id	sid	tid	token	lemma	pos
ejpam-488	1	1	15_488_aouf.dvi	15_488_aouf.dvi	NUM
ejpam-488	1	2	european	european	ADJ
ejpam-488	1	3	journal	journal	NOUN
ejpam-488	1	4	of	of	ADP
ejpam-488	1	5	pure	pure	ADJ
ejpam-488	1	6	and	and	CCONJ
ejpam-488	1	7	applied	apply	VERB
ejpam-488	1	8	mathematics	mathematic	NOUN
ejpam-488	1	9	vol	vol	NOUN
ejpam-488	1	10	.	.	PUNCT
ejpam-488	2	1	3	3	NUM
ejpam-488	2	2	,	,	PUNCT
ejpam-488	2	3	no	no	INTJ
ejpam-488	2	4	.	.	NOUN
ejpam-488	2	5	2	2	NUM
ejpam-488	2	6	,	,	PUNCT
ejpam-488	2	7	2010	2010	NUM
ejpam-488	2	8	,	,	PUNCT
ejpam-488	2	9	317	317	NUM
ejpam-488	2	10	-	-	SYM
ejpam-488	2	11	330	330	NUM
ejpam-488	2	12	issn	issn	PROPN
ejpam-488	2	13	1307	1307	NUM
ejpam-488	2	14	-	-	SYM
ejpam-488	2	15	5543	5543	NUM
ejpam-488	2	16	–	–	PUNCT
ejpam-488	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-488	2	18	argument	argument	NOUN
ejpam-488	2	19	estimates	estimate	NOUN
ejpam-488	2	20	of	of	ADP
ejpam-488	2	21	certain	certain	ADJ
ejpam-488	2	22	analytic	analytic	ADJ
ejpam-488	2	23	functions	function	NOUN
ejpam-488	2	24	associated	associate	VERB
ejpam-488	2	25	with	with	ADP
ejpam-488	2	26	a	a	DET
ejpam-488	2	27	family	family	NOUN
ejpam-488	2	28	of	of	ADP
ejpam-488	2	29	multiplier	multipli	ADJ
ejpam-488	2	30	transformations	transformation	NOUN
ejpam-488	2	31	m.	m.	NOUN
ejpam-488	2	32	k.	k.	PROPN
ejpam-488	2	33	aouf1∗	aouf1∗	PROPN
ejpam-488	2	34	,	,	PUNCT
ejpam-488	2	35	a.	a.	PROPN
ejpam-488	2	36	shamandy2	shamandy2	PROPN
ejpam-488	2	37	,	,	PUNCT
ejpam-488	2	38	r.	r.	PROPN
ejpam-488	2	39	m.	m.	PROPN
ejpam-488	3	1	el	el	PROPN
ejpam-488	3	2	-	-	PROPN
ejpam-488	3	3	ashwah3	ashwah3	PROPN
ejpam-488	3	4	,	,	PUNCT
ejpam-488	3	5	and	and	CCONJ
ejpam-488	3	6	e.	e.	PROPN
ejpam-488	3	7	e.	e.	PROPN
ejpam-488	3	8	ali4	ali4	PROPN
ejpam-488	3	9	1	1	NUM
ejpam-488	3	10	department	department	NOUN
ejpam-488	3	11	of	of	ADP
ejpam-488	3	12	mathematics	mathematic	NOUN
ejpam-488	3	13	,	,	PUNCT
ejpam-488	3	14	faculty	faculty	NOUN
ejpam-488	3	15	of	of	ADP
ejpam-488	3	16	science	science	NOUN
ejpam-488	3	17	,	,	PUNCT
ejpam-488	3	18	mansoura	mansoura	PROPN
ejpam-488	3	19	university	university	NOUN
ejpam-488	3	20	,	,	PUNCT
ejpam-488	3	21	mansoura	mansoura	PROPN
ejpam-488	3	22	,	,	PUNCT
ejpam-488	3	23	egypt	egypt	PROPN
ejpam-488	3	24	abstract	abstract	PROPN
ejpam-488	3	25	.	.	PUNCT
ejpam-488	4	1	the	the	DET
ejpam-488	4	2	purpose	purpose	NOUN
ejpam-488	4	3	of	of	ADP
ejpam-488	4	4	the	the	DET
ejpam-488	4	5	present	present	ADJ
ejpam-488	4	6	paper	paper	NOUN
ejpam-488	4	7	is	be	AUX
ejpam-488	4	8	to	to	PART
ejpam-488	4	9	derive	derive	VERB
ejpam-488	4	10	some	some	DET
ejpam-488	4	11	inclusion	inclusion	NOUN
ejpam-488	4	12	properties	property	NOUN
ejpam-488	4	13	and	and	CCONJ
ejpam-488	4	14	argument	argument	NOUN
ejpam-488	4	15	estimates	estimate	NOUN
ejpam-488	4	16	of	of	ADP
ejpam-488	4	17	certain	certain	ADJ
ejpam-488	4	18	normalized	normalize	VERB
ejpam-488	4	19	analytic	analytic	ADJ
ejpam-488	4	20	functions	function	NOUN
ejpam-488	4	21	in	in	ADP
ejpam-488	4	22	the	the	DET
ejpam-488	4	23	open	open	ADJ
ejpam-488	4	24	unit	unit	NOUN
ejpam-488	4	25	disk	disk	NOUN
ejpam-488	4	26	,	,	PUNCT
ejpam-488	4	27	which	which	PRON
ejpam-488	4	28	are	be	AUX
ejpam-488	4	29	defined	define	VERB
ejpam-488	4	30	by	by	ADP
ejpam-488	4	31	means	mean	NOUN
ejpam-488	4	32	of	of	ADP
ejpam-488	4	33	a	a	DET
ejpam-488	4	34	class	class	NOUN
ejpam-488	4	35	of	of	ADP
ejpam-488	4	36	multiplier	multipli	ADJ
ejpam-488	4	37	transformations	transformation	NOUN
ejpam-488	4	38	.	.	PUNCT
ejpam-488	5	1	furthermore	furthermore	ADV
ejpam-488	5	2	,	,	PUNCT
ejpam-488	5	3	the	the	DET
ejpam-488	5	4	integral	integral	ADJ
ejpam-488	5	5	preserving	preserving	ADJ
ejpam-488	5	6	properties	property	NOUN
ejpam-488	5	7	in	in	ADP
ejpam-488	5	8	a	a	DET
ejpam-488	5	9	sector	sector	NOUN
ejpam-488	5	10	are	be	AUX
ejpam-488	5	11	investigated	investigate	VERB
ejpam-488	5	12	for	for	ADP
ejpam-488	5	13	these	these	DET
ejpam-488	5	14	multiplier	multipli	ADJ
ejpam-488	5	15	transformations	transformation	NOUN
ejpam-488	5	16	.	.	PUNCT
ejpam-488	6	1	2000	2000	NUM
ejpam-488	6	2	mathematics	mathematic	NOUN
ejpam-488	6	3	subject	subject	NOUN
ejpam-488	6	4	classifications	classification	NOUN
ejpam-488	6	5	:	:	PUNCT
ejpam-488	6	6	30c45	30c45	NUM
ejpam-488	6	7	key	key	ADJ
ejpam-488	6	8	words	word	NOUN
ejpam-488	6	9	and	and	CCONJ
ejpam-488	6	10	phrases	phrase	NOUN
ejpam-488	6	11	:	:	PUNCT
ejpam-488	6	12	analytic	analytic	ADJ
ejpam-488	6	13	functions	function	NOUN
ejpam-488	6	14	,	,	PUNCT
ejpam-488	6	15	multiplier	multipli	ADJ
ejpam-488	6	16	transformation	transformation	NOUN
ejpam-488	6	17	,	,	PUNCT
ejpam-488	6	18	differential	differential	ADJ
ejpam-488	6	19	subordination	subordination	NOUN
ejpam-488	6	20	,	,	PUNCT
ejpam-488	6	21	closeto	closeto	NOUN
ejpam-488	6	22	-	-	PUNCT
ejpam-488	6	23	convex	convex	NOUN
ejpam-488	6	24	functions	function	NOUN
ejpam-488	6	25	,	,	PUNCT
ejpam-488	6	26	argument	argument	NOUN
ejpam-488	6	27	estimates	estimate	NOUN
ejpam-488	6	28	.	.	PUNCT
ejpam-488	7	1	1	1	X
ejpam-488	7	2	.	.	X
ejpam-488	7	3	introduction	introduction	NOUN
ejpam-488	7	4	let	let	VERB
ejpam-488	7	5	a	a	DET
ejpam-488	7	6	denote	denote	NOUN
ejpam-488	7	7	the	the	DET
ejpam-488	7	8	class	class	NOUN
ejpam-488	7	9	of	of	ADP
ejpam-488	7	10	the	the	DET
ejpam-488	7	11	functions	function	NOUN
ejpam-488	7	12	of	of	ADP
ejpam-488	7	13	the	the	DET
ejpam-488	7	14	form	form	NOUN
ejpam-488	7	15	:	:	PUNCT
ejpam-488	7	16	f	f	PROPN
ejpam-488	7	17	(	(	PUNCT
ejpam-488	7	18	z	z	NOUN
ejpam-488	7	19	)	)	PUNCT
ejpam-488	7	20	=	=	SYM
ejpam-488	8	1	z	z	NOUN
ejpam-488	9	1	+	+	NUM
ejpam-488	9	2	∞	∞	NUM
ejpam-488	9	3	∑	∑	PROPN
ejpam-488	9	4	k=2	k=2	PROPN
ejpam-488	9	5	akzk	akzk	PROPN
ejpam-488	9	6	,	,	PUNCT
ejpam-488	9	7	(	(	PUNCT
ejpam-488	9	8	1	1	X
ejpam-488	9	9	)	)	PUNCT
ejpam-488	9	10	which	which	PRON
ejpam-488	9	11	are	be	AUX
ejpam-488	9	12	analytic	analytic	ADJ
ejpam-488	9	13	in	in	ADP
ejpam-488	9	14	the	the	DET
ejpam-488	9	15	open	open	ADJ
ejpam-488	9	16	unit	unit	NOUN
ejpam-488	9	17	disc	disc	VERB
ejpam-488	9	18	u	u	NOUN
ejpam-488	9	19	=	=	PUNCT
ejpam-488	9	20	{	{	PUNCT
ejpam-488	9	21	z	z	NOUN
ejpam-488	9	22	:	:	PUNCT
ejpam-488	9	23	|z|	|z|	NOUN
ejpam-488	9	24	<	<	X
ejpam-488	9	25	1	1	NUM
ejpam-488	9	26	}	}	PUNCT
ejpam-488	9	27	.	.	PUNCT
ejpam-488	10	1	if	if	SCONJ
ejpam-488	10	2	f	f	PROPN
ejpam-488	10	3	(	(	PUNCT
ejpam-488	10	4	z	z	NOUN
ejpam-488	10	5	)	)	PUNCT
ejpam-488	10	6	and	and	CCONJ
ejpam-488	10	7	g(z	g(z	PROPN
ejpam-488	10	8	)	)	PUNCT
ejpam-488	10	9	are	be	AUX
ejpam-488	10	10	analytic	analytic	ADJ
ejpam-488	10	11	in	in	ADP
ejpam-488	10	12	u	u	PROPN
ejpam-488	10	13	,	,	PUNCT
ejpam-488	10	14	we	we	PRON
ejpam-488	10	15	say	say	VERB
ejpam-488	10	16	that	that	SCONJ
ejpam-488	10	17	f	f	PROPN
ejpam-488	10	18	(	(	PUNCT
ejpam-488	10	19	z	z	NOUN
ejpam-488	10	20	)	)	PUNCT
ejpam-488	10	21	is	be	AUX
ejpam-488	10	22	subordinate	subordinate	ADJ
ejpam-488	10	23	to	to	ADP
ejpam-488	10	24	g(z	g(z	PROPN
ejpam-488	10	25	)	)	PUNCT
ejpam-488	10	26	written	write	VERB
ejpam-488	10	27	symbolically	symbolically	ADV
ejpam-488	10	28	as	as	SCONJ
ejpam-488	10	29	follows	follow	VERB
ejpam-488	10	30	:	:	PUNCT
ejpam-488	10	31	f	f	PROPN
ejpam-488	10	32	≺	≺	NOUN
ejpam-488	10	33	g	g	PROPN
ejpam-488	10	34	(	(	PUNCT
ejpam-488	10	35	z	z	NOUN
ejpam-488	10	36	∈	∈	PROPN
ejpam-488	10	37	u	u	NOUN
ejpam-488	10	38	)	)	PUNCT
ejpam-488	10	39	or	or	CCONJ
ejpam-488	10	40	f	f	X
ejpam-488	10	41	(	(	PUNCT
ejpam-488	10	42	z)≺	z)≺	PROPN
ejpam-488	10	43	g(z	g(z	PROPN
ejpam-488	10	44	)	)	PUNCT
ejpam-488	10	45	(	(	PUNCT
ejpam-488	10	46	z	z	NOUN
ejpam-488	10	47	∈	∈	PROPN
ejpam-488	10	48	u	u	NOUN
ejpam-488	10	49	)	)	PUNCT
ejpam-488	10	50	,	,	PUNCT
ejpam-488	10	51	if	if	SCONJ
ejpam-488	10	52	there	there	PRON
ejpam-488	10	53	exists	exist	VERB
ejpam-488	10	54	a	a	DET
ejpam-488	10	55	schwarz	schwarz	NOUN
ejpam-488	10	56	function	function	NOUN
ejpam-488	10	57	w(z	w(z	NOUN
ejpam-488	10	58	)	)	PUNCT
ejpam-488	10	59	,	,	PUNCT
ejpam-488	10	60	which	which	PRON
ejpam-488	10	61	(	(	PUNCT
ejpam-488	10	62	by	by	ADP
ejpam-488	10	63	definition	definition	NOUN
ejpam-488	10	64	)	)	PUNCT
ejpam-488	10	65	is	be	AUX
ejpam-488	10	66	analytic	analytic	ADJ
ejpam-488	10	67	in	in	ADP
ejpam-488	10	68	u	u	NOUN
ejpam-488	10	69	with	with	ADP
ejpam-488	10	70	w(0	w(0	PROPN
ejpam-488	10	71	)	)	PUNCT
ejpam-488	11	1	=	=	SYM
ejpam-488	11	2	0	0	NUM
ejpam-488	12	1	and	and	CCONJ
ejpam-488	12	2	|w(z)|	|w(z)|	VERB
ejpam-488	12	3	<	<	X
ejpam-488	12	4	1	1	NUM
ejpam-488	12	5	(	(	PUNCT
ejpam-488	12	6	z	z	NOUN
ejpam-488	12	7	∈	∈	PROPN
ejpam-488	12	8	u	u	NOUN
ejpam-488	12	9	)	)	PUNCT
ejpam-488	12	10	,	,	PUNCT
ejpam-488	12	11	such	such	ADJ
ejpam-488	12	12	that	that	SCONJ
ejpam-488	12	13	f	f	PROPN
ejpam-488	12	14	(	(	PUNCT
ejpam-488	12	15	z	z	NOUN
ejpam-488	12	16	)	)	PUNCT
ejpam-488	12	17	=	=	PUNCT
ejpam-488	12	18	g(w(z	g(w(z	PROPN
ejpam-488	12	19	)	)	PUNCT
ejpam-488	12	20	)	)	PUNCT
ejpam-488	13	1	(	(	PUNCT
ejpam-488	13	2	z	z	NOUN
ejpam-488	13	3	∈	∈	PROPN
ejpam-488	13	4	u	u	NOUN
ejpam-488	13	5	)	)	PUNCT
ejpam-488	13	6	.	.	PUNCT
ejpam-488	14	1	in	in	ADP
ejpam-488	14	2	particular	particular	ADJ
ejpam-488	14	3	,	,	PUNCT
ejpam-488	14	4	if	if	SCONJ
ejpam-488	14	5	the	the	DET
ejpam-488	14	6	function	function	NOUN
ejpam-488	14	7	g(z	g(z	PROPN
ejpam-488	14	8	)	)	PUNCT
ejpam-488	14	9	is	be	AUX
ejpam-488	14	10	univalent	univalent	ADJ
ejpam-488	14	11	in	in	ADP
ejpam-488	14	12	u	u	PROPN
ejpam-488	14	13	,	,	PUNCT
ejpam-488	14	14	then	then	ADV
ejpam-488	14	15	we	we	PRON
ejpam-488	14	16	have	have	VERB
ejpam-488	14	17	the	the	DET
ejpam-488	14	18	following	follow	VERB
ejpam-488	14	19	equivalent	equivalent	NOUN
ejpam-488	14	20	(	(	PUNCT
ejpam-488	14	21	cf	cf	NOUN
ejpam-488	14	22	.	.	NOUN
ejpam-488	14	23	,	,	PUNCT
ejpam-488	14	24	e.g.	e.g.	ADV
ejpam-488	14	25	,	,	PUNCT
ejpam-488	14	26	[	[	X
ejpam-488	14	27	2	2	NUM
ejpam-488	14	28	]	]	PUNCT
ejpam-488	14	29	;	;	PUNCT
ejpam-488	14	30	see	see	VERB
ejpam-488	14	31	also	also	ADV
ejpam-488	14	32	[	[	X
ejpam-488	14	33	10	10	NUM
ejpam-488	14	34	]	]	PUNCT
ejpam-488	14	35	,	,	PUNCT
ejpam-488	15	1	[	[	X
ejpam-488	15	2	11	11	NUM
ejpam-488	15	3	,	,	PUNCT
ejpam-488	15	4	p.	p.	NOUN
ejpam-488	15	5	4	4	NUM
ejpam-488	15	6	]	]	SYM
ejpam-488	15	7	)	)	PUNCT
ejpam-488	15	8	f	f	PROPN
ejpam-488	15	9	(	(	PUNCT
ejpam-488	15	10	z	z	NOUN
ejpam-488	15	11	)	)	PUNCT
ejpam-488	15	12	≺	≺	NOUN
ejpam-488	15	13	g(z)(z	g(z)(z	X
ejpam-488	15	14	∈	∈	PROPN
ejpam-488	15	15	u)⇔	u)⇔	PROPN
ejpam-488	15	16	f	f	X
ejpam-488	15	17	(	(	PUNCT
ejpam-488	15	18	0	0	NUM
ejpam-488	15	19	)	)	PUNCT
ejpam-488	15	20	=	=	SYM
ejpam-488	15	21	g(0	g(0	PROPN
ejpam-488	15	22	)	)	PUNCT
ejpam-488	15	23	and	and	CCONJ
ejpam-488	15	24	f	f	PROPN
ejpam-488	15	25	(	(	PUNCT
ejpam-488	15	26	u)⊂	u)⊂	CCONJ
ejpam-488	15	27	g(u	g(u	PROPN
ejpam-488	15	28	)	)	PUNCT
ejpam-488	15	29	.	.	PUNCT
ejpam-488	16	1	many	many	ADJ
ejpam-488	16	2	essentially	essentially	ADV
ejpam-488	16	3	equivalent	equivalent	ADJ
ejpam-488	16	4	definitions	definition	NOUN
ejpam-488	16	5	of	of	ADP
ejpam-488	16	6	multiplier	multipli	ADJ
ejpam-488	16	7	transformation	transformation	NOUN
ejpam-488	16	8	have	have	AUX
ejpam-488	16	9	been	be	AUX
ejpam-488	16	10	given	give	VERB
ejpam-488	16	11	in	in	ADP
ejpam-488	16	12	literature	literature	NOUN
ejpam-488	16	13	(	(	PUNCT
ejpam-488	16	14	see	see	VERB
ejpam-488	16	15	[	[	X
ejpam-488	16	16	4	4	NUM
ejpam-488	16	17	]	]	PUNCT
ejpam-488	16	18	,	,	PUNCT
ejpam-488	16	19	[	[	X
ejpam-488	16	20	5	5	NUM
ejpam-488	16	21	]	]	PUNCT
ejpam-488	16	22	,	,	PUNCT
ejpam-488	16	23	and	and	CCONJ
ejpam-488	16	24	[	[	X
ejpam-488	16	25	20	20	NUM
ejpam-488	16	26	]	]	PUNCT
ejpam-488	16	27	)	)	PUNCT
ejpam-488	16	28	.	.	PUNCT
ejpam-488	17	1	in	in	ADP
ejpam-488	17	2	[	[	X
ejpam-488	17	3	3	3	NUM
ejpam-488	17	4	]	]	X
ejpam-488	17	5	catas	cata	NOUN
ejpam-488	17	6	defined	define	VERB
ejpam-488	17	7	the	the	DET
ejpam-488	17	8	operator	operator	NOUN
ejpam-488	17	9	im(λ,ℓ	im(λ,ℓ	NOUN
ejpam-488	17	10	)	)	PUNCT
ejpam-488	17	11	as	as	SCONJ
ejpam-488	17	12	follows	follow	VERB
ejpam-488	17	13	:	:	PUNCT
ejpam-488	17	14	∗corresponding	∗corresponde	VERB
ejpam-488	17	15	author	author	NOUN
ejpam-488	17	16	.	.	PUNCT
ejpam-488	18	1	email	email	NOUN
ejpam-488	18	2	addresses	address	NOUN
ejpam-488	18	3	:	:	PUNCT
ejpam-488	18	4	mkaouf127	mkaouf127	PROPN
ejpam-488	18	5	�	�	PROPN
ejpam-488	18	6	yahoo	yahoo	PROPN
ejpam-488	18	7	.	.	PUNCT
ejpam-488	19	1	om	om	PROPN
ejpam-488	19	2	(	(	PUNCT
ejpam-488	19	3	m.	m.	PROPN
ejpam-488	19	4	aouf	aouf	PROPN
ejpam-488	19	5	)	)	PUNCT
ejpam-488	19	6	,	,	PUNCT
ejpam-488	19	7	shamandy16	shamandy16	NOUN
ejpam-488	19	8	�	�	NOUN
ejpam-488	19	9	hotmail	hotmail	NOUN
ejpam-488	19	10	.	.	PUNCT
ejpam-488	20	1	om	om	PROPN
ejpam-488	20	2	(	(	PUNCT
ejpam-488	20	3	a.	a.	NOUN
ejpam-488	20	4	shamandy),r_elashwah	shamandy),r_elashwah	PROPN
ejpam-488	20	5	�	�	PROPN
ejpam-488	20	6	yahoo	yahoo	PROPN
ejpam-488	20	7	.	.	PUNCT
ejpam-488	21	1	om	om	PROPN
ejpam-488	21	2	(	(	PUNCT
ejpam-488	21	3	r.	r.	PROPN
ejpam-488	21	4	el	el	PROPN
ejpam-488	21	5	-	-	PUNCT
ejpam-488	21	6	ashway	ashway	NOUN
ejpam-488	21	7	)	)	PUNCT
ejpam-488	21	8	,	,	PUNCT
ejpam-488	21	9	ekram_008eg	ekram_008eg	PROPN
ejpam-488	21	10	�	�	PROPN
ejpam-488	21	11	yahoo	yahoo	PROPN
ejpam-488	21	12	.	.	PUNCT
ejpam-488	22	1	om	om	PROPN
ejpam-488	22	2	(	(	PUNCT
ejpam-488	22	3	e.	e.	PROPN
ejpam-488	22	4	ali	ali	PROPN
ejpam-488	22	5	)	)	PUNCT
ejpam-488	22	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-488	23	1	317	317	NUM
ejpam-488	23	2	c	c	X
ejpam-488	23	3	©	©	PROPN
ejpam-488	23	4	2010	2010	NUM
ejpam-488	23	5	ejpam	ejpam	NOUN
ejpam-488	23	6	all	all	DET
ejpam-488	23	7	rights	right	NOUN
ejpam-488	23	8	reserved	reserve	VERB
ejpam-488	23	9	.	.	PUNCT
ejpam-488	24	1	m.	m.	PROPN
ejpam-488	24	2	aouf	aouf	PROPN
ejpam-488	24	3	,	,	PUNCT
ejpam-488	24	4	a.	a.	NOUN
ejpam-488	24	5	shamandy	shamandy	PROPN
ejpam-488	24	6	,	,	PUNCT
ejpam-488	24	7	r.	r.	PROPN
ejpam-488	24	8	el	el	PROPN
ejpam-488	24	9	-	-	PUNCT
ejpam-488	24	10	ashway	ashway	PROPN
ejpam-488	24	11	,	,	PUNCT
ejpam-488	24	12	e.	e.	PROPN
ejpam-488	24	13	ali	ali	PROPN
ejpam-488	24	14	/	/	SYM
ejpam-488	24	15	eur	eur	PROPN
ejpam-488	24	16	.	.	PUNCT
ejpam-488	25	1	j.	j.	PROPN
ejpam-488	25	2	pure	pure	PROPN
ejpam-488	25	3	appl	appl	PROPN
ejpam-488	25	4	.	.	PROPN
ejpam-488	25	5	math	math	PROPN
ejpam-488	25	6	,	,	PUNCT
ejpam-488	25	7	3	3	NUM
ejpam-488	25	8	(	(	PUNCT
ejpam-488	25	9	2010	2010	NUM
ejpam-488	25	10	)	)	PUNCT
ejpam-488	25	11	,	,	PUNCT
ejpam-488	25	12	317	317	NUM
ejpam-488	25	13	-	-	SYM
ejpam-488	25	14	330	330	NUM
ejpam-488	25	15	318	318	NUM
ejpam-488	25	16	definition	definition	NOUN
ejpam-488	25	17	1	1	NUM
ejpam-488	25	18	.	.	PUNCT
ejpam-488	26	1	[	[	X
ejpam-488	26	2	3	3	X
ejpam-488	26	3	]	]	PUNCT
ejpam-488	26	4	let	let	VERB
ejpam-488	26	5	the	the	DET
ejpam-488	26	6	function	function	NOUN
ejpam-488	26	7	f	f	PROPN
ejpam-488	26	8	(	(	PUNCT
ejpam-488	26	9	z	z	NOUN
ejpam-488	26	10	)	)	PUNCT
ejpam-488	26	11	∈	∈	PROPN
ejpam-488	26	12	a.	a.	NOUN
ejpam-488	26	13	for	for	ADP
ejpam-488	26	14	m	m	PROPN
ejpam-488	26	15	∈	∈	PROPN
ejpam-488	26	16	n0	n0	X
ejpam-488	26	17	=	=	SYM
ejpam-488	26	18	n	n	PRON
ejpam-488	26	19	∪	∪	X
ejpam-488	26	20	{	{	PUNCT
ejpam-488	26	21	0	0	NUM
ejpam-488	26	22	}	}	PUNCT
ejpam-488	26	23	,	,	PUNCT
ejpam-488	26	24	where	where	SCONJ
ejpam-488	26	25	n	n	ADV
ejpam-488	26	26	=	=	SYM
ejpam-488	26	27	{	{	PUNCT
ejpam-488	26	28	1,2	1,2	NUM
ejpam-488	26	29	,	,	PUNCT
ejpam-488	26	30	.	.	PUNCT
ejpam-488	26	31	.	.	PUNCT
ejpam-488	26	32	.	.	PUNCT
ejpam-488	27	1	}	}	PUNCT
ejpam-488	27	2	,	,	PUNCT
ejpam-488	27	3	λ≥	λ≥	ADP
ejpam-488	27	4	0	0	NUM
ejpam-488	27	5	,	,	PUNCT
ejpam-488	27	6	ℓ≥	ℓ≥	PROPN
ejpam-488	27	7	0	0	NUM
ejpam-488	27	8	.	.	PUNCT
ejpam-488	28	1	the	the	DET
ejpam-488	28	2	extended	extend	VERB
ejpam-488	28	3	multiplier	multipli	ADJ
ejpam-488	28	4	transformation	transformation	NOUN
ejpam-488	28	5	im(λ,ℓ	im(λ,ℓ	PROPN
ejpam-488	28	6	)	)	PUNCT
ejpam-488	28	7	on	on	ADP
ejpam-488	28	8	a	a	PRON
ejpam-488	28	9	is	be	AUX
ejpam-488	28	10	defined	define	VERB
ejpam-488	28	11	by	by	ADP
ejpam-488	28	12	the	the	DET
ejpam-488	28	13	following	follow	VERB
ejpam-488	28	14	infinite	infinite	ADJ
ejpam-488	28	15	series	series	NOUN
ejpam-488	28	16	:	:	PUNCT
ejpam-488	28	17	im(λ,ℓ	im(λ,ℓ	NOUN
ejpam-488	29	1	)	)	PUNCT
ejpam-488	29	2	f	f	NOUN
ejpam-488	29	3	(	(	PUNCT
ejpam-488	29	4	z	z	NOUN
ejpam-488	29	5	)	)	PUNCT
ejpam-488	29	6	=	=	SYM
ejpam-488	30	1	z	z	NOUN
ejpam-488	31	1	+	+	NUM
ejpam-488	31	2	∞	∞	NUM
ejpam-488	31	3	∑	∑	SYM
ejpam-488	31	4	k=2	k=2	PROPN
ejpam-488	31	5	�	�	PROPN
ejpam-488	31	6	ℓ+	ℓ+	PUNCT
ejpam-488	31	7	1+λ(k−	1+λ(k−	NUM
ejpam-488	31	8	1	1	NUM
ejpam-488	31	9	)	)	PUNCT
ejpam-488	31	10	ℓ+	ℓ+	PUNCT
ejpam-488	31	11	1	1	NUM
ejpam-488	31	12	�	�	PROPN
ejpam-488	31	13	m	m	VERB
ejpam-488	31	14	akzk	akzk	NOUN
ejpam-488	31	15	(	(	PUNCT
ejpam-488	31	16	2	2	NUM
ejpam-488	31	17	)	)	PUNCT
ejpam-488	31	18	(	(	PUNCT
ejpam-488	31	19	f	f	PROPN
ejpam-488	31	20	∈	∈	PROPN
ejpam-488	31	21	a;λ≥	a;λ≥	NOUN
ejpam-488	31	22	0;ℓ≥	0;ℓ≥	PROPN
ejpam-488	31	23	0	0	NUM
ejpam-488	31	24	;	;	PUNCT
ejpam-488	31	25	m	m	PROPN
ejpam-488	31	26	∈	∈	PROPN
ejpam-488	31	27	n0	n0	NUM
ejpam-488	31	28	;	;	PUNCT
ejpam-488	31	29	z	z	PROPN
ejpam-488	31	30	∈	∈	PROPN
ejpam-488	31	31	u	u	NOUN
ejpam-488	31	32	)	)	PUNCT
ejpam-488	31	33	.	.	PUNCT
ejpam-488	32	1	we	we	PRON
ejpam-488	32	2	can	can	AUX
ejpam-488	32	3	write	write	VERB
ejpam-488	32	4	(	(	PUNCT
ejpam-488	32	5	2	2	NUM
ejpam-488	32	6	)	)	PUNCT
ejpam-488	32	7	as	as	SCONJ
ejpam-488	32	8	follows	follow	VERB
ejpam-488	32	9	:	:	PUNCT
ejpam-488	32	10	im(λ,ℓ	im(λ,ℓ	X
ejpam-488	32	11	)	)	PUNCT
ejpam-488	32	12	f	f	NOUN
ejpam-488	32	13	(	(	PUNCT
ejpam-488	32	14	z	z	NOUN
ejpam-488	32	15	)	)	PUNCT
ejpam-488	32	16	=	=	SYM
ejpam-488	32	17	(	(	PUNCT
ejpam-488	32	18	φ	φ	PROPN
ejpam-488	32	19	,	,	PUNCT
ejpam-488	32	20	m	m	PROPN
ejpam-488	32	21	λ,ℓ	λ,ℓ	NOUN
ejpam-488	32	22	∗	∗	X
ejpam-488	32	23	f	f	PROPN
ejpam-488	32	24	)	)	PUNCT
ejpam-488	32	25	(	(	PUNCT
ejpam-488	32	26	z	z	NOUN
ejpam-488	32	27	)	)	PUNCT
ejpam-488	32	28	,	,	PUNCT
ejpam-488	32	29	(	(	PUNCT
ejpam-488	32	30	3	3	X
ejpam-488	32	31	)	)	PUNCT
ejpam-488	32	32	where	where	SCONJ
ejpam-488	32	33	φm	φm	X
ejpam-488	32	34	λ,ℓ(z	λ,ℓ(z	PROPN
ejpam-488	32	35	)	)	PUNCT
ejpam-488	33	1	=	=	SYM
ejpam-488	33	2	z	z	NOUN
ejpam-488	34	1	+	+	NUM
ejpam-488	34	2	∞	∞	NUM
ejpam-488	34	3	∑	∑	SYM
ejpam-488	34	4	k=2	k=2	PROPN
ejpam-488	34	5	�	�	PROPN
ejpam-488	34	6	ℓ+	ℓ+	PUNCT
ejpam-488	34	7	1+λ(k−	1+λ(k−	NUM
ejpam-488	34	8	1	1	NUM
ejpam-488	34	9	)	)	PUNCT
ejpam-488	34	10	ℓ+	ℓ+	PUNCT
ejpam-488	34	11	1	1	NUM
ejpam-488	34	12	�	�	PROPN
ejpam-488	34	13	m	m	NOUN
ejpam-488	34	14	zk	zk	PROPN
ejpam-488	34	15	.	.	PUNCT
ejpam-488	35	1	it	it	PRON
ejpam-488	35	2	is	be	AUX
ejpam-488	35	3	easily	easily	ADV
ejpam-488	35	4	verified	verify	VERB
ejpam-488	35	5	from	from	ADP
ejpam-488	35	6	(	(	PUNCT
ejpam-488	35	7	2	2	NUM
ejpam-488	35	8	)	)	PUNCT
ejpam-488	35	9	,	,	PUNCT
ejpam-488	35	10	that	that	SCONJ
ejpam-488	35	11	λz(im(λ,ℓ	λz(im(λ,ℓ	X
ejpam-488	35	12	)	)	PUNCT
ejpam-488	35	13	f	f	NOUN
ejpam-488	35	14	(	(	PUNCT
ejpam-488	35	15	z	z	NOUN
ejpam-488	35	16	)	)	PUNCT
ejpam-488	35	17	)	)	PUNCT
ejpam-488	36	1	′	′	NUM
ejpam-488	37	1	=	=	PUNCT
ejpam-488	37	2	(	(	PUNCT
ejpam-488	37	3	1	1	NUM
ejpam-488	37	4	+	+	NUM
ejpam-488	37	5	ℓ)im+1(λ,ℓ	ℓ)im+1(λ,ℓ	NOUN
ejpam-488	37	6	)	)	PUNCT
ejpam-488	37	7	f	f	NOUN
ejpam-488	37	8	(	(	PUNCT
ejpam-488	37	9	z)−	z)−	PROPN
ejpam-488	38	1	[	[	PUNCT
ejpam-488	38	2	1−λ+	1−λ+	NUM
ejpam-488	38	3	ℓ]im(λ,ℓ	ℓ]im(λ,ℓ	NOUN
ejpam-488	38	4	)	)	PUNCT
ejpam-488	38	5	f	f	PROPN
ejpam-488	38	6	(	(	PUNCT
ejpam-488	38	7	z	z	NOUN
ejpam-488	38	8	)	)	PUNCT
ejpam-488	38	9	(	(	PUNCT
ejpam-488	38	10	λ	λ	X
ejpam-488	38	11	>	>	X
ejpam-488	38	12	0	0	NUM
ejpam-488	38	13	)	)	PUNCT
ejpam-488	38	14	.	.	PUNCT
ejpam-488	39	1	(	(	PUNCT
ejpam-488	39	2	4	4	X
ejpam-488	39	3	)	)	PUNCT
ejpam-488	39	4	we	we	PRON
ejpam-488	39	5	note	note	VERB
ejpam-488	39	6	that	that	SCONJ
ejpam-488	39	7	:	:	PUNCT
ejpam-488	39	8	i0(λ,ℓ	i0(λ,ℓ	X
ejpam-488	39	9	)	)	PUNCT
ejpam-488	39	10	f	f	NOUN
ejpam-488	39	11	(	(	PUNCT
ejpam-488	39	12	z	z	NOUN
ejpam-488	39	13	)	)	PUNCT
ejpam-488	40	1	=	=	SYM
ejpam-488	40	2	f	f	X
ejpam-488	40	3	(	(	PUNCT
ejpam-488	40	4	z	z	NOUN
ejpam-488	40	5	)	)	PUNCT
ejpam-488	40	6	and	and	CCONJ
ejpam-488	40	7	i1(1,0	i1(1,0	NOUN
ejpam-488	40	8	)	)	PUNCT
ejpam-488	40	9	f	f	PROPN
ejpam-488	40	10	(	(	PUNCT
ejpam-488	40	11	z	z	NOUN
ejpam-488	40	12	)	)	PUNCT
ejpam-488	40	13	=	=	PUNCT
ejpam-488	41	1	z	z	NOUN
ejpam-488	41	2	f	f	NOUN
ejpam-488	42	1	′	′	NUM
ejpam-488	42	2	(	(	PUNCT
ejpam-488	42	3	z	z	NOUN
ejpam-488	42	4	)	)	PUNCT
ejpam-488	42	5	.	.	PUNCT
ejpam-488	43	1	also	also	ADV
ejpam-488	43	2	by	by	ADP
ejpam-488	43	3	specializing	specialize	VERB
ejpam-488	43	4	the	the	DET
ejpam-488	43	5	parameters	parameter	NOUN
ejpam-488	43	6	λ,ℓ	λ,ℓ	NOUN
ejpam-488	43	7	and	and	CCONJ
ejpam-488	43	8	m	m	VERB
ejpam-488	43	9	we	we	PRON
ejpam-488	43	10	obtain	obtain	VERB
ejpam-488	43	11	the	the	DET
ejpam-488	43	12	following	follow	VERB
ejpam-488	43	13	operators	operator	NOUN
ejpam-488	43	14	studied	study	VERB
ejpam-488	43	15	by	by	ADP
ejpam-488	43	16	various	various	ADJ
ejpam-488	43	17	authors	author	NOUN
ejpam-488	43	18	:	:	PUNCT
ejpam-488	43	19	(	(	PUNCT
ejpam-488	43	20	i	i	NOUN
ejpam-488	43	21	)	)	PUNCT
ejpam-488	43	22	im(1,ℓ	im(1,ℓ	PROPN
ejpam-488	43	23	)	)	PUNCT
ejpam-488	43	24	=	=	NOUN
ejpam-488	43	25	im(ℓ	im(ℓ	X
ejpam-488	43	26	)	)	PUNCT
ejpam-488	44	1	f	f	PROPN
ejpam-488	44	2	(	(	PUNCT
ejpam-488	44	3	z	z	NOUN
ejpam-488	44	4	)	)	PUNCT
ejpam-488	44	5	(	(	PUNCT
ejpam-488	44	6	see	see	VERB
ejpam-488	44	7	cho	cho	PROPN
ejpam-488	44	8	and	and	CCONJ
ejpam-488	44	9	srivastava	srivastava	PROPN
ejpam-488	45	1	[	[	X
ejpam-488	45	2	4	4	NUM
ejpam-488	45	3	]	]	PUNCT
ejpam-488	45	4	and	and	CCONJ
ejpam-488	45	5	cho	cho	NOUN
ejpam-488	45	6	and	and	CCONJ
ejpam-488	45	7	kim	kim	PROPN
ejpam-488	46	1	[	[	X
ejpam-488	46	2	5	5	NUM
ejpam-488	46	3	]	]	PUNCT
ejpam-488	46	4	)	)	PUNCT
ejpam-488	46	5	;	;	PUNCT
ejpam-488	46	6	(	(	PUNCT
ejpam-488	46	7	ii	ii	NOUN
ejpam-488	46	8	)	)	PUNCT
ejpam-488	46	9	im(λ	im(λ	NOUN
ejpam-488	46	10	,	,	PUNCT
ejpam-488	46	11	0	0	NUM
ejpam-488	46	12	)	)	PUNCT
ejpam-488	46	13	f	f	NOUN
ejpam-488	46	14	(	(	PUNCT
ejpam-488	46	15	z	z	NOUN
ejpam-488	46	16	)	)	PUNCT
ejpam-488	46	17	=	=	PUNCT
ejpam-488	47	1	dm	dm	NUM
ejpam-488	47	2	λ	λ	X
ejpam-488	47	3	f	f	X
ejpam-488	47	4	(	(	PUNCT
ejpam-488	47	5	z	z	NOUN
ejpam-488	47	6	)	)	PUNCT
ejpam-488	47	7	(	(	PUNCT
ejpam-488	47	8	see	see	VERB
ejpam-488	47	9	al	al	PROPN
ejpam-488	47	10	-	-	PUNCT
ejpam-488	47	11	oboudi	oboudi	NOUN
ejpam-488	47	12	[	[	X
ejpam-488	47	13	1	1	NUM
ejpam-488	47	14	]	]	NUM
ejpam-488	47	15	)	)	PUNCT
ejpam-488	47	16	;	;	PUNCT
ejpam-488	47	17	(	(	PUNCT
ejpam-488	47	18	iii	iii	X
ejpam-488	47	19	)	)	PUNCT
