id	sid	tid	token	lemma	pos
ejpam-1476	1	1	2_100137_altintas.dvi	2_100137_altintas.dvi	NUM
ejpam-1476	1	2	european	european	PROPN
ejpam-1476	1	3	journal	journal	PROPN
ejpam-1476	1	4	of	of	ADP
ejpam-1476	1	5	pure	pure	ADJ
ejpam-1476	1	6	and	and	CCONJ
ejpam-1476	1	7	applied	apply	VERB
ejpam-1476	1	8	mathematics	mathematic	NOUN
ejpam-1476	1	9	vol	vol	NOUN
ejpam-1476	1	10	.	.	PROPN
ejpam-1476	1	11	5	5	NUM
ejpam-1476	1	12	,	,	PUNCT
ejpam-1476	1	13	no	no	INTJ
ejpam-1476	1	14	.	.	NOUN
ejpam-1476	1	15	1	1	NUM
ejpam-1476	1	16	,	,	PUNCT
ejpam-1476	1	17	2012	2012	NUM
ejpam-1476	1	18	,	,	PUNCT
ejpam-1476	1	19	16	16	NUM
ejpam-1476	1	20	-	-	SYM
ejpam-1476	1	21	24	24	NUM
ejpam-1476	1	22	issn	issn	PROPN
ejpam-1476	1	23	1307	1307	NUM
ejpam-1476	1	24	-	-	SYM
ejpam-1476	1	25	5543	5543	NUM
ejpam-1476	1	26	–	–	PUNCT
ejpam-1476	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1476	1	28	special	special	ADJ
ejpam-1476	1	29	issue	issue	NOUN
ejpam-1476	1	30	for	for	ADP
ejpam-1476	1	31	the	the	DET
ejpam-1476	1	32	international	international	ADJ
ejpam-1476	1	33	conference	conference	NOUN
ejpam-1476	1	34	on	on	ADP
ejpam-1476	1	35	applied	apply	VERB
ejpam-1476	1	36	analysis	analysis	NOUN
ejpam-1476	1	37	and	and	CCONJ
ejpam-1476	1	38	algebra	algebra	NOUN
ejpam-1476	1	39	29	29	NUM
ejpam-1476	1	40	june	june	PROPN
ejpam-1476	1	41	02	02	NUM
ejpam-1476	1	42	july	july	PROPN
ejpam-1476	1	43	2011	2011	NUM
ejpam-1476	1	44	,	,	PUNCT
ejpam-1476	1	45	istanbul	istanbul	PROPN
ejpam-1476	1	46	turkey	turkey	PROPN
ejpam-1476	1	47	majorization	majorization	NOUN
ejpam-1476	1	48	for	for	ADP
ejpam-1476	1	49	certain	certain	ADJ
ejpam-1476	1	50	analytic	analytic	ADJ
ejpam-1476	1	51	functions	function	NOUN
ejpam-1476	1	52	osman	osman	PROPN
ejpam-1476	1	53	altintas	altintas	PROPN
ejpam-1476	1	54	department	department	PROPN
ejpam-1476	1	55	of	of	ADP
ejpam-1476	1	56	mathematics	mathematic	NOUN
ejpam-1476	1	57	,	,	PUNCT
ejpam-1476	1	58	faculty	faculty	NOUN
ejpam-1476	1	59	of	of	ADP
ejpam-1476	1	60	education	education	NOUN
ejpam-1476	1	61	,	,	PUNCT
ejpam-1476	1	62	başkent	başkent	ADJ
ejpam-1476	1	63	university	university	NOUN
ejpam-1476	1	64	,	,	PUNCT
ejpam-1476	1	65	ankara	ankara	PROPN
ejpam-1476	1	66	,	,	PUNCT
ejpam-1476	1	67	turkey	turkey	PROPN
ejpam-1476	1	68	abstract	abstract	NOUN
ejpam-1476	1	69	.	.	PUNCT
ejpam-1476	2	1	in	in	ADP
ejpam-1476	2	2	this	this	DET
ejpam-1476	2	3	paper	paper	NOUN
ejpam-1476	2	4	two	two	NUM
ejpam-1476	2	5	subclasses	subclass	NOUN
ejpam-1476	2	6	sδ	sδ	ADP
ejpam-1476	2	7	p	p	NOUN
ejpam-1476	2	8	,	,	PUNCT
ejpam-1476	2	9	q	q	PROPN
ejpam-1476	2	10	�	�	PROPN
ejpam-1476	2	11	γ	γ	PROPN
ejpam-1476	2	12	,	,	PUNCT
ejpam-1476	2	13	a	a	DET
ejpam-1476	2	14	,	,	PUNCT
ejpam-1476	2	15	b	b	PROPN
ejpam-1476	2	16	�	�	PROPN
ejpam-1476	2	17	and	and	CCONJ
ejpam-1476	2	18	cδ	cδ	NOUN
ejpam-1476	2	19	p	p	X
ejpam-1476	2	20	,	,	PUNCT
ejpam-1476	2	21	q	q	PROPN
ejpam-1476	2	22	�	�	PROPN
ejpam-1476	2	23	γ	γ	PROPN
ejpam-1476	2	24	,	,	PUNCT
ejpam-1476	2	25	a	a	PRON
ejpam-1476	2	26	,	,	PUNCT
ejpam-1476	2	27	b	b	PROPN
ejpam-1476	2	28	�	�	PROPN
ejpam-1476	2	29	of	of	ADP
ejpam-1476	2	30	p	p	NOUN
ejpam-1476	2	31	-	-	PUNCT
ejpam-1476	2	32	valently	valently	ADV
ejpam-1476	2	33	starlike	starlike	NOUN
ejpam-1476	2	34	and	and	CCONJ
ejpam-1476	2	35	pvalently	pvalently	ADV
ejpam-1476	2	36	convex	convex	NOUN
ejpam-1476	2	37	functions	function	NOUN
ejpam-1476	2	38	of	of	ADP
ejpam-1476	2	39	complex	complex	ADJ
ejpam-1476	2	40	order	order	NOUN
ejpam-1476	2	41	γ	γ	X
ejpam-1476	2	42	6=	6=	ADP
ejpam-1476	2	43	0	0	NUM
ejpam-1476	2	44	in	in	ADP
ejpam-1476	2	45	the	the	DET
ejpam-1476	2	46	open	open	ADJ
ejpam-1476	2	47	unit	unit	NOUN
ejpam-1476	2	48	disk	disk	NOUN
ejpam-1476	2	49	u	u	NOUN
ejpam-1476	2	50	are	be	AUX
ejpam-1476	2	51	introduced	introduce	VERB
ejpam-1476	2	52	and	and	CCONJ
ejpam-1476	2	53	for	for	ADP
ejpam-1476	2	54	these	these	DET
ejpam-1476	2	55	classes	class	NOUN
ejpam-1476	2	56	several	several	ADJ
ejpam-1476	2	57	majorization	majorization	NOUN
ejpam-1476	2	58	problems	problem	NOUN
ejpam-1476	2	59	are	be	AUX
ejpam-1476	2	60	discussed	discuss	VERB
ejpam-1476	2	61	.	.	PUNCT
ejpam-1476	3	1	2000	2000	NUM
ejpam-1476	3	2	mathematics	mathematic	NOUN
ejpam-1476	3	3	subject	subject	NOUN
ejpam-1476	3	4	classifications	classification	NOUN
ejpam-1476	3	5	:	:	PUNCT
ejpam-1476	3	6	30c45	30c45	NUM
ejpam-1476	3	7	key	key	ADJ
ejpam-1476	3	8	words	word	NOUN
ejpam-1476	3	9	and	and	CCONJ
ejpam-1476	3	10	phrases	phrase	NOUN
ejpam-1476	3	11	:	:	PUNCT
ejpam-1476	3	12	analytic	analytic	ADJ
ejpam-1476	3	13	function	function	NOUN
ejpam-1476	3	14	,	,	PUNCT
ejpam-1476	3	15	p	p	ADJ
ejpam-1476	3	16	-	-	PUNCT
ejpam-1476	3	17	valent	valent	NOUN
ejpam-1476	3	18	function	function	NOUN
ejpam-1476	3	19	,	,	PUNCT
ejpam-1476	3	20	starlike	starlike	NOUN
ejpam-1476	3	21	function	function	NOUN
ejpam-1476	3	22	,	,	PUNCT
ejpam-1476	3	23	convex	convex	NOUN
ejpam-1476	3	24	function	function	NOUN
ejpam-1476	3	25	,	,	PUNCT
ejpam-1476	3	26	majorization	majorization	NOUN
ejpam-1476	3	27	problems	problem	NOUN
ejpam-1476	3	28	,	,	PUNCT
ejpam-1476	3	29	fractional	fractional	ADJ
ejpam-1476	3	30	derivative	derivative	NOUN
ejpam-1476	3	31	.	.	PUNCT
ejpam-1476	4	1	1	1	X
ejpam-1476	4	2	.	.	X
ejpam-1476	4	3	introduction	introduction	NOUN
ejpam-1476	4	4	and	and	CCONJ
ejpam-1476	4	5	definitions	definition	NOUN
ejpam-1476	4	6	definition	definition	NOUN
ejpam-1476	4	7	1	1	NUM
ejpam-1476	4	8	(	(	PUNCT
ejpam-1476	4	9	[	[	PUNCT
ejpam-1476	4	10	see	see	VERB
ejpam-1476	4	11	5	5	NUM
ejpam-1476	4	12	]	]	PUNCT
ejpam-1476	4	13	)	)	PUNCT
ejpam-1476	4	14	.	.	PUNCT
ejpam-1476	5	1	let	let	VERB
ejpam-1476	5	2	the	the	DET
ejpam-1476	5	3	functions	function	NOUN
ejpam-1476	5	4	f	f	X
ejpam-1476	5	5	(	(	PUNCT
ejpam-1476	5	6	z	z	NOUN
ejpam-1476	5	7	)	)	PUNCT
ejpam-1476	5	8	and	and	CCONJ
ejpam-1476	5	9	g(z	g(z	PROPN
ejpam-1476	5	10	)	)	PUNCT
ejpam-1476	5	11	be	be	AUX
ejpam-1476	5	12	analytic	analytic	ADJ
ejpam-1476	5	13	in	in	ADP
ejpam-1476	5	14	the	the	DET
ejpam-1476	5	15	open	open	ADJ
ejpam-1476	5	16	unit	unit	NOUN
ejpam-1476	5	17	disk	disk	NOUN
ejpam-1476	5	18	u	u	NOUN
ejpam-1476	5	19	=	=	PUNCT
ejpam-1476	5	20	{	{	PUNCT
ejpam-1476	5	21	z	z	NOUN
ejpam-1476	5	22	:	:	PUNCT
ejpam-1476	5	23	z	z	PROPN
ejpam-1476	5	24	∈	∈	PROPN
ejpam-1476	5	25	c	c	NOUN
ejpam-1476	6	1	and	and	CCONJ
ejpam-1476	6	2	|	|	ADV
ejpam-1476	6	3	z	z	NOUN
ejpam-1476	7	1	|	|	ADV
ejpam-1476	7	2	<	<	X
ejpam-1476	7	3	1	1	NUM
ejpam-1476	7	4	}	}	PUNCT
ejpam-1476	7	5	.	.	PUNCT
ejpam-1476	8	1	we	we	PRON
ejpam-1476	8	2	say	say	VERB
ejpam-1476	8	3	that	that	SCONJ
ejpam-1476	8	4	f	f	PROPN
ejpam-1476	8	5	(	(	PUNCT
ejpam-1476	8	6	z	z	NOUN
ejpam-1476	8	7	)	)	PUNCT
ejpam-1476	8	8	is	be	AUX
ejpam-1476	8	9	majorized	majorize	VERB
ejpam-1476	8	10	by	by	ADP
ejpam-1476	8	11	g(z	g(z	PROPN
ejpam-1476	8	12	)	)	PUNCT
ejpam-1476	8	13	and	and	CCONJ
ejpam-1476	8	14	write	write	VERB
ejpam-1476	8	15	f	f	PROPN
ejpam-1476	8	16	(	(	PUNCT
ejpam-1476	8	17	z)≪	z)≪	NOUN
ejpam-1476	8	18	g(z	g(z	ADJ
ejpam-1476	8	19	)	)	PUNCT
ejpam-1476	8	20	(	(	PUNCT
ejpam-1476	8	21	1	1	X
ejpam-1476	8	22	)	)	PUNCT
ejpam-1476	8	23	if	if	SCONJ
ejpam-1476	8	24	there	there	PRON
ejpam-1476	8	25	exists	exist	VERB
ejpam-1476	8	26	a	a	DET
ejpam-1476	8	27	function	function	NOUN
ejpam-1476	8	28	φ(z	φ(z	NOUN
ejpam-1476	8	29	)	)	PUNCT
ejpam-1476	8	30	analytic	analytic	NOUN
ejpam-1476	8	31	in	in	ADP
ejpam-1476	8	32	∪	∪	NOUN
ejpam-1476	8	33	,	,	PUNCT
ejpam-1476	8	34	such	such	ADJ
ejpam-1476	8	35	that	that	SCONJ
ejpam-1476	8	36	|	|	ADV
ejpam-1476	8	37	φ(z	φ(z	PROPN
ejpam-1476	8	38	)	)	PUNCT
ejpam-1476	8	39	|≤	|≤	PROPN
ejpam-1476	8	40	1	1	NUM
ejpam-1476	8	41	and	and	CCONJ
ejpam-1476	8	42	f	f	PROPN
ejpam-1476	8	43	(	(	PUNCT
ejpam-1476	8	44	z	z	NOUN
ejpam-1476	8	45	)	)	PUNCT
ejpam-1476	8	46	=	=	NOUN
ejpam-1476	8	47	φ(z)g(z	φ(z)g(z	NUM
ejpam-1476	8	48	)	)	PUNCT
ejpam-1476	8	49	.	.	PUNCT
ejpam-1476	9	1	(	(	PUNCT
ejpam-1476	9	2	2	2	X
ejpam-1476	9	3	)	)	PUNCT
ejpam-1476	9	4	also	also	ADV
ejpam-1476	9	5	,	,	PUNCT
ejpam-1476	9	6	we	we	PRON
ejpam-1476	9	7	say	say	VERB
ejpam-1476	9	8	that	that	SCONJ
ejpam-1476	9	9	f	f	PROPN
ejpam-1476	9	10	(	(	PUNCT
ejpam-1476	9	11	z	z	NOUN
ejpam-1476	9	12	)	)	PUNCT
ejpam-1476	9	13	is	be	AUX
ejpam-1476	9	14	subordinate	subordinate	ADJ
ejpam-1476	9	15	to	to	ADP
ejpam-1476	9	16	g(z	g(z	PROPN
ejpam-1476	9	17	)	)	PUNCT
ejpam-1476	9	18	and	and	CCONJ
ejpam-1476	9	19	write	write	VERB
ejpam-1476	9	20	f	f	PROPN
ejpam-1476	9	21	(	(	PUNCT
ejpam-1476	9	22	z)≺	z)≺	PROPN
ejpam-1476	9	23	g(z	g(z	PROPN
ejpam-1476	9	24	)	)	PUNCT
ejpam-1476	9	25	if	if	SCONJ
ejpam-1476	9	26	there	there	PRON
ejpam-1476	9	27	exist	exist	VERB
ejpam-1476	9	28	a	a	DET
ejpam-1476	9	29	function	function	NOUN
ejpam-1476	9	30	w(z	w(z	NOUN
ejpam-1476	9	31	)	)	PUNCT
ejpam-1476	9	32	analytic	analytic	NOUN
ejpam-1476	9	33	in	in	ADP
ejpam-1476	9	34	u	u	PROPN
ejpam-1476	9	35	,	,	PUNCT
ejpam-1476	9	36	such	such	ADJ
ejpam-1476	9	37	that	that	SCONJ
ejpam-1476	9	38	w	w	NOUN
ejpam-1476	9	39	(	(	PUNCT
ejpam-1476	9	40	0	0	NUM
ejpam-1476	9	41	)	)	PUNCT
ejpam-1476	9	42	=	=	SYM
ejpam-1476	9	43	0	0	NUM
ejpam-1476	9	44	,	,	PUNCT
ejpam-1476	9	45	|w	|w	NOUN
ejpam-1476	9	46	(	(	PUNCT
ejpam-1476	9	47	z)|	z)|	ADP
ejpam-1476	9	48	≤	≤	NUM
ejpam-1476	9	49	|z|	|z|	NOUN
ejpam-1476	9	50	and	and	CCONJ
ejpam-1476	9	51	f	f	PROPN
ejpam-1476	9	52	(	(	PUNCT
ejpam-1476	9	53	z	z	NOUN
ejpam-1476	9	54	)	)	PUNCT
ejpam-1476	10	1	=	=	SYM
ejpam-1476	10	2	g	g	PROPN
ejpam-1476	10	3	(	(	PUNCT
ejpam-1476	10	4	w	w	PROPN
ejpam-1476	10	5	(	(	PUNCT
ejpam-1476	10	6	z	z	NOUN
ejpam-1476	10	7	)	)	PUNCT
ejpam-1476	10	8	)	)	PUNCT
ejpam-1476	10	9	.	.	PUNCT
ejpam-1476	11	1	email	email	NOUN
ejpam-1476	11	2	address	address	NOUN
ejpam-1476	11	3	:	:	PUNCT
ejpam-1476	11	4	oaltintas�baskent.edu.tr	oaltintas�baskent.edu.tr	PROPN
ejpam-1476	11	5	(	(	PUNCT
ejpam-1476	11	6	o.	o.	PROPN
ejpam-1476	11	7	altıntaş	altıntaş	PROPN
ejpam-1476	11	8	)	)	PUNCT
ejpam-1476	11	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1476	12	1	16	16	NUM
ejpam-1476	13	1	c	c	X
ejpam-1476	13	2	©	©	PROPN
ejpam-1476	13	3	2012	2012	NUM
ejpam-1476	13	4	ejpam	ejpam	VERB
ejpam-1476	13	5	all	all	DET
ejpam-1476	13	6	rights	right	NOUN
ejpam-1476	13	7	reserved	reserve	VERB
ejpam-1476	13	8	.	.	PUNCT
ejpam-1476	14	1	o.	o.	PROPN
ejpam-1476	14	2	altıntaş	altıntaş	PROPN
ejpam-1476	14	3	/	/	SYM
ejpam-1476	14	4	eur	eur	PROPN
ejpam-1476	14	5	.	.	PUNCT
ejpam-1476	15	1	j.	j.	PROPN
ejpam-1476	15	2	pure	pure	PROPN
ejpam-1476	15	3	appl	appl	PROPN
ejpam-1476	15	4	.	.	PROPN
ejpam-1476	15	5	math	math	PROPN
ejpam-1476	15	6	,	,	PUNCT
ejpam-1476	15	7	5	5	NUM
ejpam-1476	15	8	(	(	PUNCT
ejpam-1476	15	9	2012	2012	NUM
ejpam-1476	15	10	)	)	PUNCT
ejpam-1476	15	11	,	,	PUNCT
ejpam-1476	15	12	16	16	NUM
ejpam-1476	15	13	-	-	SYM
ejpam-1476	15	14	24	24	NUM
ejpam-1476	15	15	17	17	NUM
ejpam-1476	15	16	definition	definition	NOUN
ejpam-1476	15	17	2	2	NUM
ejpam-1476	15	18	(	(	PUNCT
ejpam-1476	15	19	[	[	PUNCT
ejpam-1476	15	20	see	see	VERB
ejpam-1476	15	21	8	8	NUM
ejpam-1476	15	22	]	]	PUNCT
ejpam-1476	15	23	)	)	PUNCT
ejpam-1476	15	24	.	.	PUNCT
ejpam-1476	16	1	the	the	DET
ejpam-1476	16	2	fractional	fractional	ADJ
ejpam-1476	16	3	derivative	derivative	NOUN
ejpam-1476	16	4	of	of	ADP
ejpam-1476	16	5	order	order	NOUN
ejpam-1476	16	6	δ	δ	PROPN
ejpam-1476	16	7	is	be	AUX
ejpam-1476	16	8	defined	define	VERB
ejpam-1476	16	9	by	by	ADP
ejpam-1476	16	10	dδz	dδz	PROPN
ejpam-1476	16	11	f	f	PROPN
ejpam-1476	16	12	(	(	PUNCT
ejpam-1476	16	13	z	z	NOUN
ejpam-1476	16	14	)	)	PUNCT
ejpam-1476	16	15	=	=	SYM
ejpam-1476	16	16	1	1	NUM
ejpam-1476	16	17	γ(1−δ	γ(1−δ	NOUN
ejpam-1476	16	18	)	)	PUNCT
ejpam-1476	17	1	d	d	X
ejpam-1476	17	2	dz	dz	PROPN
ejpam-1476	17	3	z	z	PROPN
ejpam-1476	17	4	∫	∫	PROPN
ejpam-1476	17	5	0	0	PUNCT
ejpam-1476	18	1	f	f	PROPN
ejpam-1476	18	2	(	(	PUNCT
ejpam-1476	18	3	ζ	ζ	NOUN
ejpam-1476	18	4	)	)	PUNCT
ejpam-1476	18	5	(	(	PUNCT
ejpam-1476	18	6	z	z	NOUN
ejpam-1476	18	7	−	−	PROPN
ejpam-1476	18	8	ζ)δ	ζ)δ	ADJ
ejpam-1476	18	9	dζ	dζ	PROPN
ejpam-1476	18	10	(	(	PUNCT
ejpam-1476	18	11	0¶	0¶	NOUN
ejpam-1476	18	12	δ	δ	X
ejpam-1476	18	13	<	<	X
ejpam-1476	18	14	1	1	NUM
ejpam-1476	18	15	)	)	PUNCT
ejpam-1476	18	16	(	(	PUNCT
ejpam-1476	18	17	3	3	X
ejpam-1476	18	18	)	)	PUNCT
ejpam-1476	18	19	where	where	SCONJ
ejpam-1476	18	20	f	f	PROPN
ejpam-1476	18	21	(	(	PUNCT
ejpam-1476	18	22	z	z	NOUN
ejpam-1476	18	23	)	)	PUNCT
ejpam-1476	18	24	is	be	AUX
ejpam-1476	18	25	an	an	DET
ejpam-1476	18	26	analytic	analytic	ADJ
ejpam-1476	18	27	function	function	NOUN
ejpam-1476	18	28	in	in	ADP
ejpam-1476	18	29	a	a	DET
ejpam-1476	18	30	simply	simply	ADV
ejpam-1476	18	31	connected	connected	ADJ
ejpam-1476	18	32	region	region	NOUN
ejpam-1476	18	33	of	of	ADP
ejpam-1476	18	34	the	the	DET
ejpam-1476	18	35	z−plane	z−plane	NOUN
ejpam-1476	18	36	containing	contain	VERB
ejpam-1476	18	37	the	the	DET
ejpam-1476	18	38	origin	origin	NOUN
ejpam-1476	18	39	and	and	CCONJ
ejpam-1476	18	40	the	the	DET
ejpam-1476	18	41	multiplicity	multiplicity	NOUN
ejpam-1476	18	42	of	of	ADP
ejpam-1476	18	43	(	(	PUNCT
ejpam-1476	18	44	z	z	NOUN
ejpam-1476	18	45	−	−	NOUN
ejpam-1476	18	46	ζ)−δ	ζ)−δ	PROPN
ejpam-1476	18	47	is	be	AUX
ejpam-1476	18	48	removed	remove	VERB
ejpam-1476	18	49	by	by	ADP
ejpam-1476	18	50	requiring	require	VERB
ejpam-1476	18	51	log	log	NOUN
ejpam-1476	18	52	(	(	PUNCT
ejpam-1476	18	53	z	z	NOUN
ejpam-1476	18	54	−	−	PROPN
ejpam-1476	18	55	ζ	ζ	NOUN
ejpam-1476	18	56	)	)	PUNCT
ejpam-1476	18	57	to	to	PART
ejpam-1476	18	58	be	be	AUX
ejpam-1476	18	59	real	real	ADJ
ejpam-1476	18	60	when	when	SCONJ
ejpam-1476	18	61	z	z	NOUN
ejpam-1476	18	62	−	−	VERB
ejpam-1476	18	63	ζ	ζ	X
ejpam-1476	18	64	>	>	X
ejpam-1476	18	65	0	0	NUM
ejpam-1476	18	66	.	.	PUNCT
ejpam-1476	18	67	definition	definition	NOUN
ejpam-1476	18	68	3	3	NUM
ejpam-1476	18	69	(	(	PUNCT
ejpam-1476	18	70	[	[	PUNCT
ejpam-1476	18	71	see	see	VERB
ejpam-1476	18	72	8	8	NUM
ejpam-1476	18	73	]	]	PUNCT
ejpam-1476	18	74	)	)	PUNCT
ejpam-1476	18	75	.	.	PUNCT
ejpam-1476	19	1	under	under	ADP
ejpam-1476	19	2	the	the	DET
ejpam-1476	19	3	hypotheses	hypothesis	NOUN
ejpam-1476	19	4	of	of	ADP
ejpam-1476	19	5	definition	definition	NOUN
