id	sid	tid	token	lemma	pos
ejpam-144	1	1	7_ahmed.dvi	7_ahmed.dvi	NUM
ejpam-144	1	2	european	european	ADJ
ejpam-144	1	3	journal	journal	NOUN
ejpam-144	1	4	of	of	ADP
ejpam-144	1	5	pure	pure	ADJ
ejpam-144	1	6	and	and	CCONJ
ejpam-144	1	7	applied	apply	VERB
ejpam-144	1	8	mathematics	mathematic	NOUN
ejpam-144	1	9	vol	vol	NOUN
ejpam-144	1	10	.	.	PROPN
ejpam-144	2	1	2	2	NUM
ejpam-144	2	2	,	,	PUNCT
ejpam-144	2	3	no	no	INTJ
ejpam-144	2	4	.	.	NOUN
ejpam-144	2	5	2	2	NUM
ejpam-144	2	6	,	,	PUNCT
ejpam-144	2	7	2009	2009	NUM
ejpam-144	2	8	,	,	PUNCT
ejpam-144	2	9	(	(	PUNCT
ejpam-144	2	10	250	250	NUM
ejpam-144	2	11	-	-	SYM
ejpam-144	2	12	267	267	NUM
ejpam-144	2	13	)	)	PUNCT
ejpam-144	2	14	issn	issn	PROPN
ejpam-144	2	15	1307	1307	NUM
ejpam-144	2	16	-	-	SYM
ejpam-144	2	17	5543	5543	NUM
ejpam-144	2	18	–	–	PUNCT
ejpam-144	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-144	2	20	some	some	DET
ejpam-144	2	21	characterizations	characterization	NOUN
ejpam-144	2	22	of	of	ADP
ejpam-144	2	23	weighted	weight	VERB
ejpam-144	2	24	holomorphic	holomorphic	PROPN
ejpam-144	2	25	bloch	bloch	PROPN
ejpam-144	2	26	space	space	PROPN
ejpam-144	2	27	r.	r.	PROPN
ejpam-144	2	28	a.	a.	PROPN
ejpam-144	2	29	rashwan1	rashwan1	PROPN
ejpam-144	2	30	,	,	PUNCT
ejpam-144	2	31	a.	a.	PROPN
ejpam-144	2	32	el	el	PROPN
ejpam-144	2	33	-	-	PUNCT
ejpam-144	2	34	sayed	say	VERB
ejpam-144	2	35	ahmed2∗	ahmed2∗	PROPN
ejpam-144	2	36	and	and	CCONJ
ejpam-144	2	37	a.	a.	NOUN
ejpam-144	2	38	kamal3	kamal3	NOUN
ejpam-144	2	39	1	1	NUM
ejpam-144	2	40	assiut	assiut	NOUN
ejpam-144	2	41	university	university	NOUN
ejpam-144	2	42	,	,	PUNCT
ejpam-144	2	43	faculty	faculty	NOUN
ejpam-144	2	44	of	of	ADP
ejpam-144	2	45	science	science	NOUN
ejpam-144	2	46	,	,	PUNCT
ejpam-144	2	47	department	department	NOUN
ejpam-144	2	48	of	of	ADP
ejpam-144	2	49	mathematics	mathematics	PROPN
ejpam-144	2	50	,	,	PUNCT
ejpam-144	2	51	assiut	assiut	PROPN
ejpam-144	2	52	,	,	PUNCT
ejpam-144	2	53	egypt	egypt	PROPN
ejpam-144	2	54	2	2	NUM
ejpam-144	2	55	sohag	sohag	NOUN
ejpam-144	2	56	university	university	NOUN
ejpam-144	2	57	,	,	PUNCT
ejpam-144	2	58	faculty	faculty	NOUN
ejpam-144	2	59	of	of	ADP
ejpam-144	2	60	science	science	NOUN
ejpam-144	2	61	,	,	PUNCT
ejpam-144	2	62	department	department	NOUN
ejpam-144	2	63	of	of	ADP
ejpam-144	2	64	mathematics	mathematic	NOUN
ejpam-144	2	65	,	,	PUNCT
ejpam-144	2	66	sohag	sohag	NOUN
ejpam-144	2	67	82524	82524	NUM
ejpam-144	2	68	,	,	PUNCT
ejpam-144	2	69	egypt	egypt	PROPN
ejpam-144	2	70	current	current	ADJ
ejpam-144	2	71	address	address	PROPN
ejpam-144	2	72	:	:	PUNCT
ejpam-144	2	73	taif	taif	PROPN
ejpam-144	2	74	university	university	PROPN
ejpam-144	2	75	,	,	PUNCT
ejpam-144	2	76	faculty	faculty	NOUN
ejpam-144	2	77	of	of	ADP
ejpam-144	2	78	science	science	NOUN
ejpam-144	2	79	,	,	PUNCT
ejpam-144	2	80	mathematics	mathematics	PROPN
ejpam-144	2	81	department	department	PROPN
ejpam-144	2	82	,	,	PUNCT
ejpam-144	2	83	el	el	PROPN
ejpam-144	2	84	-	-	PUNCT
ejpam-144	2	85	taif	taif	PROPN
ejpam-144	2	86	p.o.box	p.o.box	PROPN
ejpam-144	2	87	888	888	NUM
ejpam-144	2	88	,	,	PUNCT
ejpam-144	2	89	el	el	PROPN
ejpam-144	2	90	-	-	PUNCT
ejpam-144	2	91	hawiyah	hawiyah	NOUN
ejpam-144	2	92	,	,	PUNCT
ejpam-144	2	93	kingdom	kingdom	NOUN
ejpam-144	2	94	of	of	ADP
ejpam-144	2	95	saudi	saudi	PROPN
ejpam-144	2	96	arabia	arabia	PROPN
ejpam-144	2	97	3	3	NUM
ejpam-144	2	98	institute	institute	PROPN
ejpam-144	2	99	of	of	ADP
ejpam-144	2	100	computer	computer	NOUN
ejpam-144	2	101	science	science	NOUN
ejpam-144	2	102	,	,	PUNCT
ejpam-144	2	103	al	al	PROPN
ejpam-144	2	104	-	-	PUNCT
ejpam-144	2	105	kawser	kawser	PROPN
ejpam-144	2	106	city	city	NOUN
ejpam-144	2	107	at	at	ADP
ejpam-144	2	108	sohag	sohag	PROPN
ejpam-144	2	109	egypt	egypt	PROPN
ejpam-144	2	110	abstract	abstract	PROPN
ejpam-144	2	111	.	.	PUNCT
ejpam-144	3	1	in	in	ADP
ejpam-144	3	2	this	this	DET
ejpam-144	3	3	paper	paper	NOUN
ejpam-144	3	4	we	we	PRON
ejpam-144	3	5	introduce	introduce	VERB
ejpam-144	3	6	a	a	DET
ejpam-144	3	7	new	new	ADJ
ejpam-144	3	8	space	space	NOUN
ejpam-144	3	9	,	,	PUNCT
ejpam-144	3	10	the	the	DET
ejpam-144	3	11	so	so	ADV
ejpam-144	3	12	called	call	VERB
ejpam-144	3	13	qk	qk	PROPN
ejpam-144	3	14	,	,	PUNCT
ejpam-144	3	15	ω	ω	NUM
ejpam-144	3	16	space	space	NOUN
ejpam-144	3	17	of	of	ADP
ejpam-144	3	18	analytic	analytic	ADJ
ejpam-144	3	19	functions	function	NOUN
ejpam-144	3	20	on	on	ADP
ejpam-144	3	21	the	the	DET
ejpam-144	3	22	unit	unit	NOUN
ejpam-144	3	23	disk	disk	NOUN
ejpam-144	3	24	in	in	ADP
ejpam-144	3	25	terms	term	NOUN
ejpam-144	3	26	of	of	ADP
ejpam-144	3	27	nondecreasing	nondecreasing	ADJ
ejpam-144	3	28	functions	function	NOUN
ejpam-144	3	29	.	.	PUNCT
ejpam-144	4	1	the	the	DET
ejpam-144	4	2	relation	relation	NOUN
ejpam-144	4	3	between	between	ADP
ejpam-144	4	4	integral	integral	ADJ
ejpam-144	4	5	norm	norm	NOUN
ejpam-144	4	6	of	of	ADP
ejpam-144	4	7	qk	qk	PROPN
ejpam-144	4	8	,	,	PUNCT
ejpam-144	4	9	ω	ω	NUM
ejpam-144	4	10	space	space	NOUN
ejpam-144	4	11	and	and	CCONJ
ejpam-144	4	12	integral	integral	ADJ
ejpam-144	4	13	norm	norm	NOUN
ejpam-144	4	14	of	of	ADP
ejpam-144	4	15	the	the	DET
ejpam-144	4	16	weighted	weight	VERB
ejpam-144	4	17	bloch	bloch	PROPN
ejpam-144	4	18	spacebαω	spacebαω	PROPN
ejpam-144	4	19	is	be	AUX
ejpam-144	4	20	also	also	ADV
ejpam-144	4	21	given	give	VERB
ejpam-144	4	22	.	.	PUNCT
ejpam-144	5	1	ams	am	NOUN
ejpam-144	5	2	subject	subject	ADJ
ejpam-144	5	3	classifications	classification	NOUN
ejpam-144	5	4	:	:	PUNCT
ejpam-144	5	5	30d45	30d45	NUM
ejpam-144	5	6	,	,	PUNCT
ejpam-144	5	7	46e15	46e15	PRON
ejpam-144	5	8	key	key	ADJ
ejpam-144	5	9	words	word	NOUN
ejpam-144	5	10	:	:	PUNCT
ejpam-144	5	11	qk	qk	NOUN
ejpam-144	5	12	,	,	PUNCT
ejpam-144	5	13	ω	ω	PROPN
ejpam-144	5	14	spaces	space	NOUN
ejpam-144	5	15	,	,	PUNCT
ejpam-144	5	16	weighted	weight	VERB
ejpam-144	5	17	bloch	bloch	PROPN
ejpam-144	5	18	functions	function	NOUN
ejpam-144	5	19	.	.	PUNCT
ejpam-144	6	1	∗corresponding	∗corresponde	VERB
ejpam-144	6	2	author	author	NOUN
ejpam-144	6	3	.	.	PUNCT
ejpam-144	7	1	email	email	NOUN
ejpam-144	7	2	addresses	address	NOUN
ejpam-144	7	3	:	:	PUNCT
ejpam-144	7	4	r_rashwan	r_rashwan	NUM
ejpam-144	7	5	�	�	PROPN
ejpam-144	7	6	yahoo	yahoo	PROPN
ejpam-144	7	7	.	.	PUNCT
ejpam-144	7	8	om	om	PROPN
ejpam-144	7	9	(	(	PUNCT
ejpam-144	7	10	r.	r.	PROPN
ejpam-144	7	11	rashwan	rashwan	PROPN
ejpam-144	7	12	)	)	PUNCT
ejpam-144	7	13	,	,	PUNCT
ejpam-144	7	14	ahsayed80	ahsayed80	PROPN
ejpam-144	7	15	�	�	NOUN
ejpam-144	7	16	hotmail	hotmail	NOUN
ejpam-144	7	17	.	.	PUNCT
ejpam-144	8	1	om	om	PROPN
ejpam-144	8	2	(	(	PUNCT
ejpam-144	8	3	a.	a.	NOUN
ejpam-144	8	4	ahmed),alaa_mohamed1	ahmed),alaa_mohamed1	PROPN
ejpam-144	8	5	�	�	PROPN
ejpam-144	8	6	yahoo	yahoo	PROPN
ejpam-144	8	7	.	.	PUNCT
ejpam-144	9	1	om	om	PROPN
ejpam-144	9	2	(	(	PUNCT
ejpam-144	9	3	a.	a.	PROPN
ejpam-144	9	4	kamal	kamal	PROPN
ejpam-144	9	5	)	)	PUNCT
ejpam-144	9	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-144	10	1	250	250	NUM
ejpam-144	10	2	c	c	X
ejpam-144	10	3	©	©	PROPN
ejpam-144	10	4	2009	2009	NUM
ejpam-144	10	5	ejpam	ejpam	NOUN
ejpam-144	10	6	all	all	DET
ejpam-144	10	7	rights	right	NOUN
ejpam-144	10	8	reserved	reserve	VERB
ejpam-144	10	9	.	.	PUNCT
ejpam-144	11	1	r.	r.	PROPN
ejpam-144	11	2	rashwan	rashwan	PROPN
ejpam-144	11	3	,	,	PUNCT
ejpam-144	11	4	a.	a.	PROPN
ejpam-144	11	5	ahmed	ahmed	PROPN
ejpam-144	11	6	and	and	CCONJ
ejpam-144	11	7	a.	a.	PROPN
ejpam-144	11	8	kamal	kamal	PROPN
ejpam-144	11	9	/	/	SYM
ejpam-144	11	10	eur	eur	PROPN
ejpam-144	11	11	.	.	PUNCT
ejpam-144	12	1	j.	j.	PROPN
ejpam-144	12	2	pure	pure	PROPN
ejpam-144	12	3	appl	appl	PROPN
ejpam-144	12	4	.	.	PROPN
ejpam-144	12	5	math	math	PROPN
ejpam-144	12	6	,	,	PUNCT
ejpam-144	12	7	2	2	NUM
ejpam-144	12	8	(	(	PUNCT
ejpam-144	12	9	2009	2009	NUM
ejpam-144	12	10	)	)	PUNCT
ejpam-144	12	11	,	,	PUNCT
ejpam-144	12	12	(	(	PUNCT
ejpam-144	12	13	250	250	NUM
ejpam-144	12	14	-	-	SYM
ejpam-144	12	15	267	267	NUM
ejpam-144	12	16	)	)	PUNCT
ejpam-144	12	17	251	251	NUM
ejpam-144	12	18	1	1	NUM
ejpam-144	12	19	.	.	PUNCT
ejpam-144	13	1	introduction	introduction	NOUN
ejpam-144	13	2	let	let	VERB
ejpam-144	13	3	∆=	∆=	VERB
ejpam-144	13	4	{	{	PUNCT
ejpam-144	13	5	z	z	NOUN
ejpam-144	13	6	:	:	PUNCT
ejpam-144	13	7	|z|	|z|	NOUN
ejpam-144	13	8	<	<	X
ejpam-144	13	9	1	1	NUM
ejpam-144	13	10	}	}	PUNCT
ejpam-144	13	11	be	be	AUX
ejpam-144	13	12	the	the	DET
ejpam-144	13	13	open	open	ADJ
ejpam-144	13	14	unit	unit	NOUN
ejpam-144	13	15	disk	disk	NOUN
ejpam-144	13	16	in	in	ADP
ejpam-144	13	17	the	the	DET
ejpam-144	13	18	complex	complex	ADJ
ejpam-144	13	19	plane	plane	NOUN
ejpam-144	13	20	c.	c.	NOUN
ejpam-144	13	21	recall	recall	VERB
ejpam-144	13	22	that	that	SCONJ
ejpam-144	13	23	the	the	DET
ejpam-144	13	24	well	well	ADV
ejpam-144	13	25	known	know	VERB
ejpam-144	13	26	bloch	bloch	NOUN
ejpam-144	13	27	space	space	NOUN
ejpam-144	13	28	(	(	PUNCT
ejpam-144	13	29	cf	cf	NOUN
ejpam-144	13	30	.	.	PUNCT
ejpam-144	14	1	[	[	X
ejpam-144	14	2	2	2	NUM
ejpam-144	14	3	]	]	PUNCT
ejpam-144	14	4	)	)	PUNCT
ejpam-144	14	5	is	be	AUX
ejpam-144	14	6	defined	define	VERB
ejpam-144	14	7	as	as	SCONJ
ejpam-144	14	8	follows	follow	VERB
ejpam-144	14	9	:	:	PUNCT
ejpam-144	14	10	b	b	X
ejpam-144	14	11	=	=	SYM
ejpam-144	14	12	{	{	PUNCT
ejpam-144	14	13	f	f	X
ejpam-144	14	14	:	:	PUNCT
ejpam-144	14	15	f	f	PROPN
ejpam-144	14	16	analytic	analytic	ADJ
ejpam-144	14	17	in	in	ADP
ejpam-144	14	18	∆	∆	PROPN
ejpam-144	14	19	and	and	CCONJ
ejpam-144	14	20	sup	sup	PROPN
ejpam-144	14	21	z∈∆	z∈∆	NUM
ejpam-144	14	22	(	(	PUNCT
ejpam-144	14	23	1−	1−	NUM
ejpam-144	14	24	|z|2)|	|z|2)|	PROPN
ejpam-144	14	25	f	f	PROPN
ejpam-144	14	26	′(z)|<∞	′(z)|<∞	PROPN
ejpam-144	14	27	}	}	PUNCT
ejpam-144	14	28	;	;	PUNCT
ejpam-144	14	29	the	the	DET
ejpam-144	14	30	little	little	ADJ
ejpam-144	14	31	bloch	bloch	PROPN
ejpam-144	14	32	spaceb0	spaceb0	NOUN
ejpam-144	14	33	(	(	PUNCT
ejpam-144	14	34	cf	cf	NOUN
ejpam-144	14	35	.	.	PUNCT
ejpam-144	15	1	[	[	X
ejpam-144	15	2	2	2	NUM
ejpam-144	15	3	]	]	PUNCT
ejpam-144	15	4	)	)	PUNCT
ejpam-144	15	5	is	be	AUX
ejpam-144	15	6	a	a	DET
ejpam-144	15	7	subspace	subspace	NOUN
ejpam-144	15	8	ofb	ofb	PROPN
ejpam-144	15	9	consisting	consist	VERB
ejpam-144	15	10	of	of	ADP
ejpam-144	15	11	all	all	DET
ejpam-144	15	12	f	f	PROPN
ejpam-144	15	13	∈b	∈b	PROPN
ejpam-144	15	14	such	such	ADJ
ejpam-144	15	15	that	that	SCONJ
ejpam-144	15	16	lim	lim	PROPN
ejpam-144	15	17	|z|→1−	|z|→1−	PROPN
ejpam-144	15	18	(	(	PUNCT
ejpam-144	15	19	1−	1−	NUM
ejpam-144	15	20	|z|2)|	|z|2)|	PROPN
ejpam-144	15	21	f	f	PROPN
ejpam-144	15	22	′(z)|=	′(z)|=	PROPN
ejpam-144	15	23	0	0	NUM
ejpam-144	15	24	.	.	PUNCT
ejpam-144	16	1	the	the	DET
ejpam-144	16	2	dirichlet	dirichlet	PROPN
ejpam-144	16	3	space	space	NOUN
ejpam-144	16	4	is	be	AUX
ejpam-144	16	5	defined	define	VERB
ejpam-144	16	6	by	by	ADP
ejpam-144	16	7	d	d	PROPN
ejpam-144	16	8	=	=	SYM
ejpam-144	16	9	{	{	PUNCT
ejpam-144	16	10	f	f	X
ejpam-144	16	11	:	:	PUNCT
ejpam-144	16	12	f	f	PROPN
ejpam-144	16	13	analytic	analytic	ADJ
ejpam-144	16	14	in	in	ADP
ejpam-144	16	15	∆	∆	PROPN
ejpam-144	16	16	and	and	CCONJ
ejpam-144	16	17	∫	∫	PROPN
ejpam-144	16	18	∆	∆	PROPN
ejpam-144	16	19	�	�	PROPN
ejpam-144	16	20	�	�	PROPN
ejpam-144	16	21	f	f	PROPN
ejpam-144	16	22	′(z	′(z	NOUN
ejpam-144	16	23	)	)	PUNCT
ejpam-144	16	24	�	�	PROPN
ejpam-144	16	25	�	�	PROPN
ejpam-144	16	26	2	2	NUM
ejpam-144	16	27	dσz	dσz	NOUN
ejpam-144	16	28	<	<	X
ejpam-144	16	29	∞	∞	NUM
ejpam-144	16	30	}	}	PUNCT
ejpam-144	16	31	,	,	PUNCT
ejpam-144	16	32	where	where	SCONJ
ejpam-144	16	33	dσz	dσz	NOUN
ejpam-144	16	34	is	be	AUX
ejpam-144	16	35	the	the	DET
ejpam-144	16	36	euclidean	euclidean	ADJ
ejpam-144	16	37	area	area	NOUN
ejpam-144	16	38	element	element	NOUN
ejpam-144	17	1	d	d	PROPN
ejpam-144	17	2	xd	xd	PROPN
ejpam-144	17	3	y.	y.	PROPN
ejpam-144	17	4	let	let	VERB
ejpam-144	17	5	0	0	PUNCT
ejpam-144	17	6	<	<	X
ejpam-144	17	7	q	q	X
ejpam-144	18	1	<	<	X
ejpam-144	18	2	∞.	∞.	PROPN
ejpam-144	18	3	then	then	ADV
ejpam-144	18	4	the	the	DET
ejpam-144	18	5	besov	besov	NOUN
ejpam-144	18	6	-	-	PUNCT
ejpam-144	18	7	type	type	NOUN
ejpam-144	18	8	spaces	space	NOUN
ejpam-144	18	9	bq	bq	X
ejpam-144	18	10	=	=	SYM
ejpam-144	18	11	�	�	PROPN
ejpam-144	18	12	f	f	PROPN
ejpam-144	18	13	:	:	PUNCT
ejpam-144	18	14	f	f	PROPN
ejpam-144	18	15	analytic	analytic	ADJ
ejpam-144	18	16	in	in	ADP
ejpam-144	18	17	∆	∆	PROPN
ejpam-144	18	18	and	and	CCONJ
ejpam-144	18	19	sup	sup	PROPN
ejpam-144	18	20	a∈∆	a∈∆	PROPN
ejpam-144	18	21	∫	∫	PROPN
ejpam-144	18	22	∆	∆	PROPN
ejpam-144	18	23	�	�	PROPN
ejpam-144	18	24	�	�	PROPN
ejpam-144	18	25	f	f	PROPN
ejpam-144	18	26	′(z	′(z	NOUN
ejpam-144	18	27	)	)	PUNCT
ejpam-144	18	28	�	�	PROPN
ejpam-144	18	29	�	�	PROPN
ejpam-144	18	30	q	q	PROPN
ejpam-144	18	31	�	�	PROPN
ejpam-144	18	32	1−	1−	NUM
ejpam-144	18	33	|z|2	|z|2	PROPN
ejpam-144	18	34	�	�	NOUN
ejpam-144	18	35	q−2	q−2	PROPN
ejpam-144	18	36	(	(	PUNCT
ejpam-144	18	37	1−	1−	NUM
ejpam-144	18	38	|ϕa(z)|	|ϕa(z)|	ADP
ejpam-144	18	39	2)2dσz	2)2dσz	NUM
ejpam-144	18	40	<	<	NOUN
ejpam-144	18	41	∞	∞	PROPN
ejpam-144	18	42	�	�	PROPN
ejpam-144	18	43	are	be	AUX
ejpam-144	18	44	introduced	introduce	VERB
ejpam-144	18	45	and	and	CCONJ
ejpam-144	18	46	studied	study	VERB
ejpam-144	18	47	intensively	intensively	ADV
ejpam-144	18	48	by	by	ADP
ejpam-144	18	49	stroethoff	stroethoff	NOUN
ejpam-144	18	50	(	(	PUNCT
ejpam-144	18	51	cf	cf	NOUN
ejpam-144	18	52	.	.	PUNCT
ejpam-144	19	1	[	[	X
ejpam-144	19	2	11	11	NUM
ejpam-144	19	3	]	]	NUM
ejpam-144	19	4	)	)	PUNCT
ejpam-144	19	5	.	.	PUNCT
ejpam-144	20	1	here	here	ADV
ejpam-144	20	2	,	,	PUNCT
ejpam-144	20	3	ϕa(z	ϕa(z	PUNCT
ejpam-144	20	4	)	)	PUNCT
ejpam-144	20	5	stands	stand	VERB
ejpam-144	20	6	for	for	ADP
ejpam-144	20	7	the	the	DET
ejpam-144	20	8	möbius	möbius	NOUN
ejpam-144	20	9	transformation	transformation	NOUN
ejpam-144	20	10	of	of	ADP
ejpam-144	20	11	∆	∆	PROPN
ejpam-144	20	12	given	give	VERB
ejpam-144	20	13	by	by	ADP
ejpam-144	20	14	ϕa(z	ϕa(z	PUNCT
ejpam-144	20	15	)	)	PUNCT
ejpam-144	20	16	=	=	SYM
ejpam-144	21	1	a−	a−	PROPN
ejpam-144	21	2	z	z	NOUN
ejpam-144	21	3	1−	1−	NUM
ejpam-144	21	4	āz	āz	ADV
ejpam-144	21	5	,	,	PUNCT
ejpam-144	21	6	where	where	SCONJ
ejpam-144	21	7	a	a	DET
ejpam-144	21	8	∈∆.	∈∆.	PROPN
ejpam-144	21	9	in	in	ADP
ejpam-144	21	10	1994	1994	NUM
ejpam-144	21	11	,	,	PUNCT
ejpam-144	21	12	aulaskari	aulaskari	PROPN
ejpam-144	21	13	and	and	CCONJ
ejpam-144	21	14	lappan	lappan	VERB
ejpam-144	22	1	[	[	X
ejpam-144	22	2	2	2	NUM
ejpam-144	22	3	]	]	PUNCT
ejpam-144	22	4	introduced	introduce	VERB
ejpam-144	22	5	a	a	DET
ejpam-144	22	6	class	class	NOUN
ejpam-144	22	7	of	of	ADP
ejpam-144	22	8	holomorphic	holomorphic	ADJ
ejpam-144	22	9	functions	function	NOUN
ejpam-144	22	10	,	,	PUNCT
ejpam-144	22	11	the	the	DET
ejpam-144	22	12	so	so	ADV
ejpam-144	22	13	called	call	VERB
ejpam-144	22	14	qp	qp	NOUN
ejpam-144	22	15	-	-	PUNCT
ejpam-144	22	16	spaces	space	NOUN
ejpam-144	22	17	as	as	SCONJ
ejpam-144	22	18	follows	follow	VERB
ejpam-144	22	19	:	:	PUNCT
ejpam-144	22	20	qp	qp	PROPN
ejpam-144	22	21	=	=	SYM
ejpam-144	22	22	�	�	PROPN
ejpam-144	22	23	f	f	PROPN
ejpam-144	22	24	:	:	PUNCT
ejpam-144	22	25	f	f	PROPN
ejpam-144	22	26	analytic	analytic	ADJ
ejpam-144	22	27	in	in	ADP
ejpam-144	22	28	∆	∆	PROPN
ejpam-144	22	29	and	and	CCONJ
ejpam-144	22	30	sup	sup	PROPN
ejpam-144	22	31	a∈∆	a∈∆	PROPN
ejpam-144	22	32	∫	∫	PROPN
ejpam-144	22	33	∆	∆	PROPN
ejpam-144	22	34	�	�	PROPN
ejpam-144	22	35	�	�	PROPN
ejpam-144	22	36	f	f	PROPN
ejpam-144	22	37	′(z	′(z	NOUN
ejpam-144	22	38	)	)	PUNCT
ejpam-144	22	39	�	�	PROPN
ejpam-144	22	40	�	�	PROPN
ejpam-144	22	41	2	2	NUM
ejpam-144	22	42	g	g	NOUN
ejpam-144	22	43	p(z	p(z	NOUN
ejpam-144	22	44	,	,	PUNCT
ejpam-144	22	45	a)dσz	a)dσz	PROPN
ejpam-144	22	46	<	<	X
ejpam-144	22	47	∞	∞	PROPN
ejpam-144	22	48	�	�	PROPN
ejpam-144	22	49	,	,	PUNCT
ejpam-144	22	50	where	where	SCONJ
ejpam-144	22	51	0	0	X
ejpam-144	22	52	<	<	X
ejpam-144	22	53	p	p	X
ejpam-144	22	54	<	<	X
ejpam-144	22	55	∞	∞	PROPN
ejpam-144	22	56	and	and	CCONJ
ejpam-144	22	57	the	the	DET
ejpam-144	22	58	weight	weight	NOUN
ejpam-144	22	59	function	function	NOUN
ejpam-144	23	1	g(z	g(z	PROPN
ejpam-144	23	2	,	,	PUNCT
ejpam-144	23	3	a	a	PRON
ejpam-144	23	4	)	)	PUNCT
ejpam-144	23	5	=	=	SYM
ejpam-144	23	6	log	log	PROPN
ejpam-144	23	7	�	�	PROPN
ejpam-144	23	8	�	�	PROPN
ejpam-144	23	9	�	�	PROPN
ejpam-144	23	10	�	�	PROPN
ejpam-144	23	11	1−	1−	NUM
ejpam-144	23	12	āz	āz	PROPN
ejpam-144	23	13	a−	a−	PROPN
ejpam-144	23	14	z	z	PROPN
ejpam-144	23	15	�	�	PROPN
ejpam-144	23	16	�	�	PROPN
ejpam-144	23	17	�	�	PROPN
ejpam-144	23	18	�	�	PROPN
ejpam-144	23	19	r.	r.	PROPN
ejpam-144	23	20	rashwan	rashwan	PROPN
ejpam-144	23	21	,	,	PUNCT
ejpam-144	23	22	a.	a.	PROPN
ejpam-144	23	23	ahmed	ahmed	PROPN
ejpam-144	23	24	and	and	CCONJ
ejpam-144	23	25	a.	a.	PROPN
ejpam-144	23	26	kamal	kamal	PROPN
ejpam-144	23	27	/	/	SYM
ejpam-144	23	28	eur	eur	PROPN
ejpam-144	23	29	.	.	PUNCT
ejpam-144	24	1	j.	j.	PROPN
ejpam-144	24	2	pure	pure	PROPN
ejpam-144	24	3	appl	appl	PROPN
ejpam-144	24	4	.	.	PROPN
ejpam-144	24	5	math	math	PROPN
ejpam-144	24	6	,	,	PUNCT
ejpam-144	24	7	2	2	NUM
ejpam-144	24	8	(	(	PUNCT
ejpam-144	24	9	2009	2009	NUM
ejpam-144	24	10	)	)	PUNCT
ejpam-144	24	11	,	,	PUNCT
ejpam-144	24	12	(	(	PUNCT
ejpam-144	24	13	250	250	NUM
ejpam-144	24	14	-	-	SYM
ejpam-144	24	15	267	267	NUM
ejpam-144	24	16	)	)	PUNCT
ejpam-144	24	17	252	252	NUM
ejpam-144	24	18	is	be	AUX
ejpam-144	24	19	defined	define	VERB
ejpam-144	24	20	as	as	ADP
ejpam-144	24	21	the	the	DET
ejpam-144	24	22	composition	composition	NOUN
ejpam-144	24	23	of	of	ADP
ejpam-144	24	24	the	the	DET
ejpam-144	24	25	möbius	möbius	NOUN
ejpam-144	24	26	transformation	transformation	NOUN
ejpam-144	24	27	ϕa	ϕa	PROPN
ejpam-144	24	28	and	and	CCONJ
ejpam-144	24	29	the	the	DET
ejpam-144	24	30	fundamental	fundamental	ADJ
ejpam-144	24	31	solution	solution	NOUN
ejpam-144	24	32	of	of	ADP
ejpam-144	24	33	the	the	DET
ejpam-144	24	34	two	two	NUM
ejpam-144	24	35	-	-	PUNCT
ejpam-144	24	36	dimensional	dimensional	ADJ
ejpam-144	24	37	real	real	ADJ
ejpam-144	24	38	laplacian	laplacian	NOUN
ejpam-144	24	39	.	.	PUNCT
ejpam-144	25	1	the	the	DET
ejpam-144	25	2	weight	weight	NOUN
ejpam-144	25	3	function	function	NOUN
ejpam-144	25	4	g(z	g(z	PROPN
ejpam-144	25	5	,	,	PUNCT
ejpam-144	25	6	a	a	PRON
ejpam-144	25	7	)	)	PUNCT
ejpam-144	25	8	is	be	AUX
ejpam-144	25	9	actually	actually	ADV
ejpam-144	25	10	green	green	ADJ
ejpam-144	25	11	’s	’s	PART
ejpam-144	25	12	function	function	NOUN
ejpam-144	25	13	in	in	ADP
ejpam-144	25	14	∆	∆	PROPN
ejpam-144	25	15	with	with	ADP
ejpam-144	25	16	pole	pole	NOUN
ejpam-144	25	17	at	at	ADP
ejpam-144	25	18	a	a	DET
ejpam-144	25	19	∈∆.	∈∆.	PROPN
ejpam-144	25	20	for	for	ADP
ejpam-144	25	21	0	0	NUM
ejpam-144	25	22	<	<	X
ejpam-144	25	23	p	p	X
ejpam-144	25	24	<	<	X
ejpam-144	25	25	∞,−2	∞,−2	PROPN
ejpam-144	25	26	<	<	X
ejpam-144	25	27	q	q	X
ejpam-144	25	28	<	<	X
ejpam-144	25	29	∞	∞	PROPN
ejpam-144	25	30	,	,	PUNCT
ejpam-144	25	31	we	we	PRON
ejpam-144	25	32	say	say	VERB
ejpam-144	25	33	that	that	SCONJ
ejpam-144	25	34	a	a	DET
ejpam-144	25	35	function	function	NOUN
ejpam-144	25	36	f	f	PROPN
ejpam-144	25	37	analytic	analytic	NOUN
ejpam-144	25	38	in	in	ADP
ejpam-144	25	39	∆	∆	PROPN
ejpam-144	25	40	belongs	belong	VERB
ejpam-144	25	41	to	to	ADP
ejpam-144	25	42	the	the	DET
ejpam-144	25	43	space	space	NOUN
ejpam-144	25	44	qk(p	qk(p	NOUN
ejpam-144	25	45	,	,	PUNCT
ejpam-144	25	46	q	q	X
ejpam-144	25	47	)	)	PUNCT
ejpam-144	25	48	(	(	PUNCT
ejpam-144	25	49	cf	cf	NOUN
ejpam-144	25	50	.	.	PUNCT
ejpam-144	26	1	[	[	X
ejpam-144	26	2	14	14	NUM
ejpam-144	26	3	]	]	PUNCT
ejpam-144	26	4	)	)	PUNCT
ejpam-144	26	5	,	,	PUNCT
ejpam-144	26	6	if	if	SCONJ
ejpam-144	26	7	‖	‖	PROPN
ejpam-144	26	8	f	f	PROPN
ejpam-144	26	9	‖k	‖k	PROPN
ejpam-144	26	10	,	,	PUNCT
ejpam-144	26	11	p	p	X
ejpam-144	26	12	,	,	PUNCT
ejpam-144	26	13	q	q	NOUN
ejpam-144	26	14	=	=	NOUN
ejpam-144	26	15	sup	sup	PROPN
ejpam-144	26	16	a∈∆	a∈∆	NOUN
ejpam-144	26	17	∫	∫	PROPN
ejpam-144	26	18	∆	∆	PROPN
ejpam-144	26	19	�	�	PROPN
ejpam-144	26	20	�	�	PROPN
ejpam-144	26	21	f	f	PROPN
ejpam-144	26	22	′(z	′(z	NOUN
ejpam-144	26	23	)	)	PUNCT
ejpam-144	26	24	�	�	PROPN
ejpam-144	26	25	�	�	PROPN
ejpam-144	26	26	p	p	PROPN
ejpam-144	26	27	�	�	PROPN
ejpam-144	26	28	1−	1−	NUM
ejpam-144	26	29	|z|2	|z|2	PROPN
ejpam-144	26	30	�	�	PROPN
ejpam-144	26	31	q	q	NOUN
ejpam-144	26	32	k(g(z	k(g(z	NOUN
ejpam-144	26	33	,	,	PUNCT
ejpam-144	26	34	a))dσz	a))dσz	ADJ
ejpam-144	26	35	<	<	AUX
ejpam-144	26	36	∞.	∞.	PROPN
ejpam-144	26	37	recall	recall	VERB
ejpam-144	26	38	that	that	SCONJ
ejpam-144	26	39	the	the	DET
ejpam-144	26	40	analytic	analytic	ADJ
ejpam-144	26	41	function	function	NOUN
ejpam-144	26	42	f	f	PROPN
ejpam-144	26	43	(	(	PUNCT
ejpam-144	26	44	z	z	NOUN
ejpam-144	26	45	)	)	PUNCT
ejpam-144	26	46	=	=	SYM
ejpam-144	27	1	∞	∞	NUM
ejpam-144	27	2	∑	∑	PUNCT
ejpam-144	27	3	k	k	X
ejpam-144	27	4	akznk	akznk	PROPN
ejpam-144	27	5	(	(	PUNCT
ejpam-144	27	6	with	with	ADP
ejpam-144	27	7	nk	nk	PROPN
ejpam-144	27	8	∈	∈	PROPN
ejpam-144	27	9	n	n	CCONJ
ejpam-144	27	10	;	;	PUNCT
ejpam-144	27	11	for	for	ADP
ejpam-144	27	12	all	all	DET
ejpam-144	27	13	k	k	PROPN
ejpam-144	27	14	∈	∈	PROPN
ejpam-144	27	15	n=	n=	ADJ
ejpam-144	27	16	{	{	PUNCT
ejpam-144	27	17	1	1	NUM
ejpam-144	27	18	,	,	PUNCT
ejpam-144	27	19	2	2	NUM
ejpam-144	27	20	,	,	PUNCT
ejpam-144	27	21	3	3	NUM
ejpam-144	27	22	,	,	PUNCT
ejpam-144	27	23	.	.	PUNCT
ejpam-144	27	24	.	.	PUNCT
ejpam-144	27	25	.	.	PUNCT
ejpam-144	28	1	}	}	PUNCT
ejpam-144	28	2	)	)	PUNCT
ejpam-144	28	3	is	be	AUX
ejpam-144	28	4	said	say	VERB
ejpam-144	28	5	to	to	PART
ejpam-144	28	6	belong	belong	VERB
ejpam-144	28	7	to	to	ADP
ejpam-144	28	8	the	the	DET
ejpam-144	28	9	hadamard	hadamard	ADJ
ejpam-144	28	10	gap	gap	NOUN
ejpam-144	28	11	class	class	NOUN
ejpam-144	28	12	(	(	PUNCT
ejpam-144	28	13	also	also	ADV
ejpam-144	28	14	known	know	VERB
ejpam-144	28	15	as	as	ADP
ejpam-144	28	16	lacunary	lacunary	ADJ
ejpam-144	28	17	series	series	NOUN
ejpam-144	28	18	)	)	PUNCT
ejpam-144	28	19	if	if	SCONJ
ejpam-144	28	20	there	there	PRON
ejpam-144	28	21	exists	exist	VERB
ejpam-144	28	22	a	a	DET
ejpam-144	28	23	constant	constant	ADJ
ejpam-144	28	24	c	c	NOUN
ejpam-144	28	25	>	>	X
ejpam-144	28	26	1	1	NUM
ejpam-144	28	27	such	such	ADJ
ejpam-144	28	28	that	that	SCONJ
ejpam-144	28	29	nk+1	nk+1	NUM
ejpam-144	28	30	nk	nk	PROPN
ejpam-144	28	31	≥	≥	PROPN
ejpam-144	28	32	c	c	NOUN
ejpam-144	28	33	for	for	ADP
ejpam-144	28	34	all	all	DET
ejpam-144	28	35	k	k	PROPN
ejpam-144	28	36	∈	∈	PROPN
ejpam-144	28	37	n	n	CCONJ
ejpam-144	28	38	(	(	PUNCT
ejpam-144	28	39	see	see	VERB
ejpam-144	29	1	e.g.	e.g.	ADV
ejpam-144	29	2	[	[	X
ejpam-144	29	3	17	17	NUM
ejpam-144	29	4	]	]	NUM
ejpam-144	29	5	)	)	PUNCT
ejpam-144	29	6	.	.	PUNCT
ejpam-144	30	1	two	two	NUM
ejpam-144	30	2	quantities	quantity	NOUN
ejpam-144	30	3	a	a	DET
ejpam-144	30	4	f	f	NOUN
ejpam-144	30	5	and	and	CCONJ
ejpam-144	30	6	b	b	PROPN
ejpam-144	30	7	f	f	PROPN
ejpam-144	30	8	,	,	PUNCT
ejpam-144	30	9	both	both	PRON
ejpam-144	30	10	depending	depend	VERB
ejpam-144	30	11	on	on	ADP
ejpam-144	30	12	an	an	DET
ejpam-144	30	13	analytic	analytic	ADJ
ejpam-144	30	14	function	function	NOUN
ejpam-144	30	15	f	f	PROPN
ejpam-144	30	16	on	on	ADP
ejpam-144	30	17	∆	∆	PROPN
ejpam-144	30	18	,	,	PUNCT
ejpam-144	30	19	are	be	AUX
ejpam-144	30	20	said	say	VERB
ejpam-144	30	21	to	to	PART
ejpam-144	30	22	be	be	AUX
ejpam-144	30	23	equivalent	equivalent	ADJ
ejpam-144	30	24	,	,	PUNCT
ejpam-144	30	25	written	write	VERB
ejpam-144	30	26	as	as	ADP
ejpam-144	30	27	a	a	DET
ejpam-144	30	28	f	f	PROPN
ejpam-144	30	29	≈	≈	PROPN
ejpam-144	30	30	b	b	PROPN
ejpam-144	30	31	f	f	X
ejpam-144	30	32	,	,	PUNCT
ejpam-144	30	33	if	if	SCONJ
ejpam-144	30	34	there	there	PRON
ejpam-144	30	35	exists	exist	VERB
ejpam-144	30	36	a	a	DET
ejpam-144	30	37	finite	finite	ADJ
ejpam-144	30	38	positive	positive	ADJ
ejpam-144	30	39	constant	constant	ADJ
ejpam-144	30	40	c	c	NOUN
ejpam-144	30	41	not	not	PART
ejpam-144	30	42	depending	depend	VERB
ejpam-144	30	43	on	on	ADP
ejpam-144	30	44	f	f	PROPN
ejpam-144	30	45	such	such	ADJ
ejpam-144	30	46	that	that	PRON
ejpam-144	30	47	for	for	ADP
ejpam-144	30	48	every	every	DET
ejpam-144	30	49	analytic	analytic	ADJ
ejpam-144	30	50	function	function	NOUN
ejpam-144	30	51	f	f	PROPN
ejpam-144	30	52	on	on	ADP
ejpam-144	30	53	∆	∆	PROPN
ejpam-144	30	54	we	we	PRON
ejpam-144	30	55	have	have	VERB
ejpam-144	30	56	:	:	PUNCT
ejpam-144	30	57	1	1	NUM
ejpam-144	30	58	c	c	NOUN
ejpam-144	30	59	b	b	X
ejpam-144	30	60	f	f	X
ejpam-144	30	61	≤	≤	NOUN
ejpam-144	30	62	a	a	DET
ejpam-144	30	63	f	f	PROPN
ejpam-144	30	64	≤	≤	PROPN
ejpam-144	30	65	cb	cb	PROPN
ejpam-144	30	66	f	f	PROPN
ejpam-144	30	67	.	.	PUNCT
ejpam-144	31	1	if	if	SCONJ
ejpam-144	31	2	the	the	DET
ejpam-144	31	3	quantities	quantity	NOUN
ejpam-144	31	4	a	a	DET
ejpam-144	31	5	f	f	NOUN
ejpam-144	31	6	and	and	CCONJ
ejpam-144	31	7	b	b	PROPN
ejpam-144	31	8	f	f	PROPN
ejpam-144	31	9	,	,	PUNCT