ejpam-488	47	20	im(1,0	im(1,0	PROPN
ejpam-488	47	21	)	)	PUNCT
ejpam-488	48	1	=	=	PUNCT
ejpam-488	48	2	dm	dm	PRON
ejpam-488	48	3	f	f	X
ejpam-488	48	4	(	(	PUNCT
ejpam-488	48	5	z	z	NOUN
ejpam-488	48	6	)	)	PUNCT
ejpam-488	48	7	(	(	PUNCT
ejpam-488	48	8	see	see	VERB
ejpam-488	48	9	salagean	salagean	ADJ
ejpam-488	48	10	[	[	X
ejpam-488	48	11	18	18	NUM
ejpam-488	48	12	]	]	PUNCT
ejpam-488	48	13	)	)	PUNCT
ejpam-488	48	14	;	;	PUNCT
ejpam-488	48	15	(	(	PUNCT
ejpam-488	48	16	iv	iv	X
ejpam-488	48	17	)	)	PUNCT
ejpam-488	48	18	im(1,1	im(1,1	PROPN
ejpam-488	48	19	)	)	PUNCT
ejpam-488	49	1	=	=	PUNCT
ejpam-488	50	1	i	i	PRON
ejpam-488	50	2	m	m	VERB
ejpam-488	50	3	f	f	X
ejpam-488	50	4	(	(	PUNCT
ejpam-488	50	5	z	z	NOUN
ejpam-488	50	6	)	)	PUNCT
ejpam-488	50	7	(	(	PUNCT
ejpam-488	50	8	see	see	VERB
ejpam-488	50	9	uralegaddi	uralegaddi	ADJ
ejpam-488	50	10	and	and	CCONJ
ejpam-488	50	11	somanatha	somanatha	NOUN
ejpam-488	51	1	[	[	X
ejpam-488	51	2	20	20	NUM
ejpam-488	51	3	]	]	PUNCT
ejpam-488	51	4	)	)	PUNCT
ejpam-488	51	5	.	.	PUNCT
ejpam-488	52	1	let	let	VERB
ejpam-488	52	2	the	the	DET
ejpam-488	52	3	functions	function	NOUN
ejpam-488	52	4	g1	g1	VERB
ejpam-488	52	5	,	,	PUNCT
ejpam-488	52	6	...	...	PUNCT
ejpam-488	52	7	,	,	PUNCT
ejpam-488	52	8	gq	gq	NOUN
ejpam-488	52	9	be	be	AUX
ejpam-488	52	10	in	in	ADP
ejpam-488	52	11	the	the	DET
ejpam-488	52	12	class	class	NOUN
ejpam-488	52	13	a.	a.	NOUN
ejpam-488	52	14	then	then	ADV
ejpam-488	52	15	we	we	PRON
ejpam-488	52	16	say	say	VERB
ejpam-488	52	17	that	that	SCONJ
ejpam-488	52	18	the	the	DET
ejpam-488	52	19	functions	function	NOUN
ejpam-488	52	20	g1	g1	VERB
ejpam-488	52	21	,	,	PUNCT
ejpam-488	52	22	...	...	PUNCT
ejpam-488	52	23	,	,	PUNCT
ejpam-488	52	24	gq	gq	PROPN
ejpam-488	52	25	are	be	AUX
ejpam-488	52	26	in	in	ADP
ejpam-488	52	27	the	the	DET
ejpam-488	52	28	class	class	NOUN
ejpam-488	52	29	ωm	ωm	NOUN
ejpam-488	52	30	,	,	PUNCT
ejpam-488	52	31	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	52	32	;	;	PUNCT
ejpam-488	52	33	a	a	DET
ejpam-488	52	34	,	,	PUNCT
ejpam-488	52	35	b	b	NOUN
ejpam-488	52	36	)	)	PUNCT
ejpam-488	52	37	if	if	SCONJ
ejpam-488	52	38	they	they	PRON
ejpam-488	52	39	satisfy	satisfy	VERB
ejpam-488	52	40	the	the	DET
ejpam-488	52	41	subordination	subordination	NOUN
ejpam-488	52	42	condition	condition	NOUN
ejpam-488	52	43	:	:	PUNCT
ejpam-488	52	44	z(im(λ,ℓ)gi(z	z(im(λ,ℓ)gi(z	NOUN
ejpam-488	52	45	)	)	PUNCT
ejpam-488	52	46	)	)	PUNCT
ejpam-488	53	1	′	′	NUM
ejpam-488	53	2	�	�	PROPN
ejpam-488	53	3	1	1	NUM
ejpam-488	53	4	q	q	PROPN
ejpam-488	53	5	�	�	PROPN
ejpam-488	53	6	q	q	PROPN
ejpam-488	53	7	∑	∑	PROPN
ejpam-488	53	8	j=1	j=1	ADJ
ejpam-488	53	9	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	53	10	j(z	j(z	PROPN
ejpam-488	53	11	)	)	PUNCT
ejpam-488	53	12	≺	≺	NOUN
ejpam-488	53	13	1	1	NUM
ejpam-488	53	14	+	+	NUM
ejpam-488	53	15	az	az	PROPN
ejpam-488	53	16	1	1	NUM
ejpam-488	53	17	+	+	CCONJ
ejpam-488	53	18	bz	bz	PROPN
ejpam-488	53	19	(	(	PUNCT
ejpam-488	53	20	z	z	NOUN
ejpam-488	53	21	∈	∈	PROPN
ejpam-488	53	22	u	u	NOUN
ejpam-488	53	23	;	;	PUNCT
ejpam-488	53	24	i	i	NOUN
ejpam-488	53	25	=	=	NOUN
ejpam-488	53	26	1	1	NUM
ejpam-488	53	27	,	,	PUNCT
ejpam-488	53	28	...	...	PUNCT
ejpam-488	53	29	,	,	PUNCT
ejpam-488	53	30	q;−1≤	q;−1≤	PRON
ejpam-488	53	31	b	b	X
ejpam-488	53	32	<	<	X
ejpam-488	53	33	a≤	a≤	ADP
ejpam-488	53	34	1	1	NUM
ejpam-488	53	35	)	)	PUNCT
ejpam-488	53	36	,	,	PUNCT
ejpam-488	53	37	(	(	PUNCT
ejpam-488	53	38	5	5	X
ejpam-488	53	39	)	)	PUNCT
ejpam-488	53	40	where	where	SCONJ
ejpam-488	53	41	n	n	AUX
ejpam-488	53	42	∑	∑	ADP
ejpam-488	53	43	j=1	j=1	NOUN
ejpam-488	53	44	1	1	NUM
ejpam-488	53	45	z	z	NOUN
ejpam-488	53	46	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	53	47	j(z	j(z	PROPN
ejpam-488	53	48	)	)	PUNCT
ejpam-488	53	49	6=	6=	ADP
ejpam-488	53	50	0	0	NUM
ejpam-488	53	51	(	(	PUNCT
ejpam-488	53	52	z	z	NOUN
ejpam-488	53	53	∈	∈	PROPN
ejpam-488	53	54	u	u	NOUN
ejpam-488	53	55	)	)	PUNCT
ejpam-488	53	56	.	.	PUNCT
ejpam-488	54	1	for	for	ADP
ejpam-488	54	2	λ=	λ=	NOUN
ejpam-488	54	3	1	1	NUM
ejpam-488	54	4	,	,	PUNCT
ejpam-488	54	5	m	m	VERB
ejpam-488	54	6	=	=	ADJ
ejpam-488	54	7	ℓ=	ℓ=	NOUN
ejpam-488	54	8	0	0	PUNCT
ejpam-488	54	9	and	and	CCONJ
ejpam-488	54	10	g	g	PROPN
ejpam-488	54	11	j(z	j(z	PROPN
ejpam-488	54	12	)	)	PUNCT
ejpam-488	55	1	=	=	PUNCT
ejpam-488	55	2	w−	w−	PROPN
ejpam-488	55	3	j	j	PROPN
ejpam-488	55	4	f	f	PROPN
ejpam-488	55	5	(	(	PUNCT
ejpam-488	55	6	w	w	PROPN
ejpam-488	55	7	jz	jz	PROPN
ejpam-488	55	8	)	)	PUNCT
ejpam-488	55	9	(	(	PUNCT
ejpam-488	55	10	f	f	PROPN
ejpam-488	55	11	∈	∈	PROPN
ejpam-488	55	12	a	a	PRON
ejpam-488	55	13	;	;	PUNCT
ejpam-488	55	14	j	j	PROPN
ejpam-488	55	15	=	=	SYM
ejpam-488	55	16	1	1	NUM
ejpam-488	55	17	,	,	PUNCT
ejpam-488	55	18	...	...	PUNCT
ejpam-488	55	19	,	,	PUNCT
ejpam-488	55	20	q	q	NOUN
ejpam-488	55	21	;	;	PUNCT
ejpam-488	55	22	w	w	NOUN
ejpam-488	55	23	=	=	SYM
ejpam-488	55	24	e2πi	e2πi	X
ejpam-488	55	25	/	/	SYM
ejpam-488	55	26	n	n	CCONJ
ejpam-488	55	27	)	)	PUNCT
ejpam-488	55	28	,	,	PUNCT
ejpam-488	55	29	m.	m.	NOUN
ejpam-488	55	30	aouf	aouf	PROPN
ejpam-488	55	31	,	,	PUNCT
ejpam-488	55	32	a.	a.	NOUN
ejpam-488	55	33	shamandy	shamandy	PROPN
ejpam-488	55	34	,	,	PUNCT
ejpam-488	55	35	r.	r.	PROPN
ejpam-488	55	36	el	el	PROPN
ejpam-488	55	37	-	-	PUNCT
ejpam-488	55	38	ashway	ashway	PROPN
ejpam-488	55	39	,	,	PUNCT
ejpam-488	55	40	e.	e.	PROPN
ejpam-488	55	41	ali	ali	PROPN
ejpam-488	55	42	/	/	SYM
ejpam-488	55	43	eur	eur	PROPN
ejpam-488	55	44	.	.	PUNCT
ejpam-488	56	1	j.	j.	PROPN
ejpam-488	56	2	pure	pure	PROPN
ejpam-488	56	3	appl	appl	PROPN
ejpam-488	56	4	.	.	PROPN
ejpam-488	56	5	math	math	PROPN
ejpam-488	56	6	,	,	PUNCT
ejpam-488	56	7	3	3	NUM
ejpam-488	56	8	(	(	PUNCT
ejpam-488	56	9	2010	2010	NUM
ejpam-488	56	10	)	)	PUNCT
ejpam-488	56	11	,	,	PUNCT
ejpam-488	56	12	317	317	NUM
ejpam-488	56	13	-	-	SYM
ejpam-488	56	14	330	330	NUM
ejpam-488	56	15	319	319	NUM
ejpam-488	56	16	ωm	ωm	NOUN
ejpam-488	56	17	,	,	PUNCT
ejpam-488	56	18	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	56	19	;	;	PUNCT
ejpam-488	56	20	a	a	DET
ejpam-488	56	21	,	,	PUNCT
ejpam-488	56	22	b	b	NOUN
ejpam-488	56	23	)	)	PUNCT
ejpam-488	56	24	reduces	reduce	VERB
ejpam-488	56	25	to	to	ADP
ejpam-488	56	26	the	the	DET
ejpam-488	56	27	class	class	NOUN
ejpam-488	56	28	of	of	ADP
ejpam-488	56	29	starlike	starlike	NOUN
ejpam-488	56	30	functions	function	NOUN
ejpam-488	56	31	in	in	ADP
ejpam-488	56	32	u	u	NOUN
ejpam-488	56	33	with	with	ADP
ejpam-488	56	34	respect	respect	NOUN
ejpam-488	56	35	to	to	ADP
ejpam-488	56	36	q	q	PROPN
ejpam-488	56	37	symmetric	symmetric	ADJ
ejpam-488	56	38	points	point	NOUN
ejpam-488	57	1	[	[	X
ejpam-488	57	2	12	12	NUM
ejpam-488	57	3	]	]	PUNCT
ejpam-488	57	4	(	(	PUNCT
ejpam-488	57	5	see	see	VERB
ejpam-488	57	6	also	also	ADV
ejpam-488	57	7	[	[	X
ejpam-488	57	8	17	17	NUM
ejpam-488	57	9	]	]	PUNCT
ejpam-488	57	10	)	)	PUNCT
ejpam-488	57	11	.	.	PUNCT
ejpam-488	58	1	if	if	SCONJ
ejpam-488	58	2	we	we	PRON
ejpam-488	58	3	take	take	VERB
ejpam-488	58	4	λ	λ	NOUN
ejpam-488	58	5	=	=	SYM
ejpam-488	58	6	1	1	NUM
ejpam-488	58	7	,	,	PUNCT
ejpam-488	58	8	ℓ	ℓ	PROPN
ejpam-488	58	9	=	=	SYM
ejpam-488	58	10	0	0	NUM
ejpam-488	58	11	,	,	PUNCT
ejpam-488	58	12	m	m	VERB
ejpam-488	58	13	=	=	NOUN
ejpam-488	58	14	0	0	NUM
ejpam-488	58	15	,	,	PUNCT
ejpam-488	58	16	q	q	NOUN
ejpam-488	58	17	=	=	SYM
ejpam-488	58	18	2	2	NUM
ejpam-488	58	19	,	,	PUNCT
ejpam-488	58	20	a	a	DET
ejpam-488	58	21	=	=	SYM
ejpam-488	58	22	1	1	NUM
ejpam-488	58	23	and	and	CCONJ
ejpam-488	58	24	b	b	NOUN
ejpam-488	58	25	=	=	SYM
ejpam-488	58	26	−1	−1	NOUN
ejpam-488	58	27	in	in	ADV
ejpam-488	58	28	(	(	PUNCT
ejpam-488	58	29	5	5	NUM
ejpam-488	58	30	)	)	PUNCT
ejpam-488	58	31	,	,	PUNCT
ejpam-488	58	32	then	then	ADV
ejpam-488	58	33	we	we	PRON
ejpam-488	58	34	obtain	obtain	VERB
ejpam-488	58	35	the	the	DET
ejpam-488	58	36	class	class	NOUN
ejpam-488	58	37	of	of	ADP
ejpam-488	58	38	mutually	mutually	ADV
ejpam-488	58	39	adjoint	adjoint	VERB
ejpam-488	58	40	close	close	ADJ
ejpam-488	58	41	-	-	PUNCT
ejpam-488	58	42	to	to	ADP
ejpam-488	58	43	-	-	PUNCT
ejpam-488	58	44	convex	convex	NOUN
ejpam-488	58	45	functions	function	NOUN
ejpam-488	58	46	in	in	ADP
ejpam-488	58	47	u	u	NOUN
ejpam-488	58	48	considered	consider	VERB
ejpam-488	58	49	by	by	ADP
ejpam-488	58	50	lewandowski	lewandowski	PROPN
ejpam-488	58	51	and	and	CCONJ
ejpam-488	58	52	stankiewicz	stankiewicz	VERB
ejpam-488	59	1	[	[	X
ejpam-488	59	2	9	9	NUM
ejpam-488	59	3	]	]	PUNCT
ejpam-488	59	4	.	.	PUNCT
ejpam-488	60	1	let	let	VERB
ejpam-488	60	2	cm	cm	NOUN
ejpam-488	60	3	,	,	PUNCT
ejpam-488	60	4	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	60	5	;	;	PUNCT
ejpam-488	60	6	a	a	DET
ejpam-488	60	7	,	,	PUNCT
ejpam-488	60	8	b	b	X
ejpam-488	60	9	)	)	PUNCT
ejpam-488	60	10	be	be	AUX
ejpam-488	60	11	the	the	DET
ejpam-488	60	12	class	class	NOUN
ejpam-488	60	13	of	of	ADP
ejpam-488	60	14	functions	function	NOUN
ejpam-488	60	15	of	of	ADP
ejpam-488	60	16	functions	function	NOUN
ejpam-488	60	17	f	f	PROPN
ejpam-488	60	18	∈	∈	PROPN
ejpam-488	60	19	a	a	DET
ejpam-488	60	20	satisfying	satisfying	NOUN
ejpam-488	60	21	the	the	DET
ejpam-488	60	22	argument	argument	NOUN
ejpam-488	60	23	inequality	inequality	NOUN
ejpam-488	60	24	�	�	PROPN
ejpam-488	60	25	�	�	PROPN
ejpam-488	60	26	�	�	PROPN
ejpam-488	60	27	�	�	PROPN
ejpam-488	60	28	�	�	PROPN
ejpam-488	60	29	�	�	PROPN
ejpam-488	60	30	�	�	PROPN
ejpam-488	60	31	�	�	PROPN
ejpam-488	60	32	�	�	PROPN
ejpam-488	60	33	arg	arg	NOUN
ejpam-488	60	34			PROPN
ejpam-488	60	35			NOUN
ejpam-488	60	36			NOUN
ejpam-488	60	37			NOUN
ejpam-488	60	38			NOUN
ejpam-488	60	39			NOUN
ejpam-488	60	40	z(im(λ,ℓ	z(im(λ,ℓ	NUM
ejpam-488	60	41	)	)	PUNCT
ejpam-488	60	42	f	f	PROPN
ejpam-488	60	43	(	(	PUNCT
ejpam-488	60	44	z	z	NOUN
ejpam-488	60	45	)	)	PUNCT
ejpam-488	60	46	)	)	PUNCT
ejpam-488	61	1	′	′	NUM
ejpam-488	61	2	�	�	PROPN
ejpam-488	61	3	1	1	NUM
ejpam-488	61	4	q	q	PROPN
ejpam-488	61	5	�	�	PROPN
ejpam-488	61	6	q	q	PROPN
ejpam-488	61	7	∑	∑	PROPN
ejpam-488	61	8	j=1	j=1	ADJ
ejpam-488	61	9	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	61	10	j(z	j(z	PROPN
ejpam-488	61	11	)	)	PUNCT
ejpam-488	61	12			PROPN
ejpam-488	61	13			NOUN
ejpam-488	61	14			VERB
ejpam-488	61	15			NOUN
ejpam-488	61	16			NOUN
ejpam-488	61	17			PUNCT
ejpam-488	61	18	�	�	PROPN
ejpam-488	61	19	�	�	PROPN
ejpam-488	61	20	�	�	PROPN
ejpam-488	61	21	�	�	PROPN
ejpam-488	61	22	�	�	PROPN
ejpam-488	61	23	�	�	PROPN
ejpam-488	61	24	�	�	PROPN
ejpam-488	61	25	�	�	PROPN
ejpam-488	61	26	�	�	PROPN
ejpam-488	61	27	<	<	X
ejpam-488	61	28	π	π	PROPN
ejpam-488	61	29	2	2	NUM
ejpam-488	61	30	α	α	NOUN
ejpam-488	61	31	(	(	PUNCT
ejpam-488	61	32	6	6	NUM
ejpam-488	61	33	)	)	PUNCT
ejpam-488	61	34	(	(	PUNCT
ejpam-488	61	35	z	z	NOUN
ejpam-488	61	36	∈	∈	PROPN
ejpam-488	61	37	u	u	NOUN
ejpam-488	61	38	,	,	PUNCT
ejpam-488	61	39	m	m	PROPN
ejpam-488	61	40	∈	∈	PROPN
ejpam-488	61	41	n0	n0	PROPN
ejpam-488	61	42	,	,	PUNCT
ejpam-488	61	43	0	0	PUNCT
ejpam-488	61	44	<	<	X
ejpam-488	61	45	α≤	α≤	PROPN
ejpam-488	61	46	1	1	NUM
ejpam-488	61	47	;	;	PUNCT
ejpam-488	61	48	g	g	PROPN
ejpam-488	61	49	j	j	PROPN
ejpam-488	61	50	∈	∈	PROPN
ejpam-488	61	51	ωm	ωm	VERB
ejpam-488	61	52	,	,	PUNCT
ejpam-488	61	53	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	61	54	;	;	PUNCT
ejpam-488	61	55	a	a	DET
ejpam-488	61	56	,	,	PUNCT
ejpam-488	61	57	b	b	NOUN
ejpam-488	61	58	)	)	PUNCT
ejpam-488	61	59	;	;	PUNCT
ejpam-488	62	1	j	j	PROPN
ejpam-488	62	2	=	=	SYM
ejpam-488	62	3	1	1	NUM
ejpam-488	62	4	,	,	PUNCT
ejpam-488	62	5	...	...	PUNCT
ejpam-488	62	6	,	,	PUNCT
ejpam-488	62	7	q	q	NOUN
ejpam-488	62	8	)	)	PUNCT
ejpam-488	62	9	.	.	PUNCT
ejpam-488	63	1	if	if	SCONJ
ejpam-488	63	2	we	we	PRON
ejpam-488	63	3	take	take	VERB
ejpam-488	63	4	m	m	NOUN
ejpam-488	63	5	=	=	SYM
ejpam-488	63	6	ℓ	ℓ	PROPN
ejpam-488	63	7	=	=	SYM
ejpam-488	63	8	0	0	PROPN
ejpam-488	63	9	,	,	PUNCT
ejpam-488	63	10	λ	λ	X
ejpam-488	63	11	=	=	NOUN
ejpam-488	63	12	1	1	NUM
ejpam-488	63	13	,	,	PUNCT
ejpam-488	63	14	q	q	NOUN
ejpam-488	63	15	=	=	SYM
ejpam-488	63	16	1	1	NUM
ejpam-488	63	17	,	,	PUNCT
ejpam-488	63	18	α	α	NOUN
ejpam-488	63	19	=	=	SYM
ejpam-488	63	20	1	1	NUM
ejpam-488	63	21	,	,	PUNCT
ejpam-488	63	22	a	a	DET
ejpam-488	63	23	=	=	SYM
ejpam-488	63	24	1	1	NUM
ejpam-488	63	25	and	and	CCONJ
ejpam-488	63	26	b	b	NOUN
ejpam-488	63	27	=	=	SYM
ejpam-488	63	28	−1	−1	NOUN
ejpam-488	63	29	in	in	ADV
ejpam-488	63	30	(	(	PUNCT
ejpam-488	63	31	6	6	NUM
ejpam-488	63	32	)	)	PUNCT
ejpam-488	63	33	,	,	PUNCT
ejpam-488	63	34	cm	cm	NOUN
ejpam-488	63	35	,	,	PUNCT
ejpam-488	63	36	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	63	37	;	;	PUNCT
ejpam-488	63	38	a	a	DET
ejpam-488	63	39	,	,	PUNCT
ejpam-488	63	40	b	b	NOUN
ejpam-488	63	41	)	)	PUNCT
ejpam-488	63	42	becomes	become	VERB
ejpam-488	63	43	the	the	DET
ejpam-488	63	44	familiar	familiar	ADJ
ejpam-488	63	45	class	class	NOUN
ejpam-488	63	46	of	of	ADP
ejpam-488	63	47	close	close	NOUN
ejpam-488	63	48	-	-	PUNCT
ejpam-488	63	49	to	to	ADP
ejpam-488	63	50	-	-	PUNCT
ejpam-488	63	51	convex	convex	NOUN
ejpam-488	63	52	functions	function	NOUN
ejpam-488	63	53	in	in	ADP
ejpam-488	63	54	u	u	NOUN
ejpam-488	63	55	introduce	introduce	NOUN
ejpam-488	63	56	by	by	ADP
ejpam-488	63	57	kaplan	kaplan	PROPN
ejpam-488	63	58	[	[	X
ejpam-488	63	59	8	8	NUM
ejpam-488	63	60	]	]	PUNCT
ejpam-488	63	61	.	.	PUNCT
ejpam-488	64	1	further	far	ADV
ejpam-488	64	2	,	,	PUNCT
ejpam-488	64	3	for	for	ADP
ejpam-488	64	4	m	m	PROPN
ejpam-488	64	5	=	=	SYM
ejpam-488	64	6	ℓ	ℓ	PROPN
ejpam-488	64	7	=	=	SYM
ejpam-488	64	8	0	0	PROPN
ejpam-488	64	9	,	,	PUNCT
ejpam-488	64	10	λ	λ	X
ejpam-488	64	11	=	=	NOUN
ejpam-488	64	12	1	1	NUM
ejpam-488	64	13	,	,	PUNCT
ejpam-488	64	14	q	q	NOUN
ejpam-488	64	15	=	=	SYM
ejpam-488	64	16	2	2	NUM
ejpam-488	64	17	,	,	PUNCT
ejpam-488	64	18	α	α	NOUN
ejpam-488	64	19	=	=	SYM
ejpam-488	64	20	1	1	NUM
ejpam-488	64	21	,	,	PUNCT
ejpam-488	64	22	a	a	DET
ejpam-488	64	23	=	=	SYM
ejpam-488	64	24	1	1	NUM
ejpam-488	64	25	and	and	CCONJ
ejpam-488	64	26	b	b	NOUN
ejpam-488	64	27	=	=	SYM
ejpam-488	64	28	−1	−1	NOUN
ejpam-488	64	29	,	,	PUNCT
ejpam-488	64	30	cm	cm	NOUN
ejpam-488	64	31	,	,	PUNCT
ejpam-488	64	32	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	64	33	;	;	PUNCT
ejpam-488	64	34	a	a	DET
ejpam-488	64	35	,	,	PUNCT
ejpam-488	64	36	b	b	NOUN
ejpam-488	64	37	)	)	PUNCT
ejpam-488	64	38	covers	cover	VERB
ejpam-488	64	39	the	the	DET
ejpam-488	64	40	class	class	NOUN
ejpam-488	64	41	of	of	ADP
ejpam-488	64	42	close	close	NOUN
ejpam-488	64	43	-	-	PUNCT
ejpam-488	64	44	to	to	ADP
ejpam-488	64	45	-	-	PUNCT
ejpam-488	64	46	convex	convex	NOUN
ejpam-488	64	47	functions	function	NOUN
ejpam-488	64	48	in	in	ADP
ejpam-488	64	49	u	u	NOUN
ejpam-488	64	50	with	with	ADP
ejpam-488	64	51	respect	respect	NOUN
ejpam-488	64	52	to	to	ADP
ejpam-488	64	53	symmetric	symmetric	ADJ
ejpam-488	64	54	points	point	NOUN
ejpam-488	64	55	studied	study	VERB
ejpam-488	64	56	by	by	ADP
ejpam-488	64	57	das	das	PROPN
ejpam-488	64	58	and	and	CCONJ
ejpam-488	64	59	singh	singh	NOUN
ejpam-488	65	1	[	[	X
ejpam-488	65	2	6	6	NUM
ejpam-488	65	3	]	]	PUNCT
ejpam-488	65	4	.	.	PUNCT
ejpam-488	66	1	in	in	ADP
ejpam-488	66	2	this	this	DET
ejpam-488	66	3	present	present	ADJ
ejpam-488	66	4	paper	paper	NOUN
ejpam-488	66	5	,	,	PUNCT
ejpam-488	66	6	we	we	PRON
ejpam-488	66	7	give	give	VERB
ejpam-488	66	8	some	some	DET
ejpam-488	66	9	argument	argument	NOUN
ejpam-488	66	10	properties	property	NOUN
ejpam-488	66	11	and	and	CCONJ
ejpam-488	66	12	estimates	estimate	NOUN
ejpam-488	66	13	of	of	ADP
ejpam-488	66	14	analytic	analytic	ADJ
ejpam-488	66	15	functions	function	NOUN
ejpam-488	66	16	belonging	belong	VERB
ejpam-488	66	17	to	to	ADP
ejpam-488	66	18	a	a	PRON
ejpam-488	66	19	,	,	PUNCT
ejpam-488	66	20	which	which	PRON
ejpam-488	66	21	contain	contain	VERB
ejpam-488	66	22	the	the	DET
ejpam-488	66	23	basic	basic	ADJ
ejpam-488	66	24	inclusion	inclusion	NOUN
ejpam-488	66	25	relationships	relationship	NOUN
ejpam-488	66	26	among	among	ADP
ejpam-488	66	27	the	the	DET
ejpam-488	66	28	classesωm	classesωm	NOUN
ejpam-488	66	29	,	,	PUNCT
ejpam-488	66	30	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	66	31	;	;	PUNCT
ejpam-488	66	32	a	a	DET
ejpam-488	66	33	,	,	PUNCT
ejpam-488	66	34	b	b	NOUN
ejpam-488	66	35	)	)	PUNCT
ejpam-488	66	36	and	and	CCONJ
ejpam-488	66	37	cm	cm	NOUN
ejpam-488	66	38	,	,	PUNCT
ejpam-488	66	39	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	66	40	;	;	PUNCT
ejpam-488	66	41	a	a	DET
ejpam-488	66	42	,	,	PUNCT
ejpam-488	66	43	b	b	NOUN
ejpam-488	66	44	)	)	PUNCT
ejpam-488	66	45	.	.	PUNCT
ejpam-488	67	1	the	the	DET
ejpam-488	67	2	integral	integral	ADJ
ejpam-488	67	3	preserving	preserve	VERB
ejpam-488	67	4	properties	property	NOUN
ejpam-488	67	5	in	in	ADP
ejpam-488	67	6	connection	connection	NOUN
ejpam-488	67	7	with	with	ADP
ejpam-488	67	8	the	the	DET
ejpam-488	67	9	operator	operator	NOUN
ejpam-488	67	10	im(λ,ℓ	im(λ,ℓ	NOUN
ejpam-488	67	11	)	)	PUNCT
ejpam-488	67	12	defined	define	VERB
ejpam-488	67	13	by	by	ADP
ejpam-488	67	14	(	(	PUNCT
ejpam-488	67	15	2	2	X
ejpam-488	67	16	)	)	PUNCT
ejpam-488	67	17	are	be	AUX
ejpam-488	67	18	also	also	ADV
ejpam-488	67	19	considered	consider	VERB
ejpam-488	67	20	.	.	PUNCT
ejpam-488	68	1	2	2	X
ejpam-488	68	2	.	.	X
ejpam-488	68	3	the	the	DET
ejpam-488	68	4	main	main	ADJ
ejpam-488	68	5	results	result	NOUN
ejpam-488	68	6	and	and	CCONJ
ejpam-488	68	7	their	their	PRON
ejpam-488	68	8	consequences	consequence	NOUN
ejpam-488	68	9	unless	unless	SCONJ
ejpam-488	68	10	otherwise	otherwise	ADV
ejpam-488	68	11	mentioned	mention	VERB
ejpam-488	68	12	,	,	PUNCT
ejpam-488	68	13	we	we	PRON
ejpam-488	68	14	shall	shall	AUX
ejpam-488	68	15	assume	assume	VERB
ejpam-488	68	16	in	in	ADP
ejpam-488	68	17	the	the	DET
ejpam-488	68	18	reminder	reminder	NOUN
ejpam-488	68	19	of	of	ADP
ejpam-488	68	20	this	this	DET
ejpam-488	68	21	paper	paper	NOUN
ejpam-488	68	22	that	that	PRON
ejpam-488	68	23	λ	λ	PROPN
ejpam-488	68	24	>	>	X
ejpam-488	68	25	0,ℓ	0,ℓ	X
ejpam-488	68	26	≥	≥	X
ejpam-488	68	27	0	0	NUM
ejpam-488	68	28	and	and	CCONJ
ejpam-488	68	29	m	m	PROPN
ejpam-488	68	30	∈	∈	PROPN
ejpam-488	68	31	n0	n0	PROPN
ejpam-488	68	32	.	.	PUNCT
ejpam-488	69	1	in	in	ADP
ejpam-488	69	2	proving	prove	VERB
ejpam-488	69	3	our	our	PRON
ejpam-488	69	4	main	main	ADJ
ejpam-488	69	5	results	result	NOUN
ejpam-488	69	6	,	,	PUNCT
ejpam-488	69	7	we	we	PRON
ejpam-488	69	8	need	need	VERB
ejpam-488	69	9	the	the	DET
ejpam-488	69	10	following	follow	VERB
ejpam-488	69	11	lemmas	lemmas	NOUN
ejpam-488	69	12	.	.	PUNCT
ejpam-488	70	1	lemma	lemma	PROPN
ejpam-488	70	2	1	1	NUM
ejpam-488	70	3	.	.	PUNCT
ejpam-488	71	1	[	[	X
ejpam-488	71	2	7	7	X
ejpam-488	71	3	]	]	PUNCT
ejpam-488	71	4	let	let	VERB
ejpam-488	71	5	h	h	PRON
ejpam-488	71	6	be	be	AUX
ejpam-488	71	7	convex	convex	ADJ
ejpam-488	71	8	univalent	univalent	ADJ
ejpam-488	71	9	in	in	ADP
ejpam-488	71	10	u	u	NOUN
ejpam-488	71	11	with	with	ADP
ejpam-488	71	12	h(0	h(0	PROPN
ejpam-488	71	13	)	)	PUNCT
ejpam-488	71	14	=	=	SYM
ejpam-488	71	15	1	1	NUM
ejpam-488	71	16	and	and	CCONJ
ejpam-488	71	17	r(βh(z	r(βh(z	NUM
ejpam-488	71	18	)	)	PUNCT
ejpam-488	72	1	+	+	CCONJ
ejpam-488	72	2	γ	γ	X
ejpam-488	72	3	)	)	PUNCT
ejpam-488	72	4	>	>	X
ejpam-488	72	5	0	0	PUNCT
ejpam-488	73	1	(	(	PUNCT
ejpam-488	73	2	z	z	NOUN
ejpam-488	73	3	∈	∈	PROPN
ejpam-488	73	4	u;β	u;β	NOUN
ejpam-488	73	5	,	,	PUNCT
ejpam-488	73	6	γ	γ	PROPN
ejpam-488	73	7	∈	∈	PROPN
ejpam-488	73	8	c	c	X
ejpam-488	73	9	)	)	PUNCT
ejpam-488	73	10	.	.	PUNCT
ejpam-488	74	1	if	if	SCONJ
ejpam-488	74	2	p	p	NOUN
ejpam-488	74	3	is	be	AUX
ejpam-488	74	4	analytic	analytic	ADJ
ejpam-488	74	5	in	in	ADP
ejpam-488	74	6	u	u	NOUN
ejpam-488	74	7	with	with	ADP
ejpam-488	74	8	p(0	p(0	PROPN
ejpam-488	74	9	)	)	PUNCT
ejpam-488	74	10	=	=	SYM
ejpam-488	74	11	1	1	NUM
ejpam-488	74	12	,	,	PUNCT
ejpam-488	74	13	then	then	ADV
ejpam-488	74	14	p(z	p(z	PROPN
ejpam-488	74	15	)	)	PUNCT
ejpam-488	75	1	+	+	CCONJ
ejpam-488	75	2	zp	zp	NOUN
ejpam-488	75	3	′	′	NUM
ejpam-488	75	4	(	(	PUNCT
ejpam-488	75	5	z	z	NOUN
ejpam-488	75	6	)	)	PUNCT
ejpam-488	75	7	βp(z	βp(z	PUNCT
ejpam-488	75	8	)	)	PUNCT
ejpam-488	75	9	+	+	CCONJ
ejpam-488	75	10	γ	γ	PROPN
ejpam-488	75	11	≺	≺	NOUN
ejpam-488	75	12	h(z	h(z	NOUN
ejpam-488	75	13	)	)	PUNCT
ejpam-488	75	14	(	(	PUNCT
ejpam-488	75	15	z	z	NOUN
ejpam-488	75	16	∈	∈	PROPN
ejpam-488	75	17	u	u	NOUN
ejpam-488	75	18	)	)	PUNCT
ejpam-488	75	19	,	,	PUNCT
ejpam-488	75	20	implies	imply	VERB
ejpam-488	75	21	that	that	SCONJ
ejpam-488	75	22	p(z	p(z	NOUN
ejpam-488	75	23	)	)	PUNCT
ejpam-488	75	24	≺	≺	NOUN
ejpam-488	75	25	h(z	h(z	NOUN
ejpam-488	75	26	)	)	PUNCT
ejpam-488	75	27	(	(	PUNCT
ejpam-488	75	28	z	z	NOUN
ejpam-488	75	29	∈	∈	PROPN
ejpam-488	75	30	u	u	NOUN
ejpam-488	75	31	)	)	PUNCT
ejpam-488	75	32	.	.	PUNCT
ejpam-488	76	1	lemma	lemma	PROPN
ejpam-488	76	2	2	2	NUM
ejpam-488	76	3	.	.	PUNCT
ejpam-488	77	1	[	[	X
ejpam-488	77	2	10	10	NUM
ejpam-488	77	3	]	]	PUNCT
ejpam-488	77	4	let	let	VERB
ejpam-488	77	5	h	h	PRON
ejpam-488	77	6	be	be	AUX
ejpam-488	77	7	convex	convex	ADJ
ejpam-488	77	8	univalent	univalent	ADJ
ejpam-488	77	9	in	in	ADP
ejpam-488	77	10	u	u	PROPN
ejpam-488	77	11	and	and	CCONJ
ejpam-488	77	12	φ	φ	PROPN
ejpam-488	77	13	be	be	AUX
ejpam-488	77	14	analytic	analytic	ADJ
ejpam-488	77	15	in	in	ADP
ejpam-488	77	16	u	u	NOUN
ejpam-488	77	17	with	with	ADP
ejpam-488	77	18	r(φ(z))≥	r(φ(z))≥	PROPN
ejpam-488	77	19	0	0	NUM
ejpam-488	78	1	(	(	PUNCT
ejpam-488	78	2	z	z	NOUN
ejpam-488	78	3	∈	∈	PROPN
ejpam-488	78	4	u	u	NOUN
ejpam-488	78	5	)	)	PUNCT
ejpam-488	78	6	.	.	PUNCT
ejpam-488	78	7	implies	imply	VERB
ejpam-488	78	8	that	that	SCONJ
ejpam-488	78	9	p(z	p(z	NOUN
ejpam-488	78	10	)	)	PUNCT
ejpam-488	78	11	≺	≺	NOUN
ejpam-488	78	12	h(z	h(z	NOUN
ejpam-488	78	13	)	)	PUNCT
ejpam-488	78	14	(	(	PUNCT
ejpam-488	78	15	z	z	NOUN
ejpam-488	78	16	∈	∈	PROPN
ejpam-488	78	17	u	u	NOUN
ejpam-488	78	18	)	)	PUNCT
ejpam-488	78	19	.	.	PUNCT
ejpam-488	79	1	m.	m.	PROPN
ejpam-488	79	2	aouf	aouf	PROPN
ejpam-488	79	3	,	,	PUNCT
ejpam-488	79	4	a.	a.	NOUN
ejpam-488	79	5	shamandy	shamandy	PROPN
ejpam-488	79	6	,	,	PUNCT
ejpam-488	79	7	r.	r.	PROPN
ejpam-488	79	8	el	el	PROPN
ejpam-488	79	9	-	-	PUNCT
ejpam-488	79	10	ashway	ashway	PROPN
ejpam-488	79	11	,	,	PUNCT
ejpam-488	79	12	e.	e.	PROPN
ejpam-488	79	13	ali	ali	PROPN
ejpam-488	79	14	/	/	SYM
ejpam-488	79	15	eur	eur	PROPN
ejpam-488	79	16	.	.	PUNCT
ejpam-488	80	1	j.	j.	PROPN
ejpam-488	80	2	pure	pure	PROPN
ejpam-488	80	3	appl	appl	PROPN
ejpam-488	80	4	.	.	PROPN
ejpam-488	80	5	math	math	PROPN
ejpam-488	80	6	,	,	PUNCT
ejpam-488	80	7	3	3	NUM
ejpam-488	80	8	(	(	PUNCT
ejpam-488	80	9	2010	2010	NUM
ejpam-488	80	10	)	)	PUNCT
ejpam-488	80	11	,	,	PUNCT
ejpam-488	80	12	317	317	NUM
ejpam-488	80	13	-	-	SYM
ejpam-488	80	14	330	330	NUM
ejpam-488	80	15	320	320	NUM
ejpam-488	80	16	lemma	lemma	PROPN
ejpam-488	80	17	3	3	NUM
ejpam-488	80	18	.	.	PUNCT
ejpam-488	81	1	[	[	X
ejpam-488	81	2	14	14	NUM
ejpam-488	81	3	]	]	PUNCT
ejpam-488	81	4	let	let	VERB
ejpam-488	81	5	p	p	PRON
