id	sid	tid	token	lemma	pos
ejpam-676	1	1	5_aouf.dvi	5_aouf.dvi	NUM
ejpam-676	1	2	european	european	ADJ
ejpam-676	1	3	journal	journal	NOUN
ejpam-676	1	4	of	of	ADP
ejpam-676	1	5	pure	pure	ADJ
ejpam-676	1	6	and	and	CCONJ
ejpam-676	1	7	applied	apply	VERB
ejpam-676	1	8	mathematics	mathematic	NOUN
ejpam-676	1	9	vol	vol	NOUN
ejpam-676	1	10	.	.	PROPN
ejpam-676	1	11	5	5	NUM
ejpam-676	1	12	,	,	PUNCT
ejpam-676	1	13	no	no	INTJ
ejpam-676	1	14	.	.	NOUN
ejpam-676	1	15	2	2	NUM
ejpam-676	1	16	,	,	PUNCT
ejpam-676	1	17	2012	2012	NUM
ejpam-676	1	18	,	,	PUNCT
ejpam-676	1	19	141	141	NUM
ejpam-676	1	20	-	-	SYM
ejpam-676	1	21	159	159	NUM
ejpam-676	1	22	issn	issn	PROPN
ejpam-676	1	23	1307	1307	NUM
ejpam-676	1	24	-	-	SYM
ejpam-676	1	25	5543	5543	NUM
ejpam-676	1	26	–	–	PUNCT
ejpam-676	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-676	1	28	applications	application	NOUN
ejpam-676	1	29	of	of	ADP
ejpam-676	1	30	differential	differential	ADJ
ejpam-676	1	31	subordination	subordination	NOUN
ejpam-676	1	32	to	to	ADP
ejpam-676	1	33	certain	certain	ADJ
ejpam-676	1	34	subclasses	subclass	NOUN
ejpam-676	1	35	of	of	ADP
ejpam-676	1	36	meromorphically	meromorphically	ADV
ejpam-676	1	37	multivalent	multivalent	NOUN
ejpam-676	1	38	functions	function	NOUN
ejpam-676	1	39	associated	associate	VERB
ejpam-676	1	40	with	with	ADP
ejpam-676	1	41	generalized	generalized	ADJ
ejpam-676	1	42	hypergeometric	hypergeometric	ADJ
ejpam-676	1	43	function	function	NOUN
ejpam-676	1	44	m.	m.	NOUN
ejpam-676	1	45	k.	k.	PROPN
ejpam-676	1	46	aouf	aouf	PROPN
ejpam-676	1	47	faculty	faculty	NOUN
ejpam-676	1	48	of	of	ADP
ejpam-676	1	49	science	science	NOUN
ejpam-676	1	50	,	,	PUNCT
ejpam-676	1	51	mansoura	mansoura	PROPN
ejpam-676	1	52	university	university	NOUN
ejpam-676	1	53	,	,	PUNCT
ejpam-676	1	54	mansoura	mansoura	PROPN
ejpam-676	1	55	35516	35516	NUM
ejpam-676	1	56	,	,	PUNCT
ejpam-676	1	57	egypt	egypt	PROPN
ejpam-676	1	58	.	.	PUNCT
ejpam-676	2	1	abstract	abstract	PROPN
ejpam-676	2	2	.	.	PUNCT
ejpam-676	3	1	by	by	ADP
ejpam-676	3	2	making	make	VERB
ejpam-676	3	3	use	use	NOUN
ejpam-676	3	4	of	of	ADP
ejpam-676	3	5	the	the	DET
ejpam-676	3	6	principle	principle	NOUN
ejpam-676	3	7	of	of	ADP
ejpam-676	3	8	differential	differential	ADJ
ejpam-676	3	9	subordination	subordination	NOUN
ejpam-676	3	10	,	,	PUNCT
ejpam-676	3	11	we	we	PRON
ejpam-676	3	12	investigate	investigate	VERB
ejpam-676	3	13	several	several	ADJ
ejpam-676	3	14	inclusion	inclusion	NOUN
ejpam-676	3	15	relationships	relationship	NOUN
ejpam-676	3	16	and	and	CCONJ
ejpam-676	3	17	other	other	ADJ
ejpam-676	3	18	interesting	interesting	ADJ
ejpam-676	3	19	properties	property	NOUN
ejpam-676	3	20	of	of	ADP
ejpam-676	3	21	certain	certain	ADJ
ejpam-676	3	22	subclasses	subclass	NOUN
ejpam-676	3	23	of	of	ADP
ejpam-676	3	24	meromorphically	meromorphically	ADV
ejpam-676	3	25	multivalent	multivalent	NOUN
ejpam-676	3	26	functions	function	NOUN
ejpam-676	3	27	which	which	PRON
ejpam-676	3	28	are	be	AUX
ejpam-676	3	29	defined	define	VERB
ejpam-676	3	30	by	by	ADP
ejpam-676	3	31	certain	certain	ADJ
ejpam-676	3	32	linear	linear	ADJ
ejpam-676	3	33	operator	operator	NOUN
ejpam-676	3	34	involving	involve	VERB
ejpam-676	3	35	the	the	DET
ejpam-676	3	36	generalized	generalized	ADJ
ejpam-676	3	37	hypergeometric	hypergeometric	ADJ
ejpam-676	3	38	function	function	NOUN
ejpam-676	3	39	.	.	PUNCT
ejpam-676	4	1	2010	2010	NUM
ejpam-676	4	2	mathematics	mathematic	NOUN
ejpam-676	4	3	subject	subject	NOUN
ejpam-676	4	4	classifications	classification	NOUN
ejpam-676	4	5	:	:	PUNCT
ejpam-676	4	6	30c45	30c45	NUM
ejpam-676	4	7	key	key	ADJ
ejpam-676	4	8	words	word	NOUN
ejpam-676	4	9	and	and	CCONJ
ejpam-676	4	10	phrases	phrase	NOUN
ejpam-676	4	11	:	:	PUNCT
ejpam-676	4	12	differential	differential	ADJ
ejpam-676	4	13	subordination	subordination	NOUN
ejpam-676	4	14	,	,	PUNCT
ejpam-676	4	15	hadamard	hadamard	ADJ
ejpam-676	4	16	product	product	NOUN
ejpam-676	4	17	,	,	PUNCT
ejpam-676	4	18	meromorphic	meromorphic	ADJ
ejpam-676	4	19	function	function	NOUN
ejpam-676	4	20	,	,	PUNCT
ejpam-676	4	21	hypergeometric	hypergeometric	ADJ
ejpam-676	4	22	function	function	NOUN
ejpam-676	4	23	.	.	PUNCT
ejpam-676	5	1	1	1	X
ejpam-676	5	2	.	.	X
ejpam-676	5	3	introduction	introduction	NOUN
ejpam-676	5	4	for	for	ADP
ejpam-676	5	5	any	any	DET
ejpam-676	5	6	integer	integer	NOUN
ejpam-676	5	7	m	m	NOUN
ejpam-676	5	8	>	>	X
ejpam-676	5	9	−p	−p	NOUN
ejpam-676	5	10	,	,	PUNCT
ejpam-676	5	11	let	let	VERB
ejpam-676	5	12	∑	∑	PROPN
ejpam-676	5	13	p	p	X
ejpam-676	5	14	,	,	PUNCT
ejpam-676	5	15	m	m	VERB
ejpam-676	5	16	denote	denote	VERB
ejpam-676	5	17	the	the	DET
ejpam-676	5	18	class	class	NOUN
ejpam-676	5	19	of	of	ADP
ejpam-676	5	20	all	all	DET
ejpam-676	5	21	meromorphic	meromorphic	ADJ
ejpam-676	5	22	functions	function	NOUN
ejpam-676	5	23	f	f	PROPN
ejpam-676	5	24	of	of	ADP
ejpam-676	5	25	the	the	DET
ejpam-676	5	26	form	form	NOUN
ejpam-676	5	27	:	:	PUNCT
ejpam-676	5	28	f	f	PROPN
ejpam-676	5	29	(	(	PUNCT
ejpam-676	5	30	z	z	NOUN
ejpam-676	5	31	)	)	PUNCT
ejpam-676	5	32	=	=	PUNCT
ejpam-676	5	33	z−p	z−p	NOUN
ejpam-676	5	34	+	+	CCONJ
ejpam-676	6	1	∞	∞	NUM
ejpam-676	6	2	∑	∑	PUNCT
ejpam-676	6	3	k	k	X
ejpam-676	6	4	=	=	NOUN
ejpam-676	6	5	m	m	VERB
ejpam-676	6	6	akzk	akzk	ADJ
ejpam-676	6	7	(	(	PUNCT
ejpam-676	6	8	p	p	NOUN
ejpam-676	6	9	∈	∈	PROPN
ejpam-676	6	10	n	n	NOUN
ejpam-676	6	11	=	=	SYM
ejpam-676	6	12	{	{	PUNCT
ejpam-676	6	13	1,2	1,2	NUM
ejpam-676	6	14	,	,	PUNCT
ejpam-676	6	15	.	.	PUNCT
ejpam-676	6	16	.	.	PUNCT
ejpam-676	6	17	.	.	PUNCT
ejpam-676	6	18	}	}	PUNCT
ejpam-676	6	19	)	)	PUNCT
ejpam-676	6	20	,	,	PUNCT
ejpam-676	6	21	(	(	PUNCT
ejpam-676	6	22	1	1	X
ejpam-676	6	23	)	)	PUNCT
ejpam-676	6	24	which	which	PRON
ejpam-676	6	25	are	be	AUX
ejpam-676	6	26	analytic	analytic	ADJ
ejpam-676	6	27	and	and	CCONJ
ejpam-676	6	28	p	p	NOUN
ejpam-676	6	29	-	-	PUNCT
ejpam-676	6	30	valent	valent	NOUN
ejpam-676	6	31	in	in	ADP
ejpam-676	6	32	the	the	DET
ejpam-676	6	33	punctured	punctured	ADJ
ejpam-676	6	34	disc	disc	NOUN
ejpam-676	6	35	u∗	u∗	NOUN
ejpam-676	6	36	=	=	SYM
ejpam-676	6	37	{	{	PUNCT
ejpam-676	6	38	z	z	NOUN
ejpam-676	6	39	:	:	PUNCT
ejpam-676	6	40	z	z	PROPN
ejpam-676	6	41	∈	∈	PROPN
ejpam-676	6	42	c	c	NOUN
ejpam-676	6	43	and	and	CCONJ
ejpam-676	6	44	0	0	NUM
ejpam-676	6	45	<	<	X
ejpam-676	6	46	|z|	|z|	PROPN
ejpam-676	6	47	<	<	X
ejpam-676	6	48	1}=	1}=	NUM
ejpam-676	6	49	u\{0	u\{0	PROPN
ejpam-676	6	50	}	}	PUNCT
ejpam-676	6	51	.	.	PUNCT
ejpam-676	7	1	for	for	ADP
ejpam-676	7	2	convenience	convenience	NOUN
ejpam-676	7	3	,	,	PUNCT
ejpam-676	7	4	we	we	PRON
ejpam-676	7	5	write	write	VERB
ejpam-676	7	6	∑	∑	PROPN
ejpam-676	7	7	p,−p+1	p,−p+1	NOUN
ejpam-676	7	8	=	=	PUNCT
ejpam-676	7	9	∑	∑	PUNCT
ejpam-676	8	1	p.	p.	NOUN
ejpam-676	8	2	if	if	SCONJ
ejpam-676	8	3	f	f	PROPN
ejpam-676	8	4	and	and	CCONJ
ejpam-676	8	5	g	g	PROPN
ejpam-676	8	6	are	be	AUX
ejpam-676	8	7	analytic	analytic	ADJ
ejpam-676	8	8	in	in	ADP
ejpam-676	8	9	u	u	PROPN
ejpam-676	8	10	,	,	PUNCT
ejpam-676	8	11	we	we	PRON
ejpam-676	8	12	say	say	VERB
ejpam-676	8	13	that	that	SCONJ
ejpam-676	8	14	f	f	PROPN
ejpam-676	8	15	is	be	AUX
ejpam-676	8	16	subordinate	subordinate	ADJ
ejpam-676	8	17	to	to	ADP
ejpam-676	8	18	g	g	NOUN
ejpam-676	8	19	,	,	PUNCT
ejpam-676	8	20	written	write	VERB
ejpam-676	8	21	symbolically	symbolically	ADV
ejpam-676	8	22	as	as	SCONJ
ejpam-676	8	23	follows	follow	VERB
ejpam-676	8	24	:	:	PUNCT
ejpam-676	8	25	f	f	NOUN
ejpam-676	8	26	≺	≺	NOUN
ejpam-676	8	27	g	g	PROPN
ejpam-676	8	28	or	or	CCONJ
ejpam-676	8	29	f	f	PROPN
ejpam-676	8	30	(	(	PUNCT
ejpam-676	8	31	z)≺	z)≺	PROPN
ejpam-676	8	32	g(z	g(z	PROPN
ejpam-676	8	33	)	)	PUNCT
ejpam-676	8	34	,	,	PUNCT
ejpam-676	8	35	if	if	SCONJ
ejpam-676	8	36	there	there	PRON
ejpam-676	8	37	exists	exist	VERB
ejpam-676	8	38	a	a	DET
ejpam-676	8	39	schwarz	schwarz	PROPN
ejpam-676	8	40	function	function	PROPN
ejpam-676	8	41	w	w	PROPN
ejpam-676	8	42	,	,	PUNCT
ejpam-676	8	43	which	which	PRON
ejpam-676	8	44	(	(	PUNCT
ejpam-676	8	45	by	by	ADP
ejpam-676	8	46	definition	definition	NOUN
ejpam-676	8	47	)	)	PUNCT
ejpam-676	8	48	is	be	AUX
ejpam-676	8	49	analytic	analytic	ADJ
ejpam-676	8	50	in	in	ADP
ejpam-676	8	51	u	u	NOUN
ejpam-676	8	52	with	with	ADP
ejpam-676	8	53	w(0	w(0	PROPN
ejpam-676	8	54	)	)	PUNCT
ejpam-676	8	55	=	=	SYM
ejpam-676	8	56	0	0	NUM
ejpam-676	8	57	and	and	CCONJ
ejpam-676	8	58	|w(z)|	|w(z)|	VERB
ejpam-676	8	59	<	<	X
ejpam-676	8	60	1	1	NUM
ejpam-676	8	61	(	(	PUNCT
ejpam-676	8	62	z	z	NOUN
ejpam-676	8	63	∈	∈	PROPN
ejpam-676	8	64	u	u	NOUN
ejpam-676	8	65	)	)	PUNCT
ejpam-676	8	66	such	such	ADJ
ejpam-676	8	67	that	that	SCONJ
ejpam-676	8	68	f	f	PROPN
ejpam-676	8	69	(	(	PUNCT
ejpam-676	8	70	z	z	NOUN
ejpam-676	8	71	)	)	PUNCT
ejpam-676	8	72	=	=	PUNCT
ejpam-676	8	73	g(w(z	g(w(z	PROPN
ejpam-676	8	74	)	)	PUNCT
ejpam-676	8	75	)	)	PUNCT
ejpam-676	9	1	(	(	PUNCT
ejpam-676	9	2	z	z	NOUN
ejpam-676	9	3	∈	∈	PROPN
ejpam-676	9	4	u	u	NOUN
ejpam-676	9	5	)	)	PUNCT
ejpam-676	9	6	.	.	PUNCT
ejpam-676	10	1	in	in	ADP
ejpam-676	10	2	particular	particular	ADJ
ejpam-676	10	3	,	,	PUNCT
ejpam-676	10	4	if	if	SCONJ
ejpam-676	10	5	the	the	DET
ejpam-676	10	6	function	function	NOUN
ejpam-676	10	7	g	g	PROPN
ejpam-676	10	8	is	be	AUX
ejpam-676	10	9	univalent	univalent	ADJ
ejpam-676	10	10	in	in	ADP
ejpam-676	10	11	u	u	PROPN
ejpam-676	10	12	,	,	PUNCT
ejpam-676	10	13	we	we	PRON
ejpam-676	10	14	have	have	VERB
ejpam-676	10	15	the	the	DET
ejpam-676	10	16	equivalence	equivalence	NOUN
ejpam-676	10	17	(	(	PUNCT
ejpam-676	10	18	cf	cf	NOUN
ejpam-676	10	19	.	.	PROPN
ejpam-676	10	20	,	,	PUNCT
ejpam-676	10	21	e.	e.	PROPN
ejpam-676	10	22	g.	g.	PROPN
ejpam-676	10	23	,	,	PUNCT
ejpam-676	11	1	[	[	X
ejpam-676	11	2	7	7	NUM
ejpam-676	11	3	]	]	PUNCT
ejpam-676	11	4	;	;	PUNCT
ejpam-676	11	5	see	see	VERB
ejpam-676	11	6	also	also	ADV
ejpam-676	11	7	[	[	X
ejpam-676	11	8	8	8	NUM
ejpam-676	11	9	,	,	PUNCT
ejpam-676	11	10	p.	p.	NOUN
ejpam-676	11	11	4	4	NUM
ejpam-676	11	12	]	]	PUNCT
ejpam-676	11	13	):	):	PUNCT
ejpam-676	11	14	f	f	PROPN
ejpam-676	11	15	(	(	PUNCT
ejpam-676	11	16	z)≺	z)≺	PROPN
ejpam-676	11	17	g(z)⇔	g(z)⇔	PROPN
ejpam-676	11	18	f	f	PROPN
ejpam-676	11	19	(	(	PUNCT
ejpam-676	11	20	0	0	NUM
ejpam-676	11	21	)	)	PUNCT
ejpam-676	11	22	=	=	SYM
ejpam-676	11	23	g(0	g(0	PROPN
ejpam-676	11	24	)	)	PUNCT
ejpam-676	11	25	and	and	CCONJ
ejpam-676	11	26	f	f	PROPN
ejpam-676	11	27	(	(	PUNCT
ejpam-676	11	28	u)⊂	u)⊂	CCONJ
ejpam-676	11	29	g(u	g(u	PROPN
ejpam-676	11	30	)	)	PUNCT
ejpam-676	11	31	.	.	PUNCT
ejpam-676	12	1	email	email	NOUN
ejpam-676	12	2	address	address	NOUN
ejpam-676	12	3	:	:	PUNCT
ejpam-676	12	4	mkaouf127	mkaouf127	PROPN
ejpam-676	12	5	�	�	PROPN
ejpam-676	12	6	yahoo	yahoo	PROPN
ejpam-676	12	7	.	.	PUNCT
ejpam-676	13	1	om	om	PROPN
ejpam-676	13	2	(	(	PUNCT
ejpam-676	13	3	m.	m.	PROPN
ejpam-676	13	4	aouf	aouf	PROPN
ejpam-676	13	5	)	)	PUNCT
ejpam-676	13	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-676	14	1	141	141	NUM
ejpam-676	14	2	c	c	X
ejpam-676	14	3	©	©	PROPN
ejpam-676	14	4	2012	2012	NUM
ejpam-676	14	5	ejpam	ejpam	VERB
ejpam-676	14	6	all	all	DET
ejpam-676	14	7	rights	right	NOUN
ejpam-676	14	8	reserved	reserve	VERB
ejpam-676	14	9	.	.	PUNCT
ejpam-676	15	1	m.	m.	PROPN
ejpam-676	15	2	aouf	aouf	PROPN
ejpam-676	15	3	/	/	SYM
ejpam-676	15	4	eur	eur	PROPN
ejpam-676	15	5	.	.	PUNCT
ejpam-676	16	1	j.	j.	PROPN
ejpam-676	16	2	pure	pure	PROPN
ejpam-676	16	3	appl	appl	PROPN
ejpam-676	16	4	.	.	PROPN
ejpam-676	16	5	math	math	PROPN
ejpam-676	16	6	,	,	PUNCT
ejpam-676	16	7	5	5	NUM
ejpam-676	16	8	(	(	PUNCT
ejpam-676	16	9	2012	2012	NUM
ejpam-676	16	10	)	)	PUNCT
ejpam-676	16	11	,	,	PUNCT
ejpam-676	16	12	141	141	NUM
ejpam-676	16	13	-	-	SYM
ejpam-676	16	14	159	159	NUM
ejpam-676	16	15	142	142	NUM
ejpam-676	16	16	for	for	ADP
ejpam-676	16	17	functions	function	NOUN
ejpam-676	16	18	f	f	PROPN
ejpam-676	16	19	∈∑p	∈∑p	NOUN
ejpam-676	16	20	,	,	PUNCT
ejpam-676	16	21	m	m	PRON
ejpam-676	16	22	,	,	PUNCT
ejpam-676	16	23	given	give	VERB
ejpam-676	16	24	by	by	ADP
ejpam-676	16	25	(	(	PUNCT
ejpam-676	16	26	1	1	NUM
ejpam-676	16	27	)	)	PUNCT
ejpam-676	16	28	,	,	PUNCT
ejpam-676	16	29	and	and	CCONJ
ejpam-676	16	30	g	g	PROPN
ejpam-676	16	31	∈∑p	∈∑p	NOUN
ejpam-676	16	32	,	,	PUNCT
ejpam-676	16	33	m	m	AUX
ejpam-676	16	34	defined	define	VERB
ejpam-676	16	35	by	by	ADP
ejpam-676	16	36	g(z	g(z	PROPN
ejpam-676	16	37	)	)	PUNCT
ejpam-676	16	38	=	=	PUNCT
ejpam-676	16	39	z−p	z−p	NOUN
ejpam-676	16	40	+	+	CCONJ
ejpam-676	16	41	∞	∞	NUM
ejpam-676	16	42	∑	∑	PUNCT
ejpam-676	16	43	k	k	X
ejpam-676	16	44	=	=	NOUN
ejpam-676	16	45	m	m	VERB
ejpam-676	16	46	bkzk	bkzk	NOUN
ejpam-676	16	47	(	(	PUNCT
ejpam-676	16	48	m	m	NOUN
ejpam-676	16	49	>	>	X
ejpam-676	16	50	−p	−p	NOUN
ejpam-676	16	51	;	;	PUNCT
ejpam-676	16	52	p	p	PROPN
ejpam-676	16	53	∈	∈	PROPN
ejpam-676	16	54	n	n	CCONJ
ejpam-676	16	55	)	)	PUNCT
ejpam-676	16	56	,	,	PUNCT
ejpam-676	16	57	(	(	PUNCT
ejpam-676	16	58	2	2	X
ejpam-676	16	59	)	)	PUNCT
ejpam-676	16	60	then	then	ADV
ejpam-676	16	61	the	the	DET
ejpam-676	16	62	hadamard	hadamard	ADJ
ejpam-676	16	63	product	product	NOUN
ejpam-676	16	64	(	(	PUNCT
ejpam-676	16	65	or	or	CCONJ
ejpam-676	16	66	convolution	convolution	NOUN
ejpam-676	16	67	)	)	PUNCT
ejpam-676	16	68	of	of	ADP
ejpam-676	16	69	f	f	PROPN
ejpam-676	16	70	and	and	CCONJ
ejpam-676	16	71	g	g	PROPN
ejpam-676	16	72	is	be	AUX
ejpam-676	16	73	given	give	VERB
ejpam-676	16	74	by	by	ADP
ejpam-676	16	75	(	(	PUNCT
ejpam-676	16	76	f	f	PROPN
ejpam-676	16	77	∗	∗	X
ejpam-676	16	78	g	g	NOUN
ejpam-676	16	79	)	)	PUNCT
ejpam-676	16	80	=	=	PUNCT
ejpam-676	16	81	z−p	z−p	NOUN
ejpam-676	16	82	+	+	CCONJ
ejpam-676	17	1	∞	∞	NUM
ejpam-676	17	2	∑	∑	PUNCT
ejpam-676	17	3	k	k	X
ejpam-676	17	4	=	=	PROPN
ejpam-676	17	5	m	m	PROPN
ejpam-676	17	6	ak	ak	NOUN
ejpam-676	17	7	bkzk	bkzk	NOUN
ejpam-676	17	8	=	=	PUNCT
ejpam-676	17	9	(	(	PUNCT
ejpam-676	17	10	g	g	PROPN
ejpam-676	17	11	∗	∗	X
ejpam-676	17	12	f	f	PROPN
ejpam-676	17	13	)	)	PUNCT
ejpam-676	17	14	(	(	PUNCT
ejpam-676	17	15	z	z	NOUN
ejpam-676	17	16	)	)	PUNCT
ejpam-676	17	17	(	(	PUNCT
ejpam-676	17	18	m	m	X
ejpam-676	17	19	>	>	X
ejpam-676	17	20	−p	−p	NOUN
ejpam-676	17	21	;	;	PUNCT
ejpam-676	17	22	p	p	PROPN
ejpam-676	17	23	∈	∈	PROPN
ejpam-676	17	24	n	n	CCONJ
ejpam-676	17	25	)	)	PUNCT
ejpam-676	17	26	.	.	PUNCT
ejpam-676	18	1	(	(	PUNCT
ejpam-676	18	2	3	3	X
ejpam-676	18	3	)	)	PUNCT
ejpam-676	18	4	for	for	ADP
ejpam-676	18	5	complex	complex	ADJ
ejpam-676	18	6	parameters	parameter	NOUN
ejpam-676	18	7	α1	α1	PROPN
ejpam-676	18	8	,	,	PUNCT
ejpam-676	18	9	.	.	PUNCT
ejpam-676	18	10	.	.	PUNCT
ejpam-676	19	1	.αq	.αq	PUNCT
ejpam-676	19	2	β1	β1	PROPN
ejpam-676	19	3	,	,	PUNCT
ejpam-676	19	4	.	.	PUNCT
ejpam-676	19	5	.	.	PUNCT
ejpam-676	19	6	.	.	PUNCT
ejpam-676	20	1	,	,	PUNCT
ejpam-676	20	2	β	β	X
ejpam-676	20	3	s	s	X
ejpam-676	20	4	(	(	PUNCT
ejpam-676	20	5	β	β	X
ejpam-676	20	6	j	j	PROPN
ejpam-676	20	7	/∈	/∈	PUNCT
ejpam-676	21	1	z−0	z−0	NUM
ejpam-676	21	2	=	=	SYM
ejpam-676	21	3	{	{	PUNCT
ejpam-676	21	4	0,−1,−2	0,−1,−2	NUM
ejpam-676	21	5	,	,	PUNCT
ejpam-676	21	6	.	.	PUNCT
ejpam-676	21	7	.	.	PUNCT
ejpam-676	22	1	.	.	PUNCT
ejpam-676	22	2	}	}	PUNCT
ejpam-676	22	3	;	;	PUNCT
ejpam-676	22	4	j	j	PROPN
ejpam-676	22	5	=	=	SYM
ejpam-676	22	6	1,2	1,2	NUM
ejpam-676	22	7	,	,	PUNCT
ejpam-676	22	8	.	.	PUNCT
ejpam-676	22	9	.	.	PUNCT
ejpam-676	23	1	.	.	PUNCT
ejpam-676	24	1	,	,	PUNCT
ejpam-676	24	2	s	s	X
ejpam-676	24	3	)	)	PUNCT
ejpam-676	24	4	,	,	PUNCT
ejpam-676	24	5	we	we	PRON
ejpam-676	24	6	now	now	ADV
ejpam-676	24	7	define	define	VERB
ejpam-676	24	8	the	the	DET
ejpam-676	24	9	generalized	generalized	ADJ
ejpam-676	24	10	hypergeometric	hypergeometric	ADJ
ejpam-676	24	11	function	function	NOUN
ejpam-676	24	12	qfs(α1	qfs(α1	NOUN
ejpam-676	24	13	,	,	PUNCT
ejpam-676	24	14	.	.	PUNCT
ejpam-676	24	15	.	.	PUNCT
ejpam-676	25	1	.	.	PUNCT
ejpam-676	26	1	,	,	PUNCT
ejpam-676	26	2	αq;β1	αq;β1	NOUN
ejpam-676	26	3	,	,	PUNCT
ejpam-676	26	4	.	.	PUNCT
ejpam-676	26	5	.	.	PUNCT
ejpam-676	27	1	.	.	PUNCT
ejpam-676	28	1	,	,	PUNCT
ejpam-676	28	2	β	β	PROPN
ejpam-676	28	3	s	s	X
ejpam-676	28	4	;	;	PUNCT
ejpam-676	28	5	z	z	X
ejpam-676	28	6	)	)	PUNCT
ejpam-676	28	7	by	by	ADP
ejpam-676	28	8	(	(	PUNCT
ejpam-676	28	9	see	see	VERB
ejpam-676	28	10	,	,	PUNCT
ejpam-676	28	11	for	for	ADP
ejpam-676	28	12	example	example	NOUN
ejpam-676	28	13	,	,	PUNCT
ejpam-676	28	14	[	[	X
ejpam-676	28	15	14	14	NUM
ejpam-676	28	16	,	,	PUNCT
ejpam-676	28	17	p.19	p.19	NOUN
ejpam-676	28	18	]	]	PUNCT
ejpam-676	28	19	)	)	PUNCT
ejpam-676	28	20	qfs(α1	qfs(α1	NOUN
ejpam-676	28	21	,	,	PUNCT
ejpam-676	28	22	.	.	PUNCT
ejpam-676	28	23	.	.	PUNCT
ejpam-676	28	24	.	.	PUNCT
ejpam-676	29	1	,	,	PUNCT
ejpam-676	29	2	αq;β1	αq;β1	NOUN
ejpam-676	29	3	,	,	PUNCT
ejpam-676	29	4	.	.	PUNCT
ejpam-676	29	5	.	.	PUNCT
ejpam-676	30	1	.	.	PUNCT
ejpam-676	31	1	,	,	PUNCT
ejpam-676	31	2	β	β	PROPN
ejpam-676	31	3	s	s	X
ejpam-676	31	4	;	;	PUNCT
ejpam-676	31	5	z	z	X
ejpam-676	31	6	)	)	PUNCT
ejpam-676	32	1	=	=	SYM
ejpam-676	32	2	∞	∞	PROPN
ejpam-676	32	3	∑	∑	PUNCT
ejpam-676	32	4	k=0	k=0	PROPN
ejpam-676	32	5	(	(	PUNCT
ejpam-676	32	6	α1)k	α1)k	ADV
ejpam-676	32	7	.	.	PUNCT
ejpam-676	32	8	.	.	PUNCT
ejpam-676	32	9	.	.	PUNCT
ejpam-676	33	1	(	(	PUNCT
ejpam-676	33	2	αq)k	αq)k	PROPN
ejpam-676	33	3	(	(	PUNCT
ejpam-676	33	4	β1)k	β1)k	PROPN
ejpam-676	33	5	.	.	PUNCT
ejpam-676	33	6	.	.	PUNCT
ejpam-676	33	7	.	.	PUNCT
ejpam-676	34	1	(	(	PUNCT
ejpam-676	34	2	β	β	X
ejpam-676	34	3	s)k	s)k	NOUN
ejpam-676	34	4	·	·	PUNCT
ejpam-676	34	5	z	z	X
ejpam-676	35	1	k	k	PUNCT
ejpam-676	35	2	k	k	X
ejpam-676	35	3	!	!	PUNCT
ejpam-676	36	1	(	(	PUNCT
ejpam-676	36	2	q	q	NOUN
ejpam-676	36	3	≤	≤	ADJ
ejpam-676	36	4	s+	s+	PUNCT
ejpam-676	36	5	1	1	NUM
ejpam-676	36	6	;	;	PUNCT
ejpam-676	36	7	q	q	X
ejpam-676	36	8	,	,	PUNCT
ejpam-676	36	9	s	s	NOUN
ejpam-676	36	10	∈	∈	PROPN
ejpam-676	36	11	n0	n0	X
ejpam-676	36	12	=	=	PROPN
ejpam-676	36	13	n	n	PART
ejpam-676	36	14	∪	∪	X
ejpam-676	36	15	{	{	PUNCT
ejpam-676	36	16	0	0	NUM
ejpam-676	36	17	}	}	PUNCT
ejpam-676	36	18	;	;	PUNCT
ejpam-676	36	19	z	z	PROPN
ejpam-676	36	20	∈	∈	PROPN
ejpam-676	36	21	u	u	NOUN
ejpam-676	36	22	)	)	PUNCT
ejpam-676	36	23	,	,	PUNCT
ejpam-676	36	24	(	(	PUNCT
ejpam-676	36	25	4	4	X
ejpam-676	36	26	)	)	PUNCT
ejpam-676	36	27	where	where	SCONJ
ejpam-676	36	28	(	(	PUNCT
ejpam-676	36	29	θ)ν	θ)ν	X
ejpam-676	36	30	is	be	AUX
ejpam-676	36	31	the	the	DET
ejpam-676	36	32	pochhammer	pochhammer	NOUN
ejpam-676	36	33	symbol	symbol	NOUN
ejpam-676	36	34	defined	define	VERB
ejpam-676	36	35	,	,	PUNCT
ejpam-676	36	36	in	in	ADP
ejpam-676	36	37	terms	term	NOUN
ejpam-676	36	38	of	of	ADP
ejpam-676	36	39	the	the	DET
ejpam-676	36	40	gamma	gamma	NOUN
ejpam-676	36	41	function	function	PROPN
ejpam-676	36	42	γ	γ	PROPN
ejpam-676	36	43	,	,	PUNCT
ejpam-676	36	44	by	by	ADP
ejpam-676	36	45	(	(	PUNCT
ejpam-676	36	46	θ	θ	NOUN
ejpam-676	36	47	)	)	PUNCT
ejpam-676	36	48	ν	ν	PROPN
ejpam-676	36	49	=	=	PUNCT
ejpam-676	36	50	γ(θ	γ(θ	PROPN
ejpam-676	36	51	+	+	CCONJ
ejpam-676	36	52	ν	ν	X
ejpam-676	36	53	)	)	PUNCT
ejpam-676	36	54	γ(θ	γ(θ	PROPN
ejpam-676	36	55	)	)	PUNCT
ejpam-676	37	1	=	=	SYM
ejpam-676	37	2	¨	¨	NOUN
ejpam-676	37	3	1	1	NUM
ejpam-676	37	4	(	(	PUNCT
ejpam-676	37	5	ν	ν	NOUN
ejpam-676	37	6	=	=	SYM
ejpam-676	37	7	0;θ	0;θ	NOUN
ejpam-676	37	8	∈	∈	PROPN
ejpam-676	37	9	c\{0	c\{0	NOUN
ejpam-676	37	10	}	}	PUNCT
ejpam-676	37	11	)	)	PUNCT
ejpam-676	37	12	,	,	PUNCT
ejpam-676	37	13	θ(θ	θ(θ	VERB
ejpam-676	37	14	−	−	PROPN
ejpam-676	37	15	1	1	NUM
ejpam-676	37	16	)	)	PUNCT
ejpam-676	37	17	.	.	PUNCT
ejpam-676	37	18	.	.	PUNCT
ejpam-676	37	19	.	.	PUNCT
ejpam-676	38	1	(	(	PUNCT
ejpam-676	38	2	θ	θ	NOUN
ejpam-676	38	3	+	+	PUNCT
ejpam-676	38	4	ν	ν	X
ejpam-676	38	5	−	−	NOUN
ejpam-676	38	6	1	1	NUM
ejpam-676	38	7	)	)	PUNCT
ejpam-676	38	8	(	(	PUNCT
ejpam-676	38	9	ν	ν	X
ejpam-676	38	10	∈	∈	PROPN
ejpam-676	38	11	n	n	NOUN
ejpam-676	38	12	;	;	PUNCT
ejpam-676	38	13	θ	θ	PROPN
ejpam-676	38	14	∈	∈	PROPN
ejpam-676	38	15	c	c	NOUN
ejpam-676	38	16	)	)	PUNCT
ejpam-676	38	17	.	.	PUNCT
ejpam-676	39	1	(	(	PUNCT
ejpam-676	39	2	5	5	X
ejpam-676	39	3	)	)	PUNCT
ejpam-676	39	4	corresponding	correspond	VERB
ejpam-676	39	5	to	to	ADP
ejpam-676	39	6	the	the	DET
ejpam-676	39	7	function	function	NOUN
ejpam-676	39	8	hp(α1	hp(α1	NOUN
ejpam-676	39	9	,	,	PUNCT
ejpam-676	39	10	.	.	PUNCT
ejpam-676	39	11	.	.	PUNCT
ejpam-676	40	1	.	.	PUNCT
ejpam-676	41	1	,	,	PUNCT
ejpam-676	41	2	αq;β1	αq;β1	NOUN
ejpam-676	41	3	,	,	PUNCT
ejpam-676	41	4	.	.	PUNCT
ejpam-676	41	5	.	.	PUNCT
ejpam-676	42	1	.	.	PUNCT
ejpam-676	43	1	,	,	PUNCT
ejpam-676	43	2	β	β	PROPN
ejpam-676	43	3	s	s	X
ejpam-676	43	4	;	;	PUNCT
ejpam-676	43	5	z	z	X
ejpam-676	43	6	)	)	PUNCT
ejpam-676	43	7	,	,	PUNCT
ejpam-676	43	8	defined	define	VERB
ejpam-676	43	9	by	by	ADP
ejpam-676	43	10	hp(α1	hp(α1	NOUN
ejpam-676	43	11	,	,	PUNCT
ejpam-676	43	12	.	.	PUNCT
ejpam-676	43	13	.	.	PUNCT
ejpam-676	44	1	.	.	PUNCT
ejpam-676	45	1	,	,	PUNCT
ejpam-676	45	2	αq;β1	αq;β1	NOUN
ejpam-676	45	3	,	,	PUNCT
ejpam-676	45	4	.	.	PUNCT
ejpam-676	45	5	.	.	PUNCT
ejpam-676	46	1	.	.	PUNCT
ejpam-676	47	1	,	,	PUNCT
ejpam-676	47	2	β	β	PROPN
ejpam-676	47	3	s	s	X
ejpam-676	47	4	;	;	PUNCT
ejpam-676	47	5	z	z	X
ejpam-676	47	6	)	)	PUNCT
ejpam-676	47	7	=	=	NOUN
ejpam-676	47	8	z−p	z−p	NUM
ejpam-676	47	9	qfs(α1	qfs(α1	NOUN
ejpam-676	47	10	,	,	PUNCT
ejpam-676	47	11	.	.	PUNCT
ejpam-676	47	12	.	.	PUNCT
ejpam-676	48	1	.	.	PUNCT
ejpam-676	49	1	,	,	PUNCT
ejpam-676	49	2	αq;β1	αq;β1	NOUN
ejpam-676	49	3	,	,	PUNCT
ejpam-676	49	4	.	.	PUNCT
ejpam-676	49	5	.	.	PUNCT
ejpam-676	50	1	.	.	PUNCT
ejpam-676	51	1	,	,	PUNCT
ejpam-676	51	2	β	β	PROPN
ejpam-676	51	3	s	s	X
ejpam-676	51	4	;	;	PUNCT
ejpam-676	51	5	z	z	X
ejpam-676	51	6	)	)	PUNCT
ejpam-676	51	7	,	,	PUNCT
ejpam-676	51	8	(	(	PUNCT
ejpam-676	51	9	6	6	X
ejpam-676	51	10	)	)	PUNCT
ejpam-676	51	11	we	we	PRON
ejpam-676	51	12	consider	consider	VERB
ejpam-676	51	13	a	a	DET
ejpam-676	51	14	linear	linear	ADJ
ejpam-676	51	15	operator	operator	NOUN
ejpam-676	51	16	hp(α1	hp(α1	NOUN
ejpam-676	51	17	,	,	PUNCT
ejpam-676	51	18	.	.	PUNCT
ejpam-676	51	19	.	.	PUNCT
ejpam-676	52	1	.	.	PUNCT
ejpam-676	53	1	,	,	PUNCT
ejpam-676	53	2	αq;β1	αq;β1	NOUN
ejpam-676	53	3	,	,	PUNCT
ejpam-676	53	4	.	.	PUNCT
ejpam-676	53	5	.	.	PUNCT
ejpam-676	54	1	.	.	PUNCT
ejpam-676	55	1	,	,	PUNCT
ejpam-676	55	2	β	β	PROPN
ejpam-676	55	3	s	s	X
ejpam-676	55	4	;	;	PUNCT
ejpam-676	55	5	z	z	X
ejpam-676	55	6	)	)	PUNCT
ejpam-676	55	7	:	:	PUNCT
ejpam-676	55	8	σp→	σp→	ADV
ejpam-676	55	9	σp	σp	NOUN
ejpam-676	55	10	,	,	PUNCT
ejpam-676	55	11	which	which	PRON
ejpam-676	55	12	is	be	AUX
ejpam-676	55	13	defined	define	VERB
ejpam-676	55	14	by	by	ADP
ejpam-676	55	15	the	the	DET
ejpam-676	55	16	following	follow	VERB
ejpam-676	55	17	hadamard	hadamard	ADJ
ejpam-676	55	18	product	product	NOUN
ejpam-676	55	19	(	(	PUNCT
ejpam-676	55	20	or	or	CCONJ
ejpam-676	55	21	convolution	convolution	NOUN
ejpam-676	55	22	):	):	PUNCT
ejpam-676	55	23	hp(α1	hp(α1	NOUN
ejpam-676	55	24	,	,	PUNCT
ejpam-676	55	25	.	.	PUNCT
ejpam-676	55	26	.	.	PUNCT
ejpam-676	55	27	.	.	PUNCT
ejpam-676	56	1	,	,	PUNCT
ejpam-676	56	2	αq;β1	αq;β1	NOUN
ejpam-676	56	3	,	,	PUNCT
ejpam-676	56	4	.	.	PUNCT
ejpam-676	56	5	.	.	PUNCT
ejpam-676	57	1	.	.	PUNCT
ejpam-676	58	1	,	,	PUNCT
ejpam-676	58	2	β	β	X
ejpam-676	58	3	s	s	PROPN
ejpam-676	58	4	)	)	PUNCT
ejpam-676	58	5	f	f	NOUN
ejpam-676	58	6	(	(	PUNCT
ejpam-676	58	7	z	z	NOUN
ejpam-676	58	8	)	)	PUNCT
ejpam-676	58	9	=	=	SYM
ejpam-676	58	10	hp(α1	hp(α1	NOUN
ejpam-676	58	11	,	,	PUNCT
ejpam-676	58	12	.	.	PUNCT
ejpam-676	58	13	.	.	PUNCT
ejpam-676	59	1	.	.	PUNCT
ejpam-676	60	1	,	,	PUNCT
ejpam-676	60	2	αq;β1	αq;β1	NOUN
ejpam-676	60	3	,	,	PUNCT
ejpam-676	60	4	.	.	PUNCT
ejpam-676	60	5	.	.	PUNCT
ejpam-676	61	1	.	.	PUNCT
ejpam-676	62	1	,	,	PUNCT
ejpam-676	62	2	β	β	PROPN
ejpam-676	62	3	s	s	X
ejpam-676	62	4	;	;	PUNCT
ejpam-676	62	5	z	z	X
ejpam-676	62	6	)	)	PUNCT
ejpam-676	62	7	∗	∗	NOUN
ejpam-676	62	8	f	f	PROPN
ejpam-676	62	9	(	(	PUNCT
ejpam-676	62	10	z	z	NOUN
ejpam-676	62	11	)	)	PUNCT
ejpam-676	62	12	.	.	PUNCT
ejpam-676	63	1	(	(	PUNCT
ejpam-676	63	2	7	7	X
ejpam-676	63	3	)	)	PUNCT
ejpam-676	63	4	we	we	PRON
ejpam-676	63	5	observe	observe	VERB
ejpam-676	63	6	that	that	SCONJ
ejpam-676	63	7	,	,	PUNCT
ejpam-676	63	8	for	for	ADP
ejpam-676	63	9	a	a	DET
ejpam-676	63	10	function	function	NOUN
ejpam-676	63	11	f	f	X
ejpam-676	63	12	(	(	PUNCT
ejpam-676	63	13	z	z	NOUN
ejpam-676	63	14	)	)	PUNCT
ejpam-676	63	15	of	of	ADP
ejpam-676	63	16	the	the	DET
ejpam-676	63	17	form	form	NOUN
ejpam-676	63	18	(	(	PUNCT
ejpam-676	63	19	1	1	NUM
ejpam-676	63	20	)	)	PUNCT
ejpam-676	63	21	,	,	PUNCT
ejpam-676	63	22	we	we	PRON
ejpam-676	63	23	have	have	VERB
ejpam-676	63	24	hp(α1	hp(α1	NOUN
ejpam-676	63	25	,	,	PUNCT
ejpam-676	63	26	.	.	PUNCT
ejpam-676	63	27	.	.	PUNCT
ejpam-676	64	1	.	.	PUNCT
ejpam-676	65	1	,	,	PUNCT
ejpam-676	65	2	αq;β1	αq;β1	NOUN
ejpam-676	65	3	,	,	PUNCT
ejpam-676	65	4	.	.	PUNCT
ejpam-676	65	5	.	.	PUNCT
ejpam-676	66	1	.	.	PUNCT
ejpam-676	67	1	,	,	PUNCT
ejpam-676	67	2	β	β	X
ejpam-676	67	3	s	s	PROPN
ejpam-676	67	4	)	)	PUNCT
ejpam-676	67	5	f	f	NOUN
ejpam-676	67	6	(	(	PUNCT
ejpam-676	67	7	z	z	NOUN
ejpam-676	67	8	)	)	PUNCT
ejpam-676	67	9	=	=	PUNCT
ejpam-676	67	10	z−p	z−p	NOUN
ejpam-676	67	11	+	+	CCONJ
ejpam-676	68	1	∞	∞	NUM
ejpam-676	68	2	∑	∑	PUNCT
ejpam-676	68	3	k	k	X
ejpam-676	68	4	=	=	NOUN
ejpam-676	68	5	m	m	X
ejpam-676	68	6	(	(	PUNCT
ejpam-676	68	7	α1)k+p	α1)k+p	PROPN
ejpam-676	68	8	.	.	PUNCT
ejpam-676	68	9	.	.	PUNCT
ejpam-676	68	10	.	.	PUNCT
ejpam-676	69	1	(	(	PUNCT
ejpam-676	69	2	αq)k+p	αq)k+p	INTJ
ejpam-676	69	3	(	(	PUNCT
ejpam-676	69	4	β1)k+p	β1)k+p	INTJ
ejpam-676	69	5	.	.	PUNCT
ejpam-676	69	6	.	.	PUNCT
ejpam-676	69	7	.	.	PUNCT
ejpam-676	70	1	(	(	PUNCT
ejpam-676	70	2	β	β	X
ejpam-676	70	3	s)k+p	s)k+p	X
ejpam-676	70	4	·	·	PUNCT
ejpam-676	70	5	ak	ak	PROPN
ejpam-676	70	6	(	(	PUNCT
ejpam-676	70	7	k+	k+	NOUN
ejpam-676	70	8	p	p	NOUN
ejpam-676	70	9	)	)	PUNCT
ejpam-676	70	10	!	!	PUNCT
ejpam-676	71	1	zk	zk	PROPN
ejpam-676	71	2	.	.	PUNCT
ejpam-676	72	1	(	(	PUNCT
ejpam-676	72	2	8)	8)	NUM
ejpam-676	72	3	if	if	SCONJ
ejpam-676	72	4	,	,	PUNCT
ejpam-676	72	5	for	for	ADP
ejpam-676	72	6	convenience	convenience	NOUN
ejpam-676	72	7	,	,	PUNCT
ejpam-676	72	8	we	we	PRON
ejpam-676	72	9	write	write	VERB
ejpam-676	72	10	hp	hp	PROPN
ejpam-676	72	11	,	,	PUNCT
ejpam-676	72	12	q	q	NOUN
ejpam-676	72	13	,	,	PUNCT
ejpam-676	72	14	s(α1	s(α1	NOUN
ejpam-676	72	15	)	)	PUNCT
ejpam-676	72	16	=	=	SYM
ejpam-676	72	17	hp(α1	hp(α1	NOUN
ejpam-676	72	18	,	,	PUNCT
ejpam-676	72	19	.	.	PUNCT
ejpam-676	72	20	.	.	PUNCT
ejpam-676	72	21	.	.	PUNCT
ejpam-676	73	1	,	,	PUNCT
ejpam-676	73	2	αq;β1	αq;β1	NOUN
ejpam-676	73	3	,	,	PUNCT
ejpam-676	73	4	.	.	PUNCT
ejpam-676	73	5	.	.	PUNCT
ejpam-676	74	1	.	.	PUNCT
ejpam-676	75	1	,	,	PUNCT
ejpam-676	75	2	β	β	X
ejpam-676	75	3	s	s	PROPN
ejpam-676	75	4	)	)	PUNCT
ejpam-676	76	1	,	,	PUNCT
ejpam-676	76	2	(	(	PUNCT
ejpam-676	76	3	9	9	X
ejpam-676	76	4	)	)	PUNCT
ejpam-676	76	5	m.	m.	NOUN
ejpam-676	76	6	aouf	aouf	PROPN
ejpam-676	76	7	/	/	SYM
ejpam-676	76	8	eur	eur	PROPN
ejpam-676	76	9	.	.	PUNCT
ejpam-676	77	1	j.	j.	PROPN
ejpam-676	77	2	pure	pure	PROPN
ejpam-676	77	3	appl	appl	PROPN
ejpam-676	77	4	.	.	PROPN
ejpam-676	77	5	math	math	PROPN
ejpam-676	77	6	,	,	PUNCT
ejpam-676	77	7	5	5	NUM
ejpam-676	77	8	(	(	PUNCT
ejpam-676	77	9	2012	2012	NUM
ejpam-676	77	10	)	)	PUNCT
ejpam-676	77	11	,	,	PUNCT
ejpam-676	77	12	141	141	NUM
ejpam-676	77	13	-	-	SYM
ejpam-676	77	14	159	159	NUM
ejpam-676	77	15	143	143	NUM
ejpam-676	77	16	then	then	ADV
ejpam-676	77	17	one	one	PRON
ejpam-676	77	18	can	can	AUX
ejpam-676	77	19	easily	easily	ADV
ejpam-676	77	20	verify	verify	VERB
ejpam-676	77	21	from	from	ADP
ejpam-676	77	22	the	the	DET
ejpam-676	77	23	definition	definition	NOUN
ejpam-676	77	24	(	(	PUNCT
ejpam-676	77	25	7	7	NUM
ejpam-676	77	26	)	)	PUNCT
ejpam-676	77	27	that	that	PRON
ejpam-676	77	28	z(hp	z(hp	VERB
ejpam-676	77	29	,	,	PUNCT
ejpam-676	77	30	q	q	NOUN
ejpam-676	77	31	,	,	PUNCT
ejpam-676	77	32	s(α1	s(α1	NOUN
ejpam-676	77	33	)	)	PUNCT
ejpam-676	77	34	f	f	PROPN
ejpam-676	77	35	(	(	PUNCT
ejpam-676	77	36	z	z	NOUN
ejpam-676	77	37	)	)	PUNCT
ejpam-676	77	38	)	)	PUNCT
ejpam-676	78	1	′	′	NUM
ejpam-676	79	1	=	=	PUNCT
ejpam-676	79	2	α1hp	α1hp	NUM
ejpam-676	79	3	,	,	PUNCT
ejpam-676	79	4	q	q	NOUN
ejpam-676	79	5	,	,	PUNCT
ejpam-676	79	6	s(α1	s(α1	NOUN
ejpam-676	79	7	+	+	CCONJ
ejpam-676	79	8	1	1	X
ejpam-676	79	9	)	)	PUNCT
ejpam-676	79	10	f	f	NOUN
ejpam-676	79	11	(	(	PUNCT
ejpam-676	79	12	z)−	z)−	PROPN
ejpam-676	79	13	(	(	PUNCT
ejpam-676	79	14	α1	α1	PROPN
ejpam-676	79	15	+	+	CCONJ
ejpam-676	79	16	p)hp	p)hp	PROPN
ejpam-676	79	17	,	,	PUNCT
ejpam-676	79	18	q	q	NOUN
ejpam-676	79	19	,	,	PUNCT
ejpam-676	79	20	s(α1	s(α1	NOUN
ejpam-676	79	21	)	)	PUNCT
ejpam-676	80	1	f	f	PROPN
ejpam-676	80	2	(	(	PUNCT
ejpam-676	80	3	z	z	NOUN
ejpam-676	80	4	)	)	PUNCT
ejpam-676	80	5	.	.	PUNCT
ejpam-676	81	1	(	(	PUNCT
ejpam-676	81	2	10	10	NUM
ejpam-676	81	3	)	)	PUNCT
ejpam-676	81	4	for	for	ADP
ejpam-676	81	5	m	m	NOUN
ejpam-676	81	6	=	=	SYM
ejpam-676	81	7	−p	−p	ADJ
ejpam-676	81	8	+	+	NOUN
ejpam-676	81	9	1	1	NUM
ejpam-676	81	10	(	(	PUNCT
ejpam-676	81	11	p	p	NOUN
ejpam-676	81	12	∈	∈	PROPN
ejpam-676	81	13	n	n	CCONJ
ejpam-676	81	14	)	)	PUNCT
ejpam-676	81	15	,	,	PUNCT
ejpam-676	81	16	the	the	DET
ejpam-676	81	17	linear	linear	ADJ
ejpam-676	81	18	operator	operator	NOUN
ejpam-676	81	19	hp	hp	NOUN
ejpam-676	81	20	,	,	PUNCT
ejpam-676	81	21	q	q	NOUN
ejpam-676	81	22	,	,	PUNCT
ejpam-676	81	23	s(α1	s(α1	NOUN
ejpam-676	81	24	)	)	PUNCT
ejpam-676	81	25	was	be	AUX
ejpam-676	81	26	investigated	investigate	VERB
ejpam-676	81	27	recently	recently	ADV
ejpam-676	81	28	by	by	ADP
ejpam-676	81	29	liu	liu	PROPN
ejpam-676	81	30	and	and	CCONJ
ejpam-676	81	31	srivastava	srivastava	PROPN
ejpam-676	82	1	[	[	X
ejpam-676	82	2	5	5	NUM
ejpam-676	82	3	]	]	PUNCT
ejpam-676	82	4	and	and	CCONJ
ejpam-676	82	5	aouf	aouf	PROPN
ejpam-676	83	1	[	[	X
ejpam-676	83	2	1	1	NUM
ejpam-676	83	3	]	]	PUNCT
ejpam-676	83	4	.	.	PUNCT
ejpam-676	84	1	in	in	ADP
ejpam-676	84	2	particular	particular	ADJ
ejpam-676	84	3	,	,	PUNCT
ejpam-676	84	4	for	for	ADP
ejpam-676	84	5	s	s	NOUN
ejpam-676	84	6	=	=	SYM
ejpam-676	84	7	1,q	1,q	NUM
ejpam-676	84	8	=	=	SYM
ejpam-676	84	9	2,α1	2,α1	NUM
ejpam-676	84	10	>	>	PUNCT
ejpam-676	84	11	0,β1	0,β1	PROPN
ejpam-676	84	12	>	>	X
ejpam-676	84	13	0	0	PUNCT
ejpam-676	85	1	and	and	CCONJ
ejpam-676	85	2	α2	α2	ADJ
ejpam-676	85	3	=	=	SYM
ejpam-676	86	1	1	1	NUM
ejpam-676	86	2	,	,	PUNCT
ejpam-676	86	3	we	we	PRON
ejpam-676	86	4	obtain	obtain	VERB
ejpam-676	86	5	the	the	DET
ejpam-676	86	6	linear	linear	ADJ
ejpam-676	86	7	operator	operator	NOUN
ejpam-676	86	8	ℓp(α1,β1	ℓp(α1,β1	PROPN
ejpam-676	86	9	)	)	PUNCT
ejpam-676	86	10	f	f	NOUN
ejpam-676	86	11	(	(	PUNCT
ejpam-676	86	12	z	z	NOUN
ejpam-676	86	13	)	)	PUNCT
ejpam-676	86	14	=	=	SYM
ejpam-676	86	15	hp(α1	hp(α1	NOUN
ejpam-676	86	16	,	,	PUNCT
ejpam-676	86	17	1;β1	1;β1	NUM
ejpam-676	86	18	)	)	PUNCT
ejpam-676	87	1	f	f	NOUN
ejpam-676	87	2	(	(	PUNCT
ejpam-676	87	3	z	z	NOUN
ejpam-676	87	4	)	)	PUNCT
ejpam-676	87	5	(	(	PUNCT
ejpam-676	87	6	f	f	PROPN
ejpam-676	87	7	∈∑p	∈∑p	NOUN
ejpam-676	87	8	)	)	PUNCT
ejpam-676	87	9	,	,	PUNCT
ejpam-676	87	10	which	which	PRON
ejpam-676	87	11	was	be	AUX
ejpam-676	87	12	introduced	introduce	VERB
ejpam-676	87	13	and	and	CCONJ
ejpam-676	87	14	studied	study	VERB
ejpam-676	87	15	by	by	ADP
ejpam-676	87	16	liu	liu	PROPN
ejpam-676	87	17	and	and	CCONJ
ejpam-676	87	18	srivastava	srivastava	PROPN
ejpam-676	88	1	[	[	X
ejpam-676	88	2	4	4	NUM
ejpam-676	88	3	]	]	PUNCT
ejpam-676	88	4	.	.	PUNCT
ejpam-676	89	1	we	we	PRON
ejpam-676	89	2	note	note	VERB
ejpam-676	89	3	that	that	SCONJ
ejpam-676	89	4	,	,	PUNCT
ejpam-676	89	5	for	for	ADP
