id	sid	tid	token	lemma	pos
ejpam-901	1	1	16_914_cho.dvi	16_914_cho.dvi	PROPN
ejpam-901	1	2	european	european	PROPN
ejpam-901	1	3	journal	journal	PROPN
ejpam-901	1	4	of	of	ADP
ejpam-901	1	5	pure	pure	ADJ
ejpam-901	1	6	and	and	CCONJ
ejpam-901	1	7	applied	apply	VERB
ejpam-901	1	8	mathematics	mathematic	NOUN
ejpam-901	1	9	vol	vol	NOUN
ejpam-901	1	10	.	.	PUNCT
ejpam-901	2	1	3	3	NUM
ejpam-901	2	2	,	,	PUNCT
ejpam-901	2	3	no	no	INTJ
ejpam-901	2	4	.	.	NOUN
ejpam-901	2	5	6	6	NUM
ejpam-901	2	6	,	,	PUNCT
ejpam-901	2	7	2010	2010	NUM
ejpam-901	2	8	,	,	PUNCT
ejpam-901	2	9	1124	1124	NUM
ejpam-901	2	10	-	-	SYM
ejpam-901	2	11	1136	1136	NUM
ejpam-901	2	12	issn	issn	PROPN
ejpam-901	2	13	1307	1307	NUM
ejpam-901	2	14	-	-	SYM
ejpam-901	2	15	5543	5543	NUM
ejpam-901	2	16	–	–	PUNCT
ejpam-901	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-901	2	18	special	special	ADJ
ejpam-901	2	19	issue	issue	NOUN
ejpam-901	2	20	on	on	ADP
ejpam-901	2	21	complex	complex	ADJ
ejpam-901	2	22	analysis	analysis	NOUN
ejpam-901	2	23	:	:	PUNCT
ejpam-901	2	24	theory	theory	NOUN
ejpam-901	2	25	and	and	CCONJ
ejpam-901	2	26	applications	application	NOUN
ejpam-901	2	27	dedicated	dedicate	VERB
ejpam-901	2	28	to	to	ADP
ejpam-901	2	29	professor	professor	PROPN
ejpam-901	2	30	hari	hari	PROPN
ejpam-901	2	31	m.	m.	PROPN
ejpam-901	2	32	srivastava	srivastava	PROPN
ejpam-901	2	33	,	,	PUNCT
ejpam-901	2	34	on	on	ADP
ejpam-901	2	35	the	the	DET
ejpam-901	2	36	occasion	occasion	NOUN
ejpam-901	2	37	of	of	ADP
ejpam-901	2	38	his	his	PRON
ejpam-901	2	39	70th	70th	ADJ
ejpam-901	2	40	birthday	birthday	NOUN
ejpam-901	2	41	inclusion	inclusion	NOUN
ejpam-901	2	42	properties	property	NOUN
ejpam-901	2	43	for	for	ADP
ejpam-901	2	44	certain	certain	ADJ
ejpam-901	2	45	subclasses	subclass	NOUN
ejpam-901	2	46	of	of	ADP
ejpam-901	2	47	analytic	analytic	ADJ
ejpam-901	2	48	functions	function	NOUN
ejpam-901	2	49	defined	define	VERB
ejpam-901	2	50	by	by	ADP
ejpam-901	2	51	a	a	DET
ejpam-901	2	52	multiplier	multipli	ADJ
ejpam-901	2	53	transformation	transformation	NOUN
ejpam-901	3	1	oh	oh	INTJ
ejpam-901	3	2	sang	sing	VERB
ejpam-901	3	3	kwon1	kwon1	PROPN
ejpam-901	3	4	,	,	PUNCT
ejpam-901	3	5	nak	nak	PROPN
ejpam-901	3	6	eun	eun	PROPN
ejpam-901	3	7	cho2,∗	cho2,∗	PROPN
ejpam-901	3	8	1	1	NUM
ejpam-901	3	9	department	department	NOUN
ejpam-901	3	10	of	of	ADP
ejpam-901	3	11	mathematics	mathematic	NOUN
ejpam-901	3	12	,	,	PUNCT
ejpam-901	3	13	kyungsung	kyungsung	PROPN
ejpam-901	3	14	university	university	PROPN
ejpam-901	3	15	,	,	PUNCT
ejpam-901	3	16	busan	busan	PROPN
ejpam-901	3	17	608	608	NUM
ejpam-901	3	18	-	-	PUNCT
ejpam-901	3	19	736	736	NUM
ejpam-901	3	20	,	,	PUNCT
ejpam-901	3	21	korea	korea	PROPN
ejpam-901	3	22	2	2	NUM
ejpam-901	3	23	department	department	NOUN
ejpam-901	3	24	of	of	ADP
ejpam-901	3	25	applied	apply	VERB
ejpam-901	3	26	mathematics	mathematic	NOUN
ejpam-901	3	27	,	,	PUNCT
ejpam-901	3	28	pukyong	pukyong	PROPN
ejpam-901	3	29	national	national	PROPN
ejpam-901	3	30	university	university	PROPN
ejpam-901	3	31	,	,	PUNCT
ejpam-901	3	32	busan	busan	PROPN
ejpam-901	3	33	608	608	NUM
ejpam-901	3	34	-	-	SYM
ejpam-901	3	35	737	737	NUM
ejpam-901	3	36	,	,	PUNCT
ejpam-901	3	37	korea	korea	PROPN
ejpam-901	3	38	abstract	abstract	NOUN
ejpam-901	3	39	.	.	PUNCT
ejpam-901	4	1	the	the	DET
ejpam-901	4	2	purpose	purpose	NOUN
ejpam-901	4	3	of	of	ADP
ejpam-901	4	4	the	the	DET
ejpam-901	4	5	present	present	ADJ
ejpam-901	4	6	paper	paper	NOUN
ejpam-901	4	7	is	be	AUX
ejpam-901	4	8	to	to	PART
ejpam-901	4	9	investigate	investigate	VERB
ejpam-901	4	10	some	some	DET
ejpam-901	4	11	inclusion	inclusion	NOUN
ejpam-901	4	12	properties	property	NOUN
ejpam-901	4	13	of	of	ADP
ejpam-901	4	14	certain	certain	ADJ
ejpam-901	4	15	subclasses	subclass	NOUN
ejpam-901	4	16	of	of	ADP
ejpam-901	4	17	analytic	analytic	ADJ
ejpam-901	4	18	functions	function	NOUN
ejpam-901	4	19	associated	associate	VERB
ejpam-901	4	20	with	with	ADP
ejpam-901	4	21	a	a	DET
ejpam-901	4	22	family	family	NOUN
ejpam-901	4	23	of	of	ADP
ejpam-901	4	24	multiplier	multipli	ADJ
ejpam-901	4	25	transformations	transformation	NOUN
ejpam-901	4	26	,	,	PUNCT
ejpam-901	4	27	which	which	PRON
ejpam-901	4	28	are	be	AUX
ejpam-901	4	29	defined	define	VERB
ejpam-901	4	30	by	by	ADP
ejpam-901	4	31	means	mean	NOUN
ejpam-901	4	32	of	of	ADP
ejpam-901	4	33	the	the	DET
ejpam-901	4	34	hadamard	hadamard	ADJ
ejpam-901	4	35	product	product	NOUN
ejpam-901	4	36	(	(	PUNCT
ejpam-901	4	37	or	or	CCONJ
ejpam-901	4	38	convolution	convolution	NOUN
ejpam-901	4	39	)	)	PUNCT
ejpam-901	4	40	.	.	PUNCT
ejpam-901	5	1	2000	2000	NUM
ejpam-901	5	2	mathematics	mathematic	NOUN
ejpam-901	5	3	subject	subject	NOUN
ejpam-901	5	4	classifications	classification	NOUN
ejpam-901	5	5	:	:	PUNCT
ejpam-901	5	6	30c45	30c45	NUM
ejpam-901	5	7	key	key	ADJ
ejpam-901	5	8	words	word	NOUN
ejpam-901	5	9	and	and	CCONJ
ejpam-901	5	10	phrases	phrase	NOUN
ejpam-901	5	11	:	:	PUNCT
ejpam-901	5	12	analytic	analytic	ADJ
ejpam-901	5	13	function	function	NOUN
ejpam-901	5	14	,	,	PUNCT
ejpam-901	5	15	starlike	starlike	NOUN
ejpam-901	5	16	function	function	NOUN
ejpam-901	5	17	,	,	PUNCT
ejpam-901	5	18	convex	convex	NOUN
ejpam-901	5	19	function	function	NOUN
ejpam-901	5	20	,	,	PUNCT
ejpam-901	5	21	hadamard	hadamard	ADJ
ejpam-901	5	22	product	product	NOUN
ejpam-901	5	23	,	,	PUNCT
ejpam-901	5	24	choi	choi	NOUN
ejpam-901	5	25	-	-	PUNCT
ejpam-901	5	26	saigo	saigo	NOUN
ejpam-901	5	27	-	-	PUNCT
ejpam-901	5	28	srivastava	srivastava	PROPN
ejpam-901	5	29	operator	operator	NOUN
ejpam-901	5	30	,	,	PUNCT
ejpam-901	5	31	multiplier	multipli	ADJ
ejpam-901	5	32	transformation	transformation	NOUN
ejpam-901	5	33	,	,	PUNCT
ejpam-901	5	34	inclusion	inclusion	NOUN
ejpam-901	5	35	relation	relation	NOUN
ejpam-901	5	36	,	,	PUNCT
ejpam-901	5	37	convolution	convolution	NOUN
ejpam-901	5	38	property	property	NOUN
ejpam-901	5	39	,	,	PUNCT
ejpam-901	5	40	integral	integral	ADJ
ejpam-901	5	41	preserving	preserving	ADJ
ejpam-901	5	42	property	property	NOUN
ejpam-901	5	43	1	1	NUM
ejpam-901	5	44	.	.	PUNCT
ejpam-901	6	1	introduction	introduction	NOUN
ejpam-901	6	2	leta	leta	PROPN
ejpam-901	6	3	denote	denote	VERB
ejpam-901	6	4	the	the	DET
ejpam-901	6	5	class	class	NOUN
ejpam-901	6	6	of	of	ADP
ejpam-901	6	7	functions	function	NOUN
ejpam-901	6	8	of	of	ADP
ejpam-901	6	9	the	the	DET
ejpam-901	6	10	form	form	NOUN
ejpam-901	6	11	f	f	X
ejpam-901	6	12	(	(	PUNCT
ejpam-901	6	13	z	z	NOUN
ejpam-901	6	14	)	)	PUNCT
ejpam-901	6	15	=	=	SYM
ejpam-901	7	1	z	z	NOUN
ejpam-901	8	1	+	+	NOUN
ejpam-901	8	2	∞∑	∞∑	DET
ejpam-901	8	3	k=2	k=2	PROPN
ejpam-901	8	4	akzk	akzk	NOUN
ejpam-901	8	5	(	(	PUNCT
ejpam-901	8	6	1	1	X
ejpam-901	8	7	)	)	PUNCT
ejpam-901	8	8	which	which	PRON
ejpam-901	8	9	are	be	AUX
ejpam-901	8	10	analytic	analytic	ADJ
ejpam-901	8	11	in	in	ADP
ejpam-901	8	12	the	the	DET
ejpam-901	8	13	open	open	ADJ
ejpam-901	8	14	unit	unit	NOUN
ejpam-901	8	15	disk	disk	NOUN
ejpam-901	8	16	u	u	NOUN
ejpam-901	8	17	=	=	PUNCT
ejpam-901	8	18	{	{	PUNCT
ejpam-901	8	19	z	z	PROPN
ejpam-901	8	20	∈	∈	PROPN
ejpam-901	8	21	c	c	NOUN
ejpam-901	8	22	:	:	PUNCT
ejpam-901	8	23	|z|	|z|	NOUN
ejpam-901	8	24	<	<	X
ejpam-901	8	25	1	1	NUM
ejpam-901	8	26	}	}	PUNCT
ejpam-901	8	27	.	.	PUNCT
ejpam-901	9	1	let	let	VERB
ejpam-901	9	2	s	s	PRON
ejpam-901	9	3	∗(α	∗(α	PROPN
ejpam-901	9	4	)	)	PUNCT
ejpam-901	9	5	and	and	CCONJ
ejpam-901	9	6	k	k	PROPN
ejpam-901	9	7	(	(	PUNCT
ejpam-901	9	8	α	α	NOUN
ejpam-901	9	9	)	)	PUNCT
ejpam-901	9	10	denote	denote	VERB
ejpam-901	9	11	the	the	DET
ejpam-901	9	12	subclasses	subclass	NOUN
ejpam-901	9	13	of	of	ADP
ejpam-901	9	14	a	a	DET
ejpam-901	9	15	consisting	consisting	NOUN
ejpam-901	9	16	of	of	ADP
ejpam-901	9	17	starlike	starlike	NOUN
ejpam-901	9	18	and	and	CCONJ
ejpam-901	9	19	convex	convex	NOUN
ejpam-901	9	20	functions	function	NOUN
ejpam-901	9	21	of	of	ADP
ejpam-901	9	22	order	order	NOUN
ejpam-901	9	23	α	α	PROPN
ejpam-901	9	24	(	(	PUNCT
ejpam-901	9	25	0	0	NUM
ejpam-901	9	26	≤	≤	NUM
ejpam-901	9	27	α	α	NOUN
ejpam-901	9	28	<	<	X
ejpam-901	9	29	1	1	NUM
ejpam-901	9	30	)	)	PUNCT
ejpam-901	9	31	and	and	CCONJ
ejpam-901	9	32	let	let	VERB
ejpam-901	9	33	s	s	PRON
ejpam-901	9	34	∗(0	∗(0	PART
ejpam-901	9	35	)	)	PUNCT
ejpam-901	10	1	=	=	SYM
ejpam-901	10	2	s	s	NOUN
ejpam-901	10	3	∗	∗	NOUN
ejpam-901	10	4	and	and	CCONJ
ejpam-901	10	5	k	k	X
ejpam-901	10	6	(	(	PUNCT
ejpam-901	10	7	0	0	NUM
ejpam-901	10	8	)	)	PUNCT
ejpam-901	10	9	=	=	SYM
ejpam-901	11	1	k	k	PROPN
ejpam-901	11	2	.	.	PUNCT
ejpam-901	12	1	if	if	SCONJ
ejpam-901	12	2	f	f	PROPN
ejpam-901	12	3	and	and	CCONJ
ejpam-901	12	4	g	g	PROPN
ejpam-901	12	5	are	be	AUX
ejpam-901	12	6	analytic	analytic	ADJ
ejpam-901	12	7	in	in	ADP
ejpam-901	12	8	u	u	NOUN
ejpam-901	12	9	,	,	PUNCT
ejpam-901	12	10	we	we	PRON
ejpam-901	12	11	say	say	VERB
ejpam-901	12	12	that	that	SCONJ
ejpam-901	12	13	f	f	PROPN
ejpam-901	12	14	is	be	AUX
ejpam-901	12	15	subordinate	subordinate	ADJ
ejpam-901	12	16	to	to	ADP
ejpam-901	12	17	g	g	PROPN
ejpam-901	12	18	in	in	ADP
ejpam-901	12	19	u	u	NOUN
ejpam-901	12	20	,	,	PUNCT
ejpam-901	12	21	written	write	VERB
ejpam-901	12	22	as	as	ADP
ejpam-901	12	23	f	f	PROPN
ejpam-901	12	24	≺	≺	NOUN
ejpam-901	12	25	g	g	PROPN
ejpam-901	12	26	or	or	CCONJ
ejpam-901	12	27	f	f	PROPN
ejpam-901	12	28	(	(	PUNCT
ejpam-901	12	29	z	z	NOUN
ejpam-901	12	30	)	)	PUNCT
ejpam-901	12	31	≺	≺	NOUN
ejpam-901	12	32	g(z	g(z	PROPN
ejpam-901	12	33	)	)	PUNCT
ejpam-901	12	34	,	,	PUNCT
ejpam-901	12	35	if	if	SCONJ
ejpam-901	12	36	there	there	PRON
ejpam-901	12	37	exists	exist	VERB
ejpam-901	12	38	a	a	DET
ejpam-901	12	39	schwarz	schwarz	PROPN
ejpam-901	12	40	function	function	NOUN
ejpam-901	12	41	w	w	ADP
ejpam-901	12	42	such	such	ADJ
ejpam-901	12	43	that	that	SCONJ
ejpam-901	12	44	f	f	PROPN
ejpam-901	12	45	(	(	PUNCT
ejpam-901	12	46	z	z	NOUN
ejpam-901	12	47	)	)	PUNCT
ejpam-901	12	48	=	=	PUNCT
ejpam-901	12	49	g(w(z	g(w(z	PROPN
ejpam-901	12	50	)	)	PUNCT
ejpam-901	12	51	)	)	PUNCT
ejpam-901	12	52	for	for	ADP
ejpam-901	12	53	z	z	PROPN
ejpam-901	12	54	∈	∈	PROPN
ejpam-901	12	55	u.	u.	PROPN
ejpam-901	12	56	∗corresponding	∗corresponde	VERB
ejpam-901	12	57	author	author	NOUN
ejpam-901	12	58	.	.	PUNCT
ejpam-901	13	1	email	email	NOUN
ejpam-901	13	2	addresses	address	NOUN
ejpam-901	13	3	:	:	PUNCT
ejpam-901	13	4	oskwon	oskwon	VERB
ejpam-901	13	5	�	�	PROPN
ejpam-901	13	6	ks.a	ks.a	NOUN
ejpam-901	13	7	.kr	.kr	PUNCT
ejpam-901	13	8	(	(	PUNCT
ejpam-901	13	9	o.	o.	PROPN
ejpam-901	13	10	kwon	kwon	PROPN
ejpam-901	13	11	)	)	PUNCT
ejpam-901	13	12	,	,	PUNCT
ejpam-901	13	13	ne	ne	PROPN
ejpam-901	13	14	ho	ho	PROPN
ejpam-901	13	15	�	�	PROPN
ejpam-901	13	16	pknu.a	pknu.a	PROPN
ejpam-901	13	17	.kr	.kr	PUNCT
ejpam-901	13	18	(	(	PUNCT
ejpam-901	13	19	n.	n.	PROPN
ejpam-901	13	20	cho	cho	PROPN
ejpam-901	13	21	)	)	PUNCT
ejpam-901	13	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-901	14	1	1124	1124	NUM
ejpam-901	15	1	c	c	X
ejpam-901	15	2	©	©	PROPN
ejpam-901	15	3	2010	2010	NUM
ejpam-901	15	4	ejpam	ejpam	NOUN
ejpam-901	15	5	all	all	DET
ejpam-901	15	6	rights	right	NOUN
ejpam-901	15	7	reserved	reserve	VERB
ejpam-901	15	8	.	.	PUNCT
ejpam-901	16	1	o.	o.	PROPN
ejpam-901	16	2	kwon	kwon	PROPN
ejpam-901	16	3	,	,	PUNCT
ejpam-901	16	4	n.	n.	PROPN
ejpam-901	16	5	cho	cho	PROPN
ejpam-901	16	6	/	/	SYM
ejpam-901	16	7	eur	eur	PROPN
ejpam-901	16	8	.	.	PUNCT
ejpam-901	17	1	j.	j.	PROPN
ejpam-901	17	2	pure	pure	PROPN
ejpam-901	17	3	appl	appl	PROPN
ejpam-901	17	4	.	.	PROPN
ejpam-901	17	5	math	math	PROPN
ejpam-901	17	6	,	,	PUNCT
ejpam-901	17	7	3	3	NUM
ejpam-901	17	8	(	(	PUNCT
ejpam-901	17	9	2010	2010	NUM
ejpam-901	17	10	)	)	PUNCT
ejpam-901	17	11	,	,	PUNCT
ejpam-901	17	12	1124	1124	NUM
ejpam-901	17	13	-	-	SYM
ejpam-901	17	14	1136	1136	NUM
ejpam-901	17	15	1125	1125	NUM
ejpam-901	17	16	a	a	DET
ejpam-901	17	17	function	function	NOUN
ejpam-901	17	18	f	f	PROPN
ejpam-901	17	19	∈a	∈a	PROPN
ejpam-901	17	20	is	be	AUX
ejpam-901	17	21	said	say	VERB
ejpam-901	17	22	to	to	PART
ejpam-901	17	23	be	be	AUX
ejpam-901	17	24	prestarlike	prestarlike	ADP
ejpam-901	17	25	of	of	ADP
ejpam-901	17	26	order	order	NOUN
ejpam-901	17	27	α	α	NOUN
ejpam-901	17	28	in	in	ADP
ejpam-901	17	29	u	u	PRON
ejpam-901	17	30	if	if	SCONJ
ejpam-901	17	31	z	z	PROPN
ejpam-901	17	32	(	(	PUNCT
ejpam-901	17	33	1−	1−	NUM
ejpam-901	17	34	z)2(1−α	z)2(1−α	NUM
ejpam-901	17	35	)	)	PUNCT
ejpam-901	17	36	∗	∗	PROPN
ejpam-901	17	37	f	f	PROPN
ejpam-901	17	38	(	(	PUNCT
ejpam-901	17	39	z	z	NOUN
ejpam-901	17	40	)	)	PUNCT
ejpam-901	17	41	∈	∈	PROPN
ejpam-901	17	42	s	s	PART
ejpam-901	17	43	∗(α	∗(α	PROPN
ejpam-901	17	44	)	)	PUNCT
ejpam-901	17	45	(	(	PUNCT
ejpam-901	17	46	0≤	0≤	NUM
ejpam-901	17	47	α	α	X
ejpam-901	17	48	<	<	X
ejpam-901	17	49	1	1	NUM
ejpam-901	17	50	)	)	PUNCT
ejpam-901	17	51	,	,	PUNCT
ejpam-901	17	52	where	where	SCONJ
ejpam-901	17	53	the	the	DET
ejpam-901	17	54	symbol	symbol	NOUN
ejpam-901	17	55	(	(	PUNCT
ejpam-901	17	56	∗	∗	NOUN
ejpam-901	17	57	)	)	PUNCT
ejpam-901	17	58	means	mean	VERB
ejpam-901	17	59	the	the	DET
ejpam-901	17	60	familiar	familiar	ADJ
ejpam-901	17	61	hadamard	hadamard	ADJ
ejpam-901	17	62	product	product	NOUN
ejpam-901	17	63	(	(	PUNCT
ejpam-901	17	64	or	or	CCONJ
ejpam-901	17	65	convolution	convolution	NOUN
ejpam-901	17	66	)	)	PUNCT
ejpam-901	17	67	of	of	ADP
ejpam-901	17	68	two	two	NUM
ejpam-901	17	69	analytic	analytic	ADJ
ejpam-901	17	70	functions	function	NOUN
ejpam-901	17	71	in	in	ADP
ejpam-901	17	72	u.	u.	NOUN
ejpam-901	17	73	we	we	PRON
ejpam-901	17	74	denote	denote	VERB
ejpam-901	17	75	this	this	DET
ejpam-901	17	76	class	class	NOUN
ejpam-901	17	77	by	by	ADP
ejpam-901	17	78	r(α	r(α	PROPN
ejpam-901	17	79	)	)	PUNCT
ejpam-901	17	80	(	(	PUNCT
ejpam-901	17	81	see	see	VERB
ejpam-901	17	82	,	,	PUNCT
ejpam-901	17	83	for	for	ADP
ejpam-901	17	84	details	detail	NOUN
ejpam-901	17	85	,	,	PUNCT
ejpam-901	17	86	[	[	X
ejpam-901	17	87	9	9	NUM
ejpam-901	17	88	]	]	PUNCT
ejpam-901	17	89	)	)	PUNCT
ejpam-901	17	90	.	.	PUNCT
ejpam-901	18	1	we	we	PRON
ejpam-901	18	2	note	note	VERB
ejpam-901	18	3	that	that	SCONJ
ejpam-901	18	4	a	a	DET
ejpam-901	18	5	function	function	NOUN
ejpam-901	18	6	f	f	PROPN
ejpam-901	18	7	∈a	∈a	PROPN
ejpam-901	18	8	is	be	AUX
ejpam-901	18	9	in	in	ADP
ejpam-901	18	10	the	the	DET
ejpam-901	18	11	class	class	NOUN
ejpam-901	18	12	r(0	r(0	PROPN
ejpam-901	18	13	)	)	PUNCT
ejpam-901	18	14	if	if	SCONJ
ejpam-901	18	15	and	and	CCONJ
ejpam-901	18	16	only	only	ADV
ejpam-901	18	17	if	if	SCONJ
ejpam-901	18	18	f	f	PROPN
ejpam-901	18	19	is	be	AUX
ejpam-901	18	20	convex	convex	ADJ
ejpam-901	18	21	univalent	univalent	ADJ
ejpam-901	18	22	in	in	ADP
ejpam-901	18	23	u	u	NOUN
ejpam-901	18	24	,	,	PUNCT
ejpam-901	18	25	and	and	CCONJ
ejpam-901	18	26	r(1/2	r(1/2	NUM
ejpam-901	18	27	)	)	PUNCT
ejpam-901	18	28	=	=	PRON
ejpam-901	18	29	s	s	VERB
ejpam-901	18	30	∗(1/2	∗(1/2	ADJ
ejpam-901	18	31	)	)	PUNCT
ejpam-901	18	32	.	.	PUNCT
ejpam-901	19	1	let	let	VERB
ejpam-901	19	2	n	n	PRON
ejpam-901	19	3	be	be	AUX
ejpam-901	19	4	the	the	DET
ejpam-901	19	5	class	class	NOUN
ejpam-901	19	6	of	of	ADP
ejpam-901	19	7	all	all	DET
ejpam-901	19	8	analytic	analytic	ADJ
ejpam-901	19	9	functions	function	NOUN
ejpam-901	19	10	h	h	NOUN
ejpam-901	19	11	which	which	PRON
ejpam-901	19	12	are	be	AUX
ejpam-901	19	13	univalent	univalent	ADJ
ejpam-901	19	14	in	in	ADP
ejpam-901	19	15	u	u	NOUN
ejpam-901	19	16	and	and	CCONJ
ejpam-901	19	17	for	for	ADP
ejpam-901	19	18	which	which	PRON
ejpam-901	19	19	h(u	h(u	PROPN
ejpam-901	19	20	)	)	PUNCT
ejpam-901	19	21	is	be	AUX
ejpam-901	19	22	convex	convex	ADJ
ejpam-901	19	23	with	with	ADP
ejpam-901	19	24	h(0	h(0	PROPN
ejpam-901	19	25	)	)	PUNCT
ejpam-901	19	26	=	=	SYM
ejpam-901	19	27	1	1	NUM
ejpam-901	19	28	and	and	CCONJ
ejpam-901	19	29	and	and	CCONJ
ejpam-901	19	30	re{h(z	re{h(z	NOUN
ejpam-901	19	31	)	)	PUNCT
ejpam-901	19	32	}	}	PUNCT
ejpam-901	19	33	>	>	X
ejpam-901	19	34	0	0	PUNCT
ejpam-901	20	1	in	in	ADP
ejpam-901	20	2	u.	u.	NOUN
ejpam-901	20	3	for	for	ADP
ejpam-901	20	4	any	any	DET
ejpam-901	20	5	real	real	ADJ
ejpam-901	20	6	number	number	NOUN
ejpam-901	20	7	s	s	PART
ejpam-901	20	8	,	,	PUNCT
ejpam-901	20	9	we	we	PRON
ejpam-901	20	10	define	define	VERB
ejpam-901	20	11	the	the	DET
ejpam-901	20	12	multiplier	multipli	ADJ
ejpam-901	20	13	transformations	transformation	NOUN
ejpam-901	20	14	i	i	PRON
ejpam-901	20	15	s	s	VERB
ejpam-901	20	16	λ	λ	PROPN
ejpam-901	20	17	of	of	ADP
ejpam-901	20	18	functions	function	NOUN
ejpam-901	20	19	f	f	PROPN
ejpam-901	20	20	∈	∈	PROPN
ejpam-901	20	21	a	a	PRON
ejpam-901	20	22	by	by	ADP
ejpam-901	20	23	i	i	PRON
ejpam-901	20	24	s	s	PROPN
ejpam-901	20	25	λ	λ	X
ejpam-901	20	26	f	f	X
ejpam-901	20	27	(	(	PUNCT
ejpam-901	20	28	z	z	NOUN
ejpam-901	20	29	)	)	PUNCT
ejpam-901	20	30	=	=	SYM
ejpam-901	21	1	z	z	NOUN
ejpam-901	22	1	+	+	NOUN
ejpam-901	22	2	∞∑	∞∑	NUM
ejpam-901	22	3	k=2	k=2	PROPN
ejpam-901	22	4	�	�	PROPN
ejpam-901	22	5	k+λ	k+λ	X
ejpam-901	22	6	1+λ	1+λ	NUM
ejpam-901	22	7	�	�	PROPN
ejpam-901	22	8	s	s	PART
ejpam-901	22	9	akzk	akzk	NOUN
ejpam-901	22	10	(	(	PUNCT
ejpam-901	22	11	λ	λ	X
ejpam-901	22	12	>	>	X
ejpam-901	22	13	−1	−1	NOUN
ejpam-901	22	14	)	)	PUNCT
ejpam-901	22	15	.	.	PUNCT
ejpam-901	23	1	obviously	obviously	ADV
ejpam-901	23	2	,	,	PUNCT
ejpam-901	23	3	we	we	PRON
ejpam-901	23	4	observe	observe	VERB
ejpam-901	23	5	that	that	SCONJ
ejpam-901	23	6	i	i	PRON
ejpam-901	23	7	s	s	VERB
ejpam-901	23	8	λ(i	λ(i	PROPN
ejpam-901	23	9	t	t	PROPN
ejpam-901	23	10	λ	λ	X
ejpam-901	23	11	f	f	X
ejpam-901	23	12	(	(	PUNCT
ejpam-901	23	13	z	z	NOUN
ejpam-901	23	14	)	)	PUNCT
ejpam-901	23	15	)	)	PUNCT
ejpam-901	24	1	=	=	PUNCT
ejpam-901	25	1	i	i	PRON
ejpam-901	25	2	s+t	s+t	PROPN
ejpam-901	26	1	λ	λ	X
ejpam-901	26	2	f	f	X
ejpam-901	26	3	(	(	PUNCT
ejpam-901	26	4	z	z	NOUN
ejpam-901	26	5	)	)	PUNCT
ejpam-901	26	6	for	for	ADP
ejpam-901	26	7	all	all	DET
ejpam-901	26	8	real	real	ADJ
ejpam-901	26	9	numbers	number	NOUN
ejpam-901	26	10	s	s	NOUN
ejpam-901	26	11	and	and	CCONJ
ejpam-901	26	12	t.	t.	NOUN
ejpam-901	26	13	for	for	ADP
ejpam-901	26	14	λ	λ	PROPN
ejpam-901	26	15	=	=	SYM
ejpam-901	26	16	1	1	NUM
ejpam-901	26	17	and	and	CCONJ
ejpam-901	26	18	any	any	DET
ejpam-901	26	19	integer	integer	NOUN
ejpam-901	26	20	s	s	PROPN
ejpam-901	26	21	,	,	PUNCT
ejpam-901	26	22	the	the	DET
ejpam-901	26	23	operator	operator	NOUN
ejpam-901	27	1	i	i	PRON
ejpam-901	27	2	s	s	VERB
ejpam-901	27	3	λ	λ	PROPN
ejpam-901	27	4	was	be	AUX
ejpam-901	27	5	studied	study	VERB
ejpam-901	27	6	by	by	ADP
ejpam-901	27	7	uralegaddi	uralegaddi	ADJ
