id	sid	tid	token	lemma	pos
ejpam-490	1	1	10_490_aouf.dvi	10_490_aouf.dvi	NUM
ejpam-490	1	2	european	european	PROPN
ejpam-490	1	3	journal	journal	PROPN
ejpam-490	1	4	of	of	ADP
ejpam-490	1	5	pure	pure	ADJ
ejpam-490	1	6	and	and	CCONJ
ejpam-490	1	7	applied	apply	VERB
ejpam-490	1	8	mathematics	mathematic	NOUN
ejpam-490	1	9	vol	vol	NOUN
ejpam-490	1	10	.	.	PUNCT
ejpam-490	2	1	3	3	NUM
ejpam-490	2	2	,	,	PUNCT
ejpam-490	2	3	no	no	INTJ
ejpam-490	2	4	.	.	NOUN
ejpam-490	2	5	5	5	NUM
ejpam-490	2	6	,	,	PUNCT
ejpam-490	2	7	2010	2010	NUM
ejpam-490	2	8	,	,	PUNCT
ejpam-490	2	9	903	903	NUM
ejpam-490	2	10	-	-	SYM
ejpam-490	2	11	917	917	NUM
ejpam-490	2	12	issn	issn	PROPN
ejpam-490	2	13	1307	1307	NUM
ejpam-490	2	14	-	-	SYM
ejpam-490	2	15	5543	5543	NUM
ejpam-490	2	16	–	–	PUNCT
ejpam-490	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-490	2	18	subordination	subordination	NOUN
ejpam-490	2	19	results	result	VERB
ejpam-490	2	20	for	for	ADP
ejpam-490	2	21	certain	certain	ADJ
ejpam-490	2	22	subclasses	subclass	NOUN
ejpam-490	2	23	of	of	ADP
ejpam-490	2	24	uniformly	uniformly	ADJ
ejpam-490	2	25	starlike	starlike	NOUN
ejpam-490	2	26	and	and	CCONJ
ejpam-490	2	27	convex	convex	NOUN
ejpam-490	2	28	functions	function	NOUN
ejpam-490	2	29	defined	define	VERB
ejpam-490	2	30	by	by	ADP
ejpam-490	2	31	convolution	convolution	NOUN
ejpam-490	2	32	m.	m.	PROPN
ejpam-490	2	33	k.	k.	PROPN
ejpam-490	2	34	aouf1,∗	aouf1,∗	PROPN
ejpam-490	2	35	,	,	PUNCT
ejpam-490	2	36	r.	r.	PROPN
ejpam-490	2	37	m.	m.	PROPN
ejpam-490	3	1	el	el	PROPN
ejpam-490	3	2	-	-	PROPN
ejpam-490	3	3	ashwah2	ashwah2	PROPN
ejpam-490	3	4	and	and	CCONJ
ejpam-490	3	5	s.	s.	PROPN
ejpam-490	3	6	m.	m.	PROPN
ejpam-490	3	7	el	el	PROPN
ejpam-490	3	8	-	-	PUNCT
ejpam-490	3	9	deeb2	deeb2	PROPN
ejpam-490	3	10	1	1	NUM
ejpam-490	3	11	department	department	NOUN
ejpam-490	3	12	of	of	ADP
ejpam-490	3	13	mathematics	mathematic	NOUN
ejpam-490	3	14	,	,	PUNCT
ejpam-490	3	15	faculty	faculty	NOUN
ejpam-490	3	16	of	of	ADP
ejpam-490	3	17	science	science	NOUN
ejpam-490	3	18	,	,	PUNCT
ejpam-490	3	19	university	university	NOUN
ejpam-490	3	20	of	of	ADP
ejpam-490	3	21	mansoura	mansoura	NOUN
ejpam-490	3	22	,	,	PUNCT
ejpam-490	3	23	mansoura	mansoura	PROPN
ejpam-490	3	24	33516	33516	NUM
ejpam-490	3	25	,	,	PUNCT
ejpam-490	3	26	egypt	egypt	PROPN
ejpam-490	3	27	2	2	NUM
ejpam-490	3	28	department	department	NOUN
ejpam-490	3	29	of	of	ADP
ejpam-490	3	30	mathematics	mathematic	NOUN
ejpam-490	3	31	,	,	PUNCT
ejpam-490	3	32	faculty	faculty	NOUN
ejpam-490	3	33	of	of	ADP
ejpam-490	3	34	science	science	NOUN
ejpam-490	3	35	at	at	ADP
ejpam-490	3	36	damietta	damietta	PROPN
ejpam-490	3	37	,	,	PUNCT
ejpam-490	3	38	university	university	NOUN
ejpam-490	3	39	of	of	ADP
ejpam-490	3	40	mansoura	mansoura	PROPN
ejpam-490	3	41	,	,	PUNCT
ejpam-490	3	42	new	new	PROPN
ejpam-490	3	43	damietta	damietta	PROPN
ejpam-490	3	44	34517	34517	NUM
ejpam-490	3	45	,	,	PUNCT
ejpam-490	3	46	egypt	egypt	PROPN
ejpam-490	3	47	abstract	abstract	PROPN
ejpam-490	3	48	.	.	PUNCT
ejpam-490	4	1	in	in	ADP
ejpam-490	4	2	this	this	DET
ejpam-490	4	3	paper	paper	NOUN
ejpam-490	4	4	we	we	PRON
ejpam-490	4	5	derive	derive	VERB
ejpam-490	4	6	several	several	ADJ
ejpam-490	4	7	subordination	subordination	NOUN
ejpam-490	4	8	results	result	NOUN
ejpam-490	4	9	for	for	ADP
ejpam-490	4	10	certain	certain	ADJ
ejpam-490	4	11	subclasses	subclass	NOUN
ejpam-490	4	12	of	of	ADP
ejpam-490	4	13	uniformly	uniformly	ADJ
ejpam-490	4	14	starlike	starlike	NOUN
ejpam-490	4	15	and	and	CCONJ
ejpam-490	4	16	convex	convex	NOUN
ejpam-490	4	17	functions	function	NOUN
ejpam-490	4	18	defined	define	VERB
ejpam-490	4	19	by	by	ADP
ejpam-490	4	20	convolution	convolution	NOUN
ejpam-490	4	21	.	.	PUNCT
ejpam-490	5	1	2000	2000	NUM
ejpam-490	5	2	mathematics	mathematic	NOUN
ejpam-490	5	3	subject	subject	NOUN
ejpam-490	5	4	classifications	classification	NOUN
ejpam-490	5	5	:	:	PUNCT
ejpam-490	5	6	30c45	30c45	NUM
ejpam-490	5	7	key	key	ADJ
ejpam-490	5	8	words	word	NOUN
ejpam-490	5	9	and	and	CCONJ
ejpam-490	5	10	phrases	phrase	NOUN
ejpam-490	5	11	:	:	PUNCT
ejpam-490	5	12	analytic	analytic	ADJ
ejpam-490	5	13	,	,	PUNCT
ejpam-490	5	14	univalent	univalent	ADJ
ejpam-490	5	15	,	,	PUNCT
ejpam-490	5	16	uniformly	uniformly	ADJ
ejpam-490	5	17	,	,	PUNCT
ejpam-490	5	18	convolution	convolution	NOUN
ejpam-490	5	19	,	,	PUNCT
ejpam-490	5	20	subordinating	subordinating	NOUN
ejpam-490	5	21	factor	factor	NOUN
ejpam-490	5	22	sequence	sequence	NOUN
ejpam-490	5	23	.	.	PUNCT
ejpam-490	6	1	1	1	X
ejpam-490	6	2	.	.	X
ejpam-490	6	3	introduction	introduction	NOUN
ejpam-490	6	4	let	let	VERB
ejpam-490	6	5	a	a	DET
ejpam-490	6	6	denote	denote	NOUN
ejpam-490	6	7	the	the	DET
ejpam-490	6	8	class	class	NOUN
ejpam-490	6	9	of	of	ADP
ejpam-490	6	10	functions	function	NOUN
ejpam-490	6	11	of	of	ADP
ejpam-490	6	12	the	the	DET
ejpam-490	6	13	form	form	NOUN
ejpam-490	6	14	:	:	PUNCT
ejpam-490	6	15	f	f	PROPN
ejpam-490	6	16	(	(	PUNCT
ejpam-490	6	17	z	z	NOUN
ejpam-490	6	18	)	)	PUNCT
ejpam-490	6	19	=	=	SYM
ejpam-490	7	1	z	z	NOUN
ejpam-490	8	1	+	+	NUM
ejpam-490	8	2	∞	∞	NUM
ejpam-490	8	3	∑	∑	PROPN
ejpam-490	8	4	k=2	k=2	PROPN
ejpam-490	8	5	akzk	akzk	PROPN
ejpam-490	8	6	,	,	PUNCT
ejpam-490	8	7	(	(	PUNCT
ejpam-490	8	8	1	1	X
ejpam-490	8	9	)	)	PUNCT
ejpam-490	8	10	that	that	PRON
ejpam-490	8	11	are	be	AUX
ejpam-490	8	12	analytic	analytic	ADJ
ejpam-490	8	13	and	and	CCONJ
ejpam-490	8	14	univalent	univalent	ADJ
ejpam-490	8	15	in	in	ADP
ejpam-490	8	16	the	the	DET
ejpam-490	8	17	open	open	ADJ
ejpam-490	8	18	unit	unit	NOUN
ejpam-490	8	19	disk	disk	NOUN
ejpam-490	8	20	u	u	NOUN
ejpam-490	8	21	=	=	PUNCT
ejpam-490	8	22	{	{	PUNCT
ejpam-490	8	23	z	z	NOUN
ejpam-490	8	24	:	:	PUNCT
ejpam-490	8	25	|z|	|z|	NOUN
ejpam-490	8	26	<	<	X
ejpam-490	8	27	1	1	NUM
ejpam-490	8	28	}	}	PUNCT
ejpam-490	8	29	.	.	PUNCT
ejpam-490	9	1	let	let	VERB
ejpam-490	9	2	f	f	PRON
ejpam-490	9	3	∈	∈	PROPN
ejpam-490	9	4	a	a	PRON
ejpam-490	9	5	be	be	AUX
ejpam-490	9	6	given	give	VERB
ejpam-490	9	7	by	by	ADP
ejpam-490	9	8	(	(	PUNCT
ejpam-490	9	9	1	1	NUM
ejpam-490	9	10	)	)	PUNCT
ejpam-490	9	11	and	and	CCONJ
ejpam-490	9	12	φ	φ	PROPN
ejpam-490	9	13	∈	∈	PROPN
ejpam-490	9	14	a	a	PRON
ejpam-490	9	15	be	be	AUX
ejpam-490	9	16	given	give	VERB
ejpam-490	9	17	by	by	ADP
ejpam-490	9	18	φ(z	φ(z	PROPN
ejpam-490	9	19	)	)	PUNCT
ejpam-490	9	20	=	=	SYM
ejpam-490	10	1	z	z	NOUN
ejpam-490	11	1	+	+	NUM
ejpam-490	11	2	∞	∞	NUM
ejpam-490	11	3	∑	∑	PROPN
ejpam-490	11	4	k=2	k=2	PROPN
ejpam-490	11	5	ckzk	ckzk	PROPN
ejpam-490	11	6	.	.	PUNCT
ejpam-490	12	1	(	(	PUNCT
ejpam-490	12	2	2	2	X
ejpam-490	12	3	)	)	PUNCT
ejpam-490	12	4	definition	definition	NOUN
ejpam-490	12	5	1	1	NUM
ejpam-490	12	6	(	(	PUNCT
ejpam-490	12	7	hadamard	hadamard	ADJ
ejpam-490	12	8	product	product	NOUN
ejpam-490	12	9	or	or	CCONJ
ejpam-490	12	10	convolution	convolution	NOUN
ejpam-490	12	11	)	)	PUNCT
ejpam-490	12	12	.	.	PUNCT
ejpam-490	13	1	given	give	VERB
ejpam-490	13	2	two	two	NUM
ejpam-490	13	3	functions	function	NOUN
ejpam-490	13	4	f	f	PROPN
ejpam-490	13	5	and	and	CCONJ
ejpam-490	13	6	φ	φ	PROPN
ejpam-490	13	7	in	in	ADP
ejpam-490	13	8	the	the	DET
ejpam-490	13	9	class	class	NOUN
ejpam-490	13	10	a	a	NOUN
ejpam-490	13	11	,	,	PUNCT
ejpam-490	13	12	where	where	SCONJ
ejpam-490	13	13	f	f	PROPN
ejpam-490	13	14	(	(	PUNCT
ejpam-490	13	15	z	z	NOUN
ejpam-490	13	16	)	)	PUNCT
ejpam-490	13	17	is	be	AUX
ejpam-490	13	18	given	give	VERB
ejpam-490	13	19	by	by	ADP
ejpam-490	13	20	(	(	PUNCT
ejpam-490	13	21	1	1	NUM
ejpam-490	13	22	)	)	PUNCT
ejpam-490	13	23	and	and	CCONJ
ejpam-490	13	24	φ(z	φ(z	PROPN
ejpam-490	13	25	)	)	PUNCT
ejpam-490	13	26	is	be	AUX
ejpam-490	13	27	given	give	VERB
ejpam-490	13	28	by	by	ADP
ejpam-490	13	29	(	(	PUNCT
ejpam-490	13	30	2	2	X
ejpam-490	13	31	)	)	PUNCT
ejpam-490	13	32	the	the	DET
ejpam-490	13	33	hadamard	hadamard	ADJ
ejpam-490	13	34	product	product	NOUN
ejpam-490	13	35	(	(	PUNCT
ejpam-490	13	36	or	or	CCONJ
ejpam-490	13	37	convolution	convolution	NOUN
ejpam-490	13	38	)	)	PUNCT
ejpam-490	13	39	f	f	PROPN
ejpam-490	13	40	∗φ	∗φ	PROPN
ejpam-490	13	41	of	of	ADP
ejpam-490	13	42	f	f	PROPN
ejpam-490	13	43	and	and	CCONJ
ejpam-490	13	44	φ	φ	PROPN
ejpam-490	13	45	is	be	AUX
ejpam-490	13	46	defined	define	VERB
ejpam-490	13	47	(	(	PUNCT
ejpam-490	13	48	as	as	ADP
ejpam-490	13	49	usual	usual	ADJ
ejpam-490	13	50	)	)	PUNCT
ejpam-490	13	51	by	by	ADP
ejpam-490	13	52	(	(	PUNCT
ejpam-490	13	53	f	f	PROPN
ejpam-490	13	54	∗φ)(z	∗φ)(z	PROPN
ejpam-490	13	55	)	)	PUNCT
ejpam-490	13	56	=	=	SYM
ejpam-490	14	1	z	z	NOUN
ejpam-490	15	1	+	+	NUM
ejpam-490	15	2	∞	∞	NUM
ejpam-490	15	3	∑	∑	PROPN
ejpam-490	15	4	k=2	k=2	PROPN
ejpam-490	15	5	akckzk	akckzk	PROPN
ejpam-490	15	6	=	=	SYM
ejpam-490	15	7	(	(	PUNCT
ejpam-490	15	8	φ	φ	PROPN
ejpam-490	15	9	∗	∗	PROPN
ejpam-490	15	10	f	f	PROPN
ejpam-490	15	11	)	)	PUNCT
ejpam-490	15	12	(	(	PUNCT
ejpam-490	15	13	z	z	NOUN
ejpam-490	15	14	)	)	PUNCT
ejpam-490	15	15	.	.	PUNCT
ejpam-490	16	1	(	(	PUNCT
ejpam-490	16	2	3	3	X
ejpam-490	16	3	)	)	PUNCT
ejpam-490	16	4	we	we	PRON
ejpam-490	16	5	also	also	ADV
ejpam-490	16	6	denote	denote	VERB
ejpam-490	16	7	by	by	ADP
ejpam-490	16	8	k	k	PROPN
ejpam-490	16	9	the	the	DET
ejpam-490	16	10	class	class	NOUN
ejpam-490	16	11	of	of	ADP
ejpam-490	16	12	functions	function	NOUN
ejpam-490	16	13	f	f	X
ejpam-490	16	14	(	(	PUNCT
ejpam-490	16	15	z	z	NOUN
ejpam-490	16	16	)	)	PUNCT
ejpam-490	16	17	∈	∈	PROPN
ejpam-490	16	18	a	a	PRON
ejpam-490	16	19	that	that	PRON
ejpam-490	16	20	are	be	AUX
ejpam-490	16	21	convex	convex	ADJ
ejpam-490	16	22	in	in	ADP
ejpam-490	16	23	u.	u.	NOUN
ejpam-490	16	24	∗corresponding	∗corresponde	VERB
ejpam-490	16	25	author	author	NOUN
ejpam-490	16	26	.	.	PUNCT
ejpam-490	17	1	email	email	NOUN
ejpam-490	17	2	addresses	address	NOUN
ejpam-490	17	3	:	:	PUNCT
ejpam-490	17	4	mkaouf127	mkaouf127	PROPN
ejpam-490	17	5	�	�	PROPN
ejpam-490	17	6	yahoo	yahoo	PROPN
ejpam-490	17	7	.	.	PUNCT
ejpam-490	18	1	om	om	PROPN
ejpam-490	18	2	(	(	PUNCT
ejpam-490	18	3	m.	m.	PROPN
ejpam-490	18	4	aouf	aouf	PROPN
ejpam-490	18	5	)	)	PUNCT
ejpam-490	18	6	,	,	PUNCT
ejpam-490	18	7	r_elashwah	r_elashwah	NOUN
ejpam-490	18	8	�	�	PROPN
ejpam-490	18	9	yahoo	yahoo	PROPN
ejpam-490	18	10	.	.	PUNCT
ejpam-490	19	1	om	om	PROPN
ejpam-490	19	2	(	(	PUNCT
ejpam-490	19	3	r.	r.	PROPN
ejpam-490	19	4	el	el	PROPN
ejpam-490	19	5	-	-	PUNCT
ejpam-490	19	6	ashwah),shezaeldeeb	ashwah),shezaeldeeb	NUM
ejpam-490	19	7	�	�	PROPN
ejpam-490	19	8	yahoo	yahoo	PROPN
ejpam-490	19	9	.	.	PUNCT
ejpam-490	20	1	om	om	PROPN
ejpam-490	20	2	(	(	PUNCT
ejpam-490	20	3	s.	s.	PROPN
ejpam-490	20	4	el	el	PROPN
ejpam-490	20	5	-	-	PROPN
ejpam-490	20	6	deeb	deeb	PROPN
ejpam-490	20	7	)	)	PUNCT
ejpam-490	20	8	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-490	21	1	903	903	NUM
ejpam-490	22	1	c	c	NOUN
ejpam-490	22	2	©	©	PROPN
ejpam-490	22	3	2010	2010	NUM
ejpam-490	22	4	ejpam	ejpam	NOUN
ejpam-490	22	5	all	all	DET
ejpam-490	22	6	rights	right	NOUN
ejpam-490	22	7	reserved	reserve	VERB
ejpam-490	22	8	.	.	PUNCT
ejpam-490	23	1	m.	m.	PROPN
ejpam-490	23	2	aouf	aouf	PROPN
ejpam-490	23	3	,	,	PUNCT
ejpam-490	23	4	r.	r.	PROPN
ejpam-490	23	5	el	el	PROPN
ejpam-490	23	6	-	-	PUNCT
ejpam-490	23	7	ashwah	ashwah	PROPN
ejpam-490	23	8	,	,	PUNCT
ejpam-490	23	9	s.	s.	PROPN
ejpam-490	23	10	el	el	PROPN
ejpam-490	23	11	-	-	PUNCT
ejpam-490	23	12	deeb	deeb	PROPN
ejpam-490	23	13	/	/	SYM
ejpam-490	23	14	eur	eur	PROPN
ejpam-490	23	15	.	.	PUNCT
ejpam-490	24	1	j.	j.	PROPN
ejpam-490	24	2	pure	pure	PROPN
ejpam-490	24	3	appl	appl	PROPN
ejpam-490	24	4	.	.	PROPN
ejpam-490	24	5	math	math	PROPN
ejpam-490	24	6	,	,	PUNCT
ejpam-490	24	7	3	3	NUM
ejpam-490	24	8	(	(	PUNCT
ejpam-490	24	9	2010	2010	NUM
ejpam-490	24	10	)	)	PUNCT
ejpam-490	24	11	,	,	PUNCT
ejpam-490	24	12	903	903	NUM
ejpam-490	24	13	-	-	SYM
ejpam-490	24	14	917	917	NUM
ejpam-490	24	15	904	904	NUM
ejpam-490	24	16	following	follow	VERB
ejpam-490	24	17	goodman	goodman	PROPN
ejpam-490	24	18	(	(	PUNCT
ejpam-490	24	19	[	[	X
ejpam-490	24	20	9	9	NUM
ejpam-490	24	21	]	]	PUNCT
ejpam-490	24	22	and	and	CCONJ
ejpam-490	24	23	[	[	X
ejpam-490	24	24	10	10	NUM
ejpam-490	24	25	]	]	NUM
ejpam-490	24	26	)	)	PUNCT
ejpam-490	24	27	,	,	PUNCT
ejpam-490	24	28	ronning	ronne	VERB
ejpam-490	24	29	(	(	PUNCT
ejpam-490	24	30	[	[	X
ejpam-490	24	31	19	19	NUM
ejpam-490	24	32	]	]	PUNCT
ejpam-490	24	33	and	and	CCONJ
ejpam-490	24	34	[	[	X
ejpam-490	24	35	20	20	NUM
ejpam-490	24	36	]	]	PUNCT
ejpam-490	24	37	)	)	PUNCT
ejpam-490	24	38	introduced	introduce	VERB
ejpam-490	24	39	and	and	CCONJ
ejpam-490	24	40	studied	study	VERB
ejpam-490	24	41	the	the	DET
ejpam-490	24	42	following	following	ADJ
ejpam-490	24	43	subclasses	subclass	NOUN
ejpam-490	24	44	:	:	PUNCT
ejpam-490	24	45	(	(	PUNCT
ejpam-490	24	46	i	i	NOUN
ejpam-490	24	47	)	)	PUNCT
ejpam-490	24	48	a	a	DET
ejpam-490	24	49	function	function	NOUN
ejpam-490	24	50	f	f	X
ejpam-490	24	51	(	(	PUNCT
ejpam-490	24	52	z	z	NOUN
ejpam-490	24	53	)	)	PUNCT
ejpam-490	24	54	of	of	ADP
ejpam-490	24	55	the	the	DET
ejpam-490	24	56	form	form	NOUN
ejpam-490	24	57	(	(	PUNCT
ejpam-490	24	58	1	1	X
ejpam-490	24	59	)	)	PUNCT
ejpam-490	24	60	is	be	AUX
ejpam-490	24	61	said	say	VERB
ejpam-490	24	62	to	to	PART
ejpam-490	24	63	be	be	AUX
ejpam-490	24	64	in	in	ADP
ejpam-490	24	65	the	the	DET
ejpam-490	24	66	class	class	NOUN
ejpam-490	24	67	sp(α	sp(α	NOUN
ejpam-490	24	68	,	,	PUNCT
ejpam-490	24	69	β	β	NOUN
ejpam-490	24	70	)	)	PUNCT
ejpam-490	24	71	of	of	ADP
ejpam-490	24	72	uniformly	uniformly	ADV
ejpam-490	24	73	β	β	X
ejpam-490	24	74	-starlike	-starlike	NOUN
ejpam-490	24	75	functions	function	NOUN
ejpam-490	24	76	if	if	SCONJ
ejpam-490	24	77	it	it	PRON
ejpam-490	24	78	satisfies	satisfy	VERB
ejpam-490	24	79	the	the	DET
ejpam-490	24	80	condition	condition	NOUN
ejpam-490	24	81	:	:	PUNCT
ejpam-490	24	82	re	re	X
ejpam-490	24	83	(	(	PUNCT
ejpam-490	24	84	z	z	NOUN
ejpam-490	24	85	f	f	NOUN
ejpam-490	24	86	′	′	NUM
ejpam-490	24	87	(	(	PUNCT
ejpam-490	24	88	z	z	NOUN
ejpam-490	24	89	)	)	PUNCT
ejpam-490	24	90	f	f	NOUN
ejpam-490	24	91	(	(	PUNCT
ejpam-490	24	92	z	z	NOUN
ejpam-490	24	93	)	)	PUNCT
ejpam-490	24	94	−α	−α	NOUN
ejpam-490	24	95	)	)	PUNCT
ejpam-490	25	1	>	>	PUNCT
ejpam-490	25	2	β	β	X
ejpam-490	25	3	�	�	PROPN
ejpam-490	25	4	�	�	PROPN
ejpam-490	25	5	�	�	PROPN
ejpam-490	25	6	�	�	PROPN
ejpam-490	25	7	�	�	PROPN
ejpam-490	25	8	z	z	PROPN
ejpam-490	25	9	f	f	NOUN
ejpam-490	26	1	′	′	NUM
ejpam-490	27	1	(	(	PUNCT
ejpam-490	27	2	z	z	NOUN
ejpam-490	27	3	)	)	PUNCT
ejpam-490	27	4	f	f	NOUN
ejpam-490	27	5	(	(	PUNCT
ejpam-490	27	6	z	z	NOUN
ejpam-490	27	7	)	)	PUNCT
ejpam-490	27	8	−	−	PROPN
ejpam-490	27	9	1	1	NUM
ejpam-490	27	10	�	�	PROPN
ejpam-490	27	11	�	�	PROPN
ejpam-490	27	12	�	�	PROPN
ejpam-490	27	13	�	�	PROPN
ejpam-490	27	14	�	�	PROPN
ejpam-490	27	15	(	(	PUNCT
ejpam-490	27	16	z	z	NOUN
ejpam-490	27	17	∈	∈	PROPN
ejpam-490	27	18	u	u	NOUN
ejpam-490	27	19	)	)	PUNCT
ejpam-490	27	20	,	,	PUNCT
ejpam-490	27	21	(	(	PUNCT
ejpam-490	27	22	4	4	X
ejpam-490	27	23	)	)	PUNCT
ejpam-490	27	24	where	where	SCONJ
ejpam-490	27	25	−1≤	−1≤	VERB
ejpam-490	27	26	α	α	NOUN
ejpam-490	27	27	<	<	X
ejpam-490	27	28	1	1	NUM
ejpam-490	27	29	and	and	CCONJ
ejpam-490	27	30	β	β	X
ejpam-490	27	31	≥	≥	NOUN
ejpam-490	27	32	0	0	NUM
ejpam-490	27	33	.	.	PUNCT
ejpam-490	28	1	(	(	PUNCT
ejpam-490	28	2	ii	ii	NOUN
ejpam-490	28	3	)	)	PUNCT
ejpam-490	28	4	a	a	DET
ejpam-490	28	5	function	function	NOUN
ejpam-490	28	6	f	f	X
ejpam-490	28	7	(	(	PUNCT
ejpam-490	28	8	z	z	NOUN
ejpam-490	28	9	)	)	PUNCT
ejpam-490	28	10	of	of	ADP
ejpam-490	28	11	the	the	DET
ejpam-490	28	12	form	form	NOUN
ejpam-490	28	13	(	(	PUNCT
ejpam-490	28	14	1	1	X
ejpam-490	28	15	)	)	PUNCT
ejpam-490	28	16	is	be	AUX
ejpam-490	28	17	said	say	VERB
ejpam-490	28	18	to	to	PART
ejpam-490	28	19	be	be	AUX
ejpam-490	28	20	in	in	ADP
ejpam-490	28	21	the	the	DET
ejpam-490	28	22	class	class	NOUN
ejpam-490	28	23	ucv	ucv	PROPN
ejpam-490	28	24	(	(	PUNCT
ejpam-490	28	25	α	α	X
ejpam-490	28	26	,	,	PUNCT
ejpam-490	28	27	β	β	NOUN
ejpam-490	28	28	)	)	PUNCT
ejpam-490	28	29	of	of	ADP
ejpam-490	28	30	uniformly	uniformly	ADV
ejpam-490	28	31	β	β	X
ejpam-490	28	32	convex	convex	NOUN
ejpam-490	28	33	functions	function	NOUN
ejpam-490	28	34	if	if	SCONJ
ejpam-490	28	35	it	it	PRON
ejpam-490	28	36	satisfies	satisfy	VERB
ejpam-490	28	37	the	the	DET
ejpam-490	28	38	condition	condition	NOUN
ejpam-490	28	39	:	:	PUNCT
ejpam-490	28	40	re	re	X
ejpam-490	28	41	(	(	PUNCT
ejpam-490	28	42	1	1	NUM
ejpam-490	28	43	+	+	NUM
ejpam-490	28	44	z	z	NOUN
ejpam-490	28	45	f	f	X
ejpam-490	29	1	′′	′′	PROPN
ejpam-490	29	2	(	(	PUNCT
ejpam-490	29	3	z	z	PROPN
ejpam-490	29	4	)	)	PUNCT
ejpam-490	29	5	f	f	NOUN
ejpam-490	29	6	′	′	NUM
ejpam-490	29	7	(	(	PUNCT
ejpam-490	29	8	z	z	NOUN
ejpam-490	29	9	)	)	PUNCT
ejpam-490	29	10	−α	−α	NOUN
ejpam-490	29	11	)	)	PUNCT
ejpam-490	29	12	>	>	PUNCT
ejpam-490	29	13	β	β	X
ejpam-490	29	14	�	�	PROPN
ejpam-490	29	15	�	�	PROPN
ejpam-490	29	16	�	�	PROPN
ejpam-490	29	17	�	�	PROPN
ejpam-490	29	18	�	�	PROPN
ejpam-490	29	19	z	z	PROPN
ejpam-490	29	20	f	f	X
ejpam-490	30	1	′′	′′	PROPN
ejpam-490	30	2	(	(	PUNCT
ejpam-490	30	3	z	z	PROPN
ejpam-490	30	4	)	)	PUNCT
ejpam-490	30	5	f	f	NOUN
ejpam-490	30	6	′	′	NUM
ejpam-490	30	7	(	(	PUNCT
ejpam-490	30	8	z	z	NOUN
ejpam-490	30	9	)	)	PUNCT
ejpam-490	30	10	�	�	PROPN
ejpam-490	30	11	�	�	PROPN
ejpam-490	30	12	�	�	PROPN
ejpam-490	30	13	�	�	PROPN
ejpam-490	30	14	�	�	PROPN
ejpam-490	30	15	(	(	PUNCT
ejpam-490	30	16	z	z	NOUN
ejpam-490	30	17	∈	∈	PROPN
ejpam-490	30	18	u	u	NOUN
ejpam-490	30	19	)	)	PUNCT
ejpam-490	30	20	,	,	PUNCT
ejpam-490	30	21	(	(	PUNCT
ejpam-490	30	22	5	5	X
ejpam-490	30	23	)	)	PUNCT
ejpam-490	30	24	where	where	SCONJ
ejpam-490	30	25	−1≤	−1≤	VERB
ejpam-490	30	26	α	α	NOUN
ejpam-490	30	27	<	<	X
ejpam-490	30	28	1	1	NUM
ejpam-490	30	29	and	and	CCONJ
ejpam-490	30	30	β	β	X
ejpam-490	30	31	≥	≥	NUM
ejpam-490	30	32	0	0	NUM
ejpam-490	30	33	.	.	PUNCT
ejpam-490	31	1	it	it	PRON
ejpam-490	31	2	follows	follow	VERB
ejpam-490	31	3	from	from	ADP
ejpam-490	31	4	(	(	PUNCT
ejpam-490	31	5	4	4	NUM
ejpam-490	31	6	)	)	PUNCT
ejpam-490	31	7	and	and	CCONJ
ejpam-490	31	8	(	(	PUNCT
ejpam-490	31	9	5	5	NUM
ejpam-490	31	10	)	)	PUNCT
ejpam-490	32	1	that	that	SCONJ
ejpam-490	32	2	f	f	X
ejpam-490	32	3	(	(	PUNCT
ejpam-490	32	4	z	z	NOUN
ejpam-490	32	5	)	)	PUNCT
ejpam-490	32	6	∈	∈	PROPN
ejpam-490	32	7	ucv	ucv	PROPN
ejpam-490	32	8	(	(	PUNCT
ejpam-490	32	9	α	α	X
ejpam-490	32	10	,	,	PUNCT
ejpam-490	32	11	β	β	NOUN
ejpam-490	32	12	)	)	PUNCT
ejpam-490	32	13	⇐	⇐	ADJ
ejpam-490	32	14	⇒	⇒	PROPN
ejpam-490	32	15	z	z	PROPN
ejpam-490	32	16	f	f	NOUN
ejpam-490	33	1	′	′	NUM
ejpam-490	34	1	(	(	PUNCT
ejpam-490	34	2	z	z	X
ejpam-490	34	3	)	)	PUNCT
ejpam-490	34	4	∈	∈	PROPN
ejpam-490	34	5	sp(α	sp(α	X
ejpam-490	34	6	,	,	PUNCT
ejpam-490	34	7	β	β	NOUN
ejpam-490	34	8	)	)	PUNCT
ejpam-490	34	9	.	.	PUNCT
ejpam-490	35	1	(	(	PUNCT
ejpam-490	35	2	6	6	NUM
ejpam-490	35	3	)	)	PUNCT
ejpam-490	35	4	for	for	ADP
ejpam-490	35	5	−1	−1	NOUN
ejpam-490	35	6	≤	≤	NOUN
ejpam-490	35	7	α	α	NOUN
ejpam-490	35	8	<	<	X
ejpam-490	35	9	1	1	NUM
ejpam-490	35	10	,	,	PUNCT
ejpam-490	35	11	0	0	NUM
ejpam-490	35	12	≤	≤	NUM
ejpam-490	35	13	γ	γ	X
ejpam-490	35	14	≤	≤	NOUN
ejpam-490	35	15	1	1	NUM
ejpam-490	35	16	and	and	CCONJ
ejpam-490	35	17	β	β	X
ejpam-490	35	18	≥	≥	NOUN
ejpam-490	35	19	0	0	NUM
ejpam-490	35	20	,	,	PUNCT
ejpam-490	35	21	we	we	PRON
ejpam-490	35	22	let	let	VERB
ejpam-490	35	23	sγ	sγ	INTJ
ejpam-490	35	24	(	(	PUNCT
ejpam-490	35	25	f	f	PROPN
ejpam-490	35	26	,	,	PUNCT
ejpam-490	35	27	g;α	g;α	PROPN
ejpam-490	35	28	,	,	PUNCT
ejpam-490	35	29	β	β	NOUN
ejpam-490	35	30	)	)	PUNCT
ejpam-490	35	31	be	be	VERB
ejpam-490	35	32	the	the	DET
ejpam-490	35	33	subclass	subclass	NOUN
ejpam-490	35	34	of	of	ADP
ejpam-490	35	35	a	a	DET
ejpam-490	35	36	consisting	consisting	NOUN
ejpam-490	35	37	of	of	ADP
ejpam-490	35	38	functions	function	NOUN
ejpam-490	36	1	f	f	X
ejpam-490	36	2	(	(	PUNCT
ejpam-490	36	3	z	z	NOUN
ejpam-490	36	4	)	)	PUNCT
ejpam-490	36	5	of	of	ADP
ejpam-490	36	6	the	the	DET
ejpam-490	36	7	form	form	NOUN
ejpam-490	36	8	(	(	PUNCT
ejpam-490	36	9	1	1	NUM
ejpam-490	36	10	)	)	PUNCT
ejpam-490	36	11	and	and	CCONJ
ejpam-490	36	12	functions	function	NOUN
ejpam-490	36	13	g(z	g(z	ADJ
ejpam-490	36	14	)	)	PUNCT
ejpam-490	36	15	given	give	VERB
ejpam-490	36	16	by	by	ADP
ejpam-490	36	17	g(z	g(z	PROPN
ejpam-490	36	18	)	)	PUNCT
ejpam-490	36	19	=	=	SYM
ejpam-490	37	1	z	z	NOUN
ejpam-490	38	1	+	+	NUM
ejpam-490	38	2	∞	∞	NUM
ejpam-490	38	3	∑	∑	PROPN
ejpam-490	38	4	k=2	k=2	PROPN
ejpam-490	38	5	bkzk	bkzk	NOUN
ejpam-490	38	6	(	(	PUNCT
ejpam-490	38	7	bk	bk	NOUN
ejpam-490	38	8	≥	≥	NOUN
ejpam-490	38	9	0	0	NUM
ejpam-490	38	10	)	)	PUNCT
ejpam-490	38	11	,	,	PUNCT
ejpam-490	38	12	(	(	PUNCT
ejpam-490	38	13	7	7	X
ejpam-490	38	14	)	)	PUNCT
ejpam-490	38	15	and	and	CCONJ
ejpam-490	38	16	satisfying	satisfy	VERB
ejpam-490	38	17	the	the	DET
ejpam-490	38	18	analytic	analytic	ADJ
ejpam-490	38	19	criterion	criterion	NOUN
ejpam-490	38	20	:	:	PUNCT
ejpam-490	38	21	re	re	X
ejpam-490	38	22	(	(	PUNCT
ejpam-490	38	23	z	z	X
ejpam-490	38	24	(	(	PUNCT
ejpam-490	38	25	f	f	PROPN
ejpam-490	38	26	∗	∗	PROPN
ejpam-490	38	27	g	g	NOUN
ejpam-490	38	28	)	)	PUNCT
ejpam-490	38	29	′	′	NUM
ejpam-490	39	1	(	(	PUNCT
ejpam-490	39	2	z	z	NOUN
ejpam-490	39	3	)	)	PUNCT
ejpam-490	39	4	+	+	CCONJ
ejpam-490	39	5	γz2	γz2	PROPN
ejpam-490	39	6	(	(	PUNCT
ejpam-490	39	7	f	f	PROPN
ejpam-490	39	8	∗	∗	X
ejpam-490	39	9	g	g	NOUN
ejpam-490	39	10	)	)	PUNCT
ejpam-490	40	1	′′	′′	PROPN
ejpam-490	40	2	(	(	PUNCT
ejpam-490	40	3	z	z	PROPN
ejpam-490	40	4	)	)	PUNCT
ejpam-490	40	5	�	�	PROPN
ejpam-490	40	6	1−	1−	NUM
ejpam-490	40	7	γ	γ	PROPN
ejpam-490	40	8	�	�	PROPN
ejpam-490	40	9	(	(	PUNCT
ejpam-490	40	10	f	f	PROPN
ejpam-490	40	11	∗	∗	NOUN
ejpam-490	40	12	g)(z	g)(z	PUNCT
ejpam-490	40	13	)	)	PUNCT
ejpam-490	40	14	+	+	CCONJ
ejpam-490	40	15	γz	γz	X
ejpam-490	40	16	(	(	PUNCT
ejpam-490	40	17	f	f	PROPN
ejpam-490	40	18	∗	∗	PROPN
ejpam-490	40	19	g	g	NOUN
ejpam-490	40	20	)	)	PUNCT
ejpam-490	40	21	′	′	NUM
ejpam-490	41	1	(	(	PUNCT
ejpam-490	41	2	z	z	X
ejpam-490	41	3	)	)	PUNCT
ejpam-490	41	4	−α	−α	NOUN
ejpam-490	41	5	)	)	PUNCT
ejpam-490	41	6	>	>	PUNCT
ejpam-490	42	1	β	β	X
ejpam-490	42	2	�	�	PROPN
ejpam-490	42	3	�	�	PROPN
ejpam-490	42	4	�	�	PROPN
ejpam-490	42	5	�	�	PROPN
ejpam-490	42	6	�	�	PROPN
ejpam-490	42	7	z	z	PROPN
ejpam-490	42	8	(	(	PUNCT
ejpam-490	42	9	f	f	PROPN
ejpam-490	42	10	∗	∗	PROPN
ejpam-490	42	11	g	g	NOUN
ejpam-490	42	12	)	)	PUNCT
ejpam-490	42	13	′	′	NUM
ejpam-490	43	1	(	(	PUNCT
ejpam-490	43	2	z	z	NOUN
ejpam-490	43	3	)	)	PUNCT
ejpam-490	43	4	+	+	CCONJ
ejpam-490	43	5	γz2	γz2	PROPN
ejpam-490	43	6	(	(	PUNCT
ejpam-490	43	7	f	f	PROPN
ejpam-490	43	8	∗	∗	X
ejpam-490	43	9	g	g	NOUN
ejpam-490	43	10	)	)	PUNCT
ejpam-490	44	1	′′	′′	PROPN
ejpam-490	44	2	(	(	PUNCT
ejpam-490	44	3	z	z	PROPN
ejpam-490	44	4	)	)	PUNCT
ejpam-490	44	5	�	�	PROPN
ejpam-490	44	6	1−	1−	NUM
ejpam-490	44	7	γ	γ	PROPN
ejpam-490	44	8	�	�	PROPN
ejpam-490	44	9	(	(	PUNCT
ejpam-490	44	10	f	f	PROPN
ejpam-490	44	11	∗	∗	NOUN
ejpam-490	44	12	g)(z	g)(z	PUNCT
ejpam-490	44	13	)	)	PUNCT
ejpam-490	44	14	+	+	CCONJ
ejpam-490	44	15	γz	γz	X
ejpam-490	44	16	(	(	PUNCT
ejpam-490	44	17	f	f	PROPN
ejpam-490	44	18	∗	∗	PROPN
ejpam-490	44	19	g	g	NOUN
ejpam-490	44	20	)	)	PUNCT
ejpam-490	44	21	′	′	NUM
ejpam-490	45	1	(	(	PUNCT
ejpam-490	45	2	z	z	NOUN
ejpam-490	45	3	)	)	PUNCT
ejpam-490	45	4	−	−	PROPN
ejpam-490	45	5	1	1	NUM
ejpam-490	45	6	�	�	PROPN
ejpam-490	45	7	�	�	PROPN
ejpam-490	45	8	�	�	PROPN
ejpam-490	45	9	�	�	PROPN
ejpam-490	45	10	�	�	PROPN
ejpam-490	45	11	.	.	PUNCT
ejpam-490	46	1	(	(	PUNCT
ejpam-490	46	2	8)	8)	NUM
ejpam-490	46	3	we	we	PRON
ejpam-490	46	4	note	note	VERB
ejpam-490	46	5	that	that	SCONJ
ejpam-490	46	6	:	:	PUNCT
ejpam-490	46	7	(	(	PUNCT
ejpam-490	46	8	i	i	NOUN
ejpam-490	46	9	)	)	PUNCT
ejpam-490	46	10	s0	s0	PROPN
ejpam-490	46	11	(	(	PUNCT
ejpam-490	46	12	f	f	PROPN
ejpam-490	46	13	,	,	PUNCT
ejpam-490	46	14	φ(z);α	φ(z);α	PROPN
ejpam-490	46	15	,	,	PUNCT
ejpam-490	46	16	β	β	NOUN
ejpam-490	46	17	)	)	PUNCT
ejpam-490	46	18	=	=	SYM
ejpam-490	46	19	h	h	PROPN
ejpam-490	46	20	�	�	PROPN
ejpam-490	46	21	φ	φ	PROPN
ejpam-490	46	22	,	,	PUNCT
ejpam-490	46	23	α	α	PROPN
ejpam-490	46	24	,	,	PUNCT
ejpam-490	46	25	β	β	X
ejpam-490	46	26	�	�	PROPN
ejpam-490	46	27	(	(	PUNCT
ejpam-490	46	28	−1≤	−1≤	VERB
ejpam-490	46	29	α	α	PROPN
ejpam-490	46	30	<	<	X
ejpam-490	46	31	1	1	NUM
ejpam-490	46	32	,	,	PUNCT
ejpam-490	46	33	β	β	X
ejpam-490	46	34	≥	≥	NOUN
ejpam-490	46	35	0	0	NUM
ejpam-490	46	36	)	)	PUNCT
ejpam-490	46	37	(	(	PUNCT
ejpam-490	46	38	see	see	VERB
ejpam-490	46	39	raina	raina	NOUN
ejpam-490	46	40	and	and	CCONJ
ejpam-490	46	41	bansal	bansal	NOUN
ejpam-490	46	42	[	[	X
ejpam-490	46	43	18	18	NUM
ejpam-490	46	44	]	]	NUM
ejpam-490	46	45	)	)	PUNCT
ejpam-490	46	46	,	,	PUNCT
ejpam-490	46	47	where	where	SCONJ
ejpam-490	46	48	φ(z	φ(z	NOUN
ejpam-490	46	49	)	)	PUNCT
ejpam-490	46	50	=	=	SYM
ejpam-490	47	1	z	z	NOUN
ejpam-490	48	1	+	+	NUM
ejpam-490	48	2	∞	∞	NUM
ejpam-490	48	3	∑	∑	PROPN
ejpam-490	48	4	k=2	k=2	PROPN
ejpam-490	48	5	µkzk	µkzk	PROPN
ejpam-490	48	6	(	(	PUNCT
ejpam-490	48	7	µ	µ	X
ejpam-490	48	8	≥	≥	NOUN
ejpam-490	48	9	0	0	NUM
ejpam-490	48	10	)	)	PUNCT
ejpam-490	48	11	;	;	PUNCT
ejpam-490	48	12	(	(	PUNCT
ejpam-490	48	13	ii	ii	NOUN
ejpam-490	48	14	)	)	PUNCT
ejpam-490	48	15	s0	s0	PROPN
ejpam-490	48	16	(	(	PUNCT
ejpam-490	48	17	f	f	PROPN
ejpam-490	48	18	,	,	PUNCT
ejpam-490	48	19	z	z	PROPN
ejpam-490	48	20	(	(	PUNCT
ejpam-490	48	21	1−z	1−z	NUM
ejpam-490	48	22	)	)	PUNCT
ejpam-490	48	23	;	;	PUNCT
ejpam-490	48	24	α	α	X
ejpam-490	48	25	,	,	PUNCT
ejpam-490	48	26	1	1	NUM
ejpam-490	48	27	)	)	PUNCT
ejpam-490	48	28	=	=	SYM
ejpam-490	48	29	sp(α	sp(α	X
ejpam-490	48	30	)	)	PUNCT
ejpam-490	48	31	and	and	CCONJ
ejpam-490	48	32	s0	s0	PROPN
ejpam-490	48	33	(	(	PUNCT
ejpam-490	48	34	f	f	PROPN
ejpam-490	48	35	,	,	PUNCT
ejpam-490	48	36	z	z	PROPN
ejpam-490	48	37	(	(	PUNCT
ejpam-490	48	38	1−z)2	1−z)2	NOUN
ejpam-490	48	39	;	;	PUNCT
ejpam-490	48	40	α	α	NOUN
ejpam-490	48	41	,	,	PUNCT
ejpam-490	48	42	1	1	NUM
ejpam-490	48	43	)	)	PUNCT
ejpam-490	48	44	=	=	SYM
ejpam-490	48	45	s1	s1	PROPN
ejpam-490	48	46	(	(	PUNCT
ejpam-490	48	47	f	f	PROPN
ejpam-490	48	48	,	,	PUNCT
ejpam-490	48	49	z	z	PROPN
ejpam-490	48	50	(	(	PUNCT
ejpam-490	48	51	1−z	1−z	NUM
ejpam-490	48	52	)	)	PUNCT
ejpam-490	48	53	;	;	PUNCT
ejpam-490	48	54	α	α	X
ejpam-490	48	55	,	,	PUNCT
ejpam-490	48	56	1	1	NUM
ejpam-490	48	57	)	)	PUNCT
ejpam-490	48	58	=	=	SYM
ejpam-490	48	59	ucv	ucv	PROPN
ejpam-490	48	60	(	(	PUNCT
ejpam-490	48	61	α	α	NOUN
ejpam-490	48	62	)	)	PUNCT
ejpam-490	48	63	(	(	PUNCT
ejpam-490	48	64	−1≤	−1≤	VERB
ejpam-490	48	65	α	α	PROPN
ejpam-490	48	66	<	<	X
ejpam-490	48	67	1	1	NUM
ejpam-490	48	68	)	)	PUNCT
ejpam-490	48	69	(	(	PUNCT
ejpam-490	48	70	see	see	VERB
ejpam-490	48	71	bharati	bharati	PROPN
ejpam-490	48	72	et	et	NOUN
ejpam-490	48	73	al	al	PROPN
ejpam-490	48	74	.	.	PUNCT
ejpam-490	49	1	[	[	X
ejpam-490	49	2	5	5	NUM
ejpam-490	49	3	]	]	PUNCT
ejpam-490	49	4	)	)	PUNCT
ejpam-490	49	5	;	;	PUNCT
ejpam-490	49	6	(	(	PUNCT
ejpam-490	49	7	iii	iii	X
ejpam-490	49	8	)	)	PUNCT
ejpam-490	49	9	s1	s1	NOUN
ejpam-490	49	10	(	(	PUNCT
ejpam-490	49	11	f	f	PROPN