ejpam-676	89	6	any	any	DET
ejpam-676	89	7	integer	integer	NOUN
ejpam-676	89	8	n	n	CCONJ
ejpam-676	89	9	>	>	X
ejpam-676	89	10	−p	−p	NOUN
ejpam-676	89	11	and	and	CCONJ
ejpam-676	89	12	f	f	PROPN
ejpam-676	89	13	∈∑p	∈∑p	NOUN
ejpam-676	89	14	,	,	PUNCT
ejpam-676	89	15	m	m	PROPN
ejpam-676	89	16	,	,	PUNCT
ejpam-676	89	17	hp,2,1(n+	hp,2,1(n+	PROPN
ejpam-676	89	18	p	p	X
ejpam-676	89	19	,	,	PUNCT
ejpam-676	89	20	1	1	NUM
ejpam-676	89	21	;	;	PUNCT
ejpam-676	89	22	1	1	X
ejpam-676	89	23	)	)	PUNCT
ejpam-676	89	24	f	f	NOUN
ejpam-676	89	25	(	(	PUNCT
ejpam-676	89	26	z	z	NOUN
ejpam-676	89	27	)	)	PUNCT
ejpam-676	89	28	=	=	PUNCT
ejpam-676	90	1	dn+p−1	dn+p−1	ADJ
ejpam-676	90	2	f	f	X
ejpam-676	90	3	(	(	PUNCT
ejpam-676	90	4	z	z	NOUN
ejpam-676	90	5	)	)	PUNCT
ejpam-676	90	6	=	=	SYM
ejpam-676	90	7	1	1	NUM
ejpam-676	90	8	zp(1−	zp(1−	PROPN
ejpam-676	90	9	z)n+p	z)n+p	PROPN
ejpam-676	90	10	∗	∗	NOUN
ejpam-676	90	11	f	f	PROPN
ejpam-676	90	12	(	(	PUNCT
ejpam-676	90	13	z	z	NOUN
ejpam-676	90	14	)	)	PUNCT
ejpam-676	90	15	where	where	SCONJ
ejpam-676	90	16	dn+p−1	dn+p−1	NOUN
ejpam-676	90	17	is	be	AUX
ejpam-676	90	18	the	the	DET
ejpam-676	90	19	differential	differential	ADJ
ejpam-676	90	20	operator	operator	NOUN
ejpam-676	90	21	studied	study	VERB
ejpam-676	90	22	by	by	ADP
ejpam-676	90	23	uralegaddi	uralegaddi	ADJ
ejpam-676	90	24	and	and	CCONJ
ejpam-676	90	25	somanatha	somanatha	NOUN
ejpam-676	91	1	[	[	X
ejpam-676	91	2	17	17	NUM
ejpam-676	91	3	]	]	PUNCT
ejpam-676	91	4	.	.	PUNCT
ejpam-676	92	1	making	make	VERB
ejpam-676	92	2	use	use	NOUN
ejpam-676	92	3	of	of	ADP
ejpam-676	92	4	the	the	DET
ejpam-676	92	5	principle	principle	NOUN
ejpam-676	92	6	of	of	ADP
ejpam-676	92	7	differential	differential	ADJ
ejpam-676	92	8	subordination	subordination	NOUN
ejpam-676	92	9	as	as	ADV
ejpam-676	92	10	well	well	ADV
ejpam-676	92	11	as	as	ADP
ejpam-676	92	12	the	the	DET
ejpam-676	92	13	linear	linear	ADJ
ejpam-676	92	14	operator	operator	NOUN
ejpam-676	92	15	hp	hp	NOUN
ejpam-676	92	16	,	,	PUNCT
ejpam-676	92	17	q	q	NOUN
ejpam-676	92	18	,	,	PUNCT
ejpam-676	92	19	s(α1	s(α1	NOUN
ejpam-676	92	20	)	)	PUNCT
ejpam-676	92	21	,	,	PUNCT
ejpam-676	92	22	we	we	PRON
ejpam-676	92	23	now	now	ADV
ejpam-676	92	24	introduce	introduce	VERB
ejpam-676	92	25	a	a	DET
ejpam-676	92	26	subclass	subclass	NOUN
ejpam-676	92	27	of	of	ADP
ejpam-676	92	28	the	the	DET
ejpam-676	92	29	function	function	NOUN
ejpam-676	92	30	class	class	NOUN
ejpam-676	92	31	∑	∑	PROPN
ejpam-676	92	32	p	p	PROPN
ejpam-676	92	33	,	,	PUNCT
ejpam-676	92	34	m	m	VERB
ejpam-676	92	35	as	as	SCONJ
ejpam-676	92	36	follows	follow	VERB
ejpam-676	92	37	:	:	PUNCT
ejpam-676	92	38	for	for	ADP
ejpam-676	92	39	fixed	fix	VERB
ejpam-676	92	40	parameters	parameter	NOUN
ejpam-676	92	41	a	a	PRON
ejpam-676	92	42	and	and	CCONJ
ejpam-676	92	43	b(−1	b(−1	PROPN
ejpam-676	93	1	≤	≤	PROPN
ejpam-676	93	2	b	b	ADP
ejpam-676	93	3	<	<	X
ejpam-676	93	4	a≤	a≤	ADP
ejpam-676	93	5	1	1	NUM
ejpam-676	93	6	)	)	PUNCT
ejpam-676	93	7	,	,	PUNCT
ejpam-676	93	8	we	we	PRON
ejpam-676	93	9	say	say	VERB
ejpam-676	93	10	that	that	SCONJ
ejpam-676	93	11	a	a	DET
ejpam-676	93	12	function	function	NOUN
ejpam-676	93	13	f	f	PROPN
ejpam-676	93	14	∈∑p	∈∑p	NOUN
ejpam-676	93	15	,	,	PUNCT
ejpam-676	93	16	m	m	VERB
ejpam-676	93	17	is	be	AUX
ejpam-676	93	18	in	in	ADP
ejpam-676	93	19	the	the	DET
ejpam-676	93	20	class	class	NOUN
ejpam-676	93	21	∑m	∑m	PROPN
ejpam-676	93	22	p	p	PROPN
ejpam-676	93	23	,	,	PUNCT
ejpam-676	93	24	q	q	ADJ
ejpam-676	93	25	,	,	PUNCT
ejpam-676	93	26	s(α1	s(α1	NOUN
ejpam-676	93	27	;	;	PUNCT
ejpam-676	93	28	a	a	DET
ejpam-676	93	29	,	,	PUNCT
ejpam-676	93	30	b	b	NOUN
ejpam-676	93	31	)	)	PUNCT
ejpam-676	93	32	,	,	PUNCT
ejpam-676	93	33	if	if	SCONJ
ejpam-676	93	34	it	it	PRON
ejpam-676	93	35	satisfies	satisfy	VERB
ejpam-676	93	36	the	the	DET
ejpam-676	93	37	following	follow	VERB
ejpam-676	93	38	subordination	subordination	NOUN
ejpam-676	93	39	condition	condition	NOUN
ejpam-676	93	40	:	:	PUNCT
ejpam-676	93	41	−zp+1(hp	−zp+1(hp	ADJ
ejpam-676	93	42	,	,	PUNCT
ejpam-676	93	43	q	q	NOUN
ejpam-676	93	44	,	,	PUNCT
ejpam-676	93	45	s(α1	s(α1	NOUN
ejpam-676	93	46	)	)	PUNCT
ejpam-676	94	1	f	f	PROPN
ejpam-676	94	2	(	(	PUNCT
ejpam-676	94	3	z	z	NOUN
ejpam-676	94	4	)	)	PUNCT
ejpam-676	94	5	)	)	PUNCT
ejpam-676	95	1	′	′	NUM
ejpam-676	96	1	p	p	NOUN
ejpam-676	96	2	≺	≺	NOUN
ejpam-676	96	3	1	1	NUM
ejpam-676	96	4	+	+	NUM
ejpam-676	96	5	az	az	PROPN
ejpam-676	96	6	1	1	NUM
ejpam-676	96	7	+	+	CCONJ
ejpam-676	96	8	bz	bz	PROPN
ejpam-676	96	9	.	.	PUNCT
ejpam-676	97	1	(	(	PUNCT
ejpam-676	97	2	11	11	NUM
ejpam-676	97	3	)	)	PUNCT
ejpam-676	97	4	in	in	ADP
ejpam-676	97	5	view	view	NOUN
ejpam-676	97	6	of	of	ADP
ejpam-676	97	7	the	the	DET
ejpam-676	97	8	definition	definition	NOUN
ejpam-676	97	9	of	of	ADP
ejpam-676	97	10	subordination	subordination	NOUN
ejpam-676	97	11	,	,	PUNCT
ejpam-676	97	12	(	(	PUNCT
ejpam-676	97	13	11	11	NUM
ejpam-676	97	14	)	)	PUNCT
ejpam-676	97	15	is	be	AUX
ejpam-676	97	16	equivalent	equivalent	ADJ
ejpam-676	97	17	to	to	ADP
ejpam-676	97	18	the	the	DET
ejpam-676	97	19	following	follow	VERB
ejpam-676	97	20	condition	condition	NOUN
ejpam-676	97	21	:	:	PUNCT
ejpam-676	97	22	�	�	PROPN
ejpam-676	97	23	�	�	PROPN
ejpam-676	97	24	�	�	PROPN
ejpam-676	97	25	�	�	PROPN
ejpam-676	97	26	�	�	PROPN
ejpam-676	97	27	zp+1(hp	zp+1(hp	PROPN
ejpam-676	97	28	,	,	PUNCT
ejpam-676	97	29	q	q	NOUN
ejpam-676	97	30	,	,	PUNCT
ejpam-676	97	31	s(α1	s(α1	NOUN
ejpam-676	97	32	)	)	PUNCT
ejpam-676	98	1	f	f	PROPN
ejpam-676	98	2	(	(	PUNCT
ejpam-676	98	3	z	z	NOUN
ejpam-676	98	4	)	)	PUNCT
ejpam-676	98	5	)	)	PUNCT
ejpam-676	99	1	′	′	PUNCT
ejpam-676	100	1	+	+	CCONJ
ejpam-676	100	2	p	p	X
ejpam-676	100	3	bzp+1(hp	bzp+1(hp	PROPN
ejpam-676	100	4	,	,	PUNCT
ejpam-676	100	5	q	q	NOUN
ejpam-676	100	6	,	,	PUNCT
ejpam-676	100	7	s(α1	s(α1	NOUN
ejpam-676	100	8	)	)	PUNCT
ejpam-676	100	9	f	f	PROPN
ejpam-676	100	10	(	(	PUNCT
ejpam-676	100	11	z	z	NOUN
ejpam-676	100	12	)	)	PUNCT
ejpam-676	100	13	)	)	PUNCT
ejpam-676	100	14	′	′	PUNCT
ejpam-676	101	1	+	+	CCONJ
ejpam-676	101	2	pa	pa	PROPN
ejpam-676	101	3	�	�	PROPN
ejpam-676	101	4	�	�	PROPN
ejpam-676	101	5	�	�	PROPN
ejpam-676	101	6	�	�	PROPN
ejpam-676	101	7	�	�	PROPN
ejpam-676	101	8	<	<	X
ejpam-676	101	9	1	1	NUM
ejpam-676	101	10	(	(	PUNCT
ejpam-676	101	11	z	z	NOUN
ejpam-676	101	12	∈	∈	PROPN
ejpam-676	101	13	u	u	NOUN
ejpam-676	101	14	)	)	PUNCT
ejpam-676	101	15	.	.	PUNCT
ejpam-676	102	1	for	for	ADP
ejpam-676	102	2	convenience	convenience	NOUN
ejpam-676	102	3	,	,	PUNCT
ejpam-676	102	4	we	we	PRON
ejpam-676	102	5	write	write	VERB
ejpam-676	102	6	σm	σm	ADP
ejpam-676	103	1	p	p	X
ejpam-676	103	2	,	,	PUNCT
ejpam-676	103	3	q	q	ADJ
ejpam-676	103	4	,	,	PUNCT
ejpam-676	103	5	s(α1	s(α1	NOUN
ejpam-676	103	6	;	;	PUNCT
ejpam-676	103	7	1−	1−	NUM
ejpam-676	103	8	2ζ	2ζ	NUM
ejpam-676	103	9	p	p	X
ejpam-676	103	10	,	,	PUNCT
ejpam-676	103	11	1	1	X
ejpam-676	103	12	)	)	PUNCT
ejpam-676	103	13	=	=	NOUN
ejpam-676	103	14	σm	σm	X
ejpam-676	104	1	p	p	X
ejpam-676	104	2	,	,	PUNCT
ejpam-676	104	3	q	q	NOUN
ejpam-676	104	4	,	,	PUNCT
ejpam-676	104	5	s(α1;ζ	s(α1;ζ	PROPN
ejpam-676	104	6	)	)	PUNCT
ejpam-676	104	7	,	,	PUNCT
ejpam-676	104	8	where	where	SCONJ
ejpam-676	104	9	σm	σm	INTJ
ejpam-676	104	10	p	p	X
ejpam-676	104	11	,	,	PUNCT
ejpam-676	104	12	q	q	NOUN
ejpam-676	104	13	,	,	PUNCT
ejpam-676	104	14	s(α1;ζ	s(α1;ζ	NOUN
ejpam-676	104	15	)	)	PUNCT
ejpam-676	104	16	denotes	denote	VERB
ejpam-676	104	17	the	the	DET
ejpam-676	104	18	class	class	NOUN
ejpam-676	104	19	of	of	ADP
ejpam-676	104	20	functions	function	NOUN
ejpam-676	104	21	f	f	X
ejpam-676	104	22	(	(	PUNCT
ejpam-676	104	23	z	z	NOUN
ejpam-676	104	24	)	)	PUNCT
ejpam-676	104	25	∈	∈	PROPN
ejpam-676	104	26	σp	σp	PROPN
ejpam-676	104	27	,	,	PUNCT
ejpam-676	104	28	m	m	AUX
ejpam-676	104	29	satisfying	satisfy	VERB
ejpam-676	104	30	the	the	DET
ejpam-676	104	31	following	follow	VERB
ejpam-676	104	32	inequality	inequality	NOUN
ejpam-676	104	33	:	:	PUNCT
ejpam-676	104	34	re	re	X
ejpam-676	104	35	¦	¦	PROPN
ejpam-676	104	36	−zp+1(hp	−zp+1(hp	PROPN
ejpam-676	104	37	,	,	PUNCT
ejpam-676	104	38	q	q	NOUN
ejpam-676	104	39	,	,	PUNCT
ejpam-676	104	40	s(α1	s(α1	NOUN
ejpam-676	104	41	)	)	PUNCT
ejpam-676	104	42	f	f	PROPN
ejpam-676	104	43	(	(	PUNCT
ejpam-676	104	44	z	z	NOUN
ejpam-676	104	45	)	)	PUNCT
ejpam-676	104	46	)	)	PUNCT
ejpam-676	105	1	′	′	NOUN
ejpam-676	105	2	©	©	NOUN
ejpam-676	105	3	>	>	X
ejpam-676	105	4	ζ	ζ	X
ejpam-676	105	5	(	(	PUNCT
ejpam-676	105	6	0≤	0≤	NUM
ejpam-676	105	7	ζ	ζ	NOUN
ejpam-676	105	8	<	<	X
ejpam-676	105	9	p	p	X
ejpam-676	105	10	;	;	PUNCT
ejpam-676	105	11	z	z	PROPN
ejpam-676	105	12	∈	∈	PROPN
ejpam-676	105	13	u	u	NOUN
ejpam-676	105	14	)	)	PUNCT
ejpam-676	105	15	.	.	PUNCT
ejpam-676	106	1	we	we	PRON
ejpam-676	106	2	note	note	VERB
ejpam-676	106	3	that	that	SCONJ
ejpam-676	106	4	σ	σ	PROPN
ejpam-676	106	5	−p+1	−p+1	PROPN
ejpam-676	106	6	p	p	PROPN
ejpam-676	106	7	,	,	PUNCT
ejpam-676	106	8	q	q	X
ejpam-676	106	9	,	,	PUNCT
ejpam-676	106	10	s	s	PART
ejpam-676	106	11	(	(	PUNCT
ejpam-676	106	12	α1	α1	PROPN
ejpam-676	106	13	;	;	PUNCT
ejpam-676	106	14	a+	a+	PUNCT
ejpam-676	106	15	(	(	PUNCT
ejpam-676	106	16	b	b	X
ejpam-676	106	17	−	−	PROPN
ejpam-676	106	18	a	a	X
ejpam-676	106	19	)	)	PUNCT
ejpam-676	106	20	ρ	ρ	PROPN
ejpam-676	106	21	p	p	NOUN
ejpam-676	106	22	,	,	PUNCT
ejpam-676	106	23	b	b	NOUN
ejpam-676	106	24	)	)	PUNCT
ejpam-676	106	25	=	=	SYM
ejpam-676	106	26	σp	σp	PROPN
ejpam-676	106	27	,	,	PUNCT
ejpam-676	106	28	q	q	NOUN
ejpam-676	106	29	,	,	PUNCT
ejpam-676	106	30	s(α1,a	s(α1,a	PROPN
ejpam-676	106	31	,	,	PUNCT
ejpam-676	106	32	b	b	PROPN
ejpam-676	106	33	,	,	PUNCT
ejpam-676	106	34	ρ	ρ	PROPN
ejpam-676	106	35	)	)	PUNCT
ejpam-676	106	36	,	,	PUNCT
ejpam-676	106	37	0	0	NUM
ejpam-676	106	38	≤	≤	NUM
ejpam-676	106	39	ρ	ρ	NOUN
ejpam-676	106	40	<	<	X
ejpam-676	106	41	p	p	X
ejpam-676	106	42	;	;	PUNCT
ejpam-676	106	43	p	p	PROPN
ejpam-676	106	44	∈	∈	PROPN
ejpam-676	106	45	n	n	CCONJ
ejpam-676	106	46	)	)	PUNCT
ejpam-676	106	47	,	,	PUNCT
ejpam-676	106	48	where	where	SCONJ
ejpam-676	106	49	the	the	DET
ejpam-676	106	50	class	class	NOUN
ejpam-676	106	51	σp	σp	PROPN
ejpam-676	106	52	,	,	PUNCT
ejpam-676	106	53	q	q	NOUN
ejpam-676	106	54	,	,	PUNCT
ejpam-676	106	55	s(α1,a	s(α1,a	PROPN
ejpam-676	106	56	,	,	PUNCT
ejpam-676	106	57	b	b	PROPN
ejpam-676	106	58	,	,	PUNCT
ejpam-676	106	59	ρ	ρ	PROPN
ejpam-676	106	60	)	)	PUNCT
ejpam-676	106	61	was	be	AUX
ejpam-676	106	62	introduced	introduce	VERB
ejpam-676	106	63	and	and	CCONJ
ejpam-676	106	64	studied	study	VERB
ejpam-676	106	65	by	by	ADP
ejpam-676	106	66	aouf	aouf	PROPN
ejpam-676	107	1	[	[	X
ejpam-676	107	2	1	1	NUM
ejpam-676	107	3	]	]	PUNCT
ejpam-676	107	4	.	.	PUNCT
ejpam-676	108	1	we	we	PRON
ejpam-676	108	2	also	also	ADV
ejpam-676	108	3	observe	observe	VERB
ejpam-676	108	4	that	that	SCONJ
ejpam-676	108	5	:	:	PUNCT
ejpam-676	108	6	(	(	PUNCT
ejpam-676	108	7	i	i	NOUN
ejpam-676	108	8	)	)	PUNCT
ejpam-676	108	9	∑−p+1	∑−p+1	PROPN
ejpam-676	108	10	p,2,1	p,2,1	NOUN
ejpam-676	108	11	(	(	PUNCT
ejpam-676	108	12	n+	n+	ADP
ejpam-676	108	13	p	p	X
ejpam-676	108	14	,	,	PUNCT
ejpam-676	108	15	1	1	NUM
ejpam-676	108	16	;	;	PUNCT
ejpam-676	108	17	1	1	NUM
ejpam-676	108	18	;	;	PUNCT
ejpam-676	108	19	a	a	DET
ejpam-676	108	20	,	,	PUNCT
ejpam-676	108	21	b	b	NOUN
ejpam-676	108	22	)	)	PUNCT
ejpam-676	108	23	=	=	SYM
ejpam-676	108	24	cn	cn	PROPN
ejpam-676	108	25	,	,	PUNCT
ejpam-676	108	26	p(a	p(a	PROPN
ejpam-676	108	27	,	,	PUNCT
ejpam-676	108	28	b	b	NOUN
ejpam-676	108	29	)	)	PUNCT
ejpam-676	108	30	(	(	PUNCT
ejpam-676	108	31	n	n	CCONJ
ejpam-676	108	32	>	>	X
ejpam-676	108	33	−p	−p	NOUN
ejpam-676	108	34	;	;	PUNCT
ejpam-676	108	35	p	p	PROPN
ejpam-676	108	36	∈	∈	PROPN
ejpam-676	108	37	n	n	NOUN
ejpam-676	108	38	;	;	PUNCT
ejpam-676	108	39	−1≤	−1≤	VERB
ejpam-676	108	40	b	b	ADP
ejpam-676	108	41	<	<	X
ejpam-676	108	42	a≤	a≤	ADP
ejpam-676	108	43	1	1	NUM
ejpam-676	108	44	)	)	PUNCT
ejpam-676	108	45	,	,	PUNCT
ejpam-676	108	46	is	be	AUX
ejpam-676	108	47	the	the	DET
ejpam-676	108	48	subclass	subclass	NOUN
ejpam-676	108	49	of	of	ADP
ejpam-676	108	50	∑	∑	PUNCT
ejpam-676	108	51	p	p	NOUN
ejpam-676	108	52	studied	study	VERB
ejpam-676	108	53	by	by	ADP
ejpam-676	108	54	uralegaddi	uralegaddi	ADJ
ejpam-676	108	55	and	and	CCONJ
ejpam-676	108	56	somanatha	somanatha	NOUN
ejpam-676	109	1	[	[	X
ejpam-676	109	2	17	17	NUM
ejpam-676	109	3	]	]	SYM
ejpam-676	109	4	;	;	PUNCT
ejpam-676	109	5	(	(	PUNCT
ejpam-676	109	6	ii	ii	NOUN
ejpam-676	109	7	)	)	PUNCT
ejpam-676	109	8	∑−p+1	∑−p+1	PROPN
ejpam-676	109	9	p,2,1	p,2,1	NOUN
ejpam-676	109	10	(	(	PUNCT
ejpam-676	109	11	n+	n+	ADP
ejpam-676	109	12	p	p	X
ejpam-676	109	13	,	,	PUNCT
ejpam-676	109	14	1	1	NUM
ejpam-676	109	15	;	;	PUNCT
ejpam-676	109	16	1	1	NUM
ejpam-676	109	17	;	;	PUNCT
ejpam-676	109	18	1−	1−	NUM
ejpam-676	109	19	2α	2α	NOUN
ejpam-676	109	20	p	p	NOUN
ejpam-676	109	21	,	,	PUNCT
ejpam-676	109	22	−1	−1	NOUN
ejpam-676	109	23	)	)	PUNCT
ejpam-676	109	24	=	=	SYM
ejpam-676	109	25	∑	∑	PUNCT
ejpam-676	109	26	n	n	CCONJ
ejpam-676	109	27	,	,	PUNCT
ejpam-676	109	28	p(α	p(α	PROPN
ejpam-676	109	29	)	)	PUNCT
ejpam-676	109	30	(	(	PUNCT
ejpam-676	109	31	n	n	CCONJ
ejpam-676	109	32	>	>	X
ejpam-676	109	33	−p	−p	NOUN
ejpam-676	109	34	;	;	PUNCT
ejpam-676	109	35	p	p	PROPN
ejpam-676	109	36	∈	∈	PROPN
ejpam-676	109	37	n	n	NOUN
ejpam-676	109	38	;	;	PUNCT
ejpam-676	109	39	0≤	0≤	NUM
ejpam-676	109	40	α	α	NOUN
ejpam-676	109	41	<	<	X
ejpam-676	109	42	p	p	X
ejpam-676	109	43	)	)	PUNCT
ejpam-676	109	44	,	,	PUNCT
ejpam-676	109	45	is	be	AUX
ejpam-676	109	46	the	the	DET
ejpam-676	109	47	subclass	subclass	NOUN
ejpam-676	109	48	of	of	ADP
ejpam-676	109	49	∑	∑	PUNCT
ejpam-676	109	50	p	p	NOUN
ejpam-676	109	51	studied	study	VERB
ejpam-676	109	52	by	by	ADP
ejpam-676	109	53	cho	cho	PROPN
ejpam-676	109	54	and	and	CCONJ
ejpam-676	109	55	nunokawa	nunokawa	NOUN
ejpam-676	110	1	[	[	X
ejpam-676	110	2	2	2	NUM
ejpam-676	110	3	]	]	PUNCT
ejpam-676	110	4	;	;	PUNCT
ejpam-676	110	5	m.	m.	PROPN
ejpam-676	110	6	aouf	aouf	PROPN
ejpam-676	110	7	/	/	SYM
ejpam-676	110	8	eur	eur	PROPN
ejpam-676	110	9	.	.	PUNCT
ejpam-676	111	1	j.	j.	PROPN
ejpam-676	111	2	pure	pure	PROPN
ejpam-676	111	3	appl	appl	PROPN
ejpam-676	111	4	.	.	PROPN
ejpam-676	111	5	math	math	PROPN
ejpam-676	111	6	,	,	PUNCT
ejpam-676	111	7	5	5	NUM
ejpam-676	111	8	(	(	PUNCT
ejpam-676	111	9	2012	2012	NUM
ejpam-676	111	10	)	)	PUNCT
ejpam-676	111	11	,	,	PUNCT
ejpam-676	111	12	141	141	NUM
ejpam-676	111	13	-	-	SYM
ejpam-676	111	14	159	159	NUM
ejpam-676	111	15	144	144	NUM
ejpam-676	111	16	(	(	PUNCT
ejpam-676	111	17	iii	iii	NOUN
ejpam-676	111	18	)	)	PUNCT
ejpam-676	111	19	for	for	ADP
ejpam-676	111	20	q	q	NOUN
ejpam-676	111	21	=	=	SYM
ejpam-676	111	22	2	2	NUM
ejpam-676	111	23	,	,	PUNCT
ejpam-676	111	24	s	s	PART
ejpam-676	111	25	=	=	SYM
ejpam-676	111	26	1	1	NUM
ejpam-676	111	27	,	,	PUNCT
ejpam-676	111	28	α1	α1	PROPN
ejpam-676	111	29	=	=	PUNCT
ejpam-676	111	30	a	a	PRON
ejpam-676	111	31	>	>	X
ejpam-676	111	32	0	0	NUM
ejpam-676	111	33	,	,	PUNCT
ejpam-676	111	34	β1	β1	PROPN
ejpam-676	111	35	=	=	PUNCT
ejpam-676	111	36	c	c	PROPN
ejpam-676	111	37	>	>	PUNCT
ejpam-676	111	38	0	0	PUNCT
ejpam-676	111	39	and	and	CCONJ
ejpam-676	111	40	α2	α2	ADJ
ejpam-676	111	41	=	=	SYM
ejpam-676	112	1	1	1	NUM
ejpam-676	112	2	,	,	PUNCT
ejpam-676	112	3	we	we	PRON
ejpam-676	112	4	have	have	VERB
ejpam-676	112	5	σa	σa	PROPN
ejpam-676	112	6	,	,	PUNCT
ejpam-676	112	7	c(p	c(p	NOUN
ejpam-676	112	8	;	;	PUNCT
ejpam-676	112	9	m	m	PRON
ejpam-676	112	10	,	,	PUNCT
ejpam-676	112	11	a	a	DET
ejpam-676	112	12	,	,	PUNCT
ejpam-676	112	13	b	b	NOUN
ejpam-676	112	14	)	)	PUNCT
ejpam-676	112	15	=	=	SYM
ejpam-676	113	1	(	(	PUNCT
ejpam-676	113	2	f	f	X
ejpam-676	113	3	(	(	PUNCT
ejpam-676	113	4	z	z	NOUN
ejpam-676	113	5	)	)	PUNCT
ejpam-676	113	6	∈	∈	PROPN
ejpam-676	113	7	σp	σp	PROPN
ejpam-676	113	8	,	,	PUNCT
ejpam-676	113	9	m	m	VERB
ejpam-676	113	10	:	:	PUNCT
ejpam-676	113	11	−zp+1(ℓp(a	−zp+1(ℓp(a	ADJ
ejpam-676	113	12	,	,	PUNCT
ejpam-676	113	13	c	c	X
ejpam-676	113	14	)	)	PUNCT
ejpam-676	113	15	f	f	NOUN
ejpam-676	113	16	(	(	PUNCT
ejpam-676	113	17	z	z	NOUN
ejpam-676	113	18	)	)	PUNCT
ejpam-676	113	19	)	)	PUNCT
ejpam-676	114	1	′	′	NUM
ejpam-676	115	1	p	p	NOUN
ejpam-676	115	2	≺	≺	NOUN
ejpam-676	115	3	1	1	NUM
ejpam-676	115	4	+	+	NUM
ejpam-676	115	5	az	az	PROPN
ejpam-676	115	6	1	1	NUM
ejpam-676	115	7	+	+	CCONJ
ejpam-676	115	8	bz	bz	PROPN
ejpam-676	115	9	,	,	PUNCT
ejpam-676	115	10	−1≤	−1≤	PROPN
ejpam-676	115	11	b	b	ADP
ejpam-676	115	12	<	<	X
ejpam-676	115	13	a≤	a≤	PRON
ejpam-676	115	14	1	1	NUM
ejpam-676	115	15	,	,	PUNCT
ejpam-676	115	16	z	z	NOUN
ejpam-676	115	17	∈	∈	PROPN
ejpam-676	115	18	u	u	PROPN
ejpam-676	115	19	)	)	PUNCT
ejpam-676	115	20	,	,	PUNCT
ejpam-676	115	21	(	(	PUNCT
ejpam-676	115	22	12	12	NUM
ejpam-676	115	23	)	)	PUNCT
ejpam-676	115	24	where	where	SCONJ
ejpam-676	115	25	the	the	DET
ejpam-676	115	26	class	class	NOUN
ejpam-676	115	27	σa	σa	PROPN
ejpam-676	115	28	,	,	PUNCT
ejpam-676	115	29	c(p	c(p	NOUN
ejpam-676	115	30	;	;	PUNCT
ejpam-676	115	31	m	m	PRON
ejpam-676	115	32	,	,	PUNCT
ejpam-676	115	33	a	a	DET
ejpam-676	115	34	,	,	PUNCT
ejpam-676	115	35	b	b	NOUN
ejpam-676	115	36	)	)	PUNCT
ejpam-676	115	37	was	be	AUX
ejpam-676	115	38	studied	study	VERB
ejpam-676	115	39	by	by	ADP
ejpam-676	115	40	patel	patel	NOUN
ejpam-676	115	41	and	and	CCONJ
ejpam-676	115	42	cho	cho	NOUN
ejpam-676	116	1	[	[	X
ejpam-676	116	2	12	12	NUM
ejpam-676	116	3	]	]	PUNCT
ejpam-676	116	4	.	.	PUNCT
ejpam-676	117	1	2	2	X
ejpam-676	117	2	.	.	X
ejpam-676	117	3	preliminary	preliminary	ADJ
ejpam-676	117	4	lemmas	lemma	NOUN
ejpam-676	117	5	to	to	PART
ejpam-676	117	6	establish	establish	VERB
ejpam-676	117	7	our	our	PRON
ejpam-676	117	8	main	main	ADJ
ejpam-676	117	9	results	result	NOUN
ejpam-676	117	10	,	,	PUNCT
ejpam-676	117	11	we	we	PRON
ejpam-676	117	12	need	need	VERB
ejpam-676	117	13	the	the	DET
ejpam-676	117	14	following	follow	VERB
ejpam-676	117	15	lemmas	lemmas	NOUN
ejpam-676	117	16	.	.	PUNCT
ejpam-676	118	1	lemma	lemma	PROPN
ejpam-676	118	2	1	1	NUM
ejpam-676	118	3	(	(	PUNCT
ejpam-676	118	4	[	[	X
ejpam-676	118	5	3	3	NUM
ejpam-676	118	6	]	]	PUNCT
ejpam-676	118	7	)	)	PUNCT
ejpam-676	118	8	.	.	PUNCT
ejpam-676	119	1	let	let	VERB
ejpam-676	119	2	the	the	DET
ejpam-676	119	3	function	function	NOUN
ejpam-676	119	4	h	h	NOUN
ejpam-676	119	5	be	be	AUX
ejpam-676	119	6	analytic	analytic	ADJ
ejpam-676	119	7	and	and	CCONJ
ejpam-676	119	8	convex	convex	ADJ
ejpam-676	119	9	(	(	PUNCT
ejpam-676	119	10	univalent	univalent	ADJ
ejpam-676	119	11	)	)	PUNCT
ejpam-676	119	12	in	in	ADP
ejpam-676	119	13	u	u	NOUN
ejpam-676	119	14	with	with	ADP
ejpam-676	119	15	h(0	h(0	PROPN
ejpam-676	119	16	)	)	PUNCT
ejpam-676	119	17	=	=	SYM
ejpam-676	119	18	1	1	X
ejpam-676	119	19	.	.	PUNCT
ejpam-676	119	20	suppose	suppose	VERB
ejpam-676	119	21	also	also	ADV
ejpam-676	119	22	that	that	SCONJ
ejpam-676	119	23	the	the	DET
ejpam-676	119	24	function	function	NOUN
ejpam-676	119	25	ϕ	ϕ	NOUN
ejpam-676	119	26	given	give	VERB
ejpam-676	119	27	by	by	ADP
ejpam-676	119	28	ϕ(z	ϕ(z	NOUN
ejpam-676	119	29	)	)	PUNCT
ejpam-676	119	30	=	=	SYM
ejpam-676	119	31	1	1	NUM
ejpam-676	119	32	+	+	NUM
ejpam-676	119	33	cp+mzp+m+	cp+mzp+m+	NOUN
ejpam-676	119	34	cp+m+1zp+m+1	cp+m+1zp+m+1	PROPN
ejpam-676	119	35	+	+	PUNCT
ejpam-676	119	36	.	.	PUNCT
ejpam-676	119	37	.	.	PUNCT
ejpam-676	119	38	.	.	PUNCT
ejpam-676	120	1	(	(	PUNCT
ejpam-676	120	2	13	13	NUM
ejpam-676	120	3	)	)	PUNCT
ejpam-676	120	4	in	in	ADP
ejpam-676	120	5	analytic	analytic	NOUN
ejpam-676	120	6	in	in	ADP
ejpam-676	120	7	u.	u.	PROPN
ejpam-676	120	8	if	if	SCONJ
ejpam-676	120	9	ϕ(z	ϕ(z	NOUN
ejpam-676	120	10	)	)	PUNCT
ejpam-676	121	1	+	+	CCONJ
ejpam-676	121	2	zϕ	zϕ	X
ejpam-676	121	3	′	′	NUM
ejpam-676	121	4	(	(	PUNCT
ejpam-676	121	5	z	z	X
ejpam-676	121	6	)	)	PUNCT
ejpam-676	121	7	γ	γ	PROPN
ejpam-676	121	8	≺	≺	NOUN
ejpam-676	121	9	h(z	h(z	NOUN
ejpam-676	121	10	)	)	PUNCT
ejpam-676	121	11	(	(	PUNCT
ejpam-676	121	12	re(γ)≥	re(γ)≥	PROPN
ejpam-676	121	13	0;γ	0;γ	NUM
ejpam-676	121	14	6=	6=	PROPN
ejpam-676	121	15	0	0	NUM
ejpam-676	121	16	)	)	PUNCT
ejpam-676	121	17	,	,	PUNCT
ejpam-676	121	18	(	(	PUNCT
ejpam-676	121	19	14	14	NUM
ejpam-676	121	20	)	)	PUNCT
ejpam-676	121	21	then	then	ADV
ejpam-676	121	22	ϕ(z	ϕ(z	PROPN
ejpam-676	121	23	)	)	PUNCT
ejpam-676	121	24	≺ψ(z	≺ψ(z	NOUN
ejpam-676	121	25	)	)	PUNCT
ejpam-676	121	26	=	=	SYM
ejpam-676	122	1	γ	γ	X
ejpam-676	122	2	p+m	p+m	PROPN
ejpam-676	122	3	z	z	NUM
ejpam-676	122	4	−γ	−γ	NOUN
ejpam-676	122	5	p+m	p+m	PROPN
ejpam-676	122	6	z	z	PROPN
ejpam-676	122	7	∫	∫	PROPN
ejpam-676	122	8	0	0	NUM
ejpam-676	122	9	t	t	PROPN
ejpam-676	122	10	γ	γ	X
ejpam-676	122	11	p+m	p+m	X
ejpam-676	122	12	−1	−1	NOUN
ejpam-676	122	13	h(t)d	h(t)d	PROPN
ejpam-676	122	14	t	t	PROPN
ejpam-676	122	15	≺	≺	VERB
ejpam-676	122	16	h(z	h(z	NOUN
ejpam-676	122	17	)	)	PUNCT
ejpam-676	122	18	,	,	PUNCT
ejpam-676	122	19	and	and	CCONJ
ejpam-676	122	20	ψ	ψ	NOUN
ejpam-676	122	21	is	be	AUX
ejpam-676	122	22	the	the	DET
ejpam-676	122	23	best	good	ADJ
ejpam-676	122	24	dominant	dominant	NOUN
ejpam-676	122	25	of	of	ADP
ejpam-676	122	26	(	(	PUNCT
ejpam-676	122	27	14	14	NUM
ejpam-676	122	28	)	)	PUNCT
ejpam-676	122	29	.	.	PUNCT
ejpam-676	123	1	with	with	ADP
ejpam-676	123	2	a	a	DET
ejpam-676	123	3	view	view	NOUN
ejpam-676	123	4	to	to	ADP
ejpam-676	123	5	starting	start	VERB
ejpam-676	123	6	a	a	DET
ejpam-676	123	7	well	well	ADV
ejpam-676	123	8	-	-	PUNCT
ejpam-676	123	9	known	know	VERB
ejpam-676	123	10	result	result	NOUN
ejpam-676	123	11	(	(	PUNCT
ejpam-676	123	12	lemma	lemma	PROPN
ejpam-676	123	13	2	2	NUM
ejpam-676	123	14	below	below	ADV
ejpam-676	123	15	)	)	PUNCT
ejpam-676	123	16	,	,	PUNCT
ejpam-676	123	17	we	we	PRON
ejpam-676	123	18	denote	denote	VERB
ejpam-676	123	19	by	by	ADP
ejpam-676	123	20	p(γ	p(γ	NOUN
ejpam-676	123	21	)	)	PUNCT
ejpam-676	123	22	the	the	DET
ejpam-676	123	23	class	class	NOUN
ejpam-676	123	24	of	of	ADP
ejpam-676	123	25	functions	function	NOUN
ejpam-676	123	26	ϕ	ϕ	NOUN
ejpam-676	123	27	given	give	VERB
ejpam-676	123	28	by	by	ADP
ejpam-676	123	29	ϕ(z	ϕ(z	NOUN
ejpam-676	123	30	)	)	PUNCT
ejpam-676	123	31	=	=	SYM
ejpam-676	124	1	1	1	NUM
ejpam-676	124	2	+	+	CCONJ
ejpam-676	124	3	b1z	b1z	X
ejpam-676	124	4	+	+	CCONJ
ejpam-676	124	5	b2z2	b2z2	X
ejpam-676	124	6	+	+	X
ejpam-676	124	7	.	.	PUNCT
ejpam-676	124	8	.	.	PUNCT
ejpam-676	124	9	.	.	PUNCT
ejpam-676	125	1	,	,	PUNCT
ejpam-676	125	2	(	(	PUNCT
ejpam-676	125	3	15	15	NUM
ejpam-676	125	4	)	)	PUNCT
ejpam-676	125	5	which	which	PRON
ejpam-676	125	6	are	be	AUX
ejpam-676	125	7	analytic	analytic	ADJ
ejpam-676	125	8	in	in	ADP
ejpam-676	125	9	u	u	NOUN
ejpam-676	125	10	and	and	CCONJ
ejpam-676	125	11	satisfy	satisfy	VERB
ejpam-676	125	12	the	the	DET
ejpam-676	125	13	following	follow	VERB
ejpam-676	125	14	inequality	inequality	NOUN
ejpam-676	125	15	:	:	PUNCT
ejpam-676	125	16	re	re	VERB
ejpam-676	125	17	�	�	PROPN
ejpam-676	125	18	ϕ(z	ϕ(z	PROPN
ejpam-676	125	19	)	)	PUNCT
ejpam-676	125	20	>	>	X
ejpam-676	126	1	γ	γ	X
ejpam-676	126	2	(	(	PUNCT
ejpam-676	126	3	0≤	0≤	NUM
ejpam-676	126	4	γ	γ	X
ejpam-676	126	5	<	<	X
ejpam-676	126	6	1	1	NUM
ejpam-676	126	7	;	;	PUNCT
ejpam-676	126	8	z	z	PROPN
ejpam-676	126	9	∈	∈	PROPN
ejpam-676	126	10	u	u	NOUN
ejpam-676	126	11	)	)	PUNCT
ejpam-676	126	12	.	.	PUNCT
ejpam-676	127	1	lemma	lemma	PROPN
ejpam-676	127	2	2	2	NUM
ejpam-676	127	3	(	(	PUNCT
ejpam-676	127	4	[	[	X
ejpam-676	127	5	10	10	NUM
ejpam-676	127	6	]	]	NUM
ejpam-676	127	7	)	)	PUNCT
ejpam-676	127	8	.	.	PUNCT
ejpam-676	128	1	let	let	VERB
ejpam-676	128	2	the	the	DET
ejpam-676	128	3	function	function	NOUN
ejpam-676	128	4	ϕ	ϕ	NOUN
ejpam-676	128	5	,	,	PUNCT
ejpam-676	128	6	given	give	VERB
ejpam-676	128	7	by	by	ADP
ejpam-676	128	8	(	(	PUNCT
ejpam-676	128	9	15	15	NUM
ejpam-676	128	10	)	)	PUNCT
ejpam-676	128	11	,	,	PUNCT
ejpam-676	128	12	be	be	AUX
ejpam-676	128	13	in	in	ADP
ejpam-676	128	14	the	the	DET
ejpam-676	128	15	class	class	NOUN
ejpam-676	128	16	p(γ	p(γ	NOUN
ejpam-676	128	17	)	)	PUNCT
ejpam-676	128	18	.	.	PUNCT
ejpam-676	129	1	then	then	ADV
ejpam-676	129	2	re	re	VERB
ejpam-676	129	3	�	�	PROPN
ejpam-676	129	4	ϕ(z	ϕ(z	PROPN
ejpam-676	129	5	)	)	PUNCT
ejpam-676	129	6	≥	≥	NOUN
ejpam-676	130	1	2γ−	2γ−	NUM
ejpam-676	130	2	1	1	NUM
ejpam-676	130	3	+	+	NUM
ejpam-676	130	4	2(1−	2(1−	NUM
ejpam-676	130	5	γ	γ	NOUN
ejpam-676	130	6	)	)	PUNCT
ejpam-676	130	7	1	1	NUM
ejpam-676	130	8	+	+	NUM
ejpam-676	130	9	|z|	|z|	NOUN
ejpam-676	130	10	(	(	PUNCT
ejpam-676	130	11	0≤	0≤	NUM
ejpam-676	130	12	γ	γ	X
ejpam-676	130	13	<	<	X
ejpam-676	130	14	1	1	NUM
ejpam-676	130	15	;	;	PUNCT
ejpam-676	130	16	z	z	PROPN
ejpam-676	130	17	∈	∈	PROPN
ejpam-676	130	18	u	u	NOUN
ejpam-676	130	19	)	)	PUNCT
ejpam-676	130	20	.	.	PUNCT
ejpam-676	131	1	lemma	lemma	PROPN
ejpam-676	131	2	3	3	NUM
ejpam-676	131	3	(	(	PUNCT
ejpam-676	131	4	[	[	X
ejpam-676	131	5	16	16	NUM
ejpam-676	131	6	]	]	PUNCT
ejpam-676	131	7	)	)	PUNCT
ejpam-676	131	8	.	.	PUNCT
ejpam-676	132	1	for	for	ADP
ejpam-676	132	2	0≤	0≤	NUM
ejpam-676	132	3	γ1,γ2	γ1,γ2	PROPN
ejpam-676	132	4	<	<	X
ejpam-676	132	5	1	1	NUM
ejpam-676	132	6	,	,	PUNCT
ejpam-676	132	7	we	we	PRON
ejpam-676	132	8	have	have	AUX
ejpam-676	132	9	p(γ1	p(γ1	NOUN
ejpam-676	132	10	)	)	PUNCT
ejpam-676	132	11	∗	∗	NOUN
ejpam-676	132	12	p(γ2)⊂	p(γ2)⊂	PROPN
ejpam-676	132	13	p(γ3	p(γ3	PROPN
ejpam-676	132	14	)	)	PUNCT
ejpam-676	132	15	(	(	PUNCT
ejpam-676	132	16	γ3	γ3	NOUN
ejpam-676	132	17	=	=	SYM
ejpam-676	132	18	1−	1−	NUM
ejpam-676	132	19	2(1−	2(1−	X
ejpam-676	132	20	γ1)(1−	γ1)(1−	ADJ
ejpam-676	132	21	γ2	γ2	NOUN
ejpam-676	132	22	)	)	PUNCT
ejpam-676	132	23	)	)	PUNCT
ejpam-676	132	24	.	.	PUNCT
ejpam-676	133	1	the	the	DET
ejpam-676	133	2	result	result	NOUN
ejpam-676	133	3	is	be	AUX
ejpam-676	133	4	the	the	DET
ejpam-676	133	5	best	good	ADJ
ejpam-676	133	6	possible	possible	ADJ
ejpam-676	133	7	.	.	PUNCT
ejpam-676	134	1	m.	m.	PROPN
ejpam-676	134	2	aouf	aouf	PROPN
ejpam-676	134	3	/	/	SYM
ejpam-676	134	4	eur	eur	PROPN
ejpam-676	134	5	.	.	PUNCT
ejpam-676	135	1	j.	j.	PROPN
ejpam-676	135	2	pure	pure	PROPN
ejpam-676	135	3	appl	appl	PROPN
ejpam-676	135	4	.	.	PROPN
ejpam-676	135	5	math	math	PROPN
ejpam-676	135	6	,	,	PUNCT
ejpam-676	135	7	5	5	NUM
ejpam-676	135	8	(	(	PUNCT
ejpam-676	135	9	2012	2012	NUM
ejpam-676	135	10	)	)	PUNCT
ejpam-676	135	11	,	,	PUNCT
ejpam-676	135	12	141	141	NUM
ejpam-676	135	13	-	-	SYM
ejpam-676	135	14	159	159	NUM
ejpam-676	135	15	145	145	NUM
ejpam-676	135	16	for	for	ADP
ejpam-676	135	17	real	real	ADJ
ejpam-676	135	18	or	or	CCONJ
ejpam-676	135	19	complex	complex	ADJ
ejpam-676	135	20	numbers	number	NOUN
ejpam-676	135	21	a	a	PRON
ejpam-676	135	22	,	,	PUNCT
ejpam-676	135	23	b	b	NOUN
ejpam-676	135	24	and	and	CCONJ
ejpam-676	135	25	c	c	PROPN
ejpam-676	135	26	(	(	PUNCT
ejpam-676	135	27	c	c	NOUN
ejpam-676	135	28	/∈	/∈	PUNCT
ejpam-676	136	1	z−0	z−0	NUM
ejpam-676	136	2	)	)	PUNCT
ejpam-676	137	1	,	,	PUNCT
ejpam-676	137	2	the	the	DET
ejpam-676	137	3	gaussian	gaussian	ADJ
ejpam-676	137	4	hypergeometric	hypergeometric	ADJ
ejpam-676	137	5	function	function	NOUN
ejpam-676	137	6	is	be	AUX
ejpam-676	137	7	defined	define	VERB
ejpam-676	137	8	by	by	ADP
ejpam-676	137	9	2f1(a	2f1(a	NUM
ejpam-676	137	10	,	,	PUNCT
ejpam-676	137	11	b	b	NOUN
ejpam-676	137	12	;	;	PUNCT
ejpam-676	137	13	c	c	X
ejpam-676	137	14	;	;	PUNCT
ejpam-676	137	15	z	z	X
ejpam-676	137	16	)	)	PUNCT
ejpam-676	137	17	=	=	SYM
ejpam-676	138	1	1	1	NUM
ejpam-676	138	2	+	+	NUM
ejpam-676	138	3	ab	ab	PROPN
ejpam-676	138	4	c	c	X
ejpam-676	138	5	·	·	PUNCT
ejpam-676	138	6	z	z	NOUN
ejpam-676	138	7	1	1	NUM
ejpam-676	138	8	!	!	PUNCT
ejpam-676	139	1	+	+	PUNCT
ejpam-676	139	2	a(a+	a(a+	PROPN
ejpam-676	139	3	1)b(b+	1)b(b+	NUM
ejpam-676	139	4	1	1	X
ejpam-676	139	5	)	)	PUNCT
ejpam-676	139	6	c(c	c(c	NOUN
ejpam-676	139	7	+	+	NOUN
ejpam-676	139	8	1	1	NUM
ejpam-676	139	9	)	)	PUNCT
ejpam-676	139	10	·	·	PUNCT
ejpam-676	140	1	z	z	NOUN
ejpam-676	140	2	2	2	NUM
ejpam-676	140	3	z	z	NOUN
ejpam-676	140	4	!	!	PUNCT
ejpam-676	141	1	+	+	CCONJ
ejpam-676	141	2	.	.	PUNCT
ejpam-676	141	3	.	.	PUNCT
ejpam-676	141	4	.	.	PUNCT
ejpam-676	142	1	.	.	PUNCT
ejpam-676	143	1	we	we	PRON
ejpam-676	143	2	note	note	VERB
ejpam-676	143	3	that	that	SCONJ
ejpam-676	143	4	the	the	DET
ejpam-676	143	5	above	above	ADJ
ejpam-676	143	6	series	series	NOUN
ejpam-676	143	7	converges	converge	VERB
ejpam-676	143	8	absolutely	absolutely	ADV
ejpam-676	143	9	for	for	ADP
ejpam-676	143	10	z	z	PROPN
ejpam-676	143	11	∈	∈	PROPN
ejpam-676	143	12	u	u	NOUN
ejpam-676	143	13	and	and	CCONJ
ejpam-676	143	14	hence	hence	ADV
ejpam-676	143	15	represents	represent	VERB
ejpam-676	143	16	an	an	DET
ejpam-676	143	17	analytic	analytic	ADJ
ejpam-676	143	18	function	function	NOUN
ejpam-676	143	19	in	in	ADP
ejpam-676	143	20	u	u	NOUN
ejpam-676	143	21	(	(	PUNCT
ejpam-676	143	22	see	see	VERB
ejpam-676	143	23	,	,	PUNCT
ejpam-676	143	24	for	for	ADP
ejpam-676	143	25	details	detail	NOUN
ejpam-676	143	26	[	[	X
ejpam-676	143	27	18	18	NUM
ejpam-676	143	28	,	,	PUNCT
ejpam-676	143	29	chapter	chapter	NOUN
ejpam-676	143	30	14	14	NUM
ejpam-676	143	31	]	]	PUNCT
ejpam-676	143	32	)	)	PUNCT
ejpam-676	143	33	.	.	PUNCT
ejpam-676	144	1	each	each	PRON
ejpam-676	144	2	of	of	ADP
ejpam-676	144	3	the	the	DET
ejpam-676	144	4	identities	identity	NOUN
ejpam-676	144	5	(	(	PUNCT
ejpam-676	144	6	asserted	assert	VERB
ejpam-676	144	7	by	by	ADP
ejpam-676	144	8	lemma	lemma	PROPN
ejpam-676	144	9	4	4	NUM
ejpam-676	144	10	below	below	ADV
ejpam-676	144	11	)	)	PUNCT
ejpam-676	144	12	is	be	AUX
ejpam-676	144	13	well	well	ADV
ejpam-676	144	14	-	-	PUNCT
ejpam-676	144	15	known	know	VERB
ejpam-676	144	16	(	(	PUNCT
ejpam-676	144	17	cf	cf	NOUN
ejpam-676	144	18	.	.	NOUN
ejpam-676	144	19	,	,	PUNCT
ejpam-676	144	20	e.g.	e.g.	ADV
ejpam-676	144	21	,	,	PUNCT
ejpam-676	144	22	[	[	X
ejpam-676	144	23	18	18	NUM
ejpam-676	144	24	,	,	PUNCT
ejpam-676	144	25	chapter	chapter	NOUN
ejpam-676	144	26	14	14	NUM
ejpam-676	144	27	]	]	PUNCT
ejpam-676	144	28	)	)	PUNCT
ejpam-676	144	29	.	.	PUNCT
ejpam-676	145	1	lemma	lemma	PROPN
ejpam-676	145	2	4	4	NUM
ejpam-676	145	3	(	(	PUNCT
ejpam-676	145	4	[	[	X
ejpam-676	145	5	18	18	NUM
ejpam-676	145	6	]	]	NUM
ejpam-676	145	7	)	)	PUNCT
ejpam-676	145	8	.	.	PUNCT
ejpam-676	146	1	for	for	ADP
ejpam-676	146	2	real	real	ADJ
ejpam-676	146	3	or	or	CCONJ
ejpam-676	146	4	complex	complex	ADJ
ejpam-676	146	5	parameters	parameter	NOUN
ejpam-676	146	6	a	a	DET
ejpam-676	146	7	,	,	PUNCT
ejpam-676	146	8	b	b	PROPN
ejpam-676	146	9	and	and	CCONJ
ejpam-676	146	10	c	c	PROPN
ejpam-676	146	11	(	(	PUNCT
ejpam-676	146	12	c	c	NOUN
ejpam-676	146	13	/∈	/∈	PUNCT
ejpam-676	147	1	z−0	z−0	NUM
ejpam-676	147	2	)	)	PUNCT
ejpam-676	147	3	,	,	PUNCT
ejpam-676	147	4	1	1	NUM
ejpam-676	147	5	∫	∫	NOUN
ejpam-676	147	6	0	0	NUM
ejpam-676	148	1	t	t	PROPN
ejpam-676	148	2	b−1(1−	b−1(1−	PROPN
ejpam-676	148	3	t)c−b−1(1−	t)c−b−1(1−	X
ejpam-676	148	4	zt)−ad	zt)−ad	X
ejpam-676	148	5	t	t	NOUN
ejpam-676	148	6	=	=	PUNCT
ejpam-676	148	7	γ(b)γ(c−	γ(b)γ(c−	PROPN
ejpam-676	148	8	b	b	PROPN
ejpam-676	148	9	)	)	PUNCT
ejpam-676	148	10	γ(c	γ(c	NUM
ejpam-676	148	11	)	)	PUNCT
ejpam-676	148	12	2γ1(a	2γ1(a	NUM
ejpam-676	148	13	,	,	PUNCT
ejpam-676	148	14	b	b	NOUN
ejpam-676	148	15	;	;	PUNCT
ejpam-676	148	16	c	c	X
ejpam-676	148	17	;	;	PUNCT
ejpam-676	148	18	z	z	X
ejpam-676	148	19	)	)	PUNCT
ejpam-676	148	20	(	(	PUNCT
ejpam-676	148	21	re(c	re(c	NOUN
ejpam-676	148	22	)	)	PUNCT
ejpam-676	148	23	>	>	X
ejpam-676	148	24	re(b	re(b	X
ejpam-676	148	25	)	)	PUNCT
ejpam-676	148	26	>	>	X
ejpam-676	148	27	0	0	NUM
ejpam-676	148	28	)	)	PUNCT
ejpam-676	148	29	;	;	PUNCT
ejpam-676	148	30	(	(	PUNCT
ejpam-676	148	31	16	16	NUM
ejpam-676	148	32	)	)	PUNCT
ejpam-676	148	33	2f1(a	2f1(a	NUM
ejpam-676	148	34	,	,	PUNCT