ejpam-1476	19	6	2	2	NUM
ejpam-1476	19	7	,	,	PUNCT
ejpam-1476	19	8	the	the	DET
ejpam-1476	19	9	fractional	fractional	ADJ
ejpam-1476	19	10	derivative	derivative	NOUN
ejpam-1476	19	11	of	of	ADP
ejpam-1476	19	12	order	order	NOUN
ejpam-1476	19	13	(	(	PUNCT
ejpam-1476	19	14	n+	n+	X
ejpam-1476	19	15	δ	δ	NOUN
ejpam-1476	19	16	)	)	PUNCT
ejpam-1476	19	17	is	be	AUX
ejpam-1476	19	18	defined	define	VERB
ejpam-1476	19	19	by	by	ADP
ejpam-1476	19	20	dn+δ	dn+δ	PROPN
ejpam-1476	19	21	z	z	PROPN
ejpam-1476	19	22	f	f	X
ejpam-1476	19	23	(	(	PUNCT
ejpam-1476	19	24	z	z	NOUN
ejpam-1476	19	25	)	)	PUNCT
ejpam-1476	19	26	=	=	SYM
ejpam-1476	20	1	d	d	NOUN
ejpam-1476	20	2	dzn	dzn	NOUN
ejpam-1476	20	3	dδz	dδz	PROPN
ejpam-1476	20	4	f	f	PROPN
ejpam-1476	20	5	(	(	PUNCT
ejpam-1476	20	6	z	z	NOUN
ejpam-1476	20	7	)	)	PUNCT
ejpam-1476	20	8	.	.	PUNCT
ejpam-1476	21	1	(	(	PUNCT
ejpam-1476	21	2	4	4	X
ejpam-1476	21	3	)	)	PUNCT
ejpam-1476	21	4	several	several	ADJ
ejpam-1476	21	5	majorization	majorization	NOUN
ejpam-1476	21	6	problems	problem	NOUN
ejpam-1476	21	7	investigated	investigate	VERB
ejpam-1476	21	8	by	by	ADP
ejpam-1476	21	9	altıntaş	altıntaş	PROPN
ejpam-1476	21	10	and	and	CCONJ
ejpam-1476	21	11	owa	owa	PROPN
ejpam-1476	22	1	[	[	X
ejpam-1476	22	2	1	1	NUM
ejpam-1476	22	3	]	]	PUNCT
ejpam-1476	22	4	,	,	PUNCT
ejpam-1476	22	5	altıntaş	altıntaş	PROPN
ejpam-1476	22	6	et	et	PROPN
ejpam-1476	22	7	al	al	PROPN
ejpam-1476	22	8	.	.	PUNCT
ejpam-1476	23	1	[	[	X
ejpam-1476	23	2	2	2	NUM
ejpam-1476	23	3	]	]	PUNCT
ejpam-1476	23	4	and	and	CCONJ
ejpam-1476	23	5	[	[	X
ejpam-1476	23	6	3	3	NUM
ejpam-1476	23	7	]	]	PUNCT
ejpam-1476	23	8	.	.	PUNCT
ejpam-1476	24	1	let	let	VERB
ejpam-1476	24	2	ap	ap	PROPN
ejpam-1476	24	3	denote	denote	VERB
ejpam-1476	24	4	the	the	DET
ejpam-1476	24	5	class	class	NOUN
ejpam-1476	24	6	of	of	ADP
ejpam-1476	24	7	functions	function	NOUN
ejpam-1476	24	8	f	f	PRON
ejpam-1476	24	9	normalized	normalize	VERB
ejpam-1476	24	10	by	by	ADP
ejpam-1476	24	11	f	f	PROPN
ejpam-1476	24	12	(	(	PUNCT
ejpam-1476	24	13	z	z	NOUN
ejpam-1476	24	14	)	)	PUNCT
ejpam-1476	25	1	=	=	SYM
ejpam-1476	25	2	zp	zp	PROPN
ejpam-1476	26	1	+	+	CCONJ
ejpam-1476	26	2	∞	∞	NUM
ejpam-1476	26	3	∑	∑	PUNCT
ejpam-1476	26	4	n	n	CCONJ
ejpam-1476	26	5	=	=	PROPN
ejpam-1476	26	6	p+1	p+1	PROPN
ejpam-1476	26	7	anzn	anzn	NOUN
ejpam-1476	26	8	(	(	PUNCT
ejpam-1476	26	9	p	p	NOUN
ejpam-1476	26	10	∈	∈	PROPN
ejpam-1476	26	11	n	n	NOUN
ejpam-1476	26	12	=	=	PUNCT
ejpam-1476	26	13	{	{	PUNCT
ejpam-1476	26	14	1,2,3	1,2,3	NUM
ejpam-1476	26	15	,	,	PUNCT
ejpam-1476	26	16	.	.	PUNCT
ejpam-1476	26	17	.	.	PUNCT
ejpam-1476	26	18	.	.	PUNCT
ejpam-1476	26	19	}	}	PUNCT
ejpam-1476	26	20	)	)	PUNCT
ejpam-1476	26	21	which	which	PRON
ejpam-1476	26	22	are	be	AUX
ejpam-1476	26	23	analytic	analytic	ADJ
ejpam-1476	26	24	and	and	CCONJ
ejpam-1476	26	25	p	p	NOUN
ejpam-1476	26	26	−	−	PROPN
ejpam-1476	26	27	valent	valent	NOUN
ejpam-1476	26	28	in	in	ADP
ejpam-1476	26	29	u	u	PROPN
ejpam-1476	26	30	.	.	PUNCT
ejpam-1476	27	1	also	also	ADV
ejpam-1476	27	2	let	let	VERB
ejpam-1476	27	3	a	a	DET
ejpam-1476	27	4	function	function	NOUN
ejpam-1476	27	5	f	f	PROPN
ejpam-1476	27	6	∈	∈	PROPN
ejpam-1476	27	7	ap	ap	PROPN
ejpam-1476	27	8	is	be	AUX
ejpam-1476	27	9	said	say	VERB
ejpam-1476	27	10	to	to	PART
ejpam-1476	27	11	be	be	AUX
ejpam-1476	27	12	in	in	ADP
ejpam-1476	27	13	the	the	DET
ejpam-1476	27	14	class	class	NOUN
ejpam-1476	27	15	sδp	sδp	NOUN
ejpam-1476	27	16	,	,	PUNCT
ejpam-1476	27	17	q	q	PROPN
ejpam-1476	27	18	�	�	PROPN
ejpam-1476	27	19	γ	γ	PROPN
ejpam-1476	27	20	,	,	PUNCT
ejpam-1476	27	21	a	a	PRON
ejpam-1476	27	22	,	,	PUNCT
ejpam-1476	27	23	b	b	PROPN
ejpam-1476	27	24	�	�	PROPN
ejpam-1476	28	1	if	if	SCONJ
ejpam-1476	28	2	and	and	CCONJ
ejpam-1476	28	3	only	only	ADV
ejpam-1476	28	4	if	if	SCONJ
ejpam-1476	28	5	1	1	NUM
ejpam-1476	28	6	+	+	SYM
ejpam-1476	28	7	1	1	NUM
ejpam-1476	28	8	γ	γ	X
ejpam-1476	28	9	z	z	PROPN
ejpam-1476	28	10	f	f	PROPN
ejpam-1476	28	11	(	(	PUNCT
ejpam-1476	28	12	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	28	13	)	)	PUNCT
ejpam-1476	28	14	f	f	PROPN
ejpam-1476	28	15	(	(	PUNCT
ejpam-1476	28	16	q+δ)(z	q+δ)(z	NOUN
ejpam-1476	28	17	)	)	PUNCT
ejpam-1476	28	18	−	−	PROPN
ejpam-1476	28	19	p+	p+	X
ejpam-1476	28	20	q+	q+	ADV
ejpam-1476	28	21	δ	δ	PROPN
ejpam-1476	28	22	!	!	PUNCT
ejpam-1476	29	1	≺	≺	NOUN
ejpam-1476	29	2	1	1	NUM
ejpam-1476	29	3	+	+	NUM
ejpam-1476	29	4	az	az	PROPN
ejpam-1476	29	5	1	1	NUM
ejpam-1476	29	6	+	+	CCONJ
ejpam-1476	29	7	bz	bz	PROPN
ejpam-1476	29	8	(	(	PUNCT
ejpam-1476	29	9	5	5	NUM
ejpam-1476	29	10	)	)	PUNCT
ejpam-1476	29	11	where	where	SCONJ
ejpam-1476	29	12	γ	γ	X
ejpam-1476	29	13	∈	∈	PROPN
ejpam-1476	29	14	c	c	X
ejpam-1476	29	15	\	\	X
ejpam-1476	29	16	{	{	PUNCT
ejpam-1476	29	17	0	0	NUM
ejpam-1476	29	18	}	}	PUNCT
ejpam-1476	29	19	,	,	PUNCT
ejpam-1476	29	20	p	p	PROPN
ejpam-1476	29	21	∈	∈	PROPN
ejpam-1476	29	22	n	n	CCONJ
ejpam-1476	29	23	,	,	PUNCT
ejpam-1476	29	24	q	q	PROPN
ejpam-1476	29	25	∈	∈	PROPN
ejpam-1476	29	26	n0	n0	X
ejpam-1476	29	27	=	=	SYM
ejpam-1476	29	28	n∪	n∪	PROPN
ejpam-1476	29	29	{	{	PUNCT
ejpam-1476	29	30	0	0	NUM
ejpam-1476	29	31	}	}	PUNCT
ejpam-1476	29	32	,	,	PUNCT
ejpam-1476	29	33	0¶	0¶	NOUN
ejpam-1476	29	34	δ	δ	X
ejpam-1476	29	35	<	<	X
ejpam-1476	29	36	1	1	NUM
ejpam-1476	29	37	,	,	PUNCT
ejpam-1476	29	38	−1¶	−1¶	PROPN
ejpam-1476	29	39	b	b	X
ejpam-1476	29	40	<	<	X
ejpam-1476	29	41	a¶	a¶	X
ejpam-1476	29	42	1	1	NUM
ejpam-1476	29	43	and	and	CCONJ
ejpam-1476	29	44	�	�	PROPN
ejpam-1476	29	45	�	�	PROPN
ejpam-1476	29	46	γ(a−	γ(a−	PROPN
ejpam-1476	29	47	b	b	NOUN
ejpam-1476	29	48	)	)	PUNCT
ejpam-1476	29	49	+	+	CCONJ
ejpam-1476	29	50	(	(	PUNCT
ejpam-1476	29	51	p−	p−	NOUN
ejpam-1476	29	52	q−	q−	PROPN
ejpam-1476	29	53	δ)b	δ)b	ADJ
ejpam-1476	29	54	�	�	PROPN
ejpam-1476	29	55	�	�	PROPN
ejpam-1476	29	56	¶	¶	PROPN
ejpam-1476	29	57	�	�	PROPN
ejpam-1476	29	58	�	�	PROPN
ejpam-1476	29	59	p−	p−	PROPN
ejpam-1476	29	60	q−	q−	PROPN
ejpam-1476	29	61	δ	δ	PROPN
ejpam-1476	29	62	�	�	PROPN
ejpam-1476	29	63	�	�	PROPN
ejpam-1476	29	64	.	.	PUNCT
ejpam-1476	30	1	furthermore	furthermore	ADV
ejpam-1476	30	2	a	a	DET
ejpam-1476	30	3	function	function	NOUN
ejpam-1476	30	4	f	f	PROPN
ejpam-1476	30	5	∈	∈	PROPN
ejpam-1476	30	6	ap	ap	PROPN
ejpam-1476	30	7	is	be	AUX
ejpam-1476	30	8	said	say	VERB
ejpam-1476	30	9	to	to	PART
ejpam-1476	30	10	be	be	AUX
ejpam-1476	30	11	in	in	ADP
ejpam-1476	30	12	the	the	DET
ejpam-1476	30	13	class	class	NOUN
ejpam-1476	30	14	cδp	cδp	PROPN
ejpam-1476	30	15	,	,	PUNCT
ejpam-1476	30	16	q	q	PROPN
ejpam-1476	30	17	�	�	PROPN
ejpam-1476	30	18	γ	γ	PROPN
ejpam-1476	30	19	,	,	PUNCT
ejpam-1476	30	20	a	a	PRON
ejpam-1476	30	21	,	,	PUNCT
ejpam-1476	30	22	b	b	PROPN
ejpam-1476	30	23	�	�	PROPN
ejpam-1476	30	24	if	if	SCONJ
ejpam-1476	30	25	and	and	CCONJ
ejpam-1476	30	26	only	only	ADV
ejpam-1476	30	27	if	if	SCONJ
ejpam-1476	30	28	1	1	NUM
ejpam-1476	30	29	+	+	SYM
ejpam-1476	30	30	1	1	NUM
ejpam-1476	30	31	γ	γ	SYM
ejpam-1476	30	32	1	1	NUM
ejpam-1476	30	33	+	+	PROPN
ejpam-1476	30	34	z	z	PROPN
ejpam-1476	30	35	f	f	X
ejpam-1476	30	36	(	(	PUNCT
ejpam-1476	30	37	q+δ+2)(z	q+δ+2)(z	PROPN
ejpam-1476	30	38	)	)	PUNCT
ejpam-1476	30	39	f	f	PROPN
ejpam-1476	30	40	(	(	PUNCT
ejpam-1476	30	41	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	30	42	)	)	PUNCT
ejpam-1476	30	43	−	−	PROPN
ejpam-1476	30	44	p+	p+	X
ejpam-1476	30	45	q+	q+	ADV
ejpam-1476	30	46	δ	δ	PROPN
ejpam-1476	30	47	!	!	PUNCT
ejpam-1476	31	1	≺	≺	NOUN
ejpam-1476	31	2	1	1	NUM
ejpam-1476	31	3	+	+	NUM
ejpam-1476	31	4	az	az	PROPN
ejpam-1476	31	5	1	1	NUM
ejpam-1476	31	6	+	+	CCONJ
ejpam-1476	31	7	bz	bz	PROPN
ejpam-1476	31	8	(	(	PUNCT
ejpam-1476	31	9	6	6	NUM
ejpam-1476	31	10	)	)	PUNCT
ejpam-1476	31	11	where	where	SCONJ
ejpam-1476	31	12	γ	γ	X
ejpam-1476	31	13	∈	∈	PROPN
ejpam-1476	31	14	c	c	X
ejpam-1476	31	15	\	\	X
ejpam-1476	31	16	{	{	PUNCT
ejpam-1476	31	17	0	0	NUM
ejpam-1476	31	18	}	}	PUNCT
ejpam-1476	31	19	,	,	PUNCT
ejpam-1476	31	20	p	p	PROPN
ejpam-1476	31	21	∈	∈	PROPN
ejpam-1476	31	22	n	n	CCONJ
ejpam-1476	31	23	,	,	PUNCT
ejpam-1476	31	24	q	q	PROPN
ejpam-1476	31	25	∈	∈	PROPN
ejpam-1476	31	26	n0	n0	NUM
ejpam-1476	31	27	,	,	PUNCT
ejpam-1476	31	28	0¶	0¶	NOUN
ejpam-1476	31	29	δ	δ	X
ejpam-1476	31	30	<	<	X
ejpam-1476	31	31	1	1	NUM
ejpam-1476	31	32	,	,	PUNCT
ejpam-1476	31	33	−1¶	−1¶	PROPN
ejpam-1476	31	34	b	b	X
ejpam-1476	31	35	<	<	X
ejpam-1476	31	36	a¶	a¶	X
ejpam-1476	31	37	1	1	NUM
ejpam-1476	31	38	and	and	CCONJ
ejpam-1476	31	39	�	�	PROPN
ejpam-1476	31	40	�	�	PROPN
ejpam-1476	31	41	γ(a−	γ(a−	PROPN
ejpam-1476	31	42	b	b	NOUN
ejpam-1476	31	43	)	)	PUNCT
ejpam-1476	31	44	+	+	CCONJ
ejpam-1476	31	45	(	(	PUNCT
ejpam-1476	31	46	p−	p−	NOUN
ejpam-1476	31	47	q−	q−	PROPN
ejpam-1476	31	48	δ)b	δ)b	ADJ
ejpam-1476	31	49	�	�	PROPN
ejpam-1476	31	50	�	�	PROPN
ejpam-1476	31	51	¶	¶	PROPN
ejpam-1476	31	52	�	�	PROPN
ejpam-1476	31	53	�	�	PROPN
ejpam-1476	31	54	p−	p−	PROPN
ejpam-1476	31	55	q−	q−	PROPN
ejpam-1476	31	56	δ	δ	PROPN
ejpam-1476	31	57	�	�	PROPN
ejpam-1476	31	58	�	�	PROPN
ejpam-1476	31	59	.	.	PUNCT
ejpam-1476	32	1	we	we	PRON
ejpam-1476	32	2	have	have	VERB
ejpam-1476	32	3	the	the	DET
ejpam-1476	32	4	following	follow	VERB
ejpam-1476	32	5	relationships	relationship	NOUN
ejpam-1476	32	6	(	(	PUNCT
ejpam-1476	32	7	from	from	ADP
ejpam-1476	32	8	[	[	X
ejpam-1476	32	9	3	3	NUM
ejpam-1476	32	10	,	,	PUNCT
ejpam-1476	32	11	11	11	NUM
ejpam-1476	32	12	,	,	PUNCT
ejpam-1476	32	13	2	2	NUM
ejpam-1476	32	14	]	]	PUNCT
ejpam-1476	32	15	,	,	PUNCT
ejpam-1476	32	16	respectively	respectively	ADV
ejpam-1476	32	17	)	)	PUNCT
ejpam-1476	32	18	s0	s0	PROPN
ejpam-1476	32	19	p	p	PROPN
ejpam-1476	32	20	,	,	PUNCT
ejpam-1476	32	21	q(γ	q(γ	PROPN
ejpam-1476	32	22	,	,	PUNCT
ejpam-1476	32	23	1,−1	1,−1	NUM
ejpam-1476	32	24	)	)	PUNCT
ejpam-1476	32	25	=	=	SYM
ejpam-1476	32	26	sp	sp	NOUN
ejpam-1476	32	27	,	,	PUNCT
ejpam-1476	32	28	q(γ	q(γ	PROPN
ejpam-1476	32	29	)	)	PUNCT
ejpam-1476	32	30	.	.	PUNCT
ejpam-1476	33	1	c0	c0	PROPN
ejpam-1476	33	2	p	p	PROPN
ejpam-1476	33	3	,	,	PUNCT
ejpam-1476	33	4	q(γ	q(γ	PROPN
ejpam-1476	33	5	,	,	PUNCT
ejpam-1476	33	6	1,−1	1,−1	NUM
ejpam-1476	33	7	)	)	PUNCT
ejpam-1476	33	8	=	=	SYM
ejpam-1476	33	9	cp	cp	PROPN
ejpam-1476	33	10	,	,	PUNCT
ejpam-1476	33	11	q(γ	q(γ	PROPN
ejpam-1476	33	12	)	)	PUNCT
ejpam-1476	33	13	.	.	PUNCT
ejpam-1476	34	1	o.	o.	PROPN
ejpam-1476	34	2	altıntaş	altıntaş	PROPN
ejpam-1476	34	3	/	/	SYM
ejpam-1476	34	4	eur	eur	PROPN
ejpam-1476	34	5	.	.	PUNCT
ejpam-1476	35	1	j.	j.	PROPN
ejpam-1476	35	2	pure	pure	PROPN
ejpam-1476	35	3	appl	appl	PROPN
ejpam-1476	35	4	.	.	PROPN
ejpam-1476	35	5	math	math	PROPN
ejpam-1476	35	6	,	,	PUNCT
ejpam-1476	35	7	5	5	NUM
ejpam-1476	35	8	(	(	PUNCT
ejpam-1476	35	9	2012	2012	NUM
ejpam-1476	35	10	)	)	PUNCT
ejpam-1476	35	11	,	,	PUNCT
ejpam-1476	35	12	16	16	NUM
ejpam-1476	35	13	-	-	SYM
ejpam-1476	35	14	24	24	NUM
ejpam-1476	35	15	18	18	NUM
ejpam-1476	35	16	s0	s0	PROPN
ejpam-1476	35	17	p,0(γ	p,0(γ	NOUN
ejpam-1476	35	18	,	,	PUNCT
ejpam-1476	35	19	1,−1	1,−1	NUM
ejpam-1476	35	20	)	)	PUNCT
ejpam-1476	35	21	=	=	SYM
ejpam-1476	35	22	s(γ	s(γ	PROPN
ejpam-1476	35	23	)	)	PUNCT
ejpam-1476	35	24	and	and	CCONJ
ejpam-1476	35	25	c0	c0	PROPN
ejpam-1476	35	26	p,0(γ	p,0(γ	PROPN
ejpam-1476	35	27	,	,	PUNCT
ejpam-1476	35	28	1,−1	1,−1	NUM
ejpam-1476	35	29	)	)	PUNCT
ejpam-1476	35	30	=	=	SYM
ejpam-1476	35	31	c(γ	c(γ	PROPN
ejpam-1476	35	32	)	)	PUNCT
ejpam-1476	35	33	.	.	PUNCT
ejpam-1476	36	1	s(γ	s(γ	PROPN
ejpam-1476	36	2	)	)	PUNCT
ejpam-1476	36	3	and	and	CCONJ
ejpam-1476	36	4	c(γ	c(γ	NOUN
ejpam-1476	36	5	)	)	PUNCT
ejpam-1476	36	6	were	be	AUX
ejpam-1476	36	7	considered	consider	VERB
ejpam-1476	36	8	by	by	ADP
ejpam-1476	36	9	nasr	nasr	PROPN
ejpam-1476	36	10	and	and	CCONJ
ejpam-1476	36	11	aouf	aouf	PROPN
ejpam-1476	36	12	in	in	ADP
ejpam-1476	36	13	[	[	X
ejpam-1476	36	14	6	6	NUM
ejpam-1476	36	15	]	]	PUNCT
ejpam-1476	36	16	.	.	PUNCT
ejpam-1476	37	1	s0	s0	PROPN
ejpam-1476	37	2	p,0(1−α	p,0(1−α	PROPN
ejpam-1476	37	3	,	,	PUNCT
ejpam-1476	37	4	1,−1	1,−1	NUM
ejpam-1476	37	5	)	)	PUNCT
ejpam-1476	37	6	=	=	SYM
ejpam-1476	37	7	s∗(α	s∗(α	X
ejpam-1476	37	8	)	)	PUNCT
ejpam-1476	37	9	and	and	CCONJ
ejpam-1476	37	10	c0	c0	PROPN
ejpam-1476	37	11	p,0(1−α	p,0(1−α	PROPN
ejpam-1476	37	12	,	,	PUNCT
ejpam-1476	37	13	1,−1	1,−1	NUM
ejpam-1476	37	14	)	)	PUNCT
ejpam-1476	37	15	=	=	SYM
ejpam-1476	37	16	c(α	c(α	NOUN
ejpam-1476	37	17	)	)	PUNCT
ejpam-1476	37	18	denote	denote	VERB
ejpam-1476	37	19	respectively	respectively	ADV
ejpam-1476	37	20	the	the	DET
ejpam-1476	37	21	class	class	NOUN
ejpam-1476	37	22	of	of	ADP
ejpam-1476	37	23	starlike	starlike	NOUN
ejpam-1476	37	24	and	and	CCONJ
ejpam-1476	37	25	convex	convex	NOUN
ejpam-1476	37	26	functions	function	NOUN
ejpam-1476	37	27	of	of	ADP
ejpam-1476	37	28	order	order	NOUN
ejpam-1476	37	29	α	α	NOUN
ejpam-1476	37	30	,	,	PUNCT
ejpam-1476	37	31	(	(	PUNCT
ejpam-1476	37	32	0	0	NUM
ejpam-1476	37	33	¶	¶	NOUN
ejpam-1476	37	34	α	α	PROPN
ejpam-1476	37	35	<	<	X
ejpam-1476	37	36	1	1	NUM
ejpam-1476	37	37	)	)	PUNCT
ejpam-1476	37	38	which	which	PRON
ejpam-1476	37	39	were	be	AUX
ejpam-1476	37	40	introduced	introduce	VERB
ejpam-1476	37	41	by	by	ADP
ejpam-1476	37	42	robertson	robertson	PROPN
ejpam-1476	37	43	in	in	ADP
ejpam-1476	37	44	[	[	X
ejpam-1476	37	45	9	9	NUM
ejpam-1476	37	46	]	]	SYM
ejpam-1476	37	47	.	.	PUNCT
ejpam-1476	38	1	2	2	X
ejpam-1476	38	2	.	.	X
ejpam-1476	38	3	majorization	majorization	NOUN
ejpam-1476	38	4	problems	problem	NOUN
ejpam-1476	38	5	for	for	ADP
ejpam-1476	38	6	the	the	DET
ejpam-1476	38	7	class	class	NOUN
ejpam-1476	38	8	sδ	sδ	ADP
ejpam-1476	38	9	p	p	NOUN
ejpam-1476	38	10	,	,	PUNCT
ejpam-1476	38	11	q(γ	q(γ	PROPN
ejpam-1476	38	12	,	,	PUNCT
ejpam-1476	38	13	a	a	DET
ejpam-1476	38	14	,	,	PUNCT
ejpam-1476	38	15	b	b	NOUN
ejpam-1476	38	16	)	)	PUNCT
ejpam-1476	38	17	we	we	PRON
ejpam-1476	38	18	begin	begin	VERB
ejpam-1476	38	19	by	by	ADP
ejpam-1476	38	20	proving	prove	VERB
ejpam-1476	38	21	.	.	PUNCT
ejpam-1476	39	1	theorem	theorem	NOUN
ejpam-1476	39	2	1	1	NUM
ejpam-1476	39	3	.	.	PUNCT
ejpam-1476	40	1	let	let	VERB
ejpam-1476	40	2	the	the	DET
ejpam-1476	40	3	function	function	NOUN
ejpam-1476	40	4	f	f	PROPN
ejpam-1476	40	5	(	(	PUNCT
ejpam-1476	40	6	z	z	NOUN
ejpam-1476	40	7	)	)	PUNCT
ejpam-1476	40	8	be	be	AUX
