id	sid	tid	token	lemma	pos
ejpam-5407	1	1	european	european	PROPN
ejpam-5407	1	2	journal	journal	PROPN
ejpam-5407	1	3	of	of	ADP
ejpam-5407	1	4	pure	pure	ADJ
ejpam-5407	1	5	and	and	CCONJ
ejpam-5407	1	6	applied	apply	VERB
ejpam-5407	1	7	mathematics	mathematic	NOUN
ejpam-5407	1	8	vol	vol	NOUN
ejpam-5407	1	9	.	.	PROPN
ejpam-5407	2	1	17	17	NUM
ejpam-5407	2	2	,	,	PUNCT
ejpam-5407	2	3	no	no	INTJ
ejpam-5407	2	4	.	.	NOUN
ejpam-5407	2	5	4	4	NUM
ejpam-5407	2	6	,	,	PUNCT
ejpam-5407	2	7	2024	2024	NUM
ejpam-5407	2	8	,	,	PUNCT
ejpam-5407	2	9	3386	3386	NUM
ejpam-5407	2	10	-	-	SYM
ejpam-5407	2	11	3398	3398	NUM
ejpam-5407	2	12	issn	issn	PROPN
ejpam-5407	2	13	1307	1307	NUM
ejpam-5407	2	14	-	-	SYM
ejpam-5407	2	15	5543	5543	NUM
ejpam-5407	2	16	–	–	PUNCT
ejpam-5407	2	17	ejpam.com	ejpam.com	X
ejpam-5407	2	18	published	publish	VERB
ejpam-5407	2	19	by	by	ADP
ejpam-5407	2	20	new	new	PROPN
ejpam-5407	2	21	york	york	PROPN
ejpam-5407	2	22	business	business	PROPN
ejpam-5407	2	23	global	global	PROPN
ejpam-5407	2	24	some	some	DET
ejpam-5407	2	25	inclusion	inclusion	NOUN
ejpam-5407	2	26	properties	property	NOUN
ejpam-5407	2	27	for	for	ADP
ejpam-5407	2	28	hohlov	hohlov	NOUN
ejpam-5407	2	29	operator	operator	NOUN
ejpam-5407	2	30	to	to	PART
ejpam-5407	2	31	be	be	AUX
ejpam-5407	2	32	in	in	ADP
ejpam-5407	2	33	comprehensive	comprehensive	ADJ
ejpam-5407	2	34	subfamilies	subfamily	NOUN
ejpam-5407	2	35	of	of	ADP
ejpam-5407	2	36	analytic	analytic	ADJ
ejpam-5407	2	37	functions	function	NOUN
ejpam-5407	2	38	tariq	tariq	PROPN
ejpam-5407	2	39	al	al	PROPN
ejpam-5407	2	40	-	-	PUNCT
ejpam-5407	2	41	hawary1,3,∗	hawary1,3,∗	PROPN
ejpam-5407	2	42	,	,	PUNCT
ejpam-5407	2	43	mourad	mourad	PROPN
ejpam-5407	2	44	oqla	oqla	PROPN
ejpam-5407	2	45	massa’deh1	massa’deh1	PROPN
ejpam-5407	2	46	,	,	PUNCT
ejpam-5407	2	47	ahlam	ahlam	PROPN
ejpam-5407	2	48	omar	omar	PROPN
ejpam-5407	2	49	fallatah2	fallatah2	PROPN
ejpam-5407	2	50	1	1	NUM
ejpam-5407	2	51	department	department	NOUN
ejpam-5407	2	52	of	of	ADP
ejpam-5407	2	53	applied	apply	VERB
ejpam-5407	2	54	science	science	NOUN
ejpam-5407	2	55	,	,	PUNCT
ejpam-5407	2	56	ajloun	ajloun	PROPN
ejpam-5407	2	57	college	college	NOUN
ejpam-5407	3	1	,	,	PUNCT
ejpam-5407	3	2	al	al	PROPN
ejpam-5407	3	3	balqa	balqa	NOUN
ejpam-5407	3	4	applied	apply	VERB
ejpam-5407	3	5	university	university	NOUN
ejpam-5407	3	6	,	,	PUNCT
ejpam-5407	3	7	ajloun	ajloun	NOUN
ejpam-5407	3	8	26816	26816	NUM
ejpam-5407	3	9	.	.	PUNCT
ejpam-5407	4	1	jordan	jordan	PROPN
ejpam-5407	4	2	2	2	NUM
ejpam-5407	4	3	taibah	taibah	PROPN
ejpam-5407	4	4	university	university	PROPN
ejpam-5407	4	5	,	,	PUNCT
ejpam-5407	4	6	college	college	NOUN
ejpam-5407	4	7	of	of	ADP
ejpam-5407	4	8	science	science	NOUN
ejpam-5407	4	9	,	,	PUNCT
ejpam-5407	4	10	department	department	NOUN
ejpam-5407	4	11	of	of	ADP
ejpam-5407	4	12	mathematics	mathematics	PROPN
ejpam-5407	4	13	,	,	PUNCT
ejpam-5407	4	14	madinah	madinah	PROPN
ejpam-5407	4	15	,	,	PUNCT
ejpam-5407	4	16	saudi	saudi	PROPN
ejpam-5407	4	17	arabia	arabia	PROPN
ejpam-5407	4	18	3	3	NUM
ejpam-5407	4	19	jadara	jadara	PROPN
ejpam-5407	4	20	research	research	NOUN
ejpam-5407	4	21	center	center	NOUN
ejpam-5407	4	22	,	,	PUNCT
ejpam-5407	4	23	jadara	jadara	PROPN
ejpam-5407	4	24	university	university	PROPN
ejpam-5407	4	25	,	,	PUNCT
ejpam-5407	4	26	irbid	irbid	VERB
ejpam-5407	4	27	21110	21110	NUM
ejpam-5407	4	28	,	,	PUNCT
ejpam-5407	4	29	jordan	jordan	PROPN
ejpam-5407	4	30	abstract	abstract	PROPN
ejpam-5407	4	31	.	.	PUNCT
ejpam-5407	5	1	in	in	ADP
ejpam-5407	5	2	this	this	DET
ejpam-5407	5	3	paper	paper	NOUN
ejpam-5407	5	4	,	,	PUNCT
ejpam-5407	5	5	the	the	DET
ejpam-5407	5	6	subfamilies	subfamily	NOUN
ejpam-5407	5	7	cκ3	cκ3	VERB
ejpam-5407	5	8	(	(	PUNCT
ejpam-5407	5	9	κ1	κ1	NOUN
ejpam-5407	5	10	,	,	PUNCT
ejpam-5407	5	11	κ2	κ2	NOUN
ejpam-5407	5	12	)	)	PUNCT
ejpam-5407	5	13	and	and	CCONJ
ejpam-5407	5	14	s∗κ3	s∗κ3	PRON
ejpam-5407	5	15	(	(	PUNCT
ejpam-5407	5	16	κ1	κ1	NOUN
ejpam-5407	5	17	,	,	PUNCT
ejpam-5407	5	18	κ2	κ2	PROPN
ejpam-5407	5	19	)	)	PUNCT
ejpam-5407	5	20	investigated	investigate	VERB
ejpam-5407	5	21	through	through	ADP
ejpam-5407	5	22	the	the	DET
ejpam-5407	5	23	hohlov	hohlov	NOUN
ejpam-5407	5	24	operator	operator	NOUN
ejpam-5407	5	25	.	.	PUNCT
ejpam-5407	6	1	more	more	ADV
ejpam-5407	6	2	specifically	specifically	ADV
ejpam-5407	6	3	,	,	PUNCT
ejpam-5407	6	4	a	a	DET
ejpam-5407	6	5	number	number	NOUN
ejpam-5407	6	6	of	of	ADP
ejpam-5407	6	7	sufficient	sufficient	ADJ
ejpam-5407	6	8	requirements	requirement	NOUN
ejpam-5407	6	9	are	be	AUX
ejpam-5407	6	10	given	give	VERB
ejpam-5407	6	11	in	in	ADP
ejpam-5407	6	12	order	order	NOUN
ejpam-5407	6	13	for	for	ADP
ejpam-5407	6	14	the	the	DET
ejpam-5407	6	15	aforementioned	aforementioned	ADJ
ejpam-5407	6	16	functions	function	NOUN
ejpam-5407	6	17	subfamilies	subfamily	NOUN
ejpam-5407	6	18	.	.	PUNCT
ejpam-5407	7	1	moreover	moreover	ADV
ejpam-5407	7	2	,	,	PUNCT
ejpam-5407	7	3	our	our	PRON
ejpam-5407	7	4	results	result	NOUN
ejpam-5407	7	5	will	will	AUX
ejpam-5407	7	6	imply	imply	VERB
ejpam-5407	7	7	several	several	ADJ
ejpam-5407	7	8	corollaries	corollary	NOUN
ejpam-5407	7	9	.	.	PUNCT
ejpam-5407	8	1	2020	2020	NUM
ejpam-5407	8	2	mathematics	mathematic	NOUN
ejpam-5407	8	3	subject	subject	NOUN
ejpam-5407	8	4	classifications	classification	NOUN
ejpam-5407	8	5	:	:	PUNCT
ejpam-5407	8	6	30c45	30c45	NUM
ejpam-5407	8	7	key	key	ADJ
ejpam-5407	8	8	words	word	NOUN
ejpam-5407	8	9	and	and	CCONJ
ejpam-5407	8	10	phrases	phrase	NOUN
ejpam-5407	8	11	:	:	PUNCT
ejpam-5407	8	12	analytic	analytic	ADJ
ejpam-5407	8	13	function	function	NOUN
ejpam-5407	8	14	,	,	PUNCT
ejpam-5407	8	15	geometric	geometric	ADJ
ejpam-5407	8	16	functions	function	NOUN
ejpam-5407	8	17	,	,	PUNCT
ejpam-5407	8	18	gaussian	gaussian	ADJ
ejpam-5407	8	19	function	function	NOUN
ejpam-5407	8	20	,	,	PUNCT
ejpam-5407	8	21	hohlov	hohlov	NOUN
ejpam-5407	8	22	operator	operator	NOUN
ejpam-5407	8	23	1	1	NUM
ejpam-5407	8	24	.	.	PUNCT
ejpam-5407	9	1	preliminaries	preliminary	NOUN
ejpam-5407	9	2	and	and	CCONJ
ejpam-5407	9	3	definitions	definition	NOUN
ejpam-5407	9	4	geometric	geometric	ADJ
ejpam-5407	9	5	functions	function	NOUN
ejpam-5407	9	6	are	be	AUX
ejpam-5407	9	7	a	a	DET
ejpam-5407	9	8	basic	basic	ADJ
ejpam-5407	9	9	family	family	NOUN
ejpam-5407	9	10	of	of	ADP
ejpam-5407	9	11	special	special	ADJ
ejpam-5407	9	12	functions	function	NOUN
ejpam-5407	9	13	in	in	ADP
ejpam-5407	9	14	mathematics	mathematic	NOUN
ejpam-5407	9	15	that	that	PRON
ejpam-5407	9	16	have	have	VERB
ejpam-5407	9	17	complex	complex	ADJ
ejpam-5407	9	18	mathematical	mathematical	ADJ
ejpam-5407	9	19	features	feature	NOUN
ejpam-5407	9	20	and	and	CCONJ
ejpam-5407	9	21	linkages	linkage	NOUN
ejpam-5407	9	22	and	and	CCONJ
ejpam-5407	9	23	are	be	AUX
ejpam-5407	9	24	widely	widely	ADV
ejpam-5407	9	25	used	use	VERB
ejpam-5407	9	26	in	in	ADP
ejpam-5407	9	27	many	many	ADJ
ejpam-5407	9	28	different	different	ADJ
ejpam-5407	9	29	domains	domain	NOUN
ejpam-5407	9	30	as	as	SCONJ
ejpam-5407	9	31	solutions	solution	NOUN
ejpam-5407	9	32	to	to	PART
ejpam-5407	9	33	differential	differential	VERB
ejpam-5407	9	34	equations	equation	NOUN
ejpam-5407	9	35	and	and	CCONJ
ejpam-5407	9	36	recurrence	recurrence	NOUN
ejpam-5407	9	37	relations	relation	NOUN
ejpam-5407	9	38	.	.	PUNCT
ejpam-5407	10	1	gaussian	gaussian	ADJ
ejpam-5407	10	2	hypergeometric	hypergeometric	ADJ
ejpam-5407	10	3	function	function	NOUN
ejpam-5407	10	4	is	be	AUX
ejpam-5407	10	5	one	one	NUM
ejpam-5407	10	6	of	of	ADP
ejpam-5407	10	7	the	the	DET
ejpam-5407	10	8	most	most	ADV
ejpam-5407	10	9	important	important	ADJ
ejpam-5407	10	10	in	in	ADP
ejpam-5407	10	11	geometric	geometric	ADJ
ejpam-5407	10	12	functions	function	NOUN
ejpam-5407	10	13	theory	theory	NOUN
ejpam-5407	10	14	,	,	PUNCT
ejpam-5407	10	15	it	it	PRON
ejpam-5407	10	16	is	be	AUX
ejpam-5407	10	17	foundation	foundation	NOUN
ejpam-5407	10	18	is	be	AUX
ejpam-5407	10	19	found	find	VERB
ejpam-5407	10	20	in	in	ADP
ejpam-5407	10	21	the	the	DET
ejpam-5407	10	22	research	research	NOUN
ejpam-5407	10	23	of	of	ADP
ejpam-5407	10	24	17th	17th	ADJ
ejpam-5407	10	25	-	-	PUNCT
ejpam-5407	10	26	century	century	NOUN
ejpam-5407	10	27	mathematicians	mathematician	NOUN
ejpam-5407	10	28	and	and	CCONJ
ejpam-5407	10	29	astrophysicists	astrophysicist	NOUN
ejpam-5407	10	30	.	.	PUNCT
ejpam-5407	11	1	in	in	ADP
ejpam-5407	11	2	terms	term	NOUN
ejpam-5407	11	3	of	of	ADP
ejpam-5407	11	4	measurement	measurement	NOUN
ejpam-5407	11	5	,	,	PUNCT
ejpam-5407	11	6	instrumentation	instrumentation	NOUN
ejpam-5407	11	7	,	,	PUNCT
ejpam-5407	11	8	and	and	CCONJ
ejpam-5407	11	9	statistics	statistic	NOUN
ejpam-5407	11	10	,	,	PUNCT
ejpam-5407	11	11	the	the	DET
ejpam-5407	11	12	gaussian	gaussian	ADJ
ejpam-5407	11	13	distribution	distribution	NOUN
ejpam-5407	11	14	is	be	AUX
ejpam-5407	11	15	most	most	ADV
ejpam-5407	11	16	likely	likely	ADJ
ejpam-5407	11	17	the	the	DET
ejpam-5407	11	18	most	most	ADV
ejpam-5407	11	19	employed	employ	VERB
ejpam-5407	11	20	.	.	PUNCT
ejpam-5407	12	1	indeed	indeed	ADV
ejpam-5407	12	2	,	,	PUNCT
ejpam-5407	12	3	celestial	celestial	ADJ
ejpam-5407	12	4	sources	source	NOUN
ejpam-5407	12	5	frequently	frequently	ADV
ejpam-5407	12	6	have	have	VERB
ejpam-5407	12	7	a	a	DET
ejpam-5407	12	8	gaussian	gaussian	ADJ
ejpam-5407	12	9	nature	nature	NOUN
ejpam-5407	12	10	in	in	ADP
ejpam-5407	12	11	radio	radio	NOUN
ejpam-5407	12	12	astronomy	astronomy	NOUN
ejpam-5407	12	13	[	[	X
ejpam-5407	12	14	8	8	NUM
ejpam-5407	12	15	]	]	PUNCT
ejpam-5407	12	16	.	.	PUNCT
ejpam-5407	13	1	let	let	VERB
ejpam-5407	13	2	π	π	X
ejpam-5407	13	3	be	be	AUX
ejpam-5407	13	4	the	the	DET
ejpam-5407	13	5	family	family	NOUN
ejpam-5407	13	6	of	of	ADP
ejpam-5407	13	7	all	all	DET
ejpam-5407	13	8	analytic	analytic	ADJ
ejpam-5407	13	9	and	and	CCONJ
ejpam-5407	13	10	univalent	univalent	ADJ
ejpam-5407	13	11	functions	function	NOUN
ejpam-5407	13	12	of	of	ADP
ejpam-5407	13	13	the	the	DET
ejpam-5407	13	14	form	form	NOUN
ejpam-5407	13	15	:	:	PUNCT
ejpam-5407	13	16	l(ς	l(ς	PROPN
ejpam-5407	13	17	)	)	PUNCT
ejpam-5407	13	18	=	=	PUNCT
ejpam-5407	14	1	ς	ς	PROPN
ejpam-5407	14	2	+	+	PUNCT
ejpam-5407	14	3	∞∑	∞∑	PROPN
ejpam-5407	14	4	τ=2	τ=2	SYM
ejpam-5407	14	5	rτ	rτ	NOUN
ejpam-5407	14	6	ς	ς	PROPN
ejpam-5407	14	7	τ	τ	PROPN
ejpam-5407	14	8	,	,	PUNCT
ejpam-5407	14	9	|ς|	|ς|	PROPN
ejpam-5407	14	10	<	<	X
ejpam-5407	14	11	1	1	NUM
ejpam-5407	14	12	,	,	PUNCT
ejpam-5407	14	13	(	(	PUNCT
ejpam-5407	14	14	1	1	X
ejpam-5407	14	15	)	)	PUNCT
ejpam-5407	14	16	∗corresponding	∗corresponde	VERB
ejpam-5407	14	17	author	author	NOUN
ejpam-5407	14	18	.	.	PUNCT
ejpam-5407	15	1	doi	doi	NOUN
ejpam-5407	15	2	:	:	PUNCT
ejpam-5407	15	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5407	https://doi.org/10.29020/nybg.ejpam.v17i4.5407	VERB
ejpam-5407	15	4	email	email	NOUN
ejpam-5407	15	5	addresses	address	NOUN
ejpam-5407	15	6	:	:	PUNCT
ejpam-5407	15	7	tariqamh@bau.edu.jo	tariqamh@bau.edu.jo	PROPN
ejpam-5407	15	8	(	(	PUNCT
ejpam-5407	15	9	t.al	t.al	PROPN
ejpam-5407	15	10	−hawary	−hawary	ADJ
ejpam-5407	15	11	)	)	PUNCT
ejpam-5407	15	12	,	,	PUNCT
ejpam-5407	15	13	mourad.oqla@bau.edu.jo	mourad.oqla@bau.edu.jo	PROPN
ejpam-5407	15	14	(	(	PUNCT
ejpam-5407	15	15	m.	m.	NOUN
ejpam-5407	15	16	o.	o.	PROPN
ejpam-5407	15	17	massa’deh	massa’deh	PROPN
ejpam-5407	15	18	)	)	PUNCT
ejpam-5407	15	19	,	,	PUNCT
ejpam-5407	15	20	afallatah@taibahu.edu.sa	afallatah@taibahu.edu.sa	PROPN
ejpam-5407	15	21	(	(	PUNCT
ejpam-5407	15	22	a.	a.	NOUN
ejpam-5407	15	23	o.	o.	PROPN
ejpam-5407	15	24	fallatah	fallatah	PROPN
ejpam-5407	15	25	)	)	PUNCT
ejpam-5407	15	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5407	15	27	3386	3386	NUM
ejpam-5407	16	1	copyright	copyright	NOUN
ejpam-5407	16	2	:	:	PUNCT
ejpam-5407	16	3	©	©	PROPN
ejpam-5407	16	4	2024	2024	NUM
ejpam-5407	16	5	the	the	DET
ejpam-5407	16	6	author(s	author(s	NOUN
ejpam-5407	16	7	)	)	PUNCT
ejpam-5407	16	8	.	.	PUNCT
ejpam-5407	17	1	(	(	PUNCT
ejpam-5407	17	2	cc	cc	NOUN
ejpam-5407	17	3	by	by	ADP
ejpam-5407	17	4	-	-	PUNCT
ejpam-5407	17	5	nc	nc	PROPN
ejpam-5407	17	6	4.0	4.0	NUM
ejpam-5407	17	7	)	)	PUNCT
ejpam-5407	17	8	t.	t.	PROPN
ejpam-5407	17	9	al	al	PROPN
ejpam-5407	17	10	-	-	PUNCT
ejpam-5407	17	11	hawary	hawary	PROPN
ejpam-5407	17	12	,	,	PUNCT
ejpam-5407	17	13	m.	m.	NOUN
ejpam-5407	17	14	o.	o.	PROPN
ejpam-5407	17	15	massa’deh	massa’deh	PROPN
ejpam-5407	17	16	,	,	PUNCT
ejpam-5407	17	17	a.	a.	NOUN
ejpam-5407	17	18	o	o	X
ejpam-5407	17	19	fallatah	fallatah	PROPN
ejpam-5407	17	20	/	/	SYM
ejpam-5407	17	21	eur	eur	PROPN
ejpam-5407	17	22	.	.	PUNCT
ejpam-5407	18	1	j.	j.	PROPN
ejpam-5407	18	2	pure	pure	PROPN
ejpam-5407	18	3	appl	appl	PROPN
ejpam-5407	18	4	.	.	PROPN
ejpam-5407	18	5	math	math	PROPN
ejpam-5407	18	6	,	,	PUNCT
ejpam-5407	18	7	17	17	NUM
ejpam-5407	18	8	(	(	PUNCT
ejpam-5407	18	9	4	4	NUM
ejpam-5407	18	10	)	)	PUNCT
ejpam-5407	18	11	(	(	PUNCT
ejpam-5407	18	12	2024	2024	NUM
ejpam-5407	18	13	)	)	PUNCT
ejpam-5407	18	14	,	,	PUNCT
ejpam-5407	18	15	3386	3386	NUM
ejpam-5407	18	16	-	-	SYM
ejpam-5407	18	17	3398	3398	NUM
ejpam-5407	18	18	3387	3387	NUM
ejpam-5407	18	19	which	which	PRON
ejpam-5407	18	20	are	be	AUX
ejpam-5407	18	21	normalized	normalize	VERB
ejpam-5407	18	22	by	by	ADP
ejpam-5407	18	23	l(0	l(0	PROPN
ejpam-5407	18	24	)	)	PUNCT
ejpam-5407	18	25	=	=	PUNCT
ejpam-5407	18	26	l′(0	l′(0	NOUN
ejpam-5407	18	27	)	)	PUNCT
ejpam-5407	18	28	−	−	PROPN
ejpam-5407	18	29	1	1	NUM
ejpam-5407	18	30	=	=	SYM
ejpam-5407	18	31	0	0	NUM
ejpam-5407	18	32	.	.	PUNCT
ejpam-5407	19	1	also	also	ADV
ejpam-5407	19	2	,	,	PUNCT
ejpam-5407	19	3	indicate	indicate	VERB
ejpam-5407	19	4	by	by	ADP
ejpam-5407	19	5	h	h	NOUN
ejpam-5407	19	6	the	the	DET
ejpam-5407	19	7	subfamily	subfamily	NOUN
ejpam-5407	19	8	of	of	ADP
ejpam-5407	19	9	π	π	PROPN
ejpam-5407	19	10	made	make	VERB
ejpam-5407	19	11	up	up	ADP
ejpam-5407	19	12	of	of	ADP
ejpam-5407	19	13	functions	function	NOUN
ejpam-5407	19	14	of	of	ADP
ejpam-5407	19	15	the	the	DET
ejpam-5407	19	16	form	form	NOUN
ejpam-5407	19	17	:	:	PUNCT
ejpam-5407	19	18	l(ς	l(ς	PROPN
ejpam-5407	19	19	)	)	PUNCT
ejpam-5407	20	1	=	=	PUNCT
ejpam-5407	20	2	ς	ς	PROPN
ejpam-5407	20	3	−	−	PROPN
ejpam-5407	20	4	∞∑	∞∑	NUM
ejpam-5407	20	5	τ=2	τ=2	PUNCT
ejpam-5407	20	6	rτ	rτ	NOUN
ejpam-5407	20	7	ς	ς	PROPN
ejpam-5407	20	8	τ	τ	PROPN
ejpam-5407	20	9	,	,	PUNCT
ejpam-5407	20	10	rτ	rτ	NOUN
ejpam-5407	20	11	≥	≥	PROPN
ejpam-5407	20	12	0	0	NUM
ejpam-5407	20	13	.	.	PUNCT
ejpam-5407	21	1	(	(	PUNCT
ejpam-5407	21	2	2	2	X
ejpam-5407	21	3	)	)	PUNCT
ejpam-5407	21	4	for	for	ADP
ejpam-5407	21	5	two	two	NUM
ejpam-5407	21	6	functions	function	NOUN
ejpam-5407	21	7	l	l	NOUN
ejpam-5407	21	8	,	,	PUNCT
ejpam-5407	21	9	ℓ	ℓ	PROPN
ejpam-5407	21	10	∈	∈	PROPN
ejpam-5407	21	11	π	π	PROPN
ejpam-5407	21	12	,	,	PUNCT
ejpam-5407	21	13	l	l	PROPN
ejpam-5407	21	14	given	give	VERB
ejpam-5407	21	15	by	by	ADP
ejpam-5407	21	16	(	(	PUNCT
ejpam-5407	21	17	1	1	NUM
ejpam-5407	21	18	)	)	PUNCT
ejpam-5407	21	19	and	and	CCONJ
ejpam-5407	21	20	ℓ(ς	ℓ(ς	NOUN
ejpam-5407	21	21	)	)	PUNCT
ejpam-5407	21	22	=	=	PUNCT
ejpam-5407	22	1	ς	ς	PROPN
ejpam-5407	22	2	+	+	PUNCT
ejpam-5407	22	3	∞∑	∞∑	NUM
ejpam-5407	22	4	τ=2	τ=2	PUNCT
ejpam-5407	22	5	sτ	sτ	ADP
ejpam-5407	22	6	ς	ς	PROPN
ejpam-5407	22	7	τ	τ	PROPN
ejpam-5407	22	8	,	,	PUNCT
ejpam-5407	22	9	we	we	PRON
ejpam-5407	22	10	define	define	VERB
ejpam-5407	22	11	the	the	DET
ejpam-5407	22	12	convolution	convolution	NOUN
ejpam-5407	22	13	of	of	ADP
ejpam-5407	22	14	l	l	NOUN
ejpam-5407	22	15	and	and	CCONJ