ejpam-901	27	8	and	and	CCONJ
ejpam-901	27	9	somanatha	somanatha	NOUN
ejpam-901	28	1	[	[	X
ejpam-901	28	2	13	13	NUM
ejpam-901	28	3	]	]	PUNCT
ejpam-901	28	4	.	.	PUNCT
ejpam-901	29	1	also	also	ADV
ejpam-901	29	2	,	,	PUNCT
ejpam-901	29	3	for	for	ADP
ejpam-901	29	4	s	s	NOUN
ejpam-901	29	5	=	=	SYM
ejpam-901	29	6	−1	−1	NOUN
ejpam-901	29	7	,	,	PUNCT
ejpam-901	29	8	the	the	DET
ejpam-901	29	9	operator	operator	NOUN
ejpam-901	29	10	i	i	PRON
ejpam-901	29	11	s	s	VERB
ejpam-901	29	12	λ	λ	NOUN
ejpam-901	29	13	is	be	AUX
ejpam-901	29	14	the	the	DET
ejpam-901	29	15	integral	integral	ADJ
ejpam-901	29	16	operator	operator	NOUN
ejpam-901	29	17	studied	study	VERB
ejpam-901	29	18	by	by	ADP
ejpam-901	29	19	owa	owa	PROPN
ejpam-901	29	20	and	and	CCONJ
ejpam-901	29	21	srivastava	srivastava	PROPN
ejpam-901	29	22	[	[	X
ejpam-901	29	23	8	8	NUM
ejpam-901	29	24	]	]	PUNCT
ejpam-901	29	25	.	.	PUNCT
ejpam-901	30	1	moreover	moreover	ADV
ejpam-901	30	2	,	,	PUNCT
ejpam-901	30	3	the	the	DET
ejpam-901	30	4	operator	operator	NOUN
ejpam-901	30	5	i	i	PRON
ejpam-901	30	6	s	s	VERB
ejpam-901	30	7	λ	λ	NOUN
ejpam-901	30	8	is	be	AUX
ejpam-901	30	9	closely	closely	ADV
ejpam-901	30	10	related	relate	VERB
ejpam-901	30	11	to	to	ADP
ejpam-901	30	12	the	the	DET
ejpam-901	30	13	multiplier	multipli	ADJ
ejpam-901	30	14	transformation	transformation	NOUN
ejpam-901	30	15	studied	study	VERB
ejpam-901	30	16	by	by	ADP
ejpam-901	30	17	jung	jung	PROPN
ejpam-901	30	18	et	et	PROPN
ejpam-901	30	19	al	al	PROPN
ejpam-901	30	20	.	.	PUNCT
ejpam-901	31	1	[	[	X
ejpam-901	31	2	3	3	NUM
ejpam-901	31	3	]	]	PUNCT
ejpam-901	31	4	(	(	PUNCT
ejpam-901	31	5	also	also	ADV
ejpam-901	31	6	see	see	VERB
ejpam-901	31	7	[	[	X
ejpam-901	31	8	2	2	NUM
ejpam-901	31	9	]	]	NUM
ejpam-901	31	10	)	)	PUNCT
ejpam-901	31	11	,	,	PUNCT
ejpam-901	31	12	and	and	CCONJ
ejpam-901	31	13	the	the	DET
ejpam-901	31	14	differential	differential	ADJ
ejpam-901	31	15	operator	operator	NOUN
ejpam-901	31	16	defined	define	VERB
ejpam-901	31	17	by	by	ADP
ejpam-901	31	18	sălăgean	sălăgean	NOUN
ejpam-901	31	19	[	[	X
ejpam-901	31	20	10	10	NUM
ejpam-901	31	21	]	]	PUNCT
ejpam-901	31	22	.	.	PUNCT
ejpam-901	32	1	let	let	VERB
ejpam-901	32	2	f	f	PROPN
ejpam-901	32	3	s	s	PART
ejpam-901	32	4	λ(z	λ(z	PROPN
ejpam-901	32	5	)	)	PUNCT
ejpam-901	32	6	=	=	SYM
ejpam-901	33	1	z	z	NOUN
ejpam-901	34	1	+	+	NOUN
ejpam-901	34	2	∞∑	∞∑	NUM
ejpam-901	34	3	k=2	k=2	PROPN
ejpam-901	34	4	�	�	PROPN
ejpam-901	34	5	k+λ	k+λ	X
ejpam-901	34	6	1+λ	1+λ	NUM
ejpam-901	34	7	�	�	PROPN
ejpam-901	34	8	s	s	PART
ejpam-901	34	9	zk	zk	PROPN
ejpam-901	34	10	(	(	PUNCT
ejpam-901	34	11	s	s	NOUN
ejpam-901	34	12	∈	∈	PROPN
ejpam-901	34	13	r	r	NOUN
ejpam-901	34	14	;	;	PUNCT
ejpam-901	34	15	λ	λ	X
ejpam-901	34	16	>	>	X
ejpam-901	34	17	−1	−1	NOUN
ejpam-901	34	18	)	)	PUNCT
ejpam-901	34	19	and	and	CCONJ
ejpam-901	34	20	let	let	VERB
ejpam-901	34	21	f	f	PROPN
ejpam-901	34	22	s	s	AUX
ejpam-901	34	23	λ,µ	λ,µ	NOUN
ejpam-901	34	24	be	be	AUX
ejpam-901	34	25	defined	define	VERB
ejpam-901	34	26	such	such	ADJ
ejpam-901	34	27	that	that	SCONJ
ejpam-901	34	28	f	f	PROPN
ejpam-901	34	29	s	s	PROPN
ejpam-901	34	30	λ(z	λ(z	NOUN
ejpam-901	34	31	)	)	PUNCT
ejpam-901	34	32	∗	∗	NOUN
ejpam-901	34	33	f	f	PROPN
ejpam-901	34	34	s	s	X
ejpam-901	34	35	λ,µ(z	λ,µ(z	NOUN
ejpam-901	34	36	)	)	PUNCT
ejpam-901	34	37	=	=	SYM
ejpam-901	34	38	z	z	NOUN
ejpam-901	34	39	(	(	PUNCT
ejpam-901	34	40	1−	1−	NUM
ejpam-901	34	41	z)µ	z)µ	NOUN
ejpam-901	34	42	(	(	PUNCT
ejpam-901	34	43	µ	µ	X
ejpam-901	34	44	>	>	X
ejpam-901	34	45	0	0	NUM
ejpam-901	34	46	;	;	PUNCT
ejpam-901	34	47	z	z	PROPN
ejpam-901	34	48	∈	∈	PROPN
ejpam-901	34	49	u	u	NOUN
ejpam-901	34	50	)	)	PUNCT
ejpam-901	34	51	,	,	PUNCT
ejpam-901	34	52	(	(	PUNCT
ejpam-901	34	53	2	2	X
ejpam-901	34	54	)	)	PUNCT
ejpam-901	34	55	where	where	SCONJ
ejpam-901	34	56	the	the	DET
ejpam-901	34	57	symbol	symbol	NOUN
ejpam-901	34	58	(	(	PUNCT
ejpam-901	34	59	∗	∗	NOUN
ejpam-901	34	60	)	)	PUNCT
ejpam-901	34	61	stands	stand	VERB
ejpam-901	34	62	for	for	ADP
ejpam-901	34	63	the	the	DET
ejpam-901	34	64	hadamard	hadamard	ADJ
ejpam-901	34	65	product(or	product(or	ADJ
ejpam-901	34	66	convolution	convolution	NOUN
ejpam-901	34	67	)	)	PUNCT
ejpam-901	34	68	.	.	PUNCT
ejpam-901	35	1	then	then	ADV
ejpam-901	35	2	,	,	PUNCT
ejpam-901	35	3	motivated	motivate	VERB
ejpam-901	35	4	essentially	essentially	ADV
ejpam-901	35	5	by	by	ADP
ejpam-901	35	6	the	the	DET
ejpam-901	35	7	choi	choi	NOUN
ejpam-901	35	8	-	-	PUNCT
ejpam-901	35	9	saigo	saigo	NOUN
ejpam-901	35	10	-	-	PUNCT
ejpam-901	35	11	srivastava	srivastava	PROPN
ejpam-901	35	12	operator	operator	NOUN
ejpam-901	35	13	[	[	X
ejpam-901	35	14	1	1	NUM
ejpam-901	35	15	]	]	PUNCT
ejpam-901	35	16	(	(	PUNCT
ejpam-901	35	17	see	see	VERB
ejpam-901	35	18	also	also	ADV
ejpam-901	35	19	[	[	X
ejpam-901	35	20	5	5	NUM
ejpam-901	35	21	]	]	PUNCT
ejpam-901	35	22	,	,	PUNCT
ejpam-901	35	23	[	[	X
ejpam-901	35	24	6	6	NUM
ejpam-901	35	25	]	]	PUNCT
ejpam-901	35	26	and	and	CCONJ
ejpam-901	35	27	[	[	X
ejpam-901	35	28	7	7	NUM
ejpam-901	35	29	]	]	NUM
ejpam-901	35	30	)	)	PUNCT
ejpam-901	35	31	,	,	PUNCT
ejpam-901	35	32	we	we	PRON
ejpam-901	35	33	now	now	ADV
ejpam-901	35	34	introduce	introduce	VERB
ejpam-901	35	35	the	the	DET
ejpam-901	35	36	operator	operator	NOUN
ejpam-901	35	37	i	i	PRON
ejpam-901	35	38	s	s	VERB
ejpam-901	35	39	λ,µ	λ,µ	NOUN
ejpam-901	35	40	:	:	PUNCT
ejpam-901	35	41	a	a	DET
ejpam-901	35	42	→a	→a	PROPN
ejpam-901	35	43	,	,	PUNCT
ejpam-901	35	44	which	which	PRON
ejpam-901	35	45	are	be	AUX
ejpam-901	35	46	defined	define	VERB
ejpam-901	35	47	here	here	ADV
ejpam-901	35	48	by	by	ADP
ejpam-901	35	49	i	i	PRON
ejpam-901	35	50	s	s	PROPN
ejpam-901	36	1	λ,µ	λ,µ	PROPN
ejpam-901	36	2	f	f	PROPN
ejpam-901	36	3	(	(	PUNCT
ejpam-901	36	4	z	z	NOUN
ejpam-901	36	5	)	)	PUNCT
ejpam-901	36	6	=	=	SYM
ejpam-901	36	7	�	�	X
ejpam-901	37	1	f	f	PROPN
ejpam-901	37	2	s	s	PROPN
ejpam-901	37	3	λ,µ	λ,µ	PROPN
ejpam-901	37	4	∗	∗	X
ejpam-901	37	5	f	f	PROPN
ejpam-901	37	6	�	�	PROPN
ejpam-901	37	7	(	(	PUNCT
ejpam-901	37	8	z	z	NOUN
ejpam-901	37	9	)	)	PUNCT
ejpam-901	37	10	(	(	PUNCT
ejpam-901	37	11	f	f	PROPN
ejpam-901	37	12	∈a	∈a	ADJ
ejpam-901	37	13	;	;	PUNCT
ejpam-901	37	14	s	s	X
ejpam-901	37	15	∈	∈	PROPN
ejpam-901	37	16	r	r	NOUN
ejpam-901	37	17	;	;	PUNCT
ejpam-901	37	18	λ	λ	X
ejpam-901	37	19	>	>	X
ejpam-901	37	20	−1	−1	NOUN
ejpam-901	37	21	;	;	PUNCT
ejpam-901	37	22	µ	µ	X
ejpam-901	37	23	>	>	X
ejpam-901	37	24	0	0	NUM
ejpam-901	37	25	)	)	PUNCT
ejpam-901	37	26	,	,	PUNCT
ejpam-901	37	27	(	(	PUNCT
ejpam-901	37	28	3	3	X
ejpam-901	37	29	)	)	PUNCT
ejpam-901	37	30	in	in	ADP
ejpam-901	37	31	particular	particular	ADJ
ejpam-901	37	32	,	,	PUNCT
ejpam-901	37	33	we	we	PRON
ejpam-901	37	34	note	note	VERB
ejpam-901	37	35	that	that	SCONJ
ejpam-901	37	36	i0	i0	PROPN
ejpam-901	37	37	0,2	0,2	NUM
ejpam-901	37	38	f	f	X
ejpam-901	37	39	(	(	PUNCT
ejpam-901	37	40	z	z	NOUN
ejpam-901	37	41	)	)	PUNCT
ejpam-901	37	42	=	=	PUNCT
ejpam-901	37	43	z	z	X
ejpam-901	37	44	f	f	NOUN
ejpam-901	37	45	′(z	′(z	NOUN
ejpam-901	37	46	)	)	PUNCT
ejpam-901	37	47	and	and	CCONJ
ejpam-901	37	48	i1	i1	PROPN
ejpam-901	37	49	0,2	0,2	NUM
ejpam-901	37	50	f	f	PROPN
ejpam-901	37	51	(	(	PUNCT
ejpam-901	37	52	z	z	NOUN
ejpam-901	37	53	)	)	PUNCT
ejpam-901	38	1	=	=	SYM
ejpam-901	38	2	f	f	X
ejpam-901	38	3	(	(	PUNCT
ejpam-901	38	4	z	z	NOUN
ejpam-901	38	5	)	)	PUNCT
ejpam-901	38	6	.	.	PUNCT
ejpam-901	39	1	in	in	ADP
ejpam-901	39	2	view	view	NOUN
ejpam-901	39	3	of	of	ADP
ejpam-901	39	4	(	(	PUNCT
ejpam-901	39	5	2	2	NUM
ejpam-901	39	6	)	)	PUNCT
ejpam-901	39	7	and	and	CCONJ
ejpam-901	39	8	(	(	PUNCT
ejpam-901	39	9	3	3	NUM
ejpam-901	39	10	)	)	PUNCT
ejpam-901	39	11	,	,	PUNCT
ejpam-901	39	12	we	we	PRON
ejpam-901	39	13	obtain	obtain	VERB
ejpam-901	39	14	the	the	DET
ejpam-901	39	15	following	follow	VERB
ejpam-901	39	16	relations	relation	NOUN
ejpam-901	39	17	:	:	PUNCT
ejpam-901	39	18	z	z	NOUN
ejpam-901	39	19	�	�	PROPN
ejpam-901	40	1	i	i	PRON
ejpam-901	40	2	s	s	VERB
ejpam-901	40	3	λ,µ	λ,µ	PROPN
ejpam-901	40	4	f	f	PROPN
ejpam-901	40	5	(	(	PUNCT
ejpam-901	40	6	z	z	NOUN
ejpam-901	40	7	)	)	PUNCT
ejpam-901	40	8	�	�	PROPN
ejpam-901	40	9	′	′	NOUN
ejpam-901	41	1	=	=	PUNCT
ejpam-901	42	1	µi	µi	PROPN
ejpam-901	42	2	s	s	PART
ejpam-901	42	3	λ,µ+1	λ,µ+1	PROPN
ejpam-901	42	4	f	f	X
ejpam-901	42	5	(	(	PUNCT
ejpam-901	42	6	z)−	z)−	PROPN
ejpam-901	42	7	(	(	PUNCT
ejpam-901	42	8	µ−	µ−	PROPN
ejpam-901	42	9	1)i	1)i	NUM
ejpam-901	42	10	s	s	PART
ejpam-901	42	11	λ,µ	λ,µ	PROPN
ejpam-901	42	12	f	f	PROPN
ejpam-901	42	13	(	(	PUNCT
ejpam-901	42	14	z	z	NOUN
ejpam-901	42	15	)	)	PUNCT
ejpam-901	42	16	(	(	PUNCT
ejpam-901	42	17	f	f	PROPN
ejpam-901	42	18	∈a	∈a	ADJ
ejpam-901	42	19	;	;	PUNCT
ejpam-901	42	20	λ	λ	X
ejpam-901	42	21	>	>	X
ejpam-901	42	22	−1	−1	NOUN
ejpam-901	42	23	;	;	PUNCT
ejpam-901	42	24	µ	µ	X
ejpam-901	42	25	>	>	X
ejpam-901	42	26	0	0	NUM
ejpam-901	42	27	)	)	PUNCT
ejpam-901	42	28	(	(	PUNCT
ejpam-901	42	29	4	4	NUM
ejpam-901	42	30	)	)	PUNCT
ejpam-901	42	31	and	and	CCONJ
ejpam-901	42	32	z	z	PROPN
ejpam-901	42	33	�	�	PROPN
ejpam-901	43	1	i	i	PRON
ejpam-901	43	2	s+1	s+1	VERB
ejpam-901	43	3	λ,µ	λ,µ	VERB
ejpam-901	43	4	f	f	PROPN
ejpam-901	43	5	(	(	PUNCT
ejpam-901	43	6	z	z	NOUN
ejpam-901	43	7	)	)	PUNCT
ejpam-901	43	8	�	�	PROPN
ejpam-901	43	9	′	′	NOUN
ejpam-901	43	10	=	=	PUNCT
ejpam-901	43	11	(	(	PUNCT
ejpam-901	43	12	λ+	λ+	NUM
ejpam-901	43	13	1)i	1)i	NUM
ejpam-901	43	14	s	s	PART
ejpam-901	43	15	λ,µ	λ,µ	PROPN
ejpam-901	43	16	f	f	X
ejpam-901	43	17	(	(	PUNCT
ejpam-901	43	18	z)−λi	z)−λi	PROPN
ejpam-901	44	1	s+1	s+1	PROPN
ejpam-901	44	2	λ,µ	λ,µ	PROPN
ejpam-901	44	3	f	f	PROPN
ejpam-901	44	4	(	(	PUNCT
ejpam-901	44	5	z	z	NOUN
ejpam-901	44	6	)	)	PUNCT
ejpam-901	44	7	(	(	PUNCT
ejpam-901	44	8	f	f	PROPN
ejpam-901	44	9	∈	∈	PROPN
ejpam-901	44	10	a	a	PRON
ejpam-901	44	11	;	;	PUNCT
ejpam-901	44	12	λ	λ	X
ejpam-901	44	13	>	>	X
ejpam-901	44	14	−1	−1	NOUN
ejpam-901	44	15	;	;	PUNCT
ejpam-901	44	16	µ	µ	X
ejpam-901	44	17	>	>	X
ejpam-901	44	18	0	0	NUM
ejpam-901	44	19	)	)	PUNCT
ejpam-901	44	20	.	.	PUNCT
ejpam-901	45	1	(	(	PUNCT
ejpam-901	45	2	5	5	X
ejpam-901	45	3	)	)	PUNCT
ejpam-901	45	4	o.	o.	NOUN
ejpam-901	45	5	kwon	kwon	PROPN
ejpam-901	45	6	,	,	PUNCT
ejpam-901	45	7	n.	n.	PROPN
ejpam-901	45	8	cho	cho	PROPN
ejpam-901	45	9	/	/	SYM
ejpam-901	45	10	eur	eur	PROPN
ejpam-901	45	11	.	.	PUNCT
ejpam-901	46	1	j.	j.	PROPN
ejpam-901	46	2	pure	pure	PROPN
ejpam-901	46	3	appl	appl	PROPN
ejpam-901	46	4	.	.	PROPN
ejpam-901	46	5	math	math	PROPN
ejpam-901	46	6	,	,	PUNCT
ejpam-901	46	7	3	3	NUM
ejpam-901	46	8	(	(	PUNCT
ejpam-901	46	9	2010	2010	NUM
ejpam-901	46	10	)	)	PUNCT
ejpam-901	46	11	,	,	PUNCT
ejpam-901	46	12	1124	1124	NUM
ejpam-901	46	13	-	-	SYM
ejpam-901	46	14	1136	1136	NUM
ejpam-901	46	15	1126	1126	NUM
ejpam-901	46	16	we	we	PRON
ejpam-901	46	17	also	also	ADV
ejpam-901	46	18	define	define	VERB
ejpam-901	46	19	the	the	DET
ejpam-901	46	20	function	function	NOUN
ejpam-901	46	21	φ(a	φ(a	ADJ
ejpam-901	46	22	,	,	PUNCT
ejpam-901	46	23	c	c	X
ejpam-901	46	24	;	;	PUNCT
ejpam-901	46	25	z	z	X
ejpam-901	46	26	)	)	PUNCT
ejpam-901	46	27	by	by	ADP
ejpam-901	46	28	φ(a	φ(a	ADJ
ejpam-901	46	29	,	,	PUNCT
ejpam-901	46	30	c	c	X
ejpam-901	46	31	;	;	PUNCT
ejpam-901	46	32	z	z	X
ejpam-901	46	33	)	)	PUNCT
ejpam-901	46	34	:	:	PUNCT
ejpam-901	47	1	=	=	NOUN
ejpam-901	48	1	∞∑	∞∑	NUM
ejpam-901	48	2	k=0	k=0	PROPN
ejpam-901	48	3	(	(	PUNCT
ejpam-901	48	4	a)k	a)k	ADJ
ejpam-901	48	5	(	(	PUNCT
ejpam-901	48	6	c)k	c)k	PROPN
ejpam-901	48	7	zk+1	zk+1	NUM
ejpam-901	48	8	(	(	PUNCT
ejpam-901	48	9	6	6	NUM
ejpam-901	48	10	)	)	PUNCT
ejpam-901	48	11	(	(	PUNCT
ejpam-901	48	12	z	z	NOUN
ejpam-901	48	13	∈	∈	PROPN
ejpam-901	48	14	u	u	NOUN
ejpam-901	48	15	;	;	PUNCT
ejpam-901	48	16	a	a	DET
ejpam-901	48	17	∈	∈	PROPN
ejpam-901	48	18	r	r	NOUN
ejpam-901	48	19	;	;	PUNCT
ejpam-901	48	20	c	c	PROPN
ejpam-901	48	21	∈	∈	PROPN
ejpam-901	48	22	r	r	NOUN
ejpam-901	48	23	\z−0	\z−0	NOUN
ejpam-901	48	24	;	;	PUNCT
ejpam-901	48	25	z−0	z−0	NUM
ejpam-901	48	26	:	:	PUNCT
ejpam-901	48	27	=	=	X
ejpam-901	48	28	{	{	PUNCT
ejpam-901	48	29	−1,−2	−1,−2	VERB
ejpam-901	48	30	,	,	PUNCT
ejpam-901	48	31	·	·	PUNCT
ejpam-901	48	32	·	·	PUNCT
ejpam-901	48	33	·	·	PUNCT
ejpam-901	48	34	}	}	PUNCT
ejpam-901	48	35	)	)	PUNCT
ejpam-901	48	36	,	,	PUNCT
ejpam-901	48	37	where	where	SCONJ
ejpam-901	48	38	(	(	PUNCT
ejpam-901	48	39	ν)k	ν)k	X
ejpam-901	48	40	is	be	AUX
ejpam-901	48	41	the	the	DET
ejpam-901	48	42	pochhammer	pochhammer	NOUN
ejpam-901	48	43	symbol	symbol	NOUN
ejpam-901	48	44	(	(	PUNCT
ejpam-901	48	45	or	or	CCONJ
ejpam-901	48	46	the	the	DET
ejpam-901	48	47	shifted	shift	VERB
ejpam-901	48	48	factorial	factorial	NOUN
ejpam-901	48	49	)	)	PUNCT
ejpam-901	48	50	defined	define	VERB
ejpam-901	48	51	(	(	PUNCT
ejpam-901	48	52	in	in	ADP
ejpam-901	48	53	terms	term	NOUN
ejpam-901	48	54	of	of	ADP
ejpam-901	48	55	the	the	DET
ejpam-901	48	56	gamma	gamma	NOUN
ejpam-901	48	57	function	function	NOUN
ejpam-901	48	58	)	)	PUNCT
ejpam-901	48	59	by	by	ADP
ejpam-901	48	60	(	(	PUNCT
ejpam-901	48	61	ν)k	ν)k	NOUN
ejpam-901	48	62	:	:	PUNCT
ejpam-901	48	63	=	=	SYM
ejpam-901	48	64	γ(ν	γ(ν	PROPN
ejpam-901	48	65	+	+	CCONJ
ejpam-901	48	66	k	k	PROPN
ejpam-901	48	67	)	)	PUNCT
ejpam-901	48	68	γ(ν	γ(ν	NOUN
ejpam-901	48	69	)	)	PUNCT
ejpam-901	48	70	=	=	PUNCT
ejpam-901	49	1	(	(	PUNCT
ejpam-901	49	2	1	1	NUM
ejpam-901	49	3	if	if	SCONJ
ejpam-901	49	4	k	k	PROPN
ejpam-901	49	5	=	=	PUNCT
ejpam-901	49	6	0	0	NUM
ejpam-901	49	7	and	and	CCONJ
ejpam-901	49	8	ν	ν	X
ejpam-901	49	9	∈	∈	NOUN
ejpam-901	49	10	c	c	NOUN
ejpam-901	49	11	\	\	X
ejpam-901	49	12	{	{	PUNCT
ejpam-901	49	13	0	0	NUM
ejpam-901	49	14	}	}	PUNCT
ejpam-901	49	15	,	,	PUNCT
ejpam-901	49	16	ν(ν	ν(ν	NOUN
ejpam-901	49	17	+	+	PUNCT
ejpam-901	49	18	1	1	NUM
ejpam-901	49	19	)	)	PUNCT
ejpam-901	49	20	·	·	PUNCT
ejpam-901	49	21	·	·	PUNCT
ejpam-901	49	22	·	·	PUNCT
ejpam-901	49	23	(	(	PUNCT
ejpam-901	49	24	ν	ν	X
ejpam-901	49	25	+	+	NUM
ejpam-901	49	26	k−	k−	PROPN
ejpam-901	49	27	1	1	NUM
ejpam-901	49	28	)	)	PUNCT
ejpam-901	49	29	if	if	SCONJ
ejpam-901	49	30	k	k	PROPN
ejpam-901	49	31	∈	∈	PROPN
ejpam-901	50	1	n	n	X
ejpam-901	50	2	:	:	PUNCT
ejpam-901	50	3	=	=	SYM
ejpam-901	50	4	{	{	PUNCT
ejpam-901	50	5	1,2	1,2	NUM
ejpam-901	50	6	,	,	PUNCT
ejpam-901	50	7	·	·	PUNCT
ejpam-901	50	8	·	·	PUNCT
ejpam-901	50	9	·	·	PUNCT
ejpam-901	50	10	}	}	PUNCT
ejpam-901	50	11	and	and	CCONJ
ejpam-901	50	12	ν	ν	PROPN
ejpam-901	50	13	∈	∈	PROPN
ejpam-901	50	14	c.	c.	NOUN
ejpam-901	50	15	by	by	ADP
ejpam-901	50	16	using	use	VERB
ejpam-901	50	17	the	the	DET
ejpam-901	50	18	operator	operator	NOUN
ejpam-901	50	19	i	i	PRON
ejpam-901	50	20	s	s	VERB
ejpam-901	51	1	λ,µ	λ,µ	INTJ
ejpam-901	51	2	,	,	PUNCT
ejpam-901	51	3	we	we	PRON
ejpam-901	51	4	introduce	introduce	VERB
ejpam-901	51	5	the	the	DET
ejpam-901	51	6	following	follow	VERB
ejpam-901	51	7	class	class	NOUN
ejpam-901	51	8	of	of	ADP
ejpam-901	51	9	analytic	analytic	ADJ
ejpam-901	51	10	functions	function	NOUN
ejpam-901	51	11	for	for	ADP
ejpam-901	51	12	γ	γ	X
ejpam-901	51	13	>	>	X
ejpam-901	51	14	0	0	PROPN
ejpam-901	51	15	,	,	PUNCT
ejpam-901	51	16	λ	λ	X
ejpam-901	51	17	>	>	X
ejpam-901	51	18	−1	−1	NOUN
ejpam-901	51	19	,	,	PUNCT
ejpam-901	51	20	s	s	NOUN
ejpam-901	51	21	∈	∈	PROPN
ejpam-901	51	22	r	r	NOUN
ejpam-901	51	23	,	,	PUNCT
ejpam-901	51	24	µ	µ	X
ejpam-901	51	25	>	>	SYM
ejpam-901	51	26	0	0	PUNCT
ejpam-901	52	1	and	and	CCONJ
ejpam-901	52	2	h	h	NOUN
ejpam-901	52	3	∈	∈	PROPN
ejpam-901	52	4	n	n	CCONJ
ejpam-901	52	5	:	:	PUNCT
ejpam-901	52	6	t	t	PROPN
ejpam-901	52	7	s	s	PART
ejpam-901	52	8	λ,µ(γ	λ,µ(γ	NOUN
ejpam-901	52	9	;	;	PUNCT
ejpam-901	52	10	h	h	X
ejpam-901	52	11	)	)	PUNCT
ejpam-901	52	12	:	:	PUNCT
ejpam-901	53	1	=	=	SYM
ejpam-901	53	2	(	(	PUNCT
ejpam-901	53	3	f	f	PROPN
ejpam-901	53	4	∈a	∈a	PROPN
ejpam-901	53	5	:	:	PUNCT
ejpam-901	53	6	(	(	PUNCT
ejpam-901	53	7	1−	1−	NUM
ejpam-901	53	8	γ	γ	X
ejpam-901	53	9	)	)	PUNCT
ejpam-901	53	10	i	i	PRON
ejpam-901	53	11	s	s	VERB
ejpam-901	53	12	λ,µ	λ,µ	PROPN
ejpam-901	53	13	f	f	PROPN
ejpam-901	53	14	(	(	PUNCT
ejpam-901	53	15	z	z	NOUN
ejpam-901	53	16	)	)	PUNCT
ejpam-901	53	17	z	z	NOUN
ejpam-901	54	1	+	+	NUM
ejpam-901	54	2	γ(i	γ(i	NOUN
ejpam-901	54	3	s	s	X
ejpam-901	54	4	λ,µ	λ,µ	NOUN
ejpam-901	54	5	f	f	PROPN
ejpam-901	54	6	(	(	PUNCT
ejpam-901	54	7	z))′	z))′	X
ejpam-901	54	8	≺	≺	NOUN
ejpam-901	54	9	h(z	h(z	NOUN
ejpam-901	54	10	)	)	PUNCT
ejpam-901	54	11	)	)	PUNCT
ejpam-901	54	12	.	.	PUNCT
ejpam-901	55	1	in	in	ADP
ejpam-901	55	2	the	the	DET
ejpam-901	55	3	present	present	ADJ
ejpam-901	55	4	paper	paper	NOUN
ejpam-901	55	5	,	,	PUNCT
ejpam-901	55	6	we	we	PRON
ejpam-901	55	7	derive	derive	VERB
ejpam-901	55	8	some	some	DET
ejpam-901	55	9	inclusion	inclusion	NOUN
ejpam-901	55	10	relations	relation	NOUN
ejpam-901	55	11	,	,	PUNCT
ejpam-901	55	12	convolution	convolution	NOUN
ejpam-901	55	13	properties	property	NOUN
ejpam-901	55	14	and	and	CCONJ
ejpam-901	55	15	integral	integral	ADJ
ejpam-901	55	16	preserving	preserve	VERB
ejpam-901	55	17	properties	property	NOUN
ejpam-901	55	18	for	for	ADP
ejpam-901	55	19	the	the	DET
ejpam-901	55	20	class	class	NOUN
ejpam-901	56	1	t	t	PROPN
ejpam-901	56	2	s	s	X
ejpam-901	56	3	λ,µ	λ,µ	NOUN
ejpam-901	56	4	(	(	PUNCT
ejpam-901	56	5	γ	γ	X
ejpam-901	56	6	;	;	PUNCT
ejpam-901	56	7	h	h	NOUN
ejpam-901	56	8	)	)	PUNCT
ejpam-901	56	9	.	.	PUNCT
ejpam-901	57	1	the	the	DET
ejpam-901	57	2	following	follow	VERB
ejpam-901	57	3	lemmas	lemmas	PROPN
ejpam-901	57	4	will	will	AUX
ejpam-901	57	5	be	be	AUX
ejpam-901	57	6	required	require	VERB
ejpam-901	57	7	in	in	ADP
ejpam-901	57	8	our	our	PRON
ejpam-901	57	9	investigation	investigation	NOUN
ejpam-901	57	10	.	.	PUNCT
ejpam-901	58	1	lemma	lemma	PROPN
ejpam-901	58	2	1	1	NUM
ejpam-901	58	3	.	.	PUNCT
ejpam-901	59	1	[	[	X
ejpam-901	59	2	4	4	X
ejpam-901	59	3	]	]	PUNCT
ejpam-901	59	4	let	let	VERB
ejpam-901	59	5	g	g	PRON
ejpam-901	59	6	be	be	AUX
ejpam-901	59	7	analytic	analytic	ADJ
ejpam-901	59	8	in	in	ADP
ejpam-901	59	9	u	u	NOUN
ejpam-901	59	10	and	and	CCONJ
ejpam-901	59	11	h	h	NOUN
ejpam-901	59	12	be	be	AUX
ejpam-901	59	13	analytic	analytic	ADJ
ejpam-901	59	14	and	and	CCONJ
ejpam-901	59	15	convex	convex	VERB
ejpam-901	59	16	univalent	univalent	ADJ
ejpam-901	59	17	in	in	ADP
ejpam-901	59	18	u	u	NOUN
ejpam-901	59	19	with	with	ADP
ejpam-901	59	20	h(0	h(0	PROPN
ejpam-901	59	21	)	)	PUNCT
ejpam-901	59	22	=	=	SYM
ejpam-901	59	23	g(0	g(0	NOUN
ejpam-901	59	24	)	)	PUNCT
ejpam-901	59	25	.	.	PUNCT
ejpam-901	60	1	if	if	SCONJ
ejpam-901	60	2	g(z	g(z	ADJ