ejpam-1476	40	9	in	in	ADP
ejpam-1476	40	10	the	the	DET
ejpam-1476	40	11	class	class	NOUN
ejpam-1476	40	12	ap	ap	PROPN
ejpam-1476	40	13	and	and	CCONJ
ejpam-1476	40	14	suppose	suppose	VERB
ejpam-1476	40	15	that	that	SCONJ
ejpam-1476	40	16	g	g	PROPN
ejpam-1476	40	17	∈	∈	PROPN
ejpam-1476	40	18	sδp	sδp	NOUN
ejpam-1476	40	19	,	,	PUNCT
ejpam-1476	40	20	q(γ	q(γ	PROPN
ejpam-1476	40	21	,	,	PUNCT
ejpam-1476	40	22	a	a	DET
ejpam-1476	40	23	,	,	PUNCT
ejpam-1476	40	24	b	b	NOUN
ejpam-1476	40	25	)	)	PUNCT
ejpam-1476	40	26	.	.	PUNCT
ejpam-1476	41	1	if	if	SCONJ
ejpam-1476	41	2	f	f	PROPN
ejpam-1476	41	3	(	(	PUNCT
ejpam-1476	41	4	q+δ)(z	q+δ)(z	X
ejpam-1476	41	5	)	)	PUNCT
ejpam-1476	41	6	is	be	AUX
ejpam-1476	41	7	majorized	majorize	VERB
ejpam-1476	41	8	by	by	ADP
ejpam-1476	41	9	g(q+δ)(z	g(q+δ)(z	PROPN
ejpam-1476	41	10	)	)	PUNCT
ejpam-1476	41	11	in	in	ADP
ejpam-1476	41	12	u	u	NOUN
ejpam-1476	41	13	for	for	ADP
ejpam-1476	41	14	q	q	PROPN
ejpam-1476	41	15	∈	∈	PROPN
ejpam-1476	41	16	no	no	INTJ
ejpam-1476	41	17	and	and	CCONJ
ejpam-1476	41	18	0¶	0¶	NOUN
ejpam-1476	41	19	δ	δ	NOUN
ejpam-1476	41	20	<	<	X
ejpam-1476	41	21	1	1	NUM
ejpam-1476	41	22	,	,	PUNCT
ejpam-1476	41	23	then	then	ADV
ejpam-1476	41	24	�	�	PROPN
ejpam-1476	41	25	�	�	PROPN
ejpam-1476	41	26	�	�	PROPN
ejpam-1476	41	27	f	f	PROPN
ejpam-1476	41	28	(	(	PUNCT
ejpam-1476	41	29	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	41	30	)	)	PUNCT
ejpam-1476	41	31	�	�	PROPN
ejpam-1476	41	32	�	�	PROPN
ejpam-1476	41	33	�	�	PROPN
ejpam-1476	41	34	¶	¶	PROPN
ejpam-1476	41	35	�	�	PROPN
ejpam-1476	41	36	�	�	PROPN
ejpam-1476	41	37	�	�	PROPN
ejpam-1476	41	38	g(q+δ+1)(z	g(q+δ+1)(z	PROPN
ejpam-1476	41	39	)	)	PUNCT
ejpam-1476	41	40	�	�	PROPN
ejpam-1476	41	41	�	�	PROPN
ejpam-1476	41	42	�	�	PROPN
ejpam-1476	41	43	�	�	PROPN
ejpam-1476	41	44	|z|	|z|	NOUN
ejpam-1476	41	45	¶	¶	PROPN
ejpam-1476	41	46	r1	r1	PROPN
ejpam-1476	41	47	�	�	PROPN
ejpam-1476	41	48	(	(	PUNCT
ejpam-1476	41	49	7	7	NUM
ejpam-1476	41	50	)	)	PUNCT
ejpam-1476	41	51	where	where	SCONJ
ejpam-1476	41	52	r1	r1	NOUN
ejpam-1476	41	53	=	=	SYM
ejpam-1476	41	54	r1(p	r1(p	PROPN
ejpam-1476	41	55	,	,	PUNCT
ejpam-1476	41	56	q	q	NOUN
ejpam-1476	41	57	,	,	PUNCT
ejpam-1476	41	58	δ	δ	PROPN
ejpam-1476	41	59	,	,	PUNCT
ejpam-1476	41	60	γ	γ	PROPN
ejpam-1476	41	61	,	,	PUNCT
ejpam-1476	41	62	a	a	DET
ejpam-1476	41	63	,	,	PUNCT
ejpam-1476	41	64	b	b	NOUN
ejpam-1476	41	65	)	)	PUNCT
ejpam-1476	41	66	is	be	AUX
ejpam-1476	41	67	the	the	DET
ejpam-1476	41	68	smallest	small	ADJ
ejpam-1476	41	69	positive	positive	ADJ
ejpam-1476	41	70	root	root	NOUN
ejpam-1476	41	71	of	of	ADP
ejpam-1476	41	72	the	the	DET
ejpam-1476	41	73	equation	equation	NOUN
ejpam-1476	41	74	�	�	PROPN
ejpam-1476	41	75	�	�	PROPN
ejpam-1476	41	76	γ(a−	γ(a−	PROPN
ejpam-1476	41	77	b	b	NOUN
ejpam-1476	41	78	)	)	PUNCT
ejpam-1476	41	79	+	+	CCONJ
ejpam-1476	41	80	(	(	PUNCT
ejpam-1476	41	81	p−	p−	NOUN
ejpam-1476	41	82	q−	q−	PROPN
ejpam-1476	41	83	δ)b	δ)b	ADJ
ejpam-1476	41	84	�	�	PROPN
ejpam-1476	41	85	�	�	PROPN
ejpam-1476	41	86	r3	r3	PROPN
ejpam-1476	41	87	−	−	PROPN
ejpam-1476	42	1	(	(	PUNCT
ejpam-1476	42	2	p−	p−	PROPN
ejpam-1476	42	3	q−	q−	PROPN
ejpam-1476	42	4	δ+	δ+	PUNCT
ejpam-1476	42	5	2	2	NUM
ejpam-1476	42	6	|b|)r2−	|b|)r2−	NOUN
ejpam-1476	42	7	[	[	PUNCT
ejpam-1476	42	8	�	�	PROPN
ejpam-1476	42	9	�	�	PROPN
ejpam-1476	42	10	γ(a−	γ(a−	PROPN
ejpam-1476	42	11	b	b	NOUN
ejpam-1476	42	12	)	)	PUNCT
ejpam-1476	42	13	+	+	CCONJ
ejpam-1476	42	14	(	(	PUNCT
ejpam-1476	42	15	p−	p−	NOUN
ejpam-1476	42	16	q−	q−	PROPN
ejpam-1476	42	17	δ)b	δ)b	ADJ
ejpam-1476	42	18	�	�	PROPN
ejpam-1476	42	19	�	�	PROPN
ejpam-1476	42	20	+	+	CCONJ
ejpam-1476	42	21	2]r	2]r	PROPN
ejpam-1476	42	22	+	+	ADP
ejpam-1476	42	23	p−	p−	PROPN
ejpam-1476	42	24	q−	q−	PROPN
ejpam-1476	42	25	δ	δ	NOUN
ejpam-1476	42	26	=	=	SYM
ejpam-1476	42	27	0	0	PUNCT
ejpam-1476	42	28	(	(	PUNCT
ejpam-1476	42	29	8)	8)	NUM
ejpam-1476	42	30	where	where	SCONJ
ejpam-1476	42	31	p	p	PROPN
ejpam-1476	42	32	∈	∈	PROPN
ejpam-1476	42	33	n	n	CCONJ
ejpam-1476	42	34	,	,	PUNCT
ejpam-1476	42	35	q	q	PROPN
ejpam-1476	42	36	∈	∈	PROPN
ejpam-1476	42	37	n0	n0	PROPN
ejpam-1476	42	38	,	,	PUNCT
ejpam-1476	42	39	γ	γ	PROPN
ejpam-1476	42	40	∈	∈	PROPN
ejpam-1476	42	41	c	c	X
ejpam-1476	42	42	\	\	X
ejpam-1476	42	43	{	{	PUNCT
ejpam-1476	42	44	0	0	NUM
ejpam-1476	42	45	}	}	PUNCT
ejpam-1476	42	46	,	,	PUNCT
ejpam-1476	42	47	0¶	0¶	NOUN
ejpam-1476	42	48	δ	δ	X
ejpam-1476	42	49	<	<	X
ejpam-1476	42	50	1	1	NUM
ejpam-1476	42	51	and	and	CCONJ
ejpam-1476	42	52	�	�	PROPN
ejpam-1476	42	53	�	�	PROPN
ejpam-1476	42	54	γ(a−	γ(a−	PROPN
ejpam-1476	42	55	b	b	NOUN
ejpam-1476	42	56	)	)	PUNCT
ejpam-1476	42	57	+	+	CCONJ
ejpam-1476	42	58	(	(	PUNCT
ejpam-1476	42	59	p−	p−	NOUN
ejpam-1476	42	60	q−	q−	PROPN
ejpam-1476	42	61	δ)b	δ)b	ADJ
ejpam-1476	42	62	�	�	PROPN
ejpam-1476	42	63	�	�	PROPN
ejpam-1476	42	64	¶	¶	PROPN
ejpam-1476	42	65	�	�	PROPN
ejpam-1476	42	66	�	�	PROPN
ejpam-1476	42	67	p−	p−	PROPN
ejpam-1476	42	68	q−	q−	PROPN
ejpam-1476	42	69	δ	δ	PROPN
ejpam-1476	42	70	�	�	PROPN
ejpam-1476	42	71	�	�	PROPN
ejpam-1476	42	72	.	.	PUNCT
ejpam-1476	43	1	proof	proof	NOUN
ejpam-1476	43	2	.	.	PUNCT
ejpam-1476	44	1	since	since	SCONJ
ejpam-1476	44	2	g	g	PROPN
ejpam-1476	44	3	∈	∈	PROPN
ejpam-1476	44	4	sδp	sδp	NOUN
ejpam-1476	44	5	,	,	PUNCT
ejpam-1476	44	6	q(γ	q(γ	PROPN
ejpam-1476	44	7	,	,	PUNCT
ejpam-1476	44	8	a	a	DET
ejpam-1476	44	9	,	,	PUNCT
ejpam-1476	44	10	b	b	NOUN
ejpam-1476	44	11	)	)	PUNCT
ejpam-1476	44	12	,	,	PUNCT
ejpam-1476	44	13	we	we	PRON
ejpam-1476	44	14	obtain	obtain	VERB
ejpam-1476	44	15	from	from	ADP
ejpam-1476	44	16	(	(	PUNCT
ejpam-1476	44	17	5	5	NUM
ejpam-1476	44	18	)	)	PUNCT
ejpam-1476	44	19	1	1	NUM
ejpam-1476	44	20	+	+	SYM
ejpam-1476	44	21	1	1	NUM
ejpam-1476	44	22	γ	γ	PROPN
ejpam-1476	44	23	z	z	PROPN
ejpam-1476	44	24	g(q+δ+1)(z	g(q+δ+1)(z	PROPN
ejpam-1476	44	25	)	)	PUNCT
ejpam-1476	44	26	g(q+δ)(z	g(q+δ)(z	PROPN
ejpam-1476	44	27	)	)	PUNCT
ejpam-1476	44	28	−	−	PROPN
ejpam-1476	44	29	p+	p+	X
ejpam-1476	44	30	q+	q+	ADV
ejpam-1476	44	31	δ	δ	PROPN
ejpam-1476	44	32	!	!	PUNCT
ejpam-1476	45	1	=	=	PUNCT
ejpam-1476	46	1	1	1	NUM
ejpam-1476	46	2	+	+	CCONJ
ejpam-1476	46	3	aω(z	aω(z	PUNCT
ejpam-1476	46	4	)	)	PUNCT
ejpam-1476	46	5	1	1	NUM
ejpam-1476	46	6	+	+	CCONJ
ejpam-1476	46	7	bω(z	bω(z	NUM
ejpam-1476	46	8	)	)	PUNCT
ejpam-1476	46	9	(	(	PUNCT
ejpam-1476	46	10	9	9	X
ejpam-1476	46	11	)	)	PUNCT
ejpam-1476	46	12	where	where	SCONJ
ejpam-1476	46	13	ω(0	ω(0	NOUN
ejpam-1476	46	14	)	)	PUNCT
ejpam-1476	46	15	=	=	SYM
ejpam-1476	46	16	0	0	NUM
ejpam-1476	46	17	and	and	CCONJ
ejpam-1476	46	18	|ω(z)|	|ω(z)|	PROPN
ejpam-1476	46	19	¶	¶	PROPN
ejpam-1476	46	20	|z|	|z|	NOUN
ejpam-1476	46	21	(	(	PUNCT
ejpam-1476	46	22	z	z	NOUN
ejpam-1476	46	23	∈	∈	PROPN
ejpam-1476	46	24	u	u	NOUN
ejpam-1476	46	25	)	)	PUNCT
ejpam-1476	46	26	.	.	PUNCT
ejpam-1476	47	1	(	(	PUNCT
ejpam-1476	47	2	10	10	NUM
ejpam-1476	47	3	)	)	PUNCT
ejpam-1476	47	4	from	from	ADP
ejpam-1476	47	5	(	(	PUNCT
ejpam-1476	47	6	9	9	X
ejpam-1476	47	7	)	)	PUNCT
ejpam-1476	47	8	we	we	PRON
ejpam-1476	47	9	readily	readily	ADV
ejpam-1476	47	10	obtain	obtain	VERB
ejpam-1476	47	11	z	z	NOUN
ejpam-1476	47	12	g(q+δ+1)(z	g(q+δ+1)(z	X
ejpam-1476	47	13	)	)	PUNCT
ejpam-1476	47	14	g(q+δ)(z	g(q+δ)(z	PROPN
ejpam-1476	47	15	)	)	PUNCT
ejpam-1476	47	16	=	=	PUNCT
ejpam-1476	48	1	p−	p−	NOUN
ejpam-1476	48	2	q−	q−	PROPN
ejpam-1476	48	3	δ+	δ+	PUNCT
ejpam-1476	48	4	�	�	X
ejpam-1476	48	5	γ(a−	γ(a−	PROPN
ejpam-1476	48	6	b	b	NOUN
ejpam-1476	48	7	)	)	PUNCT
ejpam-1476	48	8	+	+	CCONJ
ejpam-1476	48	9	(	(	PUNCT
ejpam-1476	48	10	p−	p−	PROPN
ejpam-1476	48	11	q−	q−	PROPN
ejpam-1476	48	12	δ)b	δ)b	ADV
ejpam-1476	48	13	�	�	PROPN
ejpam-1476	48	14	ω(z	ω(z	NUM
ejpam-1476	48	15	)	)	PUNCT
ejpam-1476	48	16	1	1	NUM
ejpam-1476	48	17	+	+	CCONJ
ejpam-1476	48	18	bω(z	bω(z	NUM
ejpam-1476	48	19	)	)	PUNCT
ejpam-1476	48	20	.	.	PUNCT
ejpam-1476	49	1	(	(	PUNCT
ejpam-1476	49	2	11	11	X
ejpam-1476	49	3	)	)	PUNCT
ejpam-1476	49	4	using	use	VERB
ejpam-1476	49	5	(	(	PUNCT
ejpam-1476	49	6	10	10	NUM
ejpam-1476	49	7	)	)	PUNCT
ejpam-1476	49	8	in	in	ADP
ejpam-1476	49	9	(	(	PUNCT
ejpam-1476	49	10	11	11	NUM
ejpam-1476	49	11	)	)	PUNCT
ejpam-1476	49	12	we	we	PRON
ejpam-1476	49	13	find	find	VERB
ejpam-1476	49	14	�	�	PROPN
ejpam-1476	49	15	�	�	PROPN
ejpam-1476	49	16	�	�	PROPN
ejpam-1476	49	17	g(q+δ)(z	g(q+δ)(z	PROPN
ejpam-1476	49	18	)	)	PUNCT
ejpam-1476	49	19	�	�	PROPN
ejpam-1476	49	20	�	�	PROPN
ejpam-1476	49	21	�	�	PROPN
ejpam-1476	49	22	¶	¶	PROPN
ejpam-1476	49	23	(	(	PUNCT
ejpam-1476	49	24	1	1	NUM
ejpam-1476	49	25	+	+	NUM
ejpam-1476	49	26	|b|	|b|	PROPN
ejpam-1476	49	27	|z|	|z|	NOUN
ejpam-1476	49	28	)	)	PUNCT
ejpam-1476	49	29	|z|	|z|	VERB
ejpam-1476	49	30	p−	p−	NOUN
ejpam-1476	49	31	q−	q−	PROPN
ejpam-1476	49	32	δ−	δ−	PROPN
ejpam-1476	49	33	�	�	PROPN
ejpam-1476	49	34	�	�	PROPN
ejpam-1476	49	35	γ(a−	γ(a−	PROPN
ejpam-1476	49	36	b	b	NOUN
ejpam-1476	49	37	)	)	PUNCT
ejpam-1476	50	1	+	+	CCONJ
ejpam-1476	50	2	(	(	PUNCT
ejpam-1476	50	3	p−	p−	NOUN
ejpam-1476	50	4	q−	q−	PROPN
ejpam-1476	50	5	δ)b	δ)b	ADJ
ejpam-1476	50	6	�	�	PROPN
ejpam-1476	50	7	�	�	PROPN
ejpam-1476	50	8	|z|	|z|	NOUN
ejpam-1476	50	9	�	�	PROPN
ejpam-1476	50	10	�	�	PROPN
ejpam-1476	50	11	�	�	PROPN
ejpam-1476	50	12	g(q+δ+1)(z	g(q+δ+1)(z	PROPN
ejpam-1476	50	13	)	)	PUNCT
ejpam-1476	50	14	�	�	PROPN
ejpam-1476	50	15	�	�	PROPN
ejpam-1476	50	16	�	�	PROPN
ejpam-1476	50	17	.	.	PUNCT
ejpam-1476	51	1	(	(	PUNCT
ejpam-1476	51	2	12	12	NUM
ejpam-1476	51	3	)	)	PUNCT
ejpam-1476	51	4	o.	o.	NOUN
ejpam-1476	51	5	altıntaş	altıntaş	PROPN
ejpam-1476	51	6	/	/	SYM
ejpam-1476	51	7	eur	eur	PROPN
ejpam-1476	51	8	.	.	PUNCT
ejpam-1476	52	1	j.	j.	PROPN
ejpam-1476	52	2	pure	pure	PROPN
ejpam-1476	52	3	appl	appl	PROPN
ejpam-1476	52	4	.	.	PROPN
ejpam-1476	52	5	math	math	PROPN
ejpam-1476	52	6	,	,	PUNCT
ejpam-1476	52	7	5	5	NUM
ejpam-1476	52	8	(	(	PUNCT
ejpam-1476	52	9	2012	2012	NUM
ejpam-1476	52	10	)	)	PUNCT
ejpam-1476	52	11	,	,	PUNCT
ejpam-1476	52	12	16	16	NUM
ejpam-1476	52	13	-	-	SYM
ejpam-1476	52	14	24	24	NUM
ejpam-1476	52	15	19	19	NUM
ejpam-1476	52	16	since	since	SCONJ
ejpam-1476	52	17	f	f	PROPN
ejpam-1476	52	18	(	(	PUNCT
ejpam-1476	52	19	q+δ)(z	q+δ)(z	X
ejpam-1476	52	20	)	)	PUNCT
ejpam-1476	52	21	is	be	AUX
ejpam-1476	52	22	majorized	majorize	VERB
ejpam-1476	52	23	by	by	ADP
ejpam-1476	52	24	g(q+δ)(z	g(q+δ)(z	PROPN
ejpam-1476	52	25	)	)	PUNCT
ejpam-1476	52	26	from	from	ADP
ejpam-1476	52	27	(	(	PUNCT
ejpam-1476	52	28	2	2	X
ejpam-1476	52	29	)	)	PUNCT
ejpam-1476	52	30	we	we	PRON
ejpam-1476	52	31	have	have	AUX
ejpam-1476	52	32	f	f	X
ejpam-1476	52	33	(	(	PUNCT
ejpam-1476	52	34	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	52	35	)	)	PUNCT
ejpam-1476	52	36	=	=	PUNCT
ejpam-1476	52	37	φ(z)g(q+δ+1)(z	φ(z)g(q+δ+1)(z	NUM
ejpam-1476	52	38	)	)	PUNCT
ejpam-1476	53	1	+	+	NUM
ejpam-1476	53	2	φ′(z)g(q+δ)(z	φ′(z)g(q+δ)(z	NOUN
ejpam-1476	53	3	)	)	PUNCT
ejpam-1476	53	4	,	,	PUNCT
ejpam-1476	53	5	(	(	PUNCT
ejpam-1476	53	6	13	13	X
ejpam-1476	53	7	)	)	PUNCT
ejpam-1476	53	8	φ(z	φ(z	PROPN
ejpam-1476	53	9	)	)	PUNCT
ejpam-1476	53	10	is	be	AUX
ejpam-1476	53	11	satisfies	satisfie	NOUN
ejpam-1476	53	12	the	the	DET
ejpam-1476	53	13	inequality	inequality	NOUN
ejpam-1476	53	14	[	[	X
ejpam-1476	53	15	cf	cf	NOUN
ejpam-1476	53	16	.	.	PUNCT
ejpam-1476	53	17	nehari	nehari	PROPN
ejpam-1476	53	18	7	7	NUM
ejpam-1476	53	19	,	,	PUNCT
ejpam-1476	53	20	p.	p.	NOUN
ejpam-1476	53	21	168	168	NUM
ejpam-1476	53	22	]	]	SYM
ejpam-1476	53	23	:	:	PUNCT
ejpam-1476	53	24	�	�	PROPN
ejpam-1476	53	25	�	�	PROPN
ejpam-1476	53	26	φ′(z	φ′(z	PROPN
ejpam-1476	53	27	)	)	PUNCT
ejpam-1476	53	28	�	�	PROPN
ejpam-1476	53	29	�	�	PROPN
ejpam-1476	53	30	¶	¶	PROPN
ejpam-1476	53	31	1−	1−	PROPN
ejpam-1476	53	32	�	�	PROPN
ejpam-1476	53	33	�	�	PROPN
ejpam-1476	53	34	φ(z	φ(z	PROPN
ejpam-1476	53	35	)	)	PUNCT
ejpam-1476	53	36	�	�	PROPN
ejpam-1476	53	37	�	�	PROPN
ejpam-1476	53	38	2	2	NUM
ejpam-1476	53	39	1−	1−	NUM
ejpam-1476	53	40	|z|2	|z|2	PROPN
ejpam-1476	53	41	(	(	PUNCT
ejpam-1476	53	42	z	z	NOUN
ejpam-1476	53	43	∈	∈	PROPN
ejpam-1476	53	44	u	u	NOUN
ejpam-1476	53	45	)	)	PUNCT
ejpam-1476	53	46	(	(	PUNCT
ejpam-1476	53	47	14	14	NUM
ejpam-1476	53	48	)	)	PUNCT
ejpam-1476	53	49	and	and	CCONJ
ejpam-1476	53	50	using	use	VERB
ejpam-1476	53	51	(	(	PUNCT
ejpam-1476	53	52	12	12	NUM
ejpam-1476	53	53	)	)	PUNCT
ejpam-1476	53	54	and	and	CCONJ
ejpam-1476	53	55	(	(	PUNCT
ejpam-1476	53	56	14	14	NUM
ejpam-1476	53	57	)	)	PUNCT
ejpam-1476	53	58	in	in	ADP
ejpam-1476	53	59	(	(	PUNCT
ejpam-1476	53	60	13	13	NUM
ejpam-1476	53	61	)	)	PUNCT
ejpam-1476	53	62	,	,	PUNCT
ejpam-1476	53	63	we	we	PRON
ejpam-1476	53	64	get	get	VERB
ejpam-1476	53	65	�	�	PROPN
ejpam-1476	53	66	�	�	PROPN
ejpam-1476	53	67	�	�	PROPN
ejpam-1476	53	68	f	f	PROPN
ejpam-1476	53	69	(	(	PUNCT
ejpam-1476	53	70	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	53	71	)	)	PUNCT
ejpam-1476	53	72	�	�	PROPN
ejpam-1476	53	73	�	�	PROPN
ejpam-1476	53	74	�	�	PROPN
ejpam-1476	53	75	¶	¶	PROPN
ejpam-1476	53	76	�	�	PROPN
ejpam-1476	53	77	�	�	PROPN
ejpam-1476	53	78	φ(z	φ(z	PROPN
ejpam-1476	53	79	)	)	PUNCT
ejpam-1476	53	80	�	�	PROPN
ejpam-1476	53	81	�	�	PROPN
ejpam-1476	53	82	+	+	PROPN
ejpam-1476	53	83	1−	1−	NUM
ejpam-1476	53	84	�	�	PROPN
ejpam-1476	53	85	�	�	PROPN
ejpam-1476	53	86	φ(z	φ(z	PROPN
ejpam-1476	53	87	)	)	PUNCT
ejpam-1476	53	88	�	�	PROPN
ejpam-1476	53	89	�	�	PROPN
ejpam-1476	53	90	2	2	NUM
ejpam-1476	53	91	1−	1−	NUM
ejpam-1476	53	92	|z|2	|z|2	NOUN
ejpam-1476	53	93	(	(	PUNCT
ejpam-1476	53	94	1	1	NUM
ejpam-1476	53	95	+	+	NUM
ejpam-1476	53	96	|b|	|b|	PROPN
ejpam-1476	53	97	|z|	|z|	NOUN
ejpam-1476	53	98	)	)	PUNCT
ejpam-1476	53	99	|z|	|z|	VERB
ejpam-1476	53	100	p−	p−	NOUN
ejpam-1476	53	101	q−	q−	PROPN
ejpam-1476	53	102	δ−	δ−	PROPN
ejpam-1476	53	103	�	�	PROPN
ejpam-1476	53	104	�	�	PROPN
ejpam-1476	53	105	γ(a−	γ(a−	PROPN
ejpam-1476	53	106	b	b	NOUN
ejpam-1476	53	107	)	)	PUNCT
ejpam-1476	54	1	+	+	CCONJ
ejpam-1476	54	2	(	(	PUNCT
ejpam-1476	54	3	p−	p−	NOUN
ejpam-1476	54	4	q−	q−	PROPN
ejpam-1476	54	5	δ)b	δ)b	ADJ
ejpam-1476	54	6	�	�	PROPN
ejpam-1476	54	7	�	�	PROPN
ejpam-1476	54	8	|z|	|z|	NOUN
ejpam-1476	54	9	�	�	PROPN
ejpam-1476	54	10	�	�	PROPN
ejpam-1476	54	11	�	�	PROPN
ejpam-1476	54	12	g(q+δ+1)(z	g(q+δ+1)(z	PROPN
