpam-544	145	8	�	�	PROPN
ejpam-544	145	9	�	�	PROPN
ejpam-544	145	10	�	�	PROPN
ejpam-544	145	11	�	�	PROPN
ejpam-544	145	12	�	�	PROPN
ejpam-544	145	13	�	�	PROPN
ejpam-544	145	14	≤	≤	PROPN
ejpam-544	145	15	ρ2	ρ2	NOUN
ejpam-544	145	16	(	(	PUNCT
ejpam-544	145	17	z	z	NOUN
ejpam-544	145	18	∈∆	∈∆	NOUN
ejpam-544	145	19	)	)	PUNCT
ejpam-544	145	20	,	,	PUNCT
ejpam-544	145	21	then	then	ADV
ejpam-544	145	22	f	f	X
ejpam-544	145	23	(	(	PUNCT
ejpam-544	145	24	z	z	NOUN
ejpam-544	145	25	)	)	PUNCT
ejpam-544	145	26	∈	∈	PROPN
ejpam-544	145	27	sn(0,−1	sn(0,−1	NOUN
ejpam-544	145	28	)	)	PUNCT
ejpam-544	145	29	.	.	PUNCT
ejpam-544	146	1	by	by	ADP
ejpam-544	146	2	taking	take	VERB
ejpam-544	146	3	n	n	X
ejpam-544	146	4	=	=	SYM
ejpam-544	146	5	1	1	NUM
ejpam-544	146	6	in	in	ADP
ejpam-544	146	7	corollary	corollary	ADJ
ejpam-544	146	8	7	7	NUM
ejpam-544	146	9	,	,	PUNCT
ejpam-544	146	10	we	we	PRON
ejpam-544	146	11	have	have	VERB
ejpam-544	146	12	u3	u3	NOUN
ejpam-544	146	13	=	=	SYM
ejpam-544	146	14	0.266048	0.266048	NUM
ejpam-544	146	15	.	.	PUNCT
ejpam-544	146	16	.	.	PUNCT
ejpam-544	147	1	.	.	PUNCT
ejpam-544	147	2	,	,	PUNCT
ejpam-544	147	3	thus	thus	ADV
ejpam-544	147	4	we	we	PRON
ejpam-544	147	5	have	have	VERB
ejpam-544	147	6	the	the	DET
ejpam-544	147	7	following	follow	VERB
ejpam-544	147	8	result	result	VERB
ejpam-544	147	9	corollary	corollary	ADJ
ejpam-544	147	10	8	8	NUM
ejpam-544	147	11	.	.	PUNCT
ejpam-544	148	1	if	if	SCONJ
ejpam-544	148	2	f	f	PROPN
ejpam-544	148	3	(	(	PUNCT
ejpam-544	148	4	z	z	NOUN
ejpam-544	148	5	)	)	PUNCT
ejpam-544	148	6	∈	∈	PROPN
ejpam-544	148	7	a	a	DET
ejpam-544	148	8	satisfies	satisfie	NOUN
ejpam-544	148	9	�	�	PROPN
ejpam-544	148	10	�	�	PROPN
ejpam-544	148	11	�	�	PROPN
ejpam-544	148	12	�	�	PROPN
ejpam-544	148	13	�	�	PROPN
ejpam-544	148	14	�	�	PROPN
ejpam-544	148	15	2z	2z	PROPN
ejpam-544	148	16	f	f	PROPN
ejpam-544	148	17	′(z	′(z	NOUN
ejpam-544	148	18	)	)	PUNCT
ejpam-544	148	19	f	f	PROPN
ejpam-544	149	1	(	(	PUNCT
ejpam-544	149	2	z)−	z)−	PROPN
ejpam-544	149	3	f	f	X
ejpam-544	149	4	(	(	PUNCT
ejpam-544	149	5	−z	−z	NOUN
ejpam-544	149	6	)	)	PUNCT
ejpam-544	149	7	−	−	PROPN
ejpam-544	149	8	1	1	NUM
ejpam-544	149	9	�	�	PROPN
ejpam-544	149	10	�	�	PROPN
ejpam-544	149	11	z	z	PROPN
ejpam-544	149	12	f	f	PROPN
ejpam-544	149	13	′′(z	′′(z	PROPN
ejpam-544	149	14	)	)	PUNCT
ejpam-544	149	15	f	f	PROPN
ejpam-544	149	16	′(z	′(z	NOUN
