id	sid	tid	token	lemma	pos
ejpam-1678	1	1	9_xiong.dvi	9_xiong.dvi	NUM
ejpam-1678	1	2	european	european	ADJ
ejpam-1678	1	3	journal	journal	NOUN
ejpam-1678	1	4	of	of	ADP
ejpam-1678	1	5	pure	pure	ADJ
ejpam-1678	1	6	and	and	CCONJ
ejpam-1678	1	7	applied	apply	VERB
ejpam-1678	1	8	mathematics	mathematic	NOUN
ejpam-1678	1	9	vol	vol	NOUN
ejpam-1678	1	10	.	.	PROPN
ejpam-1678	1	11	5	5	NUM
ejpam-1678	1	12	,	,	PUNCT
ejpam-1678	1	13	no	no	INTJ
ejpam-1678	1	14	.	.	NOUN
ejpam-1678	1	15	3	3	NUM
ejpam-1678	1	16	,	,	PUNCT
ejpam-1678	1	17	2012	2012	NUM
ejpam-1678	1	18	,	,	PUNCT
ejpam-1678	1	19	380	380	NUM
ejpam-1678	1	20	-	-	SYM
ejpam-1678	1	21	389	389	NUM
ejpam-1678	1	22	issn	issn	PROPN
ejpam-1678	1	23	1307	1307	NUM
ejpam-1678	1	24	-	-	SYM
ejpam-1678	1	25	5543	5543	NUM
ejpam-1678	1	26	–	–	PUNCT
ejpam-1678	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1678	1	28	some	some	PRON
ejpam-1678	1	29	results	result	VERB
ejpam-1678	1	30	for	for	ADP
ejpam-1678	1	31	certain	certain	ADJ
ejpam-1678	1	32	subclasses	subclass	NOUN
ejpam-1678	1	33	of	of	ADP
ejpam-1678	1	34	functions	function	NOUN
ejpam-1678	1	35	with	with	ADP
ejpam-1678	1	36	differential	differential	ADJ
ejpam-1678	1	37	equation	equation	NOUN
ejpam-1678	1	38	and	and	CCONJ
ejpam-1678	1	39	subordination	subordination	NOUN
ejpam-1678	1	40	liangpeng	liangpeng	PROPN
ejpam-1678	1	41	xiong∗	xiong∗	PROPN
ejpam-1678	1	42	,	,	PUNCT
ejpam-1678	1	43	xiaoli	xiaoli	PROPN
ejpam-1678	1	44	liu	liu	PROPN
ejpam-1678	1	45	the	the	DET
ejpam-1678	1	46	college	college	PROPN
ejpam-1678	1	47	of	of	ADP
ejpam-1678	1	48	engineering	engineering	NOUN
ejpam-1678	1	49	and	and	CCONJ
ejpam-1678	1	50	technical	technical	ADJ
ejpam-1678	1	51	,	,	PUNCT
ejpam-1678	1	52	chengdu	chengdu	PROPN
ejpam-1678	1	53	university	university	PROPN
ejpam-1678	1	54	of	of	ADP
ejpam-1678	1	55	technology	technology	PROPN
ejpam-1678	1	56	university	university	PROPN
ejpam-1678	1	57	,	,	PUNCT
ejpam-1678	1	58	leshan	leshan	NOUN
ejpam-1678	1	59	,	,	PUNCT
ejpam-1678	1	60	sichuan	sichuan	PROPN
ejpam-1678	1	61	,	,	PUNCT
ejpam-1678	1	62	614000	614000	NUM
ejpam-1678	1	63	,	,	PUNCT
ejpam-1678	1	64	p.r	p.r	PROPN
ejpam-1678	1	65	china	china	PROPN
ejpam-1678	1	66	abstract	abstract	NOUN
ejpam-1678	1	67	.	.	PUNCT
ejpam-1678	2	1	by	by	ADP
ejpam-1678	2	2	applying	apply	VERB
ejpam-1678	2	3	the	the	DET
ejpam-1678	2	4	differential	differential	ADJ
ejpam-1678	2	5	subordination	subordination	NOUN
ejpam-1678	2	6	theorem	theorem	VERB
ejpam-1678	2	7	,	,	PUNCT
ejpam-1678	2	8	we	we	PRON
ejpam-1678	2	9	further	far	ADV
ejpam-1678	2	10	investigate	investigate	VERB
ejpam-1678	2	11	the	the	DET
ejpam-1678	2	12	subclass	subclass	ADJ
ejpam-1678	2	13	h	h	NOUN
ejpam-1678	2	14	n	n	CCONJ
ejpam-1678	2	15	,	,	PUNCT
ejpam-1678	2	16	γ	γ	X
ejpam-1678	2	17	λ	λ	X
ejpam-1678	3	1	[	[	X
ejpam-1678	3	2	α	α	X
ejpam-1678	3	3	,	,	PUNCT
ejpam-1678	3	4	β	β	NOUN
ejpam-1678	3	5	]	]	PUNCT
ejpam-1678	3	6	of	of	ADP
ejpam-1678	3	7	functions	function	NOUN
ejpam-1678	3	8	which	which	PRON
ejpam-1678	3	9	are	be	AUX
ejpam-1678	3	10	analytic	analytic	ADJ
ejpam-1678	3	11	in	in	ADP
ejpam-1678	3	12	the	the	DET
ejpam-1678	3	13	unit	unit	NOUN
ejpam-1678	3	14	disk	disk	NOUN
ejpam-1678	3	15	.	.	PUNCT
ejpam-1678	4	1	several	several	ADJ
ejpam-1678	4	2	subordination	subordination	NOUN
ejpam-1678	4	3	results	result	VERB
ejpam-1678	4	4	on	on	ADP
ejpam-1678	4	5	a	a	DET
ejpam-1678	4	6	convex	convex	NOUN
ejpam-1678	4	7	function	function	NOUN
ejpam-1678	4	8	and	and	CCONJ
ejpam-1678	4	9	a	a	DET
ejpam-1678	4	10	incomplete	incomplete	ADJ
ejpam-1678	4	11	beta	beta	NOUN
ejpam-1678	4	12	function	function	NOUN
ejpam-1678	4	13	are	be	AUX
ejpam-1678	4	14	obtained	obtain	VERB
ejpam-1678	4	15	.	.	PUNCT
ejpam-1678	5	1	moreover	moreover	ADV
ejpam-1678	5	2	,	,	PUNCT
ejpam-1678	5	3	the	the	DET
ejpam-1678	5	4	function	function	NOUN
ejpam-1678	5	5	that	that	PRON
ejpam-1678	5	6	belongs	belong	VERB
ejpam-1678	5	7	to	to	ADP
ejpam-1678	5	8	the	the	DET
ejpam-1678	5	9	h	h	NOUN
ejpam-1678	5	10	n	n	CCONJ
ejpam-1678	5	11	,	,	PUNCT
ejpam-1678	5	12	γ	γ	X
ejpam-1678	5	13	λ	λ	X
ejpam-1678	6	1	[	[	X
ejpam-1678	6	2	α	α	X
ejpam-1678	6	3	,	,	PUNCT
ejpam-1678	6	4	β	β	X
ejpam-1678	6	5	]	]	PUNCT
ejpam-1678	6	6	with	with	ADP
ejpam-1678	6	7	a	a	DET
ejpam-1678	6	8	cauchy	cauchy	NOUN
ejpam-1678	6	9	-	-	PUNCT
ejpam-1678	6	10	euler	euler	NOUN
ejpam-1678	6	11	differential	differential	ADJ
ejpam-1678	6	12	equation	equation	NOUN
ejpam-1678	6	13	is	be	AUX
ejpam-1678	6	14	also	also	ADV
ejpam-1678	6	15	discussed	discuss	VERB
ejpam-1678	6	16	on	on	ADP
ejpam-1678	6	17	similar	similar	ADJ
ejpam-1678	6	18	subject	subject	NOUN
ejpam-1678	6	19	.	.	PUNCT
ejpam-1678	7	1	our	our	PRON
ejpam-1678	7	2	results	result	NOUN
ejpam-1678	7	3	extend	extend	VERB
ejpam-1678	7	4	some	some	DET
ejpam-1678	7	5	earlier	early	ADJ
ejpam-1678	7	6	works	work	NOUN
ejpam-1678	7	7	.	.	PUNCT
ejpam-1678	8	1	2010	2010	NUM
ejpam-1678	8	2	mathematics	mathematic	NOUN
ejpam-1678	8	3	subject	subject	NOUN
ejpam-1678	8	4	classifications	classification	NOUN
ejpam-1678	8	5	:	:	PUNCT
ejpam-1678	8	6	30c45	30c45	NUM
ejpam-1678	8	7	key	key	ADJ
ejpam-1678	8	8	words	word	NOUN
ejpam-1678	8	9	and	and	CCONJ
ejpam-1678	8	10	phrases	phrase	NOUN
ejpam-1678	8	11	:	:	PUNCT
ejpam-1678	8	12	analytic	analytic	ADJ
ejpam-1678	8	13	functions	function	NOUN
ejpam-1678	8	14	,	,	PUNCT
ejpam-1678	8	15	convex	convex	NOUN
ejpam-1678	8	16	function	function	NOUN
ejpam-1678	8	17	,	,	PUNCT
ejpam-1678	8	18	subordination	subordination	NOUN
ejpam-1678	8	19	,	,	PUNCT
ejpam-1678	8	20	differential	differential	ADJ
ejpam-1678	8	21	equation	equation	NOUN
ejpam-1678	8	22	1	1	NUM
ejpam-1678	8	23	.	.	PUNCT
ejpam-1678	9	1	introduction	introduction	NOUN
ejpam-1678	9	2	and	and	CCONJ
ejpam-1678	9	3	definition	definition	NOUN
ejpam-1678	9	4	let	let	VERB
ejpam-1678	9	5	a	a	DET
ejpam-1678	9	6	denote	denote	NOUN
ejpam-1678	9	7	the	the	DET
ejpam-1678	9	8	class	class	NOUN
ejpam-1678	9	9	of	of	ADP
ejpam-1678	9	10	all	all	DET
ejpam-1678	9	11	functions	function	NOUN
ejpam-1678	9	12	of	of	ADP
ejpam-1678	9	13	the	the	DET
ejpam-1678	9	14	form	form	NOUN
ejpam-1678	9	15	f	f	X
ejpam-1678	9	16	(	(	PUNCT
ejpam-1678	9	17	z	z	NOUN
ejpam-1678	9	18	)	)	PUNCT
ejpam-1678	9	19	=	=	SYM
ejpam-1678	9	20	z+	z+	NUM
ejpam-1678	9	21	∞	∞	PROPN
ejpam-1678	9	22	∑	∑	PROPN
ejpam-1678	9	23	k=2	k=2	PROPN
ejpam-1678	9	24	akzk	akzk	PROPN
ejpam-1678	9	25	,	,	PUNCT
ejpam-1678	9	26	which	which	PRON
ejpam-1678	9	27	are	be	AUX
ejpam-1678	9	28	analytic	analytic	ADJ
ejpam-1678	9	29	in	in	ADP
ejpam-1678	9	30	the	the	DET
ejpam-1678	9	31	open	open	ADJ
ejpam-1678	9	32	unit	unit	NOUN
ejpam-1678	9	33	disk	disk	NOUN
ejpam-1678	9	34	u	u	NOUN
ejpam-1678	9	35	=	=	PUNCT
ejpam-1678	9	36	{	{	PUNCT
ejpam-1678	9	37	z	z	NOUN
ejpam-1678	9	38	∈	∈	PROPN
ejpam-1678	9	39	c	c	NOUN
ejpam-1678	9	40	,	,	PUNCT
ejpam-1678	9	41	|z|	|z|	VERB
ejpam-1678	9	42	<	<	X
ejpam-1678	9	43	1	1	NUM
ejpam-1678	9	44	}	}	PUNCT
ejpam-1678	9	45	and	and	CCONJ
ejpam-1678	9	46	let	let	VERB
ejpam-1678	9	47	s	s	PRON
ejpam-1678	9	48	be	be	AUX
ejpam-1678	9	49	the	the	DET
ejpam-1678	9	50	subclass	subclass	NOUN
ejpam-1678	9	51	of	of	ADP
ejpam-1678	9	52	a	a	DET
ejpam-1678	9	53	consisting	consisting	NOUN
ejpam-1678	9	54	of	of	ADP
ejpam-1678	9	55	univalent	univalent	ADJ
ejpam-1678	9	56	functions	function	NOUN
ejpam-1678	9	57	.	.	PUNCT
ejpam-1678	10	1	k	k	PROPN
ejpam-1678	10	2	denotes	denote	VERB
ejpam-1678	10	3	the	the	DET
ejpam-1678	10	4	usual	usual	ADJ
ejpam-1678	10	5	class	class	NOUN
ejpam-1678	10	6	of	of	ADP
ejpam-1678	10	7	convex	convex	NOUN
ejpam-1678	10	8	functions	function	NOUN
ejpam-1678	10	9	.	.	PUNCT
ejpam-1678	11	1	suppose	suppose	VERB
ejpam-1678	11	2	that	that	SCONJ
ejpam-1678	11	3	the	the	DET
ejpam-1678	11	4	functions	function	NOUN
ejpam-1678	11	5	f	f	PROPN
ejpam-1678	11	6	and	and	CCONJ
ejpam-1678	11	7	g	g	PROPN
ejpam-1678	11	8	are	be	AUX
ejpam-1678	11	9	analytic	analytic	ADJ
ejpam-1678	11	10	in	in	ADP
ejpam-1678	11	11	u.	u.	NOUN
ejpam-1678	11	12	we	we	PRON
ejpam-1678	11	13	say	say	VERB
ejpam-1678	11	14	that	that	SCONJ
ejpam-1678	11	15	f	f	PROPN
ejpam-1678	11	16	is	be	AUX
ejpam-1678	11	17	subordinate	subordinate	ADJ
ejpam-1678	11	18	to	to	ADP
ejpam-1678	11	19	g	g	NOUN
ejpam-1678	11	20	in	in	ADP
ejpam-1678	11	21	u	u	NOUN
ejpam-1678	11	22	if	if	SCONJ
ejpam-1678	11	23	there	there	PRON
ejpam-1678	11	24	exists	exist	VERB
ejpam-1678	11	25	a	a	DET
ejpam-1678	11	26	functions	function	NOUN
ejpam-1678	11	27	φ	φ	X
ejpam-1678	11	28	analytic	analytic	ADJ
ejpam-1678	11	29	in	in	ADP
ejpam-1678	11	30	u	u	PRON
ejpam-1678	11	31	such	such	ADJ
ejpam-1678	11	32	that	that	PRON
ejpam-1678	11	33	φ(0	φ(0	ADJ
ejpam-1678	11	34	)	)	PUNCT
ejpam-1678	11	35	=	=	SYM
ejpam-1678	11	36	0	0	NUM
ejpam-1678	11	37	,	,	PUNCT
ejpam-1678	11	38	|φ(z)|	|φ(z)|	ADP
ejpam-1678	11	39	<	<	X
ejpam-1678	11	40	1	1	NUM
ejpam-1678	11	41	(	(	PUNCT
ejpam-1678	11	42	|z|	|z|	NOUN
ejpam-1678	11	43	<	<	X
ejpam-1678	11	44	1	1	NUM
ejpam-1678	11	45	)	)	PUNCT
ejpam-1678	11	46	and	and	CCONJ
ejpam-1678	11	47	f	f	PROPN
ejpam-1678	11	48	(	(	PUNCT
ejpam-1678	11	49	z	z	NOUN
ejpam-1678	11	50	)	)	PUNCT
ejpam-1678	11	51	=	=	SYM
ejpam-1678	11	52	g(φ(z	g(φ(z	PROPN
ejpam-1678	11	53	)	)	PUNCT
ejpam-1678	11	54	)	)	PUNCT
ejpam-1678	11	55	(	(	PUNCT
ejpam-1678	11	56	|z|	|z|	NOUN
ejpam-1678	11	57	<	<	X
ejpam-1678	11	58	1	1	NUM
ejpam-1678	11	59	)	)	PUNCT
ejpam-1678	11	60	,	,	PUNCT
ejpam-1678	11	61	written	write	VERB
ejpam-1678	11	62	f	f	PROPN
ejpam-1678	11	63	≺	≺	NOUN
ejpam-1678	11	64	g.	g.	PROPN
ejpam-1678	11	65	let	let	VERB
ejpam-1678	11	66	be	be	AUX
ejpam-1678	11	67	given	give	VERB
ejpam-1678	11	68	two	two	NUM
ejpam-1678	11	69	functions	function	NOUN
ejpam-1678	12	1	f	f	X
ejpam-1678	12	2	(	(	PUNCT
ejpam-1678	12	3	z	z	NOUN
ejpam-1678	12	4	)	)	PUNCT
ejpam-1678	12	5	=	=	SYM
ejpam-1678	13	1	z	z	NOUN
ejpam-1678	14	1	+	+	NUM
ejpam-1678	14	2	∞	∞	NUM
ejpam-1678	14	3	∑	∑	PROPN
ejpam-1678	14	4	k=2	k=2	PROPN
ejpam-1678	14	5	akzk	akzk	NOUN
ejpam-1678	14	6	and	and	CCONJ
ejpam-1678	14	7	g(z	g(z	PROPN
ejpam-1678	14	8	)	)	PUNCT
ejpam-1678	15	1	=	=	SYM
ejpam-1678	15	2	z	z	NOUN
ejpam-1678	16	1	+	+	NUM
ejpam-1678	16	2	∞	∞	NUM
ejpam-1678	16	3	∑	∑	PROPN
ejpam-1678	16	4	k=2	k=2	PROPN
ejpam-1678	16	5	bkzk	bkzk	VERB
ejpam-1678	16	6	analytic	analytic	ADJ
ejpam-1678	16	7	in	in	ADP
ejpam-1678	16	8	the	the	DET
ejpam-1678	16	9	open	open	ADJ
ejpam-1678	16	10	unit	unit	NOUN
ejpam-1678	16	11	disc	disc	VERB
ejpam-1678	16	12	u	u	NOUN
ejpam-1678	16	13	=	=	PUNCT
ejpam-1678	16	14	{	{	PUNCT
ejpam-1678	16	15	z	z	PROPN
ejpam-1678	16	16	∈	∈	PROPN
ejpam-1678	16	17	c	c	NOUN
ejpam-1678	16	18	:	:	PUNCT
ejpam-1678	16	19	|z|	|z|	NOUN
ejpam-1678	16	20	<	<	X
ejpam-1678	16	21	1	1	NUM
ejpam-1678	16	22	}	}	PUNCT
ejpam-1678	16	23	,	,	PUNCT
ejpam-1678	16	24	then	then	ADV
ejpam-1678	16	25	the	the	DET
ejpam-1678	16	26	hadamard	hadamard	ADJ
ejpam-1678	16	27	product(or	product(or	ADJ
ejpam-1678	16	28	convolution	convolution	NOUN
ejpam-1678	16	29	)	)	PUNCT
ejpam-1678	16	30	f	f	PROPN
ejpam-1678	16	31	∗	∗	NOUN
ejpam-1678	16	32	g	g	NOUN
ejpam-1678	16	33	of	of	ADP
ejpam-1678	16	34	two	two	NUM
ejpam-1678	16	35	functions	function	NOUN
ejpam-1678	16	36	f	f	NOUN
ejpam-1678	16	37	,	,	PUNCT
ejpam-1678	16	38	g	g	PROPN
ejpam-1678	16	39	is	be	AUX
ejpam-1678	16	40	defined	define	VERB
ejpam-1678	16	41	by	by	ADP
ejpam-1678	16	42	f	f	PROPN
ejpam-1678	16	43	∗	∗	NOUN
ejpam-1678	16	44	g(z	g(z	PROPN
ejpam-1678	16	45	)	)	PUNCT
ejpam-1678	17	1	=	=	SYM
ejpam-1678	17	2	z	z	NOUN
ejpam-1678	18	1	+	+	NUM
ejpam-1678	18	2	∞	∞	NUM
ejpam-1678	18	3	∑	∑	PROPN
ejpam-1678	18	4	k=2	k=2	PROPN
ejpam-1678	18	5	ak	ak	PROPN
ejpam-1678	18	6	bkzk	bkzk	NOUN
ejpam-1678	18	7	.	.	PUNCT
ejpam-1678	19	1	let	let	VERB
ejpam-1678	19	2	(	(	PUNCT
ejpam-1678	19	3	x)k	x)k	X
ejpam-1678	19	4	be	be	AUX
ejpam-1678	19	5	the	the	DET
ejpam-1678	19	6	pochhammer	pochhammer	NOUN
ejpam-1678	19	7	symbol	symbol	NOUN
ejpam-1678	19	8	defined	define	VERB
ejpam-1678	19	9	by	by	ADP
ejpam-1678	19	10	(	(	PUNCT
ejpam-1678	19	11	1	1	NUM
ejpam-1678	19	12	,	,	PUNCT
ejpam-1678	19	13	k	k	NOUN
ejpam-1678	19	14	=	=	SYM
ejpam-1678	19	15	0	0	PROPN
ejpam-1678	19	16	,	,	PUNCT
ejpam-1678	19	17	x	x	SYM
ejpam-1678	19	18	∈c/{0	∈c/{0	PROPN
ejpam-1678	19	19	}	}	PUNCT
ejpam-1678	19	20	,	,	PUNCT
ejpam-1678	19	21	x(x	x(x	PROPN
ejpam-1678	20	1	+	+	CCONJ
ejpam-1678	20	2	1)(x	1)(x	NUM
ejpam-1678	20	3	+	+	CCONJ
ejpam-1678	20	4	2	2	NUM
ejpam-1678	20	5	)	)	PUNCT
ejpam-1678	20	6	.	.	PUNCT
ejpam-1678	21	1	.	.	PUNCT
ejpam-1678	21	2	.	.	PUNCT
ejpam-1678	22	1	(	(	PUNCT
ejpam-1678	22	2	x	x	X
ejpam-1678	22	3	+	+	NUM
ejpam-1678	22	4	k−	k−	NOUN
ejpam-1678	22	5	1	1	NUM
ejpam-1678	22	6	)	)	PUNCT
ejpam-1678	22	7	,	,	PUNCT
ejpam-1678	22	8	k	k	PROPN
ejpam-1678	22	9	∈	∈	PROPN
ejpam-1678	22	10	n	n	NOUN
ejpam-1678	22	11	=	=	PUNCT
ejpam-1678	22	12	{	{	PUNCT
ejpam-1678	22	13	1,2,3	1,2,3	NUM
ejpam-1678	22	14	,	,	PUNCT
ejpam-1678	22	15	.	.	PUNCT
ejpam-1678	22	16	.	.	PUNCT
ejpam-1678	23	1	.	.	PUNCT
ejpam-1678	23	2	}	}	PUNCT
ejpam-1678	23	3	,	,	PUNCT
ejpam-1678	23	4	x	x	PROPN
ejpam-1678	23	5	∈	∈	PROPN
ejpam-1678	23	6	c.	c.	PROPN
ejpam-1678	23	7	∗corresponding	∗corresponde	VERB
ejpam-1678	23	8	author	author	NOUN
ejpam-1678	23	9	.	.	PUNCT
ejpam-1678	24	1	email	email	NOUN
ejpam-1678	24	2	addresses	address	NOUN
ejpam-1678	24	3	:	:	PUNCT
ejpam-1678	24	4	xlpwxf	xlpwxf	PROPN
ejpam-1678	24	5	�	�	PROPN
ejpam-1678	24	6	163	163	NUM
ejpam-1678	24	7	.	.	PUNCT
ejpam-1678	25	1	om	om	PROPN
ejpam-1678	25	2	(	(	PUNCT
ejpam-1678	25	3	l.	l.	PROPN
ejpam-1678	25	4	xiong	xiong	PROPN
ejpam-1678	25	5	)	)	PUNCT
ejpam-1678	25	6	,	,	PUNCT
ejpam-1678	25	7	travel	travel	NOUN
ejpam-1678	25	8	-	-	PUNCT
ejpam-1678	25	9	lxl	lxl	NOUN
ejpam-1678	25	10	�	�	PROPN
ejpam-1678	25	11	163	163	NUM
ejpam-1678	25	12	.	.	PUNCT
ejpam-1678	26	1	om	om	PROPN
ejpam-1678	26	2	(	(	PUNCT
ejpam-1678	26	3	x.	x.	PROPN
ejpam-1678	26	4	liu	liu	PROPN
ejpam-1678	26	5	)	)	PUNCT
ejpam-1678	26	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1678	27	1	380	380	NUM
ejpam-1678	27	2	c	c	NOUN
ejpam-1678	27	3	©	©	PROPN
ejpam-1678	27	4	2012	2012	NUM
ejpam-1678	27	5	ejpam	ejpam	VERB
ejpam-1678	27	6	all	all	DET
ejpam-1678	27	7	rights	right	NOUN
ejpam-1678	27	8	reserved	reserve	VERB
ejpam-1678	27	9	.	.	PUNCT
ejpam-1678	28	1	l.	l.	PROPN
ejpam-1678	28	2	xiong	xiong	PROPN
ejpam-1678	28	3	,	,	PUNCT
ejpam-1678	28	4	x.	x.	PROPN
ejpam-1678	28	5	liu	liu	PROPN
ejpam-1678	28	6	/	/	SYM
ejpam-1678	28	7	eur	eur	PROPN
ejpam-1678	28	8	.	.	PUNCT
ejpam-1678	29	1	j.	j.	PROPN
ejpam-1678	29	2	pure	pure	PROPN
ejpam-1678	29	3	appl	appl	PROPN
ejpam-1678	29	4	.	.	PROPN
ejpam-1678	29	5	math	math	PROPN
ejpam-1678	29	6	,	,	PUNCT
ejpam-1678	29	7	5	5	NUM
ejpam-1678	29	8	(	(	PUNCT
ejpam-1678	29	9	2012	2012	NUM
ejpam-1678	29	10	)	)	PUNCT
ejpam-1678	29	11	,	,	PUNCT
ejpam-1678	29	12	380	380	NUM
ejpam-1678	29	13	-	-	SYM
ejpam-1678	29	14	389	389	NUM
ejpam-1678	29	15	381	381	NUM
ejpam-1678	29	16	in	in	ADP
ejpam-1678	29	17	[	[	X
ejpam-1678	29	18	7	7	NUM
ejpam-1678	29	19	]	]	PUNCT
ejpam-1678	29	20	,	,	PUNCT
ejpam-1678	29	21	ruscheweyh	ruscheweyh	NOUN
ejpam-1678	29	22	defined	define	VERB
ejpam-1678	29	23	the	the	DET
ejpam-1678	29	24	incomplete	incomplete	ADJ
ejpam-1678	29	25	beta	beta	NOUN
ejpam-1678	29	26	function	function	NOUN
ejpam-1678	29	27	h(a	h(a	PROPN
ejpam-1678	29	28	,	,	PUNCT
ejpam-1678	29	29	c	c	X
ejpam-1678	29	30	;	;	PUNCT
ejpam-1678	29	31	z	z	X
ejpam-1678	29	32	)	)	PUNCT
ejpam-1678	29	33	=	=	SYM
ejpam-1678	30	1	z	z	NOUN
ejpam-1678	31	1	+	+	NUM
ejpam-1678	31	2	∞	∞	PROPN
ejpam-1678	31	3	∑	∑	PROPN
ejpam-1678	31	4	k=2	k=2	PROPN
ejpam-1678	31	5	(	(	PUNCT
ejpam-1678	31	6	a)k−1	a)k−1	PROPN
ejpam-1678	31	7	(	(	PUNCT
ejpam-1678	31	8	c)k−1	c)k−1	AUX
ejpam-1678	31	9	zk	zk	PROPN
ejpam-1678	31	10	|z|	|z|	VERB
ejpam-1678	31	11	<	<	X
ejpam-1678	31	12	1	1	NUM
ejpam-1678	31	13	,	,	PUNCT
ejpam-1678	31	14	(	(	PUNCT
ejpam-1678	31	15	1	1	X
ejpam-1678	31	16	)	)	PUNCT
ejpam-1678	31	17	where	where	SCONJ
ejpam-1678	31	18	a	a	PRON
ejpam-1678	31	19	is	be	AUX
ejpam-1678	31	20	any	any	DET
ejpam-1678	31	21	real	real	ADJ
ejpam-1678	31	22	number	number	NOUN
ejpam-1678	31	23	and	and	CCONJ
ejpam-1678	31	24	c	c	PROPN
ejpam-1678	31	25	6=	6=	PROPN
ejpam-1678	31	26	{	{	PUNCT
ejpam-1678	31	27	0,−1,−2	0,−1,−2	NUM
ejpam-1678	31	28	,	,	PUNCT
ejpam-1678	31	29	.	.	PUNCT
ejpam-1678	31	30	.	.	PUNCT
