id	sid	tid	token	lemma	pos
ejpam-617	1	1	2_617_dziok.dvi	2_617_dziok.dvi	NUM
ejpam-617	1	2	european	european	ADJ
ejpam-617	1	3	journal	journal	NOUN
ejpam-617	1	4	of	of	ADP
ejpam-617	1	5	pure	pure	ADJ
ejpam-617	1	6	and	and	CCONJ
ejpam-617	1	7	applied	apply	VERB
ejpam-617	1	8	mathematics	mathematic	NOUN
ejpam-617	1	9	vol	vol	NOUN
ejpam-617	1	10	.	.	PUNCT
ejpam-617	2	1	3	3	NUM
ejpam-617	2	2	,	,	PUNCT
ejpam-617	2	3	no	no	INTJ
ejpam-617	2	4	.	.	NOUN
ejpam-617	2	5	4	4	NUM
ejpam-617	2	6	,	,	PUNCT
ejpam-617	2	7	2010	2010	NUM
ejpam-617	2	8	,	,	PUNCT
ejpam-617	2	9	633	633	NUM
ejpam-617	2	10	-	-	SYM
ejpam-617	2	11	640	640	NUM
ejpam-617	2	12	issn	issn	PROPN
ejpam-617	2	13	1307	1307	NUM
ejpam-617	2	14	-	-	SYM
ejpam-617	2	15	5543	5543	NUM
ejpam-617	2	16	–	–	PUNCT
ejpam-617	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-617	2	18	certain	certain	ADJ
ejpam-617	2	19	results	result	NOUN
ejpam-617	2	20	for	for	ADP
ejpam-617	2	21	a	a	DET
ejpam-617	2	22	subclass	subclass	NOUN
ejpam-617	2	23	of	of	ADP
ejpam-617	2	24	meromorphic	meromorphic	ADJ
ejpam-617	2	25	multivalent	multivalent	NOUN
ejpam-617	2	26	functions	function	NOUN
ejpam-617	2	27	associated	associate	VERB
ejpam-617	2	28	with	with	ADP
ejpam-617	2	29	the	the	DET
ejpam-617	2	30	wright	wright	PROPN
ejpam-617	2	31	function	function	PROPN
ejpam-617	2	32	sanjay	sanjay	PROPN
ejpam-617	2	33	k.	k.	PROPN
ejpam-617	2	34	bansal1	bansal1	PROPN
ejpam-617	2	35	,	,	PUNCT
ejpam-617	2	36	jacek	jacek	PROPN
ejpam-617	2	37	dziok2,∗	dziok2,∗	PROPN
ejpam-617	2	38	,	,	PUNCT
ejpam-617	2	39	pranay	pranay	NOUN
ejpam-617	2	40	goswami	goswami	NOUN
ejpam-617	2	41	3	3	NUM
ejpam-617	2	42	1	1	NUM
ejpam-617	2	43	school	school	NOUN
ejpam-617	2	44	of	of	ADP
ejpam-617	2	45	engg	engg	PROPN
ejpam-617	2	46	.	.	PUNCT
ejpam-617	3	1	and	and	CCONJ
ejpam-617	3	2	tech	tech	NOUN
ejpam-617	3	3	.	.	PUNCT
ejpam-617	3	4	,	,	PUNCT
ejpam-617	3	5	jaipur-303904	jaipur-303904	PROPN
ejpam-617	3	6	,	,	PUNCT
ejpam-617	3	7	india	india	PROPN
ejpam-617	3	8	2	2	NUM
ejpam-617	3	9	institute	institute	NOUN
ejpam-617	3	10	of	of	ADP
ejpam-617	3	11	mathematics	mathematics	PROPN
ejpam-617	3	12	,	,	PUNCT
ejpam-617	3	13	university	university	NOUN
ejpam-617	3	14	of	of	ADP
ejpam-617	3	15	rzeszów	rzeszów	NOUN
ejpam-617	3	16	,	,	PUNCT
ejpam-617	3	17	ul.rejtana,16a	ul.rejtana,16a	NOUN
ejpam-617	3	18	,	,	PUNCT
ejpam-617	3	19	pl-35	pl-35	ADV
ejpam-617	3	20	-	-	PUNCT
ejpam-617	3	21	310	310	NUM
ejpam-617	3	22	rzeszów	rzeszów	NOUN
ejpam-617	3	23	,	,	PUNCT
ejpam-617	3	24	poland	poland	PROPN
ejpam-617	3	25	3	3	NUM
ejpam-617	3	26	department	department	NOUN
ejpam-617	3	27	of	of	ADP
ejpam-617	3	28	mathematics	mathematics	PROPN
ejpam-617	3	29	,	,	PUNCT
ejpam-617	3	30	amity	amity	NOUN
ejpam-617	3	31	university	university	NOUN
ejpam-617	3	32	,	,	PUNCT
ejpam-617	3	33	rajasthan	rajasthan	NOUN
ejpam-617	3	34	,	,	PUNCT
ejpam-617	3	35	jaipur302002	jaipur302002	PROPN
ejpam-617	3	36	,	,	PUNCT
ejpam-617	3	37	india	india	PROPN
ejpam-617	3	38	abstract	abstract	NOUN
ejpam-617	3	39	.	.	PUNCT
ejpam-617	4	1	in	in	ADP
ejpam-617	4	2	this	this	DET
ejpam-617	4	3	paper	paper	NOUN
ejpam-617	4	4	,	,	PUNCT
ejpam-617	4	5	we	we	PRON
ejpam-617	4	6	introduce	introduce	VERB
ejpam-617	4	7	a	a	DET
ejpam-617	4	8	new	new	ADJ
ejpam-617	4	9	subclass	subclass	NOUN
ejpam-617	4	10	of	of	ADP
ejpam-617	4	11	meromorphic	meromorphic	ADJ
ejpam-617	4	12	multivalent	multivalent	NOUN
ejpam-617	4	13	functions	function	NOUN
ejpam-617	4	14	associated	associate	VERB
ejpam-617	4	15	with	with	ADP
ejpam-617	4	16	wright	wright	PROPN
ejpam-617	4	17	generalized	generalize	VERB
ejpam-617	4	18	hypergeometric	hypergeometric	ADJ
ejpam-617	4	19	function	function	NOUN
ejpam-617	4	20	and	and	CCONJ
ejpam-617	4	21	obtain	obtain	VERB
ejpam-617	4	22	new	new	ADJ
ejpam-617	4	23	results	result	NOUN
ejpam-617	4	24	for	for	ADP
ejpam-617	4	25	this	this	DET
ejpam-617	4	26	class	class	NOUN
ejpam-617	4	27	by	by	ADP
ejpam-617	4	28	the	the	DET
ejpam-617	4	29	application	application	NOUN
ejpam-617	4	30	of	of	ADP
ejpam-617	4	31	briot	briot	NOUN
ejpam-617	4	32	-	-	PUNCT
ejpam-617	4	33	bouquet	bouquet	NOUN
ejpam-617	4	34	differential	differential	NOUN
ejpam-617	4	35	subordination	subordination	NOUN
ejpam-617	4	36	.	.	PUNCT
ejpam-617	5	1	key	key	ADJ
ejpam-617	5	2	words	word	NOUN
ejpam-617	5	3	and	and	CCONJ
ejpam-617	5	4	phrases	phrase	NOUN
ejpam-617	5	5	:	:	PUNCT
ejpam-617	5	6	analytic	analytic	ADJ
ejpam-617	5	7	functions	function	NOUN
ejpam-617	5	8	,	,	PUNCT
ejpam-617	5	9	wright	wright	PROPN
ejpam-617	5	10	generalized	generalize	VERB
ejpam-617	5	11	hypergeometric	hypergeometric	ADJ
ejpam-617	5	12	function	function	NOUN
ejpam-617	5	13	,	,	PUNCT
ejpam-617	5	14	the	the	DET
ejpam-617	5	15	briotbouquet	briotbouquet	NOUN
ejpam-617	5	16	differential	differential	NOUN
ejpam-617	5	17	subordination	subordination	NOUN
ejpam-617	5	18	.	.	PUNCT
ejpam-617	6	1	1	1	X
ejpam-617	6	2	.	.	X
ejpam-617	6	3	introduction	introduction	NOUN
ejpam-617	6	4	let	let	VERB
ejpam-617	6	5	σp	σp	PART
ejpam-617	6	6	denote	denote	VERB
ejpam-617	6	7	the	the	DET
ejpam-617	6	8	class	class	NOUN
ejpam-617	6	9	of	of	ADP
ejpam-617	6	10	meromorphic	meromorphic	ADJ
ejpam-617	6	11	function	function	NOUN
ejpam-617	6	12	of	of	ADP
ejpam-617	6	13	the	the	DET
ejpam-617	6	14	form	form	NOUN
ejpam-617	7	1	f	f	X
ejpam-617	7	2	(	(	PUNCT
ejpam-617	7	3	z	z	NOUN
ejpam-617	7	4	)	)	PUNCT
ejpam-617	7	5	=	=	PUNCT
ejpam-617	7	6	z−p	z−p	NOUN
ejpam-617	7	7	+	+	CCONJ
ejpam-617	8	1	∞	∞	NUM
ejpam-617	8	2	∑	∑	PUNCT
ejpam-617	8	3	k=1	k=1	PROPN
ejpam-617	8	4	akzk−p	akzk−p	PROPN
ejpam-617	8	5	(	(	PUNCT
ejpam-617	8	6	p	p	NOUN
ejpam-617	8	7	∈	∈	PROPN
ejpam-617	8	8	n	n	NOUN
ejpam-617	8	9	:	:	PUNCT
ejpam-617	8	10	=	=	SYM
ejpam-617	8	11	{	{	PUNCT
ejpam-617	8	12	1,2,3	1,2,3	NUM
ejpam-617	8	13	,	,	PUNCT
ejpam-617	8	14	.....	.....	PUNCT
ejpam-617	8	15	}	}	PUNCT
ejpam-617	8	16	)	)	PUNCT
ejpam-617	8	17	,	,	PUNCT
ejpam-617	8	18	(	(	PUNCT
ejpam-617	8	19	1	1	X
ejpam-617	8	20	)	)	PUNCT
ejpam-617	8	21	which	which	PRON
ejpam-617	8	22	are	be	AUX
ejpam-617	8	23	analytic	analytic	ADJ
ejpam-617	8	24	in	in	ADP
ejpam-617	8	25	the	the	DET
ejpam-617	8	26	punctured	puncture	VERB
ejpam-617	8	27	open	open	ADJ
ejpam-617	8	28	unit	unit	NOUN
ejpam-617	8	29	disk	disk	NOUN
ejpam-617	8	30	d	d	NOUN
ejpam-617	8	31	:	:	PUNCT
ejpam-617	8	32	=	=	SYM
ejpam-617	8	33	{	{	PUNCT
ejpam-617	8	34	z	z	NOUN
ejpam-617	8	35	∈	∈	PROPN
ejpam-617	8	36	c	c	NOUN
ejpam-617	9	1	|	|	ADV
ejpam-617	9	2	0	0	NUM
ejpam-617	9	3	<	<	X
ejpam-617	9	4	|z|	|z|	PROPN
ejpam-617	9	5	<	<	X
ejpam-617	9	6	1}=u	1}=u	NOUN
ejpam-617	9	7	\	\	PROPN
ejpam-617	9	8	{	{	PUNCT
ejpam-617	9	9	0	0	NUM
ejpam-617	9	10	}	}	PUNCT
ejpam-617	9	11	,	,	PUNCT
ejpam-617	9	12	where	where	SCONJ
ejpam-617	9	13	u	u	NOUN
ejpam-617	9	14	:	:	PUNCT
ejpam-617	9	15	=	=	SYM
ejpam-617	9	16	{	{	PUNCT
ejpam-617	9	17	z	z	NOUN
ejpam-617	9	18	∈	∈	PROPN
ejpam-617	9	19	c	c	NOUN
ejpam-617	9	20	|	|	ADV
ejpam-617	9	21	|z|	|z|	VERB
ejpam-617	9	22	<	<	X
ejpam-617	9	23	1	1	NUM
ejpam-617	9	24	}	}	PUNCT
ejpam-617	9	25	.	.	PUNCT
ejpam-617	10	1	also	also	ADV
ejpam-617	10	2	,	,	PUNCT
ejpam-617	10	3	we	we	PRON
ejpam-617	10	4	denote	denote	VERB
ejpam-617	10	5	σ	σ	PROPN
ejpam-617	10	6	=	=	PROPN
ejpam-617	10	7	σ1	σ1	PROPN
ejpam-617	10	8	.	.	PUNCT
ejpam-617	11	1	if	if	SCONJ
ejpam-617	11	2	f	f	PROPN
ejpam-617	11	3	(	(	PUNCT
ejpam-617	11	4	z	z	NOUN
ejpam-617	11	5	)	)	PUNCT
ejpam-617	11	6	and	and	CCONJ
ejpam-617	11	7	f(z	f(z	NOUN
ejpam-617	11	8	)	)	PUNCT
ejpam-617	11	9	are	be	AUX
ejpam-617	11	10	analytic	analytic	ADJ
ejpam-617	11	11	in	in	ADP
ejpam-617	11	12	u	u	PROPN
ejpam-617	11	13	,	,	PUNCT
ejpam-617	11	14	we	we	PRON
ejpam-617	11	15	say	say	VERB
ejpam-617	11	16	that	that	SCONJ
ejpam-617	11	17	f	f	PROPN
ejpam-617	11	18	(	(	PUNCT
ejpam-617	11	19	z	z	NOUN
ejpam-617	11	20	)	)	PUNCT
ejpam-617	11	21	is	be	AUX
ejpam-617	11	22	subordinate	subordinate	ADJ
ejpam-617	11	23	to	to	ADP
ejpam-617	11	24	a	a	DET
ejpam-617	11	25	function	function	NOUN
ejpam-617	11	26	f(z	f(z	NOUN
ejpam-617	11	27	)	)	PUNCT
ejpam-617	11	28	written	write	VERB
ejpam-617	11	29	symbolically	symbolically	ADV
ejpam-617	11	30	as	as	ADP
ejpam-617	11	31	f	f	PROPN
ejpam-617	11	32	≺	≺	NOUN
ejpam-617	11	33	f	f	PROPN
ejpam-617	11	34	or	or	CCONJ
ejpam-617	11	35	f	f	PROPN
ejpam-617	11	36	(	(	PUNCT
ejpam-617	11	37	z)≺	z)≺	PROPN
ejpam-617	11	38	f(z	f(z	PROPN
ejpam-617	11	39	)	)	PUNCT
ejpam-617	11	40	,	,	PUNCT
ejpam-617	11	41	(	(	PUNCT
ejpam-617	11	42	z	z	NOUN
ejpam-617	11	43	∈	∈	PROPN
ejpam-617	11	44	u	u	NOUN
ejpam-617	11	45	)	)	PUNCT
ejpam-617	11	46	,	,	PUNCT
ejpam-617	11	47	if	if	SCONJ
ejpam-617	11	48	there	there	PRON
ejpam-617	11	49	exists	exist	VERB
ejpam-617	11	50	a	a	DET
ejpam-617	11	51	schwarz	schwarz	NOUN
ejpam-617	11	52	function	function	NOUN
ejpam-617	11	53	w(z	w(z	NOUN
ejpam-617	11	54	)	)	PUNCT
ejpam-617	11	55	which	which	PRON
ejpam-617	11	56	(	(	PUNCT
ejpam-617	11	57	by	by	ADP
ejpam-617	11	58	definition	definition	NOUN
ejpam-617	11	59	)	)	PUNCT
ejpam-617	11	60	is	be	AUX
ejpam-617	11	61	analytic	analytic	ADJ
ejpam-617	11	62	in	in	ADP
ejpam-617	11	63	u	u	NOUN
ejpam-617	11	64	with	with	ADP
ejpam-617	11	65	w(0	w(0	PROPN
ejpam-617	11	66	)	)	PUNCT
ejpam-617	11	67	=	=	SYM
ejpam-617	11	68	0	0	NUM
ejpam-617	11	69	,	,	PUNCT
ejpam-617	11	70	|w(z)|	|w(z)|	VERB
ejpam-617	11	71	<	<	X
ejpam-617	11	72	1	1	NUM
ejpam-617	11	73	(	(	PUNCT
ejpam-617	11	74	z	z	NOUN
ejpam-617	11	75	∈	∈	PROPN
ejpam-617	11	76	u	u	NOUN
ejpam-617	11	77	)	)	PUNCT
ejpam-617	11	78	,	,	PUNCT
ejpam-617	11	79	∗corresponding	∗corresponde	VERB
ejpam-617	11	80	author	author	NOUN
ejpam-617	11	81	.	.	PUNCT
ejpam-617	12	1	email	email	NOUN
ejpam-617	12	2	addresses	address	NOUN
ejpam-617	12	3	:	:	PUNCT
ejpam-617	12	4	bansalindian	bansalindian	ADJ
ejpam-617	12	5	�	�	PROPN
ejpam-617	12	6	gmail	gmail	NOUN
ejpam-617	12	7	.	.	PUNCT
ejpam-617	13	1	om	om	PROPN
ejpam-617	13	2	(	(	PUNCT
ejpam-617	13	3	s.	s.	PROPN
ejpam-617	13	4	bansal	bansal	PROPN
ejpam-617	13	5	)	)	PUNCT
ejpam-617	13	6	,	,	PUNCT
ejpam-617	13	7	jdziok�univ.rzeszow.pl	jdziok�univ.rzeszow.pl	PROPN
ejpam-617	13	8	(	(	PUNCT
ejpam-617	13	9	j.	j.	PROPN
ejpam-617	13	10	dziok),pranaygoswami83	dziok),pranaygoswami83	PROPN
ejpam-617	13	11	�	�	PROPN
ejpam-617	13	12	gmail	gmail	NOUN
ejpam-617	13	13	.	.	PUNCT
ejpam-617	14	1	om	om	PROPN
ejpam-617	14	2	(	(	PUNCT
ejpam-617	14	3	p.	p.	NOUN
ejpam-617	14	4	goswami	goswami	PROPN
ejpam-617	14	5	)	)	PUNCT
ejpam-617	14	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-617	15	1	633	633	NUM
ejpam-617	15	2	c	c	X
ejpam-617	15	3	©	©	PROPN
ejpam-617	15	4	2010	2010	NUM
ejpam-617	15	5	ejpam	ejpam	NOUN
ejpam-617	15	6	all	all	DET
ejpam-617	15	7	rights	right	NOUN
ejpam-617	15	8	reserved	reserve	VERB
ejpam-617	15	9	.	.	PUNCT
ejpam-617	16	1	s.	s.	PROPN
ejpam-617	16	2	bansal	bansal	PROPN
ejpam-617	16	3	,	,	PUNCT
ejpam-617	16	4	j.	j.	PROPN
ejpam-617	16	5	dziok	dziok	PROPN
ejpam-617	16	6	,	,	PUNCT
ejpam-617	16	7	p.	p.	NOUN
ejpam-617	16	8	goswami	goswami	PROPN
ejpam-617	16	9	/	/	SYM
ejpam-617	16	10	eur	eur	PROPN
ejpam-617	16	11	.	.	PUNCT
ejpam-617	17	1	j.	j.	PROPN
ejpam-617	17	2	pure	pure	PROPN
ejpam-617	17	3	appl	appl	PROPN
ejpam-617	17	4	.	.	PROPN
ejpam-617	17	5	math	math	PROPN
ejpam-617	17	6	,	,	PUNCT
ejpam-617	17	7	3	3	NUM
ejpam-617	17	8	(	(	PUNCT
ejpam-617	17	9	2010	2010	NUM
ejpam-617	17	10	)	)	PUNCT
ejpam-617	17	11	,	,	PUNCT
ejpam-617	17	12	633	633	NUM
ejpam-617	17	13	-	-	SYM
ejpam-617	17	14	640	640	NUM
ejpam-617	17	15	634	634	NUM
ejpam-617	17	16	such	such	ADJ
ejpam-617	17	17	that	that	SCONJ
ejpam-617	17	18	f	f	PROPN
ejpam-617	17	19	(	(	PUNCT
ejpam-617	17	20	z	z	NOUN
ejpam-617	17	21	)	)	PUNCT
ejpam-617	17	22	=	=	SYM
ejpam-617	17	23	f(w(z	f(w(z	PROPN
ejpam-617	17	24	)	)	PUNCT
ejpam-617	17	25	)	)	PUNCT
ejpam-617	18	1	(	(	PUNCT
ejpam-617	18	2	z	z	NOUN
ejpam-617	18	3	∈	∈	PROPN
ejpam-617	18	4	u	u	NOUN
ejpam-617	18	5	)	)	PUNCT
ejpam-617	18	6	.	.	PUNCT
ejpam-617	19	1	in	in	ADP
ejpam-617	19	2	particular	particular	ADJ
ejpam-617	19	3	,	,	PUNCT
ejpam-617	19	4	if	if	SCONJ
ejpam-617	19	5	the	the	DET
ejpam-617	19	6	function	function	NOUN
ejpam-617	19	7	f(z	f(z	PROPN
ejpam-617	19	8	)	)	PUNCT
ejpam-617	19	9	is	be	AUX
ejpam-617	19	10	univalent	univalent	ADJ
ejpam-617	19	11	in	in	ADP
ejpam-617	19	12	u	u	PROPN
ejpam-617	19	13	,	,	PUNCT
ejpam-617	19	14	then	then	ADV
ejpam-617	19	15	we	we	PRON
ejpam-617	19	16	have	have	VERB
ejpam-617	19	17	the	the	DET
ejpam-617	19	18	following	following	ADJ
ejpam-617	19	19	equivalence	equivalence	NOUN
ejpam-617	19	20	[	[	X
ejpam-617	19	21	cf	cf	NOUN
ejpam-617	19	22	.	.	PUNCT
ejpam-617	20	1	7	7	NUM
ejpam-617	20	2	]	]	SYM
ejpam-617	20	3	:	:	PUNCT
ejpam-617	20	4	f	f	X
ejpam-617	20	5	(	(	PUNCT
ejpam-617	20	6	z)≺	z)≺	PROPN
ejpam-617	20	7	f(z)(z	f(z)(z	X
ejpam-617	20	8	∈	∈	PROPN
ejpam-617	20	9	u	u	NOUN
ejpam-617	20	10	)	)	PUNCT
ejpam-617	20	11	⇐	⇐	ADJ
ejpam-617	20	12	⇒	⇒	PROPN
ejpam-617	20	13	f	f	X
ejpam-617	20	14	(	(	PUNCT
ejpam-617	20	15	0	0	NUM
ejpam-617	20	16	)	)	PUNCT
ejpam-617	20	17	=	=	SYM
ejpam-617	20	18	f(0	f(0	NOUN
ejpam-617	20	19	)	)	PUNCT
ejpam-617	20	20	and	and	CCONJ
ejpam-617	20	21	f	f	PROPN
ejpam-617	20	22	(	(	PUNCT
ejpam-617	20	23	u	u	NOUN
ejpam-617	20	24	)	)	PUNCT
ejpam-617	20	25	⊂	⊂	PROPN
ejpam-617	20	26	f(u	f(u	PROPN
ejpam-617	20	27	)	)	PUNCT
ejpam-617	20	28	.	.	PUNCT
ejpam-617	21	1	for	for	ADP
ejpam-617	21	2	functions	function	NOUN
ejpam-617	21	3	f	f	X
ejpam-617	21	4	(	(	PUNCT
ejpam-617	21	5	z	z	NOUN
ejpam-617	21	6	)	)	PUNCT
ejpam-617	21	7	∈	∈	PROPN