ejpam-144	31	10	are	be	AUX
ejpam-144	31	11	equivalent	equivalent	ADJ
ejpam-144	31	12	,	,	PUNCT
ejpam-144	31	13	then	then	ADV
ejpam-144	31	14	in	in	ADP
ejpam-144	31	15	particular	particular	ADJ
ejpam-144	31	16	we	we	PRON
ejpam-144	31	17	have	have	VERB
ejpam-144	31	18	a	a	DET
ejpam-144	31	19	f	f	X
ejpam-144	31	20	<	<	X
ejpam-144	31	21	∞	∞	PROPN
ejpam-144	31	22	if	if	SCONJ
ejpam-144	32	1	and	and	CCONJ
ejpam-144	32	2	only	only	ADV
ejpam-144	32	3	if	if	SCONJ
ejpam-144	32	4	b	b	PROPN
ejpam-144	32	5	f	f	X
ejpam-144	32	6	<	<	X
ejpam-144	32	7	∞.	∞.	PROPN
ejpam-144	32	8	now	now	ADV
ejpam-144	32	9	,	,	PUNCT
ejpam-144	32	10	given	give	VERB
ejpam-144	32	11	a	a	DET
ejpam-144	32	12	reasonable	reasonable	ADJ
ejpam-144	32	13	function	function	NOUN
ejpam-144	32	14	ω	ω	NOUN
ejpam-144	32	15	:	:	PUNCT
ejpam-144	32	16	(	(	PUNCT
ejpam-144	32	17	0	0	NUM
ejpam-144	32	18	,	,	PUNCT
ejpam-144	32	19	1]→	1]→	NOUN
ejpam-144	33	1	[	[	X
ejpam-144	33	2	0,∞	0,∞	NOUN
ejpam-144	33	3	)	)	PUNCT
ejpam-144	33	4	,	,	PUNCT
ejpam-144	33	5	the	the	DET
ejpam-144	33	6	weighted	weight	VERB
ejpam-144	33	7	bloch	bloch	PROPN
ejpam-144	33	8	space	space	NOUN
ejpam-144	33	9	bω	bω	PROPN
ejpam-144	33	10	(	(	PUNCT
ejpam-144	33	11	see	see	VERB
ejpam-144	33	12	[	[	X
ejpam-144	33	13	4	4	NUM
ejpam-144	33	14	]	]	PUNCT
ejpam-144	33	15	)	)	PUNCT
ejpam-144	33	16	is	be	AUX
ejpam-144	33	17	defined	define	VERB
ejpam-144	33	18	as	as	ADP
ejpam-144	33	19	the	the	DET
ejpam-144	33	20	set	set	NOUN
ejpam-144	33	21	of	of	ADP
ejpam-144	33	22	all	all	DET
ejpam-144	33	23	analytic	analytic	ADJ
ejpam-144	33	24	functions	function	NOUN
ejpam-144	33	25	f	f	X
ejpam-144	33	26	on	on	ADP
ejpam-144	33	27	∆	∆	PROPN
ejpam-144	33	28	satisfying	satisfying	NOUN
ejpam-144	33	29	(	(	PUNCT
ejpam-144	33	30	1−	1−	NUM
ejpam-144	33	31	|z|)|	|z|)|	PROPN
ejpam-144	33	32	f	f	PROPN
ejpam-144	34	1	′(z)|	′(z)|	NOUN
ejpam-144	34	2	≤	≤	NOUN
ejpam-144	34	3	cω(1−	cω(1−	NUM
ejpam-144	34	4	|z|	|z|	NOUN
ejpam-144	34	5	)	)	PUNCT
ejpam-144	34	6	,	,	PUNCT
ejpam-144	34	7	z	z	NOUN
ejpam-144	34	8	∈∆	∈∆	VERB
ejpam-144	34	9	,	,	PUNCT
ejpam-144	34	10	for	for	ADP
ejpam-144	34	11	some	some	DET
ejpam-144	34	12	fixed	fix	VERB
ejpam-144	34	13	c	c	NOUN
ejpam-144	34	14	=	=	PUNCT
ejpam-144	35	1	c	c	PROPN
ejpam-144	35	2	f	f	X
ejpam-144	35	3	>	>	X
ejpam-144	35	4	0	0	X
ejpam-144	35	5	.	.	PUNCT
ejpam-144	36	1	in	in	ADP
ejpam-144	36	2	the	the	DET
ejpam-144	36	3	special	special	ADJ
ejpam-144	36	4	case	case	NOUN
ejpam-144	36	5	where	where	SCONJ
ejpam-144	36	6	ω	ω	PROPN
ejpam-144	36	7	≡	≡	PROPN
ejpam-144	36	8	1,bω	1,bω	NUM
ejpam-144	36	9	reduces	reduce	VERB
ejpam-144	36	10	to	to	ADP
ejpam-144	36	11	the	the	DET
ejpam-144	36	12	classical	classical	ADJ
ejpam-144	36	13	bloch	bloch	PROPN
ejpam-144	36	14	space	space	PROPN
ejpam-144	36	15	b	b	PROPN
ejpam-144	36	16	.	.	PUNCT
ejpam-144	37	1	here	here	ADV
ejpam-144	37	2	,	,	PUNCT
ejpam-144	37	3	the	the	DET
ejpam-144	37	4	word	word	NOUN
ejpam-144	37	5	"	"	PUNCT
ejpam-144	37	6	reasonable	reasonable	ADJ
ejpam-144	37	7	"	"	PUNCT
ejpam-144	37	8	is	be	AUX
ejpam-144	37	9	a	a	DET
ejpam-144	37	10	non	non	ADJ
ejpam-144	37	11	-	-	ADJ
ejpam-144	37	12	mathematical	mathematical	ADJ
ejpam-144	37	13	term	term	NOUN
ejpam-144	37	14	;	;	PUNCT
ejpam-144	37	15	it	it	PRON
ejpam-144	37	16	was	be	AUX
ejpam-144	37	17	just	just	ADV
ejpam-144	37	18	intended	intend	VERB
ejpam-144	37	19	to	to	PART
ejpam-144	37	20	mean	mean	VERB
ejpam-144	37	21	that	that	SCONJ
ejpam-144	37	22	the	the	DET
ejpam-144	37	23	"	"	PUNCT
ejpam-144	37	24	not	not	PART
ejpam-144	37	25	too	too	ADV
ejpam-144	37	26	bad	bad	ADJ
ejpam-144	37	27	"	"	PUNCT
ejpam-144	37	28	and	and	CCONJ
ejpam-144	37	29	the	the	DET
ejpam-144	37	30	function	function	NOUN
ejpam-144	37	31	satisfy	satisfy	VERB
ejpam-144	37	32	some	some	DET
ejpam-144	37	33	natural	natural	ADJ
ejpam-144	37	34	conditions	condition	NOUN
ejpam-144	37	35	.	.	PUNCT
ejpam-144	38	1	now	now	ADV
ejpam-144	38	2	,	,	PUNCT
ejpam-144	38	3	we	we	PRON
ejpam-144	38	4	introduce	introduce	VERB
ejpam-144	38	5	the	the	DET
ejpam-144	38	6	following	following	ADJ
ejpam-144	38	7	definitions	definition	NOUN
ejpam-144	38	8	:	:	PUNCT
ejpam-144	38	9	r.	r.	PROPN
ejpam-144	38	10	rashwan	rashwan	PROPN
ejpam-144	38	11	,	,	PUNCT
ejpam-144	38	12	a.	a.	PROPN
ejpam-144	38	13	ahmed	ahmed	PROPN
ejpam-144	38	14	and	and	CCONJ
ejpam-144	38	15	a.	a.	PROPN
ejpam-144	38	16	kamal	kamal	PROPN
ejpam-144	38	17	/	/	SYM
ejpam-144	38	18	eur	eur	PROPN
ejpam-144	38	19	.	.	PUNCT
ejpam-144	39	1	j.	j.	PROPN
ejpam-144	39	2	pure	pure	PROPN
ejpam-144	39	3	appl	appl	PROPN
ejpam-144	39	4	.	.	PROPN
ejpam-144	39	5	math	math	PROPN
ejpam-144	39	6	,	,	PUNCT
ejpam-144	39	7	2	2	NUM
ejpam-144	39	8	(	(	PUNCT
ejpam-144	39	9	2009	2009	NUM
ejpam-144	39	10	)	)	PUNCT
ejpam-144	39	11	,	,	PUNCT
ejpam-144	39	12	(	(	PUNCT
ejpam-144	39	13	250	250	NUM
ejpam-144	39	14	-	-	SYM
ejpam-144	39	15	267	267	NUM
ejpam-144	39	16	)	)	PUNCT
ejpam-144	39	17	253	253	NUM
ejpam-144	39	18	definition	definition	NOUN
ejpam-144	39	19	1.1	1.1	NUM
ejpam-144	39	20	.	.	PUNCT
ejpam-144	40	1	for	for	ADP
ejpam-144	40	2	a	a	DET
ejpam-144	40	3	given	give	VERB
ejpam-144	40	4	reasonable	reasonable	ADJ
ejpam-144	40	5	functionω	functionω	NOUN
ejpam-144	40	6	:	:	PUNCT
ejpam-144	40	7	(	(	PUNCT
ejpam-144	40	8	0	0	NUM
ejpam-144	40	9	,	,	PUNCT
ejpam-144	40	10	1]→	1]→	NOUN
ejpam-144	41	1	[	[	X
ejpam-144	41	2	0,∞	0,∞	NOUN
ejpam-144	41	3	)	)	PUNCT
ejpam-144	41	4	and	and	CCONJ
ejpam-144	41	5	for	for	ADP
ejpam-144	41	6	0	0	NUM
ejpam-144	41	7	<	<	X
ejpam-144	41	8	α<∞.	α<∞.	NOUN
ejpam-144	41	9	an	an	DET
ejpam-144	41	10	analytic	analytic	ADJ
ejpam-144	41	11	function	function	NOUN
ejpam-144	41	12	f	f	PROPN
ejpam-144	41	13	on	on	ADP
ejpam-144	41	14	∆	∆	PROPN
ejpam-144	41	15	is	be	AUX
ejpam-144	41	16	said	say	VERB
ejpam-144	41	17	to	to	PART
ejpam-144	41	18	belong	belong	VERB
ejpam-144	41	19	to	to	ADP
ejpam-144	41	20	the	the	DET
ejpam-144	41	21	α−weighted	α−weighted	ADJ
ejpam-144	41	22	bloch	bloch	NOUN
ejpam-144	41	23	space	space	NOUN
ejpam-144	41	24	bα	bα	PROPN
ejpam-144	41	25	ω	ω	PROPN
ejpam-144	41	26	if	if	SCONJ
ejpam-144	41	27	‖	‖	PROPN
ejpam-144	41	28	f	f	PROPN
ejpam-144	41	29	‖bαω	‖bαω	PROPN
ejpam-144	41	30	=	=	SYM
ejpam-144	41	31	sup	sup	NOUN
ejpam-144	41	32	z∈∆	z∈∆	PUNCT
ejpam-144	41	33	(	(	PUNCT
ejpam-144	41	34	1−	1−	NUM
ejpam-144	41	35	|z|)α	|z|)α	NOUN
ejpam-144	41	36	ω(1−	ω(1−	NOUN
ejpam-144	41	37	|z|	|z|	NOUN
ejpam-144	41	38	)	)	PUNCT
ejpam-144	42	1	|	|	ADV
ejpam-144	42	2	f	f	PROPN
ejpam-144	42	3	′(z)|	′(z)|	PROPN
ejpam-144	43	1	<	<	X
ejpam-144	43	2	∞.	∞.	PROPN
ejpam-144	43	3	definition	definition	NOUN
ejpam-144	43	4	1.2	1.2	NUM
ejpam-144	43	5	.	.	PUNCT
ejpam-144	44	1	for	for	ADP
ejpam-144	44	2	a	a	DET
ejpam-144	44	3	given	give	VERB
ejpam-144	44	4	reasonable	reasonable	ADJ
ejpam-144	44	5	functionω	functionω	NOUN
ejpam-144	44	6	:	:	PUNCT
ejpam-144	44	7	(	(	PUNCT
ejpam-144	44	8	0	0	NUM
ejpam-144	44	9	,	,	PUNCT
ejpam-144	44	10	1]→	1]→	NOUN
ejpam-144	45	1	[	[	X
ejpam-144	45	2	0,∞	0,∞	NOUN
ejpam-144	45	3	)	)	PUNCT
ejpam-144	45	4	and	and	CCONJ
ejpam-144	45	5	for	for	ADP
ejpam-144	45	6	0	0	NUM
ejpam-144	45	7	<	<	X
ejpam-144	45	8	α<∞.	α<∞.	NOUN
ejpam-144	45	9	an	an	DET
ejpam-144	45	10	analytic	analytic	ADJ
ejpam-144	45	11	function	function	NOUN
ejpam-144	45	12	f	f	PROPN
ejpam-144	45	13	on	on	ADP
ejpam-144	45	14	∆	∆	PROPN
ejpam-144	45	15	is	be	AUX
ejpam-144	45	16	said	say	VERB
ejpam-144	45	17	to	to	PART
ejpam-144	45	18	belong	belong	VERB
ejpam-144	45	19	to	to	ADP
ejpam-144	45	20	the	the	DET
ejpam-144	45	21	little	little	ADJ
ejpam-144	45	22	weighted	weight	VERB
ejpam-144	45	23	bloch	bloch	PROPN
ejpam-144	45	24	space	space	PROPN
ejpam-144	45	25	bα	bα	PROPN
ejpam-144	46	1	ω,0	ω,0	NUM
ejpam-144	46	2	if	if	SCONJ
ejpam-144	46	3	‖	‖	PROPN
ejpam-144	46	4	f	f	PROPN
ejpam-144	46	5	‖bαω,0	‖bαω,0	PROPN
ejpam-144	46	6	=	=	SYM
ejpam-144	46	7	lim	lim	PROPN
ejpam-144	46	8	|z|→1−	|z|→1−	PROPN
ejpam-144	46	9	(	(	PUNCT
ejpam-144	46	10	1−	1−	NUM
ejpam-144	46	11	|z|)α	|z|)α	VERB
ejpam-144	46	12	ω(1−	ω(1−	NOUN
ejpam-144	46	13	|z|	|z|	NOUN
ejpam-144	46	14	)	)	PUNCT
ejpam-144	46	15	|	|	ADV
ejpam-144	46	16	f	f	PROPN
ejpam-144	46	17	′(z)|=	′(z)|=	PROPN
ejpam-144	46	18	0	0	NUM
ejpam-144	46	19	.	.	PUNCT
ejpam-144	47	1	throughout	throughout	ADP
ejpam-144	47	2	this	this	DET
ejpam-144	47	3	paper	paper	NOUN
ejpam-144	47	4	and	and	CCONJ
ejpam-144	47	5	for	for	ADP
ejpam-144	47	6	some	some	DET
ejpam-144	47	7	techniques	technique	NOUN
ejpam-144	47	8	we	we	PRON
ejpam-144	47	9	consider	consider	VERB
ejpam-144	47	10	the	the	DET
ejpam-144	47	11	case	case	NOUN
ejpam-144	47	12	of	of	ADP
ejpam-144	47	13	ω	ω	NUM
ejpam-144	47	14	6≡	6≡	NUM
ejpam-144	47	15	0	0	NUM
ejpam-144	47	16	.	.	PUNCT
ejpam-144	48	1	now	now	ADV
ejpam-144	48	2	,	,	PUNCT
ejpam-144	48	3	we	we	PRON
ejpam-144	48	4	introduce	introduce	VERB
ejpam-144	48	5	the	the	DET
ejpam-144	48	6	following	follow	VERB
ejpam-144	48	7	new	new	ADJ
ejpam-144	48	8	definition	definition	NOUN
ejpam-144	48	9	:	:	PUNCT
ejpam-144	48	10	definition	definition	NOUN
ejpam-144	48	11	1.3	1.3	NUM
ejpam-144	48	12	.	.	PUNCT
ejpam-144	49	1	for	for	ADP
ejpam-144	49	2	a	a	DET
ejpam-144	49	3	nondecreasing	nondecrease	VERB
ejpam-144	49	4	function	function	NOUN
ejpam-144	49	5	k	k	NOUN
ejpam-144	49	6	:	:	PUNCT
ejpam-144	50	1	[	[	X
ejpam-144	50	2	0,∞)→	0,∞)→	NOUN
ejpam-144	50	3	[	[	X
ejpam-144	50	4	0,∞	0,∞	NUM
ejpam-144	50	5	)	)	PUNCT
ejpam-144	50	6	,	,	PUNCT
ejpam-144	50	7	0	0	PUNCT
ejpam-144	50	8	<	<	X
ejpam-144	50	9	p	p	X
ejpam-144	50	10	<	<	X
ejpam-144	50	11	∞	∞	PROPN
ejpam-144	50	12	,	,	PUNCT
ejpam-144	50	13	and	and	CCONJ
ejpam-144	50	14	for	for	ADP
ejpam-144	50	15	a	a	DET
ejpam-144	50	16	given	give	VERB
ejpam-144	50	17	reasonable	reasonable	ADJ
ejpam-144	50	18	function	function	NOUN
ejpam-144	50	19	ω	ω	NOUN
ejpam-144	50	20	:	:	PUNCT
ejpam-144	50	21	(	(	PUNCT
ejpam-144	50	22	0	0	NUM
ejpam-144	50	23	,	,	PUNCT
ejpam-144	50	24	1]→	1]→	NOUN
ejpam-144	50	25	(	(	PUNCT
ejpam-144	50	26	0,∞	0,∞	NOUN
ejpam-144	50	27	)	)	PUNCT
ejpam-144	50	28	,	,	PUNCT
ejpam-144	50	29	an	an	DET
ejpam-144	50	30	analytic	analytic	ADJ
ejpam-144	50	31	function	function	NOUN
ejpam-144	50	32	f	f	PROPN
ejpam-144	50	33	in	in	ADP
ejpam-144	50	34	∆	∆	PROPN
ejpam-144	50	35	is	be	AUX
ejpam-144	50	36	said	say	VERB
ejpam-144	50	37	to	to	PART
ejpam-144	50	38	belong	belong	VERB
ejpam-144	50	39	to	to	ADP
ejpam-144	50	40	the	the	DET
ejpam-144	50	41	space	space	NOUN
ejpam-144	50	42	qk	qk	PROPN
ejpam-144	50	43	,	,	PUNCT
ejpam-144	50	44	ω	ω	PROPN
ejpam-144	50	45	if	if	SCONJ
ejpam-144	50	46	‖	‖	PROPN
ejpam-144	50	47	f	f	PROPN
ejpam-144	50	48	‖pk	‖pk	PROPN
ejpam-144	50	49	,	,	PUNCT
ejpam-144	50	50	ω	ω	NUM
ejpam-144	50	51	=	=	SYM
ejpam-144	50	52	sup	sup	PROPN
ejpam-144	50	53	a∈∆	a∈∆	NOUN
ejpam-144	50	54	∫	∫	PROPN
ejpam-144	50	55	∆	∆	PROPN
ejpam-144	50	56	�	�	PROPN
ejpam-144	50	57	�	�	PROPN
ejpam-144	50	58	f	f	PROPN
ejpam-144	50	59	′(z	′(z	NOUN
ejpam-144	50	60	)	)	PUNCT
ejpam-144	50	61	�	�	PROPN
ejpam-144	50	62	�	�	PROPN
ejpam-144	50	63	p	p	PROPN
ejpam-144	50	64	(	(	PUNCT
ejpam-144	50	65	1−	1−	NUM
ejpam-144	50	66	|z|)p	|z|)p	PROPN
ejpam-144	50	67	k(g(z	k(g(z	PROPN
ejpam-144	50	68	,	,	PUNCT
ejpam-144	50	69	a	a	PRON
ejpam-144	50	70	)	)	PUNCT
ejpam-144	50	71	)	)	PUNCT
ejpam-144	50	72	ωp(1−	ωp(1−	ADJ
ejpam-144	50	73	|z|	|z|	NOUN
ejpam-144	50	74	)	)	PUNCT
ejpam-144	50	75	dσz	dσz	NOUN
ejpam-144	50	76	<	<	X
ejpam-144	50	77	∞.	∞.	PROPN
ejpam-144	50	78	remark	remark	VERB
ejpam-144	50	79	1.1	1.1	NUM
ejpam-144	50	80	.	.	PUNCT
ejpam-144	51	1	it	it	PRON
ejpam-144	51	2	should	should	AUX
ejpam-144	51	3	be	be	AUX
ejpam-144	51	4	remarked	remark	VERB
ejpam-144	51	5	that	that	SCONJ
ejpam-144	51	6	our	our	PRON
ejpam-144	51	7	qk	qk	PROPN
ejpam-144	51	8	,	,	PUNCT
ejpam-144	51	9	ω	ω	PROPN
ejpam-144	51	10	classes	class	NOUN
ejpam-144	51	11	are	be	AUX
ejpam-144	51	12	more	more	ADV
ejpam-144	51	13	general	general	ADJ
ejpam-144	51	14	than	than	ADP
ejpam-144	51	15	many	many	ADJ
ejpam-144	51	16	classes	class	NOUN
ejpam-144	51	17	of	of	ADP
ejpam-144	51	18	analytic	analytic	ADJ
ejpam-144	51	19	functions	function	NOUN
ejpam-144	51	20	.	.	PUNCT
ejpam-144	52	1	if	if	SCONJ
ejpam-144	52	2	ω	ω	PROPN
ejpam-144	52	3	≡	≡	PROPN
ejpam-144	52	4	1	1	NUM
ejpam-144	52	5	,	,	PUNCT
ejpam-144	52	6	we	we	PRON
ejpam-144	52	7	obtain	obtain	VERB
ejpam-144	52	8	qk(p	qk(p	PUNCT
ejpam-144	52	9	,	,	PUNCT
ejpam-144	52	10	p	p	X
ejpam-144	52	11	)	)	PUNCT
ejpam-144	52	12	type	type	NOUN
ejpam-144	52	13	spaces	space	NOUN
ejpam-144	52	14	(	(	PUNCT
ejpam-144	52	15	cf	cf	NOUN
ejpam-144	52	16	.	.	PUNCT
ejpam-144	53	1	[	[	X
ejpam-144	53	2	14	14	NUM
ejpam-144	53	3	]	]	PUNCT
ejpam-144	53	4	and	and	CCONJ
ejpam-144	53	5	[	[	X
ejpam-144	53	6	15	15	NUM
ejpam-144	53	7	]	]	PUNCT
ejpam-144	53	8	)	)	PUNCT
ejpam-144	53	9	.	.	PUNCT
ejpam-144	54	1	if	if	SCONJ
ejpam-144	54	2	p	p	NOUN
ejpam-144	54	3	=	=	NOUN
ejpam-144	54	4	2	2	NUM
ejpam-144	54	5	,	,	PUNCT
ejpam-144	54	6	and	and	CCONJ
ejpam-144	54	7	ω(t	ω(t	NOUN
ejpam-144	54	8	)	)	PUNCT
ejpam-144	54	9	=	=	SYM
ejpam-144	54	10	t	t	PROPN
ejpam-144	54	11	,	,	PUNCT
ejpam-144	54	12	we	we	PRON
ejpam-144	54	13	obtain	obtain	VERB
ejpam-144	54	14	qk	qk	NOUN
ejpam-144	54	15	spaces	space	NOUN
ejpam-144	54	16	as	as	SCONJ
ejpam-144	54	17	studied	study	VERB
ejpam-144	54	18	recently	recently	ADV
ejpam-144	54	19	in	in	ADP
ejpam-144	54	20	[	[	X
ejpam-144	54	21	5	5	NUM
ejpam-144	54	22	,	,	PUNCT
ejpam-144	54	23	6	6	NUM
ejpam-144	54	24	,	,	PUNCT
ejpam-144	54	25	9	9	NUM
ejpam-144	54	26	,	,	PUNCT
ejpam-144	54	27	12	12	NUM
ejpam-144	54	28	,	,	PUNCT
ejpam-144	54	29	13	13	NUM
ejpam-144	54	30	,	,	PUNCT
ejpam-144	54	31	16	16	NUM
ejpam-144	54	32	]	]	PUNCT
ejpam-144	54	33	and	and	CCONJ
ejpam-144	54	34	others	other	NOUN
ejpam-144	54	35	.	.	PUNCT
ejpam-144	55	1	if	if	SCONJ
ejpam-144	55	2	p	p	NOUN
ejpam-144	55	3	=	=	NOUN
ejpam-144	55	4	2	2	NUM
ejpam-144	55	5	,	,	PUNCT
ejpam-144	55	6	ω(t	ω(t	NOUN
ejpam-144	55	7	)	)	PUNCT
ejpam-144	55	8	=	=	SYM
ejpam-144	55	9	t	t	PROPN
ejpam-144	55	10	and	and	CCONJ
ejpam-144	55	11	k(t	k(t	PROPN
ejpam-144	55	12	)	)	PUNCT
ejpam-144	56	1	=	=	SYM
ejpam-144	56	2	t	t	PROPN
ejpam-144	56	3	p	p	NOUN
ejpam-144	56	4	,	,	PUNCT
ejpam-144	56	5	we	we	PRON
ejpam-144	56	6	obtain	obtain	VERB
ejpam-144	56	7	qp	qp	ADP
ejpam-144	56	8	spaces	space	NOUN
ejpam-144	56	9	as	as	SCONJ
ejpam-144	56	10	studied	study	VERB
ejpam-144	56	11	in	in	ADP
ejpam-144	56	12	[	[	X
ejpam-144	56	13	2	2	NUM
ejpam-144	56	14	,	,	PUNCT
ejpam-144	56	15	3	3	NUM
ejpam-144	56	16	,	,	PUNCT
ejpam-144	56	17	17	17	NUM
ejpam-144	56	18	]	]	PUNCT
ejpam-144	56	19	and	and	CCONJ
ejpam-144	56	20	others	other	NOUN
ejpam-144	56	21	.	.	PUNCT
ejpam-144	57	1	if	if	SCONJ
ejpam-144	57	2	ω	ω	PROPN
ejpam-144	57	3	≡	≡	PROPN
ejpam-144	57	4	1	1	NUM
ejpam-144	57	5	and	and	CCONJ
ejpam-144	57	6	k(t	k(t	PROPN
ejpam-144	57	7	)	)	PUNCT
ejpam-144	57	8	=	=	SYM
ejpam-144	57	9	t	t	PROPN
ejpam-144	57	10	s	s	PROPN
ejpam-144	57	11	,	,	PUNCT
ejpam-144	57	12	then	then	ADV
ejpam-144	57	13	qk	qk	PROPN
ejpam-144	57	14	,	,	PUNCT
ejpam-144	57	15	ω	ω	PROPN
ejpam-144	57	16	=	=	SYM
ejpam-144	57	17	f(p	f(p	PROPN
ejpam-144	57	18	,	,	PUNCT
ejpam-144	57	19	p	p	X
ejpam-144	57	20	,	,	PUNCT
ejpam-144	57	21	s	s	NOUN
ejpam-144	57	22	)	)	PUNCT
ejpam-144	57	23	classes	class	NOUN
ejpam-144	57	24	(	(	PUNCT
ejpam-144	57	25	cf	cf	NOUN
ejpam-144	57	26	.	.	PUNCT
ejpam-144	58	1	[	[	X
ejpam-144	58	2	1,18	1,18	X
ejpam-144	58	3	]	]	X
ejpam-144	58	4	)	)	PUNCT
ejpam-144	58	5	.	.	PUNCT
ejpam-144	59	1	in	in	ADP
ejpam-144	59	2	this	this	DET
ejpam-144	59	3	paper	paper	NOUN
ejpam-144	59	4	,	,	PUNCT
ejpam-144	59	5	we	we	PRON
ejpam-144	59	6	characterize	characterize	VERB
ejpam-144	59	7	the	the	DET
ejpam-144	59	8	weighted	weight	VERB
ejpam-144	59	9	bloch	bloch	PROPN
ejpam-144	59	10	space	space	PROPN
ejpam-144	59	11	bα	bα	PROPN
ejpam-144	59	12	ω	ω	PROPN
ejpam-144	59	13	by	by	ADP
ejpam-144	59	14	our	our	PRON
ejpam-144	59	15	qk	qk	PROPN
ejpam-144	59	16	,	,	PUNCT
ejpam-144	59	17	ω	ω	PROPN
ejpam-144	59	18	spaces	space	NOUN
ejpam-144	59	19	.	.	PUNCT
ejpam-144	60	1	one	one	NUM
ejpam-144	60	2	of	of	ADP
ejpam-144	60	3	the	the	DET
ejpam-144	60	4	main	main	ADJ
ejpam-144	60	5	results	result	NOUN
ejpam-144	60	6	is	be	AUX
ejpam-144	60	7	a	a	DET
ejpam-144	60	8	general	general	ADJ
ejpam-144	60	9	besov	besov	NOUN
ejpam-144	60	10	-	-	PUNCT
ejpam-144	60	11	type	type	NOUN
ejpam-144	60	12	characterization	characterization	NOUN
ejpam-144	60	13	forbα	forbα	NOUN
ejpam-144	60	14	ω	ω	NUM
ejpam-144	60	15	functions	function	NOUN
ejpam-144	60	16	that	that	PRON
ejpam-144	60	17	extends	extend	VERB
ejpam-144	60	18	and	and	CCONJ
ejpam-144	60	19	generalizes	generalize	VERB
ejpam-144	60	20	the	the	DET
ejpam-144	60	21	stroethoff	stroethoff	NOUN
ejpam-144	60	22	’s	’s	PART
ejpam-144	60	23	theorem	theorem	NOUN
ejpam-144	60	24	[	[	PUNCT
ejpam-144	60	25	11	11	NUM
ejpam-144	60	26	]	]	PUNCT
ejpam-144	60	27	.	.	PUNCT
ejpam-144	61	1	also	also	ADV
ejpam-144	61	2	,	,	PUNCT
ejpam-144	61	3	we	we	PRON
ejpam-144	61	4	extend	extend	VERB
ejpam-144	61	5	and	and	CCONJ
ejpam-144	61	6	improve	improve	VERB
ejpam-144	61	7	some	some	DET
ejpam-144	61	8	results	result	NOUN
ejpam-144	61	9	due	due	ADP
ejpam-144	61	10	to	to	ADP
ejpam-144	61	11	essén	essén	VERB
ejpam-144	61	12	et	et	NOUN
ejpam-144	61	13	.	.	PUNCT
ejpam-144	62	1	al	al	PROPN
ejpam-144	63	1	[	[	X
ejpam-144	63	2	6	6	NUM
ejpam-144	63	3	]	]	PUNCT
ejpam-144	63	4	using	use	VERB
ejpam-144	63	5	our	our	PRON
ejpam-144	63	6	new	new	ADJ
ejpam-144	63	7	definitions	definition	NOUN
ejpam-144	63	8	.	.	PUNCT
ejpam-144	64	1	r.	r.	PROPN
ejpam-144	64	2	rashwan	rashwan	PROPN
ejpam-144	64	3	,	,	PUNCT
ejpam-144	64	4	a.	a.	PROPN
ejpam-144	64	5	ahmed	ahmed	PROPN
ejpam-144	64	6	and	and	CCONJ
ejpam-144	64	7	a.	a.	PROPN
ejpam-144	64	8	kamal	kamal	PROPN
ejpam-144	64	9	/	/	SYM
ejpam-144	64	10	eur	eur	PROPN
ejpam-144	64	11	.	.	PUNCT
ejpam-144	65	1	j.	j.	PROPN
ejpam-144	65	2	pure	pure	PROPN
ejpam-144	65	3	appl	appl	PROPN
ejpam-144	65	4	.	.	PROPN
ejpam-144	65	5	math	math	PROPN
ejpam-144	65	6	,	,	PUNCT
ejpam-144	65	7	2	2	NUM
ejpam-144	65	8	(	(	PUNCT
ejpam-144	65	9	2009	2009	NUM
ejpam-144	65	10	)	)	PUNCT
ejpam-144	65	11	,	,	PUNCT
ejpam-144	65	12	(	(	PUNCT
ejpam-144	65	13	250	250	NUM
ejpam-144	65	14	-	-	SYM
ejpam-144	65	15	267	267	NUM
ejpam-144	65	16	)	)	PUNCT
ejpam-144	65	17	254	254	NUM
ejpam-144	65	18	2	2	NUM
ejpam-144	65	19	.	.	X
ejpam-144	65	20	holomorphic	holomorphic	ADJ
ejpam-144	65	21	qk	qk	PROPN
ejpam-144	65	22	,	,	PUNCT
ejpam-144	65	23	ω	ω	PROPN
ejpam-144	65	24	classes	class	NOUN
ejpam-144	65	25	in	in	ADP
ejpam-144	65	26	this	this	DET
ejpam-144	65	27	paper	paper	NOUN
ejpam-144	65	28	we	we	PRON
ejpam-144	65	29	show	show	VERB
ejpam-144	65	30	some	some	DET
ejpam-144	65	31	relations	relation	NOUN
ejpam-144	65	32	between	between	ADP
ejpam-144	65	33	qk	qk	PROPN
ejpam-144	65	34	,	,	PUNCT
ejpam-144	65	35	ω	ω	NUM
ejpam-144	65	36	norms	norm	NOUN
ejpam-144	65	37	and	and	CCONJ
ejpam-144	65	38	bα	bα	PROPN
ejpam-144	65	39	ω	ω	NUM
ejpam-144	65	40	norms	norm	NOUN
ejpam-144	65	41	for	for	ADP
ejpam-144	65	42	a	a	DET
ejpam-144	65	43	nondecreasing	nondecrease	VERB
ejpam-144	65	44	function	function	NOUN
ejpam-144	65	45	k	k	PROPN
ejpam-144	65	46	,	,	PUNCT
ejpam-144	65	47	,	,	PUNCT
ejpam-144	65	48	also	also	ADV
ejpam-144	65	49	we	we	PRON
ejpam-144	65	50	give	give	VERB
ejpam-144	65	51	a	a	DET
ejpam-144	65	52	general	general	ADJ
ejpam-144	65	53	way	way	NOUN
ejpam-144	65	54	to	to	PART
ejpam-144	65	55	construct	construct	VERB
ejpam-144	65	56	different	different	ADJ
ejpam-144	65	57	spaces	space	NOUN
ejpam-144	65	58	qk	qk	NOUN
ejpam-144	65	59	,	,	PUNCT
ejpam-144	65	60	ω1	ω1	PROPN
ejpam-144	65	61	and	and	CCONJ
ejpam-144	65	62	qk2,ω	qk2,ω	NOUN
ejpam-144	65	63	by	by	ADP
ejpam-144	65	64	using	use	VERB
ejpam-144	65	65	some	some	DET
ejpam-144	65	66	functions	function	NOUN
ejpam-144	65	67	k1	k1	NOUN
ejpam-144	65	68	and	and	CCONJ
ejpam-144	65	69	k2	k2	NOUN
ejpam-144	65	70	.	.	PUNCT
ejpam-144	66	1	before	before	ADP
ejpam-144	66	2	proving	prove	VERB
ejpam-144	66	3	theorems	theorem	NOUN
ejpam-144	66	4	we	we	PRON
ejpam-144	66	5	recall	recall	VERB
ejpam-144	66	6	few	few	ADJ
ejpam-144	66	7	facts	fact	NOUN
ejpam-144	66	8	about	about	ADP
ejpam-144	66	9	the	the	DET
ejpam-144	66	10	möbius	möbius	NOUN
ejpam-144	66	11	function	function	NOUN
ejpam-144	66	12	ϕa	ϕa	PROPN
ejpam-144	66	13	.	.	PUNCT
ejpam-144	67	1	first	first	ADV
ejpam-144	67	2	,	,	PUNCT
ejpam-144	67	3	the	the	DET
ejpam-144	67	4	function	function	NOUN
ejpam-144	67	5	ϕa	ϕa	NOUN
ejpam-144	67	6	is	be	AUX
ejpam-144	67	7	easily	easily	ADV
ejpam-144	67	8	seen	see	VERB
ejpam-144	67	9	to	to	PART
ejpam-144	67	10	be	be	AUX
ejpam-144	67	11	it	it	PRON
ejpam-144	67	12	own	own	ADJ
ejpam-144	67	13	inverse	inverse	NOUN
ejpam-144	67	14	under	under	ADP
ejpam-144	67	15	composition	composition	NOUN
ejpam-144	67	16	:	:	PUNCT
ejpam-144	67	17	(	(	PUNCT
ejpam-144	67	18	ϕa	ϕa	PROPN
ejpam-144	67	19	◦	◦	NOUN
ejpam-144	67	20	ϕa)(z	ϕa)(z	PROPN
ejpam-144	67	21	)	)	PUNCT
ejpam-144	68	1	=	=	SYM
ejpam-144	68	2	z	z	NOUN
ejpam-144	68	3	for	for	ADP
ejpam-144	68	4	all	all	DET
ejpam-144	68	5	z	z	NOUN
ejpam-144	68	6	∈∆	∈∆	VERB
ejpam-144	68	7	the	the	DET
ejpam-144	68	8	following	follow	VERB
ejpam-144	68	9	identity	identity	NOUN
ejpam-144	68	10	can	can	AUX
ejpam-144	68	11	be	be	AUX
ejpam-144	68	12	obtained	obtain	VERB
ejpam-144	68	13	by	by	ADP
ejpam-144	68	14	straight	straight	ADJ
ejpam-144	68	15	forward	forward	ADJ
ejpam-144	68	16	computation	computation	NOUN
ejpam-144	68	17	:	:	PUNCT
ejpam-144	68	18	1−	1−	NUM
ejpam-144	68	19	|ϕa(z)|	|ϕa(z)|	ADJ
ejpam-144	68	20	2	2	NUM
ejpam-144	68	21	=	=	SYM
ejpam-144	68	22	(	(	PUNCT
ejpam-144	68	23	1−	1−	NUM
ejpam-144	68	24	|a|2)(1−	|a|2)(1−	PUNCT
ejpam-144	68	25	|z|2	|z|2	PROPN
ejpam-144	68	26	)	)	PUNCT
ejpam-144	68	27	|1−	|1−	VERB
ejpam-144	68	28	az|2	az|2	NOUN
ejpam-144	68	29	,	,	PUNCT
ejpam-144	68	30	(	(	PUNCT
ejpam-144	68	31	a	a	X
ejpam-144	68	32	,	,	PUNCT
ejpam-144	68	33	z	z	NOUN
ejpam-144	68	34	∈∆	∈∆	NOUN
ejpam-144	68	35	)	)	PUNCT
ejpam-144	68	36	.	.	PUNCT
ejpam-144	69	1	a	a	DET
ejpam-144	69	2	slightly	slightly	ADV
ejpam-144	69	3	different	different	ADJ
ejpam-144	69	4	form	form	NOUN
ejpam-144	69	5	in	in	ADP
ejpam-144	69	6	which	which	PRON
ejpam-144	69	7	we	we	PRON
ejpam-144	69	8	will	will	AUX
ejpam-144	69	9	apply	apply	VERB
ejpam-144	69	10	the	the	DET
ejpam-144	69	11	above	above	ADJ
ejpam-144	69	12	identity	identity	NOUN
ejpam-144	69	13	is	be	AUX
ejpam-144	69	14	:	:	PUNCT
ejpam-144	69	15	1−	1−	NUM
ejpam-144	69	16	|ϕa(z)|	|ϕa(z)|	ADJ
ejpam-144	69	17	2	2	NUM
ejpam-144	69	18	1−	1−	NUM
ejpam-144	69	19	|z|2	|z|2	NOUN
ejpam-144	69	20	=	=	SYM
ejpam-144	69	21	|ϕ′	|ϕ′	PROPN
ejpam-144	69	22	a	a	DET
ejpam-144	69	23	(	(	PUNCT
ejpam-144	69	24	z)|	z)|	INTJ
ejpam-144	69	25	,	,	PUNCT
ejpam-144	69	26	(	(	PUNCT
ejpam-144	69	27	a	a	X
ejpam-144	69	28	,	,	PUNCT
ejpam-144	69	29	z	z	NOUN
ejpam-144	69	30	∈∆	∈∆	NOUN
ejpam-144	69	31	)	)	PUNCT
ejpam-144	69	32	.	.	PUNCT
ejpam-144	70	1	(	(	PUNCT
ejpam-144	70	2	2.1	2.1	NUM
ejpam-144	70	3	)	)	PUNCT
ejpam-144	70	4	for	for	ADP
ejpam-144	70	5	a	a	DET
ejpam-144	70	6	∈	∈	PROPN
ejpam-144	70	7	∆	∆	PROPN
ejpam-144	70	8	,	,	PUNCT
ejpam-144	70	9	the	the	DET
ejpam-144	70	10	substitution	substitution	NOUN
ejpam-144	70	11	z	z	NOUN
ejpam-144	70	12	=	=	SYM
ejpam-144	70	13	ϕa(w	ϕa(w	X
ejpam-144	70	14	)	)	PUNCT
ejpam-144	70	15	results	result	NOUN
ejpam-144	70	16	in	in	ADP
ejpam-144	70	17	the	the	DET
ejpam-144	70	18	jacobian	jacobian	ADJ
ejpam-144	70	19	change	change	NOUN
ejpam-144	70	20	in	in	ADP
ejpam-144	70	21	measure	measure	NOUN
ejpam-144	70	22	given	give	VERB
ejpam-144	70	23	by	by	ADP
ejpam-144	70	24	dσw	dσw	ADJ
ejpam-144	70	25	=	=	SYM
ejpam-144	70	26	|ϕ	|ϕ	VERB
ejpam-144	70	27	′	′	NUM
ejpam-144	70	28	a	a	DET
ejpam-144	70	29	(	(	PUNCT
ejpam-144	70	30	z)|2dσz	z)|2dσz	X
ejpam-144	70	31	.	.	PUNCT
ejpam-144	71	1	for	for	SCONJ
ejpam-144	71	2	a	a	DET
ejpam-144	71	3	lebesgue	lebesgue	NOUN
ejpam-144	71	4	integrable	integrable	ADJ
ejpam-144	71	5	or	or	CCONJ
ejpam-144	71	6	a	a	DET
ejpam-144	71	7	non	non	ADJ
ejpam-144	71	8	-	-	ADJ
ejpam-144	71	9	negative	negative	ADJ
ejpam-144	71	10	lebesgue	lebesgue	ADJ
ejpam-144	71	11	measurable	measurable	ADJ
ejpam-144	71	12	function	function	NOUN
ejpam-144	71	13	h	h	NOUN
ejpam-144	71	14	on	on	ADP
ejpam-144	71	15	∆	∆	PROPN
ejpam-144	71	16	we	we	PRON
ejpam-144	71	17	thus	thus	ADV
ejpam-144	71	18	have	have	VERB
ejpam-144	71	19	the	the	DET
ejpam-144	71	20	following	follow	VERB
ejpam-144	71	21	change	change	NOUN
ejpam-144	71	22	-	-	PUNCT
ejpam-144	71	23	of	of	ADP
ejpam-144	71	24	-	-	PUNCT
ejpam-144	71	25	variable	variable	ADJ
ejpam-144	71	26	formula	formula	NOUN
ejpam-144	71	27	:	:	PUNCT
ejpam-144	71	28	∫	∫	PROPN
ejpam-144	71	29	∆(0,r	∆(0,r	ADV
ejpam-144	71	30	)	)	PUNCT
ejpam-144	71	31	h(ϕa(w))dσw	h(ϕa(w))dσw	ADJ
ejpam-144	71	32	=	=	SYM
ejpam-144	71	33	∫	∫	PROPN