ejpam-490	49	12	,	,	PUNCT
ejpam-490	49	13	z	z	PROPN
ejpam-490	49	14	(	(	PUNCT
ejpam-490	49	15	1−z	1−z	NUM
ejpam-490	49	16	)	)	PUNCT
ejpam-490	49	17	;	;	PUNCT
ejpam-490	49	18	0,β	0,β	X
ejpam-490	49	19	)	)	PUNCT
ejpam-490	49	20	=	=	SYM
ejpam-490	49	21	ucv	ucv	PROPN
ejpam-490	49	22	(	(	PUNCT
ejpam-490	49	23	β	β	NOUN
ejpam-490	49	24	)	)	PUNCT
ejpam-490	49	25	�	�	PROPN
ejpam-490	49	26	β	β	PROPN
ejpam-490	49	27	≥	≥	NUM
ejpam-490	49	28	0	0	NUM
ejpam-490	49	29	�	�	PROPN
ejpam-490	49	30	(	(	PUNCT
ejpam-490	49	31	see	see	VERB
ejpam-490	49	32	subramanian	subramanian	PROPN
ejpam-490	49	33	et	et	PROPN
ejpam-490	49	34	al	al	PROPN
ejpam-490	49	35	.	.	PUNCT
ejpam-490	50	1	[	[	X
ejpam-490	50	2	24	24	NUM
ejpam-490	50	3	]	]	PUNCT
ejpam-490	50	4	)	)	PUNCT
ejpam-490	50	5	;	;	PUNCT
ejpam-490	50	6	m.	m.	PROPN
ejpam-490	50	7	aouf	aouf	PROPN
ejpam-490	50	8	,	,	PUNCT
ejpam-490	50	9	r.	r.	PROPN
ejpam-490	50	10	el	el	PROPN
ejpam-490	50	11	-	-	PUNCT
ejpam-490	50	12	ashwah	ashwah	PROPN
ejpam-490	50	13	,	,	PUNCT
ejpam-490	50	14	s.	s.	PROPN
ejpam-490	50	15	el	el	PROPN
ejpam-490	50	16	-	-	PUNCT
ejpam-490	50	17	deeb	deeb	PROPN
ejpam-490	50	18	/	/	SYM
ejpam-490	50	19	eur	eur	PROPN
ejpam-490	50	20	.	.	PUNCT
ejpam-490	51	1	j.	j.	PROPN
ejpam-490	51	2	pure	pure	PROPN
ejpam-490	51	3	appl	appl	PROPN
ejpam-490	51	4	.	.	PROPN
ejpam-490	51	5	math	math	PROPN
ejpam-490	51	6	,	,	PUNCT
ejpam-490	51	7	3	3	NUM
ejpam-490	51	8	(	(	PUNCT
ejpam-490	51	9	2010	2010	NUM
ejpam-490	51	10	)	)	PUNCT
ejpam-490	51	11	,	,	PUNCT
ejpam-490	51	12	903	903	NUM
ejpam-490	51	13	-	-	SYM
ejpam-490	51	14	917	917	NUM
ejpam-490	51	15	905	905	NUM
ejpam-490	51	16	(	(	PUNCT
ejpam-490	51	17	iv	iv	X
ejpam-490	51	18	)	)	PUNCT
ejpam-490	51	19	s0	s0	PROPN
ejpam-490	51	20	(	(	PUNCT
ejpam-490	51	21	f	f	PROPN
ejpam-490	51	22	,	,	PUNCT
ejpam-490	51	23	z	z	PROPN
ejpam-490	51	24	+	+	CCONJ
ejpam-490	51	25	∞	∞	PROPN
ejpam-490	51	26	∑	∑	PROPN
ejpam-490	51	27	k=2	k=2	PROPN
ejpam-490	51	28	(	(	PUNCT
ejpam-490	51	29	a)k−1	a)k−1	PROPN
ejpam-490	51	30	(	(	PUNCT
ejpam-490	51	31	c)k−1	c)k−1	PROPN
ejpam-490	51	32	zk;α	zk;α	PROPN
ejpam-490	51	33	,	,	PUNCT
ejpam-490	51	34	β	β	X
ejpam-490	51	35	)	)	PUNCT
ejpam-490	51	36	=	=	SYM
ejpam-490	51	37	s	s	PROPN
ejpam-490	51	38	�	�	PROPN
ejpam-490	51	39	α	α	PROPN
ejpam-490	51	40	,	,	PUNCT
ejpam-490	51	41	β	β	X
ejpam-490	51	42	�	�	PROPN
ejpam-490	51	43	(	(	PUNCT
ejpam-490	51	44	−1≤	−1≤	VERB
ejpam-490	51	45	α	α	NOUN
ejpam-490	51	46	<	<	X
ejpam-490	51	47	1,β	1,β	NUM
ejpam-490	51	48	≥	≥	NOUN
ejpam-490	51	49	0	0	NUM
ejpam-490	51	50	,	,	PUNCT
ejpam-490	51	51	c	c	PROPN
ejpam-490	51	52	6=	6=	NUM
ejpam-490	51	53	0,−1,−2	0,−1,−2	NUM
ejpam-490	51	54	,	,	PUNCT
ejpam-490	51	55	.	.	PUNCT
ejpam-490	51	56	.	.	PUNCT
ejpam-490	51	57	.	.	PUNCT
ejpam-490	51	58	)	)	PUNCT
ejpam-490	52	1	(	(	PUNCT
ejpam-490	52	2	see	see	VERB
ejpam-490	52	3	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-490	52	4	and	and	CCONJ
ejpam-490	52	5	magesh	magesh	ADJ
ejpam-490	53	1	[	[	X
ejpam-490	53	2	14,15	14,15	NUM
ejpam-490	53	3	]	]	PUNCT
ejpam-490	53	4	)	)	PUNCT
ejpam-490	53	5	;	;	PUNCT
ejpam-490	53	6	(	(	PUNCT
ejpam-490	53	7	v	v	NOUN
ejpam-490	53	8	)	)	PUNCT
ejpam-490	53	9	s0	s0	PROPN
ejpam-490	53	10	(	(	PUNCT
ejpam-490	53	11	f	f	PROPN
ejpam-490	53	12	,	,	PUNCT
ejpam-490	53	13	z	z	PROPN
ejpam-490	53	14	+	+	CCONJ
ejpam-490	53	15	∞	∞	NUM
ejpam-490	53	16	∑	∑	PROPN
ejpam-490	53	17	k=2	k=2	PROPN
ejpam-490	53	18	knzk;α	knzk;α	PROPN
ejpam-490	53	19	,	,	PUNCT
ejpam-490	53	20	β	β	NOUN
ejpam-490	53	21	)	)	PUNCT
ejpam-490	54	1	=	=	SYM
ejpam-490	54	2	s	s	PROPN
ejpam-490	54	3	�	�	PROPN
ejpam-490	54	4	n	n	CCONJ
ejpam-490	54	5	,	,	PUNCT
ejpam-490	54	6	α	α	PROPN
ejpam-490	54	7	,	,	PUNCT
ejpam-490	54	8	β	β	X
ejpam-490	54	9	�	�	PROPN
ejpam-490	54	10	(	(	PUNCT
ejpam-490	54	11	−1	−1	NOUN
ejpam-490	54	12	≤	≤	PUNCT
ejpam-490	54	13	α	α	NOUN
ejpam-490	54	14	<	<	X
ejpam-490	54	15	1,β	1,β	NUM
ejpam-490	54	16	≥	≥	NOUN
ejpam-490	54	17	0	0	NUM
ejpam-490	54	18	,	,	PUNCT
ejpam-490	54	19	n	n	PROPN
ejpam-490	54	20	∈	∈	PROPN
ejpam-490	54	21	n0	n0	X
ejpam-490	54	22	=	=	SYM
ejpam-490	54	23	n	n	PRON
ejpam-490	54	24	∪	∪	X
ejpam-490	54	25	{	{	PUNCT
ejpam-490	54	26	0	0	NUM
ejpam-490	54	27	}	}	PUNCT
ejpam-490	54	28	,	,	PUNCT
ejpam-490	54	29	n	n	NOUN
ejpam-490	54	30	=	=	SYM
ejpam-490	54	31	{	{	PUNCT
ejpam-490	54	32	1,2	1,2	NUM
ejpam-490	54	33	,	,	PUNCT
ejpam-490	54	34	...	...	PUNCT
ejpam-490	54	35	}	}	PUNCT
ejpam-490	54	36	)	)	PUNCT
ejpam-490	54	37	(	(	PUNCT
ejpam-490	54	38	see	see	VERB
ejpam-490	54	39	rosy	rosy	ADJ
ejpam-490	54	40	and	and	CCONJ
ejpam-490	54	41	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-490	54	42	[	[	PUNCT
ejpam-490	54	43	21	21	NUM
ejpam-490	54	44	]	]	PUNCT
ejpam-490	54	45	)	)	PUNCT
ejpam-490	54	46	;	;	PUNCT
ejpam-490	54	47	(	(	PUNCT
ejpam-490	54	48	vi	vi	NOUN
ejpam-490	54	49	)	)	PUNCT
ejpam-490	54	50	s0	s0	PROPN
ejpam-490	54	51	(	(	PUNCT
ejpam-490	54	52	f	f	PROPN
ejpam-490	54	53	,	,	PUNCT
ejpam-490	54	54	z	z	PROPN
ejpam-490	54	55	+	+	CCONJ
ejpam-490	54	56	∞	∞	NUM
ejpam-490	54	57	∑	∑	X
ejpam-490	54	58	k=2	k=2	PROPN
ejpam-490	55	1	[	[	X
ejpam-490	55	2	1+λ(k−	1+λ(k−	NUM
ejpam-490	55	3	1)]n	1)]n	NUM
ejpam-490	55	4	zk;α	zk;α	NOUN
ejpam-490	55	5	,	,	PUNCT
ejpam-490	55	6	β	β	X
ejpam-490	55	7	)	)	PUNCT
ejpam-490	55	8	=	=	SYM
ejpam-490	55	9	sλ	sλ	NOUN
ejpam-490	55	10	�	�	PROPN
ejpam-490	55	11	n	n	CCONJ
ejpam-490	55	12	,	,	PUNCT
ejpam-490	55	13	α	α	PROPN
ejpam-490	55	14	,	,	PUNCT
ejpam-490	55	15	β	β	X
ejpam-490	55	16	�	�	PROPN
ejpam-490	55	17	(	(	PUNCT
ejpam-490	55	18	−1	−1	NOUN
ejpam-490	55	19	≤	≤	PUNCT
ejpam-490	55	20	α	α	NOUN
ejpam-490	55	21	<	<	X
ejpam-490	55	22	1,β	1,β	NUM
ejpam-490	55	23	≥	≥	X
ejpam-490	55	24	0,λ	0,λ	NOUN
ejpam-490	55	25	≥	≥	PROPN
ejpam-490	55	26	0	0	NUM
ejpam-490	55	27	,	,	PUNCT
ejpam-490	55	28	n	n	PRON
ejpam-490	55	29	∈	∈	PROPN
ejpam-490	55	30	n0	n0	PROPN
ejpam-490	55	31	)	)	PUNCT
ejpam-490	55	32	(	(	PUNCT
ejpam-490	55	33	see	see	VERB
ejpam-490	55	34	aouf	aouf	PROPN
ejpam-490	55	35	and	and	CCONJ
ejpam-490	55	36	mostafa	mostafa	PROPN
ejpam-490	56	1	[	[	X
ejpam-490	56	2	2	2	NUM
ejpam-490	56	3	]	]	PUNCT
ejpam-490	56	4	)	)	PUNCT
ejpam-490	56	5	;	;	PUNCT
ejpam-490	56	6	(	(	PUNCT
ejpam-490	56	7	vii	vii	PROPN
ejpam-490	56	8	)	)	PUNCT
ejpam-490	56	9	sγ	sγ	PROPN
ejpam-490	56	10	(	(	PUNCT
ejpam-490	56	11	f	f	PROPN
ejpam-490	56	12	,	,	PUNCT
ejpam-490	56	13	z+	z+	NUM
ejpam-490	56	14	∞	∞	PROPN
ejpam-490	56	15	∑	∑	PROPN
ejpam-490	56	16	k=2	k=2	PROPN
ejpam-490	56	17	(	(	PUNCT
ejpam-490	56	18	a)k−1	a)k−1	PROPN
ejpam-490	56	19	(	(	PUNCT
ejpam-490	56	20	c)k−1	c)k−1	PROPN
ejpam-490	56	21	zk;α	zk;α	PROPN
ejpam-490	56	22	,	,	PUNCT
ejpam-490	56	23	β	β	X
ejpam-490	56	24	)	)	PUNCT
ejpam-490	56	25	=	=	SYM
ejpam-490	56	26	s	s	PART
ejpam-490	56	27	�	�	PROPN
ejpam-490	56	28	γ	γ	PROPN
ejpam-490	56	29	,	,	PUNCT
ejpam-490	56	30	α	α	PROPN
ejpam-490	56	31	,	,	PUNCT
ejpam-490	56	32	β	β	X
ejpam-490	56	33	�	�	PROPN
ejpam-490	56	34	(	(	PUNCT
ejpam-490	56	35	−1≤	−1≤	VERB
ejpam-490	56	36	α	α	NOUN
ejpam-490	56	37	<	<	X
ejpam-490	56	38	1,β	1,β	NUM
ejpam-490	56	39	≥	≥	NUM
ejpam-490	56	40	0,0≤	0,0≤	NOUN
ejpam-490	57	1	γ≤	γ≤	PRON
ejpam-490	57	2	1	1	NUM
ejpam-490	57	3	,	,	PUNCT
ejpam-490	57	4	c	c	PROPN
ejpam-490	57	5	6=	6=	PROPN
ejpam-490	57	6	0,−1,−2	0,−1,−2	NUM
ejpam-490	57	7	,	,	PUNCT
ejpam-490	57	8	.	.	PUNCT
ejpam-490	57	9	.	.	PUNCT
ejpam-490	57	10	.	.	PUNCT
ejpam-490	57	11	)	)	PUNCT
ejpam-490	58	1	(	(	PUNCT
ejpam-490	58	2	see	see	VERB
ejpam-490	58	3	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-490	58	4	et	et	PROPN
ejpam-490	58	5	al	al	PROPN
ejpam-490	58	6	.	.	PUNCT
ejpam-490	59	1	[	[	X
ejpam-490	59	2	16	16	NUM
ejpam-490	59	3	]	]	PUNCT
ejpam-490	59	4	)	)	PUNCT
ejpam-490	59	5	;	;	PUNCT
ejpam-490	59	6	(	(	PUNCT
ejpam-490	59	7	viii	viii	NOUN
ejpam-490	59	8	)	)	PUNCT
ejpam-490	59	9	sγ	sγ	PROPN
ejpam-490	59	10	(	(	PUNCT
ejpam-490	59	11	f	f	PROPN
ejpam-490	59	12	,	,	PUNCT
ejpam-490	59	13	z	z	PROPN
ejpam-490	59	14	+	+	CCONJ
ejpam-490	59	15	∞	∞	NUM
ejpam-490	59	16	∑	∑	PROPN
ejpam-490	59	17	k=2	k=2	PROPN
ejpam-490	59	18	γkzk;α	γkzk;α	PROPN
ejpam-490	59	19	,	,	PUNCT
ejpam-490	59	20	β	β	NOUN
ejpam-490	59	21	)	)	PUNCT
ejpam-490	60	1	=	=	SYM
ejpam-490	60	2	ss	ss	PROPN
ejpam-490	60	3	q(γ	q(γ	PROPN
ejpam-490	60	4	,	,	PUNCT
ejpam-490	60	5	α	α	NOUN
ejpam-490	60	6	,	,	PUNCT
ejpam-490	60	7	β	β	NOUN
ejpam-490	60	8	)	)	PUNCT
ejpam-490	60	9	(	(	PUNCT
ejpam-490	60	10	see	see	VERB
ejpam-490	60	11	ahuja	ahuja	PROPN
ejpam-490	60	12	et	et	PROPN
ejpam-490	60	13	al	al	PROPN
ejpam-490	60	14	.	.	PUNCT
ejpam-490	61	1	[	[	X
ejpam-490	61	2	1	1	NUM
ejpam-490	61	3	]	]	NUM
ejpam-490	61	4	)	)	PUNCT
ejpam-490	61	5	,	,	PUNCT
ejpam-490	61	6	where	where	SCONJ
ejpam-490	61	7	γk	γk	X
ejpam-490	61	8	=	=	PUNCT
ejpam-490	61	9	(	(	PUNCT
ejpam-490	61	10	α1)k−1	α1)k−1	NOUN
ejpam-490	61	11	...	...	PUNCT
ejpam-490	61	12	(αq)k−1	(αq)k−1	INTJ
ejpam-490	61	13	(	(	PUNCT
ejpam-490	61	14	β1)k−1	β1)k−1	NOUN
ejpam-490	61	15	...	...	PUNCT
ejpam-490	61	16	(βs)k−1	(βs)k−1	PROPN
ejpam-490	61	17	1	1	NUM
ejpam-490	61	18	(	(	PUNCT
ejpam-490	61	19	k−	k−	PROPN
ejpam-490	61	20	1	1	NUM
ejpam-490	61	21	)	)	PUNCT
ejpam-490	61	22	!	!	PUNCT
ejpam-490	62	1	(	(	PUNCT
ejpam-490	62	2	9	9	X
ejpam-490	62	3	)	)	PUNCT
ejpam-490	62	4	for	for	ADP
ejpam-490	62	5	αi	αi	INTJ
ejpam-490	62	6	>	>	X
ejpam-490	62	7	0	0	NUM
ejpam-490	62	8	,	,	PUNCT
ejpam-490	62	9	i	i	PRON
ejpam-490	62	10	=	=	NOUN
ejpam-490	62	11	1	1	NUM
ejpam-490	62	12	,	,	PUNCT
ejpam-490	62	13	.	.	PUNCT
ejpam-490	62	14	.	.	PUNCT
ejpam-490	62	15	.	.	PUNCT
ejpam-490	63	1	,	,	PUNCT
ejpam-490	63	2	q	q	NOUN
ejpam-490	63	3	;	;	PUNCT
ejpam-490	63	4	β	β	X
ejpam-490	63	5	j	j	X
ejpam-490	63	6	>	>	X
ejpam-490	63	7	0	0	PROPN
ejpam-490	63	8	,	,	PUNCT
ejpam-490	63	9	j	j	PROPN
ejpam-490	63	10	=	=	SYM
ejpam-490	63	11	1	1	NUM
ejpam-490	63	12	,	,	PUNCT
ejpam-490	63	13	.	.	PUNCT
ejpam-490	63	14	.	.	PUNCT
ejpam-490	63	15	.	.	PUNCT
ejpam-490	64	1	,	,	PUNCT
ejpam-490	64	2	s	s	X
ejpam-490	64	3	;	;	PUNCT
ejpam-490	64	4	q	q	X
ejpam-490	64	5	≤	≤	NUM
ejpam-490	64	6	s+	s+	PUNCT
ejpam-490	64	7	1	1	NUM
ejpam-490	64	8	;	;	PUNCT
ejpam-490	64	9	q	q	X
ejpam-490	64	10	,	,	PUNCT
ejpam-490	64	11	s	s	PROPN
ejpam-490	64	12	∈	∈	PROPN
ejpam-490	64	13	n0	n0	PROPN
ejpam-490	64	14	.	.	PUNCT
ejpam-490	65	1	also	also	ADV
ejpam-490	65	2	we	we	PRON
ejpam-490	65	3	note	note	VERB
ejpam-490	65	4	that	that	SCONJ
ejpam-490	65	5	:	:	PUNCT
ejpam-490	65	6	(	(	PUNCT
ejpam-490	65	7	i	i	NOUN
ejpam-490	65	8	)	)	PUNCT
ejpam-490	65	9	s0	s0	PROPN
ejpam-490	65	10	(	(	PUNCT
ejpam-490	65	11	f	f	PROPN
ejpam-490	65	12	,	,	PUNCT
ejpam-490	65	13	z	z	PROPN
ejpam-490	65	14	+	+	CCONJ
ejpam-490	66	1	∞	∞	NUM
ejpam-490	66	2	∑	∑	PROPN
ejpam-490	66	3	k=2	k=2	PROPN
ejpam-490	66	4	�	�	PROPN
ejpam-490	66	5	k+λ−	k+λ−	PROPN
ejpam-490	66	6	1	1	NUM
ejpam-490	66	7	λ	λ	PROPN
ejpam-490	66	8	�	�	PROPN
ejpam-490	66	9	zk;α	zk;α	PROPN
ejpam-490	66	10	,	,	PUNCT
ejpam-490	66	11	β	β	X
ejpam-490	66	12	)	)	PUNCT
ejpam-490	66	13	=	=	SYM
ejpam-490	66	14	s	s	PROPN
ejpam-490	66	15	�	�	PROPN
ejpam-490	66	16	α	α	PROPN
ejpam-490	66	17	,	,	PUNCT
ejpam-490	66	18	β	β	X
ejpam-490	66	19	,	,	PUNCT
ejpam-490	66	20	λ	λ	PROPN
ejpam-490	66	21	�	�	PROPN
ejpam-490	66	22	=	=	SYM
ejpam-490	66	23	�	�	PROPN
ejpam-490	66	24	f	f	PROPN
ejpam-490	66	25	∈	∈	PROPN
ejpam-490	67	1	a	a	DET
ejpam-490	67	2	:	:	PUNCT
ejpam-490	67	3	re	re	X
ejpam-490	67	4	(	(	PUNCT
ejpam-490	67	5	z(dλ	z(dλ	PROPN
ejpam-490	67	6	f	f	PROPN
ejpam-490	67	7	(	(	PUNCT
ejpam-490	67	8	z	z	NOUN
ejpam-490	67	9	)	)	PUNCT
ejpam-490	67	10	)	)	PUNCT
ejpam-490	67	11	′	′	NUM
ejpam-490	68	1	dλ	dλ	INTJ
ejpam-490	68	2	f	f	X
ejpam-490	68	3	(	(	PUNCT
ejpam-490	68	4	z	z	NOUN
ejpam-490	68	5	)	)	PUNCT
ejpam-490	68	6	−α	−α	NOUN
ejpam-490	68	7	)	)	PUNCT
ejpam-490	68	8	>	>	PUNCT
ejpam-490	69	1	β	β	X
ejpam-490	69	2	�	�	PROPN
ejpam-490	69	3	�	�	PROPN
ejpam-490	69	4	�	�	PROPN
ejpam-490	69	5	�	�	PROPN
ejpam-490	69	6	�	�	PROPN
ejpam-490	69	7	z(dλ	z(dλ	PROPN
ejpam-490	69	8	f	f	X
ejpam-490	69	9	(	(	PUNCT
ejpam-490	69	10	z	z	NOUN
ejpam-490	69	11	)	)	PUNCT
ejpam-490	69	12	)	)	PUNCT
ejpam-490	70	1	′	′	NUM
ejpam-490	71	1	dλ	dλ	INTJ
ejpam-490	71	2	f	f	X
ejpam-490	72	1	(	(	PUNCT
ejpam-490	72	2	z	z	NOUN
ejpam-490	72	3	)	)	PUNCT
ejpam-490	72	4	−	−	PROPN
ejpam-490	72	5	1	1	NUM
ejpam-490	72	6	�	�	PROPN
ejpam-490	72	7	�	�	PROPN
ejpam-490	72	8	�	�	PROPN
ejpam-490	72	9	�	�	PROPN
ejpam-490	72	10	�	�	PROPN
ejpam-490	72	11	(	(	PUNCT
ejpam-490	72	12	−1≤	−1≤	VERB
ejpam-490	72	13	α	α	NOUN
ejpam-490	72	14	<	<	X
ejpam-490	72	15	1,β	1,β	NUM
ejpam-490	72	16	≥	≥	X
ejpam-490	72	17	0,λ	0,λ	NOUN
ejpam-490	72	18	>	>	X
ejpam-490	73	1	−1	−1	NOUN
ejpam-490	73	2	,	,	PUNCT
ejpam-490	73	3	z	z	PROPN
ejpam-490	73	4	∈	∈	PROPN
ejpam-490	73	5	u	u	NOUN
ejpam-490	73	6	)	)	PUNCT
ejpam-490	73	7	,	,	PUNCT
ejpam-490	73	8	(	(	PUNCT
ejpam-490	73	9	10	10	NUM
ejpam-490	73	10	)	)	PUNCT
ejpam-490	73	11	where	where	SCONJ
ejpam-490	73	12	dλ	dλ	NOUN
ejpam-490	73	13	is	be	AUX
ejpam-490	73	14	ruscheweyh	ruscheweyh	NOUN
ejpam-490	73	15	derivative	derivative	ADJ
ejpam-490	74	1	[	[	X
ejpam-490	74	2	22	22	NUM
ejpam-490	74	3	]	]	PUNCT
ejpam-490	74	4	,	,	PUNCT
ejpam-490	74	5	defined	define	VERB
ejpam-490	74	6	by	by	ADP
ejpam-490	74	7	dλ	dλ	PROPN
ejpam-490	74	8	f	f	PROPN
ejpam-490	74	9	(	(	PUNCT
ejpam-490	74	10	z	z	NOUN
ejpam-490	74	11	)	)	PUNCT
ejpam-490	74	12	=	=	SYM
ejpam-490	75	1	z(zλ−1	z(zλ−1	X
ejpam-490	75	2	f	f	PROPN
ejpam-490	75	3	(	(	PUNCT
ejpam-490	75	4	z))λ	z))λ	PROPN
ejpam-490	75	5	λ	λ	PROPN
ejpam-490	75	6	!	!	PUNCT
ejpam-490	75	7	=	=	SYM
ejpam-490	76	1	z	z	NOUN
ejpam-490	76	2	(	(	PUNCT
ejpam-490	76	3	1−	1−	NUM
ejpam-490	76	4	z)λ+1	z)λ+1	NOUN
ejpam-490	76	5	∗	∗	NOUN
ejpam-490	76	6	f	f	PROPN
ejpam-490	77	1	(	(	PUNCT
ejpam-490	77	2	z	z	NOUN
ejpam-490	77	3	)	)	PUNCT
ejpam-490	77	4	;	;	PUNCT
ejpam-490	77	5	(	(	PUNCT
ejpam-490	77	6	ii	ii	NOUN
ejpam-490	77	7	)	)	PUNCT
ejpam-490	77	8	sγ	sγ	PROPN
ejpam-490	77	9	(	(	PUNCT
ejpam-490	77	10	f	f	PROPN
ejpam-490	77	11	,	,	PUNCT
ejpam-490	77	12	z	z	PROPN
ejpam-490	78	1	+	+	CCONJ
ejpam-490	78	2	∞	∞	NUM
ejpam-490	78	3	∑	∑	PROPN
ejpam-490	78	4	k=2	k=2	PROPN
ejpam-490	78	5	knzk;α	knzk;α	PROPN
ejpam-490	78	6	,	,	PUNCT
ejpam-490	78	7	β	β	NOUN
ejpam-490	78	8	)	)	PUNCT
ejpam-490	79	1	=	=	SYM
ejpam-490	79	2	sγ	sγ	PROPN
ejpam-490	79	3	�	�	PROPN
ejpam-490	79	4	n	n	CCONJ
ejpam-490	79	5	,	,	PUNCT
ejpam-490	79	6	α	α	PROPN
ejpam-490	79	7	,	,	PUNCT
ejpam-490	79	8	β	β	X
ejpam-490	79	9	�	�	NOUN
ejpam-490	79	10	=	=	PUNCT
ejpam-490	79	11	¨	¨	NOUN
ejpam-490	79	12	f	f	PROPN
ejpam-490	79	13	∈	∈	PROPN
ejpam-490	79	14	a	a	PRON
ejpam-490	79	15	:	:	PUNCT
ejpam-490	79	16	re	re	X
ejpam-490	79	17	(	(	PUNCT
ejpam-490	79	18	(	(	PUNCT
ejpam-490	79	19	1−	1−	NUM
ejpam-490	79	20	γ)z(dn	γ)z(dn	NUM
ejpam-490	79	21	f	f	PROPN
ejpam-490	79	22	(	(	PUNCT
ejpam-490	79	23	z	z	NOUN
ejpam-490	79	24	)	)	PUNCT
ejpam-490	79	25	)	)	PUNCT
ejpam-490	79	26	′	′	PUNCT
ejpam-490	80	1	+	+	CCONJ
ejpam-490	80	2	γz(dn+1	γz(dn+1	NOUN
ejpam-490	80	3	f	f	X
ejpam-490	80	4	(	(	PUNCT
ejpam-490	80	5	z	z	NOUN
ejpam-490	80	6	)	)	PUNCT
ejpam-490	80	7	)	)	PUNCT
ejpam-490	81	1	′	′	NUM
ejpam-490	82	1	(	(	PUNCT
ejpam-490	82	2	1−	1−	NUM
ejpam-490	82	3	γ)dn	γ)dn	PROPN
ejpam-490	82	4	f	f	PROPN
ejpam-490	82	5	(	(	PUNCT
ejpam-490	82	6	z	z	NOUN
ejpam-490	82	7	)	)	PUNCT
ejpam-490	82	8	+	+	CCONJ
ejpam-490	82	9	γdn+1	γdn+1	ADJ
ejpam-490	82	10	f	f	X
ejpam-490	82	11	(	(	PUNCT
ejpam-490	82	12	z	z	NOUN
ejpam-490	82	13	)	)	PUNCT
ejpam-490	82	14	−α	−α	NOUN
ejpam-490	82	15	)	)	PUNCT
ejpam-490	82	16	m.	m.	NOUN
ejpam-490	82	17	aouf	aouf	PROPN
ejpam-490	82	18	,	,	PUNCT
ejpam-490	82	19	r.	r.	PROPN
ejpam-490	82	20	el	el	PROPN
ejpam-490	82	21	-	-	PUNCT
ejpam-490	82	22	ashwah	ashwah	PROPN
ejpam-490	82	23	,	,	PUNCT
ejpam-490	82	24	s.	s.	PROPN
ejpam-490	82	25	el	el	PROPN
ejpam-490	82	26	-	-	PUNCT
ejpam-490	82	27	deeb	deeb	PROPN
ejpam-490	82	28	/	/	SYM
ejpam-490	82	29	eur	eur	PROPN
ejpam-490	82	30	.	.	PUNCT
ejpam-490	83	1	j.	j.	PROPN
ejpam-490	83	2	pure	pure	PROPN
ejpam-490	83	3	appl	appl	PROPN
ejpam-490	83	4	.	.	PROPN
ejpam-490	83	5	math	math	PROPN
ejpam-490	83	6	,	,	PUNCT
ejpam-490	83	7	3	3	NUM
ejpam-490	83	8	(	(	PUNCT
ejpam-490	83	9	2010	2010	NUM
ejpam-490	83	10	)	)	PUNCT
ejpam-490	83	11	,	,	PUNCT
ejpam-490	83	12	903	903	NUM
ejpam-490	83	13	-	-	SYM
ejpam-490	83	14	917	917	NUM
ejpam-490	83	15	906	906	NUM
ejpam-490	83	16	>	>	PUNCT
ejpam-490	83	17	β	β	X
ejpam-490	83	18	�	�	PROPN
ejpam-490	83	19	�	�	PROPN
ejpam-490	83	20	�	�	PROPN
ejpam-490	83	21	�	�	PROPN
ejpam-490	83	22	�	�	PROPN
ejpam-490	83	23	(	(	PUNCT
ejpam-490	83	24	1−	1−	NUM
ejpam-490	83	25	γ)z(dn	γ)z(dn	NUM
ejpam-490	83	26	f	f	PROPN
ejpam-490	83	27	(	(	PUNCT
ejpam-490	83	28	z	z	NOUN
ejpam-490	83	29	)	)	PUNCT
ejpam-490	83	30	)	)	PUNCT
ejpam-490	83	31	′	′	PUNCT
ejpam-490	84	1	+	+	CCONJ
ejpam-490	84	2	γz(dn+1	γz(dn+1	NOUN
ejpam-490	84	3	f	f	X
ejpam-490	84	4	(	(	PUNCT
ejpam-490	84	5	z	z	NOUN
ejpam-490	84	6	)	)	PUNCT
ejpam-490	84	7	)	)	PUNCT
ejpam-490	85	1	′	′	NUM
ejpam-490	86	1	(	(	PUNCT
ejpam-490	86	2	1−	1−	NUM
ejpam-490	86	3	γ)dn	γ)dn	PROPN
ejpam-490	86	4	f	f	PROPN
ejpam-490	86	5	(	(	PUNCT
ejpam-490	86	6	z	z	NOUN
ejpam-490	86	7	)	)	PUNCT
ejpam-490	86	8	+	+	CCONJ
ejpam-490	86	9	γdn+1	γdn+1	ADJ
ejpam-490	86	10	f	f	X
ejpam-490	86	11	(	(	PUNCT
ejpam-490	86	12	z	z	NOUN
ejpam-490	86	13	)	)	PUNCT
ejpam-490	86	14	−	−	PROPN
ejpam-490	86	15	1	1	NUM
ejpam-490	86	16	�	�	PROPN
ejpam-490	86	17	�	�	PROPN
ejpam-490	86	18	�	�	PROPN
ejpam-490	86	19	�	�	PROPN
ejpam-490	86	20	�	�	PROPN
ejpam-490	86	21	,	,	PUNCT
ejpam-490	86	22	�	�	PROPN
ejpam-490	86	23	−1≤	−1≤	VERB
ejpam-490	86	24	α	α	PROPN
ejpam-490	86	25	<	<	X
ejpam-490	86	26	1	1	NUM
ejpam-490	86	27	,	,	PUNCT
ejpam-490	86	28	β	β	X
ejpam-490	86	29	≥	≥	NOUN
ejpam-490	86	30	0	0	NUM
ejpam-490	86	31	,	,	PUNCT
ejpam-490	86	32	n	n	PROPN
ejpam-490	86	33	∈	∈	PROPN
ejpam-490	86	34	n0	n0	PROPN
ejpam-490	86	35	,	,	PUNCT
ejpam-490	86	36	z	z	PROPN
ejpam-490	86	37	∈	∈	PROPN
ejpam-490	86	38	u	u	PROPN
ejpam-490	86	39	�	�	PROPN
ejpam-490	86	40	«	«	PUNCT
ejpam-490	86	41	,	,	PUNCT
ejpam-490	86	42	(	(	PUNCT
ejpam-490	86	43	11	11	NUM
ejpam-490	86	44	)	)	PUNCT
ejpam-490	86	45	(	(	PUNCT
ejpam-490	86	46	iii	iii	X
ejpam-490	86	47	)	)	PUNCT
ejpam-490	86	48	sγ	sγ	PROPN
ejpam-490	86	49	(	(	PUNCT
ejpam-490	86	50	f	f	PROPN
ejpam-490	86	51	,	,	PUNCT
ejpam-490	86	52	z	z	PROPN
ejpam-490	86	53	+	+	CCONJ
ejpam-490	86	54	∞	∞	NUM
ejpam-490	86	55	∑	∑	PROPN
ejpam-490	86	56	k=2	k=2	PROPN
ejpam-490	86	57	�	�	PROPN
ejpam-490	86	58	c	c	PROPN
ejpam-490	87	1	+	+	PROPN
ejpam-490	87	2	1	1	NUM
ejpam-490	87	3	c	c	NOUN
ejpam-490	87	4	+	+	CCONJ
ejpam-490	87	5	k	k	PROPN
ejpam-490	87	6	�	�	PROPN
ejpam-490	87	7	zk;α	zk;α	PROPN
ejpam-490	87	8	,	,	PUNCT
ejpam-490	87	9	β	β	X
ejpam-490	87	10	)	)	PUNCT
ejpam-490	88	1	=	=	SYM
ejpam-490	88	2	sγ	sγ	PROPN
ejpam-490	88	3	�	�	PROPN
ejpam-490	88	4	c	c	PROPN
ejpam-490	88	5	,	,	PUNCT
ejpam-490	88	6	α	α	PROPN
ejpam-490	88	7	,	,	PUNCT
ejpam-490	88	8	β	β	X
ejpam-490	88	9	�	�	NOUN
ejpam-490	88	10	=	=	PUNCT
ejpam-490	88	11	¨	¨	NOUN
ejpam-490	88	12	f	f	PROPN
ejpam-490	88	13	∈	∈	PROPN
ejpam-490	88	14	a	a	DET
ejpam-490	88	15	:	:	PUNCT
ejpam-490	88	16	re	re	X
ejpam-490	88	17	(	(	PUNCT
ejpam-490	88	18	z(jc	z(jc	PROPN
ejpam-490	88	19	f	f	X
ejpam-490	88	20	(	(	PUNCT
ejpam-490	88	21	z	z	NOUN
ejpam-490	88	22	)	)	PUNCT
ejpam-490	88	23	)	)	PUNCT
ejpam-490	88	24	′	′	PUNCT
ejpam-490	89	1	+	+	CCONJ
ejpam-490	89	2	γz2(jc	γz2(jc	SYM
ejpam-490	89	3	f	f	X
ejpam-490	89	4	(	(	PUNCT
ejpam-490	89	5	z	z	NOUN
ejpam-490	89	6	)	)	PUNCT
ejpam-490	89	7	)	)	PUNCT
ejpam-490	90	1	′′	′′	PROPN
ejpam-490	90	2	(	(	PUNCT
ejpam-490	90	3	1−	1−	NUM
ejpam-490	90	4	γ)jc	γ)jc	PROPN
ejpam-490	90	5	f	f	PROPN
ejpam-490	90	6	(	(	PUNCT
ejpam-490	90	7	z	z	NOUN
ejpam-490	90	8	)	)	PUNCT
ejpam-490	91	1	+	+	CCONJ
ejpam-490	91	2	γz(jc	γz(jc	PROPN
ejpam-490	91	3	f	f	X
ejpam-490	91	4	(	(	PUNCT
ejpam-490	91	5	z	z	NOUN
ejpam-490	91	6	)	)	PUNCT
ejpam-490	91	7	)	)	PUNCT
ejpam-490	91	8	′	′	NUM
ejpam-490	91	9	−α	−α	NOUN
ejpam-490	91	10	)	)	PUNCT
ejpam-490	91	11	>	>	PUNCT
ejpam-490	92	1	β	β	X
ejpam-490	92	2	�	�	PROPN
ejpam-490	92	3	�	�	PROPN
ejpam-490	92	4	�	�	PROPN
ejpam-490	92	5	�	�	PROPN
ejpam-490	92	6	�	�	PROPN
ejpam-490	92	7	z(jc	z(jc	PROPN
ejpam-490	92	8	f	f	X
ejpam-490	92	9	(	(	PUNCT
ejpam-490	92	10	z	z	NOUN
ejpam-490	92	11	)	)	PUNCT
ejpam-490	92	12	)	)	PUNCT
ejpam-490	93	1	′	′	PUNCT
ejpam-490	94	1	+	+	CCONJ
ejpam-490	94	2	γz2(jc	γz2(jc	SYM
ejpam-490	94	3	f	f	X
ejpam-490	94	4	(	(	PUNCT
ejpam-490	94	5	z	z	NOUN
ejpam-490	94	6	)	)	PUNCT
ejpam-490	94	7	)	)	PUNCT
ejpam-490	95	1	′′	′′	PROPN
ejpam-490	95	2	(	(	PUNCT
ejpam-490	95	3	1−	1−	NUM
ejpam-490	95	4	γ)jc	γ)jc	PROPN
ejpam-490	95	5	f	f	PROPN
ejpam-490	95	6	(	(	PUNCT
ejpam-490	95	7	z	z	NOUN
ejpam-490	95	8	)	)	PUNCT
ejpam-490	96	1	+	+	CCONJ
ejpam-490	96	2	γz(jc	γz(jc	PROPN
ejpam-490	96	3	f	f	X
ejpam-490	96	4	(	(	PUNCT
ejpam-490	96	5	z	z	NOUN
ejpam-490	96	6	)	)	PUNCT
ejpam-490	96	7	)	)	PUNCT
ejpam-490	97	1	′	′	NUM
ejpam-490	98	1	−	−	NOUN
ejpam-490	98	2	1	1	NUM
ejpam-490	98	3	�	�	PROPN
ejpam-490	98	4	�	�	PROPN
ejpam-490	98	5	�	�	PROPN
ejpam-490	98	6	�	�	PROPN
ejpam-490	98	7	�	�	PROPN
ejpam-490	98	8	,	,	PUNCT
ejpam-490	98	9	�	�	PROPN
ejpam-490	98	10	0≤	0≤	NUM
ejpam-490	98	11	γ≤	γ≤	NUM
ejpam-490	98	12	1	1	NUM
ejpam-490	98	13	,	,	PUNCT
ejpam-490	98	14	−1≤	−1≤	VERB
ejpam-490	98	15	α	α	NOUN
ejpam-490	98	16	<	<	X
ejpam-490	98	17	1	1	NUM
ejpam-490	98	18	,	,	PUNCT
ejpam-490	98	19	β	β	X
ejpam-490	98	20	≥	≥	NOUN
ejpam-490	98	21	0	0	NUM
ejpam-490	98	22	,	,	PUNCT
ejpam-490	98	23	c	c	NOUN
ejpam-490	98	24	>	>	X
ejpam-490	98	25	−1	−1	NOUN
ejpam-490	98	26	,	,	PUNCT
ejpam-490	98	27	z	z	PROPN
ejpam-490	98	28	∈	∈	PROPN
ejpam-490	98	29	u	u	PROPN
ejpam-490	98	30	�	�	PROPN
ejpam-490	98	31	«	«	PUNCT
ejpam-490	98	32	,	,	PUNCT
ejpam-490	98	33	(	(	PUNCT
ejpam-490	98	34	12	12	NUM
ejpam-490	98	35	)	)	PUNCT
ejpam-490	98	36	where	where	SCONJ
ejpam-490	98	37	jc	jc	PROPN
ejpam-490	98	38	is	be	AUX
ejpam-490	98	39	a	a	DET
ejpam-490	98	40	bernardi	bernardi	PROPN
ejpam-490	98	41	operator	operator	NOUN
ejpam-490	98	42	[	[	X
ejpam-490	98	43	4	4	NUM
ejpam-490	98	44	]	]	PUNCT
ejpam-490	98	45	,	,	PUNCT
ejpam-490	98	46	defined	define	VERB
ejpam-490	98	47	by	by	ADP
ejpam-490	98	48	jc	jc	PROPN
ejpam-490	98	49	f	f	PROPN
ejpam-490	98	50	(	(	PUNCT
ejpam-490	98	51	z	z	NOUN
ejpam-490	98	52	)	)	PUNCT
ejpam-490	98	53	=	=	PUNCT
ejpam-490	99	1	c	c	NOUN
ejpam-490	99	2	+	+	NOUN
ejpam-490	99	3	1	1	NUM
ejpam-490	99	4	zc	zc	NOUN
ejpam-490	99	5	z	z	PROPN
ejpam-490	99	6	∫	∫	PROPN
ejpam-490	99	7	0	0	PROPN
ejpam-490	100	1	t	t	PROPN
ejpam-490	100	2	c−1	c−1	PROPN
ejpam-490	100	3	f	f	PROPN
ejpam-490	100	4	(	(	PUNCT
ejpam-490	100	5	t)d	t)d	PROPN
ejpam-490	100	6	t	t	X
ejpam-490	100	7	=	=	PUNCT
ejpam-490	100	8	z	z	NOUN
ejpam-490	101	1	+	+	NUM
ejpam-490	101	2	∞	∞	NUM
ejpam-490	101	3	∑	∑	PROPN
ejpam-490	101	4	k=2	k=2	PROPN
ejpam-490	101	5	�	�	PROPN
ejpam-490	101	6	c	c	PROPN
ejpam-490	101	7	+	+	PROPN
ejpam-490	101	8	1	1	NUM
ejpam-490	101	9	c	c	NOUN
ejpam-490	101	10	+	+	CCONJ
ejpam-490	101	11	k	k	PROPN
ejpam-490	101	12	�	�	PROPN
ejpam-490	101	13	akzk	akzk	PROPN
ejpam-490	101	14	.	.	PUNCT
ejpam-490	102	1	note	note	VERB
ejpam-490	102	2	that	that	SCONJ
ejpam-490	102	3	the	the	DET
ejpam-490	102	4	operator	operator	NOUN
ejpam-490	102	5	j1	j1	PROPN
ejpam-490	102	6	f	f	PROPN
ejpam-490	102	7	(	(	PUNCT
ejpam-490	102	8	z	z	NOUN
ejpam-490	102	9	)	)	PUNCT
ejpam-490	102	10	was	be	AUX
ejpam-490	102	11	studied	study	VERB
ejpam-490	102	12	earlier	early	ADV
ejpam-490	102	13	by	by	ADP
ejpam-490	102	14	libera	libera	NOUN
ejpam-490	103	1	[	[	X
ejpam-490	103	2	11	11	NUM
ejpam-490	103	3	]	]	PUNCT
ejpam-490	103	4	and	and	CCONJ
ejpam-490	103	5	livingston	livingston	PROPN
ejpam-490	104	1	[	[	X
ejpam-490	104	2	12	12	NUM
ejpam-490	104	3	]	]	X
ejpam-490	104	4	;	;	PUNCT
ejpam-490	104	5	(	(	PUNCT
ejpam-490	104	6	iv	iv	X
ejpam-490	104	7	)	)	PUNCT
ejpam-490	104	8	sγ	sγ	PROPN
ejpam-490	104	9	(	(	PUNCT
ejpam-490	104	10	f	f	PROPN
ejpam-490	104	11	,	,	PUNCT
ejpam-490	104	12	z	z	PROPN
ejpam-490	104	13	+	+	CCONJ
ejpam-490	104	14	∞	∞	PROPN
ejpam-490	104	15	∑	∑	PROPN
ejpam-490	104	16	k=2	k=2	PROPN
ejpam-490	104	17	(	(	PUNCT
ejpam-490	104	18	µ)k−1	µ)k−1	X
ejpam-490	104	19	(	(	PUNCT
ejpam-490	104	20	λ+	λ+	NUM
ejpam-490	104	21	1)k−1	1)k−1	NUM
ejpam-490	104	22	zk;α	zk;α	NOUN
ejpam-490	104	23	,	,	PUNCT
ejpam-490	104	24	β	β	X
ejpam-490	104	25	)	)	PUNCT
ejpam-490	104	26	=	=	SYM
ejpam-490	104	27	sγ	sγ	PROPN
ejpam-490	104	28	�	�	PROPN
ejpam-490	104	29	µ,λ;α	µ,λ;α	PROPN
ejpam-490	104	30	,	,	PUNCT
ejpam-490	104	31	β	β	X
ejpam-490	104	32	�	�	X
ejpam-490	104	33	=	=	PUNCT
ejpam-490	104	34	¨	¨	NOUN
ejpam-490	104	35	f	f	PROPN
ejpam-490	104	36	∈	∈	PROPN
ejpam-490	104	37	a	a	PRON
ejpam-490	104	38	:	:	PUNCT
ejpam-490	104	39	re	re	X
ejpam-490	104	40	(	(	PUNCT
ejpam-490	104	41	z(iλ,µ	z(iλ,µ	NOUN
ejpam-490	104	42	f	f	X
ejpam-490	104	43	(	(	PUNCT
ejpam-490	104	44	z	z	NOUN
ejpam-490	104	45	)	)	PUNCT
ejpam-490	104	46	)	)	PUNCT
ejpam-490	104	47	′	′	VERB
ejpam-490	105	1	+	+	CCONJ
ejpam-490	105	2	γz2(iλ,µ	γz2(iλ,µ	PROPN
ejpam-490	105	3	f	f	X
ejpam-490	105	4	(	(	PUNCT
ejpam-490	105	5	z	z	NOUN
ejpam-490	105	6	)	)	PUNCT
ejpam-490	105	7	)	)	PUNCT
ejpam-490	106	1	′′	′′	PROPN
ejpam-490	106	2	(	(	PUNCT
ejpam-490	106	3	1−	1−	NUM
ejpam-490	106	4	γ)iλ,µ	γ)iλ,µ	PROPN
ejpam-490	106	5	f	f	PROPN
ejpam-490	106	6	(	(	PUNCT
ejpam-490	106	7	z	z	NOUN
ejpam-490	106	8	)	)	PUNCT
ejpam-490	107	1	+	+	CCONJ
ejpam-490	107	2	γz(iλ,µ	γz(iλ,µ	NOUN
ejpam-490	107	3	f	f	X
ejpam-490	107	4	(	(	PUNCT
ejpam-490	107	5	z	z	NOUN
ejpam-490	107	6	)	)	PUNCT
ejpam-490	107	7	)	)	PUNCT
ejpam-490	107	8	′	′	NUM
ejpam-490	107	9	−α	−α	NOUN
ejpam-490	107	10	)	)	PUNCT
ejpam-490	107	11	>	>	PUNCT
ejpam-490	107	12	β	β	X
ejpam-490	107	13	�	�	PROPN
ejpam-490	107	14	�	�	PROPN
ejpam-490	107	15	�	�	PROPN
ejpam-490	107	16	�	�	PROPN
ejpam-490	107	17	�	�	PROPN
ejpam-490	107	18	z(iλ,µ	z(iλ,µ	PROPN
ejpam-490	107	19	f	f	PROPN
ejpam-490	107	20	(	(	PUNCT
ejpam-490	107	21	z	z	NOUN
ejpam-490	107	22	)	)	PUNCT
ejpam-490	107	23	)	)	PUNCT
ejpam-490	107	24	′	′	VERB
ejpam-490	108	1	+	+	CCONJ
ejpam-490	108	2	γz2(iλ,µ	γz2(iλ,µ	PROPN
ejpam-490	108	3	f	f	X
ejpam-490	108	4	(	(	PUNCT
ejpam-490	108	5	z	z	NOUN
ejpam-490	108	6	)	)	PUNCT
ejpam-490	108	7	)	)	PUNCT
ejpam-490	109	1	′′	′′	PROPN
ejpam-490	109	2	(	(	PUNCT
ejpam-490	109	3	1−	1−	NUM
ejpam-490	109	4	γ)iλ,µ	γ)iλ,µ	PROPN
ejpam-490	109	5	f	f	PROPN
ejpam-490	109	6	(	(	PUNCT
ejpam-490	109	7	z	z	NOUN
ejpam-490	109	8	)	)	PUNCT
ejpam-490	110	1	+	+	CCONJ
ejpam-490	110	2	γz(iλ,µ	γz(iλ,µ	NOUN
ejpam-490	110	3	f	f	X
ejpam-490	110	4	(	(	PUNCT
ejpam-490	110	5	z	z	NOUN
ejpam-490	110	6	)	)	PUNCT
ejpam-490	110	7	)	)	PUNCT
ejpam-490	111	1	′	′	NUM
ejpam-490	112	1	−	−	NOUN
ejpam-490	112	2	1	1	NUM
ejpam-490	112	3	�	�	PROPN
ejpam-490	112	4	�	�	PROPN
ejpam-490	112	5	�	�	PROPN
ejpam-490	112	6	�	�	PROPN
ejpam-490	112	7	�	�	PROPN
ejpam-490	112	8	,	,	PUNCT
ejpam-490	112	9	�	�	PROPN
ejpam-490	112	10	0≤	0≤	NUM
ejpam-490	112	11	γ≤	γ≤	NUM
ejpam-490	112	12	1	1	NUM
ejpam-490	112	13	,	,	PUNCT