ejpam-901	60	3	)	)	PUNCT
ejpam-901	61	1	+	+	CCONJ
ejpam-901	61	2	1	1	NUM
ejpam-901	61	3	γ	γ	X
ejpam-901	61	4	zg′(z)≺	zg′(z)≺	PUNCT
ejpam-901	61	5	h(z	h(z	NOUN
ejpam-901	61	6	)	)	PUNCT
ejpam-901	61	7	(	(	PUNCT
ejpam-901	61	8	re{γ	re{γ	NOUN
ejpam-901	61	9	}	}	PUNCT
ejpam-901	61	10	≥	≥	NUM
ejpam-901	61	11	0;γ	0;γ	NUM
ejpam-901	61	12	6=	6=	NOUN
ejpam-901	61	13	0	0	NUM
ejpam-901	61	14	)	)	PUNCT
ejpam-901	61	15	,	,	PUNCT
ejpam-901	61	16	(	(	PUNCT
ejpam-901	61	17	7	7	X
ejpam-901	61	18	)	)	PUNCT
ejpam-901	61	19	then	then	ADV
ejpam-901	61	20	g(z	g(z	PROPN
ejpam-901	61	21	)	)	PUNCT
ejpam-901	61	22	≺eh(z	≺eh(z	PROPN
ejpam-901	61	23	)	)	PUNCT
ejpam-901	62	1	=	=	SYM
ejpam-901	63	1	γz−γ	γz−γ	PROPN
ejpam-901	63	2	∫	∫	PROPN
ejpam-901	63	3	z	z	NOUN
ejpam-901	63	4	0	0	NUM
ejpam-901	63	5	tγ−1h(t)d	tγ−1h(t)d	VERB
ejpam-901	63	6	t	t	PROPN
ejpam-901	63	7	≺	≺	VERB
ejpam-901	63	8	h(z	h(z	NOUN
ejpam-901	63	9	)	)	PUNCT
ejpam-901	63	10	and	and	CCONJ
ejpam-901	63	11	eh	eh	INTJ
ejpam-901	63	12	is	be	AUX
ejpam-901	63	13	the	the	DET
ejpam-901	63	14	best	good	ADJ
ejpam-901	63	15	dominant	dominant	NOUN
ejpam-901	63	16	of	of	ADP
ejpam-901	63	17	(	(	PUNCT
ejpam-901	63	18	7	7	NUM
ejpam-901	63	19	)	)	PUNCT
ejpam-901	63	20	.	.	PUNCT
ejpam-901	64	1	lemma	lemma	PROPN
ejpam-901	64	2	2	2	NUM
ejpam-901	64	3	.	.	PUNCT
ejpam-901	65	1	[	[	X
ejpam-901	65	2	9	9	NUM
ejpam-901	65	3	]	]	PUNCT
ejpam-901	65	4	let	let	VERB
ejpam-901	65	5	f	f	PROPN
ejpam-901	65	6	∈	∈	PROPN
ejpam-901	65	7	s	s	VERB
ejpam-901	65	8	∗(α	∗(α	PROPN
ejpam-901	65	9	)	)	PUNCT
ejpam-901	65	10	and	and	CCONJ
ejpam-901	65	11	g	g	PROPN
ejpam-901	65	12	∈	∈	PROPN
ejpam-901	65	13	r(α	r(α	PROPN
ejpam-901	65	14	)	)	PUNCT
ejpam-901	65	15	.	.	PUNCT
ejpam-901	66	1	then	then	ADV
ejpam-901	66	2	for	for	ADP
ejpam-901	66	3	any	any	DET
ejpam-901	66	4	analytic	analytic	ADJ
ejpam-901	66	5	function	function	NOUN
ejpam-901	66	6	f	f	PROPN
ejpam-901	66	7	in	in	ADP
ejpam-901	66	8	u	u	PROPN
ejpam-901	66	9	,	,	PUNCT
ejpam-901	66	10	g	g	PROPN
ejpam-901	66	11	∗	∗	NOUN
ejpam-901	66	12	(	(	PUNCT
ejpam-901	66	13	f	f	PROPN
ejpam-901	66	14	f	f	X
ejpam-901	66	15	)	)	PUNCT
ejpam-901	66	16	g	g	NOUN
ejpam-901	66	17	∗	∗	X
ejpam-901	66	18	f	f	PROPN
ejpam-901	66	19	(	(	PUNCT
ejpam-901	66	20	u)⊂	u)⊂	NOUN
ejpam-901	66	21	co(f(u	co(f(u	NUM
ejpam-901	66	22	)	)	PUNCT
ejpam-901	66	23	)	)	PUNCT
ejpam-901	67	1	where	where	SCONJ
ejpam-901	67	2	co(f(u	co(f(u	NUM
ejpam-901	67	3	)	)	PUNCT
ejpam-901	67	4	)	)	PUNCT
ejpam-901	67	5	denotes	denote	VERB
ejpam-901	67	6	the	the	DET
ejpam-901	67	7	convex	convex	PROPN
ejpam-901	67	8	hull	hull	NOUN
ejpam-901	67	9	of	of	ADP
ejpam-901	67	10	f(u	f(u	PROPN
ejpam-901	67	11	)	)	PUNCT
ejpam-901	67	12	.	.	PUNCT
ejpam-901	68	1	lemma	lemma	PROPN
ejpam-901	68	2	3	3	X
ejpam-901	68	3	.	.	PUNCT
ejpam-901	69	1	[	[	X
ejpam-901	69	2	12	12	NUM
ejpam-901	69	3	]	]	PUNCT
ejpam-901	69	4	let	let	VERB
ejpam-901	69	5	0	0	NUM
ejpam-901	69	6	<	<	X
ejpam-901	69	7	a	a	DET
ejpam-901	69	8	≤	≤	ADJ
ejpam-901	69	9	c.	c.	NOUN
ejpam-901	69	10	then	then	ADV
ejpam-901	69	11	re	re	VERB
ejpam-901	69	12	�	�	PROPN
ejpam-901	69	13	φ(a	φ(a	PROPN
ejpam-901	69	14	,	,	PUNCT
ejpam-901	69	15	c	c	X
ejpam-901	69	16	;	;	PUNCT
ejpam-901	69	17	z	z	X
ejpam-901	69	18	)	)	PUNCT
ejpam-901	69	19	z	z	PROPN
ejpam-901	69	20	�	�	PROPN
ejpam-901	69	21	>	>	SYM
ejpam-901	69	22	1	1	NUM
ejpam-901	69	23	2	2	NUM
ejpam-901	69	24	(	(	PUNCT
ejpam-901	69	25	z	z	NOUN
ejpam-901	69	26	∈	∈	PROPN
ejpam-901	69	27	u	u	NOUN
ejpam-901	69	28	)	)	PUNCT
ejpam-901	69	29	,	,	PUNCT
ejpam-901	69	30	where	where	SCONJ
ejpam-901	69	31	φ	φ	PROPN
ejpam-901	69	32	is	be	AUX
ejpam-901	69	33	given	give	VERB
ejpam-901	69	34	by	by	ADP
ejpam-901	69	35	(	(	PUNCT
ejpam-901	69	36	1.6	1.6	NUM
ejpam-901	69	37	)	)	PUNCT
ejpam-901	69	38	.	.	PUNCT
ejpam-901	70	1	o.	o.	PROPN
ejpam-901	70	2	kwon	kwon	PROPN
ejpam-901	70	3	,	,	PUNCT
ejpam-901	70	4	n.	n.	PROPN
ejpam-901	70	5	cho	cho	PROPN
ejpam-901	70	6	/	/	SYM
ejpam-901	70	7	eur	eur	PROPN
ejpam-901	70	8	.	.	PUNCT
ejpam-901	71	1	j.	j.	PROPN
ejpam-901	71	2	pure	pure	PROPN
ejpam-901	71	3	appl	appl	PROPN
ejpam-901	71	4	.	.	PROPN
ejpam-901	71	5	math	math	PROPN
ejpam-901	71	6	,	,	PUNCT
ejpam-901	71	7	3	3	NUM
ejpam-901	71	8	(	(	PUNCT
ejpam-901	71	9	2010	2010	NUM
ejpam-901	71	10	)	)	PUNCT
ejpam-901	71	11	,	,	PUNCT
ejpam-901	71	12	1124	1124	NUM
ejpam-901	71	13	-	-	SYM
ejpam-901	71	14	1136	1136	NUM
ejpam-901	71	15	1127	1127	NUM
ejpam-901	71	16	2	2	NUM
ejpam-901	71	17	.	.	PUNCT
ejpam-901	71	18	inclusion	inclusion	NOUN
ejpam-901	71	19	relations	relation	NOUN
ejpam-901	71	20	theorem	theorem	VERB
ejpam-901	71	21	1	1	NUM
ejpam-901	71	22	.	.	PUNCT
ejpam-901	72	1	if	if	SCONJ
ejpam-901	72	2	0≤	0≤	NUM
ejpam-901	72	3	γ1	γ1	NOUN
ejpam-901	72	4	<	<	X
ejpam-901	72	5	γ2	γ2	PROPN
ejpam-901	72	6	,	,	PUNCT
ejpam-901	72	7	then	then	ADV
ejpam-901	72	8	t	t	PROPN
ejpam-901	72	9	s	s	PART
ejpam-901	72	10	λ,µ(γ2	λ,µ(γ2	NOUN
ejpam-901	72	11	;	;	PUNCT
ejpam-901	72	12	h)⊂	h)⊂	PROPN
ejpam-901	72	13	t	t	PROPN
ejpam-901	72	14	s	s	PART
ejpam-901	72	15	λ,µ(γ1	λ,µ(γ1	NOUN
ejpam-901	72	16	;	;	PUNCT
ejpam-901	72	17	h	h	NOUN
ejpam-901	72	18	)	)	PUNCT
ejpam-901	72	19	.	.	PUNCT
ejpam-901	73	1	proof	proof	NOUN
ejpam-901	73	2	.	.	PUNCT
ejpam-901	74	1	let	let	VERB
ejpam-901	74	2	g(z	g(z	ADJ
ejpam-901	74	3	)	)	PUNCT
ejpam-901	75	1	=	=	PUNCT
ejpam-901	76	1	i	i	PRON
ejpam-901	76	2	s	s	VERB
ejpam-901	76	3	λ,µ	λ,µ	PROPN
ejpam-901	76	4	f	f	PROPN
ejpam-901	76	5	(	(	PUNCT
ejpam-901	76	6	z	z	NOUN
ejpam-901	76	7	)	)	PUNCT
ejpam-901	76	8	z	z	NOUN
ejpam-901	77	1	(	(	PUNCT
ejpam-901	77	2	f	f	PROPN
ejpam-901	77	3	∈	∈	PROPN
ejpam-901	77	4	t	t	PROPN
ejpam-901	77	5	s	s	PART
ejpam-901	77	6	λ,µ(γ2	λ,µ(γ2	NOUN
ejpam-901	77	7	;	;	PUNCT
ejpam-901	77	8	h	h	X
ejpam-901	77	9	)	)	PUNCT
ejpam-901	77	10	:	:	PUNCT
ejpam-901	78	1	z	z	PROPN
ejpam-901	78	2	∈	∈	PROPN
ejpam-901	78	3	u	u	NOUN
ejpam-901	78	4	)	)	PUNCT
ejpam-901	78	5	.	.	PUNCT
ejpam-901	79	1	(	(	PUNCT
ejpam-901	79	2	8)	8)	NUM
ejpam-901	79	3	then	then	ADV
ejpam-901	79	4	the	the	DET
ejpam-901	79	5	function	function	NOUN
ejpam-901	79	6	g	g	PROPN
ejpam-901	79	7	is	be	AUX
ejpam-901	79	8	analytic	analytic	ADJ
ejpam-901	79	9	in	in	ADP
ejpam-901	79	10	u	u	NOUN
ejpam-901	79	11	with	with	ADP
ejpam-901	79	12	g(0	g(0	NOUN
ejpam-901	79	13	)	)	PUNCT
ejpam-901	79	14	=	=	SYM
ejpam-901	80	1	1	1	X
ejpam-901	80	2	.	.	X
ejpam-901	80	3	differentiating	differentiate	VERB
ejpam-901	80	4	both	both	DET
ejpam-901	80	5	sides	side	NOUN
ejpam-901	80	6	of	of	ADP
ejpam-901	80	7	(	(	PUNCT
ejpam-901	80	8	8)	8)	NUM
ejpam-901	80	9	,	,	PUNCT
ejpam-901	80	10	we	we	PRON
ejpam-901	80	11	have	have	VERB
ejpam-901	80	12	(	(	PUNCT
ejpam-901	80	13	1−	1−	NUM
ejpam-901	80	14	γ2	γ2	NOUN
ejpam-901	80	15	)	)	PUNCT
ejpam-901	81	1	i	i	PRON
ejpam-901	81	2	s	s	VERB
ejpam-901	81	3	λ,µ	λ,µ	PROPN
ejpam-901	81	4	f	f	PROPN
ejpam-901	81	5	(	(	PUNCT
ejpam-901	81	6	z	z	NOUN
ejpam-901	81	7	)	)	PUNCT
ejpam-901	81	8	z	z	NOUN
ejpam-901	82	1	+	+	PUNCT
ejpam-901	82	2	γ2(i	γ2(i	SYM
ejpam-901	82	3	s	s	X
ejpam-901	82	4	λ,µ	λ,µ	X
ejpam-901	82	5	f	f	X
ejpam-901	82	6	(	(	PUNCT
ejpam-901	82	7	z))′	z))′	X
ejpam-901	82	8	=	=	SYM
ejpam-901	82	9	g(z	g(z	PROPN
ejpam-901	82	10	)	)	PUNCT
ejpam-901	82	11	+	+	NUM
ejpam-901	82	12	γ2zg′(z	γ2zg′(z	NOUN
ejpam-901	82	13	)	)	PUNCT
ejpam-901	82	14	≺	≺	NOUN
ejpam-901	82	15	h(z	h(z	NOUN
ejpam-901	82	16	)	)	PUNCT
ejpam-901	82	17	.	.	PUNCT
ejpam-901	83	1	(	(	PUNCT
ejpam-901	83	2	9	9	X
ejpam-901	83	3	)	)	PUNCT
ejpam-901	83	4	hence	hence	ADV
ejpam-901	83	5	an	an	DET
ejpam-901	83	6	application	application	NOUN
ejpam-901	83	7	of	of	ADP
ejpam-901	83	8	lemma	lemma	PROPN
ejpam-901	83	9	1	1	NUM
ejpam-901	83	10	with	with	ADP
ejpam-901	83	11	µ	µ	NOUN
ejpam-901	83	12	=	=	SYM
ejpam-901	83	13	1	1	NUM
ejpam-901	83	14	/	/	SYM
ejpam-901	83	15	γ2	γ2	ADJ
ejpam-901	83	16	yields	yield	NOUN
ejpam-901	83	17	g(z	g(z	PROPN
ejpam-901	83	18	)	)	PUNCT
ejpam-901	83	19	≺	≺	NOUN
ejpam-901	83	20	h(z	h(z	NOUN
ejpam-901	83	21	)	)	PUNCT
ejpam-901	83	22	.	.	PUNCT
ejpam-901	84	1	(	(	PUNCT
ejpam-901	84	2	10	10	NUM
ejpam-901	84	3	)	)	PUNCT
ejpam-901	84	4	since	since	SCONJ
ejpam-901	84	5	0≤	0≤	NUM
ejpam-901	84	6	γ1	γ1	NOUN
ejpam-901	84	7	/	/	SYM
ejpam-901	84	8	γ2	γ2	NOUN
ejpam-901	84	9	<	<	X
ejpam-901	84	10	1	1	NUM
ejpam-901	84	11	and	and	CCONJ
ejpam-901	84	12	h	h	NOUN
ejpam-901	84	13	is	be	AUX
ejpam-901	84	14	convex	convex	ADJ
ejpam-901	84	15	univalent	univalent	ADJ
ejpam-901	84	16	in	in	ADP
ejpam-901	84	17	u	u	PROPN
ejpam-901	84	18	,	,	PUNCT
ejpam-901	84	19	it	it	PRON
ejpam-901	84	20	follows	follow	VERB
ejpam-901	84	21	from	from	ADP
ejpam-901	84	22	(	(	PUNCT
ejpam-901	84	23	8)	8)	NUM
ejpam-901	84	24	,	,	PUNCT
ejpam-901	84	25	(	(	PUNCT
ejpam-901	84	26	9	9	NUM
ejpam-901	84	27	)	)	PUNCT
ejpam-901	84	28	and	and	CCONJ
ejpam-901	84	29	(	(	PUNCT
ejpam-901	84	30	10	10	NUM
ejpam-901	84	31	)	)	PUNCT
ejpam-901	84	32	that	that	SCONJ
ejpam-901	84	33	(	(	PUNCT
ejpam-901	84	34	1−	1−	NUM
ejpam-901	84	35	γ1	γ1	NOUN
ejpam-901	84	36	)	)	PUNCT
ejpam-901	85	1	i	i	PRON
ejpam-901	85	2	s	s	VERB
ejpam-901	85	3	λ,µ	λ,µ	PROPN
ejpam-901	85	4	f	f	PROPN
ejpam-901	85	5	(	(	PUNCT
ejpam-901	85	6	z	z	NOUN
ejpam-901	85	7	)	)	PUNCT
ejpam-901	85	8	z	z	NOUN
ejpam-901	86	1	+	+	X
ejpam-901	86	2	γ1(i	γ1(i	PROPN
ejpam-901	86	3	s	s	PART
ejpam-901	86	4	λ,µ	λ,µ	NOUN
ejpam-901	86	5	f	f	PROPN
ejpam-901	86	6	(	(	PUNCT
ejpam-901	86	7	z))′	z))′	X
ejpam-901	86	8	=	=	SYM
ejpam-901	86	9	γ1	γ1	PROPN
ejpam-901	86	10	γ2	γ2	PROPN
ejpam-901	86	11			PROPN
ejpam-901	86	12	(1−	(1−	PROPN
ejpam-901	86	13	γ2	γ2	PROPN
ejpam-901	86	14	)	)	PUNCT
ejpam-901	87	1	i	i	PRON
ejpam-901	87	2	s	s	VERB
ejpam-901	87	3	λ,µ	λ,µ	PROPN
ejpam-901	87	4	f	f	PROPN
ejpam-901	87	5	(	(	PUNCT
ejpam-901	87	6	z	z	NOUN
ejpam-901	87	7	)	)	PUNCT
ejpam-901	87	8	z	z	NOUN
ejpam-901	88	1	+	+	PUNCT
ejpam-901	88	2	γ2(i	γ2(i	SYM
ejpam-901	88	3	s	s	X
ejpam-901	88	4	λ,µ	λ,µ	NOUN
ejpam-901	88	5	f	f	PROPN
ejpam-901	88	6	(	(	PUNCT
ejpam-901	88	7	z))′	z))′	X
ejpam-901	88	8			PROPN
ejpam-901	88	9	+	+	NUM
ejpam-901	88	10	�	�	PROPN
ejpam-901	88	11	1−	1−	NUM
ejpam-901	88	12	γ1	γ1	PROPN
ejpam-901	88	13	γ2	γ2	PROPN
ejpam-901	88	14	�	�	PROPN
ejpam-901	88	15	g(z	g(z	PROPN
ejpam-901	88	16	)	)	PUNCT
ejpam-901	88	17	≺	≺	NOUN
ejpam-901	88	18	h(z	h(z	NOUN
ejpam-901	88	19	)	)	PUNCT
ejpam-901	88	20	.	.	PUNCT
ejpam-901	89	1	therefore	therefore	ADV
ejpam-901	89	2	f	f	PROPN
ejpam-901	89	3	∈	∈	PROPN
ejpam-901	89	4	t	t	PROPN
ejpam-901	89	5	s	s	X
ejpam-901	89	6	λ,µ	λ,µ	PROPN
ejpam-901	89	7	(	(	PUNCT
ejpam-901	89	8	γ1	γ1	PROPN
ejpam-901	89	9	;	;	PUNCT
ejpam-901	89	10	h	h	NOUN
ejpam-901	89	11	)	)	PUNCT
ejpam-901	89	12	and	and	CCONJ
ejpam-901	89	13	so	so	ADV
ejpam-901	89	14	we	we	PRON
ejpam-901	89	15	complete	complete	VERB
ejpam-901	89	16	the	the	DET
ejpam-901	89	17	proof	proof	NOUN
ejpam-901	89	18	of	of	ADP
ejpam-901	89	19	theorem	theorem	ADJ
ejpam-901	89	20	1	1	NUM
ejpam-901	89	21	.	.	PUNCT
ejpam-901	90	1	theorem	theorem	NOUN
ejpam-901	90	2	2	2	NUM
ejpam-901	90	3	.	.	PUNCT
ejpam-901	91	1	if	if	SCONJ
ejpam-901	91	2	0	0	NUM
ejpam-901	91	3	<	<	X
ejpam-901	91	4	µ1	µ1	PROPN
ejpam-901	91	5	≤	≤	NOUN
ejpam-901	91	6	µ2	µ2	PROPN
ejpam-901	91	7	,	,	PUNCT
ejpam-901	91	8	then	then	ADV
ejpam-901	91	9	t	t	PROPN
ejpam-901	91	10	s	s	PROPN
ejpam-901	91	11	λ,µ2	λ,µ2	PROPN
ejpam-901	91	12	(	(	PUNCT
ejpam-901	91	13	γ	γ	PROPN
ejpam-901	91	14	;	;	PUNCT
ejpam-901	91	15	h)⊂	h)⊂	PROPN
ejpam-901	91	16	t	t	PROPN
ejpam-901	91	17	s	s	PART
ejpam-901	91	18	λ,µ1	λ,µ1	PROPN
ejpam-901	91	19	(	(	PUNCT
ejpam-901	91	20	γ	γ	PROPN
ejpam-901	91	21	;	;	PUNCT
ejpam-901	91	22	h	h	NOUN
ejpam-901	91	23	)	)	PUNCT
ejpam-901	91	24	.	.	PUNCT
ejpam-901	92	1	proof	proof	NOUN
ejpam-901	92	2	.	.	PUNCT
ejpam-901	93	1	let	let	VERB
ejpam-901	93	2	f	f	PROPN
ejpam-901	93	3	∈	∈	PROPN
ejpam-901	93	4	t	t	PROPN
ejpam-901	93	5	s	s	PART
ejpam-901	93	6	λ,µ2	λ,µ2	PROPN
ejpam-901	93	7	(	(	PUNCT
ejpam-901	93	8	γ	γ	PROPN
ejpam-901	93	9	;	;	PUNCT
ejpam-901	93	10	h	h	NOUN
ejpam-901	93	11	)	)	PUNCT
ejpam-901	93	12	.	.	PUNCT
ejpam-901	94	1	then	then	ADV
ejpam-901	94	2	(	(	PUNCT
ejpam-901	94	3	1−	1−	NUM
ejpam-901	94	4	γ	γ	X
ejpam-901	94	5	)	)	PUNCT
ejpam-901	94	6	i	i	PRON
ejpam-901	94	7	s	s	PART
ejpam-901	94	8	λ,µ1	λ,µ1	PROPN
ejpam-901	94	9	f	f	PROPN
ejpam-901	94	10	(	(	PUNCT
ejpam-901	94	11	z	z	NOUN
ejpam-901	94	12	)	)	PUNCT
ejpam-901	94	13	z	z	NOUN
ejpam-901	95	1	+	+	NUM
ejpam-901	95	2	γ(i	γ(i	NOUN
ejpam-901	95	3	s	s	PART
ejpam-901	95	4	λ,µ1	λ,µ1	PROPN
ejpam-901	95	5	f	f	X
ejpam-901	95	6	(	(	PUNCT
ejpam-901	95	7	z))′	z))′	X
ejpam-901	95	8	(	(	PUNCT
ejpam-901	95	9	11	11	NUM
ejpam-901	95	10	)	)	PUNCT
ejpam-901	95	11	=	=	PUNCT
ejpam-901	96	1	φ(µ1,µ2	φ(µ1,µ2	ADV
ejpam-901	96	2	;	;	PUNCT
ejpam-901	96	3	z	z	X
ejpam-901	96	4	)	)	PUNCT
ejpam-901	96	5	z	z	NOUN
ejpam-901	96	6	∗	∗	NOUN
ejpam-901	96	7			PROPN
ejpam-901	96	8	(1−	(1−	PROPN
ejpam-901	96	9	γ	γ	X
ejpam-901	96	10	)	)	PUNCT
ejpam-901	96	11	i	i	PRON
ejpam-901	96	12	s	s	VERB
ejpam-901	96	13	λ,µ2	λ,µ2	PROPN
ejpam-901	96	14	f	f	PROPN
ejpam-901	96	15	(	(	PUNCT
ejpam-901	96	16	z	z	NOUN
ejpam-901	96	17	)	)	PUNCT
ejpam-901	96	18	z	z	NOUN
ejpam-901	97	1	+	+	NUM
ejpam-901	97	2	γ(i	γ(i	NOUN
ejpam-901	97	3	s	s	PART
ejpam-901	97	4	λ,µ2	λ,µ2	PROPN
ejpam-901	97	5	f	f	PROPN
ejpam-901	97	6	(	(	PUNCT
ejpam-901	97	7	z))′	z))′	X
ejpam-901	97	8			PROPN
ejpam-901	97	9			PROPN
ejpam-901	97	10	.	.	PUNCT
ejpam-901	98	1	in	in	ADP
ejpam-901	98	2	view	view	NOUN
ejpam-901	98	3	of	of	ADP
ejpam-901	98	4	lemma	lemma	PROPN
ejpam-901	98	5	3	3	NUM
ejpam-901	98	6	,	,	PUNCT
ejpam-901	98	7	we	we	PRON
ejpam-901	98	8	see	see	VERB
ejpam-901	98	9	that	that	SCONJ
ejpam-901	98	10	the	the	DET
ejpam-901	98	11	function	function	NOUN
ejpam-901	98	12	φ(µ1,µ2	φ(µ1,µ2	ADV
ejpam-901	98	13	;	;	PUNCT
ejpam-901	98	14	z)/z	z)/z	X
ejpam-901	98	15	has	have	VERB
ejpam-901	98	16	the	the	DET
ejpam-901	98	17	herglotz	herglotz	NOUN
ejpam-901	98	18	representation	representation	NOUN
ejpam-901	98	19	φ(µ1,µ2	φ(µ1,µ2	ADV
ejpam-901	98	20	;	;	PUNCT
ejpam-901	98	21	z	z	X
ejpam-901	98	22	)	)	PUNCT
ejpam-901	98	23	z	z	NOUN
ejpam-901	98	24	=	=	SYM
ejpam-901	98	25	∫	∫	PROPN
ejpam-901	98	26	|x	|x	PROPN
ejpam-901	98	27	|=1	|=1	PROPN
ejpam-901	98	28	dµ(x	dµ(x	PUNCT
ejpam-901	98	29	)	)	PUNCT
ejpam-901	98	30	1−	1−	NUM
ejpam-901	98	31	xz	xz	PROPN
ejpam-901	98	32	(	(	PUNCT
ejpam-901	98	33	z	z	NOUN
ejpam-901	98	34	∈	∈	PROPN
ejpam-901	98	35	u	u	NOUN
ejpam-901	98	36	)	)	PUNCT
ejpam-901	98	37	,	,	PUNCT
ejpam-901	98	38	(	(	PUNCT
ejpam-901	98	39	12	12	X
ejpam-901	98	40	)	)	PUNCT
ejpam-901	98	41	o.	o.	PROPN
ejpam-901	98	42	kwon	kwon	PROPN
ejpam-901	98	43	,	,	PUNCT
ejpam-901	98	44	n.	n.	PROPN
ejpam-901	98	45	cho	cho	PROPN
ejpam-901	98	46	/	/	SYM
ejpam-901	98	47	eur	eur	PROPN
ejpam-901	98	48	.	.	PUNCT
ejpam-901	99	1	j.	j.	PROPN
ejpam-901	99	2	pure	pure	PROPN
ejpam-901	99	3	appl	appl	PROPN
ejpam-901	99	4	.	.	PROPN
ejpam-901	99	5	math	math	PROPN
ejpam-901	99	6	,	,	PUNCT
ejpam-901	99	7	3	3	NUM
ejpam-901	99	8	(	(	PUNCT
ejpam-901	99	9	2010	2010	NUM
ejpam-901	99	10	)	)	PUNCT
ejpam-901	99	11	,	,	PUNCT
ejpam-901	99	12	1124	1124	NUM
ejpam-901	99	13	-	-	SYM
ejpam-901	99	14	1136	1136	NUM
ejpam-901	99	15	1128	1128	NUM
ejpam-901	99	16	where	where	SCONJ
ejpam-901	99	17	µ(x	µ(x	VERB
ejpam-901	99	18	)	)	PUNCT
ejpam-901	99	19	is	be	AUX
ejpam-901	99	20	a	a	DET
ejpam-901	99	21	probability	probability	NOUN
ejpam-901	99	22	measure	measure	NOUN
ejpam-901	99	23	defined	define	VERB
ejpam-901	99	24	on	on	ADP
ejpam-901	99	25	the	the	DET
ejpam-901	99	26	unit	unit	NOUN
ejpam-901	99	27	circle	circle	NOUN
ejpam-901	99	28	|x	|x	PROPN
ejpam-901	100	1	|	|	ADV
ejpam-901	100	2	<	<	X
ejpam-901	100	3	1	1	NUM
ejpam-901	100	4	and	and	CCONJ
ejpam-901	100	5	∫	∫	PROPN
ejpam-901	100	6	|x	|x	PROPN
ejpam-901	100	7	|=1	|=1	PROPN
ejpam-901	100	8	dµ(x	dµ(x	PUNCT
ejpam-901	100	9	)	)	PUNCT
ejpam-901	100	10	=	=	SYM
ejpam-901	101	1	1	1	X
ejpam-901	101	2	.	.	PUNCT
ejpam-901	101	3	since	since	SCONJ
ejpam-901	101	4	h	h	NOUN
ejpam-901	101	5	is	be	AUX
ejpam-901	101	6	convex	convex	ADJ
ejpam-901	101	7	univalent	univalent	ADJ
ejpam-901	101	8	in	in	ADP
ejpam-901	101	9	u	u	PROPN
ejpam-901	101	10	,	,	PUNCT
ejpam-901	101	11	it	it	PRON
ejpam-901	101	12	follows	follow	VERB
ejpam-901	101	13	from	from	ADP
ejpam-901	101	14	(	(	PUNCT
ejpam-901	101	15	11	11	NUM
ejpam-901	101	16	)	)	PUNCT
ejpam-901	101	17	and	and	CCONJ
ejpam-901	101	18	(	(	PUNCT
ejpam-901	101	19	12	12	NUM
ejpam-901	101	20	)	)	PUNCT
ejpam-901	101	21	that	that	SCONJ
ejpam-901	101	22	(	(	PUNCT
ejpam-901	101	23	1−	1−	NUM
ejpam-901	101	24	γ	γ	X
ejpam-901	101	25	)	)	PUNCT
ejpam-901	101	26	i	i	PRON
ejpam-901	101	27	s	s	PART
ejpam-901	102	1	λ,µ1	λ,µ1	PROPN
ejpam-901	102	2	f	f	PROPN
ejpam-901	102	3	(	(	PUNCT
ejpam-901	102	4	z	z	NOUN
ejpam-901	102	5	)	)	PUNCT
ejpam-901	102	6	z	z	NOUN
ejpam-901	103	1	+	+	NUM
ejpam-901	103	2	γ(i	γ(i	NOUN
ejpam-901	103	3	s	s	PART
ejpam-901	103	4	λ,µ1	λ,µ1	PROPN
ejpam-901	103	5	f	f	X
ejpam-901	103	6	(	(	PUNCT
ejpam-901	103	7	z))′	z))′	PROPN
ejpam-901	103	8	=	=	SYM
ejpam-901	103	9	∫	∫	PROPN
ejpam-901	103	10	|x	|x	PROPN
ejpam-901	103	11	|=1	|=1	PROPN
ejpam-901	103	12	h(xz)dµ(x)≺	h(xz)dµ(x)≺	PROPN
ejpam-901	103	13	h(z	h(z	PROPN
ejpam-901	103	14	)	)	PUNCT
ejpam-901	103	15	,	,	PUNCT
ejpam-901	103	16	which	which	PRON
ejpam-901	103	17	completes	complete	VERB
ejpam-901	103	18	the	the	DET
ejpam-901	103	19	proof	proof	NOUN
ejpam-901	103	20	of	of	ADP
ejpam-901	103	21	theorem	theorem	ADJ
ejpam-901	103	22	9	9	NUM
ejpam-901	103	23	.	.	PUNCT
ejpam-901	103	24	theorem	theorem	NOUN
ejpam-901	103	25	3	3	NUM
ejpam-901	103	26	.	.	PUNCT
ejpam-901	104	1	if	if	SCONJ
ejpam-901	104	2	µ	µ	X
ejpam-901	104	3	>	>	X
ejpam-901	104	4	0	0	NUM
ejpam-901	104	5	,	,	PUNCT
ejpam-901	104	6	then	then	ADV
ejpam-901	104	7	t	t	PROPN
ejpam-901	104	8	s	s	PART
ejpam-901	104	9	λ,µ+1	λ,µ+1	PROPN
ejpam-901	104	10	(	(	PUNCT
ejpam-901	104	11	γ	γ	PROPN
ejpam-901	104	12	;	;	PUNCT
ejpam-901	104	13	h)⊂	h)⊂	PROPN
ejpam-901	104	14	t	t	PROPN
ejpam-901	104	15	s	s	PROPN
ejpam-901	104	16	λ,µ(γ;eh	λ,µ(γ;eh	PROPN
ejpam-901	104	17	)	)	PUNCT
ejpam-901	104	18	,	,	PUNCT
ejpam-901	104	19	where	where	SCONJ
ejpam-901	104	20	eh(z	eh(z	X
ejpam-901	104	21	)	)	PUNCT
ejpam-901	104	22	=	=	PRON
ejpam-901	104	23	µz−µ	µz−µ	NOUN
ejpam-901	105	1	∫	∫	PROPN
ejpam-901	105	2	z	z	NOUN
ejpam-901	105	3	0	0	NUM
ejpam-901	105	4	tµ−1h(t)d	tµ−1h(t)d	ADJ
ejpam-901	105	5	t	t	NOUN
ejpam-901	105	6	≺	≺	VERB