ejpam-544	149	17	)	)	PUNCT
ejpam-544	149	18	−	−	PROPN
ejpam-544	149	19	z	z	PROPN
ejpam-544	149	20	f	f	PROPN
ejpam-544	149	21	′(−z	′(−z	ADV
ejpam-544	149	22	)	)	PUNCT
ejpam-544	149	23	f	f	PROPN
ejpam-544	149	24	(	(	PUNCT
ejpam-544	149	25	z)−	z)−	PROPN
ejpam-544	149	26	f	f	X
ejpam-544	149	27	(	(	PUNCT
ejpam-544	149	28	−z	−z	NOUN
ejpam-544	149	29	)	)	PUNCT
ejpam-544	149	30	�	�	PROPN
ejpam-544	149	31	�	�	PROPN
ejpam-544	149	32	�	�	PROPN
ejpam-544	149	33	�	�	PROPN
ejpam-544	149	34	�	�	PROPN
ejpam-544	149	35	�	�	PROPN
ejpam-544	149	36	≤	≤	PROPN
ejpam-544	149	37	ρ3	ρ3	NOUN
ejpam-544	149	38	(	(	PUNCT
ejpam-544	149	39	z	z	NOUN
ejpam-544	149	40	∈∆	∈∆	NOUN
ejpam-544	149	41	)	)	PUNCT
ejpam-544	149	42	,	,	PUNCT
ejpam-544	149	43	where	where	SCONJ
ejpam-544	149	44	ρ3	ρ3	NOUN
ejpam-544	149	45	=	=	VERB
ejpam-544	149	46	2.0145979	2.0145979	NUM
ejpam-544	149	47	.	.	PUNCT
ejpam-544	149	48	.	.	PUNCT
ejpam-544	150	1	.	.	PUNCT
ejpam-544	151	1	,	,	PUNCT
ejpam-544	151	2	then	then	ADV
ejpam-544	151	3	f	f	X
ejpam-544	151	4	(	(	PUNCT
ejpam-544	151	5	z	z	NOUN
ejpam-544	151	6	)	)	PUNCT
ejpam-544	151	7	∈	∈	PROPN
ejpam-544	151	8	s(0,−1	s(0,−1	PROPN
ejpam-544	151	9	)	)	PUNCT
ejpam-544	151	10	.	.	PUNCT
ejpam-544	152	1	by	by	ADP
ejpam-544	152	2	taking	take	VERB
ejpam-544	152	3	t	t	NOUN
ejpam-544	152	4	=	=	SYM
ejpam-544	152	5	0	0	NUM
ejpam-544	152	6	in	in	ADP
ejpam-544	152	7	theorem	theorem	NOUN
ejpam-544	152	8	2	2	NUM
ejpam-544	152	9	,	,	PUNCT
ejpam-544	152	10	we	we	PRON
ejpam-544	152	11	get	get	VERB
ejpam-544	152	12	a	a	DET
ejpam-544	152	13	known	known	ADJ
ejpam-544	152	14	result	result	NOUN
ejpam-544	152	15	due	due	ADP
ejpam-544	152	16	to	to	ADP
ejpam-544	152	17	ravichandran	ravichandran	VERB
ejpam-544	152	18	et	et	PROPN
ejpam-544	152	19	al	al	PROPN
ejpam-544	152	20	.	.	PUNCT
ejpam-544	153	1	[	[	X
ejpam-544	153	2	6	6	NUM
ejpam-544	153	3	,	,	PUNCT
ejpam-544	153	4	thm	thm	PROPN
ejpam-544	153	5	.	.	PUNCT
ejpam-544	154	1	2.5	2.5	NUM
ejpam-544	154	2	]	]	PUNCT
ejpam-544	154	3	.	.	PUNCT
ejpam-544	155	1	for	for	ADP
ejpam-544	155	2	n	n	NOUN
ejpam-544	155	3	=	=	SYM
ejpam-544	155	4	1	1	NUM
ejpam-544	155	5	,	,	PUNCT
ejpam-544	155	6	β	β	X
ejpam-544	155	7	=	=	SYM
ejpam-544	155	8	0	0	PUNCT
ejpam-544	155	9	=	=	SYM
ejpam-544	155	10	t	t	PROPN
ejpam-544	155	11	,	,	PUNCT
ejpam-544	155	12	our	our	PRON
ejpam-544	155	13	theorem	theorem	ADJ
ejpam-544	155	14	2	2	NUM