ejpam-490	112	14	−1≤	−1≤	VERB
ejpam-490	112	15	α	α	NOUN
ejpam-490	112	16	<	<	X
ejpam-490	112	17	1	1	NUM
ejpam-490	112	18	,	,	PUNCT
ejpam-490	112	19	β	β	X
ejpam-490	112	20	≥	≥	NOUN
ejpam-490	112	21	0	0	NUM
ejpam-490	112	22	,	,	PUNCT
ejpam-490	112	23	λ	λ	X
ejpam-490	112	24	>	>	X
ejpam-490	112	25	−1	−1	NOUN
ejpam-490	112	26	,	,	PUNCT
ejpam-490	112	27	µ	µ	X
ejpam-490	112	28	>	>	X
ejpam-490	112	29	0	0	NUM
ejpam-490	112	30	,	,	PUNCT
ejpam-490	112	31	z	z	PROPN
ejpam-490	112	32	∈	∈	PROPN
ejpam-490	112	33	u	u	PROPN
ejpam-490	112	34	�	�	PROPN
ejpam-490	112	35	«	«	PUNCT
ejpam-490	112	36	,	,	PUNCT
ejpam-490	112	37	(	(	PUNCT
ejpam-490	112	38	13	13	NUM
ejpam-490	112	39	)	)	PUNCT
ejpam-490	112	40	where	where	SCONJ
ejpam-490	112	41	iλ,µ	iλ,µ	PROPN
ejpam-490	112	42	is	be	AUX
ejpam-490	112	43	a	a	DET
ejpam-490	112	44	choi	choi	NOUN
ejpam-490	112	45	-	-	PUNCT
ejpam-490	112	46	saigo	saigo	NOUN
ejpam-490	112	47	-	-	PUNCT
ejpam-490	112	48	srivastava	srivastava	PROPN
ejpam-490	112	49	operator	operator	NOUN
ejpam-490	112	50	[	[	X
ejpam-490	112	51	7	7	NUM
ejpam-490	112	52	]	]	PUNCT
ejpam-490	112	53	,	,	PUNCT
ejpam-490	112	54	defined	define	VERB
ejpam-490	112	55	by	by	ADP
ejpam-490	112	56	iλ,µ	iλ,µ	PROPN
ejpam-490	112	57	f	f	PROPN
ejpam-490	112	58	(	(	PUNCT
ejpam-490	112	59	z	z	NOUN
ejpam-490	112	60	)	)	PUNCT
ejpam-490	112	61	=	=	SYM
ejpam-490	113	1	z	z	NOUN
ejpam-490	114	1	+	+	NUM
ejpam-490	114	2	∞	∞	PROPN
ejpam-490	114	3	∑	∑	PROPN
ejpam-490	114	4	k=2	k=2	PROPN
ejpam-490	114	5	(	(	PUNCT
ejpam-490	114	6	µ)k−1	µ)k−1	X
ejpam-490	114	7	(	(	PUNCT
ejpam-490	114	8	λ+	λ+	NUM
ejpam-490	114	9	1)k−1	1)k−1	NUM
ejpam-490	114	10	akzk	akzk	NOUN
ejpam-490	114	11	(	(	PUNCT
ejpam-490	114	12	λ	λ	X
ejpam-490	114	13	>	>	X
ejpam-490	114	14	−1	−1	NOUN
ejpam-490	114	15	;	;	PUNCT
ejpam-490	114	16	µ	µ	X
ejpam-490	114	17	>	>	X
ejpam-490	114	18	0	0	NUM
ejpam-490	114	19	)	)	PUNCT
ejpam-490	114	20	;	;	PUNCT
ejpam-490	114	21	m.	m.	PROPN
ejpam-490	114	22	aouf	aouf	PROPN
ejpam-490	114	23	,	,	PUNCT
ejpam-490	114	24	r.	r.	PROPN
ejpam-490	114	25	el	el	PROPN
ejpam-490	114	26	-	-	PUNCT
ejpam-490	114	27	ashwah	ashwah	PROPN
ejpam-490	114	28	,	,	PUNCT
ejpam-490	114	29	s.	s.	PROPN
ejpam-490	114	30	el	el	PROPN
ejpam-490	114	31	-	-	PUNCT
ejpam-490	114	32	deeb	deeb	PROPN
ejpam-490	114	33	/	/	SYM
ejpam-490	114	34	eur	eur	PROPN
ejpam-490	114	35	.	.	PUNCT
ejpam-490	115	1	j.	j.	PROPN
ejpam-490	115	2	pure	pure	PROPN
ejpam-490	115	3	appl	appl	PROPN
ejpam-490	115	4	.	.	PROPN
ejpam-490	115	5	math	math	PROPN
ejpam-490	115	6	,	,	PUNCT
ejpam-490	115	7	3	3	NUM
ejpam-490	115	8	(	(	PUNCT
ejpam-490	115	9	2010	2010	NUM
ejpam-490	115	10	)	)	PUNCT
ejpam-490	115	11	,	,	PUNCT
ejpam-490	115	12	903	903	NUM
ejpam-490	115	13	-	-	SYM
ejpam-490	115	14	917	917	NUM
ejpam-490	115	15	907	907	NUM
ejpam-490	115	16	(	(	PUNCT
ejpam-490	115	17	v	v	NOUN
ejpam-490	115	18	)	)	PUNCT
ejpam-490	115	19	sγ	sγ	PROPN
ejpam-490	115	20	(	(	PUNCT
ejpam-490	115	21	f	f	PROPN
ejpam-490	115	22	,	,	PUNCT
ejpam-490	115	23	z	z	PROPN
ejpam-490	115	24	+	+	CCONJ
ejpam-490	115	25	∞	∞	PROPN
ejpam-490	115	26	∑	∑	PROPN
ejpam-490	115	27	k=2	k=2	PROPN
ejpam-490	115	28	(	(	PUNCT
ejpam-490	115	29	c)k−1	c)k−1	PROPN
ejpam-490	115	30	(	(	PUNCT
ejpam-490	115	31	a)k−1	a)k−1	PROPN
ejpam-490	115	32	(	(	PUNCT
ejpam-490	115	33	λ+	λ+	NUM
ejpam-490	115	34	1)k−1	1)k−1	NUM
ejpam-490	115	35	(	(	PUNCT
ejpam-490	115	36	1)k−1	1)k−1	NUM
ejpam-490	115	37	zk;α	zk;α	PROPN
ejpam-490	115	38	,	,	PUNCT
ejpam-490	115	39	β	β	X
ejpam-490	115	40	)	)	PUNCT
ejpam-490	115	41	=	=	SYM
ejpam-490	116	1	sγ	sγ	PROPN
ejpam-490	116	2	�	�	PROPN
ejpam-490	116	3	a	a	PRON
ejpam-490	116	4	,	,	PUNCT
ejpam-490	116	5	c	c	NOUN
ejpam-490	116	6	,	,	PUNCT
ejpam-490	116	7	λ;α	λ;α	PROPN
ejpam-490	116	8	,	,	PUNCT
ejpam-490	116	9	β	β	X
ejpam-490	116	10	�	�	X
ejpam-490	116	11	=	=	PUNCT
ejpam-490	116	12	¨	¨	NOUN
ejpam-490	116	13	f	f	PROPN
ejpam-490	116	14	∈	∈	PROPN
ejpam-490	116	15	a	a	PRON
ejpam-490	116	16	:	:	PUNCT
ejpam-490	116	17	re	re	X
ejpam-490	116	18	(	(	PUNCT
ejpam-490	116	19	z(iλ(a	z(iλ(a	NOUN
ejpam-490	116	20	,	,	PUNCT
ejpam-490	116	21	c	c	NOUN
ejpam-490	116	22	)	)	PUNCT
ejpam-490	116	23	f	f	NOUN
ejpam-490	116	24	(	(	PUNCT
ejpam-490	116	25	z	z	NOUN
ejpam-490	116	26	)	)	PUNCT
ejpam-490	116	27	)	)	PUNCT
ejpam-490	116	28	′	′	PUNCT
ejpam-490	117	1	+	+	CCONJ
ejpam-490	117	2	γz2(iλ(a	γz2(iλ(a	NOUN
ejpam-490	117	3	,	,	PUNCT
ejpam-490	117	4	c	c	NOUN
ejpam-490	117	5	)	)	PUNCT
ejpam-490	117	6	f	f	NOUN
ejpam-490	117	7	(	(	PUNCT
ejpam-490	117	8	z	z	NOUN
ejpam-490	117	9	)	)	PUNCT
ejpam-490	117	10	)	)	PUNCT
ejpam-490	118	1	′′	′′	PROPN
ejpam-490	118	2	(	(	PUNCT
ejpam-490	118	3	1−	1−	NUM
ejpam-490	118	4	γ)iλ(a	γ)iλ(a	NOUN
ejpam-490	118	5	,	,	PUNCT
ejpam-490	118	6	c	c	NOUN
ejpam-490	118	7	)	)	PUNCT
ejpam-490	118	8	f	f	NOUN
ejpam-490	118	9	(	(	PUNCT
ejpam-490	118	10	z	z	NOUN
ejpam-490	118	11	)	)	PUNCT
ejpam-490	118	12	+	+	NUM
ejpam-490	118	13	γz(iλ(a	γz(iλ(a	NOUN
ejpam-490	118	14	,	,	PUNCT
ejpam-490	118	15	c	c	NOUN
ejpam-490	118	16	)	)	PUNCT
ejpam-490	118	17	f	f	NOUN
ejpam-490	118	18	(	(	PUNCT
ejpam-490	118	19	z	z	NOUN
ejpam-490	118	20	)	)	PUNCT
ejpam-490	118	21	)	)	PUNCT
ejpam-490	118	22	′	′	NUM
ejpam-490	118	23	−α	−α	NOUN
ejpam-490	118	24	)	)	PUNCT
ejpam-490	118	25	>	>	PUNCT
ejpam-490	118	26	β	β	X
ejpam-490	118	27	�	�	PROPN
ejpam-490	118	28	�	�	PROPN
ejpam-490	118	29	�	�	PROPN
ejpam-490	118	30	�	�	PROPN
ejpam-490	118	31	�	�	PROPN
ejpam-490	118	32	z(iλ(a	z(iλ(a	PROPN
ejpam-490	118	33	,	,	PUNCT
ejpam-490	118	34	c	c	NOUN
ejpam-490	118	35	)	)	PUNCT
ejpam-490	118	36	f	f	NOUN
ejpam-490	118	37	(	(	PUNCT
ejpam-490	118	38	z	z	NOUN
ejpam-490	118	39	)	)	PUNCT
ejpam-490	118	40	)	)	PUNCT
ejpam-490	118	41	′	′	PUNCT
ejpam-490	119	1	+	+	CCONJ
ejpam-490	119	2	γz2(iλ(a	γz2(iλ(a	NOUN
ejpam-490	119	3	,	,	PUNCT
ejpam-490	119	4	c	c	NOUN
ejpam-490	119	5	)	)	PUNCT
ejpam-490	119	6	f	f	NOUN
ejpam-490	119	7	(	(	PUNCT
ejpam-490	119	8	z	z	NOUN
ejpam-490	119	9	)	)	PUNCT
ejpam-490	119	10	)	)	PUNCT
ejpam-490	120	1	′′	′′	PROPN
ejpam-490	120	2	(	(	PUNCT
ejpam-490	120	3	1−	1−	NUM
ejpam-490	120	4	γ)iλ(a	γ)iλ(a	NOUN
ejpam-490	120	5	,	,	PUNCT
ejpam-490	120	6	c	c	NOUN
ejpam-490	120	7	)	)	PUNCT
ejpam-490	120	8	f	f	NOUN
ejpam-490	120	9	(	(	PUNCT
ejpam-490	120	10	z	z	NOUN
ejpam-490	120	11	)	)	PUNCT
ejpam-490	120	12	+	+	NUM
ejpam-490	120	13	γz(iλ(a	γz(iλ(a	NOUN
ejpam-490	120	14	,	,	PUNCT
ejpam-490	120	15	c	c	NOUN
ejpam-490	120	16	)	)	PUNCT
ejpam-490	120	17	f	f	NOUN
ejpam-490	120	18	(	(	PUNCT
ejpam-490	120	19	z	z	NOUN
ejpam-490	120	20	)	)	PUNCT
ejpam-490	120	21	)	)	PUNCT
ejpam-490	120	22	′	′	NUM
ejpam-490	121	1	−	−	NOUN
ejpam-490	121	2	1	1	NUM
ejpam-490	121	3	�	�	PROPN
ejpam-490	121	4	�	�	PROPN
ejpam-490	121	5	�	�	PROPN
ejpam-490	121	6	�	�	PROPN
ejpam-490	121	7	�	�	PROPN
ejpam-490	121	8	,	,	PUNCT
ejpam-490	121	9	�	�	PROPN
ejpam-490	121	10	0≤	0≤	NUM
ejpam-490	121	11	γ	γ	X
ejpam-490	121	12	≤	≤	NOUN
ejpam-490	121	13	1	1	NUM
ejpam-490	121	14	,	,	PUNCT
ejpam-490	121	15	−1≤	−1≤	VERB
ejpam-490	121	16	α	α	NOUN
ejpam-490	121	17	<	<	X
ejpam-490	121	18	1	1	NUM
ejpam-490	121	19	,	,	PUNCT
ejpam-490	121	20	β	β	X
ejpam-490	121	21	≥	≥	NOUN
ejpam-490	121	22	0	0	NUM
ejpam-490	121	23	,	,	PUNCT
ejpam-490	121	24	a	a	PRON
ejpam-490	121	25	,	,	PUNCT
ejpam-490	121	26	c	c	PROPN
ejpam-490	121	27	∈	∈	PROPN
ejpam-490	121	28	r\z−0	r\z−0	NOUN
ejpam-490	121	29	,	,	PUNCT
ejpam-490	121	30	λ	λ	X
ejpam-490	121	31	>	>	X
ejpam-490	121	32	−1	−1	NOUN
ejpam-490	121	33	,	,	PUNCT
ejpam-490	121	34	z	z	PROPN
ejpam-490	121	35	∈	∈	PROPN
ejpam-490	121	36	u	u	PROPN
ejpam-490	121	37	�	�	PROPN
ejpam-490	121	38	«	«	PUNCT
ejpam-490	121	39	,	,	PUNCT
ejpam-490	121	40	(	(	PUNCT
ejpam-490	121	41	14	14	NUM
ejpam-490	121	42	)	)	PUNCT
ejpam-490	121	43	where	where	SCONJ
ejpam-490	121	44	iλ(a	iλ(a	NOUN
ejpam-490	121	45	,	,	PUNCT
ejpam-490	121	46	c	c	NOUN
ejpam-490	121	47	)	)	PUNCT
ejpam-490	121	48	is	be	AUX
ejpam-490	121	49	a	a	DET
ejpam-490	121	50	cho	cho	PROPN
ejpam-490	121	51	-	-	PUNCT
ejpam-490	121	52	kwon	kwon	VERB
ejpam-490	121	53	-	-	PUNCT
ejpam-490	121	54	srivastava	srivastava	PROPN
ejpam-490	121	55	operator	operator	NOUN
ejpam-490	121	56	[	[	X
ejpam-490	121	57	6	6	NUM
ejpam-490	121	58	]	]	PUNCT
ejpam-490	121	59	,	,	PUNCT
ejpam-490	121	60	defined	define	VERB
ejpam-490	121	61	by	by	ADP
ejpam-490	121	62	iλ(a	iλ(a	NOUN
ejpam-490	121	63	,	,	PUNCT
ejpam-490	121	64	c	c	NOUN
ejpam-490	121	65	)	)	PUNCT
ejpam-490	121	66	f	f	NOUN
ejpam-490	121	67	(	(	PUNCT
ejpam-490	121	68	z	z	NOUN
ejpam-490	121	69	)	)	PUNCT
ejpam-490	121	70	=	=	SYM
ejpam-490	122	1	z	z	NOUN
ejpam-490	123	1	+	+	NUM
ejpam-490	123	2	∞	∞	PROPN
ejpam-490	123	3	∑	∑	PROPN
ejpam-490	123	4	k=2	k=2	PROPN
ejpam-490	123	5	(	(	PUNCT
ejpam-490	123	6	c)k−1	c)k−1	PROPN
ejpam-490	123	7	(	(	PUNCT
ejpam-490	123	8	a)k−1	a)k−1	PROPN
ejpam-490	123	9	(	(	PUNCT
ejpam-490	123	10	λ+	λ+	NUM
ejpam-490	123	11	1)k−1	1)k−1	NUM
ejpam-490	123	12	(	(	PUNCT
ejpam-490	123	13	1)k−1	1)k−1	NUM
ejpam-490	123	14	akzk	akzk	NOUN
ejpam-490	123	15	;	;	PUNCT
ejpam-490	123	16	(	(	PUNCT
ejpam-490	123	17	vi	vi	X
ejpam-490	123	18	)	)	PUNCT
ejpam-490	123	19	sγ	sγ	PROPN
ejpam-490	123	20	(	(	PUNCT
ejpam-490	123	21	f	f	PROPN
ejpam-490	123	22	,	,	PUNCT
ejpam-490	123	23	z	z	PROPN
ejpam-490	123	24	+	+	CCONJ
ejpam-490	123	25	∞	∞	PROPN
ejpam-490	123	26	∑	∑	PROPN
ejpam-490	123	27	k=2	k=2	PROPN
ejpam-490	123	28	(	(	PUNCT
ejpam-490	123	29	2)k−1	2)k−1	NUM
ejpam-490	123	30	(	(	PUNCT
ejpam-490	123	31	n+	n+	NUM
ejpam-490	123	32	1)k−1	1)k−1	NUM
ejpam-490	123	33	zk;α	zk;α	NOUN
ejpam-490	123	34	,	,	PUNCT
ejpam-490	123	35	β	β	X
ejpam-490	123	36	)	)	PUNCT
ejpam-490	123	37	=	=	SYM
ejpam-490	123	38	sγ	sγ	PROPN
ejpam-490	123	39	�	�	PROPN
ejpam-490	123	40	n;α	n;α	PROPN
ejpam-490	123	41	,	,	PUNCT
ejpam-490	123	42	β	β	X
ejpam-490	123	43	�	�	NOUN
ejpam-490	123	44	=	=	PUNCT
ejpam-490	123	45	¨	¨	NOUN
ejpam-490	123	46	f	f	PROPN
ejpam-490	123	47	∈	∈	PROPN
ejpam-490	123	48	a	a	DET
ejpam-490	123	49	:	:	PUNCT
ejpam-490	123	50	re	re	X
ejpam-490	123	51	(	(	PUNCT
ejpam-490	123	52	z(in	z(in	X
ejpam-490	123	53	f	f	X
ejpam-490	123	54	(	(	PUNCT
ejpam-490	123	55	z	z	NOUN
ejpam-490	123	56	)	)	PUNCT
ejpam-490	123	57	)	)	PUNCT
ejpam-490	123	58	′	′	PUNCT
ejpam-490	124	1	+	+	CCONJ
ejpam-490	124	2	γz2(in	γz2(in	SYM
ejpam-490	124	3	f	f	X
ejpam-490	124	4	(	(	PUNCT
ejpam-490	124	5	z	z	NOUN
ejpam-490	124	6	)	)	PUNCT
ejpam-490	124	7	)	)	PUNCT
ejpam-490	125	1	′′	′′	PROPN
ejpam-490	125	2	(	(	PUNCT
ejpam-490	125	3	1−	1−	NUM
ejpam-490	125	4	γ)in	γ)in	PROPN
ejpam-490	125	5	f	f	PROPN
ejpam-490	125	6	(	(	PUNCT
ejpam-490	125	7	z	z	NOUN
ejpam-490	125	8	)	)	PUNCT
ejpam-490	125	9	+	+	NUM
ejpam-490	125	10	γz(in	γz(in	PROPN
ejpam-490	125	11	f	f	PROPN
ejpam-490	125	12	(	(	PUNCT
ejpam-490	125	13	z	z	NOUN
ejpam-490	125	14	)	)	PUNCT
ejpam-490	125	15	)	)	PUNCT
ejpam-490	125	16	′	′	NUM
ejpam-490	125	17	−α	−α	NOUN
ejpam-490	125	18	)	)	PUNCT
ejpam-490	125	19	>	>	PUNCT
ejpam-490	125	20	β	β	X
ejpam-490	125	21	�	�	PROPN
ejpam-490	125	22	�	�	PROPN
ejpam-490	125	23	�	�	PROPN
ejpam-490	125	24	�	�	PROPN
ejpam-490	125	25	�	�	PROPN
ejpam-490	125	26	z(in	z(in	PROPN
ejpam-490	125	27	f	f	X
ejpam-490	125	28	(	(	PUNCT
ejpam-490	125	29	z	z	NOUN
ejpam-490	125	30	)	)	PUNCT
ejpam-490	125	31	)	)	PUNCT
ejpam-490	125	32	′	′	PUNCT
ejpam-490	126	1	+	+	CCONJ
ejpam-490	126	2	γz2(in	γz2(in	SYM
ejpam-490	126	3	f	f	X
ejpam-490	126	4	(	(	PUNCT
ejpam-490	126	5	z	z	NOUN
ejpam-490	126	6	)	)	PUNCT
ejpam-490	126	7	)	)	PUNCT
ejpam-490	127	1	′′	′′	PROPN
ejpam-490	127	2	(	(	PUNCT
ejpam-490	127	3	1−	1−	NUM
ejpam-490	127	4	γ)in	γ)in	PROPN
ejpam-490	127	5	f	f	PROPN
ejpam-490	127	6	(	(	PUNCT
ejpam-490	127	7	z	z	NOUN
ejpam-490	127	8	)	)	PUNCT
ejpam-490	127	9	+	+	NUM
ejpam-490	127	10	γz(in	γz(in	PROPN
ejpam-490	127	11	f	f	PROPN
ejpam-490	127	12	(	(	PUNCT
ejpam-490	127	13	z	z	NOUN
ejpam-490	127	14	)	)	PUNCT
ejpam-490	127	15	)	)	PUNCT
ejpam-490	128	1	′	′	NUM
ejpam-490	129	1	−	−	NOUN
ejpam-490	129	2	1	1	NUM
ejpam-490	129	3	�	�	PROPN
ejpam-490	129	4	�	�	PROPN
ejpam-490	129	5	�	�	PROPN
ejpam-490	129	6	�	�	PROPN
ejpam-490	129	7	�	�	PROPN
ejpam-490	129	8	,	,	PUNCT
ejpam-490	129	9	�	�	PROPN
ejpam-490	129	10	0≤	0≤	NUM
ejpam-490	129	11	γ	γ	X
ejpam-490	129	12	≤	≤	NOUN
ejpam-490	129	13	1	1	NUM
ejpam-490	129	14	,	,	PUNCT
ejpam-490	129	15	−1≤	−1≤	VERB
ejpam-490	129	16	α	α	NOUN
ejpam-490	129	17	<	<	X
ejpam-490	129	18	1	1	NUM
ejpam-490	129	19	,	,	PUNCT
ejpam-490	129	20	β	β	X
ejpam-490	129	21	≥	≥	NOUN
ejpam-490	129	22	0	0	NUM
ejpam-490	129	23	,	,	PUNCT
ejpam-490	129	24	n	n	CCONJ
ejpam-490	129	25	>	>	X
ejpam-490	129	26	−1	−1	NOUN
ejpam-490	129	27	,	,	PUNCT
ejpam-490	129	28	z	z	PROPN
ejpam-490	129	29	∈	∈	PROPN
ejpam-490	129	30	u	u	PROPN
ejpam-490	129	31	�	�	PROPN
ejpam-490	129	32	«	«	PUNCT
ejpam-490	129	33	,	,	PUNCT
ejpam-490	129	34	(	(	PUNCT
ejpam-490	129	35	15	15	NUM
ejpam-490	129	36	)	)	PUNCT
ejpam-490	129	37	where	where	SCONJ
ejpam-490	129	38	in	in	ADP
ejpam-490	129	39	is	be	AUX
ejpam-490	129	40	a	a	DET
ejpam-490	129	41	noor	noor	PROPN
ejpam-490	129	42	integral	integral	ADJ
ejpam-490	129	43	operator	operator	NOUN
ejpam-490	129	44	[	[	X
ejpam-490	129	45	17	17	NUM
ejpam-490	129	46	]	]	PUNCT
ejpam-490	129	47	,	,	PUNCT
ejpam-490	129	48	defined	define	VERB
ejpam-490	129	49	by	by	ADP
ejpam-490	129	50	in	in	ADP
ejpam-490	129	51	f	f	PROPN
ejpam-490	129	52	(	(	PUNCT
ejpam-490	129	53	z	z	NOUN
ejpam-490	129	54	)	)	PUNCT
ejpam-490	129	55	=	=	SYM
ejpam-490	130	1	z	z	NOUN
ejpam-490	131	1	+	+	NUM
ejpam-490	131	2	∞	∞	PROPN
ejpam-490	131	3	∑	∑	PROPN
ejpam-490	131	4	k=2	k=2	PROPN
ejpam-490	131	5	(	(	PUNCT
ejpam-490	131	6	2)k−1	2)k−1	NUM
ejpam-490	131	7	(	(	PUNCT
ejpam-490	131	8	n+	n+	NUM
ejpam-490	131	9	1)k−1	1)k−1	NUM
ejpam-490	131	10	akzk	akzk	NOUN
ejpam-490	131	11	(	(	PUNCT
ejpam-490	131	12	n	n	CCONJ
ejpam-490	131	13	>	>	X
ejpam-490	131	14	−1	−1	NOUN
ejpam-490	131	15	)	)	PUNCT
ejpam-490	131	16	.	.	PUNCT
ejpam-490	132	1	definition	definition	NOUN
ejpam-490	132	2	2	2	NUM
ejpam-490	132	3	(	(	PUNCT
ejpam-490	132	4	subordination	subordination	NOUN
ejpam-490	132	5	principle	principle	NOUN
ejpam-490	132	6	)	)	PUNCT
ejpam-490	132	7	.	.	PUNCT
ejpam-490	133	1	for	for	ADP
ejpam-490	133	2	two	two	NUM
ejpam-490	133	3	functions	function	NOUN
ejpam-490	133	4	f	f	PROPN
ejpam-490	133	5	and	and	CCONJ
ejpam-490	133	6	φ	φ	NUM
ejpam-490	133	7	,	,	PUNCT
ejpam-490	133	8	analytic	analytic	ADJ
ejpam-490	133	9	in	in	ADP
ejpam-490	133	10	u	u	NOUN
ejpam-490	133	11	,	,	PUNCT
ejpam-490	133	12	we	we	PRON
ejpam-490	133	13	say	say	VERB
ejpam-490	133	14	that	that	SCONJ
ejpam-490	133	15	the	the	DET
ejpam-490	133	16	function	function	NOUN
ejpam-490	133	17	f	f	X
ejpam-490	133	18	(	(	PUNCT
ejpam-490	133	19	z	z	NOUN
ejpam-490	133	20	)	)	PUNCT
ejpam-490	133	21	is	be	AUX
ejpam-490	133	22	subordinate	subordinate	ADJ
ejpam-490	133	23	to	to	ADP
ejpam-490	133	24	φ(z	φ(z	PROPN
ejpam-490	133	25	)	)	PUNCT
ejpam-490	133	26	in	in	ADP
ejpam-490	133	27	u	u	NOUN
ejpam-490	133	28	,	,	PUNCT
ejpam-490	133	29	and	and	CCONJ
ejpam-490	133	30	write	write	VERB
ejpam-490	133	31	f	f	PROPN
ejpam-490	133	32	(	(	PUNCT
ejpam-490	133	33	z	z	NOUN
ejpam-490	133	34	)	)	PUNCT
ejpam-490	133	35	≺	≺	NOUN
ejpam-490	133	36	φ(z	φ(z	PROPN
ejpam-490	133	37	)	)	PUNCT
ejpam-490	133	38	(	(	PUNCT
ejpam-490	133	39	z	z	NOUN
ejpam-490	133	40	∈	∈	PROPN
ejpam-490	133	41	u	u	NOUN
ejpam-490	133	42	)	)	PUNCT
ejpam-490	133	43	,	,	PUNCT
ejpam-490	133	44	if	if	SCONJ
ejpam-490	133	45	there	there	PRON
ejpam-490	133	46	exists	exist	VERB
ejpam-490	133	47	a	a	DET
ejpam-490	133	48	schwarz	schwarz	NOUN
ejpam-490	133	49	function	function	NOUN
ejpam-490	133	50	w(z	w(z	NOUN
ejpam-490	133	51	)	)	PUNCT
ejpam-490	133	52	,	,	PUNCT
ejpam-490	133	53	which	which	PRON
ejpam-490	133	54	(	(	PUNCT
ejpam-490	133	55	by	by	ADP
ejpam-490	133	56	definition	definition	NOUN
ejpam-490	133	57	)	)	PUNCT
ejpam-490	133	58	is	be	AUX
ejpam-490	133	59	analytic	analytic	ADJ
ejpam-490	133	60	in	in	ADP
ejpam-490	133	61	u	u	NOUN
ejpam-490	133	62	with	with	ADP
ejpam-490	133	63	w(0	w(0	PROPN
ejpam-490	133	64	)	)	PUNCT
ejpam-490	134	1	=	=	SYM
ejpam-490	134	2	0	0	NUM
ejpam-490	135	1	and	and	CCONJ
ejpam-490	135	2	|w(z)|	|w(z)|	VERB
ejpam-490	135	3	<	<	X
ejpam-490	135	4	1	1	NUM
ejpam-490	135	5	,	,	PUNCT
ejpam-490	136	1	such	such	ADJ
ejpam-490	136	2	that	that	SCONJ
ejpam-490	136	3	f	f	PROPN
ejpam-490	136	4	(	(	PUNCT
ejpam-490	136	5	z	z	NOUN
ejpam-490	136	6	)	)	PUNCT
ejpam-490	136	7	=	=	SYM
ejpam-490	136	8	φ(w(z	φ(w(z	PROPN
ejpam-490	136	9	)	)	PUNCT
ejpam-490	136	10	)	)	PUNCT
ejpam-490	136	11	(	(	PUNCT
ejpam-490	136	12	z	z	NOUN
ejpam-490	136	13	∈	∈	PROPN
ejpam-490	136	14	u	u	NOUN
ejpam-490	136	15	)	)	PUNCT
ejpam-490	136	16	.	.	PUNCT
ejpam-490	137	1	indeed	indeed	ADV
ejpam-490	137	2	it	it	PRON
ejpam-490	137	3	is	be	AUX
ejpam-490	137	4	known	know	VERB
ejpam-490	137	5	that	that	SCONJ
ejpam-490	137	6	f	f	PROPN
ejpam-490	137	7	(	(	PUNCT
ejpam-490	137	8	z)≺	z)≺	PROPN
ejpam-490	137	9	φ(z	φ(z	PROPN
ejpam-490	137	10	)	)	PUNCT
ejpam-490	137	11	(	(	PUNCT
ejpam-490	137	12	z	z	NOUN
ejpam-490	137	13	∈	∈	PROPN
ejpam-490	137	14	u)⇒	u)⇒	NOUN
ejpam-490	137	15	f	f	X
ejpam-490	137	16	(	(	PUNCT
ejpam-490	137	17	0	0	NUM
ejpam-490	137	18	)	)	PUNCT
ejpam-490	137	19	=	=	SYM
ejpam-490	138	1	φ(0	φ(0	ADJ
ejpam-490	138	2	)	)	PUNCT
ejpam-490	138	3	and	and	CCONJ
ejpam-490	138	4	f	f	PROPN
ejpam-490	138	5	(	(	PUNCT
ejpam-490	138	6	u)⊂	u)⊂	NOUN
ejpam-490	138	7	φ(u	φ(u	NOUN
ejpam-490	138	8	)	)	PUNCT
ejpam-490	138	9	.	.	PUNCT
ejpam-490	139	1	furthermore	furthermore	ADV
ejpam-490	139	2	,	,	PUNCT
ejpam-490	139	3	if	if	SCONJ
ejpam-490	139	4	the	the	DET
ejpam-490	139	5	function	function	NOUN
ejpam-490	139	6	φ	φ	PROPN
ejpam-490	139	7	is	be	AUX
ejpam-490	139	8	univalent	univalent	ADJ
ejpam-490	139	9	in	in	ADP
ejpam-490	139	10	u	u	NOUN
ejpam-490	139	11	,	,	PUNCT
ejpam-490	139	12	then	then	ADV
ejpam-490	139	13	we	we	PRON
ejpam-490	139	14	have	have	VERB
ejpam-490	139	15	the	the	DET
ejpam-490	139	16	following	following	ADJ
ejpam-490	139	17	equivalence	equivalence	NOUN
ejpam-490	139	18	[	[	X
ejpam-490	139	19	13	13	NUM
ejpam-490	139	20	,	,	PUNCT
ejpam-490	139	21	p.	p.	NOUN
ejpam-490	139	22	4	4	NUM
ejpam-490	139	23	]	]	PUNCT
ejpam-490	139	24	:	:	PUNCT
ejpam-490	139	25	f	f	X
ejpam-490	139	26	(	(	PUNCT
ejpam-490	139	27	z)≺	z)≺	PROPN
ejpam-490	139	28	φ(z	φ(z	PROPN
ejpam-490	139	29	)	)	PUNCT
ejpam-490	139	30	(	(	PUNCT
ejpam-490	139	31	z	z	NOUN
ejpam-490	139	32	∈	∈	PROPN
ejpam-490	140	1	u)⇔	u)⇔	PROPN
ejpam-490	140	2	f	f	X
ejpam-490	140	3	(	(	PUNCT
ejpam-490	140	4	0	0	NUM
ejpam-490	140	5	)	)	PUNCT
ejpam-490	140	6	=	=	SYM
ejpam-490	141	1	φ(0	φ(0	ADJ
ejpam-490	141	2	)	)	PUNCT
ejpam-490	141	3	and	and	CCONJ
ejpam-490	141	4	f	f	PROPN
ejpam-490	141	5	(	(	PUNCT
ejpam-490	141	6	u)⊂	u)⊂	NOUN
ejpam-490	141	7	φ(u	φ(u	NOUN
ejpam-490	141	8	)	)	PUNCT
ejpam-490	141	9	.	.	PUNCT
ejpam-490	142	1	m.	m.	PROPN
ejpam-490	142	2	aouf	aouf	PROPN
ejpam-490	142	3	,	,	PUNCT
ejpam-490	142	4	r.	r.	PROPN
ejpam-490	142	5	el	el	PROPN
ejpam-490	142	6	-	-	PUNCT
ejpam-490	142	7	ashwah	ashwah	PROPN
ejpam-490	142	8	,	,	PUNCT
ejpam-490	142	9	s.	s.	PROPN
ejpam-490	142	10	el	el	PROPN
ejpam-490	142	11	-	-	PUNCT
ejpam-490	142	12	deeb	deeb	PROPN
ejpam-490	142	13	/	/	SYM
ejpam-490	142	14	eur	eur	PROPN
ejpam-490	142	15	.	.	PUNCT
ejpam-490	143	1	j.	j.	PROPN
ejpam-490	143	2	pure	pure	PROPN
ejpam-490	143	3	appl	appl	PROPN
ejpam-490	143	4	.	.	PROPN
ejpam-490	143	5	math	math	PROPN
ejpam-490	143	6	,	,	PUNCT
ejpam-490	143	7	3	3	NUM
ejpam-490	143	8	(	(	PUNCT
ejpam-490	143	9	2010	2010	NUM
ejpam-490	143	10	)	)	PUNCT
ejpam-490	143	11	,	,	PUNCT
ejpam-490	143	12	903	903	NUM
ejpam-490	143	13	-	-	SYM
ejpam-490	143	14	917	917	NUM
ejpam-490	143	15	908	908	NUM
ejpam-490	143	16	definition	definition	NOUN
ejpam-490	143	17	3	3	NUM
ejpam-490	143	18	(	(	PUNCT
ejpam-490	143	19	subordination	subordination	NOUN
ejpam-490	143	20	factor	factor	NOUN
ejpam-490	143	21	sequence	sequence	NOUN
ejpam-490	143	22	)	)	PUNCT
ejpam-490	143	23	.	.	PUNCT
ejpam-490	144	1	a	a	DET
ejpam-490	144	2	sequence	sequence	NOUN
ejpam-490	144	3	{	{	PUNCT
ejpam-490	144	4	ck	ck	NOUN
ejpam-490	144	5	}	}	PUNCT
ejpam-490	144	6	∞	∞	NUM
ejpam-490	144	7	k=1	k=1	NOUN
ejpam-490	144	8	of	of	ADP
ejpam-490	144	9	complex	complex	ADJ
ejpam-490	144	10	numbers	number	NOUN
ejpam-490	144	11	is	be	AUX
ejpam-490	144	12	said	say	VERB
ejpam-490	144	13	to	to	PART
ejpam-490	144	14	be	be	AUX
ejpam-490	144	15	a	a	DET
ejpam-490	144	16	subordinating	subordinate	VERB
ejpam-490	144	17	factor	factor	NOUN
ejpam-490	144	18	sequence	sequence	NOUN
ejpam-490	144	19	if	if	SCONJ
ejpam-490	144	20	,	,	PUNCT
ejpam-490	144	21	whenever	whenever	SCONJ
ejpam-490	144	22	f	f	PROPN
ejpam-490	144	23	(	(	PUNCT
ejpam-490	144	24	z	z	NOUN
ejpam-490	144	25	)	)	PUNCT
ejpam-490	144	26	of	of	ADP
ejpam-490	144	27	the	the	DET
ejpam-490	144	28	form	form	NOUN
ejpam-490	144	29	(	(	PUNCT
ejpam-490	144	30	1	1	X
ejpam-490	144	31	)	)	PUNCT
ejpam-490	144	32	is	be	AUX
ejpam-490	144	33	analytic	analytic	ADJ
ejpam-490	144	34	,	,	PUNCT
ejpam-490	144	35	univalent	univalent	ADJ
ejpam-490	144	36	and	and	CCONJ
ejpam-490	144	37	convex	convex	NOUN
ejpam-490	144	38	in	in	ADP
ejpam-490	144	39	u	u	NOUN
ejpam-490	144	40	,	,	PUNCT
ejpam-490	144	41	we	we	PRON
ejpam-490	144	42	have	have	VERB
ejpam-490	144	43	the	the	DET
ejpam-490	144	44	subordination	subordination	NOUN
ejpam-490	144	45	given	give	VERB
ejpam-490	144	46	by	by	ADP
ejpam-490	144	47	∞	∞	PROPN
ejpam-490	144	48	∑	∑	PROPN
ejpam-490	144	49	k=1	k=1	PROPN
ejpam-490	144	50	akckzk	akckzk	PROPN
ejpam-490	144	51	≺	≺	NOUN
ejpam-490	144	52	f	f	X
ejpam-490	144	53	(	(	PUNCT
ejpam-490	144	54	z	z	NOUN
ejpam-490	144	55	)	)	PUNCT
ejpam-490	144	56	(	(	PUNCT
ejpam-490	144	57	z	z	NOUN
ejpam-490	144	58	∈	∈	PROPN
ejpam-490	144	59	u	u	NOUN
ejpam-490	144	60	;	;	PUNCT
ejpam-490	144	61	a1	a1	NOUN
ejpam-490	144	62	=	=	SYM
ejpam-490	144	63	1	1	NUM
ejpam-490	144	64	)	)	PUNCT
ejpam-490	144	65	.	.	PUNCT
ejpam-490	145	1	(	(	PUNCT
ejpam-490	145	2	16	16	NUM
ejpam-490	145	3	)	)	PUNCT
ejpam-490	145	4	2	2	NUM
ejpam-490	145	5	.	.	X
ejpam-490	145	6	main	main	ADJ
ejpam-490	145	7	result	result	NOUN
ejpam-490	145	8	to	to	PART
ejpam-490	145	9	prove	prove	VERB
ejpam-490	145	10	our	our	PRON
ejpam-490	145	11	main	main	ADJ
ejpam-490	145	12	result	result	NOUN
ejpam-490	145	13	we	we	PRON
ejpam-490	145	14	need	need	VERB
ejpam-490	145	15	the	the	DET
ejpam-490	145	16	following	follow	VERB
ejpam-490	145	17	lemmas	lemmas	NOUN
ejpam-490	145	18	.	.	PUNCT
ejpam-490	146	1	lemma	lemma	PROPN
ejpam-490	146	2	1	1	NUM
ejpam-490	146	3	(	(	PUNCT
ejpam-490	146	4	[	[	X
ejpam-490	146	5	25	25	NUM
ejpam-490	146	6	]	]	PUNCT
ejpam-490	146	7	)	)	PUNCT
ejpam-490	146	8	.	.	PUNCT
ejpam-490	147	1	the	the	DET
ejpam-490	147	2	sequence	sequence	NOUN
ejpam-490	147	3	{	{	PUNCT
ejpam-490	147	4	ck	ck	NOUN
ejpam-490	147	5	}	}	PUNCT
ejpam-490	147	6	∞	∞	NUM
ejpam-490	147	7	k=1	k=1	PROPN
ejpam-490	147	8	is	be	AUX
ejpam-490	147	9	a	a	DET
ejpam-490	147	10	subordinating	subordinate	VERB
ejpam-490	147	11	factor	factor	NOUN
ejpam-490	147	12	sequence	sequence	NOUN
ejpam-490	147	13	if	if	SCONJ
ejpam-490	147	14	and	and	CCONJ
ejpam-490	147	15	only	only	ADV
ejpam-490	147	16	if	if	SCONJ
ejpam-490	147	17	re	re	X
ejpam-490	147	18	(	(	PUNCT
ejpam-490	147	19	1	1	NUM
ejpam-490	147	20	+	+	NUM
ejpam-490	147	21	2	2	NUM
ejpam-490	147	22	∞	∞	NUM
ejpam-490	147	23	∑	∑	PUNCT
ejpam-490	147	24	k=1	k=1	PROPN
ejpam-490	147	25	ckzk	ckzk	PROPN
ejpam-490	147	26	)	)	PUNCT
ejpam-490	147	27	>	>	X
ejpam-490	147	28	0	0	PUNCT
ejpam-490	148	1	(	(	PUNCT
ejpam-490	148	2	z	z	NOUN
ejpam-490	148	3	∈	∈	PROPN
ejpam-490	148	4	u	u	NOUN
ejpam-490	148	5	)	)	PUNCT
ejpam-490	148	6	.	.	PUNCT
ejpam-490	149	1	now	now	ADV
ejpam-490	149	2	,	,	PUNCT
ejpam-490	149	3	we	we	PRON
ejpam-490	149	4	prove	prove	VERB
ejpam-490	149	5	the	the	DET
ejpam-490	149	6	following	follow	VERB
ejpam-490	149	7	lemma	lemma	PROPN
ejpam-490	149	8	which	which	PRON
ejpam-490	149	9	gives	give	VERB
ejpam-490	149	10	a	a	DET
ejpam-490	149	11	sufficient	sufficient	ADJ
ejpam-490	149	12	condition	condition	NOUN
ejpam-490	149	13	for	for	ADP
ejpam-490	149	14	functions	function	NOUN
ejpam-490	149	15	belonging	belong	VERB
ejpam-490	149	16	to	to	ADP
ejpam-490	149	17	the	the	DET
ejpam-490	149	18	class	class	NOUN
ejpam-490	149	19	sγ	sγ	PROPN
ejpam-490	149	20	(	(	PUNCT
ejpam-490	149	21	f	f	PROPN
ejpam-490	149	22	,	,	PUNCT
ejpam-490	149	23	g;α	g;α	PROPN
ejpam-490	149	24	,	,	PUNCT
ejpam-490	149	25	β	β	NOUN
ejpam-490	149	26	)	)	PUNCT
ejpam-490	149	27	.	.	PUNCT
ejpam-490	150	1	lemma	lemma	PROPN
ejpam-490	150	2	2	2	NUM
ejpam-490	150	3	.	.	PUNCT
ejpam-490	151	1	a	a	DET
ejpam-490	151	2	function	function	NOUN
ejpam-490	151	3	f	f	X
ejpam-490	151	4	(	(	PUNCT
ejpam-490	151	5	z	z	NOUN
ejpam-490	151	6	)	)	PUNCT
ejpam-490	151	7	of	of	ADP
ejpam-490	151	8	the	the	DET
ejpam-490	151	9	form	form	NOUN
ejpam-490	151	10	(	(	PUNCT
ejpam-490	151	11	1	1	X
ejpam-490	151	12	)	)	PUNCT
ejpam-490	151	13	is	be	AUX
ejpam-490	151	14	in	in	ADP
ejpam-490	151	15	sγ	sγ	PROPN
ejpam-490	151	16	(	(	PUNCT
ejpam-490	151	17	f	f	PROPN
ejpam-490	151	18	,	,	PUNCT
ejpam-490	151	19	g;α	g;α	PROPN
ejpam-490	151	20	,	,	PUNCT
ejpam-490	151	21	β	β	NOUN
ejpam-490	151	22	)	)	PUNCT
ejpam-490	151	23	if	if	SCONJ
ejpam-490	151	24	∞	∞	PROPN
ejpam-490	151	25	∑	∑	PROPN
ejpam-490	151	26	k=2	k=2	PROPN
ejpam-490	151	27	�	�	PROPN
ejpam-490	151	28	k(1	k(1	PROPN
ejpam-490	151	29	+	+	PROPN
ejpam-490	151	30	β)−	β)−	PROPN
ejpam-490	151	31	(	(	PUNCT
ejpam-490	151	32	α+	α+	X
ejpam-490	151	33	β	β	X
ejpam-490	151	34	)	)	PUNCT
ejpam-490	151	35	�	�	PROPN
ejpam-490	151	36	�	�	PROPN
ejpam-490	151	37	1	1	NUM
ejpam-490	151	38	+	+	CCONJ
ejpam-490	151	39	γ(k−	γ(k−	NUM
ejpam-490	151	40	1	1	NUM
ejpam-490	151	41	)	)	PUNCT
ejpam-490	151	42	�	�	PROPN
ejpam-490	151	43	�	�	PROPN
ejpam-490	151	44	�	�	PROPN
ejpam-490	151	45	ak	ak	PROPN
ejpam-490	151	46	�	�	PROPN
ejpam-490	151	47	�	�	PROPN
ejpam-490	151	48	bk	bk	VERB
ejpam-490	151	49	≤	≤	ADJ
ejpam-490	151	50	1−α	1−α	NUM
ejpam-490	151	51	,	,	PUNCT
ejpam-490	151	52	(	(	PUNCT
ejpam-490	151	53	17	17	NUM
ejpam-490	151	54	)	)	PUNCT
ejpam-490	151	55	where	where	SCONJ
ejpam-490	151	56	−1≤	−1≤	VERB
ejpam-490	151	57	α	α	NOUN
ejpam-490	151	58	<	<	X
ejpam-490	151	59	1	1	NUM
ejpam-490	151	60	,	,	PUNCT
ejpam-490	151	61	β	β	X
ejpam-490	151	62	≥	≥	NOUN
ejpam-490	151	63	0	0	NUM
ejpam-490	151	64	,	,	PUNCT
ejpam-490	151	65	0≤	0≤	NUM
ejpam-490	151	66	γ≤	γ≤	NUM
ejpam-490	151	67	1	1	NUM
ejpam-490	151	68	and	and	CCONJ
ejpam-490	151	69	bk	bk	PROPN
ejpam-490	151	70	≥	≥	NOUN
ejpam-490	151	71	b2	b2	PROPN
ejpam-490	151	72	(	(	PUNCT
ejpam-490	151	73	k	k	X
ejpam-490	151	74	≥	≥	NUM
ejpam-490	151	75	2	2	NUM
ejpam-490	151	76	)	)	PUNCT
ejpam-490	151	77	.	.	PUNCT
ejpam-490	152	1	proof	proof	NOUN
ejpam-490	152	2	.	.	PUNCT
ejpam-490	153	1	it	it	PRON
ejpam-490	153	2	suffices	suffice	VERB
ejpam-490	153	3	to	to	PART
ejpam-490	153	4	show	show	VERB
ejpam-490	153	5	that	that	SCONJ
ejpam-490	153	6	β	β	PROPN
ejpam-490	153	7	�	�	PROPN
ejpam-490	153	8	�	�	PROPN
ejpam-490	153	9	�	�	PROPN
ejpam-490	153	10	�	�	PROPN