ejpam-144	71	34	∆(a	∆(a	PROPN
ejpam-144	71	35	,	,	PUNCT
ejpam-144	71	36	r	r	NOUN
ejpam-144	71	37	)	)	PUNCT
ejpam-144	71	38	h(z	h(z	PROPN
ejpam-144	71	39	)	)	PUNCT
ejpam-144	71	40	�	�	PROPN
ejpam-144	71	41	1−	1−	NUM
ejpam-144	71	42	|ϕa(z)|	|ϕa(z)|	ADJ
ejpam-144	71	43	2	2	NUM
ejpam-144	71	44	1−	1−	NUM
ejpam-144	71	45	|z|2	|z|2	NOUN
ejpam-144	71	46	�	�	NOUN
ejpam-144	71	47	2	2	NUM
ejpam-144	71	48	dσz	dσz	NOUN
ejpam-144	71	49	.	.	PUNCT
ejpam-144	72	1	(	(	PUNCT
ejpam-144	72	2	2.2	2.2	NUM
ejpam-144	72	3	)	)	PUNCT
ejpam-144	72	4	we	we	PRON
ejpam-144	72	5	assume	assume	VERB
ejpam-144	72	6	throughout	throughout	ADP
ejpam-144	72	7	this	this	DET
ejpam-144	72	8	paper	paper	NOUN
ejpam-144	72	9	that	that	PRON
ejpam-144	72	10	∫	∫	PROPN
ejpam-144	72	11	1	1	NUM
ejpam-144	72	12	0	0	NUM
ejpam-144	72	13	k	k	PROPN
ejpam-144	72	14	�	�	PROPN
ejpam-144	72	15	log	log	VERB
ejpam-144	72	16	1	1	NUM
ejpam-144	72	17	r	r	NOUN
ejpam-144	72	18	�	�	PROPN
ejpam-144	72	19	r	r	NOUN
ejpam-144	72	20	(	(	PUNCT
ejpam-144	72	21	1−	1−	NUM
ejpam-144	72	22	r2)2	r2)2	NOUN
ejpam-144	72	23	dr	dr	PROPN
ejpam-144	72	24	<	<	X
ejpam-144	72	25	∞	∞	PROPN
ejpam-144	72	26	.	.	PUNCT
ejpam-144	73	1	(	(	PUNCT
ejpam-144	73	2	2.3	2.3	NUM
ejpam-144	73	3	)	)	PUNCT
ejpam-144	73	4	we	we	PRON
ejpam-144	73	5	need	need	VERB
ejpam-144	73	6	the	the	DET
ejpam-144	73	7	following	follow	VERB
ejpam-144	73	8	lemmas	lemma	NOUN
ejpam-144	73	9	in	in	ADP
ejpam-144	73	10	the	the	DET
ejpam-144	73	11	sequel	sequel	NOUN
ejpam-144	73	12	.	.	PUNCT
ejpam-144	74	1	lemma	lemma	PROPN
ejpam-144	74	2	2.1	2.1	NUM
ejpam-144	74	3	.	.	PUNCT
ejpam-144	75	1	[	[	X
ejpam-144	75	2	17	17	NUM
ejpam-144	75	3	]	]	PUNCT
ejpam-144	75	4	let	let	VERB
ejpam-144	75	5	α	α	PRON
ejpam-144	75	6	∈	∈	PROPN
ejpam-144	75	7	(	(	PUNCT
ejpam-144	75	8	0,∞	0,∞	NOUN
ejpam-144	75	9	)	)	PUNCT
ejpam-144	75	10	and	and	CCONJ
ejpam-144	75	11	suppose	suppose	VERB
ejpam-144	75	12	that	that	SCONJ
ejpam-144	75	13	f	f	PROPN
ejpam-144	75	14	(	(	PUNCT
ejpam-144	75	15	z	z	NOUN
ejpam-144	75	16	)	)	PUNCT
ejpam-144	75	17	=	=	SYM
ejpam-144	76	1	∞	∞	NUM
ejpam-144	76	2	∑	∑	PUNCT
ejpam-144	76	3	j=1	j=1	PROPN
ejpam-144	76	4	a	a	DET
ejpam-144	76	5	jz	jz	PROPN
ejpam-144	76	6	n	n	PROPN
ejpam-144	76	7	j	j	PROPN
ejpam-144	76	8	belongs	belong	VERB
ejpam-144	76	9	to	to	ADP
ejpam-144	76	10	hadamard	hadamard	ADJ
ejpam-144	76	11	gap	gap	NOUN
ejpam-144	76	12	class	class	NOUN
ejpam-144	76	13	.	.	PUNCT
ejpam-144	77	1	then	then	ADV
ejpam-144	77	2	f	f	PROPN
ejpam-144	77	3	∈bα	∈bα	PROPN
ejpam-144	77	4	if	if	SCONJ
ejpam-144	77	5	and	and	CCONJ
ejpam-144	77	6	only	only	ADV
ejpam-144	77	7	if	if	SCONJ
ejpam-144	77	8	sup	sup	NOUN
ejpam-144	77	9	j∈n	j∈n	NOUN
ejpam-144	77	10	|a	|a	X
ejpam-144	77	11	j|n	j|n	NOUN
ejpam-144	78	1	1−α	1−α	NUM
ejpam-144	78	2	j	j	PROPN
ejpam-144	78	3	<	<	X
ejpam-144	78	4	∞	∞	PROPN
ejpam-144	78	5	,	,	PUNCT
ejpam-144	78	6	where	where	SCONJ
ejpam-144	78	7	n	n	ADV
ejpam-144	78	8	=	=	SYM
ejpam-144	78	9	{	{	PUNCT
ejpam-144	78	10	1	1	NUM
ejpam-144	78	11	,	,	PUNCT
ejpam-144	78	12	2	2	NUM
ejpam-144	78	13	,	,	PUNCT
ejpam-144	78	14	3	3	NUM
ejpam-144	78	15	,	,	PUNCT
ejpam-144	78	16	.	.	PUNCT
ejpam-144	78	17	.	.	PUNCT
ejpam-144	78	18	.	.	PUNCT
ejpam-144	78	19	}	}	PUNCT
ejpam-144	78	20	.	.	PUNCT
ejpam-144	79	1	r.	r.	PROPN
ejpam-144	79	2	rashwan	rashwan	PROPN
ejpam-144	79	3	,	,	PUNCT
ejpam-144	79	4	a.	a.	PROPN
ejpam-144	79	5	ahmed	ahmed	PROPN
ejpam-144	79	6	and	and	CCONJ
ejpam-144	79	7	a.	a.	PROPN
ejpam-144	79	8	kamal	kamal	PROPN
ejpam-144	79	9	/	/	SYM
ejpam-144	79	10	eur	eur	PROPN
ejpam-144	79	11	.	.	PUNCT
ejpam-144	80	1	j.	j.	PROPN
ejpam-144	80	2	pure	pure	PROPN
ejpam-144	80	3	appl	appl	PROPN
ejpam-144	80	4	.	.	PROPN
ejpam-144	80	5	math	math	PROPN
ejpam-144	80	6	,	,	PUNCT
ejpam-144	80	7	2	2	NUM
ejpam-144	80	8	(	(	PUNCT
ejpam-144	80	9	2009	2009	NUM
ejpam-144	80	10	)	)	PUNCT
ejpam-144	80	11	,	,	PUNCT
ejpam-144	80	12	(	(	PUNCT
ejpam-144	80	13	250	250	NUM
ejpam-144	80	14	-	-	SYM
ejpam-144	80	15	267	267	NUM
ejpam-144	80	16	)	)	PUNCT
ejpam-144	80	17	255	255	NUM
ejpam-144	81	1	lemma	lemma	PROPN
ejpam-144	81	2	2.2	2.2	NUM
ejpam-144	81	3	.	.	PUNCT
ejpam-144	82	1	let	let	VERB
ejpam-144	82	2	ω	ω	NOUN
ejpam-144	82	3	:	:	PUNCT
ejpam-144	82	4	(	(	PUNCT
ejpam-144	82	5	0	0	NUM
ejpam-144	82	6	,	,	PUNCT
ejpam-144	82	7	1]→	1]→	NOUN
ejpam-144	82	8	(	(	PUNCT
ejpam-144	82	9	0,∞	0,∞	NOUN
ejpam-144	82	10	)	)	PUNCT
ejpam-144	82	11	be	be	AUX
ejpam-144	82	12	a	a	DET
ejpam-144	82	13	nondecreasing	nondecreasing	ADJ
ejpam-144	82	14	function	function	NOUN
ejpam-144	82	15	.	.	PUNCT
ejpam-144	83	1	then	then	ADV
ejpam-144	83	2	there	there	PRON
ejpam-144	83	3	are	be	VERB
ejpam-144	83	4	two	two	NUM
ejpam-144	83	5	functions	function	NOUN
ejpam-144	83	6	f1	f1	NOUN
ejpam-144	83	7	,	,	PUNCT
ejpam-144	83	8	f2	f2	PROPN
ejpam-144	83	9	∈bω	∈bω	ADJ
ejpam-144	83	10	such	such	ADJ
ejpam-144	83	11	that	that	SCONJ
ejpam-144	84	1	|	|	INTJ
ejpam-144	84	2	f	f	NOUN
ejpam-144	85	1	′	′	NOUN
ejpam-144	85	2	1	1	NUM
ejpam-144	86	1	(	(	PUNCT
ejpam-144	86	2	z)|+	z)|+	PROPN
ejpam-144	86	3	|	|	NOUN
ejpam-144	86	4	f	f	NOUN
ejpam-144	86	5	′	′	NOUN
ejpam-144	86	6	2	2	NUM
ejpam-144	87	1	(	(	PUNCT
ejpam-144	87	2	z)|	z)|	PROPN
ejpam-144	87	3	≈	≈	PROPN
ejpam-144	87	4	ω(1−	ω(1−	PROPN
ejpam-144	87	5	|z|	|z|	NOUN
ejpam-144	87	6	)	)	PUNCT
ejpam-144	87	7	(	(	PUNCT
ejpam-144	87	8	1−	1−	NUM
ejpam-144	87	9	|z|	|z|	NOUN
ejpam-144	87	10	)	)	PUNCT
ejpam-144	87	11	,	,	PUNCT
ejpam-144	87	12	z	z	PROPN
ejpam-144	87	13	∈∆.	∈∆.	PROPN
ejpam-144	87	14	(	(	PUNCT
ejpam-144	87	15	2.4	2.4	NUM
ejpam-144	87	16	)	)	PUNCT
ejpam-144	87	17	proof	proof	NOUN
ejpam-144	87	18	.	.	PUNCT
ejpam-144	88	1	for	for	ADP
ejpam-144	88	2	a	a	DET
ejpam-144	88	3	large	large	ADJ
ejpam-144	88	4	number	number	NOUN
ejpam-144	88	5	q	q	X
ejpam-144	88	6	∈	∈	PROPN
ejpam-144	88	7	n	n	CCONJ
ejpam-144	88	8	,	,	PUNCT
ejpam-144	88	9	choose	choose	VERB
ejpam-144	88	10	a	a	DET
ejpam-144	88	11	gap	gap	NOUN
ejpam-144	88	12	series	series	NOUN
ejpam-144	88	13	:	:	PUNCT
ejpam-144	88	14	f1(z	f1(z	X
ejpam-144	88	15	)	)	PUNCT
ejpam-144	88	16	=	=	SYM
ejpam-144	89	1	∞	∞	PROPN
ejpam-144	89	2	∑	∑	PUNCT
ejpam-144	89	3	j=0	j=0	PROPN
ejpam-144	89	4	zq	zq	PROPN
ejpam-144	89	5	j	j	PROPN
ejpam-144	89	6	,	,	PUNCT
ejpam-144	89	7	z	z	PROPN
ejpam-144	89	8	∈∆.	∈∆.	PROPN
ejpam-144	89	9	then	then	ADV
ejpam-144	89	10	,	,	PUNCT
ejpam-144	89	11	apply	apply	VERB
ejpam-144	89	12	lemma	lemma	PROPN
ejpam-144	89	13	2.1	2.1	NUM
ejpam-144	89	14	to	to	PART
ejpam-144	89	15	infer	infer	VERB
ejpam-144	89	16	that	that	SCONJ
ejpam-144	89	17	(	(	PUNCT
ejpam-144	89	18	1−|z|)|	1−|z|)|	NUM
ejpam-144	89	19	f	f	PROPN
ejpam-144	89	20	′1(z)|	′1(z)|	PROPN
ejpam-144	89	21	ω((1−|z|	ω((1−|z|	NOUN
ejpam-144	89	22	)	)	PUNCT
ejpam-144	89	23	)	)	PUNCT
ejpam-144	89	24	≤	≤	NUM
ejpam-144	90	1	λ	λ	NOUN
ejpam-144	90	2	holds	hold	VERB
ejpam-144	90	3	for	for	ADP
ejpam-144	90	4	all	all	DET
ejpam-144	90	5	z	z	NOUN
ejpam-144	90	6	∈	∈	NOUN
ejpam-144	90	7	∆	∆	PROPN
ejpam-144	90	8	,	,	PUNCT
ejpam-144	90	9	where	where	SCONJ
ejpam-144	90	10	λ	λ	PROPN
ejpam-144	90	11	is	be	AUX
ejpam-144	90	12	a	a	DET
ejpam-144	90	13	constant	constant	ADJ
ejpam-144	90	14	.	.	PUNCT
ejpam-144	91	1	furthermore	furthermore	ADV
ejpam-144	91	2	,	,	PUNCT
ejpam-144	91	3	let	let	VERB
ejpam-144	91	4	us	we	PRON
ejpam-144	91	5	verify	verify	VERB
ejpam-144	91	6	(	(	PUNCT
ejpam-144	91	7	1−	1−	NUM
ejpam-144	91	8	|z|)|	|z|)|	PROPN
ejpam-144	91	9	f	f	NOUN
ejpam-144	92	1	′	′	NOUN
ejpam-144	92	2	1	1	NUM
ejpam-144	92	3	(	(	PUNCT
ejpam-144	92	4	z)|	z)|	ADP
ejpam-144	92	5	ω((1−	ω((1−	NUM
ejpam-144	92	6	|z|	|z|	NOUN
ejpam-144	92	7	)	)	PUNCT
ejpam-144	92	8	)	)	PUNCT
ejpam-144	92	9	≥	≥	PROPN
ejpam-144	93	1	λ	λ	INTJ
ejpam-144	93	2	,	,	PUNCT
ejpam-144	93	3	1−	1−	NUM
ejpam-144	93	4	q−k	q−k	PROPN
ejpam-144	93	5	≤	≤	PUNCT
ejpam-144	93	6	|z|	|z|	VERB
ejpam-144	93	7	≤	≤	NOUN
ejpam-144	93	8	1−	1−	NUM
ejpam-144	93	9	q−(k+	q−(k+	NUM
ejpam-144	93	10	1	1	NUM
ejpam-144	93	11	2	2	NUM
ejpam-144	93	12	)	)	PUNCT
ejpam-144	93	13	,	,	PUNCT
ejpam-144	93	14	k	k	PROPN
ejpam-144	93	15	∈	∈	PROPN
ejpam-144	93	16	n.	n.	NOUN
ejpam-144	93	17	(	(	PUNCT
ejpam-144	93	18	2.5	2.5	NUM
ejpam-144	93	19	)	)	PUNCT
ejpam-144	93	20	and	and	CCONJ
ejpam-144	93	21	q−(k+	q−(k+	NOUN
ejpam-144	93	22	1	1	NUM
ejpam-144	93	23	2	2	NUM
ejpam-144	93	24	)	)	PUNCT
ejpam-144	93	25	≤	≤	NOUN
ejpam-144	93	26	1−	1−	NUM
ejpam-144	93	27	|z|	|z|	NOUN
ejpam-144	93	28	≤	≤	NUM
ejpam-144	93	29	q−k⇒ω(q−(k+	q−k⇒ω(q−(k+	NOUN
ejpam-144	93	30	1	1	NUM
ejpam-144	93	31	2	2	NUM
ejpam-144	93	32	)	)	PUNCT
ejpam-144	93	33	)	)	PUNCT
ejpam-144	94	1	≤ω(1−	≤ω(1−	PROPN
ejpam-144	94	2	|z|)≤ω(q−k	|z|)≤ω(q−k	NUM
ejpam-144	94	3	)	)	PUNCT
ejpam-144	94	4	.	.	PUNCT
ejpam-144	95	1	observe	observe	VERB
ejpam-144	95	2	that	that	SCONJ
ejpam-144	95	3	for	for	SCONJ
ejpam-144	95	4	any	any	DET
ejpam-144	95	5	z	z	NOUN
ejpam-144	95	6	∈∆	∈∆	NOUN
ejpam-144	95	7	,	,	PUNCT
ejpam-144	96	1	|	|	ADV
ejpam-144	96	2	f	f	NOUN
ejpam-144	97	1	′	′	NOUN
ejpam-144	97	2	1	1	NUM
ejpam-144	97	3	(	(	PUNCT
ejpam-144	97	4	z)|	z)|	PRON
ejpam-144	97	5	≥	≥	NUM
ejpam-144	97	6	qk|z|q	qk|z|q	PROPN
ejpam-144	98	1	k	k	PROPN
ejpam-144	99	1	−	−	PROPN
ejpam-144	99	2	k−1	k−1	PROPN
ejpam-144	99	3	∑	∑	PUNCT
ejpam-144	99	4	j=0	j=0	PROPN
ejpam-144	99	5	q	q	ADJ
ejpam-144	99	6	j|z|q	j|z|q	PROPN
ejpam-144	99	7	j	j	PROPN
ejpam-144	99	8	−	−	PROPN
ejpam-144	99	9	∞	∞	PROPN
ejpam-144	99	10	∑	∑	PUNCT
ejpam-144	99	11	k+1	k+1	X
ejpam-144	99	12	q	q	PUNCT
ejpam-144	99	13	j|z|q	j|z|q	PROPN
ejpam-144	99	14	j	j	PROPN
ejpam-144	99	15	=	=	SYM
ejpam-144	99	16	t1−	t1−	PROPN
ejpam-144	99	17	t2−	t2−	NOUN
ejpam-144	99	18	t3	t3	PROPN
ejpam-144	99	19	.	.	PUNCT
ejpam-144	100	1	and	and	CCONJ
ejpam-144	100	2	then	then	ADV
ejpam-144	100	3	,	,	PUNCT
ejpam-144	100	4	fix	fix	VERB
ejpam-144	100	5	a	a	DET
ejpam-144	100	6	z	z	NOUN
ejpam-144	100	7	with	with	ADP
ejpam-144	100	8	|z|	|z|	NOUN
ejpam-144	100	9	∈	∈	PROPN
ejpam-144	101	1	[	[	X
ejpam-144	101	2	1−	1−	NUM
ejpam-144	101	3	q−k	q−k	PROPN
ejpam-144	101	4	,	,	PUNCT
ejpam-144	101	5	1−	1−	NUM
ejpam-144	101	6	q−(k+	q−(k+	NUM
ejpam-144	101	7	1	1	NUM
ejpam-144	101	8	2	2	NUM
ejpam-144	101	9	)	)	PUNCT
ejpam-144	101	10	]	]	PUNCT
ejpam-144	101	11	,	,	PUNCT
ejpam-144	101	12	k	k	PROPN
ejpam-144	101	13	∈	∈	PROPN
ejpam-144	101	14	n	n	CCONJ
ejpam-144	101	15	,	,	PUNCT
ejpam-144	101	16	and	and	CCONJ
ejpam-144	101	17	put	put	VERB
ejpam-144	101	18	x	x	X
ejpam-144	101	19	=	=	PUNCT
ejpam-144	101	20	|z|q	|z|q	NOUN
ejpam-144	101	21	k	k	X
ejpam-144	101	22	.	.	PUNCT
ejpam-144	102	1	thus	thus	ADV
ejpam-144	102	2	(	(	PUNCT
ejpam-144	102	3	1−	1−	NUM
ejpam-144	102	4	q−k)q	q−k)q	NOUN
ejpam-144	102	5	k	k	NOUN
ejpam-144	102	6	≤	≤	NUM
ejpam-144	102	7	x	x	PUNCT
ejpam-144	102	8	≤	≤	NUM
ejpam-144	103	1	[	[	X
ejpam-144	103	2	(	(	PUNCT
ejpam-144	103	3	1−	1−	NUM
ejpam-144	103	4	q−(k+	q−(k+	NOUN
ejpam-144	103	5	1	1	NUM
ejpam-144	103	6	2	2	NUM
ejpam-144	103	7	)	)	PUNCT
ejpam-144	103	8	)	)	PUNCT
ejpam-144	104	1	q	q	NOUN
ejpam-144	104	2	k+	k+	NOUN
ejpam-144	104	3	1	1	NUM
ejpam-144	104	4	2	2	NUM
ejpam-144	104	5	]	]	PUNCT
ejpam-144	104	6	q	q	X
ejpam-144	104	7	−1	−1	NOUN
ejpam-144	104	8	2	2	NUM
ejpam-144	104	9	.	.	PUNCT
ejpam-144	105	1	if	if	SCONJ
ejpam-144	105	2	q	q	NOUN
ejpam-144	105	3	is	be	AUX
ejpam-144	105	4	large	large	ADJ
ejpam-144	105	5	enough	enough	ADV
ejpam-144	105	6	,	,	PUNCT
ejpam-144	105	7	then	then	ADV
ejpam-144	105	8	for	for	SCONJ
ejpam-144	105	9	k	k	PROPN
ejpam-144	105	10	≥	≥	NUM
ejpam-144	105	11	1	1	NUM
ejpam-144	105	12	one	one	NUM
ejpam-144	105	13	has	have	VERB
ejpam-144	105	14	1	1	NUM
ejpam-144	105	15	3	3	NUM
ejpam-144	105	16	≤	≤	NUM
ejpam-144	105	17	x	x	PUNCT
ejpam-144	105	18	≤	≤	NUM
ejpam-144	105	19	(	(	PUNCT
ejpam-144	105	20	1	1	NUM
ejpam-144	105	21	2	2	NUM
ejpam-144	105	22	)	)	PUNCT
ejpam-144	105	23	q	q	PART
ejpam-144	105	24	−1	−1	NOUN
ejpam-144	105	25	2	2	NUM
ejpam-144	105	26	,	,	PUNCT
ejpam-144	105	27	(	(	PUNCT
ejpam-144	105	28	2.6	2.6	NUM
ejpam-144	105	29	)	)	PUNCT
ejpam-144	105	30	and	and	CCONJ
ejpam-144	105	31	hence	hence	ADV
ejpam-144	105	32	t1	t1	PROPN
ejpam-144	105	33	≥	≥	NUM
ejpam-144	105	34	qk	qk	ADP
ejpam-144	105	35	3	3	NUM
ejpam-144	105	36	.	.	PUNCT
ejpam-144	106	1	since	since	SCONJ
ejpam-144	106	2	it	it	PRON
ejpam-144	106	3	is	be	AUX
ejpam-144	106	4	easy	easy	ADJ
ejpam-144	106	5	to	to	PART
ejpam-144	106	6	establish	establish	VERB
ejpam-144	106	7	t2	t2	NOUN
ejpam-144	106	8	≤	≤	PUNCT
ejpam-144	106	9	k−1	k−1	PROPN
ejpam-144	106	10	∑	∑	PUNCT
ejpam-144	106	11	j=0	j=0	PROPN
ejpam-144	106	12	q	q	PROPN
ejpam-144	106	13	j	j	PROPN
ejpam-144	106	14	≤	≤	NUM
ejpam-144	106	15	qk	qk	ADP
ejpam-144	106	16	q−	q−	PROPN
ejpam-144	106	17	1	1	NUM
ejpam-144	106	18	,	,	PUNCT
ejpam-144	106	19	r.	r.	PROPN
ejpam-144	106	20	rashwan	rashwan	PROPN
ejpam-144	106	21	,	,	PUNCT
ejpam-144	106	22	a.	a.	PROPN
ejpam-144	106	23	ahmed	ahmed	PROPN
ejpam-144	106	24	and	and	CCONJ
ejpam-144	106	25	a.	a.	PROPN
ejpam-144	106	26	kamal	kamal	PROPN
ejpam-144	106	27	/	/	SYM
ejpam-144	106	28	eur	eur	PROPN
ejpam-144	106	29	.	.	PUNCT
ejpam-144	107	1	j.	j.	PROPN
ejpam-144	107	2	pure	pure	PROPN
ejpam-144	107	3	appl	appl	PROPN
ejpam-144	107	4	.	.	PROPN
ejpam-144	107	5	math	math	PROPN
ejpam-144	107	6	,	,	PUNCT
ejpam-144	107	7	2	2	NUM
ejpam-144	107	8	(	(	PUNCT
ejpam-144	107	9	2009	2009	NUM
ejpam-144	107	10	)	)	PUNCT
ejpam-144	107	11	,	,	PUNCT
ejpam-144	107	12	(	(	PUNCT
ejpam-144	107	13	250	250	NUM
ejpam-144	107	14	-	-	SYM
ejpam-144	107	15	267	267	NUM
ejpam-144	107	16	)	)	PUNCT
ejpam-144	107	17	256	256	NUM
ejpam-144	107	18	it	it	PRON
ejpam-144	107	19	remains	remain	VERB
ejpam-144	107	20	to	to	PART
ejpam-144	107	21	deal	deal	VERB
ejpam-144	107	22	with	with	ADP
ejpam-144	107	23	the	the	DET
ejpam-144	107	24	third	third	ADJ
ejpam-144	107	25	term	term	NOUN
ejpam-144	107	26	t3	t3	PROPN
ejpam-144	107	27	.	.	PUNCT
ejpam-144	108	1	noting	note	VERB
ejpam-144	108	2	that	that	SCONJ
ejpam-144	108	3	|z|q	|z|q	ADJ
ejpam-144	108	4	n(q−1	n(q−1	ADJ
ejpam-144	108	5	)	)	PUNCT
ejpam-144	108	6	≤	≤	NOUN
ejpam-144	108	7	|z|q	|z|q	VERB
ejpam-144	108	8	k+1(q−1	k+1(q−1	PROPN
ejpam-144	108	9	)	)	PUNCT
ejpam-144	108	10	,	,	PUNCT
ejpam-144	108	11	n	n	CCONJ
ejpam-144	108	12	≥	≥	NOUN
ejpam-144	108	13	k+	k+	NOUN
ejpam-144	108	14	1	1	NUM
ejpam-144	108	15	,	,	PUNCT
ejpam-144	108	16	namely	namely	ADV
ejpam-144	108	17	,	,	PUNCT
ejpam-144	108	18	in	in	ADP
ejpam-144	108	19	t3	t3	PROPN
ejpam-144	108	20	the	the	DET
ejpam-144	108	21	quotient	quotient	NOUN
ejpam-144	108	22	of	of	ADP
ejpam-144	108	23	two	two	NUM
ejpam-144	108	24	successive	successive	ADJ
ejpam-144	108	25	terms	term	NOUN
ejpam-144	108	26	is	be	AUX
ejpam-144	108	27	not	not	PART
ejpam-144	108	28	greater	great	ADJ
ejpam-144	108	29	than	than	ADP
ejpam-144	108	30	the	the	DET
ejpam-144	108	31	ratio	ratio	NOUN
ejpam-144	108	32	of	of	ADP
ejpam-144	108	33	the	the	DET
ejpam-144	108	34	first	first	ADJ
ejpam-144	108	35	two	two	NUM
ejpam-144	108	36	terms	term	NOUN
ejpam-144	108	37	,	,	PUNCT
ejpam-144	108	38	one	one	PRON
ejpam-144	108	39	finds	find	VERB
ejpam-144	108	40	that	that	SCONJ
ejpam-144	108	41	the	the	DET
ejpam-144	108	42	series	series	NOUN
ejpam-144	108	43	of	of	ADP
ejpam-144	108	44	t3	t3	PROPN
ejpam-144	108	45	is	be	AUX
ejpam-144	108	46	controlled	control	VERB
ejpam-144	108	47	by	by	ADP
ejpam-144	108	48	the	the	DET
ejpam-144	108	49	geometric	geometric	ADJ
ejpam-144	108	50	series	series	NOUN
ejpam-144	108	51	having	have	VERB
ejpam-144	108	52	the	the	DET
ejpam-144	108	53	same	same	ADJ
ejpam-144	108	54	first	first	ADJ
ejpam-144	108	55	two	two	NUM
ejpam-144	108	56	terms	term	NOUN
ejpam-144	108	57	.	.	PUNCT
ejpam-144	109	1	accordingly	accordingly	ADV
ejpam-144	109	2	(	(	PUNCT
ejpam-144	109	3	2.6	2.6	NUM
ejpam-144	109	4	)	)	PUNCT
ejpam-144	109	5	is	be	AUX
ejpam-144	109	6	applied	apply	VERB
ejpam-144	109	7	to	to	PART
ejpam-144	109	8	produce	produce	VERB
ejpam-144	109	9	t3	t3	NOUN
ejpam-144	109	10	≤	≤	PROPN
ejpam-144	109	11	qk+1|z|q	qk+1|z|q	NUM
ejpam-144	109	12	k+1	k+1	PROPN
ejpam-144	109	13	∞	∞	PROPN
ejpam-144	109	14	∑	∑	PUNCT
ejpam-144	109	15	j=0	j=0	PROPN
ejpam-144	109	16	�	�	PROPN
ejpam-144	109	17	q|z|q	q|z|q	PROPN
ejpam-144	109	18	k+2−qk+1	k+2−qk+1	VERB
ejpam-144	109	19	�	�	PROPN
ejpam-144	109	20	j	j	PROPN
ejpam-144	109	21	=	=	PUNCT
ejpam-144	110	1	qk+1|z|q	qk+1|z|q	PUNCT
ejpam-144	110	2	k+1	k+1	X
ejpam-144	110	3	1−	1−	NUM
ejpam-144	110	4	q|z|(qk+2−qk+1	q|z|(qk+2−qk+1	NOUN
ejpam-144	110	5	)	)	PUNCT
ejpam-144	111	1	=	=	NOUN
ejpam-144	111	2	qk	qk	X
ejpam-144	111	3	qxq	qxq	NOUN
ejpam-144	111	4	1−	1−	NUM
ejpam-144	111	5	qxq2−q	qxq2−q	NOUN
ejpam-144	111	6	≤	≤	NOUN
ejpam-144	111	7	qk	qk	ADP
ejpam-144	111	8	q(1	q(1	PROPN
ejpam-144	111	9	2	2	NUM
ejpam-144	111	10	)	)	PUNCT
ejpam-144	111	11	q	q	NOUN
ejpam-144	111	12	1	1	NUM
ejpam-144	111	13	2	2	NUM
ejpam-144	111	14	1−	1−	NUM
ejpam-144	111	15	q(1	q(1	PROPN
ejpam-144	111	16	2	2	NUM
ejpam-144	111	17	)	)	PUNCT
ejpam-144	111	18	q	q	NOUN
ejpam-144	111	19	3	3	NUM
ejpam-144	111	20	2	2	NUM
ejpam-144	111	21	−	−	NOUN
ejpam-144	111	22	q	q	NOUN
ejpam-144	111	23	1	1	NUM
ejpam-144	111	24	2	2	NUM
ejpam-144	111	25	.	.	PUNCT
ejpam-144	112	1	the	the	DET
ejpam-144	112	2	preceding	precede	VERB
ejpam-144	112	3	estimates	estimate	NOUN
ejpam-144	112	4	for	for	ADP
ejpam-144	112	5	t1	t1	NOUN
ejpam-144	112	6	,	,	PUNCT
ejpam-144	112	7	t2	t2	NOUN
ejpam-144	112	8	and	and	CCONJ
ejpam-144	112	9	t3	t3	NOUN
ejpam-144	112	10	imply	imply	INTJ
ejpam-144	113	1	|	|	ADV
ejpam-144	113	2	f	f	NOUN
ejpam-144	113	3	′	′	NOUN
ejpam-144	113	4	1	1	NUM
ejpam-144	113	5	(	(	PUNCT
ejpam-144	113	6	z)|	z)|	INTJ
ejpam-144	113	7	≥	≥	NOUN
ejpam-144	113	8	qk	qk	ADP
ejpam-144	113	9	4	4	NUM
ejpam-144	113	10	ω(1−	ω(1−	NOUN
ejpam-144	113	11	|z|	|z|	NOUN
ejpam-144	113	12	)	)	PUNCT
ejpam-144	113	13	ω(1−	ω(1−	NOUN
ejpam-144	113	14	|z|	|z|	NOUN
ejpam-144	113	15	)	)	PUNCT
ejpam-144	113	16	=	=	PUNCT
ejpam-144	113	17	qk+	qk+	ADJ
ejpam-144	113	18	1	1	NUM
ejpam-144	113	19	2	2	NUM
ejpam-144	113	20	4q	4q	NOUN
ejpam-144	113	21	1	1	NUM
ejpam-144	113	22	2	2	NUM
ejpam-144	113	23	ω(1−	ω(1−	NOUN
ejpam-144	113	24	|z|	|z|	NOUN
ejpam-144	113	25	)	)	PUNCT
ejpam-144	113	26	ω(1−	ω(1−	PROPN
ejpam-144	113	27	|z|	|z|	NOUN
ejpam-144	113	28	)	)	PUNCT
ejpam-144	113	29	≥	≥	NOUN
ejpam-144	113	30	ω(1−	ω(1−	NOUN
ejpam-144	113	31	|z|	|z|	NOUN
ejpam-144	113	32	)	)	PUNCT
ejpam-144	113	33	4q	4q	NOUN
ejpam-144	113	34	1	1	NUM
ejpam-144	113	35	2	2	NUM
ejpam-144	113	36	(	(	PUNCT
ejpam-144	113	37	1−	1−	NUM
ejpam-144	113	38	|z|)×ω(1−	|z|)×ω(1−	ADJ
ejpam-144	113	39	|z|	|z|	NOUN
ejpam-144	113	40	)	)	PUNCT
ejpam-144	113	41	≥	≥	NOUN
ejpam-144	113	42	ω(1−	ω(1−	NOUN
ejpam-144	113	43	|z|	|z|	NOUN
ejpam-144	113	44	)	)	PUNCT
ejpam-144	113	45	4q	4q	NOUN
ejpam-144	113	46	1	1	NUM
ejpam-144	113	47	2ω(q−k)×	2ω(q−k)×	NUM
ejpam-144	113	48	(	(	PUNCT
ejpam-144	113	49	1−	1−	NUM
ejpam-144	113	50	|z|	|z|	NOUN
ejpam-144	113	51	)	)	PUNCT
ejpam-144	113	52	;	;	PUNCT
ejpam-144	113	53	ω(q−k	ω(q−k	X
ejpam-144	113	54	)	)	PUNCT
ejpam-144	114	1	6→	6→	NUM
ejpam-144	115	1	∞.	∞.	PROPN
ejpam-144	115	2	reaching	reach	VERB
ejpam-144	115	3	(	(	PUNCT
ejpam-144	115	4	2.5	2.5	NUM
ejpam-144	115	5	)	)	PUNCT
ejpam-144	115	6	.	.	PUNCT
ejpam-144	116	1	in	in	ADP
ejpam-144	116	2	a	a	DET
ejpam-144	116	3	completely	completely	ADV
ejpam-144	116	4	similar	similar	ADJ
ejpam-144	116	5	manner	manner	NOUN
ejpam-144	116	6	one	one	PRON
ejpam-144	116	7	can	can	AUX
ejpam-144	116	8	prove	prove	VERB
ejpam-144	116	9	that	that	SCONJ
ejpam-144	116	10	if	if	SCONJ
ejpam-144	116	11	q	q	NOUN
ejpam-144	116	12	is	be	AUX
ejpam-144	116	13	a	a	DET
ejpam-144	116	14	large	large	ADJ
ejpam-144	116	15	natural	natural	ADJ
ejpam-144	116	16	number	number	NOUN
ejpam-144	116	17	,	,	PUNCT
ejpam-144	116	18	for	for	ADP
ejpam-144	116	19	example	example	NOUN
ejpam-144	116	20	q	q	X
ejpam-144	117	1	=	=	PUNCT
ejpam-144	117	2	m2	m2	PROPN
ejpam-144	117	3	where	where	SCONJ
ejpam-144	117	4	m	m	PROPN
ejpam-144	117	5	is	be	AUX
ejpam-144	117	6	a	a	DET
ejpam-144	117	7	large	large	ADJ
ejpam-144	117	8	natural	natural	ADJ
ejpam-144	117	9	number	number	NOUN
ejpam-144	117	10	,	,	PUNCT
ejpam-144	117	11	and	and	CCONJ
ejpam-144	117	12	if	if	SCONJ
ejpam-144	117	13	f2(z	f2(z	NOUN
ejpam-144	117	14	)	)	PUNCT
ejpam-144	117	15	=	=	SYM
ejpam-144	117	16	∞	∞	PROPN
ejpam-144	117	17	∑	∑	PUNCT
ejpam-144	117	18	j=0	j=0	PROPN
ejpam-144	117	19	zq	zq	PROPN
ejpam-144	117	20	j	j	PROPN
ejpam-144	117	21	,	,	PUNCT
ejpam-144	117	22	z	z	PROPN
ejpam-144	117	23	∈∆	∈∆	ADV
ejpam-144	117	24	,	,	PUNCT
ejpam-144	117	25	then	then	ADV
ejpam-144	117	26	(	(	PUNCT
ejpam-144	117	27	1−	1−	NUM
ejpam-144	117	28	|z|2)|	|z|2)|	PROPN
ejpam-144	117	29	f	f	PROPN
ejpam-144	117	30	′	′	NOUN
ejpam-144	117	31	2	2	NUM
ejpam-144	117	32	(	(	PUNCT
ejpam-144	117	33	z)|	z)|	ADP
ejpam-144	117	34	≤	≤	NUM
ejpam-144	117	35	λ	λ	NOUN
ejpam-144	117	36	for	for	ADP
ejpam-144	117	37	all	all	DET
ejpam-144	117	38	z	z	NOUN
ejpam-144	117	39	∈∆	∈∆	NOUN
ejpam-144	117	40	(	(	PUNCT
ejpam-144	117	41	owing	owe	VERB
ejpam-144	117	42	to	to	ADP
ejpam-144	117	43	lemma	lemma	PROPN
ejpam-144	117	44	2.1	2.1	NUM
ejpam-144	117	45	)	)	PUNCT
ejpam-144	117	46	and	and	CCONJ
ejpam-144	117	47	(	(	PUNCT
ejpam-144	117	48	1−	1−	NUM
ejpam-144	117	49	|z|)|	|z|)|	PROPN
ejpam-144	117	50	f	f	NOUN
ejpam-144	118	1	′	′	NOUN
ejpam-144	118	2	1	1	NUM
ejpam-144	118	3	(	(	PUNCT
ejpam-144	118	4	z)|	z)|	ADP
ejpam-144	118	5	ω((1−	ω((1−	NUM
ejpam-144	118	6	|z|	|z|	NOUN
ejpam-144	118	7	)	)	PUNCT
ejpam-144	118	8	)	)	PUNCT
ejpam-144	119	1	≤	≤	NUM
ejpam-144	119	2	λ	λ	PROPN
ejpam-144	119	3	,	,	PUNCT
ejpam-144	119	4	1−	1−	NUM
ejpam-144	119	5	q−(k+	q−(k+	NUM
ejpam-144	119	6	1	1	NUM
ejpam-144	119	7	2	2	NUM
ejpam-144	119	8	)	)	PUNCT
ejpam-144	119	9	≤	≤	NUM
ejpam-144	119	10	|z|	|z|	VERB
ejpam-144	119	11	≤	≤	NUM
ejpam-144	119	12	1−	1−	NUM
ejpam-144	119	13	q−(k+1	q−(k+1	NOUN
ejpam-144	119	14	)	)	PUNCT
ejpam-144	119	15	,	,	PUNCT
ejpam-144	119	16	k	k	PROPN
ejpam-144	119	17	∈	∈	PROPN
ejpam-144	119	18	n.	n.	NOUN
ejpam-144	119	19	(	(	PUNCT
ejpam-144	119	20	2.7	2.7	NUM
ejpam-144	119	21	)	)	PUNCT
ejpam-144	119	22	r.	r.	PROPN
ejpam-144	119	23	rashwan	rashwan	PROPN
ejpam-144	119	24	,	,	PUNCT
ejpam-144	119	25	a.	a.	PROPN
ejpam-144	119	26	ahmed	ahmed	PROPN
ejpam-144	119	27	and	and	CCONJ
ejpam-144	119	28	a.	a.	PROPN
ejpam-144	119	29	kamal	kamal	PROPN
ejpam-144	119	30	/	/	SYM
ejpam-144	119	31	eur	eur	PROPN
ejpam-144	119	32	.	.	PUNCT
ejpam-144	120	1	j.	j.	PROPN
ejpam-144	120	2	pure	pure	PROPN
ejpam-144	120	3	appl	appl	PROPN
ejpam-144	120	4	.	.	PROPN
ejpam-144	120	5	math	math	PROPN
ejpam-144	120	6	,	,	PUNCT
ejpam-144	120	7	2	2	NUM
ejpam-144	120	8	(	(	PUNCT
ejpam-144	120	9	2009	2009	NUM
ejpam-144	120	10	)	)	PUNCT
ejpam-144	120	11	,	,	PUNCT
ejpam-144	120	12	(	(	PUNCT
ejpam-144	120	13	250	250	NUM
ejpam-144	120	14	-	-	SYM
ejpam-144	120	15	267	267	NUM
ejpam-144	120	16	)	)	PUNCT
ejpam-144	120	17	257	257	NUM
ejpam-144	120	18	of	of	ADP
ejpam-144	120	19	course	course	NOUN
ejpam-144	120	20	,	,	PUNCT
ejpam-144	120	21	(	(	PUNCT
ejpam-144	120	22	2.5	2.5	NUM
ejpam-144	120	23	)	)	PUNCT
ejpam-144	120	24	and	and	CCONJ
ejpam-144	120	25	(	(	PUNCT
ejpam-144	120	26	2.7	2.7	NUM
ejpam-144	120	27	)	)	PUNCT
ejpam-144	120	28	yield	yield	NOUN
ejpam-144	120	29	(	(	PUNCT
ejpam-144	120	30	2.4	2.4	NUM
ejpam-144	120	31	)	)	PUNCT
ejpam-144	120	32	unless	unless	SCONJ
ejpam-144	120	33	it	it	PRON
ejpam-144	120	34	occurs	occur	VERB
ejpam-144	120	35	that	that	SCONJ
ejpam-144	120	36	f	f	PROPN
ejpam-144	121	1	′	′	NOUN
ejpam-144	121	2	1	1	NUM
ejpam-144	122	1	and	and	CCONJ
ejpam-144	122	2	f	f	PROPN
ejpam-144	122	3	′	′	NOUN
ejpam-144	122	4	2	2	NUM
ejpam-144	122	5	have	have	VERB
ejpam-144	122	6	common	common	ADJ
ejpam-144	122	7	zero	zero	NUM
ejpam-144	122	8	in	in	ADP
ejpam-144	122	9	{	{	PUNCT
ejpam-144	122	10	z	z	NOUN
ejpam-144	122	11	∈	∈	PROPN
ejpam-144	122	12	∆	∆	PROPN
ejpam-144	122	13	:	:	PUNCT
ejpam-144	122	14	|z|	|z|	VERB
ejpam-144	122	15	<	<	X
ejpam-144	122	16	1	1	NUM
ejpam-144	122	17	−	−	PROPN
ejpam-144	122	18	q−1	q−1	PROPN
ejpam-144	122	19	}	}	PUNCT
ejpam-144	122	20	in	in	ADP
ejpam-144	122	21	which	which	DET
ejpam-144	122	22	case	case	NOUN
ejpam-144	122	23	one	one	PRON
ejpam-144	122	24	can	can	AUX
ejpam-144	122	25	replace	replace	VERB
ejpam-144	122	26	f2	f2	ADJ
ejpam-144	122	27	with	with	ADP
ejpam-144	122	28	f2(ζz	f2(ζz	PROPN
ejpam-144	122	29	)	)	PUNCT
ejpam-144	122	30	for	for	ADP
ejpam-144	122	31	appropriate	appropriate	ADJ
ejpam-144	122	32	ζ	ζ	PROPN
ejpam-144	122	33	∈	∈	PROPN
ejpam-144	122	34	∂∆	∂∆	NOUN
ejpam-144	122	35	,	,	PUNCT
ejpam-144	122	36	where	where	SCONJ
ejpam-144	122	37	∂∆	∂∆	NOUN
ejpam-144	122	38	is	be	AUX
ejpam-144	122	39	the	the	DET
ejpam-144	122	40	boundary	boundary	NOUN
ejpam-144	122	41	of	of	ADP
ejpam-144	122	42	the	the	DET
ejpam-144	122	43	unit	unit	NOUN
ejpam-144	122	44	disk	disk	NOUN
ejpam-144	122	45	(	(	PUNCT
ejpam-144	122	46	note	note	VERB
ejpam-144	122	47	that	that	SCONJ
ejpam-144	122	48	f	f	PROPN
