id	sid	tid	token	lemma	pos
ejpam-6366	1	1	european	european	PROPN
ejpam-6366	1	2	journal	journal	PROPN
ejpam-6366	1	3	of	of	ADP
ejpam-6366	1	4	pure	pure	ADJ
ejpam-6366	1	5	and	and	CCONJ
ejpam-6366	1	6	applied	applied	ADJ
ejpam-6366	1	7	mathematics	mathematic	NOUN
ejpam-6366	1	8	2025	2025	NUM
ejpam-6366	1	9	,	,	PUNCT
ejpam-6366	1	10	vol	vol	NOUN
ejpam-6366	1	11	.	.	PROPN
ejpam-6366	1	12	18	18	NUM
ejpam-6366	1	13	,	,	PUNCT
ejpam-6366	1	14	issue	issue	NOUN
ejpam-6366	1	15	4	4	NUM
ejpam-6366	1	16	,	,	PUNCT
ejpam-6366	1	17	article	article	NOUN
ejpam-6366	1	18	number	number	NOUN
ejpam-6366	1	19	6366	6366	NUM
ejpam-6366	1	20	issn	issn	PROPN
ejpam-6366	1	21	1307	1307	NUM
ejpam-6366	1	22	-	-	SYM
ejpam-6366	1	23	5543	5543	NUM
ejpam-6366	1	24	–	–	PUNCT
ejpam-6366	1	25	ejpam.com	ejpam.com	X
ejpam-6366	1	26	published	publish	VERB
ejpam-6366	1	27	by	by	ADP
ejpam-6366	1	28	new	new	PROPN
ejpam-6366	1	29	york	york	PROPN
ejpam-6366	1	30	business	business	PROPN
ejpam-6366	1	31	global	global	ADJ
ejpam-6366	1	32	some	some	DET
ejpam-6366	1	33	geometric	geometric	ADJ
ejpam-6366	1	34	results	result	NOUN
ejpam-6366	1	35	for	for	ADP
ejpam-6366	1	36	a	a	DET
ejpam-6366	1	37	new	new	ADJ
ejpam-6366	1	38	subfamily	subfamily	NOUN
ejpam-6366	1	39	of	of	ADP
ejpam-6366	1	40	regular	regular	ADJ
ejpam-6366	1	41	functions	function	NOUN
ejpam-6366	1	42	in	in	ADP
ejpam-6366	1	43	the	the	DET
ejpam-6366	1	44	generalized	generalized	ADJ
ejpam-6366	1	45	janowski	janowski	ADJ
ejpam-6366	1	46	domain	domain	NOUN
ejpam-6366	1	47	tamer	tame	ADJ
ejpam-6366	1	48	m.	m.	NOUN
ejpam-6366	1	49	seoudy1,∗	seoudy1,∗	PROPN
ejpam-6366	1	50	,	,	PUNCT
ejpam-6366	1	51	amnah	amnah	PROPN
ejpam-6366	1	52	e.	e.	PROPN
ejpam-6366	1	53	shammaky2	shammaky2	PROPN
ejpam-6366	2	1	1	1	NUM
ejpam-6366	2	2	department	department	NOUN
ejpam-6366	2	3	of	of	ADP
ejpam-6366	2	4	mathematics	mathematic	NOUN
ejpam-6366	2	5	,	,	PUNCT
ejpam-6366	2	6	faculty	faculty	NOUN
ejpam-6366	2	7	of	of	ADP
ejpam-6366	2	8	science	science	NOUN
ejpam-6366	2	9	,	,	PUNCT
ejpam-6366	2	10	fayoum	fayoum	PROPN
ejpam-6366	2	11	university	university	PROPN
ejpam-6366	2	12	,	,	PUNCT
ejpam-6366	2	13	fayoum	fayoum	PROPN
ejpam-6366	2	14	63514	63514	NUM
ejpam-6366	2	15	,	,	PUNCT
ejpam-6366	2	16	egypt	egypt	PROPN
ejpam-6366	2	17	2	2	NUM
ejpam-6366	2	18	department	department	NOUN
ejpam-6366	2	19	of	of	ADP
ejpam-6366	2	20	mathematics	mathematic	NOUN
ejpam-6366	2	21	,	,	PUNCT
ejpam-6366	2	22	faculty	faculty	NOUN
ejpam-6366	2	23	of	of	ADP
ejpam-6366	2	24	science	science	NOUN
ejpam-6366	2	25	,	,	PUNCT
ejpam-6366	2	26	jazan	jazan	PROPN
ejpam-6366	2	27	university	university	PROPN
ejpam-6366	2	28	,	,	PUNCT
ejpam-6366	2	29	jazan	jazan	NOUN
ejpam-6366	2	30	45142	45142	NUM
ejpam-6366	2	31	,	,	PUNCT
ejpam-6366	2	32	saudi	saudi	PROPN
ejpam-6366	2	33	arabia	arabia	PROPN
ejpam-6366	2	34	abstract	abstract	NOUN
ejpam-6366	2	35	.	.	PUNCT
ejpam-6366	3	1	let	let	VERB
ejpam-6366	3	2	sk	sk	VERB
ejpam-6366	4	1	[	[	X
ejpam-6366	4	2	p	p	X
ejpam-6366	4	3	,	,	PUNCT
ejpam-6366	4	4	q;α	q;α	PROPN
ejpam-6366	4	5	,	,	PUNCT
ejpam-6366	4	6	β	β	X
ejpam-6366	4	7	]	]	X
ejpam-6366	4	8	denote	denote	VERB
ejpam-6366	4	9	the	the	DET
ejpam-6366	4	10	subfamily	subfamily	NOUN
ejpam-6366	4	11	of	of	ADP
ejpam-6366	4	12	normalized	normalize	VERB
ejpam-6366	4	13	regular	regular	ADJ
ejpam-6366	4	14	function	function	NOUN
ejpam-6366	4	15	g(ξ	g(ξ	PROPN
ejpam-6366	4	16	)	)	PUNCT
ejpam-6366	4	17	=	=	SYM
ejpam-6366	5	1	ξ	ξ	X
ejpam-6366	5	2	+	+	PUNCT
ejpam-6366	5	3	d2ξ	d2ξ	PROPN
ejpam-6366	5	4	2	2	NUM
ejpam-6366	5	5	+	+	NOUN
ejpam-6366	5	6	d3ξ	d3ξ	NOUN
ejpam-6366	5	7	3	3	NUM
ejpam-6366	5	8	+	+	NUM
ejpam-6366	5	9	d4ξ	d4ξ	NOUN
ejpam-6366	5	10	4	4	NUM
ejpam-6366	5	11	+	+	CCONJ
ejpam-6366	5	12	...	...	PUNCT
ejpam-6366	5	13	in	in	ADP
ejpam-6366	5	14	the	the	DET
ejpam-6366	5	15	open	open	ADJ
ejpam-6366	5	16	unit	unit	NOUN
ejpam-6366	5	17	disk	disk	NOUN
ejpam-6366	5	18	∆	∆	PROPN
ejpam-6366	5	19	holding	hold	VERB
ejpam-6366	5	20	the	the	DET
ejpam-6366	5	21	next	next	ADJ
ejpam-6366	5	22	subordination	subordination	NOUN
ejpam-6366	5	23	condition	condition	NOUN
ejpam-6366	5	24	:	:	PUNCT
ejpam-6366	5	25	αg	αg	NOUN
ejpam-6366	5	26	(	(	PUNCT
ejpam-6366	5	27	ξ	ξ	NOUN
ejpam-6366	5	28	)	)	PUNCT
ejpam-6366	5	29	+	+	NUM
ejpam-6366	5	30	βξg′	βξg′	NUM
ejpam-6366	5	31	(	(	PUNCT
ejpam-6366	5	32	ξ	ξ	NOUN
ejpam-6366	5	33	)	)	PUNCT
ejpam-6366	5	34	αξ	αξ	NOUN
ejpam-6366	5	35	+	+	NUM
ejpam-6366	5	36	βg	βg	PROPN
ejpam-6366	5	37	(	(	PUNCT
ejpam-6366	5	38	ξ	ξ	NOUN
ejpam-6366	5	39	)	)	PUNCT
ejpam-6366	5	40	≺	≺	NOUN
ejpam-6366	5	41	1	1	NUM
ejpam-6366	5	42	+	+	CCONJ
ejpam-6366	6	1	[	[	X
ejpam-6366	6	2	q+	q+	X
ejpam-6366	6	3	(	(	PUNCT
ejpam-6366	6	4	1−	1−	NUM
ejpam-6366	6	5	γ	γ	NOUN
ejpam-6366	6	6	)	)	PUNCT
ejpam-6366	6	7	(	(	PUNCT
ejpam-6366	6	8	p	p	NOUN
ejpam-6366	6	9	−q	−q	NOUN
ejpam-6366	6	10	)	)	PUNCT
ejpam-6366	6	11	]	]	PUNCT
ejpam-6366	6	12	ξ	ξ	X
ejpam-6366	6	13	1	1	NUM
ejpam-6366	6	14	+	+	NUM
ejpam-6366	6	15	mξ	mξ	NOUN
ejpam-6366	6	16	,	,	PUNCT
ejpam-6366	6	17	where	where	SCONJ
ejpam-6366	6	18	0	0	NUM
ejpam-6366	6	19	≤	≤	NUM
ejpam-6366	6	20	α	α	X
ejpam-6366	6	21	,	,	PUNCT
ejpam-6366	6	22	β	β	X
ejpam-6366	6	23	≤	≤	NUM
ejpam-6366	6	24	1	1	NUM
ejpam-6366	6	25	,	,	PUNCT
ejpam-6366	6	26	−1	−1	NOUN
ejpam-6366	6	27	≤	≤	NOUN
ejpam-6366	6	28	q	q	NOUN
ejpam-6366	7	1	<	<	X
ejpam-6366	7	2	p	p	X
ejpam-6366	7	3	≤	≤	NUM
ejpam-6366	7	4	1	1	NUM
ejpam-6366	7	5	,	,	PUNCT
ejpam-6366	7	6	0	0	NUM
ejpam-6366	7	7	≤	≤	NUM
ejpam-6366	7	8	γ	γ	X
ejpam-6366	7	9	<	<	X
ejpam-6366	7	10	1	1	NUM
ejpam-6366	7	11	and	and	CCONJ
ejpam-6366	7	12	ξ	ξ	PRON
ejpam-6366	7	13	∈	∈	PROPN
ejpam-6366	7	14	∆.	∆.	X
ejpam-6366	7	15	in	in	ADP
ejpam-6366	7	16	this	this	DET
ejpam-6366	7	17	article	article	NOUN
ejpam-6366	7	18	,	,	PUNCT
ejpam-6366	7	19	we	we	PRON
ejpam-6366	7	20	study	study	VERB
ejpam-6366	7	21	some	some	DET
ejpam-6366	7	22	geometric	geometric	ADJ
ejpam-6366	7	23	properties	property	NOUN
ejpam-6366	7	24	such	such	ADJ
ejpam-6366	7	25	as	as	ADP
ejpam-6366	7	26	convolution	convolution	NOUN
ejpam-6366	7	27	results	result	NOUN
ejpam-6366	7	28	,	,	PUNCT
ejpam-6366	7	29	coefficient	coefficient	NOUN
ejpam-6366	7	30	estimates	estimate	NOUN
ejpam-6366	7	31	,	,	PUNCT
ejpam-6366	7	32	upper	upper	ADJ
ejpam-6366	7	33	bounds	bound	NOUN
ejpam-6366	7	34	for	for	ADP
ejpam-6366	7	35	the	the	DET
ejpam-6366	7	36	initial	initial	ADJ
ejpam-6366	7	37	coefficients	coefficient	NOUN
ejpam-6366	7	38	of	of	ADP
ejpam-6366	7	39	the	the	DET
ejpam-6366	7	40	first	first	ADJ
ejpam-6366	7	41	four	four	NUM
ejpam-6366	7	42	coefficients	coefficient	NOUN
ejpam-6366	7	43	,	,	PUNCT
ejpam-6366	7	44	and	and	CCONJ
ejpam-6366	7	45	the	the	DET
ejpam-6366	7	46	fekete	fekete	PROPN
ejpam-6366	7	47	-	-	PUNCT
ejpam-6366	7	48	szegö	szegö	ADJ
ejpam-6366	7	49	inequalities	inequality	NOUN
ejpam-6366	7	50	for	for	ADP
ejpam-6366	7	51	this	this	DET
ejpam-6366	7	52	subfamily	subfamily	NOUN
ejpam-6366	7	53	.	.	PUNCT
ejpam-6366	8	1	2020	2020	NUM
ejpam-6366	8	2	mathematics	mathematic	NOUN
ejpam-6366	8	3	subject	subject	NOUN
ejpam-6366	8	4	classifications	classification	NOUN
ejpam-6366	8	5	:	:	PUNCT
ejpam-6366	8	6	30c45	30c45	NUM
ejpam-6366	8	7	key	key	ADJ
ejpam-6366	8	8	words	word	NOUN
ejpam-6366	8	9	and	and	CCONJ
ejpam-6366	8	10	phrases	phrase	NOUN
ejpam-6366	8	11	:	:	PUNCT
ejpam-6366	8	12	regular	regular	ADJ
ejpam-6366	8	13	function	function	NOUN
ejpam-6366	8	14	,	,	PUNCT
ejpam-6366	8	15	starlike	starlike	NOUN
ejpam-6366	8	16	,	,	PUNCT
ejpam-6366	8	17	convolution	convolution	NOUN
ejpam-6366	8	18	,	,	PUNCT
ejpam-6366	8	19	fekete	fekete	PROPN
ejpam-6366	8	20	-	-	PUNCT
ejpam-6366	8	21	szegö	szegö	PROPN
ejpam-6366	8	22	problem	problem	NOUN
ejpam-6366	8	23	1	1	NUM
ejpam-6366	8	24	.	.	PUNCT
ejpam-6366	9	1	introduction	introduction	NOUN
ejpam-6366	9	2	let	let	VERB
ejpam-6366	9	3	us	we	PRON
ejpam-6366	9	4	represent	represent	VERB
ejpam-6366	9	5	the	the	DET
ejpam-6366	9	6	family	family	NOUN
ejpam-6366	9	7	of	of	ADP
ejpam-6366	9	8	regular	regular	ADJ
ejpam-6366	9	9	(	(	PUNCT
ejpam-6366	9	10	analytic	analytic	ADJ
ejpam-6366	9	11	)	)	PUNCT
ejpam-6366	9	12	functions	function	NOUN
ejpam-6366	9	13	inside	inside	ADP
ejpam-6366	9	14	the	the	DET
ejpam-6366	9	15	symmetrical	symmetrical	ADJ
ejpam-6366	9	16	unit	unit	NOUN
ejpam-6366	9	17	disc	disc	VERB
ejpam-6366	9	18	∆	∆	PROPN
ejpam-6366	9	19	=	=	SYM
ejpam-6366	9	20	{	{	PUNCT
ejpam-6366	9	21	ξ	ξ	X
ejpam-6366	9	22	∈	∈	PROPN
ejpam-6366	9	23	c	c	NOUN
ejpam-6366	9	24	:	:	PUNCT
ejpam-6366	9	25	|ξ|	|ξ|	VERB
ejpam-6366	9	26	<	<	X
ejpam-6366	9	27	1	1	NUM
ejpam-6366	9	28	}	}	PUNCT
ejpam-6366	9	29	by	by	ADP
ejpam-6366	9	30	a	a	DET
ejpam-6366	9	31	(	(	PUNCT
ejpam-6366	9	32	∆	∆	X
ejpam-6366	9	33	)	)	PUNCT
ejpam-6366	9	34	and	and	CCONJ
ejpam-6366	9	35	let	let	VERB
ejpam-6366	9	36	h	h	NOUN
ejpam-6366	9	37	be	be	AUX
ejpam-6366	9	38	the	the	DET
ejpam-6366	9	39	subfamily	subfamily	NOUN
ejpam-6366	9	40	of	of	ADP
ejpam-6366	9	41	a	a	DET
ejpam-6366	9	42	(	(	PUNCT
ejpam-6366	9	43	∆	∆	X
ejpam-6366	9	44	)	)	PUNCT
ejpam-6366	9	45	consisting	consist	VERB
ejpam-6366	9	46	of	of	ADP
ejpam-6366	9	47	all	all	DET
ejpam-6366	9	48	functions	function	NOUN
ejpam-6366	9	49	g	g	NOUN
ejpam-6366	9	50	in	in	ADP
ejpam-6366	9	51	∆	∆	PROPN
ejpam-6366	9	52	that	that	PRON
ejpam-6366	9	53	has	have	VERB
ejpam-6366	9	54	the	the	DET
ejpam-6366	9	55	following	follow	VERB
ejpam-6366	9	56	form	form	NOUN
ejpam-6366	9	57	:	:	PUNCT
ejpam-6366	9	58	g(ξ	g(ξ	PROPN
ejpam-6366	9	59	)	)	PUNCT
ejpam-6366	9	60	=	=	SYM
ejpam-6366	10	1	ξ	ξ	PROPN
ejpam-6366	11	1	+	+	PUNCT
ejpam-6366	11	2	∞∑	∞∑	PROPN
ejpam-6366	11	3	j=2	j=2	PROPN
ejpam-6366	11	4	djξ	djξ	VERB
ejpam-6366	11	5	j	j	PROPN
ejpam-6366	11	6	(	(	PUNCT
ejpam-6366	11	7	ξ	ξ	PROPN
ejpam-6366	11	8	∈	∈	PROPN
ejpam-6366	11	9	∆	∆	X
ejpam-6366	11	10	)	)	PUNCT
ejpam-6366	11	11	.	.	PUNCT
ejpam-6366	12	1	(	(	PUNCT
ejpam-6366	12	2	1	1	X
ejpam-6366	12	3	)	)	PUNCT
ejpam-6366	12	4	also	also	ADV
ejpam-6366	12	5	,	,	PUNCT
ejpam-6366	12	6	let	let	VERB
ejpam-6366	12	7	ω	ω	NOUN
ejpam-6366	12	8	be	be	AUX
ejpam-6366	12	9	the	the	DET
ejpam-6366	12	10	family	family	NOUN
ejpam-6366	12	11	of	of	ADP
ejpam-6366	12	12	functions	function	NOUN
ejpam-6366	12	13	w	w	ADP
ejpam-6366	12	14	∈	∈	PROPN
ejpam-6366	12	15	a	a	DET
ejpam-6366	12	16	(	(	PUNCT
ejpam-6366	12	17	∆	∆	X
ejpam-6366	12	18	)	)	PUNCT
ejpam-6366	12	19	satisfying	satisfy	VERB
ejpam-6366	12	20	w(0	w(0	PROPN
ejpam-6366	12	21	)	)	PUNCT
ejpam-6366	13	1	=	=	SYM
ejpam-6366	13	2	0	0	NUM
ejpam-6366	13	3	and	and	CCONJ
ejpam-6366	13	4	|w(ξ)|	|w(ξ)|	PROPN
ejpam-6366	13	5	<	<	X
ejpam-6366	13	6	1	1	NUM
ejpam-6366	13	7	for	for	ADP
ejpam-6366	13	8	all	all	DET
ejpam-6366	13	9	ξ	ξ	PROPN
ejpam-6366	13	10	∈	∈	PROPN
ejpam-6366	13	11	∆.	∆.	NOUN
ejpam-6366	13	12	for	for	ADP
ejpam-6366	13	13	h1(ξ	h1(ξ	ADV
ejpam-6366	13	14	)	)	PUNCT
ejpam-6366	13	15	,	,	PUNCT
ejpam-6366	13	16	h2(ξ	h2(ξ	PROPN
ejpam-6366	13	17	)	)	PUNCT
ejpam-6366	13	18	∈	∈	PROPN
ejpam-6366	13	19	a	a	DET
ejpam-6366	13	20	(	(	PUNCT
ejpam-6366	13	21	∆	∆	PROPN
ejpam-6366	13	22	)	)	PUNCT
ejpam-6366	14	1	,	,	PUNCT
ejpam-6366	14	2	we	we	PRON
ejpam-6366	14	3	say	say	VERB
ejpam-6366	14	4	that	that	SCONJ
ejpam-6366	14	5	h1	h1	PROPN
ejpam-6366	14	6	(	(	PUNCT
ejpam-6366	14	7	ξ	ξ	NOUN
ejpam-6366	14	8	)	)	PUNCT
ejpam-6366	14	9	is	be	AUX
ejpam-6366	14	10	subordinate	subordinate	ADJ
ejpam-6366	14	11	to	to	ADP
ejpam-6366	14	12	h2	h2	PROPN
ejpam-6366	14	13	(	(	PUNCT
ejpam-6366	14	14	ξ	ξ	NOUN
ejpam-6366	14	15	)	)	PUNCT
ejpam-6366	14	16	,	,	PUNCT
ejpam-6366	14	17	written	write	VERB
ejpam-6366	14	18	as	as	ADP
ejpam-6366	14	19	h1(ξ	h1(ξ	NOUN
ejpam-6366	14	20	)	)	PUNCT
ejpam-6366	14	21	≺	≺	VERB
ejpam-6366	14	22	h2(ξ	h2(ξ	PROPN
ejpam-6366	14	23	)	)	PUNCT
ejpam-6366	14	24	if	if	SCONJ
ejpam-6366	14	25	there	there	PRON
ejpam-6366	14	26	exists	exist	VERB
ejpam-6366	14	27	a	a	DET
ejpam-6366	14	28	function	function	NOUN
ejpam-6366	14	29	w(ξ	w(ξ	NOUN
ejpam-6366	14	30	)	)	PUNCT
ejpam-6366	14	31	∈	∈	PROPN
ejpam-6366	14	32	ω	ω	NUM
ejpam-6366	14	33	such	such	ADJ
ejpam-6366	14	34	that	that	SCONJ
ejpam-6366	14	35	h1(ξ	h1(ξ	NOUN
ejpam-6366	14	36	)	)	PUNCT
ejpam-6366	14	37	=	=	SYM
ejpam-6366	14	38	(	(	PUNCT
ejpam-6366	14	39	h2	h2	PROPN
ejpam-6366	14	40	◦	◦	NOUN
ejpam-6366	14	41	w	w	PROPN
ejpam-6366	14	42	)	)	PUNCT
ejpam-6366	14	43	(	(	PUNCT
ejpam-6366	14	44	ξ	ξ	NOUN
ejpam-6366	14	45	)	)	PUNCT
ejpam-6366	14	46	for	for	ADP
ejpam-6366	14	47	all	all	DET
ejpam-6366	14	48	ξ	ξ	X
ejpam-6366	14	49	∈	∈	PROPN
ejpam-6366	14	50	∆.	∆.	X
ejpam-6366	14	51	moreover	moreover	ADV
ejpam-6366	14	52	,	,	PUNCT
ejpam-6366	14	53	if	if	SCONJ
ejpam-6366	14	54	h1(ξ	h1(ξ	ADV
ejpam-6366	14	55	)	)	PUNCT
ejpam-6366	14	56	is	be	AUX
ejpam-6366	14	57	univalent	univalent	ADJ
ejpam-6366	14	58	function	function	NOUN
ejpam-6366	14	59	in	in	ADP
ejpam-6366	14	60	∆	∆	PROPN
ejpam-6366	14	61	,	,	PUNCT
ejpam-6366	14	62	then	then	ADV
ejpam-6366	14	63	h1(ξ	h1(ξ	CCONJ
ejpam-6366	14	64	)	)	PUNCT
ejpam-6366	14	65	≺	≺	VERB
ejpam-6366	14	66	h2(ξ	h2(ξ	SYM
ejpam-6366	14	67	)	)	PUNCT
ejpam-6366	14	68	if	if	SCONJ
ejpam-6366	14	69	and	and	CCONJ
ejpam-6366	14	70	only	only	ADV
ejpam-6366	14	71	if	if	SCONJ
ejpam-6366	14	72	h1(0	h1(0	PROPN
ejpam-6366	14	73	)	)	PUNCT
ejpam-6366	14	74	=	=	SYM
ejpam-6366	14	75	h2(0	h2(0	NOUN
ejpam-6366	14	76	)	)	PUNCT
ejpam-6366	14	77	and	and	CCONJ
ejpam-6366	14	78	h1(∆	h1(∆	NUM
ejpam-6366	14	79	)	)	PUNCT
ejpam-6366	15	1	⊂	⊂	PROPN
ejpam-6366	15	2	h2(∆	h2(∆	PROPN
ejpam-6366	15	3	)	)	PUNCT
ejpam-6366	15	4	.	.	PUNCT
ejpam-6366	16	1	∗corresponding	∗corresponde	VERB
ejpam-6366	16	2	author	author	NOUN
ejpam-6366	16	3	.	.	PUNCT
ejpam-6366	17	1	doi	doi	NOUN
ejpam-6366	17	2	:	:	PUNCT
ejpam-6366	17	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6366	https://doi.org/10.29020/nybg.ejpam.v18i4.6366	PROPN
ejpam-6366	17	4	email	email	NOUN
ejpam-6366	17	5	addresses	address	NOUN
ejpam-6366	17	6	:	:	PUNCT
ejpam-6366	17	7	tms00@fayoum.edu.eg	tms00@fayoum.edu.eg	PROPN
ejpam-6366	17	8	(	(	PUNCT
ejpam-6366	17	9	t.	t.	PROPN
ejpam-6366	17	10	m.	m.	PROPN
ejpam-6366	17	11	seoudy	seoudy	PROPN
ejpam-6366	17	12	)	)	PUNCT
ejpam-6366	17	13	,	,	PUNCT
ejpam-6366	17	14	aeshamakhi@jazan.edu.sa	aeshamakhi@jazan.edu.sa	PROPN
ejpam-6366	17	15	(	(	PUNCT
ejpam-6366	17	16	a.	a.	PROPN
ejpam-6366	17	17	e.	e.	PROPN
ejpam-6366	17	18	shammaky	shammaky	PROPN
ejpam-6366	17	19	)	)	PUNCT
ejpam-6366	17	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6366	18	1	1	1	NUM
ejpam-6366	18	2	copyright	copyright	NOUN
ejpam-6366	18	3	:	:	PUNCT
ejpam-6366	18	4	©	©	PROPN
ejpam-6366	18	5	2025	2025	NUM
ejpam-6366	18	6	the	the	DET
ejpam-6366	18	7	author(s	author(s	NOUN
ejpam-6366	18	8	)	)	PUNCT
ejpam-6366	18	9	.	.	PUNCT
ejpam-6366	19	1	(	(	PUNCT
ejpam-6366	19	2	cc	cc	NOUN
ejpam-6366	19	3	by	by	ADP
ejpam-6366	19	4	-	-	PUNCT
ejpam-6366	19	5	nc	nc	PROPN
ejpam-6366	19	6	4.0	4.0	NUM
ejpam-6366	19	7	)	)	PUNCT
ejpam-6366	19	8	t.	t.	PROPN
ejpam-6366	19	9	m.	m.	NOUN
ejpam-6366	19	10	seoudy	seoudy	PROPN
ejpam-6366	19	11	,	,	PUNCT
ejpam-6366	19	12	a.	a.	PROPN
ejpam-6366	19	13	e.	e.	PROPN
ejpam-6366	19	14	shammaky	shammaky	PROPN
ejpam-6366	19	15	/	/	SYM
ejpam-6366	19	16	eur	eur	PROPN
ejpam-6366	19	17	.	.	PUNCT
ejpam-6366	20	1	j.	j.	PROPN
ejpam-6366	20	2	pure	pure	PROPN
ejpam-6366	20	3	appl	appl	PROPN
ejpam-6366	20	4	.	.	PROPN
ejpam-6366	20	5	math	math	PROPN
ejpam-6366	20	6	,	,	PUNCT
ejpam-6366	20	7	18	18	NUM
ejpam-6366	20	8	(	(	PUNCT
ejpam-6366	20	9	4	4	NUM
ejpam-6366	20	10	)	)	PUNCT
ejpam-6366	20	11	(	(	PUNCT
ejpam-6366	20	12	2025	2025	NUM
ejpam-6366	20	13	)	)	PUNCT
ejpam-6366	20	14	,	,	PUNCT
ejpam-6366	20	15	6366	6366	NUM
ejpam-6366	20	16	2	2	NUM
ejpam-6366	20	17	of	of	ADP
ejpam-6366	20	18	15	15	NUM
ejpam-6366	20	19	for	for	ADP
ejpam-6366	20	20	functions	function	NOUN
ejpam-6366	20	21	g	g	NOUN
ejpam-6366	20	22	,	,	PUNCT
ejpam-6366	20	23	h	h	NOUN
ejpam-6366	20	24	∈	∈	PROPN
ejpam-6366	20	25	h	h	NOUN
ejpam-6366	20	26	,	,	PUNCT
ejpam-6366	20	27	where	where	SCONJ
ejpam-6366	20	28	g	g	PROPN
ejpam-6366	20	29	is	be	AUX
ejpam-6366	20	30	given	give	VERB
ejpam-6366	20	31	by	by	ADP
ejpam-6366	20	32	(	(	PUNCT
ejpam-6366	20	33	1	1	NUM
ejpam-6366	20	34	)	)	PUNCT
ejpam-6366	20	35	and	and	CCONJ
ejpam-6366	20	36	h	h	NOUN
ejpam-6366	20	37	has	have	VERB
ejpam-6366	20	38	the	the	DET
ejpam-6366	20	39	following	follow	VERB
ejpam-6366	20	40	form	form	NOUN
ejpam-6366	20	41	:	:	PUNCT
ejpam-6366	20	42	h(ξ	h(ξ	X
ejpam-6366	20	43	)	)	PUNCT
ejpam-6366	20	44	=	=	SYM
ejpam-6366	21	1	ξ	ξ	PROPN
ejpam-6366	22	1	+	+	PUNCT
ejpam-6366	22	2	∞∑	∞∑	PROPN
ejpam-6366	22	3	j=2	j=2	PROPN
ejpam-6366	22	4	ejξ	ejξ	PROPN
ejpam-6366	22	5	j	j	PROPN
ejpam-6366	22	6	,	,	PUNCT
ejpam-6366	22	7	(	(	PUNCT
ejpam-6366	22	8	2	2	NUM
ejpam-6366	22	9	)	)	PUNCT
ejpam-6366	22	10	then	then	ADV
ejpam-6366	22	11	,	,	PUNCT
ejpam-6366	22	12	the	the	DET
ejpam-6366	22	13	convolution	convolution	NOUN
ejpam-6366	22	14	of	of	ADP
ejpam-6366	22	15	g	g	PROPN
ejpam-6366	22	16	and	and	CCONJ
ejpam-6366	22	17	h	h	NOUN
ejpam-6366	22	18	is	be	AUX
ejpam-6366	22	19	defined	define	VERB
ejpam-6366	22	20	by	by	ADP
ejpam-6366	22	21	(	(	PUNCT
ejpam-6366	22	22	g	g	PROPN
ejpam-6366	22	23	∗	∗	NOUN
ejpam-6366	22	24	h	h	NOUN
ejpam-6366	22	25	)	)	PUNCT
ejpam-6366	22	26	(	(	PUNCT
ejpam-6366	22	27	ξ	ξ	X
ejpam-6366	22	28	)	)	PUNCT
ejpam-6366	22	29	=	=	SYM
ejpam-6366	23	1	ξ	ξ	PROPN
ejpam-6366	23	2	+	+	PUNCT
ejpam-6366	23	3	∞∑	∞∑	PROPN
ejpam-6366	23	4	j=2	j=2	PROPN
ejpam-6366	23	5	djejξ	djejξ	VERB
ejpam-6366	23	6	j	j	PROPN
ejpam-6366	24	1	=	=	PRON
ejpam-6366	24	2	(	(	PUNCT
ejpam-6366	24	3	h	h	NOUN
ejpam-6366	24	4	∗	∗	NOUN
ejpam-6366	24	5	g	g	NOUN
ejpam-6366	24	6	)	)	PUNCT
ejpam-6366	24	7	(	(	PUNCT
ejpam-6366	24	8	ξ	ξ	NOUN
ejpam-6366	24	9	)	)	PUNCT
ejpam-6366	24	10	.	.	PUNCT
ejpam-6366	25	1	(	(	PUNCT
ejpam-6366	25	2	3	3	X
ejpam-6366	25	3	)	)	PUNCT
ejpam-6366	25	4	definition	definition	NOUN
ejpam-6366	25	5	1	1	NUM
ejpam-6366	25	6	.	.	PUNCT
ejpam-6366	26	1	let	let	VERB
ejpam-6366	26	2	us	we	PRON
ejpam-6366	26	3	introduce	introduce	VERB
ejpam-6366	26	4	the	the	DET
ejpam-6366	26	5	new	new	ADJ
ejpam-6366	26	6	subfamily	subfamily	NOUN
ejpam-6366	26	7	sk	sk	VERB
ejpam-6366	26	8	[	[	X
ejpam-6366	26	9	p	p	X
ejpam-6366	26	10	,	,	PUNCT
ejpam-6366	26	11	q;α	q;α	PROPN
ejpam-6366	26	12	,	,	PUNCT
ejpam-6366	26	13	β	β	X
ejpam-6366	26	14	]	]	PUNCT
ejpam-6366	26	15	of	of	ADP
ejpam-6366	26	16	h	h	NOUN
ejpam-6366	26	17	by	by	ADP
ejpam-6366	26	18	using	use	VERB
ejpam-6366	26	19	the	the	DET
ejpam-6366	26	20	subordination	subordination	NOUN
ejpam-6366	26	21	principle	principle	NOUN
ejpam-6366	26	22	between	between	ADP
ejpam-6366	26	23	two	two	NUM
ejpam-6366	26	24	analytic	analytic	ADJ
ejpam-6366	26	25	functions	function	NOUN
ejpam-6366	26	26	as	as	SCONJ
ejpam-6366	26	27	follows	follow	VERB
ejpam-6366	26	28	:	:	PUNCT
ejpam-6366	26	29	sk	sk	ADP
ejpam-6366	27	1	[	[	X
ejpam-6366	27	2	p	p	X
ejpam-6366	27	3	,	,	PUNCT
ejpam-6366	27	4	q	q	NOUN
ejpam-6366	27	5	,	,	PUNCT
ejpam-6366	27	6	γ;α	γ;α	ADV
ejpam-6366	27	7	,	,	PUNCT
ejpam-6366	27	8	β	β	X
ejpam-6366	27	9	]	]	X
ejpam-6366	27	10	=	=	X
ejpam-6366	27	11	{	{	PUNCT
ejpam-6366	27	12	g	g	PROPN
ejpam-6366	27	13	∈	∈	PROPN
ejpam-6366	27	14	h	h	NOUN
ejpam-6366	27	15	:	:	PUNCT
ejpam-6366	27	16	αg	αg	X
ejpam-6366	27	17	(	(	PUNCT
ejpam-6366	27	18	ξ	ξ	NOUN
ejpam-6366	27	19	)	)	PUNCT
ejpam-6366	27	20	+	+	NUM
ejpam-6366	27	21	βξg′	βξg′	NUM
ejpam-6366	27	22	(	(	PUNCT
ejpam-6366	27	23	ξ	ξ	NOUN
ejpam-6366	27	24	)	)	PUNCT
ejpam-6366	27	25	αξ	αξ	NOUN
ejpam-6366	28	1	+	+	NUM
ejpam-6366	28	2	βg	βg	PROPN
ejpam-6366	28	3	(	(	PUNCT
ejpam-6366	28	4	ξ	ξ	NOUN
ejpam-6366	28	5	)	)	PUNCT
ejpam-6366	28	6	≺	≺	NOUN
ejpam-6366	28	7	1	1	NUM
ejpam-6366	29	1	+	+	CCONJ
ejpam-6366	29	2	[	[	X
ejpam-6366	29	3	q+	q+	X
ejpam-6366	29	4	(	(	PUNCT
ejpam-6366	29	5	1−	1−	NUM
ejpam-6366	29	6	γ	γ	NOUN
ejpam-6366	29	7	)	)	PUNCT
ejpam-6366	29	8	(	(	PUNCT
ejpam-6366	29	9	p	p	NOUN
ejpam-6366	29	10	−q	−q	NOUN
ejpam-6366	29	11	)	)	PUNCT
ejpam-6366	29	12	]	]	PUNCT
ejpam-6366	30	1	ξ	ξ	X
ejpam-6366	30	2	1	1	NUM
ejpam-6366	30	3	+	+	NOUN
ejpam-6366	30	4	mξ	mξ	NOUN
ejpam-6366	30	5	}	}	PUNCT
ejpam-6366	30	6	,	,	PUNCT
ejpam-6366	30	7	(	(	PUNCT
ejpam-6366	30	8	4	4	X
ejpam-6366	30	9	)	)	PUNCT
ejpam-6366	30	10	where	where	SCONJ
ejpam-6366	30	11	0	0	NUM
ejpam-6366	30	12	≤	≤	NUM
ejpam-6366	30	13	α	α	X
ejpam-6366	30	14	,	,	PUNCT
ejpam-6366	30	15	β	β	X
ejpam-6366	30	16	≤	≤	NUM
ejpam-6366	30	17	1	1	NUM
ejpam-6366	30	18	,	,	PUNCT
ejpam-6366	30	19	−1	−1	NOUN
ejpam-6366	30	20	≤	≤	NOUN
ejpam-6366	30	21	q	q	NOUN
ejpam-6366	31	1	<	<	X
ejpam-6366	31	2	p	p	X
ejpam-6366	31	3	≤	≤	NUM
ejpam-6366	31	4	1	1	NUM
ejpam-6366	31	5	,	,	PUNCT
ejpam-6366	31	6	0	0	NUM
ejpam-6366	31	7	≤	≤	NUM
ejpam-6366	31	8	γ	γ	X
ejpam-6366	31	9	<	<	X
ejpam-6366	31	10	1	1	NUM
ejpam-6366	31	11	and	and	CCONJ
ejpam-6366	31	12	ξ	ξ	PROPN
ejpam-6366	31	13	∈	∈	PROPN
ejpam-6366	31	14	∆.	∆.	NOUN
ejpam-6366	31	15	remark	remark	NOUN
ejpam-6366	31	16	1	1	NUM
ejpam-6366	31	17	.	.	PUNCT
ejpam-6366	32	1	the	the	DET
ejpam-6366	32	2	function	function	NOUN
ejpam-6366	32	3	ψ	ψ	X
ejpam-6366	32	4	(	(	PUNCT
ejpam-6366	32	5	ξ	ξ	NOUN
ejpam-6366	32	6	)	)	PUNCT
ejpam-6366	32	7	=	=	SYM
ejpam-6366	32	8	1	1	NUM
ejpam-6366	32	9	+	+	CCONJ
ejpam-6366	33	1	[	[	X
ejpam-6366	33	2	q+	q+	X
ejpam-6366	33	3	(	(	PUNCT
ejpam-6366	33	4	1−	1−	NUM
ejpam-6366	33	5	γ	γ	NOUN
ejpam-6366	33	6	)	)	PUNCT
ejpam-6366	33	7	(	(	PUNCT
ejpam-6366	33	8	p	p	NOUN
ejpam-6366	33	9	−q	−q	NOUN
ejpam-6366	33	10	)	)	PUNCT
ejpam-6366	33	11	]	]	PUNCT
ejpam-6366	33	12	ξ	ξ	X
ejpam-6366	33	13	1	1	NUM
ejpam-6366	33	14	+	+	NOUN
ejpam-6366	33	15	qξ	qξ	NOUN
ejpam-6366	33	16	is	be	AUX
ejpam-6366	33	17	a	a	DET
ejpam-6366	33	18	bilinear	bilinear	ADJ
ejpam-6366	33	19	transformation	transformation	NOUN
ejpam-6366	33	20	that	that	PRON
ejpam-6366	33	21	maps	map	VERB
ejpam-6366	33	22	the	the	DET
ejpam-6366	33	23	symmetrical	symmetrical	ADJ
ejpam-6366	33	24	unit	unit	NOUN
ejpam-6366	33	25	disk	disk	NOUN
ejpam-6366	33	26	∆	∆	PROPN
ejpam-6366	33	27	onto	onto	ADP
ejpam-6366	33	28	the	the	DET
ejpam-6366	33	29	symmetrical	symmetrical	ADJ
ejpam-6366	33	30	disk	disk	NOUN
ejpam-6366	33	31	with	with	ADP
ejpam-6366	33	32	respect	respect	NOUN
ejpam-6366	33	33	to	to	ADP
ejpam-6366	33	34	positive	positive	ADJ
ejpam-6366	33	35	real	real	ADJ
ejpam-6366	33	36	axis	axis	NOUN
ejpam-6366	33	37	,	,	PUNCT
ejpam-6366	33	38	which	which	PRON
ejpam-6366	33	39	is	be	AUX
ejpam-6366	33	40	centered	center	VERB
ejpam-6366	33	41	at	at	ADP
ejpam-6366	33	42	1−[q+(1−γ)(p−q)]q	1−[q+(1−γ)(p−q)]q	NUM
ejpam-6366	33	43	1−q2	1−q2	NUM
ejpam-6366	33	44	(	(	PUNCT
ejpam-6366	33	45	q	q	NOUN
ejpam-6366	33	46	̸=	̸=	PROPN
ejpam-6366	33	47	±1	±1	VERB
ejpam-6366	33	48	)	)	PUNCT
ejpam-6366	33	49	and	and	CCONJ
ejpam-6366	33	50	,	,	PUNCT
ejpam-6366	33	51	with	with	ADP
ejpam-6366	33	52	a	a	DET
ejpam-6366	33	53	radius	radius	NOUN
ejpam-6366	33	54	(	(	PUNCT
ejpam-6366	33	55	1−γ)(p−q	1−γ)(p−q	NUM
ejpam-6366	33	56	)	)	PUNCT
ejpam-6366	33	57	1−q2	1−q2	NUM
ejpam-6366	33	58	(	(	PUNCT
ejpam-6366	33	59	q	q	NOUN
ejpam-6366	33	60	̸=	̸=	PROPN
ejpam-6366	33	61	±1	±1	VERB
ejpam-6366	33	62	)	)	PUNCT
ejpam-6366	33	63	.	.	PUNCT
ejpam-6366	34	1	(	(	PUNCT
ejpam-6366	34	2	i	i	NOUN
ejpam-6366	34	3	)	)	PUNCT
ejpam-6366	34	4	substituting	substitute	VERB
ejpam-6366	34	5	α	α	NOUN
ejpam-6366	34	6	=	=	SYM
ejpam-6366	34	7	γ	γ	X
ejpam-6366	34	8	=	=	SYM
ejpam-6366	34	9	0	0	NUM
ejpam-6366	34	10	in	in	ADP
ejpam-6366	34	11	(	(	PUNCT
ejpam-6366	34	12	4	4	NUM
ejpam-6366	34	13	)	)	PUNCT
ejpam-6366	34	14	,	,	PUNCT
ejpam-6366	34	15	we	we	PRON
ejpam-6366	34	16	get	get	VERB
ejpam-6366	34	17	the	the	DET
ejpam-6366	34	18	subfamily	subfamily	NOUN
ejpam-6366	34	19	s	s	PART
ejpam-6366	34	20	[	[	X
ejpam-6366	34	21	p	p	X
ejpam-6366	34	22	,	,	PUNCT
ejpam-6366	34	23	q	q	X
ejpam-6366	34	24	]	]	X
ejpam-6366	34	25	=	=	X
ejpam-6366	34	26	{	{	PUNCT
ejpam-6366	34	27	g	g	PROPN
ejpam-6366	34	28	∈	∈	PROPN
ejpam-6366	34	29	h	h	NOUN
ejpam-6366	34	30	:	:	PUNCT
ejpam-6366	34	31	ξg′	ξg′	X
ejpam-6366	34	32	(	(	PUNCT
ejpam-6366	34	33	ξ	ξ	NOUN
ejpam-6366	34	34	)	)	PUNCT
ejpam-6366	34	35	g	g	NOUN
ejpam-6366	34	36	(	(	PUNCT
ejpam-6366	34	37	ξ	ξ	NOUN
ejpam-6366	34	38	)	)	PUNCT
ejpam-6366	34	39	≺	≺	NOUN
ejpam-6366	34	40	1	1	NUM
ejpam-6366	34	41	+	+	CCONJ
ejpam-6366	34	42	pξ	pξ	ADP
ejpam-6366	34	43	1	1	NUM
ejpam-6366	34	44	+	+	NOUN
ejpam-6366	34	45	qξ	qξ	NOUN
ejpam-6366	34	46	}	}	PUNCT
ejpam-6366	34	47	,	,	PUNCT
ejpam-6366	34	48	which	which	PRON
ejpam-6366	34	49	was	be	AUX
ejpam-6366	34	50	introduced	introduce	VERB
ejpam-6366	34	51	by	by	ADP
ejpam-6366	34	52	janowski	janowski	NOUN
ejpam-6366	35	1	[	[	X
ejpam-6366	35	2	1	1	NUM
ejpam-6366	35	3	,	,	PUNCT
ejpam-6366	35	4	2	2	NUM
ejpam-6366	35	5	]	]	PUNCT
ejpam-6366	35	6	.	.	PUNCT
ejpam-6366	36	1	furthermore	furthermore	ADV
ejpam-6366	36	2	,	,	PUNCT
ejpam-6366	36	3	this	this	PRON
ejpam-6366	36	4	subfamily	subfamily	ADV
ejpam-6366	36	5	has	have	AUX
ejpam-6366	36	6	been	be	AUX
ejpam-6366	36	7	studied	study	VERB
ejpam-6366	36	8	by	by	ADP
ejpam-6366	36	9	the	the	DET
ejpam-6366	36	10	many	many	ADJ
ejpam-6366	36	11	authors	author	NOUN
ejpam-6366	36	12	(	(	PUNCT
ejpam-6366	36	13	see	see	VERB
ejpam-6366	36	14	[	[	X
ejpam-6366	36	15	3–13	3–13	NUM
ejpam-6366	36	16	]	]	PUNCT
ejpam-6366	36	17	)	)	PUNCT
ejpam-6366	36	18	.	.	PUNCT
ejpam-6366	37	1	by	by	ADP
ejpam-6366	37	2	taking	take	VERB
ejpam-6366	37	3	β	β	X
ejpam-6366	37	4	=	=	PUNCT
ejpam-6366	37	5	γ	γ	X
ejpam-6366	37	6	=	=	SYM
ejpam-6366	37	7	0	0	NUM
ejpam-6366	37	8	in	in	ADP
ejpam-6366	37	9	(	(	PUNCT
ejpam-6366	37	10	4	4	NUM
ejpam-6366	37	11	)	)	PUNCT
ejpam-6366	37	12	,	,	PUNCT
ejpam-6366	37	13	we	we	PRON
ejpam-6366	37	14	obtain	obtain	VERB
ejpam-6366	37	15	the	the	DET
ejpam-6366	37	16	next	next	ADJ
ejpam-6366	37	17	subfamily	subfamily	ADV
ejpam-6366	37	18	k	k	PROPN
ejpam-6366	38	1	[	[	X
ejpam-6366	38	2	p	p	X
ejpam-6366	38	3	,	,	PUNCT
ejpam-6366	38	4	q	q	X
ejpam-6366	38	5	]	]	X
ejpam-6366	38	6	=	=	X
ejpam-6366	38	7	{	{	PUNCT
ejpam-6366	38	8	g	g	PROPN
ejpam-6366	38	9	∈	∈	PROPN
ejpam-6366	38	10	h	h	NOUN
ejpam-6366	38	11	:	:	PUNCT
ejpam-6366	38	12	g	g	PROPN
ejpam-6366	38	13	(	(	PUNCT
ejpam-6366	38	14	ξ	ξ	PROPN
ejpam-6366	38	15	)	)	PUNCT
ejpam-6366	38	16	ξ	ξ	NOUN
ejpam-6366	38	17	≺	≺	NOUN
ejpam-6366	38	18	1	1	NUM
ejpam-6366	38	19	+	+	CCONJ
ejpam-6366	38	20	pξ	pξ	ADP
ejpam-6366	38	21	1	1	NUM
ejpam-6366	38	22	+	+	NOUN
ejpam-6366	38	23	qξ	qξ	NOUN
ejpam-6366	38	24	}	}	PUNCT
ejpam-6366	38	25	;	;	PUNCT
ejpam-6366	38	26	(	(	PUNCT
ejpam-6366	38	27	ii	ii	NOUN
ejpam-6366	38	28	)	)	PUNCT
ejpam-6366	38	29	putting	put	VERB
ejpam-6366	38	30	p	p	NOUN
ejpam-6366	38	31	=	=	NOUN
ejpam-6366	38	32	1	1	NUM
ejpam-6366	38	33	and	and	CCONJ
ejpam-6366	38	34	q	q	NOUN
ejpam-6366	38	35	=	=	NOUN
ejpam-6366	38	36	−1	−1	NOUN
ejpam-6366	38	37	in	in	ADV
ejpam-6366	38	38	(	(	PUNCT
ejpam-6366	38	39	4	4	NUM
ejpam-6366	38	40	)	)	PUNCT
ejpam-6366	38	41	,	,	PUNCT
ejpam-6366	38	42	we	we	PRON
ejpam-6366	38	43	obtain	obtain	VERB
ejpam-6366	38	44	the	the	DET
ejpam-6366	38	45	next	next	ADJ
ejpam-6366	38	46	subfamily	subfamily	ADV
ejpam-6366	38	47	sk	sk	VERB
ejpam-6366	38	48	[	[	X
ejpam-6366	38	49	γ;α	γ;α	X
ejpam-6366	38	50	,	,	PUNCT
ejpam-6366	38	51	β	β	X
ejpam-6366	38	52	]	]	X
ejpam-6366	39	1	=	=	X
ejpam-6366	40	1	{	{	PUNCT
ejpam-6366	40	2	g	g	PROPN
