id	sid	tid	token	lemma	pos
ejpam-486	1	1	4_486_aouf.dvi	4_486_aouf.dvi	NUM
ejpam-486	1	2	european	european	ADJ
ejpam-486	1	3	journal	journal	NOUN
ejpam-486	1	4	of	of	ADP
ejpam-486	1	5	pure	pure	ADJ
ejpam-486	1	6	and	and	CCONJ
ejpam-486	1	7	applied	apply	VERB
ejpam-486	1	8	mathematics	mathematic	NOUN
ejpam-486	1	9	vol	vol	NOUN
ejpam-486	1	10	.	.	PUNCT
ejpam-486	2	1	3	3	NUM
ejpam-486	2	2	,	,	PUNCT
ejpam-486	2	3	no	no	INTJ
ejpam-486	2	4	.	.	NOUN
ejpam-486	2	5	1	1	NUM
ejpam-486	2	6	,	,	PUNCT
ejpam-486	2	7	2010	2010	NUM
ejpam-486	2	8	,	,	PUNCT
ejpam-486	2	9	26	26	NUM
ejpam-486	2	10	-	-	SYM
ejpam-486	2	11	44	44	NUM
ejpam-486	2	12	issn	issn	PROPN
ejpam-486	2	13	1307	1307	NUM
ejpam-486	2	14	-	-	SYM
ejpam-486	2	15	5543	5543	NUM
ejpam-486	2	16	–	–	PUNCT
ejpam-486	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-486	2	18	differential	differential	ADJ
ejpam-486	2	19	subordination	subordination	NOUN
ejpam-486	2	20	and	and	CCONJ
ejpam-486	2	21	superordination	superordination	NOUN
ejpam-486	2	22	of	of	ADP
ejpam-486	2	23	analytic	analytic	ADJ
ejpam-486	2	24	functions	function	NOUN
ejpam-486	2	25	defined	define	VERB
ejpam-486	2	26	by	by	ADP
ejpam-486	2	27	an	an	DET
ejpam-486	2	28	integral	integral	ADJ
ejpam-486	2	29	operator	operator	NOUN
ejpam-486	2	30	m.	m.	NOUN
ejpam-486	2	31	k.	k.	PROPN
ejpam-486	2	32	aouf1∗	aouf1∗	PROPN
ejpam-486	2	33	and	and	CCONJ
ejpam-486	2	34	t.	t.	PROPN
ejpam-486	2	35	m.	m.	PROPN
ejpam-486	2	36	seoudy2	seoudy2	PROPN
ejpam-486	2	37	1	1	NUM
ejpam-486	2	38	department	department	NOUN
ejpam-486	2	39	of	of	ADP
ejpam-486	2	40	mathematics	mathematic	NOUN
ejpam-486	2	41	,	,	PUNCT
ejpam-486	2	42	faculty	faculty	NOUN
ejpam-486	2	43	of	of	ADP
ejpam-486	2	44	science	science	NOUN
ejpam-486	2	45	,	,	PUNCT
ejpam-486	2	46	mansoura	mansoura	PROPN
ejpam-486	2	47	35516	35516	NUM
ejpam-486	2	48	,	,	PUNCT
ejpam-486	2	49	egypt	egypt	PROPN
ejpam-486	2	50	2	2	NUM
ejpam-486	2	51	department	department	NOUN
ejpam-486	2	52	of	of	ADP
ejpam-486	2	53	mathematics	mathematic	NOUN
ejpam-486	2	54	,	,	PUNCT
ejpam-486	2	55	faculty	faculty	NOUN
ejpam-486	2	56	of	of	ADP
ejpam-486	2	57	science	science	NOUN
ejpam-486	2	58	,	,	PUNCT
ejpam-486	2	59	fayoum	fayoum	PROPN
ejpam-486	2	60	63514	63514	NUM
ejpam-486	2	61	,	,	PUNCT
ejpam-486	2	62	egypt	egypt	PROPN
ejpam-486	2	63	abstract	abstract	PROPN
ejpam-486	2	64	.	.	PUNCT
ejpam-486	3	1	differential	differential	ADJ
ejpam-486	3	2	subordination	subordination	NOUN
ejpam-486	3	3	and	and	CCONJ
ejpam-486	3	4	superordination	superordination	NOUN
ejpam-486	3	5	results	result	NOUN
ejpam-486	3	6	are	be	AUX
ejpam-486	3	7	obtained	obtain	VERB
ejpam-486	3	8	for	for	ADP
ejpam-486	3	9	analytic	analytic	ADJ
ejpam-486	3	10	functions	function	NOUN
ejpam-486	3	11	in	in	ADP
ejpam-486	3	12	the	the	DET
ejpam-486	3	13	open	open	ADJ
ejpam-486	3	14	unit	unit	NOUN
ejpam-486	3	15	disk	disk	NOUN
ejpam-486	3	16	which	which	PRON
ejpam-486	3	17	are	be	AUX
ejpam-486	3	18	associated	associate	VERB
ejpam-486	3	19	with	with	ADP
ejpam-486	3	20	the	the	DET
ejpam-486	3	21	integral	integral	ADJ
ejpam-486	3	22	operator	operator	NOUN
ejpam-486	3	23	.	.	PUNCT
ejpam-486	4	1	these	these	DET
ejpam-486	4	2	results	result	NOUN
ejpam-486	4	3	are	be	AUX
ejpam-486	4	4	obtained	obtain	VERB
ejpam-486	4	5	by	by	ADP
ejpam-486	4	6	investigating	investigate	VERB
ejpam-486	4	7	appropriate	appropriate	ADJ
ejpam-486	4	8	classes	class	NOUN
ejpam-486	4	9	of	of	ADP
ejpam-486	4	10	admissible	admissible	ADJ
ejpam-486	4	11	functions	function	NOUN
ejpam-486	4	12	.	.	PUNCT
ejpam-486	5	1	sandwich	sandwich	NOUN
ejpam-486	5	2	-	-	PUNCT
ejpam-486	5	3	type	type	NOUN
ejpam-486	5	4	results	result	NOUN
ejpam-486	5	5	are	be	AUX
ejpam-486	5	6	also	also	ADV
ejpam-486	5	7	obtained	obtain	VERB
ejpam-486	5	8	.	.	PUNCT
ejpam-486	6	1	some	some	PRON
ejpam-486	6	2	of	of	ADP
ejpam-486	6	3	the	the	DET
ejpam-486	6	4	results	result	NOUN
ejpam-486	6	5	established	establish	VERB
ejpam-486	6	6	in	in	ADP
ejpam-486	6	7	this	this	DET
ejpam-486	6	8	paper	paper	NOUN
ejpam-486	6	9	would	would	AUX
ejpam-486	6	10	provide	provide	VERB
ejpam-486	6	11	extensions	extension	NOUN
ejpam-486	6	12	of	of	ADP
ejpam-486	6	13	those	those	PRON
ejpam-486	6	14	given	give	VERB
ejpam-486	6	15	in	in	ADP
ejpam-486	6	16	earlier	early	ADJ
ejpam-486	6	17	works	work	NOUN
ejpam-486	6	18	.	.	PUNCT
ejpam-486	7	1	2000	2000	NUM
ejpam-486	7	2	mathematics	mathematic	NOUN
ejpam-486	7	3	subject	subject	NOUN
ejpam-486	7	4	classifications	classification	NOUN
ejpam-486	7	5	:	:	PUNCT
ejpam-486	7	6	30c45	30c45	NUM
ejpam-486	7	7	key	key	ADJ
ejpam-486	7	8	words	word	NOUN
ejpam-486	7	9	and	and	CCONJ
ejpam-486	7	10	phrases	phrase	NOUN
ejpam-486	7	11	:	:	PUNCT
ejpam-486	7	12	analytic	analytic	ADJ
ejpam-486	7	13	function	function	NOUN
ejpam-486	7	14	,	,	PUNCT
ejpam-486	7	15	integral	integral	ADJ
ejpam-486	7	16	operator	operator	NOUN
ejpam-486	7	17	,	,	PUNCT
ejpam-486	7	18	hadamard	hadamard	ADJ
ejpam-486	7	19	product	product	NOUN
ejpam-486	7	20	,	,	PUNCT
ejpam-486	7	21	differential	differential	ADJ
ejpam-486	7	22	subordination	subordination	NOUN
ejpam-486	7	23	,	,	PUNCT
ejpam-486	7	24	superordination	superordination	NOUN
ejpam-486	7	25	.	.	PUNCT
ejpam-486	8	1	1	1	X
ejpam-486	8	2	.	.	X
ejpam-486	8	3	introduction	introduction	NOUN
ejpam-486	8	4	let	let	VERB
ejpam-486	8	5	h(u	h(u	PROPN
ejpam-486	8	6	)	)	PUNCT
ejpam-486	8	7	be	be	AUX
ejpam-486	8	8	the	the	DET
ejpam-486	8	9	class	class	NOUN
ejpam-486	8	10	of	of	ADP
ejpam-486	8	11	functions	function	NOUN
ejpam-486	8	12	analytic	analytic	ADJ
ejpam-486	8	13	in	in	ADP
ejpam-486	8	14	u	u	NOUN
ejpam-486	8	15	=	=	PUNCT
ejpam-486	8	16	{	{	PUNCT
ejpam-486	8	17	z	z	NOUN
ejpam-486	8	18	:	:	PUNCT
ejpam-486	8	19	z	z	PROPN
ejpam-486	8	20	∈	∈	PROPN
ejpam-486	8	21	c	c	PROPN
ejpam-486	8	22	and	and	CCONJ
ejpam-486	8	23	|z|	|z|	VERB
ejpam-486	8	24	<	<	X
ejpam-486	8	25	1	1	NUM
ejpam-486	8	26	}	}	PUNCT
ejpam-486	8	27	and	and	CCONJ
ejpam-486	8	28	h[a	h[a	NUM
ejpam-486	8	29	,	,	PUNCT
ejpam-486	8	30	n	n	CCONJ
ejpam-486	8	31	]	]	PUNCT
ejpam-486	8	32	be	be	AUX
ejpam-486	8	33	the	the	DET
ejpam-486	8	34	subclass	subclass	NOUN
ejpam-486	8	35	of	of	ADP
ejpam-486	8	36	h(u	h(u	PROPN
ejpam-486	8	37	)	)	PUNCT
ejpam-486	8	38	consisting	consist	VERB
ejpam-486	8	39	of	of	ADP
ejpam-486	8	40	functions	function	NOUN
ejpam-486	8	41	of	of	ADP
ejpam-486	8	42	the	the	DET
ejpam-486	8	43	form	form	NOUN
ejpam-486	9	1	f	f	X
ejpam-486	9	2	(	(	PUNCT
ejpam-486	9	3	z	z	NOUN
ejpam-486	9	4	)	)	PUNCT
ejpam-486	9	5	=	=	PRON
ejpam-486	9	6	a+	a+	PUNCT
ejpam-486	9	7	anzn+	anzn+	PUNCT
ejpam-486	9	8	an+1zn+1	an+1zn+1	NOUN
ejpam-486	9	9	+	+	NUM
ejpam-486	9	10	...	...	PUNCT
ejpam-486	9	11	,	,	PUNCT
ejpam-486	9	12	with	with	ADP
ejpam-486	9	13	h0	h0	NOUN
ejpam-486	9	14	=	=	PROPN
ejpam-486	9	15	h[0,1	h[0,1	NOUN
ejpam-486	9	16	]	]	PUNCT
ejpam-486	9	17	and	and	CCONJ
ejpam-486	9	18	h	h	NOUN
ejpam-486	9	19	=	=	NOUN
ejpam-486	9	20	h[1,1	h[1,1	NOUN
ejpam-486	9	21	]	]	PUNCT
ejpam-486	9	22	.	.	PUNCT
ejpam-486	10	1	let	let	VERB
ejpam-486	10	2	a	a	DET
ejpam-486	10	3	�	�	PROPN
ejpam-486	10	4	p	p	X
ejpam-486	10	5	�	�	PROPN
ejpam-486	10	6	denote	denote	VERB
ejpam-486	10	7	the	the	DET
ejpam-486	10	8	class	class	NOUN
ejpam-486	10	9	of	of	ADP
ejpam-486	10	10	all	all	DET
ejpam-486	10	11	analytic	analytic	ADJ
ejpam-486	10	12	functions	function	NOUN
ejpam-486	10	13	of	of	ADP
ejpam-486	10	14	the	the	DET
ejpam-486	10	15	form	form	NOUN
ejpam-486	11	1	f	f	X
ejpam-486	11	2	(	(	PUNCT
ejpam-486	11	3	z	z	NOUN
ejpam-486	11	4	)	)	PUNCT
ejpam-486	11	5	=	=	SYM
ejpam-486	11	6	zp	zp	PROPN
ejpam-486	11	7	+	+	CCONJ
ejpam-486	11	8	∞	∞	NUM
ejpam-486	11	9	∑	∑	PUNCT
ejpam-486	11	10	n=1	n=1	PROPN
ejpam-486	11	11	ap+nzp+n	ap+nzp+n	VERB
ejpam-486	11	12	�	�	PROPN
ejpam-486	11	13	p	p	NOUN
ejpam-486	11	14	∈	∈	PROPN
ejpam-486	11	15	n	n	NOUN
ejpam-486	11	16	=	=	SYM
ejpam-486	11	17	{	{	PUNCT
ejpam-486	11	18	1,2,3	1,2,3	NUM
ejpam-486	11	19	,	,	PUNCT
ejpam-486	11	20	...	...	PUNCT
ejpam-486	11	21	}	}	PUNCT
ejpam-486	11	22	;	;	PUNCT
ejpam-486	11	23	z	z	NOUN
ejpam-486	11	24	∈	∈	PROPN
ejpam-486	11	25	u	u	PROPN
ejpam-486	11	26	�	�	PROPN
ejpam-486	11	27	(	(	PUNCT
ejpam-486	11	28	1	1	NUM
ejpam-486	11	29	)	)	PUNCT
ejpam-486	11	30	and	and	CCONJ
ejpam-486	11	31	let	let	VERB
ejpam-486	11	32	a(1	a(1	NOUN
ejpam-486	11	33	)	)	PUNCT
ejpam-486	11	34	=	=	SYM
ejpam-486	11	35	a.	a.	NOUN
ejpam-486	11	36	let	let	VERB
ejpam-486	11	37	f	f	PROPN
ejpam-486	11	38	and	and	CCONJ
ejpam-486	11	39	f	f	PROPN
ejpam-486	11	40	be	be	AUX
ejpam-486	11	41	members	member	NOUN
ejpam-486	11	42	of	of	ADP
ejpam-486	11	43	h(u	h(u	PROPN
ejpam-486	11	44	)	)	PUNCT
ejpam-486	11	45	.	.	PUNCT
ejpam-486	12	1	the	the	DET
ejpam-486	12	2	function	function	NOUN
ejpam-486	12	3	f	f	X
ejpam-486	12	4	(	(	PUNCT
ejpam-486	12	5	z	z	NOUN
ejpam-486	12	6	)	)	PUNCT
ejpam-486	12	7	is	be	AUX
ejpam-486	12	8	said	say	VERB
ejpam-486	12	9	to	to	PART
ejpam-486	12	10	be	be	AUX
ejpam-486	12	11	subordinate	subordinate	ADJ
ejpam-486	12	12	to	to	ADP
ejpam-486	12	13	f(z	f(z	PROPN
ejpam-486	12	14	)	)	PUNCT
ejpam-486	12	15	,	,	PUNCT
ejpam-486	12	16	or	or	CCONJ
ejpam-486	12	17	f(z	f(z	NOUN
ejpam-486	12	18	)	)	PUNCT
ejpam-486	12	19	is	be	AUX
ejpam-486	12	20	said	say	VERB
ejpam-486	12	21	to	to	PART
ejpam-486	12	22	be	be	AUX
ejpam-486	12	23	superordinate	superordinate	ADJ
ejpam-486	12	24	to	to	ADP
ejpam-486	12	25	f	f	PROPN
ejpam-486	12	26	(	(	PUNCT
ejpam-486	12	27	z	z	NOUN
ejpam-486	12	28	)	)	PUNCT
ejpam-486	12	29	,	,	PUNCT
ejpam-486	12	30	if	if	SCONJ
ejpam-486	12	31	there	there	PRON
ejpam-486	12	32	exists	exist	VERB
ejpam-486	12	33	a	a	DET
ejpam-486	12	34	function	function	NOUN
ejpam-486	12	35	ω(z	ω(z	PUNCT
ejpam-486	12	36	)	)	PUNCT
ejpam-486	12	37	analytic	analytic	NOUN
ejpam-486	12	38	in	in	ADP
ejpam-486	12	39	u	u	NOUN
ejpam-486	12	40	with	with	ADP
ejpam-486	12	41	ω(0	ω(0	PROPN
ejpam-486	12	42	)	)	PUNCT
ejpam-486	12	43	=	=	SYM
ejpam-486	12	44	0	0	NUM
ejpam-486	12	45	and	and	CCONJ
ejpam-486	12	46	|ω(z)|	|ω(z)|	X
ejpam-486	12	47	<	<	X
ejpam-486	12	48	1(z	1(z	NUM
ejpam-486	12	49	∈	∈	PROPN
ejpam-486	12	50	u	u	NOUN
ejpam-486	12	51	)	)	PUNCT
ejpam-486	12	52	,	,	PUNCT
ejpam-486	12	53	such	such	ADJ
ejpam-486	12	54	that	that	SCONJ
ejpam-486	12	55	f	f	PROPN
ejpam-486	12	56	(	(	PUNCT
ejpam-486	12	57	z	z	NOUN
ejpam-486	12	58	)	)	PUNCT
ejpam-486	12	59	=	=	SYM
ejpam-486	12	60	f(ω(z	f(ω(z	ADJ
ejpam-486	12	61	)	)	PUNCT
ejpam-486	12	62	)	)	PUNCT
ejpam-486	12	63	.	.	PUNCT
ejpam-486	13	1	in	in	ADP
ejpam-486	13	2	such	such	DET
ejpam-486	13	3	a	a	DET
ejpam-486	13	4	case	case	NOUN
ejpam-486	13	5	we	we	PRON
ejpam-486	13	6	write	write	VERB
ejpam-486	13	7	f	f	PROPN
ejpam-486	13	8	(	(	PUNCT
ejpam-486	13	9	z	z	NOUN
ejpam-486	13	10	)	)	PUNCT
ejpam-486	13	11	≺	≺	NOUN
ejpam-486	13	12	f(z	f(z	NOUN
ejpam-486	13	13	)	)	PUNCT
ejpam-486	13	14	.	.	PUNCT
ejpam-486	14	1	if	if	SCONJ
ejpam-486	14	2	f	f	PROPN
ejpam-486	14	3	is	be	AUX
ejpam-486	14	4	univalent	univalent	ADJ
ejpam-486	14	5	,	,	PUNCT
ejpam-486	14	6	then	then	ADV
ejpam-486	14	7	f	f	X
ejpam-486	14	8	(	(	PUNCT
ejpam-486	14	9	z	z	NOUN
ejpam-486	14	10	)	)	PUNCT
ejpam-486	14	11	≺	≺	NOUN
ejpam-486	14	12	f(z	f(z	NOUN
ejpam-486	14	13	)	)	PUNCT
ejpam-486	15	1	if	if	SCONJ
ejpam-486	15	2	and	and	CCONJ
ejpam-486	15	3	only	only	ADV
ejpam-486	15	4	if	if	SCONJ
ejpam-486	15	5	f	f	PROPN
ejpam-486	15	6	(	(	PUNCT
ejpam-486	15	7	0	0	NUM
ejpam-486	15	8	)	)	PUNCT
ejpam-486	15	9	=	=	SYM
ejpam-486	15	10	f(0	f(0	NOUN
ejpam-486	15	11	)	)	PUNCT
ejpam-486	15	12	and	and	CCONJ
ejpam-486	15	13	f	f	PROPN
ejpam-486	15	14	(	(	PUNCT
ejpam-486	15	15	u	u	NOUN
ejpam-486	15	16	)	)	PUNCT
ejpam-486	15	17	⊂	⊂	PROPN
ejpam-486	15	18	f(u	f(u	PROPN
ejpam-486	15	19	)	)	PUNCT
ejpam-486	15	20	(	(	PUNCT
ejpam-486	15	21	see	see	VERB
ejpam-486	15	22	[	[	X
ejpam-486	15	23	8	8	NUM
ejpam-486	15	24	]	]	PUNCT
ejpam-486	15	25	and	and	CCONJ
ejpam-486	15	26	[	[	X
ejpam-486	15	27	9	9	NUM
ejpam-486	15	28	]	]	PUNCT
ejpam-486	15	29	.	.	PUNCT
ejpam-486	16	1	for	for	ADP
ejpam-486	16	2	two	two	NUM
ejpam-486	16	3	functions	function	NOUN
ejpam-486	16	4	f	f	X
ejpam-486	16	5	(	(	PUNCT
ejpam-486	16	6	z	z	NOUN
ejpam-486	16	7	)	)	PUNCT
ejpam-486	16	8	given	give	VERB
ejpam-486	16	9	by	by	ADP
ejpam-486	16	10	(	(	PUNCT
ejpam-486	16	11	1	1	NUM
ejpam-486	16	12	)	)	PUNCT
ejpam-486	16	13	and	and	CCONJ
ejpam-486	16	14	g(z	g(z	PROPN
ejpam-486	16	15	)	)	PUNCT
ejpam-486	16	16	=	=	PUNCT
ejpam-486	16	17	zp	zp	PROPN
ejpam-486	16	18	+	+	CCONJ
ejpam-486	16	19	∞	∞	NUM
ejpam-486	16	20	∑	∑	PUNCT
ejpam-486	16	21	n=1	n=1	PROPN
ejpam-486	16	22	bp+nzp+n	bp+nzp+n	NOUN
ejpam-486	16	23	,	,	PUNCT
ejpam-486	16	24	∗corresponding	∗corresponde	VERB
ejpam-486	16	25	author	author	NOUN
ejpam-486	16	26	.	.	PUNCT
ejpam-486	17	1	email	email	NOUN
ejpam-486	17	2	addresses	address	NOUN
ejpam-486	17	3	:	:	PUNCT
ejpam-486	17	4	mkaouf127	mkaouf127	PROPN
ejpam-486	17	5	�	�	PROPN
ejpam-486	17	6	yahoo	yahoo	PROPN
ejpam-486	17	7	.	.	PUNCT
ejpam-486	18	1	om	om	PROPN
ejpam-486	18	2	(	(	PUNCT
ejpam-486	18	3	m.	m.	PROPN
ejpam-486	18	4	aouf	aouf	PROPN
ejpam-486	18	5	)	)	PUNCT
ejpam-486	18	6	,	,	PUNCT
ejpam-486	18	7	tmseoudy	tmseoudy	PROPN
ejpam-486	18	8	�	�	PROPN
ejpam-486	18	9	gmail	gmail	NOUN
ejpam-486	18	10	.	.	PUNCT
ejpam-486	19	1	om	om	PROPN
ejpam-486	19	2	(	(	PUNCT
ejpam-486	19	3	t.	t.	PROPN
ejpam-486	19	4	seoudy	seoudy	PROPN
ejpam-486	19	5	)	)	PUNCT
ejpam-486	19	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-486	20	1	26	26	NUM
ejpam-486	21	1	c	c	X
ejpam-486	21	2	©	©	PROPN
ejpam-486	21	3	2009	2009	NUM
ejpam-486	21	4	ejpam	ejpam	NOUN
ejpam-486	21	5	all	all	DET
ejpam-486	21	6	rights	right	NOUN
ejpam-486	21	7	reserved	reserve	VERB
ejpam-486	21	8	.	.	PUNCT
ejpam-486	22	1	m.	m.	PROPN
ejpam-486	22	2	aouf	aouf	PROPN
ejpam-486	22	3	,	,	PUNCT
ejpam-486	22	4	t.	t.	PROPN
ejpam-486	22	5	seoudy	seoudy	PROPN
ejpam-486	22	6	/	/	SYM
ejpam-486	22	7	eur	eur	PROPN
ejpam-486	22	8	.	.	PUNCT
ejpam-486	23	1	j.	j.	PROPN
ejpam-486	23	2	pure	pure	PROPN
ejpam-486	23	3	appl	appl	PROPN
ejpam-486	23	4	.	.	PROPN
ejpam-486	23	5	math	math	PROPN
ejpam-486	23	6	,	,	PUNCT
ejpam-486	23	7	3	3	NUM
ejpam-486	23	8	(	(	PUNCT
ejpam-486	23	9	2010	2010	NUM
ejpam-486	23	10	)	)	PUNCT
ejpam-486	23	11	,	,	PUNCT
ejpam-486	23	12	26	26	NUM
ejpam-486	23	13	-	-	SYM
ejpam-486	23	14	44	44	NUM
ejpam-486	23	15	27	27	NUM
ejpam-486	23	16	the	the	DET
ejpam-486	23	17	hadamard	hadamard	ADJ
ejpam-486	23	18	product	product	NOUN
ejpam-486	23	19	(	(	PUNCT
ejpam-486	23	20	or	or	CCONJ
ejpam-486	23	21	convolution	convolution	NOUN
ejpam-486	23	22	)	)	PUNCT
ejpam-486	23	23	of	of	ADP
ejpam-486	23	24	f	f	PROPN
ejpam-486	23	25	and	and	CCONJ
ejpam-486	23	26	g	g	PROPN
ejpam-486	23	27	is	be	AUX
ejpam-486	23	28	defined	define	VERB
ejpam-486	23	29	by	by	ADP
ejpam-486	23	30	�	�	PROPN
ejpam-486	23	31	f	f	PROPN
ejpam-486	23	32	∗	∗	NOUN
ejpam-486	23	33	g	g	PROPN
ejpam-486	23	34	�	�	PROPN
ejpam-486	23	35	(	(	PUNCT
ejpam-486	23	36	z	z	NOUN
ejpam-486	23	37	)	)	PUNCT
ejpam-486	23	38	=	=	SYM
ejpam-486	24	1	zp	zp	PROPN
ejpam-486	24	2	+	+	CCONJ
ejpam-486	24	3	∞	∞	NUM
ejpam-486	24	4	∑	∑	PUNCT
ejpam-486	24	5	n=1	n=1	PROPN
ejpam-486	24	6	ap+n	ap+n	VERB
ejpam-486	24	7	bp+n	bp+n	ADJ
ejpam-486	24	8	zp+n	zp+n	ADJ
ejpam-486	24	9	=	=	SYM
ejpam-486	24	10	�	�	PROPN
ejpam-486	24	11	g	g	PROPN
ejpam-486	24	12	∗	∗	X
ejpam-486	24	13	f	f	PROPN
ejpam-486	24	14	�	�	PROPN
ejpam-486	24	15	(	(	PUNCT
ejpam-486	24	16	z	z	NOUN
ejpam-486	24	17	)	)	PUNCT
ejpam-486	24	18	.	.	PUNCT
ejpam-486	25	1	motivated	motivate	VERB
ejpam-486	25	2	essentially	essentially	ADV
ejpam-486	25	3	by	by	ADP
ejpam-486	25	4	jung	jung	PROPN
ejpam-486	25	5	et	et	PROPN
ejpam-486	25	6	al	al	PROPN
ejpam-486	25	7	.	.	PUNCT
ejpam-486	26	1	liu	liu	PROPN
ejpam-486	27	1	[	[	X
ejpam-486	27	2	5	5	NUM
ejpam-486	27	3	]	]	PUNCT
ejpam-486	27	4	and	and	CCONJ
ejpam-486	27	5	owa	owa	PROPN
ejpam-486	27	6	[	[	X
ejpam-486	27	7	7	7	NUM
ejpam-486	27	8	]	]	PUNCT
ejpam-486	27	9	introduced	introduce	VERB
ejpam-486	27	10	the	the	DET
ejpam-486	27	11	integral	integral	ADJ
ejpam-486	27	12	operator	operator	NOUN
ejpam-486	27	13	qα	qα	PROPN
ejpam-486	27	14	β	β	PROPN
ejpam-486	27	15	,	,	PUNCT
ejpam-486	27	16	p	p	X
ejpam-486	27	17	:	:	PUNCT
ejpam-486	27	18	a	a	DET
ejpam-486	27	19	�	�	PROPN
ejpam-486	27	20	p	p	PROPN
ejpam-486	27	21	�	�	PROPN
ejpam-486	27	22	→	→	PUNCT
ejpam-486	27	23	a	a	DET
ejpam-486	27	24	�	�	PROPN
ejpam-486	27	25	p	p	X
ejpam-486	27	26	�	�	PROPN
ejpam-486	27	27	as	as	SCONJ
ejpam-486	27	28	follows	follow	VERB
ejpam-486	27	29	:	:	PUNCT
ejpam-486	27	30	qαβ	qαβ	INTJ
ejpam-486	27	31	,	,	PUNCT
ejpam-486	27	32	p	p	NOUN
ejpam-486	27	33	f	f	X
ejpam-486	27	34	(	(	PUNCT
ejpam-486	27	35	z	z	NOUN
ejpam-486	27	36	)	)	PUNCT
ejpam-486	27	37	=	=	SYM
ejpam-486	27	38	�	�	PROPN
ejpam-486	27	39	p+α+	p+α+	NOUN
ejpam-486	27	40	β	β	NOUN
ejpam-486	28	1	−	−	PROPN
ejpam-486	28	2	1	1	NUM
ejpam-486	28	3	p+	p+	NOUN
ejpam-486	28	4	β	β	NOUN
ejpam-486	28	5	−	−	PROPN
ejpam-486	28	6	1	1	NUM
ejpam-486	28	7	�	�	PROPN
ejpam-486	28	8	α	α	NOUN
ejpam-486	28	9	zβ	zβ	PROPN
ejpam-486	28	10	∫	∫	PROPN
ejpam-486	28	11	z	z	PROPN
ejpam-486	28	12	0	0	PROPN
ejpam-486	28	13	�	�	PROPN
ejpam-486	28	14	1−	1−	NUM
ejpam-486	28	15	t	t	PROPN
ejpam-486	28	16	z	z	PROPN
ejpam-486	28	17	�	�	PROPN
ejpam-486	28	18	α−1	α−1	PROPN
ejpam-486	28	19	tβ−1	tβ−1	NOUN
ejpam-486	28	20	f	f	PROPN
ejpam-486	28	21	(	(	PUNCT
ejpam-486	28	22	t	t	PROPN
ejpam-486	28	23	)	)	PUNCT
ejpam-486	28	24	d	d	PROPN
ejpam-486	28	25	t	t	PROPN
ejpam-486	28	26	,	,	PUNCT
ejpam-486	28	27	�	�	PROPN
ejpam-486	28	28	α	α	X
ejpam-486	28	29	>	>	X
ejpam-486	28	30	0;β	0;β	X
ejpam-486	28	31	>	>	PUNCT
ejpam-486	28	32	−1	−1	NOUN
ejpam-486	28	33	;	;	PUNCT
ejpam-486	28	34	p	p	PROPN
ejpam-486	28	35	∈	∈	PROPN
ejpam-486	28	36	n	n	PRON
ejpam-486	28	37	�	�	PROPN
ejpam-486	28	38	,	,	PUNCT
ejpam-486	28	39	(	(	PUNCT
ejpam-486	28	40	2	2	X
ejpam-486	28	41	)	)	PUNCT
ejpam-486	28	42	and	and	CCONJ
ejpam-486	28	43	q0	q0	PROPN
ejpam-486	28	44	β	β	X
ejpam-486	28	45	,	,	PUNCT
ejpam-486	28	46	p	p	PROPN
ejpam-486	28	47	f	f	X
ejpam-486	28	48	(	(	PUNCT
ejpam-486	28	49	z	z	NOUN
ejpam-486	28	50	)	)	PUNCT
ejpam-486	28	51	=	=	SYM
ejpam-486	29	1	f	f	X
ejpam-486	29	2	(	(	PUNCT
ejpam-486	29	3	z	z	NOUN
ejpam-486	29	4	)	)	PUNCT
ejpam-486	29	5	,	,	PUNCT
ejpam-486	29	6	�	�	PROPN
ejpam-486	29	7	α=	α=	NOUN
ejpam-486	29	8	0;β	0;β	PROPN
ejpam-486	29	9	>	>	X
ejpam-486	29	10	−1	−1	PROPN
ejpam-486	29	11	�	�	PROPN
ejpam-486	29	12	.	.	PUNCT
ejpam-486	30	1	for	for	ADP
ejpam-486	30	2	f	f	PROPN
ejpam-486	30	3	∈	∈	PROPN
ejpam-486	30	4	a	a	DET
ejpam-486	30	5	�	�	PROPN
ejpam-486	30	6	p	p	PRON
ejpam-486	30	7	�	�	PROPN
ejpam-486	30	8	given	give	VERB
ejpam-486	30	9	by	by	ADP
ejpam-486	30	10	(	(	PUNCT
ejpam-486	30	11	1	1	NUM
ejpam-486	30	12	)	)	PUNCT
ejpam-486	30	13	,	,	PUNCT
ejpam-486	30	14	then	then	ADV
ejpam-486	30	15	from	from	ADP
ejpam-486	30	16	(	(	PUNCT
ejpam-486	30	17	2	2	NUM
ejpam-486	30	18	)	)	PUNCT
ejpam-486	30	19	,	,	PUNCT
ejpam-486	30	20	we	we	PRON
ejpam-486	30	21	deduce	deduce	VERB
ejpam-486	30	22	that	that	PRON
ejpam-486	30	23	qαβ	qαβ	INTJ
ejpam-486	30	24	,	,	PUNCT
ejpam-486	30	25	p	p	NOUN
ejpam-486	30	26	f	f	X
ejpam-486	30	27	(	(	PUNCT
ejpam-486	30	28	z	z	NOUN
ejpam-486	30	29	)	)	PUNCT
ejpam-486	30	30	=	=	SYM
ejpam-486	31	1	zp	zp	PROPN
ejpam-486	31	2	+	+	CCONJ
ejpam-486	31	3	γ	γ	X
ejpam-486	31	4	�	�	PROPN
ejpam-486	31	5	α+	α+	X
ejpam-486	31	6	β	β	X
ejpam-486	32	1	+	+	SYM
ejpam-486	32	2	p	p	PROPN
ejpam-486	32	3	�	�	PROPN
ejpam-486	32	4	γ	γ	X
ejpam-486	32	5	�	�	PROPN
ejpam-486	32	6	β	β	PROPN
ejpam-486	32	7	+	+	CCONJ
ejpam-486	32	8	p	p	PROPN
ejpam-486	32	9	�	�	PROPN
ejpam-486	32	10	∞	∞	PROPN
ejpam-486	32	11	∑	∑	PROPN
ejpam-486	32	12	n=1	n=1	PROPN
ejpam-486	32	13	γ	γ	X
ejpam-486	32	14	�	�	PROPN
ejpam-486	32	15	β	β	PROPN
ejpam-486	32	16	+	+	PROPN
ejpam-486	32	17	p+	p+	VERB
ejpam-486	32	18	n	n	PRON
ejpam-486	32	19	�	�	PROPN
ejpam-486	32	20	γ	γ	PROPN
ejpam-486	32	21	�	�	PROPN
ejpam-486	32	22	α+	α+	X
ejpam-486	32	23	β	β	PROPN
ejpam-486	32	24	+	+	PROPN
ejpam-486	32	25	p+	p+	NOUN
ejpam-486	32	26	n	n	PRON
ejpam-486	32	27	�	�	PROPN
ejpam-486	32	28	ap+nzp+n	ap+nzp+n	VERB
ejpam-486	32	29	�	�	PROPN
ejpam-486	32	30	α	α	PRON
ejpam-486	32	31	≥	≥	NOUN
ejpam-486	32	32	0;β	0;β	X
ejpam-486	32	33	>	>	X
ejpam-486	32	34	−1	−1	NOUN
ejpam-486	32	35	;	;	PUNCT
ejpam-486	32	36	p	p	PROPN
ejpam-486	32	37	∈	∈	PROPN
ejpam-486	32	38	n	n	PRON
ejpam-486	32	39	�	�	PROPN
ejpam-486	32	40	.	.	PUNCT
ejpam-486	33	1	(	(	PUNCT
ejpam-486	33	2	3	3	X
ejpam-486	33	3	)	)	PUNCT
ejpam-486	33	4	it	it	PRON
ejpam-486	33	5	is	be	AUX
ejpam-486	33	6	easily	easily	ADV
ejpam-486	33	7	verified	verify	VERB
ejpam-486	33	8	from	from	ADP
ejpam-486	33	9	the	the	DET
ejpam-486	33	10	definition	definition	NOUN
ejpam-486	33	11	(	(	PUNCT
ejpam-486	33	12	3	3	NUM
ejpam-486	33	13	)	)	PUNCT
ejpam-486	33	14	that	that	PRON
ejpam-486	33	15	(	(	PUNCT
ejpam-486	33	16	see	see	VERB
ejpam-486	33	17	[	[	X
ejpam-486	33	18	7	7	NUM
ejpam-486	33	19	]	]	SYM
ejpam-486	33	20	)	)	PUNCT
ejpam-486	33	21	z	z	NOUN
ejpam-486	33	22	�	�	PROPN
ejpam-486	33	23	qαβ	qαβ	PROPN
ejpam-486	33	24	,	,	PUNCT
ejpam-486	33	25	p	p	NOUN
ejpam-486	33	26	f	f	X
ejpam-486	33	27	(	(	PUNCT
ejpam-486	33	28	z	z	NOUN
ejpam-486	33	29	)	)	PUNCT
ejpam-486	33	30	�	�	PROPN
ejpam-486	33	31	′	′	NOUN
ejpam-486	33	32	=	=	SYM
ejpam-486	33	33	�	�	PROPN
ejpam-486	33	34	α+	α+	PUNCT
ejpam-486	33	35	β	β	NOUN
ejpam-486	34	1	+	+	CCONJ
ejpam-486	34	2	p−	p−	NOUN
ejpam-486	34	3	1	1	NUM
ejpam-486	34	4	�	�	PROPN
ejpam-486	34	5	qα−1	qα−1	PROPN
ejpam-486	34	6	β	β	X
ejpam-486	34	7	,	,	PUNCT
ejpam-486	34	8	p	p	PROPN
ejpam-486	34	9	f	f	X
ejpam-486	34	10	(	(	PUNCT
ejpam-486	34	11	z)−	z)−	PROPN
ejpam-486	34	12	�	�	PROPN
ejpam-486	34	13	α+	α+	X
ejpam-486	34	14	β	β	NOUN
ejpam-486	34	15	−	−	PROPN
ejpam-486	34	16	1	1	NUM
ejpam-486	34	17	�	�	PROPN
ejpam-486	34	18	qαβ	qαβ	PROPN
ejpam-486	34	19	,	,	PUNCT
ejpam-486	34	20	p	p	NOUN
ejpam-486	34	21	f	f	X
ejpam-486	34	22	(	(	PUNCT
ejpam-486	34	23	z	z	NOUN
ejpam-486	34	24	)	)	PUNCT
ejpam-486	34	25	.	.	PUNCT
ejpam-486	35	1	(	(	PUNCT
ejpam-486	35	2	4	4	X
ejpam-486	35	3	)	)	PUNCT
ejpam-486	35	4	we	we	PRON
ejpam-486	35	5	note	note	VERB
ejpam-486	35	6	that	that	SCONJ
ejpam-486	35	7	the	the	DET
ejpam-486	35	8	one	one	NUM
ejpam-486	35	9	-	-	PUNCT
ejpam-486	35	10	parameter	parameter	NOUN
ejpam-486	35	11	family	family	NOUN
ejpam-486	35	12	of	of	ADP
ejpam-486	35	13	integral	integral	ADJ
ejpam-486	35	14	operator	operator	NOUN
ejpam-486	35	15	qα	qα	PROPN
ejpam-486	35	16	β	β	PROPN
ejpam-486	35	17	,	,	PUNCT
ejpam-486	35	18	1	1	NUM
ejpam-486	35	19	f	f	X
ejpam-486	35	20	(	(	PUNCT
ejpam-486	35	21	z	z	NOUN
ejpam-486	35	22	)	)	PUNCT
ejpam-486	35	23	=	=	SYM
ejpam-486	35	24	qα	qα	PROPN
ejpam-486	35	25	β	β	PROPN
ejpam-486	35	26	was	be	AUX
ejpam-486	35	27	defined	define	VERB
ejpam-486	35	28	by	by	ADP
ejpam-486	35	29	jung	jung	PROPN
ejpam-486	35	30	et	et	PROPN
ejpam-486	35	31	al	al	PROPN
ejpam-486	35	32	.	.	PUNCT
ejpam-486	36	1	[	[	X
ejpam-486	36	2	5	5	NUM
ejpam-486	36	3	]	]	PUNCT
ejpam-486	36	4	.	.	PUNCT
ejpam-486	37	1	to	to	PART
ejpam-486	37	2	prove	prove	VERB
ejpam-486	37	3	our	our	PRON
ejpam-486	37	4	results	result	NOUN
ejpam-486	37	5	,	,	PUNCT
ejpam-486	37	6	we	we	PRON
ejpam-486	37	7	need	need	VERB
ejpam-486	37	8	the	the	DET
ejpam-486	37	9	following	follow	VERB
ejpam-486	37	10	definitions	definition	NOUN
ejpam-486	37	11	and	and	CCONJ
ejpam-486	37	12	lemmas	lemmas	PROPN
ejpam-486	37	13	.	.	PUNCT
ejpam-486	38	1	denote	denote	VERB
ejpam-486	38	2	by	by	ADP
ejpam-486	38	3	f	f	PROPN
ejpam-486	38	4	the	the	DET
ejpam-486	38	5	set	set	NOUN
ejpam-486	38	6	of	of	ADP
ejpam-486	38	7	all	all	DET
ejpam-486	38	8	functions	function	NOUN
ejpam-486	38	9	q(z	q(z	PROPN
ejpam-486	38	10	)	)	PUNCT
ejpam-486	38	11	that	that	PRON
ejpam-486	38	12	are	be	AUX
ejpam-486	38	13	analytic	analytic	ADJ
ejpam-486	38	14	and	and	CCONJ
ejpam-486	38	15	injective	injective	ADJ
ejpam-486	38	16	on	on	ADP
ejpam-486	38	17	ū\e(q	ū\e(q	PROPN
ejpam-486	38	18	)	)	PUNCT
ejpam-486	38	19	where	where	SCONJ
ejpam-486	38	20	e(q	e(q	VERB
ejpam-486	38	21	)	)	PUNCT
ejpam-486	38	22	=	=	SYM
ejpam-486	38	23	�	�	PROPN
ejpam-486	38	24	ζ	ζ	PROPN
ejpam-486	38	25	∈	∈	PROPN
ejpam-486	38	26	∂	∂	NOUN
ejpam-486	38	27	u	u	NOUN
ejpam-486	38	28	:	:	PUNCT
ejpam-486	38	29	lim	lim	PROPN
ejpam-486	38	30	z→ζ	z→ζ	NUM
ejpam-486	38	31	q(z	q(z	PROPN
ejpam-486	38	32	)	)	PUNCT
ejpam-486	38	33	=	=	SYM
ejpam-486	38	34	∞	∞	PROPN
ejpam-486	38	35	�	�	PROPN
ejpam-486	38	36	,	,	PUNCT
ejpam-486	38	37	and	and	CCONJ
ejpam-486	38	38	are	be	AUX
ejpam-486	38	39	such	such	ADJ
ejpam-486	38	40	that	that	DET
ejpam-486	38	41	q′(ζ	q′(ζ	NOUN
ejpam-486	38	42	)	)	PUNCT
ejpam-486	38	43	6=	6=	ADP
ejpam-486	38	44	0	0	NUM
ejpam-486	38	45	for	for	ADP
ejpam-486	38	46	ζ	ζ	PROPN
ejpam-486	38	47	∈	∈	PROPN
ejpam-486	38	48	∂	∂	NOUN
ejpam-486	38	49	u\e(q	u\e(q	ADJ
ejpam-486	38	50	)	)	PUNCT
ejpam-486	38	51	.	.	PUNCT
ejpam-486	39	1	further	far	ADV
ejpam-486	39	2	let	let	VERB
ejpam-486	39	3	the	the	DET
ejpam-486	39	4	subclass	subclass	NOUN
ejpam-486	39	5	off	off	ADP
ejpam-486	39	6	for	for	ADP
ejpam-486	39	7	which	which	PRON
ejpam-486	39	8	q(0	q(0	PROPN
ejpam-486	39	9	)	)	PUNCT
ejpam-486	39	10	=	=	NOUN
ejpam-486	40	1	a	a	PRON
ejpam-486	40	2	be	be	AUX
ejpam-486	40	3	denoted	denote	VERB
ejpam-486	40	4	by	by	ADP
ejpam-486	40	5	f	f	PROPN
ejpam-486	40	6	(	(	PUNCT
ejpam-486	40	7	a	a	PROPN
ejpam-486	40	8	)	)	PUNCT
ejpam-486	40	9	,	,	PUNCT
ejpam-486	40	10	f	f	PROPN
ejpam-486	40	11	(	(	PUNCT
ejpam-486	40	12	0)≡f0	0)≡f0	NOUN
ejpam-486	40	13	and	and	CCONJ
ejpam-486	40	14	f	f	PROPN
ejpam-486	40	15	(	(	PUNCT
ejpam-486	40	16	1)≡f1	1)≡f1	NUM
ejpam-486	40	17	.	.	PUNCT
ejpam-486	41	1	definition	definition	NOUN
ejpam-486	41	2	1	1	NUM
ejpam-486	41	3	(	(	PUNCT
ejpam-486	41	4	[	[	X
ejpam-486	41	5	8	8	NUM
ejpam-486	41	6	]	]	PUNCT
ejpam-486	41	7	,	,	PUNCT
ejpam-486	41	8	definition	definition	NOUN
ejpam-486	41	9	2.3a	2.3a	NUM
ejpam-486	41	10	,	,	PUNCT
ejpam-486	41	11	p.	p.	NOUN
ejpam-486	41	12	27	27	NUM
ejpam-486	41	13	)	)	PUNCT
ejpam-486	41	14	.	.	PUNCT
ejpam-486	42	1	let	let	VERB
ejpam-486	42	2	ω	ω	PRON
ejpam-486	42	3	be	be	AUX
ejpam-486	42	4	a	a	DET
ejpam-486	42	5	set	set	NOUN
ejpam-486	42	6	in	in	ADP
ejpam-486	42	7	c	c	NOUN
ejpam-486	42	8	,	,	PUNCT
ejpam-486	42	9	q	q	PROPN
ejpam-486	42	10	∈	∈	PROPN
ejpam-486	42	11	f	f	PROPN
ejpam-486	42	12	and	and	CCONJ
ejpam-486	42	13	n	n	PROPN
ejpam-486	42	14	be	be	VERB
ejpam-486	42	15	a	a	DET
ejpam-486	42	16	positive	positive	ADJ
ejpam-486	42	17	integer	integer	NOUN
ejpam-486	42	18	.	.	PUNCT
ejpam-486	43	1	the	the	DET
ejpam-486	43	2	class	class	NOUN
ejpam-486	43	3	of	of	ADP
ejpam-486	43	4	admissible	admissible	ADJ
ejpam-486	43	5	functions	function	NOUN
ejpam-486	43	6	ψn[ω	ψn[ω	NOUN
ejpam-486	43	7	,	,	PUNCT
ejpam-486	43	8	q	q	NOUN
ejpam-486	43	9	]	]	X
ejpam-486	43	10	,	,	PUNCT
ejpam-486	43	11	consists	consist	VERB
ejpam-486	43	12	of	of	ADP
ejpam-486	43	13	those	those	DET
ejpam-486	43	14	functions	function	NOUN
ejpam-486	43	15	ψ	ψ	NOUN
ejpam-486	43	16	:	:	PUNCT
ejpam-486	43	17	c3	c3	PROPN
ejpam-486	43	18	×	×	PROPN
ejpam-486	43	19	u	u	PROPN
ejpam-486	43	20	→	→	SYM
ejpam-486	43	21	c	c	X
ejpam-486	43	22	that	that	PRON
ejpam-486	43	23	satisfy	satisfy	VERB
ejpam-486	43	24	the	the	DET
ejpam-486	43	25	admissibility	admissibility	NOUN
ejpam-486	43	26	condition	condition	NOUN
ejpam-486	43	27	:	:	PUNCT
ejpam-486	43	28	ψ(r	ψ(r	PROPN
ejpam-486	43	29	,	,	PUNCT
ejpam-486	43	30	s	s	X
ejpam-486	43	31	,	,	PUNCT
ejpam-486	43	32	t	t	PROPN
ejpam-486	43	33	;	;	PUNCT
ejpam-486	43	34	z	z	X
ejpam-486	43	35	)	)	PUNCT
ejpam-486	43	36	/∈	/∈	PUNCT
ejpam-486	44	1	ω	ω	NUM
ejpam-486	44	2	whenever	whenever	SCONJ
ejpam-486	44	3	r	r	NOUN
ejpam-486	44	4	=	=	SYM
ejpam-486	44	5	q(ζ	q(ζ	ADJ
ejpam-486	44	6	)	)	PUNCT
ejpam-486	44	7	,	,	PUNCT
ejpam-486	44	8	s	s	NOUN
ejpam-486	44	9	=	=	PUNCT
ejpam-486	44	10	kζq′(ζ	kζq′(ζ	NOUN
ejpam-486	44	11	)	)	PUNCT
ejpam-486	44	12	,	,	PUNCT
ejpam-486	45	1	ℜ	ℜ	PROPN
ejpam-486	45	2	§	§	PROPN
ejpam-486	45	3	t	t	NOUN
ejpam-486	45	4	s	s	PART
ejpam-486	45	5	+	+	ADJ
ejpam-486	45	6	1	1	NUM
ejpam-486	45	7	ª	ª	SYM
ejpam-486	45	8	≥	≥	NOUN
ejpam-486	45	9	kℜ	kℜ	X
ejpam-486	45	10	(	(	PUNCT
ejpam-486	45	11	1	1	NUM
ejpam-486	45	12	+	+	NUM
ejpam-486	45	13	ζq	ζq	NOUN
ejpam-486	45	14	′′	′′	PROPN
ejpam-486	45	15	(	(	PUNCT
ejpam-486	45	16	ζ	ζ	NOUN
ejpam-486	45	17	)	)	PUNCT
ejpam-486	45	18	q′	q′	NOUN
ejpam-486	45	19	(	(	PUNCT
ejpam-486	45	20	ζ	ζ	NOUN
ejpam-486	45	21	)	)	PUNCT
ejpam-486	45	22	)	)	PUNCT
ejpam-486	45	23	,	,	PUNCT
ejpam-486	45	24	where	where	SCONJ
ejpam-486	45	25	z	z	PROPN
ejpam-486	45	26	∈	∈	PROPN
ejpam-486	45	27	u	u	NOUN
ejpam-486	45	28	,	,	PUNCT
ejpam-486	45	29	ζ	ζ	PROPN
ejpam-486	45	30	∈	∈	PROPN
ejpam-486	45	31	∂	∂	NOUN
ejpam-486	45	32	u\e(q	u\e(q	ADJ
ejpam-486	45	33	)	)	PUNCT
ejpam-486	45	34	and	and	CCONJ
ejpam-486	45	35	k	k	PROPN
ejpam-486	45	36	≥	≥	PROPN
ejpam-486	45	37	n.	n.	NOUN
ejpam-486	45	38	we	we	PRON
ejpam-486	45	39	write	write	VERB
ejpam-486	45	40	ψ1[ω	ψ1[ω	PROPN
ejpam-486	45	41	,	,	PUNCT
ejpam-486	45	42	q	q	X
ejpam-486	45	43	]	]	X
ejpam-486	45	44	as	as	ADP
ejpam-486	45	45	ψ[ω	ψ[ω	NOUN
ejpam-486	45	46	,	,	PUNCT
ejpam-486	45	47	q	q	X
ejpam-486	45	48	]	]	X
ejpam-486	45	49	.	.	PUNCT
ejpam-486	46	1	m.	m.	PROPN
ejpam-486	46	2	aouf	aouf	PROPN
ejpam-486	46	3	,	,	PUNCT
ejpam-486	46	4	t.	t.	PROPN
ejpam-486	46	5	seoudy	seoudy	PROPN
ejpam-486	46	6	/	/	SYM
ejpam-486	46	7	eur	eur	PROPN
ejpam-486	46	8	.	.	PUNCT
ejpam-486	47	1	j.	j.	PROPN
ejpam-486	47	2	pure	pure	PROPN
ejpam-486	47	3	appl	appl	PROPN
ejpam-486	47	4	.	.	PROPN
ejpam-486	47	5	math	math	PROPN
ejpam-486	47	6	,	,	PUNCT
ejpam-486	47	7	3	3	NUM
ejpam-486	47	8	(	(	PUNCT
ejpam-486	47	9	2010	2010	NUM
ejpam-486	47	10	)	)	PUNCT
ejpam-486	47	11	,	,	PUNCT
ejpam-486	47	12	26	26	NUM
ejpam-486	47	13	-	-	SYM
ejpam-486	47	14	44	44	NUM
ejpam-486	47	15	28	28	NUM
ejpam-486	47	16	in	in	ADP
ejpam-486	47	17	particular	particular	ADJ
ejpam-486	47	18	when	when	SCONJ
ejpam-486	47	19	q(z	q(z	PROPN
ejpam-486	47	20	)	)	PUNCT
ejpam-486	47	21	=	=	PUNCT
ejpam-486	48	1	m	m	VERB
ejpam-486	48	2	mz+a	mz+a	ADJ
ejpam-486	48	3	m+āz	m+āz	ADJ
ejpam-486	48	4	,	,	PUNCT
ejpam-486	48	5	with	with	ADP
ejpam-486	48	6	m	m	PROPN
ejpam-486	48	7	>	>	X
ejpam-486	48	8	0	0	NUM
ejpam-486	48	9	and	and	CCONJ
ejpam-486	48	10	|a|	|a|	NOUN
ejpam-486	48	11	<	<	X
ejpam-486	48	12	m	m	NOUN
ejpam-486	48	13	,	,	PUNCT
ejpam-486	48	14	then	then	ADV
ejpam-486	48	15	q(u	q(u	X
ejpam-486	48	16	)	)	PUNCT
ejpam-486	49	1	=	=	SYM
ejpam-486	49	2	um	um	INTJ
ejpam-486	49	3	=	=	PUNCT
ejpam-486	49	4	{	{	PUNCT
ejpam-486	49	5	w	w	NOUN
ejpam-486	49	6	:	:	PUNCT
ejpam-486	49	7	|w|	|w|	VERB
ejpam-486	49	8	<	<	X
ejpam-486	49	9	m	m	NOUN
ejpam-486	49	10	}	}	PUNCT
ejpam-486	49	11	,	,	PUNCT
ejpam-486	49	12	q(0	q(0	PROPN
ejpam-486	49	13	)	)	PUNCT
ejpam-486	49	14	=	=	SYM
ejpam-486	50	1	a	a	PRON
ejpam-486	50	2	,	,	PUNCT
ejpam-486	50	3	e(q	e(q	PROPN
ejpam-486	50	4	)	)	PUNCT
ejpam-486	50	5	=	=	SYM
ejpam-486	50	6	∅	∅	NOUN
ejpam-486	50	7	and	and	CCONJ
ejpam-486	50	8	q	q	NOUN
ejpam-486	50	9	∈	∈	PROPN
ejpam-486	51	1	f	f	X
ejpam-486	51	2	.	.	PUNCT
ejpam-486	52	1	in	in	ADP
ejpam-486	52	2	this	this	DET
ejpam-486	52	3	case	case	NOUN
ejpam-486	52	4	,	,	PUNCT
ejpam-486	52	5	we	we	PRON
ejpam-486	52	6	set	set	VERB
ejpam-486	52	7	ψn[ω	ψn[ω	PROPN
ejpam-486	52	8	,	,	PUNCT
ejpam-486	52	9	m	m	PRON
ejpam-486	52	10	,	,	PUNCT
ejpam-486	52	11	a	a	X
ejpam-486	52	12	]	]	X
ejpam-486	52	13	=	=	SYM
ejpam-486	52	14	ψn[ω	ψn[ω	NOUN
ejpam-486	52	15	,	,	PUNCT
ejpam-486	52	16	q	q	NOUN
ejpam-486	52	17	]	]	X
ejpam-486	52	18	,	,	PUNCT
ejpam-486	52	19	and	and	CCONJ
ejpam-486	52	20	in	in	ADP
ejpam-486	52	21	the	the	DET
ejpam-486	52	22	special	special	ADJ
ejpam-486	52	23	case	case	NOUN
ejpam-486	52	24	when	when	SCONJ
ejpam-486	52	25	the	the	DET
ejpam-486	52	26	set	set	NOUN
ejpam-486	52	27	ω	ω	PROPN
ejpam-486	52	28	=	=	X
ejpam-486	52	29	um	um	INTJ
ejpam-486	52	30	,	,	PUNCT
ejpam-486	52	31	the	the	DET
ejpam-486	52	32	class	class	NOUN
ejpam-486	52	33	is	be	AUX
ejpam-486	52	34	simply	simply	ADV
ejpam-486	52	35	denoted	denote	VERB
ejpam-486	52	36	by	by	ADP
ejpam-486	52	37	ψn[m	ψn[m	PROPN
ejpam-486	52	38	,	,	PUNCT
ejpam-486	52	39	a	a	PRON
ejpam-486	52	40	]	]	X
ejpam-486	52	41	.	.	PUNCT
ejpam-486	53	1	definition	definition	NOUN
ejpam-486	53	2	2	2	NUM
ejpam-486	53	3	(	(	PUNCT
ejpam-486	53	4	[	[	X
ejpam-486	53	5	9	9	NUM
ejpam-486	53	6	]	]	PUNCT
ejpam-486	53	7	,	,	PUNCT
ejpam-486	53	8	definition	definition	NOUN
ejpam-486	53	9	3	3	NUM
ejpam-486	53	10	,	,	PUNCT
ejpam-486	53	11	p.	p.	NOUN
ejpam-486	53	12	817	817	NUM
ejpam-486	53	13	)	)	PUNCT
ejpam-486	53	14	.	.	PUNCT
ejpam-486	54	1	let	let	VERB
ejpam-486	54	2	ω	ω	PRON
ejpam-486	54	3	be	be	AUX
ejpam-486	54	4	a	a	DET
ejpam-486	54	5	set	set	NOUN
ejpam-486	54	6	in	in	ADP
ejpam-486	54	7	c	c	PROPN
ejpam-486	54	8	,	,	PUNCT
ejpam-486	54	9	q(z	q(z	PROPN
ejpam-486	54	10	)	)	PUNCT
ejpam-486	54	11	∈	∈	PROPN
ejpam-486	54	12	h[a	h[a	PROPN
ejpam-486	54	13	,	,	PUNCT
ejpam-486	54	14	n	n	CCONJ
ejpam-486	54	15	]	]	PUNCT
ejpam-486	54	16	with	with	ADP
ejpam-486	54	17	q′(z	q′(z	PROPN
ejpam-486	54	18	)	)	PUNCT
ejpam-486	54	19	6=	6=	ADP
ejpam-486	54	20	0	0	X
ejpam-486	54	21	.	.	PUNCT
ejpam-486	55	1	the	the	DET
ejpam-486	55	2	class	class	NOUN
ejpam-486	55	3	of	of	ADP
ejpam-486	55	4	admissible	admissible	ADJ
ejpam-486	55	5	functions	function	NOUN
ejpam-486	55	6	ψ′n[ω	ψ′n[ω	PROPN
ejpam-486	55	7	,	,	PUNCT
ejpam-486	55	8	q	q	X
ejpam-486	55	9	]	]	PUNCT
ejpam-486	55	10	consists	consist	VERB
ejpam-486	55	11	of	of	ADP
ejpam-486	55	12	those	those	DET
ejpam-486	55	13	functions	function	NOUN
ejpam-486	55	14	ψ	ψ	NOUN
ejpam-486	55	15	:	:	PUNCT
ejpam-486	55	16	c3×	c3×	VERB
ejpam-486	55	17	ū	ū	NOUN
ejpam-486	55	18	→	→	SYM
ejpam-486	55	19	c	c	X
ejpam-486	55	20	that	that	PRON
ejpam-486	55	21	satisfy	satisfy	VERB
ejpam-486	55	22	the	the	DET
ejpam-486	55	23	admissibility	admissibility	NOUN
ejpam-486	55	24	condition	condition	NOUN
ejpam-486	55	25	ψ(r	ψ(r	PROPN
ejpam-486	55	26	,	,	PUNCT
ejpam-486	55	27	s	s	NOUN
ejpam-486	55	28	,	,	PUNCT
ejpam-486	55	29	t;ζ	t;ζ	NUM
ejpam-486	55	30	)	)	PUNCT
ejpam-486	56	1	∈	∈	PROPN
ejpam-486	56	2	ω	ω	NUM
ejpam-486	56	3	whenever	whenever	SCONJ
ejpam-486	56	4	r	r	NOUN
ejpam-486	56	5	=	=	SYM
ejpam-486	56	6	q(z	q(z	PROPN
ejpam-486	56	7	)	)	PUNCT
ejpam-486	56	8	,	,	PUNCT
ejpam-486	56	9	s	s	NOUN
ejpam-486	56	10	=	=	SYM
ejpam-486	56	11	zq′(z	zq′(z	PROPN
ejpam-486	56	12	)	)	PUNCT
ejpam-486	56	13	m	m	PROPN
ejpam-486	56	14	,	,	PUNCT
ejpam-486	56	15	ℜ	ℜ	PROPN
ejpam-486	56	16	§	§	PROPN
ejpam-486	56	17	t	t	NOUN
ejpam-486	56	18	s	s	PART
ejpam-486	56	19	+	+	ADJ
ejpam-486	56	20	1	1	NUM
ejpam-486	56	21	ª	ª	SYM
ejpam-486	56	22	≥	≥	NUM
ejpam-486	56	23	1	1	NUM
ejpam-486	56	24	m	m	NOUN
ejpam-486	56	25	ℜ	ℜ	NOUN
ejpam-486	56	26	(	(	PUNCT
ejpam-486	56	27	1	1	NUM
ejpam-486	56	28	+	+	NUM
ejpam-486	56	29	zq	zq	PROPN
ejpam-486	56	30	′′	′′	PROPN
ejpam-486	56	31	(	(	PUNCT
ejpam-486	56	32	z	z	NOUN
ejpam-486	56	33	)	)	PUNCT
ejpam-486	56	34	q′	q′	NOUN
ejpam-486	56	35	(	(	PUNCT
ejpam-486	56	36	z	z	NOUN
ejpam-486	56	37	)	)	PUNCT
ejpam-486	56	38	)	)	PUNCT
ejpam-486	56	39	,	,	PUNCT
ejpam-486	56	40	where	where	SCONJ
ejpam-486	56	41	z	z	PROPN
ejpam-486	56	42	∈	∈	PROPN
ejpam-486	56	43	u	u	NOUN
ejpam-486	56	44	,	,	PUNCT
ejpam-486	56	45	ζ	ζ	PROPN
ejpam-486	56	46	∈	∈	PROPN
ejpam-486	56	47	∂	∂	NUM
ejpam-486	56	48	u	u	NOUN
ejpam-486	56	49	and	and	CCONJ
ejpam-486	56	50	m	m	PROPN
ejpam-486	56	51	≥	≥	NOUN
ejpam-486	56	52	n≥	n≥	NOUN
ejpam-486	56	53	1	1	X
ejpam-486	56	54	.	.	PUNCT
ejpam-486	57	1	in	in	ADP
ejpam-486	57	2	particular	particular	ADJ
ejpam-486	57	3	,	,	PUNCT
ejpam-486	57	4	we	we	PRON
ejpam-486	57	5	write	write	VERB
ejpam-486	57	6	ψ′1[ω	ψ′1[ω	NOUN
ejpam-486	57	7	,	,	PUNCT
ejpam-486	57	8	q	q	X
ejpam-486	57	9	]	]	X
ejpam-486	57	10	as	as	ADP
ejpam-486	57	11	ψ′[ω	ψ′[ω	PROPN
ejpam-486	57	12	,	,	PUNCT
ejpam-486	57	13	q	q	X
ejpam-486	57	14	]	]	X
ejpam-486	57	15	.	.	PUNCT
ejpam-486	58	1	lemma	lemma	PROPN
ejpam-486	58	2	1	1	NUM
ejpam-486	58	3	(	(	PUNCT
ejpam-486	58	4	[	[	X
ejpam-486	58	5	8],theorem	8],theorem	NUM
ejpam-486	58	6	2.3b	2.3b	NUM
ejpam-486	58	7	,	,	PUNCT
ejpam-486	58	8	p.	p.	NOUN
ejpam-486	58	9	28	28	NUM
ejpam-486	58	10	)	)	PUNCT
ejpam-486	58	11	.	.	PUNCT
ejpam-486	59	1	letψ	letψ	PROPN
ejpam-486	59	2	∈ψn	∈ψn	PROPN
ejpam-486	59	3	�	�	PROPN
ejpam-486	59	4	ω	ω	PROPN
ejpam-486	59	5	,	,	PUNCT
ejpam-486	59	6	q	q	PROPN
ejpam-486	59	7	�	�	PROPN
ejpam-486	59	8	with	with	ADP
ejpam-486	59	9	q(0	q(0	PROPN
ejpam-486	59	10	)	)	PUNCT
ejpam-486	59	11	=	=	PUNCT
ejpam-486	59	12	a.	a.	NOUN
ejpam-486	59	13	if	if	SCONJ
ejpam-486	59	14	the	the	DET
ejpam-486	59	15	analytic	analytic	ADJ
ejpam-486	59	16	function	function	NOUN
ejpam-486	59	17	g(z	g(z	PROPN
ejpam-486	59	18	)	)	PUNCT
ejpam-486	59	19	=	=	SYM
ejpam-486	59	20	a+	a+	PUNCT
ejpam-486	59	21	anzn	anzn	NOUN
ejpam-486	59	22	+	+	CCONJ
ejpam-486	59	23	an+1zn+1	an+1zn+1	ADJ
ejpam-486	59	24	+	+	CCONJ
ejpam-486	59	25	...	...	PUNCT
ejpam-486	59	26	satisfies	satisfie	NOUN
ejpam-486	59	27	ψ(g(z	ψ(g(z	PROPN
ejpam-486	59	28	)	)	PUNCT
ejpam-486	59	29	,	,	PUNCT
ejpam-486	59	30	zg′(z	zg′(z	PROPN
ejpam-486	59	31	)	)	PUNCT
ejpam-486	59	32	,	,	PUNCT
ejpam-486	59	33	z2	z2	PROPN
ejpam-486	59	34	g	g	PROPN
ejpam-486	59	35	′′	′′	PROPN
ejpam-486	59	36	(	(	PUNCT
ejpam-486	59	37	z	z	PROPN
ejpam-486	59	38	)	)	PUNCT
ejpam-486	59	39	;	;	PUNCT
ejpam-486	59	40	z	z	X
ejpam-486	59	41	)	)	PUNCT
ejpam-486	59	42	∈	∈	PROPN
ejpam-486	59	43	ω	ω	PROPN
ejpam-486	59	44	,	,	PUNCT
ejpam-486	59	45	then	then	ADV
ejpam-486	59	46	g(z	g(z	PROPN
ejpam-486	59	47	)	)	PUNCT
ejpam-486	59	48	≺	≺	NOUN
ejpam-486	59	49	q(z	q(z	PROPN
ejpam-486	59	50	)	)	PUNCT
ejpam-486	59	51	.	.	PUNCT
ejpam-486	60	1	lemma	lemma	PROPN
ejpam-486	60	2	2	2	NUM
ejpam-486	60	3	(	(	PUNCT
ejpam-486	60	4	[	[	X
ejpam-486	60	5	9],theorem	9],theorem	NUM
ejpam-486	60	6	1	1	NUM
ejpam-486	60	7	,	,	PUNCT
ejpam-486	60	8	p.	p.	NOUN
ejpam-486	60	9	818	818	NUM
ejpam-486	60	10	)	)	PUNCT
ejpam-486	60	11	.	.	PUNCT