ejpam-901	105	7	h(z	h(z	NOUN
ejpam-901	105	8	)	)	PUNCT
ejpam-901	105	9	.	.	PUNCT
ejpam-901	106	1	proof	proof	NOUN
ejpam-901	106	2	.	.	PUNCT
ejpam-901	107	1	let	let	VERB
ejpam-901	107	2	g(z	g(z	ADJ
ejpam-901	107	3	)	)	PUNCT
ejpam-901	107	4	=	=	PUNCT
ejpam-901	107	5	(	(	PUNCT
ejpam-901	107	6	1−	1−	NUM
ejpam-901	107	7	γ	γ	X
ejpam-901	107	8	)	)	PUNCT
ejpam-901	108	1	i	i	PRON
ejpam-901	108	2	s	s	VERB
ejpam-901	108	3	λ,µ	λ,µ	PROPN
ejpam-901	108	4	f	f	PROPN
ejpam-901	108	5	(	(	PUNCT
ejpam-901	108	6	z	z	NOUN
ejpam-901	108	7	)	)	PUNCT
ejpam-901	108	8	z	z	NOUN
ejpam-901	109	1	+	+	NUM
ejpam-901	109	2	γ(i	γ(i	NOUN
ejpam-901	109	3	s	s	X
ejpam-901	109	4	λ,µ	λ,µ	NOUN
ejpam-901	109	5	f	f	PROPN
ejpam-901	109	6	(	(	PUNCT
ejpam-901	109	7	z))′	z))′	PROPN
ejpam-901	109	8	(	(	PUNCT
ejpam-901	109	9	f	f	PROPN
ejpam-901	109	10	∈a	∈a	PROPN
ejpam-901	109	11	;	;	PUNCT
ejpam-901	109	12	z	z	PROPN
ejpam-901	109	13	∈	∈	PROPN
ejpam-901	109	14	u	u	NOUN
ejpam-901	109	15	)	)	PUNCT
ejpam-901	109	16	.	.	PUNCT
ejpam-901	110	1	(	(	PUNCT
ejpam-901	110	2	13	13	NUM
ejpam-901	110	3	)	)	PUNCT
ejpam-901	110	4	then	then	ADV
ejpam-901	110	5	from	from	ADP
ejpam-901	110	6	(	(	PUNCT
ejpam-901	110	7	4	4	NUM
ejpam-901	110	8	)	)	PUNCT
ejpam-901	110	9	and	and	CCONJ
ejpam-901	110	10	(	(	PUNCT
ejpam-901	110	11	13	13	NUM
ejpam-901	110	12	)	)	PUNCT
ejpam-901	110	13	,	,	PUNCT
ejpam-901	110	14	we	we	PRON
ejpam-901	110	15	have	have	VERB
ejpam-901	110	16	zg(z	zg(z	NUM
ejpam-901	110	17	)	)	PUNCT
ejpam-901	110	18	=	=	PUNCT
ejpam-901	111	1	γµi	γµi	PROPN
ejpam-901	111	2	s	s	X
ejpam-901	111	3	λ,µ+1	λ,µ+1	PROPN
ejpam-901	111	4	f	f	X
ejpam-901	111	5	(	(	PUNCT
ejpam-901	111	6	z	z	NOUN
ejpam-901	111	7	)	)	PUNCT
ejpam-901	112	1	+	+	CCONJ
ejpam-901	112	2	(	(	PUNCT
ejpam-901	112	3	1−	1−	NUM
ejpam-901	112	4	γµ)i	γµ)i	PROPN
ejpam-901	112	5	s	s	X
ejpam-901	112	6	λ,µ	λ,µ	NOUN
ejpam-901	112	7	f	f	PROPN
ejpam-901	112	8	(	(	PUNCT
ejpam-901	112	9	z	z	NOUN
ejpam-901	112	10	)	)	PUNCT
ejpam-901	112	11	.	.	PUNCT
ejpam-901	113	1	(	(	PUNCT
ejpam-901	113	2	14	14	X
ejpam-901	113	3	)	)	PUNCT
ejpam-901	113	4	differentiating	differentiate	VERB
ejpam-901	113	5	both	both	DET
ejpam-901	113	6	sides	side	NOUN
ejpam-901	113	7	of	of	ADP
ejpam-901	113	8	(	(	PUNCT
ejpam-901	113	9	13	13	NUM
ejpam-901	113	10	)	)	PUNCT
ejpam-901	113	11	and	and	CCONJ
ejpam-901	113	12	using	use	VERB
ejpam-901	113	13	(	(	PUNCT
ejpam-901	113	14	4	4	NUM
ejpam-901	113	15	)	)	PUNCT
ejpam-901	113	16	again	again	ADV
ejpam-901	113	17	,	,	PUNCT
ejpam-901	113	18	we	we	PRON
ejpam-901	113	19	obtain	obtain	VERB
ejpam-901	113	20	z(zg′(z	z(zg′(z	NUM
ejpam-901	113	21	)	)	PUNCT
ejpam-901	114	1	+	+	CCONJ
ejpam-901	114	2	g(z	g(z	ADJ
ejpam-901	114	3	)	)	PUNCT
ejpam-901	114	4	)	)	PUNCT
ejpam-901	115	1	=	=	PUNCT
ejpam-901	116	1	γµz(i	γµz(i	PROPN
ejpam-901	116	2	s	s	VERB
ejpam-901	116	3	λ,µ+1	λ,µ+1	NOUN
ejpam-901	116	4	f	f	X
ejpam-901	116	5	(	(	PUNCT
ejpam-901	116	6	z	z	NOUN
ejpam-901	116	7	)	)	PUNCT
ejpam-901	116	8	)	)	PUNCT
ejpam-901	117	1	+	+	CCONJ
ejpam-901	117	2	(	(	PUNCT
ejpam-901	117	3	1−	1−	NUM
ejpam-901	117	4	γµ)(µi	γµ)(µi	PUNCT
ejpam-901	117	5	s	s	VERB
ejpam-901	117	6	λ,µ+1	λ,µ+1	ADJ
ejpam-901	117	7	f	f	X
ejpam-901	117	8	(	(	PUNCT
ejpam-901	117	9	z)−	z)−	PROPN
ejpam-901	117	10	(	(	PUNCT
ejpam-901	117	11	µ−	µ−	PROPN
ejpam-901	117	12	1)i	1)i	NUM
ejpam-901	117	13	s	s	PART
ejpam-901	117	14	λ,µ	λ,µ	PROPN
ejpam-901	117	15	f	f	PROPN
ejpam-901	117	16	(	(	PUNCT
ejpam-901	117	17	z	z	NOUN
ejpam-901	117	18	)	)	PUNCT
ejpam-901	117	19	)	)	PUNCT
ejpam-901	117	20	.	.	PUNCT
ejpam-901	118	1	(	(	PUNCT
ejpam-901	118	2	15	15	NUM
ejpam-901	118	3	)	)	PUNCT
ejpam-901	118	4	by	by	ADP
ejpam-901	118	5	a	a	DET
ejpam-901	118	6	simple	simple	ADJ
ejpam-901	118	7	calculation	calculation	NOUN
ejpam-901	118	8	with	with	ADP
ejpam-901	118	9	(	(	PUNCT
ejpam-901	118	10	14	14	NUM
ejpam-901	118	11	)	)	PUNCT
ejpam-901	118	12	and	and	CCONJ
ejpam-901	118	13	(	(	PUNCT
ejpam-901	118	14	15	15	NUM
ejpam-901	118	15	)	)	PUNCT
ejpam-901	118	16	,	,	PUNCT
ejpam-901	118	17	we	we	PRON
ejpam-901	118	18	get	get	VERB
ejpam-901	118	19	g(z	g(z	ADJ
ejpam-901	118	20	)	)	PUNCT
ejpam-901	119	1	+	+	CCONJ
ejpam-901	119	2	zg′(z	zg′(z	NOUN
ejpam-901	119	3	)	)	PUNCT
ejpam-901	119	4	µ	µ	X
ejpam-901	119	5	=	=	PUNCT
ejpam-901	119	6	(	(	PUNCT
ejpam-901	119	7	1−	1−	NUM
ejpam-901	119	8	γ	γ	X
ejpam-901	119	9	)	)	PUNCT
ejpam-901	119	10	i	i	PRON
ejpam-901	119	11	s	s	VERB
ejpam-901	119	12	λ,µ+1	λ,µ+1	PROPN
ejpam-901	119	13	f	f	X
ejpam-901	119	14	(	(	PUNCT
ejpam-901	119	15	z	z	NOUN
ejpam-901	119	16	)	)	PUNCT
ejpam-901	119	17	z	z	NOUN
ejpam-901	120	1	+	+	NUM
ejpam-901	120	2	γ(i	γ(i	NOUN
ejpam-901	120	3	s	s	PART
ejpam-901	120	4	λ,µ+1	λ,µ+1	NOUN
ejpam-901	120	5	f	f	X
ejpam-901	120	6	(	(	PUNCT
ejpam-901	120	7	z))′.	z))′.	PROPN
ejpam-901	120	8	(	(	PUNCT
ejpam-901	120	9	16	16	NUM
ejpam-901	120	10	)	)	PUNCT
ejpam-901	120	11	if	if	SCONJ
ejpam-901	120	12	f	f	PROPN
ejpam-901	120	13	∈	∈	PROPN
ejpam-901	120	14	t	t	PROPN
ejpam-901	120	15	s	s	PART
ejpam-901	120	16	λ,µ+1	λ,µ+1	PROPN
ejpam-901	120	17	(	(	PUNCT
ejpam-901	120	18	γ	γ	X
ejpam-901	120	19	;	;	PUNCT
ejpam-901	120	20	h	h	NOUN
ejpam-901	120	21	)	)	PUNCT
ejpam-901	120	22	,	,	PUNCT
ejpam-901	120	23	then	then	ADV
ejpam-901	120	24	it	it	PRON
ejpam-901	120	25	follows	follow	VERB
ejpam-901	120	26	from	from	ADP
ejpam-901	120	27	(	(	PUNCT
ejpam-901	120	28	16	16	NUM
ejpam-901	120	29	)	)	PUNCT
ejpam-901	120	30	that	that	SCONJ
ejpam-901	120	31	g(z	g(z	ADJ
ejpam-901	120	32	)	)	PUNCT
ejpam-901	121	1	+	+	CCONJ
ejpam-901	121	2	zg′(z	zg′(z	NOUN
ejpam-901	121	3	)	)	PUNCT
ejpam-901	121	4	µ	µ	NOUN
ejpam-901	121	5	≺	≺	NOUN
ejpam-901	121	6	h(z	h(z	NOUN
ejpam-901	121	7	)	)	PUNCT
ejpam-901	121	8	(	(	PUNCT
ejpam-901	121	9	µ	µ	X
ejpam-901	121	10	>	>	X
ejpam-901	121	11	0	0	NUM
ejpam-901	121	12	)	)	PUNCT
ejpam-901	121	13	.	.	PUNCT
ejpam-901	122	1	hence	hence	ADV
ejpam-901	122	2	an	an	DET
ejpam-901	122	3	application	application	NOUN
ejpam-901	122	4	of	of	ADP
ejpam-901	122	5	lemma	lemma	PROPN
ejpam-901	122	6	1	1	NUM
ejpam-901	122	7	yields	yield	NOUN
ejpam-901	122	8	g(z)≺eh(z	g(z)≺eh(z	NOUN
ejpam-901	122	9	)	)	PUNCT
ejpam-901	122	10	=	=	SYM
ejpam-901	122	11	µz−µ	µz−µ	NOUN
ejpam-901	123	1	∫	∫	PROPN
ejpam-901	123	2	z	z	NOUN
ejpam-901	123	3	0	0	NUM
ejpam-901	123	4	tµ−1h(t)d	tµ−1h(t)d	ADJ
ejpam-901	123	5	t	t	NOUN
ejpam-901	123	6	≺	≺	NOUN
ejpam-901	123	7	h(z	h(z	NOUN
ejpam-901	123	8	)	)	PUNCT
ejpam-901	123	9	,	,	PUNCT
ejpam-901	123	10	which	which	PRON
ejpam-901	123	11	shows	show	VERB
ejpam-901	123	12	that	that	SCONJ
ejpam-901	123	13	f	f	PROPN
ejpam-901	123	14	∈	∈	PROPN
ejpam-901	123	15	t	t	PROPN
ejpam-901	123	16	s	s	PART
ejpam-901	123	17	λ,µ+1	λ,µ+1	PROPN
ejpam-901	123	18	(	(	PUNCT
ejpam-901	123	19	γ;eh)⊂	γ;eh)⊂	PROPN
ejpam-901	123	20	t	t	PROPN
ejpam-901	123	21	s	s	PART
ejpam-901	123	22	λ,µ(γ	λ,µ(γ	NOUN
ejpam-901	123	23	;	;	PUNCT
ejpam-901	123	24	h	h	X
ejpam-901	123	25	)	)	PUNCT
ejpam-901	123	26	.	.	PUNCT
ejpam-901	124	1	o.	o.	PROPN
ejpam-901	124	2	kwon	kwon	PROPN
ejpam-901	124	3	,	,	PUNCT
ejpam-901	124	4	n.	n.	PROPN
ejpam-901	124	5	cho	cho	PROPN
ejpam-901	124	6	/	/	SYM
ejpam-901	124	7	eur	eur	PROPN
ejpam-901	124	8	.	.	PUNCT
ejpam-901	125	1	j.	j.	PROPN
ejpam-901	125	2	pure	pure	PROPN
ejpam-901	125	3	appl	appl	PROPN
ejpam-901	125	4	.	.	PROPN
ejpam-901	125	5	math	math	PROPN
ejpam-901	125	6	,	,	PUNCT
ejpam-901	125	7	3	3	NUM
ejpam-901	125	8	(	(	PUNCT
ejpam-901	125	9	2010	2010	NUM
ejpam-901	125	10	)	)	PUNCT
ejpam-901	125	11	,	,	PUNCT
ejpam-901	125	12	1124	1124	NUM
ejpam-901	125	13	-	-	SYM
ejpam-901	125	14	1136	1136	NUM
ejpam-901	125	15	1129	1129	NUM
ejpam-901	125	16	theorem	theorem	VERB
ejpam-901	125	17	4	4	NUM
ejpam-901	125	18	.	.	PUNCT
ejpam-901	126	1	if	if	SCONJ
ejpam-901	126	2	s	s	X
ejpam-901	126	3	∈	∈	PROPN
ejpam-901	126	4	r	r	NOUN
ejpam-901	126	5	and	and	CCONJ
ejpam-901	126	6	λ	λ	X
ejpam-901	126	7	>	>	X
ejpam-901	126	8	−1	−1	NOUN
ejpam-901	126	9	,	,	PUNCT
ejpam-901	126	10	then	then	ADV
ejpam-901	126	11	t	t	PROPN
ejpam-901	126	12	s	s	PART
ejpam-901	126	13	λ,µ(γ	λ,µ(γ	ADV
ejpam-901	126	14	;	;	PUNCT
ejpam-901	126	15	h)⊂	h)⊂	PROPN
ejpam-901	126	16	t	t	PROPN
ejpam-901	126	17	s+1	s+1	PROPN
ejpam-901	126	18	λ,µ	λ,µ	PROPN
ejpam-901	126	19	(	(	PUNCT
ejpam-901	126	20	γ;eh	γ;eh	PROPN
ejpam-901	126	21	)	)	PUNCT
ejpam-901	126	22	,	,	PUNCT
ejpam-901	126	23	where	where	SCONJ
ejpam-901	126	24	eh(z	eh(z	PRON
ejpam-901	126	25	)	)	PUNCT
ejpam-901	126	26	=	=	NOUN
ejpam-901	126	27	(	(	PUNCT
ejpam-901	126	28	λ+	λ+	X
ejpam-901	126	29	1)z−(λ+1	1)z−(λ+1	NUM
ejpam-901	126	30	)	)	PUNCT
ejpam-901	126	31	∫	∫	PROPN
ejpam-901	127	1	z	z	NOUN
ejpam-901	127	2	0	0	NUM
ejpam-901	128	1	tλh(t)d	tλh(t)d	PROPN
ejpam-901	128	2	t	t	PROPN
ejpam-901	128	3	≺	≺	VERB
ejpam-901	128	4	h(z	h(z	NOUN
ejpam-901	128	5	)	)	PUNCT
ejpam-901	128	6	.	.	PUNCT
ejpam-901	129	1	proof	proof	NOUN
ejpam-901	129	2	.	.	PUNCT
ejpam-901	130	1	by	by	ADP
ejpam-901	130	2	using	use	VERB
ejpam-901	130	3	the	the	DET
ejpam-901	130	4	same	same	ADJ
ejpam-901	130	5	techniques	technique	NOUN
ejpam-901	130	6	as	as	ADP
ejpam-901	130	7	in	in	ADP
ejpam-901	130	8	the	the	DET
ejpam-901	130	9	proof	proof	NOUN
ejpam-901	130	10	of	of	ADP
ejpam-901	130	11	theorem	theorem	ADJ
ejpam-901	130	12	3	3	NUM
ejpam-901	130	13	and	and	CCONJ
ejpam-901	130	14	(	(	PUNCT
ejpam-901	130	15	5	5	NUM
ejpam-901	130	16	)	)	PUNCT
ejpam-901	130	17	,	,	PUNCT
ejpam-901	130	18	we	we	PRON
ejpam-901	130	19	have	have	AUX
ejpam-901	130	20	theorem	theorem	VERB
ejpam-901	130	21	11	11	NUM
ejpam-901	130	22	and	and	CCONJ
ejpam-901	130	23	so	so	ADV
ejpam-901	130	24	we	we	PRON
ejpam-901	130	25	omit	omit	VERB
ejpam-901	130	26	the	the	DET
ejpam-901	130	27	detailed	detailed	ADJ
ejpam-901	130	28	proof	proof	NOUN
ejpam-901	130	29	involved	involve	VERB
ejpam-901	130	30	.	.	PUNCT
ejpam-901	131	1	theorem	theorem	NOUN
ejpam-901	131	2	5	5	NUM
ejpam-901	131	3	.	.	PUNCT
ejpam-901	132	1	let	let	VERB
ejpam-901	132	2	γ	γ	X
ejpam-901	132	3	>	>	X
ejpam-901	132	4	0	0	PROPN
ejpam-901	132	5	,	,	PUNCT
ejpam-901	132	6	β	β	X
ejpam-901	132	7	>	>	X
ejpam-901	132	8	0	0	PUNCT
ejpam-901	133	1	and	and	CCONJ
ejpam-901	133	2	f	f	PROPN
ejpam-901	133	3	∈	∈	PROPN
ejpam-901	133	4	t	t	PROPN
ejpam-901	133	5	s	s	X
ejpam-901	133	6	λ,µ	λ,µ	NOUN
ejpam-901	133	7	(	(	PUNCT
ejpam-901	133	8	γ;βh+	γ;βh+	NOUN
ejpam-901	133	9	1−	1−	NUM
ejpam-901	133	10	β	β	NOUN
ejpam-901	133	11	)	)	PUNCT
ejpam-901	133	12	.	.	PUNCT
ejpam-901	134	1	if	if	SCONJ
ejpam-901	134	2	β	β	PROPN
ejpam-901	134	3	≤	≤	PROPN
ejpam-901	134	4	β0	β0	NOUN
ejpam-901	134	5	,	,	PUNCT
ejpam-901	134	6	where	where	SCONJ
ejpam-901	134	7	β0	β0	NOUN
ejpam-901	134	8	=	=	NOUN
ejpam-901	134	9	1	1	NUM
ejpam-901	134	10	2	2	NUM
ejpam-901	134	11			NOUN
ejpam-901	134	12	1−	1−	PROPN
ejpam-901	134	13	1	1	NUM
ejpam-901	134	14	γ	γ	X
ejpam-901	134	15	∫	∫	PROPN
ejpam-901	134	16	1	1	NUM
ejpam-901	134	17	0	0	NUM
ejpam-901	134	18	u	u	NOUN
ejpam-901	134	19	1	1	NUM
ejpam-901	134	20	γ	γ	NOUN
ejpam-901	134	21	−1	−1	NOUN
ejpam-901	134	22	1	1	NUM
ejpam-901	134	23	+	+	SYM
ejpam-901	134	24	u	u	X
ejpam-901	134	25	du	du	X
ejpam-901	134	26			PROPN
ejpam-901	135	1			PROPN
ejpam-901	135	2	−1	−1	NOUN
ejpam-901	135	3	,	,	PUNCT
ejpam-901	135	4	(	(	PUNCT
ejpam-901	135	5	17	17	NUM
ejpam-901	135	6	)	)	PUNCT
ejpam-901	136	1	then	then	ADV
ejpam-901	136	2	f	f	PROPN
ejpam-901	136	3	∈	∈	PROPN
ejpam-901	136	4	t	t	PROPN
ejpam-901	136	5	s	s	X
ejpam-901	136	6	λ,µ	λ,µ	NOUN
ejpam-901	136	7	(	(	PUNCT
ejpam-901	136	8	0	0	NUM
ejpam-901	136	9	;	;	PUNCT
ejpam-901	136	10	h	h	NOUN
ejpam-901	136	11	)	)	PUNCT
ejpam-901	136	12	.	.	PUNCT
ejpam-901	137	1	the	the	DET
ejpam-901	137	2	bound	bind	VERB
ejpam-901	137	3	β0	β0	NOUN
ejpam-901	137	4	is	be	AUX
ejpam-901	137	5	sharp	sharp	ADJ
ejpam-901	137	6	for	for	ADP
ejpam-901	137	7	the	the	DET
ejpam-901	137	8	function	function	NOUN
ejpam-901	137	9	h(z	h(z	NOUN
ejpam-901	137	10	)	)	PUNCT
ejpam-901	137	11	=	=	SYM
ejpam-901	137	12	1	1	NUM
ejpam-901	137	13	1−	1−	NUM
ejpam-901	137	14	z	z	NOUN
ejpam-901	137	15	(	(	PUNCT
ejpam-901	137	16	z	z	NOUN
ejpam-901	137	17	∈	∈	PROPN
ejpam-901	137	18	u	u	NOUN
ejpam-901	137	19	)	)	PUNCT
ejpam-901	137	20	.	.	PUNCT
ejpam-901	138	1	proof	proof	NOUN
ejpam-901	138	2	.	.	PUNCT
ejpam-901	139	1	let	let	VERB
ejpam-901	139	2	g(z	g(z	ADJ
ejpam-901	139	3	)	)	PUNCT
ejpam-901	140	1	=	=	PUNCT
ejpam-901	141	1	i	i	PRON
ejpam-901	141	2	s	s	VERB
ejpam-901	141	3	λ,µ	λ,µ	PROPN
ejpam-901	141	4	f	f	PROPN
ejpam-901	141	5	(	(	PUNCT
ejpam-901	141	6	z	z	NOUN
ejpam-901	141	7	)	)	PUNCT
ejpam-901	141	8	z	z	NOUN
ejpam-901	142	1	(	(	PUNCT
ejpam-901	142	2	f	f	PROPN
ejpam-901	142	3	∈	∈	PROPN
ejpam-901	142	4	t	t	PROPN
ejpam-901	142	5	s	s	PART
ejpam-901	142	6	λ,µ(γ;βh+	λ,µ(γ;βh+	X
ejpam-901	142	7	1−	1−	NUM
ejpam-901	142	8	β);γ	β);γ	NUM
ejpam-901	142	9	>	>	X
ejpam-901	142	10	0;β	0;β	X
ejpam-901	142	11	>	>	X
ejpam-901	142	12	0	0	NUM
ejpam-901	142	13	)	)	PUNCT
ejpam-901	142	14	.	.	PUNCT
ejpam-901	143	1	(	(	PUNCT
ejpam-901	143	2	18	18	NUM
ejpam-901	143	3	)	)	PUNCT
ejpam-901	143	4	then	then	ADV
ejpam-901	143	5	we	we	PRON
ejpam-901	143	6	have	have	VERB
ejpam-901	143	7	g(z	g(z	PROPN
ejpam-901	143	8	)	)	PUNCT
ejpam-901	144	1	+	+	NUM
ejpam-901	144	2	γzg′(z	γzg′(z	NOUN
ejpam-901	144	3	)	)	PUNCT
ejpam-901	144	4	=	=	SYM
ejpam-901	144	5	(	(	PUNCT
ejpam-901	144	6	1−	1−	NUM
ejpam-901	144	7	γ	γ	X
ejpam-901	144	8	)	)	PUNCT
ejpam-901	144	9	i	i	PRON
ejpam-901	144	10	s	s	VERB
ejpam-901	144	11	λ,µ	λ,µ	PROPN
ejpam-901	144	12	f	f	PROPN
ejpam-901	144	13	(	(	PUNCT
ejpam-901	144	14	z	z	NOUN
ejpam-901	144	15	)	)	PUNCT
ejpam-901	144	16	z	z	NOUN
ejpam-901	145	1	+	+	NUM
ejpam-901	145	2	γ(i	γ(i	NOUN
ejpam-901	145	3	s	s	X
ejpam-901	145	4	λ,µ	λ,µ	NOUN
ejpam-901	145	5	f	f	PROPN
ejpam-901	145	6	(	(	PUNCT
ejpam-901	145	7	z))′	z))′	X
ejpam-901	145	8	≺	≺	NOUN
ejpam-901	145	9	βh(z	βh(z	PUNCT
ejpam-901	145	10	)	)	PUNCT
ejpam-901	146	1	+	+	CCONJ
ejpam-901	146	2	1−	1−	NUM
ejpam-901	146	3	β	β	X
ejpam-901	146	4	.	.	PUNCT
ejpam-901	147	1	hence	hence	ADV
ejpam-901	147	2	an	an	DET
ejpam-901	147	3	application	application	NOUN
ejpam-901	147	4	of	of	ADP
ejpam-901	147	5	lemma	lemma	PROPN
ejpam-901	147	6	1	1	NUM
ejpam-901	147	7	yields	yield	NOUN
ejpam-901	147	8	g(z	g(z	PROPN
ejpam-901	147	9	)	)	PUNCT
ejpam-901	147	10	≺	≺	NOUN
ejpam-901	147	11	β	β	X
ejpam-901	147	12	γ	γ	X
ejpam-901	147	13	z	z	PROPN
ejpam-901	147	14	−	−	PROPN
ejpam-901	147	15	1	1	NUM
ejpam-901	147	16	γ	γ	X
ejpam-901	147	17	∫	∫	PROPN
ejpam-901	147	18	z	z	PROPN
ejpam-901	147	19	0	0	NUM
ejpam-901	147	20	t	t	PROPN
ejpam-901	147	21	1	1	NUM
ejpam-901	147	22	γ	γ	NOUN
ejpam-901	147	23	−1	−1	NOUN
ejpam-901	147	24	h(t)d	h(t)d	PROPN
ejpam-901	147	25	t	t	PROPN
ejpam-901	147	26	+	+	CCONJ
ejpam-901	147	27	1−	1−	NUM
ejpam-901	147	28	β	β	X
ejpam-901	147	29	=	=	SYM
ejpam-901	147	30	(	(	PUNCT
ejpam-901	147	31	h	h	NOUN
ejpam-901	147	32	∗ψ)(z	∗ψ)(z	NOUN
ejpam-901	147	33	)	)	PUNCT
ejpam-901	147	34	,	,	PUNCT
ejpam-901	147	35	(	(	PUNCT
ejpam-901	147	36	19	19	NUM
ejpam-901	147	37	)	)	PUNCT
ejpam-901	147	38	where	where	SCONJ
ejpam-901	147	39	ψ(z	ψ(z	NOUN
ejpam-901	147	40	)	)	PUNCT
ejpam-901	147	41	=	=	PUNCT
ejpam-901	147	42	β	β	X
ejpam-901	147	43	γ	γ	X
ejpam-901	147	44	z	z	PROPN
ejpam-901	147	45	−	−	PROPN
ejpam-901	147	46	1	1	NUM
ejpam-901	147	47	γ	γ	X
ejpam-901	147	48	∫	∫	PROPN
ejpam-901	147	49	z	z	PROPN
ejpam-901	147	50	0	0	NUM
ejpam-901	147	51	t	t	PROPN
ejpam-901	147	52	1	1	NUM
ejpam-901	147	53	γ	γ	NOUN
ejpam-901	147	54	−1	−1	NOUN
ejpam-901	147	55	1−	1−	NUM
ejpam-901	147	56	t	t	PROPN
ejpam-901	147	57	d	d	X
ejpam-901	147	58	t	t	PROPN
ejpam-901	147	59	+	+	CCONJ
ejpam-901	147	60	1−	1−	NUM
ejpam-901	147	61	β	β	X
ejpam-901	147	62	.	.	PUNCT
ejpam-901	148	1	(	(	PUNCT
ejpam-901	148	2	20	20	NUM
ejpam-901	148	3	)	)	PUNCT
ejpam-901	148	4	if	if	SCONJ
ejpam-901	148	5	0	0	NUM
ejpam-901	148	6	<	<	X
ejpam-901	148	7	β	β	X
ejpam-901	148	8	≤	≤	PROPN
ejpam-901	148	9	β0	β0	NOUN
ejpam-901	148	10	,	,	PUNCT
ejpam-901	148	11	where	where	SCONJ
ejpam-901	148	12	β0	β0	PROPN
ejpam-901	148	13	is	be	AUX
ejpam-901	148	14	given	give	VERB
ejpam-901	148	15	by	by	ADP
ejpam-901	148	16	(	(	PUNCT
ejpam-901	148	17	17	17	NUM
ejpam-901	148	18	)	)	PUNCT
ejpam-901	148	19	,	,	PUNCT
ejpam-901	148	20	then	then	ADV
ejpam-901	148	21	from	from	ADP
ejpam-901	148	22	(	(	PUNCT
ejpam-901	148	23	20	20	NUM
ejpam-901	148	24	)	)	PUNCT
ejpam-901	148	25	,	,	PUNCT
ejpam-901	148	26	we	we	PRON
ejpam-901	148	27	have	have	VERB
ejpam-901	148	28	o.	o.	PROPN
ejpam-901	148	29	kwon	kwon	PROPN
ejpam-901	148	30	,	,	PUNCT
ejpam-901	148	31	n.	n.	PROPN
ejpam-901	148	32	cho	cho	PROPN
ejpam-901	148	33	/	/	SYM
ejpam-901	148	34	eur	eur	PROPN
ejpam-901	148	35	.	.	PUNCT
ejpam-901	149	1	j.	j.	PROPN
ejpam-901	149	2	pure	pure	PROPN
ejpam-901	149	3	appl	appl	PROPN
ejpam-901	149	4	.	.	PROPN
ejpam-901	149	5	math	math	PROPN
ejpam-901	149	6	,	,	PUNCT
ejpam-901	149	7	3	3	NUM
ejpam-901	149	8	(	(	PUNCT
ejpam-901	149	9	2010	2010	NUM
ejpam-901	149	10	)	)	PUNCT
ejpam-901	149	11	,	,	PUNCT
ejpam-901	149	12	1124	1124	NUM
ejpam-901	149	13	-	-	SYM
ejpam-901	149	14	1136	1136	NUM
ejpam-901	149	15	1130	1130	NUM
ejpam-901	149	16	re{ψ(z	re{ψ(z	NOUN
ejpam-901	149	17	)	)	PUNCT
ejpam-901	149	18	}	}	PUNCT
ejpam-901	149	19	=	=	PUNCT
ejpam-901	149	20	β	β	X
ejpam-901	149	21	γ	γ	X
ejpam-901	149	22	∫	∫	PROPN
ejpam-901	149	23	1	1	NUM
ejpam-901	149	24	0	0	NUM
ejpam-901	149	25	u	u	NOUN
ejpam-901	149	26	1	1	NUM
ejpam-901	149	27	γ	γ	NOUN
ejpam-901	149	28	−1	−1	NOUN
ejpam-901	149	29	re	re	ADP
ejpam-901	149	30	�	�	PROPN
ejpam-901	149	31	1	1	NUM
ejpam-901	149	32	1−	1−	NUM
ejpam-901	149	33	uz	uz	PROPN
ejpam-901	149	34	du	du	PROPN
ejpam-901	149	35	�	�	PROPN
ejpam-901	149	36	+	+	CCONJ
ejpam-901	149	37	1−	1−	NUM
ejpam-901	149	38	β	β	X
ejpam-901	149	39	>	>	X
ejpam-901	149	40	β	β	X
ejpam-901	149	41	γ	γ	X
ejpam-901	149	42	∫	∫	PROPN
ejpam-901	149	43	1	1	NUM
ejpam-901	149	44	0	0	NUM
ejpam-901	149	45	u	u	NOUN
ejpam-901	149	46	1	1	NUM
ejpam-901	149	47	γ	γ	NOUN
ejpam-901	149	48	−1	−1	NOUN
ejpam-901	149	49	1	1	NUM
ejpam-901	149	50	+	+	NUM
ejpam-901	149	51	u	u	NOUN
ejpam-901	149	52	du+	du+	NOUN
ejpam-901	149	53	1−	1−	NUM
ejpam-901	149	54	β	β	X
ejpam-901	149	55	≥	≥	NUM
ejpam-901	149	56	1	1	NUM
ejpam-901	149	57	2	2	NUM
ejpam-901	149	58	.	.	PUNCT
ejpam-901	150	1	by	by	ADP
ejpam-901	150	2	using	use	VERB
ejpam-901	150	3	the	the	DET
ejpam-901	150	4	herglotz	herglotz	NOUN
ejpam-901	150	5	representation	representation	NOUN
ejpam-901	150	6	for	for	ADP