ejpam-490	153	11	�	�	PROPN
ejpam-490	153	12	z	z	PROPN
ejpam-490	153	13	(	(	PUNCT
ejpam-490	153	14	f	f	PROPN
ejpam-490	153	15	∗	∗	PROPN
ejpam-490	153	16	g	g	NOUN
ejpam-490	153	17	)	)	PUNCT
ejpam-490	153	18	′	′	NUM
ejpam-490	154	1	(	(	PUNCT
ejpam-490	154	2	z	z	NOUN
ejpam-490	154	3	)	)	PUNCT
ejpam-490	154	4	+	+	CCONJ
ejpam-490	154	5	γz2	γz2	PROPN
ejpam-490	154	6	(	(	PUNCT
ejpam-490	154	7	f	f	PROPN
ejpam-490	154	8	∗	∗	X
ejpam-490	154	9	g	g	NOUN
ejpam-490	154	10	)	)	PUNCT
ejpam-490	155	1	′′	′′	PROPN
ejpam-490	155	2	(	(	PUNCT
ejpam-490	155	3	z	z	NOUN
ejpam-490	155	4	)	)	PUNCT
ejpam-490	155	5	(	(	PUNCT
ejpam-490	155	6	1−	1−	NUM
ejpam-490	155	7	γ	γ	X
ejpam-490	155	8	)	)	PUNCT
ejpam-490	155	9	(	(	PUNCT
ejpam-490	155	10	f	f	PROPN
ejpam-490	155	11	∗	∗	NOUN
ejpam-490	155	12	g)(z	g)(z	PUNCT
ejpam-490	155	13	)	)	PUNCT
ejpam-490	155	14	+	+	CCONJ
ejpam-490	155	15	γz	γz	X
ejpam-490	155	16	(	(	PUNCT
ejpam-490	155	17	f	f	PROPN
ejpam-490	155	18	∗	∗	PROPN
ejpam-490	155	19	g	g	NOUN
ejpam-490	155	20	)	)	PUNCT
ejpam-490	155	21	′	′	NUM
ejpam-490	156	1	(	(	PUNCT
ejpam-490	156	2	z	z	NOUN
ejpam-490	156	3	)	)	PUNCT
ejpam-490	156	4	−	−	PROPN
ejpam-490	156	5	1	1	NUM
ejpam-490	156	6	�	�	PROPN
ejpam-490	156	7	�	�	PROPN
ejpam-490	156	8	�	�	PROPN
ejpam-490	156	9	�	�	PROPN
ejpam-490	156	10	�	�	PROPN
ejpam-490	156	11	−re	−re	PROPN
ejpam-490	157	1	(	(	PUNCT
ejpam-490	157	2	z	z	X
ejpam-490	157	3	(	(	PUNCT
ejpam-490	157	4	f	f	PROPN
ejpam-490	157	5	∗	∗	PROPN
ejpam-490	157	6	g	g	NOUN
ejpam-490	157	7	)	)	PUNCT
ejpam-490	157	8	′	′	NUM
ejpam-490	158	1	(	(	PUNCT
ejpam-490	158	2	z	z	NOUN
ejpam-490	158	3	)	)	PUNCT
ejpam-490	158	4	+	+	CCONJ
ejpam-490	158	5	γz2	γz2	PROPN
ejpam-490	158	6	(	(	PUNCT
ejpam-490	158	7	f	f	PROPN
ejpam-490	158	8	∗	∗	X
ejpam-490	158	9	g	g	NOUN
ejpam-490	158	10	)	)	PUNCT
ejpam-490	159	1	′′	′′	PROPN
ejpam-490	159	2	(	(	PUNCT
ejpam-490	159	3	z	z	NOUN
ejpam-490	159	4	)	)	PUNCT
ejpam-490	159	5	(	(	PUNCT
ejpam-490	159	6	1−	1−	NUM
ejpam-490	159	7	γ	γ	X
ejpam-490	159	8	)	)	PUNCT
ejpam-490	159	9	(	(	PUNCT
ejpam-490	159	10	f	f	PROPN
ejpam-490	159	11	∗	∗	NOUN
ejpam-490	159	12	g)(z	g)(z	PUNCT
ejpam-490	159	13	)	)	PUNCT
ejpam-490	159	14	+	+	CCONJ
ejpam-490	159	15	γz	γz	X
ejpam-490	159	16	(	(	PUNCT
ejpam-490	159	17	f	f	PROPN
ejpam-490	159	18	∗	∗	PROPN
ejpam-490	159	19	g	g	NOUN
ejpam-490	159	20	)	)	PUNCT
ejpam-490	159	21	′	′	NUM
ejpam-490	160	1	(	(	PUNCT
ejpam-490	160	2	z	z	NOUN
ejpam-490	160	3	)	)	PUNCT
ejpam-490	160	4	−	−	PROPN
ejpam-490	160	5	1	1	X
ejpam-490	160	6	)	)	PUNCT
ejpam-490	160	7	≤	≤	NOUN
ejpam-490	160	8	1−α	1−α	NUM
ejpam-490	160	9	.	.	PUNCT
ejpam-490	161	1	we	we	PRON
ejpam-490	161	2	have	have	VERB
ejpam-490	161	3	β	β	X
ejpam-490	161	4	�	�	PROPN
ejpam-490	161	5	�	�	PROPN
ejpam-490	161	6	�	�	PROPN
ejpam-490	161	7	�	�	PROPN
ejpam-490	161	8	�	�	PROPN
ejpam-490	161	9	z	z	PROPN
ejpam-490	161	10	(	(	PUNCT
ejpam-490	161	11	f	f	PROPN
ejpam-490	161	12	∗	∗	PROPN
ejpam-490	161	13	g	g	NOUN
ejpam-490	161	14	)	)	PUNCT
ejpam-490	161	15	′	′	NUM
ejpam-490	162	1	(	(	PUNCT
ejpam-490	162	2	z	z	NOUN
ejpam-490	162	3	)	)	PUNCT
ejpam-490	162	4	+	+	CCONJ
ejpam-490	162	5	γz2	γz2	PROPN
ejpam-490	162	6	(	(	PUNCT
ejpam-490	162	7	f	f	PROPN
ejpam-490	162	8	∗	∗	X
ejpam-490	162	9	g	g	NOUN
ejpam-490	162	10	)	)	PUNCT
ejpam-490	163	1	′′	′′	PROPN
ejpam-490	163	2	(	(	PUNCT
ejpam-490	163	3	z	z	NOUN
ejpam-490	163	4	)	)	PUNCT
ejpam-490	163	5	(	(	PUNCT
ejpam-490	163	6	1−	1−	NUM
ejpam-490	163	7	γ	γ	X
ejpam-490	163	8	)	)	PUNCT
ejpam-490	163	9	(	(	PUNCT
ejpam-490	163	10	f	f	PROPN
ejpam-490	163	11	∗	∗	NOUN
ejpam-490	163	12	g)(z	g)(z	PUNCT
ejpam-490	163	13	)	)	PUNCT
ejpam-490	163	14	+	+	CCONJ
ejpam-490	163	15	γz	γz	X
ejpam-490	163	16	(	(	PUNCT
ejpam-490	163	17	f	f	PROPN
ejpam-490	163	18	∗	∗	PROPN
ejpam-490	163	19	g	g	NOUN
ejpam-490	163	20	)	)	PUNCT
ejpam-490	163	21	′	′	NUM
ejpam-490	164	1	(	(	PUNCT
ejpam-490	164	2	z	z	NOUN
ejpam-490	164	3	)	)	PUNCT
ejpam-490	164	4	−	−	PROPN
ejpam-490	164	5	1	1	NUM
ejpam-490	164	6	�	�	PROPN
ejpam-490	164	7	�	�	PROPN
ejpam-490	164	8	�	�	PROPN
ejpam-490	164	9	�	�	PROPN
ejpam-490	164	10	�	�	PROPN
ejpam-490	164	11	−re	−re	PROPN
ejpam-490	165	1	(	(	PUNCT
ejpam-490	165	2	z	z	X
ejpam-490	165	3	(	(	PUNCT
ejpam-490	165	4	f	f	PROPN
ejpam-490	165	5	∗	∗	PROPN
ejpam-490	165	6	g	g	NOUN
ejpam-490	165	7	)	)	PUNCT
ejpam-490	165	8	′	′	NUM
ejpam-490	166	1	(	(	PUNCT
ejpam-490	166	2	z	z	NOUN
ejpam-490	166	3	)	)	PUNCT
ejpam-490	166	4	+	+	CCONJ
ejpam-490	166	5	γz2	γz2	PROPN
ejpam-490	166	6	(	(	PUNCT
ejpam-490	166	7	f	f	PROPN
ejpam-490	166	8	∗	∗	X
ejpam-490	166	9	g	g	NOUN
ejpam-490	166	10	)	)	PUNCT
ejpam-490	167	1	′′	′′	PROPN
ejpam-490	167	2	(	(	PUNCT
ejpam-490	167	3	z	z	NOUN
ejpam-490	167	4	)	)	PUNCT
ejpam-490	167	5	(	(	PUNCT
ejpam-490	167	6	1−	1−	NUM
ejpam-490	167	7	γ	γ	X
ejpam-490	167	8	)	)	PUNCT
ejpam-490	167	9	(	(	PUNCT
ejpam-490	167	10	f	f	PROPN
ejpam-490	167	11	∗	∗	NOUN
ejpam-490	167	12	g)(z	g)(z	PUNCT
ejpam-490	167	13	)	)	PUNCT
ejpam-490	167	14	+	+	CCONJ
ejpam-490	167	15	γz	γz	X
ejpam-490	167	16	(	(	PUNCT
ejpam-490	167	17	f	f	PROPN
ejpam-490	167	18	∗	∗	PROPN
ejpam-490	167	19	g	g	NOUN
ejpam-490	167	20	)	)	PUNCT
ejpam-490	167	21	′	′	NUM
ejpam-490	168	1	(	(	PUNCT
ejpam-490	168	2	z	z	NOUN
ejpam-490	168	3	)	)	PUNCT
ejpam-490	168	4	−	−	PROPN
ejpam-490	168	5	1	1	X
ejpam-490	168	6	)	)	PUNCT
ejpam-490	168	7	≤	≤	NOUN
ejpam-490	168	8	(	(	PUNCT
ejpam-490	168	9	1	1	NUM
ejpam-490	168	10	+	+	NUM
ejpam-490	168	11	β	β	X
ejpam-490	168	12	)	)	PUNCT
ejpam-490	168	13	�	�	PROPN
ejpam-490	168	14	�	�	PROPN
ejpam-490	168	15	�	�	PROPN
ejpam-490	168	16	�	�	PROPN
ejpam-490	168	17	�	�	PROPN
ejpam-490	168	18	z	z	PROPN
ejpam-490	168	19	(	(	PUNCT
ejpam-490	168	20	f	f	PROPN
ejpam-490	168	21	∗	∗	PROPN
ejpam-490	168	22	g	g	NOUN
ejpam-490	168	23	)	)	PUNCT
ejpam-490	168	24	′	′	NUM
ejpam-490	169	1	(	(	PUNCT
ejpam-490	169	2	z	z	NOUN
ejpam-490	169	3	)	)	PUNCT
ejpam-490	169	4	+	+	CCONJ
ejpam-490	169	5	γz2	γz2	PROPN
ejpam-490	169	6	(	(	PUNCT
ejpam-490	169	7	f	f	PROPN
ejpam-490	169	8	∗	∗	X
ejpam-490	169	9	g	g	NOUN
ejpam-490	169	10	)	)	PUNCT
ejpam-490	170	1	′′	′′	PROPN
ejpam-490	170	2	(	(	PUNCT
ejpam-490	170	3	z	z	NOUN
ejpam-490	170	4	)	)	PUNCT
ejpam-490	170	5	(	(	PUNCT
ejpam-490	170	6	1−	1−	NUM
ejpam-490	170	7	γ	γ	X
ejpam-490	170	8	)	)	PUNCT
ejpam-490	170	9	(	(	PUNCT
ejpam-490	170	10	f	f	PROPN
ejpam-490	170	11	∗	∗	NOUN
ejpam-490	170	12	g)(z	g)(z	PUNCT
ejpam-490	170	13	)	)	PUNCT
ejpam-490	170	14	+	+	CCONJ
ejpam-490	170	15	γz	γz	X
ejpam-490	170	16	(	(	PUNCT
ejpam-490	170	17	f	f	PROPN
ejpam-490	170	18	∗	∗	PROPN
ejpam-490	170	19	g	g	NOUN
ejpam-490	170	20	)	)	PUNCT
ejpam-490	170	21	′	′	NUM
ejpam-490	171	1	(	(	PUNCT
ejpam-490	171	2	z	z	NOUN
ejpam-490	171	3	)	)	PUNCT
ejpam-490	171	4	−	−	PROPN
ejpam-490	171	5	1	1	NUM
ejpam-490	171	6	�	�	PROPN
ejpam-490	171	7	�	�	PROPN
ejpam-490	171	8	�	�	PROPN
ejpam-490	171	9	�	�	PROPN
ejpam-490	171	10	�	�	PROPN
ejpam-490	171	11	≤	≤	PROPN
ejpam-490	171	12	(	(	PUNCT
ejpam-490	171	13	1	1	NUM
ejpam-490	171	14	+	+	NUM
ejpam-490	171	15	β	β	NOUN
ejpam-490	171	16	)	)	PUNCT
ejpam-490	171	17	∞	∞	PROPN
ejpam-490	171	18	∑	∑	PROPN
ejpam-490	171	19	k=2	k=2	PROPN
ejpam-490	171	20	(	(	PUNCT
ejpam-490	171	21	k−	k−	PROPN
ejpam-490	171	22	1	1	NUM
ejpam-490	171	23	)	)	PUNCT
ejpam-490	171	24	�	�	NOUN
ejpam-490	171	25	1	1	NUM
ejpam-490	171	26	+	+	CCONJ
ejpam-490	171	27	γ(k−	γ(k−	NUM
ejpam-490	171	28	1	1	NUM
ejpam-490	171	29	)	)	PUNCT
ejpam-490	171	30	�	�	PROPN
ejpam-490	171	31	�	�	PROPN
ejpam-490	171	32	�	�	PROPN
ejpam-490	171	33	ak	ak	PROPN
ejpam-490	171	34	�	�	PROPN
ejpam-490	171	35	�	�	PROPN
ejpam-490	171	36	bk	bk	ADP
ejpam-490	171	37	1−	1−	NUM
ejpam-490	171	38	∞	∞	NUM
ejpam-490	171	39	∑	∑	PROPN
ejpam-490	171	40	k=2	k=2	PROPN
ejpam-490	171	41	�	�	PROPN
ejpam-490	171	42	1	1	NUM
ejpam-490	171	43	+	+	CCONJ
ejpam-490	171	44	γ(k−	γ(k−	NUM
ejpam-490	171	45	1	1	NUM
ejpam-490	171	46	)	)	PUNCT
ejpam-490	171	47	�	�	PROPN
ejpam-490	171	48	�	�	PROPN
ejpam-490	171	49	�	�	PROPN
ejpam-490	171	50	ak	ak	PROPN
ejpam-490	171	51	�	�	PROPN
ejpam-490	171	52	�	�	PROPN
ejpam-490	171	53	bk	bk	PROPN
ejpam-490	171	54	.	.	PUNCT
ejpam-490	172	1	m.	m.	PROPN
ejpam-490	172	2	aouf	aouf	PROPN
ejpam-490	172	3	,	,	PUNCT
ejpam-490	172	4	r.	r.	PROPN
ejpam-490	172	5	el	el	PROPN
ejpam-490	172	6	-	-	PUNCT
ejpam-490	172	7	ashwah	ashwah	PROPN
ejpam-490	172	8	,	,	PUNCT
ejpam-490	172	9	s.	s.	PROPN
ejpam-490	172	10	el	el	PROPN
ejpam-490	172	11	-	-	PUNCT
ejpam-490	172	12	deeb	deeb	PROPN
ejpam-490	172	13	/	/	SYM
ejpam-490	172	14	eur	eur	PROPN
ejpam-490	172	15	.	.	PUNCT
ejpam-490	173	1	j.	j.	PROPN
ejpam-490	173	2	pure	pure	PROPN
ejpam-490	173	3	appl	appl	PROPN
ejpam-490	173	4	.	.	PROPN
ejpam-490	173	5	math	math	PROPN
ejpam-490	173	6	,	,	PUNCT
ejpam-490	173	7	3	3	NUM
ejpam-490	173	8	(	(	PUNCT
ejpam-490	173	9	2010	2010	NUM
ejpam-490	173	10	)	)	PUNCT
ejpam-490	173	11	,	,	PUNCT
ejpam-490	173	12	903	903	NUM
ejpam-490	173	13	-	-	SYM
ejpam-490	173	14	917	917	NUM
ejpam-490	173	15	909	909	NUM
ejpam-490	173	16	this	this	DET
ejpam-490	173	17	last	last	ADJ
ejpam-490	173	18	expression	expression	NOUN
ejpam-490	173	19	is	be	AUX
ejpam-490	173	20	bounded	bound	VERB
ejpam-490	173	21	above	above	ADV
ejpam-490	173	22	by	by	ADP
ejpam-490	173	23	(	(	PUNCT
ejpam-490	173	24	1−α	1−α	NUM
ejpam-490	173	25	)	)	PUNCT
ejpam-490	173	26	if	if	SCONJ
ejpam-490	173	27	∞	∞	PROPN
ejpam-490	173	28	∑	∑	PROPN
ejpam-490	173	29	k=2	k=2	PROPN
ejpam-490	173	30	�	�	PROPN
ejpam-490	173	31	k(1	k(1	PROPN
ejpam-490	173	32	+	+	PROPN
ejpam-490	173	33	β)−	β)−	PROPN
ejpam-490	173	34	(	(	PUNCT
ejpam-490	173	35	α+	α+	X
ejpam-490	173	36	β	β	X
ejpam-490	173	37	)	)	PUNCT
ejpam-490	173	38	�	�	PROPN
ejpam-490	173	39	�	�	PROPN
ejpam-490	173	40	1	1	NUM
ejpam-490	173	41	+	+	CCONJ
ejpam-490	173	42	γ(k−	γ(k−	NUM
ejpam-490	173	43	1	1	NUM
ejpam-490	173	44	)	)	PUNCT
ejpam-490	173	45	�	�	PROPN
ejpam-490	173	46	�	�	PROPN
ejpam-490	173	47	�	�	PROPN
ejpam-490	173	48	ak	ak	PROPN
ejpam-490	173	49	�	�	PROPN
ejpam-490	173	50	�	�	PROPN
ejpam-490	173	51	bk	bk	VERB
ejpam-490	173	52	≤	≤	ADJ
ejpam-490	173	53	1−α	1−α	NUM
ejpam-490	173	54	,	,	PUNCT
ejpam-490	173	55	and	and	CCONJ
ejpam-490	173	56	hence	hence	ADV
ejpam-490	173	57	the	the	DET
ejpam-490	173	58	proof	proof	NOUN
ejpam-490	173	59	is	be	AUX
ejpam-490	173	60	completed	complete	VERB
ejpam-490	173	61	.	.	PUNCT
ejpam-490	174	1	let	let	VERB
ejpam-490	174	2	s∗γ	s∗γ	NUM
ejpam-490	174	3	(	(	PUNCT
ejpam-490	174	4	f	f	PROPN
ejpam-490	174	5	,	,	PUNCT
ejpam-490	174	6	g;α	g;α	PROPN
ejpam-490	174	7	,	,	PUNCT
ejpam-490	174	8	β	β	NOUN
ejpam-490	174	9	)	)	PUNCT
ejpam-490	174	10	denote	denote	VERB
ejpam-490	174	11	the	the	DET
ejpam-490	174	12	class	class	NOUN
ejpam-490	174	13	of	of	ADP
ejpam-490	174	14	f	f	PROPN
ejpam-490	174	15	(	(	PUNCT
ejpam-490	174	16	z	z	NOUN
ejpam-490	174	17	)	)	PUNCT
ejpam-490	174	18	∈	∈	PROPN
ejpam-490	174	19	a	a	PRON
ejpam-490	174	20	whose	whose	DET
ejpam-490	174	21	coefficients	coefficient	NOUN
ejpam-490	174	22	satisfy	satisfy	VERB
ejpam-490	174	23	the	the	DET
ejpam-490	174	24	condition	condition	NOUN
ejpam-490	174	25	(	(	PUNCT
ejpam-490	174	26	17	17	NUM
ejpam-490	174	27	)	)	PUNCT
ejpam-490	174	28	.	.	PUNCT
ejpam-490	175	1	we	we	PRON
ejpam-490	175	2	note	note	VERB
ejpam-490	175	3	that	that	SCONJ
ejpam-490	175	4	s∗γ	s∗γ	ADV
ejpam-490	175	5	(	(	PUNCT
ejpam-490	175	6	f	f	PROPN
ejpam-490	175	7	,	,	PUNCT
ejpam-490	175	8	g;α	g;α	PROPN
ejpam-490	175	9	,	,	PUNCT
ejpam-490	175	10	β	β	NOUN
ejpam-490	175	11	)	)	PUNCT
ejpam-490	175	12	⊆	⊆	NUM
ejpam-490	175	13	sγ	sγ	NOUN
ejpam-490	175	14	(	(	PUNCT
ejpam-490	175	15	f	f	PROPN
ejpam-490	175	16	,	,	PUNCT
ejpam-490	175	17	g;α	g;α	PROPN
ejpam-490	175	18	,	,	PUNCT
ejpam-490	175	19	β	β	NOUN
ejpam-490	175	20	)	)	PUNCT
ejpam-490	175	21	.	.	PUNCT
ejpam-490	176	1	employing	employ	VERB
ejpam-490	176	2	the	the	DET
ejpam-490	176	3	technique	technique	NOUN
ejpam-490	176	4	used	use	VERB
ejpam-490	176	5	earlier	early	ADV
ejpam-490	176	6	by	by	ADP
ejpam-490	176	7	attiya	attiya	PROPN
ejpam-490	177	1	[	[	X
ejpam-490	177	2	3	3	NUM
ejpam-490	177	3	]	]	PUNCT
ejpam-490	177	4	and	and	CCONJ
ejpam-490	177	5	srivastava	srivastava	PROPN
ejpam-490	177	6	and	and	CCONJ
ejpam-490	177	7	attiya	attiya	VERB
ejpam-490	177	8	[	[	X
ejpam-490	177	9	23	23	NUM
ejpam-490	177	10	]	]	PUNCT
ejpam-490	177	11	,	,	PUNCT
ejpam-490	177	12	we	we	PRON
ejpam-490	177	13	prove	prove	VERB
ejpam-490	177	14	:	:	PUNCT
ejpam-490	177	15	theorem	theorem	NOUN
ejpam-490	177	16	1	1	NUM
ejpam-490	177	17	.	.	PUNCT
ejpam-490	178	1	let	let	VERB
ejpam-490	178	2	f	f	PROPN
ejpam-490	178	3	(	(	PUNCT
ejpam-490	178	4	z	z	X
ejpam-490	178	5	)	)	PUNCT
ejpam-490	178	6	∈	∈	PROPN
ejpam-490	178	7	s∗γ	s∗γ	NUM
ejpam-490	178	8	(	(	PUNCT
ejpam-490	178	9	f	f	PROPN
ejpam-490	178	10	,	,	PUNCT
ejpam-490	178	11	g;α	g;α	PROPN
ejpam-490	178	12	,	,	PUNCT
ejpam-490	178	13	β	β	NOUN
ejpam-490	178	14	)	)	PUNCT
ejpam-490	178	15	.	.	PUNCT
ejpam-490	179	1	then	then	ADV
ejpam-490	179	2	(	(	PUNCT
ejpam-490	179	3	2	2	NUM
ejpam-490	179	4	+	+	CCONJ
ejpam-490	179	5	β	β	NOUN
ejpam-490	179	6	−α)(1	−α)(1	NOUN
ejpam-490	179	7	+	+	CCONJ
ejpam-490	179	8	γ)b2	γ)b2	PROPN
ejpam-490	179	9	2	2	NUM
ejpam-490	179	10	�	�	PROPN
ejpam-490	179	11	(	(	PUNCT
ejpam-490	179	12	2	2	NUM
ejpam-490	179	13	+	+	CCONJ
ejpam-490	179	14	β	β	NOUN
ejpam-490	179	15	−α)(1	−α)(1	NOUN
ejpam-490	179	16	+	+	CCONJ
ejpam-490	179	17	γ)b2	γ)b2	PROPN
ejpam-490	179	18	+	+	CCONJ
ejpam-490	179	19	(	(	PUNCT
ejpam-490	179	20	1−α	1−α	NUM
ejpam-490	179	21	)	)	PUNCT
ejpam-490	179	22	�	�	PROPN
ejpam-490	179	23	(	(	PUNCT
ejpam-490	179	24	f	f	PROPN
ejpam-490	179	25	∗	∗	VERB
ejpam-490	179	26	h)(z)≺	h)(z)≺	PROPN
ejpam-490	179	27	h(z	h(z	NOUN
ejpam-490	179	28	)	)	PUNCT
ejpam-490	179	29	(	(	PUNCT
ejpam-490	179	30	z	z	NOUN
ejpam-490	179	31	∈	∈	PROPN
ejpam-490	179	32	u	u	NOUN
ejpam-490	179	33	)	)	PUNCT
ejpam-490	179	34	,	,	PUNCT
ejpam-490	179	35	(	(	PUNCT
ejpam-490	179	36	18	18	NUM
ejpam-490	179	37	)	)	PUNCT
ejpam-490	179	38	for	for	ADP
ejpam-490	179	39	every	every	DET
ejpam-490	179	40	function	function	NOUN
ejpam-490	179	41	h	h	NOUN
ejpam-490	179	42	in	in	ADP
ejpam-490	179	43	k	k	PROPN
ejpam-490	179	44	,	,	PUNCT
ejpam-490	179	45	and	and	CCONJ
ejpam-490	179	46	re	re	VERB
ejpam-490	179	47	(	(	PUNCT
ejpam-490	179	48	f	f	PROPN
ejpam-490	179	49	(	(	PUNCT
ejpam-490	179	50	z	z	NOUN
ejpam-490	179	51	)	)	PUNCT
ejpam-490	179	52	)	)	PUNCT
ejpam-490	179	53	>	>	X
ejpam-490	180	1	−	−	PROPN
ejpam-490	180	2	�	�	PROPN
ejpam-490	180	3	(	(	PUNCT
ejpam-490	180	4	2	2	NUM
ejpam-490	180	5	+	+	CCONJ
ejpam-490	180	6	β	β	NOUN
ejpam-490	180	7	−α)(1	−α)(1	NOUN
ejpam-490	180	8	+	+	CCONJ
ejpam-490	180	9	γ)b2	γ)b2	PROPN
ejpam-490	180	10	+	+	CCONJ
ejpam-490	180	11	(	(	PUNCT
ejpam-490	180	12	1−α	1−α	NUM
ejpam-490	180	13	)	)	PUNCT
ejpam-490	180	14	�	�	PROPN
ejpam-490	180	15	(	(	PUNCT
ejpam-490	180	16	2	2	NUM
ejpam-490	180	17	+	+	CCONJ
ejpam-490	180	18	β	β	NOUN
ejpam-490	180	19	−α)(1	−α)(1	NOUN
ejpam-490	180	20	+	+	X
ejpam-490	180	21	γ)b2	γ)b2	PROPN
ejpam-490	180	22	,	,	PUNCT
ejpam-490	180	23	(	(	PUNCT
ejpam-490	180	24	z	z	NOUN
ejpam-490	180	25	∈	∈	PROPN
ejpam-490	180	26	u	u	NOUN
ejpam-490	180	27	)	)	PUNCT
ejpam-490	180	28	.	.	PUNCT
ejpam-490	181	1	(	(	PUNCT
ejpam-490	181	2	19	19	NUM
ejpam-490	181	3	)	)	PUNCT
ejpam-490	181	4	the	the	DET
ejpam-490	181	5	constant	constant	ADJ
ejpam-490	181	6	factor	factor	NOUN
ejpam-490	181	7	(	(	PUNCT
ejpam-490	181	8	2+β−α)(1+γ)b2	2+β−α)(1+γ)b2	NUM
ejpam-490	181	9	2[(2+β−α)(1+γ)b2+(1−α	2[(2+β−α)(1+γ)b2+(1−α	NUM
ejpam-490	181	10	)	)	PUNCT
ejpam-490	181	11	]	]	PUNCT
ejpam-490	181	12	in	in	ADP
ejpam-490	181	13	the	the	DET
ejpam-490	181	14	subordination	subordination	NOUN
ejpam-490	181	15	result	result	NOUN
ejpam-490	181	16	(	(	PUNCT
ejpam-490	181	17	18	18	NUM
ejpam-490	181	18	)	)	PUNCT
ejpam-490	181	19	can	can	AUX
ejpam-490	181	20	not	not	PART
ejpam-490	181	21	be	be	AUX
ejpam-490	181	22	replaced	replace	VERB
ejpam-490	181	23	by	by	ADP
ejpam-490	181	24	a	a	DET
ejpam-490	181	25	larger	large	ADJ
ejpam-490	181	26	one	one	NOUN
ejpam-490	181	27	.	.	PUNCT
ejpam-490	182	1	proof	proof	NOUN
ejpam-490	182	2	.	.	PUNCT
ejpam-490	183	1	let	let	VERB
ejpam-490	183	2	f	f	PROPN
ejpam-490	183	3	(	(	PUNCT
ejpam-490	183	4	z	z	X
ejpam-490	183	5	)	)	PUNCT
ejpam-490	183	6	∈	∈	PROPN
ejpam-490	183	7	s∗γ	s∗γ	NUM
ejpam-490	183	8	(	(	PUNCT
ejpam-490	183	9	f	f	PROPN
ejpam-490	183	10	,	,	PUNCT
ejpam-490	183	11	g;α	g;α	PROPN
ejpam-490	183	12	,	,	PUNCT
ejpam-490	183	13	β	β	NOUN
ejpam-490	183	14	)	)	PUNCT
ejpam-490	183	15	and	and	CCONJ
ejpam-490	183	16	let	let	VERB
ejpam-490	183	17	h(z	h(z	NOUN
ejpam-490	183	18	)	)	PUNCT
ejpam-490	183	19	=	=	SYM
ejpam-490	184	1	z	z	NOUN
ejpam-490	185	1	+	+	NUM
ejpam-490	185	2	∞	∞	NUM
ejpam-490	185	3	∑	∑	PROPN
ejpam-490	185	4	k=2	k=2	PROPN
ejpam-490	185	5	ckzk	ckzk	PROPN
ejpam-490	185	6	∈	∈	PROPN
ejpam-490	185	7	k	k	PROPN
ejpam-490	185	8	.	.	PUNCT
ejpam-490	186	1	then	then	ADV
ejpam-490	186	2	we	we	PRON
ejpam-490	186	3	have	have	VERB
ejpam-490	186	4	(	(	PUNCT
ejpam-490	186	5	2	2	NUM
ejpam-490	186	6	+	+	CCONJ
ejpam-490	186	7	β	β	NOUN
ejpam-490	186	8	−α)(1	−α)(1	NOUN
ejpam-490	186	9	+	+	CCONJ
ejpam-490	186	10	γ)b2	γ)b2	PROPN
ejpam-490	186	11	2	2	NUM
ejpam-490	186	12	�	�	PROPN
ejpam-490	186	13	(	(	PUNCT
ejpam-490	186	14	2	2	NUM
ejpam-490	186	15	+	+	CCONJ
ejpam-490	186	16	β	β	NOUN
ejpam-490	186	17	−α)(1	−α)(1	NOUN
ejpam-490	187	1	+	+	CCONJ
ejpam-490	187	2	γ)b2	γ)b2	PROPN
ejpam-490	187	3	+	+	CCONJ
ejpam-490	187	4	(	(	PUNCT
ejpam-490	187	5	1−α	1−α	NUM
ejpam-490	187	6	)	)	PUNCT
ejpam-490	187	7	�	�	PROPN
ejpam-490	187	8	(	(	PUNCT
ejpam-490	187	9	f	f	PROPN
ejpam-490	187	10	∗	∗	NOUN
ejpam-490	187	11	h)(z	h)(z	NOUN
ejpam-490	187	12	)	)	PUNCT
ejpam-490	187	13	=	=	SYM
ejpam-490	188	1	(	(	PUNCT
ejpam-490	188	2	2+β	2+β	NUM
ejpam-490	188	3	−α)(1	−α)(1	NOUN
ejpam-490	188	4	+	+	X
ejpam-490	188	5	γ)b2	γ)b2	PROPN
ejpam-490	188	6	2	2	NUM
ejpam-490	188	7	�	�	PROPN
ejpam-490	188	8	(	(	PUNCT
ejpam-490	188	9	2	2	NUM
ejpam-490	188	10	+	+	CCONJ
ejpam-490	188	11	β	β	NOUN
ejpam-490	188	12	−α)(1	−α)(1	NOUN
ejpam-490	188	13	+	+	X
ejpam-490	188	14	γ)b2	γ)b2	PROPN
ejpam-490	188	15	+	+	CCONJ
ejpam-490	188	16	(	(	PUNCT
ejpam-490	188	17	1−α	1−α	NUM
ejpam-490	188	18	)	)	PUNCT
ejpam-490	188	19	�	�	PROPN
ejpam-490	188	20	z	z	PROPN
ejpam-490	188	21	+	+	CCONJ
ejpam-490	188	22	∞	∞	PROPN
ejpam-490	188	23	∑	∑	PROPN
ejpam-490	188	24	k=2	k=2	PROPN
ejpam-490	188	25	akckzk	akckzk	PROPN
ejpam-490	188	26	!	!	PUNCT
ejpam-490	188	27	.	.	PUNCT
ejpam-490	189	1	(	(	PUNCT
ejpam-490	189	2	20	20	NUM
ejpam-490	189	3	)	)	PUNCT
ejpam-490	189	4	thus	thus	ADV
ejpam-490	189	5	,	,	PUNCT
ejpam-490	189	6	by	by	ADP
ejpam-490	189	7	definition	definition	NOUN
ejpam-490	189	8	3	3	NUM
ejpam-490	189	9	,	,	PUNCT
ejpam-490	189	10	the	the	DET
ejpam-490	189	11	subordination	subordination	NOUN
ejpam-490	189	12	result	result	VERB
ejpam-490	189	13	(	(	PUNCT
ejpam-490	189	14	18	18	NUM
ejpam-490	189	15	)	)	PUNCT
ejpam-490	189	16	will	will	AUX
ejpam-490	189	17	hold	hold	VERB
ejpam-490	189	18	true	true	ADJ
ejpam-490	189	19	if	if	SCONJ
ejpam-490	189	20	the	the	DET
ejpam-490	189	21	sequence	sequence	NOUN
ejpam-490	189	22	¨	¨	NOUN
ejpam-490	189	23	(	(	PUNCT
ejpam-490	189	24	2	2	NUM
ejpam-490	189	25	+	+	CCONJ
ejpam-490	189	26	β	β	NOUN
ejpam-490	189	27	−α)(1	−α)(1	NOUN
ejpam-490	189	28	+	+	CCONJ
ejpam-490	189	29	γ)b2	γ)b2	PROPN
ejpam-490	189	30	2	2	NUM
ejpam-490	189	31	�	�	PROPN
ejpam-490	189	32	(	(	PUNCT
ejpam-490	189	33	2	2	NUM
ejpam-490	189	34	+	+	CCONJ
ejpam-490	189	35	β	β	NOUN
ejpam-490	189	36	−α)(1	−α)(1	NOUN
ejpam-490	189	37	+	+	X
ejpam-490	189	38	γ)b2	γ)b2	PROPN
ejpam-490	189	39	+	+	CCONJ
ejpam-490	189	40	(	(	PUNCT
ejpam-490	189	41	1−α	1−α	NUM
ejpam-490	189	42	)	)	PUNCT
ejpam-490	189	43	�	�	PROPN
ejpam-490	189	44	ak	ak	PROPN
ejpam-490	189	45	«	«	PUNCT
ejpam-490	189	46	∞	∞	PROPN
ejpam-490	189	47	k=1	k=1	X
ejpam-490	189	48	(	(	PUNCT
ejpam-490	189	49	21	21	NUM
ejpam-490	189	50	)	)	PUNCT
ejpam-490	189	51	is	be	AUX
ejpam-490	189	52	a	a	DET
ejpam-490	189	53	subordinating	subordinate	VERB
ejpam-490	189	54	factor	factor	NOUN
ejpam-490	189	55	sequence	sequence	NOUN
ejpam-490	189	56	,	,	PUNCT
ejpam-490	189	57	with	with	ADP
ejpam-490	189	58	a1	a1	NOUN
ejpam-490	189	59	=	=	SYM
ejpam-490	189	60	1	1	X
ejpam-490	189	61	.	.	PUNCT
ejpam-490	190	1	in	in	ADP
ejpam-490	190	2	view	view	NOUN
ejpam-490	190	3	of	of	ADP
ejpam-490	190	4	lemma	lemma	PROPN
ejpam-490	190	5	1	1	NUM
ejpam-490	190	6	,	,	PUNCT
ejpam-490	190	7	this	this	PRON
ejpam-490	190	8	is	be	AUX
ejpam-490	190	9	equivalent	equivalent	ADJ
ejpam-490	190	10	to	to	ADP
ejpam-490	190	11	the	the	DET
ejpam-490	190	12	following	follow	VERB
ejpam-490	190	13	inequality	inequality	NOUN
ejpam-490	190	14	:	:	PUNCT
ejpam-490	190	15	re	re	X
ejpam-490	190	16	(	(	PUNCT
ejpam-490	190	17	1	1	NUM
ejpam-490	190	18	+	+	NUM
ejpam-490	190	19	∞	∞	NUM
ejpam-490	190	20	∑	∑	PUNCT
ejpam-490	190	21	k=1	k=1	X
ejpam-490	190	22	(	(	PUNCT
ejpam-490	190	23	2	2	NUM
ejpam-490	190	24	+	+	CCONJ
ejpam-490	190	25	β	β	NOUN
ejpam-490	190	26	−α)(1	−α)(1	NOUN
ejpam-490	190	27	+	+	ADJ
ejpam-490	190	28	γ)b2	γ)b2	PROPN
ejpam-490	190	29	�	�	PROPN
ejpam-490	190	30	(	(	PUNCT
ejpam-490	190	31	2	2	NUM
ejpam-490	190	32	+	+	CCONJ
ejpam-490	190	33	β	β	NOUN
ejpam-490	190	34	−α)(1	−α)(1	NOUN
ejpam-490	190	35	+	+	X
ejpam-490	190	36	γ)b2	γ)b2	PROPN
ejpam-490	190	37	+	+	CCONJ
ejpam-490	190	38	(	(	PUNCT
ejpam-490	190	39	1−α	1−α	NUM
ejpam-490	190	40	)	)	PUNCT
ejpam-490	190	41	�	�	NOUN
ejpam-490	190	42	akzk	akzk	NOUN
ejpam-490	190	43	)	)	PUNCT
ejpam-490	190	44	>	>	X
ejpam-490	190	45	0	0	PUNCT
ejpam-490	191	1	(	(	PUNCT
ejpam-490	191	2	z	z	NOUN
ejpam-490	191	3	∈	∈	PROPN
ejpam-490	191	4	u	u	NOUN
ejpam-490	191	5	)	)	PUNCT
ejpam-490	191	6	.	.	PUNCT
ejpam-490	192	1	(	(	PUNCT
ejpam-490	192	2	22	22	NUM
ejpam-490	192	3	)	)	PUNCT
ejpam-490	192	4	now	now	ADV
ejpam-490	192	5	,	,	PUNCT
ejpam-490	192	6	since	since	SCONJ
ejpam-490	192	7	ψ(k	ψ(k	PROPN
ejpam-490	192	8	)	)	PUNCT
ejpam-490	192	9	=	=	SYM
ejpam-490	192	10	�	�	PROPN
ejpam-490	192	11	k(1	k(1	PROPN
ejpam-490	192	12	+	+	PROPN
ejpam-490	192	13	β)−	β)−	PROPN
ejpam-490	192	14	(	(	PUNCT
ejpam-490	192	15	α+	α+	X
ejpam-490	192	16	β	β	X
ejpam-490	192	17	)	)	PUNCT
ejpam-490	192	18	�	�	PROPN
ejpam-490	192	19	�	�	PROPN
ejpam-490	192	20	1	1	NUM
ejpam-490	192	21	+	+	CCONJ
ejpam-490	192	22	γ(k−	γ(k−	NUM
ejpam-490	192	23	1	1	NUM
ejpam-490	192	24	)	)	PUNCT
ejpam-490	192	25	�	�	PROPN
ejpam-490	192	26	bk	bk	PROPN
ejpam-490	192	27	m.	m.	PROPN
ejpam-490	192	28	aouf	aouf	PROPN
ejpam-490	192	29	,	,	PUNCT
ejpam-490	192	30	r.	r.	PROPN
ejpam-490	192	31	el	el	PROPN
ejpam-490	192	32	-	-	PUNCT
ejpam-490	192	33	ashwah	ashwah	PROPN
ejpam-490	192	34	,	,	PUNCT
ejpam-490	192	35	s.	s.	PROPN
ejpam-490	192	36	el	el	PROPN
ejpam-490	192	37	-	-	PUNCT
ejpam-490	192	38	deeb	deeb	PROPN
ejpam-490	192	39	/	/	SYM
ejpam-490	192	40	eur	eur	PROPN
ejpam-490	192	41	.	.	PUNCT
ejpam-490	193	1	j.	j.	PROPN
ejpam-490	193	2	pure	pure	PROPN
ejpam-490	193	3	appl	appl	PROPN
ejpam-490	193	4	.	.	PROPN
ejpam-490	193	5	math	math	PROPN
ejpam-490	193	6	,	,	PUNCT
ejpam-490	193	7	3	3	NUM
ejpam-490	193	8	(	(	PUNCT
ejpam-490	193	9	2010	2010	NUM
ejpam-490	193	10	)	)	PUNCT
ejpam-490	193	11	,	,	PUNCT
ejpam-490	193	12	903	903	NUM
ejpam-490	193	13	-	-	SYM
ejpam-490	193	14	917	917	NUM
ejpam-490	193	15	910	910	NUM
ejpam-490	193	16	is	be	AUX
ejpam-490	193	17	an	an	DET
ejpam-490	193	18	increasing	increase	VERB
ejpam-490	193	19	function	function	NOUN
ejpam-490	193	20	of	of	ADP
ejpam-490	193	21	k	k	PROPN
ejpam-490	193	22	(	(	PUNCT
ejpam-490	193	23	k	k	X
ejpam-490	193	24	≥	≥	NUM
ejpam-490	193	25	2	2	NUM
ejpam-490	193	26	)	)	PUNCT
ejpam-490	193	27	,	,	PUNCT
ejpam-490	193	28	we	we	PRON
ejpam-490	193	29	have	have	AUX
ejpam-490	193	30	re	re	VERB
ejpam-490	193	31	(	(	PUNCT
ejpam-490	193	32	1	1	NUM
ejpam-490	193	33	+	+	NUM
ejpam-490	193	34	∞	∞	NUM
ejpam-490	193	35	∑	∑	PUNCT
ejpam-490	193	36	k=1	k=1	X
ejpam-490	193	37	(	(	PUNCT
ejpam-490	193	38	2	2	NUM
ejpam-490	193	39	+	+	CCONJ
ejpam-490	193	40	β	β	NOUN
ejpam-490	193	41	−α)(1	−α)(1	NOUN
ejpam-490	193	42	+	+	ADJ
ejpam-490	193	43	γ)b2	γ)b2	PROPN
ejpam-490	193	44	�	�	PROPN
ejpam-490	193	45	(	(	PUNCT
ejpam-490	193	46	2+β	2+β	NUM
ejpam-490	193	47	−α)(1	−α)(1	NOUN
ejpam-490	193	48	+	+	X
ejpam-490	193	49	γ)b2	γ)b2	PROPN
ejpam-490	193	50	+	+	CCONJ
ejpam-490	193	51	(	(	PUNCT
ejpam-490	193	52	1−α	1−α	NUM
ejpam-490	193	53	)	)	PUNCT
ejpam-490	193	54	�	�	NOUN
ejpam-490	193	55	akzk	akzk	NOUN
ejpam-490	193	56	)	)	PUNCT
ejpam-490	194	1	=	=	PUNCT
ejpam-490	194	2	re	re	ADP
ejpam-490	194	3	¨	¨	NOUN
ejpam-490	194	4	1	1	NUM
ejpam-490	194	5	+	+	CCONJ
ejpam-490	194	6	(	(	PUNCT
ejpam-490	194	7	2	2	NUM
ejpam-490	194	8	+	+	CCONJ
ejpam-490	194	9	β	β	NOUN
ejpam-490	194	10	−α)(1	−α)(1	NOUN
ejpam-490	194	11	+	+	ADJ
ejpam-490	194	12	γ)b2	γ)b2	PROPN
ejpam-490	194	13	�	�	PROPN
ejpam-490	194	14	(	(	PUNCT
ejpam-490	194	15	2	2	NUM
ejpam-490	194	16	+	+	CCONJ
ejpam-490	194	17	β	β	NOUN
ejpam-490	194	18	−α)(1	−α)(1	NOUN
ejpam-490	194	19	+	+	X
ejpam-490	194	20	γ)b2	γ)b2	PROPN
ejpam-490	194	21	+	+	CCONJ
ejpam-490	194	22	(	(	PUNCT
ejpam-490	194	23	1−α	1−α	NUM
ejpam-490	194	24	)	)	PUNCT
ejpam-490	194	25	�	�	PROPN
ejpam-490	194	26	z	z	PROPN
ejpam-490	194	27	+	+	CCONJ
ejpam-490	194	28	1	1	NUM
ejpam-490	194	29	�	�	PROPN
ejpam-490	194	30	(	(	PUNCT
ejpam-490	194	31	2	2	NUM
ejpam-490	194	32	+	+	CCONJ
ejpam-490	194	33	β	β	NOUN
ejpam-490	194	34	−α)(1	−α)(1	NOUN
ejpam-490	194	35	+	+	CCONJ
ejpam-490	194	36	γ)b2	γ)b2	PROPN
ejpam-490	194	37	+	+	CCONJ
ejpam-490	194	38	(	(	PUNCT
ejpam-490	194	39	1−α	1−α	NUM
ejpam-490	194	40	)	)	PUNCT
ejpam-490	194	41	�	�	PROPN
ejpam-490	194	42	∞	∞	PROPN
ejpam-490	194	43	∑	∑	PROPN
ejpam-490	194	44	k=2	k=2	PROPN
ejpam-490	194	45	(	(	PUNCT
ejpam-490	194	46	2	2	NUM
ejpam-490	194	47	+	+	CCONJ
ejpam-490	194	48	β	β	X
ejpam-490	194	49	−α)(1	−α)(1	NOUN
ejpam-490	194	50	+	+	NUM
ejpam-490	194	51	γ)b2akzk	γ)b2akzk	ADJ
ejpam-490	194	52	«	«	PUNCT
ejpam-490	194	53	≥	≥	NUM
ejpam-490	194	54	1−	1−	NUM
ejpam-490	194	55	(	(	PUNCT
ejpam-490	194	56	2	2	NUM
ejpam-490	194	57	+	+	CCONJ
ejpam-490	194	58	β	β	NOUN
ejpam-490	194	59	−α)(1	−α)(1	NOUN
ejpam-490	194	60	+	+	ADJ
ejpam-490	194	61	γ)b2	γ)b2	PROPN
ejpam-490	194	62	�	�	PROPN
ejpam-490	194	63	(	(	PUNCT
ejpam-490	194	64	2	2	NUM
ejpam-490	194	65	+	+	CCONJ
ejpam-490	194	66	β	β	NOUN
ejpam-490	194	67	−α)(1	−α)(1	NOUN
ejpam-490	194	68	+	+	X
ejpam-490	194	69	γ)b2	γ)b2	PROPN
ejpam-490	194	70	+	+	CCONJ
ejpam-490	194	71	(	(	PUNCT
ejpam-490	194	72	1−α	1−α	NUM
ejpam-490	194	73	)	)	PUNCT
ejpam-490	194	74	�	�	PROPN
ejpam-490	194	75	r	r	NOUN
ejpam-490	194	76	−	−	PROPN
ejpam-490	194	77	1	1	NUM
ejpam-490	194	78	�	�	PROPN
ejpam-490	194	79	(	(	PUNCT
ejpam-490	194	80	2	2	NUM
ejpam-490	194	81	+	+	CCONJ
ejpam-490	194	82	β	β	NOUN
ejpam-490	194	83	−α)(1	−α)(1	NOUN
ejpam-490	194	84	+	+	CCONJ
ejpam-490	194	85	γ)b2	γ)b2	PROPN
ejpam-490	194	86	+	+	CCONJ
ejpam-490	194	87	(	(	PUNCT
ejpam-490	194	88	1−α	1−α	NUM
ejpam-490	194	89	)	)	PUNCT
ejpam-490	194	90	�	�	PROPN
ejpam-490	194	91	∞	∞	PROPN
ejpam-490	194	92	∑	∑	PROPN