ejpam-488	81	6	be	be	AUX
ejpam-488	81	7	analytic	analytic	ADJ
ejpam-488	81	8	in	in	ADP
ejpam-488	81	9	u	u	NOUN
ejpam-488	81	10	with	with	ADP
ejpam-488	81	11	p(0	p(0	PROPN
ejpam-488	81	12	)	)	PUNCT
ejpam-488	81	13	=	=	SYM
ejpam-488	81	14	1	1	NUM
ejpam-488	81	15	and	and	CCONJ
ejpam-488	81	16	p(z	p(z	NOUN
ejpam-488	81	17	)	)	PUNCT
ejpam-488	81	18	6=	6=	ADP
ejpam-488	81	19	0	0	NUM
ejpam-488	81	20	in	in	ADP
ejpam-488	81	21	u	u	NOUN
ejpam-488	81	22	.	.	PUNCT
ejpam-488	82	1	if	if	SCONJ
ejpam-488	82	2	there	there	PRON
ejpam-488	82	3	exists	exist	VERB
ejpam-488	82	4	two	two	NUM
ejpam-488	82	5	points	point	NOUN
ejpam-488	82	6	z1	z1	VERB
ejpam-488	82	7	,	,	PUNCT
ejpam-488	82	8	z2	z2	PROPN
ejpam-488	82	9	∈	∈	PROPN
ejpam-488	82	10	u	u	NOUN
ejpam-488	82	11	such	such	ADJ
ejpam-488	82	12	that	that	SCONJ
ejpam-488	82	13	−π	−π	ADJ
ejpam-488	82	14	2	2	NUM
ejpam-488	82	15	α1	α1	PROPN
ejpam-488	82	16	=	=	SYM
ejpam-488	82	17	arg(p(z1	arg(p(z1	NOUN
ejpam-488	82	18	)	)	PUNCT
ejpam-488	82	19	)	)	PUNCT
ejpam-488	82	20	<	<	X
ejpam-488	82	21	arg(p(z	arg(p(z	PROPN
ejpam-488	82	22	)	)	PUNCT
ejpam-488	82	23	)	)	PUNCT
ejpam-488	82	24	<	<	X
ejpam-488	82	25	arg(p(z2	arg(p(z2	PROPN
ejpam-488	82	26	)	)	PUNCT
ejpam-488	82	27	)	)	PUNCT
ejpam-488	83	1	=	=	PUNCT
ejpam-488	83	2	π	π	X
ejpam-488	83	3	2	2	NUM
ejpam-488	83	4	α2	α2	ADJ
ejpam-488	83	5	,	,	PUNCT
ejpam-488	83	6	(	(	PUNCT
ejpam-488	83	7	7	7	X
ejpam-488	83	8	)	)	PUNCT
ejpam-488	83	9	for	for	ADP
ejpam-488	83	10	some	some	DET
ejpam-488	83	11	α1	α1	PROPN
ejpam-488	83	12	and	and	CCONJ
ejpam-488	83	13	α2	α2	PROPN
ejpam-488	83	14	(	(	PUNCT
ejpam-488	83	15	α1,α2	α1,α2	PROPN
ejpam-488	83	16	>	>	X
ejpam-488	83	17	0	0	NUM
ejpam-488	83	18	)	)	PUNCT
ejpam-488	83	19	and	and	CCONJ
ejpam-488	83	20	for	for	SCONJ
ejpam-488	83	21	all	all	DET
ejpam-488	83	22	z	z	PROPN
ejpam-488	83	23	�	�	PROPN
ejpam-488	83	24	|z|	|z|	VERB
ejpam-488	83	25	<	<	X
ejpam-488	83	26	|z1|	|z1|	NOUN
ejpam-488	83	27	=	=	PUNCT
ejpam-488	83	28	|z2|	|z2|	PROPN
ejpam-488	83	29	�	�	PROPN
ejpam-488	83	30	,	,	PUNCT
ejpam-488	83	31	then	then	ADV
ejpam-488	83	32	z1p	z1p	INTJ
ejpam-488	83	33	′	′	NUM
ejpam-488	84	1	(	(	PUNCT
ejpam-488	84	2	z1	z1	ADJ
ejpam-488	84	3	)	)	PUNCT
ejpam-488	84	4	p(z1	p(z1	NOUN
ejpam-488	84	5	)	)	PUNCT
ejpam-488	85	1	=	=	SYM
ejpam-488	85	2	−i	−i	PROPN
ejpam-488	85	3	�	�	PROPN
ejpam-488	85	4	α1	α1	PROPN
ejpam-488	85	5	+	+	CCONJ
ejpam-488	85	6	α2	α2	ADJ
ejpam-488	85	7	2	2	NUM
ejpam-488	85	8	�	�	PROPN
ejpam-488	85	9	m	m	PROPN
ejpam-488	85	10	and	and	CCONJ
ejpam-488	85	11	z2p	z2p	PROPN
ejpam-488	85	12	′	′	NUM
ejpam-488	85	13	(	(	PUNCT
ejpam-488	85	14	z2	z2	NOUN
ejpam-488	85	15	)	)	PUNCT
ejpam-488	85	16	p(z2	p(z2	NOUN
ejpam-488	85	17	)	)	PUNCT
ejpam-488	86	1	=	=	PUNCT
ejpam-488	87	1	i	i	PRON
ejpam-488	87	2	�	�	PROPN
ejpam-488	87	3	α1+α2	α1+α2	PROPN
ejpam-488	87	4	2	2	NUM
ejpam-488	87	5	�	�	PROPN
ejpam-488	87	6	m	m	PRON
ejpam-488	87	7	,	,	PUNCT
ejpam-488	87	8	(	(	PUNCT
ejpam-488	87	9	8)	8)	NUM
ejpam-488	87	10	where	where	SCONJ
ejpam-488	87	11	m≥	m≥	PROPN
ejpam-488	87	12	1−	1−	NUM
ejpam-488	87	13	|a|	|a|	PROPN
ejpam-488	87	14	1	1	NUM
ejpam-488	87	15	+	+	NUM
ejpam-488	87	16	|a|	|a|	PROPN
ejpam-488	87	17	and	and	CCONJ
ejpam-488	87	18	a	a	PRON
ejpam-488	87	19	=	=	X
ejpam-488	88	1	i	i	PRON
ejpam-488	88	2	tan	tan	VERB
ejpam-488	88	3	π	π	PROPN
ejpam-488	88	4	4	4	NUM
ejpam-488	88	5	�	�	PROPN
ejpam-488	88	6	α2	α2	PROPN
ejpam-488	88	7	−α1	−α1	VERB
ejpam-488	88	8	α1	α1	PROPN
ejpam-488	88	9	+	+	ADJ
ejpam-488	88	10	α2	α2	ADJ
ejpam-488	88	11	�	�	PROPN
ejpam-488	88	12	(	(	PUNCT
ejpam-488	88	13	9	9	NUM
ejpam-488	88	14	)	)	PUNCT
ejpam-488	88	15	first	first	ADV
ejpam-488	88	16	of	of	ADP
ejpam-488	88	17	all	all	PRON
ejpam-488	88	18	,	,	PUNCT
ejpam-488	88	19	with	with	ADP
ejpam-488	88	20	the	the	DET
ejpam-488	88	21	help	help	NOUN
ejpam-488	88	22	of	of	ADP
ejpam-488	88	23	lemma	lemma	PROPN
ejpam-488	88	24	1	1	NUM
ejpam-488	88	25	and	and	CCONJ
ejpam-488	88	26	2	2	NUM
ejpam-488	88	27	,	,	PUNCT
ejpam-488	88	28	we	we	PRON
ejpam-488	88	29	obtain	obtain	VERB
ejpam-488	88	30	the	the	DET
ejpam-488	88	31	following	following	NOUN
ejpam-488	88	32	.	.	PUNCT
ejpam-488	89	1	proposition	proposition	NOUN
ejpam-488	89	2	1	1	NUM
ejpam-488	89	3	.	.	PUNCT
ejpam-488	90	1	if	if	SCONJ
ejpam-488	90	2	g1	g1	NOUN
ejpam-488	90	3	,	,	PUNCT
ejpam-488	90	4	...	...	PUNCT
ejpam-488	90	5	,	,	PUNCT
ejpam-488	90	6	gq	gq	PROPN
ejpam-488	90	7	∈	∈	PROPN
ejpam-488	90	8	ωm+1,λ,ℓ(q	ωm+1,λ,ℓ(q	PROPN
ejpam-488	90	9	;	;	PUNCT
ejpam-488	90	10	a	a	DET
ejpam-488	90	11	,	,	PUNCT
ejpam-488	90	12	b	b	NOUN
ejpam-488	90	13	)	)	PUNCT
ejpam-488	90	14	,	,	PUNCT
ejpam-488	90	15	then	then	ADV
ejpam-488	90	16	g1	g1	VERB
ejpam-488	90	17	,	,	PUNCT
ejpam-488	90	18	...	...	PUNCT
ejpam-488	90	19	,	,	PUNCT
ejpam-488	90	20	gq	gq	PROPN
ejpam-488	90	21	∈	∈	PROPN
ejpam-488	90	22	ωm	ωm	VERB
ejpam-488	90	23	,	,	PUNCT
ejpam-488	90	24	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	90	25	;	;	PUNCT
ejpam-488	90	26	a	a	DET
ejpam-488	90	27	,	,	PUNCT
ejpam-488	90	28	b	b	NOUN
ejpam-488	90	29	)	)	PUNCT
ejpam-488	90	30	.	.	PUNCT
ejpam-488	91	1	proof	proof	NOUN
ejpam-488	91	2	.	.	PUNCT
ejpam-488	92	1	let	let	VERB
ejpam-488	92	2	pi(z	pi(z	NOUN
ejpam-488	92	3	)	)	PUNCT
ejpam-488	92	4	=	=	SYM
ejpam-488	92	5	z(im(λ,ℓ)gi(z	z(im(λ,ℓ)gi(z	NOUN
ejpam-488	92	6	)	)	PUNCT
ejpam-488	92	7	)	)	PUNCT
ejpam-488	93	1	′	′	NUM
ejpam-488	93	2	�	�	PROPN
ejpam-488	93	3	1	1	NUM
ejpam-488	93	4	q	q	PROPN
ejpam-488	93	5	�	�	PROPN
ejpam-488	93	6	q	q	PROPN
ejpam-488	93	7	∑	∑	PROPN
ejpam-488	93	8	j=1	j=1	ADJ
ejpam-488	93	9	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	93	10	j(z	j(z	PROPN
ejpam-488	93	11	)	)	PUNCT
ejpam-488	93	12	(	(	PUNCT
ejpam-488	93	13	i	i	NOUN
ejpam-488	93	14	=	=	NOUN
ejpam-488	93	15	1	1	NUM
ejpam-488	93	16	,	,	PUNCT
ejpam-488	93	17	...	...	PUNCT
ejpam-488	93	18	,	,	PUNCT
ejpam-488	93	19	q	q	NOUN
ejpam-488	93	20	)	)	PUNCT
ejpam-488	93	21	.	.	PUNCT
ejpam-488	94	1	(	(	PUNCT
ejpam-488	94	2	10	10	NUM
ejpam-488	94	3	)	)	PUNCT
ejpam-488	94	4	by	by	ADP
ejpam-488	94	5	using	use	VERB
ejpam-488	94	6	the	the	DET
ejpam-488	94	7	identity	identity	NOUN
ejpam-488	94	8	(	(	PUNCT
ejpam-488	94	9	4	4	NUM
ejpam-488	94	10	)	)	PUNCT
ejpam-488	94	11	,	,	PUNCT
ejpam-488	94	12	we	we	PRON
ejpam-488	94	13	get	get	VERB
ejpam-488	94	14	1	1	NUM
ejpam-488	94	15	q	q	NOUN
ejpam-488	94	16	q	q	NOUN
ejpam-488	94	17	∑	∑	PUNCT
ejpam-488	94	18	j=1	j=1	NOUN
ejpam-488	94	19	(	(	PUNCT
ejpam-488	94	20	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	94	21	j(z))pi(z	j(z))pi(z	VERB
ejpam-488	94	22	)	)	PUNCT
ejpam-488	94	23	+	+	CCONJ
ejpam-488	94	24	1−λ+	1−λ+	NUM
ejpam-488	94	25	ℓ	ℓ	PROPN
ejpam-488	94	26	λ	λ	PROPN
ejpam-488	94	27	(	(	PUNCT
ejpam-488	94	28	im(λ,ℓ)gi(z	im(λ,ℓ)gi(z	NOUN
ejpam-488	94	29	)	)	PUNCT
ejpam-488	94	30	)	)	PUNCT
ejpam-488	95	1	=	=	PUNCT
ejpam-488	95	2	1	1	NUM
ejpam-488	95	3	+	+	NUM
ejpam-488	95	4	ℓ	ℓ	PROPN
ejpam-488	95	5	λ	λ	PROPN
ejpam-488	95	6	(	(	PUNCT
ejpam-488	95	7	im+1(λ,ℓ)gi(z	im+1(λ,ℓ)gi(z	NOUN
ejpam-488	95	8	)	)	PUNCT
ejpam-488	95	9	)	)	PUNCT
ejpam-488	95	10	.	.	PUNCT
ejpam-488	96	1	(	(	PUNCT
ejpam-488	96	2	11	11	X
ejpam-488	96	3	)	)	PUNCT
ejpam-488	96	4	differentiating	differentiate	VERB
ejpam-488	96	5	both	both	DET
ejpam-488	96	6	sides	side	NOUN
ejpam-488	96	7	of	of	ADP
ejpam-488	96	8	(	(	PUNCT
ejpam-488	96	9	11	11	NUM
ejpam-488	96	10	)	)	PUNCT
ejpam-488	96	11	with	with	ADP
ejpam-488	96	12	respect	respect	NOUN
ejpam-488	96	13	to	to	ADP
ejpam-488	96	14	z	z	NOUN
ejpam-488	96	15	,	,	PUNCT
ejpam-488	96	16	and	and	CCONJ
ejpam-488	96	17	simplifying	simplify	VERB
ejpam-488	96	18	,	,	PUNCT
ejpam-488	96	19	we	we	PRON
ejpam-488	96	20	obtain	obtain	VERB
ejpam-488	96	21	pi(z	pi(z	NOUN
ejpam-488	96	22	)	)	PUNCT
ejpam-488	97	1	+	+	CCONJ
ejpam-488	97	2	zp	zp	NOUN
ejpam-488	98	1	′	′	NUM
ejpam-488	99	1	i	i	PRON
ejpam-488	99	2	(	(	PUNCT
ejpam-488	99	3	z	z	NOUN
ejpam-488	99	4	)	)	PUNCT
ejpam-488	99	5	�	�	PROPN
ejpam-488	99	6	1	1	NUM
ejpam-488	99	7	q	q	PROPN
ejpam-488	99	8	�	�	PROPN
ejpam-488	99	9	q	q	PROPN
ejpam-488	99	10	∑	∑	PROPN
ejpam-488	99	11	i=1	i=1	PROPN
ejpam-488	99	12	pi(z	pi(z	NOUN
ejpam-488	99	13	)	)	PUNCT
ejpam-488	100	1	+	+	CCONJ
ejpam-488	100	2	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	100	3	λ	λ	NOUN
ejpam-488	100	4	=	=	SYM
ejpam-488	100	5	z(im+1(λ,ℓ)gi(z	z(im+1(λ,ℓ)gi(z	NOUN
ejpam-488	100	6	)	)	PUNCT
ejpam-488	100	7	)	)	PUNCT
ejpam-488	101	1	′	′	NUM
ejpam-488	101	2	�	�	PROPN
ejpam-488	101	3	1	1	NUM
ejpam-488	101	4	q	q	PROPN
ejpam-488	101	5	�	�	PROPN
ejpam-488	101	6	q	q	PROPN
ejpam-488	101	7	∑	∑	PROPN
ejpam-488	101	8	j=1	j=1	PROPN
ejpam-488	101	9	im+1(λ,ℓ)g	im+1(λ,ℓ)g	PUNCT
ejpam-488	101	10	j(z	j(z	PROPN
ejpam-488	101	11	)	)	PUNCT
ejpam-488	101	12	≺	≺	NOUN
ejpam-488	101	13	1	1	NUM
ejpam-488	101	14	+	+	NUM
ejpam-488	101	15	az	az	PROPN
ejpam-488	101	16	1	1	NUM
ejpam-488	101	17	+	+	CCONJ
ejpam-488	101	18	bz	bz	PROPN
ejpam-488	101	19	≡	≡	PROPN
ejpam-488	101	20	h(z	h(z	PROPN
ejpam-488	101	21	)	)	PUNCT
ejpam-488	101	22	,	,	PUNCT
ejpam-488	101	23	(	(	PUNCT
ejpam-488	101	24	z	z	NOUN
ejpam-488	101	25	∈	∈	PROPN
ejpam-488	101	26	u	u	NOUN
ejpam-488	101	27	;	;	PUNCT
ejpam-488	101	28	i	i	NOUN
ejpam-488	101	29	=	=	NOUN
ejpam-488	101	30	1	1	NUM
ejpam-488	101	31	,	,	PUNCT
ejpam-488	101	32	...	...	PUNCT
ejpam-488	101	33	,	,	PUNCT
ejpam-488	101	34	q	q	X
ejpam-488	101	35	)	)	PUNCT
ejpam-488	101	36	,	,	PUNCT
ejpam-488	101	37	(	(	PUNCT
ejpam-488	101	38	12	12	NUM
ejpam-488	101	39	)	)	PUNCT
ejpam-488	101	40	g1	g1	NOUN
ejpam-488	101	41	,	,	PUNCT
ejpam-488	101	42	...	...	PUNCT
ejpam-488	101	43	,	,	PUNCT
ejpam-488	101	44	gq	gq	PROPN
ejpam-488	101	45	∈	∈	PROPN
ejpam-488	101	46	ωm+1,λ,ℓ(q	ωm+1,λ,ℓ(q	PROPN
ejpam-488	101	47	;	;	PUNCT
ejpam-488	101	48	a	a	DET
ejpam-488	101	49	,	,	PUNCT
ejpam-488	101	50	b	b	NOUN
ejpam-488	101	51	)	)	PUNCT
ejpam-488	101	52	.	.	PUNCT
ejpam-488	102	1	since	since	SCONJ
ejpam-488	102	2	h	h	PROPN
ejpam-488	102	3	is	be	AUX
ejpam-488	102	4	convex	convex	PROPN
ejpam-488	102	5	,	,	PUNCT
ejpam-488	102	6	for	for	ADP
ejpam-488	102	7	any	any	DET
ejpam-488	102	8	z0	z0	PROPN
ejpam-488	102	9	∈	∈	PROPN
ejpam-488	102	10	u	u	NOUN
ejpam-488	102	11	,	,	PUNCT
ejpam-488	102	12	there	there	PRON
ejpam-488	102	13	exists	exist	VERB
ejpam-488	102	14	a	a	DET
ejpam-488	102	15	point	point	NOUN
ejpam-488	102	16	ζ0	ζ0	NOUN
ejpam-488	102	17	∈	∈	PROPN
ejpam-488	102	18	u	u	NOUN
ejpam-488	102	19	such	such	ADJ
ejpam-488	102	20	that	that	SCONJ
ejpam-488	102	21	x	x	PUNCT
ejpam-488	102	22	(	(	PUNCT
ejpam-488	102	23	z0	z0	PROPN
ejpam-488	102	24	)	)	PUNCT
ejpam-488	102	25	+	+	PROPN
ejpam-488	102	26	z0x	z0x	PROPN
ejpam-488	102	27	′	′	NUM
ejpam-488	102	28	(	(	PUNCT
ejpam-488	102	29	z0	z0	PROPN
ejpam-488	102	30	)	)	PUNCT
ejpam-488	102	31	x	x	X
ejpam-488	102	32	(	(	PUNCT
ejpam-488	102	33	z0	z0	PROPN
ejpam-488	102	34	)	)	PUNCT
ejpam-488	102	35	+	+	NUM
ejpam-488	102	36	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	102	37	λ	λ	NOUN
ejpam-488	102	38	=	=	SYM
ejpam-488	102	39	h(ζ0	h(ζ0	PROPN
ejpam-488	102	40	)	)	PUNCT
ejpam-488	102	41	,	,	PUNCT
ejpam-488	102	42	where	where	SCONJ
ejpam-488	102	43	x	x	X
ejpam-488	102	44	(	(	PUNCT
ejpam-488	102	45	z	z	NOUN
ejpam-488	102	46	)	)	PUNCT
ejpam-488	102	47	=	=	SYM
ejpam-488	102	48	1	1	NUM
ejpam-488	102	49	q	q	NOUN
ejpam-488	102	50	q	q	X
ejpam-488	102	51	∑	∑	PUNCT
ejpam-488	102	52	i=1	i=1	PROPN
ejpam-488	102	53	pi(z	pi(z	NOUN
ejpam-488	102	54	)	)	PUNCT
ejpam-488	102	55	.	.	PUNCT
ejpam-488	103	1	m.	m.	PROPN
ejpam-488	103	2	aouf	aouf	PROPN
ejpam-488	103	3	,	,	PUNCT
ejpam-488	103	4	a.	a.	NOUN
ejpam-488	103	5	shamandy	shamandy	PROPN
ejpam-488	103	6	,	,	PUNCT
ejpam-488	103	7	r.	r.	PROPN
ejpam-488	103	8	el	el	PROPN
ejpam-488	103	9	-	-	PUNCT
ejpam-488	103	10	ashway	ashway	PROPN
ejpam-488	103	11	,	,	PUNCT
ejpam-488	103	12	e.	e.	PROPN
ejpam-488	103	13	ali	ali	PROPN
ejpam-488	103	14	/	/	SYM
ejpam-488	103	15	eur	eur	PROPN
ejpam-488	103	16	.	.	PUNCT
ejpam-488	104	1	j.	j.	PROPN
ejpam-488	104	2	pure	pure	PROPN
ejpam-488	104	3	appl	appl	PROPN
ejpam-488	104	4	.	.	PROPN
ejpam-488	104	5	math	math	PROPN
ejpam-488	104	6	,	,	PUNCT
ejpam-488	104	7	3	3	NUM
ejpam-488	104	8	(	(	PUNCT
ejpam-488	104	9	2010	2010	NUM
ejpam-488	104	10	)	)	PUNCT
ejpam-488	104	11	,	,	PUNCT
ejpam-488	104	12	317	317	NUM
ejpam-488	104	13	-	-	SYM
ejpam-488	104	14	330	330	NUM
ejpam-488	104	15	321	321	NUM
ejpam-488	104	16	then	then	ADV
ejpam-488	104	17	we	we	PRON
ejpam-488	104	18	find	find	VERB
ejpam-488	104	19	from	from	ADP
ejpam-488	104	20	lemma	lemma	PROPN
ejpam-488	104	21	1	1	NUM
ejpam-488	105	1	that	that	SCONJ
ejpam-488	105	2	x	x	SYM
ejpam-488	105	3	≺	≺	AUX
ejpam-488	105	4	h.	h.	NOUN
ejpam-488	105	5	applying	apply	VERB
ejpam-488	105	6	lemma	lemma	PROPN
ejpam-488	105	7	2	2	NUM
ejpam-488	105	8	with	with	ADP
ejpam-488	105	9	φ(z	φ(z	PROPN
ejpam-488	105	10	)	)	PUNCT
ejpam-488	105	11	=	=	SYM
ejpam-488	106	1	1	1	NUM
ejpam-488	106	2	x	x	SYM
ejpam-488	106	3	(	(	PUNCT
ejpam-488	106	4	z	z	NOUN
ejpam-488	106	5	)	)	PUNCT
ejpam-488	106	6	+	+	CCONJ
ejpam-488	106	7	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	106	8	λ	λ	NOUN
ejpam-488	106	9	to	to	ADP
ejpam-488	106	10	(	(	PUNCT
ejpam-488	106	11	12	12	NUM
ejpam-488	106	12	)	)	PUNCT
ejpam-488	106	13	again	again	ADV
ejpam-488	106	14	,	,	PUNCT
ejpam-488	106	15	we	we	PRON
ejpam-488	106	16	find	find	VERB
ejpam-488	106	17	that	that	SCONJ
ejpam-488	106	18	pi	pi	NOUN
ejpam-488	106	19	≺	≺	NOUN
ejpam-488	106	20	h	h	NOUN
ejpam-488	106	21	for	for	ADP
ejpam-488	106	22	all	all	DET
ejpam-488	106	23	i(i	i(i	PROPN
ejpam-488	106	24	=	=	SYM
ejpam-488	106	25	1	1	NUM
ejpam-488	106	26	,	,	PUNCT
ejpam-488	106	27	...	...	PUNCT
ejpam-488	106	28	,	,	PUNCT
ejpam-488	106	29	q	q	NOUN
ejpam-488	106	30	)	)	PUNCT
ejpam-488	106	31	.	.	PUNCT
ejpam-488	107	1	next	next	ADV
ejpam-488	107	2	,	,	PUNCT
ejpam-488	107	3	we	we	PRON
ejpam-488	107	4	prove	prove	VERB
ejpam-488	107	5	that	that	SCONJ
ejpam-488	107	6	q	q	PUNCT
ejpam-488	107	7	∑	∑	PUNCT
ejpam-488	107	8	j=1	j=1	NOUN
ejpam-488	107	9	1	1	NUM
ejpam-488	107	10	z	z	NOUN
ejpam-488	107	11	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	107	12	j(z	j(z	PROPN
ejpam-488	107	13	)	)	PUNCT
ejpam-488	107	14	6=	6=	ADP
ejpam-488	107	15	0	0	NUM
ejpam-488	108	1	(	(	PUNCT
ejpam-488	108	2	z	z	NOUN
ejpam-488	108	3	∈	∈	PROPN
ejpam-488	108	4	u	u	NOUN
ejpam-488	108	5	)	)	PUNCT
ejpam-488	108	6	.	.	PUNCT
ejpam-488	109	1	since	since	SCONJ
ejpam-488	109	2	g1	g1	PROPN
ejpam-488	109	3	,	,	PUNCT
ejpam-488	109	4	...	...	PUNCT
ejpam-488	109	5	,	,	PUNCT
ejpam-488	109	6	gq	gq	PROPN
ejpam-488	109	7	∈	∈	PROPN
ejpam-488	109	8	ωm+1,λ,ℓ(q	ωm+1,λ,ℓ(q	PROPN
ejpam-488	109	9	;	;	PUNCT
ejpam-488	109	10	a	a	DET
ejpam-488	109	11	,	,	PUNCT
ejpam-488	109	12	b	b	NOUN
ejpam-488	109	13	)	)	PUNCT
ejpam-488	109	14	and	and	CCONJ
ejpam-488	109	15	h	h	NOUN
ejpam-488	109	16	is	be	AUX
ejpam-488	109	17	convex	convex	PROPN
ejpam-488	109	18	,	,	PUNCT
ejpam-488	109	19	we	we	PRON
ejpam-488	109	20	find	find	VERB
ejpam-488	109	21	that	that	SCONJ
ejpam-488	109	22	there	there	PRON
ejpam-488	109	23	exists	exist	VERB
ejpam-488	109	24	a	a	DET
ejpam-488	109	25	point	point	NOUN
ejpam-488	109	26	ζ0	ζ0	NOUN
ejpam-488	109	27	∈	∈	PROPN
ejpam-488	109	28	u	u	NOUN
ejpam-488	109	29	such	such	ADJ
ejpam-488	109	30	that	that	SCONJ
ejpam-488	109	31	,	,	PUNCT
ejpam-488	109	32	for	for	ADP
ejpam-488	109	33	any	any	DET
ejpam-488	109	34	z0	z0	PROPN
ejpam-488	109	35	∈	∈	PROPN
ejpam-488	109	36	u	u	NOUN
ejpam-488	109	37	,	,	PUNCT
ejpam-488	109	38	r(z0	r(z0	ADV
ejpam-488	109	39	)	)	PUNCT
ejpam-488	109	40	=	=	SYM
ejpam-488	109	41	z0	z0	PROPN
ejpam-488	109	42	q	q	PUNCT
ejpam-488	109	43	∑	∑	PROPN
ejpam-488	109	44	j=1	j=1	PROPN
ejpam-488	109	45	im+1(λ,ℓ)g	im+1(λ,ℓ)g	PUNCT
ejpam-488	109	46	j(z0	j(z0	NOUN
ejpam-488	109	47	)	)	PUNCT
ejpam-488	109	48	!	!	PUNCT
ejpam-488	110	1	′	′	NUM
ejpam-488	111	1	q	q	NOUN
ejpam-488	112	1	∑	∑	PUNCT
ejpam-488	112	2	j=1	j=1	PROPN
ejpam-488	112	3	im+1(λ,ℓ)g	im+1(λ,ℓ)g	PUNCT
ejpam-488	112	4	j(z0	j(z0	NOUN
ejpam-488	112	5	)	)	PUNCT
ejpam-488	112	6	=	=	SYM
ejpam-488	112	7	h(ζ0	h(ζ0	PROPN
ejpam-488	112	8	)	)	PUNCT
ejpam-488	112	9	,	,	PUNCT
ejpam-488	112	10	and	and	CCONJ
ejpam-488	112	11	hence	hence	ADV
ejpam-488	112	12	,	,	PUNCT
ejpam-488	112	13	r	r	NOUN
ejpam-488	112	14	≺	≺	NOUN
ejpam-488	112	15	h.	h.	NOUN
ejpam-488	112	16	we	we	PRON
ejpam-488	112	17	note	note	VERB
ejpam-488	112	18	also	also	ADV
ejpam-488	112	19	that	that	SCONJ
ejpam-488	112	20	q	q	PUNCT
ejpam-488	112	21	∑	∑	PUNCT
ejpam-488	112	22	j=1	j=1	ADJ
ejpam-488	112	23	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	112	24	j(z	j(z	PROPN
ejpam-488	112	25	)	)	PUNCT
ejpam-488	112	26	=	=	SYM
ejpam-488	112	27	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	112	28	λ	λ	NOUN
ejpam-488	112	29	+	+	NOUN
ejpam-488	112	30	1	1	NUM
ejpam-488	112	31	z(1−λ+ℓ)/λ	z(1−λ+ℓ)/λ	NOUN
ejpam-488	112	32	z	z	NOUN
ejpam-488	112	33	∫	∫	PROPN
ejpam-488	112	34	0	0	NUM
ejpam-488	112	35	t	t	PROPN
ejpam-488	112	36	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	112	37	λ	λ	NOUN
ejpam-488	112	38	−1	−1	NOUN
ejpam-488	112	39	q	q	NOUN
ejpam-488	112	40	∑	∑	PUNCT
ejpam-488	112	41	j=1	j=1	PROPN
ejpam-488	112	42	im+1(λ,ℓ)g	im+1(λ,ℓ)g	PROPN
ejpam-488	112	43	j(t)d	j(t)d	PROPN
ejpam-488	112	44	t	t	PROPN
ejpam-488	112	45	.	.	PUNCT
ejpam-488	113	1	thus	thus	ADV
ejpam-488	113	2	,	,	PUNCT
ejpam-488	113	3	by	by	ADP
ejpam-488	113	4	applying	apply	VERB
ejpam-488	113	5	lemma	lemma	PROPN
ejpam-488	113	6	a	a	PRON
ejpam-488	113	7	of	of	ADP
ejpam-488	113	8	[	[	X
ejpam-488	113	9	12	12	NUM
ejpam-488	113	10	]	]	PUNCT
ejpam-488	113	11	,	,	PUNCT
ejpam-488	113	12	we	we	PRON
ejpam-488	113	13	conclude	conclude	VERB
ejpam-488	113	14	that	that	PRON
ejpam-488	113	15	q	q	PUNCT
ejpam-488	113	16	∑	∑	PUNCT
ejpam-488	113	17	j=1	j=1	NOUN
ejpam-488	113	18	1	1	NUM
ejpam-488	113	19	z	z	NOUN
ejpam-488	113	20	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	113	21	j(z	j(z	PROPN
ejpam-488	113	22	)	)	PUNCT
ejpam-488	113	23	6=	6=	ADP
ejpam-488	113	24	0	0	NUM
ejpam-488	114	1	(	(	PUNCT
ejpam-488	114	2	z	z	NOUN
ejpam-488	114	3	∈	∈	PROPN
ejpam-488	114	4	u	u	NOUN
ejpam-488	114	5	)	)	PUNCT
ejpam-488	114	6	.	.	PUNCT
ejpam-488	115	1	this	this	PRON
ejpam-488	115	2	evidently	evidently	ADV
ejpam-488	115	3	completes	complete	VERB
ejpam-488	115	4	the	the	DET
ejpam-488	115	5	proof	proof	NOUN
ejpam-488	115	6	of	of	ADP
ejpam-488	115	7	proposition	proposition	NOUN
ejpam-488	115	8	1	1	NUM
ejpam-488	115	9	.	.	PUNCT
ejpam-488	115	10	proposition	proposition	NOUN
ejpam-488	115	11	2	2	NUM
ejpam-488	115	12	.	.	PUNCT
ejpam-488	116	1	if	if	SCONJ
ejpam-488	116	2	g1	g1	NOUN
ejpam-488	116	3	,	,	PUNCT
ejpam-488	116	4	...	...	PUNCT
ejpam-488	116	5	,	,	PUNCT
ejpam-488	116	6	gq	gq	PROPN
ejpam-488	116	7	∈	∈	PROPN
ejpam-488	116	8	ωm	ωm	VERB
ejpam-488	116	9	,	,	PUNCT
ejpam-488	116	10	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	116	11	;	;	PUNCT
ejpam-488	116	12	a	a	DET
ejpam-488	116	13	,	,	PUNCT
ejpam-488	116	14	b	b	NOUN
ejpam-488	116	15	)	)	PUNCT
ejpam-488	116	16	,	,	PUNCT
ejpam-488	116	17	then	then	ADV
ejpam-488	116	18	fc(g1	fc(g1	NOUN
ejpam-488	116	19	)	)	PUNCT
ejpam-488	116	20	,	,	PUNCT
ejpam-488	116	21	...	...	PUNCT
ejpam-488	116	22	,	,	PUNCT
ejpam-488	116	23	fc(gq	fc(gq	PROPN
ejpam-488	116	24	)	)	PUNCT
ejpam-488	116	25	∈	∈	PROPN
ejpam-488	117	1	ωm	ωm	VERB
ejpam-488	117	2	,	,	PUNCT
ejpam-488	117	3	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	117	4	;	;	PUNCT
ejpam-488	117	5	a	a	DET
ejpam-488	117	6	,	,	PUNCT
ejpam-488	117	7	b	b	NOUN
ejpam-488	117	8	)	)	PUNCT
ejpam-488	117	9	,	,	PUNCT
ejpam-488	117	10	where	where	SCONJ
ejpam-488	117	11	fc	fc	PROPN
ejpam-488	117	12	is	be	AUX
ejpam-488	117	13	the	the	DET
ejpam-488	117	14	integral	integral	ADJ
ejpam-488	117	15	operator	operator	NOUN
ejpam-488	117	16	defined	define	VERB
ejpam-488	117	17	by	by	ADP
ejpam-488	117	18	fc(gi	fc(gi	PROPN
ejpam-488	117	19	)	)	PUNCT
ejpam-488	118	1	=	=	SYM
ejpam-488	118	2	fc(gi)(z	fc(gi)(z	NOUN
ejpam-488	118	3	)	)	PUNCT
ejpam-488	118	4	=	=	PUNCT
ejpam-488	119	1	c	c	NOUN
ejpam-488	119	2	+	+	NOUN
ejpam-488	119	3	1	1	NUM
ejpam-488	119	4	zc	zc	NOUN
ejpam-488	119	5	z	z	PROPN
ejpam-488	119	6	∫	∫	PROPN
ejpam-488	119	7	0	0	PROPN
ejpam-488	120	1	t	t	PROPN
ejpam-488	120	2	c−1	c−1	PROPN
ejpam-488	120	3	gi(t)d	gi(t)d	VERB
ejpam-488	120	4	t	t	PROPN
ejpam-488	120	5	(	(	PUNCT
ejpam-488	120	6	i	i	NOUN
ejpam-488	120	7	=	=	NOUN
ejpam-488	120	8	1	1	NUM
ejpam-488	120	9	,	,	PUNCT
ejpam-488	120	10	...	...	PUNCT
ejpam-488	120	11	,	,	PUNCT
ejpam-488	120	12	q	q	X
ejpam-488	120	13	,	,	PUNCT
ejpam-488	120	14	c	c	X
ejpam-488	120	15	≥	≥	NOUN
ejpam-488	120	16	0	0	NUM
ejpam-488	120	17	)	)	PUNCT
ejpam-488	120	18	.	.	PUNCT
ejpam-488	121	1	(	(	PUNCT
ejpam-488	121	2	13	13	NUM
ejpam-488	121	3	)	)	PUNCT
ejpam-488	121	4	proof	proof	NOUN
ejpam-488	121	5	.	.	PUNCT
ejpam-488	122	1	from	from	ADP
ejpam-488	122	2	(	(	PUNCT
ejpam-488	122	3	13	13	NUM
ejpam-488	122	4	)	)	PUNCT
ejpam-488	122	5	,	,	PUNCT
ejpam-488	122	6	we	we	PRON
ejpam-488	122	7	have	have	VERB
ejpam-488	122	8	z(im(λ,ℓ)fc(gi)(z	z(im(λ,ℓ)fc(gi)(z	NOUN
ejpam-488	122	9	)	)	PUNCT
ejpam-488	122	10	)	)	PUNCT
ejpam-488	123	1	′	′	NUM
ejpam-488	124	1	=	=	PUNCT
ejpam-488	124	2	(	(	PUNCT
ejpam-488	124	3	c	c	X
ejpam-488	124	4	+	+	NOUN
ejpam-488	125	1	1)im(λ,ℓ)gi(z)−	1)im(λ,ℓ)gi(z)−	NUM
ejpam-488	125	2	cim(λ,ℓ)fc(gi)(z	cim(λ,ℓ)fc(gi)(z	NOUN
ejpam-488	125	3	)	)	PUNCT
ejpam-488	125	4	.	.	PUNCT
ejpam-488	126	1	(	(	PUNCT
ejpam-488	126	2	14	14	X
ejpam-488	126	3	)	)	PUNCT
ejpam-488	126	4	let	let	VERB
ejpam-488	126	5	pi(z	pi(z	NOUN
ejpam-488	126	6	)	)	PUNCT
ejpam-488	126	7	=	=	SYM
ejpam-488	126	8	z(im(λ,ℓ)fc(gi)(z	z(im(λ,ℓ)fc(gi)(z	PROPN
ejpam-488	126	9	)	)	PUNCT
ejpam-488	126	10	)	)	PUNCT
ejpam-488	127	1	′	′	NUM
ejpam-488	127	2	�	�	PROPN
ejpam-488	127	3	1	1	NUM
ejpam-488	127	4	q	q	PROPN
ejpam-488	127	5	�	�	PROPN
ejpam-488	127	6	q	q	PROPN
ejpam-488	127	7	∑	∑	PROPN
ejpam-488	127	8	j=1	j=1	PROPN
ejpam-488	127	9	im(λ,ℓ)fc(g	im(λ,ℓ)fc(g	NOUN
ejpam-488	127	10	j)(z	j)(z	PUNCT
ejpam-488	127	11	)	)	PUNCT
ejpam-488	127	12	(	(	PUNCT
ejpam-488	127	13	i	i	NOUN
ejpam-488	127	14	=	=	NOUN
ejpam-488	127	15	1	1	NUM
ejpam-488	127	16	,	,	PUNCT
ejpam-488	127	17	...	...	PUNCT
ejpam-488	127	18	,	,	PUNCT
ejpam-488	127	19	q	q	NOUN
ejpam-488	127	20	)	)	PUNCT
ejpam-488	127	21	.	.	PUNCT
ejpam-488	128	1	m.	m.	PROPN
ejpam-488	128	2	aouf	aouf	PROPN
ejpam-488	128	3	,	,	PUNCT
ejpam-488	128	4	a.	a.	NOUN
ejpam-488	128	5	shamandy	shamandy	PROPN
ejpam-488	128	6	,	,	PUNCT
ejpam-488	128	7	r.	r.	PROPN
ejpam-488	128	8	el	el	PROPN
ejpam-488	128	9	-	-	PUNCT
ejpam-488	128	10	ashway	ashway	PROPN
ejpam-488	128	11	,	,	PUNCT
ejpam-488	128	12	e.	e.	PROPN
ejpam-488	128	13	ali	ali	PROPN
ejpam-488	128	14	/	/	SYM
ejpam-488	128	15	eur	eur	PROPN
ejpam-488	128	16	.	.	PUNCT
ejpam-488	129	1	j.	j.	PROPN
ejpam-488	129	2	pure	pure	PROPN
ejpam-488	129	3	appl	appl	PROPN
ejpam-488	129	4	.	.	PROPN
ejpam-488	129	5	math	math	PROPN