ejpam-1678	31	31	.	.	PUNCT
ejpam-1678	31	32	}	}	PUNCT
ejpam-1678	31	33	.	.	PUNCT
ejpam-1678	32	1	now	now	ADV
ejpam-1678	32	2	we	we	PRON
ejpam-1678	32	3	recall	recall	VERB
ejpam-1678	32	4	the	the	DET
ejpam-1678	32	5	linear	linear	ADJ
ejpam-1678	32	6	multiplier	multipli	ADJ
ejpam-1678	32	7	fractional	fractional	ADJ
ejpam-1678	32	8	differential	differential	NOUN
ejpam-1678	32	9	operator	operator	NOUN
ejpam-1678	32	10	d	d	PROPN
ejpam-1678	32	11	n	n	CCONJ
ejpam-1678	32	12	,	,	PUNCT
ejpam-1678	32	13	γ	γ	PROPN
ejpam-1678	32	14	λ	λ	PROPN
ejpam-1678	32	15	introduced	introduce	VERB
ejpam-1678	32	16	and	and	CCONJ
ejpam-1678	32	17	studied	study	VERB
ejpam-1678	32	18	by	by	ADP
ejpam-1678	32	19	al	al	PROPN
ejpam-1678	32	20	-	-	PUNCT
ejpam-1678	32	21	oboudi	oboudi	PROPN
ejpam-1678	32	22	and	and	CCONJ
ejpam-1678	32	23	al	al	PROPN
ejpam-1678	32	24	-	-	PUNCT
ejpam-1678	32	25	amoudi	amoudi	PROPN
ejpam-1678	33	1	[	[	X
ejpam-1678	33	2	1	1	NUM
ejpam-1678	33	3	]	]	PUNCT
ejpam-1678	33	4	as	as	SCONJ
ejpam-1678	33	5	follows	follow	VERB
ejpam-1678	33	6	:	:	PUNCT
ejpam-1678	33	7	d	d	NOUN
ejpam-1678	33	8	0,0	0,0	NUM
ejpam-1678	34	1	λ	λ	X
ejpam-1678	34	2	f	f	X
ejpam-1678	34	3	(	(	PUNCT
ejpam-1678	34	4	z	z	NOUN
ejpam-1678	34	5	)	)	PUNCT
ejpam-1678	34	6	=	=	SYM
ejpam-1678	34	7	f	f	X
ejpam-1678	34	8	(	(	PUNCT
ejpam-1678	34	9	z	z	NOUN
ejpam-1678	34	10	)	)	PUNCT
ejpam-1678	34	11	,	,	PUNCT
ejpam-1678	35	1	d	d	PROPN
ejpam-1678	35	2	1,γ	1,γ	NUM
ejpam-1678	35	3	λ	λ	X
ejpam-1678	35	4	f	f	X
ejpam-1678	35	5	(	(	PUNCT
ejpam-1678	35	6	z	z	NOUN
ejpam-1678	35	7	)	)	PUNCT
ejpam-1678	35	8	=	=	PRON
ejpam-1678	35	9	λz(ωγ	λz(ωγ	VERB
ejpam-1678	35	10	f	f	X
ejpam-1678	35	11	(	(	PUNCT
ejpam-1678	35	12	z))′+	z))′+	X
ejpam-1678	35	13	(	(	PUNCT
ejpam-1678	35	14	1−	1−	NUM
ejpam-1678	35	15	γ)ωγ	γ)ωγ	PROPN
ejpam-1678	35	16	f	f	PROPN
ejpam-1678	35	17	(	(	PUNCT
ejpam-1678	35	18	z	z	NOUN
ejpam-1678	35	19	)	)	PUNCT
ejpam-1678	35	20	=	=	PUNCT
ejpam-1678	36	1	d	d	X
ejpam-1678	36	2	γ	γ	X
ejpam-1678	36	3	λ	λ	X
ejpam-1678	36	4	f	f	X
ejpam-1678	36	5	(	(	PUNCT
ejpam-1678	36	6	z	z	NOUN
ejpam-1678	36	7	)	)	PUNCT
ejpam-1678	36	8	,	,	PUNCT
ejpam-1678	37	1	d	d	PROPN
ejpam-1678	37	2	2,γ	2,γ	NUM
ejpam-1678	38	1	λ	λ	X
ejpam-1678	38	2	f	f	X
ejpam-1678	38	3	(	(	PUNCT
ejpam-1678	38	4	z	z	NOUN
ejpam-1678	38	5	)	)	PUNCT
ejpam-1678	38	6	=	=	PUNCT
ejpam-1678	39	1	d	d	X
ejpam-1678	39	2	γ	γ	X
ejpam-1678	39	3	λ	λ	X
ejpam-1678	39	4	(	(	PUNCT
ejpam-1678	39	5	d	d	PROPN
ejpam-1678	39	6	1,γ	1,γ	PROPN
ejpam-1678	39	7	λ	λ	SYM
ejpam-1678	39	8	f	f	X
ejpam-1678	39	9	(	(	PUNCT
ejpam-1678	39	10	z	z	NOUN
ejpam-1678	39	11	)	)	PUNCT
ejpam-1678	39	12	)	)	PUNCT
ejpam-1678	39	13	,	,	PUNCT
ejpam-1678	39	14	.	.	PUNCT
ejpam-1678	39	15	.	.	PUNCT
ejpam-1678	39	16	.	.	PUNCT
ejpam-1678	39	17	.	.	PUNCT
ejpam-1678	39	18	.	.	PUNCT
ejpam-1678	39	19	.	.	PUNCT
ejpam-1678	40	1	d	d	NOUN
ejpam-1678	40	2	n	n	CCONJ
ejpam-1678	40	3	,	,	PUNCT
ejpam-1678	40	4	γ	γ	X
ejpam-1678	40	5	λ	λ	X
ejpam-1678	40	6	f	f	X
ejpam-1678	40	7	(	(	PUNCT
ejpam-1678	40	8	z	z	NOUN
ejpam-1678	40	9	)	)	PUNCT
ejpam-1678	40	10	=	=	PUNCT
ejpam-1678	41	1	d	d	X
ejpam-1678	41	2	γ	γ	X
ejpam-1678	41	3	λ	λ	X
ejpam-1678	41	4	(	(	PUNCT
ejpam-1678	41	5	d	d	PROPN
ejpam-1678	41	6	n−1,γ	n−1,γ	NOUN
ejpam-1678	41	7	λ	λ	X
ejpam-1678	41	8	f	f	PROPN
ejpam-1678	41	9	(	(	PUNCT
ejpam-1678	41	10	z	z	NOUN
ejpam-1678	41	11	)	)	PUNCT
ejpam-1678	41	12	)	)	PUNCT
ejpam-1678	41	13	,	,	PUNCT
ejpam-1678	41	14	for	for	ADP
ejpam-1678	41	15	n	n	PRON
ejpam-1678	41	16	∈	∈	PROPN
ejpam-1678	41	17	n	n	CCONJ
ejpam-1678	41	18	,	,	PUNCT
ejpam-1678	41	19	λ	λ	X
ejpam-1678	41	20	¾	¾	NOUN
ejpam-1678	41	21	0	0	NUM
ejpam-1678	41	22	and	and	CCONJ
ejpam-1678	41	23	0	0	NUM
ejpam-1678	41	24	¶	¶	NOUN
ejpam-1678	41	25	γ	γ	X
ejpam-1678	41	26	<	<	X
ejpam-1678	41	27	1	1	NUM
ejpam-1678	41	28	,	,	PUNCT
ejpam-1678	41	29	where	where	SCONJ
ejpam-1678	41	30	ωγ	ωγ	ADP
ejpam-1678	41	31	f	f	PROPN
ejpam-1678	41	32	(	(	PUNCT
ejpam-1678	41	33	z	z	NOUN
ejpam-1678	41	34	)	)	PUNCT
ejpam-1678	41	35	=	=	SYM
ejpam-1678	42	1	γ(2−	γ(2−	PROPN
ejpam-1678	42	2	γ)zγd	γ)zγd	PROPN
ejpam-1678	42	3	γ	γ	PROPN
ejpam-1678	42	4	z	z	PROPN
ejpam-1678	42	5	f	f	X
ejpam-1678	42	6	(	(	PUNCT
ejpam-1678	42	7	z	z	NOUN
ejpam-1678	42	8	)	)	PUNCT
ejpam-1678	42	9	is	be	AUX
ejpam-1678	42	10	an	an	DET
ejpam-1678	42	11	extension	extension	NOUN
ejpam-1678	42	12	of	of	ADP
ejpam-1678	42	13	the	the	DET
ejpam-1678	42	14	fractional	fractional	ADJ
ejpam-1678	42	15	derivative	derivative	ADJ
ejpam-1678	42	16	and	and	CCONJ
ejpam-1678	42	17	fractional	fractional	ADJ
ejpam-1678	42	18	integral	integral	ADJ
ejpam-1678	42	19	defined	define	VERB
ejpam-1678	42	20	by	by	ADP
ejpam-1678	42	21	owa	owa	PROPN
ejpam-1678	42	22	and	and	CCONJ
ejpam-1678	42	23	srivastava	srivastava	PROPN
ejpam-1678	43	1	[	[	X
ejpam-1678	43	2	6	6	NUM
ejpam-1678	43	3	]	]	PUNCT
ejpam-1678	43	4	.	.	PUNCT
ejpam-1678	44	1	suppose	suppose	VERB
ejpam-1678	45	1	f	f	X
ejpam-1678	45	2	(	(	PUNCT
ejpam-1678	45	3	z	z	NOUN
ejpam-1678	45	4	)	)	PUNCT
ejpam-1678	45	5	=	=	SYM
ejpam-1678	45	6	z	z	NOUN
ejpam-1678	46	1	+	+	NUM
ejpam-1678	46	2	∞	∞	NUM
ejpam-1678	46	3	∑	∑	PROPN
ejpam-1678	46	4	k=2	k=2	PROPN
ejpam-1678	46	5	akzk	akzk	PROPN
ejpam-1678	46	6	,	,	PUNCT
ejpam-1678	46	7	in	in	ADP
ejpam-1678	46	8	the	the	DET
ejpam-1678	46	9	light	light	NOUN
ejpam-1678	46	10	of	of	ADP
ejpam-1678	46	11	the	the	DET
ejpam-1678	46	12	above	above	ADJ
ejpam-1678	46	13	definitions	definition	NOUN
ejpam-1678	46	14	,	,	PUNCT
ejpam-1678	46	15	it	it	PRON
ejpam-1678	46	16	is	be	AUX
ejpam-1678	46	17	easy	easy	ADJ
ejpam-1678	46	18	to	to	PART
ejpam-1678	46	19	conclude	conclude	VERB
ejpam-1678	46	20	that	that	SCONJ
ejpam-1678	46	21	d	d	PROPN
ejpam-1678	46	22	n	n	CCONJ
ejpam-1678	46	23	,	,	PUNCT
ejpam-1678	46	24	γ	γ	X
ejpam-1678	46	25	λ	λ	NOUN
ejpam-1678	46	26	=	=	PUNCT
ejpam-1678	46	27	z	z	NOUN
ejpam-1678	47	1	+	+	NUM
ejpam-1678	47	2	∞	∞	NUM
ejpam-1678	47	3	∑	∑	X
ejpam-1678	47	4	k=2	k=2	PROPN
ejpam-1678	48	1	[	[	X
ejpam-1678	48	2	ψk(γ	ψk(γ	NUM
ejpam-1678	48	3	,	,	PUNCT
ejpam-1678	48	4	λ)]nakzk	λ)]nakzk	PROPN
ejpam-1678	48	5	,	,	PUNCT
ejpam-1678	48	6	n	n	PROPN
ejpam-1678	48	7	∈	∈	PROPN
ejpam-1678	48	8	n0	n0	X
ejpam-1678	48	9	=	=	SYM
ejpam-1678	48	10	n∪	n∪	PROPN
ejpam-1678	48	11	{	{	PUNCT
ejpam-1678	48	12	0	0	NUM
ejpam-1678	48	13	}	}	PUNCT
ejpam-1678	48	14	,	,	PUNCT
ejpam-1678	48	15	where	where	SCONJ
ejpam-1678	48	16	ψk(γ	ψk(γ	ADJ
ejpam-1678	48	17	,	,	PUNCT
ejpam-1678	48	18	λ	λ	NOUN
ejpam-1678	48	19	)	)	PUNCT
ejpam-1678	48	20	=	=	SYM
ejpam-1678	48	21	γ(k+	γ(k+	PROPN
ejpam-1678	48	22	1)γ(2−	1)γ(2−	NUM
ejpam-1678	48	23	γ	γ	NOUN
ejpam-1678	48	24	)	)	PUNCT
ejpam-1678	48	25	γ(k+	γ(k+	NOUN
ejpam-1678	48	26	1−	1−	NUM
ejpam-1678	48	27	γ	γ	X
ejpam-1678	48	28	)	)	PUNCT
ejpam-1678	49	1	[	[	X
ejpam-1678	49	2	1+λ(k−	1+λ(k−	NUM
ejpam-1678	49	3	1	1	NUM
ejpam-1678	49	4	)	)	PUNCT
ejpam-1678	49	5	]	]	PUNCT
ejpam-1678	50	1	(	(	PUNCT
ejpam-1678	50	2	k	k	X
ejpam-1678	50	3	=	=	SYM
ejpam-1678	50	4	2,3	2,3	NUM
ejpam-1678	50	5	,	,	PUNCT
ejpam-1678	50	6	.	.	PUNCT
ejpam-1678	50	7	.	.	PUNCT
ejpam-1678	50	8	.	.	PUNCT
ejpam-1678	50	9	)	)	PUNCT
ejpam-1678	50	10	.	.	PUNCT
ejpam-1678	51	1	(	(	PUNCT
ejpam-1678	51	2	2	2	X
ejpam-1678	51	3	)	)	PUNCT
ejpam-1678	51	4	let	let	VERB
ejpam-1678	51	5	t	t	NOUN
ejpam-1678	51	6	denote	denote	VERB
ejpam-1678	51	7	the	the	DET
ejpam-1678	51	8	subclass	subclass	NOUN
ejpam-1678	51	9	of	of	ADP
ejpam-1678	51	10	s	s	VERB
ejpam-1678	51	11	whose	whose	DET
ejpam-1678	51	12	elements	element	NOUN
ejpam-1678	51	13	can	can	AUX
ejpam-1678	51	14	be	be	AUX
ejpam-1678	51	15	expressed	express	VERB
ejpam-1678	51	16	in	in	ADP
ejpam-1678	51	17	the	the	DET
ejpam-1678	51	18	form	form	NOUN
ejpam-1678	51	19	f	f	X
ejpam-1678	51	20	(	(	PUNCT
ejpam-1678	51	21	z	z	NOUN
ejpam-1678	51	22	)	)	PUNCT
ejpam-1678	51	23	=	=	SYM
ejpam-1678	52	1	z	z	NOUN
ejpam-1678	53	1	+	+	NUM
ejpam-1678	53	2	∞	∞	NUM
ejpam-1678	53	3	∑	∑	PROPN
ejpam-1678	53	4	k=2	k=2	PROPN
ejpam-1678	53	5	akzk	akzk	PROPN
ejpam-1678	53	6	ak	ak	PROPN
ejpam-1678	53	7	¶	¶	PROPN
ejpam-1678	53	8	0	0	NUM
ejpam-1678	53	9	.	.	PUNCT
ejpam-1678	54	1	using	use	VERB
ejpam-1678	54	2	the	the	DET
ejpam-1678	54	3	differential	differential	ADJ
ejpam-1678	54	4	operator	operator	NOUN
ejpam-1678	54	5	d	d	PROPN
ejpam-1678	54	6	n	n	CCONJ
ejpam-1678	54	7	,	,	PUNCT
ejpam-1678	54	8	γ	γ	PROPN
ejpam-1678	54	9	λ	λ	PROPN
ejpam-1678	54	10	,	,	PUNCT
ejpam-1678	54	11	marouf	marouf	PROPN
ejpam-1678	55	1	[	[	X
ejpam-1678	55	2	5	5	NUM
ejpam-1678	55	3	]	]	PUNCT
ejpam-1678	55	4	introduced	introduce	VERB
ejpam-1678	55	5	and	and	CCONJ
ejpam-1678	55	6	studied	study	VERB
ejpam-1678	55	7	the	the	DET
ejpam-1678	55	8	class	class	NOUN
ejpam-1678	55	9	h	h	NOUN
ejpam-1678	55	10	n	n	CCONJ
ejpam-1678	55	11	,	,	PUNCT
ejpam-1678	55	12	γ	γ	X
ejpam-1678	55	13	λ	λ	X
ejpam-1678	56	1	[	[	X
ejpam-1678	56	2	α	α	X
ejpam-1678	56	3	,	,	PUNCT
ejpam-1678	56	4	β	β	X
ejpam-1678	56	5	]	]	X
ejpam-1678	56	6	.	.	PUNCT
ejpam-1678	57	1	as	as	ADP
ejpam-1678	57	2	a	a	DET
ejpam-1678	57	3	function	function	NOUN
ejpam-1678	57	4	f	f	X
ejpam-1678	57	5	(	(	PUNCT
ejpam-1678	57	6	z	z	NOUN
ejpam-1678	57	7	)	)	PUNCT
ejpam-1678	57	8	∈	∈	PROPN
ejpam-1678	57	9	t	t	PROPN
ejpam-1678	57	10	is	be	AUX
ejpam-1678	57	11	in	in	ADP
ejpam-1678	57	12	the	the	DET
ejpam-1678	57	13	h	h	NOUN
ejpam-1678	57	14	n	n	CCONJ
ejpam-1678	57	15	,	,	PUNCT
ejpam-1678	57	16	γ	γ	X
ejpam-1678	57	17	λ	λ	X
ejpam-1678	58	1	[	[	X
ejpam-1678	58	2	α	α	X
ejpam-1678	58	3	,	,	PUNCT
ejpam-1678	58	4	β	β	X
ejpam-1678	58	5	]	]	X
ejpam-1678	58	6	if	if	SCONJ
ejpam-1678	58	7	and	and	CCONJ
ejpam-1678	58	8	only	only	ADV
ejpam-1678	58	9	if	if	SCONJ
ejpam-1678	58	10	it	it	PRON
ejpam-1678	58	11	satisfies	satisfy	VERB
ejpam-1678	58	12	ℜ	ℜ	PROPN
ejpam-1678	58	13	�	�	PROPN
ejpam-1678	58	14	α	α	PROPN
ejpam-1678	58	15	d	d	PROPN
ejpam-1678	58	16	n+2,γ	n+2,γ	PROPN
ejpam-1678	58	17	λ	λ	X
ejpam-1678	58	18	f	f	X
ejpam-1678	58	19	(	(	PUNCT
ejpam-1678	58	20	z	z	NOUN
ejpam-1678	58	21	)	)	PUNCT
ejpam-1678	58	22	d	d	NOUN
ejpam-1678	58	23	n	n	CCONJ
ejpam-1678	58	24	,	,	PUNCT
ejpam-1678	58	25	γ	γ	X
ejpam-1678	58	26	λ	λ	X
ejpam-1678	58	27	f	f	X
ejpam-1678	58	28	(	(	PUNCT
ejpam-1678	58	29	z	z	NOUN
ejpam-1678	58	30	)	)	PUNCT
ejpam-1678	59	1	+	+	CCONJ
ejpam-1678	59	2	(	(	PUNCT
ejpam-1678	59	3	1−α	1−α	NUM
ejpam-1678	59	4	)	)	PUNCT
ejpam-1678	60	1	d	d	NOUN
ejpam-1678	60	2	n+1,γ	n+1,γ	PROPN
ejpam-1678	60	3	λ	λ	X
ejpam-1678	60	4	f	f	X
ejpam-1678	60	5	(	(	PUNCT
ejpam-1678	60	6	z	z	NOUN
ejpam-1678	60	7	)	)	PUNCT
ejpam-1678	60	8	d	d	NOUN
ejpam-1678	60	9	n	n	CCONJ
ejpam-1678	60	10	,	,	PUNCT
ejpam-1678	60	11	γ	γ	X
ejpam-1678	60	12	λ	λ	X
ejpam-1678	60	13	f	f	X
ejpam-1678	60	14	(	(	PUNCT
ejpam-1678	60	15	z	z	NOUN
ejpam-1678	60	16	)	)	PUNCT
ejpam-1678	60	17	�	�	PROPN
ejpam-1678	60	18	>	>	X
ejpam-1678	60	19	β	β	X
ejpam-1678	60	20	(	(	PUNCT
ejpam-1678	60	21	α¾	α¾	PROPN
ejpam-1678	60	22	0	0	NUM
ejpam-1678	60	23	;	;	PUNCT
ejpam-1678	60	24	0¶	0¶	NOUN
ejpam-1678	60	25	β	β	X
ejpam-1678	60	26	<	<	X
ejpam-1678	60	27	0	0	NUM
ejpam-1678	60	28	)	)	PUNCT
ejpam-1678	60	29	.	.	PUNCT
ejpam-1678	61	1	in	in	ADP
ejpam-1678	61	2	particular	particular	ADJ
ejpam-1678	61	3	,	,	PUNCT
ejpam-1678	61	4	the	the	DET
ejpam-1678	61	5	class	class	NOUN
ejpam-1678	61	6	h	h	NOUN
ejpam-1678	61	7	0,0	0,0	NUM
ejpam-1678	61	8	1	1	NUM
ejpam-1678	61	9	[	[	X
ejpam-1678	61	10	α	α	X
ejpam-1678	61	11	,	,	PUNCT
ejpam-1678	61	12	β	β	NOUN
ejpam-1678	61	13	]	]	X
ejpam-1678	61	14	≡	≡	PROPN
ejpam-1678	61	15	h̄[α	h̄[α	PROPN
ejpam-1678	61	16	,	,	PUNCT
ejpam-1678	61	17	β	β	PROPN
ejpam-1678	61	18	]	]	PUNCT
ejpam-1678	61	19	was	be	AUX
ejpam-1678	61	20	studied	study	VERB
ejpam-1678	61	21	by	by	ADP
ejpam-1678	61	22	lashin	lashin	NOUN
ejpam-1678	61	23	[	[	X
ejpam-1678	61	24	3	3	NUM
ejpam-1678	61	25	]	]	PUNCT
ejpam-1678	61	26	and	and	CCONJ
ejpam-1678	61	27	the	the	DET
ejpam-1678	61	28	classes	class	NOUN
ejpam-1678	61	29	h	h	NOUN
ejpam-1678	61	30	0,0	0,0	NUM
ejpam-1678	61	31	1	1	NUM
ejpam-1678	61	32	[	[	X
ejpam-1678	61	33	0,β]≡	0,β]≡	NOUN
ejpam-1678	61	34	t	t	PROPN
ejpam-1678	61	35	∗(β	∗(β	PROPN
ejpam-1678	61	36	)	)	PUNCT
ejpam-1678	61	37	and	and	CCONJ
ejpam-1678	61	38	h	h	NOUN
ejpam-1678	61	39	0,0	0,0	NUM
ejpam-1678	61	40	1	1	NUM
ejpam-1678	62	1	[	[	X
ejpam-1678	62	2	1,β]≡	1,β]≡	NOUN
ejpam-1678	62	3	c(β	c(β	NOUN
ejpam-1678	62	4	)	)	PUNCT
ejpam-1678	62	5	were	be	AUX
ejpam-1678	62	6	studied	study	VERB
ejpam-1678	62	7	by	by	ADP
ejpam-1678	62	8	silverman	silverman	NOUN
ejpam-1678	62	9	[	[	X
ejpam-1678	62	10	8	8	NUM
ejpam-1678	62	11	]	]	PUNCT
ejpam-1678	62	12	.	.	PUNCT
ejpam-1678	63	1	to	to	PART
ejpam-1678	63	2	prove	prove	VERB
ejpam-1678	63	3	our	our	PRON
ejpam-1678	63	4	results	result	NOUN
ejpam-1678	63	5	we	we	PRON
ejpam-1678	63	6	shall	shall	AUX
ejpam-1678	63	7	need	need	VERB
ejpam-1678	63	8	the	the	DET
ejpam-1678	63	9	following	follow	VERB
ejpam-1678	63	10	definition	definition	NOUN
ejpam-1678	63	11	and	and	CCONJ
ejpam-1678	63	12	lemma	lemma	PROPN
ejpam-1678	63	13	:	:	PUNCT
ejpam-1678	63	14	definition	definition	NOUN
ejpam-1678	63	15	1	1	NUM
ejpam-1678	63	16	.	.	PUNCT
ejpam-1678	64	1	[	[	X
ejpam-1678	64	2	see	see	VERB
ejpam-1678	64	3	9	9	NUM
ejpam-1678	64	4	]	]	X
ejpam-1678	64	5	an	an	DET
ejpam-1678	64	6	infinite	infinite	ADJ
ejpam-1678	64	7	sequence	sequence	NOUN
ejpam-1678	64	8	{	{	PUNCT
ejpam-1678	64	9	bn	bn	NOUN
ejpam-1678	64	10	}	}	PUNCT
ejpam-1678	64	11	∞	∞	NUM
ejpam-1678	64	12	n=1	n=1	PROPN
ejpam-1678	64	13	of	of	ADP
ejpam-1678	64	14	complex	complex	ADJ
ejpam-1678	64	15	numbers	number	NOUN
ejpam-1678	64	16	will	will	AUX
ejpam-1678	64	17	be	be	AUX
ejpam-1678	64	18	called	call	VERB
ejpam-1678	64	19	a	a	DET
ejpam-1678	64	20	subordinating	subordinate	VERB
ejpam-1678	64	21	factor	factor	NOUN
ejpam-1678	64	22	sequence	sequence	NOUN
ejpam-1678	64	23	if	if	SCONJ
ejpam-1678	64	24	whenever	whenever	SCONJ
ejpam-1678	64	25	f	f	PROPN
ejpam-1678	64	26	∈k	∈k	VERB
ejpam-1678	64	27	,	,	PUNCT
ejpam-1678	64	28	we	we	PRON
ejpam-1678	64	29	have	have	VERB
ejpam-1678	64	30	the	the	DET
ejpam-1678	64	31	subordination	subordination	NOUN
ejpam-1678	64	32	given	give	VERB
ejpam-1678	64	33	by	by	ADP
ejpam-1678	64	34	∞	∞	PROPN
ejpam-1678	64	35	∑	∑	PROPN
ejpam-1678	64	36	n=1	n=1	PROPN
ejpam-1678	64	37	an	an	DET
ejpam-1678	64	38	bnzn	bnzn	NOUN
ejpam-1678	64	39	≺	≺	VERB
ejpam-1678	64	40	f	f	X
ejpam-1678	64	41	(	(	PUNCT
ejpam-1678	64	42	z	z	NOUN
ejpam-1678	64	43	)	)	PUNCT
ejpam-1678	64	44	(	(	PUNCT
ejpam-1678	64	45	z	z	NOUN
ejpam-1678	64	46	∈	∈	PROPN
ejpam-1678	64	47	u	u	NOUN
ejpam-1678	64	48	,	,	PUNCT
ejpam-1678	64	49	a1	a1	NOUN
ejpam-1678	64	50	=	=	SYM
ejpam-1678	64	51	1	1	NUM
ejpam-1678	64	52	)	)	PUNCT
ejpam-1678	64	53	.	.	PUNCT
ejpam-1678	65	1	l.	l.	PROPN
ejpam-1678	65	2	xiong	xiong	PROPN
ejpam-1678	65	3	,	,	PUNCT
ejpam-1678	65	4	x.	x.	PROPN
ejpam-1678	65	5	liu	liu	PROPN
ejpam-1678	65	6	/	/	SYM
ejpam-1678	65	7	eur	eur	PROPN
ejpam-1678	65	8	.	.	PUNCT
ejpam-1678	66	1	j.	j.	PROPN
ejpam-1678	66	2	pure	pure	PROPN
ejpam-1678	66	3	appl	appl	PROPN
ejpam-1678	66	4	.	.	PROPN
ejpam-1678	66	5	math	math	PROPN
ejpam-1678	66	6	,	,	PUNCT
ejpam-1678	66	7	5	5	NUM
ejpam-1678	66	8	(	(	PUNCT
ejpam-1678	66	9	2012	2012	NUM
ejpam-1678	66	10	)	)	PUNCT
ejpam-1678	66	11	,	,	PUNCT
ejpam-1678	66	12	380	380	NUM
ejpam-1678	66	13	-	-	SYM
ejpam-1678	66	14	389	389	NUM
ejpam-1678	66	15	382	382	NUM
ejpam-1678	66	16	lemma	lemma	PROPN
ejpam-1678	66	17	1	1	NUM
ejpam-1678	66	18	.	.	PUNCT
ejpam-1678	67	1	[	[	X
ejpam-1678	67	2	see	see	VERB
ejpam-1678	67	3	9	9	NUM
ejpam-1678	67	4	]	]	X
ejpam-1678	67	5	the	the	DET
ejpam-1678	67	6	sequence	sequence	NOUN
ejpam-1678	67	7	{	{	PUNCT
ejpam-1678	67	8	bn	bn	NOUN
ejpam-1678	67	9	}	}	PUNCT
ejpam-1678	67	10	∞	∞	NUM
ejpam-1678	67	11	n=1	n=1	PROPN
ejpam-1678	67	12	is	be	AUX
ejpam-1678	67	13	subordinating	subordinate	VERB
ejpam-1678	67	14	factor	factor	NOUN
ejpam-1678	67	15	sequence	sequence	NOUN
ejpam-1678	67	16	if	if	SCONJ
ejpam-1678	67	17	and	and	CCONJ
ejpam-1678	67	18	only	only	ADV
ejpam-1678	67	19	if	if	SCONJ
ejpam-1678	67	20	ℜ	ℜ	ADJ
ejpam-1678	67	21	�	�	PROPN
ejpam-1678	67	22	1	1	NUM
ejpam-1678	67	23	+	+	NUM
ejpam-1678	67	24	2	2	NUM
ejpam-1678	67	25	∞	∞	NUM
ejpam-1678	67	26	∑	∑	PUNCT
ejpam-1678	67	27	n=1	n=1	PROPN
ejpam-1678	67	28	bnzn	bnzn	NOUN
ejpam-1678	67	29	>	>	X
ejpam-1678	67	30	0	0	PUNCT
ejpam-1678	68	1	(	(	PUNCT
