id	sid	tid	token	lemma	pos
ejpam-834	1	1	2_834_frasin.dvi	2_834_frasin.dvi	NUM
ejpam-834	1	2	european	european	ADJ
ejpam-834	1	3	journal	journal	NOUN
ejpam-834	1	4	of	of	ADP
ejpam-834	1	5	pure	pure	ADJ
ejpam-834	1	6	and	and	CCONJ
ejpam-834	1	7	applied	apply	VERB
ejpam-834	1	8	mathematics	mathematic	NOUN
ejpam-834	1	9	vol	vol	NOUN
ejpam-834	1	10	.	.	PROPN
ejpam-834	1	11	4	4	NUM
ejpam-834	1	12	,	,	PUNCT
ejpam-834	1	13	no	no	INTJ
ejpam-834	1	14	.	.	NOUN
ejpam-834	1	15	1	1	NUM
ejpam-834	1	16	,	,	PUNCT
ejpam-834	1	17	2011	2011	NUM
ejpam-834	1	18	,	,	PUNCT
ejpam-834	1	19	14	14	NUM
ejpam-834	1	20	-	-	SYM
ejpam-834	1	21	19	19	NUM
ejpam-834	1	22	issn	issn	PROPN
ejpam-834	1	23	1307	1307	NUM
ejpam-834	1	24	-	-	SYM
ejpam-834	1	25	5543	5543	NUM
ejpam-834	1	26	–	–	PUNCT
ejpam-834	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-834	1	28	(	(	PUNCT
ejpam-834	1	29	α	α	X
ejpam-834	1	30	,	,	PUNCT
ejpam-834	1	31	β	β	X
ejpam-834	1	32	,	,	PUNCT
ejpam-834	1	33	δ)−neighborhood	δ)−neighborhood	PROPN
ejpam-834	1	34	for	for	ADP
ejpam-834	1	35	certain	certain	ADJ
ejpam-834	1	36	analytic	analytic	ADJ
ejpam-834	1	37	functions	function	NOUN
ejpam-834	1	38	with	with	ADP
ejpam-834	1	39	negative	negative	ADJ
ejpam-834	1	40	coefficients	coefficient	NOUN
ejpam-834	1	41	b.a	b.a	PROPN
ejpam-834	1	42	.	.	PROPN
ejpam-834	1	43	frasin	frasin	PROPN
ejpam-834	1	44	faculty	faculty	NOUN
ejpam-834	1	45	of	of	ADP
ejpam-834	1	46	science	science	NOUN
ejpam-834	1	47	,	,	PUNCT
ejpam-834	1	48	department	department	NOUN
ejpam-834	1	49	of	of	ADP
ejpam-834	1	50	mathematics	mathematics	PROPN
ejpam-834	1	51	,	,	PUNCT
ejpam-834	1	52	al	al	PROPN
ejpam-834	1	53	al	al	PROPN
ejpam-834	1	54	-	-	PUNCT
ejpam-834	1	55	bayt	bayt	ADJ
ejpam-834	1	56	university	university	NOUN
ejpam-834	1	57	,	,	PUNCT
ejpam-834	1	58	p.o	p.o	PROPN
ejpam-834	1	59	.	.	PROPN
ejpam-834	1	60	box	box	PROPN
ejpam-834	1	61	:	:	PUNCT
ejpam-834	1	62	130095	130095	NUM
ejpam-834	1	63	mafraq	mafraq	NOUN
ejpam-834	1	64	,	,	PUNCT
ejpam-834	1	65	jordan	jordan	PROPN
ejpam-834	1	66	abstract	abstract	PROPN
ejpam-834	1	67	.	.	PUNCT
ejpam-834	2	1	in	in	ADP
ejpam-834	2	2	this	this	DET
ejpam-834	2	3	paper	paper	NOUN
ejpam-834	2	4	,	,	PUNCT
ejpam-834	2	5	we	we	PRON
ejpam-834	2	6	introduce	introduce	VERB
ejpam-834	2	7	(	(	PUNCT
ejpam-834	2	8	α	α	NOUN
ejpam-834	2	9	,	,	PUNCT
ejpam-834	2	10	β	β	NOUN
ejpam-834	2	11	,	,	PUNCT
ejpam-834	2	12	δ)−neighborhoods	δ)−neighborhoods	PROPN
ejpam-834	2	13	of	of	ADP
ejpam-834	2	14	analytic	analytic	ADJ
ejpam-834	2	15	functions	function	NOUN
ejpam-834	2	16	with	with	ADP
ejpam-834	2	17	negative	negative	ADJ
ejpam-834	2	18	coefficients	coefficient	NOUN
ejpam-834	2	19	.	.	PUNCT
ejpam-834	3	1	furthermore	furthermore	ADV
ejpam-834	3	2	,	,	PUNCT
ejpam-834	3	3	we	we	PRON
ejpam-834	3	4	obtain	obtain	VERB
ejpam-834	3	5	some	some	DET
ejpam-834	3	6	interesting	interesting	ADJ
ejpam-834	3	7	results	result	NOUN
ejpam-834	3	8	for	for	ADP
ejpam-834	3	9	functions	function	NOUN
ejpam-834	3	10	belonging	belong	VERB
ejpam-834	3	11	to	to	ADP
ejpam-834	3	12	this	this	DET
ejpam-834	3	13	neighborhoods	neighborhood	NOUN
ejpam-834	3	14	.	.	PUNCT
ejpam-834	4	1	2000	2000	NUM
ejpam-834	4	2	mathematics	mathematic	NOUN
ejpam-834	4	3	subject	subject	NOUN
ejpam-834	4	4	classifications	classification	NOUN
ejpam-834	4	5	:	:	PUNCT
ejpam-834	4	6	30c45	30c45	NUM
ejpam-834	4	7	key	key	ADJ
ejpam-834	4	8	words	word	NOUN
ejpam-834	4	9	and	and	CCONJ
ejpam-834	4	10	phrases	phrase	NOUN
ejpam-834	4	11	:	:	PUNCT
ejpam-834	4	12	analytic	analytic	ADJ
ejpam-834	4	13	functions	function	NOUN
ejpam-834	4	14	,	,	PUNCT
ejpam-834	4	15	neighborhood	neighborhood	NOUN
ejpam-834	4	16	1	1	NUM
ejpam-834	4	17	.	.	PUNCT
ejpam-834	5	1	introduction	introduction	NOUN
ejpam-834	5	2	and	and	CCONJ
ejpam-834	5	3	definitions	definition	NOUN
ejpam-834	5	4	let	let	VERB
ejpam-834	5	5	t	t	NOUN
ejpam-834	5	6	denote	denote	VERB
ejpam-834	5	7	the	the	DET
ejpam-834	5	8	class	class	NOUN
ejpam-834	5	9	of	of	ADP
ejpam-834	5	10	functions	function	NOUN
ejpam-834	5	11	of	of	ADP
ejpam-834	5	12	the	the	DET
ejpam-834	5	13	form	form	NOUN
ejpam-834	5	14	:	:	PUNCT
ejpam-834	6	1	f	f	X
ejpam-834	6	2	(	(	PUNCT
ejpam-834	6	3	z	z	NOUN
ejpam-834	6	4	)	)	PUNCT
ejpam-834	6	5	=	=	PUNCT
ejpam-834	7	1	z	z	NOUN
ejpam-834	7	2	−	−	NOUN
ejpam-834	7	3	∞	∞	PROPN
ejpam-834	7	4	∑	∑	PROPN
ejpam-834	7	5	n=2	n=2	PART
ejpam-834	7	6	anzn	anzn	NOUN
ejpam-834	7	7	,	,	PUNCT
ejpam-834	7	8	(	(	PUNCT
ejpam-834	7	9	an	an	DET
ejpam-834	7	10	≥	≥	NOUN
ejpam-834	7	11	0	0	NUM
ejpam-834	7	12	)	)	PUNCT
ejpam-834	7	13	.	.	PUNCT
ejpam-834	8	1	(	(	PUNCT
ejpam-834	8	2	1	1	X
ejpam-834	8	3	)	)	PUNCT
ejpam-834	8	4	which	which	PRON
ejpam-834	8	5	are	be	AUX
ejpam-834	8	6	analytic	analytic	ADJ
ejpam-834	8	7	in	in	ADP
ejpam-834	8	8	the	the	DET
ejpam-834	8	9	open	open	ADJ
ejpam-834	8	10	unit	unit	NOUN
ejpam-834	8	11	disk	disk	NOUN
ejpam-834	8	12	u	u	NOUN
ejpam-834	8	13	=	=	PUNCT
ejpam-834	8	14	{	{	PUNCT
ejpam-834	8	15	z	z	NOUN
ejpam-834	8	16	:	:	PUNCT
ejpam-834	8	17	|z|	|z|	NOUN
ejpam-834	8	18	<	<	X
ejpam-834	8	19	1}.for	1}.for	PROPN
ejpam-834	8	20	a	a	DET
ejpam-834	8	21	function	function	NOUN
ejpam-834	8	22	f	f	X
ejpam-834	8	23	(	(	PUNCT
ejpam-834	8	24	z	z	NOUN
ejpam-834	8	25	)	)	PUNCT
ejpam-834	8	26	∈	∈	PROPN
ejpam-834	8	27	t	t	NOUN
ejpam-834	8	28	,	,	PUNCT
ejpam-834	8	29	we	we	PRON
ejpam-834	8	30	define	define	VERB
ejpam-834	8	31	d0	d0	PROPN
ejpam-834	8	32	f	f	PROPN
ejpam-834	8	33	(	(	PUNCT
ejpam-834	8	34	z	z	NOUN
ejpam-834	8	35	)	)	PUNCT
ejpam-834	9	1	=	=	SYM
ejpam-834	9	2	f	f	X
ejpam-834	9	3	(	(	PUNCT
ejpam-834	9	4	z	z	NOUN
ejpam-834	9	5	)	)	PUNCT
ejpam-834	9	6	,	,	PUNCT
ejpam-834	9	7	d1	d1	PROPN
ejpam-834	9	8	f	f	PROPN
ejpam-834	9	9	(	(	PUNCT
ejpam-834	9	10	z	z	NOUN
ejpam-834	9	11	)	)	PUNCT
ejpam-834	9	12	=	=	PUNCT
ejpam-834	10	1	d	d	X
ejpam-834	10	2	f	f	X
ejpam-834	10	3	(	(	PUNCT
ejpam-834	10	4	z	z	NOUN
ejpam-834	10	5	)	)	PUNCT
ejpam-834	10	6	=	=	PUNCT
ejpam-834	10	7	z	z	X
ejpam-834	10	8	f	f	PROPN
ejpam-834	10	9	′(z	′(z	NOUN
ejpam-834	10	10	)	)	PUNCT
ejpam-834	10	11	,	,	PUNCT
ejpam-834	10	12	and	and	CCONJ
ejpam-834	10	13	dk	dk	PROPN
ejpam-834	10	14	f	f	PROPN
ejpam-834	10	15	(	(	PUNCT
ejpam-834	10	16	z	z	NOUN
ejpam-834	10	17	)	)	PUNCT
ejpam-834	10	18	=	=	PRON
ejpam-834	10	19	d(dk−1	d(dk−1	PROPN
ejpam-834	10	20	f	f	PROPN
ejpam-834	10	21	(	(	PUNCT
ejpam-834	10	22	z	z	NOUN
ejpam-834	10	23	)	)	PUNCT
ejpam-834	10	24	)	)	PUNCT
ejpam-834	11	1	=	=	PUNCT
ejpam-834	11	2	z	z	NOUN
ejpam-834	12	1	−	−	NOUN
ejpam-834	12	2	∞	∞	NUM
ejpam-834	12	3	∑	∑	PROPN
ejpam-834	12	4	n=2	n=2	PRON
ejpam-834	12	5	nkanzn	nkanzn	ADV
ejpam-834	12	6	(	(	PUNCT
ejpam-834	12	7	k	k	PROPN
ejpam-834	12	8	∈	∈	PROPN
ejpam-834	12	9	n0	n0	PROPN
ejpam-834	12	10	=	=	SYM
ejpam-834	12	11	n∪	n∪	PROPN
ejpam-834	12	12	{	{	PUNCT
ejpam-834	12	13	0	0	NUM
ejpam-834	12	14	}	}	PUNCT
ejpam-834	12	15	)	)	PUNCT
ejpam-834	12	16	.	.	PUNCT
ejpam-834	13	1	the	the	DET
ejpam-834	13	2	differential	differential	ADJ
ejpam-834	13	3	operator	operator	NOUN
ejpam-834	13	4	dk	dk	PROPN
ejpam-834	13	5	was	be	AUX
ejpam-834	13	6	introduced	introduce	VERB
ejpam-834	13	7	by	by	ADP
ejpam-834	13	8	sălăgean	sălăgean	PROPN
ejpam-834	13	9	[	[	X
ejpam-834	13	10	12	12	NUM
ejpam-834	13	11	]	]	PUNCT
ejpam-834	13	12	.	.	PUNCT
ejpam-834	14	1	email	email	NOUN
ejpam-834	14	2	address	address	NOUN
ejpam-834	14	3	:	:	PUNCT
ejpam-834	14	4	bafrasin	bafrasin	PROPN
ejpam-834	14	5	�	�	PROPN
ejpam-834	14	6	yahoo	yahoo	PROPN
ejpam-834	14	7	.	.	PUNCT
ejpam-834	15	1	om	om	PROPN
ejpam-834	15	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-834	16	1	14	14	NUM
ejpam-834	16	2	c	c	X
ejpam-834	16	3	©	©	PROPN
ejpam-834	16	4	2010	2010	NUM
ejpam-834	16	5	ejpam	ejpam	NOUN
ejpam-834	16	6	all	all	DET
ejpam-834	16	7	rights	right	NOUN
ejpam-834	16	8	reserved	reserve	VERB
ejpam-834	16	9	.	.	PUNCT
ejpam-834	17	1	b.	b.	PROPN
ejpam-834	17	2	frasin	frasin	PROPN
ejpam-834	17	3	/	/	SYM
ejpam-834	17	4	eur	eur	PROPN
ejpam-834	17	5	.	.	PUNCT
ejpam-834	18	1	j.	j.	PROPN
ejpam-834	18	2	pure	pure	PROPN
ejpam-834	18	3	appl	appl	PROPN
ejpam-834	18	4	.	.	PROPN
ejpam-834	18	5	math	math	PROPN
ejpam-834	18	6	,	,	PUNCT
ejpam-834	18	7	4	4	NUM
ejpam-834	18	8	(	(	PUNCT
ejpam-834	18	9	2011	2011	NUM
ejpam-834	18	10	)	)	PUNCT
ejpam-834	18	11	,	,	PUNCT
ejpam-834	18	12	14	14	NUM
ejpam-834	18	13	-	-	SYM
ejpam-834	18	14	19	19	NUM