ejpam-486	60	12	.	.	PUNCT
ejpam-486	61	1	let	let	VERB
ejpam-486	61	2	ψ	ψ	SYM
ejpam-486	61	3	∈ψ′n[ω	∈ψ′n[ω	NOUN
ejpam-486	61	4	,	,	PUNCT
ejpam-486	61	5	q	q	X
ejpam-486	61	6	]	]	X
ejpam-486	61	7	with	with	ADP
ejpam-486	61	8	q(0	q(0	PROPN
ejpam-486	61	9	)	)	PUNCT
ejpam-486	62	1	=	=	PUNCT
ejpam-486	62	2	a.	a.	NOUN
ejpam-486	62	3	if	if	SCONJ
ejpam-486	62	4	g(z	g(z	PROPN
ejpam-486	62	5	)	)	PUNCT
ejpam-486	62	6	∈	∈	PROPN
ejpam-486	62	7	f	f	X
ejpam-486	62	8	(	(	PUNCT
ejpam-486	62	9	a	a	NOUN
ejpam-486	62	10	)	)	PUNCT
ejpam-486	62	11	and	and	CCONJ
ejpam-486	62	12	ψ(g(z	ψ(g(z	PROPN
ejpam-486	62	13	)	)	PUNCT
ejpam-486	62	14	,	,	PUNCT
ejpam-486	62	15	zg′(z	zg′(z	PROPN
ejpam-486	62	16	)	)	PUNCT
ejpam-486	62	17	,	,	PUNCT
ejpam-486	62	18	z2	z2	PROPN
ejpam-486	62	19	g	g	PROPN
ejpam-486	62	20	′′	′′	PROPN
ejpam-486	62	21	(	(	PUNCT
ejpam-486	62	22	z	z	PROPN
ejpam-486	62	23	)	)	PUNCT
ejpam-486	62	24	;	;	PUNCT
ejpam-486	63	1	z	z	X
ejpam-486	63	2	)	)	PUNCT
ejpam-486	63	3	is	be	AUX
ejpam-486	63	4	univalent	univalent	ADJ
ejpam-486	63	5	in	in	ADP
ejpam-486	63	6	u	u	PROPN
ejpam-486	63	7	then	then	ADV
ejpam-486	63	8	ω⊂	ω⊂	PROPN
ejpam-486	63	9	{	{	PUNCT
ejpam-486	63	10	ψ(g(z	ψ(g(z	PROPN
ejpam-486	63	11	)	)	PUNCT
ejpam-486	63	12	,	,	PUNCT
ejpam-486	63	13	zg′(z	zg′(z	PROPN
ejpam-486	63	14	)	)	PUNCT
ejpam-486	63	15	,	,	PUNCT
ejpam-486	63	16	z2	z2	PROPN
ejpam-486	63	17	g	g	PROPN
ejpam-486	63	18	′′	′′	PROPN
ejpam-486	63	19	(	(	PUNCT
ejpam-486	63	20	z	z	PROPN
ejpam-486	63	21	)	)	PUNCT
ejpam-486	63	22	;	;	PUNCT
ejpam-486	64	1	z	z	X
ejpam-486	64	2	)	)	PUNCT
ejpam-486	64	3	:	:	PUNCT
ejpam-486	64	4	z	z	X
ejpam-486	64	5	∈	∈	PROPN
ejpam-486	64	6	u	u	NOUN
ejpam-486	64	7	}	}	PUNCT
ejpam-486	64	8	,	,	PUNCT
ejpam-486	64	9	implies	imply	VERB
ejpam-486	64	10	q(z)≺	q(z)≺	ADP
ejpam-486	64	11	g(z	g(z	PROPN
ejpam-486	64	12	)	)	PUNCT
ejpam-486	64	13	.	.	PUNCT
ejpam-486	65	1	in	in	ADP
ejpam-486	65	2	the	the	DET
ejpam-486	65	3	present	present	ADJ
ejpam-486	65	4	investigation	investigation	NOUN
ejpam-486	65	5	,	,	PUNCT
ejpam-486	65	6	the	the	DET
ejpam-486	65	7	differential	differential	ADJ
ejpam-486	65	8	subordination	subordination	NOUN
ejpam-486	65	9	result	result	NOUN
ejpam-486	65	10	of	of	ADP
ejpam-486	65	11	miller	miller	PROPN
ejpam-486	65	12	and	and	CCONJ
ejpam-486	65	13	mocanu	mocanu	NOUN
ejpam-486	66	1	[	[	X
ejpam-486	66	2	8,theorem	8,theorem	NUM
ejpam-486	66	3	2.3b	2.3b	NUM
ejpam-486	66	4	,	,	PUNCT
ejpam-486	66	5	p.28	p.28	PROPN
ejpam-486	66	6	]	]	PUNCT
ejpam-486	66	7	is	be	AUX
ejpam-486	66	8	extended	extend	VERB
ejpam-486	66	9	for	for	ADP
ejpam-486	66	10	functions	function	NOUN
ejpam-486	66	11	associated	associate	VERB
ejpam-486	66	12	with	with	ADP
ejpam-486	66	13	the	the	DET
ejpam-486	66	14	integral	integral	ADJ
ejpam-486	66	15	operator	operator	NOUN
ejpam-486	66	16	qα	qα	PROPN
ejpam-486	66	17	β	β	PROPN
ejpam-486	66	18	,	,	PUNCT
ejpam-486	66	19	p	p	X
ejpam-486	66	20	,	,	PUNCT
ejpam-486	66	21	and	and	CCONJ
ejpam-486	66	22	we	we	PRON
ejpam-486	66	23	obtain	obtain	VERB
ejpam-486	66	24	certain	certain	ADJ
ejpam-486	66	25	other	other	ADJ
ejpam-486	66	26	related	related	ADJ
ejpam-486	66	27	results	result	NOUN
ejpam-486	66	28	.	.	PUNCT
ejpam-486	67	1	a	a	DET
ejpam-486	67	2	similar	similar	ADJ
ejpam-486	67	3	problem	problem	NOUN
ejpam-486	67	4	for	for	ADP
ejpam-486	67	5	analytic	analytic	ADJ
ejpam-486	67	6	functions	function	NOUN
ejpam-486	67	7	was	be	AUX
ejpam-486	67	8	studied	study	VERB
ejpam-486	67	9	by	by	ADP
ejpam-486	67	10	aghalary	aghalary	PROPN
ejpam-486	67	11	et	et	PROPN
ejpam-486	67	12	al	al	PROPN
ejpam-486	67	13	.	.	PUNCT
ejpam-486	68	1	[	[	X
ejpam-486	68	2	1	1	NUM
ejpam-486	68	3	]	]	PUNCT
ejpam-486	68	4	,	,	PUNCT
ejpam-486	68	5	ali	ali	PROPN
ejpam-486	68	6	et	et	PROPN
ejpam-486	68	7	al	al	PROPN
ejpam-486	68	8	.	.	PUNCT
ejpam-486	69	1	[	[	X
ejpam-486	69	2	2	2	NUM
ejpam-486	69	3	]	]	PUNCT
ejpam-486	69	4	,	,	PUNCT
ejpam-486	69	5	aouf	aouf	PROPN
ejpam-486	70	1	[	[	X
ejpam-486	70	2	3	3	NUM
ejpam-486	70	3	]	]	PUNCT
ejpam-486	70	4	,	,	PUNCT
ejpam-486	70	5	aouf	aouf	PROPN
ejpam-486	70	6	et	et	PROPN
ejpam-486	70	7	al	al	PROPN
ejpam-486	70	8	.	.	PUNCT
ejpam-486	71	1	[	[	X
ejpam-486	71	2	4	4	NUM
ejpam-486	71	3	]	]	PUNCT
ejpam-486	71	4	,	,	PUNCT
ejpam-486	71	5	and	and	CCONJ
ejpam-486	71	6	kim	kim	PROPN
ejpam-486	71	7	and	and	CCONJ
ejpam-486	71	8	srivastava	srivastava	PROPN
ejpam-486	72	1	[	[	X
ejpam-486	72	2	6	6	NUM
ejpam-486	72	3	]	]	PUNCT
ejpam-486	72	4	.	.	PUNCT
ejpam-486	73	1	additionally	additionally	ADV
ejpam-486	73	2	,	,	PUNCT
ejpam-486	73	3	the	the	DET
ejpam-486	73	4	corresponding	corresponding	ADJ
ejpam-486	73	5	differential	differential	ADJ
ejpam-486	73	6	superordination	superordination	NOUN
ejpam-486	73	7	problem	problem	NOUN
ejpam-486	73	8	is	be	AUX
ejpam-486	73	9	investigated	investigate	VERB
ejpam-486	73	10	,	,	PUNCT
ejpam-486	73	11	and	and	CCONJ
ejpam-486	73	12	several	several	ADJ
ejpam-486	73	13	sandwich	sandwich	NOUN
ejpam-486	73	14	-	-	PUNCT
ejpam-486	73	15	type	type	NOUN
ejpam-486	73	16	results	result	NOUN
ejpam-486	73	17	are	be	AUX
ejpam-486	73	18	obtained	obtain	VERB
ejpam-486	73	19	.	.	PUNCT
ejpam-486	74	1	2	2	X
ejpam-486	74	2	.	.	X
ejpam-486	74	3	subordination	subordination	NOUN
ejpam-486	74	4	results	result	NOUN
ejpam-486	74	5	involving	involve	VERB
ejpam-486	74	6	the	the	DET
ejpam-486	74	7	integral	integral	ADJ
ejpam-486	74	8	operator	operator	NOUN
ejpam-486	74	9	definition	definition	NOUN
ejpam-486	74	10	3	3	X
ejpam-486	74	11	.	.	PUNCT
ejpam-486	75	1	let	let	VERB
ejpam-486	75	2	ω	ω	NUM
ejpam-486	75	3	be	be	AUX
ejpam-486	75	4	a	a	DET
ejpam-486	75	5	set	set	NOUN
ejpam-486	75	6	in	in	ADP
ejpam-486	75	7	c	c	PROPN
ejpam-486	75	8	and	and	CCONJ
ejpam-486	75	9	q(z	q(z	PROPN
ejpam-486	75	10	)	)	PUNCT
ejpam-486	75	11	∈	∈	PROPN
ejpam-486	75	12	f0	f0	PROPN
ejpam-486	75	13	∩	∩	PROPN
ejpam-486	75	14	h[0	h[0	PROPN
ejpam-486	75	15	,	,	PUNCT
ejpam-486	75	16	p	p	X
ejpam-486	75	17	]	]	X
ejpam-486	75	18	.	.	PUNCT
ejpam-486	76	1	the	the	DET
ejpam-486	76	2	class	class	NOUN
ejpam-486	76	3	of	of	ADP
ejpam-486	76	4	admissible	admissible	ADJ
ejpam-486	76	5	functions	function	NOUN
ejpam-486	76	6	φq	φq	ADP
ejpam-486	76	7	�	�	PROPN
ejpam-486	76	8	ω	ω	PROPN
ejpam-486	76	9	,	,	PUNCT
ejpam-486	76	10	q	q	PROPN
ejpam-486	76	11	�	�	PROPN
ejpam-486	76	12	consists	consist	VERB
ejpam-486	76	13	of	of	ADP
ejpam-486	76	14	those	those	DET
ejpam-486	76	15	functions	function	NOUN
ejpam-486	76	16	φ	φ	NOUN
ejpam-486	76	17	:	:	PUNCT
ejpam-486	77	1	c3	c3	PROPN
ejpam-486	77	2	×	×	PROPN
ejpam-486	77	3	u	u	PROPN
ejpam-486	77	4	→	→	SYM
ejpam-486	77	5	c	c	X
ejpam-486	77	6	that	that	PRON
ejpam-486	77	7	satisfy	satisfy	VERB
ejpam-486	77	8	the	the	DET
ejpam-486	77	9	admissibility	admissibility	NOUN
ejpam-486	77	10	condition	condition	NOUN
ejpam-486	77	11	φ	φ	PROPN
ejpam-486	77	12	(	(	PUNCT
ejpam-486	77	13	u	u	NOUN
ejpam-486	77	14	,	,	PUNCT
ejpam-486	77	15	v	v	NOUN
ejpam-486	77	16	,	,	PUNCT
ejpam-486	77	17	w	w	NOUN
ejpam-486	77	18	;	;	PUNCT
ejpam-486	77	19	z	z	X
ejpam-486	77	20	)	)	PUNCT
ejpam-486	77	21	/∈	/∈	PUNCT
ejpam-486	78	1	ω	ω	NUM
ejpam-486	78	2	m.	m.	PROPN
ejpam-486	78	3	aouf	aouf	PROPN
ejpam-486	78	4	,	,	PUNCT
ejpam-486	78	5	t.	t.	PROPN
ejpam-486	78	6	seoudy	seoudy	PROPN
ejpam-486	78	7	/	/	SYM
ejpam-486	78	8	eur	eur	PROPN
ejpam-486	78	9	.	.	PUNCT
ejpam-486	79	1	j.	j.	PROPN
ejpam-486	79	2	pure	pure	PROPN
ejpam-486	79	3	appl	appl	PROPN
ejpam-486	79	4	.	.	PROPN
ejpam-486	79	5	math	math	PROPN
ejpam-486	79	6	,	,	PUNCT
ejpam-486	79	7	3	3	NUM
ejpam-486	79	8	(	(	PUNCT
ejpam-486	79	9	2010	2010	NUM
ejpam-486	79	10	)	)	PUNCT
ejpam-486	79	11	,	,	PUNCT
ejpam-486	79	12	26	26	NUM
ejpam-486	79	13	-	-	SYM
ejpam-486	79	14	44	44	NUM
ejpam-486	79	15	29	29	NUM
ejpam-486	79	16	whenever	whenever	SCONJ
ejpam-486	79	17	u	u	NOUN
ejpam-486	79	18	=	=	NOUN
ejpam-486	79	19	q	q	X
ejpam-486	79	20	(	(	PUNCT
ejpam-486	79	21	ζ	ζ	NOUN
ejpam-486	79	22	)	)	PUNCT
ejpam-486	79	23	,	,	PUNCT
ejpam-486	79	24	v	v	X
ejpam-486	79	25	=	=	SYM
ejpam-486	79	26	kζq′	kζq′	NOUN
ejpam-486	79	27	(	(	PUNCT
ejpam-486	79	28	ζ	ζ	NOUN
ejpam-486	79	29	)	)	PUNCT
ejpam-486	79	30	+	+	NUM
ejpam-486	79	31	�	�	PROPN
ejpam-486	79	32	α+	α+	X
ejpam-486	79	33	β	β	NOUN
ejpam-486	79	34	−	−	PROPN
ejpam-486	79	35	1	1	NUM
ejpam-486	79	36	�	�	PROPN
ejpam-486	79	37	q	q	PROPN
ejpam-486	79	38	(	(	PUNCT
ejpam-486	79	39	ζ	ζ	NOUN
ejpam-486	79	40	)	)	PUNCT
ejpam-486	79	41	α+	α+	PRON
ejpam-486	79	42	β	β	NOUN
ejpam-486	80	1	+	+	CCONJ
ejpam-486	80	2	p−	p−	PROPN
ejpam-486	80	3	1	1	NUM
ejpam-486	80	4	,	,	PUNCT
ejpam-486	80	5	ℜ	ℜ	PROPN
ejpam-486	80	6	¨	¨	NOUN
ejpam-486	80	7	�	�	PROPN
ejpam-486	80	8	α+	α+	PUNCT
ejpam-486	80	9	β	β	NOUN
ejpam-486	80	10	+	+	CCONJ
ejpam-486	80	11	p−	p−	PROPN
ejpam-486	80	12	1	1	NUM
ejpam-486	80	13	�	�	PROPN
ejpam-486	80	14	�	�	PROPN
ejpam-486	80	15	α+	α+	PUNCT
ejpam-486	80	16	β	β	NOUN
ejpam-486	80	17	+	+	CCONJ
ejpam-486	80	18	p−	p−	PROPN
ejpam-486	80	19	2	2	NUM
ejpam-486	80	20	�	�	PROPN
ejpam-486	80	21	w	w	PROPN
ejpam-486	80	22	−	−	PROPN
ejpam-486	80	23	�	�	PROPN
ejpam-486	80	24	α+	α+	PUNCT
ejpam-486	80	25	β	β	NOUN
ejpam-486	80	26	−	−	PROPN
ejpam-486	80	27	1	1	NUM
ejpam-486	80	28	�	�	PROPN
ejpam-486	80	29	�	�	PROPN
ejpam-486	80	30	α+	α+	PUNCT
ejpam-486	80	31	β	β	NOUN
ejpam-486	80	32	−	−	PROPN
ejpam-486	80	33	2	2	NUM
ejpam-486	80	34	�	�	PROPN
ejpam-486	80	35	u	u	PROPN
ejpam-486	80	36	�	�	PROPN
ejpam-486	80	37	α+	α+	X
ejpam-486	80	38	β	β	NOUN
ejpam-486	81	1	+	+	CCONJ
ejpam-486	81	2	p−	p−	PROPN
ejpam-486	81	3	1	1	NUM
ejpam-486	81	4	�	�	PROPN
ejpam-486	81	5	v	v	ADP
ejpam-486	81	6	−	−	PROPN
ejpam-486	81	7	�	�	PROPN
ejpam-486	81	8	α+	α+	NOUN
ejpam-486	81	9	β	β	NOUN
ejpam-486	81	10	−	−	PROPN
ejpam-486	81	11	1	1	NUM
ejpam-486	81	12	�	�	PROPN
ejpam-486	81	13	u	u	NOUN
ejpam-486	81	14	−	−	PROPN
ejpam-486	81	15	2	2	NUM
ejpam-486	81	16	�	�	PROPN
ejpam-486	81	17	α+	α+	PUNCT
ejpam-486	81	18	β	β	X
ejpam-486	81	19	�	�	PROPN
ejpam-486	81	20	+	+	CCONJ
ejpam-486	81	21	3	3	NUM
ejpam-486	81	22	«	«	SYM
ejpam-486	81	23	≥	≥	NUM
ejpam-486	81	24	kℜ	kℜ	X
ejpam-486	81	25	(	(	PUNCT
ejpam-486	81	26	1	1	NUM
ejpam-486	81	27	+	+	NUM
ejpam-486	81	28	ζq	ζq	NOUN
ejpam-486	81	29	′′	′′	PROPN
ejpam-486	81	30	(	(	PUNCT
ejpam-486	81	31	ζ	ζ	NOUN
ejpam-486	81	32	)	)	PUNCT
ejpam-486	81	33	q′	q′	NOUN
ejpam-486	81	34	(	(	PUNCT
ejpam-486	81	35	ζ	ζ	NOUN
ejpam-486	81	36	)	)	PUNCT
ejpam-486	81	37	)	)	PUNCT
ejpam-486	81	38	,	,	PUNCT
ejpam-486	81	39	where	where	SCONJ
ejpam-486	81	40	z	z	PROPN
ejpam-486	81	41	∈	∈	PROPN
ejpam-486	81	42	u	u	NOUN
ejpam-486	81	43	,	,	PUNCT
ejpam-486	81	44	ζ	ζ	PROPN
ejpam-486	81	45	∈	∈	PROPN
ejpam-486	81	46	∂	∂	NUM
ejpam-486	81	47	u\e	u\e	PROPN
ejpam-486	81	48	�	�	PROPN
ejpam-486	81	49	q	q	PROPN
ejpam-486	81	50	�	�	PROPN
ejpam-486	81	51	,	,	PUNCT
ejpam-486	81	52	and	and	CCONJ
ejpam-486	81	53	k	k	PROPN
ejpam-486	81	54	≥	≥	PROPN
ejpam-486	81	55	p.	p.	NOUN
ejpam-486	81	56	theorem	theorem	NOUN
ejpam-486	81	57	1	1	X
ejpam-486	81	58	.	.	PUNCT
ejpam-486	82	1	let	let	VERB
ejpam-486	82	2	φ	φ	PROPN
ejpam-486	82	3	∈	∈	PROPN
ejpam-486	82	4	φq	φq	PROPN
ejpam-486	82	5	�	�	PROPN
ejpam-486	82	6	ω	ω	PROPN
ejpam-486	82	7	,	,	PUNCT
ejpam-486	82	8	q	q	PROPN
ejpam-486	82	9	�	�	PROPN
ejpam-486	82	10	.	.	PUNCT
ejpam-486	83	1	if	if	SCONJ
ejpam-486	83	2	f	f	PROPN
ejpam-486	83	3	(	(	PUNCT
ejpam-486	83	4	z	z	NOUN
ejpam-486	83	5	)	)	PUNCT
ejpam-486	83	6	∈	∈	PROPN
ejpam-486	83	7	a	a	DET
ejpam-486	83	8	�	�	PROPN
ejpam-486	83	9	p	p	NOUN
ejpam-486	83	10	�	�	PROPN
ejpam-486	83	11	satisfies	satisfy	VERB
ejpam-486	83	12	n	n	NUM
ejpam-486	83	13	φ	φ	PROPN
ejpam-486	83	14	�	�	PROPN
ejpam-486	83	15	qαβ	qαβ	PROPN
ejpam-486	83	16	,	,	PUNCT
ejpam-486	83	17	p	p	PROPN
ejpam-486	83	18	f	f	X
ejpam-486	83	19	(	(	PUNCT
ejpam-486	83	20	z),qα−1	z),qα−1	PROPN
ejpam-486	83	21	β	β	X
ejpam-486	83	22	,	,	PUNCT
ejpam-486	83	23	p	p	PROPN
ejpam-486	83	24	f	f	X
ejpam-486	83	25	(	(	PUNCT
ejpam-486	83	26	z),qα−2	z),qα−2	NOUN
ejpam-486	83	27	β	β	X
ejpam-486	83	28	,	,	PUNCT
ejpam-486	83	29	p	p	PROPN
ejpam-486	83	30	f	f	X
ejpam-486	83	31	(	(	PUNCT
ejpam-486	83	32	z	z	NOUN
ejpam-486	83	33	)	)	PUNCT
ejpam-486	83	34	;	;	PUNCT
ejpam-486	83	35	z	z	PROPN
ejpam-486	83	36	�	�	PROPN
ejpam-486	83	37	:	:	PUNCT
ejpam-486	83	38	z	z	PROPN
ejpam-486	83	39	∈	∈	PROPN
ejpam-486	84	1	u	u	X
ejpam-486	84	2	o	o	X
ejpam-486	84	3	⊂	⊂	PROPN
ejpam-486	84	4	ω	ω	PROPN
ejpam-486	84	5	�	�	PROPN
ejpam-486	84	6	α	α	PROPN
ejpam-486	84	7	>	>	X
ejpam-486	84	8	2	2	NUM
ejpam-486	84	9	;	;	PUNCT
ejpam-486	84	10	β	β	X
ejpam-486	84	11	>	>	X
ejpam-486	84	12	−1	−1	NOUN
ejpam-486	84	13	;	;	PUNCT
ejpam-486	84	14	p	p	PROPN
ejpam-486	84	15	∈	∈	PROPN
ejpam-486	84	16	n	n	PRON
ejpam-486	84	17	�	�	PROPN
ejpam-486	84	18	,	,	PUNCT
ejpam-486	84	19	(	(	PUNCT
ejpam-486	84	20	5	5	X
ejpam-486	84	21	)	)	PUNCT
ejpam-486	84	22	then	then	ADV
ejpam-486	84	23	qαβ	qαβ	INTJ
ejpam-486	84	24	,	,	PUNCT
ejpam-486	84	25	p	p	NOUN
ejpam-486	84	26	f	f	X
ejpam-486	84	27	(	(	PUNCT
ejpam-486	84	28	z	z	NOUN
ejpam-486	84	29	)	)	PUNCT
ejpam-486	84	30	≺	≺	NOUN
ejpam-486	84	31	q	q	NOUN
ejpam-486	84	32	(	(	PUNCT
ejpam-486	84	33	z	z	NOUN
ejpam-486	84	34	)	)	PUNCT
ejpam-486	84	35	(	(	PUNCT
ejpam-486	84	36	z	z	NOUN
ejpam-486	84	37	∈	∈	PROPN
ejpam-486	84	38	u	u	NOUN
ejpam-486	84	39	)	)	PUNCT
ejpam-486	84	40	.	.	PUNCT
ejpam-486	85	1	proof	proof	NOUN
ejpam-486	85	2	.	.	PUNCT
ejpam-486	86	1	define	define	VERB
ejpam-486	86	2	the	the	DET
ejpam-486	86	3	analytic	analytic	ADJ
ejpam-486	86	4	function	function	NOUN
ejpam-486	86	5	g(z	g(z	PROPN
ejpam-486	86	6	)	)	PUNCT
ejpam-486	86	7	in	in	ADP
ejpam-486	86	8	u	u	NOUN
ejpam-486	86	9	by	by	ADP
ejpam-486	86	10	g(z	g(z	PROPN
ejpam-486	86	11	)	)	PUNCT
ejpam-486	87	1	=	=	PUNCT
ejpam-486	87	2	qαβ	qαβ	INTJ
ejpam-486	87	3	,	,	PUNCT
ejpam-486	87	4	p	p	NOUN
ejpam-486	87	5	f	f	X
ejpam-486	87	6	(	(	PUNCT
ejpam-486	87	7	z	z	NOUN
ejpam-486	87	8	)	)	PUNCT
ejpam-486	87	9	�	�	PROPN
ejpam-486	87	10	α	α	PROPN
ejpam-486	87	11	>	>	X
ejpam-486	87	12	2	2	NUM
ejpam-486	87	13	;	;	PUNCT
ejpam-486	87	14	β	β	X
ejpam-486	87	15	>	>	X
ejpam-486	87	16	−1	−1	NOUN
ejpam-486	87	17	;	;	PUNCT
ejpam-486	87	18	p	p	PROPN
ejpam-486	87	19	∈	∈	PROPN
ejpam-486	87	20	n	n	CCONJ
ejpam-486	87	21	;	;	PUNCT
ejpam-486	87	22	z	z	PROPN
ejpam-486	87	23	∈	∈	PROPN
ejpam-486	87	24	u	u	PROPN
ejpam-486	87	25	�	�	PROPN
ejpam-486	87	26	.	.	PUNCT
ejpam-486	88	1	(	(	PUNCT
ejpam-486	88	2	6	6	NUM
ejpam-486	88	3	)	)	PUNCT
ejpam-486	88	4	in	in	ADP
ejpam-486	88	5	view	view	NOUN
ejpam-486	88	6	of	of	ADP
ejpam-486	88	7	the	the	DET
ejpam-486	88	8	relation	relation	NOUN
ejpam-486	88	9	(	(	PUNCT
ejpam-486	88	10	4	4	NUM
ejpam-486	88	11	)	)	PUNCT
ejpam-486	88	12	from	from	ADP
ejpam-486	88	13	(	(	PUNCT
ejpam-486	88	14	6	6	NUM
ejpam-486	88	15	)	)	PUNCT
ejpam-486	88	16	,	,	PUNCT
ejpam-486	88	17	we	we	PRON
ejpam-486	88	18	get	get	VERB
ejpam-486	88	19	qα−1	qα−1	ADJ
ejpam-486	88	20	β	β	NOUN
ejpam-486	88	21	,	,	PUNCT
ejpam-486	88	22	p	p	PROPN
ejpam-486	88	23	f	f	X
ejpam-486	88	24	(	(	PUNCT
ejpam-486	88	25	z	z	NOUN
ejpam-486	88	26	)	)	PUNCT
ejpam-486	88	27	=	=	SYM
ejpam-486	88	28	zg′	zg′	X
ejpam-486	88	29	(	(	PUNCT
ejpam-486	88	30	z	z	NOUN
ejpam-486	88	31	)	)	PUNCT
ejpam-486	89	1	+	+	CCONJ
ejpam-486	89	2	�	�	PROPN
ejpam-486	89	3	α+	α+	X
ejpam-486	89	4	β	β	NOUN
ejpam-486	89	5	−	−	PROPN
ejpam-486	89	6	1	1	NUM
ejpam-486	89	7	�	�	PROPN
ejpam-486	89	8	g	g	PROPN
ejpam-486	89	9	(	(	PUNCT
ejpam-486	89	10	z	z	PROPN
ejpam-486	89	11	)	)	PUNCT
ejpam-486	89	12	α+β	α+β	PROPN
ejpam-486	90	1	+	+	CCONJ
ejpam-486	90	2	p−	p−	NOUN
ejpam-486	90	3	1	1	NUM
ejpam-486	90	4	.	.	PUNCT
ejpam-486	91	1	(	(	PUNCT
ejpam-486	91	2	7	7	X
ejpam-486	91	3	)	)	PUNCT
ejpam-486	91	4	further	further	ADJ
ejpam-486	91	5	computations	computation	NOUN
ejpam-486	91	6	show	show	VERB
ejpam-486	91	7	that	that	SCONJ
ejpam-486	91	8	qα−2	qα−2	NOUN
ejpam-486	91	9	β	β	PROPN
ejpam-486	91	10	,	,	PUNCT
ejpam-486	91	11	p	p	PROPN
ejpam-486	91	12	f	f	X
ejpam-486	91	13	(	(	PUNCT
ejpam-486	91	14	z	z	NOUN
ejpam-486	91	15	)	)	PUNCT
ejpam-486	91	16	=	=	SYM
ejpam-486	91	17	z2	z2	PROPN
ejpam-486	91	18	g	g	PROPN
ejpam-486	91	19	′′	′′	PROPN
ejpam-486	91	20	(	(	PUNCT
ejpam-486	91	21	z	z	NOUN
ejpam-486	91	22	)	)	PUNCT
ejpam-486	91	23	+	+	CCONJ
ejpam-486	91	24	2	2	NUM
ejpam-486	91	25	�	�	NOUN
ejpam-486	91	26	α+	α+	PUNCT
ejpam-486	91	27	β	β	NOUN
ejpam-486	91	28	−	−	PROPN
ejpam-486	91	29	1	1	NUM
ejpam-486	91	30	�	�	PROPN
ejpam-486	91	31	zg′	zg′	PROPN
ejpam-486	91	32	(	(	PUNCT
ejpam-486	91	33	z	z	NOUN
ejpam-486	91	34	)	)	PUNCT
ejpam-486	91	35	+	+	CCONJ
ejpam-486	91	36	�	�	PROPN
ejpam-486	91	37	α+	α+	X
ejpam-486	91	38	β	β	NOUN
ejpam-486	91	39	−	−	PROPN
ejpam-486	91	40	1	1	NUM
ejpam-486	91	41	�	�	PROPN
ejpam-486	91	42	�	�	PROPN
ejpam-486	91	43	α+	α+	PUNCT
ejpam-486	91	44	β	β	NOUN
ejpam-486	91	45	−	−	PROPN
ejpam-486	91	46	2	2	NUM
ejpam-486	91	47	�	�	PROPN
ejpam-486	91	48	g	g	PROPN
ejpam-486	91	49	(	(	PUNCT
ejpam-486	91	50	z	z	PROPN
ejpam-486	91	51	)	)	PUNCT
ejpam-486	91	52	�	�	PROPN
ejpam-486	91	53	α+	α+	PUNCT
ejpam-486	91	54	β	β	NOUN
ejpam-486	92	1	+	+	CCONJ
ejpam-486	92	2	p−	p−	PROPN
ejpam-486	92	3	1	1	NUM
ejpam-486	92	4	�	�	PROPN
ejpam-486	92	5	�	�	PROPN
ejpam-486	92	6	α+	α+	PUNCT
ejpam-486	92	7	β	β	NOUN
ejpam-486	92	8	+	+	CCONJ
ejpam-486	92	9	p−	p−	PROPN
ejpam-486	92	10	2	2	NUM
ejpam-486	92	11	�	�	NOUN
ejpam-486	92	12	.	.	PUNCT
ejpam-486	93	1	(	(	PUNCT
ejpam-486	93	2	8)	8)	NUM
ejpam-486	93	3	define	define	VERB
ejpam-486	93	4	the	the	DET
ejpam-486	93	5	transformations	transformation	NOUN
ejpam-486	93	6	from	from	ADP
ejpam-486	93	7	c3	c3	PROPN
ejpam-486	93	8	to	to	ADP
ejpam-486	93	9	c	c	NOUN
ejpam-486	93	10	by	by	ADP
ejpam-486	93	11	u	u	NOUN
ejpam-486	93	12	=	=	SYM
ejpam-486	93	13	r	r	PROPN
ejpam-486	93	14	,	,	PUNCT
ejpam-486	93	15	v	v	NOUN
ejpam-486	93	16	=	=	PUNCT
ejpam-486	93	17	s+	s+	NUM
ejpam-486	93	18	�	�	PROPN
ejpam-486	93	19	α+	α+	PUNCT
ejpam-486	93	20	β	β	NOUN
ejpam-486	93	21	−	−	PROPN
ejpam-486	93	22	1	1	NUM
ejpam-486	93	23	�	�	PROPN
ejpam-486	93	24	r	r	NOUN
ejpam-486	93	25	α+	α+	NOUN
ejpam-486	93	26	β	β	NOUN
ejpam-486	93	27	+	+	CCONJ
ejpam-486	93	28	p−	p−	NOUN
ejpam-486	93	29	1	1	NUM
ejpam-486	93	30	,	,	PUNCT
ejpam-486	93	31	w	w	PROPN
ejpam-486	93	32	=	=	SYM
ejpam-486	93	33	t	t	PROPN
ejpam-486	93	34	+	+	CCONJ
ejpam-486	93	35	2	2	NUM
ejpam-486	93	36	�	�	NOUN
ejpam-486	93	37	α+	α+	PUNCT
ejpam-486	93	38	β	β	NOUN
ejpam-486	93	39	−	−	PROPN
ejpam-486	93	40	1	1	NUM
ejpam-486	93	41	�	�	PROPN
ejpam-486	93	42	s+	s+	PUNCT
ejpam-486	93	43	�	�	PROPN
ejpam-486	93	44	α+	α+	PUNCT
ejpam-486	93	45	β	β	NOUN
ejpam-486	93	46	−	−	PROPN
ejpam-486	93	47	1	1	NUM
ejpam-486	93	48	�	�	PROPN
ejpam-486	93	49	�	�	PROPN
ejpam-486	93	50	α+	α+	PUNCT
ejpam-486	93	51	β	β	NOUN
ejpam-486	93	52	−	−	PROPN
ejpam-486	93	53	2	2	NUM
ejpam-486	93	54	�	�	PROPN
ejpam-486	93	55	r	r	NOUN
ejpam-486	93	56	�	�	PROPN
ejpam-486	93	57	α+	α+	X
ejpam-486	93	58	β	β	NOUN
ejpam-486	93	59	+	+	CCONJ
ejpam-486	93	60	p−	p−	PROPN
ejpam-486	93	61	1	1	NUM
ejpam-486	93	62	�	�	PROPN
ejpam-486	93	63	�	�	PROPN
ejpam-486	93	64	α+	α+	PUNCT
ejpam-486	93	65	β	β	NOUN
ejpam-486	93	66	+	+	CCONJ
ejpam-486	93	67	p−	p−	PROPN
ejpam-486	93	68	2	2	NUM
ejpam-486	93	69	�	�	NOUN
ejpam-486	93	70	.	.	PUNCT
ejpam-486	94	1	(	(	PUNCT
ejpam-486	94	2	9	9	X
ejpam-486	94	3	)	)	PUNCT
ejpam-486	94	4	let	let	VERB
ejpam-486	94	5	ψ(r	ψ(r	NOUN
ejpam-486	94	6	,	,	PUNCT
ejpam-486	94	7	s	s	X
ejpam-486	94	8	,	,	PUNCT
ejpam-486	94	9	t	t	PROPN
ejpam-486	94	10	;	;	PUNCT
ejpam-486	94	11	z	z	X
ejpam-486	94	12	)	)	PUNCT
ejpam-486	95	1	=	=	SYM
ejpam-486	95	2	φ	φ	PROPN
ejpam-486	95	3	(	(	PUNCT
ejpam-486	95	4	u	u	NOUN
ejpam-486	95	5	,	,	PUNCT
ejpam-486	95	6	v	v	NOUN
ejpam-486	95	7	,	,	PUNCT
ejpam-486	95	8	w	w	NOUN
ejpam-486	95	9	;	;	PUNCT
ejpam-486	95	10	z	z	X
ejpam-486	95	11	)	)	PUNCT
ejpam-486	95	12	=	=	PUNCT
ejpam-486	95	13	φ	φ	PROPN
ejpam-486	95	14	�	�	PROPN
ejpam-486	95	15	r	r	PROPN
ejpam-486	95	16	,	,	PUNCT
ejpam-486	95	17	s+	s+	PUNCT
ejpam-486	95	18	�	�	PROPN
ejpam-486	95	19	α+	α+	PUNCT
ejpam-486	95	20	β	β	NOUN
ejpam-486	95	21	−	−	PROPN
ejpam-486	95	22	1	1	NUM
ejpam-486	95	23	�	�	PROPN
ejpam-486	95	24	r	r	NOUN
ejpam-486	95	25	α+	α+	NOUN
ejpam-486	95	26	β	β	NOUN
ejpam-486	95	27	+	+	CCONJ
ejpam-486	95	28	p−	p−	PROPN
ejpam-486	95	29	1	1	NUM
ejpam-486	95	30	,	,	PUNCT
ejpam-486	95	31	t	t	PROPN
ejpam-486	95	32	+	+	CCONJ
ejpam-486	95	33	2	2	NUM
ejpam-486	95	34	�	�	NOUN
ejpam-486	95	35	α+	α+	PUNCT
ejpam-486	95	36	β	β	NOUN
ejpam-486	95	37	−	−	PROPN
ejpam-486	95	38	1	1	NUM
ejpam-486	95	39	�	�	PROPN
ejpam-486	95	40	s+	s+	PUNCT
ejpam-486	95	41	�	�	PROPN
ejpam-486	95	42	α+	α+	PUNCT
ejpam-486	95	43	β	β	NOUN
ejpam-486	95	44	−	−	PROPN
ejpam-486	95	45	1	1	NUM
ejpam-486	95	46	�	�	PROPN
ejpam-486	95	47	�	�	PROPN
ejpam-486	95	48	α+	α+	PUNCT
ejpam-486	95	49	β	β	NOUN
ejpam-486	95	50	−	−	PROPN
ejpam-486	95	51	2	2	NUM
ejpam-486	95	52	�	�	PROPN
ejpam-486	95	53	r	r	NOUN
ejpam-486	95	54	�	�	PROPN
ejpam-486	95	55	α+	α+	X
ejpam-486	95	56	β	β	NOUN
ejpam-486	95	57	+	+	CCONJ
ejpam-486	95	58	p−	p−	PROPN
ejpam-486	95	59	1	1	NUM
ejpam-486	95	60	�	�	PROPN
ejpam-486	95	61	�	�	PROPN
ejpam-486	95	62	α+	α+	PUNCT
ejpam-486	95	63	β	β	NOUN
ejpam-486	95	64	+	+	CCONJ
ejpam-486	95	65	p−	p−	PROPN
ejpam-486	95	66	2	2	NUM
ejpam-486	95	67	�	�	NOUN
ejpam-486	95	68	;	;	PUNCT
ejpam-486	95	69	z	z	PROPN
ejpam-486	95	70	�	�	PROPN
ejpam-486	95	71	.	.	PUNCT
ejpam-486	96	1	(	(	PUNCT
ejpam-486	96	2	10	10	NUM
ejpam-486	96	3	)	)	PUNCT
ejpam-486	96	4	m.	m.	NOUN
ejpam-486	96	5	aouf	aouf	PROPN
ejpam-486	96	6	,	,	PUNCT
ejpam-486	96	7	t.	t.	PROPN
ejpam-486	96	8	seoudy	seoudy	PROPN
ejpam-486	96	9	/	/	SYM
ejpam-486	96	10	eur	eur	PROPN
ejpam-486	96	11	.	.	PUNCT
ejpam-486	97	1	j.	j.	PROPN
ejpam-486	97	2	pure	pure	PROPN
ejpam-486	97	3	appl	appl	PROPN
ejpam-486	97	4	.	.	PROPN
ejpam-486	97	5	math	math	PROPN
ejpam-486	97	6	,	,	PUNCT
ejpam-486	97	7	3	3	NUM
ejpam-486	97	8	(	(	PUNCT
ejpam-486	97	9	2010	2010	NUM
ejpam-486	97	10	)	)	PUNCT
ejpam-486	97	11	,	,	PUNCT
ejpam-486	97	12	26	26	NUM
ejpam-486	97	13	-	-	SYM
ejpam-486	97	14	44	44	NUM
ejpam-486	97	15	30	30	NUM
ejpam-486	97	16	the	the	DET
ejpam-486	97	17	proof	proof	NOUN
ejpam-486	97	18	shall	shall	AUX
ejpam-486	97	19	make	make	VERB
ejpam-486	97	20	use	use	NOUN
ejpam-486	97	21	of	of	ADP
ejpam-486	97	22	lemma	lemma	PROPN
ejpam-486	97	23	1	1	NUM
ejpam-486	97	24	.	.	PUNCT
ejpam-486	97	25	using	use	VERB
ejpam-486	97	26	equations	equation	NOUN
ejpam-486	97	27	(	(	PUNCT
ejpam-486	97	28	6	6	NUM
ejpam-486	97	29	)	)	PUNCT
ejpam-486	97	30	,	,	PUNCT
ejpam-486	97	31	(	(	PUNCT
ejpam-486	97	32	7	7	X
ejpam-486	97	33	)	)	PUNCT
ejpam-486	97	34	and	and	CCONJ
ejpam-486	97	35	(	(	PUNCT
ejpam-486	97	36	8)	8)	NUM
ejpam-486	97	37	,	,	PUNCT
ejpam-486	97	38	from	from	ADP
ejpam-486	97	39	(	(	PUNCT
ejpam-486	97	40	10	10	NUM
ejpam-486	97	41	)	)	PUNCT
ejpam-486	97	42	,	,	PUNCT
ejpam-486	97	43	we	we	PRON
ejpam-486	97	44	obtain	obtain	VERB
ejpam-486	97	45	ψ(p(z	ψ(p(z	NOUN
ejpam-486	97	46	)	)	PUNCT
ejpam-486	97	47	,	,	PUNCT
ejpam-486	97	48	zp′(z	zp′(z	PROPN
ejpam-486	97	49	)	)	PUNCT
ejpam-486	97	50	,	,	PUNCT
ejpam-486	98	1	z2p	z2p	PROPN
ejpam-486	98	2	′′	′′	PROPN
ejpam-486	98	3	(	(	PUNCT
ejpam-486	98	4	z	z	PROPN
ejpam-486	98	5	)	)	PUNCT
ejpam-486	98	6	;	;	PUNCT
ejpam-486	98	7	z	z	X
ejpam-486	98	8	)	)	PUNCT
ejpam-486	98	9	=	=	PUNCT
ejpam-486	98	10	φ	φ	PROPN
ejpam-486	98	11	�	�	PROPN
ejpam-486	98	12	qαβ	qαβ	PROPN
ejpam-486	98	13	,	,	PUNCT
ejpam-486	98	14	p	p	PROPN
ejpam-486	98	15	f	f	X
ejpam-486	98	16	(	(	PUNCT
ejpam-486	98	17	z),qα−1	z),qα−1	PROPN
ejpam-486	98	18	β	β	X
ejpam-486	98	19	,	,	PUNCT
ejpam-486	98	20	p	p	PROPN
ejpam-486	98	21	f	f	X
ejpam-486	98	22	(	(	PUNCT
ejpam-486	98	23	z),qα−2	z),qα−2	NOUN
ejpam-486	98	24	β	β	X
ejpam-486	98	25	,	,	PUNCT
ejpam-486	98	26	p	p	PROPN
ejpam-486	98	27	f	f	X
ejpam-486	98	28	(	(	PUNCT
ejpam-486	98	29	z	z	NOUN
ejpam-486	98	30	)	)	PUNCT
ejpam-486	98	31	;	;	PUNCT
ejpam-486	98	32	z	z	PROPN
ejpam-486	98	33	�	�	PROPN
ejpam-486	98	34	(	(	PUNCT
ejpam-486	98	35	11	11	NUM
ejpam-486	98	36	)	)	PUNCT
ejpam-486	98	37	�	�	PROPN
ejpam-486	98	38	α	α	PROPN
ejpam-486	98	39	>	>	X
ejpam-486	98	40	2	2	NUM
ejpam-486	98	41	;	;	PUNCT
ejpam-486	98	42	β	β	X
ejpam-486	98	43	>	>	X
ejpam-486	98	44	−1	−1	NOUN
ejpam-486	98	45	;	;	PUNCT
ejpam-486	98	46	p	p	PROPN
ejpam-486	98	47	∈	∈	PROPN
ejpam-486	98	48	n	n	CCONJ
ejpam-486	98	49	;	;	PUNCT
ejpam-486	98	50	z	z	PROPN
ejpam-486	98	51	∈	∈	PROPN
ejpam-486	98	52	u	u	PROPN
ejpam-486	98	53	�	�	PROPN
ejpam-486	98	54	.	.	PUNCT
ejpam-486	99	1	hence	hence	ADV
ejpam-486	99	2	(	(	PUNCT
ejpam-486	99	3	5	5	X
ejpam-486	99	4	)	)	PUNCT
ejpam-486	99	5	becomes	become	VERB
ejpam-486	99	6	ψ(p(z	ψ(p(z	ADJ
ejpam-486	99	7	)	)	PUNCT
ejpam-486	99	8	,	,	PUNCT
ejpam-486	99	9	zp′(z	zp′(z	PROPN
ejpam-486	99	10	)	)	PUNCT
ejpam-486	99	11	,	,	PUNCT
ejpam-486	99	12	z2p	z2p	PROPN
ejpam-486	99	13	′′	′′	PROPN
ejpam-486	99	14	(	(	PUNCT
ejpam-486	99	15	z	z	PROPN
ejpam-486	99	16	)	)	PUNCT
ejpam-486	99	17	;	;	PUNCT
ejpam-486	99	18	z	z	X
ejpam-486	99	19	)	)	PUNCT
ejpam-486	99	20	∈	∈	PROPN
ejpam-486	99	21	ω	ω	PROPN
ejpam-486	99	22	.	.	PUNCT
ejpam-486	100	1	the	the	DET
ejpam-486	100	2	proof	proof	NOUN
ejpam-486	100	3	is	be	AUX
ejpam-486	100	4	completed	complete	VERB
ejpam-486	100	5	if	if	SCONJ
ejpam-486	100	6	it	it	PRON
ejpam-486	100	7	can	can	AUX
ejpam-486	100	8	be	be	AUX
ejpam-486	100	9	shown	show	VERB
ejpam-486	100	10	that	that	SCONJ
ejpam-486	100	11	the	the	DET
ejpam-486	100	12	admissibility	admissibility	NOUN
ejpam-486	100	13	condition	condition	NOUN
ejpam-486	100	14	for	for	ADP
ejpam-486	100	15	φ	φ	PROPN
ejpam-486	100	16	∈	∈	PROPN
ejpam-486	100	17	φq	φq	PROPN
ejpam-486	100	18	�	�	PROPN
ejpam-486	100	19	ω	ω	PROPN
ejpam-486	100	20	,	,	PUNCT
ejpam-486	100	21	q	q	PROPN
ejpam-486	100	22	�	�	PROPN
ejpam-486	100	23	is	be	AUX
ejpam-486	100	24	equivalent	equivalent	ADJ
ejpam-486	100	25	to	to	ADP
ejpam-486	100	26	the	the	DET
ejpam-486	100	27	admissibility	admissibility	NOUN
ejpam-486	100	28	condition	condition	NOUN
ejpam-486	100	29	for	for	ADP
ejpam-486	100	30	ψ	ψ	PRON
ejpam-486	100	31	as	as	SCONJ
ejpam-486	100	32	given	give	VERB
ejpam-486	100	33	in	in	ADP
ejpam-486	100	34	definition	definition	NOUN
ejpam-486	100	35	1	1	NUM
ejpam-486	100	36	.	.	PUNCT
ejpam-486	101	1	note	note	VERB
ejpam-486	101	2	that	that	SCONJ
ejpam-486	101	3	t	t	PROPN
ejpam-486	101	4	s	s	PART
ejpam-486	101	5	+	+	NUM
ejpam-486	101	6	1=	1=	X
ejpam-486	101	7	�	�	X
ejpam-486	101	8	α+	α+	PUNCT
ejpam-486	101	9	β	β	NOUN
ejpam-486	101	10	+	+	CCONJ
ejpam-486	101	11	p−	p−	PROPN
ejpam-486	101	12	1	1	NUM
ejpam-486	101	13	�	�	PROPN
ejpam-486	101	14	�	�	PROPN
ejpam-486	101	15	α+	α+	PUNCT
ejpam-486	101	16	β	β	NOUN
ejpam-486	101	17	+	+	CCONJ
ejpam-486	101	18	p−	p−	PROPN
ejpam-486	101	19	2	2	NUM
ejpam-486	101	20	�	�	PROPN
ejpam-486	101	21	w	w	PROPN
ejpam-486	101	22	−	−	PROPN
ejpam-486	101	23	�	�	PROPN
ejpam-486	101	24	α+	α+	PUNCT
ejpam-486	101	25	β	β	NOUN
ejpam-486	101	26	−	−	PROPN
ejpam-486	101	27	1	1	NUM
ejpam-486	101	28	�	�	PROPN
ejpam-486	101	29	�	�	PROPN
ejpam-486	101	30	α+	α+	PUNCT
ejpam-486	101	31	β	β	NOUN
ejpam-486	101	32	−	−	PROPN
ejpam-486	101	33	2	2	NUM
ejpam-486	101	34	�	�	PROPN
ejpam-486	101	35	u	u	PROPN
ejpam-486	101	36	�	�	PROPN
ejpam-486	101	37	α+	α+	X
ejpam-486	101	38	β	β	NOUN
ejpam-486	102	1	+	+	CCONJ
ejpam-486	102	2	p−	p−	PROPN
ejpam-486	102	3	1	1	NUM
ejpam-486	102	4	�	�	PROPN
ejpam-486	102	5	v	v	ADP
ejpam-486	102	6	−	−	PROPN
ejpam-486	102	7	�	�	PROPN
ejpam-486	102	8	α+	α+	NOUN
ejpam-486	102	9	β	β	NOUN
ejpam-486	102	10	−	−	PROPN
ejpam-486	102	11	1	1	NUM
ejpam-486	102	12	�	�	PROPN
ejpam-486	102	13	u	u	NOUN
ejpam-486	102	14	−	−	PROPN
ejpam-486	102	15	2	2	NUM
ejpam-486	102	16	�	�	PROPN
ejpam-486	102	17	α+	α+	PUNCT
ejpam-486	102	18	β	β	X
ejpam-486	102	19	�	�	PROPN
ejpam-486	102	20	+	+	CCONJ
ejpam-486	102	21	3	3	NUM
ejpam-486	102	22	,	,	PUNCT
ejpam-486	102	23	and	and	CCONJ
ejpam-486	102	24	hence	hence	ADV
ejpam-486	102	25	ψ	ψ	ADP
ejpam-486	102	26	∈ψp	∈ψp	PROPN
ejpam-486	102	27	�	�	PROPN
ejpam-486	102	28	ω	ω	PROPN
ejpam-486	102	29	,	,	PUNCT
ejpam-486	102	30	q	q	PROPN
ejpam-486	102	31	�	�	PROPN
ejpam-486	102	32	.	.	PUNCT
ejpam-486	103	1	by	by	ADP
ejpam-486	103	2	lemma	lemma	PROPN
ejpam-486	103	3	1	1	NUM
ejpam-486	103	4	,	,	PUNCT
ejpam-486	103	5	g(z)≺	g(z)≺	PROPN
ejpam-486	103	6	q(z	q(z	PROPN
ejpam-486	103	7	)	)	PUNCT
ejpam-486	103	8	or	or	CCONJ
ejpam-486	103	9	qαβ	qαβ	INTJ
ejpam-486	103	10	,	,	PUNCT
ejpam-486	103	11	p	p	NOUN
ejpam-486	103	12	f	f	X
ejpam-486	103	13	(	(	PUNCT
ejpam-486	103	14	z)≺	z)≺	PROPN
ejpam-486	103	15	q	q	PROPN
ejpam-486	103	16	(	(	PUNCT
ejpam-486	103	17	z	z	NOUN
ejpam-486	103	18	)	)	PUNCT
ejpam-486	103	19	(	(	PUNCT
ejpam-486	103	20	z	z	NOUN
ejpam-486	103	21	∈	∈	PROPN
ejpam-486	103	22	u	u	NOUN
ejpam-486	103	23	)	)	PUNCT
ejpam-486	103	24	.	.	PUNCT
ejpam-486	104	1	if	if	SCONJ
ejpam-486	104	2	ω	ω	PROPN
ejpam-486	104	3	6=	6=	PROPN
ejpam-486	104	4	c	c	PROPN
ejpam-486	104	5	is	be	AUX
ejpam-486	104	6	a	a	DET
ejpam-486	104	7	simply	simply	ADV
ejpam-486	104	8	connected	connected	ADJ
ejpam-486	104	9	domain	domain	NOUN
ejpam-486	104	10	,	,	PUNCT
ejpam-486	104	11	then	then	ADV
ejpam-486	104	12	ω	ω	PROPN
ejpam-486	104	13	=	=	SYM
ejpam-486	104	14	h(u	h(u	PROPN
ejpam-486	104	15	)	)	PUNCT
ejpam-486	104	16	for	for	ADP
ejpam-486	104	17	some	some	DET
ejpam-486	104	18	conformal	conformal	ADJ
ejpam-486	104	19	mapping	map	VERB
ejpam-486	104	20	h(z	h(z	NOUN
ejpam-486	104	21	)	)	PUNCT
ejpam-486	104	22	of	of	ADP
ejpam-486	104	23	u	u	PRON
ejpam-486	104	24	onto	onto	ADP
ejpam-486	104	25	ω	ω	NUM
ejpam-486	104	26	.	.	PUNCT
ejpam-486	105	1	in	in	ADP
ejpam-486	105	2	this	this	DET
ejpam-486	105	3	case	case	NOUN
ejpam-486	105	4	the	the	DET
ejpam-486	105	5	class	class	NOUN
ejpam-486	105	6	φq[h(u),q	φq[h(u),q	PROPN
ejpam-486	105	7	]	]	PUNCT
ejpam-486	105	8	is	be	AUX
ejpam-486	105	9	written	write	VERB
ejpam-486	105	10	as	as	ADP
ejpam-486	105	11	φq[h	φq[h	PROPN
ejpam-486	105	12	,	,	PUNCT
ejpam-486	105	13	q	q	X
ejpam-486	105	14	]	]	X
ejpam-486	105	15	.	.	PUNCT
ejpam-486	106	1	the	the	DET
ejpam-486	106	2	following	following	ADJ
ejpam-486	106	3	result	result	NOUN
ejpam-486	106	4	is	be	AUX
ejpam-486	106	5	an	an	DET
ejpam-486	106	6	immediate	immediate	ADJ
ejpam-486	106	7	consequence	consequence	NOUN
ejpam-486	106	8	of	of	ADP
ejpam-486	106	9	theorem	theorem	NOUN
ejpam-486	106	10	1	1	NUM
ejpam-486	106	11	.	.	PUNCT
ejpam-486	106	12	theorem	theorem	NOUN
ejpam-486	106	13	2	2	NUM
ejpam-486	106	14	.	.	PUNCT
ejpam-486	107	1	let	let	VERB
ejpam-486	107	2	φ	φ	PROPN
ejpam-486	107	3	∈	∈	PROPN
ejpam-486	107	4	φq[h	φq[h	PROPN
ejpam-486	107	5	,	,	PUNCT
ejpam-486	107	6	q	q	X
ejpam-486	107	7	]	]	X
ejpam-486	107	8	.	.	PUNCT
ejpam-486	108	1	if	if	SCONJ
ejpam-486	108	2	f	f	PROPN
ejpam-486	108	3	(	(	PUNCT
ejpam-486	108	4	z	z	NOUN
ejpam-486	108	5	)	)	PUNCT
ejpam-486	108	6	∈	∈	PROPN
ejpam-486	108	7	a	a	DET
ejpam-486	108	8	�	�	PROPN
ejpam-486	108	9	p	p	PROPN
ejpam-486	108	10	�	�	PROPN
ejpam-486	108	11	satisfies	satisfy	VERB
ejpam-486	108	12	φ	φ	PROPN
ejpam-486	108	13	�	�	PROPN
ejpam-486	108	14	qαβ	qαβ	PROPN
ejpam-486	108	15	,	,	PUNCT
ejpam-486	108	16	p	p	PROPN
ejpam-486	108	17	f	f	X
ejpam-486	108	18	(	(	PUNCT
ejpam-486	108	19	z),qα−1	z),qα−1	PROPN
ejpam-486	108	20	β	β	X
ejpam-486	108	21	,	,	PUNCT
ejpam-486	109	1	p	p	PROPN
ejpam-486	109	2	f	f	X
ejpam-486	109	3	(	(	PUNCT
ejpam-486	109	4	z),qα−2	z),qα−2	NOUN
ejpam-486	109	5	β	β	X
ejpam-486	109	6	,	,	PUNCT
ejpam-486	109	7	p	p	PROPN
ejpam-486	109	8	f	f	X
ejpam-486	109	9	(	(	PUNCT
ejpam-486	109	10	z	z	NOUN
ejpam-486	109	11	)	)	PUNCT
ejpam-486	109	12	;	;	PUNCT
ejpam-486	109	13	z	z	PROPN
ejpam-486	109	14	�	�	PROPN
ejpam-486	109	15	≺	≺	VERB
ejpam-486	109	16	h(z	h(z	NOUN
ejpam-486	109	17	)	)	PUNCT
ejpam-486	109	18	�	�	PROPN
ejpam-486	109	19	α	α	X
ejpam-486	109	20	>	>	X
ejpam-486	109	21	2;β	2;β	NUM
ejpam-486	109	22	>	>	SYM
ejpam-486	109	23	−1	−1	NOUN
ejpam-486	109	24	;	;	PUNCT
ejpam-486	109	25	p	p	PROPN
ejpam-486	109	26	∈	∈	PROPN
ejpam-486	109	27	n	n	CCONJ
ejpam-486	109	28	;	;	PUNCT
ejpam-486	109	29	z	z	PROPN
ejpam-486	109	30	∈	∈	PROPN
ejpam-486	109	31	u	u	PROPN
ejpam-486	109	32	�	�	PROPN
ejpam-486	109	33	,	,	PUNCT
ejpam-486	109	34	(	(	PUNCT
ejpam-486	109	35	12	12	NUM
ejpam-486	109	36	)	)	PUNCT
ejpam-486	109	37	then	then	ADV
ejpam-486	109	38	qαβ	qαβ	INTJ
ejpam-486	109	39	,	,	PUNCT
ejpam-486	109	40	p	p	NOUN
ejpam-486	109	41	f	f	X
ejpam-486	109	42	(	(	PUNCT
ejpam-486	109	43	z	z	NOUN
ejpam-486	109	44	)	)	PUNCT
ejpam-486	109	45	≺	≺	NOUN
ejpam-486	109	46	q	q	NOUN
ejpam-486	109	47	(	(	PUNCT
ejpam-486	109	48	z	z	NOUN
ejpam-486	109	49	)	)	PUNCT
ejpam-486	109	50	(	(	PUNCT
ejpam-486	109	51	z	z	NOUN
ejpam-486	109	52	∈	∈	PROPN
ejpam-486	109	53	u	u	NOUN
ejpam-486	109	54	)	)	PUNCT
ejpam-486	109	55	.	.	PUNCT
ejpam-486	110	1	our	our	PRON
ejpam-486	110	2	next	next	ADJ
ejpam-486	110	3	result	result	NOUN
ejpam-486	110	4	is	be	AUX
ejpam-486	110	5	an	an	DET
ejpam-486	110	6	extension	extension	NOUN
ejpam-486	110	7	of	of	ADP
ejpam-486	110	8	theorem	theorem	NOUN
ejpam-486	110	9	1	1	NUM
ejpam-486	110	10	to	to	ADP
ejpam-486	110	11	the	the	DET
ejpam-486	110	12	case	case	NOUN
ejpam-486	110	13	where	where	SCONJ
ejpam-486	110	14	the	the	DET
ejpam-486	110	15	behavior	behavior	NOUN
ejpam-486	110	16	of	of	ADP
ejpam-486	110	17	q(z	q(z	PROPN
ejpam-486	110	18	)	)	PUNCT
ejpam-486	110	19	on	on	ADP
ejpam-486	110	20	∂	∂	NUM
ejpam-486	110	21	u	u	NOUN
ejpam-486	110	22	is	be	AUX
ejpam-486	110	23	not	not	PART
ejpam-486	110	24	known	know	VERB
ejpam-486	110	25	.	.	PUNCT
ejpam-486	111	1	corollary	corollary	ADJ
ejpam-486	111	2	1	1	NUM
ejpam-486	111	3	.	.	PUNCT
ejpam-486	112	1	let	let	VERB
ejpam-486	112	2	ω	ω	PROPN
ejpam-486	112	3	⊂	⊂	PROPN
ejpam-486	112	4	c	c	PROPN
ejpam-486	112	5	and	and	CCONJ
ejpam-486	112	6	let	let	VERB
ejpam-486	112	7	q(z	q(z	PROPN
ejpam-486	112	8	)	)	PUNCT
ejpam-486	112	9	be	be	AUX
ejpam-486	112	10	univalent	univalent	ADJ
ejpam-486	112	11	in	in	ADP
ejpam-486	112	12	u	u	PROPN
ejpam-486	112	13	,	,	PUNCT
ejpam-486	112	14	q(0	q(0	PROPN
ejpam-486	112	15	)	)	PUNCT
ejpam-486	112	16	=	=	NOUN
ejpam-486	113	1	0	0	X
ejpam-486	113	2	.	.	PUNCT
ejpam-486	114	1	let	let	VERB
ejpam-486	114	2	φ	φ	PROPN
ejpam-486	114	3	∈	∈	PROPN
ejpam-486	114	4	φq[ω	φq[ω	PROPN
ejpam-486	114	5	,	,	PUNCT
ejpam-486	114	6	qρ	qρ	X
ejpam-486	114	7	]	]	PUNCT
ejpam-486	114	8	for	for	ADP
ejpam-486	114	9	some	some	DET
ejpam-486	114	10	ρ	ρ	NUM
ejpam-486	114	11	∈	∈	PROPN
ejpam-486	114	12	(	(	PUNCT
ejpam-486	114	13	0,1	0,1	NOUN
ejpam-486	114	14	)	)	PUNCT
ejpam-486	114	15	where	where	SCONJ
ejpam-486	114	16	qρ(z	qρ(z	NOUN
ejpam-486	114	17	)	)	PUNCT
ejpam-486	114	18	=	=	SYM
ejpam-486	114	19	q(ρz	q(ρz	PROPN
ejpam-486	114	20	)	)	PUNCT
ejpam-486	114	21	.	.	PUNCT
ejpam-486	115	1	if	if	SCONJ
ejpam-486	115	2	f	f	PROPN
ejpam-486	115	3	(	(	PUNCT
ejpam-486	115	4	z	z	NOUN
ejpam-486	115	5	)	)	PUNCT
ejpam-486	115	6	∈	∈	PROPN
ejpam-486	115	7	a	a	DET
ejpam-486	115	8	�	�	PROPN
ejpam-486	115	9	p	p	PROPN
ejpam-486	115	10	�	�	PROPN
ejpam-486	115	11	and	and	CCONJ
ejpam-486	115	12	φ	φ	PROPN
ejpam-486	115	13	�	�	PROPN
ejpam-486	115	14	qαβ	qαβ	PROPN
ejpam-486	115	15	,	,	PUNCT
ejpam-486	115	16	p	p	PROPN
ejpam-486	115	17	f	f	X
ejpam-486	115	18	(	(	PUNCT
ejpam-486	115	19	z),qα−1	z),qα−1	PROPN
ejpam-486	115	20	β	β	X
ejpam-486	115	21	,	,	PUNCT
ejpam-486	115	22	p	p	PROPN
ejpam-486	115	23	f	f	X
ejpam-486	115	24	(	(	PUNCT
ejpam-486	115	25	z),qα−2	z),qα−2	NOUN
ejpam-486	115	26	β	β	X
ejpam-486	115	27	,	,	PUNCT
ejpam-486	115	28	p	p	PROPN
ejpam-486	115	29	f	f	X
ejpam-486	115	30	(	(	PUNCT
ejpam-486	115	31	z	z	NOUN
ejpam-486	115	32	)	)	PUNCT
ejpam-486	115	33	;	;	PUNCT
ejpam-486	115	34	z	z	NOUN
ejpam-486	115	35	�	�	PROPN
ejpam-486	115	36	∈	∈	PROPN
ejpam-486	115	37	ω	ω	PROPN
ejpam-486	115	38	�	�	PROPN
ejpam-486	115	39	α	α	PROPN
ejpam-486	115	40	>	>	X
ejpam-486	115	41	2	2	NUM
ejpam-486	115	42	;	;	PUNCT
ejpam-486	115	43	β	β	X
ejpam-486	115	44	>	>	X
ejpam-486	115	45	−1	−1	NOUN
ejpam-486	115	46	;	;	PUNCT
ejpam-486	115	47	p	p	PROPN
ejpam-486	115	48	∈	∈	PROPN
ejpam-486	115	49	n	n	CCONJ
ejpam-486	115	50	;	;	PUNCT
ejpam-486	115	51	z	z	PROPN
ejpam-486	115	52	∈	∈	PROPN
ejpam-486	115	53	u	u	PROPN
ejpam-486	115	54	�	�	PROPN
ejpam-486	115	55	,	,	PUNCT
ejpam-486	115	56	then	then	ADV
ejpam-486	115	57	qαβ	qαβ	INTJ
ejpam-486	115	58	,	,	PUNCT
ejpam-486	115	59	p	p	NOUN
ejpam-486	115	60	f	f	X
ejpam-486	115	61	(	(	PUNCT
ejpam-486	115	62	z	z	NOUN
ejpam-486	115	63	)	)	PUNCT
ejpam-486	115	64	≺	≺	NOUN
ejpam-486	115	65	q	q	NOUN
ejpam-486	116	1	(	(	PUNCT
ejpam-486	116	2	z	z	NOUN
ejpam-486	116	3	)	)	PUNCT
ejpam-486	116	4	(	(	PUNCT
ejpam-486	116	5	z	z	NOUN
ejpam-486	116	6	∈	∈	PROPN
ejpam-486	116	7	u	u	NOUN
ejpam-486	116	8	)	)	PUNCT
ejpam-486	116	9	.	.	PUNCT
ejpam-486	117	1	proof	proof	NOUN
ejpam-486	117	2	.	.	PUNCT
ejpam-486	118	1	theorem	theorem	VERB
ejpam-486	118	2	1	1	NUM
ejpam-486	118	3	yields	yield	NOUN
ejpam-486	118	4	qα	qα	PROPN
ejpam-486	118	5	β	β	PROPN
ejpam-486	118	6	,	,	PUNCT
ejpam-486	118	7	p	p	PROPN
ejpam-486	118	8	f	f	X
ejpam-486	118	9	(	(	PUNCT
ejpam-486	118	10	z	z	NOUN
ejpam-486	118	11	)	)	PUNCT
ejpam-486	118	12	≺	≺	NOUN
ejpam-486	118	13	qρ	qρ	X
ejpam-486	118	14	(	(	PUNCT
ejpam-486	118	15	z	z	NOUN
ejpam-486	118	16	)	)	PUNCT
ejpam-486	118	17	.	.	PUNCT
ejpam-486	119	1	the	the	DET
ejpam-486	119	2	result	result	NOUN
ejpam-486	119	3	is	be	AUX
ejpam-486	119	4	now	now	ADV
ejpam-486	119	5	deduced	deduce	VERB
ejpam-486	119	6	from	from	ADP
ejpam-486	119	7	qρ(z	qρ(z	NOUN
ejpam-486	119	8	)	)	PUNCT
ejpam-486	119	9	≺	≺	NOUN
ejpam-486	119	10	q(z	q(z	PROPN
ejpam-486	119	11	)	)	PUNCT
ejpam-486	119	12	.	.	PUNCT
ejpam-486	120	1	theorem	theorem	NOUN
ejpam-486	120	2	3	3	X
ejpam-486	120	3	.	.	PUNCT
ejpam-486	121	1	let	let	VERB
ejpam-486	121	2	h(z	h(z	NOUN
ejpam-486	121	3	)	)	PUNCT
ejpam-486	121	4	and	and	CCONJ
ejpam-486	121	5	q(z	q(z	PROPN
ejpam-486	121	6	)	)	PUNCT
ejpam-486	121	7	be	be	AUX
ejpam-486	121	8	univalent	univalent	ADJ
ejpam-486	121	9	in	in	ADP
ejpam-486	121	10	u	u	NOUN
ejpam-486	121	11	with	with	ADP