ejpam-488	129	6	,	,	PUNCT
ejpam-488	129	7	3	3	NUM
ejpam-488	129	8	(	(	PUNCT
ejpam-488	129	9	2010	2010	NUM
ejpam-488	129	10	)	)	PUNCT
ejpam-488	129	11	,	,	PUNCT
ejpam-488	129	12	317	317	NUM
ejpam-488	129	13	-	-	SYM
ejpam-488	129	14	330	330	NUM
ejpam-488	129	15	322	322	NUM
ejpam-488	129	16	then	then	ADV
ejpam-488	129	17	by	by	ADP
ejpam-488	129	18	using	use	VERB
ejpam-488	129	19	(	(	PUNCT
ejpam-488	129	20	14	14	NUM
ejpam-488	129	21	)	)	PUNCT
ejpam-488	129	22	,	,	PUNCT
ejpam-488	129	23	we	we	PRON
ejpam-488	129	24	obtain	obtain	VERB
ejpam-488	129	25	�	�	PROPN
ejpam-488	129	26	1	1	NUM
ejpam-488	129	27	q	q	PROPN
ejpam-488	129	28	�	�	PROPN
ejpam-488	129	29	q	q	PROPN
ejpam-488	129	30	∑	∑	PROPN
ejpam-488	129	31	j=1	j=1	PROPN
ejpam-488	129	32	(	(	PUNCT
ejpam-488	129	33	im(λ,ℓ)fc(g	im(λ,ℓ)fc(g	NOUN
ejpam-488	129	34	j)(z))pi(z	j)(z))pi(z	NUM
ejpam-488	129	35	)	)	PUNCT
ejpam-488	129	36	+	+	CCONJ
ejpam-488	129	37	cim(λ,ℓ)fc(gi)(z	cim(λ,ℓ)fc(gi)(z	NOUN
ejpam-488	129	38	)	)	PUNCT
ejpam-488	129	39	=	=	PUNCT
ejpam-488	130	1	(	(	PUNCT
ejpam-488	130	2	c	c	NOUN
ejpam-488	130	3	+	+	X
ejpam-488	130	4	1)im+1(λ,ℓ)gi(z	1)im+1(λ,ℓ)gi(z	NUM
ejpam-488	130	5	)	)	PUNCT
ejpam-488	130	6	.	.	PUNCT
ejpam-488	131	1	(	(	PUNCT
ejpam-488	131	2	15	15	X
ejpam-488	131	3	)	)	PUNCT
ejpam-488	131	4	differentiating	differentiate	VERB
ejpam-488	131	5	both	both	DET
ejpam-488	131	6	sides	side	NOUN
ejpam-488	131	7	of	of	ADP
ejpam-488	131	8	(	(	PUNCT
ejpam-488	131	9	15	15	NUM
ejpam-488	131	10	)	)	PUNCT
ejpam-488	131	11	with	with	ADP
ejpam-488	131	12	respect	respect	NOUN
ejpam-488	131	13	to	to	ADP
ejpam-488	131	14	z	z	NOUN
ejpam-488	131	15	,	,	PUNCT
ejpam-488	131	16	and	and	CCONJ
ejpam-488	131	17	simplifying	simplify	VERB
ejpam-488	131	18	,	,	PUNCT
ejpam-488	131	19	we	we	PRON
ejpam-488	131	20	obtain	obtain	VERB
ejpam-488	131	21	pi(z	pi(z	NOUN
ejpam-488	131	22	)	)	PUNCT
ejpam-488	132	1	+	+	CCONJ
ejpam-488	132	2	zp	zp	NOUN
ejpam-488	132	3	′	′	NUM
ejpam-488	132	4	i(z	i(z	NOUN
ejpam-488	132	5	)	)	PUNCT
ejpam-488	132	6	�	�	PROPN
ejpam-488	132	7	1	1	NUM
ejpam-488	132	8	q	q	PROPN
ejpam-488	132	9	�	�	PROPN
ejpam-488	132	10	q	q	PROPN
ejpam-488	132	11	∑	∑	PROPN
ejpam-488	132	12	j=1	j=1	NOUN
ejpam-488	132	13	pi(z	pi(z	PUNCT
ejpam-488	132	14	)	)	PUNCT
ejpam-488	133	1	+	+	NUM
ejpam-488	133	2	c	c	NOUN
ejpam-488	133	3	=	=	SYM
ejpam-488	133	4	z(im(λ,ℓ)gi(z	z(im(λ,ℓ)gi(z	PROPN
ejpam-488	133	5	)	)	PUNCT
ejpam-488	133	6	)	)	PUNCT
ejpam-488	134	1	′	′	NUM
ejpam-488	134	2	�	�	PROPN
ejpam-488	134	3	1	1	NUM
ejpam-488	134	4	q	q	PROPN
ejpam-488	134	5	�	�	PROPN
ejpam-488	134	6	q	q	PROPN
ejpam-488	134	7	∑	∑	PROPN
ejpam-488	134	8	j=1	j=1	ADJ
ejpam-488	134	9	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	134	10	j(z	j(z	PROPN
ejpam-488	134	11	)	)	PUNCT
ejpam-488	134	12	.	.	PUNCT
ejpam-488	135	1	then	then	ADV
ejpam-488	135	2	,	,	PUNCT
ejpam-488	135	3	by	by	ADP
ejpam-488	135	4	the	the	DET
ejpam-488	135	5	same	same	ADJ
ejpam-488	135	6	arguments	argument	NOUN
ejpam-488	135	7	as	as	ADP
ejpam-488	135	8	in	in	ADP
ejpam-488	135	9	the	the	DET
ejpam-488	135	10	proof	proof	NOUN
ejpam-488	135	11	of	of	ADP
ejpam-488	135	12	proposition	proposition	NOUN
ejpam-488	135	13	1	1	NUM
ejpam-488	135	14	,	,	PUNCT
ejpam-488	135	15	it	it	PRON
ejpam-488	135	16	follows	follow	VERB
ejpam-488	135	17	that	that	SCONJ
ejpam-488	135	18	proposition	proposition	NOUN
ejpam-488	135	19	2	2	NUM
ejpam-488	135	20	holds	hold	VERB
ejpam-488	135	21	true	true	ADJ
ejpam-488	135	22	as	as	SCONJ
ejpam-488	135	23	stated	state	VERB
ejpam-488	135	24	.	.	PUNCT
ejpam-488	136	1	remark	remark	PROPN
ejpam-488	136	2	1	1	NUM
ejpam-488	136	3	.	.	PUNCT
ejpam-488	137	1	(	(	PUNCT
ejpam-488	137	2	i	i	NOUN
ejpam-488	137	3	)	)	PUNCT
ejpam-488	137	4	putting	put	VERB
ejpam-488	137	5	m	m	NOUN
ejpam-488	137	6	=	=	PUNCT
ejpam-488	137	7	ℓ	ℓ	X
ejpam-488	137	8	=	=	PUNCT
ejpam-488	137	9	0,λ	0,λ	NOUN
ejpam-488	138	1	=	=	SYM
ejpam-488	138	2	1	1	NUM
ejpam-488	138	3	and	and	CCONJ
ejpam-488	138	4	gi(z	gi(z	NOUN
ejpam-488	138	5	)	)	PUNCT
ejpam-488	139	1	=	=	PUNCT
ejpam-488	140	1	w−1	w−1	PROPN
ejpam-488	140	2	f	f	X
ejpam-488	140	3	(	(	PUNCT
ejpam-488	140	4	w	w	PROPN
ejpam-488	140	5	iz	iz	NOUN
ejpam-488	140	6	)	)	PUNCT
ejpam-488	140	7	(	(	PUNCT
ejpam-488	140	8	f	f	PROPN
ejpam-488	140	9	∈	∈	PROPN
ejpam-488	140	10	a	a	PRON
ejpam-488	140	11	;	;	PUNCT
ejpam-488	141	1	i	i	NOUN
ejpam-488	141	2	=	=	NOUN
ejpam-488	141	3	1	1	NUM
ejpam-488	141	4	,	,	PUNCT
ejpam-488	141	5	...	...	PUNCT
ejpam-488	141	6	,	,	PUNCT
ejpam-488	141	7	q	q	NOUN
ejpam-488	141	8	;	;	PUNCT
ejpam-488	141	9	w	w	X
ejpam-488	141	10	=	=	PUNCT
ejpam-488	141	11	e	e	NOUN
ejpam-488	141	12	2πi	2πi	NOUN
ejpam-488	141	13	q	q	X
ejpam-488	141	14	)	)	PUNCT
ejpam-488	141	15	in	in	ADP
ejpam-488	141	16	proposition	proposition	NOUN
ejpam-488	141	17	2	2	NUM
ejpam-488	141	18	,	,	PUNCT
ejpam-488	141	19	we	we	PRON
ejpam-488	141	20	obtain	obtain	VERB
ejpam-488	141	21	the	the	DET
ejpam-488	141	22	result	result	NOUN
ejpam-488	141	23	obtained	obtain	VERB
ejpam-488	141	24	by	by	ADP
ejpam-488	141	25	mocanu	mocanu	NOUN
ejpam-488	142	1	[	[	X
ejpam-488	142	2	12	12	NUM
ejpam-488	142	3	]	]	X
ejpam-488	142	4	;	;	PUNCT
ejpam-488	142	5	(	(	PUNCT
ejpam-488	142	6	ii	ii	NOUN
ejpam-488	142	7	)	)	PUNCT
ejpam-488	142	8	putting	put	VERB
ejpam-488	142	9	m	m	NOUN
ejpam-488	142	10	=	=	PUNCT
ejpam-488	142	11	ℓ	ℓ	X
ejpam-488	142	12	=	=	PUNCT
ejpam-488	142	13	0,λ	0,λ	NOUN
ejpam-488	143	1	=	=	PUNCT
ejpam-488	143	2	1,q	1,q	NUM
ejpam-488	143	3	=	=	SYM
ejpam-488	143	4	2	2	NUM
ejpam-488	143	5	,	,	PUNCT
ejpam-488	143	6	g1(z	g1(z	NOUN
ejpam-488	143	7	)	)	PUNCT
ejpam-488	143	8	=	=	SYM
ejpam-488	143	9	f	f	X
ejpam-488	143	10	(	(	PUNCT
ejpam-488	143	11	z	z	NOUN
ejpam-488	143	12	)	)	PUNCT
ejpam-488	143	13	,	,	PUNCT
ejpam-488	143	14	and	and	CCONJ
ejpam-488	143	15	g2(z	g2(z	PROPN
ejpam-488	143	16	)	)	PUNCT
ejpam-488	143	17	=	=	SYM
ejpam-488	144	1	−	−	PROPN
ejpam-488	144	2	f	f	X
ejpam-488	144	3	(	(	PUNCT
ejpam-488	144	4	−z	−z	NOUN
ejpam-488	144	5	)	)	PUNCT
ejpam-488	144	6	in	in	ADP
ejpam-488	144	7	proposition	proposition	NOUN
ejpam-488	144	8	2	2	NUM
ejpam-488	144	9	,	,	PUNCT
ejpam-488	144	10	we	we	PRON
ejpam-488	144	11	obtain	obtain	VERB
ejpam-488	144	12	the	the	DET
ejpam-488	144	13	result	result	NOUN
ejpam-488	144	14	obtained	obtain	VERB
ejpam-488	144	15	by	by	ADP
ejpam-488	144	16	padmanabhan	padmanabhan	NOUN
ejpam-488	144	17	and	and	CCONJ
ejpam-488	144	18	thangamani	thangamani	NOUN
ejpam-488	144	19	[	[	X
ejpam-488	144	20	16	16	NUM
ejpam-488	144	21	]	]	X
ejpam-488	144	22	,	,	PUNCT
ejpam-488	144	23	which	which	PRON
ejpam-488	144	24	(	(	PUNCT
ejpam-488	144	25	in	in	ADP
ejpam-488	144	26	turn	turn	NOUN
ejpam-488	144	27	)	)	PUNCT
ejpam-488	144	28	includes	include	VERB
ejpam-488	144	29	the	the	DET
ejpam-488	144	30	result	result	NOUN
ejpam-488	144	31	given	give	VERB
ejpam-488	144	32	by	by	ADP
ejpam-488	144	33	das	das	PROPN
ejpam-488	144	34	and	and	CCONJ
ejpam-488	144	35	singh	singh	NOUN
ejpam-488	145	1	[	[	X
ejpam-488	145	2	6	6	NUM
ejpam-488	145	3	]	]	PUNCT
ejpam-488	145	4	as	as	ADP
ejpam-488	145	5	a	a	DET
ejpam-488	145	6	special	special	ADJ
ejpam-488	145	7	case	case	NOUN
ejpam-488	145	8	.	.	PUNCT
ejpam-488	146	1	next	next	ADV
ejpam-488	146	2	,	,	PUNCT
ejpam-488	146	3	we	we	PRON
ejpam-488	146	4	prove	prove	VERB
ejpam-488	146	5	the	the	DET
ejpam-488	146	6	following	follow	VERB
ejpam-488	146	7	theorem	theorem	VERB
ejpam-488	146	8	.	.	PUNCT
ejpam-488	146	9	theorem	theorem	NOUN
ejpam-488	146	10	1	1	NUM
ejpam-488	146	11	.	.	PUNCT
ejpam-488	147	1	let	let	VERB
ejpam-488	147	2	f	f	PROPN
ejpam-488	147	3	∈	∈	PROPN
ejpam-488	147	4	a	a	PRON
ejpam-488	147	5	and	and	CCONJ
ejpam-488	147	6	0	0	NUM
ejpam-488	147	7	<	<	X
ejpam-488	147	8	δ1	δ1	NOUN
ejpam-488	147	9	,	,	PUNCT
ejpam-488	147	10	δ2	δ2	ADJ
ejpam-488	147	11	≤	≤	NOUN
ejpam-488	147	12	1	1	NUM
ejpam-488	147	13	.	.	PUNCT
ejpam-488	148	1	if	if	SCONJ
ejpam-488	148	2	−	−	PROPN
ejpam-488	148	3	π	π	PROPN
ejpam-488	148	4	2	2	NUM
ejpam-488	148	5	δ1	δ1	NOUN
ejpam-488	148	6	<	<	X
ejpam-488	148	7	arg	arg	NOUN
ejpam-488	148	8			PROPN
ejpam-488	148	9			NOUN
ejpam-488	148	10			NOUN
ejpam-488	148	11			NOUN
ejpam-488	148	12			NOUN
ejpam-488	148	13			NOUN
ejpam-488	148	14	z(im+1(λ,ℓ	z(im+1(λ,ℓ	NOUN
ejpam-488	148	15	)	)	PUNCT
ejpam-488	148	16	f	f	NOUN
ejpam-488	148	17	(	(	PUNCT
ejpam-488	148	18	z	z	NOUN
ejpam-488	148	19	)	)	PUNCT
ejpam-488	148	20	)	)	PUNCT
ejpam-488	148	21	′	′	NUM
ejpam-488	148	22	�	�	PROPN
ejpam-488	148	23	1	1	NUM
ejpam-488	148	24	q	q	PROPN
ejpam-488	148	25	�	�	PROPN
ejpam-488	148	26	q	q	PROPN
ejpam-488	148	27	∑	∑	PROPN
ejpam-488	148	28	j=1	j=1	PROPN
ejpam-488	148	29	im+1(λ,ℓ)g	im+1(λ,ℓ)g	PROPN
ejpam-488	148	30	j(z	j(z	PROPN
ejpam-488	148	31	)	)	PUNCT
ejpam-488	148	32			PROPN
ejpam-488	149	1			NOUN
ejpam-488	149	2			VERB
ejpam-488	149	3			NOUN
ejpam-488	149	4			NOUN
ejpam-488	149	5			PUNCT
ejpam-488	150	1	<	<	X
ejpam-488	150	2	π	π	X
ejpam-488	150	3	2	2	NUM
ejpam-488	150	4	δ2	δ2	VERB
ejpam-488	150	5	,	,	PUNCT
ejpam-488	150	6	where	where	SCONJ
ejpam-488	150	7	g1	g1	PROPN
ejpam-488	150	8	,	,	PUNCT
ejpam-488	150	9	...	...	PUNCT
ejpam-488	150	10	,	,	PUNCT
ejpam-488	150	11	gq	gq	PROPN
ejpam-488	150	12	∈	∈	PROPN
ejpam-488	150	13	ωm+1,λ,ℓ(q	ωm+1,λ,ℓ(q	PROPN
ejpam-488	150	14	;	;	PUNCT
ejpam-488	150	15	a	a	DET
ejpam-488	150	16	,	,	PUNCT
ejpam-488	150	17	b	b	NOUN
ejpam-488	150	18	)	)	PUNCT
ejpam-488	150	19	,	,	PUNCT
ejpam-488	150	20	then	then	ADV
ejpam-488	150	21	−	−	PROPN
ejpam-488	150	22	π	π	PROPN
ejpam-488	150	23	2	2	NUM
ejpam-488	150	24	α1	α1	PROPN
ejpam-488	150	25	<	<	X
ejpam-488	150	26	arg	arg	NOUN
ejpam-488	150	27			PROPN
ejpam-488	150	28			NOUN
ejpam-488	150	29			NOUN
ejpam-488	150	30			NOUN
ejpam-488	150	31			NOUN
ejpam-488	150	32			NOUN
ejpam-488	150	33	z(im(λ,ℓ	z(im(λ,ℓ	NUM
ejpam-488	150	34	)	)	PUNCT
ejpam-488	150	35	f	f	PROPN
ejpam-488	150	36	(	(	PUNCT
ejpam-488	150	37	z	z	NOUN
ejpam-488	150	38	)	)	PUNCT
ejpam-488	150	39	)	)	PUNCT
ejpam-488	151	1	′	′	NUM
ejpam-488	151	2	�	�	PROPN
ejpam-488	151	3	1	1	NUM
ejpam-488	151	4	q	q	PROPN
ejpam-488	151	5	�	�	PROPN
ejpam-488	151	6	q	q	PROPN
ejpam-488	151	7	∑	∑	PROPN
ejpam-488	151	8	j=1	j=1	ADJ
ejpam-488	151	9	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	151	10	j(z	j(z	PROPN
ejpam-488	151	11	)	)	PUNCT
ejpam-488	151	12			PROPN
ejpam-488	151	13			NOUN
ejpam-488	151	14			VERB
ejpam-488	151	15			NOUN
ejpam-488	151	16			NOUN
ejpam-488	151	17			PUNCT
ejpam-488	152	1	<	<	X
ejpam-488	152	2	π	π	X
ejpam-488	152	3	2	2	NUM
ejpam-488	152	4	α2	α2	ADJ
ejpam-488	152	5	,	,	PUNCT
ejpam-488	152	6	where	where	SCONJ
ejpam-488	152	7	α1	α1	PROPN
ejpam-488	152	8	and	and	CCONJ
ejpam-488	152	9	α2	α2	PROPN
ejpam-488	152	10	(	(	PUNCT
ejpam-488	152	11	0	0	NUM
ejpam-488	152	12	<	<	X
ejpam-488	152	13	α1	α1	PROPN
ejpam-488	152	14	,	,	PUNCT
ejpam-488	152	15	α2	α2	ADJ
ejpam-488	152	16	≤	≤	NOUN
ejpam-488	152	17	1	1	NUM
ejpam-488	152	18	)	)	PUNCT
ejpam-488	152	19	are	be	AUX
ejpam-488	152	20	the	the	DET
ejpam-488	152	21	solutions	solution	NOUN
ejpam-488	152	22	of	of	ADP
ejpam-488	152	23	the	the	DET
ejpam-488	152	24	following	follow	VERB
ejpam-488	152	25	equations	equation	NOUN
ejpam-488	152	26	:	:	PUNCT
ejpam-488	152	27	δ1	δ1	NOUN
ejpam-488	152	28	=	=	PUNCT
ejpam-488	152	29			PROPN
ejpam-488	152	30			ADP
ejpam-488	152	31			ADJ
ejpam-488	152	32	α1	α1	PROPN
ejpam-488	152	33	+	+	CCONJ
ejpam-488	152	34	�	�	PROPN
ejpam-488	152	35	2	2	NUM
ejpam-488	152	36	π	π	PROPN
ejpam-488	152	37	�	�	PROPN
ejpam-488	152	38	tan−1	tan−1	PROPN
ejpam-488	152	39	�	�	PROPN
ejpam-488	152	40	(	(	PUNCT
ejpam-488	152	41	α1+α2)(1−|a|	α1+α2)(1−|a|	NOUN
ejpam-488	152	42	)	)	PUNCT
ejpam-488	152	43	cos	cos	PROPN
ejpam-488	152	44	�	�	PROPN
ejpam-488	152	45	π	π	PROPN
ejpam-488	152	46	2	2	NUM
ejpam-488	152	47	�	�	PROPN
ejpam-488	152	48	t1	t1	NOUN
ejpam-488	152	49	2	2	NUM
ejpam-488	152	50	�	�	PROPN
ejpam-488	152	51	1+a	1+a	NUM
ejpam-488	152	52	1+b	1+b	NUM
ejpam-488	152	53	+	+	CCONJ
ejpam-488	152	54	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	152	55	λ	λ	X
ejpam-488	152	56	�	�	PROPN
ejpam-488	152	57	(	(	PUNCT
ejpam-488	152	58	1+|a|)+(α1+α2)(1−|a|	1+|a|)+(α1+α2)(1−|a|	NOUN
ejpam-488	152	59	)	)	PUNCT
ejpam-488	152	60	sin	sin	NOUN
ejpam-488	152	61	�	�	PROPN
ejpam-488	152	62	π	π	PROPN
ejpam-488	152	63	2	2	NUM
ejpam-488	152	64	�	�	PROPN
ejpam-488	152	65	t1	t1	NUM
ejpam-488	152	66	�	�	PROPN
ejpam-488	152	67	(	(	PUNCT
ejpam-488	152	68	b	b	PROPN
ejpam-488	152	69	6=	6=	NUM
ejpam-488	152	70	−1	−1	NOUN
ejpam-488	152	71	)	)	PUNCT
ejpam-488	152	72	,	,	PUNCT
ejpam-488	152	73	α1	α1	PROPN
ejpam-488	152	74	(	(	PUNCT
ejpam-488	152	75	b	b	NOUN
ejpam-488	152	76	=	=	SYM
ejpam-488	152	77	−1	−1	NOUN
ejpam-488	152	78	)	)	PUNCT
ejpam-488	152	79	,	,	PUNCT
ejpam-488	152	80	(	(	PUNCT
ejpam-488	152	81	16	16	X
ejpam-488	152	82	)	)	PUNCT
ejpam-488	152	83	m.	m.	NOUN
ejpam-488	152	84	aouf	aouf	PROPN
ejpam-488	152	85	,	,	PUNCT
ejpam-488	152	86	a.	a.	NOUN
ejpam-488	152	87	shamandy	shamandy	PROPN
ejpam-488	152	88	,	,	PUNCT
ejpam-488	152	89	r.	r.	PROPN
ejpam-488	152	90	el	el	PROPN
ejpam-488	152	91	-	-	PUNCT
ejpam-488	152	92	ashway	ashway	PROPN
ejpam-488	152	93	,	,	PUNCT
ejpam-488	152	94	e.	e.	PROPN
ejpam-488	152	95	ali	ali	PROPN
ejpam-488	152	96	/	/	SYM
ejpam-488	152	97	eur	eur	PROPN
ejpam-488	152	98	.	.	PUNCT
ejpam-488	153	1	j.	j.	PROPN
ejpam-488	153	2	pure	pure	PROPN
ejpam-488	153	3	appl	appl	PROPN
ejpam-488	153	4	.	.	PROPN
ejpam-488	153	5	math	math	PROPN
ejpam-488	153	6	,	,	PUNCT
ejpam-488	153	7	3	3	NUM
ejpam-488	153	8	(	(	PUNCT
ejpam-488	153	9	2010	2010	NUM
ejpam-488	153	10	)	)	PUNCT
ejpam-488	153	11	,	,	PUNCT
ejpam-488	153	12	317	317	NUM
ejpam-488	153	13	-	-	SYM
ejpam-488	153	14	330	330	NUM
ejpam-488	153	15	323	323	NUM
ejpam-488	153	16	and	and	CCONJ
ejpam-488	153	17	δ2	δ2	VERB
ejpam-488	153	18	=	=	PUNCT
ejpam-488	153	19			PROPN
ejpam-488	153	20			ADP
ejpam-488	153	21			ADJ
ejpam-488	153	22	α2	α2	PROPN
ejpam-488	153	23	+	+	CCONJ
ejpam-488	153	24	�	�	PROPN
ejpam-488	153	25	2	2	NUM
ejpam-488	153	26	π	π	PROPN
ejpam-488	153	27	�	�	PROPN
ejpam-488	153	28	tan−1	tan−1	PROPN
ejpam-488	153	29	�	�	PROPN
ejpam-488	153	30	(	(	PUNCT
ejpam-488	153	31	α1+α2)(1−|a|	α1+α2)(1−|a|	NOUN
ejpam-488	153	32	)	)	PUNCT
ejpam-488	153	33	cos	cos	PROPN
ejpam-488	153	34	�	�	PROPN
ejpam-488	153	35	π	π	PROPN
ejpam-488	153	36	2	2	NUM
ejpam-488	153	37	�	�	PROPN
ejpam-488	153	38	t1	t1	NOUN
ejpam-488	153	39	2	2	NUM
ejpam-488	153	40	�	�	PROPN
ejpam-488	153	41	1+a	1+a	NUM
ejpam-488	153	42	1+b	1+b	NUM
ejpam-488	153	43	+	+	CCONJ
ejpam-488	153	44	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	153	45	λ	λ	X
ejpam-488	153	46	�	�	PROPN
ejpam-488	153	47	(	(	PUNCT
ejpam-488	153	48	1+|a|)+(α1+α2)(1−|a|	1+|a|)+(α1+α2)(1−|a|	NOUN
ejpam-488	153	49	)	)	PUNCT
ejpam-488	153	50	sin	sin	NOUN
ejpam-488	153	51	�	�	PROPN
ejpam-488	153	52	π	π	PROPN
ejpam-488	153	53	2	2	NUM
ejpam-488	153	54	�	�	PROPN
ejpam-488	153	55	t1	t1	NUM
ejpam-488	153	56	�	�	PROPN
ejpam-488	153	57	(	(	PUNCT
ejpam-488	153	58	b	b	PROPN
ejpam-488	153	59	6=	6=	NUM
ejpam-488	153	60	−1	−1	NOUN
ejpam-488	153	61	)	)	PUNCT
ejpam-488	153	62	,	,	PUNCT
ejpam-488	153	63	α2	α2	PROPN
ejpam-488	153	64	(	(	PUNCT
ejpam-488	153	65	b	b	NOUN
ejpam-488	153	66	=	=	SYM
ejpam-488	153	67	−1	−1	NOUN
ejpam-488	153	68	)	)	PUNCT
ejpam-488	153	69	,	,	PUNCT
ejpam-488	153	70	(	(	PUNCT
ejpam-488	153	71	17	17	NUM
ejpam-488	153	72	)	)	PUNCT
ejpam-488	153	73	a	a	PRON
ejpam-488	153	74	being	be	AUX
ejpam-488	153	75	given	give	VERB
ejpam-488	153	76	by	by	ADP
ejpam-488	153	77	(	(	PUNCT
ejpam-488	153	78	9	9	NUM
ejpam-488	153	79	)	)	PUNCT
ejpam-488	153	80	,	,	PUNCT
ejpam-488	153	81	and	and	CCONJ
ejpam-488	153	82	t1	t1	NOUN
ejpam-488	153	83	=	=	SYM
ejpam-488	153	84	2	2	NUM
ejpam-488	153	85	π	π	NOUN
ejpam-488	153	86	sin−1	sin−1	PROPN
ejpam-488	153	87	a−	a−	PROPN
ejpam-488	153	88	b	b	PROPN
ejpam-488	153	89	1−	1−	NUM
ejpam-488	153	90	ab+	ab+	NOUN
ejpam-488	153	91	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	153	92	λ	λ	NOUN
ejpam-488	153	93	(	(	PUNCT
ejpam-488	153	94	1−	1−	NUM
ejpam-488	153	95	b2	b2	NOUN
ejpam-488	153	96	)	)	PUNCT
ejpam-488	153	97	!	!	PUNCT
ejpam-488	153	98	.	.	PUNCT
ejpam-488	154	1	(	(	PUNCT
ejpam-488	154	2	18	18	NUM
ejpam-488	154	3	)	)	PUNCT
ejpam-488	154	4	proof	proof	NOUN
ejpam-488	154	5	.	.	PUNCT
ejpam-488	155	1	let	let	VERB
ejpam-488	155	2	p(z	p(z	VERB
ejpam-488	155	3	)	)	PUNCT
ejpam-488	155	4	=	=	SYM
ejpam-488	155	5	z(im(λ,ℓ	z(im(λ,ℓ	NUM
ejpam-488	155	6	)	)	PUNCT
ejpam-488	155	7	f	f	PROPN
ejpam-488	155	8	(	(	PUNCT
ejpam-488	155	9	z	z	NOUN
ejpam-488	155	10	)	)	PUNCT
ejpam-488	155	11	)	)	PUNCT
ejpam-488	156	1	′	′	NUM
ejpam-488	156	2	�	�	PROPN
ejpam-488	156	3	1	1	NUM
ejpam-488	156	4	q	q	PROPN
ejpam-488	156	5	�	�	PROPN
ejpam-488	156	6	q	q	PROPN
ejpam-488	156	7	∑	∑	PROPN
ejpam-488	156	8	j=1	j=1	ADJ
ejpam-488	156	9	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	156	10	j(z	j(z	PROPN
ejpam-488	156	11	)	)	PUNCT
ejpam-488	156	12	and	and	CCONJ
ejpam-488	156	13	q(z	q(z	PROPN
ejpam-488	156	14	)	)	PUNCT
ejpam-488	156	15	=	=	SYM
ejpam-488	156	16	1	1	NUM
ejpam-488	156	17	q	q	NOUN
ejpam-488	156	18	q	q	X
ejpam-488	156	19	∑	∑	PUNCT
ejpam-488	156	20	i=1	i=1	PRON
ejpam-488	156	21	q	q	PUNCT
ejpam-488	156	22	i(z	i(z	PROPN
ejpam-488	156	23	)	)	PUNCT
ejpam-488	156	24	,	,	PUNCT
ejpam-488	156	25	where	where	SCONJ
ejpam-488	156	26	q	q	NOUN
ejpam-488	156	27	i(z	i(z	NOUN
ejpam-488	156	28	)	)	PUNCT
ejpam-488	156	29	=	=	SYM
ejpam-488	156	30	z(im(λ,ℓ)gi(z	z(im(λ,ℓ)gi(z	NOUN
ejpam-488	156	31	)	)	PUNCT
ejpam-488	156	32	)	)	PUNCT
ejpam-488	156	33	′	′	NUM
ejpam-488	156	34	�	�	PROPN
ejpam-488	156	35	1	1	NUM
ejpam-488	156	36	q	q	PROPN
ejpam-488	156	37	�	�	PROPN
ejpam-488	156	38	q	q	PROPN
ejpam-488	156	39	∑	∑	PROPN
ejpam-488	156	40	j=1	j=1	ADJ
ejpam-488	156	41	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	156	42	j(z	j(z	PROPN
ejpam-488	156	43	)	)	PUNCT
ejpam-488	156	44	(	(	PUNCT
ejpam-488	156	45	i	i	NOUN
ejpam-488	156	46	=	=	NOUN
ejpam-488	156	47	1	1	NUM
ejpam-488	156	48	,	,	PUNCT
ejpam-488	156	49	...	...	PUNCT
ejpam-488	156	50	,	,	PUNCT
ejpam-488	156	51	q	q	NOUN
ejpam-488	156	52	)	)	PUNCT
ejpam-488	156	53	.	.	PUNCT
ejpam-488	157	1	using	use	VERB
ejpam-488	157	2	(	(	PUNCT
ejpam-488	157	3	10	10	NUM
ejpam-488	157	4	)	)	PUNCT
ejpam-488	157	5	with	with	ADP
ejpam-488	157	6	gi	gi	NOUN
ejpam-488	157	7	replaced	replace	VERB
ejpam-488	157	8	by	by	ADP
ejpam-488	157	9	f	f	PROPN
ejpam-488	157	10	,	,	PUNCT
ejpam-488	157	11	we	we	PRON
ejpam-488	157	12	have	have	VERB
ejpam-488	157	13	�	�	PROPN
ejpam-488	157	14	1	1	NUM
ejpam-488	157	15	q	q	PROPN
ejpam-488	157	16	�	�	PROPN
ejpam-488	157	17	q	q	PROPN
ejpam-488	157	18	∑	∑	PROPN
ejpam-488	157	19	j=1	j=1	NOUN
ejpam-488	157	20	(	(	PUNCT
ejpam-488	157	21	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	157	22	j(z))p(z	j(z))p(z	NOUN
ejpam-488	157	23	)	)	PUNCT
ejpam-488	158	1	+	+	CCONJ
ejpam-488	158	2	1−λ+	1−λ+	NUM
ejpam-488	158	3	ℓ	ℓ	PROPN
ejpam-488	158	4	λ	λ	PROPN
ejpam-488	158	5	im(λ,ℓ	im(λ,ℓ	NOUN
ejpam-488	158	6	)	)	PUNCT
ejpam-488	158	7	f	f	NOUN
ejpam-488	158	8	(	(	PUNCT
ejpam-488	158	9	z	z	NOUN
ejpam-488	158	10	)	)	PUNCT
ejpam-488	158	11	=	=	SYM
ejpam-488	159	1	1	1	NUM
ejpam-488	159	2	+	+	NUM
ejpam-488	159	3	ℓ	ℓ	PROPN
ejpam-488	159	4	λ	λ	X
ejpam-488	159	5	im+1(λ,ℓ	im+1(λ,ℓ	PROPN
ejpam-488	159	6	)	)	PUNCT
ejpam-488	159	7	f	f	PROPN
ejpam-488	159	8	(	(	PUNCT
ejpam-488	159	9	z	z	NOUN
ejpam-488	159	10	)	)	PUNCT
ejpam-488	159	11	.	.	PUNCT
ejpam-488	160	1	(	(	PUNCT
ejpam-488	160	2	19	19	NUM
ejpam-488	160	3	)	)	PUNCT
ejpam-488	160	4	differentiating	differentiate	VERB
ejpam-488	160	5	(	(	PUNCT
ejpam-488	160	6	19	19	NUM
ejpam-488	160	7	)	)	PUNCT
ejpam-488	160	8	with	with	ADP
ejpam-488	160	9	respect	respect	NOUN
ejpam-488	160	10	to	to	ADP
ejpam-488	160	11	z	z	NOUN
ejpam-488	160	12	,	,	PUNCT
ejpam-488	160	13	and	and	CCONJ
ejpam-488	160	14	simplifying	simplifying	NOUN
ejpam-488	160	15	,	,	PUNCT
ejpam-488	160	16	we	we	PRON
ejpam-488	160	17	obtain	obtain	VERB
ejpam-488	160	18	z(im+1(λ,ℓ	z(im+1(λ,ℓ	NOUN
ejpam-488	160	19	)	)	PUNCT
ejpam-488	160	20	f	f	NOUN
ejpam-488	160	21	(	(	PUNCT
ejpam-488	160	22	z	z	NOUN
ejpam-488	160	23	)	)	PUNCT
ejpam-488	160	24	)	)	PUNCT
ejpam-488	161	1	′	′	NUM
ejpam-488	161	2	�	�	PROPN
ejpam-488	161	3	1	1	NUM
ejpam-488	161	4	q	q	PROPN
ejpam-488	161	5	�	�	PROPN
ejpam-488	161	6	q	q	PROPN
ejpam-488	161	7	∑	∑	PROPN
ejpam-488	161	8	j=1	j=1	PROPN
ejpam-488	161	9	im+1(λ,ℓ)g	im+1(λ,ℓ)g	PUNCT
ejpam-488	161	10	j(z	j(z	PROPN
ejpam-488	161	11	)	)	PUNCT
ejpam-488	161	12	=	=	PUNCT
ejpam-488	161	13	p(z	p(z	NOUN
ejpam-488	161	14	)	)	PUNCT
ejpam-488	162	1	+	+	CCONJ
ejpam-488	162	2	zp	zp	NOUN
ejpam-488	162	3	′	′	NUM
ejpam-488	162	4	(	(	PUNCT
ejpam-488	162	5	z	z	NOUN
ejpam-488	162	6	)	)	PUNCT
ejpam-488	162	7	q(z	q(z	PROPN
ejpam-488	162	8	)	)	PUNCT
ejpam-488	163	1	+	+	CCONJ
ejpam-488	163	2	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	163	3	λ	λ	NOUN
ejpam-488	163	4	.	.	PUNCT
ejpam-488	164	1	since	since	SCONJ
ejpam-488	164	2	g1	g1	PROPN
ejpam-488	164	3	,	,	PUNCT
ejpam-488	164	4	...	...	PUNCT
ejpam-488	164	5	,	,	PUNCT
ejpam-488	164	6	gn	gn	PROPN
ejpam-488	164	7	∈	∈	PROPN
ejpam-488	164	8	ωm+1,λ,ℓ(q	ωm+1,λ,ℓ(q	PROPN
ejpam-488	164	9	;	;	PUNCT
ejpam-488	164	10	a	a	DET
ejpam-488	164	11	,	,	PUNCT
ejpam-488	164	12	b	b	NOUN
ejpam-488	164	13	)	)	PUNCT
ejpam-488	164	14	,	,	PUNCT
ejpam-488	164	15	by	by	ADP
ejpam-488	164	16	proposition	proposition	NOUN
ejpam-488	164	17	1	1	NUM
ejpam-488	164	18	,	,	PUNCT
ejpam-488	164	19	we	we	PRON
ejpam-488	164	20	know	know	VERB
ejpam-488	164	21	that	that	SCONJ
ejpam-488	164	22	g1	g1	PROPN
ejpam-488	164	23	,	,	PUNCT
ejpam-488	164	24	...	...	PUNCT
ejpam-488	164	25	,	,	PUNCT
ejpam-488	164	26	gq	gq	PROPN
ejpam-488	164	27	∈	∈	PROPN
ejpam-488	164	28	ωm	ωm	VERB
ejpam-488	164	29	,	,	PUNCT
ejpam-488	164	30	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	164	31	;	;	PUNCT
ejpam-488	164	32	a	a	DET
ejpam-488	164	33	,	,	PUNCT
ejpam-488	164	34	b	b	NOUN
ejpam-488	164	35	)	)	PUNCT
ejpam-488	164	36	,	,	PUNCT
ejpam-488	164	37	and	and	CCONJ
ejpam-488	164	38	so	so	ADV
ejpam-488	164	39	q(z)≺	q(z)≺	ADV
ejpam-488	164	40	1	1	NUM
ejpam-488	164	41	+	+	NUM
ejpam-488	164	42	az	az	PROPN
ejpam-488	164	43	1	1	NUM
ejpam-488	164	44	+	+	CCONJ
ejpam-488	164	45	bz	bz	PROPN
ejpam-488	164	46	(	(	PUNCT
ejpam-488	164	47	z	z	NOUN
ejpam-488	164	48	∈	∈	PROPN
ejpam-488	164	49	u;−1≤	u;−1≤	NUM
ejpam-488	164	50	b	b	NOUN
ejpam-488	164	51	<	<	X
ejpam-488	164	52	a≤	a≤	DET
ejpam-488	164	53	1	1	NUM
ejpam-488	164	54	)	)	PUNCT
ejpam-488	164	55	.	.	PUNCT
ejpam-488	165	1	hence	hence	ADV
ejpam-488	165	2	,	,	PUNCT
ejpam-488	165	3	we	we	PRON
ejpam-488	165	4	observe	observe	VERB
ejpam-488	165	5	from	from	ADP
ejpam-488	165	6	[	[	X
ejpam-488	165	7	19	19	NUM
ejpam-488	165	8	]	]	PUNCT
ejpam-488	165	9	that	that	SCONJ
ejpam-488	165	10	�	�	PROPN
ejpam-488	165	11	�	�	PROPN
ejpam-488	165	12	�	�	PROPN
ejpam-488	165	13	�	�	PROPN