ejpam-6366	40	3	∈	∈	PROPN
ejpam-6366	40	4	h	h	NOUN
ejpam-6366	40	5	:	:	PUNCT
ejpam-6366	40	6	ℜ	ℜ	ADJ
ejpam-6366	40	7	{	{	PUNCT
ejpam-6366	40	8	αg	αg	X
ejpam-6366	40	9	(	(	PUNCT
ejpam-6366	40	10	ξ	ξ	NOUN
ejpam-6366	40	11	)	)	PUNCT
ejpam-6366	40	12	+	+	NUM
ejpam-6366	40	13	βξg′	βξg′	NUM
ejpam-6366	40	14	(	(	PUNCT
ejpam-6366	40	15	ξ	ξ	NOUN
ejpam-6366	40	16	)	)	PUNCT
ejpam-6366	40	17	αξ	αξ	NOUN
ejpam-6366	40	18	+	+	NUM
ejpam-6366	40	19	βg	βg	PROPN
ejpam-6366	40	20	(	(	PUNCT
ejpam-6366	40	21	ξ	ξ	NOUN
ejpam-6366	40	22	)	)	PUNCT
ejpam-6366	40	23	}	}	PUNCT
ejpam-6366	40	24	>	>	X
ejpam-6366	40	25	γ	γ	X
ejpam-6366	40	26	}	}	PUNCT
ejpam-6366	40	27	,	,	PUNCT
ejpam-6366	40	28	(	(	PUNCT
ejpam-6366	40	29	5	5	NUM
ejpam-6366	40	30	)	)	PUNCT
ejpam-6366	40	31	by	by	ADP
ejpam-6366	40	32	taking	take	VERB
ejpam-6366	40	33	α	α	NOUN
ejpam-6366	40	34	=	=	SYM
ejpam-6366	40	35	0	0	NUM
ejpam-6366	40	36	in	in	ADP
ejpam-6366	40	37	(	(	PUNCT
ejpam-6366	40	38	5	5	NUM
ejpam-6366	40	39	)	)	PUNCT
ejpam-6366	40	40	,	,	PUNCT
ejpam-6366	40	41	we	we	PRON
ejpam-6366	40	42	obtain	obtain	VERB
ejpam-6366	40	43	the	the	DET
ejpam-6366	40	44	next	next	ADJ
ejpam-6366	40	45	subfamily	subfamily	NOUN
ejpam-6366	40	46	s	s	PART
ejpam-6366	40	47	(	(	PUNCT
ejpam-6366	40	48	γ	γ	NOUN
ejpam-6366	40	49	)	)	PUNCT
ejpam-6366	40	50	=	=	NOUN
ejpam-6366	40	51	{	{	PUNCT
ejpam-6366	40	52	g	g	PROPN
ejpam-6366	40	53	∈	∈	PROPN
ejpam-6366	40	54	h	h	NOUN
ejpam-6366	40	55	:	:	PUNCT
ejpam-6366	40	56	ℜ	ℜ	X
ejpam-6366	40	57	{	{	PUNCT
ejpam-6366	40	58	ξg′	ξg′	X
ejpam-6366	40	59	(	(	PUNCT
ejpam-6366	40	60	ξ	ξ	NOUN
ejpam-6366	40	61	)	)	PUNCT
ejpam-6366	40	62	g	g	NOUN
ejpam-6366	40	63	(	(	PUNCT
ejpam-6366	40	64	ξ	ξ	NOUN
ejpam-6366	40	65	)	)	PUNCT
ejpam-6366	40	66	}	}	PUNCT
ejpam-6366	40	67	>	>	X
ejpam-6366	40	68	γ	γ	X
ejpam-6366	40	69	}	}	PUNCT
ejpam-6366	40	70	,	,	PUNCT
ejpam-6366	40	71	t.	t.	PROPN
ejpam-6366	40	72	m.	m.	PROPN
ejpam-6366	40	73	seoudy	seoudy	PROPN
ejpam-6366	40	74	,	,	PUNCT
ejpam-6366	40	75	a.	a.	PROPN
ejpam-6366	40	76	e.	e.	PROPN
ejpam-6366	40	77	shammaky	shammaky	PROPN
ejpam-6366	40	78	/	/	SYM
ejpam-6366	40	79	eur	eur	PROPN
ejpam-6366	40	80	.	.	PUNCT
ejpam-6366	41	1	j.	j.	PROPN
ejpam-6366	41	2	pure	pure	PROPN
ejpam-6366	41	3	appl	appl	PROPN
ejpam-6366	41	4	.	.	PROPN
ejpam-6366	41	5	math	math	PROPN
ejpam-6366	41	6	,	,	PUNCT
ejpam-6366	41	7	18	18	NUM
ejpam-6366	41	8	(	(	PUNCT
ejpam-6366	41	9	4	4	NUM
ejpam-6366	41	10	)	)	PUNCT
ejpam-6366	41	11	(	(	PUNCT
ejpam-6366	41	12	2025	2025	NUM
ejpam-6366	41	13	)	)	PUNCT
ejpam-6366	41	14	,	,	PUNCT
ejpam-6366	41	15	6366	6366	NUM
ejpam-6366	41	16	3	3	NUM
ejpam-6366	41	17	of	of	ADP
ejpam-6366	41	18	15	15	NUM
ejpam-6366	41	19	where	where	SCONJ
ejpam-6366	41	20	s	s	X
ejpam-6366	41	21	(	(	PUNCT
ejpam-6366	41	22	γ	γ	NOUN
ejpam-6366	41	23	)	)	PUNCT
ejpam-6366	41	24	is	be	AUX
ejpam-6366	41	25	the	the	DET
ejpam-6366	41	26	family	family	NOUN
ejpam-6366	41	27	of	of	ADP
ejpam-6366	41	28	starlike	starlike	NOUN
ejpam-6366	41	29	of	of	ADP
ejpam-6366	41	30	order	order	NOUN
ejpam-6366	41	31	γ	γ	NOUN
ejpam-6366	41	32	in	in	ADP
ejpam-6366	41	33	∆	∆	PROPN
ejpam-6366	41	34	(	(	PUNCT
ejpam-6366	41	35	see	see	VERB
ejpam-6366	41	36	[	[	X
ejpam-6366	41	37	14–19	14–19	NUM
ejpam-6366	41	38	]	]	PUNCT
ejpam-6366	41	39	)	)	PUNCT
ejpam-6366	41	40	and	and	CCONJ
ejpam-6366	41	41	by	by	ADP
ejpam-6366	41	42	putting	put	VERB
ejpam-6366	41	43	β	β	X
ejpam-6366	41	44	=	=	SYM
ejpam-6366	41	45	0	0	NUM
ejpam-6366	41	46	in	in	ADP
ejpam-6366	41	47	(	(	PUNCT
ejpam-6366	41	48	5	5	NUM
ejpam-6366	41	49	)	)	PUNCT
ejpam-6366	41	50	,	,	PUNCT
ejpam-6366	41	51	we	we	PRON
ejpam-6366	41	52	obtain	obtain	VERB
ejpam-6366	41	53	the	the	DET
ejpam-6366	41	54	next	next	ADJ
ejpam-6366	41	55	subfamily	subfamily	ADV
ejpam-6366	41	56	k	k	PROPN
ejpam-6366	41	57	(	(	PUNCT
ejpam-6366	41	58	γ	γ	NOUN
ejpam-6366	41	59	)	)	PUNCT
ejpam-6366	41	60	=	=	NOUN
ejpam-6366	41	61	{	{	PUNCT
ejpam-6366	41	62	g	g	PROPN
ejpam-6366	41	63	∈	∈	PROPN
ejpam-6366	41	64	h	h	NOUN
ejpam-6366	41	65	:	:	PUNCT
ejpam-6366	41	66	ℜ	ℜ	PROPN
ejpam-6366	41	67	{	{	PUNCT
ejpam-6366	41	68	g	g	PROPN
ejpam-6366	41	69	(	(	PUNCT
ejpam-6366	41	70	ξ	ξ	NOUN
ejpam-6366	41	71	)	)	PUNCT
ejpam-6366	41	72	ξ	ξ	PROPN
ejpam-6366	41	73	}	}	PUNCT
ejpam-6366	41	74	>	>	X
ejpam-6366	41	75	γ	γ	PROPN
ejpam-6366	41	76	}	}	PUNCT
ejpam-6366	41	77	;	;	PUNCT
ejpam-6366	41	78	(	(	PUNCT
ejpam-6366	41	79	iii	iii	X
ejpam-6366	41	80	)	)	PUNCT
ejpam-6366	41	81	substituting	substitute	VERB
ejpam-6366	41	82	the	the	DET
ejpam-6366	41	83	value	value	NOUN
ejpam-6366	41	84	of	of	ADP
ejpam-6366	41	85	p	p	NOUN
ejpam-6366	41	86	=	=	PROPN
ejpam-6366	41	87	ρ	ρ	PROPN
ejpam-6366	41	88	and	and	CCONJ
ejpam-6366	41	89	q	q	NOUN
ejpam-6366	41	90	=	=	NOUN
ejpam-6366	41	91	−ρ	−ρ	NOUN
ejpam-6366	41	92	with	with	ADP
ejpam-6366	41	93	0	0	NUM
ejpam-6366	41	94	<	<	X
ejpam-6366	41	95	ρ	ρ	PROPN
ejpam-6366	41	96	≤	≤	NUM
ejpam-6366	41	97	1	1	NUM
ejpam-6366	41	98	in	in	ADP
ejpam-6366	41	99	(	(	PUNCT
ejpam-6366	41	100	4	4	NUM
ejpam-6366	41	101	)	)	PUNCT
ejpam-6366	41	102	,	,	PUNCT
ejpam-6366	41	103	we	we	PRON
ejpam-6366	41	104	get	get	VERB
ejpam-6366	41	105	the	the	DET
ejpam-6366	41	106	following	follow	VERB
ejpam-6366	41	107	subfamily	subfamily	ADV
ejpam-6366	41	108	sk	sk	VERB
ejpam-6366	41	109	(	(	PUNCT
ejpam-6366	41	110	γ	γ	PROPN
ejpam-6366	41	111	,	,	PUNCT
ejpam-6366	41	112	ρ;α	ρ;α	PRON
ejpam-6366	41	113	,	,	PUNCT
ejpam-6366	41	114	β	β	X
ejpam-6366	41	115	)	)	PUNCT
ejpam-6366	41	116	=	=	PUNCT
ejpam-6366	41	117	g	g	PROPN
ejpam-6366	41	118	∈	∈	PROPN
ejpam-6366	41	119	h	h	NOUN
ejpam-6366	41	120	:	:	PUNCT
ejpam-6366	41	121	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-6366	41	122	αg(ξ)+βξg′(ξ	αg(ξ)+βξg′(ξ	PROPN
ejpam-6366	41	123	)	)	PUNCT
ejpam-6366	41	124	αξ+βg(ξ	αξ+βg(ξ	PROPN
ejpam-6366	41	125	)	)	PUNCT
ejpam-6366	41	126	−	−	PROPN
ejpam-6366	41	127	1	1	NUM
ejpam-6366	41	128	αg(ξ)+βξg′(ξ	αg(ξ)+βξg′(ξ	PROPN
ejpam-6366	41	129	)	)	PUNCT
ejpam-6366	41	130	αξ+βg(ξ	αξ+βg(ξ	PROPN
ejpam-6366	41	131	)	)	PUNCT
ejpam-6366	42	1	+	+	NUM
ejpam-6366	42	2	1−	1−	NUM
ejpam-6366	42	3	2γ	2γ	X
ejpam-6366	42	4	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6366	42	5	<	<	X
ejpam-6366	42	6	ρ	ρ	X
ejpam-6366	42	7			NOUN
ejpam-6366	42	8	(	(	PUNCT
ejpam-6366	42	9	6	6	NUM
ejpam-6366	42	10	)	)	PUNCT
ejpam-6366	42	11	by	by	ADP
ejpam-6366	42	12	substituting	substitute	VERB
ejpam-6366	42	13	α	α	NOUN
ejpam-6366	42	14	=	=	SYM
ejpam-6366	42	15	0	0	NUM
ejpam-6366	42	16	in	in	ADP
ejpam-6366	42	17	(	(	PUNCT
ejpam-6366	42	18	6	6	NUM
ejpam-6366	42	19	)	)	PUNCT
ejpam-6366	42	20	,	,	PUNCT
ejpam-6366	42	21	we	we	PRON
ejpam-6366	42	22	have	have	VERB
ejpam-6366	42	23	s	s	NOUN
ejpam-6366	42	24	(	(	PUNCT
ejpam-6366	42	25	γ	γ	PROPN
ejpam-6366	42	26	,	,	PUNCT
ejpam-6366	42	27	ρ	ρ	NOUN
ejpam-6366	42	28	)	)	PUNCT
ejpam-6366	42	29	=	=	PUNCT
ejpam-6366	42	30	g	g	PROPN
ejpam-6366	42	31	∈	∈	PROPN
ejpam-6366	42	32	h	h	NOUN
ejpam-6366	42	33	:	:	PUNCT
ejpam-6366	43	1	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-6366	43	2	ξg′(ξ	ξg′(ξ	PROPN
ejpam-6366	43	3	)	)	PUNCT
ejpam-6366	43	4	g(ξ	g(ξ	PROPN
ejpam-6366	43	5	)	)	PUNCT
ejpam-6366	43	6	−	−	PROPN
ejpam-6366	43	7	1	1	NUM
ejpam-6366	43	8	ξg′(ξ	ξg′(ξ	PROPN
ejpam-6366	43	9	)	)	PUNCT
ejpam-6366	43	10	g(ξ	g(ξ	PROPN
ejpam-6366	43	11	)	)	PUNCT
ejpam-6366	44	1	+	+	NUM
ejpam-6366	44	2	1−	1−	NUM
ejpam-6366	44	3	2γ	2γ	X
ejpam-6366	44	4	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6366	44	5	<	<	X
ejpam-6366	44	6	ρ	ρ	NUM
ejpam-6366	44	7			NOUN
ejpam-6366	44	8	,	,	PUNCT
ejpam-6366	44	9	where	where	SCONJ
ejpam-6366	44	10	the	the	DET
ejpam-6366	44	11	subfamily	subfamily	NOUN
ejpam-6366	44	12	s	s	X
ejpam-6366	44	13	(	(	PUNCT
ejpam-6366	44	14	γ	γ	PROPN
ejpam-6366	44	15	,	,	PUNCT
ejpam-6366	44	16	ρ	ρ	PROPN
ejpam-6366	44	17	)	)	PUNCT
ejpam-6366	44	18	was	be	AUX
ejpam-6366	44	19	introduced	introduce	VERB
ejpam-6366	44	20	in	in	ADP
ejpam-6366	44	21	[	[	X
ejpam-6366	44	22	20	20	NUM
ejpam-6366	44	23	]	]	PUNCT
ejpam-6366	44	24	and	and	CCONJ
ejpam-6366	44	25	also	also	ADV
ejpam-6366	44	26	,	,	PUNCT
ejpam-6366	44	27	by	by	ADP
ejpam-6366	44	28	putting	put	VERB
ejpam-6366	44	29	α	α	NOUN
ejpam-6366	44	30	=	=	SYM
ejpam-6366	44	31	0	0	NUM
ejpam-6366	44	32	in	in	ADP
ejpam-6366	44	33	(	(	PUNCT
ejpam-6366	44	34	6	6	NUM
ejpam-6366	44	35	)	)	PUNCT
ejpam-6366	44	36	,	,	PUNCT
ejpam-6366	44	37	we	we	PRON
ejpam-6366	44	38	get	get	VERB
ejpam-6366	44	39	the	the	DET
ejpam-6366	44	40	following	follow	VERB
ejpam-6366	44	41	subfamily	subfamily	ADV
ejpam-6366	44	42	k	k	PROPN
ejpam-6366	44	43	(	(	PUNCT
ejpam-6366	44	44	γ	γ	X
ejpam-6366	44	45	,	,	PUNCT
ejpam-6366	44	46	ρ	ρ	NOUN
ejpam-6366	44	47	)	)	PUNCT
ejpam-6366	44	48	=	=	PUNCT
ejpam-6366	44	49	g	g	PROPN
ejpam-6366	44	50	∈	∈	PROPN
ejpam-6366	44	51	h	h	NOUN
ejpam-6366	44	52	:	:	PUNCT
ejpam-6366	44	53	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-6366	44	54	g(ξ	g(ξ	PROPN
ejpam-6366	44	55	)	)	PUNCT
ejpam-6366	45	1	ξ	ξ	PROPN
ejpam-6366	45	2	−	−	PROPN
ejpam-6366	45	3	1	1	NUM
ejpam-6366	45	4	g(ξ	g(ξ	PROPN
ejpam-6366	45	5	)	)	PUNCT
ejpam-6366	46	1	ξ	ξ	PROPN
ejpam-6366	47	1	+	+	SYM
ejpam-6366	47	2	1−	1−	NUM
ejpam-6366	47	3	2γ	2γ	X
ejpam-6366	47	4	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6366	47	5	<	<	X
ejpam-6366	47	6	ρ	ρ	NUM
ejpam-6366	47	7			NOUN
ejpam-6366	47	8	.	.	PUNCT
ejpam-6366	48	1	in	in	ADP
ejpam-6366	48	2	order	order	NOUN
ejpam-6366	48	3	to	to	PART
ejpam-6366	48	4	obtain	obtain	VERB
ejpam-6366	48	5	the	the	DET
ejpam-6366	48	6	results	result	NOUN
ejpam-6366	48	7	of	of	ADP
ejpam-6366	48	8	this	this	DET
ejpam-6366	48	9	study	study	NOUN
ejpam-6366	48	10	,	,	PUNCT
ejpam-6366	48	11	we	we	PRON
ejpam-6366	48	12	will	will	AUX
ejpam-6366	48	13	mention	mention	VERB
ejpam-6366	48	14	the	the	DET
ejpam-6366	48	15	next	next	ADJ
ejpam-6366	48	16	definition	definition	NOUN
ejpam-6366	48	17	and	and	CCONJ
ejpam-6366	48	18	the	the	DET
ejpam-6366	48	19	next	next	ADJ
ejpam-6366	48	20	lemmas	lemmas	NOUN
ejpam-6366	48	21	.	.	PUNCT
ejpam-6366	49	1	definition	definition	NOUN
ejpam-6366	49	2	2	2	NUM
ejpam-6366	49	3	.	.	PUNCT
ejpam-6366	50	1	the	the	DET
ejpam-6366	50	2	family	family	NOUN
ejpam-6366	50	3	of	of	ADP
ejpam-6366	50	4	regular	regular	ADJ
ejpam-6366	50	5	functions	function	NOUN
ejpam-6366	50	6	ϕ(ξ	ϕ(ξ	PROPN
ejpam-6366	50	7	)	)	PUNCT
ejpam-6366	50	8	in	in	ADP
ejpam-6366	50	9	∆	∆	PROPN
ejpam-6366	50	10	with	with	ADP
ejpam-6366	50	11	the	the	DET
ejpam-6366	50	12	positive	positive	ADJ
ejpam-6366	50	13	real	real	ADJ
ejpam-6366	50	14	part	part	NOUN
ejpam-6366	50	15	in	in	ADP
ejpam-6366	50	16	∆	∆	PROPN
ejpam-6366	50	17	,	,	PUNCT
ejpam-6366	50	18	and	and	CCONJ
ejpam-6366	50	19	of	of	ADP
ejpam-6366	50	20	the	the	DET
ejpam-6366	50	21	form	form	NOUN
ejpam-6366	50	22	ϕ(ξ	ϕ(ξ	PROPN
ejpam-6366	50	23	)	)	PUNCT
ejpam-6366	51	1	=	=	PUNCT
ejpam-6366	51	2	1	1	NUM
ejpam-6366	51	3	+	+	CCONJ
ejpam-6366	51	4	∞∑	∞∑	NUM
ejpam-6366	51	5	j=1	j=1	PROPN
ejpam-6366	51	6	δjξ	δjξ	PROPN
ejpam-6366	51	7	j	j	PROPN
ejpam-6366	51	8	(	(	PUNCT
ejpam-6366	51	9	ξ	ξ	PROPN
ejpam-6366	51	10	∈	∈	PROPN
ejpam-6366	51	11	∆	∆	X
ejpam-6366	51	12	)	)	PUNCT
ejpam-6366	51	13	(	(	PUNCT
ejpam-6366	51	14	7	7	X
ejpam-6366	51	15	)	)	PUNCT
ejpam-6366	51	16	is	be	AUX
ejpam-6366	51	17	denoted	denote	VERB
ejpam-6366	51	18	by	by	ADP
ejpam-6366	51	19	φ	φ	PROPN
ejpam-6366	51	20	,	,	PUNCT
ejpam-6366	51	21	that	that	PRON
ejpam-6366	51	22	calls	call	VERB
ejpam-6366	51	23	the	the	DET
ejpam-6366	51	24	well	well	ADV
ejpam-6366	51	25	-	-	PUNCT
ejpam-6366	51	26	known	know	VERB
ejpam-6366	51	27	carathéodory	carathéodory	NOUN
ejpam-6366	51	28	family	family	NOUN
ejpam-6366	51	29	.	.	PUNCT
ejpam-6366	52	1	lemma	lemma	PROPN
ejpam-6366	52	2	1	1	NUM
ejpam-6366	52	3	.	.	PUNCT
ejpam-6366	53	1	if	if	SCONJ
ejpam-6366	53	2	ϕ	ϕ	NOUN
ejpam-6366	53	3	given	give	VERB
ejpam-6366	53	4	by	by	ADP
ejpam-6366	53	5	(	(	PUNCT
ejpam-6366	53	6	7	7	NUM
ejpam-6366	53	7	)	)	PUNCT
ejpam-6366	53	8	belongs	belong	VERB
ejpam-6366	53	9	to	to	ADP
ejpam-6366	53	10	φ	φ	NUM
ejpam-6366	53	11	,	,	PUNCT
ejpam-6366	53	12	then	then	ADV
ejpam-6366	53	13	|δj	|δj	NUM
ejpam-6366	53	14	|	|	ADV
ejpam-6366	53	15	≤	≤	NUM
ejpam-6366	53	16	2	2	NUM
ejpam-6366	53	17	,	,	PUNCT
ejpam-6366	53	18	for	for	ADP
ejpam-6366	53	19	j	j	PROPN
ejpam-6366	53	20	∈	∈	PROPN
ejpam-6366	53	21	n	n	PROPN
ejpam-6366	53	22	=	=	SYM
ejpam-6366	53	23	{	{	PUNCT
ejpam-6366	53	24	1	1	NUM
ejpam-6366	53	25	,	,	PUNCT
ejpam-6366	53	26	2	2	NUM
ejpam-6366	53	27	,	,	PUNCT
ejpam-6366	53	28	3	3	NUM
ejpam-6366	53	29	,	,	PUNCT
ejpam-6366	53	30	...	...	PUNCT
ejpam-6366	53	31	}	}	PUNCT
ejpam-6366	53	32	,	,	PUNCT
ejpam-6366	53	33	(	(	PUNCT
ejpam-6366	53	34	8)	8)	NUM
ejpam-6366	53	35	for	for	ADP
ejpam-6366	53	36	u	u	NOUN
ejpam-6366	53	37	,	,	PUNCT
ejpam-6366	53	38	v	v	NOUN
ejpam-6366	53	39	are	be	AUX
ejpam-6366	53	40	complex	complex	ADJ
ejpam-6366	53	41	numbers	number	NOUN
ejpam-6366	53	42	we	we	PRON
ejpam-6366	53	43	have∣∣δ2	have∣∣δ2	VERB
ejpam-6366	53	44	−	−	PROPN
ejpam-6366	54	1	uδ21	uδ21	PROPN
ejpam-6366	54	2	∣∣	∣∣	NUM
ejpam-6366	54	3	≤	≤	PROPN
ejpam-6366	54	4	2max{1	2max{1	NUM
ejpam-6366	54	5	;	;	PUNCT
ejpam-6366	54	6	|2u−	|2u−	PROPN
ejpam-6366	54	7	1|	1|	NUM
ejpam-6366	54	8	}	}	PUNCT
ejpam-6366	54	9	(	(	PUNCT
ejpam-6366	54	10	9	9	NUM
ejpam-6366	54	11	)	)	PUNCT
ejpam-6366	54	12	and	and	CCONJ
ejpam-6366	54	13	|δi+j	|δi+j	NUM
ejpam-6366	54	14	−	−	ADP
ejpam-6366	54	15	vδiδj	vδiδj	NOUN
ejpam-6366	54	16	|	|	ADV
ejpam-6366	54	17	≤	≤	PUNCT
ejpam-6366	54	18	2max{1	2max{1	NUM
ejpam-6366	54	19	;	;	PUNCT
ejpam-6366	54	20	|1−	|1−	NOUN
ejpam-6366	54	21	2v|	2v|	NUM
ejpam-6366	54	22	}	}	PUNCT
ejpam-6366	54	23	.	.	PUNCT
ejpam-6366	55	1	(	(	PUNCT
ejpam-6366	55	2	10	10	NUM
ejpam-6366	55	3	)	)	PUNCT
ejpam-6366	55	4	t.	t.	NOUN
ejpam-6366	55	5	m.	m.	NOUN
ejpam-6366	55	6	seoudy	seoudy	PROPN
ejpam-6366	55	7	,	,	PUNCT
ejpam-6366	55	8	a.	a.	PROPN
ejpam-6366	55	9	e.	e.	PROPN
ejpam-6366	55	10	shammaky	shammaky	PROPN
ejpam-6366	55	11	/	/	SYM
ejpam-6366	55	12	eur	eur	PROPN
ejpam-6366	55	13	.	.	PUNCT
ejpam-6366	56	1	j.	j.	PROPN
ejpam-6366	56	2	pure	pure	PROPN
ejpam-6366	56	3	appl	appl	PROPN
ejpam-6366	56	4	.	.	PROPN
ejpam-6366	56	5	math	math	PROPN
ejpam-6366	56	6	,	,	PUNCT
ejpam-6366	56	7	18	18	NUM
ejpam-6366	56	8	(	(	PUNCT
ejpam-6366	56	9	4	4	NUM
ejpam-6366	56	10	)	)	PUNCT
ejpam-6366	56	11	(	(	PUNCT
ejpam-6366	56	12	2025	2025	NUM
ejpam-6366	56	13	)	)	PUNCT
ejpam-6366	56	14	,	,	PUNCT
ejpam-6366	56	15	6366	6366	NUM
ejpam-6366	56	16	4	4	NUM
ejpam-6366	56	17	of	of	ADP
ejpam-6366	56	18	15	15	NUM
ejpam-6366	56	19	the	the	DET
ejpam-6366	56	20	inequality	inequality	NOUN
ejpam-6366	56	21	(	(	PUNCT
ejpam-6366	56	22	8)	8)	NUM
ejpam-6366	56	23	is	be	AUX
ejpam-6366	56	24	carathéodory	carathéodory	NOUN
ejpam-6366	56	25	’s	’s	PART
ejpam-6366	56	26	result	result	NOUN
ejpam-6366	56	27	(	(	PUNCT
ejpam-6366	56	28	see	see	VERB
ejpam-6366	56	29	[	[	X
ejpam-6366	56	30	21	21	NUM
ejpam-6366	56	31	,	,	PUNCT
ejpam-6366	56	32	22	22	NUM
ejpam-6366	56	33	]	]	PUNCT
ejpam-6366	56	34	)	)	PUNCT
ejpam-6366	56	35	,	,	PUNCT
ejpam-6366	56	36	while	while	SCONJ
ejpam-6366	56	37	the	the	DET
ejpam-6366	56	38	inequality	inequality	NOUN
ejpam-6366	56	39	(	(	PUNCT
ejpam-6366	56	40	9	9	NUM
ejpam-6366	56	41	)	)	PUNCT
ejpam-6366	56	42	may	may	AUX
ejpam-6366	56	43	be	be	AUX
ejpam-6366	56	44	detected	detect	VERB
ejpam-6366	56	45	in	in	ADP
ejpam-6366	56	46	[	[	X
ejpam-6366	56	47	23	23	NUM
ejpam-6366	56	48	]	]	PUNCT
ejpam-6366	56	49	,	,	PUNCT
ejpam-6366	56	50	and	and	CCONJ
ejpam-6366	56	51	the	the	DET
ejpam-6366	56	52	inequality	inequality	NOUN
ejpam-6366	56	53	(	(	PUNCT
ejpam-6366	56	54	10	10	NUM
ejpam-6366	56	55	)	)	PUNCT
ejpam-6366	56	56	is	be	AUX
ejpam-6366	56	57	from	from	ADP
ejpam-6366	56	58	[	[	X
ejpam-6366	56	59	24	24	NUM
ejpam-6366	56	60	]	]	PUNCT
ejpam-6366	56	61	.	.	PUNCT
ejpam-6366	57	1	lemma	lemma	PROPN
ejpam-6366	57	2	2	2	NUM
ejpam-6366	57	3	.	.	PUNCT
ejpam-6366	58	1	[	[	X
ejpam-6366	58	2	25	25	NUM
ejpam-6366	58	3	]	]	X
ejpam-6366	58	4	if	if	SCONJ
ejpam-6366	58	5	ϕ	ϕ	NOUN
ejpam-6366	58	6	given	give	VERB
ejpam-6366	58	7	by	by	ADP
ejpam-6366	58	8	(	(	PUNCT
ejpam-6366	58	9	7	7	NUM
ejpam-6366	58	10	)	)	PUNCT
ejpam-6366	58	11	belongs	belong	VERB
ejpam-6366	58	12	to	to	ADP
ejpam-6366	58	13	φ	φ	NUM
ejpam-6366	58	14	,	,	PUNCT
ejpam-6366	58	15	then	then	ADV
ejpam-6366	58	16	∣∣δ2	∣∣δ2	NOUN
ejpam-6366	58	17	−	−	PROPN
ejpam-6366	58	18	uδ21	uδ21	PROPN
ejpam-6366	58	19	∣∣	∣∣	X
ejpam-6366	58	20	≤	≤	NUM
ejpam-6366	58	21			PUNCT
ejpam-6366	58	22	−4u+	−4u+	NOUN
ejpam-6366	58	23	2	2	NUM
ejpam-6366	58	24	if	if	SCONJ
ejpam-6366	58	25	u	u	NOUN
ejpam-6366	58	26	≤	≤	ADV
ejpam-6366	58	27	0	0	NUM
ejpam-6366	58	28	,	,	PUNCT
ejpam-6366	58	29	2	2	NUM
ejpam-6366	58	30	if	if	SCONJ
ejpam-6366	58	31	0	0	NUM
ejpam-6366	58	32	≤	≤	NUM
ejpam-6366	58	33	u	u	NOUN
ejpam-6366	58	34	≤	≤	NUM
ejpam-6366	58	35	1	1	NUM
ejpam-6366	58	36	,	,	PUNCT
ejpam-6366	58	37	4u−	4u−	PROPN
ejpam-6366	58	38	2	2	NUM
ejpam-6366	58	39	if	if	SCONJ
ejpam-6366	58	40	u	u	NOUN
ejpam-6366	58	41	≥	≥	NOUN
ejpam-6366	58	42	1	1	NUM
ejpam-6366	58	43	.	.	PUNCT
ejpam-6366	58	44	(	(	PUNCT
ejpam-6366	58	45	11	11	NUM
ejpam-6366	58	46	)	)	PUNCT
ejpam-6366	58	47	also	also	ADV
ejpam-6366	58	48	the	the	DET
ejpam-6366	58	49	upper	upper	ADJ
ejpam-6366	58	50	bound	bound	ADJ
ejpam-6366	58	51	(	(	PUNCT
ejpam-6366	58	52	11	11	NUM
ejpam-6366	58	53	)	)	PUNCT
ejpam-6366	58	54	can	can	AUX
ejpam-6366	58	55	be	be	AUX
ejpam-6366	58	56	improved	improve	VERB
ejpam-6366	58	57	as	as	SCONJ
ejpam-6366	58	58	follows	follow	VERB
ejpam-6366	58	59	for	for	ADP
ejpam-6366	58	60	0	0	NUM
ejpam-6366	58	61	≤	≤	NUM
ejpam-6366	58	62	u	u	NOUN
ejpam-6366	58	63	≤	≤	NUM
ejpam-6366	58	64	1	1	NUM
ejpam-6366	58	65	2	2	NUM
ejpam-6366	58	66	,	,	PUNCT
ejpam-6366	58	67	we	we	PRON
ejpam-6366	58	68	have∣∣δ2	have∣∣δ2	VERB
ejpam-6366	58	69	−	−	PROPN
ejpam-6366	58	70	uδ21	uδ21	PROPN
ejpam-6366	58	71	∣∣+	∣∣+	PROPN
ejpam-6366	58	72	u	u	PROPN
ejpam-6366	58	73	|δ1|2	|δ1|2	PROPN
ejpam-6366	58	74	≤	≤	NOUN
ejpam-6366	58	75	2	2	NUM
ejpam-6366	58	76	,	,	PUNCT
ejpam-6366	58	77	and	and	CCONJ
ejpam-6366	58	78	for	for	ADP
ejpam-6366	58	79	1	1	NUM
ejpam-6366	58	80	2	2	NUM
ejpam-6366	58	81	≤	≤	NUM
ejpam-6366	58	82	u	u	NOUN
ejpam-6366	58	83	≤	≤	NOUN
ejpam-6366	58	84	1	1	NUM
ejpam-6366	58	85	,	,	PUNCT
ejpam-6366	58	86	we	we	PRON
ejpam-6366	58	87	have	have	VERB
ejpam-6366	58	88	∣∣δ2	∣∣δ2	NOUN
ejpam-6366	58	89	−	−	PROPN
ejpam-6366	58	90	uδ21	uδ21	PROPN
ejpam-6366	58	91	∣∣+	∣∣+	X
ejpam-6366	58	92	(	(	PUNCT
ejpam-6366	58	93	1−	1−	NUM
ejpam-6366	58	94	u	u	NOUN
ejpam-6366	58	95	)	)	PUNCT
ejpam-6366	58	96	|δ1|2	|δ1|2	PROPN
ejpam-6366	58	97	≤	≤	ADV
ejpam-6366	58	98	2	2	NUM
ejpam-6366	58	99	.	.	PUNCT
ejpam-6366	59	1	in	in	ADP
ejpam-6366	59	2	the	the	DET
ejpam-6366	59	3	following	follow	VERB
ejpam-6366	59	4	sections	section	NOUN
ejpam-6366	59	5	,	,	PUNCT
ejpam-6366	59	6	for	for	ADP
ejpam-6366	59	7	the	the	DET
ejpam-6366	59	8	function	function	NOUN
ejpam-6366	59	9	subfamily	subfamily	ADV
ejpam-6366	59	10	sk	sk	VERB
ejpam-6366	59	11	[	[	X
ejpam-6366	59	12	p	p	X
ejpam-6366	59	13	,	,	PUNCT
ejpam-6366	59	14	q;α	q;α	PROPN
ejpam-6366	59	15	,	,	PUNCT
ejpam-6366	59	16	β	β	X
ejpam-6366	59	17	]	]	PUNCT
ejpam-6366	59	18	and	and	CCONJ
ejpam-6366	59	19	its	its	PRON
ejpam-6366	59	20	special	special	ADJ
ejpam-6366	59	21	subfamilies	subfamily	NOUN
ejpam-6366	59	22	s	s	VERB
ejpam-6366	59	23	[	[	X
ejpam-6366	59	24	p	p	X
ejpam-6366	59	25	,	,	PUNCT
ejpam-6366	59	26	q	q	X
ejpam-6366	59	27	]	]	X
ejpam-6366	59	28	and	and	CCONJ
ejpam-6366	59	29	k	k	X
ejpam-6366	60	1	[	[	X
ejpam-6366	60	2	p	p	X
ejpam-6366	60	3	,	,	PUNCT
ejpam-6366	60	4	q	q	X
ejpam-6366	60	5	]	]	X
ejpam-6366	60	6	,	,	PUNCT
ejpam-6366	60	7	we	we	PRON
ejpam-6366	60	8	study	study	VERB
ejpam-6366	60	9	the	the	DET
ejpam-6366	60	10	well	well	ADV
ejpam-6366	60	11	-	-	PUNCT
ejpam-6366	60	12	known	know	VERB
ejpam-6366	60	13	results	result	NOUN
ejpam-6366	60	14	,	,	PUNCT
ejpam-6366	60	15	like	like	ADP
ejpam-6366	60	16	convolution	convolution	NOUN
ejpam-6366	60	17	properties	property	NOUN
ejpam-6366	60	18	,	,	PUNCT
ejpam-6366	60	19	necessary	necessary	ADJ
ejpam-6366	60	20	and	and	CCONJ
ejpam-6366	60	21	sufficient	sufficient	ADJ
ejpam-6366	60	22	conditions	condition	NOUN
ejpam-6366	60	23	,	,	PUNCT
ejpam-6366	60	24	coefficient	coefficient	NOUN
ejpam-6366	60	25	estimates	estimate	NOUN
ejpam-6366	60	26	,	,	PUNCT
ejpam-6366	60	27	and	and	CCONJ
ejpam-6366	60	28	fekete	fekete	PROPN
ejpam-6366	60	29	-	-	PUNCT
ejpam-6366	60	30	szegö	szegö	ADJ
ejpam-6366	60	31	inequalities	inequality	NOUN
ejpam-6366	60	32	.	.	PUNCT
ejpam-6366	61	1	2	2	X
ejpam-6366	61	2	.	.	X
ejpam-6366	61	3	convolution	convolution	NOUN
ejpam-6366	61	4	properties	property	NOUN
ejpam-6366	61	5	unless	unless	SCONJ
ejpam-6366	61	6	otherwise	otherwise	ADV
ejpam-6366	61	7	stated	state	VERB
ejpam-6366	61	8	,	,	PUNCT
ejpam-6366	61	9	we	we	PRON
ejpam-6366	61	10	suppose	suppose	VERB
ejpam-6366	61	11	throughout	throughout	ADP
ejpam-6366	61	12	this	this	DET
ejpam-6366	61	13	article	article	NOUN
ejpam-6366	61	14	that	that	SCONJ
ejpam-6366	61	15	0	0	NUM
ejpam-6366	61	16	≤	≤	NUM
ejpam-6366	61	17	θ	θ	NOUN
ejpam-6366	61	18	<	<	X
ejpam-6366	61	19	2π	2π	NOUN
ejpam-6366	61	20	;	;	PUNCT
ejpam-6366	61	21	0	0	NUM
ejpam-6366	61	22	≤	≤	NUM
ejpam-6366	61	23	α	α	X
ejpam-6366	61	24	,	,	PUNCT
ejpam-6366	61	25	β	β	X
ejpam-6366	61	26	≤	≤	NUM
ejpam-6366	61	27	1	1	NUM
ejpam-6366	61	28	;	;	PUNCT
ejpam-6366	61	29	α+	α+	X
ejpam-6366	61	30	β	β	X
ejpam-6366	61	31	̸=	̸=	PROPN
ejpam-6366	61	32	0	0	NUM
ejpam-6366	61	33	;	;	PUNCT
ejpam-6366	61	34	−1	−1	NOUN
ejpam-6366	61	35	≤	≤	PUNCT
ejpam-6366	61	36	q	q	NOUN
ejpam-6366	62	1	<	<	X
ejpam-6366	62	2	p	p	X
ejpam-6366	62	3	≤	≤	NUM
ejpam-6366	62	4	1	1	NUM
ejpam-6366	62	5	;	;	PUNCT
ejpam-6366	62	6	0	0	NUM
ejpam-6366	62	7	≤	≤	NUM
ejpam-6366	62	8	γ	γ	X
ejpam-6366	62	9	<	<	X
ejpam-6366	62	10	1	1	NUM
ejpam-6366	62	11	and	and	CCONJ
ejpam-6366	62	12	g	g	PROPN
ejpam-6366	62	13	∈	∈	PROPN
ejpam-6366	62	14	h	h	NOUN
ejpam-6366	62	15	has	have	VERB
ejpam-6366	62	16	the	the	DET
ejpam-6366	62	17	series	series	NOUN
ejpam-6366	62	18	form	form	NOUN
ejpam-6366	62	19	(	(	PUNCT
ejpam-6366	62	20	1	1	NUM
ejpam-6366	62	21	)	)	PUNCT
ejpam-6366	62	22	.	.	PUNCT
ejpam-6366	63	1	theorem	theorem	NOUN
ejpam-6366	63	2	1	1	NUM
ejpam-6366	63	3	.	.	PUNCT
ejpam-6366	64	1	the	the	DET
ejpam-6366	64	2	function	function	NOUN
ejpam-6366	64	3	g	g	PROPN
ejpam-6366	64	4	∈	∈	PROPN
ejpam-6366	64	5	sk	sk	NOUN
ejpam-6366	65	1	[	[	X
ejpam-6366	65	2	p	p	X
ejpam-6366	65	3	,	,	PUNCT
ejpam-6366	65	4	q;α	q;α	PROPN
ejpam-6366	65	5	,	,	PUNCT
ejpam-6366	65	6	β	β	X
ejpam-6366	65	7	]	]	X
ejpam-6366	65	8	if	if	SCONJ
ejpam-6366	65	9	and	and	CCONJ
ejpam-6366	66	1	only	only	ADV
ejpam-6366	66	2	if	if	SCONJ
ejpam-6366	66	3	1	1	NUM
ejpam-6366	66	4	ξ	ξ	PROPN
ejpam-6366	66	5	g	g	PROPN
ejpam-6366	66	6	(	(	PUNCT
ejpam-6366	66	7	ξ	ξ	NOUN
ejpam-6366	66	8	)	)	PUNCT
ejpam-6366	66	9	∗	∗	NOUN
ejpam-6366	66	10	ξ	ξ	X
ejpam-6366	66	11	−	−	PROPN
ejpam-6366	66	12	(	(	PUNCT
ejpam-6366	66	13	α+(α+β)r	α+(α+β)r	PROPN
ejpam-6366	66	14	α+β	α+β	NUM
ejpam-6366	66	15	)	)	PUNCT
ejpam-6366	66	16	ξ2	ξ2	NOUN
ejpam-6366	67	1	+	+	CCONJ
ejpam-6366	67	2	(	(	PUNCT
ejpam-6366	67	3	αr	αr	NUM
ejpam-6366	67	4	α+β	α+β	NUM
ejpam-6366	67	5	)	)	PUNCT
ejpam-6366	67	6	ξ3	ξ3	NOUN
ejpam-6366	67	7	(	(	PUNCT
ejpam-6366	67	8	1−	1−	NUM
ejpam-6366	67	9	ξ)2	ξ)2	NOUN
ejpam-6366	67	10			PROPN
ejpam-6366	67	11	̸=	̸=	PROPN
ejpam-6366	67	12	0	0	NUM
ejpam-6366	67	13	,	,	PUNCT
ejpam-6366	67	14	(	(	PUNCT
ejpam-6366	67	15	12	12	NUM
ejpam-6366	67	16	)	)	PUNCT
ejpam-6366	67	17	where	where	SCONJ
ejpam-6366	67	18	r	r	NOUN
ejpam-6366	67	19	is	be	AUX
ejpam-6366	67	20	defined	define	VERB
ejpam-6366	67	21	by	by	ADP
ejpam-6366	67	22	r	r	NOUN
ejpam-6366	67	23	=	=	SYM
ejpam-6366	67	24	r	r	NOUN
ejpam-6366	67	25	(	(	PUNCT
ejpam-6366	67	26	θ	θ	PROPN
ejpam-6366	67	27	,	,	PUNCT
ejpam-6366	67	28	p	p	X
ejpam-6366	67	29	,	,	PUNCT
ejpam-6366	67	30	q	q	ADJ
ejpam-6366	67	31	,	,	PUNCT
ejpam-6366	67	32	γ	γ	NOUN
ejpam-6366	67	33	)	)	PUNCT
ejpam-6366	67	34	=	=	X
ejpam-6366	67	35	e−iθ	e−iθ	NOUN
ejpam-6366	68	1	+	+	ADJ
ejpam-6366	68	2	q	q	X
ejpam-6366	68	3	(	(	PUNCT
ejpam-6366	68	4	1−	1−	NUM
ejpam-6366	68	5	γ	γ	X
ejpam-6366	68	6	)	)	PUNCT
ejpam-6366	68	7	(	(	PUNCT
ejpam-6366	68	8	p	p	NOUN
ejpam-6366	68	9	−q	−q	NOUN
ejpam-6366	68	10	)	)	PUNCT
ejpam-6366	68	11	+	+	NUM
ejpam-6366	68	12	1	1	X
ejpam-6366	68	13	.	.	X
ejpam-6366	68	14	(	(	PUNCT
ejpam-6366	68	15	13	13	NUM
ejpam-6366	68	16	)	)	PUNCT
ejpam-6366	68	17	proof	proof	NOUN
ejpam-6366	68	18	.	.	PUNCT
ejpam-6366	69	1	it	it	PRON
ejpam-6366	69	2	is	be	AUX
ejpam-6366	69	3	clear	clear	ADJ
ejpam-6366	69	4	to	to	PART
ejpam-6366	69	5	check	check	VERB
ejpam-6366	69	6	the	the	DET
ejpam-6366	69	7	next	next	ADJ
ejpam-6366	69	8	:	:	PUNCT
ejpam-6366	69	9	g	g	PROPN
ejpam-6366	69	10	(	(	PUNCT
ejpam-6366	69	11	ξ	ξ	PROPN
ejpam-6366	69	12	)	)	PUNCT
ejpam-6366	69	13	=	=	SYM
ejpam-6366	69	14	g	g	PROPN
ejpam-6366	69	15	(	(	PUNCT
ejpam-6366	69	16	ξ	ξ	NOUN
ejpam-6366	69	17	)	)	PUNCT
ejpam-6366	69	18	∗	∗	NOUN
ejpam-6366	69	19	ξ	ξ	PROPN
ejpam-6366	69	20	1−	1−	NUM
ejpam-6366	69	21	ξ	ξ	PROPN
ejpam-6366	69	22	,	,	PUNCT
ejpam-6366	69	23	ξg′	ξg′	PROPN
ejpam-6366	69	24	(	(	PUNCT
ejpam-6366	69	25	ξ	ξ	NOUN
ejpam-6366	69	26	)	)	PUNCT
ejpam-6366	69	27	=	=	SYM
ejpam-6366	69	28	g	g	PROPN
ejpam-6366	69	29	(	(	PUNCT
ejpam-6366	69	30	ξ	ξ	NOUN
ejpam-6366	69	31	)	)	PUNCT
ejpam-6366	69	32	∗	∗	NOUN
ejpam-6366	69	33	ξ	ξ	PROPN
ejpam-6366	69	34	(	(	PUNCT
ejpam-6366	69	35	1−	1−	NUM
ejpam-6366	69	36	ξ)2	ξ)2	NOUN
ejpam-6366	69	37	.	.	PUNCT
ejpam-6366	70	1			PROPN
ejpam-6366	70	2	(	(	PUNCT
ejpam-6366	70	3	14	14	NUM
ejpam-6366	70	4	)	)	PUNCT
ejpam-6366	70	5	to	to	PART
ejpam-6366	70	6	show	show	VERB
ejpam-6366	70	7	that	that	SCONJ
ejpam-6366	70	8	(	(	PUNCT
ejpam-6366	70	9	12	12	NUM
ejpam-6366	70	10	)	)	PUNCT
ejpam-6366	70	11	is	be	AUX
ejpam-6366	70	12	true	true	ADJ
ejpam-6366	70	13	,	,	PUNCT
ejpam-6366	70	14	we	we	PRON
ejpam-6366	70	15	will	will	AUX
ejpam-6366	70	16	write	write	VERB
ejpam-6366	70	17	(	(	PUNCT
ejpam-6366	70	18	4	4	NUM
ejpam-6366	70	19	)	)	PUNCT
ejpam-6366	70	20	as	as	SCONJ
ejpam-6366	70	21	follows	follow	VERB
ejpam-6366	70	22	αg	αg	X
ejpam-6366	70	23	(	(	PUNCT
ejpam-6366	70	24	ξ	ξ	NOUN
ejpam-6366	70	25	)	)	PUNCT
ejpam-6366	70	26	+	+	NUM
ejpam-6366	70	27	βξg′	βξg′	NUM
ejpam-6366	70	28	(	(	PUNCT
ejpam-6366	70	29	ξ	ξ	NOUN
ejpam-6366	70	30	)	)	PUNCT
ejpam-6366	70	31	αξ	αξ	NOUN
ejpam-6366	71	1	+	+	NUM
ejpam-6366	71	2	βg	βg	PROPN
ejpam-6366	71	3	(	(	PUNCT
ejpam-6366	71	4	ξ	ξ	NOUN
ejpam-6366	71	5	)	)	PUNCT
ejpam-6366	71	6	=	=	SYM
ejpam-6366	71	7	1	1	NUM
ejpam-6366	71	8	+	+	CCONJ
ejpam-6366	71	9	[	[	X
ejpam-6366	71	10	q+	q+	X
ejpam-6366	71	11	(	(	PUNCT
ejpam-6366	71	12	1−	1−	NUM
ejpam-6366	71	13	γ	γ	NOUN
ejpam-6366	71	14	)	)	PUNCT
ejpam-6366	71	15	(	(	PUNCT
ejpam-6366	71	16	p	p	PROPN
ejpam-6366	71	17	−q)]w	−q)]w	PROPN
ejpam-6366	71	18	(	(	PUNCT
ejpam-6366	71	19	ξ	ξ	NOUN
ejpam-6366	71	20	)	)	PUNCT
ejpam-6366	71	21	1	1	NUM
ejpam-6366	71	22	+	+	SYM
ejpam-6366	71	23	qw	qw	X
ejpam-6366	71	24	(	(	PUNCT
ejpam-6366	71	25	ξ	ξ	NOUN
ejpam-6366	71	26	)	)	PUNCT
ejpam-6366	71	27	,	,	PUNCT
ejpam-6366	71	28	(	(	PUNCT
ejpam-6366	71	29	15	15	X
ejpam-6366	71	30	)	)	PUNCT
ejpam-6366	71	31	t.	t.	NOUN