ejpam-486	121	12	q(0	q(0	PROPN
ejpam-486	121	13	)	)	PUNCT
ejpam-486	121	14	=	=	SYM
ejpam-486	121	15	0	0	NUM
ejpam-486	121	16	and	and	CCONJ
ejpam-486	121	17	set	set	VERB
ejpam-486	121	18	qρ(z	qρ(z	NOUN
ejpam-486	121	19	)	)	PUNCT
ejpam-486	121	20	=	=	SYM
ejpam-486	121	21	q(ρz	q(ρz	PROPN
ejpam-486	121	22	)	)	PUNCT
ejpam-486	121	23	and	and	CCONJ
ejpam-486	121	24	hρ(z	hρ(z	NUM
ejpam-486	121	25	)	)	PUNCT
ejpam-486	122	1	=	=	SYM
ejpam-486	122	2	h(ρz	h(ρz	NOUN
ejpam-486	122	3	)	)	PUNCT
ejpam-486	122	4	.	.	PUNCT
ejpam-486	123	1	letφ	letφ	PROPN
ejpam-486	123	2	:	:	PUNCT
ejpam-486	123	3	c3×	c3×	VERB
ejpam-486	123	4	u	u	PROPN
ejpam-486	123	5	→	→	SYM
ejpam-486	123	6	c	c	AUX
ejpam-486	123	7	satisfy	satisfy	VERB
ejpam-486	123	8	one	one	NUM
ejpam-486	123	9	of	of	ADP
ejpam-486	123	10	the	the	DET
ejpam-486	123	11	following	following	ADJ
ejpam-486	123	12	conditions	condition	NOUN
ejpam-486	123	13	:	:	PUNCT
ejpam-486	123	14	(	(	PUNCT
ejpam-486	123	15	1	1	X
ejpam-486	123	16	)	)	PUNCT
ejpam-486	123	17	φ	φ	PROPN
ejpam-486	123	18	∈	∈	PROPN
ejpam-486	123	19	φq[h	φq[h	PROPN
ejpam-486	123	20	,	,	PUNCT
ejpam-486	123	21	qρ	qρ	PROPN
ejpam-486	123	22	]	]	PUNCT
ejpam-486	123	23	,	,	PUNCT
ejpam-486	123	24	for	for	ADP
ejpam-486	123	25	some	some	DET
ejpam-486	123	26	ρ	ρ	NUM
ejpam-486	123	27	∈	∈	PROPN
ejpam-486	123	28	(	(	PUNCT
ejpam-486	123	29	0,1	0,1	NOUN
ejpam-486	123	30	)	)	PUNCT
ejpam-486	123	31	,	,	PUNCT
ejpam-486	123	32	or	or	CCONJ
ejpam-486	123	33	m.	m.	NOUN
ejpam-486	123	34	aouf	aouf	PROPN
ejpam-486	123	35	,	,	PUNCT
ejpam-486	123	36	t.	t.	PROPN
ejpam-486	123	37	seoudy	seoudy	PROPN
ejpam-486	123	38	/	/	SYM
ejpam-486	123	39	eur	eur	PROPN
ejpam-486	123	40	.	.	PUNCT
ejpam-486	124	1	j.	j.	PROPN
ejpam-486	124	2	pure	pure	PROPN
ejpam-486	124	3	appl	appl	PROPN
ejpam-486	124	4	.	.	PROPN
ejpam-486	124	5	math	math	PROPN
ejpam-486	124	6	,	,	PUNCT
ejpam-486	124	7	3	3	NUM
ejpam-486	124	8	(	(	PUNCT
ejpam-486	124	9	2010	2010	NUM
ejpam-486	124	10	)	)	PUNCT
ejpam-486	124	11	,	,	PUNCT
ejpam-486	124	12	26	26	NUM
ejpam-486	124	13	-	-	SYM
ejpam-486	124	14	44	44	NUM
ejpam-486	124	15	31	31	NUM
ejpam-486	124	16	(	(	PUNCT
ejpam-486	124	17	2	2	X
ejpam-486	124	18	)	)	PUNCT
ejpam-486	124	19	there	there	PRON
ejpam-486	124	20	exists	exist	VERB
ejpam-486	124	21	ρ0	ρ0	PROPN
ejpam-486	124	22	∈	∈	PROPN
ejpam-486	124	23	(	(	PUNCT
ejpam-486	124	24	0,1	0,1	NOUN
ejpam-486	124	25	)	)	PUNCT
ejpam-486	124	26	such	such	ADJ
ejpam-486	124	27	that	that	SCONJ
ejpam-486	124	28	φ	φ	PROPN
ejpam-486	124	29	∈	∈	PROPN
ejpam-486	124	30	φq[hρ	φq[hρ	PROPN
ejpam-486	124	31	,	,	PUNCT
ejpam-486	124	32	qρ	qρ	PROPN
ejpam-486	124	33	]	]	PUNCT
ejpam-486	124	34	,	,	PUNCT
ejpam-486	124	35	for	for	ADP
ejpam-486	124	36	all	all	PRON
ejpam-486	124	37	ρ	ρ	NUM
ejpam-486	124	38	∈	∈	NOUN
ejpam-486	124	39	(	(	PUNCT
ejpam-486	124	40	ρ0	ρ0	PROPN
ejpam-486	124	41	,	,	PUNCT
ejpam-486	124	42	1	1	NUM
ejpam-486	124	43	)	)	PUNCT
ejpam-486	124	44	.	.	PUNCT
ejpam-486	125	1	if	if	SCONJ
ejpam-486	125	2	f	f	PROPN
ejpam-486	125	3	(	(	PUNCT
ejpam-486	125	4	z	z	NOUN
ejpam-486	125	5	)	)	PUNCT
ejpam-486	125	6	∈	∈	PROPN
ejpam-486	125	7	a	a	DET
ejpam-486	125	8	�	�	PROPN
ejpam-486	125	9	p	p	PROPN
ejpam-486	125	10	�	�	PROPN
ejpam-486	125	11	satisfies	satisfie	NOUN
ejpam-486	125	12	(	(	PUNCT
ejpam-486	125	13	12	12	NUM
ejpam-486	125	14	)	)	PUNCT
ejpam-486	125	15	,	,	PUNCT
ejpam-486	125	16	then	then	ADV
ejpam-486	125	17	qαβ	qαβ	INTJ
ejpam-486	125	18	,	,	PUNCT
ejpam-486	125	19	p	p	NOUN
ejpam-486	125	20	f	f	X
ejpam-486	125	21	(	(	PUNCT
ejpam-486	125	22	z	z	NOUN
ejpam-486	125	23	)	)	PUNCT
ejpam-486	125	24	≺	≺	NOUN
ejpam-486	125	25	q	q	NOUN
ejpam-486	125	26	(	(	PUNCT
ejpam-486	125	27	z	z	NOUN
ejpam-486	125	28	)	)	PUNCT
ejpam-486	125	29	(	(	PUNCT
ejpam-486	125	30	z	z	NOUN
ejpam-486	125	31	∈	∈	PROPN
ejpam-486	125	32	u	u	NOUN
ejpam-486	125	33	)	)	PUNCT
ejpam-486	125	34	.	.	PUNCT
ejpam-486	126	1	proof	proof	NOUN
ejpam-486	126	2	.	.	PUNCT
ejpam-486	127	1	the	the	DET
ejpam-486	127	2	proof	proof	NOUN
ejpam-486	127	3	is	be	AUX
ejpam-486	127	4	similar	similar	ADJ
ejpam-486	127	5	to	to	ADP
ejpam-486	127	6	the	the	DET
ejpam-486	127	7	proof	proof	NOUN
ejpam-486	127	8	of	of	ADP
ejpam-486	127	9	[	[	X
ejpam-486	127	10	8	8	NUM
ejpam-486	127	11	,	,	PUNCT
ejpam-486	127	12	theorem	theorem	VERB
ejpam-486	127	13	2.3d	2.3d	NUM
ejpam-486	127	14	,	,	PUNCT
ejpam-486	127	15	p.30	p.30	X
ejpam-486	127	16	]	]	PUNCT
ejpam-486	127	17	and	and	CCONJ
ejpam-486	127	18	is	be	AUX
ejpam-486	127	19	therefore	therefore	ADV
ejpam-486	127	20	omitted	omit	VERB
ejpam-486	127	21	.	.	PUNCT
ejpam-486	128	1	the	the	DET
ejpam-486	128	2	next	next	ADJ
ejpam-486	128	3	theorem	theorem	NOUN
ejpam-486	128	4	yields	yield	VERB
ejpam-486	128	5	the	the	DET
ejpam-486	128	6	best	good	ADJ
ejpam-486	128	7	dominant	dominant	NOUN
ejpam-486	128	8	of	of	ADP
ejpam-486	128	9	the	the	DET
ejpam-486	128	10	differential	differential	ADJ
ejpam-486	128	11	subordination	subordination	NOUN
ejpam-486	128	12	(	(	PUNCT
ejpam-486	128	13	12	12	NUM
ejpam-486	128	14	)	)	PUNCT
ejpam-486	128	15	.	.	PUNCT
ejpam-486	129	1	theorem	theorem	ADJ
ejpam-486	129	2	4	4	NUM
ejpam-486	129	3	.	.	PUNCT
ejpam-486	129	4	let	let	VERB
ejpam-486	129	5	h(z	h(z	NOUN
ejpam-486	129	6	)	)	PUNCT
ejpam-486	129	7	be	be	AUX
ejpam-486	129	8	univalent	univalent	ADJ
ejpam-486	129	9	in	in	ADP
ejpam-486	129	10	u.	u.	PROPN
ejpam-486	130	1	let	let	VERB
ejpam-486	130	2	φ	φ	PROPN
ejpam-486	130	3	:	:	PUNCT
ejpam-486	131	1	c3	c3	PROPN
ejpam-486	131	2	×	×	PROPN
ejpam-486	131	3	u	u	PROPN
ejpam-486	131	4	→	→	PROPN
ejpam-486	131	5	c.	c.	PROPN
ejpam-486	131	6	suppose	suppose	VERB
ejpam-486	131	7	that	that	SCONJ
ejpam-486	131	8	the	the	DET
ejpam-486	131	9	differential	differential	ADJ
ejpam-486	131	10	equation	equation	NOUN
ejpam-486	131	11	φ(q(z	φ(q(z	PROPN
ejpam-486	131	12	)	)	PUNCT
ejpam-486	131	13	,	,	PUNCT
ejpam-486	131	14	zq′(z	zq′(z	PROPN
ejpam-486	131	15	)	)	PUNCT
ejpam-486	131	16	,	,	PUNCT
ejpam-486	131	17	z2q	z2q	PUNCT
ejpam-486	131	18	′′	′′	PROPN
ejpam-486	131	19	(	(	PUNCT
ejpam-486	131	20	z	z	PROPN
ejpam-486	131	21	)	)	PUNCT
ejpam-486	131	22	;	;	PUNCT
ejpam-486	131	23	z	z	X
ejpam-486	131	24	)	)	PUNCT
ejpam-486	131	25	=	=	SYM
ejpam-486	131	26	h(z	h(z	NOUN
ejpam-486	131	27	)	)	PUNCT
ejpam-486	131	28	(	(	PUNCT
ejpam-486	131	29	13	13	NUM
ejpam-486	131	30	)	)	PUNCT
ejpam-486	131	31	has	have	VERB
ejpam-486	131	32	a	a	DET
ejpam-486	131	33	solution	solution	NOUN
ejpam-486	131	34	q(z	q(z	PROPN
ejpam-486	131	35	)	)	PUNCT
ejpam-486	131	36	with	with	ADP
ejpam-486	131	37	q(0	q(0	PROPN
ejpam-486	131	38	)	)	PUNCT
ejpam-486	131	39	=	=	SYM
ejpam-486	131	40	0	0	PUNCT
ejpam-486	131	41	and	and	CCONJ
ejpam-486	131	42	satisfy	satisfy	VERB
ejpam-486	131	43	one	one	NUM
ejpam-486	131	44	of	of	ADP
ejpam-486	131	45	the	the	DET
ejpam-486	131	46	following	following	ADJ
ejpam-486	131	47	conditions	condition	NOUN
ejpam-486	131	48	:	:	PUNCT
ejpam-486	131	49	(	(	PUNCT
ejpam-486	131	50	1	1	X
ejpam-486	131	51	)	)	PUNCT
ejpam-486	131	52	q(z	q(z	PROPN
ejpam-486	131	53	)	)	PUNCT
ejpam-486	131	54	∈	∈	PROPN
ejpam-486	131	55	f0	f0	PROPN
ejpam-486	131	56	and	and	CCONJ
ejpam-486	131	57	φ	φ	NOUN
ejpam-486	131	58	∈	∈	PROPN
ejpam-486	131	59	φq[h	φq[h	PROPN
ejpam-486	131	60	,	,	PUNCT
ejpam-486	131	61	q	q	X
ejpam-486	131	62	]	]	X
ejpam-486	131	63	,	,	PUNCT
ejpam-486	131	64	(	(	PUNCT
ejpam-486	131	65	2	2	X
ejpam-486	131	66	)	)	PUNCT
ejpam-486	131	67	q(z	q(z	PROPN
ejpam-486	131	68	)	)	PUNCT
ejpam-486	131	69	is	be	AUX
ejpam-486	131	70	univalent	univalent	ADJ
ejpam-486	131	71	in	in	ADP
ejpam-486	131	72	u	u	NOUN
ejpam-486	131	73	and	and	CCONJ
ejpam-486	131	74	φ	φ	PROPN
ejpam-486	131	75	∈	∈	PROPN
ejpam-486	131	76	φq[h	φq[h	PROPN
ejpam-486	131	77	,	,	PUNCT
ejpam-486	131	78	qρ	qρ	PROPN
ejpam-486	131	79	]	]	PUNCT
ejpam-486	131	80	,	,	PUNCT
ejpam-486	131	81	for	for	SCONJ
ejpam-486	131	82	some	some	DET
ejpam-486	131	83	ρ	ρ	NUM
ejpam-486	131	84	∈	∈	PROPN
ejpam-486	131	85	(	(	PUNCT
ejpam-486	131	86	0,1	0,1	NUM
ejpam-486	131	87	)	)	PUNCT
ejpam-486	131	88	,	,	PUNCT
ejpam-486	131	89	or	or	CCONJ
ejpam-486	131	90	(	(	PUNCT
ejpam-486	131	91	3	3	X
ejpam-486	131	92	)	)	PUNCT
ejpam-486	131	93	q(z	q(z	PROPN
ejpam-486	131	94	)	)	PUNCT
ejpam-486	131	95	is	be	AUX
ejpam-486	131	96	univalent	univalent	ADJ
ejpam-486	131	97	in	in	ADP
ejpam-486	131	98	u	u	NOUN
ejpam-486	131	99	and	and	CCONJ
ejpam-486	131	100	there	there	PRON
ejpam-486	131	101	exists	exist	VERB
ejpam-486	131	102	ρ0	ρ0	PROPN
ejpam-486	131	103	∈	∈	PROPN
ejpam-486	131	104	(	(	PUNCT
ejpam-486	131	105	0,1	0,1	NOUN
ejpam-486	131	106	)	)	PUNCT
ejpam-486	131	107	such	such	ADJ
ejpam-486	131	108	that	that	SCONJ
ejpam-486	131	109	φ	φ	PROPN
ejpam-486	131	110	∈	∈	PROPN
ejpam-486	131	111	φq[hρ	φq[hρ	PROPN
ejpam-486	131	112	,	,	PUNCT
ejpam-486	131	113	qρ	qρ	PROPN
ejpam-486	131	114	]	]	PUNCT
ejpam-486	131	115	,	,	PUNCT
ejpam-486	131	116	for	for	ADP
ejpam-486	131	117	all	all	PRON
ejpam-486	131	118	ρ	ρ	NUM
ejpam-486	131	119	∈	∈	NOUN
ejpam-486	131	120	(	(	PUNCT
ejpam-486	131	121	ρ0	ρ0	PROPN
ejpam-486	131	122	,	,	PUNCT
ejpam-486	131	123	1	1	NUM
ejpam-486	131	124	)	)	PUNCT
ejpam-486	131	125	.	.	PUNCT
ejpam-486	132	1	if	if	SCONJ
ejpam-486	132	2	f	f	PROPN
ejpam-486	132	3	(	(	PUNCT
ejpam-486	132	4	z	z	NOUN
ejpam-486	132	5	)	)	PUNCT
ejpam-486	132	6	∈	∈	PROPN
ejpam-486	132	7	a	a	DET
ejpam-486	132	8	�	�	PROPN
ejpam-486	132	9	p	p	PROPN
ejpam-486	132	10	�	�	PROPN
ejpam-486	132	11	satisfies	satisfie	NOUN
ejpam-486	132	12	(	(	PUNCT
ejpam-486	132	13	12	12	NUM
ejpam-486	132	14	)	)	PUNCT
ejpam-486	132	15	,	,	PUNCT
ejpam-486	132	16	then	then	ADV
ejpam-486	132	17	qαβ	qαβ	INTJ
ejpam-486	132	18	,	,	PUNCT
ejpam-486	132	19	p	p	NOUN
ejpam-486	132	20	f	f	X
ejpam-486	132	21	(	(	PUNCT
ejpam-486	132	22	z	z	NOUN
ejpam-486	132	23	)	)	PUNCT
ejpam-486	132	24	≺	≺	NOUN
ejpam-486	132	25	q	q	NOUN
ejpam-486	132	26	(	(	PUNCT
ejpam-486	132	27	z	z	NOUN
ejpam-486	132	28	)	)	PUNCT
ejpam-486	132	29	(	(	PUNCT
ejpam-486	132	30	z	z	NOUN
ejpam-486	132	31	∈	∈	PROPN
ejpam-486	132	32	u	u	NOUN
ejpam-486	132	33	)	)	PUNCT
ejpam-486	132	34	,	,	PUNCT
ejpam-486	132	35	and	and	CCONJ
ejpam-486	132	36	q(z	q(z	PROPN
ejpam-486	132	37	)	)	PUNCT
ejpam-486	132	38	is	be	AUX
ejpam-486	132	39	the	the	DET
ejpam-486	132	40	best	good	ADJ
ejpam-486	132	41	dominant	dominant	ADJ
ejpam-486	132	42	.	.	PUNCT
ejpam-486	133	1	proof	proof	NOUN
ejpam-486	133	2	.	.	PUNCT
ejpam-486	134	1	following	follow	VERB
ejpam-486	134	2	the	the	DET
ejpam-486	134	3	same	same	ADJ
ejpam-486	134	4	arguments	argument	NOUN
ejpam-486	134	5	in	in	ADP
ejpam-486	134	6	[	[	X
ejpam-486	134	7	8	8	NUM
ejpam-486	134	8	,	,	PUNCT
ejpam-486	134	9	theorem	theorem	VERB
ejpam-486	134	10	2.3e	2.3e	NUM
ejpam-486	134	11	,	,	PUNCT
ejpam-486	134	12	p.	p.	NOUN
ejpam-486	134	13	31	31	NUM
ejpam-486	134	14	]	]	PUNCT
ejpam-486	134	15	,	,	PUNCT
ejpam-486	134	16	we	we	PRON
ejpam-486	134	17	deduce	deduce	VERB
ejpam-486	134	18	that	that	SCONJ
ejpam-486	134	19	q(z	q(z	PROPN
ejpam-486	134	20	)	)	PUNCT
ejpam-486	134	21	is	be	AUX
ejpam-486	134	22	a	a	DET
ejpam-486	134	23	dominant	dominant	NOUN
ejpam-486	134	24	from	from	ADP
ejpam-486	134	25	theorems	theorem	NOUN
ejpam-486	134	26	2	2	NUM
ejpam-486	134	27	and	and	CCONJ
ejpam-486	134	28	3	3	NUM
ejpam-486	134	29	.	.	PUNCT
ejpam-486	135	1	since	since	SCONJ
ejpam-486	135	2	q(z	q(z	PROPN
ejpam-486	135	3	)	)	PUNCT
ejpam-486	135	4	satisfies	satisfie	NOUN
ejpam-486	135	5	(	(	PUNCT
ejpam-486	135	6	13	13	NUM
ejpam-486	135	7	)	)	PUNCT
ejpam-486	135	8	it	it	PRON
ejpam-486	135	9	is	be	AUX
ejpam-486	135	10	also	also	ADV
ejpam-486	135	11	a	a	DET
ejpam-486	135	12	solution	solution	NOUN
ejpam-486	135	13	of	of	ADP
ejpam-486	135	14	(	(	PUNCT
ejpam-486	135	15	12	12	NUM
ejpam-486	135	16	)	)	PUNCT
ejpam-486	135	17	and	and	CCONJ
ejpam-486	135	18	therefore	therefore	ADV
ejpam-486	135	19	q(z	q(z	PROPN
ejpam-486	135	20	)	)	PUNCT
ejpam-486	135	21	will	will	AUX
ejpam-486	135	22	be	be	AUX
ejpam-486	135	23	dominated	dominate	VERB
ejpam-486	135	24	by	by	ADP
ejpam-486	135	25	all	all	DET
ejpam-486	135	26	dominants	dominant	NOUN
ejpam-486	135	27	.	.	PUNCT
ejpam-486	136	1	hence	hence	ADV
ejpam-486	136	2	q(z	q(z	PROPN
ejpam-486	136	3	)	)	PUNCT
ejpam-486	136	4	is	be	AUX
ejpam-486	136	5	the	the	DET
ejpam-486	136	6	best	good	ADJ
ejpam-486	136	7	dominant	dominant	NOUN
ejpam-486	136	8	.	.	PUNCT
ejpam-486	137	1	in	in	ADP
ejpam-486	137	2	the	the	DET
ejpam-486	137	3	particular	particular	ADJ
ejpam-486	137	4	case	case	NOUN
ejpam-486	137	5	q(z	q(z	PROPN
ejpam-486	137	6	)	)	PUNCT
ejpam-486	137	7	=	=	SYM
ejpam-486	137	8	mz	mz	PROPN
ejpam-486	137	9	,	,	PUNCT
ejpam-486	137	10	m	m	VERB
ejpam-486	137	11	>	>	X
ejpam-486	137	12	0	0	NUM
ejpam-486	137	13	,	,	PUNCT
ejpam-486	137	14	and	and	CCONJ
ejpam-486	137	15	in	in	ADP
ejpam-486	137	16	view	view	NOUN
ejpam-486	137	17	of	of	ADP
ejpam-486	137	18	the	the	DET
ejpam-486	137	19	definition	definition	NOUN
ejpam-486	137	20	1	1	NUM
ejpam-486	137	21	,	,	PUNCT
ejpam-486	137	22	the	the	DET
ejpam-486	137	23	class	class	NOUN
ejpam-486	137	24	of	of	ADP
ejpam-486	137	25	admissible	admissible	ADJ
ejpam-486	137	26	functions	function	NOUN
ejpam-486	137	27	φq[ω	φq[ω	PROPN
ejpam-486	137	28	,	,	PUNCT
ejpam-486	137	29	q	q	X
ejpam-486	137	30	]	]	X
ejpam-486	137	31	,	,	PUNCT
ejpam-486	137	32	denoted	denote	VERB
ejpam-486	137	33	by	by	ADP
ejpam-486	137	34	φq[ω	φq[ω	PROPN
ejpam-486	137	35	,	,	PUNCT
ejpam-486	137	36	m	m	VERB
ejpam-486	137	37	]	]	PUNCT
ejpam-486	137	38	,	,	PUNCT
ejpam-486	137	39	is	be	AUX
ejpam-486	137	40	described	describe	VERB
ejpam-486	137	41	below	below	ADV
ejpam-486	137	42	.	.	PUNCT
ejpam-486	138	1	definition	definition	NOUN
ejpam-486	138	2	4	4	NUM
ejpam-486	138	3	.	.	PUNCT
ejpam-486	139	1	let	let	VERB
ejpam-486	139	2	ω	ω	PRON
ejpam-486	139	3	be	be	AUX
ejpam-486	139	4	a	a	DET
ejpam-486	139	5	set	set	NOUN
ejpam-486	139	6	in	in	ADP
ejpam-486	139	7	c	c	PROPN
ejpam-486	139	8	and	and	CCONJ
ejpam-486	139	9	m	m	PROPN
ejpam-486	139	10	>	>	X
ejpam-486	139	11	0	0	X
ejpam-486	139	12	.	.	PUNCT
ejpam-486	140	1	the	the	DET
ejpam-486	140	2	class	class	NOUN
ejpam-486	140	3	of	of	ADP
ejpam-486	140	4	admissible	admissible	ADJ
ejpam-486	140	5	functions	function	NOUN
ejpam-486	140	6	φq[ω	φq[ω	PROPN
ejpam-486	140	7	,	,	PUNCT
ejpam-486	140	8	m	m	PRON
ejpam-486	140	9	]	]	PUNCT
ejpam-486	140	10	consists	consist	VERB
ejpam-486	140	11	of	of	ADP
ejpam-486	140	12	those	those	DET
ejpam-486	140	13	functions	function	NOUN
ejpam-486	140	14	φ	φ	NOUN
ejpam-486	140	15	:	:	PUNCT
ejpam-486	141	1	c3	c3	PROPN
ejpam-486	141	2	×	×	PROPN
ejpam-486	141	3	u	u	PROPN
ejpam-486	141	4	→	→	SYM
ejpam-486	141	5	c	c	NOUN
ejpam-486	141	6	such	such	ADJ
ejpam-486	141	7	that	that	SCONJ
ejpam-486	141	8	φ	φ	PROPN
ejpam-486	141	9	�	�	PROPN
ejpam-486	141	10	meiθ	meiθ	PROPN
ejpam-486	141	11	,	,	PUNCT
ejpam-486	141	12	k+α+	k+α+	PROPN
ejpam-486	141	13	β	β	X
ejpam-486	141	14	−	−	PROPN
ejpam-486	141	15	1	1	NUM
ejpam-486	141	16	α+	α+	NOUN
ejpam-486	141	17	β	β	NOUN
ejpam-486	141	18	+	+	CCONJ
ejpam-486	141	19	p−	p−	NOUN
ejpam-486	141	20	1	1	NUM
ejpam-486	141	21	meiθ	meiθ	NOUN
ejpam-486	141	22	,	,	PUNCT
ejpam-486	141	23	l	l	PROPN
ejpam-486	141	24	+	+	CCONJ
ejpam-486	141	25	�	�	PROPN
ejpam-486	141	26	2	2	NUM
ejpam-486	141	27	�	�	PROPN
ejpam-486	141	28	α+	α+	PUNCT
ejpam-486	141	29	β	β	NOUN
ejpam-486	141	30	−	−	PROPN
ejpam-486	141	31	1	1	NUM
ejpam-486	141	32	�	�	PROPN
ejpam-486	141	33	k+	k+	X
ejpam-486	141	34	�	�	PROPN
ejpam-486	141	35	α+	α+	PUNCT
ejpam-486	141	36	β	β	NOUN
ejpam-486	141	37	−	−	PROPN
ejpam-486	141	38	1	1	NUM
ejpam-486	141	39	�	�	PROPN
ejpam-486	141	40	�	�	PROPN
ejpam-486	141	41	α+	α+	PUNCT
ejpam-486	141	42	β	β	NOUN
ejpam-486	141	43	−	−	PROPN
ejpam-486	141	44	2	2	NUM
ejpam-486	141	45	�	�	PROPN
ejpam-486	141	46	�	�	PROPN
ejpam-486	141	47	meiθ	meiθ	PROPN
ejpam-486	141	48	�	�	PROPN
ejpam-486	141	49	α+	α+	X
ejpam-486	141	50	β	β	NOUN
ejpam-486	141	51	+	+	CCONJ
ejpam-486	141	52	p−	p−	PROPN
ejpam-486	141	53	1	1	NUM
ejpam-486	141	54	�	�	PROPN
ejpam-486	141	55	�	�	PROPN
ejpam-486	141	56	α+	α+	PUNCT
ejpam-486	141	57	β	β	NOUN
ejpam-486	141	58	+	+	CCONJ
ejpam-486	141	59	p−	p−	PROPN
ejpam-486	141	60	2	2	NUM
ejpam-486	141	61	�	�	NOUN
ejpam-486	141	62	;	;	PUNCT
ejpam-486	141	63	z	z	PROPN
ejpam-486	141	64	�	�	PROPN
ejpam-486	141	65	/∈	/∈	PUNCT
ejpam-486	142	1	ω	ω	PROPN
ejpam-486	142	2	(	(	PUNCT
ejpam-486	142	3	14	14	NUM
ejpam-486	142	4	)	)	PUNCT
ejpam-486	142	5	whenever	whenever	SCONJ
ejpam-486	142	6	z	z	PROPN
ejpam-486	142	7	∈	∈	PROPN
ejpam-486	142	8	u	u	PROPN
ejpam-486	142	9	,	,	PUNCT
ejpam-486	142	10	θ	θ	PROPN
ejpam-486	142	11	∈	∈	PROPN
ejpam-486	142	12	r	r	NOUN
ejpam-486	142	13	,	,	PUNCT
ejpam-486	142	14	ℜ	ℜ	ADJ
ejpam-486	142	15	�	�	PROPN
ejpam-486	142	16	le−iθ	le−iθ	PROPN
ejpam-486	142	17	�	�	PROPN
ejpam-486	142	18	≥	≥	PROPN
ejpam-486	142	19	(	(	PUNCT
ejpam-486	142	20	k−	k−	PROPN
ejpam-486	142	21	1)km	1)km	PROPN
ejpam-486	142	22	for	for	ADP
ejpam-486	142	23	all	all	DET
ejpam-486	142	24	real	real	ADJ
ejpam-486	142	25	θ	θ	NOUN
ejpam-486	142	26	,	,	PUNCT
ejpam-486	142	27	α	α	X
ejpam-486	142	28	>	>	X
ejpam-486	142	29	2	2	NUM
ejpam-486	142	30	,	,	PUNCT
ejpam-486	142	31	β	β	X
ejpam-486	142	32	>	>	X
ejpam-486	142	33	−1	−1	NOUN
ejpam-486	142	34	,	,	PUNCT
ejpam-486	142	35	p	p	PROPN
ejpam-486	142	36	∈	∈	PROPN
ejpam-486	142	37	n	n	NOUN
ejpam-486	142	38	and	and	CCONJ
ejpam-486	142	39	k	k	PROPN
ejpam-486	142	40	≥	≥	PROPN
ejpam-486	143	1	p.	p.	NOUN
ejpam-486	143	2	corollary	corollary	NOUN
ejpam-486	144	1	2	2	NUM
ejpam-486	144	2	.	.	PUNCT
ejpam-486	145	1	let	let	VERB
ejpam-486	145	2	φ	φ	PROPN
ejpam-486	145	3	∈	∈	PROPN
ejpam-486	145	4	φq[ω	φq[ω	PROPN
ejpam-486	145	5	,	,	PUNCT
ejpam-486	145	6	m	m	VERB
ejpam-486	145	7	]	]	X
ejpam-486	145	8	.	.	PUNCT
ejpam-486	146	1	if	if	SCONJ
ejpam-486	146	2	f	f	PROPN
ejpam-486	146	3	(	(	PUNCT
ejpam-486	146	4	z	z	NOUN
ejpam-486	146	5	)	)	PUNCT
ejpam-486	146	6	∈	∈	PROPN
ejpam-486	146	7	a	a	DET
ejpam-486	146	8	�	�	PROPN
ejpam-486	146	9	p	p	PROPN
ejpam-486	146	10	�	�	PROPN
ejpam-486	146	11	satisfies	satisfy	VERB
ejpam-486	146	12	φ	φ	PROPN
ejpam-486	146	13	�	�	PROPN
ejpam-486	146	14	qαβ	qαβ	PROPN
ejpam-486	146	15	,	,	PUNCT
ejpam-486	146	16	p	p	PROPN
ejpam-486	146	17	f	f	X
ejpam-486	146	18	(	(	PUNCT
ejpam-486	146	19	z),qα−1	z),qα−1	PROPN
ejpam-486	146	20	β	β	X
ejpam-486	146	21	,	,	PUNCT
ejpam-486	146	22	p	p	PROPN
ejpam-486	146	23	f	f	X
ejpam-486	146	24	(	(	PUNCT
ejpam-486	146	25	z),qα−2	z),qα−2	NOUN
ejpam-486	146	26	β	β	X
ejpam-486	146	27	,	,	PUNCT
ejpam-486	146	28	p	p	PROPN
ejpam-486	146	29	f	f	X
ejpam-486	146	30	(	(	PUNCT
ejpam-486	146	31	z	z	NOUN
ejpam-486	146	32	)	)	PUNCT
ejpam-486	146	33	;	;	PUNCT
ejpam-486	146	34	z	z	NOUN
ejpam-486	146	35	�	�	PROPN
ejpam-486	146	36	∈	∈	PROPN
ejpam-486	146	37	ω	ω	PROPN
ejpam-486	146	38	�	�	PROPN
ejpam-486	146	39	α	α	PROPN
ejpam-486	146	40	>	>	X
ejpam-486	146	41	2	2	NUM
ejpam-486	146	42	;	;	PUNCT
ejpam-486	146	43	β	β	X
ejpam-486	146	44	>	>	X
ejpam-486	146	45	−1	−1	NOUN
ejpam-486	146	46	;	;	PUNCT
ejpam-486	146	47	p	p	PROPN
ejpam-486	146	48	∈	∈	PROPN
ejpam-486	146	49	n	n	CCONJ
ejpam-486	146	50	;	;	PUNCT
ejpam-486	146	51	z	z	PROPN
ejpam-486	146	52	∈	∈	PROPN
ejpam-486	146	53	u	u	PROPN
ejpam-486	146	54	�	�	PROPN
ejpam-486	146	55	,	,	PUNCT
ejpam-486	146	56	then	then	ADV
ejpam-486	146	57	�	�	PROPN
ejpam-486	146	58	�	�	PROPN
ejpam-486	146	59	�	�	PROPN
ejpam-486	146	60	qαβ	qαβ	PROPN
ejpam-486	146	61	,	,	PUNCT
ejpam-486	146	62	p	p	NOUN
ejpam-486	146	63	f	f	X
ejpam-486	146	64	(	(	PUNCT
ejpam-486	146	65	z	z	NOUN
ejpam-486	146	66	)	)	PUNCT
ejpam-486	146	67	�	�	PROPN
ejpam-486	146	68	�	�	PROPN
ejpam-486	146	69	�	�	PROPN
ejpam-486	146	70	<	<	X
ejpam-486	146	71	m	m	PROPN
ejpam-486	146	72	(	(	PUNCT
ejpam-486	146	73	z	z	NOUN
ejpam-486	146	74	∈	∈	PROPN
ejpam-486	146	75	u	u	NOUN
ejpam-486	146	76	)	)	PUNCT
ejpam-486	146	77	.	.	PUNCT
ejpam-486	147	1	m.	m.	PROPN
ejpam-486	147	2	aouf	aouf	PROPN
ejpam-486	147	3	,	,	PUNCT
ejpam-486	147	4	t.	t.	PROPN
ejpam-486	147	5	seoudy	seoudy	PROPN
ejpam-486	147	6	/	/	SYM
ejpam-486	147	7	eur	eur	PROPN
ejpam-486	147	8	.	.	PUNCT
ejpam-486	148	1	j.	j.	PROPN
ejpam-486	148	2	pure	pure	PROPN
ejpam-486	148	3	appl	appl	PROPN
ejpam-486	148	4	.	.	PROPN
ejpam-486	148	5	math	math	PROPN
ejpam-486	148	6	,	,	PUNCT
ejpam-486	148	7	3	3	NUM
ejpam-486	148	8	(	(	PUNCT
ejpam-486	148	9	2010	2010	NUM
ejpam-486	148	10	)	)	PUNCT
ejpam-486	148	11	,	,	PUNCT
ejpam-486	148	12	26	26	NUM
ejpam-486	148	13	-	-	SYM
ejpam-486	148	14	44	44	NUM
ejpam-486	148	15	32	32	NUM
ejpam-486	148	16	in	in	ADP
ejpam-486	148	17	the	the	DET
ejpam-486	148	18	special	special	ADJ
ejpam-486	148	19	case	case	NOUN
ejpam-486	148	20	ω	ω	NOUN
ejpam-486	148	21	=	=	SYM
ejpam-486	148	22	q(u	q(u	PROPN
ejpam-486	148	23	)	)	PUNCT
ejpam-486	148	24	=	=	SYM
ejpam-486	148	25	{	{	PUNCT
ejpam-486	148	26	ω	ω	NOUN
ejpam-486	148	27	:	:	PUNCT
ejpam-486	148	28	|ω|	|ω|	VERB
ejpam-486	148	29	<	<	X
ejpam-486	148	30	m	m	PRON
ejpam-486	148	31	}	}	PUNCT
ejpam-486	148	32	,	,	PUNCT
ejpam-486	148	33	the	the	DET
ejpam-486	148	34	class	class	NOUN
ejpam-486	148	35	φq[ω	φq[ω	PROPN
ejpam-486	148	36	,	,	PUNCT
ejpam-486	148	37	m	m	PROPN
ejpam-486	148	38	]	]	PUNCT
ejpam-486	148	39	is	be	AUX
ejpam-486	148	40	simply	simply	ADV
ejpam-486	148	41	denoted	denote	VERB
ejpam-486	148	42	by	by	ADP
ejpam-486	148	43	φq[m	φq[m	NOUN
ejpam-486	148	44	]	]	PUNCT
ejpam-486	148	45	.	.	PUNCT
ejpam-486	149	1	corollary	corollary	ADJ
ejpam-486	149	2	3	3	X
ejpam-486	149	3	.	.	PUNCT
ejpam-486	150	1	let	let	VERB
ejpam-486	150	2	φ	φ	PROPN
ejpam-486	150	3	∈	∈	PROPN
ejpam-486	150	4	φq[m	φq[m	PROPN
ejpam-486	150	5	]	]	PUNCT
ejpam-486	150	6	.	.	PUNCT
ejpam-486	151	1	if	if	SCONJ
ejpam-486	151	2	f	f	PROPN
ejpam-486	151	3	(	(	PUNCT
ejpam-486	151	4	z	z	NOUN
ejpam-486	151	5	)	)	PUNCT
ejpam-486	151	6	∈	∈	PROPN
ejpam-486	151	7	a	a	DET
ejpam-486	151	8	�	�	PROPN
ejpam-486	151	9	p	p	NOUN
ejpam-486	151	10	�	�	PROPN
ejpam-486	151	11	satisfies	satisfy	VERB
ejpam-486	151	12	�	�	PROPN
ejpam-486	151	13	�	�	PROPN
ejpam-486	151	14	�	�	PROPN
ejpam-486	151	15	φ	φ	PROPN
ejpam-486	151	16	�	�	PROPN
ejpam-486	151	17	qαβ	qαβ	PROPN
ejpam-486	151	18	,	,	PUNCT
ejpam-486	151	19	p	p	PROPN
ejpam-486	151	20	f	f	X
ejpam-486	151	21	(	(	PUNCT
ejpam-486	151	22	z),qα−1	z),qα−1	PROPN
ejpam-486	151	23	β	β	X
ejpam-486	151	24	,	,	PUNCT
ejpam-486	152	1	p	p	PROPN
ejpam-486	152	2	f	f	X
ejpam-486	152	3	(	(	PUNCT
ejpam-486	152	4	z),qα−2	z),qα−2	NOUN
ejpam-486	152	5	β	β	X
ejpam-486	152	6	,	,	PUNCT
ejpam-486	152	7	p	p	PROPN
ejpam-486	152	8	f	f	X
ejpam-486	152	9	(	(	PUNCT
ejpam-486	152	10	z	z	NOUN
ejpam-486	152	11	)	)	PUNCT
ejpam-486	152	12	;	;	PUNCT
ejpam-486	152	13	z	z	PROPN
ejpam-486	152	14	�	�	PROPN
ejpam-486	152	15	�	�	PROPN
ejpam-486	152	16	�	�	PROPN
ejpam-486	152	17	�	�	PROPN
ejpam-486	152	18	<	<	X
ejpam-486	152	19	m	m	PROPN
ejpam-486	152	20	�	�	PROPN
ejpam-486	152	21	α	α	X
ejpam-486	152	22	>	>	X
ejpam-486	152	23	2;β	2;β	NUM
ejpam-486	152	24	>	>	SYM
ejpam-486	152	25	−1	−1	NOUN
ejpam-486	152	26	;	;	PUNCT
ejpam-486	152	27	p	p	PROPN
ejpam-486	152	28	∈	∈	PROPN
ejpam-486	152	29	n	n	CCONJ
ejpam-486	152	30	;	;	PUNCT
ejpam-486	152	31	z	z	PROPN
ejpam-486	152	32	∈	∈	PROPN
ejpam-486	152	33	u	u	PROPN
ejpam-486	152	34	�	�	PROPN
ejpam-486	152	35	,	,	PUNCT
ejpam-486	152	36	then	then	ADV
ejpam-486	152	37	�	�	PROPN
ejpam-486	152	38	�	�	PROPN
ejpam-486	152	39	�	�	PROPN
ejpam-486	152	40	qαβ	qαβ	PROPN
ejpam-486	152	41	,	,	PUNCT
ejpam-486	152	42	p	p	NOUN
ejpam-486	152	43	f	f	X
ejpam-486	152	44	(	(	PUNCT
ejpam-486	152	45	z	z	NOUN
ejpam-486	152	46	)	)	PUNCT
ejpam-486	152	47	�	�	PROPN
ejpam-486	152	48	�	�	PROPN
ejpam-486	152	49	�	�	PROPN
ejpam-486	152	50	<	<	X
ejpam-486	152	51	m	m	PROPN
ejpam-486	152	52	(	(	PUNCT
ejpam-486	152	53	z	z	NOUN
ejpam-486	152	54	∈	∈	PROPN
ejpam-486	152	55	u	u	NOUN
ejpam-486	152	56	)	)	PUNCT
ejpam-486	152	57	.	.	PUNCT
ejpam-486	153	1	remark	remark	PROPN
ejpam-486	153	2	1	1	NUM
ejpam-486	153	3	.	.	PUNCT
ejpam-486	154	1	putting	put	VERB
ejpam-486	154	2	m	m	NOUN
ejpam-486	154	3	=	=	NOUN
ejpam-486	154	4	1	1	NUM
ejpam-486	154	5	in	in	ADP
ejpam-486	154	6	the	the	DET
ejpam-486	154	7	corollary	corollary	ADJ
ejpam-486	154	8	3	3	NUM
ejpam-486	154	9	we	we	PRON
ejpam-486	154	10	obtain	obtain	VERB
ejpam-486	154	11	the	the	DET
ejpam-486	154	12	result	result	NOUN
ejpam-486	154	13	obtained	obtain	VERB
ejpam-486	154	14	by	by	ADP
ejpam-486	154	15	aouf	aouf	PROPN
ejpam-486	155	1	[	[	X
ejpam-486	155	2	3	3	NUM
ejpam-486	155	3	,	,	PUNCT
ejpam-486	155	4	theorem	theorem	VERB
ejpam-486	155	5	2	2	NUM
ejpam-486	155	6	]	]	PUNCT
ejpam-486	155	7	.	.	PUNCT
ejpam-486	156	1	corollary	corollary	ADJ
ejpam-486	156	2	4	4	NUM
ejpam-486	156	3	.	.	PUNCT
ejpam-486	157	1	if	if	SCONJ
ejpam-486	157	2	k	k	PROPN
ejpam-486	157	3	≥	≥	PUNCT
ejpam-486	157	4	p	p	NOUN
ejpam-486	157	5	and	and	CCONJ
ejpam-486	157	6	f	f	PROPN
ejpam-486	157	7	(	(	PUNCT
ejpam-486	157	8	z	z	X
ejpam-486	157	9	)	)	PUNCT
ejpam-486	157	10	∈	∈	PROPN
ejpam-486	157	11	a	a	DET
ejpam-486	157	12	�	�	PROPN
ejpam-486	157	13	p	p	NOUN
ejpam-486	157	14	�	�	PROPN
ejpam-486	157	15	satisfies	satisfy	VERB
ejpam-486	157	16	�	�	PROPN
ejpam-486	157	17	�	�	PROPN
ejpam-486	157	18	�	�	PROPN
ejpam-486	157	19	qα−1	qα−1	PROPN
ejpam-486	157	20	β	β	NOUN
ejpam-486	157	21	,	,	PUNCT
ejpam-486	157	22	p	p	PROPN
ejpam-486	157	23	f	f	X
ejpam-486	157	24	(	(	PUNCT
ejpam-486	157	25	z	z	NOUN
ejpam-486	157	26	)	)	PUNCT
ejpam-486	157	27	�	�	PROPN
ejpam-486	157	28	�	�	PROPN
ejpam-486	157	29	�	�	PROPN
ejpam-486	157	30	<	<	X
ejpam-486	157	31	m	m	PROPN
ejpam-486	157	32	�	�	PROPN
ejpam-486	157	33	α	α	PROPN
ejpam-486	157	34	>	>	X
ejpam-486	157	35	1;β	1;β	NUM
ejpam-486	157	36	>	>	PUNCT
ejpam-486	157	37	−1	−1	NOUN
ejpam-486	157	38	;	;	PUNCT
ejpam-486	157	39	p	p	PROPN
ejpam-486	157	40	∈	∈	PROPN
ejpam-486	157	41	n	n	CCONJ
ejpam-486	157	42	;	;	PUNCT
ejpam-486	157	43	z	z	PROPN
ejpam-486	157	44	∈	∈	PROPN
ejpam-486	157	45	u	u	PROPN
ejpam-486	157	46	�	�	PROPN
ejpam-486	157	47	.	.	PUNCT
ejpam-486	158	1	then	then	ADV
ejpam-486	158	2	�	�	PROPN
ejpam-486	158	3	�	�	PROPN
ejpam-486	158	4	�	�	PROPN
ejpam-486	158	5	qαβ	qαβ	PROPN
ejpam-486	158	6	,	,	PUNCT
ejpam-486	158	7	p	p	NOUN
ejpam-486	158	8	f	f	X
ejpam-486	158	9	(	(	PUNCT
ejpam-486	158	10	z	z	NOUN
ejpam-486	158	11	)	)	PUNCT
ejpam-486	158	12	�	�	PROPN
ejpam-486	158	13	�	�	PROPN
ejpam-486	158	14	�	�	PROPN
ejpam-486	158	15	<	<	X
ejpam-486	158	16	m	m	PROPN
ejpam-486	158	17	(	(	PUNCT
ejpam-486	158	18	z	z	NOUN
ejpam-486	158	19	∈	∈	PROPN
ejpam-486	158	20	u	u	NOUN
ejpam-486	158	21	)	)	PUNCT
ejpam-486	158	22	.	.	PUNCT
ejpam-486	159	1	proof	proof	NOUN
ejpam-486	159	2	.	.	PUNCT
ejpam-486	160	1	this	this	PRON
ejpam-486	160	2	follows	follow	VERB
ejpam-486	160	3	from	from	ADP
ejpam-486	160	4	corollary	corollary	ADJ
ejpam-486	160	5	3	3	NUM
ejpam-486	160	6	by	by	ADP
ejpam-486	160	7	taking	take	VERB
ejpam-486	160	8	φ	φ	PROPN
ejpam-486	160	9	(	(	PUNCT
ejpam-486	160	10	u	u	PROPN
ejpam-486	160	11	,	,	PUNCT
ejpam-486	160	12	v	v	NOUN
ejpam-486	160	13	,	,	PUNCT
ejpam-486	160	14	w	w	NOUN
ejpam-486	160	15	;	;	PUNCT
ejpam-486	160	16	z	z	X
ejpam-486	160	17	)	)	PUNCT
ejpam-486	160	18	=	=	SYM
ejpam-486	160	19	v	v	NOUN
ejpam-486	160	20	=	=	PUNCT
ejpam-486	160	21	k+α+β−1	k+α+β−1	X
ejpam-486	160	22	α+β+p−1	α+β+p−1	NOUN
ejpam-486	160	23	meiθ	meiθ	NOUN
ejpam-486	160	24	.	.	PUNCT
ejpam-486	161	1	remark	remark	PROPN
ejpam-486	161	2	2	2	NUM
ejpam-486	161	3	.	.	PUNCT
ejpam-486	162	1	for	for	ADP
ejpam-486	162	2	m	m	PROPN
ejpam-486	162	3	=	=	SYM
ejpam-486	162	4	1	1	NUM
ejpam-486	162	5	,	,	PUNCT
ejpam-486	162	6	corollary	corollary	ADJ
ejpam-486	162	7	4	4	NUM
ejpam-486	162	8	yields	yield	NOUN
ejpam-486	162	9	the	the	DET
ejpam-486	162	10	result	result	NOUN
ejpam-486	162	11	obtained	obtain	VERB
ejpam-486	162	12	by	by	ADP
ejpam-486	162	13	aouf	aouf	PROPN
ejpam-486	163	1	[	[	X
ejpam-486	163	2	3	3	NUM
ejpam-486	163	3	,	,	PUNCT
ejpam-486	163	4	corollary	corollary	ADJ
ejpam-486	163	5	2	2	NUM
ejpam-486	163	6	]	]	PUNCT
ejpam-486	163	7	.	.	PUNCT
ejpam-486	164	1	definition	definition	NOUN
ejpam-486	164	2	5	5	NUM
ejpam-486	164	3	.	.	PUNCT
ejpam-486	165	1	let	let	VERB
ejpam-486	165	2	ω	ω	NUM
ejpam-486	165	3	be	be	AUX
ejpam-486	165	4	a	a	DET
ejpam-486	165	5	set	set	NOUN
ejpam-486	165	6	in	in	ADP
ejpam-486	165	7	c	c	PROPN
ejpam-486	165	8	and	and	CCONJ
ejpam-486	165	9	q(z	q(z	PROPN
ejpam-486	165	10	)	)	PUNCT
ejpam-486	165	11	∈	∈	PROPN
ejpam-486	165	12	f0	f0	PROPN
ejpam-486	165	13	∩	∩	PROPN
ejpam-486	165	14	h0	h0	PROPN
ejpam-486	165	15	.	.	PUNCT
ejpam-486	166	1	the	the	DET
ejpam-486	166	2	class	class	NOUN
ejpam-486	166	3	of	of	ADP
ejpam-486	166	4	admissible	admissible	ADJ
ejpam-486	166	5	functions	function	NOUN
ejpam-486	166	6	φq,1	φq,1	PROPN
ejpam-486	166	7	�	�	PROPN
ejpam-486	166	8	ω	ω	PROPN
ejpam-486	166	9	,	,	PUNCT
ejpam-486	166	10	q	q	PROPN
ejpam-486	166	11	�	�	PROPN
ejpam-486	166	12	consists	consist	VERB
ejpam-486	166	13	of	of	ADP
ejpam-486	166	14	those	those	DET
ejpam-486	166	15	functions	function	NOUN
ejpam-486	166	16	φ	φ	NOUN
ejpam-486	166	17	:	:	PUNCT
ejpam-486	167	1	c3	c3	PROPN
ejpam-486	167	2	×	×	PROPN
ejpam-486	167	3	u	u	PROPN
ejpam-486	167	4	→	→	SYM
ejpam-486	167	5	c	c	X
ejpam-486	167	6	that	that	PRON
ejpam-486	167	7	satisfy	satisfy	VERB
ejpam-486	167	8	the	the	DET
ejpam-486	167	9	admissibility	admissibility	NOUN
ejpam-486	167	10	condition	condition	NOUN
ejpam-486	167	11	:	:	PUNCT
ejpam-486	167	12	φ	φ	PROPN
ejpam-486	167	13	(	(	PUNCT
ejpam-486	167	14	u	u	NOUN
ejpam-486	167	15	,	,	PUNCT
ejpam-486	167	16	v	v	NOUN
ejpam-486	167	17	,	,	PUNCT
ejpam-486	167	18	w	w	NOUN
ejpam-486	167	19	;	;	PUNCT
ejpam-486	167	20	z	z	X
ejpam-486	167	21	)	)	PUNCT
ejpam-486	167	22	/∈	/∈	PUNCT
ejpam-486	168	1	ω	ω	NUM
ejpam-486	168	2	whenever	whenever	SCONJ
ejpam-486	168	3	u=	u=	ADV
ejpam-486	168	4	q	q	NOUN
ejpam-486	168	5	(	(	PUNCT
ejpam-486	168	6	ζ	ζ	NOUN
ejpam-486	168	7	)	)	PUNCT
ejpam-486	168	8	,	,	PUNCT
ejpam-486	168	9	v	v	X
ejpam-486	168	10	=	=	SYM
ejpam-486	168	11	kζq′	kζq′	NOUN
ejpam-486	168	12	(	(	PUNCT
ejpam-486	168	13	ζ	ζ	NOUN
ejpam-486	168	14	)	)	PUNCT
ejpam-486	168	15	+	+	CCONJ
ejpam-486	168	16	�	�	PROPN
ejpam-486	168	17	α+	α+	X
ejpam-486	168	18	β	β	NOUN
ejpam-486	168	19	+	+	CCONJ
ejpam-486	168	20	p−	p−	PROPN
ejpam-486	168	21	2	2	NUM
ejpam-486	168	22	�	�	PROPN
ejpam-486	168	23	q	q	PROPN
ejpam-486	168	24	(	(	PUNCT
ejpam-486	168	25	ζ	ζ	NOUN
ejpam-486	168	26	)	)	PUNCT
ejpam-486	168	27	α+	α+	PRON
ejpam-486	168	28	β	β	NOUN
ejpam-486	168	29	+	+	CCONJ
ejpam-486	168	30	p−	p−	PROPN
ejpam-486	168	31	1	1	NUM
ejpam-486	168	32	,	,	PUNCT
ejpam-486	168	33	ℜ	ℜ	PROPN
ejpam-486	168	34	¨	¨	NOUN
ejpam-486	168	35	�	�	PROPN
ejpam-486	168	36	α+	α+	PUNCT
ejpam-486	168	37	β	β	NOUN
ejpam-486	168	38	+	+	CCONJ
ejpam-486	168	39	p−	p−	PROPN
ejpam-486	168	40	2	2	NUM
ejpam-486	168	41	�	�	PROPN
ejpam-486	168	42	�	�	PROPN
ejpam-486	168	43	�	�	PROPN
ejpam-486	168	44	α+	α+	X
ejpam-486	168	45	β	β	NOUN
ejpam-486	168	46	+	+	CCONJ
ejpam-486	168	47	p−	p−	PROPN
ejpam-486	168	48	1	1	NUM
ejpam-486	168	49	�	�	PROPN
ejpam-486	168	50	w	w	PROPN
ejpam-486	168	51	−	−	PROPN
ejpam-486	168	52	�	�	PROPN
ejpam-486	168	53	α+	α+	PUNCT
ejpam-486	168	54	β	β	NOUN
ejpam-486	168	55	+	+	CCONJ
ejpam-486	168	56	p−	p−	PROPN
ejpam-486	168	57	3	3	NUM
ejpam-486	168	58	�	�	PROPN
ejpam-486	168	59	u	u	PROPN
ejpam-486	168	60	�	�	PROPN
ejpam-486	168	61	�	�	PROPN
ejpam-486	168	62	α+	α+	X
ejpam-486	168	63	β	β	NOUN
ejpam-486	168	64	+	+	CCONJ
ejpam-486	168	65	p−	p−	PROPN
ejpam-486	168	66	1	1	NUM
ejpam-486	168	67	�	�	PROPN
ejpam-486	168	68	v	v	ADP
ejpam-486	168	69	−	−	PROPN
ejpam-486	168	70	�	�	PROPN
ejpam-486	168	71	α+	α+	PUNCT
ejpam-486	168	72	β	β	NOUN
ejpam-486	169	1	+	+	CCONJ
ejpam-486	169	2	p−	p−	PROPN
ejpam-486	169	3	2	2	NUM
ejpam-486	169	4	�	�	PROPN
ejpam-486	169	5	u	u	NOUN
ejpam-486	169	6	−	−	PROPN
ejpam-486	169	7	2	2	NUM
ejpam-486	169	8	�	�	PROPN
ejpam-486	169	9	α+	α+	PUNCT
ejpam-486	169	10	β	β	X
ejpam-486	169	11	�	�	PROPN
ejpam-486	169	12	+	+	CCONJ
ejpam-486	169	13	5	5	NUM
ejpam-486	169	14	«	«	PUNCT
ejpam-486	169	15	≥	≥	NUM
ejpam-486	169	16	kℜ	kℜ	X
ejpam-486	169	17	(	(	PUNCT
ejpam-486	169	18	1	1	NUM
ejpam-486	169	19	+	+	NUM
ejpam-486	169	20	ζq	ζq	NOUN
ejpam-486	169	21	′′	′′	PROPN
ejpam-486	169	22	(	(	PUNCT
ejpam-486	169	23	ζ	ζ	NOUN
ejpam-486	169	24	)	)	PUNCT
ejpam-486	169	25	q′	q′	NOUN
ejpam-486	169	26	(	(	PUNCT
ejpam-486	169	27	ζ	ζ	NOUN
ejpam-486	169	28	)	)	PUNCT
ejpam-486	169	29	)	)	PUNCT
ejpam-486	169	30	,	,	PUNCT
ejpam-486	169	31	where	where	SCONJ
ejpam-486	169	32	z	z	PROPN
ejpam-486	169	33	∈	∈	PROPN
ejpam-486	169	34	u	u	NOUN
ejpam-486	169	35	,	,	PUNCT
ejpam-486	169	36	ζ	ζ	PROPN
ejpam-486	169	37	∈	∈	PROPN
ejpam-486	169	38	∂	∂	NUM
ejpam-486	169	39	u\e	u\e	PROPN
ejpam-486	169	40	�	�	PROPN
ejpam-486	169	41	q	q	PROPN
ejpam-486	169	42	�	�	PROPN
ejpam-486	169	43	,	,	PUNCT
ejpam-486	169	44	α	α	NOUN
ejpam-486	169	45	>	>	X
ejpam-486	169	46	2,β	2,β	X
ejpam-486	169	47	>	>	PUNCT
ejpam-486	169	48	−1	−1	NOUN
ejpam-486	169	49	;	;	PUNCT
ejpam-486	169	50	p	p	PROPN
ejpam-486	169	51	∈	∈	PROPN
ejpam-486	169	52	n	n	NOUN
ejpam-486	169	53	and	and	CCONJ
ejpam-486	169	54	k	k	PROPN
ejpam-486	169	55	≥	≥	NUM
ejpam-486	169	56	1	1	NUM
ejpam-486	169	57	.	.	PUNCT
ejpam-486	169	58	theorem	theorem	NOUN
ejpam-486	169	59	5	5	NUM
ejpam-486	169	60	.	.	PUNCT
ejpam-486	169	61	let	let	VERB
ejpam-486	169	62	φ	φ	NUM
ejpam-486	169	63	∈	∈	PROPN
ejpam-486	169	64	φq,1	φq,1	PROPN
ejpam-486	169	65	�	�	PROPN
ejpam-486	169	66	ω	ω	PROPN
ejpam-486	169	67	,	,	PUNCT
ejpam-486	169	68	q	q	PROPN
ejpam-486	169	69	�	�	PROPN
ejpam-486	169	70	.	.	PUNCT
ejpam-486	170	1	if	if	SCONJ
ejpam-486	170	2	f	f	PROPN
ejpam-486	170	3	(	(	PUNCT
ejpam-486	170	4	z	z	NOUN
ejpam-486	170	5	)	)	PUNCT
ejpam-486	170	6	∈	∈	PROPN
ejpam-486	170	7	a	a	DET
ejpam-486	170	8	�	�	PROPN
ejpam-486	170	9	p	p	PROPN
ejpam-486	170	10	�	�	PROPN
ejpam-486	170	11	satisfies	satisfie	NOUN
ejpam-486	170	12	(	(	PUNCT
ejpam-486	170	13	φ	φ	PROPN
ejpam-486	170	14	qα	qα	PROPN
ejpam-486	170	15	β	β	PROPN
ejpam-486	170	16	,	,	PUNCT
ejpam-486	170	17	p	p	PROPN
ejpam-486	170	18	f	f	X
ejpam-486	170	19	(	(	PUNCT
ejpam-486	170	20	z	z	NOUN
ejpam-486	170	21	)	)	PUNCT
ejpam-486	170	22	zp−1	zp−1	PROPN
ejpam-486	170	23	,	,	PUNCT
ejpam-486	170	24	qα−1	qα−1	PROPN
ejpam-486	170	25	β	β	X
ejpam-486	170	26	,	,	PUNCT
ejpam-486	170	27	p	p	PROPN
ejpam-486	170	28	f	f	X
ejpam-486	170	29	(	(	PUNCT
ejpam-486	170	30	z	z	NOUN
ejpam-486	170	31	)	)	PUNCT
ejpam-486	170	32	zp−1	zp−1	PROPN
ejpam-486	170	33	,	,	PUNCT
ejpam-486	170	34	qα−2	qα−2	PROPN
ejpam-486	170	35	β	β	PROPN
ejpam-486	170	36	,	,	PUNCT
ejpam-486	170	37	p	p	PROPN
ejpam-486	170	38	f	f	X
ejpam-486	170	39	(	(	PUNCT
ejpam-486	170	40	z	z	NOUN
ejpam-486	170	41	)	)	PUNCT
ejpam-486	170	42	zp−1	zp−1	PROPN
ejpam-486	170	43	;	;	PUNCT
ejpam-486	170	44	z	z	X
ejpam-486	170	45	!	!	PUNCT
ejpam-486	171	1	:	:	PUNCT
ejpam-486	171	2	z	z	X
ejpam-486	171	3	∈	∈	PROPN
ejpam-486	171	4	u	u	PROPN
ejpam-486	171	5	)	)	PUNCT
ejpam-486	172	1	⊂	⊂	PROPN
ejpam-486	172	2	ω	ω	PROPN
ejpam-486	172	3	�	�	PROPN
ejpam-486	172	4	α	α	X
ejpam-486	172	5	>	>	X
ejpam-486	172	6	2;β	2;β	NUM
ejpam-486	172	7	>	>	SYM
ejpam-486	172	8	−1	−1	NOUN
ejpam-486	172	9	�	�	PROPN
ejpam-486	172	10	,	,	PUNCT
ejpam-486	172	11	(	(	PUNCT
ejpam-486	172	12	15	15	NUM
ejpam-486	172	13	)	)	PUNCT
ejpam-486	172	14	then	then	ADV
ejpam-486	172	15	qα	qα	PROPN
ejpam-486	172	16	β	β	PROPN
ejpam-486	172	17	,	,	PUNCT
ejpam-486	172	18	p	p	PROPN
ejpam-486	172	19	f	f	X
ejpam-486	172	20	(	(	PUNCT
ejpam-486	172	21	z	z	NOUN
ejpam-486	172	22	)	)	PUNCT
ejpam-486	172	23	zp−1	zp−1	PROPN
ejpam-486	172	24	≺	≺	NOUN
ejpam-486	172	25	q	q	PUNCT
ejpam-486	172	26	(	(	PUNCT
ejpam-486	172	27	z	z	NOUN
ejpam-486	172	28	)	)	PUNCT
ejpam-486	172	29	(	(	PUNCT
ejpam-486	172	30	z	z	NOUN
ejpam-486	172	31	∈	∈	PROPN
ejpam-486	172	32	u	u	NOUN
ejpam-486	172	33	)	)	PUNCT
ejpam-486	172	34	.	.	PUNCT
ejpam-486	173	1	m.	m.	PROPN
ejpam-486	173	2	aouf	aouf	PROPN
ejpam-486	173	3	,	,	PUNCT
ejpam-486	173	4	t.	t.	PROPN
ejpam-486	173	5	seoudy	seoudy	PROPN
ejpam-486	173	6	/	/	SYM
ejpam-486	173	7	eur	eur	PROPN
ejpam-486	173	8	.	.	PUNCT
ejpam-486	174	1	j.	j.	PROPN
ejpam-486	174	2	pure	pure	PROPN
ejpam-486	174	3	appl	appl	PROPN
ejpam-486	174	4	.	.	PROPN
ejpam-486	174	5	math	math	PROPN
ejpam-486	174	6	,	,	PUNCT
ejpam-486	174	7	3	3	NUM
ejpam-486	174	8	(	(	PUNCT
ejpam-486	174	9	2010	2010	NUM
ejpam-486	174	10	)	)	PUNCT
ejpam-486	174	11	,	,	PUNCT
ejpam-486	174	12	26	26	NUM
ejpam-486	174	13	-	-	SYM
ejpam-486	174	14	44	44	NUM
ejpam-486	174	15	33	33	NUM
ejpam-486	174	16	proof	proof	NOUN
ejpam-486	174	17	.	.	PUNCT
ejpam-486	175	1	define	define	VERB
ejpam-486	175	2	an	an	DET
ejpam-486	175	3	analytic	analytic	ADJ
ejpam-486	175	4	function	function	NOUN
ejpam-486	175	5	g(z	g(z	PROPN
ejpam-486	175	6	)	)	PUNCT
ejpam-486	175	7	in	in	ADP
ejpam-486	175	8	u	u	NOUN
ejpam-486	175	9	by	by	ADP
ejpam-486	175	10	g	g	PROPN
ejpam-486	175	11	(	(	PUNCT
ejpam-486	175	12	z	z	NOUN
ejpam-486	175	13	)	)	PUNCT
ejpam-486	175	14	=	=	SYM
ejpam-486	175	15	qα	qα	PROPN
ejpam-486	175	16	β	β	PROPN
ejpam-486	175	17	,	,	PUNCT
ejpam-486	175	18	p	p	PROPN
ejpam-486	175	19	f	f	X
ejpam-486	175	20	(	(	PUNCT
ejpam-486	175	21	z	z	NOUN
ejpam-486	175	22	)	)	PUNCT
ejpam-486	175	23	zp−1	zp−1	PROPN
ejpam-486	175	24	�	�	PROPN
ejpam-486	175	25	α	α	PROPN
ejpam-486	175	26	>	>	X
ejpam-486	175	27	2	2	NUM
ejpam-486	175	28	;	;	PUNCT
ejpam-486	175	29	β	β	X
ejpam-486	175	30	>	>	X
ejpam-486	175	31	−1	−1	NOUN
ejpam-486	175	32	;	;	PUNCT
ejpam-486	175	33	p	p	PROPN
ejpam-486	175	34	∈	∈	PROPN
ejpam-486	175	35	n	n	CCONJ
ejpam-486	175	36	;	;	PUNCT
ejpam-486	175	37	z	z	PROPN
ejpam-486	175	38	∈	∈	PROPN
ejpam-486	175	39	u	u	PROPN
ejpam-486	175	40	�	�	PROPN
ejpam-486	175	41	.	.	PUNCT
ejpam-486	176	1	(	(	PUNCT
ejpam-486	176	2	16	16	NUM
ejpam-486	176	3	)	)	PUNCT
ejpam-486	176	4	by	by	ADP
ejpam-486	176	5	making	make	VERB
ejpam-486	176	6	use	use	NOUN
ejpam-486	176	7	of	of	ADP
ejpam-486	176	8	(	(	PUNCT
ejpam-486	176	9	4	4	NUM
ejpam-486	176	10	)	)	PUNCT
ejpam-486	176	11	and	and	CCONJ