ejpam-1678	68	2	z	z	NOUN
ejpam-1678	68	3	∈	∈	PROPN
ejpam-1678	68	4	u	u	NOUN
ejpam-1678	68	5	)	)	PUNCT
ejpam-1678	68	6	.	.	PUNCT
ejpam-1678	69	1	lemma	lemma	PROPN
ejpam-1678	69	2	2	2	NUM
ejpam-1678	69	3	.	.	PUNCT
ejpam-1678	70	1	[	[	AUX
ejpam-1678	70	2	see	see	VERB
ejpam-1678	70	3	7	7	NUM
ejpam-1678	70	4	]	]	X
ejpam-1678	70	5	let	let	VERB
ejpam-1678	70	6	0	0	NUM
ejpam-1678	70	7	<	<	X
ejpam-1678	70	8	a	a	DET
ejpam-1678	70	9	¶	¶	PROPN
ejpam-1678	70	10	c.	c.	NOUN
ejpam-1678	70	11	if	if	SCONJ
ejpam-1678	70	12	c	c	PROPN
ejpam-1678	70	13	¾	¾	PROPN
ejpam-1678	70	14	2	2	NUM
ejpam-1678	70	15	or	or	CCONJ
ejpam-1678	70	16	a+	a+	PRON
ejpam-1678	70	17	c	c	PROPN
ejpam-1678	70	18	¾	¾	PROPN
ejpam-1678	70	19	3	3	NUM
ejpam-1678	70	20	,	,	PUNCT
ejpam-1678	70	21	then	then	ADV
ejpam-1678	70	22	the	the	DET
ejpam-1678	70	23	function	function	PROPN
ejpam-1678	70	24	h(a	h(a	PROPN
ejpam-1678	70	25	,	,	PUNCT
ejpam-1678	70	26	c	c	X
ejpam-1678	70	27	;	;	PUNCT
ejpam-1678	70	28	z	z	X
ejpam-1678	70	29	)	)	PUNCT
ejpam-1678	70	30	=	=	SYM
ejpam-1678	71	1	z	z	NOUN
ejpam-1678	72	1	+	+	NUM
ejpam-1678	72	2	∞	∞	PROPN
ejpam-1678	72	3	∑	∑	PROPN
ejpam-1678	72	4	k=2	k=2	PROPN
ejpam-1678	72	5	(	(	PUNCT
ejpam-1678	72	6	a)k−1	a)k−1	PROPN
ejpam-1678	72	7	(	(	PUNCT
ejpam-1678	72	8	c)k−1	c)k−1	PROPN
ejpam-1678	72	9	zk	zk	PROPN
ejpam-1678	72	10	(	(	PUNCT
ejpam-1678	72	11	z	z	NOUN
ejpam-1678	72	12	∈	∈	PROPN
ejpam-1678	72	13	u	u	NOUN
ejpam-1678	72	14	)	)	PUNCT
ejpam-1678	72	15	belongs	belong	VERB
ejpam-1678	72	16	to	to	ADP
ejpam-1678	72	17	the	the	DET
ejpam-1678	72	18	class	class	NOUN
ejpam-1678	72	19	k	k	PROPN
ejpam-1678	72	20	of	of	ADP
ejpam-1678	72	21	convex	convex	PROPN
ejpam-1678	72	22	functions	function	NOUN
ejpam-1678	72	23	.	.	PUNCT
ejpam-1678	73	1	in	in	ADP
ejpam-1678	73	2	[	[	X
ejpam-1678	73	3	5	5	NUM
ejpam-1678	73	4	]	]	PUNCT
ejpam-1678	73	5	,	,	PUNCT
ejpam-1678	73	6	marouf	marouf	NOUN
ejpam-1678	73	7	proved	prove	VERB
ejpam-1678	73	8	the	the	DET
ejpam-1678	73	9	sufficient	sufficient	ADJ
ejpam-1678	73	10	and	and	CCONJ
ejpam-1678	73	11	necessary	necessary	ADJ
ejpam-1678	73	12	condition	condition	NOUN
ejpam-1678	73	13	on	on	ADP
ejpam-1678	73	14	a	a	DET
ejpam-1678	73	15	function	function	NOUN
ejpam-1678	73	16	f	f	NOUN
ejpam-1678	73	17	(	(	PUNCT
ejpam-1678	73	18	z	z	NOUN
ejpam-1678	73	19	)	)	PUNCT
ejpam-1678	73	20	=	=	SYM
ejpam-1678	74	1	z	z	NOUN
ejpam-1678	75	1	+	+	NUM
ejpam-1678	75	2	∞	∞	NUM
ejpam-1678	75	3	∑	∑	PROPN
ejpam-1678	75	4	k=2	k=2	PROPN
ejpam-1678	75	5	akzk	akzk	PROPN
ejpam-1678	75	6	∈	∈	PROPN
ejpam-1678	75	7	t	t	PROPN
ejpam-1678	75	8	to	to	PART
ejpam-1678	75	9	be	be	AUX
ejpam-1678	75	10	h	h	NOUN
ejpam-1678	75	11	n	n	NOUN
ejpam-1678	75	12	,	,	PUNCT
ejpam-1678	75	13	γ	γ	X
ejpam-1678	75	14	λ	λ	X
ejpam-1678	76	1	[	[	X
ejpam-1678	76	2	α	α	X
ejpam-1678	76	3	,	,	PUNCT
ejpam-1678	76	4	β	β	X
ejpam-1678	76	5	]	]	X
ejpam-1678	76	6	,	,	PUNCT
ejpam-1678	76	7	which	which	PRON
ejpam-1678	76	8	is	be	AUX
ejpam-1678	76	9	equivalent	equivalent	ADJ
ejpam-1678	76	10	to	to	ADP
ejpam-1678	76	11	the	the	DET
ejpam-1678	76	12	following	follow	VERB
ejpam-1678	76	13	lemma	lemma	PROPN
ejpam-1678	76	14	:	:	PUNCT
ejpam-1678	76	15	lemma	lemma	PROPN
ejpam-1678	76	16	3	3	X
ejpam-1678	76	17	.	.	PUNCT
ejpam-1678	77	1	[	[	X
ejpam-1678	77	2	see	see	VERB
ejpam-1678	77	3	5	5	NUM
ejpam-1678	77	4	]	]	PUNCT
ejpam-1678	77	5	a	a	DET
ejpam-1678	77	6	function	function	NOUN
ejpam-1678	77	7	f	f	X
ejpam-1678	77	8	(	(	PUNCT
ejpam-1678	77	9	z	z	NOUN
ejpam-1678	77	10	)	)	PUNCT
ejpam-1678	77	11	∈	∈	PROPN
ejpam-1678	77	12	t	t	PROPN
ejpam-1678	77	13	is	be	AUX
ejpam-1678	77	14	in	in	ADP
ejpam-1678	77	15	the	the	DET
ejpam-1678	77	16	h	h	NOUN
ejpam-1678	77	17	n	n	CCONJ
ejpam-1678	77	18	,	,	PUNCT
ejpam-1678	77	19	γ	γ	X
ejpam-1678	77	20	λ	λ	X
ejpam-1678	78	1	[	[	X
ejpam-1678	78	2	α	α	X
ejpam-1678	78	3	,	,	PUNCT
ejpam-1678	78	4	β	β	X
ejpam-1678	78	5	]	]	X
ejpam-1678	78	6	if	if	SCONJ
ejpam-1678	78	7	and	and	CCONJ
ejpam-1678	78	8	only	only	ADV
ejpam-1678	78	9	if	if	SCONJ
ejpam-1678	78	10	∞	∞	PROPN
ejpam-1678	78	11	∑	∑	X
ejpam-1678	78	12	k=2	k=2	PROPN
ejpam-1678	79	1	[	[	X
ejpam-1678	79	2	(	(	PUNCT
ejpam-1678	79	3	αψk(γ	αψk(γ	PROPN
ejpam-1678	79	4	,	,	PUNCT
ejpam-1678	79	5	λ	λ	X
ejpam-1678	79	6	)	)	PUNCT
ejpam-1678	79	7	+	+	NOUN
ejpam-1678	79	8	1)(ψk(γ	1)(ψk(γ	NUM
ejpam-1678	79	9	,	,	PUNCT
ejpam-1678	79	10	λ)−	λ)−	PROPN
ejpam-1678	79	11	1)+	1)+	NUM
ejpam-1678	79	12	1−	1−	NUM
ejpam-1678	79	13	β][ψk(γ	β][ψk(γ	PROPN
ejpam-1678	79	14	,	,	PUNCT
ejpam-1678	79	15	λ)]n|ak|	λ)]n|ak|	NUM
ejpam-1678	79	16	¶	¶	NOUN
ejpam-1678	79	17	1−	1−	NUM
ejpam-1678	79	18	β	β	X
ejpam-1678	79	19	(	(	PUNCT
ejpam-1678	79	20	3	3	X
ejpam-1678	79	21	)	)	PUNCT
ejpam-1678	79	22	which	which	PRON
ejpam-1678	79	23	ψk(γ	ψk(γ	NUM
ejpam-1678	79	24	,	,	PUNCT
ejpam-1678	79	25	λ	λ	X
ejpam-1678	79	26	)	)	PUNCT
ejpam-1678	79	27	is	be	AUX
ejpam-1678	79	28	defined	define	VERB
ejpam-1678	79	29	as	as	ADP
ejpam-1678	79	30	(	(	PUNCT
ejpam-1678	79	31	2	2	NUM
ejpam-1678	79	32	)	)	PUNCT
ejpam-1678	79	33	.	.	PUNCT
ejpam-1678	80	1	lemma	lemma	PROPN
ejpam-1678	80	2	4	4	NUM
ejpam-1678	80	3	.	.	PUNCT
ejpam-1678	81	1	[	[	X
ejpam-1678	81	2	see	see	VERB
ejpam-1678	81	3	4	4	NUM
ejpam-1678	81	4	]	]	PUNCT
ejpam-1678	81	5	if	if	SCONJ
ejpam-1678	81	6	the	the	DET
ejpam-1678	81	7	functions	function	NOUN
ejpam-1678	81	8	f	f	X
ejpam-1678	81	9	(	(	PUNCT
ejpam-1678	81	10	z	z	NOUN
ejpam-1678	81	11	)	)	PUNCT
ejpam-1678	81	12	and	and	CCONJ
ejpam-1678	81	13	g(z	g(z	PROPN
ejpam-1678	81	14	)	)	PUNCT
ejpam-1678	81	15	are	be	AUX
ejpam-1678	81	16	analytic	analytic	ADJ
ejpam-1678	81	17	in	in	ADP
ejpam-1678	81	18	u	u	NOUN
ejpam-1678	81	19	with	with	ADP
ejpam-1678	81	20	g(z	g(z	PROPN
ejpam-1678	81	21	)	)	PUNCT
ejpam-1678	81	22	≺	≺	NOUN
ejpam-1678	81	23	f	f	X
ejpam-1678	81	24	(	(	PUNCT
ejpam-1678	81	25	z	z	NOUN
ejpam-1678	81	26	)	)	PUNCT
ejpam-1678	81	27	,	,	PUNCT
ejpam-1678	81	28	then	then	ADV
ejpam-1678	81	29	for	for	ADP
ejpam-1678	81	30	s	s	PROPN
ejpam-1678	81	31	>	>	X
ejpam-1678	81	32	0	0	PROPN
ejpam-1678	81	33	and	and	CCONJ
ejpam-1678	81	34	z	z	NOUN
ejpam-1678	81	35	=	=	SYM
ejpam-1678	81	36	reiθ	reiθ	PROPN
ejpam-1678	81	37	(	(	PUNCT
ejpam-1678	81	38	0	0	NUM
ejpam-1678	81	39	<	<	X
ejpam-1678	81	40	r	r	NOUN
ejpam-1678	81	41	<	<	X
ejpam-1678	81	42	1	1	NUM
ejpam-1678	81	43	)	)	PUNCT
ejpam-1678	81	44	,	,	PUNCT
ejpam-1678	81	45	we	we	PRON
ejpam-1678	81	46	have	have	VERB
ejpam-1678	81	47	∫	∫	PROPN
ejpam-1678	81	48	2π	2π	NOUN
ejpam-1678	81	49	0	0	PUNCT
ejpam-1678	82	1	|	|	ADV
ejpam-1678	82	2	f	f	X
ejpam-1678	82	3	(	(	PUNCT
ejpam-1678	82	4	reiθ	reiθ	PROPN
ejpam-1678	82	5	)	)	PUNCT
ejpam-1678	82	6	|s	|s	PROPN
ejpam-1678	83	1	¶	¶	NUM
ejpam-1678	83	2	∫	∫	PROPN
ejpam-1678	83	3	2π	2π	PROPN
ejpam-1678	83	4	0	0	NUM
ejpam-1678	84	1	|g(reiθ	|g(reiθ	PROPN
ejpam-1678	84	2	)	)	PUNCT
ejpam-1678	84	3	|s	|s	PROPN
ejpam-1678	84	4	.	.	PROPN
ejpam-1678	85	1	2	2	NUM
ejpam-1678	85	2	.	.	X
ejpam-1678	86	1	some	some	DET
ejpam-1678	86	2	results	result	NOUN
ejpam-1678	86	3	on	on	ADP
ejpam-1678	86	4	the	the	DET
ejpam-1678	86	5	class	class	NOUN
ejpam-1678	86	6	h	h	NOUN
ejpam-1678	86	7	n	n	CCONJ
ejpam-1678	86	8	,	,	PUNCT
ejpam-1678	86	9	γ	γ	X
ejpam-1678	86	10	λ	λ	X
ejpam-1678	87	1	[	[	X
ejpam-1678	87	2	α	α	X
ejpam-1678	87	3	,	,	PUNCT
ejpam-1678	87	4	β	β	X
ejpam-1678	87	5	]	]	X
ejpam-1678	87	6	we	we	PRON
ejpam-1678	87	7	begin	begin	VERB
ejpam-1678	87	8	with	with	ADP
ejpam-1678	87	9	the	the	DET
ejpam-1678	87	10	following	follow	VERB
ejpam-1678	87	11	theorem	theorem	NOUN
ejpam-1678	87	12	:	:	PUNCT
ejpam-1678	87	13	theorem	theorem	NOUN
ejpam-1678	87	14	1	1	NUM
ejpam-1678	87	15	.	.	PUNCT
ejpam-1678	88	1	if	if	SCONJ
ejpam-1678	88	2	f	f	PROPN
ejpam-1678	88	3	∈	∈	PROPN
ejpam-1678	88	4	h	h	NOUN
ejpam-1678	88	5	n	n	CCONJ
ejpam-1678	88	6	,	,	PUNCT
ejpam-1678	88	7	γ	γ	X
ejpam-1678	88	8	λ	λ	X
ejpam-1678	89	1	[	[	X
ejpam-1678	89	2	α	α	X
ejpam-1678	89	3	,	,	PUNCT
ejpam-1678	89	4	β	β	X
ejpam-1678	89	5	]	]	PUNCT
ejpam-1678	89	6	in	in	ADP
ejpam-1678	89	7	u	u	NOUN
ejpam-1678	89	8	and	and	CCONJ
ejpam-1678	89	9	s	s	PROPN
ejpam-1678	89	10	>	>	X
ejpam-1678	89	11	0	0	NUM
ejpam-1678	89	12	,	,	PUNCT
ejpam-1678	89	13	0	0	NUM
ejpam-1678	89	14	<	<	X
ejpam-1678	89	15	|z|	|z|	NOUN
ejpam-1678	89	16	=	=	SYM
ejpam-1678	89	17	r	r	NOUN
ejpam-1678	89	18	<	<	X
ejpam-1678	89	19	1	1	NUM
ejpam-1678	89	20	,	,	PUNCT
ejpam-1678	89	21	then	then	ADV
ejpam-1678	89	22	for	for	ADP
ejpam-1678	89	23	function	function	NOUN
ejpam-1678	89	24	g	g	PROPN
ejpam-1678	89	25	∈k	∈k	PROPN
ejpam-1678	89	26	φ(2	φ(2	PROPN
ejpam-1678	89	27	)	)	PUNCT
ejpam-1678	89	28	φ(2)+	φ(2)+	VERB
ejpam-1678	89	29	1−	1−	NUM
ejpam-1678	89	30	β	β	X
ejpam-1678	89	31	f	f	PROPN
ejpam-1678	89	32	∗	∗	NOUN
ejpam-1678	89	33	g(z	g(z	PROPN
ejpam-1678	89	34	)	)	PUNCT
ejpam-1678	89	35	≺	≺	NOUN
ejpam-1678	89	36	2g(z	2g(z	NUM
ejpam-1678	89	37	)	)	PUNCT
ejpam-1678	89	38	(	(	PUNCT
ejpam-1678	89	39	4	4	NUM
ejpam-1678	89	40	)	)	PUNCT
ejpam-1678	89	41	and	and	CCONJ
ejpam-1678	89	42	φ(2	φ(2	PROPN
ejpam-1678	89	43	)	)	PUNCT
ejpam-1678	89	44	φ(2)+	φ(2)+	VERB
ejpam-1678	89	45	1−	1−	NUM
ejpam-1678	89	46	β	β	X
ejpam-1678	89	47	∫	∫	PROPN
ejpam-1678	90	1	2π	2π	PROPN
ejpam-1678	90	2	0	0	PUNCT
ejpam-1678	91	1	|	|	ADV
ejpam-1678	91	2	f	f	PROPN
ejpam-1678	91	3	∗	∗	NOUN
ejpam-1678	91	4	g(reiθ	g(reiθ	NOUN
ejpam-1678	91	5	)	)	PUNCT
ejpam-1678	91	6	|sdθ	|sdθ	NOUN
ejpam-1678	91	7	¶	¶	NOUN
ejpam-1678	91	8	2	2	NUM
ejpam-1678	91	9	∫	∫	PROPN
ejpam-1678	91	10	2π	2π	PROPN
ejpam-1678	91	11	0	0	NUM
ejpam-1678	92	1	|g(reiθ	|g(reiθ	NOUN
ejpam-1678	92	2	)	)	PUNCT
ejpam-1678	92	3	|sdθ	|sdθ	NOUN
ejpam-1678	92	4	(	(	PUNCT
ejpam-1678	92	5	5	5	NUM
ejpam-1678	92	6	)	)	PUNCT
ejpam-1678	92	7	where	where	SCONJ
ejpam-1678	92	8	φ(2	φ(2	NOUN
ejpam-1678	92	9	)	)	PUNCT
ejpam-1678	92	10	=	=	PUNCT
ejpam-1678	93	1	[	[	X
ejpam-1678	93	2	(	(	PUNCT
ejpam-1678	93	3	αψ2(γ	αψ2(γ	NOUN
ejpam-1678	93	4	,	,	PUNCT
ejpam-1678	93	5	λ	λ	NOUN
ejpam-1678	93	6	)	)	PUNCT
ejpam-1678	93	7	+	+	NUM
ejpam-1678	93	8	1)(ψ2(γ	1)(ψ2(γ	NUM
ejpam-1678	93	9	,	,	PUNCT
ejpam-1678	93	10	λ)−	λ)−	PROPN
ejpam-1678	93	11	1	1	NUM
ejpam-1678	93	12	)	)	PUNCT
ejpam-1678	93	13	+	+	SYM
ejpam-1678	93	14	1−	1−	NUM
ejpam-1678	93	15	β][ψ2(γ	β][ψ2(γ	NOUN
ejpam-1678	93	16	,	,	PUNCT
ejpam-1678	93	17	λ)]n	λ)]n	NOUN
ejpam-1678	93	18	.	.	PUNCT
ejpam-1678	93	19	l.	l.	PROPN
ejpam-1678	93	20	xiong	xiong	PROPN
ejpam-1678	93	21	,	,	PUNCT
ejpam-1678	93	22	x.	x.	PROPN
ejpam-1678	93	23	liu	liu	PROPN
ejpam-1678	93	24	/	/	SYM
ejpam-1678	93	25	eur	eur	PROPN
ejpam-1678	93	26	.	.	PUNCT
ejpam-1678	94	1	j.	j.	PROPN
ejpam-1678	94	2	pure	pure	PROPN
ejpam-1678	94	3	appl	appl	PROPN
ejpam-1678	94	4	.	.	PROPN
ejpam-1678	94	5	math	math	PROPN
ejpam-1678	94	6	,	,	PUNCT
ejpam-1678	94	7	5	5	NUM
ejpam-1678	94	8	(	(	PUNCT
ejpam-1678	94	9	2012	2012	NUM
ejpam-1678	94	10	)	)	PUNCT
ejpam-1678	94	11	,	,	PUNCT
ejpam-1678	94	12	380	380	NUM
ejpam-1678	94	13	-	-	SYM
ejpam-1678	94	14	389	389	NUM
ejpam-1678	94	15	383	383	NUM
ejpam-1678	94	16	proof	proof	NOUN
ejpam-1678	94	17	.	.	PUNCT
ejpam-1678	95	1	suppose	suppose	VERB
ejpam-1678	95	2	we	we	PRON
ejpam-1678	95	3	take	take	VERB
ejpam-1678	95	4	f	f	PROPN
ejpam-1678	95	5	(	(	PUNCT
ejpam-1678	95	6	z	z	NOUN
ejpam-1678	95	7	)	)	PUNCT
ejpam-1678	95	8	=	=	SYM
ejpam-1678	96	1	z	z	NOUN
ejpam-1678	97	1	+	+	NUM
ejpam-1678	97	2	∞	∞	NUM
ejpam-1678	97	3	∑	∑	PROPN
ejpam-1678	97	4	k=2	k=2	PROPN
ejpam-1678	97	5	akzk	akzk	PROPN
ejpam-1678	97	6	∈	∈	PROPN
ejpam-1678	97	7	h	h	PROPN
ejpam-1678	97	8	n	n	CCONJ
ejpam-1678	97	9	,	,	PUNCT
ejpam-1678	97	10	γ	γ	X
ejpam-1678	97	11	λ	λ	X
ejpam-1678	98	1	[	[	X
ejpam-1678	98	2	α	α	X
ejpam-1678	98	3	,	,	PUNCT
ejpam-1678	98	4	β	β	NOUN
ejpam-1678	98	5	]	]	X
ejpam-1678	98	6	and	and	CCONJ
ejpam-1678	98	7	g(z	g(z	ADJ
ejpam-1678	98	8	)	)	PUNCT
ejpam-1678	99	1	=	=	SYM
ejpam-1678	99	2	z	z	NOUN
ejpam-1678	100	1	+	+	NUM
ejpam-1678	100	2	∞	∞	NUM
ejpam-1678	100	3	∑	∑	PROPN
ejpam-1678	100	4	k=2	k=2	PROPN
ejpam-1678	100	5	bkzk	bkzk	NOUN
ejpam-1678	100	6	∈	∈	PROPN
ejpam-1678	101	1	k	k	NOUN
ejpam-1678	101	2	,	,	PUNCT
ejpam-1678	101	3	then	then	ADV
ejpam-1678	101	4	φ(2	φ(2	PROPN
ejpam-1678	101	5	)	)	PUNCT
ejpam-1678	102	1	2φ(2)+	2φ(2)+	NUM
ejpam-1678	102	2	2(1−β	2(1−β	NUM
ejpam-1678	102	3	)	)	PUNCT
ejpam-1678	102	4	f	f	PROPN
ejpam-1678	102	5	∗	∗	NOUN
ejpam-1678	102	6	g(z	g(z	PROPN
ejpam-1678	102	7	)	)	PUNCT
ejpam-1678	102	8	=	=	SYM
ejpam-1678	102	9	φ(2	φ(2	PROPN
ejpam-1678	102	10	)	)	PUNCT
ejpam-1678	103	1	2φ(2)+	2φ(2)+	NUM
ejpam-1678	103	2	2(1−	2(1−	NUM
ejpam-1678	103	3	β	β	X
ejpam-1678	103	4	)	)	PUNCT
ejpam-1678	103	5	z	z	NOUN
ejpam-1678	104	1	+	+	CCONJ
ejpam-1678	104	2	∞	∞	NUM
ejpam-1678	104	3	∑	∑	PROPN
ejpam-1678	104	4	k=2	k=2	PROPN
ejpam-1678	104	5	φ(2	φ(2	PROPN
ejpam-1678	104	6	)	)	PUNCT
ejpam-1678	105	1	2φ(2)+	2φ(2)+	NUM
ejpam-1678	105	2	2(1−	2(1−	NUM
ejpam-1678	105	3	β	β	X
ejpam-1678	105	4	)	)	PUNCT
ejpam-1678	105	5	ak	ak	NOUN
ejpam-1678	105	6	bkzk	bkzk	NOUN
ejpam-1678	105	7	.	.	PUNCT
ejpam-1678	106	1	if	if	SCONJ
ejpam-1678	106	2	we	we	PRON
ejpam-1678	106	3	can	can	AUX
ejpam-1678	106	4	know	know	VERB
ejpam-1678	106	5	ℜ	ℜ	PROPN
ejpam-1678	106	6	�	�	PROPN
ejpam-1678	106	7	1	1	NUM
ejpam-1678	106	8	+	+	NUM
ejpam-1678	106	9	2	2	NUM
ejpam-1678	106	10	∞	∞	NUM
ejpam-1678	106	11	∑	∑	PROPN
ejpam-1678	106	12	k=2	k=2	PROPN
ejpam-1678	106	13	φ(2	φ(2	PROPN
ejpam-1678	106	14	)	)	PUNCT
ejpam-1678	107	1	2φ(2)+	2φ(2)+	NUM
ejpam-1678	107	2	2(1−	2(1−	NUM
ejpam-1678	107	3	β	β	X
ejpam-1678	107	4	)	)	PUNCT
ejpam-1678	107	5	akzk	akzk	PROPN
ejpam-1678	107	6	�	�	PROPN
ejpam-1678	107	7	>	>	X
ejpam-1678	107	8	0	0	PUNCT
ejpam-1678	107	9	from	from	ADP
ejpam-1678	107	10	lemma	lemma	PROPN
ejpam-1678	107	11	1	1	NUM
ejpam-1678	107	12	,	,	PUNCT
ejpam-1678	107	13	it	it	PRON
ejpam-1678	107	14	implies	imply	VERB
ejpam-1678	107	15	that	that	SCONJ
ejpam-1678	107	16	the	the	DET
ejpam-1678	107	17	sequence	sequence	NOUN
ejpam-1678	107	18	�	�	PROPN
ejpam-1678	107	19	φ(2	φ(2	PROPN
ejpam-1678	107	20	)	)	PUNCT
ejpam-1678	108	1	2φ(2)+	2φ(2)+	NUM
ejpam-1678	108	2	2(1−	2(1−	NUM
ejpam-1678	108	3	β	β	X
ejpam-1678	108	4	)	)	PUNCT
ejpam-1678	108	5	ak	ak	PROPN
ejpam-1678	108	6	�	�	PROPN
ejpam-1678	108	7	∞	∞	PROPN
ejpam-1678	108	8	1	1	NUM
ejpam-1678	108	9	is	be	AUX
ejpam-1678	108	10	a	a	DET
ejpam-1678	108	11	subordination	subordination	NOUN
ejpam-1678	108	12	factor	factor	NOUN
ejpam-1678	108	13	sequence	sequence	NOUN
ejpam-1678	108	14	,	,	PUNCT
ejpam-1678	108	15	with	with	ADP
ejpam-1678	108	16	a1	a1	NOUN
ejpam-1678	108	17	=	=	SYM
ejpam-1678	108	18	1	1	X
ejpam-1678	108	19	.	.	PUNCT
ejpam-1678	109	1	now	now	ADV
ejpam-1678	109	2	ℜ	ℜ	ADJ
ejpam-1678	109	3	�	�	PROPN
ejpam-1678	109	4	1	1	NUM
ejpam-1678	109	5	+	+	NUM
ejpam-1678	109	6	2	2	NUM
ejpam-1678	109	7	∞	∞	NUM
ejpam-1678	109	8	∑	∑	PROPN
ejpam-1678	109	9	k=2	k=2	PROPN
ejpam-1678	109	10	φ(2	φ(2	PROPN
ejpam-1678	109	11	)	)	PUNCT
ejpam-1678	110	1	2φ(2)+	2φ(2)+	NUM
ejpam-1678	110	2	2(1−	2(1−	NUM
ejpam-1678	110	3	β	β	X
ejpam-1678	110	4	)	)	PUNCT
ejpam-1678	110	5	akzk	akzk	PROPN
ejpam-1678	110	6	�	�	PROPN
ejpam-1678	110	7	=	=	SYM
ejpam-1678	110	8	ℜ	ℜ	PROPN
ejpam-1678	110	9	�	�	NOUN
ejpam-1678	110	10	1	1	NUM
ejpam-1678	110	11	+	+	NUM
ejpam-1678	110	12	∞	∞	NUM
ejpam-1678	110	13	∑	∑	PROPN
ejpam-1678	110	14	k=2	k=2	PROPN
ejpam-1678	110	15	φ(2	φ(2	PROPN
ejpam-1678	110	16	)	)	PUNCT
ejpam-1678	110	17	φ(2)+	φ(2)+	VERB
ejpam-1678	110	18	1−	1−	NUM
ejpam-1678	110	19	β	β	X
ejpam-1678	110	20	akzk	akzk	NOUN
ejpam-1678	110	21	�	�	PROPN
ejpam-1678	110	22	=	=	SYM
ejpam-1678	110	23	ℜ	ℜ	PROPN
ejpam-1678	110	24	�	�	NOUN
ejpam-1678	110	25	1	1	NUM
ejpam-1678	110	26	+	+	NUM
ejpam-1678	110	27	φ(2	φ(2	PROPN
ejpam-1678	110	28	)	)	PUNCT
ejpam-1678	110	29	φ(2	φ(2	PROPN
ejpam-1678	110	30	)	)	PUNCT
ejpam-1678	111	1	+	+	CCONJ
ejpam-1678	112	1	1−	1−	NUM
ejpam-1678	112	2	β	β	X
ejpam-1678	112	3	z	z	NOUN
ejpam-1678	113	1	+	+	NOUN
ejpam-1678	113	2	1	1	NUM
ejpam-1678	113	3	φ(2)+	φ(2)+	VERB
ejpam-1678	113	4	1−	1−	NUM
ejpam-1678	113	5	β	β	X
ejpam-1678	113	6	∞	∞	NUM
ejpam-1678	113	7	∑	∑	PROPN
ejpam-1678	113	8	k=2	k=2	PROPN
ejpam-1678	113	9	φ(2)akzk	φ(2)akzk	PROPN
ejpam-1678	113	10	�	�	PROPN
ejpam-1678	113	11	¾	¾	PROPN
ejpam-1678	113	12	1−	1−	NUM
ejpam-1678	113	13	φ(2	φ(2	PROPN
ejpam-1678	113	14	)	)	PUNCT
ejpam-1678	113	15	φ(2	φ(2	PROPN
ejpam-1678	113	16	)	)	PUNCT
ejpam-1678	114	1	+	+	CCONJ
ejpam-1678	114	2	1−	1−	NUM