ejpam-6366	71	32	m.	m.	NOUN
ejpam-6366	71	33	seoudy	seoudy	PROPN
ejpam-6366	71	34	,	,	PUNCT
ejpam-6366	71	35	a.	a.	PROPN
ejpam-6366	71	36	e.	e.	PROPN
ejpam-6366	71	37	shammaky	shammaky	PROPN
ejpam-6366	71	38	/	/	SYM
ejpam-6366	71	39	eur	eur	PROPN
ejpam-6366	71	40	.	.	PUNCT
ejpam-6366	72	1	j.	j.	PROPN
ejpam-6366	72	2	pure	pure	PROPN
ejpam-6366	72	3	appl	appl	PROPN
ejpam-6366	72	4	.	.	PROPN
ejpam-6366	72	5	math	math	PROPN
ejpam-6366	72	6	,	,	PUNCT
ejpam-6366	72	7	18	18	NUM
ejpam-6366	72	8	(	(	PUNCT
ejpam-6366	72	9	4	4	NUM
ejpam-6366	72	10	)	)	PUNCT
ejpam-6366	72	11	(	(	PUNCT
ejpam-6366	72	12	2025	2025	NUM
ejpam-6366	72	13	)	)	PUNCT
ejpam-6366	72	14	,	,	PUNCT
ejpam-6366	72	15	6366	6366	NUM
ejpam-6366	72	16	5	5	NUM
ejpam-6366	72	17	of	of	ADP
ejpam-6366	72	18	15	15	NUM
ejpam-6366	72	19	where	where	SCONJ
ejpam-6366	72	20	w	w	PROPN
ejpam-6366	72	21	(	(	PUNCT
ejpam-6366	72	22	ξ	ξ	NOUN
ejpam-6366	72	23	)	)	PUNCT
ejpam-6366	72	24	∈	∈	PROPN
ejpam-6366	72	25	ω	ω	PROPN
ejpam-6366	72	26	,	,	PUNCT
ejpam-6366	72	27	hence	hence	ADV
ejpam-6366	72	28	we	we	PRON
ejpam-6366	72	29	have	have	VERB
ejpam-6366	72	30	αg	αg	NUM
ejpam-6366	72	31	(	(	PUNCT
ejpam-6366	72	32	ξ	ξ	NOUN
ejpam-6366	72	33	)	)	PUNCT
ejpam-6366	73	1	+	+	NUM
ejpam-6366	73	2	βξg′	βξg′	NUM
ejpam-6366	73	3	(	(	PUNCT
ejpam-6366	73	4	ξ	ξ	NOUN
ejpam-6366	73	5	)	)	PUNCT
ejpam-6366	73	6	αξ	αξ	NOUN
ejpam-6366	74	1	+	+	NUM
ejpam-6366	74	2	βg	βg	PROPN
ejpam-6366	74	3	(	(	PUNCT
ejpam-6366	74	4	ξ	ξ	NOUN
ejpam-6366	74	5	)	)	PUNCT
ejpam-6366	74	6	̸=	̸=	NOUN
ejpam-6366	74	7	1	1	NUM
ejpam-6366	75	1	+	+	CCONJ
ejpam-6366	75	2	[	[	X
ejpam-6366	75	3	q+	q+	X
ejpam-6366	75	4	(	(	PUNCT
ejpam-6366	75	5	1−	1−	NUM
ejpam-6366	75	6	γ	γ	NOUN
ejpam-6366	75	7	)	)	PUNCT
ejpam-6366	75	8	(	(	PUNCT
ejpam-6366	75	9	p	p	NOUN
ejpam-6366	75	10	−q	−q	NOUN
ejpam-6366	75	11	)	)	PUNCT
ejpam-6366	75	12	]	]	PUNCT
ejpam-6366	76	1	eiθ	eiθ	PROPN
ejpam-6366	76	2	1	1	NUM
ejpam-6366	76	3	+	+	NOUN
ejpam-6366	76	4	qeiθ	qeiθ	NOUN
ejpam-6366	76	5	,	,	PUNCT
ejpam-6366	76	6	which	which	PRON
ejpam-6366	76	7	is	be	AUX
ejpam-6366	76	8	equivalent	equivalent	ADJ
ejpam-6366	76	9	to	to	ADP
ejpam-6366	76	10	1	1	NUM
ejpam-6366	76	11	ξ	ξ	NOUN
ejpam-6366	76	12	{	{	PUNCT
ejpam-6366	76	13	(	(	PUNCT
ejpam-6366	76	14	1	1	NUM
ejpam-6366	76	15	+	+	NOUN
ejpam-6366	76	16	qeiθ	qeiθ	NOUN
ejpam-6366	76	17	)	)	PUNCT
ejpam-6366	76	18	[	[	PUNCT
ejpam-6366	76	19	αg	αg	X
ejpam-6366	76	20	(	(	PUNCT
ejpam-6366	76	21	ξ	ξ	NOUN
ejpam-6366	76	22	)	)	PUNCT
ejpam-6366	76	23	+	+	NUM
ejpam-6366	76	24	βξg′	βξg′	NUM
ejpam-6366	76	25	(	(	PUNCT
ejpam-6366	76	26	ξ	ξ	NOUN
ejpam-6366	76	27	)	)	PUNCT
ejpam-6366	76	28	]	]	PUNCT
ejpam-6366	77	1	−	−	PROPN
ejpam-6366	77	2	(	(	PUNCT
ejpam-6366	77	3	1	1	NUM
ejpam-6366	78	1	+	+	CCONJ
ejpam-6366	78	2	[	[	X
ejpam-6366	78	3	q+	q+	X
ejpam-6366	78	4	(	(	PUNCT
ejpam-6366	78	5	1−	1−	NUM
ejpam-6366	78	6	γ	γ	NOUN
ejpam-6366	78	7	)	)	PUNCT
ejpam-6366	78	8	(	(	PUNCT
ejpam-6366	78	9	p	p	NOUN
ejpam-6366	78	10	−q	−q	NOUN
ejpam-6366	78	11	)	)	PUNCT
ejpam-6366	78	12	]	]	PUNCT
ejpam-6366	78	13	eiθ	eiθ	PROPN
ejpam-6366	78	14	)	)	PUNCT
ejpam-6366	79	1	[	[	X
ejpam-6366	79	2	αξ	αξ	NOUN
ejpam-6366	79	3	+	+	NUM
ejpam-6366	79	4	βg	βg	ADJ
ejpam-6366	79	5	(	(	PUNCT
ejpam-6366	79	6	ξ	ξ	NOUN
ejpam-6366	79	7	)	)	PUNCT
ejpam-6366	79	8	]	]	PUNCT
ejpam-6366	79	9	}	}	PUNCT
ejpam-6366	79	10	̸=	̸=	PROPN
ejpam-6366	79	11	0	0	NUM
ejpam-6366	79	12	.	.	PUNCT
ejpam-6366	80	1	(	(	PUNCT
ejpam-6366	80	2	16	16	NUM
ejpam-6366	80	3	)	)	PUNCT
ejpam-6366	80	4	by	by	ADP
ejpam-6366	80	5	using	use	VERB
ejpam-6366	80	6	(	(	PUNCT
ejpam-6366	80	7	14	14	NUM
ejpam-6366	80	8	)	)	PUNCT
ejpam-6366	80	9	in	in	ADP
ejpam-6366	80	10	(	(	PUNCT
ejpam-6366	80	11	16	16	NUM
ejpam-6366	80	12	)	)	PUNCT
ejpam-6366	80	13	,	,	PUNCT
ejpam-6366	80	14	we	we	PRON
ejpam-6366	80	15	get	get	VERB
ejpam-6366	80	16	1	1	NUM
ejpam-6366	80	17	ξ	ξ	NOUN
ejpam-6366	80	18			PUNCT
ejpam-6366	80	19	g	g	PROPN
ejpam-6366	80	20	(	(	PUNCT
ejpam-6366	80	21	ξ	ξ	NOUN
ejpam-6366	80	22	)	)	PUNCT
ejpam-6366	80	23	∗	∗	NOUN
ejpam-6366	80	24	(	(	PUNCT
ejpam-6366	80	25	αξ	αξ	NOUN
ejpam-6366	80	26	1−ξ	1−ξ	NUM
ejpam-6366	81	1	+	+	CCONJ
ejpam-6366	81	2	βξ	βξ	PROPN
ejpam-6366	81	3	(	(	PUNCT
ejpam-6366	81	4	1−ξ)2	1−ξ)2	NUM
ejpam-6366	81	5	)	)	PUNCT
ejpam-6366	81	6	(	(	PUNCT
ejpam-6366	81	7	1	1	NUM
ejpam-6366	81	8	+	+	NOUN
ejpam-6366	81	9	qeiθ	qeiθ	NOUN
ejpam-6366	81	10	)	)	PUNCT
ejpam-6366	81	11	−g	−g	NOUN
ejpam-6366	81	12	(	(	PUNCT
ejpam-6366	81	13	ξ	ξ	NOUN
ejpam-6366	81	14	)	)	PUNCT
ejpam-6366	81	15	∗	∗	NOUN
ejpam-6366	81	16	(	(	PUNCT
ejpam-6366	81	17	αξ	αξ	NOUN
ejpam-6366	81	18	+	+	CCONJ
ejpam-6366	81	19	βξ	βξ	PROPN
ejpam-6366	81	20	1−ξ	1−ξ	NUM
ejpam-6366	81	21	)	)	PUNCT
ejpam-6366	81	22	(	(	PUNCT
ejpam-6366	81	23	1	1	NUM
ejpam-6366	81	24	+	+	CCONJ
ejpam-6366	82	1	[	[	X
ejpam-6366	82	2	q+	q+	X
ejpam-6366	82	3	(	(	PUNCT
ejpam-6366	82	4	1−	1−	NUM
ejpam-6366	82	5	γ	γ	NOUN
ejpam-6366	82	6	)	)	PUNCT
ejpam-6366	82	7	(	(	PUNCT
ejpam-6366	82	8	p	p	NOUN
ejpam-6366	82	9	−q	−q	NOUN
ejpam-6366	82	10	)	)	PUNCT
ejpam-6366	82	11	]	]	PUNCT
ejpam-6366	82	12	eiθ	eiθ	PROPN
ejpam-6366	82	13	)	)	PUNCT
ejpam-6366	83	1			NOUN
ejpam-6366	83	2	=	=	NOUN
ejpam-6366	83	3	1	1	NUM
ejpam-6366	83	4	ξ	ξ	X
ejpam-6366	83	5			PUNCT
ejpam-6366	83	6	g	g	PROPN
ejpam-6366	83	7	(	(	PUNCT
ejpam-6366	83	8	ξ	ξ	NOUN
ejpam-6366	83	9	)	)	PUNCT
ejpam-6366	83	10	∗	∗	NOUN
ejpam-6366	83	11	(	(	PUNCT
ejpam-6366	83	12	(	(	PUNCT
ejpam-6366	83	13	α+β)ξ−αξ2	α+β)ξ−αξ2	NOUN
ejpam-6366	83	14	(	(	PUNCT
ejpam-6366	83	15	1−ξ)2	1−ξ)2	NUM
ejpam-6366	83	16	)	)	PUNCT
ejpam-6366	83	17	(	(	PUNCT
ejpam-6366	83	18	1	1	NUM
ejpam-6366	83	19	+	+	NOUN
ejpam-6366	83	20	qeiθ	qeiθ	NOUN
ejpam-6366	83	21	)	)	PUNCT
ejpam-6366	83	22	−g	−g	NOUN
ejpam-6366	83	23	(	(	PUNCT
ejpam-6366	83	24	ξ	ξ	NOUN
ejpam-6366	83	25	)	)	PUNCT
ejpam-6366	83	26	∗	∗	NOUN
ejpam-6366	83	27	(	(	PUNCT
ejpam-6366	83	28	(	(	PUNCT
ejpam-6366	83	29	α+β)ξ−(2α+β)ξ2+αξ3	α+β)ξ−(2α+β)ξ2+αξ3	INTJ
ejpam-6366	83	30	(	(	PUNCT
ejpam-6366	83	31	1−ξ)2	1−ξ)2	NUM
ejpam-6366	83	32	)	)	PUNCT
ejpam-6366	83	33	(	(	PUNCT
ejpam-6366	83	34	1	1	NUM
ejpam-6366	83	35	+	+	CCONJ
ejpam-6366	83	36	[	[	X
ejpam-6366	83	37	q+	q+	X
ejpam-6366	83	38	(	(	PUNCT
ejpam-6366	83	39	1−	1−	NUM
ejpam-6366	83	40	γ	γ	NOUN
ejpam-6366	83	41	)	)	PUNCT
ejpam-6366	83	42	(	(	PUNCT
ejpam-6366	83	43	p	p	NOUN
ejpam-6366	83	44	−q	−q	NOUN
ejpam-6366	83	45	)	)	PUNCT
ejpam-6366	83	46	]	]	PUNCT
ejpam-6366	83	47	eiθ	eiθ	PROPN
ejpam-6366	83	48	)	)	PUNCT
ejpam-6366	84	1			NOUN
ejpam-6366	84	2	=	=	PUNCT
ejpam-6366	84	3	−	−	PROPN
ejpam-6366	84	4	(	(	PUNCT
ejpam-6366	84	5	α+β)(1−γ)(p−q)eiθ	α+β)(1−γ)(p−q)eiθ	NOUN
ejpam-6366	84	6	ξ	ξ	X
ejpam-6366	84	7	g	g	NOUN
ejpam-6366	84	8	(	(	PUNCT
ejpam-6366	84	9	ξ	ξ	NOUN
ejpam-6366	84	10	)	)	PUNCT
ejpam-6366	84	11	∗	∗	NOUN
ejpam-6366	84	12	ξ	ξ	NOUN
ejpam-6366	84	13	−	−	NOUN
ejpam-6366	84	14	α+(α+β	α+(α+β	NOUN
ejpam-6366	84	15	)	)	PUNCT
ejpam-6366	84	16	(	(	PUNCT
ejpam-6366	84	17	e−iθ+q	e−iθ+q	X
ejpam-6366	84	18	(	(	PUNCT
ejpam-6366	84	19	1−γ)(p−q	1−γ)(p−q	NUM
ejpam-6366	84	20	)	)	PUNCT
ejpam-6366	84	21	+1	+1	NOUN
ejpam-6366	84	22	)	)	PUNCT
ejpam-6366	84	23	α+β	α+β	PROPN
ejpam-6366	85	1	ξ2	ξ2	NOUN
ejpam-6366	85	2	+	+	CCONJ
ejpam-6366	85	3	α	α	PROPN
ejpam-6366	85	4	(	(	PUNCT
ejpam-6366	85	5	e−iθ+q	e−iθ+q	X
ejpam-6366	85	6	(	(	PUNCT
ejpam-6366	85	7	1−γ)(p−q	1−γ)(p−q	NUM
ejpam-6366	85	8	)	)	PUNCT
ejpam-6366	85	9	+1	+1	NOUN
ejpam-6366	85	10	)	)	PUNCT
ejpam-6366	85	11	α+β	α+β	PROPN
ejpam-6366	85	12	ξ3	ξ3	NOUN
ejpam-6366	85	13	(	(	PUNCT
ejpam-6366	85	14	1−	1−	NUM
ejpam-6366	85	15	ξ)2	ξ)2	PROPN
ejpam-6366	85	16			NUM
ejpam-6366	85	17	̸=	̸=	PROPN
ejpam-6366	85	18	0	0	NUM
ejpam-6366	85	19	which	which	PRON
ejpam-6366	85	20	explains	explain	VERB
ejpam-6366	85	21	the	the	DET
ejpam-6366	85	22	necessary	necessary	ADJ
ejpam-6366	85	23	condition	condition	NOUN
ejpam-6366	85	24	(	(	PUNCT
ejpam-6366	85	25	12	12	NUM
ejpam-6366	85	26	)	)	PUNCT
ejpam-6366	85	27	for	for	ADP
ejpam-6366	85	28	this	this	DET
ejpam-6366	85	29	theorem	theorem	NOUN
ejpam-6366	85	30	.	.	PUNCT
ejpam-6366	85	31	reversely	reversely	ADV
ejpam-6366	85	32	,	,	PUNCT
ejpam-6366	85	33	assume	assume	VERB
ejpam-6366	85	34	that	that	SCONJ
ejpam-6366	85	35	g	g	PROPN
ejpam-6366	85	36	∈	∈	PROPN
ejpam-6366	85	37	h	h	NOUN
ejpam-6366	85	38	satisfies	satisfie	NOUN
ejpam-6366	85	39	(	(	PUNCT
ejpam-6366	85	40	12	12	NUM
ejpam-6366	85	41	)	)	PUNCT
ejpam-6366	85	42	.	.	PUNCT
ejpam-6366	86	1	since	since	SCONJ
ejpam-6366	86	2	the	the	DET
ejpam-6366	86	3	first	first	ADJ
ejpam-6366	86	4	part	part	NOUN
ejpam-6366	86	5	has	have	AUX
ejpam-6366	86	6	been	be	AUX
ejpam-6366	86	7	proven	prove	VERB
ejpam-6366	86	8	,	,	PUNCT
ejpam-6366	86	9	assumption	assumption	NOUN
ejpam-6366	86	10	(	(	PUNCT
ejpam-6366	86	11	12	12	NUM
ejpam-6366	86	12	)	)	PUNCT
ejpam-6366	86	13	is	be	AUX
ejpam-6366	86	14	equivalent	equivalent	ADJ
ejpam-6366	86	15	to	to	ADP
ejpam-6366	86	16	(	(	PUNCT
ejpam-6366	86	17	16	16	NUM
ejpam-6366	86	18	)	)	PUNCT
ejpam-6366	86	19	,	,	PUNCT
ejpam-6366	86	20	so	so	ADV
ejpam-6366	86	21	we	we	PRON
ejpam-6366	86	22	get	get	VERB
ejpam-6366	86	23	that	that	DET
ejpam-6366	86	24	αg	αg	NOUN
ejpam-6366	86	25	(	(	PUNCT
ejpam-6366	86	26	ξ	ξ	NOUN
ejpam-6366	86	27	)	)	PUNCT
ejpam-6366	86	28	+	+	NUM
ejpam-6366	86	29	βξg′	βξg′	NUM
ejpam-6366	86	30	(	(	PUNCT
ejpam-6366	86	31	ξ	ξ	NOUN
ejpam-6366	86	32	)	)	PUNCT
ejpam-6366	86	33	αξ	αξ	NOUN
ejpam-6366	87	1	+	+	NUM
ejpam-6366	87	2	βg	βg	PROPN
ejpam-6366	87	3	(	(	PUNCT
ejpam-6366	87	4	ξ	ξ	NOUN
ejpam-6366	87	5	)	)	PUNCT
ejpam-6366	87	6	̸=	̸=	NOUN
ejpam-6366	87	7	1	1	NUM
ejpam-6366	88	1	+	+	CCONJ
ejpam-6366	88	2	[	[	X
ejpam-6366	88	3	q+	q+	X
ejpam-6366	88	4	(	(	PUNCT
ejpam-6366	88	5	1−	1−	NUM
ejpam-6366	88	6	γ	γ	NOUN
ejpam-6366	88	7	)	)	PUNCT
ejpam-6366	88	8	(	(	PUNCT
ejpam-6366	88	9	p	p	NOUN
ejpam-6366	88	10	−q	−q	NOUN
ejpam-6366	88	11	)	)	PUNCT
ejpam-6366	88	12	]	]	PUNCT
ejpam-6366	89	1	eiθ	eiθ	PROPN
ejpam-6366	89	2	1	1	NUM
ejpam-6366	89	3	+	+	NOUN
ejpam-6366	89	4	qeiθ	qeiθ	NOUN
ejpam-6366	89	5	,	,	PUNCT
ejpam-6366	89	6	(	(	PUNCT
ejpam-6366	89	7	17	17	NUM
ejpam-6366	89	8	)	)	PUNCT
ejpam-6366	89	9	if	if	SCONJ
ejpam-6366	89	10	we	we	PRON
ejpam-6366	89	11	assume	assume	VERB
ejpam-6366	89	12	to	to	ADP
ejpam-6366	89	13	φ	φ	PROPN
ejpam-6366	89	14	(	(	PUNCT
ejpam-6366	89	15	ξ	ξ	PROPN
ejpam-6366	89	16	)	)	PUNCT
ejpam-6366	89	17	=	=	SYM
ejpam-6366	89	18	αg(ξ)+βξg′(ξ	αg(ξ)+βξg′(ξ	PROPN
ejpam-6366	89	19	)	)	PUNCT
ejpam-6366	89	20	αξ+βg(ξ	αξ+βg(ξ	PROPN
ejpam-6366	89	21	)	)	PUNCT
ejpam-6366	89	22	and	and	CCONJ
ejpam-6366	89	23	ψ	ψ	X
ejpam-6366	89	24	(	(	PUNCT
ejpam-6366	89	25	ξ	ξ	NOUN
ejpam-6366	89	26	)	)	PUNCT
ejpam-6366	89	27	=	=	SYM
ejpam-6366	90	1	1+[q+(1−γ)(p−q)]ξ	1+[q+(1−γ)(p−q)]ξ	NUM
ejpam-6366	90	2	1+qξ	1+qξ	NUM
ejpam-6366	90	3	,	,	PUNCT
ejpam-6366	90	4	the	the	DET
ejpam-6366	90	5	relationship	relationship	NOUN
ejpam-6366	90	6	(	(	PUNCT
ejpam-6366	90	7	17	17	NUM
ejpam-6366	90	8	)	)	PUNCT
ejpam-6366	90	9	indicates	indicate	VERB
ejpam-6366	90	10	that	that	SCONJ
ejpam-6366	90	11	φ	φ	PROPN
ejpam-6366	90	12	(	(	PUNCT
ejpam-6366	90	13	∆	∆	PROPN
ejpam-6366	90	14	)	)	PUNCT
ejpam-6366	90	15	∩	∩	NOUN
ejpam-6366	90	16	ψ	ψ	X
ejpam-6366	90	17	(	(	PUNCT
ejpam-6366	90	18	∂∆	∂∆	NOUN
ejpam-6366	90	19	)	)	PUNCT
ejpam-6366	90	20	=	=	PUNCT
ejpam-6366	90	21	∅.	∅.	VERB
ejpam-6366	90	22	therefore	therefore	ADV
ejpam-6366	90	23	,	,	PUNCT
ejpam-6366	90	24	the	the	DET
ejpam-6366	90	25	simply	simply	ADV
ejpam-6366	90	26	connected	connected	ADJ
ejpam-6366	90	27	domain	domain	NOUN
ejpam-6366	90	28	φ	φ	X
ejpam-6366	90	29	(	(	PUNCT
ejpam-6366	90	30	∆	∆	PROPN
ejpam-6366	90	31	)	)	PUNCT
ejpam-6366	90	32	lies	lie	VERB
ejpam-6366	90	33	inside	inside	ADP
ejpam-6366	90	34	a	a	DET
ejpam-6366	90	35	connected	connected	ADJ
ejpam-6366	90	36	component	component	NOUN
ejpam-6366	90	37	of	of	ADP
ejpam-6366	90	38	c\ψ	c\ψ	PROPN
ejpam-6366	90	39	(	(	PUNCT
ejpam-6366	90	40	∂∆	∂∆	NOUN
ejpam-6366	90	41	)	)	PUNCT
ejpam-6366	90	42	.	.	PUNCT
ejpam-6366	91	1	thus	thus	ADV
ejpam-6366	91	2	,	,	PUNCT
ejpam-6366	91	3	using	use	VERB
ejpam-6366	91	4	the	the	DET
ejpam-6366	91	5	fact	fact	NOUN
ejpam-6366	91	6	that	that	SCONJ
ejpam-6366	91	7	the	the	DET
ejpam-6366	91	8	function	function	NOUN
ejpam-6366	91	9	ψ(ξ	ψ(ξ	PROPN
ejpam-6366	91	10	)	)	PUNCT
ejpam-6366	91	11	is	be	AUX
ejpam-6366	91	12	univalent	univalent	ADJ
ejpam-6366	91	13	and	and	CCONJ
ejpam-6366	91	14	φ	φ	PROPN
ejpam-6366	91	15	(	(	PUNCT
ejpam-6366	91	16	0	0	NUM
ejpam-6366	91	17	)	)	PUNCT
ejpam-6366	91	18	=	=	SYM
ejpam-6366	91	19	ψ	ψ	X
ejpam-6366	91	20	(	(	PUNCT
ejpam-6366	91	21	0	0	NUM
ejpam-6366	91	22	)	)	PUNCT
ejpam-6366	91	23	,	,	PUNCT
ejpam-6366	91	24	it	it	PRON
ejpam-6366	91	25	follows	follow	VERB
ejpam-6366	91	26	that	that	SCONJ
ejpam-6366	91	27	φ	φ	PROPN
ejpam-6366	91	28	(	(	PUNCT
ejpam-6366	91	29	ξ	ξ	NOUN
ejpam-6366	91	30	)	)	PUNCT
ejpam-6366	91	31	≺	≺	NOUN
ejpam-6366	91	32	ψ	ψ	X
ejpam-6366	91	33	(	(	PUNCT
ejpam-6366	91	34	ξ	ξ	NOUN
ejpam-6366	91	35	)	)	PUNCT
ejpam-6366	91	36	,	,	PUNCT
ejpam-6366	91	37	which	which	PRON
ejpam-6366	91	38	means	mean	VERB
ejpam-6366	91	39	that	that	SCONJ
ejpam-6366	91	40	g	g	PROPN
ejpam-6366	91	41	∈	∈	PROPN
ejpam-6366	91	42	sk	sk	VERB
ejpam-6366	92	1	[	[	X
ejpam-6366	92	2	p	p	X
ejpam-6366	92	3	,	,	PUNCT
ejpam-6366	92	4	q	q	NOUN
ejpam-6366	92	5	,	,	PUNCT
ejpam-6366	92	6	γ;α	γ;α	ADV
ejpam-6366	92	7	,	,	PUNCT
ejpam-6366	92	8	β	β	X
ejpam-6366	92	9	]	]	X
ejpam-6366	92	10	.	.	PUNCT
ejpam-6366	93	1	this	this	DET
ejpam-6366	93	2	finishes	finish	NOUN
ejpam-6366	93	3	theorem	theorem	VERB
ejpam-6366	93	4	1	1	NUM
ejpam-6366	93	5	.	.	X
ejpam-6366	93	6	letting	let	VERB
ejpam-6366	93	7	p	p	X
ejpam-6366	93	8	=	=	NOUN
ejpam-6366	93	9	1	1	NUM
ejpam-6366	93	10	and	and	CCONJ
ejpam-6366	93	11	q	q	NOUN
ejpam-6366	93	12	=	=	PUNCT
ejpam-6366	93	13	−1	−1	NOUN
ejpam-6366	93	14	in	in	ADP
ejpam-6366	93	15	theorem	theorem	NOUN
ejpam-6366	93	16	1	1	NUM
ejpam-6366	93	17	,	,	PUNCT
ejpam-6366	93	18	we	we	PRON
ejpam-6366	93	19	get	get	VERB
ejpam-6366	93	20	the	the	DET
ejpam-6366	93	21	following	follow	VERB
ejpam-6366	93	22	result	result	NOUN
ejpam-6366	93	23	.	.	PUNCT
ejpam-6366	94	1	corollary	corollary	ADJ
ejpam-6366	94	2	1	1	NUM
ejpam-6366	94	3	.	.	PUNCT
ejpam-6366	95	1	the	the	DET
ejpam-6366	95	2	function	function	NOUN
ejpam-6366	95	3	g	g	PROPN
ejpam-6366	95	4	∈	∈	PROPN
ejpam-6366	95	5	sk	sk	NOUN
ejpam-6366	95	6	[	[	X
ejpam-6366	95	7	γ;α	γ;α	X
ejpam-6366	95	8	,	,	PUNCT
ejpam-6366	95	9	β	β	X
ejpam-6366	95	10	]	]	X
ejpam-6366	95	11	if	if	SCONJ
ejpam-6366	95	12	and	and	CCONJ
ejpam-6366	95	13	only	only	ADV
ejpam-6366	95	14	if	if	SCONJ
ejpam-6366	95	15	1	1	NUM
ejpam-6366	95	16	ξ	ξ	PROPN
ejpam-6366	95	17	g	g	PROPN
ejpam-6366	95	18	(	(	PUNCT
ejpam-6366	95	19	ξ	ξ	NOUN
ejpam-6366	95	20	)	)	PUNCT
ejpam-6366	95	21	∗	∗	NOUN
ejpam-6366	95	22	ξ	ξ	X
ejpam-6366	95	23	−	−	PROPN
ejpam-6366	96	1	(	(	PUNCT
ejpam-6366	96	2	α+(α+β)t	α+(α+β)t	PROPN
ejpam-6366	96	3	α+β	α+β	NUM
ejpam-6366	96	4	)	)	PUNCT
ejpam-6366	96	5	ξ2	ξ2	NOUN
ejpam-6366	97	1	+	+	CCONJ
ejpam-6366	97	2	(	(	PUNCT
ejpam-6366	97	3	αt	αt	PROPN
ejpam-6366	97	4	α+β	α+β	NUM
ejpam-6366	97	5	)	)	PUNCT
ejpam-6366	97	6	ξ3	ξ3	NOUN
ejpam-6366	97	7	(	(	PUNCT
ejpam-6366	97	8	1−	1−	NUM
ejpam-6366	97	9	ξ)2	ξ)2	NOUN
ejpam-6366	97	10			PROPN
ejpam-6366	97	11	̸=	̸=	PROPN
ejpam-6366	97	12	0	0	NUM
ejpam-6366	97	13	,	,	PUNCT
ejpam-6366	97	14	where	where	SCONJ
ejpam-6366	97	15	t	t	PROPN
ejpam-6366	97	16	is	be	AUX
ejpam-6366	97	17	given	give	VERB
ejpam-6366	97	18	by	by	ADP
ejpam-6366	97	19	t	t	PROPN
ejpam-6366	97	20	=	=	SYM
ejpam-6366	97	21	t	t	PROPN
ejpam-6366	97	22	(	(	PUNCT
ejpam-6366	97	23	θ	θ	PROPN
ejpam-6366	97	24	,	,	PUNCT
ejpam-6366	97	25	γ	γ	NOUN
ejpam-6366	97	26	)	)	PUNCT
ejpam-6366	97	27	=	=	SYM
ejpam-6366	97	28	e−iθ	e−iθ	NOUN
ejpam-6366	97	29	−	−	NOUN
ejpam-6366	97	30	1	1	NUM
ejpam-6366	97	31	2	2	NUM
ejpam-6366	97	32	(	(	PUNCT
ejpam-6366	97	33	1−	1−	NUM
ejpam-6366	97	34	γ	γ	X
ejpam-6366	97	35	)	)	PUNCT
ejpam-6366	97	36	+	+	NOUN
ejpam-6366	97	37	1	1	X
ejpam-6366	97	38	.	.	PUNCT
ejpam-6366	97	39	(	(	PUNCT
ejpam-6366	97	40	18	18	NUM
ejpam-6366	97	41	)	)	PUNCT
ejpam-6366	97	42	t.	t.	NOUN
ejpam-6366	97	43	m.	m.	NOUN
ejpam-6366	97	44	seoudy	seoudy	PROPN
ejpam-6366	97	45	,	,	PUNCT
ejpam-6366	97	46	a.	a.	PROPN
ejpam-6366	97	47	e.	e.	PROPN
ejpam-6366	97	48	shammaky	shammaky	PROPN
ejpam-6366	97	49	/	/	SYM
ejpam-6366	97	50	eur	eur	PROPN
ejpam-6366	97	51	.	.	PUNCT
ejpam-6366	98	1	j.	j.	PROPN
ejpam-6366	98	2	pure	pure	PROPN
ejpam-6366	98	3	appl	appl	PROPN
ejpam-6366	98	4	.	.	PROPN
ejpam-6366	98	5	math	math	PROPN
ejpam-6366	98	6	,	,	PUNCT
ejpam-6366	98	7	18	18	NUM
ejpam-6366	98	8	(	(	PUNCT
ejpam-6366	98	9	4	4	NUM
ejpam-6366	98	10	)	)	PUNCT
ejpam-6366	98	11	(	(	PUNCT
ejpam-6366	98	12	2025	2025	NUM
ejpam-6366	98	13	)	)	PUNCT
ejpam-6366	98	14	,	,	PUNCT
ejpam-6366	98	15	6366	6366	NUM
ejpam-6366	98	16	6	6	NUM
ejpam-6366	98	17	of	of	ADP
ejpam-6366	98	18	15	15	NUM
ejpam-6366	98	19	putting	put	VERB
ejpam-6366	98	20	α	α	NOUN
ejpam-6366	98	21	=	=	SYM
ejpam-6366	98	22	γ	γ	X
ejpam-6366	98	23	=	=	SYM
ejpam-6366	98	24	0	0	NUM
ejpam-6366	98	25	in	in	ADP
ejpam-6366	98	26	theorem	theorem	NOUN
ejpam-6366	98	27	1	1	NUM
ejpam-6366	98	28	,	,	PUNCT
ejpam-6366	98	29	we	we	PRON
ejpam-6366	98	30	have	have	VERB
ejpam-6366	98	31	the	the	DET
ejpam-6366	98	32	next	next	ADJ
ejpam-6366	98	33	corollary	corollary	NOUN
ejpam-6366	98	34	.	.	PUNCT
ejpam-6366	99	1	corollary	corollary	ADJ
ejpam-6366	99	2	2	2	NUM
ejpam-6366	99	3	.	.	PUNCT
ejpam-6366	100	1	the	the	DET
ejpam-6366	100	2	function	function	NOUN
ejpam-6366	100	3	g	g	PROPN
ejpam-6366	100	4	∈	∈	PROPN
ejpam-6366	100	5	s	s	PART
ejpam-6366	101	1	[	[	X
ejpam-6366	101	2	p	p	X
ejpam-6366	101	3	,	,	PUNCT
ejpam-6366	101	4	q	q	X
ejpam-6366	101	5	]	]	X
ejpam-6366	101	6	if	if	SCONJ
ejpam-6366	101	7	and	and	CCONJ
ejpam-6366	101	8	only	only	ADV
ejpam-6366	101	9	if	if	SCONJ
ejpam-6366	101	10	1	1	NUM
ejpam-6366	101	11	ξ	ξ	X
ejpam-6366	101	12	{	{	PUNCT
ejpam-6366	101	13	g	g	PROPN
ejpam-6366	101	14	(	(	PUNCT
ejpam-6366	101	15	ξ	ξ	NOUN
ejpam-6366	101	16	)	)	PUNCT
ejpam-6366	101	17	∗	∗	NOUN
ejpam-6366	101	18	ξ	ξ	X
ejpam-6366	101	19	−rξ2	−rξ2	NUM
ejpam-6366	101	20	(	(	PUNCT
ejpam-6366	101	21	1−	1−	NUM
ejpam-6366	101	22	ξ)2	ξ)2	NOUN
ejpam-6366	101	23	}	}	PUNCT
ejpam-6366	101	24	̸=	̸=	PROPN
ejpam-6366	101	25	0	0	NUM
ejpam-6366	101	26	,	,	PUNCT
ejpam-6366	101	27	where	where	SCONJ
ejpam-6366	101	28	r	r	NOUN
ejpam-6366	101	29	is	be	AUX
ejpam-6366	101	30	given	give	VERB
ejpam-6366	101	31	by	by	ADP
ejpam-6366	101	32	(	(	PUNCT
ejpam-6366	101	33	13	13	NUM
ejpam-6366	101	34	)	)	PUNCT
ejpam-6366	101	35	.	.	PUNCT
ejpam-6366	102	1	putting	put	VERB
ejpam-6366	102	2	β	β	X
ejpam-6366	102	3	=	=	PUNCT
ejpam-6366	102	4	γ	γ	X
ejpam-6366	102	5	=	=	SYM
ejpam-6366	102	6	0	0	NUM
ejpam-6366	102	7	in	in	ADP
ejpam-6366	102	8	theorem	theorem	NOUN
ejpam-6366	102	9	1	1	NUM
ejpam-6366	102	10	,	,	PUNCT
ejpam-6366	102	11	we	we	PRON
ejpam-6366	102	12	get	get	VERB
ejpam-6366	102	13	the	the	DET
ejpam-6366	102	14	next	next	ADJ
ejpam-6366	102	15	.	.	PUNCT
ejpam-6366	103	1	corollary	corollary	ADJ
ejpam-6366	103	2	3	3	NUM
ejpam-6366	103	3	.	.	PUNCT
ejpam-6366	104	1	the	the	DET
ejpam-6366	104	2	function	function	NOUN
ejpam-6366	104	3	g	g	PROPN
ejpam-6366	104	4	∈	∈	PROPN
ejpam-6366	104	5	k	k	PROPN
ejpam-6366	105	1	[	[	X
ejpam-6366	105	2	p	p	X
ejpam-6366	105	3	,	,	PUNCT
ejpam-6366	105	4	q	q	X
ejpam-6366	105	5	]	]	X
ejpam-6366	105	6	if	if	SCONJ
ejpam-6366	105	7	and	and	CCONJ
ejpam-6366	105	8	only	only	ADV
ejpam-6366	105	9	if	if	SCONJ
ejpam-6366	105	10	1	1	NUM
ejpam-6366	105	11	ξ	ξ	X
ejpam-6366	105	12	{	{	PUNCT
ejpam-6366	105	13	g	g	PROPN
ejpam-6366	105	14	(	(	PUNCT
ejpam-6366	105	15	ξ	ξ	NOUN
ejpam-6366	105	16	)	)	PUNCT
ejpam-6366	105	17	∗	∗	NOUN
ejpam-6366	105	18	ξ	ξ	PROPN
ejpam-6366	105	19	−rξ2	−rξ2	NUM
ejpam-6366	105	20	1−	1−	NUM
ejpam-6366	105	21	ξ	ξ	X
ejpam-6366	105	22	}	}	PUNCT
ejpam-6366	105	23	̸=	̸=	PROPN
ejpam-6366	105	24	0	0	NUM
ejpam-6366	105	25	,	,	PUNCT
ejpam-6366	105	26	where	where	SCONJ
ejpam-6366	105	27	r	r	NOUN
ejpam-6366	105	28	is	be	AUX
ejpam-6366	105	29	given	give	VERB
ejpam-6366	105	30	by	by	ADP
ejpam-6366	105	31	(	(	PUNCT
ejpam-6366	105	32	13	13	NUM
ejpam-6366	105	33	)	)	PUNCT
ejpam-6366	105	34	.	.	PUNCT
ejpam-6366	106	1	theorem	theorem	NOUN
ejpam-6366	106	2	2	2	NUM
ejpam-6366	106	3	.	.	PUNCT
ejpam-6366	107	1	the	the	DET
ejpam-6366	107	2	function	function	NOUN
ejpam-6366	107	3	g	g	PROPN
ejpam-6366	107	4	∈	∈	PROPN
ejpam-6366	107	5	sk	sk	NOUN
ejpam-6366	108	1	[	[	X
ejpam-6366	108	2	p	p	X
ejpam-6366	108	3	,	,	PUNCT
ejpam-6366	108	4	q	q	NOUN
ejpam-6366	108	5	,	,	PUNCT
ejpam-6366	108	6	γ;α	γ;α	ADV
ejpam-6366	108	7	,	,	PUNCT
ejpam-6366	108	8	β	β	X
ejpam-6366	108	9	]	]	X
ejpam-6366	108	10	if	if	SCONJ
ejpam-6366	108	11	and	and	CCONJ
ejpam-6366	108	12	only	only	ADV
ejpam-6366	108	13	if	if	SCONJ
ejpam-6366	108	14	1−	1−	NUM
ejpam-6366	108	15	∞∑	∞∑	NUM
ejpam-6366	108	16	j=2	j=2	NOUN
ejpam-6366	108	17	α	α	NOUN
ejpam-6366	108	18	(	(	PUNCT
ejpam-6366	108	19	e−iθ	e−iθ	VERB
ejpam-6366	108	20	+	+	NOUN
ejpam-6366	108	21	q	q	X
ejpam-6366	108	22	)	)	PUNCT
ejpam-6366	109	1	+	+	CCONJ
ejpam-6366	109	2	β	β	X
ejpam-6366	109	3	[	[	PUNCT
ejpam-6366	109	4	(	(	PUNCT
ejpam-6366	109	5	j	j	PROPN
ejpam-6366	109	6	−	−	PROPN
ejpam-6366	109	7	1	1	NUM
ejpam-6366	109	8	)	)	PUNCT
ejpam-6366	109	9	(	(	PUNCT
ejpam-6366	109	10	e−iθ	e−iθ	VERB
ejpam-6366	110	1	+	+	ADJ
ejpam-6366	110	2	q	q	NOUN
ejpam-6366	110	3	)	)	PUNCT
ejpam-6366	110	4	−	−	PROPN
ejpam-6366	110	5	(	(	PUNCT
ejpam-6366	110	6	1−	1−	NUM
ejpam-6366	110	7	γ	γ	NOUN
ejpam-6366	110	8	)	)	PUNCT
ejpam-6366	111	1	(	(	PUNCT
ejpam-6366	111	2	p	p	NOUN
ejpam-6366	111	3	−q	−q	NOUN
ejpam-6366	111	4	)	)	PUNCT
ejpam-6366	111	5	]	]	PUNCT
ejpam-6366	111	6	(	(	PUNCT
ejpam-6366	111	7	α+	α+	X
ejpam-6366	111	8	β	β	X
ejpam-6366	111	9	)	)	PUNCT
ejpam-6366	111	10	(	(	PUNCT
ejpam-6366	111	11	1−	1−	NUM
ejpam-6366	111	12	γ	γ	X
ejpam-6366	111	13	)	)	PUNCT
ejpam-6366	111	14	(	(	PUNCT
ejpam-6366	111	15	p	p	NOUN
ejpam-6366	111	16	−q	−q	NOUN
ejpam-6366	111	17	)	)	PUNCT
ejpam-6366	111	18	djξ	djξ	VERB
ejpam-6366	111	19	j−1	j−1	PROPN
ejpam-6366	111	20	̸=	̸=	PROPN
ejpam-6366	111	21	0	0	NUM
ejpam-6366	111	22	.	.	PUNCT
ejpam-6366	112	1	(	(	PUNCT
ejpam-6366	112	2	19	19	NUM
ejpam-6366	112	3	)	)	PUNCT
ejpam-6366	112	4	proof	proof	NOUN
ejpam-6366	112	5	.	.	PUNCT
ejpam-6366	113	1	from	from	ADP
ejpam-6366	113	2	theorem	theorem	NOUN
ejpam-6366	113	3	1	1	NUM
ejpam-6366	113	4	,	,	PUNCT
ejpam-6366	113	5	we	we	PRON
ejpam-6366	113	6	find	find	VERB
ejpam-6366	113	7	that	that	SCONJ
ejpam-6366	113	8	g(ξ	g(ξ	PROPN
ejpam-6366	113	9	)	)	PUNCT
ejpam-6366	113	10	∈	∈	PROPN
ejpam-6366	113	11	sk	sk	VERB
ejpam-6366	113	12	[	[	X
ejpam-6366	113	13	p	p	X
ejpam-6366	113	14	,	,	PUNCT
ejpam-6366	113	15	q	q	NOUN
ejpam-6366	113	16	,	,	PUNCT
ejpam-6366	113	17	γ;α	γ;α	ADV
ejpam-6366	113	18	,	,	PUNCT
ejpam-6366	113	19	β	β	X
ejpam-6366	113	20	]	]	X
ejpam-6366	113	21	if	if	SCONJ
ejpam-6366	113	22	and	and	CCONJ
ejpam-6366	113	23	only	only	ADV
ejpam-6366	113	24	if	if	SCONJ
ejpam-6366	113	25	1	1	NUM
ejpam-6366	113	26	ξ	ξ	X
ejpam-6366	113	27	g(ξ	g(ξ	NOUN
ejpam-6366	113	28	)	)	PUNCT
ejpam-6366	113	29	∗	∗	NOUN
ejpam-6366	113	30	ξ	ξ	X
ejpam-6366	113	31	−	−	NOUN
ejpam-6366	113	32	α+(α+β)r	α+(α+β)r	PROPN
ejpam-6366	113	33	α+β	α+β	NUM
ejpam-6366	113	34	ξ2	ξ2	NOUN
ejpam-6366	113	35	+	+	CCONJ
ejpam-6366	114	1	αr	αr	NUM
ejpam-6366	114	2	α+β	α+β	NUM
ejpam-6366	114	3	ξ	ξ	SYM
ejpam-6366	114	4	3	3	NUM
ejpam-6366	114	5	(	(	PUNCT
ejpam-6366	114	6	1−	1−	NUM
ejpam-6366	114	7	ξ)2	ξ)2	NOUN
ejpam-6366	114	8			NOUN
ejpam-6366	114	9	̸=	̸=	PROPN
ejpam-6366	114	10	0	0	NUM
ejpam-6366	114	11	(	(	PUNCT
ejpam-6366	114	12	20	20	NUM
ejpam-6366	114	13	)	)	PUNCT
ejpam-6366	114	14	for	for	ADP
ejpam-6366	114	15	all	all	DET
ejpam-6366	114	16	r	r	NOUN
ejpam-6366	114	17	given	give	VERB
ejpam-6366	114	18	by	by	ADP
ejpam-6366	114	19	(	(	PUNCT
ejpam-6366	114	20	13	13	NUM
ejpam-6366	114	21	)	)	PUNCT
ejpam-6366	114	22	.	.	PUNCT
ejpam-6366	115	1	the	the	DET
ejpam-6366	115	2	left	left	ADJ
ejpam-6366	115	3	hand	hand	NOUN
ejpam-6366	115	4	side	side	NOUN
ejpam-6366	115	5	of	of	ADP
ejpam-6366	115	6	(	(	PUNCT
ejpam-6366	115	7	20	20	NUM
ejpam-6366	115	8	)	)	PUNCT
ejpam-6366	115	9	can	can	AUX
ejpam-6366	115	10	be	be	AUX
ejpam-6366	115	11	written	write	VERB
ejpam-6366	115	12	as	as	ADP
ejpam-6366	115	13	1	1	NUM
ejpam-6366	115	14	ξ	ξ	PROPN
ejpam-6366	115	15	g(ξ	g(ξ	NOUN
ejpam-6366	115	16	)	)	PUNCT
ejpam-6366	115	17	∗	∗	VERB
ejpam-6366	115	18			PROPN
ejpam-6366	115	19	αr	αr	ADP
ejpam-6366	115	20	α+	α+	NOUN
ejpam-6366	115	21	β	β	X
ejpam-6366	115	22	ξ	ξ	PROPN
ejpam-6366	115	23	+	+	CCONJ
ejpam-6366	115	24	(	(	PUNCT
ejpam-6366	115	25	α+(β−α)r	α+(β−α)r	NOUN
ejpam-6366	115	26	α+β	α+β	NUM
ejpam-6366	115	27	)	)	PUNCT
ejpam-6366	116	1	ξ	ξ	PROPN
ejpam-6366	116	2	1−	1−	NUM
ejpam-6366	116	3	ξ	ξ	NOUN
ejpam-6366	116	4	+	+	CCONJ
ejpam-6366	116	5	(	(	PUNCT
ejpam-6366	116	6	β(1−r	β(1−r	ADJ
ejpam-6366	116	7	)	)	PUNCT
ejpam-6366	116	8	α+β	α+β	NUM
ejpam-6366	116	9	)	)	PUNCT
ejpam-6366	117	1	ξ	ξ	PROPN
ejpam-6366	117	2	(	(	PUNCT
ejpam-6366	117	3	1−	1−	NUM
ejpam-6366	117	4	ξ)2	ξ)2	NOUN
ejpam-6366	117	5			NOUN
ejpam-6366	118	1	=	=	NOUN
ejpam-6366	118	2	1	1	NUM
ejpam-6366	118	3	ξ	ξ	X
ejpam-6366	118	4	{	{	PUNCT
ejpam-6366	118	5	(	(	PUNCT
ejpam-6366	118	6	αr	αr	INTJ
ejpam-6366	118	7	α+	α+	NOUN
ejpam-6366	118	8	β	β	X
ejpam-6366	118	9	)	)	PUNCT
ejpam-6366	119	1	ξ	ξ	PROPN
ejpam-6366	120	1	+	+	PUNCT
ejpam-6366	120	2	(	(	PUNCT
ejpam-6366	120	3	α+	α+	X
ejpam-6366	120	4	(	(	PUNCT
ejpam-6366	120	5	β	β	NOUN
ejpam-6366	120	6	−	−	NOUN
ejpam-6366	120	7	α)r	α)r	X
ejpam-6366	120	8	α+	α+	PRON
ejpam-6366	120	9	β	β	X
ejpam-6366	120	10	)	)	PUNCT
ejpam-6366	120	11	g	g	PROPN
ejpam-6366	120	12	(	(	PUNCT
ejpam-6366	120	13	ξ	ξ	NOUN
ejpam-6366	120	14	)	)	PUNCT
ejpam-6366	120	15	+	+	CCONJ
ejpam-6366	120	16	(	(	PUNCT
ejpam-6366	120	17	β	β	X
ejpam-6366	120	18	(	(	PUNCT
ejpam-6366	120	19	1−r	1−r	NUM
ejpam-6366	120	20	)	)	PUNCT
ejpam-6366	120	21	α+	α+	PRON
ejpam-6366	120	22	β	β	X
ejpam-6366	120	23	)	)	PUNCT
ejpam-6366	120	24	ξg′	ξg′	PROPN
ejpam-6366	120	25	(	(	PUNCT
ejpam-6366	120	26	ξ	ξ	NOUN
ejpam-6366	120	27	)	)	PUNCT
ejpam-6366	120	28	}	}	PUNCT
ejpam-6366	120	29	=	=	SYM
ejpam-6366	121	1	1−	1−	NUM
ejpam-6366	121	2	∞∑	∞∑	NUM
ejpam-6366	121	3	j=2	j=2	PROPN
ejpam-6366	121	4	α	α	NOUN
ejpam-6366	121	5	(	(	PUNCT
ejpam-6366	121	6	r−	r−	PROPN
ejpam-6366	121	7	1	1	NUM
ejpam-6366	121	8	)	)	PUNCT
ejpam-6366	121	9	+	+	CCONJ
ejpam-6366	121	10	β	β	X
ejpam-6366	121	11	(	(	PUNCT
ejpam-6366	121	12	j	j	PROPN
ejpam-6366	121	13	(	(	PUNCT
ejpam-6366	121	14	r−	r−	PROPN
ejpam-6366	121	15	1)−r	1)−r	NUM
ejpam-6366	121	16	)	)	PUNCT
ejpam-6366	121	17	α+	α+	X
ejpam-6366	121	18	β	β	X
ejpam-6366	121	19	djξ	djξ	VERB
ejpam-6366	121	20	j−1	j−1	PROPN
ejpam-6366	121	21	=	=	SYM
ejpam-6366	121	22	1−	1−	NUM
ejpam-6366	122	1	∞∑	∞∑	NUM
ejpam-6366	122	2	j=2	j=2	PROPN
ejpam-6366	122	3	α	α	NOUN
ejpam-6366	122	4	(	(	PUNCT
ejpam-6366	122	5	e−iθ	e−iθ	VERB
ejpam-6366	122	6	+	+	NOUN
ejpam-6366	122	7	q	q	X
ejpam-6366	122	8	)	)	PUNCT
ejpam-6366	123	1	+	+	CCONJ
ejpam-6366	123	2	β	β	X
ejpam-6366	123	3	[	[	PUNCT
ejpam-6366	123	4	(	(	PUNCT
ejpam-6366	123	5	j	j	PROPN