ejpam-617	21	8	σp	σp	NOUN
ejpam-617	21	9	given	give	VERB
ejpam-617	21	10	by	by	ADP
ejpam-617	21	11	(	(	PUNCT
ejpam-617	21	12	1	1	NUM
ejpam-617	21	13	)	)	PUNCT
ejpam-617	21	14	and	and	CCONJ
ejpam-617	21	15	g(z	g(z	PROPN
ejpam-617	21	16	)	)	PUNCT
ejpam-617	21	17	∈	∈	PROPN
ejpam-617	21	18	σp	σp	NOUN
ejpam-617	21	19	given	give	VERB
ejpam-617	21	20	by	by	ADP
ejpam-617	21	21	g(z	g(z	PROPN
ejpam-617	21	22	)	)	PUNCT
ejpam-617	22	1	=	=	PUNCT
ejpam-617	22	2	z−p	z−p	NOUN
ejpam-617	22	3	+	+	CCONJ
ejpam-617	23	1	∞	∞	NUM
ejpam-617	23	2	∑	∑	PUNCT
ejpam-617	23	3	k=1	k=1	PROPN
ejpam-617	23	4	bkzk−p	bkzk−p	NOUN
ejpam-617	23	5	,	,	PUNCT
ejpam-617	23	6	(	(	PUNCT
ejpam-617	23	7	2	2	X
ejpam-617	23	8	)	)	PUNCT
ejpam-617	23	9	the	the	DET
ejpam-617	23	10	hadamard	hadamard	ADJ
ejpam-617	23	11	product	product	NOUN
ejpam-617	23	12	(	(	PUNCT
ejpam-617	23	13	or	or	CCONJ
ejpam-617	23	14	convolution	convolution	NOUN
ejpam-617	23	15	)	)	PUNCT
ejpam-617	23	16	of	of	ADP
ejpam-617	23	17	f	f	PROPN
ejpam-617	23	18	and	and	CCONJ
ejpam-617	23	19	g	g	PROPN
ejpam-617	23	20	is	be	AUX
ejpam-617	23	21	defined	define	VERB
ejpam-617	23	22	by	by	ADP
ejpam-617	23	23	(	(	PUNCT
ejpam-617	23	24	f	f	PROPN
ejpam-617	23	25	∗	∗	PROPN
ejpam-617	23	26	g)(z	g)(z	PUNCT
ejpam-617	23	27	)	)	PUNCT
ejpam-617	23	28	:	:	PUNCT
ejpam-617	23	29	=	=	PUNCT
ejpam-617	23	30	z−p	z−p	PROPN
ejpam-617	23	31	+	+	CCONJ
ejpam-617	23	32	∞	∞	NUM
ejpam-617	23	33	∑	∑	PUNCT
ejpam-617	23	34	k=1	k=1	PROPN
ejpam-617	23	35	ak	ak	PROPN
ejpam-617	23	36	bkzk−p	bkzk−p	PROPN
ejpam-617	23	37	=	=	NOUN
ejpam-617	23	38	:	:	PUNCT
ejpam-617	23	39	(	(	PUNCT
ejpam-617	23	40	g	g	NOUN
ejpam-617	23	41	∗	∗	X
ejpam-617	23	42	f	f	PROPN
ejpam-617	23	43	)	)	PUNCT
ejpam-617	23	44	(	(	PUNCT
ejpam-617	23	45	z	z	NOUN
ejpam-617	23	46	)	)	PUNCT
ejpam-617	23	47	(	(	PUNCT
ejpam-617	23	48	p	p	NOUN
ejpam-617	23	49	∈	∈	PROPN
ejpam-617	23	50	n	n	CCONJ
ejpam-617	23	51	;	;	PUNCT
ejpam-617	23	52	z	z	PROPN
ejpam-617	23	53	∈	∈	PROPN
ejpam-617	23	54	d	d	NOUN
ejpam-617	23	55	)	)	PUNCT
ejpam-617	23	56	.	.	PUNCT
ejpam-617	24	1	(	(	PUNCT
ejpam-617	24	2	3	3	X
ejpam-617	24	3	)	)	PUNCT
ejpam-617	24	4	let	let	VERB
ejpam-617	24	5	l	l	NOUN
ejpam-617	24	6	,	,	PUNCT
ejpam-617	24	7	s	s	PROPN
ejpam-617	24	8	∈	∈	PROPN
ejpam-617	24	9	n.	n.	NOUN
ejpam-617	24	10	for	for	ADP
ejpam-617	24	11	positive	positive	ADJ
ejpam-617	24	12	real	real	ADJ
ejpam-617	24	13	parameters	parameter	NOUN
ejpam-617	24	14	α	α	PROPN
ejpam-617	24	15	j	j	PROPN
ejpam-617	24	16	,	,	PUNCT
ejpam-617	24	17	a	a	DET
ejpam-617	24	18	j	j	PROPN
ejpam-617	24	19	�	�	PROPN
ejpam-617	24	20	j	j	PROPN
ejpam-617	24	21	=	=	NOUN
ejpam-617	24	22	1	1	NUM
ejpam-617	24	23	,	,	PUNCT
ejpam-617	24	24	.	.	PUNCT
ejpam-617	24	25	.	.	PUNCT
ejpam-617	25	1	.	.	PUNCT
ejpam-617	26	1	,	,	PUNCT
ejpam-617	26	2	q	q	PROPN
ejpam-617	26	3	�	�	PROPN
ejpam-617	26	4	;	;	PUNCT
ejpam-617	26	5	β	β	X
ejpam-617	26	6	j	j	PROPN
ejpam-617	26	7	,	,	PUNCT
ejpam-617	26	8	b	b	PROPN
ejpam-617	26	9	j	j	PROPN
ejpam-617	26	10	>	>	SYM
ejpam-617	26	11	0	0	NUM
ejpam-617	26	12	�	�	PROPN
ejpam-617	26	13	j	j	PROPN
ejpam-617	26	14	=	=	NOUN
ejpam-617	26	15	1	1	NUM
ejpam-617	26	16	,	,	PUNCT
ejpam-617	26	17	.	.	PUNCT
ejpam-617	26	18	.	.	PUNCT
ejpam-617	26	19	.	.	PUNCT
ejpam-617	27	1	,	,	PUNCT
ejpam-617	27	2	s	s	PROPN
ejpam-617	27	3	�	�	PROPN
ejpam-617	27	4	,	,	PUNCT
ejpam-617	27	5	with	with	ADP
ejpam-617	27	6	1	1	NUM
ejpam-617	27	7	+	+	SYM
ejpam-617	27	8	s	s	NOUN
ejpam-617	27	9	∑	∑	PROPN
ejpam-617	27	10	j=1	j=1	PROPN
ejpam-617	27	11	b	b	PROPN
ejpam-617	27	12	j	j	PROPN
ejpam-617	27	13	−	−	PROPN
ejpam-617	27	14	q	q	NOUN
ejpam-617	28	1	∑	∑	PUNCT
ejpam-617	28	2	j=1	j=1	PROPN
ejpam-617	28	3	a	a	DET
ejpam-617	28	4	j	j	PROPN
ejpam-617	28	5	≥	≥	NUM
ejpam-617	28	6	0	0	NUM
ejpam-617	28	7	,	,	PUNCT
ejpam-617	28	8	the	the	DET
ejpam-617	28	9	fox	fox	PROPN
ejpam-617	28	10	-	-	PUNCT
ejpam-617	28	11	wright	wright	PROPN
ejpam-617	28	12	function	function	PROPN
ejpam-617	28	13	lψs	lψs	NOUN
ejpam-617	28	14	is	be	AUX
ejpam-617	28	15	defined	define	VERB
ejpam-617	28	16	by	by	ADP
ejpam-617	28	17	[	[	PUNCT
ejpam-617	28	18	see	see	VERB
ejpam-617	28	19	8	8	NUM
ejpam-617	28	20	]	]	SYM
ejpam-617	28	21	lψs[(α	lψs[(α	PROPN
ejpam-617	28	22	j	j	PROPN
ejpam-617	28	23	,	,	PUNCT
ejpam-617	28	24	a	a	DET
ejpam-617	28	25	j)1,l	j)1,l	NOUN
ejpam-617	28	26	;	;	PUNCT
ejpam-617	28	27	(	(	PUNCT
ejpam-617	28	28	β	β	X
ejpam-617	28	29	j	j	PROPN
ejpam-617	28	30	,	,	PUNCT
ejpam-617	28	31	b	b	PROPN
ejpam-617	28	32	j)1,s	j)1,s	PROPN
ejpam-617	28	33	;	;	PUNCT
ejpam-617	29	1	z	z	X
ejpam-617	29	2	]	]	X
ejpam-617	29	3	=	=	SYM
ejpam-617	29	4	∞	∞	NUM
ejpam-617	29	5	∑	∑	PUNCT
ejpam-617	29	6	n=1	n=1	PROPN
ejpam-617	29	7	πl	πl	PROPN
ejpam-617	29	8	j=1	j=1	PROPN
ejpam-617	29	9	γ(α	γ(α	PROPN
ejpam-617	29	10	j	j	PROPN
ejpam-617	29	11	+	+	CCONJ
ejpam-617	29	12	na	na	NOUN
ejpam-617	29	13	j)z	j)z	NOUN
ejpam-617	30	1	n	n	CCONJ
ejpam-617	30	2	πs	πs	ADV
ejpam-617	30	3	j=1	j=1	PROPN
ejpam-617	30	4	γ(β	γ(β	PROPN
ejpam-617	30	5	j	j	PROPN
ejpam-617	31	1	+	+	CCONJ
ejpam-617	31	2	nb	nb	PROPN
ejpam-617	31	3	j)n	j)n	PROPN
ejpam-617	31	4	!	!	PUNCT
ejpam-617	32	1	(	(	PUNCT
ejpam-617	32	2	z	z	NOUN
ejpam-617	32	3	∈	∈	PROPN
ejpam-617	32	4	u	u	NOUN
ejpam-617	32	5	)	)	PUNCT
ejpam-617	32	6	.	.	PUNCT
ejpam-617	33	1	(	(	PUNCT
ejpam-617	33	2	4	4	X
ejpam-617	33	3	)	)	PUNCT
ejpam-617	33	4	in	in	ADP
ejpam-617	33	5	particular	particular	ADJ
ejpam-617	33	6	,	,	PUNCT
ejpam-617	33	7	when	when	SCONJ
ejpam-617	33	8	ai	ai	VERB
ejpam-617	33	9	=	=	SYM
ejpam-617	33	10	b	b	PROPN
ejpam-617	33	11	j	j	PROPN
ejpam-617	33	12	=	=	SYM
ejpam-617	33	13	1	1	NUM
ejpam-617	33	14	�	�	NOUN
ejpam-617	33	15	i	i	NOUN
ejpam-617	33	16	=	=	NOUN
ejpam-617	33	17	1	1	NUM
ejpam-617	33	18	,	,	PUNCT
ejpam-617	33	19	...	...	PUNCT
ejpam-617	33	20	,	,	PUNCT
ejpam-617	33	21	l	l	NOUN
ejpam-617	33	22	;	;	PUNCT
ejpam-617	33	23	j	j	PROPN
ejpam-617	33	24	=	=	SYM
ejpam-617	33	25	1	1	NUM
ejpam-617	33	26	,	,	PUNCT
ejpam-617	33	27	...	...	PUNCT
ejpam-617	33	28	,	,	PUNCT
ejpam-617	33	29	s	s	PROPN
ejpam-617	33	30	�	�	PROPN
ejpam-617	33	31	,	,	PUNCT
ejpam-617	33	32	we	we	PRON
ejpam-617	33	33	have	have	VERB
ejpam-617	33	34	the	the	DET
ejpam-617	33	35	following	follow	VERB
ejpam-617	33	36	relationship	relationship	NOUN
ejpam-617	33	37	:	:	PUNCT
ejpam-617	33	38	l	l	NOUN
ejpam-617	33	39	fs(α1	fs(α1	NOUN
ejpam-617	33	40	,	,	PUNCT
ejpam-617	33	41	...	...	PUNCT
ejpam-617	33	42	,	,	PUNCT
ejpam-617	33	43	αl	αl	ADP
ejpam-617	33	44	;	;	PUNCT
ejpam-617	33	45	β1	β1	PROPN
ejpam-617	33	46	,	,	PUNCT
ejpam-617	33	47	..	..	PUNCT
ejpam-617	33	48	,	,	PUNCT
ejpam-617	33	49	βs	βs	CCONJ
ejpam-617	33	50	;	;	PUNCT
ejpam-617	33	51	z	z	X
ejpam-617	33	52	)	)	PUNCT
ejpam-617	33	53	=	=	SYM
ejpam-617	33	54	ω	ω	NUM
ejpam-617	33	55	lψs[(α1	lψs[(α1	NOUN
ejpam-617	33	56	,	,	PUNCT
ejpam-617	33	57	1)1,l	1)1,l	NUM
ejpam-617	33	58	;	;	PUNCT
ejpam-617	33	59	(	(	PUNCT
ejpam-617	33	60	β	β	X
ejpam-617	33	61	j	j	PROPN
ejpam-617	33	62	,	,	PUNCT
ejpam-617	33	63	1)1,s	1)1,s	NUM
ejpam-617	33	64	;	;	PUNCT
ejpam-617	33	65	z	z	NOUN
ejpam-617	33	66	]	]	X
ejpam-617	33	67	(	(	PUNCT
ejpam-617	33	68	l	l	NOUN
ejpam-617	33	69	≤	≤	NUM
ejpam-617	33	70	s+	s+	PUNCT
ejpam-617	33	71	1	1	NUM
ejpam-617	33	72	;	;	PUNCT
ejpam-617	33	73	z	z	PROPN
ejpam-617	33	74	∈	∈	PROPN
ejpam-617	33	75	u	u	PROPN
ejpam-617	33	76	)	)	PUNCT
ejpam-617	33	77	(	(	PUNCT
ejpam-617	33	78	5	5	X
ejpam-617	33	79	)	)	PUNCT
ejpam-617	33	80	where	where	SCONJ
ejpam-617	33	81	ω	ω	X
ejpam-617	33	82	:	:	PUNCT
ejpam-617	33	83	=	=	SYM
ejpam-617	33	84	γ(β1)	γ(β1)	NOUN
ejpam-617	33	85	...	...	PUNCT
ejpam-617	33	86	γ(βs	γ(β	NOUN
ejpam-617	33	87	)	)	PUNCT
ejpam-617	33	88	γ(α1)	γ(α1)	NOUN
ejpam-617	33	89	...	...	PUNCT
ejpam-617	33	90	(αl	(αl	PUNCT
ejpam-617	33	91	)	)	PUNCT
ejpam-617	33	92	.	.	PUNCT
ejpam-617	34	1	(	(	PUNCT
ejpam-617	34	2	6	6	X
ejpam-617	34	3	)	)	PUNCT
ejpam-617	34	4	let	let	VERB
ejpam-617	34	5	φp[(α	φp[(α	PROPN
ejpam-617	34	6	j	j	PROPN
ejpam-617	34	7	,	,	PUNCT
ejpam-617	34	8	a	a	DET
ejpam-617	34	9	j)1,l	j)1,l	NOUN
ejpam-617	34	10	;	;	PUNCT
ejpam-617	34	11	(	(	PUNCT
ejpam-617	34	12	β	β	X
ejpam-617	34	13	j	j	PROPN
ejpam-617	34	14	,	,	PUNCT
ejpam-617	34	15	b	b	PROPN
ejpam-617	34	16	j)1,s	j)1,s	PROPN
ejpam-617	34	17	;	;	PUNCT
ejpam-617	34	18	z	z	NOUN
ejpam-617	34	19	]	]	X
ejpam-617	34	20	=	=	PUNCT
ejpam-617	34	21	ωz−p	ωz−p	PROPN
ejpam-617	34	22	lψs[(α	lψs[(α	PROPN
ejpam-617	34	23	j	j	PROPN
ejpam-617	34	24	,	,	PUNCT
ejpam-617	34	25	a	a	DET
ejpam-617	34	26	j)1,l	j)1,l	NOUN
ejpam-617	34	27	;	;	PUNCT
ejpam-617	34	28	(	(	PUNCT
ejpam-617	34	29	β	β	X
ejpam-617	34	30	j	j	PROPN
ejpam-617	34	31	,	,	PUNCT
ejpam-617	34	32	b	b	PROPN
ejpam-617	34	33	j)1,s	j)1,s	PROPN
ejpam-617	34	34	;	;	PUNCT
ejpam-617	34	35	z	z	NOUN
ejpam-617	34	36	]	]	X
ejpam-617	34	37	(	(	PUNCT
ejpam-617	34	38	z	z	NOUN
ejpam-617	34	39	∈	∈	PROPN
ejpam-617	34	40	d	d	NOUN
ejpam-617	34	41	)	)	PUNCT
ejpam-617	34	42	.	.	PUNCT
ejpam-617	35	1	(	(	PUNCT
ejpam-617	35	2	7	7	X
ejpam-617	35	3	)	)	PUNCT
ejpam-617	35	4	due	due	ADP
ejpam-617	35	5	to	to	ADP
ejpam-617	35	6	dziok	dziok	NOUN
ejpam-617	35	7	and	and	CCONJ
ejpam-617	35	8	raina	raina	VERB
ejpam-617	35	9	[	[	X
ejpam-617	35	10	2	2	NUM
ejpam-617	35	11	]	]	PUNCT
ejpam-617	35	12	(	(	PUNCT
ejpam-617	35	13	see	see	VERB
ejpam-617	35	14	also	also	ADV
ejpam-617	35	15	[	[	X
ejpam-617	35	16	1	1	X
ejpam-617	35	17	]	]	PUNCT
ejpam-617	35	18	and	and	CCONJ
ejpam-617	36	1	[	[	X
ejpam-617	36	2	3	3	NUM
ejpam-617	36	3	]	]	PUNCT
ejpam-617	36	4	)	)	PUNCT
ejpam-617	36	5	we	we	PRON
ejpam-617	36	6	consider	consider	VERB
ejpam-617	36	7	a	a	DET
ejpam-617	36	8	linear	linear	ADJ
ejpam-617	36	9	operator	operator	NOUN
ejpam-617	36	10	θ	θ	PROPN
ejpam-617	36	11	l	l	NOUN
ejpam-617	36	12	,	,	PUNCT
ejpam-617	36	13	s	s	PROPN
ejpam-617	36	14	p	p	ADJ
ejpam-617	36	15	�	�	PROPN
ejpam-617	36	16	�	�	PROPN
ejpam-617	36	17	α1,a1	α1,a1	PROPN
ejpam-617	36	18	�	�	PROPN
ejpam-617	36	19	f	f	PROPN
ejpam-617	36	20	(	(	PUNCT
ejpam-617	36	21	z	z	NOUN
ejpam-617	36	22	)	)	PUNCT
ejpam-617	36	23	=	=	SYM
ejpam-617	36	24	θp[(α1,a1	θp[(α1,a1	NOUN
ejpam-617	36	25	)	)	PUNCT
ejpam-617	36	26	,	,	PUNCT
ejpam-617	36	27	...	...	PUNCT
ejpam-617	36	28	,	,	PUNCT
ejpam-617	36	29	(	(	PUNCT
ejpam-617	36	30	αl	αl	ADP
ejpam-617	36	31	,	,	PUNCT
ejpam-617	36	32	al	al	PROPN
ejpam-617	36	33	)	)	PUNCT
ejpam-617	36	34	;	;	PUNCT
ejpam-617	36	35	(	(	PUNCT
ejpam-617	36	36	β1	β1	NOUN
ejpam-617	36	37	,	,	PUNCT
ejpam-617	36	38	b1	b1	NOUN
ejpam-617	36	39	)	)	PUNCT
ejpam-617	36	40	,	,	PUNCT
ejpam-617	36	41	...	...	PUNCT
ejpam-617	36	42	,	,	PUNCT
ejpam-617	36	43	(	(	PUNCT
ejpam-617	36	44	βs	βs	X
ejpam-617	36	45	,	,	PUNCT
ejpam-617	36	46	bs	bs	NOUN
ejpam-617	36	47	)	)	PUNCT
ejpam-617	36	48	]	]	PUNCT
ejpam-617	36	49	:	:	PUNCT
ejpam-617	36	50	σp	σp	PART
ejpam-617	36	51	−→	−→	ADJ
ejpam-617	36	52	σp	σp	NOUN
ejpam-617	36	53	defined	define	VERB
ejpam-617	36	54	by	by	ADP
ejpam-617	36	55	the	the	DET
ejpam-617	36	56	following	follow	VERB
ejpam-617	36	57	hadmard	hadmard	ADJ
ejpam-617	36	58	product	product	NOUN
ejpam-617	36	59	θ	θ	PROPN
ejpam-617	36	60	l	l	NOUN
ejpam-617	36	61	,	,	PUNCT
ejpam-617	36	62	s	s	PROPN
ejpam-617	37	1	p	p	ADJ
ejpam-617	37	2	�	�	PROPN
ejpam-617	37	3	�	�	PROPN
ejpam-617	37	4	α1,a1	α1,a1	PROPN
ejpam-617	37	5	�	�	PROPN
ejpam-617	37	6	f	f	PROPN
ejpam-617	37	7	(	(	PUNCT
ejpam-617	37	8	z	z	NOUN
ejpam-617	37	9	)	)	PUNCT
ejpam-617	37	10	:	:	PUNCT
ejpam-617	38	1	=	=	SYM
ejpam-617	38	2	φp[(α	φp[(α	PROPN
ejpam-617	38	3	j	j	PROPN
ejpam-617	38	4	,	,	PUNCT
ejpam-617	38	5	a	a	DET
ejpam-617	38	6	j)1,l	j)1,l	NOUN
ejpam-617	38	7	;	;	PUNCT
ejpam-617	38	8	(	(	PUNCT
ejpam-617	38	9	b	b	X
ejpam-617	38	10	j	j	PROPN
ejpam-617	38	11	,	,	PUNCT
ejpam-617	38	12	β	β	X
ejpam-617	38	13	j)1,s	j)1,s	NUM
ejpam-617	38	14	;	;	PUNCT
ejpam-617	38	15	z	z	X
ejpam-617	38	16	]	]	X
ejpam-617	38	17	∗	∗	X
ejpam-617	38	18	f	f	PROPN
ejpam-617	38	19	(	(	PUNCT
ejpam-617	38	20	z	z	NOUN
ejpam-617	38	21	)	)	PUNCT
ejpam-617	38	22	.	.	PUNCT
ejpam-617	39	1	(	(	PUNCT
ejpam-617	39	2	8)	8)	NUM
ejpam-617	39	3	s.	s.	PROPN
ejpam-617	39	4	bansal	bansal	PROPN
ejpam-617	39	5	,	,	PUNCT
ejpam-617	39	6	j.	j.	PROPN
ejpam-617	39	7	dziok	dziok	PROPN
ejpam-617	39	8	,	,	PUNCT
ejpam-617	39	9	p.	p.	NOUN
ejpam-617	39	10	goswami	goswami	PROPN
ejpam-617	39	11	/	/	SYM
ejpam-617	39	12	eur	eur	PROPN
ejpam-617	39	13	.	.	PUNCT
ejpam-617	40	1	j.	j.	PROPN
ejpam-617	40	2	pure	pure	PROPN
ejpam-617	40	3	appl	appl	PROPN
ejpam-617	40	4	.	.	PROPN
ejpam-617	40	5	math	math	PROPN
ejpam-617	40	6	,	,	PUNCT
ejpam-617	40	7	3	3	NUM
ejpam-617	40	8	(	(	PUNCT
ejpam-617	40	9	2010	2010	NUM
ejpam-617	40	10	)	)	PUNCT
ejpam-617	40	11	,	,	PUNCT
ejpam-617	40	12	633	633	NUM
ejpam-617	40	13	-	-	SYM
ejpam-617	40	14	640	640	NUM
ejpam-617	40	15	635	635	NUM
ejpam-617	40	16	if	if	SCONJ
ejpam-617	40	17	f	f	PROPN
ejpam-617	40	18	∈	∈	PROPN
ejpam-617	40	19	σp	σp	PROPN
ejpam-617	40	20	is	be	AUX
ejpam-617	40	21	given	give	VERB
ejpam-617	40	22	by	by	ADP
ejpam-617	40	23	the	the	DET
ejpam-617	40	24	equation	equation	NOUN
ejpam-617	40	25	(	(	PUNCT
ejpam-617	40	26	1	1	NUM
ejpam-617	40	27	)	)	PUNCT
ejpam-617	40	28	,	,	PUNCT
ejpam-617	40	29	then	then	ADV
ejpam-617	40	30	we	we	PRON
ejpam-617	40	31	have	have	VERB
ejpam-617	40	32	θ	θ	PROPN
ejpam-617	40	33	l	l	NOUN
ejpam-617	40	34	,	,	PUNCT
ejpam-617	40	35	s	s	PROPN
ejpam-617	40	36	p	p	ADJ
ejpam-617	40	37	�	�	PROPN
ejpam-617	40	38	�	�	PROPN
ejpam-617	40	39	α1,a1	α1,a1	PROPN
ejpam-617	40	40	�	�	PROPN
ejpam-617	40	41	f	f	PROPN
ejpam-617	40	42	(	(	PUNCT