ejpam-901	150	7	ψ	ψ	NOUN
ejpam-901	150	8	,	,	PUNCT
ejpam-901	150	9	it	it	PRON
ejpam-901	150	10	follows	follow	VERB
ejpam-901	150	11	from	from	ADP
ejpam-901	150	12	(	(	PUNCT
ejpam-901	150	13	18	18	NUM
ejpam-901	150	14	)	)	PUNCT
ejpam-901	150	15	and	and	CCONJ
ejpam-901	150	16	(	(	PUNCT
ejpam-901	150	17	19	19	NUM
ejpam-901	150	18	)	)	PUNCT
ejpam-901	150	19	that	that	SCONJ
ejpam-901	150	20	i	i	PRON
ejpam-901	150	21	s	s	VERB
ejpam-901	150	22	λ,µ	λ,µ	PROPN
ejpam-901	150	23	f	f	PROPN
ejpam-901	150	24	(	(	PUNCT
ejpam-901	150	25	z	z	NOUN
ejpam-901	150	26	)	)	PUNCT
ejpam-901	150	27	z	z	NOUN
ejpam-901	150	28	≺	≺	NOUN
ejpam-901	150	29	(	(	PUNCT
ejpam-901	150	30	h	h	NOUN
ejpam-901	150	31	∗ψ)(z)≺	∗ψ)(z)≺	NUM
ejpam-901	150	32	h(z	h(z	NOUN
ejpam-901	150	33	)	)	PUNCT
ejpam-901	150	34	,	,	PUNCT
ejpam-901	150	35	since	since	SCONJ
ejpam-901	150	36	h	h	NOUN
ejpam-901	150	37	is	be	AUX
ejpam-901	150	38	convex	convex	ADJ
ejpam-901	150	39	univalent	univalent	ADJ
ejpam-901	150	40	in	in	ADP
ejpam-901	150	41	u.	u.	PROPN
ejpam-901	150	42	this	this	PRON
ejpam-901	150	43	shows	show	VERB
ejpam-901	150	44	that	that	SCONJ
ejpam-901	150	45	f	f	PROPN
ejpam-901	150	46	∈	∈	PROPN
ejpam-901	150	47	t	t	PROPN
ejpam-901	150	48	s	s	X
ejpam-901	150	49	λ,µ	λ,µ	NOUN
ejpam-901	150	50	(	(	PUNCT
ejpam-901	150	51	0	0	NUM
ejpam-901	150	52	;	;	PUNCT
ejpam-901	150	53	h	h	NOUN
ejpam-901	150	54	)	)	PUNCT
ejpam-901	150	55	.	.	PUNCT
ejpam-901	151	1	for	for	ADP
ejpam-901	151	2	h(z	h(z	NOUN
ejpam-901	151	3	)	)	PUNCT
ejpam-901	151	4	=	=	PUNCT
ejpam-901	151	5	1/(1−	1/(1−	NUM
ejpam-901	151	6	z	z	NOUN
ejpam-901	151	7	)	)	PUNCT
ejpam-901	151	8	and	and	CCONJ
ejpam-901	151	9	f	f	PROPN
ejpam-901	151	10	∈a	∈a	VERB
ejpam-901	151	11	defined	define	VERB
ejpam-901	151	12	by	by	ADP
ejpam-901	151	13	i	i	PRON
ejpam-901	151	14	s	s	PROPN
ejpam-901	151	15	λ,µ	λ,µ	PROPN
ejpam-901	151	16	f	f	PROPN
ejpam-901	151	17	(	(	PUNCT
ejpam-901	151	18	z	z	NOUN
ejpam-901	151	19	)	)	PUNCT
ejpam-901	151	20	z	z	NOUN
ejpam-901	151	21	=	=	PUNCT
ejpam-901	151	22	β	β	X
ejpam-901	151	23	γ	γ	X
ejpam-901	151	24	z	z	PROPN
ejpam-901	151	25	−	−	PROPN
ejpam-901	151	26	1	1	NUM
ejpam-901	151	27	γ	γ	X
ejpam-901	151	28	∫	∫	PROPN
ejpam-901	151	29	z	z	PROPN
ejpam-901	151	30	0	0	NUM
ejpam-901	151	31	t	t	PROPN
ejpam-901	151	32	1	1	NUM
ejpam-901	151	33	γ	γ	NOUN
ejpam-901	151	34	−1	−1	NOUN
ejpam-901	151	35	1−	1−	NUM
ejpam-901	151	36	t	t	PROPN
ejpam-901	151	37	d	d	X
ejpam-901	151	38	t	t	PROPN
ejpam-901	151	39	+	+	CCONJ
ejpam-901	151	40	1−	1−	NUM
ejpam-901	151	41	β	β	X
ejpam-901	151	42	,	,	PUNCT
ejpam-901	151	43	it	it	PRON
ejpam-901	151	44	is	be	AUX
ejpam-901	151	45	easy	easy	ADJ
ejpam-901	151	46	to	to	PART
ejpam-901	151	47	verify	verify	VERB
ejpam-901	151	48	that	that	SCONJ
ejpam-901	151	49	(	(	PUNCT
ejpam-901	151	50	1−	1−	NUM
ejpam-901	151	51	γ	γ	X
ejpam-901	151	52	)	)	PUNCT
ejpam-901	151	53	i	i	PRON
ejpam-901	151	54	s	s	VERB
ejpam-901	151	55	λ,µ	λ,µ	PROPN
ejpam-901	151	56	f	f	PROPN
ejpam-901	151	57	(	(	PUNCT
ejpam-901	151	58	z	z	NOUN
ejpam-901	151	59	)	)	PUNCT
ejpam-901	151	60	z	z	NOUN
ejpam-901	152	1	+	+	NUM
ejpam-901	152	2	γ(i	γ(i	NOUN
ejpam-901	152	3	s	s	X
ejpam-901	152	4	λ,µ	λ,µ	NOUN
ejpam-901	152	5	f	f	PROPN
ejpam-901	152	6	(	(	PUNCT
ejpam-901	152	7	z))′	z))′	PROPN
ejpam-901	152	8	=	=	PUNCT
ejpam-901	152	9	βh(z	βh(z	X
ejpam-901	152	10	)	)	PUNCT
ejpam-901	153	1	+	+	CCONJ
ejpam-901	153	2	1−	1−	NUM
ejpam-901	153	3	β	β	X
ejpam-901	153	4	.	.	PUNCT
ejpam-901	154	1	thus	thus	ADV
ejpam-901	154	2	f	f	PROPN
ejpam-901	154	3	∈	∈	PROPN
ejpam-901	154	4	t	t	PROPN
ejpam-901	154	5	s	s	X
ejpam-901	154	6	λ,µ	λ,µ	NOUN
ejpam-901	154	7	(	(	PUNCT
ejpam-901	154	8	γ;βh+	γ;βh+	NOUN
ejpam-901	154	9	1−	1−	NUM
ejpam-901	154	10	β	β	NOUN
ejpam-901	154	11	)	)	PUNCT
ejpam-901	154	12	.	.	PUNCT
ejpam-901	155	1	furthermore	furthermore	ADV
ejpam-901	155	2	,	,	PUNCT
ejpam-901	155	3	for	for	ADP
ejpam-901	155	4	β	β	X
ejpam-901	155	5	>	>	X
ejpam-901	155	6	β0	β0	PROPN
ejpam-901	155	7	,	,	PUNCT
ejpam-901	155	8	we	we	PRON
ejpam-901	155	9	have	have	AUX
ejpam-901	155	10	re	re	VERB
ejpam-901	155	11	(	(	PUNCT
ejpam-901	155	12	i	i	PRON
ejpam-901	155	13	s	s	VERB
ejpam-901	155	14	λ,µ	λ,µ	PROPN
ejpam-901	155	15	f	f	PROPN
ejpam-901	155	16	(	(	PUNCT
ejpam-901	155	17	z	z	NOUN
ejpam-901	155	18	)	)	PUNCT
ejpam-901	155	19	z	z	NOUN
ejpam-901	155	20	)	)	PUNCT
ejpam-901	155	21	to	to	ADP
ejpam-901	155	22	β	β	PROPN
ejpam-901	155	23	γ	γ	X
ejpam-901	155	24	∫	∫	PROPN
ejpam-901	155	25	1	1	NUM
ejpam-901	155	26	0	0	NUM
ejpam-901	155	27	u	u	NOUN
ejpam-901	155	28	1	1	NUM
ejpam-901	155	29	γ	γ	NOUN
ejpam-901	155	30	−1	−1	NOUN
ejpam-901	155	31	1	1	NUM
ejpam-901	155	32	+	+	NUM
ejpam-901	155	33	u	u	NOUN
ejpam-901	155	34	du+	du+	NOUN
ejpam-901	155	35	1−	1−	NUM
ejpam-901	155	36	β	β	X
ejpam-901	155	37	<	<	X
ejpam-901	155	38	1	1	NUM
ejpam-901	155	39	2	2	NUM
ejpam-901	155	40	(	(	PUNCT
ejpam-901	155	41	z→−1	z→−1	NUM
ejpam-901	155	42	)	)	PUNCT
ejpam-901	155	43	,	,	PUNCT
ejpam-901	155	44	which	which	PRON
ejpam-901	155	45	implies	imply	VERB
ejpam-901	155	46	that	that	SCONJ
ejpam-901	155	47	f	f	PROPN
ejpam-901	155	48	6∈	6∈	PROPN
ejpam-901	155	49	t	t	PROPN
ejpam-901	155	50	s	s	X
ejpam-901	155	51	λ,µ	λ,µ	NOUN
ejpam-901	155	52	(	(	PUNCT
ejpam-901	155	53	0	0	NUM
ejpam-901	155	54	;	;	PUNCT
ejpam-901	155	55	h	h	NOUN
ejpam-901	155	56	)	)	PUNCT
ejpam-901	155	57	.	.	PUNCT
ejpam-901	156	1	hence	hence	ADV
ejpam-901	156	2	the	the	DET
ejpam-901	156	3	bound	bind	VERB
ejpam-901	156	4	β0	β0	NOUN
ejpam-901	156	5	can	can	AUX
ejpam-901	156	6	not	not	PART
ejpam-901	156	7	be	be	AUX
ejpam-901	156	8	increased	increase	VERB
ejpam-901	156	9	when	when	SCONJ
ejpam-901	156	10	h(z	h(z	NOUN
ejpam-901	156	11	)	)	PUNCT
ejpam-901	156	12	=	=	PUNCT
ejpam-901	157	1	1/(1−	1/(1−	NUM
ejpam-901	157	2	z	z	NOUN
ejpam-901	157	3	)	)	PUNCT
ejpam-901	157	4	(	(	PUNCT
ejpam-901	157	5	z	z	NOUN
ejpam-901	157	6	∈	∈	PROPN
ejpam-901	157	7	u	u	NOUN
ejpam-901	157	8	)	)	PUNCT
ejpam-901	157	9	.	.	PUNCT
ejpam-901	158	1	3	3	X
ejpam-901	158	2	.	.	X
ejpam-901	158	3	convolution	convolution	NOUN
ejpam-901	158	4	properties	property	NOUN
ejpam-901	158	5	theorem	theorem	VERB
ejpam-901	158	6	6	6	NUM
ejpam-901	158	7	.	.	PUNCT
ejpam-901	159	1	if	if	SCONJ
ejpam-901	159	2	f	f	PROPN
ejpam-901	159	3	∈	∈	PROPN
ejpam-901	159	4	t	t	PROPN
ejpam-901	159	5	s	s	X
ejpam-901	159	6	λ,µ	λ,µ	X
ejpam-901	159	7	(	(	PUNCT
ejpam-901	159	8	γ	γ	X
ejpam-901	159	9	;	;	PUNCT
ejpam-901	159	10	h	h	NOUN
ejpam-901	159	11	)	)	PUNCT
ejpam-901	159	12	and	and	CCONJ
ejpam-901	159	13	re	re	VERB
ejpam-901	159	14	�	�	PROPN
ejpam-901	159	15	g(z	g(z	PROPN
ejpam-901	159	16	)	)	PUNCT
ejpam-901	159	17	z	z	PROPN
ejpam-901	159	18	�	�	PROPN
ejpam-901	159	19	>	>	SYM
ejpam-901	159	20	1	1	NUM
ejpam-901	159	21	2	2	NUM
ejpam-901	159	22	(	(	PUNCT
ejpam-901	159	23	g	g	PROPN
ejpam-901	159	24	∈a	∈a	NUM
ejpam-901	159	25	;	;	PUNCT
ejpam-901	159	26	z	z	PROPN
ejpam-901	159	27	∈	∈	PROPN
ejpam-901	159	28	u	u	NOUN
ejpam-901	159	29	)	)	PUNCT
ejpam-901	159	30	,	,	PUNCT
ejpam-901	159	31	then	then	ADV
ejpam-901	159	32	f	f	PROPN
ejpam-901	159	33	∗	∗	VERB
ejpam-901	159	34	g	g	PROPN
ejpam-901	159	35	∈	∈	PROPN
ejpam-901	159	36	t	t	PROPN
ejpam-901	159	37	s	s	PART
ejpam-901	159	38	λ,µ(γ	λ,µ(γ	NOUN
ejpam-901	159	39	;	;	PUNCT
ejpam-901	159	40	h	h	X
ejpam-901	159	41	)	)	PUNCT
ejpam-901	159	42	.	.	PUNCT
ejpam-901	160	1	o.	o.	PROPN
ejpam-901	160	2	kwon	kwon	PROPN
ejpam-901	160	3	,	,	PUNCT
ejpam-901	160	4	n.	n.	PROPN
ejpam-901	160	5	cho	cho	PROPN
ejpam-901	160	6	/	/	SYM
ejpam-901	160	7	eur	eur	PROPN
ejpam-901	160	8	.	.	PUNCT
ejpam-901	161	1	j.	j.	PROPN
ejpam-901	161	2	pure	pure	PROPN
ejpam-901	161	3	appl	appl	PROPN
ejpam-901	161	4	.	.	PROPN
ejpam-901	161	5	math	math	PROPN
ejpam-901	161	6	,	,	PUNCT
ejpam-901	161	7	3	3	NUM
ejpam-901	161	8	(	(	PUNCT
ejpam-901	161	9	2010	2010	NUM
ejpam-901	161	10	)	)	PUNCT
ejpam-901	161	11	,	,	PUNCT
ejpam-901	161	12	1124	1124	NUM
ejpam-901	161	13	-	-	SYM
ejpam-901	161	14	1136	1136	NUM
ejpam-901	161	15	1131	1131	NUM
ejpam-901	161	16	proof	proof	NOUN
ejpam-901	161	17	.	.	PUNCT
ejpam-901	162	1	let	let	VERB
ejpam-901	162	2	f	f	PROPN
ejpam-901	162	3	∈	∈	PROPN
ejpam-901	162	4	t	t	PROPN
ejpam-901	162	5	s	s	X
ejpam-901	162	6	λ,µ	λ,µ	X
ejpam-901	162	7	(	(	PUNCT
ejpam-901	162	8	γ	γ	X
ejpam-901	162	9	;	;	PUNCT
ejpam-901	162	10	h	h	NOUN
ejpam-901	162	11	)	)	PUNCT
ejpam-901	162	12	and	and	CCONJ
ejpam-901	162	13	g	g	PROPN
ejpam-901	162	14	∈a	∈a	PROPN
ejpam-901	162	15	.	.	PUNCT
ejpam-901	163	1	then	then	ADV
ejpam-901	163	2	we	we	PRON
ejpam-901	163	3	have	have	VERB
ejpam-901	163	4	(	(	PUNCT
ejpam-901	163	5	1−	1−	NUM
ejpam-901	163	6	γ	γ	X
ejpam-901	163	7	)	)	PUNCT
ejpam-901	163	8	i	i	PRON
ejpam-901	163	9	s	s	VERB
ejpam-901	163	10	λ,µ	λ,µ	INTJ
ejpam-901	164	1	(	(	PUNCT
ejpam-901	164	2	f	f	PROPN
ejpam-901	164	3	∗	∗	PROPN
ejpam-901	164	4	g)(z	g)(z	PROPN
ejpam-901	164	5	)	)	PUNCT
ejpam-901	164	6	z	z	NOUN
ejpam-901	165	1	+	+	NUM
ejpam-901	165	2	γ(i	γ(i	NOUN
ejpam-901	165	3	s	s	X
ejpam-901	165	4	λ,µ	λ,µ	NOUN
ejpam-901	165	5	(	(	PUNCT
ejpam-901	165	6	f	f	PROPN
ejpam-901	165	7	∗	∗	NOUN
ejpam-901	165	8	g)(z))′	g)(z))′	X
ejpam-901	165	9	=	=	PUNCT
ejpam-901	165	10	g(z	g(z	PROPN
ejpam-901	165	11	)	)	PUNCT
ejpam-901	165	12	z	z	NOUN
ejpam-901	165	13	∗ψ(z	∗ψ(z	PROPN
ejpam-901	165	14	)	)	PUNCT
ejpam-901	165	15	,	,	PUNCT
ejpam-901	165	16	where	where	SCONJ
ejpam-901	165	17	ψ(z	ψ(z	NOUN
ejpam-901	165	18	)	)	PUNCT
ejpam-901	165	19	=	=	PUNCT
ejpam-901	165	20	(	(	PUNCT
ejpam-901	165	21	1−	1−	NUM
ejpam-901	165	22	γ	γ	X
ejpam-901	165	23	)	)	PUNCT
ejpam-901	165	24	i	i	PRON
ejpam-901	165	25	s	s	VERB
ejpam-901	165	26	λ,µ	λ,µ	PROPN
ejpam-901	165	27	f	f	PROPN
ejpam-901	165	28	(	(	PUNCT
ejpam-901	165	29	z	z	NOUN
ejpam-901	165	30	)	)	PUNCT
ejpam-901	165	31	z	z	NOUN
ejpam-901	166	1	+	+	NUM
ejpam-901	166	2	γ(i	γ(i	NOUN
ejpam-901	166	3	s	s	X
ejpam-901	166	4	λ,µ	λ,µ	NOUN
ejpam-901	166	5	f	f	PROPN
ejpam-901	166	6	(	(	PUNCT
ejpam-901	166	7	z))′	z))′	X
ejpam-901	166	8	≺	≺	NOUN
ejpam-901	166	9	h(z	h(z	NOUN
ejpam-901	166	10	)	)	PUNCT
ejpam-901	166	11	.	.	PUNCT
ejpam-901	167	1	the	the	DET
ejpam-901	167	2	remaining	remain	VERB
ejpam-901	167	3	part	part	NOUN
ejpam-901	167	4	of	of	ADP
ejpam-901	167	5	the	the	DET
ejpam-901	167	6	proof	proof	NOUN
ejpam-901	167	7	of	of	ADP
ejpam-901	167	8	theorem	theorem	NOUN
ejpam-901	167	9	6	6	NUM
ejpam-901	167	10	is	be	AUX
ejpam-901	167	11	similar	similar	ADJ
ejpam-901	167	12	to	to	ADP
ejpam-901	167	13	that	that	PRON
ejpam-901	167	14	of	of	ADP
ejpam-901	167	15	theorem	theorem	ADJ
ejpam-901	167	16	2	2	NUM
ejpam-901	168	1	and	and	CCONJ
ejpam-901	168	2	so	so	ADV
ejpam-901	168	3	we	we	PRON
ejpam-901	168	4	omit	omit	VERB
ejpam-901	168	5	the	the	DET
ejpam-901	168	6	details	detail	NOUN
ejpam-901	168	7	involved	involve	VERB
ejpam-901	168	8	.	.	PUNCT
ejpam-901	169	1	corollary	corollary	ADJ
ejpam-901	169	2	1	1	NUM
ejpam-901	169	3	.	.	PUNCT
ejpam-901	170	1	let	let	VERB
ejpam-901	170	2	f	f	PROPN
ejpam-901	170	3	∈	∈	PROPN
ejpam-901	170	4	t	t	PROPN
ejpam-901	170	5	s	s	X
ejpam-901	170	6	λ,µ	λ,µ	X
ejpam-901	170	7	(	(	PUNCT
ejpam-901	170	8	γ	γ	X
ejpam-901	170	9	;	;	PUNCT
ejpam-901	170	10	h	h	X
ejpam-901	170	11	)	)	PUNCT
ejpam-901	170	12	be	be	AUX
ejpam-901	170	13	given	give	VERB
ejpam-901	170	14	by	by	ADP
ejpam-901	170	15	(	(	PUNCT
ejpam-901	170	16	1	1	NUM
ejpam-901	170	17	)	)	PUNCT
ejpam-901	170	18	.	.	PUNCT
ejpam-901	171	1	then	then	ADV
ejpam-901	171	2	the	the	DET
ejpam-901	171	3	function	function	NOUN
ejpam-901	171	4	σm(z	σm(z	PUNCT
ejpam-901	171	5	)	)	PUNCT
ejpam-901	171	6	=	=	SYM
ejpam-901	172	1	∫	∫	PROPN
ejpam-901	172	2	1	1	NUM
ejpam-901	172	3	0	0	NUM
ejpam-901	172	4	sm(tz	sm(tz	NOUN
ejpam-901	172	5	)	)	PUNCT
ejpam-901	173	1	t	t	PROPN
ejpam-901	173	2	d	d	X
ejpam-901	173	3	t	t	PROPN
ejpam-901	173	4	(	(	PUNCT
ejpam-901	173	5	z	z	NOUN
ejpam-901	173	6	∈	∈	PROPN
ejpam-901	173	7	u	u	NOUN
ejpam-901	173	8	)	)	PUNCT
ejpam-901	173	9	,	,	PUNCT
ejpam-901	173	10	where	where	SCONJ
ejpam-901	173	11	sm(z	sm(z	PUNCT
ejpam-901	173	12	)	)	PUNCT
ejpam-901	173	13	=	=	SYM
ejpam-901	174	1	z	z	NOUN
ejpam-901	174	2	+	+	NOUN
ejpam-901	174	3	m−1∑	m−1∑	PROPN
ejpam-901	174	4	n=1	n=1	PROPN
ejpam-901	174	5	an+1zn+1	an+1zn+1	VERB
ejpam-901	174	6	m	m	PROPN
ejpam-901	174	7	∈	∈	PROPN
ejpam-901	174	8	n	n	PRON
ejpam-901	174	9	\	\	NOUN
ejpam-901	174	10	{	{	PUNCT
ejpam-901	174	11	1	1	NUM
ejpam-901	174	12	}	}	PUNCT
ejpam-901	174	13	;	;	PUNCT
ejpam-901	174	14	z	z	PROPN
ejpam-901	174	15	∈	∈	PROPN
ejpam-901	174	16	u	u	NOUN
ejpam-901	174	17	)	)	PUNCT
ejpam-901	174	18	,	,	PUNCT
ejpam-901	174	19	is	be	AUX
ejpam-901	174	20	also	also	ADV
ejpam-901	174	21	in	in	ADP
ejpam-901	174	22	the	the	DET
ejpam-901	174	23	class	class	NOUN
ejpam-901	175	1	t	t	PROPN
ejpam-901	175	2	s	s	X
ejpam-901	175	3	λ,µ	λ,µ	NOUN
ejpam-901	175	4	(	(	PUNCT
ejpam-901	175	5	γ	γ	X
ejpam-901	175	6	;	;	PUNCT
ejpam-901	175	7	h	h	NOUN
ejpam-901	175	8	)	)	PUNCT
ejpam-901	175	9	.	.	PUNCT
ejpam-901	176	1	proof	proof	NOUN
ejpam-901	176	2	.	.	PUNCT
ejpam-901	177	1	we	we	PRON
ejpam-901	177	2	have	have	VERB
ejpam-901	177	3	σm(z	σm(z	ADV
ejpam-901	177	4	)	)	PUNCT
ejpam-901	178	1	=	=	SYM
ejpam-901	178	2	z	z	NOUN
ejpam-901	179	1	+	+	NOUN
ejpam-901	179	2	m−1∑	m−1∑	NUM
ejpam-901	179	3	n=1	n=1	NUM
ejpam-901	179	4	an+1	an+1	NOUN
ejpam-901	179	5	n+	n+	ADP
ejpam-901	179	6	1	1	NUM
ejpam-901	179	7	zn+1	zn+1	NOUN
ejpam-901	179	8	=	=	SYM
ejpam-901	179	9	(	(	PUNCT
ejpam-901	179	10	f	f	PROPN
ejpam-901	179	11	∗	∗	X
ejpam-901	179	12	gm)(z	gm)(z	PROPN
ejpam-901	179	13	)	)	PUNCT
ejpam-901	179	14	(	(	PUNCT
ejpam-901	179	15	m	m	VERB
ejpam-901	179	16	∈	∈	PROPN
ejpam-901	179	17	n	n	PRON
ejpam-901	179	18	\	\	NOUN
ejpam-901	179	19	{	{	PUNCT
ejpam-901	179	20	1	1	NUM
ejpam-901	179	21	}	}	PUNCT
ejpam-901	179	22	)	)	PUNCT
ejpam-901	179	23	,	,	PUNCT
ejpam-901	179	24	(	(	PUNCT
ejpam-901	179	25	21	21	NUM
ejpam-901	179	26	)	)	PUNCT
ejpam-901	179	27	where	where	SCONJ
ejpam-901	179	28	f	f	PROPN
ejpam-901	179	29	(	(	PUNCT
ejpam-901	179	30	z	z	NOUN
ejpam-901	179	31	)	)	PUNCT
ejpam-901	179	32	=	=	SYM
ejpam-901	179	33	z	z	NOUN
ejpam-901	180	1	+	+	NOUN
ejpam-901	180	2	∞∑	∞∑	NUM
ejpam-901	180	3	n=1	n=1	PROPN
ejpam-901	180	4	an+1zn+1	an+1zn+1	VERB
ejpam-901	180	5	∈	∈	PROPN
ejpam-901	180	6	t	t	PROPN
ejpam-901	180	7	n	n	CCONJ
ejpam-901	180	8	λ,µ(γ	λ,µ(γ	ADV
ejpam-901	180	9	;	;	PUNCT
ejpam-901	180	10	h	h	X
ejpam-901	180	11	)	)	PUNCT
ejpam-901	180	12	and	and	CCONJ
ejpam-901	180	13	gm(z	gm(z	PROPN
ejpam-901	180	14	)	)	PUNCT
ejpam-901	180	15	=	=	SYM
ejpam-901	181	1	z	z	NOUN
ejpam-901	182	1	+	+	NOUN
ejpam-901	182	2	m−1∑	m−1∑	NUM
ejpam-901	182	3	n=1	n=1	SYM
ejpam-901	182	4	zn+1	zn+1	PROPN
ejpam-901	182	5	n+	n+	X
ejpam-901	182	6	1	1	NUM
ejpam-901	182	7	∈a	∈a	ADJ
ejpam-901	182	8	,	,	PUNCT
ejpam-901	182	9	while	while	SCONJ
ejpam-901	182	10	,	,	PUNCT
ejpam-901	182	11	it	it	PRON
ejpam-901	182	12	is	be	AUX
ejpam-901	182	13	known	know	VERB
ejpam-901	182	14	[	[	PUNCT
ejpam-901	182	15	11	11	NUM
ejpam-901	182	16	]	]	PUNCT
ejpam-901	182	17	that	that	PRON
ejpam-901	182	18	re	re	VERB
ejpam-901	182	19	�	�	PROPN
ejpam-901	182	20	gm(z	gm(z	NOUN
ejpam-901	182	21	)	)	PUNCT
ejpam-901	182	22	z	z	NOUN
ejpam-901	182	23	�	�	PROPN
ejpam-901	182	24	=	=	SYM
ejpam-901	182	25	re	re	X
ejpam-901	182	26	(	(	PUNCT
ejpam-901	182	27	1	1	NUM
ejpam-901	182	28	+	+	NUM
ejpam-901	182	29	m−1∑	m−1∑	NUM
ejpam-901	182	30	n=1	n=1	PROPN
ejpam-901	182	31	zn	zn	PROPN
ejpam-901	182	32	n+	n+	ADP
ejpam-901	182	33	1	1	NUM
ejpam-901	182	34	)	)	PUNCT
ejpam-901	182	35	>	>	PUNCT
ejpam-901	182	36	1	1	NUM
ejpam-901	182	37	2	2	NUM
ejpam-901	182	38	(	(	PUNCT
ejpam-901	182	39	m	m	PROPN
ejpam-901	182	40	∈	∈	PROPN
ejpam-901	182	41	n	n	PRON
ejpam-901	182	42	\	\	NOUN
ejpam-901	182	43	{	{	PUNCT
ejpam-901	182	44	1	1	NUM
ejpam-901	182	45	}	}	PUNCT
ejpam-901	182	46	;	;	PUNCT
ejpam-901	182	47	z	z	PROPN
ejpam-901	182	48	∈	∈	PROPN
ejpam-901	182	49	u	u	NOUN
ejpam-901	182	50	)	)	PUNCT
ejpam-901	182	51	.	.	PUNCT
ejpam-901	183	1	(	(	PUNCT
ejpam-901	183	2	22	22	NUM
ejpam-901	183	3	)	)	PUNCT
ejpam-901	183	4	in	in	ADP
ejpam-901	183	5	view	view	NOUN
ejpam-901	183	6	of	of	ADP
ejpam-901	183	7	(	(	PUNCT
ejpam-901	183	8	21	21	NUM
ejpam-901	183	9	)	)	PUNCT
ejpam-901	183	10	and	and	CCONJ
ejpam-901	183	11	(	(	PUNCT
ejpam-901	183	12	22	22	NUM
ejpam-901	183	13	)	)	PUNCT
ejpam-901	183	14	,	,	PUNCT
ejpam-901	183	15	an	an	DET
ejpam-901	183	16	application	application	NOUN
ejpam-901	183	17	of	of	ADP
ejpam-901	183	18	theorem	theorem	ADJ
ejpam-901	183	19	6	6	NUM
ejpam-901	183	20	leads	lead	VERB
ejpam-901	183	21	to	to	ADP
ejpam-901	183	22	σm	σm	ADP
ejpam-901	183	23	∈	∈	PROPN
ejpam-901	183	24	t	t	NOUN
ejpam-901	183	25	s	s	X
ejpam-901	183	26	λ,µ	λ,µ	X
ejpam-901	183	27	(	(	PUNCT
ejpam-901	183	28	γ	γ	X
ejpam-901	183	29	;	;	PUNCT
ejpam-901	183	30	h	h	NOUN
ejpam-901	183	31	)	)	PUNCT
ejpam-901	183	32	.	.	PUNCT
ejpam-901	184	1	theorem	theorem	VERB
ejpam-901	184	2	7	7	NUM
ejpam-901	184	3	.	.	PUNCT
ejpam-901	185	1	if	if	SCONJ
ejpam-901	185	2	f	f	PROPN
ejpam-901	185	3	∈	∈	PROPN
ejpam-901	185	4	t	t	PROPN
ejpam-901	185	5	s	s	X
ejpam-901	185	6	λ,µ	λ,µ	X
ejpam-901	185	7	(	(	PUNCT
ejpam-901	185	8	γ	γ	X
ejpam-901	185	9	;	;	PUNCT
ejpam-901	185	10	h	h	NOUN
ejpam-901	185	11	)	)	PUNCT
ejpam-901	185	12	and	and	CCONJ
ejpam-901	185	13	g(z	g(z	PROPN
ejpam-901	185	14	)	)	PUNCT
ejpam-901	185	15	∈	∈	PROPN
ejpam-901	185	16	r(α	r(α	NOUN
ejpam-901	185	17	)	)	PUNCT
ejpam-901	185	18	(	(	PUNCT
ejpam-901	185	19	g	g	PROPN
ejpam-901	185	20	∈a	∈a	NUM
ejpam-901	185	21	;	;	PUNCT
ejpam-901	185	22	z	z	PROPN
ejpam-901	185	23	∈	∈	PROPN
ejpam-901	185	24	u	u	NOUN
ejpam-901	185	25	)	)	PUNCT
ejpam-901	185	26	,	,	PUNCT
ejpam-901	185	27	then	then	ADV
ejpam-901	185	28	f	f	PROPN
ejpam-901	185	29	∗	∗	VERB
ejpam-901	185	30	g	g	PROPN
ejpam-901	185	31	∈	∈	PROPN
ejpam-901	185	32	t	t	PROPN
ejpam-901	185	33	s	s	PART
ejpam-901	185	34	λ,µ(γ	λ,µ(γ	NOUN
ejpam-901	185	35	;	;	PUNCT
ejpam-901	185	36	h	h	X
ejpam-901	185	37	)	)	PUNCT
ejpam-901	185	38	.	.	PUNCT
ejpam-901	186	1	o.	o.	PROPN
ejpam-901	186	2	kwon	kwon	PROPN
ejpam-901	186	3	,	,	PUNCT
ejpam-901	186	4	n.	n.	PROPN
ejpam-901	186	5	cho	cho	PROPN
ejpam-901	186	6	/	/	SYM
ejpam-901	186	7	eur	eur	PROPN
ejpam-901	186	8	.	.	PUNCT
ejpam-901	187	1	j.	j.	PROPN
ejpam-901	187	2	pure	pure	PROPN
ejpam-901	187	3	appl	appl	PROPN
ejpam-901	187	4	.	.	PROPN
ejpam-901	187	5	math	math	PROPN
ejpam-901	187	6	,	,	PUNCT
ejpam-901	187	7	3	3	NUM
ejpam-901	187	8	(	(	PUNCT