ejpam-1678	114	3	β	β	NOUN
ejpam-1678	114	4	r	r	NOUN
ejpam-1678	114	5	−	−	PROPN
ejpam-1678	114	6	1	1	NUM
ejpam-1678	114	7	φ(2	φ(2	PROPN
ejpam-1678	114	8	)	)	PUNCT
ejpam-1678	115	1	+	+	CCONJ
ejpam-1678	115	2	1−	1−	NUM
ejpam-1678	115	3	β	β	X
ejpam-1678	115	4	∞	∞	NUM
ejpam-1678	115	5	∑	∑	PROPN
ejpam-1678	115	6	k=2	k=2	PROPN
ejpam-1678	115	7	φ(2)|ak|r	φ(2)|ak|r	PROPN
ejpam-1678	115	8	k.	k.	PROPN
ejpam-1678	115	9	(	(	PUNCT
ejpam-1678	115	10	6	6	NUM
ejpam-1678	115	11	)	)	PUNCT
ejpam-1678	115	12	since	since	SCONJ
ejpam-1678	115	13	φ(k	φ(k	PROPN
ejpam-1678	115	14	)	)	PUNCT
ejpam-1678	115	15	=	=	PUNCT
ejpam-1678	116	1	[	[	X
ejpam-1678	116	2	(	(	PUNCT
ejpam-1678	116	3	αψk(γ	αψk(γ	PROPN
ejpam-1678	116	4	,	,	PUNCT
ejpam-1678	116	5	λ	λ	X
ejpam-1678	116	6	)	)	PUNCT
ejpam-1678	116	7	+	+	NOUN
ejpam-1678	116	8	1)(ψk(γ	1)(ψk(γ	NUM
ejpam-1678	116	9	,	,	PUNCT
ejpam-1678	116	10	λ)−	λ)−	PROPN
ejpam-1678	116	11	1	1	NUM
ejpam-1678	116	12	)	)	PUNCT
ejpam-1678	116	13	+	+	NUM
ejpam-1678	116	14	1−	1−	NUM
ejpam-1678	116	15	β][ψk(γ	β][ψk(γ	NUM
ejpam-1678	116	16	,	,	PUNCT
ejpam-1678	116	17	λ)]n	λ)]n	ADV
ejpam-1678	116	18	(	(	PUNCT
ejpam-1678	116	19	k	k	NOUN
ejpam-1678	116	20	=	=	SYM
ejpam-1678	116	21	2,3	2,3	NUM
ejpam-1678	116	22	,	,	PUNCT
ejpam-1678	116	23	.	.	PUNCT
ejpam-1678	116	24	.	.	PUNCT
ejpam-1678	116	25	.	.	PUNCT
ejpam-1678	116	26	)	)	PUNCT
ejpam-1678	117	1	and	and	CCONJ
ejpam-1678	117	2	ψk(γ	ψk(γ	NUM
ejpam-1678	117	3	,	,	PUNCT
ejpam-1678	117	4	λ	λ	X
ejpam-1678	117	5	)	)	PUNCT
ejpam-1678	117	6	=	=	SYM
ejpam-1678	118	1	γ(k+	γ(k+	PROPN
ejpam-1678	118	2	1)γ(2−	1)γ(2−	NUM
ejpam-1678	118	3	γ	γ	NOUN
ejpam-1678	118	4	)	)	PUNCT
ejpam-1678	118	5	γ(k+	γ(k+	NOUN
ejpam-1678	118	6	1−	1−	NUM
ejpam-1678	118	7	γ	γ	X
ejpam-1678	118	8	)	)	PUNCT
ejpam-1678	119	1	[	[	X
ejpam-1678	119	2	1+λ(k−	1+λ(k−	NUM
ejpam-1678	119	3	1	1	NUM
ejpam-1678	119	4	)	)	PUNCT
ejpam-1678	119	5	]	]	PUNCT
ejpam-1678	120	1	(	(	PUNCT
ejpam-1678	120	2	k	k	X
ejpam-1678	120	3	=	=	SYM
ejpam-1678	120	4	2,3	2,3	NUM
ejpam-1678	120	5	,	,	PUNCT
ejpam-1678	120	6	.	.	PUNCT
ejpam-1678	120	7	.	.	PUNCT
ejpam-1678	120	8	.	.	PUNCT
ejpam-1678	120	9	)	)	PUNCT
ejpam-1678	121	1	is	be	AUX
ejpam-1678	121	2	a	a	DET
ejpam-1678	121	3	increasing	increase	VERB
ejpam-1678	121	4	function	function	NOUN
ejpam-1678	121	5	of	of	ADP
ejpam-1678	121	6	k	k	PROPN
ejpam-1678	121	7	,	,	PUNCT
ejpam-1678	121	8	so	so	ADV
ejpam-1678	121	9	0	0	NUM
ejpam-1678	121	10	<	<	X
ejpam-1678	121	11	φ(2)¶	φ(2)¶	X
ejpam-1678	121	12	φ(k	φ(k	PROPN
ejpam-1678	121	13	)	)	PUNCT
ejpam-1678	122	1	(	(	PUNCT
ejpam-1678	122	2	k	k	NOUN
ejpam-1678	122	3	=	=	SYM
ejpam-1678	122	4	2,3	2,3	NUM
ejpam-1678	122	5	,	,	PUNCT
ejpam-1678	122	6	.	.	PUNCT
ejpam-1678	122	7	.	.	PUNCT
ejpam-1678	122	8	.	.	PUNCT
ejpam-1678	122	9	)	)	PUNCT
ejpam-1678	122	10	.	.	PUNCT
ejpam-1678	123	1	following	follow	VERB
ejpam-1678	123	2	(	(	PUNCT
ejpam-1678	123	3	6	6	NUM
ejpam-1678	123	4	)	)	PUNCT
ejpam-1678	123	5	,	,	PUNCT
ejpam-1678	123	6	we	we	PRON
ejpam-1678	123	7	can	can	AUX
ejpam-1678	123	8	write	write	VERB
ejpam-1678	123	9	¾	¾	PROPN
ejpam-1678	123	10	1−	1−	NUM
ejpam-1678	123	11	φ(2	φ(2	PROPN
ejpam-1678	123	12	)	)	PUNCT
ejpam-1678	123	13	φ(2)+	φ(2)+	VERB
ejpam-1678	123	14	1−	1−	NUM
ejpam-1678	123	15	β	β	NOUN
ejpam-1678	123	16	r	r	NOUN
ejpam-1678	123	17	−	−	PROPN
ejpam-1678	123	18	1	1	NUM
ejpam-1678	123	19	φ(2	φ(2	PROPN
ejpam-1678	123	20	)	)	PUNCT
ejpam-1678	124	1	+	+	CCONJ
ejpam-1678	124	2	1−β	1−β	NUM
ejpam-1678	124	3	∞	∞	NUM
ejpam-1678	124	4	∑	∑	PROPN
ejpam-1678	124	5	k=2	k=2	PROPN
ejpam-1678	124	6	φ(k)|ak|r	φ(k)|ak|r	PROPN
ejpam-1678	124	7	k.	k.	PROPN
ejpam-1678	124	8	as	as	ADP
ejpam-1678	124	9	0	0	NUM
ejpam-1678	124	10	<	<	X
ejpam-1678	124	11	r	r	NOUN
ejpam-1678	124	12	<	<	X
ejpam-1678	124	13	1	1	NUM
ejpam-1678	124	14	,	,	PUNCT
ejpam-1678	124	15	it	it	PRON
ejpam-1678	124	16	can	can	AUX
ejpam-1678	124	17	make	make	VERB
ejpam-1678	124	18	sure	sure	ADJ
ejpam-1678	124	19	¾	¾	PROPN
ejpam-1678	124	20	1−	1−	NUM
ejpam-1678	124	21	φ(2	φ(2	PROPN
ejpam-1678	124	22	)	)	PUNCT
ejpam-1678	124	23	φ(2)+	φ(2)+	VERB
ejpam-1678	124	24	1−	1−	NUM
ejpam-1678	124	25	β	β	NOUN
ejpam-1678	124	26	r	r	NOUN
ejpam-1678	124	27	−	−	NOUN
ejpam-1678	124	28	r	r	NOUN
ejpam-1678	124	29	φ(2	φ(2	PROPN
ejpam-1678	124	30	)	)	PUNCT
ejpam-1678	125	1	+	+	CCONJ
ejpam-1678	125	2	1−	1−	NUM
ejpam-1678	125	3	β	β	NOUN
ejpam-1678	125	4	∞	∞	NUM
ejpam-1678	125	5	∑	∑	PROPN
ejpam-1678	125	6	k=2	k=2	PROPN
ejpam-1678	125	7	φ(k)|ak|	φ(k)|ak|	PROPN
ejpam-1678	125	8	.	.	PUNCT
ejpam-1678	126	1	(	(	PUNCT
ejpam-1678	126	2	7	7	X
ejpam-1678	126	3	)	)	PUNCT
ejpam-1678	126	4	l.	l.	PROPN
ejpam-1678	126	5	xiong	xiong	PROPN
ejpam-1678	126	6	,	,	PUNCT
ejpam-1678	126	7	x.	x.	PROPN
ejpam-1678	126	8	liu	liu	PROPN
ejpam-1678	126	9	/	/	SYM
ejpam-1678	126	10	eur	eur	PROPN
ejpam-1678	126	11	.	.	PUNCT
ejpam-1678	127	1	j.	j.	PROPN
ejpam-1678	127	2	pure	pure	PROPN
ejpam-1678	127	3	appl	appl	PROPN
ejpam-1678	127	4	.	.	PROPN
ejpam-1678	127	5	math	math	PROPN
ejpam-1678	127	6	,	,	PUNCT
ejpam-1678	127	7	5	5	NUM
ejpam-1678	127	8	(	(	PUNCT
ejpam-1678	127	9	2012	2012	NUM
ejpam-1678	127	10	)	)	PUNCT
ejpam-1678	127	11	,	,	PUNCT
ejpam-1678	127	12	380	380	NUM
ejpam-1678	127	13	-	-	SYM
ejpam-1678	127	14	389	389	NUM
ejpam-1678	127	15	384	384	NUM
ejpam-1678	127	16	using	use	VERB
ejpam-1678	127	17	lemma	lemma	PROPN
ejpam-1678	127	18	3	3	NUM
ejpam-1678	127	19	in	in	ADP
ejpam-1678	127	20	(	(	PUNCT
ejpam-1678	127	21	3	3	NUM
ejpam-1678	127	22	)	)	PUNCT
ejpam-1678	127	23	and	and	CCONJ
ejpam-1678	127	24	following	follow	VERB
ejpam-1678	127	25	(	(	PUNCT
ejpam-1678	127	26	7	7	NUM
ejpam-1678	127	27	)	)	PUNCT
ejpam-1678	128	1	,	,	PUNCT
ejpam-1678	128	2	we	we	PRON
ejpam-1678	128	3	obtain	obtain	VERB
ejpam-1678	128	4	ℜ	ℜ	ADJ
ejpam-1678	128	5	�	�	NOUN
ejpam-1678	128	6	1	1	NUM
ejpam-1678	128	7	+	+	NUM
ejpam-1678	128	8	2	2	NUM
ejpam-1678	128	9	∞	∞	NUM
ejpam-1678	128	10	∑	∑	PROPN
ejpam-1678	128	11	k=2	k=2	PROPN
ejpam-1678	128	12	φ(2	φ(2	PROPN
ejpam-1678	128	13	)	)	PUNCT
ejpam-1678	129	1	2φ(2)+	2φ(2)+	NUM
ejpam-1678	129	2	2(1−	2(1−	NUM
ejpam-1678	129	3	β	β	X
ejpam-1678	129	4	)	)	PUNCT
ejpam-1678	129	5	akzk	akzk	PROPN
ejpam-1678	129	6	�	�	PROPN
ejpam-1678	129	7	¾	¾	PROPN
ejpam-1678	129	8	1−	1−	NUM
ejpam-1678	129	9	φ(2	φ(2	PROPN
ejpam-1678	129	10	)	)	PUNCT
ejpam-1678	129	11	φ(2)+	φ(2)+	VERB
ejpam-1678	129	12	1−	1−	NUM
ejpam-1678	129	13	β	β	NOUN
ejpam-1678	129	14	r	r	NOUN
ejpam-1678	129	15	−	−	PROPN
ejpam-1678	129	16	1−	1−	NUM
ejpam-1678	129	17	β	β	X
ejpam-1678	129	18	φ(2	φ(2	PROPN
ejpam-1678	129	19	)	)	PUNCT
ejpam-1678	130	1	+	+	CCONJ
ejpam-1678	130	2	1−	1−	NUM
ejpam-1678	130	3	β	β	SYM
ejpam-1678	130	4	r	r	NOUN
ejpam-1678	130	5	=	=	SYM
ejpam-1678	130	6	1−	1−	NUM
ejpam-1678	130	7	r	r	NOUN
ejpam-1678	130	8	>	>	X
ejpam-1678	130	9	0	0	NUM
ejpam-1678	130	10	,	,	PUNCT
ejpam-1678	130	11	in	in	ADP
ejpam-1678	130	12	the	the	DET
ejpam-1678	130	13	light	light	NOUN
ejpam-1678	130	14	of	of	ADP
ejpam-1678	130	15	definition	definition	NOUN
ejpam-1678	130	16	1	1	NUM
ejpam-1678	130	17	,	,	PUNCT
ejpam-1678	130	18	we	we	PRON
ejpam-1678	130	19	have	have	VERB
ejpam-1678	130	20	φ(2	φ(2	PROPN
ejpam-1678	130	21	)	)	PUNCT
ejpam-1678	131	1	2φ(2)+	2φ(2)+	NUM
ejpam-1678	131	2	2(1−	2(1−	NUM
ejpam-1678	131	3	β	β	X
ejpam-1678	131	4	)	)	PUNCT
ejpam-1678	131	5	f	f	PROPN
ejpam-1678	131	6	∗	∗	NOUN
ejpam-1678	131	7	g(z	g(z	PROPN
ejpam-1678	131	8	)	)	PUNCT
ejpam-1678	131	9	=	=	SYM
ejpam-1678	132	1	∞	∞	NUM
ejpam-1678	132	2	∑	∑	PUNCT
ejpam-1678	132	3	k=1	k=1	PROPN
ejpam-1678	132	4	φ(2	φ(2	PROPN
ejpam-1678	132	5	)	)	PUNCT
ejpam-1678	133	1	2φ(2)+	2φ(2)+	NUM
ejpam-1678	133	2	2(1−	2(1−	NUM
ejpam-1678	133	3	β	β	X
ejpam-1678	133	4	)	)	PUNCT
ejpam-1678	133	5	bkckzk	bkckzk	VERB
ejpam-1678	133	6	≺	≺	NOUN
ejpam-1678	133	7	g(z	g(z	PROPN
ejpam-1678	133	8	)	)	PUNCT
ejpam-1678	133	9	,	,	PUNCT
ejpam-1678	133	10	furthermore	furthermore	ADV
ejpam-1678	133	11	,	,	PUNCT
ejpam-1678	133	12	it	it	PRON
ejpam-1678	133	13	is	be	AUX
ejpam-1678	133	14	easy	easy	ADJ
ejpam-1678	133	15	to	to	PART
ejpam-1678	133	16	deduce	deduce	VERB
ejpam-1678	133	17	the	the	DET
ejpam-1678	133	18	result	result	NOUN
ejpam-1678	133	19	in	in	ADP
ejpam-1678	133	20	(	(	PUNCT
ejpam-1678	133	21	5	5	NUM
ejpam-1678	133	22	)	)	PUNCT
ejpam-1678	133	23	by	by	ADP
ejpam-1678	133	24	using	use	VERB
ejpam-1678	133	25	(	(	PUNCT
ejpam-1678	133	26	4	4	NUM
ejpam-1678	133	27	)	)	PUNCT
ejpam-1678	133	28	and	and	CCONJ
ejpam-1678	133	29	lemma	lemma	PROPN
ejpam-1678	133	30	4	4	X
ejpam-1678	133	31	.	.	PUNCT
ejpam-1678	133	32	corollary	corollary	ADJ
ejpam-1678	133	33	1	1	NUM
ejpam-1678	133	34	.	.	PUNCT
ejpam-1678	134	1	if	if	SCONJ
ejpam-1678	134	2	f	f	PROPN
ejpam-1678	134	3	(	(	PUNCT
ejpam-1678	134	4	z	z	NOUN
ejpam-1678	134	5	)	)	PUNCT
ejpam-1678	134	6	=	=	SYM
ejpam-1678	134	7	z	z	NOUN
ejpam-1678	135	1	+	+	NUM
ejpam-1678	135	2	∞	∞	NUM
ejpam-1678	135	3	∑	∑	PROPN
ejpam-1678	135	4	k=2	k=2	PROPN
ejpam-1678	135	5	akzk	akzk	PROPN
ejpam-1678	135	6	∈	∈	PROPN
ejpam-1678	135	7	h	h	PROPN
ejpam-1678	135	8	n	n	CCONJ
ejpam-1678	135	9	,	,	PUNCT
ejpam-1678	135	10	γ	γ	X
ejpam-1678	135	11	λ	λ	X
ejpam-1678	136	1	[	[	X
ejpam-1678	136	2	α	α	X
ejpam-1678	136	3	,	,	PUNCT
ejpam-1678	136	4	β	β	NOUN
ejpam-1678	136	5	]	]	PUNCT
ejpam-1678	136	6	and	and	CCONJ
ejpam-1678	136	7	f(z	f(z	PROPN
ejpam-1678	136	8	)	)	PUNCT
ejpam-1678	137	1	=	=	SYM
ejpam-1678	137	2	z	z	NOUN
ejpam-1678	138	1	+	+	NUM
ejpam-1678	138	2	∞	∞	PROPN
ejpam-1678	138	3	∑	∑	PROPN
ejpam-1678	138	4	k=2	k=2	PROPN
ejpam-1678	138	5	(	(	PUNCT
ejpam-1678	138	6	a)k−1	a)k−1	PROPN
ejpam-1678	138	7	(	(	PUNCT
ejpam-1678	138	8	c)k−1	c)k−1	PROPN
ejpam-1678	138	9	akzk	akzk	PROPN
ejpam-1678	138	10	,	,	PUNCT
ejpam-1678	138	11	then	then	ADV
ejpam-1678	138	12	φ(2	φ(2	PROPN
ejpam-1678	138	13	)	)	PUNCT
ejpam-1678	138	14	φ(2)+	φ(2)+	VERB
ejpam-1678	138	15	1−	1−	NUM
ejpam-1678	138	16	β	β	X
ejpam-1678	138	17	f(z	f(z	PROPN
ejpam-1678	138	18	)	)	PUNCT
ejpam-1678	138	19	≺	≺	NOUN
ejpam-1678	138	20	2h(a	2h(a	NUM
ejpam-1678	138	21	,	,	PUNCT
ejpam-1678	138	22	c	c	X
ejpam-1678	138	23	;	;	PUNCT
ejpam-1678	138	24	z	z	X
ejpam-1678	138	25	)	)	PUNCT
ejpam-1678	138	26	(	(	PUNCT
ejpam-1678	138	27	8)	8)	NUM
ejpam-1678	138	28	and	and	CCONJ
ejpam-1678	138	29	ℜ	ℜ	ADJ
ejpam-1678	138	30	f	f	X
ejpam-1678	138	31	(	(	PUNCT
ejpam-1678	138	32	z	z	NOUN
ejpam-1678	138	33	)	)	PUNCT
ejpam-1678	138	34	>	>	X
ejpam-1678	139	1	β	β	X
ejpam-1678	139	2	−	−	PROPN
ejpam-1678	139	3	1−φ(2	1−φ(2	NUM
ejpam-1678	139	4	)	)	PUNCT
ejpam-1678	139	5	φ(2	φ(2	PROPN
ejpam-1678	139	6	)	)	PUNCT
ejpam-1678	139	7	,	,	PUNCT
ejpam-1678	139	8	(	(	PUNCT
ejpam-1678	139	9	9	9	X
ejpam-1678	139	10	)	)	PUNCT
ejpam-1678	139	11	where	where	SCONJ
ejpam-1678	139	12	φ(2	φ(2	NOUN
ejpam-1678	139	13	)	)	PUNCT
ejpam-1678	140	1	=	=	PUNCT
ejpam-1678	141	1	[	[	X
ejpam-1678	141	2	(	(	PUNCT
ejpam-1678	141	3	αψ2(γ	αψ2(γ	NOUN
ejpam-1678	141	4	,	,	PUNCT
ejpam-1678	141	5	λ)+1)(ψ2(γ	λ)+1)(ψ2(γ	NOUN
ejpam-1678	141	6	,	,	PUNCT
ejpam-1678	141	7	λ)−1)+1−β][ψ2(γ	λ)−1)+1−β][ψ2(γ	PROPN
ejpam-1678	141	8	,	,	PUNCT
ejpam-1678	141	9	λ)]n	λ)]n	NOUN
ejpam-1678	141	10	,	,	PUNCT
ejpam-1678	141	11	and	and	CCONJ
ejpam-1678	141	12	h(a	h(a	PROPN
ejpam-1678	141	13	,	,	PUNCT
ejpam-1678	141	14	c	c	PROPN
ejpam-1678	141	15	;	;	PUNCT
ejpam-1678	141	16	z	z	X
ejpam-1678	141	17	)	)	PUNCT
ejpam-1678	141	18	is	be	AUX
ejpam-1678	141	19	the	the	DET
ejpam-1678	141	20	incomplete	incomplete	ADJ
ejpam-1678	141	21	beta	beta	NOUN
ejpam-1678	141	22	function	function	NOUN
ejpam-1678	141	23	defined	define	VERB
ejpam-1678	141	24	in	in	ADP
ejpam-1678	141	25	(	(	PUNCT
ejpam-1678	141	26	1	1	NUM
ejpam-1678	141	27	)	)	PUNCT
ejpam-1678	141	28	with	with	ADP
ejpam-1678	141	29	0	0	NUM
ejpam-1678	141	30	<	<	X
ejpam-1678	141	31	a	a	DET
ejpam-1678	141	32	¶	¶	PROPN
ejpam-1678	141	33	c	c	NOUN
ejpam-1678	141	34	,	,	PUNCT
ejpam-1678	141	35	c	c	PROPN
ejpam-1678	141	36	¾	¾	PROPN
ejpam-1678	141	37	2	2	NUM
ejpam-1678	141	38	or	or	CCONJ
ejpam-1678	141	39	a+	a+	PRON
ejpam-1678	141	40	c	c	PROPN
ejpam-1678	141	41	¾	¾	PROPN
ejpam-1678	141	42	3	3	NUM
ejpam-1678	141	43	.	.	PUNCT
ejpam-1678	142	1	proof	proof	NOUN
ejpam-1678	142	2	.	.	PUNCT
ejpam-1678	143	1	since	since	SCONJ
ejpam-1678	143	2	0	0	NUM
ejpam-1678	143	3	<	<	X
ejpam-1678	143	4	a	a	DET
ejpam-1678	143	5	¶	¶	PROPN
ejpam-1678	143	6	c	c	NOUN
ejpam-1678	143	7	,	,	PUNCT
ejpam-1678	143	8	c	c	PROPN
ejpam-1678	143	9	¾	¾	PROPN
ejpam-1678	143	10	2	2	NUM
ejpam-1678	143	11	or	or	CCONJ
ejpam-1678	143	12	a+	a+	PRON
ejpam-1678	143	13	c	c	PROPN
ejpam-1678	143	14	¾	¾	PROPN
ejpam-1678	143	15	3	3	NUM
ejpam-1678	143	16	,	,	PUNCT
ejpam-1678	143	17	using	use	VERB
ejpam-1678	143	18	lemma	lemma	PROPN
ejpam-1678	143	19	2	2	NUM
ejpam-1678	143	20	,	,	PUNCT
ejpam-1678	143	21	we	we	PRON
ejpam-1678	143	22	can	can	AUX
ejpam-1678	143	23	know	know	VERB
ejpam-1678	143	24	that	that	PRON
ejpam-1678	143	25	h(a	h(a	PROPN
ejpam-1678	143	26	,	,	PUNCT
ejpam-1678	143	27	c	c	PROPN
ejpam-1678	143	28	;	;	PUNCT
ejpam-1678	143	29	z	z	X
ejpam-1678	143	30	)	)	PUNCT
ejpam-1678	143	31	=	=	SYM
ejpam-1678	144	1	z	z	NOUN
ejpam-1678	145	1	+	+	NUM
ejpam-1678	145	2	∞	∞	PROPN
ejpam-1678	145	3	∑	∑	PROPN
ejpam-1678	145	4	k=2	k=2	PROPN
ejpam-1678	145	5	(	(	PUNCT
ejpam-1678	145	6	a)k−1	a)k−1	PROPN
ejpam-1678	145	7	(	(	PUNCT
ejpam-1678	145	8	c)k−1	c)k−1	VERB
ejpam-1678	145	9	zk	zk	PROPN
ejpam-1678	145	10	∈k	∈k	ADV
ejpam-1678	145	11	.	.	PUNCT
ejpam-1678	146	1	taking	take	VERB
ejpam-1678	146	2	g(z	g(z	PROPN
ejpam-1678	146	3	)	)	PUNCT
ejpam-1678	146	4	=	=	SYM
ejpam-1678	146	5	h(a	h(a	PROPN
ejpam-1678	146	6	,	,	PUNCT
ejpam-1678	146	7	c	c	X
ejpam-1678	146	8	;	;	PUNCT
ejpam-1678	146	9	z	z	X
ejpam-1678	146	10	)	)	PUNCT
ejpam-1678	146	11	and	and	CCONJ
ejpam-1678	146	12	g(z	g(z	PROPN
ejpam-1678	146	13	)	)	PUNCT
ejpam-1678	146	14	=	=	PUNCT
ejpam-1678	147	1	z	z	PROPN
ejpam-1678	147	2	1−z	1−z	PROPN
ejpam-1678	147	3	in	in	ADP
ejpam-1678	147	4	theorem	theorem	NOUN
ejpam-1678	147	5	1	1	NUM
ejpam-1678	147	6	,	,	PUNCT
ejpam-1678	147	7	respectively	respectively	ADV
ejpam-1678	147	8	,	,	PUNCT
ejpam-1678	147	9	the	the	DET
ejpam-1678	147	10	results	result	NOUN
ejpam-1678	147	11	(	(	PUNCT
ejpam-1678	147	12	8)	8)	NUM
ejpam-1678	147	13	and	and	CCONJ
ejpam-1678	147	14	(	(	PUNCT
ejpam-1678	147	15	9	9	NUM
ejpam-1678	147	16	)	)	PUNCT
ejpam-1678	147	17	are	be	AUX
ejpam-1678	147	18	obtained	obtain	VERB
ejpam-1678	147	19	.	.	PUNCT
ejpam-1678	148	1	corollary	corollary	ADJ
ejpam-1678	148	2	2	2	NUM
ejpam-1678	148	3	.	.	PUNCT
ejpam-1678	149	1	if	if	SCONJ
ejpam-1678	149	2	f	f	PROPN
ejpam-1678	149	3	∈	∈	PROPN
ejpam-1678	149	4	h̄[α	h̄[α	PROPN
ejpam-1678	149	5	,	,	PUNCT
ejpam-1678	149	6	β	β	X
ejpam-1678	149	7	]	]	PUNCT
ejpam-1678	149	8	in	in	ADP
ejpam-1678	149	9	u	u	NOUN
ejpam-1678	149	10	and	and	CCONJ
ejpam-1678	149	11	s	s	PROPN
ejpam-1678	149	12	>	>	X
ejpam-1678	149	13	0	0	NUM
ejpam-1678	149	14	,	,	PUNCT
ejpam-1678	149	15	0	0	NUM
ejpam-1678	149	16	<	<	X
ejpam-1678	149	17	|z|	|z|	NOUN
ejpam-1678	149	18	=	=	SYM
ejpam-1678	149	19	r	r	NOUN
ejpam-1678	149	20	<	<	X
ejpam-1678	149	21	1	1	NUM
ejpam-1678	149	22	,	,	PUNCT
ejpam-1678	149	23	then	then	ADV
ejpam-1678	149	24	for	for	ADP
ejpam-1678	149	25	function	function	NOUN
ejpam-1678	149	26	g	g	PROPN
ejpam-1678	149	27	∈k	∈k	PROPN
ejpam-1678	149	28	2(α+	2(α+	NUM
ejpam-1678	149	29	1)−	1)−	NUM
ejpam-1678	149	30	β	β	SYM
ejpam-1678	149	31	2(α−	2(α−	NUM
ejpam-1678	149	32	β	β	X
ejpam-1678	149	33	)	)	PUNCT
ejpam-1678	150	1	+	+	CCONJ
ejpam-1678	150	2	3	3	NUM
ejpam-1678	150	3	f	f	NOUN
ejpam-1678	150	4	∗	∗	NOUN
ejpam-1678	150	5	g(z	g(z	PROPN
ejpam-1678	150	6	)	)	PUNCT
ejpam-1678	150	7	≺	≺	NOUN
ejpam-1678	150	8	2g(z	2g(z	NUM
ejpam-1678	150	9	)	)	PUNCT
ejpam-1678	150	10	and	and	CCONJ
ejpam-1678	151	1	[	[	X
ejpam-1678	151	2	2(α+	2(α+	NUM
ejpam-1678	151	3	1)−	1)−	NUM
ejpam-1678	151	4	β	β	NOUN
ejpam-1678	151	5	]	]	X
ejpam-1678	151	6	2(α−	2(α−	NUM
ejpam-1678	151	7	β	β	X
ejpam-1678	151	8	)	)	PUNCT
ejpam-1678	151	9	+	+	CCONJ
ejpam-1678	151	10	3	3	NUM
ejpam-1678	151	11	∫	∫	PROPN
ejpam-1678	151	12	2π	2π	PROPN
ejpam-1678	151	13	0	0	PUNCT
ejpam-1678	152	1	|	|	ADV
ejpam-1678	152	2	f	f	PROPN
ejpam-1678	152	3	∗	∗	NOUN
ejpam-1678	152	4	g(reiθ	g(reiθ	NOUN
ejpam-1678	152	5	)	)	PUNCT
ejpam-1678	152	6	|sdθ	|sdθ	NOUN
ejpam-1678	152	7	¶	¶	NOUN
ejpam-1678	152	8	2	2	NUM
ejpam-1678	152	9	∫	∫	PROPN
ejpam-1678	152	10	2π	2π	PROPN