ejpam-490	194	93	k=2	k=2	PROPN
ejpam-490	194	94	�	�	PROPN
ejpam-490	194	95	k(1+β)−	k(1+β)−	PROPN
ejpam-490	194	96	(	(	PUNCT
ejpam-490	194	97	α+	α+	X
ejpam-490	194	98	β	β	X
ejpam-490	194	99	)	)	PUNCT
ejpam-490	194	100	�	�	PROPN
ejpam-490	194	101	�	�	PROPN
ejpam-490	194	102	1	1	NUM
ejpam-490	194	103	+	+	CCONJ
ejpam-490	194	104	γ(k−	γ(k−	NUM
ejpam-490	194	105	1	1	NUM
ejpam-490	194	106	)	)	PUNCT
ejpam-490	194	107	�	�	PROPN
ejpam-490	194	108	bk	bk	ADP
ejpam-490	194	109	�	�	PROPN
ejpam-490	194	110	�	�	PROPN
ejpam-490	194	111	ak	ak	PROPN
ejpam-490	194	112	�	�	PROPN
ejpam-490	194	113	�	�	PROPN
ejpam-490	194	114	rk	rk	VERB
ejpam-490	194	115	>	>	X
ejpam-490	194	116	1−	1−	NUM
ejpam-490	194	117	(	(	PUNCT
ejpam-490	194	118	2	2	NUM
ejpam-490	194	119	+	+	CCONJ
ejpam-490	194	120	β	β	NOUN
ejpam-490	194	121	−α)(1	−α)(1	NOUN
ejpam-490	194	122	+	+	ADJ
ejpam-490	194	123	γ)b2	γ)b2	PROPN
ejpam-490	194	124	�	�	PROPN
ejpam-490	194	125	(	(	PUNCT
ejpam-490	194	126	2	2	NUM
ejpam-490	194	127	+	+	CCONJ
ejpam-490	194	128	β	β	NOUN
ejpam-490	194	129	−α)(1	−α)(1	NOUN
ejpam-490	194	130	+	+	X
ejpam-490	194	131	γ)b2	γ)b2	PROPN
ejpam-490	194	132	+	+	CCONJ
ejpam-490	194	133	(	(	PUNCT
ejpam-490	194	134	1−α	1−α	NUM
ejpam-490	194	135	)	)	PUNCT
ejpam-490	194	136	�	�	PROPN
ejpam-490	194	137	r	r	NOUN
ejpam-490	194	138	−	−	PROPN
ejpam-490	194	139	(	(	PUNCT
ejpam-490	194	140	1−α	1−α	NUM
ejpam-490	194	141	)	)	PUNCT
ejpam-490	194	142	�	�	PROPN
ejpam-490	194	143	(	(	PUNCT
ejpam-490	194	144	2	2	NUM
ejpam-490	194	145	+	+	CCONJ
ejpam-490	194	146	β	β	NOUN
ejpam-490	194	147	−α)(1	−α)(1	NOUN
ejpam-490	194	148	+	+	X
ejpam-490	194	149	γ)b2	γ)b2	PROPN
ejpam-490	194	150	+	+	CCONJ
ejpam-490	194	151	(	(	PUNCT
ejpam-490	194	152	1−α	1−α	NUM
ejpam-490	194	153	)	)	PUNCT
ejpam-490	194	154	�	�	PROPN
ejpam-490	194	155	r	r	NOUN
ejpam-490	194	156	=	=	SYM
ejpam-490	194	157	1−	1−	NUM
ejpam-490	194	158	r	r	NOUN
ejpam-490	194	159	>	>	X
ejpam-490	194	160	0	0	PUNCT
ejpam-490	194	161	(	(	PUNCT
ejpam-490	194	162	|z|	|z|	NOUN
ejpam-490	194	163	=	=	SYM
ejpam-490	194	164	r	r	NOUN
ejpam-490	194	165	<	<	X
ejpam-490	194	166	1	1	NUM
ejpam-490	194	167	)	)	PUNCT
ejpam-490	194	168	,	,	PUNCT
ejpam-490	194	169	where	where	SCONJ
ejpam-490	194	170	we	we	PRON
ejpam-490	194	171	have	have	AUX
ejpam-490	194	172	also	also	ADV
ejpam-490	194	173	made	make	VERB
ejpam-490	194	174	use	use	NOUN
ejpam-490	194	175	of	of	ADP
ejpam-490	194	176	assertion	assertion	NOUN
ejpam-490	194	177	(	(	PUNCT
ejpam-490	194	178	17	17	NUM
ejpam-490	194	179	)	)	PUNCT
ejpam-490	194	180	of	of	ADP
ejpam-490	194	181	lemma	lemma	PROPN
ejpam-490	194	182	2	2	NUM
ejpam-490	194	183	.	.	PUNCT
ejpam-490	195	1	thus	thus	ADV
ejpam-490	195	2	(	(	PUNCT
ejpam-490	195	3	22	22	NUM
ejpam-490	195	4	)	)	PUNCT
ejpam-490	195	5	holds	hold	VERB
ejpam-490	195	6	true	true	ADJ
ejpam-490	195	7	in	in	ADP
ejpam-490	195	8	u	u	PROPN
ejpam-490	195	9	.	.	PUNCT
ejpam-490	196	1	this	this	PRON
ejpam-490	196	2	proves	prove	VERB
ejpam-490	196	3	the	the	DET
ejpam-490	196	4	inequality	inequality	NOUN
ejpam-490	196	5	(	(	PUNCT
ejpam-490	196	6	18	18	NUM
ejpam-490	196	7	)	)	PUNCT
ejpam-490	196	8	.	.	PUNCT
ejpam-490	197	1	the	the	DET
ejpam-490	197	2	inequality	inequality	NOUN
ejpam-490	197	3	(	(	PUNCT
ejpam-490	197	4	19	19	NUM
ejpam-490	197	5	)	)	PUNCT
ejpam-490	197	6	follows	follow	VERB
ejpam-490	197	7	from	from	ADP
ejpam-490	197	8	(	(	PUNCT
ejpam-490	197	9	18	18	NUM
ejpam-490	197	10	)	)	PUNCT
ejpam-490	197	11	by	by	ADP
ejpam-490	197	12	taking	take	VERB
ejpam-490	197	13	the	the	DET
ejpam-490	197	14	convex	convex	NOUN
ejpam-490	197	15	function	function	NOUN
ejpam-490	197	16	h(z	h(z	NOUN
ejpam-490	197	17	)	)	PUNCT
ejpam-490	197	18	=	=	PUNCT
ejpam-490	198	1	z	z	X
ejpam-490	198	2	1−z	1−z	NUM
ejpam-490	199	1	=	=	SYM
ejpam-490	199	2	z	z	NOUN
ejpam-490	200	1	+	+	NUM
ejpam-490	200	2	∞	∞	NUM
ejpam-490	200	3	∑	∑	PROPN
ejpam-490	200	4	k=2	k=2	PROPN
ejpam-490	200	5	zk	zk	PROPN
ejpam-490	200	6	.	.	PUNCT
ejpam-490	201	1	to	to	PART
ejpam-490	201	2	prove	prove	VERB
ejpam-490	201	3	the	the	DET
ejpam-490	201	4	sharpness	sharpness	NOUN
ejpam-490	201	5	of	of	ADP
ejpam-490	201	6	the	the	DET
ejpam-490	201	7	constant	constant	ADJ
ejpam-490	201	8	(	(	PUNCT
ejpam-490	201	9	2+β−α)(1+γ)b2	2+β−α)(1+γ)b2	NUM
ejpam-490	201	10	2[(2+β−α)(1+γ)b2+(1−α	2[(2+β−α)(1+γ)b2+(1−α	NUM
ejpam-490	201	11	)	)	PUNCT
ejpam-490	201	12	]	]	PUNCT
ejpam-490	201	13	,	,	PUNCT
ejpam-490	201	14	we	we	PRON
ejpam-490	201	15	consider	consider	VERB
ejpam-490	201	16	the	the	DET
ejpam-490	201	17	function	function	NOUN
ejpam-490	201	18	f0(z	f0(z	SYM
ejpam-490	201	19	)	)	PUNCT
ejpam-490	201	20	∈	∈	PROPN
ejpam-490	201	21	s∗γ	s∗γ	NUM
ejpam-490	201	22	(	(	PUNCT
ejpam-490	201	23	f	f	PROPN
ejpam-490	201	24	,	,	PUNCT
ejpam-490	201	25	g;α	g;α	PROPN
ejpam-490	201	26	,	,	PUNCT
ejpam-490	201	27	β	β	NOUN
ejpam-490	201	28	)	)	PUNCT
ejpam-490	201	29	given	give	VERB
ejpam-490	201	30	by	by	ADP
ejpam-490	201	31	f0(z	f0(z	PUNCT
ejpam-490	201	32	)	)	PUNCT
ejpam-490	201	33	=	=	PUNCT
ejpam-490	202	1	z	z	NOUN
ejpam-490	203	1	−	−	PROPN
ejpam-490	203	2	1−α	1−α	NUM
ejpam-490	203	3	(	(	PUNCT
ejpam-490	203	4	2	2	NUM
ejpam-490	203	5	+	+	CCONJ
ejpam-490	203	6	β	β	NOUN
ejpam-490	203	7	−α)(1	−α)(1	NOUN
ejpam-490	203	8	+	+	PROPN
ejpam-490	203	9	γ)b2	γ)b2	PROPN
ejpam-490	203	10	z2	z2	PROPN
ejpam-490	203	11	.	.	PUNCT
ejpam-490	204	1	(	(	PUNCT
ejpam-490	204	2	23	23	NUM
ejpam-490	204	3	)	)	PUNCT
ejpam-490	204	4	thus	thus	ADV
ejpam-490	204	5	from	from	ADP
ejpam-490	204	6	(	(	PUNCT
ejpam-490	204	7	18	18	NUM
ejpam-490	204	8	)	)	PUNCT
ejpam-490	204	9	,	,	PUNCT
ejpam-490	204	10	we	we	PRON
ejpam-490	204	11	have	have	VERB
ejpam-490	204	12	(	(	PUNCT
ejpam-490	204	13	2	2	NUM
ejpam-490	204	14	+	+	CCONJ
ejpam-490	204	15	β	β	NOUN
ejpam-490	204	16	−α)(1	−α)(1	NOUN
ejpam-490	204	17	+	+	CCONJ
ejpam-490	204	18	γ)b2	γ)b2	PROPN
ejpam-490	204	19	2	2	NUM
ejpam-490	204	20	�	�	PROPN
ejpam-490	204	21	(	(	PUNCT
ejpam-490	204	22	2	2	NUM
ejpam-490	204	23	+	+	CCONJ
ejpam-490	204	24	β	β	NOUN
ejpam-490	204	25	−α)(1	−α)(1	NOUN
ejpam-490	205	1	+	+	CCONJ
ejpam-490	205	2	γ)b2	γ)b2	PROPN
ejpam-490	205	3	+	+	CCONJ
ejpam-490	205	4	(	(	PUNCT
ejpam-490	205	5	1−α	1−α	NUM
ejpam-490	205	6	)	)	PUNCT
ejpam-490	205	7	�	�	PROPN
ejpam-490	205	8	f0(z	f0(z	NUM
ejpam-490	205	9	)	)	PUNCT
ejpam-490	205	10	≺	≺	NOUN
ejpam-490	205	11	z	z	NOUN
ejpam-490	205	12	1−	1−	NUM
ejpam-490	205	13	z	z	NOUN
ejpam-490	205	14	(	(	PUNCT
ejpam-490	205	15	z	z	NOUN
ejpam-490	205	16	∈	∈	PROPN
ejpam-490	205	17	u	u	NOUN
ejpam-490	205	18	)	)	PUNCT
ejpam-490	205	19	.	.	PUNCT
ejpam-490	206	1	(	(	PUNCT
ejpam-490	206	2	24	24	NUM
ejpam-490	206	3	)	)	PUNCT
ejpam-490	206	4	moreover	moreover	ADV
ejpam-490	206	5	,	,	PUNCT
ejpam-490	206	6	it	it	PRON
ejpam-490	206	7	can	can	AUX
ejpam-490	206	8	easily	easily	ADV
ejpam-490	206	9	be	be	AUX
ejpam-490	206	10	verified	verify	VERB
ejpam-490	206	11	for	for	ADP
ejpam-490	206	12	the	the	DET
ejpam-490	206	13	function	function	NOUN
ejpam-490	206	14	f0(z	f0(z	NUM
ejpam-490	206	15	)	)	PUNCT
ejpam-490	206	16	given	give	VERB
ejpam-490	206	17	by	by	ADP
ejpam-490	206	18	(	(	PUNCT
ejpam-490	206	19	23	23	NUM
ejpam-490	206	20	)	)	PUNCT
ejpam-490	206	21	that	that	PRON
ejpam-490	206	22	min	min	AUX
ejpam-490	206	23	|z|≤r	|z|≤r	PROPN
ejpam-490	206	24	¨	¨	NOUN
ejpam-490	206	25	re	re	X
ejpam-490	206	26	(	(	PUNCT
ejpam-490	206	27	2	2	NUM
ejpam-490	206	28	+	+	CCONJ
ejpam-490	206	29	β	β	NOUN
ejpam-490	206	30	−α)(1	−α)(1	NOUN
ejpam-490	207	1	+	+	CCONJ
ejpam-490	207	2	γ)b2	γ)b2	PROPN
ejpam-490	207	3	2	2	NUM
ejpam-490	207	4	�	�	PROPN
ejpam-490	207	5	(	(	PUNCT
ejpam-490	207	6	2	2	NUM
ejpam-490	207	7	+	+	CCONJ
ejpam-490	207	8	β	β	NOUN
ejpam-490	207	9	−α)(1	−α)(1	NOUN
ejpam-490	207	10	+	+	CCONJ
ejpam-490	207	11	γ)b2	γ)b2	PROPN
ejpam-490	207	12	+	+	CCONJ
ejpam-490	207	13	(	(	PUNCT
ejpam-490	207	14	1−α	1−α	NUM
ejpam-490	207	15	)	)	PUNCT
ejpam-490	207	16	�	�	PROPN
ejpam-490	207	17	f0(z	f0(z	NUM
ejpam-490	207	18	)	)	PUNCT
ejpam-490	207	19	«	«	PUNCT
ejpam-490	208	1	=	=	SYM
ejpam-490	208	2	−	−	PROPN
ejpam-490	208	3	1	1	NUM
ejpam-490	208	4	2	2	NUM
ejpam-490	208	5	.	.	PUNCT
ejpam-490	209	1	(	(	PUNCT
ejpam-490	209	2	25	25	NUM
ejpam-490	209	3	)	)	PUNCT
ejpam-490	209	4	this	this	PRON
ejpam-490	209	5	shows	show	VERB
ejpam-490	209	6	that	that	SCONJ
ejpam-490	209	7	the	the	DET
ejpam-490	209	8	constant	constant	ADJ
ejpam-490	209	9	(	(	PUNCT
ejpam-490	209	10	2+β−α)(1+γ)b2	2+β−α)(1+γ)b2	NUM
ejpam-490	209	11	2[(2+β−α)(1+γ)b2+(1−α	2[(2+β−α)(1+γ)b2+(1−α	NUM
ejpam-490	209	12	)	)	PUNCT
ejpam-490	209	13	]	]	PUNCT
ejpam-490	209	14	is	be	AUX
ejpam-490	209	15	the	the	DET
ejpam-490	209	16	best	good	ADJ
ejpam-490	209	17	possible	possible	ADJ
ejpam-490	209	18	.	.	PUNCT
ejpam-490	210	1	remark	remark	NOUN
ejpam-490	210	2	1	1	NUM
ejpam-490	210	3	.	.	PUNCT
ejpam-490	211	1	(	(	PUNCT
ejpam-490	211	2	i	i	NOUN
ejpam-490	211	3	)	)	PUNCT
ejpam-490	211	4	taking	take	VERB
ejpam-490	211	5	g(z	g(z	NOUN
ejpam-490	211	6	)	)	PUNCT
ejpam-490	211	7	=	=	SYM
ejpam-490	212	1	z	z	NOUN
ejpam-490	213	1	+	+	NUM
ejpam-490	213	2	∞	∞	PROPN
ejpam-490	213	3	∑	∑	PROPN
ejpam-490	213	4	k=2	k=2	PROPN
ejpam-490	213	5	(	(	PUNCT
ejpam-490	213	6	a)k−1	a)k−1	PROPN
ejpam-490	213	7	(	(	PUNCT
ejpam-490	213	8	c)k−1	c)k−1	PROPN
ejpam-490	213	9	zk	zk	PROPN
ejpam-490	213	10	(	(	PUNCT
ejpam-490	213	11	c	c	PROPN
ejpam-490	213	12	6=	6=	NUM
ejpam-490	213	13	0,−1,−2	0,−1,−2	NUM
ejpam-490	213	14	,	,	PUNCT
ejpam-490	213	15	.	.	PUNCT
ejpam-490	213	16	.	.	PUNCT
ejpam-490	213	17	.	.	PUNCT
ejpam-490	213	18	)	)	PUNCT
ejpam-490	214	1	and	and	CCONJ
ejpam-490	214	2	γ	γ	X
ejpam-490	214	3	=	=	SYM
ejpam-490	214	4	0	0	NUM
ejpam-490	214	5	in	in	ADP
ejpam-490	214	6	theorem	theorem	NOUN
ejpam-490	214	7	1	1	NUM
ejpam-490	214	8	,	,	PUNCT
ejpam-490	214	9	we	we	PRON
ejpam-490	214	10	obtain	obtain	VERB
ejpam-490	214	11	the	the	DET
ejpam-490	214	12	result	result	NOUN
ejpam-490	214	13	obtained	obtain	VERB
ejpam-490	214	14	by	by	ADP
ejpam-490	214	15	frasin	frasin	NOUN
ejpam-490	214	16	[	[	X
ejpam-490	214	17	8	8	NUM
ejpam-490	214	18	,	,	PUNCT
ejpam-490	214	19	theorem	theorem	VERB
ejpam-490	214	20	2.1	2.1	NUM
ejpam-490	214	21	]	]	PUNCT
ejpam-490	214	22	;	;	PUNCT
ejpam-490	214	23	m.	m.	PROPN
ejpam-490	214	24	aouf	aouf	PROPN
ejpam-490	214	25	,	,	PUNCT
ejpam-490	214	26	r.	r.	PROPN
ejpam-490	214	27	el	el	PROPN
ejpam-490	214	28	-	-	PUNCT
ejpam-490	214	29	ashwah	ashwah	PROPN
ejpam-490	214	30	,	,	PUNCT
ejpam-490	214	31	s.	s.	PROPN
ejpam-490	214	32	el	el	PROPN
ejpam-490	214	33	-	-	PUNCT
ejpam-490	214	34	deeb	deeb	PROPN
ejpam-490	214	35	/	/	SYM
ejpam-490	214	36	eur	eur	PROPN
ejpam-490	214	37	.	.	PUNCT
ejpam-490	215	1	j.	j.	PROPN
ejpam-490	215	2	pure	pure	PROPN
ejpam-490	215	3	appl	appl	PROPN
ejpam-490	215	4	.	.	PROPN
ejpam-490	215	5	math	math	PROPN
ejpam-490	215	6	,	,	PUNCT
ejpam-490	215	7	3	3	NUM
ejpam-490	215	8	(	(	PUNCT
ejpam-490	215	9	2010	2010	NUM
ejpam-490	215	10	)	)	PUNCT
ejpam-490	215	11	,	,	PUNCT
ejpam-490	215	12	903	903	NUM
ejpam-490	215	13	-	-	SYM
ejpam-490	215	14	917	917	NUM
ejpam-490	215	15	911	911	NUM
ejpam-490	215	16	(	(	PUNCT
ejpam-490	215	17	ii	ii	NOUN
ejpam-490	215	18	)	)	PUNCT
ejpam-490	215	19	taking	take	VERB
ejpam-490	215	20	g(z	g(z	NOUN
ejpam-490	215	21	)	)	PUNCT
ejpam-490	215	22	=	=	PUNCT
ejpam-490	216	1	z	z	PROPN
ejpam-490	216	2	1−z	1−z	NUM
ejpam-490	216	3	and	and	CCONJ
ejpam-490	216	4	γ	γ	X
ejpam-490	216	5	=	=	SYM
ejpam-490	216	6	0	0	NUM
ejpam-490	216	7	in	in	ADP
ejpam-490	216	8	theorem	theorem	NOUN
ejpam-490	216	9	1	1	NUM
ejpam-490	216	10	,	,	PUNCT
ejpam-490	216	11	we	we	PRON
ejpam-490	216	12	obtain	obtain	VERB
ejpam-490	216	13	the	the	DET
ejpam-490	216	14	result	result	NOUN
ejpam-490	216	15	obtained	obtain	VERB
ejpam-490	216	16	by	by	ADP
ejpam-490	216	17	frasin	frasin	NOUN
ejpam-490	216	18	[	[	X
ejpam-490	216	19	8	8	NUM
ejpam-490	216	20	,	,	PUNCT
ejpam-490	216	21	corollary	corollary	NOUN
ejpam-490	216	22	2.2	2.2	NUM
ejpam-490	216	23	]	]	PUNCT
ejpam-490	216	24	;	;	PUNCT
ejpam-490	216	25	(	(	PUNCT
ejpam-490	216	26	iii	iii	X
ejpam-490	216	27	)	)	PUNCT
ejpam-490	216	28	taking	take	VERB
ejpam-490	216	29	g(z	g(z	NOUN
ejpam-490	216	30	)	)	PUNCT
ejpam-490	217	1	=	=	PUNCT
ejpam-490	217	2	z	z	PROPN
ejpam-490	217	3	1−z	1−z	NUM
ejpam-490	217	4	and	and	CCONJ
ejpam-490	217	5	β	β	X
ejpam-490	217	6	=	=	SYM
ejpam-490	217	7	γ	γ	X
ejpam-490	217	8	=	=	SYM
ejpam-490	217	9	0	0	NUM
ejpam-490	217	10	in	in	ADP
ejpam-490	217	11	theorem	theorem	NOUN
ejpam-490	217	12	1	1	NUM
ejpam-490	217	13	,	,	PUNCT
ejpam-490	217	14	we	we	PRON
ejpam-490	217	15	obtain	obtain	VERB
ejpam-490	217	16	the	the	DET
ejpam-490	217	17	result	result	NOUN
ejpam-490	217	18	obtained	obtain	VERB
ejpam-490	217	19	by	by	ADP
ejpam-490	217	20	frasin	frasin	NOUN
ejpam-490	217	21	[	[	X
ejpam-490	217	22	8	8	NUM
ejpam-490	217	23	,	,	PUNCT
ejpam-490	217	24	corollary	corollary	ADJ
ejpam-490	217	25	2.3	2.3	NUM
ejpam-490	217	26	]	]	PUNCT
ejpam-490	217	27	;	;	PUNCT
ejpam-490	217	28	(	(	PUNCT
ejpam-490	217	29	iv	iv	X
ejpam-490	217	30	)	)	PUNCT
ejpam-490	217	31	taking	take	VERB
ejpam-490	217	32	g(z	g(z	NOUN
ejpam-490	217	33	)	)	PUNCT
ejpam-490	217	34	=	=	PUNCT
ejpam-490	218	1	z	z	PROPN
ejpam-490	218	2	1−z	1−z	NUM
ejpam-490	218	3	and	and	CCONJ
ejpam-490	218	4	α	α	NOUN
ejpam-490	218	5	=	=	X
ejpam-490	218	6	β	β	X
ejpam-490	218	7	=	=	PUNCT
ejpam-490	218	8	γ	γ	X
ejpam-490	218	9	=	=	SYM
ejpam-490	218	10	0	0	NUM
ejpam-490	218	11	in	in	ADP
ejpam-490	218	12	theorem	theorem	NOUN
ejpam-490	218	13	1	1	NUM
ejpam-490	218	14	,	,	PUNCT
ejpam-490	218	15	we	we	PRON
ejpam-490	218	16	obtain	obtain	VERB
ejpam-490	218	17	the	the	DET
ejpam-490	218	18	result	result	NOUN
ejpam-490	218	19	obtained	obtain	VERB
ejpam-490	218	20	by	by	ADP
ejpam-490	218	21	frasin	frasin	NOUN
ejpam-490	218	22	[	[	X
ejpam-490	218	23	8	8	NUM
ejpam-490	218	24	,	,	PUNCT
ejpam-490	218	25	corollary	corollary	ADJ
ejpam-490	218	26	2.4	2.4	NUM
ejpam-490	218	27	]	]	PUNCT
ejpam-490	218	28	;	;	PUNCT
ejpam-490	218	29	(	(	PUNCT
ejpam-490	218	30	v	v	NOUN
ejpam-490	218	31	)	)	PUNCT
ejpam-490	218	32	taking	take	VERB
ejpam-490	218	33	g(z	g(z	NOUN
ejpam-490	218	34	)	)	PUNCT
ejpam-490	219	1	=	=	SYM
ejpam-490	219	2	z	z	NOUN
ejpam-490	219	3	(	(	PUNCT
ejpam-490	219	4	1−z)2	1−z)2	NUM
ejpam-490	219	5	and	and	CCONJ
ejpam-490	219	6	γ	γ	X
ejpam-490	219	7	=	=	SYM
ejpam-490	219	8	0	0	NUM
ejpam-490	219	9	in	in	ADP
ejpam-490	219	10	theorem	theorem	NOUN
ejpam-490	219	11	1	1	NUM
ejpam-490	219	12	,	,	PUNCT
ejpam-490	219	13	we	we	PRON
ejpam-490	219	14	obtain	obtain	VERB
ejpam-490	219	15	the	the	DET
ejpam-490	219	16	result	result	NOUN
ejpam-490	219	17	obtained	obtain	VERB
ejpam-490	219	18	by	by	ADP
ejpam-490	219	19	frasin	frasin	NOUN
ejpam-490	219	20	[	[	X
ejpam-490	219	21	8	8	NUM
ejpam-490	219	22	,	,	PUNCT
ejpam-490	219	23	corollary	corollary	ADJ
ejpam-490	219	24	2.5	2.5	NUM
ejpam-490	219	25	]	]	PUNCT
ejpam-490	219	26	;	;	PUNCT
ejpam-490	219	27	(	(	PUNCT
ejpam-490	219	28	vi	vi	NOUN
ejpam-490	219	29	)	)	PUNCT
ejpam-490	219	30	taking	take	VERB
ejpam-490	219	31	g(z	g(z	NOUN
ejpam-490	219	32	)	)	PUNCT
ejpam-490	220	1	=	=	SYM
ejpam-490	220	2	z	z	NOUN
ejpam-490	220	3	(	(	PUNCT
ejpam-490	220	4	1−z)2	1−z)2	NUM
ejpam-490	220	5	and	and	CCONJ
ejpam-490	220	6	β	β	X
ejpam-490	220	7	=	=	SYM
ejpam-490	220	8	γ=	γ=	PROPN
ejpam-490	220	9	0	0	PUNCT
ejpam-490	220	10	in	in	ADP
ejpam-490	220	11	theorem	theorem	NOUN
ejpam-490	220	12	1	1	NUM
ejpam-490	220	13	,	,	PUNCT
ejpam-490	220	14	we	we	PRON
ejpam-490	220	15	obtain	obtain	VERB
ejpam-490	220	16	the	the	DET
ejpam-490	220	17	result	result	NOUN
ejpam-490	220	18	obtained	obtain	VERB
ejpam-490	220	19	by	by	ADP
ejpam-490	220	20	frasin	frasin	NOUN
ejpam-490	220	21	[	[	X
ejpam-490	220	22	8	8	NUM
ejpam-490	220	23	,	,	PUNCT
ejpam-490	220	24	corollary	corollary	ADJ
ejpam-490	220	25	2.6	2.6	NUM
ejpam-490	220	26	]	]	PUNCT
ejpam-490	220	27	;	;	PUNCT
ejpam-490	220	28	(	(	PUNCT
ejpam-490	220	29	vii	vii	PROPN
ejpam-490	220	30	)	)	PUNCT
ejpam-490	220	31	taking	take	VERB
ejpam-490	220	32	g(z	g(z	PROPN
ejpam-490	220	33	)	)	PUNCT
ejpam-490	221	1	=	=	SYM
ejpam-490	221	2	z	z	NOUN
ejpam-490	221	3	(	(	PUNCT
ejpam-490	221	4	1−z)2	1−z)2	NUM
ejpam-490	221	5	and	and	CCONJ
ejpam-490	221	6	α	α	NOUN
ejpam-490	221	7	=	=	X
ejpam-490	221	8	β	β	X
ejpam-490	221	9	=	=	PUNCT
ejpam-490	221	10	γ	γ	X
ejpam-490	221	11	=	=	SYM
ejpam-490	221	12	0	0	NUM
ejpam-490	221	13	in	in	ADP
ejpam-490	221	14	theorem	theorem	NOUN
ejpam-490	221	15	1	1	NUM
ejpam-490	221	16	,	,	PUNCT
ejpam-490	221	17	we	we	PRON
ejpam-490	221	18	obtain	obtain	VERB
ejpam-490	221	19	the	the	DET
ejpam-490	221	20	result	result	NOUN
ejpam-490	221	21	obtained	obtain	VERB
ejpam-490	221	22	by	by	ADP
ejpam-490	221	23	frasin	frasin	NOUN
ejpam-490	221	24	[	[	X
ejpam-490	221	25	8	8	NUM
ejpam-490	221	26	,	,	PUNCT
ejpam-490	221	27	corollary	corollary	ADJ
ejpam-490	221	28	2.7	2.7	NUM
ejpam-490	221	29	]	]	PUNCT
ejpam-490	221	30	;	;	PUNCT
ejpam-490	221	31	(	(	PUNCT
ejpam-490	221	32	viii	viii	NOUN
ejpam-490	221	33	)	)	PUNCT
ejpam-490	221	34	taking	take	VERB
ejpam-490	221	35	g(z	g(z	NOUN
ejpam-490	221	36	)	)	PUNCT
ejpam-490	221	37	=	=	SYM
ejpam-490	222	1	z	z	NOUN
ejpam-490	223	1	+	+	NUM
ejpam-490	223	2	∞	∞	NUM
ejpam-490	223	3	∑	∑	PROPN
ejpam-490	223	4	k=2	k=2	PROPN
ejpam-490	223	5	µkzk	µkzk	VERB
ejpam-490	223	6	and	and	CCONJ
ejpam-490	223	7	γ	γ	X
ejpam-490	223	8	=	=	SYM
ejpam-490	223	9	0	0	NUM
ejpam-490	223	10	in	in	ADP
ejpam-490	223	11	theorem	theorem	NOUN
ejpam-490	223	12	1	1	NUM
ejpam-490	223	13	,	,	PUNCT
ejpam-490	223	14	we	we	PRON
ejpam-490	223	15	obtain	obtain	VERB
ejpam-490	223	16	the	the	DET
ejpam-490	223	17	result	result	NOUN
ejpam-490	223	18	obtained	obtain	VERB
ejpam-490	223	19	by	by	ADP
ejpam-490	223	20	raina	raina	PROPN
ejpam-490	223	21	and	and	CCONJ
ejpam-490	223	22	bansal	bansal	NOUN
ejpam-490	223	23	[	[	X
ejpam-490	223	24	18	18	NUM
ejpam-490	223	25	,	,	PUNCT
ejpam-490	223	26	theorem	theorem	VERB
ejpam-490	223	27	5.2	5.2	NUM
ejpam-490	223	28	]	]	PUNCT
ejpam-490	223	29	.	.	PUNCT
ejpam-490	224	1	also	also	ADV
ejpam-490	224	2	,	,	PUNCT
ejpam-490	224	3	we	we	PRON
ejpam-490	224	4	establish	establish	VERB
ejpam-490	224	5	subordination	subordination	NOUN
ejpam-490	224	6	results	result	NOUN
ejpam-490	224	7	for	for	ADP
ejpam-490	224	8	the	the	DET
ejpam-490	224	9	associated	associated	ADJ
ejpam-490	224	10	sub	sub	NOUN
ejpam-490	224	11	classes	class	NOUN
ejpam-490	224	12	,	,	PUNCT
ejpam-490	224	13	s∗p(α	s∗p(α	PROPN
ejpam-490	224	14	)	)	PUNCT
ejpam-490	224	15	,	,	PUNCT
ejpam-490	224	16	ucv	ucv	PROPN
ejpam-490	224	17	∗(α	∗(α	PROPN
ejpam-490	224	18	)	)	PUNCT
ejpam-490	224	19	,	,	PUNCT
ejpam-490	224	20	ucv	ucv	PROPN
ejpam-490	224	21	∗(β	∗(β	PROPN
ejpam-490	224	22	)	)	PUNCT
ejpam-490	224	23	,	,	PUNCT
ejpam-490	224	24	s∗	s∗	PROPN
ejpam-490	224	25	�	�	PROPN
ejpam-490	224	26	n	n	CCONJ
ejpam-490	224	27	,	,	PUNCT
ejpam-490	224	28	α	α	PROPN
ejpam-490	224	29	,	,	PUNCT
ejpam-490	224	30	β	β	X
ejpam-490	224	31	�	�	PROPN
ejpam-490	224	32	,	,	PUNCT
ejpam-490	224	33	s∗	s∗	PROPN
ejpam-490	224	34	�	�	PROPN
ejpam-490	224	35	α	α	PROPN
ejpam-490	224	36	,	,	PUNCT
ejpam-490	224	37	β	β	X
ejpam-490	224	38	,	,	PUNCT
ejpam-490	224	39	λ	λ	PROPN
ejpam-490	224	40	�	�	PROPN
ejpam-490	224	41	,	,	PUNCT
ejpam-490	224	42	s∗	s∗	PROPN
ejpam-490	224	43	λ	λ	PROPN
ejpam-490	224	44	�	�	PROPN
ejpam-490	224	45	n	n	CCONJ
ejpam-490	224	46	,	,	PUNCT
ejpam-490	224	47	α	α	PROPN
ejpam-490	224	48	,	,	PUNCT
ejpam-490	224	49	β	β	X
ejpam-490	224	50	�	�	PROPN
ejpam-490	224	51	,	,	PUNCT
ejpam-490	224	52	ss,∗	ss,∗	PROPN
ejpam-490	224	53	q	q	X
ejpam-490	224	54	(	(	PUNCT
ejpam-490	224	55	γ	γ	X
ejpam-490	224	56	,	,	PUNCT
ejpam-490	224	57	α	α	NOUN
ejpam-490	224	58	,	,	PUNCT
ejpam-490	224	59	β	β	NOUN
ejpam-490	224	60	)	)	PUNCT
ejpam-490	224	61	,	,	PUNCT
ejpam-490	224	62	s∗	s∗	PROPN
ejpam-490	224	63	�	�	PROPN
ejpam-490	224	64	γ	γ	PROPN
ejpam-490	224	65	,	,	PUNCT
ejpam-490	224	66	α	α	PROPN
ejpam-490	224	67	,	,	PUNCT
ejpam-490	224	68	β	β	X
ejpam-490	224	69	�	�	PROPN
ejpam-490	224	70	,	,	PUNCT
ejpam-490	224	71	s∗γ	s∗γ	X
ejpam-490	224	72	�	�	PROPN
ejpam-490	224	73	n	n	CCONJ
ejpam-490	224	74	,	,	PUNCT
ejpam-490	224	75	α	α	PROPN
ejpam-490	224	76	,	,	PUNCT
ejpam-490	224	77	β	β	X
ejpam-490	224	78	�	�	PROPN
ejpam-490	224	79	,	,	PUNCT
ejpam-490	224	80	s∗γ	s∗γ	X
ejpam-490	224	81	�	�	PROPN
ejpam-490	224	82	c	c	PROPN
ejpam-490	224	83	,	,	PUNCT
ejpam-490	224	84	α	α	PROPN
ejpam-490	224	85	,	,	PUNCT
ejpam-490	224	86	β	β	X
ejpam-490	224	87	�	�	PROPN
ejpam-490	224	88	,	,	PUNCT
ejpam-490	224	89	s∗γ	s∗γ	X
ejpam-490	224	90	�	�	PROPN
ejpam-490	224	91	µ,λ;α	µ,λ;α	PROPN
ejpam-490	224	92	,	,	PUNCT
ejpam-490	224	93	β	β	X
ejpam-490	224	94	�	�	PROPN
ejpam-490	224	95	,	,	PUNCT
ejpam-490	224	96	s∗γ	s∗γ	X
ejpam-490	224	97	�	�	PROPN
ejpam-490	224	98	a	a	PROPN
ejpam-490	224	99	,	,	PUNCT
ejpam-490	224	100	c	c	NOUN
ejpam-490	224	101	,	,	PUNCT
ejpam-490	224	102	λ;α	λ;α	PROPN
ejpam-490	224	103	,	,	PUNCT
ejpam-490	224	104	β	β	X
ejpam-490	224	105	�	�	PROPN
ejpam-490	224	106	,	,	PUNCT
ejpam-490	224	107	s∗γ	s∗γ	X
ejpam-490	224	108	�	�	PROPN
ejpam-490	224	109	n;α	n;α	PROPN
ejpam-490	224	110	,	,	PUNCT
ejpam-490	224	111	β	β	X
ejpam-490	224	112	�	�	PROPN
ejpam-490	224	113	,	,	PUNCT
ejpam-490	224	114	whose	whose	DET
ejpam-490	224	115	coefficients	coefficient	NOUN
ejpam-490	224	116	satisfy	satisfy	VERB
ejpam-490	224	117	the	the	DET
ejpam-490	224	118	(	(	PUNCT
ejpam-490	224	119	17	17	NUM
ejpam-490	224	120	)	)	PUNCT
ejpam-490	224	121	in	in	ADP
ejpam-490	224	122	the	the	DET
ejpam-490	224	123	special	special	ADJ
ejpam-490	224	124	cases	case	NOUN
ejpam-490	224	125	as	as	SCONJ
ejpam-490	224	126	mentioned	mention	VERB
ejpam-490	224	127	in	in	ADP
ejpam-490	224	128	p.	p.	PROPN
ejpam-490	224	129	905	905	NUM
ejpam-490	224	130	907	907	NUM
ejpam-490	224	131	.	.	PUNCT
ejpam-490	225	1	putting	put	VERB
ejpam-490	225	2	g(z	g(z	PROPN
ejpam-490	225	3	)	)	PUNCT
ejpam-490	225	4	=	=	SYM
ejpam-490	225	5	z	z	NOUN
ejpam-490	225	6	(	(	PUNCT
ejpam-490	225	7	1−z	1−z	NUM
ejpam-490	225	8	)	)	PUNCT
ejpam-490	225	9	,	,	PUNCT
ejpam-490	225	10	γ=	γ=	PROPN
ejpam-490	225	11	0	0	NUM
ejpam-490	225	12	and	and	CCONJ
ejpam-490	225	13	β	β	X
ejpam-490	225	14	=	=	SYM
ejpam-490	225	15	1	1	NUM
ejpam-490	225	16	in	in	ADP
ejpam-490	225	17	theorem	theorem	NOUN
ejpam-490	225	18	1	1	NUM
ejpam-490	225	19	,	,	PUNCT
ejpam-490	225	20	we	we	PRON
ejpam-490	225	21	have	have	VERB
ejpam-490	225	22	corollary	corollary	ADJ
ejpam-490	225	23	1	1	NUM
ejpam-490	225	24	.	.	PUNCT
ejpam-490	226	1	let	let	VERB
ejpam-490	226	2	the	the	DET
ejpam-490	226	3	function	function	NOUN
ejpam-490	226	4	f	f	PROPN
ejpam-490	226	5	(	(	PUNCT
ejpam-490	226	6	z	z	NOUN
ejpam-490	226	7	)	)	PUNCT
ejpam-490	226	8	defined	define	VERB
ejpam-490	226	9	by	by	ADP
ejpam-490	226	10	(	(	PUNCT
ejpam-490	226	11	1	1	X
ejpam-490	226	12	)	)	PUNCT
ejpam-490	226	13	be	be	AUX
ejpam-490	226	14	in	in	ADP
ejpam-490	226	15	the	the	DET
ejpam-490	226	16	class	class	NOUN
ejpam-490	226	17	s∗p(α	s∗p(α	PROPN
ejpam-490	226	18	)	)	PUNCT
ejpam-490	226	19	and	and	CCONJ
ejpam-490	226	20	suppose	suppose	VERB
ejpam-490	226	21	that	that	SCONJ
ejpam-490	226	22	h(z	h(z	NOUN
ejpam-490	226	23	)	)	PUNCT
ejpam-490	226	24	∈	∈	PROPN
ejpam-490	227	1	k	k	INTJ
ejpam-490	227	2	.	.	PUNCT
ejpam-490	228	1	then	then	ADV
ejpam-490	228	2	3−α	3−α	NUM
ejpam-490	228	3	2(4−	2(4−	NUM
ejpam-490	228	4	2α	2α	NOUN
ejpam-490	228	5	)	)	PUNCT
ejpam-490	228	6	(	(	PUNCT
ejpam-490	228	7	f	f	PROPN
ejpam-490	228	8	∗	∗	VERB
ejpam-490	228	9	h)(z)≺	h)(z)≺	PROPN
ejpam-490	229	1	h(z	h(z	NOUN
ejpam-490	229	2	)	)	PUNCT
ejpam-490	229	3	(	(	PUNCT
ejpam-490	229	4	z	z	NOUN
ejpam-490	229	5	∈	∈	PROPN
ejpam-490	229	6	u	u	NOUN
ejpam-490	229	7	)	)	PUNCT
ejpam-490	229	8	(	(	PUNCT
ejpam-490	229	9	26	26	NUM
ejpam-490	229	10	)	)	PUNCT
ejpam-490	229	11	and	and	CCONJ
ejpam-490	229	12	re	re	ADP
ejpam-490	229	13	(	(	PUNCT
ejpam-490	229	14	f	f	PROPN
ejpam-490	229	15	(	(	PUNCT
ejpam-490	229	16	z	z	NOUN
ejpam-490	229	17	)	)	PUNCT
ejpam-490	229	18	)	)	PUNCT
ejpam-490	229	19	>	>	X
ejpam-490	230	1	−	−	PROPN
ejpam-490	231	1	4−	4−	NUM
ejpam-490	231	2	2α	2α	NOUN
ejpam-490	231	3	3−α	3−α	NUM
ejpam-490	231	4	(	(	PUNCT
ejpam-490	231	5	z	z	NOUN
ejpam-490	231	6	∈	∈	PROPN
ejpam-490	231	7	u	u	NOUN
ejpam-490	231	8	)	)	PUNCT
ejpam-490	231	9	.	.	PUNCT
ejpam-490	232	1	(	(	PUNCT
ejpam-490	232	2	27	27	NUM
ejpam-490	232	3	)	)	PUNCT
ejpam-490	232	4	the	the	DET
ejpam-490	232	5	constant	constant	ADJ
ejpam-490	232	6	factor	factor	NOUN
ejpam-490	232	7	3−α	3−α	NUM
ejpam-490	232	8	2(4−2α	2(4−2α	NUM
ejpam-490	232	9	)	)	PUNCT
ejpam-490	232	10	in	in	ADP
ejpam-490	232	11	the	the	DET
ejpam-490	232	12	subordination	subordination	NOUN
ejpam-490	232	13	result	result	NOUN
ejpam-490	232	14	(	(	PUNCT
ejpam-490	232	15	26	26	NUM
ejpam-490	232	16	)	)	PUNCT
ejpam-490	232	17	can	can	AUX
ejpam-490	232	18	not	not	PART
ejpam-490	232	19	be	be	AUX
ejpam-490	232	20	replaced	replace	VERB
ejpam-490	232	21	by	by	ADP
ejpam-490	232	22	a	a	DET
ejpam-490	232	23	larger	large	ADJ
ejpam-490	232	24	one	one	NOUN
ejpam-490	232	25	.	.	PUNCT
ejpam-490	233	1	putting	put	VERB
ejpam-490	233	2	g(z	g(z	PROPN
ejpam-490	233	3	)	)	PUNCT
ejpam-490	233	4	=	=	SYM
ejpam-490	233	5	z	z	NOUN
ejpam-490	233	6	(	(	PUNCT
ejpam-490	233	7	1−z)2	1−z)2	NUM
ejpam-490	233	8	,	,	PUNCT
ejpam-490	233	9	γ	γ	X
ejpam-490	233	10	=	=	SYM
ejpam-490	233	11	0	0	NUM
ejpam-490	233	12	and	and	CCONJ
ejpam-490	233	13	β	β	X
ejpam-490	233	14	=	=	SYM
ejpam-490	233	15	1	1	NUM
ejpam-490	233	16	in	in	ADP
ejpam-490	233	17	theorem	theorem	NOUN
ejpam-490	233	18	1	1	NUM
ejpam-490	233	19	,	,	PUNCT
ejpam-490	233	20	we	we	PRON
ejpam-490	233	21	have	have	VERB
ejpam-490	233	22	corollary	corollary	ADJ
ejpam-490	233	23	2	2	NUM
ejpam-490	233	24	.	.	PUNCT
ejpam-490	234	1	let	let	VERB
ejpam-490	234	2	the	the	DET
ejpam-490	234	3	function	function	NOUN
ejpam-490	234	4	f	f	PROPN
ejpam-490	234	5	(	(	PUNCT
ejpam-490	234	6	z	z	NOUN
ejpam-490	234	7	)	)	PUNCT
ejpam-490	234	8	defined	define	VERB
ejpam-490	234	9	by	by	ADP
ejpam-490	234	10	(	(	PUNCT
ejpam-490	234	11	1	1	X
ejpam-490	234	12	)	)	PUNCT
ejpam-490	234	13	be	be	AUX
ejpam-490	234	14	in	in	ADP
ejpam-490	234	15	the	the	DET
ejpam-490	234	16	class	class	NOUN
ejpam-490	234	17	ucv	ucv	PROPN
ejpam-490	234	18	∗(α	∗(α	PROPN
ejpam-490	234	19	)	)	PUNCT
ejpam-490	234	20	and	and	CCONJ
ejpam-490	234	21	suppose	suppose	VERB
ejpam-490	234	22	that	that	SCONJ
ejpam-490	234	23	h(z	h(z	NOUN
ejpam-490	234	24	)	)	PUNCT
ejpam-490	234	25	∈	∈	PROPN
ejpam-490	235	1	k	k	INTJ
ejpam-490	235	2	.	.	PUNCT
ejpam-490	236	1	then	then	ADV
ejpam-490	236	2	3−α	3−α	NUM
ejpam-490	236	3	7−	7−	NUM
ejpam-490	236	4	3α	3α	NOUN
ejpam-490	236	5	(	(	PUNCT
ejpam-490	236	6	f	f	PROPN
ejpam-490	236	7	∗	∗	NOUN
ejpam-490	236	8	h)(z)≺	h)(z)≺	PROPN
ejpam-490	236	9	h(z	h(z	NOUN
ejpam-490	236	10	)	)	PUNCT
ejpam-490	236	11	(	(	PUNCT
ejpam-490	236	12	z	z	NOUN
ejpam-490	236	13	∈	∈	PROPN
ejpam-490	236	14	u	u	NOUN
ejpam-490	236	15	)	)	PUNCT
ejpam-490	236	16	(	(	PUNCT
ejpam-490	236	17	28	28	NUM
ejpam-490	236	18	)	)	PUNCT
ejpam-490	236	19	and	and	CCONJ
ejpam-490	236	20	re	re	VERB