ejpam-544	155	15	reduces	reduce	VERB
ejpam-544	155	16	to	to	ADP
ejpam-544	155	17	another	another	DET
ejpam-544	155	18	known	know	VERB
ejpam-544	155	19	result	result	NOUN
ejpam-544	155	20	due	due	ADP
ejpam-544	155	21	to	to	ADP
ejpam-544	155	22	li	li	PROPN
ejpam-544	155	23	and	and	CCONJ
ejpam-544	155	24	owa	owa	PROPN
ejpam-544	156	1	[	[	X
ejpam-544	156	2	3	3	NUM
ejpam-544	156	3	]	]	PUNCT
ejpam-544	156	4	.	.	PUNCT
ejpam-544	157	1	acknowledgements	acknowledgement	NOUN
ejpam-544	157	2	the	the	DET
ejpam-544	157	3	first	first	ADJ
ejpam-544	157	4	author	author	NOUN
ejpam-544	157	5	(	(	PUNCT
ejpam-544	157	6	s	s	PROPN
ejpam-544	157	7	p	p	NOUN
ejpam-544	157	8	g	g	NOUN
ejpam-544	157	9	)	)	PUNCT
ejpam-544	157	10	is	be	AUX
ejpam-544	157	11	thankful	thankful	ADJ
ejpam-544	157	12	to	to	ADP
ejpam-544	157	13	csir	csir	PROPN
ejpam-544	157	14	,	,	PUNCT
ejpam-544	157	15	new	new	ADJ
ejpam-544	157	16	delhi	delhi	PROPN
ejpam-544	157	17	,	,	PUNCT
ejpam-544	157	18	india	india	PROPN
ejpam-544	157	19	for	for	ADP
ejpam-544	157	20	awarding	award	VERB
ejpam-544	157	21	emeritius	emeritius	NOUN
ejpam-544	157	22	scientist	scientist	NOUN
ejpam-544	157	23	under	under	ADP
ejpam-544	157	24	scheme	scheme	PROPN
ejpam-544	157	25	no	no	NOUN
ejpam-544	157	26	.	.	NOUN
ejpam-544	158	1	21(084)/10	21(084)/10	NUM
ejpam-544	158	2	/	/	SYM
ejpam-544	158	3	emr	emr	PROPN
ejpam-544	158	4	-	-	PUNCT
ejpam-544	158	5	ii	ii	PROPN
ejpam-544	158	6	and	and	CCONJ
ejpam-544	158	7	second	second	ADJ
ejpam-544	158	8	author	author	NOUN
ejpam-544	158	9	(	(	PUNCT
ejpam-544	158	10	p	p	NOUN
ejpam-544	158	11	v	v	NOUN
ejpam-544	158	12	)	)	PUNCT
ejpam-544	158	13	is	be	AUX
ejpam-544	158	14	thankful	thankful	ADJ
ejpam-544	158	15	to	to	ADP
ejpam-544	158	16	the	the	DET
ejpam-544	158	17	csir	csir	PROPN
ejpam-544	158	18	,	,	PUNCT
ejpam-544	158	19	india	india	PROPN
ejpam-544	158	20	,	,	PUNCT
ejpam-544	158	21	for	for	ADP
ejpam-544	158	22	providing	provide	VERB
ejpam-544	158	23	senior	senior	ADJ
ejpam-544	158	24	research	research	NOUN
ejpam-544	158	25	fellowship	fellowship	NOUN
ejpam-544	158	26	under	under	ADP
ejpam-544	158	27	research	research	NOUN
ejpam-544	158	28	scheme	scheme	NOUN
ejpam-544	158	29	no	no	INTJ
ejpam-544	158	30	.	.	PUNCT
ejpam-544	159	1	09/149(0431)/2006	09/149(0431)/2006	NOUN
ejpam-544	159	2	-	-	PUNCT
ejpam-544	159	3	emr	emr	PROPN
ejpam-544	159	4	-	-	PUNCT
ejpam-544	159	5	i.	i.	NOUN