ejpam-1678	152	11	0	0	NUM
ejpam-1678	153	1	|g(reiθ	|g(reiθ	NOUN
ejpam-1678	153	2	)	)	PUNCT
ejpam-1678	153	3	|sdθ	|sdθ	NOUN
ejpam-1678	153	4	.	.	PUNCT
ejpam-1678	154	1	proof	proof	NOUN
ejpam-1678	154	2	.	.	PUNCT
ejpam-1678	155	1	by	by	ADP
ejpam-1678	155	2	taking	take	VERB
ejpam-1678	155	3	n=	n=	ADJ
ejpam-1678	155	4	0	0	NUM
ejpam-1678	155	5	,	,	PUNCT
ejpam-1678	155	6	γ	γ	X
ejpam-1678	155	7	=	=	SYM
ejpam-1678	155	8	0	0	PUNCT
ejpam-1678	155	9	and	and	CCONJ
ejpam-1678	155	10	λ=	λ=	VERB
ejpam-1678	155	11	1	1	NUM
ejpam-1678	155	12	in	in	ADP
ejpam-1678	155	13	theorem	theorem	ADJ
ejpam-1678	155	14	1	1	NUM
ejpam-1678	155	15	,	,	PUNCT
ejpam-1678	155	16	corollary	corollary	ADJ
ejpam-1678	155	17	2	2	NUM
ejpam-1678	155	18	is	be	AUX
ejpam-1678	155	19	given	give	VERB
ejpam-1678	155	20	.	.	PUNCT
ejpam-1678	156	1	l.	l.	PROPN
ejpam-1678	156	2	xiong	xiong	PROPN
ejpam-1678	156	3	,	,	PUNCT
ejpam-1678	156	4	x.	x.	PROPN
ejpam-1678	156	5	liu	liu	PROPN
ejpam-1678	156	6	/	/	SYM
ejpam-1678	156	7	eur	eur	PROPN
ejpam-1678	156	8	.	.	PUNCT
ejpam-1678	157	1	j.	j.	PROPN
ejpam-1678	157	2	pure	pure	PROPN
ejpam-1678	157	3	appl	appl	PROPN
ejpam-1678	157	4	.	.	PROPN
ejpam-1678	157	5	math	math	PROPN
ejpam-1678	157	6	,	,	PUNCT
ejpam-1678	157	7	5	5	NUM
ejpam-1678	157	8	(	(	PUNCT
ejpam-1678	157	9	2012	2012	NUM
ejpam-1678	157	10	)	)	PUNCT
ejpam-1678	157	11	,	,	PUNCT
ejpam-1678	157	12	380	380	NUM
ejpam-1678	157	13	-	-	SYM
ejpam-1678	157	14	389	389	NUM
ejpam-1678	157	15	385	385	NUM
ejpam-1678	157	16	corollary	corollary	NOUN
ejpam-1678	157	17	3	3	NUM
ejpam-1678	157	18	.	.	PUNCT
ejpam-1678	158	1	if	if	SCONJ
ejpam-1678	158	2	f	f	PROPN
ejpam-1678	158	3	∈	∈	PROPN
ejpam-1678	158	4	t	t	PROPN
ejpam-1678	158	5	∗(β	∗(β	PROPN
ejpam-1678	158	6	)	)	PUNCT
ejpam-1678	158	7	in	in	ADP
ejpam-1678	158	8	u	u	NOUN
ejpam-1678	158	9	and	and	CCONJ
ejpam-1678	158	10	s	s	PROPN
ejpam-1678	158	11	>	>	X
ejpam-1678	158	12	0	0	NUM
ejpam-1678	158	13	,	,	PUNCT
ejpam-1678	158	14	0	0	NUM
ejpam-1678	158	15	<	<	X
ejpam-1678	158	16	|z|	|z|	NOUN
ejpam-1678	158	17	=	=	SYM
ejpam-1678	158	18	r	r	NOUN
ejpam-1678	158	19	<	<	X
ejpam-1678	158	20	1	1	NUM
ejpam-1678	158	21	,	,	PUNCT
ejpam-1678	158	22	then	then	ADV
ejpam-1678	158	23	for	for	ADP
ejpam-1678	158	24	function	function	NOUN
ejpam-1678	158	25	g	g	PROPN
ejpam-1678	158	26	∈k	∈k	ADP
ejpam-1678	158	27	2−	2−	NUM
ejpam-1678	158	28	β	β	NOUN
ejpam-1678	158	29	3−	3−	NUM
ejpam-1678	158	30	2β	2β	NOUN
ejpam-1678	158	31	f	f	NOUN
ejpam-1678	158	32	∗	∗	NOUN
ejpam-1678	158	33	g(z	g(z	PROPN
ejpam-1678	158	34	)	)	PUNCT
ejpam-1678	158	35	≺	≺	NOUN
ejpam-1678	158	36	2g(z	2g(z	NUM
ejpam-1678	158	37	)	)	PUNCT
ejpam-1678	158	38	and	and	CCONJ
ejpam-1678	158	39	2−	2−	NUM
ejpam-1678	158	40	β	β	X
ejpam-1678	158	41	3−	3−	NUM
ejpam-1678	158	42	2β	2β	NUM
ejpam-1678	158	43	∫	∫	PROPN
ejpam-1678	158	44	2π	2π	NOUN
ejpam-1678	158	45	0	0	PUNCT
ejpam-1678	159	1	|	|	ADV
ejpam-1678	159	2	f	f	PROPN
ejpam-1678	159	3	∗	∗	NOUN
ejpam-1678	159	4	g(reiθ	g(reiθ	NOUN
ejpam-1678	159	5	)	)	PUNCT
ejpam-1678	159	6	|sdθ	|sdθ	NOUN
ejpam-1678	159	7	¶	¶	NOUN
ejpam-1678	159	8	2	2	NUM
ejpam-1678	159	9	∫	∫	PROPN
ejpam-1678	159	10	2π	2π	PROPN
ejpam-1678	159	11	0	0	NUM
ejpam-1678	159	12	|g(reiθ	|g(reiθ	NOUN
ejpam-1678	159	13	)	)	PUNCT
ejpam-1678	159	14	|sdθ	|sdθ	NOUN
ejpam-1678	159	15	.	.	PUNCT
ejpam-1678	160	1	proof	proof	NOUN
ejpam-1678	160	2	.	.	PUNCT
ejpam-1678	161	1	by	by	ADP
ejpam-1678	161	2	taking	take	VERB
ejpam-1678	161	3	α	α	NOUN
ejpam-1678	161	4	=	=	NOUN
ejpam-1678	161	5	0	0	NUM
ejpam-1678	161	6	in	in	ADP
ejpam-1678	161	7	corollary	corollary	ADJ
ejpam-1678	161	8	2	2	NUM
ejpam-1678	161	9	,	,	PUNCT
ejpam-1678	161	10	corollary	corollary	ADJ
ejpam-1678	161	11	3	3	NUM
ejpam-1678	161	12	is	be	AUX
ejpam-1678	161	13	given	give	VERB
ejpam-1678	161	14	.	.	PUNCT
ejpam-1678	162	1	corollary	corollary	ADJ
ejpam-1678	162	2	4	4	NUM
ejpam-1678	162	3	.	.	PUNCT
ejpam-1678	163	1	if	if	SCONJ
ejpam-1678	163	2	f	f	PROPN
ejpam-1678	163	3	∈	∈	PROPN
ejpam-1678	163	4	c(β	c(β	PROPN
ejpam-1678	163	5	)	)	PUNCT
ejpam-1678	163	6	in	in	ADP
ejpam-1678	163	7	u	u	NOUN
ejpam-1678	163	8	and	and	CCONJ
ejpam-1678	163	9	s	s	PROPN
ejpam-1678	163	10	>	>	X
ejpam-1678	163	11	0	0	NUM
ejpam-1678	163	12	,	,	PUNCT
ejpam-1678	163	13	0	0	NUM
ejpam-1678	163	14	<	<	X
ejpam-1678	163	15	|z|	|z|	NOUN
ejpam-1678	163	16	=	=	SYM
ejpam-1678	163	17	r	r	NOUN
ejpam-1678	163	18	<	<	X
ejpam-1678	163	19	1	1	NUM
ejpam-1678	163	20	,	,	PUNCT
ejpam-1678	163	21	then	then	ADV
ejpam-1678	163	22	for	for	ADP
ejpam-1678	163	23	function	function	NOUN
ejpam-1678	163	24	g	g	PROPN
ejpam-1678	163	25	∈k	∈k	ADP
ejpam-1678	163	26	4−	4−	NUM
ejpam-1678	163	27	β	β	NOUN
ejpam-1678	163	28	5−	5−	NUM
ejpam-1678	163	29	2β	2β	NUM
ejpam-1678	163	30	f	f	NOUN
ejpam-1678	163	31	∗	∗	NOUN
ejpam-1678	163	32	g(z	g(z	PROPN
ejpam-1678	163	33	)	)	PUNCT
ejpam-1678	163	34	≺	≺	NOUN
ejpam-1678	163	35	2g(z	2g(z	NUM
ejpam-1678	163	36	)	)	PUNCT
ejpam-1678	163	37	and	and	CCONJ
ejpam-1678	163	38	4−	4−	NUM
ejpam-1678	163	39	β	β	NOUN
ejpam-1678	163	40	5−	5−	NUM
ejpam-1678	164	1	2β	2β	NUM
ejpam-1678	164	2	∫	∫	PROPN
ejpam-1678	164	3	2π	2π	NOUN
ejpam-1678	164	4	0	0	PUNCT
ejpam-1678	165	1	|	|	ADV
ejpam-1678	165	2	f	f	PROPN
ejpam-1678	165	3	∗	∗	NOUN
ejpam-1678	165	4	g(reiθ	g(reiθ	NOUN
ejpam-1678	165	5	)	)	PUNCT
ejpam-1678	165	6	|sdθ	|sdθ	NOUN
ejpam-1678	165	7	¶	¶	NOUN
ejpam-1678	165	8	2	2	NUM
ejpam-1678	165	9	∫	∫	PROPN
ejpam-1678	165	10	2π	2π	PROPN
ejpam-1678	165	11	0	0	NUM
ejpam-1678	165	12	|g(reiθ	|g(reiθ	NOUN
ejpam-1678	165	13	)	)	PUNCT
ejpam-1678	165	14	|sdθ	|sdθ	NOUN
ejpam-1678	165	15	.	.	PUNCT
ejpam-1678	166	1	proof	proof	NOUN
ejpam-1678	166	2	.	.	PUNCT
ejpam-1678	167	1	by	by	ADP
ejpam-1678	167	2	taking	take	VERB
ejpam-1678	167	3	α	α	NOUN
ejpam-1678	167	4	=	=	SYM
ejpam-1678	167	5	1	1	NUM
ejpam-1678	167	6	in	in	ADP
ejpam-1678	167	7	corollary	corollary	ADJ
ejpam-1678	167	8	2	2	NUM
ejpam-1678	167	9	,	,	PUNCT
ejpam-1678	167	10	corollary	corollary	ADJ
ejpam-1678	167	11	4	4	NUM
ejpam-1678	167	12	is	be	AUX
ejpam-1678	167	13	given	give	VERB
ejpam-1678	167	14	.	.	PUNCT
ejpam-1678	168	1	3	3	X
ejpam-1678	168	2	.	.	X
ejpam-1678	169	1	some	some	DET
ejpam-1678	169	2	results	result	NOUN
ejpam-1678	169	3	on	on	ADP
ejpam-1678	169	4	the	the	DET
ejpam-1678	169	5	class	class	NOUN
ejpam-1678	169	6	h	h	NOUN
ejpam-1678	169	7	n	n	CCONJ
ejpam-1678	169	8	,	,	PUNCT
ejpam-1678	169	9	γ	γ	X
ejpam-1678	169	10	λ	λ	X
ejpam-1678	170	1	[	[	X
ejpam-1678	170	2	α	α	X
ejpam-1678	170	3	,	,	PUNCT
ejpam-1678	170	4	β	β	X
ejpam-1678	170	5	]	]	PUNCT
ejpam-1678	170	6	with	with	ADP
ejpam-1678	170	7	fixed	fix	VERB
ejpam-1678	170	8	equation	equation	NOUN
ejpam-1678	170	9	in	in	ADP
ejpam-1678	170	10	this	this	DET
ejpam-1678	170	11	section	section	NOUN
ejpam-1678	170	12	,	,	PUNCT
ejpam-1678	170	13	we	we	PRON
ejpam-1678	170	14	shall	shall	AUX
ejpam-1678	170	15	obtain	obtain	VERB
ejpam-1678	170	16	several	several	ADJ
ejpam-1678	170	17	interesting	interesting	ADJ
ejpam-1678	170	18	results	result	NOUN
ejpam-1678	170	19	on	on	ADP
ejpam-1678	170	20	the	the	DET
ejpam-1678	170	21	functions	function	NOUN
ejpam-1678	170	22	which	which	PRON
ejpam-1678	170	23	are	be	AUX
ejpam-1678	170	24	defined	define	VERB
ejpam-1678	170	25	by	by	ADP
ejpam-1678	170	26	the	the	DET
ejpam-1678	170	27	class	class	NOUN
ejpam-1678	170	28	h	h	NOUN
ejpam-1678	170	29	n	n	CCONJ
ejpam-1678	170	30	,	,	PUNCT
ejpam-1678	170	31	γ	γ	X
ejpam-1678	170	32	λ	λ	X
ejpam-1678	171	1	[	[	X
ejpam-1678	171	2	α	α	X
ejpam-1678	171	3	,	,	PUNCT
ejpam-1678	171	4	β	β	X
ejpam-1678	171	5	]	]	PUNCT
ejpam-1678	171	6	with	with	ADP
ejpam-1678	171	7	the	the	DET
ejpam-1678	171	8	following	follow	VERB
ejpam-1678	171	9	nonhomogeneous	nonhomogeneous	ADJ
ejpam-1678	171	10	cauchy	cauchy	PROPN
ejpam-1678	171	11	-	-	PUNCT
ejpam-1678	171	12	euler	euler	NOUN
ejpam-1678	171	13	differential	differential	ADJ
ejpam-1678	171	14	equation	equation	NOUN
ejpam-1678	171	15	:	:	PUNCT
ejpam-1678	171	16	z2	z2	PROPN
ejpam-1678	171	17	d2	d2	PROPN
ejpam-1678	171	18	l	l	PROPN
ejpam-1678	171	19	dz2	dz2	NOUN
ejpam-1678	171	20	+	+	CCONJ
ejpam-1678	171	21	2(µ+	2(µ+	NUM
ejpam-1678	171	22	1)z	1)z	NUM
ejpam-1678	172	1	d	d	X
ejpam-1678	172	2	l	l	NOUN
ejpam-1678	172	3	dz	dz	X
ejpam-1678	173	1	+	+	NOUN
ejpam-1678	173	2	µ(µ+	µ(µ+	VERB
ejpam-1678	173	3	1)l	1)l	NUM
ejpam-1678	173	4	=	=	SYM
ejpam-1678	173	5	(	(	PUNCT
ejpam-1678	173	6	1+µ)(2+µ	1+µ)(2+µ	NUM
ejpam-1678	173	7	)	)	PUNCT
ejpam-1678	173	8	f	f	NOUN
ejpam-1678	173	9	(	(	PUNCT
ejpam-1678	173	10	z	z	NOUN
ejpam-1678	173	11	)	)	PUNCT
ejpam-1678	173	12	(	(	PUNCT
ejpam-1678	173	13	10	10	NUM
ejpam-1678	173	14	)	)	PUNCT
ejpam-1678	173	15	where	where	SCONJ
ejpam-1678	173	16	l(z	l(z	NOUN
ejpam-1678	173	17	)	)	PUNCT
ejpam-1678	173	18	∈	∈	PROPN
ejpam-1678	173	19	t	t	PROPN
ejpam-1678	173	20	,	,	PUNCT
ejpam-1678	173	21	f	f	PROPN
ejpam-1678	173	22	(	(	PUNCT
ejpam-1678	173	23	z	z	NOUN
ejpam-1678	173	24	)	)	PUNCT
ejpam-1678	173	25	∈	∈	PROPN
ejpam-1678	173	26	h	h	NOUN
ejpam-1678	173	27	n	n	CCONJ
ejpam-1678	173	28	,	,	PUNCT
ejpam-1678	173	29	γ	γ	X
ejpam-1678	173	30	λ	λ	X
ejpam-1678	173	31	[	[	X
ejpam-1678	173	32	α	α	X
ejpam-1678	173	33	,	,	PUNCT
ejpam-1678	173	34	β	β	X
ejpam-1678	173	35	]	]	X
ejpam-1678	173	36	,	,	PUNCT
ejpam-1678	173	37	µ+	µ+	X
ejpam-1678	173	38	1	1	NUM
ejpam-1678	173	39	>	>	SYM
ejpam-1678	173	40	0	0	NUM
ejpam-1678	173	41	,	,	PUNCT
ejpam-1678	173	42	µ	µ	PROPN
ejpam-1678	173	43	∈	∈	PROPN
ejpam-1678	173	44	r.	r.	NOUN
ejpam-1678	173	45	the	the	DET
ejpam-1678	173	46	cauchy	cauchy	PROPN
ejpam-1678	173	47	-	-	PUNCT
ejpam-1678	173	48	euler	euler	NOUN
ejpam-1678	173	49	differential	differential	ADJ
ejpam-1678	173	50	equation	equation	NOUN
ejpam-1678	173	51	was	be	AUX
ejpam-1678	173	52	introduced	introduce	VERB
ejpam-1678	173	53	earlier	early	ADV
ejpam-1678	173	54	to	to	PART
ejpam-1678	173	55	study	study	VERB
ejpam-1678	173	56	the	the	DET
ejpam-1678	173	57	distortion	distortion	NOUN
ejpam-1678	173	58	inequalities	inequality	NOUN
ejpam-1678	173	59	and	and	CCONJ
ejpam-1678	173	60	neighborhoods	neighborhood	NOUN
ejpam-1678	173	61	problems	problem	NOUN
ejpam-1678	173	62	of	of	ADP
ejpam-1678	173	63	the	the	DET
ejpam-1678	173	64	other	other	ADJ
ejpam-1678	173	65	class	class	NOUN
ejpam-1678	173	66	of	of	ADP
ejpam-1678	173	67	functions	function	NOUN
ejpam-1678	173	68	by	by	ADP
ejpam-1678	173	69	o.	o.	PROPN
ejpam-1678	173	70	altintaş	altintaş	PROPN
ejpam-1678	173	71	et	et	PROPN
ejpam-1678	173	72	al	al	PROPN
ejpam-1678	173	73	.	.	PUNCT
ejpam-1678	174	1	[	[	X
ejpam-1678	174	2	2	2	NUM
ejpam-1678	174	3	]	]	PUNCT
ejpam-1678	174	4	.	.	PUNCT
ejpam-1678	175	1	theorem	theorem	NOUN
ejpam-1678	175	2	2	2	NUM
ejpam-1678	175	3	.	.	PUNCT
ejpam-1678	176	1	if	if	SCONJ
ejpam-1678	176	2	the	the	DET
ejpam-1678	176	3	function	function	NOUN
ejpam-1678	176	4	l(z	l(z	NOUN
ejpam-1678	176	5	)	)	PUNCT
ejpam-1678	176	6	=	=	SYM
ejpam-1678	176	7	z	z	NOUN
ejpam-1678	177	1	+	+	NUM
ejpam-1678	177	2	∞	∞	NUM
ejpam-1678	177	3	∑	∑	PROPN
ejpam-1678	177	4	k=2	k=2	PROPN
ejpam-1678	177	5	ckzk	ckzk	PROPN
ejpam-1678	177	6	∈	∈	PROPN
ejpam-1678	177	7	t	t	PROPN
ejpam-1678	177	8	satisfy	satisfy	VERB
ejpam-1678	177	9	the	the	DET
ejpam-1678	177	10	equation	equation	NOUN
ejpam-1678	177	11	(	(	PUNCT
ejpam-1678	177	12	10	10	NUM
ejpam-1678	177	13	)	)	PUNCT
ejpam-1678	177	14	with	with	ADP
ejpam-1678	177	15	f	f	PROPN
ejpam-1678	177	16	(	(	PUNCT
ejpam-1678	177	17	z	z	NOUN
ejpam-1678	177	18	)	)	PUNCT
ejpam-1678	177	19	=	=	SYM
ejpam-1678	178	1	z	z	NOUN
ejpam-1678	179	1	+	+	NUM
ejpam-1678	179	2	∞	∞	NUM
ejpam-1678	179	3	∑	∑	PROPN
ejpam-1678	179	4	k=2	k=2	PROPN
ejpam-1678	179	5	akzk	akzk	PROPN
ejpam-1678	179	6	∈	∈	PROPN
ejpam-1678	179	7	h	h	PROPN
ejpam-1678	179	8	n	n	CCONJ
ejpam-1678	179	9	,	,	PUNCT
ejpam-1678	179	10	γ	γ	X
ejpam-1678	179	11	λ	λ	X
ejpam-1678	180	1	[	[	X
ejpam-1678	180	2	α	α	X
ejpam-1678	180	3	,	,	PUNCT
ejpam-1678	180	4	β	β	X
ejpam-1678	180	5	]	]	X
ejpam-1678	180	6	,	,	PUNCT
ejpam-1678	180	7	then	then	ADV
ejpam-1678	180	8	for	for	ADP
ejpam-1678	180	9	function	function	NOUN
ejpam-1678	180	10	g(z	g(z	PROPN
ejpam-1678	180	11	)	)	PUNCT
ejpam-1678	180	12	∈k	∈k	ADV
ejpam-1678	180	13	,	,	PUNCT
ejpam-1678	180	14	(	(	PUNCT
ejpam-1678	180	15	µ+	µ+	X
ejpam-1678	180	16	3)φ(2	3)φ(2	NOUN
ejpam-1678	180	17	)	)	PUNCT
ejpam-1678	180	18	(	(	PUNCT
ejpam-1678	180	19	µ+	µ+	PROPN
ejpam-1678	180	20	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	180	21	(	(	PUNCT
ejpam-1678	180	22	µ+	µ+	X
ejpam-1678	180	23	1)(1−	1)(1−	NUM
ejpam-1678	180	24	β	β	X
ejpam-1678	180	25	)	)	PUNCT
ejpam-1678	180	26	l	l	NOUN
ejpam-1678	180	27	∗	∗	NOUN
ejpam-1678	180	28	g(z	g(z	PROPN
ejpam-1678	180	29	)	)	PUNCT
ejpam-1678	180	30	≺	≺	NOUN
ejpam-1678	180	31	2g(z	2g(z	NUM
ejpam-1678	180	32	)	)	PUNCT
ejpam-1678	180	33	(	(	PUNCT
ejpam-1678	180	34	11	11	NUM
ejpam-1678	180	35	)	)	PUNCT
ejpam-1678	180	36	and	and	CCONJ
ejpam-1678	180	37	(	(	PUNCT
ejpam-1678	180	38	µ+	µ+	X
ejpam-1678	180	39	3)φ(2	3)φ(2	NOUN
ejpam-1678	180	40	)	)	PUNCT
ejpam-1678	180	41	(	(	PUNCT
ejpam-1678	180	42	µ+	µ+	PROPN
ejpam-1678	180	43	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	180	44	(	(	PUNCT
ejpam-1678	180	45	µ+	µ+	X
ejpam-1678	180	46	1)(1−	1)(1−	NUM
ejpam-1678	180	47	β	β	X
ejpam-1678	180	48	)	)	PUNCT
ejpam-1678	180	49	∫	∫	PROPN
ejpam-1678	180	50	2π	2π	PROPN
ejpam-1678	180	51	0	0	NUM
ejpam-1678	181	1	|l	|l	PROPN
ejpam-1678	181	2	∗	∗	NOUN
ejpam-1678	181	3	g(reiθ	g(reiθ	NOUN
ejpam-1678	181	4	)	)	PUNCT
ejpam-1678	181	5	|sdθ	|sdθ	NOUN
ejpam-1678	181	6	¶	¶	NOUN
ejpam-1678	181	7	2	2	NUM
ejpam-1678	181	8	∫	∫	PROPN
ejpam-1678	181	9	2π	2π	PROPN
ejpam-1678	181	10	0	0	NUM
ejpam-1678	181	11	|g(reiθ	|g(reiθ	NOUN
ejpam-1678	181	12	)	)	PUNCT
ejpam-1678	181	13	|sdθ	|sdθ	NOUN
ejpam-1678	181	14	,	,	PUNCT
ejpam-1678	181	15	(	(	PUNCT
ejpam-1678	181	16	12	12	NUM
ejpam-1678	181	17	)	)	PUNCT
ejpam-1678	181	18	where	where	SCONJ
ejpam-1678	181	19	φ(2	φ(2	NOUN
ejpam-1678	181	20	)	)	PUNCT
ejpam-1678	182	1	=	=	PUNCT
ejpam-1678	183	1	[	[	X
ejpam-1678	183	2	(	(	PUNCT
ejpam-1678	183	3	αψ2(γ	αψ2(γ	NOUN
ejpam-1678	183	4	,	,	PUNCT
ejpam-1678	183	5	λ	λ	NOUN
ejpam-1678	183	6	)	)	PUNCT
ejpam-1678	183	7	+	+	NUM
ejpam-1678	183	8	1)(ψ2(γ	1)(ψ2(γ	NUM
ejpam-1678	183	9	,	,	PUNCT
ejpam-1678	183	10	λ)−	λ)−	PROPN
ejpam-1678	183	11	1	1	NUM
ejpam-1678	183	12	)	)	PUNCT
ejpam-1678	183	13	+	+	SYM
ejpam-1678	183	14	1−	1−	NUM
ejpam-1678	183	15	β][ψ2(γ	β][ψ2(γ	NOUN
ejpam-1678	183	16	,	,	PUNCT
ejpam-1678	183	17	λ)]n	λ)]n	NOUN
ejpam-1678	183	18	,	,	PUNCT
ejpam-1678	183	19	0	0	PUNCT
ejpam-1678	183	20	<	<	X
ejpam-1678	183	21	|z|	|z|	NOUN
ejpam-1678	183	22	=	=	SYM
ejpam-1678	183	23	r	r	NOUN
ejpam-1678	183	24	<	<	X
ejpam-1678	183	25	1	1	NUM
ejpam-1678	183	26	,	,	PUNCT
ejpam-1678	183	27	s	s	VERB
ejpam-1678	183	28	>	>	X
ejpam-1678	183	29	0	0	PROPN
ejpam-1678	183	30	.	.	PUNCT
ejpam-1678	184	1	l.	l.	PROPN
ejpam-1678	184	2	xiong	xiong	PROPN
ejpam-1678	184	3	,	,	PUNCT
ejpam-1678	184	4	x.	x.	PROPN
ejpam-1678	184	5	liu	liu	PROPN
ejpam-1678	184	6	/	/	SYM
ejpam-1678	184	7	eur	eur	PROPN
ejpam-1678	184	8	.	.	PUNCT
ejpam-1678	185	1	j.	j.	PROPN
ejpam-1678	185	2	pure	pure	PROPN
ejpam-1678	185	3	appl	appl	PROPN
ejpam-1678	185	4	.	.	PROPN
ejpam-1678	185	5	math	math	PROPN
ejpam-1678	185	6	,	,	PUNCT
ejpam-1678	185	7	5	5	NUM
ejpam-1678	185	8	(	(	PUNCT
ejpam-1678	185	9	2012	2012	NUM
ejpam-1678	185	10	)	)	PUNCT
ejpam-1678	185	11	,	,	PUNCT
ejpam-1678	185	12	380	380	NUM
ejpam-1678	185	13	-	-	SYM
ejpam-1678	185	14	389	389	NUM
ejpam-1678	185	15	386	386	NUM
ejpam-1678	185	16	proof	proof	NOUN
ejpam-1678	185	17	.	.	PUNCT
ejpam-1678	186	1	suppose	suppose	VERB
ejpam-1678	186	2	g(z	g(z	ADJ
ejpam-1678	186	3	)	)	PUNCT
ejpam-1678	186	4	=	=	SYM
ejpam-1678	187	1	z	z	NOUN
ejpam-1678	188	1	+	+	NUM
ejpam-1678	188	2	∞	∞	NUM
ejpam-1678	188	3	∑	∑	PROPN
ejpam-1678	188	4	k=2	k=2	PROPN
ejpam-1678	188	5	bkzk	bkzk	VERB
ejpam-1678	188	6	∈k	∈k	ADV
ejpam-1678	188	7	,	,	PUNCT
ejpam-1678	188	8	then	then	ADV
ejpam-1678	188	9	(	(	PUNCT
ejpam-1678	188	10	µ+	µ+	X
ejpam-1678	188	11	3)φ(2	3)φ(2	NOUN
ejpam-1678	188	12	)	)	PUNCT
ejpam-1678	188	13	2(µ+	2(µ+	PROPN
ejpam-1678	189	1	3)φ(2)+	3)φ(2)+	NUM
ejpam-1678	189	2	2(µ+	2(µ+	NUM
ejpam-1678	189	3	1)(1−	1)(1−	NUM
ejpam-1678	189	4	β	β	X
ejpam-1678	189	5	)	)	PUNCT
ejpam-1678	189	6	l	l	NOUN
ejpam-1678	189	7	∗	∗	NOUN
ejpam-1678	189	8	g(z	g(z	PROPN