ejpam-617	40	43	z	z	NOUN
ejpam-617	40	44	)	)	PUNCT
ejpam-617	40	45	=	=	PUNCT
ejpam-617	41	1	z−p	z−p	NOUN
ejpam-617	41	2	+	+	PROPN
ejpam-617	41	3	ω	ω	NOUN
ejpam-617	41	4	∞	∞	NUM
ejpam-617	41	5	∑	∑	PUNCT
ejpam-617	41	6	n=1	n=1	PROPN
ejpam-617	41	7	πl	πl	PROPN
ejpam-617	42	1	j=1γ(α	j=1γ(α	PROPN
ejpam-617	42	2	j	j	PROPN
ejpam-617	42	3	+	+	CCONJ
ejpam-617	42	4	na	na	PART
ejpam-617	42	5	j)z	j)z	NOUN
ejpam-617	42	6	n−p	n−p	PROPN
ejpam-617	42	7	πs	πs	ADP
ejpam-617	42	8	j=1	j=1	PROPN
ejpam-617	42	9	γ(β	γ(β	PROPN
ejpam-617	42	10	j	j	PROPN
ejpam-617	43	1	+	+	CCONJ
ejpam-617	43	2	nb	nb	PROPN
ejpam-617	43	3	j)n	j)n	PROPN
ejpam-617	43	4	!	!	PUNCT
ejpam-617	44	1	an	an	DET
ejpam-617	44	2	(	(	PUNCT
ejpam-617	44	3	z	z	NOUN
ejpam-617	44	4	∈	∈	PROPN
ejpam-617	44	5	d	d	NOUN
ejpam-617	44	6	)	)	PUNCT
ejpam-617	44	7	.	.	PUNCT
ejpam-617	45	1	(	(	PUNCT
ejpam-617	45	2	9	9	X
ejpam-617	45	3	)	)	PUNCT
ejpam-617	45	4	in	in	ADP
ejpam-617	45	5	particular	particular	ADJ
ejpam-617	45	6	,	,	PUNCT
ejpam-617	45	7	for	for	ADP
ejpam-617	45	8	ai	ai	PROPN
ejpam-617	45	9	=	=	SYM
ejpam-617	45	10	b	b	PROPN
ejpam-617	45	11	j	j	PROPN
ejpam-617	45	12	=	=	SYM
ejpam-617	45	13	1(i	1(i	NUM
ejpam-617	45	14	=	=	SYM
ejpam-617	45	15	1	1	NUM
ejpam-617	45	16	,	,	PUNCT
ejpam-617	45	17	...	...	PUNCT
ejpam-617	45	18	,	,	PUNCT
ejpam-617	45	19	l	l	NOUN
ejpam-617	45	20	,	,	PUNCT
ejpam-617	45	21	j	j	PROPN
ejpam-617	45	22	=	=	SYM
ejpam-617	45	23	1	1	NUM
ejpam-617	45	24	,	,	PUNCT
ejpam-617	45	25	...	...	PUNCT
ejpam-617	45	26	,	,	PUNCT
ejpam-617	45	27	s	s	X
ejpam-617	45	28	)	)	PUNCT
ejpam-617	45	29	,	,	PUNCT
ejpam-617	45	30	we	we	PRON
ejpam-617	45	31	get	get	VERB
ejpam-617	45	32	the	the	DET
ejpam-617	45	33	linear	linear	ADJ
ejpam-617	45	34	operator	operator	NOUN
ejpam-617	45	35	hp[α1	hp[α1	PROPN
ejpam-617	45	36	]	]	X
ejpam-617	45	37	f	f	X
ejpam-617	45	38	(	(	PUNCT
ejpam-617	45	39	z	z	NOUN
ejpam-617	45	40	)	)	PUNCT
ejpam-617	45	41	=	=	PUNCT
ejpam-617	45	42	z−p	z−p	NOUN
ejpam-617	45	43	+	+	CCONJ
ejpam-617	46	1	∞	∞	NUM
ejpam-617	46	2	∑	∑	PUNCT
ejpam-617	46	3	n=1	n=1	PROPN
ejpam-617	46	4	πl	πl	ADP
ejpam-617	46	5	j=1	j=1	PROPN
ejpam-617	46	6	(	(	PUNCT
ejpam-617	46	7	α	α	NOUN
ejpam-617	46	8	j)n	j)n	NOUN
ejpam-617	46	9	πs	πs	ADP
ejpam-617	46	10	j=1	j=1	NOUN
ejpam-617	46	11	(	(	PUNCT
ejpam-617	46	12	β	β	X
ejpam-617	46	13	j)nn	j)nn	PROPN
ejpam-617	46	14	!	!	PROPN
ejpam-617	47	1	anzn−p	anzn−p	PROPN
ejpam-617	47	2	(	(	PUNCT
ejpam-617	47	3	z	z	NOUN
ejpam-617	47	4	∈	∈	PROPN
ejpam-617	47	5	u	u	NOUN
ejpam-617	47	6	)	)	PUNCT
ejpam-617	47	7	,	,	PUNCT
ejpam-617	47	8	(	(	PUNCT
ejpam-617	47	9	10	10	NUM
ejpam-617	47	10	)	)	PUNCT
ejpam-617	47	11	studied	study	VERB
ejpam-617	47	12	by	by	ADP
ejpam-617	47	13	liu	liu	PROPN
ejpam-617	47	14	and	and	CCONJ
ejpam-617	47	15	srivastava	srivastava	PROPN
ejpam-617	48	1	[	[	X
ejpam-617	48	2	6	6	NUM
ejpam-617	48	3	]	]	PUNCT
ejpam-617	48	4	.	.	PUNCT
ejpam-617	49	1	obviously	obviously	ADV
ejpam-617	49	2	,	,	PUNCT
ejpam-617	49	3	for	for	ADP
ejpam-617	49	4	l	l	NOUN
ejpam-617	49	5	=	=	SYM
ejpam-617	49	6	2	2	NUM
ejpam-617	49	7	,	,	PUNCT
ejpam-617	49	8	s	s	VERB
ejpam-617	49	9	=	=	NOUN
ejpam-617	49	10	p	p	NOUN
ejpam-617	49	11	=	=	SYM
ejpam-617	49	12	1	1	NUM
ejpam-617	49	13	and	and	CCONJ
ejpam-617	49	14	α2	α2	ADJ
ejpam-617	49	15	=	=	SYM
ejpam-617	50	1	1	1	NUM
ejpam-617	50	2	,	,	PUNCT
ejpam-617	50	3	we	we	PRON
ejpam-617	50	4	get	get	VERB
ejpam-617	50	5	l	l	NOUN
ejpam-617	50	6	(	(	PUNCT
ejpam-617	50	7	α1,β1	α1,β1	PROPN
ejpam-617	50	8	)	)	PUNCT
ejpam-617	50	9	f	f	NOUN
ejpam-617	50	10	(	(	PUNCT
ejpam-617	50	11	z	z	NOUN
ejpam-617	50	12	)	)	PUNCT
ejpam-617	51	1	=	=	SYM
ejpam-617	51	2	z−1	z−1	PROPN
ejpam-617	51	3	+	+	CCONJ
ejpam-617	51	4	∞	∞	NUM
ejpam-617	51	5	∑	∑	PUNCT
ejpam-617	51	6	n=1	n=1	PROPN
ejpam-617	51	7	(	(	PUNCT
ejpam-617	51	8	α1)n	α1)n	NOUN
ejpam-617	51	9	(	(	PUNCT
ejpam-617	51	10	β1)n	β1)n	NOUN
ejpam-617	51	11	anzn−1	anzn−1	PROPN
ejpam-617	51	12	(	(	PUNCT
ejpam-617	51	13	z	z	NOUN
ejpam-617	51	14	∈	∈	PROPN
ejpam-617	51	15	u	u	NOUN
ejpam-617	51	16	)	)	PUNCT
ejpam-617	51	17	.	.	PUNCT
ejpam-617	52	1	it	it	PRON
ejpam-617	52	2	is	be	AUX
ejpam-617	52	3	easy	easy	ADJ
ejpam-617	52	4	to	to	PART
ejpam-617	52	5	verify	verify	VERB
ejpam-617	52	6	that	that	SCONJ
ejpam-617	53	1	z	z	NOUN
ejpam-617	53	2	h	h	NOUN
ejpam-617	53	3	θ	θ	X
ejpam-617	53	4	l	l	NOUN
ejpam-617	53	5	,	,	PUNCT
ejpam-617	53	6	s	s	AUX
ejpam-617	53	7	p	p	ADJ
ejpam-617	53	8	�	�	PROPN
ejpam-617	53	9	�	�	PROPN
ejpam-617	53	10	α1,a1	α1,a1	PROPN
ejpam-617	53	11	�	�	PROPN
ejpam-617	53	12	f	f	PROPN
ejpam-617	53	13	(	(	PUNCT
ejpam-617	53	14	z	z	NOUN
ejpam-617	53	15	)	)	PUNCT
ejpam-617	53	16	i′	i′	NOUN
ejpam-617	53	17	=	=	SYM
ejpam-617	53	18	α1	α1	PROPN
ejpam-617	53	19	a1	a1	NOUN
ejpam-617	53	20	θ	θ	PROPN
ejpam-617	53	21	l	l	NOUN
ejpam-617	53	22	,	,	PUNCT
ejpam-617	53	23	s	s	PROPN
ejpam-617	53	24	p	p	X
ejpam-617	53	25	�	�	PROPN
ejpam-617	53	26	(	(	PUNCT
ejpam-617	53	27	α1	α1	PROPN
ejpam-617	53	28	+	+	CCONJ
ejpam-617	53	29	1,a1	1,a1	NUM
ejpam-617	53	30	)	)	PUNCT
ejpam-617	53	31	f	f	NOUN
ejpam-617	53	32	(	(	PUNCT
ejpam-617	53	33	z)−	z)−	PROPN
ejpam-617	53	34	�	�	PROPN
ejpam-617	53	35	α1	α1	PROPN
ejpam-617	53	36	a1	a1	NOUN
ejpam-617	53	37	+	+	CCONJ
ejpam-617	53	38	p	p	X
ejpam-617	53	39	�	�	PROPN
ejpam-617	53	40	θ	θ	PROPN
ejpam-617	53	41	l	l	NOUN
ejpam-617	53	42	,	,	PUNCT
ejpam-617	53	43	s	s	PROPN
ejpam-617	53	44	p	p	ADJ
ejpam-617	53	45	�	�	PROPN
ejpam-617	53	46	�	�	PROPN
ejpam-617	53	47	α1,a1	α1,a1	PROPN
ejpam-617	53	48	�	�	PROPN
ejpam-617	53	49	f	f	PROPN
ejpam-617	53	50	(	(	PUNCT
ejpam-617	53	51	z	z	NOUN
ejpam-617	53	52	)	)	PUNCT
ejpam-617	53	53	(	(	PUNCT
ejpam-617	53	54	11	11	NUM
ejpam-617	53	55	)	)	PUNCT
ejpam-617	53	56	also	also	ADV
ejpam-617	53	57	,	,	PUNCT
ejpam-617	53	58	for	for	ADP
ejpam-617	53	59	−1≤	−1≤	ADJ
ejpam-617	53	60	b	b	NOUN
ejpam-617	53	61	<	<	X
ejpam-617	53	62	a≤	a≤	ADP
ejpam-617	53	63	1	1	NUM
ejpam-617	53	64	we	we	PRON
ejpam-617	53	65	denote	denote	VERB
ejpam-617	53	66	by	by	ADP
ejpam-617	53	67	v	v	NOUN
ejpam-617	53	68	(	(	PUNCT
ejpam-617	53	69	(	(	PUNCT
ejpam-617	53	70	α1,a1	α1,a1	PROPN
ejpam-617	53	71	)	)	PUNCT
ejpam-617	53	72	;	;	PUNCT
ejpam-617	54	1	a	a	DET
ejpam-617	54	2	,	,	PUNCT
ejpam-617	54	3	b	b	NOUN
ejpam-617	54	4	)	)	PUNCT
ejpam-617	54	5	=	=	NOUN
ejpam-617	54	6	v	v	NOUN
ejpam-617	54	7	(	(	PUNCT
ejpam-617	54	8	(	(	PUNCT
ejpam-617	54	9	α1,a1	α1,a1	PROPN
ejpam-617	54	10	)	)	PUNCT
ejpam-617	54	11	,	,	PUNCT
ejpam-617	54	12	...	...	PUNCT
ejpam-617	54	13	,	,	PUNCT
ejpam-617	54	14	(	(	PUNCT
ejpam-617	54	15	αl	αl	ADP
ejpam-617	54	16	,	,	PUNCT
ejpam-617	54	17	al	al	PROPN
ejpam-617	54	18	)	)	PUNCT
ejpam-617	54	19	;	;	PUNCT
ejpam-617	54	20	a	a	DET
ejpam-617	54	21	,	,	PUNCT
ejpam-617	54	22	b	b	NOUN
ejpam-617	54	23	)	)	PUNCT
ejpam-617	54	24	the	the	DET
ejpam-617	54	25	class	class	NOUN
ejpam-617	54	26	of	of	ADP
ejpam-617	54	27	functions	function	NOUN
ejpam-617	54	28	f	f	PROPN
ejpam-617	54	29	∈	∈	PROPN
ejpam-617	54	30	σp	σp	NOUN
ejpam-617	54	31	which	which	PRON
ejpam-617	54	32	satisfy	satisfy	VERB
ejpam-617	54	33	the	the	DET
ejpam-617	54	34	following	follow	VERB
ejpam-617	54	35	condition	condition	NOUN
ejpam-617	54	36	:	:	PUNCT
ejpam-617	54	37	�	�	PROPN
ejpam-617	54	38	α1	α1	PROPN
ejpam-617	54	39	a1	a1	NOUN
ejpam-617	54	40	+	+	CCONJ
ejpam-617	54	41	p	p	PROPN
ejpam-617	54	42	�	�	PROPN
ejpam-617	54	43	−	−	PROPN
ejpam-617	54	44	�	�	PROPN
ejpam-617	54	45	α1	α1	PROPN
ejpam-617	54	46	a1	a1	NOUN
ejpam-617	54	47	�	�	PROPN
ejpam-617	54	48	θ	θ	PROPN
ejpam-617	54	49	l	l	NOUN
ejpam-617	54	50	,	,	PUNCT
ejpam-617	54	51	s	s	PROPN
ejpam-617	54	52	p	p	ADJ
ejpam-617	54	53	�	�	PROPN
ejpam-617	54	54	α1	α1	PROPN
ejpam-617	54	55	+	+	CCONJ
ejpam-617	54	56	1,a1	1,a1	NUM
ejpam-617	54	57	�	�	PROPN
ejpam-617	54	58	f	f	PROPN
ejpam-617	54	59	(	(	PUNCT
ejpam-617	54	60	z	z	NOUN
ejpam-617	54	61	)	)	PUNCT
ejpam-617	54	62	θ	θ	PROPN
ejpam-617	54	63	l	l	NOUN
ejpam-617	54	64	,	,	PUNCT
ejpam-617	54	65	s	s	PROPN
ejpam-617	54	66	p	p	X
ejpam-617	54	67	�	�	PROPN
ejpam-617	54	68	α1,a1	α1,a1	PROPN
ejpam-617	54	69	�	�	PROPN
ejpam-617	54	70	f	f	PROPN
ejpam-617	54	71	(	(	PUNCT
ejpam-617	54	72	z	z	NOUN
ejpam-617	54	73	)	)	PUNCT
ejpam-617	54	74	≺	≺	NOUN
ejpam-617	54	75	p	p	X
ejpam-617	54	76	1	1	NUM
ejpam-617	54	77	+	+	NUM
ejpam-617	54	78	az	az	PROPN
ejpam-617	54	79	1	1	NUM
ejpam-617	54	80	+	+	CCONJ
ejpam-617	54	81	bz	bz	PROPN
ejpam-617	54	82	.	.	PUNCT
ejpam-617	55	1	(	(	PUNCT
ejpam-617	55	2	12	12	NUM
ejpam-617	55	3	)	)	PUNCT
ejpam-617	55	4	let	let	VERB
ejpam-617	55	5	h	h	NOUN
ejpam-617	55	6	and	and	CCONJ
ejpam-617	55	7	q	q	AUX
ejpam-617	55	8	be	be	AUX
ejpam-617	55	9	analytic	analytic	ADJ
ejpam-617	55	10	functions	function	NOUN
ejpam-617	55	11	in	in	ADP
ejpam-617	55	12	u	u	NOUN
ejpam-617	55	13	with	with	ADP
ejpam-617	55	14	h(0	h(0	PROPN
ejpam-617	55	15	)	)	PUNCT
ejpam-617	56	1	=	=	SYM
ejpam-617	56	2	q(0	q(0	NOUN
ejpam-617	56	3	)	)	PUNCT
ejpam-617	57	1	=	=	SYM
ejpam-617	57	2	p	p	NOUN
ejpam-617	57	3	and	and	CCONJ
ejpam-617	57	4	let	let	VERB
ejpam-617	57	5	q	q	PUNCT
ejpam-617	57	6	be	be	AUX
ejpam-617	57	7	univalent	univalent	ADJ
ejpam-617	57	8	convex	convex	NOUN
ejpam-617	57	9	function	function	NOUN
ejpam-617	57	10	.	.	PUNCT
ejpam-617	58	1	the	the	DET
ejpam-617	58	2	first	first	ADJ
ejpam-617	58	3	-	-	PUNCT
ejpam-617	58	4	order	order	NOUN
ejpam-617	58	5	differential	differential	ADJ
ejpam-617	58	6	subordination	subordination	NOUN
ejpam-617	58	7	h(z	h(z	NOUN
ejpam-617	58	8	)	)	PUNCT
ejpam-617	58	9	+	+	CCONJ
ejpam-617	58	10	zh′(z	zh′(z	PROPN
ejpam-617	58	11	)	)	PUNCT
ejpam-617	58	12	βh(z	βh(z	PUNCT
ejpam-617	58	13	)	)	PUNCT
ejpam-617	59	1	+	+	CCONJ
ejpam-617	59	2	γ	γ	X
ejpam-617	59	3	≺	≺	NOUN
ejpam-617	59	4	q(z	q(z	PROPN
ejpam-617	59	5	)	)	PUNCT
ejpam-617	59	6	,	,	PUNCT
ejpam-617	59	7	(	(	PUNCT
ejpam-617	59	8	13	13	NUM
ejpam-617	59	9	)	)	PUNCT
ejpam-617	59	10	is	be	AUX
ejpam-617	59	11	called	call	VERB
ejpam-617	59	12	the	the	DET
ejpam-617	59	13	briot	briot	NOUN
ejpam-617	59	14	-	-	PUNCT
ejpam-617	59	15	bouquet	bouquet	NOUN
ejpam-617	59	16	differential	differential	NOUN
ejpam-617	59	17	subordination	subordination	NOUN
ejpam-617	59	18	.	.	PUNCT
ejpam-617	60	1	this	this	DET
ejpam-617	60	2	particular	particular	ADJ
ejpam-617	60	3	differential	differential	NOUN
ejpam-617	60	4	subordination	subordination	NOUN
ejpam-617	60	5	has	have	VERB
ejpam-617	60	6	a	a	DET
ejpam-617	60	7	surprising	surprising	ADJ
ejpam-617	60	8	number	number	NOUN
ejpam-617	60	9	of	of	ADP
ejpam-617	60	10	important	important	ADJ
ejpam-617	60	11	applications	application	NOUN
ejpam-617	60	12	in	in	ADP
ejpam-617	60	13	the	the	DET
ejpam-617	60	14	theory	theory	NOUN
ejpam-617	60	15	of	of	ADP
ejpam-617	60	16	analytic	analytic	ADJ
ejpam-617	60	17	functions	function	NOUN
ejpam-617	60	18	(	(	PUNCT
ejpam-617	60	19	for	for	ADP
ejpam-617	60	20	details	detail	NOUN
ejpam-617	60	21	see	see	VERB
ejpam-617	60	22	[	[	X
ejpam-617	60	23	7	7	NUM
ejpam-617	60	24	]	]	NUM
ejpam-617	60	25	)	)	PUNCT
ejpam-617	60	26	.	.	PUNCT
ejpam-617	61	1	in	in	ADP
ejpam-617	61	2	this	this	DET
ejpam-617	61	3	paper	paper	NOUN
ejpam-617	61	4	we	we	PRON
ejpam-617	61	5	present	present	VERB
ejpam-617	61	6	one	one	NUM
ejpam-617	61	7	more	more	ADJ
ejpam-617	61	8	application	application	NOUN
ejpam-617	61	9	of	of	ADP
ejpam-617	61	10	the	the	DET
ejpam-617	61	11	briot	briot	NOUN
ejpam-617	61	12	-	-	PUNCT
ejpam-617	61	13	bouquet	bouquet	NOUN
ejpam-617	61	14	differential	differential	NOUN
ejpam-617	61	15	subordination	subordination	NOUN
ejpam-617	61	16	.	.	PUNCT
ejpam-617	62	1	s.	s.	PROPN
ejpam-617	62	2	bansal	bansal	PROPN
ejpam-617	62	3	,	,	PUNCT
ejpam-617	62	4	j.	j.	PROPN
ejpam-617	62	5	dziok	dziok	PROPN
ejpam-617	62	6	,	,	PUNCT
ejpam-617	62	7	p.	p.	NOUN
ejpam-617	62	8	goswami	goswami	PROPN
ejpam-617	62	9	/	/	SYM
ejpam-617	62	10	eur	eur	PROPN
ejpam-617	62	11	.	.	PUNCT
ejpam-617	63	1	j.	j.	PROPN
ejpam-617	63	2	pure	pure	PROPN
ejpam-617	63	3	appl	appl	PROPN
ejpam-617	63	4	.	.	PROPN
ejpam-617	63	5	math	math	PROPN
ejpam-617	63	6	,	,	PUNCT
ejpam-617	63	7	3	3	NUM
ejpam-617	63	8	(	(	PUNCT
ejpam-617	63	9	2010	2010	NUM
ejpam-617	63	10	)	)	PUNCT
ejpam-617	63	11	,	,	PUNCT
ejpam-617	63	12	633	633	NUM
ejpam-617	63	13	-	-	SYM
ejpam-617	63	14	640	640	NUM
ejpam-617	63	15	636	636	NUM
ejpam-617	63	16	2	2	NUM
ejpam-617	63	17	.	.	PUNCT
ejpam-617	63	18	main	main	ADJ
ejpam-617	63	19	result	result	NOUN
ejpam-617	63	20	to	to	PART
ejpam-617	63	21	prove	prove	VERB
ejpam-617	63	22	our	our	PRON
ejpam-617	63	23	main	main	ADJ
ejpam-617	63	24	results	result	NOUN
ejpam-617	63	25	we	we	PRON
ejpam-617	63	26	need	need	VERB
ejpam-617	63	27	the	the	DET
ejpam-617	63	28	following	follow	VERB
ejpam-617	63	29	lemmas	lemmas	NOUN
ejpam-617	63	30	:	:	PUNCT
ejpam-617	63	31	lemma	lemma	PROPN
ejpam-617	63	32	1	1	NUM
ejpam-617	63	33	(	(	PUNCT
ejpam-617	63	34	[	[	X
ejpam-617	63	35	7	7	NUM
ejpam-617	63	36	]	]	PUNCT
ejpam-617	63	37	,	,	PUNCT
ejpam-617	63	38	see	see	VERB
ejpam-617	63	39	also	also	ADV
ejpam-617	63	40	[	[	X
ejpam-617	63	41	4	4	NUM
ejpam-617	63	42	]	]	PUNCT
ejpam-617	63	43	)	)	PUNCT
ejpam-617	63	44	.	.	PUNCT
ejpam-617	64	1	let	let	VERB
ejpam-617	64	2	β	β	PRON
ejpam-617	64	3	,	,	PUNCT
ejpam-617	64	4	γ	γ	PROPN
ejpam-617	64	5	∈	∈	PROPN
ejpam-617	64	6	c	c	PROPN
ejpam-617	64	7	and	and	CCONJ
ejpam-617	64	8	suppose	suppose	VERB
ejpam-617	64	9	q(z	q(z	PROPN
ejpam-617	64	10	)	)	PUNCT
ejpam-617	64	11	is	be	AUX
ejpam-617	64	12	convex	convex	ADJ
ejpam-617	64	13	univalent	univalent	ADJ
ejpam-617	64	14	in	in	ADP