ejpam-488	165	14	q(z)−	q(z)−	PROPN
ejpam-488	165	15	1−	1−	NUM
ejpam-488	165	16	ab	ab	PROPN
ejpam-488	165	17	1−	1−	NUM
ejpam-488	165	18	b2	b2	PROPN
ejpam-488	165	19	�	�	PROPN
ejpam-488	165	20	�	�	PROPN
ejpam-488	165	21	�	�	PROPN
ejpam-488	165	22	�	�	PROPN
ejpam-488	165	23	<	<	X
ejpam-488	165	24	a−	a−	PROPN
ejpam-488	165	25	b	b	PROPN
ejpam-488	165	26	1−	1−	NUM
ejpam-488	165	27	b2	b2	NOUN
ejpam-488	165	28	(	(	PUNCT
ejpam-488	165	29	z	z	NOUN
ejpam-488	165	30	∈	∈	PROPN
ejpam-488	165	31	u	u	NOUN
ejpam-488	165	32	;	;	PUNCT
ejpam-488	165	33	b	b	PROPN
ejpam-488	165	34	6=	6=	NUM
ejpam-488	165	35	−1	−1	NOUN
ejpam-488	165	36	)	)	PUNCT
ejpam-488	165	37	,	,	PUNCT
ejpam-488	165	38	(	(	PUNCT
ejpam-488	165	39	20	20	NUM
ejpam-488	165	40	)	)	PUNCT
ejpam-488	165	41	and	and	CCONJ
ejpam-488	165	42	re(q(z	re(q(z	NOUN
ejpam-488	165	43	)	)	PUNCT
ejpam-488	165	44	)	)	PUNCT
ejpam-488	165	45	>	>	X
ejpam-488	166	1	1−	1−	NUM
ejpam-488	166	2	a	a	DET
ejpam-488	166	3	2	2	NUM
ejpam-488	166	4	(	(	PUNCT
ejpam-488	166	5	z	z	NOUN
ejpam-488	166	6	∈	∈	PROPN
ejpam-488	166	7	u	u	NOUN
ejpam-488	166	8	;	;	PUNCT
ejpam-488	166	9	b	b	X
ejpam-488	166	10	=	=	SYM
ejpam-488	166	11	−1	−1	NOUN
ejpam-488	166	12	)	)	PUNCT
ejpam-488	166	13	.	.	PUNCT
ejpam-488	167	1	(	(	PUNCT
ejpam-488	167	2	21	21	NUM
ejpam-488	167	3	)	)	PUNCT
ejpam-488	167	4	m.	m.	NOUN
ejpam-488	167	5	aouf	aouf	PROPN
ejpam-488	167	6	,	,	PUNCT
ejpam-488	167	7	a.	a.	NOUN
ejpam-488	167	8	shamandy	shamandy	PROPN
ejpam-488	167	9	,	,	PUNCT
ejpam-488	167	10	r.	r.	PROPN
ejpam-488	167	11	el	el	PROPN
ejpam-488	167	12	-	-	PUNCT
ejpam-488	167	13	ashway	ashway	PROPN
ejpam-488	167	14	,	,	PUNCT
ejpam-488	167	15	e.	e.	PROPN
ejpam-488	167	16	ali	ali	PROPN
ejpam-488	167	17	/	/	SYM
ejpam-488	167	18	eur	eur	PROPN
ejpam-488	167	19	.	.	PUNCT
ejpam-488	168	1	j.	j.	PROPN
ejpam-488	168	2	pure	pure	PROPN
ejpam-488	168	3	appl	appl	PROPN
ejpam-488	168	4	.	.	PROPN
ejpam-488	168	5	math	math	PROPN
ejpam-488	168	6	,	,	PUNCT
ejpam-488	168	7	3	3	NUM
ejpam-488	168	8	(	(	PUNCT
ejpam-488	168	9	2010	2010	NUM
ejpam-488	168	10	)	)	PUNCT
ejpam-488	168	11	,	,	PUNCT
ejpam-488	168	12	317	317	NUM
ejpam-488	168	13	-	-	SYM
ejpam-488	168	14	330	330	NUM
ejpam-488	168	15	324	324	NUM
ejpam-488	168	16	then	then	ADV
ejpam-488	168	17	,	,	PUNCT
ejpam-488	168	18	by	by	ADP
ejpam-488	168	19	using	use	VERB
ejpam-488	168	20	(	(	PUNCT
ejpam-488	168	21	20	20	NUM
ejpam-488	168	22	)	)	PUNCT
ejpam-488	168	23	and	and	CCONJ
ejpam-488	168	24	(	(	PUNCT
ejpam-488	168	25	21	21	NUM
ejpam-488	168	26	)	)	PUNCT
ejpam-488	169	1	,	,	PUNCT
ejpam-488	169	2	we	we	PRON
ejpam-488	169	3	have	have	VERB
ejpam-488	169	4	q(z	q(z	PROPN
ejpam-488	169	5	)	)	PUNCT
ejpam-488	170	1	+	+	CCONJ
ejpam-488	170	2	1−λ+	1−λ+	NUM
ejpam-488	170	3	ℓ	ℓ	NOUN
ejpam-488	170	4	λ	λ	PROPN
ejpam-488	170	5	=	=	SYM
ejpam-488	170	6	ρeφπi/2	ρeφπi/2	PROPN
ejpam-488	170	7	,	,	PUNCT
ejpam-488	170	8	where	where	SCONJ
ejpam-488	170	9	1−	1−	NUM
ejpam-488	170	10	a	a	DET
ejpam-488	170	11	1−	1−	NUM
ejpam-488	170	12	b	b	NOUN
ejpam-488	170	13	+	+	CCONJ
ejpam-488	170	14	1−λ+	1−λ+	NUM
ejpam-488	170	15	ℓ	ℓ	PROPN
ejpam-488	170	16	λ	λ	PROPN
ejpam-488	170	17	<	<	X
ejpam-488	170	18	ρ	ρ	X
ejpam-488	170	19	<	<	X
ejpam-488	170	20	1	1	NUM
ejpam-488	170	21	+	+	CCONJ
ejpam-488	170	22	a	a	DET
ejpam-488	170	23	1	1	NUM
ejpam-488	170	24	+	+	SYM
ejpam-488	170	25	b	b	NOUN
ejpam-488	170	26	+	+	CCONJ
ejpam-488	170	27	1−λ+	1−λ+	NUM
ejpam-488	170	28	ℓ	ℓ	PROPN
ejpam-488	170	29	λ	λ	PROPN
ejpam-488	170	30	,	,	PUNCT
ejpam-488	170	31	−t1	−t1	PROPN
ejpam-488	170	32	<	<	X
ejpam-488	170	33	φ	φ	X
ejpam-488	170	34	<	<	X
ejpam-488	170	35	t1	t1	PROPN
ejpam-488	170	36	(	(	PUNCT
ejpam-488	170	37	b	b	PROPN
ejpam-488	170	38	6=	6=	NUM
ejpam-488	170	39	−1	−1	NOUN
ejpam-488	170	40	)	)	PUNCT
ejpam-488	170	41	,	,	PUNCT
ejpam-488	171	1	t1	t1	NOUN
ejpam-488	171	2	being	be	AUX
ejpam-488	171	3	given	give	VERB
ejpam-488	171	4	by	by	ADP
ejpam-488	171	5	(	(	PUNCT
ejpam-488	171	6	18	18	NUM
ejpam-488	171	7	)	)	PUNCT
ejpam-488	171	8	,	,	PUNCT
ejpam-488	171	9	and	and	CCONJ
ejpam-488	171	10	1−	1−	NUM
ejpam-488	171	11	a	a	DET
ejpam-488	171	12	2	2	NUM
ejpam-488	171	13	+	+	NUM
ejpam-488	171	14	1−λ+	1−λ+	NUM
ejpam-488	171	15	ℓ	ℓ	NUM
ejpam-488	171	16	λ	λ	PROPN
ejpam-488	171	17	<	<	X
ejpam-488	171	18	ρ	ρ	PROPN
ejpam-488	171	19	<	<	X
ejpam-488	171	20	∞	∞	PROPN
ejpam-488	171	21	−1	−1	NOUN
ejpam-488	171	22	<	<	X
ejpam-488	171	23	φ	φ	X
ejpam-488	171	24	<	<	X
ejpam-488	171	25	1	1	NUM
ejpam-488	171	26	(	(	PUNCT
ejpam-488	171	27	b	b	NOUN
ejpam-488	171	28	=	=	SYM
ejpam-488	171	29	−1	−1	NOUN
ejpam-488	171	30	)	)	PUNCT
ejpam-488	171	31	.	.	PUNCT
ejpam-488	172	1	we	we	PRON
ejpam-488	172	2	note	note	VERB
ejpam-488	172	3	that	that	SCONJ
ejpam-488	172	4	p	p	NOUN
ejpam-488	172	5	is	be	AUX
ejpam-488	172	6	analytic	analytic	ADJ
ejpam-488	172	7	in	in	ADP
ejpam-488	172	8	u	u	NOUN
ejpam-488	172	9	with	with	ADP
ejpam-488	172	10	p(0	p(0	PROPN
ejpam-488	172	11	)	)	PUNCT
ejpam-488	172	12	=	=	SYM
ejpam-488	173	1	1	1	X
ejpam-488	173	2	.	.	PUNCT
ejpam-488	173	3	let	let	VERB
ejpam-488	173	4	h	h	NOUN
ejpam-488	173	5	be	be	AUX
ejpam-488	173	6	the	the	DET
ejpam-488	173	7	function	function	NOUN
ejpam-488	173	8	which	which	PRON
ejpam-488	173	9	maps	map	VERB
ejpam-488	173	10	u	u	NOUN
ejpam-488	173	11	onto	onto	ADP
ejpam-488	173	12	the	the	DET
ejpam-488	173	13	angular	angular	ADJ
ejpam-488	173	14	domain	domain	NOUN
ejpam-488	173	15	§	§	PROPN
ejpam-488	173	16	φ	φ	NOUN
ejpam-488	173	17	:	:	PUNCT
ejpam-488	173	18	−	−	PROPN
ejpam-488	173	19	π	π	PROPN
ejpam-488	173	20	2	2	NUM
ejpam-488	173	21	δ1	δ1	NOUN
ejpam-488	173	22	<	<	X
ejpam-488	173	23	arg(φ	arg(φ	PROPN
ejpam-488	173	24	)	)	PUNCT
ejpam-488	173	25	<	<	X
ejpam-488	173	26	π	π	PROPN
ejpam-488	173	27	2	2	NUM
ejpam-488	173	28	δ2	δ2	VERB
ejpam-488	173	29	ª	ª	PRON
ejpam-488	173	30	,	,	PUNCT
ejpam-488	173	31	with	with	ADP
ejpam-488	173	32	h(0	h(0	PROPN
ejpam-488	173	33	)	)	PUNCT
ejpam-488	173	34	=	=	SYM
ejpam-488	173	35	1	1	X
ejpam-488	173	36	.	.	X
ejpam-488	173	37	applying	apply	VERB
ejpam-488	173	38	lemma	lemma	PROPN
ejpam-488	173	39	1	1	NUM
ejpam-488	173	40	for	for	ADP
ejpam-488	173	41	this	this	DET
ejpam-488	173	42	h	h	NOUN
ejpam-488	173	43	with	with	ADP
ejpam-488	173	44	φ(z	φ(z	PROPN
ejpam-488	173	45	)	)	PUNCT
ejpam-488	173	46	=	=	SYM
ejpam-488	173	47	1	1	NUM
ejpam-488	173	48	q(z	q(z	PROPN
ejpam-488	173	49	)	)	PUNCT
ejpam-488	173	50	+	+	CCONJ
ejpam-488	173	51	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	173	52	λ	λ	NOUN
ejpam-488	173	53	,	,	PUNCT
ejpam-488	173	54	we	we	PRON
ejpam-488	173	55	see	see	VERB
ejpam-488	173	56	that	that	DET
ejpam-488	173	57	r(p(z	r(p(z	NOUN
ejpam-488	173	58	)	)	PUNCT
ejpam-488	173	59	)	)	PUNCT
ejpam-488	173	60	>	>	X
ejpam-488	173	61	0	0	PUNCT
ejpam-488	174	1	(	(	PUNCT
ejpam-488	174	2	z	z	NOUN
ejpam-488	174	3	∈	∈	PROPN
ejpam-488	174	4	u	u	NOUN
ejpam-488	174	5	)	)	PUNCT
ejpam-488	174	6	,	,	PUNCT
ejpam-488	174	7	and	and	CCONJ
ejpam-488	174	8	hence	hence	ADV
ejpam-488	174	9	,	,	PUNCT
ejpam-488	174	10	p(z	p(z	PROPN
ejpam-488	174	11	)	)	PUNCT
ejpam-488	175	1	6=	6=	ADP
ejpam-488	175	2	0	0	NUM
ejpam-488	175	3	in	in	ADP
ejpam-488	175	4	u	u	NOUN
ejpam-488	175	5	.	.	PUNCT
ejpam-488	176	1	if	if	SCONJ
ejpam-488	176	2	there	there	PRON
ejpam-488	176	3	exist	exist	VERB
ejpam-488	176	4	two	two	NUM
ejpam-488	176	5	points	point	NOUN
ejpam-488	176	6	z1	z1	NOUN
ejpam-488	176	7	and	and	CCONJ
ejpam-488	176	8	z2	z2	PROPN
ejpam-488	176	9	in	in	ADP
ejpam-488	176	10	u	u	PRON
ejpam-488	176	11	such	such	ADJ
ejpam-488	176	12	that	that	DET
ejpam-488	176	13	condition	condition	NOUN
ejpam-488	176	14	(	(	PUNCT
ejpam-488	176	15	7	7	X
ejpam-488	176	16	)	)	PUNCT
ejpam-488	176	17	is	be	AUX
ejpam-488	176	18	satisfied	satisfied	ADJ
ejpam-488	176	19	,	,	PUNCT
ejpam-488	176	20	then	then	ADV
ejpam-488	176	21	(	(	PUNCT
ejpam-488	176	22	by	by	ADP
ejpam-488	176	23	lemma	lemma	PROPN
ejpam-488	176	24	3	3	X
ejpam-488	176	25	)	)	PUNCT
ejpam-488	176	26	we	we	PRON
ejpam-488	176	27	obtain	obtain	VERB
ejpam-488	176	28	(	(	PUNCT
ejpam-488	176	29	8)	8)	NUM
ejpam-488	176	30	under	under	ADP
ejpam-488	176	31	restriction	restriction	NOUN
ejpam-488	176	32	(	(	PUNCT
ejpam-488	176	33	9	9	NUM
ejpam-488	176	34	)	)	PUNCT
ejpam-488	176	35	.	.	PUNCT
ejpam-488	177	1	for	for	ADP
ejpam-488	177	2	the	the	DET
ejpam-488	177	3	case	case	NOUN
ejpam-488	177	4	b	b	PROPN
ejpam-488	177	5	6=	6=	NUM
ejpam-488	177	6	−1	−1	NOUN
ejpam-488	177	7	,	,	PUNCT
ejpam-488	177	8	we	we	PRON
ejpam-488	177	9	first	first	ADV
ejpam-488	177	10	obtain	obtain	VERB
ejpam-488	177	11	arg	arg	NOUN
ejpam-488	177	12	p(z1	p(z1	NOUN
ejpam-488	177	13	)	)	PUNCT
ejpam-488	178	1	+	+	CCONJ
ejpam-488	178	2	z1p	z1p	NUM
ejpam-488	178	3	′	′	NUM
ejpam-488	178	4	(	(	PUNCT
ejpam-488	178	5	z1	z1	NOUN
ejpam-488	178	6	)	)	PUNCT
ejpam-488	178	7	q(z1	q(z1	NOUN
ejpam-488	178	8	)	)	PUNCT
ejpam-488	178	9	+	+	CCONJ
ejpam-488	178	10	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	178	11	λ	λ	NOUN
ejpam-488	178	12	!	!	PUNCT
ejpam-488	178	13	=	=	PUNCT
ejpam-488	179	1	−	−	PROPN
ejpam-488	179	2	π	π	PROPN
ejpam-488	179	3	2	2	NUM
ejpam-488	179	4	α1	α1	PROPN
ejpam-488	179	5	+	+	CCONJ
ejpam-488	179	6	arg	arg	NOUN
ejpam-488	179	7	�	�	PROPN
ejpam-488	179	8	1−	1−	NUM
ejpam-488	179	9	i	i	PRON
ejpam-488	179	10	α1	α1	VERB
ejpam-488	179	11	+	+	ADV
ejpam-488	179	12	α2	α2	ADJ
ejpam-488	179	13	2	2	NUM
ejpam-488	179	14	m	m	NOUN
ejpam-488	179	15	�	�	PROPN
ejpam-488	179	16	ρeφπi/2	ρeφπi/2	PROPN
ejpam-488	179	17	�	�	PROPN
ejpam-488	179	18	−1	−1	NOUN
ejpam-488	179	19	�	�	PROPN
ejpam-488	179	20	≤	≤	NUM
ejpam-488	180	1	−	−	PROPN
ejpam-488	180	2	π	π	PROPN
ejpam-488	180	3	2	2	NUM
ejpam-488	180	4	α1	α1	PROPN
ejpam-488	180	5	−	−	PROPN
ejpam-488	180	6	tan−1	tan−1	PROPN
ejpam-488	180	7	(	(	PUNCT
ejpam-488	180	8	α1	α1	PROPN
ejpam-488	180	9	+	+	NOUN
ejpam-488	180	10	α2)m	α2)m	NOUN
ejpam-488	180	11	sin	sin	VERB
ejpam-488	180	12	�	�	PROPN
ejpam-488	180	13	π	π	PROPN
ejpam-488	180	14	2	2	NUM
ejpam-488	180	15	�	�	PROPN
ejpam-488	180	16	(	(	PUNCT
ejpam-488	180	17	1−φ	1−φ	NUM
ejpam-488	180	18	)	)	PUNCT
ejpam-488	180	19	2ρ+	2ρ+	NUM
ejpam-488	180	20	(	(	PUNCT
ejpam-488	180	21	α1+α2)m	α1+α2)m	PROPN
ejpam-488	180	22	cos	cos	PROPN
ejpam-488	180	23	�	�	PROPN
ejpam-488	180	24	π	π	PROPN
ejpam-488	180	25	2	2	NUM
ejpam-488	180	26	�	�	PROPN
ejpam-488	180	27	(	(	PUNCT
ejpam-488	180	28	1−φ	1−φ	NUM
ejpam-488	180	29	)	)	PUNCT
ejpam-488	180	30	!	!	PUNCT
ejpam-488	181	1	≤	≤	NUM
ejpam-488	182	1	−	−	PUNCT
ejpam-488	182	2	π	π	PROPN
ejpam-488	182	3	2	2	NUM
ejpam-488	182	4	α1	α1	PROPN
ejpam-488	182	5	−	−	PROPN
ejpam-488	182	6	tan−1	tan−1	PROPN
ejpam-488	182	7			NOUN
ejpam-488	182	8			NOUN
ejpam-488	182	9			NOUN
ejpam-488	182	10	(	(	PUNCT
ejpam-488	182	11	α1	α1	PROPN
ejpam-488	182	12	+	+	PROPN
ejpam-488	182	13	α2)(1−	α2)(1−	PROPN
ejpam-488	182	14	|a|	|a|	NUM
ejpam-488	182	15	)	)	PUNCT
ejpam-488	182	16	cos	cos	PROPN
ejpam-488	182	17	�	�	PROPN
ejpam-488	182	18	π	π	PROPN
ejpam-488	182	19	2	2	NUM
ejpam-488	182	20	�	�	PROPN
ejpam-488	182	21	t1	t1	NOUN
ejpam-488	182	22	2	2	NUM
ejpam-488	182	23	�	�	PROPN
ejpam-488	182	24	1+a	1+a	NUM
ejpam-488	182	25	1+b	1+b	NUM
ejpam-488	182	26	+	+	CCONJ
ejpam-488	182	27	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	182	28	λ	λ	X
ejpam-488	182	29	�	�	X
ejpam-488	182	30	(	(	PUNCT
ejpam-488	182	31	1	1	NUM
ejpam-488	182	32	+	+	NUM
ejpam-488	182	33	|a|)+	|a|)+	NOUN
ejpam-488	182	34	(	(	PUNCT
ejpam-488	182	35	α1	α1	PROPN
ejpam-488	182	36	+	+	PROPN
ejpam-488	182	37	α2)(1−	α2)(1−	PROPN
ejpam-488	182	38	|a|	|a|	NOUN
ejpam-488	182	39	)	)	PUNCT
ejpam-488	182	40	sin	sin	NOUN
ejpam-488	182	41	�	�	PROPN
ejpam-488	182	42	π	π	PROPN
ejpam-488	182	43	2	2	NUM
ejpam-488	182	44	�	�	PROPN
ejpam-488	182	45	t1	t1	PROPN
ejpam-488	182	46			PROPN
ejpam-488	182	47			VERB
ejpam-488	182	48			PUNCT
ejpam-488	183	1	=	=	PUNCT
ejpam-488	183	2	−	−	PROPN
ejpam-488	183	3	π	π	PROPN
ejpam-488	183	4	2	2	NUM
ejpam-488	183	5	δ1	δ1	NOUN
ejpam-488	183	6	m.	m.	NOUN
ejpam-488	183	7	aouf	aouf	PROPN
ejpam-488	183	8	,	,	PUNCT
ejpam-488	183	9	a.	a.	NOUN
ejpam-488	183	10	shamandy	shamandy	PROPN
ejpam-488	183	11	,	,	PUNCT
ejpam-488	183	12	r.	r.	PROPN
ejpam-488	183	13	el	el	PROPN
ejpam-488	183	14	-	-	PUNCT
ejpam-488	183	15	ashway	ashway	PROPN
ejpam-488	183	16	,	,	PUNCT
ejpam-488	183	17	e.	e.	PROPN
ejpam-488	183	18	ali	ali	PROPN
ejpam-488	183	19	/	/	SYM
ejpam-488	183	20	eur	eur	PROPN
ejpam-488	183	21	.	.	PUNCT
ejpam-488	184	1	j.	j.	PROPN
ejpam-488	184	2	pure	pure	PROPN
ejpam-488	184	3	appl	appl	PROPN
ejpam-488	184	4	.	.	PROPN
ejpam-488	184	5	math	math	PROPN
ejpam-488	184	6	,	,	PUNCT
ejpam-488	184	7	3	3	NUM
ejpam-488	184	8	(	(	PUNCT
ejpam-488	184	9	2010	2010	NUM
ejpam-488	184	10	)	)	PUNCT
ejpam-488	184	11	,	,	PUNCT
ejpam-488	184	12	317	317	NUM
ejpam-488	184	13	-	-	SYM
ejpam-488	184	14	330	330	NUM
ejpam-488	184	15	325	325	NUM
ejpam-488	184	16	and	and	CCONJ
ejpam-488	184	17	arg	arg	VERB
ejpam-488	184	18	p(z2	p(z2	NOUN
ejpam-488	184	19	)	)	PUNCT
ejpam-488	185	1	+	+	PUNCT
ejpam-488	185	2	z2p	z2p	NUM
ejpam-488	185	3	′	′	NUM
ejpam-488	185	4	(	(	PUNCT
ejpam-488	185	5	z2	z2	PROPN
ejpam-488	185	6	)	)	PUNCT
ejpam-488	185	7	q(z2	q(z2	NOUN
ejpam-488	185	8	)	)	PUNCT
ejpam-488	186	1	+	+	CCONJ
ejpam-488	186	2	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	186	3	λ	λ	NOUN
ejpam-488	186	4	!	!	PUNCT
ejpam-488	186	5	≥	≥	PROPN
ejpam-488	187	1	π	π	PROPN
ejpam-488	187	2	2	2	NUM
ejpam-488	187	3	α2	α2	ADJ
ejpam-488	187	4	+	+	CCONJ
ejpam-488	187	5	tan−1	tan−1	PROPN
ejpam-488	187	6			NOUN
ejpam-488	187	7			NOUN
ejpam-488	187	8			NOUN
ejpam-488	187	9	(	(	PUNCT
ejpam-488	187	10	α1+α2)(1−	α1+α2)(1−	NUM
ejpam-488	187	11	|a|	|a|	NOUN
ejpam-488	187	12	)	)	PUNCT
ejpam-488	187	13	cos	cos	PROPN
ejpam-488	187	14	�	�	PROPN
ejpam-488	187	15	π	π	PROPN
ejpam-488	187	16	2	2	NUM
ejpam-488	187	17	�	�	PROPN
ejpam-488	187	18	t1	t1	NOUN
ejpam-488	187	19	2	2	NUM
ejpam-488	187	20	�	�	PROPN
ejpam-488	187	21	1+a	1+a	NUM
ejpam-488	187	22	1+b	1+b	NUM
ejpam-488	188	1	+	+	CCONJ
ejpam-488	188	2	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	188	3	λ	λ	X
ejpam-488	188	4	�	�	X
ejpam-488	188	5	(	(	PUNCT
ejpam-488	188	6	1	1	NUM
ejpam-488	188	7	+	+	NUM
ejpam-488	188	8	|a|)+	|a|)+	NOUN
ejpam-488	188	9	(	(	PUNCT
ejpam-488	188	10	α1	α1	PROPN
ejpam-488	188	11	+	+	PROPN
ejpam-488	188	12	α2)(1−	α2)(1−	PROPN
ejpam-488	188	13	|a|	|a|	NOUN
ejpam-488	188	14	)	)	PUNCT
ejpam-488	188	15	sin	sin	NOUN
ejpam-488	188	16	�	�	PROPN
ejpam-488	188	17	π	π	PROPN
ejpam-488	188	18	2	2	NUM
ejpam-488	188	19	�	�	PROPN
ejpam-488	188	20	t1	t1	PROPN
ejpam-488	188	21			PROPN
ejpam-488	188	22			VERB
ejpam-488	188	23			PUNCT
ejpam-488	189	1	=	=	PUNCT
ejpam-488	189	2	π	π	PROPN
ejpam-488	189	3	2	2	NUM
ejpam-488	189	4	δ2	δ2	VERB
ejpam-488	189	5	,	,	PUNCT
ejpam-488	189	6	where	where	SCONJ
ejpam-488	189	7	we	we	PRON
ejpam-488	189	8	have	have	AUX
ejpam-488	189	9	used	use	VERB
ejpam-488	189	10	inequality	inequality	NOUN
ejpam-488	189	11	(	(	PUNCT
ejpam-488	189	12	9	9	NUM
ejpam-488	189	13	)	)	PUNCT
ejpam-488	189	14	,	,	PUNCT
ejpam-488	189	15	δ1	δ1	NOUN
ejpam-488	189	16	,	,	PUNCT
ejpam-488	189	17	δ2	δ2	VERB
ejpam-488	189	18	and	and	CCONJ
ejpam-488	189	19	t1	t1	NOUN
ejpam-488	189	20	being	be	AUX
ejpam-488	189	21	given	give	VERB
ejpam-488	189	22	by	by	ADP
ejpam-488	189	23	(	(	PUNCT
ejpam-488	189	24	16	16	NUM
ejpam-488	189	25	)	)	PUNCT
ejpam-488	189	26	,	,	PUNCT
ejpam-488	189	27	(	(	PUNCT
ejpam-488	189	28	17	17	NUM
ejpam-488	189	29	)	)	PUNCT
ejpam-488	189	30	,	,	PUNCT
ejpam-488	189	31	and	and	CCONJ
ejpam-488	189	32	(	(	PUNCT
ejpam-488	189	33	18	18	NUM
ejpam-488	189	34	)	)	PUNCT
ejpam-488	189	35	,	,	PUNCT
ejpam-488	189	36	respectively	respectively	ADV
ejpam-488	189	37	.	.	PUNCT
ejpam-488	190	1	similarly	similarly	ADV
ejpam-488	190	2	,	,	PUNCT
ejpam-488	190	3	for	for	ADP
ejpam-488	190	4	the	the	DET
ejpam-488	190	5	case	case	NOUN
ejpam-488	190	6	b	b	NOUN
ejpam-488	190	7	=	=	SYM
ejpam-488	190	8	−1	−1	NOUN
ejpam-488	190	9	,	,	PUNCT
ejpam-488	190	10	we	we	PRON
ejpam-488	190	11	have	have	VERB
ejpam-488	190	12	arg	arg	NOUN
ejpam-488	190	13	p(z1	p(z1	NOUN
ejpam-488	190	14	)	)	PUNCT
ejpam-488	191	1	+	+	CCONJ
ejpam-488	191	2	z1p	z1p	NUM
ejpam-488	191	3	′	′	NUM
ejpam-488	191	4	(	(	PUNCT
ejpam-488	191	5	z1	z1	NOUN
ejpam-488	191	6	)	)	PUNCT
ejpam-488	191	7	q(z1	q(z1	NOUN
ejpam-488	191	8	)	)	PUNCT
ejpam-488	191	9	+	+	CCONJ
ejpam-488	191	10	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	191	11	λ	λ	NOUN
ejpam-488	191	12	!	!	PUNCT
ejpam-488	191	13	≤	≤	NUM
ejpam-488	192	1	−	−	PUNCT
ejpam-488	192	2	π	π	PROPN
ejpam-488	192	3	2	2	NUM
ejpam-488	192	4	α1	α1	PROPN
ejpam-488	192	5	and	and	CCONJ
ejpam-488	192	6	arg	arg	NOUN
ejpam-488	192	7	p(z2	p(z2	NOUN
ejpam-488	192	8	)	)	PUNCT
ejpam-488	193	1	+	+	PUNCT
ejpam-488	193	2	z2p	z2p	NUM
ejpam-488	193	3	′	′	NUM
ejpam-488	193	4	(	(	PUNCT
ejpam-488	193	5	z2	z2	PROPN
ejpam-488	193	6	)	)	PUNCT
ejpam-488	193	7	q(z2	q(z2	NOUN
ejpam-488	193	8	)	)	PUNCT
ejpam-488	194	1	+	+	CCONJ
ejpam-488	194	2	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	194	3	λ	λ	NOUN
ejpam-488	194	4	!	!	PUNCT
ejpam-488	194	5	≥	≥	PROPN
ejpam-488	195	1	π	π	PROPN
ejpam-488	195	2	2	2	NUM
ejpam-488	195	3	α2	α2	ADJ
ejpam-488	195	4	.	.	PUNCT
ejpam-488	196	1	these	these	PRON
ejpam-488	196	2	obviously	obviously	ADV
ejpam-488	196	3	contradict	contradict	VERB
ejpam-488	196	4	the	the	DET
ejpam-488	196	5	assumption	assumption	NOUN
ejpam-488	196	6	of	of	ADP
ejpam-488	196	7	theorem	theorem	NOUN
ejpam-488	196	8	1	1	NUM
ejpam-488	196	9	.	.	PUNCT
ejpam-488	197	1	the	the	DET
ejpam-488	197	2	proof	proof	NOUN
ejpam-488	197	3	of	of	ADP
ejpam-488	197	4	theorem	theorem	ADJ
ejpam-488	197	5	1	1	NUM
ejpam-488	197	6	is	be	AUX
ejpam-488	197	7	thus	thus	ADV
ejpam-488	197	8	completed	complete	VERB
ejpam-488	197	9	.	.	PUNCT
ejpam-488	198	1	putting	put	VERB
ejpam-488	198	2	δ1	δ1	NOUN
ejpam-488	198	3	=	=	SYM
ejpam-488	198	4	δ2	δ2	VERB
ejpam-488	198	5	=	=	SYM
ejpam-488	198	6	δ	δ	PROPN
ejpam-488	198	7	in	in	ADP
ejpam-488	198	8	theorem	theorem	NOUN
ejpam-488	198	9	1	1	NUM
ejpam-488	198	10	,	,	PUNCT
ejpam-488	198	11	we	we	PRON
ejpam-488	198	12	obtain	obtain	VERB
ejpam-488	198	13	the	the	DET
ejpam-488	198	14	following	follow	VERB
ejpam-488	198	15	corollary	corollary	NOUN
ejpam-488	198	16	.	.	PUNCT
ejpam-488	199	1	corollary	corollary	ADJ
ejpam-488	199	2	1	1	NUM
ejpam-488	199	3	.	.	PUNCT
ejpam-488	200	1	let	let	VERB
ejpam-488	200	2	f	f	PROPN
ejpam-488	200	3	∈	∈	PROPN
ejpam-488	200	4	a	a	PRON
ejpam-488	200	5	and	and	CCONJ
ejpam-488	200	6	0	0	NUM
ejpam-488	200	7	<	<	X
ejpam-488	200	8	δ	δ	NOUN
ejpam-488	200	9	≤	≤	ADV
ejpam-488	200	10	1	1	NUM
ejpam-488	200	11	.	.	PUNCT
ejpam-488	201	1	if	if	SCONJ
ejpam-488	201	2	�	�	PROPN
ejpam-488	201	3	�	�	PROPN
ejpam-488	201	4	�	�	PROPN
ejpam-488	201	5	�	�	PROPN
ejpam-488	201	6	�	�	PROPN
ejpam-488	201	7	�	�	PROPN
ejpam-488	201	8	�	�	PROPN
ejpam-488	201	9	�	�	PROPN
ejpam-488	201	10	�	�	PROPN
ejpam-488	201	11	arg	arg	NOUN
ejpam-488	201	12			PROPN
ejpam-488	201	13			NOUN
ejpam-488	201	14			NOUN
ejpam-488	201	15			NOUN
ejpam-488	201	16			NOUN
ejpam-488	201	17			NOUN
ejpam-488	201	18	z(im+1(λ,ℓ	z(im+1(λ,ℓ	NOUN
ejpam-488	201	19	)	)	PUNCT
ejpam-488	201	20	f	f	NOUN
ejpam-488	201	21	(	(	PUNCT
ejpam-488	201	22	z	z	NOUN
ejpam-488	201	23	)	)	PUNCT
ejpam-488	201	24	)	)	PUNCT
ejpam-488	202	1	′	′	NUM
ejpam-488	202	2	�	�	PROPN
ejpam-488	202	3	1	1	NUM
ejpam-488	202	4	q	q	PROPN
ejpam-488	202	5	�	�	PROPN
ejpam-488	202	6	q	q	PROPN
ejpam-488	202	7	∑	∑	PROPN
ejpam-488	202	8	j=1	j=1	PROPN
ejpam-488	202	9	im+1(λ,ℓ)g	im+1(λ,ℓ)g	PROPN
ejpam-488	202	10	j(z	j(z	PROPN
ejpam-488	202	11	)	)	PUNCT
ejpam-488	202	12			PROPN
ejpam-488	202	13			NOUN
ejpam-488	202	14			VERB
ejpam-488	202	15			NOUN
ejpam-488	202	16			NOUN
ejpam-488	202	17			PUNCT
ejpam-488	203	1	�	�	PROPN
ejpam-488	203	2	�	�	PROPN
ejpam-488	203	3	�	�	PROPN
ejpam-488	203	4	�	�	PROPN
ejpam-488	203	5	�	�	PROPN
ejpam-488	203	6	�	�	PROPN
ejpam-488	203	7	�	�	PROPN
ejpam-488	203	8	�	�	PROPN
ejpam-488	203	9	�	�	PROPN
ejpam-488	203	10	<	<	X
ejpam-488	203	11	π	π	PROPN
ejpam-488	203	12	2	2	NUM
ejpam-488	203	13	δ	δ	PROPN
ejpam-488	203	14	,	,	PUNCT
ejpam-488	203	15	where	where	SCONJ
ejpam-488	203	16	g1	g1	PROPN
ejpam-488	203	17	,	,	PUNCT
ejpam-488	203	18	...	...	PUNCT
ejpam-488	203	19	,	,	PUNCT
ejpam-488	203	20	gq	gq	PROPN
ejpam-488	203	21	∈	∈	PROPN
ejpam-488	203	22	ωm	ωm	VERB
ejpam-488	203	23	,	,	PUNCT
ejpam-488	203	24	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	203	25	;	;	PUNCT
ejpam-488	203	26	a	a	DET
ejpam-488	203	27	,	,	PUNCT
ejpam-488	203	28	b	b	NOUN
ejpam-488	203	29	)	)	PUNCT
ejpam-488	203	30	,	,	PUNCT
ejpam-488	203	31	then	then	ADV
ejpam-488	203	32	�	�	PROPN
ejpam-488	203	33	�	�	PROPN
ejpam-488	203	34	�	�	PROPN
ejpam-488	203	35	�	�	PROPN
ejpam-488	203	36	�	�	PROPN
ejpam-488	203	37	�	�	PROPN
ejpam-488	203	38	�	�	PROPN
ejpam-488	203	39	�	�	PROPN
ejpam-488	203	40	�	�	PROPN
ejpam-488	203	41	arg	arg	NOUN
ejpam-488	203	42			PROPN
ejpam-488	203	43			NOUN
ejpam-488	203	44			NOUN
ejpam-488	203	45			NOUN
ejpam-488	203	46			NOUN
ejpam-488	203	47			NOUN
ejpam-488	203	48	z(im(λ,ℓ	z(im(λ,ℓ	NUM
ejpam-488	203	49	)	)	PUNCT
ejpam-488	203	50	f	f	PROPN
ejpam-488	204	1	(	(	PUNCT
ejpam-488	204	2	z	z	NOUN
ejpam-488	204	3	)	)	PUNCT
ejpam-488	204	4	)	)	PUNCT
ejpam-488	205	1	′	′	NUM
ejpam-488	205	2	�	�	PROPN
ejpam-488	205	3	1	1	NUM
ejpam-488	205	4	q	q	PROPN
ejpam-488	205	5	�	�	PROPN
ejpam-488	205	6	q	q	PROPN
ejpam-488	205	7	∑	∑	PROPN
ejpam-488	205	8	j=1	j=1	ADJ
ejpam-488	205	9	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	205	10	j(z	j(z	PROPN
ejpam-488	205	11	)	)	PUNCT
ejpam-488	205	12			PROPN
ejpam-488	205	13			NOUN
ejpam-488	205	14			VERB
ejpam-488	205	15			NOUN
ejpam-488	205	16			NOUN
ejpam-488	205	17			PUNCT
ejpam-488	205	18	�	�	PROPN
ejpam-488	205	19	�	�	PROPN
ejpam-488	205	20	�	�	PROPN
ejpam-488	205	21	�	�	PROPN
ejpam-488	205	22	�	�	PROPN
ejpam-488	205	23	�	�	PROPN
ejpam-488	205	24	�	�	PROPN
ejpam-488	205	25	�	�	PROPN
ejpam-488	205	26	�	�	PROPN
ejpam-488	205	27	<	<	X
ejpam-488	205	28	π	π	PROPN
ejpam-488	205	29	2	2	NUM
ejpam-488	205	30	α	α	NOUN
ejpam-488	205	31	,	,	PUNCT
ejpam-488	205	32	where	where	SCONJ
ejpam-488	205	33	α	α	X
ejpam-488	205	34	(	(	PUNCT
ejpam-488	205	35	0	0	NUM
ejpam-488	205	36	<	<	X
ejpam-488	205	37	α	α	PRON
ejpam-488	205	38	≤	≤	NUM
ejpam-488	205	39	1	1	NUM
ejpam-488	205	40	)	)	PUNCT
ejpam-488	205	41	is	be	AUX
ejpam-488	205	42	the	the	DET
ejpam-488	205	43	solution	solution	NOUN
ejpam-488	205	44	of	of	ADP
ejpam-488	205	45	the	the	DET
ejpam-488	205	46	equation	equation	NOUN
ejpam-488	205	47	δ	δ	NOUN
ejpam-488	205	48	=	=	PUNCT
ejpam-488	205	49			PROPN
ejpam-488	205	50			PRON
ejpam-488	205	51			NOUN
ejpam-488	205	52	α+	α+	X
ejpam-488	205	53	2	2	NUM
ejpam-488	205	54	π	π	PROPN
ejpam-488	205	55	tan−1	tan−1	PROPN
ejpam-488	205	56	�	�	PROPN
ejpam-488	205	57	α	α	PROPN
ejpam-488	205	58	cos	cos	PROPN
ejpam-488	205	59	�	�	PROPN
ejpam-488	205	60	π	π	PROPN