ejpam-1678	189	9	)	)	PUNCT
ejpam-1678	189	10	=	=	PUNCT
ejpam-1678	189	11	(	(	PUNCT
ejpam-1678	189	12	µ+	µ+	X
ejpam-1678	189	13	3)φ(2	3)φ(2	NOUN
ejpam-1678	189	14	)	)	PUNCT
ejpam-1678	189	15	2(µ+	2(µ+	PROPN
ejpam-1678	190	1	3)φ(2)+	3)φ(2)+	NUM
ejpam-1678	190	2	2(µ+	2(µ+	NUM
ejpam-1678	190	3	1)(1−β	1)(1−β	NUM
ejpam-1678	190	4	)	)	PUNCT
ejpam-1678	190	5	z	z	NOUN
ejpam-1678	191	1	+	+	NUM
ejpam-1678	191	2	∞	∞	NUM
ejpam-1678	191	3	∑	∑	PROPN
ejpam-1678	191	4	k=2	k=2	PROPN
ejpam-1678	191	5	(	(	PUNCT
ejpam-1678	191	6	µ+	µ+	X
ejpam-1678	191	7	3)φ(2	3)φ(2	NOUN
ejpam-1678	191	8	)	)	PUNCT
ejpam-1678	191	9	2(µ+	2(µ+	PROPN
ejpam-1678	192	1	3)φ(2)+	3)φ(2)+	NUM
ejpam-1678	192	2	2(µ+	2(µ+	NUM
ejpam-1678	192	3	1)(1−	1)(1−	NUM
ejpam-1678	192	4	β	β	NOUN
ejpam-1678	192	5	)	)	PUNCT
ejpam-1678	192	6	bkckzk	bkckzk	NOUN
ejpam-1678	192	7	.	.	PUNCT
ejpam-1678	193	1	if	if	SCONJ
ejpam-1678	193	2	we	we	PRON
ejpam-1678	193	3	show	show	VERB
ejpam-1678	193	4	that	that	SCONJ
ejpam-1678	193	5	ℜ{1	ℜ{1	VERB
ejpam-1678	193	6	+	+	ADP
ejpam-1678	193	7	2	2	NUM
ejpam-1678	193	8	∞	∞	NUM
ejpam-1678	193	9	∑	∑	PROPN
ejpam-1678	193	10	k=2	k=2	PROPN
ejpam-1678	193	11	(	(	PUNCT
ejpam-1678	193	12	µ+	µ+	X
ejpam-1678	193	13	3)φ(2	3)φ(2	NOUN
ejpam-1678	193	14	)	)	PUNCT
ejpam-1678	193	15	2(µ+	2(µ+	PROPN
ejpam-1678	194	1	3)φ(2)+	3)φ(2)+	NUM
ejpam-1678	194	2	2(µ+	2(µ+	NUM
ejpam-1678	194	3	1)(1−	1)(1−	NUM
ejpam-1678	194	4	β	β	SYM
ejpam-1678	194	5	)	)	PUNCT
ejpam-1678	194	6	ckzk	ckzk	NOUN
ejpam-1678	194	7	}	}	PUNCT
ejpam-1678	194	8	>	>	X
ejpam-1678	194	9	0	0	PUNCT
ejpam-1678	195	1	then	then	ADV
ejpam-1678	195	2	from	from	ADP
ejpam-1678	195	3	lemma	lemma	PROPN
ejpam-1678	195	4	1	1	NUM
ejpam-1678	195	5	,	,	PUNCT
ejpam-1678	195	6	we	we	PRON
ejpam-1678	195	7	say	say	VERB
ejpam-1678	195	8	that	that	SCONJ
ejpam-1678	195	9	the	the	DET
ejpam-1678	195	10	sequence	sequence	NOUN
ejpam-1678	195	11	�	�	PROPN
ejpam-1678	195	12	(	(	PUNCT
ejpam-1678	195	13	µ+	µ+	X
ejpam-1678	195	14	3)φ(2	3)φ(2	NOUN
ejpam-1678	195	15	)	)	PUNCT
ejpam-1678	195	16	2(µ+	2(µ+	PROPN
ejpam-1678	196	1	3)φ(2)+	3)φ(2)+	NUM
ejpam-1678	196	2	2(µ+	2(µ+	NUM
ejpam-1678	196	3	1)(1−	1)(1−	NUM
ejpam-1678	196	4	β	β	NOUN
ejpam-1678	196	5	)	)	PUNCT
ejpam-1678	196	6	ck	ck	PROPN
ejpam-1678	196	7	�	�	PROPN
ejpam-1678	196	8	∞	∞	PROPN
ejpam-1678	196	9	1	1	NUM
ejpam-1678	196	10	is	be	AUX
ejpam-1678	196	11	a	a	DET
ejpam-1678	196	12	subordination	subordination	NOUN
ejpam-1678	196	13	factor	factor	NOUN
ejpam-1678	196	14	sequence	sequence	NOUN
ejpam-1678	196	15	,	,	PUNCT
ejpam-1678	196	16	with	with	ADP
ejpam-1678	196	17	c1	c1	PROPN
ejpam-1678	196	18	=	=	PUNCT
ejpam-1678	197	1	1	1	X
ejpam-1678	197	2	.	.	PUNCT
ejpam-1678	197	3	now	now	ADV
ejpam-1678	197	4	ℜ	ℜ	ADJ
ejpam-1678	197	5	�	�	PROPN
ejpam-1678	197	6	1	1	NUM
ejpam-1678	197	7	+	+	NUM
ejpam-1678	197	8	2	2	NUM
ejpam-1678	197	9	∞	∞	NUM
ejpam-1678	197	10	∑	∑	PROPN
ejpam-1678	197	11	k=2	k=2	PROPN
ejpam-1678	197	12	(	(	PUNCT
ejpam-1678	197	13	µ+	µ+	X
ejpam-1678	197	14	3)φ(2	3)φ(2	NOUN
ejpam-1678	197	15	)	)	PUNCT
ejpam-1678	197	16	2(µ+	2(µ+	PROPN
ejpam-1678	198	1	3)φ(2)+	3)φ(2)+	NUM
ejpam-1678	198	2	2(µ+	2(µ+	NUM
ejpam-1678	198	3	1)(1−β	1)(1−β	NUM
ejpam-1678	198	4	)	)	PUNCT
ejpam-1678	198	5	ckzk	ckzk	NOUN
ejpam-1678	198	6	�	�	PROPN
ejpam-1678	198	7	=	=	SYM
ejpam-1678	198	8	ℜ	ℜ	PROPN
ejpam-1678	198	9	�	�	NOUN
ejpam-1678	198	10	1	1	NUM
ejpam-1678	198	11	+	+	NUM
ejpam-1678	198	12	∞	∞	NUM
ejpam-1678	198	13	∑	∑	PROPN
ejpam-1678	198	14	k=2	k=2	PROPN
ejpam-1678	198	15	(	(	PUNCT
ejpam-1678	198	16	µ+	µ+	X
ejpam-1678	198	17	3)φ(2	3)φ(2	NOUN
ejpam-1678	198	18	)	)	PUNCT
ejpam-1678	198	19	(	(	PUNCT
ejpam-1678	198	20	µ+	µ+	PROPN
ejpam-1678	198	21	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	198	22	(	(	PUNCT
ejpam-1678	198	23	µ+	µ+	X
ejpam-1678	198	24	1)(1−	1)(1−	NUM
ejpam-1678	198	25	β	β	SYM
ejpam-1678	198	26	)	)	PUNCT
ejpam-1678	198	27	ckzk	ckzk	NOUN
ejpam-1678	198	28	�	�	PROPN
ejpam-1678	198	29	=	=	SYM
ejpam-1678	198	30	ℜ	ℜ	PROPN
ejpam-1678	198	31	�	�	NOUN
ejpam-1678	198	32	1	1	NUM
ejpam-1678	198	33	+	+	CCONJ
ejpam-1678	198	34	(	(	PUNCT
ejpam-1678	198	35	µ+	µ+	X
ejpam-1678	198	36	3)φ(2	3)φ(2	NOUN
ejpam-1678	198	37	)	)	PUNCT
ejpam-1678	198	38	(	(	PUNCT
ejpam-1678	198	39	µ+	µ+	PROPN
ejpam-1678	198	40	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	198	41	(	(	PUNCT
ejpam-1678	198	42	µ+	µ+	X
ejpam-1678	198	43	1)(1−	1)(1−	NUM
ejpam-1678	198	44	β	β	X
ejpam-1678	198	45	)	)	PUNCT
ejpam-1678	198	46	z	z	NOUN
ejpam-1678	199	1	+	+	CCONJ
ejpam-1678	199	2	(	(	PUNCT
ejpam-1678	199	3	µ+	µ+	X
ejpam-1678	199	4	3	3	NUM
ejpam-1678	199	5	)	)	PUNCT
ejpam-1678	199	6	(	(	PUNCT
ejpam-1678	199	7	µ+	µ+	PROPN
ejpam-1678	199	8	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	199	9	(	(	PUNCT
ejpam-1678	199	10	µ+	µ+	X
ejpam-1678	199	11	1)(1−	1)(1−	NUM
ejpam-1678	199	12	β	β	NOUN
ejpam-1678	199	13	)	)	PUNCT
ejpam-1678	199	14	∞	∞	PROPN
ejpam-1678	199	15	∑	∑	PROPN
ejpam-1678	199	16	k=2	k=2	PROPN
ejpam-1678	199	17	φ(2)ckzk	φ(2)ckzk	PROPN
ejpam-1678	199	18	�	�	PROPN
ejpam-1678	199	19	¾	¾	PROPN
ejpam-1678	199	20	1−	1−	NUM
ejpam-1678	199	21	(	(	PUNCT
ejpam-1678	199	22	µ+	µ+	X
ejpam-1678	199	23	3)φ(2	3)φ(2	NOUN
ejpam-1678	199	24	)	)	PUNCT
ejpam-1678	199	25	(	(	PUNCT
ejpam-1678	199	26	µ+	µ+	PROPN
ejpam-1678	199	27	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	199	28	(	(	PUNCT
ejpam-1678	199	29	µ+	µ+	X
ejpam-1678	199	30	1)(1−	1)(1−	NUM
ejpam-1678	199	31	β	β	X
ejpam-1678	199	32	)	)	PUNCT
ejpam-1678	199	33	r	r	NOUN
ejpam-1678	199	34	−	−	PROPN
ejpam-1678	199	35	(	(	PUNCT
ejpam-1678	199	36	µ+	µ+	X
ejpam-1678	199	37	3	3	NUM
ejpam-1678	199	38	)	)	PUNCT
ejpam-1678	199	39	(	(	PUNCT
ejpam-1678	199	40	µ+	µ+	PROPN
ejpam-1678	199	41	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	199	42	(	(	PUNCT
ejpam-1678	199	43	µ+	µ+	X
ejpam-1678	199	44	1)(1−	1)(1−	NUM
ejpam-1678	199	45	β	β	NOUN
ejpam-1678	199	46	)	)	PUNCT
ejpam-1678	199	47	∞	∞	PROPN
ejpam-1678	199	48	∑	∑	PROPN
ejpam-1678	199	49	k=2	k=2	PROPN
ejpam-1678	200	1	φ(2)|ck|r	φ(2)|ck|r	PROPN
ejpam-1678	200	2	k	k	PROPN
ejpam-1678	200	3	(	(	PUNCT
ejpam-1678	200	4	13	13	NUM
ejpam-1678	200	5	)	)	PUNCT
ejpam-1678	200	6	because	because	SCONJ
ejpam-1678	200	7	l(z	l(z	NOUN
ejpam-1678	200	8	)	)	PUNCT
ejpam-1678	200	9	satisfies	satisfy	VERB
ejpam-1678	200	10	the	the	DET
ejpam-1678	200	11	differential	differential	ADJ
ejpam-1678	200	12	equation	equation	NOUN
ejpam-1678	200	13	with	with	ADP
ejpam-1678	200	14	the	the	DET
ejpam-1678	200	15	f	f	PROPN
ejpam-1678	200	16	(	(	PUNCT
ejpam-1678	200	17	z	z	NOUN
ejpam-1678	200	18	)	)	PUNCT
ejpam-1678	200	19	∈	∈	PROPN
ejpam-1678	200	20	h	h	NOUN
ejpam-1678	200	21	n	n	CCONJ
ejpam-1678	200	22	,	,	PUNCT
ejpam-1678	200	23	γ	γ	X
ejpam-1678	200	24	λ	λ	X
ejpam-1678	201	1	[	[	X
ejpam-1678	201	2	α	α	X
ejpam-1678	201	3	,	,	PUNCT
ejpam-1678	201	4	β	β	X
ejpam-1678	201	5	]	]	X
ejpam-1678	201	6	,	,	PUNCT
ejpam-1678	201	7	so	so	ADV
ejpam-1678	201	8	ck	ck	ADV
ejpam-1678	201	9	=	=	SYM
ejpam-1678	201	10	(	(	PUNCT
ejpam-1678	201	11	µ+	µ+	PROPN
ejpam-1678	201	12	1)(µ+	1)(µ+	NUM
ejpam-1678	201	13	2	2	NUM
ejpam-1678	201	14	)	)	PUNCT
ejpam-1678	201	15	(	(	PUNCT
ejpam-1678	201	16	k+µ)(k+µ+	k+µ)(k+µ+	PROPN
ejpam-1678	201	17	1	1	NUM
ejpam-1678	201	18	)	)	PUNCT
ejpam-1678	201	19	ak	ak	PROPN
ejpam-1678	201	20	following	follow	VERB
ejpam-1678	201	21	(	(	PUNCT
ejpam-1678	201	22	13	13	NUM
ejpam-1678	201	23	)	)	PUNCT
ejpam-1678	201	24	,	,	PUNCT
ejpam-1678	201	25	we	we	PRON
ejpam-1678	201	26	have	have	VERB
ejpam-1678	201	27	¾1−	¾1−	NUM
ejpam-1678	201	28	(	(	PUNCT
ejpam-1678	201	29	µ+	µ+	X
ejpam-1678	201	30	3)φ(2	3)φ(2	NOUN
ejpam-1678	201	31	)	)	PUNCT
ejpam-1678	201	32	(	(	PUNCT
ejpam-1678	201	33	µ+	µ+	PROPN
ejpam-1678	201	34	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	201	35	(	(	PUNCT
ejpam-1678	201	36	µ+	µ+	X
ejpam-1678	201	37	1)(1−	1)(1−	NUM
ejpam-1678	201	38	β	β	X
ejpam-1678	201	39	)	)	PUNCT
ejpam-1678	201	40	r	r	NOUN
ejpam-1678	201	41	−	−	PROPN
ejpam-1678	201	42	(	(	PUNCT
ejpam-1678	201	43	µ+	µ+	X
ejpam-1678	201	44	3	3	NUM
ejpam-1678	201	45	)	)	PUNCT
ejpam-1678	201	46	(	(	PUNCT
ejpam-1678	201	47	µ+	µ+	PROPN
ejpam-1678	201	48	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	201	49	(	(	PUNCT
ejpam-1678	201	50	µ+	µ+	X
ejpam-1678	201	51	1)(1−β	1)(1−β	NUM
ejpam-1678	201	52	)	)	PUNCT
ejpam-1678	201	53	∞	∞	PROPN
ejpam-1678	201	54	∑	∑	PROPN
ejpam-1678	201	55	k=2	k=2	PROPN
ejpam-1678	201	56	φ(2	φ(2	PROPN
ejpam-1678	201	57	)	)	PUNCT
ejpam-1678	201	58	(	(	PUNCT
ejpam-1678	201	59	µ+	µ+	ADJ
ejpam-1678	201	60	1)(µ+	1)(µ+	NUM
ejpam-1678	201	61	2	2	NUM
ejpam-1678	201	62	)	)	PUNCT
ejpam-1678	201	63	(	(	PUNCT
ejpam-1678	201	64	k+µ)(k+µ+	k+µ)(k+µ+	PROPN
ejpam-1678	201	65	1	1	NUM
ejpam-1678	201	66	)	)	PUNCT
ejpam-1678	201	67	|ak|r	|ak|r	ADP
ejpam-1678	201	68	k	k	PROPN
ejpam-1678	201	69	¾1−	¾1−	NUM
ejpam-1678	201	70	(	(	PUNCT
ejpam-1678	201	71	µ+	µ+	X
ejpam-1678	201	72	3)φ(2	3)φ(2	NOUN
ejpam-1678	201	73	)	)	PUNCT
ejpam-1678	201	74	(	(	PUNCT
ejpam-1678	201	75	µ+	µ+	PROPN
ejpam-1678	201	76	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	201	77	(	(	PUNCT
ejpam-1678	201	78	µ+	µ+	X
ejpam-1678	201	79	1)(1−	1)(1−	NUM
ejpam-1678	201	80	β	β	X
ejpam-1678	201	81	)	)	PUNCT
ejpam-1678	201	82	r	r	NOUN
ejpam-1678	201	83	−	−	PROPN
ejpam-1678	201	84	(	(	PUNCT
ejpam-1678	201	85	µ+	µ+	X
ejpam-1678	201	86	3	3	NUM
ejpam-1678	201	87	)	)	PUNCT
ejpam-1678	201	88	(	(	PUNCT
ejpam-1678	201	89	µ+	µ+	PROPN
ejpam-1678	201	90	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	201	91	(	(	PUNCT
ejpam-1678	201	92	µ+	µ+	X
ejpam-1678	201	93	1)(1−β	1)(1−β	NUM
ejpam-1678	201	94	)	)	PUNCT
ejpam-1678	201	95	∞	∞	PROPN
ejpam-1678	201	96	∑	∑	PROPN
ejpam-1678	201	97	k=2	k=2	PROPN
ejpam-1678	201	98	φ(2	φ(2	PROPN
ejpam-1678	201	99	)	)	PUNCT
ejpam-1678	201	100	(	(	PUNCT
ejpam-1678	201	101	µ+	µ+	ADJ
ejpam-1678	201	102	1)(µ+	1)(µ+	NUM
ejpam-1678	201	103	2	2	NUM
ejpam-1678	201	104	)	)	PUNCT
ejpam-1678	201	105	(	(	PUNCT
ejpam-1678	201	106	2+µ)(µ+	2+µ)(µ+	NOUN
ejpam-1678	201	107	3	3	NUM
ejpam-1678	201	108	)	)	PUNCT
ejpam-1678	201	109	|ak|r	|ak|r	ADP
ejpam-1678	201	110	k	k	PROPN
ejpam-1678	201	111	¾1−	¾1−	NUM
ejpam-1678	201	112	(	(	PUNCT
ejpam-1678	201	113	µ+	µ+	X
ejpam-1678	201	114	3)φ(2	3)φ(2	NOUN
ejpam-1678	201	115	)	)	PUNCT
ejpam-1678	201	116	(	(	PUNCT
ejpam-1678	201	117	µ+	µ+	PROPN
ejpam-1678	201	118	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	201	119	(	(	PUNCT
ejpam-1678	201	120	µ+	µ+	X
ejpam-1678	201	121	1)(1−	1)(1−	NUM
ejpam-1678	201	122	β	β	X
ejpam-1678	201	123	)	)	PUNCT
ejpam-1678	201	124	r	r	NOUN
ejpam-1678	201	125	−	−	PROPN
ejpam-1678	201	126	(	(	PUNCT
ejpam-1678	201	127	µ+	µ+	X
ejpam-1678	201	128	1	1	NUM
ejpam-1678	201	129	)	)	PUNCT
ejpam-1678	201	130	(	(	PUNCT
ejpam-1678	201	131	µ+	µ+	PROPN
ejpam-1678	201	132	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	201	133	(	(	PUNCT
ejpam-1678	201	134	µ+	µ+	X
ejpam-1678	201	135	1)(1−β	1)(1−β	NUM
ejpam-1678	201	136	)	)	PUNCT
ejpam-1678	201	137	∞	∞	PROPN
ejpam-1678	201	138	∑	∑	PROPN
ejpam-1678	201	139	k=2	k=2	PROPN
ejpam-1678	201	140	φ(2)|ak|r	φ(2)|ak|r	ADP
ejpam-1678	201	141	k	k	X
ejpam-1678	201	142	(	(	PUNCT
ejpam-1678	201	143	14	14	NUM
ejpam-1678	201	144	)	)	PUNCT
ejpam-1678	201	145	l.	l.	PROPN
ejpam-1678	201	146	xiong	xiong	PROPN
ejpam-1678	201	147	,	,	PUNCT
ejpam-1678	201	148	x.	x.	PROPN
ejpam-1678	201	149	liu	liu	PROPN
ejpam-1678	201	150	/	/	SYM
ejpam-1678	201	151	eur	eur	PROPN
ejpam-1678	201	152	.	.	PUNCT
ejpam-1678	202	1	j.	j.	PROPN
ejpam-1678	202	2	pure	pure	PROPN
ejpam-1678	202	3	appl	appl	PROPN
ejpam-1678	202	4	.	.	PROPN
ejpam-1678	202	5	math	math	PROPN
ejpam-1678	202	6	,	,	PUNCT
ejpam-1678	202	7	5	5	NUM
ejpam-1678	202	8	(	(	PUNCT
ejpam-1678	202	9	2012	2012	NUM
ejpam-1678	202	10	)	)	PUNCT
ejpam-1678	202	11	,	,	PUNCT
ejpam-1678	202	12	380	380	NUM
ejpam-1678	202	13	-	-	SYM
ejpam-1678	202	14	389	389	NUM
ejpam-1678	202	15	387	387	NUM
ejpam-1678	202	16	since	since	SCONJ
ejpam-1678	202	17	φ(k	φ(k	PROPN
ejpam-1678	202	18	)	)	PUNCT
ejpam-1678	202	19	=	=	PUNCT
ejpam-1678	203	1	[	[	X
ejpam-1678	203	2	(	(	PUNCT
ejpam-1678	203	3	αψk(γ	αψk(γ	PROPN
ejpam-1678	203	4	,	,	PUNCT
ejpam-1678	203	5	λ	λ	X
ejpam-1678	203	6	)	)	PUNCT
ejpam-1678	203	7	+	+	NOUN
ejpam-1678	203	8	1)(ψk(γ	1)(ψk(γ	NUM
ejpam-1678	203	9	,	,	PUNCT
ejpam-1678	203	10	λ)−	λ)−	PROPN
ejpam-1678	203	11	1	1	NUM
ejpam-1678	203	12	)	)	PUNCT
ejpam-1678	203	13	+	+	NUM
ejpam-1678	203	14	1−	1−	NUM
ejpam-1678	203	15	β][ψk(γ	β][ψk(γ	NUM
ejpam-1678	203	16	,	,	PUNCT
ejpam-1678	203	17	λ)]n	λ)]n	ADV
ejpam-1678	203	18	(	(	PUNCT
ejpam-1678	203	19	k	k	NOUN
ejpam-1678	203	20	=	=	SYM
ejpam-1678	203	21	2,3	2,3	NUM
ejpam-1678	203	22	,	,	PUNCT
ejpam-1678	203	23	.	.	PUNCT
ejpam-1678	203	24	.	.	PUNCT
ejpam-1678	203	25	.	.	PUNCT
ejpam-1678	203	26	)	)	PUNCT
ejpam-1678	204	1	and	and	CCONJ
ejpam-1678	204	2	ψk(γ	ψk(γ	NUM
ejpam-1678	204	3	,	,	PUNCT
ejpam-1678	204	4	λ	λ	X
ejpam-1678	204	5	)	)	PUNCT
ejpam-1678	204	6	=	=	SYM
ejpam-1678	205	1	γ(k+	γ(k+	PROPN
ejpam-1678	205	2	1)γ(2−	1)γ(2−	NUM
ejpam-1678	205	3	γ	γ	NOUN
ejpam-1678	205	4	)	)	PUNCT
ejpam-1678	205	5	γ(k+	γ(k+	NOUN
ejpam-1678	205	6	1−	1−	NUM
ejpam-1678	205	7	γ	γ	X
ejpam-1678	205	8	)	)	PUNCT
ejpam-1678	206	1	[	[	X
ejpam-1678	206	2	1+λ(k−	1+λ(k−	NUM
ejpam-1678	206	3	1	1	NUM
ejpam-1678	206	4	)	)	PUNCT
ejpam-1678	206	5	]	]	PUNCT
ejpam-1678	207	1	(	(	PUNCT
ejpam-1678	207	2	k	k	X
ejpam-1678	207	3	=	=	SYM
ejpam-1678	207	4	2,3	2,3	NUM
ejpam-1678	207	5	,	,	PUNCT
ejpam-1678	207	6	.	.	PUNCT
ejpam-1678	207	7	.	.	PUNCT
ejpam-1678	207	8	.	.	PUNCT
ejpam-1678	207	9	)	)	PUNCT
ejpam-1678	208	1	is	be	AUX
ejpam-1678	208	2	a	a	DET
ejpam-1678	208	3	increasing	increase	VERB
ejpam-1678	208	4	function	function	NOUN
ejpam-1678	208	5	of	of	ADP
ejpam-1678	208	6	k	k	PROPN
ejpam-1678	208	7	,	,	PUNCT
ejpam-1678	208	8	so	so	ADV
ejpam-1678	208	9	0	0	NUM
ejpam-1678	208	10	<	<	X
ejpam-1678	208	11	φ(2)¶	φ(2)¶	X
ejpam-1678	208	12	φ(k	φ(k	PROPN
ejpam-1678	208	13	)	)	PUNCT
ejpam-1678	209	1	(	(	PUNCT
ejpam-1678	209	2	k	k	NOUN
ejpam-1678	209	3	=	=	SYM
ejpam-1678	209	4	2,3	2,3	NUM
ejpam-1678	209	5	,	,	PUNCT
ejpam-1678	209	6	.	.	PUNCT
ejpam-1678	209	7	.	.	PUNCT
ejpam-1678	209	8	.	.	PUNCT
ejpam-1678	209	9	)	)	PUNCT
ejpam-1678	209	10	.	.	PUNCT
ejpam-1678	210	1	following	follow	VERB
ejpam-1678	210	2	(	(	PUNCT
ejpam-1678	210	3	14	14	NUM
ejpam-1678	210	4	)	)	PUNCT
ejpam-1678	210	5	,	,	PUNCT
ejpam-1678	210	6	we	we	PRON
ejpam-1678	210	7	can	can	AUX
ejpam-1678	210	8	write	write	VERB
ejpam-1678	210	9	¾	¾	PROPN
ejpam-1678	210	10	1−	1−	NUM
ejpam-1678	210	11	(	(	PUNCT
ejpam-1678	210	12	µ+	µ+	X
ejpam-1678	210	13	3)φ(2	3)φ(2	NOUN
ejpam-1678	210	14	)	)	PUNCT
ejpam-1678	210	15	(	(	PUNCT
ejpam-1678	210	16	µ+	µ+	PROPN
ejpam-1678	210	17	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	210	18	(	(	PUNCT
ejpam-1678	210	19	µ+	µ+	X
ejpam-1678	210	20	1)(1−	1)(1−	NUM
ejpam-1678	210	21	β	β	X
ejpam-1678	210	22	)	)	PUNCT
ejpam-1678	210	23	r	r	NOUN
ejpam-1678	210	24	−	−	PROPN
ejpam-1678	210	25	(	(	PUNCT
ejpam-1678	210	26	µ+	µ+	X
ejpam-1678	210	27	1	1	NUM
ejpam-1678	210	28	)	)	PUNCT
ejpam-1678	210	29	(	(	PUNCT
ejpam-1678	210	30	µ+	µ+	PROPN
ejpam-1678	210	31	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	210	32	(	(	PUNCT
ejpam-1678	210	33	µ+	µ+	X
ejpam-1678	210	34	1)(1−	1)(1−	NUM
ejpam-1678	210	35	β	β	NOUN
ejpam-1678	210	36	)	)	PUNCT
ejpam-1678	210	37	∞	∞	PROPN
ejpam-1678	210	38	∑	∑	PROPN
ejpam-1678	210	39	k=2	k=2	PROPN
ejpam-1678	210	40	φ(k)|ak|r	φ(k)|ak|r	PROPN
ejpam-1678	210	41	k.	k.	PROPN
ejpam-1678	210	42	as	as	ADP
ejpam-1678	210	43	0	0	NUM
ejpam-1678	210	44	<	<	X
ejpam-1678	210	45	r	r	NOUN
ejpam-1678	210	46	<	<	X
ejpam-1678	210	47	1	1	NUM
ejpam-1678	210	48	,	,	PUNCT
ejpam-1678	210	49	it	it	PRON
ejpam-1678	210	50	can	can	AUX
ejpam-1678	210	51	make	make	VERB
ejpam-1678	210	52	sure	sure	ADJ
ejpam-1678	210	53	¾	¾	NOUN
ejpam-1678	210	54	1−	1−	NUM
ejpam-1678	210	55	(	(	PUNCT
ejpam-1678	210	56	µ+	µ+	X
ejpam-1678	210	57	3)φ(2	3)φ(2	NOUN
ejpam-1678	210	58	)	)	PUNCT
ejpam-1678	210	59	(	(	PUNCT
ejpam-1678	210	60	µ+	µ+	PROPN
ejpam-1678	210	61	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	210	62	(	(	PUNCT
ejpam-1678	210	63	µ+	µ+	X
ejpam-1678	210	64	1)(1−	1)(1−	NUM
ejpam-1678	210	65	β	β	X
ejpam-1678	210	66	)	)	PUNCT
ejpam-1678	210	67	r	r	NOUN
ejpam-1678	210	68	−	−	PROPN
ejpam-1678	210	69	(	(	PUNCT