ejpam-490	236	21	(	(	PUNCT
ejpam-490	236	22	f	f	PROPN
ejpam-490	236	23	(	(	PUNCT
ejpam-490	236	24	z	z	NOUN
ejpam-490	236	25	)	)	PUNCT
ejpam-490	236	26	)	)	PUNCT
ejpam-490	236	27	>	>	X
ejpam-490	237	1	−	−	PROPN
ejpam-490	237	2	7−	7−	NUM
ejpam-490	237	3	3α	3α	NUM
ejpam-490	237	4	2(3−α	2(3−α	NUM
ejpam-490	237	5	)	)	PUNCT
ejpam-490	237	6	(	(	PUNCT
ejpam-490	237	7	z	z	NOUN
ejpam-490	237	8	∈	∈	PROPN
ejpam-490	237	9	u	u	NOUN
ejpam-490	237	10	)	)	PUNCT
ejpam-490	237	11	.	.	PUNCT
ejpam-490	238	1	(	(	PUNCT
ejpam-490	238	2	29	29	NUM
ejpam-490	238	3	)	)	PUNCT
ejpam-490	238	4	the	the	DET
ejpam-490	238	5	constant	constant	ADJ
ejpam-490	238	6	factor	factor	NOUN
ejpam-490	238	7	3−α	3−α	NUM
ejpam-490	238	8	7−3α	7−3α	NUM
ejpam-490	238	9	in	in	ADP
ejpam-490	238	10	the	the	DET
ejpam-490	238	11	subordination	subordination	NOUN
ejpam-490	238	12	result	result	NOUN
ejpam-490	238	13	(	(	PUNCT
ejpam-490	238	14	28	28	NUM
ejpam-490	238	15	)	)	PUNCT
ejpam-490	238	16	can	can	AUX
ejpam-490	238	17	not	not	PART
ejpam-490	238	18	be	be	AUX
ejpam-490	238	19	replaced	replace	VERB
ejpam-490	238	20	by	by	ADP
ejpam-490	238	21	a	a	DET
ejpam-490	238	22	larger	large	ADJ
ejpam-490	238	23	one	one	NUM
ejpam-490	238	24	.	.	PUNCT
ejpam-490	239	1	m.	m.	PROPN
ejpam-490	239	2	aouf	aouf	PROPN
ejpam-490	239	3	,	,	PUNCT
ejpam-490	239	4	r.	r.	PROPN
ejpam-490	239	5	el	el	PROPN
ejpam-490	239	6	-	-	PUNCT
ejpam-490	239	7	ashwah	ashwah	PROPN
ejpam-490	239	8	,	,	PUNCT
ejpam-490	239	9	s.	s.	PROPN
ejpam-490	239	10	el	el	PROPN
ejpam-490	239	11	-	-	PUNCT
ejpam-490	239	12	deeb	deeb	PROPN
ejpam-490	239	13	/	/	SYM
ejpam-490	239	14	eur	eur	PROPN
ejpam-490	239	15	.	.	PUNCT
ejpam-490	240	1	j.	j.	PROPN
ejpam-490	240	2	pure	pure	PROPN
ejpam-490	240	3	appl	appl	PROPN
ejpam-490	240	4	.	.	PROPN
ejpam-490	240	5	math	math	PROPN
ejpam-490	240	6	,	,	PUNCT
ejpam-490	240	7	3	3	NUM
ejpam-490	240	8	(	(	PUNCT
ejpam-490	240	9	2010	2010	NUM
ejpam-490	240	10	)	)	PUNCT
ejpam-490	240	11	,	,	PUNCT
ejpam-490	240	12	903	903	NUM
ejpam-490	240	13	-	-	SYM
ejpam-490	240	14	917	917	NUM
ejpam-490	240	15	912	912	NUM
ejpam-490	240	16	putting	put	VERB
ejpam-490	240	17	g(z	g(z	PROPN
ejpam-490	240	18	)	)	PUNCT
ejpam-490	241	1	=	=	SYM
ejpam-490	241	2	z	z	NOUN
ejpam-490	241	3	(	(	PUNCT
ejpam-490	241	4	1−z	1−z	NUM
ejpam-490	241	5	)	)	PUNCT
ejpam-490	241	6	,	,	PUNCT
ejpam-490	241	7	γ=	γ=	PROPN
ejpam-490	241	8	1	1	NUM
ejpam-490	241	9	and	and	CCONJ
ejpam-490	241	10	α	α	NOUN
ejpam-490	241	11	=	=	NOUN
ejpam-490	241	12	0	0	NUM
ejpam-490	241	13	in	in	ADP
ejpam-490	241	14	theorem	theorem	NOUN
ejpam-490	241	15	1	1	NUM
ejpam-490	241	16	,	,	PUNCT
ejpam-490	241	17	we	we	PRON
ejpam-490	241	18	have	have	VERB
ejpam-490	241	19	corollary	corollary	ADJ
ejpam-490	241	20	3	3	NUM
ejpam-490	241	21	.	.	PUNCT
ejpam-490	242	1	let	let	VERB
ejpam-490	242	2	the	the	DET
ejpam-490	242	3	function	function	NOUN
ejpam-490	242	4	f	f	PROPN
ejpam-490	242	5	(	(	PUNCT
ejpam-490	242	6	z	z	NOUN
ejpam-490	242	7	)	)	PUNCT
ejpam-490	242	8	defined	define	VERB
ejpam-490	242	9	by	by	ADP
ejpam-490	242	10	(	(	PUNCT
ejpam-490	242	11	1	1	X
ejpam-490	242	12	)	)	PUNCT
ejpam-490	242	13	be	be	AUX
ejpam-490	242	14	in	in	ADP
ejpam-490	242	15	the	the	DET
ejpam-490	242	16	class	class	NOUN
ejpam-490	242	17	ucv	ucv	PROPN
ejpam-490	242	18	∗(β	∗(β	PROPN
ejpam-490	242	19	)	)	PUNCT
ejpam-490	242	20	and	and	CCONJ
ejpam-490	242	21	suppose	suppose	VERB
ejpam-490	242	22	that	that	SCONJ
ejpam-490	242	23	h(z	h(z	NOUN
ejpam-490	242	24	)	)	PUNCT
ejpam-490	242	25	∈	∈	PROPN
ejpam-490	243	1	k	k	INTJ
ejpam-490	243	2	.	.	PUNCT
ejpam-490	244	1	then	then	ADV
ejpam-490	244	2	2	2	NUM
ejpam-490	244	3	+	+	NUM
ejpam-490	244	4	β	β	NOUN
ejpam-490	244	5	5	5	NUM
ejpam-490	244	6	+	+	NUM
ejpam-490	244	7	2β	2β	NUM
ejpam-490	244	8	(	(	PUNCT
ejpam-490	244	9	f	f	PROPN
ejpam-490	244	10	∗	∗	VERB
ejpam-490	244	11	h)(z)≺	h)(z)≺	PROPN
ejpam-490	244	12	h(z	h(z	NOUN
ejpam-490	244	13	)	)	PUNCT
ejpam-490	244	14	(	(	PUNCT
ejpam-490	244	15	z	z	NOUN
ejpam-490	244	16	∈	∈	PROPN
ejpam-490	244	17	u	u	NOUN
ejpam-490	244	18	)	)	PUNCT
ejpam-490	244	19	(	(	PUNCT
ejpam-490	244	20	30	30	NUM
ejpam-490	244	21	)	)	PUNCT
ejpam-490	244	22	and	and	CCONJ
ejpam-490	244	23	re	re	ADP
ejpam-490	244	24	(	(	PUNCT
ejpam-490	244	25	f	f	PROPN
ejpam-490	244	26	(	(	PUNCT
ejpam-490	244	27	z	z	NOUN
ejpam-490	244	28	)	)	PUNCT
ejpam-490	244	29	)	)	PUNCT
ejpam-490	244	30	>	>	X
ejpam-490	245	1	−	−	NUM
ejpam-490	245	2	5	5	NUM
ejpam-490	245	3	+	+	NUM
ejpam-490	245	4	2β	2β	NUM
ejpam-490	245	5	2(2	2(2	NUM
ejpam-490	245	6	+	+	SYM
ejpam-490	245	7	β	β	X
ejpam-490	245	8	)	)	PUNCT
ejpam-490	245	9	(	(	PUNCT
ejpam-490	245	10	z	z	NOUN
ejpam-490	245	11	∈	∈	PROPN
ejpam-490	245	12	u	u	NOUN
ejpam-490	245	13	)	)	PUNCT
ejpam-490	245	14	.	.	PUNCT
ejpam-490	246	1	(	(	PUNCT
ejpam-490	246	2	31	31	NUM
ejpam-490	246	3	)	)	PUNCT
ejpam-490	246	4	the	the	DET
ejpam-490	246	5	constant	constant	ADJ
ejpam-490	246	6	factor	factor	NOUN
ejpam-490	246	7	2+β	2+β	NUM
ejpam-490	246	8	5	5	NUM
ejpam-490	246	9	+	+	NOUN
ejpam-490	246	10	2β	2β	NOUN
ejpam-490	246	11	in	in	ADP
ejpam-490	246	12	the	the	DET
ejpam-490	246	13	subordination	subordination	NOUN
ejpam-490	246	14	result	result	NOUN
ejpam-490	246	15	(	(	PUNCT
ejpam-490	246	16	30	30	NUM
ejpam-490	246	17	)	)	PUNCT
ejpam-490	246	18	can	can	AUX
ejpam-490	246	19	not	not	PART
ejpam-490	246	20	be	be	AUX
ejpam-490	246	21	replaced	replace	VERB
ejpam-490	246	22	by	by	ADP
ejpam-490	246	23	a	a	DET
ejpam-490	246	24	larger	large	ADJ
ejpam-490	246	25	one	one	NOUN
ejpam-490	246	26	.	.	PUNCT
ejpam-490	247	1	putting	put	VERB
ejpam-490	247	2	g(z	g(z	PROPN
ejpam-490	247	3	)	)	PUNCT
ejpam-490	248	1	=	=	SYM
ejpam-490	248	2	z	z	NOUN
ejpam-490	249	1	+	+	NUM
ejpam-490	249	2	∞	∞	NUM
ejpam-490	249	3	∑	∑	PROPN
ejpam-490	249	4	k=2	k=2	PROPN
ejpam-490	249	5	knzk	knzk	PROPN
ejpam-490	249	6	(	(	PUNCT
ejpam-490	249	7	n	n	CCONJ
ejpam-490	249	8	∈	∈	PROPN
ejpam-490	249	9	n0	n0	PROPN
ejpam-490	249	10	)	)	PUNCT
ejpam-490	249	11	and	and	CCONJ
ejpam-490	249	12	γ	γ	X
ejpam-490	249	13	=	=	SYM
ejpam-490	249	14	0	0	NUM
ejpam-490	249	15	in	in	ADP
ejpam-490	249	16	theorem	theorem	NOUN
ejpam-490	249	17	1	1	NUM
ejpam-490	249	18	,	,	PUNCT
ejpam-490	249	19	we	we	PRON
ejpam-490	249	20	have	have	VERB
ejpam-490	249	21	corollary	corollary	ADJ
ejpam-490	249	22	4	4	NUM
ejpam-490	249	23	.	.	PUNCT
ejpam-490	250	1	let	let	VERB
ejpam-490	250	2	the	the	DET
ejpam-490	250	3	function	function	NOUN
ejpam-490	250	4	f	f	PROPN
ejpam-490	250	5	(	(	PUNCT
ejpam-490	250	6	z	z	NOUN
ejpam-490	250	7	)	)	PUNCT
ejpam-490	250	8	defined	define	VERB
ejpam-490	250	9	by	by	ADP
ejpam-490	250	10	(	(	PUNCT
ejpam-490	250	11	1	1	X
ejpam-490	250	12	)	)	PUNCT
ejpam-490	250	13	be	be	AUX
ejpam-490	250	14	in	in	ADP
ejpam-490	250	15	the	the	DET
ejpam-490	250	16	class	class	NOUN
ejpam-490	250	17	s∗	s∗	PROPN
ejpam-490	250	18	�	�	PROPN
ejpam-490	250	19	n	n	CCONJ
ejpam-490	250	20	,	,	PUNCT
ejpam-490	250	21	α	α	PROPN
ejpam-490	250	22	,	,	PUNCT
ejpam-490	250	23	β	β	X
ejpam-490	250	24	�	�	PROPN
ejpam-490	250	25	and	and	CCONJ
ejpam-490	250	26	suppose	suppose	VERB
ejpam-490	250	27	that	that	SCONJ
ejpam-490	250	28	h(z	h(z	NOUN
ejpam-490	250	29	)	)	PUNCT
ejpam-490	250	30	∈	∈	PROPN
ejpam-490	251	1	k	k	INTJ
ejpam-490	251	2	.	.	PUNCT
ejpam-490	252	1	then	then	ADV
ejpam-490	252	2	2n(2−α+	2n(2−α+	NUM
ejpam-490	252	3	β	β	X
ejpam-490	252	4	)	)	PUNCT
ejpam-490	252	5	2	2	NUM
ejpam-490	252	6	�	�	PROPN
ejpam-490	252	7	2n(2−α+	2n(2−α+	NUM
ejpam-490	252	8	β	β	NOUN
ejpam-490	252	9	)	)	PUNCT
ejpam-490	253	1	+	+	CCONJ
ejpam-490	253	2	(	(	PUNCT
ejpam-490	253	3	1−α	1−α	NUM
ejpam-490	253	4	)	)	PUNCT
ejpam-490	253	5	�	�	PROPN
ejpam-490	253	6	(	(	PUNCT
ejpam-490	253	7	f	f	PROPN
ejpam-490	253	8	∗	∗	NOUN
ejpam-490	253	9	h)(z)≺	h)(z)≺	PROPN
ejpam-490	254	1	h(z	h(z	NOUN
ejpam-490	254	2	)	)	PUNCT
ejpam-490	254	3	(	(	PUNCT
ejpam-490	254	4	z	z	NOUN
ejpam-490	254	5	∈	∈	PROPN
ejpam-490	254	6	u	u	NOUN
ejpam-490	254	7	)	)	PUNCT
ejpam-490	254	8	(	(	PUNCT
ejpam-490	254	9	32	32	NUM
ejpam-490	254	10	)	)	PUNCT
ejpam-490	254	11	and	and	CCONJ
ejpam-490	254	12	re	re	ADP
ejpam-490	254	13	(	(	PUNCT
ejpam-490	254	14	f	f	PROPN
ejpam-490	254	15	(	(	PUNCT
ejpam-490	254	16	z	z	NOUN
ejpam-490	254	17	)	)	PUNCT
ejpam-490	254	18	)	)	PUNCT
ejpam-490	254	19	>	>	X
ejpam-490	255	1	−	−	PROPN
ejpam-490	255	2	�	�	PROPN
ejpam-490	255	3	2n(2−α+	2n(2−α+	NUM
ejpam-490	255	4	β	β	X
ejpam-490	255	5	)	)	PUNCT
ejpam-490	255	6	+	+	CCONJ
ejpam-490	255	7	(	(	PUNCT
ejpam-490	255	8	1−α	1−α	NUM
ejpam-490	255	9	)	)	PUNCT
ejpam-490	255	10	�	�	PROPN
ejpam-490	255	11	2n(2−α+	2n(2−α+	NUM
ejpam-490	255	12	β	β	NOUN
ejpam-490	255	13	)	)	PUNCT
ejpam-490	255	14	(	(	PUNCT
ejpam-490	255	15	z	z	NOUN
ejpam-490	255	16	∈	∈	PROPN
ejpam-490	255	17	u	u	NOUN
ejpam-490	255	18	)	)	PUNCT
ejpam-490	255	19	.	.	PUNCT
ejpam-490	256	1	(	(	PUNCT
ejpam-490	256	2	33	33	NUM
ejpam-490	256	3	)	)	PUNCT
ejpam-490	256	4	the	the	DET
ejpam-490	256	5	constant	constant	ADJ
ejpam-490	256	6	factor	factor	NOUN
ejpam-490	256	7	2n(2−α+β	2n(2−α+β	NUM
ejpam-490	256	8	)	)	PUNCT
ejpam-490	256	9	2[2n(2−α+β)+(1−α	2[2n(2−α+β)+(1−α	NUM
ejpam-490	256	10	)	)	PUNCT
ejpam-490	256	11	]	]	PUNCT
ejpam-490	256	12	in	in	ADP
ejpam-490	256	13	the	the	DET
ejpam-490	256	14	subordination	subordination	NOUN
ejpam-490	256	15	result	result	NOUN
ejpam-490	256	16	(	(	PUNCT
ejpam-490	256	17	32	32	NUM
ejpam-490	256	18	)	)	PUNCT
ejpam-490	256	19	can	can	AUX
ejpam-490	256	20	not	not	PART
ejpam-490	256	21	be	be	AUX
ejpam-490	256	22	replaced	replace	VERB
ejpam-490	256	23	by	by	ADP
ejpam-490	256	24	a	a	DET
ejpam-490	256	25	larger	large	ADJ
ejpam-490	256	26	one	one	NOUN
ejpam-490	256	27	.	.	PUNCT
ejpam-490	257	1	putting	put	VERB
ejpam-490	257	2	g(z	g(z	PROPN
ejpam-490	257	3	)	)	PUNCT
ejpam-490	258	1	=	=	SYM
ejpam-490	258	2	z	z	NOUN
ejpam-490	259	1	+	+	NUM
ejpam-490	259	2	∞	∞	NUM
ejpam-490	259	3	∑	∑	PROPN
ejpam-490	259	4	k=2	k=2	PROPN
ejpam-490	259	5	�	�	PROPN
ejpam-490	259	6	k+λ−	k+λ−	PROPN
ejpam-490	259	7	1	1	NUM
ejpam-490	259	8	λ	λ	PROPN
ejpam-490	259	9	�	�	PROPN
ejpam-490	259	10	zk	zk	PROPN
ejpam-490	259	11	(	(	PUNCT
ejpam-490	259	12	λ	λ	X
ejpam-490	259	13	>	>	X
ejpam-490	259	14	−1	−1	NOUN
ejpam-490	259	15	)	)	PUNCT
ejpam-490	259	16	and	and	CCONJ
ejpam-490	259	17	γ=	γ=	PROPN
ejpam-490	259	18	0	0	NUM
ejpam-490	259	19	in	in	ADP
ejpam-490	259	20	theorem	theorem	NOUN
ejpam-490	259	21	1	1	NUM
ejpam-490	259	22	,	,	PUNCT
ejpam-490	259	23	we	we	PRON
ejpam-490	259	24	have	have	VERB
ejpam-490	259	25	corollary	corollary	ADJ
ejpam-490	259	26	5	5	NUM
ejpam-490	259	27	.	.	PUNCT
ejpam-490	260	1	let	let	VERB
ejpam-490	260	2	the	the	DET
ejpam-490	260	3	function	function	NOUN
ejpam-490	260	4	f	f	PROPN
ejpam-490	260	5	(	(	PUNCT
ejpam-490	260	6	z	z	NOUN
ejpam-490	260	7	)	)	PUNCT
ejpam-490	260	8	defined	define	VERB
ejpam-490	260	9	by	by	ADP
ejpam-490	260	10	(	(	PUNCT
ejpam-490	260	11	1	1	X
ejpam-490	260	12	)	)	PUNCT
ejpam-490	260	13	be	be	AUX
ejpam-490	260	14	in	in	ADP
ejpam-490	260	15	the	the	DET
ejpam-490	260	16	class	class	NOUN
ejpam-490	260	17	s∗	s∗	PROPN
ejpam-490	260	18	�	�	PROPN
ejpam-490	260	19	α	α	PROPN
ejpam-490	260	20	,	,	PUNCT
ejpam-490	260	21	β	β	X
ejpam-490	260	22	,	,	PUNCT
ejpam-490	260	23	λ	λ	PROPN
ejpam-490	260	24	�	�	PROPN
ejpam-490	260	25	and	and	CCONJ
ejpam-490	260	26	suppose	suppose	VERB
ejpam-490	260	27	that	that	SCONJ
ejpam-490	260	28	h(z	h(z	NOUN
ejpam-490	260	29	)	)	PUNCT
ejpam-490	260	30	∈	∈	PROPN
ejpam-490	261	1	k	k	INTJ
ejpam-490	261	2	.	.	PUNCT
ejpam-490	262	1	then	then	ADV
ejpam-490	262	2	(	(	PUNCT
ejpam-490	262	3	2−α+	2−α+	NUM
ejpam-490	262	4	β)(1+λ	β)(1+λ	NUM
ejpam-490	262	5	)	)	PUNCT
ejpam-490	262	6	2	2	NUM
ejpam-490	262	7	�	�	PROPN
ejpam-490	262	8	2λ+	2λ+	NUM
ejpam-490	262	9	3−α(λ+	3−α(λ+	NOUN
ejpam-490	262	10	2)+	2)+	NUM
ejpam-490	262	11	(	(	PUNCT
ejpam-490	262	12	1+λ)β	1+λ)β	NUM
ejpam-490	262	13	�	�	NOUN
ejpam-490	262	14	(	(	PUNCT
ejpam-490	262	15	f	f	PROPN
ejpam-490	262	16	∗	∗	NOUN
ejpam-490	262	17	h)(z)≺	h)(z)≺	PROPN
ejpam-490	263	1	h(z	h(z	NOUN
ejpam-490	263	2	)	)	PUNCT
ejpam-490	263	3	(	(	PUNCT
ejpam-490	263	4	z	z	NOUN
ejpam-490	263	5	∈	∈	PROPN
ejpam-490	263	6	u	u	NOUN
ejpam-490	263	7	)	)	PUNCT
ejpam-490	263	8	(	(	PUNCT
ejpam-490	263	9	34	34	NUM
ejpam-490	263	10	)	)	PUNCT
ejpam-490	263	11	and	and	CCONJ
ejpam-490	263	12	re	re	ADP
ejpam-490	263	13	(	(	PUNCT
ejpam-490	263	14	f	f	PROPN
ejpam-490	263	15	(	(	PUNCT
ejpam-490	263	16	z	z	NOUN
ejpam-490	263	17	)	)	PUNCT
ejpam-490	263	18	)	)	PUNCT
ejpam-490	264	1	>	>	X
ejpam-490	265	1	−	−	PROPN
ejpam-490	265	2	�	�	PROPN
ejpam-490	265	3	2λ+	2λ+	NUM
ejpam-490	265	4	3−α(λ+	3−α(λ+	NOUN
ejpam-490	265	5	2)+	2)+	NUM
ejpam-490	265	6	(	(	PUNCT
ejpam-490	265	7	1+λ)β	1+λ)β	NUM
ejpam-490	265	8	�	�	PROPN
ejpam-490	265	9	(	(	PUNCT
ejpam-490	265	10	2−α+	2−α+	PROPN
ejpam-490	265	11	β)(1+λ	β)(1+λ	NUM
ejpam-490	265	12	)	)	PUNCT
ejpam-490	265	13	(	(	PUNCT
ejpam-490	265	14	z	z	NOUN
ejpam-490	265	15	∈	∈	PROPN
ejpam-490	265	16	u	u	NOUN
ejpam-490	265	17	)	)	PUNCT
ejpam-490	265	18	.	.	PUNCT
ejpam-490	266	1	(	(	PUNCT
ejpam-490	266	2	35	35	NUM
ejpam-490	266	3	)	)	PUNCT
ejpam-490	266	4	the	the	DET
ejpam-490	266	5	constant	constant	ADJ
ejpam-490	266	6	factor	factor	NOUN
ejpam-490	266	7	(	(	PUNCT
ejpam-490	266	8	2−α+β)(1+λ	2−α+β)(1+λ	NUM
ejpam-490	266	9	)	)	PUNCT
ejpam-490	266	10	2[2λ+3−α(λ+2)+(1+λ)β	2[2λ+3−α(λ+2)+(1+λ)β	NUM
ejpam-490	266	11	]	]	PUNCT
ejpam-490	266	12	in	in	ADP
ejpam-490	266	13	the	the	DET
ejpam-490	266	14	subordination	subordination	NOUN
ejpam-490	266	15	result	result	NOUN
ejpam-490	266	16	(	(	PUNCT
ejpam-490	266	17	34	34	NUM
ejpam-490	266	18	)	)	PUNCT
ejpam-490	266	19	can	can	AUX
ejpam-490	266	20	not	not	PART
ejpam-490	266	21	be	be	AUX
ejpam-490	266	22	replaced	replace	VERB
ejpam-490	266	23	by	by	ADP
ejpam-490	266	24	a	a	DET
ejpam-490	266	25	larger	large	ADJ
ejpam-490	266	26	one	one	NOUN
ejpam-490	266	27	.	.	PUNCT
ejpam-490	267	1	putting	put	VERB
ejpam-490	267	2	g(z	g(z	PROPN
ejpam-490	267	3	)	)	PUNCT
ejpam-490	268	1	=	=	PUNCT
ejpam-490	268	2	z+	z+	NUM
ejpam-490	268	3	∞	∞	NUM
ejpam-490	268	4	∑	∑	PUNCT
ejpam-490	268	5	k=2	k=2	PROPN
ejpam-490	269	1	[	[	X
ejpam-490	269	2	1+λ(k−	1+λ(k−	NUM
ejpam-490	269	3	1)]n	1)]n	NUM
ejpam-490	269	4	zk	zk	PROPN
ejpam-490	269	5	(	(	PUNCT
ejpam-490	269	6	λ≥	λ≥	PROPN
ejpam-490	269	7	0	0	NUM
ejpam-490	269	8	,	,	PUNCT
ejpam-490	269	9	n	n	PRON
ejpam-490	269	10	∈	∈	PROPN
ejpam-490	269	11	n0	n0	NUM
ejpam-490	269	12	)	)	PUNCT
ejpam-490	269	13	and	and	CCONJ
ejpam-490	269	14	γ	γ	X
ejpam-490	269	15	=	=	SYM
ejpam-490	269	16	0	0	NUM
ejpam-490	269	17	in	in	ADP
ejpam-490	269	18	theorem	theorem	NOUN
ejpam-490	269	19	1	1	NUM
ejpam-490	269	20	,	,	PUNCT
ejpam-490	269	21	we	we	PRON
ejpam-490	269	22	have	have	VERB
ejpam-490	269	23	m.	m.	PROPN
ejpam-490	269	24	aouf	aouf	PROPN
ejpam-490	269	25	,	,	PUNCT
ejpam-490	269	26	r.	r.	PROPN
ejpam-490	269	27	el	el	PROPN
ejpam-490	269	28	-	-	PUNCT
ejpam-490	269	29	ashwah	ashwah	PROPN
ejpam-490	269	30	,	,	PUNCT
ejpam-490	269	31	s.	s.	PROPN
ejpam-490	269	32	el	el	PROPN
ejpam-490	269	33	-	-	PUNCT
ejpam-490	269	34	deeb	deeb	PROPN
ejpam-490	269	35	/	/	SYM
ejpam-490	269	36	eur	eur	PROPN
ejpam-490	269	37	.	.	PUNCT
ejpam-490	270	1	j.	j.	PROPN
ejpam-490	270	2	pure	pure	PROPN
ejpam-490	270	3	appl	appl	PROPN
ejpam-490	270	4	.	.	PROPN
ejpam-490	270	5	math	math	PROPN
ejpam-490	270	6	,	,	PUNCT
ejpam-490	270	7	3	3	NUM
ejpam-490	270	8	(	(	PUNCT
ejpam-490	270	9	2010	2010	NUM
ejpam-490	270	10	)	)	PUNCT
ejpam-490	270	11	,	,	PUNCT
ejpam-490	270	12	903	903	NUM
ejpam-490	270	13	-	-	SYM
ejpam-490	270	14	917	917	NUM
ejpam-490	270	15	913	913	NUM
ejpam-490	270	16	corollary	corollary	ADJ
ejpam-490	270	17	6	6	NUM
ejpam-490	270	18	.	.	PUNCT
ejpam-490	271	1	let	let	VERB
ejpam-490	271	2	the	the	DET
ejpam-490	271	3	function	function	NOUN
ejpam-490	271	4	f	f	PROPN
ejpam-490	271	5	(	(	PUNCT
ejpam-490	271	6	z	z	NOUN
ejpam-490	271	7	)	)	PUNCT
ejpam-490	271	8	defined	define	VERB
ejpam-490	271	9	by	by	ADP
ejpam-490	271	10	(	(	PUNCT
ejpam-490	271	11	1	1	X
ejpam-490	271	12	)	)	PUNCT
ejpam-490	271	13	be	be	AUX
ejpam-490	271	14	in	in	ADP
ejpam-490	271	15	the	the	DET
ejpam-490	271	16	class	class	NOUN
ejpam-490	271	17	s∗	s∗	PROPN
ejpam-490	271	18	λ	λ	PROPN
ejpam-490	271	19	�	�	PROPN
ejpam-490	271	20	n	n	CCONJ
ejpam-490	271	21	,	,	PUNCT
ejpam-490	271	22	α	α	PROPN
ejpam-490	271	23	,	,	PUNCT
ejpam-490	271	24	β	β	X
ejpam-490	271	25	�	�	PROPN
ejpam-490	271	26	and	and	CCONJ
ejpam-490	271	27	suppose	suppose	VERB
ejpam-490	271	28	that	that	SCONJ
ejpam-490	271	29	h(z	h(z	NOUN
ejpam-490	271	30	)	)	PUNCT
ejpam-490	271	31	∈	∈	PROPN
ejpam-490	272	1	k	k	INTJ
ejpam-490	272	2	.	.	PUNCT
ejpam-490	273	1	then	then	ADV
ejpam-490	273	2	(	(	PUNCT
ejpam-490	273	3	2−α+	2−α+	NUM
ejpam-490	273	4	β)(1+λ)n	β)(1+λ)n	ADJ
ejpam-490	273	5	2	2	NUM
ejpam-490	273	6	�	�	PROPN
ejpam-490	273	7	(	(	PUNCT
ejpam-490	273	8	2−α+	2−α+	NUM
ejpam-490	273	9	β)(1+λ)n+	β)(1+λ)n+	NUM
ejpam-490	273	10	(	(	PUNCT
ejpam-490	273	11	1−α	1−α	NUM
ejpam-490	273	12	)	)	PUNCT
ejpam-490	273	13	�	�	PROPN
ejpam-490	273	14	(	(	PUNCT
ejpam-490	273	15	f	f	PROPN
ejpam-490	273	16	∗	∗	NOUN
ejpam-490	273	17	h)(z	h)(z	NOUN
ejpam-490	273	18	)	)	PUNCT
ejpam-490	273	19	≺	≺	NOUN
ejpam-490	273	20	h(z	h(z	NOUN
ejpam-490	273	21	)	)	PUNCT
ejpam-490	273	22	(	(	PUNCT
ejpam-490	273	23	z	z	NOUN
ejpam-490	273	24	∈	∈	PROPN
ejpam-490	273	25	u	u	NOUN
ejpam-490	273	26	)	)	PUNCT
ejpam-490	273	27	(	(	PUNCT
ejpam-490	273	28	36	36	NUM
ejpam-490	273	29	)	)	PUNCT
ejpam-490	273	30	and	and	CCONJ
ejpam-490	273	31	re	re	VERB
ejpam-490	273	32	(	(	PUNCT
ejpam-490	273	33	f	f	PROPN
ejpam-490	273	34	(	(	PUNCT
ejpam-490	273	35	z	z	NOUN
ejpam-490	273	36	)	)	PUNCT
ejpam-490	273	37	)	)	PUNCT
ejpam-490	273	38	>	>	X
ejpam-490	274	1	−	−	PROPN
ejpam-490	274	2	�	�	PROPN
ejpam-490	274	3	(	(	PUNCT
ejpam-490	274	4	2−α+	2−α+	NUM
ejpam-490	274	5	β)(1+λ)n+	β)(1+λ)n+	NUM
ejpam-490	274	6	(	(	PUNCT
ejpam-490	274	7	1−α	1−α	NUM
ejpam-490	274	8	)	)	PUNCT
ejpam-490	274	9	�	�	PROPN
ejpam-490	274	10	(	(	PUNCT
ejpam-490	274	11	2−α+	2−α+	PROPN
ejpam-490	274	12	β)(1+λ)n	β)(1+λ)n	PROPN
ejpam-490	274	13	(	(	PUNCT
ejpam-490	274	14	z	z	NOUN
ejpam-490	274	15	∈	∈	PROPN
ejpam-490	274	16	u	u	NOUN
ejpam-490	274	17	)	)	PUNCT
ejpam-490	274	18	.	.	PUNCT
ejpam-490	275	1	(	(	PUNCT
ejpam-490	275	2	37	37	NUM
ejpam-490	275	3	)	)	PUNCT
ejpam-490	275	4	the	the	DET
ejpam-490	275	5	constant	constant	ADJ
ejpam-490	275	6	factor	factor	NOUN
ejpam-490	275	7	(	(	PUNCT
ejpam-490	275	8	2−α+β)(1+λ)n	2−α+β)(1+λ)n	NOUN
ejpam-490	275	9	2[(2−α+β)(1+λ)n+(1−α	2[(2−α+β)(1+λ)n+(1−α	NUM
ejpam-490	275	10	)	)	PUNCT
ejpam-490	275	11	]	]	PUNCT
ejpam-490	275	12	in	in	ADP
ejpam-490	275	13	the	the	DET
ejpam-490	275	14	subordination	subordination	NOUN
ejpam-490	275	15	result	result	NOUN
ejpam-490	275	16	(	(	PUNCT
ejpam-490	275	17	36	36	NUM
ejpam-490	275	18	)	)	PUNCT
ejpam-490	275	19	can	can	AUX
ejpam-490	275	20	not	not	PART
ejpam-490	275	21	be	be	AUX
ejpam-490	275	22	replaced	replace	VERB
ejpam-490	275	23	by	by	ADP
ejpam-490	275	24	a	a	DET
ejpam-490	275	25	larger	large	ADJ
ejpam-490	275	26	one	one	NOUN
ejpam-490	275	27	.	.	PUNCT
ejpam-490	276	1	putting	put	VERB
ejpam-490	276	2	g(z	g(z	PROPN
ejpam-490	276	3	)	)	PUNCT
ejpam-490	277	1	=	=	SYM
ejpam-490	277	2	z	z	NOUN
ejpam-490	278	1	+	+	NUM
ejpam-490	278	2	∞	∞	NUM
ejpam-490	278	3	∑	∑	PROPN
ejpam-490	278	4	k=2	k=2	PROPN
ejpam-490	278	5	γkzk	γkzk	NOUN
ejpam-490	278	6	where	where	SCONJ
ejpam-490	278	7	γk	γk	PROPN
ejpam-490	278	8	is	be	AUX
ejpam-490	278	9	defined	define	VERB
ejpam-490	278	10	by	by	ADP
ejpam-490	278	11	(	(	PUNCT
ejpam-490	278	12	9	9	NUM
ejpam-490	278	13	)	)	PUNCT
ejpam-490	278	14	in	in	ADP
ejpam-490	278	15	theorem	theorem	NOUN
ejpam-490	278	16	1	1	NUM
ejpam-490	278	17	,	,	PUNCT
ejpam-490	278	18	we	we	PRON
ejpam-490	278	19	have	have	VERB
ejpam-490	278	20	corollary	corollary	ADJ
ejpam-490	278	21	7	7	NUM
ejpam-490	278	22	.	.	PUNCT
ejpam-490	279	1	let	let	VERB
ejpam-490	279	2	the	the	DET
ejpam-490	279	3	function	function	NOUN
ejpam-490	279	4	f	f	PROPN
ejpam-490	279	5	(	(	PUNCT
ejpam-490	279	6	z	z	NOUN
ejpam-490	279	7	)	)	PUNCT
ejpam-490	279	8	defined	define	VERB
ejpam-490	279	9	by	by	ADP
ejpam-490	279	10	(	(	PUNCT
ejpam-490	279	11	1	1	X
ejpam-490	279	12	)	)	PUNCT
ejpam-490	279	13	be	be	AUX
ejpam-490	279	14	in	in	ADP
ejpam-490	279	15	the	the	DET
ejpam-490	279	16	class	class	NOUN
ejpam-490	279	17	ss,∗	ss,∗	NOUN
ejpam-490	279	18	q	q	X
ejpam-490	279	19	(	(	PUNCT
ejpam-490	279	20	γ	γ	X
ejpam-490	279	21	,	,	PUNCT
ejpam-490	279	22	α	α	NOUN
ejpam-490	279	23	,	,	PUNCT
ejpam-490	279	24	β	β	NOUN
ejpam-490	279	25	)	)	PUNCT
ejpam-490	279	26	and	and	CCONJ
ejpam-490	279	27	suppose	suppose	VERB
ejpam-490	279	28	that	that	SCONJ
ejpam-490	279	29	h(z	h(z	NOUN
ejpam-490	279	30	)	)	PUNCT
ejpam-490	279	31	∈	∈	PROPN
ejpam-490	280	1	k	k	INTJ
ejpam-490	280	2	.	.	PUNCT
ejpam-490	281	1	then	then	ADV
ejpam-490	281	2	(	(	PUNCT
ejpam-490	281	3	2−α+	2−α+	NUM
ejpam-490	281	4	β)(1	β)(1	PUNCT
ejpam-490	281	5	+	+	X
ejpam-490	281	6	γ)γ2	γ)γ2	PROPN
ejpam-490	281	7	2	2	NUM
ejpam-490	281	8	�	�	PROPN
ejpam-490	281	9	(	(	PUNCT
ejpam-490	281	10	2−α+	2−α+	NUM
ejpam-490	281	11	β)(1	β)(1	PUNCT
ejpam-490	281	12	+	+	X
ejpam-490	281	13	γ)γ2	γ)γ2	NOUN
ejpam-490	281	14	+	+	SYM
ejpam-490	281	15	(	(	PUNCT
ejpam-490	281	16	1−α	1−α	NUM
ejpam-490	281	17	)	)	PUNCT
ejpam-490	281	18	�	�	PROPN
ejpam-490	281	19	(	(	PUNCT
ejpam-490	281	20	f	f	PROPN
ejpam-490	281	21	∗	∗	NOUN
ejpam-490	281	22	h)(z)≺	h)(z)≺	PROPN
ejpam-490	281	23	h(z	h(z	NOUN
ejpam-490	281	24	)	)	PUNCT
ejpam-490	281	25	(	(	PUNCT
ejpam-490	281	26	z	z	NOUN
ejpam-490	281	27	∈	∈	PROPN
ejpam-490	281	28	u	u	NOUN
ejpam-490	281	29	)	)	PUNCT
ejpam-490	281	30	(	(	PUNCT
ejpam-490	281	31	38	38	NUM
ejpam-490	281	32	)	)	PUNCT
ejpam-490	281	33	where	where	SCONJ
ejpam-490	281	34	γ2	γ2	PROPN
ejpam-490	281	35	defined	define	VERB
ejpam-490	281	36	by	by	ADP
ejpam-490	281	37	(	(	PUNCT
ejpam-490	281	38	8)	8)	NUM
ejpam-490	281	39	,	,	PUNCT
ejpam-490	281	40	and	and	CCONJ
ejpam-490	281	41	re	re	VERB
ejpam-490	281	42	(	(	PUNCT
ejpam-490	281	43	f	f	PROPN
ejpam-490	281	44	(	(	PUNCT
ejpam-490	281	45	z	z	NOUN
ejpam-490	281	46	)	)	PUNCT
ejpam-490	281	47	)	)	PUNCT
ejpam-490	281	48	>	>	X
ejpam-490	282	1	−	−	PROPN
ejpam-490	282	2	�	�	PROPN
ejpam-490	282	3	(	(	PUNCT
ejpam-490	282	4	2−α+	2−α+	NUM
ejpam-490	282	5	β)(1	β)(1	PUNCT
ejpam-490	282	6	+	+	X
ejpam-490	282	7	γ)γ2	γ)γ2	NOUN
ejpam-490	282	8	+	+	SYM
ejpam-490	282	9	(	(	PUNCT
ejpam-490	282	10	1−α	1−α	NUM
ejpam-490	282	11	)	)	PUNCT
ejpam-490	282	12	�	�	PROPN
ejpam-490	282	13	(	(	PUNCT
ejpam-490	282	14	2−α+	2−α+	NUM
ejpam-490	282	15	β)(1	β)(1	PUNCT
ejpam-490	282	16	+	+	X
ejpam-490	282	17	γ)γ2	γ)γ2	NOUN
ejpam-490	282	18	(	(	PUNCT
ejpam-490	282	19	z	z	NOUN
ejpam-490	282	20	∈	∈	PROPN
ejpam-490	282	21	u	u	NOUN
ejpam-490	282	22	)	)	PUNCT
ejpam-490	282	23	.	.	PUNCT
ejpam-490	283	1	(	(	PUNCT
ejpam-490	283	2	39	39	NUM
ejpam-490	283	3	)	)	PUNCT
ejpam-490	283	4	the	the	DET
ejpam-490	283	5	constant	constant	ADJ
ejpam-490	283	6	factor	factor	NOUN
ejpam-490	283	7	(	(	PUNCT
ejpam-490	283	8	2−α+β)(1+γ)γ2	2−α+β)(1+γ)γ2	NOUN
ejpam-490	283	9	2[(2−α+β)(1+γ)γ2+(1−α	2[(2−α+β)(1+γ)γ2+(1−α	NOUN
ejpam-490	283	10	)	)	PUNCT
ejpam-490	283	11	]	]	PUNCT
ejpam-490	283	12	in	in	ADP
ejpam-490	283	13	the	the	DET
ejpam-490	283	14	subordination	subordination	NOUN
ejpam-490	283	15	result	result	NOUN
ejpam-490	283	16	(	(	PUNCT
ejpam-490	283	17	38	38	NUM
ejpam-490	283	18	)	)	PUNCT
ejpam-490	283	19	can	can	AUX
ejpam-490	283	20	not	not	PART
ejpam-490	283	21	be	be	AUX
ejpam-490	283	22	replaced	replace	VERB
ejpam-490	283	23	by	by	ADP
ejpam-490	283	24	a	a	DET
ejpam-490	283	25	larger	large	ADJ
ejpam-490	283	26	one	one	NOUN
ejpam-490	283	27	.	.	PUNCT
ejpam-490	284	1	putting	put	VERB
ejpam-490	284	2	g(z	g(z	PROPN
ejpam-490	284	3	)	)	PUNCT
ejpam-490	285	1	=	=	SYM
ejpam-490	285	2	z	z	NOUN
ejpam-490	286	1	+	+	NUM
ejpam-490	286	2	∞	∞	PROPN
ejpam-490	286	3	∑	∑	PROPN
ejpam-490	286	4	k=2	k=2	PROPN
ejpam-490	286	5	(	(	PUNCT
ejpam-490	286	6	a)k−1	a)k−1	PROPN
ejpam-490	286	7	(	(	PUNCT
ejpam-490	286	8	c)k−1	c)k−1	PROPN
ejpam-490	286	9	zk	zk	PROPN
ejpam-490	286	10	(	(	PUNCT
ejpam-490	286	11	c	c	PROPN
ejpam-490	286	12	6=	6=	NUM
ejpam-490	286	13	0,−1,−2	0,−1,−2	NUM
ejpam-490	286	14	,	,	PUNCT
ejpam-490	286	15	.	.	PUNCT
ejpam-490	286	16	.	.	PUNCT
ejpam-490	286	17	.	.	PUNCT
ejpam-490	286	18	)	)	PUNCT
ejpam-490	287	1	in	in	ADP
ejpam-490	287	2	theorem	theorem	NOUN
ejpam-490	287	3	1	1	NUM
ejpam-490	287	4	,	,	PUNCT
ejpam-490	287	5	we	we	PRON
ejpam-490	287	6	have	have	VERB
ejpam-490	287	7	corollary	corollary	ADJ
ejpam-490	287	8	8	8	NUM
ejpam-490	287	9	.	.	PUNCT
ejpam-490	288	1	let	let	VERB
ejpam-490	288	2	the	the	DET
ejpam-490	288	3	function	function	NOUN
ejpam-490	288	4	f	f	PROPN
ejpam-490	288	5	(	(	PUNCT
ejpam-490	288	6	z	z	NOUN
ejpam-490	288	7	)	)	PUNCT
ejpam-490	288	8	defined	define	VERB
ejpam-490	288	9	by	by	ADP
ejpam-490	288	10	(	(	PUNCT
ejpam-490	288	11	1	1	X
ejpam-490	288	12	)	)	PUNCT
ejpam-490	288	13	be	be	AUX
ejpam-490	288	14	in	in	ADP
ejpam-490	288	15	the	the	DET
ejpam-490	288	16	class	class	NOUN
ejpam-490	288	17	s∗	s∗	PROPN
ejpam-490	288	18	�	�	PROPN
ejpam-490	288	19	γ	γ	PROPN
ejpam-490	288	20	,	,	PUNCT
ejpam-490	288	21	α	α	PROPN
ejpam-490	288	22	,	,	PUNCT
ejpam-490	288	23	β	β	X
ejpam-490	288	24	�	�	PROPN
ejpam-490	288	25	and	and	CCONJ
ejpam-490	288	26	suppose	suppose	VERB
ejpam-490	288	27	that	that	SCONJ
ejpam-490	288	28	h(z	h(z	NOUN
ejpam-490	288	29	)	)	PUNCT
ejpam-490	288	30	∈	∈	PROPN
ejpam-490	289	1	k	k	INTJ
ejpam-490	289	2	.	.	PUNCT
ejpam-490	290	1	then	then	ADV
ejpam-490	290	2	(	(	PUNCT
ejpam-490	290	3	2−α+	2−α+	NUM
ejpam-490	290	4	β)(1	β)(1	PUNCT
ejpam-490	290	5	+	+	CCONJ
ejpam-490	290	6	γ)a	γ)a	SYM
ejpam-490	290	7	2	2	NUM
ejpam-490	290	8	�	�	PROPN
ejpam-490	290	9	(	(	PUNCT
ejpam-490	290	10	2−α+	2−α+	NUM
ejpam-490	290	11	β)(1	β)(1	NOUN
ejpam-490	290	12	+	+	X
ejpam-490	290	13	γ)a+	γ)a+	NUM
ejpam-490	290	14	(	(	PUNCT
ejpam-490	290	15	1−α)c	1−α)c	NUM
ejpam-490	290	16	�	�	PROPN
ejpam-490	290	17	(	(	PUNCT
ejpam-490	290	18	f	f	PROPN
ejpam-490	290	19	∗	∗	VERB
ejpam-490	290	20	h)(z	h)(z	NOUN
ejpam-490	290	21	)	)	PUNCT
ejpam-490	290	22	≺	≺	NOUN
ejpam-490	290	23	h(z	h(z	NOUN
ejpam-490	290	24	)	)	PUNCT
ejpam-490	290	25	(	(	PUNCT
ejpam-490	290	26	z	z	NOUN
ejpam-490	290	27	∈	∈	PROPN
ejpam-490	290	28	u	u	NOUN
ejpam-490	290	29	)	)	PUNCT
ejpam-490	290	30	(	(	PUNCT
ejpam-490	290	31	40	40	NUM
ejpam-490	290	32	)	)	PUNCT
ejpam-490	290	33	and	and	CCONJ
ejpam-490	290	34	re	re	ADP
ejpam-490	290	35	(	(	PUNCT
ejpam-490	290	36	f	f	PROPN
ejpam-490	290	37	(	(	PUNCT
ejpam-490	290	38	z	z	NOUN
ejpam-490	290	39	)	)	PUNCT
ejpam-490	290	40	)	)	PUNCT
ejpam-490	290	41	>	>	X
ejpam-490	291	1	−	−	PROPN
ejpam-490	291	2	�	�	PROPN
ejpam-490	291	3	(	(	PUNCT
ejpam-490	291	4	2−α+β)(1	2−α+β)(1	NOUN
ejpam-490	291	5	+	+	X
ejpam-490	291	6	γ)a+	γ)a+	NUM
ejpam-490	291	7	(	(	PUNCT
ejpam-490	291	8	1−α)c	1−α)c	NUM
ejpam-490	291	9	�	�	PROPN
ejpam-490	291	10	(	(	PUNCT
ejpam-490	291	11	2−α+	2−α+	NUM
ejpam-490	291	12	β)(1	β)(1	PUNCT