ejpam-488	205	61	2	2	NUM
ejpam-488	205	62	�	�	PROPN
ejpam-488	205	63	t1	t1	NOUN
ejpam-488	205	64	�	�	PROPN
ejpam-488	205	65	1+a	1+a	NUM
ejpam-488	205	66	1+b	1+b	NUM
ejpam-488	205	67	+	+	CCONJ
ejpam-488	205	68	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	205	69	λ	λ	X
ejpam-488	205	70	�	�	NOUN
ejpam-488	205	71	+	+	NOUN
ejpam-488	205	72	α	α	PROPN
ejpam-488	205	73	sin	sin	NOUN
ejpam-488	205	74	�	�	PROPN
ejpam-488	205	75	π	π	PROPN
ejpam-488	205	76	2	2	NUM
ejpam-488	205	77	�	�	PROPN
ejpam-488	205	78	t1	t1	NUM
ejpam-488	205	79	�	�	PROPN
ejpam-488	205	80	(	(	PUNCT
ejpam-488	205	81	b	b	PROPN
ejpam-488	205	82	6=	6=	NUM
ejpam-488	205	83	−1	−1	NOUN
ejpam-488	205	84	)	)	PUNCT
ejpam-488	205	85	α	α	PROPN
ejpam-488	205	86	(	(	PUNCT
ejpam-488	205	87	b	b	NOUN
ejpam-488	205	88	=	=	SYM
ejpam-488	205	89	−1	−1	NOUN
ejpam-488	205	90	)	)	PUNCT
ejpam-488	205	91	,	,	PUNCT
ejpam-488	205	92	t1	t1	NOUN
ejpam-488	205	93	being	be	AUX
ejpam-488	205	94	given	give	VERB
ejpam-488	205	95	by	by	ADP
ejpam-488	205	96	(	(	PUNCT
ejpam-488	205	97	18	18	NUM
ejpam-488	205	98	)	)	PUNCT
ejpam-488	205	99	.	.	PUNCT
ejpam-488	206	1	m.	m.	PROPN
ejpam-488	206	2	aouf	aouf	PROPN
ejpam-488	206	3	,	,	PUNCT
ejpam-488	206	4	a.	a.	NOUN
ejpam-488	206	5	shamandy	shamandy	PROPN
ejpam-488	206	6	,	,	PUNCT
ejpam-488	206	7	r.	r.	PROPN
ejpam-488	206	8	el	el	PROPN
ejpam-488	206	9	-	-	PUNCT
ejpam-488	206	10	ashway	ashway	PROPN
ejpam-488	206	11	,	,	PUNCT
ejpam-488	206	12	e.	e.	PROPN
ejpam-488	206	13	ali	ali	PROPN
ejpam-488	206	14	/	/	SYM
ejpam-488	206	15	eur	eur	PROPN
ejpam-488	206	16	.	.	PUNCT
ejpam-488	207	1	j.	j.	PROPN
ejpam-488	207	2	pure	pure	PROPN
ejpam-488	207	3	appl	appl	PROPN
ejpam-488	207	4	.	.	PROPN
ejpam-488	207	5	math	math	PROPN
ejpam-488	207	6	,	,	PUNCT
ejpam-488	207	7	3	3	NUM
ejpam-488	207	8	(	(	PUNCT
ejpam-488	207	9	2010	2010	NUM
ejpam-488	207	10	)	)	PUNCT
ejpam-488	207	11	,	,	PUNCT
ejpam-488	207	12	317	317	NUM
ejpam-488	207	13	-	-	SYM
ejpam-488	207	14	330	330	NUM
ejpam-488	207	15	326	326	NUM
ejpam-488	207	16	from	from	ADP
ejpam-488	207	17	corollary	corollary	ADJ
ejpam-488	207	18	1	1	NUM
ejpam-488	207	19	,	,	PUNCT
ejpam-488	207	20	we	we	PRON
ejpam-488	207	21	immediately	immediately	ADV
ejpam-488	207	22	obtain	obtain	VERB
ejpam-488	207	23	the	the	DET
ejpam-488	207	24	following	follow	VERB
ejpam-488	207	25	corollary	corollary	NOUN
ejpam-488	207	26	.	.	PUNCT
ejpam-488	208	1	corollary	corollary	ADJ
ejpam-488	208	2	2	2	NUM
ejpam-488	208	3	.	.	PUNCT
ejpam-488	209	1	the	the	DET
ejpam-488	209	2	inclusion	inclusion	NOUN
ejpam-488	209	3	relation	relation	NOUN
ejpam-488	209	4	cm+1,λ,ℓ(q	cm+1,λ,ℓ(q	PROPN
ejpam-488	209	5	;	;	PUNCT
ejpam-488	209	6	a	a	PRON
ejpam-488	209	7	,	,	PUNCT
ejpam-488	209	8	b)⊂	b)⊂	PROPN
ejpam-488	209	9	cm	cm	NOUN
ejpam-488	209	10	,	,	PUNCT
ejpam-488	209	11	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	209	12	;	;	PUNCT
ejpam-488	209	13	a	a	DET
ejpam-488	209	14	,	,	PUNCT
ejpam-488	209	15	b	b	NOUN
ejpam-488	209	16	)	)	PUNCT
ejpam-488	209	17	holds	hold	VERB
ejpam-488	209	18	true	true	ADJ
ejpam-488	209	19	for	for	ADP
ejpam-488	209	20	any	any	DET
ejpam-488	209	21	integer	integer	NOUN
ejpam-488	209	22	m.	m.	NOUN
ejpam-488	209	23	remark	remark	NOUN
ejpam-488	209	24	2	2	NUM
ejpam-488	209	25	.	.	PUNCT
ejpam-488	209	26	for	for	ADP
ejpam-488	209	27	m	m	PROPN
ejpam-488	209	28	=	=	SYM
ejpam-488	209	29	ℓ	ℓ	X
ejpam-488	209	30	=	=	PUNCT
ejpam-488	209	31	0,λ	0,λ	NOUN
ejpam-488	210	1	=	=	PUNCT
ejpam-488	210	2	1,q	1,q	X
ejpam-488	210	3	=	=	SYM
ejpam-488	211	1	1,δ	1,δ	NUM
ejpam-488	211	2	=	=	SYM
ejpam-488	211	3	1,a	1,a	NUM
ejpam-488	211	4	=	=	SYM
ejpam-488	211	5	1	1	NUM
ejpam-488	211	6	and	and	CCONJ
ejpam-488	211	7	b	b	NOUN
ejpam-488	211	8	=	=	SYM
ejpam-488	211	9	−1	−1	NOUN
ejpam-488	211	10	,	,	PUNCT
ejpam-488	211	11	the	the	DET
ejpam-488	211	12	class	class	NOUN
ejpam-488	211	13	cm	cm	NOUN
ejpam-488	211	14	,	,	PUNCT
ejpam-488	211	15	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	211	16	;	;	PUNCT
ejpam-488	211	17	a	a	DET
ejpam-488	211	18	,	,	PUNCT
ejpam-488	211	19	b	b	NOUN
ejpam-488	211	20	)	)	PUNCT
ejpam-488	211	21	reduces	reduce	VERB
ejpam-488	211	22	to	to	ADP
ejpam-488	211	23	the	the	DET
ejpam-488	211	24	class	class	NOUN
ejpam-488	211	25	of	of	ADP
ejpam-488	211	26	quasiconvex	quasiconvex	NOUN
ejpam-488	211	27	functions	function	NOUN
ejpam-488	211	28	in	in	ADP
ejpam-488	211	29	u	u	NOUN
ejpam-488	211	30	introduced	introduce	VERB
ejpam-488	211	31	by	by	ADP
ejpam-488	211	32	sakaguchi	sakaguchi	ADJ
ejpam-488	211	33	[	[	X
ejpam-488	211	34	17	17	NUM
ejpam-488	211	35	]	]	PUNCT
ejpam-488	211	36	(	(	PUNCT
ejpam-488	211	37	see	see	VERB
ejpam-488	211	38	also	also	ADV
ejpam-488	211	39	[	[	X
ejpam-488	211	40	13	13	NUM
ejpam-488	211	41	]	]	NUM
ejpam-488	211	42	)	)	PUNCT
ejpam-488	211	43	.	.	PUNCT
ejpam-488	212	1	hence	hence	ADV
ejpam-488	212	2	,	,	PUNCT
ejpam-488	212	3	we	we	PRON
ejpam-488	212	4	see	see	VERB
ejpam-488	212	5	from	from	ADP
ejpam-488	212	6	corollary	corollary	ADJ
ejpam-488	212	7	2	2	NUM
ejpam-488	212	8	that	that	PRON
ejpam-488	212	9	every	every	DET
ejpam-488	212	10	quasiconvex	quasiconvex	NOUN
ejpam-488	212	11	function	function	NOUN
ejpam-488	212	12	in	in	ADP
ejpam-488	212	13	u	u	NOUN
ejpam-488	212	14	is	be	AUX
ejpam-488	212	15	close	close	ADJ
ejpam-488	212	16	-	-	PUNCT
ejpam-488	212	17	to	to	ADP
ejpam-488	212	18	-	-	PUNCT
ejpam-488	212	19	convex	convex	NOUN
ejpam-488	212	20	in	in	ADP
ejpam-488	212	21	u.	u.	PROPN
ejpam-488	212	22	next	next	ADV
ejpam-488	212	23	,	,	PUNCT
ejpam-488	212	24	we	we	PRON
ejpam-488	212	25	prove	prove	VERB
ejpam-488	212	26	the	the	DET
ejpam-488	212	27	following	follow	VERB
ejpam-488	212	28	theorem	theorem	VERB
ejpam-488	212	29	.	.	PUNCT
ejpam-488	212	30	theorem	theorem	NOUN
ejpam-488	212	31	2	2	NUM
ejpam-488	212	32	.	.	PUNCT
ejpam-488	213	1	let	let	VERB
ejpam-488	213	2	f	f	PROPN
ejpam-488	213	3	∈	∈	PROPN
ejpam-488	213	4	a	a	PRON
ejpam-488	213	5	,	,	PUNCT
ejpam-488	213	6	0	0	NUM
ejpam-488	213	7	<	<	X
ejpam-488	213	8	δ1	δ1	NOUN
ejpam-488	213	9	,	,	PUNCT
ejpam-488	213	10	δ2	δ2	ADJ
ejpam-488	213	11	≤	≤	NOUN
ejpam-488	213	12	1	1	NUM
ejpam-488	213	13	and	and	CCONJ
ejpam-488	213	14	c	c	X
ejpam-488	213	15	≥	≥	NOUN
ejpam-488	213	16	0	0	NUM
ejpam-488	213	17	.	.	PUNCT
ejpam-488	214	1	if	if	SCONJ
ejpam-488	214	2	−	−	PROPN
ejpam-488	214	3	π	π	PROPN
ejpam-488	214	4	2	2	NUM
ejpam-488	214	5	δ1	δ1	NOUN
ejpam-488	214	6	<	<	X
ejpam-488	214	7	arg	arg	NOUN
ejpam-488	214	8			PROPN
ejpam-488	214	9			NOUN
ejpam-488	214	10			NOUN
ejpam-488	214	11			NOUN
ejpam-488	214	12			NOUN
ejpam-488	214	13			NOUN
ejpam-488	214	14	z(im(λ,ℓ	z(im(λ,ℓ	NUM
ejpam-488	214	15	)	)	PUNCT
ejpam-488	214	16	f	f	PROPN
ejpam-488	214	17	(	(	PUNCT
ejpam-488	214	18	z	z	NOUN
ejpam-488	214	19	)	)	PUNCT
ejpam-488	214	20	)	)	PUNCT
ejpam-488	215	1	′	′	NUM
ejpam-488	215	2	�	�	PROPN
ejpam-488	215	3	1	1	NUM
ejpam-488	215	4	q	q	PROPN
ejpam-488	215	5	�	�	PROPN
ejpam-488	215	6	q	q	PROPN
ejpam-488	215	7	∑	∑	PROPN
ejpam-488	215	8	j=1	j=1	ADJ
ejpam-488	215	9	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	215	10	j(z	j(z	PROPN
ejpam-488	215	11	)	)	PUNCT
ejpam-488	215	12			PROPN
ejpam-488	215	13			NOUN
ejpam-488	215	14			VERB
ejpam-488	215	15			NOUN
ejpam-488	215	16			NOUN
ejpam-488	215	17			PUNCT
ejpam-488	216	1	<	<	X
ejpam-488	216	2	π	π	X
ejpam-488	216	3	2	2	NUM
ejpam-488	216	4	δ2	δ2	VERB
ejpam-488	216	5	,	,	PUNCT
ejpam-488	216	6	where	where	SCONJ
ejpam-488	216	7	g1	g1	PROPN
ejpam-488	216	8	,	,	PUNCT
ejpam-488	216	9	...	...	PUNCT
ejpam-488	216	10	,	,	PUNCT
ejpam-488	216	11	gq	gq	PROPN
ejpam-488	216	12	∈	∈	PROPN
ejpam-488	216	13	ωm	ωm	VERB
ejpam-488	216	14	,	,	PUNCT
ejpam-488	216	15	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	216	16	;	;	PUNCT
ejpam-488	216	17	a	a	DET
ejpam-488	216	18	,	,	PUNCT
ejpam-488	216	19	b	b	NOUN
ejpam-488	216	20	)	)	PUNCT
ejpam-488	216	21	,	,	PUNCT
ejpam-488	216	22	then	then	ADV
ejpam-488	216	23	−	−	PROPN
ejpam-488	216	24	π	π	PROPN
ejpam-488	216	25	2	2	NUM
ejpam-488	216	26	α1	α1	PROPN
ejpam-488	216	27	<	<	X
ejpam-488	216	28	arg	arg	NOUN
ejpam-488	216	29			PROPN
ejpam-488	216	30			NOUN
ejpam-488	216	31			NOUN
ejpam-488	216	32			NOUN
ejpam-488	216	33			NOUN
ejpam-488	216	34			NOUN
ejpam-488	216	35	z(im(λ,ℓ)fc	z(im(λ,ℓ)fc	NOUN
ejpam-488	216	36	(	(	PUNCT
ejpam-488	216	37	f	f	NOUN
ejpam-488	216	38	)	)	PUNCT
ejpam-488	216	39	(	(	PUNCT
ejpam-488	216	40	z	z	NOUN
ejpam-488	216	41	)	)	PUNCT
ejpam-488	216	42	)	)	PUNCT
ejpam-488	217	1	′	′	NUM
ejpam-488	217	2	�	�	PROPN
ejpam-488	217	3	1	1	NUM
ejpam-488	217	4	q	q	PROPN
ejpam-488	217	5	�	�	PROPN
ejpam-488	217	6	q	q	PROPN
ejpam-488	217	7	∑	∑	PROPN
ejpam-488	217	8	j=1	j=1	PROPN
ejpam-488	217	9	im(λ,ℓ)fc(g	im(λ,ℓ)fc(g	NOUN
ejpam-488	217	10	j)(z	j)(z	PUNCT
ejpam-488	217	11	)	)	PUNCT
ejpam-488	217	12			PROPN
ejpam-488	217	13			NOUN
ejpam-488	217	14			VERB
ejpam-488	217	15			NOUN
ejpam-488	217	16			NOUN
ejpam-488	217	17			PUNCT
ejpam-488	218	1	<	<	X
ejpam-488	218	2	π	π	X
ejpam-488	218	3	2	2	NUM
ejpam-488	218	4	α2	α2	ADJ
ejpam-488	218	5	,	,	PUNCT
ejpam-488	218	6	where	where	SCONJ
ejpam-488	218	7	fc	fc	PROPN
ejpam-488	218	8	is	be	AUX
ejpam-488	218	9	the	the	DET
ejpam-488	218	10	integral	integral	ADJ
ejpam-488	218	11	operator	operator	NOUN
ejpam-488	218	12	defined	define	VERB
ejpam-488	218	13	by	by	ADP
ejpam-488	218	14	(	(	PUNCT
ejpam-488	218	15	13	13	NUM
ejpam-488	218	16	)	)	PUNCT
ejpam-488	218	17	,	,	PUNCT
ejpam-488	218	18	and	and	CCONJ
ejpam-488	218	19	α1	α1	PROPN
ejpam-488	218	20	and	and	CCONJ
ejpam-488	218	21	α2	α2	PROPN
ejpam-488	218	22	(	(	PUNCT
ejpam-488	218	23	0	0	NUM
ejpam-488	218	24	<	<	X
ejpam-488	218	25	α1	α1	PROPN
ejpam-488	218	26	,	,	PUNCT
ejpam-488	218	27	α2	α2	ADJ
ejpam-488	218	28	≤	≤	NOUN
ejpam-488	218	29	1	1	NUM
ejpam-488	218	30	)	)	PUNCT
ejpam-488	218	31	are	be	AUX
ejpam-488	218	32	the	the	DET
ejpam-488	218	33	solutions	solution	NOUN
ejpam-488	218	34	of	of	ADP
ejpam-488	218	35	the	the	DET
ejpam-488	218	36	following	follow	VERB
ejpam-488	218	37	equations	equation	NOUN
ejpam-488	218	38	:	:	PUNCT
ejpam-488	218	39	δ1	δ1	NOUN
ejpam-488	218	40	=	=	PUNCT
ejpam-488	218	41			PROPN
ejpam-488	218	42			ADP
ejpam-488	218	43			ADJ
ejpam-488	218	44	α1	α1	PROPN
ejpam-488	218	45	+	+	CCONJ
ejpam-488	218	46	2	2	NUM
ejpam-488	218	47	π	π	PROPN
ejpam-488	218	48	tan−1	tan−1	PROPN
ejpam-488	218	49	�	�	PROPN
ejpam-488	218	50	(	(	PUNCT
ejpam-488	218	51	α1+α2)(1−|a|	α1+α2)(1−|a|	NOUN
ejpam-488	218	52	)	)	PUNCT
ejpam-488	218	53	cos	cos	PROPN
ejpam-488	218	54	�	�	PROPN
ejpam-488	218	55	π	π	PROPN
ejpam-488	218	56	2	2	NUM
ejpam-488	218	57	�	�	PROPN
ejpam-488	218	58	t2	t2	PROPN
ejpam-488	218	59	2	2	NUM
ejpam-488	218	60	�	�	PROPN
ejpam-488	218	61	1+a	1+a	NUM
ejpam-488	218	62	1+b	1+b	NUM
ejpam-488	218	63	+	+	PROPN
ejpam-488	218	64	c	c	PROPN
ejpam-488	218	65	�	�	PROPN
ejpam-488	218	66	(	(	PUNCT
ejpam-488	218	67	1+|a|)+(α1+α2)(1−|a|	1+|a|)+(α1+α2)(1−|a|	NOUN
ejpam-488	218	68	)	)	PUNCT
ejpam-488	218	69	sin	sin	NOUN
ejpam-488	218	70	�	�	PROPN
ejpam-488	218	71	π	π	PROPN
ejpam-488	218	72	2	2	NUM
ejpam-488	218	73	�	�	PROPN
ejpam-488	218	74	t2	t2	PROPN
ejpam-488	218	75	�	�	PROPN
ejpam-488	218	76	(	(	PUNCT
ejpam-488	218	77	b	b	PROPN
ejpam-488	218	78	6=−1	6=−1	NUM
ejpam-488	218	79	)	)	PUNCT
ejpam-488	218	80	α1	α1	PROPN
ejpam-488	218	81	(	(	PUNCT
ejpam-488	218	82	b	b	NOUN
ejpam-488	218	83	=	=	NOUN
ejpam-488	218	84	−1	−1	NOUN
ejpam-488	218	85	)	)	PUNCT
ejpam-488	218	86	,	,	PUNCT
ejpam-488	218	87	and	and	CCONJ
ejpam-488	218	88	δ2	δ2	VERB
ejpam-488	218	89	=	=	PUNCT
ejpam-488	218	90			PROPN
ejpam-488	218	91			PRON
ejpam-488	218	92			NOUN
ejpam-488	218	93	α2	α2	ADJ
ejpam-488	218	94	+	+	CCONJ
ejpam-488	218	95	2	2	NUM
ejpam-488	218	96	π	π	PROPN
ejpam-488	218	97	tan−1	tan−1	PROPN
ejpam-488	218	98	�	�	PROPN
ejpam-488	218	99	(	(	PUNCT
ejpam-488	218	100	α1+α2)(1−|a|	α1+α2)(1−|a|	NOUN
ejpam-488	218	101	)	)	PUNCT
ejpam-488	218	102	cos	cos	PROPN
ejpam-488	218	103	�	�	PROPN
ejpam-488	218	104	π	π	PROPN
ejpam-488	218	105	2	2	NUM
ejpam-488	218	106	�	�	PROPN
ejpam-488	218	107	t2	t2	PROPN
ejpam-488	218	108	2	2	NUM
ejpam-488	218	109	�	�	PROPN
ejpam-488	218	110	1+a	1+a	NUM
ejpam-488	218	111	1+b	1+b	NUM
ejpam-488	218	112	+	+	PROPN
ejpam-488	218	113	c	c	PROPN
ejpam-488	218	114	�	�	PROPN
ejpam-488	218	115	(	(	PUNCT
ejpam-488	218	116	1+|a|)+(α1+α2)(1−|a|	1+|a|)+(α1+α2)(1−|a|	NOUN
ejpam-488	218	117	)	)	PUNCT
ejpam-488	218	118	sin	sin	NOUN
ejpam-488	218	119	�	�	PROPN
ejpam-488	218	120	π	π	PROPN
ejpam-488	218	121	2	2	NUM
ejpam-488	218	122	�	�	PROPN
ejpam-488	218	123	t2	t2	PROPN
ejpam-488	218	124	�	�	PROPN
ejpam-488	218	125	(	(	PUNCT
ejpam-488	218	126	b	b	PROPN
ejpam-488	218	127	6=−1	6=−1	NUM
ejpam-488	218	128	)	)	PUNCT
ejpam-488	218	129	,	,	PUNCT
ejpam-488	218	130	α1	α1	PROPN
ejpam-488	218	131	(	(	PUNCT
ejpam-488	218	132	b	b	NOUN
ejpam-488	218	133	=	=	SYM
ejpam-488	218	134	−1	−1	NOUN
ejpam-488	218	135	)	)	PUNCT
ejpam-488	218	136	,	,	PUNCT
ejpam-488	219	1	a	a	PRON
ejpam-488	219	2	being	be	AUX
ejpam-488	219	3	given	give	VERB
ejpam-488	219	4	by	by	ADP
ejpam-488	219	5	(	(	PUNCT
ejpam-488	219	6	9	9	NUM
ejpam-488	219	7	)	)	PUNCT
ejpam-488	219	8	and	and	CCONJ
ejpam-488	219	9	t2	t2	NOUN
ejpam-488	219	10	being	be	AUX
ejpam-488	219	11	the	the	DET
ejpam-488	219	12	same	same	ADJ
ejpam-488	219	13	as	as	ADP
ejpam-488	219	14	t1	t1	NOUN
ejpam-488	219	15	given	give	VERB
ejpam-488	219	16	by	by	ADP
ejpam-488	219	17	(	(	PUNCT
ejpam-488	219	18	18	18	NUM
ejpam-488	219	19	)	)	PUNCT
ejpam-488	219	20	with	with	ADP
ejpam-488	219	21	c	c	NOUN
ejpam-488	219	22	=	=	SYM
ejpam-488	219	23	1−λ+	1−λ+	NUM
ejpam-488	219	24	ℓ	ℓ	PROPN
ejpam-488	219	25	λ	λ	PROPN
ejpam-488	219	26	.	.	PUNCT
ejpam-488	220	1	m.	m.	PROPN
ejpam-488	220	2	aouf	aouf	PROPN
ejpam-488	220	3	,	,	PUNCT
ejpam-488	220	4	a.	a.	NOUN
ejpam-488	220	5	shamandy	shamandy	PROPN
ejpam-488	220	6	,	,	PUNCT
ejpam-488	220	7	r.	r.	PROPN
ejpam-488	220	8	el	el	PROPN
ejpam-488	220	9	-	-	PUNCT
ejpam-488	220	10	ashway	ashway	PROPN
ejpam-488	220	11	,	,	PUNCT
ejpam-488	220	12	e.	e.	PROPN
ejpam-488	220	13	ali	ali	PROPN
ejpam-488	220	14	/	/	SYM
ejpam-488	220	15	eur	eur	PROPN
ejpam-488	220	16	.	.	PUNCT
ejpam-488	221	1	j.	j.	PROPN
ejpam-488	221	2	pure	pure	PROPN
ejpam-488	221	3	appl	appl	PROPN
ejpam-488	221	4	.	.	PROPN
ejpam-488	221	5	math	math	PROPN
ejpam-488	221	6	,	,	PUNCT
ejpam-488	221	7	3	3	NUM
ejpam-488	221	8	(	(	PUNCT
ejpam-488	221	9	2010	2010	NUM
ejpam-488	221	10	)	)	PUNCT
ejpam-488	221	11	,	,	PUNCT
ejpam-488	221	12	317	317	NUM
ejpam-488	221	13	-	-	SYM
ejpam-488	221	14	330	330	NUM
ejpam-488	221	15	327	327	NUM
ejpam-488	221	16	proof	proof	NOUN
ejpam-488	221	17	.	.	PUNCT
ejpam-488	222	1	let	let	VERB
ejpam-488	222	2	p(z	p(z	VERB
ejpam-488	222	3	)	)	PUNCT
ejpam-488	223	1	=	=	SYM
ejpam-488	223	2	z(im(λ,ℓ)fc	z(im(λ,ℓ)fc	NOUN
ejpam-488	223	3	(	(	PUNCT
ejpam-488	223	4	f	f	NOUN
ejpam-488	223	5	)	)	PUNCT
ejpam-488	223	6	(	(	PUNCT
ejpam-488	223	7	z	z	NOUN
ejpam-488	223	8	)	)	PUNCT
ejpam-488	223	9	)	)	PUNCT
ejpam-488	224	1	′	′	NUM
ejpam-488	224	2	�	�	PROPN
ejpam-488	224	3	1	1	NUM
ejpam-488	224	4	q	q	PROPN
ejpam-488	224	5	�	�	PROPN
ejpam-488	224	6	q	q	PROPN
ejpam-488	224	7	∑	∑	PROPN
ejpam-488	224	8	j=1	j=1	PROPN
ejpam-488	224	9	im(λ,ℓ)fc(g	im(λ,ℓ)fc(g	NOUN
ejpam-488	224	10	j)(z	j)(z	PUNCT
ejpam-488	224	11	)	)	PUNCT
ejpam-488	224	12	and	and	CCONJ
ejpam-488	224	13	q(z	q(z	PROPN
ejpam-488	224	14	)	)	PUNCT
ejpam-488	224	15	=	=	SYM
ejpam-488	224	16	1	1	NUM
ejpam-488	224	17	q	q	NOUN
ejpam-488	224	18	q	q	X
ejpam-488	224	19	∑	∑	PUNCT
ejpam-488	224	20	k=1	k=1	X
ejpam-488	224	21	qk(z	qk(z	PROPN
ejpam-488	224	22	)	)	PUNCT
ejpam-488	224	23	,	,	PUNCT
ejpam-488	224	24	qk(z	qk(z	X
ejpam-488	224	25	)	)	PUNCT
ejpam-488	224	26	=	=	SYM
ejpam-488	224	27	z(im(λ,ℓ)fc(gk)(z	z(im(λ,ℓ)fc(gk)(z	NOUN
ejpam-488	224	28	)	)	PUNCT
ejpam-488	224	29	)	)	PUNCT
ejpam-488	225	1	′	′	NUM
ejpam-488	225	2	�	�	PROPN
ejpam-488	225	3	1	1	NUM
ejpam-488	225	4	q	q	PROPN
ejpam-488	225	5	�	�	PROPN
ejpam-488	225	6	q	q	PROPN
ejpam-488	225	7	∑	∑	PROPN
ejpam-488	225	8	j=1	j=1	PROPN
ejpam-488	225	9	im(λ,ℓ)fc(g	im(λ,ℓ)fc(g	NOUN
ejpam-488	225	10	j)(z	j)(z	PUNCT
ejpam-488	225	11	)	)	PUNCT
ejpam-488	225	12	.	.	PUNCT
ejpam-488	226	1	using	use	VERB
ejpam-488	226	2	the	the	DET
ejpam-488	226	3	relationship	relationship	NOUN
ejpam-488	226	4	(	(	PUNCT
ejpam-488	226	5	14	14	NUM
ejpam-488	226	6	)	)	PUNCT
ejpam-488	226	7	,	,	PUNCT
ejpam-488	226	8	we	we	PRON
ejpam-488	226	9	obtain	obtain	VERB
ejpam-488	226	10	�	�	PROPN
ejpam-488	226	11	1	1	NUM
ejpam-488	226	12	q	q	PROPN
ejpam-488	226	13	�	�	PROPN
ejpam-488	226	14	q	q	PROPN
ejpam-488	226	15	∑	∑	PROPN
ejpam-488	226	16	j=1	j=1	PROPN
ejpam-488	226	17	(	(	PUNCT
ejpam-488	226	18	im(λ,ℓ)fc(g	im(λ,ℓ)fc(g	PROPN
ejpam-488	226	19	j)(z))p(z	j)(z))p(z	NUM
ejpam-488	226	20	)	)	PUNCT
ejpam-488	226	21	+	+	CCONJ
ejpam-488	226	22	cim(λ,ℓ)fc	cim(λ,ℓ)fc	PROPN
ejpam-488	226	23	(	(	PUNCT
ejpam-488	226	24	f	f	NOUN
ejpam-488	226	25	)	)	PUNCT
ejpam-488	226	26	(	(	PUNCT
ejpam-488	226	27	z	z	NOUN
ejpam-488	226	28	)	)	PUNCT
ejpam-488	226	29	=	=	PUNCT
ejpam-488	227	1	(	(	PUNCT
ejpam-488	227	2	c	c	NOUN
ejpam-488	227	3	+	+	NOUN
ejpam-488	227	4	1)im(λ,ℓ	1)im(λ,ℓ	X
ejpam-488	227	5	)	)	PUNCT
ejpam-488	227	6	f	f	NOUN
ejpam-488	227	7	(	(	PUNCT
ejpam-488	227	8	z	z	NOUN
ejpam-488	227	9	)	)	PUNCT
ejpam-488	227	10	.	.	PUNCT
ejpam-488	228	1	(	(	PUNCT
ejpam-488	228	2	22	22	X
ejpam-488	228	3	)	)	PUNCT
ejpam-488	228	4	differentiating	differentiate	VERB
ejpam-488	228	5	(	(	PUNCT
ejpam-488	228	6	22	22	NUM
ejpam-488	228	7	)	)	PUNCT
ejpam-488	228	8	with	with	ADP
ejpam-488	228	9	respect	respect	NOUN
ejpam-488	228	10	to	to	ADP
ejpam-488	228	11	z	z	NOUN
ejpam-488	228	12	,	,	PUNCT
ejpam-488	228	13	and	and	CCONJ
ejpam-488	228	14	simplifying	simplify	VERB
ejpam-488	228	15	,	,	PUNCT
ejpam-488	228	16	we	we	PRON
ejpam-488	228	17	get	get	VERB
ejpam-488	228	18	z(im(λ,ℓ	z(im(λ,ℓ	NUM
ejpam-488	228	19	)	)	PUNCT
ejpam-488	228	20	f	f	PROPN
ejpam-488	228	21	(	(	PUNCT
ejpam-488	228	22	z	z	NOUN
ejpam-488	228	23	)	)	PUNCT
ejpam-488	228	24	)	)	PUNCT
ejpam-488	229	1	′	′	NUM
ejpam-488	229	2	�	�	PROPN
ejpam-488	229	3	1	1	NUM
ejpam-488	229	4	q	q	PROPN
ejpam-488	229	5	�	�	PROPN
ejpam-488	229	6	q	q	PROPN
ejpam-488	229	7	∑	∑	PROPN
ejpam-488	229	8	j=1	j=1	ADJ
ejpam-488	229	9	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	229	10	j(z	j(z	PROPN
ejpam-488	229	11	)	)	PUNCT
ejpam-488	229	12	=	=	PUNCT
ejpam-488	229	13	p(z	p(z	NOUN
ejpam-488	229	14	)	)	PUNCT
ejpam-488	230	1	+	+	CCONJ
ejpam-488	230	2	zp	zp	NOUN
ejpam-488	230	3	′	′	NUM
ejpam-488	230	4	(	(	PUNCT
ejpam-488	230	5	z	z	NOUN
ejpam-488	230	6	)	)	PUNCT
ejpam-488	230	7	q(z	q(z	PROPN
ejpam-488	230	8	)	)	PUNCT
ejpam-488	231	1	+	+	NUM
ejpam-488	232	1	c	c	NOUN
ejpam-488	232	2	.	.	PUNCT
ejpam-488	233	1	since	since	SCONJ
ejpam-488	233	2	g1	g1	PROPN
ejpam-488	233	3	,	,	PUNCT
ejpam-488	233	4	...	...	PUNCT
ejpam-488	233	5	,	,	PUNCT
ejpam-488	233	6	gq	gq	PROPN
ejpam-488	233	7	∈	∈	PROPN
ejpam-488	233	8	ωm	ωm	VERB
ejpam-488	233	9	,	,	PUNCT
ejpam-488	233	10	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	233	11	;	;	PUNCT
ejpam-488	233	12	a	a	DET
ejpam-488	233	13	,	,	PUNCT
ejpam-488	233	14	b	b	NOUN
ejpam-488	233	15	)	)	PUNCT
ejpam-488	233	16	,	,	PUNCT
ejpam-488	233	17	by	by	ADP
ejpam-488	233	18	proposition	proposition	NOUN
ejpam-488	233	19	2	2	NUM
ejpam-488	233	20	,	,	PUNCT
ejpam-488	233	21	we	we	PRON
ejpam-488	233	22	have	have	VERB
ejpam-488	233	23	fc(g1	fc(g1	NOUN
ejpam-488	233	24	)	)	PUNCT
ejpam-488	233	25	,	,	PUNCT
ejpam-488	233	26	...	...	PUNCT
ejpam-488	233	27	,	,	PUNCT
ejpam-488	233	28	fc(gq	fc(gq	PROPN
ejpam-488	233	29	)	)	PUNCT
ejpam-488	233	30	∈	∈	PROPN
ejpam-488	233	31	ωm	ωm	VERB
ejpam-488	233	32	,	,	PUNCT
ejpam-488	233	33	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	233	34	;	;	PUNCT
ejpam-488	233	35	a	a	DET
ejpam-488	233	36	,	,	PUNCT
ejpam-488	233	37	b	b	NOUN
ejpam-488	233	38	)	)	PUNCT
ejpam-488	233	39	.	.	PUNCT
ejpam-488	234	1	hence	hence	ADV
ejpam-488	234	2	,	,	PUNCT
ejpam-488	234	3	we	we	PRON
ejpam-488	234	4	find	find	VERB
ejpam-488	234	5	that	that	SCONJ
ejpam-488	234	6	q(z)≺	q(z)≺	ADV
ejpam-488	234	7	1	1	NUM
ejpam-488	234	8	+	+	NUM
ejpam-488	234	9	az	az	PROPN
ejpam-488	234	10	1	1	NUM
ejpam-488	234	11	+	+	CCONJ
ejpam-488	234	12	bz	bz	PROPN
ejpam-488	234	13	(	(	PUNCT
ejpam-488	234	14	z	z	NOUN
ejpam-488	234	15	∈	∈	PROPN
ejpam-488	234	16	u;−1≤	u;−1≤	NUM
ejpam-488	234	17	b	b	NOUN
ejpam-488	234	18	<	<	X
ejpam-488	234	19	a≤	a≤	DET
ejpam-488	234	20	1	1	NUM
ejpam-488	234	21	)	)	PUNCT
ejpam-488	234	22	.	.	PUNCT
ejpam-488	235	1	the	the	DET
ejpam-488	235	2	remaining	remain	VERB
ejpam-488	235	3	part	part	NOUN
ejpam-488	235	4	of	of	ADP
ejpam-488	235	5	the	the	DET
ejpam-488	235	6	proof	proof	NOUN
ejpam-488	235	7	is	be	AUX
ejpam-488	235	8	similar	similar	ADJ
ejpam-488	235	9	to	to	ADP
ejpam-488	235	10	that	that	PRON
ejpam-488	235	11	in	in	ADP
ejpam-488	235	12	the	the	DET
ejpam-488	235	13	proof	proof	NOUN
ejpam-488	235	14	of	of	ADP
ejpam-488	235	15	theorem	theorem	NOUN
ejpam-488	235	16	1	1	NUM
ejpam-488	235	17	,	,	PUNCT
ejpam-488	235	18	and	and	CCONJ
ejpam-488	235	19	so	so	ADV
ejpam-488	235	20	we	we	PRON
ejpam-488	235	21	omit	omit	VERB
ejpam-488	235	22	the	the	DET
ejpam-488	235	23	details	detail	NOUN
ejpam-488	235	24	involved	involve	VERB
ejpam-488	235	25	.	.	PUNCT
ejpam-488	236	1	putting	put	VERB
ejpam-488	236	2	δ1	δ1	NOUN
ejpam-488	236	3	=	=	SYM
ejpam-488	236	4	δ2	δ2	PROPN
ejpam-488	236	5	in	in	ADP
ejpam-488	236	6	theorem	theorem	NOUN
ejpam-488	236	7	2	2	NUM
ejpam-488	236	8	we	we	PRON
ejpam-488	236	9	obtain	obtain	VERB
ejpam-488	236	10	the	the	DET
ejpam-488	236	11	following	follow	VERB
ejpam-488	236	12	corollary	corollary	NOUN
ejpam-488	236	13	.	.	PUNCT
ejpam-488	237	1	corollary	corollary	ADJ
ejpam-488	237	2	3	3	X
ejpam-488	237	3	.	.	PUNCT
ejpam-488	238	1	let	let	VERB
ejpam-488	238	2	f	f	PROPN
ejpam-488	238	3	∈	∈	PROPN
ejpam-488	238	4	a	a	PRON
ejpam-488	238	5	,	,	PUNCT
ejpam-488	238	6	0	0	NUM
ejpam-488	238	7	<	<	X
ejpam-488	238	8	δ	δ	NOUN
ejpam-488	238	9	≤	≤	ADV
ejpam-488	238	10	1	1	NUM
ejpam-488	238	11	and	and	CCONJ
ejpam-488	238	12	c	c	X
ejpam-488	238	13	≥	≥	NOUN
ejpam-488	238	14	0	0	NUM
ejpam-488	238	15	.	.	PUNCT
ejpam-488	239	1	if	if	SCONJ
ejpam-488	239	2	�	�	PROPN
ejpam-488	239	3	�	�	PROPN
ejpam-488	239	4	�	�	PROPN
ejpam-488	239	5	�	�	PROPN
ejpam-488	239	6	�	�	PROPN
ejpam-488	239	7	�	�	PROPN
ejpam-488	239	8	�	�	PROPN
ejpam-488	239	9	�	�	PROPN
ejpam-488	239	10	�	�	PROPN
ejpam-488	239	11	arg	arg	NOUN
ejpam-488	239	12			PROPN
ejpam-488	239	13			NOUN
ejpam-488	239	14			NOUN
ejpam-488	239	15			NOUN
ejpam-488	239	16			NOUN
ejpam-488	239	17			NOUN
ejpam-488	239	18	z(im(λ,ℓ	z(im(λ,ℓ	NUM
ejpam-488	239	19	)	)	PUNCT
ejpam-488	239	20	f	f	PROPN
ejpam-488	239	21	(	(	PUNCT
ejpam-488	239	22	z	z	NOUN
ejpam-488	239	23	)	)	PUNCT
ejpam-488	239	24	)	)	PUNCT
ejpam-488	240	1	′	′	NUM
ejpam-488	240	2	�	�	PROPN
ejpam-488	240	3	1	1	NUM
ejpam-488	240	4	q	q	PROPN