ejpam-5407	22	16	ℓ	ℓ	NUM
ejpam-5407	22	17	by	by	ADP
ejpam-5407	22	18	:	:	PUNCT
ejpam-5407	22	19	(	(	PUNCT
ejpam-5407	22	20	l∗ℓ)(ς	l∗ℓ)(ς	NOUN
ejpam-5407	22	21	)	)	PUNCT
ejpam-5407	22	22	=	=	PUNCT
ejpam-5407	23	1	ς	ς	PROPN
ejpam-5407	23	2	+	+	PUNCT
ejpam-5407	23	3	∞∑	∞∑	NUM
ejpam-5407	23	4	τ=2	τ=2	PUNCT
ejpam-5407	23	5	rτsτ	rτsτ	NOUN
ejpam-5407	23	6	ς	ς	PROPN
ejpam-5407	23	7	τ	τ	PROPN
ejpam-5407	23	8	.	.	PUNCT
ejpam-5407	24	1	the	the	DET
ejpam-5407	24	2	subfamily	subfamily	ADV
ejpam-5407	24	3	ξ	ξ	PROPN
ejpam-5407	24	4	−	−	PROPN
ejpam-5407	24	5	st	st	PROPN
ejpam-5407	24	6	meeting	meet	VERB
ejpam-5407	24	7	the	the	DET
ejpam-5407	24	8	requirements	requirement	NOUN
ejpam-5407	24	9	ξ	ξ	PROPN
ejpam-5407	24	10	−	−	PROPN
ejpam-5407	24	11	st	st	NOUN
ejpam-5407	25	1	=	=	X
ejpam-5407	25	2	{	{	PUNCT
ejpam-5407	25	3	l∈	l∈	NOUN
ejpam-5407	25	4	π	π	NOUN
ejpam-5407	25	5	:	:	PUNCT
ejpam-5407	25	6	re	re	X
ejpam-5407	25	7	(	(	PUNCT
ejpam-5407	25	8	ςl′(ς	ςl′(ς	PROPN
ejpam-5407	25	9	)	)	PUNCT
ejpam-5407	25	10	l(ς	l(ς	PROPN
ejpam-5407	25	11	)	)	PUNCT
ejpam-5407	25	12	)	)	PUNCT
ejpam-5407	25	13	>	>	X
ejpam-5407	26	1	ξ	ξ	X
ejpam-5407	26	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5407	26	3	ςl′(ς	ςl′(ς	PROPN
ejpam-5407	26	4	)	)	PUNCT
ejpam-5407	26	5	l(ς	l(ς	PROPN
ejpam-5407	26	6	)	)	PUNCT
ejpam-5407	26	7	−	−	PROPN
ejpam-5407	26	8	1	1	NUM
ejpam-5407	26	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	26	10	,	,	PUNCT
ejpam-5407	26	11	(	(	PUNCT
ejpam-5407	26	12	0	0	NUM
ejpam-5407	26	13	≤	≤	NOUN
ejpam-5407	26	14	ξ	ξ	PUNCT
ejpam-5407	26	15	<	<	X
ejpam-5407	26	16	∞	∞	PROPN
ejpam-5407	26	17	,	,	PUNCT
ejpam-5407	26	18	|ς|	|ς|	PROPN
ejpam-5407	26	19	<	<	X
ejpam-5407	26	20	1	1	NUM
ejpam-5407	26	21	)	)	PUNCT
ejpam-5407	26	22	}	}	PUNCT
ejpam-5407	26	23	and	and	CCONJ
ejpam-5407	26	24	l(ς	l(ς	PROPN
ejpam-5407	26	25	)	)	PUNCT
ejpam-5407	26	26	∈	∈	PROPN
ejpam-5407	27	1	ξ	ξ	X
ejpam-5407	27	2	−	−	PROPN
ejpam-5407	27	3	ucv	ucv	PROPN
ejpam-5407	27	4	⇔	⇔	PROPN
ejpam-5407	27	5	ςl′(ς	ςl′(ς	PROPN
ejpam-5407	27	6	)	)	PUNCT
ejpam-5407	27	7	∈	∈	PROPN
ejpam-5407	28	1	ξ	ξ	X
ejpam-5407	28	2	−	−	PROPN
ejpam-5407	28	3	st	st	PROPN
ejpam-5407	28	4	,	,	PUNCT
ejpam-5407	28	5	was	be	AUX
ejpam-5407	28	6	presented	present	VERB
ejpam-5407	28	7	by	by	ADP
ejpam-5407	28	8	kanas	kanas	PROPN
ejpam-5407	28	9	and	and	CCONJ
ejpam-5407	28	10	wísniowska	wísniowska	PROPN
ejpam-5407	29	1	[	[	X
ejpam-5407	29	2	13	13	NUM
ejpam-5407	29	3	]	]	PUNCT
ejpam-5407	29	4	and	and	CCONJ
ejpam-5407	29	5	[	[	X
ejpam-5407	29	6	14	14	NUM
ejpam-5407	29	7	]	]	PUNCT
ejpam-5407	29	8	.	.	PUNCT
ejpam-5407	30	1	in	in	ADP
ejpam-5407	30	2	particular	particular	ADJ
ejpam-5407	30	3	,	,	PUNCT
ejpam-5407	30	4	when	when	SCONJ
ejpam-5407	30	5	ξ	ξ	X
ejpam-5407	30	6	=	=	SYM
ejpam-5407	30	7	1	1	NUM
ejpam-5407	30	8	,	,	PUNCT
ejpam-5407	30	9	we	we	PRON
ejpam-5407	30	10	obtain	obtain	VERB
ejpam-5407	30	11	the	the	DET
ejpam-5407	30	12	comprehensive	comprehensive	ADJ
ejpam-5407	30	13	subfamilies	subfamily	NOUN
ejpam-5407	30	14	of	of	ADP
ejpam-5407	30	15	uniformly	uniformly	ADV
ejpam-5407	30	16	convex	convex	NOUN
ejpam-5407	30	17	functions	function	NOUN
ejpam-5407	30	18	ucv	ucv	PROPN
ejpam-5407	30	19	and	and	CCONJ
ejpam-5407	30	20	parabolic	parabolic	ADJ
ejpam-5407	30	21	starlike	starlike	NOUN
ejpam-5407	30	22	functions	function	NOUN
ejpam-5407	30	23	sp	sp	ADP
ejpam-5407	30	24	in	in	ADP
ejpam-5407	30	25	u	u	NOUN
ejpam-5407	30	26	=	=	PUNCT
ejpam-5407	30	27	{	{	PUNCT
ejpam-5407	30	28	ς	ς	PROPN
ejpam-5407	30	29	∈	∈	PROPN
ejpam-5407	30	30	c	c	NOUN
ejpam-5407	30	31	:	:	PUNCT
ejpam-5407	31	1	|ς|	|ς|	PROPN
ejpam-5407	31	2	<	<	X
ejpam-5407	31	3	1	1	NUM
ejpam-5407	31	4	}	}	PUNCT
ejpam-5407	31	5	.	.	PUNCT
ejpam-5407	32	1	also	also	ADV
ejpam-5407	32	2	,	,	PUNCT
ejpam-5407	32	3	when	when	SCONJ
ejpam-5407	32	4	ξ	ξ	X
ejpam-5407	32	5	=	=	SYM
ejpam-5407	32	6	0	0	NUM
ejpam-5407	32	7	,	,	PUNCT
ejpam-5407	32	8	we	we	PRON
ejpam-5407	32	9	obtain	obtain	VERB
ejpam-5407	32	10	the	the	DET
ejpam-5407	32	11	renowned	renowned	ADJ
ejpam-5407	32	12	subfamilies	subfamily	NOUN
ejpam-5407	32	13	of	of	ADP
ejpam-5407	32	14	convex	convex	NOUN
ejpam-5407	32	15	functions	function	NOUN
ejpam-5407	32	16	cv	cv	PROPN
ejpam-5407	32	17	and	and	CCONJ
ejpam-5407	32	18	starlike	starlike	PROPN
ejpam-5407	32	19	functions	function	NOUN
ejpam-5407	32	20	st	st	PROPN
ejpam-5407	32	21	in	in	ADP
ejpam-5407	32	22	u	u	PROPN
ejpam-5407	32	23	(	(	PUNCT
ejpam-5407	32	24	see	see	VERB
ejpam-5407	32	25	for	for	ADP
ejpam-5407	32	26	details	detail	NOUN
ejpam-5407	32	27	,	,	PUNCT
ejpam-5407	32	28	[	[	X
ejpam-5407	32	29	10	10	NUM
ejpam-5407	32	30	]	]	PUNCT
ejpam-5407	32	31	)	)	PUNCT
ejpam-5407	32	32	.	.	PUNCT
ejpam-5407	33	1	let	let	AUX
ejpam-5407	33	2	(	(	PUNCT
ejpam-5407	33	3	see	see	VERB
ejpam-5407	33	4	[	[	X
ejpam-5407	33	5	13	13	NUM
ejpam-5407	33	6	]	]	PUNCT
ejpam-5407	33	7	and	and	CCONJ
ejpam-5407	34	1	[	[	X
ejpam-5407	34	2	14	14	NUM
ejpam-5407	34	3	]	]	SYM
ejpam-5407	34	4	)	)	PUNCT
ejpam-5407	34	5	υ1	υ1	PROPN
ejpam-5407	34	6	=	=	NOUN
ejpam-5407	34	7	:	:	PUNCT
ejpam-5407	34	8	υ1(ξ	υ1(ξ	X
ejpam-5407	34	9	)	)	PUNCT
ejpam-5407	34	10	=	=	SYM
ejpam-5407	35	1			NUM
ejpam-5407	35	2	8(cos−1	8(cos−1	NUM
ejpam-5407	35	3	ξ	ξ	X
ejpam-5407	35	4	)	)	PUNCT
ejpam-5407	35	5	2	2	NUM
ejpam-5407	35	6	π2(1−ξ2	π2(1−ξ2	NOUN
ejpam-5407	35	7	)	)	PUNCT
ejpam-5407	35	8	for	for	ADP
ejpam-5407	35	9	0	0	NUM
ejpam-5407	35	10	≤	≤	NOUN
ejpam-5407	35	11	ξ	ξ	X
ejpam-5407	35	12	<	<	X
ejpam-5407	35	13	1	1	NUM
ejpam-5407	35	14	8	8	NUM
ejpam-5407	35	15	π2	π2	NOUN
ejpam-5407	35	16	for	for	ADP
ejpam-5407	35	17	ξ	ξ	NOUN
ejpam-5407	35	18	=	=	SYM
ejpam-5407	35	19	1	1	NUM
ejpam-5407	35	20	π2	π2	NUM
ejpam-5407	35	21	4	4	NUM
ejpam-5407	35	22	√	√	NUM
ejpam-5407	35	23	v(v+1)(ξ2−1)ψ2(v	v(v+1)(ξ2−1)ψ2(v	NUM
ejpam-5407	35	24	)	)	PUNCT
ejpam-5407	35	25	for	for	ADP
ejpam-5407	35	26	ξ	ξ	PROPN
ejpam-5407	35	27	>	>	SYM
ejpam-5407	35	28	1	1	NUM
ejpam-5407	35	29	,	,	PUNCT
ejpam-5407	35	30	(	(	PUNCT
ejpam-5407	35	31	3	3	X
ejpam-5407	35	32	)	)	PUNCT
ejpam-5407	35	33	where	where	SCONJ
ejpam-5407	35	34	v	v	X
ejpam-5407	35	35	∈	∈	PROPN
ejpam-5407	35	36	(	(	PUNCT
ejpam-5407	35	37	0	0	NUM
ejpam-5407	35	38	,	,	PUNCT
ejpam-5407	35	39	1	1	NUM
ejpam-5407	35	40	)	)	PUNCT
ejpam-5407	35	41	is	be	AUX
ejpam-5407	35	42	determined	determine	VERB
ejpam-5407	35	43	by	by	ADP
ejpam-5407	35	44	ξ	ξ	PROPN
ejpam-5407	35	45	=	=	SYM
ejpam-5407	35	46	cosh	cosh	PROPN
ejpam-5407	35	47	(	(	PUNCT
ejpam-5407	35	48	πf	πf	INTJ
ejpam-5407	35	49	′(v)⧸4f	′(v)⧸4f	NOUN
ejpam-5407	35	50	(	(	PUNCT
ejpam-5407	35	51	v	v	NOUN
ejpam-5407	35	52	)	)	PUNCT
ejpam-5407	35	53	)	)	PUNCT
ejpam-5407	35	54	,	,	PUNCT
ejpam-5407	35	55	f	f	PROPN
ejpam-5407	35	56	is	be	AUX
ejpam-5407	35	57	the	the	DET
ejpam-5407	35	58	legendre	legendre	PROPN
ejpam-5407	35	59	’s	’s	PART
ejpam-5407	35	60	complete	complete	ADJ
ejpam-5407	35	61	elliptic	elliptic	ADJ
ejpam-5407	35	62	integral	integral	NOUN
ejpam-5407	35	63	of	of	ADP
ejpam-5407	35	64	the	the	DET
ejpam-5407	35	65	first	first	ADJ
ejpam-5407	35	66	kind	kind	NOUN
ejpam-5407	35	67	f	f	PROPN
ejpam-5407	35	68	(	(	PUNCT
ejpam-5407	35	69	v	v	NOUN
ejpam-5407	35	70	)	)	PUNCT
ejpam-5407	35	71	=	=	PUNCT
ejpam-5407	36	1	1∫	1∫	NUM
ejpam-5407	36	2	0	0	NUM
ejpam-5407	36	3	dt	dt	NOUN
ejpam-5407	36	4	(	(	PUNCT
ejpam-5407	36	5	1−t2)(1−v2t2	1−t2)(1−v2t2	NUM
ejpam-5407	36	6	)	)	PUNCT
ejpam-5407	36	7	and	and	CCONJ
ejpam-5407	36	8	f	f	PROPN
ejpam-5407	36	9	′(v	′(v	PROPN
ejpam-5407	36	10	)	)	PUNCT
ejpam-5407	37	1	=	=	SYM
ejpam-5407	37	2	f	f	PROPN
ejpam-5407	37	3	(	(	PUNCT
ejpam-5407	37	4	√	√	PROPN
ejpam-5407	37	5	1−	1−	NUM
ejpam-5407	37	6	v2	v2	PROPN
ejpam-5407	37	7	)	)	PUNCT
ejpam-5407	37	8	is	be	AUX
ejpam-5407	37	9	the	the	DET
ejpam-5407	37	10	complementary	complementary	ADJ
ejpam-5407	37	11	integral	integral	NOUN
ejpam-5407	37	12	of	of	ADP
ejpam-5407	37	13	f	f	PROPN
ejpam-5407	37	14	(	(	PUNCT
ejpam-5407	37	15	v	v	NOUN
ejpam-5407	37	16	)	)	PUNCT
ejpam-5407	37	17	.	.	PUNCT
ejpam-5407	38	1	let	let	VERB
ejpam-5407	38	2	l∈	l∈	NOUN
ejpam-5407	38	3	π	π	PROPN
ejpam-5407	38	4	be	be	AUX
ejpam-5407	38	5	of	of	ADP
ejpam-5407	38	6	the	the	DET
ejpam-5407	38	7	form	form	NOUN
ejpam-5407	38	8	(	(	PUNCT
ejpam-5407	38	9	2	2	NUM
ejpam-5407	38	10	)	)	PUNCT
ejpam-5407	38	11	and	and	CCONJ
ejpam-5407	38	12	in	in	ADP
ejpam-5407	38	13	the	the	DET
ejpam-5407	38	14	subfamily	subfamily	ADV
ejpam-5407	38	15	ξ−ucv	ξ−ucv	NOUN
ejpam-5407	38	16	,	,	PUNCT
ejpam-5407	38	17	then	then	ADV
ejpam-5407	38	18	the	the	DET
ejpam-5407	38	19	following	follow	VERB
ejpam-5407	38	20	inequalities	inequality	NOUN
ejpam-5407	38	21	hold	hold	VERB
ejpam-5407	38	22	true	true	ADJ
ejpam-5407	38	23	[	[	X
ejpam-5407	38	24	13	13	NUM
ejpam-5407	38	25	]	]	SYM
ejpam-5407	38	26	|rτ	|rτ	PUNCT
ejpam-5407	39	1	|	|	ADV
ejpam-5407	39	2	≤	≤	X
ejpam-5407	39	3	(	(	PUNCT
ejpam-5407	39	4	υ1(ξ))τ−1	υ1(ξ))τ−1	X
ejpam-5407	39	5	τ	τ	PROPN
ejpam-5407	39	6	!	!	PUNCT
ejpam-5407	39	7	,	,	PUNCT
ejpam-5407	39	8	τ	τ	PROPN
ejpam-5407	39	9	∈	∈	PROPN
ejpam-5407	39	10	n−	n−	PROPN
ejpam-5407	39	11	{	{	PUNCT
ejpam-5407	39	12	1	1	NUM
ejpam-5407	39	13	}	}	PUNCT
ejpam-5407	39	14	.	.	PUNCT
ejpam-5407	40	1	(	(	PUNCT
ejpam-5407	40	2	4	4	X
ejpam-5407	40	3	)	)	PUNCT
ejpam-5407	40	4	also	also	ADV
ejpam-5407	40	5	,	,	PUNCT
ejpam-5407	40	6	if	if	SCONJ
ejpam-5407	40	7	l∈	l∈	NOUN
ejpam-5407	40	8	π	π	NOUN
ejpam-5407	40	9	be	be	VERB
ejpam-5407	40	10	of	of	ADP
ejpam-5407	40	11	the	the	DET
ejpam-5407	40	12	form	form	NOUN
ejpam-5407	40	13	(	(	PUNCT
ejpam-5407	40	14	2	2	NUM
ejpam-5407	40	15	)	)	PUNCT
ejpam-5407	40	16	in	in	ADP
ejpam-5407	40	17	the	the	DET
ejpam-5407	40	18	subfamily	subfamily	ADV
ejpam-5407	40	19	ξ	ξ	PROPN
ejpam-5407	40	20	−	−	PROPN
ejpam-5407	40	21	st	st	PROPN
ejpam-5407	40	22	,	,	PUNCT
ejpam-5407	40	23	then	then	ADV
ejpam-5407	40	24	[	[	X
ejpam-5407	40	25	14	14	NUM
ejpam-5407	40	26	]	]	SYM
ejpam-5407	40	27	|rτ	|rτ	PUNCT
ejpam-5407	41	1	|	|	ADV
ejpam-5407	41	2	≤	≤	X
ejpam-5407	41	3	(	(	PUNCT
ejpam-5407	41	4	υ1(ξ))τ−1	υ1(ξ))τ−1	X
ejpam-5407	41	5	(	(	PUNCT
ejpam-5407	41	6	τ−1	τ−1	PROPN
ejpam-5407	41	7	)	)	PUNCT
ejpam-5407	41	8	!	!	PUNCT
ejpam-5407	41	9	,	,	PUNCT
ejpam-5407	41	10	τ	τ	PROPN
ejpam-5407	41	11	∈	∈	PROPN
ejpam-5407	41	12	n−	n−	PROPN
ejpam-5407	41	13	{	{	PUNCT
ejpam-5407	41	14	1	1	NUM
ejpam-5407	41	15	}	}	PUNCT
ejpam-5407	41	16	.	.	PUNCT
ejpam-5407	42	1	(	(	PUNCT
ejpam-5407	42	2	5	5	X
ejpam-5407	42	3	)	)	PUNCT
ejpam-5407	42	4	the	the	DET
ejpam-5407	42	5	gaussian	gaussian	ADJ
ejpam-5407	42	6	hypergeometric	hypergeometric	ADJ
ejpam-5407	42	7	function	function	NOUN
ejpam-5407	42	8	g(ℶ1,ℶ2;ℶ3	g(ℶ1,ℶ2;ℶ3	PROPN
ejpam-5407	42	9	;	;	PUNCT
ejpam-5407	42	10	ς	ς	NOUN
ejpam-5407	42	11	)	)	PUNCT
ejpam-5407	42	12	given	give	VERB
ejpam-5407	42	13	by	by	ADP
ejpam-5407	42	14	:	:	PUNCT
ejpam-5407	42	15	g(ℶ1,ℶ2;ℶ3	g(ℶ1,ℶ2;ℶ3	PROPN
ejpam-5407	42	16	;	;	PUNCT
ejpam-5407	42	17	ς	ς	X
ejpam-5407	42	18	)	)	PUNCT
ejpam-5407	42	19	=	=	NOUN
ejpam-5407	43	1	∞∑	∞∑	NUM
ejpam-5407	43	2	τ=0	τ=0	PUNCT
ejpam-5407	43	3	(	(	PUNCT
ejpam-5407	43	4	ℶ1)τ	ℶ1)τ	PROPN
ejpam-5407	43	5	(	(	PUNCT
ejpam-5407	43	6	ℶ2)τ	ℶ2)τ	PROPN
ejpam-5407	43	7	(	(	PUNCT
ejpam-5407	43	8	ℶ3)τ	ℶ3)τ	ADJ
ejpam-5407	43	9	(	(	PUNCT
ejpam-5407	43	10	1)τ	1)τ	NUM
ejpam-5407	43	11	ςτ	ςτ	NOUN
ejpam-5407	43	12	,	,	PUNCT
ejpam-5407	43	13	|ς|	|ς|	PROPN
ejpam-5407	43	14	<	<	X
ejpam-5407	43	15	1	1	NUM
ejpam-5407	43	16	t.	t.	PROPN
ejpam-5407	43	17	al	al	PROPN
ejpam-5407	43	18	-	-	PUNCT
ejpam-5407	43	19	hawary	hawary	PROPN
ejpam-5407	43	20	,	,	PUNCT
ejpam-5407	43	21	m.	m.	NOUN
ejpam-5407	43	22	o.	o.	PROPN
ejpam-5407	43	23	massa’deh	massa’deh	PROPN
ejpam-5407	43	24	,	,	PUNCT
ejpam-5407	43	25	a.	a.	NOUN
ejpam-5407	43	26	o	o	X
ejpam-5407	43	27	fallatah	fallatah	PROPN
ejpam-5407	43	28	/	/	SYM
ejpam-5407	43	29	eur	eur	PROPN
ejpam-5407	43	30	.	.	PUNCT
ejpam-5407	44	1	j.	j.	PROPN
ejpam-5407	44	2	pure	pure	PROPN
ejpam-5407	44	3	appl	appl	PROPN
ejpam-5407	44	4	.	.	PROPN
ejpam-5407	44	5	math	math	PROPN
ejpam-5407	44	6	,	,	PUNCT
ejpam-5407	44	7	17	17	NUM
ejpam-5407	44	8	(	(	PUNCT
ejpam-5407	44	9	4	4	NUM
ejpam-5407	44	10	)	)	PUNCT
ejpam-5407	44	11	(	(	PUNCT
ejpam-5407	44	12	2024	2024	NUM
ejpam-5407	44	13	)	)	PUNCT
ejpam-5407	44	14	,	,	PUNCT
ejpam-5407	44	15	3386	3386	NUM
ejpam-5407	44	16	-	-	SYM
ejpam-5407	44	17	3398	3398	NUM
ejpam-5407	44	18	3388	3388	NUM
ejpam-5407	44	19	where	where	SCONJ
ejpam-5407	44	20	ℶ1,ℶ2,ℶ3	ℶ1,ℶ2,ℶ3	ADP
ejpam-5407	44	21	∈	∈	PROPN
ejpam-5407	44	22	c	c	NOUN
ejpam-5407	44	23	such	such	ADJ
ejpam-5407	44	24	that	that	DET
ejpam-5407	44	25	ℶ3	ℶ3	PROPN
ejpam-5407	44	26	̸=	̸=	PROPN
ejpam-5407	44	27	0,−1,−2	0,−1,−2	NUM
ejpam-5407	44	28	,	,	PUNCT
ejpam-5407	44	29	·	·	PUNCT
ejpam-5407	44	30	·	·	PUNCT
ejpam-5407	44	31	·	·	PUNCT
ejpam-5407	44	32	,	,	PUNCT
ejpam-5407	44	33	(	(	PUNCT
ejpam-5407	44	34	ℶ1)0	ℶ1)0	NOUN
ejpam-5407	44	35	=	=	SYM
ejpam-5407	44	36	1	1	NUM
ejpam-5407	44	37	for	for	ADP
ejpam-5407	44	38	ℶ1	ℶ1	NOUN
ejpam-5407	44	39	̸=	̸=	PROPN
ejpam-5407	44	40	0	0	NUM
ejpam-5407	44	41	and	and	CCONJ
ejpam-5407	44	42	for	for	ADP
ejpam-5407	44	43	τ	τ	PROPN
ejpam-5407	44	44	∈	∈	PROPN
ejpam-5407	44	45	n	n	CCONJ
ejpam-5407	44	46	,	,	PUNCT
ejpam-5407	44	47	(	(	PUNCT
ejpam-5407	44	48	ℶ1)τ	ℶ1)τ	NOUN
ejpam-5407	44	49	=	=	PUNCT
ejpam-5407	44	50	ℶ1(ℶ1	ℶ1(ℶ1	PRON
ejpam-5407	44	51	+	+	NOUN
ejpam-5407	44	52	1)(ℶ1	1)(ℶ1	NUM
ejpam-5407	44	53	+	+	CCONJ
ejpam-5407	44	54	2	2	NUM
ejpam-5407	44	55	)	)	PUNCT
ejpam-5407	44	56	·	·	PUNCT
ejpam-5407	44	57	·	·	PUNCT
ejpam-5407	44	58	·	·	PUNCT
ejpam-5407	45	1	(	(	PUNCT
ejpam-5407	45	2	ℶ1	ℶ1	NOUN
ejpam-5407	45	3	+	+	CCONJ
ejpam-5407	45	4	τ	τ	PROPN
ejpam-5407	45	5	−	−	PROPN
ejpam-5407	45	6	1	1	NUM
ejpam-5407	45	7	)	)	PUNCT
ejpam-5407	45	8	is	be	AUX
ejpam-5407	45	9	the	the	DET
ejpam-5407	45	10	pochhammer	pochhammer	NOUN
ejpam-5407	45	11	symbol	symbol	NOUN
ejpam-5407	45	12	,	,	PUNCT
ejpam-5407	45	13	and	and	CCONJ
ejpam-5407	45	14	it	it	PRON
ejpam-5407	45	15	represents	represent	VERB
ejpam-5407	45	16	the	the	DET
ejpam-5407	45	17	solution	solution	NOUN
ejpam-5407	45	18	of	of	ADP
ejpam-5407	45	19	the	the	DET
ejpam-5407	45	20	homogenous	homogenous	ADJ
ejpam-5407	45	21	differential	differential	NOUN
ejpam-5407	45	22	equation	equation	NOUN
ejpam-5407	45	23	ς(1−	ς(1−	PROPN
ejpam-5407	45	24	ς)y′′(ς	ς)y′′(ς	NUM
ejpam-5407	45	25	)	)	PUNCT
ejpam-5407	46	1	+	+	CCONJ
ejpam-5407	46	2	(	(	PUNCT
ejpam-5407	46	3	ℶ3	ℶ3	INTJ
ejpam-5407	46	4	−	−	PROPN
ejpam-5407	46	5	(	(	PUNCT
ejpam-5407	46	6	ℶ1	ℶ1	NOUN
ejpam-5407	46	7	+	+	CCONJ
ejpam-5407	46	8	ℶ2	ℶ2	PROPN
ejpam-5407	46	9	+	+	NOUN
ejpam-5407	46	10	1)ς	1)ς	NOUN
ejpam-5407	46	11	)	)	PUNCT
ejpam-5407	47	1	y′(ς)−	y′(ς)−	NOUN
ejpam-5407	47	2	ℶ1ℶ2y(ς)=0	ℶ1ℶ2y(ς)=0	NOUN
ejpam-5407	47	3	has	have	VERB
ejpam-5407	47	4	several	several	ADJ
ejpam-5407	47	5	uses	use	NOUN
ejpam-5407	47	6	in	in	ADP
ejpam-5407	47	7	a	a	DET
ejpam-5407	47	8	variety	variety	NOUN
ejpam-5407	47	9	of	of	ADP
ejpam-5407	47	10	fields	field	NOUN
ejpam-5407	47	11	,	,	PUNCT
ejpam-5407	47	12	including	include	VERB
ejpam-5407	47	13	continued	continue	VERB
ejpam-5407	47	14	fractions	fraction	NOUN
ejpam-5407	47	15	,	,	PUNCT
ejpam-5407	47	16	quasi	quasi	ADJ
ejpam-5407	47	17	-	-	ADJ
ejpam-5407	47	18	conformal	conformal	ADJ
ejpam-5407	47	19	theory	theory	NOUN
ejpam-5407	47	20	,	,	PUNCT
ejpam-5407	47	21	conformal	conformal	NOUN
ejpam-5407	47	22	mappings	mapping	NOUN
ejpam-5407	47	23	,	,	PUNCT
ejpam-5407	47	24	and	and	CCONJ
ejpam-5407	47	25	more	more	ADJ