ejpam-617	64	15	u	u	NOUN
ejpam-617	64	16	with	with	ADP
ejpam-617	64	17	q(0	q(0	PROPN
ejpam-617	64	18	)	)	PUNCT
ejpam-617	64	19	=	=	SYM
ejpam-617	65	1	p	p	PROPN
ejpam-617	65	2	and	and	CCONJ
ejpam-617	65	3	re	re	ADJ
ejpam-617	65	4	�	�	PROPN
ejpam-617	65	5	βq(z	βq(z	NUM
ejpam-617	65	6	)	)	PUNCT
ejpam-617	66	1	+	+	CCONJ
ejpam-617	66	2	γ	γ	X
ejpam-617	66	3	>	>	X
ejpam-617	66	4	0	0	PUNCT
ejpam-617	67	1	(	(	PUNCT
ejpam-617	67	2	z	z	NOUN
ejpam-617	67	3	∈	∈	PROPN
ejpam-617	67	4	u	u	NOUN
ejpam-617	67	5	)	)	PUNCT
ejpam-617	67	6	if	if	SCONJ
ejpam-617	67	7	h(z	h(z	NOUN
ejpam-617	67	8	)	)	PUNCT
ejpam-617	67	9	is	be	AUX
ejpam-617	67	10	analytic	analytic	ADJ
ejpam-617	67	11	in	in	ADP
ejpam-617	67	12	u	u	NOUN
ejpam-617	67	13	with	with	ADP
ejpam-617	67	14	h(0	h(0	PROPN
ejpam-617	67	15	)	)	PUNCT
ejpam-617	67	16	=	=	SYM
ejpam-617	67	17	p	p	X
ejpam-617	67	18	,	,	PUNCT
ejpam-617	67	19	and	and	CCONJ
ejpam-617	67	20	:	:	PUNCT
ejpam-617	67	21	h(z	h(z	NOUN
ejpam-617	67	22	)	)	PUNCT
ejpam-617	67	23	+	+	CCONJ
ejpam-617	67	24	zh′(z	zh′(z	PROPN
ejpam-617	67	25	)	)	PUNCT
ejpam-617	67	26	βh(z	βh(z	PUNCT
ejpam-617	67	27	)	)	PUNCT
ejpam-617	68	1	+	+	CCONJ
ejpam-617	68	2	γ	γ	X
ejpam-617	68	3	≺	≺	NOUN
ejpam-617	68	4	q(z	q(z	PROPN
ejpam-617	68	5	)	)	PUNCT
ejpam-617	68	6	(	(	PUNCT
ejpam-617	68	7	z	z	NOUN
ejpam-617	68	8	∈	∈	PROPN
ejpam-617	68	9	u	u	NOUN
ejpam-617	68	10	)	)	PUNCT
ejpam-617	68	11	,	,	PUNCT
ejpam-617	68	12	(	(	PUNCT
ejpam-617	68	13	14	14	NUM
ejpam-617	68	14	)	)	PUNCT
ejpam-617	68	15	then	then	ADV
ejpam-617	68	16	h(z	h(z	NOUN
ejpam-617	68	17	)	)	PUNCT
ejpam-617	68	18	≺	≺	NOUN
ejpam-617	68	19	q(z	q(z	PROPN
ejpam-617	68	20	)	)	PUNCT
ejpam-617	68	21	.	.	PUNCT
ejpam-617	69	1	lemma	lemma	PROPN
ejpam-617	69	2	2	2	NUM
ejpam-617	69	3	(	(	PUNCT
ejpam-617	69	4	[	[	X
ejpam-617	69	5	7	7	NUM
ejpam-617	69	6	]	]	NUM
ejpam-617	69	7	)	)	PUNCT
ejpam-617	69	8	.	.	PUNCT
ejpam-617	70	1	let	let	VERB
ejpam-617	70	2	the	the	DET
ejpam-617	70	3	function	function	NOUN
ejpam-617	70	4	w(z	w(z	NOUN
ejpam-617	70	5	)	)	PUNCT
ejpam-617	70	6	be	be	AUX
ejpam-617	70	7	(	(	PUNCT
ejpam-617	70	8	nonconstant	nonconstant	ADJ
ejpam-617	70	9	)	)	PUNCT
ejpam-617	70	10	analytic	analytic	NOUN
ejpam-617	70	11	in	in	ADP
ejpam-617	70	12	u	u	NOUN
ejpam-617	70	13	with	with	ADP
ejpam-617	70	14	w(0	w(0	PROPN
ejpam-617	70	15	)	)	PUNCT
ejpam-617	70	16	=	=	NOUN
ejpam-617	71	1	0	0	X
ejpam-617	71	2	.	.	PUNCT
ejpam-617	72	1	if	if	SCONJ
ejpam-617	72	2	|w(z)|	|w(z)|	ADJ
ejpam-617	72	3	attains	attain	NOUN
ejpam-617	72	4	its	its	PRON
ejpam-617	72	5	maximum	maximum	ADJ
ejpam-617	72	6	value	value	NOUN
ejpam-617	72	7	on	on	ADP
ejpam-617	72	8	the	the	DET
ejpam-617	72	9	circle	circle	NOUN
ejpam-617	72	10	|z|	|z|	NOUN
ejpam-617	72	11	=	=	SYM
ejpam-617	72	12	r	r	NOUN
ejpam-617	72	13	<	<	X
ejpam-617	72	14	1	1	NUM
ejpam-617	72	15	at	at	ADP
ejpam-617	72	16	a	a	DET
ejpam-617	72	17	point	point	NOUN
ejpam-617	72	18	z0	z0	PROPN
ejpam-617	72	19	∈	∈	PROPN
ejpam-617	72	20	u	u	PROPN
ejpam-617	72	21	,	,	PUNCT
ejpam-617	72	22	then	then	ADV
ejpam-617	72	23	z0w′(z0	z0w′(z0	NOUN
ejpam-617	72	24	)	)	PUNCT
ejpam-617	72	25	=	=	SYM
ejpam-617	72	26	kw(z0	kw(z0	NOUN
ejpam-617	72	27	)	)	PUNCT
ejpam-617	72	28	,	,	PUNCT
ejpam-617	72	29	(	(	PUNCT
ejpam-617	72	30	15	15	NUM
ejpam-617	72	31	)	)	PUNCT
ejpam-617	72	32	where	where	SCONJ
ejpam-617	72	33	k	k	PROPN
ejpam-617	72	34	is	be	AUX
ejpam-617	72	35	real	real	ADJ
ejpam-617	72	36	and	and	CCONJ
ejpam-617	72	37	k	k	PROPN
ejpam-617	72	38	≥	≥	NUM
ejpam-617	72	39	1	1	NUM
ejpam-617	72	40	.	.	PUNCT
ejpam-617	73	1	making	make	VERB
ejpam-617	73	2	use	use	NOUN
ejpam-617	73	3	of	of	ADP
ejpam-617	73	4	lemma	lemma	PROPN
ejpam-617	73	5	1	1	NUM
ejpam-617	73	6	,	,	PUNCT
ejpam-617	73	7	we	we	PRON
ejpam-617	73	8	get	get	VERB
ejpam-617	73	9	the	the	DET
ejpam-617	73	10	following	follow	VERB
ejpam-617	73	11	theorem	theorem	NOUN
ejpam-617	73	12	:	:	PUNCT
ejpam-617	73	13	theorem	theorem	NOUN
ejpam-617	73	14	1	1	NUM
ejpam-617	73	15	.	.	PUNCT
ejpam-617	74	1	if	if	SCONJ
ejpam-617	74	2	α1	α1	PROPN
ejpam-617	74	3	(	(	PUNCT
ejpam-617	74	4	1	1	NUM
ejpam-617	74	5	+	+	NUM
ejpam-617	74	6	b	b	NOUN
ejpam-617	74	7	)	)	PUNCT
ejpam-617	74	8	>	>	X
ejpam-617	74	9	pa1	pa1	PROPN
ejpam-617	74	10	(	(	PUNCT
ejpam-617	74	11	a−	a−	PROPN
ejpam-617	74	12	b	b	PROPN
ejpam-617	74	13	)	)	PUNCT
ejpam-617	74	14	,	,	PUNCT
ejpam-617	74	15	then	then	ADV
ejpam-617	74	16	v	v	X
ejpam-617	74	17	(	(	PUNCT
ejpam-617	74	18	(	(	PUNCT
ejpam-617	74	19	α1	α1	PROPN
ejpam-617	74	20	+	+	PROPN
ejpam-617	74	21	m	m	PROPN
ejpam-617	74	22	,	,	PUNCT
ejpam-617	74	23	a1	a1	PROPN
ejpam-617	74	24	)	)	PUNCT
ejpam-617	74	25	;	;	PUNCT
ejpam-617	74	26	a	a	DET
ejpam-617	74	27	,	,	PUNCT
ejpam-617	74	28	b	b	NOUN
ejpam-617	74	29	)	)	PUNCT
ejpam-617	74	30	⊂	⊂	PROPN
ejpam-617	74	31	v	v	X
ejpam-617	74	32	(	(	PUNCT
ejpam-617	74	33	(	(	PUNCT
ejpam-617	74	34	α1,a1	α1,a1	PROPN
ejpam-617	74	35	)	)	PUNCT
ejpam-617	74	36	;	;	PUNCT
ejpam-617	74	37	a	a	DET
ejpam-617	74	38	,	,	PUNCT
ejpam-617	74	39	b	b	NOUN
ejpam-617	74	40	)	)	PUNCT
ejpam-617	74	41	(	(	PUNCT
ejpam-617	74	42	m	m	PROPN
ejpam-617	74	43	∈	∈	PROPN
ejpam-617	74	44	n	n	CCONJ
ejpam-617	74	45	)	)	PUNCT
ejpam-617	74	46	.	.	PUNCT
ejpam-617	75	1	proof	proof	NOUN
ejpam-617	75	2	.	.	PUNCT
ejpam-617	76	1	obviously	obviously	ADV
ejpam-617	76	2	,	,	PUNCT
ejpam-617	76	3	it	it	PRON
ejpam-617	76	4	is	be	AUX
ejpam-617	76	5	sufficient	sufficient	ADJ
ejpam-617	76	6	to	to	PART
ejpam-617	76	7	prove	prove	VERB
ejpam-617	76	8	the	the	DET
ejpam-617	76	9	theorem	theorem	NOUN
ejpam-617	76	10	for	for	ADP
ejpam-617	76	11	m	m	PROPN
ejpam-617	76	12	=	=	NOUN
ejpam-617	76	13	1	1	X
ejpam-617	76	14	.	.	PUNCT
ejpam-617	77	1	let	let	VERB
ejpam-617	77	2	a	a	DET
ejpam-617	77	3	function	function	NOUN
ejpam-617	77	4	f	f	PROPN
ejpam-617	77	5	belong	belong	VERB
ejpam-617	77	6	to	to	ADP
ejpam-617	77	7	the	the	DET
ejpam-617	77	8	class	class	NOUN
ejpam-617	77	9	v	v	NOUN
ejpam-617	77	10	(	(	PUNCT
ejpam-617	77	11	(	(	PUNCT
ejpam-617	77	12	α1	α1	PROPN
ejpam-617	77	13	+	+	CCONJ
ejpam-617	77	14	1,a1	1,a1	NUM
ejpam-617	77	15	)	)	PUNCT
ejpam-617	77	16	;	;	PUNCT
ejpam-617	77	17	a	a	DET
ejpam-617	77	18	,	,	PUNCT
ejpam-617	77	19	b	b	NOUN
ejpam-617	77	20	)	)	PUNCT
ejpam-617	77	21	or	or	CCONJ
ejpam-617	77	22	equivalently	equivalently	ADV
ejpam-617	77	23	−z	−z	NOUN
ejpam-617	77	24	h	h	NOUN
ejpam-617	77	25	θ	θ	PROPN
ejpam-617	77	26	l	l	NOUN
ejpam-617	77	27	,	,	PUNCT
ejpam-617	77	28	s	s	PROPN
ejpam-617	77	29	p	p	X
ejpam-617	77	30	(	(	PUNCT
ejpam-617	77	31	α1	α1	PROPN
ejpam-617	77	32	+	+	CCONJ
ejpam-617	77	33	1,a1	1,a1	NUM
ejpam-617	77	34	)	)	SYM
ejpam-617	77	35	f	f	NOUN
ejpam-617	77	36	(	(	PUNCT
ejpam-617	77	37	z	z	NOUN
ejpam-617	77	38	)	)	PUNCT
ejpam-617	77	39	i′	i′	NOUN
ejpam-617	77	40	θ	θ	NOUN
ejpam-617	77	41	l	l	NOUN
ejpam-617	77	42	,	,	PUNCT
ejpam-617	77	43	s	s	PROPN
ejpam-617	77	44	p	p	X
ejpam-617	77	45	(	(	PUNCT
ejpam-617	77	46	α1	α1	PROPN
ejpam-617	77	47	+	+	CCONJ
ejpam-617	77	48	1,a1	1,a1	NUM
ejpam-617	77	49	)	)	SYM
ejpam-617	77	50	f	f	NOUN
ejpam-617	77	51	(	(	PUNCT
ejpam-617	77	52	z	z	NOUN
ejpam-617	77	53	)	)	PUNCT
ejpam-617	77	54	≺	≺	NOUN
ejpam-617	77	55	p	p	X
ejpam-617	77	56	1	1	NUM
ejpam-617	77	57	+	+	NUM
ejpam-617	77	58	az	az	PROPN
ejpam-617	77	59	1	1	NUM
ejpam-617	77	60	+	+	CCONJ
ejpam-617	77	61	bz	bz	PROPN
ejpam-617	77	62	.	.	PUNCT
ejpam-617	78	1	(	(	PUNCT
ejpam-617	78	2	16	16	NUM
ejpam-617	78	3	)	)	PUNCT
ejpam-617	78	4	then	then	ADV
ejpam-617	78	5	the	the	DET
ejpam-617	78	6	function	function	NOUN
ejpam-617	78	7	h(z	h(z	NOUN
ejpam-617	78	8	)	)	PUNCT
ejpam-617	78	9	=	=	PUNCT
ejpam-617	79	1	−z	−z	NOUN
ejpam-617	79	2	h	h	NOUN
ejpam-617	79	3	θ	θ	NOUN
ejpam-617	79	4	l	l	NOUN
ejpam-617	79	5	,	,	PUNCT
ejpam-617	79	6	s	s	X
ejpam-617	79	7	p	p	X
ejpam-617	79	8	(	(	PUNCT
ejpam-617	79	9	α1,a1	α1,a1	PROPN
ejpam-617	79	10	)	)	PUNCT
ejpam-617	79	11	f	f	PROPN
ejpam-617	79	12	(	(	PUNCT
ejpam-617	79	13	z	z	NOUN
ejpam-617	79	14	)	)	PUNCT
ejpam-617	79	15	i′	i′	NOUN
ejpam-617	79	16	θ	θ	NOUN
ejpam-617	79	17	l	l	NOUN
ejpam-617	79	18	,	,	PUNCT
ejpam-617	79	19	s	s	PART
ejpam-617	79	20	p	p	X
ejpam-617	79	21	(	(	PUNCT
ejpam-617	79	22	α1,a1	α1,a1	PROPN
ejpam-617	79	23	)	)	PUNCT
ejpam-617	79	24	f	f	PROPN
ejpam-617	79	25	(	(	PUNCT
ejpam-617	79	26	z	z	NOUN
ejpam-617	79	27	)	)	PUNCT
ejpam-617	79	28	,	,	PUNCT
ejpam-617	79	29	(	(	PUNCT
ejpam-617	79	30	17	17	NUM
ejpam-617	79	31	)	)	PUNCT
ejpam-617	79	32	is	be	AUX
ejpam-617	79	33	analytic	analytic	ADJ
ejpam-617	79	34	in	in	ADP
ejpam-617	79	35	u	u	NOUN
ejpam-617	79	36	and	and	CCONJ
ejpam-617	79	37	h(0	h(0	PROPN
ejpam-617	79	38	)	)	PUNCT
ejpam-617	80	1	=	=	PUNCT
ejpam-617	81	1	p.	p.	NOUN
ejpam-617	81	2	using	use	VERB
ejpam-617	81	3	equation	equation	NOUN
ejpam-617	81	4	(	(	PUNCT
ejpam-617	81	5	11	11	NUM
ejpam-617	81	6	)	)	PUNCT
ejpam-617	81	7	the	the	DET
ejpam-617	81	8	equation	equation	NOUN
ejpam-617	81	9	(	(	PUNCT
ejpam-617	81	10	17	17	NUM
ejpam-617	81	11	)	)	PUNCT
ejpam-617	81	12	can	can	AUX
ejpam-617	81	13	be	be	AUX
ejpam-617	81	14	rewritten	rewrite	VERB
ejpam-617	81	15	as	as	ADP
ejpam-617	81	16	−h(z	−h(z	NOUN
ejpam-617	81	17	)	)	PUNCT
ejpam-617	81	18	+	+	CCONJ
ejpam-617	81	19	�	�	PROPN
ejpam-617	81	20	α1	α1	PROPN
ejpam-617	81	21	a1	a1	NOUN
ejpam-617	81	22	+	+	CCONJ
ejpam-617	81	23	p	p	X
ejpam-617	81	24	�	�	PROPN
ejpam-617	81	25	=	=	SYM
ejpam-617	81	26	α1	α1	PROPN
ejpam-617	81	27	a1	a1	NOUN
ejpam-617	81	28	θ	θ	PROPN
ejpam-617	81	29	l	l	NOUN
ejpam-617	81	30	,	,	PUNCT
ejpam-617	81	31	s	s	PROPN
ejpam-617	81	32	p	p	X
ejpam-617	81	33	(	(	PUNCT
ejpam-617	81	34	α1	α1	PROPN
ejpam-617	81	35	+	+	CCONJ
ejpam-617	81	36	1,a1	1,a1	NUM
ejpam-617	81	37	)	)	SYM
ejpam-617	81	38	f	f	NOUN
ejpam-617	81	39	(	(	PUNCT
ejpam-617	81	40	z	z	NOUN
ejpam-617	81	41	)	)	PUNCT
ejpam-617	81	42	θ	θ	PROPN
ejpam-617	81	43	l	l	NOUN
ejpam-617	81	44	,	,	PUNCT
ejpam-617	81	45	s	s	X
ejpam-617	81	46	p	p	X
ejpam-617	81	47	(	(	PUNCT
ejpam-617	81	48	α1,a1	α1,a1	PROPN
ejpam-617	81	49	)	)	PUNCT
ejpam-617	81	50	f	f	PROPN
ejpam-617	81	51	(	(	PUNCT
ejpam-617	81	52	z	z	NOUN
ejpam-617	81	53	)	)	PUNCT
ejpam-617	81	54	.	.	PUNCT
ejpam-617	82	1	(	(	PUNCT
ejpam-617	82	2	18	18	NUM
ejpam-617	82	3	)	)	PUNCT
ejpam-617	82	4	s.	s.	PROPN
ejpam-617	82	5	bansal	bansal	PROPN
ejpam-617	82	6	,	,	PUNCT
ejpam-617	82	7	j.	j.	PROPN
ejpam-617	82	8	dziok	dziok	PROPN
ejpam-617	82	9	,	,	PUNCT
ejpam-617	82	10	p.	p.	NOUN
ejpam-617	82	11	goswami	goswami	PROPN
ejpam-617	82	12	/	/	SYM
ejpam-617	82	13	eur	eur	PROPN
ejpam-617	82	14	.	.	PUNCT
ejpam-617	83	1	j.	j.	PROPN
ejpam-617	83	2	pure	pure	PROPN
ejpam-617	83	3	appl	appl	PROPN
ejpam-617	83	4	.	.	PROPN
ejpam-617	83	5	math	math	PROPN
ejpam-617	83	6	,	,	PUNCT
ejpam-617	83	7	3	3	NUM
ejpam-617	83	8	(	(	PUNCT
ejpam-617	83	9	2010	2010	NUM
ejpam-617	83	10	)	)	PUNCT
ejpam-617	83	11	,	,	PUNCT
ejpam-617	83	12	633	633	NUM
ejpam-617	83	13	-	-	SYM
ejpam-617	83	14	640	640	NUM
ejpam-617	83	15	637	637	NUM
ejpam-617	83	16	taking	take	VERB
ejpam-617	83	17	the	the	DET
ejpam-617	83	18	logarithmic	logarithmic	ADJ
ejpam-617	83	19	derivative	derivative	NOUN
ejpam-617	83	20	of	of	ADP
ejpam-617	83	21	equation	equation	NOUN
ejpam-617	83	22	(	(	PUNCT
ejpam-617	83	23	18	18	NUM
ejpam-617	83	24	)	)	PUNCT
ejpam-617	83	25	,	,	PUNCT
ejpam-617	83	26	we	we	PRON
ejpam-617	83	27	get	get	VERB
ejpam-617	83	28	−zh′(z	−zh′(z	PRON
ejpam-617	83	29	)	)	PUNCT
ejpam-617	83	30	�	�	PROPN
ejpam-617	83	31	α1	α1	PROPN
ejpam-617	83	32	a1	a1	NOUN
ejpam-617	83	33	+	+	CCONJ
ejpam-617	83	34	p	p	X
ejpam-617	83	35	�	�	PROPN
ejpam-617	83	36	−	−	PROPN
ejpam-617	83	37	h(z	h(z	NOUN
ejpam-617	83	38	)	)	PUNCT
ejpam-617	83	39	=	=	PUNCT
ejpam-617	84	1	z	z	NOUN
ejpam-617	84	2	h	h	NOUN
ejpam-617	84	3	θ	θ	NOUN
ejpam-617	84	4	l	l	NOUN
ejpam-617	84	5	,	,	PUNCT
ejpam-617	84	6	s	s	PROPN
ejpam-617	84	7	p	p	X
ejpam-617	84	8	(	(	PUNCT
ejpam-617	84	9	α1	α1	PROPN
ejpam-617	84	10	+	+	CCONJ
ejpam-617	84	11	1,a1	1,a1	NUM
ejpam-617	84	12	)	)	SYM
ejpam-617	84	13	f	f	NOUN
ejpam-617	84	14	(	(	PUNCT
ejpam-617	84	15	z	z	NOUN
ejpam-617	84	16	)	)	PUNCT
ejpam-617	84	17	i′	i′	NOUN
ejpam-617	84	18	θ	θ	NOUN
ejpam-617	84	19	l	l	NOUN
ejpam-617	84	20	,	,	PUNCT
ejpam-617	84	21	s	s	PROPN
ejpam-617	84	22	p	p	X
ejpam-617	84	23	(	(	PUNCT
ejpam-617	84	24	α1	α1	PROPN
ejpam-617	84	25	+	+	CCONJ
ejpam-617	84	26	1,a1	1,a1	NUM
ejpam-617	84	27	)	)	SYM
ejpam-617	84	28	f	f	NOUN
ejpam-617	84	29	(	(	PUNCT
ejpam-617	84	30	z	z	NOUN
ejpam-617	84	31	)	)	PUNCT
ejpam-617	85	1	−	−	PROPN
ejpam-617	86	1	z	z	NOUN
ejpam-617	86	2	h	h	NOUN
ejpam-617	86	3	θ	θ	NOUN
ejpam-617	86	4	l	l	NOUN
ejpam-617	86	5	,	,	PUNCT
ejpam-617	86	6	s	s	X
ejpam-617	86	7	p	p	X
ejpam-617	86	8	(	(	PUNCT
ejpam-617	86	9	α1,a1	α1,a1	PROPN
ejpam-617	86	10	)	)	PUNCT
ejpam-617	86	11	f	f	PROPN
ejpam-617	86	12	(	(	PUNCT
ejpam-617	86	13	z	z	NOUN
ejpam-617	86	14	)	)	PUNCT
ejpam-617	86	15	i′	i′	NOUN
ejpam-617	86	16	θ	θ	NOUN
ejpam-617	86	17	l	l	NOUN
ejpam-617	86	18	,	,	PUNCT
ejpam-617	86	19	s	s	PART
ejpam-617	86	20	p	p	X
ejpam-617	86	21	(	(	PUNCT
ejpam-617	86	22	α1,a1	α1,a1	PROPN
ejpam-617	86	23	)	)	PUNCT
ejpam-617	86	24	f	f	PROPN
ejpam-617	86	25	(	(	PUNCT
ejpam-617	86	26	z	z	NOUN
ejpam-617	86	27	)	)	PUNCT
ejpam-617	86	28	.	.	PUNCT
ejpam-617	87	1	(	(	PUNCT
ejpam-617	87	2	19	19	NUM
ejpam-617	87	3	)	)	PUNCT
ejpam-617	87	4	using	use	VERB
ejpam-617	87	5	(	(	PUNCT
ejpam-617	87	6	17	17	NUM
ejpam-617	87	7	)	)	PUNCT
ejpam-617	87	8	in	in	ADP
ejpam-617	87	9	the	the	DET
ejpam-617	87	10	above	above	ADJ
ejpam-617	87	11	equation	equation	NOUN
ejpam-617	87	12	we	we	PRON