ejpam-834	18	15	15	15	NUM
ejpam-834	18	16	following	follow	VERB
ejpam-834	18	17	a	a	DET
ejpam-834	18	18	recent	recent	ADJ
ejpam-834	18	19	investigation	investigation	NOUN
ejpam-834	18	20	by	by	ADP
ejpam-834	18	21	frasin	frasin	NOUN
ejpam-834	18	22	and	and	CCONJ
ejpam-834	18	23	darus	darus	NOUN
ejpam-834	18	24	[	[	X
ejpam-834	18	25	6	6	NUM
ejpam-834	18	26	]	]	PUNCT
ejpam-834	19	1	[	[	X
ejpam-834	19	2	see	see	VERB
ejpam-834	19	3	also	also	ADV
ejpam-834	19	4	1	1	NUM
ejpam-834	19	5	]	]	PUNCT
ejpam-834	19	6	,	,	PUNCT
ejpam-834	19	7	if	if	SCONJ
ejpam-834	19	8	f	f	PROPN
ejpam-834	19	9	(	(	PUNCT
ejpam-834	19	10	z	z	NOUN
ejpam-834	19	11	)	)	PUNCT
ejpam-834	19	12	∈	∈	PROPN
ejpam-834	19	13	t	t	PROPN
ejpam-834	19	14	and	and	CCONJ
ejpam-834	19	15	µ	µ	X
ejpam-834	19	16	≥	≥	NOUN
ejpam-834	19	17	0	0	NUM
ejpam-834	19	18	,	,	PUNCT
ejpam-834	19	19	then	then	ADV
ejpam-834	19	20	we	we	PRON
ejpam-834	19	21	define	define	VERB
ejpam-834	19	22	the	the	DET
ejpam-834	19	23	(	(	PUNCT
ejpam-834	19	24	k,µ)-neighborhood	k,µ)-neighborhood	NOUN
ejpam-834	19	25	for	for	ADP
ejpam-834	19	26	the	the	DET
ejpam-834	19	27	function	function	NOUN
ejpam-834	19	28	f	f	PROPN
ejpam-834	19	29	(	(	PUNCT
ejpam-834	19	30	z	z	NOUN
ejpam-834	19	31	)	)	PUNCT
ejpam-834	19	32	by	by	ADP
ejpam-834	19	33	n	n	PROPN
ejpam-834	19	34	k	k	PROPN
ejpam-834	19	35	µ	µ	X
ejpam-834	19	36	(	(	PUNCT
ejpam-834	19	37	f	f	PROPN
ejpam-834	19	38	)	)	PUNCT
ejpam-834	20	1	=	=	PRON
ejpam-834	20	2	{	{	PUNCT
ejpam-834	20	3	g	g	PROPN
ejpam-834	20	4	∈	∈	PROPN
ejpam-834	20	5	t	t	NOUN
ejpam-834	20	6	:	:	PUNCT
ejpam-834	20	7	g(z	g(z	ADJ
ejpam-834	20	8	)	)	PUNCT
ejpam-834	20	9	=	=	PUNCT
ejpam-834	20	10	z	z	NOUN
ejpam-834	21	1	−	−	NOUN
ejpam-834	21	2	∞	∞	PROPN
ejpam-834	21	3	∑	∑	PROPN
ejpam-834	21	4	n=2	n=2	PART
ejpam-834	21	5	bnzn	bnzn	NOUN
ejpam-834	21	6	,	,	PUNCT
ejpam-834	21	7	∞	∞	PROPN
ejpam-834	21	8	∑	∑	PUNCT
ejpam-834	21	9	n=2	n=2	PRON
ejpam-834	21	10	nk+1	nk+1	NUM
ejpam-834	21	11	�	�	PROPN
ejpam-834	21	12	�	�	PROPN
ejpam-834	21	13	an−	an−	PROPN
ejpam-834	21	14	bn	bn	NUM
ejpam-834	21	15	�	�	PROPN
ejpam-834	21	16	�	�	PROPN
ejpam-834	21	17	≤	≤	PROPN
ejpam-834	21	18	µ	µ	NUM
ejpam-834	21	19	}	}	PUNCT
ejpam-834	21	20	.	.	PUNCT
ejpam-834	22	1	(	(	PUNCT
ejpam-834	22	2	2	2	X
ejpam-834	22	3	)	)	PUNCT
ejpam-834	22	4	in	in	ADP
ejpam-834	22	5	particular	particular	ADJ
ejpam-834	22	6	,	,	PUNCT
ejpam-834	22	7	for	for	ADP
ejpam-834	22	8	the	the	DET
ejpam-834	22	9	identity	identity	NOUN
ejpam-834	22	10	function	function	NOUN
ejpam-834	22	11	e(z	e(z	PROPN
ejpam-834	22	12	)	)	PUNCT
ejpam-834	22	13	=	=	SYM
ejpam-834	23	1	z	z	X
ejpam-834	23	2	,	,	PUNCT
ejpam-834	23	3	we	we	PRON
ejpam-834	23	4	immediately	immediately	ADV
ejpam-834	23	5	have	have	VERB
ejpam-834	23	6	n	n	PROPN
ejpam-834	23	7	k	k	PROPN
ejpam-834	23	8	µ	µ	X
ejpam-834	23	9	(	(	PUNCT
ejpam-834	23	10	e	e	NOUN
ejpam-834	23	11	)	)	PUNCT
ejpam-834	23	12	=	=	PRON
ejpam-834	23	13	{	{	PUNCT
ejpam-834	23	14	g	g	PROPN
ejpam-834	23	15	∈	∈	PROPN
ejpam-834	23	16	t	t	NOUN
ejpam-834	23	17	:	:	PUNCT
ejpam-834	24	1	g(z	g(z	ADJ
ejpam-834	24	2	)	)	PUNCT
ejpam-834	24	3	=	=	PUNCT
ejpam-834	24	4	z	z	NOUN
ejpam-834	25	1	−	−	NOUN
ejpam-834	25	2	∞	∞	PROPN
ejpam-834	25	3	∑	∑	PROPN
ejpam-834	25	4	n=2	n=2	PART
ejpam-834	25	5	bnzn	bnzn	NOUN
ejpam-834	25	6	,	,	PUNCT
ejpam-834	25	7	∞	∞	PROPN
ejpam-834	25	8	∑	∑	PUNCT
ejpam-834	25	9	n=2	n=2	PRON
ejpam-834	25	10	nk+1	nk+1	NUM
ejpam-834	25	11	�	�	PROPN
ejpam-834	25	12	�	�	PROPN
ejpam-834	25	13	bn	bn	PROPN
ejpam-834	25	14	�	�	PROPN
ejpam-834	25	15	�	�	PROPN
ejpam-834	25	16	≤	≤	PROPN
ejpam-834	25	17	µ	µ	NUM
ejpam-834	25	18	}	}	PUNCT
ejpam-834	25	19	,	,	PUNCT
ejpam-834	25	20	(	(	PUNCT
ejpam-834	25	21	3	3	X
ejpam-834	25	22	)	)	PUNCT
ejpam-834	25	23	we	we	PRON
ejpam-834	25	24	observe	observe	VERB
ejpam-834	25	25	that	that	SCONJ
ejpam-834	25	26	n	n	PROPN
ejpam-834	25	27	0	0	NUM
ejpam-834	25	28	µ	µ	X
ejpam-834	25	29	(	(	PUNCT
ejpam-834	25	30	f	f	PROPN
ejpam-834	25	31	)	)	PUNCT
ejpam-834	25	32	≡	≡	PROPN
ejpam-834	25	33	n	n	CCONJ
ejpam-834	25	34	µ	µ	X
ejpam-834	25	35	(	(	PUNCT
ejpam-834	25	36	f	f	PROPN
ejpam-834	25	37	)	)	PUNCT
ejpam-834	25	38	and	and	CCONJ
ejpam-834	25	39	n	n	PROPN
ejpam-834	25	40	1	1	NUM
ejpam-834	25	41	µ	µ	X
ejpam-834	25	42	(	(	PUNCT
ejpam-834	25	43	f	f	PROPN
ejpam-834	25	44	)	)	PUNCT
ejpam-834	25	45	≡	≡	PROPN
ejpam-834	25	46	m	m	PROPN
ejpam-834	25	47	µ	µ	X
ejpam-834	25	48	(	(	PUNCT
ejpam-834	25	49	f	f	PROPN
ejpam-834	25	50	)	)	PUNCT
ejpam-834	25	51	,	,	PUNCT
ejpam-834	25	52	where	where	SCONJ
ejpam-834	25	53	n	n	PROPN
ejpam-834	25	54	k	k	PROPN
ejpam-834	25	55	µ	µ	X
ejpam-834	25	56	(	(	PUNCT
ejpam-834	25	57	f	f	PROPN
ejpam-834	25	58	)	)	PUNCT
ejpam-834	25	59	and	and	CCONJ
ejpam-834	25	60	mµ	mµ	INTJ
ejpam-834	25	61	(	(	PUNCT
ejpam-834	25	62	f	f	PROPN
ejpam-834	25	63	)	)	PUNCT
ejpam-834	25	64	denote	denote	NOUN
ejpam-834	25	65	,	,	PUNCT
ejpam-834	25	66	respectively	respectively	ADV
ejpam-834	25	67	,	,	PUNCT
ejpam-834	25	68	the	the	DET
ejpam-834	25	69	µ-neighborhoods	µ-neighborhood	NOUN
ejpam-834	25	70	of	of	ADP
ejpam-834	25	71	f	f	PROPN
ejpam-834	25	72	as	as	SCONJ
ejpam-834	25	73	defined	define	VERB
ejpam-834	25	74	by	by	ADP
ejpam-834	25	75	ruscheweyh	ruscheweyh	NOUN
ejpam-834	26	1	[	[	X
ejpam-834	26	2	11	11	NUM
ejpam-834	26	3	]	]	PUNCT
ejpam-834	26	4	and	and	CCONJ
ejpam-834	26	5	silverman	silverman	NOUN
ejpam-834	26	6	[	[	X
ejpam-834	26	7	13	13	NUM
ejpam-834	26	8	]	]	PUNCT
ejpam-834	26	9	.	.	PUNCT
ejpam-834	27	1	for	for	ADP
ejpam-834	27	2	further	further	ADJ
ejpam-834	27	3	details	detail	NOUN
ejpam-834	27	4	about	about	ADP
ejpam-834	27	5	the	the	DET
ejpam-834	27	6	neighborhood	neighborhood	NOUN
ejpam-834	27	7	of	of	ADP
ejpam-834	27	8	analytic	analytic	ADJ
ejpam-834	27	9	functions	function	NOUN
ejpam-834	27	10	see	see	VERB
ejpam-834	27	11	(	(	PUNCT
ejpam-834	27	12	as	as	ADP
ejpam-834	27	13	examples	example	NOUN
ejpam-834	27	14	)	)	PUNCT
ejpam-834	27	15	the	the	DET
ejpam-834	27	16	papers	paper	NOUN
ejpam-834	27	17	in	in	ADP
ejpam-834	27	18	[	[	X
ejpam-834	27	19	2	2	NUM
ejpam-834	27	20	,	,	PUNCT
ejpam-834	27	21	3	3	NUM
ejpam-834	27	22	,	,	PUNCT
ejpam-834	27	23	4	4	NUM
ejpam-834	27	24	,	,	PUNCT
ejpam-834	27	25	7	7	NUM
ejpam-834	27	26	,	,	PUNCT
ejpam-834	27	27	5	5	NUM
ejpam-834	27	28	,	,	PUNCT
ejpam-834	27	29	8	8	NUM
ejpam-834	27	30	,	,	PUNCT
ejpam-834	27	31	9	9	NUM
ejpam-834	27	32	]	]	PUNCT
ejpam-834	27	33	.	.	PUNCT
ejpam-834	28	1	very	very	ADV
ejpam-834	28	2	recently	recently	ADV
ejpam-834	28	3	,	,	PUNCT
ejpam-834	28	4	orhan	orhan	PROPN
ejpam-834	28	5	et	et	PROPN
ejpam-834	28	6	al	al	PROPN
ejpam-834	28	7	.	.	PUNCT
ejpam-834	29	1	[	[	X
ejpam-834	29	2	10	10	NUM
ejpam-834	29	3	]	]	PUNCT
ejpam-834	29	4	,	,	PUNCT
ejpam-834	29	5	introduced	introduce	VERB
ejpam-834	29	6	new	new	ADJ
ejpam-834	29	7	definition	definition	NOUN
ejpam-834	29	8	of	of	ADP
ejpam-834	29	9	(	(	PUNCT
ejpam-834	29	10	α	α	NOUN
ejpam-834	29	11	,	,	PUNCT
ejpam-834	29	12	δ)-neighborhood	δ)-neighborhood	PUNCT
ejpam-834	29	13	for	for	ADP
ejpam-834	29	14	analytic	analytic	ADJ
ejpam-834	29	15	function	function	NOUN
ejpam-834	29	16	f	f	PROPN
ejpam-834	29	17	(	(	PUNCT
ejpam-834	29	18	z	z	NOUN
ejpam-834	29	19	)	)	PUNCT
ejpam-834	29	20	in	in	ADP
ejpam-834	29	21	the	the	DET
ejpam-834	29	22	form	form	NOUN
ejpam-834	29	23	f	f	X
ejpam-834	29	24	(	(	PUNCT
ejpam-834	29	25	z	z	NOUN
ejpam-834	29	26	)	)	PUNCT
ejpam-834	29	27	=	=	SYM
ejpam-834	30	1	z	z	NOUN
ejpam-834	31	1	+	+	NUM
ejpam-834	31	2	∞	∞	NUM
ejpam-834	31	3	∑	∑	CCONJ
ejpam-834	31	4	n=2	n=2	PART
ejpam-834	31	5	anzn	anzn	NOUN
ejpam-834	31	6	,	,	PUNCT
ejpam-834	31	7	(	(	PUNCT
ejpam-834	31	8	4	4	NUM
ejpam-834	31	9	)	)	PUNCT
ejpam-834	31	10	in	in	ADP
ejpam-834	31	11	this	this	DET
ejpam-834	31	12	paper	paper	NOUN
ejpam-834	31	13	,	,	PUNCT
ejpam-834	31	14	we	we	PRON
ejpam-834	31	15	introduce	introduce	VERB
ejpam-834	31	16	the	the	DET
ejpam-834	31	17	following	follow	VERB
ejpam-834	31	18	new	new	ADJ
ejpam-834	31	19	definition	definition	NOUN
ejpam-834	31	20	of	of	ADP
ejpam-834	31	21	(	(	PUNCT
ejpam-834	31	22	α	α	X
ejpam-834	31	23	,	,	PUNCT
ejpam-834	31	24	β	β	X
ejpam-834	31	25	,	,	PUNCT
ejpam-834	31	26	δ)-neighborhood	δ)-neighborhood	PUNCT
ejpam-834	31	27	for	for	ADP
ejpam-834	31	28	a	a	DET
ejpam-834	31	29	function	function	NOUN
ejpam-834	31	30	given	give	VERB
ejpam-834	31	31	by	by	ADP