ejpam-676	148	35	b	b	X
ejpam-676	148	36	;	;	PUNCT
ejpam-676	148	37	c	c	X
ejpam-676	148	38	;	;	PUNCT
ejpam-676	148	39	z	z	X
ejpam-676	148	40	)	)	PUNCT
ejpam-676	148	41	=	=	PUNCT
ejpam-676	148	42	(	(	PUNCT
ejpam-676	148	43	1−	1−	NUM
ejpam-676	148	44	z)−a	z)−a	PROPN
ejpam-676	148	45	2f1(a	2f1(a	NUM
ejpam-676	148	46	,	,	PUNCT
ejpam-676	148	47	b	b	NOUN
ejpam-676	148	48	;	;	PUNCT
ejpam-676	148	49	c	c	X
ejpam-676	148	50	;	;	PUNCT
ejpam-676	148	51	z	z	NOUN
ejpam-676	148	52	z	z	NOUN
ejpam-676	148	53	−	−	NUM
ejpam-676	148	54	1	1	NUM
ejpam-676	148	55	)	)	PUNCT
ejpam-676	148	56	;	;	PUNCT
ejpam-676	148	57	(	(	PUNCT
ejpam-676	148	58	17	17	NUM
ejpam-676	148	59	)	)	PUNCT
ejpam-676	148	60	2f1(a	2f1(a	NUM
ejpam-676	148	61	,	,	PUNCT
ejpam-676	148	62	b	b	X
ejpam-676	148	63	;	;	PUNCT
ejpam-676	148	64	c	c	X
ejpam-676	148	65	;	;	PUNCT
ejpam-676	148	66	z	z	X
ejpam-676	148	67	)	)	PUNCT
ejpam-676	148	68	=	=	PUNCT
ejpam-676	149	1	2f1(a	2f1(a	NUM
ejpam-676	149	2	,	,	PUNCT
ejpam-676	149	3	b−	b−	NOUN
ejpam-676	149	4	1	1	NUM
ejpam-676	149	5	;	;	PUNCT
ejpam-676	149	6	c	c	X
ejpam-676	149	7	;	;	PUNCT
ejpam-676	149	8	z	z	X
ejpam-676	149	9	)	)	PUNCT
ejpam-676	150	1	+	+	CCONJ
ejpam-676	150	2	az	az	PROPN
ejpam-676	150	3	c	c	NOUN
ejpam-676	150	4	2f1(a+	2f1(a+	NUM
ejpam-676	150	5	1	1	NUM
ejpam-676	150	6	,	,	PUNCT
ejpam-676	150	7	b	b	NOUN
ejpam-676	150	8	;	;	PUNCT
ejpam-676	150	9	c	c	X
ejpam-676	150	10	+	+	NOUN
ejpam-676	150	11	1	1	NUM
ejpam-676	150	12	;	;	PUNCT
ejpam-676	150	13	z	z	X
ejpam-676	150	14	)	)	PUNCT
ejpam-676	150	15	;	;	PUNCT
ejpam-676	150	16	(	(	PUNCT
ejpam-676	150	17	18	18	NUM
ejpam-676	150	18	)	)	PUNCT
ejpam-676	150	19	2f1(a	2f1(a	NUM
ejpam-676	150	20	,	,	PUNCT
ejpam-676	150	21	b	b	NOUN
ejpam-676	150	22	;	;	PUNCT
ejpam-676	150	23	a+	a+	X
ejpam-676	150	24	b+	b+	ADJ
ejpam-676	150	25	1	1	NUM
ejpam-676	150	26	2	2	NUM
ejpam-676	150	27	;	;	PUNCT
ejpam-676	150	28	1	1	NUM
ejpam-676	150	29	2	2	NUM
ejpam-676	150	30	)	)	PUNCT
ejpam-676	150	31	=	=	NOUN
ejpam-676	151	1	p	p	X
ejpam-676	151	2	πγ	πγ	PROPN
ejpam-676	151	3	(	(	PUNCT
ejpam-676	151	4	a+b+1	a+b+1	NOUN
ejpam-676	151	5	2	2	NUM
ejpam-676	151	6	)	)	PUNCT
ejpam-676	151	7	γ	γ	PROPN
ejpam-676	151	8	(	(	PUNCT
ejpam-676	151	9	a+1	a+1	PROPN
ejpam-676	151	10	2	2	NUM
ejpam-676	151	11	)	)	PUNCT
ejpam-676	151	12	γ	γ	PROPN
ejpam-676	151	13	(	(	PUNCT
ejpam-676	151	14	b+1	b+1	NOUN
ejpam-676	151	15	2	2	NUM
ejpam-676	151	16	)	)	PUNCT
ejpam-676	151	17	.	.	PUNCT
ejpam-676	152	1	(	(	PUNCT
ejpam-676	152	2	19	19	NUM
ejpam-676	152	3	)	)	PUNCT
ejpam-676	152	4	lemma	lemma	PROPN
ejpam-676	152	5	5	5	NUM
ejpam-676	152	6	(	(	PUNCT
ejpam-676	152	7	[	[	X
ejpam-676	152	8	13	13	NUM
ejpam-676	152	9	]	]	NUM
ejpam-676	152	10	)	)	PUNCT
ejpam-676	152	11	.	.	PUNCT
ejpam-676	153	1	let	let	VERB
ejpam-676	153	2	φ	φ	PRON
ejpam-676	153	3	be	be	AUX
ejpam-676	153	4	analytic	analytic	ADJ
ejpam-676	153	5	in	in	ADP
ejpam-676	153	6	u	u	NOUN
ejpam-676	153	7	with	with	ADP
ejpam-676	153	8	φ(0	φ(0	ADJ
ejpam-676	153	9	)	)	PUNCT
ejpam-676	153	10	=	=	SYM
ejpam-676	153	11	1	1	NUM
ejpam-676	153	12	and	and	CCONJ
ejpam-676	153	13	re	re	ADJ
ejpam-676	153	14	{	{	PUNCT
ejpam-676	153	15	φ(z	φ(z	PROPN
ejpam-676	153	16	)	)	PUNCT
ejpam-676	153	17	}	}	PUNCT
ejpam-676	153	18	>	>	PUNCT
ejpam-676	154	1	1	1	NUM
ejpam-676	154	2	2	2	NUM
ejpam-676	154	3	(	(	PUNCT
ejpam-676	154	4	z	z	NOUN
ejpam-676	154	5	∈	∈	PROPN
ejpam-676	154	6	u	u	NOUN
ejpam-676	154	7	)	)	PUNCT
ejpam-676	154	8	.	.	PUNCT
ejpam-676	155	1	then	then	ADV
ejpam-676	155	2	,	,	PUNCT
ejpam-676	155	3	for	for	ADP
ejpam-676	155	4	any	any	DET
ejpam-676	155	5	function	function	NOUN
ejpam-676	155	6	f	f	PROPN
ejpam-676	155	7	analytic	analytic	NOUN
ejpam-676	155	8	in	in	ADP
ejpam-676	155	9	u	u	PROPN
ejpam-676	155	10	,	,	PUNCT
ejpam-676	155	11	(	(	PUNCT
ejpam-676	155	12	φ	φ	PROPN
ejpam-676	155	13	∗	∗	PROPN
ejpam-676	155	14	f	f	PROPN
ejpam-676	155	15	)	)	PUNCT
ejpam-676	155	16	(	(	PUNCT
ejpam-676	155	17	u	u	NOUN
ejpam-676	155	18	)	)	PUNCT
ejpam-676	155	19	is	be	AUX
ejpam-676	155	20	contained	contain	VERB
ejpam-676	155	21	in	in	ADP
ejpam-676	155	22	the	the	DET
ejpam-676	155	23	convex	convex	PROPN
ejpam-676	155	24	hull	hull	NOUN
ejpam-676	155	25	of	of	ADP
ejpam-676	155	26	f(u	f(u	PROPN
ejpam-676	155	27	)	)	PUNCT
ejpam-676	155	28	.	.	PUNCT
ejpam-676	156	1	3	3	X
ejpam-676	156	2	.	.	X
ejpam-676	156	3	main	main	ADJ
ejpam-676	156	4	results	result	NOUN
ejpam-676	156	5	remark	remark	VERB
ejpam-676	156	6	1	1	NUM
ejpam-676	156	7	.	.	PUNCT
ejpam-676	157	1	throughout	throughout	ADP
ejpam-676	157	2	our	our	PRON
ejpam-676	157	3	present	present	ADJ
ejpam-676	157	4	paper	paper	NOUN
ejpam-676	157	5	,	,	PUNCT
ejpam-676	157	6	we	we	PRON
ejpam-676	157	7	assume	assume	VERB
ejpam-676	157	8	that	that	SCONJ
ejpam-676	157	9	:	:	PUNCT
ejpam-676	157	10	−1≤	−1≤	VERB
ejpam-676	157	11	b	b	NOUN
ejpam-676	157	12	<	<	X
ejpam-676	157	13	a≤	a≤	PRON
ejpam-676	157	14	1,λ	1,λ	PROPN
ejpam-676	157	15	>	>	X
ejpam-676	157	16	0	0	NUM
ejpam-676	157	17	,	,	PUNCT
ejpam-676	157	18	p	p	NOUN
ejpam-676	157	19	∈	∈	PROPN
ejpam-676	157	20	n	n	NOUN
ejpam-676	157	21	and	and	CCONJ
ejpam-676	157	22	α1	α1	PROPN
ejpam-676	157	23	∈	∈	PROPN
ejpam-676	157	24	c\{0	c\{0	PROPN
ejpam-676	157	25	}	}	PUNCT
ejpam-676	157	26	.	.	PUNCT
ejpam-676	158	1	theorem	theorem	NOUN
ejpam-676	158	2	1	1	NUM
ejpam-676	158	3	.	.	PUNCT
ejpam-676	159	1	let	let	VERB
ejpam-676	159	2	the	the	DET
ejpam-676	159	3	function	function	NOUN
ejpam-676	159	4	f	f	PROPN
ejpam-676	159	5	defined	define	VERB
ejpam-676	159	6	by	by	ADP
ejpam-676	159	7	(	(	PUNCT
ejpam-676	159	8	1	1	X
ejpam-676	159	9	)	)	PUNCT
ejpam-676	159	10	satisfying	satisfy	VERB
ejpam-676	159	11	the	the	DET
ejpam-676	159	12	following	follow	VERB
ejpam-676	159	13	subordination	subordination	NOUN
ejpam-676	159	14	condition	condition	NOUN
ejpam-676	159	15	:	:	PUNCT
ejpam-676	159	16	−	−	PROPN
ejpam-676	159	17	(	(	PUNCT
ejpam-676	159	18	1−λ)z	1−λ)z	NUM
ejpam-676	159	19	p+1(hp	p+1(hp	VERB
ejpam-676	159	20	,	,	PUNCT
ejpam-676	159	21	q	q	NOUN
ejpam-676	159	22	,	,	PUNCT
ejpam-676	159	23	s(α1	s(α1	NOUN
ejpam-676	159	24	)	)	PUNCT
ejpam-676	160	1	f	f	PROPN
ejpam-676	160	2	(	(	PUNCT
ejpam-676	160	3	z	z	NOUN
ejpam-676	160	4	)	)	PUNCT
ejpam-676	160	5	)	)	PUNCT
ejpam-676	161	1	′	′	NUM
ejpam-676	162	1	+	+	PUNCT
ejpam-676	162	2	λzp+1(hp	λzp+1(hp	PROPN
ejpam-676	162	3	,	,	PUNCT
ejpam-676	162	4	q	q	NOUN
ejpam-676	162	5	,	,	PUNCT
ejpam-676	162	6	s(α1	s(α1	NOUN
ejpam-676	162	7	+	+	CCONJ
ejpam-676	162	8	1	1	X
ejpam-676	162	9	)	)	PUNCT
ejpam-676	162	10	f	f	NOUN
ejpam-676	162	11	(	(	PUNCT
ejpam-676	162	12	z	z	NOUN
ejpam-676	162	13	)	)	PUNCT
ejpam-676	162	14	)	)	PUNCT
ejpam-676	163	1	′	′	NUM
ejpam-676	164	1	p	p	NOUN
ejpam-676	164	2	≺	≺	NOUN
ejpam-676	164	3	1	1	NUM
ejpam-676	164	4	+	+	NUM
ejpam-676	164	5	az	az	PROPN
ejpam-676	164	6	1	1	NUM
ejpam-676	164	7	+	+	CCONJ
ejpam-676	164	8	bz	bz	PROPN
ejpam-676	164	9	.	.	PUNCT
ejpam-676	165	1	then	then	ADV
ejpam-676	165	2	−zp+1(hp	−zp+1(hp	ADJ
ejpam-676	165	3	,	,	PUNCT
ejpam-676	165	4	q	q	NOUN
ejpam-676	165	5	,	,	PUNCT
ejpam-676	165	6	s(α1	s(α1	NOUN
ejpam-676	165	7	)	)	PUNCT
ejpam-676	166	1	f	f	PROPN
ejpam-676	166	2	(	(	PUNCT
ejpam-676	166	3	z	z	NOUN
ejpam-676	166	4	)	)	PUNCT
ejpam-676	166	5	)	)	PUNCT
ejpam-676	167	1	′	′	NUM
ejpam-676	168	1	p	p	NOUN
ejpam-676	168	2	≺	≺	NOUN
ejpam-676	168	3	q(z	q(z	PROPN
ejpam-676	168	4	)	)	PUNCT
ejpam-676	168	5	≺	≺	NOUN
ejpam-676	168	6	1	1	NUM
ejpam-676	168	7	+	+	NUM
ejpam-676	168	8	az	az	PROPN
ejpam-676	168	9	1	1	NUM
ejpam-676	168	10	+	+	CCONJ
ejpam-676	168	11	bz	bz	PROPN
ejpam-676	168	12	,	,	PUNCT
ejpam-676	168	13	(	(	PUNCT
ejpam-676	168	14	20	20	NUM
ejpam-676	168	15	)	)	PUNCT
ejpam-676	168	16	m.	m.	NOUN
ejpam-676	168	17	aouf	aouf	PROPN
ejpam-676	168	18	/	/	SYM
ejpam-676	168	19	eur	eur	PROPN
ejpam-676	168	20	.	.	PUNCT
ejpam-676	169	1	j.	j.	PROPN
ejpam-676	169	2	pure	pure	PROPN
ejpam-676	169	3	appl	appl	PROPN
ejpam-676	169	4	.	.	PROPN
ejpam-676	169	5	math	math	PROPN
ejpam-676	169	6	,	,	PUNCT
ejpam-676	169	7	5	5	NUM
ejpam-676	169	8	(	(	PUNCT
ejpam-676	169	9	2012	2012	NUM
ejpam-676	169	10	)	)	PUNCT
ejpam-676	169	11	,	,	PUNCT
ejpam-676	169	12	141	141	NUM
ejpam-676	169	13	-	-	SYM
ejpam-676	169	14	159	159	NUM
ejpam-676	169	15	146	146	NUM
ejpam-676	169	16	where	where	SCONJ
ejpam-676	169	17	the	the	DET
ejpam-676	169	18	function	function	NOUN
ejpam-676	169	19	q	q	NOUN
ejpam-676	169	20	given	give	VERB
ejpam-676	169	21	by	by	ADP
ejpam-676	169	22	q(z	q(z	PROPN
ejpam-676	169	23	)	)	PUNCT
ejpam-676	169	24	=	=	PUNCT
ejpam-676	170	1			PROPN
ejpam-676	170	2			VERB
ejpam-676	170	3			NOUN
ejpam-676	170	4	a	a	DET
ejpam-676	170	5	b	b	NOUN
ejpam-676	170	6	+	+	CCONJ
ejpam-676	170	7	(	(	PUNCT
ejpam-676	170	8	1−	1−	NUM
ejpam-676	170	9	a	a	DET
ejpam-676	170	10	b	b	NOUN
ejpam-676	170	11	)	)	PUNCT
ejpam-676	170	12	(	(	PUNCT
ejpam-676	170	13	1	1	NUM
ejpam-676	170	14	+	+	NUM
ejpam-676	170	15	bz)−1	bz)−1	NOUN
ejpam-676	170	16	2f1(1,1	2f1(1,1	NUM
ejpam-676	170	17	;	;	PUNCT
ejpam-676	170	18	α1	α1	PROPN
ejpam-676	170	19	λ(p+m	λ(p+m	NOUN
ejpam-676	170	20	)	)	PUNCT
ejpam-676	170	21	+	+	CCONJ
ejpam-676	170	22	1	1	NUM
ejpam-676	170	23	;	;	PUNCT
ejpam-676	170	24	bz	bz	PROPN
ejpam-676	170	25	1+bz	1+bz	NUM
ejpam-676	170	26	)	)	PUNCT
ejpam-676	170	27	(	(	PUNCT
ejpam-676	170	28	b	b	X
ejpam-676	170	29	6=	6=	NUM
ejpam-676	170	30	0	0	NUM
ejpam-676	170	31	)	)	PUNCT
ejpam-676	170	32	1	1	NUM
ejpam-676	170	33	+	+	CCONJ
ejpam-676	170	34	α1a	α1a	PROPN
ejpam-676	170	35	λ(p+m)+α1	λ(p+m)+α1	PROPN
ejpam-676	170	36	z	z	NOUN
ejpam-676	170	37	(	(	PUNCT
ejpam-676	170	38	b	b	NOUN
ejpam-676	170	39	=	=	SYM
ejpam-676	170	40	0	0	NUM
ejpam-676	170	41	)	)	PUNCT
ejpam-676	170	42	is	be	AUX
ejpam-676	170	43	the	the	DET
ejpam-676	170	44	best	good	ADJ
ejpam-676	170	45	dominant	dominant	NOUN
ejpam-676	170	46	of	of	ADP
ejpam-676	170	47	(	(	PUNCT
ejpam-676	170	48	20	20	NUM
ejpam-676	170	49	)	)	PUNCT
ejpam-676	170	50	.	.	PUNCT
ejpam-676	171	1	furthermore	furthermore	ADV
ejpam-676	171	2	,	,	PUNCT
ejpam-676	171	3	re	re	X
ejpam-676	171	4	(	(	PUNCT
ejpam-676	171	5	−zp+1(hp	−zp+1(hp	PROPN
ejpam-676	171	6	,	,	PUNCT
ejpam-676	171	7	q	q	NOUN
ejpam-676	171	8	,	,	PUNCT
ejpam-676	171	9	s(α1	s(α1	NOUN
ejpam-676	171	10	)	)	PUNCT
ejpam-676	171	11	f	f	PROPN
ejpam-676	171	12	(	(	PUNCT
ejpam-676	171	13	z	z	NOUN
ejpam-676	171	14	)	)	PUNCT
ejpam-676	171	15	)	)	PUNCT
ejpam-676	172	1	′	′	NUM
ejpam-676	172	2	p	p	NOUN
ejpam-676	172	3	)	)	PUNCT
ejpam-676	172	4	>	>	X
ejpam-676	173	1	ξ	ξ	X
ejpam-676	173	2	(	(	PUNCT
ejpam-676	173	3	z	z	NOUN
ejpam-676	173	4	∈	∈	PROPN
ejpam-676	173	5	u	u	NOUN
ejpam-676	173	6	)	)	PUNCT
ejpam-676	173	7	,	,	PUNCT
ejpam-676	173	8	(	(	PUNCT
ejpam-676	173	9	21	21	NUM
ejpam-676	173	10	)	)	PUNCT
ejpam-676	173	11	where	where	SCONJ
ejpam-676	173	12	ξ	ξ	X
ejpam-676	173	13	=	=	SYM
ejpam-676	173	14			PROPN
ejpam-676	173	15			PROPN
ejpam-676	173	16			NOUN
ejpam-676	173	17	a	a	DET
ejpam-676	173	18	b	b	NOUN
ejpam-676	173	19	+	+	CCONJ
ejpam-676	173	20	(	(	PUNCT
ejpam-676	173	21	1−	1−	NUM
ejpam-676	173	22	a	a	DET
ejpam-676	173	23	b	b	NOUN
ejpam-676	173	24	)	)	PUNCT
ejpam-676	173	25	(	(	PUNCT
ejpam-676	173	26	1−	1−	NUM
ejpam-676	173	27	b)−1	b)−1	NOUN
ejpam-676	173	28	2f1(1,1	2f1(1,1	NUM
ejpam-676	173	29	;	;	PUNCT
ejpam-676	173	30	α1	α1	PROPN
ejpam-676	173	31	λ(p+m	λ(p+m	NOUN
ejpam-676	173	32	)	)	PUNCT
ejpam-676	173	33	+	+	CCONJ
ejpam-676	173	34	1	1	NUM
ejpam-676	173	35	;	;	PUNCT
ejpam-676	173	36	b	b	X
ejpam-676	173	37	b−1	b−1	PROPN
ejpam-676	173	38	)	)	PUNCT
ejpam-676	173	39	(	(	PUNCT
ejpam-676	173	40	b	b	X
ejpam-676	173	41	6=	6=	NUM
ejpam-676	173	42	0	0	NUM
ejpam-676	173	43	)	)	PUNCT
ejpam-676	173	44	1−	1−	NUM
ejpam-676	174	1	α1a	α1a	ADV
ejpam-676	174	2	λ(p+m)+α1	λ(p+m)+α1	PROPN
ejpam-676	174	3	(	(	PUNCT
ejpam-676	174	4	b	b	NOUN
ejpam-676	174	5	=	=	NOUN
ejpam-676	174	6	0	0	NUM
ejpam-676	174	7	)	)	PUNCT
ejpam-676	174	8	.	.	PUNCT
ejpam-676	175	1	the	the	DET
ejpam-676	175	2	estimate	estimate	NOUN
ejpam-676	175	3	in	in	ADP
ejpam-676	175	4	(	(	PUNCT
ejpam-676	175	5	21	21	NUM
ejpam-676	175	6	)	)	PUNCT
ejpam-676	175	7	is	be	AUX
ejpam-676	175	8	the	the	DET
ejpam-676	175	9	best	good	ADJ
ejpam-676	175	10	possible	possible	ADJ
ejpam-676	175	11	.	.	PUNCT
ejpam-676	176	1	proof	proof	NOUN
ejpam-676	176	2	.	.	PUNCT
ejpam-676	177	1	consider	consider	VERB
ejpam-676	177	2	the	the	DET
ejpam-676	177	3	function	function	NOUN
ejpam-676	177	4	ϕ	ϕ	NOUN
ejpam-676	177	5	defined	define	VERB
ejpam-676	177	6	by	by	ADP
ejpam-676	177	7	ϕ(z	ϕ(z	NOUN
ejpam-676	177	8	)	)	PUNCT
ejpam-676	178	1	=	=	SYM
ejpam-676	178	2	−zp+1(hp	−zp+1(hp	PROPN
ejpam-676	178	3	,	,	PUNCT
ejpam-676	178	4	q	q	NOUN
ejpam-676	178	5	,	,	PUNCT
ejpam-676	178	6	s(α1	s(α1	NOUN
ejpam-676	178	7	)	)	PUNCT
ejpam-676	178	8	f	f	PROPN
ejpam-676	178	9	(	(	PUNCT
ejpam-676	178	10	z	z	NOUN
ejpam-676	178	11	)	)	PUNCT
ejpam-676	178	12	)	)	PUNCT
ejpam-676	179	1	′	′	NUM
ejpam-676	180	1	p	p	X
ejpam-676	180	2	(	(	PUNCT
ejpam-676	180	3	z	z	NOUN
ejpam-676	180	4	∈	∈	PROPN
ejpam-676	180	5	u	u	NOUN
ejpam-676	180	6	)	)	PUNCT
ejpam-676	180	7	.	.	PUNCT
ejpam-676	181	1	(	(	PUNCT
ejpam-676	181	2	22	22	NUM
ejpam-676	181	3	)	)	PUNCT
ejpam-676	181	4	then	then	ADV
ejpam-676	181	5	ϕ	ϕ	PROPN
ejpam-676	181	6	is	be	AUX
ejpam-676	181	7	of	of	ADP
ejpam-676	181	8	the	the	DET
ejpam-676	181	9	form	form	NOUN
ejpam-676	181	10	(	(	PUNCT
ejpam-676	181	11	13	13	NUM
ejpam-676	181	12	)	)	PUNCT
ejpam-676	181	13	and	and	CCONJ
ejpam-676	181	14	is	be	AUX
ejpam-676	181	15	analytic	analytic	ADJ
ejpam-676	181	16	in	in	ADP
ejpam-676	181	17	u	u	PROPN
ejpam-676	181	18	.	.	PUNCT
ejpam-676	182	1	differentiating	differentiate	VERB
ejpam-676	182	2	(	(	PUNCT
ejpam-676	182	3	22	22	NUM
ejpam-676	182	4	)	)	PUNCT
ejpam-676	182	5	with	with	ADP
ejpam-676	182	6	respect	respect	NOUN
ejpam-676	182	7	to	to	ADP
ejpam-676	182	8	z	z	NOUN
ejpam-676	182	9	and	and	CCONJ
ejpam-676	182	10	using	use	VERB
ejpam-676	182	11	(	(	PUNCT
ejpam-676	182	12	10	10	NUM
ejpam-676	182	13	)	)	PUNCT
ejpam-676	182	14	,	,	PUNCT
ejpam-676	182	15	we	we	PRON
ejpam-676	182	16	obtain	obtain	VERB
ejpam-676	182	17	−	−	PROPN
ejpam-676	182	18	(	(	PUNCT
ejpam-676	182	19	1−λ)z	1−λ)z	NUM
ejpam-676	182	20	p+1(hp	p+1(hp	VERB
ejpam-676	182	21	,	,	PUNCT
ejpam-676	182	22	q	q	NOUN
ejpam-676	182	23	,	,	PUNCT
ejpam-676	182	24	s(α1	s(α1	NOUN
ejpam-676	182	25	)	)	PUNCT
ejpam-676	183	1	f	f	PROPN
ejpam-676	183	2	(	(	PUNCT
ejpam-676	183	3	z	z	NOUN
ejpam-676	183	4	)	)	PUNCT
ejpam-676	183	5	)	)	PUNCT
ejpam-676	184	1	′	′	NUM
ejpam-676	185	1	+	+	PUNCT
ejpam-676	185	2	λzp+1(hp	λzp+1(hp	PROPN
ejpam-676	185	3	,	,	PUNCT
ejpam-676	185	4	q	q	NOUN
ejpam-676	185	5	,	,	PUNCT
ejpam-676	185	6	s(α1	s(α1	NOUN
ejpam-676	185	7	)	)	PUNCT
ejpam-676	185	8	f	f	PROPN
ejpam-676	185	9	(	(	PUNCT
ejpam-676	185	10	z	z	NOUN
ejpam-676	185	11	)	)	PUNCT
ejpam-676	185	12	)	)	PUNCT
ejpam-676	186	1	′	′	NUM
ejpam-676	187	1	p	p	NOUN
ejpam-676	187	2	=	=	PUNCT
ejpam-676	187	3	ϕ(z	ϕ(z	PROPN
ejpam-676	187	4	)	)	PUNCT
ejpam-676	188	1	+	+	NUM
ejpam-676	188	2	λ	λ	PROPN
ejpam-676	188	3	α1	α1	PROPN
ejpam-676	188	4	zϕ	zϕ	INTJ
ejpam-676	188	5	′	′	NUM
ejpam-676	189	1	(	(	PUNCT
ejpam-676	189	2	z)≺	z)≺	PROPN
ejpam-676	189	3	1	1	NUM
ejpam-676	189	4	+	+	NUM
ejpam-676	189	5	az	az	PROPN
ejpam-676	189	6	1	1	NUM
ejpam-676	189	7	+	+	CCONJ
ejpam-676	189	8	bz	bz	PROPN
ejpam-676	189	9	(	(	PUNCT
ejpam-676	189	10	z	z	NOUN
ejpam-676	189	11	∈	∈	PROPN
ejpam-676	189	12	u	u	NOUN
ejpam-676	189	13	)	)	PUNCT
ejpam-676	189	14	.	.	PUNCT
ejpam-676	190	1	now	now	ADV
ejpam-676	190	2	,	,	PUNCT
ejpam-676	190	3	by	by	ADP
ejpam-676	190	4	using	use	VERB
ejpam-676	190	5	lemma	lemma	PROPN
ejpam-676	190	6	1	1	NUM
ejpam-676	190	7	for	for	ADP
ejpam-676	190	8	β	β	X
ejpam-676	190	9	=	=	SYM
ejpam-676	190	10	α1	α1	PROPN
ejpam-676	190	11	λ	λ	PROPN
ejpam-676	190	12	,	,	PUNCT
ejpam-676	190	13	we	we	PRON
ejpam-676	190	14	obtain	obtain	VERB
ejpam-676	190	15	−zp+1(hp	−zp+1(hp	ADJ
ejpam-676	190	16	,	,	PUNCT
ejpam-676	190	17	q	q	NOUN
ejpam-676	190	18	,	,	PUNCT
ejpam-676	190	19	s(α1	s(α1	NOUN
ejpam-676	190	20	)	)	PUNCT
ejpam-676	191	1	f	f	PROPN
ejpam-676	191	2	(	(	PUNCT
ejpam-676	191	3	z	z	NOUN
ejpam-676	191	4	)	)	PUNCT
ejpam-676	191	5	)	)	PUNCT
ejpam-676	192	1	′	′	NUM
ejpam-676	193	1	p	p	NOUN
ejpam-676	193	2	≺	≺	NOUN
ejpam-676	193	3	q(z	q(z	PROPN
ejpam-676	193	4	)	)	PUNCT
ejpam-676	193	5	=	=	SYM
ejpam-676	193	6	α1	α1	PROPN
ejpam-676	193	7	λ(p+m	λ(p+m	NOUN
ejpam-676	193	8	)	)	PUNCT
ejpam-676	194	1	z	z	NOUN
ejpam-676	194	2	−	−	PROPN
ejpam-676	194	3	α1	α1	PROPN
ejpam-676	194	4	λ(p+m	λ(p+m	NOUN
ejpam-676	194	5	)	)	PUNCT
ejpam-676	194	6	z	z	NOUN
ejpam-676	194	7	∫	∫	PROPN
ejpam-676	194	8	0	0	NUM
ejpam-676	194	9	t	t	PROPN
ejpam-676	194	10	α1	α1	PROPN
ejpam-676	194	11	λ(p+m	λ(p+m	NOUN
ejpam-676	194	12	)	)	PUNCT
ejpam-676	194	13	−1	−1	NOUN
ejpam-676	194	14	�	�	PROPN
ejpam-676	194	15	1+at	1+at	NUM
ejpam-676	194	16	1	1	NUM
ejpam-676	194	17	+	+	NUM
ejpam-676	194	18	bt	bt	PROPN
ejpam-676	194	19	�	�	PROPN
ejpam-676	194	20	d	d	PROPN
ejpam-676	194	21	t	t	PROPN
ejpam-676	194	22	=	=	PUNCT
ejpam-676	194	23			PROPN
ejpam-676	194	24			PROPN
ejpam-676	194	25			NOUN
ejpam-676	194	26	a	a	DET
ejpam-676	194	27	b	b	NOUN
ejpam-676	194	28	+	+	CCONJ
ejpam-676	194	29	(	(	PUNCT
ejpam-676	194	30	1−	1−	NUM
ejpam-676	194	31	a	a	DET
ejpam-676	194	32	b	b	NOUN
ejpam-676	194	33	)	)	PUNCT
ejpam-676	194	34	(	(	PUNCT
ejpam-676	194	35	1	1	NUM
ejpam-676	194	36	+	+	NUM
ejpam-676	194	37	bz)−1	bz)−1	NOUN
ejpam-676	194	38	2f1(1,1	2f1(1,1	NUM
ejpam-676	194	39	;	;	PUNCT
ejpam-676	194	40	α1	α1	PROPN
ejpam-676	194	41	λ(p+m	λ(p+m	NOUN
ejpam-676	194	42	)	)	PUNCT
ejpam-676	194	43	+	+	CCONJ
ejpam-676	194	44	1	1	NUM
ejpam-676	194	45	;	;	PUNCT
ejpam-676	194	46	bz	bz	PROPN
ejpam-676	194	47	1+bz	1+bz	NUM
ejpam-676	194	48	)	)	PUNCT
ejpam-676	194	49	(	(	PUNCT
ejpam-676	194	50	b	b	X
ejpam-676	194	51	6=	6=	NUM
ejpam-676	194	52	0	0	NUM
ejpam-676	194	53	)	)	PUNCT
ejpam-676	194	54	1	1	NUM
ejpam-676	194	55	+	+	CCONJ
ejpam-676	194	56	α1a	α1a	PROPN
ejpam-676	194	57	λ(p+m)+α1	λ(p+m)+α1	PROPN
ejpam-676	194	58	z	z	NOUN
ejpam-676	194	59	(	(	PUNCT
ejpam-676	194	60	b	b	NOUN
ejpam-676	194	61	=	=	NOUN
ejpam-676	194	62	0	0	NUM
ejpam-676	194	63	)	)	PUNCT
ejpam-676	194	64	,	,	PUNCT
ejpam-676	194	65	m.	m.	PROPN
ejpam-676	194	66	aouf	aouf	PROPN
ejpam-676	194	67	/	/	SYM
ejpam-676	194	68	eur	eur	PROPN
ejpam-676	194	69	.	.	PUNCT
ejpam-676	195	1	j.	j.	PROPN
ejpam-676	195	2	pure	pure	PROPN
ejpam-676	195	3	appl	appl	PROPN
ejpam-676	195	4	.	.	PROPN
ejpam-676	195	5	math	math	PROPN
ejpam-676	195	6	,	,	PUNCT
ejpam-676	195	7	5	5	NUM
ejpam-676	195	8	(	(	PUNCT
ejpam-676	195	9	2012	2012	NUM
ejpam-676	195	10	)	)	PUNCT
ejpam-676	195	11	,	,	PUNCT
ejpam-676	195	12	141	141	NUM
ejpam-676	195	13	-	-	SYM
ejpam-676	195	14	159	159	NUM
ejpam-676	195	15	147	147	NUM
ejpam-676	195	16	by	by	ADP
ejpam-676	195	17	change	change	NOUN
ejpam-676	195	18	of	of	ADP
ejpam-676	195	19	variables	variable	NOUN
ejpam-676	195	20	followed	follow	VERB
ejpam-676	195	21	by	by	ADP
ejpam-676	195	22	the	the	DET
ejpam-676	195	23	use	use	NOUN
ejpam-676	195	24	of	of	ADP
ejpam-676	195	25	the	the	DET
ejpam-676	195	26	identities	identity	NOUN
ejpam-676	195	27	(	(	PUNCT
ejpam-676	195	28	16	16	NUM
ejpam-676	195	29	)	)	PUNCT
ejpam-676	195	30	,	,	PUNCT
ejpam-676	195	31	(	(	PUNCT
ejpam-676	195	32	17	17	NUM
ejpam-676	195	33	)	)	PUNCT
ejpam-676	195	34	and	and	CCONJ
ejpam-676	195	35	(	(	PUNCT
ejpam-676	195	36	18	18	NUM
ejpam-676	195	37	)	)	PUNCT
ejpam-676	195	38	(	(	PUNCT
ejpam-676	195	39	with	with	ADP
ejpam-676	195	40	a	a	DET
ejpam-676	195	41	=	=	SYM
ejpam-676	195	42	1	1	NUM
ejpam-676	195	43	,	,	PUNCT
ejpam-676	195	44	c	c	NOUN
ejpam-676	195	45	=	=	PUNCT
ejpam-676	195	46	b+	b+	PUNCT
ejpam-676	195	47	1	1	NUM
ejpam-676	195	48	,	,	PUNCT
ejpam-676	195	49	b	b	X
ejpam-676	195	50	=	=	SYM
ejpam-676	195	51	α1	α1	PROPN
ejpam-676	195	52	λ(p+m	λ(p+m	NOUN
ejpam-676	195	53	)	)	PUNCT
ejpam-676	195	54	)	)	PUNCT
ejpam-676	195	55	.	.	PUNCT
ejpam-676	196	1	this	this	PRON
ejpam-676	196	2	proves	prove	VERB
ejpam-676	196	3	the	the	DET
ejpam-676	196	4	assertion	assertion	NOUN
ejpam-676	196	5	(	(	PUNCT
ejpam-676	196	6	20	20	NUM
ejpam-676	196	7	)	)	PUNCT
ejpam-676	196	8	of	of	ADP
ejpam-676	196	9	theorem	theorem	NOUN
ejpam-676	196	10	1	1	NUM
ejpam-676	196	11	.	.	PUNCT
ejpam-676	197	1	next	next	ADV
ejpam-676	197	2	,	,	PUNCT
ejpam-676	197	3	in	in	ADP
ejpam-676	197	4	order	order	NOUN
ejpam-676	197	5	to	to	PART
ejpam-676	197	6	prove	prove	VERB
ejpam-676	197	7	the	the	DET
ejpam-676	197	8	assertion	assertion	NOUN
ejpam-676	197	9	(	(	PUNCT
ejpam-676	197	10	21	21	NUM
ejpam-676	197	11	)	)	PUNCT
ejpam-676	197	12	of	of	ADP
ejpam-676	197	13	theorem	theorem	NOUN
ejpam-676	197	14	1	1	NUM
ejpam-676	197	15	,	,	PUNCT
ejpam-676	197	16	it	it	PRON
ejpam-676	197	17	suffices	suffice	VERB
ejpam-676	197	18	to	to	PART
ejpam-676	197	19	show	show	VERB
ejpam-676	197	20	that	that	DET
ejpam-676	197	21	inf	inf	PROPN
ejpam-676	197	22	|z|<1	|z|<1	X
ejpam-676	197	23	{	{	PUNCT
ejpam-676	197	24	re(q(z))}=	re(q(z))}=	PROPN
ejpam-676	197	25	q(−1	q(−1	NOUN
ejpam-676	197	26	)	)	PUNCT
ejpam-676	197	27	.	.	PUNCT
ejpam-676	198	1	(	(	PUNCT
ejpam-676	198	2	23	23	NUM
ejpam-676	198	3	)	)	PUNCT
ejpam-676	198	4	indeed	indeed	ADV
ejpam-676	198	5	we	we	PRON
ejpam-676	198	6	have	have	VERB
ejpam-676	198	7	,	,	PUNCT
ejpam-676	198	8	for	for	ADP
ejpam-676	198	9	|z|	|z|	NOUN
ejpam-676	198	10	≤	≤	NUM
ejpam-676	198	11	r	r	NOUN
ejpam-676	198	12	<	<	X
ejpam-676	198	13	1	1	NUM
ejpam-676	198	14	,	,	PUNCT
ejpam-676	198	15	re	re	VERB
ejpam-676	198	16	�	�	PROPN
ejpam-676	198	17	1	1	NUM
ejpam-676	198	18	+	+	NUM
ejpam-676	198	19	az	az	PROPN
ejpam-676	198	20	1	1	NUM
ejpam-676	198	21	+	+	CCONJ
ejpam-676	198	22	bz	bz	PROPN
ejpam-676	198	23	�	�	PROPN
ejpam-676	198	24	≥	≥	NUM
ejpam-676	198	25	1−	1−	NUM
ejpam-676	198	26	ar	ar	PROPN
ejpam-676	198	27	1−	1−	NUM
ejpam-676	198	28	br	br	NOUN
ejpam-676	198	29	.	.	PUNCT
ejpam-676	199	1	upon	upon	SCONJ
ejpam-676	199	2	setting	set	VERB
ejpam-676	199	3	g(ζ	g(ζ	PROPN
ejpam-676	199	4	,	,	PUNCT
ejpam-676	199	5	z	z	NOUN
ejpam-676	199	6	)	)	PUNCT
ejpam-676	199	7	=	=	SYM
ejpam-676	199	8	1	1	NUM
ejpam-676	199	9	+	+	NUM
ejpam-676	199	10	aζz	aζz	NOUN
ejpam-676	199	11	1	1	NUM
ejpam-676	199	12	+	+	NUM
ejpam-676	199	13	bζz	bζz	NOUN
ejpam-676	199	14	and	and	CCONJ
ejpam-676	199	15	dν(ζ	dν(ζ	NOUN
ejpam-676	199	16	)	)	PUNCT
ejpam-676	200	1	=	=	SYM
ejpam-676	200	2	α1	α1	PROPN
ejpam-676	200	3	λ(p+m	λ(p+m	NOUN
ejpam-676	200	4	)	)	PUNCT
ejpam-676	200	5	ζ	ζ	PROPN
ejpam-676	200	6	α1	α1	PROPN
ejpam-676	200	7	λ(p+m	λ(p+m	NOUN
ejpam-676	200	8	)	)	PUNCT
ejpam-676	200	9	−1	−1	NOUN
ejpam-676	200	10	dζ	dζ	PROPN
ejpam-676	200	11	(	(	PUNCT
ejpam-676	200	12	0≤	0≤	PROPN
ejpam-676	200	13	ζ≤	ζ≤	ADJ
ejpam-676	200	14	1	1	NUM
ejpam-676	200	15	)	)	PUNCT
ejpam-676	200	16	,	,	PUNCT
ejpam-676	200	17	which	which	PRON
ejpam-676	200	18	is	be	AUX
ejpam-676	200	19	a	a	DET
ejpam-676	200	20	positive	positive	ADJ
ejpam-676	200	21	measure	measure	NOUN
ejpam-676	200	22	on	on	ADP
ejpam-676	200	23	the	the	DET
ejpam-676	200	24	closed	closed	ADJ
ejpam-676	200	25	interval	interval	NOUN
ejpam-676	200	26	[	[	X
ejpam-676	200	27	0,1	0,1	NUM
ejpam-676	200	28	]	]	PUNCT
ejpam-676	200	29	,	,	PUNCT
ejpam-676	200	30	we	we	PRON
ejpam-676	200	31	get	get	VERB
ejpam-676	200	32	q(z	q(z	PROPN
ejpam-676	200	33	)	)	PUNCT
ejpam-676	200	34	=	=	SYM
ejpam-676	200	35	1	1	NUM
ejpam-676	200	36	∫	∫	NOUN
ejpam-676	200	37	0	0	NUM
ejpam-676	200	38	g(ζ	g(ζ	PROPN
ejpam-676	200	39	,	,	PUNCT
ejpam-676	200	40	z)dν(ζ	z)dν(ζ	NUM
ejpam-676	200	41	)	)	PUNCT
ejpam-676	200	42	,	,	PUNCT
ejpam-676	200	43	so	so	SCONJ
ejpam-676	200	44	that	that	SCONJ
ejpam-676	200	45	re	re	ADP
ejpam-676	200	46	{	{	PUNCT
ejpam-676	200	47	q(z	q(z	PROPN
ejpam-676	200	48	)	)	PUNCT
ejpam-676	200	49	}	}	PUNCT
ejpam-676	200	50	≥	≥	NOUN
ejpam-676	200	51	1	1	NUM
ejpam-676	200	52	∫	∫	NOUN
ejpam-676	200	53	0	0	PROPN
ejpam-676	200	54	�	�	PROPN
ejpam-676	200	55	1−	1−	NUM
ejpam-676	200	56	aζr	aζr	PROPN
ejpam-676	200	57	1−	1−	NUM
ejpam-676	200	58	bζr	bζr	PROPN
ejpam-676	200	59	�	�	PROPN
ejpam-676	200	60	dν(ζ	dν(ζ	NOUN
ejpam-676	200	61	)	)	PUNCT
ejpam-676	200	62	=	=	SYM
ejpam-676	200	63	q(−r	q(−r	X
ejpam-676	200	64	)	)	PUNCT
ejpam-676	200	65	(	(	PUNCT
ejpam-676	200	66	|z|	|z|	VERB
ejpam-676	200	67	≤	≤	NUM
ejpam-676	201	1	r	r	NOUN
ejpam-676	201	2	<	<	X
ejpam-676	201	3	1	1	NUM
ejpam-676	201	4	)	)	PUNCT
ejpam-676	201	5	.	.	PUNCT
ejpam-676	202	1	letting	let	VERB
ejpam-676	202	2	r	r	PRON
ejpam-676	202	3	→	→	SYM
ejpam-676	202	4	1−	1−	NUM
ejpam-676	202	5	in	in	ADP
ejpam-676	202	6	the	the	DET
ejpam-676	202	7	above	above	ADJ
ejpam-676	202	8	inequality	inequality	NOUN
ejpam-676	202	9	,	,	PUNCT
ejpam-676	202	10	we	we	PRON
ejpam-676	202	11	obtain	obtain	VERB
ejpam-676	202	12	the	the	DET
ejpam-676	202	13	assertion	assertion	NOUN
ejpam-676	202	14	(	(	PUNCT
ejpam-676	202	15	21	21	NUM
ejpam-676	202	16	)	)	PUNCT
ejpam-676	202	17	of	of	ADP
ejpam-676	202	18	theorem	theorem	NOUN
ejpam-676	202	19	1	1	NUM
ejpam-676	202	20	.	.	PUNCT
ejpam-676	203	1	finally	finally	ADV
ejpam-676	203	2	,	,	PUNCT
ejpam-676	203	3	the	the	DET
ejpam-676	203	4	estimate	estimate	NOUN
ejpam-676	203	5	in	in	ADP
ejpam-676	203	6	(	(	PUNCT
ejpam-676	203	7	21	21	NUM
ejpam-676	203	8	)	)	PUNCT
ejpam-676	203	9	is	be	AUX
ejpam-676	203	10	the	the	DET
ejpam-676	203	11	best	good	ADJ
ejpam-676	203	12	possible	possible	ADJ
ejpam-676	203	13	as	as	ADP
ejpam-676	203	14	the	the	DET
ejpam-676	203	15	function	function	NOUN
ejpam-676	203	16	q	q	NOUN
ejpam-676	203	17	is	be	AUX
ejpam-676	203	18	the	the	DET
ejpam-676	203	19	best	good	ADJ
ejpam-676	203	20	dominant	dominant	NOUN
ejpam-676	203	21	of	of	ADP
ejpam-676	203	22	(	(	PUNCT
ejpam-676	203	23	20	20	NUM
ejpam-676	203	24	)	)	PUNCT
ejpam-676	203	25	.	.	PUNCT
ejpam-676	204	1	taking	take	VERB
ejpam-676	204	2	λ	λ	PROPN
ejpam-676	204	3	=	=	SYM
ejpam-676	204	4	1	1	NUM
ejpam-676	204	5	,	,	PUNCT
ejpam-676	204	6	a=	a=	PROPN
ejpam-676	205	1	1−	1−	NUM
ejpam-676	205	2	2σ	2σ	NOUN
ejpam-676	206	1	p	p	X
ejpam-676	206	2	(	(	PUNCT
ejpam-676	206	3	0	0	NUM
ejpam-676	206	4	≤	≤	NUM
ejpam-676	206	5	σ	σ	NOUN
ejpam-676	206	6	<	<	X
ejpam-676	206	7	p	p	X
ejpam-676	206	8	)	)	PUNCT
ejpam-676	206	9	and	and	CCONJ
ejpam-676	206	10	b	b	X
ejpam-676	206	11	=	=	SYM
ejpam-676	206	12	−1	−1	NOUN
ejpam-676	206	13	in	in	ADP
ejpam-676	206	14	theorem	theorem	NOUN
ejpam-676	206	15	1	1	NUM
ejpam-676	206	16	,	,	PUNCT
ejpam-676	206	17	we	we	PRON
ejpam-676	206	18	obtain	obtain	VERB
ejpam-676	206	19	the	the	DET
ejpam-676	206	20	following	follow	VERB
ejpam-676	206	21	corollary	corollary	NOUN
ejpam-676	206	22	.	.	PUNCT
ejpam-676	207	1	corollary	corollary	ADJ
ejpam-676	207	2	1	1	NUM
ejpam-676	207	3	.	.	PUNCT
ejpam-676	208	1	the	the	DET
ejpam-676	208	2	following	follow	VERB
ejpam-676	208	3	inclusion	inclusion	NOUN
ejpam-676	208	4	property	property	NOUN
ejpam-676	208	5	holds	hold	VERB
ejpam-676	208	6	true	true	ADJ
ejpam-676	208	7	for	for	ADP
ejpam-676	208	8	the	the	DET
ejpam-676	208	9	function	function	NOUN
ejpam-676	208	10	class	class	NOUN
ejpam-676	208	11	σm	σm	X
ejpam-676	208	12	p	p	X
ejpam-676	208	13	,	,	PUNCT
ejpam-676	208	14	q	q	X
ejpam-676	208	15	,	,	PUNCT
ejpam-676	208	16	s(α1;σ	s(α1;σ	VERB
ejpam-676	208	17	):	):	PUNCT
ejpam-676	208	18	σm	σm	X
ejpam-676	208	19	p	p	X
ejpam-676	208	20	,	,	PUNCT
ejpam-676	208	21	q	q	NOUN
ejpam-676	208	22	,	,	PUNCT
ejpam-676	208	23	s(α1	s(α1	NOUN
ejpam-676	209	1	+	+	CCONJ
ejpam-676	209	2	1;σ)⊂	1;σ)⊂	NUM
ejpam-676	209	3	σm	σm	ADP
ejpam-676	209	4	p	p	X
ejpam-676	209	5	,	,	PUNCT
ejpam-676	209	6	q	q	NOUN
ejpam-676	209	7	,	,	PUNCT
ejpam-676	209	8	s(α1;β(p	s(α1;β(p	NOUN
ejpam-676	209	9	,	,	PUNCT
ejpam-676	209	10	m	m	PRON
ejpam-676	209	11	,	,	PUNCT
ejpam-676	209	12	α1,σ))⊂	α1,σ))⊂	NUM
ejpam-676	209	13	σm	σm	ADP
ejpam-676	210	1	p	p	X
ejpam-676	210	2	,	,	PUNCT
ejpam-676	210	3	q	q	ADJ
ejpam-676	210	4	,	,	PUNCT
ejpam-676	210	5	s(α1;σ	s(α1;σ	NOUN
ejpam-676	210	6	)	)	PUNCT
ejpam-676	210	7	,	,	PUNCT
ejpam-676	210	8	where	where	SCONJ
ejpam-676	210	9	β(p	β(p	PROPN
ejpam-676	210	10	,	,	PUNCT
ejpam-676	210	11	m	m	PROPN
ejpam-676	210	12	,	,	PUNCT
ejpam-676	210	13	α1,σ	α1,σ	PROPN
ejpam-676	210	14	)	)	PUNCT
ejpam-676	210	15	=	=	SYM
ejpam-676	210	16	σ+	σ+	X
ejpam-676	210	17	(	(	PUNCT
ejpam-676	210	18	p−σ	p−σ	PROPN
ejpam-676	210	19	)	)	PUNCT
ejpam-676	210	20	�	�	PROPN
ejpam-676	210	21	2f1(1,1	2f1(1,1	NUM
ejpam-676	210	22	;	;	PUNCT
ejpam-676	210	23	α1	α1	PROPN
ejpam-676	210	24	p+m	p+m	NOUN
ejpam-676	210	25	+	+	CCONJ
ejpam-676	210	26	1	1	NUM
ejpam-676	210	27	;	;	PUNCT
ejpam-676	210	28	1	1	NUM
ejpam-676	210	29	2	2	NUM
ejpam-676	210	30	)	)	PUNCT
ejpam-676	210	31	−	−	PROPN
ejpam-676	210	32	1	1	NUM
ejpam-676	210	33	�	�	PROPN
ejpam-676	210	34	.	.	PUNCT
ejpam-676	211	1	the	the	DET
ejpam-676	211	2	result	result	NOUN
ejpam-676	211	3	is	be	AUX
ejpam-676	211	4	the	the	DET
ejpam-676	211	5	best	good	ADJ
ejpam-676	211	6	possible	possible	ADJ
ejpam-676	211	7	.	.	PUNCT
ejpam-676	212	1	taking	take	VERB
ejpam-676	212	2	λ=	λ=	NOUN
ejpam-676	212	3	1	1	NUM
ejpam-676	212	4	and	and	CCONJ
ejpam-676	212	5	m=	m=	X
ejpam-676	212	6	1−	1−	NUM
ejpam-676	213	1	p	p	X
ejpam-676	213	2	(	(	PUNCT
ejpam-676	213	3	p	p	NOUN
ejpam-676	213	4	∈	∈	PROPN
ejpam-676	213	5	n	n	CCONJ
ejpam-676	213	6	)	)	PUNCT
ejpam-676	213	7	in	in	ADP
ejpam-676	213	8	theorem	theorem	NOUN
ejpam-676	213	9	1	1	NUM
ejpam-676	213	10	,	,	PUNCT
ejpam-676	213	11	we	we	PRON
ejpam-676	213	12	obtain	obtain	VERB
ejpam-676	213	13	the	the	DET
ejpam-676	213	14	following	follow	VERB
ejpam-676	213	15	corollary	corollary	NOUN
ejpam-676	213	16	.	.	PUNCT
ejpam-676	214	1	m.	m.	PROPN
ejpam-676	214	2	aouf	aouf	PROPN
ejpam-676	214	3	/	/	SYM
ejpam-676	214	4	eur	eur	PROPN
ejpam-676	214	5	.	.	PUNCT
ejpam-676	215	1	j.	j.	PROPN
ejpam-676	215	2	pure	pure	PROPN
ejpam-676	215	3	appl	appl	PROPN
ejpam-676	215	4	.	.	PROPN
ejpam-676	215	5	math	math	PROPN
ejpam-676	215	6	,	,	PUNCT
ejpam-676	215	7	5	5	NUM
ejpam-676	215	8	(	(	PUNCT
ejpam-676	215	9	2012	2012	NUM
ejpam-676	215	10	)	)	PUNCT
ejpam-676	215	11	,	,	PUNCT
ejpam-676	215	12	141	141	NUM
ejpam-676	215	13	-	-	SYM
ejpam-676	215	14	159	159	NUM
ejpam-676	215	15	148	148	NUM
ejpam-676	215	16	corollary	corollary	ADJ
ejpam-676	215	17	2	2	NUM
ejpam-676	215	18	.	.	PUNCT
ejpam-676	216	1	the	the	DET
ejpam-676	216	2	following	follow	VERB
ejpam-676	216	3	inclusion	inclusion	NOUN
ejpam-676	216	4	property	property	NOUN
ejpam-676	216	5	holds	hold	VERB
ejpam-676	216	6	true	true	ADJ
ejpam-676	216	7	for	for	ADP
ejpam-676	216	8	the	the	DET
ejpam-676	216	9	function	function	NOUN
ejpam-676	216	10	class	class	NOUN
ejpam-676	216	11	σp	σp	PROPN
ejpam-676	216	12	,	,	PUNCT
ejpam-676	216	13	q	q	NOUN
ejpam-676	216	14	,	,	PUNCT
ejpam-676	216	15	s(α1	s(α1	NOUN
ejpam-676	216	16	;	;	PUNCT
ejpam-676	216	17	a	a	DET
ejpam-676	216	18	,	,	PUNCT
ejpam-676	216	19	b	b	NOUN
ejpam-676	216	20	):	):	PUNCT
ejpam-676	216	21	σp	σp	PROPN
ejpam-676	216	22	,	,	PUNCT
ejpam-676	216	23	q	q	NOUN
ejpam-676	216	24	,	,	PUNCT
ejpam-676	216	25	s(α1	s(α1	NOUN
ejpam-676	216	26	+	+	CCONJ
ejpam-676	216	27	1	1	NUM
ejpam-676	216	28	;	;	PUNCT
ejpam-676	216	29	a	a	DET
ejpam-676	216	30	,	,	PUNCT
ejpam-676	216	31	b	b	NOUN
ejpam-676	216	32	)	)	PUNCT
ejpam-676	216	33	⊂	⊂	PROPN
ejpam-676	216	34	σp	σp	PROPN
ejpam-676	216	35	,	,	PUNCT
ejpam-676	216	36	q	q	NOUN
ejpam-676	216	37	,	,	PUNCT
ejpam-676	216	38	s(α1	s(α1	NOUN
ejpam-676	216	39	;	;	PUNCT
ejpam-676	216	40	1−	1−	NUM
ejpam-676	216	41	2σ	2σ	NOUN
ejpam-676	217	1	p	p	X
ejpam-676	217	2	,	,	PUNCT
ejpam-676	217	3	−1)⊂	−1)⊂	PROPN
ejpam-676	217	4	σp	σp	NOUN
ejpam-676	217	5	,	,	PUNCT