ejpam-5407	47	26	.	.	PUNCT
ejpam-5407	48	1	using	use	VERB
ejpam-5407	48	2	gauss	gauss	ADJ
ejpam-5407	48	3	summation	summation	NOUN
ejpam-5407	48	4	theorem	theorem	PROPN
ejpam-5407	48	5	,	,	PUNCT
ejpam-5407	48	6	it	it	PRON
ejpam-5407	48	7	is	be	AUX
ejpam-5407	48	8	possible	possible	ADJ
ejpam-5407	48	9	to	to	PART
ejpam-5407	48	10	write	write	VERB
ejpam-5407	48	11	g(ℶ1,ℶ2;ℶ3	g(ℶ1,ℶ2;ℶ3	NOUN
ejpam-5407	48	12	;	;	PUNCT
ejpam-5407	48	13	1	1	X
ejpam-5407	48	14	)	)	PUNCT
ejpam-5407	48	15	=	=	NOUN
ejpam-5407	49	1	∞∑	∞∑	NUM
ejpam-5407	49	2	τ=0	τ=0	PUNCT
ejpam-5407	49	3	(	(	PUNCT
ejpam-5407	49	4	ℶ1)τ	ℶ1)τ	PROPN
ejpam-5407	49	5	(	(	PUNCT
ejpam-5407	49	6	ℶ2)τ	ℶ2)τ	PROPN
ejpam-5407	49	7	(	(	PUNCT
ejpam-5407	49	8	ℶ3)τ	ℶ3)τ	ADJ
ejpam-5407	49	9	(	(	PUNCT
ejpam-5407	49	10	1)τ	1)τ	NUM
ejpam-5407	49	11	=	=	NOUN
ejpam-5407	49	12	γ(ℶ3	γ(ℶ3	NOUN
ejpam-5407	49	13	−	−	PROPN
ejpam-5407	49	14	ℶ2	ℶ2	PROPN
ejpam-5407	49	15	−	−	PROPN
ejpam-5407	49	16	ℶ1)γ(ℶ3	ℶ1)γ(ℶ3	PROPN
ejpam-5407	49	17	)	)	PUNCT
ejpam-5407	49	18	γ(ℶ3	γ(ℶ3	NOUN
ejpam-5407	49	19	−	−	PROPN
ejpam-5407	49	20	ℶ1)γ(ℶ3	ℶ1)γ(ℶ3	NOUN
ejpam-5407	49	21	−	−	PROPN
ejpam-5407	49	22	ℶ2	ℶ2	PROPN
ejpam-5407	49	23	)	)	PUNCT
ejpam-5407	49	24	,	,	PUNCT
ejpam-5407	49	25	for	for	ADP
ejpam-5407	49	26	re(ℶ3	re(ℶ3	VERB
ejpam-5407	49	27	−	−	PROPN
ejpam-5407	49	28	ℶ2	ℶ2	PROPN
ejpam-5407	49	29	−	−	PROPN
ejpam-5407	49	30	ℶ1	ℶ1	NOUN
ejpam-5407	49	31	)	)	PUNCT
ejpam-5407	49	32	>	>	X
ejpam-5407	49	33	0	0	X
ejpam-5407	49	34	.	.	PUNCT
ejpam-5407	49	35	(	(	PUNCT
ejpam-5407	49	36	6	6	NUM
ejpam-5407	49	37	)	)	PUNCT
ejpam-5407	49	38	for	for	ADP
ejpam-5407	49	39	l∈	l∈	PROPN
ejpam-5407	49	40	π	π	PROPN
ejpam-5407	49	41	,	,	PUNCT
ejpam-5407	49	42	we	we	PRON
ejpam-5407	49	43	recall	recall	VERB
ejpam-5407	49	44	the	the	DET
ejpam-5407	49	45	operator	operator	NOUN
ejpam-5407	49	46	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	VERB
ejpam-5407	49	47	)	)	PUNCT
ejpam-5407	49	48	:	:	PUNCT
ejpam-5407	50	1	π	π	X
ejpam-5407	50	2	→	→	SYM
ejpam-5407	50	3	π	π	PROPN
ejpam-5407	50	4	of	of	ADP
ejpam-5407	50	5	hohlov	hohlov	NOUN
ejpam-5407	50	6	[	[	X
ejpam-5407	50	7	11	11	NUM
ejpam-5407	50	8	]	]	PUNCT
ejpam-5407	50	9	defined	define	VERB
ejpam-5407	50	10	as	as	ADP
ejpam-5407	50	11	:	:	PUNCT
ejpam-5407	50	12	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	50	13	)	)	PUNCT
ejpam-5407	50	14	≡	≡	PROPN
ejpam-5407	50	15	hoℶ1,ℶ2,ℶ3(l)(ς	hoℶ1,ℶ2,ℶ3(l)(ς	X
ejpam-5407	50	16	)	)	PUNCT
ejpam-5407	50	17	=	=	SYM
ejpam-5407	51	1	ςg(ℶ1,ℶ2;ℶ3	ςg(ℶ1,ℶ2;ℶ3	X
ejpam-5407	51	2	;	;	PUNCT
ejpam-5407	51	3	ς	ς	X
ejpam-5407	51	4	)	)	PUNCT
ejpam-5407	51	5	∗	∗	NOUN
ejpam-5407	51	6	l(ς	l(ς	PROPN
ejpam-5407	51	7	)	)	PUNCT
ejpam-5407	51	8	=	=	PUNCT
ejpam-5407	52	1	ς	ς	PROPN
ejpam-5407	52	2	+	+	PUNCT
ejpam-5407	52	3	∞∑	∞∑	NUM
ejpam-5407	52	4	τ=2	τ=2	PUNCT
ejpam-5407	52	5	(	(	PUNCT
ejpam-5407	52	6	ℶ1)τ−1(ℶ2)τ−1	ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	52	7	(	(	PUNCT
ejpam-5407	52	8	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	PROPN
ejpam-5407	52	9	rτ	rτ	PROPN
ejpam-5407	52	10	ς	ς	PROPN
ejpam-5407	52	11	τ	τ	PROPN
ejpam-5407	52	12	.	.	PUNCT
ejpam-5407	53	1	remark	remark	PROPN
ejpam-5407	53	2	1	1	NUM
ejpam-5407	53	3	.	.	NOUN
ejpam-5407	53	4	1	1	NUM
ejpam-5407	53	5	)	)	PUNCT
ejpam-5407	53	6	if	if	SCONJ
ejpam-5407	53	7	ℶ1	ℶ1	NOUN
ejpam-5407	53	8	=	=	NOUN
ejpam-5407	53	9	1	1	NUM
ejpam-5407	53	10	,	,	PUNCT
ejpam-5407	53	11	ℶ2	ℶ2	NOUN
ejpam-5407	53	12	=	=	SYM
ejpam-5407	53	13	α	α	PROPN
ejpam-5407	54	1	+	+	NOUN
ejpam-5407	54	2	1	1	NUM
ejpam-5407	54	3	,	,	PUNCT
ejpam-5407	54	4	ℶ3	ℶ3	NOUN
ejpam-5407	54	5	=	=	SYM
ejpam-5407	54	6	α	α	PROPN
ejpam-5407	55	1	+	+	NOUN
ejpam-5407	55	2	2	2	NUM
ejpam-5407	55	3	with	with	ADP
ejpam-5407	55	4	re(α	re(α	NOUN
ejpam-5407	55	5	)	)	PUNCT
ejpam-5407	55	6	>	>	X
ejpam-5407	56	1	−1	−1	NOUN
ejpam-5407	56	2	,	,	PUNCT
ejpam-5407	56	3	then	then	ADV
ejpam-5407	56	4	the	the	DET
ejpam-5407	56	5	operator	operator	NOUN
ejpam-5407	56	6	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	VERB
ejpam-5407	56	7	)	)	PUNCT
ejpam-5407	56	8	turns	turn	VERB
ejpam-5407	56	9	into	into	ADP
ejpam-5407	56	10	ho1,α+1,α+2(l	ho1,α+1,α+2(l	NOUN
ejpam-5407	56	11	)	)	PUNCT
ejpam-5407	56	12	bernardi	bernardi	PROPN
ejpam-5407	56	13	operator	operator	NOUN
ejpam-5407	57	1	[	[	X
ejpam-5407	57	2	7	7	NUM
ejpam-5407	57	3	]	]	PUNCT
ejpam-5407	57	4	,	,	PUNCT
ejpam-5407	57	5	2	2	X
ejpam-5407	57	6	)	)	PUNCT
ejpam-5407	57	7	ho1,1,2(l	ho1,1,2(l	NOUN
ejpam-5407	57	8	)	)	PUNCT
ejpam-5407	57	9	alexander	alexander	NOUN
ejpam-5407	57	10	operator	operator	NOUN
ejpam-5407	57	11	[	[	X
ejpam-5407	57	12	3	3	NUM
ejpam-5407	57	13	]	]	PUNCT
ejpam-5407	57	14	,	,	PUNCT
ejpam-5407	57	15	3	3	X
ejpam-5407	57	16	)	)	PUNCT
ejpam-5407	57	17	ho1,2,3(l	ho1,2,3(l	NOUN
ejpam-5407	57	18	)	)	PUNCT
ejpam-5407	57	19	libera	libera	NOUN
ejpam-5407	57	20	operator	operator	NOUN
ejpam-5407	57	21	[	[	X
ejpam-5407	57	22	16	16	NUM
ejpam-5407	57	23	]	]	PUNCT
ejpam-5407	57	24	.	.	PUNCT
ejpam-5407	58	1	we	we	PRON
ejpam-5407	58	2	examine	examine	VERB
ejpam-5407	58	3	the	the	DET
ejpam-5407	58	4	following	follow	VERB
ejpam-5407	58	5	subfamilies	subfamily	NOUN
ejpam-5407	58	6	of	of	ADP
ejpam-5407	58	7	analytic	analytic	ADJ
ejpam-5407	58	8	functions	function	NOUN
ejpam-5407	58	9	investigated	investigate	VERB
ejpam-5407	58	10	by	by	ADP
ejpam-5407	58	11	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-5407	58	12	et	et	PROPN
ejpam-5407	58	13	al	al	PROPN
ejpam-5407	58	14	.	.	PROPN
ejpam-5407	58	15	,	,	PUNCT
ejpam-5407	59	1	[	[	X
ejpam-5407	59	2	18	18	NUM
ejpam-5407	59	3	]	]	PUNCT
ejpam-5407	59	4	and	and	CCONJ
ejpam-5407	59	5	ali	ali	PROPN
ejpam-5407	59	6	et	et	PROPN
ejpam-5407	59	7	al	al	PROPN
ejpam-5407	59	8	.	.	PROPN
ejpam-5407	59	9	,	,	PUNCT
ejpam-5407	60	1	[	[	X
ejpam-5407	60	2	20	20	NUM
ejpam-5407	60	3	]	]	PUNCT
ejpam-5407	60	4	,	,	PUNCT
ejpam-5407	60	5	respectively	respectively	ADV
ejpam-5407	60	6	.	.	PUNCT
ejpam-5407	61	1	definition	definition	NOUN
ejpam-5407	61	2	1	1	NUM
ejpam-5407	61	3	.	.	PUNCT
ejpam-5407	62	1	for	for	ADP
ejpam-5407	62	2	some	some	DET
ejpam-5407	62	3	κ1(0	κ1(0	NOUN
ejpam-5407	62	4	≤	≤	NOUN
ejpam-5407	62	5	κ1	κ1	NOUN
ejpam-5407	62	6	<	<	X
ejpam-5407	62	7	1	1	NUM
ejpam-5407	62	8	)	)	PUNCT
ejpam-5407	62	9	,	,	PUNCT
ejpam-5407	62	10	κ2(κ2	κ2(κ2	X
ejpam-5407	62	11	≥	≥	NUM
ejpam-5407	62	12	0	0	NUM
ejpam-5407	62	13	)	)	PUNCT
ejpam-5407	62	14	and	and	CCONJ
ejpam-5407	62	15	κ3(0	κ3(0	PROPN
ejpam-5407	62	16	≤	≤	NOUN
ejpam-5407	62	17	κ3	κ3	PROPN
ejpam-5407	62	18	≤	≤	NUM
ejpam-5407	62	19	1	1	NUM
ejpam-5407	62	20	)	)	PUNCT
ejpam-5407	62	21	.	.	PUNCT
ejpam-5407	63	1	let	let	VERB
ejpam-5407	63	2	the	the	DET
ejpam-5407	63	3	subfamily	subfamily	ADV
ejpam-5407	63	4	cκ3(κ1	cκ3(κ1	ADJ
ejpam-5407	63	5	,	,	PUNCT
ejpam-5407	63	6	κ2	κ2	NOUN
ejpam-5407	63	7	)	)	PUNCT
ejpam-5407	63	8	consists	consist	VERB
ejpam-5407	63	9	of	of	ADP
ejpam-5407	63	10	functions	function	NOUN
ejpam-5407	63	11	in	in	ADP
ejpam-5407	63	12	π	π	PROPN
ejpam-5407	63	13	satisfying	satisfy	VERB
ejpam-5407	63	14	the	the	DET
ejpam-5407	63	15	inequality	inequality	NOUN
ejpam-5407	63	16	re	re	ADP
ejpam-5407	63	17	(	(	PUNCT
ejpam-5407	63	18	ςl′(ς	ςl′(ς	PROPN
ejpam-5407	63	19	)	)	PUNCT
ejpam-5407	63	20	+	+	NUM
ejpam-5407	63	21	ς2l′′(ς	ς2l′′(ς	NUM
ejpam-5407	63	22	)	)	PUNCT
ejpam-5407	64	1	(	(	PUNCT
ejpam-5407	64	2	1−	1−	NUM
ejpam-5407	64	3	κ3)ς	κ3)ς	NOUN
ejpam-5407	64	4	+	+	CCONJ
ejpam-5407	64	5	κ3ςl′(ς	κ3ςl′(ς	NOUN
ejpam-5407	64	6	)	)	PUNCT
ejpam-5407	64	7	−	−	PROPN
ejpam-5407	64	8	κ1	κ1	NOUN
ejpam-5407	64	9	)	)	PUNCT
ejpam-5407	64	10	>	>	PUNCT
ejpam-5407	64	11	κ2	κ2	PROPN
ejpam-5407	64	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5407	64	13	ςl′(ς	ςl′(ς	PROPN
ejpam-5407	64	14	)	)	PUNCT
ejpam-5407	65	1	+	+	NUM
ejpam-5407	65	2	ς2l′′(ς	ς2l′′(ς	NUM
ejpam-5407	65	3	)	)	PUNCT
ejpam-5407	65	4	(	(	PUNCT
ejpam-5407	65	5	1−	1−	NUM
ejpam-5407	65	6	κ3)ς	κ3)ς	NOUN
ejpam-5407	65	7	+	+	CCONJ
ejpam-5407	65	8	κ3ςl′(ς	κ3ςl′(ς	NOUN
ejpam-5407	65	9	)	)	PUNCT
ejpam-5407	66	1	−	−	PROPN
ejpam-5407	66	2	1	1	NUM
ejpam-5407	66	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	66	4	,	,	PUNCT
ejpam-5407	66	5	|ς|	|ς|	PROPN
ejpam-5407	66	6	<	<	X
ejpam-5407	66	7	1	1	NUM
ejpam-5407	66	8	and	and	CCONJ
ejpam-5407	66	9	the	the	DET
ejpam-5407	66	10	subfamily	subfamily	ADV
ejpam-5407	66	11	s∗κ3(κ1	s∗κ3(κ1	ADJ
ejpam-5407	66	12	,	,	PUNCT
ejpam-5407	66	13	κ2	κ2	NOUN
ejpam-5407	66	14	)	)	PUNCT
ejpam-5407	66	15	consists	consist	VERB
ejpam-5407	66	16	of	of	ADP
ejpam-5407	66	17	functions	function	NOUN
ejpam-5407	66	18	in	in	ADP
ejpam-5407	66	19	π	π	PROPN
ejpam-5407	66	20	satisfying	satisfy	VERB
ejpam-5407	66	21	the	the	DET
ejpam-5407	66	22	inequality	inequality	NOUN
ejpam-5407	66	23	re	re	ADP
ejpam-5407	66	24	(	(	PUNCT
ejpam-5407	66	25	ςl′(ς	ςl′(ς	PROPN
ejpam-5407	66	26	)	)	PUNCT
ejpam-5407	66	27	(	(	PUNCT
ejpam-5407	66	28	1−	1−	NUM
ejpam-5407	66	29	κ3)ς	κ3)ς	PROPN
ejpam-5407	66	30	+	+	CCONJ
ejpam-5407	66	31	κ3l(ς	κ3l(ς	PROPN
ejpam-5407	66	32	)	)	PUNCT
ejpam-5407	66	33	−	−	PROPN
ejpam-5407	66	34	κ1	κ1	NOUN
ejpam-5407	66	35	)	)	PUNCT
ejpam-5407	66	36	>	>	PUNCT
ejpam-5407	66	37	κ2	κ2	PROPN
ejpam-5407	66	38	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5407	66	39	ςl′(ς	ςl′(ς	PROPN
ejpam-5407	66	40	)	)	PUNCT
ejpam-5407	66	41	(	(	PUNCT
ejpam-5407	66	42	1−	1−	NUM
ejpam-5407	66	43	κ3)ς	κ3)ς	PROPN
ejpam-5407	66	44	+	+	CCONJ
ejpam-5407	66	45	κ3l(ς	κ3l(ς	PROPN
ejpam-5407	66	46	)	)	PUNCT
ejpam-5407	66	47	−	−	PROPN
ejpam-5407	66	48	1	1	NUM
ejpam-5407	66	49	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	66	50	,	,	PUNCT
ejpam-5407	66	51	|ς|	|ς|	PROPN
ejpam-5407	66	52	<	<	X
ejpam-5407	66	53	1	1	X
ejpam-5407	66	54	.	.	PUNCT
ejpam-5407	66	55	example	example	NOUN
ejpam-5407	67	1	1	1	NUM
ejpam-5407	67	2	.	.	PUNCT
ejpam-5407	68	1	[	[	X
ejpam-5407	68	2	12	12	NUM
ejpam-5407	68	3	,	,	PUNCT
ejpam-5407	68	4	19	19	NUM
ejpam-5407	68	5	]	]	PUNCT
ejpam-5407	68	6	for	for	ADP
ejpam-5407	68	7	some	some	DET
ejpam-5407	68	8	κ1(0	κ1(0	NOUN
ejpam-5407	68	9	≤	≤	NOUN
ejpam-5407	68	10	κ1	κ1	NOUN
ejpam-5407	68	11	<	<	X
ejpam-5407	68	12	1	1	NUM
ejpam-5407	68	13	)	)	PUNCT
ejpam-5407	68	14	,	,	PUNCT
ejpam-5407	68	15	κ2(κ2	κ2(κ2	X
ejpam-5407	68	16	≥	≥	NUM
ejpam-5407	68	17	0	0	NUM
ejpam-5407	68	18	)	)	PUNCT
ejpam-5407	68	19	,	,	PUNCT
ejpam-5407	68	20	κ3	κ3	PROPN
ejpam-5407	68	21	=	=	SYM
ejpam-5407	68	22	1	1	NUM
ejpam-5407	68	23	and	and	CCONJ
ejpam-5407	68	24	l(ς	l(ς	PROPN
ejpam-5407	68	25	)	)	PUNCT
ejpam-5407	68	26	of	of	ADP
ejpam-5407	68	27	the	the	DET
ejpam-5407	68	28	form	form	NOUN
ejpam-5407	68	29	(	(	PUNCT
ejpam-5407	68	30	1	1	NUM
ejpam-5407	68	31	)	)	PUNCT
ejpam-5407	68	32	,	,	PUNCT
ejpam-5407	68	33	let	let	VERB
ejpam-5407	68	34	the	the	DET
ejpam-5407	68	35	subfamily	subfamily	ADV
ejpam-5407	68	36	c1(κ1	c1(κ1	ADJ
ejpam-5407	68	37	,	,	PUNCT
ejpam-5407	68	38	κ2	κ2	NOUN
ejpam-5407	68	39	)	)	PUNCT
ejpam-5407	68	40	consists	consist	VERB
ejpam-5407	68	41	of	of	ADP
ejpam-5407	68	42	functions	function	NOUN
ejpam-5407	68	43	in	in	ADP
ejpam-5407	68	44	π	π	PROPN
ejpam-5407	68	45	satisfying	satisfy	VERB
ejpam-5407	68	46	re	re	ADP
ejpam-5407	68	47	(	(	PUNCT
ejpam-5407	68	48	ςl′′(ς	ςl′′(ς	NOUN
ejpam-5407	68	49	)	)	PUNCT
ejpam-5407	68	50	l′(ς	l′(ς	PUNCT
ejpam-5407	68	51	)	)	PUNCT
ejpam-5407	69	1	+	+	CCONJ
ejpam-5407	69	2	1−	1−	NUM
ejpam-5407	69	3	κ1	κ1	NOUN
ejpam-5407	69	4	)	)	PUNCT
ejpam-5407	69	5	>	>	PUNCT
ejpam-5407	69	6	κ2	κ2	PROPN
ejpam-5407	69	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	69	8	ςl′′(ς	ςl′′(ς	NOUN
ejpam-5407	69	9	)	)	PUNCT
ejpam-5407	69	10	l′(ς	l′(ς	NOUN
ejpam-5407	69	11	)	)	PUNCT
ejpam-5407	69	12	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	69	13	,	,	PUNCT
ejpam-5407	69	14	|ς|	|ς|	PROPN
ejpam-5407	69	15	<	<	X
ejpam-5407	69	16	1	1	NUM
ejpam-5407	69	17	and	and	CCONJ
ejpam-5407	69	18	the	the	DET
ejpam-5407	69	19	subfamily	subfamily	ADV
ejpam-5407	69	20	s∗1(κ1	s∗1(κ1	NOUN
ejpam-5407	69	21	,	,	PUNCT
ejpam-5407	69	22	κ2	κ2	NOUN
ejpam-5407	69	23	)	)	PUNCT
ejpam-5407	69	24	consists	consist	VERB
ejpam-5407	69	25	of	of	ADP
ejpam-5407	69	26	functions	function	NOUN
ejpam-5407	69	27	in	in	ADP
ejpam-5407	69	28	π	π	PROPN
ejpam-5407	69	29	satisfying	satisfy	VERB
ejpam-5407	69	30	re	re	ADP
ejpam-5407	69	31	(	(	PUNCT
ejpam-5407	69	32	ςl′(ς	ςl′(ς	PROPN
ejpam-5407	69	33	)	)	PUNCT
ejpam-5407	69	34	l(ς	l(ς	PROPN
ejpam-5407	69	35	)	)	PUNCT
ejpam-5407	69	36	−	−	PROPN
ejpam-5407	69	37	κ1	κ1	NOUN
ejpam-5407	69	38	)	)	PUNCT
ejpam-5407	69	39	>	>	PUNCT
ejpam-5407	69	40	κ2	κ2	PROPN
ejpam-5407	69	41	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5407	69	42	ςl′(ς	ςl′(ς	PROPN
ejpam-5407	69	43	)	)	PUNCT
ejpam-5407	69	44	l(ς	l(ς	PROPN
ejpam-5407	69	45	)	)	PUNCT
ejpam-5407	69	46	−	−	PROPN
ejpam-5407	69	47	1	1	NUM
ejpam-5407	69	48	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	69	49	,	,	PUNCT
ejpam-5407	69	50	|ς|	|ς|	PROPN
ejpam-5407	69	51	<	<	X
ejpam-5407	69	52	1	1	X
ejpam-5407	69	53	.	.	PUNCT
ejpam-5407	70	1	t.	t.	PROPN
ejpam-5407	70	2	al	al	PROPN
ejpam-5407	70	3	-	-	PUNCT
ejpam-5407	70	4	hawary	hawary	PROPN
ejpam-5407	70	5	,	,	PUNCT
ejpam-5407	70	6	m.	m.	NOUN
ejpam-5407	70	7	o.	o.	PROPN
ejpam-5407	70	8	massa’deh	massa’deh	PROPN
ejpam-5407	70	9	,	,	PUNCT
ejpam-5407	70	10	a.	a.	NOUN
ejpam-5407	70	11	o	o	X
ejpam-5407	70	12	fallatah	fallatah	PROPN
ejpam-5407	70	13	/	/	SYM
ejpam-5407	70	14	eur	eur	PROPN
ejpam-5407	70	15	.	.	PUNCT
ejpam-5407	71	1	j.	j.	PROPN
ejpam-5407	71	2	pure	pure	PROPN
ejpam-5407	71	3	appl	appl	PROPN
ejpam-5407	71	4	.	.	PROPN
ejpam-5407	71	5	math	math	PROPN
ejpam-5407	71	6	,	,	PUNCT
ejpam-5407	71	7	17	17	NUM
ejpam-5407	71	8	(	(	PUNCT
ejpam-5407	71	9	4	4	NUM
ejpam-5407	71	10	)	)	PUNCT
ejpam-5407	71	11	(	(	PUNCT
ejpam-5407	71	12	2024	2024	NUM
ejpam-5407	71	13	)	)	PUNCT
ejpam-5407	71	14	,	,	PUNCT
ejpam-5407	71	15	3386	3386	NUM
ejpam-5407	71	16	-	-	SYM
ejpam-5407	71	17	3398	3398	NUM
ejpam-5407	71	18	3389	3389	NUM
ejpam-5407	71	19	example	example	NOUN
ejpam-5407	71	20	2	2	NUM
ejpam-5407	71	21	.	.	PUNCT
ejpam-5407	72	1	[	[	X
ejpam-5407	72	2	18	18	NUM
ejpam-5407	72	3	]	]	PUNCT
ejpam-5407	72	4	for	for	ADP
ejpam-5407	72	5	some	some	DET
ejpam-5407	72	6	κ1(0	κ1(0	NOUN
ejpam-5407	72	7	≤	≤	NOUN
ejpam-5407	72	8	κ1	κ1	NOUN
ejpam-5407	72	9	<	<	X
ejpam-5407	72	10	1	1	NUM
ejpam-5407	72	11	)	)	PUNCT
ejpam-5407	72	12	,	,	PUNCT
ejpam-5407	72	13	κ2(κ2	κ2(κ2	X
ejpam-5407	72	14	≥	≥	NUM
ejpam-5407	72	15	0	0	NUM
ejpam-5407	72	16	)	)	PUNCT
ejpam-5407	72	17	,	,	PUNCT
ejpam-5407	72	18	κ3	κ3	PROPN
ejpam-5407	72	19	=	=	SYM
ejpam-5407	72	20	0	0	NUM
ejpam-5407	72	21	and	and	CCONJ
ejpam-5407	72	22	l(ς	l(ς	PROPN
ejpam-5407	72	23	)	)	PUNCT
ejpam-5407	72	24	of	of	ADP
ejpam-5407	72	25	the	the	DET
ejpam-5407	72	26	form	form	NOUN
ejpam-5407	72	27	(	(	PUNCT
ejpam-5407	72	28	1	1	NUM
ejpam-5407	72	29	)	)	PUNCT
ejpam-5407	72	30	,	,	PUNCT
ejpam-5407	72	31	let	let	VERB
ejpam-5407	72	32	the	the	DET
ejpam-5407	72	33	subfamily	subfamily	ADV
ejpam-5407	72	34	c0(κ1	c0(κ1	NOUN
ejpam-5407	72	35	,	,	PUNCT
ejpam-5407	72	36	κ2	κ2	NOUN
ejpam-5407	72	37	)	)	PUNCT
ejpam-5407	72	38	consists	consist	VERB
ejpam-5407	72	39	of	of	ADP
ejpam-5407	72	40	functions	function	NOUN
ejpam-5407	72	41	in	in	ADP
ejpam-5407	72	42	π	π	PROPN
ejpam-5407	72	43	satisfying	satisfy	VERB
ejpam-5407	72	44	re	re	ADP
ejpam-5407	72	45	(	(	PUNCT
ejpam-5407	72	46	(	(	PUNCT
ejpam-5407	72	47	ςl′(ς	ςl′(ς	NOUN
ejpam-5407	72	48	)	)	PUNCT
ejpam-5407	72	49	)	)	PUNCT