ejpam-834	31	32	1	1	NUM
ejpam-834	31	33	.	.	PUNCT
ejpam-834	31	34	definition	definition	NOUN
ejpam-834	31	35	1	1	NUM
ejpam-834	31	36	.	.	PUNCT
ejpam-834	32	1	a	a	DET
ejpam-834	32	2	function	function	NOUN
ejpam-834	32	3	f	f	X
ejpam-834	32	4	(	(	PUNCT
ejpam-834	32	5	z	z	NOUN
ejpam-834	32	6	)	)	PUNCT
ejpam-834	32	7	∈	∈	PROPN
ejpam-834	32	8	t	t	PROPN
ejpam-834	32	9	is	be	AUX
ejpam-834	32	10	said	say	VERB
ejpam-834	32	11	to	to	PART
ejpam-834	32	12	be	be	AUX
ejpam-834	32	13	(	(	PUNCT
ejpam-834	32	14	α	α	X
ejpam-834	32	15	,	,	PUNCT
ejpam-834	32	16	β	β	X
ejpam-834	32	17	,	,	PUNCT
ejpam-834	32	18	δ)-neighborhood	δ)-neighborhood	PUNCT
ejpam-834	32	19	for	for	ADP
ejpam-834	32	20	g(z	g(z	PROPN
ejpam-834	32	21	)	)	PUNCT
ejpam-834	33	1	=	=	SYM
ejpam-834	33	2	z	z	NOUN
ejpam-834	34	1	−	−	NOUN
ejpam-834	34	2	∞	∞	NUM
ejpam-834	34	3	∑	∑	ADP
ejpam-834	34	4	n=2	n=2	PRON
ejpam-834	34	5	bnzn	bnzn	NOUN
ejpam-834	34	6	∈	∈	PROPN
ejpam-834	34	7	t	t	NOUN
ejpam-834	34	8	if	if	SCONJ
ejpam-834	34	9	it	it	PRON
ejpam-834	34	10	satisfies	satisfy	VERB
ejpam-834	34	11	�	�	PROPN
ejpam-834	34	12	�	�	PROPN
ejpam-834	34	13	eiα(dk	eiα(dk	PROPN
ejpam-834	34	14	f	f	X
ejpam-834	34	15	(	(	PUNCT
ejpam-834	34	16	z))′	z))′	X
ejpam-834	34	17	−	−	PROPN
ejpam-834	35	1	eiβ	eiβ	NOUN
ejpam-834	35	2	(	(	PUNCT
ejpam-834	35	3	dk	dk	PROPN
ejpam-834	35	4	g(z))′	g(z))′	PROPN
ejpam-834	35	5	�	�	PROPN
ejpam-834	35	6	�	�	PROPN
ejpam-834	35	7	<	<	X
ejpam-834	35	8	δ	δ	PROPN
ejpam-834	35	9	(	(	PUNCT
ejpam-834	35	10	z	z	NOUN
ejpam-834	35	11	∈	∈	PROPN
ejpam-834	35	12	u	u	NOUN
ejpam-834	35	13	)	)	PUNCT
ejpam-834	35	14	(	(	PUNCT
ejpam-834	35	15	5	5	NUM
ejpam-834	35	16	)	)	PUNCT
ejpam-834	35	17	for	for	ADP
ejpam-834	35	18	some	some	DET
ejpam-834	35	19	−π≤	−π≤	PROPN
ejpam-834	35	20	α	α	NOUN
ejpam-834	35	21	,	,	PUNCT
ejpam-834	35	22	β	β	NOUN
ejpam-834	35	23	≤	≤	ADJ
ejpam-834	35	24	π	π	PROPN
ejpam-834	35	25	and	and	CCONJ
ejpam-834	35	26	δ	δ	PROPN
ejpam-834	35	27	>	>	X
ejpam-834	35	28	p	p	X
ejpam-834	35	29	2(1−	2(1−	NUM
ejpam-834	35	30	cos(α−β	cos(α−β	NOUN
ejpam-834	35	31	)	)	PUNCT
ejpam-834	35	32	)	)	PUNCT
ejpam-834	35	33	.	.	PUNCT
ejpam-834	36	1	we	we	PRON
ejpam-834	36	2	denote	denote	VERB
ejpam-834	36	3	this	this	DET
ejpam-834	36	4	neighborhood	neighborhood	NOUN
ejpam-834	36	5	by	by	ADP
ejpam-834	36	6	(	(	PUNCT
ejpam-834	36	7	α	α	X
ejpam-834	36	8	,	,	PUNCT
ejpam-834	36	9	β	β	X
ejpam-834	36	10	,	,	PUNCT
ejpam-834	36	11	δ)−n	δ)−n	PROPN
ejpam-834	36	12	(	(	PUNCT
ejpam-834	36	13	g	g	NOUN
ejpam-834	36	14	)	)	PUNCT
ejpam-834	36	15	.	.	PUNCT
ejpam-834	37	1	now	now	ADV
ejpam-834	37	2	we	we	PRON
ejpam-834	37	3	show	show	VERB
ejpam-834	37	4	some	some	DET
ejpam-834	37	5	results	result	NOUN
ejpam-834	37	6	for	for	ADP
ejpam-834	37	7	functions	function	NOUN
ejpam-834	37	8	belonging	belong	VERB
ejpam-834	37	9	to	to	ADP
ejpam-834	37	10	(	(	PUNCT
ejpam-834	37	11	α	α	X
ejpam-834	37	12	,	,	PUNCT
ejpam-834	37	13	β	β	X
ejpam-834	37	14	,	,	PUNCT
ejpam-834	37	15	δ)−n	δ)−n	PROPN
ejpam-834	37	16	(	(	PUNCT
ejpam-834	37	17	g	g	NOUN
ejpam-834	37	18	)	)	PUNCT
ejpam-834	37	19	.	.	PUNCT
ejpam-834	38	1	2	2	X
ejpam-834	38	2	.	.	X
ejpam-834	38	3	main	main	ADJ
ejpam-834	38	4	results	result	NOUN
ejpam-834	38	5	in	in	ADP
ejpam-834	38	6	our	our	PRON
ejpam-834	38	7	first	first	ADJ
ejpam-834	38	8	theorem	theorem	NOUN
ejpam-834	38	9	,	,	PUNCT
ejpam-834	38	10	we	we	PRON
ejpam-834	38	11	introduce	introduce	VERB
ejpam-834	38	12	a	a	DET
ejpam-834	38	13	sufficient	sufficient	ADJ
ejpam-834	38	14	condition	condition	NOUN
ejpam-834	38	15	to	to	PART
ejpam-834	38	16	be	be	AUX
ejpam-834	38	17	in	in	ADP
ejpam-834	38	18	(	(	PUNCT
ejpam-834	38	19	α	α	X
ejpam-834	38	20	,	,	PUNCT
ejpam-834	38	21	β	β	X
ejpam-834	38	22	,	,	PUNCT
ejpam-834	38	23	δ)−n	δ)−n	PROPN
ejpam-834	38	24	(	(	PUNCT
ejpam-834	38	25	g	g	NOUN
ejpam-834	38	26	)	)	PUNCT
ejpam-834	38	27	.	.	PUNCT
ejpam-834	39	1	theorem	theorem	NOUN
ejpam-834	39	2	1	1	NUM
ejpam-834	39	3	.	.	PUNCT
ejpam-834	40	1	if	if	SCONJ
ejpam-834	40	2	f	f	PROPN
ejpam-834	40	3	(	(	PUNCT
ejpam-834	40	4	z	z	NOUN
ejpam-834	40	5	)	)	PUNCT
ejpam-834	40	6	∈	∈	PROPN
ejpam-834	40	7	t	t	NOUN
ejpam-834	40	8	satisfies	satisfy	VERB
ejpam-834	40	9	∞	∞	PROPN
ejpam-834	40	10	∑	∑	ADV
ejpam-834	40	11	n=2	n=2	PRON
ejpam-834	40	12	nk+1	nk+1	NUM
ejpam-834	40	13	�	�	PROPN
ejpam-834	40	14	�	�	PROPN
ejpam-834	40	15	eiαan−	eiαan−	ADJ
ejpam-834	40	16	eiβ	eiβ	X
ejpam-834	40	17	bn	bn	PROPN
ejpam-834	40	18	�	�	PROPN
ejpam-834	40	19	�	�	PROPN
ejpam-834	40	20	≤	≤	PROPN
ejpam-834	40	21	δ−	δ−	PROPN
ejpam-834	40	22	p	p	NOUN
ejpam-834	40	23	2(1−	2(1−	NUM
ejpam-834	40	24	cos(α−	cos(α−	VERB
ejpam-834	40	25	β	β	X
ejpam-834	40	26	)	)	PUNCT
ejpam-834	40	27	)	)	PUNCT
ejpam-834	40	28	(	(	PUNCT
ejpam-834	40	29	6	6	NUM
ejpam-834	40	30	)	)	PUNCT
ejpam-834	40	31	for	for	ADP
ejpam-834	40	32	some	some	DET
ejpam-834	40	33	−π≤	−π≤	PROPN
ejpam-834	40	34	α	α	NOUN
ejpam-834	40	35	,	,	PUNCT
ejpam-834	40	36	β	β	NOUN
ejpam-834	40	37	≤	≤	ADJ
ejpam-834	40	38	π	π	PROPN
ejpam-834	40	39	and	and	CCONJ
ejpam-834	40	40	δ	δ	PROPN
ejpam-834	40	41	>	>	X
ejpam-834	40	42	p	p	X
ejpam-834	40	43	2(1−	2(1−	NUM
ejpam-834	40	44	cos(α−β	cos(α−β	NOUN
ejpam-834	40	45	)	)	PUNCT
ejpam-834	40	46	)	)	PUNCT
ejpam-834	41	1	then	then	ADV
ejpam-834	41	2	f	f	X
ejpam-834	41	3	(	(	PUNCT
ejpam-834	41	4	z	z	NOUN
ejpam-834	41	5	)	)	PUNCT
ejpam-834	41	6	∈	∈	PROPN
ejpam-834	41	7	(	(	PUNCT
ejpam-834	41	8	α	α	NOUN
ejpam-834	41	9	,	,	PUNCT
ejpam-834	41	10	β	β	X
ejpam-834	41	11	,	,	PUNCT
ejpam-834	41	12	δ)−n	δ)−n	PROPN
ejpam-834	41	13	(	(	PUNCT
ejpam-834	41	14	g	g	NOUN
ejpam-834	41	15	)	)	PUNCT
ejpam-834	41	16	.	.	PUNCT
ejpam-834	42	1	b.	b.	PROPN
ejpam-834	42	2	frasin	frasin	PROPN
ejpam-834	42	3	/	/	SYM
ejpam-834	42	4	eur	eur	PROPN
ejpam-834	42	5	.	.	PUNCT
ejpam-834	43	1	j.	j.	PROPN
ejpam-834	43	2	pure	pure	PROPN
ejpam-834	43	3	appl	appl	PROPN
ejpam-834	43	4	.	.	PROPN
ejpam-834	43	5	math	math	PROPN
ejpam-834	43	6	,	,	PUNCT
ejpam-834	43	7	4	4	NUM
ejpam-834	43	8	(	(	PUNCT
ejpam-834	43	9	2011	2011	NUM
ejpam-834	43	10	)	)	PUNCT
ejpam-834	43	11	,	,	PUNCT
ejpam-834	43	12	14	14	NUM
ejpam-834	43	13	-	-	SYM
ejpam-834	43	14	19	19	NUM
ejpam-834	43	15	16	16	NUM
ejpam-834	43	16	proof	proof	NOUN
ejpam-834	43	17	.	.	PUNCT
ejpam-834	44	1	we	we	PRON
ejpam-834	44	2	observe	observe	VERB
ejpam-834	44	3	that	that	SCONJ
ejpam-834	44	4	�	�	PROPN
ejpam-834	44	5	�	�	PROPN
ejpam-834	44	6	eiα(dk	eiα(dk	PROPN
ejpam-834	44	7	f	f	X
ejpam-834	44	8	(	(	PUNCT
ejpam-834	44	9	z))′	z))′	PROPN
ejpam-834	44	10	−	−	PROPN
ejpam-834	44	11	eiβ(dk	eiβ(dk	X
ejpam-834	44	12	g(z))′	g(z))′	PROPN
ejpam-834	44	13	�	�	PROPN
ejpam-834	44	14	�	�	PROPN
ejpam-834	44	15	=	=	SYM
ejpam-834	44	16	�	�	PROPN
ejpam-834	44	17	�	�	PROPN
ejpam-834	44	18	�	�	PROPN
ejpam-834	44	19	�	�	PROPN
ejpam-834	44	20	�	�	PROPN
ejpam-834	44	21	eiα	eiα	PROPN
ejpam-834	44	22	−	−	PROPN
ejpam-834	45	1	eiβ	eiβ	NOUN
ejpam-834	46	1	−	−	NOUN
ejpam-834	46	2	∞	∞	NUM
ejpam-834	46	3	∑	∑	PUNCT
ejpam-834	46	4	n=2	n=2	PRON
ejpam-834	46	5	nk+1(eiαan	nk+1(eiαan	NOUN
ejpam-834	46	6	−	−	NOUN
ejpam-834	47	1	eiβ	eiβ	X
ejpam-834	47	2	bn)z	bn)z	PROPN
ejpam-834	47	3	n−1	n−1	PROPN
ejpam-834	47	4	�	�	PROPN
ejpam-834	47	5	�	�	PROPN
ejpam-834	47	6	�	�	PROPN
ejpam-834	47	7	�	�	PROPN
ejpam-834	47	8	�	�	PROPN
ejpam-834	47	9	≤	≤	PROPN
ejpam-834	47	10	�	�	PROPN
ejpam-834	47	11	�	�	PROPN
ejpam-834	47	12	eiα	eiα	NOUN
ejpam-834	47	13	−	−	PROPN
ejpam-834	47	14	eiβ	eiβ	X
ejpam-834	47	15	�	�	PROPN
ejpam-834	47	16	�	�	PROPN
ejpam-834	47	17	+	+	NUM
ejpam-834	47	18	∞	∞	NUM
ejpam-834	47	19	∑	∑	ADP
ejpam-834	47	20	n=2	n=2	PRON
ejpam-834	47	21	nk+1	nk+1	NUM
ejpam-834	47	22	�	�	PROPN
ejpam-834	47	23	�	�	PROPN
ejpam-834	47	24	eiαan	eiαan	NOUN
ejpam-834	47	25	−	−	NOUN
ejpam-834	48	1	eiβ	eiβ	PROPN
ejpam-834	48	2	bn	bn	PROPN
ejpam-834	48	3	�	�	PROPN
ejpam-834	48	4	�	�	PROPN
ejpam-834	48	5	|z|n−1	|z|n−1	PROPN
ejpam-834	48	6	≤	≤	PUNCT
ejpam-834	48	7	p	p	NOUN
ejpam-834	48	8	2(1−	2(1−	NUM
ejpam-834	48	9	cos(α−	cos(α−	NOUN
ejpam-834	48	10	β	β	X
ejpam-834	48	11	)	)	PUNCT
ejpam-834	48	12	)	)	PUNCT
ejpam-834	49	1	+	+	CCONJ
ejpam-834	49	2	∞	∞	NUM
ejpam-834	49	3	∑	∑	ADP
ejpam-834	49	4	n=2	n=2	PRON
ejpam-834	49	5	nk+1	nk+1	NUM
ejpam-834	49	6	�	�	PROPN
ejpam-834	49	7	�	�	PROPN
ejpam-834	49	8	eiαan−	eiαan−	ADJ
ejpam-834	49	9	eiβ	eiβ	X
ejpam-834	49	10	bn	bn	PROPN
ejpam-834	49	11	�	�	PROPN