ejpam-617	87	13	have	have	VERB
ejpam-617	87	14	,	,	PUNCT
ejpam-617	87	15	−zh′(z	−zh′(z	NUM
ejpam-617	87	16	)	)	PUNCT
ejpam-617	87	17	�	�	PROPN
ejpam-617	87	18	α1	α1	PROPN
ejpam-617	87	19	a1	a1	NOUN
ejpam-617	87	20	+	+	CCONJ
ejpam-617	87	21	p	p	X
ejpam-617	87	22	�	�	PROPN
ejpam-617	87	23	−	−	PROPN
ejpam-617	87	24	h(z	h(z	NOUN
ejpam-617	87	25	)	)	PUNCT
ejpam-617	87	26	=	=	PUNCT
ejpam-617	87	27	z	z	NOUN
ejpam-617	87	28	h	h	NOUN
ejpam-617	87	29	θ	θ	NOUN
ejpam-617	87	30	l	l	NOUN
ejpam-617	87	31	,	,	PUNCT
ejpam-617	87	32	s	s	PROPN
ejpam-617	87	33	p	p	X
ejpam-617	87	34	(	(	PUNCT
ejpam-617	87	35	α1	α1	PROPN
ejpam-617	87	36	+	+	CCONJ
ejpam-617	87	37	1,a1	1,a1	NUM
ejpam-617	87	38	)	)	SYM
ejpam-617	87	39	f	f	NOUN
ejpam-617	87	40	(	(	PUNCT
ejpam-617	87	41	z	z	NOUN
ejpam-617	87	42	)	)	PUNCT
ejpam-617	87	43	i′	i′	NOUN
ejpam-617	87	44	θ	θ	NOUN
ejpam-617	87	45	l	l	NOUN
ejpam-617	87	46	,	,	PUNCT
ejpam-617	87	47	s	s	PROPN
ejpam-617	87	48	p	p	X
ejpam-617	87	49	(	(	PUNCT
ejpam-617	87	50	α1	α1	PROPN
ejpam-617	87	51	+	+	CCONJ
ejpam-617	87	52	1,a1	1,a1	NUM
ejpam-617	87	53	)	)	SYM
ejpam-617	87	54	f	f	NOUN
ejpam-617	87	55	(	(	PUNCT
ejpam-617	87	56	z	z	NOUN
ejpam-617	87	57	)	)	PUNCT
ejpam-617	88	1	+	+	CCONJ
ejpam-617	89	1	h(z	h(z	NOUN
ejpam-617	89	2	)	)	PUNCT
ejpam-617	89	3	,	,	PUNCT
ejpam-617	89	4	(	(	PUNCT
ejpam-617	89	5	20	20	X
ejpam-617	89	6	)	)	PUNCT
ejpam-617	89	7	h(z	h(z	NOUN
ejpam-617	89	8	)	)	PUNCT
ejpam-617	89	9	+	+	CCONJ
ejpam-617	89	10	zh′(z	zh′(z	X
ejpam-617	89	11	)	)	PUNCT
ejpam-617	89	12	�	�	PROPN
ejpam-617	89	13	α1	α1	PROPN
ejpam-617	89	14	a1	a1	NOUN
ejpam-617	89	15	+	+	CCONJ
ejpam-617	89	16	p	p	X
ejpam-617	89	17	�	�	PROPN
ejpam-617	89	18	−	−	PROPN
ejpam-617	89	19	h(z	h(z	NOUN
ejpam-617	89	20	)	)	PUNCT
ejpam-617	89	21	=	=	SYM
ejpam-617	90	1	−	−	NOUN
ejpam-617	90	2	z	z	NOUN
ejpam-617	90	3	h	h	NOUN
ejpam-617	90	4	θ	θ	NOUN
ejpam-617	90	5	l	l	NOUN
ejpam-617	90	6	,	,	PUNCT
ejpam-617	90	7	s	s	PROPN
ejpam-617	90	8	p	p	X
ejpam-617	90	9	(	(	PUNCT
ejpam-617	90	10	α1	α1	PROPN
ejpam-617	90	11	+	+	CCONJ
ejpam-617	90	12	1,a1	1,a1	NUM
ejpam-617	90	13	)	)	SYM
ejpam-617	90	14	f	f	NOUN
ejpam-617	90	15	(	(	PUNCT
ejpam-617	90	16	z	z	NOUN
ejpam-617	90	17	)	)	PUNCT
ejpam-617	90	18	i′	i′	NOUN
ejpam-617	90	19	θ	θ	NOUN
ejpam-617	90	20	l	l	NOUN
ejpam-617	90	21	,	,	PUNCT
ejpam-617	90	22	s	s	PROPN
ejpam-617	90	23	p	p	X
ejpam-617	90	24	(	(	PUNCT
ejpam-617	90	25	α1	α1	PROPN
ejpam-617	90	26	+	+	CCONJ
ejpam-617	90	27	1,a1	1,a1	NUM
ejpam-617	90	28	)	)	SYM
ejpam-617	90	29	f	f	NOUN
ejpam-617	90	30	(	(	PUNCT
ejpam-617	90	31	z	z	NOUN
ejpam-617	90	32	)	)	PUNCT
ejpam-617	90	33	.	.	PUNCT
ejpam-617	91	1	(	(	PUNCT
ejpam-617	91	2	21	21	NUM
ejpam-617	91	3	)	)	PUNCT
ejpam-617	91	4	thus	thus	ADV
ejpam-617	91	5	by	by	ADP
ejpam-617	91	6	(	(	PUNCT
ejpam-617	91	7	16	16	NUM
ejpam-617	91	8	)	)	PUNCT
ejpam-617	91	9	we	we	PRON
ejpam-617	91	10	have	have	VERB
ejpam-617	91	11	h(z	h(z	NOUN
ejpam-617	91	12	)	)	PUNCT
ejpam-617	91	13	+	+	CCONJ
ejpam-617	91	14	zh′(z	zh′(z	X
ejpam-617	91	15	)	)	PUNCT
ejpam-617	91	16	�	�	PROPN
ejpam-617	91	17	α1	α1	PROPN
ejpam-617	91	18	a1	a1	NOUN
ejpam-617	91	19	+	+	CCONJ
ejpam-617	91	20	p	p	X
ejpam-617	91	21	�	�	PROPN
ejpam-617	91	22	−	−	PROPN
ejpam-617	91	23	h(z	h(z	NOUN
ejpam-617	91	24	)	)	PUNCT
ejpam-617	91	25	≺	≺	NOUN
ejpam-617	91	26	p	p	X
ejpam-617	91	27	1	1	NUM
ejpam-617	91	28	+	+	NUM
ejpam-617	91	29	az	az	PROPN
ejpam-617	91	30	1	1	NUM
ejpam-617	91	31	+	+	CCONJ
ejpam-617	91	32	bz	bz	PROPN
ejpam-617	91	33	.	.	PUNCT
ejpam-617	92	1	(	(	PUNCT
ejpam-617	92	2	22	22	X
ejpam-617	92	3	)	)	PUNCT
ejpam-617	92	4	lemma	lemma	PROPN
ejpam-617	92	5	1	1	NUM
ejpam-617	92	6	now	now	ADV
ejpam-617	92	7	yields	yield	VERB
ejpam-617	92	8	h(z	h(z	NOUN
ejpam-617	92	9	)	)	PUNCT
ejpam-617	92	10	≺	≺	NOUN
ejpam-617	92	11	p	p	X
ejpam-617	92	12	1	1	NUM
ejpam-617	92	13	+	+	NUM
ejpam-617	92	14	az	az	PROPN
ejpam-617	92	15	1	1	NUM
ejpam-617	92	16	+	+	CCONJ
ejpam-617	92	17	bz	bz	PROPN
ejpam-617	92	18	.	.	PUNCT
ejpam-617	93	1	thus	thus	ADV
ejpam-617	93	2	,	,	PUNCT
ejpam-617	93	3	by	by	ADP
ejpam-617	93	4	(	(	PUNCT
ejpam-617	93	5	17	17	NUM
ejpam-617	93	6	)	)	PUNCT
ejpam-617	93	7	and	and	CCONJ
ejpam-617	93	8	(	(	PUNCT
ejpam-617	93	9	11	11	NUM
ejpam-617	93	10	)	)	PUNCT
ejpam-617	93	11	we	we	PRON
ejpam-617	93	12	conclude	conclude	VERB
ejpam-617	93	13	that	that	SCONJ
ejpam-617	93	14	f	f	PROPN
ejpam-617	93	15	(	(	PUNCT
ejpam-617	93	16	z	z	X
ejpam-617	93	17	)	)	PUNCT
ejpam-617	93	18	∈	∈	NOUN
ejpam-617	93	19	v	v	NOUN
ejpam-617	93	20	(	(	PUNCT
ejpam-617	93	21	(	(	PUNCT
ejpam-617	93	22	α1,a1	α1,a1	PROPN
ejpam-617	93	23	)	)	PUNCT
ejpam-617	93	24	;	;	PUNCT
ejpam-617	93	25	a	a	DET
ejpam-617	93	26	,	,	PUNCT
ejpam-617	93	27	b	b	NOUN
ejpam-617	93	28	)	)	PUNCT
ejpam-617	93	29	.	.	PUNCT
ejpam-617	94	1	this	this	PRON
ejpam-617	94	2	completes	complete	VERB
ejpam-617	94	3	the	the	DET
ejpam-617	94	4	proof	proof	NOUN
ejpam-617	94	5	of	of	ADP
ejpam-617	94	6	the	the	DET
ejpam-617	94	7	theorem	theorem	NOUN
ejpam-617	94	8	1	1	X
ejpam-617	94	9	.	.	PUNCT
ejpam-617	94	10	using	use	VERB
ejpam-617	94	11	lemma	lemma	PROPN
ejpam-617	94	12	2	2	NUM
ejpam-617	94	13	we	we	PRON
ejpam-617	94	14	now	now	ADV
ejpam-617	94	15	show	show	VERB
ejpam-617	94	16	the	the	DET
ejpam-617	94	17	following	follow	VERB
ejpam-617	94	18	sufficient	sufficient	ADJ
ejpam-617	94	19	conditions	condition	NOUN
ejpam-617	94	20	for	for	SCONJ
ejpam-617	94	21	functions	function	NOUN
ejpam-617	94	22	to	to	PART
ejpam-617	94	23	belong	belong	VERB
ejpam-617	94	24	to	to	ADP
ejpam-617	94	25	the	the	DET
ejpam-617	94	26	class	class	NOUN
ejpam-617	94	27	v	v	NOUN
ejpam-617	94	28	(	(	PUNCT
ejpam-617	94	29	(	(	PUNCT
ejpam-617	94	30	α1,a1	α1,a1	PROPN
ejpam-617	94	31	)	)	PUNCT
ejpam-617	94	32	;	;	PUNCT
ejpam-617	94	33	a	a	DET
ejpam-617	94	34	,	,	PUNCT
ejpam-617	94	35	b	b	NOUN
ejpam-617	94	36	)	)	PUNCT
ejpam-617	94	37	.	.	PUNCT
ejpam-617	95	1	theorem	theorem	NOUN
ejpam-617	95	2	2	2	NUM
ejpam-617	95	3	.	.	PUNCT
ejpam-617	96	1	let	let	VERB
ejpam-617	96	2	m	m	PRON
ejpam-617	96	3	∈	∈	VERB
ejpam-617	96	4	n	n	NOUN
ejpam-617	96	5	and	and	CCONJ
ejpam-617	96	6	α1	α1	PROPN
ejpam-617	96	7	(	(	PUNCT
ejpam-617	96	8	1	1	NUM
ejpam-617	96	9	+	+	NUM
ejpam-617	96	10	b	b	NOUN
ejpam-617	96	11	)	)	PUNCT
ejpam-617	96	12	>	>	X
ejpam-617	96	13	pa1	pa1	PROPN
ejpam-617	96	14	(	(	PUNCT
ejpam-617	96	15	a−	a−	PROPN
ejpam-617	96	16	b	b	PROPN
ejpam-617	96	17	)	)	PUNCT
ejpam-617	96	18	,	,	PUNCT
ejpam-617	96	19	2	2	NUM
ejpam-617	96	20	�	�	PROPN
ejpam-617	96	21	α1	α1	PROPN
ejpam-617	96	22	+	+	PROPN
ejpam-617	96	23	m−	m−	PROPN
ejpam-617	96	24	1	1	NUM
ejpam-617	96	25	�	�	PROPN
ejpam-617	96	26	b2	b2	NOUN
ejpam-617	96	27	≤	≤	NOUN
ejpam-617	96	28	a1p[(a−	a1p[(a−	NOUN
ejpam-617	96	29	b)(2b+	b)(2b+	NOUN
ejpam-617	96	30	1	1	NUM
ejpam-617	96	31	)	)	PUNCT
ejpam-617	96	32	]	]	PUNCT
ejpam-617	96	33	.	.	PUNCT
ejpam-617	97	1	(	(	PUNCT
ejpam-617	97	2	23	23	NUM
ejpam-617	97	3	)	)	PUNCT
ejpam-617	97	4	if	if	SCONJ
ejpam-617	97	5	a	a	DET
ejpam-617	97	6	function	function	NOUN
ejpam-617	97	7	f	f	PROPN
ejpam-617	97	8	∈	∈	PROPN
ejpam-617	97	9	σp	σp	PROPN
ejpam-617	97	10	satisfies	satisfy	VERB
ejpam-617	97	11	the	the	DET
ejpam-617	97	12	inequality	inequality	NOUN
ejpam-617	97	13	�	�	PROPN
ejpam-617	97	14	α1+m	α1+m	PROPN
ejpam-617	97	15	a1	a1	PROPN
ejpam-617	97	16	�	�	PROPN
ejpam-617	97	17	�	�	PROPN
ejpam-617	97	18	�	�	PROPN
ejpam-617	97	19	�	�	PROPN
ejpam-617	97	20	�	�	PROPN
ejpam-617	97	21	�	�	PROPN
ejpam-617	97	22	θ	θ	PROPN
ejpam-617	97	23	l	l	NOUN
ejpam-617	97	24	,	,	PUNCT
ejpam-617	97	25	s	s	VERB
ejpam-617	97	26	p	p	X
ejpam-617	97	27	(	(	PUNCT
ejpam-617	97	28	α1+m+	α1+m+	NUM
ejpam-617	97	29	1	1	NUM
ejpam-617	97	30	;	;	PUNCT
ejpam-617	97	31	a1	a1	PROPN
ejpam-617	97	32	)	)	PUNCT
ejpam-617	97	33	f	f	NOUN
ejpam-617	97	34	(	(	PUNCT
ejpam-617	97	35	z	z	NOUN
ejpam-617	97	36	)	)	PUNCT
ejpam-617	97	37	θ	θ	PROPN
ejpam-617	97	38	l	l	NOUN
ejpam-617	97	39	,	,	PUNCT
ejpam-617	97	40	s	s	PROPN
ejpam-617	97	41	p	p	X
ejpam-617	97	42	(	(	PUNCT
ejpam-617	97	43	α1+m	α1+m	PROPN
ejpam-617	97	44	;	;	PUNCT
ejpam-617	97	45	a1	a1	PROPN
ejpam-617	97	46	)	)	PUNCT
ejpam-617	97	47	f	f	NOUN
ejpam-617	97	48	(	(	PUNCT
ejpam-617	97	49	z	z	NOUN
ejpam-617	97	50	)	)	PUNCT
ejpam-617	98	1	−	−	PROPN
ejpam-617	98	2	1	1	NUM
ejpam-617	98	3	�	�	PROPN
ejpam-617	98	4	�	�	PROPN
ejpam-617	98	5	�	�	PROPN
ejpam-617	98	6	�	�	PROPN
ejpam-617	98	7	�	�	PROPN
ejpam-617	98	8	<	<	X
ejpam-617	98	9	a−	a−	PROPN
ejpam-617	98	10	b	b	PROPN
ejpam-617	98	11	−	−	PROPN
ejpam-617	98	12	α1	α1	PROPN
ejpam-617	98	13	pa1	pa1	PROPN
ejpam-617	98	14	b	b	PROPN
ejpam-617	98	15	a−	a−	PROPN
ejpam-617	98	16	b+	b+	ADJ
ejpam-617	98	17	α1	α1	PROPN
ejpam-617	98	18	pa1	pa1	PROPN
ejpam-617	98	19	(	(	PUNCT
ejpam-617	98	20	1−	1−	NUM
ejpam-617	98	21	b	b	NOUN
ejpam-617	98	22	)	)	PUNCT
ejpam-617	98	23	(	(	PUNCT
ejpam-617	98	24	24	24	NUM
ejpam-617	98	25	)	)	PUNCT
ejpam-617	98	26	+	+	CCONJ
ejpam-617	98	27	b+	b+	NOUN
ejpam-617	98	28	p	p	X
ejpam-617	98	29	(	(	PUNCT
ejpam-617	98	30	a−	a−	PROPN
ejpam-617	98	31	b	b	PROPN
ejpam-617	98	32	)	)	PUNCT
ejpam-617	98	33	1	1	NUM
ejpam-617	98	34	+	+	NUM
ejpam-617	98	35	b	b	NOUN
ejpam-617	98	36	,	,	PUNCT
ejpam-617	98	37	(	(	PUNCT
ejpam-617	98	38	z	z	NOUN
ejpam-617	98	39	∈	∈	PROPN
ejpam-617	98	40	u	u	NOUN
ejpam-617	98	41	)	)	PUNCT
ejpam-617	98	42	,	,	PUNCT
ejpam-617	98	43	then	then	ADV
ejpam-617	98	44	f	f	PROPN
ejpam-617	98	45	∈	∈	PROPN
ejpam-617	98	46	v	v	PROPN
ejpam-617	98	47	(	(	PUNCT
ejpam-617	98	48	(	(	PUNCT
ejpam-617	98	49	α1,a1	α1,a1	PROPN
ejpam-617	98	50	)	)	PUNCT
ejpam-617	98	51	;	;	PUNCT
ejpam-617	98	52	a	a	DET
ejpam-617	98	53	,	,	PUNCT
ejpam-617	98	54	b	b	NOUN
ejpam-617	98	55	)	)	PUNCT
ejpam-617	98	56	.	.	PUNCT
ejpam-617	99	1	proof	proof	NOUN
ejpam-617	99	2	.	.	PUNCT
ejpam-617	100	1	it	it	PRON
ejpam-617	100	2	is	be	AUX
ejpam-617	100	3	sufficient	sufficient	ADJ
ejpam-617	100	4	to	to	PART
ejpam-617	100	5	consider	consider	VERB
ejpam-617	100	6	the	the	DET
ejpam-617	100	7	case	case	NOUN
ejpam-617	100	8	m	m	NOUN
ejpam-617	100	9	=	=	NOUN
ejpam-617	100	10	1	1	X
ejpam-617	100	11	.	.	PUNCT
ejpam-617	101	1	let	let	VERB
ejpam-617	101	2	a	a	DET
ejpam-617	101	3	function	function	NOUN
ejpam-617	101	4	f	f	PROPN
ejpam-617	101	5	belong	belong	VERB
ejpam-617	101	6	to	to	ADP
ejpam-617	101	7	the	the	DET
ejpam-617	101	8	class	class	NOUN
ejpam-617	101	9	σp	σp	PROPN
ejpam-617	101	10	.	.	PUNCT
ejpam-617	102	1	on	on	ADP
ejpam-617	102	2	putting	put	VERB
ejpam-617	102	3	h(z	h(z	NOUN
ejpam-617	102	4	)	)	PUNCT
ejpam-617	102	5	=	=	PUNCT
ejpam-617	102	6	p	p	VERB
ejpam-617	102	7	1	1	NUM
ejpam-617	102	8	+	+	CCONJ
ejpam-617	102	9	aw(z	aw(z	VERB
ejpam-617	102	10	)	)	PUNCT
ejpam-617	102	11	1	1	NUM
ejpam-617	102	12	+	+	NUM
ejpam-617	102	13	bw(z	bw(z	NOUN
ejpam-617	102	14	)	)	PUNCT
ejpam-617	102	15	(	(	PUNCT
ejpam-617	102	16	z	z	NOUN
ejpam-617	102	17	∈	∈	PROPN
ejpam-617	102	18	u	u	NOUN
ejpam-617	102	19	)	)	PUNCT
ejpam-617	102	20	.	.	PUNCT
ejpam-617	103	1	(	(	PUNCT
ejpam-617	103	2	25	25	NUM
ejpam-617	103	3	)	)	PUNCT
ejpam-617	103	4	s.	s.	PROPN
ejpam-617	103	5	bansal	bansal	PROPN
ejpam-617	103	6	,	,	PUNCT
ejpam-617	103	7	j.	j.	PROPN
ejpam-617	103	8	dziok	dziok	PROPN
ejpam-617	103	9	,	,	PUNCT
ejpam-617	103	10	p.	p.	NOUN
ejpam-617	103	11	goswami	goswami	PROPN
ejpam-617	103	12	/	/	SYM
ejpam-617	103	13	eur	eur	PROPN
ejpam-617	103	14	.	.	PUNCT
ejpam-617	104	1	j.	j.	PROPN
ejpam-617	104	2	pure	pure	PROPN
ejpam-617	104	3	appl	appl	PROPN
ejpam-617	104	4	.	.	PROPN
ejpam-617	104	5	math	math	PROPN
ejpam-617	104	6	,	,	PUNCT
ejpam-617	104	7	3	3	NUM
ejpam-617	104	8	(	(	PUNCT
ejpam-617	104	9	2010	2010	NUM
ejpam-617	104	10	)	)	PUNCT
ejpam-617	104	11	,	,	PUNCT
ejpam-617	104	12	633	633	NUM
ejpam-617	104	13	-	-	SYM
ejpam-617	104	14	640	640	NUM
ejpam-617	104	15	638	638	NUM
ejpam-617	104	16	in	in	ADP
ejpam-617	104	17	(	(	PUNCT
ejpam-617	104	18	21	21	NUM
ejpam-617	104	19	)	)	PUNCT
ejpam-617	104	20	,	,	PUNCT
ejpam-617	104	21	we	we	PRON
ejpam-617	104	22	obtain	obtain	VERB
ejpam-617	104	23	�	�	PROPN
ejpam-617	104	24	α1	α1	PROPN
ejpam-617	104	25	+	+	CCONJ
ejpam-617	104	26	1	1	NUM
ejpam-617	104	27	a1	a1	NOUN
ejpam-617	104	28	+	+	CCONJ
ejpam-617	104	29	p	p	PROPN
ejpam-617	104	30	�	�	PROPN
ejpam-617	104	31	−	−	PROPN
ejpam-617	104	32	�	�	PROPN
ejpam-617	104	33	α1	α1	PROPN
ejpam-617	104	34	+	+	CCONJ
ejpam-617	104	35	1	1	NUM
ejpam-617	104	36	a1	a1	NOUN
ejpam-617	104	37	�	�	PROPN
ejpam-617	104	38	θ	θ	PROPN
ejpam-617	104	39	l	l	NOUN
ejpam-617	104	40	,	,	PUNCT
ejpam-617	104	41	s	s	PROPN
ejpam-617	104	42	p	p	X
ejpam-617	104	43	(	(	PUNCT
ejpam-617	104	44	α1	α1	PROPN
ejpam-617	104	45	+	+	CCONJ
ejpam-617	104	46	2,a1	2,a1	NUM
ejpam-617	104	47	)	)	SYM
ejpam-617	104	48	f	f	NOUN
ejpam-617	104	49	(	(	PUNCT
ejpam-617	104	50	z	z	NOUN
ejpam-617	105	1	)	)	PUNCT
ejpam-617	105	2	θ	θ	PROPN
ejpam-617	105	3	l	l	NOUN
ejpam-617	105	4	,	,	PUNCT
ejpam-617	105	5	s	s	PROPN
ejpam-617	105	6	p	p	X
ejpam-617	105	7	(	(	PUNCT
ejpam-617	105	8	α1	α1	PROPN
ejpam-617	105	9	+	+	CCONJ
ejpam-617	105	10	1,a1	1,a1	NUM
ejpam-617	105	11	)	)	SYM
ejpam-617	105	12	f	f	NOUN
ejpam-617	105	13	(	(	PUNCT
ejpam-617	105	14	z	z	NOUN
ejpam-617	105	15	)	)	PUNCT
ejpam-617	105	16	=	=	SYM
ejpam-617	105	17	(	(	PUNCT
ejpam-617	105	18	a−	a−	PROPN
ejpam-617	105	19	b−	b−	PROPN
ejpam-617	105	20	α1	α1	PROPN
ejpam-617	105	21	pa1	pa1	PROPN
ejpam-617	105	22	b)zw′(z	b)zw′(z	PROPN
ejpam-617	105	23	)	)	PUNCT
ejpam-617	105	24	α1	α1	PROPN
ejpam-617	105	25	pa1	pa1	NOUN
ejpam-617	105	26	+	+	CCONJ
ejpam-617	105	27	{	{	PUNCT