ejpam-1678	210	70	µ+	µ+	PROPN
ejpam-1678	210	71	1)r	1)r	NUM
ejpam-1678	210	72	(	(	PUNCT
ejpam-1678	210	73	µ+	µ+	PROPN
ejpam-1678	210	74	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	210	75	(	(	PUNCT
ejpam-1678	210	76	µ+	µ+	X
ejpam-1678	210	77	1)(1−	1)(1−	NUM
ejpam-1678	210	78	β	β	NOUN
ejpam-1678	210	79	)	)	PUNCT
ejpam-1678	210	80	∞	∞	PROPN
ejpam-1678	210	81	∑	∑	PROPN
ejpam-1678	210	82	k=2	k=2	PROPN
ejpam-1678	211	1	φ(k)|ak|	φ(k)|ak|	PROPN
ejpam-1678	211	2	.	.	PUNCT
ejpam-1678	212	1	(	(	PUNCT
ejpam-1678	212	2	15	15	NUM
ejpam-1678	212	3	)	)	PUNCT
ejpam-1678	212	4	since	since	SCONJ
ejpam-1678	212	5	f	f	PROPN
ejpam-1678	212	6	(	(	PUNCT
ejpam-1678	212	7	z	z	NOUN
ejpam-1678	212	8	)	)	PUNCT
ejpam-1678	212	9	=	=	SYM
ejpam-1678	213	1	z	z	NOUN
ejpam-1678	214	1	+	+	NUM
ejpam-1678	214	2	∞	∞	NUM
ejpam-1678	214	3	∑	∑	PUNCT
ejpam-1678	214	4	k=2	k=2	PROPN
ejpam-1678	214	5	∈	∈	PROPN
ejpam-1678	214	6	h	h	PROPN
ejpam-1678	214	7	n	n	CCONJ
ejpam-1678	214	8	,	,	PUNCT
ejpam-1678	214	9	γ	γ	X
ejpam-1678	214	10	λ	λ	X
ejpam-1678	215	1	[	[	X
ejpam-1678	215	2	α	α	X
ejpam-1678	215	3	,	,	PUNCT
ejpam-1678	215	4	β	β	X
ejpam-1678	215	5	]	]	X
ejpam-1678	215	6	,	,	PUNCT
ejpam-1678	215	7	using	use	VERB
ejpam-1678	215	8	lemma	lemma	PROPN
ejpam-1678	215	9	3	3	NUM
ejpam-1678	215	10	and	and	CCONJ
ejpam-1678	215	11	following	follow	VERB
ejpam-1678	215	12	(	(	PUNCT
ejpam-1678	215	13	15	15	NUM
ejpam-1678	215	14	)	)	PUNCT
ejpam-1678	215	15	,	,	PUNCT
ejpam-1678	215	16	we	we	PRON
ejpam-1678	215	17	obtain	obtain	VERB
ejpam-1678	215	18	ℜ{1	ℜ{1	VERB
ejpam-1678	215	19	+	+	NOUN
ejpam-1678	215	20	2	2	NUM
ejpam-1678	215	21	∞	∞	NUM
ejpam-1678	215	22	∑	∑	PROPN
ejpam-1678	215	23	k=2	k=2	PROPN
ejpam-1678	215	24	(	(	PUNCT
ejpam-1678	215	25	µ+	µ+	X
ejpam-1678	215	26	3)φ(2	3)φ(2	NOUN
ejpam-1678	215	27	)	)	PUNCT
ejpam-1678	215	28	2(µ+	2(µ+	PROPN
ejpam-1678	216	1	3)φ(2)+	3)φ(2)+	NUM
ejpam-1678	216	2	2(µ+	2(µ+	NUM
ejpam-1678	216	3	1)(1−	1)(1−	NUM
ejpam-1678	216	4	β	β	SYM
ejpam-1678	216	5	)	)	PUNCT
ejpam-1678	216	6	ckzk	ckzk	NOUN
ejpam-1678	216	7	}	}	PUNCT
ejpam-1678	216	8	¾	¾	PROPN
ejpam-1678	216	9	1−	1−	NUM
ejpam-1678	216	10	(	(	PUNCT
ejpam-1678	216	11	µ+	µ+	X
ejpam-1678	216	12	3)φ(2	3)φ(2	NOUN
ejpam-1678	216	13	)	)	PUNCT
ejpam-1678	216	14	(	(	PUNCT
ejpam-1678	216	15	µ+	µ+	PROPN
ejpam-1678	216	16	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	216	17	(	(	PUNCT
ejpam-1678	216	18	µ+	µ+	X
ejpam-1678	216	19	1)(1−	1)(1−	NUM
ejpam-1678	216	20	β	β	X
ejpam-1678	216	21	)	)	PUNCT
ejpam-1678	216	22	r	r	NOUN
ejpam-1678	216	23	−	−	PROPN
ejpam-1678	216	24	(	(	PUNCT
ejpam-1678	216	25	1−β)(µ+	1−β)(µ+	NUM
ejpam-1678	216	26	1	1	NUM
ejpam-1678	216	27	)	)	PUNCT
ejpam-1678	216	28	(	(	PUNCT
ejpam-1678	216	29	µ+	µ+	PROPN
ejpam-1678	216	30	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	216	31	(	(	PUNCT
ejpam-1678	216	32	µ+	µ+	X
ejpam-1678	216	33	1)(1−	1)(1−	NUM
ejpam-1678	216	34	β	β	X
ejpam-1678	216	35	)	)	PUNCT
ejpam-1678	216	36	r	r	NOUN
ejpam-1678	216	37	=	=	SYM
ejpam-1678	216	38	1−	1−	NUM
ejpam-1678	216	39	r	r	NOUN
ejpam-1678	216	40	>	>	X
ejpam-1678	216	41	0	0	NUM
ejpam-1678	216	42	.	.	PUNCT
ejpam-1678	217	1	in	in	ADP
ejpam-1678	217	2	the	the	DET
ejpam-1678	217	3	light	light	NOUN
ejpam-1678	217	4	of	of	ADP
ejpam-1678	217	5	definition	definition	NOUN
ejpam-1678	217	6	1	1	NUM
ejpam-1678	217	7	,	,	PUNCT
ejpam-1678	217	8	we	we	PRON
ejpam-1678	217	9	have	have	VERB
ejpam-1678	217	10	(	(	PUNCT
ejpam-1678	217	11	µ+	µ+	X
ejpam-1678	217	12	3)φ(2	3)φ(2	NOUN
ejpam-1678	217	13	)	)	PUNCT
ejpam-1678	217	14	2(µ+	2(µ+	PROPN
ejpam-1678	218	1	3)φ(2)+	3)φ(2)+	NUM
ejpam-1678	218	2	2(µ+	2(µ+	NUM
ejpam-1678	218	3	1)(1−	1)(1−	NUM
ejpam-1678	218	4	β	β	X
ejpam-1678	218	5	)	)	PUNCT
ejpam-1678	218	6	l	l	NOUN
ejpam-1678	218	7	∗	∗	NOUN
ejpam-1678	218	8	g(z	g(z	ADJ
ejpam-1678	218	9	)	)	PUNCT
ejpam-1678	218	10	=	=	SYM
ejpam-1678	219	1	∞	∞	NUM
ejpam-1678	219	2	∑	∑	PUNCT
ejpam-1678	219	3	k=1	k=1	X
ejpam-1678	219	4	(	(	PUNCT
ejpam-1678	219	5	µ+	µ+	X
ejpam-1678	219	6	3)φ(2	3)φ(2	NOUN
ejpam-1678	219	7	)	)	PUNCT
ejpam-1678	219	8	2(µ+	2(µ+	PROPN
ejpam-1678	220	1	3)φ(2)+	3)φ(2)+	NUM
ejpam-1678	220	2	2(µ+	2(µ+	NUM
ejpam-1678	220	3	1)(1−β	1)(1−β	NUM
ejpam-1678	220	4	)	)	PUNCT
ejpam-1678	220	5	bkckzk	bkckzk	VERB
ejpam-1678	220	6	≺	≺	NOUN
ejpam-1678	220	7	g(z	g(z	PROPN
ejpam-1678	220	8	)	)	PUNCT
ejpam-1678	220	9	.	.	PUNCT
ejpam-1678	221	1	furthermore	furthermore	ADV
ejpam-1678	221	2	,	,	PUNCT
ejpam-1678	221	3	it	it	PRON
ejpam-1678	221	4	is	be	AUX
ejpam-1678	221	5	easy	easy	ADJ
ejpam-1678	221	6	to	to	PART
ejpam-1678	221	7	deduce	deduce	VERB
ejpam-1678	221	8	the	the	DET
ejpam-1678	221	9	result	result	NOUN
ejpam-1678	221	10	in	in	ADP
ejpam-1678	221	11	(	(	PUNCT
ejpam-1678	221	12	12	12	NUM
ejpam-1678	221	13	)	)	PUNCT
ejpam-1678	221	14	by	by	ADP
ejpam-1678	221	15	using	use	VERB
ejpam-1678	221	16	(	(	PUNCT
ejpam-1678	221	17	11	11	NUM
ejpam-1678	221	18	)	)	PUNCT
ejpam-1678	221	19	and	and	CCONJ
ejpam-1678	221	20	lemma	lemma	PROPN
ejpam-1678	221	21	4	4	X
ejpam-1678	221	22	.	.	PUNCT
ejpam-1678	221	23	corollary	corollary	ADJ
ejpam-1678	221	24	5	5	NUM
ejpam-1678	221	25	.	.	PUNCT
ejpam-1678	222	1	if	if	SCONJ
ejpam-1678	222	2	the	the	DET
ejpam-1678	222	3	function	function	NOUN
ejpam-1678	222	4	l(z	l(z	NOUN
ejpam-1678	222	5	)	)	PUNCT
ejpam-1678	222	6	=	=	SYM
ejpam-1678	222	7	z	z	NOUN
ejpam-1678	223	1	+	+	NUM
ejpam-1678	223	2	∞	∞	NUM
ejpam-1678	223	3	∑	∑	PROPN
ejpam-1678	223	4	k=2	k=2	PROPN
ejpam-1678	223	5	ckzk	ckzk	PROPN
ejpam-1678	223	6	∈	∈	PROPN
ejpam-1678	223	7	t	t	PROPN
ejpam-1678	223	8	satisfy	satisfy	VERB
ejpam-1678	223	9	the	the	DET
ejpam-1678	223	10	equation	equation	NOUN
ejpam-1678	223	11	(	(	PUNCT
ejpam-1678	223	12	10	10	NUM
ejpam-1678	223	13	)	)	PUNCT
ejpam-1678	223	14	with	with	ADP
ejpam-1678	223	15	f	f	PROPN
ejpam-1678	223	16	(	(	PUNCT
ejpam-1678	223	17	z	z	NOUN
ejpam-1678	223	18	)	)	PUNCT
ejpam-1678	223	19	=	=	SYM
ejpam-1678	224	1	z	z	NOUN
ejpam-1678	225	1	+	+	NUM
ejpam-1678	225	2	∞	∞	NUM
ejpam-1678	225	3	∑	∑	PROPN
ejpam-1678	225	4	k=2	k=2	PROPN
ejpam-1678	225	5	akzk	akzk	PROPN
ejpam-1678	225	6	∈	∈	PROPN
ejpam-1678	225	7	h	h	PROPN
ejpam-1678	225	8	n	n	CCONJ
ejpam-1678	225	9	,	,	PUNCT
ejpam-1678	225	10	γ	γ	X
ejpam-1678	225	11	λ	λ	X
ejpam-1678	226	1	[	[	X
ejpam-1678	226	2	α	α	X
ejpam-1678	226	3	,	,	PUNCT
ejpam-1678	226	4	β	β	NOUN
ejpam-1678	226	5	]	]	PUNCT
ejpam-1678	226	6	and	and	CCONJ
ejpam-1678	226	7	f(z	f(z	PROPN
ejpam-1678	226	8	)	)	PUNCT
ejpam-1678	227	1	=	=	SYM
ejpam-1678	227	2	z	z	NOUN
ejpam-1678	228	1	+	+	NUM
ejpam-1678	228	2	∞	∞	PROPN
ejpam-1678	228	3	∑	∑	PROPN
ejpam-1678	228	4	k=2	k=2	PROPN
ejpam-1678	228	5	(	(	PUNCT
ejpam-1678	228	6	a)k−1	a)k−1	PROPN
ejpam-1678	228	7	(	(	PUNCT
ejpam-1678	228	8	c)k−1	c)k−1	PROPN
ejpam-1678	228	9	ckzk	ckzk	PROPN
ejpam-1678	228	10	,	,	PUNCT
ejpam-1678	228	11	then	then	ADV
ejpam-1678	228	12	(	(	PUNCT
ejpam-1678	228	13	µ+	µ+	X
ejpam-1678	228	14	3)φ(2	3)φ(2	NOUN
ejpam-1678	228	15	)	)	PUNCT
ejpam-1678	228	16	(	(	PUNCT
ejpam-1678	228	17	µ+	µ+	PROPN
ejpam-1678	228	18	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	228	19	(	(	PUNCT
ejpam-1678	228	20	µ+	µ+	X
ejpam-1678	228	21	1)(1−	1)(1−	NUM
ejpam-1678	228	22	β	β	SYM
ejpam-1678	228	23	)	)	PUNCT
ejpam-1678	228	24	f(z	f(z	PROPN
ejpam-1678	228	25	)	)	PUNCT
ejpam-1678	228	26	≺	≺	NOUN
ejpam-1678	228	27	2h(a	2h(a	NUM
ejpam-1678	228	28	,	,	PUNCT
ejpam-1678	228	29	c	c	X
ejpam-1678	228	30	;	;	PUNCT
ejpam-1678	228	31	z	z	X
ejpam-1678	228	32	)	)	PUNCT
ejpam-1678	228	33	(	(	PUNCT
ejpam-1678	228	34	16	16	NUM
ejpam-1678	228	35	)	)	PUNCT
ejpam-1678	228	36	and	and	CCONJ
ejpam-1678	228	37	ℜl(z	ℜl(z	NOUN
ejpam-1678	228	38	)	)	PUNCT
ejpam-1678	228	39	>	>	X
ejpam-1678	229	1	−	−	PROPN
ejpam-1678	230	1	(	(	PUNCT
ejpam-1678	230	2	µ+	µ+	PROPN
ejpam-1678	230	3	3)φ(2)+	3)φ(2)+	PROPN
ejpam-1678	230	4	(	(	PUNCT
ejpam-1678	230	5	µ+	µ+	X
ejpam-1678	230	6	1)(1−	1)(1−	NUM
ejpam-1678	230	7	β	β	X
ejpam-1678	230	8	)	)	PUNCT
ejpam-1678	230	9	(	(	PUNCT
ejpam-1678	230	10	µ+	µ+	X
ejpam-1678	230	11	3)φ(2	3)φ(2	NOUN
ejpam-1678	230	12	)	)	PUNCT
ejpam-1678	230	13	,	,	PUNCT
ejpam-1678	230	14	(	(	PUNCT
ejpam-1678	230	15	17	17	NUM
ejpam-1678	230	16	)	)	PUNCT
ejpam-1678	230	17	where	where	SCONJ
ejpam-1678	230	18	φ(2	φ(2	NOUN
ejpam-1678	230	19	)	)	PUNCT
ejpam-1678	231	1	=	=	PUNCT
ejpam-1678	232	1	[	[	X
ejpam-1678	232	2	(	(	PUNCT
ejpam-1678	232	3	αψ2(γ	αψ2(γ	NOUN
ejpam-1678	232	4	,	,	PUNCT
ejpam-1678	232	5	λ)+1)(ψ2(γ	λ)+1)(ψ2(γ	NOUN
ejpam-1678	232	6	,	,	PUNCT
ejpam-1678	232	7	λ)−1)+1−β][ψ2(γ	λ)−1)+1−β][ψ2(γ	PROPN
ejpam-1678	232	8	,	,	PUNCT
ejpam-1678	232	9	λ)]n	λ)]n	NOUN
ejpam-1678	232	10	,	,	PUNCT
ejpam-1678	232	11	and	and	CCONJ
ejpam-1678	232	12	h(a	h(a	PROPN
ejpam-1678	232	13	,	,	PUNCT
ejpam-1678	232	14	c	c	PROPN
ejpam-1678	232	15	;	;	PUNCT
ejpam-1678	232	16	z	z	X
ejpam-1678	232	17	)	)	PUNCT
ejpam-1678	232	18	is	be	AUX
ejpam-1678	232	19	the	the	DET
ejpam-1678	232	20	incomplete	incomplete	ADJ
ejpam-1678	232	21	beta	beta	ADJ
ejpam-1678	232	22	function	function	NOUN
ejpam-1678	232	23	with	with	ADP
ejpam-1678	232	24	0	0	NUM
ejpam-1678	232	25	<	<	X
ejpam-1678	232	26	a	a	DET
ejpam-1678	232	27	¶	¶	PROPN
ejpam-1678	232	28	c	c	NOUN
ejpam-1678	232	29	,	,	PUNCT
ejpam-1678	232	30	c	c	PROPN
ejpam-1678	232	31	¾	¾	PROPN
ejpam-1678	232	32	2	2	NUM
ejpam-1678	232	33	or	or	CCONJ
ejpam-1678	232	34	a+	a+	PRON
ejpam-1678	232	35	c	c	PROPN
ejpam-1678	232	36	¾	¾	PROPN
ejpam-1678	232	37	3	3	NUM
ejpam-1678	232	38	and	and	CCONJ
ejpam-1678	232	39	0	0	NUM
ejpam-1678	232	40	<	<	X
ejpam-1678	232	41	|z|	|z|	NOUN
ejpam-1678	232	42	=	=	SYM
ejpam-1678	232	43	r	r	NOUN
ejpam-1678	232	44	<	<	X
ejpam-1678	232	45	1	1	NUM
ejpam-1678	232	46	,	,	PUNCT
ejpam-1678	232	47	s	s	VERB
ejpam-1678	232	48	>	>	X
ejpam-1678	232	49	0	0	PROPN
ejpam-1678	232	50	.	.	PUNCT
ejpam-1678	233	1	l.	l.	PROPN
ejpam-1678	233	2	xiong	xiong	PROPN
ejpam-1678	233	3	,	,	PUNCT
ejpam-1678	233	4	x.	x.	PROPN
ejpam-1678	233	5	liu	liu	PROPN
ejpam-1678	233	6	/	/	SYM
ejpam-1678	233	7	eur	eur	PROPN
ejpam-1678	233	8	.	.	PUNCT
ejpam-1678	234	1	j.	j.	PROPN
ejpam-1678	234	2	pure	pure	PROPN
ejpam-1678	234	3	appl	appl	PROPN
ejpam-1678	234	4	.	.	PROPN
ejpam-1678	234	5	math	math	PROPN
ejpam-1678	234	6	,	,	PUNCT
ejpam-1678	234	7	5	5	NUM
ejpam-1678	234	8	(	(	PUNCT
ejpam-1678	234	9	2012	2012	NUM
ejpam-1678	234	10	)	)	PUNCT
ejpam-1678	234	11	,	,	PUNCT
ejpam-1678	234	12	380	380	NUM
ejpam-1678	234	13	-	-	SYM
ejpam-1678	234	14	389	389	NUM
ejpam-1678	234	15	388	388	NUM
ejpam-1678	234	16	proof	proof	NOUN
ejpam-1678	234	17	.	.	PUNCT
ejpam-1678	235	1	since	since	SCONJ
ejpam-1678	235	2	0	0	NUM
ejpam-1678	235	3	<	<	X
ejpam-1678	235	4	a	a	DET
ejpam-1678	235	5	¶	¶	PROPN
ejpam-1678	235	6	c	c	NOUN
ejpam-1678	235	7	,	,	PUNCT
ejpam-1678	235	8	c	c	PROPN
ejpam-1678	235	9	¾	¾	PROPN
ejpam-1678	235	10	2	2	NUM
ejpam-1678	235	11	or	or	CCONJ
ejpam-1678	235	12	a+	a+	PRON
ejpam-1678	235	13	c	c	PROPN
ejpam-1678	235	14	¾	¾	PROPN
ejpam-1678	235	15	3	3	NUM
ejpam-1678	235	16	,	,	PUNCT
ejpam-1678	235	17	using	use	VERB
ejpam-1678	235	18	lemma	lemma	PROPN
ejpam-1678	235	19	2	2	NUM
ejpam-1678	235	20	,	,	PUNCT
ejpam-1678	235	21	we	we	PRON
ejpam-1678	235	22	can	can	AUX
ejpam-1678	235	23	know	know	VERB
ejpam-1678	235	24	that	that	PRON
ejpam-1678	235	25	h(a	h(a	PROPN
ejpam-1678	235	26	,	,	PUNCT
ejpam-1678	235	27	c	c	PROPN
ejpam-1678	235	28	;	;	PUNCT
ejpam-1678	235	29	z	z	X
ejpam-1678	235	30	)	)	PUNCT
ejpam-1678	235	31	=	=	SYM
ejpam-1678	236	1	z	z	NOUN
ejpam-1678	237	1	+	+	NUM
ejpam-1678	237	2	∞	∞	PROPN
ejpam-1678	237	3	∑	∑	PROPN
ejpam-1678	237	4	k=2	k=2	PROPN
ejpam-1678	237	5	(	(	PUNCT
ejpam-1678	237	6	a)k−1	a)k−1	PROPN
ejpam-1678	237	7	(	(	PUNCT
ejpam-1678	237	8	c)k−1	c)k−1	VERB
ejpam-1678	237	9	zk	zk	PROPN
ejpam-1678	237	10	∈k	∈k	ADV
ejpam-1678	237	11	.	.	PUNCT
ejpam-1678	238	1	taking	take	VERB
ejpam-1678	238	2	g(z	g(z	PROPN
ejpam-1678	238	3	)	)	PUNCT
ejpam-1678	238	4	=	=	SYM
ejpam-1678	238	5	h(a	h(a	PROPN
ejpam-1678	238	6	,	,	PUNCT
ejpam-1678	238	7	c	c	X
ejpam-1678	238	8	;	;	PUNCT
ejpam-1678	238	9	z	z	X
ejpam-1678	238	10	)	)	PUNCT
ejpam-1678	238	11	and	and	CCONJ
ejpam-1678	238	12	g(z	g(z	PROPN
ejpam-1678	238	13	)	)	PUNCT
ejpam-1678	238	14	=	=	PUNCT
ejpam-1678	239	1	z	z	PROPN
ejpam-1678	239	2	1−z	1−z	PROPN
ejpam-1678	239	3	in	in	ADP
ejpam-1678	239	4	theorem	theorem	NOUN
ejpam-1678	239	5	2	2	NUM
ejpam-1678	239	6	,	,	PUNCT
ejpam-1678	239	7	respectively	respectively	ADV
ejpam-1678	239	8	,	,	PUNCT
ejpam-1678	239	9	the	the	DET
ejpam-1678	239	10	results	result	NOUN
ejpam-1678	239	11	(	(	PUNCT
ejpam-1678	239	12	16	16	NUM
ejpam-1678	239	13	)	)	PUNCT
ejpam-1678	239	14	and	and	CCONJ
ejpam-1678	239	15	(	(	PUNCT
ejpam-1678	239	16	17	17	NUM
ejpam-1678	239	17	)	)	PUNCT
ejpam-1678	239	18	are	be	AUX
ejpam-1678	239	19	obtained	obtain	VERB
ejpam-1678	239	20	.	.	PUNCT
ejpam-1678	240	1	corollary	corollary	ADJ
ejpam-1678	240	2	6	6	NUM
ejpam-1678	240	3	.	.	PUNCT
ejpam-1678	241	1	if	if	SCONJ
ejpam-1678	241	2	the	the	DET
ejpam-1678	241	3	function	function	NOUN
ejpam-1678	241	4	l(z	l(z	NOUN
ejpam-1678	241	5	)	)	PUNCT
ejpam-1678	241	6	=	=	SYM
ejpam-1678	241	7	z	z	NOUN
ejpam-1678	242	1	+	+	NUM
ejpam-1678	242	2	∞	∞	NUM
ejpam-1678	242	3	∑	∑	PROPN
ejpam-1678	242	4	k=2	k=2	PROPN
ejpam-1678	242	5	ckzk	ckzk	PROPN
ejpam-1678	242	6	∈	∈	PROPN
ejpam-1678	242	7	t	t	PROPN
ejpam-1678	242	8	satisfy	satisfy	VERB
ejpam-1678	242	9	the	the	DET
ejpam-1678	242	10	equation	equation	NOUN
ejpam-1678	242	11	(	(	PUNCT
ejpam-1678	242	12	10	10	NUM
ejpam-1678	242	13	)	)	PUNCT
ejpam-1678	242	14	with	with	ADP
ejpam-1678	242	15	f	f	PROPN
ejpam-1678	242	16	(	(	PUNCT
ejpam-1678	242	17	z	z	NOUN
ejpam-1678	242	18	)	)	PUNCT
ejpam-1678	242	19	=	=	SYM
ejpam-1678	243	1	z	z	NOUN
ejpam-1678	244	1	+	+	NUM
ejpam-1678	244	2	∞	∞	NUM
ejpam-1678	244	3	∑	∑	PROPN
ejpam-1678	244	4	k=2	k=2	PROPN
ejpam-1678	244	5	akzk	akzk	PROPN
ejpam-1678	244	6	∈	∈	PROPN
ejpam-1678	244	7	h̄[α	h̄[α	PROPN
ejpam-1678	244	8	,	,	PUNCT
ejpam-1678	244	9	β	β	X
ejpam-1678	244	10	]	]	X
ejpam-1678	244	11	,	,	PUNCT
ejpam-1678	244	12	then	then	ADV
ejpam-1678	244	13	for	for	ADP
ejpam-1678	244	14	function	function	NOUN
ejpam-1678	244	15	g(z	g(z	PROPN
ejpam-1678	244	16	)	)	PUNCT
ejpam-1678	244	17	∈k	∈k	ADV
ejpam-1678	244	18	,	,	PUNCT
ejpam-1678	244	19	(	(	PUNCT
ejpam-1678	244	20	µ+	µ+	X
ejpam-1678	244	21	3)[2(α+	3)[2(α+	NUM
ejpam-1678	244	22	1)−	1)−	NUM
ejpam-1678	244	23	β	β	SYM
ejpam-1678	244	24	]	]	X
ejpam-1678	244	25	(	(	PUNCT
ejpam-1678	244	26	µ+	µ+	X
ejpam-1678	244	27	3)[2(α+	3)[2(α+	NUM
ejpam-1678	244	28	1)−	1)−	NUM
ejpam-1678	244	29	β	β	SYM
ejpam-1678	244	30	]	]	X
ejpam-1678	245	1	+	+	CCONJ
ejpam-1678	245	2	(	(	PUNCT
ejpam-1678	245	3	µ+	µ+	X
ejpam-1678	245	4	1)(1−	1)(1−	NUM
ejpam-1678	245	5	β	β	X
ejpam-1678	245	6	)	)	PUNCT
ejpam-1678	245	7	l	l	NOUN
ejpam-1678	245	8	∗	∗	NOUN
ejpam-1678	245	9	g(z	g(z	PROPN
ejpam-1678	245	10	)	)	PUNCT
ejpam-1678	245	11	≺	≺	NOUN
ejpam-1678	245	12	2g(z	2g(z	NUM
ejpam-1678	245	13	)	)	PUNCT
ejpam-1678	245	14	and	and	CCONJ
ejpam-1678	245	15	(	(	PUNCT
ejpam-1678	245	16	µ+	µ+	X
ejpam-1678	245	17	3)[2(α+	3)[2(α+	NUM
ejpam-1678	245	18	1)−	1)−	NUM
ejpam-1678	245	19	β	β	SYM
ejpam-1678	245	20	]	]	X
ejpam-1678	245	21	(	(	PUNCT
ejpam-1678	245	22	µ+	µ+	X
ejpam-1678	245	23	3)[2(α+	3)[2(α+	NUM
ejpam-1678	245	24	1)−	1)−	NUM
ejpam-1678	245	25	β	β	SYM
ejpam-1678	245	26	]	]	X
ejpam-1678	245	27	+	+	CCONJ
ejpam-1678	245	28	(	(	PUNCT
ejpam-1678	245	29	µ+	µ+	X
ejpam-1678	245	30	1)(1−	1)(1−	NUM
ejpam-1678	245	31	β	β	X
ejpam-1678	245	32	)	)	PUNCT
ejpam-1678	245	33	∫	∫	PROPN
ejpam-1678	245	34	2π	2π	PROPN
ejpam-1678	245	35	0	0	NUM
ejpam-1678	245	36	|l	|l	PROPN
ejpam-1678	245	37	∗	∗	NOUN
ejpam-1678	245	38	g(reiθ	g(reiθ	NOUN
ejpam-1678	245	39	)	)	PUNCT
ejpam-1678	245	40	|sdθ	|sdθ	NOUN
ejpam-1678	245	41	¶	¶	NOUN
ejpam-1678	245	42	2	2	NUM
ejpam-1678	245	43	∫	∫	PROPN
ejpam-1678	245	44	2π	2π	PROPN
ejpam-1678	245	45	0	0	NUM
ejpam-1678	245	46	|g(reiθ	|g(reiθ	NOUN
ejpam-1678	245	47	)	)	PUNCT
ejpam-1678	245	48	|sdθ	|sdθ	NOUN
ejpam-1678	245	49	.	.	PUNCT
ejpam-1678	246	1	proof	proof	NOUN
ejpam-1678	246	2	.	.	PUNCT
ejpam-1678	247	1	by	by	ADP
ejpam-1678	247	2	taking	take	VERB
ejpam-1678	247	3	n=	n=	ADJ
ejpam-1678	247	4	0	0	NUM
ejpam-1678	247	5	,	,	PUNCT
ejpam-1678	247	6	γ	γ	X
ejpam-1678	247	7	=	=	SYM
ejpam-1678	247	8	0	0	PUNCT
ejpam-1678	247	9	and	and	CCONJ