ejpam-834	49	12	�	�	PROPN
ejpam-834	49	13	.	.	PUNCT
ejpam-834	50	1	if	if	SCONJ
ejpam-834	50	2	∞	∞	PROPN
ejpam-834	50	3	∑	∑	ADP
ejpam-834	50	4	n=2	n=2	PRON
ejpam-834	50	5	nk+1	nk+1	NUM
ejpam-834	50	6	�	�	PROPN
ejpam-834	50	7	�	�	PROPN
ejpam-834	50	8	eiαan	eiαan	NOUN
ejpam-834	50	9	−	−	PROPN
ejpam-834	50	10	eiβ	eiβ	PROPN
ejpam-834	50	11	bn	bn	PROPN
ejpam-834	50	12	�	�	PROPN
ejpam-834	50	13	�	�	PROPN
ejpam-834	50	14	≤	≤	PROPN
ejpam-834	50	15	δ−	δ−	PROPN
ejpam-834	50	16	p	p	NOUN
ejpam-834	50	17	2(1−	2(1−	NUM
ejpam-834	50	18	cos(α−β	cos(α−β	NOUN
ejpam-834	50	19	)	)	PUNCT
ejpam-834	50	20	)	)	PUNCT
ejpam-834	50	21	,	,	PUNCT
ejpam-834	50	22	then	then	ADV
ejpam-834	50	23	we	we	PRON
ejpam-834	50	24	have	have	VERB
ejpam-834	50	25	�	�	PROPN
ejpam-834	50	26	�	�	PROPN
ejpam-834	50	27	eiα(dk	eiα(dk	PROPN
ejpam-834	50	28	f	f	X
ejpam-834	50	29	(	(	PUNCT
ejpam-834	50	30	z))′	z))′	PROPN
ejpam-834	50	31	−	−	PROPN
ejpam-834	50	32	eiβ(dk	eiβ(dk	PROPN
ejpam-834	50	33	g(z))′	g(z))′	PROPN
ejpam-834	50	34	�	�	PROPN
ejpam-834	50	35	�	�	PROPN
ejpam-834	50	36	<	<	X
ejpam-834	50	37	δ	δ	PROPN
ejpam-834	50	38	(	(	PUNCT
ejpam-834	50	39	z	z	NOUN
ejpam-834	50	40	∈	∈	PROPN
ejpam-834	50	41	u	u	NOUN
ejpam-834	50	42	)	)	PUNCT
ejpam-834	50	43	.	.	PUNCT
ejpam-834	51	1	this	this	PRON
ejpam-834	51	2	shows	show	VERB
ejpam-834	51	3	that	that	SCONJ
ejpam-834	51	4	f	f	PROPN
ejpam-834	51	5	(	(	PUNCT
ejpam-834	51	6	z	z	NOUN
ejpam-834	51	7	)	)	PUNCT
ejpam-834	51	8	∈	∈	PROPN
ejpam-834	51	9	(	(	PUNCT
ejpam-834	51	10	α	α	NOUN
ejpam-834	51	11	,	,	PUNCT
ejpam-834	51	12	β	β	X
ejpam-834	51	13	,	,	PUNCT
ejpam-834	51	14	δ)−n	δ)−n	PROPN
ejpam-834	51	15	(	(	PUNCT
ejpam-834	51	16	g	g	NOUN
ejpam-834	51	17	)	)	PUNCT
ejpam-834	51	18	.	.	PUNCT
ejpam-834	52	1	corollary	corollary	ADJ
ejpam-834	52	2	1	1	NUM
ejpam-834	52	3	.	.	PUNCT
ejpam-834	53	1	let	let	VERB
ejpam-834	53	2	f	f	PROPN
ejpam-834	53	3	(	(	PUNCT
ejpam-834	53	4	z	z	X
ejpam-834	53	5	)	)	PUNCT
ejpam-834	53	6	∈	∈	PROPN
ejpam-834	53	7	t	t	PROPN
ejpam-834	53	8	.	.	PUNCT
ejpam-834	54	1	then	then	ADV
ejpam-834	54	2	for	for	ADP
ejpam-834	54	3	0	0	NUM
ejpam-834	54	4	<	<	X
ejpam-834	54	5	µ	µ	PRON
ejpam-834	54	6	≤	≤	NUM
ejpam-834	54	7	δ	δ	PROPN
ejpam-834	54	8	,	,	PUNCT
ejpam-834	54	9	we	we	PRON
ejpam-834	54	10	have	have	VERB
ejpam-834	54	11	n	n	PROPN
ejpam-834	54	12	k	k	PROPN
ejpam-834	54	13	µ	µ	X
ejpam-834	54	14	(	(	PUNCT
ejpam-834	54	15	g)⊆	g)⊆	NOUN
ejpam-834	54	16	(	(	PUNCT
ejpam-834	54	17	α	α	PROPN
ejpam-834	54	18	,	,	PUNCT
ejpam-834	54	19	α	α	NOUN
ejpam-834	54	20	,	,	PUNCT
ejpam-834	54	21	δ)−n	δ)−n	PROPN
ejpam-834	54	22	k	k	PROPN
ejpam-834	54	23	δ	δ	PROPN
ejpam-834	54	24	(	(	PUNCT
ejpam-834	54	25	g	g	NOUN
ejpam-834	54	26	)	)	PUNCT
ejpam-834	54	27	.	.	PUNCT
ejpam-834	55	1	proof	proof	NOUN
ejpam-834	55	2	.	.	PUNCT
ejpam-834	56	1	assuming	assume	VERB
ejpam-834	56	2	that	that	SCONJ
ejpam-834	56	3	f	f	PROPN
ejpam-834	56	4	(	(	PUNCT
ejpam-834	56	5	z	z	X
ejpam-834	56	6	)	)	PUNCT
ejpam-834	56	7	∈	∈	PROPN
ejpam-834	56	8	n	n	CCONJ
ejpam-834	56	9	k	k	PROPN
ejpam-834	56	10	µ	µ	X
ejpam-834	56	11	(	(	PUNCT
ejpam-834	56	12	g	g	NOUN
ejpam-834	56	13	)	)	PUNCT
ejpam-834	56	14	.	.	PUNCT
ejpam-834	57	1	we	we	PRON
ejpam-834	57	2	find	find	VERB
ejpam-834	57	3	from	from	ADP
ejpam-834	57	4	the	the	DET
ejpam-834	57	5	definition	definition	NOUN
ejpam-834	57	6	(	(	PUNCT
ejpam-834	57	7	2	2	NUM
ejpam-834	57	8	)	)	PUNCT
ejpam-834	57	9	that	that	SCONJ
ejpam-834	57	10	∞	∞	PROPN
ejpam-834	57	11	∑	∑	ADV
ejpam-834	57	12	n=2	n=2	PRON
ejpam-834	57	13	nk+1	nk+1	NUM
ejpam-834	57	14	�	�	PROPN
ejpam-834	57	15	�	�	PROPN
ejpam-834	57	16	an	an	DET
ejpam-834	57	17	−	−	PROPN
ejpam-834	57	18	bn	bn	INTJ
ejpam-834	57	19	�	�	PROPN
ejpam-834	57	20	�	�	PROPN
ejpam-834	57	21	≤	≤	PROPN
ejpam-834	57	22	µ.	µ.	NOUN
ejpam-834	57	23	now	now	ADV
ejpam-834	57	24	∞	∞	NUM
ejpam-834	57	25	∑	∑	ADV
ejpam-834	57	26	n=2	n=2	PRON
ejpam-834	57	27	nk+1	nk+1	NUM
ejpam-834	57	28	�	�	PROPN
ejpam-834	57	29	�	�	PROPN
ejpam-834	57	30	eiαan−	eiαan−	PROPN
ejpam-834	57	31	eiαbn	eiαbn	PROPN
ejpam-834	57	32	�	�	PROPN
ejpam-834	57	33	�	�	PROPN
ejpam-834	57	34	=	=	SYM
ejpam-834	57	35	∞	∞	PROPN
ejpam-834	57	36	∑	∑	ADP
ejpam-834	57	37	n=2	n=2	PRON
ejpam-834	57	38	nk+1	nk+1	NUM
ejpam-834	57	39	�	�	PROPN
ejpam-834	57	40	�	�	PROPN
ejpam-834	57	41	eiα	eiα	PROPN
ejpam-834	57	42	�	�	PROPN
ejpam-834	57	43	�	�	PROPN
ejpam-834	57	44	�	�	PROPN
ejpam-834	57	45	�	�	PROPN
ejpam-834	57	46	an−	an−	PROPN
ejpam-834	57	47	bn	bn	NUM
ejpam-834	57	48	�	�	PROPN
ejpam-834	57	49	�	�	PROPN
ejpam-834	57	50	=	=	SYM
ejpam-834	57	51	∞	∞	PROPN
ejpam-834	57	52	∑	∑	ADP
ejpam-834	57	53	n=2	n=2	PRON
ejpam-834	57	54	nk+1	nk+1	NUM
ejpam-834	57	55	�	�	PROPN
ejpam-834	57	56	�	�	PROPN
ejpam-834	57	57	an	an	DET
ejpam-834	57	58	−	−	PROPN
ejpam-834	57	59	bn	bn	INTJ
ejpam-834	57	60	�	�	PROPN
ejpam-834	57	61	�	�	PROPN
ejpam-834	57	62	≤	≤	PROPN
ejpam-834	57	63	δ	δ	PROPN
ejpam-834	57	64	.	.	PUNCT
ejpam-834	58	1	thus	thus	ADV
ejpam-834	58	2	by	by	ADP
ejpam-834	58	3	theorem	theorem	NOUN
ejpam-834	58	4	1	1	NUM
ejpam-834	58	5	,	,	PUNCT
ejpam-834	58	6	we	we	PRON
ejpam-834	58	7	have	have	VERB
ejpam-834	58	8	f	f	PROPN
ejpam-834	58	9	(	(	PUNCT
ejpam-834	58	10	z	z	NOUN
ejpam-834	58	11	)	)	PUNCT
ejpam-834	58	12	∈	∈	PROPN
ejpam-834	58	13	(	(	PUNCT
ejpam-834	58	14	α	α	NOUN
ejpam-834	58	15	,	,	PUNCT
ejpam-834	58	16	α	α	NOUN
ejpam-834	58	17	,	,	PUNCT
ejpam-834	58	18	δ)−n	δ)−n	PROPN
ejpam-834	58	19	(	(	PUNCT
ejpam-834	58	20	g	g	NOUN
ejpam-834	58	21	)	)	PUNCT
ejpam-834	58	22	.	.	PUNCT
ejpam-834	59	1	corollary	corollary	ADJ
ejpam-834	59	2	2	2	NUM
ejpam-834	59	3	.	.	PUNCT
ejpam-834	60	1	if	if	SCONJ
ejpam-834	60	2	f	f	PROPN
ejpam-834	60	3	(	(	PUNCT
ejpam-834	60	4	z	z	NOUN
ejpam-834	60	5	)	)	PUNCT
ejpam-834	60	6	∈	∈	PROPN
ejpam-834	60	7	t	t	NOUN
ejpam-834	60	8	satisfies	satisfy	VERB
ejpam-834	60	9	∞	∞	PROPN
ejpam-834	60	10	∑	∑	ADV
ejpam-834	60	11	n=2	n=2	PRON
ejpam-834	60	12	nk+1	nk+1	NUM
ejpam-834	60	13	�	�	PROPN
ejpam-834	60	14	�	�	PROPN
ejpam-834	60	15	�	�	PROPN
ejpam-834	60	16	�	�	PROPN
ejpam-834	60	17	an	an	DET
ejpam-834	60	18	�	�	PROPN
ejpam-834	60	19	�	�	PROPN
ejpam-834	60	20	−	−	PROPN
ejpam-834	60	21	�	�	PROPN
ejpam-834	60	22	�	�	PROPN
ejpam-834	60	23	bn	bn	PROPN
ejpam-834	60	24	�	�	PROPN
ejpam-834	60	25	�	�	PROPN
ejpam-834	60	26	�	�	PROPN
ejpam-834	60	27	�	�	PROPN
ejpam-834	60	28	≤	≤	PROPN
ejpam-834	60	29	δ−	δ−	PROPN
ejpam-834	60	30	p	p	NOUN
ejpam-834	60	31	2(1−	2(1−	NUM
ejpam-834	60	32	cos(α−	cos(α−	VERB
ejpam-834	60	33	β	β	X
ejpam-834	60	34	)	)	PUNCT
ejpam-834	60	35	)	)	PUNCT
ejpam-834	60	36	(	(	PUNCT
ejpam-834	60	37	7	7	X
ejpam-834	60	38	)	)	PUNCT
ejpam-834	60	39	for	for	ADP
ejpam-834	60	40	some	some	DET
ejpam-834	60	41	−π≤	−π≤	PROPN
ejpam-834	60	42	α	α	NOUN
ejpam-834	60	43	,	,	PUNCT
ejpam-834	60	44	β	β	X
ejpam-834	60	45	≤	≤	NUM
ejpam-834	60	46	π	π	PROPN
ejpam-834	60	47	,	,	PUNCT
ejpam-834	60	48	δ	δ	PROPN
ejpam-834	60	49	>	>	X
ejpam-834	60	50	p	p	X
ejpam-834	60	51	2(1−	2(1−	NUM
ejpam-834	60	52	cos(α−	cos(α−	NOUN
ejpam-834	60	53	β	β	X
ejpam-834	60	54	)	)	PUNCT
ejpam-834	60	55	)	)	PUNCT
ejpam-834	60	56	and	and	CCONJ
ejpam-834	60	57	arg	arg	VERB
ejpam-834	60	58	an−	an−	X
ejpam-834	60	59	arg	arg	NOUN
ejpam-834	60	60	bn	bn	NOUN
ejpam-834	60	61	=	=	SYM
ejpam-834	60	62	β	β	X
ejpam-834	60	63	−α	−α	PROPN
ejpam-834	60	64	(	(	PUNCT
ejpam-834	60	65	n=	n=	ADJ
ejpam-834	60	66	2,3,4	2,3,4	NUM
ejpam-834	60	67	,	,	PUNCT
ejpam-834	60	68	...	...	PUNCT
ejpam-834	60	69	)	)	PUNCT
ejpam-834	60	70	,	,	PUNCT
ejpam-834	60	71	then	then	ADV
ejpam-834	60	72	f	f	X
ejpam-834	60	73	(	(	PUNCT
ejpam-834	60	74	z	z	NOUN
ejpam-834	60	75	)	)	PUNCT
ejpam-834	60	76	∈	∈	PROPN
ejpam-834	60	77	(	(	PUNCT
ejpam-834	60	78	α	α	NOUN
ejpam-834	60	79	,	,	PUNCT
ejpam-834	60	80	β	β	X
ejpam-834	60	81	,	,	PUNCT
ejpam-834	60	82	δ)−n	δ)−n	PROPN
ejpam-834	60	83	(	(	PUNCT
ejpam-834	60	84	g	g	NOUN
ejpam-834	60	85	)	)	PUNCT
ejpam-834	60	86	.	.	PUNCT
ejpam-834	61	1	b.	b.	PROPN
ejpam-834	61	2	frasin	frasin	PROPN
ejpam-834	61	3	/	/	SYM
ejpam-834	61	4	eur	eur	PROPN
ejpam-834	61	5	.	.	PUNCT
ejpam-834	62	1	j.	j.	PROPN
ejpam-834	62	2	pure	pure	PROPN
ejpam-834	62	3	appl	appl	PROPN
ejpam-834	62	4	.	.	PROPN
ejpam-834	62	5	math	math	PROPN
ejpam-834	62	6	,	,	PUNCT
ejpam-834	62	7	4	4	NUM
ejpam-834	62	8	(	(	PUNCT
ejpam-834	62	9	2011	2011	NUM
ejpam-834	62	10	)	)	PUNCT
ejpam-834	62	11	,	,	PUNCT