ejpam-486	176	12	(	(	PUNCT
ejpam-486	176	13	16	16	NUM
ejpam-486	176	14	)	)	PUNCT
ejpam-486	176	15	,	,	PUNCT
ejpam-486	176	16	we	we	PRON
ejpam-486	176	17	get	get	VERB
ejpam-486	176	18	qα−1	qα−1	ADJ
ejpam-486	176	19	β	β	NOUN
ejpam-486	176	20	,	,	PUNCT
ejpam-486	176	21	p	p	PROPN
ejpam-486	176	22	f	f	X
ejpam-486	176	23	(	(	PUNCT
ejpam-486	176	24	z	z	NOUN
ejpam-486	176	25	)	)	PUNCT
ejpam-486	176	26	zp−1	zp−1	PROPN
ejpam-486	176	27	=	=	PUNCT
ejpam-486	176	28	zg′	zg′	PROPN
ejpam-486	176	29	(	(	PUNCT
ejpam-486	176	30	z	z	NOUN
ejpam-486	176	31	)	)	PUNCT
ejpam-486	177	1	+	+	CCONJ
ejpam-486	177	2	�	�	PROPN
ejpam-486	177	3	α+	α+	X
ejpam-486	177	4	β	β	NOUN
ejpam-486	177	5	+	+	CCONJ
ejpam-486	177	6	p−	p−	PROPN
ejpam-486	177	7	2	2	NUM
ejpam-486	177	8	�	�	PROPN
ejpam-486	177	9	g	g	PROPN
ejpam-486	177	10	(	(	PUNCT
ejpam-486	177	11	z	z	NOUN
ejpam-486	177	12	)	)	PUNCT
ejpam-486	177	13	α+	α+	PRON
ejpam-486	177	14	β	β	X
ejpam-486	178	1	+	+	CCONJ
ejpam-486	178	2	p−	p−	NOUN
ejpam-486	178	3	1	1	NUM
ejpam-486	178	4	.	.	PUNCT
ejpam-486	179	1	(	(	PUNCT
ejpam-486	179	2	17	17	NUM
ejpam-486	179	3	)	)	PUNCT
ejpam-486	179	4	further	further	ADJ
ejpam-486	179	5	computations	computation	NOUN
ejpam-486	179	6	show	show	VERB
ejpam-486	179	7	that	that	SCONJ
ejpam-486	179	8	qα−2	qα−2	NOUN
ejpam-486	179	9	β	β	PROPN
ejpam-486	179	10	,	,	PUNCT
ejpam-486	179	11	p	p	PROPN
ejpam-486	179	12	f	f	X
ejpam-486	179	13	(	(	PUNCT
ejpam-486	179	14	z	z	NOUN
ejpam-486	179	15	)	)	PUNCT
ejpam-486	179	16	zp−1	zp−1	PROPN
ejpam-486	179	17	=	=	SYM
ejpam-486	179	18	z2	z2	PROPN
ejpam-486	179	19	g	g	PROPN
ejpam-486	179	20	′′	′′	PROPN
ejpam-486	179	21	(	(	PUNCT
ejpam-486	179	22	z	z	NOUN
ejpam-486	179	23	)	)	PUNCT
ejpam-486	179	24	+	+	CCONJ
ejpam-486	179	25	2	2	NUM
ejpam-486	179	26	�	�	NOUN
ejpam-486	179	27	α+	α+	PUNCT
ejpam-486	179	28	β	β	NOUN
ejpam-486	180	1	+	+	CCONJ
ejpam-486	180	2	p−	p−	PROPN
ejpam-486	180	3	2	2	NUM
ejpam-486	180	4	�	�	PROPN
ejpam-486	180	5	zg′	zg′	PROPN
ejpam-486	180	6	(	(	PUNCT
ejpam-486	180	7	z	z	NOUN
ejpam-486	180	8	)	)	PUNCT
ejpam-486	180	9	+	+	CCONJ
ejpam-486	180	10	�	�	PROPN
ejpam-486	180	11	α+	α+	X
ejpam-486	180	12	β	β	NOUN
ejpam-486	180	13	+	+	CCONJ
ejpam-486	180	14	p−	p−	PROPN
ejpam-486	180	15	2	2	NUM
ejpam-486	180	16	�	�	PROPN
ejpam-486	180	17	�	�	PROPN
ejpam-486	180	18	α+	α+	X
ejpam-486	180	19	β	β	NOUN
ejpam-486	180	20	+	+	CCONJ
ejpam-486	180	21	p−	p−	PROPN
ejpam-486	180	22	3	3	NUM
ejpam-486	180	23	�	�	PROPN
ejpam-486	180	24	g	g	PROPN
ejpam-486	180	25	(	(	PUNCT
ejpam-486	180	26	z	z	PROPN
ejpam-486	180	27	)	)	PUNCT
ejpam-486	180	28	�	�	PROPN
ejpam-486	180	29	α+	α+	PUNCT
ejpam-486	180	30	β	β	NOUN
ejpam-486	180	31	+	+	CCONJ
ejpam-486	180	32	p−	p−	PROPN
ejpam-486	180	33	1	1	NUM
ejpam-486	180	34	�	�	PROPN
ejpam-486	180	35	�	�	PROPN
ejpam-486	180	36	α+	α+	PUNCT
ejpam-486	180	37	β	β	NOUN
ejpam-486	180	38	+	+	CCONJ
ejpam-486	180	39	p−	p−	PROPN
ejpam-486	180	40	2	2	NUM
ejpam-486	180	41	�	�	NOUN
ejpam-486	180	42	.	.	PUNCT
ejpam-486	181	1	(	(	PUNCT
ejpam-486	181	2	18	18	NUM
ejpam-486	181	3	)	)	PUNCT
ejpam-486	181	4	define	define	VERB
ejpam-486	181	5	the	the	DET
ejpam-486	181	6	transformations	transformation	NOUN
ejpam-486	181	7	from	from	ADP
ejpam-486	181	8	c3	c3	PROPN
ejpam-486	181	9	to	to	ADP
ejpam-486	181	10	c	c	NOUN
ejpam-486	181	11	by	by	ADP
ejpam-486	181	12	u	u	NOUN
ejpam-486	181	13	=	=	SYM
ejpam-486	181	14	r	r	PROPN
ejpam-486	181	15	,	,	PUNCT
ejpam-486	181	16	v	v	NOUN
ejpam-486	181	17	=	=	PUNCT
ejpam-486	181	18	s+	s+	NUM
ejpam-486	181	19	�	�	PROPN
ejpam-486	181	20	α+	α+	PUNCT
ejpam-486	181	21	β	β	X
ejpam-486	181	22	+	+	CCONJ
ejpam-486	181	23	p−	p−	NOUN
ejpam-486	181	24	2	2	NUM
ejpam-486	181	25	�	�	NOUN
ejpam-486	181	26	r	r	NOUN
ejpam-486	181	27	α+	α+	NOUN
ejpam-486	181	28	β	β	NOUN
ejpam-486	181	29	+	+	CCONJ
ejpam-486	181	30	p−	p−	NOUN
ejpam-486	181	31	1	1	NUM
ejpam-486	181	32	,	,	PUNCT
ejpam-486	181	33	w	w	PROPN
ejpam-486	181	34	=	=	SYM
ejpam-486	181	35	t	t	PROPN
ejpam-486	181	36	+	+	CCONJ
ejpam-486	181	37	2	2	NUM
ejpam-486	181	38	�	�	NOUN
ejpam-486	181	39	α+	α+	PUNCT
ejpam-486	181	40	β	β	NOUN
ejpam-486	181	41	+	+	CCONJ
ejpam-486	181	42	p−	p−	PROPN
ejpam-486	181	43	2	2	NUM
ejpam-486	181	44	�	�	PROPN
ejpam-486	181	45	s+	s+	PUNCT
ejpam-486	181	46	�	�	PROPN
ejpam-486	181	47	α+	α+	PUNCT
ejpam-486	181	48	β	β	X
ejpam-486	181	49	+	+	CCONJ
ejpam-486	181	50	p−	p−	PROPN
ejpam-486	181	51	2	2	NUM
ejpam-486	181	52	�	�	PROPN
ejpam-486	181	53	�	�	PROPN
ejpam-486	181	54	α+	α+	X
ejpam-486	181	55	β	β	NOUN
ejpam-486	181	56	+	+	CCONJ
ejpam-486	181	57	p−	p−	PROPN
ejpam-486	181	58	3	3	NUM
ejpam-486	181	59	�	�	PROPN
ejpam-486	181	60	r	r	NOUN
ejpam-486	181	61	�	�	PROPN
ejpam-486	181	62	α+	α+	X
ejpam-486	181	63	β	β	NOUN
ejpam-486	181	64	+	+	CCONJ
ejpam-486	181	65	p−	p−	PROPN
ejpam-486	181	66	1	1	NUM
ejpam-486	181	67	�	�	PROPN
ejpam-486	181	68	�	�	PROPN
ejpam-486	181	69	α+β	α+β	PROPN
ejpam-486	181	70	+	+	CCONJ
ejpam-486	181	71	p−	p−	PROPN
ejpam-486	181	72	2	2	NUM
ejpam-486	181	73	�	�	NOUN
ejpam-486	181	74	.	.	PUNCT
ejpam-486	182	1	(	(	PUNCT
ejpam-486	182	2	19	19	NUM
ejpam-486	182	3	)	)	PUNCT
ejpam-486	182	4	let	let	VERB
ejpam-486	182	5	ψ	ψ	X
ejpam-486	182	6	(	(	PUNCT
ejpam-486	182	7	r	r	NOUN
ejpam-486	182	8	,	,	PUNCT
ejpam-486	182	9	s	s	PROPN
ejpam-486	182	10	,	,	PUNCT
ejpam-486	182	11	t	t	PROPN
ejpam-486	182	12	;	;	PUNCT
ejpam-486	182	13	z	z	X
ejpam-486	183	1	)	)	PUNCT
ejpam-486	183	2	=	=	SYM
ejpam-486	183	3	φ	φ	PROPN
ejpam-486	183	4	(	(	PUNCT
ejpam-486	183	5	u	u	NOUN
ejpam-486	183	6	,	,	PUNCT
ejpam-486	183	7	v	v	NOUN
ejpam-486	183	8	,	,	PUNCT
ejpam-486	183	9	w	w	NOUN
ejpam-486	183	10	;	;	PUNCT
ejpam-486	183	11	z	z	X
ejpam-486	183	12	)	)	PUNCT
ejpam-486	183	13	=	=	PUNCT
ejpam-486	183	14	φ	φ	PROPN
ejpam-486	183	15	�	�	PROPN
ejpam-486	183	16	r	r	PROPN
ejpam-486	183	17	,	,	PUNCT
ejpam-486	183	18	s+	s+	PUNCT
ejpam-486	183	19	�	�	PROPN
ejpam-486	183	20	α+	α+	PUNCT
ejpam-486	183	21	β	β	X
ejpam-486	183	22	+	+	CCONJ
ejpam-486	183	23	p−	p−	NOUN
ejpam-486	183	24	2	2	NUM
ejpam-486	183	25	�	�	NOUN
ejpam-486	183	26	r	r	NOUN
ejpam-486	183	27	α+β	α+β	PROPN
ejpam-486	183	28	+	+	CCONJ
ejpam-486	183	29	p−	p−	NOUN
ejpam-486	183	30	1	1	NUM
ejpam-486	183	31	,	,	PUNCT
ejpam-486	183	32	t	t	PROPN
ejpam-486	183	33	+	+	CCONJ
ejpam-486	183	34	2	2	NUM
ejpam-486	183	35	�	�	NOUN
ejpam-486	183	36	α+	α+	PUNCT
ejpam-486	183	37	β	β	NOUN
ejpam-486	183	38	+	+	CCONJ
ejpam-486	183	39	p−	p−	PROPN
ejpam-486	183	40	2	2	NUM
ejpam-486	183	41	�	�	PROPN
ejpam-486	183	42	s+	s+	PUNCT
ejpam-486	183	43	�	�	PROPN
ejpam-486	183	44	α+	α+	PUNCT
ejpam-486	183	45	β	β	X
ejpam-486	184	1	+	+	CCONJ
ejpam-486	184	2	p−	p−	PROPN
ejpam-486	184	3	2	2	NUM
ejpam-486	184	4	�	�	PROPN
ejpam-486	184	5	�	�	PROPN
ejpam-486	184	6	α+β	α+β	PROPN
ejpam-486	184	7	+	+	CCONJ
ejpam-486	184	8	p−	p−	NOUN
ejpam-486	184	9	3	3	NUM
ejpam-486	184	10	�	�	NOUN
ejpam-486	184	11	r	r	NOUN
ejpam-486	184	12	�	�	PROPN
ejpam-486	184	13	α+	α+	X
ejpam-486	184	14	β	β	NOUN
ejpam-486	184	15	+	+	CCONJ
ejpam-486	184	16	p−	p−	PROPN
ejpam-486	184	17	1	1	NUM
ejpam-486	184	18	�	�	PROPN
ejpam-486	184	19	�	�	PROPN
ejpam-486	184	20	α+	α+	PUNCT
ejpam-486	184	21	β	β	NOUN
ejpam-486	184	22	+	+	CCONJ
ejpam-486	184	23	p−	p−	PROPN
ejpam-486	184	24	2	2	NUM
ejpam-486	184	25	�	�	NOUN
ejpam-486	184	26	;	;	PUNCT
ejpam-486	184	27	z	z	PROPN
ejpam-486	184	28	�	�	PROPN
ejpam-486	184	29	.	.	PUNCT
ejpam-486	185	1	(	(	PUNCT
ejpam-486	185	2	20	20	NUM
ejpam-486	185	3	)	)	PUNCT
ejpam-486	185	4	the	the	DET
ejpam-486	185	5	proof	proof	NOUN
ejpam-486	185	6	shall	shall	AUX
ejpam-486	185	7	make	make	VERB
ejpam-486	185	8	use	use	NOUN
ejpam-486	185	9	of	of	ADP
ejpam-486	185	10	lemma	lemma	PROPN
ejpam-486	185	11	1	1	NUM
ejpam-486	185	12	.	.	PUNCT
ejpam-486	185	13	using	use	VERB
ejpam-486	185	14	equations	equation	NOUN
ejpam-486	185	15	(	(	PUNCT
ejpam-486	185	16	16)-(18	16)-(18	NOUN
ejpam-486	185	17	)	)	PUNCT
ejpam-486	185	18	,	,	PUNCT
ejpam-486	185	19	and	and	CCONJ
ejpam-486	185	20	from	from	ADP
ejpam-486	185	21	(	(	PUNCT
ejpam-486	185	22	20	20	NUM
ejpam-486	185	23	)	)	PUNCT
ejpam-486	185	24	,	,	PUNCT
ejpam-486	185	25	we	we	PRON
ejpam-486	185	26	obtain	obtain	VERB
ejpam-486	185	27	ψ	ψ	ADP
ejpam-486	185	28	�	�	PROPN
ejpam-486	185	29	g	g	PROPN
ejpam-486	185	30	(	(	PUNCT
ejpam-486	185	31	z	z	PROPN
ejpam-486	185	32	)	)	PUNCT
ejpam-486	185	33	,	,	PUNCT
ejpam-486	185	34	zg′	zg′	X
ejpam-486	185	35	(	(	PUNCT
ejpam-486	185	36	z	z	NOUN
ejpam-486	185	37	)	)	PUNCT
ejpam-486	185	38	,	,	PUNCT
ejpam-486	185	39	z2	z2	PROPN
ejpam-486	185	40	g	g	PROPN
ejpam-486	185	41	′′	′′	PROPN
ejpam-486	185	42	(	(	PUNCT
ejpam-486	185	43	z	z	PROPN
ejpam-486	185	44	)	)	PUNCT
ejpam-486	185	45	;	;	PUNCT
ejpam-486	185	46	z	z	PROPN
ejpam-486	185	47	�	�	PROPN
ejpam-486	185	48	=	=	SYM
ejpam-486	185	49	φ	φ	PROPN
ejpam-486	185	50	�	�	PROPN
ejpam-486	185	51	qα	qα	PROPN
ejpam-486	185	52	β	β	PROPN
ejpam-486	185	53	,	,	PUNCT
ejpam-486	185	54	p	p	PROPN
ejpam-486	185	55	f	f	X
ejpam-486	185	56	(	(	PUNCT
ejpam-486	185	57	z	z	NOUN
ejpam-486	185	58	)	)	PUNCT
ejpam-486	185	59	zp−1	zp−1	PROPN
ejpam-486	185	60	,	,	PUNCT
ejpam-486	185	61	qα	qα	PROPN
ejpam-486	185	62	β	β	PROPN
ejpam-486	185	63	,	,	PUNCT
ejpam-486	185	64	p	p	PROPN
ejpam-486	185	65	f	f	X
ejpam-486	185	66	(	(	PUNCT
ejpam-486	185	67	z	z	NOUN
ejpam-486	185	68	)	)	PUNCT
ejpam-486	185	69	zp−1	zp−1	PROPN
ejpam-486	185	70	,	,	PUNCT
ejpam-486	185	71	qα	qα	PROPN
ejpam-486	185	72	β	β	PROPN
ejpam-486	185	73	,	,	PUNCT
ejpam-486	185	74	p	p	PROPN
ejpam-486	185	75	f	f	X
ejpam-486	185	76	(	(	PUNCT
ejpam-486	185	77	z	z	NOUN
ejpam-486	185	78	)	)	PUNCT
ejpam-486	185	79	zp−1	zp−1	PROPN
ejpam-486	185	80	;	;	PUNCT
ejpam-486	185	81	z	z	PROPN
ejpam-486	185	82	�	�	PROPN
ejpam-486	185	83	.	.	PUNCT
ejpam-486	186	1	(	(	PUNCT
ejpam-486	186	2	21	21	NUM
ejpam-486	186	3	)	)	PUNCT
ejpam-486	186	4	hence	hence	ADV
ejpam-486	186	5	(	(	PUNCT
ejpam-486	186	6	15	15	NUM
ejpam-486	186	7	)	)	PUNCT
ejpam-486	186	8	becomes	become	VERB
ejpam-486	186	9	ψ	ψ	ADP
ejpam-486	186	10	�	�	PROPN
ejpam-486	186	11	g	g	PROPN
ejpam-486	186	12	(	(	PUNCT
ejpam-486	186	13	z	z	PROPN
ejpam-486	186	14	)	)	PUNCT
ejpam-486	186	15	,	,	PUNCT
ejpam-486	186	16	zg′	zg′	X
ejpam-486	186	17	(	(	PUNCT
ejpam-486	186	18	z	z	NOUN
ejpam-486	186	19	)	)	PUNCT
ejpam-486	186	20	,	,	PUNCT
ejpam-486	186	21	z2	z2	PROPN
ejpam-486	186	22	g	g	PROPN
ejpam-486	186	23	′′	′′	PROPN
ejpam-486	186	24	(	(	PUNCT
ejpam-486	186	25	z	z	PROPN
ejpam-486	186	26	)	)	PUNCT
ejpam-486	186	27	;	;	PUNCT
ejpam-486	186	28	z	z	NOUN
ejpam-486	186	29	�	�	PROPN
ejpam-486	186	30	∈	∈	PROPN
ejpam-486	186	31	ω	ω	PROPN
ejpam-486	186	32	.	.	PUNCT
ejpam-486	187	1	the	the	DET
ejpam-486	187	2	proof	proof	NOUN
ejpam-486	187	3	is	be	AUX
ejpam-486	187	4	completed	complete	VERB
ejpam-486	187	5	if	if	SCONJ
ejpam-486	187	6	it	it	PRON
ejpam-486	187	7	can	can	AUX
ejpam-486	187	8	be	be	AUX
ejpam-486	187	9	shown	show	VERB
ejpam-486	187	10	that	that	SCONJ
ejpam-486	187	11	the	the	DET
ejpam-486	187	12	admissibility	admissibility	NOUN
ejpam-486	187	13	condition	condition	NOUN
ejpam-486	187	14	for	for	ADP
ejpam-486	187	15	φ	φ	PROPN
ejpam-486	187	16	∈	∈	PROPN
ejpam-486	187	17	φq,1	φq,1	PROPN
ejpam-486	187	18	�	�	PROPN
ejpam-486	187	19	ω	ω	PROPN
ejpam-486	187	20	,	,	PUNCT
ejpam-486	187	21	q	q	PROPN
ejpam-486	187	22	�	�	PROPN
ejpam-486	187	23	is	be	AUX
ejpam-486	187	24	equivalent	equivalent	ADJ
ejpam-486	187	25	to	to	ADP
ejpam-486	187	26	the	the	DET
ejpam-486	187	27	admissibility	admissibility	NOUN
ejpam-486	187	28	condition	condition	NOUN
ejpam-486	187	29	for	for	ADP
ejpam-486	187	30	ψ	ψ	PRON
ejpam-486	187	31	as	as	SCONJ
ejpam-486	187	32	given	give	VERB
ejpam-486	187	33	in	in	ADP
ejpam-486	187	34	definition	definition	NOUN
ejpam-486	187	35	1	1	NUM
ejpam-486	187	36	.	.	PUNCT
ejpam-486	188	1	note	note	VERB
ejpam-486	188	2	that	that	SCONJ
ejpam-486	188	3	t	t	PROPN
ejpam-486	188	4	s	s	PART
ejpam-486	188	5	+	+	NUM
ejpam-486	188	6	1=	1=	X
ejpam-486	188	7	�	�	X
ejpam-486	188	8	α+	α+	PUNCT
ejpam-486	188	9	β	β	NOUN
ejpam-486	188	10	+	+	CCONJ
ejpam-486	188	11	p−	p−	PROPN
ejpam-486	188	12	2	2	NUM
ejpam-486	188	13	�	�	PROPN
ejpam-486	188	14	�	�	PROPN
ejpam-486	188	15	�	�	PROPN
ejpam-486	188	16	α+	α+	X
ejpam-486	188	17	β	β	NOUN
ejpam-486	188	18	+	+	CCONJ
ejpam-486	188	19	p−	p−	PROPN
ejpam-486	188	20	1	1	NUM
ejpam-486	188	21	�	�	PROPN
ejpam-486	188	22	w	w	PROPN
ejpam-486	188	23	−	−	PROPN
ejpam-486	188	24	�	�	PROPN
ejpam-486	188	25	α+	α+	PUNCT
ejpam-486	188	26	β	β	NOUN
ejpam-486	188	27	+	+	CCONJ
ejpam-486	188	28	p−	p−	PROPN
ejpam-486	188	29	3	3	NUM
ejpam-486	188	30	�	�	PROPN
ejpam-486	188	31	u	u	PROPN
ejpam-486	188	32	�	�	PROPN
ejpam-486	188	33	�	�	PROPN
ejpam-486	188	34	α+	α+	X
ejpam-486	188	35	β	β	NOUN
ejpam-486	188	36	+	+	CCONJ
ejpam-486	188	37	p−	p−	PROPN
ejpam-486	188	38	1	1	NUM
ejpam-486	188	39	�	�	PROPN
ejpam-486	188	40	v	v	ADP
ejpam-486	188	41	−	−	PROPN
ejpam-486	188	42	�	�	PROPN
ejpam-486	188	43	α+	α+	PUNCT
ejpam-486	188	44	β	β	NOUN
ejpam-486	188	45	+	+	CCONJ
ejpam-486	188	46	p−	p−	PROPN
ejpam-486	188	47	2	2	NUM
ejpam-486	188	48	�	�	PROPN
ejpam-486	188	49	u	u	NOUN
ejpam-486	188	50	−	−	PROPN
ejpam-486	188	51	2	2	NUM
ejpam-486	188	52	�	�	PROPN
ejpam-486	188	53	α+	α+	PUNCT
ejpam-486	188	54	β	β	X
ejpam-486	188	55	�	�	PROPN
ejpam-486	188	56	+	+	CCONJ
ejpam-486	188	57	5	5	NUM
ejpam-486	188	58	,	,	PUNCT
ejpam-486	188	59	and	and	CCONJ
ejpam-486	188	60	hence	hence	ADV
ejpam-486	188	61	ψ	ψ	VERB
ejpam-486	188	62	∈ψ	∈ψ	PROPN
ejpam-486	188	63	�	�	PROPN
ejpam-486	188	64	ω	ω	PROPN
ejpam-486	188	65	,	,	PUNCT
ejpam-486	188	66	q	q	PROPN
ejpam-486	188	67	�	�	PROPN
ejpam-486	188	68	.	.	PUNCT
ejpam-486	189	1	by	by	ADP
ejpam-486	189	2	lemma	lemma	PROPN
ejpam-486	189	3	1	1	NUM
ejpam-486	189	4	,	,	PUNCT
ejpam-486	189	5	g	g	PROPN
ejpam-486	189	6	(	(	PUNCT
ejpam-486	189	7	z	z	NOUN
ejpam-486	189	8	)	)	PUNCT
ejpam-486	189	9	≺	≺	NOUN
ejpam-486	189	10	q	q	NOUN
ejpam-486	189	11	(	(	PUNCT
ejpam-486	189	12	z	z	NOUN
ejpam-486	189	13	)	)	PUNCT
ejpam-486	189	14	or	or	CCONJ
ejpam-486	189	15	qα	qα	PROPN
ejpam-486	189	16	β	β	PROPN
ejpam-486	189	17	,	,	PUNCT
ejpam-486	189	18	p	p	PROPN
ejpam-486	189	19	f	f	X
ejpam-486	189	20	(	(	PUNCT
ejpam-486	189	21	z	z	NOUN
ejpam-486	189	22	)	)	PUNCT
ejpam-486	189	23	zp−1	zp−1	PROPN
ejpam-486	189	24	≺	≺	NOUN
ejpam-486	189	25	q	q	PUNCT
ejpam-486	189	26	(	(	PUNCT
ejpam-486	189	27	z	z	NOUN
ejpam-486	189	28	)	)	PUNCT
ejpam-486	189	29	(	(	PUNCT
ejpam-486	189	30	z	z	NOUN
ejpam-486	189	31	∈	∈	PROPN
ejpam-486	189	32	u	u	NOUN
ejpam-486	189	33	)	)	PUNCT
ejpam-486	189	34	.	.	PUNCT
ejpam-486	190	1	m.	m.	PROPN
ejpam-486	190	2	aouf	aouf	PROPN
ejpam-486	190	3	,	,	PUNCT
ejpam-486	190	4	t.	t.	PROPN
ejpam-486	190	5	seoudy	seoudy	PROPN
ejpam-486	190	6	/	/	SYM
ejpam-486	190	7	eur	eur	PROPN
ejpam-486	190	8	.	.	PUNCT
ejpam-486	191	1	j.	j.	PROPN
ejpam-486	191	2	pure	pure	PROPN
ejpam-486	191	3	appl	appl	PROPN
ejpam-486	191	4	.	.	PROPN
ejpam-486	191	5	math	math	PROPN
ejpam-486	191	6	,	,	PUNCT
ejpam-486	191	7	3	3	NUM
ejpam-486	191	8	(	(	PUNCT
ejpam-486	191	9	2010	2010	NUM
ejpam-486	191	10	)	)	PUNCT
ejpam-486	191	11	,	,	PUNCT
ejpam-486	191	12	26	26	NUM
ejpam-486	191	13	-	-	SYM
ejpam-486	191	14	44	44	NUM
ejpam-486	191	15	34	34	NUM
ejpam-486	191	16	if	if	SCONJ
ejpam-486	191	17	ω	ω	PROPN
ejpam-486	191	18	6=	6=	PROPN
ejpam-486	191	19	c	c	PROPN
ejpam-486	191	20	is	be	AUX
ejpam-486	191	21	a	a	DET
ejpam-486	191	22	simply	simply	ADV
ejpam-486	191	23	connected	connected	ADJ
ejpam-486	191	24	domain	domain	NOUN
ejpam-486	191	25	,	,	PUNCT
ejpam-486	191	26	then	then	ADV
ejpam-486	191	27	ω	ω	PROPN
ejpam-486	191	28	=	=	SYM
ejpam-486	191	29	h(u	h(u	PROPN
ejpam-486	191	30	)	)	PUNCT
ejpam-486	191	31	,	,	PUNCT
ejpam-486	191	32	for	for	ADP
ejpam-486	191	33	some	some	DET
ejpam-486	191	34	conformal	conformal	ADJ
ejpam-486	191	35	mapping	map	VERB
ejpam-486	191	36	h(z	h(z	NOUN
ejpam-486	191	37	)	)	PUNCT
ejpam-486	191	38	of	of	ADP
ejpam-486	191	39	u	u	PRON
ejpam-486	191	40	onto	onto	ADP
ejpam-486	191	41	ω	ω	NUM
ejpam-486	191	42	.	.	PUNCT
ejpam-486	192	1	in	in	ADP
ejpam-486	192	2	this	this	DET
ejpam-486	192	3	case	case	NOUN
ejpam-486	192	4	the	the	DET
ejpam-486	192	5	class	class	NOUN
ejpam-486	192	6	φq,1	φq,1	PROPN
ejpam-486	192	7	�	�	PROPN
ejpam-486	192	8	h(u	h(u	PROPN
ejpam-486	192	9	)	)	PUNCT
ejpam-486	192	10	,	,	PUNCT
ejpam-486	192	11	q	q	PROPN
ejpam-486	192	12	�	�	PROPN
ejpam-486	192	13	is	be	AUX
ejpam-486	192	14	written	write	VERB
ejpam-486	192	15	as	as	ADP
ejpam-486	192	16	φq,1	φq,1	ADJ
ejpam-486	192	17	�	�	PROPN
ejpam-486	192	18	h	h	NOUN
ejpam-486	192	19	,	,	PUNCT
ejpam-486	192	20	q	q	PROPN
ejpam-486	192	21	�	�	PROPN
ejpam-486	192	22	.	.	PUNCT
ejpam-486	193	1	in	in	ADP
ejpam-486	193	2	the	the	DET
ejpam-486	193	3	particular	particular	ADJ
ejpam-486	193	4	case	case	NOUN
ejpam-486	193	5	q(z	q(z	PROPN
ejpam-486	193	6	)	)	PUNCT
ejpam-486	193	7	=	=	SYM
ejpam-486	193	8	mz	mz	PROPN
ejpam-486	193	9	,	,	PUNCT
ejpam-486	193	10	m	m	VERB
ejpam-486	193	11	>	>	X
ejpam-486	193	12	0	0	NUM
ejpam-486	193	13	,	,	PUNCT
ejpam-486	193	14	the	the	DET
ejpam-486	193	15	class	class	NOUN
ejpam-486	193	16	of	of	ADP
ejpam-486	193	17	admissible	admissible	ADJ
ejpam-486	193	18	functions	function	NOUN
ejpam-486	193	19	φq,1	φq,1	PROPN
ejpam-486	193	20	�	�	PROPN
ejpam-486	193	21	ω	ω	PROPN
ejpam-486	193	22	,	,	PUNCT
ejpam-486	193	23	q	q	PROPN
ejpam-486	193	24	�	�	PROPN
ejpam-486	193	25	,	,	PUNCT
ejpam-486	193	26	denoted	denote	VERB
ejpam-486	193	27	by	by	ADP
ejpam-486	193	28	φq,1	φq,1	PROPN
ejpam-486	193	29	[	[	X
ejpam-486	193	30	ω	ω	NOUN
ejpam-486	193	31	,	,	PUNCT
ejpam-486	193	32	m	m	PROPN
ejpam-486	193	33	]	]	PUNCT
ejpam-486	193	34	.	.	PUNCT
ejpam-486	194	1	proceeding	proceed	VERB
ejpam-486	194	2	similarly	similarly	ADV
ejpam-486	194	3	as	as	ADP
ejpam-486	194	4	in	in	ADP
ejpam-486	194	5	the	the	DET
ejpam-486	194	6	previous	previous	ADJ
ejpam-486	194	7	section	section	NOUN
ejpam-486	194	8	,	,	PUNCT
ejpam-486	194	9	the	the	DET
ejpam-486	194	10	following	following	ADJ
ejpam-486	194	11	result	result	NOUN
ejpam-486	194	12	is	be	AUX
ejpam-486	194	13	an	an	DET
ejpam-486	194	14	immediate	immediate	ADJ
ejpam-486	194	15	consequence	consequence	NOUN
ejpam-486	194	16	of	of	ADP
ejpam-486	194	17	theorem	theorem	NOUN
ejpam-486	194	18	5	5	NUM
ejpam-486	194	19	.	.	PUNCT
ejpam-486	194	20	theorem	theorem	NOUN
ejpam-486	194	21	6	6	NUM
ejpam-486	194	22	.	.	PUNCT
ejpam-486	195	1	let	let	VERB
ejpam-486	195	2	φ	φ	NUM
ejpam-486	195	3	∈	∈	PROPN
ejpam-486	195	4	φq,1	φq,1	ADJ
ejpam-486	195	5	�	�	PROPN
ejpam-486	195	6	h	h	NOUN
ejpam-486	195	7	,	,	PUNCT
ejpam-486	195	8	q	q	PROPN
ejpam-486	195	9	�	�	PROPN
ejpam-486	195	10	.	.	PUNCT
ejpam-486	196	1	if	if	SCONJ
ejpam-486	196	2	f	f	PROPN
ejpam-486	196	3	(	(	PUNCT
ejpam-486	196	4	z	z	NOUN
ejpam-486	196	5	)	)	PUNCT
ejpam-486	196	6	∈	∈	PROPN
ejpam-486	196	7	a	a	DET
ejpam-486	196	8	�	�	PROPN
ejpam-486	196	9	p	p	PROPN
ejpam-486	196	10	�	�	PROPN
ejpam-486	196	11	satisfies	satisfy	VERB
ejpam-486	196	12	φ	φ	PROPN
ejpam-486	196	13	qα	qα	PROPN
ejpam-486	196	14	β	β	PROPN
ejpam-486	196	15	,	,	PUNCT
ejpam-486	196	16	p	p	PROPN
ejpam-486	196	17	f	f	X
ejpam-486	196	18	(	(	PUNCT
ejpam-486	196	19	z	z	NOUN
ejpam-486	196	20	)	)	PUNCT
ejpam-486	196	21	zp−1	zp−1	PROPN
ejpam-486	196	22	,	,	PUNCT
ejpam-486	196	23	qα−1	qα−1	PROPN
ejpam-486	196	24	β	β	X
ejpam-486	196	25	,	,	PUNCT
ejpam-486	196	26	p	p	PROPN
ejpam-486	196	27	f	f	X
ejpam-486	196	28	(	(	PUNCT
ejpam-486	196	29	z	z	NOUN
ejpam-486	196	30	)	)	PUNCT
ejpam-486	196	31	zp−1	zp−1	PROPN
ejpam-486	196	32	,	,	PUNCT
ejpam-486	196	33	qα−2	qα−2	PROPN
ejpam-486	196	34	β	β	PROPN
ejpam-486	196	35	,	,	PUNCT
ejpam-486	196	36	p	p	PROPN
ejpam-486	196	37	f	f	X
ejpam-486	196	38	(	(	PUNCT
ejpam-486	196	39	z	z	NOUN
ejpam-486	196	40	)	)	PUNCT
ejpam-486	196	41	zp−1	zp−1	PROPN
ejpam-486	196	42	;	;	PUNCT
ejpam-486	196	43	z	z	NOUN
ejpam-486	196	44	!	!	PUNCT
ejpam-486	197	1	≺	≺	NOUN
ejpam-486	197	2	h(z	h(z	NOUN
ejpam-486	197	3	)	)	PUNCT
ejpam-486	197	4	�	�	PROPN
ejpam-486	197	5	α	α	X
ejpam-486	197	6	>	>	X
ejpam-486	197	7	2;β	2;β	NUM
ejpam-486	197	8	>	>	SYM
ejpam-486	197	9	−1	−1	NOUN
ejpam-486	197	10	;	;	PUNCT
ejpam-486	197	11	p	p	PROPN
ejpam-486	197	12	∈	∈	PROPN
ejpam-486	197	13	n	n	CCONJ
ejpam-486	197	14	;	;	PUNCT
ejpam-486	197	15	z	z	PROPN
ejpam-486	197	16	∈	∈	PROPN
ejpam-486	197	17	u	u	PROPN
ejpam-486	197	18	�	�	PROPN
ejpam-486	197	19	,	,	PUNCT
ejpam-486	197	20	(	(	PUNCT
ejpam-486	197	21	22	22	NUM
ejpam-486	197	22	)	)	PUNCT
ejpam-486	197	23	then	then	ADV
ejpam-486	197	24	qα	qα	PROPN
ejpam-486	197	25	β	β	PROPN
ejpam-486	197	26	,	,	PUNCT
ejpam-486	197	27	p	p	PROPN
ejpam-486	197	28	f	f	X
ejpam-486	197	29	(	(	PUNCT
ejpam-486	197	30	z	z	NOUN
ejpam-486	197	31	)	)	PUNCT
ejpam-486	197	32	zp−1	zp−1	PROPN
ejpam-486	197	33	≺	≺	NOUN
ejpam-486	197	34	q	q	PUNCT
ejpam-486	197	35	(	(	PUNCT
ejpam-486	197	36	z	z	NOUN
ejpam-486	197	37	)	)	PUNCT
ejpam-486	197	38	(	(	PUNCT
ejpam-486	197	39	z	z	NOUN
ejpam-486	197	40	∈	∈	PROPN
ejpam-486	197	41	u	u	NOUN
ejpam-486	197	42	)	)	PUNCT
ejpam-486	197	43	.	.	PUNCT
ejpam-486	198	1	definition	definition	NOUN
ejpam-486	198	2	6	6	NUM
ejpam-486	198	3	.	.	PUNCT
ejpam-486	199	1	let	let	VERB
ejpam-486	199	2	ω	ω	NUM
ejpam-486	199	3	be	be	AUX
ejpam-486	199	4	a	a	DET
ejpam-486	199	5	set	set	NOUN
ejpam-486	199	6	in	in	ADP
ejpam-486	199	7	c	c	PROPN
ejpam-486	199	8	and	and	CCONJ
ejpam-486	199	9	m	m	PROPN
ejpam-486	199	10	>	>	X
ejpam-486	199	11	0	0	X
ejpam-486	199	12	.	.	PUNCT
ejpam-486	200	1	the	the	DET
ejpam-486	200	2	class	class	NOUN
ejpam-486	200	3	of	of	ADP
ejpam-486	200	4	admissible	admissible	ADJ
ejpam-486	200	5	functions	function	NOUN
ejpam-486	200	6	φq,1	φq,1	ADJ
ejpam-486	200	7	[	[	X
ejpam-486	200	8	ω	ω	NOUN
ejpam-486	200	9	,	,	PUNCT
ejpam-486	200	10	m	m	PRON
ejpam-486	200	11	]	]	PUNCT
ejpam-486	200	12	consists	consist	VERB
ejpam-486	200	13	of	of	ADP
ejpam-486	200	14	those	those	DET
ejpam-486	200	15	functions	function	NOUN
ejpam-486	200	16	φ	φ	NOUN
ejpam-486	200	17	:	:	PUNCT
ejpam-486	201	1	c3	c3	PROPN
ejpam-486	201	2	×	×	PROPN
ejpam-486	201	3	u	u	PROPN
ejpam-486	201	4	→	→	SYM
ejpam-486	201	5	c	c	NOUN
ejpam-486	201	6	such	such	ADJ
ejpam-486	201	7	that	that	SCONJ
ejpam-486	201	8	φ	φ	PROPN
ejpam-486	201	9	�	�	PROPN
ejpam-486	201	10	meiθ	meiθ	PROPN
ejpam-486	201	11	,	,	PUNCT
ejpam-486	201	12	k+α+	k+α+	NOUN
ejpam-486	201	13	β	β	X
ejpam-486	201	14	+	+	CCONJ
ejpam-486	201	15	p−	p−	PROPN
ejpam-486	201	16	2	2	NUM
ejpam-486	201	17	α+	α+	NOUN
ejpam-486	201	18	β	β	NOUN
ejpam-486	201	19	+	+	CCONJ
ejpam-486	201	20	p−	p−	NOUN
ejpam-486	201	21	1	1	NUM
ejpam-486	201	22	meiθ	meiθ	NOUN
ejpam-486	201	23	,	,	PUNCT
ejpam-486	201	24	l	l	PROPN
ejpam-486	201	25	+	+	X
ejpam-486	201	26	�	�	PROPN
ejpam-486	201	27	α+	α+	X
ejpam-486	201	28	β	β	NOUN
ejpam-486	201	29	+	+	CCONJ
ejpam-486	201	30	p−	p−	PROPN
ejpam-486	201	31	2	2	NUM
ejpam-486	201	32	�	�	NOUN
ejpam-486	201	33	�	�	PROPN
ejpam-486	201	34	2k+α+	2k+α+	NUM
ejpam-486	201	35	β	β	X
ejpam-486	201	36	+	+	CCONJ
ejpam-486	201	37	p−	p−	PROPN
ejpam-486	201	38	3	3	NUM
ejpam-486	201	39	�	�	NOUN
ejpam-486	201	40	meiθ	meiθ	NOUN
ejpam-486	201	41	�	�	PROPN
ejpam-486	201	42	α+	α+	X
ejpam-486	201	43	β	β	NOUN
ejpam-486	201	44	+	+	CCONJ
ejpam-486	201	45	p−	p−	PROPN
ejpam-486	201	46	1	1	NUM
ejpam-486	201	47	�	�	PROPN
ejpam-486	201	48	�	�	PROPN
ejpam-486	201	49	α+	α+	PUNCT
ejpam-486	201	50	β	β	NOUN
ejpam-486	201	51	+	+	CCONJ
ejpam-486	201	52	p−	p−	PROPN
ejpam-486	201	53	2	2	NUM
ejpam-486	201	54	�	�	NOUN
ejpam-486	201	55	;	;	PUNCT
ejpam-486	201	56	z	z	PROPN
ejpam-486	201	57	�	�	PROPN
ejpam-486	201	58	/∈	/∈	PUNCT
ejpam-486	202	1	ω	ω	PROPN
ejpam-486	202	2	(	(	PUNCT
ejpam-486	202	3	23	23	NUM
ejpam-486	202	4	)	)	PUNCT
ejpam-486	202	5	whenever	whenever	SCONJ
ejpam-486	202	6	z	z	PROPN
ejpam-486	202	7	∈	∈	PROPN
ejpam-486	202	8	u	u	PROPN
ejpam-486	202	9	,	,	PUNCT
ejpam-486	202	10	θ	θ	PROPN
ejpam-486	202	11	∈	∈	PROPN
ejpam-486	202	12	r	r	NOUN
ejpam-486	202	13	,	,	PUNCT
ejpam-486	202	14	ℜ	ℜ	ADJ
ejpam-486	202	15	�	�	PROPN
ejpam-486	202	16	le−iθ	le−iθ	PROPN
ejpam-486	202	17	�	�	PROPN
ejpam-486	202	18	≥	≥	PROPN
ejpam-486	202	19	(	(	PUNCT
ejpam-486	202	20	k−	k−	PROPN
ejpam-486	202	21	1)km	1)km	PROPN
ejpam-486	202	22	for	for	ADP
ejpam-486	202	23	all	all	DET
ejpam-486	202	24	real	real	ADJ
ejpam-486	202	25	θ	θ	NOUN
ejpam-486	202	26	,	,	PUNCT
ejpam-486	202	27	p	p	PROPN
ejpam-486	202	28	∈	∈	PROPN
ejpam-486	202	29	n	n	NOUN
ejpam-486	202	30	and	and	CCONJ
ejpam-486	202	31	k	k	PROPN
ejpam-486	202	32	≥	≥	NUM
ejpam-486	202	33	1	1	NUM
ejpam-486	202	34	.	.	PUNCT
ejpam-486	202	35	corollary	corollary	ADJ
ejpam-486	202	36	5	5	NUM
ejpam-486	202	37	.	.	PUNCT
ejpam-486	203	1	let	let	VERB
ejpam-486	203	2	φ	φ	NUM
ejpam-486	203	3	∈	∈	PROPN
ejpam-486	203	4	φq,1	φq,1	ADJ
ejpam-486	203	5	[	[	X
ejpam-486	203	6	ω	ω	NOUN
ejpam-486	203	7	,	,	PUNCT
ejpam-486	203	8	m	m	X
ejpam-486	203	9	]	]	X
ejpam-486	203	10	.	.	PUNCT
ejpam-486	204	1	if	if	SCONJ
ejpam-486	204	2	f	f	PROPN
ejpam-486	204	3	(	(	PUNCT
ejpam-486	204	4	z	z	NOUN
ejpam-486	204	5	)	)	PUNCT
ejpam-486	204	6	∈	∈	PROPN
ejpam-486	204	7	a	a	DET
ejpam-486	204	8	�	�	PROPN
ejpam-486	204	9	p	p	PROPN
ejpam-486	204	10	�	�	PROPN
ejpam-486	204	11	satisfies	satisfy	VERB
ejpam-486	204	12	φ	φ	PROPN
ejpam-486	204	13	qα	qα	PROPN
ejpam-486	204	14	β	β	PROPN
ejpam-486	204	15	,	,	PUNCT
ejpam-486	204	16	p	p	PROPN
ejpam-486	204	17	f	f	X
ejpam-486	204	18	(	(	PUNCT
ejpam-486	204	19	z	z	NOUN
ejpam-486	204	20	)	)	PUNCT
ejpam-486	204	21	zp−1	zp−1	PROPN
ejpam-486	204	22	,	,	PUNCT
ejpam-486	204	23	qα−1	qα−1	PROPN
ejpam-486	204	24	β	β	X
ejpam-486	204	25	,	,	PUNCT
ejpam-486	204	26	p	p	PROPN
ejpam-486	204	27	f	f	X
ejpam-486	204	28	(	(	PUNCT
ejpam-486	204	29	z	z	NOUN
ejpam-486	204	30	)	)	PUNCT
ejpam-486	204	31	zp−1	zp−1	PROPN
ejpam-486	204	32	,	,	PUNCT
ejpam-486	204	33	qα−2	qα−2	PROPN
ejpam-486	204	34	β	β	PROPN
ejpam-486	204	35	,	,	PUNCT
ejpam-486	204	36	p	p	PROPN
ejpam-486	204	37	f	f	X
ejpam-486	204	38	(	(	PUNCT
ejpam-486	204	39	z	z	NOUN
ejpam-486	204	40	)	)	PUNCT
ejpam-486	204	41	zp−1	zp−1	PROPN
ejpam-486	204	42	;	;	PUNCT
ejpam-486	204	43	z	z	X
ejpam-486	204	44	!	!	PUNCT
ejpam-486	205	1	∈	∈	PROPN
ejpam-486	205	2	ω	ω	NUM
ejpam-486	205	3	�	�	PROPN
ejpam-486	205	4	α	α	X
ejpam-486	205	5	>	>	X
ejpam-486	205	6	2;β	2;β	NUM
ejpam-486	205	7	>	>	SYM
ejpam-486	205	8	−1	−1	NOUN
ejpam-486	205	9	;	;	PUNCT
ejpam-486	205	10	p	p	PROPN
ejpam-486	205	11	∈	∈	PROPN
ejpam-486	205	12	n	n	CCONJ
ejpam-486	205	13	;	;	PUNCT
ejpam-486	205	14	z	z	PROPN
ejpam-486	205	15	∈	∈	PROPN
ejpam-486	205	16	u	u	PROPN
ejpam-486	205	17	�	�	PROPN
ejpam-486	205	18	,	,	PUNCT
ejpam-486	205	19	then	then	ADV
ejpam-486	205	20	�	�	PROPN
ejpam-486	205	21	�	�	PROPN
ejpam-486	205	22	�	�	PROPN
ejpam-486	205	23	�	�	PROPN
ejpam-486	205	24	�	�	PROPN
ejpam-486	205	25	qα	qα	PROPN
ejpam-486	205	26	β	β	PROPN
ejpam-486	205	27	,	,	PUNCT
ejpam-486	205	28	p	p	PROPN
ejpam-486	205	29	f	f	X
ejpam-486	205	30	(	(	PUNCT
ejpam-486	205	31	z	z	NOUN
ejpam-486	205	32	)	)	PUNCT
ejpam-486	205	33	zp−1	zp−1	PROPN
ejpam-486	205	34	�	�	PROPN
ejpam-486	205	35	�	�	PROPN
ejpam-486	205	36	�	�	PROPN
ejpam-486	205	37	�	�	PROPN
ejpam-486	205	38	�	�	PROPN
ejpam-486	205	39	<	<	X
ejpam-486	205	40	m	m	PROPN
ejpam-486	205	41	(	(	PUNCT
ejpam-486	205	42	z	z	NOUN
ejpam-486	205	43	∈	∈	PROPN
ejpam-486	205	44	u	u	NOUN
ejpam-486	205	45	)	)	PUNCT
ejpam-486	205	46	.	.	PUNCT
ejpam-486	206	1	in	in	ADP
ejpam-486	206	2	the	the	DET
ejpam-486	206	3	special	special	ADJ
ejpam-486	206	4	case	case	NOUN
ejpam-486	206	5	ω	ω	X
ejpam-486	206	6	=	=	SYM
ejpam-486	206	7	{	{	PUNCT
ejpam-486	206	8	ω	ω	NOUN
ejpam-486	206	9	:	:	PUNCT
ejpam-486	206	10	|ω|	|ω|	VERB
ejpam-486	206	11	<	<	X
ejpam-486	206	12	m	m	PRON
ejpam-486	206	13	}	}	PUNCT
ejpam-486	206	14	,	,	PUNCT
ejpam-486	206	15	the	the	DET
ejpam-486	206	16	class	class	NOUN
ejpam-486	206	17	φq,1	φq,1	PROPN
ejpam-486	206	18	[	[	X
ejpam-486	206	19	ω	ω	NOUN
ejpam-486	206	20	,	,	PUNCT
ejpam-486	206	21	m	m	X
ejpam-486	206	22	]	]	X
ejpam-486	206	23	is	be	AUX
ejpam-486	206	24	simply	simply	ADV
ejpam-486	206	25	denoted	denote	VERB
ejpam-486	206	26	by	by	ADP
ejpam-486	206	27	φq,1	φq,1	ADJ
ejpam-486	206	28	[	[	X
ejpam-486	206	29	m	m	X
ejpam-486	206	30	]	]	X
ejpam-486	206	31	.	.	PUNCT
ejpam-486	207	1	corollary	corollary	ADJ
ejpam-486	207	2	6	6	NUM
ejpam-486	207	3	.	.	PUNCT
ejpam-486	208	1	let	let	VERB
ejpam-486	208	2	φ	φ	NUM
ejpam-486	208	3	∈	∈	PROPN
ejpam-486	208	4	φq,1	φq,1	ADJ
ejpam-486	208	5	[	[	X
ejpam-486	208	6	m	m	X
ejpam-486	208	7	]	]	X
ejpam-486	208	8	.	.	PUNCT
ejpam-486	209	1	if	if	SCONJ
ejpam-486	209	2	f	f	PROPN
ejpam-486	209	3	(	(	PUNCT
ejpam-486	209	4	z	z	NOUN
ejpam-486	209	5	)	)	PUNCT
ejpam-486	209	6	∈	∈	PROPN
ejpam-486	209	7	a	a	DET
ejpam-486	209	8	�	�	PROPN
ejpam-486	209	9	p	p	NOUN
ejpam-486	209	10	�	�	PROPN
ejpam-486	209	11	satisfies	satisfy	VERB
ejpam-486	209	12	�	�	PROPN
ejpam-486	209	13	�	�	PROPN
ejpam-486	209	14	�	�	PROPN
ejpam-486	209	15	�	�	PROPN
ejpam-486	209	16	�	�	PROPN
ejpam-486	209	17	φ	φ	PROPN
ejpam-486	209	18	qα	qα	PROPN
ejpam-486	209	19	β	β	PROPN
ejpam-486	209	20	,	,	PUNCT
ejpam-486	209	21	p	p	PROPN
ejpam-486	209	22	f	f	X
ejpam-486	209	23	(	(	PUNCT
ejpam-486	209	24	z	z	NOUN
ejpam-486	209	25	)	)	PUNCT
ejpam-486	209	26	zp−1	zp−1	PROPN
ejpam-486	209	27	,	,	PUNCT
ejpam-486	209	28	qα−1	qα−1	PROPN
ejpam-486	209	29	β	β	X
ejpam-486	209	30	,	,	PUNCT
ejpam-486	209	31	p	p	PROPN
ejpam-486	209	32	f	f	X
ejpam-486	209	33	(	(	PUNCT
ejpam-486	209	34	z	z	NOUN
ejpam-486	209	35	)	)	PUNCT
ejpam-486	209	36	zp−1	zp−1	PROPN
ejpam-486	209	37	,	,	PUNCT
ejpam-486	209	38	qα−2	qα−2	PROPN
ejpam-486	209	39	β	β	PROPN
ejpam-486	209	40	,	,	PUNCT
ejpam-486	209	41	p	p	PROPN
ejpam-486	209	42	f	f	X
ejpam-486	209	43	(	(	PUNCT
ejpam-486	209	44	z	z	NOUN
ejpam-486	209	45	)	)	PUNCT
ejpam-486	209	46	zp−1	zp−1	PROPN
ejpam-486	209	47	;	;	PUNCT
ejpam-486	209	48	z	z	X
ejpam-486	209	49	!	!	PUNCT
ejpam-486	210	1	�	�	PROPN
ejpam-486	210	2	�	�	PROPN
ejpam-486	210	3	�	�	PROPN
ejpam-486	210	4	�	�	PROPN
ejpam-486	210	5	�	�	PROPN
ejpam-486	210	6	<	<	X
ejpam-486	210	7	m	m	PROPN
ejpam-486	210	8	�	�	PROPN
ejpam-486	210	9	α	α	PROPN
ejpam-486	210	10	>	>	X
ejpam-486	210	11	2	2	NUM
ejpam-486	210	12	;	;	PUNCT
ejpam-486	210	13	β	β	X
ejpam-486	210	14	>	>	X
ejpam-486	210	15	−1	−1	NOUN
ejpam-486	210	16	;	;	PUNCT
ejpam-486	210	17	p	p	PROPN
ejpam-486	210	18	∈	∈	PROPN
ejpam-486	210	19	n	n	CCONJ
ejpam-486	210	20	;	;	PUNCT
ejpam-486	210	21	z	z	PROPN
ejpam-486	210	22	∈	∈	PROPN
ejpam-486	210	23	u	u	PROPN
ejpam-486	210	24	�	�	PROPN
ejpam-486	210	25	,	,	PUNCT
ejpam-486	210	26	then	then	ADV
ejpam-486	210	27	�	�	PROPN
ejpam-486	210	28	�	�	PROPN
ejpam-486	210	29	�	�	PROPN
ejpam-486	210	30	�	�	PROPN
ejpam-486	210	31	�	�	PROPN
ejpam-486	210	32	qα	qα	PROPN
ejpam-486	210	33	β	β	PROPN
ejpam-486	210	34	,	,	PUNCT
ejpam-486	210	35	p	p	PROPN
ejpam-486	210	36	f	f	X
ejpam-486	210	37	(	(	PUNCT
ejpam-486	210	38	z	z	NOUN
ejpam-486	210	39	)	)	PUNCT
ejpam-486	210	40	zp−1	zp−1	PROPN
ejpam-486	210	41	�	�	PROPN
ejpam-486	210	42	�	�	PROPN
ejpam-486	210	43	�	�	PROPN
ejpam-486	210	44	�	�	PROPN
ejpam-486	210	45	�	�	PROPN
ejpam-486	210	46	<	<	X
ejpam-486	210	47	m	m	PROPN
ejpam-486	210	48	(	(	PUNCT
ejpam-486	210	49	z	z	NOUN
ejpam-486	210	50	∈	∈	PROPN
ejpam-486	210	51	u	u	NOUN
ejpam-486	210	52	)	)	PUNCT
ejpam-486	210	53	.	.	PUNCT
ejpam-486	211	1	m.	m.	PROPN
ejpam-486	211	2	aouf	aouf	PROPN
ejpam-486	211	3	,	,	PUNCT
ejpam-486	211	4	t.	t.	PROPN
ejpam-486	211	5	seoudy	seoudy	PROPN
ejpam-486	211	6	/	/	SYM
ejpam-486	211	7	eur	eur	PROPN
ejpam-486	211	8	.	.	PUNCT
ejpam-486	212	1	j.	j.	PROPN
ejpam-486	212	2	pure	pure	PROPN
ejpam-486	212	3	appl	appl	PROPN
ejpam-486	212	4	.	.	PROPN
ejpam-486	212	5	math	math	PROPN
ejpam-486	212	6	,	,	PUNCT
ejpam-486	212	7	3	3	NUM
ejpam-486	212	8	(	(	PUNCT
ejpam-486	212	9	2010	2010	NUM
ejpam-486	212	10	)	)	PUNCT
ejpam-486	212	11	,	,	PUNCT
ejpam-486	212	12	26	26	NUM
ejpam-486	212	13	-	-	SYM
ejpam-486	212	14	44	44	NUM
ejpam-486	212	15	35	35	NUM
ejpam-486	212	16	corollary	corollary	NOUN
ejpam-486	212	17	7	7	NUM
ejpam-486	212	18	.	.	PUNCT
ejpam-486	213	1	if	if	SCONJ
ejpam-486	213	2	k	k	PROPN
ejpam-486	213	3	≥	≥	VERB
ejpam-486	213	4	1	1	NUM
ejpam-486	213	5	and	and	CCONJ
ejpam-486	213	6	f	f	PROPN
ejpam-486	213	7	(	(	PUNCT
ejpam-486	213	8	z	z	X
ejpam-486	213	9	)	)	PUNCT
ejpam-486	213	10	∈	∈	PROPN
ejpam-486	213	11	a	a	DET
ejpam-486	213	12	�	�	PROPN
ejpam-486	213	13	p	p	NOUN
ejpam-486	213	14	�	�	PROPN
ejpam-486	213	15	satisfies	satisfy	VERB
ejpam-486	213	16	�	�	PROPN
ejpam-486	213	17	�	�	PROPN
ejpam-486	213	18	�	�	PROPN
ejpam-486	213	19	�	�	PROPN
ejpam-486	213	20	�	�	PROPN
ejpam-486	213	21	qα−1	qα−1	PROPN
ejpam-486	213	22	β	β	X
ejpam-486	213	23	,	,	PUNCT
ejpam-486	213	24	p	p	PROPN
ejpam-486	213	25	f	f	X
ejpam-486	213	26	(	(	PUNCT
ejpam-486	213	27	z	z	NOUN
ejpam-486	213	28	)	)	PUNCT
ejpam-486	213	29	zp−1	zp−1	PROPN
ejpam-486	213	30	�	�	PROPN
ejpam-486	213	31	�	�	PROPN
ejpam-486	213	32	�	�	PROPN
ejpam-486	213	33	�	�	PROPN
ejpam-486	213	34	�	�	PROPN
ejpam-486	213	35	<	<	X
ejpam-486	213	36	m	m	PROPN
ejpam-486	213	37	�	�	PROPN
ejpam-486	213	38	α	α	PROPN
ejpam-486	213	39	>	>	X
ejpam-486	213	40	1	1	NUM
ejpam-486	213	41	;	;	PUNCT
ejpam-486	213	42	β	β	X
ejpam-486	213	43	>	>	X
ejpam-486	213	44	−1	−1	NOUN
ejpam-486	213	45	;	;	PUNCT
ejpam-486	213	46	p	p	PROPN
ejpam-486	213	47	∈	∈	PROPN
ejpam-486	213	48	n	n	CCONJ
ejpam-486	213	49	;	;	PUNCT
ejpam-486	213	50	z	z	PROPN
ejpam-486	213	51	∈	∈	PROPN
ejpam-486	213	52	u	u	PROPN
ejpam-486	213	53	�	�	PROPN
ejpam-486	213	54	.	.	PUNCT
ejpam-486	214	1	then	then	ADV
ejpam-486	214	2	�	�	PROPN
ejpam-486	214	3	�	�	PROPN
ejpam-486	214	4	�	�	PROPN
ejpam-486	214	5	�	�	PROPN
ejpam-486	214	6	�	�	PROPN
ejpam-486	214	7	qα	qα	PROPN
ejpam-486	214	8	β	β	PROPN
ejpam-486	214	9	,	,	PUNCT
ejpam-486	214	10	p	p	PROPN
ejpam-486	214	11	f	f	X
ejpam-486	214	12	(	(	PUNCT
ejpam-486	214	13	z	z	NOUN
ejpam-486	214	14	)	)	PUNCT
ejpam-486	214	15	zp−1	zp−1	PROPN
ejpam-486	214	16	�	�	PROPN
ejpam-486	214	17	�	�	PROPN
ejpam-486	214	18	�	�	PROPN
ejpam-486	214	19	�	�	PROPN
ejpam-486	214	20	�	�	PROPN
ejpam-486	214	21	<	<	X
ejpam-486	214	22	m	m	PROPN
ejpam-486	214	23	(	(	PUNCT
ejpam-486	214	24	z	z	NOUN
ejpam-486	214	25	∈	∈	PROPN
ejpam-486	214	26	u	u	NOUN
ejpam-486	214	27	)	)	PUNCT
ejpam-486	214	28	.	.	PUNCT
ejpam-486	215	1	proof	proof	NOUN
ejpam-486	215	2	.	.	PUNCT
ejpam-486	216	1	this	this	PRON
ejpam-486	216	2	follows	follow	VERB
ejpam-486	216	3	from	from	ADP
ejpam-486	216	4	corollary	corollary	ADJ
ejpam-486	216	5	6	6	NUM
ejpam-486	216	6	by	by	ADP
ejpam-486	216	7	taking	take	VERB
ejpam-486	216	8	φ(u	φ(u	NOUN
ejpam-486	216	9	,	,	PUNCT
ejpam-486	216	10	v	v	NOUN
ejpam-486	216	11	,	,	PUNCT
ejpam-486	216	12	w	w	NOUN
ejpam-486	216	13	;	;	PUNCT
ejpam-486	216	14	z	z	X
ejpam-486	216	15	)	)	PUNCT
ejpam-486	216	16	=	=	SYM
ejpam-486	216	17	v	v	X
ejpam-486	216	18	=	=	SYM
ejpam-486	216	19	k+α+β+p−2	k+α+β+p−2	PROPN
ejpam-486	216	20	α+β+p−1	α+β+p−1	INTJ
ejpam-486	216	21	meiθ	meiθ	NOUN
ejpam-486	216	22	.	.	PUNCT
ejpam-486	217	1	definition	definition	NOUN
ejpam-486	217	2	7	7	NUM
ejpam-486	217	3	.	.	PUNCT
ejpam-486	218	1	let	let	VERB
ejpam-486	218	2	ω	ω	NUM
ejpam-486	218	3	be	be	AUX
ejpam-486	218	4	a	a	DET
ejpam-486	218	5	set	set	NOUN
ejpam-486	218	6	in	in	ADP
ejpam-486	218	7	c	c	PROPN
ejpam-486	218	8	and	and	CCONJ
ejpam-486	218	9	q(z	q(z	PROPN
ejpam-486	218	10	)	)	PUNCT
ejpam-486	218	11	∈	∈	PROPN
ejpam-486	218	12	f1∩h	f1∩h	ADV
ejpam-486	218	13	.	.	PUNCT
ejpam-486	219	1	the	the	DET
ejpam-486	219	2	class	class	NOUN
ejpam-486	219	3	of	of	ADP
ejpam-486	219	4	admissible	admissible	ADJ
ejpam-486	219	5	functions	function	NOUN
ejpam-486	219	6	φq,2	φq,2	PUNCT
ejpam-486	219	7	�	�	PROPN
ejpam-486	219	8	ω	ω	PROPN
ejpam-486	219	9	,	,	PUNCT
ejpam-486	219	10	q	q	PROPN
ejpam-486	219	11	�	�	PROPN
ejpam-486	219	12	consists	consist	VERB
ejpam-486	219	13	of	of	ADP
ejpam-486	219	14	those	those	DET
ejpam-486	219	15	functions	function	NOUN
ejpam-486	219	16	φ	φ	NOUN
ejpam-486	219	17	:	:	PUNCT
ejpam-486	220	1	c3	c3	PROPN
ejpam-486	220	2	×	×	PROPN
ejpam-486	220	3	u	u	PROPN
ejpam-486	220	4	→	→	SYM
ejpam-486	220	5	c	c	X
ejpam-486	220	6	that	that	PRON
ejpam-486	220	7	satisfy	satisfy	VERB
ejpam-486	220	8	the	the	DET
ejpam-486	220	9	admissibility	admissibility	NOUN
ejpam-486	220	10	condition	condition	NOUN
ejpam-486	220	11	φ	φ	PROPN
ejpam-486	220	12	(	(	PUNCT
ejpam-486	220	13	u	u	NOUN
ejpam-486	220	14	,	,	PUNCT
ejpam-486	220	15	v	v	NOUN
ejpam-486	220	16	,	,	PUNCT
ejpam-486	220	17	w	w	NOUN
ejpam-486	220	18	;	;	PUNCT
ejpam-486	220	19	z	z	X
ejpam-486	220	20	)	)	PUNCT
ejpam-486	220	21	/∈	/∈	PUNCT
ejpam-486	221	1	ω	ω	NUM
ejpam-486	221	2	whenever	whenever	SCONJ
ejpam-486	221	3	u	u	NOUN
ejpam-486	221	4	=	=	NOUN
ejpam-486	221	5	q	q	X
ejpam-486	221	6	(	(	PUNCT
ejpam-486	221	7	ζ	ζ	NOUN
ejpam-486	221	8	)	)	PUNCT
ejpam-486	221	9	,	,	PUNCT
ejpam-486	221	10	v	v	NOUN
ejpam-486	221	11	=	=	SYM
ejpam-486	221	12	1	1	NUM
ejpam-486	221	13	α+	α+	NOUN
ejpam-486	221	14	β	β	NOUN
ejpam-486	221	15	+	+	CCONJ
ejpam-486	221	16	p−	p−	PROPN
ejpam-486	221	17	2	2	NUM
ejpam-486	221	18	¨	¨	NOUN
ejpam-486	221	19	−1	−1	NOUN
ejpam-486	221	20	+	+	CCONJ
ejpam-486	221	21	�	�	PROPN
ejpam-486	221	22	α+β	α+β	NUM
ejpam-486	221	23	+	+	CCONJ
ejpam-486	221	24	p−	p−	NOUN
ejpam-486	221	25	1	1	NUM
ejpam-486	221	26	�	�	PROPN
ejpam-486	221	27	q	q	PROPN
ejpam-486	221	28	(	(	PUNCT
ejpam-486	221	29	ζ	ζ	NOUN
ejpam-486	221	30	)	)	PUNCT
ejpam-486	221	31	+	+	NOUN
ejpam-486	221	32	kζq′	kζq′	ADJ
ejpam-486	221	33	(	(	PUNCT
ejpam-486	221	34	ζ	ζ	NOUN
ejpam-486	221	35	)	)	PUNCT
ejpam-486	221	36	q	q	NOUN
ejpam-486	221	37	(	(	PUNCT
ejpam-486	221	38	ζ	ζ	NOUN
ejpam-486	221	39	)	)	PUNCT
ejpam-486	221	40	«	«	PUNCT
ejpam-486	221	41	,	,	PUNCT
ejpam-486	221	42	ℜ	ℜ	PROPN
ejpam-486	221	43	�	�	PROPN
ejpam-486	221	44	�	�	PROPN
ejpam-486	221	45	�	�	PROPN
ejpam-486	221	46	α+	α+	X
ejpam-486	221	47	β	β	NOUN
ejpam-486	221	48	+	+	CCONJ
ejpam-486	221	49	p−	p−	PROPN
ejpam-486	221	50	3	3	NUM
ejpam-486	221	51	�	�	PROPN