ejpam-676	217	6	q	q	NOUN
ejpam-676	217	7	,	,	PUNCT
ejpam-676	217	8	s(α1	s(α1	NOUN
ejpam-676	217	9	;	;	PUNCT
ejpam-676	217	10	a	a	DET
ejpam-676	217	11	,	,	PUNCT
ejpam-676	217	12	b	b	NOUN
ejpam-676	217	13	)	)	PUNCT
ejpam-676	217	14	,	,	PUNCT
ejpam-676	217	15	where	where	SCONJ
ejpam-676	217	16	σ	σ	NOUN
ejpam-676	217	17	=	=	PUNCT
ejpam-676	217	18			PROPN
ejpam-676	217	19			PROPN
ejpam-676	217	20			NOUN
ejpam-676	217	21	a	a	DET
ejpam-676	217	22	b	b	NOUN
ejpam-676	217	23	+	+	CCONJ
ejpam-676	217	24	(	(	PUNCT
ejpam-676	217	25	1−	1−	NUM
ejpam-676	217	26	a	a	DET
ejpam-676	217	27	b	b	NOUN
ejpam-676	217	28	)	)	PUNCT
ejpam-676	217	29	(	(	PUNCT
ejpam-676	217	30	1	1	NUM
ejpam-676	217	31	+	+	NUM
ejpam-676	217	32	b)−1	b)−1	NOUN
ejpam-676	217	33	2f1(1,1;α1	2f1(1,1;α1	NOUN
ejpam-676	217	34	+	+	CCONJ
ejpam-676	217	35	1	1	NUM
ejpam-676	217	36	;	;	PUNCT
ejpam-676	217	37	b	b	X
ejpam-676	217	38	b−1	b−1	PROPN
ejpam-676	217	39	)	)	PUNCT
ejpam-676	217	40	(	(	PUNCT
ejpam-676	217	41	b	b	X
ejpam-676	217	42	6=	6=	NUM
ejpam-676	217	43	0	0	NUM
ejpam-676	217	44	)	)	PUNCT
ejpam-676	217	45	1−	1−	NUM
ejpam-676	218	1	α1a	α1a	NUM
ejpam-676	218	2	1+α1	1+α1	NUM
ejpam-676	218	3	(	(	PUNCT
ejpam-676	218	4	b	b	NOUN
ejpam-676	218	5	=	=	NOUN
ejpam-676	218	6	0	0	NUM
ejpam-676	218	7	)	)	PUNCT
ejpam-676	218	8	.	.	PUNCT
ejpam-676	219	1	the	the	DET
ejpam-676	219	2	result	result	NOUN
ejpam-676	219	3	is	be	AUX
ejpam-676	219	4	the	the	DET
ejpam-676	219	5	best	good	ADJ
ejpam-676	219	6	possible	possible	ADJ
ejpam-676	219	7	.	.	PUNCT
ejpam-676	220	1	remark	remark	NOUN
ejpam-676	220	2	2	2	NUM
ejpam-676	220	3	.	.	PUNCT
ejpam-676	221	1	(	(	PUNCT
ejpam-676	221	2	i	i	NOUN
ejpam-676	221	3	)	)	PUNCT
ejpam-676	221	4	taking	take	VERB
ejpam-676	221	5	λ	λ	X
ejpam-676	221	6	=	=	SYM
ejpam-676	221	7	1	1	NUM
ejpam-676	221	8	,	,	PUNCT
ejpam-676	221	9	q	q	NOUN
ejpam-676	221	10	=	=	SYM
ejpam-676	221	11	2	2	NUM
ejpam-676	221	12	,	,	PUNCT
ejpam-676	221	13	s	s	PART
ejpam-676	221	14	=	=	SYM
ejpam-676	221	15	1	1	NUM
ejpam-676	221	16	,	,	PUNCT
ejpam-676	221	17	α1	α1	PROPN
ejpam-676	221	18	=	=	SYM
ejpam-676	221	19	a	a	NOUN
ejpam-676	221	20	,	,	PUNCT
ejpam-676	222	1	β1	β1	PROPN
ejpam-676	222	2	=	=	PUNCT
ejpam-676	222	3	c	c	PROPN
ejpam-676	222	4	(	(	PUNCT
ejpam-676	222	5	a	a	DET
ejpam-676	222	6	>	>	X
ejpam-676	222	7	0	0	NUM
ejpam-676	222	8	;	;	PUNCT
ejpam-676	222	9	c	c	X
ejpam-676	222	10	>	>	X
ejpam-676	222	11	0	0	NUM
ejpam-676	222	12	)	)	PUNCT
ejpam-676	222	13	and	and	CCONJ
ejpam-676	222	14	α2	α2	NOUN
ejpam-676	222	15	=	=	SYM
ejpam-676	222	16	1	1	NUM
ejpam-676	222	17	in	in	ADP
ejpam-676	222	18	theorem	theorem	NOUN
ejpam-676	222	19	1	1	NUM
ejpam-676	222	20	,	,	PUNCT
ejpam-676	222	21	we	we	PRON
ejpam-676	222	22	obtain	obtain	VERB
ejpam-676	222	23	the	the	DET
ejpam-676	222	24	result	result	NOUN
ejpam-676	222	25	obtained	obtain	VERB
ejpam-676	222	26	by	by	ADP
ejpam-676	222	27	patel	patel	NOUN
ejpam-676	222	28	and	and	CCONJ
ejpam-676	222	29	cho	cho	NOUN
ejpam-676	223	1	[	[	X
ejpam-676	223	2	12	12	NUM
ejpam-676	223	3	,	,	PUNCT
ejpam-676	223	4	theorem	theorem	VERB
ejpam-676	223	5	1	1	NUM
ejpam-676	223	6	]	]	PUNCT
ejpam-676	223	7	;	;	PUNCT
ejpam-676	223	8	(	(	PUNCT
ejpam-676	223	9	ii	ii	NOUN
ejpam-676	223	10	)	)	PUNCT
ejpam-676	223	11	taking	take	VERB
ejpam-676	223	12	m	m	NOUN
ejpam-676	223	13	=	=	NOUN
ejpam-676	223	14	−p+	−p+	NOUN
ejpam-676	223	15	1	1	NUM
ejpam-676	223	16	,	,	PUNCT
ejpam-676	223	17	λ	λ	X
ejpam-676	223	18	=	=	SYM
ejpam-676	223	19	1	1	NUM
ejpam-676	223	20	,	,	PUNCT
ejpam-676	223	21	q	q	NOUN
ejpam-676	223	22	=	=	SYM
ejpam-676	223	23	2	2	NUM
ejpam-676	223	24	,	,	PUNCT
ejpam-676	223	25	s	s	PART
ejpam-676	223	26	=	=	SYM
ejpam-676	223	27	1	1	NUM
ejpam-676	223	28	,	,	PUNCT
ejpam-676	223	29	α1	α1	PROPN
ejpam-676	223	30	=	=	SYM
ejpam-676	223	31	n+	n+	ADP
ejpam-676	223	32	p(n	p(n	PROPN
ejpam-676	223	33	>	>	X
ejpam-676	223	34	−p	−p	NOUN
ejpam-676	223	35	)	)	PUNCT
ejpam-676	223	36	,	,	PUNCT
ejpam-676	223	37	α2	α2	PROPN
ejpam-676	223	38	=	=	SYM
ejpam-676	223	39	β1	β1	PROPN
ejpam-676	224	1	=	=	PUNCT
ejpam-676	224	2	1	1	NUM
ejpam-676	224	3	in	in	ADP
ejpam-676	224	4	theorem	theorem	NOUN
ejpam-676	224	5	1	1	NUM
ejpam-676	224	6	,	,	PUNCT
ejpam-676	224	7	we	we	PRON
ejpam-676	224	8	obtain	obtain	VERB
ejpam-676	224	9	the	the	DET
ejpam-676	224	10	result	result	NOUN
ejpam-676	224	11	obtained	obtain	VERB
ejpam-676	224	12	by	by	ADP
ejpam-676	224	13	patel	patel	NOUN
ejpam-676	224	14	and	and	CCONJ
ejpam-676	224	15	cho	cho	NOUN
ejpam-676	225	1	[	[	X
ejpam-676	225	2	12	12	NUM
ejpam-676	225	3	,	,	PUNCT
ejpam-676	225	4	corollary	corollary	ADJ
ejpam-676	225	5	2	2	NUM
ejpam-676	225	6	]	]	PUNCT
ejpam-676	225	7	which	which	PRON
ejpam-676	225	8	improves	improve	VERB
ejpam-676	225	9	the	the	DET
ejpam-676	225	10	corresponding	corresponding	ADJ
ejpam-676	225	11	result	result	NOUN
ejpam-676	225	12	obtained	obtain	VERB
ejpam-676	225	13	by	by	ADP
ejpam-676	225	14	uralegaddi	uralegaddi	ADJ
ejpam-676	225	15	and	and	CCONJ
ejpam-676	225	16	somanatha	somanatha	NOUN
ejpam-676	226	1	[	[	X
ejpam-676	226	2	17	17	NUM
ejpam-676	226	3	]	]	SYM
ejpam-676	226	4	;	;	PUNCT
ejpam-676	226	5	(	(	PUNCT
ejpam-676	226	6	iii	iii	X
ejpam-676	226	7	)	)	PUNCT
ejpam-676	226	8	taking	take	VERB
ejpam-676	226	9	q	q	NOUN
ejpam-676	226	10	=	=	NUM
ejpam-676	226	11	2	2	NUM
ejpam-676	226	12	,	,	PUNCT
ejpam-676	226	13	s	s	PART
ejpam-676	226	14	=	=	SYM
ejpam-676	226	15	1	1	NUM
ejpam-676	226	16	,	,	PUNCT
ejpam-676	226	17	α1	α1	PROPN
ejpam-676	226	18	=	=	PUNCT
ejpam-676	226	19	a	a	DET
ejpam-676	226	20	>	>	X
ejpam-676	226	21	0	0	NUM
ejpam-676	226	22	,	,	PUNCT
ejpam-676	227	1	β1	β1	PROPN
ejpam-676	227	2	=	=	PUNCT
ejpam-676	227	3	c	c	PROPN
ejpam-676	227	4	>	>	PUNCT
ejpam-676	227	5	0	0	PUNCT
ejpam-676	228	1	and	and	CCONJ
ejpam-676	228	2	α2	α2	ADJ
ejpam-676	228	3	=	=	SYM
ejpam-676	228	4	1	1	NUM
ejpam-676	228	5	in	in	ADP
ejpam-676	228	6	corollary	corollary	ADJ
ejpam-676	228	7	2	2	NUM
ejpam-676	228	8	,	,	PUNCT
ejpam-676	228	9	we	we	PRON
ejpam-676	228	10	obtain	obtain	VERB
ejpam-676	228	11	the	the	DET
ejpam-676	228	12	result	result	NOUN
ejpam-676	228	13	obtained	obtain	VERB
ejpam-676	228	14	by	by	ADP
ejpam-676	228	15	patel	patel	NOUN
ejpam-676	228	16	and	and	CCONJ
ejpam-676	228	17	cho	cho	NOUN
ejpam-676	229	1	[	[	X
ejpam-676	229	2	12	12	NUM
ejpam-676	229	3	,	,	PUNCT
ejpam-676	229	4	corollary	corollary	ADJ
ejpam-676	229	5	1	1	NUM
ejpam-676	229	6	]	]	PUNCT
ejpam-676	229	7	.	.	PUNCT
ejpam-676	230	1	theorem	theorem	NOUN
ejpam-676	230	2	2	2	NUM
ejpam-676	230	3	.	.	PUNCT
ejpam-676	231	1	if	if	SCONJ
ejpam-676	231	2	f	f	PROPN
ejpam-676	231	3	∈	∈	PROPN
ejpam-676	231	4	σm	σm	X
ejpam-676	231	5	p	p	X
ejpam-676	231	6	,	,	PUNCT
ejpam-676	231	7	q	q	ADJ
ejpam-676	231	8	,	,	PUNCT
ejpam-676	231	9	s(α1;θ	s(α1;θ	NOUN
ejpam-676	231	10	)	)	PUNCT
ejpam-676	231	11	(	(	PUNCT
ejpam-676	231	12	0≤	0≤	NUM
ejpam-676	231	13	θ	θ	X
ejpam-676	231	14	<	<	X
ejpam-676	231	15	p	p	X
ejpam-676	231	16	)	)	PUNCT
ejpam-676	231	17	,	,	PUNCT
ejpam-676	231	18	then	then	ADV
ejpam-676	231	19	re	re	VERB
ejpam-676	231	20	¦	¦	PROPN
ejpam-676	231	21	−zp+1	−zp+1	PROPN
ejpam-676	231	22	�	�	PROPN
ejpam-676	231	23	(	(	PUNCT
ejpam-676	231	24	1−λ)(hp	1−λ)(hp	NUM
ejpam-676	231	25	,	,	PUNCT
ejpam-676	231	26	q	q	NOUN
ejpam-676	231	27	,	,	PUNCT
ejpam-676	231	28	s(α1	s(α1	NOUN
ejpam-676	231	29	)	)	PUNCT
ejpam-676	232	1	f	f	PROPN
ejpam-676	232	2	(	(	PUNCT
ejpam-676	232	3	z	z	NOUN
ejpam-676	232	4	)	)	PUNCT
ejpam-676	232	5	)	)	PUNCT
ejpam-676	233	1	′	′	NUM
ejpam-676	234	1	+	+	PUNCT
ejpam-676	234	2	λ(hp	λ(hp	NOUN
ejpam-676	234	3	,	,	PUNCT
ejpam-676	234	4	q	q	NOUN
ejpam-676	234	5	,	,	PUNCT
ejpam-676	234	6	s(α1	s(α1	NOUN
ejpam-676	234	7	+	+	CCONJ
ejpam-676	234	8	1	1	X
ejpam-676	234	9	)	)	PUNCT
ejpam-676	234	10	f	f	NOUN
ejpam-676	234	11	(	(	PUNCT
ejpam-676	234	12	z	z	NOUN
ejpam-676	234	13	)	)	PUNCT
ejpam-676	234	14	)	)	PUNCT
ejpam-676	234	15	′	′	NUM
ejpam-676	235	1	�	�	X
ejpam-676	235	2	©	©	NOUN
ejpam-676	235	3	>	>	X
ejpam-676	235	4	θ	θ	PROPN
ejpam-676	235	5	(	(	PUNCT
ejpam-676	235	6	|z|	|z|	NOUN
ejpam-676	235	7	<	<	X
ejpam-676	235	8	r	r	NOUN
ejpam-676	235	9	)	)	PUNCT
ejpam-676	235	10	,	,	PUNCT
ejpam-676	235	11	(	(	PUNCT
ejpam-676	235	12	24	24	NUM
ejpam-676	235	13	)	)	PUNCT
ejpam-676	235	14	where	where	SCONJ
ejpam-676	235	15	r=	r=	ADJ
ejpam-676	235	16			VERB
ejpam-676	235	17			ADP
ejpam-676	235	18			NOUN
ejpam-676	235	19	p	p	PROPN
ejpam-676	235	20	α2	α2	PROPN
ejpam-676	235	21	1	1	NUM
ejpam-676	235	22	+	+	NOUN
ejpam-676	235	23	λ	λ	X
ejpam-676	235	24	2(p+m)2	2(p+m)2	NUM
ejpam-676	235	25	−λ(p+m	−λ(p+m	NOUN
ejpam-676	235	26	)	)	PUNCT
ejpam-676	235	27	α1	α1	PROPN
ejpam-676	235	28			PROPN
ejpam-676	235	29			PROPN
ejpam-676	235	30			NOUN
ejpam-676	235	31	1	1	NUM
ejpam-676	235	32	p+m	p+m	NOUN
ejpam-676	235	33	.	.	PUNCT
ejpam-676	236	1	the	the	DET
ejpam-676	236	2	result	result	NOUN
ejpam-676	236	3	is	be	AUX
ejpam-676	236	4	the	the	DET
ejpam-676	236	5	best	good	ADJ
ejpam-676	236	6	possible	possible	ADJ
ejpam-676	236	7	.	.	PUNCT
ejpam-676	237	1	proof	proof	NOUN
ejpam-676	237	2	.	.	PUNCT
ejpam-676	238	1	since	since	SCONJ
ejpam-676	238	2	f	f	PROPN
ejpam-676	238	3	∈	∈	PROPN
ejpam-676	238	4	σm	σm	X
ejpam-676	238	5	p	p	X
ejpam-676	238	6	,	,	PUNCT
ejpam-676	238	7	q	q	ADJ
ejpam-676	238	8	,	,	PUNCT
ejpam-676	238	9	s(α1;θ	s(α1;θ	NOUN
ejpam-676	238	10	)	)	PUNCT
ejpam-676	238	11	,	,	PUNCT
ejpam-676	238	12	we	we	PRON
ejpam-676	238	13	write	write	VERB
ejpam-676	238	14	−zp+1(hp	−zp+1(hp	ADJ
ejpam-676	238	15	,	,	PUNCT
ejpam-676	238	16	q	q	NOUN
ejpam-676	238	17	,	,	PUNCT
ejpam-676	238	18	s(α1	s(α1	NOUN
ejpam-676	238	19	)	)	PUNCT
ejpam-676	239	1	f	f	PROPN
ejpam-676	239	2	(	(	PUNCT
ejpam-676	239	3	z	z	NOUN
ejpam-676	239	4	)	)	PUNCT
ejpam-676	239	5	)	)	PUNCT
ejpam-676	240	1	′	′	NUM
ejpam-676	241	1	=	=	PUNCT
ejpam-676	241	2	θ	θ	NOUN
ejpam-676	241	3	+	+	PUNCT
ejpam-676	241	4	(	(	PUNCT
ejpam-676	241	5	p−	p−	NOUN
ejpam-676	241	6	θ)u(z	θ)u(z	NOUN
ejpam-676	241	7	)	)	PUNCT
ejpam-676	241	8	(	(	PUNCT
ejpam-676	241	9	z	z	NOUN
ejpam-676	241	10	∈	∈	PROPN
ejpam-676	241	11	u	u	NOUN
ejpam-676	241	12	)	)	PUNCT
ejpam-676	241	13	.	.	PUNCT
ejpam-676	242	1	(	(	PUNCT
ejpam-676	242	2	25	25	NUM
ejpam-676	242	3	)	)	PUNCT
ejpam-676	242	4	then	then	ADV
ejpam-676	242	5	,	,	PUNCT
ejpam-676	242	6	clearly	clearly	ADV
ejpam-676	242	7	,	,	PUNCT
ejpam-676	242	8	u	u	NOUN
ejpam-676	242	9	is	be	AUX
ejpam-676	242	10	of	of	ADP
ejpam-676	242	11	the	the	DET
ejpam-676	242	12	form	form	NOUN
ejpam-676	242	13	(	(	PUNCT
ejpam-676	242	14	13	13	NUM
ejpam-676	242	15	)	)	PUNCT
ejpam-676	242	16	,	,	PUNCT
ejpam-676	242	17	is	be	AUX
ejpam-676	242	18	analytic	analytic	ADJ
ejpam-676	242	19	in	in	ADP
ejpam-676	242	20	u	u	PROPN
ejpam-676	242	21	,	,	PUNCT
ejpam-676	242	22	and	and	CCONJ
ejpam-676	242	23	has	have	VERB
ejpam-676	242	24	a	a	DET
ejpam-676	242	25	positive	positive	ADJ
ejpam-676	242	26	real	real	ADJ
ejpam-676	242	27	part	part	NOUN
ejpam-676	242	28	in	in	ADP
ejpam-676	242	29	u	u	PROPN
ejpam-676	242	30	.	.	PUNCT
ejpam-676	243	1	differentiating	differentiate	VERB
ejpam-676	243	2	(	(	PUNCT
ejpam-676	243	3	25	25	NUM
ejpam-676	243	4	)	)	PUNCT
ejpam-676	243	5	with	with	ADP
ejpam-676	243	6	respect	respect	NOUN
ejpam-676	243	7	to	to	ADP
ejpam-676	243	8	z	z	NOUN
ejpam-676	243	9	and	and	CCONJ
ejpam-676	243	10	using	use	VERB
ejpam-676	243	11	(	(	PUNCT
ejpam-676	243	12	10	10	NUM
ejpam-676	243	13	)	)	PUNCT
ejpam-676	243	14	,	,	PUNCT
ejpam-676	243	15	we	we	PRON
ejpam-676	243	16	obtain	obtain	VERB
ejpam-676	243	17	−	−	NUM
ejpam-676	243	18	zp+1	zp+1	NUM
ejpam-676	243	19	�	�	PROPN
ejpam-676	243	20	(	(	PUNCT
ejpam-676	243	21	1−λ)(hp	1−λ)(hp	NUM
ejpam-676	243	22	,	,	PUNCT
ejpam-676	243	23	q	q	NOUN
ejpam-676	243	24	,	,	PUNCT
ejpam-676	243	25	s(α1	s(α1	NOUN
ejpam-676	243	26	)	)	PUNCT
ejpam-676	243	27	f	f	PROPN
ejpam-676	243	28	(	(	PUNCT
ejpam-676	243	29	z	z	NOUN
ejpam-676	243	30	)	)	PUNCT
ejpam-676	243	31	)	)	PUNCT
ejpam-676	243	32	′	′	NUM
ejpam-676	244	1	+	+	PUNCT
ejpam-676	244	2	λ(hp	λ(hp	NOUN
ejpam-676	244	3	,	,	PUNCT
ejpam-676	244	4	q	q	NOUN
ejpam-676	244	5	,	,	PUNCT
ejpam-676	244	6	s(α1	s(α1	NOUN
ejpam-676	244	7	+	+	CCONJ
ejpam-676	244	8	1	1	X
ejpam-676	244	9	)	)	PUNCT
ejpam-676	244	10	f	f	NOUN
ejpam-676	244	11	(	(	PUNCT
ejpam-676	244	12	z	z	NOUN
ejpam-676	244	13	)	)	PUNCT
ejpam-676	244	14	)	)	PUNCT
ejpam-676	244	15	′	′	NUM
ejpam-676	244	16	�	�	PROPN
ejpam-676	244	17	+	+	NUM
ejpam-676	244	18	θ	θ	PROPN
ejpam-676	244	19	p−	p−	NOUN
ejpam-676	244	20	θ	θ	NOUN
ejpam-676	244	21	=	=	SYM
ejpam-676	244	22	u(z	u(z	NOUN
ejpam-676	244	23	)	)	PUNCT
ejpam-676	244	24	+	+	NUM
ejpam-676	244	25	λ	λ	X
ejpam-676	244	26	α1	α1	PROPN
ejpam-676	244	27	zu	zu	ADJ
ejpam-676	244	28	′	′	NUM
ejpam-676	244	29	(	(	PUNCT
ejpam-676	244	30	z	z	NOUN
ejpam-676	244	31	)	)	PUNCT
ejpam-676	244	32	.	.	PUNCT
ejpam-676	245	1	(	(	PUNCT
ejpam-676	245	2	26	26	NUM
ejpam-676	245	3	)	)	PUNCT
ejpam-676	245	4	m.	m.	NOUN
ejpam-676	245	5	aouf	aouf	PROPN
ejpam-676	245	6	/	/	SYM
ejpam-676	245	7	eur	eur	PROPN
ejpam-676	245	8	.	.	PUNCT
ejpam-676	246	1	j.	j.	PROPN
ejpam-676	246	2	pure	pure	PROPN
ejpam-676	246	3	appl	appl	PROPN
ejpam-676	246	4	.	.	PROPN
ejpam-676	246	5	math	math	PROPN
ejpam-676	246	6	,	,	PUNCT
ejpam-676	246	7	5	5	NUM
ejpam-676	246	8	(	(	PUNCT
ejpam-676	246	9	2012	2012	NUM
ejpam-676	246	10	)	)	PUNCT
ejpam-676	246	11	,	,	PUNCT
ejpam-676	246	12	141	141	NUM
ejpam-676	246	13	-	-	SYM
ejpam-676	246	14	159	159	NUM
ejpam-676	246	15	149	149	NUM
ejpam-676	246	16	now	now	ADV
ejpam-676	246	17	,	,	PUNCT
ejpam-676	246	18	by	by	ADP
ejpam-676	246	19	applying	apply	VERB
ejpam-676	246	20	the	the	DET
ejpam-676	246	21	well	well	ADV
ejpam-676	246	22	-	-	PUNCT
ejpam-676	246	23	known	know	VERB
ejpam-676	246	24	estimate	estimate	NOUN
ejpam-676	246	25	[	[	X
ejpam-676	246	26	6	6	NUM
ejpam-676	246	27	]	]	SYM
ejpam-676	246	28	�	�	PROPN
ejpam-676	246	29	�	�	PROPN
ejpam-676	246	30	�	�	PROPN
ejpam-676	246	31	zu	zu	NOUN
ejpam-676	246	32	′	′	NUM
ejpam-676	246	33	(	(	PUNCT
ejpam-676	246	34	z	z	X
ejpam-676	246	35	)	)	PUNCT
ejpam-676	246	36	�	�	PROPN
ejpam-676	246	37	�	�	PROPN
ejpam-676	246	38	�	�	PROPN
ejpam-676	246	39	re{u(z	re{u(z	PROPN
ejpam-676	246	40	)	)	PUNCT
ejpam-676	246	41	}	}	PUNCT
ejpam-676	246	42	≤	≤	NUM
ejpam-676	246	43	2(p+m)r	2(p+m)r	NUM
ejpam-676	246	44	p+m	p+m	X
ejpam-676	246	45	1−	1−	NUM
ejpam-676	246	46	r2(p+m	r2(p+m	NOUN
ejpam-676	246	47	)	)	PUNCT
ejpam-676	246	48	(	(	PUNCT
ejpam-676	246	49	|z|	|z|	NOUN
ejpam-676	246	50	=	=	SYM
ejpam-676	246	51	r	r	NOUN
ejpam-676	246	52	<	<	X
ejpam-676	246	53	1	1	NUM
ejpam-676	246	54	)	)	PUNCT
ejpam-676	246	55	in	in	ADP
ejpam-676	246	56	(	(	PUNCT
ejpam-676	246	57	26	26	NUM
ejpam-676	246	58	)	)	PUNCT
ejpam-676	246	59	,	,	PUNCT
ejpam-676	246	60	we	we	PRON
ejpam-676	246	61	obtain	obtain	VERB
ejpam-676	246	62	re	re	ADP
ejpam-676	246	63	(	(	PUNCT
ejpam-676	246	64	−	−	PROPN
ejpam-676	246	65	zp+1	zp+1	NUM
ejpam-676	246	66	�	�	PROPN
ejpam-676	246	67	(	(	PUNCT
ejpam-676	246	68	1−λ)(hp	1−λ)(hp	NUM
ejpam-676	246	69	,	,	PUNCT
ejpam-676	246	70	q	q	NOUN
ejpam-676	246	71	,	,	PUNCT
ejpam-676	246	72	s(α1	s(α1	NOUN
ejpam-676	246	73	)	)	PUNCT
ejpam-676	247	1	f	f	PROPN
ejpam-676	248	1	(	(	PUNCT
ejpam-676	248	2	z	z	NOUN
ejpam-676	248	3	)	)	PUNCT
ejpam-676	248	4	)	)	PUNCT
ejpam-676	249	1	′	′	NUM
ejpam-676	250	1	+	+	PUNCT
ejpam-676	250	2	λ(hp	λ(hp	NOUN
ejpam-676	250	3	,	,	PUNCT
ejpam-676	250	4	q	q	NOUN
ejpam-676	250	5	,	,	PUNCT
ejpam-676	250	6	s(α1	s(α1	NOUN
ejpam-676	250	7	+	+	CCONJ
ejpam-676	250	8	1	1	X
ejpam-676	250	9	)	)	PUNCT
ejpam-676	250	10	f	f	NOUN
ejpam-676	250	11	(	(	PUNCT
ejpam-676	250	12	z	z	NOUN
ejpam-676	250	13	)	)	PUNCT
ejpam-676	250	14	)	)	PUNCT
ejpam-676	250	15	′	′	NUM
ejpam-676	250	16	�	�	PROPN
ejpam-676	250	17	+	+	NUM
ejpam-676	250	18	θ	θ	PROPN
ejpam-676	250	19	p−	p−	NOUN
ejpam-676	250	20	θ	θ	NOUN
ejpam-676	250	21	)	)	PUNCT
ejpam-676	250	22	≥	≥	NOUN
ejpam-676	250	23	re{u(z	re{u(z	PROPN
ejpam-676	250	24	)	)	PUNCT
ejpam-676	250	25	}	}	PUNCT
ejpam-676	250	26	·	·	PUNCT
ejpam-676	250	27	�	�	PROPN
ejpam-676	250	28	1−	1−	NUM
ejpam-676	250	29	2λ(p+m)r	2λ(p+m)r	PROPN
ejpam-676	250	30	p+m	p+m	NOUN
ejpam-676	250	31	α1(1−	α1(1−	X
ejpam-676	250	32	r2(p+m	r2(p+m	NOUN
ejpam-676	250	33	)	)	PUNCT
ejpam-676	250	34	)	)	PUNCT
ejpam-676	250	35	�	�	PROPN
ejpam-676	250	36	.	.	PUNCT
ejpam-676	251	1	(	(	PUNCT
ejpam-676	251	2	27	27	NUM
ejpam-676	251	3	)	)	PUNCT
ejpam-676	251	4	it	it	PRON
ejpam-676	251	5	is	be	AUX
ejpam-676	251	6	easily	easily	ADV
ejpam-676	251	7	seen	see	VERB
ejpam-676	251	8	that	that	SCONJ
ejpam-676	251	9	the	the	DET
ejpam-676	251	10	right	right	ADJ
ejpam-676	251	11	-	-	PUNCT
ejpam-676	251	12	hand	hand	NOUN
ejpam-676	251	13	side	side	NOUN
ejpam-676	251	14	of	of	ADP
ejpam-676	251	15	(	(	PUNCT
ejpam-676	251	16	27	27	NUM
ejpam-676	251	17	)	)	PUNCT
ejpam-676	251	18	is	be	AUX
ejpam-676	251	19	positive	positive	ADJ
ejpam-676	251	20	provided	provide	VERB
ejpam-676	251	21	that	that	SCONJ
ejpam-676	251	22	r	r	NOUN
ejpam-676	251	23	<	<	X
ejpam-676	251	24	r	r	NOUN
ejpam-676	251	25	,	,	PUNCT
ejpam-676	251	26	where	where	SCONJ
ejpam-676	251	27	r	r	NOUN
ejpam-676	251	28	is	be	AUX
ejpam-676	251	29	given	give	VERB
ejpam-676	251	30	as	as	ADP
ejpam-676	251	31	in	in	ADP
ejpam-676	251	32	theorem	theorem	NOUN
ejpam-676	251	33	2	2	NUM
ejpam-676	251	34	.	.	PUNCT
ejpam-676	252	1	this	this	PRON
ejpam-676	252	2	proves	prove	VERB
ejpam-676	252	3	the	the	DET
ejpam-676	252	4	assertion	assertion	NOUN
ejpam-676	252	5	(	(	PUNCT
ejpam-676	252	6	24	24	NUM
ejpam-676	252	7	)	)	PUNCT
ejpam-676	252	8	of	of	ADP
ejpam-676	252	9	theorem	theorem	NOUN
ejpam-676	252	10	2	2	NUM
ejpam-676	252	11	.	.	PUNCT
ejpam-676	253	1	in	in	ADP
ejpam-676	253	2	order	order	NOUN
ejpam-676	253	3	to	to	PART
ejpam-676	253	4	show	show	VERB
ejpam-676	253	5	that	that	SCONJ
ejpam-676	253	6	the	the	DET
ejpam-676	253	7	bound	bound	ADJ
ejpam-676	253	8	r	r	NOUN
ejpam-676	253	9	is	be	AUX
ejpam-676	253	10	the	the	DET
ejpam-676	253	11	best	good	ADJ
ejpam-676	253	12	possible	possible	ADJ
ejpam-676	253	13	,	,	PUNCT
ejpam-676	253	14	we	we	PRON
ejpam-676	253	15	consider	consider	VERB
ejpam-676	253	16	the	the	DET
ejpam-676	253	17	function	function	NOUN
ejpam-676	253	18	f	f	PROPN
ejpam-676	253	19	∈	∈	PROPN
ejpam-676	253	20	σp	σp	PROPN
ejpam-676	253	21	,	,	PUNCT
ejpam-676	253	22	m	m	AUX
ejpam-676	253	23	defined	define	VERB
ejpam-676	253	24	by	by	ADP
ejpam-676	253	25	−zp+1(hp	−zp+1(hp	ADJ
ejpam-676	253	26	,	,	PUNCT
ejpam-676	253	27	q	q	NOUN
ejpam-676	253	28	,	,	PUNCT
ejpam-676	253	29	s(α1	s(α1	NOUN
ejpam-676	254	1	)	)	PUNCT
ejpam-676	254	2	f	f	PROPN
ejpam-676	254	3	(	(	PUNCT
ejpam-676	254	4	z	z	NOUN
ejpam-676	254	5	)	)	PUNCT
ejpam-676	254	6	)	)	PUNCT
ejpam-676	255	1	′	′	NUM
ejpam-676	256	1	=	=	PUNCT
ejpam-676	256	2	θ	θ	NOUN
ejpam-676	256	3	+	+	PUNCT
ejpam-676	256	4	(	(	PUNCT
ejpam-676	256	5	p−	p−	NOUN
ejpam-676	256	6	θ	θ	NOUN
ejpam-676	256	7	)	)	PUNCT
ejpam-676	256	8	1	1	NUM
ejpam-676	257	1	+	+	SYM
ejpam-676	257	2	zp+m	zp+m	ADJ
ejpam-676	257	3	1−	1−	NUM
ejpam-676	257	4	zp+m	zp+m	NOUN
ejpam-676	257	5	(	(	PUNCT
ejpam-676	257	6	0≤	0≤	NUM
ejpam-676	257	7	θ	θ	X
ejpam-676	257	8	<	<	X
ejpam-676	257	9	p	p	X
ejpam-676	257	10	;	;	PUNCT
ejpam-676	257	11	p	p	PROPN
ejpam-676	257	12	∈	∈	PROPN
ejpam-676	257	13	n	n	NOUN
ejpam-676	257	14	;	;	PUNCT
ejpam-676	257	15	z	z	PROPN
ejpam-676	257	16	∈	∈	PROPN
ejpam-676	257	17	u	u	NOUN
ejpam-676	257	18	)	)	PUNCT
ejpam-676	257	19	.	.	PUNCT
ejpam-676	258	1	noting	note	VERB
ejpam-676	258	2	that	that	SCONJ
ejpam-676	258	3	−	−	PROPN
ejpam-676	258	4	zp+1	zp+1	NUM
ejpam-676	258	5	�	�	PROPN
ejpam-676	258	6	(	(	PUNCT
ejpam-676	258	7	1−λ)(hp	1−λ)(hp	NUM
ejpam-676	258	8	,	,	PUNCT
ejpam-676	258	9	q	q	NOUN
ejpam-676	258	10	,	,	PUNCT
ejpam-676	258	11	s(α1	s(α1	NOUN
ejpam-676	258	12	)	)	PUNCT
ejpam-676	258	13	f	f	PROPN
ejpam-676	258	14	(	(	PUNCT
ejpam-676	258	15	z	z	NOUN
ejpam-676	258	16	)	)	PUNCT
ejpam-676	258	17	)	)	PUNCT
ejpam-676	258	18	′	′	NUM
ejpam-676	259	1	+	+	PUNCT
ejpam-676	259	2	λ(hp	λ(hp	NOUN
ejpam-676	259	3	,	,	PUNCT
ejpam-676	259	4	q	q	NOUN
ejpam-676	259	5	,	,	PUNCT
ejpam-676	259	6	s(α1	s(α1	NOUN
ejpam-676	259	7	+	+	CCONJ
ejpam-676	259	8	1	1	X
ejpam-676	259	9	)	)	PUNCT
ejpam-676	259	10	f	f	NOUN
ejpam-676	259	11	(	(	PUNCT
ejpam-676	259	12	z	z	NOUN
ejpam-676	259	13	)	)	PUNCT
ejpam-676	259	14	)	)	PUNCT
ejpam-676	259	15	′	′	NUM
ejpam-676	259	16	�	�	PROPN
ejpam-676	259	17	+	+	NUM
ejpam-676	259	18	θ	θ	PROPN
ejpam-676	259	19	p−	p−	NOUN
ejpam-676	259	20	θ	θ	NOUN
ejpam-676	259	21	=	=	SYM
ejpam-676	259	22	α1−α1z2(p+m	α1−α1z2(p+m	NOUN
ejpam-676	259	23	)	)	PUNCT
ejpam-676	260	1	+	+	CCONJ
ejpam-676	260	2	2λ(p+m)zp+m	2λ(p+m)zp+m	NUM
ejpam-676	260	3	α1(1−	α1(1−	VERB
ejpam-676	260	4	zp+m)2	zp+m)2	NUM
ejpam-676	260	5	=	=	SYM
ejpam-676	260	6	0	0	NUM
ejpam-676	261	1	for	for	ADP
ejpam-676	261	2	z	z	NOUN
ejpam-676	261	3	=	=	SYM
ejpam-676	261	4	r	r	NOUN
ejpam-676	261	5	1	1	NUM
ejpam-676	261	6	p+m	p+m	NOUN
ejpam-676	261	7	exp	exp	NOUN
ejpam-676	261	8	�	�	PROPN
ejpam-676	261	9	iπ	iπ	PRON
ejpam-676	261	10	p+m	p+m	PROPN
ejpam-676	261	11	�	�	PROPN
ejpam-676	261	12	,	,	PUNCT
ejpam-676	261	13	we	we	PRON
ejpam-676	261	14	complete	complete	VERB
ejpam-676	261	15	the	the	DET
ejpam-676	261	16	proof	proof	NOUN
ejpam-676	261	17	of	of	ADP
ejpam-676	261	18	theorem	theorem	NOUN
ejpam-676	261	19	2	2	NUM
ejpam-676	261	20	.	.	PUNCT
ejpam-676	261	21	putting	put	VERB
ejpam-676	261	22	λ=	λ=	NOUN
ejpam-676	261	23	1	1	NUM
ejpam-676	261	24	in	in	ADP
ejpam-676	261	25	theorem	theorem	NOUN
ejpam-676	261	26	2	2	NUM
ejpam-676	261	27	,	,	PUNCT
ejpam-676	261	28	we	we	PRON
ejpam-676	261	29	obtain	obtain	VERB
ejpam-676	261	30	the	the	DET
ejpam-676	261	31	following	follow	VERB
ejpam-676	261	32	result	result	NOUN
ejpam-676	261	33	.	.	PUNCT
ejpam-676	262	1	corollary	corollary	ADJ
ejpam-676	262	2	3	3	X
ejpam-676	262	3	.	.	PUNCT
ejpam-676	263	1	if	if	SCONJ
ejpam-676	263	2	f	f	PROPN
ejpam-676	263	3	∈	∈	PROPN
ejpam-676	263	4	σm	σm	X
ejpam-676	263	5	p	p	X
ejpam-676	263	6	,	,	PUNCT
ejpam-676	263	7	q	q	ADJ
ejpam-676	263	8	,	,	PUNCT
ejpam-676	263	9	s(α1;θ	s(α1;θ	NOUN
ejpam-676	263	10	)	)	PUNCT
ejpam-676	263	11	(	(	PUNCT
ejpam-676	263	12	0	0	NUM
ejpam-676	263	13	≤	≤	NUM
ejpam-676	263	14	θ	θ	NOUN
ejpam-676	263	15	<	<	X
ejpam-676	263	16	p	p	X
ejpam-676	263	17	;	;	PUNCT
ejpam-676	263	18	p	p	PROPN
ejpam-676	263	19	∈	∈	PROPN
ejpam-676	263	20	n	n	CCONJ
ejpam-676	263	21	)	)	PUNCT
ejpam-676	263	22	,	,	PUNCT
ejpam-676	263	23	then	then	ADV
ejpam-676	263	24	f	f	PROPN
ejpam-676	263	25	∈	∈	PROPN
ejpam-676	263	26	σm	σm	X
ejpam-676	264	1	p	p	X
ejpam-676	264	2	,	,	PUNCT
ejpam-676	264	3	q	q	NOUN
ejpam-676	264	4	,	,	PUNCT
ejpam-676	264	5	s(α1	s(α1	NOUN
ejpam-676	264	6	+	+	CCONJ
ejpam-676	264	7	1;θ	1;θ	NUM
ejpam-676	264	8	)	)	PUNCT
ejpam-676	264	9	for	for	ADP
ejpam-676	264	10	|z|	|z|	NOUN
ejpam-676	264	11	<	<	X
ejpam-676	264	12	r∗	r∗	PROPN
ejpam-676	264	13	,	,	PUNCT
ejpam-676	264	14	where	where	SCONJ
ejpam-676	264	15	r∗	r∗	NOUN
ejpam-676	264	16	=	=	PUNCT
ejpam-676	264	17			PROPN
ejpam-676	264	18			PRON
ejpam-676	264	19			NOUN
ejpam-676	264	20	p	p	PROPN
ejpam-676	264	21	α2	α2	PROPN
ejpam-676	264	22	1	1	NUM
ejpam-676	264	23	+	+	CCONJ
ejpam-676	264	24	(	(	PUNCT
ejpam-676	264	25	p+m)2	p+m)2	NUM
ejpam-676	264	26	−	−	PROPN
ejpam-676	264	27	(	(	PUNCT
ejpam-676	264	28	p+m	p+m	NOUN
ejpam-676	264	29	)	)	PUNCT
ejpam-676	264	30	α1	α1	PROPN
ejpam-676	264	31			PROPN
ejpam-676	264	32			PROPN
ejpam-676	264	33			NOUN
ejpam-676	264	34	1	1	NUM
ejpam-676	264	35	p+m	p+m	NOUN
ejpam-676	264	36	.	.	PUNCT
ejpam-676	265	1	the	the	DET
ejpam-676	265	2	result	result	NOUN
ejpam-676	265	3	is	be	AUX
ejpam-676	265	4	the	the	DET
ejpam-676	265	5	best	good	ADJ
ejpam-676	265	6	possible	possible	ADJ
ejpam-676	265	7	.	.	PUNCT
ejpam-676	266	1	remark	remark	PROPN
ejpam-676	266	2	3	3	NUM
ejpam-676	266	3	.	.	PUNCT
ejpam-676	267	1	taking	take	VERB
ejpam-676	267	2	s	s	PART
ejpam-676	267	3	=	=	SYM
ejpam-676	267	4	1	1	NUM
ejpam-676	267	5	,	,	PUNCT
ejpam-676	267	6	q	q	NOUN
ejpam-676	267	7	=	=	SYM
ejpam-676	267	8	2	2	NUM
ejpam-676	267	9	,	,	PUNCT
ejpam-676	267	10	α1	α1	PROPN
ejpam-676	267	11	=	=	PUNCT
ejpam-676	267	12	a	a	PROPN
ejpam-676	267	13	and	and	CCONJ
ejpam-676	268	1	β1	β1	PROPN
ejpam-676	268	2	=	=	PUNCT
ejpam-676	268	3	c	c	PROPN
ejpam-676	268	4	(	(	PUNCT
ejpam-676	268	5	a	a	DET
ejpam-676	268	6	>	>	X
ejpam-676	268	7	0	0	NUM
ejpam-676	268	8	;	;	PUNCT
ejpam-676	268	9	c	c	X
ejpam-676	268	10	>	>	X
ejpam-676	268	11	0	0	NUM
ejpam-676	268	12	)	)	PUNCT
ejpam-676	268	13	and	and	CCONJ
ejpam-676	268	14	α2	α2	NOUN
ejpam-676	268	15	=	=	SYM
ejpam-676	268	16	1	1	NUM
ejpam-676	268	17	in	in	ADP
ejpam-676	268	18	corollary	corollary	ADJ
ejpam-676	268	19	3	3	NUM
ejpam-676	268	20	,	,	PUNCT
ejpam-676	268	21	we	we	PRON
ejpam-676	268	22	obtain	obtain	VERB
ejpam-676	268	23	the	the	DET
ejpam-676	268	24	result	result	NOUN
ejpam-676	268	25	obtained	obtain	VERB
ejpam-676	268	26	by	by	ADP
ejpam-676	268	27	patel	patel	NOUN
ejpam-676	268	28	and	and	CCONJ
ejpam-676	268	29	cho	cho	NOUN
ejpam-676	269	1	[	[	X
ejpam-676	269	2	12	12	NUM
ejpam-676	269	3	,	,	PUNCT
ejpam-676	269	4	theorem	theorem	VERB
ejpam-676	269	5	2	2	NUM
ejpam-676	269	6	]	]	PUNCT
ejpam-676	269	7	.	.	PUNCT
ejpam-676	270	1	m.	m.	PROPN
ejpam-676	270	2	aouf	aouf	PROPN
ejpam-676	270	3	/	/	SYM
ejpam-676	270	4	eur	eur	PROPN
ejpam-676	270	5	.	.	PUNCT
ejpam-676	271	1	j.	j.	PROPN
ejpam-676	271	2	pure	pure	PROPN
ejpam-676	271	3	appl	appl	PROPN
ejpam-676	271	4	.	.	PROPN
ejpam-676	271	5	math	math	PROPN
ejpam-676	271	6	,	,	PUNCT
ejpam-676	271	7	5	5	NUM
ejpam-676	271	8	(	(	PUNCT
ejpam-676	271	9	2012	2012	NUM
ejpam-676	271	10	)	)	PUNCT
ejpam-676	271	11	,	,	PUNCT
ejpam-676	271	12	141	141	NUM
ejpam-676	271	13	-	-	SYM
ejpam-676	271	14	159	159	NUM
ejpam-676	271	15	150	150	NUM
ejpam-676	271	16	theorem	theorem	NOUN
ejpam-676	271	17	3	3	X
ejpam-676	271	18	.	.	PUNCT
ejpam-676	272	1	let	let	VERB
ejpam-676	272	2	f	f	PRON
ejpam-676	272	3	∈	∈	PROPN
ejpam-676	272	4	σm	σm	ADP
ejpam-676	273	1	p	p	X
ejpam-676	273	2	,	,	PUNCT
ejpam-676	273	3	q	q	ADJ
ejpam-676	273	4	,	,	PUNCT
ejpam-676	273	5	s(α1	s(α1	NOUN
ejpam-676	273	6	;	;	PUNCT
ejpam-676	273	7	a	a	DET
ejpam-676	273	8	,	,	PUNCT
ejpam-676	273	9	b	b	NOUN
ejpam-676	273	10	)	)	PUNCT
ejpam-676	274	1	and	and	CCONJ
ejpam-676	274	2	let	let	VERB
ejpam-676	274	3	fδ	fδ	PRON
ejpam-676	274	4	,	,	PUNCT
ejpam-676	274	5	p	p	X
ejpam-676	274	6	(	(	PUNCT
ejpam-676	274	7	f	f	PROPN
ejpam-676	274	8	)	)	PUNCT
ejpam-676	274	9	(	(	PUNCT
ejpam-676	274	10	z	z	NOUN
ejpam-676	274	11	)	)	PUNCT
ejpam-676	275	1	=	=	SYM
ejpam-676	275	2	δ	δ	X
ejpam-676	275	3	zδ+p	zδ+p	NUM
ejpam-676	275	4	z	z	NOUN
ejpam-676	275	5	∫	∫	PROPN
ejpam-676	275	6	0	0	NUM
ejpam-676	276	1	tδ+p−1	tδ+p−1	PRON
ejpam-676	276	2	f	f	X
ejpam-676	276	3	(	(	PUNCT
ejpam-676	276	4	t)d	t)d	PROPN
ejpam-676	276	5	t	t	PROPN
ejpam-676	276	6	(	(	PUNCT
ejpam-676	276	7	δ	δ	PROPN
ejpam-676	276	8	>	>	X
ejpam-676	276	9	0	0	NUM
ejpam-676	276	10	;	;	PUNCT
ejpam-676	276	11	z	z	PROPN
ejpam-676	276	12	∈	∈	PROPN
ejpam-676	276	13	u	u	NOUN
ejpam-676	276	14	)	)	PUNCT
ejpam-676	276	15	.	.	PUNCT
ejpam-676	277	1	(	(	PUNCT
ejpam-676	277	2	28	28	NUM
ejpam-676	277	3	)	)	PUNCT
ejpam-676	277	4	then	then	ADV
ejpam-676	277	5	−zp+1(hp	−zp+1(hp	ADJ
ejpam-676	277	6	,	,	PUNCT
ejpam-676	277	7	q	q	NOUN
ejpam-676	277	8	,	,	PUNCT
ejpam-676	277	9	s(α1)fδ	s(α1)fδ	ADJ
ejpam-676	277	10	,	,	PUNCT
ejpam-676	277	11	p	p	PROPN
ejpam-676	277	12	f	f	X
ejpam-676	277	13	(	(	PUNCT
ejpam-676	277	14	z	z	NOUN
ejpam-676	277	15	)	)	PUNCT
ejpam-676	277	16	)	)	PUNCT
ejpam-676	278	1	′	′	NUM
ejpam-676	279	1	p	p	NOUN
ejpam-676	279	2	≺	≺	NOUN
ejpam-676	279	3	φ(z)≺	φ(z)≺	X
ejpam-676	279	4	1	1	NUM
ejpam-676	279	5	+	+	NUM
ejpam-676	279	6	az	az	PROPN
ejpam-676	279	7	1	1	NUM
ejpam-676	279	8	+	+	CCONJ
ejpam-676	279	9	bz	bz	PROPN
ejpam-676	279	10	,	,	PUNCT
ejpam-676	279	11	(	(	PUNCT
ejpam-676	279	12	29	29	NUM
ejpam-676	279	13	)	)	PUNCT
ejpam-676	280	1	where	where	SCONJ
ejpam-676	280	2	the	the	DET
ejpam-676	280	3	function	function	NOUN
ejpam-676	280	4	φ	φ	NOUN
ejpam-676	280	5	given	give	VERB
ejpam-676	280	6	by	by	ADP
ejpam-676	280	7	φ(z	φ(z	PROPN
ejpam-676	280	8	)	)	PUNCT
ejpam-676	280	9	=	=	PUNCT
ejpam-676	280	10			PROPN
ejpam-676	280	11			VERB
ejpam-676	280	12			NOUN
ejpam-676	280	13	a	a	DET
ejpam-676	280	14	b	b	NOUN
ejpam-676	280	15	+	+	CCONJ
ejpam-676	280	16	(	(	PUNCT
ejpam-676	280	17	1−	1−	NUM
ejpam-676	280	18	a	a	DET
ejpam-676	280	19	b	b	NOUN
ejpam-676	280	20	)	)	PUNCT
ejpam-676	280	21	(	(	PUNCT
ejpam-676	280	22	1	1	NUM
ejpam-676	280	23	+	+	NUM
ejpam-676	280	24	bz)−1	bz)−1	NOUN
ejpam-676	280	25	2f1(1,1	2f1(1,1	NUM
ejpam-676	280	26	;	;	PUNCT
ejpam-676	280	27	δ	δ	PROPN
ejpam-676	280	28	p+m	p+m	PROPN
ejpam-676	280	29	+	+	ADP
ejpam-676	280	30	1	1	NUM
ejpam-676	280	31	;	;	PUNCT
ejpam-676	280	32	bz	bz	PROPN
ejpam-676	280	33	bz+1	bz+1	PROPN
ejpam-676	280	34	)	)	PUNCT
ejpam-676	281	1	(	(	PUNCT
ejpam-676	281	2	b	b	X
ejpam-676	281	3	6=	6=	NUM
ejpam-676	281	4	0	0	NUM
ejpam-676	281	5	)	)	PUNCT
ejpam-676	281	6	1	1	NUM
ejpam-676	281	7	+	+	NUM
ejpam-676	281	8	δ	δ	PROPN
ejpam-676	281	9	δ+p+m	δ+p+m	NOUN
ejpam-676	281	10	az	az	PROPN
ejpam-676	281	11	(	(	PUNCT
ejpam-676	281	12	b	b	NOUN
ejpam-676	281	13	=	=	NOUN
ejpam-676	281	14	0	0	NUM
ejpam-676	281	15	)	)	PUNCT
ejpam-676	281	16	,	,	PUNCT
ejpam-676	281	17	is	be	AUX
ejpam-676	281	18	the	the	DET
ejpam-676	281	19	best	good	ADJ
ejpam-676	281	20	dominant	dominant	NOUN
ejpam-676	281	21	of	of	ADP
ejpam-676	281	22	(	(	PUNCT
ejpam-676	281	23	29	29	NUM
ejpam-676	281	24	)	)	PUNCT
ejpam-676	281	25	.	.	PUNCT
ejpam-676	282	1	furthermore	furthermore	ADV
ejpam-676	282	2	,	,	PUNCT
ejpam-676	282	3	re	re	X
ejpam-676	282	4	(	(	PUNCT
ejpam-676	282	5	−zp+1(hp	−zp+1(hp	PROPN
ejpam-676	282	6	,	,	PUNCT
ejpam-676	282	7	q	q	NOUN
ejpam-676	282	8	,	,	PUNCT
ejpam-676	282	9	s(α1)fδ	s(α1)fδ	ADJ
ejpam-676	282	10	,	,	PUNCT
ejpam-676	282	11	p	p	X
ejpam-676	282	12	(	(	PUNCT
ejpam-676	282	13	f	f	PROPN
ejpam-676	282	14	)	)	PUNCT
ejpam-676	282	15	(	(	PUNCT
ejpam-676	282	16	z	z	NOUN
ejpam-676	282	17	)	)	PUNCT
ejpam-676	282	18	)	)	PUNCT
ejpam-676	283	1	′	′	NUM
ejpam-676	283	2	p	p	NOUN
ejpam-676	283	3	)	)	PUNCT
ejpam-676	283	4	>	>	X
ejpam-676	284	1	ξ∗	ξ∗	PROPN
ejpam-676	284	2	(	(	PUNCT
ejpam-676	284	3	z	z	NOUN
ejpam-676	284	4	∈	∈	PROPN
ejpam-676	284	5	u	u	NOUN
ejpam-676	284	6	)	)	PUNCT
ejpam-676	284	7	,	,	PUNCT
ejpam-676	284	8	(	(	PUNCT
ejpam-676	284	9	30	30	NUM
ejpam-676	284	10	)	)	PUNCT
ejpam-676	284	11	where	where	SCONJ
ejpam-676	284	12	ξ∗	ξ∗	NOUN
ejpam-676	284	13	=	=	PUNCT
ejpam-676	284	14			PROPN
ejpam-676	284	15			PROPN
ejpam-676	284	16			NOUN
ejpam-676	284	17	a	a	DET
ejpam-676	284	18	b	b	NOUN
ejpam-676	284	19	+	+	CCONJ
ejpam-676	284	20	(	(	PUNCT
ejpam-676	284	21	1−	1−	NUM
ejpam-676	284	22	a	a	DET
ejpam-676	284	23	b	b	NOUN
ejpam-676	284	24	)	)	PUNCT
ejpam-676	284	25	(	(	PUNCT
ejpam-676	284	26	1−	1−	NUM
ejpam-676	284	27	b)−1	b)−1	NOUN
ejpam-676	284	28	2f1(1,1	2f1(1,1	NUM
ejpam-676	284	29	;	;	PUNCT
ejpam-676	284	30	δ	δ	PROPN
ejpam-676	284	31	p+m	p+m	PROPN
ejpam-676	284	32	+	+	CCONJ
ejpam-676	284	33	1	1	NUM
ejpam-676	284	34	;	;	PUNCT
ejpam-676	284	35	b	b	X
ejpam-676	284	36	b−1	b−1	PROPN
ejpam-676	284	37	)	)	PUNCT
ejpam-676	284	38	(	(	PUNCT
ejpam-676	284	39	b	b	X
ejpam-676	284	40	6=	6=	NUM
ejpam-676	284	41	0	0	NUM
ejpam-676	284	42	)	)	PUNCT
ejpam-676	284	43	1−	1−	NUM
ejpam-676	284	44	δ	δ	PROPN
ejpam-676	284	45	δ+p+m	δ+p+m	NOUN
ejpam-676	284	46	a	a	DET
ejpam-676	284	47	(	(	PUNCT
ejpam-676	284	48	b	b	NOUN
ejpam-676	284	49	=	=	NOUN
ejpam-676	284	50	0	0	NUM
ejpam-676	284	51	)	)	PUNCT
ejpam-676	284	52	.	.	PUNCT