ejpam-834	62	12	14	14	NUM
ejpam-834	62	13	-	-	SYM
ejpam-834	62	14	19	19	NUM
ejpam-834	62	15	17	17	NUM
ejpam-834	62	16	proof	proof	NOUN
ejpam-834	62	17	.	.	PUNCT
ejpam-834	63	1	let	let	VERB
ejpam-834	63	2	arg	arg	VERB
ejpam-834	63	3	an−	an−	PUNCT
ejpam-834	63	4	arg	arg	VERB
ejpam-834	63	5	bn	bn	NOUN
ejpam-834	63	6	=	=	SYM
ejpam-834	63	7	β	β	X
ejpam-834	63	8	−α	−α	NOUN
ejpam-834	63	9	and	and	CCONJ
ejpam-834	63	10	arg	arg	VERB
ejpam-834	63	11	an	an	DET
ejpam-834	63	12	=	=	SYM
ejpam-834	63	13	θ	θ	PROPN
ejpam-834	63	14	n.	n.	NOUN
ejpam-834	63	15	then	then	ADV
ejpam-834	63	16	arg	arg	VERB
ejpam-834	63	17	bn	bn	NOUN
ejpam-834	63	18	=	=	SYM
ejpam-834	63	19	θ	θ	PROPN
ejpam-834	63	20	n+α−β	n+α−β	PROPN
ejpam-834	63	21	.	.	PUNCT
ejpam-834	64	1	therefore	therefore	ADV
ejpam-834	64	2	,	,	PUNCT
ejpam-834	64	3	eiαan	eiαan	NOUN
ejpam-834	64	4	−	−	PROPN
ejpam-834	64	5	eiβ	eiβ	NOUN
ejpam-834	64	6	bn	bn	PROPN
ejpam-834	64	7	=	=	SYM
ejpam-834	64	8	�	�	PROPN
ejpam-834	64	9	�	�	PROPN
ejpam-834	64	10	an	an	DET
ejpam-834	64	11	�	�	PROPN
ejpam-834	64	12	�	�	PROPN
ejpam-834	64	13	ei(α+θ	ei(α+θ	PROPN
ejpam-834	64	14	n	n	CCONJ
ejpam-834	64	15	)	)	PUNCT
ejpam-834	64	16	−	−	PROPN
ejpam-834	64	17	�	�	PROPN
ejpam-834	64	18	�	�	PROPN
ejpam-834	64	19	bn	bn	PROPN
ejpam-834	64	20	�	�	PROPN
ejpam-834	64	21	�	�	PROPN
ejpam-834	64	22	ei(α+θ	ei(α+θ	PROPN
ejpam-834	64	23	n	n	CCONJ
ejpam-834	64	24	)	)	PUNCT
ejpam-834	64	25	,	,	PUNCT
ejpam-834	64	26	which	which	PRON
ejpam-834	64	27	implies	imply	VERB
ejpam-834	64	28	�	�	PROPN
ejpam-834	64	29	�	�	PROPN
ejpam-834	64	30	eiαan−	eiαan−	ADJ
ejpam-834	64	31	eiβ	eiβ	X
ejpam-834	64	32	bn	bn	PROPN
ejpam-834	64	33	�	�	PROPN
ejpam-834	64	34	�	�	PROPN
ejpam-834	64	35	=	=	SYM
ejpam-834	64	36	�	�	PROPN
ejpam-834	64	37	�	�	PROPN
ejpam-834	64	38	�	�	PROPN
ejpam-834	64	39	�	�	PROPN
ejpam-834	64	40	an	an	DET
ejpam-834	64	41	�	�	PROPN
ejpam-834	64	42	�	�	PROPN
ejpam-834	64	43	−	−	PROPN
ejpam-834	64	44	�	�	PROPN
ejpam-834	64	45	�	�	PROPN
ejpam-834	64	46	bn	bn	PROPN
ejpam-834	64	47	�	�	PROPN
ejpam-834	64	48	�	�	PROPN
ejpam-834	64	49	�	�	PROPN
ejpam-834	64	50	�	�	PROPN
ejpam-834	64	51	.	.	PUNCT
ejpam-834	65	1	(	(	PUNCT
ejpam-834	65	2	8)	8)	NUM
ejpam-834	65	3	from	from	ADP
ejpam-834	65	4	the	the	DET
ejpam-834	65	5	hypotheses	hypothesis	NOUN
ejpam-834	65	6	(	(	PUNCT
ejpam-834	65	7	7	7	NUM
ejpam-834	65	8	)	)	PUNCT
ejpam-834	65	9	and	and	CCONJ
ejpam-834	65	10	(	(	PUNCT
ejpam-834	65	11	8)	8)	NUM
ejpam-834	65	12	,	,	PUNCT
ejpam-834	65	13	we	we	PRON
ejpam-834	65	14	get	get	VERB
ejpam-834	65	15	(	(	PUNCT
ejpam-834	65	16	6	6	NUM
ejpam-834	65	17	)	)	PUNCT
ejpam-834	65	18	.	.	PUNCT
ejpam-834	66	1	thus	thus	ADV
ejpam-834	66	2	by	by	ADP
ejpam-834	66	3	theorem	theorem	NOUN
ejpam-834	66	4	1	1	NUM
ejpam-834	66	5	,	,	PUNCT
ejpam-834	66	6	it	it	PRON
ejpam-834	66	7	follows	follow	VERB
ejpam-834	66	8	that	that	SCONJ
ejpam-834	66	9	f	f	PROPN
ejpam-834	66	10	(	(	PUNCT
ejpam-834	66	11	z	z	X
ejpam-834	66	12	)	)	PUNCT
ejpam-834	66	13	∈	∈	PROPN
ejpam-834	66	14	(	(	PUNCT
ejpam-834	66	15	α	α	NOUN
ejpam-834	66	16	,	,	PUNCT
ejpam-834	66	17	β	β	X
ejpam-834	66	18	,	,	PUNCT
ejpam-834	66	19	δ)−n	δ)−n	PROPN
ejpam-834	66	20	(	(	PUNCT
ejpam-834	66	21	g	g	NOUN
ejpam-834	66	22	)	)	PUNCT
ejpam-834	66	23	.	.	PUNCT
ejpam-834	67	1	furthermore	furthermore	ADV
ejpam-834	67	2	,	,	PUNCT
ejpam-834	67	3	from	from	ADP
ejpam-834	67	4	theorem	theorem	NOUN
ejpam-834	67	5	1	1	NUM
ejpam-834	67	6	,	,	PUNCT
ejpam-834	67	7	we	we	PRON
ejpam-834	67	8	easily	easily	ADV
ejpam-834	67	9	get	get	VERB
ejpam-834	67	10	corollary	corollary	ADJ
ejpam-834	67	11	3	3	NUM
ejpam-834	67	12	.	.	PUNCT
ejpam-834	68	1	if	if	SCONJ
ejpam-834	68	2	f	f	PROPN
ejpam-834	68	3	(	(	PUNCT
ejpam-834	68	4	z	z	NOUN
ejpam-834	68	5	)	)	PUNCT
ejpam-834	68	6	∈	∈	PROPN
ejpam-834	68	7	t	t	NOUN
ejpam-834	68	8	satisfies	satisfy	VERB
ejpam-834	68	9	∞	∞	PROPN
ejpam-834	68	10	∑	∑	PROPN
ejpam-834	68	11	n=2	n=2	SYM
ejpam-834	68	12	nk+1	nk+1	ADJ
ejpam-834	68	13	(	(	PUNCT
ejpam-834	68	14	�	�	PROPN
ejpam-834	68	15	�	�	PROPN
ejpam-834	68	16	an	an	DET
ejpam-834	68	17	�	�	PROPN
ejpam-834	68	18	�	�	PROPN
ejpam-834	68	19	+	+	PROPN
ejpam-834	68	20	�	�	PROPN
ejpam-834	68	21	�	�	PROPN
ejpam-834	68	22	bn	bn	PROPN
ejpam-834	68	23	�	�	PROPN
ejpam-834	68	24	�	�	PROPN
ejpam-834	68	25	)	)	PUNCT
ejpam-834	68	26	≤	≤	NUM
ejpam-834	69	1	δ−	δ−	PROPN
ejpam-834	69	2	p	p	NOUN
ejpam-834	69	3	2(1−	2(1−	NUM
ejpam-834	69	4	cos(α−	cos(α−	VERB
ejpam-834	69	5	β	β	X
ejpam-834	69	6	)	)	PUNCT
ejpam-834	69	7	)	)	PUNCT
ejpam-834	69	8	(	(	PUNCT
ejpam-834	69	9	9	9	X
ejpam-834	69	10	)	)	PUNCT
ejpam-834	69	11	for	for	ADP
ejpam-834	69	12	some	some	DET
ejpam-834	69	13	−π≤	−π≤	PROPN
ejpam-834	69	14	α	α	NOUN
ejpam-834	69	15	,	,	PUNCT
ejpam-834	69	16	β	β	NOUN
ejpam-834	69	17	≤	≤	ADJ
ejpam-834	69	18	π	π	PROPN
ejpam-834	69	19	and	and	CCONJ
ejpam-834	69	20	δ	δ	PROPN
ejpam-834	69	21	>	>	X
ejpam-834	69	22	p	p	X
ejpam-834	69	23	2(1−	2(1−	NUM
ejpam-834	69	24	cos(α−β	cos(α−β	NOUN
ejpam-834	69	25	)	)	PUNCT
ejpam-834	70	1	then	then	ADV
ejpam-834	70	2	f	f	X
ejpam-834	70	3	(	(	PUNCT
ejpam-834	70	4	z	z	NOUN
ejpam-834	70	5	)	)	PUNCT
ejpam-834	70	6	∈	∈	PROPN
ejpam-834	70	7	(	(	PUNCT
ejpam-834	70	8	α	α	NOUN
ejpam-834	70	9	,	,	PUNCT
ejpam-834	70	10	β	β	X
ejpam-834	70	11	,	,	PUNCT
ejpam-834	70	12	δ)−n	δ)−n	PROPN
ejpam-834	70	13	(	(	PUNCT
ejpam-834	70	14	g	g	NOUN
ejpam-834	70	15	)	)	PUNCT
ejpam-834	70	16	.	.	PUNCT
ejpam-834	71	1	next	next	ADV
ejpam-834	71	2	,	,	PUNCT
ejpam-834	71	3	we	we	PRON
ejpam-834	71	4	prove	prove	VERB
ejpam-834	71	5	theorem	theorem	ADJ
ejpam-834	71	6	2	2	X
ejpam-834	71	7	.	.	PUNCT
ejpam-834	72	1	if	if	SCONJ
ejpam-834	72	2	f	f	PROPN
ejpam-834	72	3	(	(	PUNCT
ejpam-834	72	4	z	z	NOUN
ejpam-834	72	5	)	)	PUNCT
ejpam-834	72	6	∈	∈	PROPN
ejpam-834	72	7	(	(	PUNCT
ejpam-834	72	8	α	α	NOUN
ejpam-834	72	9	,	,	PUNCT
ejpam-834	72	10	β	β	X
ejpam-834	72	11	,	,	PUNCT
ejpam-834	72	12	δ)−n	δ)−n	PROPN
ejpam-834	72	13	(	(	PUNCT
ejpam-834	72	14	g	g	NOUN
ejpam-834	72	15	)	)	PUNCT
ejpam-834	72	16	and	and	CCONJ
ejpam-834	72	17	arg(eiαan	arg(eiαan	NOUN
ejpam-834	72	18	−	−	PROPN
ejpam-834	72	19	eiβ	eiβ	NOUN
ejpam-834	72	20	bn	bn	NOUN
ejpam-834	72	21	)	)	PUNCT
ejpam-834	72	22	=	=	SYM
ejpam-834	73	1	(	(	PUNCT
ejpam-834	73	2	n−	n−	NOUN
ejpam-834	73	3	1)ϕ	1)ϕ	NUM
ejpam-834	73	4	(	(	PUNCT
ejpam-834	73	5	n	n	NOUN
ejpam-834	73	6	=	=	SYM
ejpam-834	73	7	2,3,4	2,3,4	NUM
ejpam-834	73	8	,	,	PUNCT
ejpam-834	73	9	.	.	PUNCT
ejpam-834	73	10	.	.	PUNCT
ejpam-834	73	11	.	.	PUNCT
ejpam-834	73	12	)	)	PUNCT
ejpam-834	74	1	,	,	PUNCT
ejpam-834	74	2	then	then	ADV
ejpam-834	74	3	∞	∞	NUM
ejpam-834	74	4	∑	∑	ADP
ejpam-834	74	5	n=2	n=2	PRON
ejpam-834	74	6	nk+1	nk+1	NUM
ejpam-834	74	7	�	�	PROPN
ejpam-834	74	8	�	�	PROPN
ejpam-834	74	9	eiαan−	eiαan−	ADJ
ejpam-834	74	10	eiβ	eiβ	X
ejpam-834	74	11	bn	bn	PROPN
ejpam-834	74	12	�	�	PROPN
ejpam-834	74	13	�	�	PROPN
ejpam-834	74	14	>	>	X
ejpam-834	74	15	δ+	δ+	PUNCT
ejpam-834	74	16	cosα−	cosα−	NOUN
ejpam-834	74	17	cosβ	cosβ	NOUN
ejpam-834	74	18	.	.	PUNCT
ejpam-834	75	1	(	(	PUNCT
ejpam-834	75	2	10	10	NUM
ejpam-834	75	3	)	)	PUNCT
ejpam-834	75	4	proof	proof	NOUN
ejpam-834	75	5	.	.	PUNCT
ejpam-834	76	1	let	let	VERB
ejpam-834	76	2	f	f	PROPN
ejpam-834	76	3	(	(	PUNCT
ejpam-834	76	4	z	z	NOUN
ejpam-834	76	5	)	)	PUNCT
ejpam-834	76	6	∈	∈	PROPN
ejpam-834	76	7	(	(	PUNCT
ejpam-834	76	8	α	α	NOUN
ejpam-834	76	9	,	,	PUNCT
ejpam-834	76	10	β	β	X
ejpam-834	76	11	,	,	PUNCT
ejpam-834	76	12	δ)−n	δ)−n	PROPN
ejpam-834	76	13	(	(	PUNCT
ejpam-834	76	14	g	g	NOUN
ejpam-834	76	15	)	)	PUNCT
ejpam-834	76	16	and	and	CCONJ
ejpam-834	76	17	arg	arg	NOUN
ejpam-834	76	18	z	z	NOUN
ejpam-834	76	19	=	=	PUNCT
ejpam-834	76	20	−ϕ.	−ϕ.	ADV
ejpam-834	76	21	then	then	ADV
ejpam-834	76	22	for	for	ADP
ejpam-834	76	23	all	all	DET
ejpam-834	76	24	z	z	NOUN
ejpam-834	76	25	∈	∈	PROPN
ejpam-834	76	26	u	u	NOUN
ejpam-834	76	27	,	,	PUNCT
ejpam-834	76	28	we	we	PRON
ejpam-834	76	29	have	have	VERB
ejpam-834	76	30	�	�	PROPN
ejpam-834	76	31	�	�	PROPN
ejpam-834	76	32	eiα(dk	eiα(dk	PROPN
ejpam-834	76	33	f	f	X
ejpam-834	76	34	(	(	PUNCT
ejpam-834	76	35	z))′−	z))′−	X
ejpam-834	76	36	eiβ	eiβ	NOUN
ejpam-834	76	37	(	(	PUNCT
ejpam-834	76	38	dk	dk	PROPN
ejpam-834	76	39	g(z))′	g(z))′	PROPN
ejpam-834	76	40	�	�	PROPN
ejpam-834	76	41	�	�	PROPN
ejpam-834	76	42	=	=	SYM
ejpam-834	76	43	�	�	PROPN
ejpam-834	76	44	�	�	PROPN