ejpam-486	221	52	w	w	PROPN
ejpam-486	221	53	−	−	PROPN
ejpam-486	221	54	�	�	PROPN
ejpam-486	221	55	α+	α+	PUNCT
ejpam-486	221	56	β	β	NOUN
ejpam-486	221	57	+	+	CCONJ
ejpam-486	221	58	p−	p−	PROPN
ejpam-486	221	59	2	2	NUM
ejpam-486	221	60	�	�	NOUN
ejpam-486	221	61	v+	v+	ADP
ejpam-486	221	62	1	1	NUM
ejpam-486	221	63	�	�	PROPN
ejpam-486	221	64	v	v	NUM
ejpam-486	221	65	�	�	PROPN
ejpam-486	221	66	α+	α+	PUNCT
ejpam-486	221	67	β	β	NOUN
ejpam-486	221	68	+	+	CCONJ
ejpam-486	221	69	p−	p−	PROPN
ejpam-486	221	70	2	2	NUM
ejpam-486	221	71	�	�	NOUN
ejpam-486	221	72	v	v	ADP
ejpam-486	221	73	−	−	PROPN
ejpam-486	221	74	�	�	PROPN
ejpam-486	221	75	α+	α+	PUNCT
ejpam-486	221	76	β	β	NOUN
ejpam-486	221	77	+	+	CCONJ
ejpam-486	221	78	p−	p−	NOUN
ejpam-486	221	79	1	1	NUM
ejpam-486	221	80	�	�	PROPN
ejpam-486	221	81	u+	u+	NOUN
ejpam-486	221	82	1	1	NUM
ejpam-486	221	83	+	+	NUM
ejpam-486	221	84	�	�	X
ejpam-486	221	85	α+	α+	X
ejpam-486	221	86	β	β	NOUN
ejpam-486	222	1	+	+	CCONJ
ejpam-486	222	2	p−	p−	PROPN
ejpam-486	222	3	2	2	NUM
ejpam-486	222	4	�	�	PROPN
ejpam-486	222	5	v−	v−	NOUN
ejpam-486	222	6	2	2	NUM
ejpam-486	222	7	�	�	NOUN
ejpam-486	222	8	α+	α+	PUNCT
ejpam-486	222	9	β	β	NOUN
ejpam-486	222	10	+	+	CCONJ
ejpam-486	222	11	p−	p−	NOUN
ejpam-486	222	12	1	1	NUM
ejpam-486	222	13	�	�	PROPN
ejpam-486	222	14	u+	u+	NUM
ejpam-486	222	15	1	1	NUM
ejpam-486	222	16	�	�	PROPN
ejpam-486	222	17	≥	≥	NUM
ejpam-486	222	18	kℜ	kℜ	PROPN
ejpam-486	222	19	(	(	PUNCT
ejpam-486	222	20	1	1	NUM
ejpam-486	222	21	+	+	NUM
ejpam-486	222	22	ζq	ζq	NOUN
ejpam-486	222	23	′′	′′	PROPN
ejpam-486	222	24	(	(	PUNCT
ejpam-486	222	25	ζ	ζ	NOUN
ejpam-486	222	26	)	)	PUNCT
ejpam-486	222	27	q′	q′	NOUN
ejpam-486	223	1	(	(	PUNCT
ejpam-486	223	2	ζ	ζ	NOUN
ejpam-486	223	3	)	)	PUNCT
ejpam-486	223	4	)	)	PUNCT
ejpam-486	223	5	,	,	PUNCT
ejpam-486	223	6	where	where	SCONJ
ejpam-486	223	7	z	z	PROPN
ejpam-486	223	8	∈	∈	PROPN
ejpam-486	223	9	u	u	NOUN
ejpam-486	223	10	,	,	PUNCT
ejpam-486	223	11	ζ	ζ	PROPN
ejpam-486	223	12	∈	∈	PROPN
ejpam-486	223	13	∂	∂	NUM
ejpam-486	223	14	u\e	u\e	PROPN
ejpam-486	223	15	�	�	PROPN
ejpam-486	223	16	q	q	PROPN
ejpam-486	223	17	�	�	PROPN
ejpam-486	223	18	,	,	PUNCT
ejpam-486	223	19	p	p	NOUN
ejpam-486	223	20	∈	∈	PROPN
ejpam-486	223	21	n	n	NOUN
ejpam-486	223	22	and	and	CCONJ
ejpam-486	223	23	k	k	PROPN
ejpam-486	223	24	≥	≥	NUM
ejpam-486	223	25	1	1	NUM
ejpam-486	223	26	.	.	PUNCT
ejpam-486	223	27	theorem	theorem	VERB
ejpam-486	223	28	7	7	NUM
ejpam-486	223	29	.	.	PUNCT
ejpam-486	224	1	let	let	VERB
ejpam-486	224	2	φ	φ	PROPN
ejpam-486	224	3	∈	∈	PROPN
ejpam-486	224	4	φq,2	φq,2	PUNCT
ejpam-486	224	5	�	�	PROPN
ejpam-486	224	6	ω	ω	PROPN
ejpam-486	224	7	,	,	PUNCT
ejpam-486	224	8	q	q	PROPN
ejpam-486	224	9	�	�	PROPN
ejpam-486	224	10	and	and	CCONJ
ejpam-486	224	11	qα	qα	PROPN
ejpam-486	224	12	β	β	PROPN
ejpam-486	224	13	,	,	PUNCT
ejpam-486	224	14	p	p	PROPN
ejpam-486	224	15	f	f	X
ejpam-486	224	16	(	(	PUNCT
ejpam-486	224	17	z	z	NOUN
ejpam-486	224	18	)	)	PUNCT
ejpam-486	224	19	6=	6=	ADP
ejpam-486	224	20	0	0	X
ejpam-486	224	21	.	.	PUNCT
ejpam-486	225	1	if	if	SCONJ
ejpam-486	225	2	f	f	PROPN
ejpam-486	225	3	(	(	PUNCT
ejpam-486	225	4	z	z	NOUN
ejpam-486	225	5	)	)	PUNCT
ejpam-486	225	6	∈	∈	PROPN
ejpam-486	225	7	a	a	DET
ejpam-486	225	8	�	�	PROPN
ejpam-486	225	9	p	p	PROPN
ejpam-486	225	10	�	�	PROPN
ejpam-486	225	11	satisfies	satisfie	NOUN
ejpam-486	225	12	(	(	PUNCT
ejpam-486	225	13	φ	φ	PROPN
ejpam-486	225	14	qα−1	qα−1	PROPN
ejpam-486	225	15	β	β	X
ejpam-486	225	16	,	,	PUNCT
ejpam-486	225	17	p	p	X
ejpam-486	225	18	(	(	PUNCT
ejpam-486	225	19	z	z	NOUN
ejpam-486	225	20	)	)	PUNCT
ejpam-486	225	21	qα	qα	PROPN
ejpam-486	226	1	β	β	PROPN
ejpam-486	226	2	,	,	PUNCT
ejpam-486	226	3	p	p	PROPN
ejpam-486	226	4	f	f	X
ejpam-486	226	5	(	(	PUNCT
ejpam-486	226	6	z	z	NOUN
ejpam-486	226	7	)	)	PUNCT
ejpam-486	226	8	,	,	PUNCT
ejpam-486	226	9	qα−2	qα−2	PROPN
ejpam-486	226	10	β	β	PROPN
ejpam-486	226	11	,	,	PUNCT
ejpam-486	226	12	p	p	PROPN
ejpam-486	226	13	f	f	X
ejpam-486	226	14	(	(	PUNCT
ejpam-486	226	15	z	z	NOUN
ejpam-486	226	16	)	)	PUNCT
ejpam-486	226	17	qα−1	qα−1	PROPN
ejpam-486	226	18	β	β	X
ejpam-486	226	19	,	,	PUNCT
ejpam-486	226	20	p	p	PROPN
ejpam-486	226	21	f	f	X
ejpam-486	226	22	(	(	PUNCT
ejpam-486	226	23	z	z	NOUN
ejpam-486	226	24	)	)	PUNCT
ejpam-486	226	25	,	,	PUNCT
ejpam-486	226	26	qα−3	qα−3	NOUN
ejpam-486	226	27	β	β	X
ejpam-486	226	28	,	,	PUNCT
ejpam-486	226	29	p	p	PROPN
ejpam-486	226	30	f	f	X
ejpam-486	226	31	(	(	PUNCT
ejpam-486	226	32	z	z	NOUN
ejpam-486	226	33	)	)	PUNCT
ejpam-486	226	34	qα−2	qα−2	NOUN
ejpam-486	226	35	β	β	NOUN
ejpam-486	226	36	,	,	PUNCT
ejpam-486	226	37	p	p	PROPN
ejpam-486	226	38	f	f	X
ejpam-486	226	39	(	(	PUNCT
ejpam-486	226	40	z	z	NOUN
ejpam-486	226	41	)	)	PUNCT
ejpam-486	226	42	;	;	PUNCT
ejpam-486	226	43	z	z	X
ejpam-486	226	44	!	!	PUNCT
ejpam-486	226	45	:	:	PUNCT
ejpam-486	227	1	z	z	X
ejpam-486	227	2	∈	∈	PROPN
ejpam-486	227	3	u	u	PROPN
ejpam-486	227	4	)	)	PUNCT
ejpam-486	228	1	⊂	⊂	PROPN
ejpam-486	228	2	ω	ω	PROPN
ejpam-486	228	3	�	�	PROPN
ejpam-486	228	4	α	α	PROPN
ejpam-486	228	5	>	>	X
ejpam-486	228	6	3;β	3;β	NUM
ejpam-486	228	7	>	>	SYM
ejpam-486	228	8	−1	−1	NOUN
ejpam-486	228	9	;	;	PUNCT
ejpam-486	228	10	p	p	PROPN
ejpam-486	228	11	∈	∈	PROPN
ejpam-486	228	12	n	n	PRON
ejpam-486	228	13	�	�	PROPN
ejpam-486	228	14	,	,	PUNCT
ejpam-486	228	15	(	(	PUNCT
ejpam-486	228	16	24	24	NUM
ejpam-486	228	17	)	)	PUNCT
ejpam-486	228	18	then	then	ADV
ejpam-486	228	19	qα−1	qα−1	VERB
ejpam-486	228	20	β	β	PROPN
ejpam-486	228	21	,	,	PUNCT
ejpam-486	228	22	p	p	PROPN
ejpam-486	228	23	f	f	X
ejpam-486	228	24	(	(	PUNCT
ejpam-486	228	25	z	z	NOUN
ejpam-486	228	26	)	)	PUNCT
ejpam-486	228	27	qα	qα	PROPN
ejpam-486	228	28	β	β	PROPN
ejpam-486	228	29	,	,	PUNCT
ejpam-486	228	30	p	p	PROPN
ejpam-486	228	31	f	f	X
ejpam-486	228	32	(	(	PUNCT
ejpam-486	228	33	z	z	NOUN
ejpam-486	228	34	)	)	PUNCT
ejpam-486	228	35	≺	≺	NOUN
ejpam-486	228	36	q	q	NOUN
ejpam-486	228	37	(	(	PUNCT
ejpam-486	228	38	z	z	NOUN
ejpam-486	228	39	)	)	PUNCT
ejpam-486	228	40	(	(	PUNCT
ejpam-486	228	41	z	z	NOUN
ejpam-486	228	42	∈	∈	PROPN
ejpam-486	228	43	u	u	NOUN
ejpam-486	228	44	)	)	PUNCT
ejpam-486	228	45	.	.	PUNCT
ejpam-486	229	1	proof	proof	NOUN
ejpam-486	229	2	.	.	PUNCT
ejpam-486	230	1	define	define	VERB
ejpam-486	230	2	an	an	DET
ejpam-486	230	3	analytic	analytic	ADJ
ejpam-486	230	4	function	function	NOUN
ejpam-486	230	5	g(z	g(z	PROPN
ejpam-486	230	6	)	)	PUNCT
ejpam-486	230	7	in	in	ADP
ejpam-486	230	8	u	u	NOUN
ejpam-486	230	9	by	by	ADP
ejpam-486	230	10	g	g	PROPN
ejpam-486	230	11	(	(	PUNCT
ejpam-486	230	12	z	z	NOUN
ejpam-486	230	13	)	)	PUNCT
ejpam-486	230	14	=	=	SYM
ejpam-486	230	15	qα−1	qα−1	NOUN
ejpam-486	230	16	β	β	X
ejpam-486	230	17	,	,	PUNCT
ejpam-486	230	18	p	p	PROPN
ejpam-486	230	19	f	f	X
ejpam-486	230	20	(	(	PUNCT
ejpam-486	230	21	z	z	NOUN
ejpam-486	230	22	)	)	PUNCT
ejpam-486	230	23	qα	qα	PROPN
ejpam-486	230	24	β	β	PROPN
ejpam-486	230	25	,	,	PUNCT
ejpam-486	230	26	p	p	PROPN
ejpam-486	230	27	f	f	X
ejpam-486	230	28	(	(	PUNCT
ejpam-486	230	29	z	z	NOUN
ejpam-486	230	30	)	)	PUNCT
ejpam-486	230	31	�	�	PROPN
ejpam-486	230	32	α	α	NOUN
ejpam-486	230	33	>	>	X
ejpam-486	230	34	3;β	3;β	NUM
ejpam-486	230	35	>	>	SYM
ejpam-486	230	36	−1	−1	NOUN
ejpam-486	230	37	;	;	PUNCT
ejpam-486	230	38	p	p	PROPN
ejpam-486	230	39	∈	∈	PROPN
ejpam-486	230	40	n	n	CCONJ
ejpam-486	230	41	;	;	PUNCT
ejpam-486	230	42	z	z	PROPN
ejpam-486	230	43	∈	∈	PROPN
ejpam-486	230	44	u	u	PROPN
ejpam-486	230	45	�	�	PROPN
ejpam-486	230	46	.	.	PUNCT
ejpam-486	231	1	(	(	PUNCT
ejpam-486	231	2	25	25	NUM
ejpam-486	231	3	)	)	PUNCT
ejpam-486	231	4	m.	m.	NOUN
ejpam-486	231	5	aouf	aouf	PROPN
ejpam-486	231	6	,	,	PUNCT
ejpam-486	231	7	t.	t.	PROPN
ejpam-486	231	8	seoudy	seoudy	PROPN
ejpam-486	231	9	/	/	SYM
ejpam-486	231	10	eur	eur	PROPN
ejpam-486	231	11	.	.	PUNCT
ejpam-486	232	1	j.	j.	PROPN
ejpam-486	232	2	pure	pure	PROPN
ejpam-486	232	3	appl	appl	PROPN
ejpam-486	232	4	.	.	PROPN
ejpam-486	232	5	math	math	PROPN
ejpam-486	232	6	,	,	PUNCT
ejpam-486	232	7	3	3	NUM
ejpam-486	232	8	(	(	PUNCT
ejpam-486	232	9	2010	2010	NUM
ejpam-486	232	10	)	)	PUNCT
ejpam-486	232	11	,	,	PUNCT
ejpam-486	232	12	26	26	NUM
ejpam-486	232	13	-	-	SYM
ejpam-486	232	14	44	44	NUM
ejpam-486	232	15	36	36	NUM
ejpam-486	232	16	using	use	VERB
ejpam-486	232	17	(	(	PUNCT
ejpam-486	232	18	25	25	NUM
ejpam-486	232	19	)	)	PUNCT
ejpam-486	232	20	,	,	PUNCT
ejpam-486	232	21	we	we	PRON
ejpam-486	232	22	get	get	VERB
ejpam-486	232	23	zg′	zg′	NOUN
ejpam-486	232	24	(	(	PUNCT
ejpam-486	232	25	z	z	NOUN
ejpam-486	232	26	)	)	PUNCT
ejpam-486	232	27	g	g	NOUN
ejpam-486	232	28	(	(	PUNCT
ejpam-486	232	29	z	z	NOUN
ejpam-486	232	30	)	)	PUNCT
ejpam-486	232	31	=	=	SYM
ejpam-486	232	32	z	z	NUM
ejpam-486	232	33	�	�	PROPN
ejpam-486	232	34	qα−1	qα−1	PROPN
ejpam-486	232	35	β	β	X
ejpam-486	232	36	,	,	PUNCT
ejpam-486	232	37	p	p	PROPN
ejpam-486	232	38	f	f	X
ejpam-486	232	39	(	(	PUNCT
ejpam-486	232	40	z	z	NOUN
ejpam-486	232	41	)	)	PUNCT
ejpam-486	232	42	�	�	PROPN
ejpam-486	232	43	′	′	NUM
ejpam-486	232	44	qα−1	qα−1	PROPN
ejpam-486	232	45	β	β	X
ejpam-486	232	46	,	,	PUNCT
ejpam-486	232	47	p	p	PROPN
ejpam-486	232	48	f	f	X
ejpam-486	232	49	(	(	PUNCT
ejpam-486	232	50	z	z	NOUN
ejpam-486	232	51	)	)	PUNCT
ejpam-486	232	52	−	−	PROPN
ejpam-486	232	53	z	z	PROPN
ejpam-486	232	54	�	�	PROPN
ejpam-486	232	55	qα	qα	PROPN
ejpam-486	232	56	β	β	PROPN
ejpam-486	232	57	,	,	PUNCT
ejpam-486	232	58	p	p	PROPN
ejpam-486	232	59	f	f	X
ejpam-486	232	60	(	(	PUNCT
ejpam-486	232	61	z	z	NOUN
ejpam-486	232	62	)	)	PUNCT
ejpam-486	232	63	�	�	PROPN
ejpam-486	232	64	′	′	NUM
ejpam-486	232	65	qα	qα	PROPN
ejpam-486	232	66	β	β	PROPN
ejpam-486	232	67	,	,	PUNCT
ejpam-486	232	68	p	p	PROPN
ejpam-486	232	69	f	f	X
ejpam-486	232	70	(	(	PUNCT
ejpam-486	232	71	z	z	NOUN
ejpam-486	232	72	)	)	PUNCT
ejpam-486	232	73	.	.	PUNCT
ejpam-486	233	1	(	(	PUNCT
ejpam-486	233	2	26	26	NUM
ejpam-486	233	3	)	)	PUNCT
ejpam-486	233	4	by	by	ADP
ejpam-486	233	5	making	make	VERB
ejpam-486	233	6	use	use	NOUN
ejpam-486	233	7	of	of	ADP
ejpam-486	233	8	(	(	PUNCT
ejpam-486	233	9	4	4	NUM
ejpam-486	233	10	)	)	PUNCT
ejpam-486	233	11	in	in	ADP
ejpam-486	233	12	(	(	PUNCT
ejpam-486	233	13	26	26	NUM
ejpam-486	233	14	)	)	PUNCT
ejpam-486	233	15	,	,	PUNCT
ejpam-486	233	16	we	we	PRON
ejpam-486	233	17	get	get	VERB
ejpam-486	233	18	qα−2	qα−2	NOUN
ejpam-486	233	19	β	β	NOUN
ejpam-486	233	20	,	,	PUNCT
ejpam-486	233	21	p	p	PROPN
ejpam-486	233	22	f	f	X
ejpam-486	233	23	(	(	PUNCT
ejpam-486	233	24	z	z	NOUN
ejpam-486	233	25	)	)	PUNCT
ejpam-486	233	26	qα−1	qα−1	PROPN
ejpam-486	233	27	β	β	X
ejpam-486	233	28	,	,	PUNCT
ejpam-486	233	29	p	p	PROPN
ejpam-486	233	30	f	f	X
ejpam-486	233	31	(	(	PUNCT
ejpam-486	233	32	z	z	NOUN
ejpam-486	233	33	)	)	PUNCT
ejpam-486	233	34	=	=	SYM
ejpam-486	234	1	1	1	NUM
ejpam-486	234	2	α+	α+	NOUN
ejpam-486	234	3	β	β	NOUN
ejpam-486	234	4	+	+	CCONJ
ejpam-486	234	5	p−	p−	PROPN
ejpam-486	234	6	2	2	NUM
ejpam-486	234	7	¨	¨	NOUN
ejpam-486	234	8	−1	−1	NOUN
ejpam-486	234	9	+	+	CCONJ
ejpam-486	234	10	�	�	PROPN
ejpam-486	234	11	α+	α+	X
ejpam-486	234	12	β	β	NOUN
ejpam-486	234	13	+	+	CCONJ
ejpam-486	234	14	p−	p−	PROPN
ejpam-486	234	15	1	1	NUM
ejpam-486	234	16	�	�	PROPN
ejpam-486	234	17	g	g	PROPN
ejpam-486	234	18	(	(	PUNCT
ejpam-486	234	19	z	z	NOUN
ejpam-486	234	20	)	)	PUNCT
ejpam-486	234	21	+	+	CCONJ
ejpam-486	234	22	zg′	zg′	NOUN
ejpam-486	234	23	(	(	PUNCT
ejpam-486	234	24	z	z	NOUN
ejpam-486	234	25	)	)	PUNCT
ejpam-486	234	26	g	g	NOUN
ejpam-486	234	27	(	(	PUNCT
ejpam-486	234	28	z	z	NOUN
ejpam-486	234	29	)	)	PUNCT
ejpam-486	234	30	«	«	PUNCT
ejpam-486	234	31	.	.	PUNCT
ejpam-486	235	1	(	(	PUNCT
ejpam-486	235	2	27	27	NUM
ejpam-486	235	3	)	)	PUNCT
ejpam-486	235	4	further	further	ADJ
ejpam-486	235	5	computations	computation	NOUN
ejpam-486	235	6	show	show	VERB
ejpam-486	235	7	that	that	SCONJ
ejpam-486	235	8	qα−3	qα−3	NOUN
ejpam-486	235	9	β	β	NOUN
ejpam-486	235	10	,	,	PUNCT
ejpam-486	235	11	p	p	PROPN
ejpam-486	235	12	f	f	X
ejpam-486	235	13	(	(	PUNCT
ejpam-486	235	14	z	z	NOUN
ejpam-486	235	15	)	)	PUNCT
ejpam-486	235	16	qα−2	qα−2	NOUN
ejpam-486	235	17	β	β	NOUN
ejpam-486	235	18	,	,	PUNCT
ejpam-486	235	19	p	p	PROPN
ejpam-486	235	20	f	f	X
ejpam-486	235	21	(	(	PUNCT
ejpam-486	235	22	z	z	NOUN
ejpam-486	235	23	)	)	PUNCT
ejpam-486	235	24	=	=	SYM
ejpam-486	235	25	1	1	NUM
ejpam-486	235	26	α+	α+	NOUN
ejpam-486	235	27	β	β	NOUN
ejpam-486	236	1	+	+	CCONJ
ejpam-486	236	2	p−	p−	PROPN
ejpam-486	236	3	2	2	NUM
ejpam-486	236	4	¨	¨	NOUN
ejpam-486	236	5	−2	−2	NOUN
ejpam-486	236	6	+	+	CCONJ
ejpam-486	236	7	�	�	PROPN
ejpam-486	236	8	α+	α+	X
ejpam-486	236	9	β	β	NOUN
ejpam-486	236	10	+	+	CCONJ
ejpam-486	236	11	p−	p−	PROPN
ejpam-486	236	12	1	1	NUM
ejpam-486	236	13	�	�	PROPN
ejpam-486	236	14	g	g	PROPN
ejpam-486	236	15	(	(	PUNCT
ejpam-486	236	16	z	z	NOUN
ejpam-486	236	17	)	)	PUNCT
ejpam-486	237	1	+	+	CCONJ
ejpam-486	237	2	zg′	zg′	NOUN
ejpam-486	237	3	(	(	PUNCT
ejpam-486	237	4	z	z	NOUN
ejpam-486	237	5	)	)	PUNCT
ejpam-486	237	6	g	g	NOUN
ejpam-486	237	7	(	(	PUNCT
ejpam-486	237	8	z	z	NOUN
ejpam-486	237	9	)	)	PUNCT
ejpam-486	237	10	+	+	CCONJ
ejpam-486	237	11	�	�	PROPN
ejpam-486	237	12	α+	α+	X
ejpam-486	237	13	β	β	NOUN
ejpam-486	237	14	+	+	CCONJ
ejpam-486	237	15	p−	p−	PROPN
ejpam-486	237	16	1	1	NUM
ejpam-486	237	17	�	�	PROPN
ejpam-486	237	18	zg′	zg′	PROPN
ejpam-486	237	19	(	(	PUNCT
ejpam-486	237	20	z	z	NOUN
ejpam-486	237	21	)	)	PUNCT
ejpam-486	237	22	+	+	CCONJ
ejpam-486	237	23	zg	zg	PROPN
ejpam-486	237	24	′(z	′(z	NOUN
ejpam-486	237	25	)	)	PUNCT
ejpam-486	237	26	g(z	g(z	ADJ
ejpam-486	237	27	)	)	PUNCT
ejpam-486	238	1	+	+	NOUN
ejpam-486	238	2	z2	z2	NUM
ejpam-486	238	3	g	g	PROPN
ejpam-486	238	4	′′	′′	PROPN
ejpam-486	238	5	(	(	PUNCT
ejpam-486	238	6	z	z	NOUN
ejpam-486	238	7	)	)	PUNCT
ejpam-486	238	8	g(z	g(z	ADJ
ejpam-486	238	9	)	)	PUNCT
ejpam-486	239	1	−	−	PROPN
ejpam-486	239	2	�	�	PROPN
ejpam-486	239	3	zg	zg	PROPN
ejpam-486	239	4	′(z	′(z	NOUN
ejpam-486	239	5	)	)	PUNCT
ejpam-486	239	6	g(z	g(z	PROPN
ejpam-486	239	7	)	)	PUNCT
ejpam-486	239	8	�	�	PROPN
ejpam-486	239	9	2	2	NUM
ejpam-486	239	10	−1	−1	NOUN
ejpam-486	239	11	+	+	CCONJ
ejpam-486	239	12	�	�	PROPN
ejpam-486	239	13	α+	α+	X
ejpam-486	239	14	β	β	NOUN
ejpam-486	239	15	+	+	CCONJ
ejpam-486	239	16	p−	p−	PROPN
ejpam-486	239	17	1	1	NUM
ejpam-486	239	18	�	�	PROPN
ejpam-486	239	19	g	g	PROPN
ejpam-486	239	20	(	(	PUNCT
ejpam-486	239	21	z	z	NOUN
ejpam-486	239	22	)	)	PUNCT
ejpam-486	239	23	+	+	CCONJ
ejpam-486	239	24	zg	zg	PROPN
ejpam-486	239	25	′(z	′(z	NOUN
ejpam-486	239	26	)	)	PUNCT
ejpam-486	239	27	g(z	g(z	PROPN
ejpam-486	239	28	)	)	PUNCT
ejpam-486	239	29			PROPN
ejpam-486	239	30			PROPN
ejpam-486	239	31			NOUN
ejpam-486	239	32	.	.	PUNCT
ejpam-486	240	1	(	(	PUNCT
ejpam-486	240	2	28	28	NUM
ejpam-486	240	3	)	)	PUNCT
ejpam-486	240	4	define	define	VERB
ejpam-486	240	5	the	the	DET
ejpam-486	240	6	transformations	transformation	NOUN
ejpam-486	240	7	from	from	ADP
ejpam-486	240	8	c3	c3	PROPN
ejpam-486	240	9	to	to	ADP
ejpam-486	240	10	c	c	NOUN
ejpam-486	240	11	by	by	ADP
ejpam-486	240	12	u	u	NOUN
ejpam-486	240	13	=	=	SYM
ejpam-486	240	14	r	r	PROPN
ejpam-486	240	15	,	,	PUNCT
ejpam-486	240	16	v	v	NOUN
ejpam-486	240	17	=	=	SYM
ejpam-486	240	18	1	1	NUM
ejpam-486	240	19	α+	α+	NOUN
ejpam-486	240	20	β	β	NOUN
ejpam-486	240	21	+	+	CCONJ
ejpam-486	240	22	p−	p−	PROPN
ejpam-486	240	23	2	2	NUM
ejpam-486	240	24	§	§	PROPN
ejpam-486	240	25	−1	−1	NOUN
ejpam-486	240	26	+	+	CCONJ
ejpam-486	240	27	�	�	PROPN
ejpam-486	240	28	α+	α+	X
ejpam-486	240	29	β	β	NOUN
ejpam-486	240	30	+	+	CCONJ
ejpam-486	240	31	p−	p−	NOUN
ejpam-486	240	32	1	1	NUM
ejpam-486	240	33	�	�	NOUN
ejpam-486	240	34	r	r	NOUN
ejpam-486	240	35	+	+	SYM
ejpam-486	240	36	s	s	NOUN
ejpam-486	240	37	r	r	NOUN
ejpam-486	240	38	ª	ª	PROPN
ejpam-486	240	39	,	,	PUNCT
ejpam-486	240	40	(	(	PUNCT
ejpam-486	240	41	29	29	NUM
ejpam-486	240	42	)	)	PUNCT
ejpam-486	240	43	w	w	NOUN
ejpam-486	240	44	=	=	SYM
ejpam-486	240	45	1	1	NUM
ejpam-486	240	46	α+	α+	NOUN
ejpam-486	240	47	β	β	NOUN
ejpam-486	240	48	+	+	CCONJ
ejpam-486	240	49	p−	p−	NOUN
ejpam-486	240	50	2	2	NUM
ejpam-486	240	51			NOUN
ejpam-486	240	52			ADJ
ejpam-486	240	53			ADJ
ejpam-486	240	54	−2	−2	PROPN
ejpam-486	240	55	+	+	X
ejpam-486	240	56	�	�	PROPN
ejpam-486	240	57	α+	α+	X
ejpam-486	240	58	β	β	NOUN
ejpam-486	240	59	+	+	CCONJ
ejpam-486	240	60	p−	p−	NOUN
ejpam-486	240	61	1	1	NUM
ejpam-486	240	62	�	�	NOUN
ejpam-486	240	63	r	r	NOUN
ejpam-486	240	64	+	+	CCONJ
ejpam-486	240	65	s	s	NOUN
ejpam-486	240	66	r	r	NOUN
ejpam-486	240	67	+	+	NUM
ejpam-486	240	68	�	�	PROPN
ejpam-486	240	69	α+	α+	X
ejpam-486	240	70	β	β	NOUN
ejpam-486	240	71	+	+	CCONJ
ejpam-486	240	72	p−	p−	PROPN
ejpam-486	240	73	1	1	NUM
ejpam-486	240	74	�	�	PROPN
ejpam-486	240	75	s+	s+	ADP
ejpam-486	240	76	s	s	PART
ejpam-486	240	77	r	r	NOUN
ejpam-486	240	78	+	+	NOUN
ejpam-486	240	79	l	l	NOUN
ejpam-486	240	80	r	r	NOUN
ejpam-486	240	81	−	−	PROPN
ejpam-486	240	82	�	�	PROPN
ejpam-486	240	83	s	s	PART
ejpam-486	240	84	r	r	NOUN
ejpam-486	240	85	�	�	PROPN
ejpam-486	240	86	2	2	NUM
ejpam-486	240	87	−1	−1	NOUN
ejpam-486	240	88	+	+	CCONJ
ejpam-486	240	89	�	�	PROPN
ejpam-486	240	90	α+	α+	X
ejpam-486	240	91	β	β	NOUN
ejpam-486	240	92	+	+	CCONJ
ejpam-486	240	93	p−	p−	NOUN
ejpam-486	240	94	1	1	NUM
ejpam-486	240	95	�	�	NOUN
ejpam-486	240	96	r	r	NOUN
ejpam-486	240	97	+	+	CCONJ
ejpam-486	240	98	s	s	NOUN
ejpam-486	240	99	r	r	NOUN
ejpam-486	240	100			PROPN
ejpam-486	240	101			PROPN
ejpam-486	240	102			NOUN
ejpam-486	240	103	.	.	PUNCT
ejpam-486	241	1	let	let	VERB
ejpam-486	241	2	ψ	ψ	X
ejpam-486	241	3	(	(	PUNCT
ejpam-486	241	4	r	r	NOUN
ejpam-486	241	5	,	,	PUNCT
ejpam-486	241	6	s	s	PROPN
ejpam-486	241	7	,	,	PUNCT
ejpam-486	241	8	t	t	PROPN
ejpam-486	241	9	;	;	PUNCT
ejpam-486	242	1	z	z	X
ejpam-486	242	2	)	)	PUNCT
ejpam-486	242	3	=	=	SYM
ejpam-486	242	4	φ	φ	PROPN
ejpam-486	242	5	(	(	PUNCT
ejpam-486	242	6	u	u	NOUN
ejpam-486	242	7	,	,	PUNCT
ejpam-486	242	8	v	v	NOUN
ejpam-486	242	9	,	,	PUNCT
ejpam-486	242	10	w	w	NOUN
ejpam-486	242	11	;	;	PUNCT
ejpam-486	242	12	z	z	X
ejpam-486	242	13	)	)	PUNCT
ejpam-486	242	14	=	=	PUNCT
ejpam-486	243	1	φ	φ	PROPN
ejpam-486	243	2	�	�	PROPN
ejpam-486	243	3	r	r	PROPN
ejpam-486	243	4	,	,	PUNCT
ejpam-486	243	5	1	1	NUM
ejpam-486	243	6	α+	α+	NOUN
ejpam-486	243	7	β	β	NOUN
ejpam-486	243	8	+	+	CCONJ
ejpam-486	243	9	p−	p−	PROPN
ejpam-486	243	10	2	2	NUM
ejpam-486	243	11	§	§	PROPN
ejpam-486	243	12	−1	−1	NOUN
ejpam-486	243	13	+	+	CCONJ
ejpam-486	243	14	�	�	PROPN
ejpam-486	243	15	α+β	α+β	NUM
ejpam-486	243	16	+	+	CCONJ
ejpam-486	243	17	p−	p−	NOUN
ejpam-486	243	18	1	1	NUM
ejpam-486	243	19	�	�	NOUN
ejpam-486	243	20	r	r	NOUN
ejpam-486	243	21	+	+	SYM
ejpam-486	243	22	s	s	NOUN
ejpam-486	243	23	r	r	NOUN
ejpam-486	243	24	ª	ª	NOUN
ejpam-486	243	25	,	,	PUNCT
ejpam-486	243	26	1	1	NUM
ejpam-486	243	27	α+	α+	NOUN
ejpam-486	243	28	β	β	NOUN
ejpam-486	243	29	+	+	CCONJ
ejpam-486	243	30	p−	p−	NOUN
ejpam-486	243	31	2	2	NUM
ejpam-486	243	32			NOUN
ejpam-486	243	33			ADJ
ejpam-486	243	34			ADJ
ejpam-486	243	35	−2	−2	PROPN
ejpam-486	243	36	+	+	X
ejpam-486	243	37	�	�	PROPN
ejpam-486	243	38	α+	α+	X
ejpam-486	243	39	β	β	NOUN
ejpam-486	243	40	+	+	CCONJ
ejpam-486	243	41	p−	p−	NOUN
ejpam-486	243	42	1	1	NUM
ejpam-486	243	43	�	�	NOUN
ejpam-486	243	44	r	r	NOUN
ejpam-486	243	45	+	+	CCONJ
ejpam-486	243	46	s	s	NOUN
ejpam-486	243	47	r	r	NOUN
ejpam-486	243	48	+	+	NUM
ejpam-486	243	49	�	�	PROPN
ejpam-486	243	50	α+	α+	X
ejpam-486	243	51	β	β	NOUN
ejpam-486	243	52	+	+	CCONJ
ejpam-486	243	53	p−	p−	PROPN
ejpam-486	243	54	1	1	NUM
ejpam-486	243	55	�	�	PROPN
ejpam-486	243	56	s+	s+	ADP
ejpam-486	243	57	s	s	PART
ejpam-486	243	58	r	r	NOUN
ejpam-486	243	59	+	+	NOUN
ejpam-486	243	60	l	l	NOUN
ejpam-486	243	61	r	r	NOUN
ejpam-486	243	62	−	−	PROPN
ejpam-486	243	63	�	�	PROPN
ejpam-486	243	64	s	s	PART
ejpam-486	243	65	r	r	NOUN
ejpam-486	243	66	�	�	PROPN
ejpam-486	243	67	2	2	NUM
ejpam-486	243	68	−1	−1	NOUN
ejpam-486	243	69	+	+	CCONJ
ejpam-486	243	70	�	�	PROPN
ejpam-486	243	71	α+	α+	X
ejpam-486	243	72	β	β	NOUN
ejpam-486	243	73	+	+	CCONJ
ejpam-486	243	74	p−	p−	NOUN
ejpam-486	243	75	1	1	NUM
ejpam-486	243	76	�	�	NOUN
ejpam-486	243	77	r	r	NOUN
ejpam-486	243	78	+	+	CCONJ
ejpam-486	243	79	s	s	NOUN
ejpam-486	243	80	r	r	NOUN
ejpam-486	243	81			PROPN
ejpam-486	243	82			PROPN
ejpam-486	243	83			NOUN
ejpam-486	243	84	;	;	PUNCT
ejpam-486	243	85	z	z	PROPN
ejpam-486	243	86	�	�	PROPN
ejpam-486	243	87	.	.	PUNCT
ejpam-486	244	1	(	(	PUNCT
ejpam-486	244	2	30	30	NUM
ejpam-486	244	3	)	)	PUNCT
ejpam-486	244	4	the	the	DET
ejpam-486	244	5	proof	proof	NOUN
ejpam-486	244	6	shall	shall	AUX
ejpam-486	244	7	make	make	VERB
ejpam-486	244	8	use	use	NOUN
ejpam-486	244	9	of	of	ADP
ejpam-486	244	10	lemma	lemma	PROPN
ejpam-486	244	11	1	1	NUM
ejpam-486	244	12	.	.	PUNCT
ejpam-486	244	13	using	use	VERB
ejpam-486	244	14	equations	equation	NOUN
ejpam-486	244	15	(	(	PUNCT
ejpam-486	244	16	25	25	NUM
ejpam-486	244	17	)	)	PUNCT
ejpam-486	244	18	,	,	PUNCT
ejpam-486	244	19	(	(	PUNCT
ejpam-486	244	20	27	27	NUM
ejpam-486	244	21	)	)	PUNCT
ejpam-486	244	22	and	and	CCONJ
ejpam-486	244	23	(	(	PUNCT
ejpam-486	244	24	28	28	NUM
ejpam-486	244	25	)	)	PUNCT
ejpam-486	244	26	,	,	PUNCT
ejpam-486	244	27	from	from	ADP
ejpam-486	244	28	(	(	PUNCT
ejpam-486	244	29	30	30	NUM
ejpam-486	244	30	)	)	PUNCT
ejpam-486	244	31	,	,	PUNCT
ejpam-486	244	32	we	we	PRON
ejpam-486	244	33	obtain	obtain	VERB
ejpam-486	244	34	ψ(p(z	ψ(p(z	NOUN
ejpam-486	244	35	)	)	PUNCT
ejpam-486	244	36	,	,	PUNCT
ejpam-486	244	37	zp′(z	zp′(z	PROPN
ejpam-486	244	38	)	)	PUNCT
ejpam-486	244	39	,	,	PUNCT
ejpam-486	245	1	z2p	z2p	PROPN
ejpam-486	245	2	′′	′′	PROPN
ejpam-486	245	3	(	(	PUNCT
ejpam-486	245	4	z	z	PROPN
ejpam-486	245	5	)	)	PUNCT
ejpam-486	245	6	;	;	PUNCT
ejpam-486	245	7	z	z	X
ejpam-486	245	8	)	)	PUNCT
ejpam-486	245	9	=	=	PUNCT
ejpam-486	246	1	φ	φ	PROPN
ejpam-486	246	2	qα−1	qα−1	PROPN
ejpam-486	246	3	β	β	X
ejpam-486	246	4	,	,	PUNCT
ejpam-486	246	5	p	p	X
ejpam-486	246	6	(	(	PUNCT
ejpam-486	246	7	z	z	NOUN
ejpam-486	246	8	)	)	PUNCT
ejpam-486	246	9	qα	qα	PROPN
ejpam-486	246	10	β	β	PROPN
ejpam-486	246	11	,	,	PUNCT
ejpam-486	246	12	p	p	PROPN
ejpam-486	246	13	f	f	X
ejpam-486	246	14	(	(	PUNCT
ejpam-486	246	15	z	z	NOUN
ejpam-486	246	16	)	)	PUNCT
ejpam-486	246	17	,	,	PUNCT
ejpam-486	246	18	qα−2	qα−2	PROPN
ejpam-486	246	19	β	β	PROPN
ejpam-486	246	20	,	,	PUNCT
ejpam-486	246	21	p	p	PROPN
ejpam-486	246	22	f	f	X
ejpam-486	246	23	(	(	PUNCT
ejpam-486	246	24	z	z	NOUN
ejpam-486	246	25	)	)	PUNCT
ejpam-486	246	26	qα−1	qα−1	PROPN
ejpam-486	246	27	β	β	X
ejpam-486	246	28	,	,	PUNCT
ejpam-486	246	29	p	p	PROPN
ejpam-486	246	30	f	f	X
ejpam-486	246	31	(	(	PUNCT
ejpam-486	246	32	z	z	NOUN
ejpam-486	246	33	)	)	PUNCT
ejpam-486	246	34	,	,	PUNCT
ejpam-486	246	35	qα−3	qα−3	NOUN
ejpam-486	246	36	β	β	X
ejpam-486	246	37	,	,	PUNCT
ejpam-486	246	38	p	p	PROPN
ejpam-486	246	39	f	f	X
ejpam-486	246	40	(	(	PUNCT
ejpam-486	246	41	z	z	NOUN
ejpam-486	246	42	)	)	PUNCT
ejpam-486	246	43	qα−2	qα−2	NOUN
ejpam-486	246	44	β	β	NOUN
ejpam-486	246	45	,	,	PUNCT
ejpam-486	246	46	p	p	PROPN
ejpam-486	246	47	f	f	X
ejpam-486	246	48	(	(	PUNCT
ejpam-486	246	49	z	z	NOUN
ejpam-486	246	50	)	)	PUNCT
ejpam-486	246	51	;	;	PUNCT
ejpam-486	246	52	z	z	X
ejpam-486	246	53	!	!	PUNCT
ejpam-486	246	54	.	.	PUNCT
ejpam-486	247	1	(	(	PUNCT
ejpam-486	247	2	31	31	NUM
ejpam-486	247	3	)	)	PUNCT
ejpam-486	247	4	m.	m.	NOUN
ejpam-486	247	5	aouf	aouf	PROPN
ejpam-486	247	6	,	,	PUNCT
ejpam-486	247	7	t.	t.	PROPN
ejpam-486	247	8	seoudy	seoudy	PROPN
ejpam-486	247	9	/	/	SYM
ejpam-486	247	10	eur	eur	PROPN
ejpam-486	247	11	.	.	PUNCT
ejpam-486	248	1	j.	j.	PROPN
ejpam-486	248	2	pure	pure	PROPN
ejpam-486	248	3	appl	appl	PROPN
ejpam-486	248	4	.	.	PROPN
ejpam-486	248	5	math	math	PROPN
ejpam-486	248	6	,	,	PUNCT
ejpam-486	248	7	3	3	NUM
ejpam-486	248	8	(	(	PUNCT
ejpam-486	248	9	2010	2010	NUM
ejpam-486	248	10	)	)	PUNCT
ejpam-486	248	11	,	,	PUNCT
ejpam-486	248	12	26	26	NUM
ejpam-486	248	13	-	-	SYM
ejpam-486	248	14	44	44	NUM
ejpam-486	248	15	37	37	NUM
ejpam-486	248	16	hence	hence	ADV
ejpam-486	248	17	(	(	PUNCT
ejpam-486	248	18	24	24	NUM
ejpam-486	248	19	)	)	PUNCT
ejpam-486	248	20	becomes	become	VERB
ejpam-486	248	21	ψ(p(z	ψ(p(z	ADJ
ejpam-486	248	22	)	)	PUNCT
ejpam-486	248	23	,	,	PUNCT
ejpam-486	248	24	zp′(z	zp′(z	PROPN
ejpam-486	248	25	)	)	PUNCT
ejpam-486	248	26	,	,	PUNCT
ejpam-486	249	1	z2p	z2p	PROPN
ejpam-486	249	2	′′	′′	PROPN
ejpam-486	249	3	(	(	PUNCT
ejpam-486	249	4	z	z	PROPN
ejpam-486	249	5	)	)	PUNCT
ejpam-486	249	6	;	;	PUNCT
ejpam-486	249	7	z	z	X
ejpam-486	249	8	)	)	PUNCT
ejpam-486	249	9	∈	∈	PROPN
ejpam-486	249	10	ω	ω	PROPN
ejpam-486	249	11	.	.	PUNCT
ejpam-486	250	1	the	the	DET
ejpam-486	250	2	proof	proof	NOUN
ejpam-486	250	3	is	be	AUX
ejpam-486	250	4	completed	complete	VERB
ejpam-486	250	5	if	if	SCONJ
ejpam-486	250	6	it	it	PRON
ejpam-486	250	7	can	can	AUX
ejpam-486	250	8	be	be	AUX
ejpam-486	250	9	shown	show	VERB
ejpam-486	250	10	that	that	SCONJ
ejpam-486	250	11	the	the	DET
ejpam-486	250	12	admissibility	admissibility	NOUN
ejpam-486	250	13	condition	condition	NOUN
ejpam-486	250	14	for	for	ADP
ejpam-486	250	15	φ	φ	PROPN
ejpam-486	250	16	∈	∈	PROPN
ejpam-486	250	17	φi	φi	ADV
ejpam-486	250	18	,	,	PUNCT
ejpam-486	250	19	2	2	NUM
ejpam-486	250	20	�	�	PROPN
ejpam-486	250	21	ω	ω	PROPN
ejpam-486	250	22	,	,	PUNCT
ejpam-486	250	23	q	q	PROPN
ejpam-486	250	24	�	�	PROPN
ejpam-486	250	25	is	be	AUX
ejpam-486	250	26	equivalent	equivalent	ADJ
ejpam-486	250	27	to	to	ADP
ejpam-486	250	28	the	the	DET
ejpam-486	250	29	admissibility	admissibility	NOUN
ejpam-486	250	30	condition	condition	NOUN
ejpam-486	250	31	for	for	ADP
ejpam-486	250	32	ψ	ψ	PRON
ejpam-486	250	33	as	as	SCONJ
ejpam-486	250	34	given	give	VERB
ejpam-486	250	35	in	in	ADP
ejpam-486	250	36	definition	definition	NOUN
ejpam-486	250	37	1	1	NUM
ejpam-486	250	38	.	.	PUNCT
ejpam-486	251	1	note	note	VERB
ejpam-486	251	2	that	that	SCONJ
ejpam-486	251	3	t	t	PROPN
ejpam-486	251	4	s	s	PART
ejpam-486	251	5	+	+	ADJ
ejpam-486	251	6	1	1	NUM
ejpam-486	251	7	=	=	SYM
ejpam-486	251	8	�	�	PROPN
ejpam-486	251	9	�	�	PROPN
ejpam-486	251	10	α+	α+	X
ejpam-486	251	11	β	β	NOUN
ejpam-486	251	12	+	+	CCONJ
ejpam-486	251	13	p−	p−	PROPN
ejpam-486	251	14	3	3	NUM
ejpam-486	251	15	�	�	PROPN
ejpam-486	251	16	w	w	PROPN
ejpam-486	251	17	−	−	PROPN
ejpam-486	251	18	�	�	PROPN
ejpam-486	251	19	α+	α+	PUNCT
ejpam-486	251	20	β	β	NOUN
ejpam-486	251	21	+	+	CCONJ
ejpam-486	251	22	p−	p−	PROPN
ejpam-486	251	23	2	2	NUM
ejpam-486	251	24	�	�	NOUN
ejpam-486	251	25	v	v	ADP
ejpam-486	251	26	+	+	NOUN
ejpam-486	251	27	1	1	NUM
ejpam-486	251	28	�	�	PROPN
ejpam-486	251	29	v	v	ADP
ejpam-486	251	30	�	�	PROPN
ejpam-486	251	31	α+	α+	PUNCT
ejpam-486	251	32	β	β	NOUN
ejpam-486	251	33	+	+	CCONJ
ejpam-486	251	34	p−	p−	PROPN
ejpam-486	251	35	2	2	NUM
ejpam-486	251	36	�	�	PROPN
ejpam-486	251	37	v−	v−	NOUN
ejpam-486	251	38	�	�	PROPN
ejpam-486	251	39	α+	α+	X
ejpam-486	251	40	β	β	NOUN
ejpam-486	251	41	+	+	CCONJ
ejpam-486	251	42	p−	p−	NOUN
ejpam-486	251	43	1	1	NUM
ejpam-486	251	44	�	�	PROPN
ejpam-486	251	45	u+	u+	NOUN
ejpam-486	251	46	1	1	NUM
ejpam-486	251	47	+	+	NUM
ejpam-486	251	48	�	�	X
ejpam-486	251	49	α+	α+	X
ejpam-486	251	50	β	β	NOUN
ejpam-486	252	1	+	+	CCONJ
ejpam-486	252	2	p−	p−	PROPN
ejpam-486	252	3	2	2	NUM
ejpam-486	252	4	�	�	PROPN
ejpam-486	252	5	v−	v−	NOUN
ejpam-486	252	6	2	2	NUM
ejpam-486	252	7	�	�	NOUN
ejpam-486	252	8	α+	α+	PUNCT
ejpam-486	252	9	β	β	NOUN
ejpam-486	252	10	+	+	CCONJ
ejpam-486	252	11	p−	p−	NOUN
ejpam-486	252	12	1	1	NUM
ejpam-486	252	13	�	�	PROPN
ejpam-486	252	14	u+	u+	NUM
ejpam-486	252	15	1	1	NUM
ejpam-486	252	16	,	,	PUNCT
ejpam-486	252	17	and	and	CCONJ
ejpam-486	252	18	hence	hence	ADV
ejpam-486	252	19	ψ	ψ	VERB
ejpam-486	252	20	∈ψ	∈ψ	PROPN
ejpam-486	252	21	�	�	PROPN
ejpam-486	252	22	ω	ω	PROPN
ejpam-486	252	23	,	,	PUNCT
ejpam-486	252	24	q	q	PROPN
ejpam-486	252	25	�	�	PROPN
ejpam-486	252	26	.	.	PUNCT
ejpam-486	253	1	by	by	ADP
ejpam-486	253	2	lemma	lemma	PROPN
ejpam-486	253	3	1	1	NUM
ejpam-486	253	4	,	,	PUNCT
ejpam-486	253	5	g(z)≺	g(z)≺	PROPN
ejpam-486	253	6	q(z	q(z	PROPN
ejpam-486	253	7	)	)	PUNCT
ejpam-486	253	8	or	or	CCONJ
ejpam-486	253	9	qα−1	qα−1	PROPN
ejpam-486	253	10	β	β	X
ejpam-486	253	11	,	,	PUNCT
ejpam-486	253	12	p	p	X
ejpam-486	253	13	(	(	PUNCT
ejpam-486	253	14	z	z	NOUN
ejpam-486	253	15	)	)	PUNCT
ejpam-486	253	16	qα	qα	PROPN
ejpam-486	254	1	β	β	PROPN
ejpam-486	254	2	,	,	PUNCT
ejpam-486	254	3	p	p	PROPN
ejpam-486	254	4	f	f	X
ejpam-486	254	5	(	(	PUNCT
ejpam-486	254	6	z	z	NOUN
ejpam-486	254	7	)	)	PUNCT
ejpam-486	254	8	≺	≺	NOUN
ejpam-486	254	9	q(z	q(z	PROPN
ejpam-486	254	10	)	)	PUNCT
ejpam-486	254	11	(	(	PUNCT
ejpam-486	254	12	z	z	NOUN
ejpam-486	254	13	∈	∈	PROPN
ejpam-486	254	14	u	u	NOUN
ejpam-486	254	15	)	)	PUNCT
ejpam-486	254	16	.	.	PUNCT
ejpam-486	255	1	if	if	SCONJ
ejpam-486	255	2	ω	ω	PROPN
ejpam-486	255	3	6=	6=	PROPN
ejpam-486	255	4	c	c	PROPN
ejpam-486	255	5	is	be	AUX
ejpam-486	255	6	a	a	DET
ejpam-486	255	7	simply	simply	ADV
ejpam-486	255	8	connected	connected	ADJ
ejpam-486	255	9	domain	domain	NOUN
ejpam-486	255	10	,	,	PUNCT
ejpam-486	255	11	then	then	ADV
ejpam-486	255	12	ω	ω	PROPN
ejpam-486	255	13	=	=	SYM
ejpam-486	255	14	h(u	h(u	PROPN
ejpam-486	255	15	)	)	PUNCT
ejpam-486	255	16	,	,	PUNCT
ejpam-486	255	17	for	for	ADP
ejpam-486	255	18	some	some	DET
ejpam-486	255	19	conformal	conformal	ADJ
ejpam-486	255	20	mapping	map	VERB
ejpam-486	255	21	h(z	h(z	NOUN
ejpam-486	255	22	)	)	PUNCT
ejpam-486	255	23	of	of	ADP
ejpam-486	255	24	u	u	PRON
ejpam-486	255	25	onto	onto	ADP
ejpam-486	255	26	ω	ω	NUM
ejpam-486	255	27	.	.	PUNCT
ejpam-486	256	1	in	in	ADP
ejpam-486	256	2	this	this	DET
ejpam-486	256	3	case	case	NOUN
ejpam-486	256	4	the	the	DET
ejpam-486	256	5	class	class	NOUN
ejpam-486	256	6	φq,2	φq,2	PUNCT
ejpam-486	256	7	�	�	PROPN
ejpam-486	256	8	h(u	h(u	PROPN
ejpam-486	256	9	)	)	PUNCT
ejpam-486	256	10	,	,	PUNCT
ejpam-486	256	11	q	q	PROPN
ejpam-486	256	12	�	�	PROPN
ejpam-486	256	13	is	be	AUX
ejpam-486	256	14	written	write	VERB
ejpam-486	256	15	as	as	ADP
ejpam-486	256	16	φq,2	φq,2	PUNCT
ejpam-486	256	17	�	�	PROPN
ejpam-486	256	18	h	h	PROPN
ejpam-486	256	19	,	,	PUNCT
ejpam-486	256	20	q	q	PROPN
ejpam-486	256	21	�	�	PROPN
ejpam-486	256	22	.	.	PUNCT
ejpam-486	257	1	in	in	ADP
ejpam-486	257	2	the	the	DET
ejpam-486	257	3	particular	particular	ADJ
ejpam-486	257	4	case	case	NOUN
ejpam-486	257	5	q(z	q(z	PROPN
ejpam-486	257	6	)	)	PUNCT
ejpam-486	257	7	=	=	SYM
ejpam-486	257	8	mz	mz	PROPN
ejpam-486	257	9	,	,	PUNCT
ejpam-486	257	10	m	m	VERB
ejpam-486	257	11	>	>	X
ejpam-486	257	12	0	0	NUM
ejpam-486	257	13	,	,	PUNCT
ejpam-486	257	14	the	the	DET
ejpam-486	257	15	class	class	NOUN
ejpam-486	257	16	of	of	ADP
ejpam-486	257	17	admissible	admissible	ADJ
ejpam-486	257	18	functions	function	NOUN
ejpam-486	257	19	φq,2	φq,2	PUNCT
ejpam-486	257	20	�	�	PROPN
ejpam-486	257	21	ω	ω	PROPN
ejpam-486	257	22	,	,	PUNCT
ejpam-486	257	23	q	q	PROPN
ejpam-486	257	24	�	�	PROPN
ejpam-486	257	25	becomes	become	VERB
ejpam-486	257	26	the	the	DET
ejpam-486	257	27	class	class	NOUN
ejpam-486	257	28	φq,2	φq,2	PUNCT
ejpam-486	257	29	[	[	X
ejpam-486	257	30	ω	ω	NOUN
ejpam-486	257	31	,	,	PUNCT
ejpam-486	257	32	m	m	PRON
ejpam-486	257	33	]	]	PUNCT
ejpam-486	257	34	.	.	PUNCT
ejpam-486	258	1	proceeding	proceed	VERB
ejpam-486	258	2	similarly	similarly	ADV
ejpam-486	258	3	as	as	ADP
ejpam-486	258	4	in	in	ADP
ejpam-486	258	5	the	the	DET
ejpam-486	258	6	previous	previous	ADJ
ejpam-486	258	7	section	section	NOUN
ejpam-486	258	8	,	,	PUNCT
ejpam-486	258	9	the	the	DET
ejpam-486	258	10	following	following	ADJ
ejpam-486	258	11	result	result	NOUN
ejpam-486	258	12	is	be	AUX
ejpam-486	258	13	an	an	DET
ejpam-486	258	14	immediate	immediate	ADJ
ejpam-486	258	15	consequence	consequence	NOUN
ejpam-486	258	16	of	of	ADP
ejpam-486	258	17	theorem	theorem	ADJ
ejpam-486	258	18	7	7	NUM
ejpam-486	258	19	.	.	PUNCT
ejpam-486	258	20	theorem	theorem	NOUN
ejpam-486	258	21	8	8	NUM
ejpam-486	258	22	.	.	PUNCT
ejpam-486	259	1	let	let	VERB
ejpam-486	259	2	φ	φ	PROPN
ejpam-486	259	3	∈	∈	PROPN
ejpam-486	259	4	φq,2	φq,2	PUNCT
ejpam-486	259	5	�	�	PROPN
ejpam-486	259	6	h	h	PROPN
ejpam-486	259	7	,	,	PUNCT
ejpam-486	259	8	q	q	PROPN
ejpam-486	259	9	�	�	PROPN
ejpam-486	259	10	.	.	PUNCT
ejpam-486	260	1	if	if	SCONJ
ejpam-486	260	2	f	f	PROPN
ejpam-486	260	3	(	(	PUNCT
ejpam-486	260	4	z	z	NOUN
ejpam-486	260	5	)	)	PUNCT
ejpam-486	260	6	∈	∈	PROPN
ejpam-486	260	7	a	a	DET
ejpam-486	260	8	�	�	PROPN
ejpam-486	260	9	p	p	PROPN
ejpam-486	260	10	�	�	PROPN
ejpam-486	260	11	satisfies	satisfy	VERB
ejpam-486	260	12	φ	φ	PROPN
ejpam-486	260	13	qα−1	qα−1	PROPN
ejpam-486	260	14	β	β	PROPN
ejpam-486	260	15	,	,	PUNCT
ejpam-486	260	16	p	p	X
ejpam-486	260	17	(	(	PUNCT
ejpam-486	260	18	z	z	NOUN
ejpam-486	260	19	)	)	PUNCT
ejpam-486	260	20	qα	qα	PROPN
ejpam-486	260	21	β	β	PROPN
ejpam-486	260	22	,	,	PUNCT
ejpam-486	260	23	p	p	PROPN
ejpam-486	260	24	f	f	X
ejpam-486	260	25	(	(	PUNCT
ejpam-486	260	26	z	z	NOUN
ejpam-486	260	27	)	)	PUNCT
ejpam-486	260	28	,	,	PUNCT
ejpam-486	260	29	qα−2	qα−2	PROPN
ejpam-486	260	30	β	β	PROPN
ejpam-486	260	31	,	,	PUNCT
ejpam-486	260	32	p	p	PROPN
ejpam-486	260	33	f	f	X
ejpam-486	260	34	(	(	PUNCT
ejpam-486	260	35	z	z	NOUN
ejpam-486	260	36	)	)	PUNCT
ejpam-486	260	37	qα−1	qα−1	PROPN
ejpam-486	260	38	β	β	X
ejpam-486	260	39	,	,	PUNCT
ejpam-486	260	40	p	p	PROPN
ejpam-486	260	41	f	f	X
ejpam-486	260	42	(	(	PUNCT
ejpam-486	260	43	z	z	NOUN
ejpam-486	260	44	)	)	PUNCT
ejpam-486	260	45	,	,	PUNCT
ejpam-486	260	46	qα−3	qα−3	NOUN
ejpam-486	260	47	β	β	X
ejpam-486	260	48	,	,	PUNCT
ejpam-486	260	49	p	p	PROPN
ejpam-486	260	50	f	f	X
ejpam-486	260	51	(	(	PUNCT
ejpam-486	260	52	z	z	NOUN
ejpam-486	260	53	)	)	PUNCT
ejpam-486	260	54	qα−2	qα−2	NOUN
ejpam-486	260	55	β	β	NOUN
ejpam-486	260	56	,	,	PUNCT
ejpam-486	260	57	p	p	PROPN
ejpam-486	260	58	f	f	X
ejpam-486	260	59	(	(	PUNCT
ejpam-486	260	60	z	z	NOUN
ejpam-486	260	61	)	)	PUNCT
ejpam-486	260	62	;	;	PUNCT
ejpam-486	261	1	z	z	X
ejpam-486	261	2	!	!	PUNCT
ejpam-486	262	1	≺	≺	NOUN
ejpam-486	262	2	h(z	h(z	NOUN
ejpam-486	262	3	)	)	PUNCT
ejpam-486	262	4	�	�	PROPN
ejpam-486	262	5	α	α	PROPN
ejpam-486	262	6	>	>	X
ejpam-486	262	7	3	3	NUM
ejpam-486	262	8	,	,	PUNCT
ejpam-486	262	9	β	β	X
ejpam-486	262	10	>	>	X
ejpam-486	262	11	−1	−1	NOUN
ejpam-486	262	12	;	;	PUNCT
ejpam-486	262	13	p	p	PROPN
ejpam-486	262	14	∈	∈	PROPN
ejpam-486	262	15	n	n	CCONJ
ejpam-486	262	16	;	;	PUNCT
ejpam-486	262	17	z	z	PROPN
ejpam-486	262	18	∈	∈	PROPN
ejpam-486	262	19	u	u	PROPN
ejpam-486	262	20	�	�	PROPN
ejpam-486	262	21	,	,	PUNCT
ejpam-486	262	22	(	(	PUNCT
ejpam-486	262	23	32	32	NUM
ejpam-486	262	24	)	)	PUNCT
ejpam-486	262	25	then	then	ADV
ejpam-486	262	26	qα−1	qα−1	VERB
ejpam-486	262	27	β	β	PROPN
ejpam-486	262	28	,	,	PUNCT
ejpam-486	262	29	p	p	X
ejpam-486	262	30	(	(	PUNCT
ejpam-486	262	31	z	z	NOUN
ejpam-486	262	32	)	)	PUNCT
ejpam-486	262	33	qα	qα	PROPN
ejpam-486	262	34	β	β	PROPN
ejpam-486	262	35	,	,	PUNCT
ejpam-486	262	36	p	p	PROPN
ejpam-486	262	37	f	f	X
ejpam-486	262	38	(	(	PUNCT
ejpam-486	262	39	z	z	NOUN
ejpam-486	262	40	)	)	PUNCT
ejpam-486	262	41	≺	≺	NOUN
ejpam-486	262	42	q	q	NOUN
ejpam-486	262	43	(	(	PUNCT
ejpam-486	262	44	z	z	NOUN
ejpam-486	262	45	)	)	PUNCT
ejpam-486	262	46	(	(	PUNCT
ejpam-486	262	47	z	z	NOUN
ejpam-486	262	48	∈	∈	PROPN
ejpam-486	262	49	u	u	NOUN
ejpam-486	262	50	)	)	PUNCT
ejpam-486	262	51	.	.	PUNCT
ejpam-486	263	1	definition	definition	NOUN
ejpam-486	263	2	8	8	NUM
ejpam-486	263	3	.	.	PUNCT
ejpam-486	264	1	let	let	VERB
ejpam-486	264	2	ω	ω	PRON
ejpam-486	264	3	be	be	AUX
ejpam-486	264	4	a	a	DET
ejpam-486	264	5	set	set	NOUN
ejpam-486	264	6	in	in	ADP
ejpam-486	264	7	c	c	PROPN
ejpam-486	264	8	and	and	CCONJ
ejpam-486	264	9	m	m	PROPN
ejpam-486	264	10	>	>	X
ejpam-486	264	11	0	0	X
ejpam-486	264	12	.	.	PUNCT
ejpam-486	265	1	the	the	DET
ejpam-486	265	2	class	class	NOUN
ejpam-486	265	3	of	of	ADP
ejpam-486	265	4	admissible	admissible	ADJ
ejpam-486	265	5	functions	function	NOUN
ejpam-486	265	6	φq,2	φq,2	PUNCT
ejpam-486	265	7	[	[	X
ejpam-486	265	8	ω	ω	NOUN
ejpam-486	265	9	,	,	PUNCT
ejpam-486	265	10	m	m	PRON
ejpam-486	265	11	]	]	PUNCT
ejpam-486	265	12	consists	consist	VERB
ejpam-486	265	13	of	of	ADP
ejpam-486	265	14	those	those	DET
ejpam-486	265	15	functions	function	NOUN
ejpam-486	265	16	φ	φ	NOUN
ejpam-486	265	17	:	:	PUNCT
ejpam-486	266	1	c3	c3	PROPN
ejpam-486	266	2	×	×	PROPN
ejpam-486	266	3	u	u	PROPN
ejpam-486	266	4	→	→	SYM
ejpam-486	266	5	c	c	NOUN
ejpam-486	266	6	such	such	ADJ
ejpam-486	266	7	that	that	SCONJ
ejpam-486	266	8	φ	φ	PROPN
ejpam-486	266	9	�	�	PROPN
ejpam-486	266	10	meiθ	meiθ	PROPN
ejpam-486	266	11	,	,	PUNCT
ejpam-486	266	12	k−	k−	PROPN
ejpam-486	266	13	1	1	NUM
ejpam-486	266	14	+	+	NUM
ejpam-486	266	15	�	�	X
ejpam-486	266	16	α+	α+	X
ejpam-486	266	17	β	β	NOUN
ejpam-486	266	18	+	+	CCONJ
ejpam-486	266	19	p−	p−	NOUN
ejpam-486	266	20	1	1	NUM
ejpam-486	266	21	�	�	NOUN
ejpam-486	266	22	meiθ	meiθ	NOUN
ejpam-486	266	23	α+	α+	X
ejpam-486	266	24	β	β	X
ejpam-486	266	25	+	+	CCONJ
ejpam-486	266	26	p−	p−	PROPN
ejpam-486	266	27	2	2	NUM
ejpam-486	266	28	,	,	PUNCT
ejpam-486	266	29	1	1	NUM
ejpam-486	266	30	α+	α+	NOUN
ejpam-486	266	31	β	β	NOUN
ejpam-486	266	32	+	+	CCONJ
ejpam-486	266	33	p−	p−	NOUN
ejpam-486	266	34	2	2	NUM
ejpam-486	266	35	¦	¦	PROPN
ejpam-486	266	36	k−	k−	PROPN
ejpam-486	266	37	2	2	NUM
ejpam-486	266	38	+	+	NUM
ejpam-486	266	39	�	�	X
ejpam-486	266	40	α+	α+	X
ejpam-486	266	41	β	β	NOUN
ejpam-486	266	42	+	+	CCONJ
ejpam-486	266	43	p−	p−	NOUN
ejpam-486	266	44	1	1	NUM
ejpam-486	266	45	�	�	NOUN
ejpam-486	266	46	meiθ	meiθ	NOUN
ejpam-486	266	47	+	+	CCONJ
ejpam-486	266	48	�	�	PROPN
ejpam-486	266	49	α+	α+	PUNCT
ejpam-486	266	50	β	β	NOUN
ejpam-486	266	51	+	+	CCONJ
ejpam-486	266	52	p−	p−	NOUN
ejpam-486	266	53	1	1	NUM
ejpam-486	266	54	�	�	PROPN
ejpam-486	266	55	km2eiθ	km2eiθ	PROPN
ejpam-486	266	56	+	+	PROPN
ejpam-486	266	57	km	km	NOUN
ejpam-486	266	58	+	+	CCONJ
ejpam-486	266	59	le−iθ	le−iθ	ADJ
ejpam-486	266	60	−	−	PROPN
ejpam-486	266	61	k2	k2	PROPN
ejpam-486	266	62	m	m	PROPN
ejpam-486	266	63	(	(	PUNCT
ejpam-486	266	64	k−	k−	PROPN
ejpam-486	266	65	1)m	1)m	PROPN