ejpam-5407	73	1	′	′	NUM
ejpam-5407	74	1	−	−	PROPN
ejpam-5407	74	2	κ1	κ1	NOUN
ejpam-5407	74	3	)	)	PUNCT
ejpam-5407	74	4	>	>	X
ejpam-5407	74	5	κ2	κ2	PROPN
ejpam-5407	74	6	∣∣∣(ςl′(ς	∣∣∣(ςl′(ς	ADJ
ejpam-5407	74	7	)	)	PUNCT
ejpam-5407	74	8	)	)	PUNCT
ejpam-5407	75	1	′	′	NUM
ejpam-5407	76	1	−	−	NOUN
ejpam-5407	76	2	1	1	NUM
ejpam-5407	76	3	∣∣∣	∣∣∣	NOUN
ejpam-5407	76	4	,	,	PUNCT
ejpam-5407	76	5	|ς|	|ς|	PROPN
ejpam-5407	76	6	<	<	X
ejpam-5407	76	7	1	1	NUM
ejpam-5407	76	8	and	and	CCONJ
ejpam-5407	76	9	the	the	DET
ejpam-5407	76	10	subfamily	subfamily	ADV
ejpam-5407	76	11	s∗0(κ1	s∗0(κ1	ADJ
ejpam-5407	76	12	,	,	PUNCT
ejpam-5407	76	13	κ2	κ2	NOUN
ejpam-5407	76	14	)	)	PUNCT
ejpam-5407	76	15	consists	consist	VERB
ejpam-5407	76	16	of	of	ADP
ejpam-5407	76	17	functions	function	NOUN
ejpam-5407	76	18	in	in	ADP
ejpam-5407	76	19	π	π	PROPN
ejpam-5407	76	20	satisfying	satisfy	VERB
ejpam-5407	76	21	re	re	ADP
ejpam-5407	76	22	(	(	PUNCT
ejpam-5407	76	23	l′(ς)−	l′(ς)−	PROPN
ejpam-5407	76	24	κ1	κ1	NOUN
ejpam-5407	76	25	)	)	PUNCT
ejpam-5407	76	26	>	>	PUNCT
ejpam-5407	76	27	κ2	κ2	PROPN
ejpam-5407	76	28	∣∣l′(ς)−	∣∣l′(ς)−	NOUN
ejpam-5407	76	29	1	1	NUM
ejpam-5407	76	30	∣∣	∣∣	NUM
ejpam-5407	76	31	,	,	PUNCT
ejpam-5407	76	32	|ς|	|ς|	PROPN
ejpam-5407	76	33	<	<	X
ejpam-5407	76	34	1	1	X
ejpam-5407	76	35	.	.	PUNCT
ejpam-5407	76	36	example	example	NOUN
ejpam-5407	77	1	3	3	NUM
ejpam-5407	77	2	.	.	PUNCT
ejpam-5407	78	1	[	[	X
ejpam-5407	78	2	21	21	NUM
ejpam-5407	78	3	]	]	PUNCT
ejpam-5407	78	4	for	for	ADP
ejpam-5407	78	5	some	some	DET
ejpam-5407	78	6	κ1(0	κ1(0	NOUN
ejpam-5407	78	7	≤	≤	NOUN
ejpam-5407	78	8	κ1	κ1	NOUN
ejpam-5407	78	9	<	<	X
ejpam-5407	78	10	1	1	NUM
ejpam-5407	78	11	)	)	PUNCT
ejpam-5407	78	12	,	,	PUNCT
ejpam-5407	78	13	κ2	κ2	PROPN
ejpam-5407	78	14	=	=	SYM
ejpam-5407	78	15	0	0	NUM
ejpam-5407	78	16	,	,	PUNCT
ejpam-5407	78	17	κ3	κ3	PROPN
ejpam-5407	78	18	=	=	SYM
ejpam-5407	78	19	1	1	NUM
ejpam-5407	78	20	and	and	CCONJ
ejpam-5407	78	21	l(ς	l(ς	PROPN
ejpam-5407	78	22	)	)	PUNCT
ejpam-5407	78	23	of	of	ADP
ejpam-5407	78	24	the	the	DET
ejpam-5407	78	25	form	form	NOUN
ejpam-5407	78	26	(	(	PUNCT
ejpam-5407	78	27	1	1	NUM
ejpam-5407	78	28	)	)	PUNCT
ejpam-5407	78	29	,	,	PUNCT
ejpam-5407	78	30	let	let	VERB
ejpam-5407	78	31	the	the	DET
ejpam-5407	78	32	subfamily	subfamily	ADV
ejpam-5407	78	33	c∗	c∗	PROPN
ejpam-5407	78	34	1(κ1	1(κ1	NUM
ejpam-5407	78	35	,	,	PUNCT
ejpam-5407	78	36	0	0	NUM
ejpam-5407	78	37	)	)	PUNCT
ejpam-5407	78	38	≡	≡	PROPN
ejpam-5407	78	39	cv(κ1	cv(κ1	NOUN
ejpam-5407	78	40	)	)	PUNCT
ejpam-5407	78	41	consists	consist	VERB
ejpam-5407	78	42	of	of	ADP
ejpam-5407	78	43	functions	function	NOUN
ejpam-5407	78	44	in	in	ADP
ejpam-5407	78	45	π	π	PROPN
ejpam-5407	78	46	satisfying	satisfy	VERB
ejpam-5407	78	47	re	re	ADP
ejpam-5407	78	48	(	(	PUNCT
ejpam-5407	78	49	ςl′′(ς	ςl′′(ς	NOUN
ejpam-5407	78	50	)	)	PUNCT
ejpam-5407	78	51	l′(ς	l′(ς	PUNCT
ejpam-5407	78	52	)	)	PUNCT
ejpam-5407	79	1	+	+	CCONJ
ejpam-5407	79	2	1	1	X
ejpam-5407	79	3	)	)	PUNCT
ejpam-5407	79	4	>	>	X
ejpam-5407	79	5	κ1	κ1	PROPN
ejpam-5407	79	6	,	,	PUNCT
ejpam-5407	79	7	|ς|	|ς|	PROPN
ejpam-5407	79	8	<	<	X
ejpam-5407	79	9	1	1	NUM
ejpam-5407	79	10	and	and	CCONJ
ejpam-5407	79	11	the	the	DET
ejpam-5407	79	12	subfamily	subfamily	ADV
ejpam-5407	79	13	s∗1(κ1	s∗1(κ1	NOUN
ejpam-5407	79	14	,	,	PUNCT
ejpam-5407	79	15	0	0	NUM
ejpam-5407	79	16	)	)	PUNCT
ejpam-5407	79	17	≡	≡	PROPN
ejpam-5407	79	18	st	st	PROPN
ejpam-5407	79	19	(	(	PUNCT
ejpam-5407	79	20	κ1	κ1	NOUN
ejpam-5407	79	21	)	)	PUNCT
ejpam-5407	79	22	consists	consist	VERB
ejpam-5407	79	23	of	of	ADP
ejpam-5407	79	24	functions	function	NOUN
ejpam-5407	79	25	in	in	ADP
ejpam-5407	79	26	π	π	PROPN
ejpam-5407	79	27	satisfying	satisfy	VERB
ejpam-5407	79	28	re	re	ADP
ejpam-5407	79	29	(	(	PUNCT
ejpam-5407	79	30	ςl′(ς	ςl′(ς	PROPN
ejpam-5407	79	31	)	)	PUNCT
ejpam-5407	79	32	l(ς	l(ς	PROPN
ejpam-5407	79	33	)	)	PUNCT
ejpam-5407	79	34	)	)	PUNCT
ejpam-5407	80	1	>	>	X
ejpam-5407	80	2	κ1	κ1	PROPN
ejpam-5407	80	3	,	,	PUNCT
ejpam-5407	80	4	|ς|	|ς|	PROPN
ejpam-5407	80	5	<	<	X
ejpam-5407	80	6	1	1	X
ejpam-5407	80	7	.	.	PUNCT
ejpam-5407	81	1	both	both	DET
ejpam-5407	81	2	subfamilies	subfamily	NOUN
ejpam-5407	81	3	cv	cv	NOUN
ejpam-5407	81	4	(	(	PUNCT
ejpam-5407	81	5	κ1	κ1	NOUN
ejpam-5407	81	6	)	)	PUNCT
ejpam-5407	81	7	and	and	CCONJ
ejpam-5407	81	8	st	st	PROPN
ejpam-5407	81	9	(	(	PUNCT
ejpam-5407	81	10	κ1	κ1	NOUN
ejpam-5407	81	11	)	)	PUNCT
ejpam-5407	81	12	are	be	AUX
ejpam-5407	81	13	well	well	ADV
ejpam-5407	81	14	known	know	VERB
ejpam-5407	81	15	subfamilies	subfamily	NOUN
ejpam-5407	81	16	of	of	ADP
ejpam-5407	81	17	convex	convex	NOUN
ejpam-5407	81	18	and	and	CCONJ
ejpam-5407	81	19	starlike	starlike	NOUN
ejpam-5407	81	20	functions	function	NOUN
ejpam-5407	81	21	of	of	ADP
ejpam-5407	81	22	order	order	NOUN
ejpam-5407	81	23	κ1	κ1	NOUN
ejpam-5407	81	24	,	,	PUNCT
ejpam-5407	81	25	respectively	respectively	ADV
ejpam-5407	81	26	.	.	PUNCT
ejpam-5407	82	1	moreover	moreover	ADV
ejpam-5407	82	2	,	,	PUNCT
ejpam-5407	82	3	if	if	SCONJ
ejpam-5407	82	4	κ1	κ1	NOUN
ejpam-5407	82	5	=	=	SYM
ejpam-5407	82	6	κ2	κ2	NOUN
ejpam-5407	82	7	=	=	SYM
ejpam-5407	82	8	0	0	NUM
ejpam-5407	82	9	,	,	PUNCT
ejpam-5407	82	10	κ3	κ3	PROPN
ejpam-5407	82	11	=	=	SYM
ejpam-5407	82	12	1	1	NUM
ejpam-5407	82	13	,	,	PUNCT
ejpam-5407	82	14	we	we	PRON
ejpam-5407	82	15	get	get	VERB
ejpam-5407	82	16	the	the	DET
ejpam-5407	82	17	subfamilies	subfamily	NOUN
ejpam-5407	82	18	of	of	ADP
ejpam-5407	82	19	convex	convex	NOUN
ejpam-5407	82	20	functions	function	NOUN
ejpam-5407	82	21	cv	cv	PROPN
ejpam-5407	82	22	and	and	CCONJ
ejpam-5407	82	23	starlike	starlike	PROPN
ejpam-5407	82	24	functions	function	NOUN
ejpam-5407	82	25	st	st	PROPN
ejpam-5407	82	26	,	,	PUNCT
ejpam-5407	82	27	respectively	respectively	ADV
ejpam-5407	82	28	(	(	PUNCT
ejpam-5407	82	29	see	see	VERB
ejpam-5407	82	30	[	[	X
ejpam-5407	82	31	21	21	NUM
ejpam-5407	82	32	]	]	PUNCT
ejpam-5407	82	33	)	)	PUNCT
ejpam-5407	82	34	.	.	PUNCT
ejpam-5407	83	1	lemma	lemma	PROPN
ejpam-5407	83	2	1	1	NUM
ejpam-5407	83	3	.	.	PUNCT
ejpam-5407	84	1	[	[	X
ejpam-5407	84	2	18	18	NUM
ejpam-5407	84	3	]	]	PUNCT
ejpam-5407	84	4	a	a	DET
ejpam-5407	84	5	function	function	NOUN
ejpam-5407	84	6	l	l	PROPN
ejpam-5407	84	7	∈	∈	PROPN
ejpam-5407	84	8	cκ3(κ1	cκ3(κ1	NOUN
ejpam-5407	84	9	,	,	PUNCT
ejpam-5407	84	10	κ2	κ2	NOUN
ejpam-5407	84	11	)	)	PUNCT
ejpam-5407	84	12	if	if	SCONJ
ejpam-5407	84	13	and	and	CCONJ
ejpam-5407	84	14	only	only	ADV
ejpam-5407	84	15	if	if	SCONJ
ejpam-5407	84	16	∞∑	∞∑	NUM
ejpam-5407	84	17	τ=2	τ=2	PUNCT
ejpam-5407	84	18	τ	τ	PROPN
ejpam-5407	85	1	[	[	X
ejpam-5407	85	2	(	(	PUNCT
ejpam-5407	85	3	τ(κ2	τ(κ2	NOUN
ejpam-5407	85	4	+	+	X
ejpam-5407	85	5	1)−	1)−	NUM
ejpam-5407	85	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	85	7	+	+	NUM
ejpam-5407	85	8	κ2	κ2	NOUN
ejpam-5407	85	9	)	)	PUNCT
ejpam-5407	85	10	]	]	PUNCT
ejpam-5407	85	11	|rτ	|rτ	PUNCT
ejpam-5407	86	1	|	|	ADV
ejpam-5407	86	2	≤	≤	NOUN
ejpam-5407	86	3	1−	1−	NUM
ejpam-5407	86	4	κ1	κ1	NOUN
ejpam-5407	86	5	(	(	PUNCT
ejpam-5407	86	6	7	7	NUM
ejpam-5407	86	7	)	)	PUNCT
ejpam-5407	86	8	and	and	CCONJ
ejpam-5407	86	9	l	l	NOUN
ejpam-5407	86	10	∈	∈	PROPN
ejpam-5407	86	11	s∗κ3(κ1	s∗κ3(κ1	NOUN
ejpam-5407	86	12	,	,	PUNCT
ejpam-5407	86	13	κ2	κ2	NOUN
ejpam-5407	86	14	)	)	PUNCT
ejpam-5407	86	15	if	if	SCONJ
ejpam-5407	86	16	and	and	CCONJ
ejpam-5407	86	17	only	only	ADV
ejpam-5407	86	18	if	if	SCONJ
ejpam-5407	86	19	∞∑	∞∑	PRON
ejpam-5407	86	20	τ=2	τ=2	PUNCT
ejpam-5407	87	1	[	[	X
ejpam-5407	87	2	(	(	PUNCT
ejpam-5407	87	3	τ(κ2	τ(κ2	NOUN
ejpam-5407	87	4	+	+	X
ejpam-5407	87	5	1)−	1)−	NUM
ejpam-5407	87	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	87	7	+	+	NUM
ejpam-5407	87	8	κ2	κ2	NOUN
ejpam-5407	87	9	)	)	PUNCT
ejpam-5407	87	10	]	]	PUNCT
ejpam-5407	87	11	|rτ	|rτ	PUNCT
ejpam-5407	88	1	|	|	ADV
ejpam-5407	88	2	≤	≤	ADJ
ejpam-5407	88	3	1−	1−	NUM
ejpam-5407	88	4	κ1	κ1	NOUN
ejpam-5407	88	5	.	.	PUNCT
ejpam-5407	89	1	(	(	PUNCT
ejpam-5407	89	2	8)	8)	NUM
ejpam-5407	89	3	the	the	DET
ejpam-5407	89	4	geometric	geometric	ADJ
ejpam-5407	89	5	characteristics	characteristic	NOUN
ejpam-5407	89	6	of	of	ADP
ejpam-5407	89	7	numerous	numerous	ADJ
ejpam-5407	89	8	types	type	NOUN
ejpam-5407	89	9	of	of	ADP
ejpam-5407	89	10	special	special	ADJ
ejpam-5407	89	11	functions	function	NOUN
ejpam-5407	89	12	are	be	AUX
ejpam-5407	89	13	covered	cover	VERB
ejpam-5407	89	14	in	in	ADP
ejpam-5407	89	15	a	a	DET
ejpam-5407	89	16	substantial	substantial	ADJ
ejpam-5407	89	17	body	body	NOUN
ejpam-5407	89	18	of	of	ADP
ejpam-5407	89	19	literature	literature	NOUN
ejpam-5407	89	20	(	(	PUNCT
ejpam-5407	89	21	see	see	VERB
ejpam-5407	89	22	[	[	X
ejpam-5407	89	23	1	1	NUM
ejpam-5407	89	24	]	]	PUNCT
ejpam-5407	89	25	,	,	PUNCT
ejpam-5407	89	26	[	[	X
ejpam-5407	89	27	6	6	NUM
ejpam-5407	89	28	]	]	PUNCT
ejpam-5407	89	29	,	,	PUNCT
ejpam-5407	89	30	[	[	X
ejpam-5407	89	31	9	9	NUM
ejpam-5407	89	32	]	]	PUNCT
ejpam-5407	89	33	,	,	PUNCT
ejpam-5407	89	34	[	[	X
ejpam-5407	89	35	4	4	NUM
ejpam-5407	89	36	]	]	PUNCT
ejpam-5407	89	37	,	,	PUNCT
ejpam-5407	89	38	[	[	X
ejpam-5407	89	39	11	11	NUM
ejpam-5407	89	40	]	]	PUNCT
ejpam-5407	89	41	,	,	PUNCT
ejpam-5407	89	42	[	[	X
ejpam-5407	89	43	2	2	NUM
ejpam-5407	89	44	]	]	NUM
ejpam-5407	89	45	)	)	PUNCT
ejpam-5407	89	46	.	.	PUNCT
ejpam-5407	90	1	the	the	DET
ejpam-5407	90	2	current	current	ADJ
ejpam-5407	90	3	paper	paper	NOUN
ejpam-5407	90	4	aims	aim	VERB
ejpam-5407	90	5	to	to	PART
ejpam-5407	90	6	create	create	VERB
ejpam-5407	90	7	connections	connection	NOUN
ejpam-5407	90	8	between	between	ADP
ejpam-5407	90	9	hohlov	hohlov	NOUN
ejpam-5407	90	10	operator	operator	NOUN
ejpam-5407	90	11	and	and	CCONJ
ejpam-5407	90	12	geometric	geometric	ADJ
ejpam-5407	90	13	function	function	NOUN
ejpam-5407	90	14	theory	theory	NOUN
ejpam-5407	90	15	.	.	PUNCT
ejpam-5407	91	1	by	by	ADP
ejpam-5407	91	2	findings	finding	NOUN
ejpam-5407	91	3	the	the	DET
ejpam-5407	91	4	relationships	relationship	NOUN
ejpam-5407	91	5	between	between	ADP
ejpam-5407	91	6	different	different	ADJ
ejpam-5407	91	7	subfamilies	subfamily	NOUN
ejpam-5407	91	8	of	of	ADP
ejpam-5407	91	9	analytic	analytic	ADJ
ejpam-5407	91	10	univalent	univalent	ADJ
ejpam-5407	91	11	functions	function	NOUN
ejpam-5407	91	12	.	.	PUNCT
ejpam-5407	92	1	inspired	inspire	VERB
ejpam-5407	92	2	by	by	ADP
ejpam-5407	92	3	numerous	numerous	ADJ
ejpam-5407	92	4	works	work	NOUN
ejpam-5407	92	5	,	,	PUNCT
ejpam-5407	92	6	for	for	ADP
ejpam-5407	92	7	example	example	NOUN
ejpam-5407	92	8	ahmad	ahmad	PROPN
ejpam-5407	92	9	et	et	PROPN
ejpam-5407	92	10	al	al	PROPN
ejpam-5407	92	11	.	.	PUNCT
ejpam-5407	93	1	[	[	X
ejpam-5407	93	2	17	17	NUM
ejpam-5407	93	3	]	]	PUNCT
ejpam-5407	93	4	deduced	deduce	VERB
ejpam-5407	93	5	sufficient	sufficient	ADJ
ejpam-5407	93	6	conditions	condition	NOUN
ejpam-5407	93	7	and	and	CCONJ
ejpam-5407	93	8	some	some	DET
ejpam-5407	93	9	properties	property	NOUN
ejpam-5407	93	10	for	for	ADP
ejpam-5407	93	11	mittag	mittag	ADJ
ejpam-5407	93	12	-	-	PUNCT
ejpam-5407	93	13	leffler	leffler	NOUN
ejpam-5407	93	14	.	.	PUNCT
ejpam-5407	94	1	frasin	frasin	PROPN
ejpam-5407	94	2	et	et	PROPN
ejpam-5407	94	3	al	al	PROPN
ejpam-5407	94	4	.	.	PUNCT
ejpam-5407	95	1	[	[	X
ejpam-5407	95	2	5	5	NUM
ejpam-5407	95	3	]	]	PUNCT
ejpam-5407	95	4	deduced	deduce	VERB
ejpam-5407	95	5	necessary	necessary	ADJ
ejpam-5407	95	6	and	and	CCONJ
ejpam-5407	95	7	sufficient	sufficient	ADJ
ejpam-5407	95	8	conditions	condition	NOUN
ejpam-5407	95	9	for	for	SCONJ
ejpam-5407	95	10	struve	struve	PROPN
ejpam-5407	95	11	functions	function	NOUN
ejpam-5407	95	12	to	to	PART
ejpam-5407	95	13	be	be	AUX
ejpam-5407	95	14	in	in	ADP
ejpam-5407	95	15	some	some	DET
ejpam-5407	95	16	classes	class	NOUN
ejpam-5407	95	17	.	.	PUNCT
ejpam-5407	96	1	kasthuri	kasthuri	PROPN
ejpam-5407	96	2	et	et	PROPN
ejpam-5407	96	3	al	al	PROPN
ejpam-5407	96	4	.	.	PUNCT
ejpam-5407	97	1	[	[	X
ejpam-5407	97	2	15	15	NUM
ejpam-5407	97	3	]	]	PUNCT
ejpam-5407	97	4	introduced	introduce	VERB
ejpam-5407	97	5	a	a	DET
ejpam-5407	97	6	new	new	ADJ
ejpam-5407	97	7	class	class	NOUN
ejpam-5407	97	8	by	by	ADP
ejpam-5407	97	9	hohlov	hohlov	NOUN
ejpam-5407	97	10	operator	operator	NOUN
ejpam-5407	97	11	and	and	CCONJ
ejpam-5407	97	12	obtain	obtain	VERB
ejpam-5407	97	13	some	some	DET
ejpam-5407	97	14	inclusion	inclusion	NOUN
ejpam-5407	97	15	relations	relation	NOUN
ejpam-5407	97	16	.	.	PUNCT
ejpam-5407	98	1	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-5407	98	2	et	et	PROPN
ejpam-5407	98	3	al	al	PROPN
ejpam-5407	98	4	.	.	PUNCT
ejpam-5407	99	1	[	[	X
ejpam-5407	99	2	18	18	NUM
ejpam-5407	99	3	]	]	PUNCT
ejpam-5407	99	4	introduced	introduce	VERB
ejpam-5407	99	5	a	a	DET
ejpam-5407	99	6	class	class	NOUN
ejpam-5407	99	7	of	of	ADP
ejpam-5407	99	8	starlike	starlike	NOUN
ejpam-5407	99	9	functions	function	NOUN
ejpam-5407	99	10	and	and	CCONJ
ejpam-5407	99	11	subordination	subordination	NOUN
ejpam-5407	99	12	results	result	NOUN
ejpam-5407	99	13	for	for	ADP
ejpam-5407	99	14	some	some	DET
ejpam-5407	99	15	classes	class	NOUN
ejpam-5407	99	16	of	of	ADP
ejpam-5407	99	17	starlike	starlike	NOUN
ejpam-5407	99	18	functions	function	NOUN
ejpam-5407	99	19	.	.	PUNCT
ejpam-5407	100	1	swaminathan	swaminathan	ADV
ejpam-5407	100	2	[	[	X
ejpam-5407	100	3	22	22	NUM
ejpam-5407	100	4	]	]	PUNCT
ejpam-5407	100	5	introduced	introduce	VERB
ejpam-5407	100	6	some	some	DET
ejpam-5407	100	7	conditions	condition	NOUN
ejpam-5407	100	8	for	for	ADP
ejpam-5407	100	9	normalized	normalize	VERB
ejpam-5407	100	10	gaussian	gaussian	ADJ
ejpam-5407	100	11	hypergeometric	hypergeometric	ADJ
ejpam-5407	100	12	function	function	NOUN
ejpam-5407	100	13	.	.	PUNCT
ejpam-5407	101	1	t.	t.	PROPN
ejpam-5407	101	2	al	al	PROPN
ejpam-5407	101	3	-	-	PUNCT
ejpam-5407	101	4	hawary	hawary	PROPN
ejpam-5407	101	5	,	,	PUNCT
ejpam-5407	101	6	m.	m.	NOUN
ejpam-5407	101	7	o.	o.	PROPN
ejpam-5407	101	8	massa’deh	massa’deh	PROPN
ejpam-5407	101	9	,	,	PUNCT
ejpam-5407	101	10	a.	a.	NOUN
ejpam-5407	101	11	o	o	X
ejpam-5407	101	12	fallatah	fallatah	PROPN
ejpam-5407	101	13	/	/	SYM
ejpam-5407	101	14	eur	eur	PROPN
ejpam-5407	101	15	.	.	PUNCT
ejpam-5407	102	1	j.	j.	PROPN
ejpam-5407	102	2	pure	pure	PROPN
ejpam-5407	102	3	appl	appl	PROPN
ejpam-5407	102	4	.	.	PROPN
ejpam-5407	102	5	math	math	PROPN
ejpam-5407	102	6	,	,	PUNCT
ejpam-5407	102	7	17	17	NUM
ejpam-5407	102	8	(	(	PUNCT
ejpam-5407	102	9	4	4	NUM
ejpam-5407	102	10	)	)	PUNCT
ejpam-5407	102	11	(	(	PUNCT
ejpam-5407	102	12	2024	2024	NUM
ejpam-5407	102	13	)	)	PUNCT
ejpam-5407	102	14	,	,	PUNCT
ejpam-5407	102	15	3386	3386	NUM
ejpam-5407	102	16	-	-	SYM
ejpam-5407	102	17	3398	3398	NUM
ejpam-5407	102	18	3390	3390	NUM
ejpam-5407	102	19	2	2	NUM
ejpam-5407	102	20	.	.	PUNCT
ejpam-5407	102	21	main	main	ADJ
ejpam-5407	102	22	results	result	NOUN
ejpam-5407	102	23	this	this	DET
ejpam-5407	102	24	section	section	NOUN
ejpam-5407	102	25	will	will	AUX
ejpam-5407	102	26	provide	provide	VERB
ejpam-5407	102	27	sufficient	sufficient	ADJ
ejpam-5407	102	28	conditions	condition	NOUN
ejpam-5407	102	29	for	for	ADP
ejpam-5407	102	30	hohlov	hohlov	NOUN
ejpam-5407	102	31	operator	operator	NOUN
ejpam-5407	102	32	function	function	NOUN
ejpam-5407	102	33	to	to	PART
ejpam-5407	102	34	be	be	AUX
ejpam-5407	102	35	in	in	ADP
ejpam-5407	102	36	the	the	DET
ejpam-5407	102	37	subfamilies	subfamily	NOUN
ejpam-5407	102	38	cκ3(κ1	cκ3(κ1	NOUN
ejpam-5407	102	39	,	,	PUNCT
ejpam-5407	102	40	κ2	κ2	NOUN
ejpam-5407	102	41	)	)	PUNCT
ejpam-5407	102	42	and	and	CCONJ
ejpam-5407	102	43	s∗κ3(κ1	s∗κ3(κ1	ADJ