ejpam-488	240	5	�	�	PROPN
ejpam-488	240	6	q	q	PROPN
ejpam-488	240	7	∑	∑	PROPN
ejpam-488	240	8	j=1	j=1	ADJ
ejpam-488	240	9	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	240	10	j(z	j(z	PROPN
ejpam-488	240	11	)	)	PUNCT
ejpam-488	240	12			PROPN
ejpam-488	240	13			NOUN
ejpam-488	240	14			VERB
ejpam-488	240	15			NOUN
ejpam-488	240	16			NOUN
ejpam-488	240	17			PUNCT
ejpam-488	240	18	�	�	PROPN
ejpam-488	240	19	�	�	PROPN
ejpam-488	240	20	�	�	PROPN
ejpam-488	240	21	�	�	PROPN
ejpam-488	240	22	�	�	PROPN
ejpam-488	240	23	�	�	PROPN
ejpam-488	240	24	�	�	PROPN
ejpam-488	240	25	�	�	PROPN
ejpam-488	240	26	�	�	PROPN
ejpam-488	240	27	<	<	X
ejpam-488	240	28	π	π	PROPN
ejpam-488	240	29	2	2	NUM
ejpam-488	240	30	δ	δ	PROPN
ejpam-488	240	31	,	,	PUNCT
ejpam-488	240	32	where	where	SCONJ
ejpam-488	240	33	g1	g1	PROPN
ejpam-488	240	34	,	,	PUNCT
ejpam-488	240	35	...	...	PUNCT
ejpam-488	240	36	,	,	PUNCT
ejpam-488	240	37	gq	gq	PROPN
ejpam-488	240	38	∈	∈	PROPN
ejpam-488	240	39	ωm	ωm	VERB
ejpam-488	240	40	,	,	PUNCT
ejpam-488	240	41	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	240	42	;	;	PUNCT
ejpam-488	240	43	a	a	DET
ejpam-488	240	44	,	,	PUNCT
ejpam-488	240	45	b	b	NOUN
ejpam-488	240	46	)	)	PUNCT
ejpam-488	240	47	,	,	PUNCT
ejpam-488	240	48	then	then	ADV
ejpam-488	240	49	�	�	PROPN
ejpam-488	240	50	�	�	PROPN
ejpam-488	240	51	�	�	PROPN
ejpam-488	240	52	�	�	PROPN
ejpam-488	240	53	�	�	PROPN
ejpam-488	240	54	�	�	PROPN
ejpam-488	240	55	�	�	PROPN
ejpam-488	240	56	�	�	PROPN
ejpam-488	240	57	�	�	PROPN
ejpam-488	240	58	arg	arg	NOUN
ejpam-488	240	59			PROPN
ejpam-488	240	60			NOUN
ejpam-488	240	61			NOUN
ejpam-488	240	62			NOUN
ejpam-488	240	63			NOUN
ejpam-488	240	64			NOUN
ejpam-488	240	65	z(im(λ,ℓ)fc	z(im(λ,ℓ)fc	NOUN
ejpam-488	240	66	(	(	PUNCT
ejpam-488	240	67	f	f	NOUN
ejpam-488	240	68	)	)	PUNCT
ejpam-488	240	69	(	(	PUNCT
ejpam-488	240	70	z	z	NOUN
ejpam-488	240	71	)	)	PUNCT
ejpam-488	240	72	)	)	PUNCT
ejpam-488	241	1	′	′	NUM
ejpam-488	241	2	�	�	PROPN
ejpam-488	241	3	1	1	NUM
ejpam-488	241	4	q	q	PROPN
ejpam-488	241	5	�	�	PROPN
ejpam-488	241	6	q	q	PROPN
ejpam-488	241	7	∑	∑	PROPN
ejpam-488	241	8	j=1	j=1	PROPN
ejpam-488	241	9	im(λ,ℓ)fc(g	im(λ,ℓ)fc(g	NOUN
ejpam-488	241	10	j)(z	j)(z	PUNCT
ejpam-488	241	11	)	)	PUNCT
ejpam-488	241	12			PROPN
ejpam-488	241	13			NOUN
ejpam-488	241	14			VERB
ejpam-488	241	15			NOUN
ejpam-488	241	16			NOUN
ejpam-488	241	17			PUNCT
ejpam-488	242	1	�	�	PROPN
ejpam-488	242	2	�	�	PROPN
ejpam-488	242	3	�	�	PROPN
ejpam-488	242	4	�	�	PROPN
ejpam-488	242	5	�	�	PROPN
ejpam-488	242	6	�	�	PROPN
ejpam-488	242	7	�	�	PROPN
ejpam-488	242	8	�	�	PROPN
ejpam-488	242	9	�	�	PROPN
ejpam-488	242	10	<	<	X
ejpam-488	242	11	π	π	PROPN
ejpam-488	242	12	2	2	NUM
ejpam-488	242	13	α	α	NOUN
ejpam-488	242	14	,	,	PUNCT
ejpam-488	242	15	m.	m.	NOUN
ejpam-488	242	16	aouf	aouf	PROPN
ejpam-488	242	17	,	,	PUNCT
ejpam-488	242	18	a.	a.	NOUN
ejpam-488	242	19	shamandy	shamandy	PROPN
ejpam-488	242	20	,	,	PUNCT
ejpam-488	242	21	r.	r.	PROPN
ejpam-488	242	22	el	el	PROPN
ejpam-488	242	23	-	-	PUNCT
ejpam-488	242	24	ashway	ashway	PROPN
ejpam-488	242	25	,	,	PUNCT
ejpam-488	242	26	e.	e.	PROPN
ejpam-488	242	27	ali	ali	PROPN
ejpam-488	242	28	/	/	SYM
ejpam-488	242	29	eur	eur	PROPN
ejpam-488	242	30	.	.	PUNCT
ejpam-488	243	1	j.	j.	PROPN
ejpam-488	243	2	pure	pure	PROPN
ejpam-488	243	3	appl	appl	PROPN
ejpam-488	243	4	.	.	PROPN
ejpam-488	243	5	math	math	PROPN
ejpam-488	243	6	,	,	PUNCT
ejpam-488	243	7	3	3	NUM
ejpam-488	243	8	(	(	PUNCT
ejpam-488	243	9	2010	2010	NUM
ejpam-488	243	10	)	)	PUNCT
ejpam-488	243	11	,	,	PUNCT
ejpam-488	243	12	317	317	NUM
ejpam-488	243	13	-	-	SYM
ejpam-488	243	14	330	330	NUM
ejpam-488	243	15	328	328	NUM
ejpam-488	243	16	where	where	SCONJ
ejpam-488	243	17	α	α	PROPN
ejpam-488	243	18	(	(	PUNCT
ejpam-488	243	19	0	0	NUM
ejpam-488	243	20	<	<	X
ejpam-488	243	21	α	α	PRON
ejpam-488	243	22	≤	≤	NUM
ejpam-488	243	23	1	1	NUM
ejpam-488	243	24	)	)	PUNCT
ejpam-488	243	25	is	be	AUX
ejpam-488	243	26	the	the	DET
ejpam-488	243	27	solution	solution	NOUN
ejpam-488	243	28	of	of	ADP
ejpam-488	243	29	the	the	DET
ejpam-488	243	30	following	follow	VERB
ejpam-488	243	31	equation	equation	NOUN
ejpam-488	243	32	δ	δ	NOUN
ejpam-488	243	33	=	=	PUNCT
ejpam-488	244	1			PROPN
ejpam-488	244	2			PRON
ejpam-488	244	3			NOUN
ejpam-488	244	4	α+	α+	X
ejpam-488	244	5	2	2	NUM
ejpam-488	244	6	π	π	PROPN
ejpam-488	244	7	tan−1	tan−1	PROPN
ejpam-488	244	8	�	�	PROPN
ejpam-488	244	9	α	α	PROPN
ejpam-488	244	10	cos	cos	PROPN
ejpam-488	244	11	�	�	PROPN
ejpam-488	244	12	π	π	PROPN
ejpam-488	244	13	2	2	NUM
ejpam-488	244	14	�	�	PROPN
ejpam-488	244	15	t2	t2	PROPN
ejpam-488	244	16	�	�	PROPN
ejpam-488	244	17	1+a	1+a	NUM
ejpam-488	244	18	1+b	1+b	NUM
ejpam-488	244	19	+	+	NOUN
ejpam-488	244	20	c	c	PROPN
ejpam-488	244	21	�	�	NOUN
ejpam-488	244	22	+	+	NOUN
ejpam-488	244	23	α	α	PROPN
ejpam-488	244	24	sin	sin	NOUN
ejpam-488	244	25	�	�	PROPN
ejpam-488	244	26	π	π	PROPN
ejpam-488	244	27	2	2	NUM
ejpam-488	244	28	�	�	PROPN
ejpam-488	244	29	t2	t2	PROPN
ejpam-488	244	30	�	�	PROPN
ejpam-488	244	31	(	(	PUNCT
ejpam-488	244	32	b	b	PROPN
ejpam-488	244	33	6=	6=	NUM
ejpam-488	244	34	−1	−1	NOUN
ejpam-488	244	35	)	)	PUNCT
ejpam-488	244	36	,	,	PUNCT
ejpam-488	244	37	α	α	PROPN
ejpam-488	244	38	(	(	PUNCT
ejpam-488	244	39	b	b	NOUN
ejpam-488	244	40	=	=	SYM
ejpam-488	244	41	−1	−1	NOUN
ejpam-488	244	42	)	)	PUNCT
ejpam-488	244	43	,	,	PUNCT
ejpam-488	244	44	t2	t2	NOUN
ejpam-488	244	45	being	be	AUX
ejpam-488	244	46	the	the	DET
ejpam-488	244	47	same	same	ADJ
ejpam-488	244	48	as	as	ADP
ejpam-488	244	49	t1	t1	NOUN
ejpam-488	244	50	given	give	VERB
ejpam-488	244	51	by	by	ADP
ejpam-488	244	52	(	(	PUNCT
ejpam-488	244	53	18	18	NUM
ejpam-488	244	54	)	)	PUNCT
ejpam-488	244	55	with	with	ADP
ejpam-488	244	56	c	c	NOUN
ejpam-488	244	57	=	=	SYM
ejpam-488	244	58	1−λ+	1−λ+	NUM
ejpam-488	244	59	ℓ	ℓ	NOUN
ejpam-488	244	60	λ	λ	PROPN
ejpam-488	244	61	.	.	PUNCT
ejpam-488	245	1	from	from	ADP
ejpam-488	245	2	corollary	corollary	ADJ
ejpam-488	245	3	3	3	NUM
ejpam-488	245	4	,	,	PUNCT
ejpam-488	245	5	we	we	PRON
ejpam-488	245	6	readily	readily	ADV
ejpam-488	245	7	obtain	obtain	VERB
ejpam-488	245	8	the	the	DET
ejpam-488	245	9	following	follow	VERB
ejpam-488	245	10	corollary	corollary	NOUN
ejpam-488	245	11	.	.	PUNCT
ejpam-488	246	1	corollary	corollary	ADJ
ejpam-488	246	2	4	4	NUM
ejpam-488	246	3	.	.	PUNCT
ejpam-488	247	1	let	let	VERB
ejpam-488	247	2	f	f	PROPN
ejpam-488	247	3	∈	∈	PROPN
ejpam-488	247	4	cm	cm	PROPN
ejpam-488	247	5	,	,	PUNCT
ejpam-488	247	6	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	247	7	;	;	PUNCT
ejpam-488	247	8	a	a	DET
ejpam-488	247	9	,	,	PUNCT
ejpam-488	247	10	b	b	NOUN
ejpam-488	247	11	)	)	PUNCT
ejpam-488	247	12	.	.	PUNCT
ejpam-488	248	1	then	then	ADV
ejpam-488	248	2	fc	fc	PROPN
ejpam-488	248	3	(	(	PUNCT
ejpam-488	248	4	f	f	PROPN
ejpam-488	248	5	)	)	PUNCT
ejpam-488	248	6	∈	∈	PROPN
ejpam-488	248	7	cm	cm	NOUN
ejpam-488	248	8	,	,	PUNCT
ejpam-488	248	9	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	248	10	;	;	PUNCT
ejpam-488	248	11	a	a	DET
ejpam-488	248	12	,	,	PUNCT
ejpam-488	248	13	b	b	NOUN
ejpam-488	248	14	)	)	PUNCT
ejpam-488	248	15	,	,	PUNCT
ejpam-488	248	16	where	where	SCONJ
ejpam-488	248	17	fc	fc	PROPN
ejpam-488	248	18	is	be	AUX
ejpam-488	248	19	the	the	DET
ejpam-488	248	20	integral	integral	ADJ
ejpam-488	248	21	operator	operator	NOUN
ejpam-488	248	22	defined	define	VERB
ejpam-488	248	23	by	by	ADP
ejpam-488	248	24	(	(	PUNCT
ejpam-488	248	25	13	13	NUM
ejpam-488	248	26	)	)	PUNCT
ejpam-488	248	27	.	.	PUNCT
ejpam-488	249	1	remark	remark	PROPN
ejpam-488	249	2	3	3	NUM
ejpam-488	249	3	.	.	PROPN
ejpam-488	249	4	from	from	ADP
ejpam-488	249	5	theorem	theorem	ADJ
ejpam-488	249	6	2	2	NUM
ejpam-488	249	7	or	or	CCONJ
ejpam-488	249	8	corollary	corollary	ADJ
ejpam-488	249	9	4	4	NUM
ejpam-488	249	10	,	,	PUNCT
ejpam-488	249	11	we	we	PRON
ejpam-488	249	12	see	see	VERB
ejpam-488	249	13	that	that	SCONJ
ejpam-488	249	14	every	every	DET
ejpam-488	249	15	function	function	NOUN
ejpam-488	249	16	in	in	ADP
ejpam-488	249	17	cm	cm	PROPN
ejpam-488	249	18	,	,	PUNCT
ejpam-488	249	19	λ,ℓ(q	λ,ℓ(q	ADP
ejpam-488	249	20	;	;	PUNCT
ejpam-488	249	21	a	a	DET
ejpam-488	249	22	,	,	PUNCT
ejpam-488	249	23	b	b	NOUN
ejpam-488	249	24	)	)	PUNCT
ejpam-488	249	25	preserves	preserve	VERB
ejpam-488	249	26	the	the	DET
ejpam-488	249	27	angles	angle	NOUN
ejpam-488	249	28	under	under	ADP
ejpam-488	249	29	the	the	DET
ejpam-488	249	30	integral	integral	ADJ
ejpam-488	249	31	operator	operator	NOUN
ejpam-488	249	32	defined	define	VERB
ejpam-488	249	33	by	by	ADP
ejpam-488	249	34	(	(	PUNCT
ejpam-488	249	35	13	13	NUM
ejpam-488	249	36	)	)	PUNCT
ejpam-488	249	37	.	.	PUNCT
ejpam-488	250	1	if	if	SCONJ
ejpam-488	250	2	we	we	PRON
ejpam-488	250	3	put	put	VERB
ejpam-488	250	4	m	m	NOUN
ejpam-488	250	5	=	=	NOUN
ejpam-488	250	6	ℓ=	ℓ=	NOUN
ejpam-488	250	7	0	0	NUM
ejpam-488	250	8	,	,	PUNCT
ejpam-488	250	9	λ=	λ=	VERB
ejpam-488	250	10	1	1	NUM
ejpam-488	250	11	,	,	PUNCT
ejpam-488	250	12	q	q	NOUN
ejpam-488	250	13	=	=	SYM
ejpam-488	250	14	2	2	NUM
ejpam-488	250	15	,	,	PUNCT
ejpam-488	250	16	a=	a=	X
ejpam-488	250	17	1	1	NUM
ejpam-488	250	18	and	and	CCONJ
ejpam-488	250	19	b	b	NOUN
ejpam-488	250	20	=	=	SYM
ejpam-488	250	21	−1	−1	NOUN
ejpam-488	250	22	in	in	ADP
ejpam-488	250	23	corollary	corollary	ADJ
ejpam-488	250	24	4	4	NUM
ejpam-488	250	25	,	,	PUNCT
ejpam-488	250	26	we	we	PRON
ejpam-488	250	27	are	be	AUX
ejpam-488	250	28	easily	easily	ADV
ejpam-488	250	29	led	lead	VERB
ejpam-488	250	30	to	to	ADP
ejpam-488	250	31	the	the	DET
ejpam-488	250	32	result	result	NOUN
ejpam-488	250	33	given	give	VERB
ejpam-488	250	34	earlier	early	ADV
ejpam-488	250	35	by	by	ADP
ejpam-488	250	36	das	das	PROPN
ejpam-488	250	37	and	and	CCONJ
ejpam-488	250	38	singh	singh	NOUN
ejpam-488	251	1	[	[	X
ejpam-488	251	2	6	6	NUM
ejpam-488	251	3	]	]	PUNCT
ejpam-488	251	4	.	.	PUNCT
ejpam-488	252	1	finally	finally	ADV
ejpam-488	252	2	,	,	PUNCT
ejpam-488	252	3	we	we	PRON
ejpam-488	252	4	state	state	NOUN
ejpam-488	252	5	theorem	theorem	VERB
ejpam-488	252	6	3	3	NUM
ejpam-488	252	7	below	below	ADV
ejpam-488	252	8	.	.	PUNCT
ejpam-488	253	1	the	the	DET
ejpam-488	253	2	proof	proof	NOUN
ejpam-488	253	3	is	be	AUX
ejpam-488	253	4	much	much	ADV
ejpam-488	253	5	akin	akin	ADJ
ejpam-488	253	6	to	to	ADP
ejpam-488	253	7	that	that	PRON
ejpam-488	253	8	of	of	ADP
ejpam-488	253	9	theorem	theorem	NOUN
ejpam-488	253	10	1	1	NUM
ejpam-488	253	11	,	,	PUNCT
ejpam-488	253	12	and	and	CCONJ
ejpam-488	253	13	so	so	ADV
ejpam-488	253	14	that	that	SCONJ
ejpam-488	253	15	details	detail	NOUN
ejpam-488	253	16	may	may	AUX
ejpam-488	253	17	be	be	AUX
ejpam-488	253	18	omitted	omit	VERB
ejpam-488	253	19	.	.	PUNCT
ejpam-488	254	1	theorem	theorem	NOUN
ejpam-488	254	2	3	3	X
ejpam-488	254	3	.	.	PUNCT
ejpam-488	255	1	let	let	VERB
ejpam-488	255	2	f	f	PROPN
ejpam-488	255	3	∈	∈	PROPN
ejpam-488	255	4	a	a	PRON
ejpam-488	255	5	,	,	PUNCT
ejpam-488	255	6	0	0	NUM
ejpam-488	255	7	<	<	X
ejpam-488	255	8	δ1	δ1	NOUN
ejpam-488	255	9	,	,	PUNCT
ejpam-488	255	10	δ2	δ2	ADJ
ejpam-488	255	11	≤	≤	NOUN
ejpam-488	255	12	1	1	NUM
ejpam-488	255	13	and	and	CCONJ
ejpam-488	255	14	γ≥	γ≥	NOUN
ejpam-488	255	15	0	0	NUM
ejpam-488	255	16	.	.	PUNCT
ejpam-488	256	1	if	if	SCONJ
ejpam-488	256	2	−	−	PROPN
ejpam-488	256	3	π	π	PROPN
ejpam-488	256	4	2	2	NUM
ejpam-488	256	5	δ1	δ1	NOUN
ejpam-488	256	6	<	<	X
ejpam-488	256	7	arg	arg	NOUN
ejpam-488	256	8			PROPN
ejpam-488	256	9			NOUN
ejpam-488	256	10			NOUN
ejpam-488	256	11			NOUN
ejpam-488	256	12			NOUN
ejpam-488	256	13			PROPN
ejpam-488	256	14	γ	γ	X
ejpam-488	256	15	z(im+1(λ,ℓ	z(im+1(λ,ℓ	PROPN
ejpam-488	256	16	)	)	PUNCT
ejpam-488	256	17	f	f	PROPN
ejpam-488	256	18	(	(	PUNCT
ejpam-488	256	19	z	z	NOUN
ejpam-488	256	20	)	)	PUNCT
ejpam-488	256	21	)	)	PUNCT
ejpam-488	257	1	′	′	NUM
ejpam-488	257	2	�	�	PROPN
ejpam-488	257	3	1	1	NUM
ejpam-488	257	4	q	q	PROPN
ejpam-488	257	5	�	�	PROPN
ejpam-488	257	6	q	q	PROPN
ejpam-488	257	7	∑	∑	PROPN
ejpam-488	257	8	j=1	j=1	PROPN
ejpam-488	257	9	im+1(λ,ℓ)g	im+1(λ,ℓ)g	PUNCT
ejpam-488	257	10	j(z	j(z	PROPN
ejpam-488	257	11	)	)	PUNCT
ejpam-488	257	12	+	+	CCONJ
ejpam-488	257	13	(	(	PUNCT
ejpam-488	257	14	1−	1−	NUM
ejpam-488	257	15	γ	γ	NOUN
ejpam-488	257	16	)	)	PUNCT
ejpam-488	257	17	z(im(λ,ℓ	z(im(λ,ℓ	NUM
ejpam-488	257	18	)	)	PUNCT
ejpam-488	257	19	f	f	PROPN
ejpam-488	257	20	(	(	PUNCT
ejpam-488	257	21	z	z	NOUN
ejpam-488	257	22	)	)	PUNCT
ejpam-488	257	23	)	)	PUNCT
ejpam-488	258	1	′	′	NUM
ejpam-488	258	2	�	�	PROPN
ejpam-488	258	3	1	1	NUM
ejpam-488	258	4	q	q	PROPN
ejpam-488	258	5	�	�	PROPN
ejpam-488	258	6	q	q	PROPN
ejpam-488	258	7	∑	∑	PROPN
ejpam-488	258	8	j=1	j=1	ADJ
ejpam-488	258	9	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	258	10	j(z	j(z	PROPN
ejpam-488	258	11	)	)	PUNCT
ejpam-488	258	12			PROPN
ejpam-488	258	13			NOUN
ejpam-488	258	14			VERB
ejpam-488	258	15			NOUN
ejpam-488	258	16			NOUN
ejpam-488	258	17			PUNCT
ejpam-488	259	1	<	<	X
ejpam-488	259	2	π	π	X
ejpam-488	259	3	2	2	NUM
ejpam-488	259	4	δ2	δ2	VERB
ejpam-488	259	5	,	,	PUNCT
ejpam-488	259	6	where	where	SCONJ
ejpam-488	259	7	g1	g1	PROPN
ejpam-488	259	8	,	,	PUNCT
ejpam-488	259	9	...	...	PUNCT
ejpam-488	259	10	,	,	PUNCT
ejpam-488	259	11	gq	gq	PROPN
ejpam-488	259	12	∈	∈	PROPN
ejpam-488	259	13	ωm+1,λ,ℓ(q	ωm+1,λ,ℓ(q	PROPN
ejpam-488	259	14	;	;	PUNCT
ejpam-488	259	15	a	a	DET
ejpam-488	259	16	,	,	PUNCT
ejpam-488	259	17	b	b	NOUN
ejpam-488	259	18	)	)	PUNCT
ejpam-488	259	19	,	,	PUNCT
ejpam-488	259	20	then	then	ADV
ejpam-488	259	21	−	−	PROPN
ejpam-488	259	22	π	π	PROPN
ejpam-488	259	23	2	2	NUM
ejpam-488	259	24	α1	α1	PROPN
ejpam-488	259	25	<	<	X
ejpam-488	259	26	arg	arg	NOUN
ejpam-488	259	27			PROPN
ejpam-488	259	28			NOUN
ejpam-488	259	29			NOUN
ejpam-488	259	30			NOUN
ejpam-488	259	31			NOUN
ejpam-488	259	32			NOUN
ejpam-488	259	33	z(im(λ,ℓ	z(im(λ,ℓ	NUM
ejpam-488	259	34	)	)	PUNCT
ejpam-488	259	35	f	f	PROPN
ejpam-488	259	36	(	(	PUNCT
ejpam-488	259	37	z	z	NOUN
ejpam-488	259	38	)	)	PUNCT
ejpam-488	259	39	)	)	PUNCT
ejpam-488	260	1	′	′	NUM
ejpam-488	260	2	1	1	NUM
ejpam-488	260	3	q	q	NOUN
ejpam-488	260	4	q	q	NOUN
ejpam-488	260	5	∑	∑	PUNCT
ejpam-488	260	6	j=1	j=1	ADJ
ejpam-488	260	7	im(λ,ℓ)g	im(λ,ℓ)g	NOUN
ejpam-488	260	8	j(z	j(z	PROPN
ejpam-488	260	9	)	)	PUNCT
ejpam-488	260	10			PROPN
ejpam-488	260	11			NOUN
ejpam-488	260	12			VERB
ejpam-488	260	13			NOUN
ejpam-488	260	14			NOUN
ejpam-488	260	15			PUNCT
ejpam-488	261	1	<	<	X
ejpam-488	261	2	π	π	X
ejpam-488	261	3	2	2	NUM
ejpam-488	261	4	α2	α2	ADJ
ejpam-488	261	5	,	,	PUNCT
ejpam-488	261	6	where	where	SCONJ
ejpam-488	261	7	α1	α1	PROPN
ejpam-488	261	8	and	and	CCONJ
ejpam-488	261	9	α2	α2	NOUN
ejpam-488	261	10	are	be	AUX
ejpam-488	261	11	the	the	DET
ejpam-488	261	12	solutions	solution	NOUN
ejpam-488	261	13	of	of	ADP
ejpam-488	261	14	the	the	DET
ejpam-488	261	15	following	follow	VERB
ejpam-488	261	16	equation	equation	NOUN
ejpam-488	261	17	:	:	PUNCT
ejpam-488	261	18	δ1	δ1	NOUN
ejpam-488	261	19	=	=	PUNCT
ejpam-488	261	20			PROPN
ejpam-488	261	21			ADP
ejpam-488	261	22			ADJ
ejpam-488	261	23	α1	α1	PROPN
ejpam-488	261	24	+	+	CCONJ
ejpam-488	261	25	2	2	NUM
ejpam-488	261	26	π	π	PROPN
ejpam-488	261	27	tan−1	tan−1	PROPN
ejpam-488	261	28	�	�	PROPN
ejpam-488	261	29	(	(	PUNCT
ejpam-488	261	30	α1+α2)(1−|a|)γ	α1+α2)(1−|a|)γ	PROPN
ejpam-488	261	31	cos	cos	PROPN
ejpam-488	261	32	�	�	PROPN
ejpam-488	261	33	π	π	PROPN
ejpam-488	261	34	2	2	NUM
ejpam-488	261	35	�	�	PROPN
ejpam-488	261	36	t1	t1	NOUN
ejpam-488	261	37	2	2	NUM
ejpam-488	261	38	�	�	PROPN
ejpam-488	261	39	1+a	1+a	NUM
ejpam-488	261	40	1+b	1+b	NUM
ejpam-488	261	41	+	+	CCONJ
ejpam-488	261	42	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	261	43	λ	λ	X
ejpam-488	261	44	�	�	PROPN
ejpam-488	261	45	(	(	PUNCT
ejpam-488	261	46	1+|a|)+(α1+α2)(1−|a|	1+|a|)+(α1+α2)(1−|a|	NOUN
ejpam-488	261	47	)	)	PUNCT
ejpam-488	261	48	sin	sin	NOUN
ejpam-488	261	49	�	�	PROPN
ejpam-488	261	50	π	π	PROPN
ejpam-488	261	51	2	2	NUM
ejpam-488	261	52	�	�	PROPN
ejpam-488	261	53	t1	t1	NUM
ejpam-488	261	54	�	�	PROPN
ejpam-488	261	55	(	(	PUNCT
ejpam-488	261	56	b	b	PROPN
ejpam-488	261	57	6=−1	6=−1	NUM
ejpam-488	261	58	)	)	PUNCT
ejpam-488	261	59	,	,	PUNCT
ejpam-488	261	60	α1	α1	PROPN
ejpam-488	261	61	(	(	PUNCT
ejpam-488	261	62	b	b	NOUN
ejpam-488	261	63	=	=	NOUN
ejpam-488	261	64	−1	−1	NOUN
ejpam-488	261	65	)	)	PUNCT
ejpam-488	261	66	,	,	PUNCT
ejpam-488	261	67	and	and	CCONJ
ejpam-488	261	68	δ2	δ2	VERB
ejpam-488	261	69	=	=	PUNCT
ejpam-488	261	70			PROPN
ejpam-488	261	71			PRON
ejpam-488	261	72			NOUN
ejpam-488	261	73	α2	α2	ADJ
ejpam-488	261	74	+	+	CCONJ
ejpam-488	261	75	2	2	NUM
ejpam-488	261	76	π	π	PROPN
ejpam-488	261	77	tan−1	tan−1	PROPN
ejpam-488	261	78	�	�	PROPN
ejpam-488	261	79	(	(	PUNCT
ejpam-488	261	80	α1+α2)(1−|a|)γ	α1+α2)(1−|a|)γ	PROPN
ejpam-488	261	81	cos	cos	PROPN
ejpam-488	261	82	�	�	PROPN
ejpam-488	261	83	π	π	PROPN
ejpam-488	261	84	2	2	NUM
ejpam-488	261	85	�	�	PROPN
ejpam-488	261	86	t1	t1	NOUN
ejpam-488	261	87	2	2	NUM
ejpam-488	261	88	�	�	PROPN
ejpam-488	261	89	1+a	1+a	NUM
ejpam-488	261	90	1+b	1+b	NUM
ejpam-488	261	91	+	+	CCONJ
ejpam-488	261	92	1−λ+ℓ	1−λ+ℓ	NUM
ejpam-488	261	93	λ	λ	X
ejpam-488	261	94	�	�	X
ejpam-488	261	95	(	(	PUNCT
ejpam-488	261	96	1+|a|)+(α1+α2)(1−|a|)γ	1+|a|)+(α1+α2)(1−|a|)γ	ADJ
ejpam-488	261	97	sin	sin	NOUN
ejpam-488	261	98	�	�	PROPN
ejpam-488	261	99	π	π	PROPN
ejpam-488	261	100	2	2	NUM
ejpam-488	261	101	�	�	PROPN
ejpam-488	261	102	t1	t1	NUM
ejpam-488	261	103	�	�	PROPN
ejpam-488	261	104	(	(	PUNCT
ejpam-488	261	105	b	b	PROPN
ejpam-488	261	106	6=	6=	NUM
ejpam-488	261	107	−1	−1	NOUN
ejpam-488	261	108	)	)	PUNCT
ejpam-488	261	109	,	,	PUNCT
ejpam-488	261	110	α2	α2	PROPN
ejpam-488	261	111	(	(	PUNCT
ejpam-488	261	112	b	b	NOUN
ejpam-488	261	113	=	=	SYM
ejpam-488	261	114	−1	−1	NOUN
ejpam-488	261	115	)	)	PUNCT
ejpam-488	261	116	,	,	PUNCT
ejpam-488	261	117	a	a	PRON
ejpam-488	261	118	and	and	CCONJ
ejpam-488	261	119	t1	t1	NOUN
ejpam-488	261	120	being	be	AUX
ejpam-488	261	121	given	give	VERB
ejpam-488	261	122	by	by	ADP
ejpam-488	261	123	(	(	PUNCT
ejpam-488	261	124	9	9	NUM
ejpam-488	261	125	)	)	PUNCT
ejpam-488	261	126	and	and	CCONJ
ejpam-488	261	127	(	(	PUNCT
ejpam-488	261	128	18	18	NUM
ejpam-488	261	129	)	)	PUNCT
ejpam-488	261	130	,	,	PUNCT
ejpam-488	261	131	respectively	respectively	ADV
ejpam-488	261	132	.	.	PUNCT
ejpam-488	262	1	references	reference	NOUN
ejpam-488	262	2	329	329	NUM
ejpam-488	262	3	remark	remark	NOUN
ejpam-488	262	4	4	4	NUM
ejpam-488	262	5	.	.	PUNCT
ejpam-488	262	6	for	for	ADP
ejpam-488	262	7	m=	m=	NOUN
ejpam-488	262	8	ℓ	ℓ	X
ejpam-488	262	9	=	=	SYM
ejpam-488	262	10	0	0	NUM
ejpam-488	262	11	,	,	PUNCT
ejpam-488	262	12	λ=	λ=	VERB
ejpam-488	262	13	1	1	NUM
ejpam-488	262	14	,	,	PUNCT
ejpam-488	262	15	q	q	NOUN
ejpam-488	262	16	=	=	SYM
ejpam-488	262	17	2	2	NUM
ejpam-488	262	18	,	,	PUNCT
ejpam-488	262	19	a=	a=	X
ejpam-488	262	20	1	1	NUM
ejpam-488	262	21	,	,	PUNCT
ejpam-488	263	1	b	b	NOUN
ejpam-488	263	2	=	=	SYM
ejpam-488	263	3	−1	−1	NOUN
ejpam-488	263	4	and	and	CCONJ
ejpam-488	263	5	δ	δ	NOUN
ejpam-488	263	6	=	=	SYM
ejpam-488	263	7	1	1	NUM
ejpam-488	263	8	,	,	PUNCT
ejpam-488	263	9	theorem	theorem	VERB
ejpam-488	263	10	3	3	NUM
ejpam-488	263	11	reduces	reduce	VERB
ejpam-488	263	12	at	at	ADP
ejpam-488	263	13	once	once	ADV
ejpam-488	263	14	to	to	ADP
ejpam-488	263	15	the	the	DET
ejpam-488	263	16	result	result	NOUN
ejpam-488	263	17	given	give	VERB
ejpam-488	263	18	earlier	early	ADV
ejpam-488	263	19	by	by	ADP
ejpam-488	263	20	padmanabhan	padmanabhan	NOUN
ejpam-488	263	21	and	and	CCONJ
ejpam-488	263	22	thangamani	thangamani	NOUN
ejpam-488	264	1	[	[	X
ejpam-488	264	2	15	15	NUM
ejpam-488	264	3	]	]	PUNCT
ejpam-488	264	4	.	.	PUNCT
ejpam-488	265	1	remark	remark	PROPN
ejpam-488	265	2	5	5	NUM
ejpam-488	265	3	.	.	PUNCT
ejpam-488	266	1	putting	put	VERB
ejpam-488	266	2	λ	λ	NOUN
ejpam-488	266	3	=	=	NOUN
ejpam-488	266	4	1	1	NUM
ejpam-488	266	5	in	in	ADP
ejpam-488	266	6	the	the	DET
ejpam-488	266	7	above	above	ADJ
ejpam-488	266	8	results	result	NOUN
ejpam-488	266	9	,	,	PUNCT
ejpam-488	266	10	we	we	PRON
ejpam-488	266	11	obtain	obtain	VERB
ejpam-488	266	12	the	the	DET
ejpam-488	266	13	results	result	NOUN
ejpam-488	266	14	obtained	obtain	VERB
ejpam-488	266	15	by	by	ADP
ejpam-488	266	16	cho	cho	PROPN
ejpam-488	266	17	and	and	CCONJ
ejpam-488	266	18	srivastava	srivastava	PROPN
ejpam-488	267	1	[	[	X
ejpam-488	267	2	5	5	NUM
ejpam-488	267	3	]	]	PUNCT
ejpam-488	267	4	.	.	PUNCT
ejpam-488	268	1	remark	remark	PROPN
ejpam-488	268	2	6	6	NUM
ejpam-488	268	3	.	.	PUNCT
ejpam-488	269	1	putting	put	VERB
ejpam-488	269	2	ℓ=	ℓ=	NOUN
ejpam-488	269	3	0	0	NUM
ejpam-488	270	1	in	in	ADP
ejpam-488	270	2	the	the	DET
ejpam-488	270	3	above	above	ADJ
ejpam-488	270	4	results	result	NOUN
ejpam-488	270	5	,	,	PUNCT
ejpam-488	270	6	we	we	PRON
ejpam-488	270	7	obtain	obtain	VERB
ejpam-488	270	8	the	the	DET
ejpam-488	270	9	corresponding	corresponding	ADJ
ejpam-488	270	10	results	result	NOUN
ejpam-488	270	11	for	for	ADP
ejpam-488	270	12	the	the	DET
ejpam-488	270	13	operator	operator	NOUN
ejpam-488	270	14	dm	dm	PROPN
ejpam-488	270	15	λ	λ	PROPN
ejpam-488	270	16	.	.	PUNCT
ejpam-488	271	1	references	reference	NOUN
ejpam-488	271	2	[	[	X
ejpam-488	271	3	1	1	NUM
ejpam-488	271	4	]	]	PUNCT
ejpam-488	271	5	f.	f.	PROPN
ejpam-488	271	6	m.	m.	PROPN
ejpam-488	271	7	al	al	PROPN
ejpam-488	271	8	.	.	PROPN
ejpam-488	271	9	oboudi	oboudi	PROPN
ejpam-488	271	10	,	,	PUNCT
ejpam-488	271	11	on	on	ADP
ejpam-488	271	12	univalent	univalent	ADJ
ejpam-488	271	13	functions	function	NOUN
ejpam-488	271	14	defined	define	VERB
ejpam-488	271	15	by	by	ADP
ejpam-488	271	16	a	a	DET
ejpam-488	271	17	generalized	generalize	VERB
ejpam-488	271	18	salagean	salagean	ADJ
ejpam-488	271	19	operator	operator	NOUN
ejpam-488	271	20	,	,	PUNCT
ejpam-488	271	21	internat	internat	PROPN
ejpam-488	271	22	.	.	PUNCT
ejpam-488	272	1	j.	j.	PROPN
ejpam-488	272	2	math	math	PROPN
ejpam-488	272	3	.	.	PUNCT
ejpam-488	273	1	math	math	NOUN
ejpam-488	273	2	.	.	PUNCT
ejpam-488	274	1	sci	sci	PROPN
ejpam-488	274	2	.	.	PROPN
ejpam-488	274	3	,	,	PUNCT
ejpam-488	274	4	27(2004	27(2004	NUM
ejpam-488	274	5	)	)	PUNCT
ejpam-488	274	6	,	,	PUNCT
ejpam-488	274	7	1429	1429	NUM
ejpam-488	274	8	-	-	SYM
ejpam-488	274	9	1436	1436	NUM
ejpam-488	274	10	.	.	PUNCT
ejpam-488	275	1	[	[	X
ejpam-488	275	2	2	2	X
ejpam-488	275	3	]	]	PUNCT
ejpam-488	275	4	t.	t.	NOUN
ejpam-488	275	5	bulboaca	bulboaca	NOUN
ejpam-488	275	6	,	,	PUNCT
ejpam-488	275	7	differential	differential	ADJ
ejpam-488	275	8	subordinations	subordination	NOUN
ejpam-488	275	9	and	and	CCONJ
ejpam-488	275	10	superordinations	superordination	NOUN
ejpam-488	275	11	,	,	PUNCT
ejpam-488	275	12	recent	recent	ADJ
ejpam-488	275	13	results	result	NOUN
ejpam-488	275	14	,	,	PUNCT
ejpam-488	275	15	house	house	NOUN
ejpam-488	275	16	of	of	ADP
ejpam-488	275	17	scientific	scientific	ADJ
ejpam-488	275	18	book	book	NOUN
ejpam-488	275	19	publ	publ	NOUN
ejpam-488	275	20	.	.	PUNCT
ejpam-488	275	21	,	,	PUNCT