ejpam-544	159	6	references	reference	NOUN
ejpam-544	159	7	236	236	NUM
ejpam-544	159	8	references	reference	NOUN
ejpam-544	159	9	[	[	X
ejpam-544	159	10	1	1	NUM
ejpam-544	159	11	]	]	X
ejpam-544	159	12	n.e	n.e	PROPN
ejpam-544	159	13	.	.	PUNCT
ejpam-544	159	14	cho	cho	PROPN
ejpam-544	159	15	,	,	PUNCT
ejpam-544	159	16	o.s	o.s	PROPN
ejpam-544	159	17	.	.	PROPN
ejpam-544	159	18	kwon	kwon	PROPN
ejpam-544	159	19	and	and	CCONJ
ejpam-544	159	20	s.owa	s.owa	PROPN
ejpam-544	159	21	,	,	PUNCT
ejpam-544	159	22	certain	certain	ADJ
ejpam-544	159	23	subclasses	subclass	NOUN
ejpam-544	159	24	of	of	ADP
ejpam-544	159	25	sakaguchi	sakaguchi	ADJ
ejpam-544	159	26	functions	function	NOUN
ejpam-544	159	27	,	,	PUNCT
ejpam-544	159	28	southeast	southeast	ADJ
ejpam-544	159	29	asian	asian	ADJ
ejpam-544	159	30	bull	bull	NOUN
ejpam-544	159	31	.	.	PUNCT
ejpam-544	160	1	math	math	NOUN
ejpam-544	160	2	.	.	PUNCT
ejpam-544	160	3	,	,	PUNCT
ejpam-544	160	4	17	17	NUM
ejpam-544	160	5	,	,	PUNCT
ejpam-544	160	6	121	121	NUM
ejpam-544	160	7	-	-	SYM
ejpam-544	160	8	126	126	NUM
ejpam-544	160	9	.	.	PUNCT
ejpam-544	160	10	1993	1993	NUM
ejpam-544	160	11	.	.	PUNCT
ejpam-544	161	1	[	[	X
ejpam-544	161	2	2	2	NUM
ejpam-544	161	3	]	]	X
ejpam-544	161	4	s.p	s.p	PROPN
ejpam-544	161	5	.	.	PUNCT
ejpam-544	161	6	goyal	goyal	PROPN
ejpam-544	161	7	and	and	CCONJ
ejpam-544	161	8	p.	p.	PROPN
ejpam-544	161	9	goswami	goswami	PROPN
ejpam-544	161	10	,	,	PUNCT
ejpam-544	161	11	certain	certain	ADJ
ejpam-544	161	12	coefficient	coefficient	NOUN
ejpam-544	161	13	inequalities	inequality	NOUN
ejpam-544	161	14	for	for	ADP
ejpam-544	161	15	sakaguchi	sakaguchi	ADJ
ejpam-544	161	16	type	type	NOUN
ejpam-544	161	17	functions	function	NOUN
ejpam-544	161	18	and	and	CCONJ
ejpam-544	161	19	applications	application	NOUN
ejpam-544	161	20	to	to	PART
ejpam-544	161	21	fractional	fractional	VERB
ejpam-544	161	22	derivative	derivative	ADJ
ejpam-544	161	23	operator	operator	NOUN
ejpam-544	161	24	,	,	PUNCT
ejpam-544	161	25	acta	acta	PROPN
ejpam-544	161	26	universitaties	universitatie	NOUN
ejpam-544	161	27	apulensis	apulensis	NOUN
ejpam-544	161	28	,	,	PUNCT
ejpam-544	161	29	19	19	NUM
ejpam-544	161	30	,	,	PUNCT
ejpam-544	161	31	159166	159166	NUM
ejpam-544	161	32	.	.	PUNCT
ejpam-544	162	1	2009	2009	NUM
ejpam-544	162	2	.	.	PUNCT
ejpam-544	163	1	[	[	X
ejpam-544	163	2	3	3	X
ejpam-544	163	3	]	]	SYM