ejpam-5407	102	44	,	,	PUNCT
ejpam-5407	102	45	κ2	κ2	NOUN
ejpam-5407	102	46	)	)	PUNCT
ejpam-5407	102	47	.	.	PUNCT
ejpam-5407	103	1	theorem	theorem	NOUN
ejpam-5407	103	2	1	1	NUM
ejpam-5407	103	3	.	.	PUNCT
ejpam-5407	104	1	if	if	SCONJ
ejpam-5407	104	2	l	l	PROPN
ejpam-5407	104	3	∈	∈	PROPN
ejpam-5407	104	4	st	st	PROPN
ejpam-5407	104	5	and	and	CCONJ
ejpam-5407	104	6	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	104	7	∈	∈	PROPN
ejpam-5407	104	8	c−{0	c−{0	ADV
ejpam-5407	104	9	}	}	PUNCT
ejpam-5407	104	10	,	,	PUNCT
ejpam-5407	104	11	ℶ3	ℶ3	PROPN
ejpam-5407	104	12	∈	∈	PROPN
ejpam-5407	104	13	r	r	NOUN
ejpam-5407	104	14	,	,	PUNCT
ejpam-5407	104	15	then	then	ADV
ejpam-5407	104	16	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	104	17	)	)	PUNCT
ejpam-5407	104	18	∈	∈	PROPN
ejpam-5407	104	19	cκ3(κ1	cκ3(κ1	NOUN
ejpam-5407	104	20	,	,	PUNCT
ejpam-5407	104	21	κ2	κ2	NOUN
ejpam-5407	104	22	)	)	PUNCT
ejpam-5407	104	23	if	if	SCONJ
ejpam-5407	104	24	the	the	DET
ejpam-5407	104	25	following	follow	VERB
ejpam-5407	104	26	condition	condition	NOUN
ejpam-5407	104	27	is	be	AUX
ejpam-5407	104	28	satisfied	satisfied	ADJ
ejpam-5407	104	29	:	:	PUNCT
ejpam-5407	104	30	(	(	PUNCT
ejpam-5407	104	31	κ2	κ2	NOUN
ejpam-5407	104	32	+	+	CCONJ
ejpam-5407	104	33	1	1	X
ejpam-5407	104	34	)	)	PUNCT
ejpam-5407	104	35	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	104	36	(	(	PUNCT
ejpam-5407	104	37	|ℶ1|+	|ℶ1|+	X
ejpam-5407	104	38	1	1	NUM
ejpam-5407	104	39	)	)	PUNCT
ejpam-5407	104	40	(	(	PUNCT
ejpam-5407	104	41	|ℶ2|+	|ℶ2|+	X
ejpam-5407	104	42	1	1	NUM
ejpam-5407	104	43	)	)	PUNCT
ejpam-5407	104	44	(	(	PUNCT
ejpam-5407	104	45	|ℶ1|+	|ℶ1|+	X
ejpam-5407	104	46	2	2	NUM
ejpam-5407	104	47	)	)	PUNCT
ejpam-5407	104	48	(	(	PUNCT
ejpam-5407	104	49	|ℶ2|+	|ℶ2|+	X
ejpam-5407	104	50	2	2	NUM
ejpam-5407	104	51	)	)	PUNCT
ejpam-5407	104	52	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	104	53	+	+	CCONJ
ejpam-5407	104	54	1)(ℶ3	1)(ℶ3	NUM
ejpam-5407	104	55	+	+	CCONJ
ejpam-5407	104	56	2	2	X
ejpam-5407	104	57	)	)	PUNCT
ejpam-5407	104	58	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	104	59	3	3	NUM
ejpam-5407	104	60	,	,	PUNCT
ejpam-5407	104	61	|ℶ2|+	|ℶ2|+	X
ejpam-5407	104	62	3;ℶ3	3;ℶ3	NUM
ejpam-5407	104	63	+	+	SYM
ejpam-5407	104	64	3,1	3,1	NUM
ejpam-5407	104	65	)	)	PUNCT
ejpam-5407	105	1	+	+	CCONJ
ejpam-5407	105	2	(	(	PUNCT
ejpam-5407	105	3	6(κ2	6(κ2	NUM
ejpam-5407	105	4	+	+	CCONJ
ejpam-5407	105	5	1)−	1)−	NUM
ejpam-5407	105	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	105	7	+	+	NUM
ejpam-5407	105	8	κ2	κ2	NOUN
ejpam-5407	105	9	)	)	PUNCT
ejpam-5407	105	10	)	)	PUNCT
ejpam-5407	105	11	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	105	12	(	(	PUNCT
ejpam-5407	105	13	|ℶ1|+	|ℶ1|+	X
ejpam-5407	105	14	1	1	NUM
ejpam-5407	105	15	)	)	PUNCT
ejpam-5407	105	16	(	(	PUNCT
ejpam-5407	105	17	|ℶ2|+	|ℶ2|+	X
ejpam-5407	105	18	1	1	NUM
ejpam-5407	105	19	)	)	PUNCT
ejpam-5407	105	20	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	105	21	+	+	NOUN
ejpam-5407	105	22	1	1	X
ejpam-5407	105	23	)	)	PUNCT
ejpam-5407	105	24	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	105	25	2	2	NUM
ejpam-5407	105	26	,	,	PUNCT
ejpam-5407	105	27	|ℶ2|+	|ℶ2|+	X
ejpam-5407	105	28	2;ℶ3	2;ℶ3	NUM
ejpam-5407	105	29	+	+	NUM
ejpam-5407	105	30	2,1	2,1	NUM
ejpam-5407	105	31	)	)	PUNCT
ejpam-5407	105	32	+	+	CCONJ
ejpam-5407	106	1	(	(	PUNCT
ejpam-5407	106	2	7(κ2	7(κ2	X
ejpam-5407	107	1	+	+	CCONJ
ejpam-5407	107	2	1)−	1)−	NUM
ejpam-5407	107	3	3κ3(κ1	3κ3(κ1	NUM
ejpam-5407	107	4	+	+	NUM
ejpam-5407	107	5	κ2	κ2	NOUN
ejpam-5407	107	6	)	)	PUNCT
ejpam-5407	107	7	)	)	PUNCT
ejpam-5407	108	1	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	108	2	ℶ3	ℶ3	PROPN
ejpam-5407	108	3	g2,1(|ℶ1|+	g2,1(|ℶ1|+	PROPN
ejpam-5407	108	4	1	1	NUM
ejpam-5407	108	5	,	,	PUNCT
ejpam-5407	108	6	|ℶ2|+	|ℶ2|+	X
ejpam-5407	108	7	1;ℶ3	1;ℶ3	NUM
ejpam-5407	108	8	+	+	SYM
ejpam-5407	108	9	1,1	1,1	NUM
ejpam-5407	108	10	)	)	PUNCT
ejpam-5407	108	11	+	+	CCONJ
ejpam-5407	108	12	(	(	PUNCT
ejpam-5407	108	13	κ2	κ2	NOUN
ejpam-5407	108	14	−	−	PROPN
ejpam-5407	108	15	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	108	16	+	+	NUM
ejpam-5407	108	17	κ2	κ2	NOUN
ejpam-5407	108	18	)	)	PUNCT
ejpam-5407	108	19	+	+	CCONJ
ejpam-5407	109	1	1	1	X
ejpam-5407	109	2	)	)	PUNCT
ejpam-5407	110	1	[	[	X
ejpam-5407	110	2	g2,1	g2,1	ADJ
ejpam-5407	110	3	|ℶ1|	|ℶ1|	NOUN
ejpam-5407	110	4	,	,	PUNCT
ejpam-5407	110	5	|ℶ2|	|ℶ2|	ADJ
ejpam-5407	110	6	;	;	PUNCT
ejpam-5407	110	7	ℶ3,1)−	ℶ3,1)−	PROPN
ejpam-5407	110	8	1	1	NUM
ejpam-5407	110	9	]	]	PUNCT
ejpam-5407	110	10	≤	≤	NUM
ejpam-5407	110	11	1−	1−	NUM
ejpam-5407	110	12	κ1	κ1	NOUN
ejpam-5407	110	13	.	.	PUNCT
ejpam-5407	111	1	proof	proof	NOUN
ejpam-5407	111	2	.	.	PUNCT
ejpam-5407	112	1	by	by	ADP
ejpam-5407	112	2	equation	equation	NOUN
ejpam-5407	112	3	(	(	PUNCT
ejpam-5407	112	4	7	7	NUM
ejpam-5407	112	5	)	)	PUNCT
ejpam-5407	112	6	,	,	PUNCT
ejpam-5407	112	7	to	to	PART
ejpam-5407	112	8	prove	prove	VERB
ejpam-5407	112	9	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	NOUN
ejpam-5407	112	10	)	)	PUNCT
ejpam-5407	112	11	∈	∈	PROPN
ejpam-5407	112	12	cκ3(κ1	cκ3(κ1	NOUN
ejpam-5407	112	13	,	,	PUNCT
ejpam-5407	112	14	κ2	κ2	PROPN
ejpam-5407	112	15	)	)	PUNCT
ejpam-5407	112	16	,	,	PUNCT
ejpam-5407	112	17	it	it	PRON
ejpam-5407	112	18	suffices	suffice	VERB
ejpam-5407	112	19	to	to	PART
ejpam-5407	112	20	show	show	VERB
ejpam-5407	112	21	that	that	SCONJ
ejpam-5407	112	22	∞∑	∞∑	NUM
ejpam-5407	112	23	τ=2	τ=2	PUNCT
ejpam-5407	112	24	τ	τ	PROPN
ejpam-5407	113	1	[	[	X
ejpam-5407	113	2	(	(	PUNCT
ejpam-5407	113	3	τ(κ2	τ(κ2	NOUN
ejpam-5407	113	4	+	+	X
ejpam-5407	113	5	1)−	1)−	NUM
ejpam-5407	113	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	113	7	+	+	NUM
ejpam-5407	113	8	κ2	κ2	NOUN
ejpam-5407	113	9	)	)	PUNCT
ejpam-5407	113	10	]	]	PUNCT
ejpam-5407	113	11	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	113	12	(	(	PUNCT
ejpam-5407	113	13	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	NOUN
ejpam-5407	113	14	rτ	rτ	PROPN
ejpam-5407	113	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	113	16	≤	≤	NOUN
ejpam-5407	113	17	1−	1−	NUM
ejpam-5407	113	18	κ1	κ1	NOUN
ejpam-5407	113	19	.	.	PUNCT
ejpam-5407	114	1	since	since	SCONJ
ejpam-5407	114	2	l	l	PROPN
ejpam-5407	114	3	∈	∈	PROPN
ejpam-5407	114	4	st	st	NOUN
ejpam-5407	114	5	we	we	PRON
ejpam-5407	114	6	have	have	VERB
ejpam-5407	114	7	|rτ	|rτ	NUM
ejpam-5407	115	1	|	|	ADV
ejpam-5407	115	2	≤	≤	X
ejpam-5407	115	3	τ	τ	X
ejpam-5407	115	4	,	,	PUNCT
ejpam-5407	115	5	from	from	ADP
ejpam-5407	115	6	above	above	ADP
ejpam-5407	115	7	equation	equation	NOUN
ejpam-5407	115	8	we	we	PRON
ejpam-5407	115	9	get	get	VERB
ejpam-5407	115	10	∞∑	∞∑	NUM
ejpam-5407	115	11	τ=2	τ=2	PUNCT
ejpam-5407	116	1	[	[	X
ejpam-5407	116	2	(	(	PUNCT
ejpam-5407	116	3	τ3(κ2	τ3(κ2	ADV
ejpam-5407	116	4	+	+	ADP
ejpam-5407	116	5	1	1	X
ejpam-5407	116	6	)	)	PUNCT
ejpam-5407	116	7	−	−	ADP
ejpam-5407	116	8	τ2κ3(κ1	τ2κ3(κ1	ADV
ejpam-5407	116	9	+	+	NUM
ejpam-5407	116	10	κ2	κ2	NOUN
ejpam-5407	116	11	)	)	PUNCT
ejpam-5407	116	12	]	]	PUNCT
ejpam-5407	117	1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	117	2	(	(	PUNCT
ejpam-5407	117	3	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	PROPN
ejpam-5407	117	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5407	117	5	≤	≤	PROPN
ejpam-5407	117	6	1−	1−	NUM
ejpam-5407	117	7	κ1	κ1	NOUN
ejpam-5407	117	8	.	.	PUNCT
ejpam-5407	118	1	writing	write	VERB
ejpam-5407	118	2			PUNCT
ejpam-5407	118	3	τ	τ	X
ejpam-5407	118	4	=	=	PUNCT
ejpam-5407	118	5	(	(	PUNCT
ejpam-5407	118	6	τ	τ	PROPN
ejpam-5407	118	7	−	−	PROPN
ejpam-5407	118	8	1	1	NUM
ejpam-5407	118	9	)	)	PUNCT
ejpam-5407	118	10	+	+	NUM
ejpam-5407	118	11	1	1	NUM
ejpam-5407	118	12	,	,	PUNCT
ejpam-5407	118	13	τ2	τ2	NOUN
ejpam-5407	118	14	=	=	PUNCT
ejpam-5407	118	15	(	(	PUNCT
ejpam-5407	118	16	τ	τ	PROPN
ejpam-5407	118	17	−	−	PROPN
ejpam-5407	118	18	1)(τ	1)(τ	NUM
ejpam-5407	118	19	−	−	NOUN
ejpam-5407	118	20	2	2	NUM
ejpam-5407	118	21	)	)	PUNCT
ejpam-5407	118	22	+	+	CCONJ
ejpam-5407	118	23	3(τ	3(τ	NUM
ejpam-5407	118	24	−	−	NOUN
ejpam-5407	118	25	1	1	NUM
ejpam-5407	118	26	)	)	PUNCT
ejpam-5407	118	27	+	+	NUM
ejpam-5407	118	28	1	1	NUM
ejpam-5407	118	29	,	,	PUNCT
ejpam-5407	118	30	τ3	τ3	NOUN
ejpam-5407	118	31	=	=	SYM
ejpam-5407	118	32	(	(	PUNCT
ejpam-5407	118	33	τ	τ	PROPN
ejpam-5407	118	34	−	−	PROPN
ejpam-5407	119	1	1)(τ	1)(τ	NUM
ejpam-5407	119	2	−	−	NOUN
ejpam-5407	119	3	2)(τ	2)(τ	NUM
ejpam-5407	119	4	−	−	NOUN
ejpam-5407	119	5	3	3	NUM
ejpam-5407	119	6	)	)	PUNCT
ejpam-5407	119	7	+	+	NUM
ejpam-5407	119	8	6(τ	6(τ	NUM
ejpam-5407	119	9	−	−	NOUN
ejpam-5407	120	1	1)(τ	1)(τ	NUM
ejpam-5407	120	2	−	−	NOUN
ejpam-5407	120	3	2	2	NUM
ejpam-5407	120	4	)	)	PUNCT
ejpam-5407	120	5	+	+	CCONJ
ejpam-5407	120	6	7(τ	7(τ	NUM
ejpam-5407	120	7	−	−	NOUN
ejpam-5407	120	8	1	1	NUM
ejpam-5407	120	9	)	)	PUNCT
ejpam-5407	120	10	+	+	CCONJ
ejpam-5407	120	11	1	1	NUM
ejpam-5407	120	12	and	and	CCONJ
ejpam-5407	120	13	use	use	VERB
ejpam-5407	120	14	the	the	DET
ejpam-5407	120	15	relations	relation	NOUN
ejpam-5407	120	16	(	(	PUNCT
ejpam-5407	120	17	ℶ1)τ	ℶ1)τ	NOUN
ejpam-5407	120	18	=	=	PUNCT
ejpam-5407	120	19	ℶ1(ℶ1	ℶ1(ℶ1	NOUN
ejpam-5407	120	20	+	+	X
ejpam-5407	120	21	1)τ−1	1)τ−1	NUM
ejpam-5407	120	22	and	and	CCONJ
ejpam-5407	120	23	|(ℶ1)τ	|(ℶ1)τ	PROPN
ejpam-5407	120	24	|	|	ADV
ejpam-5407	120	25	≤	≤	PROPN
ejpam-5407	120	26	(	(	PUNCT
ejpam-5407	120	27	|ℶ1|)τ	|ℶ1|)τ	NOUN
ejpam-5407	120	28	,	,	PUNCT
ejpam-5407	120	29	(	(	PUNCT
ejpam-5407	120	30	9	9	X
ejpam-5407	120	31	)	)	PUNCT
ejpam-5407	120	32	we	we	PRON
ejpam-5407	120	33	have	have	VERB
ejpam-5407	120	34	∞∑	∞∑	NUM
ejpam-5407	120	35	τ=2	τ=2	PUNCT
ejpam-5407	121	1	[	[	X
ejpam-5407	121	2	(	(	PUNCT
ejpam-5407	121	3	τ3(κ2	τ3(κ2	ADV
ejpam-5407	121	4	+	+	ADP
ejpam-5407	121	5	1	1	X
ejpam-5407	121	6	)	)	PUNCT
ejpam-5407	121	7	−	−	ADP
ejpam-5407	121	8	τ2κ3(κ1	τ2κ3(κ1	ADV
ejpam-5407	121	9	+	+	NUM
ejpam-5407	121	10	κ2	κ2	NOUN
ejpam-5407	121	11	)	)	PUNCT
ejpam-5407	121	12	]	]	PUNCT
ejpam-5407	121	13	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	121	14	(	(	PUNCT
ejpam-5407	121	15	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	NOUN
ejpam-5407	121	16	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	121	17	=	=	PUNCT
ejpam-5407	121	18	(	(	PUNCT
ejpam-5407	121	19	κ2	κ2	NOUN
ejpam-5407	121	20	+	+	CCONJ
ejpam-5407	121	21	1	1	X
ejpam-5407	121	22	)	)	PUNCT
ejpam-5407	121	23	∞∑	∞∑	NOUN
ejpam-5407	121	24	τ=2	τ=2	PUNCT
ejpam-5407	121	25	(	(	PUNCT
ejpam-5407	121	26	τ	τ	X
ejpam-5407	121	27	−	−	PROPN
ejpam-5407	122	1	1)(τ	1)(τ	NUM
ejpam-5407	122	2	−	−	NOUN
ejpam-5407	122	3	2)(τ	2)(τ	NUM
ejpam-5407	122	4	−	−	NOUN
ejpam-5407	122	5	3	3	NUM
ejpam-5407	122	6	)	)	PUNCT
ejpam-5407	122	7	(	(	PUNCT
ejpam-5407	122	8	|ℶ1|)τ−1	|ℶ1|)τ−1	NOUN
ejpam-5407	122	9	(	(	PUNCT
ejpam-5407	122	10	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	122	11	(	(	PUNCT
ejpam-5407	122	12	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	122	13	(	(	PUNCT
ejpam-5407	122	14	1)τ−1	1)τ−1	NUM
ejpam-5407	122	15	+	+	ADJ
ejpam-5407	122	16	(	(	PUNCT
ejpam-5407	122	17	6(κ2	6(κ2	NUM
ejpam-5407	122	18	+	+	CCONJ
ejpam-5407	122	19	1)−	1)−	NUM
ejpam-5407	122	20	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	122	21	+	+	NUM
ejpam-5407	122	22	κ2	κ2	NOUN
ejpam-5407	122	23	)	)	PUNCT
ejpam-5407	122	24	)	)	PUNCT
ejpam-5407	123	1	∞∑	∞∑	NUM
ejpam-5407	123	2	τ=2	τ=2	PUNCT
ejpam-5407	123	3	(	(	PUNCT
ejpam-5407	123	4	τ	τ	X
ejpam-5407	123	5	−	−	PROPN
ejpam-5407	123	6	1)(τ	1)(τ	NUM
ejpam-5407	123	7	−	−	NOUN
ejpam-5407	123	8	2	2	NUM
ejpam-5407	123	9	)	)	PUNCT
ejpam-5407	123	10	(	(	PUNCT
ejpam-5407	123	11	|ℶ1|)τ−1	|ℶ1|)τ−1	NOUN
ejpam-5407	123	12	(	(	PUNCT
ejpam-5407	123	13	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	123	14	(	(	PUNCT
ejpam-5407	123	15	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	123	16	(	(	PUNCT
ejpam-5407	123	17	1)τ−1	1)τ−1	NUM
ejpam-5407	123	18	t.	t.	PROPN
ejpam-5407	123	19	al	al	PROPN
ejpam-5407	123	20	-	-	PUNCT
ejpam-5407	123	21	hawary	hawary	PROPN
ejpam-5407	123	22	,	,	PUNCT
ejpam-5407	123	23	m.	m.	NOUN
ejpam-5407	123	24	o.	o.	PROPN
ejpam-5407	123	25	massa’deh	massa’deh	PROPN
ejpam-5407	123	26	,	,	PUNCT
ejpam-5407	123	27	a.	a.	NOUN
ejpam-5407	123	28	o	o	X
ejpam-5407	123	29	fallatah	fallatah	PROPN
ejpam-5407	123	30	/	/	SYM
ejpam-5407	123	31	eur	eur	PROPN
ejpam-5407	123	32	.	.	PUNCT
ejpam-5407	124	1	j.	j.	PROPN
ejpam-5407	124	2	pure	pure	PROPN
ejpam-5407	124	3	appl	appl	PROPN
ejpam-5407	124	4	.	.	PROPN
ejpam-5407	124	5	math	math	PROPN
ejpam-5407	124	6	,	,	PUNCT
ejpam-5407	124	7	17	17	NUM
ejpam-5407	124	8	(	(	PUNCT
ejpam-5407	124	9	4	4	NUM
ejpam-5407	124	10	)	)	PUNCT
ejpam-5407	124	11	(	(	PUNCT
ejpam-5407	124	12	2024	2024	NUM
ejpam-5407	124	13	)	)	PUNCT
ejpam-5407	124	14	,	,	PUNCT
ejpam-5407	124	15	3386	3386	NUM
ejpam-5407	124	16	-	-	SYM
ejpam-5407	124	17	3398	3398	NUM
ejpam-5407	124	18	3391	3391	NUM
ejpam-5407	124	19	+	+	PROPN
ejpam-5407	124	20	(	(	PUNCT
ejpam-5407	125	1	7(κ2	7(κ2	NOUN
ejpam-5407	126	1	+	+	CCONJ
ejpam-5407	127	1	1)−	1)−	NUM
ejpam-5407	127	2	3κ3(κ1	3κ3(κ1	NUM
ejpam-5407	127	3	+	+	NUM
ejpam-5407	127	4	κ2	κ2	NOUN
ejpam-5407	127	5	)	)	PUNCT
ejpam-5407	127	6	)	)	PUNCT
ejpam-5407	128	1	∞∑	∞∑	NUM
ejpam-5407	128	2	τ=2	τ=2	PUNCT
ejpam-5407	128	3	(	(	PUNCT
ejpam-5407	128	4	τ	τ	X
ejpam-5407	128	5	−	−	PROPN
ejpam-5407	128	6	1	1	NUM
ejpam-5407	128	7	)	)	PUNCT
ejpam-5407	128	8	(	(	PUNCT
ejpam-5407	128	9	|ℶ1|)τ−1	|ℶ1|)τ−1	NOUN
ejpam-5407	128	10	(	(	PUNCT
ejpam-5407	128	11	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	128	12	(	(	PUNCT
ejpam-5407	128	13	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	128	14	(	(	PUNCT
ejpam-5407	128	15	1)τ−1	1)τ−1	NUM
ejpam-5407	128	16	+	+	ADJ
ejpam-5407	128	17	(	(	PUNCT
ejpam-5407	128	18	κ2	κ2	NOUN
ejpam-5407	128	19	−	−	PROPN
ejpam-5407	128	20	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	128	21	+	+	NUM
ejpam-5407	128	22	κ2	κ2	NOUN
ejpam-5407	128	23	)	)	PUNCT
ejpam-5407	128	24	+	+	CCONJ
ejpam-5407	128	25	1	1	X
ejpam-5407	128	26	)	)	PUNCT
ejpam-5407	128	27	∞∑	∞∑	PROPN
ejpam-5407	128	28	τ=2	τ=2	PUNCT
ejpam-5407	128	29	(	(	PUNCT
ejpam-5407	128	30	|ℶ1|)τ−1	|ℶ1|)τ−1	PROPN
ejpam-5407	128	31	(	(	PUNCT
ejpam-5407	128	32	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	128	33	(	(	PUNCT
ejpam-5407	128	34	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	128	35	(	(	PUNCT
ejpam-5407	128	36	1)τ−1	1)τ−1	NUM
ejpam-5407	128	37	≤	≤	NOUN
ejpam-5407	128	38	(	(	PUNCT
ejpam-5407	128	39	κ2	κ2	NOUN
ejpam-5407	128	40	+	+	CCONJ
ejpam-5407	128	41	1	1	X
ejpam-5407	128	42	)	)	PUNCT
ejpam-5407	128	43	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	128	44	(	(	PUNCT
ejpam-5407	128	45	|ℶ1|+	|ℶ1|+	X
ejpam-5407	128	46	1	1	NUM
ejpam-5407	128	47	)	)	PUNCT
ejpam-5407	128	48	(	(	PUNCT
ejpam-5407	128	49	|ℶ2|+	|ℶ2|+	X
ejpam-5407	128	50	1	1	NUM
ejpam-5407	128	51	)	)	PUNCT
ejpam-5407	128	52	(	(	PUNCT
ejpam-5407	128	53	|ℶ1|+	|ℶ1|+	X
ejpam-5407	128	54	2	2	NUM
ejpam-5407	128	55	)	)	PUNCT
ejpam-5407	128	56	(	(	PUNCT
ejpam-5407	128	57	|ℶ2|+	|ℶ2|+	X
ejpam-5407	128	58	2	2	NUM
ejpam-5407	128	59	)	)	PUNCT
ejpam-5407	128	60	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	128	61	+	+	CCONJ
ejpam-5407	128	62	1)(ℶ3	1)(ℶ3	NUM
ejpam-5407	128	63	+	+	CCONJ
ejpam-5407	128	64	2	2	X
ejpam-5407	128	65	)	)	PUNCT
ejpam-5407	128	66	∞∑	∞∑	NUM
ejpam-5407	128	67	τ=4	τ=4	PUNCT
ejpam-5407	128	68	(	(	PUNCT
ejpam-5407	128	69	|ℶ1|+	|ℶ1|+	X
ejpam-5407	128	70	3)τ−4	3)τ−4	NUM