ejpam-144	122	49	′(0	′(0	PROPN
ejpam-144	122	50	)	)	PUNCT
ejpam-144	123	1	=	=	SYM
ejpam-144	123	2	1	1	NUM
ejpam-144	123	3	)	)	PUNCT
ejpam-144	123	4	.	.	PUNCT
ejpam-144	124	1	our	our	PRON
ejpam-144	124	2	lemma	lemma	PROPN
ejpam-144	124	3	is	be	AUX
ejpam-144	124	4	therefore	therefore	ADV
ejpam-144	124	5	proved	prove	VERB
ejpam-144	124	6	.	.	PUNCT
ejpam-144	125	1	using	use	VERB
ejpam-144	125	2	the	the	DET
ejpam-144	125	3	same	same	ADJ
ejpam-144	125	4	steps	step	NOUN
ejpam-144	125	5	of	of	ADP
ejpam-144	125	6	lemma	lemma	PROPN
ejpam-144	125	7	2.2	2.2	NUM
ejpam-144	125	8	,	,	PUNCT
ejpam-144	125	9	it	it	PRON
ejpam-144	125	10	is	be	AUX
ejpam-144	125	11	not	not	PART
ejpam-144	125	12	hard	hard	ADJ
ejpam-144	125	13	to	to	PART
ejpam-144	125	14	prove	prove	VERB
ejpam-144	125	15	the	the	DET
ejpam-144	125	16	following	follow	VERB
ejpam-144	125	17	lemma	lemma	PROPN
ejpam-144	125	18	.	.	PUNCT
ejpam-144	126	1	lemma	lemma	PROPN
ejpam-144	126	2	2.3	2.3	NUM
ejpam-144	126	3	.	.	PUNCT
ejpam-144	127	1	let	let	VERB
ejpam-144	127	2	ω	ω	NOUN
ejpam-144	127	3	:	:	PUNCT
ejpam-144	127	4	(	(	PUNCT
ejpam-144	127	5	0	0	NUM
ejpam-144	127	6	,	,	PUNCT
ejpam-144	127	7	1]→	1]→	NOUN
ejpam-144	127	8	(	(	PUNCT
ejpam-144	127	9	0,∞	0,∞	NOUN
ejpam-144	127	10	)	)	PUNCT
ejpam-144	127	11	be	be	AUX
ejpam-144	127	12	a	a	DET
ejpam-144	127	13	nondecreasing	nondecrease	VERB
ejpam-144	127	14	function	function	NOUN
ejpam-144	127	15	and	and	CCONJ
ejpam-144	127	16	let	let	VERB
ejpam-144	127	17	1	1	NUM
ejpam-144	127	18	≤	≤	NUM
ejpam-144	127	19	α	α	PRON
ejpam-144	127	20	<	<	X
ejpam-144	127	21	∞.	∞.	PROPN
ejpam-144	127	22	then	then	ADV
ejpam-144	127	23	there	there	PRON
ejpam-144	127	24	are	be	VERB
ejpam-144	127	25	two	two	NUM
ejpam-144	127	26	functions	function	NOUN
ejpam-144	127	27	f1	f1	NOUN
ejpam-144	127	28	,	,	PUNCT
ejpam-144	127	29	f2	f2	PROPN
ejpam-144	127	30	∈b	∈b	PROPN
ejpam-144	127	31	α	α	PROPN
ejpam-144	127	32	ω	ω	PROPN
ejpam-144	127	33	such	such	ADJ
ejpam-144	127	34	that	that	SCONJ
ejpam-144	128	1	|	|	INTJ
ejpam-144	129	1	f	f	NOUN
ejpam-144	130	1	′	′	NOUN
ejpam-144	130	2	1	1	NUM
ejpam-144	131	1	(	(	PUNCT
ejpam-144	131	2	z)|+	z)|+	PROPN
ejpam-144	131	3	|	|	NOUN
ejpam-144	131	4	f	f	NOUN
ejpam-144	131	5	′	′	NOUN
ejpam-144	131	6	2	2	NUM
ejpam-144	132	1	(	(	PUNCT
ejpam-144	132	2	z)|	z)|	PROPN
ejpam-144	132	3	≈	≈	PROPN
ejpam-144	132	4	ω(1−	ω(1−	PROPN
ejpam-144	132	5	|z|	|z|	NOUN
ejpam-144	132	6	)	)	PUNCT
ejpam-144	132	7	(	(	PUNCT
ejpam-144	132	8	1−	1−	NUM
ejpam-144	132	9	|z|)α	|z|)α	PROPN
ejpam-144	132	10	,	,	PUNCT
ejpam-144	132	11	z	z	PROPN
ejpam-144	132	12	∈∆.	∈∆.	PROPN
ejpam-144	132	13	(	(	PUNCT
ejpam-144	132	14	2.8	2.8	NUM
ejpam-144	132	15	)	)	PUNCT
ejpam-144	132	16	proof	proof	NOUN
ejpam-144	132	17	.	.	PUNCT
ejpam-144	133	1	the	the	DET
ejpam-144	133	2	proof	proof	NOUN
ejpam-144	133	3	is	be	AUX
ejpam-144	133	4	very	very	ADV
ejpam-144	133	5	similar	similar	ADJ
ejpam-144	133	6	to	to	ADP
ejpam-144	133	7	the	the	DET
ejpam-144	133	8	proof	proof	NOUN
ejpam-144	133	9	of	of	ADP
ejpam-144	133	10	lemma	lemma	PROPN
ejpam-144	133	11	2.2	2.2	NUM
ejpam-144	133	12	and	and	CCONJ
ejpam-144	133	13	lemma	lemma	PROPN
ejpam-144	133	14	3.1	3.1	NUM
ejpam-144	133	15	in	in	ADP
ejpam-144	133	16	[	[	X
ejpam-144	133	17	7	7	NUM
ejpam-144	133	18	]	]	PUNCT
ejpam-144	133	19	,	,	PUNCT
ejpam-144	133	20	so	so	SCONJ
ejpam-144	133	21	it	it	PRON
ejpam-144	133	22	will	will	AUX
ejpam-144	133	23	be	be	AUX
ejpam-144	133	24	omitted	omit	VERB
ejpam-144	133	25	.	.	PUNCT
ejpam-144	134	1	theorem	theorem	VERB
ejpam-144	134	2	2.1	2.1	NUM
ejpam-144	134	3	.	.	PUNCT
ejpam-144	135	1	for	for	ADP
ejpam-144	135	2	each	each	DET
ejpam-144	135	3	non	non	ADJ
ejpam-144	135	4	-	-	ADJ
ejpam-144	135	5	decreasing	decrease	VERB
ejpam-144	135	6	function	function	NOUN
ejpam-144	135	7	k	k	NOUN
ejpam-144	136	1	:	:	PUNCT
ejpam-144	136	2	[	[	X
ejpam-144	136	3	0,∞	0,∞	NOUN
ejpam-144	136	4	)	)	PUNCT
ejpam-144	136	5	→	→	PUNCT
ejpam-144	137	1	[	[	X
ejpam-144	137	2	0,∞	0,∞	NUM
ejpam-144	137	3	)	)	PUNCT
ejpam-144	137	4	,	,	PUNCT
ejpam-144	137	5	0	0	PUNCT
ejpam-144	137	6	<	<	X
ejpam-144	138	1	p	p	X
ejpam-144	138	2	<	<	X
ejpam-144	138	3	∞	∞	PROPN
ejpam-144	138	4	and	and	CCONJ
ejpam-144	138	5	for	for	ADP
ejpam-144	138	6	a	a	DET
ejpam-144	138	7	given	give	VERB
ejpam-144	138	8	reasonable	reasonable	ADJ
ejpam-144	138	9	non	non	ADJ
ejpam-144	138	10	-	-	ADJ
ejpam-144	138	11	decreasing	decrease	VERB
ejpam-144	138	12	function	function	NOUN
ejpam-144	138	13	ω	ω	NOUN
ejpam-144	138	14	:	:	PUNCT
ejpam-144	138	15	(	(	PUNCT
ejpam-144	138	16	0	0	NUM
ejpam-144	138	17	,	,	PUNCT
ejpam-144	138	18	1]→	1]→	NOUN
ejpam-144	138	19	(	(	PUNCT
ejpam-144	138	20	0,∞	0,∞	NOUN
ejpam-144	138	21	)	)	PUNCT
ejpam-144	138	22	with	with	ADP
ejpam-144	138	23	ω(α	ω(α	PROPN
ejpam-144	138	24	t	t	PROPN
ejpam-144	138	25	)	)	PUNCT
ejpam-144	138	26	≈	≈	PROPN
ejpam-144	138	27	ω(t	ω(t	NOUN
ejpam-144	138	28	)	)	PUNCT
ejpam-144	138	29	,	,	PUNCT
ejpam-144	138	30	α	α	X
ejpam-144	138	31	>	>	X
ejpam-144	138	32	0	0	NUM
ejpam-144	138	33	,	,	PUNCT
ejpam-144	138	34	we	we	PRON
ejpam-144	138	35	have	have	VERB
ejpam-144	138	36	that	that	PRON
ejpam-144	138	37	(	(	PUNCT
ejpam-144	138	38	i	i	NOUN
ejpam-144	138	39	)	)	PUNCT
ejpam-144	138	40	qk	qk	PROPN
ejpam-144	138	41	,	,	PUNCT
ejpam-144	138	42	ω	ω	PROPN
ejpam-144	138	43	⊂b	⊂b	PROPN
ejpam-144	138	44	p+2	p+2	PROPN
ejpam-144	138	45	p	p	PROPN
ejpam-144	138	46	ω	ω	PROPN
ejpam-144	138	47	and	and	CCONJ
ejpam-144	138	48	(	(	PUNCT
ejpam-144	138	49	ii	ii	NOUN
ejpam-144	138	50	)	)	PUNCT
ejpam-144	138	51	qk	qk	PROPN
ejpam-144	138	52	,	,	PUNCT
ejpam-144	138	53	ω	ω	PROPN
ejpam-144	139	1	=	=	PROPN
ejpam-144	139	2	b	b	PROPN
ejpam-144	139	3	p+2	p+2	PROPN
ejpam-144	139	4	p	p	PROPN
ejpam-144	139	5	ω	ω	PROPN
ejpam-144	139	6	,	,	PUNCT
ejpam-144	139	7	iff	iff	PROPN
ejpam-144	139	8	∫	∫	PROPN
ejpam-144	139	9	1	1	NUM
ejpam-144	139	10	0	0	NUM
ejpam-144	139	11	k	k	PROPN
ejpam-144	139	12	�	�	PROPN
ejpam-144	139	13	log	log	VERB
ejpam-144	139	14	1	1	NUM
ejpam-144	139	15	r	r	NOUN
ejpam-144	139	16	�	�	PROPN
ejpam-144	139	17	r	r	NOUN
ejpam-144	139	18	(	(	PUNCT
ejpam-144	139	19	1−	1−	NUM
ejpam-144	139	20	r2)2	r2)2	NOUN
ejpam-144	139	21	dr	dr	PROPN
ejpam-144	139	22	<	<	PROPN
ejpam-144	139	23	∞.	∞.	PROPN
ejpam-144	139	24	proof	proof	NOUN
ejpam-144	139	25	.	.	PUNCT
ejpam-144	140	1	for	for	ADP
ejpam-144	140	2	a	a	PRON
ejpam-144	140	3	fixed	fix	VERB
ejpam-144	140	4	r	r	NOUN
ejpam-144	140	5	∈	∈	PROPN
ejpam-144	140	6	(	(	PUNCT
ejpam-144	140	7	0	0	NUM
ejpam-144	140	8	,	,	PUNCT
ejpam-144	140	9	1	1	NUM
ejpam-144	140	10	)	)	PUNCT
ejpam-144	140	11	and	and	CCONJ
ejpam-144	140	12	a	a	DET
ejpam-144	140	13	∈∆	∈∆	NOUN
ejpam-144	140	14	,	,	PUNCT
ejpam-144	140	15	let	let	VERB
ejpam-144	140	16	e(a	e(a	NOUN
ejpam-144	140	17	,	,	PUNCT
ejpam-144	140	18	r	r	NOUN
ejpam-144	140	19	)	)	PUNCT
ejpam-144	140	20	=	=	SYM
ejpam-144	140	21	�	�	PROPN
ejpam-144	140	22	z	z	PROPN
ejpam-144	140	23	∈∆	∈∆	NOUN
ejpam-144	140	24	,	,	PUNCT
ejpam-144	140	25	|z−	|z−	VERB
ejpam-144	140	26	a|	a|	PROPN
ejpam-144	140	27	<	<	X
ejpam-144	140	28	r(1−	r(1−	PROPN
ejpam-144	140	29	|a|	|a|	PROPN
ejpam-144	140	30	)	)	PUNCT
ejpam-144	140	31	�	�	PROPN
ejpam-144	140	32	.	.	PUNCT
ejpam-144	141	1	we	we	PRON
ejpam-144	141	2	know	know	VERB
ejpam-144	141	3	that	that	SCONJ
ejpam-144	141	4	e(a	e(a	NOUN
ejpam-144	141	5	,	,	PUNCT
ejpam-144	141	6	r	r	NOUN
ejpam-144	141	7	)	)	PUNCT
ejpam-144	141	8	⊂∆(a	⊂∆(a	NOUN
ejpam-144	141	9	,	,	PUNCT
ejpam-144	141	10	r	r	NOUN
ejpam-144	141	11	)	)	PUNCT
ejpam-144	141	12	and	and	CCONJ
ejpam-144	141	13	for	for	ADP
ejpam-144	141	14	any	any	DET
ejpam-144	141	15	z	z	PROPN
ejpam-144	141	16	∈	∈	PROPN
ejpam-144	141	17	e(a	e(a	PROPN
ejpam-144	141	18	,	,	PUNCT
ejpam-144	141	19	r	r	NOUN
ejpam-144	141	20	)	)	PUNCT
ejpam-144	141	21	,	,	PUNCT
ejpam-144	141	22	we	we	PRON
ejpam-144	141	23	have	have	VERB
ejpam-144	141	24	(	(	PUNCT
ejpam-144	141	25	1−	1−	NUM
ejpam-144	141	26	r)(1−	r)(1−	PROPN
ejpam-144	141	27	|a|	|a|	NOUN
ejpam-144	141	28	)	)	PUNCT
ejpam-144	141	29	≤	≤	NOUN
ejpam-144	141	30	1−	1−	NUM
ejpam-144	141	31	|z|	|z|	NOUN
ejpam-144	141	32	≤	≤	NUM
ejpam-144	141	33	(	(	PUNCT
ejpam-144	141	34	1	1	NUM
ejpam-144	141	35	+	+	CCONJ
ejpam-144	141	36	r)(1−	r)(1−	PROPN
ejpam-144	141	37	|a|	|a|	NUM
ejpam-144	141	38	)	)	PUNCT
ejpam-144	141	39	,	,	PUNCT
ejpam-144	141	40	which	which	PRON
ejpam-144	141	41	means	mean	VERB
ejpam-144	141	42	that	that	SCONJ
ejpam-144	141	43	1−	1−	NUM
ejpam-144	141	44	|z|2	|z|2	PROPN
ejpam-144	141	45	≃	≃	NOUN
ejpam-144	141	46	1−	1−	NUM
ejpam-144	141	47	|a|2	|a|2	PROPN
ejpam-144	141	48	for	for	ADP
ejpam-144	141	49	any	any	DET
ejpam-144	141	50	z	z	PROPN
ejpam-144	141	51	∈	∈	PROPN
ejpam-144	141	52	e(a	e(a	PROPN
ejpam-144	141	53	,	,	PUNCT
ejpam-144	141	54	r	r	NOUN
ejpam-144	141	55	)	)	PUNCT
ejpam-144	141	56	.	.	PUNCT
ejpam-144	142	1	denote	denote	VERB
ejpam-144	142	2	fω	fω	PROPN
ejpam-144	142	3	,	,	PUNCT
ejpam-144	142	4	p	p	X
ejpam-144	142	5	(	(	PUNCT
ejpam-144	142	6	f	f	PROPN
ejpam-144	142	7	)	)	PUNCT
ejpam-144	142	8	(	(	PUNCT
ejpam-144	142	9	z	z	NOUN
ejpam-144	142	10	)	)	PUNCT
ejpam-144	142	11	=	=	SYM
ejpam-144	142	12	�	�	PROPN
ejpam-144	142	13	�	�	PROPN
ejpam-144	142	14	f	f	PROPN
ejpam-144	142	15	′(z	′(z	NOUN
ejpam-144	142	16	)	)	PUNCT
ejpam-144	142	17	�	�	PROPN
ejpam-144	142	18	�	�	PROPN
ejpam-144	142	19	p	p	PROPN
ejpam-144	142	20	(	(	PUNCT
ejpam-144	142	21	1−	1−	NUM
ejpam-144	142	22	|z|)p	|z|)p	PROPN
ejpam-144	142	23	ωp(1−	ωp(1−	ADJ
ejpam-144	142	24	|z|	|z|	NOUN
ejpam-144	142	25	)	)	PUNCT
ejpam-144	142	26	r.	r.	PROPN
ejpam-144	142	27	rashwan	rashwan	PROPN
ejpam-144	142	28	,	,	PUNCT
ejpam-144	142	29	a.	a.	PROPN
ejpam-144	142	30	ahmed	ahmed	PROPN
ejpam-144	142	31	and	and	CCONJ
ejpam-144	142	32	a.	a.	PROPN
ejpam-144	142	33	kamal	kamal	PROPN
ejpam-144	142	34	/	/	SYM
ejpam-144	142	35	eur	eur	PROPN
ejpam-144	142	36	.	.	PUNCT
ejpam-144	143	1	j.	j.	PROPN
ejpam-144	143	2	pure	pure	PROPN
ejpam-144	143	3	appl	appl	PROPN
ejpam-144	143	4	.	.	PROPN
ejpam-144	143	5	math	math	PROPN
ejpam-144	143	6	,	,	PUNCT
ejpam-144	143	7	2	2	NUM
ejpam-144	143	8	(	(	PUNCT
ejpam-144	143	9	2009	2009	NUM
ejpam-144	143	10	)	)	PUNCT
ejpam-144	143	11	,	,	PUNCT
ejpam-144	143	12	(	(	PUNCT
ejpam-144	143	13	250	250	NUM
ejpam-144	143	14	-	-	SYM
ejpam-144	143	15	267	267	NUM
ejpam-144	143	16	)	)	PUNCT
ejpam-144	143	17	258	258	NUM
ejpam-144	143	18	then	then	ADV
ejpam-144	143	19	,	,	PUNCT
ejpam-144	143	20	we	we	PRON
ejpam-144	143	21	obtain	obtain	VERB
ejpam-144	143	22	∫	∫	PROPN
ejpam-144	143	23	∆	∆	PROPN
ejpam-144	143	24	fω	fω	PROPN
ejpam-144	143	25	,	,	PUNCT
ejpam-144	143	26	p	p	X
ejpam-144	143	27	(	(	PUNCT
ejpam-144	143	28	f	f	PROPN
ejpam-144	143	29	)	)	PUNCT
ejpam-144	143	30	(	(	PUNCT
ejpam-144	143	31	z)k	z)k	X
ejpam-144	143	32	�	�	PROPN
ejpam-144	143	33	g(z	g(z	PROPN
ejpam-144	143	34	,	,	PUNCT
ejpam-144	143	35	a	a	PRON
ejpam-144	143	36	)	)	PUNCT
ejpam-144	143	37	�	�	PROPN
ejpam-144	143	38	dσz	dσz	ADJ
ejpam-144	143	39	≥	≥	PROPN
ejpam-144	143	40	∫	∫	PROPN
ejpam-144	143	41	∆(a	∆(a	PROPN
ejpam-144	143	42	,	,	PUNCT
ejpam-144	143	43	r	r	NOUN
ejpam-144	143	44	)	)	PUNCT
ejpam-144	143	45	fω	fω	PROPN
ejpam-144	143	46	,	,	PUNCT
ejpam-144	143	47	p	p	X
ejpam-144	143	48	(	(	PUNCT
ejpam-144	143	49	f	f	PROPN
ejpam-144	143	50	)	)	PUNCT
ejpam-144	143	51	(	(	PUNCT
ejpam-144	143	52	z)k	z)k	X
ejpam-144	143	53	�	�	PROPN
ejpam-144	143	54	g(z	g(z	PROPN
ejpam-144	143	55	,	,	PUNCT
ejpam-144	143	56	a	a	PRON
ejpam-144	143	57	)	)	PUNCT
ejpam-144	143	58	�	�	PROPN
ejpam-144	143	59	dσz	dσz	NOUN
ejpam-144	143	60	≥	≥	PROPN
ejpam-144	143	61	k	k	PROPN
ejpam-144	143	62	�	�	PROPN
ejpam-144	143	63	log	log	VERB
ejpam-144	143	64	1	1	NUM
ejpam-144	143	65	r	r	NOUN
ejpam-144	143	66	�	�	PROPN
ejpam-144	143	67	∫	∫	PROPN
ejpam-144	143	68	∆(a	∆(a	PROPN
ejpam-144	143	69	,	,	PUNCT
ejpam-144	143	70	r	r	NOUN
ejpam-144	143	71	)	)	PUNCT
ejpam-144	143	72	fω	fω	PROPN
ejpam-144	143	73	,	,	PUNCT
ejpam-144	143	74	p	p	X
ejpam-144	143	75	(	(	PUNCT
ejpam-144	143	76	f	f	PROPN
ejpam-144	143	77	)	)	PUNCT
ejpam-144	143	78	(	(	PUNCT
ejpam-144	143	79	z	z	NOUN
ejpam-144	143	80	)	)	PUNCT
ejpam-144	143	81	dσz	dσz	PROPN
ejpam-144	143	82	≥	≥	PROPN
ejpam-144	143	83	k	k	PROPN
ejpam-144	143	84	�	�	PROPN
ejpam-144	143	85	log	log	VERB
ejpam-144	143	86	1	1	NUM
ejpam-144	143	87	r	r	NOUN
ejpam-144	143	88	�	�	PROPN
ejpam-144	143	89	∫	∫	PROPN
ejpam-144	143	90	e(a	e(a	PROPN
ejpam-144	143	91	,	,	PUNCT
ejpam-144	143	92	r	r	NOUN
ejpam-144	143	93	)	)	PUNCT
ejpam-144	143	94	fω	fω	PROPN
ejpam-144	143	95	,	,	PUNCT
ejpam-144	143	96	p	p	X
ejpam-144	143	97	(	(	PUNCT
ejpam-144	143	98	f	f	PROPN
ejpam-144	143	99	)	)	PUNCT
ejpam-144	143	100	(	(	PUNCT
ejpam-144	143	101	z	z	NOUN
ejpam-144	143	102	)	)	PUNCT
ejpam-144	143	103	dσz	dσz	NOUN
ejpam-144	143	104	.	.	NOUN
ejpam-144	144	1	for	for	ADP
ejpam-144	144	2	every	every	DET
ejpam-144	144	3	z	z	PROPN
ejpam-144	144	4	∈	∈	PROPN
ejpam-144	144	5	e(a	e(a	PROPN
ejpam-144	144	6	,	,	PUNCT
ejpam-144	144	7	r	r	NOUN
ejpam-144	144	8	)	)	PUNCT
ejpam-144	144	9	,	,	PUNCT
ejpam-144	144	10	we	we	PRON
ejpam-144	144	11	have	have	VERB
ejpam-144	144	12	that	that	PRON
ejpam-144	144	13	(	(	PUNCT
ejpam-144	144	14	1−	1−	NUM
ejpam-144	144	15	r)(1−	r)(1−	PROPN
ejpam-144	144	16	|a|	|a|	NOUN
ejpam-144	144	17	)	)	PUNCT
ejpam-144	144	18	≤	≤	NOUN
ejpam-144	144	19	1−	1−	NUM
ejpam-144	144	20	|z|	|z|	NOUN
ejpam-144	144	21	≤	≤	NUM
ejpam-144	144	22	(	(	PUNCT
ejpam-144	144	23	1	1	NUM
ejpam-144	144	24	+	+	CCONJ
ejpam-144	144	25	r)(1−	r)(1−	PROPN
ejpam-144	144	26	|a|	|a|	NUM
ejpam-144	144	27	)	)	PUNCT
ejpam-144	144	28	,	,	PUNCT
ejpam-144	144	29	then	then	ADV
ejpam-144	144	30	,	,	PUNCT
ejpam-144	144	31	(	(	PUNCT
ejpam-144	144	32	1−	1−	NUM
ejpam-144	144	33	|z|)p	|z|)p	NUM
ejpam-144	144	34	≥	≥	X
ejpam-144	144	35	(	(	PUNCT
ejpam-144	144	36	1−	1−	NUM
ejpam-144	144	37	r)p(1−	r)p(1−	PROPN
ejpam-144	144	38	|a|)p	|a|)p	PROPN
ejpam-144	144	39	,	,	PUNCT
ejpam-144	144	40	∀	∀	X
ejpam-144	144	41	p	p	X
ejpam-144	144	42	>	>	X
ejpam-144	144	43	0	0	X
ejpam-144	144	44	.	.	PUNCT
ejpam-144	145	1	now	now	ADV
ejpam-144	145	2	,	,	PUNCT
ejpam-144	145	3	since	since	SCONJ
ejpam-144	145	4	we	we	PRON
ejpam-144	145	5	assume	assume	VERB
ejpam-144	145	6	that	that	SCONJ
ejpam-144	145	7	ω	ω	PROPN
ejpam-144	145	8	is	be	AUX
ejpam-144	145	9	non	non	ADJ
ejpam-144	145	10	-	-	ADJ
ejpam-144	145	11	decreasing	decrease	VERB
ejpam-144	145	12	,	,	PUNCT
ejpam-144	145	13	then	then	ADV
ejpam-144	145	14	we	we	PRON
ejpam-144	145	15	obtain	obtain	VERB
ejpam-144	145	16	that	that	SCONJ
ejpam-144	145	17	∫	∫	PROPN
ejpam-144	145	18	e(a	e(a	NOUN
ejpam-144	145	19	,	,	PUNCT
ejpam-144	145	20	r	r	NOUN
ejpam-144	145	21	)	)	PUNCT
ejpam-144	145	22	fω	fω	PROPN
ejpam-144	145	23	,	,	PUNCT
ejpam-144	145	24	p	p	X
ejpam-144	145	25	(	(	PUNCT
ejpam-144	145	26	f	f	PROPN
ejpam-144	145	27	)	)	PUNCT
ejpam-144	145	28	(	(	PUNCT
ejpam-144	145	29	z	z	NOUN
ejpam-144	145	30	)	)	PUNCT
ejpam-144	145	31	dσz	dσz	NOUN
ejpam-144	145	32	≥	≥	NOUN
ejpam-144	145	33	(	(	PUNCT
ejpam-144	145	34	1−	1−	NUM
ejpam-144	145	35	r)p(1−	r)p(1−	PROPN
ejpam-144	145	36	|a|)p	|a|)p	PROPN
ejpam-144	145	37	ωp((1−	ωp((1−	PROPN
ejpam-144	145	38	r)(1−	r)(1−	PROPN
ejpam-144	145	39	|a|	|a|	NUM
ejpam-144	145	40	)	)	PUNCT
ejpam-144	145	41	)	)	PUNCT
ejpam-144	145	42	∫	∫	PROPN
ejpam-144	146	1	e(a	e(a	NOUN
ejpam-144	146	2	,	,	PUNCT
ejpam-144	146	3	r	r	NOUN
ejpam-144	146	4	)	)	PUNCT
ejpam-144	146	5	�	�	PROPN
ejpam-144	146	6	�	�	PROPN
ejpam-144	146	7	f	f	PROPN
ejpam-144	146	8	′(z	′(z	NOUN
ejpam-144	146	9	)	)	PUNCT
ejpam-144	146	10	�	�	PROPN
ejpam-144	146	11	�	�	PROPN
ejpam-144	146	12	p	p	NOUN
ejpam-144	146	13	dσz	dσz	NOUN
ejpam-144	146	14	.	.	PUNCT
ejpam-144	147	1	since	since	SCONJ
ejpam-144	147	2	|	|	ADV
ejpam-144	147	3	f	f	PROPN
ejpam-144	147	4	′(z)|p	′(z)|p	PROPN
ejpam-144	147	5	is	be	AUX
ejpam-144	147	6	a	a	DET
ejpam-144	147	7	subharmonic	subharmonic	ADJ
ejpam-144	147	8	function	function	NOUN
ejpam-144	147	9	,	,	PUNCT
ejpam-144	147	10	then	then	ADV
ejpam-144	147	11	∫	∫	PROPN
ejpam-144	147	12	e(a	e(a	PROPN
ejpam-144	147	13	,	,	PUNCT
ejpam-144	148	1	r	r	NOUN
ejpam-144	148	2	)	)	PUNCT
ejpam-144	148	3	�	�	PROPN
ejpam-144	148	4	�	�	PROPN
ejpam-144	148	5	f	f	PROPN
ejpam-144	148	6	′(z	′(z	NOUN
ejpam-144	148	7	)	)	PUNCT
ejpam-144	148	8	�	�	PROPN
ejpam-144	148	9	�	�	PROPN
ejpam-144	148	10	p	p	PROPN
ejpam-144	148	11	dσz	dσz	ADJ
ejpam-144	148	12	≥	≥	NOUN
ejpam-144	148	13	|e(a	|e(a	PROPN
ejpam-144	148	14	,	,	PUNCT
ejpam-144	148	15	r)|	r)|	NOUN
ejpam-144	148	16	.	.	PUNCT
ejpam-144	149	1	|	|	ADV
ejpam-144	149	2	f	f	PROPN
ejpam-144	149	3	′(a	′(a	ADV
ejpam-144	149	4	)	)	PUNCT
ejpam-144	149	5	�	�	PROPN
ejpam-144	149	6	�	�	PROPN
ejpam-144	149	7	p	p	X
ejpam-144	149	8	=	=	NOUN
ejpam-144	149	9	r2(1−	r2(1−	PROPN
ejpam-144	149	10	|a|)2|	|a|)2|	PROPN
ejpam-144	149	11	f	f	PROPN
ejpam-144	149	12	′(a	′(a	ADV
ejpam-144	149	13	)	)	PUNCT
ejpam-144	149	14	�	�	PROPN
ejpam-144	149	15	�	�	PROPN
ejpam-144	149	16	p	p	PROPN
ejpam-144	149	17	.	.	PUNCT
ejpam-144	150	1	then	then	ADV
ejpam-144	150	2	we	we	PRON
ejpam-144	150	3	obtain	obtain	VERB
ejpam-144	150	4	∫	∫	PROPN
ejpam-144	150	5	∆	∆	PROPN
ejpam-144	150	6	fω	fω	PROPN
ejpam-144	150	7	,	,	PUNCT
ejpam-144	150	8	p	p	X
ejpam-144	150	9	(	(	PUNCT
ejpam-144	150	10	f	f	PROPN
ejpam-144	150	11	)	)	PUNCT
ejpam-144	150	12	(	(	PUNCT
ejpam-144	150	13	z)k	z)k	X
ejpam-144	150	14	�	�	PROPN
ejpam-144	150	15	g(z	g(z	PROPN
ejpam-144	150	16	,	,	PUNCT
ejpam-144	150	17	a	a	PRON
ejpam-144	150	18	)	)	PUNCT
ejpam-144	150	19	�	�	PROPN
ejpam-144	150	20	dσz	dσz	NOUN
ejpam-144	150	21	≥	≥	PROPN
ejpam-144	150	22	k	k	PROPN
ejpam-144	150	23	�	�	PROPN
ejpam-144	150	24	log	log	VERB
ejpam-144	150	25	1	1	NUM
ejpam-144	150	26	r	r	NOUN
ejpam-144	150	27	�	�	PROPN
ejpam-144	150	28	(	(	PUNCT
ejpam-144	150	29	1−	1−	NUM
ejpam-144	150	30	r)p(1−	r)p(1−	PROPN
ejpam-144	150	31	|a|)p+2	|a|)p+2	PROPN
ejpam-144	150	32	ωp((1−	ωp((1−	PROPN
ejpam-144	150	33	r)(1−	r)(1−	PROPN
ejpam-144	150	34	|a|	|a|	NUM
ejpam-144	150	35	)	)	PUNCT
ejpam-144	150	36	)	)	PUNCT
ejpam-144	151	1	|	|	ADV
ejpam-144	151	2	f	f	PROPN
ejpam-144	151	3	′(a	′(a	ADV
ejpam-144	151	4	)	)	PUNCT
ejpam-144	151	5	�	�	PROPN
ejpam-144	151	6	�	�	PROPN
ejpam-144	151	7	p	p	PROPN
ejpam-144	151	8	≥	≥	PROPN
ejpam-144	151	9	λk	λk	PRON
ejpam-144	151	10	�	�	PROPN
ejpam-144	151	11	log	log	VERB
ejpam-144	151	12	1	1	NUM
ejpam-144	151	13	r	r	NOUN
ejpam-144	151	14	�	�	PROPN
ejpam-144	151	15	(	(	PUNCT
ejpam-144	151	16	1−	1−	NUM
ejpam-144	151	17	r)p(1−	r)p(1−	PROPN
ejpam-144	151	18	|a|)p+2	|a|)p+2	PROPN
ejpam-144	151	19	ωp(1−	ωp(1−	PROPN
ejpam-144	151	20	|a|	|a|	NOUN
ejpam-144	151	21	)	)	PUNCT
ejpam-144	152	1	|	|	ADV
ejpam-144	152	2	f	f	NOUN
ejpam-144	152	3	′(a	′(a	ADV
ejpam-144	152	4	)	)	PUNCT
ejpam-144	152	5	�	�	PROPN
ejpam-144	152	6	�	�	PROPN
ejpam-144	153	1	p	p	PROPN
ejpam-144	153	2	where	where	SCONJ
ejpam-144	153	3	λ	λ	PROPN
ejpam-144	153	4	is	be	AUX
ejpam-144	153	5	a	a	DET
ejpam-144	153	6	constant	constant	ADJ
ejpam-144	153	7	.	.	PUNCT
ejpam-144	154	1	if	if	SCONJ
ejpam-144	154	2	f	f	PROPN
ejpam-144	154	3	∈	∈	PROPN
ejpam-144	154	4	qk	qk	PROPN
ejpam-144	154	5	,	,	PUNCT
ejpam-144	154	6	ω	ω	PROPN
ejpam-144	154	7	,	,	PUNCT
ejpam-144	154	8	then	then	ADV
ejpam-144	154	9	by	by	ADP
ejpam-144	154	10	the	the	DET
ejpam-144	154	11	above	above	ADJ
ejpam-144	154	12	estimate	estimate	NOUN
ejpam-144	154	13	we	we	PRON
ejpam-144	154	14	have	have	VERB
ejpam-144	154	15	that	that	DET
ejpam-144	154	16	sup	sup	NOUN
ejpam-144	154	17	a∈∆	a∈∆	NOUN
ejpam-144	154	18	(	(	PUNCT
ejpam-144	154	19	1−	1−	NUM
ejpam-144	154	20	|a|)p+2|	|a|)p+2|	NOUN
ejpam-144	154	21	f	f	PROPN
ejpam-144	154	22	′(z)|p	′(z)|p	PROPN
ejpam-144	154	23	ωp(1−	ωp(1−	PROPN
ejpam-144	154	24	|a|	|a|	PROPN
ejpam-144	154	25	)	)	PUNCT
ejpam-144	154	26	<	<	X
ejpam-144	154	27	∞.	∞.	PROPN
ejpam-144	154	28	r.	r.	PROPN
ejpam-144	154	29	rashwan	rashwan	PROPN
ejpam-144	154	30	,	,	PUNCT
ejpam-144	154	31	a.	a.	PROPN
ejpam-144	154	32	ahmed	ahmed	PROPN
ejpam-144	154	33	and	and	CCONJ
ejpam-144	154	34	a.	a.	PROPN
ejpam-144	154	35	kamal	kamal	PROPN
ejpam-144	154	36	/	/	SYM
ejpam-144	154	37	eur	eur	PROPN
ejpam-144	154	38	.	.	PUNCT
ejpam-144	155	1	j.	j.	PROPN
ejpam-144	155	2	pure	pure	PROPN
ejpam-144	155	3	appl	appl	PROPN
ejpam-144	155	4	.	.	PROPN
ejpam-144	155	5	math	math	PROPN
ejpam-144	155	6	,	,	PUNCT
ejpam-144	155	7	2	2	NUM
ejpam-144	155	8	(	(	PUNCT
ejpam-144	155	9	2009	2009	NUM
ejpam-144	155	10	)	)	PUNCT
ejpam-144	155	11	,	,	PUNCT
ejpam-144	155	12	(	(	PUNCT
ejpam-144	155	13	250	250	NUM
ejpam-144	155	14	-	-	SYM
ejpam-144	155	15	267	267	NUM
ejpam-144	155	16	)	)	PUNCT
ejpam-144	155	17	259	259	NUM
ejpam-144	155	18	the	the	DET
ejpam-144	155	19	proof	proof	NOUN
ejpam-144	155	20	of	of	ADP
ejpam-144	155	21	(	(	PUNCT
ejpam-144	155	22	i	i	NOUN
ejpam-144	155	23	)	)	PUNCT
ejpam-144	155	24	is	be	AUX
ejpam-144	155	25	therefore	therefore	ADV
ejpam-144	155	26	completed	complete	VERB
ejpam-144	155	27	.	.	PUNCT
ejpam-144	156	1	now	now	ADV
ejpam-144	156	2	,	,	PUNCT
ejpam-144	156	3	we	we	PRON
ejpam-144	156	4	show	show	VERB
ejpam-144	156	5	that	that	SCONJ
ejpam-144	156	6	b	b	NOUN
ejpam-144	156	7	p+2	p+2	X
ejpam-144	156	8	p	p	PROPN
ejpam-144	156	9	ω	ω	PROPN
ejpam-144	156	10	⊂	⊂	PROPN
ejpam-144	156	11	qk	qk	PROPN
ejpam-144	156	12	,	,	PUNCT
ejpam-144	156	13	ω	ω	PROPN
ejpam-144	156	14	provided	provide	VERB
ejpam-144	156	15	that	that	SCONJ
ejpam-144	156	16	k	k	PROPN
ejpam-144	156	17	satisfies	satisfy	VERB
ejpam-144	156	18	condition	condition	NOUN
ejpam-144	156	19	(	(	PUNCT
ejpam-144	156	20	2.3	2.3	NUM
ejpam-144	156	21	)	)	PUNCT
ejpam-144	156	22	.	.	PUNCT
ejpam-144	157	1	for	for	ADP
ejpam-144	157	2	f	f	PROPN
ejpam-144	157	3	∈	∈	PROPN
ejpam-144	157	4	b	b	PROPN
ejpam-144	157	5	p+2	p+2	X
ejpam-144	157	6	p	p	PROPN
ejpam-144	157	7	ω	ω	PROPN
ejpam-144	157	8	,	,	PUNCT
ejpam-144	157	9	we	we	PRON
ejpam-144	157	10	have	have	VERB
ejpam-144	157	11	that	that	PRON
ejpam-144	157	12	,	,	PUNCT
ejpam-144	157	13	∫	∫	PROPN
ejpam-144	157	14	∆	∆	PROPN
ejpam-144	157	15	fω	fω	PROPN
ejpam-144	157	16	,	,	PUNCT
ejpam-144	157	17	p	p	X
ejpam-144	157	18	(	(	PUNCT
ejpam-144	157	19	f	f	PROPN
ejpam-144	157	20	)	)	PUNCT
ejpam-144	157	21	(	(	PUNCT
ejpam-144	157	22	z)k	z)k	X
ejpam-144	157	23	�	�	PROPN
ejpam-144	157	24	g(z	g(z	PROPN
ejpam-144	157	25	,	,	PUNCT
ejpam-144	157	26	a	a	PRON
ejpam-144	157	27	)	)	PUNCT
ejpam-144	157	28	�	�	PROPN
ejpam-144	157	29	dσz	dσz	NOUN
ejpam-144	157	30	≤	≤	NUM
ejpam-144	157	31	f	f	PROPN
ejpam-144	157	32	p	p	X
ejpam-144	157	33	b	b	PROPN
ejpam-144	158	1	p+2	p+2	PRON
ejpam-144	158	2	p	p	PROPN
ejpam-144	158	3	ω	ω	PROPN
ejpam-144	158	4	∫	∫	PROPN
ejpam-144	158	5	∆	∆	PROPN
ejpam-144	158	6	(	(	PUNCT
ejpam-144	158	7	1−	1−	NUM
ejpam-144	158	8	|z|2)−2k	|z|2)−2k	PROPN
ejpam-144	158	9	�	�	PROPN
ejpam-144	158	10	g(z	g(z	PROPN
ejpam-144	158	11	,	,	PUNCT
ejpam-144	158	12	a	a	PRON
ejpam-144	158	13	)	)	PUNCT
ejpam-144	158	14	�	�	PROPN
ejpam-144	158	15	dσz	dσz	NOUN
ejpam-144	158	16	=	=	SYM
ejpam-144	158	17	2π	2π	PROPN
ejpam-144	158	18	f	f	NOUN
ejpam-144	158	19	p	p	X
ejpam-144	158	20	b	b	PROPN
ejpam-144	158	21	p+2	p+2	PRON
ejpam-144	158	22	p	p	PROPN
ejpam-144	158	23	ω	ω	PROPN
ejpam-144	158	24	∫	∫	PROPN
ejpam-144	158	25	1	1	NUM
ejpam-144	158	26	0	0	NUM
ejpam-144	158	27	k	k	PROPN
ejpam-144	158	28	�	�	PROPN
ejpam-144	158	29	log	log	VERB
ejpam-144	158	30	1	1	NUM
ejpam-144	158	31	r	r	NOUN
ejpam-144	158	32	�	�	PROPN
ejpam-144	158	33	r	r	NOUN
ejpam-144	158	34	(	(	PUNCT
ejpam-144	158	35	1−	1−	NUM
ejpam-144	158	36	r2)2	r2)2	NOUN
ejpam-144	158	37	dr	dr	PROPN
ejpam-144	158	38	<	<	PROPN
ejpam-144	158	39	∞	∞	PROPN
ejpam-144	158	40	,	,	PUNCT
ejpam-144	158	41	which	which	PRON
ejpam-144	158	42	shows	show	VERB
ejpam-144	158	43	that	that	SCONJ
ejpam-144	158	44	b	b	X
ejpam-144	158	45	p+2	p+2	X
ejpam-144	158	46	p	p	PROPN
ejpam-144	158	47	ω	ω	PROPN
ejpam-144	158	48	⊂	⊂	PROPN
ejpam-144	158	49	qk	qk	PROPN
ejpam-144	158	50	,	,	PUNCT
ejpam-144	158	51	ω	ω	PROPN
ejpam-144	158	52	.	.	PUNCT
ejpam-144	159	1	now	now	ADV
ejpam-144	159	2	we	we	PRON
ejpam-144	159	3	assume	assume	VERB
ejpam-144	159	4	thatb	thatb	PROPN
ejpam-144	159	5	p+2	p+2	PROPN
ejpam-144	159	6	p	p	PROPN
ejpam-144	159	7	ω	ω	PROPN
ejpam-144	159	8	=	=	SYM
ejpam-144	159	9	qk	qk	PROPN
ejpam-144	159	10	,	,	PUNCT
ejpam-144	159	11	ω	ω	PROPN
ejpam-144	159	12	and	and	CCONJ
ejpam-144	159	13	we	we	PRON
ejpam-144	159	14	verify	verify	VERB
ejpam-144	159	15	(	(	PUNCT
ejpam-144	159	16	2.3	2.3	NUM
ejpam-144	159	17	)	)	PUNCT
ejpam-144	159	18	holds	hold	VERB
ejpam-144	159	19	.	.	PUNCT
ejpam-144	160	1	from	from	ADP
ejpam-144	160	2	lemma	lemma	PROPN
ejpam-144	160	3	2.3	2.3	NUM
ejpam-144	160	4	,	,	PUNCT
ejpam-144	160	5	for	for	ADP
ejpam-144	160	6	f1	f1	NOUN
ejpam-144	160	7	and	and	CCONJ
ejpam-144	160	8	f2	f2	PROPN
ejpam-144	160	9	inb	inb	VERB
ejpam-144	160	10	p+2	p+2	PROPN
ejpam-144	160	11	p	p	PROPN
ejpam-144	160	12	ω	ω	PROPN
ejpam-144	160	13	,	,	PUNCT
ejpam-144	160	14	we	we	PRON