ejpam-617	105	28	α1	α1	PROPN
ejpam-617	105	29	pa1	pa1	PROPN
ejpam-617	105	30	b+	b+	ADP
ejpam-617	105	31	b−	b−	PROPN
ejpam-617	105	32	a}w(z	a}w(z	NOUN
ejpam-617	105	33	)	)	PUNCT
ejpam-617	105	34	+	+	NUM
ejpam-617	105	35	bzw′(z	bzw′(z	NOUN
ejpam-617	105	36	)	)	PUNCT
ejpam-617	105	37	1	1	NUM
ejpam-617	105	38	+	+	NOUN
ejpam-617	105	39	bw(z	bw(z	NOUN
ejpam-617	105	40	)	)	PUNCT
ejpam-617	106	1	+	+	CCONJ
ejpam-617	106	2	p	p	NOUN
ejpam-617	106	3	1	1	NUM
ejpam-617	106	4	+	+	NUM
ejpam-617	106	5	aw(z	aw(z	VERB
ejpam-617	106	6	)	)	PUNCT
ejpam-617	106	7	1	1	NUM
ejpam-617	106	8	+	+	NUM
ejpam-617	106	9	bw(z	bw(z	NOUN
ejpam-617	106	10	)	)	PUNCT
ejpam-617	106	11	consequently	consequently	ADV
ejpam-617	106	12	,	,	PUNCT
ejpam-617	106	13	we	we	PRON
ejpam-617	106	14	have	have	AUX
ejpam-617	106	15	f(z	f(z	NOUN
ejpam-617	106	16	)	)	PUNCT
ejpam-617	106	17	=	=	PUNCT
ejpam-617	107	1	w(z	w(z	PROPN
ejpam-617	107	2	)	)	PUNCT
ejpam-617	107	3			PROPN
ejpam-617	107	4			PRON
ejpam-617	107	5			NOUN
ejpam-617	107	6	zw′(z	zw′(z	NOUN
ejpam-617	107	7	)	)	PUNCT
ejpam-617	107	8	w(z	w(z	PROPN
ejpam-617	107	9	)	)	PUNCT
ejpam-617	107	10			VERB
ejpam-617	107	11			NOUN
ejpam-617	107	12	a−	a−	NOUN
ejpam-617	107	13	b−	b−	PROPN
ejpam-617	107	14	α1	α1	PROPN
ejpam-617	107	15	pa1	pa1	PROPN
ejpam-617	107	16	b	b	PROPN
ejpam-617	107	17	α1	α1	PROPN
ejpam-617	107	18	pa1	pa1	NOUN
ejpam-617	107	19	+	+	CCONJ
ejpam-617	107	20	{	{	PUNCT
ejpam-617	107	21	α1	α1	PROPN
ejpam-617	107	22	pa1	pa1	PROPN
ejpam-617	107	23	b	b	PROPN
ejpam-617	107	24	+	+	CCONJ
ejpam-617	107	25	b−	b−	PROPN
ejpam-617	107	26	a}w(z	a}w(z	NOUN
ejpam-617	107	27	)	)	PUNCT
ejpam-617	108	1	+	+	SYM
ejpam-617	108	2	b	b	X
ejpam-617	108	3	1	1	NUM
ejpam-617	108	4	+	+	NUM
ejpam-617	108	5	bw(z	bw(z	NOUN
ejpam-617	108	6	)	)	PUNCT
ejpam-617	108	7			PUNCT
ejpam-617	109	1	+	+	X
ejpam-617	109	2	p	p	X
ejpam-617	109	3	(	(	PUNCT
ejpam-617	109	4	a−	a−	PROPN
ejpam-617	109	5	b	b	PROPN
ejpam-617	109	6	)	)	PUNCT
ejpam-617	109	7	1	1	NUM
ejpam-617	109	8	+	+	NUM
ejpam-617	109	9	bw(z	bw(z	NOUN
ejpam-617	109	10	)	)	PUNCT
ejpam-617	109	11			PROPN
ejpam-617	109	12			PROPN
ejpam-617	109	13			NOUN
ejpam-617	109	14	,	,	PUNCT
ejpam-617	109	15	(	(	PUNCT
ejpam-617	109	16	26	26	NUM
ejpam-617	109	17	)	)	PUNCT
ejpam-617	109	18	where	where	SCONJ
ejpam-617	109	19	f(z	f(z	NOUN
ejpam-617	109	20	)	)	PUNCT
ejpam-617	109	21	=	=	SYM
ejpam-617	109	22	�	�	PROPN
ejpam-617	109	23	α1	α1	PROPN
ejpam-617	109	24	+	+	CCONJ
ejpam-617	109	25	1	1	NUM
ejpam-617	109	26	a1	a1	NOUN
ejpam-617	109	27	+	+	CCONJ
ejpam-617	109	28	p	p	PROPN
ejpam-617	109	29	�	�	PROPN
ejpam-617	109	30	−	−	PROPN
ejpam-617	109	31	�	�	PROPN
ejpam-617	109	32	α1	α1	PROPN
ejpam-617	109	33	+	+	CCONJ
ejpam-617	109	34	1	1	NUM
ejpam-617	109	35	a1	a1	NOUN
ejpam-617	109	36	�	�	PROPN
ejpam-617	109	37	h	h	NOUN
ejpam-617	109	38	θ	θ	NOUN
ejpam-617	109	39	l	l	NOUN
ejpam-617	109	40	,	,	PUNCT
ejpam-617	109	41	s	s	PROPN
ejpam-617	109	42	p	p	X
ejpam-617	109	43	(	(	PUNCT
ejpam-617	109	44	α1	α1	PROPN
ejpam-617	109	45	+	+	CCONJ
ejpam-617	109	46	2,a1	2,a1	NUM
ejpam-617	109	47	)	)	SYM
ejpam-617	109	48	f	f	NOUN
ejpam-617	109	49	(	(	PUNCT
ejpam-617	109	50	z	z	NOUN
ejpam-617	109	51	)	)	PUNCT
ejpam-617	109	52	i	i	PRON
ejpam-617	110	1	θ	θ	X
ejpam-617	110	2	l	l	NOUN
ejpam-617	110	3	,	,	PUNCT
ejpam-617	110	4	s	s	PROPN
ejpam-617	110	5	p	p	X
ejpam-617	110	6	(	(	PUNCT
ejpam-617	110	7	α1	α1	PROPN
ejpam-617	110	8	+	+	CCONJ
ejpam-617	110	9	1,a1	1,a1	NUM
ejpam-617	110	10	)	)	SYM
ejpam-617	110	11	f	f	NOUN
ejpam-617	110	12	(	(	PUNCT
ejpam-617	110	13	z	z	NOUN
ejpam-617	110	14	)	)	PUNCT
ejpam-617	110	15	−	−	PROPN
ejpam-617	111	1	p.	p.	NOUN
ejpam-617	111	2	by	by	ADP
ejpam-617	111	3	(	(	PUNCT
ejpam-617	111	4	12	12	NUM
ejpam-617	111	5	)	)	PUNCT
ejpam-617	111	6	,	,	PUNCT
ejpam-617	111	7	(	(	PUNCT
ejpam-617	111	8	17	17	NUM
ejpam-617	111	9	)	)	PUNCT
ejpam-617	111	10	and	and	CCONJ
ejpam-617	111	11	(	(	PUNCT
ejpam-617	111	12	25	25	NUM
ejpam-617	111	13	)	)	PUNCT
ejpam-617	111	14	,	,	PUNCT
ejpam-617	111	15	it	it	PRON
ejpam-617	111	16	is	be	AUX
ejpam-617	111	17	sufficient	sufficient	ADJ
ejpam-617	111	18	to	to	PART
ejpam-617	111	19	verify	verify	VERB
ejpam-617	111	20	that	that	SCONJ
ejpam-617	111	21	w	w	NOUN
ejpam-617	111	22	is	be	AUX
ejpam-617	111	23	analytic	analytic	ADJ
ejpam-617	111	24	in	in	ADP
ejpam-617	111	25	u	u	NOUN
ejpam-617	111	26	and	and	CCONJ
ejpam-617	111	27	|w(z)|	|w(z)|	VERB
ejpam-617	111	28	<	<	X
ejpam-617	111	29	1	1	NUM
ejpam-617	111	30	(	(	PUNCT
ejpam-617	111	31	z	z	NOUN
ejpam-617	111	32	∈	∈	PROPN
ejpam-617	111	33	u	u	NOUN
ejpam-617	111	34	)	)	PUNCT
ejpam-617	111	35	.	.	PUNCT
ejpam-617	112	1	now	now	ADV
ejpam-617	112	2	,	,	PUNCT
ejpam-617	112	3	suppose	suppose	VERB
ejpam-617	112	4	that	that	SCONJ
ejpam-617	112	5	there	there	PRON
ejpam-617	112	6	exists	exist	VERB
ejpam-617	112	7	a	a	DET
ejpam-617	112	8	point	point	NOUN
ejpam-617	112	9	z0	z0	PROPN
ejpam-617	112	10	∈	∈	PROPN
ejpam-617	112	11	u	u	NOUN
ejpam-617	112	12	such	such	ADJ
ejpam-617	112	13	that	that	SCONJ
ejpam-617	112	14	�	�	PROPN
ejpam-617	112	15	�	�	PROPN
ejpam-617	112	16	w(z0	w(z0	NOUN
ejpam-617	112	17	)	)	PUNCT
ejpam-617	112	18	�	�	PROPN
ejpam-617	112	19	�	�	PROPN
ejpam-617	112	20	=	=	SYM
ejpam-617	112	21	1	1	NUM
ejpam-617	112	22	,	,	PUNCT
ejpam-617	112	23	|w(z)|	|w(z)|	VERB
ejpam-617	112	24	<	<	X
ejpam-617	112	25	1	1	NUM
ejpam-617	112	26	(	(	PUNCT
ejpam-617	112	27	|z|	|z|	NOUN
ejpam-617	112	28	<	<	X
ejpam-617	112	29	�	�	PROPN
ejpam-617	112	30	�	�	PROPN
ejpam-617	112	31	z0	z0	PROPN
ejpam-617	112	32	�	�	PROPN
ejpam-617	112	33	�	�	PROPN
ejpam-617	112	34	)	)	PUNCT
ejpam-617	112	35	.	.	PUNCT
ejpam-617	113	1	then	then	ADV
ejpam-617	113	2	,	,	PUNCT
ejpam-617	113	3	applying	apply	VERB
ejpam-617	113	4	lemma	lemma	PROPN
ejpam-617	113	5	2	2	NUM
ejpam-617	113	6	,	,	PUNCT
ejpam-617	113	7	we	we	PRON
ejpam-617	113	8	can	can	AUX
ejpam-617	113	9	write	write	VERB
ejpam-617	113	10	z0w′(z0	z0w′(z0	NOUN
ejpam-617	113	11	)	)	PUNCT
ejpam-617	113	12	=	=	SYM
ejpam-617	113	13	kw(z0	kw(z0	NOUN
ejpam-617	113	14	)	)	PUNCT
ejpam-617	113	15	,	,	PUNCT
ejpam-617	113	16	w(z0	w(z0	NOUN
ejpam-617	113	17	)	)	PUNCT
ejpam-617	114	1	=	=	SYM
ejpam-617	114	2	eiθ	eiθ	PROPN
ejpam-617	114	3	(	(	PUNCT
ejpam-617	114	4	k	k	X
ejpam-617	114	5	≥	≥	NUM
ejpam-617	114	6	1	1	NUM
ejpam-617	114	7	)	)	PUNCT
ejpam-617	114	8	.	.	PUNCT
ejpam-617	115	1	combining	combine	VERB
ejpam-617	115	2	these	these	PRON
ejpam-617	115	3	with	with	ADP
ejpam-617	115	4	(	(	PUNCT
ejpam-617	115	5	26	26	NUM
ejpam-617	115	6	)	)	PUNCT
ejpam-617	115	7	,	,	PUNCT
ejpam-617	115	8	we	we	PRON
ejpam-617	115	9	obtain	obtain	VERB
ejpam-617	115	10	�	�	PROPN
ejpam-617	115	11	�	�	NOUN
ejpam-617	115	12	f(z0	f(z0	NOUN
ejpam-617	115	13	)	)	PUNCT
ejpam-617	115	14	�	�	PROPN
ejpam-617	115	15	�	�	PROPN
ejpam-617	115	16	≥	≥	PROPN
ejpam-617	115	17	kre	kre	PROPN
ejpam-617	115	18			PROPN
ejpam-617	115	19			NOUN
ejpam-617	116	1	a−	a−	PROPN
ejpam-617	116	2	b	b	NOUN
ejpam-617	116	3	−	−	PROPN
ejpam-617	116	4	α1	α1	PROPN
ejpam-617	116	5	pa1	pa1	PROPN
ejpam-617	116	6	b	b	PROPN
ejpam-617	116	7	α1	α1	PROPN
ejpam-617	116	8	pa1	pa1	NOUN
ejpam-617	116	9	+	+	CCONJ
ejpam-617	116	10	{	{	PUNCT
ejpam-617	116	11	α1	α1	PROPN
ejpam-617	116	12	pa1	pa1	PROPN
ejpam-617	116	13	b+	b+	ADP
ejpam-617	116	14	b−	b−	PROPN
ejpam-617	117	1	a}eiθ	a}eiθ	PROPN
ejpam-617	118	1	+	+	CCONJ
ejpam-617	118	2	b	b	SYM
ejpam-617	118	3	1	1	NUM
ejpam-617	118	4	+	+	NUM
ejpam-617	118	5	beiθ	beiθ	ADJ
ejpam-617	118	6			NOUN
ejpam-617	118	7	+	+	NOUN
ejpam-617	119	1	p	p	X
ejpam-617	119	2	(	(	PUNCT
ejpam-617	119	3	a−	a−	PROPN
ejpam-617	119	4	b	b	PROPN
ejpam-617	119	5	)	)	PUNCT
ejpam-617	119	6	1	1	NUM
ejpam-617	119	7	+	+	SYM
ejpam-617	119	8	b	b	NOUN
ejpam-617	119	9	≥	≥	NOUN
ejpam-617	119	10	k	k	PROPN
ejpam-617	119	11			PROPN
ejpam-617	119	12			NOUN
ejpam-617	119	13	a−	a−	PROPN
ejpam-617	119	14	b−	b−	PROPN
ejpam-617	119	15	α1	α1	PROPN
ejpam-617	119	16	pa1	pa1	PROPN
ejpam-617	119	17	b	b	PROPN
ejpam-617	119	18	α1	α1	PROPN
ejpam-617	119	19	pa1	pa1	NOUN
ejpam-617	119	20	+	+	CCONJ
ejpam-617	119	21	a−	a−	PROPN
ejpam-617	119	22	b−	b−	PROPN
ejpam-617	119	23	α1	α1	PROPN
ejpam-617	119	24	pa1	pa1	PROPN
ejpam-617	119	25	b	b	PROPN
ejpam-617	119	26	+	+	CCONJ
ejpam-617	119	27	b	b	PROPN
ejpam-617	119	28	1	1	NUM
ejpam-617	119	29	+	+	NUM
ejpam-617	119	30	b	b	NOUN
ejpam-617	119	31			NOUN
ejpam-617	119	32	+	+	NOUN
ejpam-617	119	33	p	p	X
ejpam-617	119	34	(	(	PUNCT
ejpam-617	119	35	a−	a−	PROPN
ejpam-617	119	36	b	b	PROPN
ejpam-617	119	37	)	)	PUNCT
ejpam-617	119	38	1	1	NUM
ejpam-617	119	39	+	+	NUM
ejpam-617	119	40	b	b	NOUN
ejpam-617	119	41	≥	≥	NOUN
ejpam-617	119	42	a−	a−	PROPN
ejpam-617	119	43	b	b	PROPN
ejpam-617	119	44	−	−	PROPN
ejpam-617	119	45	α1	α1	PROPN
ejpam-617	119	46	pa1	pa1	PROPN
ejpam-617	119	47	b	b	PROPN
ejpam-617	119	48	a−	a−	PROPN
ejpam-617	119	49	b+	b+	ADJ
ejpam-617	119	50	α1	α1	PROPN
ejpam-617	119	51	pa1	pa1	PROPN
ejpam-617	119	52	(	(	PUNCT
ejpam-617	119	53	1−	1−	NUM
ejpam-617	119	54	b	b	NOUN
ejpam-617	119	55	)	)	PUNCT
ejpam-617	120	1	+	+	NUM
ejpam-617	120	2	b	b	X
ejpam-617	120	3	+	+	CCONJ
ejpam-617	120	4	p	p	X
ejpam-617	120	5	(	(	PUNCT
ejpam-617	120	6	a−	a−	PROPN
ejpam-617	120	7	b	b	PROPN
ejpam-617	120	8	)	)	PUNCT
ejpam-617	120	9	1	1	NUM
ejpam-617	120	10	+	+	SYM
ejpam-617	120	11	b	b	NOUN
ejpam-617	120	12	.	.	PUNCT
ejpam-617	121	1	since	since	SCONJ
ejpam-617	121	2	this	this	DET
ejpam-617	121	3	results	result	NOUN
ejpam-617	121	4	contradicts	contradict	VERB
ejpam-617	121	5	(	(	PUNCT
ejpam-617	121	6	24	24	NUM
ejpam-617	121	7	)	)	PUNCT
ejpam-617	121	8	,	,	PUNCT
ejpam-617	121	9	we	we	PRON
ejpam-617	121	10	conclude	conclude	VERB
ejpam-617	121	11	that	that	SCONJ
ejpam-617	121	12	w	w	NOUN
ejpam-617	121	13	is	be	AUX
ejpam-617	121	14	the	the	DET
ejpam-617	121	15	analytic	analytic	ADJ
ejpam-617	121	16	function	function	NOUN
ejpam-617	121	17	in	in	ADP
ejpam-617	121	18	u	u	NOUN
ejpam-617	121	19	and	and	CCONJ
ejpam-617	121	20	|w(z)|	|w(z)|	VERB
ejpam-617	121	21	<	<	X
ejpam-617	121	22	1	1	NUM
ejpam-617	121	23	(	(	PUNCT
ejpam-617	121	24	z	z	NOUN
ejpam-617	121	25	∈	∈	PROPN
ejpam-617	121	26	u	u	PROPN
ejpam-617	121	27	)	)	PUNCT
ejpam-617	121	28	,	,	PUNCT
ejpam-617	121	29	which	which	PRON
ejpam-617	121	30	completes	complete	VERB
ejpam-617	121	31	the	the	DET
ejpam-617	121	32	proof	proof	NOUN
ejpam-617	121	33	of	of	ADP
ejpam-617	121	34	the	the	DET
ejpam-617	121	35	theorem	theorem	NOUN
ejpam-617	121	36	2	2	NUM
ejpam-617	121	37	.	.	PUNCT
ejpam-617	121	38	putting	put	VERB
ejpam-617	121	39	p	p	NOUN
ejpam-617	121	40	=	=	NOUN
ejpam-617	121	41	1	1	NUM
ejpam-617	121	42	,	,	PUNCT
ejpam-617	121	43	a=	a=	PROPN
ejpam-617	121	44	1−α	1−α	NUM
ejpam-617	121	45	,	,	PUNCT
ejpam-617	121	46	and	and	CCONJ
ejpam-617	121	47	b	b	X
ejpam-617	121	48	=	=	SYM
ejpam-617	121	49	0	0	NUM
ejpam-617	121	50	in	in	ADP
ejpam-617	121	51	theorem	theorem	NOUN
ejpam-617	121	52	2	2	NUM
ejpam-617	121	53	,	,	PUNCT
ejpam-617	121	54	we	we	PRON
ejpam-617	121	55	obtain	obtain	VERB
ejpam-617	121	56	the	the	DET
ejpam-617	121	57	following	following	ADJ
ejpam-617	121	58	result	result	NOUN
ejpam-617	121	59	.	.	PUNCT
ejpam-617	122	1	s.	s.	PROPN
ejpam-617	122	2	bansal	bansal	PROPN
ejpam-617	122	3	,	,	PUNCT
ejpam-617	122	4	j.	j.	PROPN
ejpam-617	122	5	dziok	dziok	PROPN
ejpam-617	122	6	,	,	PUNCT
ejpam-617	122	7	p.	p.	NOUN
ejpam-617	122	8	goswami	goswami	PROPN
ejpam-617	122	9	/	/	SYM
ejpam-617	122	10	eur	eur	PROPN
ejpam-617	122	11	.	.	PUNCT
ejpam-617	123	1	j.	j.	PROPN
ejpam-617	123	2	pure	pure	PROPN
ejpam-617	123	3	appl	appl	PROPN
ejpam-617	123	4	.	.	PROPN
ejpam-617	123	5	math	math	PROPN
ejpam-617	123	6	,	,	PUNCT
ejpam-617	123	7	3	3	NUM
ejpam-617	123	8	(	(	PUNCT
ejpam-617	123	9	2010	2010	NUM
ejpam-617	123	10	)	)	PUNCT
ejpam-617	123	11	,	,	PUNCT
ejpam-617	123	12	633	633	NUM
ejpam-617	123	13	-	-	SYM
ejpam-617	123	14	640	640	NUM
ejpam-617	123	15	639	639	NUM
ejpam-617	123	16	corollary	corollary	ADJ
ejpam-617	123	17	1	1	NUM
ejpam-617	123	18	.	.	PUNCT
ejpam-617	124	1	let	let	VERB
ejpam-617	124	2	m	m	PRON
ejpam-617	124	3	∈	∈	VERB
ejpam-617	124	4	n	n	CCONJ
ejpam-617	124	5	,	,	PUNCT
ejpam-617	124	6	0	0	NUM
ejpam-617	124	7	≤	≤	NUM
ejpam-617	124	8	α	α	NOUN
ejpam-617	124	9	<	<	X
ejpam-617	124	10	1	1	NUM
ejpam-617	124	11	and	and	CCONJ
ejpam-617	124	12	α1	α1	PROPN
ejpam-617	124	13	>	>	X
ejpam-617	124	14	a1	a1	PROPN
ejpam-617	124	15	(	(	PUNCT
ejpam-617	124	16	1−α	1−α	NUM
ejpam-617	124	17	)	)	PUNCT
ejpam-617	124	18	.	.	PUNCT
ejpam-617	125	1	if	if	SCONJ
ejpam-617	125	2	a	a	DET
ejpam-617	125	3	function	function	NOUN
ejpam-617	125	4	f	f	PROPN
ejpam-617	125	5	∈	∈	PROPN
ejpam-617	125	6	σ	σ	NOUN
ejpam-617	125	7	satisfies	satisfy	VERB
ejpam-617	125	8	the	the	DET
ejpam-617	125	9	following	follow	VERB
ejpam-617	125	10	inequality	inequality	NOUN
ejpam-617	125	11	:	:	PUNCT
ejpam-617	125	12	�	�	PROPN
ejpam-617	125	13	�	�	PROPN
ejpam-617	125	14	�	�	PROPN
ejpam-617	125	15	�	�	PROPN
ejpam-617	125	16	�	�	PROPN
ejpam-617	125	17	θ	θ	PROPN
ejpam-617	125	18	l	l	NOUN
ejpam-617	125	19	,	,	PUNCT
ejpam-617	125	20	s	s	VERB
ejpam-617	125	21	p	p	X
ejpam-617	125	22	(	(	PUNCT
ejpam-617	125	23	α1+m+	α1+m+	NUM
ejpam-617	125	24	1	1	NUM
ejpam-617	125	25	;	;	PUNCT
ejpam-617	125	26	a1	a1	PROPN
ejpam-617	125	27	)	)	PUNCT
ejpam-617	125	28	f	f	NOUN
ejpam-617	125	29	(	(	PUNCT
ejpam-617	125	30	z	z	NOUN
ejpam-617	126	1	)	)	PUNCT
ejpam-617	126	2	θ	θ	PROPN
ejpam-617	126	3	l	l	NOUN
ejpam-617	126	4	,	,	PUNCT
ejpam-617	126	5	s	s	PROPN
ejpam-617	126	6	p	p	X
ejpam-617	126	7	(	(	PUNCT