ejpam-901	187	9	2010	2010	NUM
ejpam-901	187	10	)	)	PUNCT
ejpam-901	187	11	,	,	PUNCT
ejpam-901	187	12	1124	1124	NUM
ejpam-901	187	13	-	-	SYM
ejpam-901	187	14	1136	1136	NUM
ejpam-901	187	15	1132	1132	NUM
ejpam-901	187	16	proof	proof	NOUN
ejpam-901	187	17	.	.	PUNCT
ejpam-901	188	1	by	by	ADP
ejpam-901	188	2	using	use	VERB
ejpam-901	188	3	a	a	DET
ejpam-901	188	4	similar	similar	ADJ
ejpam-901	188	5	method	method	NOUN
ejpam-901	188	6	as	as	ADP
ejpam-901	188	7	in	in	ADP
ejpam-901	188	8	the	the	DET
ejpam-901	188	9	proof	proof	NOUN
ejpam-901	188	10	of	of	ADP
ejpam-901	188	11	theorem	theorem	NOUN
ejpam-901	188	12	21	21	NUM
ejpam-901	188	13	,	,	PUNCT
ejpam-901	188	14	we	we	PRON
ejpam-901	188	15	have	have	VERB
ejpam-901	188	16	(	(	PUNCT
ejpam-901	188	17	1−	1−	NUM
ejpam-901	188	18	γ	γ	X
ejpam-901	188	19	)	)	PUNCT
ejpam-901	188	20	i	i	PRON
ejpam-901	188	21	s	s	VERB
ejpam-901	188	22	λ,µ	λ,µ	INTJ
ejpam-901	189	1	(	(	PUNCT
ejpam-901	189	2	f	f	PROPN
ejpam-901	189	3	∗	∗	PROPN
ejpam-901	189	4	g)(z	g)(z	PROPN
ejpam-901	189	5	)	)	PUNCT
ejpam-901	189	6	z	z	NOUN
ejpam-901	190	1	+	+	NUM
ejpam-901	190	2	γ(i	γ(i	NOUN
ejpam-901	190	3	s	s	X
ejpam-901	190	4	λ,µ	λ,µ	NOUN
ejpam-901	190	5	(	(	PUNCT
ejpam-901	190	6	f	f	PROPN
ejpam-901	190	7	∗	∗	NOUN
ejpam-901	190	8	g)(z))′	g)(z))′	X
ejpam-901	190	9	=	=	PUNCT
ejpam-901	190	10	g(z	g(z	PROPN
ejpam-901	190	11	)	)	PUNCT
ejpam-901	190	12	∗	∗	NOUN
ejpam-901	190	13	(	(	PUNCT
ejpam-901	190	14	zψ(z	zψ(z	NOUN
ejpam-901	190	15	)	)	PUNCT
ejpam-901	190	16	)	)	PUNCT
ejpam-901	191	1	g(z	g(z	ADJ
ejpam-901	191	2	)	)	PUNCT
ejpam-901	191	3	∗	∗	NOUN
ejpam-901	191	4	z	z	NOUN
ejpam-901	191	5	(	(	PUNCT
ejpam-901	191	6	z	z	NOUN
ejpam-901	191	7	∈	∈	PROPN
ejpam-901	191	8	u	u	NOUN
ejpam-901	191	9	)	)	PUNCT
ejpam-901	191	10	,	,	PUNCT
ejpam-901	191	11	(	(	PUNCT
ejpam-901	191	12	23	23	NUM
ejpam-901	191	13	)	)	PUNCT
ejpam-901	191	14	where	where	SCONJ
ejpam-901	191	15	ψ(z	ψ(z	NOUN
ejpam-901	191	16	)	)	PUNCT
ejpam-901	191	17	=	=	PUNCT
ejpam-901	191	18	(	(	PUNCT
ejpam-901	191	19	1−	1−	NUM
ejpam-901	191	20	γ	γ	X
ejpam-901	191	21	)	)	PUNCT
ejpam-901	191	22	i	i	PRON
ejpam-901	191	23	s	s	VERB
ejpam-901	191	24	λ,µ	λ,µ	PROPN
ejpam-901	191	25	f	f	PROPN
ejpam-901	191	26	(	(	PUNCT
ejpam-901	191	27	z	z	NOUN
ejpam-901	191	28	)	)	PUNCT
ejpam-901	191	29	z	z	NOUN
ejpam-901	192	1	+	+	NUM
ejpam-901	192	2	γ(i	γ(i	NOUN
ejpam-901	192	3	s	s	X
ejpam-901	192	4	λ,µ	λ,µ	NOUN
ejpam-901	192	5	f	f	PROPN
ejpam-901	192	6	(	(	PUNCT
ejpam-901	192	7	z))′	z))′	X
ejpam-901	192	8	≺	≺	NOUN
ejpam-901	192	9	h(z	h(z	NOUN
ejpam-901	192	10	)	)	PUNCT
ejpam-901	192	11	.	.	PUNCT
ejpam-901	193	1	since	since	SCONJ
ejpam-901	193	2	h	h	NOUN
ejpam-901	193	3	is	be	AUX
ejpam-901	193	4	convex	convex	ADJ
ejpam-901	193	5	univalent	univalent	ADJ
ejpam-901	193	6	in	in	ADP
ejpam-901	193	7	u	u	PROPN
ejpam-901	193	8	,	,	PUNCT
ejpam-901	193	9	it	it	PRON
ejpam-901	193	10	follows	follow	VERB
ejpam-901	193	11	from	from	ADP
ejpam-901	193	12	(	(	PUNCT
ejpam-901	193	13	23	23	NUM
ejpam-901	193	14	)	)	PUNCT
ejpam-901	193	15	and	and	CCONJ
ejpam-901	193	16	lemma	lemma	PROPN
ejpam-901	193	17	2	2	PROPN
ejpam-901	193	18	that	that	PRON
ejpam-901	193	19	theorem	theorem	VERB
ejpam-901	193	20	7	7	NUM
ejpam-901	193	21	holds	hold	NOUN
ejpam-901	193	22	true	true	ADJ
ejpam-901	193	23	.	.	PUNCT
ejpam-901	194	1	if	if	SCONJ
ejpam-901	194	2	we	we	PRON
ejpam-901	194	3	take	take	VERB
ejpam-901	194	4	α=	α=	NOUN
ejpam-901	194	5	0	0	NUM
ejpam-901	194	6	and	and	CCONJ
ejpam-901	194	7	α=	α=	NOUN
ejpam-901	194	8	1/2	1/2	NUM
ejpam-901	194	9	in	in	ADP
ejpam-901	194	10	theorem	theorem	NOUN
ejpam-901	194	11	7	7	NUM
ejpam-901	194	12	,	,	PUNCT
ejpam-901	194	13	we	we	PRON
ejpam-901	194	14	have	have	VERB
ejpam-901	194	15	the	the	DET
ejpam-901	194	16	following	follow	VERB
ejpam-901	194	17	corollary	corollary	NOUN
ejpam-901	194	18	.	.	PUNCT
ejpam-901	195	1	corollary	corollary	ADJ
ejpam-901	195	2	2	2	NUM
ejpam-901	195	3	.	.	PUNCT
ejpam-901	196	1	if	if	SCONJ
ejpam-901	196	2	f	f	PROPN
ejpam-901	196	3	∈	∈	PROPN
ejpam-901	196	4	t	t	PROPN
ejpam-901	196	5	s	s	X
ejpam-901	196	6	λ,µ	λ,µ	X
ejpam-901	196	7	(	(	PUNCT
ejpam-901	196	8	γ	γ	X
ejpam-901	196	9	;	;	PUNCT
ejpam-901	196	10	h	h	NOUN
ejpam-901	196	11	)	)	PUNCT
ejpam-901	196	12	and	and	CCONJ
ejpam-901	196	13	g	g	PROPN
ejpam-901	196	14	∈a	∈a	ADJ
ejpam-901	196	15	satisfies	satisfie	NOUN
ejpam-901	196	16	one	one	NUM
ejpam-901	196	17	of	of	ADP
ejpam-901	196	18	the	the	DET
ejpam-901	196	19	following	following	ADJ
ejpam-901	196	20	conditions	condition	NOUN
ejpam-901	196	21	:	:	PUNCT
ejpam-901	196	22	(	(	PUNCT
ejpam-901	196	23	i	i	NOUN
ejpam-901	196	24	)	)	PUNCT
ejpam-901	196	25	g(z	g(z	PROPN
ejpam-901	196	26	)	)	PUNCT
ejpam-901	196	27	is	be	AUX
ejpam-901	196	28	convex	convex	ADJ
ejpam-901	196	29	univalent	univalent	ADJ
ejpam-901	196	30	in	in	ADP
ejpam-901	196	31	u	u	PROPN
ejpam-901	196	32	or	or	CCONJ
ejpam-901	196	33	(	(	PUNCT
ejpam-901	196	34	ii	ii	NOUN
ejpam-901	196	35	)	)	PUNCT
ejpam-901	196	36	g(z	g(z	PROPN
ejpam-901	196	37	)	)	PUNCT
ejpam-901	196	38	∈	∈	PROPN
ejpam-901	196	39	s∗(1	s∗(1	NOUN
ejpam-901	196	40	2	2	NUM
ejpam-901	196	41	)	)	PUNCT
ejpam-901	196	42	,	,	PUNCT
ejpam-901	196	43	then	then	ADV
ejpam-901	196	44	f	f	PROPN
ejpam-901	196	45	∗	∗	VERB
ejpam-901	196	46	g	g	PROPN
ejpam-901	196	47	∈	∈	PROPN
ejpam-901	196	48	t	t	PROPN
ejpam-901	196	49	s	s	X
ejpam-901	196	50	λ,µ	λ,µ	X
ejpam-901	196	51	(	(	PUNCT
ejpam-901	196	52	γ	γ	X
ejpam-901	196	53	;	;	PUNCT
ejpam-901	196	54	h	h	NOUN
ejpam-901	196	55	)	)	PUNCT
ejpam-901	196	56	.	.	PUNCT
ejpam-901	197	1	4	4	X
ejpam-901	197	2	.	.	X
ejpam-901	197	3	integral	integral	ADJ
ejpam-901	197	4	operators	operator	NOUN
ejpam-901	197	5	theorem	theorem	VERB
ejpam-901	197	6	8	8	NUM
ejpam-901	197	7	.	.	PUNCT
ejpam-901	198	1	if	if	SCONJ
ejpam-901	198	2	f	f	PROPN
ejpam-901	198	3	∈	∈	PROPN
ejpam-901	198	4	t	t	PROPN
ejpam-901	198	5	s	s	X
ejpam-901	198	6	λ,µ	λ,µ	X
ejpam-901	198	7	(	(	PUNCT
ejpam-901	198	8	γ	γ	X
ejpam-901	198	9	;	;	PUNCT
ejpam-901	198	10	h	h	NOUN
ejpam-901	198	11	)	)	PUNCT
ejpam-901	198	12	,	,	PUNCT
ejpam-901	198	13	then	then	ADV
ejpam-901	198	14	the	the	DET
ejpam-901	198	15	function	function	NOUN
ejpam-901	198	16	f	f	PROPN
ejpam-901	198	17	defined	define	VERB
ejpam-901	198	18	by	by	ADP
ejpam-901	198	19	f(z	f(z	NOUN
ejpam-901	198	20	)	)	PUNCT
ejpam-901	198	21	=	=	PUNCT
ejpam-901	199	1	c	c	NOUN
ejpam-901	199	2	+	+	NOUN
ejpam-901	199	3	1	1	NUM
ejpam-901	199	4	zc	zc	NUM
ejpam-901	199	5	∫	∫	PROPN
ejpam-901	199	6	z	z	PROPN
ejpam-901	199	7	0	0	PROPN
ejpam-901	200	1	t	t	PROPN
ejpam-901	200	2	c−1	c−1	PROPN
ejpam-901	200	3	f	f	PROPN
ejpam-901	200	4	(	(	PUNCT
ejpam-901	200	5	t)d	t)d	PROPN
ejpam-901	200	6	t	t	PROPN
ejpam-901	200	7	(	(	PUNCT
ejpam-901	200	8	re{c	re{c	NOUN
ejpam-901	200	9	}	}	PUNCT
ejpam-901	200	10	>	>	PUNCT
ejpam-901	200	11	−1	−1	NOUN
ejpam-901	200	12	)	)	PUNCT
ejpam-901	200	13	(	(	PUNCT
ejpam-901	200	14	24	24	NUM
ejpam-901	200	15	)	)	PUNCT
ejpam-901	200	16	is	be	AUX
ejpam-901	200	17	in	in	ADP
ejpam-901	200	18	the	the	DET
ejpam-901	200	19	class	class	NOUN
ejpam-901	200	20	t	t	PROPN
ejpam-901	200	21	s	s	X
ejpam-901	200	22	λ,µ	λ,µ	PROPN
ejpam-901	200	23	(	(	PUNCT
ejpam-901	200	24	γ;eh	γ;eh	PROPN
ejpam-901	200	25	)	)	PUNCT
ejpam-901	200	26	,	,	PUNCT
ejpam-901	200	27	where	where	SCONJ
ejpam-901	200	28	eh(z	eh(z	PRON
ejpam-901	200	29	)	)	PUNCT
ejpam-901	200	30	=	=	PUNCT
ejpam-901	201	1	(	(	PUNCT
ejpam-901	201	2	c	c	NOUN
ejpam-901	201	3	+	+	NOUN
ejpam-901	201	4	1)z−(c+1	1)z−(c+1	NUM
ejpam-901	201	5	)	)	PUNCT
ejpam-901	201	6	∫	∫	PROPN
ejpam-901	201	7	z	z	NOUN
ejpam-901	201	8	0	0	NUM
ejpam-901	201	9	t	t	PROPN
ejpam-901	201	10	ch(t)d	ch(t)d	PROPN
ejpam-901	201	11	t	t	PROPN
ejpam-901	201	12	≺	≺	VERB
ejpam-901	201	13	h(z	h(z	NOUN
ejpam-901	201	14	)	)	PUNCT
ejpam-901	201	15	.	.	PUNCT
ejpam-901	202	1	proof	proof	NOUN
ejpam-901	202	2	.	.	PUNCT
ejpam-901	203	1	let	let	VERB
ejpam-901	203	2	f	f	PROPN
ejpam-901	203	3	∈	∈	PROPN
ejpam-901	203	4	t	t	PROPN
ejpam-901	203	5	s	s	X
ejpam-901	203	6	λ,µ	λ,µ	X
ejpam-901	203	7	(	(	PUNCT
ejpam-901	203	8	γ	γ	X
ejpam-901	203	9	;	;	PUNCT
ejpam-901	203	10	h	h	NOUN
ejpam-901	203	11	)	)	PUNCT
ejpam-901	203	12	.	.	PUNCT
ejpam-901	204	1	then	then	ADV
ejpam-901	204	2	from	from	ADP
ejpam-901	204	3	(	(	PUNCT
ejpam-901	204	4	24	24	NUM
ejpam-901	204	5	)	)	PUNCT
ejpam-901	204	6	,	,	PUNCT
ejpam-901	204	7	we	we	PRON
ejpam-901	204	8	obtain	obtain	VERB
ejpam-901	204	9	(	(	PUNCT
ejpam-901	204	10	c	c	NOUN
ejpam-901	204	11	+	+	NOUN
ejpam-901	204	12	1	1	X
ejpam-901	204	13	)	)	PUNCT
ejpam-901	204	14	f	f	NOUN
ejpam-901	204	15	(	(	PUNCT
ejpam-901	204	16	z	z	NOUN
ejpam-901	204	17	)	)	PUNCT
ejpam-901	204	18	=	=	SYM
ejpam-901	204	19	zf	zf	PROPN
ejpam-901	204	20	′(z	′(z	NOUN
ejpam-901	204	21	)	)	PUNCT
ejpam-901	204	22	+	+	CCONJ
ejpam-901	204	23	cf(z	cf(z	NOUN
ejpam-901	204	24	)	)	PUNCT
ejpam-901	204	25	.	.	PUNCT
ejpam-901	205	1	(	(	PUNCT
ejpam-901	205	2	25	25	NUM
ejpam-901	205	3	)	)	PUNCT
ejpam-901	205	4	define	define	VERB
ejpam-901	205	5	the	the	DET
ejpam-901	205	6	function	function	NOUN
ejpam-901	205	7	g	g	NOUN
ejpam-901	205	8	by	by	ADP
ejpam-901	205	9	zg(z	zg(z	NUM
ejpam-901	205	10	)	)	PUNCT
ejpam-901	205	11	=	=	SYM
ejpam-901	205	12	(	(	PUNCT
ejpam-901	205	13	1−	1−	NUM
ejpam-901	205	14	γ)i	γ)i	NOUN
ejpam-901	205	15	s	s	PART
ejpam-901	205	16	λ,µf(z	λ,µf(z	VERB
ejpam-901	205	17	)	)	PUNCT
ejpam-901	206	1	+	+	CCONJ
ejpam-901	206	2	γz(i	γz(i	NUM
ejpam-901	206	3	s	s	VERB
ejpam-901	206	4	λ,µf(z))′	λ,µf(z))′	PROPN
ejpam-901	206	5	(	(	PUNCT
ejpam-901	206	6	z	z	NOUN
ejpam-901	206	7	∈	∈	PROPN
ejpam-901	206	8	u	u	NOUN
ejpam-901	206	9	)	)	PUNCT
ejpam-901	206	10	.	.	PUNCT
ejpam-901	207	1	(	(	PUNCT
ejpam-901	207	2	26	26	NUM
ejpam-901	207	3	)	)	PUNCT
ejpam-901	207	4	differentiating	differentiate	VERB
ejpam-901	207	5	both	both	DET
ejpam-901	207	6	sides	side	NOUN
ejpam-901	207	7	of	of	ADP
ejpam-901	207	8	(	(	PUNCT
ejpam-901	207	9	26	26	NUM
ejpam-901	207	10	)	)	PUNCT
ejpam-901	207	11	with	with	ADP
ejpam-901	207	12	respect	respect	NOUN
ejpam-901	207	13	to	to	ADP
ejpam-901	207	14	z	z	NOUN
ejpam-901	207	15	,	,	PUNCT
ejpam-901	207	16	we	we	PRON
ejpam-901	207	17	get	get	VERB
ejpam-901	207	18	g(z	g(z	ADJ
ejpam-901	207	19	)	)	PUNCT
ejpam-901	208	1	+	+	CCONJ
ejpam-901	208	2	zg′(z	zg′(z	NOUN
ejpam-901	208	3	)	)	PUNCT
ejpam-901	208	4	=	=	PUNCT
ejpam-901	209	1	(	(	PUNCT
ejpam-901	209	2	1−	1−	NUM
ejpam-901	209	3	γ	γ	X
ejpam-901	209	4	)	)	PUNCT
ejpam-901	209	5	i	i	PRON
ejpam-901	209	6	s	s	VERB
ejpam-901	209	7	λ,µ	λ,µ	INTJ
ejpam-901	209	8	(	(	PUNCT
ejpam-901	209	9	zf	zf	PROPN
ejpam-901	209	10	′(z	′(z	NOUN
ejpam-901	209	11	)	)	PUNCT
ejpam-901	209	12	)	)	PUNCT
ejpam-901	210	1	z	z	NOUN
ejpam-901	211	1	+	+	NUM
ejpam-901	211	2	γ(i	γ(i	NOUN
ejpam-901	211	3	s	s	PART
ejpam-901	211	4	λ,µ(zf	λ,µ(zf	PROPN
ejpam-901	211	5	′(z)))′.	′(z)))′.	NUM
ejpam-901	211	6	(	(	PUNCT
ejpam-901	211	7	27	27	NUM
ejpam-901	211	8	)	)	PUNCT
ejpam-901	211	9	o.	o.	PROPN
ejpam-901	211	10	kwon	kwon	PROPN
ejpam-901	211	11	,	,	PUNCT
ejpam-901	211	12	n.	n.	PROPN
ejpam-901	211	13	cho	cho	PROPN
ejpam-901	211	14	/	/	SYM
ejpam-901	211	15	eur	eur	PROPN
ejpam-901	211	16	.	.	PUNCT
ejpam-901	212	1	j.	j.	PROPN
ejpam-901	212	2	pure	pure	PROPN
ejpam-901	212	3	appl	appl	PROPN
ejpam-901	212	4	.	.	PROPN
ejpam-901	212	5	math	math	PROPN
ejpam-901	212	6	,	,	PUNCT
ejpam-901	212	7	3	3	NUM
ejpam-901	212	8	(	(	PUNCT
ejpam-901	212	9	2010	2010	NUM
ejpam-901	212	10	)	)	PUNCT
ejpam-901	212	11	,	,	PUNCT
ejpam-901	212	12	1124	1124	NUM
ejpam-901	212	13	-	-	SYM
ejpam-901	212	14	1136	1136	NUM
ejpam-901	212	15	1133	1133	NUM
ejpam-901	212	16	furthermore	furthermore	ADV
ejpam-901	212	17	,	,	PUNCT
ejpam-901	212	18	it	it	PRON
ejpam-901	212	19	follows	follow	VERB
ejpam-901	212	20	from	from	ADP
ejpam-901	212	21	(	(	PUNCT
ejpam-901	212	22	25	25	NUM
ejpam-901	212	23	)	)	PUNCT
ejpam-901	212	24	,	,	PUNCT
ejpam-901	212	25	(	(	PUNCT
ejpam-901	212	26	26	26	NUM
ejpam-901	212	27	)	)	PUNCT
ejpam-901	212	28	and	and	CCONJ
ejpam-901	212	29	(	(	PUNCT
ejpam-901	212	30	27	27	NUM
ejpam-901	212	31	)	)	PUNCT
ejpam-901	212	32	that	that	SCONJ
ejpam-901	212	33	(	(	PUNCT
ejpam-901	212	34	1−	1−	NUM
ejpam-901	212	35	γ	γ	X
ejpam-901	212	36	)	)	PUNCT
ejpam-901	212	37	i	i	PRON
ejpam-901	212	38	s	s	VERB
ejpam-901	212	39	λ,µ	λ,µ	PROPN
ejpam-901	212	40	f	f	PROPN
ejpam-901	212	41	(	(	PUNCT
ejpam-901	212	42	z	z	NOUN
ejpam-901	212	43	)	)	PUNCT
ejpam-901	212	44	z	z	NOUN
ejpam-901	213	1	+	+	NUM
ejpam-901	213	2	γ(i	γ(i	NOUN
ejpam-901	213	3	s	s	X
ejpam-901	213	4	λ,µ	λ,µ	NOUN
ejpam-901	213	5	f	f	PROPN
ejpam-901	213	6	(	(	PUNCT
ejpam-901	213	7	z))′	z))′	X
ejpam-901	213	8	=	=	SYM
ejpam-901	213	9	(	(	PUNCT
ejpam-901	213	10	1−	1−	NUM
ejpam-901	213	11	γ)z−1	γ)z−1	NOUN
ejpam-901	213	12	i	i	PRON
ejpam-901	213	13	s	s	VERB
ejpam-901	213	14	λ,µ	λ,µ	PROPN
ejpam-901	213	15	�	�	PROPN
ejpam-901	213	16	zf	zf	PROPN
ejpam-901	213	17	′(z	′(z	ADV
ejpam-901	213	18	)	)	PUNCT
ejpam-901	213	19	+	+	CCONJ
ejpam-901	213	20	cf(z	cf(z	NOUN
ejpam-901	213	21	)	)	PUNCT
ejpam-901	213	22	c	c	NOUN
ejpam-901	214	1	+	+	SYM
ejpam-901	214	2	1	1	NUM
ejpam-901	214	3	�	�	NOUN
ejpam-901	214	4	+	+	CCONJ
ejpam-901	214	5	γ	γ	X
ejpam-901	214	6	�	�	PROPN
ejpam-901	215	1	i	i	PRON
ejpam-901	215	2	s	s	VERB
ejpam-901	215	3	λ,µ	λ,µ	PROPN
ejpam-901	215	4	�	�	PROPN
ejpam-901	215	5	zf	zf	PROPN
ejpam-901	215	6	′(z	′(z	ADV
ejpam-901	215	7	)	)	PUNCT
ejpam-901	215	8	+	+	CCONJ
ejpam-901	215	9	cf(z	cf(z	NOUN
ejpam-901	215	10	)	)	PUNCT
ejpam-901	215	11	c	c	NOUN
ejpam-901	216	1	+	+	NOUN
ejpam-901	216	2	1	1	NUM
ejpam-901	216	3	�	�	NOUN
ejpam-901	216	4	�	�	NOUN
ejpam-901	216	5	′	′	NOUN
ejpam-901	216	6	=	=	PUNCT
ejpam-901	216	7	g(z	g(z	PROPN
ejpam-901	216	8	)	)	PUNCT
ejpam-901	217	1	+	+	CCONJ
ejpam-901	217	2	1	1	NUM
ejpam-901	217	3	c	c	NOUN
ejpam-901	217	4	+	+	NOUN
ejpam-901	217	5	1	1	NUM
ejpam-901	217	6	zg′(z	zg′(z	NOUN
ejpam-901	217	7	)	)	PUNCT
ejpam-901	217	8	.	.	PUNCT
ejpam-901	218	1	(	(	PUNCT
ejpam-901	218	2	28	28	NUM
ejpam-901	218	3	)	)	PUNCT
ejpam-901	218	4	since	since	SCONJ
ejpam-901	218	5	f	f	PROPN
ejpam-901	218	6	∈	∈	PROPN
ejpam-901	218	7	t	t	PROPN
ejpam-901	218	8	s	s	X
ejpam-901	218	9	λ,µ	λ,µ	X
ejpam-901	218	10	(	(	PUNCT
ejpam-901	218	11	γ	γ	X
ejpam-901	218	12	;	;	PUNCT
ejpam-901	218	13	h	h	NOUN
ejpam-901	218	14	)	)	PUNCT
ejpam-901	218	15	,	,	PUNCT
ejpam-901	218	16	from	from	ADP
ejpam-901	218	17	(	(	PUNCT
ejpam-901	218	18	28	28	NUM
ejpam-901	218	19	)	)	PUNCT
ejpam-901	218	20	,	,	PUNCT
ejpam-901	218	21	we	we	PRON
ejpam-901	218	22	have	have	VERB
ejpam-901	218	23	g(z	g(z	VERB
ejpam-901	218	24	)	)	PUNCT
ejpam-901	219	1	+	+	CCONJ
ejpam-901	219	2	1	1	NUM
ejpam-901	219	3	c	c	NOUN
ejpam-901	219	4	+	+	CCONJ
ejpam-901	219	5	1	1	NUM
ejpam-901	219	6	zg′(z	zg′(z	NOUN
ejpam-901	219	7	)	)	PUNCT
ejpam-901	219	8	≺	≺	NOUN
ejpam-901	219	9	h(z	h(z	NOUN
ejpam-901	219	10	)	)	PUNCT
ejpam-901	219	11	(	(	PUNCT
ejpam-901	219	12	re{c	re{c	NOUN
ejpam-901	219	13	}	}	PUNCT
ejpam-901	219	14	>	>	PUNCT
ejpam-901	219	15	−1	−1	NOUN
ejpam-901	219	16	)	)	PUNCT
ejpam-901	219	17	,	,	PUNCT
ejpam-901	219	18	and	and	CCONJ
ejpam-901	219	19	so	so	ADV
ejpam-901	219	20	an	an	DET
ejpam-901	219	21	application	application	NOUN
ejpam-901	219	22	of	of	ADP
ejpam-901	219	23	lemma	lemma	PROPN
ejpam-901	219	24	1	1	NUM
ejpam-901	219	25	yields	yield	NOUN
ejpam-901	219	26	g(z	g(z	PROPN
ejpam-901	219	27	)	)	PUNCT
ejpam-901	219	28	≺eh(z	≺eh(z	PROPN
ejpam-901	219	29	)	)	PUNCT
ejpam-901	220	1	=	=	PUNCT
ejpam-901	221	1	c	c	NOUN
ejpam-901	221	2	+	+	NOUN
ejpam-901	221	3	1	1	NUM
ejpam-901	221	4	zc+1	zc+1	NUM
ejpam-901	221	5	∫	∫	PROPN
ejpam-901	221	6	z	z	NOUN
ejpam-901	221	7	0	0	NUM
ejpam-901	221	8	t	t	PROPN
ejpam-901	221	9	ch(t)d	ch(t)d	PROPN
ejpam-901	221	10	t	t	PROPN
ejpam-901	221	11	≺	≺	VERB
ejpam-901	221	12	h(z	h(z	NOUN
ejpam-901	221	13	)	)	PUNCT
ejpam-901	221	14	.	.	PUNCT
ejpam-901	222	1	therefore	therefore	ADV
ejpam-901	222	2	we	we	PRON
ejpam-901	222	3	conclude	conclude	VERB
ejpam-901	222	4	that	that	SCONJ
ejpam-901	222	5	f	f	PROPN
ejpam-901	222	6	∈	∈	PROPN
ejpam-901	222	7	t	t	PROPN
ejpam-901	222	8	s	s	PART
ejpam-901	222	9	λ,µ(γ;eh)⊂	λ,µ(γ;eh)⊂	NUM
ejpam-901	222	10	t	t	PROPN
ejpam-901	222	11	s	s	PART
ejpam-901	222	12	λ,µ(γ	λ,µ(γ	NOUN
ejpam-901	222	13	;	;	PUNCT
ejpam-901	222	14	h	h	X
ejpam-901	222	15	)	)	PUNCT
ejpam-901	222	16	.	.	PUNCT
ejpam-901	223	1	theorem	theorem	VERB
ejpam-901	223	2	9	9	NUM
ejpam-901	223	3	.	.	PUNCT
ejpam-901	224	1	if	if	SCONJ
ejpam-901	224	2	f	f	PROPN
ejpam-901	224	3	∈	∈	PROPN
ejpam-901	224	4	a	a	PROPN
ejpam-901	224	5	and	and	CCONJ
ejpam-901	224	6	f	f	PROPN
ejpam-901	224	7	be	be	AUX
ejpam-901	224	8	defined	define	VERB
ejpam-901	224	9	as	as	ADP
ejpam-901	224	10	in	in	ADP
ejpam-901	224	11	theorem	theorem	NOUN
ejpam-901	224	12	8	8	NUM
ejpam-901	224	13	.	.	PUNCT
ejpam-901	225	1	if	if	SCONJ
ejpam-901	225	2	(	(	PUNCT
ejpam-901	225	3	1−α	1−α	NUM
ejpam-901	225	4	)	)	PUNCT
ejpam-901	225	5	i	i	PRON
ejpam-901	225	6	s	s	VERB
ejpam-901	225	7	λ,µ	λ,µ	NOUN
ejpam-901	225	8	f(z	f(z	PROPN
ejpam-901	225	9	)	)	PUNCT
ejpam-901	225	10	z	z	NOUN
ejpam-901	226	1	+	+	NOUN
ejpam-901	226	2	α	α	NOUN
ejpam-901	227	1	i	i	PRON
ejpam-901	227	2	s	s	VERB
ejpam-901	227	3	λ,µ	λ,µ	PROPN
ejpam-901	227	4	f	f	PROPN
ejpam-901	227	5	(	(	PUNCT
ejpam-901	227	6	z	z	NOUN
ejpam-901	227	7	)	)	PUNCT
ejpam-901	227	8	z	z	NOUN
ejpam-901	227	9	≺	≺	NOUN
ejpam-901	227	10	h(z	h(z	NOUN
ejpam-901	227	11	)	)	PUNCT
ejpam-901	227	12	(	(	PUNCT
ejpam-901	227	13	α	α	X
ejpam-901	227	14	>	>	X
ejpam-901	227	15	0	0	NUM
ejpam-901	227	16	)	)	PUNCT
ejpam-901	227	17	,	,	PUNCT
ejpam-901	227	18	(	(	PUNCT
ejpam-901	227	19	29	29	NUM
ejpam-901	227	20	)	)	PUNCT
ejpam-901	228	1	then	then	ADV
ejpam-901	228	2	f	f	PROPN
ejpam-901	228	3	∈	∈	PROPN
ejpam-901	228	4	t	t	PROPN
ejpam-901	228	5	s	s	X
ejpam-901	228	6	λ,µ	λ,µ	PROPN
ejpam-901	228	7	(	(	PUNCT
ejpam-901	228	8	0;eh	0;eh	NUM
ejpam-901	228	9	)	)	PUNCT
ejpam-901	228	10	,	,	PUNCT
ejpam-901	228	11	where	where	SCONJ
ejpam-901	228	12	eh(z	eh(z	X
ejpam-901	228	13	)	)	PUNCT
ejpam-901	228	14	=	=	PUNCT
ejpam-901	229	1	c	c	NOUN
ejpam-901	230	1	+	+	NOUN
ejpam-901	230	2	1	1	NUM
ejpam-901	230	3	α	α	NOUN
ejpam-901	230	4	z	z	NOUN
ejpam-901	230	5	−	−	NOUN
ejpam-901	231	1	α	α	NOUN
ejpam-901	231	2	c+1	c+1	NUM
ejpam-901	231	3	∫	∫	PROPN
ejpam-901	231	4	z	z	NOUN
ejpam-901	231	5	0	0	PROPN
ejpam-901	231	6	t	t	PROPN
ejpam-901	231	7	c+1	c+1	NUM
ejpam-901	231	8	α	α	PRON