ejpam-834	76	45	�	�	PROPN
ejpam-834	76	46	�	�	PROPN
ejpam-834	76	47	�	�	PROPN
ejpam-834	76	48	(	(	PUNCT
ejpam-834	76	49	eiα−	eiα−	NOUN
ejpam-834	76	50	eiβ	eiβ	NOUN
ejpam-834	76	51	)	)	PUNCT
ejpam-834	77	1	−	−	PROPN
ejpam-834	77	2	∞	∞	PROPN
ejpam-834	77	3	∑	∑	PUNCT
ejpam-834	77	4	n=2	n=2	PRON
ejpam-834	77	5	nk+1(eiαan	nk+1(eiαan	NOUN
ejpam-834	77	6	−	−	NOUN
ejpam-834	78	1	eiβ	eiβ	X
ejpam-834	79	1	bn)z	bn)z	PROPN
ejpam-834	79	2	n−1	n−1	PROPN
ejpam-834	79	3	�	�	PROPN
ejpam-834	79	4	�	�	PROPN
ejpam-834	79	5	�	�	PROPN
ejpam-834	79	6	�	�	PROPN
ejpam-834	79	7	�	�	PROPN
ejpam-834	79	8	=	=	SYM
ejpam-834	79	9	�	�	PROPN
ejpam-834	79	10	�	�	PROPN
ejpam-834	79	11	�	�	PROPN
ejpam-834	79	12	�	�	PROPN
ejpam-834	79	13	�	�	PROPN
ejpam-834	79	14	(	(	PUNCT
ejpam-834	79	15	eiα−	eiα−	NOUN
ejpam-834	79	16	eiβ	eiβ	NOUN
ejpam-834	79	17	)	)	PUNCT
ejpam-834	79	18	−	−	PROPN
ejpam-834	80	1	∞	∞	PROPN
ejpam-834	80	2	∑	∑	PROPN
ejpam-834	80	3	n=2	n=2	PRON
ejpam-834	80	4	nk+1	nk+1	NUM
ejpam-834	80	5	�	�	PROPN
ejpam-834	80	6	�	�	PROPN
ejpam-834	80	7	eiαan−	eiαan−	ADJ
ejpam-834	80	8	eiβ	eiβ	X
ejpam-834	80	9	bn	bn	PROPN
ejpam-834	80	10	�	�	PROPN
ejpam-834	80	11	�	�	PROPN
ejpam-834	80	12	ei(n−1)ϕ	ei(n−1)ϕ	PROPN
ejpam-834	80	13	|z|n−1	|z|n−1	NUM
ejpam-834	80	14	e−i(n−1)ϕ	e−i(n−1)ϕ	NUM
ejpam-834	80	15	�	�	PROPN
ejpam-834	80	16	�	�	PROPN
ejpam-834	80	17	�	�	PROPN
ejpam-834	80	18	�	�	PROPN
ejpam-834	80	19	�	�	PROPN
ejpam-834	80	20	=	=	SYM
ejpam-834	80	21	�	�	PROPN
ejpam-834	80	22	�	�	PROPN
ejpam-834	80	23	�	�	PROPN
ejpam-834	80	24	�	�	PROPN
ejpam-834	80	25	�	�	PROPN
ejpam-834	80	26	(	(	PUNCT
ejpam-834	80	27	eiα−	eiα−	NOUN
ejpam-834	80	28	eiβ	eiβ	NOUN
ejpam-834	80	29	)	)	PUNCT
ejpam-834	80	30	−	−	PROPN
ejpam-834	81	1	∞	∞	PROPN
ejpam-834	81	2	∑	∑	PROPN
ejpam-834	81	3	n=2	n=2	PRON
ejpam-834	81	4	nk+1	nk+1	NUM
ejpam-834	81	5	�	�	PROPN
ejpam-834	81	6	�	�	PROPN
ejpam-834	81	7	eiαan−	eiαan−	ADJ
ejpam-834	81	8	eiβ	eiβ	X
ejpam-834	81	9	bn	bn	PROPN
ejpam-834	81	10	�	�	PROPN
ejpam-834	81	11	�	�	PROPN
ejpam-834	81	12	|z|n−1	|z|n−1	NUM
ejpam-834	81	13	�	�	PROPN
ejpam-834	81	14	�	�	PROPN
ejpam-834	81	15	�	�	PROPN
ejpam-834	81	16	�	�	PROPN
ejpam-834	81	17	�	�	PROPN
ejpam-834	81	18	=	=	PUNCT
ejpam-834	82	1	[	[	X
ejpam-834	82	2	(	(	PUNCT
ejpam-834	82	3	cosα−	cosα−	NOUN
ejpam-834	82	4	cosβ)−	cosβ)−	NOUN
ejpam-834	82	5	∞	∞	PROPN
ejpam-834	82	6	∑	∑	PUNCT
ejpam-834	82	7	n=2	n=2	PRON
ejpam-834	82	8	nk+1	nk+1	NUM
ejpam-834	82	9	�	�	PROPN
ejpam-834	82	10	�	�	PROPN
ejpam-834	82	11	eiαan−	eiαan−	ADJ
ejpam-834	82	12	eiβ	eiβ	X
ejpam-834	82	13	bn	bn	PROPN
ejpam-834	82	14	�	�	PROPN
ejpam-834	82	15	�	�	PROPN
ejpam-834	82	16	|z|n−1]2	|z|n−1]2	NOUN
ejpam-834	82	17	+	+	CCONJ
ejpam-834	82	18	(	(	PUNCT
ejpam-834	82	19	sinα−	sinα−	VERB
ejpam-834	82	20	sinβ)2	sinβ)2	PROPN
ejpam-834	82	21	�	�	PROPN
ejpam-834	82	22	1/2	1/2	NUM
ejpam-834	82	23	<	<	X
ejpam-834	82	24	δ	δ	PROPN
ejpam-834	82	25	for	for	ADP
ejpam-834	82	26	z	z	PROPN
ejpam-834	82	27	∈	∈	PROPN
ejpam-834	82	28	u	u	NOUN
ejpam-834	82	29	.	.	PUNCT
ejpam-834	83	1	this	this	PRON
ejpam-834	83	2	implies	imply	VERB
ejpam-834	83	3	that	that	SCONJ
ejpam-834	83	4	(	(	PUNCT
ejpam-834	83	5	cosα−	cosα−	NOUN
ejpam-834	83	6	cosβ)−	cosβ)−	NOUN
ejpam-834	83	7	∞	∞	PROPN
ejpam-834	83	8	∑	∑	PUNCT
ejpam-834	83	9	n=2	n=2	PRON
ejpam-834	83	10	nk+1	nk+1	NUM
ejpam-834	83	11	�	�	PROPN
ejpam-834	83	12	�	�	PROPN
ejpam-834	83	13	eiαan	eiαan	NOUN
ejpam-834	83	14	−	−	NOUN
ejpam-834	83	15	eiβ	eiβ	PROPN
ejpam-834	83	16	bn	bn	PROPN
ejpam-834	83	17	�	�	PROPN
ejpam-834	83	18	�	�	PROPN
ejpam-834	83	19	|z|n−1	|z|n−1	PROPN
ejpam-834	83	20	<	<	X
ejpam-834	83	21	δ	δ	PROPN
ejpam-834	83	22	references	reference	VERB
ejpam-834	83	23	18	18	NUM
ejpam-834	83	24	for	for	ADP
ejpam-834	83	25	z	z	PROPN
ejpam-834	83	26	∈	∈	PROPN
ejpam-834	83	27	u	u	PROPN
ejpam-834	83	28	.	.	PUNCT
ejpam-834	84	1	letting	let	VERB
ejpam-834	84	2	|z|	|z|	NOUN
ejpam-834	84	3	→	→	SYM
ejpam-834	84	4	1−	1−	NUM
ejpam-834	84	5	,	,	PUNCT
ejpam-834	84	6	we	we	PRON
ejpam-834	84	7	have	have	VERB
ejpam-834	84	8	∞	∞	PROPN
ejpam-834	84	9	∑	∑	ADV
ejpam-834	84	10	n=2	n=2	PRON
ejpam-834	84	11	nk+1	nk+1	NUM
ejpam-834	84	12	�	�	PROPN
ejpam-834	84	13	�	�	PROPN
ejpam-834	84	14	eiαan−	eiαan−	ADJ
ejpam-834	84	15	eiβ	eiβ	X
ejpam-834	84	16	bn	bn	PROPN
ejpam-834	84	17	�	�	PROPN
ejpam-834	84	18	�	�	PROPN
ejpam-834	84	19	>	>	X
ejpam-834	84	20	δ+	δ+	PUNCT
ejpam-834	84	21	cosα−	cosα−	NOUN
ejpam-834	84	22	cosβ	cosβ	NOUN
ejpam-834	84	23	.	.	PUNCT
ejpam-834	85	1	finally	finally	ADV
ejpam-834	85	2	,	,	PUNCT
ejpam-834	85	3	we	we	PRON
ejpam-834	85	4	prove	prove	VERB
ejpam-834	85	5	theorem	theorem	ADJ
ejpam-834	85	6	3	3	X
ejpam-834	85	7	.	.	PUNCT
ejpam-834	86	1	if	if	SCONJ
ejpam-834	86	2	f	f	PROPN
ejpam-834	86	3	(	(	PUNCT
ejpam-834	86	4	z	z	NOUN
ejpam-834	86	5	)	)	PUNCT
ejpam-834	86	6	∈	∈	PROPN
ejpam-834	86	7	t	t	NOUN
ejpam-834	86	8	satisfies	satisfy	VERB
ejpam-834	86	9	∞	∞	PROPN
ejpam-834	86	10	∑	∑	ADV
ejpam-834	86	11	n=2	n=2	PRON
ejpam-834	86	12	nk+1	nk+1	NUM
ejpam-834	86	13	�	�	PROPN
ejpam-834	86	14	�	�	PROPN
ejpam-834	86	15	eiαan−	eiαan−	ADJ
ejpam-834	86	16	eiβ	eiβ	X
ejpam-834	86	17	bn	bn	PROPN
ejpam-834	86	18	�	�	PROPN
ejpam-834	86	19	�	�	PROPN
ejpam-834	86	20	<	<	X
ejpam-834	86	21	µ−	µ−	PROPN
ejpam-834	86	22	p	p	NOUN
ejpam-834	86	23	2(1−	2(1−	NUM
ejpam-834	86	24	cos(α−β	cos(α−β	NOUN
ejpam-834	86	25	)	)	PUNCT
ejpam-834	86	26	)	)	PUNCT
ejpam-834	87	1	(	(	PUNCT
ejpam-834	87	2	11	11	NUM
ejpam-834	87	3	)	)	PUNCT
ejpam-834	87	4	for	for	ADP
ejpam-834	87	5	some	some	DET
ejpam-834	87	6	−π≤	−π≤	PROPN
ejpam-834	87	7	α	α	NOUN
ejpam-834	87	8	,	,	PUNCT
ejpam-834	87	9	β	β	NOUN
ejpam-834	87	10	≤	≤	ADJ
ejpam-834	87	11	π	π	PROPN
ejpam-834	87	12	and	and	CCONJ
ejpam-834	87	13	µ	µ	X
ejpam-834	87	14	>	>	X
ejpam-834	87	15	p	p	X
ejpam-834	87	16	2(1−	2(1−	NUM
ejpam-834	87	17	cos(α−	cos(α−	NOUN
ejpam-834	87	18	β	β	X
ejpam-834	87	19	)	)	PUNCT
ejpam-834	87	20	)	)	PUNCT
ejpam-834	87	21	,	,	PUNCT
ejpam-834	87	22	then	then	ADV
ejpam-834	87	23	re	re	VERB
ejpam-834	87	24	�	�	PROPN
ejpam-834	87	25	eiα(dk	eiα(dk	X
ejpam-834	87	26	f	f	X
ejpam-834	87	27	(	(	PUNCT
ejpam-834	87	28	z))′	z))′	X
ejpam-834	87	29	eiβ	eiβ	X
ejpam-834	87	30	(	(	PUNCT
ejpam-834	88	1	dk	dk	PROPN
ejpam-834	88	2	g(z))′	g(z))′	PROPN
ejpam-834	88	3	�	�	PROPN
ejpam-834	88	4	>	>	X
ejpam-834	88	5	0	0	PUNCT
ejpam-834	88	6	(	(	PUNCT
ejpam-834	88	7	12	12	NUM
ejpam-834	88	8	)	)	PUNCT
ejpam-834	88	9	where	where	SCONJ
ejpam-834	88	10	g(z	g(z	ADJ
ejpam-834	88	11	)	)	PUNCT
ejpam-834	88	12	∈	∈	PROPN
ejpam-834	88	13	n	n	CCONJ
ejpam-834	88	14	k	k	PROPN
ejpam-834	88	15	1−µ(e	1−µ(e	NUM
ejpam-834	88	16	)	)	PUNCT
ejpam-834	88	17	.	.	PUNCT
ejpam-834	89	1	proof	proof	NOUN
ejpam-834	89	2	.	.	PUNCT
ejpam-834	90	1	note	note	VERB
ejpam-834	90	2	that	that	SCONJ
ejpam-834	90	3	�	�	PROPN
ejpam-834	90	4	�	�	PROPN
ejpam-834	90	5	�	�	PROPN
ejpam-834	90	6	�	�	PROPN
ejpam-834	90	7	�	�	PROPN
ejpam-834	90	8	eiα(dk	eiα(dk	X
ejpam-834	90	9	f	f	X
ejpam-834	90	10	(	(	PUNCT
ejpam-834	90	11	z))′	z))′	X
ejpam-834	90	12	eiβ(dk	eiβ(dk	X
ejpam-834	90	13	g(z))′	g(z))′	PROPN
ejpam-834	90	14	−	−	PROPN
ejpam-834	90	15	1	1	NUM
ejpam-834	90	16	�	�	PROPN
ejpam-834	90	17	�	�	PROPN
ejpam-834	90	18	�	�	PROPN
ejpam-834	90	19	�	�	PROPN
ejpam-834	90	20	�	�	PROPN
ejpam-834	90	21	≤	≤	PROPN
ejpam-834	90	22	p	p	PRON
ejpam-834	90	23	2(1−	2(1−	NUM
ejpam-834	90	24	cos(α−	cos(α−	NOUN
ejpam-834	90	25	β	β	X
ejpam-834	90	26	)	)	PUNCT
ejpam-834	90	27	)	)	PUNCT
ejpam-834	91	1	+	+	CCONJ
ejpam-834	91	2	∞	∞	NUM
ejpam-834	91	3	∑	∑	ADP
ejpam-834	91	4	n=2	n=2	PRON
ejpam-834	91	5	nk+1	nk+1	NUM
ejpam-834	91	6	�	�	PROPN
ejpam-834	91	7	�	�	PROPN
ejpam-834	91	8	eiαan	eiαan	NOUN
ejpam-834	91	9	−	−	NOUN
ejpam-834	91	10	eiβ	eiβ	PROPN
ejpam-834	91	11	bn	bn	PROPN
ejpam-834	91	12	�	�	PROPN
ejpam-834	91	13	�	�	PROPN
ejpam-834	91	14	1−	1−	NUM
ejpam-834	91	15	∞	∞	NUM
ejpam-834	91	16	∑	∑	PUNCT
ejpam-834	91	17	n=2	n=2	PRON
ejpam-834	91	18	nk+1bn	nk+1bn	VERB
ejpam-834	91	19	≤	≤	NOUN
ejpam-834	91	20	p	p	PRON
ejpam-834	91	21	2(1−	2(1−	NUM
ejpam-834	91	22	cos(α−	cos(α−	X
ejpam-834	91	23	β	β	X
ejpam-834	91	24	)	)	PUNCT
ejpam-834	91	25	)	)	PUNCT
ejpam-834	92	1	+	+	CCONJ
ejpam-834	92	2	∞	∞	NUM
ejpam-834	92	3	∑	∑	ADP
ejpam-834	92	4	n=2	n=2	PRON
ejpam-834	92	5	nk+1	nk+1	NUM
ejpam-834	92	6	�	�	PROPN
ejpam-834	92	7	�	�	PROPN
ejpam-834	92	8	eiαan	eiαan	NOUN