ejpam-617	126	8	α1+m	α1+m	PROPN
ejpam-617	126	9	;	;	PUNCT
ejpam-617	126	10	a1	a1	PROPN
ejpam-617	126	11	)	)	PUNCT
ejpam-617	126	12	f	f	NOUN
ejpam-617	126	13	(	(	PUNCT
ejpam-617	126	14	z	z	NOUN
ejpam-617	126	15	)	)	PUNCT
ejpam-617	126	16	−	−	PROPN
ejpam-617	126	17	1	1	NUM
ejpam-617	126	18	�	�	PROPN
ejpam-617	126	19	�	�	PROPN
ejpam-617	126	20	�	�	PROPN
ejpam-617	126	21	�	�	PROPN
ejpam-617	126	22	�	�	PROPN
ejpam-617	126	23	<	<	X
ejpam-617	126	24	(	(	PUNCT
ejpam-617	126	25	1−α	1−α	NUM
ejpam-617	126	26	)	)	PUNCT
ejpam-617	126	27	�	�	PROPN
ejpam-617	126	28	2	2	NUM
ejpam-617	126	29	+	+	NUM
ejpam-617	126	30	α1	α1	PROPN
ejpam-617	126	31	a1	a1	NOUN
ejpam-617	126	32	−α	−α	PROPN
ejpam-617	126	33	�	�	PROPN
ejpam-617	126	34	α1+m	α1+m	PROPN
ejpam-617	126	35	a1	a1	PROPN
ejpam-617	126	36	�	�	PROPN
ejpam-617	126	37	α1	α1	PROPN
ejpam-617	126	38	a1	a1	NOUN
ejpam-617	126	39	+	+	CCONJ
ejpam-617	126	40	1−α	1−α	NUM
ejpam-617	126	41	�	�	PROPN
ejpam-617	126	42	,	,	PUNCT
ejpam-617	126	43	then	then	ADV
ejpam-617	126	44	�	�	PROPN
ejpam-617	126	45	�	�	PROPN
ejpam-617	126	46	�	�	PROPN
ejpam-617	126	47	�	�	PROPN
ejpam-617	126	48	�	�	PROPN
ejpam-617	126	49	α1	α1	PROPN
ejpam-617	126	50	a1	a1	NOUN
ejpam-617	126	51	1−	1−	NUM
ejpam-617	126	52	θ	θ	NOUN
ejpam-617	126	53	l	l	NOUN
ejpam-617	126	54	,	,	PUNCT
ejpam-617	126	55	s	s	PROPN
ejpam-617	126	56	p	p	X
ejpam-617	126	57	(	(	PUNCT
ejpam-617	126	58	α1	α1	PROPN
ejpam-617	126	59	+	+	CCONJ
ejpam-617	126	60	1,a1	1,a1	NUM
ejpam-617	126	61	)	)	SYM
ejpam-617	126	62	f	f	NOUN
ejpam-617	126	63	(	(	PUNCT
ejpam-617	126	64	z	z	NOUN
ejpam-617	126	65	)	)	PUNCT
ejpam-617	126	66	θ	θ	PROPN
ejpam-617	126	67	l	l	NOUN
ejpam-617	126	68	,	,	PUNCT
ejpam-617	126	69	s	s	PART
ejpam-617	126	70	p	p	X
ejpam-617	126	71	(	(	PUNCT
ejpam-617	126	72	α1+,a1	α1+,a1	PROPN
ejpam-617	126	73	)	)	PUNCT
ejpam-617	126	74	f	f	NOUN
ejpam-617	126	75	(	(	PUNCT
ejpam-617	126	76	z	z	NOUN
ejpam-617	126	77	)	)	PUNCT
ejpam-617	126	78	!	!	PUNCT
ejpam-617	127	1	�	�	PROPN
ejpam-617	127	2	�	�	PROPN
ejpam-617	127	3	�	�	PROPN
ejpam-617	127	4	�	�	PROPN
ejpam-617	127	5	�	�	PROPN
ejpam-617	127	6	<	<	X
ejpam-617	127	7	1−α	1−α	NUM
ejpam-617	127	8	.	.	PUNCT
ejpam-617	128	1	putting	put	VERB
ejpam-617	128	2	ai	ai	NOUN
ejpam-617	128	3	=	=	PROPN
ejpam-617	128	4	b	b	PROPN
ejpam-617	128	5	j	j	PROPN
ejpam-617	128	6	=	=	SYM
ejpam-617	128	7	1(i	1(i	NUM
ejpam-617	128	8	=	=	SYM
ejpam-617	128	9	1	1	NUM
ejpam-617	128	10	,	,	PUNCT
ejpam-617	128	11	...	...	PUNCT
ejpam-617	128	12	,	,	PUNCT
ejpam-617	128	13	l	l	NOUN
ejpam-617	128	14	,	,	PUNCT
ejpam-617	128	15	j	j	PROPN
ejpam-617	128	16	=	=	SYM
ejpam-617	128	17	1	1	NUM
ejpam-617	128	18	,	,	PUNCT
ejpam-617	128	19	...	...	PUNCT
ejpam-617	128	20	,	,	PUNCT
ejpam-617	128	21	s	s	X
ejpam-617	128	22	)	)	PUNCT
ejpam-617	128	23	in	in	ADP
ejpam-617	128	24	corollary	corollary	ADJ
ejpam-617	128	25	1	1	NUM
ejpam-617	128	26	,	,	PUNCT
ejpam-617	128	27	we	we	PRON
ejpam-617	128	28	obtain	obtain	VERB
ejpam-617	128	29	the	the	DET
ejpam-617	128	30	following	follow	VERB
ejpam-617	128	31	result	result	NOUN
ejpam-617	128	32	.	.	PUNCT
ejpam-617	129	1	corollary	corollary	ADJ
ejpam-617	129	2	2	2	NUM
ejpam-617	129	3	.	.	PUNCT
ejpam-617	130	1	let	let	VERB
ejpam-617	130	2	m	m	PRON
ejpam-617	130	3	∈	∈	VERB
ejpam-617	130	4	n	n	CCONJ
ejpam-617	130	5	,	,	PUNCT
ejpam-617	130	6	0	0	NUM
ejpam-617	130	7	≤	≤	NUM
ejpam-617	131	1	α	α	NOUN
ejpam-617	131	2	<	<	X
ejpam-617	131	3	1	1	NUM
ejpam-617	131	4	and	and	CCONJ
ejpam-617	131	5	α1	α1	PROPN
ejpam-617	131	6	+	+	CCONJ
ejpam-617	131	7	α	α	X
ejpam-617	131	8	>	>	X
ejpam-617	131	9	1	1	NUM
ejpam-617	131	10	.	.	PUNCT
ejpam-617	132	1	if	if	SCONJ
ejpam-617	132	2	a	a	DET
ejpam-617	132	3	function	function	NOUN
ejpam-617	132	4	f	f	PROPN
ejpam-617	132	5	∈	∈	PROPN
ejpam-617	132	6	σ	σ	NOUN
ejpam-617	132	7	satisfies	satisfy	VERB
ejpam-617	132	8	the	the	DET
ejpam-617	132	9	following	follow	VERB
ejpam-617	132	10	inequality	inequality	NOUN
ejpam-617	132	11	:	:	PUNCT
ejpam-617	132	12	�	�	PROPN
ejpam-617	132	13	�	�	PROPN
ejpam-617	132	14	�	�	PROPN
ejpam-617	132	15	�	�	PROPN
ejpam-617	132	16	h	h	PROPN
ejpam-617	132	17	(	(	PUNCT
ejpam-617	132	18	α1+m+	α1+m+	NUM
ejpam-617	132	19	1	1	NUM
ejpam-617	132	20	)	)	PUNCT
ejpam-617	132	21	f	f	NOUN
ejpam-617	132	22	(	(	PUNCT
ejpam-617	132	23	z	z	NOUN
ejpam-617	132	24	)	)	PUNCT
ejpam-617	132	25	h	h	NOUN
ejpam-617	132	26	(	(	PUNCT
ejpam-617	132	27	α1	α1	PROPN
ejpam-617	132	28	+	+	PROPN
ejpam-617	132	29	m	m	NOUN
ejpam-617	132	30	)	)	PUNCT
ejpam-617	132	31	f	f	PROPN
ejpam-617	132	32	(	(	PUNCT
ejpam-617	132	33	z	z	NOUN
ejpam-617	132	34	)	)	PUNCT
ejpam-617	132	35	−	−	PROPN
ejpam-617	132	36	1	1	NUM
ejpam-617	132	37	�	�	PROPN
ejpam-617	132	38	�	�	PROPN
ejpam-617	132	39	�	�	PROPN
ejpam-617	132	40	�	�	PROPN
ejpam-617	132	41	<	<	X
ejpam-617	132	42	(	(	PUNCT
ejpam-617	132	43	1−α	1−α	NUM
ejpam-617	132	44	)	)	PUNCT
ejpam-617	132	45	�	�	PROPN
ejpam-617	132	46	2+α1	2+α1	NUM
ejpam-617	132	47	−α	−α	PROPN
ejpam-617	132	48	�	�	PROPN
ejpam-617	132	49	�	�	PROPN
ejpam-617	132	50	α1	α1	PROPN
ejpam-617	133	1	+	+	PROPN
ejpam-617	133	2	m	m	PROPN
ejpam-617	133	3	�	�	PROPN
ejpam-617	133	4	�	�	PROPN
ejpam-617	133	5	α1	α1	PROPN
ejpam-617	133	6	+	+	CCONJ
ejpam-617	133	7	1−α	1−α	NUM
ejpam-617	133	8	�	�	PROPN
ejpam-617	134	1	,	,	PUNCT
ejpam-617	134	2	then	then	ADV
ejpam-617	134	3	�	�	PROPN
ejpam-617	134	4	�	�	PROPN
ejpam-617	134	5	�	�	PROPN
ejpam-617	134	6	�	�	PROPN
ejpam-617	134	7	α1	α1	PROPN
ejpam-617	134	8	+	+	CCONJ
ejpam-617	134	9	1−α1	1−α1	NUM
ejpam-617	134	10	h	h	NOUN
ejpam-617	134	11	(	(	PUNCT
ejpam-617	134	12	α1	α1	PROPN
ejpam-617	134	13	+	+	CCONJ
ejpam-617	134	14	1	1	NUM
ejpam-617	134	15	)	)	PUNCT
ejpam-617	134	16	f	f	NOUN
ejpam-617	134	17	(	(	PUNCT
ejpam-617	134	18	z	z	NOUN
ejpam-617	134	19	)	)	PUNCT
ejpam-617	134	20	h	h	NOUN
ejpam-617	134	21	(	(	PUNCT
ejpam-617	134	22	α1	α1	PROPN
ejpam-617	134	23	)	)	PUNCT
ejpam-617	134	24	f	f	NOUN
ejpam-617	134	25	(	(	PUNCT
ejpam-617	134	26	z	z	NOUN
ejpam-617	134	27	)	)	PUNCT
ejpam-617	134	28	�	�	PROPN
ejpam-617	134	29	�	�	PROPN
ejpam-617	134	30	�	�	PROPN
ejpam-617	134	31	�	�	PROPN
ejpam-617	134	32	<	<	X
ejpam-617	134	33	1−α	1−α	NUM
ejpam-617	134	34	.	.	PUNCT
ejpam-617	135	1	putting	put	VERB
ejpam-617	135	2	l	l	NOUN
ejpam-617	135	3	=	=	SYM
ejpam-617	135	4	2	2	NUM
ejpam-617	135	5	,	,	PUNCT
ejpam-617	135	6	s	s	VERB
ejpam-617	135	7	=	=	X
ejpam-617	135	8	p	p	NOUN
ejpam-617	135	9	=	=	NOUN
ejpam-617	135	10	a1	a1	NOUN
ejpam-617	135	11	=	=	PROPN
ejpam-617	135	12	a2	a2	PROPN
ejpam-617	135	13	=	=	SYM
ejpam-617	135	14	b1	b1	PROPN
ejpam-617	135	15	=	=	SYM
ejpam-617	135	16	1	1	NUM
ejpam-617	135	17	,	,	PUNCT
ejpam-617	135	18	and	and	CCONJ
ejpam-617	135	19	α2	α2	NOUN
ejpam-617	135	20	=	=	SYM
ejpam-617	135	21	1	1	NUM
ejpam-617	135	22	in	in	ADP
ejpam-617	135	23	theorems	theorem	NOUN
ejpam-617	135	24	1	1	NUM
ejpam-617	135	25	and	and	CCONJ
ejpam-617	135	26	2	2	NUM
ejpam-617	135	27	,	,	PUNCT
ejpam-617	135	28	we	we	PRON
ejpam-617	135	29	get	get	VERB
ejpam-617	135	30	the	the	DET
ejpam-617	135	31	following	follow	VERB
ejpam-617	135	32	two	two	NUM
ejpam-617	135	33	results	result	NOUN
ejpam-617	135	34	:	:	PUNCT
ejpam-617	135	35	corollary	corollary	ADJ
ejpam-617	135	36	3	3	X
ejpam-617	135	37	.	.	PUNCT
ejpam-617	136	1	let	let	VERB
ejpam-617	136	2	m	m	PRON
ejpam-617	136	3	∈	∈	PROPN
ejpam-617	136	4	n	n	CCONJ
ejpam-617	136	5	,	,	PUNCT
ejpam-617	136	6	α1	α1	PROPN
ejpam-617	136	7	(	(	PUNCT
ejpam-617	136	8	1	1	NUM
ejpam-617	136	9	+	+	NUM
ejpam-617	136	10	b	b	NOUN
ejpam-617	136	11	)	)	PUNCT
ejpam-617	136	12	>	>	X
ejpam-617	137	1	(	(	PUNCT
ejpam-617	137	2	a−	a−	PROPN
ejpam-617	137	3	b	b	PROPN
ejpam-617	137	4	)	)	PUNCT
ejpam-617	137	5	.	.	PUNCT
ejpam-617	138	1	if	if	SCONJ
ejpam-617	138	2	a	a	DET
ejpam-617	138	3	function	function	NOUN
ejpam-617	138	4	f	f	PROPN
ejpam-617	138	5	∈	∈	PROPN
ejpam-617	138	6	σ	σ	NOUN
ejpam-617	138	7	satisfies	satisfy	VERB
ejpam-617	138	8	the	the	DET
ejpam-617	138	9	following	follow	VERB
ejpam-617	138	10	condition	condition	NOUN
ejpam-617	138	11	:	:	PUNCT
ejpam-617	138	12	(	(	PUNCT
ejpam-617	138	13	α1	α1	PROPN
ejpam-617	138	14	+	+	PROPN
ejpam-617	138	15	m+	m+	PROPN
ejpam-617	138	16	1)−	1)−	PROPN
ejpam-617	138	17	(	(	PUNCT
ejpam-617	138	18	α1+m	α1+m	PROPN
ejpam-617	138	19	)	)	PUNCT
ejpam-617	138	20	l	l	NOUN
ejpam-617	138	21	(	(	PUNCT
ejpam-617	138	22	α1	α1	PROPN
ejpam-617	138	23	+	+	PROPN
ejpam-617	138	24	m+	m+	NUM
ejpam-617	138	25	1,β1	1,β1	NUM
ejpam-617	138	26	)	)	PUNCT
ejpam-617	138	27	f	f	PROPN
ejpam-617	138	28	(	(	PUNCT
ejpam-617	138	29	z	z	NOUN
ejpam-617	138	30	)	)	PUNCT
ejpam-617	138	31	l	l	NOUN
ejpam-617	138	32	(	(	PUNCT
ejpam-617	138	33	α1	α1	PROPN
ejpam-617	138	34	+	+	PROPN
ejpam-617	138	35	m	m	PROPN
ejpam-617	138	36	,	,	PUNCT
ejpam-617	138	37	β1	β1	PROPN
ejpam-617	138	38	)	)	PUNCT
ejpam-617	139	1	f	f	PROPN
ejpam-617	139	2	(	(	PUNCT
ejpam-617	139	3	z	z	NOUN
ejpam-617	139	4	)	)	PUNCT
ejpam-617	139	5	≺	≺	NOUN
ejpam-617	139	6	1	1	NUM
ejpam-617	139	7	+	+	NUM
ejpam-617	139	8	az	az	PROPN
ejpam-617	139	9	1	1	NUM
ejpam-617	139	10	+	+	CCONJ
ejpam-617	139	11	bz	bz	PROPN
ejpam-617	139	12	,	,	PUNCT
ejpam-617	139	13	then	then	ADV
ejpam-617	139	14	(	(	PUNCT
ejpam-617	139	15	α1	α1	PROPN
ejpam-617	139	16	+	+	CCONJ
ejpam-617	139	17	1)−α1	1)−α1	NUM
ejpam-617	139	18	l	l	NOUN
ejpam-617	139	19	(	(	PUNCT
ejpam-617	139	20	α1	α1	PROPN
ejpam-617	139	21	+	+	CCONJ
ejpam-617	139	22	1,β1	1,β1	NUM
ejpam-617	139	23	)	)	PUNCT
ejpam-617	139	24	f	f	PROPN
ejpam-617	139	25	(	(	PUNCT
ejpam-617	139	26	z	z	NOUN
ejpam-617	139	27	)	)	PUNCT
ejpam-617	139	28	l	l	NOUN
ejpam-617	139	29	(	(	PUNCT
ejpam-617	139	30	α1,β1	α1,β1	PROPN
ejpam-617	139	31	)	)	PUNCT
ejpam-617	139	32	f	f	NOUN
ejpam-617	139	33	(	(	PUNCT
ejpam-617	139	34	z	z	NOUN
ejpam-617	139	35	)	)	PUNCT
ejpam-617	139	36	≺	≺	NOUN
ejpam-617	139	37	1	1	NUM
ejpam-617	139	38	+	+	NUM
ejpam-617	139	39	az	az	PROPN
ejpam-617	139	40	1	1	NUM
ejpam-617	139	41	+	+	CCONJ
ejpam-617	139	42	bz	bz	PROPN
ejpam-617	139	43	.	.	PUNCT
ejpam-617	140	1	corollary	corollary	ADJ
ejpam-617	140	2	4	4	NUM
ejpam-617	140	3	.	.	PUNCT
ejpam-617	141	1	let	let	VERB
ejpam-617	141	2	m	m	PRON
ejpam-617	141	3	∈	∈	PROPN
ejpam-617	141	4	n	n	CCONJ
ejpam-617	141	5	,	,	PUNCT
ejpam-617	141	6	α1	α1	PROPN
ejpam-617	141	7	(	(	PUNCT
ejpam-617	141	8	1	1	NUM
ejpam-617	141	9	+	+	NUM
ejpam-617	141	10	b	b	NOUN
ejpam-617	141	11	)	)	PUNCT
ejpam-617	141	12	>	>	PUNCT
ejpam-617	141	13	a−	a−	PROPN
ejpam-617	141	14	b	b	PROPN
ejpam-617	141	15	and	and	CCONJ
ejpam-617	141	16	2	2	NUM
ejpam-617	141	17	�	�	PROPN
ejpam-617	141	18	α1	α1	PROPN
ejpam-617	141	19	+	+	PROPN
ejpam-617	141	20	m−	m−	PROPN
ejpam-617	141	21	1	1	NUM
ejpam-617	141	22	�	�	PROPN
ejpam-617	141	23	b2	b2	NOUN
ejpam-617	141	24	≤	≤	NOUN
ejpam-617	141	25	(	(	PUNCT
ejpam-617	141	26	a−	a−	PROPN
ejpam-617	141	27	b)(2b	b)(2b	PROPN
ejpam-617	141	28	+	+	PROPN
ejpam-617	141	29	1	1	NUM
ejpam-617	141	30	)	)	PUNCT
ejpam-617	141	31	,	,	PUNCT
ejpam-617	141	32	if	if	SCONJ
ejpam-617	141	33	a	a	DET
ejpam-617	141	34	function	function	NOUN
ejpam-617	141	35	f	f	PROPN
ejpam-617	141	36	∈	∈	PROPN
ejpam-617	141	37	σ	σ	NOUN
ejpam-617	141	38	satisfies	satisfy	VERB
ejpam-617	141	39	the	the	DET
ejpam-617	141	40	inequality	inequality	NOUN
ejpam-617	141	41	:	:	PUNCT
ejpam-617	141	42	�	�	PROPN
ejpam-617	141	43	α1+m	α1+m	PROPN
ejpam-617	141	44	�	�	PROPN
ejpam-617	141	45	�	�	PROPN
ejpam-617	141	46	�	�	PROPN
ejpam-617	141	47	�	�	PROPN
ejpam-617	141	48	�	�	PROPN
ejpam-617	141	49	l	l	PROPN
ejpam-617	141	50	(	(	PUNCT
ejpam-617	141	51	α1+m+	α1+m+	NUM
ejpam-617	141	52	1,β1	1,β1	NUM
ejpam-617	141	53	)	)	PUNCT
ejpam-617	141	54	f	f	PROPN
ejpam-617	141	55	(	(	PUNCT
ejpam-617	141	56	z	z	NOUN
ejpam-617	141	57	)	)	PUNCT
ejpam-617	141	58	l	l	NOUN
ejpam-617	141	59	(	(	PUNCT
ejpam-617	141	60	α1	α1	PROPN
ejpam-617	141	61	+	+	PROPN
ejpam-617	141	62	m	m	PROPN
ejpam-617	141	63	,	,	PUNCT
ejpam-617	141	64	β1	β1	PROPN
ejpam-617	141	65	)	)	PUNCT
ejpam-617	142	1	f	f	PROPN
ejpam-617	142	2	(	(	PUNCT
ejpam-617	142	3	z	z	NOUN
ejpam-617	142	4	)	)	PUNCT
ejpam-617	142	5	−	−	PROPN
ejpam-617	142	6	1	1	NUM
ejpam-617	142	7	�	�	PROPN
ejpam-617	142	8	�	�	PROPN
ejpam-617	142	9	�	�	PROPN
ejpam-617	142	10	�	�	PROPN
ejpam-617	142	11	<	<	X
ejpam-617	142	12	a−	a−	PROPN
ejpam-617	142	13	b	b	PROPN
ejpam-617	142	14	−α1b	−α1b	NUM
ejpam-617	142	15	a−	a−	PROPN
ejpam-617	142	16	b+α1	b+α1	NOUN
ejpam-617	142	17	(	(	PUNCT
ejpam-617	142	18	1−	1−	NUM
ejpam-617	142	19	b	b	NOUN
ejpam-617	142	20	)	)	PUNCT
ejpam-617	143	1	+	+	CCONJ
ejpam-617	143	2	a	a	DET
ejpam-617	143	3	1	1	NUM
ejpam-617	143	4	+	+	SYM
ejpam-617	143	5	b	b	NOUN
ejpam-617	143	6	(	(	PUNCT
ejpam-617	143	7	z	z	NOUN
ejpam-617	143	8	∈	∈	PROPN
ejpam-617	143	9	u	u	NOUN
ejpam-617	143	10	)	)	PUNCT
ejpam-617	143	11	,	,	PUNCT
ejpam-617	143	12	then	then	ADV
ejpam-617	143	13	α1	α1	PROPN
ejpam-617	143	14	+	+	CCONJ
ejpam-617	143	15	1−α1	1−α1	NUM
ejpam-617	143	16	l	l	NOUN
ejpam-617	143	17	(	(	PUNCT
ejpam-617	143	18	α1	α1	PROPN
ejpam-617	143	19	+	+	CCONJ
ejpam-617	143	20	1,β1	1,β1	NUM
ejpam-617	143	21	)	)	PUNCT
ejpam-617	143	22	f	f	PROPN
ejpam-617	143	23	(	(	PUNCT
ejpam-617	143	24	z	z	NOUN
ejpam-617	143	25	)	)	PUNCT
ejpam-617	143	26	l	l	NOUN
ejpam-617	143	27	(	(	PUNCT
ejpam-617	143	28	α1,β1	α1,β1	PROPN
ejpam-617	143	29	)	)	PUNCT
ejpam-617	143	30	f	f	NOUN
ejpam-617	143	31	(	(	PUNCT
ejpam-617	143	32	z	z	NOUN
ejpam-617	143	33	)	)	PUNCT
ejpam-617	143	34	≺	≺	NOUN
ejpam-617	143	35	1+az	1+az	PUNCT
ejpam-617	143	36	1	1	NUM
ejpam-617	143	37	+	+	CCONJ