ejpam-1476	54	13	)	)	PUNCT
ejpam-1476	54	14	�	�	PROPN
ejpam-1476	54	15	�	�	PROPN
ejpam-1476	54	16	�	�	PROPN
ejpam-1476	54	17	(	(	PUNCT
ejpam-1476	54	18	15	15	NUM
ejpam-1476	54	19	)	)	PUNCT
ejpam-1476	54	20	which	which	PRON
ejpam-1476	54	21	,	,	PUNCT
ejpam-1476	54	22	upon	upon	SCONJ
ejpam-1476	54	23	setting	set	VERB
ejpam-1476	54	24	|z|	|z|	NOUN
ejpam-1476	54	25	=	=	SYM
ejpam-1476	54	26	r	r	NOUN
ejpam-1476	54	27	,	,	PUNCT
ejpam-1476	54	28	�	�	PROPN
ejpam-1476	54	29	�	�	PROPN
ejpam-1476	54	30	φ(z	φ(z	PROPN
ejpam-1476	54	31	)	)	PUNCT
ejpam-1476	54	32	�	�	PROPN
ejpam-1476	54	33	�	�	PROPN
ejpam-1476	54	34	=	=	SYM
ejpam-1476	54	35	ρ	ρ	PROPN
ejpam-1476	54	36	(	(	PUNCT
ejpam-1476	54	37	0¶	0¶	NOUN
ejpam-1476	54	38	ρ	ρ	PROPN
ejpam-1476	54	39	¶	¶	PROPN
ejpam-1476	54	40	1	1	NUM
ejpam-1476	54	41	)	)	PUNCT
ejpam-1476	54	42	leads	lead	VERB
ejpam-1476	54	43	us	we	PRON
ejpam-1476	54	44	to	to	ADP
ejpam-1476	54	45	the	the	DET
ejpam-1476	54	46	inequality	inequality	NOUN
ejpam-1476	54	47	�	�	PROPN
ejpam-1476	54	48	�	�	PROPN
ejpam-1476	54	49	�	�	PROPN
ejpam-1476	54	50	f	f	PROPN
ejpam-1476	54	51	(	(	PUNCT
ejpam-1476	54	52	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	54	53	)	)	PUNCT
ejpam-1476	54	54	�	�	PROPN
ejpam-1476	54	55	�	�	PROPN
ejpam-1476	54	56	�	�	PROPN
ejpam-1476	54	57	¶	¶	PROPN
ejpam-1476	54	58	θ(ρ	θ(ρ	PROPN
ejpam-1476	54	59	)	)	PUNCT
ejpam-1476	54	60	(	(	PUNCT
ejpam-1476	54	61	1−	1−	NUM
ejpam-1476	54	62	r2	r2	PROPN
ejpam-1476	54	63	)	)	PUNCT
ejpam-1476	54	64	�	�	PROPN
ejpam-1476	55	1	p−	p−	PROPN
ejpam-1476	55	2	q−	q−	PROPN
ejpam-1476	55	3	δ−	δ−	PROPN
ejpam-1476	55	4	�	�	PROPN
ejpam-1476	55	5	�	�	PROPN
ejpam-1476	55	6	γ(a−	γ(a−	PROPN
ejpam-1476	55	7	b	b	NOUN
ejpam-1476	55	8	)	)	PUNCT
ejpam-1476	56	1	+	+	CCONJ
ejpam-1476	56	2	(	(	PUNCT
ejpam-1476	56	3	p−	p−	NOUN
ejpam-1476	56	4	q−	q−	PROPN
ejpam-1476	56	5	δ)b	δ)b	ADJ
ejpam-1476	56	6	�	�	PROPN
ejpam-1476	56	7	�	�	PROPN
ejpam-1476	56	8	r	r	PROPN
ejpam-1476	56	9	�	�	PROPN
ejpam-1476	56	10	g(q+δ+1)(z	g(q+δ+1)(z	PROPN
ejpam-1476	56	11	)	)	PUNCT
ejpam-1476	56	12	(	(	PUNCT
ejpam-1476	56	13	16	16	NUM
ejpam-1476	56	14	)	)	PUNCT
ejpam-1476	56	15	where	where	SCONJ
ejpam-1476	56	16	θ(ρ	θ(ρ	PROPN
ejpam-1476	56	17	)	)	PUNCT
ejpam-1476	57	1	=	=	PUNCT
ejpam-1476	58	1	−(r+	−(r+	NUM
ejpam-1476	58	2	|b|	|b|	PROPN
ejpam-1476	59	1	r2)ρ2+(1−	r2)ρ2+(1−	NOUN
ejpam-1476	59	2	r2)p−q−δ−	r2)p−q−δ−	X
ejpam-1476	59	3	�	�	PROPN
ejpam-1476	59	4	�	�	PROPN
ejpam-1476	59	5	γ(a−	γ(a−	PROPN
ejpam-1476	59	6	b	b	NOUN
ejpam-1476	59	7	)	)	PUNCT
ejpam-1476	60	1	+	+	CCONJ
ejpam-1476	60	2	(	(	PUNCT
ejpam-1476	60	3	p−	p−	PROPN
ejpam-1476	60	4	q−δ)b	q−δ)b	PROPN
ejpam-1476	60	5	�	�	PROPN
ejpam-1476	60	6	�	�	PROPN
ejpam-1476	60	7	r]ρ+(r+	r]ρ+(r+	PRON
ejpam-1476	60	8	|b|	|b|	PROPN
ejpam-1476	60	9	r2	r2	PROPN
ejpam-1476	60	10	)	)	PUNCT
ejpam-1476	60	11	(	(	PUNCT
ejpam-1476	60	12	17	17	NUM
ejpam-1476	60	13	)	)	PUNCT
ejpam-1476	60	14	takes	take	VERB
ejpam-1476	60	15	on	on	ADP
ejpam-1476	60	16	its	its	PRON
ejpam-1476	60	17	maximum	maximum	ADJ
ejpam-1476	60	18	value	value	NOUN
ejpam-1476	60	19	at	at	ADP
ejpam-1476	60	20	ρ	ρ	PROPN
ejpam-1476	60	21	=	=	SYM
ejpam-1476	60	22	1	1	NUM
ejpam-1476	60	23	with	with	ADP
ejpam-1476	60	24	r	r	NOUN
ejpam-1476	60	25	=	=	SYM
ejpam-1476	60	26	r1(p	r1(p	PROPN
ejpam-1476	60	27	,	,	PUNCT
ejpam-1476	60	28	q	q	NOUN
ejpam-1476	60	29	,	,	PUNCT
ejpam-1476	60	30	δ	δ	PROPN
ejpam-1476	60	31	,	,	PUNCT
ejpam-1476	60	32	γ	γ	PROPN
ejpam-1476	60	33	,	,	PUNCT
ejpam-1476	60	34	a	a	DET
ejpam-1476	60	35	,	,	PUNCT
ejpam-1476	60	36	b	b	NOUN
ejpam-1476	60	37	)	)	PUNCT
ejpam-1476	60	38	gives	give	VERB
ejpam-1476	60	39	by	by	ADP
ejpam-1476	60	40	(	(	PUNCT
ejpam-1476	60	41	8)	8)	NUM
ejpam-1476	60	42	if	if	SCONJ
ejpam-1476	60	43	0¶	0¶	NOUN
ejpam-1476	60	44	σ	σ	PROPN
ejpam-1476	60	45	¶	¶	PROPN
ejpam-1476	60	46	r1(p	r1(p	PROPN
ejpam-1476	60	47	,	,	PUNCT
ejpam-1476	60	48	q	q	NOUN
ejpam-1476	60	49	,	,	PUNCT
ejpam-1476	60	50	δ	δ	PROPN
ejpam-1476	60	51	,	,	PUNCT
ejpam-1476	60	52	γ	γ	PROPN
ejpam-1476	60	53	,	,	PUNCT
ejpam-1476	60	54	a	a	DET
ejpam-1476	60	55	,	,	PUNCT
ejpam-1476	60	56	b	b	NOUN
ejpam-1476	60	57	)	)	PUNCT
ejpam-1476	60	58	then	then	ADV
ejpam-1476	60	59	the	the	DET
ejpam-1476	60	60	function	function	NOUN
ejpam-1476	60	61	∧(ρ	∧(ρ	PROPN
ejpam-1476	60	62	)	)	PUNCT
ejpam-1476	60	63	defined	define	VERB
ejpam-1476	60	64	by	by	ADP
ejpam-1476	60	65	∧(ρ	∧(ρ	PROPN
ejpam-1476	60	66	)	)	PUNCT
ejpam-1476	61	1	=	=	VERB
ejpam-1476	61	2	−(σ+σ2	−(σ+σ2	NUM
ejpam-1476	61	3	|b|)ρ2+(1−σ2	|b|)ρ2+(1−σ2	ADJ
ejpam-1476	61	4	)	)	PUNCT
ejpam-1476	61	5	�	�	PROPN
ejpam-1476	61	6	p−	p−	PROPN
ejpam-1476	61	7	q−	q−	PROPN
ejpam-1476	61	8	δ−	δ−	PROPN
ejpam-1476	61	9	�	�	PROPN
ejpam-1476	61	10	�	�	PROPN
ejpam-1476	61	11	γ(a−	γ(a−	PROPN
ejpam-1476	61	12	b	b	NOUN
ejpam-1476	61	13	)	)	PUNCT
ejpam-1476	61	14	+	+	CCONJ
ejpam-1476	61	15	(	(	PUNCT
ejpam-1476	61	16	p−	p−	NOUN
ejpam-1476	61	17	q−	q−	PROPN
ejpam-1476	61	18	δ)b	δ)b	ADJ
ejpam-1476	61	19	�	�	PROPN
ejpam-1476	61	20	�	�	PROPN
ejpam-1476	61	21	σ	σ	PROPN
ejpam-1476	61	22	�	�	PROPN
ejpam-1476	61	23	ρ+(σ+σ2	ρ+(σ+σ2	PROPN
ejpam-1476	61	24	|b|	|b|	PROPN
ejpam-1476	61	25	)	)	PUNCT
ejpam-1476	61	26	(	(	PUNCT
ejpam-1476	61	27	18	18	NUM
ejpam-1476	61	28	)	)	PUNCT
ejpam-1476	61	29	is	be	AUX
ejpam-1476	61	30	an	an	DET
ejpam-1476	61	31	increasing	increase	VERB
ejpam-1476	61	32	function	function	NOUN
ejpam-1476	61	33	on	on	ADP
ejpam-1476	61	34	the	the	DET
ejpam-1476	61	35	interval	interval	NOUN
ejpam-1476	61	36	0¶	0¶	NOUN
ejpam-1476	61	37	ρ	ρ	PROPN
ejpam-1476	61	38	¶	¶	NOUN
ejpam-1476	61	39	1	1	NUM
ejpam-1476	61	40	so	so	SCONJ
ejpam-1476	61	41	that	that	SCONJ
ejpam-1476	61	42	∧(ρ)¶	∧(ρ)¶	ADJ
ejpam-1476	61	43	∧(1	∧(1	NOUN
ejpam-1476	61	44	)	)	PUNCT
ejpam-1476	61	45	=	=	PUNCT
ejpam-1476	61	46	(	(	PUNCT
ejpam-1476	61	47	1−σ2	1−σ2	NUM
ejpam-1476	61	48	)	)	PUNCT
ejpam-1476	61	49	�	�	PROPN
ejpam-1476	61	50	p−	p−	PROPN
ejpam-1476	61	51	q−	q−	PROPN
ejpam-1476	61	52	δ−	δ−	PROPN
ejpam-1476	61	53	�	�	PROPN
ejpam-1476	61	54	�	�	PROPN
ejpam-1476	61	55	γ(a−	γ(a−	PROPN
ejpam-1476	61	56	b	b	NOUN
ejpam-1476	61	57	)	)	PUNCT
ejpam-1476	62	1	+	+	CCONJ
ejpam-1476	62	2	(	(	PUNCT
ejpam-1476	62	3	p−	p−	NOUN
ejpam-1476	62	4	q−	q−	PROPN
ejpam-1476	62	5	δ)b	δ)b	ADJ
ejpam-1476	62	6	�	�	PROPN
ejpam-1476	62	7	�	�	PROPN
ejpam-1476	62	8	σ	σ	PROPN
ejpam-1476	62	9	�	�	PROPN
ejpam-1476	62	10	(	(	PUNCT
ejpam-1476	62	11	0¶	0¶	NOUN
ejpam-1476	62	12	ρ	ρ	PROPN
ejpam-1476	62	13	¶	¶	PROPN
ejpam-1476	62	14	1	1	NUM
ejpam-1476	62	15	;	;	PUNCT
ejpam-1476	62	16	0¶	0¶	NOUN
ejpam-1476	62	17	σ	σ	PROPN
ejpam-1476	62	18	¶	¶	PROPN
ejpam-1476	62	19	r1(p	r1(p	PROPN
ejpam-1476	62	20	,	,	PUNCT
ejpam-1476	62	21	q	q	NOUN
ejpam-1476	62	22	,	,	PUNCT
ejpam-1476	62	23	δ	δ	PROPN
ejpam-1476	62	24	,	,	PUNCT
ejpam-1476	62	25	γ	γ	PROPN
ejpam-1476	62	26	,	,	PUNCT
ejpam-1476	62	27	a	a	DET
ejpam-1476	62	28	,	,	PUNCT
ejpam-1476	62	29	b	b	NOUN
ejpam-1476	62	30	)	)	PUNCT
ejpam-1476	62	31	)	)	PUNCT
ejpam-1476	62	32	.	.	PUNCT
ejpam-1476	63	1	hence	hence	ADV
ejpam-1476	63	2	,	,	PUNCT
ejpam-1476	63	3	by	by	ADP
ejpam-1476	63	4	setting	set	VERB
ejpam-1476	63	5	ρ	ρ	NOUN
ejpam-1476	63	6	=	=	SYM
ejpam-1476	63	7	1	1	NUM
ejpam-1476	63	8	in	in	ADP
ejpam-1476	63	9	(	(	PUNCT
ejpam-1476	63	10	16	16	NUM
ejpam-1476	63	11	)	)	PUNCT
ejpam-1476	63	12	,	,	PUNCT
ejpam-1476	63	13	we	we	PRON
ejpam-1476	63	14	conclude	conclude	VERB
ejpam-1476	63	15	that	that	SCONJ
ejpam-1476	63	16	theorem	theorem	VERB
ejpam-1476	63	17	1	1	NUM
ejpam-1476	63	18	holds	hold	VERB
ejpam-1476	63	19	true	true	ADJ
ejpam-1476	63	20	for	for	ADP
ejpam-1476	63	21	|z|	|z|	NOUN
ejpam-1476	63	22	¶	¶	PROPN
ejpam-1476	63	23	r1(p	r1(p	NOUN
ejpam-1476	63	24	,	,	PUNCT
ejpam-1476	63	25	q	q	NOUN
ejpam-1476	63	26	,	,	PUNCT
ejpam-1476	63	27	δ	δ	PROPN
ejpam-1476	63	28	,	,	PUNCT
ejpam-1476	63	29	γ	γ	PROPN
ejpam-1476	63	30	,	,	PUNCT
ejpam-1476	63	31	a	a	DET
ejpam-1476	63	32	,	,	PUNCT
ejpam-1476	63	33	b	b	NOUN
ejpam-1476	63	34	)	)	PUNCT
ejpam-1476	63	35	is	be	AUX
ejpam-1476	63	36	given	give	VERB
ejpam-1476	63	37	by	by	ADP
ejpam-1476	63	38	(	(	PUNCT
ejpam-1476	63	39	8)	8)	NUM
ejpam-1476	63	40	.	.	PUNCT
ejpam-1476	64	1	this	this	PRON
ejpam-1476	64	2	completes	complete	VERB
ejpam-1476	64	3	the	the	DET
ejpam-1476	64	4	proof	proof	NOUN
ejpam-1476	64	5	of	of	ADP
ejpam-1476	64	6	theorem	theorem	ADJ
ejpam-1476	64	7	1	1	NUM
ejpam-1476	64	8	.	.	PUNCT
ejpam-1476	64	9	corollary	corollary	ADJ
ejpam-1476	64	10	1	1	NUM
ejpam-1476	64	11	(	(	PUNCT
ejpam-1476	64	12	[	[	PUNCT
ejpam-1476	64	13	see	see	VERB
ejpam-1476	64	14	3	3	NUM
ejpam-1476	64	15	]	]	PUNCT
ejpam-1476	64	16	)	)	PUNCT
ejpam-1476	64	17	.	.	PUNCT
ejpam-1476	65	1	let	let	VERB
ejpam-1476	65	2	the	the	DET
ejpam-1476	65	3	function	function	NOUN
ejpam-1476	65	4	f	f	PROPN
ejpam-1476	65	5	(	(	PUNCT
ejpam-1476	65	6	z	z	NOUN
ejpam-1476	65	7	)	)	PUNCT
ejpam-1476	65	8	be	be	AUX
ejpam-1476	65	9	in	in	ADP
ejpam-1476	65	10	the	the	DET
ejpam-1476	65	11	class	class	NOUN
ejpam-1476	65	12	ap	ap	PROPN
ejpam-1476	65	13	and	and	CCONJ
ejpam-1476	65	14	suppose	suppose	VERB
ejpam-1476	65	15	that	that	SCONJ
ejpam-1476	65	16	g	g	PROPN
ejpam-1476	65	17	∈	∈	PROPN
ejpam-1476	65	18	s0	s0	PROPN
ejpam-1476	65	19	p	p	PROPN
ejpam-1476	65	20	,	,	PUNCT
ejpam-1476	65	21	q(γ	q(γ	PROPN
ejpam-1476	65	22	,	,	PUNCT
ejpam-1476	65	23	1,−1	1,−1	NUM
ejpam-1476	65	24	)	)	PUNCT
ejpam-1476	65	25	.	.	PUNCT
ejpam-1476	66	1	if	if	SCONJ
ejpam-1476	66	2	f	f	PROPN
ejpam-1476	66	3	(	(	PUNCT
ejpam-1476	66	4	q)(z	q)(z	NOUN
ejpam-1476	66	5	)	)	PUNCT
ejpam-1476	66	6	is	be	AUX
ejpam-1476	66	7	majorized	majorize	VERB
ejpam-1476	66	8	by	by	ADP
ejpam-1476	66	9	g(q)(z	g(q)(z	NOUN
ejpam-1476	66	10	)	)	PUNCT
ejpam-1476	66	11	in	in	ADP
ejpam-1476	66	12	u	u	NOUN
ejpam-1476	66	13	,	,	PUNCT
ejpam-1476	66	14	then	then	ADV
ejpam-1476	66	15	�	�	PROPN
ejpam-1476	66	16	�	�	PROPN
ejpam-1476	66	17	�	�	PROPN
ejpam-1476	66	18	f	f	PROPN
ejpam-1476	66	19	(	(	PUNCT
ejpam-1476	66	20	q+1)(z	q+1)(z	PROPN
ejpam-1476	66	21	)	)	PUNCT
ejpam-1476	66	22	�	�	PROPN
ejpam-1476	66	23	�	�	PROPN
ejpam-1476	66	24	�	�	PROPN
ejpam-1476	66	25	¶	¶	PROPN
ejpam-1476	66	26	�	�	PROPN
ejpam-1476	66	27	�	�	PROPN
ejpam-1476	66	28	�	�	PROPN
ejpam-1476	66	29	g(q+1)(z	g(q+1)(z	NOUN
ejpam-1476	66	30	)	)	PUNCT
ejpam-1476	66	31	�	�	PROPN
ejpam-1476	66	32	�	�	PROPN
ejpam-1476	66	33	�	�	PROPN
ejpam-1476	66	34	(	(	PUNCT
ejpam-1476	66	35	|z|	|z|	NOUN
ejpam-1476	66	36	¶	¶	NUM
ejpam-1476	66	37	r1	r1	PROPN
ejpam-1476	66	38	)	)	PUNCT
ejpam-1476	66	39	o.	o.	PROPN
ejpam-1476	66	40	altıntaş	altıntaş	PROPN
ejpam-1476	66	41	/	/	SYM
ejpam-1476	66	42	eur	eur	PROPN
ejpam-1476	66	43	.	.	PUNCT
ejpam-1476	67	1	j.	j.	PROPN
ejpam-1476	67	2	pure	pure	PROPN
ejpam-1476	67	3	appl	appl	PROPN
ejpam-1476	67	4	.	.	PROPN
ejpam-1476	67	5	math	math	PROPN
ejpam-1476	67	6	,	,	PUNCT
ejpam-1476	67	7	5	5	NUM
ejpam-1476	67	8	(	(	PUNCT
ejpam-1476	67	9	2012	2012	NUM
ejpam-1476	67	10	)	)	PUNCT
ejpam-1476	67	11	,	,	PUNCT
ejpam-1476	67	12	16	16	NUM
ejpam-1476	67	13	-	-	SYM
ejpam-1476	67	14	24	24	NUM
ejpam-1476	67	15	20	20	NUM
ejpam-1476	67	16	where	where	SCONJ
ejpam-1476	67	17	r1	r1	NOUN
ejpam-1476	67	18	=	=	SYM
ejpam-1476	67	19	r1(p	r1(p	PROPN
ejpam-1476	67	20	,	,	PUNCT
ejpam-1476	67	21	q	q	NOUN
ejpam-1476	67	22	,	,	PUNCT
ejpam-1476	67	23	δ	δ	NOUN
ejpam-1476	67	24	)	)	PUNCT
ejpam-1476	67	25	=	=	SYM
ejpam-1476	67	26	k−	k−	PROPN
ejpam-1476	67	27	æ	æ	PROPN
ejpam-1476	67	28	k2	k2	PROPN
ejpam-1476	67	29	−	−	PROPN
ejpam-1476	67	30	4(p−	4(p−	PROPN
ejpam-1476	67	31	q	q	NOUN
ejpam-1476	67	32	)	)	PUNCT
ejpam-1476	67	33	�	�	PROPN
ejpam-1476	67	34	�	�	PROPN
ejpam-1476	68	1	2γ−	2γ−	PROPN
ejpam-1476	68	2	p+	p+	NOUN
ejpam-1476	68	3	q	q	PROPN
ejpam-1476	68	4	�	�	PROPN
ejpam-1476	68	5	�	�	PROPN
ejpam-1476	68	6	2	2	NUM
ejpam-1476	68	7	�	�	PROPN
ejpam-1476	68	8	�	�	PROPN
ejpam-1476	68	9	2γ−	2γ−	PROPN
ejpam-1476	68	10	p+	p+	NOUN
ejpam-1476	68	11	q	q	PROPN
ejpam-1476	68	12	�	�	PROPN
ejpam-1476	68	13	�	�	PROPN
ejpam-1476	68	14	(	(	PUNCT
ejpam-1476	68	15	19	19	NUM
ejpam-1476	68	16	)	)	PUNCT
ejpam-1476	68	17	(	(	PUNCT
ejpam-1476	68	18	k	k	NOUN
ejpam-1476	68	19	=	=	PUNCT
ejpam-1476	68	20	p−	p−	NOUN
ejpam-1476	68	21	q+	q+	ADP
ejpam-1476	68	22	2	2	NUM
ejpam-1476	68	23	+	+	NUM
ejpam-1476	68	24	�	�	PROPN
ejpam-1476	68	25	�	�	PROPN
ejpam-1476	68	26	2γ−	2γ−	PROPN
ejpam-1476	68	27	p+	p+	NOUN
ejpam-1476	68	28	q	q	PROPN
ejpam-1476	68	29	�	�	PROPN
ejpam-1476	68	30	�	�	PROPN
ejpam-1476	68	31	,	,	PUNCT
ejpam-1476	68	32	p	p	PROPN
ejpam-1476	68	33	∈	∈	PROPN
ejpam-1476	68	34	n	n	CCONJ
ejpam-1476	68	35	,	,	PUNCT
ejpam-1476	68	36	q	q	PROPN
ejpam-1476	68	37	∈	∈	PROPN
ejpam-1476	68	38	n0,γ	n0,γ	PROPN
ejpam-1476	68	39	∈	∈	PROPN
ejpam-1476	68	40	c	c	NOUN
ejpam-1476	68	41	\	\	X
ejpam-1476	68	42	{	{	PUNCT
ejpam-1476	68	43	0	0	NUM
ejpam-1476	68	44	}	}	PUNCT
ejpam-1476	68	45	)	)	PUNCT
ejpam-1476	68	46	.	.	PUNCT
ejpam-1476	69	1	proof	proof	NOUN
ejpam-1476	69	2	.	.	PUNCT
ejpam-1476	70	1	if	if	SCONJ
ejpam-1476	70	2	we	we	PRON
ejpam-1476	70	3	set	set	VERB
ejpam-1476	70	4	δ	δ	PROPN
ejpam-1476	70	5	=	=	SYM
ejpam-1476	70	6	0	0	NUM
ejpam-1476	70	7	,	,	PUNCT
ejpam-1476	70	8	a=	a=	X
ejpam-1476	70	9	1	1	NUM
ejpam-1476	70	10	,	,	PUNCT
ejpam-1476	70	11	b	b	NOUN
ejpam-1476	70	12	=	=	SYM
ejpam-1476	70	13	−1	−1	NOUN
ejpam-1476	70	14	in	in	ADP
ejpam-1476	70	15	theorem	theorem	NOUN
ejpam-1476	70	16	1	1	NUM
ejpam-1476	70	17	,	,	PUNCT
ejpam-1476	70	18	then	then	ADV
ejpam-1476	70	19	�	�	PROPN
ejpam-1476	70	20	�	�	PROPN
ejpam-1476	70	21	�	�	PROPN
ejpam-1476	70	22	f	f	PROPN
ejpam-1476	70	23	(	(	PUNCT
ejpam-1476	70	24	q+1)(z	q+1)(z	PROPN
ejpam-1476	70	25	)	)	PUNCT
ejpam-1476	70	26	�	�	PROPN
ejpam-1476	70	27	�	�	PROPN
ejpam-1476	70	28	�	�	PROPN
ejpam-1476	70	29	¶	¶	PROPN
ejpam-1476	70	30	�	�	PROPN
ejpam-1476	70	31	�	�	PROPN
ejpam-1476	70	32	�	�	PROPN
ejpam-1476	70	33	g(q+1)(z	g(q+1)(z	NOUN
ejpam-1476	70	34	)	)	PUNCT
ejpam-1476	70	35	�	�	PROPN
ejpam-1476	70	36	�	�	PROPN
ejpam-1476	70	37	�	�	PROPN
ejpam-1476	70	38	|z|	|z|	PROPN
ejpam-1476	70	39	¶	¶	PROPN
ejpam-1476	70	40	r1	r1	PROPN
ejpam-1476	70	41	where	where	SCONJ
ejpam-1476	70	42	r1	r1	NOUN
ejpam-1476	70	43	=	=	SYM
ejpam-1476	70	44	r1(p	r1(p	PROPN