ejpam-144	160	15	have	have	VERB
ejpam-144	160	16	that	that	PRON
ejpam-144	161	1	|	|	INTJ
ejpam-144	161	2	f	f	NOUN
ejpam-144	161	3	′	′	NOUN
ejpam-144	161	4	1	1	NUM
ejpam-144	162	1	(	(	PUNCT
ejpam-144	162	2	z)|+	z)|+	PROPN
ejpam-144	162	3	|	|	NOUN
ejpam-144	162	4	f	f	NOUN
ejpam-144	162	5	′	′	NOUN
ejpam-144	162	6	2	2	NUM
ejpam-144	162	7	(	(	PUNCT
ejpam-144	162	8	z)|	z)|	PRON
ejpam-144	162	9	≥	≥	NOUN
ejpam-144	162	10	ω(1−	ω(1−	PROPN
ejpam-144	162	11	|z|	|z|	NOUN
ejpam-144	162	12	)	)	PUNCT
ejpam-144	162	13	(	(	PUNCT
ejpam-144	162	14	1−	1−	NUM
ejpam-144	162	15	|z|	|z|	NOUN
ejpam-144	162	16	)	)	PUNCT
ejpam-144	162	17	p+2	p+2	PROPN
ejpam-144	162	18	p	p	NOUN
ejpam-144	162	19	.	.	PUNCT
ejpam-144	163	1	(	(	PUNCT
ejpam-144	163	2	2.9	2.9	NUM
ejpam-144	163	3	)	)	PUNCT
ejpam-144	163	4	then	then	ADV
ejpam-144	163	5	f1	f1	NOUN
ejpam-144	163	6	,	,	PUNCT
ejpam-144	163	7	f2	f2	PROPN
ejpam-144	163	8	∈	∈	PROPN
ejpam-144	163	9	qk	qk	PROPN
ejpam-144	163	10	,	,	PUNCT
ejpam-144	163	11	ω	ω	PROPN
ejpam-144	163	12	and	and	CCONJ
ejpam-144	163	13	∞	∞	NUM
ejpam-144	163	14	>	>	X
ejpam-144	163	15	sup	sup	PROPN
ejpam-144	163	16	a∈∆	a∈∆	PROPN
ejpam-144	163	17	∫	∫	PROPN
ejpam-144	163	18	∆	∆	PROPN
ejpam-144	163	19	�	�	PROPN
ejpam-144	163	20	�	�	PROPN
ejpam-144	163	21	�	�	PROPN
ejpam-144	163	22	f	f	PROPN
ejpam-144	164	1	′	′	NOUN
ejpam-144	164	2	1	1	NUM
ejpam-144	164	3	(	(	PUNCT
ejpam-144	164	4	z	z	NOUN
ejpam-144	164	5	)	)	PUNCT
ejpam-144	164	6	�	�	PROPN
ejpam-144	164	7	�	�	PROPN
ejpam-144	164	8	p	p	PROPN
ejpam-144	164	9	+	+	PROPN
ejpam-144	164	10	�	�	PROPN
ejpam-144	164	11	�	�	PROPN
ejpam-144	164	12	f	f	PROPN
ejpam-144	164	13	′	′	NOUN
ejpam-144	164	14	2	2	NUM
ejpam-144	164	15	(	(	PUNCT
ejpam-144	164	16	z	z	NOUN
ejpam-144	164	17	)	)	PUNCT
ejpam-144	164	18	�	�	PROPN
ejpam-144	164	19	�	�	PROPN
ejpam-144	164	20	p	p	PROPN
ejpam-144	164	21	�	�	PROPN
ejpam-144	164	22	(	(	PUNCT
ejpam-144	164	23	1−	1−	NUM
ejpam-144	164	24	|z|)p	|z|)p	PROPN
ejpam-144	164	25	k	k	PROPN
ejpam-144	164	26	�	�	PROPN
ejpam-144	164	27	g(z	g(z	PROPN
ejpam-144	164	28	,	,	PUNCT
ejpam-144	164	29	a	a	PRON
ejpam-144	164	30	)	)	PUNCT
ejpam-144	164	31	�	�	PROPN
ejpam-144	164	32	ωp(1−	ωp(1−	ADJ
ejpam-144	164	33	|z|	|z|	NOUN
ejpam-144	164	34	)	)	PUNCT
ejpam-144	164	35	dσz	dσz	ADJ
ejpam-144	164	36	≥	≥	PROPN
ejpam-144	164	37	∫	∫	PROPN
ejpam-144	164	38	∆	∆	PROPN
ejpam-144	164	39	�	�	PROPN
ejpam-144	164	40	�	�	PROPN
ejpam-144	164	41	�	�	PROPN
ejpam-144	164	42	f	f	PROPN
ejpam-144	164	43	′	′	NOUN
ejpam-144	164	44	1	1	NUM
ejpam-144	164	45	(	(	PUNCT
ejpam-144	164	46	z	z	NOUN
ejpam-144	164	47	)	)	PUNCT
ejpam-144	164	48	�	�	PROPN
ejpam-144	164	49	�	�	PROPN
ejpam-144	164	50	+	+	PROPN
ejpam-144	164	51	�	�	PROPN
ejpam-144	164	52	�	�	PROPN
ejpam-144	164	53	f	f	PROPN
ejpam-144	164	54	′	′	NOUN
ejpam-144	164	55	2	2	NUM
ejpam-144	164	56	(	(	PUNCT
ejpam-144	164	57	z	z	NOUN
ejpam-144	164	58	)	)	PUNCT
ejpam-144	164	59	�	�	PROPN
ejpam-144	164	60	�	�	PROPN
ejpam-144	164	61	�	�	PROPN
ejpam-144	164	62	p	p	PROPN
ejpam-144	164	63	(	(	PUNCT
ejpam-144	164	64	1−	1−	NUM
ejpam-144	164	65	|z|)p	|z|)p	PROPN
ejpam-144	164	66	k	k	PROPN
ejpam-144	164	67	�	�	PROPN
ejpam-144	164	68	g(z	g(z	PROPN
ejpam-144	164	69	,	,	PUNCT
ejpam-144	164	70	0	0	NUM
ejpam-144	164	71	)	)	PUNCT
ejpam-144	164	72	�	�	PROPN
ejpam-144	164	73	ωp(1−	ωp(1−	ADJ
ejpam-144	164	74	|z|	|z|	NOUN
ejpam-144	164	75	)	)	PUNCT
ejpam-144	164	76	dσz	dσz	NOUN
ejpam-144	164	77	(	(	PUNCT
ejpam-144	164	78	2.10	2.10	NUM
ejpam-144	164	79	)	)	PUNCT
ejpam-144	164	80	from	from	ADP
ejpam-144	164	81	(	(	PUNCT
ejpam-144	164	82	2.9	2.9	NUM
ejpam-144	164	83	)	)	PUNCT
ejpam-144	164	84	and	and	CCONJ
ejpam-144	164	85	(	(	PUNCT
ejpam-144	164	86	2.10	2.10	NUM
ejpam-144	164	87	)	)	PUNCT
ejpam-144	164	88	,	,	PUNCT
ejpam-144	164	89	we	we	PRON
ejpam-144	164	90	obtain	obtain	VERB
ejpam-144	164	91	∫	∫	PROPN
ejpam-144	164	92	∆	∆	PROPN
ejpam-144	164	93	�	�	PROPN
ejpam-144	164	94	�	�	PROPN
ejpam-144	164	95	�	�	PROPN
ejpam-144	164	96	f	f	PROPN
ejpam-144	165	1	′	′	NOUN
ejpam-144	165	2	1	1	NUM
ejpam-144	165	3	(	(	PUNCT
ejpam-144	165	4	z	z	NOUN
ejpam-144	165	5	)	)	PUNCT
ejpam-144	165	6	�	�	PROPN
ejpam-144	165	7	�	�	PROPN
ejpam-144	165	8	p	p	PROPN
ejpam-144	165	9	+	+	PROPN
ejpam-144	165	10	�	�	PROPN
ejpam-144	165	11	�	�	PROPN
ejpam-144	165	12	f	f	PROPN
ejpam-144	165	13	′	′	NOUN
ejpam-144	165	14	2	2	NUM
ejpam-144	165	15	(	(	PUNCT
ejpam-144	165	16	z	z	NOUN
ejpam-144	165	17	)	)	PUNCT
ejpam-144	165	18	�	�	PROPN
ejpam-144	165	19	�	�	PROPN
ejpam-144	165	20	p	p	PROPN
ejpam-144	165	21	�	�	PROPN
ejpam-144	165	22	(	(	PUNCT
ejpam-144	165	23	1−	1−	NUM
ejpam-144	165	24	|z|)p	|z|)p	PROPN
ejpam-144	165	25	k	k	PROPN
ejpam-144	165	26	�	�	PROPN
ejpam-144	165	27	g(z	g(z	PROPN
ejpam-144	165	28	,	,	PUNCT
ejpam-144	165	29	0	0	NUM
ejpam-144	165	30	)	)	PUNCT
ejpam-144	165	31	�	�	PROPN
ejpam-144	165	32	ωp(1−	ωp(1−	ADJ
ejpam-144	165	33	|z|	|z|	NOUN
ejpam-144	165	34	)	)	PUNCT
ejpam-144	165	35	dσz	dσz	NOUN
ejpam-144	165	36	≈	≈	PROPN
ejpam-144	165	37	2π	2π	PROPN
ejpam-144	165	38	∫	∫	NOUN
ejpam-144	166	1	1	1	NUM
ejpam-144	166	2	0	0	NUM
ejpam-144	166	3	k	k	PROPN
ejpam-144	166	4	�	�	PROPN
ejpam-144	166	5	log	log	VERB
ejpam-144	166	6	1	1	NUM
ejpam-144	166	7	r	r	NOUN
ejpam-144	166	8	�	�	PROPN
ejpam-144	166	9	r	r	NOUN
ejpam-144	166	10	(	(	PUNCT
ejpam-144	166	11	1−	1−	NUM
ejpam-144	166	12	r2)2	r2)2	NOUN
ejpam-144	166	13	dr	dr	PROPN
ejpam-144	166	14	.	.	PROPN
ejpam-144	167	1	thus	thus	ADV
ejpam-144	167	2	(	(	PUNCT
ejpam-144	167	3	2.3	2.3	NUM
ejpam-144	167	4	)	)	PUNCT
ejpam-144	167	5	holds	hold	VERB
ejpam-144	167	6	,	,	PUNCT
ejpam-144	167	7	and	and	CCONJ
ejpam-144	167	8	this	this	PRON
ejpam-144	167	9	completes	complete	VERB
ejpam-144	167	10	the	the	DET
ejpam-144	167	11	proof	proof	NOUN
ejpam-144	167	12	.	.	PUNCT
ejpam-144	168	1	3	3	X
ejpam-144	168	2	.	.	X
ejpam-144	168	3	the	the	DET
ejpam-144	168	4	classes	class	NOUN
ejpam-144	168	5	qk	qk	VERB
ejpam-144	168	6	,	,	PUNCT
ejpam-144	168	7	ω,0	ω,0	PROPN
ejpam-144	168	8	and	and	CCONJ
ejpam-144	168	9	bα	bα	PROPN
ejpam-144	169	1	ω,0	ω,0	NOUN
ejpam-144	170	1	we	we	PRON
ejpam-144	170	2	say	say	VERB
ejpam-144	170	3	that	that	SCONJ
ejpam-144	170	4	f	f	PROPN
ejpam-144	170	5	∈	∈	PROPN
ejpam-144	170	6	qk	qk	PROPN
ejpam-144	170	7	,	,	PUNCT
ejpam-144	170	8	ω,0	ω,0	PROPN
ejpam-144	170	9	if	if	SCONJ
ejpam-144	170	10	lim	lim	PROPN
ejpam-144	170	11	|a|→1−	|a|→1−	PROPN
ejpam-144	170	12	∫	∫	PROPN
ejpam-144	170	13	∆	∆	PROPN
ejpam-144	170	14	�	�	PROPN
ejpam-144	170	15	�	�	PROPN
ejpam-144	170	16	f	f	PROPN
ejpam-144	170	17	′(z	′(z	NOUN
ejpam-144	170	18	)	)	PUNCT
ejpam-144	170	19	�	�	PROPN
ejpam-144	170	20	�	�	PROPN
ejpam-144	170	21	p	p	PROPN
ejpam-144	170	22	(	(	PUNCT
ejpam-144	170	23	1−	1−	NUM
ejpam-144	170	24	|z|)p	|z|)p	PROPN
ejpam-144	170	25	k(g(z	k(g(z	PROPN
ejpam-144	170	26	,	,	PUNCT
ejpam-144	170	27	a	a	PRON
ejpam-144	170	28	)	)	PUNCT
ejpam-144	170	29	)	)	PUNCT
ejpam-144	170	30	ωp(1−	ωp(1−	ADJ
ejpam-144	170	31	|z|	|z|	NOUN
ejpam-144	170	32	)	)	PUNCT
ejpam-144	170	33	dσz	dσz	NOUN
ejpam-144	170	34	=	=	SYM
ejpam-144	170	35	0	0	PROPN
ejpam-144	170	36	.	.	PUNCT
ejpam-144	171	1	(	(	PUNCT
ejpam-144	171	2	3.1	3.1	NUM
ejpam-144	171	3	)	)	PUNCT
ejpam-144	171	4	r.	r.	PROPN
ejpam-144	171	5	rashwan	rashwan	PROPN
ejpam-144	171	6	,	,	PUNCT
ejpam-144	171	7	a.	a.	PROPN
ejpam-144	171	8	ahmed	ahmed	PROPN
ejpam-144	171	9	and	and	CCONJ
ejpam-144	171	10	a.	a.	PROPN
ejpam-144	171	11	kamal	kamal	PROPN
ejpam-144	171	12	/	/	SYM
ejpam-144	171	13	eur	eur	PROPN
ejpam-144	171	14	.	.	PUNCT
ejpam-144	172	1	j.	j.	PROPN
ejpam-144	172	2	pure	pure	PROPN
ejpam-144	172	3	appl	appl	PROPN
ejpam-144	172	4	.	.	PROPN
ejpam-144	172	5	math	math	PROPN
ejpam-144	172	6	,	,	PUNCT
ejpam-144	172	7	2	2	NUM
ejpam-144	172	8	(	(	PUNCT
ejpam-144	172	9	2009	2009	NUM
ejpam-144	172	10	)	)	PUNCT
ejpam-144	172	11	,	,	PUNCT
ejpam-144	172	12	(	(	PUNCT
ejpam-144	172	13	250	250	NUM
ejpam-144	172	14	-	-	SYM
ejpam-144	172	15	267	267	NUM
ejpam-144	172	16	)	)	PUNCT
ejpam-144	172	17	260	260	NUM
ejpam-144	172	18	also	also	ADV
ejpam-144	172	19	,	,	PUNCT
ejpam-144	172	20	as	as	ADP
ejpam-144	172	21	a	a	DET
ejpam-144	172	22	subspace	subspace	NOUN
ejpam-144	172	23	ofbα	ofbα	PROPN
ejpam-144	172	24	ω	ω	PROPN
ejpam-144	172	25	,	,	PUNCT
ejpam-144	172	26	we	we	PRON
ejpam-144	172	27	define	define	VERB
ejpam-144	172	28	the	the	DET
ejpam-144	172	29	little	little	ADJ
ejpam-144	172	30	weighted	weight	VERB
ejpam-144	172	31	bloch	bloch	PROPN
ejpam-144	172	32	spacebα	spacebα	PROPN
ejpam-144	172	33	ω,0	ω,0	PROPN
ejpam-144	172	34	as	as	ADP
ejpam-144	172	35	the	the	DET
ejpam-144	172	36	space	space	NOUN
ejpam-144	172	37	which	which	PRON
ejpam-144	172	38	consists	consist	VERB
ejpam-144	172	39	of	of	ADP
ejpam-144	172	40	analytic	analytic	ADJ
ejpam-144	172	41	functions	function	NOUN
ejpam-144	172	42	f	f	PROPN
ejpam-144	172	43	on	on	ADP
ejpam-144	172	44	∆	∆	PROPN
ejpam-144	172	45	such	such	ADJ
ejpam-144	172	46	that	that	SCONJ
ejpam-144	172	47	lim	lim	PROPN
ejpam-144	172	48	|z|→1−	|z|→1−	PROPN
ejpam-144	172	49	(	(	PUNCT
ejpam-144	172	50	1−	1−	NUM
ejpam-144	172	51	|z|)α|	|z|)α|	NOUN
ejpam-144	172	52	f	f	PROPN
ejpam-144	172	53	′(z)|	′(z)|	NOUN
ejpam-144	172	54	ω(1−	ω(1−	PROPN
ejpam-144	172	55	|z|	|z|	NOUN
ejpam-144	172	56	)	)	PUNCT
ejpam-144	172	57	=	=	SYM
ejpam-144	172	58	0	0	NUM
ejpam-144	173	1	where	where	SCONJ
ejpam-144	173	2	0	0	X
ejpam-144	173	3	<	<	X
ejpam-144	173	4	α	α	X
ejpam-144	173	5	<	<	X
ejpam-144	173	6	∞.	∞.	PROPN
ejpam-144	173	7	thus	thus	ADV
ejpam-144	173	8	we	we	PRON
ejpam-144	173	9	can	can	AUX
ejpam-144	173	10	obtain	obtain	VERB
ejpam-144	173	11	the	the	DET
ejpam-144	173	12	following	follow	VERB
ejpam-144	173	13	theorem	theorem	NOUN
ejpam-144	173	14	:	:	PUNCT
ejpam-144	173	15	theorem	theorem	ADJ
ejpam-144	173	16	3.1	3.1	NUM
ejpam-144	173	17	.	.	PUNCT
ejpam-144	174	1	for	for	ADP
ejpam-144	174	2	each	each	DET
ejpam-144	174	3	nondecreasing	nondecrease	VERB
ejpam-144	174	4	function	function	NOUN
ejpam-144	174	5	k	k	NOUN
ejpam-144	175	1	:	:	PUNCT
ejpam-144	176	1	[	[	X
ejpam-144	176	2	0,∞)→	0,∞)→	NOUN
ejpam-144	176	3	[	[	X
ejpam-144	176	4	0,∞	0,∞	NUM
ejpam-144	176	5	)	)	PUNCT
ejpam-144	176	6	,	,	PUNCT
ejpam-144	176	7	0	0	PUNCT
ejpam-144	176	8	<	<	X
ejpam-144	176	9	p	p	X
ejpam-144	176	10	<	<	X
ejpam-144	176	11	∞	∞	PROPN
ejpam-144	176	12	,	,	PUNCT
ejpam-144	176	13	for	for	ADP
ejpam-144	176	14	a	a	DET
ejpam-144	176	15	given	give	VERB
ejpam-144	176	16	reasonable	reasonable	ADJ
ejpam-144	176	17	non	non	ADJ
ejpam-144	176	18	-	-	ADJ
ejpam-144	176	19	decreasing	decrease	VERB
ejpam-144	176	20	function	function	NOUN
ejpam-144	176	21	ω	ω	NOUN
ejpam-144	176	22	:	:	PUNCT
ejpam-144	176	23	(	(	PUNCT
ejpam-144	176	24	0	0	NUM
ejpam-144	176	25	,	,	PUNCT
ejpam-144	176	26	1]→	1]→	NOUN
ejpam-144	176	27	(	(	PUNCT
ejpam-144	176	28	0,∞	0,∞	NOUN
ejpam-144	176	29	)	)	PUNCT
ejpam-144	176	30	withω(α	withω(α	NOUN
ejpam-144	176	31	t)≈ω(t	t)≈ω(t	NOUN
ejpam-144	176	32	)	)	PUNCT
ejpam-144	176	33	,	,	PUNCT
ejpam-144	176	34	α	α	X
ejpam-144	176	35	>	>	X
ejpam-144	176	36	0	0	PROPN
ejpam-144	176	37	.	.	PUNCT
ejpam-144	177	1	then	then	ADV
ejpam-144	177	2	(	(	PUNCT
ejpam-144	177	3	i	i	NOUN
ejpam-144	177	4	)	)	PUNCT
ejpam-144	177	5	qk	qk	PROPN
ejpam-144	177	6	,	,	PUNCT
ejpam-144	177	7	ω,0	ω,0	PROPN
ejpam-144	177	8	⊂b	⊂b	PROPN
ejpam-144	177	9	p+2	p+2	PROPN
ejpam-144	177	10	p	p	NOUN
ejpam-144	177	11	ω,0	ω,0	PROPN
ejpam-144	177	12	and	and	CCONJ
ejpam-144	177	13	(	(	PUNCT
ejpam-144	177	14	ii	ii	NOUN
ejpam-144	177	15	)	)	PUNCT
ejpam-144	177	16	qk	qk	PROPN
ejpam-144	177	17	,	,	PUNCT
ejpam-144	177	18	ω,0	ω,0	PROPN
ejpam-144	178	1	=	=	SYM
ejpam-144	178	2	b	b	X
ejpam-144	178	3	p+2	p+2	PRON
ejpam-144	178	4	p	p	NOUN
ejpam-144	178	5	ω,0	ω,0	PROPN
ejpam-144	178	6	,	,	PUNCT
ejpam-144	178	7	if	if	SCONJ
ejpam-144	178	8	and	and	CCONJ
ejpam-144	178	9	only	only	ADV
ejpam-144	178	10	if	if	SCONJ
ejpam-144	178	11	(	(	PUNCT
ejpam-144	178	12	2.3	2.3	NUM
ejpam-144	178	13	)	)	PUNCT
ejpam-144	178	14	holds	hold	VERB
ejpam-144	178	15	.	.	PUNCT
ejpam-144	179	1	proof	proof	NOUN
ejpam-144	179	2	.	.	PUNCT
ejpam-144	180	1	without	without	ADP
ejpam-144	180	2	loss	loss	NOUN
ejpam-144	180	3	of	of	ADP
ejpam-144	180	4	generality	generality	NOUN
ejpam-144	180	5	,	,	PUNCT
ejpam-144	180	6	we	we	PRON
ejpam-144	180	7	assume	assume	VERB
ejpam-144	180	8	that	that	SCONJ
ejpam-144	180	9	k(1	k(1	PROPN
ejpam-144	180	10	)	)	PUNCT
ejpam-144	180	11	>	>	X
ejpam-144	181	1	0	0	X
ejpam-144	181	2	.	.	PUNCT
ejpam-144	182	1	from	from	ADP
ejpam-144	182	2	the	the	DET
ejpam-144	182	3	proof	proof	NOUN
ejpam-144	182	4	of	of	ADP
ejpam-144	182	5	theorem	theorem	ADJ
ejpam-144	182	6	2.1	2.1	NUM
ejpam-144	182	7	,	,	PUNCT
ejpam-144	182	8	we	we	PRON
ejpam-144	182	9	have	have	VERB
ejpam-144	182	10	that	that	DET
ejpam-144	182	11	π(1	π(1	PROPN
ejpam-144	182	12	e	e	NOUN
ejpam-144	182	13	)	)	PUNCT
ejpam-144	182	14	2	2	PROPN
ejpam-144	182	15	k(1	k(1	NOUN
ejpam-144	182	16	)	)	PUNCT
ejpam-144	182	17	(	(	PUNCT
ejpam-144	182	18	1−|a|)p+2	1−|a|)p+2	NUM
ejpam-144	182	19	ωp(1−|a|	ωp(1−|a|	NOUN
ejpam-144	182	20	)	)	PUNCT
ejpam-144	182	21	|	|	ADV
ejpam-144	182	22	f	f	PROPN
ejpam-144	182	23	′(a)|p	′(a)|p	PROPN
ejpam-144	182	24	≤	≤	PROPN
ejpam-144	182	25	k(1	k(1	PROPN
ejpam-144	182	26	)	)	PUNCT
ejpam-144	182	27	∫	∫	PROPN
ejpam-144	182	28	e(a	e(a	PROPN
ejpam-144	182	29	)	)	PUNCT
ejpam-144	182	30	fω	fω	PROPN
ejpam-144	182	31	,	,	PUNCT
ejpam-144	182	32	p	p	X
ejpam-144	182	33	(	(	PUNCT
ejpam-144	182	34	f	f	PROPN
ejpam-144	182	35	)	)	PUNCT
ejpam-144	182	36	(	(	PUNCT
ejpam-144	182	37	z	z	NOUN
ejpam-144	182	38	)	)	PUNCT
ejpam-144	182	39	dσz	dσz	ADJ
ejpam-144	182	40	≤	≤	PROPN
ejpam-144	182	41	k(1	k(1	PROPN
ejpam-144	182	42	)	)	PUNCT
ejpam-144	182	43	∫	∫	PROPN
ejpam-144	182	44	∆(a	∆(a	PROPN
ejpam-144	182	45	,	,	PUNCT
ejpam-144	182	46	1	1	NUM
ejpam-144	182	47	e	e	NOUN
ejpam-144	182	48	)	)	PUNCT
ejpam-144	182	49	fω	fω	PROPN
ejpam-144	182	50	,	,	PUNCT
ejpam-144	182	51	p	p	X
ejpam-144	182	52	(	(	PUNCT
ejpam-144	182	53	f	f	PROPN
ejpam-144	182	54	)	)	PUNCT
ejpam-144	182	55	(	(	PUNCT
ejpam-144	182	56	z	z	NOUN
ejpam-144	182	57	)	)	PUNCT
ejpam-144	182	58	dσz	dσz	ADJ
ejpam-144	182	59	≤	≤	NUM
ejpam-144	182	60	∫	∫	PROPN
ejpam-144	182	61	∆	∆	PROPN
ejpam-144	182	62	fω	fω	PROPN
ejpam-144	182	63	,	,	PUNCT
ejpam-144	182	64	p	p	X
ejpam-144	182	65	(	(	PUNCT
ejpam-144	182	66	f	f	PROPN
ejpam-144	182	67	)	)	PUNCT
ejpam-144	182	68	(	(	PUNCT
ejpam-144	182	69	z)k	z)k	X
ejpam-144	182	70	�	�	PROPN
ejpam-144	182	71	g(z	g(z	PROPN
ejpam-144	182	72	,	,	PUNCT
ejpam-144	182	73	a	a	DET
ejpam-144	182	74	)	)	PUNCT
ejpam-144	182	75	�	�	PROPN
ejpam-144	182	76	dσz	dσz	NOUN
ejpam-144	182	77	,	,	PUNCT
ejpam-144	182	78	where	where	SCONJ
ejpam-144	182	79	e(a	e(a	NOUN
ejpam-144	182	80	)	)	PUNCT
ejpam-144	182	81	=	=	SYM
ejpam-144	182	82	�	�	PROPN
ejpam-144	182	83	z	z	PROPN
ejpam-144	182	84	∈∆	∈∆	NOUN
ejpam-144	182	85	,	,	PUNCT
ejpam-144	182	86	|z−	|z−	VERB
ejpam-144	182	87	a|	a|	PROPN
ejpam-144	182	88	<	<	X
ejpam-144	182	89	1	1	NUM
ejpam-144	182	90	e	e	X
ejpam-144	182	91	(	(	PUNCT
ejpam-144	182	92	1−	1−	NUM
ejpam-144	182	93	|a|	|a|	NOUN
ejpam-144	182	94	)	)	PUNCT
ejpam-144	182	95	�	�	PROPN
ejpam-144	182	96	.	.	PUNCT
ejpam-144	183	1	if	if	SCONJ
ejpam-144	183	2	f	f	PROPN
ejpam-144	183	3	∈	∈	PROPN
ejpam-144	183	4	qk	qk	PROPN
ejpam-144	183	5	,	,	PUNCT
ejpam-144	183	6	ω,0	ω,0	PROPN
ejpam-144	183	7	,	,	PUNCT
ejpam-144	183	8	we	we	PRON
ejpam-144	183	9	obtain	obtain	VERB
ejpam-144	183	10	that	that	SCONJ
ejpam-144	183	11	lim	lim	PROPN
ejpam-144	183	12	|a|→1−	|a|→1−	PROPN
ejpam-144	183	13	(	(	PUNCT
ejpam-144	183	14	1−	1−	NUM
ejpam-144	183	15	|a|)p+2|	|a|)p+2|	NOUN
ejpam-144	183	16	f	f	PROPN
ejpam-144	183	17	′(a)|p	′(a)|p	PROPN
ejpam-144	183	18	ωp(1−	ωp(1−	PROPN
ejpam-144	183	19	|a|	|a|	PROPN
ejpam-144	183	20	)	)	PUNCT
ejpam-144	183	21	=	=	SYM
ejpam-144	183	22	0	0	X
ejpam-144	183	23	.	.	PUNCT
ejpam-144	183	24	(	(	PUNCT
ejpam-144	183	25	ii	ii	NOUN
ejpam-144	183	26	)	)	PUNCT
ejpam-144	183	27	we	we	PRON
ejpam-144	183	28	only	only	ADV
ejpam-144	183	29	need	need	VERB
ejpam-144	183	30	to	to	PART
ejpam-144	183	31	prove	prove	VERB
ejpam-144	183	32	thatb	thatb	PROPN
ejpam-144	183	33	p+2	p+2	PROPN
ejpam-144	184	1	p	p	PROPN
ejpam-144	185	1	ω,0	ω,0	PROPN
ejpam-144	185	2	⊂qk	⊂qk	PROPN
ejpam-144	185	3	,	,	PUNCT
ejpam-144	185	4	w,0	w,0	PROPN
ejpam-144	185	5	.	.	PUNCT
ejpam-144	186	1	assume	assume	VERB
ejpam-144	186	2	that	that	SCONJ
ejpam-144	186	3	a=	a=	NOUN
ejpam-144	186	4	∫	∫	PROPN
ejpam-144	186	5	1	1	NUM
ejpam-144	186	6	0	0	NUM
ejpam-144	186	7	k	k	PROPN
ejpam-144	186	8	�	�	PROPN
ejpam-144	186	9	log	log	VERB
ejpam-144	186	10	1	1	NUM
ejpam-144	186	11	r	r	NOUN
ejpam-144	186	12	�	�	PROPN
ejpam-144	186	13	r	r	NOUN
ejpam-144	186	14	(	(	PUNCT
ejpam-144	186	15	1−	1−	NUM
ejpam-144	186	16	r2)2	r2)2	NOUN
ejpam-144	186	17	dr	dr	PROPN
ejpam-144	186	18	<	<	PROPN
ejpam-144	186	19	∞.	∞.	PROPN
ejpam-144	186	20	r.	r.	PROPN
ejpam-144	186	21	rashwan	rashwan	PROPN
ejpam-144	186	22	,	,	PUNCT
ejpam-144	186	23	a.	a.	PROPN
ejpam-144	186	24	ahmed	ahmed	PROPN
ejpam-144	186	25	and	and	CCONJ
ejpam-144	186	26	a.	a.	PROPN
ejpam-144	186	27	kamal	kamal	PROPN
ejpam-144	186	28	/	/	SYM
ejpam-144	186	29	eur	eur	PROPN
ejpam-144	186	30	.	.	PUNCT
ejpam-144	187	1	j.	j.	PROPN
ejpam-144	187	2	pure	pure	PROPN
ejpam-144	187	3	appl	appl	PROPN
ejpam-144	187	4	.	.	PROPN
ejpam-144	187	5	math	math	PROPN
ejpam-144	187	6	,	,	PUNCT
ejpam-144	187	7	2	2	NUM
ejpam-144	187	8	(	(	PUNCT
ejpam-144	187	9	2009	2009	NUM
ejpam-144	187	10	)	)	PUNCT
ejpam-144	187	11	,	,	PUNCT
ejpam-144	187	12	(	(	PUNCT
ejpam-144	187	13	250	250	NUM
ejpam-144	187	14	-	-	SYM
ejpam-144	187	15	267	267	NUM
ejpam-144	187	16	)	)	PUNCT
ejpam-144	187	17	261	261	NUM
ejpam-144	187	18	for	for	ADP
ejpam-144	187	19	a	a	DET
ejpam-144	187	20	given	give	VERB
ejpam-144	187	21	ε	ε	PROPN
ejpam-144	187	22	>	>	X
ejpam-144	187	23	0	0	PUNCT
ejpam-144	188	1	there	there	PRON
ejpam-144	188	2	exists	exist	VERB
ejpam-144	188	3	an	an	DET
ejpam-144	188	4	r1	r1	NOUN
ejpam-144	188	5	,	,	PUNCT
ejpam-144	188	6	0	0	PUNCT
ejpam-144	188	7	<	<	X
ejpam-144	188	8	r1	r1	PROPN
ejpam-144	188	9	<	<	X
ejpam-144	188	10	1	1	NUM
ejpam-144	188	11	,	,	PUNCT
ejpam-144	188	12	such	such	ADJ
ejpam-144	188	13	that	that	PRON
ejpam-144	188	14	∫	∫	PROPN
ejpam-144	188	15	1	1	NUM
ejpam-144	188	16	r1	r1	PROPN
ejpam-144	188	17	k	k	PROPN
ejpam-144	188	18	�	�	PROPN
ejpam-144	188	19	log	log	VERB
ejpam-144	188	20	1	1	NUM
ejpam-144	188	21	r	r	NOUN
ejpam-144	188	22	�	�	PROPN
ejpam-144	188	23	r	r	NOUN
ejpam-144	188	24	(	(	PUNCT
ejpam-144	188	25	1−	1−	NUM
ejpam-144	188	26	r2)2	r2)2	NOUN
ejpam-144	188	27	dr	dr	PROPN
ejpam-144	188	28	<	<	X
ejpam-144	188	29	ε	ε	PROPN
ejpam-144	188	30	.	.	PUNCT
ejpam-144	188	31	(	(	PUNCT
ejpam-144	188	32	3.2	3.2	NUM
ejpam-144	188	33	)	)	PUNCT
ejpam-144	188	34	then	then	ADV
ejpam-144	188	35	we	we	PRON
ejpam-144	188	36	have	have	VERB
ejpam-144	188	37	that	that	PRON
ejpam-144	188	38	,	,	PUNCT
ejpam-144	189	1	∫	∫	PROPN
ejpam-144	189	2	∆\∆(a	∆\∆(a	PROPN
ejpam-144	189	3	,	,	PUNCT
ejpam-144	189	4	r1	r1	PROPN
ejpam-144	189	5	)	)	PUNCT
ejpam-144	189	6	�	�	PROPN
ejpam-144	189	7	�	�	PROPN
ejpam-144	189	8	f	f	PROPN
ejpam-144	189	9	′(z	′(z	NOUN
ejpam-144	189	10	)	)	PUNCT
ejpam-144	189	11	�	�	PROPN
ejpam-144	189	12	�	�	PROPN
ejpam-144	189	13	p	p	PROPN
ejpam-144	189	14	(	(	PUNCT
ejpam-144	189	15	1−	1−	NUM
ejpam-144	189	16	|z|)p	|z|)p	PROPN
ejpam-144	189	17	k(g(z	k(g(z	PROPN
ejpam-144	189	18	,	,	PUNCT
ejpam-144	189	19	a	a	PRON
ejpam-144	189	20	)	)	PUNCT
ejpam-144	189	21	)	)	PUNCT
ejpam-144	189	22	ωp(1−	ωp(1−	ADJ
ejpam-144	189	23	|z|	|z|	NOUN
ejpam-144	189	24	)	)	PUNCT
ejpam-144	189	25	dσz	dσz	ADJ
ejpam-144	189	26	≤	≤	NUM
ejpam-144	189	27	f	f	PROPN
ejpam-144	189	28	p	p	X
ejpam-144	189	29	b	b	PROPN
ejpam-144	190	1	p+2	p+2	DET
ejpam-144	190	2	p	p	NOUN
ejpam-144	190	3	ω,0	ω,0	NUM
ejpam-144	190	4	∫	∫	PROPN
ejpam-144	190	5	∆\∆(a	∆\∆(a	PROPN
ejpam-144	190	6	,	,	PUNCT
ejpam-144	190	7	r1	r1	NOUN
ejpam-144	190	8	)	)	PUNCT
ejpam-144	190	9	k(g(z	k(g(z	PROPN
ejpam-144	190	10	,	,	PUNCT
ejpam-144	190	11	a	a	NOUN
ejpam-144	190	12	)	)	PUNCT
ejpam-144	190	13	)	)	PUNCT
ejpam-144	190	14	(	(	PUNCT
ejpam-144	190	15	1−	1−	NUM
ejpam-144	190	16	|z|2)2	|z|2)2	PROPN
ejpam-144	190	17	dσz	dσz	NOUN
ejpam-144	190	18	=	=	SYM
ejpam-144	190	19	f	f	PROPN
ejpam-144	190	20	p	p	X
ejpam-144	190	21	b	b	PROPN
ejpam-144	190	22	p+2	p+2	PRON
ejpam-144	190	23	p	p	NOUN
ejpam-144	190	24	ω,0	ω,0	NUM
ejpam-144	190	25	∫	∫	NOUN
ejpam-144	191	1	r1<|w|<1	r1<|w|<1	PROPN
ejpam-144	192	1	k	k	PROPN
ejpam-144	192	2	�	�	PROPN
ejpam-144	192	3	log	log	VERB
ejpam-144	192	4	1	1	NUM
ejpam-144	192	5	|w|	|w|	PROPN
ejpam-144	192	6	�	�	NOUN
ejpam-144	192	7	1	1	NUM
ejpam-144	192	8	(	(	PUNCT
ejpam-144	192	9	1−	1−	NUM
ejpam-144	192	10	|w|2)2	|w|2)2	NOUN
ejpam-144	192	11	dσw	dσw	VERB
ejpam-144	192	12	=	=	PUNCT
ejpam-144	192	13	f	f	PROPN
ejpam-144	192	14	p	p	X
ejpam-144	192	15	b	b	PROPN
ejpam-144	193	1	p+2	p+2	DET
ejpam-144	193	2	p	p	NOUN
ejpam-144	193	3	ω,0	ω,0	NUM
ejpam-144	193	4	∫	∫	PROPN
ejpam-144	193	5	1	1	NUM
ejpam-144	193	6	r1	r1	PROPN
ejpam-144	193	7	k	k	PROPN
ejpam-144	193	8	�	�	PROPN
ejpam-144	193	9	log	log	VERB
ejpam-144	193	10	1	1	NUM
ejpam-144	193	11	r	r	NOUN
ejpam-144	193	12	�	�	PROPN
ejpam-144	193	13	r	r	NOUN
ejpam-144	193	14	(	(	PUNCT
ejpam-144	193	15	1−	1−	NUM
ejpam-144	193	16	r2)2	r2)2	NOUN
ejpam-144	193	17	dr	dr	PROPN
ejpam-144	193	18	≤	≤	NUM
ejpam-144	193	19	2πε	2πε	NOUN
ejpam-144	194	1	f	f	X
ejpam-144	194	2	p	p	X
ejpam-144	194	3	b	b	PROPN
ejpam-144	194	4	p+2	p+2	PRON
ejpam-144	194	5	p	p	NOUN
ejpam-144	194	6	ω,0	ω,0	PROPN
ejpam-144	194	7	.	.	PUNCT
ejpam-144	195	1	(	(	PUNCT
ejpam-144	195	2	3.3	3.3	NUM
ejpam-144	195	3	)	)	PUNCT
ejpam-144	195	4	similarly	similarly	ADV
ejpam-144	195	5	,	,	PUNCT
ejpam-144	195	6	if	if	SCONJ
ejpam-144	195	7	f	f	PROPN
ejpam-144	195	8	∈b	∈b	PROPN
ejpam-144	195	9	p+2	p+2	PROPN
ejpam-144	195	10	p	p	PROPN
ejpam-144	195	11	ω,0	ω,0	PROPN
ejpam-144	195	12	,	,	PUNCT
ejpam-144	195	13	we	we	PRON
ejpam-144	195	14	obtain	obtain	VERB
ejpam-144	195	15	that	that	SCONJ
ejpam-144	196	1	|	|	ADV
ejpam-144	196	2	f	f	PROPN
ejpam-144	196	3	′(ϕa(w))|	′(ϕa(w))|	PROPN
ejpam-144	196	4	p	p	X
ejpam-144	196	5	(	(	PUNCT
ejpam-144	196	6	1−	1−	NUM
ejpam-144	196	7	|ϕa(w)|	|ϕa(w)|	PROPN
ejpam-144	196	8	2	2	NUM
ejpam-144	196	9	)	)	PUNCT
ejpam-144	196	10	p+2	p+2	PROPN
ejpam-144	196	11	p	p	PROPN
ejpam-144	196	12	ωp(1−	ωp(1−	PROPN
ejpam-144	196	13	|ϕa(w)|	|ϕa(w)|	ADJ
ejpam-144	196	14	)	)	PUNCT
ejpam-144	196	15	−→	−→	NOUN
ejpam-144	196	16	0	0	NUM
ejpam-144	196	17	converges	converge	VERB
ejpam-144	196	18	uniformly	uniformly	ADV
ejpam-144	196	19	for	for	ADP
ejpam-144	196	20	|w|	|w|	ADJ
ejpam-144	196	21	≤	≤	NUM
ejpam-144	196	22	r	r	NOUN
ejpam-144	196	23	if	if	SCONJ
ejpam-144	196	24	|a|	|a|	PROPN
ejpam-144	196	25	→	→	SYM
ejpam-144	196	26	1−	1−	NUM
ejpam-144	196	27	,	,	PUNCT
ejpam-144	196	28	where	where	SCONJ
ejpam-144	196	29	r	r	NOUN
ejpam-144	196	30	is	be	AUX
ejpam-144	196	31	fixed	fix	VERB
ejpam-144	196	32	and	and	CCONJ
ejpam-144	196	33	0	0	NUM
ejpam-144	196	34	<	<	X
ejpam-144	196	35	r	r	X
ejpam-144	196	36	<	<	X
ejpam-144	196	37	1	1	NUM
ejpam-144	196	38	.	.	PUNCT
ejpam-144	197	1	then	then	ADV
ejpam-144	197	2	,	,	PUNCT
ejpam-144	197	3	we	we	PRON
ejpam-144	197	4	obtain	obtain	VERB
ejpam-144	197	5	that	that	SCONJ
ejpam-144	197	6	lim	lim	PROPN
ejpam-144	197	7	|a|→1−	|a|→1−	PROPN
ejpam-144	197	8	∫	∫	PROPN
ejpam-144	197	9	∆	∆	PROPN
ejpam-144	197	10	�	�	PROPN
ejpam-144	197	11	�	�	PROPN
ejpam-144	197	12	f	f	PROPN
ejpam-144	197	13	′(z	′(z	NOUN
ejpam-144	197	14	)	)	PUNCT
ejpam-144	197	15	�	�	PROPN
ejpam-144	197	16	�	�	PROPN
ejpam-144	197	17	p	p	PROPN
ejpam-144	197	18	(	(	PUNCT
ejpam-144	197	19	1−	1−	NUM
ejpam-144	197	20	|z|)p	|z|)p	PROPN
ejpam-144	197	21	k	k	PROPN
ejpam-144	197	22	�	�	PROPN
ejpam-144	197	23	g(z	g(z	PROPN
ejpam-144	197	24	,	,	PUNCT
ejpam-144	197	25	a	a	PRON
ejpam-144	197	26	)	)	PUNCT
ejpam-144	197	27	�	�	PROPN
ejpam-144	197	28	ωp(1−	ωp(1−	ADJ
ejpam-144	197	29	|z|	|z|	NOUN
ejpam-144	197	30	)	)	PUNCT
ejpam-144	197	31	dσz	dσz	NOUN
ejpam-144	197	32	=	=	PROPN
ejpam-144	197	33	lim	lim	PROPN
ejpam-144	197	34	|a|→1−	|a|→1−	PROPN
ejpam-144	197	35	∫	∫	PROPN
ejpam-144	197	36	|w|<r	|w|<r	PROPN
ejpam-144	197	37	�	�	PROPN
ejpam-144	197	38	�	�	PROPN
ejpam-144	197	39	f	f	PROPN
ejpam-144	197	40	′(ϕa(w	′(ϕa(w	PROPN
ejpam-144	197	41	)	)	PUNCT
ejpam-144	197	42	)	)	PUNCT
ejpam-144	198	1	�	�	PROPN
ejpam-144	198	2	�	�	PROPN
ejpam-144	198	3	p	p	PROPN
ejpam-144	198	4	(	(	PUNCT
ejpam-144	198	5	1−	1−	NUM
ejpam-144	198	6	|ϕa(w)|	|ϕa(w)|	PROPN
ejpam-144	198	7	)	)	PUNCT
ejpam-144	198	8	p	p	PROPN
ejpam-144	198	9	k	k	PROPN
ejpam-144	198	10	�	�	PROPN
ejpam-144	198	11	log	log	VERB
ejpam-144	198	12	1	1	NUM
ejpam-144	198	13	|w|	|w|	PROPN
ejpam-144	198	14	�	�	PROPN
ejpam-144	198	15	ωp(1−	ωp(1−	ADJ
ejpam-144	198	16	|ϕa(w)|	|ϕa(w)|	PROPN
ejpam-144	198	17	)	)	PUNCT