ejpam-6366	123	6	−	−	PROPN
ejpam-6366	123	7	1	1	NUM
ejpam-6366	123	8	)	)	PUNCT
ejpam-6366	123	9	(	(	PUNCT
ejpam-6366	123	10	e−iθ	e−iθ	VERB
ejpam-6366	124	1	+	+	ADJ
ejpam-6366	124	2	q	q	NOUN
ejpam-6366	124	3	)	)	PUNCT
ejpam-6366	124	4	−	−	PROPN
ejpam-6366	124	5	(	(	PUNCT
ejpam-6366	124	6	1−	1−	NUM
ejpam-6366	124	7	γ	γ	NOUN
ejpam-6366	124	8	)	)	PUNCT
ejpam-6366	125	1	(	(	PUNCT
ejpam-6366	125	2	p	p	NOUN
ejpam-6366	125	3	−q	−q	NOUN
ejpam-6366	125	4	)	)	PUNCT
ejpam-6366	125	5	]	]	PUNCT
ejpam-6366	125	6	(	(	PUNCT
ejpam-6366	125	7	α+	α+	X
ejpam-6366	125	8	β	β	X
ejpam-6366	125	9	)	)	PUNCT
ejpam-6366	125	10	(	(	PUNCT
ejpam-6366	125	11	1−	1−	NUM
ejpam-6366	125	12	γ	γ	X
ejpam-6366	125	13	)	)	PUNCT
ejpam-6366	125	14	(	(	PUNCT
ejpam-6366	125	15	p	p	NOUN
ejpam-6366	125	16	−q	−q	NOUN
ejpam-6366	125	17	)	)	PUNCT
ejpam-6366	125	18	djξ	djξ	VERB
ejpam-6366	125	19	j−1	j−1	PROPN
ejpam-6366	125	20	.	.	PUNCT
ejpam-6366	126	1	thus	thus	ADV
ejpam-6366	126	2	,	,	PUNCT
ejpam-6366	126	3	the	the	DET
ejpam-6366	126	4	proof	proof	NOUN
ejpam-6366	126	5	of	of	ADP
ejpam-6366	126	6	theorem	theorem	ADJ
ejpam-6366	126	7	2	2	NUM
ejpam-6366	126	8	is	be	AUX
ejpam-6366	126	9	completed	complete	VERB
ejpam-6366	126	10	.	.	PUNCT
ejpam-6366	127	1	putting	put	VERB
ejpam-6366	127	2	p	p	NOUN
ejpam-6366	127	3	=	=	SYM
ejpam-6366	127	4	1	1	NUM
ejpam-6366	127	5	andq	andq	NOUN
ejpam-6366	127	6	=	=	SYM
ejpam-6366	127	7	−1	−1	NOUN
ejpam-6366	127	8	in	in	ADP
ejpam-6366	127	9	theorem	theorem	NOUN
ejpam-6366	127	10	2	2	NUM
ejpam-6366	127	11	,	,	PUNCT
ejpam-6366	127	12	we	we	PRON
ejpam-6366	127	13	obtain	obtain	VERB
ejpam-6366	127	14	the	the	DET
ejpam-6366	127	15	following	following	ADJ
ejpam-6366	127	16	result	result	NOUN
ejpam-6366	127	17	for	for	ADP
ejpam-6366	127	18	sk	sk	PROPN
ejpam-6366	127	19	[	[	X
ejpam-6366	127	20	γ;α	γ;α	X
ejpam-6366	127	21	,	,	PUNCT
ejpam-6366	127	22	β	β	X
ejpam-6366	127	23	]	]	X
ejpam-6366	127	24	.	.	PUNCT
ejpam-6366	128	1	t.	t.	PROPN
ejpam-6366	128	2	m.	m.	PROPN
ejpam-6366	128	3	seoudy	seoudy	PROPN
ejpam-6366	128	4	,	,	PUNCT
ejpam-6366	128	5	a.	a.	PROPN
ejpam-6366	128	6	e.	e.	PROPN
ejpam-6366	128	7	shammaky	shammaky	PROPN
ejpam-6366	128	8	/	/	SYM
ejpam-6366	128	9	eur	eur	PROPN
ejpam-6366	128	10	.	.	PUNCT
ejpam-6366	129	1	j.	j.	PROPN
ejpam-6366	129	2	pure	pure	PROPN
ejpam-6366	129	3	appl	appl	PROPN
ejpam-6366	129	4	.	.	PROPN
ejpam-6366	129	5	math	math	PROPN
ejpam-6366	129	6	,	,	PUNCT
ejpam-6366	129	7	18	18	NUM
ejpam-6366	129	8	(	(	PUNCT
ejpam-6366	129	9	4	4	NUM
ejpam-6366	129	10	)	)	PUNCT
ejpam-6366	129	11	(	(	PUNCT
ejpam-6366	129	12	2025	2025	NUM
ejpam-6366	129	13	)	)	PUNCT
ejpam-6366	129	14	,	,	PUNCT
ejpam-6366	129	15	6366	6366	NUM
ejpam-6366	129	16	7	7	NUM
ejpam-6366	129	17	of	of	ADP
ejpam-6366	129	18	15	15	NUM
ejpam-6366	129	19	corollary	corollary	ADJ
ejpam-6366	129	20	4	4	NUM
ejpam-6366	129	21	.	.	PUNCT
ejpam-6366	130	1	the	the	DET
ejpam-6366	130	2	function	function	NOUN
ejpam-6366	130	3	g	g	PROPN
ejpam-6366	130	4	∈	∈	PROPN
ejpam-6366	130	5	sk	sk	NOUN
ejpam-6366	130	6	[	[	X
ejpam-6366	130	7	γ;α	γ;α	X
ejpam-6366	130	8	,	,	PUNCT
ejpam-6366	130	9	β	β	X
ejpam-6366	130	10	]	]	X
ejpam-6366	130	11	if	if	SCONJ
ejpam-6366	130	12	and	and	CCONJ
ejpam-6366	130	13	only	only	ADV
ejpam-6366	130	14	if	if	SCONJ
ejpam-6366	130	15	1−	1−	NUM
ejpam-6366	130	16	∞∑	∞∑	NUM
ejpam-6366	130	17	j=2	j=2	NOUN
ejpam-6366	130	18	α	α	NOUN
ejpam-6366	130	19	(	(	PUNCT
ejpam-6366	130	20	e−iθ	e−iθ	NOUN
ejpam-6366	130	21	−	−	PROPN
ejpam-6366	130	22	1	1	NUM
ejpam-6366	130	23	)	)	PUNCT
ejpam-6366	130	24	+	+	CCONJ
ejpam-6366	130	25	β	β	X
ejpam-6366	130	26	[	[	PUNCT
ejpam-6366	130	27	(	(	PUNCT
ejpam-6366	130	28	j	j	PROPN
ejpam-6366	130	29	−	−	PROPN
ejpam-6366	130	30	1	1	NUM
ejpam-6366	130	31	)	)	PUNCT
ejpam-6366	130	32	(	(	PUNCT
ejpam-6366	130	33	e−iθ	e−iθ	NOUN
ejpam-6366	130	34	−	−	PROPN
ejpam-6366	130	35	1	1	NUM
ejpam-6366	130	36	)	)	PUNCT
ejpam-6366	130	37	−	−	PROPN
ejpam-6366	130	38	2	2	NUM
ejpam-6366	130	39	(	(	PUNCT
ejpam-6366	130	40	1−	1−	NUM
ejpam-6366	130	41	γ	γ	NOUN
ejpam-6366	130	42	)	)	PUNCT
ejpam-6366	130	43	]	]	PUNCT
ejpam-6366	130	44	2	2	NUM
ejpam-6366	130	45	(	(	PUNCT
ejpam-6366	130	46	α+	α+	X
ejpam-6366	130	47	β	β	X
ejpam-6366	130	48	)	)	PUNCT
ejpam-6366	130	49	(	(	PUNCT
ejpam-6366	130	50	1−	1−	NUM
ejpam-6366	130	51	γ	γ	X
ejpam-6366	130	52	)	)	PUNCT
ejpam-6366	130	53	djξ	djξ	VERB
ejpam-6366	130	54	j−1	j−1	PROPN
ejpam-6366	130	55	̸=	̸=	PROPN
ejpam-6366	130	56	0	0	NUM
ejpam-6366	130	57	.	.	PUNCT
ejpam-6366	131	1	putting	put	VERB
ejpam-6366	131	2	α	α	NOUN
ejpam-6366	131	3	=	=	SYM
ejpam-6366	131	4	γ	γ	X
ejpam-6366	131	5	=	=	SYM
ejpam-6366	131	6	0	0	NUM
ejpam-6366	131	7	in	in	ADP
ejpam-6366	131	8	theorem	theorem	NOUN
ejpam-6366	131	9	2	2	NUM
ejpam-6366	131	10	,	,	PUNCT
ejpam-6366	131	11	we	we	PRON
ejpam-6366	131	12	obtain	obtain	VERB
ejpam-6366	131	13	the	the	DET
ejpam-6366	131	14	following	following	ADJ
ejpam-6366	131	15	result	result	NOUN
ejpam-6366	131	16	for	for	ADP
ejpam-6366	131	17	s	s	PROPN
ejpam-6366	131	18	[	[	X
ejpam-6366	131	19	p	p	X
ejpam-6366	131	20	,	,	PUNCT
ejpam-6366	131	21	q	q	NOUN
ejpam-6366	131	22	]	]	X
ejpam-6366	131	23	.	.	PUNCT
ejpam-6366	132	1	corollary	corollary	ADJ
ejpam-6366	132	2	5	5	NUM
ejpam-6366	132	3	.	.	PUNCT
ejpam-6366	133	1	the	the	DET
ejpam-6366	133	2	function	function	NOUN
ejpam-6366	133	3	g	g	PROPN
ejpam-6366	133	4	∈	∈	PROPN
ejpam-6366	133	5	s	s	PART
ejpam-6366	134	1	[	[	X
ejpam-6366	134	2	p	p	X
ejpam-6366	134	3	,	,	PUNCT
ejpam-6366	134	4	q	q	X
ejpam-6366	134	5	]	]	X
ejpam-6366	134	6	if	if	SCONJ
ejpam-6366	134	7	and	and	CCONJ
ejpam-6366	134	8	only	only	ADV
ejpam-6366	134	9	if	if	SCONJ
ejpam-6366	134	10	1−	1−	NUM
ejpam-6366	134	11	∞∑	∞∑	NUM
ejpam-6366	134	12	j=2	j=2	PROPN
ejpam-6366	134	13	(	(	PUNCT
ejpam-6366	134	14	j	j	PROPN
ejpam-6366	134	15	−	−	PROPN
ejpam-6366	134	16	1	1	NUM
ejpam-6366	134	17	)	)	PUNCT
ejpam-6366	134	18	(	(	PUNCT
ejpam-6366	134	19	e−iθ	e−iθ	VERB
ejpam-6366	134	20	+	+	ADJ
ejpam-6366	134	21	q	q	NOUN
ejpam-6366	134	22	)	)	PUNCT
ejpam-6366	134	23	−	−	PROPN
ejpam-6366	135	1	p	p	NOUN
ejpam-6366	136	1	+	+	NOUN
ejpam-6366	136	2	q	q	NOUN
ejpam-6366	136	3	p	p	NOUN
ejpam-6366	136	4	−q	−q	ADJ
ejpam-6366	136	5	djξ	djξ	VERB
ejpam-6366	136	6	j−1	j−1	PROPN
ejpam-6366	136	7	̸=	̸=	PROPN
ejpam-6366	136	8	0	0	NUM
ejpam-6366	136	9	.	.	PUNCT
ejpam-6366	137	1	putting	put	VERB
ejpam-6366	137	2	β	β	X
ejpam-6366	137	3	=	=	PUNCT
ejpam-6366	137	4	γ	γ	X
ejpam-6366	137	5	=	=	SYM
ejpam-6366	137	6	0	0	NUM
ejpam-6366	137	7	in	in	ADP
ejpam-6366	137	8	theorem	theorem	NOUN
ejpam-6366	137	9	2	2	NUM
ejpam-6366	137	10	,	,	PUNCT
ejpam-6366	137	11	we	we	PRON
ejpam-6366	137	12	obtain	obtain	VERB
ejpam-6366	137	13	the	the	DET
ejpam-6366	137	14	following	following	ADJ
ejpam-6366	137	15	result	result	NOUN
ejpam-6366	137	16	for	for	ADP
ejpam-6366	137	17	k	k	PROPN
ejpam-6366	138	1	[	[	X
ejpam-6366	138	2	p	p	X
ejpam-6366	138	3	,	,	PUNCT
ejpam-6366	138	4	q	q	NOUN
ejpam-6366	138	5	]	]	X
ejpam-6366	138	6	.	.	PUNCT
ejpam-6366	139	1	corollary	corollary	ADJ
ejpam-6366	139	2	6	6	NUM
ejpam-6366	139	3	.	.	PUNCT
ejpam-6366	140	1	the	the	DET
ejpam-6366	140	2	function	function	NOUN
ejpam-6366	140	3	g	g	PROPN
ejpam-6366	140	4	∈	∈	PROPN
ejpam-6366	140	5	k	k	PROPN
ejpam-6366	141	1	[	[	X
ejpam-6366	141	2	p	p	X
ejpam-6366	141	3	,	,	PUNCT
ejpam-6366	141	4	q	q	X
ejpam-6366	141	5	]	]	X
ejpam-6366	141	6	if	if	SCONJ
ejpam-6366	141	7	and	and	CCONJ
ejpam-6366	141	8	only	only	ADV
ejpam-6366	141	9	if	if	SCONJ
ejpam-6366	141	10	1−	1−	NUM
ejpam-6366	141	11	∞∑	∞∑	NUM
ejpam-6366	141	12	j=2	j=2	NOUN
ejpam-6366	141	13	e−iθ	e−iθ	NOUN
ejpam-6366	141	14	+	+	ADP
ejpam-6366	141	15	q	q	X
ejpam-6366	141	16	p	p	NOUN
ejpam-6366	141	17	−q	−q	ADJ
ejpam-6366	141	18	djξ	djξ	VERB
ejpam-6366	141	19	j−1	j−1	PROPN
ejpam-6366	141	20	̸=	̸=	PROPN
ejpam-6366	141	21	0	0	NUM
ejpam-6366	141	22	.	.	PUNCT
ejpam-6366	142	1	theorem	theorem	NOUN
ejpam-6366	142	2	3	3	NUM
ejpam-6366	142	3	.	.	PUNCT
ejpam-6366	143	1	if	if	SCONJ
ejpam-6366	143	2	the	the	DET
ejpam-6366	143	3	function	function	NOUN
ejpam-6366	143	4	g(ξ	g(ξ	PROPN
ejpam-6366	143	5	)	)	PUNCT
ejpam-6366	143	6	satisfy	satisfy	VERB
ejpam-6366	143	7	the	the	DET
ejpam-6366	143	8	inequality	inequality	NOUN
ejpam-6366	143	9	∞∑	∞∑	PROPN
ejpam-6366	143	10	j=2	j=2	PROPN
ejpam-6366	143	11	{	{	PUNCT
ejpam-6366	143	12	α	α	PROPN
ejpam-6366	143	13	(	(	PUNCT
ejpam-6366	143	14	1−q	1−q	NUM
ejpam-6366	143	15	)	)	PUNCT
ejpam-6366	143	16	+	+	NOUN
ejpam-6366	143	17	β	β	X
ejpam-6366	144	1	[	[	X
ejpam-6366	144	2	(	(	PUNCT
ejpam-6366	144	3	j	j	PROPN
ejpam-6366	144	4	−	−	PROPN
ejpam-6366	144	5	1	1	NUM
ejpam-6366	144	6	)	)	PUNCT
ejpam-6366	144	7	(	(	PUNCT
ejpam-6366	144	8	1−q	1−q	NUM
ejpam-6366	144	9	)	)	PUNCT
ejpam-6366	144	10	+	+	CCONJ
ejpam-6366	144	11	(	(	PUNCT
ejpam-6366	144	12	1−	1−	NUM
ejpam-6366	144	13	γ	γ	X
ejpam-6366	144	14	)	)	PUNCT
ejpam-6366	144	15	(	(	PUNCT
ejpam-6366	144	16	p	p	NOUN
ejpam-6366	144	17	−q	−q	NOUN
ejpam-6366	144	18	)	)	PUNCT
ejpam-6366	144	19	]	]	PUNCT
ejpam-6366	144	20	}	}	PUNCT
ejpam-6366	144	21	|dj	|dj	PUNCT
ejpam-6366	144	22	|	|	ADV
ejpam-6366	144	23	≤	≤	NUM
ejpam-6366	144	24	(	(	PUNCT
ejpam-6366	144	25	α+	α+	X
ejpam-6366	144	26	β	β	X
ejpam-6366	144	27	)	)	PUNCT
ejpam-6366	144	28	(	(	PUNCT
ejpam-6366	144	29	p	p	NOUN
ejpam-6366	144	30	−q	−q	NOUN
ejpam-6366	144	31	)	)	PUNCT
ejpam-6366	144	32	,	,	PUNCT
ejpam-6366	144	33	(	(	PUNCT
ejpam-6366	144	34	21	21	NUM
ejpam-6366	144	35	)	)	PUNCT
ejpam-6366	144	36	then	then	ADV
ejpam-6366	144	37	g	g	PROPN
ejpam-6366	144	38	∈	∈	PROPN
ejpam-6366	144	39	sk	sk	VERB
ejpam-6366	145	1	[	[	X
ejpam-6366	145	2	p	p	X
ejpam-6366	145	3	,	,	PUNCT
ejpam-6366	145	4	q	q	NOUN
ejpam-6366	145	5	,	,	PUNCT
ejpam-6366	145	6	γ;α	γ;α	ADV
ejpam-6366	145	7	,	,	PUNCT
ejpam-6366	145	8	β	β	X
ejpam-6366	145	9	]	]	PUNCT
ejpam-6366	145	10	.	.	PUNCT
ejpam-6366	146	1	proof	proof	NOUN
ejpam-6366	146	2	.	.	PUNCT
ejpam-6366	147	1	note	note	VERB
ejpam-6366	147	2	that∣∣∣∣∣∣1−	that∣∣∣∣∣∣1−	PROPN
ejpam-6366	147	3	∞∑	∞∑	ADJ
ejpam-6366	147	4	j=2	j=2	PROPN
ejpam-6366	147	5	α	α	NOUN
ejpam-6366	147	6	(	(	PUNCT
ejpam-6366	147	7	e−iθ	e−iθ	VERB
ejpam-6366	147	8	+	+	NOUN
ejpam-6366	147	9	q	q	X
ejpam-6366	147	10	)	)	PUNCT
ejpam-6366	148	1	+	+	CCONJ
ejpam-6366	148	2	β	β	X
ejpam-6366	148	3	[	[	PUNCT
ejpam-6366	148	4	(	(	PUNCT
ejpam-6366	148	5	j	j	PROPN
ejpam-6366	148	6	−	−	PROPN
ejpam-6366	148	7	1	1	NUM
ejpam-6366	148	8	)	)	PUNCT
ejpam-6366	148	9	(	(	PUNCT
ejpam-6366	148	10	e−iθ	e−iθ	VERB
ejpam-6366	149	1	+	+	ADJ
ejpam-6366	149	2	q	q	NOUN
ejpam-6366	149	3	)	)	PUNCT
ejpam-6366	149	4	−	−	PROPN
ejpam-6366	149	5	(	(	PUNCT
ejpam-6366	149	6	1−	1−	NUM
ejpam-6366	149	7	γ	γ	NOUN
ejpam-6366	149	8	)	)	PUNCT
ejpam-6366	150	1	(	(	PUNCT
ejpam-6366	150	2	p	p	NOUN
ejpam-6366	150	3	−q	−q	NOUN
ejpam-6366	150	4	)	)	PUNCT
ejpam-6366	150	5	]	]	PUNCT
ejpam-6366	150	6	(	(	PUNCT
ejpam-6366	150	7	α+	α+	X
ejpam-6366	150	8	β	β	X
ejpam-6366	150	9	)	)	PUNCT
ejpam-6366	150	10	(	(	PUNCT
ejpam-6366	150	11	1−	1−	NUM
ejpam-6366	150	12	γ	γ	X
ejpam-6366	150	13	)	)	PUNCT
ejpam-6366	150	14	(	(	PUNCT
ejpam-6366	150	15	p	p	NOUN
ejpam-6366	150	16	−q	−q	NOUN
ejpam-6366	150	17	)	)	PUNCT
ejpam-6366	150	18	djξ	djξ	VERB
ejpam-6366	150	19	j−1	j−1	PROPN
ejpam-6366	150	20	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6366	150	21	≥	≥	NOUN
ejpam-6366	150	22	1−	1−	NUM
ejpam-6366	150	23	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6366	150	24	∞∑	∞∑	NUM
ejpam-6366	150	25	j=2	j=2	PROPN
ejpam-6366	150	26	α	α	NOUN
ejpam-6366	150	27	(	(	PUNCT
ejpam-6366	150	28	e−iθ	e−iθ	VERB
ejpam-6366	151	1	+	+	NOUN
ejpam-6366	151	2	q	q	X
ejpam-6366	151	3	)	)	PUNCT
ejpam-6366	152	1	+	+	CCONJ
ejpam-6366	152	2	(	(	PUNCT
ejpam-6366	152	3	β	β	NOUN
ejpam-6366	152	4	)	)	PUNCT
ejpam-6366	152	5	[	[	PUNCT
ejpam-6366	152	6	(	(	PUNCT
ejpam-6366	152	7	j	j	NOUN
ejpam-6366	152	8	−	−	PROPN
ejpam-6366	152	9	1	1	NUM
ejpam-6366	152	10	)	)	PUNCT
ejpam-6366	152	11	(	(	PUNCT
ejpam-6366	152	12	e−iθ	e−iθ	VERB
ejpam-6366	152	13	+	+	ADJ
ejpam-6366	152	14	q	q	NOUN
ejpam-6366	152	15	)	)	PUNCT
ejpam-6366	152	16	−	−	PROPN
ejpam-6366	152	17	(	(	PUNCT
ejpam-6366	152	18	1−	1−	NUM
ejpam-6366	152	19	γ	γ	NOUN
ejpam-6366	152	20	)	)	PUNCT
ejpam-6366	152	21	(	(	PUNCT
ejpam-6366	152	22	p	p	NOUN
ejpam-6366	152	23	−q	−q	NOUN
ejpam-6366	152	24	)	)	PUNCT
ejpam-6366	152	25	]	]	PUNCT
ejpam-6366	153	1	(	(	PUNCT
ejpam-6366	153	2	α+	α+	X
ejpam-6366	153	3	β	β	X
ejpam-6366	153	4	)	)	PUNCT
ejpam-6366	153	5	(	(	PUNCT
ejpam-6366	153	6	1−	1−	NUM
ejpam-6366	153	7	γ	γ	X
ejpam-6366	153	8	)	)	PUNCT
ejpam-6366	153	9	(	(	PUNCT
ejpam-6366	153	10	p	p	NOUN
ejpam-6366	153	11	−q	−q	NOUN
ejpam-6366	153	12	)	)	PUNCT
ejpam-6366	153	13	djξ	djξ	VERB
ejpam-6366	153	14	j−1	j−1	PROPN
ejpam-6366	153	15	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6366	153	16	≥	≥	NOUN
ejpam-6366	153	17	1−	1−	NUM
ejpam-6366	154	1	∞∑	∞∑	NUM
ejpam-6366	154	2	j=2	j=2	PROPN
ejpam-6366	154	3	α	α	NOUN
ejpam-6366	154	4	(	(	PUNCT
ejpam-6366	154	5	1−q	1−q	NUM
ejpam-6366	154	6	)	)	PUNCT
ejpam-6366	155	1	+	+	NOUN
ejpam-6366	155	2	β	β	X
ejpam-6366	156	1	[	[	X
ejpam-6366	156	2	(	(	PUNCT
ejpam-6366	156	3	j	j	PROPN
ejpam-6366	156	4	−	−	PROPN
ejpam-6366	156	5	1	1	NUM
ejpam-6366	156	6	)	)	PUNCT
ejpam-6366	156	7	(	(	PUNCT
ejpam-6366	156	8	1−q	1−q	NUM
ejpam-6366	156	9	)	)	PUNCT
ejpam-6366	156	10	+	+	CCONJ
ejpam-6366	156	11	(	(	PUNCT
ejpam-6366	156	12	1−	1−	NUM
ejpam-6366	156	13	γ	γ	X
ejpam-6366	156	14	)	)	PUNCT
ejpam-6366	156	15	(	(	PUNCT
ejpam-6366	156	16	p	p	NOUN
ejpam-6366	156	17	−q	−q	NOUN
ejpam-6366	156	18	)	)	PUNCT
ejpam-6366	156	19	]	]	PUNCT
ejpam-6366	156	20	(	(	PUNCT
ejpam-6366	156	21	α+	α+	X
ejpam-6366	156	22	β	β	X
ejpam-6366	156	23	)	)	PUNCT
ejpam-6366	156	24	(	(	PUNCT
ejpam-6366	156	25	1−	1−	NUM
ejpam-6366	156	26	γ	γ	X
ejpam-6366	156	27	)	)	PUNCT
ejpam-6366	156	28	(	(	PUNCT
ejpam-6366	156	29	p	p	NOUN
ejpam-6366	156	30	−q	−q	NOUN
ejpam-6366	156	31	)	)	PUNCT
ejpam-6366	156	32	|dj	|dj	PUNCT
ejpam-6366	156	33	|	|	ADV
ejpam-6366	156	34	>	>	X
ejpam-6366	156	35	0	0	X
ejpam-6366	156	36	.	.	PUNCT
ejpam-6366	157	1	thus	thus	ADV
ejpam-6366	157	2	,	,	PUNCT
ejpam-6366	157	3	the	the	DET
ejpam-6366	157	4	inequality	inequality	NOUN
ejpam-6366	157	5	(	(	PUNCT
ejpam-6366	157	6	21	21	NUM
ejpam-6366	157	7	)	)	PUNCT
ejpam-6366	157	8	holds	hold	VERB
ejpam-6366	157	9	and	and	CCONJ
ejpam-6366	157	10	our	our	PRON
ejpam-6366	157	11	result	result	NOUN
ejpam-6366	157	12	follows	follow	VERB
ejpam-6366	157	13	from	from	ADP
ejpam-6366	157	14	theorem	theorem	ADJ
ejpam-6366	157	15	3	3	NUM
ejpam-6366	157	16	.	.	PUNCT
ejpam-6366	157	17	putting	put	VERB
ejpam-6366	157	18	p	p	NOUN
ejpam-6366	157	19	=	=	SYM
ejpam-6366	157	20	1	1	NUM
ejpam-6366	157	21	andq	andq	NOUN
ejpam-6366	157	22	=	=	SYM
ejpam-6366	157	23	−1	−1	NOUN
ejpam-6366	157	24	in	in	ADP
ejpam-6366	157	25	theorem	theorem	NOUN
ejpam-6366	157	26	3	3	NUM
ejpam-6366	157	27	,	,	PUNCT
ejpam-6366	157	28	we	we	PRON
ejpam-6366	157	29	obtain	obtain	VERB
ejpam-6366	157	30	the	the	DET
ejpam-6366	157	31	following	following	ADJ
ejpam-6366	157	32	result	result	NOUN
ejpam-6366	157	33	for	for	ADP
ejpam-6366	157	34	sk	sk	PROPN
ejpam-6366	157	35	[	[	X
ejpam-6366	157	36	γ;α	γ;α	X
ejpam-6366	157	37	,	,	PUNCT
ejpam-6366	157	38	β	β	X
ejpam-6366	157	39	]	]	X
ejpam-6366	157	40	.	.	PUNCT
ejpam-6366	158	1	t.	t.	PROPN
ejpam-6366	158	2	m.	m.	PROPN
ejpam-6366	158	3	seoudy	seoudy	PROPN
ejpam-6366	158	4	,	,	PUNCT
ejpam-6366	158	5	a.	a.	PROPN
ejpam-6366	158	6	e.	e.	PROPN
ejpam-6366	158	7	shammaky	shammaky	PROPN
ejpam-6366	158	8	/	/	SYM
ejpam-6366	158	9	eur	eur	PROPN
ejpam-6366	158	10	.	.	PUNCT
ejpam-6366	159	1	j.	j.	PROPN
ejpam-6366	159	2	pure	pure	PROPN
ejpam-6366	159	3	appl	appl	PROPN
ejpam-6366	159	4	.	.	PROPN
ejpam-6366	159	5	math	math	PROPN
ejpam-6366	159	6	,	,	PUNCT
ejpam-6366	159	7	18	18	NUM
ejpam-6366	159	8	(	(	PUNCT
ejpam-6366	159	9	4	4	NUM
ejpam-6366	159	10	)	)	PUNCT
ejpam-6366	159	11	(	(	PUNCT
ejpam-6366	159	12	2025	2025	NUM
ejpam-6366	159	13	)	)	PUNCT
ejpam-6366	159	14	,	,	PUNCT
ejpam-6366	159	15	6366	6366	NUM
ejpam-6366	159	16	8	8	NUM
ejpam-6366	159	17	of	of	ADP
ejpam-6366	159	18	15	15	NUM
ejpam-6366	159	19	corollary	corollary	ADJ
ejpam-6366	159	20	7	7	NUM
ejpam-6366	159	21	.	.	PUNCT
ejpam-6366	160	1	if	if	SCONJ
ejpam-6366	160	2	the	the	DET
ejpam-6366	160	3	function	function	NOUN
ejpam-6366	160	4	g(ξ	g(ξ	PROPN
ejpam-6366	160	5	)	)	PUNCT
ejpam-6366	160	6	satisfy	satisfy	VERB
ejpam-6366	160	7	the	the	DET
ejpam-6366	160	8	inequality	inequality	NOUN
ejpam-6366	160	9	∞∑	∞∑	PROPN
ejpam-6366	160	10	j=2	j=2	PROPN
ejpam-6366	161	1	[	[	X
ejpam-6366	161	2	α+	α+	X
ejpam-6366	161	3	β	β	X
ejpam-6366	161	4	(	(	PUNCT
ejpam-6366	161	5	j	j	PROPN
ejpam-6366	161	6	−	−	PROPN
ejpam-6366	161	7	γ	γ	PROPN
ejpam-6366	161	8	)	)	PUNCT
ejpam-6366	161	9	]	]	PUNCT
ejpam-6366	161	10	|dj	|dj	PROPN
ejpam-6366	161	11	|	|	ADV
ejpam-6366	161	12	≤	≤	NUM
ejpam-6366	161	13	(	(	PUNCT
ejpam-6366	161	14	α+	α+	X
ejpam-6366	161	15	β	β	X
ejpam-6366	161	16	)	)	PUNCT
ejpam-6366	161	17	(	(	PUNCT
ejpam-6366	161	18	1−	1−	NUM
ejpam-6366	161	19	γ	γ	X
ejpam-6366	161	20	)	)	PUNCT
ejpam-6366	161	21	,	,	PUNCT
ejpam-6366	161	22	then	then	ADV
ejpam-6366	161	23	g	g	PROPN
ejpam-6366	161	24	∈	∈	PROPN
ejpam-6366	161	25	sk	sk	NOUN
ejpam-6366	162	1	[	[	X
ejpam-6366	162	2	γ;α	γ;α	X
ejpam-6366	162	3	,	,	PUNCT
ejpam-6366	162	4	β	β	X
ejpam-6366	162	5	]	]	PUNCT
ejpam-6366	162	6	.	.	PUNCT
ejpam-6366	163	1	putting	put	VERB
ejpam-6366	163	2	α	α	NOUN
ejpam-6366	163	3	=	=	SYM
ejpam-6366	163	4	γ	γ	X
ejpam-6366	163	5	=	=	SYM
ejpam-6366	163	6	0	0	NUM
ejpam-6366	163	7	in	in	ADP
ejpam-6366	163	8	theorem	theorem	NOUN
ejpam-6366	163	9	3	3	NUM
ejpam-6366	163	10	,	,	PUNCT
ejpam-6366	163	11	we	we	PRON
ejpam-6366	163	12	obtain	obtain	VERB
ejpam-6366	163	13	the	the	DET
ejpam-6366	163	14	following	following	ADJ
ejpam-6366	163	15	result	result	NOUN
ejpam-6366	163	16	for	for	ADP
ejpam-6366	163	17	s	s	PROPN
ejpam-6366	163	18	[	[	X
ejpam-6366	163	19	p	p	X
ejpam-6366	163	20	,	,	PUNCT
ejpam-6366	163	21	q	q	NOUN
ejpam-6366	163	22	]	]	X
ejpam-6366	163	23	.	.	PUNCT
ejpam-6366	164	1	corollary	corollary	ADJ
ejpam-6366	164	2	8	8	NUM
ejpam-6366	164	3	.	.	PUNCT
ejpam-6366	165	1	if	if	SCONJ
ejpam-6366	165	2	g(ξ	g(ξ	PROPN
ejpam-6366	165	3	)	)	PUNCT
ejpam-6366	165	4	satisfy	satisfy	VERB
ejpam-6366	165	5	the	the	DET
ejpam-6366	165	6	inequality	inequality	NOUN
ejpam-6366	165	7	∞∑	∞∑	PROPN
ejpam-6366	165	8	j=2	j=2	PROPN
ejpam-6366	166	1	[	[	X
ejpam-6366	166	2	(	(	PUNCT
ejpam-6366	166	3	j	j	PROPN
ejpam-6366	166	4	−	−	PROPN
ejpam-6366	166	5	1	1	NUM
ejpam-6366	166	6	)	)	PUNCT
ejpam-6366	166	7	(	(	PUNCT
ejpam-6366	166	8	1−q	1−q	NUM
ejpam-6366	166	9	)	)	PUNCT
ejpam-6366	166	10	+	+	CCONJ
ejpam-6366	166	11	p	p	NOUN
ejpam-6366	166	12	−q	−q	NOUN
ejpam-6366	166	13	]	]	PUNCT
ejpam-6366	166	14	|dj	|dj	PUNCT
ejpam-6366	166	15	|	|	ADV
ejpam-6366	166	16	≤	≤	NOUN
ejpam-6366	166	17	p	p	NOUN
ejpam-6366	166	18	−q	−q	NOUN
ejpam-6366	166	19	,	,	PUNCT
ejpam-6366	166	20	then	then	ADV
ejpam-6366	166	21	g	g	PROPN
ejpam-6366	166	22	∈	∈	PROPN
ejpam-6366	166	23	s	s	PART
ejpam-6366	167	1	[	[	X
ejpam-6366	167	2	p	p	X
ejpam-6366	167	3	,	,	PUNCT
ejpam-6366	167	4	q	q	X
ejpam-6366	167	5	]	]	X
ejpam-6366	167	6	.	.	PUNCT
ejpam-6366	168	1	putting	put	VERB
ejpam-6366	168	2	β	β	NOUN
ejpam-6366	168	3	=	=	PUNCT
ejpam-6366	168	4	γ	γ	X
ejpam-6366	168	5	=	=	SYM
ejpam-6366	168	6	0	0	NUM
ejpam-6366	168	7	in	in	ADP
ejpam-6366	168	8	theorem	theorem	NOUN
ejpam-6366	168	9	3	3	NUM
ejpam-6366	168	10	,	,	PUNCT
ejpam-6366	168	11	we	we	PRON
ejpam-6366	168	12	obtain	obtain	VERB
ejpam-6366	168	13	the	the	DET
ejpam-6366	168	14	following	following	ADJ
ejpam-6366	168	15	result	result	NOUN
ejpam-6366	168	16	for	for	ADP
ejpam-6366	168	17	k	k	PROPN
ejpam-6366	169	1	[	[	X
ejpam-6366	169	2	p	p	X
ejpam-6366	169	3	,	,	PUNCT
ejpam-6366	169	4	q	q	NOUN
ejpam-6366	169	5	]	]	X
ejpam-6366	169	6	.	.	PUNCT
ejpam-6366	170	1	corollary	corollary	ADJ
ejpam-6366	170	2	9	9	NUM
ejpam-6366	170	3	.	.	PUNCT
ejpam-6366	171	1	if	if	SCONJ
ejpam-6366	171	2	g(ξ	g(ξ	PROPN
ejpam-6366	171	3	)	)	PUNCT
ejpam-6366	171	4	satisfy	satisfy	VERB
ejpam-6366	171	5	the	the	DET
ejpam-6366	171	6	inequality	inequality	NOUN
ejpam-6366	171	7	∞∑	∞∑	PROPN
ejpam-6366	171	8	j=2	j=2	PROPN
ejpam-6366	171	9	(	(	PUNCT
ejpam-6366	171	10	1−q	1−q	NUM
ejpam-6366	171	11	)	)	PUNCT
ejpam-6366	171	12	|dj	|dj	PUNCT
ejpam-6366	171	13	|	|	ADV
ejpam-6366	171	14	≤	≤	NOUN
ejpam-6366	171	15	p	p	NOUN
ejpam-6366	171	16	−q	−q	NOUN
ejpam-6366	171	17	,	,	PUNCT
ejpam-6366	171	18	then	then	ADV
ejpam-6366	171	19	g	g	PROPN
ejpam-6366	171	20	∈	∈	PROPN
ejpam-6366	171	21	k	k	PROPN
ejpam-6366	172	1	[	[	X
ejpam-6366	172	2	p	p	X
ejpam-6366	172	3	,	,	PUNCT
ejpam-6366	172	4	q	q	X
ejpam-6366	172	5	]	]	X
ejpam-6366	172	6	.	.	PUNCT
ejpam-6366	173	1	3	3	X
ejpam-6366	173	2	.	.	X
ejpam-6366	173	3	initial	initial	ADJ
ejpam-6366	173	4	coefficient	coefficient	NOUN
ejpam-6366	173	5	estimates	estimate	NOUN
ejpam-6366	173	6	and	and	CCONJ
ejpam-6366	173	7	fekete	fekete	PROPN
ejpam-6366	173	8	–	–	PUNCT
ejpam-6366	173	9	szegő	szegő	PROPN
ejpam-6366	173	10	problems	problem	VERB
ejpam-6366	173	11	the	the	DET
ejpam-6366	173	12	fekete	fekete	PROPN
ejpam-6366	173	13	-	-	PUNCT
ejpam-6366	173	14	szegő	szegő	PROPN
ejpam-6366	173	15	problems	problem	NOUN
ejpam-6366	173	16	are	be	AUX
ejpam-6366	173	17	a	a	DET
ejpam-6366	173	18	major	major	ADJ
ejpam-6366	173	19	area	area	NOUN
ejpam-6366	173	20	of	of	ADP
ejpam-6366	173	21	research	research	NOUN
ejpam-6366	173	22	in	in	ADP
ejpam-6366	173	23	complex	complex	ADJ
ejpam-6366	173	24	analysis	analysis	NOUN
ejpam-6366	173	25	concerning	concern	VERB
ejpam-6366	173	26	the	the	DET
ejpam-6366	173	27	maximum	maximum	ADJ
ejpam-6366	173	28	value	value	NOUN
ejpam-6366	173	29	of	of	ADP
ejpam-6366	173	30	functionals	functional	NOUN
ejpam-6366	173	31	of	of	ADP
ejpam-6366	173	32	the	the	DET
ejpam-6366	173	33	form	form	NOUN
ejpam-6366	173	34	∣∣d3	∣∣d3	NOUN
ejpam-6366	173	35	−	−	ADP
ejpam-6366	173	36	µd22	µd22	PROPN
ejpam-6366	173	37	∣∣	∣∣	X
ejpam-6366	173	38	over	over	ADP
ejpam-6366	173	39	families	family	NOUN
ejpam-6366	173	40	of	of	ADP
ejpam-6366	173	41	univalent	univalent	ADJ
ejpam-6366	173	42	functions	function	NOUN
ejpam-6366	173	43	found	find	VERB
ejpam-6366	173	44	by	by	ADP
ejpam-6366	173	45	fekete	fekete	PROPN
ejpam-6366	173	46	and	and	CCONJ
ejpam-6366	173	47	szegő	szegő	PROPN
ejpam-6366	174	1	[	[	X
ejpam-6366	174	2	26	26	NUM
ejpam-6366	174	3	]	]	PUNCT
ejpam-6366	174	4	(	(	PUNCT
ejpam-6366	174	5	see	see	VERB
ejpam-6366	174	6	also	also	ADV
ejpam-6366	174	7	,	,	PUNCT
ejpam-6366	174	8	[	[	X
ejpam-6366	174	9	27–32	27–32	NUM
ejpam-6366	174	10	]	]	PUNCT
ejpam-6366	174	11	)	)	PUNCT
ejpam-6366	174	12	.	.	PUNCT
ejpam-6366	175	1	in	in	ADP
ejpam-6366	175	2	the	the	DET
ejpam-6366	175	3	following	follow	VERB
ejpam-6366	175	4	theorems	theorem	NOUN
ejpam-6366	175	5	,	,	PUNCT
ejpam-6366	175	6	we	we	PRON
ejpam-6366	175	7	determine	determine	VERB
ejpam-6366	175	8	the	the	DET
ejpam-6366	175	9	upper	upper	ADJ
ejpam-6366	175	10	bounds	bound	NOUN
ejpam-6366	175	11	for	for	ADP
ejpam-6366	175	12	the	the	DET
ejpam-6366	175	13	coefficients	coefficient	NOUN
ejpam-6366	175	14	|d2|	|d2|	NOUN
ejpam-6366	175	15	,	,	PUNCT
ejpam-6366	175	16	|d3|	|d3|	NOUN
ejpam-6366	175	17	,	,	PUNCT
ejpam-6366	175	18	|d4|	|d4|	NOUN
ejpam-6366	175	19	and	and	CCONJ
ejpam-6366	175	20	the	the	DET
ejpam-6366	175	21	fekete	fekete	PROPN
ejpam-6366	175	22	–	–	PUNCT
ejpam-6366	175	23	szegő	szegő	VERB
ejpam-6366	175	24	functional	functional	NOUN
ejpam-6366	175	25	for	for	ADP
ejpam-6366	175	26	the	the	DET
ejpam-6366	175	27	subfamily	subfamily	ADV
ejpam-6366	175	28	sk	sk	VERB
ejpam-6366	175	29	[	[	X
ejpam-6366	175	30	p	p	X
ejpam-6366	175	31	,	,	PUNCT
ejpam-6366	175	32	q	q	NOUN
ejpam-6366	175	33	,	,	PUNCT
ejpam-6366	175	34	γ;α	γ;α	ADV
ejpam-6366	175	35	,	,	PUNCT
ejpam-6366	175	36	β	β	X
ejpam-6366	175	37	]	]	PUNCT
ejpam-6366	175	38	.	.	PUNCT
ejpam-6366	176	1	theorem	theorem	ADJ
ejpam-6366	176	2	4	4	NUM
ejpam-6366	176	3	.	.	PUNCT
ejpam-6366	177	1	if	if	SCONJ
ejpam-6366	177	2	g	g	PROPN
ejpam-6366	177	3	∈	∈	PROPN
ejpam-6366	177	4	sk	sk	VERB
ejpam-6366	178	1	[	[	X
ejpam-6366	178	2	p	p	X
ejpam-6366	178	3	,	,	PUNCT
ejpam-6366	178	4	q	q	NOUN
ejpam-6366	178	5	,	,	PUNCT
ejpam-6366	178	6	γ;α	γ;α	ADV
ejpam-6366	178	7	,	,	PUNCT
ejpam-6366	178	8	β	β	X
ejpam-6366	178	9	]	]	X
ejpam-6366	178	10	,	,	PUNCT
ejpam-6366	178	11	then	then	ADV
ejpam-6366	178	12	|d2|	|d2|	VERB
ejpam-6366	178	13	≤	≤	NUM
ejpam-6366	178	14	(	(	PUNCT
ejpam-6366	178	15	1−	1−	NUM
ejpam-6366	178	16	γ	γ	NOUN
ejpam-6366	178	17	)	)	PUNCT
ejpam-6366	178	18	(	(	PUNCT
ejpam-6366	178	19	p	p	NOUN
ejpam-6366	178	20	−q	−q	NOUN
ejpam-6366	178	21	)	)	PUNCT
ejpam-6366	178	22	,	,	PUNCT
ejpam-6366	178	23	|d3|	|d3|	NOUN
ejpam-6366	178	24	≤	≤	NUM
ejpam-6366	178	25	(	(	PUNCT
ejpam-6366	178	26	α+	α+	X
ejpam-6366	178	27	β	β	X
ejpam-6366	178	28	)	)	PUNCT
ejpam-6366	178	29	(	(	PUNCT
ejpam-6366	178	30	1−	1−	NUM
ejpam-6366	178	31	γ	γ	X
ejpam-6366	178	32	)	)	PUNCT
ejpam-6366	178	33	(	(	PUNCT
ejpam-6366	178	34	p	p	NOUN
ejpam-6366	178	35	−q	−q	NOUN
ejpam-6366	178	36	)	)	PUNCT
ejpam-6366	178	37	α+	α+	DET
ejpam-6366	178	38	2β	2β	NOUN
ejpam-6366	178	39	max	max	NOUN
ejpam-6366	178	40	{	{	PUNCT
ejpam-6366	178	41	1	1	NUM
ejpam-6366	178	42	;	;	PUNCT
ejpam-6366	178	43	∣∣∣∣q−	∣∣∣∣q−	NUM
ejpam-6366	178	44	β	β	X
ejpam-6366	178	45	(	(	PUNCT
ejpam-6366	178	46	1−	1−	NUM
ejpam-6366	178	47	γ	γ	X
ejpam-6366	178	48	)	)	PUNCT
ejpam-6366	178	49	(	(	PUNCT
ejpam-6366	178	50	p	p	NOUN
ejpam-6366	178	51	−q	−q	NOUN
ejpam-6366	178	52	)	)	PUNCT
ejpam-6366	178	53	α+	α+	PRON
ejpam-6366	178	54	β	β	X
ejpam-6366	178	55	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6366	178	56	}	}	PUNCT
ejpam-6366	178	57	,	,	PUNCT
ejpam-6366	178	58	|d4|	|d4|	PROPN
ejpam-6366	178	59	≤	≤	PROPN
ejpam-6366	178	60	(	(	PUNCT
ejpam-6366	178	61	α+β)(1−γ)(p−q	α+β)(1−γ)(p−q	NUM
ejpam-6366	178	62	)	)	PUNCT
ejpam-6366	178	63	(	(	PUNCT
ejpam-6366	178	64	α+3β	α+3β	NOUN
ejpam-6366	178	65	)	)	PUNCT
ejpam-6366	178	66			NOUN
ejpam-6366	178	67	max	max	NOUN
ejpam-6366	178	68	{	{	PUNCT
ejpam-6366	178	69	1	1	NUM
ejpam-6366	178	70	;	;	PUNCT
ejpam-6366	178	71	∣∣∣	∣∣∣	X
ejpam-6366	178	72	(	(	PUNCT
ejpam-6366	178	73	2α+3β)β(1−γ)(p−q	2α+3β)β(1−γ)(p−q	NUM
ejpam-6366	178	74	)	)	PUNCT
ejpam-6366	178	75	(	(	PUNCT
ejpam-6366	178	76	α+β)(α+2β	α+β)(α+2β	NOUN
ejpam-6366	178	77	)	)	PUNCT
ejpam-6366	178	78	−	−	PROPN
ejpam-6366	178	79	1−	1−	NUM
ejpam-6366	178	80	2q	2q	NUM
ejpam-6366	178	81	∣∣∣	∣∣∣	ADJ
ejpam-6366	178	82	}	}	PUNCT
ejpam-6366	178	83	+	+	NUM
ejpam-6366	178	84	∣∣∣1	∣∣∣1	ADJ
ejpam-6366	178	85	+	+	PROPN
ejpam-6366	178	86	q−	q−	PROPN
ejpam-6366	178	87	β(1−γ)(p−q	β(1−γ)(p−q	PROPN
ejpam-6366	178	88	)	)	PUNCT
ejpam-6366	178	89	α+β	α+β	PROPN
ejpam-6366	178	90	∣∣∣	∣∣∣	ADP
ejpam-6366	178	91	∣∣∣1	∣∣∣1	ADJ
ejpam-6366	179	1	+	+	PROPN
ejpam-6366	179	2	q−	q−	PROPN
ejpam-6366	179	3	β(1−γ)(p−q	β(1−γ)(p−q	PROPN
ejpam-6366	179	4	)	)	PUNCT
ejpam-6366	179	5	(	(	PUNCT
ejpam-6366	179	6	α+2β	α+2β	NOUN
ejpam-6366	179	7	)	)	PUNCT
ejpam-6366	179	8	∣∣∣	∣∣∣	ADJ
ejpam-6366	179	9			NOUN
ejpam-6366	179	10	.	.	PUNCT
ejpam-6366	180	1	t.	t.	PROPN
ejpam-6366	180	2	m.	m.	PROPN
ejpam-6366	180	3	seoudy	seoudy	PROPN
ejpam-6366	180	4	,	,	PUNCT
ejpam-6366	180	5	a.	a.	PROPN