ejpam-488	275	22	cluj	cluj	NOUN
ejpam-488	275	23	-	-	PUNCT
ejpam-488	275	24	napoca	napoca	NOUN
ejpam-488	275	25	,	,	PUNCT
ejpam-488	275	26	2005	2005	NUM
ejpam-488	275	27	.	.	PUNCT
ejpam-488	276	1	[	[	X
ejpam-488	276	2	3	3	NUM
ejpam-488	276	3	]	]	PUNCT
ejpam-488	276	4	a.	a.	NOUN
ejpam-488	276	5	catas	cata	NOUN
ejpam-488	276	6	,	,	PUNCT
ejpam-488	276	7	on	on	ADP
ejpam-488	276	8	certain	certain	ADJ
ejpam-488	276	9	classes	class	NOUN
ejpam-488	276	10	of	of	ADP
ejpam-488	276	11	p	p	NOUN
ejpam-488	276	12	-	-	PUNCT
ejpam-488	276	13	valent	valent	NOUN
ejpam-488	276	14	functions	function	NOUN
ejpam-488	276	15	defined	define	VERB
ejpam-488	276	16	by	by	ADP
ejpam-488	276	17	multiplier	multipli	ADJ
ejpam-488	276	18	transformations	transformation	NOUN
ejpam-488	276	19	,	,	PUNCT
ejpam-488	276	20	in	in	ADP
ejpam-488	276	21	proceedings	proceeding	NOUN
ejpam-488	276	22	of	of	ADP
ejpam-488	276	23	the	the	DET
ejpam-488	276	24	international	international	ADJ
ejpam-488	276	25	symposium	symposium	NOUN
ejpam-488	276	26	on	on	ADP
ejpam-488	276	27	geometric	geometric	ADJ
ejpam-488	276	28	function	function	NOUN
ejpam-488	276	29	theory	theory	NOUN
ejpam-488	276	30	and	and	CCONJ
ejpam-488	276	31	applications	application	NOUN
ejpam-488	276	32	:	:	PUNCT
ejpam-488	276	33	gfta	gfta	VERB
ejpam-488	276	34	2007	2007	NUM
ejpam-488	276	35	proceedings	proceeding	NOUN
ejpam-488	276	36	(	(	PUNCT
ejpam-488	276	37	̇istanbul	̇istanbul	PROPN
ejpam-488	276	38	,	,	PUNCT
ejpam-488	276	39	turkey	turkey	NOUN
ejpam-488	276	40	;	;	PUNCT
ejpam-488	276	41	20	20	NUM
ejpam-488	276	42	-	-	SYM
ejpam-488	276	43	24	24	NUM
ejpam-488	276	44	august	august	NOUN
ejpam-488	276	45	2007	2007	NUM
ejpam-488	276	46	)	)	PUNCT
ejpam-488	276	47	(	(	PUNCT
ejpam-488	276	48	s.	s.	PROPN
ejpam-488	276	49	owa	owa	PROPN
ejpam-488	276	50	and	and	CCONJ
ejpam-488	276	51	y.	y.	PROPN
ejpam-488	276	52	polatoģlu	polatoģlu	NUM
ejpam-488	276	53	,	,	PUNCT
ejpam-488	276	54	editors	editor	NOUN
ejpam-488	276	55	)	)	PUNCT
ejpam-488	276	56	,	,	PUNCT
ejpam-488	276	57	pp	pp	ADP
ejpam-488	276	58	.	.	PUNCT
ejpam-488	277	1	241–250	241–250	NUM
ejpam-488	277	2	,	,	PUNCT
ejpam-488	277	3	tc	tc	NOUN
ejpam-488	277	4	i̇stanbul	i̇stanbul	NOUN
ejpam-488	277	5	kűltűr	kűltűr	PROPN
ejpam-488	277	6	university	university	NOUN
ejpam-488	277	7	publications	publication	NOUN
ejpam-488	277	8	,	,	PUNCT
ejpam-488	277	9	vol	vol	NOUN
ejpam-488	277	10	.	.	PROPN
ejpam-488	277	11	91	91	NUM
ejpam-488	277	12	,	,	PUNCT
ejpam-488	277	13	tc	tc	NOUN
ejpam-488	277	14	i̇stanbul	i̇stanbul	NOUN
ejpam-488	278	1	kűltűr	kűltűr	PROPN
ejpam-488	278	2	university	university	PROPN
ejpam-488	278	3	,	,	PUNCT
ejpam-488	278	4	i̇stanbul	i̇stanbul	ADV
ejpam-488	278	5	,	,	PUNCT
ejpam-488	278	6	turkey	turkey	NOUN
ejpam-488	278	7	,	,	PUNCT
ejpam-488	278	8	2008	2008	NUM
ejpam-488	278	9	.	.	PUNCT
ejpam-488	279	1	[	[	X
ejpam-488	279	2	4	4	X
ejpam-488	279	3	]	]	X
ejpam-488	279	4	n.	n.	PROPN
ejpam-488	279	5	e.	e.	PROPN
ejpam-488	279	6	cho	cho	PROPN
ejpam-488	279	7	and	and	CCONJ
ejpam-488	279	8	t.	t.	PROPN
ejpam-488	279	9	h.	h.	PROPN
ejpam-488	279	10	kim	kim	PROPN
ejpam-488	279	11	,	,	PUNCT
ejpam-488	279	12	multiplier	multipli	ADJ
ejpam-488	279	13	transformations	transformation	NOUN
ejpam-488	279	14	and	and	CCONJ
ejpam-488	279	15	strongly	strongly	ADV
ejpam-488	279	16	close	close	ADV
ejpam-488	279	17	-	-	PUNCT
ejpam-488	279	18	to	to	ADP
ejpam-488	279	19	-	-	PUNCT
ejpam-488	279	20	convex	convex	NOUN
ejpam-488	279	21	functions	function	NOUN
ejpam-488	279	22	,	,	PUNCT
ejpam-488	279	23	bull	bull	NOUN
ejpam-488	279	24	.	.	PUNCT
ejpam-488	280	1	korean	korean	ADJ
ejpam-488	280	2	math	math	PROPN
ejpam-488	280	3	.	.	PUNCT
ejpam-488	281	1	soc	soc	PROPN
ejpam-488	281	2	.	.	PUNCT
ejpam-488	281	3	,	,	PUNCT
ejpam-488	281	4	40(2003	40(2003	NOUN
ejpam-488	281	5	)	)	PUNCT
ejpam-488	281	6	,	,	PUNCT
ejpam-488	281	7	no	no	INTJ
ejpam-488	281	8	.	.	NOUN
ejpam-488	281	9	3	3	NUM
ejpam-488	281	10	,	,	PUNCT
ejpam-488	281	11	399	399	NUM
ejpam-488	281	12	-	-	SYM
ejpam-488	281	13	410	410	NUM
ejpam-488	281	14	.	.	PUNCT
ejpam-488	282	1	[	[	X
ejpam-488	282	2	5	5	NUM
ejpam-488	282	3	]	]	X
ejpam-488	282	4	n.	n.	PROPN
ejpam-488	282	5	e.	e.	PROPN
ejpam-488	282	6	cho	cho	PROPN
ejpam-488	282	7	and	and	CCONJ
ejpam-488	282	8	h.	h.	PROPN
ejpam-488	282	9	m.	m.	PROPN
ejpam-488	282	10	srivastava	srivastava	PROPN
ejpam-488	282	11	,	,	PUNCT
ejpam-488	282	12	argument	argument	NOUN
ejpam-488	282	13	estimates	estimate	NOUN
ejpam-488	282	14	of	of	ADP
ejpam-488	282	15	certain	certain	ADJ
ejpam-488	282	16	analytic	analytic	ADJ
ejpam-488	282	17	functions	function	NOUN
ejpam-488	282	18	defined	define	VERB
ejpam-488	282	19	by	by	ADP
ejpam-488	282	20	a	a	DET
ejpam-488	282	21	class	class	NOUN
ejpam-488	282	22	of	of	ADP
ejpam-488	282	23	multiplier	multipli	ADJ
ejpam-488	282	24	transformations	transformation	NOUN
ejpam-488	282	25	,	,	PUNCT
ejpam-488	282	26	math	math	NOUN
ejpam-488	282	27	.	.	PUNCT
ejpam-488	283	1	comput	comput	NOUN
ejpam-488	283	2	.	.	PUNCT
ejpam-488	284	1	modelling	modelling	NOUN
ejpam-488	284	2	,	,	PUNCT
ejpam-488	284	3	37(1	37(1	NUM
ejpam-488	284	4	-	-	SYM
ejpam-488	284	5	2)(2003	2)(2003	NUM
ejpam-488	284	6	)	)	PUNCT
ejpam-488	284	7	,	,	PUNCT
ejpam-488	284	8	3949	3949	NUM
ejpam-488	284	9	.	.	PUNCT
ejpam-488	285	1	[	[	X
ejpam-488	285	2	6	6	NUM
ejpam-488	285	3	]	]	PUNCT
ejpam-488	285	4	r.	r.	PROPN
ejpam-488	285	5	n.	n.	PROPN
ejpam-488	285	6	das	das	PROPN
ejpam-488	285	7	and	and	CCONJ
ejpam-488	285	8	p.	p.	PROPN
ejpam-488	285	9	singh	singh	PROPN
ejpam-488	285	10	,	,	PUNCT
ejpam-488	285	11	on	on	ADP
ejpam-488	285	12	subclasses	subclass	NOUN
ejpam-488	285	13	of	of	ADP
ejpam-488	285	14	schicht	schicht	NOUN
ejpam-488	285	15	mapping	mapping	NOUN
ejpam-488	285	16	,	,	PUNCT
ejpam-488	285	17	indian	indian	PROPN
ejpam-488	285	18	j.	j.	PROPN
ejpam-488	285	19	pure	pure	PROPN
ejpam-488	285	20	appl	appl	PROPN
ejpam-488	285	21	.	.	PUNCT
ejpam-488	285	22	math	math	NOUN
ejpam-488	285	23	.	.	PUNCT
ejpam-488	286	1	8(1977	8(1977	NUM
ejpam-488	286	2	)	)	PUNCT
ejpam-488	286	3	,	,	PUNCT
ejpam-488	286	4	864	864	NUM
ejpam-488	286	5	-	-	SYM
ejpam-488	286	6	872	872	NUM
ejpam-488	286	7	.	.	PUNCT
ejpam-488	287	1	[	[	X
ejpam-488	287	2	7	7	X
ejpam-488	287	3	]	]	X
ejpam-488	287	4	p.	p.	NOUN
ejpam-488	287	5	eenigenburg	eenigenburg	PROPN
ejpam-488	287	6	,	,	PUNCT
ejpam-488	287	7	s.	s.	PROPN
ejpam-488	287	8	s.	s.	PROPN
ejpam-488	287	9	miller	miller	PROPN
ejpam-488	287	10	,	,	PUNCT
ejpam-488	287	11	p.	p.	PROPN
ejpam-488	287	12	t.	t.	PROPN
ejpam-488	287	13	mocanu	mocanu	PROPN
ejpam-488	287	14	and	and	CCONJ
ejpam-488	287	15	m.	m.	PROPN
ejpam-488	287	16	o.	o.	PROPN
ejpam-488	287	17	reade	reade	PROPN
ejpam-488	287	18	,	,	PUNCT
ejpam-488	287	19	on	on	ADP
ejpam-488	287	20	a	a	DET
ejpam-488	287	21	briot	briot	ADJ
ejpam-488	287	22	-	-	PUNCT
ejpam-488	287	23	bouquet	bouquet	NOUN
ejpam-488	287	24	differential	differential	NOUN
ejpam-488	287	25	subordination	subordination	NOUN
ejpam-488	287	26	,	,	PUNCT
ejpam-488	287	27	in	in	ADP
ejpam-488	287	28	general	general	ADJ
ejpam-488	287	29	inequalities	inequality	NOUN
ejpam-488	287	30	,	,	PUNCT
ejpam-488	287	31	volume	volume	NOUN
ejpam-488	287	32	3	3	NUM
ejpam-488	287	33	,	,	PUNCT
ejpam-488	287	34	oberwolfach	oberwolfach	ADV
ejpam-488	287	35	,	,	PUNCT
ejpam-488	287	36	(	(	PUNCT
ejpam-488	287	37	1981	1981	NUM
ejpam-488	287	38	)	)	PUNCT
ejpam-488	287	39	;	;	PUNCT
ejpam-488	287	40	internat	internat	PROPN
ejpam-488	287	41	.	.	PUNCT
ejpam-488	288	1	schriftenreihe	schriftenreihe	PROPN
ejpam-488	288	2	number	number	PROPN
ejpam-488	288	3	.	.	PUNCT
ejpam-488	289	1	math	math	NOUN
ejpam-488	289	2	.	.	PUNCT
ejpam-488	290	1	64	64	NUM
ejpam-488	290	2	,	,	PUNCT
ejpam-488	290	3	339	339	NUM
ejpam-488	290	4	-	-	SYM
ejpam-488	290	5	348	348	NUM
ejpam-488	290	6	,	,	PUNCT
ejpam-488	290	7	birkhauser	birkhaus	ADJ
ejpam-488	290	8	verlag	verlag	NOUN
ejpam-488	290	9	,	,	PUNCT
ejpam-488	290	10	basel	basel	PROPN
ejpam-488	290	11	(	(	PUNCT
ejpam-488	290	12	1983	1983	NUM
ejpam-488	290	13	)	)	PUNCT
ejpam-488	290	14	;	;	PUNCT
ejpam-488	290	15	rev	rev	PROPN
ejpam-488	290	16	.	.	PROPN
ejpam-488	290	17	roumaine	roumaine	PROPN
ejpam-488	290	18	math	math	NOUN
ejpam-488	290	19	.	.	PUNCT
ejpam-488	291	1	pures	pure	NOUN
ejpam-488	291	2	appl	appl	PROPN
ejpam-488	291	3	.	.	PUNCT
ejpam-488	291	4	29(1984	29(1984	NUM
ejpam-488	291	5	)	)	PUNCT
ejpam-488	291	6	,	,	PUNCT
ejpam-488	291	7	567	567	NUM
ejpam-488	291	8	-	-	SYM
ejpam-488	291	9	573	573	NUM
ejpam-488	291	10	.	.	PUNCT
ejpam-488	292	1	[	[	X
ejpam-488	292	2	8	8	NUM
ejpam-488	292	3	]	]	X
ejpam-488	292	4	w.	w.	PROPN
ejpam-488	292	5	kalplan	kalplan	PROPN
ejpam-488	292	6	,	,	PUNCT
ejpam-488	292	7	close	close	NOUN
ejpam-488	292	8	-	-	PUNCT
ejpam-488	292	9	to	to	ADP
ejpam-488	292	10	-	-	PUNCT
ejpam-488	292	11	convex	convex	NOUN
ejpam-488	292	12	schlicht	schlicht	NOUN
ejpam-488	292	13	functions	function	NOUN
ejpam-488	292	14	,	,	PUNCT
ejpam-488	292	15	michigan	michigan	PROPN
ejpam-488	292	16	math	math	PROPN
ejpam-488	292	17	.	.	PUNCT
ejpam-488	293	1	j.	j.	PROPN
ejpam-488	293	2	1(1952	1(1952	PROPN
ejpam-488	293	3	)	)	PUNCT
ejpam-488	293	4	,	,	PUNCT
ejpam-488	293	5	169	169	NUM
ejpam-488	293	6	-	-	SYM
ejpam-488	293	7	195	195	NUM
ejpam-488	293	8	.	.	PUNCT
ejpam-488	294	1	[	[	X
ejpam-488	294	2	9	9	NUM
ejpam-488	294	3	]	]	PUNCT
ejpam-488	294	4	z.	z.	PROPN
ejpam-488	294	5	lewandowska	lewandowska	PROPN
ejpam-488	294	6	and	and	CCONJ
ejpam-488	294	7	j.	j.	PROPN
ejpam-488	294	8	stankiewicz	stankiewicz	PROPN
ejpam-488	294	9	,	,	PUNCT
ejpam-488	294	10	on	on	ADP
ejpam-488	294	11	mutually	mutually	ADV
ejpam-488	294	12	adjoint	adjoint	VERB
ejpam-488	294	13	close	close	VERB
ejpam-488	294	14	-	-	PUNCT
ejpam-488	294	15	to	to	ADP
ejpam-488	294	16	-	-	PUNCT
ejpam-488	294	17	convex	convex	NOUN
ejpam-488	294	18	functions	function	NOUN
ejpam-488	294	19	,	,	PUNCT
ejpam-488	294	20	ann	ann	PROPN
ejpam-488	294	21	.	.	PROPN
ejpam-488	294	22	univ	univ	PROPN
ejpam-488	294	23	.	.	PUNCT
ejpam-488	295	1	mariae	mariae	PROPN
ejpam-488	295	2	curie	curie	PROPN
ejpam-488	295	3	-	-	PUNCT
ejpam-488	295	4	sktodowska	sktodowska	PROPN
ejpam-488	295	5	sect	sect	NOUN
ejpam-488	295	6	.	.	PUNCT
ejpam-488	296	1	a	a	DET
ejpam-488	296	2	,	,	PUNCT
ejpam-488	296	3	19(1965	19(1965	NUM
ejpam-488	296	4	)	)	PUNCT
ejpam-488	296	5	,	,	PUNCT
ejpam-488	296	6	47	47	NUM
ejpam-488	296	7	-	-	SYM
ejpam-488	296	8	51	51	NUM
ejpam-488	296	9	.	.	PUNCT
ejpam-488	297	1	[	[	X
ejpam-488	297	2	10	10	NUM
ejpam-488	297	3	]	]	PUNCT
ejpam-488	297	4	s.	s.	PROPN
ejpam-488	297	5	s.	s.	PROPN
ejpam-488	297	6	miller	miller	PROPN
ejpam-488	297	7	and	and	CCONJ
ejpam-488	297	8	p.	p.	PROPN
ejpam-488	297	9	t.	t.	PROPN
ejpam-488	297	10	mocanu	mocanu	PROPN
ejpam-488	297	11	,	,	PUNCT
ejpam-488	297	12	differential	differential	ADJ
ejpam-488	297	13	subordinations	subordination	NOUN
ejpam-488	297	14	and	and	CCONJ
ejpam-488	297	15	univalent	univalent	ADJ
ejpam-488	297	16	functions	function	NOUN
ejpam-488	297	17	,	,	PUNCT
ejpam-488	297	18	michigan	michigan	PROPN
ejpam-488	297	19	math	math	PROPN
ejpam-488	297	20	.	.	PUNCT
ejpam-488	298	1	j.	j.	PROPN
ejpam-488	298	2	28(1981	28(1981	PROPN
ejpam-488	298	3	)	)	PUNCT
ejpam-488	298	4	,	,	PUNCT
ejpam-488	298	5	157	157	NUM
ejpam-488	298	6	-	-	SYM
ejpam-488	298	7	171	171	NUM
ejpam-488	298	8	.	.	PUNCT
ejpam-488	299	1	references	reference	NOUN
ejpam-488	299	2	330	330	NUM
ejpam-488	299	3	[	[	SYM
ejpam-488	299	4	11	11	NUM
ejpam-488	299	5	]	]	PUNCT
ejpam-488	299	6	s.	s.	PROPN
ejpam-488	299	7	s.	s.	PROPN
ejpam-488	299	8	miller	miller	PROPN
ejpam-488	299	9	and	and	CCONJ
ejpam-488	299	10	p.	p.	PROPN
ejpam-488	299	11	t.	t.	PROPN
ejpam-488	299	12	mocanu	mocanu	PROPN
ejpam-488	299	13	,	,	PUNCT
ejpam-488	299	14	differential	differential	ADJ
ejpam-488	299	15	subordinations	subordination	NOUN
ejpam-488	299	16	:	:	PUNCT
ejpam-488	299	17	theory	theory	NOUN
ejpam-488	299	18	and	and	CCONJ
ejpam-488	299	19	applications	application	NOUN
ejpam-488	299	20	,	,	PUNCT
ejpam-488	299	21	series	series	NOUN
ejpam-488	299	22	on	on	ADP
ejpam-488	299	23	monographs	monograph	NOUN
ejpam-488	299	24	and	and	CCONJ
ejpam-488	299	25	texbooks	texbook	NOUN
ejpam-488	299	26	in	in	ADP
ejpam-488	299	27	pure	pure	ADJ
ejpam-488	299	28	and	and	CCONJ
ejpam-488	299	29	applied	applied	ADJ
ejpam-488	299	30	mathematics	mathematic	NOUN
ejpam-488	299	31	,	,	PUNCT
ejpam-488	299	32	vol.225	vol.225	PROPN
ejpam-488	299	33	,	,	PUNCT
ejpam-488	299	34	marcel	marcel	PROPN
ejpam-488	299	35	dekker	dekker	PROPN
ejpam-488	299	36	,	,	PUNCT
ejpam-488	299	37	new	new	PROPN
ejpam-488	299	38	york	york	PROPN
ejpam-488	299	39	and	and	CCONJ
ejpam-488	299	40	basel	basel	PROPN
ejpam-488	299	41	,	,	PUNCT
ejpam-488	299	42	2000	2000	NUM
ejpam-488	299	43	.	.	PUNCT
ejpam-488	300	1	[	[	X
ejpam-488	300	2	12	12	NUM
ejpam-488	300	3	]	]	PUNCT
ejpam-488	300	4	p.	p.	NOUN
ejpam-488	300	5	t.	t.	PROPN
ejpam-488	300	6	mocanu	mocanu	PROPN
ejpam-488	300	7	,	,	PUNCT
ejpam-488	300	8	on	on	ADP
ejpam-488	300	9	starlike	starlike	NOUN
ejpam-488	300	10	functions	function	NOUN
ejpam-488	300	11	with	with	ADP
ejpam-488	300	12	respect	respect	NOUN
ejpam-488	300	13	to	to	ADP
ejpam-488	300	14	symmetric	symmetric	ADJ
ejpam-488	300	15	points	point	NOUN
ejpam-488	300	16	,	,	PUNCT
ejpam-488	300	17	bull	bull	NOUN
ejpam-488	300	18	.	.	PUNCT
ejpam-488	301	1	math	math	NOUN
ejpam-488	301	2	.	.	PUNCT
ejpam-488	302	1	soc	soc	PROPN
ejpam-488	302	2	.	.	PUNCT
ejpam-488	303	1	sci	sci	PROPN
ejpam-488	303	2	.	.	PROPN
ejpam-488	303	3	math	math	PROPN
ejpam-488	303	4	.	.	PUNCT
ejpam-488	304	1	r.	r.	PROPN
ejpam-488	304	2	s.	s.	PROPN
ejpam-488	304	3	roumanie	roumanie	PROPN
ejpam-488	304	4	(	(	PUNCT
ejpam-488	304	5	n.	n.	PROPN
ejpam-488	304	6	s.	s.	PROPN
ejpam-488	304	7	)	)	PUNCT
ejpam-488	304	8	28(1984	28(1984	NUM
ejpam-488	304	9	)	)	PUNCT
ejpam-488	304	10	,	,	PUNCT
ejpam-488	304	11	no	no	INTJ
ejpam-488	304	12	.	.	NOUN
ejpam-488	304	13	67	67	NUM
ejpam-488	304	14	,	,	PUNCT
ejpam-488	304	15	47	47	NUM
ejpam-488	304	16	-	-	SYM
ejpam-488	304	17	50	50	NUM
ejpam-488	304	18	.	.	PUNCT
ejpam-488	305	1	[	[	X
ejpam-488	305	2	13	13	NUM
ejpam-488	305	3	]	]	X
ejpam-488	305	4	k.i	k.i	PROPN
ejpam-488	305	5	.	.	PUNCT
ejpam-488	306	1	noor	noor	PROPN
ejpam-488	306	2	,	,	PUNCT
ejpam-488	306	3	on	on	ADP
ejpam-488	306	4	quasi	quasi	ADJ
ejpam-488	306	5	-	-	ADJ
ejpam-488	306	6	convex	convex	ADJ
ejpam-488	306	7	functions	function	NOUN
ejpam-488	306	8	and	and	CCONJ
ejpam-488	306	9	related	related	ADJ
ejpam-488	306	10	topics	topic	NOUN
ejpam-488	306	11	,	,	PUNCT
ejpam-488	306	12	10(1987	10(1987	NUM
ejpam-488	306	13	)	)	PUNCT
ejpam-488	306	14	,	,	PUNCT
ejpam-488	306	15	241	241	NUM
ejpam-488	306	16	-	-	SYM
ejpam-488	306	17	258	258	NUM
ejpam-488	306	18	.	.	PUNCT
ejpam-488	307	1	[	[	X
ejpam-488	307	2	14	14	NUM
ejpam-488	307	3	]	]	PUNCT
ejpam-488	307	4	m.	m.	NOUN
ejpam-488	307	5	nunokawa	nunokawa	PROPN
ejpam-488	307	6	,	,	PUNCT
ejpam-488	307	7	s.	s.	PROPN
ejpam-488	307	8	owa	owa	PROPN
ejpam-488	307	9	,	,	PUNCT
ejpam-488	307	10	h.	h.	PROPN
ejpam-488	307	11	saitoh	saitoh	PROPN
ejpam-488	307	12	,	,	PUNCT
ejpam-488	307	13	n.	n.	PROPN
ejpam-488	307	14	e.	e.	PROPN
ejpam-488	307	15	cho	cho	PROPN
ejpam-488	307	16	and	and	CCONJ
ejpam-488	307	17	n.	n.	PROPN
ejpam-488	307	18	takahashi	takahashi	PROPN
ejpam-488	307	19	,	,	PUNCT
ejpam-488	307	20	some	some	DET
ejpam-488	307	21	properties	property	NOUN
ejpam-488	307	22	of	of	ADP
ejpam-488	307	23	analytic	analytic	ADJ
ejpam-488	307	24	functions	function	NOUN
ejpam-488	307	25	at	at	ADP
ejpam-488	307	26	extremal	extremal	ADJ
ejpam-488	307	27	points	point	NOUN
ejpam-488	307	28	for	for	ADP
ejpam-488	307	29	arguments	argument	NOUN
ejpam-488	307	30	,	,	PUNCT
ejpam-488	307	31	(	(	PUNCT
ejpam-488	307	32	preprint	preprint	NOUN
ejpam-488	307	33	2002	2002	NUM
ejpam-488	307	34	)	)	PUNCT
ejpam-488	307	35	.	.	PUNCT
ejpam-488	308	1	[	[	X
ejpam-488	308	2	15	15	NUM
ejpam-488	308	3	]	]	PUNCT
ejpam-488	308	4	k.	k.	PROPN
ejpam-488	308	5	s.	s.	PROPN
ejpam-488	308	6	padmanabhanand	padmanabhanand	PROPN
ejpam-488	308	7	j.	j.	PROPN
ejpam-488	308	8	thangamani	thangamani	PROPN
ejpam-488	308	9	,	,	PUNCT
ejpam-488	308	10	on	on	ADP
ejpam-488	308	11	α	α	NOUN
ejpam-488	308	12	-	-	NOUN
ejpam-488	308	13	starlike	starlike	NOUN
ejpam-488	308	14	and	and	CCONJ
ejpam-488	308	15	α	α	NOUN
ejpam-488	308	16	-	-	PUNCT
ejpam-488	308	17	close	close	VERB
ejpam-488	308	18	-	-	PUNCT
ejpam-488	308	19	to	to	ADP
ejpam-488	308	20	-	-	PUNCT
ejpam-488	308	21	convex	convex	NOUN
ejpam-488	308	22	functions	function	NOUN
ejpam-488	308	23	with	with	ADP
ejpam-488	308	24	respect	respect	NOUN
ejpam-488	308	25	to	to	ADP
ejpam-488	308	26	symmetric	symmetric	ADJ
ejpam-488	308	27	points	point	NOUN
ejpam-488	308	28	,	,	PUNCT
ejpam-488	308	29	j.	j.	PROPN
ejpam-488	308	30	madras	madras	PROPN
ejpam-488	308	31	univ	univ	PROPN
ejpam-488	308	32	.	.	PUNCT
ejpam-488	309	1	42(1979	42(1979	PROPN
ejpam-488	309	2	)	)	PUNCT
ejpam-488	309	3	,	,	PUNCT
ejpam-488	309	4	8	8	NUM
ejpam-488	309	5	-	-	SYM
ejpam-488	309	6	11	11	NUM
ejpam-488	309	7	.	.	PUNCT
ejpam-488	310	1	[	[	X
ejpam-488	310	2	16	16	NUM
ejpam-488	310	3	]	]	X
ejpam-488	310	4	k.s	k.s	PROPN
ejpam-488	310	5	.	.	PROPN
ejpam-488	310	6	padmanabhan	padmanabhan	PROPN
ejpam-488	310	7	and	and	CCONJ
ejpam-488	310	8	j.	j.	PROPN
ejpam-488	310	9	thangamani	thangamani	PROPN
ejpam-488	310	10	,	,	PUNCT
ejpam-488	310	11	the	the	DET
ejpam-488	310	12	effect	effect	NOUN
ejpam-488	310	13	of	of	ADP
ejpam-488	310	14	certain	certain	ADJ
ejpam-488	310	15	integral	integral	ADJ
ejpam-488	310	16	operators	operator	NOUN
ejpam-488	310	17	on	on	ADP
ejpam-488	310	18	some	some	DET
ejpam-488	310	19	classes	class	NOUN
ejpam-488	310	20	of	of	ADP
ejpam-488	310	21	starlike	starlike	NOUN
ejpam-488	310	22	functions	function	NOUN
ejpam-488	310	23	with	with	ADP
ejpam-488	310	24	respect	respect	NOUN
ejpam-488	310	25	to	to	ADP
ejpam-488	310	26	symmetric	symmetric	ADJ
ejpam-488	310	27	points	point	NOUN
ejpam-488	310	28	,	,	PUNCT
ejpam-488	310	29	bull	bull	NOUN
ejpam-488	310	30	.	.	PUNCT
ejpam-488	311	1	math	math	NOUN
ejpam-488	311	2	.	.	PUNCT
ejpam-488	312	1	soc	soc	PROPN
ejpam-488	312	2	.	.	PUNCT
ejpam-488	313	1	sci	sci	PROPN
ejpam-488	313	2	.	.	PROPN
ejpam-488	313	3	math	math	PROPN
ejpam-488	313	4	.	.	PUNCT
ejpam-488	314	1	r.s	r.s	PROPN
ejpam-488	314	2	.	.	PROPN
ejpam-488	314	3	roumanie	roumanie	PROPN
ejpam-488	314	4	(	(	PUNCT
ejpam-488	314	5	n.s	n.s	PROPN
ejpam-488	314	6	.	.	PROPN
ejpam-488	314	7	)	)	PUNCT
ejpam-488	314	8	26(1982	26(1982	NUM
ejpam-488	314	9	)	)	PUNCT
ejpam-488	314	10	,	,	PUNCT
ejpam-488	314	11	no	no	INTJ
ejpam-488	314	12	.	.	NOUN
ejpam-488	314	13	74	74	NUM
ejpam-488	314	14	,	,	PUNCT
ejpam-488	314	15	355	355	NUM
ejpam-488	314	16	-	-	SYM
ejpam-488	314	17	360	360	NUM
ejpam-488	314	18	.	.	PUNCT
ejpam-488	315	1	[	[	X
ejpam-488	315	2	17	17	NUM
ejpam-488	315	3	]	]	PUNCT
ejpam-488	315	4	k.	k.	PROPN
ejpam-488	315	5	sakaguchi	sakaguchi	PROPN
ejpam-488	315	6	,	,	PUNCT
ejpam-488	315	7	on	on	ADP
ejpam-488	315	8	a	a	DET
ejpam-488	315	9	certain	certain	ADJ
ejpam-488	315	10	univalent	univalent	ADJ
ejpam-488	315	11	mapping	mapping	NOUN
ejpam-488	315	12	,	,	PUNCT
ejpam-488	315	13	j.	j.	PROPN
ejpam-488	315	14	math	math	PROPN
ejpam-488	315	15	.	.	PUNCT
ejpam-488	316	1	soc	soc	PROPN
ejpam-488	316	2	.	.	PUNCT
ejpam-488	317	1	japan	japan	PROPN
ejpam-488	317	2	11(1959	11(1959	NUM
ejpam-488	317	3	)	)	PUNCT
ejpam-488	317	4	,	,	PUNCT
ejpam-488	317	5	72	72	NUM
ejpam-488	317	6	-	-	SYM
ejpam-488	317	7	75	75	NUM
ejpam-488	317	8	.	.	PUNCT
ejpam-488	318	1	[	[	X
ejpam-488	318	2	18	18	NUM
ejpam-488	318	3	]	]	X
ejpam-488	318	4	g.	g.	PROPN
ejpam-488	318	5	s.	s.	PROPN
ejpam-488	318	6	salagean	salagean	PROPN
ejpam-488	318	7	,	,	PUNCT
ejpam-488	318	8	subclasses	subclass	NOUN
ejpam-488	318	9	of	of	ADP
ejpam-488	318	10	univalent	univalent	ADJ
ejpam-488	318	11	functions	function	NOUN
ejpam-488	318	12	,	,	PUNCT
ejpam-488	318	13	lecture	lecture	NOUN
ejpam-488	318	14	notes	note	NOUN
ejpam-488	318	15	in	in	ADP
ejpam-488	318	16	math	math	NOUN
ejpam-488	318	17	.	.	PUNCT
ejpam-488	319	1	(	(	PUNCT
ejpam-488	319	2	springerverlag	springerverlag	NOUN
ejpam-488	319	3	)	)	PUNCT
ejpam-488	319	4	1013(1983	1013(1983	NUM
ejpam-488	319	5	)	)	PUNCT
ejpam-488	319	6	,	,	PUNCT
ejpam-488	319	7	362	362	NUM
ejpam-488	319	8	-	-	SYM
ejpam-488	319	9	372	372	NUM
ejpam-488	319	10	.	.	PUNCT
ejpam-488	320	1	[	[	X
ejpam-488	320	2	19	19	NUM
ejpam-488	320	3	]	]	X
ejpam-488	320	4	h.	h.	PROPN
ejpam-488	320	5	silverman	silverman	PROPN
ejpam-488	320	6	and	and	CCONJ
ejpam-488	320	7	e.	e.	PROPN
ejpam-488	320	8	m.	m.	PROPN
ejpam-488	320	9	silvia	silvia	PROPN
ejpam-488	320	10	,	,	PUNCT
ejpam-488	320	11	subclasses	subclass	NOUN
ejpam-488	320	12	of	of	ADP
ejpam-488	320	13	starlike	starlike	NOUN
ejpam-488	320	14	functions	function	NOUN
ejpam-488	320	15	subordinate	subordinate	VERB
ejpam-488	320	16	to	to	PART
ejpam-488	320	17	convex	convex	NOUN
ejpam-488	320	18	functions	function	NOUN
ejpam-488	320	19	,	,	PUNCT
ejpam-488	320	20	canada	canada	PROPN
ejpam-488	320	21	.	.	PUNCT
ejpam-488	321	1	j.	j.	PROPN
ejpam-488	321	2	math	math	PROPN
ejpam-488	321	3	.	.	PUNCT
ejpam-488	322	1	37(1985	37(1985	NUM
ejpam-488	322	2	)	)	PUNCT
ejpam-488	322	3	,	,	PUNCT
ejpam-488	322	4	48	48	NUM
ejpam-488	322	5	-	-	SYM
ejpam-488	322	6	61	61	NUM
ejpam-488	322	7	.	.	PUNCT
ejpam-488	323	1	[	[	X
ejpam-488	323	2	20	20	NUM
ejpam-488	323	3	]	]	PUNCT
ejpam-488	323	4	b.	b.	PROPN
ejpam-488	323	5	a.	a.	PROPN
ejpam-488	323	6	uralegaddi	uralegaddi	PROPN
ejpam-488	323	7	,	,	PUNCT
ejpam-488	323	8	c.	c.	PROPN
ejpam-488	323	9	somanatha	somanatha	PROPN
ejpam-488	323	10	,	,	PUNCT
ejpam-488	323	11	certain	certain	ADJ
ejpam-488	323	12	classes	class	NOUN
ejpam-488	323	13	of	of	ADP
ejpam-488	323	14	univalent	univalent	ADJ
ejpam-488	323	15	functions	function	NOUN
ejpam-488	323	16	,	,	PUNCT
ejpam-488	323	17	in	in	ADP
ejpam-488	323	18	current	current	ADJ
ejpam-488	323	19	topics	topic	NOUN
ejpam-488	323	20	in	in	ADP
ejpam-488	323	21	analytic	analytic	ADJ
ejpam-488	323	22	function	function	NOUN
ejpam-488	323	23	theory	theory	NOUN
ejpam-488	323	24	,	,	PUNCT
ejpam-488	323	25	(	(	PUNCT
ejpam-488	323	26	edited	edit	VERB
ejpam-488	323	27	by	by	ADP
ejpam-488	323	28	h.	h.	PROPN
ejpam-488	323	29	m.	m.	PROPN
ejpam-488	323	30	srivastava	srivastava	PROPN
ejpam-488	323	31	and	and	CCONJ
ejpam-488	323	32	s.	s.	PROPN
ejpam-488	323	33	owa	owa	PROPN
ejpam-488	323	34	)	)	PUNCT
ejpam-488	323	35	,	,	PUNCT
ejpam-488	323	36	world	world	PROPN
ejpam-488	323	37	scientfic	scientfic	PROPN
ejpam-488	323	38	publishing	publishing	PROPN
ejpam-488	323	39	company	company	NOUN
ejpam-488	323	40	,	,	PUNCT
ejpam-488	323	41	singapore	singapore	PROPN
ejpam-488	323	42	,	,	PUNCT
ejpam-488	323	43	1992	1992	NUM
ejpam-488	323	44	,	,	PUNCT
ejpam-488	323	45	371	371	NUM
ejpam-488	323	46	-	-	SYM
ejpam-488	323	47	374	374	NUM
ejpam-488	323	48	.	.	PUNCT