ejpam-490	291	13	+	+	X
ejpam-490	291	14	γ)a	γ)a	X
ejpam-490	291	15	(	(	PUNCT
ejpam-490	291	16	z	z	NOUN
ejpam-490	291	17	∈	∈	PROPN
ejpam-490	291	18	u	u	NOUN
ejpam-490	291	19	)	)	PUNCT
ejpam-490	291	20	.	.	PUNCT
ejpam-490	292	1	(	(	PUNCT
ejpam-490	292	2	41	41	NUM
ejpam-490	292	3	)	)	PUNCT
ejpam-490	292	4	the	the	DET
ejpam-490	292	5	constant	constant	ADJ
ejpam-490	292	6	factor	factor	NOUN
ejpam-490	292	7	(	(	PUNCT
ejpam-490	292	8	2−α+β)(1+γ)a	2−α+β)(1+γ)a	NOUN
ejpam-490	292	9	2[(2−α+β)(1+γ)a+(1−α)c	2[(2−α+β)(1+γ)a+(1−α)c	NUM
ejpam-490	292	10	]	]	PUNCT
ejpam-490	292	11	in	in	ADP
ejpam-490	292	12	the	the	DET
ejpam-490	292	13	subordination	subordination	NOUN
ejpam-490	292	14	result	result	NOUN
ejpam-490	292	15	(	(	PUNCT
ejpam-490	292	16	40	40	NUM
ejpam-490	292	17	)	)	PUNCT
ejpam-490	292	18	can	can	AUX
ejpam-490	292	19	not	not	PART
ejpam-490	292	20	be	be	AUX
ejpam-490	292	21	replaced	replace	VERB
ejpam-490	292	22	by	by	ADP
ejpam-490	292	23	a	a	DET
ejpam-490	292	24	larger	large	ADJ
ejpam-490	292	25	one	one	NOUN
ejpam-490	292	26	.	.	PUNCT
ejpam-490	293	1	putting	put	VERB
ejpam-490	293	2	g(z	g(z	PROPN
ejpam-490	293	3	)	)	PUNCT
ejpam-490	294	1	=	=	SYM
ejpam-490	294	2	z	z	NOUN
ejpam-490	295	1	+	+	NUM
ejpam-490	295	2	∞	∞	NUM
ejpam-490	295	3	∑	∑	PROPN
ejpam-490	295	4	k=2	k=2	PROPN
ejpam-490	295	5	knzk	knzk	PROPN
ejpam-490	295	6	,	,	PUNCT
ejpam-490	295	7	(	(	PUNCT
ejpam-490	295	8	n	n	CCONJ
ejpam-490	295	9	∈	∈	PROPN
ejpam-490	295	10	n0	n0	NUM
ejpam-490	295	11	)	)	PUNCT
ejpam-490	295	12	in	in	ADP
ejpam-490	295	13	theorem	theorem	NOUN
ejpam-490	295	14	1	1	NUM
ejpam-490	295	15	,	,	PUNCT
ejpam-490	295	16	we	we	PRON
ejpam-490	295	17	have	have	VERB
ejpam-490	295	18	m.	m.	PROPN
ejpam-490	295	19	aouf	aouf	PROPN
ejpam-490	295	20	,	,	PUNCT
ejpam-490	295	21	r.	r.	PROPN
ejpam-490	295	22	el	el	PROPN
ejpam-490	295	23	-	-	PUNCT
ejpam-490	295	24	ashwah	ashwah	PROPN
ejpam-490	295	25	,	,	PUNCT
ejpam-490	295	26	s.	s.	PROPN
ejpam-490	295	27	el	el	PROPN
ejpam-490	295	28	-	-	PUNCT
ejpam-490	295	29	deeb	deeb	PROPN
ejpam-490	295	30	/	/	SYM
ejpam-490	295	31	eur	eur	PROPN
ejpam-490	295	32	.	.	PUNCT
ejpam-490	296	1	j.	j.	PROPN
ejpam-490	296	2	pure	pure	PROPN
ejpam-490	296	3	appl	appl	PROPN
ejpam-490	296	4	.	.	PROPN
ejpam-490	296	5	math	math	PROPN
ejpam-490	296	6	,	,	PUNCT
ejpam-490	296	7	3	3	NUM
ejpam-490	296	8	(	(	PUNCT
ejpam-490	296	9	2010	2010	NUM
ejpam-490	296	10	)	)	PUNCT
ejpam-490	296	11	,	,	PUNCT
ejpam-490	296	12	903	903	NUM
ejpam-490	296	13	-	-	SYM
ejpam-490	296	14	917	917	NUM
ejpam-490	296	15	914	914	NUM
ejpam-490	296	16	corollary	corollary	ADJ
ejpam-490	296	17	9	9	NUM
ejpam-490	296	18	.	.	PUNCT
ejpam-490	297	1	let	let	VERB
ejpam-490	297	2	the	the	DET
ejpam-490	297	3	function	function	NOUN
ejpam-490	297	4	f	f	PROPN
ejpam-490	297	5	(	(	PUNCT
ejpam-490	297	6	z	z	NOUN
ejpam-490	297	7	)	)	PUNCT
ejpam-490	297	8	defined	define	VERB
ejpam-490	297	9	by	by	ADP
ejpam-490	297	10	(	(	PUNCT
ejpam-490	297	11	1	1	X
ejpam-490	297	12	)	)	PUNCT
ejpam-490	297	13	be	be	AUX
ejpam-490	297	14	in	in	ADP
ejpam-490	297	15	the	the	DET
ejpam-490	297	16	class	class	NOUN
ejpam-490	297	17	s∗γ	s∗γ	PUNCT
ejpam-490	297	18	�	�	PROPN
ejpam-490	297	19	n	n	CCONJ
ejpam-490	297	20	,	,	PUNCT
ejpam-490	297	21	α	α	PROPN
ejpam-490	297	22	,	,	PUNCT
ejpam-490	297	23	β	β	X
ejpam-490	297	24	�	�	PROPN
ejpam-490	297	25	and	and	CCONJ
ejpam-490	297	26	suppose	suppose	VERB
ejpam-490	297	27	that	that	SCONJ
ejpam-490	297	28	h(z	h(z	NOUN
ejpam-490	297	29	)	)	PUNCT
ejpam-490	297	30	∈	∈	PROPN
ejpam-490	298	1	k	k	INTJ
ejpam-490	298	2	.	.	PUNCT
ejpam-490	299	1	then	then	ADV
ejpam-490	299	2	2n(2−α+	2n(2−α+	NUM
ejpam-490	299	3	β)(1	β)(1	SYM
ejpam-490	299	4	+	+	ADJ
ejpam-490	299	5	γ	γ	X
ejpam-490	299	6	)	)	PUNCT
ejpam-490	299	7	2	2	NUM
ejpam-490	299	8	�	�	PROPN
ejpam-490	299	9	2n(2−α+	2n(2−α+	NUM
ejpam-490	299	10	β)(1	β)(1	NOUN
ejpam-490	299	11	+	+	ADJ
ejpam-490	299	12	γ	γ	X
ejpam-490	299	13	)	)	PUNCT
ejpam-490	299	14	+	+	CCONJ
ejpam-490	299	15	(	(	PUNCT
ejpam-490	299	16	1−α	1−α	NUM
ejpam-490	299	17	)	)	PUNCT
ejpam-490	299	18	�	�	PROPN
ejpam-490	299	19	(	(	PUNCT
ejpam-490	299	20	f	f	PROPN
ejpam-490	299	21	∗	∗	NOUN
ejpam-490	299	22	h)(z)≺	h)(z)≺	PROPN
ejpam-490	299	23	h(z	h(z	NOUN
ejpam-490	299	24	)	)	PUNCT
ejpam-490	299	25	(	(	PUNCT
ejpam-490	299	26	z	z	NOUN
ejpam-490	299	27	∈	∈	PROPN
ejpam-490	299	28	u	u	NOUN
ejpam-490	299	29	)	)	PUNCT
ejpam-490	299	30	(	(	PUNCT
ejpam-490	299	31	42	42	NUM
ejpam-490	299	32	)	)	PUNCT
ejpam-490	299	33	and	and	CCONJ
ejpam-490	299	34	re	re	VERB
ejpam-490	299	35	(	(	PUNCT
ejpam-490	299	36	f	f	PROPN
ejpam-490	299	37	(	(	PUNCT
ejpam-490	299	38	z	z	NOUN
ejpam-490	299	39	)	)	PUNCT
ejpam-490	299	40	)	)	PUNCT
ejpam-490	299	41	>	>	X
ejpam-490	300	1	−	−	PROPN
ejpam-490	300	2	�	�	PROPN
ejpam-490	300	3	2n(2−α+	2n(2−α+	NUM
ejpam-490	300	4	β)(1	β)(1	NOUN
ejpam-490	300	5	+	+	ADJ
ejpam-490	300	6	γ	γ	X
ejpam-490	300	7	)	)	PUNCT
ejpam-490	300	8	+	+	CCONJ
ejpam-490	300	9	(	(	PUNCT
ejpam-490	300	10	1−α	1−α	NUM
ejpam-490	300	11	)	)	PUNCT
ejpam-490	300	12	�	�	PROPN
ejpam-490	301	1	2n(2−α+	2n(2−α+	NUM
ejpam-490	301	2	β)(1	β)(1	NOUN
ejpam-490	301	3	+	+	ADJ
ejpam-490	301	4	γ	γ	X
ejpam-490	301	5	)	)	PUNCT
ejpam-490	301	6	(	(	PUNCT
ejpam-490	301	7	z	z	NOUN
ejpam-490	301	8	∈	∈	PROPN
ejpam-490	301	9	u	u	NOUN
ejpam-490	301	10	)	)	PUNCT
ejpam-490	301	11	.	.	PUNCT
ejpam-490	302	1	(	(	PUNCT
ejpam-490	302	2	43	43	NUM
ejpam-490	302	3	)	)	PUNCT
ejpam-490	302	4	the	the	DET
ejpam-490	302	5	constant	constant	ADJ
ejpam-490	302	6	factor	factor	NOUN
ejpam-490	302	7	2n(2−α+β)(1+γ	2n(2−α+β)(1+γ	NUM
ejpam-490	302	8	)	)	PUNCT
ejpam-490	302	9	2[2n(2−α+β)(1+γ)+(1−α	2[2n(2−α+β)(1+γ)+(1−α	NUM
ejpam-490	302	10	)	)	PUNCT
ejpam-490	302	11	]	]	PUNCT
ejpam-490	302	12	in	in	ADP
ejpam-490	302	13	the	the	DET
ejpam-490	302	14	subordination	subordination	NOUN
ejpam-490	302	15	result	result	NOUN
ejpam-490	302	16	(	(	PUNCT
ejpam-490	302	17	42	42	NUM
ejpam-490	302	18	)	)	PUNCT
ejpam-490	302	19	can	can	AUX
ejpam-490	302	20	not	not	PART
ejpam-490	302	21	be	be	AUX
ejpam-490	302	22	replaced	replace	VERB
ejpam-490	302	23	by	by	ADP
ejpam-490	302	24	a	a	DET
ejpam-490	302	25	larger	large	ADJ
ejpam-490	302	26	one	one	NOUN
ejpam-490	302	27	.	.	PUNCT
ejpam-490	303	1	putting	put	VERB
ejpam-490	303	2	g(z	g(z	PROPN
ejpam-490	303	3	)	)	PUNCT
ejpam-490	304	1	=	=	SYM
ejpam-490	304	2	z	z	NOUN
ejpam-490	305	1	+	+	NUM
ejpam-490	305	2	∞	∞	NUM
ejpam-490	305	3	∑	∑	PROPN
ejpam-490	305	4	k=2	k=2	PROPN
ejpam-490	305	5	�	�	PROPN
ejpam-490	305	6	c+1	c+1	PROPN
ejpam-490	305	7	c+k	c+k	NUM
ejpam-490	305	8	�	�	X
ejpam-490	305	9	zk	zk	PROPN
ejpam-490	305	10	(	(	PUNCT
ejpam-490	305	11	c	c	NOUN
ejpam-490	305	12	>	>	X
ejpam-490	305	13	−1	−1	NOUN
ejpam-490	305	14	)	)	PUNCT
ejpam-490	305	15	in	in	ADP
ejpam-490	305	16	theorem	theorem	NOUN
ejpam-490	305	17	1	1	NUM
ejpam-490	305	18	,	,	PUNCT
ejpam-490	305	19	we	we	PRON
ejpam-490	305	20	have	have	VERB
ejpam-490	305	21	corollary	corollary	ADJ
ejpam-490	305	22	10	10	NUM
ejpam-490	305	23	.	.	PUNCT
ejpam-490	306	1	let	let	VERB
ejpam-490	306	2	the	the	DET
ejpam-490	306	3	function	function	NOUN
ejpam-490	306	4	f	f	PROPN
ejpam-490	306	5	(	(	PUNCT
ejpam-490	306	6	z	z	NOUN
ejpam-490	306	7	)	)	PUNCT
ejpam-490	306	8	defined	define	VERB
ejpam-490	306	9	by	by	ADP
ejpam-490	306	10	(	(	PUNCT
ejpam-490	306	11	1	1	X
ejpam-490	306	12	)	)	PUNCT
ejpam-490	306	13	be	be	AUX
ejpam-490	306	14	in	in	ADP
ejpam-490	306	15	the	the	DET
ejpam-490	306	16	class	class	NOUN
ejpam-490	306	17	s∗γ	s∗γ	PUNCT
ejpam-490	306	18	�	�	PROPN
ejpam-490	306	19	c	c	PROPN
ejpam-490	306	20	,	,	PUNCT
ejpam-490	306	21	α	α	PROPN
ejpam-490	306	22	,	,	PUNCT
ejpam-490	306	23	β	β	X
ejpam-490	306	24	�	�	PROPN
ejpam-490	306	25	and	and	CCONJ
ejpam-490	306	26	suppose	suppose	VERB
ejpam-490	306	27	that	that	SCONJ
ejpam-490	306	28	h(z	h(z	NOUN
ejpam-490	306	29	)	)	PUNCT
ejpam-490	306	30	∈	∈	PROPN
ejpam-490	307	1	k	k	INTJ
ejpam-490	307	2	.	.	PUNCT
ejpam-490	308	1	then	then	ADV
ejpam-490	308	2	(	(	PUNCT
ejpam-490	308	3	2−α+	2−α+	NUM
ejpam-490	308	4	β)(1	β)(1	PUNCT
ejpam-490	308	5	+	+	NUM
ejpam-490	308	6	γ)(c	γ)(c	X
ejpam-490	309	1	+	+	CCONJ
ejpam-490	309	2	1	1	X
ejpam-490	309	3	)	)	SYM
ejpam-490	309	4	2	2	NUM
ejpam-490	309	5	�	�	NOUN
ejpam-490	309	6	(	(	PUNCT
ejpam-490	309	7	2−α+	2−α+	NUM
ejpam-490	309	8	β)(1	β)(1	PUNCT
ejpam-490	309	9	+	+	NUM
ejpam-490	309	10	γ)(c	γ)(c	X
ejpam-490	310	1	+	+	CCONJ
ejpam-490	310	2	1	1	X
ejpam-490	310	3	)	)	PUNCT
ejpam-490	310	4	+	+	CCONJ
ejpam-490	310	5	(	(	PUNCT
ejpam-490	310	6	1−α)(c	1−α)(c	NUM
ejpam-490	310	7	+	+	CCONJ
ejpam-490	310	8	2	2	X
ejpam-490	310	9	)	)	PUNCT
ejpam-490	310	10	�	�	PROPN
ejpam-490	310	11	(	(	PUNCT
ejpam-490	310	12	f	f	PROPN
ejpam-490	310	13	∗	∗	NOUN
ejpam-490	310	14	h)(z)≺	h)(z)≺	PROPN
ejpam-490	310	15	h(z	h(z	NOUN
ejpam-490	310	16	)	)	PUNCT
ejpam-490	310	17	(	(	PUNCT
ejpam-490	310	18	z	z	NOUN
ejpam-490	310	19	∈	∈	PROPN
ejpam-490	310	20	u	u	NOUN
ejpam-490	310	21	)	)	PUNCT
ejpam-490	310	22	(	(	PUNCT
ejpam-490	310	23	44	44	NUM
ejpam-490	310	24	)	)	PUNCT
ejpam-490	310	25	and	and	CCONJ
ejpam-490	310	26	re	re	VERB
ejpam-490	310	27	(	(	PUNCT
ejpam-490	310	28	f	f	PROPN
ejpam-490	310	29	(	(	PUNCT
ejpam-490	310	30	z	z	NOUN
ejpam-490	310	31	)	)	PUNCT
ejpam-490	310	32	)	)	PUNCT
ejpam-490	310	33	>	>	X
ejpam-490	311	1	−	−	PROPN
ejpam-490	311	2	�	�	PROPN
ejpam-490	311	3	(	(	PUNCT
ejpam-490	311	4	2−α+	2−α+	NUM
ejpam-490	311	5	β)(1	β)(1	PUNCT
ejpam-490	311	6	+	+	NUM
ejpam-490	311	7	γ)(c	γ)(c	NOUN
ejpam-490	311	8	+	+	CCONJ
ejpam-490	311	9	1)+	1)+	NUM
ejpam-490	311	10	(	(	PUNCT
ejpam-490	311	11	1−α)(c	1−α)(c	NUM
ejpam-490	311	12	+	+	CCONJ
ejpam-490	311	13	2	2	X
ejpam-490	311	14	)	)	PUNCT
ejpam-490	311	15	�	�	PROPN
ejpam-490	311	16	(	(	PUNCT
ejpam-490	311	17	2−α+	2−α+	NUM
ejpam-490	311	18	β)(1	β)(1	NOUN
ejpam-490	311	19	+	+	SYM
ejpam-490	311	20	γ)(c+	γ)(c+	NOUN
ejpam-490	311	21	1	1	NUM
ejpam-490	311	22	)	)	PUNCT
ejpam-490	311	23	(	(	PUNCT
ejpam-490	311	24	z	z	NOUN
ejpam-490	311	25	∈	∈	PROPN
ejpam-490	311	26	u	u	NOUN
ejpam-490	311	27	)	)	PUNCT
ejpam-490	311	28	.	.	PUNCT
ejpam-490	312	1	(	(	PUNCT
ejpam-490	312	2	45	45	NUM
ejpam-490	312	3	)	)	PUNCT
ejpam-490	312	4	the	the	DET
ejpam-490	312	5	constant	constant	ADJ
ejpam-490	312	6	factor	factor	NOUN
ejpam-490	312	7	(	(	PUNCT
ejpam-490	312	8	2−α+β)(1+γ)(c+1	2−α+β)(1+γ)(c+1	NUM
ejpam-490	312	9	)	)	PUNCT
ejpam-490	312	10	2[(2−α+β)(1+γ)(c+1)+(1−α)(c+2	2[(2−α+β)(1+γ)(c+1)+(1−α)(c+2	NUM
ejpam-490	312	11	)	)	PUNCT
ejpam-490	312	12	]	]	PUNCT
ejpam-490	312	13	in	in	ADP
ejpam-490	312	14	the	the	DET
ejpam-490	312	15	subordination	subordination	NOUN
ejpam-490	312	16	result	result	NOUN
ejpam-490	312	17	(	(	PUNCT
ejpam-490	312	18	44	44	NUM
ejpam-490	312	19	)	)	PUNCT
ejpam-490	312	20	can	can	AUX
ejpam-490	312	21	not	not	PART
ejpam-490	312	22	be	be	AUX
ejpam-490	312	23	replaced	replace	VERB
ejpam-490	312	24	by	by	ADP
ejpam-490	312	25	a	a	DET
ejpam-490	312	26	larger	large	ADJ
ejpam-490	312	27	one	one	NOUN
ejpam-490	312	28	.	.	PUNCT
ejpam-490	313	1	putting	put	VERB
ejpam-490	313	2	g(z	g(z	PROPN
ejpam-490	313	3	)	)	PUNCT
ejpam-490	314	1	=	=	SYM
ejpam-490	314	2	z	z	NOUN
ejpam-490	315	1	+	+	NUM
ejpam-490	315	2	∞	∞	PROPN
ejpam-490	315	3	∑	∑	PROPN
ejpam-490	315	4	k=2	k=2	PROPN
ejpam-490	315	5	(	(	PUNCT
ejpam-490	315	6	µ)k−1	µ)k−1	X
ejpam-490	315	7	(	(	PUNCT
ejpam-490	315	8	λ+1)k−1	λ+1)k−1	PROPN
ejpam-490	315	9	zk	zk	PROPN
ejpam-490	315	10	(	(	PUNCT
ejpam-490	315	11	λ	λ	X
ejpam-490	315	12	>	>	X
ejpam-490	315	13	−1	−1	NOUN
ejpam-490	315	14	,	,	PUNCT
ejpam-490	315	15	µ	µ	X
ejpam-490	315	16	>	>	X
ejpam-490	315	17	0	0	NUM
ejpam-490	315	18	)	)	PUNCT
ejpam-490	315	19	in	in	ADP
ejpam-490	315	20	theorem	theorem	NOUN
ejpam-490	315	21	1	1	NUM
ejpam-490	315	22	,	,	PUNCT
ejpam-490	315	23	we	we	PRON
ejpam-490	315	24	have	have	VERB
ejpam-490	315	25	corollary	corollary	ADJ
ejpam-490	315	26	11	11	NUM
ejpam-490	315	27	.	.	PUNCT
ejpam-490	316	1	let	let	VERB
ejpam-490	316	2	the	the	DET
ejpam-490	316	3	function	function	NOUN
ejpam-490	316	4	f	f	PROPN
ejpam-490	316	5	(	(	PUNCT
ejpam-490	316	6	z	z	NOUN
ejpam-490	316	7	)	)	PUNCT
ejpam-490	316	8	defined	define	VERB
ejpam-490	316	9	by	by	ADP
ejpam-490	316	10	(	(	PUNCT
ejpam-490	316	11	1	1	X
ejpam-490	316	12	)	)	PUNCT
ejpam-490	316	13	be	be	AUX
ejpam-490	316	14	in	in	ADP
ejpam-490	316	15	the	the	DET
ejpam-490	316	16	class	class	NOUN
ejpam-490	316	17	s∗γ	s∗γ	PUNCT
ejpam-490	316	18	�	�	PROPN
ejpam-490	316	19	µ,λ;α	µ,λ;α	PROPN
ejpam-490	316	20	,	,	PUNCT
ejpam-490	316	21	β	β	X
ejpam-490	316	22	�	�	PROPN
ejpam-490	316	23	and	and	CCONJ
ejpam-490	316	24	suppose	suppose	VERB
ejpam-490	316	25	that	that	SCONJ
ejpam-490	316	26	h(z	h(z	NOUN
ejpam-490	316	27	)	)	PUNCT
ejpam-490	316	28	∈	∈	PROPN
ejpam-490	317	1	k	k	INTJ
ejpam-490	317	2	.	.	PUNCT
ejpam-490	318	1	then	then	ADV
ejpam-490	318	2	(	(	PUNCT
ejpam-490	318	3	2−α+	2−α+	NUM
ejpam-490	318	4	β)(1	β)(1	PUNCT
ejpam-490	318	5	+	+	PRON
ejpam-490	318	6	γ)µ	γ)µ	ADJ
ejpam-490	318	7	2	2	NUM
ejpam-490	318	8	�	�	NOUN
ejpam-490	318	9	(	(	PUNCT
ejpam-490	318	10	2−α+	2−α+	NUM
ejpam-490	318	11	β)(1	β)(1	NOUN
ejpam-490	319	1	+	+	NUM
ejpam-490	319	2	γ)µ+	γ)µ+	NOUN
ejpam-490	319	3	(	(	PUNCT
ejpam-490	319	4	1−α)(λ+	1−α)(λ+	NOUN
ejpam-490	319	5	1	1	NUM
ejpam-490	319	6	)	)	PUNCT
ejpam-490	319	7	�	�	PROPN
ejpam-490	319	8	(	(	PUNCT
ejpam-490	319	9	f	f	PROPN
ejpam-490	319	10	∗	∗	NOUN
ejpam-490	319	11	h)(z)≺	h)(z)≺	PROPN
ejpam-490	319	12	h(z	h(z	NOUN
ejpam-490	319	13	)	)	PUNCT
ejpam-490	319	14	(	(	PUNCT
ejpam-490	319	15	z	z	NOUN
ejpam-490	319	16	∈	∈	PROPN
ejpam-490	319	17	u	u	NOUN
ejpam-490	319	18	)	)	PUNCT
ejpam-490	319	19	(	(	PUNCT
ejpam-490	319	20	46	46	NUM
ejpam-490	319	21	)	)	PUNCT
ejpam-490	319	22	and	and	CCONJ
ejpam-490	319	23	re	re	ADP
ejpam-490	319	24	(	(	PUNCT
ejpam-490	319	25	f	f	PROPN
ejpam-490	319	26	(	(	PUNCT
ejpam-490	319	27	z	z	NOUN
ejpam-490	319	28	)	)	PUNCT
ejpam-490	319	29	)	)	PUNCT
ejpam-490	319	30	>	>	X
ejpam-490	320	1	−	−	PROPN
ejpam-490	320	2	�	�	PROPN
ejpam-490	320	3	(	(	PUNCT
ejpam-490	320	4	2−α+	2−α+	NUM
ejpam-490	320	5	β)(1	β)(1	NOUN
ejpam-490	320	6	+	+	NUM
ejpam-490	320	7	γ)µ+	γ)µ+	NOUN
ejpam-490	320	8	(	(	PUNCT
ejpam-490	320	9	1−α)(λ+	1−α)(λ+	NOUN
ejpam-490	320	10	1	1	NUM
ejpam-490	320	11	)	)	PUNCT
ejpam-490	320	12	�	�	PROPN
ejpam-490	320	13	(	(	PUNCT
ejpam-490	320	14	2−α+	2−α+	NUM
ejpam-490	320	15	β)(1	β)(1	PUNCT
ejpam-490	320	16	+	+	NUM
ejpam-490	320	17	γ)µ	γ)µ	ADJ
ejpam-490	320	18	(	(	PUNCT
ejpam-490	320	19	z	z	NOUN
ejpam-490	320	20	∈	∈	PROPN
ejpam-490	320	21	u	u	NOUN
ejpam-490	320	22	)	)	PUNCT
ejpam-490	320	23	.	.	PUNCT
ejpam-490	321	1	(	(	PUNCT
ejpam-490	321	2	47	47	NUM
ejpam-490	321	3	)	)	PUNCT
ejpam-490	321	4	the	the	DET
ejpam-490	321	5	constant	constant	ADJ
ejpam-490	321	6	factor	factor	NOUN
ejpam-490	321	7	(	(	PUNCT
ejpam-490	321	8	2−α+β)(1+γ)µ	2−α+β)(1+γ)µ	NOUN
ejpam-490	321	9	2[(2−α+β)(1+γ)µ+(1−α)(λ+1	2[(2−α+β)(1+γ)µ+(1−α)(λ+1	NUM
ejpam-490	321	10	)	)	PUNCT
ejpam-490	321	11	]	]	PUNCT
ejpam-490	321	12	in	in	ADP
ejpam-490	321	13	the	the	DET
ejpam-490	321	14	subordination	subordination	NOUN
ejpam-490	321	15	result	result	NOUN
ejpam-490	321	16	(	(	PUNCT
ejpam-490	321	17	46	46	NUM
ejpam-490	321	18	)	)	PUNCT
ejpam-490	321	19	can	can	AUX
ejpam-490	321	20	not	not	PART
ejpam-490	321	21	be	be	AUX
ejpam-490	321	22	replaced	replace	VERB
ejpam-490	321	23	by	by	ADP
ejpam-490	321	24	a	a	DET
ejpam-490	321	25	larger	large	ADJ
ejpam-490	321	26	one	one	NOUN
ejpam-490	321	27	.	.	PUNCT
ejpam-490	322	1	putting	put	VERB
ejpam-490	322	2	g(z	g(z	PROPN
ejpam-490	322	3	)	)	PUNCT
ejpam-490	323	1	=	=	SYM
ejpam-490	323	2	z	z	NOUN
ejpam-490	324	1	+	+	NUM
ejpam-490	324	2	∞	∞	PROPN
ejpam-490	324	3	∑	∑	PROPN
ejpam-490	324	4	k=2	k=2	PROPN
ejpam-490	324	5	(	(	PUNCT
ejpam-490	324	6	c)k−1	c)k−1	PROPN
ejpam-490	324	7	(	(	PUNCT
ejpam-490	324	8	a)k−1	a)k−1	PROPN
ejpam-490	324	9	(	(	PUNCT
ejpam-490	324	10	λ+1)k−1	λ+1)k−1	X
ejpam-490	324	11	(	(	PUNCT
ejpam-490	324	12	1)k−1	1)k−1	NUM
ejpam-490	324	13	zk	zk	PROPN
ejpam-490	324	14	(	(	PUNCT
ejpam-490	324	15	a	a	PROPN
ejpam-490	324	16	,	,	PUNCT
ejpam-490	324	17	c	c	PROPN
ejpam-490	324	18	∈	∈	PROPN
ejpam-490	324	19	r\z−0	r\z−0	NOUN
ejpam-490	324	20	,	,	PUNCT
ejpam-490	324	21	λ	λ	X
ejpam-490	324	22	>	>	X
ejpam-490	324	23	−1	−1	NOUN
ejpam-490	324	24	)	)	PUNCT
ejpam-490	324	25	in	in	ADP
ejpam-490	324	26	theorem	theorem	NOUN
ejpam-490	324	27	1	1	NUM
ejpam-490	324	28	,	,	PUNCT
ejpam-490	324	29	we	we	PRON
ejpam-490	324	30	have	have	VERB
ejpam-490	324	31	references	reference	NOUN
ejpam-490	324	32	915	915	NUM
ejpam-490	324	33	corollary	corollary	ADJ
ejpam-490	324	34	12	12	NUM
ejpam-490	324	35	.	.	PUNCT
ejpam-490	325	1	let	let	VERB
ejpam-490	325	2	the	the	DET
ejpam-490	325	3	function	function	NOUN
ejpam-490	325	4	f	f	PROPN
ejpam-490	325	5	(	(	PUNCT
ejpam-490	325	6	z	z	NOUN
ejpam-490	325	7	)	)	PUNCT
ejpam-490	325	8	defined	define	VERB
ejpam-490	325	9	by	by	ADP
ejpam-490	325	10	(	(	PUNCT
ejpam-490	325	11	1	1	X
ejpam-490	325	12	)	)	PUNCT
ejpam-490	325	13	be	be	AUX
ejpam-490	325	14	in	in	ADP
ejpam-490	325	15	the	the	DET
ejpam-490	325	16	class	class	NOUN
ejpam-490	325	17	s∗γ	s∗γ	PUNCT
ejpam-490	325	18	�	�	PROPN
ejpam-490	325	19	a	a	PROPN
ejpam-490	325	20	,	,	PUNCT
ejpam-490	325	21	c	c	NOUN
ejpam-490	325	22	,	,	PUNCT
ejpam-490	325	23	λ;α	λ;α	PROPN
ejpam-490	325	24	,	,	PUNCT
ejpam-490	325	25	β	β	X
ejpam-490	325	26	�	�	PROPN
ejpam-490	325	27	and	and	CCONJ
ejpam-490	325	28	suppose	suppose	VERB
ejpam-490	325	29	that	that	SCONJ
ejpam-490	325	30	h(z	h(z	NOUN
ejpam-490	325	31	)	)	PUNCT
ejpam-490	325	32	∈	∈	PROPN
ejpam-490	326	1	k	k	INTJ
ejpam-490	326	2	.	.	PUNCT
ejpam-490	327	1	then	then	ADV
ejpam-490	327	2	(	(	PUNCT
ejpam-490	327	3	2−α+	2−α+	NUM
ejpam-490	327	4	β)(1	β)(1	PUNCT
ejpam-490	328	1	+	+	NUM
ejpam-490	328	2	γ)(λ+	γ)(λ+	NOUN
ejpam-490	328	3	1)c	1)c	PROPN
ejpam-490	328	4	2	2	NUM
ejpam-490	328	5	�	�	PROPN
ejpam-490	328	6	(	(	PUNCT
ejpam-490	328	7	2−α+	2−α+	NUM
ejpam-490	328	8	β)(1	β)(1	PUNCT
ejpam-490	329	1	+	+	NUM
ejpam-490	329	2	γ)(λ+	γ)(λ+	NOUN
ejpam-490	329	3	1)c+	1)c+	NUM
ejpam-490	329	4	(	(	PUNCT
ejpam-490	329	5	1−α)a	1−α)a	NUM
ejpam-490	329	6	�	�	PROPN
ejpam-490	329	7	(	(	PUNCT
ejpam-490	329	8	f	f	PROPN
ejpam-490	329	9	∗	∗	NOUN
ejpam-490	329	10	h)(z	h)(z	NOUN
ejpam-490	329	11	)	)	PUNCT
ejpam-490	329	12	≺	≺	NOUN
ejpam-490	329	13	h(z	h(z	NOUN
ejpam-490	329	14	)	)	PUNCT
ejpam-490	329	15	(	(	PUNCT
ejpam-490	329	16	z	z	NOUN
ejpam-490	329	17	∈	∈	PROPN
ejpam-490	329	18	u	u	NOUN
ejpam-490	329	19	)	)	PUNCT
ejpam-490	329	20	(	(	PUNCT
ejpam-490	329	21	48	48	NUM
ejpam-490	329	22	)	)	PUNCT
ejpam-490	329	23	and	and	CCONJ
ejpam-490	329	24	re	re	VERB
ejpam-490	329	25	(	(	PUNCT
ejpam-490	329	26	f	f	PROPN
ejpam-490	329	27	(	(	PUNCT
ejpam-490	329	28	z	z	NOUN
ejpam-490	329	29	)	)	PUNCT
ejpam-490	329	30	)	)	PUNCT
ejpam-490	330	1	>	>	X
ejpam-490	331	1	−	−	PROPN
ejpam-490	331	2	�	�	PROPN
ejpam-490	331	3	(	(	PUNCT
ejpam-490	331	4	2−α+β)(1	2−α+β)(1	NOUN
ejpam-490	331	5	+	+	CCONJ
ejpam-490	331	6	γ)(λ+	γ)(λ+	NOUN
ejpam-490	331	7	1)c+	1)c+	NUM
ejpam-490	331	8	(	(	PUNCT
ejpam-490	331	9	1−α)a	1−α)a	NUM
ejpam-490	331	10	�	�	PROPN
ejpam-490	331	11	(	(	PUNCT
ejpam-490	331	12	2−α+	2−α+	NUM
ejpam-490	331	13	β)(1	β)(1	PUNCT
ejpam-490	331	14	+	+	NUM
ejpam-490	331	15	γ)(λ+	γ)(λ+	NOUN
ejpam-490	331	16	1)c	1)c	PROPN
ejpam-490	331	17	(	(	PUNCT
ejpam-490	331	18	z	z	NOUN
ejpam-490	331	19	∈	∈	PROPN
ejpam-490	331	20	u	u	NOUN
ejpam-490	331	21	)	)	PUNCT
ejpam-490	331	22	.	.	PUNCT
ejpam-490	332	1	(	(	PUNCT
ejpam-490	332	2	49	49	NUM
ejpam-490	332	3	)	)	PUNCT
ejpam-490	332	4	the	the	DET
ejpam-490	332	5	constant	constant	ADJ
ejpam-490	332	6	factor	factor	NOUN
ejpam-490	332	7	(	(	PUNCT
ejpam-490	332	8	2−α+β)(1+γ)(λ+1)c	2−α+β)(1+γ)(λ+1)c	NUM
ejpam-490	332	9	2[(2−α+β)(1+γ)(λ+1)c+(1−α)a	2[(2−α+β)(1+γ)(λ+1)c+(1−α)a	NUM
ejpam-490	332	10	]	]	PUNCT
ejpam-490	332	11	in	in	ADP
ejpam-490	332	12	the	the	DET
ejpam-490	332	13	subordination	subordination	NOUN
ejpam-490	332	14	result	result	NOUN
ejpam-490	332	15	(	(	PUNCT
ejpam-490	332	16	48	48	NUM
ejpam-490	332	17	)	)	PUNCT
ejpam-490	332	18	can	can	AUX
ejpam-490	332	19	not	not	PART
ejpam-490	332	20	be	be	AUX
ejpam-490	332	21	replaced	replace	VERB
ejpam-490	332	22	by	by	ADP
ejpam-490	332	23	a	a	DET
ejpam-490	332	24	larger	large	ADJ
ejpam-490	332	25	one	one	NOUN
ejpam-490	332	26	.	.	PUNCT
ejpam-490	333	1	putting	put	VERB
ejpam-490	333	2	g(z	g(z	PROPN
ejpam-490	333	3	)	)	PUNCT
ejpam-490	334	1	=	=	SYM
ejpam-490	334	2	z	z	NOUN
ejpam-490	335	1	+	+	NUM
ejpam-490	335	2	∞	∞	PROPN
ejpam-490	335	3	∑	∑	PROPN
ejpam-490	335	4	k=2	k=2	PROPN
ejpam-490	335	5	(	(	PUNCT
ejpam-490	335	6	2)k−1	2)k−1	NUM
ejpam-490	335	7	(	(	PUNCT
ejpam-490	335	8	n+1)k−1	n+1)k−1	PROPN
ejpam-490	335	9	zk	zk	PROPN
ejpam-490	335	10	(	(	PUNCT
ejpam-490	335	11	n	n	CCONJ
ejpam-490	335	12	>	>	X
ejpam-490	335	13	−1	−1	NOUN
ejpam-490	335	14	)	)	PUNCT
ejpam-490	335	15	in	in	ADP
ejpam-490	335	16	theorem	theorem	NOUN
ejpam-490	335	17	1	1	NUM
ejpam-490	335	18	,	,	PUNCT
ejpam-490	335	19	we	we	PRON
ejpam-490	335	20	have	have	VERB
ejpam-490	335	21	corollary	corollary	ADJ
ejpam-490	335	22	13	13	NUM
ejpam-490	335	23	.	.	PUNCT
ejpam-490	336	1	let	let	VERB
ejpam-490	336	2	the	the	DET
ejpam-490	336	3	function	function	NOUN
ejpam-490	336	4	f	f	PROPN
ejpam-490	336	5	(	(	PUNCT
ejpam-490	336	6	z	z	NOUN
ejpam-490	336	7	)	)	PUNCT
ejpam-490	336	8	defined	define	VERB
ejpam-490	336	9	by	by	ADP
ejpam-490	336	10	(	(	PUNCT
ejpam-490	336	11	1	1	X
ejpam-490	336	12	)	)	PUNCT
ejpam-490	336	13	be	be	AUX
ejpam-490	336	14	in	in	ADP
ejpam-490	336	15	the	the	DET
ejpam-490	336	16	class	class	NOUN
ejpam-490	336	17	s∗γ	s∗γ	PUNCT
ejpam-490	336	18	�	�	PROPN
ejpam-490	336	19	n;α	n;α	PROPN
ejpam-490	336	20	,	,	PUNCT
ejpam-490	336	21	β	β	X
ejpam-490	336	22	�	�	PROPN
ejpam-490	336	23	and	and	CCONJ
ejpam-490	336	24	suppose	suppose	VERB
ejpam-490	336	25	that	that	SCONJ
ejpam-490	336	26	h(z	h(z	NOUN
ejpam-490	336	27	)	)	PUNCT
ejpam-490	336	28	∈	∈	PROPN
ejpam-490	337	1	k	k	INTJ
ejpam-490	337	2	.	.	PUNCT
ejpam-490	338	1	then	then	ADV
ejpam-490	338	2	(	(	PUNCT
ejpam-490	338	3	2−α+	2−α+	NUM
ejpam-490	338	4	β)(1	β)(1	NOUN
ejpam-490	338	5	+	+	CCONJ
ejpam-490	338	6	γ	γ	X
ejpam-490	338	7	)	)	PUNCT
ejpam-490	338	8	�	�	PROPN
ejpam-490	338	9	2(2−α+	2(2−α+	NUM
ejpam-490	338	10	β)(1	β)(1	PUNCT
ejpam-490	339	1	+	+	X
ejpam-490	339	2	γ	γ	X
ejpam-490	339	3	)	)	PUNCT
ejpam-490	339	4	+	+	CCONJ
ejpam-490	339	5	(	(	PUNCT
ejpam-490	339	6	1−α)(n+	1−α)(n+	NUM
ejpam-490	339	7	1	1	NUM
ejpam-490	339	8	)	)	PUNCT
ejpam-490	339	9	�	�	PROPN
ejpam-490	339	10	(	(	PUNCT
ejpam-490	339	11	f	f	PROPN
ejpam-490	339	12	∗	∗	NOUN
ejpam-490	339	13	h)(z)≺	h)(z)≺	PROPN
ejpam-490	339	14	h(z	h(z	NOUN
ejpam-490	339	15	)	)	PUNCT
ejpam-490	339	16	(	(	PUNCT
ejpam-490	339	17	z	z	NOUN
ejpam-490	339	18	∈	∈	PROPN
ejpam-490	339	19	u	u	NOUN
ejpam-490	339	20	)	)	PUNCT
ejpam-490	339	21	(	(	PUNCT
ejpam-490	339	22	50	50	NUM
ejpam-490	339	23	)	)	PUNCT
ejpam-490	339	24	and	and	CCONJ
ejpam-490	339	25	re	re	ADP
ejpam-490	339	26	(	(	PUNCT
ejpam-490	339	27	f	f	PROPN
ejpam-490	339	28	(	(	PUNCT
ejpam-490	339	29	z	z	NOUN
ejpam-490	339	30	)	)	PUNCT
ejpam-490	339	31	)	)	PUNCT
ejpam-490	339	32	>	>	X
ejpam-490	340	1	−	−	PROPN
ejpam-490	340	2	�	�	PROPN
ejpam-490	340	3	2(2−α+	2(2−α+	NUM
ejpam-490	340	4	β)(1	β)(1	PUNCT
ejpam-490	340	5	+	+	X
ejpam-490	340	6	γ	γ	X
ejpam-490	340	7	)	)	PUNCT
ejpam-490	340	8	+	+	CCONJ
ejpam-490	340	9	(	(	PUNCT
ejpam-490	340	10	1−α)(n+	1−α)(n+	NUM
ejpam-490	340	11	1	1	NUM
ejpam-490	340	12	)	)	PUNCT
ejpam-490	340	13	�	�	PROPN
ejpam-490	340	14	2(2−α+	2(2−α+	NUM
ejpam-490	340	15	β)(1	β)(1	PUNCT
ejpam-490	340	16	+	+	X
ejpam-490	340	17	γ	γ	X
ejpam-490	340	18	)	)	PUNCT
ejpam-490	340	19	(	(	PUNCT
ejpam-490	340	20	z	z	NOUN
ejpam-490	340	21	∈	∈	PROPN
ejpam-490	340	22	u	u	NOUN
ejpam-490	340	23	)	)	PUNCT
ejpam-490	340	24	.	.	PUNCT
ejpam-490	341	1	(	(	PUNCT
ejpam-490	341	2	51	51	NUM
ejpam-490	341	3	)	)	PUNCT
ejpam-490	341	4	the	the	DET
ejpam-490	341	5	constant	constant	ADJ
ejpam-490	341	6	factor	factor	NOUN
ejpam-490	341	7	(	(	PUNCT
ejpam-490	341	8	2−α+β)(1+γ	2−α+β)(1+γ	NUM
ejpam-490	341	9	)	)	PUNCT
ejpam-490	341	10	[	[	X
ejpam-490	341	11	2(2−α+β)(1+γ)+(1−α)(n+1	2(2−α+β)(1+γ)+(1−α)(n+1	NUM
ejpam-490	341	12	)	)	PUNCT
ejpam-490	341	13	]	]	PUNCT
ejpam-490	341	14	in	in	ADP
ejpam-490	341	15	the	the	DET
ejpam-490	341	16	subordination	subordination	NOUN
ejpam-490	341	17	result	result	NOUN
ejpam-490	341	18	(	(	PUNCT
ejpam-490	341	19	50	50	NUM
ejpam-490	341	20	)	)	PUNCT
ejpam-490	341	21	can	can	AUX
ejpam-490	341	22	not	not	PART
ejpam-490	341	23	be	be	AUX
ejpam-490	341	24	replaced	replace	VERB
ejpam-490	341	25	by	by	ADP
ejpam-490	341	26	a	a	DET
ejpam-490	341	27	larger	large	ADJ
ejpam-490	341	28	one	one	NUM
ejpam-490	341	29	.	.	PUNCT
ejpam-490	342	1	references	reference	NOUN
ejpam-490	342	2	[	[	X
ejpam-490	342	3	1	1	X
ejpam-490	342	4	]	]	X
ejpam-490	342	5	o.	o.	PROPN
ejpam-490	342	6	ahuja	ahuja	PROPN
ejpam-490	342	7	,	,	PUNCT
ejpam-490	342	8	g.	g.	PROPN
ejpam-490	342	9	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-490	342	10	and	and	CCONJ
ejpam-490	342	11	n.	n.	PROPN
ejpam-490	342	12	magesh	magesh	PROPN
ejpam-490	342	13	,	,	PUNCT
ejpam-490	342	14	integral	integral	ADJ
ejpam-490	342	15	means	mean	NOUN
ejpam-490	342	16	for	for	ADP
ejpam-490	342	17	uniformly	uniformly	ADV
ejpam-490	342	18	convex	convex	NOUN
ejpam-490	342	19	and	and	CCONJ
ejpam-490	342	20	starlike	starlike	NOUN
ejpam-490	342	21	functions	function	NOUN
ejpam-490	342	22	associated	associate	VERB
ejpam-490	342	23	with	with	ADP
ejpam-490	342	24	generalized	generalized	ADJ
ejpam-490	342	25	hypergeometric	hypergeometric	ADJ
ejpam-490	342	26	functions	function	NOUN
ejpam-490	342	27	,	,	PUNCT
ejpam-490	342	28	j.	j.	PROPN
ejpam-490	342	29	inequal	inequal	PROPN
ejpam-490	342	30	.	.	PUNCT
ejpam-490	343	1	pure	pure	ADJ
ejpam-490	343	2	appl	appl	PROPN
ejpam-490	343	3	.	.	PUNCT
ejpam-490	343	4	math	math	NOUN
ejpam-490	343	5	.	.	PUNCT
ejpam-490	344	1	8	8	NUM
ejpam-490	344	2	,	,	PUNCT
ejpam-490	344	3	no	no	INTJ
ejpam-490	344	4	.	.	NOUN
ejpam-490	344	5	4	4	NUM
ejpam-490	344	6	,	,	PUNCT
ejpam-490	344	7	art	art	NOUN
ejpam-490	344	8	.	.	PUNCT
ejpam-490	345	1	118	118	NUM
ejpam-490	345	2	,	,	PUNCT
ejpam-490	345	3	1	1	NUM
ejpam-490	345	4	-	-	SYM
ejpam-490	345	5	9	9	NUM
ejpam-490	345	6	.	.	NOUN
ejpam-490	345	7	2007	2007	NUM
ejpam-490	345	8	.	.	PUNCT
ejpam-490	346	1	[	[	X
ejpam-490	346	2	2	2	NUM
ejpam-490	346	3	]	]	PUNCT
ejpam-490	346	4	m.	m.	NOUN
ejpam-490	346	5	k.	k.	PROPN
ejpam-490	346	6	aouf	aouf	PROPN
ejpam-490	346	7	and	and	CCONJ
ejpam-490	346	8	a.	a.	PROPN
ejpam-490	346	9	o.	o.	PROPN
ejpam-490	346	10	mostafa	mostafa	PROPN
ejpam-490	346	11	,	,	PUNCT
ejpam-490	346	12	some	some	DET
ejpam-490	346	13	properties	property	NOUN
ejpam-490	346	14	of	of	ADP
ejpam-490	346	15	a	a	DET
ejpam-490	346	16	subclass	subclass	NOUN
ejpam-490	346	17	of	of	ADP
ejpam-490	346	18	uniformly	uniformly	ADJ
ejpam-490	346	19	convex	convex	NOUN
ejpam-490	346	20	functions	function	NOUN
ejpam-490	346	21	with	with	ADP