ejpam-5407	128	71	(	(	PUNCT
ejpam-5407	128	72	|ℶ2|+	|ℶ2|+	X
ejpam-5407	128	73	3)τ−4	3)τ−4	NUM
ejpam-5407	128	74	(	(	PUNCT
ejpam-5407	128	75	ℶ3	ℶ3	NOUN
ejpam-5407	128	76	+	+	NOUN
ejpam-5407	128	77	3)τ−4	3)τ−4	NUM
ejpam-5407	128	78	(	(	PUNCT
ejpam-5407	128	79	1)τ−4	1)τ−4	NUM
ejpam-5407	128	80	+	+	CCONJ
ejpam-5407	128	81	(	(	PUNCT
ejpam-5407	128	82	6(κ2	6(κ2	NUM
ejpam-5407	128	83	+	+	CCONJ
ejpam-5407	128	84	1)−	1)−	NUM
ejpam-5407	128	85	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	128	86	+	+	NUM
ejpam-5407	128	87	κ2	κ2	NOUN
ejpam-5407	128	88	)	)	PUNCT
ejpam-5407	128	89	)	)	PUNCT
ejpam-5407	128	90	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	128	91	(	(	PUNCT
ejpam-5407	128	92	|ℶ1|+	|ℶ1|+	X
ejpam-5407	128	93	1	1	NUM
ejpam-5407	128	94	)	)	PUNCT
ejpam-5407	128	95	(	(	PUNCT
ejpam-5407	128	96	|ℶ2|+	|ℶ2|+	X
ejpam-5407	128	97	1	1	NUM
ejpam-5407	128	98	)	)	PUNCT
ejpam-5407	128	99	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	128	100	+	+	NOUN
ejpam-5407	128	101	1	1	X
ejpam-5407	128	102	)	)	PUNCT
ejpam-5407	128	103	∞∑	∞∑	NUM
ejpam-5407	128	104	τ=3	τ=3	PUNCT
ejpam-5407	128	105	(	(	PUNCT
ejpam-5407	128	106	|ℶ1|+	|ℶ1|+	X
ejpam-5407	128	107	2)τ−3	2)τ−3	NUM
ejpam-5407	128	108	(	(	PUNCT
ejpam-5407	128	109	|ℶ2|+	|ℶ2|+	X
ejpam-5407	128	110	2)τ−3	2)τ−3	NUM
ejpam-5407	128	111	(	(	PUNCT
ejpam-5407	128	112	ℶ3	ℶ3	PROPN
ejpam-5407	128	113	+	+	CCONJ
ejpam-5407	128	114	2)τ−3	2)τ−3	NUM
ejpam-5407	128	115	(	(	PUNCT
ejpam-5407	128	116	1)τ−3	1)τ−3	NUM
ejpam-5407	128	117	+	+	CCONJ
ejpam-5407	128	118	(	(	PUNCT
ejpam-5407	128	119	7(κ2	7(κ2	NUM
ejpam-5407	129	1	+	+	CCONJ
ejpam-5407	129	2	1)−	1)−	NUM
ejpam-5407	129	3	3κ3(κ1	3κ3(κ1	NUM
ejpam-5407	129	4	+	+	NUM
ejpam-5407	129	5	κ2	κ2	NOUN
ejpam-5407	129	6	)	)	PUNCT
ejpam-5407	129	7	)	)	PUNCT
ejpam-5407	130	1	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	130	2	ℶ3	ℶ3	NOUN
ejpam-5407	130	3	∞∑	∞∑	PROPN
ejpam-5407	130	4	τ=2	τ=2	PUNCT
ejpam-5407	130	5	(	(	PUNCT
ejpam-5407	130	6	|ℶ1|+	|ℶ1|+	X
ejpam-5407	130	7	1)τ−2	1)τ−2	NUM
ejpam-5407	130	8	(	(	PUNCT
ejpam-5407	130	9	|ℶ2|+	|ℶ2|+	PROPN
ejpam-5407	130	10	1)τ−2	1)τ−2	NUM
ejpam-5407	130	11	(	(	PUNCT
ejpam-5407	130	12	ℶ3	ℶ3	NOUN
ejpam-5407	130	13	+	+	NOUN
ejpam-5407	130	14	1)τ−2	1)τ−2	NUM
ejpam-5407	130	15	(	(	PUNCT
ejpam-5407	130	16	1)τ−2	1)τ−2	NUM
ejpam-5407	130	17	+	+	PROPN
ejpam-5407	130	18	(	(	PUNCT
ejpam-5407	130	19	κ2	κ2	NOUN
ejpam-5407	130	20	−	−	PROPN
ejpam-5407	130	21	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	130	22	+	+	NUM
ejpam-5407	130	23	κ2	κ2	NOUN
ejpam-5407	130	24	)	)	PUNCT
ejpam-5407	130	25	+	+	CCONJ
ejpam-5407	130	26	1	1	X
ejpam-5407	130	27	)	)	PUNCT
ejpam-5407	130	28	∞∑	∞∑	PROPN
ejpam-5407	130	29	τ=2	τ=2	PUNCT
ejpam-5407	130	30	(	(	PUNCT
ejpam-5407	130	31	|ℶ1|)τ−1	|ℶ1|)τ−1	PROPN
ejpam-5407	130	32	(	(	PUNCT
ejpam-5407	130	33	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	130	34	(	(	PUNCT
ejpam-5407	130	35	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	130	36	(	(	PUNCT
ejpam-5407	130	37	1)τ−1	1)τ−1	NUM
ejpam-5407	130	38	.	.	PUNCT
ejpam-5407	131	1	by	by	ADP
ejpam-5407	131	2	gauss	gauss	ADJ
ejpam-5407	131	3	summation	summation	NOUN
ejpam-5407	131	4	theorem	theorem	PROPN
ejpam-5407	131	5	,	,	PUNCT
ejpam-5407	131	6	we	we	PRON
ejpam-5407	131	7	can	can	AUX
ejpam-5407	131	8	write	write	VERB
ejpam-5407	131	9	∞∑	∞∑	NOUN
ejpam-5407	131	10	τ=2	τ=2	PUNCT
ejpam-5407	132	1	[	[	X
ejpam-5407	132	2	(	(	PUNCT
ejpam-5407	132	3	τ2(κ2	τ2(κ2	ADV
ejpam-5407	132	4	+	+	NUM
ejpam-5407	132	5	1	1	X
ejpam-5407	132	6	)	)	PUNCT
ejpam-5407	132	7	−	−	NOUN
ejpam-5407	132	8	τκ3(κ1	τκ3(κ1	NUM
ejpam-5407	133	1	+	+	NUM
ejpam-5407	133	2	κ2	κ2	NOUN
ejpam-5407	133	3	)	)	PUNCT
ejpam-5407	133	4	]	]	PUNCT
ejpam-5407	133	5	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	133	6	(	(	PUNCT
ejpam-5407	133	7	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	PROPN
ejpam-5407	133	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5407	133	9	≤	≤	NOUN
ejpam-5407	133	10	(	(	PUNCT
ejpam-5407	133	11	κ2	κ2	NOUN
ejpam-5407	133	12	+	+	CCONJ
ejpam-5407	133	13	1	1	X
ejpam-5407	133	14	)	)	PUNCT
ejpam-5407	133	15	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	133	16	(	(	PUNCT
ejpam-5407	133	17	|ℶ1|+	|ℶ1|+	X
ejpam-5407	133	18	1	1	NUM
ejpam-5407	133	19	)	)	PUNCT
ejpam-5407	133	20	(	(	PUNCT
ejpam-5407	133	21	|ℶ2|+	|ℶ2|+	X
ejpam-5407	133	22	1	1	NUM
ejpam-5407	133	23	)	)	PUNCT
ejpam-5407	133	24	(	(	PUNCT
ejpam-5407	133	25	|ℶ1|+	|ℶ1|+	X
ejpam-5407	133	26	2	2	NUM
ejpam-5407	133	27	)	)	PUNCT
ejpam-5407	133	28	(	(	PUNCT
ejpam-5407	133	29	|ℶ2|+	|ℶ2|+	X
ejpam-5407	133	30	2	2	NUM
ejpam-5407	133	31	)	)	PUNCT
ejpam-5407	133	32	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	134	1	+	+	CCONJ
ejpam-5407	134	2	1)(ℶ3	1)(ℶ3	NUM
ejpam-5407	134	3	+	+	CCONJ
ejpam-5407	134	4	2	2	X
ejpam-5407	134	5	)	)	PUNCT
ejpam-5407	134	6	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	134	7	3	3	NUM
ejpam-5407	134	8	,	,	PUNCT
ejpam-5407	134	9	|ℶ2|+	|ℶ2|+	X
ejpam-5407	134	10	3;ℶ3	3;ℶ3	NUM
ejpam-5407	134	11	+	+	SYM
ejpam-5407	134	12	3,1	3,1	NUM
ejpam-5407	134	13	)	)	PUNCT
ejpam-5407	135	1	+	+	CCONJ
ejpam-5407	135	2	(	(	PUNCT
ejpam-5407	135	3	6(κ2	6(κ2	NUM
ejpam-5407	135	4	+	+	CCONJ
ejpam-5407	135	5	1)−	1)−	NUM
ejpam-5407	135	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	135	7	+	+	NUM
ejpam-5407	135	8	κ2	κ2	NOUN
ejpam-5407	135	9	)	)	PUNCT
ejpam-5407	135	10	)	)	PUNCT
ejpam-5407	135	11	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	135	12	(	(	PUNCT
ejpam-5407	135	13	|ℶ1|+	|ℶ1|+	X
ejpam-5407	135	14	1	1	NUM
ejpam-5407	135	15	)	)	PUNCT
ejpam-5407	135	16	(	(	PUNCT
ejpam-5407	135	17	|ℶ2|+	|ℶ2|+	X
ejpam-5407	135	18	1	1	NUM
ejpam-5407	135	19	)	)	PUNCT
ejpam-5407	135	20	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	135	21	+	+	NOUN
ejpam-5407	135	22	1	1	X
ejpam-5407	135	23	)	)	PUNCT
ejpam-5407	135	24	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	135	25	2	2	NUM
ejpam-5407	135	26	,	,	PUNCT
ejpam-5407	135	27	|ℶ2|+	|ℶ2|+	X
ejpam-5407	135	28	2;ℶ3	2;ℶ3	NUM
ejpam-5407	135	29	+	+	NUM
ejpam-5407	135	30	2,1	2,1	NUM
ejpam-5407	135	31	)	)	PUNCT
ejpam-5407	135	32	+	+	CCONJ
ejpam-5407	136	1	(	(	PUNCT
ejpam-5407	136	2	7(κ2	7(κ2	X
ejpam-5407	137	1	+	+	CCONJ
ejpam-5407	137	2	1)−	1)−	NUM
ejpam-5407	137	3	3κ3(κ1	3κ3(κ1	NUM
ejpam-5407	137	4	+	+	NUM
ejpam-5407	137	5	κ2	κ2	NOUN
ejpam-5407	137	6	)	)	PUNCT
ejpam-5407	137	7	)	)	PUNCT
ejpam-5407	138	1	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	138	2	ℶ3	ℶ3	PROPN
ejpam-5407	138	3	g2,1(|ℶ1|+	g2,1(|ℶ1|+	PROPN
ejpam-5407	138	4	1	1	NUM
ejpam-5407	138	5	,	,	PUNCT
ejpam-5407	138	6	|ℶ2|+	|ℶ2|+	X
ejpam-5407	138	7	1;ℶ3	1;ℶ3	NUM
ejpam-5407	138	8	+	+	SYM
ejpam-5407	138	9	1	1	NUM
ejpam-5407	138	10	,	,	PUNCT
ejpam-5407	138	11	1	1	NUM
ejpam-5407	138	12	)	)	PUNCT
ejpam-5407	138	13	+	+	CCONJ
ejpam-5407	138	14	(	(	PUNCT
ejpam-5407	138	15	κ2	κ2	NOUN
ejpam-5407	138	16	−	−	PROPN
ejpam-5407	138	17	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	138	18	+	+	NUM
ejpam-5407	138	19	κ2	κ2	NOUN
ejpam-5407	138	20	)	)	PUNCT
ejpam-5407	138	21	+	+	CCONJ
ejpam-5407	139	1	1	1	X
ejpam-5407	139	2	)	)	PUNCT
ejpam-5407	139	3	[	[	X
ejpam-5407	139	4	g2,1(|ℶ1|	g2,1(|ℶ1|	NOUN
ejpam-5407	139	5	,	,	PUNCT
ejpam-5407	139	6	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	139	7	;	;	PUNCT
ejpam-5407	139	8	ℶ3,1)−	ℶ3,1)−	PROPN
ejpam-5407	139	9	1	1	NUM
ejpam-5407	139	10	]	]	PUNCT
ejpam-5407	139	11	.	.	PUNCT
ejpam-5407	140	1	(	(	PUNCT
ejpam-5407	140	2	10	10	NUM
ejpam-5407	140	3	)	)	PUNCT
ejpam-5407	140	4	but	but	CCONJ
ejpam-5407	140	5	the	the	DET
ejpam-5407	140	6	expression	expression	NOUN
ejpam-5407	140	7	(	(	PUNCT
ejpam-5407	140	8	10	10	NUM
ejpam-5407	140	9	)	)	PUNCT
ejpam-5407	140	10	is	be	AUX
ejpam-5407	140	11	bounded	bound	VERB
ejpam-5407	140	12	above	above	ADV
ejpam-5407	140	13	by	by	ADP
ejpam-5407	140	14	1−	1−	NUM
ejpam-5407	140	15	κ1	κ1	NOUN
ejpam-5407	140	16	,	,	PUNCT
ejpam-5407	140	17	thus	thus	ADV
ejpam-5407	140	18	the	the	DET
ejpam-5407	140	19	proof	proof	NOUN
ejpam-5407	140	20	is	be	AUX
ejpam-5407	140	21	completed	complete	VERB
ejpam-5407	140	22	.	.	PUNCT
ejpam-5407	141	1	theorem	theorem	NOUN
ejpam-5407	141	2	2	2	NUM
ejpam-5407	141	3	.	.	PUNCT
ejpam-5407	142	1	if	if	SCONJ
ejpam-5407	142	2	l	l	PROPN
ejpam-5407	142	3	∈	∈	PROPN
ejpam-5407	142	4	cv	cv	PROPN
ejpam-5407	142	5	and	and	CCONJ
ejpam-5407	142	6	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	142	7	∈	∈	PROPN
ejpam-5407	142	8	c−	c−	NOUN
ejpam-5407	142	9	{	{	PUNCT
ejpam-5407	142	10	0	0	NUM
ejpam-5407	142	11	}	}	PUNCT
ejpam-5407	142	12	,	,	PUNCT
ejpam-5407	142	13	ℶ3	ℶ3	PROPN
ejpam-5407	142	14	∈	∈	PROPN
ejpam-5407	142	15	r	r	NOUN
ejpam-5407	142	16	,	,	PUNCT
ejpam-5407	142	17	then	then	ADV
ejpam-5407	142	18	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	142	19	)	)	PUNCT
ejpam-5407	142	20	∈	∈	PROPN
ejpam-5407	142	21	cκ3(κ1	cκ3(κ1	NOUN
ejpam-5407	142	22	,	,	PUNCT
ejpam-5407	142	23	κ2	κ2	NOUN
ejpam-5407	142	24	)	)	PUNCT
ejpam-5407	142	25	if	if	SCONJ
ejpam-5407	142	26	the	the	DET
ejpam-5407	142	27	following	follow	VERB
ejpam-5407	142	28	condition	condition	NOUN
ejpam-5407	142	29	is	be	AUX
ejpam-5407	142	30	satisfied	satisfied	ADJ
ejpam-5407	142	31	:	:	PUNCT
ejpam-5407	142	32	(	(	PUNCT
ejpam-5407	142	33	κ2	κ2	NOUN
ejpam-5407	142	34	+	+	CCONJ
ejpam-5407	142	35	1	1	X
ejpam-5407	142	36	)	)	PUNCT
ejpam-5407	142	37	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	142	38	(	(	PUNCT
ejpam-5407	142	39	|ℶ1|+	|ℶ1|+	X
ejpam-5407	142	40	1	1	NUM
ejpam-5407	142	41	)	)	PUNCT
ejpam-5407	142	42	(	(	PUNCT
ejpam-5407	142	43	|ℶ2|+	|ℶ2|+	X
ejpam-5407	142	44	1	1	NUM
ejpam-5407	142	45	)	)	PUNCT
ejpam-5407	142	46	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	142	47	+	+	NOUN
ejpam-5407	142	48	1	1	X
ejpam-5407	142	49	)	)	PUNCT
ejpam-5407	142	50	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	142	51	2	2	NUM
ejpam-5407	142	52	,	,	PUNCT
ejpam-5407	142	53	|ℶ2|+	|ℶ2|+	X
ejpam-5407	142	54	2;ℶ3	2;ℶ3	NUM
ejpam-5407	142	55	+	+	NUM
ejpam-5407	142	56	2,1	2,1	NUM
ejpam-5407	142	57	)	)	PUNCT
ejpam-5407	143	1	+	+	CCONJ
ejpam-5407	143	2	(	(	PUNCT
ejpam-5407	143	3	3(κ2	3(κ2	NUM
ejpam-5407	143	4	+	+	SYM
ejpam-5407	143	5	1)−	1)−	NUM
ejpam-5407	143	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	143	7	+	+	NUM
ejpam-5407	143	8	κ2	κ2	NOUN
ejpam-5407	143	9	)	)	PUNCT
ejpam-5407	143	10	)	)	PUNCT
ejpam-5407	143	11	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	143	12	ℶ3	ℶ3	PROPN
ejpam-5407	143	13	g2,1(|ℶ1|+	g2,1(|ℶ1|+	PROPN
ejpam-5407	143	14	1	1	NUM
ejpam-5407	143	15	,	,	PUNCT
ejpam-5407	143	16	|ℶ2|+	|ℶ2|+	X
ejpam-5407	143	17	1;ℶ3	1;ℶ3	NUM
ejpam-5407	143	18	+	+	SYM
ejpam-5407	143	19	1,1	1,1	NUM
ejpam-5407	143	20	)	)	PUNCT
ejpam-5407	143	21	+	+	CCONJ
ejpam-5407	143	22	(	(	PUNCT
ejpam-5407	143	23	κ2	κ2	NOUN
ejpam-5407	143	24	−	−	PROPN
ejpam-5407	143	25	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	143	26	+	+	NUM
ejpam-5407	143	27	κ2	κ2	NOUN
ejpam-5407	143	28	)	)	PUNCT
ejpam-5407	143	29	+	+	CCONJ
ejpam-5407	143	30	1	1	X
ejpam-5407	143	31	)	)	PUNCT
ejpam-5407	144	1	[	[	X
ejpam-5407	144	2	g2,1(|ℶ1|	g2,1(|ℶ1|	NOUN
ejpam-5407	144	3	,	,	PUNCT
ejpam-5407	144	4	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	144	5	;	;	PUNCT
ejpam-5407	144	6	ℶ3,1)−	ℶ3,1)−	PROPN
ejpam-5407	144	7	1	1	NUM
ejpam-5407	144	8	]	]	PUNCT
ejpam-5407	144	9	≤	≤	NUM
ejpam-5407	144	10	1−	1−	NUM
ejpam-5407	144	11	κ1	κ1	NOUN
ejpam-5407	144	12	.	.	PUNCT
ejpam-5407	145	1	proof	proof	NOUN
ejpam-5407	145	2	.	.	PUNCT
ejpam-5407	146	1	since	since	SCONJ
ejpam-5407	146	2	l	l	PROPN
ejpam-5407	146	3	∈	∈	PROPN
ejpam-5407	146	4	cv	cv	NOUN
ejpam-5407	146	5	we	we	PRON
ejpam-5407	146	6	have	have	VERB
ejpam-5407	146	7	|rτ	|rτ	NUM
ejpam-5407	146	8	|	|	ADV
ejpam-5407	146	9	≤	≤	NUM
ejpam-5407	146	10	1	1	NUM
ejpam-5407	146	11	and	and	CCONJ
ejpam-5407	146	12	by	by	ADP
ejpam-5407	146	13	equation	equation	NOUN
ejpam-5407	146	14	(	(	PUNCT
ejpam-5407	146	15	8)	8)	NUM
ejpam-5407	146	16	,	,	PUNCT
ejpam-5407	146	17	to	to	PART
ejpam-5407	146	18	prove	prove	VERB
ejpam-5407	146	19	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	NOUN
ejpam-5407	146	20	)	)	PUNCT
ejpam-5407	146	21	∈	∈	PROPN
ejpam-5407	146	22	cκ3(κ1	cκ3(κ1	NOUN
ejpam-5407	146	23	,	,	PUNCT
ejpam-5407	146	24	κ2	κ2	PROPN
ejpam-5407	146	25	)	)	PUNCT
ejpam-5407	146	26	,	,	PUNCT
ejpam-5407	146	27	it	it	PRON
ejpam-5407	146	28	suffices	suffice	VERB
ejpam-5407	146	29	to	to	PART
ejpam-5407	146	30	show	show	VERB
ejpam-5407	146	31	that	that	SCONJ
ejpam-5407	146	32	∞∑	∞∑	NUM
ejpam-5407	146	33	τ=2	τ=2	PUNCT
ejpam-5407	146	34	τ	τ	PROPN
ejpam-5407	147	1	[	[	X
ejpam-5407	147	2	(	(	PUNCT
ejpam-5407	147	3	τ(κ2	τ(κ2	NOUN
ejpam-5407	147	4	+	+	X
ejpam-5407	147	5	1)−	1)−	NUM
ejpam-5407	147	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	147	7	+	+	NUM
ejpam-5407	147	8	κ2	κ2	NOUN
ejpam-5407	147	9	)	)	PUNCT
ejpam-5407	147	10	]	]	PUNCT
ejpam-5407	147	11	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	147	12	(	(	PUNCT
ejpam-5407	147	13	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	PROPN
ejpam-5407	147	14	rτ	rτ	PROPN
ejpam-5407	147	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5407	147	16	t.	t.	PROPN
ejpam-5407	147	17	al	al	PROPN
ejpam-5407	147	18	-	-	PUNCT
ejpam-5407	147	19	hawary	hawary	PROPN
ejpam-5407	147	20	,	,	PUNCT
ejpam-5407	147	21	m.	m.	NOUN
ejpam-5407	147	22	o.	o.	PROPN
ejpam-5407	147	23	massa’deh	massa’deh	PROPN
ejpam-5407	147	24	,	,	PUNCT
ejpam-5407	147	25	a.	a.	NOUN
ejpam-5407	147	26	o	o	X
ejpam-5407	147	27	fallatah	fallatah	PROPN
ejpam-5407	147	28	/	/	SYM
ejpam-5407	147	29	eur	eur	PROPN
ejpam-5407	147	30	.	.	PUNCT
ejpam-5407	148	1	j.	j.	PROPN
ejpam-5407	148	2	pure	pure	PROPN
ejpam-5407	148	3	appl	appl	PROPN
ejpam-5407	148	4	.	.	PROPN
ejpam-5407	148	5	math	math	PROPN
ejpam-5407	148	6	,	,	PUNCT
ejpam-5407	148	7	17	17	NUM
ejpam-5407	148	8	(	(	PUNCT
ejpam-5407	148	9	4	4	NUM
ejpam-5407	148	10	)	)	PUNCT
ejpam-5407	148	11	(	(	PUNCT
ejpam-5407	148	12	2024	2024	NUM
ejpam-5407	148	13	)	)	PUNCT
ejpam-5407	148	14	,	,	PUNCT
ejpam-5407	148	15	3386	3386	NUM
ejpam-5407	148	16	-	-	SYM
ejpam-5407	148	17	3398	3398	NUM
ejpam-5407	148	18	3392	3392	NUM
ejpam-5407	148	19	≤	≤	NOUN
ejpam-5407	149	1	∞∑	∞∑	NUM
ejpam-5407	149	2	τ=2	τ=2	PUNCT
ejpam-5407	150	1	[	[	X
ejpam-5407	150	2	(	(	PUNCT
ejpam-5407	150	3	τ2(κ2	τ2(κ2	ADV
ejpam-5407	150	4	+	+	NUM
ejpam-5407	150	5	1	1	X
ejpam-5407	150	6	)	)	PUNCT
ejpam-5407	150	7	−	−	NOUN
ejpam-5407	150	8	τκ3(κ1	τκ3(κ1	NUM
ejpam-5407	151	1	+	+	NUM
ejpam-5407	151	2	κ2	κ2	NOUN
ejpam-5407	151	3	)	)	PUNCT
ejpam-5407	151	4	]	]	PUNCT
ejpam-5407	151	5	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	151	6	(	(	PUNCT
ejpam-5407	151	7	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	PROPN
ejpam-5407	151	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5407	151	9	≤	≤	PROPN
ejpam-5407	151	10	1−	1−	NUM
ejpam-5407	151	11	κ1	κ1	NOUN
ejpam-5407	151	12	.	.	PUNCT
ejpam-5407	152	1	writing	write	VERB
ejpam-5407	152	2	τ=	τ=	PROPN
ejpam-5407	152	3	(	(	PUNCT
ejpam-5407	152	4	τ−1	τ−1	PROPN
ejpam-5407	152	5	)	)	PUNCT
ejpam-5407	152	6	+	+	NUM
ejpam-5407	152	7	1	1	NUM
ejpam-5407	152	8	,	,	PUNCT
ejpam-5407	152	9	τ2	τ2	NOUN
ejpam-5407	152	10	=	=	SYM
ejpam-5407	152	11	(	(	PUNCT
ejpam-5407	152	12	τ−1)(τ−2	τ−1)(τ−2	NUM
ejpam-5407	152	13	)	)	PUNCT
ejpam-5407	152	14	+	+	NUM
ejpam-5407	152	15	3(τ−1	3(τ−1	NUM
ejpam-5407	152	16	)	)	PUNCT
ejpam-5407	153	1	+	+	CCONJ
ejpam-5407	153	2	1	1	NUM
ejpam-5407	153	3	and	and	CCONJ