ejpam-144	198	18	1	1	NUM
ejpam-144	198	19	(	(	PUNCT
ejpam-144	198	20	1−	1−	NUM
ejpam-144	198	21	|w|2)2	|w|2)2	NOUN
ejpam-144	198	22	dσw	dσw	VERB
ejpam-144	198	23	.	.	PUNCT
ejpam-144	199	1	≤	≤	NOUN
ejpam-144	199	2	a	a	DET
ejpam-144	199	3	lim	lim	PROPN
ejpam-144	199	4	|a|→1−	|a|→1−	PROPN
ejpam-144	199	5	sup	sup	PROPN
ejpam-144	199	6	|w|≤r1	|w|≤r1	PROPN
ejpam-144	199	7	�	�	PROPN
ejpam-144	199	8	�	�	PROPN
ejpam-144	199	9	f	f	PROPN
ejpam-144	199	10	′(ϕa(w	′(ϕa(w	PROPN
ejpam-144	199	11	)	)	PUNCT
ejpam-144	199	12	)	)	PUNCT
ejpam-144	200	1	�	�	PROPN
ejpam-144	200	2	�	�	PROPN
ejpam-144	200	3	p	p	PROPN
ejpam-144	200	4	(	(	PUNCT
ejpam-144	200	5	1−	1−	NUM
ejpam-144	200	6	|ϕa(w)|	|ϕa(w)|	PROPN
ejpam-144	200	7	)	)	PUNCT
ejpam-144	200	8	p+2	p+2	PROPN
ejpam-144	200	9	ωp(1−	ωp(1−	PROPN
ejpam-144	200	10	|ϕa(w)|	|ϕa(w)|	PROPN
ejpam-144	200	11	)	)	PUNCT
ejpam-144	200	12	=	=	SYM
ejpam-144	200	13	0	0	NUM
ejpam-144	200	14	(	(	PUNCT
ejpam-144	200	15	3.4	3.4	NUM
ejpam-144	200	16	)	)	PUNCT
ejpam-144	200	17	where	where	SCONJ
ejpam-144	200	18	by	by	ADP
ejpam-144	200	19	(	(	PUNCT
ejpam-144	200	20	3.2	3.2	NUM
ejpam-144	200	21	)	)	PUNCT
ejpam-144	200	22	and	and	CCONJ
ejpam-144	200	23	(	(	PUNCT
ejpam-144	200	24	3.3	3.3	NUM
ejpam-144	200	25	)	)	PUNCT
ejpam-144	200	26	it	it	PRON
ejpam-144	200	27	is	be	AUX
ejpam-144	200	28	easy	easy	ADJ
ejpam-144	200	29	to	to	PART
ejpam-144	200	30	obtain	obtain	VERB
ejpam-144	200	31	that	that	SCONJ
ejpam-144	200	32	lim	lim	PROPN
ejpam-144	200	33	|a|→1−	|a|→1−	PROPN
ejpam-144	200	34	∫	∫	PROPN
ejpam-144	200	35	∆	∆	PROPN
ejpam-144	200	36	�	�	PROPN
ejpam-144	200	37	�	�	PROPN
ejpam-144	200	38	f	f	PROPN
ejpam-144	200	39	′(z	′(z	NOUN
ejpam-144	200	40	)	)	PUNCT
ejpam-144	200	41	�	�	PROPN
ejpam-144	200	42	�	�	PROPN
ejpam-144	200	43	p	p	PROPN
ejpam-144	200	44	(	(	PUNCT
ejpam-144	200	45	1−	1−	NUM
ejpam-144	200	46	|z|)p	|z|)p	PROPN
ejpam-144	200	47	k	k	PROPN
ejpam-144	200	48	�	�	PROPN
ejpam-144	200	49	g(z	g(z	PROPN
ejpam-144	200	50	,	,	PUNCT
ejpam-144	200	51	a	a	PRON
ejpam-144	200	52	)	)	PUNCT
ejpam-144	200	53	�	�	PROPN
ejpam-144	200	54	ωp(1−	ωp(1−	ADJ
ejpam-144	200	55	|z|	|z|	NOUN
ejpam-144	200	56	)	)	PUNCT
ejpam-144	200	57	dσz	dσz	NOUN
ejpam-144	200	58	=	=	SYM
ejpam-144	200	59	0	0	PROPN
ejpam-144	200	60	.	.	PUNCT
ejpam-144	201	1	(	(	PUNCT
ejpam-144	201	2	3.5	3.5	NUM
ejpam-144	201	3	)	)	PUNCT
ejpam-144	201	4	conversely	conversely	ADV
ejpam-144	201	5	,	,	PUNCT
ejpam-144	201	6	suppose	suppose	VERB
ejpam-144	201	7	that	that	SCONJ
ejpam-144	201	8	(	(	PUNCT
ejpam-144	201	9	2.3	2.3	NUM
ejpam-144	201	10	)	)	PUNCT
ejpam-144	201	11	does	do	AUX
ejpam-144	201	12	not	not	PART
ejpam-144	201	13	hold	hold	VERB
ejpam-144	201	14	;	;	PUNCT
ejpam-144	201	15	that	that	PRON
ejpam-144	201	16	is	be	AUX
ejpam-144	201	17	∫	∫	PROPN
ejpam-144	201	18	1	1	NUM
ejpam-144	201	19	0	0	NUM
ejpam-144	201	20	k	k	PROPN
ejpam-144	201	21	�	�	PROPN
ejpam-144	201	22	log	log	VERB
ejpam-144	201	23	1	1	NUM
ejpam-144	201	24	r	r	NOUN
ejpam-144	201	25	�	�	PROPN
ejpam-144	201	26	r	r	NOUN
ejpam-144	201	27	(	(	PUNCT
ejpam-144	201	28	1−	1−	NUM
ejpam-144	201	29	r2)2	r2)2	NOUN
ejpam-144	201	30	dr	dr	PROPN
ejpam-144	201	31	=	=	PROPN
ejpam-144	201	32	∞.	∞.	PROPN
ejpam-144	201	33	r.	r.	PROPN
ejpam-144	201	34	rashwan	rashwan	PROPN
ejpam-144	201	35	,	,	PUNCT
ejpam-144	201	36	a.	a.	PROPN
ejpam-144	201	37	ahmed	ahmed	PROPN
ejpam-144	201	38	and	and	CCONJ
ejpam-144	201	39	a.	a.	PROPN
ejpam-144	201	40	kamal	kamal	PROPN
ejpam-144	201	41	/	/	SYM
ejpam-144	201	42	eur	eur	PROPN
ejpam-144	201	43	.	.	PUNCT
ejpam-144	202	1	j.	j.	PROPN
ejpam-144	202	2	pure	pure	PROPN
ejpam-144	202	3	appl	appl	PROPN
ejpam-144	202	4	.	.	PROPN
ejpam-144	202	5	math	math	PROPN
ejpam-144	202	6	,	,	PUNCT
ejpam-144	202	7	2	2	NUM
ejpam-144	202	8	(	(	PUNCT
ejpam-144	202	9	2009	2009	NUM
ejpam-144	202	10	)	)	PUNCT
ejpam-144	202	11	,	,	PUNCT
ejpam-144	202	12	(	(	PUNCT
ejpam-144	202	13	250	250	NUM
ejpam-144	202	14	-	-	SYM
ejpam-144	202	15	267	267	NUM
ejpam-144	202	16	)	)	PUNCT
ejpam-144	202	17	262	262	NUM
ejpam-144	202	18	thus	thus	ADV
ejpam-144	202	19	we	we	PRON
ejpam-144	202	20	find	find	VERB
ejpam-144	202	21	a	a	DET
ejpam-144	202	22	continuous	continuous	ADJ
ejpam-144	202	23	strictly	strictly	ADV
ejpam-144	202	24	decreasing	decrease	VERB
ejpam-144	202	25	function	function	NOUN
ejpam-144	202	26	g	g	NOUN
ejpam-144	202	27	:	:	PUNCT
ejpam-144	203	1	[	[	X
ejpam-144	203	2	0	0	NUM
ejpam-144	203	3	,	,	PUNCT
ejpam-144	203	4	1	1	X
ejpam-144	203	5	)	)	PUNCT
ejpam-144	203	6	−→	−→	NOUN
ejpam-144	203	7	[	[	X
ejpam-144	203	8	0,∞	0,∞	NOUN
ejpam-144	203	9	)	)	PUNCT
ejpam-144	203	10	tending	tend	VERB
ejpam-144	203	11	to	to	ADP
ejpam-144	203	12	zero	zero	NUM
ejpam-144	203	13	at	at	ADP
ejpam-144	203	14	1	1	NUM
ejpam-144	203	15	such	such	ADJ
ejpam-144	203	16	that	that	PRON
ejpam-144	203	17	∫	∫	PROPN
ejpam-144	203	18	1	1	NUM
ejpam-144	203	19	0	0	NUM
ejpam-144	203	20	k	k	PROPN
ejpam-144	203	21	�	�	PROPN
ejpam-144	203	22	log	log	VERB
ejpam-144	203	23	1	1	NUM
ejpam-144	203	24	r	r	NOUN
ejpam-144	203	25	�	�	PROPN
ejpam-144	203	26	g(r	g(r	PROPN
ejpam-144	203	27	)	)	PUNCT
ejpam-144	203	28	(	(	PUNCT
ejpam-144	203	29	1−	1−	NUM
ejpam-144	203	30	r2)2	r2)2	NOUN
ejpam-144	203	31	r	r	NOUN
ejpam-144	203	32	dr	dr	PROPN
ejpam-144	203	33	=	=	PROPN
ejpam-144	203	34	∞.	∞.	PROPN
ejpam-144	203	35	(	(	PUNCT
ejpam-144	203	36	3.6	3.6	NUM
ejpam-144	203	37	)	)	PUNCT
ejpam-144	203	38	it	it	PRON
ejpam-144	203	39	is	be	AUX
ejpam-144	203	40	easy	easy	ADJ
ejpam-144	203	41	to	to	PART
ejpam-144	203	42	see	see	VERB
ejpam-144	203	43	that	that	SCONJ
ejpam-144	203	44	r2k+1−2	r2k+1−2	PROPN
ejpam-144	203	45	≥	≥	NUM
ejpam-144	203	46	exp{−2k+2(1	exp{−2k+2(1	NOUN
ejpam-144	203	47	+	+	X
ejpam-144	203	48	r	r	NOUN
ejpam-144	203	49	)	)	PUNCT
ejpam-144	203	50	}	}	PUNCT
ejpam-144	203	51	,	,	PUNCT
ejpam-144	203	52	r	r	NOUN
ejpam-144	203	53	∈	∈	PROPN
ejpam-144	204	1	[	[	X
ejpam-144	204	2	0.5	0.5	NUM
ejpam-144	204	3	,	,	PUNCT
ejpam-144	204	4	1	1	NUM
ejpam-144	204	5	)	)	PUNCT
ejpam-144	204	6	.	.	PUNCT
ejpam-144	205	1	(	(	PUNCT
ejpam-144	205	2	3.7	3.7	NUM
ejpam-144	205	3	)	)	PUNCT
ejpam-144	205	4	we	we	PRON
ejpam-144	205	5	know	know	VERB
ejpam-144	205	6	for	for	ADP
ejpam-144	205	7	β	β	X
ejpam-144	205	8	>	>	X
ejpam-144	205	9	0	0	PUNCT
ejpam-144	206	1	that	that	PRON
ejpam-144	206	2	,	,	PUNCT
ejpam-144	206	3	t2β	t2β	PROPN
ejpam-144	206	4	exp{−4	exp{−4	NOUN
ejpam-144	206	5	t	t	PROPN
ejpam-144	206	6	}	}	PUNCT
ejpam-144	206	7	t=	t=	NOUN
ejpam-144	206	8	β	β	X
ejpam-144	206	9	2	2	NUM
ejpam-144	206	10	=	=	SYM
ejpam-144	206	11	�	�	PROPN
ejpam-144	206	12	β	β	PROPN
ejpam-144	206	13	2	2	NUM
ejpam-144	206	14	�	�	PROPN
ejpam-144	206	15	2β	2β	NOUN
ejpam-144	206	16	exp{−2β	exp{−2β	NOUN
ejpam-144	206	17	}	}	PUNCT
ejpam-144	206	18	.	.	PUNCT
ejpam-144	207	1	then	then	ADV
ejpam-144	207	2	,	,	PUNCT
ejpam-144	207	3	there	there	PRON
ejpam-144	207	4	exists	exist	VERB
ejpam-144	207	5	an	an	DET
ejpam-144	207	6	integer	integer	NOUN
ejpam-144	207	7	k	k	PROPN
ejpam-144	207	8	for	for	ADP
ejpam-144	207	9	3	3	NUM
ejpam-144	207	10	4	4	NUM
ejpam-144	207	11	≤	≤	NOUN
ejpam-144	207	12	r	r	NOUN
ejpam-144	207	13	<	<	X
ejpam-144	207	14	1	1	NUM
ejpam-144	207	15	such	such	ADJ
ejpam-144	207	16	that	that	SCONJ
ejpam-144	207	17	β	β	PROPN
ejpam-144	207	18	2	2	NUM
ejpam-144	207	19	≤	≤	NOUN
ejpam-144	207	20	2k(1−	2k(1−	NUM
ejpam-144	207	21	r	r	NOUN
ejpam-144	207	22	)	)	PUNCT
ejpam-144	207	23	<	<	X
ejpam-144	207	24	β+1	β+1	NUM
ejpam-144	207	25	2	2	NUM
ejpam-144	207	26	and	and	CCONJ
ejpam-144	207	27	2βk	2βk	ADJ
ejpam-144	207	28	exp{−2k+2(1−	exp{−2k+2(1−	PROPN
ejpam-144	207	29	r	r	NOUN
ejpam-144	207	30	)	)	PUNCT
ejpam-144	207	31	}	}	PUNCT
ejpam-144	207	32	=	=	SYM
ejpam-144	207	33	(	(	PUNCT
ejpam-144	207	34	1−	1−	NUM
ejpam-144	207	35	r)−2β	r)−2β	NOUN
ejpam-144	207	36	�	�	PROPN
ejpam-144	207	37	2k(1−	2k(1−	NUM
ejpam-144	207	38	r	r	NOUN
ejpam-144	207	39	)	)	PUNCT
ejpam-144	207	40	�	�	NOUN
ejpam-144	207	41	2β	2β	NOUN
ejpam-144	207	42	exp{−2k+2(1−	exp{−2k+2(1−	PROPN
ejpam-144	207	43	r	r	NOUN
ejpam-144	207	44	)	)	PUNCT
ejpam-144	207	45	}	}	PUNCT
ejpam-144	207	46	>	>	PUNCT
ejpam-144	207	47	�	�	PROPN
ejpam-144	207	48	1	1	NUM
ejpam-144	207	49	+	+	CCONJ
ejpam-144	207	50	β	β	PROPN
ejpam-144	207	51	2	2	NUM
ejpam-144	207	52	�	�	NOUN
ejpam-144	207	53	2β	2β	NOUN
ejpam-144	207	54	(	(	PUNCT
ejpam-144	207	55	1−	1−	NUM
ejpam-144	207	56	r)−2β	r)−2β	NOUN
ejpam-144	207	57	exp{−2(β	exp{−2(β	PROPN
ejpam-144	207	58	+	+	CCONJ
ejpam-144	207	59	1	1	NUM
ejpam-144	207	60	)	)	PUNCT
ejpam-144	207	61	}	}	PUNCT
ejpam-144	207	62	.	.	PUNCT
ejpam-144	208	1	(	(	PUNCT
ejpam-144	208	2	3.8	3.8	NUM
ejpam-144	208	3	)	)	PUNCT
ejpam-144	208	4	for	for	ADP
ejpam-144	208	5	3	3	NUM
ejpam-144	208	6	4	4	NUM
ejpam-144	208	7	≤	≤	NOUN
ejpam-144	208	8	r	r	NOUN
ejpam-144	208	9	<	<	X
ejpam-144	208	10	1	1	NUM
ejpam-144	208	11	we	we	PRON
ejpam-144	208	12	define	define	VERB
ejpam-144	208	13	f0(z	f0(z	PUNCT
ejpam-144	208	14	)	)	PUNCT
ejpam-144	208	15	=	=	SYM
ejpam-144	209	1	∞	∞	NUM
ejpam-144	209	2	∑	∑	PUNCT
ejpam-144	209	3	k=0	k=0	PROPN
ejpam-144	209	4	ak	ak	PROPN
ejpam-144	209	5	2	2	NUM
ejpam-144	209	6	2k	2k	NOUN
ejpam-144	209	7	p	p	ADJ
ejpam-144	209	8	z2k	z2k	PROPN
ejpam-144	209	9	,	,	PUNCT
ejpam-144	209	10	where	where	SCONJ
ejpam-144	209	11	ak	ak	PROPN
ejpam-144	209	12	=	=	PROPN
ejpam-144	209	13	g	g	PROPN
ejpam-144	209	14	�	�	PROPN
ejpam-144	209	15	1−	1−	NUM
ejpam-144	209	16	(	(	PUNCT
ejpam-144	209	17	p+1	p+1	NOUN
ejpam-144	209	18	)	)	PUNCT
ejpam-144	209	19	p	p	NOUN
ejpam-144	209	20	2k	2k	PROPN
ejpam-144	209	21	�	�	PROPN
ejpam-144	209	22	,	,	PUNCT
ejpam-144	209	23	k	k	PROPN
ejpam-144	209	24	=	=	SYM
ejpam-144	209	25	0	0	NUM
ejpam-144	209	26	,	,	PUNCT
ejpam-144	209	27	1	1	NUM
ejpam-144	209	28	,	,	PUNCT
ejpam-144	209	29	2	2	NUM
ejpam-144	209	30	,	,	PUNCT
ejpam-144	209	31	.	.	PUNCT
ejpam-144	209	32	.	.	PUNCT
ejpam-144	209	33	.	.	PUNCT
ejpam-144	209	34	.	.	PUNCT
ejpam-144	210	1	by	by	ADP
ejpam-144	210	2	(	(	PUNCT
ejpam-144	210	3	3.7	3.7	NUM
ejpam-144	210	4	)	)	PUNCT
ejpam-144	210	5	and	and	CCONJ
ejpam-144	210	6	(	(	PUNCT
ejpam-144	210	7	3.8	3.8	NUM
ejpam-144	210	8	)	)	PUNCT
ejpam-144	210	9	,	,	PUNCT
ejpam-144	210	10	we	we	PRON
ejpam-144	210	11	deduce	deduce	VERB
ejpam-144	210	12	that	that	SCONJ
ejpam-144	210	13	m2	m2	PROPN
ejpam-144	210	14	2	2	NUM
ejpam-144	210	15	(	(	PUNCT
ejpam-144	210	16	r	r	NOUN
ejpam-144	210	17	,	,	PUNCT
ejpam-144	210	18	f	f	NOUN
ejpam-144	210	19	′	′	NUM
ejpam-144	210	20	0	0	NUM
ejpam-144	210	21	)	)	PUNCT
ejpam-144	210	22	=	=	SYM
ejpam-144	211	1	∫	∫	PROPN
ejpam-144	211	2	2π	2π	NOUN
ejpam-144	211	3	0	0	PUNCT
ejpam-144	212	1	|	|	ADV
ejpam-144	212	2	f	f	X
ejpam-144	212	3	′0(r	′0(r	PROPN
ejpam-144	212	4	eiθ	eiθ	PROPN
ejpam-144	212	5	)	)	PUNCT
ejpam-144	212	6	|2	|2	NUM
ejpam-144	212	7	dθ	dθ	PROPN
ejpam-144	212	8	=	=	PROPN
ejpam-144	212	9	2π	2π	PROPN
ejpam-144	212	10	∞	∞	NUM
ejpam-144	212	11	∑	∑	PROPN
ejpam-144	212	12	k=0	k=0	PROPN
ejpam-144	212	13	a2	a2	PROPN
ejpam-144	212	14	k	k	PROPN
ejpam-144	212	15	2	2	NUM
ejpam-144	212	16	2k(p+2	2k(p+2	NUM
ejpam-144	212	17	)	)	PUNCT
ejpam-144	213	1	p	p	PROPN
ejpam-144	213	2	z2k−2	z2k−2	PROPN
ejpam-144	213	3	≥	≥	NOUN
ejpam-144	213	4	2πg	2πg	ADJ
ejpam-144	213	5	2	2	NUM
ejpam-144	213	6	p	p	NOUN
ejpam-144	213	7	(	(	PUNCT
ejpam-144	213	8	r	r	NOUN
ejpam-144	213	9	)	)	PUNCT
ejpam-144	213	10	2	2	NUM
ejpam-144	213	11	2k(p+2	2k(p+2	NOUN
ejpam-144	213	12	)	)	PUNCT
ejpam-144	213	13	p	p	PROPN
ejpam-144	213	14	exp{−2k+2(1−	exp{−2k+2(1−	PROPN
ejpam-144	213	15	r	r	NOUN
ejpam-144	213	16	)	)	PUNCT
ejpam-144	213	17	}	}	PUNCT
ejpam-144	213	18	≥	≥	X
ejpam-144	213	19	λ	λ	NOUN
ejpam-144	213	20	g	g	PROPN
ejpam-144	213	21	2	2	NUM
ejpam-144	213	22	p	p	NOUN
ejpam-144	213	23	(	(	PUNCT
ejpam-144	213	24	r)(1−	r)(1−	PROPN
ejpam-144	213	25	r	r	NOUN
ejpam-144	213	26	)	)	PUNCT
ejpam-144	213	27	−2(p+2	−2(p+2	X
ejpam-144	213	28	)	)	PUNCT
ejpam-144	213	29	p	p	NOUN
ejpam-144	213	30	,	,	PUNCT
ejpam-144	213	31	(	(	PUNCT
ejpam-144	213	32	3.9	3.9	NUM
ejpam-144	213	33	)	)	PUNCT
ejpam-144	213	34	where	where	SCONJ
ejpam-144	213	35	λ	λ	PROPN
ejpam-144	213	36	is	be	AUX
ejpam-144	213	37	a	a	DET
ejpam-144	213	38	constant	constant	ADJ
ejpam-144	213	39	.	.	PUNCT
ejpam-144	214	1	since	since	SCONJ
ejpam-144	214	2	f0	f0	PROPN
ejpam-144	214	3	is	be	AUX
ejpam-144	214	4	defined	define	VERB
ejpam-144	214	5	by	by	ADP
ejpam-144	214	6	a	a	DET
ejpam-144	214	7	gap	gap	NOUN
ejpam-144	214	8	series	series	NOUN
ejpam-144	214	9	with	with	ADP
ejpam-144	214	10	hadamard	hadamard	ADJ
ejpam-144	214	11	condition	condition	NOUN
ejpam-144	214	12	,	,	PUNCT
ejpam-144	214	13	we	we	PRON
ejpam-144	214	14	have	have	VERB
ejpam-144	214	15	m2(r	m2(r	PROPN
ejpam-144	214	16	,	,	PUNCT
ejpam-144	214	17	f	f	PROPN
ejpam-144	214	18	′	′	NUM
ejpam-144	214	19	0	0	NUM
ejpam-144	214	20	)	)	PUNCT
ejpam-144	215	1	≈	≈	PROPN
ejpam-144	215	2	mp(r	mp(r	PROPN
ejpam-144	215	3	,	,	PUNCT
ejpam-144	215	4	f	f	PROPN
ejpam-144	215	5	′	′	NUM
ejpam-144	215	6	0	0	NUM
ejpam-144	215	7	)	)	PUNCT
ejpam-144	215	8	,	,	PUNCT
ejpam-144	215	9	where	where	SCONJ
ejpam-144	215	10	mp(r	mp(r	NOUN
ejpam-144	215	11	,	,	PUNCT
ejpam-144	215	12	f	f	PROPN
ejpam-144	215	13	′	′	NOUN
ejpam-144	215	14	0	0	NUM
ejpam-144	215	15	)	)	PUNCT
ejpam-144	216	1	=	=	SYM
ejpam-144	216	2	�	�	PROPN
ejpam-144	216	3	∫	∫	PROPN
ejpam-144	216	4	2π	2π	PROPN
ejpam-144	216	5	0	0	PUNCT
ejpam-144	217	1	|	|	ADV
ejpam-144	217	2	f	f	X
ejpam-144	217	3	′0(r	′0(r	PROPN
ejpam-144	217	4	eiθ	eiθ	PROPN
ejpam-144	217	5	)	)	PUNCT
ejpam-144	217	6	|p	|p	PART
ejpam-144	217	7	dθ	dθ	PROPN
ejpam-144	217	8	�	�	PROPN
ejpam-144	217	9	1	1	NUM
ejpam-144	217	10	p	p	NOUN
ejpam-144	217	11	.	.	PUNCT
ejpam-144	218	1	r.	r.	PROPN
ejpam-144	218	2	rashwan	rashwan	PROPN
ejpam-144	218	3	,	,	PUNCT
ejpam-144	218	4	a.	a.	PROPN
ejpam-144	218	5	ahmed	ahmed	PROPN
ejpam-144	218	6	and	and	CCONJ
ejpam-144	218	7	a.	a.	PROPN
ejpam-144	218	8	kamal	kamal	PROPN
ejpam-144	218	9	/	/	SYM
ejpam-144	218	10	eur	eur	PROPN
ejpam-144	218	11	.	.	PUNCT
ejpam-144	219	1	j.	j.	PROPN
ejpam-144	219	2	pure	pure	PROPN
ejpam-144	219	3	appl	appl	PROPN
ejpam-144	219	4	.	.	PROPN
ejpam-144	219	5	math	math	PROPN
ejpam-144	219	6	,	,	PUNCT
ejpam-144	219	7	2	2	NUM
ejpam-144	219	8	(	(	PUNCT
ejpam-144	219	9	2009	2009	NUM
ejpam-144	219	10	)	)	PUNCT
ejpam-144	219	11	,	,	PUNCT
ejpam-144	219	12	(	(	PUNCT
ejpam-144	219	13	250	250	NUM
ejpam-144	219	14	-	-	SYM
ejpam-144	219	15	267	267	NUM
ejpam-144	219	16	)	)	PUNCT
ejpam-144	219	17	263	263	NUM
ejpam-144	219	18	therefore	therefore	ADV
ejpam-144	219	19	,	,	PUNCT
ejpam-144	219	20	sup	sup	PROPN
ejpam-144	219	21	a∈∆	a∈∆	NOUN
ejpam-144	219	22	∫	∫	PROPN
ejpam-144	219	23	∆	∆	PROPN
ejpam-144	219	24	�	�	PROPN
ejpam-144	219	25	�	�	PROPN
ejpam-144	219	26	f	f	PROPN
ejpam-144	220	1	′	′	NOUN
ejpam-144	220	2	0	0	NUM
ejpam-144	221	1	(	(	PUNCT
ejpam-144	221	2	z	z	NOUN
ejpam-144	221	3	)	)	PUNCT
ejpam-144	221	4	�	�	PROPN
ejpam-144	221	5	�	�	PROPN
ejpam-144	221	6	p	p	PROPN
ejpam-144	221	7	(	(	PUNCT
ejpam-144	221	8	1−	1−	NUM
ejpam-144	221	9	|z|)p	|z|)p	PROPN
ejpam-144	221	10	k(g(z	k(g(z	PROPN
ejpam-144	221	11	,	,	PUNCT
ejpam-144	221	12	a	a	PRON
ejpam-144	221	13	)	)	PUNCT
ejpam-144	221	14	)	)	PUNCT
ejpam-144	221	15	ωp(1−	ωp(1−	ADJ
ejpam-144	221	16	|z|	|z|	NOUN
ejpam-144	221	17	)	)	PUNCT
ejpam-144	221	18	dσz	dσz	NOUN
ejpam-144	221	19	≥	≥	NOUN
ejpam-144	221	20	∫	∫	PROPN
ejpam-144	221	21	1	1	NUM
ejpam-144	221	22	0	0	NUM
ejpam-144	221	23	m	m	PROPN
ejpam-144	221	24	p	p	X
ejpam-144	221	25	p	p	X
ejpam-144	221	26	(	(	PUNCT
ejpam-144	221	27	r	r	NOUN
ejpam-144	221	28	,	,	PUNCT
ejpam-144	221	29	f	f	NOUN
ejpam-144	221	30	′	′	NUM
ejpam-144	221	31	0	0	NUM
ejpam-144	221	32	)	)	PUNCT
ejpam-144	221	33	(	(	PUNCT
ejpam-144	221	34	1−	1−	NUM
ejpam-144	221	35	r2)pk	r2)pk	PROPN
ejpam-144	221	36	�	�	PROPN
ejpam-144	221	37	log	log	VERB
ejpam-144	221	38	1	1	NUM
ejpam-144	221	39	r	r	NOUN
ejpam-144	221	40	�	�	PROPN
ejpam-144	221	41	r	r	PROPN
ejpam-144	221	42	dr	dr	PROPN
ejpam-144	221	43	≈	≈	PROPN
ejpam-144	221	44	∫	∫	PROPN
ejpam-144	221	45	1	1	NUM
ejpam-144	221	46	0	0	NUM
ejpam-144	221	47	m	m	VERB
ejpam-144	221	48	p	p	ADJ
ejpam-144	221	49	2	2	NUM
ejpam-144	221	50	(	(	PUNCT
ejpam-144	221	51	r	r	NOUN
ejpam-144	221	52	,	,	PUNCT
ejpam-144	221	53	f	f	NOUN
ejpam-144	221	54	′	′	NUM
ejpam-144	221	55	0	0	NUM
ejpam-144	221	56	)	)	PUNCT
ejpam-144	221	57	(	(	PUNCT
ejpam-144	221	58	1−	1−	NUM
ejpam-144	221	59	r2)pk	r2)pk	PROPN
ejpam-144	221	60	�	�	PROPN
ejpam-144	221	61	log	log	VERB
ejpam-144	221	62	1	1	NUM
ejpam-144	221	63	r	r	NOUN
ejpam-144	221	64	�	�	PROPN
ejpam-144	221	65	r	r	PROPN
ejpam-144	221	66	dr	dr	PROPN
ejpam-144	221	67	≥	≥	PROPN
ejpam-144	221	68	∫	∫	PROPN
ejpam-144	221	69	1	1	NUM
ejpam-144	221	70	3	3	NUM
ejpam-144	221	71	4	4	NUM
ejpam-144	221	72	k	k	PROPN
ejpam-144	221	73	�	�	PROPN
ejpam-144	221	74	log	log	VERB
ejpam-144	221	75	1	1	NUM
ejpam-144	221	76	r	r	NOUN
ejpam-144	221	77	�	�	PROPN
ejpam-144	221	78	g(r	g(r	PROPN
ejpam-144	221	79	)	)	PUNCT
ejpam-144	221	80	(	(	PUNCT
ejpam-144	221	81	1−	1−	NUM
ejpam-144	221	82	r2)2	r2)2	NOUN
ejpam-144	221	83	r	r	NOUN
ejpam-144	221	84	dr	dr	PROPN
ejpam-144	221	85	=	=	PROPN
ejpam-144	221	86	∞.	∞.	PROPN
ejpam-144	221	87	this	this	PRON
ejpam-144	221	88	means	mean	VERB
ejpam-144	221	89	that	that	SCONJ
ejpam-144	221	90	f0	f0	PROPN
ejpam-144	221	91	∈	∈	PROPN
ejpam-144	222	1	b	b	X
ejpam-144	222	2	p+2	p+2	PRON
ejpam-144	222	3	p	p	PROPN
ejpam-144	222	4	ω,0	ω,0	PROPN
ejpam-144	222	5	\qk	\qk	PROPN
ejpam-144	222	6	,	,	PUNCT
ejpam-144	222	7	w,0	w,0	NOUN
ejpam-144	222	8	,	,	PUNCT
ejpam-144	222	9	which	which	PRON
ejpam-144	222	10	is	be	AUX
ejpam-144	222	11	a	a	DET
ejpam-144	222	12	contraction	contraction	NOUN
ejpam-144	222	13	.	.	PUNCT
ejpam-144	223	1	hence	hence	ADV
ejpam-144	223	2	(	(	PUNCT
ejpam-144	223	3	2.3	2.3	NUM
ejpam-144	223	4	)	)	PUNCT
ejpam-144	223	5	holds	hold	VERB
ejpam-144	223	6	.	.	PUNCT
ejpam-144	224	1	this	this	PRON
ejpam-144	224	2	completes	complete	VERB
ejpam-144	224	3	the	the	DET
ejpam-144	224	4	proof	proof	NOUN
ejpam-144	224	5	of	of	ADP
ejpam-144	224	6	our	our	PRON
ejpam-144	224	7	theorem	theorem	NOUN
ejpam-144	224	8	.	.	PROPN
ejpam-144	224	9	4	4	NUM
ejpam-144	224	10	.	.	X
ejpam-144	224	11	more	more	ADJ
ejpam-144	224	12	results	result	NOUN
ejpam-144	224	13	on	on	ADP
ejpam-144	224	14	qk	qk	PROPN
ejpam-144	224	15	,	,	PUNCT
ejpam-144	224	16	ω	ω	NOUN
ejpam-144	224	17	-	-	NOUN
ejpam-144	224	18	spaces	space	VERB
ejpam-144	224	19	the	the	DET
ejpam-144	224	20	following	follow	VERB
ejpam-144	224	21	result	result	NOUN
ejpam-144	224	22	means	mean	VERB
ejpam-144	224	23	that	that	SCONJ
ejpam-144	224	24	the	the	DET
ejpam-144	224	25	kernel	kernel	PROPN
ejpam-144	224	26	function	function	PROPN
ejpam-144	224	27	k	k	PROPN
ejpam-144	224	28	can	can	AUX
ejpam-144	224	29	be	be	AUX
ejpam-144	224	30	chosen	choose	VERB
ejpam-144	224	31	as	as	ADP
ejpam-144	224	32	bounded	bound	VERB
ejpam-144	224	33	.	.	PUNCT
ejpam-144	225	1	theorem	theorem	VERB
ejpam-144	225	2	4.1	4.1	NUM
ejpam-144	225	3	.	.	PUNCT
ejpam-144	226	1	assume	assume	VERB
ejpam-144	226	2	that	that	SCONJ
ejpam-144	226	3	k(1	k(1	PROPN
ejpam-144	226	4	)	)	PUNCT
ejpam-144	226	5	>	>	X
ejpam-144	227	1	0	0	X
ejpam-144	227	2	.	.	PUNCT
ejpam-144	228	1	let	let	VERB
ejpam-144	228	2	k1(r	k1(r	NOUN
ejpam-144	228	3	)	)	PUNCT
ejpam-144	229	1	=	=	SYM
ejpam-144	229	2	inf{k(r	inf{k(r	PROPN
ejpam-144	229	3	)	)	PUNCT
ejpam-144	229	4	,	,	PUNCT
ejpam-144	229	5	k(1	k(1	PROPN
ejpam-144	229	6	)	)	PUNCT
ejpam-144	229	7	}	}	PUNCT
ejpam-144	229	8	,	,	PUNCT
ejpam-144	229	9	then	then	ADV
ejpam-144	229	10	qk	qk	NOUN
ejpam-144	229	11	,	,	PUNCT
ejpam-144	229	12	w	w	PROPN
ejpam-144	229	13	=	=	SYM
ejpam-144	229	14	qk1,w	qk1,w	PROPN
ejpam-144	229	15	.	.	PUNCT
ejpam-144	230	1	proof	proof	NOUN
ejpam-144	230	2	.	.	PUNCT
ejpam-144	231	1	since	since	SCONJ
ejpam-144	231	2	k1	k1	NOUN
ejpam-144	231	3	≤	≤	PROPN
ejpam-144	231	4	k	k	PROPN
ejpam-144	231	5	and	and	CCONJ
ejpam-144	231	6	k1	k1	PROPN
ejpam-144	231	7	is	be	AUX
ejpam-144	231	8	nondecreasing	nondecrease	VERB
ejpam-144	231	9	,	,	PUNCT
ejpam-144	231	10	it	it	PRON
ejpam-144	231	11	is	be	AUX
ejpam-144	231	12	clear	clear	ADJ
ejpam-144	231	13	that	that	SCONJ
ejpam-144	231	14	qk	qk	NOUN
ejpam-144	231	15	,	,	PUNCT
ejpam-144	231	16	ω	ω	PROPN
ejpam-144	231	17	⊂	⊂	PROPN
ejpam-144	231	18	qk1,w	qk1,w	PROPN
ejpam-144	231	19	.	.	PUNCT
ejpam-144	232	1	it	it	PRON
ejpam-144	232	2	remains	remain	VERB
ejpam-144	232	3	to	to	PART
ejpam-144	232	4	prove	prove	VERB
ejpam-144	232	5	that	that	SCONJ
ejpam-144	232	6	qk1,ω	qk1,ω	PROPN
ejpam-144	232	7	⊂	⊂	PROPN
ejpam-144	232	8	qk	qk	PROPN
ejpam-144	232	9	,	,	PUNCT
ejpam-144	232	10	ω	ω	PROPN
ejpam-144	232	11	.	.	PUNCT
ejpam-144	233	1	we	we	PRON
ejpam-144	233	2	note	note	VERB
ejpam-144	233	3	that	that	SCONJ
ejpam-144	233	4	g(z	g(z	PROPN
ejpam-144	233	5	,	,	PUNCT
ejpam-144	233	6	a	a	PRON
ejpam-144	233	7	)	)	PUNCT
ejpam-144	233	8	>	>	X
ejpam-144	233	9	1	1	NUM
ejpam-144	233	10	,	,	PUNCT
ejpam-144	233	11	z	z	NOUN
ejpam-144	233	12	∈∆(a	∈∆(a	NOUN
ejpam-144	233	13	,	,	PUNCT
ejpam-144	233	14	1	1	NUM
ejpam-144	233	15	e	e	NOUN
ejpam-144	233	16	)	)	PUNCT
ejpam-144	233	17	and	and	CCONJ
ejpam-144	233	18	g(z	g(z	PROPN
ejpam-144	233	19	,	,	PUNCT
ejpam-144	233	20	a	a	PRON
ejpam-144	233	21	)	)	PUNCT
ejpam-144	233	22	≤	≤	NUM
ejpam-144	233	23	1	1	NUM
ejpam-144	233	24	,	,	PUNCT
ejpam-144	233	25	z	z	NOUN
ejpam-144	233	26	∈∆	∈∆	NOUN
ejpam-144	233	27	\∆(a	\∆(a	NOUN
ejpam-144	233	28	,	,	PUNCT
ejpam-144	233	29	1	1	NUM
ejpam-144	233	30	e	e	NOUN
ejpam-144	233	31	)	)	PUNCT
ejpam-144	233	32	.	.	PUNCT
ejpam-144	234	1	thus	thus	ADV
ejpam-144	234	2	k(g(z	k(g(z	VERB
ejpam-144	234	3	,	,	PUNCT
ejpam-144	234	4	a	a	PRON
ejpam-144	234	5	)	)	PUNCT
ejpam-144	234	6	)	)	PUNCT
ejpam-144	235	1	=	=	SYM
ejpam-144	235	2	k1(g(z	k1(g(z	PROPN
ejpam-144	235	3	,	,	PUNCT
ejpam-144	235	4	a	a	PRON
ejpam-144	235	5	)	)	PUNCT
ejpam-144	235	6	)	)	PUNCT
ejpam-144	235	7	in	in	ADP
ejpam-144	235	8	∆\∆(a	∆\∆(a	PROPN
ejpam-144	235	9	,	,	PUNCT
ejpam-144	235	10	1	1	NUM
ejpam-144	235	11	e	e	NOUN
ejpam-144	235	12	)	)	PUNCT
ejpam-144	235	13	.	.	PUNCT
ejpam-144	236	1	it	it	PRON
ejpam-144	236	2	suffices	suffice	VERB
ejpam-144	236	3	to	to	PART
ejpam-144	236	4	deal	deal	VERB
ejpam-144	236	5	with	with	ADP
ejpam-144	236	6	integrals	integral	NOUN
ejpam-144	236	7	over	over	ADP
ejpam-144	236	8	∆(a	∆(a	NOUN
ejpam-144	236	9	,	,	PUNCT
ejpam-144	236	10	1	1	NUM
ejpam-144	236	11	e	e	NOUN
ejpam-144	236	12	)	)	PUNCT
ejpam-144	236	13	.	.	PUNCT
ejpam-144	237	1	if	if	SCONJ
ejpam-144	237	2	f	f	PROPN
ejpam-144	237	3	∈qk1,ω	∈qk1,ω	NOUN
ejpam-144	237	4	and	and	CCONJ
ejpam-144	237	5	f	f	PROPN
ejpam-144	237	6	is	be	AUX
ejpam-144	237	7	a	a	DET
ejpam-144	237	8	weighted	weighted	ADJ
ejpam-144	237	9	bloch	bloch	PROPN
ejpam-144	237	10	function	function	PROPN
ejpam-144	237	11	i.e	i.e	PROPN
ejpam-144	237	12	,	,	PUNCT
ejpam-144	237	13	f	f	PROPN
ejpam-144	237	14	∈bω	∈bω	PROPN
ejpam-144	237	15	then	then	ADV
ejpam-144	237	16	by	by	ADP
ejpam-144	237	17	theorem	theorem	NOUN
ejpam-144	237	18	2.1	2.1	NUM
ejpam-144	237	19	,	,	PUNCT
ejpam-144	237	20	it	it	PRON
ejpam-144	237	21	follows	follow	VERB
ejpam-144	237	22	that	that	SCONJ
ejpam-144	237	23	∫	∫	PROPN
ejpam-144	237	24	∆(a	∆(a	PROPN
ejpam-144	237	25	,	,	PUNCT
ejpam-144	237	26	1	1	NUM
ejpam-144	237	27	e	e	NOUN
ejpam-144	237	28	)	)	PUNCT
ejpam-144	238	1	|	|	ADV
ejpam-144	238	2	f	f	PROPN
ejpam-144	238	3	′(z)|p	′(z)|p	PROPN
ejpam-144	238	4	(	(	PUNCT
ejpam-144	238	5	1−	1−	NUM
ejpam-144	238	6	|z|)p	|z|)p	PROPN
ejpam-144	238	7	k	k	PROPN
ejpam-144	238	8	�	�	PROPN
ejpam-144	238	9	g(z	g(z	PROPN
ejpam-144	238	10	,	,	PUNCT
ejpam-144	238	11	a	a	PRON
ejpam-144	238	12	)	)	PUNCT
ejpam-144	238	13	�	�	PROPN
ejpam-144	238	14	ωp(1−	ωp(1−	ADJ
ejpam-144	238	15	|z|	|z|	NOUN
ejpam-144	238	16	)	)	PUNCT
ejpam-144	238	17	dσz	dσz	ADJ
ejpam-144	238	18	≤	≤	NUM
ejpam-144	238	19	f	f	PROPN
ejpam-144	238	20	p	p	X
ejpam-144	238	21	b	b	PROPN
ejpam-144	239	1	p+2	p+2	PRON
ejpam-144	239	2	p	p	PROPN
ejpam-144	239	3	ω	ω	NUM
ejpam-144	239	4	∫	∫	PROPN
ejpam-144	239	5	∆(a	∆(a	PROPN
ejpam-144	239	6	,	,	PUNCT
ejpam-144	239	7	1	1	NUM
ejpam-144	239	8	e	e	NOUN
ejpam-144	239	9	)	)	PUNCT
ejpam-144	239	10	k	k	PROPN
ejpam-144	239	11	�	�	PROPN
ejpam-144	239	12	g(z	g(z	PROPN
ejpam-144	239	13	,	,	PUNCT
ejpam-144	239	14	a	a	PRON
ejpam-144	239	15	)	)	PUNCT
ejpam-144	239	16	�	�	PROPN
ejpam-144	239	17	1	1	NUM
ejpam-144	239	18	(	(	PUNCT
ejpam-144	239	19	1−	1−	NUM
ejpam-144	239	20	|z|2)2	|z|2)2	PROPN
ejpam-144	239	21	dσz	dσz	NOUN
ejpam-144	239	22	=	=	SYM
ejpam-144	239	23	f	f	PROPN
ejpam-144	239	24	p	p	X
ejpam-144	239	25	b	b	PROPN
ejpam-144	239	26	p+2	p+2	PRON
ejpam-144	239	27	p	p	PROPN
ejpam-144	239	28	ω	ω	PROPN
ejpam-144	239	29	∫	∫	PROPN
ejpam-144	239	30	∆(0	∆(0	NOUN
ejpam-144	239	31	,	,	PUNCT
ejpam-144	239	32	1	1	NUM
ejpam-144	239	33	e	e	NOUN
ejpam-144	239	34	)	)	PUNCT
ejpam-144	239	35	k	k	PROPN
ejpam-144	239	36	�	�	PROPN