ejpam-834	92	9	−	−	NOUN
ejpam-834	92	10	eiβ	eiβ	PROPN
ejpam-834	92	11	bn	bn	PROPN
ejpam-834	92	12	�	�	PROPN
ejpam-834	92	13	�	�	PROPN
ejpam-834	92	14	µ	µ	PROPN
ejpam-834	92	15	.	.	PUNCT
ejpam-834	93	1	hence	hence	ADV
ejpam-834	93	2	by	by	ADP
ejpam-834	93	3	the	the	DET
ejpam-834	93	4	condition	condition	NOUN
ejpam-834	93	5	(	(	PUNCT
ejpam-834	93	6	11	11	NUM
ejpam-834	93	7	)	)	PUNCT
ejpam-834	93	8	,	,	PUNCT
ejpam-834	93	9	we	we	PRON
ejpam-834	93	10	have	have	VERB
ejpam-834	93	11	�	�	PROPN
ejpam-834	93	12	�	�	PROPN
ejpam-834	93	13	�	�	PROPN
ejpam-834	93	14	�	�	PROPN
ejpam-834	93	15	�	�	PROPN
ejpam-834	93	16	eiα(dk	eiα(dk	X
ejpam-834	93	17	f	f	X
ejpam-834	93	18	(	(	PUNCT
ejpam-834	93	19	z))′	z))′	X
ejpam-834	93	20	eiβ	eiβ	X
ejpam-834	94	1	(	(	PUNCT
ejpam-834	94	2	dk	dk	PROPN
ejpam-834	94	3	g(z))′	g(z))′	NOUN
ejpam-834	94	4	−	−	PROPN
ejpam-834	94	5	1	1	NUM
ejpam-834	94	6	�	�	PROPN
ejpam-834	94	7	�	�	PROPN
ejpam-834	94	8	�	�	PROPN
ejpam-834	94	9	�	�	PROPN
ejpam-834	94	10	�	�	PROPN
ejpam-834	94	11	<	<	X
ejpam-834	94	12	1	1	NUM
ejpam-834	94	13	.	.	PUNCT
ejpam-834	95	1	this	this	PRON
ejpam-834	95	2	evidently	evidently	ADV
ejpam-834	95	3	proves	prove	VERB
ejpam-834	95	4	theorem	theorem	ADJ
ejpam-834	95	5	3	3	NUM
ejpam-834	95	6	.	.	PUNCT
ejpam-834	95	7	references	reference	NOUN
ejpam-834	95	8	[	[	X
ejpam-834	95	9	1	1	NUM
ejpam-834	95	10	]	]	X
ejpam-834	95	11	o.p	o.p	PROPN
ejpam-834	95	12	.	.	PROPN
ejpam-834	95	13	ahuja	ahuja	PROPN
ejpam-834	95	14	and	and	CCONJ
ejpam-834	95	15	m.	m.	PROPN
ejpam-834	95	16	nunokawa	nunokawa	PROPN
ejpam-834	95	17	,	,	PUNCT
ejpam-834	95	18	neighborhoods	neighborhood	NOUN
ejpam-834	95	19	of	of	ADP
ejpam-834	95	20	analytic	analytic	ADJ
ejpam-834	95	21	functions	function	NOUN
ejpam-834	95	22	defined	define	VERB
ejpam-834	95	23	by	by	ADP
ejpam-834	95	24	ruscheweyh	ruscheweyh	NOUN
ejpam-834	95	25	derivatives	derivative	NOUN
ejpam-834	95	26	,	,	PUNCT
ejpam-834	95	27	math	math	NOUN
ejpam-834	95	28	.	.	PUNCT
ejpam-834	96	1	japonica	japonica	PROPN
ejpam-834	96	2	51	51	NUM
ejpam-834	96	3	.	.	PUNCT
ejpam-834	97	1	no.3	no.3	VERB
ejpam-834	97	2	,	,	PUNCT
ejpam-834	97	3	487	487	NUM
ejpam-834	97	4	-	-	SYM
ejpam-834	97	5	492	492	NUM
ejpam-834	97	6	.	.	PUNCT
ejpam-834	97	7	2000	2000	NUM
ejpam-834	97	8	.	.	PUNCT
ejpam-834	98	1	[	[	X
ejpam-834	98	2	2	2	X
ejpam-834	98	3	]	]	PUNCT
ejpam-834	98	4	o.	o.	PROPN
ejpam-834	98	5	altintaş	altintaş	PROPN
ejpam-834	98	6	,	,	PUNCT
ejpam-834	98	7	neighborhoods	neighborhood	NOUN
ejpam-834	98	8	of	of	ADP
ejpam-834	98	9	certain	certain	ADJ
ejpam-834	98	10	p	p	NOUN
ejpam-834	98	11	-	-	PUNCT
ejpam-834	98	12	valently	valently	ADV
ejpam-834	98	13	analytic	analytic	ADJ
ejpam-834	98	14	functions	function	NOUN
ejpam-834	98	15	with	with	ADP
ejpam-834	98	16	negative	negative	ADJ
ejpam-834	98	17	coefficients	coefficient	NOUN
ejpam-834	98	18	,	,	PUNCT
ejpam-834	98	19	appl	appl	PROPN
ejpam-834	98	20	.	.	PROPN
ejpam-834	98	21	math	math	PROPN
ejpam-834	98	22	.	.	PUNCT
ejpam-834	99	1	comp	comp	PROPN
ejpam-834	99	2	.	.	PUNCT
ejpam-834	99	3	,	,	PUNCT
ejpam-834	99	4	187	187	NUM
ejpam-834	99	5	,	,	PUNCT
ejpam-834	99	6	47–53	47–53	NUM
ejpam-834	99	7	.	.	PUNCT
ejpam-834	100	1	2007	2007	NUM
ejpam-834	100	2	.	.	PUNCT
ejpam-834	101	1	references	reference	NOUN
ejpam-834	101	2	19	19	NUM
ejpam-834	101	3	[	[	X
ejpam-834	101	4	3	3	NUM
ejpam-834	101	5	]	]	PUNCT
ejpam-834	101	6	o.	o.	PROPN
ejpam-834	101	7	altintaş	altintaş	PROPN
ejpam-834	101	8	,	,	PUNCT
ejpam-834	101	9	ö.	ö.	VERB
ejpam-834	101	10	özkan	özkan	PROPN
ejpam-834	101	11	and	and	CCONJ
ejpam-834	101	12	h.m	h.m	PROPN
ejpam-834	101	13	.	.	PROPN
ejpam-834	101	14	srivastava	srivastava	PROPN
ejpam-834	101	15	,	,	PUNCT
ejpam-834	101	16	neighborhoods	neighborhood	NOUN
ejpam-834	101	17	of	of	ADP
ejpam-834	101	18	a	a	DET
ejpam-834	101	19	class	class	NOUN
ejpam-834	101	20	of	of	ADP
ejpam-834	101	21	analytic	analytic	ADJ
ejpam-834	101	22	functions	function	NOUN
ejpam-834	101	23	with	with	ADP
ejpam-834	101	24	negative	negative	ADJ
ejpam-834	101	25	coefficients	coefficient	NOUN
ejpam-834	101	26	,	,	PUNCT
ejpam-834	101	27	appl	appl	PROPN
ejpam-834	101	28	.	.	PROPN
ejpam-834	101	29	math	math	PROPN
ejpam-834	101	30	.	.	PUNCT
ejpam-834	102	1	lett	lett	PROPN
ejpam-834	102	2	.	.	PROPN
ejpam-834	102	3	,	,	PUNCT
ejpam-834	102	4	13	13	NUM
ejpam-834	102	5	(	(	PUNCT
ejpam-834	102	6	3	3	NUM
ejpam-834	102	7	)	)	PUNCT
ejpam-834	102	8	,	,	PUNCT
ejpam-834	102	9	63–67	63–67	PROPN
ejpam-834	102	10	.	.	PUNCT
ejpam-834	102	11	2000	2000	NUM
ejpam-834	102	12	.	.	PUNCT
ejpam-834	103	1	[	[	X
ejpam-834	103	2	4	4	X
ejpam-834	103	3	]	]	X
ejpam-834	103	4	m.k	m.k	PROPN
ejpam-834	103	5	.	.	PROPN
ejpam-834	103	6	aouf	aouf	PROPN
ejpam-834	103	7	,	,	PUNCT
ejpam-834	103	8	neighborhoods	neighborhood	NOUN
ejpam-834	103	9	of	of	ADP
ejpam-834	103	10	certain	certain	ADJ
ejpam-834	103	11	classes	class	NOUN
ejpam-834	103	12	of	of	ADP
ejpam-834	103	13	analytic	analytic	ADJ
ejpam-834	103	14	functions	function	NOUN
ejpam-834	103	15	with	with	ADP
ejpam-834	103	16	negative	negative	ADJ
ejpam-834	103	17	coefficients	coefficient	NOUN
ejpam-834	103	18	,	,	PUNCT
ejpam-834	103	19	ijmms	ijmms	NOUN
ejpam-834	103	20	.	.	PUNCT
ejpam-834	103	21	,	,	PUNCT
ejpam-834	103	22	article	article	NOUN
ejpam-834	103	23	i	i	PROPN
ejpam-834	103	24	d	d	PROPN
ejpam-834	103	25	38258	38258	NUM
ejpam-834	103	26	,	,	PUNCT
ejpam-834	103	27	pp	pp	ADJ
ejpam-834	103	28	.	.	PUNCT
ejpam-834	104	1	1	1	NUM
ejpam-834	104	2	-	-	SYM
ejpam-834	104	3	6	6	NUM
ejpam-834	104	4	.	.	NOUN
ejpam-834	104	5	2006	2006	NUM
ejpam-834	104	6	.	.	PUNCT
ejpam-834	105	1	[	[	X
ejpam-834	105	2	5	5	NUM
ejpam-834	105	3	]	]	X
ejpam-834	105	4	b.a	b.a	PROPN
ejpam-834	105	5	.	.	PROPN
ejpam-834	105	6	frasin	frasin	PROPN
ejpam-834	105	7	,	,	PUNCT
ejpam-834	105	8	neighborhoods	neighborhood	NOUN
ejpam-834	105	9	of	of	ADP
ejpam-834	105	10	certain	certain	ADJ
ejpam-834	105	11	subclasses	subclass	NOUN
ejpam-834	105	12	of	of	ADP
ejpam-834	105	13	analytic	analytic	ADJ
ejpam-834	105	14	functions	function	NOUN
ejpam-834	105	15	of	of	ADP
ejpam-834	105	16	complex	complex	ADJ
ejpam-834	105	17	order	order	NOUN
ejpam-834	105	18	with	with	ADP
ejpam-834	105	19	negative	negative	ADJ
ejpam-834	105	20	coefficients	coefficient	NOUN
ejpam-834	105	21	,	,	PUNCT
ejpam-834	105	22	aust	aust	PROPN
ejpam-834	105	23	.	.	PUNCT
ejpam-834	106	1	j.	j.	PROPN
ejpam-834	106	2	math	math	PROPN
ejpam-834	106	3	.	.	PUNCT
ejpam-834	107	1	ana	ana	PROPN
ejpam-834	107	2	.	.	PUNCT
ejpam-834	107	3	appl	appl	PROPN
ejpam-834	107	4	.	.	PROPN
ejpam-834	108	1	,vol.7	,vol.7	PROPN
ejpam-834	108	2	,	,	PUNCT
ejpam-834	108	3	issue1	issue1	ADV
ejpam-834	108	4	,	,	PUNCT
ejpam-834	108	5	article	article	NOUN
ejpam-834	108	6	6	6	NUM
ejpam-834	108	7	,	,	PUNCT
ejpam-834	108	8	pp	pp	ADJ
ejpam-834	108	9	.	.	PUNCT
ejpam-834	109	1	1	1	NUM
ejpam-834	109	2	-	-	SYM
ejpam-834	109	3	7	7	NUM
ejpam-834	109	4	,	,	PUNCT
ejpam-834	109	5	2010	2010	NUM
ejpam-834	109	6	.	.	PUNCT
ejpam-834	110	1	[	[	X
ejpam-834	110	2	6	6	NUM
ejpam-834	110	3	]	]	X
ejpam-834	110	4	b.a	b.a	PROPN
ejpam-834	110	5	.	.	PROPN
ejpam-834	110	6	frasin	frasin	PROPN
ejpam-834	110	7	and	and	CCONJ
ejpam-834	110	8	m.	m.	NOUN
ejpam-834	110	9	darus	darus	NOUN
ejpam-834	110	10	,	,	PUNCT
ejpam-834	110	11	integral	integral	ADJ
ejpam-834	110	12	means	mean	NOUN
ejpam-834	110	13	and	and	CCONJ
ejpam-834	110	14	neighborhoods	neighborhood	NOUN
ejpam-834	110	15	for	for	ADP
ejpam-834	110	16	certain	certain	ADJ
ejpam-834	110	17	analytic	analytic	ADJ
ejpam-834	110	18	univalent	univalent	ADJ
ejpam-834	110	19	functions	function	NOUN
ejpam-834	110	20	with	with	ADP
ejpam-834	110	21	negative	negative	ADJ
ejpam-834	110	22	coefficients	coefficient	NOUN
ejpam-834	110	23	,	,	PUNCT
ejpam-834	110	24	soochow	soochow	PROPN
ejpam-834	110	25	j.	j.	PROPN
ejpam-834	110	26	math	math	PROPN
ejpam-834	110	27	.	.	PUNCT
ejpam-834	111	1	comp	comp	PROPN
ejpam-834	111	2	.	.	PUNCT
ejpam-834	111	3	,	,	PUNCT
ejpam-834	112	1	vol	vol	NOUN
ejpam-834	112	2	.	.	PROPN
ejpam-834	112	3	30	30	NUM
ejpam-834	112	4	no.3	no.3	PROPN
ejpam-834	112	5	,	,	PUNCT
ejpam-834	112	6	217	217	NUM
ejpam-834	112	7	-	-	SYM
ejpam-834	112	8	223	223	NUM
ejpam-834	112	9	.	.	PUNCT
ejpam-834	113	1	2004	2004	NUM
ejpam-834	113	2	.	.	PUNCT
ejpam-834	114	1	[	[	X
ejpam-834	114	2	7	7	X
ejpam-834	114	3	]	]	X
ejpam-834	114	4	b.s	b.s	PROPN