ejpam-5407	153	4	use	use	NOUN
ejpam-5407	153	5	of	of	ADP
ejpam-5407	153	6	(	(	PUNCT
ejpam-5407	153	7	9	9	NUM
ejpam-5407	153	8	)	)	PUNCT
ejpam-5407	153	9	,	,	PUNCT
ejpam-5407	153	10	we	we	PRON
ejpam-5407	153	11	get	get	VERB
ejpam-5407	153	12	∞∑	∞∑	NUM
ejpam-5407	153	13	τ=2	τ=2	PUNCT
ejpam-5407	154	1	[	[	X
ejpam-5407	154	2	(	(	PUNCT
ejpam-5407	154	3	τ2(κ2	τ2(κ2	ADV
ejpam-5407	154	4	+	+	NUM
ejpam-5407	154	5	1	1	X
ejpam-5407	154	6	)	)	PUNCT
ejpam-5407	154	7	−	−	NOUN
ejpam-5407	154	8	τκ3(κ1	τκ3(κ1	NUM
ejpam-5407	155	1	+	+	NUM
ejpam-5407	155	2	κ2	κ2	NOUN
ejpam-5407	155	3	)	)	PUNCT
ejpam-5407	155	4	]	]	PUNCT
ejpam-5407	155	5	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	155	6	(	(	PUNCT
ejpam-5407	155	7	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	NOUN
ejpam-5407	155	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	155	9	=	=	PUNCT
ejpam-5407	155	10	(	(	PUNCT
ejpam-5407	155	11	κ2	κ2	NOUN
ejpam-5407	155	12	+	+	CCONJ
ejpam-5407	155	13	1	1	X
ejpam-5407	155	14	)	)	PUNCT
ejpam-5407	155	15	∞∑	∞∑	NOUN
ejpam-5407	155	16	τ=2	τ=2	PUNCT
ejpam-5407	155	17	(	(	PUNCT
ejpam-5407	155	18	τ	τ	X
ejpam-5407	155	19	−	−	PROPN
ejpam-5407	156	1	1)(τ	1)(τ	NUM
ejpam-5407	156	2	−	−	NOUN
ejpam-5407	156	3	2	2	NUM
ejpam-5407	156	4	)	)	PUNCT
ejpam-5407	156	5	(	(	PUNCT
ejpam-5407	156	6	|ℶ1|)τ−1	|ℶ1|)τ−1	NOUN
ejpam-5407	156	7	(	(	PUNCT
ejpam-5407	156	8	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	156	9	(	(	PUNCT
ejpam-5407	156	10	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	156	11	(	(	PUNCT
ejpam-5407	156	12	1)τ−1	1)τ−1	NUM
ejpam-5407	156	13	+	+	ADJ
ejpam-5407	156	14	(	(	PUNCT
ejpam-5407	156	15	3(κ2	3(κ2	NUM
ejpam-5407	156	16	+	+	SYM
ejpam-5407	156	17	1)−	1)−	NUM
ejpam-5407	156	18	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	156	19	+	+	NUM
ejpam-5407	156	20	κ2	κ2	NOUN
ejpam-5407	156	21	)	)	PUNCT
ejpam-5407	156	22	)	)	PUNCT
ejpam-5407	157	1	∞∑	∞∑	NUM
ejpam-5407	157	2	τ=2	τ=2	PUNCT
ejpam-5407	157	3	(	(	PUNCT
ejpam-5407	157	4	τ	τ	X
ejpam-5407	157	5	−	−	PROPN
ejpam-5407	157	6	1	1	NUM
ejpam-5407	157	7	)	)	PUNCT
ejpam-5407	157	8	(	(	PUNCT
ejpam-5407	157	9	|ℶ1|)τ−1	|ℶ1|)τ−1	NOUN
ejpam-5407	157	10	(	(	PUNCT
ejpam-5407	157	11	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	157	12	(	(	PUNCT
ejpam-5407	157	13	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	157	14	(	(	PUNCT
ejpam-5407	157	15	1)τ−1	1)τ−1	NUM
ejpam-5407	157	16	+	+	ADJ
ejpam-5407	157	17	(	(	PUNCT
ejpam-5407	157	18	κ2	κ2	NOUN
ejpam-5407	157	19	−	−	PROPN
ejpam-5407	157	20	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	157	21	+	+	NUM
ejpam-5407	157	22	κ2	κ2	NOUN
ejpam-5407	157	23	)	)	PUNCT
ejpam-5407	157	24	+	+	CCONJ
ejpam-5407	157	25	1	1	X
ejpam-5407	157	26	)	)	PUNCT
ejpam-5407	157	27	∞∑	∞∑	PROPN
ejpam-5407	157	28	τ=2	τ=2	PUNCT
ejpam-5407	157	29	(	(	PUNCT
ejpam-5407	157	30	|ℶ1|)τ−1	|ℶ1|)τ−1	PROPN
ejpam-5407	157	31	(	(	PUNCT
ejpam-5407	157	32	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	157	33	(	(	PUNCT
ejpam-5407	157	34	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	157	35	(	(	PUNCT
ejpam-5407	157	36	1)τ−1	1)τ−1	NUM
ejpam-5407	157	37	≤	≤	NOUN
ejpam-5407	157	38	(	(	PUNCT
ejpam-5407	157	39	κ2	κ2	NOUN
ejpam-5407	157	40	+	+	CCONJ
ejpam-5407	157	41	1	1	X
ejpam-5407	157	42	)	)	PUNCT
ejpam-5407	157	43	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	157	44	(	(	PUNCT
ejpam-5407	157	45	|ℶ1|+	|ℶ1|+	X
ejpam-5407	157	46	1	1	NUM
ejpam-5407	157	47	)	)	PUNCT
ejpam-5407	157	48	(	(	PUNCT
ejpam-5407	157	49	|ℶ2|+	|ℶ2|+	X
ejpam-5407	157	50	1	1	NUM
ejpam-5407	157	51	)	)	PUNCT
ejpam-5407	157	52	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	157	53	+	+	NOUN
ejpam-5407	157	54	1	1	X
ejpam-5407	157	55	)	)	PUNCT
ejpam-5407	157	56	∞∑	∞∑	NUM
ejpam-5407	157	57	τ=3	τ=3	PUNCT
ejpam-5407	157	58	(	(	PUNCT
ejpam-5407	157	59	|ℶ1|+	|ℶ1|+	X
ejpam-5407	157	60	2)τ−3	2)τ−3	NUM
ejpam-5407	157	61	(	(	PUNCT
ejpam-5407	157	62	|ℶ2|+	|ℶ2|+	X
ejpam-5407	157	63	2)τ−3	2)τ−3	NUM
ejpam-5407	157	64	(	(	PUNCT
ejpam-5407	157	65	ℶ3	ℶ3	PROPN
ejpam-5407	157	66	+	+	CCONJ
ejpam-5407	157	67	2)τ−3	2)τ−3	NUM
ejpam-5407	157	68	(	(	PUNCT
ejpam-5407	157	69	1)τ−3	1)τ−3	NUM
ejpam-5407	157	70	+	+	CCONJ
ejpam-5407	157	71	(	(	PUNCT
ejpam-5407	157	72	3(κ2	3(κ2	NUM
ejpam-5407	157	73	+	+	SYM
ejpam-5407	157	74	1)−	1)−	NUM
ejpam-5407	157	75	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	157	76	+	+	NUM
ejpam-5407	157	77	κ2	κ2	NOUN
ejpam-5407	157	78	)	)	PUNCT
ejpam-5407	157	79	)	)	PUNCT
ejpam-5407	157	80	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	158	1	ℶ3	ℶ3	NOUN
ejpam-5407	158	2	∞∑	∞∑	PROPN
ejpam-5407	158	3	τ=2	τ=2	PUNCT
ejpam-5407	158	4	(	(	PUNCT
ejpam-5407	158	5	|ℶ1|+	|ℶ1|+	X
ejpam-5407	158	6	1)τ−2	1)τ−2	NUM
ejpam-5407	158	7	(	(	PUNCT
ejpam-5407	158	8	|ℶ2|+	|ℶ2|+	PROPN
ejpam-5407	158	9	1)τ−2	1)τ−2	NUM
ejpam-5407	158	10	(	(	PUNCT
ejpam-5407	158	11	ℶ3	ℶ3	NOUN
ejpam-5407	158	12	+	+	NOUN
ejpam-5407	158	13	1)τ−2	1)τ−2	NUM
ejpam-5407	158	14	(	(	PUNCT
ejpam-5407	158	15	1)τ−2	1)τ−2	NUM
ejpam-5407	158	16	+	+	PROPN
ejpam-5407	158	17	(	(	PUNCT
ejpam-5407	158	18	κ2	κ2	NOUN
ejpam-5407	158	19	−	−	PROPN
ejpam-5407	158	20	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	158	21	+	+	NUM
ejpam-5407	158	22	κ2	κ2	NOUN
ejpam-5407	158	23	)	)	PUNCT
ejpam-5407	158	24	+	+	CCONJ
ejpam-5407	158	25	1	1	X
ejpam-5407	158	26	)	)	PUNCT
ejpam-5407	158	27	∞∑	∞∑	PROPN
ejpam-5407	158	28	τ=2	τ=2	PUNCT
ejpam-5407	158	29	(	(	PUNCT
ejpam-5407	158	30	|ℶ1|)τ−1	|ℶ1|)τ−1	PROPN
ejpam-5407	158	31	(	(	PUNCT
ejpam-5407	158	32	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	158	33	(	(	PUNCT
ejpam-5407	158	34	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	158	35	(	(	PUNCT
ejpam-5407	158	36	1)τ−1	1)τ−1	NUM
ejpam-5407	158	37	.	.	PUNCT
ejpam-5407	159	1	by	by	ADP
ejpam-5407	159	2	gauss	gauss	ADJ
ejpam-5407	159	3	summation	summation	NOUN
ejpam-5407	159	4	theorem	theorem	PROPN
ejpam-5407	159	5	,	,	PUNCT
ejpam-5407	159	6	we	we	PRON
ejpam-5407	159	7	have	have	VERB
ejpam-5407	159	8	∞∑	∞∑	NUM
ejpam-5407	159	9	τ=2	τ=2	PUNCT
ejpam-5407	160	1	[	[	X
ejpam-5407	160	2	(	(	PUNCT
ejpam-5407	160	3	τ2(κ2	τ2(κ2	ADV
ejpam-5407	160	4	+	+	NUM
ejpam-5407	160	5	1	1	X
ejpam-5407	160	6	)	)	PUNCT
ejpam-5407	160	7	−	−	NOUN
ejpam-5407	160	8	τκ3(κ1	τκ3(κ1	NUM
ejpam-5407	161	1	+	+	NUM
ejpam-5407	161	2	κ2	κ2	NOUN
ejpam-5407	161	3	)	)	PUNCT
ejpam-5407	161	4	]	]	PUNCT
ejpam-5407	161	5	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	161	6	(	(	PUNCT
ejpam-5407	161	7	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	PROPN
ejpam-5407	161	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5407	161	9	≤	≤	NOUN
ejpam-5407	161	10	(	(	PUNCT
ejpam-5407	161	11	κ2	κ2	NOUN
ejpam-5407	161	12	+	+	CCONJ
ejpam-5407	161	13	1	1	X
ejpam-5407	161	14	)	)	PUNCT
ejpam-5407	161	15	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	161	16	(	(	PUNCT
ejpam-5407	161	17	|ℶ1|+	|ℶ1|+	X
ejpam-5407	161	18	1	1	NUM
ejpam-5407	161	19	)	)	PUNCT
ejpam-5407	161	20	(	(	PUNCT
ejpam-5407	161	21	|ℶ2|+	|ℶ2|+	X
ejpam-5407	161	22	1	1	NUM
ejpam-5407	161	23	)	)	PUNCT
ejpam-5407	161	24	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	161	25	+	+	NOUN
ejpam-5407	161	26	1	1	X
ejpam-5407	161	27	)	)	PUNCT
ejpam-5407	161	28	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	161	29	2	2	NUM
ejpam-5407	161	30	,	,	PUNCT
ejpam-5407	161	31	|ℶ2|+	|ℶ2|+	X
ejpam-5407	161	32	2;ℶ3	2;ℶ3	NUM
ejpam-5407	161	33	+	+	CCONJ
ejpam-5407	161	34	2	2	NUM
ejpam-5407	161	35	,	,	PUNCT
ejpam-5407	161	36	1	1	NUM
ejpam-5407	161	37	)	)	PUNCT
ejpam-5407	161	38	+	+	CCONJ
ejpam-5407	161	39	(	(	PUNCT
ejpam-5407	161	40	3(κ2	3(κ2	NUM
ejpam-5407	161	41	+	+	SYM
ejpam-5407	161	42	1)−	1)−	NUM
ejpam-5407	161	43	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	161	44	+	+	NUM
ejpam-5407	161	45	κ2	κ2	NOUN
ejpam-5407	161	46	)	)	PUNCT
ejpam-5407	161	47	)	)	PUNCT
ejpam-5407	161	48	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	161	49	ℶ3	ℶ3	PROPN
ejpam-5407	161	50	g2,1(|ℶ1|+	g2,1(|ℶ1|+	PROPN
ejpam-5407	161	51	1	1	NUM
ejpam-5407	161	52	,	,	PUNCT
ejpam-5407	161	53	|ℶ2|+	|ℶ2|+	X
ejpam-5407	161	54	1;ℶ3	1;ℶ3	NUM
ejpam-5407	161	55	+	+	SYM
ejpam-5407	161	56	1	1	NUM
ejpam-5407	161	57	,	,	PUNCT
ejpam-5407	161	58	1	1	NUM
ejpam-5407	161	59	)	)	PUNCT
ejpam-5407	161	60	+	+	CCONJ
ejpam-5407	161	61	(	(	PUNCT
ejpam-5407	161	62	κ2	κ2	NOUN
ejpam-5407	161	63	−	−	PROPN
ejpam-5407	161	64	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	161	65	+	+	NUM
ejpam-5407	161	66	κ2	κ2	NOUN
ejpam-5407	161	67	)	)	PUNCT
ejpam-5407	161	68	+	+	CCONJ
ejpam-5407	161	69	1	1	X
ejpam-5407	161	70	)	)	PUNCT
ejpam-5407	162	1	[	[	X
ejpam-5407	162	2	g2,1(|ℶ1|	g2,1(|ℶ1|	NOUN
ejpam-5407	162	3	,	,	PUNCT
ejpam-5407	162	4	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	162	5	;	;	PUNCT
ejpam-5407	162	6	ℶ3	ℶ3	PROPN
ejpam-5407	162	7	,	,	PUNCT
ejpam-5407	162	8	1)−	1)−	PROPN
ejpam-5407	162	9	1	1	NUM
ejpam-5407	162	10	]	]	PUNCT
ejpam-5407	162	11	.	.	PUNCT
ejpam-5407	163	1	(	(	PUNCT
ejpam-5407	163	2	11	11	NUM
ejpam-5407	163	3	)	)	PUNCT
ejpam-5407	163	4	but	but	CCONJ
ejpam-5407	163	5	the	the	DET
ejpam-5407	163	6	expression	expression	NOUN
ejpam-5407	163	7	(	(	PUNCT
ejpam-5407	163	8	11	11	NUM
ejpam-5407	163	9	)	)	PUNCT
ejpam-5407	163	10	is	be	AUX
ejpam-5407	163	11	bounded	bound	VERB
ejpam-5407	163	12	above	above	ADV
ejpam-5407	163	13	by	by	ADP
ejpam-5407	163	14	1−	1−	NUM
ejpam-5407	163	15	κ1	κ1	NOUN
ejpam-5407	163	16	,	,	PUNCT
ejpam-5407	163	17	thus	thus	ADV
ejpam-5407	163	18	the	the	DET
ejpam-5407	163	19	proof	proof	NOUN
ejpam-5407	163	20	is	be	AUX
ejpam-5407	163	21	completed	complete	VERB
ejpam-5407	163	22	.	.	PUNCT
ejpam-5407	164	1	theorem	theorem	NOUN
ejpam-5407	164	2	3	3	X
ejpam-5407	164	3	.	.	PUNCT
ejpam-5407	165	1	let	let	VERB
ejpam-5407	165	2	υ1	υ1	PROPN
ejpam-5407	165	3	given	give	VERB
ejpam-5407	165	4	by	by	ADP
ejpam-5407	165	5	(	(	PUNCT
ejpam-5407	165	6	3	3	NUM
ejpam-5407	165	7	)	)	PUNCT
ejpam-5407	165	8	and	and	CCONJ
ejpam-5407	165	9	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	165	10	∈	∈	PROPN
ejpam-5407	165	11	c−{0	c−{0	ADV
ejpam-5407	165	12	}	}	PUNCT
ejpam-5407	165	13	,	,	PUNCT
ejpam-5407	165	14	ℶ3	ℶ3	PROPN
ejpam-5407	165	15	∈	∈	PROPN
ejpam-5407	165	16	r.	r.	PROPN
ejpam-5407	165	17	if	if	SCONJ
ejpam-5407	165	18	l	l	PROPN
ejpam-5407	165	19	∈	∈	PROPN
ejpam-5407	165	20	ξ−ucv	ξ−ucv	NOUN
ejpam-5407	165	21	for	for	ADP
ejpam-5407	165	22	some	some	DET
ejpam-5407	165	23	ξ(0	ξ(0	SYM
ejpam-5407	165	24	≤	≤	PUNCT
ejpam-5407	166	1	ξ	ξ	X
ejpam-5407	166	2	<	<	X
ejpam-5407	166	3	∞	∞	NUM
ejpam-5407	166	4	)	)	PUNCT
ejpam-5407	166	5	and	and	CCONJ
ejpam-5407	166	6	satisfies	satisfy	VERB
ejpam-5407	166	7	the	the	DET
ejpam-5407	166	8	inequality	inequality	NOUN
ejpam-5407	166	9	(	(	PUNCT
ejpam-5407	166	10	κ2	κ2	NOUN
ejpam-5407	166	11	+	+	CCONJ
ejpam-5407	166	12	1	1	X
ejpam-5407	166	13	)	)	PUNCT
ejpam-5407	166	14	|ℶ1ℶ2|υ1	|ℶ1ℶ2|υ1	NOUN
ejpam-5407	166	15	ℶ3(1)1	ℶ3(1)1	PROPN
ejpam-5407	166	16	g3,2(|ℶ1|+	g3,2(|ℶ1|+	PROPN
ejpam-5407	166	17	1	1	NUM
ejpam-5407	166	18	,	,	PUNCT
ejpam-5407	166	19	|ℶ2|+	|ℶ2|+	X
ejpam-5407	167	1	1,υ1	1,υ1	NUM
ejpam-5407	167	2	+	+	NUM
ejpam-5407	167	3	1;ℶ3	1;ℶ3	NUM
ejpam-5407	167	4	+	+	CCONJ
ejpam-5407	167	5	1	1	NUM
ejpam-5407	167	6	,	,	PUNCT
ejpam-5407	167	7	2	2	NUM
ejpam-5407	167	8	;	;	PUNCT
ejpam-5407	167	9	1	1	NUM
ejpam-5407	167	10	)	)	PUNCT
ejpam-5407	167	11	+	+	CCONJ
ejpam-5407	167	12	(	(	PUNCT
ejpam-5407	167	13	κ2	κ2	NOUN
ejpam-5407	167	14	−	−	PROPN
ejpam-5407	167	15	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	167	16	+	+	NUM
ejpam-5407	167	17	κ2	κ2	NOUN
ejpam-5407	167	18	)	)	PUNCT
ejpam-5407	168	1	+	+	CCONJ
ejpam-5407	169	1	1	1	X
ejpam-5407	169	2	)	)	PUNCT
ejpam-5407	169	3	[	[	X
ejpam-5407	169	4	g3,2(|ℶ1|	g3,2(|ℶ1|	NOUN
ejpam-5407	169	5	,	,	PUNCT
ejpam-5407	169	6	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	169	7	,	,	PUNCT
ejpam-5407	169	8	υ1;ℶ3	υ1;ℶ3	PROPN
ejpam-5407	169	9	,	,	PUNCT
ejpam-5407	169	10	1	1	NUM
ejpam-5407	169	11	;	;	PUNCT
ejpam-5407	169	12	1)−	1)−	PROPN
ejpam-5407	169	13	1	1	NUM
ejpam-5407	169	14	]	]	PUNCT
ejpam-5407	169	15	≤	≤	NUM
ejpam-5407	169	16	1−	1−	NUM
ejpam-5407	169	17	κ1	κ1	NOUN
ejpam-5407	169	18	,	,	PUNCT
ejpam-5407	169	19	then	then	ADV
ejpam-5407	169	20	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	169	21	)	)	PUNCT
ejpam-5407	169	22	∈	∈	PROPN
ejpam-5407	169	23	cκ3(κ1	cκ3(κ1	NOUN
ejpam-5407	169	24	,	,	PUNCT
ejpam-5407	169	25	κ2	κ2	PROPN
ejpam-5407	169	26	)	)	PUNCT
ejpam-5407	169	27	.	.	PUNCT
ejpam-5407	170	1	t.	t.	PROPN
ejpam-5407	170	2	al	al	PROPN
ejpam-5407	170	3	-	-	PUNCT
ejpam-5407	170	4	hawary	hawary	PROPN
ejpam-5407	170	5	,	,	PUNCT
ejpam-5407	170	6	m.	m.	NOUN
ejpam-5407	170	7	o.	o.	PROPN
ejpam-5407	170	8	massa’deh	massa’deh	PROPN
ejpam-5407	170	9	,	,	PUNCT
ejpam-5407	170	10	a.	a.	NOUN
ejpam-5407	170	11	o	o	X
ejpam-5407	170	12	fallatah	fallatah	PROPN
ejpam-5407	170	13	/	/	SYM
ejpam-5407	170	14	eur	eur	PROPN
ejpam-5407	170	15	.	.	PUNCT
ejpam-5407	171	1	j.	j.	PROPN
ejpam-5407	171	2	pure	pure	PROPN
ejpam-5407	171	3	appl	appl	PROPN
ejpam-5407	171	4	.	.	PROPN
ejpam-5407	171	5	math	math	PROPN
ejpam-5407	171	6	,	,	PUNCT
ejpam-5407	171	7	17	17	NUM
ejpam-5407	171	8	(	(	PUNCT
ejpam-5407	171	9	4	4	NUM
ejpam-5407	171	10	)	)	PUNCT
ejpam-5407	171	11	(	(	PUNCT
ejpam-5407	171	12	2024	2024	NUM
ejpam-5407	171	13	)	)	PUNCT
ejpam-5407	171	14	,	,	PUNCT
ejpam-5407	171	15	3386	3386	NUM
ejpam-5407	171	16	-	-	SYM
ejpam-5407	171	17	3398	3398	NUM
ejpam-5407	171	18	3393	3393	NUM
ejpam-5407	171	19	proof	proof	NOUN
ejpam-5407	171	20	.	.	PUNCT
ejpam-5407	172	1	to	to	PART
ejpam-5407	172	2	prove	prove	VERB
ejpam-5407	172	3	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	NOUN
ejpam-5407	172	4	)	)	PUNCT
ejpam-5407	172	5	∈	∈	PROPN
ejpam-5407	172	6	cκ3(κ1	cκ3(κ1	NOUN
ejpam-5407	172	7	,	,	PUNCT
ejpam-5407	172	8	κ2	κ2	PROPN
ejpam-5407	172	9	)	)	PUNCT
ejpam-5407	172	10	,	,	PUNCT
ejpam-5407	172	11	it	it	PRON
ejpam-5407	172	12	suffices	suffice	VERB
ejpam-5407	172	13	to	to	PART
ejpam-5407	172	14	show	show	VERB
ejpam-5407	172	15	that	that	SCONJ
ejpam-5407	172	16	∞∑	∞∑	NUM
ejpam-5407	172	17	τ=2	τ=2	PUNCT
ejpam-5407	172	18	τ	τ	PROPN
ejpam-5407	173	1	[	[	X
ejpam-5407	173	2	(	(	PUNCT
ejpam-5407	173	3	τ(κ2	τ(κ2	NOUN
ejpam-5407	173	4	+	+	X
ejpam-5407	173	5	1)−	1)−	NUM
ejpam-5407	173	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	173	7	+	+	NUM
ejpam-5407	173	8	κ2	κ2	NOUN
ejpam-5407	173	9	)	)	PUNCT
ejpam-5407	173	10	]	]	PUNCT
ejpam-5407	173	11	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	173	12	(	(	PUNCT
ejpam-5407	173	13	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	NOUN
ejpam-5407	173	14	rτ	rτ	PROPN
ejpam-5407	173	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	173	16	≤	≤	NOUN
ejpam-5407	173	17	1−	1−	NUM
ejpam-5407	173	18	κ1	κ1	NOUN
ejpam-5407	173	19	.	.	PUNCT
ejpam-5407	174	1	applying	apply	VERB
ejpam-5407	174	2	the	the	DET
ejpam-5407	174	3	inequality	inequality	NOUN
ejpam-5407	174	4	(	(	PUNCT
ejpam-5407	174	5	4	4	NUM
ejpam-5407	174	6	)	)	PUNCT
ejpam-5407	174	7	and	and	CCONJ
ejpam-5407	174	8	use	use	NOUN
ejpam-5407	174	9	of	of	ADP
ejpam-5407	174	10	(	(	PUNCT
ejpam-5407	174	11	9	9	NUM
ejpam-5407	174	12	)	)	PUNCT
ejpam-5407	174	13	,	,	PUNCT
ejpam-5407	174	14	and	and	CCONJ
ejpam-5407	174	15	then	then	ADV
ejpam-5407	174	16	write	write	VERB
ejpam-5407	174	17	τ	τ	PROPN
ejpam-5407	174	18	=	=	SYM
ejpam-5407	174	19	(	(	PUNCT
ejpam-5407	174	20	τ	τ	PROPN
ejpam-5407	174	21	−	−	PROPN