ejpam-6366	180	6	e.	e.	PROPN
ejpam-6366	180	7	shammaky	shammaky	PROPN
ejpam-6366	180	8	/	/	SYM
ejpam-6366	180	9	eur	eur	PROPN
ejpam-6366	180	10	.	.	PUNCT
ejpam-6366	181	1	j.	j.	PROPN
ejpam-6366	181	2	pure	pure	PROPN
ejpam-6366	181	3	appl	appl	PROPN
ejpam-6366	181	4	.	.	PROPN
ejpam-6366	181	5	math	math	PROPN
ejpam-6366	181	6	,	,	PUNCT
ejpam-6366	181	7	18	18	NUM
ejpam-6366	181	8	(	(	PUNCT
ejpam-6366	181	9	4	4	NUM
ejpam-6366	181	10	)	)	PUNCT
ejpam-6366	181	11	(	(	PUNCT
ejpam-6366	181	12	2025	2025	NUM
ejpam-6366	181	13	)	)	PUNCT
ejpam-6366	181	14	,	,	PUNCT
ejpam-6366	181	15	6366	6366	NUM
ejpam-6366	181	16	9	9	NUM
ejpam-6366	181	17	of	of	ADP
ejpam-6366	181	18	15	15	NUM
ejpam-6366	181	19	proof	proof	NOUN
ejpam-6366	181	20	.	.	PUNCT
ejpam-6366	182	1	if	if	SCONJ
ejpam-6366	182	2	g	g	PROPN
ejpam-6366	182	3	∈	∈	PROPN
ejpam-6366	182	4	sk	sk	VERB
ejpam-6366	182	5	[	[	X
ejpam-6366	182	6	p	p	X
ejpam-6366	182	7	,	,	PUNCT
ejpam-6366	182	8	q	q	NOUN
ejpam-6366	182	9	,	,	PUNCT
ejpam-6366	182	10	γ;α	γ;α	ADV
ejpam-6366	182	11	,	,	PUNCT
ejpam-6366	182	12	β	β	X
ejpam-6366	182	13	]	]	X
ejpam-6366	182	14	,	,	PUNCT
ejpam-6366	182	15	then	then	ADV
ejpam-6366	182	16	there	there	PRON
ejpam-6366	182	17	exists	exist	VERB
ejpam-6366	182	18	a	a	DET
ejpam-6366	182	19	function	function	NOUN
ejpam-6366	182	20	w	w	PROPN
ejpam-6366	182	21	(	(	PUNCT
ejpam-6366	182	22	ξ	ξ	NOUN
ejpam-6366	182	23	)	)	PUNCT
ejpam-6366	182	24	∈	∈	PROPN
ejpam-6366	182	25	ω	ω	PROPN
ejpam-6366	182	26	in	in	ADP
ejpam-6366	182	27	∆	∆	PROPN
ejpam-6366	182	28	such	such	ADJ
ejpam-6366	182	29	that	that	DET
ejpam-6366	182	30	αg	αg	NOUN
ejpam-6366	182	31	(	(	PUNCT
ejpam-6366	182	32	ξ	ξ	NOUN
ejpam-6366	182	33	)	)	PUNCT
ejpam-6366	182	34	+	+	NUM
ejpam-6366	182	35	βξg′	βξg′	NUM
ejpam-6366	182	36	(	(	PUNCT
ejpam-6366	182	37	ξ	ξ	NOUN
ejpam-6366	182	38	)	)	PUNCT
ejpam-6366	182	39	αξ	αξ	NOUN
ejpam-6366	183	1	+	+	NUM
ejpam-6366	183	2	βg	βg	PROPN
ejpam-6366	183	3	(	(	PUNCT
ejpam-6366	183	4	ξ	ξ	NOUN
ejpam-6366	183	5	)	)	PUNCT
ejpam-6366	183	6	=	=	SYM
ejpam-6366	183	7	1	1	NUM
ejpam-6366	183	8	+	+	CCONJ
ejpam-6366	183	9	[	[	X
ejpam-6366	183	10	q+	q+	X
ejpam-6366	183	11	(	(	PUNCT
ejpam-6366	183	12	1−	1−	NUM
ejpam-6366	183	13	γ	γ	NOUN
ejpam-6366	183	14	)	)	PUNCT
ejpam-6366	183	15	(	(	PUNCT
ejpam-6366	183	16	p	p	PROPN
ejpam-6366	183	17	−q)]w	−q)]w	PROPN
ejpam-6366	183	18	(	(	PUNCT
ejpam-6366	183	19	ξ	ξ	NOUN
ejpam-6366	183	20	)	)	PUNCT
ejpam-6366	183	21	1	1	NUM
ejpam-6366	183	22	+	+	SYM
ejpam-6366	183	23	qw	qw	X
ejpam-6366	183	24	(	(	PUNCT
ejpam-6366	183	25	ξ	ξ	NOUN
ejpam-6366	183	26	)	)	PUNCT
ejpam-6366	183	27	=	=	SYM
ejpam-6366	183	28	j	j	PROPN
ejpam-6366	183	29	(	(	PUNCT
ejpam-6366	183	30	w	w	PROPN
ejpam-6366	183	31	(	(	PUNCT
ejpam-6366	183	32	ξ	ξ	NOUN
ejpam-6366	183	33	)	)	PUNCT
ejpam-6366	183	34	)	)	PUNCT
ejpam-6366	183	35	.	.	PUNCT
ejpam-6366	184	1	(	(	PUNCT
ejpam-6366	184	2	22	22	NUM
ejpam-6366	184	3	)	)	PUNCT
ejpam-6366	184	4	since	since	SCONJ
ejpam-6366	184	5	g	g	PROPN
ejpam-6366	184	6	(	(	PUNCT
ejpam-6366	184	7	ξ	ξ	NOUN
ejpam-6366	184	8	)	)	PUNCT
ejpam-6366	184	9	is	be	AUX
ejpam-6366	184	10	given	give	VERB
ejpam-6366	184	11	by	by	ADP
ejpam-6366	184	12	(	(	PUNCT
ejpam-6366	184	13	1	1	NUM
ejpam-6366	184	14	)	)	PUNCT
ejpam-6366	184	15	,	,	PUNCT
ejpam-6366	184	16	it	it	PRON
ejpam-6366	184	17	follows	follow	VERB
ejpam-6366	184	18	that	that	SCONJ
ejpam-6366	184	19	αg	αg	NOUN
ejpam-6366	184	20	(	(	PUNCT
ejpam-6366	184	21	ξ	ξ	NOUN
ejpam-6366	184	22	)	)	PUNCT
ejpam-6366	184	23	+	+	NUM
ejpam-6366	184	24	βξg′	βξg′	NUM
ejpam-6366	184	25	(	(	PUNCT
ejpam-6366	184	26	ξ	ξ	NOUN
ejpam-6366	184	27	)	)	PUNCT
ejpam-6366	184	28	αξ	αξ	NOUN
ejpam-6366	185	1	+	+	NUM
ejpam-6366	185	2	βg	βg	PROPN
ejpam-6366	185	3	(	(	PUNCT
ejpam-6366	185	4	ξ	ξ	NOUN
ejpam-6366	185	5	)	)	PUNCT
ejpam-6366	185	6	=	=	SYM
ejpam-6366	185	7	1	1	NUM
ejpam-6366	185	8	+	+	NUM
ejpam-6366	185	9	d2ξ	d2ξ	PROPN
ejpam-6366	185	10	+	+	CCONJ
ejpam-6366	185	11	[	[	PUNCT
ejpam-6366	185	12	α+2β	α+2β	PROPN
ejpam-6366	185	13	α+β	α+β	NUM
ejpam-6366	185	14	d3	d3	PROPN
ejpam-6366	185	15	−	−	NOUN
ejpam-6366	185	16	β	β	NOUN
ejpam-6366	185	17	α+βd	α+βd	X
ejpam-6366	185	18	2	2	NUM
ejpam-6366	185	19	2	2	NUM
ejpam-6366	185	20	]	]	PUNCT
ejpam-6366	185	21	ξ2	ξ2	NOUN
ejpam-6366	186	1	+	+	CCONJ
ejpam-6366	187	1	[	[	PUNCT
ejpam-6366	187	2	α+3β	α+3β	NOUN
ejpam-6366	187	3	α+β	α+β	NUM
ejpam-6366	187	4	d4	d4	PROPN
ejpam-6366	187	5	−	−	PROPN
ejpam-6366	187	6	(	(	PUNCT
ejpam-6366	187	7	2α+3β)β	2α+3β)β	NUM
ejpam-6366	187	8	(	(	PUNCT
ejpam-6366	187	9	α+β)2	α+β)2	NOUN
ejpam-6366	187	10	d2d3	d2d3	PROPN
ejpam-6366	187	11	+	+	NUM
ejpam-6366	187	12	β2	β2	NOUN
ejpam-6366	187	13	(	(	PUNCT
ejpam-6366	187	14	α+β)2	α+β)2	NOUN
ejpam-6366	187	15	d32	d32	NOUN
ejpam-6366	187	16	]	]	X
ejpam-6366	187	17	ξ3	ξ3	PROPN
ejpam-6366	187	18	+	+	CCONJ
ejpam-6366	187	19	...	...	PUNCT
ejpam-6366	187	20	.	.	PUNCT
ejpam-6366	188	1	(	(	PUNCT
ejpam-6366	188	2	23	23	X
ejpam-6366	188	3	)	)	PUNCT
ejpam-6366	188	4	define	define	VERB
ejpam-6366	188	5	the	the	DET
ejpam-6366	188	6	function	function	NOUN
ejpam-6366	188	7	ϕ	ϕ	X
ejpam-6366	188	8	(	(	PUNCT
ejpam-6366	188	9	ξ	ξ	NOUN
ejpam-6366	188	10	)	)	PUNCT
ejpam-6366	188	11	by	by	ADP
ejpam-6366	188	12	ϕ	ϕ	X
ejpam-6366	188	13	(	(	PUNCT
ejpam-6366	188	14	ξ	ξ	NOUN
ejpam-6366	188	15	)	)	PUNCT
ejpam-6366	188	16	=	=	SYM
ejpam-6366	189	1	1	1	NUM
ejpam-6366	190	1	+	+	NUM
ejpam-6366	190	2	w	w	PROPN
ejpam-6366	190	3	(	(	PUNCT
ejpam-6366	190	4	ξ	ξ	NOUN
ejpam-6366	190	5	)	)	PUNCT
ejpam-6366	190	6	1−	1−	NUM
ejpam-6366	190	7	w	w	PROPN
ejpam-6366	190	8	(	(	PUNCT
ejpam-6366	190	9	ξ	ξ	NOUN
ejpam-6366	190	10	)	)	PUNCT
ejpam-6366	190	11	=	=	SYM
ejpam-6366	190	12	1	1	NUM
ejpam-6366	190	13	+	+	NUM
ejpam-6366	190	14	δ1ξ	δ1ξ	X
ejpam-6366	190	15	+	+	CCONJ
ejpam-6366	190	16	δ2ξ	δ2ξ	PROPN
ejpam-6366	190	17	2	2	NUM
ejpam-6366	190	18	+	+	CCONJ
ejpam-6366	190	19	δ3ξ	δ3ξ	ADJ
ejpam-6366	190	20	3	3	NUM
ejpam-6366	190	21	+	+	CCONJ
ejpam-6366	190	22	...	...	PUNCT
ejpam-6366	190	23	,	,	PUNCT
ejpam-6366	190	24	since	since	SCONJ
ejpam-6366	190	25	w	w	PROPN
ejpam-6366	190	26	(	(	PUNCT
ejpam-6366	190	27	ξ	ξ	NOUN
ejpam-6366	190	28	)	)	PUNCT
ejpam-6366	190	29	∈	∈	PROPN
ejpam-6366	190	30	ω	ω	NOUN
ejpam-6366	190	31	,	,	PUNCT
ejpam-6366	190	32	we	we	PRON
ejpam-6366	190	33	see	see	VERB
ejpam-6366	190	34	that	that	SCONJ
ejpam-6366	190	35	ϕ	ϕ	PROPN
ejpam-6366	190	36	∈	∈	PROPN
ejpam-6366	190	37	φ	φ	PROPN
ejpam-6366	190	38	and	and	CCONJ
ejpam-6366	190	39	w	w	PROPN
ejpam-6366	190	40	(	(	PUNCT
ejpam-6366	190	41	ξ	ξ	NOUN
ejpam-6366	190	42	)	)	PUNCT
ejpam-6366	190	43	=	=	SYM
ejpam-6366	190	44	ϕ	ϕ	PROPN
ejpam-6366	190	45	(	(	PUNCT
ejpam-6366	190	46	ξ)−	ξ)−	PROPN
ejpam-6366	190	47	1	1	NUM
ejpam-6366	190	48	ϕ	ϕ	X
ejpam-6366	190	49	(	(	PUNCT
ejpam-6366	190	50	ξ	ξ	NOUN
ejpam-6366	190	51	)	)	PUNCT
ejpam-6366	190	52	+	+	CCONJ
ejpam-6366	190	53	1	1	NUM
ejpam-6366	190	54	=	=	SYM
ejpam-6366	190	55	δ1ξ	δ1ξ	X
ejpam-6366	190	56	+	+	CCONJ
ejpam-6366	190	57	δ2ξ	δ2ξ	PROPN
ejpam-6366	190	58	2	2	NUM
ejpam-6366	190	59	+	+	CCONJ
ejpam-6366	190	60	δ3ξ	δ3ξ	ADJ
ejpam-6366	190	61	3	3	NUM
ejpam-6366	190	62	+	+	CCONJ
ejpam-6366	190	63	...	...	SYM
ejpam-6366	190	64	2	2	NUM
ejpam-6366	190	65	+	+	NUM
ejpam-6366	190	66	δ1ξ	δ1ξ	X
ejpam-6366	190	67	+	+	CCONJ
ejpam-6366	190	68	δ2ξ2	δ2ξ2	X
ejpam-6366	190	69	+	+	X
ejpam-6366	190	70	δ3ξ3	δ3ξ3	X
ejpam-6366	190	71	+	+	NUM
ejpam-6366	190	72	...	...	PUNCT
ejpam-6366	190	73	.	.	PUNCT
ejpam-6366	191	1	(	(	PUNCT
ejpam-6366	191	2	24	24	NUM
ejpam-6366	191	3	)	)	PUNCT
ejpam-6366	191	4	according	accord	VERB
ejpam-6366	191	5	to	to	ADP
ejpam-6366	191	6	(	(	PUNCT
ejpam-6366	191	7	24	24	NUM
ejpam-6366	191	8	)	)	PUNCT
ejpam-6366	191	9	,	,	PUNCT
ejpam-6366	191	10	we	we	PRON
ejpam-6366	191	11	have	have	VERB
ejpam-6366	191	12	j	j	PROPN
ejpam-6366	191	13	(	(	PUNCT
ejpam-6366	191	14	w	w	PROPN
ejpam-6366	191	15	(	(	PUNCT
ejpam-6366	191	16	ξ	ξ	NOUN
ejpam-6366	191	17	)	)	PUNCT
ejpam-6366	191	18	)	)	PUNCT
ejpam-6366	192	1	=	=	SYM
ejpam-6366	192	2	1	1	NUM
ejpam-6366	192	3	+	+	CCONJ
ejpam-6366	193	1	[	[	X
ejpam-6366	193	2	q+	q+	X
ejpam-6366	193	3	(	(	PUNCT
ejpam-6366	193	4	1−	1−	NUM
ejpam-6366	193	5	γ	γ	NOUN
ejpam-6366	193	6	)	)	PUNCT
ejpam-6366	193	7	(	(	PUNCT
ejpam-6366	193	8	p	p	PROPN
ejpam-6366	193	9	−q)]w	−q)]w	PROPN
ejpam-6366	193	10	(	(	PUNCT
ejpam-6366	193	11	ξ	ξ	NOUN
ejpam-6366	193	12	)	)	PUNCT
ejpam-6366	193	13	1	1	NUM
ejpam-6366	193	14	+	+	SYM
ejpam-6366	193	15	qw	qw	X
ejpam-6366	193	16	(	(	PUNCT
ejpam-6366	193	17	ξ	ξ	NOUN
ejpam-6366	193	18	)	)	PUNCT
ejpam-6366	193	19	=	=	SYM
ejpam-6366	193	20	1	1	NUM
ejpam-6366	193	21	+	+	CCONJ
ejpam-6366	193	22	(	(	PUNCT
ejpam-6366	193	23	1−γ)(p−q	1−γ)(p−q	NUM
ejpam-6366	193	24	)	)	PUNCT
ejpam-6366	193	25	2	2	NUM
ejpam-6366	193	26	δ1ξ+	δ1ξ+	NOUN
ejpam-6366	193	27	(	(	PUNCT
ejpam-6366	193	28	1−γ)(p−q	1−γ)(p−q	NUM
ejpam-6366	193	29	)	)	PUNCT
ejpam-6366	193	30	2	2	NUM
ejpam-6366	193	31	[	[	PUNCT
ejpam-6366	193	32	δ2	δ2	ADJ
ejpam-6366	193	33	−	−	PROPN
ejpam-6366	193	34	(	(	PUNCT
ejpam-6366	193	35	1+q	1+q	NUM
ejpam-6366	193	36	)	)	PUNCT
ejpam-6366	193	37	2	2	NUM
ejpam-6366	193	38	δ21	δ21	NOUN
ejpam-6366	193	39	]	]	PUNCT
ejpam-6366	193	40	ξ2	ξ2	NOUN
ejpam-6366	193	41	+	+	CCONJ
ejpam-6366	193	42	(	(	PUNCT
ejpam-6366	193	43	1−	1−	NUM
ejpam-6366	193	44	γ	γ	X
ejpam-6366	193	45	)	)	PUNCT
ejpam-6366	193	46	(	(	PUNCT
ejpam-6366	193	47	p	p	NOUN
ejpam-6366	193	48	−q	−q	NOUN
ejpam-6366	193	49	)	)	PUNCT
ejpam-6366	193	50	2	2	NUM
ejpam-6366	193	51	[	[	PUNCT
ejpam-6366	193	52	δ3	δ3	PROPN
ejpam-6366	193	53	−	−	PROPN
ejpam-6366	193	54	(	(	PUNCT
ejpam-6366	193	55	1	1	NUM
ejpam-6366	193	56	+	+	NOUN
ejpam-6366	193	57	q	q	NOUN
ejpam-6366	193	58	)	)	PUNCT
ejpam-6366	193	59	δ1δ2	δ1δ2	PUNCT
ejpam-6366	194	1	+	+	PUNCT
ejpam-6366	194	2	(	(	PUNCT
ejpam-6366	194	3	1	1	NUM
ejpam-6366	194	4	+	+	NOUN
ejpam-6366	194	5	q)2	q)2	PROPN
ejpam-6366	194	6	4	4	NUM
ejpam-6366	194	7	δ31	δ31	NOUN
ejpam-6366	194	8	]	]	PUNCT
ejpam-6366	194	9	ξ3	ξ3	PROPN
ejpam-6366	194	10	+	+	CCONJ
ejpam-6366	194	11	...	...	PUNCT
ejpam-6366	194	12	.	.	PUNCT
ejpam-6366	195	1	(	(	PUNCT
ejpam-6366	195	2	25	25	NUM
ejpam-6366	195	3	)	)	PUNCT
ejpam-6366	195	4	equating	equate	VERB
ejpam-6366	195	5	the	the	DET
ejpam-6366	195	6	corresponding	corresponding	ADJ
ejpam-6366	195	7	coefficients	coefficient	NOUN
ejpam-6366	195	8	of	of	ADP
ejpam-6366	195	9	(	(	PUNCT
ejpam-6366	195	10	23	23	NUM
ejpam-6366	195	11	)	)	PUNCT
ejpam-6366	195	12	and	and	CCONJ
ejpam-6366	195	13	(	(	PUNCT
ejpam-6366	195	14	25	25	NUM
ejpam-6366	195	15	)	)	PUNCT
ejpam-6366	195	16	,	,	PUNCT
ejpam-6366	195	17	we	we	PRON
ejpam-6366	195	18	obtain	obtain	VERB
ejpam-6366	195	19	d2	d2	PROPN
ejpam-6366	195	20	=	=	SYM
ejpam-6366	195	21	(	(	PUNCT
ejpam-6366	195	22	1−	1−	NUM
ejpam-6366	195	23	γ	γ	NOUN
ejpam-6366	195	24	)	)	PUNCT
ejpam-6366	195	25	(	(	PUNCT
ejpam-6366	195	26	p	p	NOUN
ejpam-6366	195	27	−q	−q	ADJ
ejpam-6366	195	28	)	)	PUNCT
ejpam-6366	195	29	δ1	δ1	NOUN
ejpam-6366	195	30	2	2	NUM
ejpam-6366	195	31	,	,	PUNCT
ejpam-6366	195	32	(	(	PUNCT
ejpam-6366	195	33	26	26	NUM
ejpam-6366	195	34	)	)	PUNCT
ejpam-6366	195	35	d3	d3	PROPN
ejpam-6366	195	36	=	=	SYM
ejpam-6366	195	37	(	(	PUNCT
ejpam-6366	195	38	α+	α+	X
ejpam-6366	195	39	β	β	X
ejpam-6366	195	40	)	)	PUNCT
ejpam-6366	195	41	(	(	PUNCT
ejpam-6366	195	42	1−	1−	NUM
ejpam-6366	195	43	γ	γ	X
ejpam-6366	195	44	)	)	PUNCT
ejpam-6366	195	45	(	(	PUNCT
ejpam-6366	195	46	p	p	NOUN
ejpam-6366	195	47	−q	−q	NOUN
ejpam-6366	195	48	)	)	PUNCT
ejpam-6366	195	49	2	2	NUM
ejpam-6366	195	50	(	(	PUNCT
ejpam-6366	195	51	α+	α+	NOUN
ejpam-6366	195	52	2β	2β	NOUN
ejpam-6366	195	53	)	)	PUNCT
ejpam-6366	195	54	{	{	PUNCT
ejpam-6366	195	55	δ2	δ2	VERB
ejpam-6366	195	56	−	−	NOUN
ejpam-6366	195	57	1	1	NUM
ejpam-6366	195	58	2	2	NUM
ejpam-6366	195	59	[	[	PUNCT
ejpam-6366	195	60	1	1	NUM
ejpam-6366	195	61	+	+	NOUN
ejpam-6366	195	62	q−	q−	PROPN
ejpam-6366	195	63	β	β	X
ejpam-6366	195	64	(	(	PUNCT
ejpam-6366	195	65	1−	1−	NUM
ejpam-6366	195	66	γ	γ	NOUN
ejpam-6366	195	67	)	)	PUNCT
ejpam-6366	195	68	(	(	PUNCT
ejpam-6366	195	69	p	p	NOUN
ejpam-6366	195	70	−q	−q	NOUN
ejpam-6366	195	71	)	)	PUNCT
ejpam-6366	195	72	α+	α+	PRON
ejpam-6366	195	73	β	β	X
ejpam-6366	195	74	]	]	PUNCT
ejpam-6366	195	75	δ21	δ21	NOUN
ejpam-6366	195	76	}	}	PUNCT
ejpam-6366	195	77	(	(	PUNCT
ejpam-6366	195	78	27	27	NUM
ejpam-6366	195	79	)	)	PUNCT
ejpam-6366	195	80	d4	d4	PROPN
ejpam-6366	195	81	=	=	SYM
ejpam-6366	195	82	(	(	PUNCT
ejpam-6366	195	83	α+β)(1−γ)(p−q	α+β)(1−γ)(p−q	NUM
ejpam-6366	195	84	)	)	PUNCT
ejpam-6366	195	85	2(α+3β	2(α+3β	NUM
ejpam-6366	195	86	)	)	PUNCT
ejpam-6366	196	1			PRON
ejpam-6366	196	2	δ3	δ3	ADV
ejpam-6366	196	3	−	−	PROPN
ejpam-6366	196	4	[	[	PUNCT
ejpam-6366	196	5	1	1	NUM
ejpam-6366	196	6	+	+	NOUN
ejpam-6366	196	7	q−	q−	PROPN
ejpam-6366	196	8	(	(	PUNCT
ejpam-6366	196	9	2α+3β)β(1−γ)(p−q	2α+3β)β(1−γ)(p−q	NUM
ejpam-6366	196	10	)	)	PUNCT
ejpam-6366	196	11	2(α+β)(α+2β	2(α+β)(α+2β	NUM
ejpam-6366	196	12	)	)	PUNCT
ejpam-6366	196	13	]	]	PUNCT
ejpam-6366	197	1	δ1δ2	δ1δ2	PUNCT
ejpam-6366	197	2	+	+	PUNCT
ejpam-6366	197	3	{	{	PUNCT
ejpam-6366	197	4	(	(	PUNCT
ejpam-6366	197	5	1+q	1+q	NUM
ejpam-6366	197	6	2	2	NUM
ejpam-6366	197	7	)	)	SYM
ejpam-6366	197	8	2	2	NUM
ejpam-6366	197	9	−	−	PROPN
ejpam-6366	197	10	(	(	PUNCT
ejpam-6366	197	11	2α+3β)β(1+q)(1−γ)(p−q	2α+3β)β(1+q)(1−γ)(p−q	NUM
ejpam-6366	197	12	)	)	PUNCT
ejpam-6366	197	13	4(α+β)(α+2β	4(α+β)(α+2β	NUM
ejpam-6366	197	14	)	)	PUNCT
ejpam-6366	198	1	+	+	CCONJ
ejpam-6366	198	2	β2(p−q)2(1−γ)2	β2(p−q)2(1−γ)2	NUM
ejpam-6366	198	3	4(α+β)(α+2β	4(α+β)(α+2β	NUM
ejpam-6366	198	4	)	)	PUNCT
ejpam-6366	198	5	}	}	PUNCT
ejpam-6366	198	6	δ31	δ31	VERB
ejpam-6366	198	7			X
ejpam-6366	198	8	(	(	PUNCT
ejpam-6366	198	9	28	28	NUM
ejpam-6366	198	10	)	)	PUNCT
ejpam-6366	198	11	using	use	VERB
ejpam-6366	198	12	(	(	PUNCT
ejpam-6366	198	13	26	26	NUM
ejpam-6366	198	14	)	)	PUNCT
ejpam-6366	198	15	,	,	PUNCT
ejpam-6366	198	16	we	we	PRON
ejpam-6366	198	17	have	have	VERB
ejpam-6366	198	18	|d2|	|d2|	NOUN
ejpam-6366	198	19	=	=	SYM
ejpam-6366	198	20	(	(	PUNCT
ejpam-6366	198	21	1−	1−	NUM
ejpam-6366	198	22	γ	γ	NOUN
ejpam-6366	198	23	)	)	PUNCT
ejpam-6366	198	24	(	(	PUNCT
ejpam-6366	198	25	p	p	NOUN
ejpam-6366	198	26	−q	−q	NOUN
ejpam-6366	198	27	)	)	PUNCT
ejpam-6366	198	28	2	2	NUM
ejpam-6366	198	29	|δ1|	|δ1|	NOUN
ejpam-6366	198	30	,	,	PUNCT
ejpam-6366	198	31	and	and	CCONJ
ejpam-6366	198	32	from	from	ADP
ejpam-6366	198	33	(	(	PUNCT
ejpam-6366	198	34	8)	8)	NUM
ejpam-6366	198	35	,	,	PUNCT
ejpam-6366	198	36	we	we	PRON
ejpam-6366	198	37	have	have	VERB
ejpam-6366	198	38	|δ1|	|δ1|	ADJ
ejpam-6366	198	39	≤	≤	NUM
ejpam-6366	198	40	2	2	NUM
ejpam-6366	198	41	,	,	PUNCT
ejpam-6366	198	42	therefore	therefore	ADV
ejpam-6366	198	43	|d2|	|d2|	VERB
ejpam-6366	198	44	≤	≤	NUM
ejpam-6366	198	45	(	(	PUNCT
ejpam-6366	198	46	1−	1−	NUM
ejpam-6366	198	47	γ	γ	NOUN
ejpam-6366	198	48	)	)	PUNCT
ejpam-6366	198	49	(	(	PUNCT
ejpam-6366	198	50	p	p	NOUN
ejpam-6366	198	51	−q	−q	NOUN
ejpam-6366	198	52	)	)	PUNCT
ejpam-6366	198	53	.	.	PUNCT
ejpam-6366	199	1	t.	t.	PROPN
ejpam-6366	199	2	m.	m.	PROPN
ejpam-6366	199	3	seoudy	seoudy	PROPN
ejpam-6366	199	4	,	,	PUNCT
ejpam-6366	199	5	a.	a.	PROPN
ejpam-6366	199	6	e.	e.	PROPN
ejpam-6366	199	7	shammaky	shammaky	PROPN
ejpam-6366	199	8	/	/	SYM
ejpam-6366	199	9	eur	eur	PROPN
ejpam-6366	199	10	.	.	PUNCT
ejpam-6366	200	1	j.	j.	PROPN
ejpam-6366	200	2	pure	pure	PROPN
ejpam-6366	200	3	appl	appl	PROPN
ejpam-6366	200	4	.	.	PROPN
ejpam-6366	200	5	math	math	PROPN
ejpam-6366	200	6	,	,	PUNCT
ejpam-6366	200	7	18	18	NUM
ejpam-6366	200	8	(	(	PUNCT
ejpam-6366	200	9	4	4	NUM
ejpam-6366	200	10	)	)	PUNCT
ejpam-6366	200	11	(	(	PUNCT
ejpam-6366	200	12	2025	2025	NUM
ejpam-6366	200	13	)	)	PUNCT
ejpam-6366	200	14	,	,	PUNCT
ejpam-6366	200	15	6366	6366	NUM
ejpam-6366	200	16	10	10	NUM
ejpam-6366	200	17	of	of	ADP
ejpam-6366	200	18	15	15	NUM
ejpam-6366	200	19	the	the	DET
ejpam-6366	200	20	relation	relation	NOUN
ejpam-6366	200	21	(	(	PUNCT
ejpam-6366	200	22	27	27	NUM
ejpam-6366	200	23	)	)	PUNCT
ejpam-6366	200	24	yields	yield	NOUN
ejpam-6366	200	25	to	to	PART
ejpam-6366	200	26	|d3|	|d3|	NOUN
ejpam-6366	200	27	=	=	SYM
ejpam-6366	200	28	(	(	PUNCT
ejpam-6366	200	29	α+	α+	X
ejpam-6366	200	30	β	β	X
ejpam-6366	200	31	)	)	PUNCT
ejpam-6366	200	32	(	(	PUNCT
ejpam-6366	200	33	1−	1−	NUM
ejpam-6366	200	34	γ	γ	X
ejpam-6366	200	35	)	)	PUNCT
ejpam-6366	200	36	(	(	PUNCT
ejpam-6366	200	37	p	p	NOUN
ejpam-6366	200	38	−q	−q	NOUN
ejpam-6366	200	39	)	)	PUNCT
ejpam-6366	200	40	2	2	NUM
ejpam-6366	200	41	(	(	PUNCT
ejpam-6366	200	42	α+	α+	NOUN
ejpam-6366	200	43	2β	2β	NOUN
ejpam-6366	200	44	)	)	PUNCT
ejpam-6366	200	45	∣∣∣∣δ2	∣∣∣∣δ2	PUNCT
ejpam-6366	201	1	−	−	NOUN
ejpam-6366	201	2	1	1	NUM
ejpam-6366	201	3	2	2	NUM
ejpam-6366	201	4	[	[	PUNCT
ejpam-6366	201	5	1	1	NUM
ejpam-6366	201	6	+	+	NOUN
ejpam-6366	201	7	q−	q−	PROPN
ejpam-6366	201	8	β	β	X
ejpam-6366	201	9	(	(	PUNCT
ejpam-6366	201	10	1−	1−	NUM
ejpam-6366	201	11	γ	γ	NOUN
ejpam-6366	201	12	)	)	PUNCT
ejpam-6366	201	13	(	(	PUNCT
ejpam-6366	201	14	p	p	NOUN
ejpam-6366	201	15	−q	−q	NOUN
ejpam-6366	201	16	)	)	PUNCT
ejpam-6366	201	17	α+	α+	DET
ejpam-6366	201	18	β	β	X
ejpam-6366	201	19	]	]	PUNCT
ejpam-6366	201	20	δ21	δ21	NOUN
ejpam-6366	201	21	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6366	201	22	and	and	CCONJ
ejpam-6366	201	23	according	accord	VERB
ejpam-6366	201	24	to	to	ADP
ejpam-6366	201	25	(	(	PUNCT
ejpam-6366	201	26	9	9	NUM
ejpam-6366	201	27	)	)	PUNCT
ejpam-6366	201	28	,	,	PUNCT
ejpam-6366	201	29	we	we	PRON
ejpam-6366	201	30	get	get	VERB
ejpam-6366	201	31	|d3|	|d3|	NOUN
ejpam-6366	201	32	≤	≤	NOUN
ejpam-6366	201	33	(	(	PUNCT
ejpam-6366	201	34	α+	α+	X
ejpam-6366	201	35	β	β	X
ejpam-6366	201	36	)	)	PUNCT
ejpam-6366	201	37	(	(	PUNCT
ejpam-6366	201	38	1−	1−	NUM
ejpam-6366	201	39	γ	γ	X
ejpam-6366	201	40	)	)	PUNCT
ejpam-6366	201	41	(	(	PUNCT
ejpam-6366	201	42	p	p	NOUN
ejpam-6366	201	43	−q	−q	NOUN
ejpam-6366	201	44	)	)	PUNCT
ejpam-6366	201	45	2	2	NUM
ejpam-6366	201	46	(	(	PUNCT
ejpam-6366	201	47	α+	α+	NOUN
ejpam-6366	201	48	2β	2β	NOUN
ejpam-6366	201	49	)	)	PUNCT
ejpam-6366	201	50	.2.max	.2.max	NOUN
ejpam-6366	201	51	{	{	PUNCT
ejpam-6366	201	52	1	1	NUM
ejpam-6366	201	53	;	;	PUNCT
ejpam-6366	201	54	∣∣∣∣2.12	∣∣∣∣2.12	NOUN
ejpam-6366	201	55	[	[	PUNCT
ejpam-6366	201	56	1	1	NUM
ejpam-6366	201	57	+	+	NOUN
ejpam-6366	201	58	q−	q−	PROPN
ejpam-6366	201	59	β	β	X
ejpam-6366	201	60	(	(	PUNCT
ejpam-6366	201	61	1−	1−	NUM
ejpam-6366	201	62	γ	γ	NOUN
ejpam-6366	201	63	)	)	PUNCT
ejpam-6366	201	64	(	(	PUNCT
ejpam-6366	201	65	p	p	NOUN
ejpam-6366	201	66	−q	−q	NOUN
ejpam-6366	201	67	)	)	PUNCT
ejpam-6366	202	1	α+	α+	PRON
ejpam-6366	202	2	β	β	X
ejpam-6366	202	3	]	]	PUNCT
ejpam-6366	202	4	−	−	PROPN
ejpam-6366	202	5	1	1	NUM
ejpam-6366	202	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6366	202	7	}	}	PUNCT
ejpam-6366	202	8	=	=	SYM
ejpam-6366	202	9	(	(	PUNCT
ejpam-6366	202	10	α+	α+	X
ejpam-6366	202	11	β	β	X
ejpam-6366	202	12	)	)	PUNCT
ejpam-6366	202	13	(	(	PUNCT
ejpam-6366	202	14	1−	1−	NUM
ejpam-6366	202	15	γ	γ	X
ejpam-6366	202	16	)	)	PUNCT
ejpam-6366	202	17	(	(	PUNCT
ejpam-6366	202	18	p	p	NOUN
ejpam-6366	202	19	−q	−q	NOUN
ejpam-6366	202	20	)	)	PUNCT
ejpam-6366	202	21	α+	α+	DET
ejpam-6366	202	22	2β	2β	NOUN
ejpam-6366	202	23	max	max	NOUN
ejpam-6366	202	24	{	{	PUNCT
ejpam-6366	202	25	1	1	NUM
ejpam-6366	202	26	;	;	PUNCT
ejpam-6366	202	27	∣∣∣∣q−	∣∣∣∣q−	NUM
ejpam-6366	202	28	β	β	X
ejpam-6366	202	29	(	(	PUNCT
ejpam-6366	202	30	1−	1−	NUM
ejpam-6366	202	31	γ	γ	X
ejpam-6366	202	32	)	)	PUNCT
ejpam-6366	202	33	(	(	PUNCT
ejpam-6366	202	34	p	p	NOUN
ejpam-6366	202	35	−q	−q	NOUN
ejpam-6366	202	36	)	)	PUNCT
ejpam-6366	202	37	α+	α+	PRON
ejpam-6366	202	38	β	β	X
ejpam-6366	202	39	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6366	202	40	}	}	PUNCT
ejpam-6366	202	41	.	.	PUNCT
ejpam-6366	203	1	the	the	DET
ejpam-6366	203	2	equality	equality	NOUN
ejpam-6366	203	3	(	(	PUNCT
ejpam-6366	203	4	28	28	NUM
ejpam-6366	203	5	)	)	PUNCT
ejpam-6366	203	6	leads	lead	VERB
ejpam-6366	203	7	to	to	ADP
ejpam-6366	203	8	|d4|	|d4|	NOUN
ejpam-6366	203	9	=	=	SYM
ejpam-6366	203	10	(	(	PUNCT
ejpam-6366	203	11	α+β)(1−γ)(p−q	α+β)(1−γ)(p−q	NUM
ejpam-6366	203	12	)	)	PUNCT
ejpam-6366	203	13	2(α+3β	2(α+3β	NUM
ejpam-6366	203	14	)	)	PUNCT
ejpam-6366	204	1	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-6366	204	2	δ3	δ3	PROPN
ejpam-6366	204	3	−	−	PROPN
ejpam-6366	204	4	[	[	PUNCT
ejpam-6366	204	5	1	1	NUM
ejpam-6366	204	6	+	+	NOUN
ejpam-6366	204	7	q−	q−	PROPN
ejpam-6366	204	8	(	(	PUNCT
ejpam-6366	204	9	2α+3β)β(1−γ)(p−q	2α+3β)β(1−γ)(p−q	NUM
ejpam-6366	204	10	)	)	PUNCT
ejpam-6366	204	11	2(α+β)(α+2β	2(α+β)(α+2β	NUM
ejpam-6366	204	12	)	)	PUNCT
ejpam-6366	204	13	]	]	PUNCT
ejpam-6366	205	1	δ1δ2	δ1δ2	PUNCT
ejpam-6366	205	2	+	+	PUNCT
ejpam-6366	205	3	{	{	PUNCT
ejpam-6366	205	4	(	(	PUNCT
ejpam-6366	205	5	1+q	1+q	NUM
ejpam-6366	205	6	2	2	NUM
ejpam-6366	205	7	)	)	SYM
ejpam-6366	205	8	2	2	NUM
ejpam-6366	205	9	−	−	PROPN
ejpam-6366	205	10	(	(	PUNCT
ejpam-6366	205	11	2α+3β)β(1+q)(1−γ)(p−q	2α+3β)β(1+q)(1−γ)(p−q	NUM
ejpam-6366	205	12	)	)	PUNCT
ejpam-6366	205	13	4(α+β)(α+2β	4(α+β)(α+2β	NUM
ejpam-6366	205	14	)	)	PUNCT
ejpam-6366	206	1	+	+	CCONJ
ejpam-6366	206	2	β2(p−q)2(1−γ)2	β2(p−q)2(1−γ)2	NUM
ejpam-6366	206	3	4(α+β)(α+2β	4(α+β)(α+2β	NUM
ejpam-6366	206	4	)	)	PUNCT
ejpam-6366	206	5	}	}	PUNCT
ejpam-6366	206	6	δ31	δ31	VERB
ejpam-6366	206	7	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PROPN
ejpam-6366	206	8	and	and	CCONJ
ejpam-6366	206	9	using	use	VERB
ejpam-6366	206	10	the	the	DET
ejpam-6366	206	11	triangle	triangle	NOUN
ejpam-6366	206	12	inequality	inequality	NOUN
ejpam-6366	206	13	we	we	PRON
ejpam-6366	206	14	have	have	VERB
ejpam-6366	206	15	|d4|	|d4|	NOUN
ejpam-6366	206	16	≤	≤	PROPN
ejpam-6366	206	17	(	(	PUNCT
ejpam-6366	206	18	α+β)(1−γ)(p−q	α+β)(1−γ)(p−q	NUM
ejpam-6366	206	19	)	)	PUNCT
ejpam-6366	206	20	2(α+3β	2(α+3β	NUM
ejpam-6366	206	21	)	)	PUNCT
ejpam-6366	207	1			PRON
ejpam-6366	207	2	∣∣∣δ3	∣∣∣δ3	VERB
ejpam-6366	207	3	−	−	NOUN
ejpam-6366	208	1	[	[	PUNCT
ejpam-6366	208	2	1	1	NUM
ejpam-6366	208	3	+	+	NOUN
ejpam-6366	208	4	q−	q−	PROPN
ejpam-6366	208	5	(	(	PUNCT
ejpam-6366	208	6	2α+3β)β(1−γ)(p−q	2α+3β)β(1−γ)(p−q	NUM
ejpam-6366	208	7	)	)	PUNCT
ejpam-6366	208	8	2(α+β)(α+2β	2(α+β)(α+2β	NUM
ejpam-6366	208	9	)	)	PUNCT
ejpam-6366	208	10	]	]	PUNCT
ejpam-6366	209	1	δ1δ2	δ1δ2	X
ejpam-6366	209	2	∣∣∣	∣∣∣	NOUN
ejpam-6366	209	3	+	+	CCONJ
ejpam-6366	209	4	∣∣∣∣(1+q	∣∣∣∣(1+q	NOUN
ejpam-6366	209	5	2	2	NUM
ejpam-6366	209	6	)	)	PUNCT
ejpam-6366	209	7	2	2	NUM
ejpam-6366	209	8	−	−	PROPN
ejpam-6366	209	9	(	(	PUNCT
ejpam-6366	209	10	2α+3β)β(1+q)(1−γ)(p−q	2α+3β)β(1+q)(1−γ)(p−q	NUM
ejpam-6366	209	11	)	)	PUNCT
ejpam-6366	209	12	4(α+β)(α+2β	4(α+β)(α+2β	NUM
ejpam-6366	209	13	)	)	PUNCT
ejpam-6366	210	1	+	+	CCONJ
ejpam-6366	210	2	β2(p−q)2(1−γ)2	β2(p−q)2(1−γ)2	NUM
ejpam-6366	210	3	4(α+β)(α+2β	4(α+β)(α+2β	NUM
ejpam-6366	210	4	)	)	PUNCT
ejpam-6366	210	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6366	210	6	|δ1|3	|δ1|3	PUNCT
ejpam-6366	210	7			PROPN
ejpam-6366	210	8	,	,	PUNCT
ejpam-6366	210	9	from	from	ADP
ejpam-6366	210	10	(	(	PUNCT
ejpam-6366	210	11	8)	8)	NUM
ejpam-6366	210	12	and	and	CCONJ
ejpam-6366	210	13	(	(	PUNCT
ejpam-6366	210	14	10	10	NUM
ejpam-6366	210	15	)	)	PUNCT
ejpam-6366	210	16	,	,	PUNCT
ejpam-6366	210	17	the	the	DET
ejpam-6366	210	18	above	above	ADJ
ejpam-6366	210	19	inequality	inequality	NOUN
ejpam-6366	210	20	implies	imply	VERB
ejpam-6366	210	21	that	that	SCONJ
ejpam-6366	210	22	|d4|	|d4|	PROPN
ejpam-6366	210	23	≤	≤	PROPN
ejpam-6366	210	24	(	(	PUNCT
ejpam-6366	210	25	α+β)(1−γ)(p−q	α+β)(1−γ)(p−q	NUM
ejpam-6366	210	26	)	)	PUNCT
ejpam-6366	210	27	2(α+3β	2(α+3β	NUM
ejpam-6366	210	28	)	)	PUNCT
ejpam-6366	210	29			PROPN
ejpam-6366	210	30	max	max	PROPN
ejpam-6366	210	31	{	{	PUNCT
ejpam-6366	210	32	1	1	NUM
ejpam-6366	210	33	;	;	PUNCT
ejpam-6366	210	34	∣∣∣	∣∣∣	X
ejpam-6366	210	35	(	(	PUNCT
ejpam-6366	210	36	2α+3β)β(1−γ)(p−q	2α+3β)β(1−γ)(p−q	NUM
ejpam-6366	210	37	)	)	PUNCT
ejpam-6366	210	38	(	(	PUNCT
ejpam-6366	210	39	α+β)(α+2β	α+β)(α+2β	NOUN
ejpam-6366	210	40	)	)	PUNCT
ejpam-6366	210	41	−	−	PROPN
ejpam-6366	210	42	1−	1−	NUM
ejpam-6366	210	43	2q	2q	NUM
ejpam-6366	210	44	∣∣∣	∣∣∣	ADJ
ejpam-6366	210	45	}	}	PUNCT
ejpam-6366	210	46	+	+	NUM
ejpam-6366	210	47	∣∣∣1	∣∣∣1	ADJ
ejpam-6366	211	1	+	+	PROPN
ejpam-6366	211	2	q−	q−	PROPN
ejpam-6366	211	3	β(1−γ)(p−q	β(1−γ)(p−q	PROPN
ejpam-6366	211	4	)	)	PUNCT
ejpam-6366	211	5	α+β	α+β	PROPN
ejpam-6366	211	6	∣∣∣	∣∣∣	ADP
ejpam-6366	211	7	∣∣∣1	∣∣∣1	ADJ
ejpam-6366	211	8	+	+	PROPN
ejpam-6366	211	9	q−	q−	PROPN
ejpam-6366	211	10	β(1−γ)(p−q	β(1−γ)(p−q	ADJ
ejpam-6366	211	11	)	)	PUNCT
ejpam-6366	212	1	α+2β	α+2β	NOUN
ejpam-6366	212	2	∣∣∣	∣∣∣	ADJ
ejpam-6366	212	3			NOUN
ejpam-6366	212	4	.	.	PUNCT
ejpam-6366	213	1	this	this	PRON
ejpam-6366	213	2	completes	complete	VERB
ejpam-6366	213	3	the	the	DET
ejpam-6366	213	4	proof	proof	NOUN
ejpam-6366	213	5	of	of	ADP
ejpam-6366	213	6	theorem	theorem	ADJ
ejpam-6366	213	7	4	4	NUM
ejpam-6366	213	8	.	.	PUNCT
ejpam-6366	213	9	putting	put	VERB
ejpam-6366	213	10	p	p	NOUN
ejpam-6366	213	11	=	=	NOUN
ejpam-6366	213	12	1	1	NUM
ejpam-6366	213	13	and	and	CCONJ
ejpam-6366	213	14	q	q	NOUN
ejpam-6366	213	15	=	=	PUNCT
ejpam-6366	213	16	−1	−1	NOUN
ejpam-6366	213	17	in	in	ADP
ejpam-6366	213	18	theorem	theorem	NOUN
ejpam-6366	213	19	4	4	NUM
ejpam-6366	213	20	,	,	PUNCT
ejpam-6366	213	21	we	we	PRON
ejpam-6366	213	22	get	get	VERB
ejpam-6366	213	23	the	the	DET
ejpam-6366	213	24	following	following	NOUN
ejpam-6366	213	25	.	.	PUNCT
ejpam-6366	214	1	corollary	corollary	ADJ
ejpam-6366	214	2	10	10	NUM
ejpam-6366	214	3	.	.	PUNCT
ejpam-6366	215	1	if	if	SCONJ
ejpam-6366	215	2	g	g	PROPN
ejpam-6366	215	3	∈	∈	PROPN
ejpam-6366	215	4	sk	sk	X
ejpam-6366	215	5	[	[	X
ejpam-6366	215	6	γ;α	γ;α	X
ejpam-6366	215	7	,	,	PUNCT
ejpam-6366	215	8	β	β	X
ejpam-6366	215	9	]	]	X
ejpam-6366	215	10	,	,	PUNCT
ejpam-6366	215	11	then	then	ADV
ejpam-6366	215	12	|d2|	|d2|	VERB
ejpam-6366	215	13	≤	≤	ADJ
ejpam-6366	215	14	2	2	NUM
ejpam-6366	215	15	(	(	PUNCT
ejpam-6366	215	16	1−	1−	NUM
ejpam-6366	215	17	γ	γ	NOUN
ejpam-6366	215	18	)	)	PUNCT
ejpam-6366	215	19	,	,	PUNCT
ejpam-6366	215	20	|d3|	|d3|	NOUN
ejpam-6366	215	21	≤	≤	ADV
ejpam-6366	215	22	2	2	NUM
ejpam-6366	216	1	[	[	X
ejpam-6366	216	2	2β	2β	NUM
ejpam-6366	216	3	(	(	PUNCT
ejpam-6366	216	4	1−	1−	NUM
ejpam-6366	216	5	γ	γ	X
ejpam-6366	216	6	)	)	PUNCT
ejpam-6366	216	7	+	+	CCONJ
ejpam-6366	216	8	α+	α+	X
ejpam-6366	216	9	β	β	X
ejpam-6366	216	10	]	]	X
ejpam-6366	216	11	(	(	PUNCT
ejpam-6366	216	12	1−	1−	NUM
ejpam-6366	216	13	γ	γ	NOUN
ejpam-6366	216	14	)	)	PUNCT
ejpam-6366	216	15	α+	α+	DET
ejpam-6366	216	16	2β	2β	NOUN
ejpam-6366	216	17	,	,	PUNCT
ejpam-6366	216	18	|d4|	|d4|	NOUN
ejpam-6366	216	19	≤	≤	NOUN
ejpam-6366	216	20	2	2	NUM
ejpam-6366	216	21	[	[	X
ejpam-6366	216	22	2β	2β	NUM
ejpam-6366	216	23	(	(	PUNCT
ejpam-6366	216	24	1−	1−	NUM
ejpam-6366	216	25	γ	γ	X
ejpam-6366	216	26	)	)	PUNCT
ejpam-6366	216	27	+	+	CCONJ
ejpam-6366	216	28	α+	α+	X
ejpam-6366	216	29	β	β	X
ejpam-6366	216	30	]	]	X
ejpam-6366	217	1	[	[	X
ejpam-6366	217	2	2β	2β	NOUN
ejpam-6366	217	3	(	(	PUNCT
ejpam-6366	217	4	1−	1−	NUM
ejpam-6366	217	5	γ	γ	X
ejpam-6366	217	6	)	)	PUNCT
ejpam-6366	217	7	+	+	CCONJ
ejpam-6366	217	8	α+	α+	DET
ejpam-6366	217	9	2β	2β	NOUN