ejpam-490	346	22	negative	negative	ADJ
ejpam-490	346	23	coefficients	coefficient	NOUN
ejpam-490	346	24	,	,	PUNCT
ejpam-490	346	25	demonstration	demonstration	NOUN
ejpam-490	346	26	math	math	NOUN
ejpam-490	346	27	.	.	PUNCT
ejpam-490	347	1	2	2	NUM
ejpam-490	347	2	,	,	PUNCT
ejpam-490	347	3	353	353	NUM
ejpam-490	347	4	-	-	SYM
ejpam-490	347	5	370	370	NUM
ejpam-490	347	6	.	.	PUNCT
ejpam-490	348	1	2008	2008	NUM
ejpam-490	348	2	.	.	PUNCT
ejpam-490	349	1	[	[	X
ejpam-490	349	2	3	3	NUM
ejpam-490	349	3	]	]	PUNCT
ejpam-490	349	4	a.	a.	NOUN
ejpam-490	349	5	a.	a.	NOUN
ejpam-490	349	6	attiya	attiya	PROPN
ejpam-490	349	7	,	,	PUNCT
ejpam-490	349	8	on	on	ADP
ejpam-490	349	9	some	some	DET
ejpam-490	349	10	application	application	NOUN
ejpam-490	349	11	of	of	ADP
ejpam-490	349	12	a	a	DET
ejpam-490	349	13	subordination	subordination	NOUN
ejpam-490	349	14	theorems	theorem	NOUN
ejpam-490	349	15	,	,	PUNCT
ejpam-490	349	16	j.	j.	PROPN
ejpam-490	349	17	math	math	PROPN
ejpam-490	349	18	.	.	PUNCT
ejpam-490	350	1	anal	anal	PROPN
ejpam-490	350	2	.	.	PUNCT
ejpam-490	350	3	appl	appl	PROPN
ejpam-490	350	4	.	.	PROPN
ejpam-490	351	1	311	311	NUM
ejpam-490	351	2	,	,	PUNCT
ejpam-490	351	3	489	489	NUM
ejpam-490	351	4	-	-	SYM
ejpam-490	351	5	494	494	NUM
ejpam-490	351	6	.	.	NUM
ejpam-490	351	7	2005	2005	NUM
ejpam-490	351	8	.	.	PUNCT
ejpam-490	352	1	[	[	X
ejpam-490	352	2	4	4	X
ejpam-490	352	3	]	]	PUNCT
ejpam-490	352	4	s.	s.	PROPN
ejpam-490	352	5	d.	d.	PROPN
ejpam-490	352	6	bernardi	bernardi	PROPN
ejpam-490	352	7	,	,	PUNCT
ejpam-490	352	8	convex	convex	NOUN
ejpam-490	352	9	and	and	CCONJ
ejpam-490	352	10	starlike	starlike	NOUN
ejpam-490	352	11	univalent	univalent	ADJ
ejpam-490	352	12	functions	function	NOUN
ejpam-490	352	13	,	,	PUNCT
ejpam-490	352	14	trans	trans	PROPN
ejpam-490	352	15	.	.	PROPN
ejpam-490	352	16	amer	amer	PROPN
ejpam-490	352	17	.	.	PUNCT
ejpam-490	352	18	math	math	PROPN
ejpam-490	352	19	.	.	PUNCT
ejpam-490	353	1	soc	soc	PROPN
ejpam-490	353	2	.	.	PROPN
ejpam-490	353	3	,	,	PUNCT
ejpam-490	353	4	135	135	NUM
ejpam-490	353	5	,	,	PUNCT
ejpam-490	353	6	429	429	NUM
ejpam-490	353	7	-	-	SYM
ejpam-490	353	8	446	446	NUM
ejpam-490	353	9	.	.	NOUN
ejpam-490	353	10	1969	1969	NUM
ejpam-490	353	11	.	.	PUNCT
ejpam-490	354	1	[	[	X
ejpam-490	354	2	5	5	NUM
ejpam-490	354	3	]	]	PUNCT
ejpam-490	354	4	r.	r.	PROPN
ejpam-490	354	5	bharati	bharati	PROPN
ejpam-490	354	6	,	,	PUNCT
ejpam-490	354	7	r.	r.	PROPN
ejpam-490	354	8	parvatham	parvatham	PROPN
ejpam-490	354	9	and	and	CCONJ
ejpam-490	354	10	a.	a.	NOUN
ejpam-490	354	11	swaminathan	swaminathan	ADV
ejpam-490	354	12	,	,	PUNCT
ejpam-490	354	13	on	on	ADP
ejpam-490	354	14	subclasses	subclass	NOUN
ejpam-490	354	15	of	of	ADP
ejpam-490	354	16	uniformly	uniformly	ADJ
ejpam-490	354	17	convex	convex	NOUN
ejpam-490	354	18	functions	function	NOUN
ejpam-490	354	19	and	and	CCONJ
ejpam-490	354	20	corresponding	correspond	VERB
ejpam-490	354	21	class	class	NOUN
ejpam-490	354	22	of	of	ADP
ejpam-490	354	23	starlike	starlike	NOUN
ejpam-490	354	24	functions	function	NOUN
ejpam-490	354	25	,	,	PUNCT
ejpam-490	354	26	tamakang	tamakang	PROPN
ejpam-490	354	27	j.	j.	PROPN
ejpam-490	354	28	math	math	PROPN
ejpam-490	354	29	.	.	PUNCT
ejpam-490	355	1	28	28	NUM
ejpam-490	355	2	,	,	PUNCT
ejpam-490	355	3	17	17	NUM
ejpam-490	355	4	-	-	SYM
ejpam-490	355	5	32	32	NUM
ejpam-490	355	6	.	.	PUNCT
ejpam-490	356	1	1997	1997	NUM
ejpam-490	356	2	.	.	PUNCT
ejpam-490	357	1	references	reference	NOUN
ejpam-490	357	2	916	916	NUM
ejpam-490	357	3	[	[	X
ejpam-490	357	4	6	6	NUM
ejpam-490	357	5	]	]	PUNCT
ejpam-490	357	6	n.	n.	PROPN
ejpam-490	357	7	e.	e.	PROPN
ejpam-490	357	8	cho	cho	PROPN
ejpam-490	357	9	,	,	PUNCT
ejpam-490	357	10	o.	o.	PROPN
ejpam-490	357	11	s.	s.	PROPN
ejpam-490	357	12	kwon	kwon	PROPN
ejpam-490	357	13	and	and	CCONJ
ejpam-490	357	14	h.	h.	PROPN
ejpam-490	357	15	m.	m.	PROPN
ejpam-490	357	16	srivastava	srivastava	PROPN
ejpam-490	357	17	,	,	PUNCT
ejpam-490	357	18	inclusion	inclusion	NOUN
ejpam-490	357	19	relationships	relationship	NOUN
ejpam-490	357	20	and	and	CCONJ
ejpam-490	357	21	argument	argument	NOUN
ejpam-490	357	22	properties	property	NOUN
ejpam-490	357	23	for	for	ADP
ejpam-490	357	24	certain	certain	ADJ
ejpam-490	357	25	subclasses	subclass	NOUN
ejpam-490	357	26	of	of	ADP
ejpam-490	357	27	multivalent	multivalent	NOUN
ejpam-490	357	28	functions	function	NOUN
ejpam-490	357	29	associated	associate	VERB
ejpam-490	357	30	with	with	ADP
ejpam-490	357	31	a	a	DET
ejpam-490	357	32	family	family	NOUN
ejpam-490	357	33	of	of	ADP
ejpam-490	357	34	linear	linear	PROPN
ejpam-490	357	35	operators	operator	NOUN
ejpam-490	357	36	,	,	PUNCT
ejpam-490	357	37	j.	j.	PROPN
ejpam-490	357	38	math	math	PROPN
ejpam-490	357	39	.	.	PUNCT
ejpam-490	358	1	anal	anal	PROPN
ejpam-490	358	2	.	.	PUNCT
ejpam-490	359	1	appl	appl	PROPN
ejpam-490	359	2	.	.	PUNCT
ejpam-490	360	1	292	292	NUM
ejpam-490	360	2	,	,	PUNCT
ejpam-490	360	3	470	470	NUM
ejpam-490	360	4	-	-	SYM
ejpam-490	360	5	483	483	NUM
ejpam-490	360	6	.	.	PUNCT
ejpam-490	361	1	2004	2004	NUM
ejpam-490	361	2	.	.	PUNCT
ejpam-490	362	1	[	[	X
ejpam-490	362	2	7	7	X
ejpam-490	362	3	]	]	X
ejpam-490	362	4	j.	j.	PROPN
ejpam-490	362	5	h.	h.	PROPN
ejpam-490	362	6	choi	choi	PROPN
ejpam-490	362	7	,	,	PUNCT
ejpam-490	362	8	m.	m.	NOUN
ejpam-490	362	9	saigo	saigo	PROPN
ejpam-490	362	10	,	,	PUNCT
ejpam-490	362	11	h.	h.	PROPN
ejpam-490	362	12	m.	m.	PROPN
ejpam-490	362	13	srivastava	srivastava	PROPN
ejpam-490	362	14	,	,	PUNCT
ejpam-490	362	15	some	some	DET
ejpam-490	362	16	inclusion	inclusion	NOUN
ejpam-490	362	17	properties	property	NOUN
ejpam-490	362	18	of	of	ADP
ejpam-490	362	19	a	a	DET
ejpam-490	362	20	certain	certain	ADJ
ejpam-490	362	21	family	family	NOUN
ejpam-490	362	22	of	of	ADP
ejpam-490	362	23	integral	integral	ADJ
ejpam-490	362	24	operators	operator	NOUN
ejpam-490	362	25	,	,	PUNCT
ejpam-490	362	26	j.	j.	PROPN
ejpam-490	362	27	math	math	PROPN
ejpam-490	362	28	.	.	PUNCT
ejpam-490	363	1	anal	anal	PROPN
ejpam-490	363	2	.	.	PUNCT
ejpam-490	364	1	appl	appl	PROPN
ejpam-490	364	2	.	.	PROPN
ejpam-490	364	3	276	276	NUM
ejpam-490	364	4	,	,	PUNCT
ejpam-490	364	5	432	432	NUM
ejpam-490	364	6	-	-	SYM
ejpam-490	364	7	445	445	NUM
ejpam-490	364	8	.	.	PUNCT
ejpam-490	365	1	2002	2002	NUM
ejpam-490	365	2	.	.	PUNCT
ejpam-490	366	1	[	[	X
ejpam-490	366	2	8	8	NUM
ejpam-490	366	3	]	]	X
ejpam-490	366	4	b.	b.	PROPN
ejpam-490	366	5	a.	a.	PROPN
ejpam-490	366	6	frasin	frasin	PROPN
ejpam-490	366	7	,	,	PUNCT
ejpam-490	366	8	subordination	subordination	NOUN
ejpam-490	366	9	results	result	VERB
ejpam-490	366	10	for	for	ADP
ejpam-490	366	11	a	a	DET
ejpam-490	366	12	class	class	NOUN
ejpam-490	366	13	of	of	ADP
ejpam-490	366	14	analytic	analytic	ADJ
ejpam-490	366	15	functions	function	NOUN
ejpam-490	366	16	defined	define	VERB
ejpam-490	366	17	by	by	ADP
ejpam-490	366	18	a	a	DET
ejpam-490	366	19	linear	linear	ADJ
ejpam-490	366	20	operator	operator	NOUN
ejpam-490	366	21	,	,	PUNCT
ejpam-490	366	22	j.	j.	PROPN
ejpam-490	366	23	inequal	inequal	PROPN
ejpam-490	366	24	.	.	PUNCT
ejpam-490	367	1	pure	pure	ADJ
ejpam-490	367	2	appl	appl	PROPN
ejpam-490	367	3	.	.	PUNCT
ejpam-490	367	4	math	math	NOUN
ejpam-490	367	5	.	.	PUNCT
ejpam-490	368	1	7	7	NUM
ejpam-490	368	2	,	,	PUNCT
ejpam-490	368	3	no	no	INTJ
ejpam-490	368	4	.	.	NOUN
ejpam-490	368	5	4	4	NUM
ejpam-490	368	6	,	,	PUNCT
ejpam-490	368	7	art	art	NOUN
ejpam-490	368	8	.	.	PUNCT
ejpam-490	369	1	134	134	NUM
ejpam-490	369	2	,	,	PUNCT
ejpam-490	369	3	1	1	NUM
ejpam-490	369	4	-	-	SYM
ejpam-490	369	5	7	7	NUM
ejpam-490	369	6	.	.	NOUN
ejpam-490	369	7	2006	2006	NUM
ejpam-490	369	8	.	.	PUNCT
ejpam-490	370	1	[	[	X
ejpam-490	370	2	9	9	NUM
ejpam-490	370	3	]	]	PUNCT
ejpam-490	370	4	a.	a.	PROPN
ejpam-490	370	5	w.	w.	PROPN
ejpam-490	370	6	goodman	goodman	PROPN
ejpam-490	370	7	,	,	PUNCT
ejpam-490	370	8	on	on	ADP
ejpam-490	370	9	uniformly	uniformly	ADV
ejpam-490	370	10	convex	convex	NOUN
ejpam-490	370	11	functions	function	NOUN
ejpam-490	370	12	,	,	PUNCT
ejpam-490	370	13	ann	ann	PROPN
ejpam-490	370	14	.	.	PROPN
ejpam-490	370	15	polon	polon	PROPN
ejpam-490	370	16	.	.	PUNCT
ejpam-490	371	1	math	math	NOUN
ejpam-490	371	2	.	.	PUNCT
ejpam-490	372	1	56	56	NUM
ejpam-490	372	2	,	,	PUNCT
ejpam-490	372	3	87	87	NUM
ejpam-490	372	4	-	-	SYM
ejpam-490	372	5	92	92	NUM
ejpam-490	372	6	.	.	PUNCT
ejpam-490	373	1	1991	1991	NUM
ejpam-490	373	2	.	.	PUNCT
ejpam-490	374	1	[	[	X
ejpam-490	374	2	10	10	NUM
ejpam-490	374	3	]	]	PUNCT
ejpam-490	374	4	a.	a.	PROPN
ejpam-490	374	5	w.	w.	PROPN
ejpam-490	374	6	goodman	goodman	PROPN
ejpam-490	374	7	,	,	PUNCT
ejpam-490	374	8	on	on	ADP
ejpam-490	374	9	uniformly	uniformly	ADJ
ejpam-490	374	10	starlike	starlike	NOUN
ejpam-490	374	11	functions	function	NOUN
ejpam-490	374	12	,	,	PUNCT
ejpam-490	374	13	j.	j.	PROPN
ejpam-490	374	14	math	math	PROPN
ejpam-490	374	15	.	.	PUNCT
ejpam-490	375	1	anal	anal	PROPN
ejpam-490	375	2	.	.	PUNCT
ejpam-490	376	1	appl	appl	PROPN
ejpam-490	376	2	.	.	PROPN
ejpam-490	377	1	155	155	NUM
ejpam-490	377	2	,	,	PUNCT
ejpam-490	377	3	364	364	NUM
ejpam-490	377	4	-	-	SYM
ejpam-490	377	5	370	370	NUM
ejpam-490	377	6	.	.	PUNCT
ejpam-490	378	1	1991	1991	NUM
ejpam-490	378	2	.	.	PUNCT
ejpam-490	379	1	[	[	X
ejpam-490	379	2	11	11	NUM
ejpam-490	379	3	]	]	PUNCT
ejpam-490	379	4	r.	r.	PROPN
ejpam-490	379	5	j.	j.	PROPN
ejpam-490	379	6	libera	libera	PROPN
ejpam-490	379	7	,	,	PUNCT
ejpam-490	379	8	some	some	DET
ejpam-490	379	9	classes	class	NOUN
ejpam-490	379	10	of	of	ADP
ejpam-490	379	11	regular	regular	ADJ
ejpam-490	379	12	univalent	univalent	ADJ
ejpam-490	379	13	functions	function	NOUN
ejpam-490	379	14	,	,	PUNCT
ejpam-490	379	15	proc	proc	NOUN
ejpam-490	379	16	.	.	PUNCT
ejpam-490	380	1	amer	amer	PROPN
ejpam-490	380	2	.	.	PUNCT
ejpam-490	380	3	math	math	PROPN
ejpam-490	380	4	.	.	PUNCT
ejpam-490	381	1	soc	soc	PROPN
ejpam-490	381	2	.	.	PUNCT
ejpam-490	382	1	16	16	NUM
ejpam-490	382	2	,	,	PUNCT
ejpam-490	382	3	755	755	NUM
ejpam-490	382	4	-	-	SYM
ejpam-490	382	5	758	758	NUM
ejpam-490	382	6	.	.	PUNCT
ejpam-490	383	1	1965	1965	NUM
ejpam-490	383	2	.	.	PUNCT
ejpam-490	384	1	[	[	X
ejpam-490	384	2	12	12	NUM
ejpam-490	384	3	]	]	PUNCT
ejpam-490	384	4	a.	a.	PROPN
ejpam-490	384	5	e.	e.	PROPN
ejpam-490	384	6	livingston	livingston	PROPN
ejpam-490	384	7	,	,	PUNCT
ejpam-490	384	8	on	on	ADP
ejpam-490	384	9	the	the	DET
ejpam-490	384	10	radius	radius	NOUN
ejpam-490	384	11	of	of	ADP
ejpam-490	384	12	univalence	univalence	NOUN
ejpam-490	384	13	of	of	ADP
ejpam-490	384	14	certain	certain	ADJ
ejpam-490	384	15	analytic	analytic	ADJ
ejpam-490	384	16	functions	function	NOUN
ejpam-490	384	17	,	,	PUNCT
ejpam-490	384	18	proc	proc	NOUN
ejpam-490	384	19	.	.	PUNCT
ejpam-490	385	1	amer	amer	PROPN
ejpam-490	385	2	.	.	PUNCT
ejpam-490	385	3	math	math	PROPN
ejpam-490	385	4	.	.	PUNCT
ejpam-490	386	1	soc	soc	PROPN
ejpam-490	386	2	.	.	PUNCT
ejpam-490	387	1	17	17	NUM
ejpam-490	387	2	,	,	PUNCT
ejpam-490	387	3	352	352	NUM
ejpam-490	387	4	-	-	SYM
ejpam-490	387	5	357	357	NUM
ejpam-490	387	6	.	.	PUNCT
ejpam-490	388	1	1966	1966	NUM
ejpam-490	388	2	.	.	PUNCT
ejpam-490	389	1	[	[	X
ejpam-490	389	2	13	13	NUM
ejpam-490	389	3	]	]	PUNCT
ejpam-490	389	4	s.	s.	PROPN
ejpam-490	389	5	s.	s.	PROPN
ejpam-490	389	6	miller	miller	PROPN
ejpam-490	389	7	and	and	CCONJ
ejpam-490	389	8	p.	p.	PROPN
ejpam-490	389	9	t.	t.	PROPN
ejpam-490	389	10	mocanu	mocanu	PROPN
ejpam-490	389	11	,	,	PUNCT
ejpam-490	389	12	differenatial	differenatial	ADJ
ejpam-490	389	13	subordinations	subordination	NOUN
ejpam-490	389	14	:	:	PUNCT
ejpam-490	389	15	theory	theory	NOUN
ejpam-490	389	16	and	and	CCONJ
ejpam-490	389	17	applications	application	NOUN
ejpam-490	389	18	,	,	PUNCT
ejpam-490	389	19	series	series	NOUN
ejpam-490	389	20	on	on	ADP
ejpam-490	389	21	monographs	monograph	NOUN
ejpam-490	389	22	and	and	CCONJ
ejpam-490	389	23	textbooks	textbook	NOUN
ejpam-490	389	24	in	in	ADP
ejpam-490	389	25	pure	pure	ADJ
ejpam-490	389	26	and	and	CCONJ
ejpam-490	389	27	appl	appl	NOUN
ejpam-490	389	28	.	.	PROPN
ejpam-490	389	29	math	math	NOUN
ejpam-490	389	30	.	.	PUNCT
ejpam-490	390	1	no	no	INTJ
ejpam-490	390	2	.	.	PUNCT
ejpam-490	390	3	255	255	NUM
ejpam-490	390	4	marcel	marcel	PROPN
ejpam-490	390	5	dekker	dekker	PROPN
ejpam-490	390	6	,	,	PUNCT
ejpam-490	390	7	inc	inc	PROPN
ejpam-490	390	8	.	.	PROPN
ejpam-490	390	9	,	,	PUNCT
ejpam-490	390	10	new	new	PROPN
ejpam-490	390	11	york	york	PROPN
ejpam-490	390	12	,	,	PUNCT
ejpam-490	390	13	2000	2000	NUM
ejpam-490	390	14	.	.	PUNCT
ejpam-490	391	1	[	[	X
ejpam-490	391	2	14	14	NUM
ejpam-490	391	3	]	]	X
ejpam-490	391	4	g.	g.	PROPN
ejpam-490	391	5	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-490	391	6	and	and	CCONJ
ejpam-490	391	7	n.	n.	PROPN
ejpam-490	391	8	magesh	magesh	PROPN
ejpam-490	391	9	,	,	PUNCT
ejpam-490	391	10	a	a	DET
ejpam-490	391	11	new	new	ADJ
ejpam-490	391	12	subclass	subclass	NOUN
ejpam-490	391	13	of	of	ADP
ejpam-490	391	14	uniformly	uniformly	ADJ
ejpam-490	391	15	convex	convex	NOUN
ejpam-490	391	16	functions	function	NOUN
ejpam-490	391	17	and	and	CCONJ
ejpam-490	391	18	corresponding	correspond	VERB
ejpam-490	391	19	subclass	subclass	NOUN
ejpam-490	391	20	of	of	ADP
ejpam-490	391	21	starlike	starlike	NOUN
ejpam-490	391	22	functions	function	NOUN
ejpam-490	391	23	with	with	ADP
ejpam-490	391	24	fixed	fix	VERB
ejpam-490	391	25	second	second	ADJ
ejpam-490	391	26	coefficient	coefficient	NOUN
ejpam-490	391	27	,	,	PUNCT
ejpam-490	391	28	j.	j.	PROPN
ejpam-490	391	29	inequal	inequal	PROPN
ejpam-490	391	30	.	.	PUNCT
ejpam-490	392	1	pure	pure	ADJ
ejpam-490	392	2	appl	appl	PROPN
ejpam-490	392	3	.	.	PUNCT
ejpam-490	392	4	math	math	NOUN
ejpam-490	392	5	.	.	PUNCT
ejpam-490	393	1	5	5	NUM
ejpam-490	393	2	,	,	PUNCT
ejpam-490	393	3	no	no	INTJ
ejpam-490	393	4	.	.	NOUN
ejpam-490	393	5	4	4	NUM
ejpam-490	393	6	,	,	PUNCT
ejpam-490	393	7	art	art	NOUN
ejpam-490	393	8	.	.	PUNCT
ejpam-490	394	1	85	85	NUM
ejpam-490	394	2	,	,	PUNCT
ejpam-490	394	3	1	1	NUM
ejpam-490	394	4	-	-	NUM
ejpam-490	394	5	10.2004	10.2004	NUM
ejpam-490	394	6	.	.	PUNCT
ejpam-490	395	1	[	[	X
ejpam-490	395	2	15	15	NUM
ejpam-490	395	3	]	]	X
ejpam-490	395	4	g.	g.	PROPN
ejpam-490	395	5	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-490	395	6	and	and	CCONJ
ejpam-490	395	7	n.	n.	PROPN
ejpam-490	395	8	magesh	magesh	PROPN
ejpam-490	395	9	,	,	PUNCT
ejpam-490	395	10	linear	linear	PROPN
ejpam-490	395	11	operators	operator	NOUN
ejpam-490	395	12	associated	associate	VERB
ejpam-490	395	13	with	with	ADP
ejpam-490	395	14	a	a	DET
ejpam-490	395	15	subclass	subclass	NOUN
ejpam-490	395	16	of	of	ADP
ejpam-490	395	17	uniformly	uniformly	ADJ
ejpam-490	395	18	convex	convex	NOUN
ejpam-490	395	19	functions	function	NOUN
ejpam-490	395	20	,	,	PUNCT
ejpam-490	395	21	internat	internat	PROPN
ejpam-490	395	22	.	.	PUNCT
ejpam-490	396	1	j.	j.	PROPN
ejpam-490	396	2	pure	pure	PROPN
ejpam-490	396	3	appl	appl	PROPN
ejpam-490	396	4	.	.	PUNCT
ejpam-490	396	5	math	math	PROPN
ejpam-490	396	6	.	.	PUNCT
ejpam-490	397	1	sci	sci	PROPN
ejpam-490	397	2	.	.	PROPN
ejpam-490	398	1	3	3	NUM
ejpam-490	398	2	,	,	PUNCT
ejpam-490	398	3	no	no	INTJ
ejpam-490	398	4	.	.	NOUN
ejpam-490	398	5	2	2	NUM
ejpam-490	398	6	,	,	PUNCT
ejpam-490	398	7	113	113	NUM
ejpam-490	398	8	-	-	SYM
ejpam-490	398	9	125	125	NUM
ejpam-490	398	10	.	.	PUNCT
ejpam-490	399	1	2006	2006	NUM
ejpam-490	399	2	.	.	PUNCT
ejpam-490	400	1	[	[	X
ejpam-490	400	2	16	16	NUM
ejpam-490	400	3	]	]	X
ejpam-490	400	4	g.	g.	PROPN
ejpam-490	400	5	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-490	400	6	,	,	PUNCT
ejpam-490	400	7	t.	t.	PROPN
ejpam-490	400	8	rosy	rosy	PROPN
ejpam-490	400	9	and	and	CCONJ
ejpam-490	400	10	k.	k.	PROPN
ejpam-490	400	11	muthunagai	muthunagai	PROPN
ejpam-490	400	12	,	,	PUNCT
ejpam-490	400	13	carlson	carlson	PROPN
ejpam-490	400	14	-	-	PUNCT
ejpam-490	400	15	shaffer	shaffer	NOUN
ejpam-490	400	16	operator	operator	NOUN
ejpam-490	400	17	and	and	CCONJ
ejpam-490	400	18	their	their	PRON
ejpam-490	400	19	applications	application	NOUN
ejpam-490	400	20	to	to	ADP
ejpam-490	400	21	certain	certain	ADJ
ejpam-490	400	22	subclass	subclass	NOUN
ejpam-490	400	23	of	of	ADP
ejpam-490	400	24	uniformly	uniformly	ADJ
ejpam-490	400	25	convex	convex	NOUN
ejpam-490	400	26	function	function	NOUN
ejpam-490	400	27	,	,	PUNCT
ejpam-490	400	28	general	general	ADJ
ejpam-490	400	29	math	math	NOUN
ejpam-490	400	30	.	.	PUNCT
ejpam-490	401	1	15	15	NUM
ejpam-490	401	2	,	,	PUNCT
ejpam-490	401	3	no	no	INTJ
ejpam-490	401	4	.	.	NOUN
ejpam-490	401	5	4	4	NUM
ejpam-490	401	6	,	,	PUNCT
ejpam-490	401	7	131	131	NUM
ejpam-490	401	8	-	-	SYM
ejpam-490	401	9	143	143	NUM
ejpam-490	401	10	.	.	PUNCT
ejpam-490	402	1	2007	2007	NUM
ejpam-490	402	2	.	.	PUNCT
ejpam-490	403	1	[	[	X
ejpam-490	403	2	17	17	NUM
ejpam-490	403	3	]	]	PUNCT
ejpam-490	403	4	k.	k.	PROPN
ejpam-490	403	5	i.	i.	PROPN
ejpam-490	403	6	noor	noor	PROPN
ejpam-490	403	7	,	,	PUNCT
ejpam-490	403	8	on	on	ADP
ejpam-490	403	9	new	new	ADJ
ejpam-490	403	10	classes	class	NOUN
ejpam-490	403	11	of	of	ADP
ejpam-490	403	12	integral	integral	ADJ
ejpam-490	403	13	operators	operator	NOUN
ejpam-490	403	14	,	,	PUNCT
ejpam-490	403	15	j.	j.	PROPN
ejpam-490	403	16	natur	natur	PROPN
ejpam-490	403	17	.	.	PUNCT
ejpam-490	404	1	geem	geem	PROPN
ejpam-490	404	2	.	.	PUNCT
ejpam-490	405	1	16	16	NUM
ejpam-490	405	2	,	,	PUNCT
ejpam-490	405	3	71	71	NUM
ejpam-490	405	4	-	-	SYM
ejpam-490	405	5	80	80	NUM
ejpam-490	405	6	.	.	PUNCT
ejpam-490	406	1	1999	1999	NUM
ejpam-490	406	2	.	.	PUNCT
ejpam-490	407	1	[	[	X
ejpam-490	407	2	18	18	NUM
ejpam-490	407	3	]	]	PUNCT
ejpam-490	407	4	r.	r.	PROPN
ejpam-490	407	5	k.	k.	PROPN
ejpam-490	407	6	raina	raina	PROPN
ejpam-490	407	7	and	and	CCONJ
ejpam-490	407	8	deepak	deepak	PROPN
ejpam-490	407	9	bansal	bansal	PROPN
ejpam-490	407	10	,	,	PUNCT
ejpam-490	407	11	some	some	DET
ejpam-490	407	12	properties	property	NOUN
ejpam-490	407	13	of	of	ADP
ejpam-490	407	14	a	a	DET
ejpam-490	407	15	new	new	ADJ
ejpam-490	407	16	class	class	NOUN
ejpam-490	407	17	of	of	ADP
ejpam-490	407	18	analytic	analytic	ADJ
ejpam-490	407	19	functions	function	NOUN
ejpam-490	407	20	defined	define	VERB
ejpam-490	407	21	in	in	ADP
ejpam-490	407	22	terms	term	NOUN
ejpam-490	407	23	of	of	ADP
ejpam-490	407	24	a	a	DET
ejpam-490	407	25	hadamard	hadamard	ADJ
ejpam-490	407	26	product	product	NOUN
ejpam-490	407	27	,	,	PUNCT
ejpam-490	407	28	j.	j.	PROPN
ejpam-490	407	29	inequal	inequal	PROPN
ejpam-490	407	30	.	.	PUNCT
ejpam-490	408	1	pure	pure	ADJ
ejpam-490	408	2	appl	appl	PROPN
ejpam-490	408	3	.	.	PUNCT
ejpam-490	408	4	math	math	NOUN
ejpam-490	408	5	.	.	PUNCT
ejpam-490	409	1	9	9	NUM
ejpam-490	409	2	,	,	PUNCT
ejpam-490	409	3	no	no	INTJ
ejpam-490	409	4	.	.	NOUN
ejpam-490	409	5	1	1	NUM
ejpam-490	409	6	,	,	PUNCT
ejpam-490	409	7	art	art	NOUN
ejpam-490	409	8	.	.	PUNCT
ejpam-490	410	1	22	22	NUM
ejpam-490	410	2	,	,	PUNCT
ejpam-490	410	3	1	1	NUM
ejpam-490	410	4	-	-	SYM
ejpam-490	410	5	9	9	NUM
ejpam-490	410	6	.	.	NUM
ejpam-490	410	7	2008	2008	NUM
ejpam-490	410	8	.	.	PUNCT
ejpam-490	411	1	[	[	X
ejpam-490	411	2	19	19	NUM
ejpam-490	411	3	]	]	X
ejpam-490	411	4	f.	f.	PROPN
ejpam-490	411	5	ronning	ronning	PROPN
ejpam-490	411	6	,	,	PUNCT
ejpam-490	411	7	on	on	ADP
ejpam-490	411	8	starlike	starlike	NOUN
ejpam-490	411	9	functions	function	NOUN
ejpam-490	411	10	associated	associate	VERB
ejpam-490	411	11	with	with	ADP
ejpam-490	411	12	parabolic	parabolic	ADJ
ejpam-490	411	13	regions	region	NOUN
ejpam-490	411	14	,	,	PUNCT
ejpam-490	411	15	ann	ann	PROPN
ejpam-490	411	16	.	.	PROPN
ejpam-490	411	17	univ	univ	PROPN
ejpam-490	411	18	.	.	PUNCT
ejpam-490	412	1	mariaecurie	mariaecurie	ADJ
ejpam-490	412	2	-	-	PUNCT
ejpam-490	412	3	sklodowska	sklodowska	NOUN
ejpam-490	412	4	,	,	PUNCT
ejpam-490	412	5	sect	sect	NOUN
ejpam-490	412	6	.	.	PUNCT
ejpam-490	413	1	a	a	DET
ejpam-490	413	2	45	45	NUM
ejpam-490	413	3	,	,	PUNCT
ejpam-490	413	4	117	117	NUM
ejpam-490	413	5	-	-	SYM
ejpam-490	413	6	122	122	NUM
ejpam-490	413	7	.	.	PUNCT
ejpam-490	413	8	1991	1991	NUM
ejpam-490	413	9	.	.	PUNCT
ejpam-490	414	1	[	[	X
ejpam-490	414	2	20	20	NUM
ejpam-490	414	3	]	]	X
ejpam-490	414	4	f.	f.	PROPN
ejpam-490	414	5	ronning	ronning	PROPN
ejpam-490	414	6	,	,	PUNCT
ejpam-490	414	7	uinformly	uinformly	ADV
ejpam-490	414	8	convex	convex	NOUN
ejpam-490	414	9	functions	function	NOUN
ejpam-490	414	10	and	and	CCONJ
ejpam-490	414	11	a	a	DET
ejpam-490	414	12	corresponding	corresponding	ADJ
ejpam-490	414	13	class	class	NOUN
ejpam-490	414	14	of	of	ADP
ejpam-490	414	15	starlike	starlike	NOUN
ejpam-490	414	16	functions	function	NOUN
ejpam-490	414	17	,	,	PUNCT
ejpam-490	414	18	proc	proc	NOUN
ejpam-490	414	19	.	.	PUNCT
ejpam-490	415	1	amer	amer	PROPN
ejpam-490	415	2	.	.	PUNCT
ejpam-490	415	3	math	math	PROPN
ejpam-490	415	4	.	.	PUNCT
ejpam-490	416	1	soc	soc	PROPN
ejpam-490	416	2	.	.	PUNCT
ejpam-490	417	1	118	118	NUM
ejpam-490	417	2	,	,	PUNCT
ejpam-490	417	3	189	189	NUM
ejpam-490	417	4	-	-	SYM
ejpam-490	417	5	196	196	NUM
ejpam-490	417	6	.	.	PUNCT
ejpam-490	418	1	1993	1993	NUM
ejpam-490	418	2	.	.	PUNCT
ejpam-490	419	1	references	reference	NOUN
ejpam-490	419	2	917	917	NUM
ejpam-490	420	1	[	[	X
ejpam-490	420	2	21	21	NUM
ejpam-490	420	3	]	]	X
ejpam-490	420	4	t.	t.	PROPN
ejpam-490	420	5	rosy	rosy	ADJ
ejpam-490	420	6	and	and	CCONJ
ejpam-490	420	7	g.	g.	PROPN
ejpam-490	420	8	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-490	420	9	,	,	PUNCT
ejpam-490	420	10	fractional	fractional	ADJ
ejpam-490	420	11	calculus	calculus	NOUN
ejpam-490	420	12	and	and	CCONJ
ejpam-490	420	13	their	their	PRON
ejpam-490	420	14	applications	application	NOUN
ejpam-490	420	15	to	to	ADP
ejpam-490	420	16	certain	certain	ADJ
ejpam-490	420	17	subclass	subclass	NOUN
ejpam-490	420	18	of	of	ADP
ejpam-490	420	19	uniformly	uniformly	ADJ
ejpam-490	420	20	convex	convex	NOUN
ejpam-490	420	21	functions	function	NOUN
ejpam-490	420	22	,	,	PUNCT
ejpam-490	420	23	far	far	PROPN
ejpam-490	420	24	east	east	PROPN
ejpam-490	420	25	j.	j.	PROPN
ejpam-490	420	26	math	math	PROPN
ejpam-490	420	27	.	.	PUNCT
ejpam-490	421	1	sci	sci	PROPN
ejpam-490	421	2	.	.	PUNCT
ejpam-490	421	3	(	(	PUNCT
ejpam-490	421	4	fjms	fjms	PROPN
ejpam-490	421	5	)	)	PUNCT
ejpam-490	421	6	,	,	PUNCT
ejpam-490	421	7	15	15	NUM
ejpam-490	421	8	,	,	PUNCT
ejpam-490	421	9	no	no	INTJ
ejpam-490	421	10	.	.	NOUN
ejpam-490	421	11	2	2	NUM
ejpam-490	421	12	,	,	PUNCT
ejpam-490	421	13	231	231	NUM
ejpam-490	421	14	-	-	SYM
ejpam-490	421	15	242	242	NUM
ejpam-490	421	16	.	.	PUNCT
ejpam-490	421	17	2004	2004	NUM
ejpam-490	421	18	.	.	PUNCT
ejpam-490	422	1	[	[	X
ejpam-490	422	2	22	22	NUM
ejpam-490	422	3	]	]	X
ejpam-490	422	4	st	st	PROPN
ejpam-490	422	5	.	.	PROPN
ejpam-490	422	6	ruscheweyh	ruscheweyh	PROPN
ejpam-490	422	7	,	,	PUNCT
ejpam-490	422	8	new	new	ADJ
ejpam-490	422	9	criteria	criterion	NOUN
ejpam-490	422	10	for	for	ADP
ejpam-490	422	11	univalent	univalent	ADJ
ejpam-490	422	12	functions	function	NOUN
ejpam-490	422	13	,	,	PUNCT
ejpam-490	422	14	proc	proc	NOUN
ejpam-490	422	15	.	.	PUNCT
ejpam-490	423	1	amer	amer	PROPN
ejpam-490	423	2	.	.	PUNCT
ejpam-490	423	3	math	math	PROPN
ejpam-490	423	4	.	.	PUNCT
ejpam-490	424	1	soc	soc	PROPN
ejpam-490	424	2	.	.	PUNCT
ejpam-490	425	1	49	49	NUM
ejpam-490	425	2	,	,	PUNCT
ejpam-490	425	3	109	109	NUM
ejpam-490	425	4	–	–	PUNCT
ejpam-490	425	5	115	115	NUM
ejpam-490	425	6	.	.	PUNCT
ejpam-490	426	1	1975	1975	NUM
ejpam-490	426	2	.	.	PUNCT
ejpam-490	427	1	[	[	X
ejpam-490	427	2	23	23	NUM
ejpam-490	427	3	]	]	X
ejpam-490	427	4	h.	h.	PROPN
ejpam-490	427	5	m.	m.	PROPN
ejpam-490	427	6	srivastava	srivastava	PROPN
ejpam-490	427	7	and	and	CCONJ
ejpam-490	427	8	a.	a.	PROPN
ejpam-490	427	9	a.	a.	PROPN
ejpam-490	427	10	attiya	attiya	PROPN
ejpam-490	427	11	,	,	PUNCT
ejpam-490	427	12	some	some	DET
ejpam-490	427	13	subordination	subordination	NOUN
ejpam-490	427	14	results	result	NOUN
ejpam-490	427	15	associated	associate	VERB
ejpam-490	427	16	with	with	ADP
ejpam-490	427	17	certain	certain	ADJ
ejpam-490	427	18	subclass	subclass	NOUN
ejpam-490	427	19	of	of	ADP
ejpam-490	427	20	analytic	analytic	ADJ
ejpam-490	427	21	functions	function	NOUN
ejpam-490	427	22	,	,	PUNCT
ejpam-490	427	23	j.	j.	PROPN
ejpam-490	427	24	inequal	inequal	PROPN
ejpam-490	427	25	.	.	PUNCT
ejpam-490	428	1	pure	pure	ADJ
ejpam-490	428	2	appl	appl	PROPN
ejpam-490	428	3	.	.	PUNCT
ejpam-490	428	4	math	math	NOUN
ejpam-490	428	5	.	.	PUNCT
ejpam-490	429	1	5	5	NUM
ejpam-490	429	2	,	,	PUNCT
ejpam-490	429	3	no	no	INTJ
ejpam-490	429	4	.	.	NOUN
ejpam-490	429	5	4	4	NUM
ejpam-490	429	6	,	,	PUNCT
ejpam-490	429	7	art	art	NOUN
ejpam-490	429	8	.	.	PUNCT
ejpam-490	430	1	82	82	NUM
ejpam-490	430	2	,	,	PUNCT
ejpam-490	430	3	1	1	NUM
ejpam-490	430	4	-	-	SYM
ejpam-490	430	5	6	6	NUM
ejpam-490	430	6	.	.	PUNCT
ejpam-490	430	7	2004	2004	NUM
ejpam-490	430	8	.	.	PUNCT
ejpam-490	431	1	[	[	X
ejpam-490	431	2	24	24	NUM
ejpam-490	431	3	]	]	PUNCT
ejpam-490	431	4	k.	k.	PROPN
ejpam-490	431	5	g.	g.	PROPN
ejpam-490	431	6	subramanian	subramanian	PROPN
ejpam-490	431	7	,	,	PUNCT
ejpam-490	431	8	g.	g.	PROPN
ejpam-490	431	9	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-490	431	10	,	,	PUNCT
ejpam-490	431	11	p.	p.	NOUN
ejpam-490	431	12	balasubrahma	balasubrahma	PROPN
ejpam-490	431	13	and	and	CCONJ
ejpam-490	431	14	h.	h.	PROPN
ejpam-490	431	15	silverman	silverman	PROPN
ejpam-490	431	16	,	,	PUNCT
ejpam-490	431	17	subclasses	subclass	NOUN
ejpam-490	431	18	of	of	ADP
ejpam-490	431	19	uniformly	uniformly	ADV
ejpam-490	431	20	convex	convex	NOUN
ejpam-490	431	21	and	and	CCONJ
ejpam-490	431	22	uniformly	uniformly	ADV
ejpam-490	431	23	starlike	starlike	NOUN
ejpam-490	431	24	functions	function	NOUN
ejpam-490	431	25	,	,	PUNCT
ejpam-490	431	26	math	math	NOUN
ejpam-490	431	27	.	.	PUNCT
ejpam-490	432	1	japon	japon	PROPN
ejpam-490	432	2	.	.	PUNCT
ejpam-490	433	1	42	42	NUM
ejpam-490	433	2	,	,	PUNCT
ejpam-490	433	3	no	no	INTJ
ejpam-490	433	4	.	.	NOUN
ejpam-490	433	5	3	3	NUM
ejpam-490	433	6	,	,	PUNCT
ejpam-490	433	7	517	517	NUM
ejpam-490	433	8	-	-	SYM
ejpam-490	433	9	522	522	NUM
ejpam-490	433	10	.	.	PUNCT
ejpam-490	433	11	1995	1995	NUM
ejpam-490	433	12	.	.	PUNCT
ejpam-490	434	1	[	[	X
ejpam-490	434	2	25	25	NUM
ejpam-490	434	3	]	]	PUNCT
ejpam-490	434	4	h.	h.	PROPN
ejpam-490	434	5	s.	s.	PROPN
ejpam-490	434	6	wilf	wilf	PROPN
ejpam-490	434	7	,	,	PUNCT
ejpam-490	434	8	subordinating	subordinating	NOUN
ejpam-490	434	9	factor	factor	NOUN
ejpam-490	434	10	sequence	sequence	NOUN
ejpam-490	434	11	for	for	ADP
ejpam-490	434	12	convex	convex	NOUN
ejpam-490	434	13	maps	map	NOUN
ejpam-490	434	14	of	of	ADP
ejpam-490	434	15	the	the	DET
ejpam-490	434	16	unit	unit	NOUN
ejpam-490	434	17	circle	circle	NOUN
ejpam-490	434	18	,	,	PUNCT
ejpam-490	434	19	proc	proc	PROPN
ejpam-490	434	20	.	.	PUNCT
ejpam-490	435	1	amer	amer	PROPN
ejpam-490	435	2	.	.	PUNCT
ejpam-490	435	3	math	math	PROPN
ejpam-490	435	4	.	.	PUNCT
ejpam-490	436	1	soc	soc	PROPN
ejpam-490	436	2	.	.	PUNCT
ejpam-490	437	1	12	12	NUM
ejpam-490	437	2	,	,	PUNCT
ejpam-490	437	3	689	689	NUM
ejpam-490	437	4	-	-	SYM
ejpam-490	437	5	693	693	NUM
ejpam-490	437	6	.	.	PUNCT
ejpam-490	438	1	1961	1961	NUM
ejpam-490	438	2	.	.	PUNCT