ejpam-144	239	37	log	log	VERB
ejpam-144	239	38	1	1	NUM
ejpam-144	239	39	|w|	|w|	PROPN
ejpam-144	239	40	�	�	NOUN
ejpam-144	239	41	1	1	NUM
ejpam-144	239	42	(	(	PUNCT
ejpam-144	239	43	1−	1−	NUM
ejpam-144	239	44	|z|2)2	|z|2)2	NOUN
ejpam-144	239	45	dσw	dσw	VERB
ejpam-144	239	46	≤	≤	NUM
ejpam-144	240	1	c	c	X
ejpam-144	240	2	f	f	PROPN
ejpam-144	240	3	p	p	X
ejpam-144	240	4	b	b	PROPN
ejpam-144	240	5	p+2	p+2	PROPN
ejpam-144	240	6	p	p	PROPN
ejpam-144	240	7	ω	ω	PROPN
ejpam-144	240	8	r.	r.	PROPN
ejpam-144	240	9	rashwan	rashwan	PROPN
ejpam-144	240	10	,	,	PUNCT
ejpam-144	240	11	a.	a.	PROPN
ejpam-144	240	12	ahmed	ahmed	PROPN
ejpam-144	240	13	and	and	CCONJ
ejpam-144	240	14	a.	a.	PROPN
ejpam-144	240	15	kamal	kamal	PROPN
ejpam-144	240	16	/	/	SYM
ejpam-144	240	17	eur	eur	PROPN
ejpam-144	240	18	.	.	PUNCT
ejpam-144	241	1	j.	j.	PROPN
ejpam-144	241	2	pure	pure	PROPN
ejpam-144	241	3	appl	appl	PROPN
ejpam-144	241	4	.	.	PROPN
ejpam-144	241	5	math	math	PROPN
ejpam-144	241	6	,	,	PUNCT
ejpam-144	241	7	2	2	NUM
ejpam-144	241	8	(	(	PUNCT
ejpam-144	241	9	2009	2009	NUM
ejpam-144	241	10	)	)	PUNCT
ejpam-144	241	11	,	,	PUNCT
ejpam-144	241	12	(	(	PUNCT
ejpam-144	241	13	250	250	NUM
ejpam-144	241	14	-	-	SYM
ejpam-144	241	15	267	267	NUM
ejpam-144	241	16	)	)	PUNCT
ejpam-144	241	17	264	264	NUM
ejpam-144	242	1	thus	thus	ADV
ejpam-144	242	2	,	,	PUNCT
ejpam-144	242	3	f	f	PROPN
ejpam-144	242	4	∈qk	∈qk	PROPN
ejpam-144	242	5	,	,	PUNCT
ejpam-144	242	6	ω	ω	NUM
ejpam-144	242	7	and	and	CCONJ
ejpam-144	242	8	theorem	theorem	VERB
ejpam-144	242	9	4.1	4.1	NUM
ejpam-144	242	10	is	be	AUX
ejpam-144	242	11	proved	prove	VERB
ejpam-144	242	12	.	.	PUNCT
ejpam-144	243	1	corollary	corollary	ADJ
ejpam-144	243	2	4.1	4.1	NUM
ejpam-144	243	3	.	.	PUNCT
ejpam-144	244	1	let	let	VERB
ejpam-144	244	2	0	0	NUM
ejpam-144	244	3	<	<	X
ejpam-144	244	4	p	p	X
ejpam-144	244	5	<	<	X
ejpam-144	244	6	∞	∞	PROPN
ejpam-144	244	7	,	,	PUNCT
ejpam-144	244	8	ω	ω	NUM
ejpam-144	244	9	:	:	PUNCT
ejpam-144	244	10	(	(	PUNCT
ejpam-144	244	11	0	0	NUM
ejpam-144	244	12	,	,	PUNCT
ejpam-144	244	13	1]→	1]→	NOUN
ejpam-144	244	14	(	(	PUNCT
ejpam-144	244	15	0,∞	0,∞	NOUN
ejpam-144	244	16	)	)	PUNCT
ejpam-144	244	17	.	.	PUNCT
ejpam-144	245	1	then	then	ADV
ejpam-144	245	2	f	f	PROPN
ejpam-144	245	3	∈	∈	PROPN
ejpam-144	245	4	qk	qk	PROPN
ejpam-144	245	5	,	,	PUNCT
ejpam-144	245	6	w	w	ADP
ejpam-144	245	7	if	if	SCONJ
ejpam-144	246	1	and	and	CCONJ
ejpam-144	246	2	only	only	ADV
ejpam-144	246	3	if	if	SCONJ
ejpam-144	246	4	sup	sup	PROPN
ejpam-144	246	5	a∈∆	a∈∆	NOUN
ejpam-144	246	6	∫	∫	NOUN
ejpam-144	246	7	∆	∆	PROPN
ejpam-144	247	1	|	|	ADV
ejpam-144	247	2	f	f	PROPN
ejpam-144	247	3	′(z)|p	′(z)|p	PROPN
ejpam-144	247	4	(	(	PUNCT
ejpam-144	247	5	1−	1−	NUM
ejpam-144	247	6	|z|)p	|z|)p	PROPN
ejpam-144	247	7	k(1−	k(1−	PROPN
ejpam-144	247	8	|ϕa(z)|	|ϕa(z)|	ADJ
ejpam-144	247	9	2	2	NUM
ejpam-144	247	10	)	)	PUNCT
ejpam-144	247	11	ωp(1−	ωp(1−	ADJ
ejpam-144	247	12	|z|	|z|	NOUN
ejpam-144	247	13	)	)	PUNCT
ejpam-144	247	14	dσz	dσz	NOUN
ejpam-144	247	15	<	<	X
ejpam-144	247	16	∞.	∞.	PROPN
ejpam-144	247	17	for	for	ADP
ejpam-144	247	18	the	the	DET
ejpam-144	247	19	application	application	NOUN
ejpam-144	247	20	of	of	ADP
ejpam-144	247	21	the	the	DET
ejpam-144	247	22	above	above	ADJ
ejpam-144	247	23	results	result	NOUN
ejpam-144	247	24	,	,	PUNCT
ejpam-144	247	25	we	we	PRON
ejpam-144	247	26	state	state	VERB
ejpam-144	247	27	the	the	DET
ejpam-144	247	28	following	follow	VERB
ejpam-144	247	29	lemma	lemma	PROPN
ejpam-144	247	30	which	which	PRON
ejpam-144	247	31	is	be	AUX
ejpam-144	247	32	needed	need	VERB
ejpam-144	247	33	later	later	ADV
ejpam-144	247	34	.	.	PUNCT
ejpam-144	248	1	lemma	lemma	PROPN
ejpam-144	248	2	4.1	4.1	NUM
ejpam-144	248	3	.	.	PUNCT
ejpam-144	249	1	let	let	VERB
ejpam-144	249	2	k	k	NOUN
ejpam-144	249	3	:	:	PUNCT
ejpam-144	250	1	[	[	X
ejpam-144	250	2	0,∞)→	0,∞)→	NOUN
ejpam-144	250	3	[	[	X
ejpam-144	250	4	0,∞	0,∞	NUM
ejpam-144	250	5	)	)	PUNCT
ejpam-144	250	6	,	,	PUNCT
ejpam-144	250	7	0	0	PUNCT
ejpam-144	250	8	<	<	X
ejpam-144	250	9	p	p	X
ejpam-144	250	10	<	<	X
ejpam-144	250	11	∞	∞	PROPN
ejpam-144	250	12	,	,	PUNCT
ejpam-144	250	13	for	for	ADP
ejpam-144	250	14	a	a	DET
ejpam-144	250	15	given	give	VERB
ejpam-144	250	16	reasonable	reasonable	ADJ
ejpam-144	250	17	function	function	NOUN
ejpam-144	250	18	ω	ω	NOUN
ejpam-144	250	19	:	:	PUNCT
ejpam-144	250	20	(	(	PUNCT
ejpam-144	250	21	0	0	NUM
ejpam-144	250	22	,	,	PUNCT
ejpam-144	250	23	1]→	1]→	NOUN
ejpam-144	250	24	(	(	PUNCT
ejpam-144	250	25	0,∞	0,∞	NOUN
ejpam-144	250	26	)	)	PUNCT
ejpam-144	250	27	.	.	PUNCT
ejpam-144	251	1	then	then	ADV
ejpam-144	251	2	(	(	PUNCT
ejpam-144	251	3	i	i	NOUN
ejpam-144	251	4	)	)	PUNCT
ejpam-144	251	5	f	f	PROPN
ejpam-144	251	6	∈b	∈b	PROPN
ejpam-144	251	7	p+2	p+2	PROPN
ejpam-144	251	8	p	p	PROPN
ejpam-144	251	9	ω	ω	PROPN
ejpam-144	251	10	if	if	SCONJ
ejpam-144	252	1	and	and	CCONJ
ejpam-144	252	2	only	only	ADV
ejpam-144	252	3	if	if	SCONJ
ejpam-144	252	4	there	there	PRON
ejpam-144	252	5	exists	exist	VERB
ejpam-144	252	6	r	r	NOUN
ejpam-144	252	7	∈	∈	PROPN
ejpam-144	252	8	(	(	PUNCT
ejpam-144	252	9	0	0	NUM
ejpam-144	252	10	,	,	PUNCT
ejpam-144	252	11	1	1	NUM
ejpam-144	252	12	)	)	PUNCT
ejpam-144	252	13	such	such	ADJ
ejpam-144	252	14	that	that	DET
ejpam-144	252	15	sup	sup	PROPN
ejpam-144	252	16	a∈∆	a∈∆	NOUN
ejpam-144	252	17	∫	∫	PROPN
ejpam-144	252	18	∆(a	∆(a	PROPN
ejpam-144	252	19	,	,	PUNCT
ejpam-144	252	20	r	r	NOUN
ejpam-144	252	21	)	)	PUNCT
ejpam-144	253	1	|	|	ADV
ejpam-144	253	2	f	f	PROPN
ejpam-144	253	3	′(z)|p	′(z)|p	PROPN
ejpam-144	253	4	(	(	PUNCT
ejpam-144	253	5	1−	1−	NUM
ejpam-144	253	6	|z|)p	|z|)p	PROPN
ejpam-144	253	7	(	(	PUNCT
ejpam-144	253	8	1−	1−	NUM
ejpam-144	253	9	|z|)k(g(z	|z|)k(g(z	PROPN
ejpam-144	253	10	,	,	PUNCT
ejpam-144	253	11	a	a	PRON
ejpam-144	253	12	)	)	PUNCT
ejpam-144	253	13	)	)	PUNCT
ejpam-144	253	14	ωp(1−	ωp(1−	ADJ
ejpam-144	253	15	|z|	|z|	NOUN
ejpam-144	253	16	)	)	PUNCT
ejpam-144	253	17	dσz	dσz	NOUN
ejpam-144	253	18	<	<	X
ejpam-144	253	19	∞	∞	PROPN
ejpam-144	253	20	,	,	PUNCT
ejpam-144	253	21	(	(	PUNCT
ejpam-144	253	22	4.1	4.1	NUM
ejpam-144	253	23	)	)	PUNCT
ejpam-144	253	24	(	(	PUNCT
ejpam-144	253	25	ii	ii	NOUN
ejpam-144	253	26	)	)	PUNCT
ejpam-144	253	27	f	f	PROPN
ejpam-144	253	28	∈b	∈b	PROPN
ejpam-144	254	1	p+2	p+2	PROPN
ejpam-144	254	2	p	p	PROPN
ejpam-144	254	3	ω,0	ω,0	PROPN
ejpam-144	254	4	if	if	SCONJ
ejpam-144	254	5	and	and	CCONJ
ejpam-144	254	6	only	only	ADV
ejpam-144	254	7	if	if	SCONJ
ejpam-144	254	8	there	there	PRON
ejpam-144	254	9	exists	exist	VERB
ejpam-144	254	10	r	r	NOUN
ejpam-144	254	11	∈	∈	PROPN
ejpam-144	254	12	(	(	PUNCT
ejpam-144	254	13	0	0	NUM
ejpam-144	254	14	,	,	PUNCT
ejpam-144	254	15	1	1	NUM
ejpam-144	254	16	)	)	PUNCT
ejpam-144	254	17	such	such	ADJ
ejpam-144	254	18	that	that	SCONJ
ejpam-144	254	19	lim	lim	PROPN
ejpam-144	254	20	|a|→1−	|a|→1−	PROPN
ejpam-144	254	21	∫	∫	PROPN
ejpam-144	254	22	∆(a	∆(a	PROPN
ejpam-144	254	23	,	,	PUNCT
ejpam-144	254	24	r	r	NOUN
ejpam-144	254	25	)	)	PUNCT
ejpam-144	255	1	|	|	ADV
ejpam-144	255	2	f	f	PROPN
ejpam-144	255	3	′(z)|p	′(z)|p	PROPN
ejpam-144	255	4	(	(	PUNCT
ejpam-144	255	5	1−	1−	NUM
ejpam-144	255	6	|z|)p	|z|)p	PROPN
ejpam-144	255	7	k(g(z	k(g(z	PROPN
ejpam-144	255	8	,	,	PUNCT
ejpam-144	255	9	a	a	PRON
ejpam-144	255	10	)	)	PUNCT
ejpam-144	255	11	)	)	PUNCT
ejpam-144	255	12	ωp(1−	ωp(1−	ADJ
ejpam-144	255	13	|z|	|z|	NOUN
ejpam-144	255	14	)	)	PUNCT
ejpam-144	255	15	dσz	dσz	NOUN
ejpam-144	255	16	=	=	SYM
ejpam-144	255	17	0	0	PROPN
ejpam-144	255	18	.	.	PUNCT
ejpam-144	256	1	(	(	PUNCT
ejpam-144	256	2	4.2	4.2	NUM
ejpam-144	256	3	)	)	PUNCT
ejpam-144	256	4	proof	proof	NOUN
ejpam-144	256	5	.	.	PUNCT
ejpam-144	257	1	(	(	PUNCT
ejpam-144	257	2	i	i	NOUN
ejpam-144	257	3	)	)	PUNCT
ejpam-144	257	4	assume	assume	VERB
ejpam-144	257	5	f	f	PROPN
ejpam-144	257	6	∈b	∈b	PROPN
ejpam-144	257	7	p+2	p+2	PROPN
ejpam-144	257	8	p	p	PROPN
ejpam-144	257	9	ω	ω	PROPN
ejpam-144	257	10	.	.	PUNCT
ejpam-144	258	1	for	for	ADP
ejpam-144	258	2	any	any	DET
ejpam-144	258	3	r	r	NOUN
ejpam-144	258	4	∈	∈	PROPN
ejpam-144	258	5	(	(	PUNCT
ejpam-144	258	6	0	0	NUM
ejpam-144	258	7	,	,	PUNCT
ejpam-144	258	8	1	1	NUM
ejpam-144	258	9	)	)	PUNCT
ejpam-144	258	10	and	and	CCONJ
ejpam-144	258	11	a	a	DET
ejpam-144	258	12	∈∆	∈∆	NOUN
ejpam-144	258	13	,	,	PUNCT
ejpam-144	258	14	we	we	PRON
ejpam-144	258	15	have	have	VERB
ejpam-144	258	16	∫	∫	PROPN
ejpam-144	258	17	∆(a	∆(a	PROPN
ejpam-144	258	18	,	,	PUNCT
ejpam-144	258	19	r	r	NOUN
ejpam-144	258	20	)	)	PUNCT
ejpam-144	259	1	|	|	ADV
ejpam-144	259	2	f	f	PROPN
ejpam-144	259	3	′(z)|p	′(z)|p	PROPN
ejpam-144	259	4	(	(	PUNCT
ejpam-144	259	5	1−	1−	NUM
ejpam-144	259	6	|z|)p	|z|)p	PROPN
ejpam-144	259	7	k(g(z	k(g(z	PROPN
ejpam-144	259	8	,	,	PUNCT
ejpam-144	259	9	a	a	PRON
ejpam-144	259	10	)	)	PUNCT
ejpam-144	259	11	)	)	PUNCT
ejpam-144	259	12	ωp(1−	ωp(1−	ADJ
ejpam-144	259	13	|z|	|z|	NOUN
ejpam-144	259	14	)	)	PUNCT
ejpam-144	259	15	dσz	dσz	NOUN
ejpam-144	259	16	=	=	SYM
ejpam-144	259	17	∫	∫	PROPN
ejpam-144	259	18	∆(0,r	∆(0,r	NOUN
ejpam-144	259	19	)	)	PUNCT
ejpam-144	260	1	|	|	ADV
ejpam-144	260	2	f	f	X
ejpam-144	260	3	′(ϕa(z))|	′(ϕa(z))|	PROPN
ejpam-144	260	4	p	p	X
ejpam-144	260	5	(	(	PUNCT
ejpam-144	260	6	1−	1−	NUM
ejpam-144	260	7	|ϕa(z)|	|ϕa(z)|	PROPN
ejpam-144	260	8	2)p+2	2)p+2	NUM
ejpam-144	260	9	(	(	PUNCT
ejpam-144	260	10	1	1	NUM
ejpam-144	260	11	+	+	NUM
ejpam-144	260	12	|ϕa(z)|)p+2	|ϕa(z)|)p+2	PROPN
ejpam-144	260	13	k	k	PROPN
ejpam-144	260	14	�	�	PROPN
ejpam-144	260	15	1	1	NUM
ejpam-144	260	16	|z|	|z|	PROPN
ejpam-144	260	17	�	�	PROPN
ejpam-144	260	18	(	(	PUNCT
ejpam-144	260	19	1−	1−	NUM
ejpam-144	260	20	|z|2)2ωp(1−	|z|2)2ωp(1−	NOUN
ejpam-144	260	21	|z|	|z|	NOUN
ejpam-144	260	22	)	)	PUNCT
ejpam-144	260	23	dσz	dσz	ADJ
ejpam-144	260	24	≤	≤	PROPN
ejpam-144	260	25	‖	‖	PROPN
ejpam-144	260	26	f	f	PROPN
ejpam-144	260	27	‖p	‖p	PROPN
ejpam-144	261	1	b	b	PROPN
ejpam-144	262	1	p+2	p+2	PROPN
ejpam-144	262	2	p	p	PROPN
ejpam-144	262	3	ω	ω	PROPN
ejpam-144	262	4	∫	∫	PROPN
ejpam-144	262	5	∆(0,r	∆(0,r	NOUN
ejpam-144	262	6	)	)	PUNCT
ejpam-144	263	1	k	k	PROPN
ejpam-144	263	2	�	�	PROPN
ejpam-144	263	3	log	log	VERB
ejpam-144	263	4	1	1	NUM
ejpam-144	263	5	|z|	|z|	NOUN
ejpam-144	263	6	�	�	PROPN
ejpam-144	263	7	1	1	NUM
ejpam-144	263	8	(	(	PUNCT
ejpam-144	263	9	1−	1−	NUM
ejpam-144	263	10	|z|2)2	|z|2)2	NOUN
ejpam-144	263	11	dσz	dσz	NOUN
ejpam-144	263	12	≤	≤	X
ejpam-144	263	13	λ1‖	λ1‖	PROPN
ejpam-144	263	14	f	f	PROPN
ejpam-144	263	15	‖	‖	PROPN
ejpam-144	263	16	p	p	PROPN
ejpam-144	263	17	b	b	PROPN
ejpam-144	264	1	p+2	p+2	PRON
ejpam-144	264	2	p	p	PROPN
ejpam-144	264	3	ω	ω	PROPN
ejpam-144	264	4	,	,	PUNCT
ejpam-144	264	5	where	where	SCONJ
ejpam-144	264	6	1	1	X
ejpam-144	264	7	<	<	X
ejpam-144	264	8	(	(	PUNCT
ejpam-144	264	9	1+|ϕa(z)|	1+|ϕa(z)|	NUM
ejpam-144	264	10	)	)	PUNCT
ejpam-144	264	11	p+2	p+2	X
ejpam-144	264	12	<	<	X
ejpam-144	264	13	2p+2	2p+2	NUM
ejpam-144	264	14	and	and	CCONJ
ejpam-144	264	15	λ1	λ1	PROPN
ejpam-144	264	16	is	be	AUX
ejpam-144	264	17	a	a	DET
ejpam-144	264	18	constant	constant	ADJ
ejpam-144	264	19	.	.	PUNCT
ejpam-144	265	1	conversely	conversely	ADV
ejpam-144	265	2	,	,	PUNCT
ejpam-144	265	3	suppose	suppose	VERB
ejpam-144	265	4	that	that	SCONJ
ejpam-144	265	5	(	(	PUNCT
ejpam-144	265	6	4.1	4.1	NUM
ejpam-144	265	7	)	)	PUNCT
ejpam-144	265	8	holds	hold	VERB
ejpam-144	265	9	for	for	ADP
ejpam-144	265	10	some	some	DET
ejpam-144	265	11	r	r	NOUN
ejpam-144	265	12	,	,	PUNCT
ejpam-144	265	13	0	0	NUM
ejpam-144	265	14	<	<	X
ejpam-144	265	15	r	r	X
ejpam-144	265	16	<	<	X
ejpam-144	265	17	1	1	NUM
ejpam-144	265	18	,	,	PUNCT
ejpam-144	265	19	by	by	ADP
ejpam-144	265	20	the	the	DET
ejpam-144	265	21	proof	proof	NOUN
ejpam-144	265	22	of	of	ADP
ejpam-144	265	23	theorem	theorem	ADJ
ejpam-144	265	24	2.1	2.1	NUM
ejpam-144	265	25	(	(	PUNCT
ejpam-144	265	26	i	i	NOUN
ejpam-144	265	27	)	)	PUNCT
ejpam-144	265	28	with	with	ADP
ejpam-144	265	29	1−	1−	NUM
ejpam-144	265	30	|a|	|a|	PROPN
ejpam-144	265	31	≈	≈	PROPN
ejpam-144	265	32	1−	1−	NUM
ejpam-144	265	33	|z|	|z|	NOUN
ejpam-144	265	34	on	on	ADP
ejpam-144	265	35	r.	r.	PROPN
ejpam-144	265	36	rashwan	rashwan	PROPN
ejpam-144	265	37	,	,	PUNCT
ejpam-144	265	38	a.	a.	PROPN
ejpam-144	265	39	ahmed	ahmed	PROPN
ejpam-144	265	40	and	and	CCONJ
ejpam-144	265	41	a.	a.	PROPN
ejpam-144	265	42	kamal	kamal	PROPN
ejpam-144	265	43	/	/	SYM
ejpam-144	265	44	eur	eur	PROPN
ejpam-144	265	45	.	.	PUNCT
ejpam-144	266	1	j.	j.	PROPN
ejpam-144	266	2	pure	pure	PROPN
ejpam-144	266	3	appl	appl	PROPN
ejpam-144	266	4	.	.	PROPN
ejpam-144	266	5	math	math	PROPN
ejpam-144	266	6	,	,	PUNCT
ejpam-144	266	7	2	2	NUM
ejpam-144	266	8	(	(	PUNCT
ejpam-144	266	9	2009	2009	NUM
ejpam-144	266	10	)	)	PUNCT
ejpam-144	266	11	,	,	PUNCT
ejpam-144	266	12	(	(	PUNCT
ejpam-144	266	13	250	250	NUM
ejpam-144	266	14	-	-	SYM
ejpam-144	266	15	267	267	NUM
ejpam-144	266	16	)	)	PUNCT
ejpam-144	266	17	265	265	NUM
ejpam-144	266	18	e(a	e(a	NOUN
ejpam-144	266	19	,	,	PUNCT
ejpam-144	266	20	r	r	NOUN
ejpam-144	266	21	)	)	PUNCT
ejpam-144	266	22	;	;	PUNCT
ejpam-144	266	23	a	a	DET
ejpam-144	266	24	,	,	PUNCT
ejpam-144	266	25	z	z	NOUN
ejpam-144	266	26	∈∆	∈∆	ADV
ejpam-144	266	27	,	,	PUNCT
ejpam-144	266	28	we	we	PRON
ejpam-144	266	29	obtain	obtain	VERB
ejpam-144	266	30	∫	∫	PROPN
ejpam-144	266	31	∆(a	∆(a	PROPN
ejpam-144	266	32	,	,	PUNCT
ejpam-144	266	33	r	r	NOUN
ejpam-144	266	34	)	)	PUNCT
ejpam-144	267	1	|	|	ADV
ejpam-144	267	2	f	f	PROPN
ejpam-144	267	3	′(z)|p	′(z)|p	PROPN
ejpam-144	267	4	(	(	PUNCT
ejpam-144	267	5	1−	1−	NUM
ejpam-144	267	6	|z|)p	|z|)p	PROPN
ejpam-144	267	7	k(g(z	k(g(z	PROPN
ejpam-144	267	8	,	,	PUNCT
ejpam-144	267	9	a	a	PRON
ejpam-144	267	10	)	)	PUNCT
ejpam-144	267	11	)	)	PUNCT
ejpam-144	267	12	ωp(1−	ωp(1−	ADJ
ejpam-144	267	13	|z|	|z|	NOUN
ejpam-144	267	14	)	)	PUNCT
ejpam-144	267	15	dσz	dσz	NOUN
ejpam-144	267	16	≥	≥	NOUN
ejpam-144	267	17	k(log	k(log	NOUN
ejpam-144	267	18	1	1	NUM
ejpam-144	267	19	r	r	NOUN
ejpam-144	267	20	)	)	PUNCT
ejpam-144	267	21	∫	∫	PROPN
ejpam-144	267	22	∆(a	∆(a	PROPN
ejpam-144	267	23	,	,	PUNCT
ejpam-144	267	24	r	r	NOUN
ejpam-144	267	25	)	)	PUNCT
ejpam-144	267	26	|	|	ADV
ejpam-144	267	27	f	f	PROPN
ejpam-144	267	28	′(z)|p	′(z)|p	PROPN
ejpam-144	267	29	(	(	PUNCT
ejpam-144	267	30	1−	1−	NUM
ejpam-144	267	31	|z|)p	|z|)p	PROPN
ejpam-144	267	32	ωp(1−	ωp(1−	ADJ
ejpam-144	267	33	|z|	|z|	NOUN
ejpam-144	267	34	)	)	PUNCT
ejpam-144	267	35	dσz	dσz	NOUN
ejpam-144	267	36	≥	≥	NOUN
ejpam-144	267	37	λ2	λ2	NOUN
ejpam-144	267	38	k	k	PROPN
ejpam-144	267	39	�	�	PROPN
ejpam-144	267	40	log	log	VERB
ejpam-144	267	41	1	1	NUM
ejpam-144	267	42	r	r	NOUN
ejpam-144	267	43	�	�	PROPN
ejpam-144	267	44	ω−p(1−	ω−p(1−	NUM
ejpam-144	267	45	|a|	|a|	NOUN
ejpam-144	267	46	)	)	PUNCT
ejpam-144	267	47	∫	∫	NOUN
ejpam-144	267	48	e(a	e(a	NOUN
ejpam-144	267	49	,	,	PUNCT
ejpam-144	267	50	r	r	NOUN
ejpam-144	267	51	)	)	PUNCT
ejpam-144	268	1	|	|	ADV
ejpam-144	268	2	f	f	PROPN
ejpam-144	268	3	′(z)|p	′(z)|p	PROPN
ejpam-144	268	4	(	(	PUNCT
ejpam-144	268	5	1−	1−	NUM
ejpam-144	268	6	|z|)p	|z|)p	NUM
ejpam-144	268	7	dσz	dσz	ADJ
ejpam-144	268	8	≥	≥	PROPN
ejpam-144	268	9	πλ2r2k	πλ2r2k	PROPN
ejpam-144	268	10	�	�	PROPN
ejpam-144	268	11	log	log	VERB
ejpam-144	268	12	1	1	NUM
ejpam-144	268	13	r	r	NOUN
ejpam-144	268	14	�	�	PROPN
ejpam-144	268	15	(	(	PUNCT
ejpam-144	268	16	1−	1−	NUM
ejpam-144	268	17	|a|)p	|a|)p	ADJ
ejpam-144	268	18	ωp(1−	ωp(1−	ADJ
ejpam-144	268	19	|a|	|a|	NOUN
ejpam-144	268	20	)	)	PUNCT
ejpam-144	268	21	|	|	NOUN
ejpam-144	268	22	f	f	PROPN
ejpam-144	268	23	′(a)|p	′(a)|p	PROPN
ejpam-144	268	24	,	,	PUNCT
ejpam-144	268	25	where	where	SCONJ
ejpam-144	268	26	λ2	λ2	NOUN
ejpam-144	268	27	is	be	AUX
ejpam-144	268	28	a	a	DET
ejpam-144	268	29	constant	constant	ADJ
ejpam-144	268	30	.	.	PUNCT
ejpam-144	269	1	the	the	DET
ejpam-144	269	2	last	last	ADJ
ejpam-144	269	3	inequality	inequality	NOUN
ejpam-144	269	4	shows	show	VERB
ejpam-144	269	5	that	that	SCONJ
ejpam-144	269	6	f	f	PROPN
ejpam-144	269	7	∈	∈	PROPN
ejpam-144	269	8	b	b	X
ejpam-144	269	9	p+2	p+2	X
ejpam-144	269	10	p	p	PROPN
ejpam-144	269	11	ω	ω	PROPN
ejpam-144	269	12	the	the	DET
ejpam-144	269	13	proof	proof	NOUN
ejpam-144	269	14	of	of	ADP
ejpam-144	269	15	(	(	PUNCT
ejpam-144	269	16	ii	ii	NOUN
ejpam-144	269	17	)	)	PUNCT
ejpam-144	269	18	is	be	AUX
ejpam-144	269	19	similar	similar	ADJ
ejpam-144	269	20	to	to	ADP
ejpam-144	269	21	proof	proof	NOUN
ejpam-144	269	22	(	(	PUNCT
ejpam-144	269	23	i	i	NOUN
ejpam-144	269	24	)	)	PUNCT
ejpam-144	269	25	by	by	ADP
ejpam-144	269	26	taking	take	VERB
ejpam-144	269	27	the	the	DET
ejpam-144	269	28	limit	limit	NOUN
ejpam-144	269	29	when	when	SCONJ
ejpam-144	269	30	|a|	|a|	NUM
ejpam-144	269	31	−→	−→	NOUN
ejpam-144	269	32	1−	1−	NUM
ejpam-144	269	33	in	in	ADP
ejpam-144	269	34	(	(	PUNCT
ejpam-144	269	35	i	i	NOUN
ejpam-144	269	36	)	)	PUNCT
ejpam-144	269	37	,	,	PUNCT
ejpam-144	269	38	hence	hence	ADV
ejpam-144	269	39	it	it	PRON
ejpam-144	269	40	can	can	AUX
ejpam-144	269	41	be	be	AUX
ejpam-144	269	42	omitted	omit	VERB
ejpam-144	269	43	.	.	PUNCT
ejpam-144	270	1	theorem	theorem	VERB
ejpam-144	270	2	4.2	4.2	NUM
ejpam-144	270	3	.	.	PUNCT
ejpam-144	271	1	let	let	VERB
ejpam-144	271	2	0	0	NUM
ejpam-144	271	3	<	<	X
ejpam-144	271	4	p	p	X
ejpam-144	271	5	<	<	X
ejpam-144	271	6	∞	∞	PROPN
ejpam-144	271	7	,	,	PUNCT
ejpam-144	271	8	ω	ω	NUM
ejpam-144	271	9	:	:	PUNCT
ejpam-144	271	10	(	(	PUNCT
ejpam-144	271	11	0	0	NUM
ejpam-144	271	12	,	,	PUNCT
ejpam-144	271	13	1]→	1]→	NOUN
ejpam-144	271	14	(	(	PUNCT
ejpam-144	271	15	0,∞	0,∞	NOUN
ejpam-144	271	16	)	)	PUNCT
ejpam-144	271	17	.	.	PUNCT
ejpam-144	272	1	assume	assume	VERB
ejpam-144	272	2	k1(r)≤	k1(r)≤	PROPN
ejpam-144	272	3	k2(r	k2(r	PROPN
ejpam-144	272	4	)	)	PUNCT
ejpam-144	272	5	for	for	ADP
ejpam-144	272	6	r	r	PROPN
ejpam-144	272	7	∈	∈	PROPN
ejpam-144	272	8	(	(	PUNCT
ejpam-144	272	9	0	0	NUM
ejpam-144	272	10	,	,	PUNCT
ejpam-144	272	11	1	1	NUM
ejpam-144	272	12	)	)	PUNCT
ejpam-144	272	13	and	and	CCONJ
ejpam-144	272	14	k1(r	k1(r	NOUN
ejpam-144	272	15	)	)	PUNCT
ejpam-144	272	16	k2(r	k2(r	NOUN
ejpam-144	272	17	)	)	PUNCT
ejpam-144	272	18	→	→	SYM
ejpam-144	272	19	0	0	NUM
ejpam-144	272	20	as	as	ADP
ejpam-144	272	21	r	r	NOUN
ejpam-144	272	22	→	→	SYM
ejpam-144	272	23	0	0	NUM
ejpam-144	272	24	.	.	PUNCT
ejpam-144	273	1	if	if	SCONJ
ejpam-144	273	2	the	the	DET
ejpam-144	273	3	integral	integral	ADJ
ejpam-144	273	4	in	in	ADP
ejpam-144	273	5	(	(	PUNCT
ejpam-144	273	6	2.3	2.3	NUM
ejpam-144	273	7	)	)	PUNCT
ejpam-144	273	8	is	be	AUX
ejpam-144	273	9	divergent	divergent	ADJ
ejpam-144	273	10	for	for	ADP
ejpam-144	273	11	k2	k2	NOUN
ejpam-144	273	12	,	,	PUNCT
ejpam-144	273	13	then	then	ADV
ejpam-144	273	14	qk2,ω	qk2,ω	NOUN
ejpam-144	273	15	$	$	SYM
ejpam-144	273	16	qk1,ω	qk1,ω	NOUN
ejpam-144	273	17	.	.	PUNCT
ejpam-144	274	1	proof	proof	NOUN
ejpam-144	274	2	.	.	PUNCT
ejpam-144	275	1	it	it	PRON
ejpam-144	275	2	is	be	AUX
ejpam-144	275	3	clear	clear	ADJ
ejpam-144	275	4	that	that	SCONJ
ejpam-144	275	5	qk2,ω	qk2,ω	PROPN
ejpam-144	275	6	⊂	⊂	PROPN
ejpam-144	275	7	qk1,ω	qk1,ω	PROPN
ejpam-144	275	8	.	.	PUNCT
ejpam-144	275	9	suppose	suppose	VERB
ejpam-144	275	10	that	that	SCONJ
ejpam-144	275	11	qk2,ω	qk2,ω	NOUN
ejpam-144	275	12	=	=	NOUN
ejpam-144	275	13	qk1,ω	qk1,ω	NOUN
ejpam-144	275	14	.	.	PUNCT
ejpam-144	276	1	by	by	ADP
ejpam-144	276	2	the	the	DET
ejpam-144	276	3	open	open	ADJ
ejpam-144	276	4	mapping	mapping	NOUN
ejpam-144	276	5	theorem	theorem	NOUN
ejpam-144	276	6	(	(	PUNCT
ejpam-144	276	7	see	see	VERB
ejpam-144	276	8	[	[	X
ejpam-144	276	9	8	8	NUM
ejpam-144	276	10	]	]	NUM
ejpam-144	276	11	)	)	PUNCT
ejpam-144	276	12	,	,	PUNCT
ejpam-144	276	13	we	we	PRON
ejpam-144	276	14	know	know	VERB
ejpam-144	276	15	that	that	SCONJ
ejpam-144	276	16	the	the	DET
ejpam-144	276	17	identity	identity	NOUN
ejpam-144	276	18	map	map	NOUN
ejpam-144	276	19	from	from	ADP
ejpam-144	276	20	one	one	NUM
ejpam-144	276	21	of	of	ADP
ejpam-144	276	22	these	these	DET
ejpam-144	276	23	spaces	space	NOUN
ejpam-144	276	24	into	into	ADP
ejpam-144	276	25	the	the	DET
ejpam-144	276	26	other	other	ADJ
ejpam-144	276	27	one	one	NOUN
ejpam-144	276	28	is	be	AUX
ejpam-144	276	29	continuous	continuous	ADJ
ejpam-144	276	30	.	.	PUNCT
ejpam-144	277	1	thus	thus	ADV
ejpam-144	277	2	there	there	PRON
ejpam-144	277	3	exists	exist	VERB
ejpam-144	277	4	a	a	DET
ejpam-144	277	5	constant	constant	ADJ
ejpam-144	277	6	c	c	NOUN
ejpam-144	277	7	such	such	ADJ
ejpam-144	277	8	that	that	DET
ejpam-144	277	9	‖	‖	PROPN
ejpam-144	277	10	f	f	PROPN
ejpam-144	277	11	‖k2,ω	‖k2,ω	ADP
ejpam-144	277	12	≤	≤	ADJ
ejpam-144	277	13	c‖	c‖	PROPN
ejpam-144	278	1	f	f	PROPN
ejpam-144	278	2	‖k1,ω	‖k1,ω	PROPN
ejpam-144	278	3	.	.	PUNCT
ejpam-144	279	1	since	since	SCONJ
ejpam-144	279	2	k1(r	k1(r	PROPN
ejpam-144	279	3	)	)	PUNCT
ejpam-144	279	4	k2(r	k2(r	NOUN
ejpam-144	279	5	)	)	PUNCT
ejpam-144	279	6	→	→	SYM
ejpam-144	279	7	0	0	NUM
ejpam-144	279	8	as	as	ADP
ejpam-144	279	9	r	r	NOUN
ejpam-144	279	10	→	→	SYM
ejpam-144	279	11	0	0	NUM
ejpam-144	279	12	,	,	PUNCT
ejpam-144	279	13	then	then	ADV
ejpam-144	279	14	there	there	PRON
ejpam-144	279	15	exists	exist	VERB
ejpam-144	279	16	r0	r0	NOUN
ejpam-144	279	17	∈	∈	PROPN
ejpam-144	279	18	(	(	PUNCT
ejpam-144	279	19	0	0	NUM
ejpam-144	279	20	,	,	PUNCT
ejpam-144	279	21	1	1	NUM
ejpam-144	279	22	)	)	PUNCT
ejpam-144	279	23	such	such	ADJ
ejpam-144	279	24	that	that	SCONJ
ejpam-144	279	25	k1(r	k1(r	NOUN
ejpam-144	279	26	)	)	PUNCT
ejpam-144	279	27	≤	≤	NOUN
ejpam-144	279	28	(	(	PUNCT
ejpam-144	279	29	2c)−1k2(r	2c)−1k2(r	NUM
ejpam-144	279	30	)	)	PUNCT
ejpam-144	279	31	for	for	ADP
ejpam-144	279	32	0	0	NUM
ejpam-144	279	33	<	<	X
ejpam-144	279	34	r	r	NOUN
ejpam-144	279	35	≤	≤	NUM
ejpam-144	279	36	r0	r0	NOUN
ejpam-144	279	37	.	.	PUNCT
ejpam-144	280	1	choose	choose	VERB
ejpam-144	280	2	t0	t0	X
ejpam-144	280	3	=	=	PUNCT
ejpam-144	280	4	e−r0	e−r0	PUNCT
ejpam-144	280	5	and	and	CCONJ
ejpam-144	280	6	we	we	PRON
ejpam-144	280	7	deduce	deduce	VERB
ejpam-144	280	8	that	that	SCONJ
ejpam-144	280	9	if	if	SCONJ
ejpam-144	280	10	f	f	PROPN
ejpam-144	280	11	∈	∈	PROPN
ejpam-144	280	12	qk2,ω	qk2,ω	PROPN
ejpam-144	280	13	,	,	PUNCT
ejpam-144	280	14	then	then	ADV
ejpam-144	280	15	sup	sup	PROPN
ejpam-144	280	16	a∈∆	a∈∆	PROPN
ejpam-144	280	17	∫	∫	PROPN
ejpam-144	280	18	∆	∆	PROPN
ejpam-144	281	1	|	|	ADV
ejpam-144	281	2	f	f	PROPN
ejpam-144	281	3	′(z)|p	′(z)|p	PROPN
ejpam-144	281	4	(	(	PUNCT
ejpam-144	281	5	1−	1−	NUM
ejpam-144	281	6	|z|)p	|z|)p	PROPN
ejpam-144	281	7	k2	k2	PROPN
ejpam-144	281	8	�	�	PROPN
ejpam-144	281	9	g(z	g(z	PROPN
ejpam-144	281	10	,	,	PUNCT
ejpam-144	281	11	a	a	PRON
ejpam-144	281	12	)	)	PUNCT
ejpam-144	281	13	�	�	PROPN
ejpam-144	281	14	ωp(1−	ωp(1−	ADJ
ejpam-144	281	15	|z|	|z|	NOUN
ejpam-144	281	16	)	)	PUNCT
ejpam-144	281	17	dσz	dσz	ADJ
ejpam-144	281	18	≤	≤	NUM
ejpam-144	281	19	c	c	NOUN
ejpam-144	281	20	sup	sup	NOUN
ejpam-144	281	21	a∈∆	a∈∆	NOUN
ejpam-144	281	22	∫	∫	PROPN
ejpam-144	281	23	∆(a	∆(a	PROPN
ejpam-144	281	24	,	,	PUNCT
ejpam-144	281	25	t0	t0	NOUN
ejpam-144	281	26	)	)	PUNCT
ejpam-144	282	1	|	|	ADV
ejpam-144	282	2	f	f	PROPN
ejpam-144	282	3	′(z)|p	′(z)|p	PROPN
ejpam-144	282	4	(	(	PUNCT
ejpam-144	282	5	1−	1−	NUM
ejpam-144	282	6	|z|)p	|z|)p	PROPN
ejpam-144	282	7	k1	k1	PROPN
ejpam-144	282	8	�	�	PROPN
ejpam-144	282	9	g(z	g(z	PROPN
ejpam-144	282	10	,	,	PUNCT
ejpam-144	282	11	a	a	PRON
ejpam-144	282	12	)	)	PUNCT
ejpam-144	282	13	�	�	PROPN
ejpam-144	282	14	ωp(1−	ωp(1−	ADJ
ejpam-144	282	15	|z|	|z|	NOUN
ejpam-144	282	16	)	)	PUNCT
ejpam-144	282	17	dσz	dσz	NOUN
ejpam-144	282	18	+	+	CCONJ
ejpam-144	282	19	1	1	NUM
ejpam-144	282	20	2	2	NUM
ejpam-144	282	21	sup	sup	NOUN
ejpam-144	282	22	a∈∆	a∈∆	NOUN
ejpam-144	282	23	∫	∫	NOUN
ejpam-144	282	24	∆	∆	PROPN
ejpam-144	283	1	|	|	ADV
ejpam-144	283	2	f	f	PROPN
ejpam-144	283	3	′(z)|p	′(z)|p	PROPN
ejpam-144	283	4	(	(	PUNCT
ejpam-144	283	5	1−	1−	NUM
ejpam-144	283	6	|z|)p	|z|)p	PROPN
ejpam-144	283	7	k2	k2	PROPN
ejpam-144	283	8	�	�	PROPN
ejpam-144	283	9	g(z	g(z	PROPN
ejpam-144	283	10	,	,	PUNCT
ejpam-144	283	11	a	a	DET
ejpam-144	283	12	)	)	PUNCT
ejpam-144	283	13	�	�	PROPN
ejpam-144	283	14	ωp(1−	ωp(1−	ADJ
ejpam-144	283	15	|z|	|z|	NOUN
ejpam-144	283	16	)	)	PUNCT
ejpam-144	283	17	dσz	dσz	NOUN
ejpam-144	283	18	.	.	PUNCT
ejpam-144	284	1	therefore	therefore	ADV
ejpam-144	284	2	,	,	PUNCT
ejpam-144	284	3	sup	sup	PROPN
ejpam-144	284	4	a∈∆	a∈∆	NOUN
ejpam-144	284	5	∫	∫	NOUN
ejpam-144	284	6	∆	∆	PROPN
ejpam-144	285	1	|	|	ADV
ejpam-144	285	2	f	f	PROPN
ejpam-144	285	3	′(z)|p	′(z)|p	PROPN
ejpam-144	285	4	(	(	PUNCT
ejpam-144	285	5	1−|z|)p	1−|z|)p	NUM
ejpam-144	285	6	k2	k2	PROPN
ejpam-144	285	7	�	�	PROPN
ejpam-144	285	8	g(z	g(z	PROPN
ejpam-144	285	9	,	,	PUNCT
ejpam-144	285	10	a	a	PRON
ejpam-144	285	11	)	)	PUNCT
ejpam-144	285	12	�	�	PROPN
ejpam-144	285	13	ωp(1−	ωp(1−	ADJ
ejpam-144	285	14	|z|	|z|	NOUN
ejpam-144	285	15	)	)	PUNCT
ejpam-144	285	16	dσz	dσz	ADJ
ejpam-144	285	17	≤	≤	NOUN
ejpam-144	285	18	2c	2c	NUM
ejpam-144	285	19	sup	sup	NOUN
ejpam-144	285	20	a∈∆	a∈∆	NOUN
ejpam-144	285	21	∫	∫	PROPN