ejpam-1476	70	45	,	,	PUNCT
ejpam-1476	70	46	q	q	NOUN
ejpam-1476	70	47	,	,	PUNCT
ejpam-1476	70	48	δ	δ	PROPN
ejpam-1476	70	49	)	)	PUNCT
ejpam-1476	70	50	is	be	AUX
ejpam-1476	70	51	the	the	DET
ejpam-1476	70	52	smallest	small	ADJ
ejpam-1476	70	53	positive	positive	ADJ
ejpam-1476	70	54	root	root	NOUN
ejpam-1476	70	55	of	of	ADP
ejpam-1476	70	56	the	the	DET
ejpam-1476	70	57	equation	equation	NOUN
ejpam-1476	70	58	�	�	PROPN
ejpam-1476	70	59	�	�	PROPN
ejpam-1476	70	60	2γ−	2γ−	PROPN
ejpam-1476	70	61	p+	p+	NOUN
ejpam-1476	70	62	q	q	PROPN
ejpam-1476	70	63	�	�	PROPN
ejpam-1476	70	64	�	�	PROPN
ejpam-1476	70	65	r3	r3	PROPN
ejpam-1476	70	66	−	−	PROPN
ejpam-1476	70	67	(	(	PUNCT
ejpam-1476	70	68	p−	p−	X
ejpam-1476	70	69	q+	q+	NOUN
ejpam-1476	70	70	2)r2−	2)r2−	NUM
ejpam-1476	70	71	[	[	PUNCT
ejpam-1476	70	72	�	�	PROPN
ejpam-1476	70	73	�	�	PROPN
ejpam-1476	70	74	2γ−	2γ−	PROPN
ejpam-1476	70	75	p+	p+	NOUN
ejpam-1476	70	76	q	q	PROPN
ejpam-1476	70	77	�	�	PROPN
ejpam-1476	70	78	�	�	PROPN
ejpam-1476	70	79	+	+	PROPN
ejpam-1476	70	80	2]r	2]r	NUM
ejpam-1476	71	1	+	+	ADP
ejpam-1476	71	2	p−	p−	NOUN
ejpam-1476	71	3	q	q	NOUN
ejpam-1476	71	4	=	=	SYM
ejpam-1476	71	5	0	0	NUM
ejpam-1476	71	6	r	r	NOUN
ejpam-1476	71	7	=	=	NOUN
ejpam-1476	71	8	−1	−1	NOUN
ejpam-1476	71	9	is	be	AUX
ejpam-1476	71	10	the	the	DET
ejpam-1476	71	11	root	root	NOUN
ejpam-1476	71	12	of	of	ADP
ejpam-1476	71	13	the	the	DET
ejpam-1476	71	14	above	above	ADJ
ejpam-1476	71	15	equation	equation	NOUN
ejpam-1476	71	16	and	and	CCONJ
ejpam-1476	71	17	we	we	PRON
ejpam-1476	71	18	obtain	obtain	VERB
ejpam-1476	71	19	�	�	PROPN
ejpam-1476	71	20	�	�	PROPN
ejpam-1476	71	21	2γ−	2γ−	PROPN
ejpam-1476	71	22	p+	p+	NOUN
ejpam-1476	71	23	q	q	PROPN
ejpam-1476	71	24	�	�	PROPN
ejpam-1476	71	25	�	�	PROPN
ejpam-1476	71	26	r2	r2	PROPN
ejpam-1476	71	27	−	−	PROPN
ejpam-1476	72	1	(	(	PUNCT
ejpam-1476	72	2	�	�	PROPN
ejpam-1476	72	3	�	�	PROPN
ejpam-1476	72	4	2γ−	2γ−	PROPN
ejpam-1476	72	5	p+	p+	NOUN
ejpam-1476	72	6	q	q	PROPN
ejpam-1476	72	7	�	�	PROPN
ejpam-1476	72	8	�	�	PROPN
ejpam-1476	72	9	+	+	PROPN
ejpam-1476	72	10	p−	p−	NOUN
ejpam-1476	72	11	q+	q+	NOUN
ejpam-1476	72	12	2)r	2)r	NOUN
ejpam-1476	73	1	+	+	CCONJ
ejpam-1476	73	2	p−	p−	NOUN
ejpam-1476	73	3	q	q	NOUN
ejpam-1476	73	4	=	=	NOUN
ejpam-1476	73	5	0	0	NUM
ejpam-1476	73	6	.	.	PUNCT
ejpam-1476	73	7	(	(	PUNCT
ejpam-1476	73	8	20	20	NUM
ejpam-1476	73	9	)	)	PUNCT
ejpam-1476	73	10	and	and	CCONJ
ejpam-1476	73	11	the	the	DET
ejpam-1476	73	12	positive	positive	ADJ
ejpam-1476	73	13	root	root	NOUN
ejpam-1476	73	14	of	of	ADP
ejpam-1476	73	15	the	the	DET
ejpam-1476	73	16	equation	equation	NOUN
ejpam-1476	73	17	(	(	PUNCT
ejpam-1476	73	18	20	20	NUM
ejpam-1476	73	19	)	)	PUNCT
ejpam-1476	73	20	is	be	AUX
ejpam-1476	73	21	r1	r1	NOUN
ejpam-1476	73	22	=	=	PUNCT
ejpam-1476	73	23	r1(p	r1(p	PROPN
ejpam-1476	73	24	,	,	PUNCT
ejpam-1476	73	25	q	q	NOUN
ejpam-1476	73	26	,	,	PUNCT
ejpam-1476	73	27	δ	δ	PROPN
ejpam-1476	73	28	)	)	PUNCT
ejpam-1476	73	29	.	.	PUNCT
ejpam-1476	74	1	corollary	corollary	ADJ
ejpam-1476	74	2	2	2	NUM
ejpam-1476	74	3	(	(	PUNCT
ejpam-1476	74	4	[	[	PUNCT
ejpam-1476	74	5	see	see	VERB
ejpam-1476	74	6	2	2	NUM
ejpam-1476	74	7	]	]	PUNCT
ejpam-1476	74	8	)	)	PUNCT
ejpam-1476	74	9	.	.	PUNCT
ejpam-1476	75	1	let	let	VERB
ejpam-1476	75	2	the	the	DET
ejpam-1476	75	3	function	function	NOUN
ejpam-1476	75	4	f	f	PROPN
ejpam-1476	75	5	(	(	PUNCT
ejpam-1476	75	6	z	z	NOUN
ejpam-1476	75	7	)	)	PUNCT
ejpam-1476	75	8	be	be	AUX
ejpam-1476	75	9	in	in	ADP
ejpam-1476	75	10	the	the	DET
ejpam-1476	75	11	class	class	NOUN
ejpam-1476	75	12	a1	a1	NOUN
ejpam-1476	75	13	and	and	CCONJ
ejpam-1476	75	14	suppose	suppose	VERB
ejpam-1476	75	15	that	that	SCONJ
ejpam-1476	75	16	g	g	PROPN
ejpam-1476	75	17	∈	∈	PROPN
ejpam-1476	75	18	s0	s0	PROPN
ejpam-1476	75	19	1,0(γ	1,0(γ	PROPN
ejpam-1476	75	20	,	,	PUNCT
ejpam-1476	75	21	1,−1	1,−1	NUM
ejpam-1476	75	22	)	)	PUNCT
ejpam-1476	75	23	.	.	PUNCT
ejpam-1476	76	1	if	if	SCONJ
ejpam-1476	76	2	f	f	PROPN
ejpam-1476	76	3	(	(	PUNCT
ejpam-1476	76	4	z	z	NOUN
ejpam-1476	76	5	)	)	PUNCT
ejpam-1476	76	6	is	be	AUX
ejpam-1476	76	7	majorized	majorize	VERB
ejpam-1476	76	8	by	by	ADP
ejpam-1476	76	9	g(z	g(z	PROPN
ejpam-1476	76	10	)	)	PUNCT
ejpam-1476	76	11	in	in	ADP
ejpam-1476	76	12	u	u	NOUN
ejpam-1476	76	13	,	,	PUNCT
ejpam-1476	76	14	then	then	ADV
ejpam-1476	76	15	�	�	PROPN
ejpam-1476	76	16	�	�	PROPN
ejpam-1476	76	17	�	�	PROPN
ejpam-1476	76	18	f	f	PROPN
ejpam-1476	77	1	′	′	NUM
ejpam-1476	77	2	(	(	PUNCT
ejpam-1476	77	3	z	z	NOUN
ejpam-1476	77	4	)	)	PUNCT
ejpam-1476	77	5	�	�	PROPN
ejpam-1476	77	6	�	�	PROPN
ejpam-1476	77	7	�	�	PROPN
ejpam-1476	77	8	¶	¶	PROPN
ejpam-1476	77	9	�	�	PROPN
ejpam-1476	77	10	�	�	PROPN
ejpam-1476	77	11	�	�	PROPN
ejpam-1476	77	12	g	g	NOUN
ejpam-1476	77	13	′	′	NUM
ejpam-1476	77	14	(	(	PUNCT
ejpam-1476	77	15	z	z	NOUN
ejpam-1476	77	16	)	)	PUNCT
ejpam-1476	77	17	�	�	PROPN
ejpam-1476	77	18	�	�	PROPN
ejpam-1476	77	19	�	�	PROPN
ejpam-1476	77	20	(	(	PUNCT
ejpam-1476	77	21	|z|	|z|	NOUN
ejpam-1476	77	22	¶	¶	NUM
ejpam-1476	77	23	r2	r2	PROPN
ejpam-1476	77	24	)	)	PUNCT
ejpam-1476	77	25	where	where	SCONJ
ejpam-1476	77	26	r2	r2	PROPN
ejpam-1476	77	27	=	=	SYM
ejpam-1476	77	28	r2(γ	r2(γ	NOUN
ejpam-1476	77	29	)	)	PUNCT
ejpam-1476	77	30	=	=	SYM
ejpam-1476	77	31	3	3	NUM
ejpam-1476	77	32	+	+	NUM
ejpam-1476	77	33	�	�	PROPN
ejpam-1476	77	34	�	�	PROPN
ejpam-1476	77	35	2γ−	2γ−	NUM
ejpam-1476	77	36	1	1	NUM
ejpam-1476	77	37	�	�	PROPN
ejpam-1476	77	38	�	�	PROPN
ejpam-1476	77	39	−	−	PROPN
ejpam-1476	77	40	æ	æ	PROPN
ejpam-1476	77	41	9	9	NUM
ejpam-1476	77	42	+	+	SYM
ejpam-1476	77	43	2	2	NUM
ejpam-1476	77	44	�	�	PROPN
ejpam-1476	77	45	�	�	PROPN
ejpam-1476	77	46	2γ−	2γ−	NUM
ejpam-1476	77	47	1	1	NUM
ejpam-1476	77	48	�	�	PROPN
ejpam-1476	77	49	�	�	PROPN
ejpam-1476	77	50	+	+	PROPN
ejpam-1476	77	51	�	�	PROPN
ejpam-1476	77	52	�	�	PROPN
ejpam-1476	77	53	2γ−	2γ−	NUM
ejpam-1476	77	54	1	1	NUM
ejpam-1476	77	55	�	�	PROPN
ejpam-1476	77	56	�	�	PROPN
ejpam-1476	77	57	2	2	NUM
ejpam-1476	77	58	2	2	NUM
ejpam-1476	77	59	�	�	PROPN
ejpam-1476	77	60	�	�	PROPN
ejpam-1476	77	61	2γ−	2γ−	NUM
ejpam-1476	77	62	1	1	NUM
ejpam-1476	77	63	�	�	PROPN
ejpam-1476	77	64	�	�	PROPN
ejpam-1476	77	65	corollary	corollary	NOUN
ejpam-1476	77	66	3	3	NUM
ejpam-1476	77	67	(	(	PUNCT
ejpam-1476	77	68	[	[	PUNCT
ejpam-1476	77	69	see	see	VERB
ejpam-1476	77	70	5	5	NUM
ejpam-1476	77	71	]	]	PUNCT
ejpam-1476	77	72	)	)	PUNCT
ejpam-1476	77	73	.	.	PUNCT
ejpam-1476	78	1	let	let	VERB
ejpam-1476	78	2	f	f	PROPN
ejpam-1476	78	3	(	(	PUNCT
ejpam-1476	78	4	z	z	NOUN
ejpam-1476	78	5	)	)	PUNCT
ejpam-1476	78	6	be	be	AUX
ejpam-1476	78	7	in	in	ADP
ejpam-1476	78	8	the	the	DET
ejpam-1476	78	9	class	class	NOUN
ejpam-1476	78	10	a1	a1	NOUN
ejpam-1476	78	11	and	and	CCONJ
ejpam-1476	78	12	suppose	suppose	VERB
ejpam-1476	78	13	that	that	SCONJ
ejpam-1476	78	14	g(z	g(z	ADJ
ejpam-1476	78	15	)	)	PUNCT
ejpam-1476	78	16	∈	∈	PROPN
ejpam-1476	78	17	s0	s0	PROPN
ejpam-1476	78	18	1,0(1,1,−1	1,0(1,1,−1	NUM
ejpam-1476	78	19	)	)	PUNCT
ejpam-1476	78	20	.	.	PUNCT
ejpam-1476	79	1	if	if	SCONJ
ejpam-1476	79	2	f	f	PROPN
ejpam-1476	79	3	(	(	PUNCT
ejpam-1476	79	4	z	z	NOUN
ejpam-1476	79	5	)	)	PUNCT
ejpam-1476	79	6	is	be	AUX
ejpam-1476	79	7	majorized	majorize	VERB
ejpam-1476	79	8	by	by	ADP
ejpam-1476	79	9	g(z	g(z	PROPN
ejpam-1476	79	10	)	)	PUNCT
ejpam-1476	79	11	in	in	ADP
ejpam-1476	79	12	u	u	NOUN
ejpam-1476	79	13	,	,	PUNCT
ejpam-1476	79	14	then	then	ADV
ejpam-1476	79	15	�	�	PROPN
ejpam-1476	79	16	�	�	PROPN
ejpam-1476	79	17	�	�	PROPN
ejpam-1476	79	18	f	f	PROPN
ejpam-1476	80	1	′	′	NUM
ejpam-1476	80	2	(	(	PUNCT
ejpam-1476	80	3	z	z	NOUN
ejpam-1476	80	4	)	)	PUNCT
ejpam-1476	80	5	�	�	PROPN
ejpam-1476	80	6	�	�	PROPN
ejpam-1476	80	7	�	�	PROPN
ejpam-1476	80	8	¶	¶	PROPN
ejpam-1476	80	9	�	�	PROPN
ejpam-1476	80	10	�	�	PROPN
ejpam-1476	80	11	g′(z	g′(z	NOUN
ejpam-1476	80	12	)	)	PUNCT
ejpam-1476	80	13	�	�	PROPN
ejpam-1476	80	14	�	�	PROPN
ejpam-1476	80	15	(	(	PUNCT
ejpam-1476	80	16	|z|	|z|	NOUN
ejpam-1476	80	17	¶	¶	NUM
ejpam-1476	80	18	r3	r3	PROPN
ejpam-1476	80	19	)	)	PUNCT
ejpam-1476	80	20	where	where	SCONJ
ejpam-1476	80	21	r3	r3	PROPN
ejpam-1476	80	22	=	=	SYM
ejpam-1476	80	23	2−p3	2−p3	NUM
ejpam-1476	80	24	.	.	PUNCT
ejpam-1476	81	1	3	3	X
ejpam-1476	81	2	.	.	X
ejpam-1476	81	3	majorization	majorization	NOUN
ejpam-1476	81	4	problems	problem	NOUN
ejpam-1476	81	5	for	for	ADP
ejpam-1476	81	6	the	the	DET
ejpam-1476	81	7	class	class	NOUN
ejpam-1476	81	8	cδ	cδ	NOUN
ejpam-1476	81	9	p	p	NOUN
ejpam-1476	81	10	,	,	PUNCT
ejpam-1476	81	11	q(γ	q(γ	PROPN
ejpam-1476	81	12	,	,	PUNCT
ejpam-1476	81	13	a	a	DET
ejpam-1476	81	14	,	,	PUNCT
ejpam-1476	81	15	b	b	NOUN
ejpam-1476	81	16	)	)	PUNCT
ejpam-1476	81	17	.	.	PUNCT
ejpam-1476	82	1	the	the	DET
ejpam-1476	82	2	proof	proof	NOUN
ejpam-1476	82	3	theorem	theorem	VERB
ejpam-1476	82	4	2	2	NUM
ejpam-1476	82	5	is	be	AUX
ejpam-1476	82	6	based	base	VERB
ejpam-1476	82	7	upon	upon	SCONJ
ejpam-1476	82	8	the	the	DET
ejpam-1476	82	9	following	following	ADJ
ejpam-1476	82	10	lemmas	lemmas	NOUN
ejpam-1476	82	11	.	.	PUNCT
ejpam-1476	83	1	lemma	lemma	PROPN
ejpam-1476	83	2	1	1	NUM
ejpam-1476	83	3	(	(	PUNCT
ejpam-1476	83	4	[	[	PUNCT
ejpam-1476	83	5	see	see	VERB
ejpam-1476	83	6	10	10	NUM
ejpam-1476	83	7	,	,	PUNCT
ejpam-1476	83	8	theorem	theorem	VERB
ejpam-1476	83	9	1	1	NUM
ejpam-1476	83	10	]	]	PUNCT
ejpam-1476	83	11	)	)	PUNCT
ejpam-1476	83	12	.	.	PUNCT
ejpam-1476	84	1	if	if	SCONJ
ejpam-1476	84	2	f	f	PROPN
ejpam-1476	84	3	∈	∈	PROPN
ejpam-1476	84	4	cδp	cδp	PROPN
ejpam-1476	84	5	,	,	PUNCT
ejpam-1476	84	6	q(γ	q(γ	PROPN
ejpam-1476	84	7	,	,	PUNCT
ejpam-1476	84	8	a	a	DET
ejpam-1476	84	9	,	,	PUNCT
ejpam-1476	84	10	b	b	NOUN
ejpam-1476	84	11	)	)	PUNCT
ejpam-1476	84	12	(	(	PUNCT
ejpam-1476	84	13	γ	γ	X
ejpam-1476	84	14	∈	∈	PROPN
ejpam-1476	84	15	c	c	X
ejpam-1476	84	16	\	\	X
ejpam-1476	84	17	{	{	PUNCT
ejpam-1476	84	18	0	0	NUM
ejpam-1476	84	19	}	}	PUNCT
ejpam-1476	84	20	)	)	PUNCT
ejpam-1476	84	21	then	then	ADV
ejpam-1476	84	22	re	re	VERB
ejpam-1476	84	23	�	�	PROPN
ejpam-1476	84	24	1	1	NUM
ejpam-1476	84	25	+	+	NUM
ejpam-1476	84	26	1	1	NUM
ejpam-1476	84	27	γ	γ	X
ejpam-1476	84	28	�	�	PROPN
ejpam-1476	84	29	z	z	PROPN
ejpam-1476	84	30	f	f	PROPN
ejpam-1476	84	31	(	(	PUNCT
ejpam-1476	84	32	q+δ+2)(z	q+δ+2)(z	PROPN
ejpam-1476	84	33	)	)	PUNCT
ejpam-1476	84	34	f	f	PROPN
ejpam-1476	84	35	(	(	PUNCT
ejpam-1476	84	36	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	84	37	)	)	PUNCT
ejpam-1476	84	38	−	−	PROPN
ejpam-1476	84	39	p+	p+	NOUN
ejpam-1476	84	40	q+	q+	ADV
ejpam-1476	84	41	δ+	δ+	PUNCT
ejpam-1476	84	42	1	1	NUM
ejpam-1476	84	43	�	�	PROPN
ejpam-1476	84	44	�	�	PROPN
ejpam-1476	84	45	>	>	X
ejpam-1476	84	46	1−	1−	NUM
ejpam-1476	85	1	a	a	DET
ejpam-1476	85	2	1−	1−	NUM
ejpam-1476	85	3	b	b	PROPN
ejpam-1476	85	4	(	(	PUNCT
ejpam-1476	85	5	21	21	NUM
ejpam-1476	85	6	)	)	PUNCT
ejpam-1476	85	7	o.	o.	NOUN
ejpam-1476	85	8	altıntaş	altıntaş	PROPN
ejpam-1476	85	9	/	/	SYM
ejpam-1476	85	10	eur	eur	PROPN
ejpam-1476	85	11	.	.	PUNCT
ejpam-1476	86	1	j.	j.	PROPN
ejpam-1476	86	2	pure	pure	PROPN
ejpam-1476	86	3	appl	appl	PROPN
ejpam-1476	86	4	.	.	PROPN
ejpam-1476	86	5	math	math	PROPN
ejpam-1476	86	6	,	,	PUNCT
ejpam-1476	86	7	5	5	NUM
ejpam-1476	86	8	(	(	PUNCT
ejpam-1476	86	9	2012	2012	NUM
ejpam-1476	86	10	)	)	PUNCT
ejpam-1476	86	11	,	,	PUNCT
ejpam-1476	86	12	16	16	NUM
ejpam-1476	86	13	-	-	SYM
ejpam-1476	86	14	24	24	NUM
ejpam-1476	86	15	21	21	NUM
ejpam-1476	86	16	proof	proof	NOUN
ejpam-1476	86	17	.	.	PUNCT
ejpam-1476	87	1	if	if	SCONJ
ejpam-1476	87	2	f	f	PROPN
ejpam-1476	87	3	∈	∈	PROPN
ejpam-1476	87	4	cδp	cδp	PROPN
ejpam-1476	87	5	,	,	PUNCT
ejpam-1476	87	6	q(γ	q(γ	PROPN
ejpam-1476	87	7	,	,	PUNCT
ejpam-1476	87	8	a	a	DET
ejpam-1476	87	9	,	,	PUNCT
ejpam-1476	87	10	b	b	NOUN
ejpam-1476	87	11	)	)	PUNCT
ejpam-1476	87	12	then	then	ADV
ejpam-1476	87	13	we	we	PRON
ejpam-1476	87	14	have	have	VERB
ejpam-1476	87	15	from	from	ADP
ejpam-1476	87	16	(	(	PUNCT
ejpam-1476	87	17	6	6	NUM
ejpam-1476	87	18	)	)	PUNCT
ejpam-1476	87	19	1	1	NUM
ejpam-1476	88	1	+	+	SYM
ejpam-1476	88	2	1	1	NUM
ejpam-1476	88	3	γ	γ	X
ejpam-1476	88	4	(	(	PUNCT
ejpam-1476	88	5	z	z	PROPN
ejpam-1476	88	6	f	f	PROPN
ejpam-1476	88	7	(	(	PUNCT
ejpam-1476	88	8	q+δ+2)(z	q+δ+2)(z	PROPN
ejpam-1476	88	9	)	)	PUNCT
ejpam-1476	88	10	f	f	PROPN
ejpam-1476	88	11	(	(	PUNCT
ejpam-1476	88	12	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	88	13	)	)	PUNCT
ejpam-1476	88	14	−	−	PROPN
ejpam-1476	88	15	p+	p+	VERB
ejpam-1476	88	16	q+δ+	q+δ+	X
ejpam-1476	88	17	1	1	NUM
ejpam-1476	88	18	)	)	PUNCT
ejpam-1476	88	19	=	=	SYM
ejpam-1476	88	20	1	1	NUM
ejpam-1476	88	21	+	+	CCONJ
ejpam-1476	88	22	aw(z	aw(z	VERB
ejpam-1476	88	23	)	)	PUNCT
ejpam-1476	88	24	1	1	NUM
ejpam-1476	89	1	+	+	NUM
ejpam-1476	89	2	bw(z	bw(z	NOUN
ejpam-1476	89	3	)	)	PUNCT
ejpam-1476	89	4	(	(	PUNCT
ejpam-1476	89	5	22	22	NUM
ejpam-1476	89	6	)	)	PUNCT
ejpam-1476	89	7	where	where	SCONJ
ejpam-1476	89	8	w(0	w(0	NOUN
ejpam-1476	89	9	)	)	PUNCT
ejpam-1476	89	10	=	=	SYM
ejpam-1476	89	11	0	0	NUM
ejpam-1476	89	12	and	and	CCONJ
ejpam-1476	89	13	|w(z)|	|w(z)|	PROPN
ejpam-1476	89	14	¶	¶	NOUN
ejpam-1476	89	15	|z|	|z|	NOUN
ejpam-1476	89	16	,	,	PUNCT
ejpam-1476	89	17	(	(	PUNCT
ejpam-1476	89	18	−1¶	−1¶	PROPN
ejpam-1476	89	19	b	b	X
ejpam-1476	89	20	<	<	X
ejpam-1476	89	21	a¶	a¶	X
ejpam-1476	89	22	1	1	NUM
ejpam-1476	89	23	)	)	PUNCT
ejpam-1476	89	24	.	.	PUNCT
ejpam-1476	90	1	we	we	PRON
ejpam-1476	90	2	let	let	VERB
ejpam-1476	90	3	h(z	h(z	NOUN
ejpam-1476	90	4	)	)	PUNCT
ejpam-1476	90	5	=	=	PUNCT
ejpam-1476	90	6	1+aw(z	1+aw(z	NUM
ejpam-1476	90	7	)	)	PUNCT
ejpam-1476	90	8	1	1	NUM
ejpam-1476	90	9	+	+	NUM
ejpam-1476	90	10	bw(z	bw(z	NOUN
ejpam-1476	90	11	)	)	PUNCT
ejpam-1476	90	12	(	(	PUNCT
ejpam-1476	90	13	23	23	NUM
ejpam-1476	90	14	)	)	PUNCT
ejpam-1476	90	15	and	and	CCONJ
ejpam-1476	90	16	h(z	h(z	NOUN
ejpam-1476	90	17	)	)	PUNCT
ejpam-1476	90	18	=	=	PUNCT
ejpam-1476	90	19	u+	u+	NUM
ejpam-1476	90	20	iv	iv	NUM
ejpam-1476	90	21	,	,	PUNCT
ejpam-1476	90	22	|w(z)|2	|w(z)|2	PRON
ejpam-1476	90	23	=	=	SYM
ejpam-1476	90	24	�	�	PROPN
ejpam-1476	90	25	�	�	PROPN
ejpam-1476	90	26	�	�	PROPN
ejpam-1476	90	27	�	�	PROPN
ejpam-1476	90	28	h(z)−	h(z)−	PROPN
ejpam-1476	90	29	1	1	NUM