ejpam-486	267	1	+	+	NUM
ejpam-486	267	2	�	�	PROPN
ejpam-486	267	3	α+	α+	X
ejpam-486	267	4	β	β	NOUN
ejpam-486	267	5	+	+	CCONJ
ejpam-486	267	6	p−	p−	NOUN
ejpam-486	267	7	1	1	NUM
ejpam-486	267	8	�	�	NOUN
ejpam-486	267	9	m2eiθ	m2eiθ	PROPN
ejpam-486	267	10	«	«	PUNCT
ejpam-486	267	11	;	;	PUNCT
ejpam-486	267	12	z	z	PROPN
ejpam-486	267	13	�	�	PROPN
ejpam-486	267	14	/∈	/∈	PUNCT
ejpam-486	268	1	ω	ω	PROPN
ejpam-486	268	2	,	,	PUNCT
ejpam-486	268	3	(	(	PUNCT
ejpam-486	268	4	33	33	NUM
ejpam-486	268	5	)	)	PUNCT
ejpam-486	268	6	whenever	whenever	SCONJ
ejpam-486	268	7	z	z	PROPN
ejpam-486	268	8	∈	∈	PROPN
ejpam-486	268	9	u	u	PROPN
ejpam-486	268	10	,	,	PUNCT
ejpam-486	268	11	θ	θ	PROPN
ejpam-486	268	12	∈	∈	PROPN
ejpam-486	268	13	r	r	NOUN
ejpam-486	268	14	,	,	PUNCT
ejpam-486	268	15	ℜ	ℜ	ADJ
ejpam-486	268	16	�	�	PROPN
ejpam-486	268	17	le−iθ	le−iθ	PROPN
ejpam-486	268	18	�	�	PROPN
ejpam-486	268	19	≥	≥	PROPN
ejpam-486	268	20	(	(	PUNCT
ejpam-486	268	21	k−	k−	PROPN
ejpam-486	268	22	1)km	1)km	PROPN
ejpam-486	268	23	for	for	ADP
ejpam-486	268	24	all	all	DET
ejpam-486	268	25	real	real	ADJ
ejpam-486	268	26	θ	θ	NOUN
ejpam-486	268	27	,	,	PUNCT
ejpam-486	268	28	α	α	X
ejpam-486	268	29	>	>	X
ejpam-486	268	30	3,β	3,β	NUM
ejpam-486	268	31	>	>	SYM
ejpam-486	268	32	−1	−1	NOUN
ejpam-486	268	33	,	,	PUNCT
ejpam-486	268	34	p	p	PROPN
ejpam-486	268	35	∈	∈	PROPN
ejpam-486	268	36	n	n	NOUN
ejpam-486	268	37	and	and	CCONJ
ejpam-486	268	38	k	k	PROPN
ejpam-486	268	39	≥	≥	NUM
ejpam-486	268	40	1	1	NUM
ejpam-486	268	41	.	.	PUNCT
ejpam-486	268	42	m.	m.	PROPN
ejpam-486	268	43	aouf	aouf	PROPN
ejpam-486	268	44	,	,	PUNCT
ejpam-486	268	45	t.	t.	PROPN
ejpam-486	268	46	seoudy	seoudy	PROPN
ejpam-486	268	47	/	/	SYM
ejpam-486	268	48	eur	eur	PROPN
ejpam-486	268	49	.	.	PUNCT
ejpam-486	269	1	j.	j.	PROPN
ejpam-486	269	2	pure	pure	PROPN
ejpam-486	269	3	appl	appl	PROPN
ejpam-486	269	4	.	.	PROPN
ejpam-486	269	5	math	math	PROPN
ejpam-486	269	6	,	,	PUNCT
ejpam-486	269	7	3	3	NUM
ejpam-486	269	8	(	(	PUNCT
ejpam-486	269	9	2010	2010	NUM
ejpam-486	269	10	)	)	PUNCT
ejpam-486	269	11	,	,	PUNCT
ejpam-486	269	12	26	26	NUM
ejpam-486	269	13	-	-	SYM
ejpam-486	269	14	44	44	NUM
ejpam-486	269	15	38	38	NUM
ejpam-486	269	16	corollary	corollary	ADJ
ejpam-486	269	17	8	8	NUM
ejpam-486	269	18	.	.	PUNCT
ejpam-486	270	1	let	let	VERB
ejpam-486	270	2	φ	φ	PROPN
ejpam-486	270	3	∈	∈	PROPN
ejpam-486	270	4	φq,2	φq,2	PUNCT
ejpam-486	271	1	[	[	X
ejpam-486	271	2	ω	ω	X
ejpam-486	271	3	,	,	PUNCT
ejpam-486	271	4	m	m	X
ejpam-486	271	5	]	]	X
ejpam-486	271	6	.	.	PUNCT
ejpam-486	272	1	if	if	SCONJ
ejpam-486	272	2	f	f	PROPN
ejpam-486	272	3	(	(	PUNCT
ejpam-486	272	4	z	z	NOUN
ejpam-486	272	5	)	)	PUNCT
ejpam-486	272	6	∈	∈	PROPN
ejpam-486	272	7	a	a	DET
ejpam-486	272	8	�	�	PROPN
ejpam-486	272	9	p	p	PROPN
ejpam-486	272	10	�	�	PROPN
ejpam-486	272	11	satisfies	satisfy	VERB
ejpam-486	272	12	φ	φ	PROPN
ejpam-486	272	13	qα−1	qα−1	PROPN
ejpam-486	272	14	β	β	PROPN
ejpam-486	272	15	,	,	PUNCT
ejpam-486	272	16	p	p	X
ejpam-486	272	17	(	(	PUNCT
ejpam-486	272	18	z	z	NOUN
ejpam-486	272	19	)	)	PUNCT
ejpam-486	272	20	qα	qα	PROPN
ejpam-486	272	21	β	β	PROPN
ejpam-486	272	22	,	,	PUNCT
ejpam-486	272	23	p	p	PROPN
ejpam-486	272	24	f	f	X
ejpam-486	272	25	(	(	PUNCT
ejpam-486	272	26	z	z	NOUN
ejpam-486	272	27	)	)	PUNCT
ejpam-486	272	28	,	,	PUNCT
ejpam-486	272	29	qα−2	qα−2	PROPN
ejpam-486	272	30	β	β	PROPN
ejpam-486	272	31	,	,	PUNCT
ejpam-486	272	32	p	p	PROPN
ejpam-486	272	33	f	f	X
ejpam-486	272	34	(	(	PUNCT
ejpam-486	272	35	z	z	NOUN
ejpam-486	272	36	)	)	PUNCT
ejpam-486	272	37	qα−1	qα−1	PROPN
ejpam-486	272	38	β	β	X
ejpam-486	272	39	,	,	PUNCT
ejpam-486	272	40	p	p	PROPN
ejpam-486	272	41	f	f	X
ejpam-486	272	42	(	(	PUNCT
ejpam-486	272	43	z	z	NOUN
ejpam-486	272	44	)	)	PUNCT
ejpam-486	272	45	,	,	PUNCT
ejpam-486	272	46	qα−3	qα−3	NOUN
ejpam-486	272	47	β	β	X
ejpam-486	272	48	,	,	PUNCT
ejpam-486	272	49	p	p	PROPN
ejpam-486	272	50	f	f	X
ejpam-486	272	51	(	(	PUNCT
ejpam-486	272	52	z	z	NOUN
ejpam-486	272	53	)	)	PUNCT
ejpam-486	272	54	qα−2	qα−2	NOUN
ejpam-486	272	55	β	β	NOUN
ejpam-486	272	56	,	,	PUNCT
ejpam-486	272	57	p	p	PROPN
ejpam-486	272	58	f	f	X
ejpam-486	272	59	(	(	PUNCT
ejpam-486	272	60	z	z	NOUN
ejpam-486	272	61	)	)	PUNCT
ejpam-486	272	62	;	;	PUNCT
ejpam-486	273	1	z	z	X
ejpam-486	273	2	!	!	PUNCT
ejpam-486	274	1	∈	∈	PROPN
ejpam-486	274	2	ω	ω	NUM
ejpam-486	274	3	�	�	PROPN
ejpam-486	274	4	α	α	PROPN
ejpam-486	274	5	>	>	X
ejpam-486	274	6	3;β	3;β	NUM
ejpam-486	274	7	>	>	SYM
ejpam-486	274	8	−1	−1	NOUN
ejpam-486	274	9	;	;	PUNCT
ejpam-486	274	10	p	p	PROPN
ejpam-486	274	11	∈	∈	PROPN
ejpam-486	274	12	n	n	CCONJ
ejpam-486	274	13	;	;	PUNCT
ejpam-486	274	14	z	z	PROPN
ejpam-486	274	15	∈	∈	PROPN
ejpam-486	274	16	u	u	PROPN
ejpam-486	274	17	�	�	PROPN
ejpam-486	274	18	,	,	PUNCT
ejpam-486	274	19	then	then	ADV
ejpam-486	274	20	�	�	PROPN
ejpam-486	274	21	�	�	PROPN
ejpam-486	274	22	�	�	PROPN
ejpam-486	274	23	�	�	PROPN
ejpam-486	274	24	�	�	PROPN
ejpam-486	274	25	qα−1	qα−1	PROPN
ejpam-486	274	26	β	β	X
ejpam-486	274	27	,	,	PUNCT
ejpam-486	274	28	p	p	X
ejpam-486	274	29	(	(	PUNCT
ejpam-486	274	30	z	z	NOUN
ejpam-486	274	31	)	)	PUNCT
ejpam-486	274	32	qα	qα	PROPN
ejpam-486	274	33	β	β	PROPN
ejpam-486	274	34	,	,	PUNCT
ejpam-486	274	35	p	p	PROPN
ejpam-486	274	36	f	f	X
ejpam-486	274	37	(	(	PUNCT
ejpam-486	274	38	z	z	NOUN
ejpam-486	274	39	)	)	PUNCT
ejpam-486	274	40	�	�	PROPN
ejpam-486	274	41	�	�	PROPN
ejpam-486	274	42	�	�	PROPN
ejpam-486	274	43	�	�	PROPN
ejpam-486	274	44	�	�	PROPN
ejpam-486	274	45	<	<	X
ejpam-486	274	46	m	m	PROPN
ejpam-486	274	47	(	(	PUNCT
ejpam-486	274	48	z	z	NOUN
ejpam-486	274	49	∈	∈	PROPN
ejpam-486	274	50	u	u	NOUN
ejpam-486	274	51	)	)	PUNCT
ejpam-486	274	52	.	.	PUNCT
ejpam-486	275	1	in	in	ADP
ejpam-486	275	2	the	the	DET
ejpam-486	275	3	special	special	ADJ
ejpam-486	275	4	caseω	caseω	NOUN
ejpam-486	275	5	=	=	SYM
ejpam-486	275	6	q	q	X
ejpam-486	275	7	(	(	PUNCT
ejpam-486	275	8	u	u	NOUN
ejpam-486	275	9	)	)	PUNCT
ejpam-486	275	10	=	=	SYM
ejpam-486	275	11	{	{	PUNCT
ejpam-486	275	12	ω	ω	NOUN
ejpam-486	275	13	:	:	PUNCT
ejpam-486	275	14	|ω|	|ω|	VERB
ejpam-486	275	15	<	<	X
ejpam-486	275	16	m	m	PRON
ejpam-486	275	17	}	}	PUNCT
ejpam-486	275	18	,	,	PUNCT
ejpam-486	275	19	the	the	DET
ejpam-486	275	20	classφq,2	classφq,2	ADJ
ejpam-486	275	21	[	[	X
ejpam-486	275	22	ω	ω	NOUN
ejpam-486	275	23	,	,	PUNCT
ejpam-486	275	24	m	m	VERB
ejpam-486	275	25	]	]	PUNCT
ejpam-486	275	26	is	be	AUX
ejpam-486	275	27	denoted	denote	VERB
ejpam-486	275	28	by	by	ADP
ejpam-486	275	29	φq,2	φq,2	NOUN
ejpam-486	275	30	[	[	X
ejpam-486	275	31	m	m	X
ejpam-486	275	32	]	]	X
ejpam-486	275	33	.	.	PUNCT
ejpam-486	276	1	corollary	corollary	ADJ
ejpam-486	276	2	9	9	NUM
ejpam-486	276	3	.	.	PUNCT
ejpam-486	277	1	let	let	VERB
ejpam-486	277	2	φ	φ	PROPN
ejpam-486	277	3	∈	∈	PROPN
ejpam-486	277	4	φq,2	φq,2	PUNCT
ejpam-486	278	1	[	[	X
ejpam-486	278	2	m	m	X
ejpam-486	278	3	]	]	X
ejpam-486	278	4	.	.	PUNCT
ejpam-486	279	1	if	if	SCONJ
ejpam-486	279	2	f	f	PROPN
ejpam-486	279	3	(	(	PUNCT
ejpam-486	279	4	z	z	NOUN
ejpam-486	279	5	)	)	PUNCT
ejpam-486	279	6	∈	∈	PROPN
ejpam-486	279	7	a	a	DET
ejpam-486	279	8	�	�	PROPN
ejpam-486	279	9	p	p	NOUN
ejpam-486	279	10	�	�	PROPN
ejpam-486	279	11	satisfies	satisfy	VERB
ejpam-486	279	12	�	�	PROPN
ejpam-486	279	13	�	�	PROPN
ejpam-486	279	14	�	�	PROPN
ejpam-486	279	15	�	�	PROPN
ejpam-486	279	16	�	�	PROPN
ejpam-486	279	17	φ	φ	PROPN
ejpam-486	279	18	qα−1	qα−1	PROPN
ejpam-486	279	19	β	β	PROPN
ejpam-486	279	20	,	,	PUNCT
ejpam-486	279	21	p	p	X
ejpam-486	279	22	(	(	PUNCT
ejpam-486	279	23	z	z	NOUN
ejpam-486	279	24	)	)	PUNCT
ejpam-486	279	25	qα	qα	PROPN
ejpam-486	280	1	β	β	PROPN
ejpam-486	280	2	,	,	PUNCT
ejpam-486	280	3	p	p	PROPN
ejpam-486	280	4	f	f	X
ejpam-486	280	5	(	(	PUNCT
ejpam-486	280	6	z	z	NOUN
ejpam-486	280	7	)	)	PUNCT
ejpam-486	280	8	,	,	PUNCT
ejpam-486	280	9	qα−2	qα−2	PROPN
ejpam-486	280	10	β	β	PROPN
ejpam-486	280	11	,	,	PUNCT
ejpam-486	280	12	p	p	PROPN
ejpam-486	280	13	f	f	X
ejpam-486	280	14	(	(	PUNCT
ejpam-486	280	15	z	z	NOUN
ejpam-486	280	16	)	)	PUNCT
ejpam-486	280	17	qα−1	qα−1	PROPN
ejpam-486	280	18	β	β	X
ejpam-486	280	19	,	,	PUNCT
ejpam-486	280	20	p	p	PROPN
ejpam-486	280	21	f	f	X
ejpam-486	280	22	(	(	PUNCT
ejpam-486	280	23	z	z	NOUN
ejpam-486	280	24	)	)	PUNCT
ejpam-486	280	25	,	,	PUNCT
ejpam-486	280	26	qα−3	qα−3	NOUN
ejpam-486	280	27	β	β	X
ejpam-486	280	28	,	,	PUNCT
ejpam-486	280	29	p	p	PROPN
ejpam-486	280	30	f	f	X
ejpam-486	280	31	(	(	PUNCT
ejpam-486	280	32	z	z	NOUN
ejpam-486	280	33	)	)	PUNCT
ejpam-486	280	34	qα−2	qα−2	NOUN
ejpam-486	280	35	β	β	NOUN
ejpam-486	280	36	,	,	PUNCT
ejpam-486	280	37	p	p	PROPN
ejpam-486	280	38	f	f	X
ejpam-486	280	39	(	(	PUNCT
ejpam-486	280	40	z	z	NOUN
ejpam-486	280	41	)	)	PUNCT
ejpam-486	280	42	;	;	PUNCT
ejpam-486	281	1	z	z	X
ejpam-486	281	2	!	!	PUNCT
ejpam-486	282	1	�	�	PROPN
ejpam-486	282	2	�	�	PROPN
ejpam-486	282	3	�	�	PROPN
ejpam-486	282	4	�	�	PROPN
ejpam-486	282	5	�	�	PROPN
ejpam-486	282	6	<	<	X
ejpam-486	282	7	m	m	PROPN
ejpam-486	282	8	�	�	PROPN
ejpam-486	282	9	α	α	PROPN
ejpam-486	282	10	>	>	X
ejpam-486	282	11	3	3	NUM
ejpam-486	282	12	;	;	PUNCT
ejpam-486	282	13	β	β	X
ejpam-486	282	14	>	>	X
ejpam-486	282	15	−1	−1	NOUN
ejpam-486	282	16	;	;	PUNCT
ejpam-486	282	17	p	p	PROPN
ejpam-486	282	18	∈	∈	PROPN
ejpam-486	282	19	n	n	CCONJ
ejpam-486	282	20	;	;	PUNCT
ejpam-486	282	21	z	z	PROPN
ejpam-486	282	22	∈	∈	PROPN
ejpam-486	282	23	u	u	PROPN
ejpam-486	282	24	�	�	PROPN
ejpam-486	282	25	,	,	PUNCT
ejpam-486	282	26	then	then	ADV
ejpam-486	282	27	�	�	PROPN
ejpam-486	282	28	�	�	PROPN
ejpam-486	282	29	�	�	PROPN
ejpam-486	282	30	�	�	PROPN
ejpam-486	282	31	�	�	PROPN
ejpam-486	282	32	qα−1	qα−1	PROPN
ejpam-486	282	33	β	β	X
ejpam-486	282	34	,	,	PUNCT
ejpam-486	282	35	p	p	X
ejpam-486	282	36	(	(	PUNCT
ejpam-486	282	37	z	z	NOUN
ejpam-486	282	38	)	)	PUNCT
ejpam-486	282	39	qα	qα	PROPN
ejpam-486	282	40	β	β	PROPN
ejpam-486	282	41	,	,	PUNCT
ejpam-486	282	42	p	p	PROPN
ejpam-486	282	43	f	f	X
ejpam-486	282	44	(	(	PUNCT
ejpam-486	282	45	z	z	NOUN
ejpam-486	282	46	)	)	PUNCT
ejpam-486	282	47	�	�	PROPN
ejpam-486	282	48	�	�	PROPN
ejpam-486	282	49	�	�	PROPN
ejpam-486	282	50	�	�	PROPN
ejpam-486	282	51	�	�	PROPN
ejpam-486	282	52	<	<	X
ejpam-486	282	53	m	m	PROPN
ejpam-486	282	54	(	(	PUNCT
ejpam-486	282	55	z	z	NOUN
ejpam-486	282	56	∈	∈	PROPN
ejpam-486	282	57	u	u	NOUN
ejpam-486	282	58	)	)	PUNCT
ejpam-486	282	59	.	.	PUNCT
ejpam-486	283	1	remark	remark	VERB
ejpam-486	283	2	3	3	NUM
ejpam-486	283	3	.	.	PUNCT
ejpam-486	284	1	the	the	DET
ejpam-486	284	2	result	result	NOUN
ejpam-486	284	3	in	in	ADP
ejpam-486	284	4	the	the	DET
ejpam-486	284	5	corollary	corollary	ADJ
ejpam-486	284	6	9	9	NUM
ejpam-486	284	7	is	be	AUX
ejpam-486	284	8	extension	extension	NOUN
ejpam-486	284	9	of	of	ADP
ejpam-486	284	10	the	the	DET
ejpam-486	284	11	result	result	NOUN
ejpam-486	284	12	obtained	obtain	VERB
ejpam-486	284	13	by	by	ADP
ejpam-486	284	14	aouf	aouf	PROPN
ejpam-486	285	1	[	[	X
ejpam-486	285	2	3	3	NUM
ejpam-486	285	3	,	,	PUNCT
ejpam-486	285	4	theorem	theorem	VERB
ejpam-486	285	5	4	4	NUM
ejpam-486	285	6	]	]	PUNCT
ejpam-486	285	7	.	.	PUNCT
ejpam-486	286	1	3	3	X
ejpam-486	286	2	.	.	X
ejpam-486	286	3	superordination	superordination	NOUN
ejpam-486	286	4	of	of	ADP
ejpam-486	286	5	the	the	DET
ejpam-486	286	6	integral	integral	ADJ
ejpam-486	286	7	operator	operator	NOUN
ejpam-486	286	8	the	the	DET
ejpam-486	286	9	dual	dual	ADJ
ejpam-486	286	10	problem	problem	NOUN
ejpam-486	286	11	of	of	ADP
ejpam-486	286	12	differential	differential	ADJ
ejpam-486	286	13	subordination	subordination	NOUN
ejpam-486	286	14	,	,	PUNCT
ejpam-486	286	15	that	that	ADV
ejpam-486	286	16	is	is	ADV
ejpam-486	286	17	,	,	PUNCT
ejpam-486	286	18	differential	differential	ADJ
ejpam-486	286	19	superordination	superordination	NOUN
ejpam-486	286	20	of	of	ADP
ejpam-486	286	21	the	the	DET
ejpam-486	286	22	integral	integral	ADJ
ejpam-486	286	23	operator	operator	NOUN
ejpam-486	286	24	qα	qα	PROPN
ejpam-486	286	25	β	β	PROPN
ejpam-486	286	26	,	,	PUNCT
ejpam-486	286	27	p	p	PROPN
ejpam-486	286	28	is	be	AUX
ejpam-486	286	29	investigated	investigate	VERB
ejpam-486	286	30	in	in	ADP
ejpam-486	286	31	this	this	DET
ejpam-486	286	32	section	section	NOUN
ejpam-486	286	33	.	.	PUNCT
ejpam-486	287	1	for	for	ADP
ejpam-486	287	2	this	this	DET
ejpam-486	287	3	purpose	purpose	NOUN
ejpam-486	287	4	the	the	DET
ejpam-486	287	5	class	class	NOUN
ejpam-486	287	6	ofvadmissible	ofvadmissible	ADJ
ejpam-486	287	7	functions	function	NOUN
ejpam-486	287	8	is	be	AUX
ejpam-486	287	9	given	give	VERB
ejpam-486	287	10	in	in	ADP
ejpam-486	287	11	the	the	DET
ejpam-486	287	12	following	follow	VERB
ejpam-486	287	13	definition	definition	NOUN
ejpam-486	287	14	.	.	PUNCT
ejpam-486	288	1	definition	definition	NOUN
ejpam-486	288	2	9	9	NUM
ejpam-486	288	3	.	.	PUNCT
ejpam-486	289	1	let	let	VERB
ejpam-486	289	2	ω	ω	PRON
ejpam-486	289	3	be	be	AUX
ejpam-486	289	4	a	a	DET
ejpam-486	289	5	set	set	NOUN
ejpam-486	289	6	in	in	ADP
ejpam-486	289	7	c	c	PROPN
ejpam-486	289	8	and	and	CCONJ
ejpam-486	289	9	q(z	q(z	PROPN
ejpam-486	289	10	)	)	PUNCT
ejpam-486	289	11	∈	∈	PROPN
ejpam-486	289	12	h[0	h[0	PROPN
ejpam-486	289	13	,	,	PUNCT
ejpam-486	289	14	p	p	X
ejpam-486	289	15	]	]	PUNCT
ejpam-486	289	16	with	with	ADP
ejpam-486	289	17	zq′(z	zq′(z	PROPN
ejpam-486	289	18	)	)	PUNCT
ejpam-486	289	19	6=	6=	ADP
ejpam-486	289	20	0	0	X
ejpam-486	289	21	.	.	PUNCT
ejpam-486	290	1	the	the	DET
ejpam-486	290	2	class	class	NOUN
ejpam-486	290	3	of	of	ADP
ejpam-486	290	4	admissible	admissible	ADJ
ejpam-486	290	5	functions	function	NOUN
ejpam-486	290	6	φ′q	φ′q	PROPN
ejpam-486	290	7	�	�	PROPN
ejpam-486	290	8	ω	ω	PROPN
ejpam-486	290	9	,	,	PUNCT
ejpam-486	290	10	q	q	PROPN
ejpam-486	290	11	�	�	PROPN
ejpam-486	290	12	consists	consist	VERB
ejpam-486	290	13	of	of	ADP
ejpam-486	290	14	those	those	DET
ejpam-486	290	15	functions	function	NOUN
ejpam-486	290	16	φ	φ	NOUN
ejpam-486	290	17	:	:	PUNCT
ejpam-486	291	1	c3	c3	PROPN
ejpam-486	291	2	×	×	PROPN
ejpam-486	291	3	ū	ū	NOUN
ejpam-486	291	4	→	→	SYM
ejpam-486	291	5	c	c	NOUN
ejpam-486	291	6	that	that	PRON
ejpam-486	291	7	satisfy	satisfy	VERB
ejpam-486	291	8	the	the	DET
ejpam-486	291	9	admissibility	admissibility	NOUN
ejpam-486	291	10	condition	condition	NOUN
ejpam-486	291	11	:	:	PUNCT
ejpam-486	291	12	φ	φ	PROPN
ejpam-486	291	13	(	(	PUNCT
ejpam-486	291	14	u	u	NOUN
ejpam-486	291	15	,	,	PUNCT
ejpam-486	291	16	v	v	NOUN
ejpam-486	291	17	,	,	PUNCT
ejpam-486	291	18	w;ζ	w;ζ	NUM
ejpam-486	291	19	)	)	PUNCT
ejpam-486	292	1	∈	∈	PROPN
ejpam-486	292	2	ω	ω	NUM
ejpam-486	292	3	whenever	whenever	SCONJ
ejpam-486	292	4	u=	u=	ADV
ejpam-486	292	5	q	q	X
ejpam-486	292	6	(	(	PUNCT
ejpam-486	292	7	z	z	NOUN
ejpam-486	292	8	)	)	PUNCT
ejpam-486	292	9	,	,	PUNCT
ejpam-486	292	10	v	v	X
ejpam-486	292	11	=	=	SYM
ejpam-486	292	12	ζq′	ζq′	ADJ
ejpam-486	292	13	(	(	PUNCT
ejpam-486	292	14	z	z	NOUN
ejpam-486	292	15	)	)	PUNCT
ejpam-486	293	1	+	+	PROPN
ejpam-486	293	2	m	m	VERB
ejpam-486	293	3	�	�	INTJ
ejpam-486	293	4	α+	α+	PUNCT
ejpam-486	293	5	β	β	NOUN
ejpam-486	293	6	−	−	PROPN
ejpam-486	293	7	1	1	NUM
ejpam-486	293	8	�	�	PROPN
ejpam-486	293	9	q	q	PROPN
ejpam-486	293	10	(	(	PUNCT
ejpam-486	293	11	z	z	NOUN
ejpam-486	293	12	)	)	PUNCT
ejpam-486	293	13	m	m	VERB
ejpam-486	293	14	�	�	INTJ
ejpam-486	293	15	α+	α+	PUNCT
ejpam-486	293	16	β	β	NOUN
ejpam-486	293	17	+	+	CCONJ
ejpam-486	293	18	p−	p−	PROPN
ejpam-486	293	19	1	1	NUM
ejpam-486	293	20	�	�	PROPN
ejpam-486	293	21	,	,	PUNCT
ejpam-486	293	22	ℜ	ℜ	PROPN
ejpam-486	293	23	¨	¨	NOUN
ejpam-486	293	24	�	�	PROPN
ejpam-486	293	25	α+	α+	PUNCT
ejpam-486	293	26	β	β	NOUN
ejpam-486	293	27	+	+	CCONJ
ejpam-486	293	28	p−	p−	PROPN
ejpam-486	293	29	1	1	NUM
ejpam-486	293	30	�	�	PROPN
ejpam-486	293	31	�	�	PROPN
ejpam-486	293	32	α+	α+	PUNCT
ejpam-486	293	33	β	β	NOUN
ejpam-486	293	34	+	+	CCONJ
ejpam-486	293	35	p−	p−	PROPN
ejpam-486	293	36	2	2	NUM
ejpam-486	293	37	�	�	PROPN
ejpam-486	293	38	w	w	PROPN
ejpam-486	293	39	−	−	PROPN
ejpam-486	293	40	�	�	PROPN
ejpam-486	293	41	α+	α+	PUNCT
ejpam-486	293	42	β	β	NOUN
ejpam-486	293	43	−	−	PROPN
ejpam-486	293	44	1	1	NUM
ejpam-486	293	45	�	�	PROPN
ejpam-486	293	46	�	�	PROPN
ejpam-486	293	47	α+	α+	PUNCT
ejpam-486	293	48	β	β	NOUN
ejpam-486	293	49	−	−	PROPN
ejpam-486	293	50	2	2	NUM
ejpam-486	293	51	�	�	PROPN
ejpam-486	293	52	u	u	PROPN
ejpam-486	293	53	�	�	PROPN
ejpam-486	293	54	α+	α+	X
ejpam-486	293	55	β	β	NOUN
ejpam-486	293	56	+	+	CCONJ
ejpam-486	293	57	p−	p−	PROPN
ejpam-486	293	58	1	1	NUM
ejpam-486	293	59	�	�	PROPN
ejpam-486	293	60	v	v	ADP
ejpam-486	293	61	−	−	PROPN
ejpam-486	293	62	�	�	PROPN
ejpam-486	293	63	α+	α+	NOUN
ejpam-486	293	64	β	β	NOUN
ejpam-486	293	65	−	−	PROPN
ejpam-486	293	66	1	1	NUM
ejpam-486	293	67	�	�	PROPN
ejpam-486	293	68	u	u	NOUN
ejpam-486	293	69	−	−	PROPN
ejpam-486	293	70	2	2	NUM
ejpam-486	293	71	�	�	PROPN
ejpam-486	293	72	α+	α+	PUNCT
ejpam-486	293	73	β	β	X
ejpam-486	293	74	�	�	PROPN
ejpam-486	293	75	+	+	CCONJ
ejpam-486	293	76	3	3	NUM
ejpam-486	293	77	«	«	SYM
ejpam-486	293	78	≤	≤	NUM
ejpam-486	293	79	1	1	NUM
ejpam-486	293	80	m	m	NOUN
ejpam-486	293	81	ℜ	ℜ	NOUN
ejpam-486	293	82	(	(	PUNCT
ejpam-486	293	83	1	1	NUM
ejpam-486	293	84	+	+	NUM
ejpam-486	293	85	zq	zq	PROPN
ejpam-486	293	86	′′	′′	PROPN
ejpam-486	293	87	(	(	PUNCT
ejpam-486	293	88	z	z	NOUN
ejpam-486	293	89	)	)	PUNCT
ejpam-486	293	90	q′	q′	NOUN
ejpam-486	293	91	(	(	PUNCT
ejpam-486	293	92	z	z	NOUN
ejpam-486	293	93	)	)	PUNCT
ejpam-486	293	94	)	)	PUNCT
ejpam-486	293	95	,	,	PUNCT
ejpam-486	293	96	where	where	SCONJ
ejpam-486	293	97	z	z	PROPN
ejpam-486	293	98	∈	∈	PROPN
ejpam-486	293	99	u	u	NOUN
ejpam-486	293	100	,	,	PUNCT
ejpam-486	293	101	ζ	ζ	PROPN
ejpam-486	293	102	∈	∈	PROPN
ejpam-486	293	103	∂	∂	NUM
ejpam-486	293	104	u	u	NOUN
ejpam-486	293	105	,	,	PUNCT
ejpam-486	293	106	α	α	X
ejpam-486	293	107	>	>	X
ejpam-486	293	108	2,β	2,β	PROPN
ejpam-486	293	109	>	>	PUNCT
ejpam-486	293	110	−1	−1	NOUN
ejpam-486	293	111	,	,	PUNCT
ejpam-486	293	112	p	p	PROPN
ejpam-486	293	113	∈	∈	PROPN
ejpam-486	293	114	n	n	NOUN
ejpam-486	293	115	and	and	CCONJ
ejpam-486	293	116	m	m	PROPN
ejpam-486	293	117	≥	≥	NOUN
ejpam-486	293	118	p.	p.	NOUN
ejpam-486	293	119	m.	m.	PROPN
ejpam-486	293	120	aouf	aouf	PROPN
ejpam-486	293	121	,	,	PUNCT
ejpam-486	293	122	t.	t.	PROPN
ejpam-486	293	123	seoudy	seoudy	PROPN
ejpam-486	293	124	/	/	SYM
ejpam-486	293	125	eur	eur	PROPN
ejpam-486	293	126	.	.	PUNCT
ejpam-486	294	1	j.	j.	PROPN
ejpam-486	294	2	pure	pure	PROPN
ejpam-486	294	3	appl	appl	PROPN
ejpam-486	294	4	.	.	PROPN
ejpam-486	294	5	math	math	PROPN
ejpam-486	294	6	,	,	PUNCT
ejpam-486	294	7	3	3	NUM
ejpam-486	294	8	(	(	PUNCT
ejpam-486	294	9	2010	2010	NUM
ejpam-486	294	10	)	)	PUNCT
ejpam-486	294	11	,	,	PUNCT
ejpam-486	294	12	26	26	NUM
ejpam-486	294	13	-	-	SYM
ejpam-486	294	14	44	44	NUM
ejpam-486	294	15	39	39	NUM
ejpam-486	294	16	theorem	theorem	NOUN
ejpam-486	294	17	9	9	NUM
ejpam-486	294	18	.	.	PUNCT
ejpam-486	295	1	let	let	VERB
ejpam-486	295	2	φ	φ	PROPN
ejpam-486	295	3	∈	∈	PROPN
ejpam-486	295	4	φ′q	φ′q	PROPN
ejpam-486	295	5	�	�	PROPN
ejpam-486	295	6	ω	ω	PROPN
ejpam-486	295	7	,	,	PUNCT
ejpam-486	295	8	q	q	PROPN
ejpam-486	295	9	�	�	PROPN
ejpam-486	295	10	.	.	PUNCT
ejpam-486	296	1	if	if	SCONJ
ejpam-486	296	2	f	f	PROPN
ejpam-486	296	3	(	(	PUNCT
ejpam-486	296	4	z	z	NOUN
ejpam-486	296	5	)	)	PUNCT
ejpam-486	296	6	∈	∈	PROPN
ejpam-486	296	7	a	a	DET
ejpam-486	296	8	�	�	PROPN
ejpam-486	296	9	p	p	PROPN
ejpam-486	296	10	�	�	PROPN
ejpam-486	296	11	,	,	PUNCT
ejpam-486	296	12	qα	qα	PROPN
ejpam-486	296	13	β	β	PROPN
ejpam-486	296	14	,	,	PUNCT
ejpam-486	296	15	p	p	PROPN
ejpam-486	296	16	f	f	X
ejpam-486	296	17	(	(	PUNCT
ejpam-486	296	18	z	z	NOUN
ejpam-486	296	19	)	)	PUNCT
ejpam-486	296	20	∈	∈	PROPN
ejpam-486	296	21	f0	f0	PROPN
ejpam-486	296	22	and	and	CCONJ
ejpam-486	296	23	φ	φ	PROPN
ejpam-486	296	24	�	�	PROPN
ejpam-486	296	25	qαβ	qαβ	PROPN
ejpam-486	296	26	,	,	PUNCT
ejpam-486	296	27	p	p	PROPN
ejpam-486	296	28	f	f	X
ejpam-486	296	29	(	(	PUNCT
ejpam-486	296	30	z),qα−1	z),qα−1	PROPN
ejpam-486	296	31	β	β	X
ejpam-486	296	32	,	,	PUNCT
ejpam-486	296	33	p	p	PROPN
ejpam-486	296	34	f	f	X
ejpam-486	296	35	(	(	PUNCT
ejpam-486	296	36	z),qα−2	z),qα−2	NOUN
ejpam-486	296	37	β	β	X
ejpam-486	296	38	,	,	PUNCT
ejpam-486	296	39	p	p	PROPN
ejpam-486	296	40	f	f	X
ejpam-486	296	41	(	(	PUNCT
ejpam-486	296	42	z	z	NOUN
ejpam-486	296	43	)	)	PUNCT
ejpam-486	296	44	;	;	PUNCT
ejpam-486	296	45	z	z	PROPN
ejpam-486	296	46	�	�	PROPN
ejpam-486	296	47	is	be	AUX
ejpam-486	296	48	univalent	univalent	ADJ
ejpam-486	296	49	in	in	ADP
ejpam-486	296	50	u	u	NOUN
ejpam-486	296	51	,	,	PUNCT
ejpam-486	296	52	then	then	ADV
ejpam-486	296	53	ω⊂	ω⊂	PROPN
ejpam-486	296	54	n	n	NUM
ejpam-486	296	55	φ	φ	PROPN
ejpam-486	296	56	�	�	PROPN
ejpam-486	296	57	qαβ	qαβ	PROPN
ejpam-486	296	58	,	,	PUNCT
ejpam-486	296	59	p	p	PROPN
ejpam-486	296	60	f	f	X
ejpam-486	296	61	(	(	PUNCT
ejpam-486	296	62	z),qα−1	z),qα−1	PROPN
ejpam-486	296	63	β	β	X
ejpam-486	296	64	,	,	PUNCT
ejpam-486	296	65	p	p	PROPN
ejpam-486	296	66	f	f	X
ejpam-486	296	67	(	(	PUNCT
ejpam-486	296	68	z),qα−2	z),qα−2	NOUN
ejpam-486	296	69	β	β	X
ejpam-486	296	70	,	,	PUNCT
ejpam-486	296	71	p	p	PROPN
ejpam-486	296	72	f	f	X
ejpam-486	296	73	(	(	PUNCT
ejpam-486	296	74	z	z	NOUN
ejpam-486	296	75	)	)	PUNCT
ejpam-486	296	76	;	;	PUNCT
ejpam-486	297	1	z	z	PROPN
ejpam-486	297	2	�	�	PROPN
ejpam-486	297	3	:	:	PUNCT
ejpam-486	297	4	z	z	PROPN
ejpam-486	297	5	∈	∈	PROPN
ejpam-486	297	6	u	u	X
ejpam-486	297	7	o	o	PROPN
ejpam-486	297	8	�	�	PROPN
ejpam-486	297	9	α	α	X
ejpam-486	297	10	>	>	X
ejpam-486	297	11	2;β	2;β	NUM
ejpam-486	297	12	>	>	SYM
ejpam-486	297	13	−1	−1	NOUN
ejpam-486	297	14	;	;	PUNCT
ejpam-486	297	15	p	p	PROPN
ejpam-486	297	16	∈	∈	PROPN
ejpam-486	297	17	n	n	PRON
ejpam-486	297	18	�	�	PROPN
ejpam-486	297	19	,	,	PUNCT
ejpam-486	297	20	(	(	PUNCT
ejpam-486	297	21	34	34	NUM
ejpam-486	297	22	)	)	PUNCT
ejpam-486	297	23	implies	imply	VERB
ejpam-486	297	24	q	q	PROPN
ejpam-486	297	25	(	(	PUNCT
ejpam-486	297	26	z	z	NOUN
ejpam-486	297	27	)	)	PUNCT
ejpam-486	297	28	≺	≺	NOUN
ejpam-486	297	29	qαβ	qαβ	INTJ
ejpam-486	297	30	,	,	PUNCT
ejpam-486	297	31	p	p	NOUN
ejpam-486	297	32	f	f	X
ejpam-486	297	33	(	(	PUNCT
ejpam-486	297	34	z	z	NOUN
ejpam-486	297	35	)	)	PUNCT
ejpam-486	297	36	(	(	PUNCT
ejpam-486	297	37	z	z	NOUN
ejpam-486	297	38	∈	∈	PROPN
ejpam-486	297	39	u	u	NOUN
ejpam-486	297	40	)	)	PUNCT
ejpam-486	297	41	.	.	PUNCT
ejpam-486	298	1	proof	proof	NOUN
ejpam-486	298	2	.	.	PUNCT
ejpam-486	299	1	from	from	ADP
ejpam-486	299	2	(	(	PUNCT
ejpam-486	299	3	11	11	NUM
ejpam-486	299	4	)	)	PUNCT
ejpam-486	299	5	and	and	CCONJ
ejpam-486	299	6	(	(	PUNCT
ejpam-486	299	7	34	34	NUM
ejpam-486	299	8	)	)	PUNCT
ejpam-486	299	9	,	,	PUNCT
ejpam-486	299	10	we	we	PRON
ejpam-486	299	11	have	have	VERB
ejpam-486	299	12	ω⊂	ω⊂	PROPN
ejpam-486	299	13	¦	¦	PROPN
ejpam-486	299	14	ψ(g(z	ψ(g(z	PROPN
ejpam-486	299	15	)	)	PUNCT
ejpam-486	299	16	,	,	PUNCT
ejpam-486	299	17	zg′(z	zg′(z	PROPN
ejpam-486	299	18	)	)	PUNCT
ejpam-486	299	19	,	,	PUNCT
ejpam-486	299	20	z2	z2	PROPN
ejpam-486	299	21	g	g	PROPN
ejpam-486	299	22	′′	′′	PROPN
ejpam-486	299	23	(	(	PUNCT
ejpam-486	299	24	z	z	PROPN
ejpam-486	299	25	)	)	PUNCT
ejpam-486	299	26	;	;	PUNCT
ejpam-486	300	1	z	z	X
ejpam-486	300	2	)	)	PUNCT
ejpam-486	300	3	:	:	PUNCT
ejpam-486	300	4	z	z	PROPN
ejpam-486	300	5	∈	∈	PROPN
ejpam-486	300	6	u	u	NOUN
ejpam-486	300	7	©	©	PROPN
ejpam-486	300	8	.	.	PUNCT
ejpam-486	301	1	from	from	ADP
ejpam-486	301	2	(	(	PUNCT
ejpam-486	301	3	9	9	NUM
ejpam-486	301	4	)	)	PUNCT
ejpam-486	301	5	,	,	PUNCT
ejpam-486	301	6	we	we	PRON
ejpam-486	301	7	see	see	VERB
ejpam-486	301	8	that	that	SCONJ
ejpam-486	301	9	the	the	DET
ejpam-486	301	10	admissibility	admissibility	NOUN
ejpam-486	301	11	condition	condition	NOUN
ejpam-486	301	12	for	for	ADP
ejpam-486	301	13	φ	φ	PROPN
ejpam-486	301	14	∈	∈	PROPN
ejpam-486	301	15	φ′q	φ′q	PROPN
ejpam-486	301	16	�	�	PROPN
ejpam-486	301	17	ω	ω	PROPN
ejpam-486	301	18	,	,	PUNCT
ejpam-486	301	19	q	q	PROPN
ejpam-486	301	20	�	�	PROPN
ejpam-486	301	21	is	be	AUX
ejpam-486	301	22	equivalent	equivalent	ADJ
ejpam-486	301	23	to	to	ADP
ejpam-486	301	24	the	the	DET
ejpam-486	301	25	admissibility	admissibility	NOUN
ejpam-486	301	26	condition	condition	NOUN
ejpam-486	301	27	for	for	ADP
ejpam-486	301	28	ψ	ψ	PRON
ejpam-486	301	29	as	as	SCONJ
ejpam-486	301	30	given	give	VERB
ejpam-486	301	31	in	in	ADP
ejpam-486	301	32	definition	definition	NOUN
ejpam-486	301	33	2	2	NUM
ejpam-486	301	34	.	.	PUNCT
ejpam-486	301	35	hence	hence	ADV
ejpam-486	301	36	ψ	ψ	X
ejpam-486	301	37	∈ψ′p	∈ψ′p	PROPN
ejpam-486	301	38	�	�	PROPN
ejpam-486	301	39	ω	ω	PROPN
ejpam-486	301	40	,	,	PUNCT
ejpam-486	301	41	q	q	PROPN
ejpam-486	301	42	�	�	PROPN
ejpam-486	301	43	,	,	PUNCT
ejpam-486	301	44	and	and	CCONJ
ejpam-486	301	45	by	by	ADP
ejpam-486	301	46	lemma	lemma	PROPN
ejpam-486	301	47	2	2	NUM
ejpam-486	301	48	,	,	PUNCT
ejpam-486	301	49	q(z)≺	q(z)≺	X
ejpam-486	301	50	g(z	g(z	PROPN
ejpam-486	301	51	)	)	PUNCT
ejpam-486	301	52	or	or	CCONJ
ejpam-486	301	53	q	q	ADJ
ejpam-486	301	54	(	(	PUNCT
ejpam-486	301	55	z	z	NOUN
ejpam-486	301	56	)	)	PUNCT
ejpam-486	301	57	≺	≺	NOUN
ejpam-486	301	58	qαβ	qαβ	INTJ
ejpam-486	301	59	,	,	PUNCT
ejpam-486	301	60	p	p	NOUN
ejpam-486	301	61	f	f	X
ejpam-486	301	62	(	(	PUNCT
ejpam-486	301	63	z	z	NOUN
ejpam-486	301	64	)	)	PUNCT
ejpam-486	301	65	(	(	PUNCT
ejpam-486	301	66	z	z	NOUN
ejpam-486	301	67	∈	∈	PROPN
ejpam-486	301	68	u	u	NOUN
ejpam-486	301	69	)	)	PUNCT
ejpam-486	301	70	.	.	PUNCT
ejpam-486	302	1	if	if	SCONJ
ejpam-486	302	2	ω	ω	PROPN
ejpam-486	302	3	6=	6=	PROPN
ejpam-486	302	4	c	c	PROPN
ejpam-486	302	5	is	be	AUX
ejpam-486	302	6	a	a	DET
ejpam-486	302	7	simply	simply	ADV
ejpam-486	302	8	connected	connected	ADJ
ejpam-486	302	9	domain	domain	NOUN
ejpam-486	302	10	,	,	PUNCT
ejpam-486	302	11	then	then	ADV
ejpam-486	302	12	ω	ω	PROPN
ejpam-486	302	13	=	=	SYM
ejpam-486	302	14	h(u	h(u	PROPN
ejpam-486	302	15	)	)	PUNCT
ejpam-486	302	16	for	for	ADP
ejpam-486	302	17	some	some	DET
ejpam-486	302	18	conformal	conformal	ADJ
ejpam-486	302	19	mapping	map	VERB
ejpam-486	302	20	h(z	h(z	NOUN
ejpam-486	302	21	)	)	PUNCT
ejpam-486	302	22	of	of	ADP
ejpam-486	302	23	u	u	PRON
ejpam-486	302	24	onto	onto	ADP
ejpam-486	302	25	ω	ω	NUM
ejpam-486	302	26	.	.	PUNCT
ejpam-486	303	1	in	in	ADP
ejpam-486	303	2	this	this	DET
ejpam-486	303	3	case	case	NOUN
ejpam-486	303	4	the	the	DET
ejpam-486	303	5	class	class	NOUN
ejpam-486	303	6	φ′q	φ′q	PROPN
ejpam-486	303	7	�	�	PROPN
ejpam-486	303	8	h(u	h(u	PROPN
ejpam-486	303	9	)	)	PUNCT
ejpam-486	303	10	,	,	PUNCT
ejpam-486	303	11	q	q	PROPN
ejpam-486	303	12	�	�	PROPN
ejpam-486	303	13	is	be	AUX
ejpam-486	303	14	written	write	VERB
ejpam-486	303	15	as	as	ADP
ejpam-486	303	16	φ′q	φ′q	PROPN
ejpam-486	303	17	�	�	PROPN
ejpam-486	303	18	h	h	PROPN
ejpam-486	303	19	,	,	PUNCT
ejpam-486	303	20	q	q	PROPN
ejpam-486	303	21	�	�	PROPN
ejpam-486	303	22	.	.	PUNCT
ejpam-486	304	1	proceeding	proceed	VERB
ejpam-486	304	2	similarly	similarly	ADV
ejpam-486	304	3	as	as	ADP
ejpam-486	304	4	in	in	ADP
ejpam-486	304	5	the	the	DET
ejpam-486	304	6	previous	previous	ADJ
ejpam-486	304	7	section	section	NOUN
ejpam-486	304	8	,	,	PUNCT
ejpam-486	304	9	the	the	DET
ejpam-486	304	10	following	following	ADJ
ejpam-486	304	11	result	result	NOUN
ejpam-486	304	12	is	be	AUX
ejpam-486	304	13	an	an	DET
ejpam-486	304	14	immediate	immediate	ADJ
ejpam-486	304	15	consequence	consequence	NOUN
ejpam-486	304	16	of	of	ADP
ejpam-486	304	17	theorem	theorem	ADJ
ejpam-486	304	18	9	9	NUM
ejpam-486	304	19	.	.	PUNCT
ejpam-486	304	20	theorem	theorem	NOUN
ejpam-486	304	21	10	10	NUM
ejpam-486	304	22	.	.	PUNCT
ejpam-486	305	1	let	let	VERB
ejpam-486	305	2	h(z	h(z	NOUN
ejpam-486	305	3	)	)	PUNCT
ejpam-486	305	4	is	be	AUX
ejpam-486	305	5	analytic	analytic	ADJ
ejpam-486	305	6	on	on	ADP
ejpam-486	305	7	u	u	NOUN
ejpam-486	305	8	and	and	CCONJ
ejpam-486	306	1	φ	φ	PROPN
ejpam-486	306	2	∈	∈	PROPN
ejpam-486	306	3	φ′q	φ′q	PROPN
ejpam-486	306	4	�	�	PROPN
ejpam-486	306	5	h	h	PROPN
ejpam-486	306	6	,	,	PUNCT
ejpam-486	306	7	q	q	PROPN
ejpam-486	306	8	�	�	PROPN
ejpam-486	306	9	.	.	PUNCT
ejpam-486	307	1	if	if	SCONJ
ejpam-486	307	2	f	f	PROPN
ejpam-486	307	3	(	(	PUNCT
ejpam-486	307	4	z	z	NOUN
ejpam-486	307	5	)	)	PUNCT
ejpam-486	307	6	∈	∈	PROPN
ejpam-486	307	7	a	a	DET
ejpam-486	307	8	�	�	PROPN
ejpam-486	307	9	p	p	PROPN
ejpam-486	307	10	�	�	PROPN
ejpam-486	307	11	,	,	PUNCT
ejpam-486	307	12	qα	qα	PROPN
ejpam-486	307	13	β	β	PROPN
ejpam-486	307	14	,	,	PUNCT
ejpam-486	307	15	p	p	PROPN
ejpam-486	307	16	f	f	X
ejpam-486	307	17	(	(	PUNCT
ejpam-486	307	18	z	z	NOUN
ejpam-486	307	19	)	)	PUNCT
ejpam-486	307	20	∈	∈	PROPN
ejpam-486	307	21	f0	f0	PROPN
ejpam-486	307	22	and	and	CCONJ
ejpam-486	307	23	φ	φ	PROPN
ejpam-486	307	24	�	�	PROPN
ejpam-486	307	25	qαβ	qαβ	PROPN
ejpam-486	307	26	,	,	PUNCT
ejpam-486	307	27	p	p	PROPN
ejpam-486	307	28	f	f	X
ejpam-486	307	29	(	(	PUNCT
ejpam-486	307	30	z),qα−1	z),qα−1	PROPN
ejpam-486	307	31	β	β	X
ejpam-486	307	32	,	,	PUNCT
ejpam-486	307	33	p	p	PROPN
ejpam-486	307	34	f	f	X
ejpam-486	307	35	(	(	PUNCT
ejpam-486	307	36	z),qα−2	z),qα−2	NOUN
ejpam-486	307	37	β	β	X
ejpam-486	307	38	,	,	PUNCT
ejpam-486	307	39	p	p	PROPN
ejpam-486	307	40	f	f	X
ejpam-486	307	41	(	(	PUNCT
ejpam-486	307	42	z	z	NOUN
ejpam-486	307	43	)	)	PUNCT
ejpam-486	307	44	;	;	PUNCT
ejpam-486	307	45	z	z	PROPN
ejpam-486	307	46	�	�	PROPN
ejpam-486	307	47	is	be	AUX
ejpam-486	307	48	univalent	univalent	ADJ
ejpam-486	307	49	in	in	ADP
ejpam-486	307	50	u	u	NOUN
ejpam-486	307	51	,	,	PUNCT
ejpam-486	307	52	then	then	ADV
ejpam-486	307	53	h(z	h(z	NOUN
ejpam-486	307	54	)	)	PUNCT
ejpam-486	307	55	≺	≺	NOUN
ejpam-486	307	56	φ	φ	PROPN
ejpam-486	307	57	�	�	PROPN
ejpam-486	307	58	qαβ	qαβ	PROPN
ejpam-486	307	59	,	,	PUNCT
ejpam-486	307	60	p	p	PROPN
ejpam-486	307	61	f	f	X
ejpam-486	307	62	(	(	PUNCT
ejpam-486	307	63	z),qα−1	z),qα−1	PROPN
ejpam-486	307	64	β	β	X
ejpam-486	307	65	,	,	PUNCT
ejpam-486	307	66	p	p	PROPN
ejpam-486	307	67	f	f	X
ejpam-486	307	68	(	(	PUNCT
ejpam-486	307	69	z),qα−2	z),qα−2	NOUN
ejpam-486	307	70	β	β	X
ejpam-486	307	71	,	,	PUNCT
ejpam-486	307	72	p	p	PROPN
ejpam-486	307	73	f	f	X
ejpam-486	307	74	(	(	PUNCT
ejpam-486	307	75	z	z	NOUN
ejpam-486	307	76	)	)	PUNCT
ejpam-486	307	77	;	;	PUNCT
ejpam-486	307	78	z	z	PROPN
ejpam-486	307	79	�	�	PROPN
ejpam-486	307	80	�	�	PROPN
ejpam-486	307	81	α	α	PROPN
ejpam-486	307	82	>	>	X
ejpam-486	307	83	2	2	NUM
ejpam-486	307	84	;	;	PUNCT
ejpam-486	307	85	β	β	X
ejpam-486	307	86	>	>	X
ejpam-486	307	87	−1	−1	NOUN
ejpam-486	307	88	;	;	PUNCT
ejpam-486	307	89	p	p	PROPN
ejpam-486	307	90	∈	∈	PROPN
ejpam-486	307	91	n	n	CCONJ
ejpam-486	307	92	;	;	PUNCT
ejpam-486	307	93	z	z	PROPN
ejpam-486	307	94	∈	∈	PROPN
ejpam-486	307	95	u	u	PROPN
ejpam-486	307	96	�	�	PROPN
ejpam-486	307	97	,	,	PUNCT
ejpam-486	307	98	(	(	PUNCT
ejpam-486	307	99	35	35	NUM
ejpam-486	307	100	)	)	PUNCT
ejpam-486	307	101	implies	imply	VERB
ejpam-486	307	102	q	q	PROPN
ejpam-486	307	103	(	(	PUNCT
ejpam-486	307	104	z	z	NOUN
ejpam-486	307	105	)	)	PUNCT
ejpam-486	307	106	≺	≺	NOUN
ejpam-486	307	107	qαβ	qαβ	INTJ
ejpam-486	307	108	,	,	PUNCT
ejpam-486	307	109	p	p	NOUN
ejpam-486	307	110	f	f	X
ejpam-486	307	111	(	(	PUNCT
ejpam-486	307	112	z	z	NOUN
ejpam-486	307	113	)	)	PUNCT
ejpam-486	307	114	(	(	PUNCT
ejpam-486	307	115	z	z	NOUN
ejpam-486	307	116	∈	∈	PROPN
ejpam-486	307	117	u	u	NOUN
ejpam-486	307	118	)	)	PUNCT
ejpam-486	307	119	.	.	PUNCT
ejpam-486	308	1	theorems	theorem	NOUN
ejpam-486	308	2	9	9	NUM
ejpam-486	308	3	and	and	CCONJ
ejpam-486	308	4	10	10	NUM
ejpam-486	308	5	can	can	AUX
ejpam-486	308	6	only	only	ADV
ejpam-486	308	7	be	be	AUX
ejpam-486	308	8	used	use	VERB
ejpam-486	308	9	to	to	PART
ejpam-486	308	10	obtain	obtain	VERB
ejpam-486	308	11	subordinants	subordinant	NOUN
ejpam-486	308	12	of	of	ADP
ejpam-486	308	13	differential	differential	ADJ
ejpam-486	308	14	superordination	superordination	NOUN
ejpam-486	308	15	of	of	ADP
ejpam-486	308	16	the	the	DET
ejpam-486	308	17	form	form	NOUN
ejpam-486	308	18	(	(	PUNCT
ejpam-486	308	19	34	34	NUM
ejpam-486	308	20	)	)	PUNCT
ejpam-486	308	21	or	or	CCONJ
ejpam-486	308	22	(	(	PUNCT
ejpam-486	308	23	35	35	NUM
ejpam-486	308	24	)	)	PUNCT
ejpam-486	308	25	.	.	PUNCT
ejpam-486	309	1	the	the	DET
ejpam-486	309	2	following	follow	VERB
ejpam-486	309	3	theorem	theorem	NOUN
ejpam-486	309	4	proves	prove	VERB
ejpam-486	309	5	the	the	DET
ejpam-486	309	6	existence	existence	NOUN
ejpam-486	309	7	of	of	ADP
ejpam-486	309	8	the	the	DET
ejpam-486	309	9	best	good	ADJ
ejpam-486	309	10	subordinant	subordinant	NOUN
ejpam-486	309	11	of	of	ADP
ejpam-486	309	12	(	(	PUNCT
ejpam-486	309	13	35	35	NUM
ejpam-486	309	14	)	)	PUNCT
ejpam-486	309	15	for	for	ADP
ejpam-486	309	16	certain	certain	ADJ
ejpam-486	309	17	φ	φ	PROPN
ejpam-486	309	18	.	.	PUNCT
ejpam-486	309	19	theorem	theorem	VERB
ejpam-486	309	20	11	11	NUM
ejpam-486	309	21	.	.	PUNCT
ejpam-486	310	1	let	let	VERB
ejpam-486	310	2	h(z	h(z	NOUN
ejpam-486	310	3	)	)	PUNCT
ejpam-486	310	4	be	be	AUX
ejpam-486	310	5	analytic	analytic	ADJ
ejpam-486	310	6	in	in	ADP
ejpam-486	310	7	u	u	NOUN
ejpam-486	310	8	and	and	CCONJ
ejpam-486	310	9	φ	φ	NOUN
ejpam-486	310	10	:	:	PUNCT
ejpam-486	311	1	c3	c3	PROPN
ejpam-486	311	2	×	×	PROPN
ejpam-486	311	3	ū	ū	PROPN
ejpam-486	311	4	→	→	PUNCT
ejpam-486	311	5	c.	c.	PROPN
ejpam-486	311	6	suppose	suppose	VERB
ejpam-486	311	7	that	that	SCONJ
ejpam-486	311	8	the	the	DET
ejpam-486	311	9	differential	differential	ADJ
ejpam-486	311	10	equation	equation	NOUN
ejpam-486	311	11	φ	φ	PROPN
ejpam-486	311	12	�	�	PROPN
ejpam-486	311	13	q(z	q(z	PROPN
ejpam-486	311	14	)	)	PUNCT
ejpam-486	311	15	,	,	PUNCT
ejpam-486	311	16	zq′(z	zq′(z	PROPN
ejpam-486	311	17	)	)	PUNCT
ejpam-486	311	18	,	,	PUNCT
ejpam-486	311	19	z2q	z2q	PUNCT
ejpam-486	311	20	′′	′′	PROPN
ejpam-486	311	21	(	(	PUNCT
ejpam-486	311	22	z	z	PROPN
ejpam-486	311	23	)	)	PUNCT
ejpam-486	311	24	;	;	PUNCT
ejpam-486	311	25	z	z	PROPN
ejpam-486	311	26	�	�	PROPN
ejpam-486	311	27	=	=	SYM
ejpam-486	311	28	h(z	h(z	NOUN
ejpam-486	311	29	)	)	PUNCT
ejpam-486	311	30	has	have	VERB
ejpam-486	311	31	a	a	DET
ejpam-486	311	32	solution	solution	NOUN
ejpam-486	311	33	q(z	q(z	PROPN
ejpam-486	311	34	)	)	PUNCT
ejpam-486	311	35	∈	∈	PROPN
ejpam-486	311	36	f0	f0	PROPN
ejpam-486	311	37	.	.	PUNCT
ejpam-486	312	1	if	if	SCONJ
ejpam-486	312	2	φ	φ	PROPN
ejpam-486	312	3	∈	∈	PROPN
ejpam-486	312	4	φ′q	φ′q	PROPN
ejpam-486	312	5	�	�	PROPN
ejpam-486	312	6	h	h	PROPN
ejpam-486	312	7	,	,	PUNCT
ejpam-486	312	8	q	q	PROPN
ejpam-486	312	9	�	�	PROPN
ejpam-486	312	10	,	,	PUNCT
ejpam-486	312	11	f	f	PROPN
ejpam-486	312	12	(	(	PUNCT
ejpam-486	312	13	z	z	NOUN
ejpam-486	312	14	)	)	PUNCT
ejpam-486	312	15	∈	∈	PROPN
ejpam-486	312	16	a	a	DET
ejpam-486	312	17	�	�	PROPN
ejpam-486	312	18	p	p	PROPN
ejpam-486	312	19	�	�	PROPN
ejpam-486	312	20	,	,	PUNCT
ejpam-486	312	21	qα	qα	PROPN
ejpam-486	312	22	β	β	PROPN
ejpam-486	312	23	,	,	PUNCT
ejpam-486	312	24	p	p	PROPN
ejpam-486	312	25	f	f	X
ejpam-486	312	26	(	(	PUNCT
ejpam-486	312	27	z	z	NOUN
ejpam-486	312	28	)	)	PUNCT
ejpam-486	312	29	∈	∈	PROPN
ejpam-486	312	30	f0	f0	PROPN
ejpam-486	312	31	and	and	CCONJ
ejpam-486	312	32	φ	φ	PROPN
ejpam-486	312	33	�	�	PROPN
ejpam-486	312	34	qαβ	qαβ	PROPN
ejpam-486	312	35	,	,	PUNCT
ejpam-486	312	36	p	p	PROPN
ejpam-486	312	37	f	f	X
ejpam-486	312	38	(	(	PUNCT
ejpam-486	312	39	z),qα−1	z),qα−1	PROPN
ejpam-486	312	40	β	β	X
ejpam-486	312	41	,	,	PUNCT
ejpam-486	312	42	p	p	PROPN
ejpam-486	312	43	f	f	X
ejpam-486	312	44	(	(	PUNCT
ejpam-486	312	45	z),qα−2	z),qα−2	NOUN
ejpam-486	312	46	β	β	X
ejpam-486	312	47	,	,	PUNCT
ejpam-486	312	48	p	p	PROPN
ejpam-486	312	49	f	f	X
ejpam-486	312	50	(	(	PUNCT
ejpam-486	312	51	z	z	NOUN
ejpam-486	312	52	)	)	PUNCT
ejpam-486	312	53	;	;	PUNCT
ejpam-486	312	54	z	z	PROPN
ejpam-486	312	55	�	�	PROPN
ejpam-486	312	56	m.	m.	PROPN
ejpam-486	312	57	aouf	aouf	PROPN
ejpam-486	312	58	,	,	PUNCT
ejpam-486	312	59	t.	t.	PROPN
ejpam-486	312	60	seoudy	seoudy	PROPN
ejpam-486	312	61	/	/	SYM
ejpam-486	312	62	eur	eur	PROPN
ejpam-486	312	63	.	.	PUNCT
ejpam-486	313	1	j.	j.	PROPN
ejpam-486	313	2	pure	pure	PROPN
ejpam-486	313	3	appl	appl	PROPN
ejpam-486	313	4	.	.	PROPN
ejpam-486	313	5	math	math	PROPN
ejpam-486	313	6	,	,	PUNCT
ejpam-486	313	7	3	3	NUM
ejpam-486	313	8	(	(	PUNCT
ejpam-486	313	9	2010	2010	NUM
ejpam-486	313	10	)	)	PUNCT
ejpam-486	313	11	,	,	PUNCT
ejpam-486	313	12	26	26	NUM
ejpam-486	313	13	-	-	SYM
ejpam-486	313	14	44	44	NUM
ejpam-486	313	15	40	40	NUM
ejpam-486	313	16	is	be	AUX
ejpam-486	313	17	univalent	univalent	ADJ
ejpam-486	313	18	in	in	ADP
ejpam-486	313	19	u	u	NOUN
ejpam-486	313	20	,	,	PUNCT
ejpam-486	313	21	then	then	ADV
ejpam-486	313	22	h(z	h(z	NOUN
ejpam-486	313	23	)	)	PUNCT
ejpam-486	313	24	≺	≺	NOUN
ejpam-486	313	25	φ	φ	PROPN
ejpam-486	313	26	�	�	PROPN
ejpam-486	313	27	qαβ	qαβ	PROPN
ejpam-486	313	28	,	,	PUNCT
ejpam-486	313	29	p	p	PROPN
ejpam-486	313	30	f	f	X
ejpam-486	313	31	(	(	PUNCT
ejpam-486	313	32	z),qα−1	z),qα−1	PROPN
ejpam-486	313	33	β	β	X
ejpam-486	313	34	,	,	PUNCT
ejpam-486	313	35	p	p	PROPN
ejpam-486	313	36	f	f	X
ejpam-486	313	37	(	(	PUNCT
ejpam-486	313	38	z),qα−2	z),qα−2	NOUN
ejpam-486	313	39	β	β	X
ejpam-486	313	40	,	,	PUNCT
ejpam-486	313	41	p	p	PROPN
ejpam-486	313	42	f	f	X
ejpam-486	313	43	(	(	PUNCT
ejpam-486	313	44	z	z	NOUN
ejpam-486	313	45	)	)	PUNCT
ejpam-486	313	46	;	;	PUNCT
ejpam-486	313	47	z	z	PROPN
ejpam-486	313	48	�	�	PROPN
ejpam-486	313	49	�	�	PROPN
ejpam-486	313	50	α	α	PROPN
ejpam-486	313	51	>	>	X
ejpam-486	313	52	2	2	NUM
ejpam-486	313	53	;	;	PUNCT
ejpam-486	313	54	β	β	X
ejpam-486	313	55	>	>	X
ejpam-486	313	56	−1	−1	NOUN
ejpam-486	313	57	;	;	PUNCT
ejpam-486	313	58	p	p	PROPN
ejpam-486	313	59	∈	∈	PROPN
ejpam-486	313	60	n	n	CCONJ
ejpam-486	313	61	;	;	PUNCT
ejpam-486	313	62	z	z	PROPN
ejpam-486	313	63	∈	∈	PROPN
ejpam-486	313	64	u	u	PROPN
ejpam-486	313	65	�	�	PROPN
ejpam-486	313	66	implies	imply	VERB
ejpam-486	313	67	q	q	X
ejpam-486	313	68	(	(	PUNCT
ejpam-486	313	69	z	z	NOUN
ejpam-486	313	70	)	)	PUNCT
ejpam-486	313	71	≺	≺	NOUN
ejpam-486	313	72	qαβ	qαβ	INTJ
ejpam-486	313	73	,	,	PUNCT
ejpam-486	313	74	p	p	NOUN
ejpam-486	313	75	f	f	X