ejpam-676	285	1	the	the	DET
ejpam-676	285	2	result	result	NOUN
ejpam-676	285	3	is	be	AUX
ejpam-676	285	4	the	the	DET
ejpam-676	285	5	best	good	ADJ
ejpam-676	285	6	possible	possible	ADJ
ejpam-676	285	7	.	.	PUNCT
ejpam-676	286	1	proof	proof	NOUN
ejpam-676	286	2	.	.	PUNCT
ejpam-676	287	1	defining	define	VERB
ejpam-676	287	2	the	the	DET
ejpam-676	287	3	function	function	NOUN
ejpam-676	287	4	ϕ	ϕ	NOUN
ejpam-676	287	5	by	by	ADP
ejpam-676	287	6	ϕ(z	ϕ(z	NOUN
ejpam-676	287	7	)	)	PUNCT
ejpam-676	287	8	=	=	SYM
ejpam-676	287	9	−zp+1(hp	−zp+1(hp	PROPN
ejpam-676	287	10	,	,	PUNCT
ejpam-676	287	11	q	q	NOUN
ejpam-676	287	12	,	,	PUNCT
ejpam-676	287	13	s(α1)fδ	s(α1)fδ	ADJ
ejpam-676	287	14	,	,	PUNCT
ejpam-676	287	15	p	p	X
ejpam-676	287	16	(	(	PUNCT
ejpam-676	287	17	f	f	PROPN
ejpam-676	287	18	)	)	PUNCT
ejpam-676	287	19	(	(	PUNCT
ejpam-676	287	20	z	z	NOUN
ejpam-676	287	21	)	)	PUNCT
ejpam-676	287	22	)	)	PUNCT
ejpam-676	288	1	′	′	NUM
ejpam-676	289	1	p	p	X
ejpam-676	289	2	(	(	PUNCT
ejpam-676	289	3	z	z	NOUN
ejpam-676	289	4	∈	∈	PROPN
ejpam-676	289	5	u	u	NOUN
ejpam-676	289	6	)	)	PUNCT
ejpam-676	289	7	,	,	PUNCT
ejpam-676	289	8	(	(	PUNCT
ejpam-676	289	9	31	31	NUM
ejpam-676	289	10	)	)	PUNCT
ejpam-676	289	11	we	we	PRON
ejpam-676	289	12	note	note	VERB
ejpam-676	289	13	that	that	SCONJ
ejpam-676	289	14	ϕ	ϕ	NOUN
ejpam-676	289	15	is	be	AUX
ejpam-676	289	16	of	of	ADP
ejpam-676	289	17	the	the	DET
ejpam-676	289	18	form	form	NOUN
ejpam-676	289	19	(	(	PUNCT
ejpam-676	289	20	13	13	NUM
ejpam-676	289	21	)	)	PUNCT
ejpam-676	289	22	and	and	CCONJ
ejpam-676	289	23	is	be	AUX
ejpam-676	289	24	analytic	analytic	ADJ
ejpam-676	289	25	in	in	ADP
ejpam-676	289	26	u	u	PROPN
ejpam-676	289	27	.	.	PUNCT
ejpam-676	290	1	using	use	VERB
ejpam-676	290	2	the	the	DET
ejpam-676	290	3	following	follow	VERB
ejpam-676	290	4	operator	operator	NOUN
ejpam-676	290	5	identity	identity	NOUN
ejpam-676	290	6	:	:	PUNCT
ejpam-676	290	7	z(hp	z(hp	NUM
ejpam-676	290	8	,	,	PUNCT
ejpam-676	290	9	q	q	ADJ
ejpam-676	290	10	,	,	PUNCT
ejpam-676	290	11	s(α1)fδ	s(α1)fδ	ADJ
ejpam-676	290	12	,	,	PUNCT
ejpam-676	290	13	p	p	X
ejpam-676	290	14	(	(	PUNCT
ejpam-676	290	15	f	f	PROPN
ejpam-676	290	16	)	)	PUNCT
ejpam-676	290	17	(	(	PUNCT
ejpam-676	290	18	z	z	NOUN
ejpam-676	290	19	)	)	PUNCT
ejpam-676	290	20	)	)	PUNCT
ejpam-676	291	1	′	′	NUM
ejpam-676	292	1	=	=	PUNCT
ejpam-676	292	2	δhp	δhp	ADJ
ejpam-676	292	3	,	,	PUNCT
ejpam-676	292	4	q	q	NOUN
ejpam-676	292	5	,	,	PUNCT
ejpam-676	292	6	s(α1	s(α1	NOUN
ejpam-676	292	7	)	)	PUNCT
ejpam-676	292	8	f	f	PROPN
ejpam-676	292	9	(	(	PUNCT
ejpam-676	292	10	z)−	z)−	X
ejpam-676	292	11	(	(	PUNCT
ejpam-676	292	12	δ+	δ+	X
ejpam-676	292	13	p)hp	p)hp	PROPN
ejpam-676	292	14	,	,	PUNCT
ejpam-676	292	15	q	q	NOUN
ejpam-676	292	16	,	,	PUNCT
ejpam-676	292	17	s(α1)fδ	s(α1)fδ	ADJ
ejpam-676	292	18	,	,	PUNCT
ejpam-676	292	19	p	p	X
ejpam-676	292	20	(	(	PUNCT
ejpam-676	292	21	f	f	PROPN
ejpam-676	292	22	)	)	PUNCT
ejpam-676	292	23	(	(	PUNCT
ejpam-676	292	24	z	z	NOUN
ejpam-676	292	25	)	)	PUNCT
ejpam-676	292	26	(	(	PUNCT
ejpam-676	292	27	32	32	NUM
ejpam-676	292	28	)	)	PUNCT
ejpam-676	292	29	in	in	ADP
ejpam-676	292	30	(	(	PUNCT
ejpam-676	292	31	31	31	NUM
ejpam-676	292	32	)	)	PUNCT
ejpam-676	292	33	and	and	CCONJ
ejpam-676	292	34	differentiating	differentiate	VERB
ejpam-676	292	35	the	the	DET
ejpam-676	292	36	resulting	result	VERB
ejpam-676	292	37	equation	equation	NOUN
ejpam-676	292	38	with	with	ADP
ejpam-676	292	39	respect	respect	NOUN
ejpam-676	292	40	to	to	ADP
ejpam-676	292	41	z	z	NOUN
ejpam-676	292	42	,	,	PUNCT
ejpam-676	292	43	we	we	PRON
ejpam-676	292	44	find	find	VERB
ejpam-676	292	45	that	that	SCONJ
ejpam-676	292	46	−zp+1(hp	−zp+1(hp	ADJ
ejpam-676	292	47	,	,	PUNCT
ejpam-676	292	48	q	q	NOUN
ejpam-676	292	49	,	,	PUNCT
ejpam-676	292	50	s(α1	s(α1	NOUN
ejpam-676	292	51	)	)	PUNCT
ejpam-676	293	1	f	f	PROPN
ejpam-676	293	2	(	(	PUNCT
ejpam-676	293	3	z	z	NOUN
ejpam-676	293	4	)	)	PUNCT
ejpam-676	293	5	)	)	PUNCT
ejpam-676	294	1	′	′	NUM
ejpam-676	295	1	p	p	NOUN
ejpam-676	295	2	≺	≺	NOUN
ejpam-676	295	3	ϕ(z	ϕ(z	NOUN
ejpam-676	295	4	)	)	PUNCT
ejpam-676	296	1	+	+	CCONJ
ejpam-676	296	2	zϕ	zϕ	X
ejpam-676	296	3	′	′	NUM
ejpam-676	296	4	(	(	PUNCT
ejpam-676	296	5	z	z	X
ejpam-676	296	6	)	)	PUNCT
ejpam-676	296	7	δ	δ	PROPN
ejpam-676	296	8	≺	≺	NOUN
ejpam-676	296	9	1	1	NUM
ejpam-676	296	10	+	+	NUM
ejpam-676	296	11	az	az	PROPN
ejpam-676	296	12	1	1	NUM
ejpam-676	296	13	+	+	CCONJ
ejpam-676	296	14	bz	bz	PROPN
ejpam-676	296	15	.	.	PUNCT
ejpam-676	297	1	now	now	ADV
ejpam-676	297	2	the	the	DET
ejpam-676	297	3	remaining	remain	VERB
ejpam-676	297	4	part	part	NOUN
ejpam-676	297	5	of	of	ADP
ejpam-676	297	6	theorem	theorem	ADJ
ejpam-676	297	7	3	3	NUM
ejpam-676	297	8	follows	follow	VERB
ejpam-676	297	9	by	by	ADP
ejpam-676	297	10	employing	employ	VERB
ejpam-676	297	11	the	the	DET
ejpam-676	297	12	techniques	technique	NOUN
ejpam-676	297	13	that	that	PRON
ejpam-676	297	14	we	we	PRON
ejpam-676	297	15	used	use	VERB
ejpam-676	297	16	in	in	ADP
ejpam-676	297	17	proving	prove	VERB
ejpam-676	297	18	theorem	theorem	ADJ
ejpam-676	297	19	1	1	NUM
ejpam-676	297	20	above	above	ADV
ejpam-676	297	21	.	.	PUNCT
ejpam-676	298	1	putting	put	VERB
ejpam-676	298	2	m=	m=	X
ejpam-676	298	3	1−	1−	NUM
ejpam-676	298	4	p	p	NOUN
ejpam-676	298	5	(	(	PUNCT
ejpam-676	298	6	p	p	NOUN
ejpam-676	298	7	∈	∈	PROPN
ejpam-676	298	8	n	n	CCONJ
ejpam-676	298	9	)	)	PUNCT
ejpam-676	298	10	in	in	ADP
ejpam-676	298	11	theorem	theorem	NOUN
ejpam-676	298	12	3	3	NUM
ejpam-676	298	13	,	,	PUNCT
ejpam-676	298	14	we	we	PRON
ejpam-676	298	15	obtain	obtain	VERB
ejpam-676	298	16	the	the	DET
ejpam-676	298	17	following	follow	VERB
ejpam-676	298	18	corollary	corollary	NOUN
ejpam-676	298	19	.	.	PUNCT
ejpam-676	299	1	m.	m.	PROPN
ejpam-676	299	2	aouf	aouf	PROPN
ejpam-676	299	3	/	/	SYM
ejpam-676	299	4	eur	eur	PROPN
ejpam-676	299	5	.	.	PUNCT
ejpam-676	300	1	j.	j.	PROPN
ejpam-676	300	2	pure	pure	PROPN
ejpam-676	300	3	appl	appl	PROPN
ejpam-676	300	4	.	.	PROPN
ejpam-676	300	5	math	math	PROPN
ejpam-676	300	6	,	,	PUNCT
ejpam-676	300	7	5	5	NUM
ejpam-676	300	8	(	(	PUNCT
ejpam-676	300	9	2012	2012	NUM
ejpam-676	300	10	)	)	PUNCT
ejpam-676	300	11	,	,	PUNCT
ejpam-676	300	12	141	141	NUM
ejpam-676	300	13	-	-	SYM
ejpam-676	300	14	159	159	NUM
ejpam-676	300	15	151	151	NUM
ejpam-676	300	16	corollary	corollary	ADJ
ejpam-676	300	17	4	4	NUM
ejpam-676	300	18	.	.	PUNCT
ejpam-676	301	1	if	if	SCONJ
ejpam-676	301	2	δ	δ	PROPN
ejpam-676	301	3	>	>	X
ejpam-676	301	4	0	0	PUNCT
ejpam-676	302	1	and	and	CCONJ
ejpam-676	302	2	f	f	PROPN
ejpam-676	302	3	∈	∈	PROPN
ejpam-676	302	4	σp	σp	PROPN
ejpam-676	302	5	,	,	PUNCT
ejpam-676	302	6	q	q	NOUN
ejpam-676	302	7	,	,	PUNCT
ejpam-676	302	8	s(α1	s(α1	NOUN
ejpam-676	302	9	;	;	PUNCT
ejpam-676	302	10	a	a	DET
ejpam-676	302	11	,	,	PUNCT
ejpam-676	302	12	b	b	NOUN
ejpam-676	302	13	)	)	PUNCT
ejpam-676	302	14	,	,	PUNCT
ejpam-676	302	15	then	then	ADV
ejpam-676	302	16	fδ	fδ	VERB
ejpam-676	302	17	,	,	PUNCT
ejpam-676	302	18	p	p	X
ejpam-676	302	19	(	(	PUNCT
ejpam-676	302	20	f	f	PROPN
ejpam-676	302	21	)	)	PUNCT
ejpam-676	302	22	(	(	PUNCT
ejpam-676	302	23	z	z	X
ejpam-676	302	24	)	)	PUNCT
ejpam-676	302	25	∈	∈	PROPN
ejpam-676	302	26	σp	σp	PROPN
ejpam-676	302	27	,	,	PUNCT
ejpam-676	302	28	q	q	NOUN
ejpam-676	302	29	,	,	PUNCT
ejpam-676	302	30	s(α1	s(α1	NOUN
ejpam-676	302	31	;	;	PUNCT
ejpam-676	302	32	1−	1−	NUM
ejpam-676	302	33	2ξ	2ξ	NUM
ejpam-676	302	34	p	p	X
ejpam-676	302	35	,	,	PUNCT
ejpam-676	302	36	−1)⊂	−1)⊂	PROPN
ejpam-676	302	37	σp	σp	NOUN
ejpam-676	302	38	,	,	PUNCT
ejpam-676	302	39	q	q	NOUN
ejpam-676	302	40	,	,	PUNCT
ejpam-676	302	41	s(α1	s(α1	NOUN
ejpam-676	302	42	;	;	PUNCT
ejpam-676	302	43	a	a	DET
ejpam-676	302	44	,	,	PUNCT
ejpam-676	302	45	b	b	NOUN
ejpam-676	302	46	)	)	PUNCT
ejpam-676	302	47	,	,	PUNCT
ejpam-676	302	48	where	where	SCONJ
ejpam-676	302	49	ξ=	ξ=	NOUN
ejpam-676	302	50			NOUN
ejpam-676	302	51			PROPN
ejpam-676	302	52			NOUN
ejpam-676	302	53	a	a	DET
ejpam-676	302	54	b	b	NOUN
ejpam-676	302	55	+	+	CCONJ
ejpam-676	302	56	(	(	PUNCT
ejpam-676	302	57	1−	1−	NUM
ejpam-676	302	58	a	a	DET
ejpam-676	302	59	b	b	NOUN
ejpam-676	302	60	)	)	PUNCT
ejpam-676	302	61	(	(	PUNCT
ejpam-676	302	62	1	1	NUM
ejpam-676	302	63	+	+	NUM
ejpam-676	302	64	b)−1	b)−1	NOUN
ejpam-676	302	65	2f1(1,1;δ+	2f1(1,1;δ+	NOUN
ejpam-676	302	66	1	1	NUM
ejpam-676	302	67	;	;	PUNCT
ejpam-676	302	68	b	b	X
ejpam-676	302	69	b−1	b−1	PROPN
ejpam-676	302	70	)	)	PUNCT
ejpam-676	302	71	(	(	PUNCT
ejpam-676	302	72	b	b	X
ejpam-676	302	73	6=	6=	NUM
ejpam-676	302	74	0	0	NUM
ejpam-676	302	75	)	)	PUNCT
ejpam-676	302	76	1−	1−	NUM
ejpam-676	302	77	δ	δ	PROPN
ejpam-676	302	78	δ+1	δ+1	PROPN
ejpam-676	302	79	a	a	DET
ejpam-676	302	80	(	(	PUNCT
ejpam-676	302	81	b	b	NOUN
ejpam-676	302	82	=	=	NOUN
ejpam-676	302	83	0	0	NUM
ejpam-676	302	84	)	)	PUNCT
ejpam-676	302	85	.	.	PUNCT
ejpam-676	303	1	the	the	DET
ejpam-676	303	2	result	result	NOUN
ejpam-676	303	3	is	be	AUX
ejpam-676	303	4	the	the	DET
ejpam-676	303	5	best	good	ADJ
ejpam-676	303	6	possible	possible	ADJ
ejpam-676	303	7	.	.	PUNCT
ejpam-676	304	1	remark	remark	PROPN
ejpam-676	304	2	4	4	NUM
ejpam-676	304	3	.	.	PUNCT
ejpam-676	304	4	by	by	ADP
ejpam-676	304	5	observing	observe	VERB
ejpam-676	304	6	that	that	PRON
ejpam-676	304	7	zp+1(hp	zp+1(hp	ADJ
ejpam-676	304	8	,	,	PUNCT
ejpam-676	304	9	q	q	NOUN
ejpam-676	304	10	,	,	PUNCT
ejpam-676	304	11	s(α1)fδ	s(α1)fδ	ADJ
ejpam-676	304	12	,	,	PUNCT
ejpam-676	304	13	p	p	X
ejpam-676	304	14	(	(	PUNCT
ejpam-676	304	15	f	f	PROPN
ejpam-676	304	16	)	)	PUNCT
ejpam-676	304	17	(	(	PUNCT
ejpam-676	304	18	z	z	NOUN
ejpam-676	304	19	)	)	PUNCT
ejpam-676	304	20	)	)	PUNCT
ejpam-676	305	1	′	′	NUM
ejpam-676	306	1	=	=	PUNCT
ejpam-676	306	2	δ	δ	PROPN
ejpam-676	306	3	zδ	zδ	NOUN
ejpam-676	306	4	z	z	PROPN
ejpam-676	306	5	∫	∫	PROPN
ejpam-676	306	6	0	0	NUM
ejpam-676	307	1	tδ+p(hp	tδ+p(hp	ADJ
ejpam-676	307	2	,	,	PUNCT
ejpam-676	307	3	q	q	NOUN
ejpam-676	307	4	,	,	PUNCT
ejpam-676	307	5	s(α1	s(α1	NOUN
ejpam-676	307	6	)	)	PUNCT
ejpam-676	308	1	f	f	PROPN
ejpam-676	308	2	(	(	PUNCT
ejpam-676	308	3	t	t	PROPN
ejpam-676	308	4	)	)	PUNCT
ejpam-676	308	5	)	)	PUNCT
ejpam-676	309	1	′	′	NUM
ejpam-676	310	1	d	d	NOUN
ejpam-676	310	2	t	t	PROPN
ejpam-676	310	3	(	(	PUNCT
ejpam-676	310	4	f	f	PROPN
ejpam-676	310	5	∈	∈	PROPN
ejpam-676	310	6	σp	σp	PROPN
ejpam-676	310	7	,	,	PUNCT
ejpam-676	310	8	m	m	PROPN
ejpam-676	310	9	;	;	PUNCT
ejpam-676	310	10	z	z	PROPN
ejpam-676	310	11	∈	∈	PROPN
ejpam-676	310	12	u	u	NOUN
ejpam-676	310	13	)	)	PUNCT
ejpam-676	310	14	,	,	PUNCT
ejpam-676	310	15	(	(	PUNCT
ejpam-676	310	16	33	33	NUM
ejpam-676	310	17	)	)	PUNCT
ejpam-676	310	18	corollary	corollary	NOUN
ejpam-676	310	19	4	4	NUM
ejpam-676	310	20	can	can	AUX
ejpam-676	310	21	be	be	AUX
ejpam-676	310	22	restated	restate	VERB
ejpam-676	310	23	as	as	SCONJ
ejpam-676	310	24	follows	follow	VERB
ejpam-676	310	25	:	:	PUNCT
ejpam-676	310	26	if	if	SCONJ
ejpam-676	310	27	δ	δ	PROPN
ejpam-676	310	28	>	>	X
ejpam-676	310	29	0	0	PUNCT
ejpam-676	310	30	and	and	CCONJ
ejpam-676	310	31	f	f	PROPN
ejpam-676	310	32	∈	∈	PROPN
ejpam-676	310	33	σp	σp	PROPN
ejpam-676	310	34	,	,	PUNCT
ejpam-676	310	35	q	q	NOUN
ejpam-676	310	36	,	,	PUNCT
ejpam-676	310	37	s(α1	s(α1	NOUN
ejpam-676	310	38	;	;	PUNCT
ejpam-676	310	39	a	a	DET
ejpam-676	310	40	,	,	PUNCT
ejpam-676	310	41	b	b	NOUN
ejpam-676	310	42	)	)	PUNCT
ejpam-676	310	43	,	,	PUNCT
ejpam-676	310	44	then	then	ADV
ejpam-676	310	45	re	re	VERB
ejpam-676	310	46			PROPN
ejpam-676	310	47			PRON
ejpam-676	310	48			NOUN
ejpam-676	310	49	−	−	PROPN
ejpam-676	310	50	δ	δ	PROPN
ejpam-676	310	51	pzδ	pzδ	PROPN
ejpam-676	310	52	z	z	PROPN
ejpam-676	310	53	∫	∫	PROPN
ejpam-676	310	54	0	0	NUM
ejpam-676	311	1	tδ+p(hp	tδ+p(hp	ADJ
ejpam-676	311	2	,	,	PUNCT
ejpam-676	311	3	q	q	NOUN
ejpam-676	311	4	,	,	PUNCT
ejpam-676	311	5	s(α1	s(α1	NOUN
ejpam-676	311	6	)	)	PUNCT
ejpam-676	312	1	f	f	PROPN
ejpam-676	312	2	(	(	PUNCT
ejpam-676	312	3	t	t	PROPN
ejpam-676	312	4	)	)	PUNCT
ejpam-676	312	5	)	)	PUNCT
ejpam-676	313	1	′	′	NUM
ejpam-676	314	1	d	d	NOUN
ejpam-676	314	2	t	t	PROPN
ejpam-676	314	3			PROPN
ejpam-676	314	4			PROPN
ejpam-676	314	5			PROPN
ejpam-676	314	6	>	>	X
ejpam-676	314	7	ξ	ξ	X
ejpam-676	314	8	(	(	PUNCT
ejpam-676	314	9	z	z	NOUN
ejpam-676	314	10	∈	∈	PROPN
ejpam-676	314	11	u	u	NOUN
ejpam-676	314	12	)	)	PUNCT
ejpam-676	314	13	.	.	PUNCT
ejpam-676	315	1	where	where	SCONJ
ejpam-676	315	2	ξ	ξ	PROPN
ejpam-676	315	3	is	be	AUX
ejpam-676	315	4	given	give	VERB
ejpam-676	315	5	as	as	ADP
ejpam-676	315	6	in	in	ADP
ejpam-676	315	7	corollary	corollary	ADJ
ejpam-676	315	8	4	4	NUM
ejpam-676	315	9	.	.	PUNCT
ejpam-676	316	1	in	in	ADP
ejpam-676	316	2	view	view	NOUN
ejpam-676	316	3	of	of	ADP
ejpam-676	316	4	(	(	PUNCT
ejpam-676	316	5	33	33	NUM
ejpam-676	316	6	)	)	PUNCT
ejpam-676	316	7	,	,	PUNCT
ejpam-676	316	8	theorem	theorem	VERB
ejpam-676	316	9	3	3	NUM
ejpam-676	316	10	for	for	ADP
ejpam-676	316	11	a=	a=	NOUN
ejpam-676	316	12	1−	1−	NUM
ejpam-676	316	13	2θ	2θ	NUM
ejpam-676	317	1	p	p	X
ejpam-676	317	2	(	(	PUNCT
ejpam-676	317	3	0≤	0≤	NUM
ejpam-676	317	4	θ	θ	X
ejpam-676	317	5	<	<	X
ejpam-676	317	6	p	p	X
ejpam-676	317	7	;	;	PUNCT
ejpam-676	317	8	p	p	PROPN
ejpam-676	317	9	∈	∈	PROPN
ejpam-676	317	10	n	n	CCONJ
ejpam-676	317	11	)	)	PUNCT
ejpam-676	317	12	and	and	CCONJ
ejpam-676	317	13	b	b	X
ejpam-676	317	14	=	=	SYM
ejpam-676	317	15	−1	−1	NOUN
ejpam-676	317	16	yields	yield	NOUN
ejpam-676	317	17	corollary	corollary	ADJ
ejpam-676	317	18	5	5	NUM
ejpam-676	317	19	.	.	PUNCT
ejpam-676	318	1	if	if	SCONJ
ejpam-676	318	2	δ	δ	PROPN
ejpam-676	318	3	>	>	X
ejpam-676	318	4	0	0	PUNCT
ejpam-676	319	1	and	and	CCONJ
ejpam-676	319	2	if	if	SCONJ
ejpam-676	319	3	f	f	PROPN
ejpam-676	319	4	∈	∈	PROPN
ejpam-676	319	5	σp	σp	PROPN
ejpam-676	319	6	,	,	PUNCT
ejpam-676	319	7	m	m	VERB
ejpam-676	319	8	satisfies	satisfy	VERB
ejpam-676	319	9	the	the	DET
ejpam-676	319	10	following	follow	VERB
ejpam-676	319	11	inequality	inequality	NOUN
ejpam-676	319	12	:	:	PUNCT
ejpam-676	319	13	re	re	X
ejpam-676	319	14	¦	¦	PROPN
ejpam-676	319	15	−zp+1(hp	−zp+1(hp	PROPN
ejpam-676	319	16	,	,	PUNCT
ejpam-676	319	17	q	q	NOUN
ejpam-676	319	18	,	,	PUNCT
ejpam-676	319	19	s(α1	s(α1	NOUN
ejpam-676	319	20	)	)	PUNCT
ejpam-676	320	1	f	f	PROPN
ejpam-676	320	2	(	(	PUNCT
ejpam-676	320	3	z	z	NOUN
ejpam-676	320	4	)	)	PUNCT
ejpam-676	320	5	)	)	PUNCT
ejpam-676	321	1	′	′	NOUN
ejpam-676	321	2	©	©	NOUN
ejpam-676	321	3	>	>	X
ejpam-676	321	4	θ	θ	PROPN
ejpam-676	321	5	(	(	PUNCT
ejpam-676	321	6	0≤	0≤	NUM
ejpam-676	321	7	θ	θ	X
ejpam-676	321	8	<	<	X
ejpam-676	321	9	p	p	X
ejpam-676	321	10	;	;	PUNCT
ejpam-676	321	11	p	p	PROPN
ejpam-676	321	12	∈	∈	PROPN
ejpam-676	321	13	n	n	NOUN
ejpam-676	321	14	;	;	PUNCT
ejpam-676	321	15	z	z	PROPN
ejpam-676	321	16	∈	∈	PROPN
ejpam-676	321	17	u	u	NOUN
ejpam-676	321	18	)	)	PUNCT
ejpam-676	321	19	,	,	PUNCT
ejpam-676	321	20	then	then	ADV
ejpam-676	321	21	re	re	VERB
ejpam-676	321	22			PROPN
ejpam-676	321	23			NOUN
ejpam-676	321	24			ADJ
ejpam-676	321	25	−δ	−δ	ADJ
ejpam-676	321	26	zδ	zδ	X
ejpam-676	321	27	z	z	PROPN
ejpam-676	321	28	∫	∫	PROPN
ejpam-676	321	29	0	0	PUNCT
ejpam-676	322	1	(	(	PUNCT
ejpam-676	322	2	hp	hp	PROPN
ejpam-676	322	3	,	,	PUNCT
ejpam-676	322	4	q	q	NOUN
ejpam-676	322	5	,	,	PUNCT
ejpam-676	322	6	s(α1	s(α1	NOUN
ejpam-676	322	7	)	)	PUNCT
ejpam-676	322	8	f	f	PROPN
ejpam-676	322	9	(	(	PUNCT
ejpam-676	322	10	t	t	PROPN
ejpam-676	322	11	)	)	PUNCT
ejpam-676	322	12	)	)	PUNCT
ejpam-676	323	1	′	′	NUM
ejpam-676	324	1	d	d	NOUN
ejpam-676	324	2	t	t	PROPN
ejpam-676	324	3			PROPN
ejpam-676	324	4			PROPN
ejpam-676	324	5			NOUN
ejpam-676	324	6	>	>	X
ejpam-676	324	7	θ	θ	PROPN
ejpam-676	325	1	+	+	PUNCT
ejpam-676	325	2	(	(	PUNCT
ejpam-676	325	3	p−	p−	NOUN
ejpam-676	325	4	θ	θ	NOUN
ejpam-676	325	5	)	)	PUNCT
ejpam-676	325	6	�	�	PROPN
ejpam-676	325	7	2f1(1,1	2f1(1,1	NUM
ejpam-676	325	8	;	;	PUNCT
ejpam-676	325	9	δ	δ	PROPN
ejpam-676	325	10	p+m	p+m	PROPN
ejpam-676	325	11	+	+	CCONJ
ejpam-676	325	12	1	1	NUM
ejpam-676	325	13	;	;	PUNCT
ejpam-676	325	14	1	1	NUM
ejpam-676	325	15	2	2	NUM
ejpam-676	325	16	)	)	PUNCT
ejpam-676	325	17	−	−	PROPN
ejpam-676	325	18	1	1	NUM
ejpam-676	325	19	�	�	PROPN
ejpam-676	325	20	(	(	PUNCT
ejpam-676	325	21	z	z	NOUN
ejpam-676	325	22	∈	∈	PROPN
ejpam-676	325	23	u	u	NOUN
ejpam-676	325	24	)	)	PUNCT
ejpam-676	325	25	.	.	PUNCT
ejpam-676	326	1	the	the	DET
ejpam-676	326	2	result	result	NOUN
ejpam-676	326	3	is	be	AUX
ejpam-676	326	4	the	the	DET
ejpam-676	326	5	best	good	ADJ
ejpam-676	326	6	possible	possible	ADJ
ejpam-676	326	7	.	.	PUNCT
ejpam-676	327	1	remark	remark	NOUN
ejpam-676	327	2	5	5	NUM
ejpam-676	327	3	.	.	PUNCT
ejpam-676	328	1	putting	put	VERB
ejpam-676	328	2	s	s	PART
ejpam-676	328	3	=	=	SYM
ejpam-676	328	4	1	1	NUM
ejpam-676	328	5	,	,	PUNCT
ejpam-676	328	6	q	q	NOUN
ejpam-676	328	7	=	=	SYM
ejpam-676	328	8	2	2	NUM
ejpam-676	328	9	,	,	PUNCT
ejpam-676	328	10	α1	α1	PROPN
ejpam-676	328	11	=	=	SYM
ejpam-676	328	12	a	a	NOUN
ejpam-676	328	13	,	,	PUNCT
ejpam-676	328	14	β1	β1	PROPN
ejpam-676	328	15	=	=	PUNCT
ejpam-676	328	16	c	c	PROPN
ejpam-676	328	17	(	(	PUNCT
ejpam-676	328	18	a	a	DET
ejpam-676	328	19	>	>	X
ejpam-676	328	20	0	0	NUM
ejpam-676	328	21	;	;	PUNCT
ejpam-676	328	22	c	c	X
ejpam-676	328	23	>	>	X
ejpam-676	328	24	0	0	NUM
ejpam-676	328	25	)	)	PUNCT
ejpam-676	328	26	and	and	CCONJ
ejpam-676	328	27	α2	α2	NOUN
ejpam-676	328	28	=	=	SYM
ejpam-676	328	29	1	1	NUM
ejpam-676	328	30	in	in	ADP
ejpam-676	328	31	theorem	theorem	NOUN
ejpam-676	328	32	3	3	NUM
ejpam-676	328	33	,	,	PUNCT
ejpam-676	328	34	we	we	PRON
ejpam-676	328	35	obtain	obtain	VERB
ejpam-676	328	36	the	the	DET
ejpam-676	328	37	result	result	NOUN
ejpam-676	328	38	obtained	obtain	VERB
ejpam-676	328	39	by	by	ADP
ejpam-676	328	40	patel	patel	NOUN
ejpam-676	328	41	and	and	CCONJ
ejpam-676	328	42	cho	cho	NOUN
ejpam-676	329	1	[	[	X
ejpam-676	329	2	12	12	NUM
ejpam-676	329	3	,	,	PUNCT
ejpam-676	329	4	theorem	theorem	VERB
ejpam-676	329	5	3	3	NUM
ejpam-676	329	6	]	]	PUNCT
ejpam-676	329	7	.	.	PUNCT
ejpam-676	330	1	m.	m.	PROPN
ejpam-676	330	2	aouf	aouf	PROPN
ejpam-676	330	3	/	/	SYM
ejpam-676	330	4	eur	eur	PROPN
ejpam-676	330	5	.	.	PUNCT
ejpam-676	331	1	j.	j.	PROPN
ejpam-676	331	2	pure	pure	PROPN
ejpam-676	331	3	appl	appl	PROPN
ejpam-676	331	4	.	.	PROPN
ejpam-676	331	5	math	math	PROPN
ejpam-676	331	6	,	,	PUNCT
ejpam-676	331	7	5	5	NUM
ejpam-676	331	8	(	(	PUNCT
ejpam-676	331	9	2012	2012	NUM
ejpam-676	331	10	)	)	PUNCT
ejpam-676	331	11	,	,	PUNCT
ejpam-676	331	12	141	141	NUM
ejpam-676	331	13	-	-	SYM
ejpam-676	331	14	159	159	NUM
ejpam-676	331	15	152	152	NUM
ejpam-676	331	16	theorem	theorem	NOUN
ejpam-676	331	17	4	4	NUM
ejpam-676	331	18	.	.	PUNCT
ejpam-676	332	1	let	let	VERB
ejpam-676	332	2	f	f	PROPN
ejpam-676	332	3	∈	∈	PROPN
ejpam-676	332	4	σp	σp	PROPN
ejpam-676	332	5	,	,	PUNCT
ejpam-676	332	6	m.	m.	NOUN
ejpam-676	332	7	suppose	suppose	VERB
ejpam-676	332	8	also	also	ADV
ejpam-676	332	9	that	that	SCONJ
ejpam-676	332	10	g	g	PROPN
ejpam-676	332	11	∈	∈	PROPN
ejpam-676	332	12	σp	σp	PROPN
ejpam-676	332	13	,	,	PUNCT
ejpam-676	332	14	m	m	VERB
ejpam-676	332	15	satisfies	satisfy	VERB
ejpam-676	332	16	the	the	DET
ejpam-676	332	17	following	follow	VERB
ejpam-676	332	18	inequality	inequality	NOUN
ejpam-676	332	19	:	:	PUNCT
ejpam-676	332	20	re	re	ADP
ejpam-676	332	21	¦	¦	PROPN
ejpam-676	332	22	zp(hp	zp(hp	PROPN
ejpam-676	332	23	,	,	PUNCT
ejpam-676	332	24	q	q	NOUN
ejpam-676	332	25	,	,	PUNCT
ejpam-676	332	26	s(α1)g(z	s(α1)g(z	NOUN
ejpam-676	332	27	)	)	PUNCT
ejpam-676	332	28	)	)	PUNCT
ejpam-676	333	1	©	©	ADP
ejpam-676	333	2	>	>	X
ejpam-676	333	3	0	0	PUNCT
ejpam-676	334	1	(	(	PUNCT
ejpam-676	334	2	z	z	NOUN
ejpam-676	334	3	∈	∈	PROPN
ejpam-676	334	4	u	u	NOUN
ejpam-676	334	5	)	)	PUNCT
ejpam-676	334	6	.	.	PUNCT
ejpam-676	335	1	if	if	SCONJ
ejpam-676	335	2	�	�	PROPN
ejpam-676	335	3	�	�	PROPN
ejpam-676	335	4	�	�	PROPN
ejpam-676	335	5	�	�	PROPN
ejpam-676	335	6	�	�	PROPN
ejpam-676	335	7	hp	hp	PROPN
ejpam-676	335	8	,	,	PUNCT
ejpam-676	335	9	q	q	NOUN
ejpam-676	335	10	,	,	PUNCT
ejpam-676	335	11	s(α1	s(α1	NOUN
ejpam-676	335	12	)	)	PUNCT
ejpam-676	335	13	f	f	PROPN
ejpam-676	335	14	(	(	PUNCT
ejpam-676	335	15	z	z	NOUN
ejpam-676	335	16	)	)	PUNCT
ejpam-676	335	17	hp	hp	PROPN
ejpam-676	335	18	,	,	PUNCT
ejpam-676	335	19	q	q	NOUN
ejpam-676	335	20	,	,	PUNCT
ejpam-676	335	21	s(α1)g(z	s(α1)g(z	ADJ
ejpam-676	335	22	)	)	PUNCT
ejpam-676	335	23	−	−	PROPN
ejpam-676	335	24	1	1	NUM
ejpam-676	335	25	�	�	PROPN
ejpam-676	335	26	�	�	PROPN
ejpam-676	335	27	�	�	PROPN
ejpam-676	335	28	�	�	PROPN
ejpam-676	335	29	�	�	PROPN
ejpam-676	335	30	<	<	X
ejpam-676	335	31	1	1	NUM
ejpam-676	335	32	(	(	PUNCT
ejpam-676	335	33	z	z	NOUN
ejpam-676	335	34	∈	∈	PROPN
ejpam-676	335	35	u	u	NOUN
ejpam-676	335	36	)	)	PUNCT
ejpam-676	335	37	,	,	PUNCT
ejpam-676	335	38	then	then	ADV
ejpam-676	335	39	re	re	X
ejpam-676	335	40	(	(	PUNCT
ejpam-676	335	41	−z(hp	−z(hp	PROPN
ejpam-676	335	42	,	,	PUNCT
ejpam-676	335	43	q	q	NOUN
ejpam-676	335	44	,	,	PUNCT
ejpam-676	335	45	s(α1	s(α1	NOUN
ejpam-676	335	46	)	)	PUNCT
ejpam-676	336	1	f	f	PROPN
ejpam-676	336	2	(	(	PUNCT
ejpam-676	336	3	z	z	NOUN
ejpam-676	336	4	)	)	PUNCT
ejpam-676	336	5	)	)	PUNCT
ejpam-676	337	1	′	′	NUM
ejpam-676	338	1	hp	hp	PROPN
ejpam-676	338	2	,	,	PUNCT
ejpam-676	338	3	q	q	NOUN
ejpam-676	338	4	,	,	PUNCT
ejpam-676	338	5	s(α1	s(α1	NOUN
ejpam-676	338	6	)	)	PUNCT
ejpam-676	338	7	f	f	PROPN
ejpam-676	338	8	(	(	PUNCT
ejpam-676	338	9	z	z	NOUN
ejpam-676	338	10	)	)	PUNCT
ejpam-676	338	11	)	)	PUNCT
ejpam-676	339	1	>	>	X
ejpam-676	339	2	0	0	PUNCT
ejpam-676	340	1	(	(	PUNCT
ejpam-676	340	2	|z|	|z|	NOUN
ejpam-676	340	3	<	<	X
ejpam-676	340	4	r0	r0	NOUN
ejpam-676	340	5	)	)	PUNCT
ejpam-676	340	6	,	,	PUNCT
ejpam-676	340	7	where	where	SCONJ
ejpam-676	340	8	r0	r0	NOUN
ejpam-676	340	9	=	=	PROPN
ejpam-676	340	10	p	p	X
ejpam-676	340	11	g(p+m)2	g(p+m)2	PROPN
ejpam-676	340	12	+	+	CCONJ
ejpam-676	340	13	4p(2p+m)−	4p(2p+m)−	NUM
ejpam-676	341	1	3(p+m	3(p+m	NUM
ejpam-676	341	2	)	)	PUNCT
ejpam-676	341	3	2(2p+m	2(2p+m	NUM
ejpam-676	341	4	)	)	PUNCT
ejpam-676	341	5	.	.	PUNCT
ejpam-676	342	1	proof	proof	NOUN
ejpam-676	342	2	.	.	PUNCT
ejpam-676	343	1	letting	let	VERB
ejpam-676	343	2	w(z	w(z	NOUN
ejpam-676	343	3	)	)	PUNCT
ejpam-676	343	4	=	=	SYM
ejpam-676	343	5	hp	hp	PROPN
ejpam-676	343	6	,	,	PUNCT
ejpam-676	343	7	q	q	NOUN
ejpam-676	343	8	,	,	PUNCT
ejpam-676	343	9	s(α1	s(α1	NOUN
ejpam-676	343	10	)	)	PUNCT
ejpam-676	344	1	f	f	PROPN
ejpam-676	344	2	(	(	PUNCT
ejpam-676	344	3	z	z	NOUN
ejpam-676	344	4	)	)	PUNCT
ejpam-676	344	5	hp	hp	PROPN
ejpam-676	344	6	,	,	PUNCT
ejpam-676	344	7	q	q	NOUN
ejpam-676	344	8	,	,	PUNCT
ejpam-676	344	9	s(α1)g(z	s(α1)g(z	ADJ
ejpam-676	344	10	)	)	PUNCT
ejpam-676	344	11	−	−	NOUN
ejpam-676	344	12	1=	1=	NUM
ejpam-676	344	13	tp+mzp+m+	tp+mzp+m+	NOUN
ejpam-676	344	14	tp+m+1zp+m+1	tp+m+1zp+m+1	PROPN
ejpam-676	344	15	+	+	X
ejpam-676	344	16	.	.	PUNCT
ejpam-676	344	17	.	.	PUNCT
ejpam-676	344	18	.	.	PUNCT
ejpam-676	345	1	(	(	PUNCT
ejpam-676	345	2	34	34	NUM
ejpam-676	345	3	)	)	PUNCT
ejpam-676	345	4	we	we	PRON
ejpam-676	345	5	note	note	VERB
ejpam-676	345	6	that	that	SCONJ
ejpam-676	345	7	w	w	NOUN
ejpam-676	345	8	is	be	AUX
ejpam-676	345	9	analytic	analytic	ADJ
ejpam-676	345	10	in	in	ADP
ejpam-676	345	11	u	u	PROPN
ejpam-676	345	12	,	,	PUNCT
ejpam-676	345	13	with	with	ADP
ejpam-676	345	14	w(0	w(0	PROPN
ejpam-676	345	15	)	)	PUNCT
ejpam-676	345	16	=	=	SYM
ejpam-676	345	17	0	0	NUM
ejpam-676	345	18	and	and	CCONJ
ejpam-676	345	19	|w(z)|	|w(z)|	VERB
ejpam-676	345	20	≤	≤	NOUN
ejpam-676	345	21	|z|p+m	|z|p+m	X
ejpam-676	345	22	(	(	PUNCT
ejpam-676	345	23	z	z	NOUN
ejpam-676	345	24	∈	∈	PROPN
ejpam-676	345	25	u	u	NOUN
ejpam-676	345	26	)	)	PUNCT
ejpam-676	345	27	.	.	PUNCT
ejpam-676	346	1	then	then	ADV
ejpam-676	346	2	,	,	PUNCT
ejpam-676	346	3	by	by	ADP
ejpam-676	346	4	applying	apply	VERB
ejpam-676	346	5	the	the	DET
ejpam-676	346	6	familiar	familiar	ADJ
ejpam-676	346	7	schwarz	schwarz	NOUN
ejpam-676	346	8	lemma	lemma	PROPN
ejpam-676	347	1	[	[	X
ejpam-676	347	2	9	9	NUM
ejpam-676	347	3	]	]	PUNCT
ejpam-676	347	4	,	,	PUNCT
ejpam-676	347	5	we	we	PRON
ejpam-676	347	6	obtain	obtain	VERB
ejpam-676	347	7	w(z	w(z	NOUN
ejpam-676	347	8	)	)	PUNCT
ejpam-676	347	9	=	=	SYM
ejpam-676	347	10	zp+mψ(z	zp+mψ(z	PROPN
ejpam-676	347	11	)	)	PUNCT
ejpam-676	347	12	,	,	PUNCT
ejpam-676	347	13	where	where	SCONJ
ejpam-676	347	14	the	the	DET
ejpam-676	347	15	functions	function	NOUN
ejpam-676	347	16	ψ	ψ	NOUN
ejpam-676	347	17	is	be	AUX
ejpam-676	347	18	analytic	analytic	ADJ
ejpam-676	347	19	in	in	ADP
ejpam-676	347	20	u	u	NOUN
ejpam-676	347	21	and	and	CCONJ
ejpam-676	347	22	|ψ(z)|	|ψ(z)|	DET
ejpam-676	347	23	≤	≤	NOUN
ejpam-676	347	24	1	1	NUM
ejpam-676	347	25	(	(	PUNCT
ejpam-676	347	26	z	z	NOUN
ejpam-676	347	27	∈	∈	PROPN
ejpam-676	347	28	u	u	NOUN
ejpam-676	347	29	)	)	PUNCT
ejpam-676	347	30	.	.	PUNCT
ejpam-676	348	1	therefore	therefore	ADV
ejpam-676	348	2	,	,	PUNCT
ejpam-676	348	3	(	(	PUNCT
ejpam-676	348	4	34	34	NUM
ejpam-676	348	5	)	)	PUNCT
ejpam-676	348	6	leads	lead	VERB
ejpam-676	348	7	us	we	PRON
ejpam-676	348	8	to	to	ADP
ejpam-676	348	9	hp	hp	PROPN
ejpam-676	348	10	,	,	PUNCT
ejpam-676	348	11	q	q	NOUN
ejpam-676	348	12	,	,	PUNCT
ejpam-676	348	13	s(α1	s(α1	NOUN
ejpam-676	348	14	)	)	PUNCT
ejpam-676	349	1	f	f	PROPN
ejpam-676	349	2	(	(	PUNCT
ejpam-676	349	3	z	z	NOUN
ejpam-676	349	4	)	)	PUNCT
ejpam-676	349	5	=	=	SYM
ejpam-676	349	6	hp	hp	PROPN
ejpam-676	349	7	,	,	PUNCT
ejpam-676	349	8	q	q	NOUN
ejpam-676	349	9	,	,	PUNCT
ejpam-676	349	10	s(α1)g(z	s(α1)g(z	PROPN
ejpam-676	349	11	)	)	PUNCT
ejpam-676	349	12	(	(	PUNCT
ejpam-676	349	13	1	1	NUM
ejpam-676	349	14	+	+	NUM
ejpam-676	349	15	zp+mψ(z	zp+mψ(z	NOUN
ejpam-676	349	16	)	)	PUNCT
ejpam-676	349	17	)	)	PUNCT
ejpam-676	350	1	(	(	PUNCT
ejpam-676	350	2	z	z	NOUN
ejpam-676	350	3	∈	∈	PROPN
ejpam-676	350	4	u	u	NOUN
ejpam-676	350	5	)	)	PUNCT
ejpam-676	350	6	.	.	PUNCT
ejpam-676	351	1	(	(	PUNCT
ejpam-676	351	2	35	35	NUM
ejpam-676	351	3	)	)	PUNCT
ejpam-676	351	4	differentiating	differentiating	NOUN
ejpam-676	351	5	(	(	PUNCT
ejpam-676	351	6	35	35	NUM
ejpam-676	351	7	)	)	PUNCT
ejpam-676	351	8	logarithmically	logarithmically	ADV
ejpam-676	351	9	with	with	ADP
ejpam-676	351	10	respect	respect	NOUN
ejpam-676	351	11	to	to	ADP
ejpam-676	351	12	z	z	NOUN
ejpam-676	351	13	,	,	PUNCT
ejpam-676	351	14	we	we	PRON
ejpam-676	351	15	obtain	obtain	VERB
ejpam-676	351	16	z(hp	z(hp	NUM
ejpam-676	351	17	,	,	PUNCT
ejpam-676	351	18	q	q	NOUN
ejpam-676	351	19	,	,	PUNCT
ejpam-676	351	20	s(α1	s(α1	NOUN
ejpam-676	351	21	)	)	PUNCT
ejpam-676	352	1	f	f	PROPN
ejpam-676	352	2	(	(	PUNCT
ejpam-676	352	3	z	z	NOUN
ejpam-676	352	4	)	)	PUNCT
ejpam-676	352	5	)	)	PUNCT
ejpam-676	353	1	′	′	NUM
ejpam-676	354	1	hp	hp	PROPN
ejpam-676	354	2	,	,	PUNCT
ejpam-676	354	3	q	q	NOUN
ejpam-676	354	4	,	,	PUNCT
ejpam-676	354	5	s(α1	s(α1	NOUN
ejpam-676	354	6	)	)	PUNCT
ejpam-676	354	7	f	f	PROPN
ejpam-676	354	8	(	(	PUNCT
ejpam-676	354	9	z	z	NOUN
ejpam-676	354	10	)	)	PUNCT
ejpam-676	354	11	=	=	SYM
ejpam-676	355	1	z(hp	z(hp	PROPN
ejpam-676	355	2	,	,	PUNCT
ejpam-676	355	3	q	q	NOUN
ejpam-676	355	4	,	,	PUNCT
ejpam-676	355	5	s(α1)g(z	s(α1)g(z	NOUN
ejpam-676	355	6	)	)	PUNCT
ejpam-676	355	7	)	)	PUNCT
ejpam-676	356	1	′	′	NUM
ejpam-676	357	1	hp	hp	PROPN
ejpam-676	357	2	,	,	PUNCT
ejpam-676	357	3	q	q	NOUN
ejpam-676	357	4	,	,	PUNCT
ejpam-676	357	5	s(α1)g(z	s(α1)g(z	ADJ
ejpam-676	357	6	)	)	PUNCT
ejpam-676	357	7	+	+	CCONJ
ejpam-676	357	8	zp+m	zp+m	PROPN
ejpam-676	357	9	¦	¦	PROPN
ejpam-676	357	10	(	(	PUNCT
ejpam-676	357	11	p+m)ψ(z	p+m)ψ(z	NOUN
ejpam-676	357	12	)	)	PUNCT
ejpam-676	358	1	+	+	CCONJ
ejpam-676	358	2	zψ	zψ	PROPN
ejpam-676	359	1	′	′	NUM
ejpam-676	359	2	(	(	PUNCT
ejpam-676	359	3	z	z	X
ejpam-676	359	4	)	)	PUNCT
ejpam-676	359	5	©	©	PROPN
ejpam-676	359	6	1	1	NUM
ejpam-676	359	7	+	+	NUM
ejpam-676	359	8	zp+mψ(z	zp+mψ(z	NOUN
ejpam-676	359	9	)	)	PUNCT
ejpam-676	359	10	.	.	PUNCT
ejpam-676	360	1	(	(	PUNCT
ejpam-676	360	2	36	36	X
ejpam-676	360	3	)	)	PUNCT
ejpam-676	360	4	putting	put	VERB
ejpam-676	360	5	ϕ(z	ϕ(z	NOUN
ejpam-676	360	6	)	)	PUNCT
ejpam-676	361	1	=	=	SYM
ejpam-676	361	2	zphp	zphp	VERB
ejpam-676	361	3	,	,	PUNCT
ejpam-676	361	4	q	q	NOUN
ejpam-676	361	5	,	,	PUNCT
ejpam-676	361	6	s(α1)g(z	s(α1)g(z	NOUN
ejpam-676	361	7	)	)	PUNCT
ejpam-676	361	8	,	,	PUNCT
ejpam-676	361	9	we	we	PRON
ejpam-676	361	10	see	see	VERB
ejpam-676	361	11	that	that	SCONJ
ejpam-676	361	12	the	the	DET
ejpam-676	361	13	function	function	NOUN
ejpam-676	361	14	ϕ	ϕ	NOUN
ejpam-676	361	15	is	be	AUX
ejpam-676	361	16	of	of	ADP
ejpam-676	361	17	the	the	DET
ejpam-676	361	18	form	form	NOUN
ejpam-676	361	19	(	(	PUNCT
ejpam-676	361	20	13	13	NUM
ejpam-676	361	21	)	)	PUNCT
ejpam-676	361	22	,	,	PUNCT
ejpam-676	361	23	is	be	AUX
ejpam-676	361	24	analytic	analytic	ADJ
ejpam-676	361	25	in	in	ADP
ejpam-676	361	26	u	u	PROPN
ejpam-676	361	27	,	,	PUNCT
ejpam-676	361	28	re{ϕ(z	re{ϕ(z	PROPN
ejpam-676	361	29	)	)	PUNCT
ejpam-676	361	30	}	}	PUNCT
ejpam-676	361	31	>	>	X
ejpam-676	361	32	0	0	PUNCT
ejpam-676	362	1	(	(	PUNCT
ejpam-676	362	2	z	z	NOUN
ejpam-676	362	3	∈	∈	PROPN
ejpam-676	362	4	u	u	NOUN
ejpam-676	362	5	)	)	PUNCT
ejpam-676	362	6	and	and	CCONJ
ejpam-676	362	7	z(hp	z(hp	NUM
ejpam-676	362	8	,	,	PUNCT
ejpam-676	362	9	q	q	NOUN
ejpam-676	362	10	,	,	PUNCT
ejpam-676	362	11	s(α1)g(z	s(α1)g(z	NOUN
ejpam-676	362	12	)	)	PUNCT
ejpam-676	362	13	)	)	PUNCT
ejpam-676	363	1	′	′	NUM
ejpam-676	364	1	hp	hp	PROPN
ejpam-676	364	2	,	,	PUNCT
ejpam-676	364	3	q	q	NOUN
ejpam-676	364	4	,	,	PUNCT
ejpam-676	364	5	s(α1)g(z	s(α1)g(z	ADJ
ejpam-676	364	6	)	)	PUNCT
ejpam-676	364	7	=	=	SYM
ejpam-676	364	8	zϕ	zϕ	NOUN
ejpam-676	365	1	′	′	NUM
ejpam-676	365	2	(	(	PUNCT
ejpam-676	365	3	z	z	X
ejpam-676	365	4	)	)	PUNCT
ejpam-676	365	5	ϕ(z	ϕ(z	PROPN
ejpam-676	365	6	)	)	PUNCT
ejpam-676	366	1	−	−	PROPN
ejpam-676	366	2	p	p	X
ejpam-676	366	3	,	,	PUNCT
ejpam-676	366	4	so	so	SCONJ
ejpam-676	366	5	that	that	SCONJ
ejpam-676	366	6	we	we	PRON
ejpam-676	366	7	find	find	VERB
ejpam-676	366	8	from	from	ADP
ejpam-676	366	9	(	(	PUNCT
ejpam-676	366	10	36	36	NUM
ejpam-676	366	11	)	)	PUNCT
ejpam-676	366	12	that	that	PRON
ejpam-676	366	13	re	re	VERB
ejpam-676	366	14	(	(	PUNCT
ejpam-676	366	15	−z(hp	−z(hp	PROPN
ejpam-676	366	16	,	,	PUNCT
ejpam-676	366	17	q	q	NOUN
ejpam-676	366	18	,	,	PUNCT
ejpam-676	366	19	s(α1	s(α1	NOUN
ejpam-676	366	20	)	)	PUNCT
ejpam-676	366	21	f	f	PROPN
ejpam-676	366	22	(	(	PUNCT
ejpam-676	366	23	z	z	NOUN
ejpam-676	366	24	)	)	PUNCT
ejpam-676	366	25	)	)	PUNCT
ejpam-676	366	26	′	′	NUM
ejpam-676	367	1	hp	hp	PROPN
ejpam-676	367	2	,	,	PUNCT
ejpam-676	367	3	q	q	NOUN
ejpam-676	367	4	,	,	PUNCT
ejpam-676	367	5	s(α1	s(α1	NOUN
ejpam-676	367	6	)	)	PUNCT
ejpam-676	367	7	f	f	PROPN
ejpam-676	367	8	(	(	PUNCT
ejpam-676	367	9	z	z	NOUN
ejpam-676	367	10	)	)	PUNCT
ejpam-676	367	11	)	)	PUNCT
ejpam-676	368	1	≥	≥	PROPN
ejpam-676	368	2	p−	p−	PROPN
ejpam-676	368	3	�	�	PROPN
ejpam-676	368	4	�	�	PROPN
ejpam-676	368	5	�	�	PROPN
ejpam-676	368	6	�	�	PROPN
ejpam-676	368	7	�	�	PROPN
ejpam-676	368	8	zϕ	zϕ	PROPN
ejpam-676	369	1	′	′	NUM
ejpam-676	369	2	(	(	PUNCT
ejpam-676	369	3	z	z	X
ejpam-676	369	4	)	)	PUNCT
ejpam-676	369	5	ϕ(z	ϕ(z	PROPN
ejpam-676	369	6	)	)	PUNCT
ejpam-676	369	7	�	�	PROPN
ejpam-676	369	8	�	�	PROPN
ejpam-676	369	9	�	�	PROPN
ejpam-676	369	10	�	�	PROPN
ejpam-676	369	11	�	�	PROPN
ejpam-676	369	12	−	−	PROPN
ejpam-676	369	13	�	�	PROPN
ejpam-676	369	14	�	�	PROPN
ejpam-676	369	15	�	�	PROPN
ejpam-676	369	16	�	�	PROPN
ejpam-676	369	17	�	�	PROPN
ejpam-676	369	18	zp+m	zp+m	PROPN
ejpam-676	369	19	¦	¦	PROPN
ejpam-676	369	20	(	(	PUNCT
ejpam-676	369	21	p+m)ψ(z	p+m)ψ(z	NOUN
ejpam-676	369	22	)	)	PUNCT
ejpam-676	370	1	+	+	CCONJ
ejpam-676	370	2	zψ	zψ	PROPN