ejpam-6366	217	10	]	]	PUNCT
ejpam-6366	217	11	(	(	PUNCT
ejpam-6366	217	12	1−	1−	NUM
ejpam-6366	217	13	γ	γ	X
ejpam-6366	217	14	)	)	PUNCT
ejpam-6366	217	15	(	(	PUNCT
ejpam-6366	217	16	α+	α+	NOUN
ejpam-6366	217	17	2β	2β	NOUN
ejpam-6366	217	18	)	)	PUNCT
ejpam-6366	217	19	(	(	PUNCT
ejpam-6366	217	20	α+	α+	NOUN
ejpam-6366	217	21	3β	3β	NUM
ejpam-6366	217	22	)	)	PUNCT
ejpam-6366	217	23	.	.	PUNCT
ejpam-6366	218	1	putting	put	VERB
ejpam-6366	218	2	α	α	NOUN
ejpam-6366	218	3	=	=	SYM
ejpam-6366	218	4	γ	γ	X
ejpam-6366	218	5	=	=	SYM
ejpam-6366	218	6	0	0	NUM
ejpam-6366	218	7	in	in	ADP
ejpam-6366	218	8	theorem	theorem	NOUN
ejpam-6366	218	9	4	4	NUM
ejpam-6366	218	10	,	,	PUNCT
ejpam-6366	218	11	we	we	PRON
ejpam-6366	218	12	get	get	VERB
ejpam-6366	218	13	the	the	DET
ejpam-6366	218	14	following	following	NOUN
ejpam-6366	218	15	.	.	PUNCT
ejpam-6366	219	1	corollary	corollary	ADJ
ejpam-6366	219	2	11	11	NUM
ejpam-6366	219	3	.	.	PUNCT
ejpam-6366	220	1	if	if	SCONJ
ejpam-6366	220	2	g	g	PROPN
ejpam-6366	220	3	∈	∈	PROPN
ejpam-6366	220	4	s	s	PART
ejpam-6366	220	5	[	[	X
ejpam-6366	220	6	p	p	X
ejpam-6366	220	7	,	,	PUNCT
ejpam-6366	220	8	q	q	X
ejpam-6366	220	9	]	]	X
ejpam-6366	220	10	,	,	PUNCT
ejpam-6366	220	11	then	then	ADV
ejpam-6366	220	12	|d2|	|d2|	VERB
ejpam-6366	220	13	≤	≤	ADJ
ejpam-6366	220	14	p	p	NOUN
ejpam-6366	220	15	−q	−q	NOUN
ejpam-6366	220	16	,	,	PUNCT
ejpam-6366	220	17	|d3|	|d3|	NOUN
ejpam-6366	220	18	≤	≤	VERB
ejpam-6366	221	1	p	p	NOUN
ejpam-6366	221	2	−q	−q	ADJ
ejpam-6366	221	3	2	2	NUM
ejpam-6366	221	4	max	max	NOUN
ejpam-6366	221	5	{	{	PUNCT
ejpam-6366	221	6	1	1	NUM
ejpam-6366	221	7	;	;	PUNCT
ejpam-6366	221	8	|2q−	|2q−	PRON
ejpam-6366	221	9	p	p	NOUN
ejpam-6366	221	10	|	|	NOUN
ejpam-6366	221	11	}	}	PUNCT
ejpam-6366	221	12	,	,	PUNCT
ejpam-6366	221	13	|d4|	|d4|	ADJ
ejpam-6366	221	14	≤	≤	PROPN
ejpam-6366	221	15	p−q	p−q	NOUN
ejpam-6366	221	16	3	3	NUM
ejpam-6366	221	17	[	[	PUNCT
ejpam-6366	221	18	max	max	X
ejpam-6366	221	19	{	{	PUNCT
ejpam-6366	221	20	1	1	NUM
ejpam-6366	221	21	;	;	PUNCT
ejpam-6366	221	22	∣∣1	∣∣1	NUM
ejpam-6366	221	23	+	+	SYM
ejpam-6366	221	24	7	7	NUM
ejpam-6366	221	25	2q−	2q−	NUM
ejpam-6366	221	26	3	3	NUM
ejpam-6366	221	27	2p	2p	NOUN
ejpam-6366	221	28	∣∣}+	∣∣}+	VERB
ejpam-6366	221	29	|1	|1	PRON
ejpam-6366	221	30	+	+	NUM
ejpam-6366	222	1	2q−	2q−	PROPN
ejpam-6366	222	2	p	p	NOUN
ejpam-6366	222	3	|	|	NOUN
ejpam-6366	222	4	∣∣∣∣1	∣∣∣∣1	NOUN
ejpam-6366	222	5	+	+	CCONJ
ejpam-6366	222	6	3	3	NUM
ejpam-6366	222	7	2	2	NUM
ejpam-6366	222	8	q−	q−	PROPN
ejpam-6366	222	9	1	1	NUM
ejpam-6366	222	10	2	2	NUM
ejpam-6366	222	11	p	p	NOUN
ejpam-6366	222	12	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6366	222	13	]	]	PUNCT
ejpam-6366	222	14	.	.	PUNCT
ejpam-6366	223	1	t.	t.	PROPN
ejpam-6366	223	2	m.	m.	PROPN
ejpam-6366	223	3	seoudy	seoudy	PROPN
ejpam-6366	223	4	,	,	PUNCT
ejpam-6366	223	5	a.	a.	PROPN
ejpam-6366	223	6	e.	e.	PROPN
ejpam-6366	223	7	shammaky	shammaky	PROPN
ejpam-6366	223	8	/	/	SYM
ejpam-6366	223	9	eur	eur	PROPN
ejpam-6366	223	10	.	.	PUNCT
ejpam-6366	224	1	j.	j.	PROPN
ejpam-6366	224	2	pure	pure	PROPN
ejpam-6366	224	3	appl	appl	PROPN
ejpam-6366	224	4	.	.	PROPN
ejpam-6366	224	5	math	math	PROPN
ejpam-6366	224	6	,	,	PUNCT
ejpam-6366	224	7	18	18	NUM
ejpam-6366	224	8	(	(	PUNCT
ejpam-6366	224	9	4	4	NUM
ejpam-6366	224	10	)	)	PUNCT
ejpam-6366	224	11	(	(	PUNCT
ejpam-6366	224	12	2025	2025	NUM
ejpam-6366	224	13	)	)	PUNCT
ejpam-6366	224	14	,	,	PUNCT
ejpam-6366	224	15	6366	6366	NUM
ejpam-6366	224	16	11	11	NUM
ejpam-6366	224	17	of	of	ADP
ejpam-6366	224	18	15	15	NUM
ejpam-6366	224	19	putting	put	VERB
ejpam-6366	224	20	β	β	X
ejpam-6366	224	21	=	=	PUNCT
ejpam-6366	224	22	γ	γ	X
ejpam-6366	224	23	=	=	SYM
ejpam-6366	224	24	0	0	NUM
ejpam-6366	224	25	in	in	ADP
ejpam-6366	224	26	theorem	theorem	NOUN
ejpam-6366	224	27	4	4	NUM
ejpam-6366	224	28	,	,	PUNCT
ejpam-6366	224	29	we	we	PRON
ejpam-6366	224	30	get	get	VERB
ejpam-6366	224	31	the	the	DET
ejpam-6366	224	32	next	next	ADJ
ejpam-6366	224	33	.	.	PUNCT
ejpam-6366	225	1	corollary	corollary	ADJ
ejpam-6366	225	2	12	12	NUM
ejpam-6366	225	3	.	.	PUNCT
ejpam-6366	226	1	if	if	SCONJ
ejpam-6366	226	2	g	g	PROPN
ejpam-6366	226	3	∈	∈	PROPN
ejpam-6366	226	4	k	k	PROPN
ejpam-6366	227	1	[	[	X
ejpam-6366	227	2	p	p	X
ejpam-6366	227	3	,	,	PUNCT
ejpam-6366	227	4	q	q	X
ejpam-6366	227	5	]	]	X
ejpam-6366	227	6	,	,	PUNCT
ejpam-6366	227	7	then	then	ADV
ejpam-6366	227	8	|d2|	|d2|	VERB
ejpam-6366	227	9	≤	≤	ADJ
ejpam-6366	227	10	p	p	NOUN
ejpam-6366	227	11	−q	−q	NOUN
ejpam-6366	227	12	,	,	PUNCT
ejpam-6366	227	13	|d3|	|d3|	NOUN
ejpam-6366	227	14	≤	≤	VERB
ejpam-6366	227	15	p	p	NOUN
ejpam-6366	227	16	−q	−q	NOUN
ejpam-6366	227	17	,	,	PUNCT
ejpam-6366	227	18	|d4|	|d4|	ADJ
ejpam-6366	227	19	≤	≤	PROPN
ejpam-6366	227	20	(	(	PUNCT
ejpam-6366	227	21	p	p	NOUN
ejpam-6366	227	22	−q	−q	NOUN
ejpam-6366	227	23	)	)	PUNCT
ejpam-6366	227	24	[	[	PUNCT
ejpam-6366	227	25	max	max	X
ejpam-6366	227	26	{	{	PUNCT
ejpam-6366	227	27	1	1	NUM
ejpam-6366	227	28	;	;	PUNCT
ejpam-6366	227	29	|1	|1	PRON
ejpam-6366	227	30	+	+	NUM
ejpam-6366	227	31	2q|}+	2q|}+	NUM
ejpam-6366	227	32	(	(	PUNCT
ejpam-6366	227	33	1	1	NUM
ejpam-6366	227	34	+	+	NOUN
ejpam-6366	227	35	q)2	q)2	X
ejpam-6366	227	36	]	]	PUNCT
ejpam-6366	227	37	.	.	PUNCT
ejpam-6366	228	1	theorem	theorem	ADJ
ejpam-6366	228	2	5	5	NUM
ejpam-6366	228	3	.	.	PUNCT
ejpam-6366	229	1	if	if	SCONJ
ejpam-6366	229	2	g	g	PROPN
ejpam-6366	229	3	∈	∈	PROPN
ejpam-6366	229	4	sk	sk	VERB
ejpam-6366	230	1	[	[	X
ejpam-6366	230	2	p	p	X
ejpam-6366	230	3	,	,	PUNCT
ejpam-6366	230	4	q	q	NOUN
ejpam-6366	230	5	,	,	PUNCT
ejpam-6366	230	6	γ;α	γ;α	ADV
ejpam-6366	230	7	,	,	PUNCT
ejpam-6366	230	8	β	β	X
ejpam-6366	230	9	]	]	X
ejpam-6366	230	10	,	,	PUNCT
ejpam-6366	230	11	then∣∣d3	then∣∣d3	NOUN
ejpam-6366	230	12	−	−	PROPN
ejpam-6366	230	13	µd22	µd22	PROPN
ejpam-6366	230	14	∣∣	∣∣	NUM
ejpam-6366	230	15	≤	≤	NOUN
ejpam-6366	230	16	(	(	PUNCT
ejpam-6366	230	17	α+	α+	X
ejpam-6366	230	18	β	β	X
ejpam-6366	230	19	)	)	PUNCT
ejpam-6366	230	20	(	(	PUNCT
ejpam-6366	230	21	1−	1−	NUM
ejpam-6366	230	22	γ	γ	X
ejpam-6366	230	23	)	)	PUNCT
ejpam-6366	230	24	(	(	PUNCT
ejpam-6366	230	25	p	p	NOUN
ejpam-6366	230	26	−q	−q	NOUN
ejpam-6366	230	27	)	)	PUNCT
ejpam-6366	230	28	α+	α+	DET
ejpam-6366	230	29	2β	2β	NOUN
ejpam-6366	230	30	max	max	NOUN
ejpam-6366	230	31	{	{	PUNCT
ejpam-6366	230	32	1	1	NUM
ejpam-6366	230	33	;	;	PUNCT
ejpam-6366	230	34	∣∣∣∣q−	∣∣∣∣q−	NUM
ejpam-6366	230	35	β(1−γ)(p−q	β(1−γ)(p−q	PROPN
ejpam-6366	230	36	)	)	PUNCT
ejpam-6366	230	37	α+β	α+β	PROPN
ejpam-6366	230	38	(	(	PUNCT
ejpam-6366	230	39	1−	1−	NUM
ejpam-6366	230	40	α+	α+	PRON
ejpam-6366	230	41	2β	2β	NOUN
ejpam-6366	230	42	β	β	X
ejpam-6366	230	43	µ	µ	X
ejpam-6366	230	44	)	)	PUNCT
ejpam-6366	230	45	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6366	230	46	}	}	PUNCT
ejpam-6366	230	47	.	.	PUNCT
ejpam-6366	231	1	(	(	PUNCT
ejpam-6366	231	2	29	29	NUM
ejpam-6366	231	3	)	)	PUNCT
ejpam-6366	231	4	proof	proof	NOUN
ejpam-6366	231	5	.	.	PUNCT
ejpam-6366	232	1	if	if	SCONJ
ejpam-6366	232	2	g	g	PROPN
ejpam-6366	232	3	∈	∈	PROPN
ejpam-6366	232	4	sk	sk	VERB
ejpam-6366	232	5	[	[	X
ejpam-6366	232	6	p	p	X
ejpam-6366	232	7	,	,	PUNCT
ejpam-6366	232	8	q	q	NOUN
ejpam-6366	232	9	,	,	PUNCT
ejpam-6366	232	10	γ;α	γ;α	ADV
ejpam-6366	232	11	,	,	PUNCT
ejpam-6366	232	12	β	β	X
ejpam-6366	232	13	]	]	X
ejpam-6366	232	14	,	,	PUNCT
ejpam-6366	232	15	then	then	ADV
ejpam-6366	232	16	from	from	ADP
ejpam-6366	232	17	(	(	PUNCT
ejpam-6366	232	18	26	26	NUM
ejpam-6366	232	19	)	)	PUNCT
ejpam-6366	232	20	and	and	CCONJ
ejpam-6366	232	21	(	(	PUNCT
ejpam-6366	232	22	27	27	NUM
ejpam-6366	232	23	)	)	PUNCT
ejpam-6366	232	24	we	we	PRON
ejpam-6366	232	25	get	get	VERB
ejpam-6366	232	26	d3	d3	PROPN
ejpam-6366	232	27	−	−	PROPN
ejpam-6366	232	28	µd22	µd22	PROPN
ejpam-6366	232	29	=	=	SYM
ejpam-6366	232	30	(	(	PUNCT
ejpam-6366	232	31	α+	α+	X
ejpam-6366	232	32	β	β	X
ejpam-6366	232	33	)	)	PUNCT
ejpam-6366	232	34	(	(	PUNCT
ejpam-6366	232	35	1−	1−	NUM
ejpam-6366	232	36	γ	γ	X
ejpam-6366	232	37	)	)	PUNCT
ejpam-6366	232	38	(	(	PUNCT
ejpam-6366	232	39	p	p	NOUN
ejpam-6366	232	40	−q	−q	NOUN
ejpam-6366	232	41	)	)	PUNCT
ejpam-6366	232	42	2	2	NUM
ejpam-6366	232	43	(	(	PUNCT
ejpam-6366	232	44	α+	α+	NOUN
ejpam-6366	232	45	2β	2β	NOUN
ejpam-6366	232	46	)	)	PUNCT
ejpam-6366	232	47	{	{	PUNCT
ejpam-6366	232	48	δ2	δ2	VERB
ejpam-6366	232	49	−	−	PROPN
ejpam-6366	232	50	uδ21	uδ21	PROPN
ejpam-6366	232	51	}	}	PUNCT
ejpam-6366	232	52	,	,	PUNCT
ejpam-6366	232	53	(	(	PUNCT
ejpam-6366	232	54	30	30	NUM
ejpam-6366	232	55	)	)	PUNCT
ejpam-6366	232	56	where	where	SCONJ
ejpam-6366	232	57	u	u	NOUN
ejpam-6366	232	58	=	=	NOUN
ejpam-6366	232	59	1	1	NUM
ejpam-6366	232	60	2	2	NUM
ejpam-6366	232	61	[	[	PUNCT
ejpam-6366	232	62	1	1	NUM
ejpam-6366	232	63	+	+	NOUN
ejpam-6366	232	64	q−	q−	PROPN
ejpam-6366	232	65	β	β	X
ejpam-6366	232	66	(	(	PUNCT
ejpam-6366	232	67	1−	1−	NUM
ejpam-6366	232	68	γ	γ	NOUN
ejpam-6366	232	69	)	)	PUNCT
ejpam-6366	232	70	(	(	PUNCT
ejpam-6366	232	71	p	p	NOUN
ejpam-6366	232	72	−q	−q	NOUN
ejpam-6366	232	73	)	)	PUNCT
ejpam-6366	233	1	α+	α+	DET
ejpam-6366	233	2	β	β	X
ejpam-6366	233	3	(	(	PUNCT
ejpam-6366	233	4	1−	1−	NUM
ejpam-6366	233	5	α+	α+	PRON
ejpam-6366	233	6	2β	2β	NOUN
ejpam-6366	233	7	β	β	X
ejpam-6366	233	8	µ	µ	NOUN
ejpam-6366	233	9	)	)	PUNCT
ejpam-6366	233	10	]	]	PUNCT
ejpam-6366	233	11	.	.	PUNCT
ejpam-6366	234	1	(	(	PUNCT
ejpam-6366	234	2	31	31	NUM
ejpam-6366	234	3	)	)	PUNCT
ejpam-6366	234	4	applying	apply	VERB
ejpam-6366	234	5	(	(	PUNCT
ejpam-6366	234	6	9	9	NUM
ejpam-6366	234	7	)	)	PUNCT
ejpam-6366	234	8	to	to	ADP
ejpam-6366	234	9	(	(	PUNCT
ejpam-6366	234	10	30	30	NUM
ejpam-6366	234	11	)	)	PUNCT
ejpam-6366	234	12	,	,	PUNCT
ejpam-6366	234	13	it	it	PRON
ejpam-6366	234	14	follows	follow	VERB
ejpam-6366	234	15	that∣∣d3	that∣∣d3	PROPN
ejpam-6366	234	16	−	−	PROPN
ejpam-6366	235	1	µd22	µd22	PROPN
ejpam-6366	235	2	∣∣	∣∣	NUM
ejpam-6366	235	3	≤	≤	PROPN
ejpam-6366	235	4	(	(	PUNCT
ejpam-6366	235	5	α+β)(1−γ)(p−q	α+β)(1−γ)(p−q	NUM
ejpam-6366	235	6	)	)	PUNCT
ejpam-6366	235	7	2(α+2β	2(α+2β	X
ejpam-6366	235	8	)	)	PUNCT
ejpam-6366	235	9	.2max	.2max	NOUN
ejpam-6366	235	10	{	{	PUNCT
ejpam-6366	235	11	1	1	NUM
ejpam-6366	235	12	;	;	PUNCT
ejpam-6366	235	13	∣∣∣∣2.12	∣∣∣∣2.12	NOUN
ejpam-6366	235	14	[	[	PUNCT
ejpam-6366	235	15	1	1	NUM
ejpam-6366	235	16	+	+	NOUN
ejpam-6366	235	17	q−	q−	PROPN
ejpam-6366	235	18	β(1−γ)(p−q	β(1−γ)(p−q	PROPN
ejpam-6366	235	19	)	)	PUNCT
ejpam-6366	235	20	α+β	α+β	PROPN
ejpam-6366	236	1	(	(	PUNCT
ejpam-6366	236	2	1−	1−	NUM
ejpam-6366	236	3	α+2β	α+2β	PROPN
ejpam-6366	236	4	β	β	X
ejpam-6366	236	5	µ	µ	X
ejpam-6366	236	6	)	)	PUNCT
ejpam-6366	236	7	]	]	PUNCT
ejpam-6366	237	1	−	−	PROPN
ejpam-6366	237	2	1	1	NUM
ejpam-6366	237	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6366	237	4	}	}	PUNCT
ejpam-6366	237	5	=	=	PUNCT
ejpam-6366	237	6	(	(	PUNCT
ejpam-6366	237	7	α+β)(1−γ)(p−q	α+β)(1−γ)(p−q	NUM
ejpam-6366	237	8	)	)	PUNCT
ejpam-6366	237	9	α+2β	α+2β	PROPN
ejpam-6366	237	10	max	max	NOUN
ejpam-6366	237	11	{	{	PUNCT
ejpam-6366	237	12	1	1	NUM
ejpam-6366	237	13	;	;	PUNCT
ejpam-6366	237	14	∣∣∣q−	∣∣∣q−	VERB
ejpam-6366	237	15	β(1−γ)(p−q	β(1−γ)(p−q	NOUN
ejpam-6366	237	16	)	)	PUNCT
ejpam-6366	237	17	α+β	α+β	NUM
ejpam-6366	237	18	(	(	PUNCT
ejpam-6366	237	19	1−	1−	NUM
ejpam-6366	237	20	α+2β	α+2β	PROPN
ejpam-6366	237	21	β	β	X
ejpam-6366	237	22	µ	µ	X
ejpam-6366	237	23	)	)	PUNCT
ejpam-6366	237	24	∣∣∣	∣∣∣	ADJ
ejpam-6366	237	25	}	}	PUNCT
ejpam-6366	237	26	.	.	PUNCT
ejpam-6366	238	1	this	this	PRON
ejpam-6366	238	2	completes	complete	VERB
ejpam-6366	238	3	the	the	DET
ejpam-6366	238	4	proof	proof	NOUN
ejpam-6366	238	5	of	of	ADP
ejpam-6366	238	6	theorem	theorem	NOUN
ejpam-6366	238	7	5	5	NUM
ejpam-6366	238	8	.	.	PUNCT
ejpam-6366	238	9	putting	put	VERB
ejpam-6366	238	10	p	p	NOUN
ejpam-6366	238	11	=	=	NOUN
ejpam-6366	238	12	1	1	NUM
ejpam-6366	238	13	and	and	CCONJ
ejpam-6366	238	14	q	q	NOUN
ejpam-6366	238	15	=	=	PUNCT
ejpam-6366	238	16	−1	−1	NOUN
ejpam-6366	238	17	in	in	ADP
ejpam-6366	238	18	theorem	theorem	NOUN
ejpam-6366	238	19	5	5	NUM
ejpam-6366	238	20	,	,	PUNCT
ejpam-6366	238	21	we	we	PRON
ejpam-6366	238	22	get	get	VERB
ejpam-6366	238	23	the	the	DET
ejpam-6366	238	24	following	following	NOUN
ejpam-6366	238	25	.	.	PUNCT
ejpam-6366	239	1	corollary	corollary	ADJ
ejpam-6366	239	2	13	13	NUM
ejpam-6366	239	3	.	.	PUNCT
ejpam-6366	240	1	if	if	SCONJ
ejpam-6366	240	2	g	g	PROPN
ejpam-6366	240	3	∈	∈	PROPN
ejpam-6366	240	4	sk	sk	X
ejpam-6366	240	5	[	[	X
ejpam-6366	240	6	γ;α	γ;α	X
ejpam-6366	240	7	,	,	PUNCT
ejpam-6366	240	8	β	β	X
ejpam-6366	240	9	]	]	X
ejpam-6366	240	10	,	,	PUNCT
ejpam-6366	240	11	then∣∣d3	then∣∣d3	NOUN
ejpam-6366	240	12	−	−	PROPN
ejpam-6366	240	13	µd22	µd22	PROPN
ejpam-6366	240	14	∣∣	∣∣	NUM
ejpam-6366	240	15	≤	≤	ADV
ejpam-6366	240	16	2	2	NUM
ejpam-6366	240	17	(	(	PUNCT
ejpam-6366	240	18	α+	α+	X
ejpam-6366	240	19	β	β	X
ejpam-6366	240	20	)	)	PUNCT
ejpam-6366	240	21	(	(	PUNCT
ejpam-6366	240	22	1−	1−	NUM
ejpam-6366	240	23	γ	γ	NOUN
ejpam-6366	240	24	)	)	PUNCT
ejpam-6366	240	25	α+	α+	PUNCT
ejpam-6366	240	26	2β	2β	NOUN
ejpam-6366	240	27	max	max	NOUN
ejpam-6366	240	28	{	{	PUNCT
ejpam-6366	240	29	1	1	NUM
ejpam-6366	240	30	;	;	PUNCT
ejpam-6366	240	31	∣∣∣∣q−	∣∣∣∣q−	NUM
ejpam-6366	240	32	2β	2β	NOUN
ejpam-6366	240	33	(	(	PUNCT
ejpam-6366	240	34	1−	1−	NUM
ejpam-6366	240	35	γ	γ	NOUN
ejpam-6366	240	36	)	)	PUNCT
ejpam-6366	240	37	α+	α+	PRON
ejpam-6366	240	38	β	β	X
ejpam-6366	240	39	(	(	PUNCT
ejpam-6366	240	40	1−	1−	NUM
ejpam-6366	240	41	α+	α+	PRON
ejpam-6366	240	42	2β	2β	NOUN
ejpam-6366	240	43	β	β	X
ejpam-6366	240	44	µ	µ	X
ejpam-6366	240	45	)	)	PUNCT
ejpam-6366	240	46	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6366	240	47	}	}	PUNCT
ejpam-6366	240	48	.	.	PUNCT
ejpam-6366	241	1	putting	put	VERB
ejpam-6366	241	2	α	α	NOUN
ejpam-6366	241	3	=	=	SYM
ejpam-6366	241	4	γ	γ	X
ejpam-6366	241	5	=	=	SYM
ejpam-6366	241	6	0	0	NUM
ejpam-6366	241	7	in	in	ADP
ejpam-6366	241	8	theorem	theorem	NOUN
ejpam-6366	241	9	5	5	NUM
ejpam-6366	241	10	,	,	PUNCT
ejpam-6366	241	11	we	we	PRON
ejpam-6366	241	12	get	get	VERB
ejpam-6366	241	13	the	the	DET
ejpam-6366	241	14	following	following	NOUN
ejpam-6366	241	15	.	.	PUNCT
ejpam-6366	242	1	corollary	corollary	ADJ
ejpam-6366	242	2	14	14	NUM
ejpam-6366	242	3	.	.	PUNCT
ejpam-6366	243	1	if	if	SCONJ
ejpam-6366	243	2	g	g	PROPN
ejpam-6366	243	3	∈	∈	PROPN
ejpam-6366	243	4	s	s	PART
ejpam-6366	243	5	[	[	X
ejpam-6366	243	6	p	p	X
ejpam-6366	243	7	,	,	PUNCT
ejpam-6366	243	8	q	q	X
ejpam-6366	243	9	]	]	X
ejpam-6366	243	10	,	,	PUNCT
ejpam-6366	243	11	then∣∣d3	then∣∣d3	NOUN
ejpam-6366	243	12	−	−	PROPN
ejpam-6366	243	13	µd22	µd22	PROPN
ejpam-6366	243	14	∣∣	∣∣	NUM
ejpam-6366	243	15	≤	≤	NUM
ejpam-6366	243	16	p−q	p−q	NOUN
ejpam-6366	243	17	2	2	NUM
ejpam-6366	243	18	max	max	NOUN
ejpam-6366	243	19	{	{	PUNCT
ejpam-6366	243	20	1	1	NUM
ejpam-6366	243	21	;	;	PUNCT
ejpam-6366	243	22	|q−	|q−	NOUN
ejpam-6366	243	23	(	(	PUNCT
ejpam-6366	243	24	p	p	NOUN
ejpam-6366	243	25	−q	−q	NOUN
ejpam-6366	243	26	)	)	PUNCT
ejpam-6366	243	27	(	(	PUNCT
ejpam-6366	243	28	1−	1−	NUM
ejpam-6366	243	29	2µ)|	2µ)|	NUM
ejpam-6366	243	30	}	}	PUNCT
ejpam-6366	243	31	.	.	PUNCT
ejpam-6366	244	1	putting	put	VERB
ejpam-6366	244	2	β	β	X
ejpam-6366	244	3	=	=	PUNCT
ejpam-6366	244	4	γ	γ	X
ejpam-6366	244	5	=	=	SYM
ejpam-6366	244	6	0	0	NUM
ejpam-6366	244	7	in	in	ADP
ejpam-6366	244	8	theorem	theorem	NOUN
ejpam-6366	244	9	5	5	NUM
ejpam-6366	244	10	,	,	PUNCT
ejpam-6366	244	11	we	we	PRON
ejpam-6366	244	12	get	get	VERB
ejpam-6366	244	13	the	the	DET
ejpam-6366	244	14	following	following	NOUN
ejpam-6366	244	15	.	.	PUNCT
ejpam-6366	245	1	corollary	corollary	ADJ
ejpam-6366	245	2	15	15	NUM
ejpam-6366	245	3	.	.	PUNCT
ejpam-6366	246	1	if	if	SCONJ
ejpam-6366	246	2	g	g	PROPN
ejpam-6366	246	3	∈	∈	PROPN
ejpam-6366	246	4	k	k	PROPN
ejpam-6366	247	1	[	[	X
ejpam-6366	247	2	p	p	X
ejpam-6366	247	3	,	,	PUNCT
ejpam-6366	247	4	q	q	X
ejpam-6366	247	5	]	]	X
ejpam-6366	247	6	,	,	PUNCT
ejpam-6366	247	7	then∣∣d3	then∣∣d3	NOUN
ejpam-6366	247	8	−	−	PROPN
ejpam-6366	247	9	µd22	µd22	PROPN
ejpam-6366	247	10	∣∣	∣∣	VERB
ejpam-6366	247	11	≤	≤	ADV
ejpam-6366	247	12	p	p	NOUN
ejpam-6366	247	13	−q	−q	NOUN
ejpam-6366	247	14	.	.	PUNCT
ejpam-6366	248	1	t.	t.	PROPN
ejpam-6366	248	2	m.	m.	PROPN
ejpam-6366	248	3	seoudy	seoudy	PROPN
ejpam-6366	248	4	,	,	PUNCT
ejpam-6366	248	5	a.	a.	PROPN
ejpam-6366	248	6	e.	e.	PROPN
ejpam-6366	248	7	shammaky	shammaky	PROPN
ejpam-6366	248	8	/	/	SYM
ejpam-6366	248	9	eur	eur	PROPN
ejpam-6366	248	10	.	.	PUNCT
ejpam-6366	249	1	j.	j.	PROPN
ejpam-6366	249	2	pure	pure	PROPN
ejpam-6366	249	3	appl	appl	PROPN
ejpam-6366	249	4	.	.	PROPN
ejpam-6366	249	5	math	math	PROPN
ejpam-6366	249	6	,	,	PUNCT
ejpam-6366	249	7	18	18	NUM
ejpam-6366	249	8	(	(	PUNCT
ejpam-6366	249	9	4	4	NUM
ejpam-6366	249	10	)	)	PUNCT
ejpam-6366	249	11	(	(	PUNCT
ejpam-6366	249	12	2025	2025	NUM
ejpam-6366	249	13	)	)	PUNCT
ejpam-6366	249	14	,	,	PUNCT
ejpam-6366	249	15	6366	6366	NUM
ejpam-6366	249	16	12	12	NUM
ejpam-6366	249	17	of	of	ADP
ejpam-6366	249	18	15	15	NUM
ejpam-6366	249	19	theorem	theorem	NOUN
ejpam-6366	249	20	6	6	NUM
ejpam-6366	249	21	.	.	PUNCT
ejpam-6366	250	1	let	let	VERB
ejpam-6366	250	2	σ1	σ1	PROPN
ejpam-6366	250	3	=	=	PUNCT
ejpam-6366	250	4	β	β	X
ejpam-6366	250	5	(	(	PUNCT
ejpam-6366	250	6	1−	1−	NUM
ejpam-6366	250	7	γ	γ	NOUN
ejpam-6366	250	8	)	)	PUNCT
ejpam-6366	250	9	(	(	PUNCT
ejpam-6366	250	10	p	p	NOUN
ejpam-6366	250	11	−q)−	−q)−	PROPN
ejpam-6366	250	12	(	(	PUNCT
ejpam-6366	250	13	α+	α+	X
ejpam-6366	250	14	β	β	X
ejpam-6366	250	15	)	)	PUNCT
ejpam-6366	250	16	(	(	PUNCT
ejpam-6366	250	17	1	1	NUM
ejpam-6366	250	18	+	+	NOUN
ejpam-6366	250	19	q	q	NOUN
ejpam-6366	250	20	)	)	PUNCT
ejpam-6366	250	21	(	(	PUNCT
ejpam-6366	250	22	α+	α+	NOUN
ejpam-6366	250	23	2β	2β	NOUN
ejpam-6366	250	24	)	)	PUNCT
ejpam-6366	250	25	(	(	PUNCT
ejpam-6366	250	26	1−	1−	NUM
ejpam-6366	250	27	γ	γ	X
ejpam-6366	250	28	)	)	PUNCT
ejpam-6366	250	29	(	(	PUNCT
ejpam-6366	250	30	p	p	NOUN
ejpam-6366	250	31	−q	−q	NOUN
ejpam-6366	250	32	)	)	PUNCT
ejpam-6366	250	33	,	,	PUNCT
ejpam-6366	250	34	σ2	σ2	NOUN
ejpam-6366	250	35	=	=	SYM
ejpam-6366	250	36	β	β	X
ejpam-6366	250	37	(	(	PUNCT
ejpam-6366	250	38	1−	1−	NUM
ejpam-6366	250	39	γ	γ	X
ejpam-6366	250	40	)	)	PUNCT
ejpam-6366	250	41	(	(	PUNCT
ejpam-6366	250	42	p	p	NOUN
ejpam-6366	250	43	−q	−q	NOUN
ejpam-6366	250	44	)	)	PUNCT
ejpam-6366	251	1	+	+	CCONJ
ejpam-6366	251	2	(	(	PUNCT
ejpam-6366	251	3	α+	α+	X
ejpam-6366	251	4	β	β	X
ejpam-6366	251	5	)	)	PUNCT
ejpam-6366	251	6	(	(	PUNCT
ejpam-6366	251	7	1−q	1−q	NUM
ejpam-6366	251	8	)	)	PUNCT
ejpam-6366	251	9	(	(	PUNCT
ejpam-6366	251	10	α+	α+	NOUN
ejpam-6366	251	11	2β	2β	NOUN
ejpam-6366	251	12	)	)	PUNCT
ejpam-6366	251	13	(	(	PUNCT
ejpam-6366	251	14	1−	1−	NUM
ejpam-6366	251	15	γ	γ	X
ejpam-6366	251	16	)	)	PUNCT
ejpam-6366	251	17	(	(	PUNCT
ejpam-6366	251	18	p	p	NOUN
ejpam-6366	251	19	−q	−q	NOUN
ejpam-6366	251	20	)	)	PUNCT
ejpam-6366	251	21	,	,	PUNCT
ejpam-6366	251	22	σ3	σ3	NOUN
ejpam-6366	251	23	=	=	PUNCT
ejpam-6366	251	24	β	β	X
ejpam-6366	251	25	(	(	PUNCT
ejpam-6366	251	26	1−	1−	NUM
ejpam-6366	251	27	γ	γ	NOUN
ejpam-6366	251	28	)	)	PUNCT
ejpam-6366	251	29	(	(	PUNCT
ejpam-6366	251	30	p	p	NOUN
ejpam-6366	251	31	−q)−	−q)−	PROPN
ejpam-6366	251	32	(	(	PUNCT
ejpam-6366	251	33	α+	α+	X
ejpam-6366	251	34	β)q	β)q	X
ejpam-6366	251	35	(	(	PUNCT
ejpam-6366	251	36	α+	α+	NOUN
ejpam-6366	251	37	2β	2β	NOUN
ejpam-6366	251	38	)	)	PUNCT
ejpam-6366	251	39	(	(	PUNCT
ejpam-6366	251	40	1−	1−	NUM
ejpam-6366	251	41	γ	γ	X
ejpam-6366	251	42	)	)	PUNCT
ejpam-6366	251	43	(	(	PUNCT
ejpam-6366	251	44	p	p	NOUN
ejpam-6366	251	45	−q	−q	NOUN
ejpam-6366	251	46	)	)	PUNCT
ejpam-6366	251	47	.	.	PUNCT
ejpam-6366	252	1	if	if	SCONJ
ejpam-6366	252	2	g	g	PROPN
ejpam-6366	252	3	∈	∈	PROPN
ejpam-6366	252	4	sk	sk	VERB
ejpam-6366	253	1	[	[	X
ejpam-6366	253	2	p	p	X
ejpam-6366	253	3	,	,	PUNCT
ejpam-6366	253	4	q	q	NOUN
ejpam-6366	253	5	,	,	PUNCT
ejpam-6366	253	6	γ;α	γ;α	ADV
ejpam-6366	253	7	,	,	PUNCT
ejpam-6366	253	8	β	β	X
ejpam-6366	253	9	]	]	X
ejpam-6366	253	10	,	,	PUNCT
ejpam-6366	253	11	then	then	ADV
ejpam-6366	253	12	∣∣d3	∣∣d3	VERB
ejpam-6366	253	13	−	−	PROPN
ejpam-6366	253	14	µd22	µd22	PROPN
ejpam-6366	253	15	∣∣	∣∣	PUNCT
ejpam-6366	253	16	≤	≤	NUM
ejpam-6366	253	17			NUM
ejpam-6366	253	18	−	−	PROPN
ejpam-6366	253	19	(	(	PUNCT
ejpam-6366	253	20	α+β)(1−γ)(p−q	α+β)(1−γ)(p−q	NUM
ejpam-6366	253	21	)	)	PUNCT
ejpam-6366	253	22	(	(	PUNCT
ejpam-6366	253	23	α+2β	α+2β	NUM
ejpam-6366	253	24	)	)	PUNCT
ejpam-6366	253	25	[	[	PUNCT
ejpam-6366	253	26	q−	q−	PROPN
ejpam-6366	253	27	β(1−γ)(p−q	β(1−γ)(p−q	PROPN
ejpam-6366	253	28	)	)	PUNCT
ejpam-6366	253	29	α+β	α+β	PROPN
ejpam-6366	254	1	(	(	PUNCT
ejpam-6366	254	2	1−	1−	NUM
ejpam-6366	254	3	α+2β	α+2β	PROPN
ejpam-6366	254	4	β	β	X
ejpam-6366	254	5	µ	µ	X
ejpam-6366	254	6	)	)	PUNCT
ejpam-6366	254	7	]	]	PUNCT
ejpam-6366	254	8	(	(	PUNCT
ejpam-6366	254	9	µ	µ	X
ejpam-6366	254	10	≤	≤	NUM
ejpam-6366	254	11	σ1	σ1	PROPN
ejpam-6366	254	12	)	)	PUNCT
ejpam-6366	254	13	,	,	PUNCT
ejpam-6366	254	14	(	(	PUNCT
ejpam-6366	254	15	α+β)(1−γ)(p−q	α+β)(1−γ)(p−q	NUM
ejpam-6366	254	16	)	)	PUNCT
ejpam-6366	254	17	(	(	PUNCT
ejpam-6366	254	18	α+2β	α+2β	NUM
ejpam-6366	254	19	)	)	PUNCT
ejpam-6366	254	20	(	(	PUNCT
ejpam-6366	254	21	σ1	σ1	PROPN
ejpam-6366	254	22	≤	≤	PROPN
ejpam-6366	254	23	µ	µ	PRON
ejpam-6366	254	24	≤	≤	PROPN
ejpam-6366	254	25	σ2	σ2	NOUN
ejpam-6366	254	26	)	)	PUNCT
ejpam-6366	254	27	,	,	PUNCT
ejpam-6366	254	28	(	(	PUNCT
ejpam-6366	254	29	α+β)(1−γ)(p−q	α+β)(1−γ)(p−q	NUM
ejpam-6366	254	30	)	)	PUNCT
ejpam-6366	254	31	(	(	PUNCT
ejpam-6366	254	32	α+2β	α+2β	NUM
ejpam-6366	254	33	)	)	PUNCT
ejpam-6366	254	34	[	[	PUNCT
ejpam-6366	254	35	q−	q−	PROPN
ejpam-6366	254	36	β(1−γ)(p−q	β(1−γ)(p−q	PROPN
ejpam-6366	254	37	)	)	PUNCT
ejpam-6366	254	38	α+β	α+β	PROPN
ejpam-6366	254	39	(	(	PUNCT
ejpam-6366	254	40	1−	1−	NUM
ejpam-6366	254	41	α+2β	α+2β	PROPN
ejpam-6366	254	42	β	β	X
ejpam-6366	254	43	µ	µ	X
ejpam-6366	254	44	)	)	PUNCT
ejpam-6366	254	45	]	]	PUNCT
ejpam-6366	254	46	(	(	PUNCT
ejpam-6366	254	47	µ	µ	X
ejpam-6366	254	48	≥	≥	NOUN
ejpam-6366	254	49	σ2	σ2	PROPN
ejpam-6366	254	50	)	)	PUNCT
ejpam-6366	254	51	.	.	PUNCT
ejpam-6366	255	1	further	far	ADV
ejpam-6366	255	2	,	,	PUNCT
ejpam-6366	255	3	if	if	SCONJ
ejpam-6366	255	4	σ1	σ1	PROPN
ejpam-6366	255	5	≤	≤	NOUN
ejpam-6366	255	6	µ	µ	PRON
ejpam-6366	255	7	≤	≤	PROPN
ejpam-6366	255	8	σ3	σ3	NOUN
ejpam-6366	255	9	,	,	PUNCT
ejpam-6366	255	10	then∣∣d3	then∣∣d3	PROPN
ejpam-6366	255	11	−	−	PROPN
ejpam-6366	255	12	µd22	µd22	PROPN
ejpam-6366	255	13	∣∣+	∣∣+	X
ejpam-6366	255	14	α+	α+	X
ejpam-6366	255	15	β	β	X
ejpam-6366	255	16	α+	α+	X
ejpam-6366	255	17	2β	2β	NOUN
ejpam-6366	255	18	[	[	PUNCT
ejpam-6366	255	19	1	1	NUM
ejpam-6366	255	20	+	+	NOUN
ejpam-6366	255	21	q	q	X
ejpam-6366	255	22	(	(	PUNCT
ejpam-6366	255	23	1−	1−	NUM
ejpam-6366	255	24	γ	γ	X
ejpam-6366	255	25	)	)	PUNCT
ejpam-6366	255	26	(	(	PUNCT
ejpam-6366	255	27	p	p	NOUN
ejpam-6366	255	28	−q	−q	NOUN
ejpam-6366	255	29	)	)	PUNCT
ejpam-6366	255	30	−	−	NOUN
ejpam-6366	255	31	β	β	INTJ
ejpam-6366	255	32	α+	α+	X
ejpam-6366	255	33	β	β	X
ejpam-6366	255	34	(	(	PUNCT
ejpam-6366	255	35	1−	1−	NUM
ejpam-6366	255	36	α+	α+	DET
ejpam-6366	255	37	2β	2β	NOUN
ejpam-6366	255	38	β	β	X
ejpam-6366	255	39	µ	µ	NOUN
ejpam-6366	255	40	)	)	PUNCT
ejpam-6366	255	41	]	]	PUNCT
ejpam-6366	255	42	|d2|2	|d2|2	X
ejpam-6366	255	43	≤	≤	NOUN
ejpam-6366	255	44	(	(	PUNCT
ejpam-6366	255	45	α+	α+	X
ejpam-6366	255	46	β	β	X
ejpam-6366	255	47	)	)	PUNCT
ejpam-6366	255	48	(	(	PUNCT
ejpam-6366	255	49	1−	1−	NUM
ejpam-6366	255	50	γ	γ	X
ejpam-6366	255	51	)	)	PUNCT
ejpam-6366	255	52	(	(	PUNCT
ejpam-6366	255	53	p	p	NOUN
ejpam-6366	255	54	−q	−q	NOUN
ejpam-6366	255	55	)	)	PUNCT
ejpam-6366	255	56	α+	α+	DET
ejpam-6366	255	57	2β	2β	NOUN
ejpam-6366	255	58	.	.	PUNCT
ejpam-6366	256	1	if	if	SCONJ
ejpam-6366	256	2	σ3	σ3	PROPN
ejpam-6366	256	3	≤	≤	PROPN
ejpam-6366	256	4	µ	µ	PRON
ejpam-6366	256	5	≤	≤	PROPN
ejpam-6366	256	6	σ2	σ2	NOUN
ejpam-6366	256	7	,	,	PUNCT
ejpam-6366	256	8	then∣∣d3	then∣∣d3	PROPN
ejpam-6366	256	9	−	−	PROPN
ejpam-6366	256	10	µd22	µd22	PROPN
ejpam-6366	256	11	∣∣+	∣∣+	X
ejpam-6366	256	12	α+	α+	X
ejpam-6366	256	13	β	β	X
ejpam-6366	256	14	α+	α+	X
ejpam-6366	256	15	2β	2β	NOUN
ejpam-6366	256	16	[	[	PUNCT
ejpam-6366	256	17	1−q	1−q	NUM
ejpam-6366	256	18	(	(	PUNCT
ejpam-6366	256	19	1−	1−	NUM
ejpam-6366	256	20	γ	γ	NOUN
ejpam-6366	256	21	)	)	PUNCT
ejpam-6366	256	22	(	(	PUNCT
ejpam-6366	256	23	p	p	NOUN
ejpam-6366	256	24	−q	−q	NOUN
ejpam-6366	256	25	)	)	PUNCT
ejpam-6366	257	1	+	+	NUM
ejpam-6366	257	2	β	β	X
ejpam-6366	257	3	α+	α+	X
ejpam-6366	257	4	β	β	X
ejpam-6366	257	5	(	(	PUNCT
ejpam-6366	257	6	1−	1−	NUM
ejpam-6366	257	7	α+	α+	DET
ejpam-6366	257	8	2β	2β	NOUN
ejpam-6366	257	9	β	β	X
ejpam-6366	257	10	µ	µ	NOUN
ejpam-6366	257	11	)	)	PUNCT
ejpam-6366	257	12	]	]	PUNCT
ejpam-6366	257	13	|d2|2	|d2|2	X
ejpam-6366	257	14	≤	≤	NOUN
ejpam-6366	257	15	(	(	PUNCT
ejpam-6366	257	16	α+	α+	X
ejpam-6366	257	17	β	β	X
ejpam-6366	257	18	)	)	PUNCT
ejpam-6366	257	19	(	(	PUNCT
ejpam-6366	257	20	1−	1−	NUM
ejpam-6366	257	21	γ	γ	X
ejpam-6366	257	22	)	)	PUNCT
ejpam-6366	257	23	(	(	PUNCT
ejpam-6366	257	24	p	p	NOUN
ejpam-6366	257	25	−q	−q	NOUN
ejpam-6366	257	26	)	)	PUNCT
ejpam-6366	257	27	α+	α+	DET
ejpam-6366	257	28	2β	2β	NOUN
ejpam-6366	257	29	.	.	PUNCT
ejpam-6366	258	1	proof	proof	NOUN
ejpam-6366	258	2	.	.	PUNCT
ejpam-6366	259	1	using	use	VERB
ejpam-6366	259	2	lemma	lemma	PROPN
ejpam-6366	259	3	2	2	NUM
ejpam-6366	259	4	to	to	ADP
ejpam-6366	259	5	(	(	PUNCT
ejpam-6366	259	6	30	30	NUM
ejpam-6366	259	7	)	)	PUNCT
ejpam-6366	259	8	and	and	CCONJ
ejpam-6366	259	9	(	(	PUNCT
ejpam-6366	259	10	31	31	NUM
ejpam-6366	259	11	)	)	PUNCT
ejpam-6366	259	12	,	,	PUNCT
ejpam-6366	259	13	we	we	PRON
ejpam-6366	259	14	can	can	AUX
ejpam-6366	259	15	derive	derive	VERB
ejpam-6366	259	16	our	our	PRON
ejpam-6366	259	17	results	result	NOUN
ejpam-6366	259	18	,	,	PUNCT
ejpam-6366	259	19	which	which	PRON
ejpam-6366	259	20	are	be	AUX
ejpam-6366	259	21	confirmed	confirm	VERB
ejpam-6366	259	22	by	by	ADP
ejpam-6366	259	23	theorem	theorem	NOUN
ejpam-6366	259	24	6	6	NUM
ejpam-6366	259	25	.	.	PUNCT
ejpam-6366	259	26	taking	take	VERB
ejpam-6366	259	27	p	p	NOUN
ejpam-6366	259	28	=	=	NOUN
ejpam-6366	259	29	1	1	NUM
ejpam-6366	259	30	and	and	CCONJ
ejpam-6366	259	31	q	q	NOUN
ejpam-6366	259	32	=	=	PUNCT
ejpam-6366	259	33	−1	−1	NOUN
ejpam-6366	259	34	in	in	ADP
ejpam-6366	259	35	theorem	theorem	NOUN
ejpam-6366	259	36	6	6	NUM
ejpam-6366	259	37	,	,	PUNCT
ejpam-6366	259	38	we	we	PRON
ejpam-6366	259	39	derive	derive	VERB
ejpam-6366	259	40	the	the	DET
ejpam-6366	259	41	following	following	NOUN
ejpam-6366	259	42	.	.	PUNCT
ejpam-6366	260	1	corollary	corollary	ADJ
ejpam-6366	260	2	16	16	NUM
ejpam-6366	260	3	.	.	PUNCT
ejpam-6366	261	1	let	let	VERB
ejpam-6366	261	2	σ4	σ4	NOUN
ejpam-6366	261	3	=	=	PUNCT
ejpam-6366	261	4	β	β	X
ejpam-6366	261	5	α+	α+	PRON
ejpam-6366	261	6	2β	2β	NOUN
ejpam-6366	261	7	,	,	PUNCT
ejpam-6366	261	8	σ5	σ5	X
ejpam-6366	261	9	=	=	SYM
ejpam-6366	261	10	β	β	X
ejpam-6366	261	11	(	(	PUNCT
ejpam-6366	261	12	1−	1−	NUM
ejpam-6366	261	13	γ	γ	X
ejpam-6366	261	14	)	)	PUNCT
ejpam-6366	262	1	+	+	CCONJ
ejpam-6366	262	2	α+	α+	X
ejpam-6366	262	3	β	β	X
ejpam-6366	262	4	(	(	PUNCT
ejpam-6366	262	5	α+	α+	NOUN
ejpam-6366	262	6	2β	2β	NOUN