ejpam-901	231	9	−1h(t	−1h(t	NOUN
ejpam-901	231	10	)	)	PUNCT
ejpam-901	231	11	≺	≺	NOUN
ejpam-901	231	12	h(z	h(z	NOUN
ejpam-901	231	13	)	)	PUNCT
ejpam-901	231	14	(	(	PUNCT
ejpam-901	231	15	re{c	re{c	NOUN
ejpam-901	231	16	}	}	PUNCT
ejpam-901	231	17	>	>	PUNCT
ejpam-901	231	18	−1	−1	NOUN
ejpam-901	231	19	)	)	PUNCT
ejpam-901	231	20	.	.	PUNCT
ejpam-901	232	1	proof	proof	NOUN
ejpam-901	232	2	.	.	PUNCT
ejpam-901	233	1	let	let	VERB
ejpam-901	233	2	g(z	g(z	ADJ
ejpam-901	233	3	)	)	PUNCT
ejpam-901	234	1	=	=	PUNCT
ejpam-901	235	1	i	i	PRON
ejpam-901	235	2	s	s	VERB
ejpam-901	235	3	λ,µ	λ,µ	NOUN
ejpam-901	235	4	f(z	f(z	PROPN
ejpam-901	235	5	)	)	PUNCT
ejpam-901	235	6	z	z	NOUN
ejpam-901	236	1	(	(	PUNCT
ejpam-901	236	2	z	z	NOUN
ejpam-901	236	3	∈	∈	PROPN
ejpam-901	236	4	u	u	NOUN
ejpam-901	236	5	)	)	PUNCT
ejpam-901	236	6	.	.	PUNCT
ejpam-901	237	1	(	(	PUNCT
ejpam-901	237	2	30	30	NUM
ejpam-901	237	3	)	)	PUNCT
ejpam-901	237	4	then	then	ADV
ejpam-901	237	5	g	g	PROPN
ejpam-901	237	6	is	be	AUX
ejpam-901	237	7	analytic	analytic	ADJ
ejpam-901	237	8	in	in	ADP
ejpam-901	237	9	u	u	NOUN
ejpam-901	237	10	with	with	ADP
ejpam-901	237	11	g(0	g(0	NOUN
ejpam-901	237	12	)	)	PUNCT
ejpam-901	238	1	=	=	SYM
ejpam-901	238	2	1	1	NUM
ejpam-901	238	3	and	and	CCONJ
ejpam-901	238	4	zg′(z	zg′(z	NOUN
ejpam-901	238	5	)	)	PUNCT
ejpam-901	238	6	=	=	PUNCT
ejpam-901	239	1	(	(	PUNCT
ejpam-901	239	2	i	i	PRON
ejpam-901	239	3	s	s	VERB
ejpam-901	239	4	λ,µf(z))′	λ,µf(z))′	PROPN
ejpam-901	239	5	−	−	PROPN
ejpam-901	239	6	g(z	g(z	PROPN
ejpam-901	239	7	)	)	PUNCT
ejpam-901	239	8	.	.	PUNCT
ejpam-901	240	1	(	(	PUNCT
ejpam-901	240	2	31	31	NUM
ejpam-901	240	3	)	)	PUNCT
ejpam-901	240	4	it	it	PRON
ejpam-901	240	5	follows	follow	VERB
ejpam-901	240	6	from	from	ADP
ejpam-901	240	7	(	(	PUNCT
ejpam-901	240	8	25	25	NUM
ejpam-901	240	9	)	)	PUNCT
ejpam-901	240	10	,	,	PUNCT
ejpam-901	240	11	(	(	PUNCT
ejpam-901	240	12	29	29	NUM
ejpam-901	240	13	)	)	PUNCT
ejpam-901	240	14	,	,	PUNCT
ejpam-901	240	15	(	(	PUNCT
ejpam-901	240	16	30	30	NUM
ejpam-901	240	17	)	)	PUNCT
ejpam-901	240	18	,	,	PUNCT
ejpam-901	240	19	and	and	CCONJ
ejpam-901	240	20	(	(	PUNCT
ejpam-901	240	21	31	31	NUM
ejpam-901	240	22	)	)	PUNCT
ejpam-901	240	23	that	that	SCONJ
ejpam-901	240	24	(	(	PUNCT
ejpam-901	240	25	1−α	1−α	NUM
ejpam-901	240	26	)	)	PUNCT
ejpam-901	240	27	i	i	PRON
ejpam-901	240	28	s	s	VERB
ejpam-901	240	29	λ,µ	λ,µ	NOUN
ejpam-901	240	30	f(z	f(z	PROPN
ejpam-901	240	31	)	)	PUNCT
ejpam-901	240	32	z	z	NOUN
ejpam-901	241	1	+	+	NOUN
ejpam-901	241	2	α	α	NOUN
ejpam-901	242	1	i	i	PRON
ejpam-901	242	2	s	s	VERB
ejpam-901	242	3	λ,µ	λ,µ	PROPN
ejpam-901	242	4	f	f	PROPN
ejpam-901	242	5	(	(	PUNCT
ejpam-901	242	6	z	z	NOUN
ejpam-901	242	7	)	)	PUNCT
ejpam-901	242	8	z	z	NOUN
ejpam-901	243	1	=	=	SYM
ejpam-901	243	2	(	(	PUNCT
ejpam-901	243	3	1−α	1−α	NUM
ejpam-901	243	4	)	)	PUNCT
ejpam-901	244	1	i	i	PRON
ejpam-901	244	2	s	s	VERB
ejpam-901	244	3	λ,µ	λ,µ	NOUN
ejpam-901	244	4	f(z	f(z	PROPN
ejpam-901	244	5	)	)	PUNCT
ejpam-901	244	6	z	z	NOUN
ejpam-901	245	1	+	+	NOUN
ejpam-901	245	2	α	α	PROPN
ejpam-901	245	3	c	c	NOUN
ejpam-901	245	4	+	+	CCONJ
ejpam-901	245	5	1	1	NUM
ejpam-901	245	6			NOUN
ejpam-901	245	7			NOUN
ejpam-901	245	8	ci	ci	PROPN
ejpam-901	245	9	s	s	PART
ejpam-901	245	10	λ,µ	λ,µ	NOUN
ejpam-901	245	11	f(z	f(z	PROPN
ejpam-901	245	12	)	)	PUNCT
ejpam-901	246	1	z	z	NOUN
ejpam-901	247	1	+	+	CCONJ
ejpam-901	247	2	(	(	PUNCT
ejpam-901	247	3	i	i	PRON
ejpam-901	247	4	s	s	VERB
ejpam-901	247	5	λ,µf(z))′	λ,µf(z))′	PROPN
ejpam-901	247	6			PROPN
ejpam-901	247	7			PROPN
ejpam-901	247	8	o.	o.	NOUN
ejpam-901	247	9	kwon	kwon	PROPN
ejpam-901	247	10	,	,	PUNCT
ejpam-901	247	11	n.	n.	PROPN
ejpam-901	247	12	cho	cho	PROPN
ejpam-901	247	13	/	/	SYM
ejpam-901	247	14	eur	eur	PROPN
ejpam-901	247	15	.	.	PUNCT
ejpam-901	248	1	j.	j.	PROPN
ejpam-901	248	2	pure	pure	PROPN
ejpam-901	248	3	appl	appl	PROPN
ejpam-901	248	4	.	.	PROPN
ejpam-901	248	5	math	math	PROPN
ejpam-901	248	6	,	,	PUNCT
ejpam-901	248	7	3	3	NUM
ejpam-901	248	8	(	(	PUNCT
ejpam-901	248	9	2010	2010	NUM
ejpam-901	248	10	)	)	PUNCT
ejpam-901	248	11	,	,	PUNCT
ejpam-901	248	12	1124	1124	NUM
ejpam-901	248	13	-	-	SYM
ejpam-901	248	14	1136	1136	NUM
ejpam-901	248	15	1134	1134	NUM
ejpam-901	248	16	=	=	SYM
ejpam-901	248	17	g(z	g(z	PROPN
ejpam-901	248	18	)	)	PUNCT
ejpam-901	249	1	+	+	CCONJ
ejpam-901	249	2	α	α	PRON
ejpam-901	249	3	c	c	NOUN
ejpam-901	249	4	+	+	CCONJ
ejpam-901	249	5	1	1	NUM
ejpam-901	249	6	zg′(z	zg′(z	NOUN
ejpam-901	249	7	)	)	PUNCT
ejpam-901	249	8	≺	≺	NOUN
ejpam-901	249	9	h(z	h(z	NOUN
ejpam-901	249	10	)	)	PUNCT
ejpam-901	249	11	(	(	PUNCT
ejpam-901	249	12	re{c	re{c	NOUN
ejpam-901	249	13	}	}	PUNCT
ejpam-901	249	14	>	>	X
ejpam-901	249	15	1;α	1;α	NUM
ejpam-901	249	16	>	>	X
ejpam-901	249	17	0	0	NUM
ejpam-901	249	18	)	)	PUNCT
ejpam-901	249	19	.	.	PUNCT
ejpam-901	250	1	therefore	therefore	ADV
ejpam-901	250	2	,	,	PUNCT
ejpam-901	250	3	by	by	ADP
ejpam-901	250	4	lemma	lemma	PROPN
ejpam-901	250	5	1	1	NUM
ejpam-901	250	6	,	,	PUNCT
ejpam-901	250	7	we	we	PRON
ejpam-901	250	8	conclude	conclude	VERB
ejpam-901	250	9	that	that	SCONJ
ejpam-901	250	10	theorem	theorem	VERB
ejpam-901	250	11	9	9	NUM
ejpam-901	250	12	holds	hold	NOUN
ejpam-901	250	13	true	true	ADJ
ejpam-901	250	14	as	as	SCONJ
ejpam-901	250	15	stated	state	VERB
ejpam-901	250	16	.	.	PUNCT
ejpam-901	251	1	theorem	theorem	ADJ
ejpam-901	251	2	10	10	NUM
ejpam-901	251	3	.	.	PUNCT
ejpam-901	252	1	let	let	VERB
ejpam-901	252	2	f	f	PROPN
ejpam-901	252	3	∈	∈	PROPN
ejpam-901	252	4	t	t	PROPN
ejpam-901	252	5	s	s	X
ejpam-901	252	6	λ,µ	λ,µ	X
ejpam-901	252	7	(	(	PUNCT
ejpam-901	252	8	γ	γ	X
ejpam-901	252	9	;	;	PUNCT
ejpam-901	252	10	h	h	NOUN
ejpam-901	252	11	)	)	PUNCT
ejpam-901	252	12	.	.	PUNCT
ejpam-901	253	1	if	if	SCONJ
ejpam-901	253	2	the	the	DET
ejpam-901	253	3	function	function	NOUN
ejpam-901	253	4	f	f	PROPN
ejpam-901	253	5	is	be	AUX
ejpam-901	253	6	defined	define	VERB
ejpam-901	253	7	by	by	ADP
ejpam-901	253	8	f(z	f(z	NOUN
ejpam-901	253	9	)	)	PUNCT
ejpam-901	254	1	=	=	PUNCT
ejpam-901	254	2	c	c	NOUN
ejpam-901	254	3	+	+	NOUN
ejpam-901	254	4	1	1	NUM
ejpam-901	254	5	zc	zc	NUM
ejpam-901	254	6	∫	∫	PROPN
ejpam-901	254	7	z	z	PROPN
ejpam-901	254	8	0	0	PROPN
ejpam-901	255	1	t	t	PROPN
ejpam-901	255	2	c−1	c−1	PROPN
ejpam-901	255	3	f	f	PROPN
ejpam-901	255	4	(	(	PUNCT
ejpam-901	255	5	t)d	t)d	PROPN
ejpam-901	255	6	t	t	PROPN
ejpam-901	255	7	(	(	PUNCT
ejpam-901	255	8	c	c	NOUN
ejpam-901	255	9	>	>	X
ejpam-901	255	10	−1	−1	NOUN
ejpam-901	255	11	)	)	PUNCT
ejpam-901	255	12	,	,	PUNCT
ejpam-901	255	13	(	(	PUNCT
ejpam-901	255	14	32	32	NUM
ejpam-901	255	15	)	)	PUNCT
ejpam-901	255	16	then	then	ADV
ejpam-901	255	17	f	f	X
ejpam-901	255	18	(	(	PUNCT
ejpam-901	255	19	σz	σz	PROPN
ejpam-901	255	20	)	)	PUNCT
ejpam-901	255	21	σ	σ	PROPN
ejpam-901	255	22	∈	∈	PROPN
ejpam-901	255	23	t	t	NOUN
ejpam-901	255	24	s	s	PART
ejpam-901	255	25	λ,µ(γ	λ,µ(γ	NOUN
ejpam-901	255	26	;	;	PUNCT
ejpam-901	255	27	h	h	X
ejpam-901	255	28	)	)	PUNCT
ejpam-901	255	29	,	,	PUNCT
ejpam-901	255	30	where	where	SCONJ
ejpam-901	255	31	σ	σ	NOUN
ejpam-901	255	32	=	=	SYM
ejpam-901	255	33	σ(c	σ(c	PROPN
ejpam-901	255	34	)	)	PUNCT
ejpam-901	255	35	=	=	PUNCT
ejpam-901	256	1	p	p	NOUN
ejpam-901	256	2	1	1	NUM
ejpam-901	256	3	+	+	CCONJ
ejpam-901	256	4	(	(	PUNCT
ejpam-901	256	5	c	c	X
ejpam-901	256	6	+	+	NOUN
ejpam-901	257	1	1)2	1)2	NUM
ejpam-901	257	2	−	−	NOUN
ejpam-901	257	3	1	1	NUM
ejpam-901	257	4	c	c	NOUN
ejpam-901	257	5	+	+	NOUN
ejpam-901	257	6	1	1	NUM
ejpam-901	257	7	.	.	PUNCT
ejpam-901	258	1	(	(	PUNCT
ejpam-901	258	2	33	33	NUM
ejpam-901	258	3	)	)	PUNCT
ejpam-901	258	4	the	the	DET
ejpam-901	258	5	bound	bind	VERB
ejpam-901	258	6	σ	σ	PROPN
ejpam-901	258	7	is	be	AUX
ejpam-901	258	8	sharp	sharp	ADJ
ejpam-901	258	9	for	for	ADP
ejpam-901	258	10	the	the	DET
ejpam-901	258	11	function	function	NOUN
ejpam-901	258	12	h(z	h(z	NOUN
ejpam-901	258	13	)	)	PUNCT
ejpam-901	258	14	=	=	PUNCT
ejpam-901	259	1	β	β	X
ejpam-901	259	2	+	+	X
ejpam-901	259	3	(	(	PUNCT
ejpam-901	259	4	1−	1−	NUM
ejpam-901	259	5	β	β	NOUN
ejpam-901	259	6	)	)	PUNCT
ejpam-901	259	7	1	1	NUM
ejpam-901	260	1	+	+	SYM
ejpam-901	260	2	z	z	NOUN
ejpam-901	260	3	1−	1−	NUM
ejpam-901	260	4	z	z	NOUN
ejpam-901	260	5	(	(	PUNCT
ejpam-901	260	6	β	β	X
ejpam-901	260	7	6=	6=	ADP
ejpam-901	260	8	1	1	NUM
ejpam-901	260	9	;	;	PUNCT
ejpam-901	260	10	z	z	PROPN
ejpam-901	260	11	∈	∈	PROPN
ejpam-901	260	12	u	u	NOUN
ejpam-901	260	13	)	)	PUNCT
ejpam-901	260	14	.	.	PUNCT
ejpam-901	261	1	(	(	PUNCT
ejpam-901	261	2	34	34	NUM
ejpam-901	261	3	)	)	PUNCT
ejpam-901	261	4	proof	proof	NOUN
ejpam-901	261	5	.	.	PUNCT
ejpam-901	262	1	we	we	PRON
ejpam-901	262	2	note	note	VERB
ejpam-901	262	3	that	that	SCONJ
ejpam-901	262	4	for	for	ADP
ejpam-901	262	5	f	f	PROPN
ejpam-901	262	6	∈a	∈a	PROPN
ejpam-901	262	7	,	,	PUNCT
ejpam-901	262	8	f(z	f(z	PROPN
ejpam-901	262	9	)	)	PUNCT
ejpam-901	262	10	=	=	SYM
ejpam-901	262	11	f(z	f(z	PROPN
ejpam-901	262	12	)	)	PUNCT
ejpam-901	262	13	∗	∗	NOUN
ejpam-901	262	14	z	z	NOUN
ejpam-901	262	15	1−	1−	NUM
ejpam-901	262	16	z	z	NOUN
ejpam-901	262	17	and	and	CCONJ
ejpam-901	262	18	zf	zf	PROPN
ejpam-901	262	19	′(z	′(z	NOUN
ejpam-901	262	20	)	)	PUNCT
ejpam-901	263	1	=	=	SYM
ejpam-901	263	2	f(z	f(z	PROPN
ejpam-901	263	3	)	)	PUNCT
ejpam-901	263	4	∗	∗	NOUN
ejpam-901	263	5	z	z	NOUN
ejpam-901	263	6	(	(	PUNCT
ejpam-901	263	7	1−	1−	NUM
ejpam-901	263	8	z)2	z)2	NOUN
ejpam-901	263	9	.	.	PUNCT
ejpam-901	264	1	then	then	ADV
ejpam-901	264	2	from	from	ADP
ejpam-901	264	3	(	(	PUNCT
ejpam-901	264	4	32	32	NUM
ejpam-901	264	5	)	)	PUNCT
ejpam-901	264	6	,	,	PUNCT
ejpam-901	264	7	we	we	PRON
ejpam-901	264	8	have	have	VERB
ejpam-901	264	9	f	f	PROPN
ejpam-901	264	10	(	(	PUNCT
ejpam-901	264	11	z	z	NOUN
ejpam-901	264	12	)	)	PUNCT
ejpam-901	264	13	=	=	PUNCT
ejpam-901	264	14	cf(z	cf(z	X
ejpam-901	264	15	)	)	PUNCT
ejpam-901	265	1	+	+	CCONJ
ejpam-901	265	2	zf	zf	PROPN
ejpam-901	265	3	′(z	′(z	NOUN
ejpam-901	265	4	)	)	PUNCT
ejpam-901	265	5	c	c	NOUN
ejpam-901	266	1	+	+	NOUN
ejpam-901	266	2	1	1	NUM
ejpam-901	266	3	=	=	SYM
ejpam-901	266	4	(	(	PUNCT
ejpam-901	266	5	f	f	PROPN
ejpam-901	266	6	∗	∗	PROPN
ejpam-901	266	7	g)(z	g)(z	PUNCT
ejpam-901	266	8	)	)	PUNCT
ejpam-901	266	9	(	(	PUNCT
ejpam-901	266	10	c	c	X
ejpam-901	266	11	>	>	X
ejpam-901	266	12	−1	−1	NOUN
ejpam-901	266	13	;	;	PUNCT
ejpam-901	266	14	z	z	PROPN
ejpam-901	266	15	∈	∈	PROPN
ejpam-901	266	16	u	u	NOUN
ejpam-901	266	17	)	)	PUNCT
ejpam-901	266	18	,	,	PUNCT
ejpam-901	266	19	(	(	PUNCT
ejpam-901	266	20	35	35	NUM
ejpam-901	266	21	)	)	PUNCT
ejpam-901	266	22	where	where	SCONJ
ejpam-901	266	23	g(z	g(z	ADJ
ejpam-901	266	24	)	)	PUNCT
ejpam-901	266	25	=	=	SYM
ejpam-901	266	26	1	1	NUM
ejpam-901	266	27	c	c	NOUN
ejpam-901	266	28	+	+	SYM
ejpam-901	266	29	1	1	NUM
ejpam-901	266	30	�	�	PROPN
ejpam-901	266	31	c	c	PROPN
ejpam-901	266	32	z	z	PROPN
ejpam-901	266	33	1−	1−	NUM
ejpam-901	266	34	z	z	NOUN
ejpam-901	266	35	+	+	NUM
ejpam-901	266	36	z	z	X
ejpam-901	266	37	(	(	PUNCT
ejpam-901	266	38	1−	1−	NUM
ejpam-901	266	39	z)2	z)2	PROPN
ejpam-901	266	40	�	�	PROPN
ejpam-901	266	41	∈a	∈a	PROPN
ejpam-901	266	42	.	.	PUNCT
ejpam-901	267	1	(	(	PUNCT
ejpam-901	267	2	36	36	NUM
ejpam-901	267	3	)	)	PUNCT
ejpam-901	267	4	next	next	ADV
ejpam-901	267	5	,	,	PUNCT
ejpam-901	267	6	we	we	PRON
ejpam-901	267	7	show	show	VERB
ejpam-901	267	8	that	that	SCONJ
ejpam-901	267	9	re	re	VERB
ejpam-901	267	10	�	�	PROPN
ejpam-901	267	11	g(z	g(z	PROPN
ejpam-901	267	12	)	)	PUNCT
ejpam-901	267	13	z	z	PROPN
ejpam-901	267	14	�	�	PROPN
ejpam-901	267	15	>	>	SYM
ejpam-901	267	16	1	1	NUM
ejpam-901	267	17	2	2	NUM
ejpam-901	267	18	(	(	PUNCT
ejpam-901	267	19	|z|	|z|	NOUN
ejpam-901	267	20	<	<	X
ejpam-901	267	21	σ	σ	PROPN
ejpam-901	267	22	)	)	PUNCT
ejpam-901	267	23	,	,	PUNCT
ejpam-901	267	24	(	(	PUNCT
ejpam-901	267	25	37	37	NUM
ejpam-901	267	26	)	)	PUNCT
ejpam-901	267	27	where	where	SCONJ
ejpam-901	267	28	σ	σ	NOUN
ejpam-901	267	29	=	=	SYM
ejpam-901	267	30	σ(c	σ(c	PROPN
ejpam-901	267	31	)	)	PUNCT
ejpam-901	267	32	is	be	AUX
ejpam-901	267	33	given	give	VERB
ejpam-901	267	34	by	by	ADP
ejpam-901	267	35	(	(	PUNCT
ejpam-901	267	36	4.10	4.10	NUM
ejpam-901	267	37	)	)	PUNCT
ejpam-901	267	38	.	.	PUNCT
ejpam-901	268	1	letting	let	VERB
ejpam-901	268	2	1	1	NUM
ejpam-901	268	3	1−	1−	NUM
ejpam-901	268	4	z	z	NOUN
ejpam-901	268	5	=	=	SYM
ejpam-901	268	6	reiθ	reiθ	PROPN
ejpam-901	268	7	(	(	PUNCT
ejpam-901	268	8	|z|	|z|	NOUN
ejpam-901	268	9	=	=	SYM
ejpam-901	268	10	r	r	NOUN
ejpam-901	268	11	<	<	X
ejpam-901	268	12	1	1	NUM
ejpam-901	268	13	;	;	PUNCT
ejpam-901	268	14	r	r	NOUN
ejpam-901	268	15	>	>	X
ejpam-901	268	16	0	0	NUM
ejpam-901	268	17	)	)	PUNCT
ejpam-901	268	18	,	,	PUNCT
ejpam-901	268	19	we	we	PRON
ejpam-901	268	20	see	see	VERB
ejpam-901	268	21	that	that	SCONJ
ejpam-901	268	22	cosθ	cosθ	PROPN
ejpam-901	268	23	=	=	SYM
ejpam-901	268	24	1+r2(1−	1+r2(1−	NUM
ejpam-901	268	25	r2	r2	NOUN
ejpam-901	268	26	)	)	PUNCT
ejpam-901	268	27	2r	2r	NUM
ejpam-901	268	28	and	and	CCONJ
ejpam-901	268	29	r≥	r≥	ADJ
ejpam-901	268	30	1	1	NUM
ejpam-901	268	31	1	1	NUM
ejpam-901	268	32	+	+	NUM
ejpam-901	268	33	r	r	NOUN
ejpam-901	268	34	.	.	PUNCT
ejpam-901	269	1	(	(	PUNCT
ejpam-901	269	2	38	38	NUM
ejpam-901	269	3	)	)	PUNCT
ejpam-901	269	4	o.	o.	PROPN
ejpam-901	269	5	kwon	kwon	PROPN
ejpam-901	269	6	,	,	PUNCT
ejpam-901	269	7	n.	n.	PROPN
ejpam-901	269	8	cho	cho	PROPN
ejpam-901	269	9	/	/	SYM
ejpam-901	269	10	eur	eur	PROPN
ejpam-901	269	11	.	.	PUNCT
ejpam-901	270	1	j.	j.	PROPN
ejpam-901	270	2	pure	pure	PROPN
ejpam-901	270	3	appl	appl	PROPN
ejpam-901	270	4	.	.	PROPN
ejpam-901	270	5	math	math	PROPN
ejpam-901	270	6	,	,	PUNCT
ejpam-901	270	7	3	3	NUM
ejpam-901	270	8	(	(	PUNCT
ejpam-901	270	9	2010	2010	NUM
ejpam-901	270	10	)	)	PUNCT
ejpam-901	270	11	,	,	PUNCT
ejpam-901	270	12	1124	1124	NUM
ejpam-901	270	13	-	-	SYM
ejpam-901	270	14	1136	1136	NUM
ejpam-901	270	15	1135	1135	NUM
ejpam-901	270	16	then	then	ADV
ejpam-901	270	17	for	for	ADP
ejpam-901	270	18	(	(	PUNCT
ejpam-901	270	19	36	36	NUM
ejpam-901	270	20	)	)	PUNCT
ejpam-901	270	21	and	and	CCONJ
ejpam-901	270	22	(	(	PUNCT
ejpam-901	270	23	38	38	NUM
ejpam-901	270	24	)	)	PUNCT
ejpam-901	271	1	,	,	PUNCT
ejpam-901	271	2	we	we	PRON
ejpam-901	271	3	have	have	VERB
ejpam-901	271	4	2re	2re	ADJ
ejpam-901	271	5	�	�	PROPN
ejpam-901	271	6	g(z	g(z	PROPN
ejpam-901	271	7	)	)	PUNCT
ejpam-901	271	8	z	z	NOUN
ejpam-901	271	9	�	�	PROPN
ejpam-901	271	10	=	=	SYM
ejpam-901	271	11	2	2	NUM
ejpam-901	271	12	c	c	NOUN
ejpam-901	271	13	+	+	SYM
ejpam-901	271	14	1	1	NUM
ejpam-901	271	15	�	�	PROPN
ejpam-901	271	16	cr	cr	PROPN
ejpam-901	271	17	cosθ	cosθ	PROPN
ejpam-901	271	18	+	+	PROPN
ejpam-901	271	19	r2(2	r2(2	PROPN
ejpam-901	271	20	cos2	cos2	NOUN
ejpam-901	271	21	θ	θ	PROPN
ejpam-901	271	22	−	−	NOUN
ejpam-901	271	23	1	1	NUM
ejpam-901	271	24	)	)	PUNCT
ejpam-901	271	25	�	�	PROPN
ejpam-901	271	26	=	=	SYM
ejpam-901	271	27	r2	r2	PROPN
ejpam-901	271	28	c	c	PROPN
ejpam-901	271	29	+	+	NOUN
ejpam-901	271	30	1	1	NUM
ejpam-901	271	31	�	�	PROPN
ejpam-901	271	32	c(1−	c(1−	NOUN
ejpam-901	271	33	r2	r2	NOUN
ejpam-901	271	34	)	)	PUNCT
ejpam-901	272	1	+	+	NOUN
ejpam-901	272	2	r2(1−	r2(1−	VERB
ejpam-901	272	3	r2)2	r2)2	NUM
ejpam-901	272	4	−	−	NUM
ejpam-901	272	5	2	2	NUM
ejpam-901	272	6	�	�	NOUN
ejpam-901	272	7	+	+	CCONJ
ejpam-901	272	8	1	1	NUM
ejpam-901	272	9	≥	≥	NOUN
ejpam-901	272	10	r2	r2	PROPN
ejpam-901	272	11	c	c	PROPN
ejpam-901	273	1	+	+	CCONJ
ejpam-901	273	2	1	1	NUM
ejpam-901	273	3	�	�	PROPN
ejpam-901	273	4	c	c	PROPN
ejpam-901	273	5	+	+	PROPN
ejpam-901	273	6	1−	1−	NUM
ejpam-901	273	7	2r	2r	NUM
ejpam-901	273	8	−	−	PROPN
ejpam-901	273	9	(	(	PUNCT
ejpam-901	273	10	c	c	NOUN
ejpam-901	273	11	+	+	CCONJ
ejpam-901	273	12	1)r2	1)r2	NUM
ejpam-901	273	13	�	�	NOUN
ejpam-901	273	14	+	+	CCONJ
ejpam-901	273	15	1	1	X
ejpam-901	273	16	.	.	X
ejpam-901	273	17	this	this	PRON
ejpam-901	273	18	evidently	evidently	ADV
ejpam-901	273	19	gives	give	VERB
ejpam-901	273	20	(	(	PUNCT
ejpam-901	273	21	37	37	NUM
ejpam-901	273	22	)	)	PUNCT
ejpam-901	273	23	,	,	PUNCT
ejpam-901	273	24	which	which	PRON
ejpam-901	273	25	is	be	AUX
ejpam-901	273	26	equivalent	equivalent	ADJ
ejpam-901	273	27	to	to	PART
ejpam-901	273	28	re	re	VERB
ejpam-901	273	29	�	�	PROPN
ejpam-901	273	30	g(σz	g(σz	PROPN
ejpam-901	273	31	)	)	PUNCT
ejpam-901	273	32	zσ	zσ	PROPN
ejpam-901	273	33	�	�	PROPN
ejpam-901	273	34	>	>	X
ejpam-901	273	35	1	1	NUM
ejpam-901	273	36	2	2	NUM
ejpam-901	273	37	z	z	NOUN
ejpam-901	273	38	∈	∈	NOUN
ejpam-901	273	39	u	u	NOUN
ejpam-901	273	40	)	)	PUNCT
ejpam-901	273	41	.	.	PUNCT
ejpam-901	274	1	(	(	PUNCT
ejpam-901	274	2	39	39	NUM
ejpam-901	274	3	)	)	PUNCT
ejpam-901	274	4	let	let	VERB
ejpam-901	274	5	f	f	PROPN
ejpam-901	274	6	∈	∈	PROPN
ejpam-901	274	7	t	t	PROPN
ejpam-901	274	8	s	s	X
ejpam-901	274	9	λ,µ	λ,µ	X
ejpam-901	274	10	(	(	PUNCT
ejpam-901	274	11	γ	γ	X
ejpam-901	274	12	;	;	PUNCT
ejpam-901	274	13	h	h	NOUN
ejpam-901	274	14	)	)	PUNCT
ejpam-901	274	15	.	.	PUNCT
ejpam-901	275	1	then	then	ADV
ejpam-901	275	2	,	,	PUNCT
ejpam-901	275	3	by	by	ADP
ejpam-901	275	4	using	use	VERB
ejpam-901	275	5	(	(	PUNCT
ejpam-901	275	6	35	35	NUM
ejpam-901	275	7	)	)	PUNCT
ejpam-901	275	8	and	and	CCONJ
ejpam-901	275	9	(	(	PUNCT
ejpam-901	275	10	39	39	NUM
ejpam-901	275	11	)	)	PUNCT
ejpam-901	275	12	,	,	PUNCT
ejpam-901	275	13	an	an	DET
ejpam-901	275	14	application	application	NOUN
ejpam-901	275	15	of	of	ADP
ejpam-901	275	16	theorem	theorem	ADJ
ejpam-901	275	17	6	6	NUM
ejpam-901	275	18	yields	yield	NOUN
ejpam-901	275	19	f	f	X
ejpam-901	275	20	(	(	PUNCT
ejpam-901	275	21	σz	σz	NOUN
ejpam-901	275	22	)	)	PUNCT
ejpam-901	275	23	σ	σ	NOUN
ejpam-901	275	24	=	=	SYM
ejpam-901	275	25	f(z	f(z	PROPN
ejpam-901	275	26	)	)	PUNCT
ejpam-901	275	27	∗	∗	NOUN
ejpam-901	275	28	g(σz	g(σz	NOUN
ejpam-901	275	29	)	)	PUNCT
ejpam-901	275	30	σ	σ	PROPN
ejpam-901	275	31	∈	∈	PROPN
ejpam-901	275	32	t	t	NOUN
ejpam-901	275	33	s	s	PART
ejpam-901	275	34	λ,µ(γ	λ,µ(γ	NOUN
ejpam-901	275	35	;	;	PUNCT
ejpam-901	275	36	h	h	X
ejpam-901	275	37	)	)	PUNCT
ejpam-901	275	38	.	.	PUNCT
ejpam-901	276	1	for	for	ADP
ejpam-901	276	2	h	h	NOUN
ejpam-901	276	3	given	give	VERB
ejpam-901	276	4	by	by	ADP
ejpam-901	276	5	(	(	PUNCT
ejpam-901	276	6	34	34	NUM
ejpam-901	276	7	)	)	PUNCT
ejpam-901	276	8	,	,	PUNCT
ejpam-901	276	9	we	we	PRON
ejpam-901	276	10	consider	consider	VERB
ejpam-901	276	11	the	the	DET
ejpam-901	276	12	function	function	NOUN
ejpam-901	276	13	f	f	PROPN
ejpam-901	276	14	∈a	∈a	VERB
ejpam-901	276	15	defined	define	VERB