ejpam-676	371	1	′	′	NUM
ejpam-676	371	2	(	(	PUNCT
ejpam-676	371	3	z	z	X
ejpam-676	371	4	)	)	PUNCT
ejpam-676	371	5	©	©	PROPN
ejpam-676	371	6	1	1	NUM
ejpam-676	371	7	+	+	CCONJ
ejpam-676	371	8	zp+mψ(z	zp+mψ(z	PROPN
ejpam-676	371	9	)	)	PUNCT
ejpam-676	371	10	�	�	PROPN
ejpam-676	371	11	�	�	PROPN
ejpam-676	371	12	�	�	PROPN
ejpam-676	371	13	�	�	PROPN
ejpam-676	371	14	�	�	PROPN
ejpam-676	371	15	(	(	PUNCT
ejpam-676	371	16	z	z	NOUN
ejpam-676	371	17	∈	∈	PROPN
ejpam-676	371	18	u	u	NOUN
ejpam-676	371	19	)	)	PUNCT
ejpam-676	371	20	.	.	PUNCT
ejpam-676	372	1	(	(	PUNCT
ejpam-676	372	2	37	37	NUM
ejpam-676	372	3	)	)	PUNCT
ejpam-676	372	4	m.	m.	NOUN
ejpam-676	372	5	aouf	aouf	PROPN
ejpam-676	372	6	/	/	SYM
ejpam-676	372	7	eur	eur	PROPN
ejpam-676	372	8	.	.	PUNCT
ejpam-676	373	1	j.	j.	PROPN
ejpam-676	373	2	pure	pure	PROPN
ejpam-676	373	3	appl	appl	PROPN
ejpam-676	373	4	.	.	PROPN
ejpam-676	373	5	math	math	PROPN
ejpam-676	373	6	,	,	PUNCT
ejpam-676	373	7	5	5	NUM
ejpam-676	373	8	(	(	PUNCT
ejpam-676	373	9	2012	2012	NUM
ejpam-676	373	10	)	)	PUNCT
ejpam-676	373	11	,	,	PUNCT
ejpam-676	373	12	141	141	NUM
ejpam-676	373	13	-	-	SYM
ejpam-676	373	14	159	159	NUM
ejpam-676	373	15	153	153	NUM
ejpam-676	373	16	now	now	ADV
ejpam-676	373	17	,	,	PUNCT
ejpam-676	373	18	by	by	ADP
ejpam-676	373	19	using	use	VERB
ejpam-676	373	20	the	the	DET
ejpam-676	373	21	following	follow	VERB
ejpam-676	373	22	known	know	VERB
ejpam-676	373	23	estimates	estimate	NOUN
ejpam-676	373	24	[	[	X
ejpam-676	373	25	11	11	NUM
ejpam-676	373	26	]	]	PUNCT
ejpam-676	373	27	(	(	PUNCT
ejpam-676	373	28	see	see	VERB
ejpam-676	373	29	also	also	ADV
ejpam-676	373	30	[	[	X
ejpam-676	373	31	6	6	NUM
ejpam-676	373	32	]	]	PUNCT
ejpam-676	373	33	):	):	PUNCT
ejpam-676	373	34	�	�	PROPN
ejpam-676	373	35	�	�	PROPN
ejpam-676	373	36	�	�	PROPN
ejpam-676	373	37	�	�	PROPN
ejpam-676	373	38	�	�	PROPN
ejpam-676	373	39	ϕ	ϕ	PROPN
ejpam-676	373	40	′	′	NUM
ejpam-676	373	41	(	(	PUNCT
ejpam-676	373	42	z	z	NOUN
ejpam-676	373	43	)	)	PUNCT
ejpam-676	373	44	ϕ(z	ϕ(z	PROPN
ejpam-676	373	45	)	)	PUNCT
ejpam-676	374	1	�	�	PROPN
ejpam-676	374	2	�	�	PROPN
ejpam-676	374	3	�	�	PROPN
ejpam-676	374	4	�	�	PROPN
ejpam-676	374	5	�	�	PROPN
ejpam-676	374	6	≤	≤	PROPN
ejpam-676	374	7	2(p+m)r	2(p+m)r	NUM
ejpam-676	374	8	p+m−1	p+m−1	PROPN
ejpam-676	374	9	1−	1−	NUM
ejpam-676	374	10	r2(p+m	r2(p+m	NOUN
ejpam-676	374	11	)	)	PUNCT
ejpam-676	374	12	(	(	PUNCT
ejpam-676	374	13	|z|	|z|	NOUN
ejpam-676	374	14	=	=	SYM
ejpam-676	374	15	r	r	NOUN
ejpam-676	374	16	<	<	X
ejpam-676	374	17	1	1	NUM
ejpam-676	374	18	)	)	PUNCT
ejpam-676	374	19	and	and	CCONJ
ejpam-676	374	20	�	�	PROPN
ejpam-676	374	21	�	�	PROPN
ejpam-676	374	22	�	�	PROPN
ejpam-676	374	23	�	�	PROPN
ejpam-676	374	24	�	�	PROPN
ejpam-676	374	25	(	(	PUNCT
ejpam-676	374	26	p+m)ψ(z	p+m)ψ(z	NOUN
ejpam-676	374	27	)	)	PUNCT
ejpam-676	375	1	+	+	CCONJ
ejpam-676	375	2	zψ	zψ	PROPN
ejpam-676	376	1	′	′	NUM
ejpam-676	376	2	(	(	PUNCT
ejpam-676	376	3	z	z	NOUN
ejpam-676	376	4	)	)	PUNCT
ejpam-676	376	5	1	1	NUM
ejpam-676	376	6	+	+	NUM
ejpam-676	376	7	zp+mψ(z	zp+mψ(z	NOUN
ejpam-676	376	8	)	)	PUNCT
ejpam-676	376	9	�	�	PROPN
ejpam-676	376	10	�	�	PROPN
ejpam-676	376	11	�	�	PROPN
ejpam-676	376	12	�	�	PROPN
ejpam-676	376	13	�	�	PROPN
ejpam-676	376	14	≤	≤	PROPN
ejpam-676	376	15	(	(	PUNCT
ejpam-676	376	16	p+m	p+m	NOUN
ejpam-676	376	17	)	)	PUNCT
ejpam-676	376	18	1−	1−	NUM
ejpam-676	376	19	r	r	NOUN
ejpam-676	376	20	p+m	p+m	X
ejpam-676	376	21	(	(	PUNCT
ejpam-676	376	22	|z|	|z|	NOUN
ejpam-676	376	23	=	=	SYM
ejpam-676	376	24	r	r	NOUN
ejpam-676	376	25	<	<	X
ejpam-676	376	26	1	1	NUM
ejpam-676	376	27	)	)	PUNCT
ejpam-676	376	28	in	in	ADP
ejpam-676	376	29	(	(	PUNCT
ejpam-676	376	30	37	37	NUM
ejpam-676	376	31	)	)	PUNCT
ejpam-676	376	32	,	,	PUNCT
ejpam-676	376	33	we	we	PRON
ejpam-676	376	34	obtain	obtain	VERB
ejpam-676	376	35	re	re	ADP
ejpam-676	376	36	(	(	PUNCT
ejpam-676	376	37	−z(hp	−z(hp	PROPN
ejpam-676	376	38	,	,	PUNCT
ejpam-676	376	39	q	q	NOUN
ejpam-676	376	40	,	,	PUNCT
ejpam-676	376	41	s(α1	s(α1	NOUN
ejpam-676	376	42	)	)	PUNCT
ejpam-676	377	1	f	f	PROPN
ejpam-676	377	2	(	(	PUNCT
ejpam-676	377	3	z	z	NOUN
ejpam-676	377	4	)	)	PUNCT
ejpam-676	377	5	)	)	PUNCT
ejpam-676	378	1	′	′	NUM
ejpam-676	379	1	hp	hp	PROPN
ejpam-676	379	2	,	,	PUNCT
ejpam-676	379	3	q	q	NOUN
ejpam-676	379	4	,	,	PUNCT
ejpam-676	379	5	s(α1	s(α1	NOUN
ejpam-676	379	6	)	)	PUNCT
ejpam-676	379	7	f	f	PROPN
ejpam-676	379	8	(	(	PUNCT
ejpam-676	379	9	z	z	NOUN
ejpam-676	379	10	)	)	PUNCT
ejpam-676	379	11	)	)	PUNCT
ejpam-676	380	1	≥	≥	PROPN
ejpam-676	380	2	p−	p−	NOUN
ejpam-676	380	3	3(p+m)r	3(p+m)r	NUM
ejpam-676	380	4	p+m−	p+m−	NOUN
ejpam-676	380	5	(	(	PUNCT
ejpam-676	380	6	2p+m)r2(p+m	2p+m)r2(p+m	NOUN
ejpam-676	380	7	)	)	PUNCT
ejpam-676	380	8	1−	1−	NUM
ejpam-676	380	9	r2(p+m	r2(p+m	NOUN
ejpam-676	380	10	)	)	PUNCT
ejpam-676	380	11	(	(	PUNCT
ejpam-676	380	12	|z|=	|z|=	NOUN
ejpam-676	380	13	r	r	NOUN
ejpam-676	380	14	<	<	X
ejpam-676	380	15	1	1	NUM
ejpam-676	380	16	)	)	PUNCT
ejpam-676	380	17	,	,	PUNCT
ejpam-676	380	18	which	which	PRON
ejpam-676	380	19	is	be	AUX
ejpam-676	380	20	certainly	certainly	ADV
ejpam-676	380	21	positive	positive	ADJ
ejpam-676	380	22	,	,	PUNCT
ejpam-676	380	23	provided	provide	VERB
ejpam-676	380	24	that	that	SCONJ
ejpam-676	380	25	r	r	NOUN
ejpam-676	380	26	<	<	X
ejpam-676	380	27	r0	r0	NOUN
ejpam-676	380	28	,	,	PUNCT
ejpam-676	380	29	r0	r0	NOUN
ejpam-676	380	30	being	be	AUX
ejpam-676	380	31	given	give	VERB
ejpam-676	380	32	as	as	ADP
ejpam-676	380	33	in	in	ADP
ejpam-676	380	34	theorem	theorem	ADJ
ejpam-676	380	35	4	4	NUM
ejpam-676	380	36	.	.	PUNCT
ejpam-676	380	37	theorem	theorem	NOUN
ejpam-676	380	38	5	5	NUM
ejpam-676	380	39	.	.	PUNCT
ejpam-676	381	1	let	let	VERB
ejpam-676	381	2	−1	−1	NOUN
ejpam-676	381	3	≤	≤	NUM
ejpam-676	381	4	b	b	X
ejpam-676	381	5	j	j	X
ejpam-676	381	6	<	<	X
ejpam-676	381	7	a	a	DET
ejpam-676	381	8	j	j	PROPN
ejpam-676	381	9	≤	≤	ADV
ejpam-676	381	10	1	1	NUM
ejpam-676	381	11	(	(	PUNCT
ejpam-676	381	12	j	j	NOUN
ejpam-676	381	13	=	=	SYM
ejpam-676	381	14	1,2	1,2	NUM
ejpam-676	381	15	)	)	PUNCT
ejpam-676	381	16	.	.	PUNCT
ejpam-676	382	1	if	if	SCONJ
ejpam-676	382	2	each	each	PRON
ejpam-676	382	3	of	of	ADP
ejpam-676	382	4	the	the	DET
ejpam-676	382	5	functions	function	NOUN
ejpam-676	382	6	f	f	PROPN
ejpam-676	382	7	j	j	PROPN
ejpam-676	382	8	∈	∈	PROPN
ejpam-676	382	9	σp	σp	PROPN
ejpam-676	382	10	satisfies	satisfy	VERB
ejpam-676	382	11	the	the	DET
ejpam-676	382	12	following	follow	VERB
ejpam-676	382	13	subordination	subordination	NOUN
ejpam-676	382	14	condition	condition	NOUN
ejpam-676	382	15	:	:	PUNCT
ejpam-676	382	16	(	(	PUNCT
ejpam-676	382	17	1−λ)zphp	1−λ)zphp	NUM
ejpam-676	382	18	,	,	PUNCT
ejpam-676	382	19	q	q	NOUN
ejpam-676	382	20	,	,	PUNCT
ejpam-676	382	21	s(α1	s(α1	NOUN
ejpam-676	382	22	)	)	PUNCT
ejpam-676	383	1	f	f	PROPN
ejpam-676	383	2	j(z	j(z	PROPN
ejpam-676	383	3	)	)	PUNCT
ejpam-676	384	1	+	+	NOUN
ejpam-676	384	2	λzphp	λzphp	ADJ
ejpam-676	384	3	,	,	PUNCT
ejpam-676	384	4	q	q	NOUN
ejpam-676	384	5	,	,	PUNCT
ejpam-676	384	6	s(α1	s(α1	NOUN
ejpam-676	384	7	+	+	CCONJ
ejpam-676	384	8	1	1	X
ejpam-676	384	9	)	)	PUNCT
ejpam-676	384	10	f	f	PROPN
ejpam-676	384	11	j(z	j(z	PROPN
ejpam-676	384	12	)	)	PUNCT
ejpam-676	384	13	≺	≺	NOUN
ejpam-676	385	1	1+a	1+a	NUM
ejpam-676	385	2	jz	jz	PROPN
ejpam-676	385	3	1	1	NUM
ejpam-676	385	4	+	+	SYM
ejpam-676	385	5	b	b	PROPN
ejpam-676	385	6	jz	jz	PROPN
ejpam-676	385	7	(	(	PUNCT
ejpam-676	385	8	j	j	PROPN
ejpam-676	385	9	=	=	SYM
ejpam-676	385	10	1,2	1,2	NUM
ejpam-676	385	11	;	;	PUNCT
ejpam-676	385	12	z	z	PROPN
ejpam-676	385	13	∈	∈	PROPN
ejpam-676	385	14	u	u	NOUN
ejpam-676	385	15	)	)	PUNCT
ejpam-676	385	16	,	,	PUNCT
ejpam-676	385	17	(	(	PUNCT
ejpam-676	385	18	38	38	NUM
ejpam-676	385	19	)	)	PUNCT
ejpam-676	385	20	then	then	ADV
ejpam-676	385	21	(	(	PUNCT
ejpam-676	385	22	1−λ)zphp	1−λ)zphp	NUM
ejpam-676	385	23	,	,	PUNCT
ejpam-676	385	24	q	q	NOUN
ejpam-676	385	25	,	,	PUNCT
ejpam-676	385	26	s(α1)g(z	s(α1)g(z	ADJ
ejpam-676	385	27	)	)	PUNCT
ejpam-676	385	28	+	+	NOUN
ejpam-676	385	29	λzphp	λzphp	ADJ
ejpam-676	385	30	,	,	PUNCT
ejpam-676	385	31	q	q	NOUN
ejpam-676	385	32	,	,	PUNCT
ejpam-676	385	33	s(α1	s(α1	NOUN
ejpam-676	385	34	+	+	CCONJ
ejpam-676	385	35	1)g(z)≺	1)g(z)≺	NUM
ejpam-676	385	36	1	1	NUM
ejpam-676	385	37	+	+	CCONJ
ejpam-676	385	38	(	(	PUNCT
ejpam-676	385	39	1−	1−	NUM
ejpam-676	385	40	2ζ)z	2ζ)z	PROPN
ejpam-676	385	41	1−	1−	NUM
ejpam-676	386	1	z	z	NOUN
ejpam-676	387	1	(	(	PUNCT
ejpam-676	387	2	z	z	NOUN
ejpam-676	387	3	∈	∈	PROPN
ejpam-676	387	4	u	u	NOUN
ejpam-676	387	5	)	)	PUNCT
ejpam-676	387	6	,	,	PUNCT
ejpam-676	387	7	(	(	PUNCT
ejpam-676	387	8	39	39	NUM
ejpam-676	387	9	)	)	PUNCT
ejpam-676	388	1	where	where	SCONJ
ejpam-676	388	2	g(z	g(z	ADJ
ejpam-676	388	3	)	)	PUNCT
ejpam-676	388	4	=	=	SYM
ejpam-676	388	5	hp	hp	PROPN
ejpam-676	388	6	,	,	PUNCT
ejpam-676	388	7	q	q	NOUN
ejpam-676	388	8	,	,	PUNCT
ejpam-676	388	9	s(α1	s(α1	NOUN
ejpam-676	388	10	)	)	PUNCT
ejpam-676	388	11	(	(	PUNCT
ejpam-676	388	12	f1	f1	NOUN
ejpam-676	388	13	∗	∗	NOUN
ejpam-676	388	14	f2)(z	f2)(z	PROPN
ejpam-676	388	15	)	)	PUNCT
ejpam-676	388	16	and	and	CCONJ
ejpam-676	388	17	ζ	ζ	NOUN
ejpam-676	388	18	=	=	SYM
ejpam-676	388	19	1−	1−	NUM
ejpam-676	388	20	4(a1−	4(a1−	NUM
ejpam-676	388	21	b1)(a2−	b1)(a2−	PROPN
ejpam-676	388	22	b2	b2	NOUN
ejpam-676	388	23	)	)	PUNCT
ejpam-676	388	24	(	(	PUNCT
ejpam-676	388	25	1−	1−	NUM
ejpam-676	388	26	b1)(1−	b1)(1−	PROPN
ejpam-676	388	27	b2	b2	NOUN
ejpam-676	388	28	)	)	PUNCT
ejpam-676	388	29	�	�	NOUN
ejpam-676	388	30	1−	1−	NUM
ejpam-676	388	31	1	1	NUM
ejpam-676	388	32	2	2	NUM
ejpam-676	388	33	2f1(1,1	2f1(1,1	NUM
ejpam-676	388	34	;	;	PUNCT
ejpam-676	388	35	α1	α1	PROPN
ejpam-676	388	36	λ	λ	PROPN
ejpam-676	388	37	+	+	PROPN
ejpam-676	388	38	1	1	NUM
ejpam-676	388	39	;	;	PUNCT
ejpam-676	388	40	1	1	NUM
ejpam-676	388	41	2	2	X
ejpam-676	388	42	)	)	PUNCT
ejpam-676	388	43	�	�	PROPN
ejpam-676	388	44	.	.	PUNCT
ejpam-676	389	1	the	the	DET
ejpam-676	389	2	result	result	NOUN
ejpam-676	389	3	is	be	AUX
ejpam-676	389	4	the	the	DET
ejpam-676	389	5	best	good	ADJ
ejpam-676	389	6	possible	possible	ADJ
ejpam-676	389	7	when	when	SCONJ
ejpam-676	389	8	b1	b1	NOUN
ejpam-676	389	9	=	=	SYM
ejpam-676	389	10	b2	b2	NOUN
ejpam-676	389	11	=	=	SYM
ejpam-676	389	12	−1	−1	NOUN
ejpam-676	389	13	.	.	PUNCT
ejpam-676	390	1	proof	proof	NOUN
ejpam-676	390	2	.	.	PUNCT
ejpam-676	391	1	suppose	suppose	VERB
ejpam-676	391	2	that	that	SCONJ
ejpam-676	391	3	each	each	PRON
ejpam-676	391	4	of	of	ADP
ejpam-676	391	5	the	the	DET
ejpam-676	391	6	functions	function	NOUN
ejpam-676	391	7	f	f	PROPN
ejpam-676	391	8	j	j	PROPN
ejpam-676	391	9	∈	∈	PROPN
ejpam-676	391	10	σp	σp	PROPN
ejpam-676	391	11	(	(	PUNCT
ejpam-676	391	12	j	j	PROPN
ejpam-676	391	13	=	=	SYM
ejpam-676	391	14	1,2	1,2	NUM
ejpam-676	391	15	)	)	PUNCT
ejpam-676	391	16	satisfies	satisfy	VERB
ejpam-676	391	17	the	the	DET
ejpam-676	391	18	condition	condition	NOUN
ejpam-676	391	19	(	(	PUNCT
ejpam-676	391	20	38	38	NUM
ejpam-676	391	21	)	)	PUNCT
ejpam-676	391	22	.	.	PUNCT
ejpam-676	392	1	then	then	ADV
ejpam-676	392	2	,	,	PUNCT
ejpam-676	392	3	by	by	ADP
ejpam-676	392	4	letting	let	VERB
ejpam-676	392	5	φ	φ	PROPN
ejpam-676	392	6	j(z	j(z	PROPN
ejpam-676	392	7	)	)	PUNCT
ejpam-676	392	8	=	=	PUNCT
ejpam-676	393	1	(	(	PUNCT
ejpam-676	393	2	1−λ)zphp	1−λ)zphp	NUM
ejpam-676	393	3	,	,	PUNCT
ejpam-676	393	4	q	q	NOUN
ejpam-676	393	5	,	,	PUNCT
ejpam-676	393	6	s(α1	s(α1	NOUN
ejpam-676	393	7	)	)	PUNCT
ejpam-676	393	8	f	f	PROPN
ejpam-676	393	9	j(z	j(z	PROPN
ejpam-676	393	10	)	)	PUNCT
ejpam-676	394	1	+	+	NOUN
ejpam-676	394	2	λzphp	λzphp	ADJ
ejpam-676	394	3	,	,	PUNCT
ejpam-676	394	4	q	q	NOUN
ejpam-676	394	5	,	,	PUNCT
ejpam-676	394	6	s(α1	s(α1	NOUN
ejpam-676	394	7	+	+	CCONJ
ejpam-676	394	8	1	1	X
ejpam-676	394	9	)	)	PUNCT
ejpam-676	394	10	f	f	NOUN
ejpam-676	394	11	j(z	j(z	PROPN
ejpam-676	394	12	)	)	PUNCT
ejpam-676	394	13	(	(	PUNCT
ejpam-676	394	14	j	j	NOUN
ejpam-676	394	15	=	=	SYM
ejpam-676	394	16	1,2	1,2	NUM
ejpam-676	394	17	)	)	PUNCT
ejpam-676	394	18	,	,	PUNCT
ejpam-676	394	19	(	(	PUNCT
ejpam-676	394	20	40	40	NUM
ejpam-676	394	21	)	)	PUNCT
ejpam-676	394	22	we	we	PRON
ejpam-676	394	23	have	have	VERB
ejpam-676	394	24	ϕ	ϕ	NOUN
ejpam-676	394	25	j(z	j(z	PROPN
ejpam-676	394	26	)	)	PUNCT
ejpam-676	394	27	∈	∈	PROPN
ejpam-676	394	28	p(γ	p(γ	NUM
ejpam-676	394	29	j	j	NOUN
ejpam-676	394	30	)	)	PUNCT
ejpam-676	394	31	(	(	PUNCT
ejpam-676	394	32	γ	γ	X
ejpam-676	394	33	j	j	PROPN
ejpam-676	394	34	=	=	SYM
ejpam-676	394	35	1−	1−	PROPN
ejpam-676	394	36	a	a	DET
ejpam-676	394	37	j	j	PROPN
ejpam-676	394	38	1−	1−	NUM
ejpam-676	394	39	b	b	PROPN
ejpam-676	394	40	j	j	PROPN
ejpam-676	394	41	;	;	PUNCT
ejpam-676	394	42	j	j	PROPN
ejpam-676	394	43	=	=	SYM
ejpam-676	394	44	1,2	1,2	NUM
ejpam-676	394	45	)	)	PUNCT
ejpam-676	394	46	.	.	PUNCT
ejpam-676	395	1	using	use	VERB
ejpam-676	395	2	the	the	DET
ejpam-676	395	3	identity	identity	NOUN
ejpam-676	395	4	(	(	PUNCT
ejpam-676	395	5	10	10	NUM
ejpam-676	395	6	)	)	PUNCT
ejpam-676	395	7	in	in	ADP
ejpam-676	395	8	(	(	PUNCT
ejpam-676	395	9	40	40	NUM
ejpam-676	395	10	)	)	PUNCT
ejpam-676	395	11	,	,	PUNCT
ejpam-676	395	12	we	we	PRON
ejpam-676	395	13	observe	observe	VERB
ejpam-676	395	14	that	that	SCONJ
ejpam-676	395	15	hp	hp	PROPN
ejpam-676	395	16	,	,	PUNCT
ejpam-676	395	17	q	q	NOUN
ejpam-676	395	18	,	,	PUNCT
ejpam-676	395	19	s(α1	s(α1	NOUN
ejpam-676	395	20	)	)	PUNCT
ejpam-676	396	1	f	f	PROPN
ejpam-676	397	1	j(z	j(z	PROPN
ejpam-676	397	2	)	)	PUNCT
ejpam-676	397	3	=	=	SYM
ejpam-676	397	4	α1	α1	PROPN
ejpam-676	397	5	λ	λ	PROPN
ejpam-676	397	6	z−p−	z−p−	NUM
ejpam-676	397	7	α1	α1	PROPN
ejpam-676	397	8	λ	λ	PROPN
ejpam-676	397	9	z	z	PROPN
ejpam-676	397	10	∫	∫	PROPN
ejpam-676	397	11	0	0	NUM
ejpam-676	397	12	t	t	PROPN
ejpam-676	397	13	α1	α1	PROPN
ejpam-676	397	14	λ	λ	X
ejpam-676	397	15	−1φ	−1φ	PROPN
ejpam-676	397	16	j(t)d	j(t)d	PROPN
ejpam-676	397	17	t	t	PROPN
ejpam-676	397	18	(	(	PUNCT
ejpam-676	397	19	j	j	PROPN
ejpam-676	397	20	=	=	SYM
ejpam-676	397	21	1,2	1,2	NUM
ejpam-676	397	22	)	)	PUNCT
ejpam-676	397	23	,	,	PUNCT
ejpam-676	397	24	m.	m.	PROPN
ejpam-676	397	25	aouf	aouf	PROPN
ejpam-676	397	26	/	/	SYM
ejpam-676	397	27	eur	eur	PROPN
ejpam-676	397	28	.	.	PUNCT
ejpam-676	398	1	j.	j.	PROPN
ejpam-676	398	2	pure	pure	PROPN
ejpam-676	398	3	appl	appl	PROPN
ejpam-676	398	4	.	.	PROPN
ejpam-676	398	5	math	math	PROPN
ejpam-676	398	6	,	,	PUNCT
ejpam-676	398	7	5	5	NUM
ejpam-676	398	8	(	(	PUNCT
ejpam-676	398	9	2012	2012	NUM
ejpam-676	398	10	)	)	PUNCT
ejpam-676	398	11	,	,	PUNCT
ejpam-676	398	12	141	141	NUM
ejpam-676	398	13	-	-	SYM
ejpam-676	398	14	159	159	NUM
ejpam-676	398	15	154	154	NUM
ejpam-676	398	16	which	which	PRON
ejpam-676	398	17	,	,	PUNCT
ejpam-676	398	18	in	in	ADP
ejpam-676	398	19	view	view	NOUN
ejpam-676	398	20	of	of	ADP
ejpam-676	398	21	the	the	DET
ejpam-676	398	22	definition	definition	NOUN
ejpam-676	398	23	of	of	ADP
ejpam-676	398	24	g	g	NOUN
ejpam-676	398	25	given	give	VERB
ejpam-676	398	26	already	already	ADV
ejpam-676	398	27	with	with	ADP
ejpam-676	398	28	(	(	PUNCT
ejpam-676	398	29	39	39	NUM
ejpam-676	398	30	)	)	PUNCT
ejpam-676	398	31	,	,	PUNCT
ejpam-676	398	32	yields	yield	NOUN
ejpam-676	398	33	hp	hp	PROPN
ejpam-676	398	34	,	,	PUNCT
ejpam-676	398	35	q	q	NOUN
ejpam-676	398	36	,	,	PUNCT
ejpam-676	398	37	s(α1)g(z	s(α1)g(z	ADJ
ejpam-676	398	38	)	)	PUNCT
ejpam-676	398	39	=	=	SYM
ejpam-676	398	40	α1	α1	PROPN
ejpam-676	398	41	λ	λ	PROPN
ejpam-676	398	42	z−p−	z−p−	NUM
ejpam-676	398	43	α1	α1	PROPN
ejpam-676	398	44	λ	λ	PROPN
ejpam-676	398	45	z	z	PROPN
ejpam-676	398	46	∫	∫	PROPN
ejpam-676	398	47	0	0	NUM
ejpam-676	398	48	t	t	PROPN
ejpam-676	398	49	α1	α1	PROPN
ejpam-676	398	50	λ	λ	PROPN
ejpam-676	398	51	−1ϕ0(t)d	−1ϕ0(t)d	PROPN
ejpam-676	398	52	t	t	PROPN
ejpam-676	398	53	,	,	PUNCT
ejpam-676	398	54	(	(	PUNCT
ejpam-676	398	55	41	41	NUM
ejpam-676	398	56	)	)	PUNCT
ejpam-676	399	1	where	where	SCONJ
ejpam-676	399	2	,	,	PUNCT
ejpam-676	399	3	for	for	ADP
ejpam-676	399	4	convenience	convenience	NOUN
ejpam-676	399	5	,	,	PUNCT
ejpam-676	399	6	φ0(z	φ0(z	NOUN
ejpam-676	399	7	)	)	PUNCT
ejpam-676	400	1	=	=	SYM
ejpam-676	400	2	(	(	PUNCT
ejpam-676	400	3	1−λ)zphp	1−λ)zphp	NUM
ejpam-676	400	4	,	,	PUNCT
ejpam-676	400	5	q	q	NOUN
ejpam-676	400	6	,	,	PUNCT
ejpam-676	400	7	s(α1)g(z	s(α1)g(z	ADJ
ejpam-676	400	8	)	)	PUNCT
ejpam-676	400	9	+	+	NOUN
ejpam-676	400	10	λzphp	λzphp	ADJ
ejpam-676	400	11	,	,	PUNCT
ejpam-676	400	12	q	q	NOUN
ejpam-676	400	13	,	,	PUNCT
ejpam-676	400	14	s(α1	s(α1	NOUN
ejpam-676	400	15	+	+	CCONJ
ejpam-676	400	16	1)g(z	1)g(z	NUM
ejpam-676	400	17	)	)	PUNCT
ejpam-676	400	18	=	=	SYM
ejpam-676	401	1	α1	α1	PROPN
ejpam-676	401	2	λ	λ	PROPN
ejpam-676	401	3	z−	z−	PROPN
ejpam-676	401	4	α1	α1	PROPN
ejpam-676	401	5	λ	λ	PROPN
ejpam-676	401	6	z	z	PROPN
ejpam-676	401	7	∫	∫	PROPN
ejpam-676	401	8	0	0	NUM
ejpam-676	401	9	t	t	PROPN
ejpam-676	401	10	α1	α1	PROPN
ejpam-676	401	11	λ	λ	PROPN
ejpam-676	401	12	−1	−1	NOUN
ejpam-676	401	13	(	(	PUNCT
ejpam-676	401	14	ϕ1	ϕ1	PROPN
ejpam-676	401	15	∗ϕ2)(t)d	∗ϕ2)(t)d	PROPN
ejpam-676	401	16	t.	t.	PROPN
ejpam-676	401	17	(	(	PUNCT
ejpam-676	401	18	42	42	NUM
ejpam-676	401	19	)	)	PUNCT
ejpam-676	401	20	since	since	SCONJ
ejpam-676	401	21	ϕ1	ϕ1	PROPN
ejpam-676	401	22	∈	∈	PROPN
ejpam-676	401	23	p(γ1	p(γ1	NOUN
ejpam-676	401	24	)	)	PUNCT
ejpam-676	401	25	and	and	CCONJ
ejpam-676	401	26	ϕ2	ϕ2	ADV
ejpam-676	401	27	∈	∈	PROPN
ejpam-676	401	28	p(γ2	p(γ2	NOUN
ejpam-676	401	29	)	)	PUNCT
ejpam-676	401	30	,	,	PUNCT
ejpam-676	401	31	it	it	PRON
ejpam-676	401	32	follows	follow	VERB
ejpam-676	401	33	from	from	ADP
ejpam-676	401	34	lemma	lemma	PROPN
ejpam-676	401	35	3	3	NUM
ejpam-676	401	36	that	that	PRON
ejpam-676	401	37	(	(	PUNCT
ejpam-676	401	38	ϕ1	ϕ1	NOUN
ejpam-676	401	39	∗ϕ2	∗ϕ2	NOUN
ejpam-676	401	40	)	)	PUNCT
ejpam-676	401	41	∈	∈	PROPN
ejpam-676	401	42	p(γ3	p(γ3	PROPN
ejpam-676	401	43	)	)	PUNCT
ejpam-676	401	44	(	(	PUNCT
ejpam-676	401	45	γ3	γ3	NOUN
ejpam-676	401	46	=	=	SYM
ejpam-676	401	47	1−	1−	NUM
ejpam-676	401	48	2(1−	2(1−	X
ejpam-676	401	49	γ1)(1−	γ1)(1−	ADJ
ejpam-676	401	50	γ2	γ2	NOUN
ejpam-676	401	51	)	)	PUNCT
ejpam-676	401	52	)	)	PUNCT
ejpam-676	401	53	.	.	PUNCT
ejpam-676	402	1	(	(	PUNCT
ejpam-676	402	2	43	43	NUM
ejpam-676	402	3	)	)	PUNCT
ejpam-676	402	4	now	now	ADV
ejpam-676	402	5	,	,	PUNCT
ejpam-676	402	6	by	by	ADP
ejpam-676	402	7	using	use	VERB
ejpam-676	402	8	(	(	PUNCT
ejpam-676	402	9	43	43	NUM
ejpam-676	402	10	)	)	PUNCT
ejpam-676	402	11	in	in	ADP
ejpam-676	402	12	(	(	PUNCT
ejpam-676	402	13	42	42	NUM
ejpam-676	402	14	)	)	PUNCT
ejpam-676	402	15	and	and	CCONJ
ejpam-676	402	16	then	then	ADV
ejpam-676	402	17	appealing	appeal	VERB
ejpam-676	402	18	to	to	PART
ejpam-676	402	19	lemma	lemma	PROPN
ejpam-676	402	20	2	2	PROPN
ejpam-676	402	21	and	and	CCONJ
ejpam-676	402	22	lemma	lemma	PROPN
ejpam-676	402	23	4	4	NUM
ejpam-676	402	24	,	,	PUNCT
ejpam-676	402	25	we	we	PRON
ejpam-676	402	26	obtain	obtain	VERB
ejpam-676	402	27	re{ϕ0(z	re{ϕ0(z	NOUN
ejpam-676	402	28	)	)	PUNCT
ejpam-676	402	29	}	}	PUNCT
ejpam-676	403	1	=	=	SYM
ejpam-676	403	2	α1	α1	PROPN
ejpam-676	403	3	λ	λ	NOUN
ejpam-676	403	4	1	1	NUM
ejpam-676	403	5	∫	∫	NOUN
ejpam-676	403	6	0	0	NUM
ejpam-676	403	7	u	u	PROPN
ejpam-676	403	8	α1	α1	PROPN
ejpam-676	403	9	λ	λ	PROPN
ejpam-676	403	10	−1	−1	NOUN
ejpam-676	403	11	re{ϕ1	re{ϕ1	NOUN
ejpam-676	404	1	∗ϕ2}(uz)du	∗ϕ2}(uz)du	PROPN
ejpam-676	404	2	≥	≥	NUM
ejpam-676	404	3	α1	α1	PROPN
ejpam-676	404	4	λ	λ	PROPN
ejpam-676	404	5	1	1	NUM
ejpam-676	404	6	∫	∫	NOUN
ejpam-676	404	7	0	0	NUM
ejpam-676	404	8	u	u	PROPN
ejpam-676	404	9	α1	α1	PROPN
ejpam-676	404	10	λ	λ	X
ejpam-676	404	11	−1(2γ3−	−1(2γ3−	NOUN
ejpam-676	404	12	1	1	NUM
ejpam-676	404	13	+	+	SYM
ejpam-676	404	14	2(1−	2(1−	NUM
ejpam-676	404	15	γ3	γ3	NOUN
ejpam-676	404	16	)	)	PUNCT
ejpam-676	404	17	1	1	NUM
ejpam-676	405	1	+	+	NUM
ejpam-676	405	2	u|z|	u|z|	NOUN
ejpam-676	405	3	)	)	PUNCT
ejpam-676	405	4	du	du	PROPN
ejpam-676	405	5	>	>	X
ejpam-676	405	6	α1	α1	PROPN
ejpam-676	405	7	λ	λ	PROPN
ejpam-676	405	8	1	1	NUM
ejpam-676	405	9	∫	∫	NOUN
ejpam-676	405	10	0	0	NUM
ejpam-676	405	11	u	u	PROPN
ejpam-676	405	12	α1	α1	PROPN
ejpam-676	405	13	λ	λ	X
ejpam-676	405	14	−1(2γ3−	−1(2γ3−	NOUN
ejpam-676	405	15	1	1	NUM
ejpam-676	405	16	+	+	SYM
ejpam-676	405	17	2(1−	2(1−	NUM
ejpam-676	405	18	γ3	γ3	NOUN
ejpam-676	405	19	)	)	PUNCT
ejpam-676	405	20	1	1	NUM
ejpam-676	405	21	+	+	NUM
ejpam-676	405	22	u	u	NOUN
ejpam-676	405	23	)	)	PUNCT
ejpam-676	405	24	du	du	PROPN
ejpam-676	405	25	=	=	SYM
ejpam-676	405	26	1−	1−	NUM
ejpam-676	405	27	4(a1−	4(a1−	PROPN
ejpam-676	405	28	b1)(a2	b1)(a2	PROPN
ejpam-676	405	29	−	−	PROPN
ejpam-676	405	30	b2	b2	PROPN
ejpam-676	405	31	)	)	PUNCT
ejpam-676	405	32	(	(	PUNCT
ejpam-676	405	33	1−	1−	NUM
ejpam-676	405	34	b1)(1−	b1)(1−	PROPN
ejpam-676	405	35	b2	b2	NOUN
ejpam-676	405	36	)	)	PUNCT
ejpam-676	405	37	(	(	PUNCT
ejpam-676	405	38	1−	1−	NUM
ejpam-676	405	39	α1	α1	PROPN
ejpam-676	405	40	λ	λ	PROPN
ejpam-676	405	41	1	1	NUM
ejpam-676	405	42	∫	∫	NOUN
ejpam-676	405	43	0	0	NUM
ejpam-676	405	44	u	u	PROPN
ejpam-676	405	45	α1	α1	PROPN
ejpam-676	405	46	λ	λ	X
ejpam-676	405	47	−1(1	−1(1	X
ejpam-676	405	48	+	+	CCONJ
ejpam-676	405	49	u)−1du	u)−1du	X
ejpam-676	405	50	)	)	PUNCT
ejpam-676	405	51	=	=	SYM
ejpam-676	405	52	1−	1−	NUM
ejpam-676	405	53	4(a1−	4(a1−	PROPN
ejpam-676	405	54	b1)(a2	b1)(a2	PROPN
ejpam-676	405	55	−	−	PROPN
ejpam-676	405	56	b2	b2	PROPN
ejpam-676	405	57	)	)	PUNCT
ejpam-676	405	58	(	(	PUNCT
ejpam-676	405	59	1−	1−	NUM
ejpam-676	405	60	b1)(1−	b1)(1−	PROPN
ejpam-676	405	61	b2	b2	NOUN
ejpam-676	405	62	)	)	PUNCT
ejpam-676	405	63	�	�	NOUN
ejpam-676	405	64	1−	1−	NUM
ejpam-676	405	65	1	1	NUM
ejpam-676	405	66	2	2	NUM
ejpam-676	405	67	2f1(1,1	2f1(1,1	NUM
ejpam-676	405	68	;	;	PUNCT
ejpam-676	405	69	α1	α1	PROPN
ejpam-676	405	70	λ	λ	PROPN
ejpam-676	405	71	+	+	PROPN
ejpam-676	405	72	1	1	NUM
ejpam-676	405	73	;	;	PUNCT
ejpam-676	405	74	1	1	NUM
ejpam-676	405	75	2	2	X
ejpam-676	405	76	)	)	PUNCT
ejpam-676	405	77	�	�	NOUN
ejpam-676	405	78	=	=	SYM
ejpam-676	405	79	ζ	ζ	PROPN
ejpam-676	405	80	(	(	PUNCT
ejpam-676	405	81	z	z	NOUN
ejpam-676	405	82	∈	∈	PROPN
ejpam-676	405	83	u	u	NOUN
ejpam-676	405	84	)	)	PUNCT
ejpam-676	405	85	.	.	PUNCT
ejpam-676	406	1	when	when	SCONJ
ejpam-676	406	2	b1	b1	NOUN
ejpam-676	406	3	=	=	SYM
ejpam-676	406	4	b2	b2	NOUN
ejpam-676	406	5	=	=	SYM
ejpam-676	406	6	−1	−1	NOUN
ejpam-676	406	7	,	,	PUNCT
ejpam-676	406	8	we	we	PRON
ejpam-676	406	9	consider	consider	VERB
ejpam-676	406	10	the	the	DET
ejpam-676	406	11	functions	function	NOUN
ejpam-676	406	12	f	f	PROPN
ejpam-676	406	13	j	j	PROPN
ejpam-676	406	14	∈	∈	PROPN
ejpam-676	406	15	σp	σp	PROPN
ejpam-676	406	16	(	(	PUNCT
ejpam-676	406	17	j	j	PROPN
ejpam-676	406	18	=	=	SYM
ejpam-676	406	19	1,2	1,2	NUM
ejpam-676	406	20	)	)	PUNCT
ejpam-676	406	21	,	,	PUNCT
ejpam-676	406	22	which	which	PRON
ejpam-676	406	23	satisfy	satisfy	VERB
ejpam-676	406	24	the	the	DET
ejpam-676	406	25	hypothesis	hypothesis	NOUN
ejpam-676	406	26	(	(	PUNCT
ejpam-676	406	27	38	38	NUM
ejpam-676	406	28	)	)	PUNCT
ejpam-676	406	29	of	of	ADP
ejpam-676	406	30	theorem	theorem	NOUN
ejpam-676	406	31	5	5	NUM
ejpam-676	406	32	and	and	CCONJ
ejpam-676	406	33	are	be	AUX
ejpam-676	406	34	defined	define	VERB
ejpam-676	406	35	by	by	ADP
ejpam-676	406	36	hp	hp	PROPN
ejpam-676	406	37	,	,	PUNCT
ejpam-676	406	38	q	q	NOUN
ejpam-676	406	39	,	,	PUNCT
ejpam-676	406	40	s(α1	s(α1	NOUN
ejpam-676	406	41	)	)	PUNCT
ejpam-676	407	1	f	f	PROPN
ejpam-676	407	2	j(z	j(z	PROPN
ejpam-676	407	3	)	)	PUNCT
ejpam-676	407	4	=	=	SYM
ejpam-676	407	5	α1	α1	PROPN
ejpam-676	407	6	λ	λ	PROPN
ejpam-676	407	7	z−	z−	PROPN
ejpam-676	407	8	α1	α1	PROPN
ejpam-676	407	9	λ	λ	PROPN
ejpam-676	407	10	z	z	PROPN
ejpam-676	407	11	∫	∫	PROPN
ejpam-676	407	12	0	0	NUM
ejpam-676	407	13	t	t	PROPN
ejpam-676	407	14	α1	α1	PROPN
ejpam-676	407	15	λ	λ	PROPN
ejpam-676	407	16	−1	−1	NOUN
ejpam-676	407	17	(	(	PUNCT
ejpam-676	407	18	1+a	1+a	NUM
ejpam-676	407	19	j	j	NOUN
ejpam-676	407	20	t	t	NOUN
ejpam-676	407	21	1−	1−	NUM
ejpam-676	407	22	t	t	NOUN
ejpam-676	407	23	)	)	PUNCT
ejpam-676	407	24	d	d	NOUN
ejpam-676	407	25	t	t	PROPN
ejpam-676	408	1	(	(	PUNCT
ejpam-676	408	2	j	j	PROPN
ejpam-676	408	3	=	=	SYM
ejpam-676	408	4	1,2	1,2	NUM
ejpam-676	408	5	)	)	PUNCT
ejpam-676	408	6	.	.	PUNCT
ejpam-676	409	1	m.	m.	PROPN
ejpam-676	409	2	aouf	aouf	PROPN
ejpam-676	409	3	/	/	SYM
ejpam-676	409	4	eur	eur	PROPN
ejpam-676	409	5	.	.	PUNCT
ejpam-676	410	1	j.	j.	PROPN
ejpam-676	410	2	pure	pure	PROPN
ejpam-676	410	3	appl	appl	PROPN
ejpam-676	410	4	.	.	PROPN
ejpam-676	410	5	math	math	PROPN
ejpam-676	410	6	,	,	PUNCT
ejpam-676	410	7	5	5	NUM
ejpam-676	410	8	(	(	PUNCT
ejpam-676	410	9	2012	2012	NUM
ejpam-676	410	10	)	)	PUNCT
ejpam-676	410	11	,	,	PUNCT
ejpam-676	410	12	141	141	NUM
ejpam-676	410	13	-	-	SYM
ejpam-676	410	14	159	159	NUM
ejpam-676	410	15	155	155	NUM
ejpam-676	410	16	thus	thus	ADV
ejpam-676	410	17	it	it	PRON
ejpam-676	410	18	follows	follow	VERB
ejpam-676	410	19	from	from	ADP
ejpam-676	410	20	(	(	PUNCT
ejpam-676	410	21	42	42	NUM
ejpam-676	410	22	)	)	PUNCT
ejpam-676	410	23	and	and	CCONJ
ejpam-676	410	24	lemma	lemma	PROPN
ejpam-676	410	25	4	4	NUM
ejpam-676	410	26	that	that	PRON
ejpam-676	410	27	ϕ0(z	ϕ0(z	X
ejpam-676	410	28	)	)	PUNCT
ejpam-676	410	29	=	=	SYM
ejpam-676	410	30	α1	α1	PROPN
ejpam-676	410	31	λ	λ	NOUN
ejpam-676	410	32	1	1	NUM
ejpam-676	410	33	∫	∫	NOUN
ejpam-676	410	34	0	0	NUM
ejpam-676	410	35	u	u	PROPN
ejpam-676	410	36	α1	α1	PROPN
ejpam-676	410	37	λ	λ	PROPN
ejpam-676	410	38	−1	−1	NOUN
ejpam-676	410	39	�	�	PROPN
ejpam-676	410	40	1−	1−	NUM
ejpam-676	410	41	(	(	PUNCT
ejpam-676	410	42	1	1	NUM
ejpam-676	410	43	+	+	NUM
ejpam-676	410	44	a1)(1	a1)(1	PROPN
ejpam-676	410	45	+	+	SYM
ejpam-676	410	46	a2	a2	NOUN
ejpam-676	410	47	)	)	PUNCT
ejpam-676	411	1	+	+	CCONJ
ejpam-676	411	2	(	(	PUNCT
ejpam-676	411	3	1	1	NUM
ejpam-676	411	4	+	+	NUM
ejpam-676	411	5	a1)(1	a1)(1	PROPN
ejpam-676	411	6	+	+	SYM
ejpam-676	411	7	a2	a2	NOUN
ejpam-676	411	8	)	)	PUNCT
ejpam-676	411	9	1−	1−	NUM
ejpam-676	412	1	uz	uz	PROPN
ejpam-676	412	2	�	�	PROPN
ejpam-676	412	3	du	du	PROPN
ejpam-676	412	4	=	=	SYM
ejpam-676	412	5	1−	1−	NUM
ejpam-676	412	6	(	(	PUNCT
ejpam-676	412	7	1	1	NUM
ejpam-676	412	8	+	+	NUM
ejpam-676	412	9	a1)(1+a2	a1)(1+a2	NOUN
ejpam-676	412	10	)	)	PUNCT
ejpam-676	413	1	+	+	CCONJ
ejpam-676	413	2	(	(	PUNCT
ejpam-676	413	3	1	1	NUM
ejpam-676	413	4	+	+	NOUN
ejpam-676	413	5	a1)(1	a1)(1	PROPN
ejpam-676	413	6	+	+	ADJ
ejpam-676	413	7	a2)(1−	a2)(1−	PROPN
ejpam-676	413	8	z)−1	z)−1	NUM
ejpam-676	413	9	.	.	PUNCT
ejpam-676	413	10	2f1(1,1	2f1(1,1	NUM
ejpam-676	413	11	;	;	PUNCT
ejpam-676	413	12	α1	α1	PROPN
ejpam-676	413	13	λ	λ	PROPN
ejpam-676	413	14	+	+	PROPN
ejpam-676	413	15	1	1	NUM
ejpam-676	413	16	;	;	PUNCT
ejpam-676	413	17	z	z	NOUN
ejpam-676	413	18	z	z	NOUN
ejpam-676	413	19	−	−	NOUN
ejpam-676	413	20	1	1	NUM
ejpam-676	413	21	)	)	PUNCT
ejpam-676	413	22	→	→	SYM
ejpam-676	413	23	1−	1−	NUM
ejpam-676	413	24	(	(	PUNCT
ejpam-676	413	25	1+a1)(1	1+a1)(1	NUM
ejpam-676	413	26	+	+	NUM
ejpam-676	413	27	a2	a2	PROPN
ejpam-676	413	28	)	)	PUNCT
ejpam-676	413	29	+	+	CCONJ
ejpam-676	413	30	1	1	NUM
ejpam-676	413	31	2	2	NUM
ejpam-676	413	32	(	(	PUNCT
ejpam-676	413	33	1	1	NUM
ejpam-676	413	34	+	+	NUM
ejpam-676	413	35	a1)(1	a1)(1	PROPN
ejpam-676	413	36	+	+	SYM
ejpam-676	413	37	a2	a2	PROPN
ejpam-676	413	38	)	)	PUNCT
ejpam-676	413	39	·	·	SYM
ejpam-676	413	40	2	2	NUM
ejpam-676	413	41	f1(1,1	f1(1,1	NOUN
ejpam-676	413	42	;	;	PUNCT
ejpam-676	413	43	α1	α1	PROPN
ejpam-676	413	44	λ	λ	PROPN
ejpam-676	413	45	+	+	PROPN
ejpam-676	413	46	1	1	NUM
ejpam-676	413	47	;	;	PUNCT
ejpam-676	413	48	1	1	NUM
ejpam-676	413	49	2	2	NUM
ejpam-676	413	50	)	)	PUNCT
ejpam-676	413	51	as	as	ADP
ejpam-676	413	52	z→−1	z→−1	NOUN
ejpam-676	413	53	,	,	PUNCT
ejpam-676	413	54	which	which	PRON
ejpam-676	413	55	evidently	evidently	ADV
ejpam-676	413	56	completes	complete	VERB
ejpam-676	413	57	the	the	DET
ejpam-676	413	58	proof	proof	NOUN
ejpam-676	413	59	of	of	ADP
ejpam-676	413	60	theorem	theorem	NOUN
ejpam-676	413	61	5	5	NUM
ejpam-676	413	62	.	.	PUNCT
ejpam-676	413	63	putting	put	VERB
ejpam-676	413	64	a	a	DET
ejpam-676	413	65	j	j	NOUN
ejpam-676	413	66	=	=	SYM
ejpam-676	413	67	1−	1−	NUM
ejpam-676	413	68	2θ	2θ	NUM
ejpam-676	413	69	j	j	PROPN
ejpam-676	413	70	,	,	PUNCT
ejpam-676	413	71	b	b	PROPN
ejpam-676	413	72	j	j	PROPN
ejpam-676	413	73	=	=	SYM
ejpam-676	413	74	−1	−1	NOUN
ejpam-676	413	75	(	(	PUNCT
ejpam-676	413	76	j	j	NOUN
ejpam-676	413	77	=	=	SYM
ejpam-676	413	78	1,2	1,2	NUM
ejpam-676	413	79	;	;	PUNCT
ejpam-676	413	80	0≤	0≤	NUM
ejpam-676	413	81	θ	θ	NOUN
ejpam-676	413	82	j	j	X
ejpam-676	413	83	<	<	X
ejpam-676	413	84	1	1	NUM
ejpam-676	413	85	)	)	PUNCT
ejpam-676	413	86	,	,	PUNCT
ejpam-676	413	87	s	s	NOUN
ejpam-676	413	88	=	=	SYM
ejpam-676	413	89	1	1	NUM
ejpam-676	413	90	,	,	PUNCT
ejpam-676	413	91	q	q	NOUN
ejpam-676	413	92	=	=	SYM
ejpam-676	413	93	2	2	NUM
ejpam-676	413	94	,	,	PUNCT
ejpam-676	413	95	α1	α1	PROPN
ejpam-676	413	96	=	=	PUNCT
ejpam-676	413	97	a	a	PRON
ejpam-676	413	98	>	>	X
ejpam-676	413	99	0	0	NUM
ejpam-676	413	100	,	,	PUNCT
ejpam-676	413	101	β1	β1	PROPN
ejpam-676	413	102	=	=	PUNCT
ejpam-676	413	103	c	c	PROPN
ejpam-676	413	104	>	>	PUNCT
ejpam-676	413	105	0	0	PUNCT
ejpam-676	413	106	and	and	CCONJ
ejpam-676	413	107	α2	α2	ADJ
ejpam-676	413	108	=	=	SYM
ejpam-676	413	109	1	1	NUM
ejpam-676	413	110	in	in	ADP
ejpam-676	413	111	theorem	theorem	NOUN
ejpam-676	413	112	5	5	NUM
ejpam-676	413	113	,	,	PUNCT
ejpam-676	413	114	we	we	PRON
ejpam-676	413	115	obtain	obtain	VERB
ejpam-676	413	116	the	the	DET
ejpam-676	413	117	following	follow	VERB
ejpam-676	413	118	corollary	corollary	NOUN
ejpam-676	413	119	.	.	PUNCT
ejpam-676	414	1	corollary	corollary	ADJ
ejpam-676	414	2	6	6	NUM
ejpam-676	414	3	.	.	PUNCT
ejpam-676	415	1	if	if	SCONJ
ejpam-676	415	2	the	the	DET
ejpam-676	415	3	functions	function	NOUN
ejpam-676	415	4	f	f	PROPN
ejpam-676	415	5	j	j	PROPN
ejpam-676	415	6	∈	∈	PROPN
ejpam-676	415	7	σp	σp	PROPN
ejpam-676	415	8	(	(	PUNCT
ejpam-676	415	9	j	j	PROPN
ejpam-676	415	10	=	=	SYM
ejpam-676	415	11	1,2	1,2	NUM
ejpam-676	415	12	)	)	PUNCT
ejpam-676	415	13	satisfy	satisfy	VERB
ejpam-676	415	14	the	the	DET
ejpam-676	415	15	following	follow	VERB
ejpam-676	415	16	inequality	inequality	NOUN
ejpam-676	415	17	:	:	PUNCT
ejpam-676	415	18	re	re	X
ejpam-676	415	19	¦	¦	X
ejpam-676	415	20	(	(	PUNCT
ejpam-676	415	21	1+λp)zpℓp(a	1+λp)zpℓp(a	NUM
ejpam-676	415	22	,	,	PUNCT
ejpam-676	415	23	c	c	NOUN
ejpam-676	415	24	)	)	PUNCT
ejpam-676	415	25	f	f	PROPN
ejpam-676	415	26	j(z	j(z	PROPN
ejpam-676	415	27	)	)	PUNCT
ejpam-676	416	1	+	+	NOUN
ejpam-676	416	2	λzp+1	λzp+1	X
ejpam-676	416	3	(	(	PUNCT
ejpam-676	416	4	ℓp(a	ℓp(a	PROPN
ejpam-676	416	5	,	,	PUNCT
ejpam-676	416	6	c	c	NOUN
ejpam-676	416	7	)	)	PUNCT
ejpam-676	416	8	f	f	PROPN
ejpam-676	416	9	j(z	j(z	PROPN
ejpam-676	416	10	)	)	PUNCT
ejpam-676	416	11	)	)	PUNCT
ejpam-676	416	12	′	′	NOUN
ejpam-676	417	1	©	©	NOUN
ejpam-676	417	2	>	>	PUNCT
ejpam-676	417	3	θ	θ	PROPN
ejpam-676	417	4	j	j	PROPN
ejpam-676	417	5	(	(	PUNCT
ejpam-676	417	6	0≤	0≤	NUM
ejpam-676	417	7	θ	θ	X
ejpam-676	417	8	j	j	NOUN
ejpam-676	417	9	<	<	X
ejpam-676	417	10	1	1	NUM
ejpam-676	417	11	;	;	PUNCT
ejpam-676	417	12	j	j	PROPN
ejpam-676	417	13	=	=	SYM
ejpam-676	417	14	1,2	1,2	NUM
ejpam-676	417	15	;	;	PUNCT
ejpam-676	417	16	z	z	PROPN
ejpam-676	417	17	∈	∈	PROPN
ejpam-676	417	18	u	u	NOUN
ejpam-676	417	19	)	)	PUNCT
ejpam-676	417	20	,	,	PUNCT
ejpam-676	417	21	(	(	PUNCT
ejpam-676	417	22	44	44	NUM
ejpam-676	417	23	)	)	PUNCT
ejpam-676	417	24	then	then	ADV
ejpam-676	417	25	re	re	X
ejpam-676	417	26	¦	¦	X
ejpam-676	417	27	(	(	PUNCT
ejpam-676	417	28	1+λp)zpℓp(a	1+λp)zpℓp(a	NUM