ejpam-144	285	22	∆(a	∆(a	PROPN
ejpam-144	285	23	,	,	PUNCT
ejpam-144	285	24	t0	t0	NOUN
ejpam-144	285	25	)	)	PUNCT
ejpam-144	286	1	|	|	ADV
ejpam-144	286	2	f	f	PROPN
ejpam-144	286	3	′(z)|p	′(z)|p	PROPN
ejpam-144	286	4	(	(	PUNCT
ejpam-144	286	5	1−|z|)p	1−|z|)p	NUM
ejpam-144	286	6	k1	k1	PROPN
ejpam-144	286	7	�	�	PROPN
ejpam-144	286	8	g(z	g(z	PROPN
ejpam-144	286	9	,	,	PUNCT
ejpam-144	286	10	a	a	DET
ejpam-144	286	11	)	)	PUNCT
ejpam-144	286	12	�	�	PROPN
ejpam-144	286	13	ωp(1−	ωp(1−	ADJ
ejpam-144	286	14	|z|	|z|	NOUN
ejpam-144	286	15	)	)	PUNCT
ejpam-144	286	16	dσz	dσz	NOUN
ejpam-144	286	17	.	.	PUNCT
ejpam-144	287	1	references	reference	NOUN
ejpam-144	287	2	266	266	NUM
ejpam-144	287	3	by	by	ADP
ejpam-144	287	4	lemma	lemma	PROPN
ejpam-144	287	5	4.1	4.1	NUM
ejpam-144	287	6	and	and	CCONJ
ejpam-144	287	7	for	for	ADP
ejpam-144	287	8	f	f	PROPN
ejpam-144	287	9	∈	∈	PROPN
ejpam-144	287	10	qk2,ω	qk2,ω	PROPN
ejpam-144	287	11	,	,	PUNCT
ejpam-144	287	12	there	there	PRON
ejpam-144	287	13	exists	exist	VERB
ejpam-144	287	14	a	a	DET
ejpam-144	287	15	constant	constant	ADJ
ejpam-144	287	16	c1	c1	NOUN
ejpam-144	287	17	such	such	ADJ
ejpam-144	287	18	that	that	DET
ejpam-144	287	19	sup	sup	PROPN
ejpam-144	287	20	a∈∆	a∈∆	NOUN
ejpam-144	287	21	∫	∫	NOUN
ejpam-144	287	22	∆	∆	PROPN
ejpam-144	288	1	|	|	ADV
ejpam-144	288	2	f	f	PROPN
ejpam-144	288	3	′(z)|p	′(z)|p	PROPN
ejpam-144	288	4	(	(	PUNCT
ejpam-144	288	5	1−	1−	NUM
ejpam-144	288	6	|z|)p	|z|)p	PROPN
ejpam-144	288	7	k2	k2	PROPN
ejpam-144	288	8	�	�	PROPN
ejpam-144	288	9	g(z	g(z	PROPN
ejpam-144	288	10	,	,	PUNCT
ejpam-144	288	11	a	a	PRON
ejpam-144	288	12	)	)	PUNCT
ejpam-144	288	13	�	�	PROPN
ejpam-144	288	14	ωp(1−	ωp(1−	ADJ
ejpam-144	288	15	|z|	|z|	NOUN
ejpam-144	288	16	)	)	PUNCT
ejpam-144	288	17	dσz	dσz	ADJ
ejpam-144	288	18	≤	≤	NUM
ejpam-144	288	19	c1‖	c1‖	NOUN
ejpam-144	288	20	f	f	PROPN
ejpam-144	288	21	‖	‖	PROPN
ejpam-144	288	22	p	p	PROPN
ejpam-144	288	23	b	b	PROPN
ejpam-144	288	24	p+2	p+2	PRON
ejpam-144	288	25	p	p	PROPN
ejpam-144	288	26	ω	ω	PROPN
ejpam-144	288	27	.	.	PUNCT
ejpam-144	289	1	(	(	PUNCT
ejpam-144	289	2	4.3	4.3	NUM
ejpam-144	289	3	)	)	PUNCT
ejpam-144	289	4	if	if	SCONJ
ejpam-144	289	5	g	g	PROPN
ejpam-144	289	6	∈	∈	PROPN
ejpam-144	289	7	b	b	X
ejpam-144	289	8	p+2	p+2	PROPN
ejpam-144	289	9	p	p	PROPN
ejpam-144	289	10	ω	ω	PROPN
ejpam-144	289	11	and	and	CCONJ
ejpam-144	289	12	gr(z	gr(z	NOUN
ejpam-144	289	13	)	)	PUNCT
ejpam-144	289	14	=	=	SYM
ejpam-144	289	15	g(rz	g(rz	PROPN
ejpam-144	289	16	)	)	PUNCT
ejpam-144	289	17	,	,	PUNCT
ejpam-144	289	18	0	0	PUNCT
ejpam-144	289	19	<	<	X
ejpam-144	289	20	r	r	X
ejpam-144	289	21	<	<	X
ejpam-144	289	22	1	1	NUM
ejpam-144	289	23	,	,	PUNCT
ejpam-144	289	24	then	then	ADV
ejpam-144	289	25	gr	gr	PROPN
ejpam-144	289	26	b	b	PROPN
ejpam-144	290	1	p+2	p+2	DET
ejpam-144	290	2	p	p	PROPN
ejpam-144	290	3	ω	ω	PROPN
ejpam-144	290	4	≤	≤	PROPN
ejpam-144	290	5	g	g	PROPN
ejpam-144	290	6	b	b	PROPN
ejpam-144	290	7	p+2	p+2	PROPN
ejpam-144	290	8	p	p	PROPN
ejpam-144	290	9	ω	ω	PROPN
ejpam-144	290	10	.	.	PUNCT
ejpam-144	291	1	since	since	SCONJ
ejpam-144	291	2	gr	gr	PROPN
ejpam-144	291	3	∈	∈	PROPN
ejpam-144	291	4	qk2,ω	qk2,ω	NOUN
ejpam-144	291	5	,	,	PUNCT
ejpam-144	291	6	0	0	PUNCT
ejpam-144	291	7	<	<	X
ejpam-144	291	8	r	r	X
ejpam-144	291	9	<	<	X
ejpam-144	291	10	1	1	NUM
ejpam-144	291	11	,	,	PUNCT
ejpam-144	291	12	we	we	PRON
ejpam-144	291	13	can	can	AUX
ejpam-144	291	14	choose	choose	VERB
ejpam-144	291	15	f	f	NOUN
ejpam-144	291	16	=	=	PUNCT
ejpam-144	291	17	gr	gr	NOUN
ejpam-144	291	18	in	in	ADP
ejpam-144	291	19	the	the	DET
ejpam-144	291	20	inequality	inequality	NOUN
ejpam-144	291	21	(	(	PUNCT
ejpam-144	291	22	4.3	4.3	NUM
ejpam-144	291	23	)	)	PUNCT
ejpam-144	291	24	.	.	PUNCT
ejpam-144	292	1	using	use	VERB
ejpam-144	292	2	fatou	fatou	NOUN
ejpam-144	292	3	’s	’s	PART
ejpam-144	292	4	lemma	lemma	PROPN
ejpam-144	292	5	(	(	PUNCT
ejpam-144	292	6	see	see	VERB
ejpam-144	292	7	[	[	X
ejpam-144	292	8	10	10	NUM
ejpam-144	292	9	]	]	NUM
ejpam-144	292	10	)	)	PUNCT
ejpam-144	292	11	,	,	PUNCT
ejpam-144	292	12	we	we	PRON
ejpam-144	292	13	deduce	deduce	VERB
ejpam-144	292	14	that	that	DET
ejpam-144	292	15	sup	sup	PROPN
ejpam-144	292	16	a∈∆	a∈∆	NOUN
ejpam-144	292	17	∫	∫	PROPN
ejpam-144	292	18	∆	∆	PROPN
ejpam-144	292	19	|g	|g	PROPN
ejpam-144	292	20	′(z)|p	′(z)|p	PROPN
ejpam-144	292	21	(	(	PUNCT
ejpam-144	292	22	1−	1−	NUM
ejpam-144	292	23	|z|)p	|z|)p	NUM
ejpam-144	292	24	k2(g(z	k2(g(z	PROPN
ejpam-144	292	25	,	,	PUNCT
ejpam-144	292	26	a	a	PRON
ejpam-144	292	27	)	)	PUNCT
ejpam-144	292	28	)	)	PUNCT
ejpam-144	292	29	ωp(1−	ωp(1−	ADJ
ejpam-144	292	30	|z|	|z|	NOUN
ejpam-144	292	31	)	)	PUNCT
ejpam-144	292	32	dσz	dσz	NOUN
ejpam-144	292	33	<	<	X
ejpam-144	292	34	c1	c1	PROPN
ejpam-144	292	35	g	g	PROPN
ejpam-144	292	36	p	p	PROPN
ejpam-144	292	37	b	b	PROPN
ejpam-144	292	38	p+2	p+2	PRON
ejpam-144	292	39	p	p	PROPN
ejpam-144	292	40	ω	ω	PROPN
ejpam-144	292	41	.	.	PUNCT
ejpam-144	293	1	we	we	PRON
ejpam-144	293	2	have	have	AUX
ejpam-144	293	3	proved	prove	VERB
ejpam-144	293	4	that	that	SCONJ
ejpam-144	293	5	g	g	PROPN
ejpam-144	293	6	∈	∈	PROPN
ejpam-144	293	7	qk2,ω	qk2,ω	NOUN
ejpam-144	293	8	.	.	PUNCT
ejpam-144	294	1	it	it	PRON
ejpam-144	294	2	means	mean	VERB
ejpam-144	294	3	that	that	SCONJ
ejpam-144	294	4	qk2,ω	qk2,ω	NOUN
ejpam-144	294	5	=	=	SYM
ejpam-144	294	6	b	b	PROPN
ejpam-144	294	7	p+2	p+2	X
ejpam-144	294	8	p	p	PROPN
ejpam-144	294	9	ω	ω	PROPN
ejpam-144	294	10	.	.	PUNCT
ejpam-144	295	1	it	it	PRON
ejpam-144	295	2	follows	follow	VERB
ejpam-144	295	3	from	from	ADP
ejpam-144	295	4	theorem	theorem	ADJ
ejpam-144	295	5	2.1	2.1	NUM
ejpam-144	295	6	that	that	SCONJ
ejpam-144	295	7	the	the	DET
ejpam-144	295	8	integral	integral	ADJ
ejpam-144	295	9	in	in	ADP
ejpam-144	295	10	(	(	PUNCT
ejpam-144	295	11	2.3	2.3	NUM
ejpam-144	295	12	)	)	PUNCT
ejpam-144	295	13	with	with	ADP
ejpam-144	295	14	k	k	PROPN
ejpam-144	295	15	=	=	SYM
ejpam-144	295	16	k2	k2	PROPN
ejpam-144	295	17	must	must	AUX
ejpam-144	295	18	be	be	AUX
ejpam-144	295	19	convergent	convergent	ADJ
ejpam-144	295	20	,	,	PUNCT
ejpam-144	295	21	a	a	DET
ejpam-144	295	22	contradiction	contradiction	NOUN
ejpam-144	295	23	.	.	PUNCT
ejpam-144	296	1	we	we	PRON
ejpam-144	296	2	obtain	obtain	VERB
ejpam-144	296	3	that	that	DET
ejpam-144	296	4	qk2,ω	qk2,ω	NOUN
ejpam-144	296	5	$	$	SYM
ejpam-144	296	6	qk1,ω	qk1,ω	NOUN
ejpam-144	296	7	.	.	PUNCT
ejpam-144	297	1	now	now	ADV
ejpam-144	297	2	,	,	PUNCT
ejpam-144	297	3	the	the	DET
ejpam-144	297	4	proof	proof	NOUN
ejpam-144	297	5	of	of	ADP
ejpam-144	297	6	theorem	theorem	ADJ
ejpam-144	297	7	4.2	4.2	NUM
ejpam-144	297	8	is	be	AUX
ejpam-144	297	9	completed	complete	VERB
ejpam-144	297	10	.	.	PUNCT
ejpam-144	298	1	acknowledgements	acknowledgement	NOUN
ejpam-144	298	2	.	.	PUNCT
ejpam-144	299	1	the	the	DET
ejpam-144	299	2	authors	author	NOUN
ejpam-144	299	3	would	would	AUX
ejpam-144	299	4	like	like	VERB
ejpam-144	299	5	to	to	PART
ejpam-144	299	6	thank	thank	VERB
ejpam-144	299	7	the	the	DET
ejpam-144	299	8	referee	referee	NOUN
ejpam-144	299	9	for	for	ADP
ejpam-144	299	10	his	his	PRON
ejpam-144	299	11	careful	careful	ADJ
ejpam-144	299	12	reading	reading	NOUN
ejpam-144	299	13	of	of	ADP
ejpam-144	299	14	the	the	DET
ejpam-144	299	15	manuscript	manuscript	NOUN
ejpam-144	299	16	and	and	CCONJ
ejpam-144	299	17	for	for	ADP
ejpam-144	299	18	the	the	DET
ejpam-144	299	19	useful	useful	ADJ
ejpam-144	299	20	suggestions	suggestion	NOUN
ejpam-144	299	21	.	.	PUNCT
ejpam-144	300	1	references	reference	NOUN
ejpam-144	300	2	[	[	X
ejpam-144	300	3	1	1	NUM
ejpam-144	300	4	]	]	PUNCT
ejpam-144	300	5	a.	a.	PROPN
ejpam-144	300	6	el	el	PROPN
ejpam-144	300	7	-	-	PUNCT
ejpam-144	300	8	sayed	say	VERB
ejpam-144	300	9	ahmed	ahmed	PROPN
ejpam-144	300	10	and	and	CCONJ
ejpam-144	300	11	m.	m.	PROPN
ejpam-144	300	12	a.	a.	PROPN
ejpam-144	300	13	bakhit	bakhit	PROPN
ejpam-144	300	14	,	,	PUNCT
ejpam-144	300	15	composition	composition	NOUN
ejpam-144	300	16	operators	operator	NOUN
ejpam-144	300	17	on	on	ADP
ejpam-144	300	18	some	some	DET
ejpam-144	300	19	holomorphic	holomorphic	ADJ
ejpam-144	300	20	banach	banach	NOUN
ejpam-144	300	21	function	function	NOUN
ejpam-144	300	22	spaces	space	NOUN
ejpam-144	300	23	,	,	PUNCT
ejpam-144	300	24	mathematica	mathematica	PROPN
ejpam-144	300	25	scandinavica	scandinavica	PROPN
ejpam-144	300	26	,	,	PUNCT
ejpam-144	300	27	vol	vol	VERB
ejpam-144	300	28	104	104	NUM
ejpam-144	300	29	(	(	PUNCT
ejpam-144	300	30	2)(2009),275	2)(2009),275	NUM
ejpam-144	300	31	-	-	SYM
ejpam-144	300	32	295	295	NUM
ejpam-144	300	33	.	.	PUNCT
ejpam-144	301	1	[	[	X
ejpam-144	301	2	2	2	NUM
ejpam-144	301	3	]	]	PUNCT
ejpam-144	301	4	r.	r.	PROPN
ejpam-144	301	5	aulaskari	aulaskari	PROPN
ejpam-144	301	6	and	and	CCONJ
ejpam-144	301	7	p.	p.	PROPN
ejpam-144	301	8	lappan	lappan	PROPN
ejpam-144	301	9	,	,	PUNCT
ejpam-144	301	10	criteria	criterion	NOUN
ejpam-144	301	11	for	for	ADP
ejpam-144	301	12	an	an	DET
ejpam-144	301	13	analytic	analytic	ADJ
ejpam-144	301	14	function	function	NOUN
ejpam-144	301	15	to	to	PART
ejpam-144	301	16	be	be	AUX
ejpam-144	301	17	bloch	bloch	PROPN
ejpam-144	301	18	and	and	CCONJ
ejpam-144	301	19	a	a	DET
ejpam-144	301	20	harmonic	harmonic	ADJ
ejpam-144	301	21	or	or	CCONJ
ejpam-144	301	22	meromorphic	meromorphic	ADJ
ejpam-144	301	23	function	function	NOUN
ejpam-144	301	24	to	to	PART
ejpam-144	301	25	be	be	AUX
ejpam-144	301	26	normal	normal	ADJ
ejpam-144	301	27	,	,	PUNCT
ejpam-144	301	28	complex	complex	ADJ
ejpam-144	301	29	analysis	analysis	NOUN
ejpam-144	301	30	and	and	CCONJ
ejpam-144	301	31	its	its	PRON
ejpam-144	301	32	applications	application	NOUN
ejpam-144	301	33	(	(	PUNCT
ejpam-144	301	34	eds	ed	NOUN
ejpam-144	301	35	y.	y.	PROPN
ejpam-144	301	36	chung	chung	PROPN
ejpam-144	301	37	-	-	PUNCT
ejpam-144	301	38	chun	chun	PROPN
ejpam-144	301	39	et	et	PROPN
ejpam-144	301	40	al	al	PROPN
ejpam-144	301	41	.	.	PROPN
ejpam-144	301	42	)	)	PUNCT
ejpam-144	301	43	,	,	PUNCT
ejpam-144	301	44	pitman	pitman	NOUN
ejpam-144	301	45	research	research	NOUN
ejpam-144	301	46	notes	note	NOUN
ejpam-144	301	47	in	in	ADP
ejpam-144	301	48	mathematics	mathematic	NOUN
ejpam-144	301	49	305	305	NUM
ejpam-144	301	50	,	,	PUNCT
ejpam-144	301	51	longman	longman	NOUN
ejpam-144	301	52	(	(	PUNCT
ejpam-144	301	53	1994	1994	NUM
ejpam-144	301	54	)	)	PUNCT
ejpam-144	301	55	,	,	PUNCT
ejpam-144	301	56	136	136	NUM
ejpam-144	301	57	-	-	SYM
ejpam-144	301	58	146	146	NUM
ejpam-144	301	59	.	.	PUNCT
ejpam-144	302	1	[	[	X
ejpam-144	302	2	3	3	X
ejpam-144	302	3	]	]	X
ejpam-144	302	4	r.	r.	PROPN
ejpam-144	302	5	aulaskari	aulaskari	PROPN
ejpam-144	302	6	,	,	PUNCT
ejpam-144	302	7	p.	p.	PROPN
ejpam-144	302	8	lappan	lappan	PROPN
ejpam-144	302	9	,	,	PUNCT
ejpam-144	302	10	peter	peter	PROPN
ejpam-144	302	11	and	and	CCONJ
ejpam-144	302	12	r.	r.	PROPN
ejpam-144	302	13	zhao	zhao	PROPN
ejpam-144	302	14	,	,	PUNCT
ejpam-144	302	15	on	on	ADP
ejpam-144	302	16	harmonic	harmonic	ADJ
ejpam-144	302	17	normal	normal	ADJ
ejpam-144	302	18	and	and	CCONJ
ejpam-144	302	19	q	q	NOUN
ejpam-144	302	20	#	#	NOUN
ejpam-144	302	21	p	p	NOUN
ejpam-144	302	22	functions	function	NOUN
ejpam-144	302	23	,	,	PUNCT
ejpam-144	302	24	ill	ill	PROPN
ejpam-144	302	25	.	.	PUNCT
ejpam-144	303	1	j.	j.	PROPN
ejpam-144	303	2	math	math	PROPN
ejpam-144	303	3	.	.	PUNCT
ejpam-144	304	1	45	45	NUM
ejpam-144	304	2	,	,	PUNCT
ejpam-144	304	3	no.2(2001	no.2(2001	NOUN
ejpam-144	304	4	)	)	PUNCT
ejpam-144	304	5	,	,	PUNCT
ejpam-144	304	6	423	423	NUM
ejpam-144	304	7	-	-	SYM
ejpam-144	304	8	440	440	NUM
ejpam-144	304	9	.	.	PUNCT
ejpam-144	305	1	references	reference	NOUN
ejpam-144	305	2	267	267	NUM
ejpam-144	305	3	[	[	X
ejpam-144	305	4	4	4	NUM
ejpam-144	305	5	]	]	PUNCT
ejpam-144	305	6	k.	k.	PROPN
ejpam-144	305	7	m.	m.	PROPN
ejpam-144	305	8	dyakonov	dyakonov	PROPN
ejpam-144	305	9	,	,	PUNCT
ejpam-144	305	10	weighted	weight	VERB
ejpam-144	305	11	bloch	bloch	PROPN
ejpam-144	305	12	spaces	space	NOUN
ejpam-144	305	13	,	,	PUNCT
ejpam-144	305	14	hp	hp	PROPN
ejpam-144	305	15	,	,	PUNCT
ejpam-144	305	16	and	and	CCONJ
ejpam-144	305	17	bmoa	bmoa	NOUN
ejpam-144	305	18	,	,	PUNCT
ejpam-144	305	19	j.	j.	PROPN
ejpam-144	305	20	lond	lond	PROPN
ejpam-144	305	21	.	.	PUNCT
ejpam-144	306	1	math	math	PROPN
ejpam-144	306	2	.	.	PUNCT
ejpam-144	307	1	soc	soc	PROPN
ejpam-144	307	2	.	.	PUNCT
ejpam-144	308	1	ii	ii	PROPN
ejpam-144	308	2	.	.	PUNCT
ejpam-144	308	3	ser	ser	PROPN
ejpam-144	308	4	.	.	PROPN
ejpam-144	309	1	65	65	NUM
ejpam-144	309	2	no	no	NOUN
ejpam-144	309	3	.	.	PUNCT
ejpam-144	310	1	2(2002	2(2002	NUM
ejpam-144	310	2	)	)	PUNCT
ejpam-144	311	1	,	,	PUNCT
ejpam-144	311	2	411	411	NUM
ejpam-144	311	3	-	-	SYM
ejpam-144	311	4	417	417	NUM
ejpam-144	311	5	.	.	PUNCT
ejpam-144	312	1	[	[	X
ejpam-144	312	2	5	5	NUM
ejpam-144	312	3	]	]	PUNCT
ejpam-144	312	4	m.	m.	NOUN
ejpam-144	312	5	essén	essén	NOUN
ejpam-144	312	6	and	and	CCONJ
ejpam-144	312	7	h.	h.	PROPN
ejpam-144	312	8	wulan	wulan	PROPN
ejpam-144	312	9	,	,	PUNCT
ejpam-144	312	10	on	on	ADP
ejpam-144	312	11	analytic	analytic	ADJ
ejpam-144	312	12	and	and	CCONJ
ejpam-144	312	13	meromorphic	meromorphic	ADJ
ejpam-144	312	14	functions	function	NOUN
ejpam-144	312	15	and	and	CCONJ
ejpam-144	312	16	spaces	space	NOUN
ejpam-144	312	17	of	of	ADP
ejpam-144	312	18	qk	qk	NOUN
ejpam-144	312	19	type	type	NOUN
ejpam-144	312	20	,	,	PUNCT
ejpam-144	312	21	illinois	illinois	PROPN
ejpam-144	312	22	j.	j.	PROPN
ejpam-144	312	23	math	math	PROPN
ejpam-144	312	24	.	.	PUNCT
ejpam-144	313	1	46(2002	46(2002	NUM
ejpam-144	313	2	)	)	PUNCT
ejpam-144	313	3	,	,	PUNCT
ejpam-144	313	4	1233	1233	NUM
ejpam-144	313	5	-	-	SYM
ejpam-144	313	6	1258	1258	NUM
ejpam-144	313	7	.	.	PUNCT
ejpam-144	314	1	[	[	X
ejpam-144	314	2	6	6	NUM
ejpam-144	314	3	]	]	PUNCT
ejpam-144	314	4	m.	m.	NOUN
ejpam-144	314	5	essén	essén	NOUN
ejpam-144	314	6	,	,	PUNCT
ejpam-144	314	7	h.	h.	PROPN
ejpam-144	314	8	wulan	wulan	PROPN
ejpam-144	314	9	and	and	CCONJ
ejpam-144	314	10	j.	j.	PROPN
ejpam-144	314	11	xiao	xiao	PROPN
ejpam-144	314	12	,	,	PUNCT
ejpam-144	314	13	several	several	ADJ
ejpam-144	314	14	function	function	NOUN
ejpam-144	314	15	-	-	PUNCT
ejpam-144	314	16	theoretic	theoretic	NOUN
ejpam-144	314	17	characterizations	characterization	NOUN
ejpam-144	314	18	of	of	ADP
ejpam-144	314	19	möbius	möbius	NOUN
ejpam-144	314	20	invariant	invariant	ADJ
ejpam-144	314	21	qk	qk	NOUN
ejpam-144	314	22	spaces	space	NOUN
ejpam-144	314	23	,	,	PUNCT
ejpam-144	314	24	j.	j.	PROPN
ejpam-144	314	25	funct	funct	PROPN
ejpam-144	314	26	.	.	PUNCT
ejpam-144	315	1	anal	anal	PROPN
ejpam-144	315	2	.	.	PUNCT
ejpam-144	316	1	230	230	NUM
ejpam-144	316	2	,	,	PUNCT
ejpam-144	316	3	no	no	INTJ
ejpam-144	316	4	.	.	NOUN
ejpam-144	316	5	1	1	NUM
ejpam-144	316	6	(	(	PUNCT
ejpam-144	316	7	2006	2006	NUM
ejpam-144	316	8	)	)	PUNCT
ejpam-144	316	9	,	,	PUNCT
ejpam-144	316	10	78	78	NUM
ejpam-144	316	11	-	-	SYM
ejpam-144	316	12	115	115	NUM
ejpam-144	316	13	.	.	PUNCT
ejpam-144	317	1	[	[	X
ejpam-144	317	2	7	7	X
ejpam-144	317	3	]	]	X
ejpam-144	317	4	p.	p.	NOUN
ejpam-144	317	5	galanopoulos	galanopoulos	PROPN
ejpam-144	317	6	,	,	PUNCT
ejpam-144	317	7	on	on	ADP
ejpam-144	317	8	blog	blog	NOUN
ejpam-144	317	9	to	to	ADP
ejpam-144	317	10	qp	qp	PROPN
ejpam-144	317	11	log	log	PROPN
ejpam-144	317	12	pullbacks	pullback	NOUN
ejpam-144	317	13	,	,	PUNCT
ejpam-144	317	14	j.	j.	PROPN
ejpam-144	317	15	math	math	PROPN
ejpam-144	317	16	.	.	PUNCT
ejpam-144	318	1	anal	anal	PROPN
ejpam-144	318	2	.	.	PUNCT
ejpam-144	319	1	appl	appl	PROPN
ejpam-144	319	2	.	.	PUNCT
ejpam-144	320	1	vol	vol	NOUN
ejpam-144	320	2	337(2008	337(2008	NOUN
ejpam-144	320	3	)	)	PUNCT
ejpam-144	320	4	,	,	PUNCT
ejpam-144	320	5	712725	712725	NUM
ejpam-144	320	6	.	.	PUNCT
ejpam-144	321	1	[	[	X
ejpam-144	321	2	8	8	NUM
ejpam-144	321	3	]	]	X
ejpam-144	321	4	e.	e.	PROPN
ejpam-144	321	5	kreyszig	kreyszig	PROPN
ejpam-144	321	6	,	,	PUNCT
ejpam-144	321	7	introductory	introductory	ADJ
ejpam-144	321	8	functional	functional	ADJ
ejpam-144	321	9	analysis	analysis	NOUN
ejpam-144	321	10	with	with	ADP
ejpam-144	321	11	applications	application	NOUN
ejpam-144	321	12	,	,	PUNCT
ejpam-144	321	13	john	john	PROPN
ejpam-144	321	14	wiley	wiley	PROPN
ejpam-144	321	15	and	and	CCONJ
ejpam-144	321	16	sons	son	NOUN
ejpam-144	321	17	(	(	PUNCT
ejpam-144	321	18	1978	1978	NUM
ejpam-144	321	19	)	)	PUNCT
ejpam-144	321	20	.	.	PUNCT
ejpam-144	322	1	[	[	X
ejpam-144	322	2	9	9	NUM
ejpam-144	322	3	]	]	PUNCT
ejpam-144	322	4	s.	s.	PROPN
ejpam-144	322	5	li	li	PROPN
ejpam-144	322	6	,	,	PUNCT
ejpam-144	322	7	songxiao	songxiao	VERB
ejpam-144	322	8	and	and	CCONJ
ejpam-144	322	9	h.	h.	PROPN
ejpam-144	322	10	wulan	wulan	NOUN
ejpam-144	322	11	,	,	PUNCT
ejpam-144	322	12	composition	composition	NOUN
ejpam-144	322	13	operators	operator	NOUN
ejpam-144	322	14	on	on	ADP
ejpam-144	322	15	qk	qk	NOUN
ejpam-144	322	16	spaces	space	NOUN
ejpam-144	322	17	,	,	PUNCT
ejpam-144	322	18	j.	j.	PROPN
ejpam-144	322	19	math	math	PROPN
ejpam-144	322	20	.	.	PUNCT
ejpam-144	323	1	anal	anal	PROPN
ejpam-144	323	2	.	.	PUNCT
ejpam-144	324	1	appl	appl	PROPN
ejpam-144	324	2	.	.	PUNCT
ejpam-144	325	1	327(2)(2007	327(2)(2007	NUM
ejpam-144	325	2	)	)	PUNCT
ejpam-144	325	3	,	,	PUNCT
ejpam-144	325	4	948	948	NUM
ejpam-144	325	5	-	-	SYM
ejpam-144	325	6	958	958	NUM
ejpam-144	325	7	.	.	PUNCT
ejpam-144	326	1	[	[	X
ejpam-144	326	2	10	10	NUM
ejpam-144	326	3	]	]	X
ejpam-144	326	4	h.	h.	PROPN
ejpam-144	326	5	l.	l.	PROPN
ejpam-144	326	6	royden	royden	PROPN
ejpam-144	326	7	,	,	PUNCT
ejpam-144	326	8	real	real	ADJ
ejpam-144	326	9	analysis	analysis	NOUN
ejpam-144	326	10	.	.	PUNCT
ejpam-144	327	1	2nd	2nd	ADJ
ejpam-144	327	2	ed	ed	NOUN
ejpam-144	327	3	.	.	PUNCT
ejpam-144	328	1	new	new	PROPN
ejpam-144	328	2	york	york	PROPN
ejpam-144	328	3	:	:	PUNCT
ejpam-144	328	4	macmillan	macmillan	PROPN
ejpam-144	328	5	,	,	PUNCT
ejpam-144	328	6	1968	1968	NUM
ejpam-144	328	7	.	.	PUNCT
ejpam-144	329	1	[	[	X
ejpam-144	329	2	11	11	NUM
ejpam-144	329	3	]	]	PUNCT
ejpam-144	329	4	k.	k.	PROPN
ejpam-144	329	5	stroethoff	stroethoff	PROPN
ejpam-144	329	6	,	,	PUNCT
ejpam-144	329	7	besov	besov	NOUN
ejpam-144	329	8	-	-	PUNCT
ejpam-144	329	9	type	type	NOUN
ejpam-144	329	10	characterisations	characterisation	NOUN
ejpam-144	329	11	for	for	ADP
ejpam-144	329	12	the	the	DET
ejpam-144	329	13	bloch	bloch	PROPN
ejpam-144	329	14	space	space	NOUN
ejpam-144	329	15	,	,	PUNCT
ejpam-144	329	16	bull	bull	NOUN
ejpam-144	329	17	.	.	PUNCT
ejpam-144	330	1	austral	austral	PROPN
ejpam-144	330	2	.	.	PUNCT
ejpam-144	331	1	math	math	NOUN
ejpam-144	331	2	.	.	PUNCT
ejpam-144	332	1	soc	soc	PROPN
ejpam-144	332	2	.	.	PUNCT
ejpam-144	333	1	39(1989	39(1989	NUM
ejpam-144	333	2	)	)	PUNCT
ejpam-144	333	3	,	,	PUNCT
ejpam-144	333	4	405	405	NUM
ejpam-144	333	5	-	-	SYM
ejpam-144	333	6	420	420	NUM
ejpam-144	333	7	.	.	PUNCT
ejpam-144	334	1	[	[	X
ejpam-144	334	2	12	12	NUM
ejpam-144	334	3	]	]	X
ejpam-144	334	4	h.	h.	NOUN
ejpam-144	334	5	wulan	wulan	NOUN
ejpam-144	334	6	and	and	CCONJ
ejpam-144	334	7	p.	p.	PROPN
ejpam-144	334	8	wu	wu	PROPN
ejpam-144	334	9	,	,	PUNCT
ejpam-144	334	10	characterizations	characterization	NOUN
ejpam-144	334	11	of	of	ADP
ejpam-144	334	12	qt	qt	NOUN
ejpam-144	334	13	spaces	space	NOUN
ejpam-144	334	14	,	,	PUNCT
ejpam-144	334	15	j.	j.	PROPN
ejpam-144	334	16	math	math	PROPN
ejpam-144	334	17	.	.	PUNCT
ejpam-144	335	1	anal	anal	PROPN
ejpam-144	335	2	.	.	PUNCT
ejpam-144	336	1	appl	appl	PROPN
ejpam-144	336	2	.	.	PROPN
ejpam-144	337	1	254	254	NUM
ejpam-144	337	2	no	no	NOUN
ejpam-144	337	3	.	.	PUNCT
ejpam-144	338	1	2(2001	2(2001	NUM
ejpam-144	338	2	)	)	PUNCT
ejpam-144	338	3	,	,	PUNCT
ejpam-144	338	4	484	484	NUM
ejpam-144	338	5	-	-	SYM
ejpam-144	338	6	497	497	NUM
ejpam-144	338	7	.	.	PUNCT
ejpam-144	339	1	[	[	X
ejpam-144	339	2	13	13	NUM
ejpam-144	339	3	]	]	X
ejpam-144	339	4	h.	h.	NOUN
ejpam-144	339	5	wulan	wulan	NOUN
ejpam-144	339	6	and	and	CCONJ
ejpam-144	339	7	y.	y.	PROPN
ejpam-144	339	8	zhang	zhang	PROPN
ejpam-144	339	9	,	,	PUNCT
ejpam-144	339	10	hadamard	hadamard	ADJ
ejpam-144	339	11	products	product	NOUN
ejpam-144	339	12	and	and	CCONJ
ejpam-144	339	13	qk	qk	NOUN
ejpam-144	339	14	spaces	space	NOUN
ejpam-144	339	15	,	,	PUNCT
ejpam-144	339	16	j.	j.	PROPN
ejpam-144	339	17	math	math	PROPN
ejpam-144	339	18	.	.	PUNCT
ejpam-144	340	1	anal	anal	PROPN
ejpam-144	340	2	.	.	PUNCT
ejpam-144	340	3	appl	appl	PROPN
ejpam-144	340	4	.	.	PUNCT
ejpam-144	341	1	337(2008	337(2008	NOUN
ejpam-144	341	2	)	)	PUNCT
ejpam-144	341	3	,	,	PUNCT
ejpam-144	341	4	1142	1142	NUM
ejpam-144	341	5	-	-	SYM
ejpam-144	341	6	1150	1150	NUM
ejpam-144	341	7	.	.	PUNCT
ejpam-144	342	1	[	[	X
ejpam-144	342	2	14	14	NUM
ejpam-144	342	3	]	]	X
ejpam-144	342	4	h.	h.	PROPN
ejpam-144	342	5	wulan	wulan	PROPN
ejpam-144	342	6	and	and	CCONJ
ejpam-144	342	7	k.	k.	PROPN
ejpam-144	342	8	zhu	zhu	PROPN
ejpam-144	342	9	,	,	PUNCT
ejpam-144	342	10	qk	qk	ADP
ejpam-144	342	11	type	type	NOUN
ejpam-144	342	12	spaces	space	NOUN
ejpam-144	342	13	of	of	ADP
ejpam-144	342	14	analytic	analytic	ADJ
ejpam-144	342	15	functions	function	NOUN
ejpam-144	342	16	,	,	PUNCT
ejpam-144	342	17	j.	j.	PROPN
ejpam-144	342	18	funct	funct	PROPN
ejpam-144	342	19	.	.	PUNCT
ejpam-144	343	1	spaces	space	NOUN
ejpam-144	343	2	appl	appl	PROPN
ejpam-144	343	3	.	.	PUNCT
ejpam-144	344	1	4(2006	4(2006	NUM
ejpam-144	344	2	)	)	PUNCT
ejpam-144	344	3	,	,	PUNCT
ejpam-144	344	4	73	73	NUM
ejpam-144	344	5	-	-	SYM
ejpam-144	344	6	84	84	NUM
ejpam-144	344	7	.	.	PUNCT
ejpam-144	345	1	[	[	X
ejpam-144	345	2	15	15	NUM
ejpam-144	345	3	]	]	X
ejpam-144	345	4	h.	h.	NOUN
ejpam-144	345	5	wulan	wulan	PROPN
ejpam-144	345	6	and	and	CCONJ
ejpam-144	345	7	j.	j.	PROPN
ejpam-144	345	8	zhou	zhou	PROPN
ejpam-144	345	9	,	,	PUNCT
ejpam-144	345	10	the	the	DET
ejpam-144	345	11	higher	high	ADJ
ejpam-144	345	12	order	order	NOUN
ejpam-144	345	13	derivatives	derivative	NOUN
ejpam-144	345	14	of	of	ADP
ejpam-144	345	15	qk	qk	NOUN
ejpam-144	345	16	type	type	NOUN
ejpam-144	345	17	spaces	space	NOUN
ejpam-144	345	18	,	,	PUNCT
ejpam-144	345	19	j.	j.	PROPN
ejpam-144	345	20	math	math	PROPN
ejpam-144	345	21	.	.	PUNCT
ejpam-144	346	1	anal	anal	PROPN
ejpam-144	346	2	.	.	PUNCT
ejpam-144	347	1	appl	appl	PROPN
ejpam-144	347	2	.	.	PUNCT
ejpam-144	348	1	332	332	NUM
ejpam-144	348	2	,	,	PUNCT
ejpam-144	348	3	no	no	INTJ
ejpam-144	348	4	.	.	PUNCT
ejpam-144	349	1	2(2007	2(2007	NUM
ejpam-144	349	2	)	)	PUNCT
ejpam-144	349	3	,	,	PUNCT
ejpam-144	349	4	1216	1216	NUM
ejpam-144	349	5	-	-	SYM
ejpam-144	349	6	1228	1228	NUM
ejpam-144	349	7	.	.	PUNCT
ejpam-144	350	1	[	[	X
ejpam-144	350	2	16	16	NUM
ejpam-144	350	3	]	]	X
ejpam-144	350	4	h.	h.	PROPN
ejpam-144	350	5	wulan	wulan	PROPN
ejpam-144	350	6	and	and	CCONJ
ejpam-144	350	7	k.	k.	PROPN
ejpam-144	350	8	zhu	zhu	PROPN
ejpam-144	350	9	,	,	PUNCT
ejpam-144	350	10	derivative	derivative	ADJ
ejpam-144	350	11	-	-	PUNCT
ejpam-144	350	12	free	free	ADJ
ejpam-144	350	13	characterizations	characterization	NOUN
ejpam-144	350	14	of	of	ADP
ejpam-144	350	15	qk	qk	NOUN
ejpam-144	350	16	spaces	space	NOUN
ejpam-144	350	17	,	,	PUNCT
ejpam-144	350	18	j.	j.	PROPN
ejpam-144	350	19	aust	aust	PROPN
ejpam-144	350	20	.	.	PUNCT
ejpam-144	351	1	math	math	PROPN
ejpam-144	351	2	.	.	PUNCT
ejpam-144	352	1	soc	soc	PROPN
ejpam-144	352	2	.	.	PUNCT
ejpam-144	353	1	82	82	NUM
ejpam-144	353	2	,	,	PUNCT
ejpam-144	353	3	no	no	INTJ
ejpam-144	353	4	.	.	PUNCT
ejpam-144	354	1	2(2007	2(2007	NUM
ejpam-144	354	2	)	)	PUNCT
ejpam-144	354	3	,	,	PUNCT
ejpam-144	354	4	283	283	NUM
ejpam-144	354	5	-	-	SYM
ejpam-144	354	6	295	295	NUM
ejpam-144	354	7	.	.	PUNCT
ejpam-144	355	1	[	[	X
ejpam-144	355	2	17	17	NUM
ejpam-144	355	3	]	]	PUNCT
ejpam-144	355	4	j.	j.	PROPN
ejpam-144	355	5	xiao	xiao	PROPN
ejpam-144	355	6	,	,	PUNCT
ejpam-144	355	7	holomorphic	holomorphic	ADJ
ejpam-144	355	8	q	q	PROPN
ejpam-144	355	9	classes	class	NOUN
ejpam-144	355	10	,	,	PUNCT
ejpam-144	355	11	springer	springer	NOUN
ejpam-144	355	12	lnm	lnm	PROPN
ejpam-144	355	13	1767	1767	NUM
ejpam-144	355	14	,	,	PUNCT
ejpam-144	355	15	berlin	berlin	PROPN
ejpam-144	355	16	,	,	PUNCT
ejpam-144	355	17	2001	2001	NUM
ejpam-144	355	18	.	.	PUNCT
ejpam-144	356	1	[	[	X
ejpam-144	356	2	18	18	NUM
ejpam-144	356	3	]	]	PUNCT
ejpam-144	356	4	r.	r.	PROPN
ejpam-144	356	5	zhao	zhao	PROPN
ejpam-144	356	6	,	,	PUNCT
ejpam-144	356	7	on	on	ADP
ejpam-144	356	8	a	a	DET
ejpam-144	356	9	general	general	ADJ
ejpam-144	356	10	family	family	NOUN
ejpam-144	356	11	of	of	ADP
ejpam-144	356	12	function	function	NOUN
ejpam-144	356	13	spaces	space	NOUN
ejpam-144	356	14	,	,	PUNCT
ejpam-144	356	15	ann	ann	PROPN
ejpam-144	356	16	.	.	PUNCT
ejpam-144	356	17	acad	acad	PROPN
ejpam-144	356	18	.	.	PUNCT
ejpam-144	357	1	sci	sci	PROPN
ejpam-144	357	2	.	.	PUNCT
ejpam-144	357	3	fenn	fenn	PROPN
ejpam-144	357	4	.	.	PUNCT
ejpam-144	357	5	math	math	PROPN
ejpam-144	357	6	.	.	PUNCT
ejpam-144	358	1	diss	diss	PROPN
ejpam-144	358	2	.	.	PROPN
ejpam-144	358	3	105	105	NUM
ejpam-144	358	4	,	,	PUNCT
ejpam-144	358	5	1996	1996	NUM
ejpam-144	358	6	.	.	PUNCT