ejpam-901	276	16	by	by	ADP
ejpam-901	276	17	(	(	PUNCT
ejpam-901	276	18	1−	1−	NUM
ejpam-901	276	19	γ	γ	X
ejpam-901	276	20	)	)	PUNCT
ejpam-901	276	21	i	i	PRON
ejpam-901	276	22	s	s	VERB
ejpam-901	276	23	λ,µ	λ,µ	NOUN
ejpam-901	276	24	f(z	f(z	PROPN
ejpam-901	276	25	)	)	PUNCT
ejpam-901	276	26	z	z	NOUN
ejpam-901	277	1	+	+	NUM
ejpam-901	277	2	γ(i	γ(i	NOUN
ejpam-901	277	3	s	s	PART
ejpam-901	277	4	λ,µf(z))′	λ,µf(z))′	PROPN
ejpam-901	277	5	=	=	PUNCT
ejpam-901	277	6	β	β	X
ejpam-901	277	7	+	+	X
ejpam-901	277	8	(	(	PUNCT
ejpam-901	277	9	1−	1−	NUM
ejpam-901	277	10	β	β	NOUN
ejpam-901	277	11	)	)	PUNCT
ejpam-901	277	12	1	1	NUM
ejpam-901	278	1	+	+	SYM
ejpam-901	278	2	z	z	NOUN
ejpam-901	278	3	1−	1−	NUM
ejpam-901	278	4	z	z	NOUN
ejpam-901	278	5	(	(	PUNCT
ejpam-901	278	6	β	β	X
ejpam-901	278	7	6=	6=	ADP
ejpam-901	278	8	1	1	NUM
ejpam-901	278	9	;	;	PUNCT
ejpam-901	278	10	z	z	PROPN
ejpam-901	278	11	∈	∈	PROPN
ejpam-901	278	12	u	u	NOUN
ejpam-901	278	13	)	)	PUNCT
ejpam-901	278	14	.	.	PUNCT
ejpam-901	279	1	(	(	PUNCT
ejpam-901	279	2	40	40	NUM
ejpam-901	279	3	)	)	PUNCT
ejpam-901	279	4	then	then	ADV
ejpam-901	279	5	from	from	ADP
ejpam-901	279	6	(	(	PUNCT
ejpam-901	279	7	26	26	NUM
ejpam-901	279	8	)	)	PUNCT
ejpam-901	279	9	,	,	PUNCT
ejpam-901	279	10	(	(	PUNCT
ejpam-901	279	11	28	28	NUM
ejpam-901	279	12	)	)	PUNCT
ejpam-901	279	13	and	and	CCONJ
ejpam-901	279	14	(	(	PUNCT
ejpam-901	279	15	40	40	NUM
ejpam-901	279	16	)	)	PUNCT
ejpam-901	279	17	,	,	PUNCT
ejpam-901	279	18	we	we	PRON
ejpam-901	279	19	find	find	VERB
ejpam-901	279	20	that	that	SCONJ
ejpam-901	279	21	(	(	PUNCT
ejpam-901	279	22	1−	1−	NUM
ejpam-901	279	23	γ	γ	X
ejpam-901	279	24	)	)	PUNCT
ejpam-901	279	25	i	i	PRON
ejpam-901	279	26	s	s	VERB
ejpam-901	279	27	λ,µ	λ,µ	PROPN
ejpam-901	279	28	f	f	PROPN
ejpam-901	279	29	(	(	PUNCT
ejpam-901	279	30	z	z	NOUN
ejpam-901	279	31	)	)	PUNCT
ejpam-901	279	32	z	z	NOUN
ejpam-901	280	1	+	+	NUM
ejpam-901	280	2	γ(i	γ(i	NOUN
ejpam-901	280	3	s	s	X
ejpam-901	280	4	λ,µ	λ,µ	NOUN
ejpam-901	280	5	f	f	X
ejpam-901	280	6	(	(	PUNCT
ejpam-901	280	7	z))′	z))′	PROPN
ejpam-901	280	8	=	=	SYM
ejpam-901	280	9	β	β	X
ejpam-901	280	10	+	+	X
ejpam-901	280	11	(	(	PUNCT
ejpam-901	280	12	1−	1−	NUM
ejpam-901	280	13	β	β	NOUN
ejpam-901	280	14	)	)	PUNCT
ejpam-901	280	15	1	1	NUM
ejpam-901	281	1	+	+	SYM
ejpam-901	281	2	z	z	NOUN
ejpam-901	281	3	1−	1−	NUM
ejpam-901	281	4	z	z	NOUN
ejpam-901	282	1	+	+	CCONJ
ejpam-901	282	2	z	z	NOUN
ejpam-901	282	3	c	c	NOUN
ejpam-901	282	4	+	+	NOUN
ejpam-901	282	5	1	1	NUM
ejpam-901	282	6	�	�	PROPN
ejpam-901	282	7	β	β	X
ejpam-901	282	8	+	+	X
ejpam-901	282	9	(	(	PUNCT
ejpam-901	282	10	1−	1−	NUM
ejpam-901	282	11	β	β	NOUN
ejpam-901	282	12	)	)	PUNCT
ejpam-901	282	13	1	1	NUM
ejpam-901	283	1	+	+	SYM
ejpam-901	283	2	z	z	NOUN
ejpam-901	283	3	1−	1−	NUM
ejpam-901	283	4	z	z	NOUN
ejpam-901	283	5	�	�	PROPN
ejpam-901	283	6	′	′	NUM
ejpam-901	283	7	=	=	PUNCT
ejpam-901	283	8	β	β	NOUN
ejpam-901	284	1	+	+	X
ejpam-901	284	2	(	(	PUNCT
ejpam-901	284	3	1−	1−	NUM
ejpam-901	284	4	β)(c+	β)(c+	SYM
ejpam-901	284	5	1	1	NUM
ejpam-901	284	6	+	+	NUM
ejpam-901	284	7	2z−	2z−	NUM
ejpam-901	284	8	(	(	PUNCT
ejpam-901	284	9	c	c	NOUN
ejpam-901	284	10	+	+	NOUN
ejpam-901	284	11	1)z2	1)z2	NUM
ejpam-901	284	12	)	)	PUNCT
ejpam-901	284	13	(	(	PUNCT
ejpam-901	284	14	c	c	NOUN
ejpam-901	284	15	+	+	SYM
ejpam-901	284	16	1)(1−	1)(1−	NUM
ejpam-901	284	17	z)2	z)2	NOUN
ejpam-901	284	18	=	=	SYM
ejpam-901	284	19	β	β	X
ejpam-901	284	20	(	(	PUNCT
ejpam-901	284	21	z	z	NOUN
ejpam-901	284	22	=	=	SYM
ejpam-901	284	23	−σ	−σ	NOUN
ejpam-901	284	24	)	)	PUNCT
ejpam-901	284	25	.	.	PUNCT
ejpam-901	285	1	therefore	therefore	ADV
ejpam-901	285	2	we	we	PRON
ejpam-901	285	3	conclude	conclude	VERB
ejpam-901	285	4	that	that	SCONJ
ejpam-901	285	5	the	the	DET
ejpam-901	285	6	bound	bound	ADJ
ejpam-901	285	7	σ	σ	NOUN
ejpam-901	285	8	=	=	SYM
ejpam-901	285	9	σ(c	σ(c	PROPN
ejpam-901	285	10	)	)	PUNCT
ejpam-901	285	11	can	can	AUX
ejpam-901	285	12	not	not	PART
ejpam-901	285	13	be	be	AUX
ejpam-901	285	14	increased	increase	VERB
ejpam-901	285	15	for	for	ADP
ejpam-901	285	16	each	each	DET
ejpam-901	285	17	c	c	NOUN
ejpam-901	285	18	(	(	PUNCT
ejpam-901	285	19	c	c	NOUN
ejpam-901	285	20	>	>	X
ejpam-901	285	21	−1	−1	NOUN
ejpam-901	285	22	)	)	PUNCT
ejpam-901	285	23	.	.	PUNCT
ejpam-901	286	1	acknowledgements	acknowledgement	NOUN
ejpam-901	286	2	this	this	DET
ejpam-901	286	3	research	research	NOUN
ejpam-901	286	4	was	be	AUX
ejpam-901	286	5	supported	support	VERB
ejpam-901	286	6	by	by	ADP
ejpam-901	286	7	the	the	DET
ejpam-901	286	8	basic	basic	ADJ
ejpam-901	286	9	science	science	NOUN
ejpam-901	286	10	research	research	NOUN
ejpam-901	286	11	program	program	NOUN
ejpam-901	286	12	through	through	ADP
ejpam-901	286	13	the	the	DET
ejpam-901	286	14	national	national	PROPN
ejpam-901	286	15	research	research	PROPN
ejpam-901	286	16	foundation	foundation	PROPN
ejpam-901	286	17	of	of	ADP
ejpam-901	286	18	korea(nrf	korea(nrf	PROPN
ejpam-901	286	19	)	)	PUNCT
ejpam-901	286	20	funded	fund	VERB
ejpam-901	286	21	by	by	ADP
ejpam-901	286	22	the	the	DET
ejpam-901	286	23	ministry	ministry	PROPN
ejpam-901	286	24	of	of	ADP
ejpam-901	286	25	education	education	PROPN
ejpam-901	286	26	,	,	PUNCT
ejpam-901	286	27	science	science	NOUN
ejpam-901	286	28	and	and	CCONJ
ejpam-901	286	29	technology	technology	NOUN
ejpam-901	286	30	(	(	PUNCT
ejpam-901	286	31	no	no	INTJ
ejpam-901	286	32	.	.	NOUN
ejpam-901	286	33	2010	2010	NUM
ejpam-901	286	34	-	-	SYM
ejpam-901	286	35	0017111	0017111	NUM
ejpam-901	286	36	)	)	PUNCT
ejpam-901	286	37	.	.	PUNCT
ejpam-901	287	1	references	reference	NOUN
ejpam-901	287	2	1136	1136	NUM
ejpam-901	287	3	references	reference	NOUN
ejpam-901	287	4	[	[	X
ejpam-901	287	5	1	1	NUM
ejpam-901	287	6	]	]	X
ejpam-901	287	7	j.h	j.h	PROPN
ejpam-901	287	8	.	.	PROPN
ejpam-901	287	9	choi	choi	PROPN
ejpam-901	287	10	,	,	PUNCT
ejpam-901	287	11	m.	m.	NOUN
ejpam-901	287	12	saigo	saigo	PROPN
ejpam-901	287	13	and	and	CCONJ
ejpam-901	287	14	h.m	h.m	PROPN
ejpam-901	287	15	.	.	PROPN
ejpam-901	287	16	srivastava	srivastava	PROPN
ejpam-901	287	17	.	.	PUNCT
ejpam-901	288	1	some	some	DET
ejpam-901	288	2	inclusion	inclusion	NOUN
ejpam-901	288	3	properties	property	NOUN
ejpam-901	288	4	of	of	ADP
ejpam-901	288	5	a	a	DET
ejpam-901	288	6	certain	certain	ADJ
ejpam-901	288	7	family	family	NOUN
ejpam-901	288	8	of	of	ADP
ejpam-901	288	9	integral	integral	ADJ
ejpam-901	288	10	operators	operator	NOUN
ejpam-901	288	11	.	.	PUNCT
ejpam-901	289	1	j.	j.	PROPN
ejpam-901	289	2	math	math	PROPN
ejpam-901	289	3	.	.	PUNCT
ejpam-901	290	1	anal	anal	PROPN
ejpam-901	290	2	.	.	PUNCT
ejpam-901	291	1	appl	appl	PROPN
ejpam-901	291	2	.	.	PROPN
ejpam-901	291	3	,	,	PUNCT
ejpam-901	291	4	276:432–445	276:432–445	NUM
ejpam-901	291	5	,	,	PUNCT
ejpam-901	291	6	2002	2002	NUM
ejpam-901	291	7	.	.	PUNCT
ejpam-901	292	1	[	[	X
ejpam-901	292	2	2	2	NUM
ejpam-901	292	3	]	]	X
ejpam-901	292	4	t.m	t.m	PROPN
ejpam-901	292	5	.	.	PROPN
ejpam-901	292	6	flett	flett	PROPN
ejpam-901	292	7	.	.	PUNCT
ejpam-901	293	1	the	the	DET
ejpam-901	293	2	dual	dual	ADJ
ejpam-901	293	3	of	of	ADP
ejpam-901	293	4	an	an	DET
ejpam-901	293	5	inequality	inequality	NOUN
ejpam-901	293	6	of	of	ADP
ejpam-901	293	7	hardy	hardy	ADJ
ejpam-901	293	8	and	and	CCONJ
ejpam-901	293	9	littlewood	littlewood	NOUN
ejpam-901	293	10	and	and	CCONJ
ejpam-901	293	11	some	some	DET
ejpam-901	293	12	related	related	ADJ
ejpam-901	293	13	inequalities	inequality	NOUN
ejpam-901	293	14	.	.	PUNCT
ejpam-901	294	1	j.	j.	PROPN
ejpam-901	294	2	math	math	PROPN
ejpam-901	294	3	.	.	PUNCT
ejpam-901	295	1	anal	anal	PROPN
ejpam-901	295	2	.	.	PUNCT
ejpam-901	296	1	appl	appl	PROPN
ejpam-901	296	2	.	.	PROPN
ejpam-901	296	3	,	,	PUNCT
ejpam-901	296	4	38:746–765	38:746–765	PROPN
ejpam-901	296	5	,	,	PUNCT
ejpam-901	296	6	2002	2002	NUM
ejpam-901	296	7	.	.	PUNCT
ejpam-901	297	1	[	[	X
ejpam-901	297	2	3	3	X
ejpam-901	297	3	]	]	X
ejpam-901	297	4	i.b	i.b	PROPN
ejpam-901	297	5	.	.	PROPN
ejpam-901	297	6	jung	jung	PROPN
ejpam-901	297	7	,	,	PUNCT
ejpam-901	297	8	y.c	y.c	PROPN
ejpam-901	297	9	.	.	PROPN
ejpam-901	297	10	kim	kim	PROPN
ejpam-901	297	11	and	and	CCONJ
ejpam-901	297	12	h.m	h.m	PROPN
ejpam-901	297	13	.	.	PROPN
ejpam-901	297	14	srivastava	srivastava	PROPN
ejpam-901	297	15	.	.	PUNCT
ejpam-901	298	1	the	the	DET
ejpam-901	298	2	hardy	hardy	ADJ
ejpam-901	298	3	space	space	NOUN
ejpam-901	298	4	of	of	ADP
ejpam-901	298	5	analytic	analytic	ADJ
ejpam-901	298	6	functions	function	NOUN
ejpam-901	298	7	associated	associate	VERB
ejpam-901	298	8	with	with	ADP
ejpam-901	298	9	certain	certain	ADJ
ejpam-901	298	10	one	one	NUM
ejpam-901	298	11	-	-	PUNCT
ejpam-901	298	12	parameter	parameter	NOUN
ejpam-901	298	13	families	family	NOUN
ejpam-901	298	14	of	of	ADP
ejpam-901	298	15	integral	integral	ADJ
ejpam-901	298	16	operators	operator	NOUN
ejpam-901	298	17	.	.	PUNCT
ejpam-901	299	1	j.	j.	PROPN
ejpam-901	299	2	math	math	PROPN
ejpam-901	299	3	.	.	PUNCT
ejpam-901	300	1	anal	anal	PROPN
ejpam-901	300	2	.	.	PUNCT
ejpam-901	301	1	appl	appl	PROPN
ejpam-901	301	2	.	.	PROPN
ejpam-901	301	3	,	,	PUNCT
ejpam-901	301	4	176:138	176:138	NUM
ejpam-901	301	5	–	–	PUNCT
ejpam-901	301	6	147	147	NUM
ejpam-901	301	7	,	,	PUNCT
ejpam-901	301	8	1993	1993	NUM
ejpam-901	301	9	.	.	PUNCT
ejpam-901	302	1	[	[	X
ejpam-901	302	2	4	4	NUM
ejpam-901	302	3	]	]	X
ejpam-901	302	4	d.j	d.j	PROPN
ejpam-901	302	5	.	.	PROPN
ejpam-901	302	6	hallenback	hallenback	PROPN
ejpam-901	302	7	and	and	CCONJ
ejpam-901	302	8	s.	s.	PROPN
ejpam-901	302	9	ruscheweyh	ruscheweyh	PROPN
ejpam-901	302	10	.	.	PUNCT
ejpam-901	303	1	subordination	subordination	NOUN
ejpam-901	303	2	by	by	ADP
ejpam-901	303	3	convex	convex	NOUN
ejpam-901	303	4	functions	function	NOUN
ejpam-901	303	5	.	.	PUNCT
ejpam-901	304	1	proc	proc	NOUN
ejpam-901	304	2	.	.	PUNCT
ejpam-901	305	1	amer	amer	PROPN
ejpam-901	305	2	.	.	PUNCT
ejpam-901	305	3	math	math	PROPN
ejpam-901	305	4	.	.	PUNCT
ejpam-901	306	1	soc	soc	PROPN
ejpam-901	306	2	.	.	PROPN
ejpam-901	306	3	,	,	PUNCT
ejpam-901	307	1	52:191–195	52:191–195	NUM
ejpam-901	307	2	,	,	PUNCT
ejpam-901	307	3	1975	1975	NUM
ejpam-901	307	4	.	.	PUNCT
ejpam-901	308	1	[	[	X
ejpam-901	308	2	5	5	NUM
ejpam-901	308	3	]	]	PUNCT
ejpam-901	308	4	j.-l	j.-l	PROPN
ejpam-901	308	5	.	.	PUNCT
ejpam-901	309	1	liu	liu	PROPN
ejpam-901	309	2	.	.	PUNCT
ejpam-901	310	1	the	the	DET
ejpam-901	310	2	noor	noor	PROPN
ejpam-901	310	3	integral	integral	ADJ
ejpam-901	310	4	and	and	CCONJ
ejpam-901	310	5	strongly	strongly	ADV
ejpam-901	310	6	starlike	starlike	ADJ
ejpam-901	310	7	functions	function	NOUN
ejpam-901	310	8	.	.	PUNCT
ejpam-901	311	1	j.	j.	PROPN
ejpam-901	311	2	math	math	PROPN
ejpam-901	311	3	.	.	PUNCT
ejpam-901	312	1	anal	anal	PROPN
ejpam-901	312	2	.	.	PUNCT
ejpam-901	313	1	appl	appl	PROPN
ejpam-901	313	2	.	.	PROPN
ejpam-901	313	3	,	,	PUNCT
ejpam-901	313	4	261:441–447	261:441–447	NUM
ejpam-901	313	5	,	,	PUNCT
ejpam-901	313	6	2001	2001	NUM
ejpam-901	313	7	.	.	PUNCT
ejpam-901	314	1	[	[	X
ejpam-901	314	2	6	6	NUM
ejpam-901	314	3	]	]	X
ejpam-901	314	4	k.i	k.i	PROPN
ejpam-901	314	5	.	.	PUNCT
ejpam-901	314	6	noor	noor	PROPN
ejpam-901	314	7	.	.	PUNCT
ejpam-901	315	1	on	on	ADP
ejpam-901	315	2	new	new	ADJ
ejpam-901	315	3	classes	class	NOUN
ejpam-901	315	4	of	of	ADP
ejpam-901	315	5	integral	integral	ADJ
ejpam-901	315	6	operators	operator	NOUN
ejpam-901	315	7	.	.	PUNCT
ejpam-901	316	1	j.	j.	PROPN
ejpam-901	316	2	natur	natur	PROPN
ejpam-901	316	3	.	.	PUNCT
ejpam-901	317	1	geom	geom	PROPN
ejpam-901	317	2	.	.	PROPN
ejpam-901	317	3	,	,	PUNCT
ejpam-901	317	4	16:71–80	16:71–80	NUM
ejpam-901	317	5	,	,	PUNCT
ejpam-901	317	6	1999	1999	NUM
ejpam-901	317	7	.	.	PUNCT
ejpam-901	318	1	[	[	X
ejpam-901	318	2	7	7	X
ejpam-901	318	3	]	]	X
ejpam-901	318	4	k.i	k.i	PROPN
ejpam-901	318	5	.	.	PUNCT
ejpam-901	319	1	noor	noor	PROPN
ejpam-901	319	2	and	and	CCONJ
ejpam-901	319	3	m.a	m.a	PROPN
ejpam-901	319	4	.	.	PROPN
ejpam-901	319	5	noor	noor	PROPN
ejpam-901	319	6	.	.	PUNCT
ejpam-901	320	1	on	on	ADP
ejpam-901	320	2	integral	integral	ADJ
ejpam-901	320	3	operators	operator	NOUN
ejpam-901	320	4	.	.	PUNCT
ejpam-901	321	1	j.	j.	PROPN
ejpam-901	321	2	math	math	PROPN
ejpam-901	321	3	.	.	PUNCT
ejpam-901	322	1	anal	anal	PROPN
ejpam-901	322	2	.	.	PUNCT
ejpam-901	322	3	appl	appl	PROPN
ejpam-901	322	4	.	.	PROPN
ejpam-901	322	5	,	,	PUNCT
ejpam-901	322	6	238:341–352	238:341–352	NUM
ejpam-901	322	7	,	,	PUNCT
ejpam-901	322	8	1999	1999	NUM
ejpam-901	322	9	.	.	PUNCT
ejpam-901	323	1	[	[	X
ejpam-901	323	2	8	8	NUM
ejpam-901	323	3	]	]	X
ejpam-901	323	4	s.owa	s.owa	PROPN
ejpam-901	323	5	and	and	CCONJ
ejpam-901	323	6	h.m	h.m	PROPN
ejpam-901	323	7	.	.	PROPN
ejpam-901	323	8	srivastava	srivastava	PROPN
ejpam-901	323	9	.	.	PUNCT
ejpam-901	324	1	some	some	DET
ejpam-901	324	2	applications	application	NOUN
ejpam-901	324	3	of	of	ADP
ejpam-901	324	4	the	the	DET
ejpam-901	324	5	generalized	generalized	ADJ
ejpam-901	324	6	libera	libera	NOUN
ejpam-901	324	7	integral	integral	ADJ
ejpam-901	324	8	operator	operator	NOUN
ejpam-901	324	9	.	.	PUNCT
ejpam-901	325	1	proc	proc	PROPN
ejpam-901	325	2	.	.	PUNCT
ejpam-901	326	1	japan	japan	PROPN
ejpam-901	326	2	acad	acad	PROPN
ejpam-901	326	3	.	.	PUNCT
ejpam-901	327	1	ser	ser	PROPN
ejpam-901	327	2	.	.	PUNCT
ejpam-901	328	1	a	a	DET
ejpam-901	328	2	math	math	NOUN
ejpam-901	328	3	.	.	PUNCT
ejpam-901	329	1	sci	sci	PROPN
ejpam-901	329	2	.	.	PROPN
ejpam-901	329	3	,	,	PUNCT
ejpam-901	329	4	62:125–128	62:125–128	PROPN
ejpam-901	329	5	,	,	PUNCT
ejpam-901	329	6	1986	1986	NUM
ejpam-901	329	7	.	.	PUNCT
ejpam-901	330	1	[	[	X
ejpam-901	330	2	9	9	NUM
ejpam-901	330	3	]	]	PUNCT
ejpam-901	330	4	st.ruscheweyh	st.ruscheweyh	NOUN
ejpam-901	330	5	.	.	PUNCT
ejpam-901	330	6	convolution	convolution	NOUN
ejpam-901	330	7	in	in	ADP
ejpam-901	330	8	geometric	geometric	ADJ
ejpam-901	330	9	function	function	NOUN
ejpam-901	330	10	theory	theory	NOUN
ejpam-901	330	11	.	.	PUNCT
ejpam-901	331	1	les	les	NOUN
ejpam-901	331	2	presses	press	NOUN
ejpam-901	331	3	de	de	ADP
ejpam-901	331	4	l’université	l’université	X
ejpam-901	331	5	de	de	X
ejpam-901	331	6	montréal	montréal	PROPN
ejpam-901	331	7	,	,	PUNCT
ejpam-901	331	8	1982	1982	NUM
ejpam-901	331	9	.	.	PUNCT
ejpam-901	332	1	[	[	X
ejpam-901	332	2	10	10	NUM
ejpam-901	332	3	]	]	X
ejpam-901	332	4	g.s	g.s	PROPN
ejpam-901	332	5	.	.	PROPN
ejpam-901	332	6	sǎlǎgean	sǎlǎgean	PROPN
ejpam-901	332	7	.	.	PUNCT
ejpam-901	332	8	subclasses	subclass	NOUN
ejpam-901	332	9	of	of	ADP
ejpam-901	332	10	univalent	univalent	ADJ
ejpam-901	332	11	functions	function	NOUN
ejpam-901	332	12	.	.	PUNCT
ejpam-901	333	1	lecture	lecture	NOUN
ejpam-901	333	2	notes	note	NOUN
ejpam-901	333	3	in	in	ADP
ejpam-901	333	4	math	math	NOUN
ejpam-901	333	5	.	.	PUNCT
ejpam-901	334	1	,	,	PUNCT
ejpam-901	334	2	springerverlag	springerverlag	NOUN
ejpam-901	334	3	,	,	PUNCT
ejpam-901	334	4	1013:362–372	1013:362–372	NOUN
ejpam-901	334	5	,	,	PUNCT
ejpam-901	334	6	1983	1983	NUM
ejpam-901	334	7	.	.	PUNCT
ejpam-901	335	1	[	[	X
ejpam-901	335	2	11	11	NUM
ejpam-901	335	3	]	]	X
ejpam-901	335	4	r.	r.	PROPN
ejpam-901	335	5	singh	singh	PROPN
ejpam-901	335	6	and	and	CCONJ
ejpam-901	335	7	s.	s.	PROPN
ejpam-901	335	8	singh	singh	PROPN
ejpam-901	335	9	.	.	PUNCT
ejpam-901	336	1	convolution	convolution	NOUN
ejpam-901	336	2	properties	property	NOUN
ejpam-901	336	3	of	of	ADP
ejpam-901	336	4	a	a	DET
ejpam-901	336	5	class	class	NOUN
ejpam-901	336	6	of	of	ADP
ejpam-901	336	7	starlike	starlike	NOUN
ejpam-901	336	8	functions	function	NOUN
ejpam-901	336	9	.	.	PUNCT
ejpam-901	337	1	proc	proc	NOUN
ejpam-901	337	2	.	.	PUNCT
ejpam-901	338	1	amer	amer	PROPN
ejpam-901	338	2	.	.	PUNCT
ejpam-901	338	3	math	math	PROPN
ejpam-901	338	4	.	.	PUNCT
ejpam-901	339	1	soc	soc	PROPN
ejpam-901	339	2	.	.	PUNCT
ejpam-901	339	3	,	,	PUNCT
ejpam-901	339	4	106:145–152	106:145–152	NUM
ejpam-901	339	5	,	,	PUNCT
ejpam-901	339	6	1989	1989	NUM
ejpam-901	339	7	.	.	PUNCT
ejpam-901	340	1	[	[	X
ejpam-901	340	2	12	12	NUM
ejpam-901	340	3	]	]	X
ejpam-901	340	4	lucyna	lucyna	NOUN
ejpam-901	340	5	trojnar	trojnar	NOUN
ejpam-901	340	6	-	-	PUNCT
ejpam-901	340	7	spelina	spelina	NOUN
ejpam-901	340	8	.	.	PUNCT
ejpam-901	341	1	on	on	ADP
ejpam-901	341	2	certain	certain	ADJ
ejpam-901	341	3	applications	application	NOUN
ejpam-901	341	4	of	of	ADP
ejpam-901	341	5	hadamard	hadamard	ADJ
ejpam-901	341	6	product	product	NOUN
ejpam-901	341	7	.	.	PUNCT
ejpam-901	342	1	applied	apply	VERB
ejpam-901	342	2	math	math	NOUN
ejpam-901	342	3	.	.	PUNCT
ejpam-901	343	1	comput	comput	NOUN
ejpam-901	343	2	.	.	PUNCT
ejpam-901	343	3	,	,	PUNCT
ejpam-901	343	4	199:653–662	199:653–662	NUM
ejpam-901	343	5	,	,	PUNCT
ejpam-901	343	6	2008	2008	NUM
ejpam-901	343	7	.	.	PUNCT
ejpam-901	344	1	[	[	X
ejpam-901	344	2	13	13	NUM
ejpam-901	344	3	]	]	SYM
ejpam-901	344	4	b.a	b.a	PROPN
ejpam-901	344	5	.	.	PROPN
ejpam-901	344	6	uralegaddi	uralegaddi	PROPN
ejpam-901	344	7	and	and	CCONJ
ejpam-901	344	8	c.	c.	PROPN
ejpam-901	344	9	somanatha	somanatha	PROPN
ejpam-901	344	10	.	.	PUNCT
ejpam-901	345	1	certain	certain	ADJ
ejpam-901	345	2	classes	class	NOUN
ejpam-901	345	3	of	of	ADP
ejpam-901	345	4	univalent	univalent	ADJ
ejpam-901	345	5	functions	function	NOUN
ejpam-901	345	6	.	.	PUNCT
ejpam-901	346	1	current	current	ADJ
ejpam-901	346	2	topics	topic	NOUN
ejpam-901	346	3	in	in	ADP
ejpam-901	346	4	analytic	analytic	ADJ
ejpam-901	346	5	function	function	NOUN
ejpam-901	346	6	theory	theory	NOUN
ejpam-901	346	7	(	(	PUNCT
ejpam-901	346	8	eds	ed	NOUN
ejpam-901	346	9	.	.	PUNCT
ejpam-901	346	10	h.	h.	PROPN
ejpam-901	346	11	m.	m.	PROPN
ejpam-901	346	12	srivastava	srivastava	PROPN
ejpam-901	346	13	and	and	CCONJ
ejpam-901	346	14	s.	s.	PROPN
ejpam-901	346	15	owa	owa	PROPN
ejpam-901	346	16	)	)	PUNCT
ejpam-901	346	17	,	,	PUNCT
ejpam-901	346	18	world	world	NOUN
ejpam-901	346	19	scientific	scientific	ADJ
ejpam-901	346	20	publishing	publishing	NOUN
ejpam-901	346	21	company	company	NOUN
ejpam-901	346	22	singapore	singapore	PROPN
ejpam-901	346	23	,	,	PUNCT
ejpam-901	346	24	new	new	PROPN
ejpam-901	346	25	jersey	jersey	PROPN
ejpam-901	346	26	,	,	PUNCT
ejpam-901	346	27	london	london	PROPN
ejpam-901	346	28	,	,	PUNCT
ejpam-901	346	29	and	and	CCONJ
ejpam-901	346	30	hong	hong	PROPN
ejpam-901	346	31	kong	kong	PROPN
ejpam-901	346	32	,	,	PUNCT
ejpam-901	346	33	pages	page	NOUN
ejpam-901	346	34	371–374	371–374	NUM
ejpam-901	346	35	,	,	PUNCT
ejpam-901	346	36	1992	1992	NUM
ejpam-901	346	37	.	.	PUNCT