ejpam-6366	262	7	)	)	PUNCT
ejpam-6366	262	8	(	(	PUNCT
ejpam-6366	262	9	1−	1−	NUM
ejpam-6366	262	10	γ	γ	X
ejpam-6366	262	11	)	)	PUNCT
ejpam-6366	262	12	,	,	PUNCT
ejpam-6366	262	13	σ6	σ6	NOUN
ejpam-6366	262	14	=	=	PUNCT
ejpam-6366	262	15	2β	2β	NOUN
ejpam-6366	262	16	(	(	PUNCT
ejpam-6366	262	17	1−	1−	NUM
ejpam-6366	262	18	γ	γ	X
ejpam-6366	262	19	)	)	PUNCT
ejpam-6366	262	20	+	+	CCONJ
ejpam-6366	262	21	α+	α+	X
ejpam-6366	262	22	β	β	PROPN
ejpam-6366	262	23	2	2	NUM
ejpam-6366	262	24	(	(	PUNCT
ejpam-6366	262	25	α+	α+	NOUN
ejpam-6366	262	26	2β	2β	NOUN
ejpam-6366	262	27	)	)	PUNCT
ejpam-6366	262	28	(	(	PUNCT
ejpam-6366	262	29	1−	1−	NUM
ejpam-6366	262	30	γ	γ	NOUN
ejpam-6366	262	31	)	)	PUNCT
ejpam-6366	262	32	.	.	PUNCT
ejpam-6366	263	1	if	if	SCONJ
ejpam-6366	263	2	g	g	PROPN
ejpam-6366	263	3	∈	∈	PROPN
ejpam-6366	263	4	sk	sk	X
ejpam-6366	263	5	[	[	X
ejpam-6366	263	6	γ;α	γ;α	X
ejpam-6366	263	7	,	,	PUNCT
ejpam-6366	263	8	β	β	X
ejpam-6366	263	9	]	]	X
ejpam-6366	263	10	,	,	PUNCT
ejpam-6366	263	11	then	then	ADV
ejpam-6366	263	12	∣∣d3	∣∣d3	VERB
ejpam-6366	263	13	−	−	PROPN
ejpam-6366	263	14	µd22	µd22	PROPN
ejpam-6366	263	15	∣∣	∣∣	PUNCT
ejpam-6366	263	16	≤	≤	NUM
ejpam-6366	263	17			NUM
ejpam-6366	263	18	2(α+β)(1−γ	2(α+β)(1−γ	NUM
ejpam-6366	263	19	)	)	PUNCT
ejpam-6366	264	1	α+2β	α+2β	NOUN
ejpam-6366	264	2	[	[	PUNCT
ejpam-6366	264	3	1	1	NUM
ejpam-6366	264	4	+	+	CCONJ
ejpam-6366	264	5	2β(1−γ	2β(1−γ	NUM
ejpam-6366	264	6	)	)	PUNCT
ejpam-6366	264	7	α+β	α+β	NUM
ejpam-6366	264	8	(	(	PUNCT
ejpam-6366	264	9	1−	1−	NUM
ejpam-6366	264	10	α+2β	α+2β	PROPN
ejpam-6366	264	11	β	β	X
ejpam-6366	264	12	µ	µ	X
ejpam-6366	264	13	)	)	PUNCT
ejpam-6366	264	14	]	]	PUNCT
ejpam-6366	264	15	(	(	PUNCT
ejpam-6366	264	16	µ	µ	X
ejpam-6366	264	17	≤	≤	NUM
ejpam-6366	264	18	σ4	σ4	NOUN
ejpam-6366	264	19	)	)	PUNCT
ejpam-6366	264	20	,	,	PUNCT
ejpam-6366	264	21	2(α+β)(1−γ	2(α+β)(1−γ	NUM
ejpam-6366	264	22	)	)	PUNCT
ejpam-6366	265	1	α+2β	α+2β	PROPN
ejpam-6366	265	2	(	(	PUNCT
ejpam-6366	265	3	σ4	σ4	NOUN
ejpam-6366	265	4	≤	≤	PROPN
ejpam-6366	265	5	µ	µ	PRON
ejpam-6366	265	6	≤	≤	NUM
ejpam-6366	265	7	σ5	σ5	NOUN
ejpam-6366	265	8	)	)	PUNCT
ejpam-6366	265	9	,	,	PUNCT
ejpam-6366	265	10	−2(α+β)(1−γ	−2(α+β)(1−γ	X
ejpam-6366	265	11	)	)	PUNCT
ejpam-6366	265	12	α+2β	α+2β	NOUN
ejpam-6366	265	13	[	[	PUNCT
ejpam-6366	265	14	1	1	NUM
ejpam-6366	265	15	+	+	CCONJ
ejpam-6366	265	16	2β(1−γ	2β(1−γ	NUM
ejpam-6366	265	17	)	)	PUNCT
ejpam-6366	265	18	α+β	α+β	NUM
ejpam-6366	265	19	(	(	PUNCT
ejpam-6366	265	20	1−	1−	NUM
ejpam-6366	265	21	α+2β	α+2β	PROPN
ejpam-6366	265	22	β	β	X
ejpam-6366	265	23	µ	µ	X
ejpam-6366	265	24	)	)	PUNCT
ejpam-6366	265	25	]	]	PUNCT
ejpam-6366	265	26	(	(	PUNCT
ejpam-6366	265	27	µ	µ	X
ejpam-6366	265	28	≥	≥	NUM
ejpam-6366	265	29	σ5	σ5	NOUN
ejpam-6366	265	30	)	)	PUNCT
ejpam-6366	265	31	.	.	PUNCT
ejpam-6366	266	1	further	far	ADV
ejpam-6366	266	2	,	,	PUNCT
ejpam-6366	266	3	if	if	SCONJ
ejpam-6366	266	4	σ4	σ4	NOUN
ejpam-6366	266	5	≤	≤	NOUN
ejpam-6366	266	6	µ	µ	PRON
ejpam-6366	266	7	≤	≤	NOUN
ejpam-6366	266	8	σ6	σ6	NOUN
ejpam-6366	266	9	,	,	PUNCT
ejpam-6366	266	10	then∣∣d3	then∣∣d3	NOUN
ejpam-6366	266	11	−	−	PROPN
ejpam-6366	266	12	µd22	µd22	PROPN
ejpam-6366	266	13	∣∣−	∣∣−	PROPN
ejpam-6366	266	14	β	β	X
ejpam-6366	266	15	α+	α+	PUNCT
ejpam-6366	266	16	2β	2β	NOUN
ejpam-6366	266	17	(	(	PUNCT
ejpam-6366	266	18	1−	1−	NUM
ejpam-6366	266	19	α+	α+	PRON
ejpam-6366	266	20	2β	2β	NOUN
ejpam-6366	266	21	β	β	X
ejpam-6366	266	22	µ	µ	X
ejpam-6366	266	23	)	)	PUNCT
ejpam-6366	266	24	|d2|2	|d2|2	SYM
ejpam-6366	266	25	≤	≤	ADV
ejpam-6366	266	26	2	2	NUM
ejpam-6366	266	27	(	(	PUNCT
ejpam-6366	266	28	α+	α+	X
ejpam-6366	266	29	β	β	X
ejpam-6366	266	30	)	)	PUNCT
ejpam-6366	266	31	(	(	PUNCT
ejpam-6366	266	32	1−	1−	NUM
ejpam-6366	266	33	γ	γ	X
ejpam-6366	266	34	)	)	PUNCT
ejpam-6366	266	35	(	(	PUNCT
ejpam-6366	266	36	α+	α+	NOUN
ejpam-6366	266	37	2β	2β	NOUN
ejpam-6366	266	38	)	)	PUNCT
ejpam-6366	266	39	.	.	PUNCT
ejpam-6366	267	1	if	if	SCONJ
ejpam-6366	267	2	σ3	σ3	PROPN
ejpam-6366	267	3	≤	≤	PROPN
ejpam-6366	267	4	µ	µ	PRON
ejpam-6366	267	5	≤	≤	PROPN
ejpam-6366	267	6	σ2	σ2	NOUN
ejpam-6366	267	7	,	,	PUNCT
ejpam-6366	267	8	then∣∣d3	then∣∣d3	PROPN
ejpam-6366	267	9	−	−	PROPN
ejpam-6366	267	10	µd22	µd22	PROPN
ejpam-6366	267	11	∣∣+	∣∣+	X
ejpam-6366	267	12	α+	α+	X
ejpam-6366	267	13	β	β	X
ejpam-6366	267	14	α+	α+	X
ejpam-6366	267	15	2β	2β	NOUN
ejpam-6366	267	16	[	[	PUNCT
ejpam-6366	267	17	1	1	NUM
ejpam-6366	267	18	1−	1−	NUM
ejpam-6366	267	19	γ	γ	X
ejpam-6366	267	20	+	+	X
ejpam-6366	267	21	β	β	X
ejpam-6366	267	22	α+	α+	X
ejpam-6366	267	23	β	β	X
ejpam-6366	267	24	(	(	PUNCT
ejpam-6366	267	25	1−	1−	NUM
ejpam-6366	267	26	α+	α+	DET
ejpam-6366	267	27	2β	2β	NOUN
ejpam-6366	267	28	β	β	X
ejpam-6366	267	29	µ	µ	NOUN
ejpam-6366	267	30	)	)	PUNCT
ejpam-6366	267	31	]	]	PUNCT
ejpam-6366	268	1	|d2|2	|d2|2	PUNCT
ejpam-6366	268	2	≤	≤	ADV
ejpam-6366	268	3	2	2	NUM
ejpam-6366	268	4	(	(	PUNCT
ejpam-6366	268	5	α+	α+	X
ejpam-6366	268	6	β	β	X
ejpam-6366	268	7	)	)	PUNCT
ejpam-6366	268	8	(	(	PUNCT
ejpam-6366	268	9	1−	1−	NUM
ejpam-6366	268	10	γ	γ	X
ejpam-6366	268	11	)	)	PUNCT
ejpam-6366	268	12	(	(	PUNCT
ejpam-6366	268	13	α+	α+	NOUN
ejpam-6366	268	14	2β	2β	NOUN
ejpam-6366	268	15	)	)	PUNCT
ejpam-6366	268	16	.	.	PUNCT
ejpam-6366	269	1	t.	t.	PROPN
ejpam-6366	269	2	m.	m.	PROPN
ejpam-6366	269	3	seoudy	seoudy	PROPN
ejpam-6366	269	4	,	,	PUNCT
ejpam-6366	269	5	a.	a.	PROPN
ejpam-6366	269	6	e.	e.	PROPN
ejpam-6366	269	7	shammaky	shammaky	PROPN
ejpam-6366	269	8	/	/	SYM
ejpam-6366	269	9	eur	eur	PROPN
ejpam-6366	269	10	.	.	PUNCT
ejpam-6366	270	1	j.	j.	PROPN
ejpam-6366	270	2	pure	pure	PROPN
ejpam-6366	270	3	appl	appl	PROPN
ejpam-6366	270	4	.	.	PROPN
ejpam-6366	270	5	math	math	PROPN
ejpam-6366	270	6	,	,	PUNCT
ejpam-6366	270	7	18	18	NUM
ejpam-6366	270	8	(	(	PUNCT
ejpam-6366	270	9	4	4	NUM
ejpam-6366	270	10	)	)	PUNCT
ejpam-6366	270	11	(	(	PUNCT
ejpam-6366	270	12	2025	2025	NUM
ejpam-6366	270	13	)	)	PUNCT
ejpam-6366	270	14	,	,	PUNCT
ejpam-6366	270	15	6366	6366	NUM
ejpam-6366	270	16	13	13	NUM
ejpam-6366	270	17	of	of	ADP
ejpam-6366	270	18	15	15	NUM
ejpam-6366	270	19	putting	put	VERB
ejpam-6366	270	20	α	α	NOUN
ejpam-6366	270	21	=	=	SYM
ejpam-6366	270	22	γ	γ	X
ejpam-6366	270	23	=	=	SYM
ejpam-6366	270	24	0	0	NUM
ejpam-6366	270	25	in	in	ADP
ejpam-6366	270	26	theorem	theorem	NOUN
ejpam-6366	270	27	6	6	NUM
ejpam-6366	270	28	,	,	PUNCT
ejpam-6366	270	29	we	we	PRON
ejpam-6366	270	30	get	get	VERB
ejpam-6366	270	31	the	the	DET
ejpam-6366	270	32	following	following	NOUN
ejpam-6366	270	33	.	.	PUNCT
ejpam-6366	271	1	corollary	corollary	ADJ
ejpam-6366	271	2	17	17	NUM
ejpam-6366	271	3	.	.	PUNCT
ejpam-6366	272	1	let	let	VERB
ejpam-6366	272	2	σ10	σ10	ADV
ejpam-6366	272	3	=	=	NOUN
ejpam-6366	273	1	p	p	NOUN
ejpam-6366	273	2	−	−	PROPN
ejpam-6366	273	3	2q−	2q−	NUM
ejpam-6366	273	4	1	1	NUM
ejpam-6366	273	5	2	2	NUM
ejpam-6366	273	6	(	(	PUNCT
ejpam-6366	273	7	p	p	NOUN
ejpam-6366	273	8	−q	−q	NOUN
ejpam-6366	273	9	)	)	PUNCT
ejpam-6366	273	10	,	,	PUNCT
ejpam-6366	273	11	σ11	σ11	NOUN
ejpam-6366	273	12	=	=	PUNCT
ejpam-6366	273	13	p	p	NOUN
ejpam-6366	273	14	−	−	PROPN
ejpam-6366	273	15	2q+	2q+	NUM
ejpam-6366	273	16	1	1	NUM
ejpam-6366	273	17	2	2	NUM
ejpam-6366	273	18	(	(	PUNCT
ejpam-6366	273	19	p	p	NOUN
ejpam-6366	273	20	−q	−q	NOUN
ejpam-6366	273	21	)	)	PUNCT
ejpam-6366	273	22	,	,	PUNCT
ejpam-6366	273	23	σ12	σ12	NOUN
ejpam-6366	273	24	=	=	SYM
ejpam-6366	273	25	p	p	NOUN
ejpam-6366	273	26	−	−	PROPN
ejpam-6366	273	27	2q	2q	NUM
ejpam-6366	273	28	2	2	NUM
ejpam-6366	273	29	(	(	PUNCT
ejpam-6366	273	30	p	p	NOUN
ejpam-6366	273	31	−q	−q	NOUN
ejpam-6366	273	32	)	)	PUNCT
ejpam-6366	273	33	.	.	PUNCT
ejpam-6366	274	1	if	if	SCONJ
ejpam-6366	274	2	g	g	PROPN
ejpam-6366	274	3	∈	∈	PROPN
ejpam-6366	274	4	s	s	PART
ejpam-6366	274	5	[	[	X
ejpam-6366	274	6	p	p	X
ejpam-6366	274	7	,	,	PUNCT
ejpam-6366	274	8	q	q	X
ejpam-6366	274	9	]	]	X
ejpam-6366	274	10	,	,	PUNCT
ejpam-6366	274	11	then	then	ADV
ejpam-6366	274	12	∣∣d3	∣∣d3	VERB
ejpam-6366	274	13	−	−	PROPN
ejpam-6366	274	14	µd22	µd22	PROPN
ejpam-6366	274	15	∣∣	∣∣	NUM
ejpam-6366	274	16	≤	≤	ADV
ejpam-6366	274	17			PROPN
ejpam-6366	274	18	−	−	PROPN
ejpam-6366	274	19	(	(	PUNCT
ejpam-6366	274	20	p−q)[q−(p−q)(1−2µ	p−q)[q−(p−q)(1−2µ	NOUN
ejpam-6366	274	21	)	)	PUNCT
ejpam-6366	274	22	]	]	PUNCT
ejpam-6366	274	23	2	2	NUM
ejpam-6366	274	24	(	(	PUNCT
ejpam-6366	274	25	µ	µ	X
ejpam-6366	274	26	≤	≤	X
ejpam-6366	274	27	σ10	σ10	ADJ
ejpam-6366	274	28	)	)	PUNCT
ejpam-6366	274	29	,	,	PUNCT
ejpam-6366	274	30	p−q	p−q	NOUN
ejpam-6366	274	31	2	2	NUM
ejpam-6366	274	32	(	(	PUNCT
ejpam-6366	274	33	σ10	σ10	ADJ
ejpam-6366	274	34	≤	≤	NUM
ejpam-6366	274	35	µ	µ	PRON
ejpam-6366	274	36	≤	≤	X
ejpam-6366	274	37	σ11	σ11	ADJ
ejpam-6366	274	38	)	)	PUNCT
ejpam-6366	274	39	,	,	PUNCT
ejpam-6366	274	40	(	(	PUNCT
ejpam-6366	274	41	p−q)[q−(p−q)(1−2µ	p−q)[q−(p−q)(1−2µ	NOUN
ejpam-6366	274	42	)	)	PUNCT
ejpam-6366	274	43	]	]	PUNCT
ejpam-6366	274	44	2	2	NUM
ejpam-6366	274	45	(	(	PUNCT
ejpam-6366	274	46	µ	µ	X
ejpam-6366	274	47	≥	≥	NOUN
ejpam-6366	274	48	σ11	σ11	PROPN
ejpam-6366	274	49	)	)	PUNCT
ejpam-6366	274	50	.	.	PUNCT
ejpam-6366	275	1	further	far	ADV
ejpam-6366	275	2	,	,	PUNCT
ejpam-6366	275	3	if	if	SCONJ
ejpam-6366	275	4	σ10	σ10	ADJ
ejpam-6366	275	5	≤	≤	NUM
ejpam-6366	275	6	µ	µ	PRON
ejpam-6366	275	7	≤	≤	NUM
ejpam-6366	275	8	σ12	σ12	NOUN
ejpam-6366	275	9	,	,	PUNCT
ejpam-6366	275	10	then∣∣d3	then∣∣d3	NOUN
ejpam-6366	275	11	−	−	PROPN
ejpam-6366	276	1	µd22	µd22	PROPN
ejpam-6366	276	2	∣∣+	∣∣+	NOUN
ejpam-6366	276	3	1	1	NUM
ejpam-6366	276	4	2	2	NUM
ejpam-6366	276	5	(	(	PUNCT
ejpam-6366	276	6	1+q	1+q	NUM
ejpam-6366	276	7	p−q	p−q	NOUN
ejpam-6366	276	8	−	−	NOUN
ejpam-6366	276	9	1	1	NUM
ejpam-6366	276	10	+	+	NUM
ejpam-6366	276	11	2µ	2µ	NUM
ejpam-6366	276	12	)	)	PUNCT
ejpam-6366	276	13	|d2|2	|d2|2	PROPN
ejpam-6366	276	14	≤	≤	NUM
ejpam-6366	276	15	p−q	p−q	NOUN
ejpam-6366	276	16	2	2	NUM
ejpam-6366	276	17	.	.	PUNCT
ejpam-6366	277	1	if	if	SCONJ
ejpam-6366	277	2	σ12	σ12	NOUN
ejpam-6366	277	3	≤	≤	NUM
ejpam-6366	277	4	µ	µ	PRON
ejpam-6366	277	5	≤	≤	NOUN
ejpam-6366	277	6	σ11	σ11	ADJ
ejpam-6366	277	7	,	,	PUNCT
ejpam-6366	277	8	then	then	ADV
ejpam-6366	277	9	∣∣d3	∣∣d3	VERB
ejpam-6366	277	10	−	−	PROPN
ejpam-6366	278	1	µd22	µd22	PROPN
ejpam-6366	278	2	∣∣+	∣∣+	NOUN
ejpam-6366	278	3	1	1	NUM
ejpam-6366	278	4	2	2	NUM
ejpam-6366	278	5	(	(	PUNCT
ejpam-6366	278	6	1−q	1−q	NUM
ejpam-6366	278	7	p−q	p−q	NOUN
ejpam-6366	278	8	+	+	CCONJ
ejpam-6366	278	9	1−	1−	NUM
ejpam-6366	278	10	2µ	2µ	NUM
ejpam-6366	278	11	)	)	PUNCT
ejpam-6366	278	12	|d2|2	|d2|2	PROPN
ejpam-6366	278	13	≤	≤	NUM
ejpam-6366	278	14	p−q	p−q	NOUN
ejpam-6366	278	15	2	2	NUM
ejpam-6366	278	16	.	.	PUNCT
ejpam-6366	279	1	putting	put	VERB
ejpam-6366	279	2	β	β	X
ejpam-6366	279	3	=	=	PUNCT
ejpam-6366	279	4	γ	γ	X
ejpam-6366	279	5	=	=	SYM
ejpam-6366	279	6	0	0	NUM
ejpam-6366	279	7	in	in	ADP
ejpam-6366	279	8	theorem	theorem	NOUN
ejpam-6366	279	9	5	5	NUM
ejpam-6366	279	10	,	,	PUNCT
ejpam-6366	279	11	we	we	PRON
ejpam-6366	279	12	obtain	obtain	VERB
ejpam-6366	279	13	the	the	DET
ejpam-6366	279	14	following	following	NOUN
ejpam-6366	279	15	.	.	PUNCT
ejpam-6366	280	1	corollary	corollary	ADJ
ejpam-6366	280	2	18	18	NUM
ejpam-6366	280	3	.	.	PUNCT
ejpam-6366	281	1	let	let	VERB
ejpam-6366	281	2	σ13	σ13	NOUN
ejpam-6366	281	3	=	=	PUNCT
ejpam-6366	281	4	−	−	PROPN
ejpam-6366	281	5	1	1	NUM
ejpam-6366	282	1	+	+	NOUN
ejpam-6366	282	2	q	q	NOUN
ejpam-6366	282	3	p	p	NOUN
ejpam-6366	282	4	−q	−q	NOUN
ejpam-6366	282	5	,	,	PUNCT
ejpam-6366	282	6	σ14	σ14	NOUN
ejpam-6366	282	7	=	=	SYM
ejpam-6366	282	8	1−q	1−q	NUM
ejpam-6366	282	9	p	p	NOUN
ejpam-6366	282	10	−q	−q	NOUN
ejpam-6366	282	11	,	,	PUNCT
ejpam-6366	282	12	σ15	σ15	NOUN
ejpam-6366	282	13	=	=	SYM
ejpam-6366	283	1	−	−	PROPN
ejpam-6366	283	2	q	q	NOUN
ejpam-6366	284	1	p	p	NOUN
ejpam-6366	284	2	−q	−q	NOUN
ejpam-6366	284	3	.	.	PUNCT
ejpam-6366	285	1	if	if	SCONJ
ejpam-6366	285	2	g	g	PROPN
ejpam-6366	285	3	∈	∈	PROPN
ejpam-6366	285	4	k	k	PROPN
ejpam-6366	286	1	[	[	X
ejpam-6366	286	2	p	p	X
ejpam-6366	286	3	,	,	PUNCT
ejpam-6366	286	4	q	q	X
ejpam-6366	286	5	]	]	X
ejpam-6366	286	6	,	,	PUNCT
ejpam-6366	286	7	then	then	ADV
ejpam-6366	286	8	∣∣d3	∣∣d3	VERB
ejpam-6366	286	9	−	−	PROPN
ejpam-6366	286	10	µd22	µd22	PROPN
ejpam-6366	286	11	∣∣	∣∣	NUM
ejpam-6366	286	12	≤	≤	NUM
ejpam-6366	286	13			PUNCT
ejpam-6366	286	14	−	−	PROPN
ejpam-6366	286	15	(	(	PUNCT
ejpam-6366	286	16	p	p	NOUN
ejpam-6366	286	17	−q)q	−q)q	NOUN
ejpam-6366	286	18	(	(	PUNCT
ejpam-6366	286	19	µ	µ	NOUN
ejpam-6366	286	20	≤	≤	NUM
ejpam-6366	286	21	σ13	σ13	NOUN
ejpam-6366	286	22	)	)	PUNCT
ejpam-6366	286	23	,	,	PUNCT
ejpam-6366	286	24	p	p	NOUN
ejpam-6366	286	25	−q	−q	NOUN
ejpam-6366	286	26	(	(	PUNCT
ejpam-6366	286	27	σ13	σ13	NOUN
ejpam-6366	286	28	≤	≤	NUM
ejpam-6366	286	29	µ	µ	PRON
ejpam-6366	286	30	≤	≤	NUM
ejpam-6366	286	31	σ14	σ14	NOUN
ejpam-6366	286	32	)	)	PUNCT
ejpam-6366	286	33	,	,	PUNCT
ejpam-6366	286	34	(	(	PUNCT
ejpam-6366	286	35	p	p	NOUN
ejpam-6366	286	36	−q)q	−q)q	NOUN
ejpam-6366	286	37	(	(	PUNCT
ejpam-6366	286	38	µ	µ	X
ejpam-6366	286	39	≥	≥	NOUN
ejpam-6366	286	40	σ14	σ14	PROPN
ejpam-6366	286	41	)	)	PUNCT
ejpam-6366	286	42	.	.	PUNCT
ejpam-6366	287	1	further	far	ADV
ejpam-6366	287	2	,	,	PUNCT
ejpam-6366	287	3	if	if	SCONJ
ejpam-6366	287	4	σ13	σ13	VERB
ejpam-6366	287	5	≤	≤	NUM
ejpam-6366	287	6	µ	µ	PRON
ejpam-6366	287	7	≤	≤	NUM
ejpam-6366	287	8	σ15	σ15	NOUN
ejpam-6366	287	9	,	,	PUNCT
ejpam-6366	287	10	then∣∣d3	then∣∣d3	PROPN
ejpam-6366	287	11	−	−	PROPN
ejpam-6366	287	12	µd22	µd22	PROPN
ejpam-6366	287	13	∣∣+	∣∣+	PART
ejpam-6366	287	14	1+q	1+q	NUM
ejpam-6366	287	15	p−q	p−q	NOUN
ejpam-6366	287	16	|d2|2	|d2|2	X
ejpam-6366	287	17	≤	≤	NOUN
ejpam-6366	287	18	p	p	NOUN
ejpam-6366	287	19	−q	−q	NOUN
ejpam-6366	287	20	.	.	PUNCT
ejpam-6366	288	1	if	if	SCONJ
ejpam-6366	288	2	σ15	σ15	PROPN
ejpam-6366	288	3	≤	≤	PROPN
ejpam-6366	288	4	µ	µ	PROPN
ejpam-6366	288	5	≤	≤	NUM
ejpam-6366	288	6	σ14	σ14	NOUN
ejpam-6366	288	7	,	,	PUNCT
ejpam-6366	288	8	then	then	ADV
ejpam-6366	288	9	∣∣d3	∣∣d3	VERB
ejpam-6366	288	10	−	−	PROPN
ejpam-6366	288	11	µd22	µd22	PROPN
ejpam-6366	288	12	∣∣+	∣∣+	NOUN
ejpam-6366	288	13	1−q	1−q	NUM
ejpam-6366	288	14	p−q	p−q	NOUN
ejpam-6366	288	15	|d2|2	|d2|2	X
ejpam-6366	288	16	≤	≤	NOUN
ejpam-6366	288	17	p	p	NOUN
ejpam-6366	288	18	−q	−q	NOUN
ejpam-6366	288	19	.	.	PUNCT
ejpam-6366	289	1	4	4	X
ejpam-6366	289	2	.	.	X
ejpam-6366	289	3	conclusion	conclusion	NOUN
ejpam-6366	289	4	this	this	DET
ejpam-6366	289	5	paper	paper	NOUN
ejpam-6366	289	6	mainly	mainly	ADV
ejpam-6366	289	7	focuses	focus	VERB
ejpam-6366	289	8	on	on	ADP
ejpam-6366	289	9	finding	find	VERB
ejpam-6366	289	10	the	the	DET
ejpam-6366	289	11	convolution	convolution	NOUN
ejpam-6366	289	12	results	result	NOUN
ejpam-6366	289	13	and	and	CCONJ
ejpam-6366	289	14	coefficient	coefficient	NOUN
ejpam-6366	289	15	estimates	estimate	NOUN
ejpam-6366	289	16	for	for	ADP
ejpam-6366	289	17	a	a	DET
ejpam-6366	289	18	new	new	ADJ
ejpam-6366	289	19	subfamily	subfamily	NOUN
ejpam-6366	289	20	sk	sk	VERB
ejpam-6366	289	21	[	[	X
ejpam-6366	289	22	p	p	X
ejpam-6366	289	23	,	,	PUNCT
ejpam-6366	289	24	q	q	NOUN
ejpam-6366	289	25	,	,	PUNCT
ejpam-6366	289	26	γ;α	γ;α	ADV
ejpam-6366	289	27	,	,	PUNCT
ejpam-6366	289	28	β	β	X
ejpam-6366	289	29	]	]	PUNCT
ejpam-6366	289	30	of	of	ADP
ejpam-6366	289	31	analytic	analytic	ADJ
ejpam-6366	289	32	functions	function	NOUN
ejpam-6366	289	33	linked	link	VERB
ejpam-6366	289	34	to	to	ADP
ejpam-6366	289	35	the	the	DET
ejpam-6366	289	36	generalized	generalized	ADJ
ejpam-6366	289	37	janowski	janowski	ADJ
ejpam-6366	289	38	domain	domain	NOUN
ejpam-6366	289	39	.	.	PUNCT
ejpam-6366	290	1	we	we	PRON
ejpam-6366	290	2	also	also	ADV
ejpam-6366	290	3	studied	study	VERB
ejpam-6366	290	4	the	the	DET
ejpam-6366	290	5	upper	upper	ADJ
ejpam-6366	290	6	bounds	bound	NOUN
ejpam-6366	290	7	of	of	ADP
ejpam-6366	290	8	the	the	DET
ejpam-6366	290	9	first	first	ADJ
ejpam-6366	290	10	four	four	NUM
ejpam-6366	290	11	coefficients	coefficient	NOUN
ejpam-6366	290	12	and	and	CCONJ
ejpam-6366	290	13	the	the	DET
ejpam-6366	290	14	fekete	fekete	PROPN
ejpam-6366	290	15	-	-	PUNCT
ejpam-6366	290	16	szegö	szegö	ADJ
ejpam-6366	290	17	inequalities	inequality	NOUN
ejpam-6366	290	18	for	for	ADP
ejpam-6366	290	19	the	the	DET
ejpam-6366	290	20	functions	function	NOUN
ejpam-6366	290	21	in	in	ADP
ejpam-6366	290	22	this	this	DET
ejpam-6366	290	23	subfamily	subfamily	NOUN
ejpam-6366	290	24	.	.	PUNCT
ejpam-6366	291	1	we	we	PRON
ejpam-6366	291	2	note	note	VERB
ejpam-6366	291	3	that	that	SCONJ
ejpam-6366	291	4	the	the	DET
ejpam-6366	291	5	results	result	NOUN
ejpam-6366	291	6	of	of	ADP
ejpam-6366	291	7	this	this	DET
ejpam-6366	291	8	study	study	NOUN
ejpam-6366	291	9	naturally	naturally	ADV
ejpam-6366	291	10	include	include	VERB
ejpam-6366	291	11	many	many	ADJ
ejpam-6366	291	12	of	of	ADP
ejpam-6366	291	13	the	the	DET
ejpam-6366	291	14	known	know	VERB
ejpam-6366	291	15	results	result	NOUN
ejpam-6366	291	16	for	for	ADP
ejpam-6366	291	17	these	these	DET
ejpam-6366	291	18	subfamilies	subfamily	NOUN
ejpam-6366	291	19	,	,	PUNCT
ejpam-6366	291	20	which	which	PRON
ejpam-6366	291	21	are	be	AUX
ejpam-6366	291	22	listed	list	VERB
ejpam-6366	291	23	in	in	ADP
ejpam-6366	291	24	the	the	DET
ejpam-6366	291	25	introduction	introduction	NOUN
ejpam-6366	291	26	section	section	NOUN
ejpam-6366	291	27	.	.	PUNCT
ejpam-6366	292	1	for	for	ADP
ejpam-6366	292	2	future	future	ADJ
ejpam-6366	292	3	studies	study	NOUN
ejpam-6366	292	4	,	,	PUNCT
ejpam-6366	292	5	we	we	PRON
ejpam-6366	292	6	can	can	AUX
ejpam-6366	292	7	derive	derive	VERB
ejpam-6366	292	8	important	important	ADJ
ejpam-6366	292	9	geometric	geometric	ADJ
ejpam-6366	292	10	properties	property	NOUN
ejpam-6366	292	11	by	by	ADP
ejpam-6366	292	12	introducing	introduce	VERB
ejpam-6366	292	13	the	the	DET
ejpam-6366	292	14	same	same	ADJ
ejpam-6366	292	15	subfamily	subfamily	ADV
ejpam-6366	292	16	in	in	ADP
ejpam-6366	292	17	the	the	DET
ejpam-6366	292	18	case	case	NOUN
ejpam-6366	292	19	of	of	ADP
ejpam-6366	292	20	multivalent	multivalent	NOUN
ejpam-6366	292	21	(	(	PUNCT
ejpam-6366	292	22	or	or	CCONJ
ejpam-6366	292	23	meromorphic	meromorphic	ADJ
ejpam-6366	292	24	)	)	PUNCT
ejpam-6366	292	25	regular	regular	ADJ
ejpam-6366	292	26	functions	function	NOUN
ejpam-6366	292	27	and	and	CCONJ
ejpam-6366	292	28	applying	apply	VERB
ejpam-6366	292	29	the	the	DET
ejpam-6366	292	30	same	same	ADJ
ejpam-6366	292	31	techniques	technique	NOUN
ejpam-6366	292	32	used	use	VERB
ejpam-6366	292	33	in	in	ADP
ejpam-6366	292	34	this	this	DET
ejpam-6366	292	35	paper	paper	NOUN
ejpam-6366	292	36	.	.	PUNCT
ejpam-6366	293	1	t.	t.	PROPN
ejpam-6366	293	2	m.	m.	PROPN
ejpam-6366	293	3	seoudy	seoudy	PROPN
ejpam-6366	293	4	,	,	PUNCT
ejpam-6366	293	5	a.	a.	PROPN
ejpam-6366	293	6	e.	e.	PROPN
ejpam-6366	293	7	shammaky	shammaky	PROPN
ejpam-6366	293	8	/	/	SYM
ejpam-6366	293	9	eur	eur	PROPN
ejpam-6366	293	10	.	.	PUNCT
ejpam-6366	294	1	j.	j.	PROPN
ejpam-6366	294	2	pure	pure	PROPN
ejpam-6366	294	3	appl	appl	PROPN
ejpam-6366	294	4	.	.	PROPN
ejpam-6366	294	5	math	math	PROPN
ejpam-6366	294	6	,	,	PUNCT
ejpam-6366	294	7	18	18	NUM
ejpam-6366	294	8	(	(	PUNCT
ejpam-6366	294	9	4	4	NUM
ejpam-6366	294	10	)	)	PUNCT
ejpam-6366	294	11	(	(	PUNCT
ejpam-6366	294	12	2025	2025	NUM
ejpam-6366	294	13	)	)	PUNCT
ejpam-6366	294	14	,	,	PUNCT
ejpam-6366	294	15	6366	6366	NUM
ejpam-6366	294	16	14	14	NUM
ejpam-6366	294	17	of	of	ADP
ejpam-6366	294	18	15	15	NUM
ejpam-6366	294	19	references	reference	NOUN
ejpam-6366	294	20	[	[	X
ejpam-6366	294	21	1	1	NUM
ejpam-6366	294	22	]	]	PUNCT
ejpam-6366	294	23	w	w	PROPN
ejpam-6366	294	24	janowski	janowski	NOUN
ejpam-6366	294	25	.	.	PUNCT
ejpam-6366	295	1	some	some	DET
ejpam-6366	295	2	extremal	extremal	ADJ
ejpam-6366	295	3	problems	problem	NOUN
ejpam-6366	295	4	for	for	ADP
ejpam-6366	295	5	certain	certain	ADJ
ejpam-6366	295	6	families	family	NOUN
ejpam-6366	295	7	of	of	ADP
ejpam-6366	295	8	analytic	analytic	ADJ
ejpam-6366	295	9	functions	function	NOUN
ejpam-6366	295	10	.	.	PUNCT
ejpam-6366	296	1	bull	bull	NOUN
ejpam-6366	296	2	.	.	PUNCT
ejpam-6366	297	1	polish	polish	PROPN
ejpam-6366	297	2	acad	acad	PROPN
ejpam-6366	297	3	.	.	PUNCT
ejpam-6366	298	1	sci	sci	PROPN
ejpam-6366	298	2	.	.	PROPN
ejpam-6366	298	3	,	,	PUNCT
ejpam-6366	298	4	21:17–25	21:17–25	NUM
ejpam-6366	298	5	,	,	PUNCT
ejpam-6366	298	6	1973	1973	NUM
ejpam-6366	298	7	.	.	PUNCT
ejpam-6366	299	1	[	[	X
ejpam-6366	299	2	2	2	X
ejpam-6366	299	3	]	]	PUNCT
ejpam-6366	299	4	w	w	PROPN
ejpam-6366	299	5	janowski	janowski	NOUN
ejpam-6366	299	6	.	.	PUNCT
ejpam-6366	300	1	some	some	DET
ejpam-6366	300	2	extremal	extremal	ADJ
ejpam-6366	300	3	problems	problem	NOUN
ejpam-6366	300	4	for	for	ADP
ejpam-6366	300	5	certain	certain	ADJ
ejpam-6366	300	6	families	family	NOUN
ejpam-6366	300	7	of	of	ADP
ejpam-6366	300	8	analytic	analytic	ADJ
ejpam-6366	300	9	functions	function	NOUN
ejpam-6366	300	10	.	.	PUNCT
ejpam-6366	301	1	ann	ann	PROPN
ejpam-6366	301	2	.	.	PUNCT
ejpam-6366	301	3	polon	polon	PROPN
ejpam-6366	301	4	.	.	PUNCT
ejpam-6366	302	1	math	math	NOUN
ejpam-6366	302	2	.	.	PUNCT
ejpam-6366	302	3	,	,	PUNCT
ejpam-6366	303	1	28:297–326	28:297–326	NUM
ejpam-6366	303	2	,	,	PUNCT
ejpam-6366	303	3	1973	1973	NUM
ejpam-6366	303	4	.	.	PUNCT
ejpam-6366	304	1	[	[	X
ejpam-6366	304	2	3	3	X
ejpam-6366	304	3	]	]	X
ejpam-6366	304	4	o	o	X
ejpam-6366	304	5	p	p	PROPN
ejpam-6366	304	6	ahuja	ahuja	PROPN
ejpam-6366	304	7	.	.	PUNCT
ejpam-6366	305	1	families	family	NOUN
ejpam-6366	305	2	of	of	ADP
ejpam-6366	305	3	analytic	analytic	ADJ
ejpam-6366	305	4	functions	function	NOUN
ejpam-6366	305	5	related	relate	VERB
ejpam-6366	305	6	to	to	ADP
ejpam-6366	305	7	ruscheweyh	ruscheweyh	VERB
ejpam-6366	305	8	derivatives	derivative	NOUN
ejpam-6366	305	9	and	and	CCONJ
ejpam-6366	305	10	subordinate	subordinate	VERB
ejpam-6366	305	11	to	to	ADP
ejpam-6366	305	12	convex	convex	NOUN
ejpam-6366	305	13	functions	function	NOUN
ejpam-6366	305	14	.	.	PUNCT
ejpam-6366	306	1	j.	j.	PROPN
ejpam-6366	306	2	yokohama	yokohama	PROPN
ejpam-6366	306	3	math	math	PROPN
ejpam-6366	306	4	.	.	PUNCT
ejpam-6366	306	5	,	,	PUNCT
ejpam-6366	306	6	41:39–50	41:39–50	PROPN
ejpam-6366	306	7	,	,	PUNCT
ejpam-6366	306	8	1993	1993	NUM
ejpam-6366	306	9	.	.	PUNCT
ejpam-6366	307	1	[	[	X
ejpam-6366	307	2	4	4	X
ejpam-6366	307	3	]	]	X
ejpam-6366	307	4	f	f	NOUN
ejpam-6366	307	5	d	d	X
ejpam-6366	307	6	alanazi	alanazi	PROPN
ejpam-6366	307	7	and	and	CCONJ
ejpam-6366	307	8	f	f	PROPN
ejpam-6366	307	9	alsarari	alsarari	ADJ
ejpam-6366	307	10	.	.	PUNCT
ejpam-6366	308	1	geometric	geometric	ADJ
ejpam-6366	308	2	convolution	convolution	NOUN
ejpam-6366	308	3	characteristics	characteristic	NOUN
ejpam-6366	308	4	of	of	ADP
ejpam-6366	308	5	q	q	ADJ
ejpam-6366	308	6	-	-	PUNCT
ejpam-6366	308	7	janowski	janowski	ADJ
ejpam-6366	308	8	type	type	NOUN
ejpam-6366	308	9	functions	function	NOUN
ejpam-6366	308	10	related	relate	VERB
ejpam-6366	308	11	to	to	ADP
ejpam-6366	308	12	(	(	PUNCT
ejpam-6366	308	13	j	j	NOUN
ejpam-6366	308	14	,	,	PUNCT
ejpam-6366	308	15	k)-symmetrical	k)-symmetrical	ADJ
ejpam-6366	308	16	functions	function	NOUN
ejpam-6366	308	17	.	.	PUNCT
ejpam-6366	309	1	aims	aim	VERB
ejpam-6366	309	2	mathematics	mathematic	NOUN
ejpam-6366	309	3	,	,	PUNCT
ejpam-6366	309	4	10(3):6652	10(3):6652	NUM
ejpam-6366	309	5	–	–	PUNCT
ejpam-6366	309	6	6663	6663	NUM
ejpam-6366	309	7	,	,	PUNCT
ejpam-6366	309	8	2025	2025	NUM
ejpam-6366	309	9	.	.	PUNCT
ejpam-6366	310	1	[	[	X
ejpam-6366	310	2	5	5	NUM
ejpam-6366	310	3	]	]	PUNCT
ejpam-6366	310	4	a	a	DET
ejpam-6366	310	5	alatawi	alatawi	ADJ
ejpam-6366	310	6	,	,	PUNCT
ejpam-6366	310	7	m	m	NOUN
ejpam-6366	310	8	darus	darus	NOUN
ejpam-6366	310	9	,	,	PUNCT
ejpam-6366	310	10	and	and	CCONJ
ejpam-6366	310	11	s	s	VERB
ejpam-6366	310	12	sivasubramanian	sivasubramanian	ADJ
ejpam-6366	310	13	.	.	PUNCT
ejpam-6366	311	1	generalised	generalise	VERB
ejpam-6366	311	2	subclasses	subclass	NOUN
ejpam-6366	311	3	of	of	ADP
ejpam-6366	311	4	meromorphically	meromorphically	ADV
ejpam-6366	311	5	q	q	ADJ
ejpam-6366	311	6	-	-	PUNCT
ejpam-6366	311	7	starlike	starlike	ADJ
ejpam-6366	311	8	function	function	NOUN
ejpam-6366	311	9	using	use	VERB
ejpam-6366	311	10	the	the	DET
ejpam-6366	311	11	janowski	janowski	ADJ
ejpam-6366	311	12	functions	function	NOUN
ejpam-6366	311	13	.	.	PUNCT
ejpam-6366	312	1	mathematical	mathematical	ADJ
ejpam-6366	312	2	foundations	foundation	NOUN
ejpam-6366	312	3	of	of	ADP
ejpam-6366	312	4	computing	computing	NOUN
ejpam-6366	312	5	,	,	PUNCT
ejpam-6366	312	6	7(4):439–446	7(4):439–446	NUM
ejpam-6366	312	7	,	,	PUNCT
ejpam-6366	312	8	2024	2024	NUM
ejpam-6366	312	9	.	.	PUNCT
ejpam-6366	313	1	[	[	X
ejpam-6366	313	2	6	6	NUM
ejpam-6366	313	3	]	]	SYM
ejpam-6366	313	4	m	m	VERB
ejpam-6366	313	5	k	k	PROPN
ejpam-6366	313	6	aouf	aouf	PROPN
ejpam-6366	313	7	and	and	CCONJ
ejpam-6366	313	8	t	t	PROPN
ejpam-6366	313	9	m	m	PROPN
ejpam-6366	313	10	seoudy	seoudy	PROPN
ejpam-6366	313	11	.	.	PUNCT
ejpam-6366	314	1	classes	class	NOUN
ejpam-6366	314	2	of	of	ADP
ejpam-6366	314	3	analytic	analytic	ADJ
ejpam-6366	314	4	functions	function	NOUN
ejpam-6366	314	5	related	relate	VERB
ejpam-6366	314	6	to	to	ADP
ejpam-6366	314	7	the	the	DET
ejpam-6366	314	8	dzioksrivastava	dzioksrivastava	NOUN
ejpam-6366	314	9	operator	operator	NOUN
ejpam-6366	314	10	.	.	PUNCT
ejpam-6366	315	1	integral	integral	ADJ
ejpam-6366	315	2	transforms	transform	VERB
ejpam-6366	315	3	spec	spec	NOUN
ejpam-6366	315	4	.	.	PUNCT
ejpam-6366	316	1	funct	funct	PROPN
ejpam-6366	316	2	.	.	PUNCT
ejpam-6366	316	3	,	,	PUNCT
ejpam-6366	317	1	22(6):423–430	22(6):423–430	PROPN
ejpam-6366	317	2	,	,	PUNCT
ejpam-6366	317	3	2011	2011	NUM
ejpam-6366	317	4	.	.	PUNCT
ejpam-6366	318	1	[	[	X
ejpam-6366	318	2	7	7	X
ejpam-6366	318	3	]	]	X
ejpam-6366	318	4	r	r	NOUN
ejpam-6366	318	5	m	m	VERB
ejpam-6366	318	6	goel	goel	NOUN
ejpam-6366	318	7	and	and	CCONJ
ejpam-6366	318	8	b	b	X
ejpam-6366	318	9	s	s	X
ejpam-6366	318	10	mehrok	mehrok	NOUN
ejpam-6366	318	11	.	.	PUNCT
ejpam-6366	319	1	on	on	ADP
ejpam-6366	319	2	the	the	DET
ejpam-6366	319	3	coefficients	coefficient	NOUN
ejpam-6366	319	4	of	of	ADP
ejpam-6366	319	5	a	a	DET
ejpam-6366	319	6	subclass	subclass	NOUN
ejpam-6366	319	7	of	of	ADP
ejpam-6366	319	8	starlike	starlike	NOUN
ejpam-6366	319	9	functions	function	NOUN
ejpam-6366	319	10	.	.	PUNCT
ejpam-6366	320	1	indian	indian	PROPN
ejpam-6366	320	2	j.	j.	PROPN
ejpam-6366	320	3	pure	pure	PROPN
ejpam-6366	320	4	appl	appl	PROPN
ejpam-6366	320	5	.	.	PUNCT
ejpam-6366	320	6	math	math	PROPN
ejpam-6366	320	7	.	.	PUNCT
ejpam-6366	320	8	,	,	PUNCT
ejpam-6366	321	1	12:634–647	12:634–647	NUM
ejpam-6366	321	2	,	,	PUNCT
ejpam-6366	321	3	1981	1981	NUM
ejpam-6366	321	4	.	.	PUNCT
ejpam-6366	322	1	[	[	X
ejpam-6366	322	2	8	8	NUM
ejpam-6366	322	3	]	]	X
ejpam-6366	322	4	h	h	NOUN
ejpam-6366	322	5	hadi	hadi	PROPN
ejpam-6366	322	6	,	,	PUNCT
ejpam-6366	322	7	m	m	NOUN
ejpam-6366	322	8	darus	darus	NOUN
ejpam-6366	322	9	,	,	PUNCT
ejpam-6366	322	10	and	and	CCONJ
ejpam-6366	322	11	a	a	DET
ejpam-6366	322	12	alb	alb	NOUN
ejpam-6366	322	13	lupas	lupa	NOUN
ejpam-6366	322	14	.	.	PUNCT
ejpam-6366	323	1	a	a	DET
ejpam-6366	323	2	class	class	NOUN
ejpam-6366	323	3	of	of	ADP
ejpam-6366	323	4	janowski	janowski	NOUN
ejpam-6366	323	5	-	-	PUNCT
ejpam-6366	323	6	type	type	NOUN
ejpam-6366	323	7	(	(	PUNCT