ejpam-676	417	29	,	,	PUNCT
ejpam-676	417	30	c	c	NOUN
ejpam-676	417	31	)	)	PUNCT
ejpam-676	417	32	(	(	PUNCT
ejpam-676	417	33	f1	f1	NOUN
ejpam-676	417	34	∗	∗	NOUN
ejpam-676	417	35	f2)(z	f2)(z	PROPN
ejpam-676	417	36	)	)	PUNCT
ejpam-676	418	1	+	+	NOUN
ejpam-676	418	2	λzp+1(ℓp(a	λzp+1(ℓp(a	ADJ
ejpam-676	418	3	,	,	PUNCT
ejpam-676	418	4	c	c	NOUN
ejpam-676	418	5	)	)	PUNCT
ejpam-676	418	6	(	(	PUNCT
ejpam-676	418	7	f1	f1	NOUN
ejpam-676	418	8	∗	∗	NOUN
ejpam-676	418	9	f2)(z	f2)(z	NUM
ejpam-676	418	10	)	)	PUNCT
ejpam-676	418	11	)	)	PUNCT
ejpam-676	419	1	′	′	NOUN
ejpam-676	419	2	©	©	NOUN
ejpam-676	419	3	>	>	X
ejpam-676	419	4	η0	η0	NOUN
ejpam-676	419	5	(	(	PUNCT
ejpam-676	419	6	z	z	NOUN
ejpam-676	419	7	∈	∈	PROPN
ejpam-676	419	8	u	u	NOUN
ejpam-676	419	9	)	)	PUNCT
ejpam-676	419	10	,	,	PUNCT
ejpam-676	419	11	where	where	SCONJ
ejpam-676	419	12	η0	η0	NOUN
ejpam-676	419	13	=	=	SYM
ejpam-676	419	14	1−	1−	NUM
ejpam-676	419	15	4(1−	4(1−	NUM
ejpam-676	419	16	θ1)(1−	θ1)(1−	PROPN
ejpam-676	419	17	θ2	θ2	PROPN
ejpam-676	419	18	)	)	PUNCT
ejpam-676	419	19	�	�	PROPN
ejpam-676	419	20	1−	1−	NUM
ejpam-676	419	21	1	1	NUM
ejpam-676	419	22	2	2	NUM
ejpam-676	419	23	2f1(1,1	2f1(1,1	NUM
ejpam-676	419	24	;	;	PUNCT
ejpam-676	419	25	a	a	DET
ejpam-676	419	26	λ	λ	NOUN
ejpam-676	419	27	+	+	NOUN
ejpam-676	419	28	1	1	NUM
ejpam-676	419	29	;	;	PUNCT
ejpam-676	419	30	1	1	NUM
ejpam-676	419	31	2	2	X
ejpam-676	419	32	)	)	PUNCT
ejpam-676	419	33	�	�	PROPN
ejpam-676	419	34	.	.	PUNCT
ejpam-676	420	1	the	the	DET
ejpam-676	420	2	result	result	NOUN
ejpam-676	420	3	is	be	AUX
ejpam-676	420	4	the	the	DET
ejpam-676	420	5	best	good	ADJ
ejpam-676	420	6	possible	possible	ADJ
ejpam-676	420	7	.	.	PUNCT
ejpam-676	421	1	choosing	choose	VERB
ejpam-676	421	2	a	a	DET
ejpam-676	421	3	j	j	NOUN
ejpam-676	421	4	=	=	SYM
ejpam-676	421	5	1−	1−	NUM
ejpam-676	421	6	2φ	2φ	NUM
ejpam-676	421	7	j	j	PROPN
ejpam-676	421	8	,	,	PUNCT
ejpam-676	421	9	b	b	PROPN
ejpam-676	421	10	j	j	PROPN
ejpam-676	421	11	=	=	SYM
ejpam-676	421	12	1	1	NUM
ejpam-676	421	13	(	(	PUNCT
ejpam-676	421	14	j	j	NOUN
ejpam-676	421	15	=	=	SYM
ejpam-676	421	16	1,2	1,2	NUM
ejpam-676	421	17	;	;	PUNCT
ejpam-676	421	18	0≤	0≤	NUM
ejpam-676	421	19	φ	φ	NUM
ejpam-676	421	20	j	j	PROPN
ejpam-676	421	21	<	<	X
ejpam-676	421	22	1	1	NUM
ejpam-676	421	23	)	)	PUNCT
ejpam-676	421	24	,	,	PUNCT
ejpam-676	421	25	q	q	NOUN
ejpam-676	421	26	=	=	PUNCT
ejpam-676	421	27	s+	s+	NUM
ejpam-676	421	28	1	1	NUM
ejpam-676	421	29	,	,	PUNCT
ejpam-676	421	30	α1	α1	PROPN
ejpam-676	421	31	=	=	SYM
ejpam-676	421	32	β1	β1	PROPN
ejpam-676	421	33	=	=	PUNCT
ejpam-676	421	34	p	p	PROPN
ejpam-676	421	35	,	,	PUNCT
ejpam-676	421	36	α	α	PROPN
ejpam-676	421	37	j	j	NOUN
ejpam-676	421	38	=	=	SYM
ejpam-676	421	39	1	1	NUM
ejpam-676	421	40	(	(	PUNCT
ejpam-676	421	41	j	j	NOUN
ejpam-676	421	42	=	=	SYM
ejpam-676	421	43	2,3	2,3	NUM
ejpam-676	421	44	,	,	PUNCT
ejpam-676	421	45	.	.	PUNCT
ejpam-676	421	46	.	.	PUNCT
ejpam-676	422	1	.	.	PUNCT
ejpam-676	423	1	,	,	PUNCT
ejpam-676	423	2	s	s	PART
ejpam-676	423	3	+	+	ADJ
ejpam-676	423	4	1	1	NUM
ejpam-676	423	5	)	)	PUNCT
ejpam-676	423	6	and	and	CCONJ
ejpam-676	423	7	β	β	X
ejpam-676	423	8	j	j	X
ejpam-676	424	1	=	=	SYM
ejpam-676	424	2	1	1	NUM
ejpam-676	424	3	(	(	PUNCT
ejpam-676	424	4	j	j	NOUN
ejpam-676	424	5	=	=	SYM
ejpam-676	424	6	2,3	2,3	NUM
ejpam-676	424	7	,	,	PUNCT
ejpam-676	424	8	.	.	PUNCT
ejpam-676	424	9	.	.	PUNCT
ejpam-676	424	10	.	.	PUNCT
ejpam-676	424	11	,	,	PUNCT
ejpam-676	424	12	s	s	X
ejpam-676	424	13	)	)	PUNCT
ejpam-676	424	14	in	in	ADP
ejpam-676	424	15	theorem	theorem	NOUN
ejpam-676	424	16	5	5	NUM
ejpam-676	424	17	,	,	PUNCT
ejpam-676	424	18	we	we	PRON
ejpam-676	424	19	obtain	obtain	VERB
ejpam-676	424	20	the	the	DET
ejpam-676	424	21	following	following	ADJ
ejpam-676	424	22	result	result	NOUN
ejpam-676	424	23	which	which	PRON
ejpam-676	424	24	refines	refine	VERB
ejpam-676	424	25	the	the	DET
ejpam-676	424	26	work	work	NOUN
ejpam-676	424	27	of	of	ADP
ejpam-676	424	28	yang	yang	PROPN
ejpam-676	425	1	[	[	X
ejpam-676	425	2	19	19	NUM
ejpam-676	425	3	,	,	PUNCT
ejpam-676	425	4	theorem	theorem	VERB
ejpam-676	425	5	4	4	NUM
ejpam-676	425	6	]	]	PUNCT
ejpam-676	425	7	and	and	CCONJ
ejpam-676	425	8	the	the	DET
ejpam-676	425	9	work	work	NOUN
ejpam-676	425	10	of	of	ADP
ejpam-676	425	11	srivastava	srivastava	PROPN
ejpam-676	425	12	and	and	CCONJ
ejpam-676	425	13	patel	patel	PROPN
ejpam-676	426	1	[	[	X
ejpam-676	426	2	15	15	NUM
ejpam-676	426	3	,	,	PUNCT
ejpam-676	426	4	corollary	corollary	ADJ
ejpam-676	426	5	6	6	NUM
ejpam-676	426	6	]	]	PUNCT
ejpam-676	426	7	.	.	PUNCT
ejpam-676	427	1	corollary	corollary	ADJ
ejpam-676	427	2	7	7	NUM
ejpam-676	427	3	.	.	PUNCT
ejpam-676	428	1	if	if	SCONJ
ejpam-676	428	2	the	the	DET
ejpam-676	428	3	functions	function	NOUN
ejpam-676	428	4	f	f	PROPN
ejpam-676	428	5	j	j	PROPN
ejpam-676	428	6	∈	∈	PROPN
ejpam-676	428	7	σp	σp	PROPN
ejpam-676	428	8	(	(	PUNCT
ejpam-676	428	9	j	j	PROPN
ejpam-676	428	10	=	=	SYM
ejpam-676	428	11	1,2	1,2	NUM
ejpam-676	428	12	)	)	PUNCT
ejpam-676	428	13	satisfy	satisfy	VERB
ejpam-676	428	14	the	the	DET
ejpam-676	428	15	following	follow	VERB
ejpam-676	428	16	inequality	inequality	NOUN
ejpam-676	428	17	:	:	PUNCT
ejpam-676	428	18	re	re	VERB
ejpam-676	428	19	�	�	PROPN
ejpam-676	428	20	(	(	PUNCT
ejpam-676	428	21	1+λ)zp	1+λ)zp	NOUN
ejpam-676	428	22	f	f	NOUN
ejpam-676	428	23	j(z	j(z	PROPN
ejpam-676	428	24	)	)	PUNCT
ejpam-676	429	1	+	+	PUNCT
ejpam-676	430	1	λ	λ	X
ejpam-676	430	2	p	p	NOUN
ejpam-676	430	3	zp+1	zp+1	NUM
ejpam-676	430	4	f	f	NOUN
ejpam-676	430	5	′	′	NUM
ejpam-676	430	6	j	j	PROPN
ejpam-676	430	7	(	(	PUNCT
ejpam-676	430	8	z	z	PROPN
ejpam-676	430	9	)	)	PUNCT
ejpam-676	430	10	�	�	PROPN
ejpam-676	430	11	>	>	X
ejpam-676	430	12	φ	φ	PROPN
ejpam-676	430	13	j	j	PROPN
ejpam-676	430	14	(	(	PUNCT
ejpam-676	430	15	0≤	0≤	PROPN
ejpam-676	430	16	φ	φ	NUM
ejpam-676	430	17	j	j	PROPN
ejpam-676	430	18	<	<	X
ejpam-676	430	19	1	1	NUM
ejpam-676	430	20	;	;	PUNCT
ejpam-676	430	21	j	j	PROPN
ejpam-676	430	22	=	=	SYM
ejpam-676	430	23	1,2	1,2	NUM
ejpam-676	430	24	;	;	PUNCT
ejpam-676	430	25	z	z	PROPN
ejpam-676	430	26	∈	∈	PROPN
ejpam-676	430	27	u	u	NOUN
ejpam-676	430	28	)	)	PUNCT
ejpam-676	430	29	,	,	PUNCT
ejpam-676	430	30	(	(	PUNCT
ejpam-676	430	31	45	45	NUM
ejpam-676	430	32	)	)	PUNCT
ejpam-676	430	33	then	then	ADV
ejpam-676	430	34	re	re	VERB
ejpam-676	430	35	�	�	PROPN
ejpam-676	430	36	(	(	PUNCT
ejpam-676	430	37	1+λ)zp	1+λ)zp	PROPN
ejpam-676	430	38	(	(	PUNCT
ejpam-676	430	39	f1	f1	NOUN
ejpam-676	430	40	∗	∗	NOUN
ejpam-676	430	41	f2)(z	f2)(z	PROPN
ejpam-676	430	42	)	)	PUNCT
ejpam-676	431	1	+	+	NUM
ejpam-676	431	2	λ	λ	X
ejpam-676	431	3	p	p	ADJ
ejpam-676	431	4	zp+1	zp+1	NUM
ejpam-676	431	5	(	(	PUNCT
ejpam-676	431	6	f1	f1	NOUN
ejpam-676	431	7	∗	∗	NOUN
ejpam-676	431	8	f2)(z	f2)(z	NUM
ejpam-676	431	9	)	)	PUNCT
ejpam-676	431	10	)	)	PUNCT
ejpam-676	432	1	′	′	NUM
ejpam-676	432	2	�	�	PROPN
ejpam-676	432	3	>	>	X
ejpam-676	432	4	ρ0	ρ0	PROPN
ejpam-676	432	5	(	(	PUNCT
ejpam-676	432	6	z	z	NOUN
ejpam-676	432	7	∈	∈	PROPN
ejpam-676	432	8	u	u	NOUN
ejpam-676	432	9	)	)	PUNCT
ejpam-676	432	10	,	,	PUNCT
ejpam-676	432	11	where	where	SCONJ
ejpam-676	432	12	ρ0	ρ0	PROPN
ejpam-676	432	13	=	=	SYM
ejpam-676	432	14	1−	1−	NUM
ejpam-676	432	15	4(1−φ1)(1−φ2	4(1−φ1)(1−φ2	NUM
ejpam-676	432	16	)	)	PUNCT
ejpam-676	432	17	�	�	PROPN
ejpam-676	432	18	1−	1−	NUM
ejpam-676	432	19	1	1	NUM
ejpam-676	432	20	2	2	NUM
ejpam-676	432	21	2f1(1,1	2f1(1,1	NUM
ejpam-676	432	22	;	;	PUNCT
ejpam-676	432	23	p	p	PROPN
ejpam-676	432	24	λ	λ	PROPN
ejpam-676	432	25	+	+	PROPN
ejpam-676	432	26	1	1	NUM
ejpam-676	432	27	;	;	PUNCT
ejpam-676	432	28	1	1	NUM
ejpam-676	432	29	2	2	X
ejpam-676	432	30	)	)	PUNCT
ejpam-676	432	31	�	�	PROPN
ejpam-676	432	32	.	.	PUNCT
ejpam-676	433	1	the	the	DET
ejpam-676	433	2	result	result	NOUN
ejpam-676	433	3	is	be	AUX
ejpam-676	433	4	the	the	DET
ejpam-676	433	5	best	good	ADJ
ejpam-676	433	6	possible	possible	ADJ
ejpam-676	433	7	.	.	PUNCT
ejpam-676	434	1	m.	m.	PROPN
ejpam-676	434	2	aouf	aouf	PROPN
ejpam-676	434	3	/	/	SYM
ejpam-676	434	4	eur	eur	PROPN
ejpam-676	434	5	.	.	PUNCT
ejpam-676	435	1	j.	j.	PROPN
ejpam-676	435	2	pure	pure	PROPN
ejpam-676	435	3	appl	appl	PROPN
ejpam-676	435	4	.	.	PROPN
ejpam-676	435	5	math	math	PROPN
ejpam-676	435	6	,	,	PUNCT
ejpam-676	435	7	5	5	NUM
ejpam-676	435	8	(	(	PUNCT
ejpam-676	435	9	2012	2012	NUM
ejpam-676	435	10	)	)	PUNCT
ejpam-676	435	11	,	,	PUNCT
ejpam-676	435	12	141	141	NUM
ejpam-676	435	13	-	-	SYM
ejpam-676	435	14	159	159	NUM
ejpam-676	435	15	156	156	NUM
ejpam-676	435	16	theorem	theorem	NOUN
ejpam-676	435	17	6	6	NUM
ejpam-676	435	18	.	.	PUNCT
ejpam-676	436	1	if	if	SCONJ
ejpam-676	436	2	f	f	PROPN
ejpam-676	436	3	∈	∈	PROPN
ejpam-676	436	4	σp	σp	PROPN
ejpam-676	436	5	,	,	PUNCT
ejpam-676	436	6	m	m	VERB
ejpam-676	436	7	satisfies	satisfy	VERB
ejpam-676	436	8	the	the	DET
ejpam-676	436	9	following	follow	VERB
ejpam-676	436	10	subordination	subordination	NOUN
ejpam-676	436	11	condition	condition	NOUN
ejpam-676	436	12	:	:	PUNCT
ejpam-676	436	13	(	(	PUNCT
ejpam-676	436	14	1−λ)zphp	1−λ)zphp	NUM
ejpam-676	436	15	,	,	PUNCT
ejpam-676	436	16	q	q	NOUN
ejpam-676	436	17	,	,	PUNCT
ejpam-676	436	18	s(α1	s(α1	NOUN
ejpam-676	436	19	)	)	PUNCT
ejpam-676	437	1	f	f	PROPN
ejpam-676	438	1	(	(	PUNCT
ejpam-676	438	2	z	z	NOUN
ejpam-676	438	3	)	)	PUNCT
ejpam-676	438	4	+	+	NOUN
ejpam-676	438	5	λzphp	λzphp	ADJ
ejpam-676	438	6	,	,	PUNCT
ejpam-676	438	7	q	q	NOUN
ejpam-676	438	8	,	,	PUNCT
ejpam-676	438	9	s(α1	s(α1	NOUN
ejpam-676	438	10	+	+	CCONJ
ejpam-676	438	11	1	1	X
ejpam-676	438	12	)	)	PUNCT
ejpam-676	438	13	f	f	NOUN
ejpam-676	439	1	(	(	PUNCT
ejpam-676	439	2	z)≺	z)≺	PROPN
ejpam-676	439	3	1	1	NUM
ejpam-676	439	4	+	+	NUM
ejpam-676	439	5	az	az	PROPN
ejpam-676	439	6	1	1	NUM
ejpam-676	439	7	+	+	CCONJ
ejpam-676	439	8	bz	bz	PROPN
ejpam-676	439	9	,	,	PUNCT
ejpam-676	439	10	then	then	ADV
ejpam-676	439	11	re	re	VERB
ejpam-676	439	12	¦	¦	PROPN
ejpam-676	439	13	zphp	zphp	PROPN
ejpam-676	439	14	,	,	PUNCT
ejpam-676	439	15	q	q	NOUN
ejpam-676	439	16	,	,	PUNCT
ejpam-676	439	17	s(α1	s(α1	NOUN
ejpam-676	439	18	)	)	PUNCT
ejpam-676	439	19	f	f	PROPN
ejpam-676	440	1	(	(	PUNCT
ejpam-676	440	2	z	z	NOUN
ejpam-676	440	3	)	)	PUNCT
ejpam-676	440	4	©	©	PROPN
ejpam-676	440	5	1	1	NUM
ejpam-676	440	6	d	d	X
ejpam-676	440	7	>	>	X
ejpam-676	440	8	ξ	ξ	PROPN
ejpam-676	440	9	1	1	NUM
ejpam-676	440	10	d	d	NOUN
ejpam-676	440	11	(	(	PUNCT
ejpam-676	440	12	d	d	PROPN
ejpam-676	440	13	∈	∈	PROPN
ejpam-676	440	14	n	n	NOUN
ejpam-676	440	15	;	;	PUNCT
ejpam-676	440	16	z	z	PROPN
ejpam-676	440	17	∈	∈	PROPN
ejpam-676	440	18	u	u	NOUN
ejpam-676	440	19	)	)	PUNCT
ejpam-676	440	20	,	,	PUNCT
ejpam-676	440	21	where	where	SCONJ
ejpam-676	440	22	ξ	ξ	PROPN
ejpam-676	440	23	is	be	AUX
ejpam-676	440	24	given	give	VERB
ejpam-676	440	25	as	as	ADP
ejpam-676	440	26	in	in	ADP
ejpam-676	440	27	theorem	theorem	NOUN
ejpam-676	440	28	1	1	NUM
ejpam-676	440	29	.	.	PUNCT
ejpam-676	441	1	the	the	DET
ejpam-676	441	2	result	result	NOUN
ejpam-676	441	3	is	be	AUX
ejpam-676	441	4	the	the	DET
ejpam-676	441	5	best	good	ADJ
ejpam-676	441	6	possible	possible	ADJ
ejpam-676	441	7	.	.	PUNCT
ejpam-676	442	1	proof	proof	NOUN
ejpam-676	442	2	.	.	PUNCT
ejpam-676	443	1	defining	define	VERB
ejpam-676	443	2	the	the	DET
ejpam-676	443	3	function	function	NOUN
ejpam-676	443	4	ϕ	ϕ	NOUN
ejpam-676	443	5	by	by	ADP
ejpam-676	443	6	ϕ(z	ϕ(z	NOUN
ejpam-676	443	7	)	)	PUNCT
ejpam-676	444	1	=	=	SYM
ejpam-676	444	2	zphp	zphp	NOUN
ejpam-676	444	3	,	,	PUNCT
ejpam-676	444	4	q	q	NOUN
ejpam-676	444	5	,	,	PUNCT
ejpam-676	444	6	s(α1	s(α1	NOUN
ejpam-676	444	7	)	)	PUNCT
ejpam-676	445	1	f	f	PROPN
ejpam-676	445	2	(	(	PUNCT
ejpam-676	445	3	z	z	NOUN
ejpam-676	445	4	)	)	PUNCT
ejpam-676	445	5	(	(	PUNCT
ejpam-676	445	6	f	f	PROPN
ejpam-676	445	7	∈	∈	PROPN
ejpam-676	445	8	σp	σp	PROPN
ejpam-676	445	9	,	,	PUNCT
ejpam-676	445	10	m	m	PROPN
ejpam-676	445	11	;	;	PUNCT
ejpam-676	445	12	z	z	PROPN
ejpam-676	445	13	∈	∈	PROPN
ejpam-676	445	14	u	u	NOUN
ejpam-676	445	15	)	)	PUNCT
ejpam-676	445	16	,	,	PUNCT
ejpam-676	445	17	(	(	PUNCT
ejpam-676	445	18	46	46	X
ejpam-676	445	19	)	)	PUNCT
ejpam-676	445	20	we	we	PRON
ejpam-676	445	21	see	see	VERB
ejpam-676	445	22	that	that	SCONJ
ejpam-676	445	23	the	the	DET
ejpam-676	445	24	function	function	NOUN
ejpam-676	445	25	ϕ	ϕ	NOUN
ejpam-676	445	26	is	be	AUX
ejpam-676	445	27	of	of	ADP
ejpam-676	445	28	the	the	DET
ejpam-676	445	29	form	form	NOUN
ejpam-676	445	30	(	(	PUNCT
ejpam-676	445	31	13	13	NUM
ejpam-676	445	32	)	)	PUNCT
ejpam-676	445	33	and	and	CCONJ
ejpam-676	445	34	is	be	AUX
ejpam-676	445	35	analytic	analytic	ADJ
ejpam-676	445	36	in	in	ADP
ejpam-676	445	37	u	u	PROPN
ejpam-676	445	38	.	.	PUNCT
ejpam-676	446	1	differentiating	differentiate	VERB
ejpam-676	446	2	(	(	PUNCT
ejpam-676	446	3	46	46	NUM
ejpam-676	446	4	)	)	PUNCT
ejpam-676	446	5	with	with	ADP
ejpam-676	446	6	respect	respect	NOUN
ejpam-676	446	7	to	to	ADP
ejpam-676	446	8	z	z	NOUN
ejpam-676	446	9	and	and	CCONJ
ejpam-676	446	10	using	use	VERB
ejpam-676	446	11	the	the	DET
ejpam-676	446	12	identity	identity	NOUN
ejpam-676	446	13	(	(	PUNCT
ejpam-676	446	14	10	10	NUM
ejpam-676	446	15	)	)	PUNCT
ejpam-676	446	16	,	,	PUNCT
ejpam-676	446	17	we	we	PRON
ejpam-676	446	18	obtain	obtain	VERB
ejpam-676	446	19	(	(	PUNCT
ejpam-676	446	20	1−λ)zphp	1−λ)zphp	NUM
ejpam-676	446	21	,	,	PUNCT
ejpam-676	446	22	q	q	NOUN
ejpam-676	446	23	,	,	PUNCT
ejpam-676	446	24	s(α1	s(α1	NOUN
ejpam-676	446	25	)	)	PUNCT
ejpam-676	447	1	f	f	PROPN
ejpam-676	447	2	(	(	PUNCT
ejpam-676	447	3	z	z	NOUN
ejpam-676	447	4	)	)	PUNCT
ejpam-676	448	1	+	+	NOUN
ejpam-676	448	2	λzphp	λzphp	ADJ
ejpam-676	448	3	,	,	PUNCT
ejpam-676	448	4	q	q	NOUN
ejpam-676	448	5	,	,	PUNCT
ejpam-676	448	6	s(α1	s(α1	NOUN
ejpam-676	448	7	+	+	CCONJ
ejpam-676	448	8	1	1	X
ejpam-676	448	9	)	)	PUNCT
ejpam-676	448	10	f	f	NOUN
ejpam-676	448	11	(	(	PUNCT
ejpam-676	448	12	z	z	NOUN
ejpam-676	448	13	)	)	PUNCT
ejpam-676	448	14	=	=	SYM
ejpam-676	448	15	ϕ(z	ϕ(z	PROPN
ejpam-676	448	16	)	)	PUNCT
ejpam-676	449	1	+	+	NUM
ejpam-676	449	2	λ	λ	PROPN
ejpam-676	449	3	α1	α1	PROPN
ejpam-676	449	4	zϕ	zϕ	INTJ
ejpam-676	449	5	′	′	NUM
ejpam-676	450	1	(	(	PUNCT
ejpam-676	450	2	z)≺	z)≺	PROPN
ejpam-676	450	3	1	1	NUM
ejpam-676	450	4	+	+	NUM
ejpam-676	450	5	az	az	PROPN
ejpam-676	450	6	1	1	NUM
ejpam-676	450	7	+	+	CCONJ
ejpam-676	450	8	bz	bz	PROPN
ejpam-676	450	9	.	.	PUNCT
ejpam-676	451	1	now	now	ADV
ejpam-676	451	2	,	,	PUNCT
ejpam-676	451	3	by	by	ADP
ejpam-676	451	4	following	follow	VERB
ejpam-676	451	5	the	the	DET
ejpam-676	451	6	lines	line	NOUN
ejpam-676	451	7	of	of	ADP
ejpam-676	451	8	the	the	DET
ejpam-676	451	9	proof	proof	NOUN
ejpam-676	451	10	of	of	ADP
ejpam-676	451	11	theorem	theorem	ADJ
ejpam-676	451	12	1	1	NUM
ejpam-676	451	13	mutates	mutate	NOUN
ejpam-676	451	14	mutandis	mutandi	NOUN
ejpam-676	451	15	,	,	PUNCT
ejpam-676	451	16	and	and	CCONJ
ejpam-676	451	17	using	use	VERB
ejpam-676	451	18	the	the	DET
ejpam-676	451	19	elementary	elementary	ADJ
ejpam-676	451	20	inequality	inequality	NOUN
ejpam-676	451	21	:	:	PUNCT
ejpam-676	451	22	re	re	VERB
ejpam-676	451	23	�	�	PROPN
ejpam-676	451	24	w	w	PROPN
ejpam-676	451	25	1	1	PROPN
ejpam-676	451	26	d	d	PROPN
ejpam-676	451	27	�	�	PROPN
ejpam-676	451	28	≥	≥	X
ejpam-676	451	29	(	(	PUNCT
ejpam-676	451	30	re	re	NOUN
ejpam-676	451	31	w	w	NOUN
ejpam-676	451	32	)	)	PUNCT
ejpam-676	451	33	1	1	NUM
ejpam-676	451	34	d	d	NOUN
ejpam-676	451	35	(	(	PUNCT
ejpam-676	451	36	re(w	re(w	NOUN
ejpam-676	451	37	)	)	PUNCT
ejpam-676	451	38	>	>	X
ejpam-676	451	39	0	0	NUM
ejpam-676	451	40	;	;	PUNCT
ejpam-676	451	41	d	d	PROPN
ejpam-676	451	42	∈	∈	PROPN
ejpam-676	451	43	n	n	CCONJ
ejpam-676	451	44	)	)	PUNCT
ejpam-676	451	45	,	,	PUNCT
ejpam-676	451	46	we	we	PRON
ejpam-676	451	47	arrive	arrive	VERB
ejpam-676	451	48	at	at	ADP
ejpam-676	451	49	the	the	DET
ejpam-676	451	50	result	result	NOUN
ejpam-676	451	51	asserted	assert	VERB
ejpam-676	451	52	by	by	ADP
ejpam-676	451	53	theorem	theorem	NOUN
ejpam-676	451	54	6	6	NUM
ejpam-676	451	55	.	.	PUNCT
ejpam-676	451	56	putting	put	VERB
ejpam-676	451	57	a=	a=	PROPN
ejpam-676	451	58	�	�	PROPN
ejpam-676	451	59	2f1(1,1	2f1(1,1	NUM
ejpam-676	451	60	;	;	PUNCT
ejpam-676	451	61	α1	α1	PROPN
ejpam-676	451	62	λ(p+m	λ(p+m	NOUN
ejpam-676	451	63	)	)	PUNCT
ejpam-676	452	1	+	+	CCONJ
ejpam-676	452	2	1	1	NUM
ejpam-676	452	3	;	;	PUNCT
ejpam-676	452	4	1	1	NUM
ejpam-676	452	5	2	2	NUM
ejpam-676	452	6	)	)	PUNCT
ejpam-676	452	7	−	−	PROPN
ejpam-676	452	8	1	1	NUM
ejpam-676	452	9	�	�	PROPN
ejpam-676	452	10	·	·	PUNCT
ejpam-676	452	11	�	�	PROPN
ejpam-676	452	12	2−	2−	NUM
ejpam-676	452	13	2f1(1,1	2f1(1,1	NUM
ejpam-676	452	14	;	;	PUNCT
ejpam-676	452	15	α1	α1	PROPN
ejpam-676	452	16	λ(p+m	λ(p+m	NOUN
ejpam-676	452	17	)	)	PUNCT
ejpam-676	452	18	+	+	CCONJ
ejpam-676	452	19	1	1	NUM
ejpam-676	452	20	;	;	PUNCT
ejpam-676	452	21	1	1	NUM
ejpam-676	452	22	2	2	NUM
ejpam-676	452	23	)	)	PUNCT
ejpam-676	452	24	�	�	PROPN
ejpam-676	452	25	−1	−1	NOUN
ejpam-676	452	26	,	,	PUNCT
ejpam-676	452	27	b	b	X
ejpam-676	452	28	=	=	SYM
ejpam-676	452	29	−1	−1	NOUN
ejpam-676	452	30	,	,	PUNCT
ejpam-676	452	31	s	s	NOUN
ejpam-676	452	32	=	=	SYM
ejpam-676	452	33	1	1	NUM
ejpam-676	452	34	,	,	PUNCT
ejpam-676	452	35	q	q	NOUN
ejpam-676	452	36	=	=	SYM
ejpam-676	452	37	2	2	NUM
ejpam-676	452	38	,	,	PUNCT
ejpam-676	452	39	α1	α1	PROPN
ejpam-676	452	40	=	=	PUNCT
ejpam-676	452	41	a	a	PRON
ejpam-676	452	42	>	>	X
ejpam-676	452	43	0,β1	0,β1	PUNCT
ejpam-676	453	1	=	=	PUNCT
ejpam-676	453	2	c	c	X
ejpam-676	453	3	>	>	X
ejpam-676	453	4	0	0	NUM
ejpam-676	453	5	,	,	PUNCT
ejpam-676	453	6	α2	α2	NOUN
ejpam-676	453	7	=	=	SYM
ejpam-676	453	8	1	1	NUM
ejpam-676	453	9	and	and	CCONJ
ejpam-676	453	10	d	d	NOUN
ejpam-676	453	11	=	=	SYM
ejpam-676	453	12	1	1	NUM
ejpam-676	453	13	in	in	ADP
ejpam-676	453	14	theorem	theorem	NOUN
ejpam-676	453	15	6	6	NUM
ejpam-676	453	16	,	,	PUNCT
ejpam-676	453	17	we	we	PRON
ejpam-676	453	18	obtain	obtain	VERB
ejpam-676	453	19	the	the	DET
ejpam-676	453	20	following	follow	VERB
ejpam-676	453	21	corollary	corollary	NOUN
ejpam-676	453	22	.	.	PUNCT
ejpam-676	454	1	corollary	corollary	ADJ
ejpam-676	454	2	8	8	NUM
ejpam-676	454	3	.	.	PUNCT
ejpam-676	455	1	if	if	SCONJ
ejpam-676	455	2	f	f	PROPN
ejpam-676	455	3	∈	∈	PROPN
ejpam-676	455	4	σp	σp	PROPN
ejpam-676	455	5	,	,	PUNCT
ejpam-676	455	6	m	m	VERB
ejpam-676	455	7	satisfies	satisfy	VERB
ejpam-676	455	8	the	the	DET
ejpam-676	455	9	following	follow	VERB
ejpam-676	455	10	inequality	inequality	NOUN
ejpam-676	455	11	:	:	PUNCT
ejpam-676	455	12	re	re	X
ejpam-676	455	13	¦	¦	X
ejpam-676	455	14	(	(	PUNCT
ejpam-676	455	15	1+λp)zpℓp(a	1+λp)zpℓp(a	NUM
ejpam-676	455	16	,	,	PUNCT
ejpam-676	455	17	c	c	NOUN
ejpam-676	455	18	)	)	PUNCT
ejpam-676	455	19	f	f	NOUN
ejpam-676	455	20	(	(	PUNCT
ejpam-676	455	21	z	z	NOUN
ejpam-676	455	22	)	)	PUNCT
ejpam-676	455	23	+	+	NOUN
ejpam-676	455	24	λzp+1(ℓp(a	λzp+1(ℓp(a	ADJ
ejpam-676	455	25	,	,	PUNCT
ejpam-676	455	26	c	c	NOUN
ejpam-676	455	27	)	)	PUNCT
ejpam-676	455	28	f	f	NOUN
ejpam-676	455	29	(	(	PUNCT
ejpam-676	455	30	z	z	NOUN
ejpam-676	455	31	)	)	PUNCT
ejpam-676	455	32	)	)	PUNCT
ejpam-676	456	1	′	′	NOUN
ejpam-676	457	1	©	©	NOUN
ejpam-676	457	2	>	>	PUNCT
ejpam-676	457	3	3−	3−	NUM
ejpam-676	457	4	2	2	NUM
ejpam-676	457	5	2f1(1,1	2f1(1,1	NUM
ejpam-676	457	6	;	;	PUNCT
ejpam-676	457	7	a	a	DET
ejpam-676	457	8	λ(p+m	λ(p+m	NOUN
ejpam-676	457	9	)	)	PUNCT
ejpam-676	457	10	+	+	CCONJ
ejpam-676	457	11	1	1	NUM
ejpam-676	457	12	;	;	PUNCT
ejpam-676	457	13	1	1	NUM
ejpam-676	457	14	2	2	NUM
ejpam-676	457	15	)	)	PUNCT
ejpam-676	457	16	2	2	NUM
ejpam-676	457	17	h	h	NOUN
ejpam-676	457	18	2−	2−	NUM
ejpam-676	457	19	2f1(1,1	2f1(1,1	NUM
ejpam-676	457	20	;	;	PUNCT
ejpam-676	457	21	a	a	DET
ejpam-676	457	22	λ(p+m	λ(p+m	NOUN
ejpam-676	457	23	)	)	PUNCT
ejpam-676	457	24	+	+	CCONJ
ejpam-676	457	25	1	1	NUM
ejpam-676	457	26	;	;	PUNCT
ejpam-676	457	27	1	1	NUM
ejpam-676	457	28	2	2	NUM
ejpam-676	457	29	)	)	PUNCT
ejpam-676	458	1	i	i	PRON
ejpam-676	458	2	z	z	NOUN
ejpam-676	458	3	∈	∈	PROPN
ejpam-676	458	4	u	u	NOUN
ejpam-676	458	5	)	)	PUNCT
ejpam-676	458	6	,	,	PUNCT
ejpam-676	458	7	(	(	PUNCT
ejpam-676	458	8	47	47	NUM
ejpam-676	458	9	)	)	PUNCT
ejpam-676	458	10	then	then	ADV
ejpam-676	458	11	re	re	X
ejpam-676	458	12	¦	¦	PROPN
ejpam-676	458	13	zpℓp(a	zpℓp(a	PROPN
ejpam-676	458	14	,	,	PUNCT
ejpam-676	458	15	c	c	NOUN
ejpam-676	458	16	)	)	PUNCT
ejpam-676	458	17	f	f	NOUN
ejpam-676	458	18	(	(	PUNCT
ejpam-676	458	19	z	z	NOUN
ejpam-676	458	20	)	)	PUNCT
ejpam-676	458	21	©	©	NOUN
ejpam-676	458	22	>	>	SYM
ejpam-676	458	23	1	1	NUM
ejpam-676	458	24	2	2	NUM
ejpam-676	458	25	(	(	PUNCT
ejpam-676	458	26	z	z	NOUN
ejpam-676	458	27	∈	∈	PROPN
ejpam-676	458	28	u	u	NOUN
ejpam-676	458	29	)	)	PUNCT
ejpam-676	458	30	.	.	PUNCT
ejpam-676	459	1	the	the	DET
ejpam-676	459	2	result	result	NOUN
ejpam-676	459	3	is	be	AUX
ejpam-676	459	4	the	the	DET
ejpam-676	459	5	best	good	ADJ
ejpam-676	459	6	possible	possible	ADJ
ejpam-676	459	7	.	.	PUNCT
ejpam-676	460	1	from	from	ADP
ejpam-676	460	2	corollary	corollary	ADJ
ejpam-676	460	3	6	6	NUM
ejpam-676	460	4	and	and	CCONJ
ejpam-676	460	5	theorem	theorem	VERB
ejpam-676	460	6	6	6	NUM
ejpam-676	460	7	(	(	PUNCT
ejpam-676	460	8	for	for	ADP
ejpam-676	460	9	m	m	PROPN
ejpam-676	460	10	=	=	SYM
ejpam-676	460	11	−p+	−p+	NOUN
ejpam-676	460	12	1	1	NUM
ejpam-676	460	13	,	,	PUNCT
ejpam-676	460	14	a=	a=	PROPN
ejpam-676	460	15	1−	1−	NUM
ejpam-676	460	16	2η0	2η0	NUM
ejpam-676	460	17	,	,	PUNCT
ejpam-676	460	18	b	b	X
ejpam-676	460	19	=	=	SYM
ejpam-676	460	20	−1	−1	NOUN
ejpam-676	460	21	and	and	CCONJ
ejpam-676	460	22	d	d	NOUN
ejpam-676	460	23	=	=	SYM
ejpam-676	460	24	1	1	NUM
ejpam-676	460	25	)	)	PUNCT
ejpam-676	460	26	,	,	PUNCT
ejpam-676	460	27	we	we	PRON
ejpam-676	460	28	obtain	obtain	VERB
ejpam-676	460	29	the	the	DET
ejpam-676	460	30	following	follow	VERB
ejpam-676	460	31	result	result	NOUN
ejpam-676	460	32	.	.	PUNCT
ejpam-676	461	1	m.	m.	NOUN
ejpam-676	461	2	aouf	aouf	PROPN
ejpam-676	461	3	/	/	SYM
ejpam-676	461	4	eur	eur	PROPN
ejpam-676	461	5	.	.	PUNCT
ejpam-676	462	1	j.	j.	PROPN
ejpam-676	462	2	pure	pure	PROPN
ejpam-676	462	3	appl	appl	PROPN
ejpam-676	462	4	.	.	PROPN
ejpam-676	462	5	math	math	PROPN
ejpam-676	462	6	,	,	PUNCT
ejpam-676	462	7	5	5	NUM
ejpam-676	462	8	(	(	PUNCT
ejpam-676	462	9	2012	2012	NUM
ejpam-676	462	10	)	)	PUNCT
ejpam-676	462	11	,	,	PUNCT
ejpam-676	462	12	141	141	NUM
ejpam-676	462	13	-	-	SYM
ejpam-676	462	14	159	159	NUM
ejpam-676	462	15	157	157	NUM
ejpam-676	462	16	corollary	corollary	ADJ
ejpam-676	462	17	9	9	NUM
ejpam-676	462	18	.	.	PUNCT
ejpam-676	463	1	if	if	SCONJ
ejpam-676	463	2	the	the	DET
ejpam-676	463	3	function	function	NOUN
ejpam-676	463	4	f	f	PROPN
ejpam-676	463	5	j	j	PROPN
ejpam-676	463	6	∈	∈	PROPN
ejpam-676	463	7	σp	σp	PROPN
ejpam-676	463	8	(	(	PUNCT
ejpam-676	463	9	j	j	PROPN
ejpam-676	463	10	=	=	SYM
ejpam-676	463	11	1,2	1,2	NUM
ejpam-676	463	12	)	)	PUNCT
ejpam-676	463	13	satisfy	satisfy	VERB
ejpam-676	463	14	the	the	DET
ejpam-676	463	15	inequality	inequality	NOUN
ejpam-676	463	16	(	(	PUNCT
ejpam-676	463	17	44	44	NUM
ejpam-676	463	18	)	)	PUNCT
ejpam-676	463	19	,	,	PUNCT
ejpam-676	463	20	then	then	ADV
ejpam-676	463	21	re	re	VERB
ejpam-676	463	22	¦	¦	PROPN
ejpam-676	463	23	zpℓp(a	zpℓp(a	PROPN
ejpam-676	463	24	,	,	PUNCT
ejpam-676	463	25	c	c	NOUN
ejpam-676	463	26	)	)	PUNCT
ejpam-676	463	27	(	(	PUNCT
ejpam-676	463	28	f1	f1	NOUN
ejpam-676	463	29	∗	∗	NOUN
ejpam-676	463	30	f2)(z	f2)(z	NOUN
ejpam-676	463	31	)	)	PUNCT
ejpam-676	463	32	©	©	NOUN
ejpam-676	463	33	>	>	X
ejpam-676	463	34	η0	η0	NOUN
ejpam-676	463	35	+	+	CCONJ
ejpam-676	463	36	(	(	PUNCT
ejpam-676	463	37	1−η0	1−η0	NUM
ejpam-676	463	38	)	)	PUNCT
ejpam-676	463	39	�	�	PROPN
ejpam-676	463	40	2f1(1,1	2f1(1,1	NUM
ejpam-676	463	41	;	;	PUNCT
ejpam-676	463	42	a	a	DET
ejpam-676	463	43	λ	λ	NOUN
ejpam-676	463	44	+	+	NOUN
ejpam-676	463	45	1	1	NUM
ejpam-676	463	46	;	;	PUNCT
ejpam-676	463	47	1	1	NUM
ejpam-676	463	48	2	2	NUM
ejpam-676	463	49	)	)	PUNCT
ejpam-676	463	50	−	−	PROPN
ejpam-676	463	51	1	1	NUM
ejpam-676	463	52	�	�	PROPN
ejpam-676	463	53	(	(	PUNCT
ejpam-676	463	54	z	z	NOUN
ejpam-676	463	55	∈	∈	PROPN
ejpam-676	463	56	u	u	NOUN
ejpam-676	463	57	)	)	PUNCT
ejpam-676	463	58	,	,	PUNCT
ejpam-676	463	59	where	where	SCONJ
ejpam-676	463	60	η0	η0	NOUN
ejpam-676	463	61	is	be	AUX
ejpam-676	463	62	given	give	VERB
ejpam-676	463	63	as	as	ADP
ejpam-676	463	64	in	in	ADP
ejpam-676	463	65	corollary	corollary	ADJ
ejpam-676	463	66	6	6	NUM
ejpam-676	463	67	.	.	PUNCT
ejpam-676	464	1	the	the	DET
ejpam-676	464	2	result	result	NOUN
ejpam-676	464	3	is	be	AUX
ejpam-676	464	4	the	the	DET
ejpam-676	464	5	best	good	ADJ
ejpam-676	464	6	possible	possible	ADJ
ejpam-676	464	7	.	.	PUNCT
ejpam-676	465	1	putting	put	VERB
ejpam-676	465	2	a=	a=	NOUN
ejpam-676	465	3	�	�	PROPN
ejpam-676	465	4	2f1(1,1	2f1(1,1	PROPN
ejpam-676	465	5	;	;	PUNCT
ejpam-676	465	6	p	p	X
ejpam-676	465	7	λ(p+m	λ(p+m	NOUN
ejpam-676	465	8	)	)	PUNCT
ejpam-676	466	1	+	+	CCONJ
ejpam-676	466	2	1	1	NUM
ejpam-676	466	3	;	;	PUNCT
ejpam-676	466	4	1	1	NUM
ejpam-676	466	5	2	2	NUM
ejpam-676	466	6	)	)	PUNCT
ejpam-676	466	7	−	−	PROPN
ejpam-676	466	8	1	1	NUM
ejpam-676	466	9	�	�	PROPN
ejpam-676	466	10	·	·	PUNCT
ejpam-676	466	11	�	�	PROPN
ejpam-676	466	12	2−	2−	NUM
ejpam-676	466	13	2f1(1,1	2f1(1,1	NUM
ejpam-676	466	14	;	;	PUNCT
ejpam-676	466	15	p	p	X
ejpam-676	466	16	λ(p+m	λ(p+m	NOUN
ejpam-676	466	17	)	)	PUNCT
ejpam-676	467	1	+	+	CCONJ
ejpam-676	467	2	1	1	NUM
ejpam-676	467	3	;	;	PUNCT
ejpam-676	467	4	1	1	NUM
ejpam-676	467	5	2	2	NUM
ejpam-676	467	6	)	)	PUNCT
ejpam-676	467	7	�	�	PROPN
ejpam-676	467	8	−1	−1	NOUN
ejpam-676	467	9	,	,	PUNCT
ejpam-676	467	10	b	b	X
ejpam-676	467	11	=	=	SYM
ejpam-676	467	12	−1	−1	NOUN
ejpam-676	467	13	,	,	PUNCT
ejpam-676	467	14	q	q	NOUN
ejpam-676	467	15	=	=	PUNCT
ejpam-676	467	16	s+	s+	NUM
ejpam-676	467	17	1	1	NUM
ejpam-676	467	18	,	,	PUNCT
ejpam-676	467	19	α1	α1	PROPN
ejpam-676	467	20	=	=	SYM
ejpam-676	467	21	β1	β1	PROPN
ejpam-676	467	22	=	=	PUNCT
ejpam-676	467	23	p	p	PROPN
ejpam-676	467	24	,	,	PUNCT
ejpam-676	467	25	α	α	PROPN
ejpam-676	467	26	j	j	NOUN
ejpam-676	467	27	=	=	SYM
ejpam-676	467	28	1	1	NUM
ejpam-676	467	29	(	(	PUNCT
ejpam-676	467	30	j	j	NOUN
ejpam-676	467	31	=	=	SYM
ejpam-676	467	32	2,3	2,3	NUM
ejpam-676	467	33	,	,	PUNCT
ejpam-676	467	34	.	.	PUNCT
ejpam-676	467	35	.	.	PUNCT
ejpam-676	467	36	.	.	PUNCT
ejpam-676	468	1	,	,	PUNCT
ejpam-676	468	2	s+	s+	X
ejpam-676	468	3	1	1	NUM
ejpam-676	468	4	)	)	PUNCT
ejpam-676	468	5	,	,	PUNCT
ejpam-676	468	6	β	β	X
ejpam-676	468	7	j	j	X
ejpam-676	468	8	=	=	SYM
ejpam-676	468	9	1	1	NUM
ejpam-676	468	10	(	(	PUNCT
ejpam-676	468	11	j	j	PROPN
ejpam-676	468	12	=	=	SYM
ejpam-676	468	13	2,2	2,2	PROPN
ejpam-676	468	14	,	,	PUNCT
ejpam-676	468	15	.	.	PUNCT
ejpam-676	468	16	.	.	PUNCT
ejpam-676	469	1	.	.	PUNCT
ejpam-676	470	1	,	,	PUNCT
ejpam-676	470	2	s	s	X
ejpam-676	470	3	)	)	PUNCT
ejpam-676	470	4	and	and	CCONJ
ejpam-676	470	5	d	d	NOUN
ejpam-676	470	6	=	=	SYM
ejpam-676	470	7	1	1	NUM
ejpam-676	470	8	in	in	ADP
ejpam-676	470	9	theorem	theorem	NOUN
ejpam-676	470	10	6	6	NUM
ejpam-676	470	11	,	,	PUNCT
ejpam-676	470	12	we	we	PRON
ejpam-676	470	13	obtain	obtain	VERB
ejpam-676	470	14	the	the	DET
ejpam-676	470	15	following	following	ADJ
ejpam-676	470	16	result	result	NOUN
ejpam-676	470	17	which	which	PRON
ejpam-676	470	18	refines	refine	VERB
ejpam-676	470	19	the	the	DET
ejpam-676	470	20	work	work	NOUN
ejpam-676	470	21	of	of	ADP
ejpam-676	470	22	srivastava	srivastava	PROPN
ejpam-676	470	23	and	and	CCONJ
ejpam-676	470	24	patel	patel	PROPN
ejpam-676	471	1	[	[	X
ejpam-676	471	2	15	15	NUM
ejpam-676	471	3	,	,	PUNCT
ejpam-676	471	4	corollary	corollary	ADJ
ejpam-676	471	5	7	7	NUM
ejpam-676	471	6	]	]	PUNCT
ejpam-676	471	7	.	.	PUNCT
ejpam-676	472	1	corollary	corollary	ADJ
ejpam-676	472	2	10	10	NUM
ejpam-676	472	3	.	.	PUNCT
ejpam-676	473	1	if	if	SCONJ
ejpam-676	473	2	f	f	PROPN
ejpam-676	473	3	∈	∈	PROPN
ejpam-676	473	4	σp	σp	PROPN
ejpam-676	473	5	,	,	PUNCT
ejpam-676	473	6	m	m	VERB
ejpam-676	473	7	satisfies	satisfy	VERB
ejpam-676	473	8	the	the	DET
ejpam-676	473	9	following	follow	VERB
ejpam-676	473	10	inequality	inequality	NOUN
ejpam-676	473	11	:	:	PUNCT
ejpam-676	473	12	re	re	VERB
ejpam-676	473	13	�	�	PROPN
ejpam-676	473	14	(	(	PUNCT
ejpam-676	473	15	1+λ)zp	1+λ)zp	PROPN
ejpam-676	473	16	f	f	X
ejpam-676	473	17	(	(	PUNCT
ejpam-676	473	18	z	z	NOUN
ejpam-676	473	19	)	)	PUNCT
ejpam-676	474	1	+	+	CCONJ
ejpam-676	474	2	λ	λ	X
ejpam-676	474	3	p	p	NOUN
ejpam-676	474	4	zp+1	zp+1	NUM
ejpam-676	474	5	f	f	NOUN
ejpam-676	474	6	′	′	NUM
ejpam-676	474	7	(	(	PUNCT
ejpam-676	474	8	z	z	NOUN
ejpam-676	474	9	)	)	PUNCT
ejpam-676	474	10	�	�	PROPN
ejpam-676	474	11	>	>	X
ejpam-676	474	12	3−	3−	NUM
ejpam-676	474	13	2	2	NUM
ejpam-676	474	14	2f1(1,1	2f1(1,1	NUM
ejpam-676	474	15	;	;	PUNCT
ejpam-676	474	16	p	p	X
ejpam-676	474	17	λ(p+m	λ(p+m	NOUN
ejpam-676	474	18	)	)	PUNCT
ejpam-676	475	1	+	+	CCONJ
ejpam-676	475	2	1	1	NUM
ejpam-676	475	3	;	;	PUNCT
ejpam-676	475	4	1	1	NUM
ejpam-676	475	5	2	2	NUM
ejpam-676	475	6	)	)	PUNCT
ejpam-676	475	7	2	2	NUM
ejpam-676	475	8	h	h	NOUN
ejpam-676	475	9	2−	2−	NUM
ejpam-676	475	10	2f1(1,1	2f1(1,1	NUM
ejpam-676	475	11	;	;	PUNCT
ejpam-676	475	12	p	p	X
ejpam-676	475	13	λ(p+m	λ(p+m	NOUN
ejpam-676	475	14	)	)	PUNCT
ejpam-676	475	15	+	+	CCONJ
ejpam-676	475	16	1	1	NUM
ejpam-676	475	17	;	;	PUNCT
ejpam-676	475	18	1	1	NUM
ejpam-676	475	19	2	2	NUM
ejpam-676	475	20	)	)	PUNCT
ejpam-676	476	1	i	i	PRON
ejpam-676	476	2	(	(	PUNCT
ejpam-676	476	3	z	z	NOUN
ejpam-676	476	4	∈	∈	PROPN
ejpam-676	476	5	u	u	NOUN
ejpam-676	476	6	)	)	PUNCT
ejpam-676	476	7	,	,	PUNCT
ejpam-676	476	8	(	(	PUNCT
ejpam-676	476	9	48	48	NUM
ejpam-676	476	10	)	)	PUNCT
ejpam-676	476	11	then	then	ADV
ejpam-676	476	12	re	re	VERB
ejpam-676	476	13	�	�	PROPN
ejpam-676	476	14	zp	zp	PROPN
ejpam-676	476	15	f	f	PROPN
ejpam-676	476	16	(	(	PUNCT
ejpam-676	476	17	z	z	NOUN
ejpam-676	476	18	)	)	PUNCT
ejpam-676	476	19	>	>	X
ejpam-676	476	20	1	1	NUM
ejpam-676	476	21	2	2	NUM
ejpam-676	476	22	(	(	PUNCT
ejpam-676	476	23	z	z	NOUN
ejpam-676	476	24	∈	∈	PROPN
ejpam-676	476	25	u	u	NOUN
ejpam-676	476	26	)	)	PUNCT
ejpam-676	476	27	.	.	PUNCT
ejpam-676	477	1	the	the	DET
ejpam-676	477	2	result	result	NOUN
ejpam-676	477	3	is	be	AUX
ejpam-676	477	4	the	the	DET
ejpam-676	477	5	best	good	ADJ
ejpam-676	477	6	possible	possible	ADJ
ejpam-676	477	7	.	.	PUNCT
ejpam-676	478	1	from	from	ADP
ejpam-676	478	2	corollary	corollary	ADJ
ejpam-676	478	3	7	7	NUM
ejpam-676	478	4	and	and	CCONJ
ejpam-676	478	5	theorem	theorem	VERB
ejpam-676	478	6	6	6	NUM
ejpam-676	478	7	(	(	PUNCT
ejpam-676	478	8	for	for	ADP
ejpam-676	478	9	m=	m=	X
ejpam-676	478	10	−p+	−p+	PROPN
ejpam-676	478	11	1	1	NUM
ejpam-676	478	12	,	,	PUNCT
ejpam-676	478	13	a=	a=	PROPN
ejpam-676	478	14	1−	1−	NUM
ejpam-676	478	15	2η0	2η0	NUM
ejpam-676	478	16	,	,	PUNCT
ejpam-676	478	17	b	b	X
ejpam-676	478	18	=	=	SYM
ejpam-676	478	19	−1	−1	NOUN
ejpam-676	478	20	,	,	PUNCT
ejpam-676	478	21	d	d	NOUN
ejpam-676	478	22	=	=	SYM
ejpam-676	478	23	1	1	NUM
ejpam-676	478	24	,	,	PUNCT
ejpam-676	478	25	q	q	NOUN
ejpam-676	478	26	=	=	PUNCT
ejpam-676	478	27	s+	s+	NUM
ejpam-676	478	28	1	1	NUM
ejpam-676	478	29	,	,	PUNCT
ejpam-676	478	30	α1	α1	PROPN
ejpam-676	478	31	=	=	SYM
ejpam-676	478	32	β1	β1	PROPN
ejpam-676	478	33	=	=	PUNCT
ejpam-676	478	34	p	p	PROPN
ejpam-676	478	35	,	,	PUNCT
ejpam-676	478	36	α	α	PROPN
ejpam-676	478	37	j	j	NOUN
ejpam-676	478	38	=	=	SYM
ejpam-676	478	39	1	1	NUM
ejpam-676	478	40	(	(	PUNCT
ejpam-676	478	41	j	j	NOUN
ejpam-676	478	42	=	=	SYM
ejpam-676	478	43	2,3	2,3	NUM
ejpam-676	478	44	,	,	PUNCT
ejpam-676	478	45	.	.	PUNCT
ejpam-676	478	46	.	.	PUNCT