ejpam-1678	247	10	λ=	λ=	VERB
ejpam-1678	247	11	1	1	NUM
ejpam-1678	247	12	in	in	ADP
ejpam-1678	247	13	theorem	theorem	ADJ
ejpam-1678	247	14	2	2	NUM
ejpam-1678	247	15	,	,	PUNCT
ejpam-1678	247	16	corollary	corollary	ADJ
ejpam-1678	247	17	6	6	NUM
ejpam-1678	247	18	is	be	AUX
ejpam-1678	247	19	given	give	VERB
ejpam-1678	247	20	.	.	PUNCT
ejpam-1678	248	1	corollary	corollary	ADJ
ejpam-1678	248	2	7	7	NUM
ejpam-1678	248	3	.	.	PUNCT
ejpam-1678	249	1	if	if	SCONJ
ejpam-1678	249	2	the	the	DET
ejpam-1678	249	3	function	function	NOUN
ejpam-1678	249	4	l(z	l(z	NOUN
ejpam-1678	249	5	)	)	PUNCT
ejpam-1678	249	6	=	=	SYM
ejpam-1678	249	7	z	z	NOUN
ejpam-1678	250	1	+	+	NUM
ejpam-1678	250	2	∞	∞	NUM
ejpam-1678	250	3	∑	∑	PROPN
ejpam-1678	250	4	k=2	k=2	PROPN
ejpam-1678	250	5	ckzk	ckzk	PROPN
ejpam-1678	250	6	∈	∈	PROPN
ejpam-1678	250	7	t	t	PROPN
ejpam-1678	250	8	satisfy	satisfy	VERB
ejpam-1678	250	9	the	the	DET
ejpam-1678	250	10	equation	equation	NOUN
ejpam-1678	250	11	(	(	PUNCT
ejpam-1678	250	12	10	10	NUM
ejpam-1678	250	13	)	)	PUNCT
ejpam-1678	250	14	with	with	ADP
ejpam-1678	250	15	f	f	PROPN
ejpam-1678	250	16	(	(	PUNCT
ejpam-1678	250	17	z	z	NOUN
ejpam-1678	250	18	)	)	PUNCT
ejpam-1678	250	19	=	=	SYM
ejpam-1678	251	1	z	z	NOUN
ejpam-1678	252	1	+	+	NUM
ejpam-1678	252	2	∞	∞	NUM
ejpam-1678	252	3	∑	∑	PROPN
ejpam-1678	252	4	k=2	k=2	PROPN
ejpam-1678	252	5	akzk	akzk	PROPN
ejpam-1678	252	6	∈	∈	PROPN
ejpam-1678	252	7	t	t	PROPN
ejpam-1678	252	8	∗(β	∗(β	PROPN
ejpam-1678	252	9	)	)	PUNCT
ejpam-1678	252	10	,	,	PUNCT
ejpam-1678	252	11	then	then	ADV
ejpam-1678	252	12	for	for	ADP
ejpam-1678	252	13	function	function	NOUN
ejpam-1678	252	14	g(z	g(z	PROPN
ejpam-1678	252	15	)	)	PUNCT
ejpam-1678	252	16	∈k	∈k	ADV
ejpam-1678	252	17	,	,	PUNCT
ejpam-1678	252	18	(	(	PUNCT
ejpam-1678	252	19	µ+	µ+	X
ejpam-1678	252	20	3)(2−	3)(2−	NUM
ejpam-1678	252	21	β	β	NOUN
ejpam-1678	252	22	)	)	PUNCT
ejpam-1678	252	23	(	(	PUNCT
ejpam-1678	252	24	µ+	µ+	X
ejpam-1678	252	25	3)(2−	3)(2−	NUM
ejpam-1678	252	26	β	β	NOUN
ejpam-1678	252	27	)	)	PUNCT
ejpam-1678	253	1	+	+	CCONJ
ejpam-1678	253	2	(	(	PUNCT
ejpam-1678	253	3	µ+	µ+	X
ejpam-1678	253	4	1)(1−	1)(1−	NUM
ejpam-1678	253	5	β	β	X
ejpam-1678	253	6	)	)	PUNCT
ejpam-1678	253	7	l	l	NOUN
ejpam-1678	253	8	∗	∗	NOUN
ejpam-1678	253	9	g(z	g(z	PROPN
ejpam-1678	253	10	)	)	PUNCT
ejpam-1678	253	11	≺	≺	NOUN
ejpam-1678	253	12	2g(z	2g(z	NUM
ejpam-1678	253	13	)	)	PUNCT
ejpam-1678	253	14	and	and	CCONJ
ejpam-1678	253	15	(	(	PUNCT
ejpam-1678	253	16	µ+	µ+	X
ejpam-1678	253	17	3)(2−	3)(2−	NUM
ejpam-1678	253	18	β	β	NOUN
ejpam-1678	253	19	)	)	PUNCT
ejpam-1678	253	20	(	(	PUNCT
ejpam-1678	253	21	µ+	µ+	X
ejpam-1678	253	22	3)(2−	3)(2−	NUM
ejpam-1678	253	23	β	β	NOUN
ejpam-1678	253	24	)	)	PUNCT
ejpam-1678	253	25	+	+	CCONJ
ejpam-1678	253	26	(	(	PUNCT
ejpam-1678	253	27	µ+	µ+	X
ejpam-1678	253	28	1)(1−	1)(1−	NUM
ejpam-1678	253	29	β	β	X
ejpam-1678	253	30	)	)	PUNCT
ejpam-1678	253	31	∫	∫	PROPN
ejpam-1678	254	1	2π	2π	PROPN
ejpam-1678	254	2	0	0	NUM
ejpam-1678	254	3	|l	|l	PROPN
ejpam-1678	254	4	∗	∗	NOUN
ejpam-1678	254	5	g(reiθ	g(reiθ	NOUN
ejpam-1678	254	6	)	)	PUNCT
ejpam-1678	254	7	|sdθ	|sdθ	NOUN
ejpam-1678	254	8	¶	¶	NOUN
ejpam-1678	254	9	2	2	NUM
ejpam-1678	254	10	∫	∫	PROPN
ejpam-1678	254	11	2π	2π	PROPN
ejpam-1678	254	12	0	0	NUM
ejpam-1678	254	13	|g(reiθ	|g(reiθ	NOUN
ejpam-1678	254	14	)	)	PUNCT
ejpam-1678	254	15	|sdθ	|sdθ	NOUN
ejpam-1678	254	16	.	.	PUNCT
ejpam-1678	255	1	proof	proof	NOUN
ejpam-1678	255	2	.	.	PUNCT
ejpam-1678	256	1	by	by	ADP
ejpam-1678	256	2	taking	take	VERB
ejpam-1678	256	3	α	α	NOUN
ejpam-1678	256	4	=	=	NOUN
ejpam-1678	256	5	0	0	NUM
ejpam-1678	256	6	in	in	ADP
ejpam-1678	256	7	corollary	corollary	ADJ
ejpam-1678	256	8	6	6	NUM
ejpam-1678	256	9	,	,	PUNCT
ejpam-1678	256	10	corollary	corollary	ADJ
ejpam-1678	256	11	7	7	NUM
ejpam-1678	256	12	is	be	AUX
ejpam-1678	256	13	given	give	VERB
ejpam-1678	256	14	.	.	PUNCT
ejpam-1678	257	1	corollary	corollary	ADJ
ejpam-1678	257	2	8	8	NUM
ejpam-1678	257	3	.	.	PUNCT
ejpam-1678	258	1	if	if	SCONJ
ejpam-1678	258	2	the	the	DET
ejpam-1678	258	3	function	function	NOUN
ejpam-1678	258	4	l(z	l(z	NOUN
ejpam-1678	258	5	)	)	PUNCT
ejpam-1678	258	6	=	=	SYM
ejpam-1678	258	7	z	z	NOUN
ejpam-1678	259	1	+	+	NUM
ejpam-1678	259	2	∞	∞	NUM
ejpam-1678	259	3	∑	∑	PROPN
ejpam-1678	259	4	k=2	k=2	PROPN
ejpam-1678	259	5	ckzk	ckzk	PROPN
ejpam-1678	259	6	∈	∈	PROPN
ejpam-1678	259	7	t	t	PROPN
ejpam-1678	259	8	satisfy	satisfy	VERB
ejpam-1678	259	9	the	the	DET
ejpam-1678	259	10	equation	equation	NOUN
ejpam-1678	259	11	(	(	PUNCT
ejpam-1678	259	12	10	10	NUM
ejpam-1678	259	13	)	)	PUNCT
ejpam-1678	259	14	with	with	ADP
ejpam-1678	259	15	f	f	PROPN
ejpam-1678	259	16	(	(	PUNCT
ejpam-1678	259	17	z	z	NOUN
ejpam-1678	259	18	)	)	PUNCT
ejpam-1678	259	19	=	=	SYM
ejpam-1678	260	1	z	z	NOUN
ejpam-1678	261	1	+	+	NUM
ejpam-1678	261	2	∞	∞	NUM
ejpam-1678	261	3	∑	∑	PROPN
ejpam-1678	261	4	k=2	k=2	PROPN
ejpam-1678	261	5	akzk	akzk	PROPN
ejpam-1678	261	6	∈	∈	PROPN
ejpam-1678	261	7	c(β	c(β	PROPN
ejpam-1678	261	8	)	)	PUNCT
ejpam-1678	261	9	,	,	PUNCT
ejpam-1678	261	10	then	then	ADV
ejpam-1678	261	11	for	for	ADP
ejpam-1678	261	12	function	function	NOUN
ejpam-1678	261	13	g(z	g(z	PROPN
ejpam-1678	261	14	)	)	PUNCT
ejpam-1678	261	15	∈k	∈k	ADV
ejpam-1678	261	16	,	,	PUNCT
ejpam-1678	261	17	(	(	PUNCT
ejpam-1678	261	18	µ+	µ+	X
ejpam-1678	261	19	3)(4−	3)(4−	NUM
ejpam-1678	261	20	β	β	SYM
ejpam-1678	261	21	)	)	PUNCT
ejpam-1678	261	22	(	(	PUNCT
ejpam-1678	261	23	µ+	µ+	X
ejpam-1678	261	24	3)(4−	3)(4−	NUM
ejpam-1678	261	25	β	β	X
ejpam-1678	261	26	)	)	PUNCT
ejpam-1678	262	1	+	+	CCONJ
ejpam-1678	262	2	(	(	PUNCT
ejpam-1678	262	3	µ+	µ+	X
ejpam-1678	262	4	1)(1−	1)(1−	NUM
ejpam-1678	262	5	β	β	X
ejpam-1678	262	6	)	)	PUNCT
ejpam-1678	262	7	l	l	NOUN
ejpam-1678	262	8	∗	∗	NOUN
ejpam-1678	262	9	g(z	g(z	PROPN
ejpam-1678	262	10	)	)	PUNCT
ejpam-1678	262	11	≺	≺	NOUN
ejpam-1678	262	12	2g(z	2g(z	NUM
ejpam-1678	262	13	)	)	PUNCT
ejpam-1678	262	14	and	and	CCONJ
ejpam-1678	262	15	(	(	PUNCT
ejpam-1678	262	16	µ+	µ+	X
ejpam-1678	262	17	3)(4−	3)(4−	NUM
ejpam-1678	262	18	β	β	SYM
ejpam-1678	262	19	)	)	PUNCT
ejpam-1678	262	20	(	(	PUNCT
ejpam-1678	262	21	µ+	µ+	X
ejpam-1678	262	22	3)(4−	3)(4−	NUM
ejpam-1678	262	23	β	β	X
ejpam-1678	262	24	)	)	PUNCT
ejpam-1678	262	25	+	+	CCONJ
ejpam-1678	262	26	(	(	PUNCT
ejpam-1678	262	27	µ+	µ+	X
ejpam-1678	262	28	1)(1−	1)(1−	NUM
ejpam-1678	262	29	β	β	X
ejpam-1678	262	30	)	)	PUNCT
ejpam-1678	262	31	∫	∫	PROPN
ejpam-1678	263	1	2π	2π	PROPN
ejpam-1678	263	2	0	0	NUM
ejpam-1678	263	3	|l	|l	PROPN
ejpam-1678	263	4	∗	∗	NOUN
ejpam-1678	263	5	g(reiθ	g(reiθ	NOUN
ejpam-1678	263	6	)	)	PUNCT
ejpam-1678	263	7	|sdθ	|sdθ	NOUN
ejpam-1678	263	8	¶	¶	NOUN
ejpam-1678	263	9	2	2	NUM
ejpam-1678	263	10	∫	∫	PROPN
ejpam-1678	263	11	2π	2π	PROPN
ejpam-1678	263	12	0	0	NUM
ejpam-1678	263	13	|g(reiθ	|g(reiθ	NOUN
ejpam-1678	263	14	)	)	PUNCT
ejpam-1678	263	15	|sdθ	|sdθ	NOUN
ejpam-1678	263	16	.	.	PUNCT
ejpam-1678	264	1	proof	proof	NOUN
ejpam-1678	264	2	.	.	PUNCT
ejpam-1678	265	1	by	by	ADP
ejpam-1678	265	2	taking	take	VERB
ejpam-1678	265	3	α	α	NOUN
ejpam-1678	265	4	=	=	SYM
ejpam-1678	265	5	1	1	NUM
ejpam-1678	265	6	in	in	ADP
ejpam-1678	265	7	corollary	corollary	ADJ
ejpam-1678	265	8	6	6	NUM
ejpam-1678	265	9	,	,	PUNCT
ejpam-1678	265	10	corollary	corollary	ADJ
ejpam-1678	265	11	8	8	NUM
ejpam-1678	265	12	is	be	AUX
ejpam-1678	265	13	given	give	VERB
ejpam-1678	265	14	.	.	PUNCT
ejpam-1678	266	1	references	reference	NOUN
ejpam-1678	266	2	389	389	NUM
ejpam-1678	266	3	references	reference	NOUN
ejpam-1678	266	4	[	[	X
ejpam-1678	266	5	1	1	NUM
ejpam-1678	266	6	]	]	X
ejpam-1678	266	7	f.m	f.m	PROPN
ejpam-1678	266	8	.	.	PROPN
ejpam-1678	266	9	al	al	PROPN
ejpam-1678	266	10	-	-	PUNCT
ejpam-1678	266	11	oboudi	oboudi	PROPN
ejpam-1678	266	12	and	and	CCONJ
ejpam-1678	266	13	k.a	k.a	PROPN
ejpam-1678	266	14	.	.	PUNCT
ejpam-1678	267	1	al	al	PROPN
ejpam-1678	267	2	-	-	PUNCT
ejpam-1678	267	3	amoudi	amoudi	PROPN
ejpam-1678	267	4	.	.	PUNCT
ejpam-1678	268	1	subordination	subordination	NOUN
ejpam-1678	268	2	results	result	VERB
ejpam-1678	268	3	for	for	ADP
ejpam-1678	268	4	classes	class	NOUN
ejpam-1678	268	5	of	of	ADP
ejpam-1678	268	6	analytic	analytic	ADJ
ejpam-1678	268	7	functions	function	NOUN
ejpam-1678	268	8	related	relate	VERB
ejpam-1678	268	9	to	to	ADP
ejpam-1678	268	10	conic	conic	ADJ
ejpam-1678	268	11	domains	domain	NOUN
ejpam-1678	268	12	defined	define	VERB
ejpam-1678	268	13	by	by	ADP
ejpam-1678	268	14	a	a	DET
ejpam-1678	268	15	fractional	fractional	ADJ
ejpam-1678	268	16	operator	operator	NOUN
ejpam-1678	268	17	.	.	PUNCT
ejpam-1678	269	1	j.	j.	PROPN
ejpam-1678	269	2	math	math	PROPN
ejpam-1678	269	3	.	.	PUNCT
ejpam-1678	270	1	anal	anal	PROPN
ejpam-1678	270	2	.	.	PUNCT
ejpam-1678	271	1	appl	appl	PROPN
ejpam-1678	271	2	,	,	PUNCT
ejpam-1678	271	3	35(4):412	35(4):412	PROPN
ejpam-1678	271	4	-	-	SYM
ejpam-1678	271	5	420	420	NUM
ejpam-1678	271	6	,	,	PUNCT
ejpam-1678	271	7	2009	2009	NUM
ejpam-1678	271	8	.	.	PUNCT
ejpam-1678	272	1	[	[	X
ejpam-1678	272	2	2	2	X
ejpam-1678	272	3	]	]	PUNCT
ejpam-1678	272	4	o.	o.	PROPN
ejpam-1678	272	5	altintaş	altintaş	PROPN
ejpam-1678	272	6	,	,	PUNCT
ejpam-1678	272	7	ö.	ö.	PROPN
ejpam-1678	272	8	özkan	özkan	PROPN
ejpam-1678	272	9	,	,	PUNCT
ejpam-1678	272	10	and	and	CCONJ
ejpam-1678	272	11	h.m	h.m	PROPN
ejpam-1678	272	12	.	.	PROPN
ejpam-1678	272	13	srivastava	srivastava	PROPN
ejpam-1678	272	14	.	.	PUNCT
ejpam-1678	273	1	neighborhoods	neighborhood	NOUN
ejpam-1678	273	2	of	of	ADP
ejpam-1678	273	3	a	a	DET
ejpam-1678	273	4	certain	certain	ADJ
ejpam-1678	273	5	family	family	NOUN
ejpam-1678	273	6	of	of	ADP
ejpam-1678	273	7	multivalent	multivalent	NOUN
ejpam-1678	273	8	functions	function	NOUN
ejpam-1678	273	9	with	with	ADP
ejpam-1678	273	10	negative	negative	ADJ
ejpam-1678	273	11	coefficients.computers	coefficients.computer	NOUN
ejpam-1678	273	12	math.applic	math.applic	NOUN
ejpam-1678	273	13	,	,	PUNCT
ejpam-1678	273	14	47:1667	47:1667	NOUN
ejpam-1678	273	15	-	-	SYM
ejpam-1678	273	16	1672	1672	NUM
ejpam-1678	273	17	,	,	PUNCT
ejpam-1678	273	18	2004	2004	NUM
ejpam-1678	273	19	.	.	PUNCT
ejpam-1678	274	1	[	[	X
ejpam-1678	274	2	3	3	NUM
ejpam-1678	274	3	]	]	X
ejpam-1678	274	4	a.y	a.y	PROPN
ejpam-1678	274	5	.	.	PROPN
ejpam-1678	274	6	lashin	lashin	PROPN
ejpam-1678	274	7	.	.	PUNCT
ejpam-1678	275	1	on	on	ADP
ejpam-1678	275	2	a	a	DET
ejpam-1678	275	3	certain	certain	ADJ
ejpam-1678	275	4	subclass	subclass	NOUN
ejpam-1678	275	5	of	of	ADP
ejpam-1678	275	6	starlike	starlike	NOUN
ejpam-1678	275	7	functions	function	NOUN
ejpam-1678	275	8	with	with	ADP
ejpam-1678	275	9	negative	negative	ADJ
ejpam-1678	275	10	coefficients.j	coefficients.j	PROPN
ejpam-1678	275	11	.	.	PUNCT
ejpam-1678	276	1	ineq	ineq	PROPN
ejpam-1678	276	2	.	.	PUNCT
ejpam-1678	277	1	pure	pure	ADJ
ejpam-1678	277	2	appl	appl	PROPN
ejpam-1678	277	3	.	.	PUNCT
ejpam-1678	277	4	math	math	PROPN
ejpam-1678	277	5	.	.	PUNCT
ejpam-1678	277	6	,	,	PUNCT
ejpam-1678	277	7	10(2):article	10(2):article	PROPN
ejpam-1678	277	8	40	40	NUM
ejpam-1678	277	9	,	,	PUNCT
ejpam-1678	277	10	2009	2009	NUM
ejpam-1678	277	11	.	.	PUNCT
ejpam-1678	278	1	[	[	X
ejpam-1678	278	2	4	4	X
ejpam-1678	278	3	]	]	X
ejpam-1678	278	4	j.e	j.e	PROPN
ejpam-1678	278	5	.	.	PROPN
ejpam-1678	278	6	littlewood	littlewood	PROPN
ejpam-1678	278	7	.	.	PUNCT
ejpam-1678	279	1	on	on	ADP
ejpam-1678	279	2	inequalities	inequality	NOUN
ejpam-1678	279	3	in	in	ADP
ejpam-1678	279	4	the	the	DET
ejpam-1678	279	5	theory	theory	NOUN
ejpam-1678	279	6	of	of	ADP
ejpam-1678	279	7	functions	function	NOUN
ejpam-1678	279	8	.	.	PUNCT
ejpam-1678	280	1	proc	proc	NOUN
ejpam-1678	280	2	.	.	PUNCT
ejpam-1678	281	1	london	london	PROPN
ejpam-1678	281	2	math	math	PROPN
ejpam-1678	281	3	.	.	PUNCT
ejpam-1678	282	1	soc	soc	PROPN
ejpam-1678	282	2	,	,	PUNCT
ejpam-1678	282	3	23:481	23:481	NUM
ejpam-1678	282	4	-	-	SYM
ejpam-1678	282	5	519	519	NUM
ejpam-1678	282	6	,	,	PUNCT
ejpam-1678	282	7	1925	1925	NUM
ejpam-1678	282	8	.	.	PUNCT
ejpam-1678	283	1	[	[	X
ejpam-1678	283	2	5	5	X
ejpam-1678	283	3	]	]	PUNCT
ejpam-1678	283	4	m.	m.	NOUN
ejpam-1678	283	5	marouf	marouf	NOUN
ejpam-1678	283	6	.	.	PUNCT
ejpam-1678	284	1	on	on	ADP
ejpam-1678	284	2	a	a	DET
ejpam-1678	284	3	subclass	subclass	NOUN
ejpam-1678	284	4	of	of	ADP
ejpam-1678	284	5	analytic	analytic	ADJ
ejpam-1678	284	6	functions	function	NOUN
ejpam-1678	284	7	with	with	ADP
ejpam-1678	284	8	negative	negative	ADJ
ejpam-1678	284	9	coefficients	coefficient	NOUN
ejpam-1678	284	10	defined	define	VERB
ejpam-1678	284	11	by	by	ADP
ejpam-1678	284	12	a	a	DET
ejpam-1678	284	13	fractional	fractional	ADJ
ejpam-1678	284	14	differential	differential	NOUN
ejpam-1678	284	15	operator	operator	NOUN
ejpam-1678	284	16	.	.	PUNCT
ejpam-1678	285	1	int.j.open	int.j.open	PROPN
ejpam-1678	285	2	problems.complex	problems.complex	PROPN
ejpam-1678	285	3	analysis	analysis	NOUN
ejpam-1678	285	4	,	,	PUNCT
ejpam-1678	285	5	2(2):140	2(2):140	NUM
ejpam-1678	285	6	-	-	SYM
ejpam-1678	285	7	153	153	NUM
ejpam-1678	285	8	,	,	PUNCT
ejpam-1678	285	9	2010	2010	NUM
ejpam-1678	285	10	.	.	PUNCT
ejpam-1678	286	1	[	[	X
ejpam-1678	286	2	6	6	NUM
ejpam-1678	286	3	]	]	PUNCT
ejpam-1678	286	4	s.	s.	PROPN
ejpam-1678	286	5	owa	owa	PROPN
ejpam-1678	286	6	and	and	CCONJ
ejpam-1678	286	7	h.m	h.m	PROPN
ejpam-1678	286	8	.	.	PROPN
ejpam-1678	286	9	srivastava	srivastava	PROPN
ejpam-1678	286	10	.	.	PUNCT
ejpam-1678	287	1	univalent	univalent	ADJ
ejpam-1678	287	2	and	and	CCONJ
ejpam-1678	287	3	starlike	starlike	ADJ
ejpam-1678	287	4	generalized	generalize	VERB
ejpam-1678	287	5	hypergeometric	hypergeometric	ADJ
ejpam-1678	287	6	functions.canad	functions.canad	NOUN
ejpam-1678	287	7	.	.	PUNCT
ejpam-1678	288	1	j.	j.	PROPN
ejpam-1678	288	2	math	math	PROPN
ejpam-1678	288	3	,	,	PUNCT
ejpam-1678	288	4	39(5):1057	39(5):1057	NUM
ejpam-1678	288	5	-	-	SYM
ejpam-1678	288	6	1077	1077	NUM
ejpam-1678	288	7	,	,	PUNCT
ejpam-1678	288	8	1987	1987	NUM
ejpam-1678	288	9	.	.	PUNCT
ejpam-1678	289	1	[	[	X
ejpam-1678	289	2	7	7	X
ejpam-1678	289	3	]	]	X
ejpam-1678	289	4	s.	s.	PROPN
ejpam-1678	289	5	ruscheweyh	ruscheweyh	PROPN
ejpam-1678	289	6	.	.	PUNCT
ejpam-1678	290	1	convolutions	convolution	NOUN
ejpam-1678	290	2	in	in	ADP
ejpam-1678	290	3	geometric	geometric	ADJ
ejpam-1678	290	4	function	function	NOUN
ejpam-1678	290	5	theory	theory	NOUN
ejpam-1678	290	6	.	.	PUNCT
ejpam-1678	291	1	les	les	NOUN
ejpam-1678	291	2	presses	press	NOUN
ejpam-1678	291	3	de	de	X
ejpam-1678	291	4	iąőuniv.de	iąőuniv.de	PROPN
ejpam-1678	291	5	montreal	montreal	PROPN
ejpam-1678	291	6	,	,	PUNCT
ejpam-1678	291	7	1982	1982	NUM
ejpam-1678	291	8	.	.	PUNCT
ejpam-1678	292	1	[	[	X
ejpam-1678	292	2	8	8	NUM
ejpam-1678	292	3	]	]	X
ejpam-1678	292	4	h.	h.	PROPN
ejpam-1678	292	5	silverman	silverman	PROPN
ejpam-1678	292	6	.	.	PUNCT
ejpam-1678	293	1	univalent	univalent	ADJ
ejpam-1678	293	2	functions	function	NOUN
ejpam-1678	293	3	with	with	ADP
ejpam-1678	293	4	negative	negative	ADJ
ejpam-1678	293	5	coefficients	coefficient	NOUN
ejpam-1678	293	6	.	.	PUNCT
ejpam-1678	294	1	proc	proc	NOUN
ejpam-1678	294	2	.	.	PUNCT
ejpam-1678	295	1	amer	amer	PROPN
ejpam-1678	295	2	.	.	PUNCT
ejpam-1678	295	3	math	math	PROPN
ejpam-1678	295	4	.	.	PUNCT
ejpam-1678	296	1	soc	soc	PROPN
ejpam-1678	296	2	,	,	PUNCT
ejpam-1678	296	3	51:109	51:109	NUM
ejpam-1678	296	4	-	-	SYM
ejpam-1678	296	5	116	116	NUM
ejpam-1678	296	6	,	,	PUNCT
ejpam-1678	296	7	1975	1975	NUM
ejpam-1678	296	8	.	.	PUNCT
ejpam-1678	297	1	[	[	X
ejpam-1678	297	2	9	9	NUM
ejpam-1678	297	3	]	]	SYM
ejpam-1678	297	4	h.s	h.s	PROPN
ejpam-1678	297	5	.	.	PROPN
ejpam-1678	297	6	wilf	wilf	PROPN
ejpam-1678	297	7	.	.	PUNCT
ejpam-1678	298	1	subordinating	subordinate	VERB
ejpam-1678	298	2	factor	factor	NOUN
ejpam-1678	298	3	sequences	sequence	NOUN
ejpam-1678	298	4	for	for	ADP
ejpam-1678	298	5	convex	convex	NOUN
ejpam-1678	298	6	maps	map	NOUN
ejpam-1678	298	7	of	of	ADP
ejpam-1678	298	8	the	the	DET
ejpam-1678	298	9	unit	unit	NOUN
ejpam-1678	298	10	circle	circle	NOUN
ejpam-1678	298	11	.	.	PUNCT
ejpam-1678	299	1	proc	proc	PROPN
ejpam-1678	299	2	.	.	PUNCT
ejpam-1678	300	1	am	be	AUX
ejpam-1678	300	2	.	.	PUNCT
ejpam-1678	301	1	math	math	NOUN
ejpam-1678	301	2	.	.	PUNCT
ejpam-1678	302	1	soc	soc	PROPN
ejpam-1678	302	2	,	,	PUNCT
ejpam-1678	302	3	12:689	12:689	NUM
ejpam-1678	302	4	-	-	SYM
ejpam-1678	302	5	693,1961	693,1961	NUM
ejpam-1678	302	6	.	.	PUNCT