ejpam-1476	90	30	a−	a−	PROPN
ejpam-1476	90	31	bh(z	bh(z	PROPN
ejpam-1476	90	32	)	)	PUNCT
ejpam-1476	90	33	�	�	PROPN
ejpam-1476	90	34	�	�	PROPN
ejpam-1476	90	35	�	�	PROPN
ejpam-1476	90	36	�	�	PROPN
ejpam-1476	90	37	2	2	NUM
ejpam-1476	90	38	¶	¶	NUM
ejpam-1476	90	39	1	1	NUM
ejpam-1476	90	40	and	and	CCONJ
ejpam-1476	90	41	(	(	PUNCT
ejpam-1476	90	42	1−	1−	NUM
ejpam-1476	90	43	b2)u2	b2)u2	NOUN
ejpam-1476	90	44	−	−	NOUN
ejpam-1476	90	45	2(1−	2(1−	NUM
ejpam-1476	90	46	ab)u+	ab)u+	NOUN
ejpam-1476	90	47	1−	1−	NUM
ejpam-1476	90	48	a2	a2	PROPN
ejpam-1476	90	49	¶	¶	PROPN
ejpam-1476	90	50	0	0	NUM
ejpam-1476	91	1	(	(	PUNCT
ejpam-1476	91	2	24	24	NUM
ejpam-1476	91	3	)	)	PUNCT
ejpam-1476	91	4	from	from	ADP
ejpam-1476	91	5	(	(	PUNCT
ejpam-1476	91	6	24	24	NUM
ejpam-1476	91	7	)	)	PUNCT
ejpam-1476	91	8	implies	imply	VERB
ejpam-1476	91	9	that	that	SCONJ
ejpam-1476	91	10	1−	1−	NUM
ejpam-1476	91	11	a	a	DET
ejpam-1476	91	12	1−	1−	NUM
ejpam-1476	91	13	b	b	PROPN
ejpam-1476	91	14	¶	¶	PROPN
ejpam-1476	91	15	reh(z	reh(z	PROPN
ejpam-1476	91	16	)	)	PUNCT
ejpam-1476	91	17	=	=	SYM
ejpam-1476	91	18	u	u	NOUN
ejpam-1476	91	19	¶	¶	NOUN
ejpam-1476	91	20	1	1	NUM
ejpam-1476	91	21	+	+	CCONJ
ejpam-1476	91	22	a	a	DET
ejpam-1476	91	23	1	1	NUM
ejpam-1476	91	24	+	+	NUM
ejpam-1476	91	25	b	b	NOUN
ejpam-1476	91	26	.	.	PUNCT
ejpam-1476	92	1	(	(	PUNCT
ejpam-1476	92	2	25	25	NUM
ejpam-1476	92	3	)	)	PUNCT
ejpam-1476	92	4	the	the	DET
ejpam-1476	92	5	following	follow	VERB
ejpam-1476	92	6	lemma	lemma	PROPN
ejpam-1476	92	7	is	be	AUX
ejpam-1476	92	8	proved	prove	VERB
ejpam-1476	92	9	in	in	ADP
ejpam-1476	92	10	[	[	X
ejpam-1476	92	11	3	3	X
ejpam-1476	92	12	]	]	PUNCT
ejpam-1476	92	13	for	for	ADP
ejpam-1476	92	14	δ	δ	PROPN
ejpam-1476	92	15	=	=	SYM
ejpam-1476	92	16	0	0	PROPN
ejpam-1476	92	17	.	.	PUNCT
ejpam-1476	93	1	lemma	lemma	PROPN
ejpam-1476	93	2	2	2	X
ejpam-1476	93	3	.	.	PUNCT
ejpam-1476	94	1	if	if	SCONJ
ejpam-1476	94	2	f	f	PROPN
ejpam-1476	94	3	∈	∈	PROPN
ejpam-1476	94	4	cδp	cδp	PROPN
ejpam-1476	94	5	,	,	PUNCT
ejpam-1476	94	6	q(γ	q(γ	PROPN
ejpam-1476	94	7	,	,	PUNCT
ejpam-1476	94	8	a	a	DET
ejpam-1476	94	9	,	,	PUNCT
ejpam-1476	94	10	b	b	NOUN
ejpam-1476	94	11	)	)	PUNCT
ejpam-1476	94	12	(	(	PUNCT
ejpam-1476	94	13	γ	γ	X
ejpam-1476	94	14	∈	∈	PROPN
ejpam-1476	94	15	c	c	X
ejpam-1476	94	16	\	\	X
ejpam-1476	94	17	{	{	PUNCT
ejpam-1476	94	18	0	0	NUM
ejpam-1476	94	19	}	}	PUNCT
ejpam-1476	94	20	)	)	PUNCT
ejpam-1476	94	21	then	then	ADV
ejpam-1476	94	22	f	f	PROPN
ejpam-1476	94	23	∈	∈	PROPN
ejpam-1476	94	24	sδp	sδp	NOUN
ejpam-1476	94	25	,	,	PUNCT
ejpam-1476	94	26	q	q	X
ejpam-1476	94	27	(	(	PUNCT
ejpam-1476	94	28	1	1	NUM
ejpam-1476	94	29	2	2	NUM
ejpam-1476	94	30	γ	γ	X
ejpam-1476	94	31	,	,	PUNCT
ejpam-1476	94	32	a	a	DET
ejpam-1476	94	33	,	,	PUNCT
ejpam-1476	94	34	b	b	NOUN
ejpam-1476	94	35	)	)	PUNCT
ejpam-1476	94	36	that	that	PRON
ejpam-1476	94	37	is	be	AUX
ejpam-1476	94	38	cδp	cδp	ADJ
ejpam-1476	94	39	,	,	PUNCT
ejpam-1476	94	40	q(γ	q(γ	PROPN
ejpam-1476	94	41	,	,	PUNCT
ejpam-1476	94	42	a	a	DET
ejpam-1476	94	43	,	,	PUNCT
ejpam-1476	94	44	b	b	NOUN
ejpam-1476	94	45	)	)	PUNCT
ejpam-1476	94	46	⊂	⊂	PROPN
ejpam-1476	94	47	sδp	sδp	PROPN
ejpam-1476	94	48	,	,	PUNCT
ejpam-1476	94	49	q	q	X
ejpam-1476	94	50	(	(	PUNCT
ejpam-1476	94	51	γ	γ	X
ejpam-1476	94	52	2	2	NUM
ejpam-1476	94	53	,	,	PUNCT
ejpam-1476	94	54	a	a	DET
ejpam-1476	94	55	,	,	PUNCT
ejpam-1476	94	56	b	b	NOUN
ejpam-1476	94	57	)	)	PUNCT
ejpam-1476	94	58	(	(	PUNCT
ejpam-1476	94	59	26	26	NUM
ejpam-1476	94	60	)	)	PUNCT
ejpam-1476	94	61	proof	proof	NOUN
ejpam-1476	94	62	.	.	PUNCT
ejpam-1476	95	1	we	we	PRON
ejpam-1476	95	2	know	know	VERB
ejpam-1476	95	3	that	that	SCONJ
ejpam-1476	95	4	all	all	DET
ejpam-1476	95	5	convex	convex	NOUN
ejpam-1476	95	6	function	function	NOUN
ejpam-1476	95	7	in	in	ADP
ejpam-1476	95	8	u	u	NOUN
ejpam-1476	95	9	is	be	AUX
ejpam-1476	95	10	starlike	starlike	NOUN
ejpam-1476	95	11	of	of	ADP
ejpam-1476	95	12	order	order	NOUN
ejpam-1476	95	13	1	1	NUM
ejpam-1476	95	14	2	2	NUM
ejpam-1476	95	15	in	in	ADP
ejpam-1476	95	16	u	u	PROPN
ejpam-1476	95	17	,	,	PUNCT
ejpam-1476	95	18	[	[	X
ejpam-1476	95	19	see	see	VERB
ejpam-1476	95	20	4	4	NUM
ejpam-1476	95	21	,	,	PUNCT
ejpam-1476	95	22	p.	p.	NOUN
ejpam-1476	95	23	7	7	NUM
ejpam-1476	95	24	]	]	PUNCT
ejpam-1476	95	25	or	or	CCONJ
ejpam-1476	95	26	,	,	PUNCT
ejpam-1476	95	27	equivalently	equivalently	ADV
ejpam-1476	95	28	re[1	re[1	VERB
ejpam-1476	95	29	+	+	CCONJ
ejpam-1476	95	30	z	z	NOUN
ejpam-1476	95	31	f	f	PROPN
ejpam-1476	95	32	′′(z	′′(z	PROPN
ejpam-1476	95	33	)	)	PUNCT
ejpam-1476	95	34	f	f	PROPN
ejpam-1476	95	35	′(z	′(z	NOUN
ejpam-1476	95	36	)	)	PUNCT
ejpam-1476	95	37	]	]	PUNCT
ejpam-1476	95	38	>	>	X
ejpam-1476	95	39	0⇒	0⇒	PROPN
ejpam-1476	95	40	re	re	PROPN
ejpam-1476	95	41	[	[	PUNCT
ejpam-1476	95	42	z	z	NOUN
ejpam-1476	95	43	f	f	PROPN
ejpam-1476	95	44	′(z	′(z	NOUN
ejpam-1476	95	45	)	)	PUNCT
ejpam-1476	95	46	f	f	PROPN
ejpam-1476	95	47	(	(	PUNCT
ejpam-1476	95	48	z	z	NOUN
ejpam-1476	95	49	)	)	PUNCT
ejpam-1476	95	50	]	]	PUNCT
ejpam-1476	95	51	>	>	X
ejpam-1476	95	52	1	1	NUM
ejpam-1476	95	53	2	2	NUM
ejpam-1476	95	54	.	.	PUNCT
ejpam-1476	96	1	(	(	PUNCT
ejpam-1476	96	2	27	27	NUM
ejpam-1476	96	3	)	)	PUNCT
ejpam-1476	96	4	if	if	SCONJ
ejpam-1476	96	5	we	we	PRON
ejpam-1476	96	6	let	let	VERB
ejpam-1476	96	7	re[1	re[1	NOUN
ejpam-1476	96	8	+	+	CCONJ
ejpam-1476	96	9	z	z	NOUN
ejpam-1476	96	10	f	f	NOUN
ejpam-1476	96	11	′′(z	′′(z	PROPN
ejpam-1476	96	12	)	)	PUNCT
ejpam-1476	96	13	f	f	PROPN
ejpam-1476	96	14	′(z	′(z	NOUN
ejpam-1476	96	15	)	)	PUNCT
ejpam-1476	97	1	]	]	PUNCT
ejpam-1476	97	2	>	>	X
ejpam-1476	97	3	α	α	PROPN
ejpam-1476	97	4	for	for	ADP
ejpam-1476	97	5	f	f	PROPN
ejpam-1476	97	6	(	(	PUNCT
ejpam-1476	97	7	z)−→	z)−→	PROPN
ejpam-1476	97	8	f	f	PROPN
ejpam-1476	97	9	(	(	PUNCT
ejpam-1476	97	10	q+δ)(z	q+δ)(z	X
ejpam-1476	97	11	)	)	PUNCT
ejpam-1476	97	12	,	,	PUNCT
ejpam-1476	97	13	and	and	CCONJ
ejpam-1476	97	14	using	use	VERB
ejpam-1476	97	15	lemma	lemma	PROPN
ejpam-1476	97	16	1	1	NUM
ejpam-1476	97	17	,	,	PUNCT
ejpam-1476	97	18	we	we	PRON
ejpam-1476	97	19	have	have	VERB
ejpam-1476	97	20	re[1	re[1	ADJ
ejpam-1476	97	21	+	+	CCONJ
ejpam-1476	97	22	z	z	NOUN
ejpam-1476	97	23	f	f	X
ejpam-1476	97	24	(	(	PUNCT
ejpam-1476	97	25	q+δ+2)(z	q+δ+2)(z	PROPN
ejpam-1476	97	26	)	)	PUNCT
ejpam-1476	98	1	f	f	PROPN
ejpam-1476	99	1	(	(	PUNCT
ejpam-1476	99	2	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	99	3	)	)	PUNCT
ejpam-1476	99	4	−	−	PROPN
ejpam-1476	99	5	p+	p+	NOUN
ejpam-1476	99	6	q+	q+	ADV
ejpam-1476	99	7	δ+	δ+	X
ejpam-1476	99	8	1	1	NUM
ejpam-1476	99	9	)	)	PUNCT
ejpam-1476	99	10	]	]	PUNCT
ejpam-1476	99	11	>	>	X
ejpam-1476	99	12	1−	1−	NUM
ejpam-1476	99	13	a	a	DET
ejpam-1476	99	14	1−	1−	NUM
ejpam-1476	99	15	b	b	PROPN
ejpam-1476	99	16	(	(	PUNCT
ejpam-1476	99	17	28	28	NUM
ejpam-1476	99	18	)	)	PUNCT
ejpam-1476	99	19	or	or	CCONJ
ejpam-1476	99	20	re[1	re[1	X
ejpam-1476	99	21	+	+	CCONJ
ejpam-1476	99	22	1	1	NUM
ejpam-1476	99	23	1−α	1−α	NUM
ejpam-1476	99	24	(	(	PUNCT
ejpam-1476	99	25	z	z	NOUN
ejpam-1476	99	26	f	f	X
ejpam-1476	99	27	(	(	PUNCT
ejpam-1476	99	28	q+δ+2)(z	q+δ+2)(z	PROPN
ejpam-1476	99	29	)	)	PUNCT
ejpam-1476	99	30	f	f	PROPN
ejpam-1476	99	31	(	(	PUNCT
ejpam-1476	99	32	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	99	33	)	)	PUNCT
ejpam-1476	99	34	−	−	PROPN
ejpam-1476	99	35	p+	p+	NOUN
ejpam-1476	99	36	q+	q+	ADV
ejpam-1476	99	37	δ+	δ+	VERB
ejpam-1476	99	38	1	1	NUM
ejpam-1476	99	39	]	]	PUNCT
ejpam-1476	99	40	>	>	X
ejpam-1476	99	41	0	0	X
ejpam-1476	99	42	.	.	PUNCT
ejpam-1476	100	1	(	(	PUNCT
ejpam-1476	100	2	29	29	NUM
ejpam-1476	100	3	)	)	PUNCT
ejpam-1476	100	4	this	this	PRON
ejpam-1476	100	5	implies	imply	VERB
ejpam-1476	100	6	that	that	SCONJ
ejpam-1476	100	7	1	1	NUM
ejpam-1476	100	8	+	+	NUM
ejpam-1476	100	9	1	1	NUM
ejpam-1476	100	10	1−α	1−α	NUM
ejpam-1476	100	11	(	(	PUNCT
ejpam-1476	100	12	z	z	NOUN
ejpam-1476	100	13	f	f	X
ejpam-1476	100	14	(	(	PUNCT
ejpam-1476	100	15	q+δ+2)(z	q+δ+2)(z	PROPN
ejpam-1476	100	16	)	)	PUNCT
ejpam-1476	100	17	f	f	PROPN
ejpam-1476	100	18	(	(	PUNCT
ejpam-1476	100	19	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	100	20	)	)	PUNCT
ejpam-1476	100	21	−	−	PROPN
ejpam-1476	100	22	p+	p+	NOUN
ejpam-1476	100	23	q+	q+	ADV
ejpam-1476	100	24	δ+	δ+	PUNCT
ejpam-1476	100	25	1=	1=	NOUN
ejpam-1476	100	26	1−w(z	1−w(z	NUM
ejpam-1476	100	27	)	)	PUNCT
ejpam-1476	100	28	1+w(z	1+w(z	NUM
ejpam-1476	100	29	)	)	PUNCT
ejpam-1476	100	30	.	.	PUNCT
ejpam-1476	101	1	(	(	PUNCT
ejpam-1476	101	2	30	30	NUM
ejpam-1476	101	3	)	)	PUNCT
ejpam-1476	101	4	o.	o.	NOUN
ejpam-1476	101	5	altıntaş	altıntaş	PROPN
ejpam-1476	101	6	/	/	SYM
ejpam-1476	101	7	eur	eur	PROPN
ejpam-1476	101	8	.	.	PUNCT
ejpam-1476	102	1	j.	j.	PROPN
ejpam-1476	102	2	pure	pure	PROPN
ejpam-1476	102	3	appl	appl	PROPN
ejpam-1476	102	4	.	.	PROPN
ejpam-1476	102	5	math	math	PROPN
ejpam-1476	102	6	,	,	PUNCT
ejpam-1476	102	7	5	5	NUM
ejpam-1476	102	8	(	(	PUNCT
ejpam-1476	102	9	2012	2012	NUM
ejpam-1476	102	10	)	)	PUNCT
ejpam-1476	102	11	,	,	PUNCT
ejpam-1476	102	12	16	16	NUM
ejpam-1476	102	13	-	-	SYM
ejpam-1476	102	14	24	24	NUM
ejpam-1476	102	15	22	22	NUM
ejpam-1476	103	1	so	so	ADV
ejpam-1476	103	2	,	,	PUNCT
ejpam-1476	103	3	we	we	PRON
ejpam-1476	103	4	have	have	VERB
ejpam-1476	103	5	1	1	NUM
ejpam-1476	103	6	+	+	SYM
ejpam-1476	103	7	1	1	NUM
ejpam-1476	103	8	γ	γ	X
ejpam-1476	103	9	(	(	PUNCT
ejpam-1476	103	10	z	z	PROPN
ejpam-1476	103	11	f	f	PROPN
ejpam-1476	103	12	(	(	PUNCT
ejpam-1476	103	13	q+δ+2)(z	q+δ+2)(z	PROPN
ejpam-1476	103	14	)	)	PUNCT
ejpam-1476	103	15	f	f	PROPN
ejpam-1476	103	16	(	(	PUNCT
ejpam-1476	103	17	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	103	18	)	)	PUNCT
ejpam-1476	103	19	−	−	PROPN
ejpam-1476	104	1	(	(	PUNCT
ejpam-1476	104	2	p+	p+	NOUN
ejpam-1476	104	3	q+	q+	ADV
ejpam-1476	104	4	δ+	δ+	VERB
ejpam-1476	104	5	1	1	NUM
ejpam-1476	104	6	)	)	PUNCT
ejpam-1476	104	7	=	=	PRON
ejpam-1476	104	8	γ+	γ+	PRON
ejpam-1476	104	9	(	(	PUNCT
ejpam-1476	104	10	γ−	γ−	PROPN
ejpam-1476	104	11	2	2	NUM
ejpam-1476	104	12	+	+	NUM
ejpam-1476	104	13	2α)w(z	2α)w(z	NUM
ejpam-1476	104	14	)	)	PUNCT
ejpam-1476	104	15	γ(1+w(z	γ(1+w(z	NOUN
ejpam-1476	104	16	)	)	PUNCT
ejpam-1476	104	17	)	)	PUNCT
ejpam-1476	104	18	.	.	PUNCT
ejpam-1476	105	1	(	(	PUNCT
ejpam-1476	105	2	31	31	NUM
ejpam-1476	105	3	)	)	PUNCT
ejpam-1476	105	4	on	on	ADP
ejpam-1476	105	5	the	the	DET
ejpam-1476	105	6	other	other	ADJ
ejpam-1476	105	7	hand	hand	NOUN
ejpam-1476	105	8	we	we	PRON
ejpam-1476	105	9	know	know	VERB
ejpam-1476	105	10	that	that	SCONJ
ejpam-1476	105	11	z	z	NOUN
ejpam-1476	105	12	f	f	PROPN
ejpam-1476	105	13	p(z	p(z	PROPN
ejpam-1476	106	1	)	)	PUNCT
ejpam-1476	106	2	f	f	NOUN
ejpam-1476	106	3	(	(	PUNCT
ejpam-1476	106	4	z	z	NOUN
ejpam-1476	106	5	)	)	PUNCT
ejpam-1476	106	6	>	>	X
ejpam-1476	107	1	α⇒	α⇒	PUNCT
ejpam-1476	107	2	re(1	re(1	X
ejpam-1476	107	3	+	+	PROPN
ejpam-1476	107	4	1	1	NUM
ejpam-1476	107	5	1−α	1−α	NUM
ejpam-1476	107	6	z	z	NOUN
ejpam-1476	107	7	f	f	NOUN
ejpam-1476	107	8	p(z	p(z	PROPN
ejpam-1476	107	9	)	)	PUNCT
ejpam-1476	107	10	f	f	NOUN
ejpam-1476	107	11	(	(	PUNCT
ejpam-1476	107	12	z	z	NOUN
ejpam-1476	107	13	)	)	PUNCT
ejpam-1476	107	14	)	)	PUNCT
ejpam-1476	107	15	>	>	X
ejpam-1476	108	1	0	0	X
ejpam-1476	108	2	.	.	PUNCT
ejpam-1476	108	3	(	(	PUNCT
ejpam-1476	108	4	32	32	NUM
ejpam-1476	108	5	)	)	PUNCT
ejpam-1476	108	6	similarly	similarly	ADV
ejpam-1476	108	7	using	use	VERB
ejpam-1476	108	8	(	(	PUNCT
ejpam-1476	108	9	27	27	NUM
ejpam-1476	108	10	)	)	PUNCT
ejpam-1476	108	11	and	and	CCONJ
ejpam-1476	108	12	(	(	PUNCT
ejpam-1476	108	13	29	29	NUM
ejpam-1476	108	14	)	)	PUNCT
ejpam-1476	108	15	we	we	PRON
ejpam-1476	108	16	obtain	obtain	VERB
ejpam-1476	108	17	the	the	DET
ejpam-1476	108	18	following	follow	VERB
ejpam-1476	108	19	relations	relation	NOUN
ejpam-1476	108	20	.	.	PUNCT
ejpam-1476	109	1	[	[	X
ejpam-1476	109	2	1	1	NUM
ejpam-1476	109	3	+	+	NUM
ejpam-1476	109	4	1	1	NUM
ejpam-1476	109	5	1−α	1−α	NUM
ejpam-1476	109	6	(	(	PUNCT
ejpam-1476	109	7	z	z	NOUN
ejpam-1476	109	8	f	f	X
ejpam-1476	109	9	(	(	PUNCT
ejpam-1476	109	10	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	109	11	)	)	PUNCT
ejpam-1476	109	12	f	f	PROPN
ejpam-1476	109	13	(	(	PUNCT
ejpam-1476	109	14	q+δ)(z	q+δ)(z	NOUN
ejpam-1476	109	15	)	)	PUNCT
ejpam-1476	109	16	−	−	PROPN
ejpam-1476	109	17	p+	p+	PROPN
ejpam-1476	109	18	q+	q+	X
ejpam-1476	109	19	δ	δ	PROPN
ejpam-1476	109	20	)	)	PUNCT
ejpam-1476	109	21	]	]	PUNCT
ejpam-1476	109	22	>	>	X
ejpam-1476	109	23	1	1	NUM
ejpam-1476	109	24	2	2	NUM
ejpam-1476	109	25	,	,	PUNCT
ejpam-1476	109	26	(	(	PUNCT
ejpam-1476	109	27	33	33	NUM
ejpam-1476	109	28	)	)	PUNCT
ejpam-1476	109	29	1	1	NUM
ejpam-1476	109	30	+	+	NUM
ejpam-1476	109	31	1	1	NUM
ejpam-1476	109	32	1−α	1−α	NUM
ejpam-1476	109	33	(	(	PUNCT
ejpam-1476	109	34	z	z	NOUN
ejpam-1476	109	35	f	f	X
ejpam-1476	109	36	(	(	PUNCT
ejpam-1476	109	37	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	109	38	)	)	PUNCT
ejpam-1476	109	39	f	f	PROPN
ejpam-1476	109	40	(	(	PUNCT
ejpam-1476	109	41	q+δ)(z	q+δ)(z	NOUN
ejpam-1476	109	42	)	)	PUNCT
ejpam-1476	109	43	−	−	PROPN
ejpam-1476	109	44	p+	p+	PROPN
ejpam-1476	109	45	q+	q+	X
ejpam-1476	109	46	δ	δ	PROPN
ejpam-1476	109	47	)	)	PUNCT
ejpam-1476	109	48	=	=	SYM
ejpam-1476	109	49	1	1	NUM
ejpam-1476	109	50	1+w(z	1+w(z	NUM
ejpam-1476	109	51	)	)	PUNCT
ejpam-1476	109	52	,	,	PUNCT
ejpam-1476	109	53	(	(	PUNCT
ejpam-1476	109	54	34	34	NUM
ejpam-1476	109	55	)	)	PUNCT
ejpam-1476	109	56	1	1	NUM
ejpam-1476	109	57	+	+	SYM
ejpam-1476	109	58	2	2	NUM
ejpam-1476	109	59	γ	γ	X
ejpam-1476	109	60	(	(	PUNCT
ejpam-1476	109	61	z	z	NOUN
ejpam-1476	109	62	f	f	X
ejpam-1476	109	63	(	(	PUNCT
ejpam-1476	109	64	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	109	65	)	)	PUNCT
ejpam-1476	109	66	f	f	PROPN
ejpam-1476	109	67	(	(	PUNCT
ejpam-1476	109	68	q+δ)(z	q+δ)(z	NOUN
ejpam-1476	109	69	)	)	PUNCT
ejpam-1476	109	70	−	−	PROPN
ejpam-1476	109	71	p+	p+	PROPN
ejpam-1476	109	72	q+	q+	NOUN
ejpam-1476	109	73	δ	δ	PROPN
ejpam-1476	109	74	)	)	PUNCT
ejpam-1476	109	75	=	=	PRON
ejpam-1476	109	76	γ+	γ+	PRON
ejpam-1476	109	77	(	(	PUNCT
ejpam-1476	109	78	γ−	γ−	NUM
ejpam-1476	109	79	2	2	NUM
ejpam-1476	109	80	+	+	NUM
ejpam-1476	109	81	2α	2α	NOUN
ejpam-1476	109	82	)	)	PUNCT