ejpam-676	478	47	.	.	PUNCT
ejpam-676	479	1	,	,	PUNCT
ejpam-676	479	2	s+	s+	X
ejpam-676	479	3	1	1	X
ejpam-676	479	4	)	)	PUNCT
ejpam-676	479	5	and	and	CCONJ
ejpam-676	479	6	β	β	X
ejpam-676	479	7	j	j	X
ejpam-676	479	8	=	=	SYM
ejpam-676	479	9	1	1	NUM
ejpam-676	479	10	(	(	PUNCT
ejpam-676	479	11	j	j	NOUN
ejpam-676	479	12	=	=	SYM
ejpam-676	479	13	2,3	2,3	NUM
ejpam-676	479	14	,	,	PUNCT
ejpam-676	479	15	.	.	PUNCT
ejpam-676	479	16	.	.	PUNCT
ejpam-676	480	1	.	.	PUNCT
ejpam-676	481	1	,	,	PUNCT
ejpam-676	481	2	s	s	X
ejpam-676	481	3	)	)	PUNCT
ejpam-676	481	4	)	)	PUNCT
ejpam-676	481	5	,	,	PUNCT
ejpam-676	481	6	we	we	PRON
ejpam-676	481	7	deduce	deduce	VERB
ejpam-676	481	8	the	the	DET
ejpam-676	481	9	following	follow	VERB
ejpam-676	481	10	result	result	NOUN
ejpam-676	481	11	.	.	PUNCT
ejpam-676	482	1	corollary	corollary	ADJ
ejpam-676	482	2	11	11	NUM
ejpam-676	482	3	.	.	PUNCT
ejpam-676	483	1	if	if	SCONJ
ejpam-676	483	2	the	the	DET
ejpam-676	483	3	functions	function	NOUN
ejpam-676	483	4	f	f	PROPN
ejpam-676	483	5	j	j	PROPN
ejpam-676	483	6	∈	∈	PROPN
ejpam-676	483	7	σp	σp	PROPN
ejpam-676	483	8	(	(	PUNCT
ejpam-676	483	9	j	j	PROPN
ejpam-676	483	10	=	=	SYM
ejpam-676	483	11	1,2	1,2	NUM
ejpam-676	483	12	)	)	PUNCT
ejpam-676	483	13	satisfy	satisfy	VERB
ejpam-676	483	14	the	the	DET
ejpam-676	483	15	inequality	inequality	NOUN
ejpam-676	483	16	(	(	PUNCT
ejpam-676	483	17	45	45	NUM
ejpam-676	483	18	)	)	PUNCT
ejpam-676	483	19	,	,	PUNCT
ejpam-676	483	20	then	then	ADV
ejpam-676	483	21	re	re	VERB
ejpam-676	483	22	�	�	PROPN
ejpam-676	483	23	zp	zp	PROPN
ejpam-676	483	24	(	(	PUNCT
ejpam-676	483	25	f1	f1	PROPN
ejpam-676	483	26	∗	∗	NOUN
ejpam-676	483	27	f2)(z	f2)(z	NOUN
ejpam-676	483	28	)	)	PUNCT
ejpam-676	483	29	�	�	PROPN
ejpam-676	483	30	>	>	X
ejpam-676	483	31	ρ0	ρ0	PROPN
ejpam-676	484	1	+	+	CCONJ
ejpam-676	484	2	(	(	PUNCT
ejpam-676	484	3	1−ρ0	1−ρ0	NUM
ejpam-676	484	4	)	)	PUNCT
ejpam-676	484	5	�	�	PROPN
ejpam-676	484	6	2f1	2f1	NUM
ejpam-676	484	7	�	�	PROPN
ejpam-676	484	8	1,1	1,1	NUM
ejpam-676	484	9	;	;	PUNCT
ejpam-676	484	10	p	p	PROPN
ejpam-676	484	11	λ	λ	X
ejpam-676	484	12	+	+	PROPN
ejpam-676	484	13	1	1	NUM
ejpam-676	484	14	;	;	PUNCT
ejpam-676	484	15	1	1	NUM
ejpam-676	484	16	2	2	NUM
ejpam-676	484	17	�	�	NOUN
ejpam-676	484	18	−	−	PROPN
ejpam-676	484	19	1	1	NUM
ejpam-676	484	20	�	�	PROPN
ejpam-676	484	21	(	(	PUNCT
ejpam-676	484	22	z	z	NOUN
ejpam-676	484	23	∈	∈	PROPN
ejpam-676	484	24	u	u	NOUN
ejpam-676	484	25	)	)	PUNCT
ejpam-676	484	26	,	,	PUNCT
ejpam-676	484	27	where	where	SCONJ
ejpam-676	484	28	ρ0	ρ0	PROPN
ejpam-676	484	29	is	be	AUX
ejpam-676	484	30	given	give	VERB
ejpam-676	484	31	as	as	ADP
ejpam-676	484	32	in	in	ADP
ejpam-676	484	33	corollary	corollary	ADJ
ejpam-676	484	34	7	7	NUM
ejpam-676	484	35	.	.	PUNCT
ejpam-676	485	1	the	the	DET
ejpam-676	485	2	result	result	NOUN
ejpam-676	485	3	is	be	AUX
ejpam-676	485	4	the	the	DET
ejpam-676	485	5	best	well	ADV
ejpam-676	485	6	possible	possible	ADJ
ejpam-676	485	7	.	.	PUNCT
ejpam-676	486	1	theorem	theorem	ADJ
ejpam-676	486	2	7	7	NUM
ejpam-676	486	3	.	.	PUNCT
ejpam-676	487	1	let	let	VERB
ejpam-676	487	2	f	f	PRON
ejpam-676	487	3	∈	∈	PROPN
ejpam-676	487	4	σm	σm	ADP
ejpam-676	488	1	p	p	X
ejpam-676	488	2	,	,	PUNCT
ejpam-676	488	3	q	q	ADJ
ejpam-676	488	4	,	,	PUNCT
ejpam-676	488	5	s(α1	s(α1	NOUN
ejpam-676	488	6	;	;	PUNCT
ejpam-676	488	7	a	a	DET
ejpam-676	488	8	,	,	PUNCT
ejpam-676	488	9	b	b	NOUN
ejpam-676	488	10	)	)	PUNCT
ejpam-676	489	1	and	and	CCONJ
ejpam-676	489	2	let	let	VERB
ejpam-676	489	3	g	g	PROPN
ejpam-676	489	4	∈	∈	PROPN
ejpam-676	489	5	σp	σp	PROPN
ejpam-676	489	6	,	,	PUNCT
ejpam-676	489	7	m	m	VERB
ejpam-676	489	8	satisfy	satisfy	VERB
ejpam-676	489	9	the	the	DET
ejpam-676	489	10	following	follow	VERB
ejpam-676	489	11	inequality	inequality	NOUN
ejpam-676	489	12	:	:	PUNCT
ejpam-676	489	13	re	re	VERB
ejpam-676	489	14	�	�	PROPN
ejpam-676	489	15	zp	zp	PROPN
ejpam-676	489	16	g(z	g(z	PROPN
ejpam-676	489	17	)	)	PUNCT
ejpam-676	489	18	>	>	SYM
ejpam-676	490	1	1	1	NUM
ejpam-676	490	2	2	2	NUM
ejpam-676	490	3	(	(	PUNCT
ejpam-676	490	4	z	z	NOUN
ejpam-676	490	5	∈	∈	PROPN
ejpam-676	490	6	u	u	NOUN
ejpam-676	490	7	)	)	PUNCT
ejpam-676	490	8	.	.	PUNCT
ejpam-676	491	1	then	then	ADV
ejpam-676	491	2	(	(	PUNCT
ejpam-676	491	3	f	f	PROPN
ejpam-676	491	4	∗	∗	X
ejpam-676	491	5	g	g	NOUN
ejpam-676	491	6	)	)	PUNCT
ejpam-676	491	7	∈	∈	NOUN
ejpam-676	491	8	σm	σm	X
ejpam-676	492	1	p	p	X
ejpam-676	492	2	,	,	PUNCT
ejpam-676	492	3	q	q	ADJ
ejpam-676	492	4	,	,	PUNCT
ejpam-676	492	5	s(α1	s(α1	NOUN
ejpam-676	492	6	;	;	PUNCT
ejpam-676	492	7	a	a	DET
ejpam-676	492	8	,	,	PUNCT
ejpam-676	492	9	b	b	NOUN
ejpam-676	492	10	)	)	PUNCT
ejpam-676	492	11	.	.	PUNCT
ejpam-676	493	1	references	reference	NOUN
ejpam-676	493	2	158	158	NUM
ejpam-676	493	3	proof	proof	NOUN
ejpam-676	493	4	.	.	PUNCT
ejpam-676	494	1	we	we	PRON
ejpam-676	494	2	have	have	AUX
ejpam-676	494	3	−zp+1(hp	−zp+1(hp	VERB
ejpam-676	494	4	,	,	PUNCT
ejpam-676	494	5	q	q	NOUN
ejpam-676	494	6	,	,	PUNCT
ejpam-676	494	7	s(α1	s(α1	NOUN
ejpam-676	494	8	)	)	PUNCT
ejpam-676	494	9	(	(	PUNCT
ejpam-676	494	10	f	f	PROPN
ejpam-676	494	11	∗	∗	NOUN
ejpam-676	494	12	g)(z	g)(z	PUNCT
ejpam-676	494	13	)	)	PUNCT
ejpam-676	494	14	)	)	PUNCT
ejpam-676	495	1	′	′	NUM
ejpam-676	496	1	p	p	NOUN
ejpam-676	496	2	=	=	SYM
ejpam-676	496	3	−zp+1(hp	−zp+1(hp	PROPN
ejpam-676	496	4	,	,	PUNCT
ejpam-676	496	5	q	q	NOUN
ejpam-676	496	6	,	,	PUNCT
ejpam-676	496	7	s(α1	s(α1	NOUN
ejpam-676	496	8	)	)	PUNCT
ejpam-676	497	1	f	f	PROPN
ejpam-676	497	2	(	(	PUNCT
ejpam-676	497	3	z	z	NOUN
ejpam-676	497	4	)	)	PUNCT
ejpam-676	497	5	)	)	PUNCT
ejpam-676	498	1	′	′	NUM
ejpam-676	499	1	p	p	NOUN
ejpam-676	499	2	∗	∗	X
ejpam-676	499	3	zp	zp	X
ejpam-676	499	4	g(z	g(z	PROPN
ejpam-676	499	5	)	)	PUNCT
ejpam-676	499	6	(	(	PUNCT
ejpam-676	499	7	z	z	NOUN
ejpam-676	499	8	∈	∈	PROPN
ejpam-676	499	9	u	u	NOUN
ejpam-676	499	10	)	)	PUNCT
ejpam-676	499	11	.	.	PUNCT
ejpam-676	500	1	since	since	SCONJ
ejpam-676	500	2	re	re	VERB
ejpam-676	500	3	�	�	PROPN
ejpam-676	500	4	zp	zp	PROPN
ejpam-676	500	5	g(z	g(z	PROPN
ejpam-676	500	6	)	)	PUNCT
ejpam-676	500	7	>	>	SYM
ejpam-676	500	8	1	1	NUM
ejpam-676	500	9	2	2	NUM
ejpam-676	500	10	(	(	PUNCT
ejpam-676	500	11	z	z	NOUN
ejpam-676	500	12	∈	∈	PROPN
ejpam-676	500	13	u	u	NOUN
ejpam-676	500	14	)	)	PUNCT
ejpam-676	500	15	and	and	CCONJ
ejpam-676	500	16	the	the	DET
ejpam-676	500	17	function	function	NOUN
ejpam-676	500	18	1	1	NUM
ejpam-676	500	19	+	+	NUM
ejpam-676	500	20	az	az	PROPN
ejpam-676	500	21	1	1	NUM
ejpam-676	500	22	+	+	CCONJ
ejpam-676	500	23	bz	bz	PROPN
ejpam-676	500	24	is	be	AUX
ejpam-676	500	25	convex	convex	ADJ
ejpam-676	500	26	(	(	PUNCT
ejpam-676	500	27	univalent	univalent	ADJ
ejpam-676	500	28	)	)	PUNCT
ejpam-676	500	29	in	in	ADP
ejpam-676	500	30	u	u	NOUN
ejpam-676	500	31	,	,	PUNCT
ejpam-676	500	32	it	it	PRON
ejpam-676	500	33	follows	follow	VERB
ejpam-676	500	34	from	from	ADP
ejpam-676	500	35	(	(	PUNCT
ejpam-676	500	36	11	11	NUM
ejpam-676	500	37	)	)	PUNCT
ejpam-676	500	38	and	and	CCONJ
ejpam-676	500	39	lemma	lemma	PROPN
ejpam-676	500	40	5	5	NUM
ejpam-676	501	1	that	that	PRON
ejpam-676	501	2	(	(	PUNCT
ejpam-676	501	3	f	f	PROPN
ejpam-676	501	4	∗	∗	PROPN
ejpam-676	501	5	g)(z	g)(z	PUNCT
ejpam-676	501	6	)	)	PUNCT
ejpam-676	501	7	∈	∈	NOUN
ejpam-676	501	8	σm	σm	X
ejpam-676	502	1	p	p	X
ejpam-676	502	2	,	,	PUNCT
ejpam-676	502	3	q	q	ADJ
ejpam-676	502	4	,	,	PUNCT
ejpam-676	502	5	s(α1	s(α1	NOUN
ejpam-676	502	6	;	;	PUNCT
ejpam-676	502	7	a	a	DET
ejpam-676	502	8	,	,	PUNCT
ejpam-676	502	9	b	b	NOUN
ejpam-676	502	10	)	)	PUNCT
ejpam-676	502	11	.	.	PUNCT
ejpam-676	503	1	this	this	PRON
ejpam-676	503	2	completes	complete	VERB
ejpam-676	503	3	the	the	DET
ejpam-676	503	4	proof	proof	NOUN
ejpam-676	503	5	of	of	ADP
ejpam-676	503	6	theorem	theorem	NOUN
ejpam-676	503	7	7	7	NUM
ejpam-676	503	8	.	.	PUNCT
ejpam-676	504	1	in	in	ADP
ejpam-676	504	2	view	view	NOUN
ejpam-676	504	3	of	of	ADP
ejpam-676	504	4	corollary	corollary	ADJ
ejpam-676	504	5	10	10	NUM
ejpam-676	504	6	and	and	CCONJ
ejpam-676	504	7	theorem	theorem	VERB
ejpam-676	504	8	7	7	NUM
ejpam-676	504	9	,	,	PUNCT
ejpam-676	504	10	we	we	PRON
ejpam-676	504	11	have	have	VERB
ejpam-676	504	12	corollary	corollary	ADJ
ejpam-676	504	13	11	11	NUM
ejpam-676	504	14	below	below	ADV
ejpam-676	504	15	.	.	PUNCT
ejpam-676	505	1	corollary	corollary	ADJ
ejpam-676	505	2	12	12	NUM
ejpam-676	505	3	.	.	PUNCT
ejpam-676	506	1	if	if	SCONJ
ejpam-676	506	2	f	f	PROPN
ejpam-676	506	3	∈	∈	PROPN
ejpam-676	506	4	σm	σm	X
ejpam-676	507	1	p	p	X
ejpam-676	507	2	,	,	PUNCT
ejpam-676	507	3	q	q	ADJ
ejpam-676	507	4	,	,	PUNCT
ejpam-676	507	5	s(α1	s(α1	NOUN
ejpam-676	507	6	;	;	PUNCT
ejpam-676	507	7	a	a	DET
ejpam-676	507	8	,	,	PUNCT
ejpam-676	507	9	b	b	NOUN
ejpam-676	507	10	)	)	PUNCT
ejpam-676	507	11	and	and	CCONJ
ejpam-676	507	12	the	the	DET
ejpam-676	507	13	function	function	NOUN
ejpam-676	507	14	g	g	PROPN
ejpam-676	507	15	∈	∈	PROPN
ejpam-676	507	16	σp	σp	PROPN
ejpam-676	507	17	,	,	PUNCT
ejpam-676	507	18	m	m	VERB
ejpam-676	507	19	satisfies	satisfy	VERB
ejpam-676	507	20	the	the	DET
ejpam-676	507	21	inequality	inequality	NOUN
ejpam-676	507	22	(	(	PUNCT
ejpam-676	507	23	48	48	NUM
ejpam-676	507	24	)	)	PUNCT
ejpam-676	507	25	,	,	PUNCT
ejpam-676	507	26	then	then	ADV
ejpam-676	507	27	(	(	PUNCT
ejpam-676	507	28	f	f	PROPN
ejpam-676	507	29	∗	∗	X
ejpam-676	507	30	g	g	NOUN
ejpam-676	507	31	)	)	PUNCT
ejpam-676	507	32	∈	∈	NOUN
ejpam-676	507	33	σm	σm	X
ejpam-676	508	1	p	p	X
ejpam-676	508	2	,	,	PUNCT
ejpam-676	508	3	q	q	ADJ
ejpam-676	508	4	,	,	PUNCT
ejpam-676	508	5	s(α1	s(α1	NOUN
ejpam-676	508	6	;	;	PUNCT
ejpam-676	508	7	a	a	DET
ejpam-676	508	8	,	,	PUNCT
ejpam-676	508	9	b	b	NOUN
ejpam-676	508	10	)	)	PUNCT
ejpam-676	508	11	.	.	PUNCT
ejpam-676	509	1	acknowledgements	acknowledgement	VERB
ejpam-676	509	2	the	the	DET
ejpam-676	509	3	author	author	NOUN
ejpam-676	509	4	is	be	AUX
ejpam-676	509	5	thankful	thankful	ADJ
ejpam-676	509	6	to	to	ADP
ejpam-676	509	7	the	the	DET
ejpam-676	509	8	referee	referee	NOUN
ejpam-676	509	9	for	for	ADP
ejpam-676	509	10	his	his	PRON
ejpam-676	509	11	comments	comment	NOUN
ejpam-676	509	12	and	and	CCONJ
ejpam-676	509	13	suggestions	suggestion	NOUN
ejpam-676	509	14	.	.	PUNCT
ejpam-676	510	1	references	reference	NOUN
ejpam-676	510	2	[	[	X
ejpam-676	510	3	1	1	NUM
ejpam-676	510	4	]	]	PUNCT
ejpam-676	510	5	m	m	VERB
ejpam-676	510	6	aouf	aouf	NOUN
ejpam-676	510	7	,	,	PUNCT
ejpam-676	510	8	certain	certain	ADJ
ejpam-676	510	9	subclasses	subclass	NOUN
ejpam-676	510	10	of	of	ADP
ejpam-676	510	11	meromorphically	meromorphically	ADV
ejpam-676	510	12	multivalent	multivalent	NOUN
ejpam-676	510	13	functions	function	NOUN
ejpam-676	510	14	associated	associate	VERB
ejpam-676	510	15	with	with	ADP
ejpam-676	510	16	generalized	generalized	ADJ
ejpam-676	510	17	hypergeometric	hypergeometric	ADJ
ejpam-676	510	18	function	function	NOUN
ejpam-676	510	19	,	,	PUNCT
ejpam-676	510	20	comput	comput	NOUN
ejpam-676	510	21	.	.	PUNCT
ejpam-676	511	1	math	math	NOUN
ejpam-676	511	2	.	.	PUNCT
ejpam-676	512	1	appl	appl	PROPN
ejpam-676	512	2	.	.	PUNCT
ejpam-676	513	1	55	55	NUM
ejpam-676	513	2	,	,	PUNCT
ejpam-676	513	3	no	no	INTJ
ejpam-676	513	4	.	.	NOUN
ejpam-676	513	5	3	3	NUM
ejpam-676	513	6	,	,	PUNCT
ejpam-676	513	7	494	494	NUM
ejpam-676	513	8	-	-	SYM
ejpam-676	513	9	509	509	NUM
ejpam-676	513	10	.	.	PUNCT
ejpam-676	513	11	2008	2008	NUM
ejpam-676	513	12	.	.	PUNCT
ejpam-676	514	1	[	[	X
ejpam-676	514	2	2	2	NUM
ejpam-676	514	3	]	]	PUNCT
ejpam-676	514	4	n	n	CCONJ
ejpam-676	514	5	cho	cho	NOUN
ejpam-676	514	6	and	and	CCONJ
ejpam-676	514	7	m	m	PROPN
ejpam-676	514	8	nunokawa	nunokawa	NOUN
ejpam-676	514	9	,	,	PUNCT
ejpam-676	514	10	on	on	ADP
ejpam-676	514	11	certain	certain	ADJ
ejpam-676	514	12	subclasses	subclass	NOUN
ejpam-676	514	13	of	of	ADP
ejpam-676	514	14	meromorphically	meromorphically	ADV
ejpam-676	514	15	multivalent	multivalent	NOUN
ejpam-676	514	16	functions	function	NOUN
ejpam-676	514	17	,	,	PUNCT
ejpam-676	514	18	chinese	chinese	PROPN
ejpam-676	514	19	j.	j.	PROPN
ejpam-676	514	20	math	math	PROPN
ejpam-676	514	21	.	.	PUNCT
ejpam-676	515	1	22	22	NUM
ejpam-676	515	2	,	,	PUNCT
ejpam-676	515	3	197	197	NUM
ejpam-676	515	4	-	-	SYM
ejpam-676	515	5	202	202	NUM
ejpam-676	515	6	.	.	NUM
ejpam-676	515	7	1994	1994	NUM
ejpam-676	515	8	.	.	PUNCT
ejpam-676	516	1	[	[	X
ejpam-676	516	2	3	3	NUM
ejpam-676	516	3	]	]	X
ejpam-676	516	4	d	d	X
ejpam-676	516	5	hallenbeck	hallenbeck	NOUN
ejpam-676	516	6	and	and	CCONJ
ejpam-676	516	7	st	st	PROPN
ejpam-676	516	8	ruscheweyh	ruscheweyh	PROPN
ejpam-676	516	9	,	,	PUNCT
ejpam-676	516	10	subordination	subordination	NOUN
ejpam-676	516	11	by	by	ADP
ejpam-676	516	12	convex	convex	NOUN
ejpam-676	516	13	functions	function	NOUN
ejpam-676	516	14	,	,	PUNCT
ejpam-676	516	15	proc	proc	NOUN
ejpam-676	516	16	.	.	PUNCT
ejpam-676	517	1	amer	amer	PROPN
ejpam-676	517	2	.	.	PUNCT
ejpam-676	517	3	math	math	PROPN
ejpam-676	517	4	.	.	PUNCT
ejpam-676	518	1	soc	soc	PROPN
ejpam-676	518	2	.	.	PUNCT
ejpam-676	519	1	52	52	NUM
ejpam-676	519	2	,	,	PUNCT
ejpam-676	519	3	191	191	NUM
ejpam-676	519	4	-	-	SYM
ejpam-676	519	5	195	195	NUM
ejpam-676	519	6	.	.	NOUN
ejpam-676	519	7	1975	1975	NUM
ejpam-676	519	8	.	.	PUNCT
ejpam-676	520	1	[	[	X
ejpam-676	520	2	4	4	X
ejpam-676	520	3	]	]	X
ejpam-676	520	4	j	j	PROPN
ejpam-676	520	5	liu	liu	PROPN
ejpam-676	520	6	and	and	CCONJ
ejpam-676	520	7	h	h	PROPN
ejpam-676	520	8	srivastava	srivastava	PROPN
ejpam-676	520	9	,	,	PUNCT
ejpam-676	520	10	a	a	DET
ejpam-676	520	11	linear	linear	ADJ
ejpam-676	520	12	operator	operator	NOUN
ejpam-676	520	13	and	and	CCONJ
ejpam-676	520	14	associated	associated	ADJ
ejpam-676	520	15	families	family	NOUN
ejpam-676	520	16	of	of	ADP
ejpam-676	520	17	meromorphically	meromorphically	ADV
ejpam-676	520	18	multivalent	multivalent	NOUN
ejpam-676	520	19	functions	function	NOUN
ejpam-676	520	20	,	,	PUNCT
ejpam-676	520	21	j.	j.	PROPN
ejpam-676	520	22	math	math	PROPN
ejpam-676	520	23	.	.	PUNCT
ejpam-676	521	1	anal	anal	PROPN
ejpam-676	521	2	.	.	PUNCT
ejpam-676	521	3	appl	appl	PROPN
ejpam-676	521	4	.	.	PUNCT
ejpam-676	522	1	259	259	NUM
ejpam-676	522	2	,	,	PUNCT
ejpam-676	522	3	566	566	NUM
ejpam-676	522	4	-	-	SYM
ejpam-676	522	5	581	581	NUM
ejpam-676	522	6	.	.	NUM
ejpam-676	522	7	2000	2000	NUM
ejpam-676	522	8	.	.	PUNCT
ejpam-676	523	1	[	[	X
ejpam-676	523	2	5	5	X
ejpam-676	523	3	]	]	X
ejpam-676	523	4	j	j	PROPN
ejpam-676	523	5	liu	liu	PROPN
ejpam-676	523	6	and	and	CCONJ
ejpam-676	523	7	h	h	PROPN
ejpam-676	523	8	srivastava	srivastava	PROPN
ejpam-676	523	9	,	,	PUNCT
ejpam-676	523	10	classes	class	NOUN
ejpam-676	523	11	of	of	ADP
ejpam-676	523	12	meromorphically	meromorphically	ADV
ejpam-676	523	13	multivalent	multivalent	NOUN
ejpam-676	523	14	functions	function	NOUN
ejpam-676	523	15	associated	associate	VERB
ejpam-676	523	16	with	with	ADP
ejpam-676	523	17	the	the	DET
ejpam-676	523	18	generalized	generalize	VERB
ejpam-676	523	19	hypergeometric	hypergeometric	ADJ
ejpam-676	523	20	function	function	NOUN
ejpam-676	523	21	,	,	PUNCT
ejpam-676	523	22	math	math	NOUN
ejpam-676	523	23	.	.	PUNCT
ejpam-676	524	1	comput	comput	NOUN
ejpam-676	524	2	.	.	PUNCT
ejpam-676	525	1	modelling	model	VERB
ejpam-676	525	2	39	39	NUM
ejpam-676	525	3	,	,	PUNCT
ejpam-676	525	4	21	21	NUM
ejpam-676	525	5	-	-	SYM
ejpam-676	525	6	34	34	NUM
ejpam-676	525	7	.	.	PUNCT
ejpam-676	525	8	2004	2004	NUM
ejpam-676	525	9	.	.	PUNCT
ejpam-676	526	1	[	[	X
ejpam-676	526	2	6	6	NUM
ejpam-676	526	3	]	]	PUNCT
ejpam-676	526	4	t	t	NOUN
ejpam-676	526	5	magregor	magregor	NOUN
ejpam-676	526	6	,	,	PUNCT
ejpam-676	526	7	radius	radius	NOUN
ejpam-676	526	8	of	of	ADP
ejpam-676	526	9	univalence	univalence	NOUN
ejpam-676	526	10	of	of	ADP
ejpam-676	526	11	certain	certain	ADJ
ejpam-676	526	12	analytic	analytic	ADJ
ejpam-676	526	13	functions	function	NOUN
ejpam-676	526	14	,	,	PUNCT
ejpam-676	526	15	proc	proc	NOUN
ejpam-676	526	16	.	.	PUNCT
ejpam-676	527	1	amer	amer	PROPN
ejpam-676	527	2	.	.	PUNCT
ejpam-676	527	3	math	math	PROPN
ejpam-676	527	4	.	.	PUNCT
ejpam-676	528	1	soc	soc	PROPN
ejpam-676	528	2	.	.	PUNCT
ejpam-676	529	1	14	14	NUM
ejpam-676	529	2	,	,	PUNCT
ejpam-676	529	3	514	514	NUM
ejpam-676	529	4	-	-	SYM
ejpam-676	529	5	520	520	NUM
ejpam-676	529	6	.	.	NUM
ejpam-676	530	1	1963	1963	NUM
ejpam-676	530	2	.	.	PUNCT
ejpam-676	531	1	[	[	X
ejpam-676	531	2	7	7	NUM
ejpam-676	531	3	]	]	X
ejpam-676	531	4	s	s	X
ejpam-676	531	5	miller	miller	NOUN
ejpam-676	531	6	and	and	CCONJ
ejpam-676	531	7	p	p	NOUN
ejpam-676	531	8	mocanu	mocanu	NOUN
ejpam-676	531	9	,	,	PUNCT
ejpam-676	531	10	differential	differential	ADJ
ejpam-676	531	11	subordinations	subordination	NOUN
ejpam-676	531	12	and	and	CCONJ
ejpam-676	531	13	univalent	univalent	ADJ
ejpam-676	531	14	functions	function	NOUN
ejpam-676	531	15	,	,	PUNCT
ejpam-676	531	16	michigan	michigan	PROPN
ejpam-676	531	17	math	math	PROPN
ejpam-676	531	18	.	.	PUNCT
ejpam-676	532	1	j.	j.	PROPN
ejpam-676	532	2	28	28	PROPN
ejpam-676	532	3	,	,	PUNCT
ejpam-676	532	4	157	157	NUM
ejpam-676	532	5	-	-	SYM
ejpam-676	532	6	171	171	NUM
ejpam-676	532	7	.	.	PUNCT
ejpam-676	532	8	1981	1981	NUM
ejpam-676	532	9	.	.	PUNCT
ejpam-676	533	1	references	reference	NOUN
ejpam-676	533	2	159	159	NUM
ejpam-676	533	3	[	[	SYM
ejpam-676	533	4	8	8	NUM
ejpam-676	533	5	]	]	SYM
ejpam-676	533	6	s	s	X
ejpam-676	533	7	miller	miller	NOUN
ejpam-676	533	8	and	and	CCONJ
ejpam-676	533	9	p	p	NOUN
ejpam-676	533	10	mocanu	mocanu	NOUN
ejpam-676	533	11	,	,	PUNCT
ejpam-676	533	12	differential	differential	ADJ
ejpam-676	533	13	subordinations	subordination	NOUN
ejpam-676	533	14	:	:	PUNCT
ejpam-676	533	15	theory	theory	NOUN
ejpam-676	533	16	and	and	CCONJ
ejpam-676	533	17	applications	application	NOUN
ejpam-676	533	18	,	,	PUNCT
ejpam-676	533	19	series	series	NOUN
ejpam-676	533	20	on	on	ADP
ejpam-676	533	21	monographs	monograph	NOUN
ejpam-676	533	22	and	and	CCONJ
ejpam-676	533	23	texbooks	texbook	NOUN
ejpam-676	533	24	in	in	ADP
ejpam-676	533	25	pure	pure	ADJ
ejpam-676	533	26	and	and	CCONJ
ejpam-676	533	27	applied	applied	ADJ
ejpam-676	533	28	mathematics	mathematic	NOUN
ejpam-676	533	29	,	,	PUNCT
ejpam-676	533	30	vol	vol	NOUN
ejpam-676	533	31	.	.	PROPN
ejpam-676	533	32	225	225	NUM
ejpam-676	533	33	,	,	PUNCT
ejpam-676	533	34	marcel	marcel	PROPN
ejpam-676	533	35	dekker	dekker	PROPN
ejpam-676	533	36	,	,	PUNCT
ejpam-676	533	37	new	new	PROPN
ejpam-676	533	38	york	york	PROPN
ejpam-676	533	39	and	and	CCONJ
ejpam-676	533	40	basel	basel	PROPN
ejpam-676	533	41	,	,	PUNCT
ejpam-676	533	42	2000	2000	NUM
ejpam-676	533	43	.	.	PUNCT
ejpam-676	534	1	[	[	X
ejpam-676	534	2	9	9	NUM
ejpam-676	534	3	]	]	SYM
ejpam-676	534	4	z	z	NOUN
ejpam-676	534	5	nehari	nehari	NOUN
ejpam-676	534	6	,	,	PUNCT
ejpam-676	534	7	conformal	conformal	NOUN
ejpam-676	534	8	mapping	mapping	NOUN
ejpam-676	534	9	,	,	PUNCT
ejpam-676	534	10	mcgraw	mcgraw	PROPN
ejpam-676	534	11	-	-	PUNCT
ejpam-676	534	12	hill	hill	PROPN
ejpam-676	534	13	,	,	PUNCT
ejpam-676	534	14	new	new	PROPN
ejpam-676	534	15	york	york	PROPN
ejpam-676	534	16	,	,	PUNCT
ejpam-676	534	17	1952	1952	NUM
ejpam-676	534	18	.	.	PUNCT
ejpam-676	535	1	[	[	X
ejpam-676	535	2	10	10	NUM
ejpam-676	535	3	]	]	X
ejpam-676	535	4	d	d	X
ejpam-676	535	5	pashkouleva	pashkouleva	PROPN
ejpam-676	535	6	,	,	PUNCT
ejpam-676	535	7	the	the	DET
ejpam-676	535	8	starlikeness	starlikeness	ADJ
ejpam-676	535	9	and	and	CCONJ
ejpam-676	535	10	spiral	spiral	ADJ
ejpam-676	535	11	-	-	PUNCT
ejpam-676	535	12	convexity	convexity	NOUN
ejpam-676	535	13	of	of	ADP
ejpam-676	535	14	certain	certain	ADJ
ejpam-676	535	15	subclasses	subclass	NOUN
ejpam-676	535	16	of	of	ADP
ejpam-676	535	17	analytic	analytic	ADJ
ejpam-676	535	18	functions	function	NOUN
ejpam-676	535	19	,	,	PUNCT
ejpam-676	535	20	in	in	ADP
ejpam-676	535	21	:	:	PUNCT
ejpam-676	535	22	h.	h.	PROPN
ejpam-676	535	23	m.	m.	PROPN
ejpam-676	535	24	srivastava	srivastava	PROPN
ejpam-676	535	25	and	and	CCONJ
ejpam-676	535	26	s.	s.	PROPN
ejpam-676	535	27	owa	owa	PROPN
ejpam-676	535	28	(	(	PUNCT
ejpam-676	535	29	editors	editor	NOUN
ejpam-676	535	30	)	)	PUNCT
ejpam-676	535	31	,	,	PUNCT
ejpam-676	535	32	current	current	ADJ
ejpam-676	535	33	topics	topic	NOUN
ejpam-676	535	34	in	in	ADP
ejpam-676	535	35	analytic	analytic	ADJ
ejpam-676	535	36	function	function	NOUN
ejpam-676	535	37	theory	theory	NOUN
ejpam-676	535	38	,	,	PUNCT
ejpam-676	535	39	266	266	NUM
ejpam-676	535	40	-	-	SYM
ejpam-676	535	41	273	273	NUM
ejpam-676	535	42	,	,	PUNCT
ejpam-676	535	43	world	world	NOUN
ejpam-676	535	44	scientific	scientific	ADJ
ejpam-676	535	45	publishing	publishing	NOUN
ejpam-676	535	46	company	company	NOUN
ejpam-676	535	47	,	,	PUNCT
ejpam-676	535	48	singapore	singapore	PROPN
ejpam-676	535	49	,	,	PUNCT
ejpam-676	535	50	new	new	PROPN
ejpam-676	535	51	jersey	jersey	PROPN
ejpam-676	535	52	,	,	PUNCT
ejpam-676	535	53	london	london	PROPN
ejpam-676	535	54	and	and	CCONJ
ejpam-676	535	55	hong	hong	PROPN
ejpam-676	535	56	kong	kong	PROPN
ejpam-676	535	57	,	,	PUNCT
ejpam-676	535	58	1992	1992	NUM
ejpam-676	535	59	.	.	PUNCT
ejpam-676	536	1	[	[	X
ejpam-676	536	2	11	11	NUM
ejpam-676	536	3	]	]	X
ejpam-676	536	4	j	j	PROPN
ejpam-676	536	5	patel	patel	PROPN
ejpam-676	536	6	,	,	PUNCT
ejpam-676	536	7	radii	radius	NOUN
ejpam-676	536	8	of	of	ADP
ejpam-676	536	9	γ	γ	NOUN
ejpam-676	536	10	-	-	NOUN
ejpam-676	536	11	spirallikeness	spirallikeness	NOUN
ejpam-676	536	12	of	of	ADP
ejpam-676	536	13	certain	certain	ADJ
ejpam-676	536	14	analytic	analytic	ADJ
ejpam-676	536	15	functions	function	NOUN
ejpam-676	536	16	,	,	PUNCT
ejpam-676	536	17	j.	j.	PROPN
ejpam-676	536	18	math	math	PROPN
ejpam-676	536	19	.	.	PUNCT
ejpam-676	537	1	phys	phy	NOUN
ejpam-676	537	2	.	.	PUNCT
ejpam-676	538	1	sci	sci	PROPN
ejpam-676	538	2	.	.	PROPN
ejpam-676	538	3	27	27	NUM
ejpam-676	538	4	,	,	PUNCT
ejpam-676	538	5	321	321	NUM
ejpam-676	538	6	-	-	SYM
ejpam-676	538	7	334	334	NUM
ejpam-676	538	8	.	.	PUNCT
ejpam-676	538	9	1993	1993	NUM
ejpam-676	538	10	.	.	PUNCT
ejpam-676	539	1	[	[	X
ejpam-676	539	2	12	12	NUM
ejpam-676	539	3	]	]	X
ejpam-676	539	4	j	j	PROPN
ejpam-676	539	5	patel	patel	PROPN
ejpam-676	539	6	and	and	CCONJ
ejpam-676	539	7	n	n	PRON
ejpam-676	539	8	cho	cho	NOUN
ejpam-676	539	9	,	,	PUNCT
ejpam-676	539	10	certain	certain	ADJ
ejpam-676	539	11	subclasses	subclass	NOUN
ejpam-676	539	12	of	of	ADP
ejpam-676	539	13	meromorphically	meromorphically	ADV
ejpam-676	539	14	p	p	ADJ
ejpam-676	539	15	-	-	PUNCT
ejpam-676	539	16	valent	valent	NOUN
ejpam-676	539	17	functions	function	NOUN
ejpam-676	539	18	involving	involve	VERB
ejpam-676	539	19	a	a	DET
ejpam-676	539	20	linear	linear	ADJ
ejpam-676	539	21	operator	operator	NOUN
ejpam-676	539	22	,	,	PUNCT
ejpam-676	539	23	math	math	NOUN
ejpam-676	539	24	.	.	PUNCT
ejpam-676	540	1	sci	sci	PROPN
ejpam-676	540	2	.	.	PUNCT
ejpam-676	540	3	res	res	PROPN
ejpam-676	540	4	.	.	PUNCT
ejpam-676	541	1	j.	j.	PROPN
ejpam-676	541	2	7	7	PROPN
ejpam-676	541	3	,	,	PUNCT
ejpam-676	541	4	no	no	INTJ
ejpam-676	541	5	.	.	NOUN
ejpam-676	541	6	4	4	NUM
ejpam-676	541	7	,	,	PUNCT
ejpam-676	541	8	117	117	NUM
ejpam-676	541	9	-	-	SYM
ejpam-676	541	10	128	128	NUM
ejpam-676	541	11	.	.	PUNCT
ejpam-676	541	12	2003	2003	NUM
ejpam-676	541	13	.	.	PUNCT
ejpam-676	542	1	[	[	X
ejpam-676	542	2	13	13	NUM
ejpam-676	542	3	]	]	X
ejpam-676	542	4	r	r	NOUN
ejpam-676	542	5	singh	singh	PROPN
ejpam-676	542	6	and	and	CCONJ
ejpam-676	542	7	s	s	PROPN
ejpam-676	542	8	singh	singh	NOUN
ejpam-676	542	9	,	,	PUNCT
ejpam-676	542	10	convolution	convolution	NOUN
ejpam-676	542	11	properties	property	NOUN
ejpam-676	542	12	of	of	ADP
ejpam-676	542	13	a	a	DET
ejpam-676	542	14	class	class	NOUN
ejpam-676	542	15	of	of	ADP
ejpam-676	542	16	starlike	starlike	NOUN
ejpam-676	542	17	functions	function	NOUN
ejpam-676	542	18	,	,	PUNCT
ejpam-676	542	19	proc	proc	NOUN
ejpam-676	542	20	.	.	PUNCT
ejpam-676	543	1	amer	amer	PROPN
ejpam-676	543	2	.	.	PUNCT
ejpam-676	543	3	math	math	PROPN
ejpam-676	543	4	.	.	PUNCT
ejpam-676	544	1	soc	soc	PROPN
ejpam-676	544	2	.	.	PUNCT
ejpam-676	545	1	106	106	NUM
ejpam-676	545	2	,	,	PUNCT
ejpam-676	545	3	145	145	NUM
ejpam-676	545	4	-	-	SYM
ejpam-676	545	5	152	152	NUM
ejpam-676	545	6	.	.	PUNCT
ejpam-676	545	7	1989	1989	NUM
ejpam-676	545	8	.	.	PUNCT
ejpam-676	546	1	[	[	X
ejpam-676	546	2	14	14	NUM
ejpam-676	546	3	]	]	X
ejpam-676	546	4	h	h	PROPN
ejpam-676	546	5	srivastava	srivastava	PROPN
ejpam-676	546	6	and	and	CCONJ
ejpam-676	546	7	p	p	PROPN
ejpam-676	546	8	karlsson	karlsson	PROPN
ejpam-676	546	9	,	,	PUNCT
ejpam-676	546	10	multiple	multiple	ADJ
ejpam-676	546	11	gaussian	gaussian	ADJ
ejpam-676	546	12	hypergeometric	hypergeometric	ADJ
ejpam-676	546	13	series	series	NOUN
ejpam-676	546	14	,	,	PUNCT
ejpam-676	546	15	halsted	halsted	ADJ
ejpam-676	546	16	press	press	PROPN
ejpam-676	546	17	,	,	PUNCT
ejpam-676	546	18	ellis	ellis	PROPN
ejpam-676	546	19	horwood	horwood	PROPN
ejpam-676	546	20	limited	limited	PROPN
ejpam-676	546	21	,	,	PUNCT
ejpam-676	546	22	chichester	chichester	PROPN
ejpam-676	546	23	,	,	PUNCT
ejpam-676	546	24	john	john	PROPN
ejpam-676	546	25	wiley	wiley	PROPN
ejpam-676	546	26	and	and	CCONJ
ejpam-676	546	27	sons	son	NOUN
ejpam-676	546	28	,	,	PUNCT
ejpam-676	546	29	new	new	PROPN
ejpam-676	546	30	york	york	PROPN
ejpam-676	546	31	,	,	PUNCT
ejpam-676	546	32	chichester	chichester	PROPN
ejpam-676	546	33	,	,	PUNCT
ejpam-676	546	34	brisbane	brisbane	PROPN
ejpam-676	546	35	,	,	PUNCT
ejpam-676	546	36	toronto	toronto	PROPN
ejpam-676	546	37	,	,	PUNCT
ejpam-676	546	38	1985	1985	NUM
ejpam-676	546	39	.	.	PUNCT
ejpam-676	547	1	[	[	X
ejpam-676	547	2	15	15	NUM
ejpam-676	547	3	]	]	X
ejpam-676	547	4	h	h	PROPN
ejpam-676	547	5	srivastava	srivastava	PROPN
ejpam-676	547	6	and	and	CCONJ
ejpam-676	547	7	j	j	PROPN
ejpam-676	547	8	patel	patel	PROPN
ejpam-676	547	9	,	,	PUNCT
ejpam-676	547	10	applications	application	NOUN
ejpam-676	547	11	of	of	ADP
ejpam-676	547	12	differential	differential	ADJ
ejpam-676	547	13	subodination	subodination	NOUN
ejpam-676	547	14	to	to	ADP
ejpam-676	547	15	certain	certain	ADJ
ejpam-676	547	16	subclasses	subclass	NOUN
ejpam-676	547	17	of	of	ADP
ejpam-676	547	18	meromorphically	meromorphically	ADV
ejpam-676	547	19	multivalent	multivalent	NOUN
ejpam-676	547	20	functions	function	NOUN
ejpam-676	547	21	,	,	PUNCT
ejpam-676	547	22	j.	j.	PROPN
ejpam-676	547	23	inequal	inequal	PROPN
ejpam-676	547	24	.	.	PUNCT
ejpam-676	548	1	pure	pure	ADJ
ejpam-676	548	2	appl	appl	PROPN
ejpam-676	548	3	.	.	PUNCT
ejpam-676	548	4	math	math	NOUN
ejpam-676	548	5	.	.	PUNCT
ejpam-676	549	1	6	6	NUM
ejpam-676	549	2	,	,	PUNCT
ejpam-676	549	3	no	no	INTJ
ejpam-676	549	4	.	.	NOUN
ejpam-676	549	5	3	3	NUM
ejpam-676	549	6	,	,	PUNCT
ejpam-676	549	7	art	art	NOUN
ejpam-676	549	8	.	.	PUNCT
ejpam-676	550	1	88	88	NUM
ejpam-676	550	2	,	,	PUNCT
ejpam-676	550	3	pp	pp	ADJ
ejpam-676	550	4	.	.	PUNCT
ejpam-676	551	1	15	15	NUM
ejpam-676	551	2	.	.	NUM
ejpam-676	552	1	2005	2005	NUM
ejpam-676	552	2	.	.	PUNCT
ejpam-676	553	1	[	[	X
ejpam-676	553	2	16	16	NUM
ejpam-676	553	3	]	]	X
ejpam-676	553	4	j	j	PROPN
ejpam-676	553	5	stankiewicz	stankiewicz	NOUN
ejpam-676	553	6	and	and	CCONJ
ejpam-676	553	7	z	z	NOUN
ejpam-676	553	8	stankiewicz	stankiewicz	NOUN
ejpam-676	553	9	,	,	PUNCT
ejpam-676	553	10	some	some	DET
ejpam-676	553	11	applications	application	NOUN
ejpam-676	553	12	of	of	ADP
ejpam-676	553	13	the	the	DET
ejpam-676	553	14	hadamard	hadamard	ADJ
ejpam-676	553	15	convolution	convolution	NOUN
ejpam-676	553	16	in	in	ADP
ejpam-676	553	17	the	the	DET
ejpam-676	553	18	theory	theory	NOUN
ejpam-676	553	19	of	of	ADP
ejpam-676	553	20	functions	function	NOUN
ejpam-676	553	21	,	,	PUNCT
ejpam-676	553	22	ann	ann	PROPN
ejpam-676	553	23	.	.	PROPN
ejpam-676	553	24	univ	univ	PROPN
ejpam-676	553	25	.	.	PUNCT
ejpam-676	554	1	mariae	mariae	PROPN
ejpam-676	554	2	curie	curie	PROPN
ejpam-676	554	3	-	-	PUNCT
ejpam-676	554	4	sklodowska	sklodowska	NOUN
ejpam-676	554	5	sect	sect	NOUN
ejpam-676	554	6	.	.	PUNCT
ejpam-676	555	1	a	a	DET
ejpam-676	555	2	40	40	NUM
ejpam-676	555	3	,	,	PUNCT
ejpam-676	555	4	251	251	NUM
ejpam-676	555	5	-	-	SYM
ejpam-676	555	6	265	265	NUM
ejpam-676	555	7	.	.	PUNCT
ejpam-676	555	8	1986	1986	NUM
ejpam-676	555	9	.	.	PUNCT
ejpam-676	556	1	[	[	X
ejpam-676	556	2	17	17	NUM
ejpam-676	556	3	]	]	SYM
ejpam-676	556	4	b	b	NOUN
ejpam-676	556	5	uralegaddi	uralegaddi	ADJ
ejpam-676	556	6	and	and	CCONJ
ejpam-676	556	7	c	c	PROPN
ejpam-676	556	8	somanatha	somanatha	NOUN
ejpam-676	556	9	,	,	PUNCT
ejpam-676	556	10	certain	certain	ADJ
ejpam-676	556	11	classes	class	NOUN
ejpam-676	556	12	of	of	ADP
ejpam-676	556	13	meromorphic	meromorphic	ADJ
ejpam-676	556	14	multivalent	multivalent	NOUN
ejpam-676	556	15	functions	function	NOUN
ejpam-676	556	16	,	,	PUNCT
ejpam-676	556	17	tamkang	tamkang	PROPN
ejpam-676	556	18	j.	j.	PROPN
ejpam-676	556	19	math	math	PROPN
ejpam-676	556	20	.	.	PUNCT
ejpam-676	557	1	23	23	NUM
ejpam-676	557	2	,	,	PUNCT
ejpam-676	557	3	223	223	NUM
ejpam-676	557	4	-	-	SYM
ejpam-676	557	5	231	231	NUM
ejpam-676	557	6	.	.	PUNCT
ejpam-676	558	1	1992	1992	NUM
ejpam-676	558	2	.	.	PUNCT
ejpam-676	559	1	[	[	X
ejpam-676	559	2	18	18	NUM
ejpam-676	559	3	]	]	X
ejpam-676	559	4	e	e	X
ejpam-676	559	5	whittaker	whittaker	PROPN
ejpam-676	559	6	and	and	CCONJ
ejpam-676	559	7	g	g	PROPN
ejpam-676	559	8	watson	watson	PROPN
ejpam-676	559	9	,	,	PUNCT
ejpam-676	559	10	a	a	DET
ejpam-676	559	11	course	course	NOUN
ejpam-676	559	12	on	on	ADP
ejpam-676	559	13	modern	modern	ADJ
ejpam-676	559	14	analysis	analysis	NOUN
ejpam-676	559	15	:	:	PUNCT
ejpam-676	559	16	an	an	DET
ejpam-676	559	17	introduction	introduction	NOUN
ejpam-676	559	18	to	to	ADP
ejpam-676	559	19	the	the	DET
ejpam-676	559	20	general	general	ADJ
ejpam-676	559	21	theory	theory	NOUN
ejpam-676	559	22	of	of	ADP
ejpam-676	559	23	infinite	infinite	ADJ
ejpam-676	559	24	processes	process	NOUN
ejpam-676	559	25	and	and	CCONJ
ejpam-676	559	26	of	of	ADP
ejpam-676	559	27	analytic	analytic	ADJ
ejpam-676	559	28	functions	function	NOUN
ejpam-676	559	29	;	;	PUNCT
ejpam-676	559	30	with	with	ADP
ejpam-676	559	31	an	an	DET
ejpam-676	559	32	account	account	NOUN
ejpam-676	559	33	of	of	ADP
ejpam-676	559	34	the	the	DET
ejpam-676	559	35	principal	principal	ADJ
ejpam-676	559	36	transcendental	transcendental	ADJ
ejpam-676	559	37	functions	function	NOUN
ejpam-676	559	38	,	,	PUNCT
ejpam-676	559	39	fourth	fourth	ADJ
ejpam-676	559	40	edition	edition	NOUN
ejpam-676	559	41	(	(	PUNCT
ejpam-676	559	42	reprinted	reprinted	PROPN
ejpam-676	559	43	)	)	PUNCT
ejpam-676	559	44	,	,	PUNCT
ejpam-676	559	45	cambridge	cambridge	PROPN
ejpam-676	559	46	university	university	PROPN
ejpam-676	559	47	press	press	PROPN
ejpam-676	559	48	,	,	PUNCT
ejpam-676	559	49	cambridge	cambridge	PROPN
ejpam-676	559	50	,	,	PUNCT
ejpam-676	559	51	1927	1927	NUM
ejpam-676	559	52	.	.	PUNCT
ejpam-676	560	1	[	[	X
ejpam-676	560	2	19	19	NUM
ejpam-676	560	3	]	]	X
ejpam-676	560	4	d	d	PROPN
ejpam-676	560	5	yang	yang	PROPN
ejpam-676	560	6	,	,	PUNCT
ejpam-676	560	7	certain	certain	ADJ
ejpam-676	560	8	convolution	convolution	NOUN
ejpam-676	560	9	operators	operator	NOUN
ejpam-676	560	10	for	for	ADP
ejpam-676	560	11	meromorphic	meromorphic	ADJ
ejpam-676	560	12	functions	function	NOUN
ejpam-676	560	13	,	,	PUNCT
ejpam-676	560	14	south	south	NOUN
ejpam-676	560	15	.	.	PUNCT
ejpam-676	561	1	asian	asian	ADJ
ejpam-676	561	2	bull	bull	PROPN
ejpam-676	561	3	.	.	PUNCT
ejpam-676	562	1	math	math	NOUN
ejpam-676	562	2	.	.	PUNCT
ejpam-676	563	1	25	25	NUM
ejpam-676	563	2	,	,	PUNCT
ejpam-676	563	3	175	175	NUM
ejpam-676	563	4	-	-	SYM
ejpam-676	563	5	186	186	NUM
ejpam-676	563	6	.	.	PUNCT
ejpam-676	564	1	2001	2001	NUM
ejpam-676	564	2	.	.	PUNCT