ejpam-617	143	38	bz	bz	PROPN
ejpam-617	143	39	.	.	PUNCT
ejpam-617	144	1	putting	put	VERB
ejpam-617	144	2	α1	α1	PROPN
ejpam-617	144	3	=	=	SYM
ejpam-617	144	4	β1	β1	PROPN
ejpam-617	144	5	=	=	PUNCT
ejpam-617	144	6	m	m	NOUN
ejpam-617	144	7	=	=	NOUN
ejpam-617	144	8	1	1	NUM
ejpam-617	144	9	in	in	ADP
ejpam-617	144	10	corollary	corollary	ADJ
ejpam-617	144	11	4	4	NUM
ejpam-617	144	12	we	we	PRON
ejpam-617	144	13	obtain	obtain	VERB
ejpam-617	144	14	the	the	DET
ejpam-617	144	15	sufficient	sufficient	ADJ
ejpam-617	144	16	conditions	condition	NOUN
ejpam-617	144	17	for	for	ADP
ejpam-617	144	18	starlikeness	starlikeness	NOUN
ejpam-617	144	19	.	.	PUNCT
ejpam-617	145	1	references	reference	NOUN
ejpam-617	145	2	640	640	NUM
ejpam-617	145	3	corollary	corollary	ADJ
ejpam-617	145	4	5	5	NUM
ejpam-617	145	5	.	.	PUNCT
ejpam-617	146	1	let	let	VERB
ejpam-617	146	2	2b2	2b2	NUM
ejpam-617	146	3	≤	≤	NUM
ejpam-617	146	4	(	(	PUNCT
ejpam-617	146	5	a−	a−	PROPN
ejpam-617	146	6	b)(2b+	b)(2b+	PROPN
ejpam-617	146	7	1	1	NUM
ejpam-617	146	8	)	)	PUNCT
ejpam-617	146	9	.	.	PUNCT
ejpam-617	147	1	if	if	SCONJ
ejpam-617	147	2	a	a	DET
ejpam-617	147	3	function	function	NOUN
ejpam-617	147	4	f	f	PROPN
ejpam-617	147	5	∈	∈	PROPN
ejpam-617	147	6	σ	σ	NOUN
ejpam-617	147	7	satisfies	satisfy	VERB
ejpam-617	147	8	the	the	DET
ejpam-617	147	9	inequality	inequality	NOUN
ejpam-617	147	10	:	:	PUNCT
ejpam-617	147	11	|	|	ADV
ejpam-617	147	12	z2	z2	PROPN
ejpam-617	147	13	f	f	PROPN
ejpam-617	147	14	′′(z	′′(z	PROPN
ejpam-617	147	15	)	)	PUNCT
ejpam-617	147	16	+	+	NUM
ejpam-617	147	17	4z	4z	NOUN
ejpam-617	147	18	f	f	PROPN
ejpam-617	147	19	′(z	′(z	NOUN
ejpam-617	147	20	)	)	PUNCT
ejpam-617	148	1	+	+	CCONJ
ejpam-617	148	2	2	2	NUM
ejpam-617	148	3	f	f	NOUN
ejpam-617	148	4	(	(	PUNCT
ejpam-617	148	5	z	z	NOUN
ejpam-617	148	6	)	)	PUNCT
ejpam-617	148	7	2	2	NUM
ejpam-617	148	8	�	�	PROPN
ejpam-617	148	9	z	z	PROPN
ejpam-617	148	10	f	f	PROPN
ejpam-617	148	11	′(z	′(z	NOUN
ejpam-617	148	12	)	)	PUNCT
ejpam-617	148	13	+	+	CCONJ
ejpam-617	148	14	2	2	NUM
ejpam-617	148	15	f	f	NOUN
ejpam-617	148	16	(	(	PUNCT
ejpam-617	148	17	z	z	NOUN
ejpam-617	148	18	)	)	PUNCT
ejpam-617	148	19	�	�	PROPN
ejpam-617	149	1	|	|	ADV
ejpam-617	149	2	<	<	X
ejpam-617	149	3	a−	a−	PROPN
ejpam-617	149	4	2b	2b	NUM
ejpam-617	149	5	1	1	NUM
ejpam-617	149	6	+	+	NUM
ejpam-617	149	7	a−	a−	PROPN
ejpam-617	149	8	2b	2b	NOUN
ejpam-617	149	9	+	+	CCONJ
ejpam-617	149	10	a	a	DET
ejpam-617	149	11	1	1	NUM
ejpam-617	149	12	+	+	SYM
ejpam-617	149	13	b	b	NOUN
ejpam-617	149	14	(	(	PUNCT
ejpam-617	149	15	z	z	NOUN
ejpam-617	149	16	∈	∈	PROPN
ejpam-617	149	17	u	u	PROPN
ejpam-617	149	18	)	)	PUNCT
ejpam-617	149	19	,	,	PUNCT
ejpam-617	149	20	then	then	ADV
ejpam-617	149	21	−z	−z	PROPN
ejpam-617	149	22	f	f	PROPN
ejpam-617	149	23	′(z	′(z	NOUN
ejpam-617	149	24	)	)	PUNCT
ejpam-617	149	25	f	f	PROPN
ejpam-617	149	26	(	(	PUNCT
ejpam-617	149	27	z	z	NOUN
ejpam-617	149	28	)	)	PUNCT
ejpam-617	149	29	≺	≺	NOUN
ejpam-617	149	30	1	1	NUM
ejpam-617	149	31	+	+	NUM
ejpam-617	149	32	az	az	PROPN
ejpam-617	149	33	1	1	NUM
ejpam-617	149	34	+	+	CCONJ
ejpam-617	149	35	bz	bz	PROPN
ejpam-617	149	36	,	,	PUNCT
ejpam-617	149	37	i.e.	i.e.	X
ejpam-617	149	38	,	,	PUNCT
ejpam-617	149	39	the	the	DET
ejpam-617	149	40	function	function	NOUN
ejpam-617	149	41	f	f	PROPN
ejpam-617	149	42	is	be	AUX
ejpam-617	149	43	starlike	starlike	NOUN
ejpam-617	149	44	in	in	ADP
ejpam-617	149	45	u	u	PROPN
ejpam-617	149	46	.	.	PUNCT
ejpam-617	150	1	acknowledgements	acknowledgement	VERB
ejpam-617	150	2	the	the	DET
ejpam-617	150	3	authors	author	NOUN
ejpam-617	150	4	s.k	s.k	PROPN
ejpam-617	150	5	.	.	PROPN
ejpam-617	150	6	bansal	bansal	NOUN
ejpam-617	150	7	and	and	CCONJ
ejpam-617	150	8	p.	p.	PROPN
ejpam-617	150	9	goswami	goswami	PROPN
ejpam-617	150	10	are	be	AUX
ejpam-617	150	11	thankful	thankful	ADJ
ejpam-617	150	12	to	to	ADP
ejpam-617	150	13	professor	professor	PROPN
ejpam-617	150	14	s.	s.	PROPN
ejpam-617	150	15	p.	p.	PROPN
ejpam-617	150	16	goyal	goyal	PROPN
ejpam-617	150	17	,	,	PUNCT
ejpam-617	150	18	university	university	NOUN
ejpam-617	150	19	of	of	ADP
ejpam-617	150	20	rajasthan	rajasthan	PROPN
ejpam-617	150	21	,	,	PUNCT
ejpam-617	150	22	jaipur	jaipur	NOUN
ejpam-617	150	23	for	for	ADP
ejpam-617	150	24	his	his	PRON
ejpam-617	150	25	valuable	valuable	ADJ
ejpam-617	150	26	help	help	NOUN
ejpam-617	150	27	and	and	CCONJ
ejpam-617	150	28	constant	constant	ADJ
ejpam-617	150	29	encouragement	encouragement	NOUN
ejpam-617	150	30	.	.	PUNCT
ejpam-617	151	1	references	reference	NOUN
ejpam-617	151	2	[	[	X
ejpam-617	151	3	1	1	X
ejpam-617	151	4	]	]	X
ejpam-617	151	5	m.k	m.k	PROPN
ejpam-617	151	6	.	.	PROPN
ejpam-617	151	7	aouf	aouf	PROPN
ejpam-617	151	8	and	and	CCONJ
ejpam-617	151	9	j.	j.	PROPN
ejpam-617	151	10	dziok	dziok	PROPN
ejpam-617	151	11	,	,	PUNCT
ejpam-617	151	12	distortion	distortion	NOUN
ejpam-617	151	13	and	and	CCONJ
ejpam-617	151	14	convolutional	convolutional	ADJ
ejpam-617	151	15	theorems	theorem	NOUN
ejpam-617	151	16	for	for	ADP
ejpam-617	151	17	operators	operator	NOUN
ejpam-617	151	18	of	of	ADP
ejpam-617	151	19	generalized	generalized	ADJ
ejpam-617	151	20	fractional	fractional	ADJ
ejpam-617	151	21	calculus	calculus	NOUN
ejpam-617	151	22	involving	involve	VERB
ejpam-617	151	23	wright	wright	PROPN
ejpam-617	151	24	function	function	PROPN
ejpam-617	151	25	.	.	PUNCT
ejpam-617	152	1	j.	j.	PROPN
ejpam-617	152	2	appl	appl	PROPN
ejpam-617	152	3	.	.	PROPN
ejpam-617	153	1	anal	anal	PROPN
ejpam-617	153	2	.	.	PUNCT
ejpam-617	154	1	14	14	NUM
ejpam-617	154	2	,	,	PUNCT
ejpam-617	154	3	183	183	NUM
ejpam-617	154	4	-	-	SYM
ejpam-617	154	5	192	192	NUM
ejpam-617	154	6	.	.	PUNCT
ejpam-617	154	7	2008	2008	NUM
ejpam-617	154	8	.	.	PUNCT
ejpam-617	155	1	[	[	X
ejpam-617	155	2	2	2	X
ejpam-617	155	3	]	]	PUNCT
ejpam-617	155	4	j.	j.	PROPN
ejpam-617	155	5	dziok	dziok	PROPN
ejpam-617	155	6	and	and	CCONJ
ejpam-617	155	7	r.	r.	PROPN
ejpam-617	155	8	k.	k.	PROPN
ejpam-617	155	9	raina	raina	PROPN
ejpam-617	155	10	,	,	PUNCT
ejpam-617	155	11	families	family	NOUN
ejpam-617	155	12	of	of	ADP
ejpam-617	155	13	analytic	analytic	ADJ
ejpam-617	155	14	functions	function	NOUN
ejpam-617	155	15	associated	associate	VERB
ejpam-617	155	16	with	with	ADP
ejpam-617	155	17	the	the	DET
ejpam-617	155	18	wright	wright	PROPN
ejpam-617	155	19	generalized	generalize	VERB
ejpam-617	155	20	hypergeometric	hypergeometric	ADJ
ejpam-617	155	21	function	function	NOUN
ejpam-617	155	22	,	,	PUNCT
ejpam-617	155	23	demonstratio	demonstratio	PROPN
ejpam-617	155	24	math	math	PROPN
ejpam-617	155	25	.	.	PUNCT
ejpam-617	156	1	37	37	NUM
ejpam-617	156	2	,	,	PUNCT
ejpam-617	156	3	533	533	NUM
ejpam-617	156	4	-	-	SYM
ejpam-617	156	5	542	542	NUM
ejpam-617	156	6	.	.	PUNCT
ejpam-617	157	1	2004	2004	NUM
ejpam-617	157	2	.	.	PUNCT
ejpam-617	158	1	[	[	X
ejpam-617	158	2	3	3	X
ejpam-617	158	3	]	]	X
ejpam-617	158	4	j.	j.	PROPN
ejpam-617	158	5	dziok	dziok	PROPN
ejpam-617	158	6	,	,	PUNCT
ejpam-617	158	7	r.k	r.k	PROPN
ejpam-617	158	8	.	.	PROPN
ejpam-617	158	9	raina	raina	PROPN
ejpam-617	158	10	and	and	CCONJ
ejpam-617	158	11	h.	h.	PROPN
ejpam-617	158	12	m.	m.	PROPN
ejpam-617	158	13	srivastava	srivastava	PROPN
ejpam-617	158	14	,	,	PUNCT
ejpam-617	158	15	some	some	DET
ejpam-617	158	16	classes	class	NOUN
ejpam-617	158	17	of	of	ADP
ejpam-617	158	18	analytic	analytic	ADJ
ejpam-617	158	19	functions	function	NOUN
ejpam-617	158	20	associated	associate	VERB
ejpam-617	158	21	with	with	ADP
ejpam-617	158	22	operators	operator	NOUN
ejpam-617	158	23	on	on	ADP
ejpam-617	158	24	hilbert	hilbert	NOUN
ejpam-617	158	25	space	space	NOUN
ejpam-617	158	26	involving	involve	VERB
ejpam-617	158	27	wright	wright	PROPN
ejpam-617	158	28	’s	’s	PART
ejpam-617	158	29	generalized	generalize	VERB
ejpam-617	158	30	hypergeometric	hypergeometric	ADJ
ejpam-617	158	31	function	function	NOUN
ejpam-617	158	32	,	,	PUNCT
ejpam-617	158	33	proc	proc	NOUN
ejpam-617	158	34	.	.	PUNCT
ejpam-617	159	1	jangjeon	jangjeon	PROPN
ejpam-617	159	2	math	math	PROPN
ejpam-617	159	3	.	.	PUNCT
ejpam-617	160	1	soc	soc	PROPN
ejpam-617	160	2	.	.	PUNCT
ejpam-617	161	1	7	7	NUM
ejpam-617	161	2	,	,	PUNCT
ejpam-617	161	3	43	43	NUM
ejpam-617	161	4	-	-	SYM
ejpam-617	161	5	55	55	NUM
ejpam-617	161	6	.	.	PUNCT
ejpam-617	162	1	2004	2004	NUM
ejpam-617	162	2	.	.	PUNCT
ejpam-617	163	1	[	[	X
ejpam-617	163	2	4	4	NUM
ejpam-617	163	3	]	]	X
ejpam-617	163	4	p.j	p.j	PROPN
ejpam-617	163	5	.	.	PROPN
ejpam-617	163	6	eenigenburg	eenigenburg	PROPN
ejpam-617	163	7	,	,	PUNCT
ejpam-617	163	8	s.s.miller	s.s.miller	PROPN
ejpam-617	163	9	,	,	PUNCT
ejpam-617	163	10	p.t	p.t	PROPN
ejpam-617	163	11	.	.	PROPN
ejpam-617	163	12	mocanu	mocanu	PROPN
ejpam-617	163	13	and	and	CCONJ
ejpam-617	163	14	o.m	o.m	PROPN
ejpam-617	163	15	.	.	PROPN
ejpam-617	163	16	reade	reade	PROPN
ejpam-617	163	17	,	,	PUNCT
ejpam-617	163	18	second	second	ADJ
ejpam-617	163	19	order	order	NOUN
ejpam-617	163	20	differential	differential	ADJ
ejpam-617	163	21	inequalities	inequality	NOUN
ejpam-617	163	22	in	in	ADP
ejpam-617	163	23	the	the	DET
ejpam-617	163	24	complex	complex	ADJ
ejpam-617	163	25	plane	plane	NOUN
ejpam-617	163	26	,	,	PUNCT
ejpam-617	163	27	j.	j.	PROPN
ejpam-617	163	28	math	math	PROPN
ejpam-617	163	29	.	.	PUNCT
ejpam-617	164	1	anal	anal	PROPN
ejpam-617	164	2	.	.	PUNCT
ejpam-617	165	1	appl	appl	PROPN
ejpam-617	165	2	.	.	PROPN
ejpam-617	166	1	65	65	NUM
ejpam-617	166	2	,	,	PUNCT
ejpam-617	166	3	289–305	289–305	NUM
ejpam-617	166	4	.	.	PUNCT
ejpam-617	167	1	1978	1978	NUM
ejpam-617	167	2	.	.	PUNCT
ejpam-617	168	1	[	[	X
ejpam-617	168	2	5	5	NUM
ejpam-617	168	3	]	]	PUNCT
ejpam-617	168	4	i.	i.	PROPN
ejpam-617	168	5	s.	s.	PROPN
ejpam-617	168	6	jack	jack	PROPN
ejpam-617	168	7	,	,	PUNCT
ejpam-617	168	8	functions	function	NOUN
ejpam-617	168	9	starlike	starlike	NOUN
ejpam-617	168	10	and	and	CCONJ
ejpam-617	168	11	convex	convex	NOUN
ejpam-617	168	12	of	of	ADP
ejpam-617	168	13	order	order	NOUN
ejpam-617	168	14	α	α	NOUN
ejpam-617	168	15	,	,	PUNCT
ejpam-617	168	16	j.	j.	PROPN
ejpam-617	168	17	london	london	PROPN
ejpam-617	168	18	math	math	PROPN
ejpam-617	168	19	.	.	PUNCT
ejpam-617	169	1	soc	soc	PROPN
ejpam-617	169	2	.	.	PUNCT
ejpam-617	170	1	2	2	NUM
ejpam-617	170	2	,	,	PUNCT
ejpam-617	170	3	469	469	NUM
ejpam-617	170	4	-	-	NUM
ejpam-617	170	5	474	474	NUM
ejpam-617	170	6	.	.	PUNCT
ejpam-617	171	1	1971	1971	NUM
ejpam-617	171	2	.	.	PUNCT
ejpam-617	172	1	[	[	X
ejpam-617	172	2	6	6	NUM
ejpam-617	172	3	]	]	X
ejpam-617	172	4	j.l	j.l	PROPN
ejpam-617	172	5	.	.	PROPN
ejpam-617	172	6	liu	liu	PROPN
ejpam-617	172	7	and	and	CCONJ
ejpam-617	172	8	h.m	h.m	PROPN
ejpam-617	172	9	.	.	PROPN
ejpam-617	172	10	srivastava	srivastava	PROPN
ejpam-617	172	11	,	,	PUNCT
ejpam-617	172	12	classes	class	NOUN
ejpam-617	172	13	of	of	ADP
ejpam-617	172	14	meromorphically	meromorphically	ADV
ejpam-617	172	15	multivalent	multivalent	NOUN
ejpam-617	172	16	functions	function	NOUN
ejpam-617	172	17	associated	associate	VERB
ejpam-617	172	18	with	with	ADP
ejpam-617	172	19	the	the	DET
ejpam-617	172	20	generalized	generalize	VERB
ejpam-617	172	21	hypergeometric	hypergeometric	ADJ
ejpam-617	172	22	function	function	NOUN
ejpam-617	172	23	,	,	PUNCT
ejpam-617	172	24	math.comput	math.comput	NOUN
ejpam-617	172	25	.	.	PUNCT
ejpam-617	173	1	modelling	model	VERB
ejpam-617	173	2	39	39	NUM
ejpam-617	173	3	,	,	PUNCT
ejpam-617	173	4	21–34	21–34	NUM
ejpam-617	173	5	.	.	PUNCT
ejpam-617	173	6	2004	2004	NUM
ejpam-617	173	7	.	.	PUNCT
ejpam-617	174	1	[	[	X
ejpam-617	174	2	7	7	X
ejpam-617	174	3	]	]	X
ejpam-617	174	4	s.s	s.s	PROPN
ejpam-617	174	5	.	.	PROPN
ejpam-617	174	6	miller	miller	PROPN
ejpam-617	174	7	and	and	CCONJ
ejpam-617	174	8	p.t	p.t	PROPN
ejpam-617	174	9	.	.	PROPN
ejpam-617	174	10	mocanu	mocanu	PROPN
ejpam-617	174	11	,	,	PUNCT
ejpam-617	174	12	differential	differential	ADJ
ejpam-617	174	13	subordinations	subordination	NOUN
ejpam-617	174	14	:	:	PUNCT
ejpam-617	174	15	theory	theory	NOUN
ejpam-617	174	16	and	and	CCONJ
ejpam-617	174	17	applications	application	NOUN
ejpam-617	174	18	,	,	PUNCT
ejpam-617	174	19	monograph	monograph	NOUN
ejpam-617	174	20	textbooks	textbook	NOUN
ejpam-617	174	21	pure	pure	ADJ
ejpam-617	174	22	and	and	CCONJ
ejpam-617	174	23	appl	appl	PROPN
ejpam-617	174	24	.	.	PROPN
ejpam-617	174	25	math	math	NOUN
ejpam-617	174	26	.	.	PUNCT
ejpam-617	175	1	225	225	NUM
ejpam-617	175	2	,	,	PUNCT
ejpam-617	175	3	dekker	dekker	NOUN
ejpam-617	175	4	,	,	PUNCT
ejpam-617	175	5	new	new	PROPN
ejpam-617	175	6	york	york	PROPN
ejpam-617	175	7	(	(	PUNCT
ejpam-617	175	8	2000	2000	NUM
ejpam-617	175	9	)	)	PUNCT
ejpam-617	175	10	.	.	PUNCT
ejpam-617	176	1	[	[	X
ejpam-617	176	2	8	8	NUM
ejpam-617	176	3	]	]	X
ejpam-617	176	4	e.m	e.m	PROPN
ejpam-617	176	5	.	.	PROPN
ejpam-617	176	6	wright	wright	PROPN
ejpam-617	176	7	,	,	PUNCT
ejpam-617	176	8	the	the	DET
ejpam-617	176	9	asymptotic	asymptotic	ADJ
ejpam-617	176	10	expansion	expansion	NOUN
ejpam-617	176	11	of	of	ADP
ejpam-617	176	12	the	the	DET
ejpam-617	176	13	generalzed	generalzed	ADJ
ejpam-617	176	14	hypergeometric	hypergeometric	ADJ
ejpam-617	176	15	function	function	NOUN
ejpam-617	176	16	,	,	PUNCT
ejpam-617	176	17	j.	j.	PROPN
ejpam-617	176	18	london	london	PROPN
ejpam-617	176	19	math	math	PROPN
ejpam-617	176	20	.	.	PUNCT
ejpam-617	177	1	soc	soc	PROPN
ejpam-617	177	2	.	.	PUNCT
ejpam-617	178	1	10	10	NUM
ejpam-617	178	2	,	,	PUNCT
ejpam-617	178	3	286	286	NUM
ejpam-617	178	4	-	-	SYM
ejpam-617	178	5	293	293	NUM
ejpam-617	178	6	.	.	PUNCT
ejpam-617	179	1	1935	1935	NUM
ejpam-617	179	2	.	.	PUNCT