ejpam-6366	323	8	p	p	NOUN
ejpam-6366	323	9	,	,	PUNCT
ejpam-6366	323	10	q)-convex	q)-convex	NOUN
ejpam-6366	323	11	harmonic	harmonic	ADJ
ejpam-6366	323	12	functions	function	NOUN
ejpam-6366	323	13	involving	involve	VERB
ejpam-6366	323	14	a	a	DET
ejpam-6366	323	15	generalized	generalized	ADJ
ejpam-6366	323	16	q	q	ADJ
ejpam-6366	323	17	-	-	PUNCT
ejpam-6366	323	18	mittag	mittag	ADJ
ejpam-6366	323	19	–	–	PUNCT
ejpam-6366	323	20	leffler	leffler	NOUN
ejpam-6366	323	21	function	function	NOUN
ejpam-6366	323	22	.	.	PUNCT
ejpam-6366	324	1	axioms	axiom	NOUN
ejpam-6366	324	2	,	,	PUNCT
ejpam-6366	324	3	12:190	12:190	NUM
ejpam-6366	324	4	,	,	PUNCT
ejpam-6366	324	5	2023	2023	NUM
ejpam-6366	324	6	.	.	PUNCT
ejpam-6366	325	1	[	[	X
ejpam-6366	325	2	9	9	NUM
ejpam-6366	325	3	]	]	SYM
ejpam-6366	325	4	s	s	PART
ejpam-6366	325	5	s	s	X
ejpam-6366	325	6	kumar	kumar	PROPN
ejpam-6366	325	7	and	and	CCONJ
ejpam-6366	325	8	p	p	PROPN
ejpam-6366	325	9	yadavc	yadavc	PROPN
ejpam-6366	325	10	.	.	PUNCT
ejpam-6366	326	1	on	on	ADP
ejpam-6366	326	2	oblique	oblique	ADJ
ejpam-6366	326	3	domains	domain	NOUN
ejpam-6366	326	4	of	of	ADP
ejpam-6366	326	5	janowski	janowski	ADJ
ejpam-6366	326	6	functions	function	NOUN
ejpam-6366	326	7	.	.	PUNCT
ejpam-6366	327	1	math	math	NOUN
ejpam-6366	327	2	.	.	PUNCT
ejpam-6366	328	1	slovaca	slovaca	PROPN
ejpam-6366	328	2	,	,	PUNCT
ejpam-6366	328	3	73(2):407–424	73(2):407–424	NUM
ejpam-6366	328	4	,	,	PUNCT
ejpam-6366	328	5	2023	2023	NUM
ejpam-6366	328	6	.	.	PUNCT
ejpam-6366	329	1	[	[	X
ejpam-6366	329	2	10	10	NUM
ejpam-6366	329	3	]	]	X
ejpam-6366	329	4	g	g	NOUN
ejpam-6366	329	5	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-6366	329	6	,	,	PUNCT
ejpam-6366	329	7	h	h	PROPN
ejpam-6366	329	8	ö	ö	X
ejpam-6366	329	9	güney	güney	PROPN
ejpam-6366	329	10	,	,	PUNCT
ejpam-6366	329	11	and	and	CCONJ
ejpam-6366	329	12	d	d	ADP
ejpam-6366	329	13	breaz	breaz	NOUN
ejpam-6366	329	14	.	.	PUNCT
ejpam-6366	330	1	starlike	starlike	NOUN
ejpam-6366	330	2	functions	function	NOUN
ejpam-6366	330	3	of	of	ADP
ejpam-6366	330	4	the	the	DET
ejpam-6366	330	5	miller	miller	PROPN
ejpam-6366	330	6	–	–	PUNCT
ejpam-6366	330	7	ross	ross	NOUN
ejpam-6366	330	8	-	-	PUNCT
ejpam-6366	330	9	type	type	NOUN
ejpam-6366	330	10	poisson	poisson	NOUN
ejpam-6366	330	11	distribution	distribution	NOUN
ejpam-6366	330	12	in	in	ADP
ejpam-6366	330	13	the	the	DET
ejpam-6366	330	14	janowski	janowski	ADJ
ejpam-6366	330	15	domain	domain	NOUN
ejpam-6366	330	16	.	.	PUNCT
ejpam-6366	331	1	mathematics	mathematic	NOUN
ejpam-6366	331	2	,	,	PUNCT
ejpam-6366	331	3	12:795	12:795	NUM
ejpam-6366	331	4	,	,	PUNCT
ejpam-6366	331	5	2024	2024	NUM
ejpam-6366	331	6	.	.	PUNCT
ejpam-6366	332	1	[	[	X
ejpam-6366	332	2	11	11	NUM
ejpam-6366	332	3	]	]	PUNCT
ejpam-6366	332	4	a	a	DET
ejpam-6366	332	5	e	e	NOUN
ejpam-6366	332	6	shammaky	shammaky	PROPN
ejpam-6366	332	7	and	and	CCONJ
ejpam-6366	332	8	t	t	PROPN
ejpam-6366	332	9	m	m	AUX
ejpam-6366	332	10	seoudy	seoudy	PROPN
ejpam-6366	332	11	.	.	PUNCT
ejpam-6366	333	1	on	on	ADP
ejpam-6366	333	2	a	a	DET
ejpam-6366	333	3	general	general	ADJ
ejpam-6366	333	4	subclass	subclass	NOUN
ejpam-6366	333	5	of	of	ADP
ejpam-6366	333	6	q	q	NOUN
ejpam-6366	333	7	-	-	PUNCT
ejpam-6366	333	8	starlike	starlike	NOUN
ejpam-6366	333	9	and	and	CCONJ
ejpam-6366	333	10	q	q	ADJ
ejpam-6366	333	11	-	-	PUNCT
ejpam-6366	333	12	convex	convex	ADJ
ejpam-6366	333	13	analytic	analytic	ADJ
ejpam-6366	333	14	functions	function	NOUN
ejpam-6366	333	15	.	.	PUNCT
ejpam-6366	334	1	contemp	contemp	NOUN
ejpam-6366	334	2	.	.	PUNCT
ejpam-6366	335	1	math	math	NOUN
ejpam-6366	335	2	.	.	PUNCT
ejpam-6366	335	3	,	,	PUNCT
ejpam-6366	335	4	5(4):6038–6055	5(4):6038–6055	NOUN
ejpam-6366	335	5	,	,	PUNCT
ejpam-6366	335	6	2024	2024	NUM
ejpam-6366	335	7	.	.	PUNCT
ejpam-6366	336	1	[	[	X
ejpam-6366	336	2	12	12	NUM
ejpam-6366	336	3	]	]	X
ejpam-6366	336	4	h	h	NOUN
ejpam-6366	336	5	silverman	silverman	NOUN
ejpam-6366	336	6	and	and	CCONJ
ejpam-6366	336	7	e	e	NOUN
ejpam-6366	336	8	m	m	PROPN
ejpam-6366	336	9	silvia	silvia	PROPN
ejpam-6366	336	10	.	.	PUNCT
ejpam-6366	337	1	subclasses	subclass	NOUN
ejpam-6366	337	2	of	of	ADP
ejpam-6366	337	3	starlike	starlike	NOUN
ejpam-6366	337	4	functions	function	NOUN
ejpam-6366	337	5	subordinate	subordinate	VERB
ejpam-6366	337	6	to	to	ADP
ejpam-6366	337	7	convex	convex	NOUN
ejpam-6366	337	8	functions	function	NOUN
ejpam-6366	337	9	.	.	PUNCT
ejpam-6366	338	1	canad	canad	PROPN
ejpam-6366	338	2	.	.	PUNCT
ejpam-6366	339	1	j.	j.	PROPN
ejpam-6366	339	2	math	math	PROPN
ejpam-6366	339	3	.	.	PUNCT
ejpam-6366	339	4	,	,	PUNCT
ejpam-6366	339	5	1:48–61	1:48–61	PROPN
ejpam-6366	339	6	,	,	PUNCT
ejpam-6366	339	7	1985	1985	NUM
ejpam-6366	339	8	.	.	PUNCT
ejpam-6366	340	1	[	[	X
ejpam-6366	340	2	13	13	NUM
ejpam-6366	340	3	]	]	PUNCT
ejpam-6366	340	4	h	h	NOUN
ejpam-6366	340	5	silverman	silverman	NOUN
ejpam-6366	340	6	,	,	PUNCT
ejpam-6366	340	7	e	e	PROPN
ejpam-6366	340	8	m	m	NOUN
ejpam-6366	340	9	silvia	silvia	NOUN
ejpam-6366	340	10	,	,	PUNCT
ejpam-6366	340	11	and	and	CCONJ
ejpam-6366	340	12	d	d	ADP
ejpam-6366	340	13	telage	telage	NOUN
ejpam-6366	340	14	.	.	PUNCT
ejpam-6366	341	1	convolution	convolution	NOUN
ejpam-6366	341	2	conditions	condition	NOUN
ejpam-6366	341	3	for	for	ADP
ejpam-6366	341	4	convexity	convexity	NOUN
ejpam-6366	341	5	,	,	PUNCT
ejpam-6366	341	6	starlikeness	starlikeness	ADJ
ejpam-6366	341	7	and	and	CCONJ
ejpam-6366	341	8	spiral	spiral	ADJ
ejpam-6366	341	9	-	-	PUNCT
ejpam-6366	341	10	likeness	likeness	NOUN
ejpam-6366	341	11	.	.	PUNCT
ejpam-6366	342	1	math	math	NOUN
ejpam-6366	342	2	.	.	PUNCT
ejpam-6366	343	1	z	z	X
ejpam-6366	343	2	,	,	PUNCT
ejpam-6366	343	3	162:125–130	162:125–130	NUM
ejpam-6366	343	4	,	,	PUNCT
ejpam-6366	343	5	1978	1978	NUM
ejpam-6366	343	6	.	.	PUNCT
ejpam-6366	344	1	[	[	X
ejpam-6366	344	2	14	14	NUM
ejpam-6366	344	3	]	]	X
ejpam-6366	344	4	t	t	PROPN
ejpam-6366	344	5	al	al	PROPN
ejpam-6366	344	6	-	-	PUNCT
ejpam-6366	344	7	hawary	hawary	PROPN
ejpam-6366	344	8	,	,	PUNCT
ejpam-6366	344	9	b	b	X
ejpam-6366	344	10	a	a	DET
ejpam-6366	344	11	frasin	frasin	NOUN
ejpam-6366	344	12	,	,	PUNCT
ejpam-6366	344	13	and	and	CCONJ
ejpam-6366	344	14	f	f	PROPN
ejpam-6366	344	15	yousef	yousef	PROPN
ejpam-6366	344	16	.	.	PUNCT
ejpam-6366	345	1	coefficients	coefficient	NOUN
ejpam-6366	345	2	estimates	estimate	NOUN
ejpam-6366	345	3	for	for	ADP
ejpam-6366	345	4	certain	certain	ADJ
ejpam-6366	345	5	classes	class	NOUN
ejpam-6366	345	6	of	of	ADP
ejpam-6366	345	7	analytic	analytic	ADJ
ejpam-6366	345	8	functions	function	NOUN
ejpam-6366	345	9	of	of	ADP
ejpam-6366	345	10	complex	complex	ADJ
ejpam-6366	345	11	order	order	NOUN
ejpam-6366	345	12	.	.	PUNCT
ejpam-6366	346	1	afr	afr	NOUN
ejpam-6366	346	2	.	.	PUNCT
ejpam-6366	347	1	mat	mat	PROPN
ejpam-6366	347	2	.	.	PROPN
ejpam-6366	347	3	,	,	PUNCT
ejpam-6366	347	4	29:12651271	29:12651271	NUM
ejpam-6366	347	5	,	,	PUNCT
ejpam-6366	347	6	2018	2018	NUM
ejpam-6366	347	7	.	.	PUNCT
ejpam-6366	348	1	[	[	X
ejpam-6366	348	2	15	15	NUM
ejpam-6366	348	3	]	]	X
ejpam-6366	348	4	m	m	VERB
ejpam-6366	348	5	k	k	PROPN
ejpam-6366	348	6	aouf	aouf	PROPN
ejpam-6366	348	7	and	and	CCONJ
ejpam-6366	348	8	t	t	PROPN
ejpam-6366	348	9	m	m	PROPN
ejpam-6366	348	10	seoudy	seoudy	PROPN
ejpam-6366	348	11	.	.	PUNCT
ejpam-6366	349	1	convolution	convolution	NOUN
ejpam-6366	349	2	properties	property	NOUN
ejpam-6366	349	3	for	for	ADP
ejpam-6366	349	4	classes	class	NOUN
ejpam-6366	349	5	of	of	ADP
ejpam-6366	349	6	bounded	bounded	ADJ
ejpam-6366	349	7	analytic	analytic	ADJ
ejpam-6366	349	8	functions	function	NOUN
ejpam-6366	349	9	with	with	ADP
ejpam-6366	349	10	complex	complex	ADJ
ejpam-6366	349	11	order	order	NOUN
ejpam-6366	349	12	defined	define	VERB
ejpam-6366	349	13	by	by	ADP
ejpam-6366	349	14	q	q	ADJ
ejpam-6366	349	15	-	-	ADJ
ejpam-6366	349	16	derivative	derivative	ADJ
ejpam-6366	349	17	operator	operator	NOUN
ejpam-6366	349	18	.	.	PUNCT
ejpam-6366	350	1	rev	rev	PROPN
ejpam-6366	350	2	.	.	PUNCT
ejpam-6366	350	3	real	real	ADJ
ejpam-6366	350	4	acad	acad	PROPN
ejpam-6366	350	5	.	.	PUNCT
ejpam-6366	351	1	cienc	cienc	PROPN
ejpam-6366	351	2	.	.	PUNCT
ejpam-6366	352	1	exactas	exactas	PROPN
ejpam-6366	352	2	fis	fis	PROPN
ejpam-6366	352	3	.	.	PUNCT
ejpam-6366	353	1	nat	nat	PROPN
ejpam-6366	353	2	.	.	PUNCT
ejpam-6366	354	1	ser	ser	PROPN
ejpam-6366	354	2	.	.	PUNCT
ejpam-6366	355	1	a	a	DET
ejpam-6366	355	2	-	-	PUNCT
ejpam-6366	355	3	mat	mat	NOUN
ejpam-6366	355	4	.	.	NOUN
ejpam-6366	355	5	,	,	PUNCT
ejpam-6366	355	6	113:1279–1288	113:1279–1288	NUM
ejpam-6366	355	7	,	,	PUNCT
ejpam-6366	355	8	2019	2019	NUM
ejpam-6366	355	9	.	.	PUNCT
ejpam-6366	356	1	[	[	X
ejpam-6366	356	2	16	16	NUM
ejpam-6366	356	3	]	]	X
ejpam-6366	356	4	m	m	PROPN
ejpam-6366	356	5	s	s	PROPN
ejpam-6366	356	6	robertson	robertson	PROPN
ejpam-6366	356	7	.	.	PUNCT
ejpam-6366	357	1	on	on	ADP
ejpam-6366	357	2	the	the	DET
ejpam-6366	357	3	theory	theory	NOUN
ejpam-6366	357	4	of	of	ADP
ejpam-6366	357	5	univalent	univalent	ADJ
ejpam-6366	357	6	functions	function	NOUN
ejpam-6366	357	7	.	.	PUNCT
ejpam-6366	358	1	ann	ann	PROPN
ejpam-6366	358	2	.	.	PUNCT
ejpam-6366	358	3	math	math	PROPN
ejpam-6366	358	4	.	.	PUNCT
ejpam-6366	358	5	,	,	PUNCT
ejpam-6366	358	6	37:374–408	37:374–408	NUM
ejpam-6366	358	7	,	,	PUNCT
ejpam-6366	358	8	1936	1936	NUM
ejpam-6366	358	9	.	.	PUNCT
ejpam-6366	359	1	[	[	X
ejpam-6366	359	2	17	17	NUM
ejpam-6366	359	3	]	]	X
ejpam-6366	359	4	t	t	PROPN
ejpam-6366	359	5	m	m	PROPN
ejpam-6366	359	6	seoudy	seoudy	PROPN
ejpam-6366	359	7	.	.	PUNCT
ejpam-6366	360	1	convolution	convolution	NOUN
ejpam-6366	360	2	results	result	NOUN
ejpam-6366	360	3	and	and	CCONJ
ejpam-6366	360	4	fekete	fekete	NOUN
ejpam-6366	360	5	-	-	PUNCT
ejpam-6366	360	6	szegö	szegö	ADJ
ejpam-6366	360	7	inequalities	inequality	NOUN
ejpam-6366	360	8	for	for	ADP
ejpam-6366	360	9	certain	certain	ADJ
ejpam-6366	360	10	classes	class	NOUN
ejpam-6366	360	11	of	of	ADP
ejpam-6366	360	12	symmetric	symmetric	ADJ
ejpam-6366	360	13	q	q	ADJ
ejpam-6366	360	14	-	-	PUNCT
ejpam-6366	360	15	starlike	starlike	NOUN
ejpam-6366	360	16	and	and	CCONJ
ejpam-6366	360	17	symmetric	symmetric	ADJ
ejpam-6366	360	18	q	q	ADJ
ejpam-6366	360	19	-	-	PUNCT
ejpam-6366	360	20	convex	convex	NOUN
ejpam-6366	360	21	functions	function	NOUN
ejpam-6366	360	22	.	.	PUNCT
ejpam-6366	361	1	j.	j.	PROPN
ejpam-6366	361	2	math	math	PROPN
ejpam-6366	361	3	.	.	PROPN
ejpam-6366	361	4	,	,	PUNCT
ejpam-6366	361	5	2022:8203921	2022:8203921	NUM
ejpam-6366	361	6	,	,	PUNCT
ejpam-6366	361	7	2022	2022	NUM
ejpam-6366	361	8	.	.	PUNCT
ejpam-6366	362	1	[	[	X
ejpam-6366	362	2	18	18	NUM
ejpam-6366	362	3	]	]	X
ejpam-6366	362	4	t	t	PROPN
ejpam-6366	362	5	m	m	VERB
ejpam-6366	362	6	seoudy	seoudy	VERB
ejpam-6366	362	7	and	and	CCONJ
ejpam-6366	362	8	m	m	PROPN
ejpam-6366	362	9	k	k	PROPN
ejpam-6366	362	10	aouf	aouf	PROPN
ejpam-6366	362	11	.	.	PUNCT
ejpam-6366	363	1	coefficient	coefficient	NOUN
ejpam-6366	363	2	estimates	estimate	NOUN
ejpam-6366	363	3	of	of	ADP
ejpam-6366	363	4	new	new	ADJ
ejpam-6366	363	5	classes	class	NOUN
ejpam-6366	363	6	of	of	ADP
ejpam-6366	363	7	q	q	NOUN
ejpam-6366	363	8	-	-	PUNCT
ejpam-6366	363	9	starlike	starlike	NOUN
ejpam-6366	363	10	and	and	CCONJ
ejpam-6366	363	11	q	q	ADJ
ejpam-6366	363	12	-	-	PUNCT
ejpam-6366	363	13	convex	convex	ADJ
ejpam-6366	363	14	functions	function	NOUN
ejpam-6366	363	15	of	of	ADP
ejpam-6366	363	16	complex	complex	ADJ
ejpam-6366	363	17	order	order	NOUN
ejpam-6366	363	18	.	.	PUNCT
ejpam-6366	364	1	j.	j.	PROPN
ejpam-6366	364	2	math	math	PROPN
ejpam-6366	364	3	.	.	PUNCT
ejpam-6366	365	1	inequal	inequal	ADJ
ejpam-6366	365	2	.	.	PUNCT
ejpam-6366	365	3	,	,	PUNCT
ejpam-6366	365	4	10(1):135–145	10(1):135–145	PROPN
ejpam-6366	365	5	,	,	PUNCT
ejpam-6366	365	6	2016	2016	NUM
ejpam-6366	365	7	.	.	PUNCT
ejpam-6366	366	1	[	[	X
ejpam-6366	366	2	19	19	NUM
ejpam-6366	366	3	]	]	PUNCT
ejpam-6366	366	4	h	h	NOUN
ejpam-6366	366	5	silverman	silverman	NOUN
ejpam-6366	366	6	.	.	PUNCT
ejpam-6366	367	1	univalent	univalent	ADJ
ejpam-6366	367	2	functions	function	NOUN
ejpam-6366	367	3	with	with	ADP
ejpam-6366	367	4	negative	negative	ADJ
ejpam-6366	367	5	coefficients	coefficient	NOUN
ejpam-6366	367	6	.	.	PUNCT
ejpam-6366	368	1	proc	proc	NOUN
ejpam-6366	368	2	.	.	PUNCT
ejpam-6366	369	1	amer	amer	PROPN
ejpam-6366	369	2	.	.	PUNCT
ejpam-6366	369	3	math	math	PROPN
ejpam-6366	369	4	.	.	PUNCT
ejpam-6366	370	1	soc	soc	PROPN
ejpam-6366	370	2	.	.	PUNCT
ejpam-6366	370	3	,	,	PUNCT
ejpam-6366	371	1	51:109–116	51:109–116	PROPN
ejpam-6366	371	2	,	,	PUNCT
ejpam-6366	371	3	1975	1975	NUM
ejpam-6366	371	4	.	.	PUNCT
ejpam-6366	372	1	t.	t.	PROPN
ejpam-6366	372	2	m.	m.	PROPN
ejpam-6366	372	3	seoudy	seoudy	PROPN
ejpam-6366	372	4	,	,	PUNCT
ejpam-6366	372	5	a.	a.	PROPN
ejpam-6366	372	6	e.	e.	PROPN
ejpam-6366	372	7	shammaky	shammaky	PROPN
ejpam-6366	372	8	/	/	SYM
ejpam-6366	372	9	eur	eur	PROPN
ejpam-6366	372	10	.	.	PUNCT
ejpam-6366	373	1	j.	j.	PROPN
ejpam-6366	373	2	pure	pure	PROPN
ejpam-6366	373	3	appl	appl	PROPN
ejpam-6366	373	4	.	.	PROPN
ejpam-6366	373	5	math	math	PROPN
ejpam-6366	373	6	,	,	PUNCT
ejpam-6366	373	7	18	18	NUM
ejpam-6366	373	8	(	(	PUNCT
ejpam-6366	373	9	4	4	NUM
ejpam-6366	373	10	)	)	PUNCT
ejpam-6366	373	11	(	(	PUNCT
ejpam-6366	373	12	2025	2025	NUM
ejpam-6366	373	13	)	)	PUNCT
ejpam-6366	373	14	,	,	PUNCT
ejpam-6366	373	15	6366	6366	NUM
ejpam-6366	373	16	15	15	NUM
ejpam-6366	373	17	of	of	ADP
ejpam-6366	373	18	15	15	NUM
ejpam-6366	374	1	[	[	SYM
ejpam-6366	374	2	20	20	NUM
ejpam-6366	374	3	]	]	SYM
ejpam-6366	374	4	v	v	ADP
ejpam-6366	374	5	p	p	X
ejpam-6366	374	6	gupta	gupta	PROPN
ejpam-6366	374	7	and	and	CCONJ
ejpam-6366	374	8	p	p	PROPN
ejpam-6366	374	9	k	k	PROPN
ejpam-6366	374	10	jain	jain	PROPN
ejpam-6366	374	11	.	.	PUNCT
ejpam-6366	375	1	certain	certain	ADJ
ejpam-6366	375	2	classes	class	NOUN
ejpam-6366	375	3	of	of	ADP
ejpam-6366	375	4	univalent	univalent	ADJ
ejpam-6366	375	5	functions	function	NOUN
ejpam-6366	375	6	with	with	ADP
ejpam-6366	375	7	negative	negative	ADJ
ejpam-6366	375	8	coefficients	coefficient	NOUN
ejpam-6366	375	9	ii	ii	PROPN
ejpam-6366	375	10	.	.	PUNCT
ejpam-6366	376	1	bull	bull	PROPN
ejpam-6366	376	2	.	.	PUNCT
ejpam-6366	377	1	austral	austral	PROPN
ejpam-6366	377	2	.	.	PUNCT
ejpam-6366	377	3	math	math	NOUN
ejpam-6366	377	4	.	.	PUNCT
ejpam-6366	378	1	soc	soc	PROPN
ejpam-6366	378	2	.	.	PUNCT
ejpam-6366	378	3	,	,	PUNCT
ejpam-6366	378	4	15(3):467–473	15(3):467–473	PROPN
ejpam-6366	378	5	,	,	PUNCT
ejpam-6366	378	6	1976	1976	NUM
ejpam-6366	378	7	.	.	PUNCT
ejpam-6366	379	1	[	[	X
ejpam-6366	379	2	21	21	NUM
ejpam-6366	379	3	]	]	X
ejpam-6366	379	4	c	c	NOUN
ejpam-6366	379	5	carathéodory	carathéodory	PROPN
ejpam-6366	379	6	.	.	PUNCT
ejpam-6366	380	1	über	über	PROPN
ejpam-6366	380	2	den	den	PROPN
ejpam-6366	380	3	variabilitä	variabilitä	PROPN
ejpam-6366	380	4	tsbereich	tsbereich	PROPN
ejpam-6366	380	5	der	der	NOUN
ejpam-6366	380	6	koeffizienten	koeffizienten	PROPN
ejpam-6366	380	7	von	von	PROPN
ejpam-6366	380	8	potenzreihen	potenzreihen	ADV
ejpam-6366	380	9	,	,	PUNCT
ejpam-6366	380	10	die	die	VERB
ejpam-6366	380	11	gegebene	gegebene	PROPN
ejpam-6366	380	12	werte	werte	NOUN
ejpam-6366	380	13	nicht	nicht	PROPN
ejpam-6366	380	14	annehmen	annehmen	PROPN
ejpam-6366	380	15	.	.	PUNCT
ejpam-6366	381	1	math	math	PROPN
ejpam-6366	381	2	.	.	PUNCT
ejpam-6366	382	1	ann	ann	PROPN
ejpam-6366	382	2	.	.	PROPN
ejpam-6366	382	3	,	,	PUNCT
ejpam-6366	382	4	64:95–115	64:95–115	NUM
ejpam-6366	382	5	,	,	PUNCT
ejpam-6366	382	6	1907	1907	NUM
ejpam-6366	382	7	.	.	PUNCT
ejpam-6366	383	1	[	[	X
ejpam-6366	383	2	22	22	NUM
ejpam-6366	383	3	]	]	X
ejpam-6366	383	4	c	c	NOUN
ejpam-6366	383	5	carathéodory	carathéodory	PROPN
ejpam-6366	383	6	.	.	PUNCT
ejpam-6366	384	1	über	über	PROPN
ejpam-6366	384	2	den	den	PROPN
ejpam-6366	384	3	variabilitärend	variabilitärend	NOUN
ejpam-6366	384	4	.	.	PUNCT
ejpam-6366	384	5	circ	circ	PROPN
ejpam-6366	384	6	.	.	PUNCT
ejpam-6366	385	1	mat	mat	NOUN
ejpam-6366	385	2	.	.	PUNCT
ejpam-6366	385	3	palermo	palermo	NOUN
ejpam-6366	385	4	,	,	PUNCT
ejpam-6366	385	5	32:193–217	32:193–217	NUM
ejpam-6366	385	6	,	,	PUNCT
ejpam-6366	385	7	1911	1911	NUM
ejpam-6366	385	8	.	.	PUNCT
ejpam-6366	386	1	[	[	X
ejpam-6366	386	2	23	23	NUM
ejpam-6366	386	3	]	]	X
ejpam-6366	386	4	f	f	PROPN
ejpam-6366	386	5	r	r	PROPN
ejpam-6366	386	6	keogh	keogh	PROPN
ejpam-6366	386	7	and	and	CCONJ
ejpam-6366	386	8	e	e	NOUN
ejpam-6366	386	9	p	p	NOUN
ejpam-6366	386	10	merkes	merke	NOUN
ejpam-6366	386	11	.	.	PUNCT
ejpam-6366	387	1	a	a	DET
ejpam-6366	387	2	coefficient	coefficient	NOUN
ejpam-6366	387	3	inequality	inequality	NOUN
ejpam-6366	387	4	for	for	ADP
ejpam-6366	387	5	certain	certain	ADJ
ejpam-6366	387	6	classes	class	NOUN
ejpam-6366	387	7	of	of	ADP
ejpam-6366	387	8	analytic	analytic	ADJ
ejpam-6366	387	9	functions	function	NOUN
ejpam-6366	387	10	.	.	PUNCT
ejpam-6366	388	1	proc	proc	NOUN
ejpam-6366	388	2	.	.	PUNCT
ejpam-6366	389	1	am	be	AUX
ejpam-6366	389	2	.	.	PUNCT
ejpam-6366	390	1	math	math	NOUN
ejpam-6366	390	2	.	.	PUNCT
ejpam-6366	391	1	soc	soc	PROPN
ejpam-6366	391	2	.	.	PROPN
ejpam-6366	391	3	,	,	PUNCT
ejpam-6366	391	4	20:8–12	20:8–12	NUM
ejpam-6366	391	5	,	,	PUNCT
ejpam-6366	391	6	1969	1969	NUM
ejpam-6366	391	7	.	.	PUNCT
ejpam-6366	392	1	[	[	X
ejpam-6366	392	2	24	24	NUM
ejpam-6366	392	3	]	]	X
ejpam-6366	392	4	c	c	NOUN
ejpam-6366	392	5	pommerenke	pommerenke	NOUN
ejpam-6366	392	6	.	.	PUNCT
ejpam-6366	393	1	univalent	univalent	ADJ
ejpam-6366	393	2	functions	function	NOUN
ejpam-6366	393	3	.	.	PUNCT
ejpam-6366	394	1	vandenhoeck	vandenhoeck	NOUN
ejpam-6366	394	2	ruprecht	ruprecht	PROPN
ejpam-6366	394	3	:	:	PUNCT
ejpam-6366	394	4	göttingen	göttingen	PROPN
ejpam-6366	394	5	,	,	PUNCT
ejpam-6366	394	6	germany	germany	PROPN
ejpam-6366	394	7	,	,	PUNCT
ejpam-6366	394	8	1975	1975	NUM
ejpam-6366	394	9	.	.	PUNCT
ejpam-6366	395	1	[	[	X
ejpam-6366	395	2	25	25	NUM
ejpam-6366	395	3	]	]	X
ejpam-6366	395	4	w	w	PROPN
ejpam-6366	395	5	c	c	PROPN
ejpam-6366	395	6	ma	ma	PROPN
ejpam-6366	395	7	and	and	CCONJ
ejpam-6366	395	8	d	d	PROPN
ejpam-6366	395	9	minda	minda	PROPN
ejpam-6366	395	10	.	.	PUNCT
ejpam-6366	396	1	a	a	DET
ejpam-6366	396	2	unified	unified	ADJ
ejpam-6366	396	3	treatment	treatment	NOUN
ejpam-6366	396	4	of	of	ADP
ejpam-6366	396	5	some	some	DET
ejpam-6366	396	6	special	special	ADJ
ejpam-6366	396	7	classes	class	NOUN
ejpam-6366	396	8	of	of	ADP
ejpam-6366	396	9	univalent	univalent	ADJ
ejpam-6366	396	10	functions	function	NOUN
ejpam-6366	396	11	.	.	PUNCT
ejpam-6366	397	1	in	in	ADP
ejpam-6366	397	2	proceedings	proceeding	NOUN
ejpam-6366	397	3	of	of	ADP
ejpam-6366	397	4	the	the	DET
ejpam-6366	397	5	conference	conference	NOUN
ejpam-6366	397	6	on	on	ADP
ejpam-6366	397	7	complex	complex	ADJ
ejpam-6366	397	8	analysis	analysis	NOUN
ejpam-6366	397	9	,	,	PUNCT
ejpam-6366	397	10	tianjin	tianjin	NOUN
ejpam-6366	397	11	,	,	PUNCT
ejpam-6366	397	12	internat	internat	PROPN
ejpam-6366	397	13	.	.	PUNCT
ejpam-6366	398	1	press	press	PROPN
ejpam-6366	398	2	,	,	PUNCT
ejpam-6366	398	3	cambridge	cambridge	PROPN
ejpam-6366	398	4	,	,	PUNCT
ejpam-6366	398	5	ma	ma	PROPN
ejpam-6366	398	6	.	.	PROPN
ejpam-6366	398	7	,	,	PUNCT
ejpam-6366	398	8	pages	page	NOUN
ejpam-6366	398	9	157–169	157–169	NUM
ejpam-6366	398	10	,	,	PUNCT
ejpam-6366	398	11	1992	1992	NUM
ejpam-6366	398	12	.	.	PUNCT
ejpam-6366	399	1	[	[	X
ejpam-6366	399	2	26	26	NUM
ejpam-6366	399	3	]	]	X
ejpam-6366	399	4	m	m	PROPN
ejpam-6366	399	5	fekete	fekete	NOUN
ejpam-6366	399	6	and	and	CCONJ
ejpam-6366	399	7	g	g	PROPN
ejpam-6366	399	8	szego	szego	NOUN
ejpam-6366	399	9	.	.	PUNCT
ejpam-6366	400	1	eine	eine	PROPN
ejpam-6366	400	2	bemerkung	bemerkung	PROPN
ejpam-6366	401	1	über	über	PROPN
ejpam-6366	401	2	ungerade	ungerade	PROPN
ejpam-6366	401	3	schlichte	schlichte	PROPN
ejpam-6366	401	4	funktionen	funktionen	PROPN
ejpam-6366	401	5	.	.	PUNCT
ejpam-6366	402	1	j.	j.	PROPN
ejpam-6366	402	2	lond	lond	PROPN
ejpam-6366	402	3	.	.	PUNCT
ejpam-6366	403	1	math	math	PROPN
ejpam-6366	403	2	.	.	PUNCT
ejpam-6366	404	1	soc	soc	PROPN
ejpam-6366	404	2	.	.	PUNCT
ejpam-6366	404	3	,	,	PUNCT
ejpam-6366	404	4	8(2):8589	8(2):8589	NUM
ejpam-6366	404	5	,	,	PUNCT
ejpam-6366	404	6	1933	1933	NUM
ejpam-6366	404	7	.	.	PUNCT
ejpam-6366	405	1	[	[	X
ejpam-6366	405	2	27	27	NUM
ejpam-6366	405	3	]	]	X
ejpam-6366	405	4	t	t	PROPN
ejpam-6366	405	5	al	al	PROPN
ejpam-6366	405	6	-	-	PUNCT
ejpam-6366	405	7	hawary	hawary	PROPN
ejpam-6366	405	8	,	,	PUNCT
ejpam-6366	405	9	a	a	DET
ejpam-6366	405	10	amourah	amourah	ADJ
ejpam-6366	405	11	,	,	PUNCT
ejpam-6366	405	12	and	and	CCONJ
ejpam-6366	405	13	b	b	ADP
ejpam-6366	405	14	a	a	DET
ejpam-6366	405	15	frasin	frasin	NOUN
ejpam-6366	405	16	.	.	PUNCT
ejpam-6366	406	1	fekete	fekete	PROPN
ejpam-6366	406	2	szego	szego	PROPN
ejpam-6366	406	3	inequality	inequality	PROPN
ejpam-6366	406	4	for	for	ADP
ejpam-6366	406	5	bi	bi	ADJ
ejpam-6366	406	6	-	-	ADJ
ejpam-6366	406	7	univalent	univalent	ADJ
ejpam-6366	406	8	functions	function	NOUN
ejpam-6366	406	9	by	by	ADP
ejpam-6366	406	10	means	mean	NOUN
ejpam-6366	406	11	of	of	ADP
ejpam-6366	406	12	horadam	horadam	NOUN
ejpam-6366	406	13	polynomials	polynomial	NOUN
ejpam-6366	406	14	.	.	PUNCT
ejpam-6366	407	1	bol	bol	NOUN
ejpam-6366	407	2	.	.	PUNCT
ejpam-6366	408	1	soc	soc	PROPN
ejpam-6366	408	2	.	.	PUNCT
ejpam-6366	409	1	mat	mat	PROPN
ejpam-6366	409	2	.	.	PUNCT
ejpam-6366	409	3	mex	mex	PROPN
ejpam-6366	409	4	.	.	PROPN
ejpam-6366	409	5	,	,	PUNCT
ejpam-6366	409	6	79:27	79:27	NUM
ejpam-6366	409	7	,	,	PUNCT
ejpam-6366	409	8	2021	2021	NUM
ejpam-6366	409	9	.	.	PUNCT
ejpam-6366	410	1	[	[	X
ejpam-6366	410	2	28	28	NUM
ejpam-6366	410	3	]	]	X
ejpam-6366	410	4	t	t	PROPN
ejpam-6366	410	5	al	al	PROPN
ejpam-6366	410	6	-	-	PUNCT
ejpam-6366	410	7	hawary	hawary	PROPN
ejpam-6366	410	8	,	,	PUNCT
ejpam-6366	410	9	m	m	NOUN
ejpam-6366	410	10	illafe	illafe	ADJ
ejpam-6366	410	11	,	,	PUNCT
ejpam-6366	410	12	and	and	CCONJ
ejpam-6366	410	13	f	f	PROPN
ejpam-6366	410	14	yousef	yousef	PROPN
ejpam-6366	410	15	.	.	PUNCT
ejpam-6366	411	1	certain	certain	ADJ
ejpam-6366	411	2	constraints	constraint	NOUN
ejpam-6366	411	3	for	for	ADP
ejpam-6366	411	4	functions	function	NOUN
ejpam-6366	411	5	provided	provide	VERB
ejpam-6366	411	6	by	by	ADP
ejpam-6366	411	7	touchard	touchard	NOUN
ejpam-6366	411	8	polynomials	polynomial	NOUN
ejpam-6366	411	9	.	.	PUNCT
ejpam-6366	412	1	internat	internat	PROPN
ejpam-6366	412	2	.	.	PUNCT
ejpam-6366	413	1	j.	j.	PROPN
ejpam-6366	413	2	math	math	PROPN
ejpam-6366	413	3	.	.	PUNCT
ejpam-6366	414	1	math	math	NOUN
ejpam-6366	414	2	.	.	PUNCT
ejpam-6366	415	1	sci	sci	PROPN
ejpam-6366	415	2	.	.	PROPN
ejpam-6366	415	3	,	,	PUNCT
ejpam-6366	415	4	2025(1):2581058	2025(1):2581058	NUM
ejpam-6366	415	5	,	,	PUNCT
ejpam-6366	415	6	2025	2025	NUM
ejpam-6366	415	7	.	.	PUNCT
ejpam-6366	416	1	[	[	X
ejpam-6366	416	2	29	29	NUM
ejpam-6366	416	3	]	]	PUNCT
ejpam-6366	416	4	a	a	DET
ejpam-6366	416	5	amourah	amourah	PROPN
ejpam-6366	416	6	,	,	PUNCT
ejpam-6366	416	7	b	b	PROPN
ejpam-6366	416	8	frasin	frasin	PROPN
ejpam-6366	416	9	,	,	PUNCT
ejpam-6366	416	10	j	j	PROPN
ejpam-6366	416	11	salah	salah	PROPN
ejpam-6366	416	12	,	,	PUNCT
ejpam-6366	416	13	and	and	CCONJ
ejpam-6366	416	14	f	f	PROPN
ejpam-6366	416	15	yousef	yousef	PROPN
ejpam-6366	416	16	.	.	PUNCT
ejpam-6366	417	1	subfamilies	subfamily	NOUN
ejpam-6366	417	2	of	of	ADP
ejpam-6366	417	3	bi	bi	ADJ
ejpam-6366	417	4	-	-	ADJ
ejpam-6366	417	5	univalent	univalent	ADJ
ejpam-6366	417	6	functions	function	NOUN
ejpam-6366	417	7	associated	associate	VERB
ejpam-6366	417	8	with	with	ADP
ejpam-6366	417	9	the	the	DET
ejpam-6366	417	10	imaginary	imaginary	ADJ
ejpam-6366	417	11	error	error	NOUN
ejpam-6366	417	12	function	function	NOUN
ejpam-6366	417	13	and	and	CCONJ
ejpam-6366	417	14	subordinate	subordinate	VERB
ejpam-6366	417	15	to	to	ADP
ejpam-6366	417	16	jacobi	jacobi	PROPN
ejpam-6366	417	17	polynomials	polynomials	PROPN
ejpam-6366	417	18	.	.	PUNCT
ejpam-6366	418	1	symmetry	symmetry	PROPN
ejpam-6366	418	2	,	,	PUNCT
ejpam-6366	418	3	17(2):157	17(2):157	NUM
ejpam-6366	418	4	,	,	PUNCT
ejpam-6366	418	5	2025	2025	NUM
ejpam-6366	418	6	.	.	PUNCT
ejpam-6366	419	1	[	[	X
ejpam-6366	419	2	30	30	NUM
ejpam-6366	419	3	]	]	X
ejpam-6366	419	4	j	j	PROPN
ejpam-6366	419	5	dziok	dziok	NOUN
ejpam-6366	419	6	.	.	PUNCT
ejpam-6366	420	1	a	a	DET
ejpam-6366	420	2	general	general	ADJ
ejpam-6366	420	3	solution	solution	NOUN
ejpam-6366	420	4	of	of	ADP
ejpam-6366	420	5	the	the	DET
ejpam-6366	420	6	fekete	fekete	PROPN
ejpam-6366	420	7	-	-	PUNCT
ejpam-6366	420	8	szegö	szegö	PROPN
ejpam-6366	420	9	problem	problem	NOUN
ejpam-6366	420	10	.	.	PUNCT
ejpam-6366	421	1	bound	bind	VERB
ejpam-6366	421	2	.	.	PUNCT
ejpam-6366	421	3	value	value	PROPN
ejpam-6366	421	4	probl	probl	PROPN
ejpam-6366	421	5	.	.	PUNCT
ejpam-6366	421	6	,	,	PUNCT
ejpam-6366	421	7	13:98	13:98	NUM
ejpam-6366	421	8	,	,	PUNCT
ejpam-6366	421	9	2013	2013	NUM
ejpam-6366	421	10	.	.	PUNCT
ejpam-6366	422	1	[	[	X
ejpam-6366	422	2	31	31	NUM
ejpam-6366	422	3	]	]	X
ejpam-6366	422	4	m	m	VERB
ejpam-6366	422	5	illafe	illafe	ADJ
ejpam-6366	422	6	,	,	PUNCT
ejpam-6366	422	7	m	m	VERB
ejpam-6366	422	8	h	h	NOUN
ejpam-6366	422	9	mohd	mohd	PROPN
ejpam-6366	422	10	,	,	PUNCT
ejpam-6366	422	11	f	f	PROPN
ejpam-6366	422	12	yousef	yousef	PROPN
ejpam-6366	422	13	,	,	PUNCT
ejpam-6366	422	14	and	and	CCONJ
ejpam-6366	422	15	s	s	VERB
ejpam-6366	422	16	supramaniam	supramaniam	NOUN
ejpam-6366	422	17	.	.	PUNCT
ejpam-6366	423	1	a	a	DET
ejpam-6366	423	2	subclass	subclass	NOUN
ejpam-6366	423	3	of	of	ADP
ejpam-6366	423	4	bi	bi	ADJ
ejpam-6366	423	5	-	-	ADJ
ejpam-6366	423	6	univalent	univalent	ADJ
ejpam-6366	423	7	functions	function	NOUN
ejpam-6366	423	8	defined	define	VERB
ejpam-6366	423	9	by	by	ADP
ejpam-6366	423	10	a	a	DET
ejpam-6366	423	11	symmetric	symmetric	ADJ
ejpam-6366	423	12	q	q	ADJ
ejpam-6366	423	13	-	-	ADJ
ejpam-6366	423	14	derivative	derivative	ADJ
ejpam-6366	423	15	operator	operator	NOUN
ejpam-6366	423	16	and	and	CCONJ
ejpam-6366	423	17	gegenbauer	gegenbauer	NOUN
ejpam-6366	423	18	polynomials	polynomial	NOUN
ejpam-6366	423	19	.	.	PUNCT
ejpam-6366	424	1	eur	eur	PROPN
ejpam-6366	424	2	.	.	PUNCT
ejpam-6366	425	1	j.	j.	PROPN
ejpam-6366	425	2	pure	pure	PROPN
ejpam-6366	425	3	appl	appl	PROPN
ejpam-6366	425	4	.	.	PUNCT
ejpam-6366	425	5	math	math	PROPN
ejpam-6366	425	6	.	.	PUNCT
ejpam-6366	425	7	,	,	PUNCT
ejpam-6366	425	8	17(4):2467–2480	17(4):2467–2480	NUM
ejpam-6366	425	9	,	,	PUNCT
ejpam-6366	425	10	2024	2024	NUM
ejpam-6366	425	11	.	.	PUNCT
ejpam-6366	426	1	[	[	X
ejpam-6366	426	2	32	32	NUM
ejpam-6366	426	3	]	]	SYM
ejpam-6366	426	4	s	s	PART
ejpam-6366	426	5	kanas	kanas	PROPN
ejpam-6366	426	6	.	.	PUNCT
ejpam-6366	427	1	an	an	DET
ejpam-6366	427	2	unified	unified	ADJ
ejpam-6366	427	3	approach	approach	NOUN
ejpam-6366	427	4	to	to	ADP
ejpam-6366	427	5	the	the	DET
ejpam-6366	427	6	fekete	fekete	PROPN
ejpam-6366	427	7	-	-	PUNCT
ejpam-6366	427	8	szego	szego	NOUN
ejpam-6366	427	9	problem	problem	NOUN
ejpam-6366	427	10	.	.	PUNCT
ejpam-6366	428	1	appl	appl	PROPN
ejpam-6366	428	2	.	.	PROPN
ejpam-6366	428	3	math	math	PROPN
ejpam-6366	428	4	.	.	PUNCT
ejpam-6366	429	1	comput	comput	NOUN
ejpam-6366	429	2	.	.	PUNCT
ejpam-6366	429	3	,	,	PUNCT
ejpam-6366	429	4	218(17):84538461	218(17):84538461	PROPN
ejpam-6366	429	5	,	,	PUNCT
ejpam-6366	429	6	2012	2012	NUM
ejpam-6366	429	7	.	.	PUNCT