ejpam-1476	109	83	γ(1+w(z	γ(1+w(z	NOUN
ejpam-1476	109	84	)	)	PUNCT
ejpam-1476	109	85	)	)	PUNCT
ejpam-1476	109	86	.	.	PUNCT
ejpam-1476	110	1	(	(	PUNCT
ejpam-1476	110	2	35	35	NUM
ejpam-1476	110	3	)	)	PUNCT
ejpam-1476	110	4	(	(	PUNCT
ejpam-1476	110	5	36	36	NUM
ejpam-1476	110	6	)	)	PUNCT
ejpam-1476	110	7	the	the	DET
ejpam-1476	110	8	inclusion	inclusion	NOUN
ejpam-1476	110	9	property	property	NOUN
ejpam-1476	110	10	(	(	PUNCT
ejpam-1476	110	11	26	26	NUM
ejpam-1476	110	12	)	)	PUNCT
ejpam-1476	110	13	is	be	AUX
ejpam-1476	110	14	easily	easily	ADV
ejpam-1476	110	15	seen	see	VERB
ejpam-1476	110	16	that	that	SCONJ
ejpam-1476	110	17	from	from	ADP
ejpam-1476	110	18	(	(	PUNCT
ejpam-1476	110	19	31	31	NUM
ejpam-1476	110	20	)	)	PUNCT
ejpam-1476	110	21	and	and	CCONJ
ejpam-1476	110	22	(	(	PUNCT
ejpam-1476	110	23	35	35	NUM
ejpam-1476	110	24	)	)	PUNCT
ejpam-1476	110	25	.	.	PUNCT
ejpam-1476	111	1	upon	upon	SCONJ
ejpam-1476	111	2	replacing	replace	VERB
ejpam-1476	111	3	γ	γ	NOUN
ejpam-1476	111	4	in	in	ADP
ejpam-1476	111	5	theorem	theorem	NOUN
ejpam-1476	111	6	1	1	NUM
ejpam-1476	111	7	by	by	ADP
ejpam-1476	111	8	1	1	NUM
ejpam-1476	111	9	2	2	NUM
ejpam-1476	111	10	γ	γ	NOUN
ejpam-1476	111	11	,	,	PUNCT
ejpam-1476	111	12	if	if	SCONJ
ejpam-1476	111	13	we	we	PRON
ejpam-1476	111	14	apply	apply	VERB
ejpam-1476	111	15	lemma	lemma	PROPN
ejpam-1476	111	16	2	2	NUM
ejpam-1476	111	17	we	we	PRON
ejpam-1476	111	18	have	have	VERB
ejpam-1476	111	19	,	,	PUNCT
ejpam-1476	111	20	theorem	theorem	VERB
ejpam-1476	111	21	2	2	NUM
ejpam-1476	111	22	.	.	PUNCT
ejpam-1476	112	1	let	let	VERB
ejpam-1476	112	2	the	the	DET
ejpam-1476	112	3	function	function	NOUN
ejpam-1476	112	4	f	f	PROPN
ejpam-1476	112	5	(	(	PUNCT
ejpam-1476	112	6	z	z	NOUN
ejpam-1476	112	7	)	)	PUNCT
ejpam-1476	112	8	be	be	AUX
ejpam-1476	112	9	in	in	ADP
ejpam-1476	112	10	the	the	DET
ejpam-1476	112	11	class	class	NOUN
ejpam-1476	112	12	ap	ap	PROPN
ejpam-1476	112	13	and	and	CCONJ
ejpam-1476	112	14	suppose	suppose	VERB
ejpam-1476	112	15	that	that	SCONJ
ejpam-1476	112	16	g(z	g(z	PROPN
ejpam-1476	112	17	)	)	PUNCT
ejpam-1476	112	18	∈	∈	PROPN
ejpam-1476	112	19	cδp	cδp	PROPN
ejpam-1476	112	20	,	,	PUNCT
ejpam-1476	112	21	q(γ	q(γ	PROPN
ejpam-1476	112	22	,	,	PUNCT
ejpam-1476	112	23	a	a	DET
ejpam-1476	112	24	,	,	PUNCT
ejpam-1476	112	25	b	b	NOUN
ejpam-1476	112	26	)	)	PUNCT
ejpam-1476	112	27	.	.	PUNCT
ejpam-1476	113	1	if	if	SCONJ
ejpam-1476	113	2	f	f	PROPN
ejpam-1476	113	3	(	(	PUNCT
ejpam-1476	113	4	q+δ)(z	q+δ)(z	X
ejpam-1476	113	5	)	)	PUNCT
ejpam-1476	113	6	is	be	AUX
ejpam-1476	113	7	majorized	majorize	VERB
ejpam-1476	113	8	by	by	ADP
ejpam-1476	113	9	g(q+δ)(z	g(q+δ)(z	PROPN
ejpam-1476	113	10	)	)	PUNCT
ejpam-1476	113	11	∈	∈	PROPN
ejpam-1476	113	12	u	u	NOUN
ejpam-1476	113	13	,	,	PUNCT
ejpam-1476	113	14	for	for	ADP
ejpam-1476	113	15	p	p	PROPN
ejpam-1476	113	16	∈	∈	PROPN
ejpam-1476	113	17	n	n	PRON
ejpam-1476	113	18	q	q	NOUN
ejpam-1476	113	19	∈	∈	PROPN
ejpam-1476	113	20	n0	n0	NOUN
ejpam-1476	113	21	and	and	CCONJ
ejpam-1476	113	22	0¶	0¶	NOUN
ejpam-1476	113	23	δ	δ	NOUN
ejpam-1476	113	24	<	<	X
ejpam-1476	113	25	1	1	NUM
ejpam-1476	113	26	then	then	ADV
ejpam-1476	113	27	�	�	PROPN
ejpam-1476	113	28	�	�	PROPN
ejpam-1476	113	29	�	�	PROPN
ejpam-1476	113	30	f	f	PROPN
ejpam-1476	113	31	(	(	PUNCT
ejpam-1476	113	32	q+δ+1)(z	q+δ+1)(z	PROPN
ejpam-1476	113	33	)	)	PUNCT
ejpam-1476	113	34	�	�	PROPN
ejpam-1476	113	35	�	�	PROPN
ejpam-1476	113	36	�	�	PROPN
ejpam-1476	113	37	¶	¶	PROPN
ejpam-1476	113	38	�	�	PROPN
ejpam-1476	113	39	�	�	PROPN
ejpam-1476	113	40	�	�	PROPN
ejpam-1476	113	41	g(q+δ+1)(z	g(q+δ+1)(z	PROPN
ejpam-1476	113	42	)	)	PUNCT
ejpam-1476	113	43	�	�	PROPN
ejpam-1476	113	44	�	�	PROPN
ejpam-1476	113	45	�	�	PROPN
ejpam-1476	113	46	(	(	PUNCT
ejpam-1476	113	47	|z|	|z|	VERB
ejpam-1476	113	48	≤	≤	NUM
ejpam-1476	113	49	r2	r2	NOUN
ejpam-1476	113	50	)	)	PUNCT
ejpam-1476	113	51	(	(	PUNCT
ejpam-1476	113	52	37	37	NUM
ejpam-1476	113	53	)	)	PUNCT
ejpam-1476	113	54	where	where	SCONJ
ejpam-1476	113	55	r2	r2	PROPN
ejpam-1476	113	56	=	=	SYM
ejpam-1476	113	57	r2(p	r2(p	PROPN
ejpam-1476	113	58	,	,	PUNCT
ejpam-1476	113	59	q	q	NOUN
ejpam-1476	113	60	,	,	PUNCT
ejpam-1476	113	61	δ	δ	PROPN
ejpam-1476	113	62	,	,	PUNCT
ejpam-1476	113	63	γ	γ	PROPN
ejpam-1476	113	64	,	,	PUNCT
ejpam-1476	113	65	a	a	DET
ejpam-1476	113	66	,	,	PUNCT
ejpam-1476	113	67	b	b	NOUN
ejpam-1476	113	68	)	)	PUNCT
ejpam-1476	113	69	is	be	AUX
ejpam-1476	113	70	the	the	DET
ejpam-1476	113	71	smallest	small	ADJ
ejpam-1476	113	72	positive	positive	ADJ
ejpam-1476	113	73	root	root	NOUN
ejpam-1476	113	74	of	of	ADP
ejpam-1476	113	75	the	the	DET
ejpam-1476	113	76	equation	equation	NOUN
ejpam-1476	113	77	�	�	PROPN
ejpam-1476	113	78	�	�	PROPN
ejpam-1476	113	79	�	�	PROPN
ejpam-1476	113	80	�	�	PROPN
ejpam-1476	113	81	1	1	NUM
ejpam-1476	113	82	2	2	NUM
ejpam-1476	113	83	γ(a−	γ(a−	PROPN
ejpam-1476	113	84	b	b	NOUN
ejpam-1476	113	85	)	)	PUNCT
ejpam-1476	114	1	+	+	CCONJ
ejpam-1476	114	2	(	(	PUNCT
ejpam-1476	114	3	p−	p−	NOUN
ejpam-1476	114	4	q−	q−	PROPN
ejpam-1476	114	5	δ)b	δ)b	ADJ
ejpam-1476	114	6	�	�	PROPN
ejpam-1476	114	7	�	�	PROPN
ejpam-1476	114	8	�	�	PROPN
ejpam-1476	114	9	�	�	PROPN
ejpam-1476	114	10	r3	r3	PROPN
ejpam-1476	114	11	−	−	PROPN
ejpam-1476	115	1	(	(	PUNCT
ejpam-1476	115	2	p−	p−	PROPN
ejpam-1476	115	3	q−	q−	PROPN
ejpam-1476	115	4	δ+	δ+	PUNCT
ejpam-1476	115	5	2	2	NUM
ejpam-1476	115	6	|b|)r2−	|b|)r2−	NOUN
ejpam-1476	115	7	[	[	PUNCT
ejpam-1476	115	8	1	1	NUM
ejpam-1476	115	9	2	2	NUM
ejpam-1476	115	10	γ(a−	γ(a−	PROPN
ejpam-1476	115	11	b	b	NOUN
ejpam-1476	115	12	)	)	PUNCT
ejpam-1476	115	13	+	+	CCONJ
ejpam-1476	115	14	(	(	PUNCT
ejpam-1476	115	15	p−	p−	PROPN
ejpam-1476	115	16	q−	q−	PROPN
ejpam-1476	115	17	δ	δ	PROPN
ejpam-1476	115	18	)	)	PUNCT
ejpam-1476	115	19	|b|	|b|	PROPN
ejpam-1476	116	1	+	+	PUNCT
ejpam-1476	117	1	2]r	2]r	NUM
ejpam-1476	117	2	+	+	ADP
ejpam-1476	117	3	p−	p−	PROPN
ejpam-1476	117	4	q−	q−	PROPN
ejpam-1476	117	5	δ	δ	NOUN
ejpam-1476	117	6	=	=	PUNCT
ejpam-1476	117	7	0	0	NUM
ejpam-1476	118	1	where	where	SCONJ
ejpam-1476	118	2	p	p	PROPN
ejpam-1476	118	3	∈	∈	PROPN
ejpam-1476	118	4	n	n	CCONJ
ejpam-1476	118	5	,	,	PUNCT
ejpam-1476	118	6	q	q	PROPN
ejpam-1476	118	7	∈	∈	PROPN
ejpam-1476	118	8	n0	n0	PROPN
ejpam-1476	118	9	,	,	PUNCT
ejpam-1476	118	10	γ	γ	PROPN
ejpam-1476	118	11	∈	∈	PROPN
ejpam-1476	118	12	c	c	X
ejpam-1476	118	13	\	\	X
ejpam-1476	118	14	{	{	PUNCT
ejpam-1476	118	15	0	0	NUM
ejpam-1476	118	16	}	}	PUNCT
ejpam-1476	118	17	,	,	PUNCT
ejpam-1476	118	18	0¶	0¶	NOUN
ejpam-1476	118	19	δ	δ	X
ejpam-1476	118	20	<	<	X
ejpam-1476	118	21	1	1	NUM
ejpam-1476	118	22	,	,	PUNCT
ejpam-1476	118	23	and	and	CCONJ
ejpam-1476	118	24	�	�	PROPN
ejpam-1476	118	25	�	�	PROPN
ejpam-1476	118	26	�	�	PROPN
ejpam-1476	118	27	�	�	PROPN
ejpam-1476	118	28	1	1	NUM
ejpam-1476	118	29	2	2	NUM
ejpam-1476	118	30	γ(a−	γ(a−	PROPN
ejpam-1476	118	31	b	b	NOUN
ejpam-1476	118	32	)	)	PUNCT
ejpam-1476	118	33	+	+	CCONJ
ejpam-1476	118	34	(	(	PUNCT
ejpam-1476	118	35	p−	p−	NOUN
ejpam-1476	118	36	q−	q−	PROPN
ejpam-1476	118	37	δ)b	δ)b	ADJ
ejpam-1476	118	38	�	�	PROPN
ejpam-1476	118	39	�	�	PROPN
ejpam-1476	118	40	�	�	PROPN
ejpam-1476	118	41	�	�	PROPN
ejpam-1476	118	42	¶	¶	PROPN
ejpam-1476	118	43	�	�	PROPN
ejpam-1476	118	44	�	�	PROPN
ejpam-1476	118	45	p−	p−	PROPN
ejpam-1476	118	46	q−	q−	PROPN
ejpam-1476	118	47	δ	δ	PROPN
ejpam-1476	118	48	�	�	PROPN
ejpam-1476	118	49	�	�	PROPN
ejpam-1476	118	50	.	.	PUNCT
ejpam-1476	118	51	corollary	corollary	ADJ
ejpam-1476	118	52	4	4	NUM
ejpam-1476	118	53	(	(	PUNCT
ejpam-1476	118	54	[	[	PUNCT
ejpam-1476	118	55	see	see	VERB
ejpam-1476	118	56	3	3	NUM
ejpam-1476	118	57	]	]	PUNCT
ejpam-1476	118	58	)	)	PUNCT
ejpam-1476	118	59	.	.	PUNCT
ejpam-1476	119	1	let	let	VERB
ejpam-1476	119	2	the	the	DET
ejpam-1476	119	3	function	function	NOUN
ejpam-1476	119	4	f	f	PROPN
ejpam-1476	119	5	(	(	PUNCT
ejpam-1476	119	6	z	z	NOUN
ejpam-1476	119	7	)	)	PUNCT
ejpam-1476	119	8	be	be	AUX
ejpam-1476	119	9	in	in	ADP
ejpam-1476	119	10	the	the	DET
ejpam-1476	119	11	class	class	NOUN
ejpam-1476	119	12	ap	ap	PROPN
ejpam-1476	119	13	and	and	CCONJ
ejpam-1476	119	14	suppose	suppose	VERB
ejpam-1476	119	15	that	that	SCONJ
ejpam-1476	119	16	g(z	g(z	ADJ
ejpam-1476	119	17	)	)	PUNCT
ejpam-1476	119	18	∈	∈	PROPN
ejpam-1476	119	19	c0	c0	NOUN
ejpam-1476	119	20	p	p	PROPN
ejpam-1476	119	21	,	,	PUNCT
ejpam-1476	119	22	q(γ	q(γ	PROPN
ejpam-1476	119	23	,	,	PUNCT
ejpam-1476	119	24	1,−1	1,−1	NUM
ejpam-1476	119	25	)	)	PUNCT
ejpam-1476	119	26	.	.	PUNCT
ejpam-1476	120	1	if	if	SCONJ
ejpam-1476	120	2	f	f	PROPN
ejpam-1476	120	3	(	(	PUNCT
ejpam-1476	120	4	q)(z	q)(z	NOUN
ejpam-1476	120	5	)	)	PUNCT
ejpam-1476	120	6	is	be	AUX
ejpam-1476	120	7	majorized	majorize	VERB
ejpam-1476	120	8	by	by	ADP
ejpam-1476	120	9	g(q)(z	g(q)(z	NOUN
ejpam-1476	120	10	)	)	PUNCT
ejpam-1476	120	11	in	in	ADP
ejpam-1476	120	12	u	u	NOUN
ejpam-1476	120	13	,	,	PUNCT
ejpam-1476	120	14	then	then	ADV
ejpam-1476	120	15	�	�	PROPN
ejpam-1476	120	16	�	�	PROPN
ejpam-1476	120	17	�	�	PROPN
ejpam-1476	120	18	f	f	PROPN
ejpam-1476	120	19	(	(	PUNCT
ejpam-1476	120	20	q+1)(z	q+1)(z	PROPN
ejpam-1476	120	21	)	)	PUNCT
ejpam-1476	120	22	�	�	PROPN
ejpam-1476	120	23	�	�	PROPN
ejpam-1476	120	24	�	�	PROPN
ejpam-1476	120	25	¶	¶	PROPN
ejpam-1476	120	26	�	�	PROPN
ejpam-1476	120	27	�	�	PROPN
ejpam-1476	120	28	�	�	PROPN
ejpam-1476	120	29	g(q+1)(z	g(q+1)(z	NOUN
ejpam-1476	120	30	)	)	PUNCT
ejpam-1476	120	31	�	�	PROPN
ejpam-1476	120	32	�	�	PROPN
ejpam-1476	120	33	�	�	PROPN
ejpam-1476	120	34	(	(	PUNCT
ejpam-1476	120	35	|z|	|z|	VERB
ejpam-1476	120	36	≤	≤	NUM
ejpam-1476	120	37	r1	r1	NOUN
ejpam-1476	120	38	)	)	PUNCT
ejpam-1476	120	39	references	reference	NOUN
ejpam-1476	120	40	23	23	NUM
ejpam-1476	120	41	where	where	SCONJ
ejpam-1476	120	42	r1	r1	NOUN
ejpam-1476	120	43	=	=	SYM
ejpam-1476	120	44	r1(p	r1(p	PROPN
ejpam-1476	120	45	,	,	PUNCT
ejpam-1476	120	46	q	q	NOUN
ejpam-1476	120	47	,	,	PUNCT
ejpam-1476	120	48	δ	δ	NOUN
ejpam-1476	120	49	)	)	PUNCT
ejpam-1476	120	50	=	=	SYM
ejpam-1476	121	1	µ−	µ−	PROPN
ejpam-1476	121	2	æ	æ	X
ejpam-1476	121	3	µ2	µ2	PROPN
ejpam-1476	121	4	−	−	PROPN
ejpam-1476	121	5	4(p−	4(p−	PROPN
ejpam-1476	121	6	q	q	NOUN
ejpam-1476	121	7	)	)	PUNCT
ejpam-1476	121	8	�	�	PROPN
ejpam-1476	121	9	�	�	PROPN
ejpam-1476	121	10	γ−	γ−	PROPN
ejpam-1476	121	11	p+	p+	PART
ejpam-1476	121	12	q	q	PROPN
ejpam-1476	121	13	�	�	PROPN
ejpam-1476	121	14	�	�	PROPN
ejpam-1476	121	15	2	2	NUM
ejpam-1476	121	16	�	�	PROPN
ejpam-1476	121	17	�	�	PROPN
ejpam-1476	121	18	γ−	γ−	PROPN
ejpam-1476	121	19	p+	p+	PART
ejpam-1476	121	20	q	q	PROPN
ejpam-1476	121	21	�	�	PROPN
ejpam-1476	121	22	�	�	PROPN
ejpam-1476	121	23	µ	µ	X
ejpam-1476	121	24	=	=	SYM
ejpam-1476	121	25	2	2	NUM
ejpam-1476	121	26	+	+	NUM
ejpam-1476	121	27	p−	p−	NOUN
ejpam-1476	121	28	q+	q+	PUNCT
ejpam-1476	121	29	�	�	PROPN
ejpam-1476	121	30	�	�	PROPN
ejpam-1476	121	31	γ−	γ−	PROPN
ejpam-1476	121	32	p+	p+	PART
ejpam-1476	121	33	q	q	PROPN
ejpam-1476	121	34	�	�	PROPN
ejpam-1476	121	35	�	�	PROPN
ejpam-1476	121	36	,	,	PUNCT
ejpam-1476	121	37	p	p	PROPN
ejpam-1476	121	38	∈	∈	PROPN
ejpam-1476	121	39	n	n	CCONJ
ejpam-1476	121	40	,	,	PUNCT
ejpam-1476	121	41	q	q	PROPN
ejpam-1476	121	42	∈	∈	PROPN
ejpam-1476	121	43	n0,γ	n0,γ	PROPN
ejpam-1476	121	44	∈	∈	PROPN
ejpam-1476	121	45	c	c	NOUN
ejpam-1476	121	46	\	\	X
ejpam-1476	121	47	{	{	PUNCT
ejpam-1476	121	48	0	0	NUM
ejpam-1476	121	49	}	}	PUNCT
ejpam-1476	121	50	proof	proof	NOUN
ejpam-1476	121	51	.	.	PUNCT
ejpam-1476	122	1	we	we	PRON
ejpam-1476	122	2	let	let	VERB
ejpam-1476	122	3	δ	δ	PROPN
ejpam-1476	122	4	=	=	SYM
ejpam-1476	122	5	0	0	PROPN
ejpam-1476	122	6	,	,	PUNCT
ejpam-1476	122	7	a=	a=	X
ejpam-1476	122	8	1	1	NUM
ejpam-1476	122	9	,	,	PUNCT
ejpam-1476	122	10	b	b	NOUN
ejpam-1476	122	11	=	=	SYM
ejpam-1476	122	12	−1	−1	NOUN
ejpam-1476	122	13	in	in	ADP
ejpam-1476	122	14	theorem	theorem	NOUN
ejpam-1476	122	15	2	2	NUM
ejpam-1476	122	16	.	.	PUNCT
ejpam-1476	122	17	corollary	corollary	ADJ
ejpam-1476	122	18	5	5	NUM
ejpam-1476	122	19	(	(	PUNCT
ejpam-1476	122	20	[	[	PUNCT
ejpam-1476	122	21	see	see	VERB
ejpam-1476	122	22	2	2	NUM
ejpam-1476	122	23	]	]	PUNCT
ejpam-1476	122	24	)	)	PUNCT
ejpam-1476	122	25	.	.	PUNCT
ejpam-1476	123	1	let	let	VERB
ejpam-1476	123	2	the	the	DET
ejpam-1476	123	3	function	function	NOUN
ejpam-1476	123	4	f	f	PROPN
ejpam-1476	123	5	(	(	PUNCT
ejpam-1476	123	6	z	z	NOUN
ejpam-1476	123	7	)	)	PUNCT
ejpam-1476	123	8	be	be	AUX
ejpam-1476	123	9	in	in	ADP
ejpam-1476	123	10	the	the	DET
ejpam-1476	123	11	class	class	NOUN
ejpam-1476	123	12	a1	a1	NOUN
ejpam-1476	123	13	and	and	CCONJ
ejpam-1476	123	14	suppose	suppose	VERB
ejpam-1476	123	15	that	that	SCONJ
ejpam-1476	123	16	g(z	g(z	ADJ
ejpam-1476	123	17	)	)	PUNCT
ejpam-1476	123	18	∈	∈	PROPN
ejpam-1476	123	19	c0	c0	NOUN
ejpam-1476	123	20	1.0(1,1,−1	1.0(1,1,−1	NUM
ejpam-1476	123	21	)	)	PUNCT
ejpam-1476	123	22	.	.	PUNCT
ejpam-1476	124	1	if	if	SCONJ
ejpam-1476	124	2	f	f	PROPN
ejpam-1476	124	3	(	(	PUNCT
ejpam-1476	124	4	z	z	NOUN
ejpam-1476	124	5	)	)	PUNCT
ejpam-1476	124	6	is	be	AUX
ejpam-1476	124	7	majorized	majorize	VERB
ejpam-1476	124	8	by	by	ADP
ejpam-1476	124	9	g(z	g(z	PROPN
ejpam-1476	124	10	)	)	PUNCT
ejpam-1476	124	11	in	in	ADP
ejpam-1476	124	12	u	u	NOUN
ejpam-1476	124	13	,	,	PUNCT
ejpam-1476	124	14	then	then	ADV
ejpam-1476	124	15	�	�	PROPN
ejpam-1476	124	16	�	�	PROPN
ejpam-1476	124	17	�	�	PROPN
ejpam-1476	124	18	f	f	PROPN
ejpam-1476	125	1	′	′	NUM
ejpam-1476	125	2	(	(	PUNCT
ejpam-1476	125	3	z	z	NOUN
ejpam-1476	125	4	)	)	PUNCT
ejpam-1476	125	5	�	�	PROPN
ejpam-1476	125	6	�	�	PROPN
ejpam-1476	125	7	�	�	PROPN
ejpam-1476	125	8	¶	¶	PROPN
ejpam-1476	125	9	�	�	PROPN
ejpam-1476	125	10	�	�	PROPN
ejpam-1476	125	11	�	�	PROPN
ejpam-1476	125	12	g	g	NOUN
ejpam-1476	125	13	′	′	NUM
ejpam-1476	125	14	(	(	PUNCT
ejpam-1476	125	15	z	z	NOUN
ejpam-1476	125	16	)	)	PUNCT
ejpam-1476	125	17	�	�	PROPN
ejpam-1476	125	18	�	�	PROPN
ejpam-1476	125	19	�	�	PROPN
ejpam-1476	125	20	(	(	PUNCT
ejpam-1476	125	21	|z|	|z|	NOUN
ejpam-1476	125	22	¶	¶	NUM
ejpam-1476	125	23	r2	r2	PROPN
ejpam-1476	125	24	)	)	PUNCT
ejpam-1476	125	25	where	where	SCONJ
ejpam-1476	125	26	r2	r2	PROPN
ejpam-1476	125	27	=	=	SYM
ejpam-1476	125	28	r2(γ	r2(γ	NOUN
ejpam-1476	125	29	)	)	PUNCT