ejpam-834	114	5	.	.	PROPN
ejpam-834	114	6	keerthi	keerthi	PROPN
ejpam-834	114	7	,	,	PUNCT
ejpam-834	114	8	b.a	b.a	PROPN
ejpam-834	114	9	.	.	PROPN
ejpam-834	114	10	stephen	stephen	PROPN
ejpam-834	114	11	,	,	PUNCT
ejpam-834	114	12	a.	a.	NOUN
ejpam-834	114	13	gangadharan	gangadharan	PROPN
ejpam-834	114	14	and	and	CCONJ
ejpam-834	114	15	s.	s.	PROPN
ejpam-834	114	16	sivasubramanian	sivasubramanian	PROPN
ejpam-834	114	17	,	,	PUNCT
ejpam-834	114	18	neighborhoods	neighborhood	NOUN
ejpam-834	114	19	of	of	ADP
ejpam-834	114	20	certain	certain	ADJ
ejpam-834	114	21	classes	class	NOUN
ejpam-834	114	22	of	of	ADP
ejpam-834	114	23	analytic	analytic	ADJ
ejpam-834	114	24	functions	function	NOUN
ejpam-834	114	25	with	with	ADP
ejpam-834	114	26	negative	negative	ADJ
ejpam-834	114	27	coefficients	coefficient	NOUN
ejpam-834	114	28	,	,	PUNCT
ejpam-834	114	29	ijmms	ijmms	NOUN
ejpam-834	114	30	.	.	PUNCT
ejpam-834	114	31	,	,	PUNCT
ejpam-834	114	32	article	article	NOUN
ejpam-834	114	33	i	i	PROPN
ejpam-834	114	34	d	d	PROPN
ejpam-834	114	35	38258	38258	NUM
ejpam-834	114	36	,	,	PUNCT
ejpam-834	114	37	pp	pp	ADJ
ejpam-834	114	38	.	.	PUNCT
ejpam-834	115	1	1	1	NUM
ejpam-834	115	2	-	-	SYM
ejpam-834	115	3	6	6	NUM
ejpam-834	115	4	.	.	NOUN
ejpam-834	115	5	2006	2006	NUM
ejpam-834	115	6	.	.	PUNCT
ejpam-834	116	1	[	[	X
ejpam-834	116	2	8	8	NUM
ejpam-834	116	3	]	]	X
ejpam-834	116	4	h.	h.	PROPN
ejpam-834	116	5	orhan	orhan	PROPN
ejpam-834	116	6	,	,	PUNCT
ejpam-834	116	7	e.	e.	PROPN
ejpam-834	116	8	kadioğlu	kadioğlu	PROPN
ejpam-834	116	9	,	,	PUNCT
ejpam-834	116	10	neighborhoods	neighborhood	NOUN
ejpam-834	116	11	of	of	ADP
ejpam-834	116	12	a	a	DET
ejpam-834	116	13	class	class	NOUN
ejpam-834	116	14	of	of	ADP
ejpam-834	116	15	analytic	analytic	ADJ
ejpam-834	116	16	functions	function	NOUN
ejpam-834	116	17	with	with	ADP
ejpam-834	116	18	negative	negative	ADJ
ejpam-834	116	19	coefficients	coefficient	NOUN
ejpam-834	116	20	,	,	PUNCT
ejpam-834	116	21	tamsui	tamsui	PROPN
ejpam-834	116	22	oxford	oxford	PROPN
ejpam-834	116	23	journal	journal	PROPN
ejpam-834	116	24	of	of	ADP
ejpam-834	116	25	math	math	NOUN
ejpam-834	116	26	.	.	PUNCT
ejpam-834	117	1	sci	sci	PROPN
ejpam-834	117	2	.	.	PROPN
ejpam-834	117	3	,	,	PUNCT
ejpam-834	117	4	20	20	NUM
ejpam-834	117	5	(	(	PUNCT
ejpam-834	117	6	2	2	NUM
ejpam-834	117	7	)	)	PUNCT
ejpam-834	117	8	135–142	135–142	NUM
ejpam-834	117	9	.	.	PUNCT
ejpam-834	117	10	2004	2004	NUM
ejpam-834	117	11	.	.	PUNCT
ejpam-834	118	1	[	[	X
ejpam-834	118	2	9	9	NUM
ejpam-834	118	3	]	]	X
ejpam-834	118	4	h.	h.	PROPN
ejpam-834	118	5	orhan	orhan	PROPN
ejpam-834	118	6	,	,	PUNCT
ejpam-834	118	7	m.	m.	NOUN
ejpam-834	118	8	kamali	kamali	PROPN
ejpam-834	118	9	,	,	PUNCT
ejpam-834	118	10	neighborhoods	neighborhood	NOUN
ejpam-834	118	11	of	of	ADP
ejpam-834	118	12	a	a	DET
ejpam-834	118	13	class	class	NOUN
ejpam-834	118	14	of	of	ADP
ejpam-834	118	15	analytic	analytic	ADJ
ejpam-834	118	16	functions	function	NOUN
ejpam-834	118	17	with	with	ADP
ejpam-834	118	18	negative	negative	ADJ
ejpam-834	118	19	coefficients	coefficient	NOUN
ejpam-834	118	20	,	,	PUNCT
ejpam-834	118	21	acta	acta	PROPN
ejpam-834	118	22	mathematica	mathematica	PROPN
ejpam-834	118	23	academiae	academiae	VERB
ejpam-834	118	24	paedagogiace	paedagogiace	PROPN
ejpam-834	118	25	nyiregyhaziensi	nyiregyhaziensi	NOUN
ejpam-834	118	26	,	,	PUNCT
ejpam-834	118	27	4	4	NUM
ejpam-834	118	28	.	.	NOUN
ejpam-834	118	29	1	1	NUM
ejpam-834	118	30	(	(	PUNCT
ejpam-834	118	31	21	21	NUM
ejpam-834	118	32	)	)	PUNCT
ejpam-834	118	33	,	,	PUNCT
ejpam-834	118	34	55–61	55–61	NUM
ejpam-834	118	35	.	.	PUNCT
ejpam-834	118	36	2005	2005	NUM
ejpam-834	118	37	.	.	PUNCT
ejpam-834	119	1	[	[	X
ejpam-834	119	2	10	10	NUM
ejpam-834	119	3	]	]	X
ejpam-834	119	4	h.	h.	PROPN
ejpam-834	119	5	orhan	orhan	PROPN
ejpam-834	119	6	,	,	PUNCT
ejpam-834	119	7	e.	e.	PROPN
ejpam-834	119	8	kadioğlu	kadioğlu	PROPN
ejpam-834	119	9	and	and	CCONJ
ejpam-834	119	10	s.	s.	PROPN
ejpam-834	119	11	owa	owa	PROPN
ejpam-834	119	12	,	,	PUNCT
ejpam-834	119	13	(	(	PUNCT
ejpam-834	119	14	α	α	X
ejpam-834	119	15	,	,	PUNCT
ejpam-834	119	16	δ)-neighborhood	δ)-neighborhood	PUNCT
ejpam-834	119	17	for	for	ADP
ejpam-834	119	18	certain	certain	ADJ
ejpam-834	119	19	analytic	analytic	ADJ
ejpam-834	119	20	functions	function	NOUN
ejpam-834	119	21	,	,	PUNCT
ejpam-834	119	22	proceeding	proceeding	NOUN
ejpam-834	119	23	of	of	ADP
ejpam-834	119	24	international	international	ADJ
ejpam-834	119	25	symposium	symposium	NOUN
ejpam-834	119	26	“	"	PUNCT
ejpam-834	119	27	geometric	geometric	ADJ
ejpam-834	119	28	function	function	NOUN
ejpam-834	119	29	theory	theory	NOUN
ejpam-834	119	30	and	and	CCONJ
ejpam-834	119	31	applications	application	NOUN
ejpam-834	119	32	”	"	PUNCT
ejpam-834	119	33	istanbul	istanbul	PROPN
ejpam-834	119	34	kultur	kultur	PROPN
ejpam-834	119	35	university	university	PROPN
ejpam-834	119	36	,	,	PUNCT
ejpam-834	119	37	207	207	NUM
ejpam-834	119	38	-	-	SYM
ejpam-834	119	39	213	213	NUM
ejpam-834	119	40	.	.	PUNCT
ejpam-834	119	41	2007	2007	NUM
ejpam-834	119	42	.	.	PUNCT
ejpam-834	120	1	[	[	X
ejpam-834	120	2	11	11	NUM
ejpam-834	120	3	]	]	PUNCT
ejpam-834	120	4	s.	s.	PROPN
ejpam-834	120	5	ruscheweyh	ruscheweyh	PROPN
ejpam-834	120	6	,	,	PUNCT
ejpam-834	120	7	neighborhoods	neighborhood	NOUN
ejpam-834	120	8	of	of	ADP
ejpam-834	120	9	univalent	univalent	ADJ
ejpam-834	120	10	functions	function	NOUN
ejpam-834	120	11	,	,	PUNCT
ejpam-834	120	12	proc	proc	NOUN
ejpam-834	120	13	.	.	PUNCT
ejpam-834	121	1	amer	amer	PROPN
ejpam-834	121	2	.	.	PUNCT
ejpam-834	122	1	math.soc	math.soc	X
ejpam-834	122	2	.	.	NOUN
ejpam-834	122	3	81(4	81(4	NUM
ejpam-834	122	4	)	)	PUNCT
ejpam-834	122	5	,	,	PUNCT
ejpam-834	122	6	521527	521527	NUM
ejpam-834	122	7	.	.	PUNCT
ejpam-834	123	1	1981	1981	NUM
ejpam-834	123	2	.	.	PUNCT
ejpam-834	124	1	[	[	X
ejpam-834	124	2	12	12	NUM
ejpam-834	124	3	]	]	X
ejpam-834	124	4	g.	g.	PROPN
ejpam-834	124	5	sălăgean	sălăgean	PROPN
ejpam-834	124	6	,	,	PUNCT
ejpam-834	124	7	subclasses	subclass	NOUN
ejpam-834	124	8	of	of	ADP
ejpam-834	124	9	univalent	univalent	ADJ
ejpam-834	124	10	functions	function	NOUN
ejpam-834	124	11	,	,	PUNCT
ejpam-834	124	12	in	in	ADP
ejpam-834	124	13	“	"	PUNCT
ejpam-834	124	14	complex	complex	ADJ
ejpam-834	124	15	analysis	analysis	NOUN
ejpam-834	124	16	:	:	PUNCT
ejpam-834	124	17	fifth	fifth	ADJ
ejpam-834	124	18	romanianfinnish	romanianfinnish	ADJ
ejpam-834	124	19	seminar	seminar	NOUN
ejpam-834	124	20	,	,	PUNCT
ejpam-834	124	21	”	"	PUNCT
ejpam-834	124	22	part	part	NOUN
ejpam-834	124	23	i	i	PRON
ejpam-834	124	24	(	(	PUNCT
ejpam-834	124	25	bucharest	buchar	ADJ
ejpam-834	124	26	,	,	PUNCT
ejpam-834	124	27	1981	1981	NUM
ejpam-834	124	28	)	)	PUNCT
ejpam-834	124	29	,	,	PUNCT
ejpam-834	124	30	pp.362	pp.362	NOUN
ejpam-834	124	31	-	-	PUNCT
ejpam-834	124	32	372	372	NUM
ejpam-834	124	33	,	,	PUNCT
ejpam-834	124	34	lecture	lecture	NOUN
ejpam-834	124	35	notes	note	NOUN
ejpam-834	124	36	in	in	ADP
ejpam-834	124	37	mathematics	mathematic	NOUN
ejpam-834	124	38	,	,	PUNCT
ejpam-834	124	39	vol	vol	NOUN
ejpam-834	124	40	.	.	NOUN
ejpam-834	124	41	1013	1013	NUM
ejpam-834	124	42	,	,	PUNCT
ejpam-834	124	43	springer	springer	NOUN
ejpam-834	124	44	-	-	PUNCT
ejpam-834	124	45	verlag	verlag	PROPN
ejpam-834	124	46	,	,	PUNCT
ejpam-834	124	47	berlin/	berlin/	NUM
ejpam-834	124	48	new	new	PROPN
ejpam-834	124	49	york	york	PROPN
ejpam-834	124	50	,	,	PUNCT
ejpam-834	124	51	1983	1983	NUM
ejpam-834	124	52	.	.	PUNCT
ejpam-834	125	1	[	[	X
ejpam-834	125	2	13	13	NUM
ejpam-834	125	3	]	]	X
ejpam-834	125	4	h.	h.	PROPN
ejpam-834	125	5	silverman	silverman	PROPN
ejpam-834	125	6	,	,	PUNCT
ejpam-834	125	7	neighborhoods	neighborhood	NOUN
ejpam-834	125	8	of	of	ADP
ejpam-834	125	9	class	class	NOUN
ejpam-834	125	10	of	of	ADP
ejpam-834	125	11	analytic	analytic	ADJ
ejpam-834	125	12	functions	function	NOUN
ejpam-834	125	13	,	,	PUNCT
ejpam-834	125	14	far	far	PROPN
ejpam-834	125	15	east	east	PROPN
ejpam-834	125	16	j.	j.	PROPN
ejpam-834	125	17	math	math	PROPN
ejpam-834	125	18	.	.	PUNCT
ejpam-834	126	1	sci	sci	PROPN
ejpam-834	126	2	.	.	PROPN
ejpam-834	126	3	,	,	PUNCT
ejpam-834	126	4	3(2	3(2	NUM
ejpam-834	126	5	)	)	PUNCT
ejpam-834	126	6	,	,	PUNCT
ejpam-834	126	7	165	165	NUM
ejpam-834	126	8	-	-	SYM
ejpam-834	126	9	169	169	NUM
ejpam-834	126	10	.	.	PUNCT
ejpam-834	126	11	1995	1995	NUM
ejpam-834	126	12	.	.	PUNCT