ejpam-544	163	4	j.-l.li	j.-l.li	NOUN
ejpam-544	163	5	and	and	CCONJ
ejpam-544	163	6	s.	s.	PROPN
ejpam-544	163	7	owa	owa	PROPN
ejpam-544	163	8	,	,	PUNCT
ejpam-544	163	9	sufficient	sufficient	ADJ
ejpam-544	163	10	conditions	condition	NOUN
ejpam-544	163	11	for	for	ADP
ejpam-544	163	12	starlikeness	starlikeness	NOUN
ejpam-544	163	13	,	,	PUNCT
ejpam-544	163	14	indian	indian	PROPN
ejpam-544	163	15	j.	j.	PROPN
ejpam-544	163	16	pure	pure	PROPN
ejpam-544	163	17	appl	appl	PROPN
ejpam-544	163	18	.	.	PUNCT
ejpam-544	163	19	math	math	PROPN
ejpam-544	163	20	.	.	PUNCT
ejpam-544	164	1	,	,	PUNCT
ejpam-544	164	2	33	33	NUM
ejpam-544	164	3	,	,	PUNCT
ejpam-544	164	4	313	313	NUM
ejpam-544	164	5	-	-	SYM
ejpam-544	164	6	318	318	NUM
ejpam-544	164	7	.	.	PUNCT
ejpam-544	165	1	2002	2002	NUM
ejpam-544	165	2	.	.	PUNCT
ejpam-544	166	1	[	[	X
ejpam-544	166	2	4	4	NUM
ejpam-544	166	3	]	]	X
ejpam-544	166	4	s.s	s.s	PROPN
ejpam-544	166	5	.	.	PROPN
ejpam-544	166	6	miller	miller	PROPN
ejpam-544	166	7	and	and	CCONJ
ejpam-544	166	8	p.t	p.t	PROPN
ejpam-544	166	9	.	.	PROPN
ejpam-544	166	10	mocanu	mocanu	PROPN
ejpam-544	166	11	,	,	PUNCT
ejpam-544	166	12	differential	differential	ADJ
ejpam-544	166	13	subordinations	subordination	NOUN
ejpam-544	166	14	and	and	CCONJ
ejpam-544	166	15	inequalities	inequality	NOUN
ejpam-544	166	16	in	in	ADP
ejpam-544	166	17	the	the	DET
ejpam-544	166	18	complex	complex	ADJ
ejpam-544	166	19	plane	plane	NOUN
ejpam-544	166	20	,	,	PUNCT
ejpam-544	166	21	j.	j.	PROPN
ejpam-544	166	22	differ	differ	VERB
ejpam-544	166	23	.	.	PUNCT
ejpam-544	167	1	equations	equation	NOUN
ejpam-544	167	2	,	,	PUNCT
ejpam-544	167	3	67	67	NUM
ejpam-544	167	4	,	,	PUNCT
ejpam-544	167	5	199	199	NUM
ejpam-544	167	6	-	-	SYM
ejpam-544	167	7	211	211	NUM
ejpam-544	167	8	.	.	PUNCT
ejpam-544	167	9	1987	1987	NUM
ejpam-544	167	10	.	.	PUNCT
ejpam-544	168	1	[	[	X
ejpam-544	168	2	5	5	X
ejpam-544	168	3	]	]	PUNCT
ejpam-544	168	4	s.	s.	PROPN
ejpam-544	168	5	owa	owa	PROPN
ejpam-544	168	6	,	,	PUNCT
ejpam-544	168	7	t.	t.	PROPN
ejpam-544	168	8	sekine	sekine	PROPN
ejpam-544	168	9	and	and	CCONJ
ejpam-544	168	10	r.	r.	PROPN
ejpam-544	168	11	yamakawa	yamakawa	PROPN
ejpam-544	168	12	,	,	PUNCT
ejpam-544	168	13	on	on	ADP
ejpam-544	168	14	sakaguchi	sakaguchi	ADJ
ejpam-544	168	15	type	type	NOUN
ejpam-544	168	16	functions	function	NOUN
ejpam-544	168	17	,	,	PUNCT
ejpam-544	168	18	appl	appl	PROPN