ejpam-486	313	76	(	(	PUNCT
ejpam-486	313	77	z	z	NOUN
ejpam-486	313	78	)	)	PUNCT
ejpam-486	313	79	(	(	PUNCT
ejpam-486	313	80	z	z	NOUN
ejpam-486	313	81	∈	∈	PROPN
ejpam-486	313	82	u	u	NOUN
ejpam-486	313	83	)	)	PUNCT
ejpam-486	313	84	.	.	PUNCT
ejpam-486	314	1	and	and	CCONJ
ejpam-486	314	2	q(z	q(z	PROPN
ejpam-486	314	3	)	)	PUNCT
ejpam-486	314	4	is	be	AUX
ejpam-486	314	5	the	the	DET
ejpam-486	314	6	best	good	ADJ
ejpam-486	314	7	subordinant	subordinant	NOUN
ejpam-486	314	8	.	.	PUNCT
ejpam-486	315	1	proof	proof	NOUN
ejpam-486	315	2	.	.	PUNCT
ejpam-486	316	1	the	the	DET
ejpam-486	316	2	proof	proof	NOUN
ejpam-486	316	3	is	be	AUX
ejpam-486	316	4	similar	similar	ADJ
ejpam-486	316	5	to	to	ADP
ejpam-486	316	6	the	the	DET
ejpam-486	316	7	proof	proof	NOUN
ejpam-486	316	8	of	of	ADP
ejpam-486	316	9	theorem	theorem	NOUN
ejpam-486	316	10	4	4	NUM
ejpam-486	316	11	and	and	CCONJ
ejpam-486	316	12	is	be	AUX
ejpam-486	316	13	therefore	therefore	ADV
ejpam-486	316	14	omitted	omit	VERB
ejpam-486	316	15	.	.	PUNCT
ejpam-486	317	1	combining	combine	VERB
ejpam-486	317	2	theorems	theorem	NOUN
ejpam-486	317	3	2	2	NUM
ejpam-486	317	4	and	and	CCONJ
ejpam-486	317	5	10	10	NUM
ejpam-486	317	6	,	,	PUNCT
ejpam-486	317	7	we	we	PRON
ejpam-486	317	8	obtain	obtain	VERB
ejpam-486	317	9	the	the	DET
ejpam-486	317	10	following	follow	VERB
ejpam-486	317	11	sandwich	sandwich	NOUN
ejpam-486	317	12	-	-	PUNCT
ejpam-486	317	13	type	type	NOUN
ejpam-486	317	14	theorem	theorem	ADJ
ejpam-486	317	15	.	.	PROPN
ejpam-486	317	16	corollary	corollary	ADJ
ejpam-486	317	17	10	10	NUM
ejpam-486	317	18	.	.	PUNCT
ejpam-486	318	1	let	let	AUX
ejpam-486	318	2	h1(z	h1(z	NUM
ejpam-486	318	3	)	)	PUNCT
ejpam-486	318	4	and	and	CCONJ
ejpam-486	318	5	q1(z	q1(z	PROPN
ejpam-486	318	6	)	)	PUNCT
ejpam-486	318	7	be	be	AUX
ejpam-486	318	8	analytic	analytic	ADJ
ejpam-486	318	9	functions	function	NOUN
ejpam-486	318	10	in	in	ADP
ejpam-486	318	11	u	u	NOUN
ejpam-486	318	12	,	,	PUNCT
ejpam-486	318	13	h2(z	h2(z	X
ejpam-486	318	14	)	)	PUNCT
ejpam-486	318	15	be	be	AUX
ejpam-486	318	16	univalent	univalent	ADJ
ejpam-486	318	17	function	function	NOUN
ejpam-486	318	18	in	in	ADP
ejpam-486	318	19	u	u	NOUN
ejpam-486	318	20	,	,	PUNCT
ejpam-486	318	21	q2(z	q2(z	NOUN
ejpam-486	318	22	)	)	PUNCT
ejpam-486	318	23	∈	∈	NOUN
ejpam-486	318	24	f0	f0	PROPN
ejpam-486	318	25	with	with	ADP
ejpam-486	318	26	q1(0	q1(0	PROPN
ejpam-486	318	27	)	)	PUNCT
ejpam-486	319	1	=	=	PUNCT
ejpam-486	319	2	q2(0	q2(0	PROPN
ejpam-486	319	3	)	)	PUNCT
ejpam-486	319	4	=	=	SYM
ejpam-486	319	5	0	0	NUM
ejpam-486	319	6	and	and	CCONJ
ejpam-486	319	7	φ	φ	PROPN
ejpam-486	319	8	∈	∈	PROPN
ejpam-486	319	9	φq	φq	ADP
ejpam-486	319	10	�	�	PROPN
ejpam-486	319	11	h2,q2	h2,q2	PROPN
ejpam-486	319	12	�	�	PROPN
ejpam-486	319	13	∩	∩	NOUN
ejpam-486	319	14	φ′q	φ′q	PROPN
ejpam-486	319	15	�	�	PROPN
ejpam-486	319	16	h1,q1	h1,q1	PROPN
ejpam-486	319	17	�	�	PROPN
ejpam-486	319	18	.	.	PUNCT
ejpam-486	320	1	if	if	SCONJ
ejpam-486	320	2	f	f	PROPN
ejpam-486	320	3	(	(	PUNCT
ejpam-486	320	4	z	z	NOUN
ejpam-486	320	5	)	)	PUNCT
ejpam-486	320	6	∈	∈	PROPN
ejpam-486	320	7	a	a	DET
ejpam-486	320	8	�	�	PROPN
ejpam-486	320	9	p	p	PROPN
ejpam-486	320	10	�	�	PROPN
ejpam-486	320	11	,	,	PUNCT
ejpam-486	320	12	qα	qα	PROPN
ejpam-486	320	13	β	β	PROPN
ejpam-486	320	14	,	,	PUNCT
ejpam-486	320	15	p	p	PROPN
ejpam-486	320	16	f	f	X
ejpam-486	320	17	(	(	PUNCT
ejpam-486	320	18	z	z	NOUN
ejpam-486	320	19	)	)	PUNCT
ejpam-486	320	20	∈	∈	PROPN
ejpam-486	320	21	h[0	h[0	PROPN
ejpam-486	320	22	,	,	PUNCT
ejpam-486	321	1	p	p	X
ejpam-486	321	2	]	]	X
ejpam-486	321	3	∩f0	∩f0	NOUN
ejpam-486	321	4	and	and	CCONJ
ejpam-486	321	5	φ	φ	PROPN
ejpam-486	321	6	�	�	PROPN
ejpam-486	321	7	qαβ	qαβ	PROPN
ejpam-486	321	8	,	,	PUNCT
ejpam-486	321	9	p	p	PROPN
ejpam-486	321	10	f	f	X
ejpam-486	321	11	(	(	PUNCT
ejpam-486	321	12	z),qα−1	z),qα−1	PROPN
ejpam-486	321	13	β	β	X
ejpam-486	321	14	,	,	PUNCT
ejpam-486	321	15	p	p	PROPN
ejpam-486	321	16	f	f	X
ejpam-486	321	17	(	(	PUNCT
ejpam-486	321	18	z),qα−2	z),qα−2	NOUN
ejpam-486	321	19	β	β	X
ejpam-486	321	20	,	,	PUNCT
ejpam-486	321	21	p	p	PROPN
ejpam-486	321	22	f	f	X
ejpam-486	321	23	(	(	PUNCT
ejpam-486	321	24	z	z	NOUN
ejpam-486	321	25	)	)	PUNCT
ejpam-486	321	26	;	;	PUNCT
ejpam-486	321	27	z	z	PROPN
ejpam-486	321	28	�	�	PROPN
ejpam-486	321	29	�	�	PROPN
ejpam-486	321	30	α	α	PROPN
ejpam-486	321	31	>	>	X
ejpam-486	321	32	2	2	NUM
ejpam-486	321	33	;	;	PUNCT
ejpam-486	321	34	β	β	X
ejpam-486	321	35	>	>	X
ejpam-486	321	36	−1	−1	NOUN
ejpam-486	321	37	;	;	PUNCT
ejpam-486	321	38	p	p	PROPN
ejpam-486	321	39	∈	∈	PROPN
ejpam-486	321	40	n	n	CCONJ
ejpam-486	321	41	;	;	PUNCT
ejpam-486	321	42	z	z	PROPN
ejpam-486	321	43	∈	∈	PROPN
ejpam-486	321	44	u	u	PROPN
ejpam-486	321	45	�	�	PROPN
ejpam-486	321	46	is	be	AUX
ejpam-486	321	47	univalent	univalent	ADJ
ejpam-486	321	48	in	in	ADP
ejpam-486	321	49	u	u	NOUN
ejpam-486	321	50	,	,	PUNCT
ejpam-486	321	51	then	then	ADV
ejpam-486	321	52	h1(z	h1(z	NOUN
ejpam-486	321	53	)	)	PUNCT
ejpam-486	321	54	≺	≺	NOUN
ejpam-486	321	55	φ	φ	PROPN
ejpam-486	321	56	�	�	PROPN
ejpam-486	321	57	qαβ	qαβ	PROPN
ejpam-486	321	58	,	,	PUNCT
ejpam-486	321	59	p	p	PROPN
ejpam-486	321	60	f	f	X
ejpam-486	321	61	(	(	PUNCT
ejpam-486	321	62	z),qα−1	z),qα−1	PROPN
ejpam-486	321	63	β	β	X
ejpam-486	321	64	,	,	PUNCT
ejpam-486	321	65	p	p	PROPN
ejpam-486	321	66	f	f	X
ejpam-486	322	1	(	(	PUNCT
ejpam-486	322	2	z),qα−2	z),qα−2	NOUN
ejpam-486	322	3	β	β	X
ejpam-486	322	4	,	,	PUNCT
ejpam-486	322	5	p	p	PROPN
ejpam-486	322	6	f	f	X
ejpam-486	322	7	(	(	PUNCT
ejpam-486	322	8	z	z	NOUN
ejpam-486	322	9	)	)	PUNCT
ejpam-486	322	10	;	;	PUNCT
ejpam-486	322	11	z	z	PROPN
ejpam-486	322	12	�	�	PROPN
ejpam-486	322	13	≺	≺	NOUN
ejpam-486	322	14	h2(z	h2(z	NUM
ejpam-486	322	15	)	)	PUNCT
ejpam-486	322	16	�	�	PROPN
ejpam-486	322	17	α	α	PROPN
ejpam-486	322	18	>	>	X
ejpam-486	322	19	2	2	NUM
ejpam-486	322	20	;	;	PUNCT
ejpam-486	322	21	p	p	PROPN
ejpam-486	322	22	∈	∈	PROPN
ejpam-486	322	23	n	n	CCONJ
ejpam-486	322	24	;	;	PUNCT
ejpam-486	322	25	z	z	PROPN
ejpam-486	322	26	∈	∈	PROPN
ejpam-486	322	27	u	u	PROPN
ejpam-486	322	28	�	�	PROPN
ejpam-486	322	29	,	,	PUNCT
ejpam-486	322	30	implies	imply	VERB
ejpam-486	322	31	q1(z	q1(z	NUM
ejpam-486	322	32	)	)	PUNCT
ejpam-486	322	33	≺	≺	NOUN
ejpam-486	322	34	qαβ	qαβ	INTJ
ejpam-486	322	35	,	,	PUNCT
ejpam-486	322	36	p	p	NOUN
ejpam-486	322	37	f	f	X
ejpam-486	322	38	(	(	PUNCT
ejpam-486	322	39	z	z	NOUN
ejpam-486	322	40	)	)	PUNCT
ejpam-486	322	41	≺	≺	NOUN
ejpam-486	322	42	q2(z	q2(z	NUM
ejpam-486	322	43	)	)	PUNCT
ejpam-486	322	44	(	(	PUNCT
ejpam-486	322	45	z	z	NOUN
ejpam-486	322	46	∈	∈	PROPN
ejpam-486	322	47	u	u	NOUN
ejpam-486	322	48	)	)	PUNCT
ejpam-486	322	49	.	.	PUNCT
ejpam-486	323	1	definition	definition	NOUN
ejpam-486	323	2	10	10	NUM
ejpam-486	323	3	.	.	PUNCT
ejpam-486	324	1	let	let	VERB
ejpam-486	324	2	ω	ω	PRON
ejpam-486	324	3	be	be	AUX
ejpam-486	324	4	a	a	DET
ejpam-486	324	5	set	set	NOUN
ejpam-486	324	6	in	in	ADP
ejpam-486	324	7	c	c	PROPN
ejpam-486	324	8	and	and	CCONJ
ejpam-486	324	9	q(z	q(z	PROPN
ejpam-486	324	10	)	)	PUNCT
ejpam-486	324	11	∈	∈	PROPN
ejpam-486	324	12	h0	h0	NOUN
ejpam-486	324	13	with	with	ADP
ejpam-486	324	14	zq′(z	zq′(z	PROPN
ejpam-486	324	15	)	)	PUNCT
ejpam-486	324	16	6=	6=	ADP
ejpam-486	324	17	0	0	X
ejpam-486	324	18	.	.	PUNCT
ejpam-486	325	1	the	the	DET
ejpam-486	325	2	class	class	NOUN
ejpam-486	325	3	of	of	ADP
ejpam-486	325	4	admissible	admissible	ADJ
ejpam-486	325	5	functions	function	NOUN
ejpam-486	325	6	φ′q,1	φ′q,1	PROPN
ejpam-486	325	7	�	�	PROPN
ejpam-486	325	8	ω	ω	PROPN
ejpam-486	325	9	,	,	PUNCT
ejpam-486	325	10	q	q	PROPN
ejpam-486	325	11	�	�	PROPN
ejpam-486	325	12	consists	consist	VERB
ejpam-486	325	13	of	of	ADP
ejpam-486	325	14	those	those	DET
ejpam-486	325	15	functions	function	NOUN
ejpam-486	325	16	φc3	φc3	PROPN
ejpam-486	325	17	×	×	NOUN
ejpam-486	325	18	ū	ū	NOUN
ejpam-486	325	19	→	→	SYM
ejpam-486	325	20	c	c	NOUN
ejpam-486	325	21	that	that	PRON
ejpam-486	325	22	satisfy	satisfy	VERB
ejpam-486	325	23	the	the	DET
ejpam-486	325	24	admissibility	admissibility	NOUN
ejpam-486	325	25	condition	condition	NOUN
ejpam-486	325	26	:	:	PUNCT
ejpam-486	325	27	φ	φ	PROPN
ejpam-486	325	28	(	(	PUNCT
ejpam-486	325	29	u	u	NOUN
ejpam-486	325	30	,	,	PUNCT
ejpam-486	325	31	v	v	NOUN
ejpam-486	325	32	,	,	PUNCT
ejpam-486	325	33	w;ζ	w;ζ	NUM
ejpam-486	325	34	)	)	PUNCT
ejpam-486	325	35	∈	∈	PROPN
ejpam-486	325	36	ω	ω	PROPN
ejpam-486	325	37	(	(	PUNCT
ejpam-486	325	38	36	36	NUM
ejpam-486	325	39	)	)	PUNCT
ejpam-486	325	40	whenever	whenever	SCONJ
ejpam-486	325	41	u	u	NOUN
ejpam-486	325	42	=	=	X
ejpam-486	325	43	q	q	X
ejpam-486	325	44	(	(	PUNCT
ejpam-486	325	45	z	z	NOUN
ejpam-486	325	46	)	)	PUNCT
ejpam-486	325	47	,	,	PUNCT
ejpam-486	325	48	v	v	X
ejpam-486	325	49	=	=	SYM
ejpam-486	325	50	zq′	zq′	X
ejpam-486	325	51	(	(	PUNCT
ejpam-486	325	52	z	z	NOUN
ejpam-486	325	53	)	)	PUNCT
ejpam-486	326	1	+	+	PROPN
ejpam-486	326	2	m	m	VERB
ejpam-486	326	3	�	�	PROPN
ejpam-486	326	4	α+β	α+β	NUM
ejpam-486	326	5	+	+	CCONJ
ejpam-486	326	6	p−	p−	PROPN
ejpam-486	326	7	2	2	NUM
ejpam-486	326	8	�	�	PROPN
ejpam-486	326	9	q	q	PROPN
ejpam-486	326	10	(	(	PUNCT
ejpam-486	326	11	z	z	NOUN
ejpam-486	326	12	)	)	PUNCT
ejpam-486	326	13	m	m	VERB
ejpam-486	326	14	�	�	INTJ
ejpam-486	326	15	α+	α+	PUNCT
ejpam-486	326	16	β	β	NOUN
ejpam-486	326	17	+	+	CCONJ
ejpam-486	326	18	p−	p−	PROPN
ejpam-486	326	19	1	1	NUM
ejpam-486	326	20	�	�	PROPN
ejpam-486	326	21	,	,	PUNCT
ejpam-486	326	22	ℜ	ℜ	PROPN
ejpam-486	326	23	¨	¨	NOUN
ejpam-486	326	24	�	�	PROPN
ejpam-486	326	25	α+	α+	PUNCT
ejpam-486	326	26	β	β	NOUN
ejpam-486	326	27	+	+	CCONJ
ejpam-486	326	28	p−	p−	PROPN
ejpam-486	326	29	2	2	NUM
ejpam-486	326	30	�	�	PROPN
ejpam-486	326	31	�	�	PROPN
ejpam-486	326	32	�	�	PROPN
ejpam-486	326	33	α+	α+	X
ejpam-486	326	34	β	β	NOUN
ejpam-486	326	35	+	+	CCONJ
ejpam-486	326	36	p−	p−	PROPN
ejpam-486	326	37	1	1	NUM
ejpam-486	326	38	�	�	PROPN
ejpam-486	326	39	w	w	PROPN
ejpam-486	326	40	−	−	PROPN
ejpam-486	326	41	�	�	PROPN
ejpam-486	326	42	α+	α+	PUNCT
ejpam-486	326	43	β	β	NOUN
ejpam-486	326	44	+	+	CCONJ
ejpam-486	326	45	p−	p−	PROPN
ejpam-486	326	46	3	3	NUM
ejpam-486	326	47	�	�	PROPN
ejpam-486	326	48	u	u	PROPN
ejpam-486	326	49	�	�	PROPN
ejpam-486	326	50	�	�	PROPN
ejpam-486	326	51	α+	α+	X
ejpam-486	326	52	β	β	NOUN
ejpam-486	326	53	+	+	CCONJ
ejpam-486	326	54	p−	p−	PROPN
ejpam-486	326	55	1	1	NUM
ejpam-486	326	56	�	�	PROPN
ejpam-486	326	57	v	v	ADP
ejpam-486	326	58	−	−	PROPN
ejpam-486	326	59	�	�	PROPN
ejpam-486	326	60	α+	α+	PUNCT
ejpam-486	326	61	β	β	NOUN
ejpam-486	326	62	+	+	CCONJ
ejpam-486	326	63	p−	p−	PROPN
ejpam-486	326	64	2	2	NUM
ejpam-486	326	65	�	�	PROPN
ejpam-486	326	66	u	u	NOUN
ejpam-486	326	67	−	−	PROPN
ejpam-486	326	68	2	2	NUM
ejpam-486	326	69	�	�	PROPN
ejpam-486	326	70	α+	α+	PUNCT
ejpam-486	326	71	β	β	X
ejpam-486	326	72	�	�	PROPN
ejpam-486	326	73	+	+	CCONJ
ejpam-486	326	74	5	5	NUM
ejpam-486	326	75	«	«	SYM
ejpam-486	326	76	≤	≤	NUM
ejpam-486	326	77	1	1	NUM
ejpam-486	326	78	m	m	NOUN
ejpam-486	326	79	ℜ	ℜ	NOUN
ejpam-486	326	80	(	(	PUNCT
ejpam-486	326	81	1	1	NUM
ejpam-486	326	82	+	+	NUM
ejpam-486	326	83	zq	zq	PROPN
ejpam-486	326	84	′′	′′	PROPN
ejpam-486	326	85	(	(	PUNCT
ejpam-486	326	86	z	z	NOUN
ejpam-486	326	87	)	)	PUNCT
ejpam-486	326	88	q′	q′	NOUN
ejpam-486	326	89	(	(	PUNCT
ejpam-486	326	90	z	z	NOUN
ejpam-486	326	91	)	)	PUNCT
ejpam-486	326	92	)	)	PUNCT
ejpam-486	326	93	,	,	PUNCT
ejpam-486	326	94	where	where	SCONJ
ejpam-486	326	95	z	z	PROPN
ejpam-486	326	96	∈	∈	PROPN
ejpam-486	326	97	u	u	NOUN
ejpam-486	326	98	,	,	PUNCT
ejpam-486	326	99	ζ	ζ	PROPN
ejpam-486	326	100	∈	∈	PROPN
ejpam-486	326	101	∂	∂	NUM
ejpam-486	326	102	u	u	NOUN
ejpam-486	326	103	and	and	CCONJ
ejpam-486	326	104	m	m	PROPN
ejpam-486	326	105	≥	≥	NOUN
ejpam-486	326	106	1	1	NUM
ejpam-486	326	107	now	now	ADV
ejpam-486	326	108	we	we	PRON
ejpam-486	326	109	will	will	AUX
ejpam-486	326	110	give	give	VERB
ejpam-486	326	111	the	the	DET
ejpam-486	326	112	dual	dual	ADJ
ejpam-486	326	113	result	result	NOUN
ejpam-486	326	114	of	of	ADP
ejpam-486	326	115	theorem	theorem	NOUN
ejpam-486	326	116	5	5	NUM
ejpam-486	326	117	for	for	ADP
ejpam-486	326	118	differential	differential	ADJ
ejpam-486	326	119	superordination	superordination	NOUN
ejpam-486	326	120	.	.	PUNCT
ejpam-486	327	1	m.	m.	PROPN
ejpam-486	327	2	aouf	aouf	PROPN
ejpam-486	327	3	,	,	PUNCT
ejpam-486	327	4	t.	t.	PROPN
ejpam-486	327	5	seoudy	seoudy	PROPN
ejpam-486	327	6	/	/	SYM
ejpam-486	327	7	eur	eur	PROPN
ejpam-486	327	8	.	.	PUNCT
ejpam-486	328	1	j.	j.	PROPN
ejpam-486	328	2	pure	pure	PROPN
ejpam-486	328	3	appl	appl	PROPN
ejpam-486	328	4	.	.	PROPN
ejpam-486	328	5	math	math	PROPN
ejpam-486	328	6	,	,	PUNCT
ejpam-486	328	7	3	3	NUM
ejpam-486	328	8	(	(	PUNCT
ejpam-486	328	9	2010	2010	NUM
ejpam-486	328	10	)	)	PUNCT
ejpam-486	328	11	,	,	PUNCT
ejpam-486	328	12	26	26	NUM
ejpam-486	328	13	-	-	SYM
ejpam-486	328	14	44	44	NUM
ejpam-486	328	15	41	41	NUM
ejpam-486	328	16	theorem	theorem	NOUN
ejpam-486	328	17	12	12	NUM
ejpam-486	328	18	.	.	PUNCT
ejpam-486	329	1	let	let	VERB
ejpam-486	329	2	φ	φ	PROPN
ejpam-486	329	3	∈	∈	PROPN
ejpam-486	329	4	φ′q,1	φ′q,1	PROPN
ejpam-486	329	5	�	�	PROPN
ejpam-486	329	6	ω	ω	PROPN
ejpam-486	329	7	,	,	PUNCT
ejpam-486	329	8	q	q	PROPN
ejpam-486	329	9	�	�	PROPN
ejpam-486	329	10	.	.	PUNCT
ejpam-486	330	1	if	if	SCONJ
ejpam-486	330	2	f	f	PROPN
ejpam-486	330	3	(	(	PUNCT
ejpam-486	330	4	z	z	NOUN
ejpam-486	330	5	)	)	PUNCT
ejpam-486	330	6	∈	∈	PROPN
ejpam-486	330	7	a	a	DET
ejpam-486	330	8	�	�	PROPN
ejpam-486	330	9	p	p	PROPN
ejpam-486	330	10	�	�	PROPN
ejpam-486	330	11	,	,	PUNCT
ejpam-486	330	12	qα	qα	PROPN
ejpam-486	330	13	β	β	PROPN
ejpam-486	330	14	,	,	PUNCT
ejpam-486	330	15	p	p	PROPN
ejpam-486	330	16	f	f	X
ejpam-486	330	17	(	(	PUNCT
ejpam-486	330	18	z	z	NOUN
ejpam-486	330	19	)	)	PUNCT
ejpam-486	330	20	zp−1	zp−1	PROPN
ejpam-486	330	21	∈	∈	PROPN
ejpam-486	330	22	f0	f0	PROPN
ejpam-486	330	23	and	and	CCONJ
ejpam-486	330	24	φ	φ	NUM
ejpam-486	330	25	qα	qα	PROPN
ejpam-486	330	26	β	β	PROPN
ejpam-486	330	27	,	,	PUNCT
ejpam-486	330	28	p	p	PROPN
ejpam-486	330	29	f	f	X
ejpam-486	330	30	(	(	PUNCT
ejpam-486	330	31	z	z	NOUN
ejpam-486	330	32	)	)	PUNCT
ejpam-486	330	33	zp−1	zp−1	PROPN
ejpam-486	330	34	,	,	PUNCT
ejpam-486	330	35	qα−1	qα−1	PROPN
ejpam-486	330	36	β	β	X
ejpam-486	330	37	,	,	PUNCT
ejpam-486	330	38	p	p	PROPN
ejpam-486	330	39	f	f	X
ejpam-486	330	40	(	(	PUNCT
ejpam-486	330	41	z	z	NOUN
ejpam-486	330	42	)	)	PUNCT
ejpam-486	330	43	zp−1	zp−1	PROPN
ejpam-486	330	44	,	,	PUNCT
ejpam-486	330	45	qα−2	qα−2	PROPN
ejpam-486	330	46	β	β	PROPN
ejpam-486	330	47	,	,	PUNCT
ejpam-486	330	48	p	p	PROPN
ejpam-486	330	49	f	f	X
ejpam-486	330	50	(	(	PUNCT
ejpam-486	330	51	z	z	NOUN
ejpam-486	330	52	)	)	PUNCT
ejpam-486	330	53	zp−1	zp−1	PROPN
ejpam-486	330	54	;	;	PUNCT
ejpam-486	330	55	z	z	X
ejpam-486	330	56	!	!	PUNCT
ejpam-486	330	57	is	be	AUX
ejpam-486	330	58	univalent	univalent	ADJ
ejpam-486	330	59	in	in	ADP
ejpam-486	330	60	u	u	NOUN
ejpam-486	330	61	,	,	PUNCT
ejpam-486	330	62	then	then	ADV
ejpam-486	330	63	ω⊂	ω⊂	PROPN
ejpam-486	330	64	(	(	PUNCT
ejpam-486	330	65	φ	φ	PROPN
ejpam-486	330	66	qα	qα	PROPN
ejpam-486	330	67	β	β	PROPN
ejpam-486	330	68	,	,	PUNCT
ejpam-486	330	69	p	p	PROPN
ejpam-486	330	70	f	f	X
ejpam-486	330	71	(	(	PUNCT
ejpam-486	330	72	z	z	NOUN
ejpam-486	330	73	)	)	PUNCT
ejpam-486	330	74	zp−1	zp−1	PROPN
ejpam-486	330	75	,	,	PUNCT
ejpam-486	330	76	qα−1	qα−1	PROPN
ejpam-486	330	77	β	β	X
ejpam-486	330	78	,	,	PUNCT
ejpam-486	330	79	p	p	PROPN
ejpam-486	330	80	f	f	X
ejpam-486	330	81	(	(	PUNCT
ejpam-486	330	82	z	z	NOUN
ejpam-486	330	83	)	)	PUNCT
ejpam-486	330	84	zp−1	zp−1	PROPN
ejpam-486	330	85	,	,	PUNCT
ejpam-486	330	86	qα−2	qα−2	PROPN
ejpam-486	330	87	β	β	PROPN
ejpam-486	330	88	,	,	PUNCT
ejpam-486	330	89	p	p	PROPN
ejpam-486	330	90	f	f	X
ejpam-486	330	91	(	(	PUNCT
ejpam-486	330	92	z	z	NOUN
ejpam-486	330	93	)	)	PUNCT
ejpam-486	330	94	zp−1	zp−1	PROPN
ejpam-486	330	95	;	;	PUNCT
ejpam-486	330	96	z	z	X
ejpam-486	330	97	!	!	PUNCT
ejpam-486	331	1	:	:	PUNCT
ejpam-486	331	2	z	z	X
ejpam-486	331	3	∈	∈	PROPN
ejpam-486	331	4	u	u	PROPN
ejpam-486	331	5	)	)	PUNCT
ejpam-486	331	6	�	�	PROPN
ejpam-486	331	7	α	α	X
ejpam-486	331	8	>	>	X
ejpam-486	331	9	2;β	2;β	NUM
ejpam-486	331	10	>	>	SYM
ejpam-486	331	11	−1	−1	NOUN
ejpam-486	331	12	;	;	PUNCT
ejpam-486	331	13	p	p	PROPN
ejpam-486	331	14	∈	∈	PROPN
ejpam-486	331	15	n	n	PRON
ejpam-486	331	16	�	�	PROPN
ejpam-486	331	17	(	(	PUNCT
ejpam-486	331	18	37	37	NUM
ejpam-486	331	19	)	)	PUNCT
ejpam-486	331	20	implies	imply	VERB
ejpam-486	331	21	q(z	q(z	PROPN
ejpam-486	331	22	)	)	PUNCT
ejpam-486	331	23	≺	≺	NOUN
ejpam-486	331	24	qα	qα	PROPN
ejpam-486	331	25	β	β	PROPN
ejpam-486	331	26	,	,	PUNCT
ejpam-486	331	27	p	p	PROPN
ejpam-486	331	28	f	f	X
ejpam-486	331	29	(	(	PUNCT
ejpam-486	331	30	z	z	NOUN
ejpam-486	331	31	)	)	PUNCT
ejpam-486	331	32	zp−1	zp−1	PROPN
ejpam-486	331	33	(	(	PUNCT
ejpam-486	331	34	z	z	NOUN
ejpam-486	331	35	∈	∈	PROPN
ejpam-486	331	36	u	u	NOUN
ejpam-486	331	37	)	)	PUNCT
ejpam-486	331	38	.	.	PUNCT
ejpam-486	332	1	proof	proof	NOUN
ejpam-486	332	2	.	.	PUNCT
ejpam-486	333	1	from	from	ADP
ejpam-486	333	2	(	(	PUNCT
ejpam-486	333	3	21	21	NUM
ejpam-486	333	4	)	)	PUNCT
ejpam-486	333	5	and	and	CCONJ
ejpam-486	333	6	(	(	PUNCT
ejpam-486	333	7	37	37	NUM
ejpam-486	333	8	)	)	PUNCT
ejpam-486	333	9	,	,	PUNCT
ejpam-486	333	10	we	we	PRON
ejpam-486	333	11	have	have	VERB
ejpam-486	333	12	ω⊂	ω⊂	PROPN
ejpam-486	333	13	¦	¦	PROPN
ejpam-486	333	14	ψ	ψ	X
ejpam-486	333	15	�	�	PROPN
ejpam-486	333	16	g	g	PROPN
ejpam-486	333	17	(	(	PUNCT
ejpam-486	333	18	z	z	PROPN
ejpam-486	333	19	)	)	PUNCT
ejpam-486	333	20	,	,	PUNCT
ejpam-486	333	21	zg′	zg′	X
ejpam-486	333	22	(	(	PUNCT
ejpam-486	333	23	z	z	NOUN
ejpam-486	333	24	)	)	PUNCT
ejpam-486	333	25	,	,	PUNCT
ejpam-486	333	26	z2	z2	PROPN
ejpam-486	333	27	g	g	PROPN
ejpam-486	333	28	′′	′′	PROPN
ejpam-486	333	29	(	(	PUNCT
ejpam-486	333	30	z	z	PROPN
ejpam-486	333	31	)	)	PUNCT
ejpam-486	333	32	;	;	PUNCT
ejpam-486	333	33	z	z	PROPN
ejpam-486	333	34	�	�	PROPN
ejpam-486	333	35	:	:	PUNCT
ejpam-486	334	1	z	z	PROPN
ejpam-486	334	2	∈	∈	PRON
ejpam-486	334	3	u	u	NOUN
ejpam-486	334	4	©	©	PROPN
ejpam-486	334	5	�	�	PROPN
ejpam-486	334	6	α	α	X
ejpam-486	334	7	>	>	X
ejpam-486	334	8	2;β	2;β	NUM
ejpam-486	334	9	>	>	SYM
ejpam-486	334	10	−1	−1	NOUN
ejpam-486	334	11	;	;	PUNCT
ejpam-486	334	12	p	p	PROPN
ejpam-486	334	13	∈	∈	PROPN
ejpam-486	334	14	n	n	PRON
ejpam-486	334	15	�	�	PROPN
ejpam-486	334	16	.	.	PUNCT
ejpam-486	335	1	from	from	ADP
ejpam-486	335	2	(	(	PUNCT
ejpam-486	335	3	19	19	NUM
ejpam-486	335	4	)	)	PUNCT
ejpam-486	335	5	,	,	PUNCT
ejpam-486	335	6	we	we	PRON
ejpam-486	335	7	see	see	VERB
ejpam-486	335	8	that	that	SCONJ
ejpam-486	335	9	the	the	DET
ejpam-486	335	10	admissibility	admissibility	NOUN
ejpam-486	335	11	condition	condition	NOUN
ejpam-486	335	12	for	for	ADP
ejpam-486	335	13	φ	φ	PROPN
ejpam-486	335	14	∈	∈	PROPN
ejpam-486	335	15	φ′q,1	φ′q,1	PROPN
ejpam-486	335	16	�	�	PROPN
ejpam-486	335	17	ω	ω	PROPN
ejpam-486	335	18	,	,	PUNCT
ejpam-486	335	19	q	q	PROPN
ejpam-486	335	20	�	�	PROPN
ejpam-486	335	21	is	be	AUX
ejpam-486	335	22	equivalent	equivalent	ADJ
ejpam-486	335	23	to	to	ADP
ejpam-486	335	24	the	the	DET
ejpam-486	335	25	admissibility	admissibility	NOUN
ejpam-486	335	26	condition	condition	NOUN
ejpam-486	335	27	for	for	ADP
ejpam-486	335	28	ψ	ψ	PRON
ejpam-486	335	29	as	as	SCONJ
ejpam-486	335	30	given	give	VERB
ejpam-486	335	31	in	in	ADP
ejpam-486	335	32	definition	definition	NOUN
ejpam-486	335	33	2	2	NUM
ejpam-486	335	34	.	.	PUNCT
ejpam-486	335	35	hence	hence	ADV
ejpam-486	335	36	ψ	ψ	X
ejpam-486	335	37	∈ψ′	∈ψ′	PROPN
ejpam-486	335	38	�	�	PROPN
ejpam-486	335	39	ω	ω	PROPN
ejpam-486	335	40	,	,	PUNCT
ejpam-486	335	41	q	q	PROPN
ejpam-486	335	42	�	�	PROPN
ejpam-486	335	43	,	,	PUNCT
ejpam-486	335	44	and	and	CCONJ
ejpam-486	335	45	by	by	ADP
ejpam-486	335	46	lemma	lemma	PROPN
ejpam-486	335	47	2	2	NUM
ejpam-486	335	48	q(z	q(z	PROPN
ejpam-486	335	49	)	)	PUNCT
ejpam-486	335	50	≺	≺	NOUN
ejpam-486	335	51	p(z	p(z	NOUN
ejpam-486	335	52	)	)	PUNCT
ejpam-486	335	53	or	or	CCONJ
ejpam-486	335	54	q(z	q(z	PROPN
ejpam-486	335	55	)	)	PUNCT
ejpam-486	335	56	≺	≺	NOUN
ejpam-486	335	57	qα	qα	PROPN
ejpam-486	335	58	β	β	PROPN
ejpam-486	335	59	,	,	PUNCT
ejpam-486	335	60	p	p	PROPN
ejpam-486	335	61	f	f	X
ejpam-486	335	62	(	(	PUNCT
ejpam-486	335	63	z	z	NOUN
ejpam-486	335	64	)	)	PUNCT
ejpam-486	335	65	zp−1	zp−1	PROPN
ejpam-486	335	66	�	�	PROPN
ejpam-486	335	67	α	α	X
ejpam-486	335	68	>	>	X
ejpam-486	335	69	2;β	2;β	NUM
ejpam-486	335	70	>	>	SYM
ejpam-486	335	71	−1	−1	NOUN
ejpam-486	335	72	;	;	PUNCT
ejpam-486	335	73	p	p	PROPN
ejpam-486	335	74	∈	∈	PROPN
ejpam-486	335	75	n	n	CCONJ
ejpam-486	335	76	;	;	PUNCT
ejpam-486	335	77	z	z	PROPN
ejpam-486	335	78	∈	∈	PROPN
ejpam-486	335	79	u	u	PROPN
ejpam-486	335	80	�	�	PROPN
ejpam-486	335	81	.	.	PUNCT
ejpam-486	336	1	if	if	SCONJ
ejpam-486	336	2	ω	ω	PROPN
ejpam-486	336	3	6=	6=	PROPN
ejpam-486	336	4	c	c	PROPN
ejpam-486	336	5	is	be	AUX
ejpam-486	336	6	a	a	DET
ejpam-486	336	7	simply	simply	ADV
ejpam-486	336	8	connected	connected	ADJ
ejpam-486	336	9	domain	domain	NOUN
ejpam-486	336	10	,	,	PUNCT
ejpam-486	336	11	and	and	CCONJ
ejpam-486	336	12	ω	ω	X
ejpam-486	336	13	=	=	SYM
ejpam-486	336	14	h(u	h(u	PROPN
ejpam-486	336	15	)	)	PUNCT
ejpam-486	336	16	for	for	ADP
ejpam-486	336	17	some	some	DET
ejpam-486	336	18	conformal	conformal	ADJ
ejpam-486	336	19	mapping	map	VERB
ejpam-486	336	20	h(z	h(z	NOUN
ejpam-486	336	21	)	)	PUNCT
ejpam-486	336	22	of	of	ADP
ejpam-486	336	23	u	u	PRON
ejpam-486	336	24	onto	onto	ADP
ejpam-486	336	25	ω	ω	PROPN
ejpam-486	336	26	and	and	CCONJ
ejpam-486	336	27	the	the	DET
ejpam-486	336	28	class	class	NOUN
ejpam-486	336	29	φ′q,1	φ′q,1	PROPN
ejpam-486	336	30	�	�	PROPN
ejpam-486	336	31	h(u	h(u	PROPN
ejpam-486	336	32	)	)	PUNCT
ejpam-486	336	33	,	,	PUNCT
ejpam-486	336	34	q	q	PROPN
ejpam-486	336	35	�	�	PROPN
ejpam-486	336	36	is	be	AUX
ejpam-486	336	37	written	write	VERB
ejpam-486	336	38	as	as	ADP
ejpam-486	336	39	φ′q,1	φ′q,1	PROPN
ejpam-486	336	40	�	�	PROPN
ejpam-486	336	41	h	h	NOUN
ejpam-486	336	42	,	,	PUNCT
ejpam-486	336	43	q	q	PROPN
ejpam-486	336	44	�	�	PROPN
ejpam-486	336	45	.	.	PUNCT
ejpam-486	337	1	proceeding	proceed	VERB
ejpam-486	337	2	similarly	similarly	ADV
ejpam-486	337	3	as	as	ADP
ejpam-486	337	4	in	in	ADP
ejpam-486	337	5	the	the	DET
ejpam-486	337	6	previous	previous	ADJ
ejpam-486	337	7	section	section	NOUN
ejpam-486	337	8	,	,	PUNCT
ejpam-486	337	9	the	the	DET
ejpam-486	337	10	following	following	ADJ
ejpam-486	337	11	result	result	NOUN
ejpam-486	337	12	is	be	AUX
ejpam-486	337	13	an	an	DET
ejpam-486	337	14	immediate	immediate	ADJ
ejpam-486	337	15	consequence	consequence	NOUN
ejpam-486	337	16	of	of	ADP
ejpam-486	337	17	theorem	theorem	NOUN
ejpam-486	337	18	12	12	NUM
ejpam-486	337	19	.	.	PUNCT
ejpam-486	338	1	theorem	theorem	VERB
ejpam-486	338	2	13	13	NUM
ejpam-486	338	3	.	.	PUNCT
ejpam-486	339	1	let	let	VERB
ejpam-486	339	2	q(z	q(z	PROPN
ejpam-486	339	3	)	)	PUNCT
ejpam-486	339	4	∈	∈	PROPN
ejpam-486	339	5	h0	h0	PROPN
ejpam-486	339	6	,	,	PUNCT
ejpam-486	339	7	h(z	h(z	NOUN
ejpam-486	339	8	)	)	PUNCT
ejpam-486	339	9	is	be	AUX
ejpam-486	339	10	analytic	analytic	ADJ
ejpam-486	339	11	on	on	ADP
ejpam-486	339	12	u	u	NOUN
ejpam-486	339	13	and	and	CCONJ
ejpam-486	339	14	φ	φ	PROPN
ejpam-486	339	15	∈	∈	PROPN
ejpam-486	339	16	φ′q,1	φ′q,1	ADJ
ejpam-486	339	17	�	�	PROPN
ejpam-486	339	18	h	h	NOUN
ejpam-486	339	19	,	,	PUNCT
ejpam-486	339	20	q	q	PROPN
ejpam-486	339	21	�	�	PROPN
ejpam-486	339	22	.	.	PUNCT
ejpam-486	340	1	if	if	SCONJ
ejpam-486	340	2	f	f	PROPN
ejpam-486	340	3	(	(	PUNCT
ejpam-486	340	4	z	z	NOUN
ejpam-486	340	5	)	)	PUNCT
ejpam-486	340	6	∈	∈	PROPN
ejpam-486	340	7	a	a	DET
ejpam-486	340	8	�	�	PROPN
ejpam-486	340	9	p	p	PROPN
ejpam-486	340	10	�	�	PROPN
ejpam-486	340	11	,	,	PUNCT
ejpam-486	340	12	qα	qα	PROPN
ejpam-486	340	13	β	β	PROPN
ejpam-486	340	14	,	,	PUNCT
ejpam-486	340	15	p	p	PROPN
ejpam-486	340	16	f	f	X
ejpam-486	340	17	(	(	PUNCT
ejpam-486	340	18	z	z	NOUN
ejpam-486	340	19	)	)	PUNCT
ejpam-486	340	20	zp−1	zp−1	PROPN
ejpam-486	340	21	∈	∈	PROPN
ejpam-486	340	22	f0	f0	PROPN
ejpam-486	340	23	and	and	CCONJ
ejpam-486	340	24	φ	φ	NUM
ejpam-486	340	25	qα	qα	PROPN
ejpam-486	340	26	β	β	PROPN
ejpam-486	340	27	,	,	PUNCT
ejpam-486	340	28	p	p	PROPN
ejpam-486	340	29	f	f	X
ejpam-486	340	30	(	(	PUNCT
ejpam-486	340	31	z	z	NOUN
ejpam-486	340	32	)	)	PUNCT
ejpam-486	340	33	zp−1	zp−1	PROPN
ejpam-486	340	34	,	,	PUNCT
ejpam-486	340	35	qα−1	qα−1	PROPN
ejpam-486	340	36	β	β	X
ejpam-486	340	37	,	,	PUNCT
ejpam-486	340	38	p	p	PROPN
ejpam-486	340	39	f	f	X
ejpam-486	340	40	(	(	PUNCT
ejpam-486	340	41	z	z	NOUN
ejpam-486	340	42	)	)	PUNCT
ejpam-486	340	43	zp−1	zp−1	PROPN
ejpam-486	340	44	,	,	PUNCT
ejpam-486	340	45	qα−2	qα−2	PROPN
ejpam-486	340	46	β	β	PROPN
ejpam-486	340	47	,	,	PUNCT
ejpam-486	340	48	p	p	PROPN
ejpam-486	340	49	f	f	X
ejpam-486	340	50	(	(	PUNCT
ejpam-486	340	51	z	z	NOUN
ejpam-486	340	52	)	)	PUNCT
ejpam-486	340	53	zp−1	zp−1	PROPN
ejpam-486	340	54	;	;	PUNCT
ejpam-486	340	55	z	z	X
ejpam-486	340	56	!	!	PUNCT
ejpam-486	340	57	is	be	AUX
ejpam-486	340	58	univalent	univalent	ADJ
ejpam-486	340	59	in	in	ADP
ejpam-486	340	60	u	u	NOUN
ejpam-486	340	61	,	,	PUNCT
ejpam-486	340	62	then	then	ADV
ejpam-486	340	63	h(z	h(z	NOUN
ejpam-486	340	64	)	)	PUNCT
ejpam-486	340	65	≺	≺	NOUN
ejpam-486	340	66	φ	φ	PROPN
ejpam-486	340	67	qα	qα	PROPN
ejpam-486	340	68	β	β	PROPN
ejpam-486	340	69	,	,	PUNCT
ejpam-486	340	70	p	p	PROPN
ejpam-486	340	71	f	f	X
ejpam-486	340	72	(	(	PUNCT
ejpam-486	340	73	z	z	NOUN
ejpam-486	340	74	)	)	PUNCT
ejpam-486	340	75	zp−1	zp−1	PROPN
ejpam-486	340	76	,	,	PUNCT
ejpam-486	340	77	qα−1	qα−1	PROPN
ejpam-486	340	78	β	β	X
ejpam-486	340	79	,	,	PUNCT
ejpam-486	340	80	p	p	PROPN
ejpam-486	340	81	f	f	X
ejpam-486	340	82	(	(	PUNCT
ejpam-486	340	83	z	z	NOUN
ejpam-486	340	84	)	)	PUNCT
ejpam-486	340	85	zp−1	zp−1	PROPN
ejpam-486	340	86	,	,	PUNCT
ejpam-486	340	87	qα−2	qα−2	PROPN
ejpam-486	340	88	β	β	PROPN
ejpam-486	340	89	,	,	PUNCT
ejpam-486	340	90	p	p	PROPN
ejpam-486	340	91	f	f	X
ejpam-486	340	92	(	(	PUNCT
ejpam-486	340	93	z	z	NOUN
ejpam-486	340	94	)	)	PUNCT
ejpam-486	340	95	zp−1	zp−1	PROPN
ejpam-486	340	96	;	;	PUNCT
ejpam-486	340	97	z	z	X
ejpam-486	340	98	!	!	PUNCT
ejpam-486	341	1	�	�	PROPN
ejpam-486	341	2	α	α	X
ejpam-486	341	3	>	>	X
ejpam-486	341	4	2	2	NUM
ejpam-486	341	5	;	;	PUNCT
ejpam-486	341	6	β	β	X
ejpam-486	341	7	>	>	X
ejpam-486	341	8	−1	−1	NOUN
ejpam-486	342	1	;	;	PUNCT
ejpam-486	342	2	p	p	PROPN
ejpam-486	342	3	∈	∈	PROPN
ejpam-486	342	4	n	n	CCONJ
ejpam-486	342	5	;	;	PUNCT
ejpam-486	342	6	z	z	PROPN
ejpam-486	342	7	∈	∈	PROPN
ejpam-486	342	8	u	u	PROPN
ejpam-486	342	9	�	�	PROPN
ejpam-486	342	10	(	(	PUNCT
ejpam-486	342	11	38	38	NUM
ejpam-486	342	12	)	)	PUNCT
ejpam-486	342	13	implies	imply	VERB
ejpam-486	342	14	q(z)≺	q(z)≺	INTJ
ejpam-486	342	15	qα	qα	PROPN
ejpam-486	342	16	β	β	PROPN
ejpam-486	342	17	,	,	PUNCT
ejpam-486	342	18	p	p	PROPN
ejpam-486	342	19	f	f	X
ejpam-486	342	20	(	(	PUNCT
ejpam-486	342	21	z	z	NOUN
ejpam-486	342	22	)	)	PUNCT
ejpam-486	342	23	zp−1	zp−1	PROPN
ejpam-486	342	24	(	(	PUNCT
ejpam-486	342	25	z	z	NOUN
ejpam-486	342	26	∈	∈	PROPN
ejpam-486	342	27	u	u	NOUN
ejpam-486	342	28	)	)	PUNCT
ejpam-486	342	29	.	.	PUNCT
ejpam-486	343	1	combining	combine	VERB
ejpam-486	343	2	theorems	theorem	NOUN
ejpam-486	343	3	6	6	NUM
ejpam-486	343	4	and	and	CCONJ
ejpam-486	343	5	13	13	NUM
ejpam-486	343	6	,	,	PUNCT
ejpam-486	343	7	we	we	PRON
ejpam-486	343	8	obtain	obtain	VERB
ejpam-486	343	9	the	the	DET
ejpam-486	343	10	following	follow	VERB
ejpam-486	343	11	sandwich	sandwich	NOUN
ejpam-486	343	12	-	-	PUNCT
ejpam-486	343	13	type	type	NOUN
ejpam-486	343	14	theorem	theorem	NOUN
ejpam-486	343	15	.	.	PROPN
ejpam-486	343	16	m.	m.	PROPN
ejpam-486	343	17	aouf	aouf	PROPN
ejpam-486	343	18	,	,	PUNCT
ejpam-486	343	19	t.	t.	PROPN
ejpam-486	343	20	seoudy	seoudy	PROPN
ejpam-486	343	21	/	/	SYM
ejpam-486	343	22	eur	eur	PROPN
ejpam-486	343	23	.	.	PUNCT
ejpam-486	344	1	j.	j.	PROPN
ejpam-486	344	2	pure	pure	PROPN
ejpam-486	344	3	appl	appl	PROPN
ejpam-486	344	4	.	.	PROPN
ejpam-486	344	5	math	math	PROPN
ejpam-486	344	6	,	,	PUNCT
ejpam-486	344	7	3	3	NUM
ejpam-486	344	8	(	(	PUNCT
ejpam-486	344	9	2010	2010	NUM
ejpam-486	344	10	)	)	PUNCT
ejpam-486	344	11	,	,	PUNCT
ejpam-486	344	12	26	26	NUM
ejpam-486	344	13	-	-	SYM
ejpam-486	344	14	44	44	NUM
ejpam-486	344	15	42	42	NUM
ejpam-486	344	16	corollary	corollary	ADJ
ejpam-486	344	17	11	11	NUM
ejpam-486	344	18	.	.	PUNCT
ejpam-486	345	1	let	let	AUX
ejpam-486	345	2	h1(z	h1(z	NUM
ejpam-486	345	3	)	)	PUNCT
ejpam-486	345	4	and	and	CCONJ
ejpam-486	345	5	q1(z	q1(z	PROPN
ejpam-486	345	6	)	)	PUNCT
ejpam-486	345	7	be	be	AUX
ejpam-486	345	8	analytic	analytic	ADJ
ejpam-486	345	9	functions	function	NOUN
ejpam-486	345	10	in	in	ADP
ejpam-486	345	11	u	u	NOUN
ejpam-486	345	12	,	,	PUNCT
ejpam-486	345	13	h2(z	h2(z	X
ejpam-486	345	14	)	)	PUNCT
ejpam-486	345	15	be	be	AUX
ejpam-486	345	16	univalent	univalent	ADJ
ejpam-486	345	17	function	function	NOUN
ejpam-486	345	18	in	in	ADP
ejpam-486	345	19	u	u	NOUN
ejpam-486	345	20	,	,	PUNCT
ejpam-486	345	21	q2(z	q2(z	NOUN
ejpam-486	345	22	)	)	PUNCT
ejpam-486	345	23	∈	∈	NOUN
ejpam-486	345	24	f0	f0	PROPN
ejpam-486	345	25	with	with	ADP
ejpam-486	345	26	q1(0	q1(0	PROPN
ejpam-486	345	27	)	)	PUNCT
ejpam-486	346	1	=	=	PUNCT
ejpam-486	346	2	q2(0	q2(0	PROPN
ejpam-486	346	3	)	)	PUNCT
ejpam-486	346	4	=	=	SYM
ejpam-486	346	5	0	0	NUM
ejpam-486	346	6	and	and	CCONJ
ejpam-486	346	7	φ	φ	PROPN
ejpam-486	346	8	∈	∈	PROPN
ejpam-486	346	9	φq,1	φq,1	ADJ
ejpam-486	346	10	�	�	PROPN
ejpam-486	346	11	h2,q2	h2,q2	PROPN
ejpam-486	346	12	�	�	PROPN
ejpam-486	346	13	∩	∩	ADJ
ejpam-486	346	14	φ′q,1	φ′q,1	ADJ
ejpam-486	346	15	�	�	PROPN
ejpam-486	346	16	h1,q1	h1,q1	PROPN
ejpam-486	346	17	�	�	PROPN
ejpam-486	346	18	.	.	PUNCT
ejpam-486	347	1	if	if	SCONJ
ejpam-486	347	2	f	f	PROPN
ejpam-486	347	3	(	(	PUNCT
ejpam-486	347	4	z	z	NOUN
ejpam-486	347	5	)	)	PUNCT
ejpam-486	347	6	∈	∈	PROPN
ejpam-486	347	7	a	a	DET
ejpam-486	347	8	�	�	PROPN
ejpam-486	347	9	p	p	PROPN
ejpam-486	347	10	�	�	PROPN
ejpam-486	347	11	,	,	PUNCT
ejpam-486	347	12	qα	qα	PROPN
ejpam-486	347	13	β	β	PROPN
ejpam-486	347	14	,	,	PUNCT
ejpam-486	347	15	p	p	PROPN
ejpam-486	347	16	f	f	X
ejpam-486	347	17	(	(	PUNCT
ejpam-486	347	18	z	z	NOUN
ejpam-486	347	19	)	)	PUNCT
ejpam-486	347	20	zp−1	zp−1	PROPN
ejpam-486	347	21	∈	∈	PROPN
ejpam-486	347	22	h0	h0	PROPN
ejpam-486	347	23	∩f0	∩f0	PROPN
ejpam-486	347	24	and	and	CCONJ
ejpam-486	347	25	φ	φ	PROPN
ejpam-486	347	26	qα	qα	PROPN
ejpam-486	347	27	β	β	PROPN
ejpam-486	347	28	,	,	PUNCT
ejpam-486	347	29	p	p	PROPN
ejpam-486	347	30	f	f	X
ejpam-486	347	31	(	(	PUNCT
ejpam-486	347	32	z	z	NOUN
ejpam-486	347	33	)	)	PUNCT
ejpam-486	347	34	zp−1	zp−1	PROPN
ejpam-486	347	35	,	,	PUNCT
ejpam-486	347	36	qα−1	qα−1	PROPN
ejpam-486	347	37	β	β	X
ejpam-486	347	38	,	,	PUNCT
ejpam-486	347	39	p	p	PROPN
ejpam-486	347	40	f	f	X
ejpam-486	347	41	(	(	PUNCT
ejpam-486	347	42	z	z	NOUN
ejpam-486	347	43	)	)	PUNCT
ejpam-486	347	44	zp−1	zp−1	PROPN
ejpam-486	347	45	,	,	PUNCT
ejpam-486	347	46	qα−2	qα−2	PROPN
ejpam-486	347	47	β	β	PROPN
ejpam-486	347	48	,	,	PUNCT
ejpam-486	347	49	p	p	PROPN
ejpam-486	347	50	f	f	X
ejpam-486	347	51	(	(	PUNCT
ejpam-486	347	52	z	z	NOUN
ejpam-486	347	53	)	)	PUNCT
ejpam-486	347	54	zp−1	zp−1	PROPN
ejpam-486	347	55	;	;	PUNCT
ejpam-486	347	56	z	z	X
ejpam-486	347	57	!	!	PUNCT
ejpam-486	347	58	is	be	AUX
ejpam-486	347	59	univalent	univalent	ADJ
ejpam-486	347	60	in	in	ADP
ejpam-486	347	61	u	u	NOUN
ejpam-486	347	62	,	,	PUNCT
ejpam-486	347	63	then	then	ADV
ejpam-486	347	64	h1	h1	PROPN
ejpam-486	347	65	(	(	PUNCT
ejpam-486	347	66	z	z	NOUN
ejpam-486	347	67	)	)	PUNCT
ejpam-486	347	68	≺	≺	NOUN
ejpam-486	347	69	φ	φ	PROPN
ejpam-486	347	70	qα	qα	PROPN
ejpam-486	347	71	β	β	PROPN
ejpam-486	347	72	,	,	PUNCT
ejpam-486	347	73	p	p	PROPN
ejpam-486	347	74	f	f	X
ejpam-486	347	75	(	(	PUNCT
ejpam-486	347	76	z	z	NOUN
ejpam-486	347	77	)	)	PUNCT
ejpam-486	347	78	zp−1	zp−1	PROPN
ejpam-486	347	79	,	,	PUNCT
ejpam-486	347	80	qα−1	qα−1	PROPN
ejpam-486	347	81	β	β	X
ejpam-486	347	82	,	,	PUNCT
ejpam-486	347	83	p	p	PROPN
ejpam-486	347	84	f	f	X
ejpam-486	347	85	(	(	PUNCT
ejpam-486	347	86	z	z	NOUN
ejpam-486	347	87	)	)	PUNCT
ejpam-486	347	88	zp−1	zp−1	PROPN
ejpam-486	347	89	,	,	PUNCT
ejpam-486	347	90	qα−2	qα−2	PROPN
ejpam-486	347	91	β	β	PROPN
ejpam-486	347	92	,	,	PUNCT
ejpam-486	347	93	p	p	PROPN
ejpam-486	347	94	f	f	X
ejpam-486	347	95	(	(	PUNCT
ejpam-486	347	96	z	z	NOUN
ejpam-486	347	97	)	)	PUNCT
ejpam-486	347	98	zp−1	zp−1	PROPN
ejpam-486	347	99	;	;	PUNCT
ejpam-486	347	100	z	z	X
ejpam-486	347	101	!	!	PUNCT
ejpam-486	348	1	≺	≺	NOUN
ejpam-486	348	2	h2	h2	NOUN
ejpam-486	348	3	(	(	PUNCT
ejpam-486	348	4	z	z	NOUN
ejpam-486	348	5	)	)	PUNCT
ejpam-486	348	6	�	�	PROPN
ejpam-486	348	7	α	α	X
ejpam-486	348	8	>	>	X
ejpam-486	348	9	2;β	2;β	NUM
ejpam-486	348	10	>	>	SYM
ejpam-486	348	11	−1	−1	NOUN
ejpam-486	348	12	;	;	PUNCT
ejpam-486	348	13	p	p	PROPN
ejpam-486	348	14	∈	∈	PROPN
ejpam-486	348	15	n	n	CCONJ
ejpam-486	348	16	;	;	PUNCT
ejpam-486	348	17	z	z	PROPN
ejpam-486	348	18	∈	∈	PROPN
ejpam-486	348	19	u	u	PROPN
ejpam-486	348	20	�	�	PROPN
ejpam-486	348	21	,	,	PUNCT
ejpam-486	348	22	implies	imply	VERB
ejpam-486	348	23	q1	q1	PROPN
ejpam-486	348	24	(	(	PUNCT
ejpam-486	348	25	z	z	NOUN
ejpam-486	348	26	)	)	PUNCT
ejpam-486	348	27	≺	≺	NOUN
ejpam-486	348	28	qα	qα	PROPN
ejpam-486	348	29	β	β	PROPN
ejpam-486	348	30	,	,	PUNCT
ejpam-486	348	31	p	p	PROPN
ejpam-486	348	32	f	f	X
ejpam-486	348	33	(	(	PUNCT
ejpam-486	348	34	z	z	NOUN
ejpam-486	348	35	)	)	PUNCT
ejpam-486	348	36	zp−1	zp−1	PROPN
ejpam-486	348	37	≺	≺	NOUN
ejpam-486	348	38	q2	q2	NOUN
ejpam-486	348	39	(	(	PUNCT
ejpam-486	348	40	z	z	NOUN
ejpam-486	348	41	)	)	PUNCT
ejpam-486	348	42	(	(	PUNCT
ejpam-486	348	43	z	z	NOUN
ejpam-486	348	44	∈	∈	PROPN
ejpam-486	348	45	u	u	NOUN
ejpam-486	348	46	)	)	PUNCT
ejpam-486	348	47	.	.	PUNCT
ejpam-486	349	1	definition	definition	NOUN
ejpam-486	349	2	11	11	NUM
ejpam-486	349	3	.	.	PUNCT
ejpam-486	350	1	let	let	VERB
ejpam-486	350	2	ω	ω	NUM
ejpam-486	350	3	be	be	AUX
ejpam-486	350	4	a	a	DET
ejpam-486	350	5	set	set	NOUN
ejpam-486	350	6	in	in	ADP
ejpam-486	350	7	c	c	PROPN
ejpam-486	350	8	,	,	PUNCT
ejpam-486	350	9	q(z	q(z	PROPN
ejpam-486	350	10	)	)	PUNCT
ejpam-486	350	11	6=	6=	ADP
ejpam-486	350	12	0	0	NUM
ejpam-486	350	13	,	,	PUNCT
ejpam-486	350	14	zq′(z	zq′(z	PROPN
ejpam-486	350	15	)	)	PUNCT
ejpam-486	350	16	6=	6=	ADP
ejpam-486	350	17	0	0	NUM
ejpam-486	350	18	and	and	CCONJ
ejpam-486	351	1	q(z	q(z	PROPN
ejpam-486	351	2	)	)	PUNCT
ejpam-486	351	3	∈	∈	PROPN
ejpam-486	351	4	h.	h.	NOUN
ejpam-486	352	1	the	the	DET
ejpam-486	352	2	class	class	NOUN
ejpam-486	352	3	of	of	ADP
ejpam-486	352	4	admissible	admissible	ADJ
ejpam-486	352	5	functions	function	NOUN
ejpam-486	352	6	φ	φ	PROPN
ejpam-486	352	7	∈	∈	PROPN
ejpam-486	352	8	φ′q,2	φ′q,2	ADP
ejpam-486	352	9	�	�	PROPN
ejpam-486	352	10	ω	ω	PROPN
ejpam-486	352	11	,	,	PUNCT
ejpam-486	352	12	q	q	PROPN
ejpam-486	352	13	�	�	PROPN
ejpam-486	352	14	consists	consist	VERB
ejpam-486	352	15	of	of	ADP
ejpam-486	352	16	those	those	DET
ejpam-486	352	17	functions	function	NOUN
ejpam-486	352	18	φ	φ	NOUN
ejpam-486	352	19	:	:	PUNCT
ejpam-486	352	20	c3×ū	c3×ū	VERB
ejpam-486	352	21	→	→	SYM
ejpam-486	352	22	c	c	NOUN
ejpam-486	352	23	that	that	PRON
ejpam-486	352	24	satisfy	satisfy	VERB
ejpam-486	352	25	the	the	DET
ejpam-486	352	26	admissibility	admissibility	NOUN
ejpam-486	352	27	condition	condition	NOUN
ejpam-486	352	28	:	:	PUNCT
ejpam-486	353	1	φ	φ	PROPN
ejpam-486	353	2	(	(	PUNCT
ejpam-486	353	3	u	u	NOUN
ejpam-486	353	4	,	,	PUNCT
ejpam-486	353	5	v	v	NOUN
ejpam-486	353	6	,	,	PUNCT
ejpam-486	353	7	w;ζ	w;ζ	NUM
ejpam-486	353	8	)	)	PUNCT
ejpam-486	353	9	∈	∈	PROPN
ejpam-486	353	10	ω	ω	NUM
ejpam-486	353	11	whenever	whenever	SCONJ
ejpam-486	353	12	u	u	NOUN
ejpam-486	353	13	=	=	NOUN
ejpam-486	353	14	q	q	X
ejpam-486	353	15	(	(	PUNCT
ejpam-486	353	16	z	z	NOUN
ejpam-486	353	17	)	)	PUNCT
ejpam-486	353	18	,	,	PUNCT
ejpam-486	353	19	v	v	NOUN
ejpam-486	353	20	=	=	SYM
ejpam-486	353	21	1	1	NUM
ejpam-486	353	22	α+	α+	NOUN
ejpam-486	353	23	β	β	X
ejpam-486	353	24	+	+	X
ejpam-486	353	25	p+	p+	PROPN
ejpam-486	353	26	2	2	NUM
ejpam-486	353	27	¨	¨	NOUN
ejpam-486	353	28	−1	−1	NOUN
ejpam-486	353	29	+	+	CCONJ
ejpam-486	353	30	�	�	PROPN
ejpam-486	353	31	α+	α+	X
ejpam-486	353	32	β	β	NOUN
ejpam-486	353	33	+	+	CCONJ
ejpam-486	353	34	p−	p−	PROPN
ejpam-486	353	35	1	1	NUM
ejpam-486	353	36	�	�	PROPN
ejpam-486	353	37	g	g	PROPN
ejpam-486	353	38	(	(	PUNCT
ejpam-486	353	39	z	z	NOUN
ejpam-486	353	40	)	)	PUNCT
ejpam-486	353	41	+	+	CCONJ
ejpam-486	353	42	zg′	zg′	NOUN
ejpam-486	353	43	(	(	PUNCT
ejpam-486	353	44	z	z	NOUN
ejpam-486	353	45	)	)	PUNCT
ejpam-486	353	46	mg	mg	PROPN
ejpam-486	353	47	(	(	PUNCT
ejpam-486	353	48	z	z	NOUN
ejpam-486	353	49	)	)	PUNCT
ejpam-486	353	50	«	«	PUNCT
ejpam-486	353	51	,	,	PUNCT
ejpam-486	353	52	ℜ	ℜ	PROPN
ejpam-486	353	53	�	�	PROPN
ejpam-486	353	54	�	�	PROPN
ejpam-486	353	55	�	�	PROPN
ejpam-486	353	56	α+	α+	X
ejpam-486	353	57	β	β	NOUN
ejpam-486	353	58	+	+	CCONJ
ejpam-486	353	59	p−	p−	PROPN
ejpam-486	353	60	3	3	NUM
ejpam-486	353	61	�	�	PROPN
ejpam-486	353	62	w	w	PROPN
ejpam-486	353	63	−	−	PROPN
ejpam-486	353	64	�	�	PROPN
ejpam-486	353	65	α+	α+	PUNCT
ejpam-486	353	66	β	β	NOUN
ejpam-486	353	67	+	+	CCONJ
ejpam-486	353	68	p−	p−	PROPN
ejpam-486	353	69	2	2	NUM
ejpam-486	353	70	�	�	NOUN
ejpam-486	353	71	v	v	ADP
ejpam-486	353	72	+	+	NOUN
ejpam-486	353	73	1	1	NUM
ejpam-486	353	74	�	�	PROPN
ejpam-486	353	75	v	v	ADP
ejpam-486	353	76	�	�	PROPN
ejpam-486	353	77	α+	α+	PUNCT
ejpam-486	353	78	β	β	NOUN
ejpam-486	353	79	+	+	CCONJ
ejpam-486	353	80	p−	p−	PROPN
ejpam-486	353	81	2	2	NUM
ejpam-486	353	82	�	�	PROPN
ejpam-486	353	83	v−	v−	NOUN
ejpam-486	353	84	�	�	PROPN
ejpam-486	353	85	α+	α+	X
ejpam-486	353	86	β	β	NOUN
ejpam-486	353	87	+	+	CCONJ
ejpam-486	353	88	p−	p−	NOUN
ejpam-486	353	89	1	1	NUM
ejpam-486	353	90	�	�	PROPN
ejpam-486	353	91	u+	u+	NOUN