ejpam-1476	125	30	=	=	SYM
ejpam-1476	125	31	3	3	NUM
ejpam-1476	125	32	+	+	NUM
ejpam-1476	125	33	�	�	PROPN
ejpam-1476	125	34	�	�	PROPN
ejpam-1476	125	35	γ−	γ−	PROPN
ejpam-1476	125	36	1	1	NUM
ejpam-1476	125	37	�	�	PROPN
ejpam-1476	125	38	�	�	PROPN
ejpam-1476	125	39	−	−	PROPN
ejpam-1476	125	40	æ	æ	SYM
ejpam-1476	125	41	9−	9−	NUM
ejpam-1476	125	42	2	2	NUM
ejpam-1476	125	43	�	�	PROPN
ejpam-1476	125	44	�	�	PROPN
ejpam-1476	125	45	γ−	γ−	PROPN
ejpam-1476	125	46	1	1	NUM
ejpam-1476	125	47	�	�	PROPN
ejpam-1476	125	48	�	�	PROPN
ejpam-1476	125	49	+	+	PROPN
ejpam-1476	125	50	�	�	PROPN
ejpam-1476	125	51	�	�	PROPN
ejpam-1476	125	52	γ−	γ−	PROPN
ejpam-1476	125	53	1	1	NUM
ejpam-1476	125	54	�	�	PROPN
ejpam-1476	125	55	�	�	PROPN
ejpam-1476	125	56	2	2	NUM
ejpam-1476	125	57	2	2	NUM
ejpam-1476	125	58	�	�	PROPN
ejpam-1476	125	59	�	�	PROPN
ejpam-1476	125	60	γ−	γ−	NOUN
ejpam-1476	125	61	1	1	NUM
ejpam-1476	125	62	�	�	PROPN
ejpam-1476	125	63	�	�	PROPN
ejpam-1476	125	64	proof	proof	NOUN
ejpam-1476	125	65	.	.	PUNCT
ejpam-1476	126	1	we	we	PRON
ejpam-1476	126	2	let	let	VERB
ejpam-1476	126	3	p	p	NOUN
ejpam-1476	126	4	=	=	NOUN
ejpam-1476	126	5	1	1	NUM
ejpam-1476	126	6	,	,	PUNCT
ejpam-1476	126	7	q	q	NOUN
ejpam-1476	126	8	=	=	SYM
ejpam-1476	126	9	0	0	NUM
ejpam-1476	126	10	,	,	PUNCT
ejpam-1476	126	11	δ	δ	X
ejpam-1476	126	12	=	=	SYM
ejpam-1476	126	13	0	0	NUM
ejpam-1476	126	14	,	,	PUNCT
ejpam-1476	126	15	a=	a=	X
ejpam-1476	126	16	1	1	NUM
ejpam-1476	126	17	,	,	PUNCT
ejpam-1476	126	18	b	b	NOUN
ejpam-1476	126	19	=	=	SYM
ejpam-1476	126	20	−1	−1	NOUN
ejpam-1476	126	21	in	in	ADP
ejpam-1476	126	22	theorem	theorem	NOUN
ejpam-1476	126	23	2	2	NUM
ejpam-1476	126	24	.	.	PUNCT
ejpam-1476	126	25	corollary	corollary	ADJ
ejpam-1476	126	26	6	6	NUM
ejpam-1476	126	27	(	(	PUNCT
ejpam-1476	126	28	[	[	PUNCT
ejpam-1476	126	29	see	see	VERB
ejpam-1476	126	30	5	5	NUM
ejpam-1476	126	31	]	]	PUNCT
ejpam-1476	126	32	)	)	PUNCT
ejpam-1476	126	33	.	.	PUNCT
ejpam-1476	127	1	let	let	VERB
ejpam-1476	127	2	the	the	DET
ejpam-1476	127	3	function	function	NOUN
ejpam-1476	127	4	f	f	PROPN
ejpam-1476	127	5	(	(	PUNCT
ejpam-1476	127	6	z	z	NOUN
ejpam-1476	127	7	)	)	PUNCT
ejpam-1476	127	8	be	be	AUX
ejpam-1476	127	9	in	in	ADP
ejpam-1476	127	10	the	the	DET
ejpam-1476	127	11	class	class	NOUN
ejpam-1476	127	12	a1	a1	NOUN
ejpam-1476	127	13	and	and	CCONJ
ejpam-1476	127	14	suppose	suppose	VERB
ejpam-1476	127	15	that	that	SCONJ
ejpam-1476	127	16	g(z	g(z	ADJ
ejpam-1476	127	17	)	)	PUNCT
ejpam-1476	127	18	∈	∈	PROPN
ejpam-1476	127	19	c0	c0	NOUN
ejpam-1476	127	20	1.0(1,1,−1	1.0(1,1,−1	NUM
ejpam-1476	127	21	)	)	PUNCT
ejpam-1476	127	22	.	.	PUNCT
ejpam-1476	128	1	if	if	SCONJ
ejpam-1476	128	2	f	f	PROPN
ejpam-1476	128	3	(	(	PUNCT
ejpam-1476	128	4	z	z	NOUN
ejpam-1476	128	5	)	)	PUNCT
ejpam-1476	128	6	is	be	AUX
ejpam-1476	128	7	majorized	majorize	VERB
ejpam-1476	128	8	by	by	ADP
ejpam-1476	128	9	g(z	g(z	PROPN
ejpam-1476	128	10	)	)	PUNCT
ejpam-1476	128	11	in	in	ADP
ejpam-1476	128	12	u	u	NOUN
ejpam-1476	128	13	,	,	PUNCT
ejpam-1476	128	14	then	then	ADV
ejpam-1476	128	15	�	�	PROPN
ejpam-1476	128	16	�	�	PROPN
ejpam-1476	128	17	�	�	PROPN
ejpam-1476	128	18	f	f	PROPN
ejpam-1476	129	1	′	′	NUM
ejpam-1476	129	2	(	(	PUNCT
ejpam-1476	129	3	z	z	NOUN
ejpam-1476	129	4	)	)	PUNCT
ejpam-1476	129	5	�	�	PROPN
ejpam-1476	129	6	�	�	PROPN
ejpam-1476	129	7	�	�	PROPN
ejpam-1476	129	8	¶	¶	PROPN
ejpam-1476	129	9	�	�	PROPN
ejpam-1476	129	10	�	�	PROPN
ejpam-1476	129	11	�	�	PROPN
ejpam-1476	129	12	g	g	NOUN
ejpam-1476	129	13	′	′	NUM
ejpam-1476	129	14	(	(	PUNCT
ejpam-1476	129	15	z	z	NOUN
ejpam-1476	129	16	)	)	PUNCT
ejpam-1476	129	17	�	�	PROPN
ejpam-1476	129	18	�	�	PROPN
ejpam-1476	129	19	�	�	PROPN
ejpam-1476	129	20	(	(	PUNCT
ejpam-1476	129	21	|z|	|z|	NOUN
ejpam-1476	129	22	¶	¶	PROPN
ejpam-1476	129	23	1	1	NUM
ejpam-1476	129	24	3	3	NUM
ejpam-1476	129	25	)	)	PUNCT
ejpam-1476	129	26	proof	proof	NOUN
ejpam-1476	129	27	.	.	PUNCT
ejpam-1476	130	1	we	we	PRON
ejpam-1476	130	2	let	let	VERB
ejpam-1476	130	3	limit	limit	VERB
ejpam-1476	130	4	for	for	ADP
ejpam-1476	130	5	γ−→	γ−→	PROPN
ejpam-1476	130	6	1	1	NUM
ejpam-1476	130	7	in	in	ADP
ejpam-1476	130	8	corollary	corollary	ADJ
ejpam-1476	130	9	5	5	NUM
ejpam-1476	130	10	or	or	CCONJ
ejpam-1476	130	11	γ−→	γ−→	PROPN
ejpam-1476	130	12	1	1	NUM
ejpam-1476	130	13	2	2	NUM
ejpam-1476	130	14	γ	γ	NOUN
ejpam-1476	130	15	in	in	ADP
ejpam-1476	130	16	corollary	corollary	ADJ
ejpam-1476	130	17	1	1	NUM
ejpam-1476	130	18	.	.	PUNCT
ejpam-1476	130	19	references	reference	NOUN
ejpam-1476	131	1	[	[	X
ejpam-1476	131	2	1	1	NUM
ejpam-1476	131	3	]	]	PUNCT
ejpam-1476	131	4	o	o	X
ejpam-1476	131	5	altintaş	altintaş	PROPN
ejpam-1476	131	6	and	and	CCONJ
ejpam-1476	131	7	s	s	VERB
ejpam-1476	131	8	owa	owa	PROPN
ejpam-1476	131	9	.	.	PROPN
ejpam-1476	131	10	majorization	majorization	NOUN
ejpam-1476	131	11	and	and	CCONJ
ejpam-1476	131	12	quasi	quasi	NOUN
ejpam-1476	131	13	-	-	NOUN
ejpam-1476	131	14	subordinations	subordination	NOUN
ejpam-1476	131	15	for	for	ADP
ejpam-1476	131	16	certain	certain	ADJ
ejpam-1476	131	17	analytic	analytic	ADJ
ejpam-1476	131	18	functions	function	NOUN
ejpam-1476	131	19	.	.	PUNCT
ejpam-1476	132	1	japan	japan	PROPN
ejpam-1476	132	2	acad	acad	PROPN
ejpam-1476	132	3	.	.	PUNCT
ejpam-1476	133	1	ser	ser	PROPN
ejpam-1476	133	2	.	.	PUNCT
ejpam-1476	134	1	a	a	DET
ejpam-1476	134	2	math	math	NOUN
ejpam-1476	134	3	.	.	PUNCT
ejpam-1476	135	1	sci	sci	PROPN
ejpam-1476	135	2	.	.	PROPN
ejpam-1476	135	3	,	,	PUNCT
ejpam-1476	135	4	68:181–185	68:181–185	NUM
ejpam-1476	135	5	,	,	PUNCT
ejpam-1476	135	6	1992	1992	NUM
ejpam-1476	135	7	.	.	PUNCT
ejpam-1476	136	1	[	[	X
ejpam-1476	136	2	2	2	X
ejpam-1476	136	3	]	]	PUNCT
ejpam-1476	136	4	o	o	X
ejpam-1476	136	5	altintaş	altintaş	PROPN
ejpam-1476	136	6	,	,	PUNCT
ejpam-1476	136	7	ö	ö	NOUN
ejpam-1476	136	8	özkan	özkan	X
ejpam-1476	136	9	,	,	PUNCT
ejpam-1476	136	10	and	and	CCONJ
ejpam-1476	136	11	h	h	PROPN
ejpam-1476	136	12	srivastava	srivastava	PROPN
ejpam-1476	136	13	.	.	PUNCT
ejpam-1476	137	1	majorization	majorization	NOUN
ejpam-1476	137	2	by	by	ADP
ejpam-1476	137	3	starlike	starlike	NOUN
ejpam-1476	137	4	functions	function	NOUN
ejpam-1476	137	5	of	of	ADP
ejpam-1476	137	6	complex	complex	ADJ
ejpam-1476	137	7	order	order	NOUN
ejpam-1476	137	8	.	.	PUNCT
ejpam-1476	138	1	complex	complex	ADJ
ejpam-1476	138	2	variables	variable	NOUN
ejpam-1476	138	3	theory	theory	NOUN
ejpam-1476	138	4	appl	appl	NOUN
ejpam-1476	138	5	,	,	PUNCT
ejpam-1476	138	6	46:207–218	46:207–218	NOUN
ejpam-1476	138	7	,	,	PUNCT
ejpam-1476	138	8	2001	2001	NUM
ejpam-1476	138	9	.	.	PUNCT
ejpam-1476	139	1	[	[	X
ejpam-1476	139	2	3	3	X
ejpam-1476	139	3	]	]	PUNCT
ejpam-1476	139	4	o.	o.	NOUN
ejpam-1476	139	5	altintaş	altintaş	PROPN
ejpam-1476	139	6	and	and	CCONJ
ejpam-1476	139	7	h	h	PROPN
ejpam-1476	139	8	srivastava	srivastava	PROPN
ejpam-1476	139	9	.	.	PUNCT
ejpam-1476	140	1	some	some	DET
ejpam-1476	140	2	majorization	majorization	NOUN
ejpam-1476	140	3	problems	problem	NOUN
ejpam-1476	140	4	associated	associate	VERB
ejpam-1476	140	5	with	with	ADP
ejpam-1476	140	6	pvalently	pvalently	ADV
ejpam-1476	140	7	starlike	starlike	NOUN
ejpam-1476	140	8	and	and	CCONJ
ejpam-1476	140	9	convex	convex	NOUN
ejpam-1476	140	10	functions	function	NOUN
ejpam-1476	140	11	of	of	ADP
ejpam-1476	140	12	complex	complex	ADJ
ejpam-1476	140	13	order	order	NOUN
ejpam-1476	140	14	.	.	PUNCT
ejpam-1476	141	1	east	east	ADJ
ejpam-1476	141	2	asian	asian	PROPN
ejpam-1476	141	3	math	math	PROPN
ejpam-1476	141	4	.	.	PUNCT
ejpam-1476	142	1	journal	journal	PROPN
ejpam-1476	142	2	,	,	PUNCT
ejpam-1476	142	3	17(2):175	17(2):175	PROPN
ejpam-1476	142	4	–	–	PUNCT
ejpam-1476	142	5	183	183	NUM
ejpam-1476	142	6	,	,	PUNCT
ejpam-1476	142	7	2001	2001	NUM
ejpam-1476	142	8	.	.	PUNCT
ejpam-1476	143	1	[	[	X
ejpam-1476	143	2	4	4	NUM
ejpam-1476	143	3	]	]	PUNCT
ejpam-1476	143	4	t	t	PROPN
ejpam-1476	143	5	macgregor	macgregor	PROPN
ejpam-1476	143	6	.	.	PUNCT
ejpam-1476	144	1	the	the	DET
ejpam-1476	144	2	radius	radius	NOUN
ejpam-1476	144	3	of	of	ADP
ejpam-1476	144	4	converity	converity	NOUN
ejpam-1476	144	5	for	for	ADP
ejpam-1476	144	6	starlike	starlike	NOUN
ejpam-1476	144	7	functions	function	NOUN
ejpam-1476	144	8	of	of	ADP
ejpam-1476	144	9	order	order	NOUN
ejpam-1476	144	10	1	1	NUM
ejpam-1476	144	11	2	2	NUM
ejpam-1476	144	12	.	.	PUNCT
ejpam-1476	145	1	amer	amer	PROPN
ejpam-1476	145	2	.	.	PUNCT
ejpam-1476	145	3	math	math	PROPN
ejpam-1476	145	4	.	.	PUNCT
ejpam-1476	146	1	soc	soc	PROPN
ejpam-1476	146	2	,	,	PUNCT
ejpam-1476	146	3	14:71–76	14:71–76	NUM
ejpam-1476	146	4	,	,	PUNCT
ejpam-1476	146	5	1963	1963	NUM
ejpam-1476	146	6	.	.	PUNCT
ejpam-1476	147	1	[	[	X
ejpam-1476	147	2	5	5	NUM
ejpam-1476	147	3	]	]	PUNCT
ejpam-1476	147	4	t	t	PROPN
ejpam-1476	147	5	macgregor	macgregor	PROPN
ejpam-1476	147	6	.	.	PUNCT
ejpam-1476	148	1	majorization	majorization	NOUN
ejpam-1476	148	2	by	by	ADP
ejpam-1476	148	3	univalent	univalent	ADJ
ejpam-1476	148	4	functions	function	NOUN
ejpam-1476	148	5	.	.	PUNCT
ejpam-1476	149	1	duke	duke	PROPN
ejpam-1476	149	2	math.j	math.j	PROPN
ejpam-1476	149	3	,	,	PUNCT
ejpam-1476	149	4	34:95–102	34:95–102	NUM
ejpam-1476	149	5	,	,	PUNCT
ejpam-1476	149	6	1967	1967	NUM
ejpam-1476	149	7	.	.	PUNCT
ejpam-1476	150	1	[	[	X
ejpam-1476	150	2	6	6	NUM
ejpam-1476	150	3	]	]	PUNCT
ejpam-1476	150	4	m	m	VERB
ejpam-1476	150	5	nasr	nasr	PROPN
ejpam-1476	150	6	and	and	CCONJ
ejpam-1476	150	7	m	m	PROPN
ejpam-1476	150	8	aouf	aouf	PROPN
ejpam-1476	150	9	.	.	PUNCT
ejpam-1476	151	1	starlike	starlike	PROPN
ejpam-1476	151	2	function	function	NOUN
ejpam-1476	151	3	of	of	ADP
ejpam-1476	151	4	complex	complex	ADJ
ejpam-1476	151	5	order	order	NOUN
ejpam-1476	151	6	.	.	PUNCT
ejpam-1476	152	1	j.	j.	PROPN
ejpam-1476	152	2	natur	natur	PROPN
ejpam-1476	152	3	.	.	PUNCT
ejpam-1476	153	1	sci	sci	PROPN
ejpam-1476	153	2	.	.	PROPN
ejpam-1476	153	3	math	math	PROPN
ejpam-1476	153	4	,	,	PUNCT
ejpam-1476	153	5	25:1–12	25:1–12	NUM
ejpam-1476	153	6	,	,	PUNCT
ejpam-1476	153	7	1985	1985	NUM
ejpam-1476	153	8	.	.	PUNCT
ejpam-1476	154	1	references	reference	NOUN
ejpam-1476	154	2	24	24	NUM
ejpam-1476	154	3	[	[	X
ejpam-1476	154	4	7	7	NUM
ejpam-1476	154	5	]	]	X
ejpam-1476	154	6	z	z	NOUN
ejpam-1476	154	7	nehari	nehari	NOUN
ejpam-1476	154	8	.	.	PUNCT
ejpam-1476	155	1	conformal	conformal	ADJ
ejpam-1476	155	2	mopping	mopping	NOUN
ejpam-1476	155	3	,	,	PUNCT
ejpam-1476	155	4	mcgraw	mcgraw	PROPN
ejpam-1476	155	5	-	-	PUNCT
ejpam-1476	155	6	hill	hill	NOUN
ejpam-1476	155	7	book	book	NOUN
ejpam-1476	155	8	company	company	NOUN
ejpam-1476	155	9	.	.	PUNCT
ejpam-1476	156	1	new	new	PROPN
ejpam-1476	156	2	york	york	PROPN
ejpam-1476	156	3	,	,	PUNCT
ejpam-1476	156	4	toronto	toronto	PROPN
ejpam-1476	156	5	and	and	CCONJ
ejpam-1476	156	6	london	london	PROPN
ejpam-1476	156	7	,	,	PUNCT
ejpam-1476	156	8	1952	1952	NUM
ejpam-1476	156	9	.	.	PUNCT
ejpam-1476	157	1	[	[	X
ejpam-1476	157	2	8	8	NUM
ejpam-1476	157	3	]	]	X
ejpam-1476	157	4	s	s	VERB
ejpam-1476	157	5	owa	owa	PROPN
ejpam-1476	157	6	.	.	PUNCT
ejpam-1476	158	1	on	on	ADP
ejpam-1476	158	2	the	the	DET
ejpam-1476	158	3	distortion	distortion	NOUN
ejpam-1476	158	4	theorems	theorems	PROPN
ejpam-1476	158	5	i.	i.	PROPN
ejpam-1476	158	6	complex	complex	PROPN
ejpam-1476	158	7	variables	variables	PROPN
ejpam-1476	158	8	theory	theory	NOUN
ejpam-1476	158	9	appl	appl	NOUN
ejpam-1476	158	10	,	,	PUNCT
ejpam-1476	158	11	18:53–59	18:53–59	NUM
ejpam-1476	158	12	,	,	PUNCT
ejpam-1476	158	13	1978	1978	NUM
ejpam-1476	158	14	.	.	PUNCT
ejpam-1476	159	1	[	[	X
ejpam-1476	159	2	9	9	NUM
ejpam-1476	159	3	]	]	X
ejpam-1476	159	4	m	m	PROPN
ejpam-1476	159	5	robertson	robertson	PROPN
ejpam-1476	159	6	.	.	PUNCT
ejpam-1476	160	1	on	on	ADP
ejpam-1476	160	2	the	the	DET
ejpam-1476	160	3	theory	theory	NOUN
ejpam-1476	160	4	of	of	ADP
ejpam-1476	160	5	univalent	univalent	ADJ
ejpam-1476	160	6	functions	function	NOUN
ejpam-1476	160	7	.	.	PUNCT
ejpam-1476	161	1	ann	ann	PROPN
ejpam-1476	161	2	.	.	PROPN
ejpam-1476	161	3	of	of	ADP
ejpam-1476	161	4	math	math	NOUN
ejpam-1476	161	5	.	.	PUNCT
ejpam-1476	161	6	,	,	PUNCT
ejpam-1476	161	7	37(2):1359–1363	37(2):1359–1363	NUM
ejpam-1476	161	8	,	,	PUNCT
ejpam-1476	161	9	1936	1936	NUM
ejpam-1476	161	10	.	.	PUNCT
ejpam-1476	162	1	[	[	X
ejpam-1476	162	2	10	10	NUM
ejpam-1476	162	3	]	]	X
ejpam-1476	162	4	h	h	PROPN
ejpam-1476	162	5	srivastava	srivastava	PROPN
ejpam-1476	162	6	,	,	PUNCT
ejpam-1476	162	7	o	o	PROPN
ejpam-1476	162	8	altıntaş	altıntaş	PROPN
ejpam-1476	162	9	,	,	PUNCT
ejpam-1476	162	10	and	and	CCONJ
ejpam-1476	162	11	s	s	AUX
ejpam-1476	162	12	serenbay	serenbay	VERB
ejpam-1476	162	13	.	.	PUNCT
ejpam-1476	163	1	coffecient	coffecient	ADJ
ejpam-1476	163	2	bounds	bound	NOUN
ejpam-1476	163	3	for	for	ADP
ejpam-1476	163	4	certain	certain	ADJ
ejpam-1476	163	5	subclass	subclass	NOUN
ejpam-1476	163	6	of	of	ADP
ejpam-1476	163	7	starlike	starlike	NOUN
ejpam-1476	163	8	functions	function	NOUN
ejpam-1476	163	9	of	of	ADP
ejpam-1476	163	10	complex	complex	ADJ
ejpam-1476	163	11	order	order	NOUN
ejpam-1476	163	12	.	.	PUNCT
ejpam-1476	164	1	applied	apply	VERB
ejpam-1476	164	2	mathematics	mathematics	NOUN
ejpam-1476	164	3	letters	letter	NOUN
ejpam-1476	164	4	,	,	PUNCT
ejpam-1476	164	5	24(8	24(8	NUM
ejpam-1476	164	6	)	)	PUNCT
ejpam-1476	164	7	,	,	PUNCT
ejpam-1476	164	8	august	august	PROPN
ejpam-1476	164	9	2011	2011	NUM
ejpam-1476	164	10	.	.	PUNCT
ejpam-1476	165	1	[	[	X
ejpam-1476	165	2	11	11	NUM
ejpam-1476	165	3	]	]	X
ejpam-1476	165	4	p	p	X
ejpam-1476	165	5	wiatrowski	wiatrowski	VERB
ejpam-1476	165	6	.	.	PUNCT
ejpam-1476	166	1	on	on	ADP
ejpam-1476	166	2	the	the	DET
ejpam-1476	166	3	coefficients	coefficient	NOUN
ejpam-1476	166	4	of	of	ADP
ejpam-1476	166	5	some	some	DET
ejpam-1476	166	6	family	family	NOUN
ejpam-1476	166	7	of	of	ADP
ejpam-1476	166	8	holomorphic	holomorphic	ADJ
ejpam-1476	166	9	functions	function	NOUN
ejpam-1476	166	10	.	.	PUNCT
ejpam-1476	167	1	nauk	nauk	PROPN
ejpam-1476	167	2	.	.	PROPN
ejpam-1476	167	3	matprzyrod	matprzyrod	PROPN
ejpam-1476	167	4	.	.	PROPN
ejpam-1476	167	5	,	,	PUNCT
ejpam-1476	167	6	39(2):75–85	39(2):75–85	NUM
ejpam-1476	167	7	,	,	PUNCT
ejpam-1476	167	8	1970	1970	NUM
ejpam-1476	167	9	.	.	PUNCT