ejpam-544	168	19	.	.	PROPN
ejpam-544	168	20	math	math	PROPN
ejpam-544	168	21	.	.	PUNCT
ejpam-544	169	1	and	and	CCONJ
ejpam-544	169	2	comp	comp	PROPN
ejpam-544	169	3	.	.	PUNCT
ejpam-544	169	4	,	,	PUNCT
ejpam-544	169	5	187(1	187(1	NUM
ejpam-544	169	6	)	)	PUNCT
ejpam-544	169	7	,	,	PUNCT
ejpam-544	169	8	356	356	NUM
ejpam-544	169	9	-	-	SYM
ejpam-544	169	10	361	361	NUM
ejpam-544	169	11	.	.	PUNCT
ejpam-544	169	12	2007	2007	NUM
ejpam-544	169	13	.	.	PUNCT
ejpam-544	170	1	[	[	X
ejpam-544	170	2	6	6	NUM
ejpam-544	170	3	]	]	PUNCT
ejpam-544	170	4	v.	v.	ADP
ejpam-544	170	5	ravichandran	ravichandran	NOUN
ejpam-544	170	6	,	,	PUNCT
ejpam-544	170	7	c.	c.	PROPN
ejpam-544	170	8	selvaraj	selvaraj	PROPN
ejpam-544	170	9	and	and	CCONJ
ejpam-544	170	10	r.	r.	PROPN
ejpam-544	170	11	rajalaksmi	rajalaksmi	PROPN
ejpam-544	170	12	,	,	PUNCT
ejpam-544	170	13	sufficient	sufficient	ADJ
ejpam-544	170	14	conditions	condition	NOUN
ejpam-544	170	15	for	for	ADP
ejpam-544	170	16	starlike	starlike	NOUN
ejpam-544	170	17	functions	function	NOUN
ejpam-544	170	18	of	of	ADP
ejpam-544	170	19	order	order	NOUN
ejpam-544	170	20	α	α	NOUN
ejpam-544	170	21	,	,	PUNCT
ejpam-544	170	22	j.inequal	j.inequal	ADJ
ejpam-544	170	23	.	.	PUNCT
ejpam-544	171	1	pure	pure	ADJ
ejpam-544	171	2	appl	appl	PROPN
ejpam-544	171	3	.	.	PUNCT
ejpam-544	172	1	math	math	PROPN
ejpam-544	172	2	.	.	PUNCT
ejpam-544	172	3	,	,	PUNCT
ejpam-544	172	4	3(5	3(5	NUM
ejpam-544	172	5	)	)	PUNCT
ejpam-544	172	6	,	,	PUNCT
ejpam-544	172	7	1	1	NUM
ejpam-544	172	8	-	-	SYM
ejpam-544	172	9	6	6	NUM
ejpam-544	172	10	.	.	NOUN
ejpam-544	172	11	2002	2002	NUM
ejpam-544	172	12	.	.	PUNCT
ejpam-544	173	1	[	[	X
ejpam-544	173	2	7	7	X
ejpam-544	173	3	]	]	PUNCT
ejpam-544	173	4	k.	k.	NOUN
ejpam-544	173	5	sakaguchi	sakaguchi	PROPN
ejpam-544	173	6	,	,	PUNCT
ejpam-544	173	7	on	on	ADP
ejpam-544	173	8	certain	certain	ADJ
ejpam-544	173	9	univalent	univalent	ADJ
ejpam-544	173	10	mapping	mapping	NOUN
ejpam-544	173	11	,	,	PUNCT
ejpam-544	173	12	j.	j.	PROPN
ejpam-544	173	13	math	math	PROPN
ejpam-544	173	14	.	.	PUNCT
ejpam-544	174	1	soc	soc	PROPN
ejpam-544	174	2	.	.	PUNCT
ejpam-544	175	1	japan	japan	PROPN
ejpam-544	175	2	,	,	PUNCT
ejpam-544	175	3	11	11	NUM
ejpam-544	175	4	,	,	PUNCT
ejpam-544	175	5	72	72	NUM
ejpam-544	175	6	-	-	SYM
ejpam-544	175	7	75	75	NUM
ejpam-544	175	8	.	.	PUNCT
ejpam-544	175	9	1959	1959	NUM
ejpam-544	175	10	.	.	PUNCT