ejpam-486	353	92	1	1	NUM
ejpam-486	353	93	+	+	NUM
ejpam-486	353	94	�	�	X
ejpam-486	353	95	α+	α+	X
ejpam-486	353	96	β	β	NOUN
ejpam-486	353	97	+	+	CCONJ
ejpam-486	353	98	p−	p−	PROPN
ejpam-486	353	99	2	2	NUM
ejpam-486	353	100	�	�	NOUN
ejpam-486	353	101	v	v	ADP
ejpam-486	353	102	−	−	PROPN
ejpam-486	353	103	2	2	NUM
ejpam-486	353	104	�	�	PROPN
ejpam-486	353	105	α+β	α+β	NUM
ejpam-486	353	106	+	+	CCONJ
ejpam-486	353	107	p−	p−	NOUN
ejpam-486	353	108	1	1	NUM
ejpam-486	353	109	�	�	PROPN
ejpam-486	353	110	u+	u+	NUM
ejpam-486	353	111	1	1	NUM
ejpam-486	353	112	�	�	PROPN
ejpam-486	353	113	≤	≤	NUM
ejpam-486	353	114	1	1	NUM
ejpam-486	353	115	m	m	NOUN
ejpam-486	353	116	ℜ	ℜ	NOUN
ejpam-486	353	117	(	(	PUNCT
ejpam-486	353	118	1	1	NUM
ejpam-486	353	119	+	+	NUM
ejpam-486	353	120	zq	zq	PROPN
ejpam-486	353	121	′′	′′	PROPN
ejpam-486	353	122	(	(	PUNCT
ejpam-486	353	123	z	z	NOUN
ejpam-486	353	124	)	)	PUNCT
ejpam-486	353	125	q′	q′	NOUN
ejpam-486	353	126	(	(	PUNCT
ejpam-486	353	127	z	z	NOUN
ejpam-486	353	128	)	)	PUNCT
ejpam-486	353	129	)	)	PUNCT
ejpam-486	353	130	,	,	PUNCT
ejpam-486	353	131	where	where	SCONJ
ejpam-486	353	132	z	z	PROPN
ejpam-486	353	133	∈	∈	PROPN
ejpam-486	353	134	u	u	NOUN
ejpam-486	353	135	,	,	PUNCT
ejpam-486	353	136	ζ	ζ	PROPN
ejpam-486	353	137	∈	∈	PROPN
ejpam-486	353	138	∂	∂	NUM
ejpam-486	353	139	u	u	NOUN
ejpam-486	353	140	,	,	PUNCT
ejpam-486	353	141	p	p	PROPN
ejpam-486	353	142	∈	∈	PROPN
ejpam-486	353	143	n	n	CCONJ
ejpam-486	353	144	and	and	CCONJ
ejpam-486	353	145	m≥	m≥	PROPN
ejpam-486	353	146	1	1	X
ejpam-486	353	147	.	.	PUNCT
ejpam-486	354	1	now	now	ADV
ejpam-486	354	2	we	we	PRON
ejpam-486	354	3	will	will	AUX
ejpam-486	354	4	give	give	VERB
ejpam-486	354	5	the	the	DET
ejpam-486	354	6	dual	dual	ADJ
ejpam-486	354	7	result	result	NOUN
ejpam-486	354	8	of	of	ADP
ejpam-486	354	9	theorem	theorem	NOUN
ejpam-486	354	10	7	7	NUM
ejpam-486	354	11	for	for	ADP
ejpam-486	354	12	the	the	DET
ejpam-486	354	13	differential	differential	ADJ
ejpam-486	354	14	superordination	superordination	NOUN
ejpam-486	354	15	.	.	PUNCT
ejpam-486	355	1	theorem	theorem	VERB
ejpam-486	355	2	14	14	NUM
ejpam-486	355	3	.	.	PUNCT
ejpam-486	356	1	let	let	VERB
ejpam-486	356	2	φ	φ	PROPN
ejpam-486	356	3	∈	∈	PROPN
ejpam-486	356	4	φ′i	φ′i	PROPN
ejpam-486	356	5	,	,	PUNCT
ejpam-486	356	6	2	2	NUM
ejpam-486	356	7	�	�	PROPN
ejpam-486	356	8	ω	ω	PROPN
ejpam-486	356	9	,	,	PUNCT
ejpam-486	356	10	q	q	PROPN
ejpam-486	356	11	�	�	PROPN
ejpam-486	356	12	.	.	PUNCT
ejpam-486	357	1	if	if	SCONJ
ejpam-486	357	2	f	f	PROPN
ejpam-486	357	3	(	(	PUNCT
ejpam-486	357	4	z	z	NOUN
ejpam-486	357	5	)	)	PUNCT
ejpam-486	357	6	∈	∈	PROPN
ejpam-486	357	7	a	a	DET
ejpam-486	357	8	�	�	PROPN
ejpam-486	357	9	p	p	PROPN
ejpam-486	357	10	�	�	PROPN
ejpam-486	357	11	,	,	PUNCT
ejpam-486	357	12	qα−1	qα−1	PROPN
ejpam-486	357	13	β	β	X
ejpam-486	357	14	,	,	PUNCT
ejpam-486	357	15	p	p	PROPN
ejpam-486	357	16	f	f	X
ejpam-486	357	17	(	(	PUNCT
ejpam-486	357	18	z	z	NOUN
ejpam-486	357	19	)	)	PUNCT
ejpam-486	357	20	qα	qα	PROPN
ejpam-486	358	1	β	β	PROPN
ejpam-486	358	2	,	,	PUNCT
ejpam-486	358	3	p	p	PROPN
ejpam-486	358	4	f	f	X
ejpam-486	358	5	(	(	PUNCT
ejpam-486	358	6	z	z	NOUN
ejpam-486	358	7	)	)	PUNCT
ejpam-486	358	8	∈	∈	PROPN
ejpam-486	358	9	f1	f1	NOUN
ejpam-486	358	10	and	and	CCONJ
ejpam-486	358	11	φ	φ	PROPN
ejpam-486	358	12	qα−1	qα−1	PROPN
ejpam-486	358	13	β	β	PROPN
ejpam-486	358	14	,	,	PUNCT
ejpam-486	358	15	p	p	PROPN
ejpam-486	358	16	f	f	X
ejpam-486	358	17	(	(	PUNCT
ejpam-486	358	18	z	z	NOUN
ejpam-486	358	19	)	)	PUNCT
ejpam-486	358	20	qα	qα	PROPN
ejpam-486	358	21	β	β	PROPN
ejpam-486	358	22	,	,	PUNCT
ejpam-486	358	23	p	p	PROPN
ejpam-486	358	24	f	f	X
ejpam-486	358	25	(	(	PUNCT
ejpam-486	358	26	z	z	NOUN
ejpam-486	358	27	)	)	PUNCT
ejpam-486	358	28	,	,	PUNCT
ejpam-486	358	29	qα−2	qα−2	PROPN
ejpam-486	358	30	β	β	PROPN
ejpam-486	358	31	,	,	PUNCT
ejpam-486	358	32	p	p	PROPN
ejpam-486	358	33	f	f	X
ejpam-486	358	34	(	(	PUNCT
ejpam-486	358	35	z	z	NOUN
ejpam-486	358	36	)	)	PUNCT
ejpam-486	358	37	qα−1	qα−1	PROPN
ejpam-486	358	38	β	β	X
ejpam-486	358	39	,	,	PUNCT
ejpam-486	358	40	p	p	PROPN
ejpam-486	358	41	f	f	X
ejpam-486	358	42	(	(	PUNCT
ejpam-486	358	43	z	z	NOUN
ejpam-486	358	44	)	)	PUNCT
ejpam-486	358	45	,	,	PUNCT
ejpam-486	358	46	qα−3	qα−3	NOUN
ejpam-486	358	47	β	β	X
ejpam-486	358	48	,	,	PUNCT
ejpam-486	358	49	p	p	PROPN
ejpam-486	358	50	f	f	X
ejpam-486	358	51	(	(	PUNCT
ejpam-486	358	52	z	z	NOUN
ejpam-486	358	53	)	)	PUNCT
ejpam-486	358	54	qα−2	qα−2	NOUN
ejpam-486	358	55	β	β	NOUN
ejpam-486	358	56	,	,	PUNCT
ejpam-486	358	57	p	p	PROPN
ejpam-486	358	58	f	f	X
ejpam-486	358	59	(	(	PUNCT
ejpam-486	358	60	z	z	NOUN
ejpam-486	358	61	)	)	PUNCT
ejpam-486	358	62	;	;	PUNCT
ejpam-486	358	63	z	z	X
ejpam-486	358	64	!	!	PUNCT
ejpam-486	358	65	m.	m.	PROPN
ejpam-486	358	66	aouf	aouf	PROPN
ejpam-486	358	67	,	,	PUNCT
ejpam-486	358	68	t.	t.	PROPN
ejpam-486	358	69	seoudy	seoudy	PROPN
ejpam-486	358	70	/	/	SYM
ejpam-486	358	71	eur	eur	PROPN
ejpam-486	358	72	.	.	PUNCT
ejpam-486	359	1	j.	j.	PROPN
ejpam-486	359	2	pure	pure	PROPN
ejpam-486	359	3	appl	appl	PROPN
ejpam-486	359	4	.	.	PROPN
ejpam-486	359	5	math	math	PROPN
ejpam-486	359	6	,	,	PUNCT
ejpam-486	359	7	3	3	NUM
ejpam-486	359	8	(	(	PUNCT
ejpam-486	359	9	2010	2010	NUM
ejpam-486	359	10	)	)	PUNCT
ejpam-486	359	11	,	,	PUNCT
ejpam-486	359	12	26	26	NUM
ejpam-486	359	13	-	-	SYM
ejpam-486	359	14	44	44	NUM
ejpam-486	359	15	43	43	NUM
ejpam-486	359	16	is	be	AUX
ejpam-486	359	17	univalent	univalent	ADJ
ejpam-486	359	18	in	in	ADP
ejpam-486	359	19	u	u	NOUN
ejpam-486	359	20	,	,	PUNCT
ejpam-486	359	21	then	then	ADV
ejpam-486	359	22	ω⊂	ω⊂	PROPN
ejpam-486	359	23	(	(	PUNCT
ejpam-486	359	24	φ	φ	PROPN
ejpam-486	359	25	qα−1	qα−1	PROPN
ejpam-486	359	26	β	β	X
ejpam-486	359	27	,	,	PUNCT
ejpam-486	359	28	p	p	PROPN
ejpam-486	359	29	f	f	X
ejpam-486	359	30	(	(	PUNCT
ejpam-486	359	31	z	z	NOUN
ejpam-486	359	32	)	)	PUNCT
ejpam-486	359	33	qα	qα	PROPN
ejpam-486	359	34	β	β	PROPN
ejpam-486	359	35	,	,	PUNCT
ejpam-486	359	36	p	p	PROPN
ejpam-486	359	37	f	f	X
ejpam-486	359	38	(	(	PUNCT
ejpam-486	359	39	z	z	NOUN
ejpam-486	359	40	)	)	PUNCT
ejpam-486	359	41	,	,	PUNCT
ejpam-486	359	42	qα−2	qα−2	PROPN
ejpam-486	359	43	β	β	PROPN
ejpam-486	359	44	,	,	PUNCT
ejpam-486	359	45	p	p	PROPN
ejpam-486	359	46	f	f	X
ejpam-486	359	47	(	(	PUNCT
ejpam-486	359	48	z	z	NOUN
ejpam-486	359	49	)	)	PUNCT
ejpam-486	359	50	qα−1	qα−1	PROPN
ejpam-486	359	51	β	β	X
ejpam-486	359	52	,	,	PUNCT
ejpam-486	359	53	p	p	PROPN
ejpam-486	359	54	f	f	X
ejpam-486	359	55	(	(	PUNCT
ejpam-486	359	56	z	z	NOUN
ejpam-486	359	57	)	)	PUNCT
ejpam-486	359	58	,	,	PUNCT
ejpam-486	359	59	qα−3	qα−3	NOUN
ejpam-486	359	60	β	β	X
ejpam-486	359	61	,	,	PUNCT
ejpam-486	359	62	p	p	PROPN
ejpam-486	359	63	f	f	X
ejpam-486	359	64	(	(	PUNCT
ejpam-486	359	65	z	z	NOUN
ejpam-486	359	66	)	)	PUNCT
ejpam-486	359	67	qα−2	qα−2	NOUN
ejpam-486	359	68	β	β	NOUN
ejpam-486	359	69	,	,	PUNCT
ejpam-486	359	70	p	p	PROPN
ejpam-486	359	71	f	f	X
ejpam-486	359	72	(	(	PUNCT
ejpam-486	359	73	z	z	NOUN
ejpam-486	359	74	)	)	PUNCT
ejpam-486	359	75	;	;	PUNCT
ejpam-486	359	76	z	z	X
ejpam-486	359	77	!	!	PUNCT
ejpam-486	360	1	:	:	PUNCT
ejpam-486	360	2	z	z	X
ejpam-486	360	3	∈	∈	PROPN
ejpam-486	360	4	u	u	PROPN
ejpam-486	360	5	)	)	PUNCT
ejpam-486	360	6	�	�	PROPN
ejpam-486	360	7	α	α	PROPN
ejpam-486	360	8	>	>	X
ejpam-486	360	9	3	3	NUM
ejpam-486	360	10	;	;	PUNCT
ejpam-486	360	11	β	β	X
ejpam-486	360	12	>	>	X
ejpam-486	360	13	−1	−1	NOUN
ejpam-486	361	1	;	;	PUNCT
ejpam-486	361	2	p	p	PROPN
ejpam-486	361	3	∈	∈	PROPN
ejpam-486	361	4	n	n	PRON
ejpam-486	361	5	�	�	PROPN
ejpam-486	361	6	(	(	PUNCT
ejpam-486	361	7	39	39	NUM
ejpam-486	361	8	)	)	PUNCT
ejpam-486	361	9	implies	imply	VERB
ejpam-486	361	10	q	q	PROPN
ejpam-486	361	11	(	(	PUNCT
ejpam-486	361	12	z	z	NOUN
ejpam-486	361	13	)	)	PUNCT
ejpam-486	361	14	≺	≺	NOUN
ejpam-486	361	15	qα−1	qα−1	NOUN
ejpam-486	361	16	β	β	X
ejpam-486	361	17	,	,	PUNCT
ejpam-486	361	18	p	p	PROPN
ejpam-486	361	19	f	f	X
ejpam-486	361	20	(	(	PUNCT
ejpam-486	361	21	z	z	NOUN
ejpam-486	361	22	)	)	PUNCT
ejpam-486	361	23	qα	qα	PROPN
ejpam-486	361	24	β	β	PROPN
ejpam-486	361	25	,	,	PUNCT
ejpam-486	361	26	p	p	PROPN
ejpam-486	361	27	f	f	X
ejpam-486	361	28	(	(	PUNCT
ejpam-486	361	29	z	z	NOUN
ejpam-486	361	30	)	)	PUNCT
ejpam-486	361	31	(	(	PUNCT
ejpam-486	361	32	z	z	NOUN
ejpam-486	361	33	∈	∈	PROPN
ejpam-486	361	34	u	u	NOUN
ejpam-486	361	35	)	)	PUNCT
ejpam-486	361	36	.	.	PUNCT
ejpam-486	362	1	proof	proof	NOUN
ejpam-486	362	2	.	.	PUNCT
ejpam-486	363	1	from	from	ADP
ejpam-486	363	2	(	(	PUNCT
ejpam-486	363	3	31	31	NUM
ejpam-486	363	4	)	)	PUNCT
ejpam-486	363	5	and	and	CCONJ
ejpam-486	363	6	(	(	PUNCT
ejpam-486	363	7	39	39	NUM
ejpam-486	363	8	)	)	PUNCT
ejpam-486	363	9	,	,	PUNCT
ejpam-486	363	10	we	we	PRON
ejpam-486	363	11	have	have	VERB
ejpam-486	363	12	ω⊂	ω⊂	PROPN
ejpam-486	363	13	¦	¦	PROPN
ejpam-486	363	14	ψ	ψ	X
ejpam-486	363	15	�	�	PROPN
ejpam-486	363	16	g	g	PROPN
ejpam-486	363	17	(	(	PUNCT
ejpam-486	363	18	z	z	PROPN
ejpam-486	363	19	)	)	PUNCT
ejpam-486	363	20	,	,	PUNCT
ejpam-486	363	21	zg′	zg′	X
ejpam-486	363	22	(	(	PUNCT
ejpam-486	363	23	z	z	NOUN
ejpam-486	363	24	)	)	PUNCT
ejpam-486	363	25	,	,	PUNCT
ejpam-486	363	26	z2	z2	PROPN
ejpam-486	363	27	g	g	PROPN
ejpam-486	363	28	′′	′′	PROPN
ejpam-486	363	29	(	(	PUNCT
ejpam-486	363	30	z	z	PROPN
ejpam-486	363	31	)	)	PUNCT
ejpam-486	363	32	;	;	PUNCT
ejpam-486	363	33	z	z	PROPN
ejpam-486	363	34	�	�	PROPN
ejpam-486	363	35	:	:	PUNCT
ejpam-486	363	36	z	z	PROPN
ejpam-486	363	37	∈	∈	PROPN
ejpam-486	363	38	u	u	NOUN
ejpam-486	363	39	©	©	PROPN
ejpam-486	363	40	.	.	PUNCT
ejpam-486	364	1	in	in	ADP
ejpam-486	364	2	view	view	NOUN
ejpam-486	364	3	of	of	ADP
ejpam-486	364	4	(	(	PUNCT
ejpam-486	364	5	29	29	NUM
ejpam-486	364	6	)	)	PUNCT
ejpam-486	364	7	,	,	PUNCT
ejpam-486	364	8	the	the	DET
ejpam-486	364	9	admissibility	admissibility	NOUN
ejpam-486	364	10	condition	condition	NOUN
ejpam-486	364	11	for	for	ADP
ejpam-486	364	12	φ	φ	PROPN
ejpam-486	364	13	∈	∈	PROPN
ejpam-486	364	14	φ′q,2	φ′q,2	ADP
ejpam-486	364	15	�	�	PROPN
ejpam-486	364	16	ω	ω	PROPN
ejpam-486	364	17	,	,	PUNCT
ejpam-486	364	18	q	q	PROPN
ejpam-486	364	19	�	�	PROPN
ejpam-486	364	20	is	be	AUX
ejpam-486	364	21	equivalent	equivalent	ADJ
ejpam-486	364	22	to	to	ADP
ejpam-486	364	23	the	the	DET
ejpam-486	364	24	admissibility	admissibility	NOUN
ejpam-486	364	25	condition	condition	NOUN
ejpam-486	364	26	for	for	ADP
ejpam-486	364	27	ψ	ψ	PRON
ejpam-486	364	28	as	as	SCONJ
ejpam-486	364	29	given	give	VERB
ejpam-486	364	30	in	in	ADP
ejpam-486	364	31	definition	definition	NOUN
ejpam-486	364	32	2	2	NUM
ejpam-486	364	33	.	.	PUNCT
ejpam-486	364	34	hence	hence	ADV
ejpam-486	364	35	ψ	ψ	X
ejpam-486	364	36	∈ψ′	∈ψ′	PROPN
ejpam-486	364	37	�	�	PROPN
ejpam-486	364	38	ω	ω	PROPN
ejpam-486	364	39	,	,	PUNCT
ejpam-486	364	40	q	q	PROPN
ejpam-486	364	41	�	�	PROPN
ejpam-486	364	42	,	,	PUNCT
ejpam-486	364	43	and	and	CCONJ
ejpam-486	364	44	by	by	ADP
ejpam-486	364	45	lemma	lemma	PROPN
ejpam-486	364	46	2	2	NUM
ejpam-486	364	47	q(z)≺	q(z)≺	ADP
ejpam-486	364	48	g(z	g(z	PROPN
ejpam-486	364	49	)	)	PUNCT
ejpam-486	364	50	or	or	CCONJ
ejpam-486	364	51	q(z	q(z	PROPN
ejpam-486	364	52	)	)	PUNCT
ejpam-486	364	53	≺	≺	NOUN
ejpam-486	364	54	qα−1	qα−1	NOUN
ejpam-486	364	55	β	β	X
ejpam-486	364	56	,	,	PUNCT
ejpam-486	364	57	p	p	PROPN
ejpam-486	364	58	f	f	X
ejpam-486	364	59	(	(	PUNCT
ejpam-486	364	60	z	z	NOUN
ejpam-486	364	61	)	)	PUNCT
ejpam-486	364	62	qα	qα	PROPN
ejpam-486	365	1	β	β	PROPN
ejpam-486	365	2	,	,	PUNCT
ejpam-486	365	3	p	p	PROPN
ejpam-486	365	4	f	f	X
ejpam-486	365	5	(	(	PUNCT
ejpam-486	365	6	z	z	NOUN
ejpam-486	365	7	)	)	PUNCT
ejpam-486	365	8	(	(	PUNCT
ejpam-486	365	9	z	z	NOUN
ejpam-486	365	10	∈	∈	PROPN
ejpam-486	365	11	u	u	NOUN
ejpam-486	365	12	)	)	PUNCT
ejpam-486	365	13	.	.	PUNCT
ejpam-486	366	1	if	if	SCONJ
ejpam-486	366	2	ω	ω	PROPN
ejpam-486	366	3	6=	6=	PROPN
ejpam-486	366	4	c	c	PROPN
ejpam-486	366	5	is	be	AUX
ejpam-486	366	6	a	a	DET
ejpam-486	366	7	simply	simply	ADV
ejpam-486	366	8	connected	connected	ADJ
ejpam-486	366	9	domain	domain	NOUN
ejpam-486	366	10	,	,	PUNCT
ejpam-486	366	11	then	then	ADV
ejpam-486	366	12	ω	ω	PROPN
ejpam-486	366	13	=	=	SYM
ejpam-486	366	14	h(u	h(u	PROPN
ejpam-486	366	15	)	)	PUNCT
ejpam-486	366	16	for	for	ADP
ejpam-486	366	17	some	some	DET
ejpam-486	366	18	conformal	conformal	ADJ
ejpam-486	366	19	mapping	map	VERB
ejpam-486	366	20	h(z	h(z	NOUN
ejpam-486	366	21	)	)	PUNCT
ejpam-486	366	22	of	of	ADP
ejpam-486	366	23	u	u	PRON
ejpam-486	366	24	onto	onto	ADP
ejpam-486	366	25	ω	ω	NUM
ejpam-486	366	26	.	.	PUNCT
ejpam-486	367	1	in	in	ADP
ejpam-486	367	2	this	this	DET
ejpam-486	367	3	case	case	NOUN
ejpam-486	367	4	the	the	DET
ejpam-486	367	5	class	class	NOUN
ejpam-486	367	6	φ′q,2	φ′q,2	ADP
ejpam-486	367	7	�	�	PROPN
ejpam-486	367	8	h(u	h(u	PROPN
ejpam-486	367	9	)	)	PUNCT
ejpam-486	367	10	,	,	PUNCT
ejpam-486	367	11	q	q	PROPN
ejpam-486	367	12	�	�	PROPN
ejpam-486	367	13	is	be	AUX
ejpam-486	367	14	written	write	VERB
ejpam-486	367	15	as	as	ADP
ejpam-486	367	16	φ′q,2	φ′q,2	ADP
ejpam-486	367	17	�	�	PROPN
ejpam-486	367	18	h	h	NOUN
ejpam-486	367	19	,	,	PUNCT
ejpam-486	367	20	q	q	PROPN
ejpam-486	367	21	�	�	PROPN
ejpam-486	367	22	.	.	PUNCT
ejpam-486	368	1	proceeding	proceed	VERB
ejpam-486	368	2	similarly	similarly	ADV
ejpam-486	368	3	as	as	ADP
ejpam-486	368	4	in	in	ADP
ejpam-486	368	5	the	the	DET
ejpam-486	368	6	previous	previous	ADJ
ejpam-486	368	7	section	section	NOUN
ejpam-486	368	8	,	,	PUNCT
ejpam-486	368	9	the	the	DET
ejpam-486	368	10	following	following	ADJ
ejpam-486	368	11	result	result	NOUN
ejpam-486	368	12	is	be	AUX
ejpam-486	368	13	an	an	DET
ejpam-486	368	14	immediate	immediate	ADJ
ejpam-486	368	15	consequence	consequence	NOUN
ejpam-486	368	16	of	of	ADP
ejpam-486	368	17	theorem	theorem	ADJ
ejpam-486	368	18	14	14	NUM
ejpam-486	368	19	.	.	PUNCT
ejpam-486	369	1	theorem	theorem	NOUN
ejpam-486	369	2	15	15	NUM
ejpam-486	369	3	.	.	PUNCT
ejpam-486	370	1	let	let	VERB
ejpam-486	370	2	q	q	NOUN
ejpam-486	370	3	(	(	PUNCT
ejpam-486	370	4	z	z	NOUN
ejpam-486	370	5	)	)	PUNCT
ejpam-486	370	6	∈	∈	PROPN
ejpam-486	370	7	h	h	NOUN
ejpam-486	370	8	,	,	PUNCT
ejpam-486	370	9	h(z	h(z	NOUN
ejpam-486	370	10	)	)	PUNCT
ejpam-486	370	11	be	be	AUX
ejpam-486	370	12	analytic	analytic	ADJ
ejpam-486	370	13	in	in	ADP
ejpam-486	370	14	u	u	NOUN
ejpam-486	370	15	and	and	CCONJ
ejpam-486	370	16	φ	φ	PROPN
ejpam-486	370	17	∈	∈	PROPN
ejpam-486	370	18	φ′q,2	φ′q,2	ADP
ejpam-486	370	19	�	�	PROPN
ejpam-486	370	20	h	h	PROPN
ejpam-486	370	21	,	,	PUNCT
ejpam-486	370	22	q	q	PROPN
ejpam-486	370	23	�	�	PROPN
ejpam-486	370	24	.	.	PUNCT
ejpam-486	371	1	if	if	SCONJ
ejpam-486	371	2	f	f	PROPN
ejpam-486	371	3	(	(	PUNCT
ejpam-486	371	4	z	z	NOUN
ejpam-486	371	5	)	)	PUNCT
ejpam-486	371	6	∈	∈	PROPN
ejpam-486	371	7	a	a	DET
ejpam-486	371	8	�	�	PROPN
ejpam-486	371	9	p	p	PROPN
ejpam-486	371	10	�	�	PROPN
ejpam-486	371	11	,	,	PUNCT
ejpam-486	371	12	qα−1	qα−1	PROPN
ejpam-486	371	13	β	β	X
ejpam-486	371	14	,	,	PUNCT
ejpam-486	371	15	p	p	PROPN
ejpam-486	371	16	f	f	X
ejpam-486	371	17	(	(	PUNCT
ejpam-486	371	18	z	z	NOUN
ejpam-486	371	19	)	)	PUNCT
ejpam-486	371	20	qα	qα	PROPN
ejpam-486	372	1	β	β	PROPN
ejpam-486	372	2	,	,	PUNCT
ejpam-486	372	3	p	p	PROPN
ejpam-486	372	4	f	f	X
ejpam-486	372	5	(	(	PUNCT
ejpam-486	372	6	z	z	NOUN
ejpam-486	372	7	)	)	PUNCT
ejpam-486	372	8	∈	∈	PROPN
ejpam-486	372	9	f1	f1	NOUN
ejpam-486	372	10	and	and	CCONJ
ejpam-486	372	11	φ	φ	PROPN
ejpam-486	372	12	qα−1	qα−1	PROPN
ejpam-486	372	13	β	β	PROPN
ejpam-486	372	14	,	,	PUNCT
ejpam-486	372	15	p	p	PROPN
ejpam-486	372	16	f	f	X
ejpam-486	372	17	(	(	PUNCT
ejpam-486	372	18	z	z	NOUN
ejpam-486	372	19	)	)	PUNCT
ejpam-486	372	20	qα	qα	PROPN
ejpam-486	372	21	β	β	PROPN
ejpam-486	372	22	,	,	PUNCT
ejpam-486	372	23	p	p	PROPN
ejpam-486	372	24	f	f	X
ejpam-486	372	25	(	(	PUNCT
ejpam-486	372	26	z	z	NOUN
ejpam-486	372	27	)	)	PUNCT
ejpam-486	372	28	,	,	PUNCT
ejpam-486	372	29	qα−2	qα−2	PROPN
ejpam-486	372	30	β	β	PROPN
ejpam-486	372	31	,	,	PUNCT
ejpam-486	372	32	p	p	PROPN
ejpam-486	372	33	f	f	X
ejpam-486	372	34	(	(	PUNCT
ejpam-486	372	35	z	z	NOUN
ejpam-486	372	36	)	)	PUNCT
ejpam-486	372	37	qα−1	qα−1	PROPN
ejpam-486	372	38	β	β	X
ejpam-486	372	39	,	,	PUNCT
ejpam-486	372	40	p	p	PROPN
ejpam-486	372	41	f	f	X
ejpam-486	372	42	(	(	PUNCT
ejpam-486	372	43	z	z	NOUN
ejpam-486	372	44	)	)	PUNCT
ejpam-486	372	45	,	,	PUNCT
ejpam-486	372	46	qα−3	qα−3	NOUN
ejpam-486	372	47	β	β	X
ejpam-486	372	48	,	,	PUNCT
ejpam-486	372	49	p	p	PROPN
ejpam-486	372	50	f	f	X
ejpam-486	372	51	(	(	PUNCT
ejpam-486	372	52	z	z	NOUN
ejpam-486	372	53	)	)	PUNCT
ejpam-486	372	54	qα−2	qα−2	NOUN
ejpam-486	372	55	β	β	NOUN
ejpam-486	372	56	,	,	PUNCT
ejpam-486	372	57	p	p	PROPN
ejpam-486	372	58	f	f	X
ejpam-486	372	59	(	(	PUNCT
ejpam-486	372	60	z	z	NOUN
ejpam-486	372	61	)	)	PUNCT
ejpam-486	372	62	;	;	PUNCT
ejpam-486	372	63	z	z	X
ejpam-486	372	64	!	!	PUNCT
ejpam-486	372	65	is	be	AUX
ejpam-486	372	66	univalent	univalent	ADJ
ejpam-486	372	67	in	in	ADP
ejpam-486	372	68	u	u	NOUN
ejpam-486	372	69	,	,	PUNCT
ejpam-486	372	70	then	then	ADV
ejpam-486	372	71	h(z	h(z	NOUN
ejpam-486	372	72	)	)	PUNCT
ejpam-486	372	73	≺	≺	NOUN
ejpam-486	372	74	φ	φ	PROPN
ejpam-486	372	75	qα−1	qα−1	PROPN
ejpam-486	372	76	β	β	X
ejpam-486	372	77	,	,	PUNCT
ejpam-486	372	78	p	p	PROPN
ejpam-486	372	79	f	f	X
ejpam-486	372	80	(	(	PUNCT
ejpam-486	372	81	z	z	NOUN
ejpam-486	372	82	)	)	PUNCT
ejpam-486	372	83	qα	qα	PROPN
ejpam-486	372	84	β	β	PROPN
ejpam-486	372	85	,	,	PUNCT
ejpam-486	372	86	p	p	PROPN
ejpam-486	372	87	f	f	X
ejpam-486	372	88	(	(	PUNCT
ejpam-486	372	89	z	z	NOUN
ejpam-486	372	90	)	)	PUNCT
ejpam-486	372	91	,	,	PUNCT
ejpam-486	372	92	qα−2	qα−2	PROPN
ejpam-486	372	93	β	β	PROPN
ejpam-486	372	94	,	,	PUNCT
ejpam-486	372	95	p	p	PROPN
ejpam-486	372	96	f	f	X
ejpam-486	372	97	(	(	PUNCT
ejpam-486	372	98	z	z	NOUN
ejpam-486	372	99	)	)	PUNCT
ejpam-486	372	100	qα−1	qα−1	PROPN
ejpam-486	372	101	β	β	X
ejpam-486	372	102	,	,	PUNCT
ejpam-486	372	103	p	p	PROPN
ejpam-486	372	104	f	f	X
ejpam-486	372	105	(	(	PUNCT
ejpam-486	372	106	z	z	NOUN
ejpam-486	372	107	)	)	PUNCT
ejpam-486	372	108	,	,	PUNCT
ejpam-486	372	109	qα−3	qα−3	NOUN
ejpam-486	372	110	β	β	X
ejpam-486	372	111	,	,	PUNCT
ejpam-486	372	112	p	p	PROPN
ejpam-486	372	113	f	f	X
ejpam-486	372	114	(	(	PUNCT
ejpam-486	372	115	z	z	NOUN
ejpam-486	372	116	)	)	PUNCT
ejpam-486	372	117	qα−2	qα−2	NOUN
ejpam-486	372	118	β	β	NOUN
ejpam-486	372	119	,	,	PUNCT
ejpam-486	372	120	p	p	PROPN
ejpam-486	372	121	f	f	X
ejpam-486	372	122	(	(	PUNCT
ejpam-486	372	123	z	z	NOUN
ejpam-486	372	124	)	)	PUNCT
ejpam-486	372	125	;	;	PUNCT
ejpam-486	372	126	z	z	X
ejpam-486	372	127	!	!	PUNCT
ejpam-486	372	128	�	�	PROPN
ejpam-486	373	1	α	α	X
ejpam-486	373	2	>	>	X
ejpam-486	373	3	3;β	3;β	NUM
ejpam-486	373	4	>	>	SYM
ejpam-486	373	5	−1	−1	NOUN
ejpam-486	373	6	;	;	PUNCT
ejpam-486	373	7	p	p	PROPN
ejpam-486	373	8	∈	∈	PROPN
ejpam-486	373	9	n	n	CCONJ
ejpam-486	373	10	;	;	PUNCT
ejpam-486	373	11	z	z	PROPN
ejpam-486	373	12	∈	∈	PROPN
ejpam-486	373	13	u	u	PROPN
ejpam-486	373	14	�	�	PROPN
ejpam-486	373	15	,	,	PUNCT
ejpam-486	373	16	(	(	PUNCT
ejpam-486	373	17	40	40	NUM
ejpam-486	373	18	)	)	PUNCT
ejpam-486	373	19	implies	imply	VERB
ejpam-486	373	20	q	q	PROPN
ejpam-486	373	21	(	(	PUNCT
ejpam-486	373	22	z	z	NOUN
ejpam-486	373	23	)	)	PUNCT
ejpam-486	373	24	≺	≺	NOUN
ejpam-486	373	25	qα−1	qα−1	NOUN
ejpam-486	373	26	β	β	X
ejpam-486	373	27	,	,	PUNCT
ejpam-486	373	28	p	p	PROPN
ejpam-486	373	29	f	f	X
ejpam-486	373	30	(	(	PUNCT
ejpam-486	373	31	z	z	NOUN
ejpam-486	373	32	)	)	PUNCT
ejpam-486	373	33	qα	qα	PROPN
ejpam-486	373	34	β	β	PROPN
ejpam-486	373	35	,	,	PUNCT
ejpam-486	373	36	p	p	PROPN
ejpam-486	373	37	f	f	X
ejpam-486	373	38	(	(	PUNCT
ejpam-486	373	39	z	z	NOUN
ejpam-486	373	40	)	)	PUNCT
ejpam-486	373	41	(	(	PUNCT
ejpam-486	373	42	z	z	NOUN
ejpam-486	373	43	∈	∈	PROPN
ejpam-486	373	44	u	u	NOUN
ejpam-486	373	45	)	)	PUNCT
ejpam-486	373	46	.	.	PUNCT
ejpam-486	374	1	combining	combine	VERB
ejpam-486	374	2	theorems	theorem	NOUN
ejpam-486	374	3	8	8	NUM
ejpam-486	374	4	and	and	CCONJ
ejpam-486	374	5	15	15	NUM
ejpam-486	374	6	,	,	PUNCT
ejpam-486	374	7	we	we	PRON
ejpam-486	374	8	obtain	obtain	VERB
ejpam-486	374	9	the	the	DET
ejpam-486	374	10	following	follow	VERB
ejpam-486	374	11	sandwich	sandwich	NOUN
ejpam-486	374	12	-	-	PUNCT
ejpam-486	374	13	type	type	NOUN
ejpam-486	374	14	theorem	theorem	VERB
ejpam-486	374	15	.	.	PROPN
ejpam-486	375	1	references	reference	NOUN
ejpam-486	375	2	44	44	NUM
ejpam-486	375	3	corollary	corollary	ADJ
ejpam-486	375	4	12	12	NUM
ejpam-486	375	5	.	.	PUNCT
ejpam-486	376	1	let	let	AUX
ejpam-486	376	2	h1(z	h1(z	NUM
ejpam-486	376	3	)	)	PUNCT
ejpam-486	376	4	and	and	CCONJ
ejpam-486	376	5	q1(z	q1(z	PROPN
ejpam-486	376	6	)	)	PUNCT
ejpam-486	376	7	be	be	AUX
ejpam-486	376	8	analytic	analytic	ADJ
ejpam-486	376	9	functions	function	NOUN
ejpam-486	376	10	in	in	ADP
ejpam-486	376	11	u	u	NOUN
ejpam-486	376	12	,	,	PUNCT
ejpam-486	376	13	h2(z	h2(z	X
ejpam-486	376	14	)	)	PUNCT
ejpam-486	376	15	be	be	AUX
ejpam-486	376	16	univalent	univalent	ADJ
ejpam-486	376	17	function	function	NOUN
ejpam-486	376	18	in	in	ADP
ejpam-486	376	19	u	u	NOUN
ejpam-486	376	20	,	,	PUNCT
ejpam-486	376	21	q2(z	q2(z	NOUN
ejpam-486	376	22	)	)	PUNCT
ejpam-486	376	23	∈	∈	PROPN
ejpam-486	376	24	f1	f1	NOUN
ejpam-486	376	25	with	with	ADP
ejpam-486	376	26	q1(0	q1(0	PROPN
ejpam-486	376	27	)	)	PUNCT
ejpam-486	376	28	=	=	SYM
ejpam-486	376	29	q20	q20	NOUN
ejpam-486	376	30	)	)	PUNCT
ejpam-486	377	1	=	=	SYM
ejpam-486	377	2	1	1	NUM
ejpam-486	377	3	and	and	CCONJ
ejpam-486	377	4	φ	φ	PROPN
ejpam-486	377	5	∈	∈	PROPN
ejpam-486	377	6	φq,2	φq,2	PUNCT
ejpam-486	377	7	�	�	PROPN
ejpam-486	377	8	h2,q2	h2,q2	PROPN
ejpam-486	377	9	�	�	PROPN
ejpam-486	377	10	∩	∩	NOUN
ejpam-486	377	11	φ′q,2	φ′q,2	ADP
ejpam-486	377	12	�	�	PROPN
ejpam-486	377	13	h1,q1	h1,q1	PROPN
ejpam-486	377	14	�	�	PROPN
ejpam-486	377	15	.	.	PUNCT
ejpam-486	378	1	if	if	SCONJ
ejpam-486	378	2	f	f	PROPN
ejpam-486	378	3	(	(	PUNCT
ejpam-486	378	4	z	z	NOUN
ejpam-486	378	5	)	)	PUNCT
ejpam-486	378	6	∈	∈	PROPN
ejpam-486	378	7	a	a	DET
ejpam-486	378	8	�	�	PROPN
ejpam-486	378	9	p	p	PROPN
ejpam-486	378	10	�	�	PROPN
ejpam-486	378	11	,	,	PUNCT
ejpam-486	378	12	qα−1	qα−1	PROPN
ejpam-486	378	13	β	β	X
ejpam-486	378	14	,	,	PUNCT
ejpam-486	378	15	p	p	PROPN
ejpam-486	378	16	f	f	X
ejpam-486	378	17	(	(	PUNCT
ejpam-486	378	18	z	z	NOUN
ejpam-486	378	19	)	)	PUNCT
ejpam-486	378	20	qα	qα	PROPN
ejpam-486	379	1	β	β	PROPN
ejpam-486	379	2	,	,	PUNCT
ejpam-486	379	3	p	p	PROPN
ejpam-486	379	4	f	f	X
ejpam-486	379	5	(	(	PUNCT
ejpam-486	379	6	z	z	NOUN
ejpam-486	379	7	)	)	PUNCT
ejpam-486	379	8	∈	∈	PROPN
ejpam-486	379	9	h	h	NOUN
ejpam-486	379	10	∩f1	∩f1	PROPN
ejpam-486	379	11	and	and	CCONJ
ejpam-486	379	12	φ	φ	PROPN
ejpam-486	379	13	qα−1	qα−1	PROPN
ejpam-486	379	14	β	β	PROPN
ejpam-486	379	15	,	,	PUNCT
ejpam-486	379	16	p	p	PROPN
ejpam-486	379	17	f	f	X
ejpam-486	379	18	(	(	PUNCT
ejpam-486	379	19	z	z	NOUN
ejpam-486	379	20	)	)	PUNCT
ejpam-486	379	21	qα	qα	PROPN
ejpam-486	379	22	β	β	PROPN
ejpam-486	379	23	,	,	PUNCT
ejpam-486	379	24	p	p	PROPN
ejpam-486	379	25	f	f	X
ejpam-486	379	26	(	(	PUNCT
ejpam-486	379	27	z	z	NOUN
ejpam-486	379	28	)	)	PUNCT
ejpam-486	379	29	,	,	PUNCT
ejpam-486	379	30	qα−2	qα−2	PROPN
ejpam-486	379	31	β	β	PROPN
ejpam-486	379	32	,	,	PUNCT
ejpam-486	379	33	p	p	PROPN
ejpam-486	379	34	f	f	X
ejpam-486	379	35	(	(	PUNCT
ejpam-486	379	36	z	z	NOUN
ejpam-486	379	37	)	)	PUNCT
ejpam-486	379	38	qα−1	qα−1	PROPN
ejpam-486	379	39	β	β	X
ejpam-486	379	40	,	,	PUNCT
ejpam-486	379	41	p	p	PROPN
ejpam-486	379	42	f	f	X
ejpam-486	379	43	(	(	PUNCT
ejpam-486	379	44	z	z	NOUN
ejpam-486	379	45	)	)	PUNCT
ejpam-486	379	46	,	,	PUNCT
ejpam-486	379	47	qα−3	qα−3	NOUN
ejpam-486	379	48	β	β	X
ejpam-486	379	49	,	,	PUNCT
ejpam-486	379	50	p	p	PROPN
ejpam-486	379	51	f	f	X
ejpam-486	379	52	(	(	PUNCT
ejpam-486	379	53	z	z	NOUN
ejpam-486	379	54	)	)	PUNCT
ejpam-486	379	55	qα−2	qα−2	NOUN
ejpam-486	379	56	β	β	NOUN
ejpam-486	379	57	,	,	PUNCT
ejpam-486	379	58	p	p	PROPN
ejpam-486	379	59	f	f	X
ejpam-486	379	60	(	(	PUNCT
ejpam-486	379	61	z	z	NOUN
ejpam-486	379	62	)	)	PUNCT
ejpam-486	379	63	;	;	PUNCT
ejpam-486	379	64	z	z	X
ejpam-486	379	65	!	!	PUNCT
ejpam-486	379	66	is	be	AUX
ejpam-486	379	67	univalent	univalent	ADJ
ejpam-486	379	68	in	in	ADP
ejpam-486	379	69	u	u	NOUN
ejpam-486	379	70	,	,	PUNCT
ejpam-486	379	71	then	then	ADV
ejpam-486	379	72	h1	h1	PROPN
ejpam-486	379	73	(	(	PUNCT
ejpam-486	379	74	z	z	NOUN
ejpam-486	379	75	)	)	PUNCT
ejpam-486	379	76	≺	≺	NOUN
ejpam-486	379	77	φ	φ	PROPN
ejpam-486	379	78	qα−1	qα−1	PROPN
ejpam-486	379	79	β	β	X
ejpam-486	379	80	,	,	PUNCT
ejpam-486	379	81	p	p	PROPN
ejpam-486	379	82	f	f	X
ejpam-486	379	83	(	(	PUNCT
ejpam-486	379	84	z	z	NOUN
ejpam-486	379	85	)	)	PUNCT
ejpam-486	379	86	qα	qα	PROPN
ejpam-486	379	87	β	β	PROPN
ejpam-486	379	88	,	,	PUNCT
ejpam-486	379	89	p	p	PROPN
ejpam-486	379	90	f	f	X
ejpam-486	379	91	(	(	PUNCT
ejpam-486	379	92	z	z	NOUN
ejpam-486	379	93	)	)	PUNCT
ejpam-486	379	94	,	,	PUNCT
ejpam-486	379	95	qα−2	qα−2	PROPN
ejpam-486	379	96	β	β	PROPN
ejpam-486	379	97	,	,	PUNCT
ejpam-486	379	98	p	p	PROPN
ejpam-486	379	99	f	f	X
ejpam-486	379	100	(	(	PUNCT
ejpam-486	379	101	z	z	NOUN
ejpam-486	379	102	)	)	PUNCT
ejpam-486	379	103	qα−1	qα−1	PROPN
ejpam-486	379	104	β	β	X
ejpam-486	379	105	,	,	PUNCT
ejpam-486	379	106	p	p	PROPN
ejpam-486	379	107	f	f	X
ejpam-486	379	108	(	(	PUNCT
ejpam-486	379	109	z	z	NOUN
ejpam-486	379	110	)	)	PUNCT
ejpam-486	379	111	,	,	PUNCT
ejpam-486	379	112	qα−3	qα−3	NOUN
ejpam-486	379	113	β	β	X
ejpam-486	379	114	,	,	PUNCT
ejpam-486	379	115	p	p	PROPN
ejpam-486	379	116	f	f	X
ejpam-486	379	117	(	(	PUNCT
ejpam-486	379	118	z	z	NOUN
ejpam-486	379	119	)	)	PUNCT
ejpam-486	379	120	qα−2	qα−2	NOUN
ejpam-486	379	121	β	β	NOUN
ejpam-486	379	122	,	,	PUNCT
ejpam-486	379	123	p	p	PROPN
ejpam-486	379	124	f	f	X
ejpam-486	379	125	(	(	PUNCT
ejpam-486	379	126	z	z	NOUN
ejpam-486	379	127	)	)	PUNCT
ejpam-486	379	128	;	;	PUNCT
ejpam-486	380	1	z	z	X
ejpam-486	380	2	!	!	PUNCT
ejpam-486	381	1	≺	≺	NOUN
ejpam-486	381	2	h2	h2	NOUN
ejpam-486	381	3	(	(	PUNCT
ejpam-486	381	4	z	z	NOUN
ejpam-486	381	5	)	)	PUNCT
ejpam-486	381	6	�	�	PROPN
ejpam-486	381	7	α	α	NOUN
ejpam-486	381	8	>	>	X
ejpam-486	381	9	3;β	3;β	NUM
ejpam-486	381	10	>	>	SYM
ejpam-486	381	11	−1	−1	NOUN
ejpam-486	381	12	;	;	PUNCT
ejpam-486	381	13	p	p	PROPN
ejpam-486	381	14	∈	∈	PROPN
ejpam-486	381	15	n	n	CCONJ
ejpam-486	381	16	;	;	PUNCT
ejpam-486	381	17	z	z	PROPN
ejpam-486	381	18	∈	∈	PROPN
ejpam-486	381	19	u	u	PROPN
ejpam-486	381	20	�	�	PROPN
ejpam-486	381	21	,	,	PUNCT
ejpam-486	381	22	implies	imply	VERB
ejpam-486	381	23	q1	q1	PROPN
ejpam-486	381	24	(	(	PUNCT
ejpam-486	381	25	z	z	NOUN
ejpam-486	381	26	)	)	PUNCT
ejpam-486	381	27	≺	≺	NOUN
ejpam-486	381	28	qα−1	qα−1	NOUN
ejpam-486	381	29	β	β	X
ejpam-486	381	30	,	,	PUNCT
ejpam-486	381	31	p	p	PROPN
ejpam-486	381	32	f	f	X
ejpam-486	381	33	(	(	PUNCT
ejpam-486	381	34	z	z	NOUN
ejpam-486	381	35	)	)	PUNCT
ejpam-486	381	36	qα	qα	PROPN
ejpam-486	381	37	β	β	PROPN
ejpam-486	381	38	,	,	PUNCT
ejpam-486	381	39	p	p	PROPN
ejpam-486	381	40	f	f	X
ejpam-486	381	41	(	(	PUNCT
ejpam-486	381	42	z	z	NOUN
ejpam-486	381	43	)	)	PUNCT
ejpam-486	381	44	≺	≺	NOUN
ejpam-486	381	45	q2	q2	NOUN
ejpam-486	381	46	(	(	PUNCT
ejpam-486	381	47	z	z	NOUN
ejpam-486	381	48	)	)	PUNCT
ejpam-486	381	49	(	(	PUNCT
ejpam-486	381	50	z	z	NOUN
ejpam-486	381	51	∈	∈	PROPN
ejpam-486	381	52	u	u	NOUN
ejpam-486	381	53	)	)	PUNCT
ejpam-486	381	54	.	.	PUNCT
ejpam-486	382	1	references	reference	NOUN
ejpam-486	382	2	[	[	X
ejpam-486	382	3	1	1	NUM
ejpam-486	382	4	]	]	X
ejpam-486	382	5	r.	r.	PROPN
ejpam-486	382	6	aghalary	aghalary	PROPN
ejpam-486	382	7	,	,	PUNCT
ejpam-486	382	8	r.	r.	PROPN
ejpam-486	382	9	m.	m.	PROPN
ejpam-486	382	10	ali	ali	PROPN
ejpam-486	382	11	,	,	PUNCT
ejpam-486	382	12	s.	s.	PROPN
ejpam-486	382	13	b.	b.	PROPN
ejpam-486	382	14	joshi	joshi	PROPN
ejpam-486	382	15	and	and	CCONJ
ejpam-486	382	16	v.	v.	ADP
ejpam-486	382	17	ravichandran	ravichandran	NOUN
ejpam-486	382	18	,	,	PUNCT
ejpam-486	382	19	inequalities	inequality	NOUN
ejpam-486	382	20	for	for	ADP
ejpam-486	382	21	analytic	analytic	ADJ
ejpam-486	382	22	functions	function	NOUN
ejpam-486	382	23	defined	define	VERB
ejpam-486	382	24	by	by	ADP
ejpam-486	382	25	certain	certain	ADJ
ejpam-486	382	26	linear	linear	ADJ
ejpam-486	382	27	operator	operator	NOUN
ejpam-486	382	28	,	,	PUNCT
ejpam-486	382	29	internat	internat	PROPN
ejpam-486	382	30	.	.	PUNCT
ejpam-486	383	1	j.	j.	PROPN
ejpam-486	383	2	math	math	PROPN
ejpam-486	383	3	.	.	PUNCT
ejpam-486	384	1	sci	sci	PROPN
ejpam-486	384	2	,	,	PUNCT
ejpam-486	384	3	4(2005	4(2005	NUM
ejpam-486	384	4	)	)	PUNCT
ejpam-486	384	5	,	,	PUNCT
ejpam-486	384	6	no.2	no.2	PROPN
ejpam-486	384	7	,	,	PUNCT
ejpam-486	384	8	267–274	267–274	NUM
ejpam-486	384	9	.	.	PUNCT
ejpam-486	385	1	[	[	X
ejpam-486	385	2	2	2	NUM
ejpam-486	385	3	]	]	X
ejpam-486	385	4	r.	r.	PROPN
ejpam-486	385	5	m.	m.	PROPN
ejpam-486	385	6	ali	ali	PROPN
ejpam-486	385	7	,	,	PUNCT
ejpam-486	385	8	v.	v.	ADP
ejpam-486	385	9	ravichandran	ravichandran	NOUN
ejpam-486	385	10	and	and	CCONJ
ejpam-486	385	11	n.	n.	PROPN
ejpam-486	385	12	seenivasagan	seenivasagan	PROPN
ejpam-486	385	13	,	,	PUNCT
ejpam-486	385	14	differential	differential	ADJ
ejpam-486	385	15	subordination	subordination	NOUN
ejpam-486	385	16	and	and	CCONJ
ejpam-486	385	17	superodination	superodination	NOUN
ejpam-486	385	18	of	of	ADP
ejpam-486	385	19	analytic	analytic	ADJ
ejpam-486	385	20	functions	function	NOUN
ejpam-486	385	21	defined	define	VERB
ejpam-486	385	22	by	by	ADP
ejpam-486	385	23	the	the	DET
ejpam-486	385	24	multiplier	multipli	ADJ
ejpam-486	385	25	transformation	transformation	NOUN
ejpam-486	385	26	,	,	PUNCT
ejpam-486	385	27	math	math	NOUN
ejpam-486	385	28	.	.	PUNCT
ejpam-486	386	1	inequal	inequal	ADJ
ejpam-486	386	2	.	.	PUNCT
ejpam-486	387	1	appl.12(2009	appl.12(2009	NOUN
ejpam-486	387	2	)	)	PUNCT
ejpam-486	387	3	,	,	PUNCT
ejpam-486	387	4	no.1,123	no.1,123	NOUN
ejpam-486	387	5	-	-	SYM
ejpam-486	387	6	139	139	NUM
ejpam-486	387	7	.	.	PUNCT
ejpam-486	388	1	[	[	X
ejpam-486	388	2	3	3	X
ejpam-486	388	3	]	]	PUNCT
ejpam-486	388	4	m.	m.	PROPN
ejpam-486	388	5	k.	k.	PROPN
ejpam-486	388	6	aouf	aouf	PROPN
ejpam-486	388	7	,	,	PUNCT
ejpam-486	388	8	inequalities	inequality	NOUN
ejpam-486	388	9	involving	involve	VERB
ejpam-486	388	10	certain	certain	ADJ
ejpam-486	388	11	integral	integral	ADJ
ejpam-486	388	12	operator	operator	NOUN
ejpam-486	388	13	,	,	PUNCT
ejpam-486	388	14	j.	j.	PROPN
ejpam-486	388	15	math	math	PROPN
ejpam-486	388	16	.	.	PUNCT
ejpam-486	389	1	inequal	inequal	ADJ
ejpam-486	389	2	.	.	PUNCT
ejpam-486	390	1	2(2008	2(2008	X
ejpam-486	390	2	)	)	PUNCT
ejpam-486	390	3	,	,	PUNCT
ejpam-486	390	4	no.2	no.2	PROPN
ejpam-486	390	5	,	,	PUNCT
ejpam-486	390	6	537	537	NUM
ejpam-486	390	7	-	-	SYM
ejpam-486	390	8	547	547	NUM
ejpam-486	390	9	.	.	PUNCT
ejpam-486	391	1	[	[	X
ejpam-486	391	2	4	4	X
ejpam-486	391	3	]	]	PUNCT
ejpam-486	391	4	m.	m.	PROPN
ejpam-486	391	5	k.	k.	PROPN
ejpam-486	391	6	aouf	aouf	PROPN
ejpam-486	391	7	,	,	PUNCT
ejpam-486	391	8	h.m	h.m	PROPN
ejpam-486	391	9	.	.	PROPN
ejpam-486	391	10	hossen	hossen	PROPN
ejpam-486	391	11	and	and	CCONJ
ejpam-486	391	12	a.	a.	PROPN
ejpam-486	391	13	y.	y.	PROPN
ejpam-486	391	14	lashin	lashin	PROPN
ejpam-486	391	15	,	,	PUNCT
ejpam-486	391	16	an	an	DET
ejpam-486	391	17	application	application	NOUN
ejpam-486	391	18	of	of	ADP
ejpam-486	391	19	certain	certain	ADJ
ejpam-486	391	20	integral	integral	ADJ
ejpam-486	391	21	operators	operator	NOUN
ejpam-486	391	22	,	,	PUNCT
ejpam-486	391	23	j.	j.	PROPN
ejpam-486	391	24	math	math	PROPN
ejpam-486	391	25	.	.	PUNCT
ejpam-486	392	1	anal	anal	PROPN
ejpam-486	392	2	.	.	PUNCT
ejpam-486	393	1	appl	appl	PROPN
ejpam-486	393	2	.	.	PUNCT
ejpam-486	394	1	248(2000	248(2000	NUM
ejpam-486	394	2	)	)	PUNCT
ejpam-486	394	3	,	,	PUNCT
ejpam-486	395	1	no	no	INTJ
ejpam-486	395	2	.	.	NOUN
ejpam-486	395	3	2	2	NUM
ejpam-486	395	4	,	,	PUNCT
ejpam-486	395	5	475–481	475–481	NUM
ejpam-486	395	6	.	.	PUNCT
ejpam-486	396	1	[	[	X
ejpam-486	396	2	5	5	X
ejpam-486	396	3	]	]	PUNCT
ejpam-486	396	4	t.	t.	PROPN
ejpam-486	396	5	b.	b.	PROPN
ejpam-486	396	6	jung	jung	PROPN
ejpam-486	396	7	,	,	PUNCT
ejpam-486	396	8	y.	y.	PROPN
ejpam-486	396	9	c.	c.	PROPN
ejpam-486	396	10	kim	kim	PROPN
ejpam-486	396	11	and	and	CCONJ
ejpam-486	396	12	h.	h.	PROPN
ejpam-486	396	13	m.	m.	PROPN
ejpam-486	396	14	srivastava	srivastava	PROPN
ejpam-486	396	15	,	,	PUNCT
ejpam-486	396	16	the	the	DET
ejpam-486	396	17	hardy	hardy	ADJ
ejpam-486	396	18	space	space	NOUN
ejpam-486	396	19	of	of	ADP
ejpam-486	396	20	analytic	analytic	ADJ
ejpam-486	396	21	functions	function	NOUN
ejpam-486	396	22	associated	associate	VERB
ejpam-486	396	23	with	with	ADP
ejpam-486	396	24	certain	certain	ADJ
ejpam-486	396	25	one	one	NUM
ejpam-486	396	26	-	-	PUNCT
ejpam-486	396	27	parameter	parameter	NOUN
ejpam-486	396	28	families	family	NOUN
ejpam-486	396	29	of	of	ADP
ejpam-486	396	30	integral	integral	ADJ
ejpam-486	396	31	operators	operator	NOUN
ejpam-486	396	32	,	,	PUNCT
ejpam-486	396	33	j.	j.	PROPN
ejpam-486	396	34	math	math	PROPN
ejpam-486	396	35	.	.	PUNCT
ejpam-486	397	1	anal	anal	PROPN
ejpam-486	397	2	.	.	PUNCT
ejpam-486	398	1	appl	appl	PROPN
ejpam-486	398	2	.	.	PROPN
ejpam-486	398	3	,	,	PUNCT
ejpam-486	398	4	176(1993	176(1993	NUM
ejpam-486	398	5	)	)	PUNCT
ejpam-486	398	6	,	,	PUNCT
ejpam-486	398	7	138	138	NUM
ejpam-486	398	8	-	-	SYM
ejpam-486	398	9	147	147	NUM
ejpam-486	398	10	.	.	PUNCT
ejpam-486	399	1	[	[	X
ejpam-486	399	2	6	6	NUM
ejpam-486	399	3	]	]	X
ejpam-486	399	4	y.	y.	PROPN
ejpam-486	399	5	c.	c.	PROPN
ejpam-486	399	6	kim	kim	PROPN
ejpam-486	399	7	and	and	CCONJ
ejpam-486	399	8	h.	h.	PROPN
ejpam-486	399	9	m.	m.	PROPN
ejpam-486	399	10	srivastava	srivastava	PROPN
ejpam-486	399	11	,	,	PUNCT
ejpam-486	399	12	inequalities	inequality	NOUN
ejpam-486	399	13	involving	involve	VERB
ejpam-486	399	14	certain	certain	ADJ
ejpam-486	399	15	families	family	NOUN
ejpam-486	399	16	of	of	ADP
ejpam-486	399	17	integral	integral	ADJ
ejpam-486	399	18	and	and	CCONJ
ejpam-486	399	19	convolution	convolution	NOUN
ejpam-486	399	20	operators	operator	NOUN
ejpam-486	399	21	,	,	PUNCT
ejpam-486	399	22	math	math	NOUN
ejpam-486	399	23	.	.	PUNCT
ejpam-486	399	24	inequal	inequal	PROPN
ejpam-486	399	25	.	.	PUNCT
ejpam-486	400	1	appl	appl	PROPN
ejpam-486	400	2	.	.	PUNCT
ejpam-486	401	1	7(2004	7(2004	NUM
ejpam-486	401	2	)	)	PUNCT
ejpam-486	401	3	,	,	PUNCT
ejpam-486	402	1	no	no	INTJ
ejpam-486	402	2	.	.	NOUN
ejpam-486	402	3	2	2	NUM
ejpam-486	402	4	,	,	PUNCT
ejpam-486	402	5	227–234	227–234	NUM
ejpam-486	402	6	.	.	PUNCT
ejpam-486	403	1	[	[	X
ejpam-486	403	2	7	7	X
ejpam-486	403	3	]	]	X
ejpam-486	403	4	j.-l	j.-l	ADV
ejpam-486	403	5	.	.	PUNCT
ejpam-486	404	1	liu	liu	PROPN
ejpam-486	404	2	and	and	CCONJ
ejpam-486	404	3	s.	s.	PROPN
ejpam-486	404	4	owa	owa	PROPN
ejpam-486	404	5	,	,	PUNCT
ejpam-486	404	6	properties	property	NOUN
ejpam-486	404	7	of	of	ADP
ejpam-486	404	8	certain	certain	ADJ
ejpam-486	404	9	integral	integral	ADJ
ejpam-486	404	10	operators	operator	NOUN
ejpam-486	404	11	,	,	PUNCT
ejpam-486	404	12	internat	internat	PROPN
ejpam-486	404	13	.	.	PUNCT
ejpam-486	405	1	j.	j.	PROPN
ejpam-486	405	2	math	math	PROPN
ejpam-486	405	3	.	.	PUNCT
ejpam-486	406	1	math	math	NOUN
ejpam-486	406	2	.	.	PUNCT
ejpam-486	407	1	sci	sci	PROPN
ejpam-486	407	2	.	.	PROPN
ejpam-486	407	3	,	,	PUNCT
ejpam-486	407	4	3(2004	3(2004	NUM
ejpam-486	407	5	)	)	PUNCT
ejpam-486	407	6	,	,	PUNCT
ejpam-486	407	7	no	no	INTJ
ejpam-486	407	8	.	.	NOUN
ejpam-486	407	9	1	1	NUM
ejpam-486	407	10	,	,	PUNCT
ejpam-486	407	11	69	69	NUM
ejpam-486	407	12	-	-	SYM
ejpam-486	407	13	75	75	NUM
ejpam-486	407	14	.	.	PUNCT
ejpam-486	408	1	[	[	X
ejpam-486	408	2	8	8	NUM
ejpam-486	408	3	]	]	PUNCT
ejpam-486	408	4	s.	s.	PROPN
ejpam-486	408	5	s.	s.	PROPN
ejpam-486	408	6	miller	miller	PROPN
ejpam-486	408	7	and	and	CCONJ
ejpam-486	408	8	p.	p.	PROPN
ejpam-486	408	9	t.	t.	PROPN
ejpam-486	408	10	mocanu	mocanu	PROPN
ejpam-486	408	11	,	,	PUNCT
ejpam-486	408	12	differential	differential	ADJ
ejpam-486	408	13	subordinations	subordination	NOUN
ejpam-486	408	14	:	:	PUNCT
ejpam-486	408	15	theory	theory	NOUN
ejpam-486	408	16	and	and	CCONJ
ejpam-486	408	17	applications	application	NOUN
ejpam-486	408	18	,	,	PUNCT
ejpam-486	408	19	series	series	NOUN
ejpam-486	408	20	on	on	ADP
ejpam-486	408	21	monographs	monograph	NOUN
ejpam-486	408	22	and	and	CCONJ
ejpam-486	408	23	textbooks	textbook	NOUN
ejpam-486	408	24	in	in	ADP
ejpam-486	408	25	pure	pure	ADJ
ejpam-486	408	26	and	and	CCONJ
ejpam-486	408	27	applied	applied	ADJ
ejpam-486	408	28	mathematics	mathematic	NOUN
ejpam-486	408	29	,	,	PUNCT
ejpam-486	408	30	vol	vol	NOUN
ejpam-486	408	31	.	.	PROPN
ejpam-486	408	32	225	225	NUM
ejpam-486	408	33	,	,	PUNCT
ejpam-486	408	34	marcel	marcel	PROPN
ejpam-486	408	35	dekker	dekker	PROPN
ejpam-486	408	36	,	,	PUNCT
ejpam-486	408	37	new	new	PROPN
ejpam-486	408	38	york	york	PROPN
ejpam-486	408	39	and	and	CCONJ
ejpam-486	408	40	basel	basel	PROPN
ejpam-486	408	41	,	,	PUNCT
ejpam-486	408	42	2000	2000	NUM
ejpam-486	408	43	.	.	PUNCT
ejpam-486	409	1	[	[	X
ejpam-486	409	2	9	9	NUM
ejpam-486	409	3	]	]	PUNCT
ejpam-486	409	4	s.	s.	PROPN
ejpam-486	409	5	miller	miller	PROPN
ejpam-486	409	6	and	and	CCONJ
ejpam-486	409	7	p.	p.	PROPN
ejpam-486	409	8	t.	t.	PROPN
ejpam-486	409	9	mocanu	mocanu	PROPN
ejpam-486	409	10	,	,	PUNCT
ejpam-486	409	11	subordinants	subordinant	NOUN
ejpam-486	409	12	of	of	ADP
ejpam-486	409	13	differential	differential	ADJ
ejpam-486	409	14	superordinations	superordination	NOUN
ejpam-486	409	15	,	,	PUNCT
ejpam-486	409	16	complex	complex	ADJ
ejpam-486	409	17	variables	variable	NOUN
ejpam-486	409	18	theory	theory	NOUN
ejpam-486	409	19	appl	appl	PROPN
ejpam-486	409	20	.	.	PUNCT
ejpam-486	410	1	48(2003	48(2003	NUM
ejpam-486	410	2	)	)	PUNCT
ejpam-486	410	3	,	,	PUNCT
ejpam-486	410	4	no.10	no.10	PROPN
ejpam-486	410	5	,	,	PUNCT
ejpam-486	410	6	815–826	815–826	NUM
ejpam-486	410	7	.	.	PUNCT