ejpam-5407	174	22	1	1	NUM
ejpam-5407	174	23	)	)	PUNCT
ejpam-5407	175	1	+	+	NUM
ejpam-5407	175	2	1	1	NUM
ejpam-5407	175	3	,	,	PUNCT
ejpam-5407	175	4	we	we	PRON
ejpam-5407	175	5	get	get	VERB
ejpam-5407	175	6	∞∑	∞∑	NUM
ejpam-5407	175	7	τ=2	τ=2	PUNCT
ejpam-5407	175	8	τ	τ	PROPN
ejpam-5407	176	1	[	[	X
ejpam-5407	176	2	(	(	PUNCT
ejpam-5407	176	3	τ(κ2	τ(κ2	NOUN
ejpam-5407	176	4	+	+	X
ejpam-5407	176	5	1)−	1)−	NUM
ejpam-5407	176	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	176	7	+	+	NUM
ejpam-5407	176	8	κ2	κ2	NOUN
ejpam-5407	176	9	)	)	PUNCT
ejpam-5407	176	10	]	]	PUNCT
ejpam-5407	176	11	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	176	12	(	(	PUNCT
ejpam-5407	176	13	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	NOUN
ejpam-5407	176	14	rτ	rτ	PROPN
ejpam-5407	176	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	176	16	≤	≤	NOUN
ejpam-5407	176	17	∞∑	∞∑	NUM
ejpam-5407	176	18	τ=2	τ=2	PUNCT
ejpam-5407	177	1	[	[	X
ejpam-5407	177	2	(	(	PUNCT
ejpam-5407	177	3	τ(κ2	τ(κ2	NOUN
ejpam-5407	177	4	+	+	X
ejpam-5407	177	5	1)−	1)−	NUM
ejpam-5407	177	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	177	7	+	+	NUM
ejpam-5407	177	8	κ2	κ2	NOUN
ejpam-5407	177	9	)	)	PUNCT
ejpam-5407	177	10	]	]	PUNCT
ejpam-5407	177	11	(	(	PUNCT
ejpam-5407	177	12	|ℶ1|)τ−1	|ℶ1|)τ−1	PROPN
ejpam-5407	177	13	(	(	PUNCT
ejpam-5407	177	14	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	177	15	(	(	PUNCT
ejpam-5407	177	16	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	177	17	(	(	PUNCT
ejpam-5407	177	18	1)τ−1	1)τ−1	NUM
ejpam-5407	177	19	(	(	PUNCT
ejpam-5407	177	20	υ1)τ−1	υ1)τ−1	PROPN
ejpam-5407	177	21	(	(	PUNCT
ejpam-5407	177	22	1)τ−1	1)τ−1	NUM
ejpam-5407	177	23	≤	≤	NOUN
ejpam-5407	177	24	(	(	PUNCT
ejpam-5407	177	25	κ2	κ2	NOUN
ejpam-5407	177	26	+	+	CCONJ
ejpam-5407	177	27	1	1	X
ejpam-5407	177	28	)	)	PUNCT
ejpam-5407	177	29	∞∑	∞∑	NOUN
ejpam-5407	177	30	τ=2	τ=2	PUNCT
ejpam-5407	177	31	(	(	PUNCT
ejpam-5407	177	32	τ	τ	X
ejpam-5407	177	33	−	−	PROPN
ejpam-5407	177	34	1	1	NUM
ejpam-5407	177	35	)	)	PUNCT
ejpam-5407	177	36	(	(	PUNCT
ejpam-5407	177	37	|ℶ1|)τ−1	|ℶ1|)τ−1	NOUN
ejpam-5407	177	38	(	(	PUNCT
ejpam-5407	177	39	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	177	40	(	(	PUNCT
ejpam-5407	177	41	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	177	42	(	(	PUNCT
ejpam-5407	177	43	1)τ−1	1)τ−1	NUM
ejpam-5407	177	44	+	+	ADJ
ejpam-5407	177	45	(	(	PUNCT
ejpam-5407	177	46	κ2	κ2	NOUN
ejpam-5407	177	47	−	−	PROPN
ejpam-5407	177	48	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	177	49	+	+	NUM
ejpam-5407	177	50	κ2	κ2	NOUN
ejpam-5407	177	51	)	)	PUNCT
ejpam-5407	177	52	+	+	CCONJ
ejpam-5407	177	53	1	1	X
ejpam-5407	177	54	)	)	PUNCT
ejpam-5407	177	55	∞∑	∞∑	PROPN
ejpam-5407	177	56	τ=2	τ=2	PUNCT
ejpam-5407	177	57	(	(	PUNCT
ejpam-5407	177	58	|ℶ1|)τ−1	|ℶ1|)τ−1	PROPN
ejpam-5407	177	59	(	(	PUNCT
ejpam-5407	177	60	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	177	61	(	(	PUNCT
ejpam-5407	177	62	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	177	63	(	(	PUNCT
ejpam-5407	177	64	1)τ−1	1)τ−1	NUM
ejpam-5407	177	65	≤	≤	NOUN
ejpam-5407	177	66	(	(	PUNCT
ejpam-5407	177	67	κ2	κ2	NOUN
ejpam-5407	177	68	+	+	CCONJ
ejpam-5407	177	69	1	1	X
ejpam-5407	177	70	)	)	PUNCT
ejpam-5407	177	71	|ℶ1ℶ2|υ1	|ℶ1ℶ2|υ1	NOUN
ejpam-5407	177	72	ℶ3(1)1	ℶ3(1)1	NOUN
ejpam-5407	177	73	∞∑	∞∑	PROPN
ejpam-5407	177	74	τ=2	τ=2	PUNCT
ejpam-5407	177	75	(	(	PUNCT
ejpam-5407	177	76	|ℶ1|+	|ℶ1|+	X
ejpam-5407	177	77	1)τ−2	1)τ−2	NUM
ejpam-5407	177	78	(	(	PUNCT
ejpam-5407	177	79	|ℶ2|+	|ℶ2|+	PROPN
ejpam-5407	177	80	1)τ−2	1)τ−2	NUM
ejpam-5407	177	81	(	(	PUNCT
ejpam-5407	177	82	υ1	υ1	PROPN
ejpam-5407	177	83	+	+	PROPN
ejpam-5407	177	84	1)τ−2	1)τ−2	NUM
ejpam-5407	177	85	(	(	PUNCT
ejpam-5407	177	86	ℶ3	ℶ3	NOUN
ejpam-5407	177	87	+	+	NOUN
ejpam-5407	177	88	1)τ−2	1)τ−2	NUM
ejpam-5407	177	89	(	(	PUNCT
ejpam-5407	177	90	1)τ−2(2)τ−2	1)τ−2(2)τ−2	NUM
ejpam-5407	177	91	+	+	PROPN
ejpam-5407	177	92	(	(	PUNCT
ejpam-5407	177	93	κ2	κ2	NOUN
ejpam-5407	177	94	−	−	PROPN
ejpam-5407	177	95	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	177	96	+	+	NUM
ejpam-5407	177	97	κ2	κ2	NOUN
ejpam-5407	177	98	)	)	PUNCT
ejpam-5407	177	99	+	+	CCONJ
ejpam-5407	177	100	1	1	X
ejpam-5407	177	101	)	)	PUNCT
ejpam-5407	177	102	∞∑	∞∑	PROPN
ejpam-5407	177	103	τ=2	τ=2	PUNCT
ejpam-5407	177	104	(	(	PUNCT
ejpam-5407	177	105	|ℶ1|)τ−1	|ℶ1|)τ−1	PROPN
ejpam-5407	177	106	(	(	PUNCT
ejpam-5407	177	107	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	177	108	(	(	PUNCT
ejpam-5407	177	109	υ1)τ−1	υ1)τ−1	PROPN
ejpam-5407	177	110	(	(	PUNCT
ejpam-5407	177	111	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	177	112	(	(	PUNCT
ejpam-5407	177	113	1)τ−1(1)τ−1	1)τ−1(1)τ−1	NUM
ejpam-5407	177	114	.	.	PUNCT
ejpam-5407	178	1	using	use	VERB
ejpam-5407	178	2	gauss	gauss	ADJ
ejpam-5407	178	3	summation	summation	NOUN
ejpam-5407	178	4	theorem	theorem	PROPN
ejpam-5407	178	5	,	,	PUNCT
ejpam-5407	178	6	we	we	PRON
ejpam-5407	178	7	can	can	AUX
ejpam-5407	178	8	write	write	VERB
ejpam-5407	178	9	∞∑	∞∑	NUM
ejpam-5407	178	10	τ=2	τ=2	PUNCT
ejpam-5407	178	11	τ	τ	PROPN
ejpam-5407	179	1	[	[	X
ejpam-5407	179	2	(	(	PUNCT
ejpam-5407	179	3	τ(κ2	τ(κ2	NOUN
ejpam-5407	179	4	+	+	X
ejpam-5407	179	5	1)−	1)−	NUM
ejpam-5407	179	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	179	7	+	+	NUM
ejpam-5407	179	8	κ2	κ2	NOUN
ejpam-5407	179	9	)	)	PUNCT
ejpam-5407	179	10	]	]	PUNCT
ejpam-5407	179	11	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	179	12	(	(	PUNCT
ejpam-5407	179	13	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	PROPN
ejpam-5407	179	14	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5407	179	15	≤	≤	NOUN
ejpam-5407	179	16	(	(	PUNCT
ejpam-5407	179	17	κ2	κ2	NOUN
ejpam-5407	179	18	+	+	CCONJ
ejpam-5407	179	19	1	1	X
ejpam-5407	179	20	)	)	PUNCT
ejpam-5407	179	21	|ℶ1ℶ2|υ1	|ℶ1ℶ2|υ1	NOUN
ejpam-5407	179	22	ℶ3(1)1	ℶ3(1)1	PROPN
ejpam-5407	179	23	g3,2(|ℶ1|+	g3,2(|ℶ1|+	PROPN
ejpam-5407	179	24	1	1	NUM
ejpam-5407	179	25	,	,	PUNCT
ejpam-5407	179	26	|ℶ2|+	|ℶ2|+	X
ejpam-5407	180	1	1,υ1	1,υ1	NUM
ejpam-5407	180	2	+	+	NUM
ejpam-5407	180	3	1;ℶ3	1;ℶ3	NUM
ejpam-5407	180	4	+	+	CCONJ
ejpam-5407	180	5	1	1	NUM
ejpam-5407	180	6	,	,	PUNCT
ejpam-5407	180	7	2	2	NUM
ejpam-5407	180	8	;	;	PUNCT
ejpam-5407	180	9	1	1	NUM
ejpam-5407	180	10	)	)	PUNCT
ejpam-5407	180	11	+	+	CCONJ
ejpam-5407	180	12	(	(	PUNCT
ejpam-5407	180	13	κ2	κ2	NOUN
ejpam-5407	180	14	−	−	PROPN
ejpam-5407	180	15	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	180	16	+	+	NUM
ejpam-5407	180	17	κ2	κ2	NOUN
ejpam-5407	180	18	)	)	PUNCT
ejpam-5407	181	1	+	+	CCONJ
ejpam-5407	182	1	1	1	X
ejpam-5407	182	2	)	)	PUNCT
ejpam-5407	182	3	[	[	X
ejpam-5407	182	4	g3,2(|ℶ1|	g3,2(|ℶ1|	NOUN
ejpam-5407	182	5	,	,	PUNCT
ejpam-5407	182	6	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	182	7	,	,	PUNCT
ejpam-5407	182	8	υ1;ℶ3	υ1;ℶ3	PROPN
ejpam-5407	182	9	,	,	PUNCT
ejpam-5407	182	10	1	1	NUM
ejpam-5407	182	11	;	;	PUNCT
ejpam-5407	182	12	1)−	1)−	PROPN
ejpam-5407	182	13	1	1	NUM
ejpam-5407	182	14	]	]	PUNCT
ejpam-5407	182	15	.	.	PUNCT
ejpam-5407	183	1	(	(	PUNCT
ejpam-5407	183	2	12	12	NUM
ejpam-5407	183	3	)	)	PUNCT
ejpam-5407	183	4	but	but	CCONJ
ejpam-5407	183	5	the	the	DET
ejpam-5407	183	6	expression	expression	NOUN
ejpam-5407	183	7	(	(	PUNCT
ejpam-5407	183	8	12	12	NUM
ejpam-5407	183	9	)	)	PUNCT
ejpam-5407	183	10	is	be	AUX
ejpam-5407	183	11	bounded	bound	VERB
ejpam-5407	183	12	above	above	ADV
ejpam-5407	183	13	by	by	ADP
ejpam-5407	183	14	1−	1−	NUM
ejpam-5407	183	15	κ1	κ1	NOUN
ejpam-5407	183	16	,	,	PUNCT
ejpam-5407	183	17	thus	thus	ADV
ejpam-5407	183	18	the	the	DET
ejpam-5407	183	19	proof	proof	NOUN
ejpam-5407	183	20	is	be	AUX
ejpam-5407	183	21	completed	complete	VERB
ejpam-5407	183	22	.	.	PUNCT
ejpam-5407	184	1	theorem	theorem	ADJ
ejpam-5407	184	2	4	4	NUM
ejpam-5407	184	3	.	.	PUNCT
ejpam-5407	185	1	let	let	VERB
ejpam-5407	185	2	υ1	υ1	PROPN
ejpam-5407	185	3	given	give	VERB
ejpam-5407	185	4	by	by	ADP
ejpam-5407	185	5	(	(	PUNCT
ejpam-5407	185	6	3	3	NUM
ejpam-5407	185	7	)	)	PUNCT
ejpam-5407	185	8	and	and	CCONJ
ejpam-5407	185	9	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	185	10	∈	∈	PROPN
ejpam-5407	185	11	c−{0	c−{0	ADV
ejpam-5407	185	12	}	}	PUNCT
ejpam-5407	185	13	,	,	PUNCT
ejpam-5407	185	14	ℶ3	ℶ3	PROPN
ejpam-5407	185	15	∈	∈	PROPN
ejpam-5407	185	16	r.	r.	PROPN
ejpam-5407	186	1	if	if	SCONJ
ejpam-5407	186	2	l	l	PROPN
ejpam-5407	186	3	∈	∈	PROPN
ejpam-5407	186	4	ξ−st	ξ−st	NOUN
ejpam-5407	186	5	for	for	ADP
ejpam-5407	186	6	some	some	DET
ejpam-5407	186	7	ξ(0	ξ(0	SYM
ejpam-5407	186	8	≤	≤	PUNCT
ejpam-5407	186	9	ξ	ξ	X
ejpam-5407	186	10	<	<	X
ejpam-5407	186	11	∞	∞	NUM
ejpam-5407	186	12	)	)	PUNCT
ejpam-5407	186	13	and	and	CCONJ
ejpam-5407	186	14	satisfies	satisfy	VERB
ejpam-5407	186	15	the	the	DET
ejpam-5407	186	16	inequality	inequality	NOUN
ejpam-5407	186	17	(	(	PUNCT
ejpam-5407	186	18	κ2	κ2	NOUN
ejpam-5407	186	19	+	+	CCONJ
ejpam-5407	186	20	1	1	X
ejpam-5407	186	21	)	)	PUNCT
ejpam-5407	186	22	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	186	23	(	(	PUNCT
ejpam-5407	186	24	|ℶ1|+	|ℶ1|+	X
ejpam-5407	186	25	1	1	NUM
ejpam-5407	186	26	)	)	PUNCT
ejpam-5407	186	27	(	(	PUNCT
ejpam-5407	186	28	|ℶ2|+	|ℶ2|+	X
ejpam-5407	186	29	1	1	NUM
ejpam-5407	186	30	)	)	PUNCT
ejpam-5407	186	31	(	(	PUNCT
ejpam-5407	186	32	υ1	υ1	NOUN
ejpam-5407	186	33	+	+	CCONJ
ejpam-5407	186	34	1)υ1	1)υ1	NUM
ejpam-5407	186	35	ℶ3(ℶ3	ℶ3(ℶ3	NUM
ejpam-5407	186	36	+	+	NOUN
ejpam-5407	186	37	1)(2)1	1)(2)1	PROPN
ejpam-5407	186	38	g3,2(|ℶ1|+	g3,2(|ℶ1|+	NOUN
ejpam-5407	186	39	2	2	NUM
ejpam-5407	186	40	,	,	PUNCT
ejpam-5407	186	41	|ℶ2|+	|ℶ2|+	PROPN
ejpam-5407	186	42	2,υ1	2,υ1	NUM
ejpam-5407	186	43	+	+	NUM
ejpam-5407	186	44	2;ℶ3	2;ℶ3	NUM
ejpam-5407	186	45	+	+	CCONJ
ejpam-5407	186	46	2	2	NUM
ejpam-5407	186	47	,	,	PUNCT
ejpam-5407	186	48	3	3	NUM
ejpam-5407	186	49	;	;	PUNCT
ejpam-5407	186	50	1	1	NUM
ejpam-5407	186	51	)	)	PUNCT
ejpam-5407	186	52	+	+	CCONJ
ejpam-5407	186	53	(	(	PUNCT
ejpam-5407	186	54	3(κ2	3(κ2	NUM
ejpam-5407	186	55	+	+	SYM
ejpam-5407	186	56	1)−	1)−	NUM
ejpam-5407	186	57	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	186	58	+	+	NUM
ejpam-5407	186	59	κ2	κ2	NOUN
ejpam-5407	186	60	)	)	PUNCT
ejpam-5407	186	61	)	)	PUNCT
ejpam-5407	187	1	|ℶ1ℶ2|υ1	|ℶ1ℶ2|υ1	NOUN
ejpam-5407	187	2	ℶ3(1)1	ℶ3(1)1	PROPN
ejpam-5407	187	3	g3,2(|ℶ1|+	g3,2(|ℶ1|+	PROPN
ejpam-5407	187	4	1	1	NUM
ejpam-5407	187	5	,	,	PUNCT
ejpam-5407	187	6	|ℶ2|+	|ℶ2|+	X
ejpam-5407	188	1	1,υ1	1,υ1	NUM
ejpam-5407	188	2	+	+	NUM
ejpam-5407	188	3	1;ℶ3	1;ℶ3	NUM
ejpam-5407	188	4	+	+	CCONJ
ejpam-5407	188	5	1	1	NUM
ejpam-5407	188	6	,	,	PUNCT
ejpam-5407	188	7	2	2	NUM
ejpam-5407	188	8	;	;	PUNCT
ejpam-5407	188	9	1	1	NUM
ejpam-5407	188	10	)	)	PUNCT
ejpam-5407	188	11	+	+	CCONJ
ejpam-5407	188	12	(	(	PUNCT
ejpam-5407	188	13	κ2	κ2	NOUN
ejpam-5407	188	14	−	−	PROPN
ejpam-5407	188	15	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	188	16	+	+	NUM
ejpam-5407	188	17	κ2	κ2	NOUN
ejpam-5407	188	18	)	)	PUNCT
ejpam-5407	189	1	+	+	CCONJ
ejpam-5407	190	1	1	1	X
ejpam-5407	190	2	)	)	PUNCT
ejpam-5407	190	3	[	[	X
ejpam-5407	190	4	g3,2(|ℶ1|	g3,2(|ℶ1|	NOUN
ejpam-5407	190	5	,	,	PUNCT
ejpam-5407	190	6	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	190	7	,	,	PUNCT
ejpam-5407	190	8	υ1;ℶ3	υ1;ℶ3	PROPN
ejpam-5407	190	9	,	,	PUNCT
ejpam-5407	190	10	1	1	NUM
ejpam-5407	190	11	;	;	PUNCT
ejpam-5407	190	12	1)−	1)−	PROPN
ejpam-5407	190	13	1	1	NUM
ejpam-5407	190	14	]	]	PUNCT
ejpam-5407	190	15	≤	≤	NUM
ejpam-5407	190	16	1−	1−	NUM
ejpam-5407	190	17	κ1	κ1	NOUN
ejpam-5407	190	18	,	,	PUNCT
ejpam-5407	190	19	then	then	ADV
ejpam-5407	190	20	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	190	21	)	)	PUNCT
ejpam-5407	190	22	∈	∈	PROPN
ejpam-5407	190	23	cκ3(κ1	cκ3(κ1	NOUN
ejpam-5407	190	24	,	,	PUNCT
ejpam-5407	190	25	κ2	κ2	PROPN
ejpam-5407	190	26	)	)	PUNCT
ejpam-5407	190	27	.	.	PUNCT
ejpam-5407	191	1	t.	t.	PROPN
ejpam-5407	191	2	al	al	PROPN
ejpam-5407	191	3	-	-	PUNCT
ejpam-5407	191	4	hawary	hawary	PROPN
ejpam-5407	191	5	,	,	PUNCT
ejpam-5407	191	6	m.	m.	NOUN
ejpam-5407	191	7	o.	o.	PROPN
ejpam-5407	191	8	massa’deh	massa’deh	PROPN
ejpam-5407	191	9	,	,	PUNCT
ejpam-5407	191	10	a.	a.	NOUN
ejpam-5407	191	11	o	o	X
ejpam-5407	191	12	fallatah	fallatah	PROPN
ejpam-5407	191	13	/	/	SYM
ejpam-5407	191	14	eur	eur	PROPN
ejpam-5407	191	15	.	.	PUNCT
ejpam-5407	192	1	j.	j.	PROPN
ejpam-5407	192	2	pure	pure	PROPN
ejpam-5407	192	3	appl	appl	PROPN
ejpam-5407	192	4	.	.	PROPN
ejpam-5407	192	5	math	math	PROPN
ejpam-5407	192	6	,	,	PUNCT
ejpam-5407	192	7	17	17	NUM
ejpam-5407	192	8	(	(	PUNCT
ejpam-5407	192	9	4	4	NUM
ejpam-5407	192	10	)	)	PUNCT
ejpam-5407	192	11	(	(	PUNCT
ejpam-5407	192	12	2024	2024	NUM
ejpam-5407	192	13	)	)	PUNCT
ejpam-5407	192	14	,	,	PUNCT
ejpam-5407	192	15	3386	3386	NUM
ejpam-5407	192	16	-	-	SYM
ejpam-5407	192	17	3398	3398	NUM
ejpam-5407	192	18	3394	3394	NUM
ejpam-5407	192	19	proof	proof	NOUN
ejpam-5407	192	20	.	.	PUNCT
ejpam-5407	193	1	to	to	PART
ejpam-5407	193	2	prove	prove	VERB
ejpam-5407	193	3	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	NOUN
ejpam-5407	193	4	)	)	PUNCT
ejpam-5407	193	5	∈	∈	PROPN
ejpam-5407	193	6	cκ3(κ1	cκ3(κ1	NOUN
ejpam-5407	193	7	,	,	PUNCT
ejpam-5407	193	8	κ2	κ2	PROPN
ejpam-5407	193	9	)	)	PUNCT
ejpam-5407	193	10	,	,	PUNCT
ejpam-5407	193	11	it	it	PRON
ejpam-5407	193	12	suffices	suffice	VERB
ejpam-5407	193	13	to	to	PART
ejpam-5407	193	14	show	show	VERB
ejpam-5407	193	15	that	that	SCONJ
ejpam-5407	193	16	∞∑	∞∑	NUM
ejpam-5407	193	17	τ=2	τ=2	PUNCT
ejpam-5407	193	18	τ	τ	PROPN
ejpam-5407	194	1	[	[	X
ejpam-5407	194	2	(	(	PUNCT
ejpam-5407	194	3	τ(κ2	τ(κ2	NOUN
ejpam-5407	194	4	+	+	X
ejpam-5407	194	5	1)−	1)−	NUM
ejpam-5407	194	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	194	7	+	+	NUM
ejpam-5407	194	8	κ2	κ2	NOUN
ejpam-5407	194	9	)	)	PUNCT
ejpam-5407	194	10	]	]	PUNCT
ejpam-5407	194	11	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	194	12	(	(	PUNCT
ejpam-5407	194	13	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	NOUN
ejpam-5407	194	14	rτ	rτ	PROPN
ejpam-5407	194	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	194	16	≤	≤	NOUN
ejpam-5407	194	17	1−	1−	NUM
ejpam-5407	194	18	κ1	κ1	NOUN
ejpam-5407	194	19	.	.	PUNCT
ejpam-5407	195	1	applying	apply	VERB
ejpam-5407	195	2	the	the	DET
ejpam-5407	195	3	inequality	inequality	NOUN
ejpam-5407	195	4	(	(	PUNCT
ejpam-5407	195	5	5	5	NUM
ejpam-5407	195	6	)	)	PUNCT
ejpam-5407	195	7	and	and	CCONJ
ejpam-5407	195	8	use	use	NOUN
ejpam-5407	195	9	of	of	ADP
ejpam-5407	195	10	(	(	PUNCT
ejpam-5407	195	11	9	9	NUM
ejpam-5407	195	12	)	)	PUNCT
ejpam-5407	195	13	,	,	PUNCT
ejpam-5407	195	14	and	and	CCONJ
ejpam-5407	195	15	then	then	ADV
ejpam-5407	195	16	write	write	VERB
ejpam-5407	195	17	τ	τ	PROPN
ejpam-5407	195	18	=	=	SYM
ejpam-5407	195	19	(	(	PUNCT
ejpam-5407	195	20	τ	τ	PROPN
ejpam-5407	195	21	−	−	PROPN
ejpam-5407	195	22	1	1	NUM
ejpam-5407	195	23	)	)	PUNCT
ejpam-5407	195	24	+	+	NUM
ejpam-5407	195	25	1	1	NUM
ejpam-5407	195	26	,	,	PUNCT
ejpam-5407	195	27	τ2	τ2	NOUN
ejpam-5407	195	28	=	=	SYM
ejpam-5407	195	29	(	(	PUNCT
ejpam-5407	195	30	τ−1)(τ−2	τ−1)(τ−2	NUM
ejpam-5407	195	31	)	)	PUNCT
ejpam-5407	195	32	+	+	NUM
ejpam-5407	195	33	3(τ−1	3(τ−1	NUM
ejpam-5407	195	34	)	)	PUNCT
ejpam-5407	196	1	+	+	NOUN
ejpam-5407	196	2	1	1	NUM
ejpam-5407	196	3	,	,	PUNCT
ejpam-5407	196	4	we	we	PRON
ejpam-5407	196	5	get	get	VERB
ejpam-5407	196	6	∞∑	∞∑	NUM
ejpam-5407	196	7	τ=2	τ=2	PUNCT
ejpam-5407	196	8	τ	τ	PROPN
ejpam-5407	197	1	[	[	X
ejpam-5407	197	2	(	(	PUNCT
ejpam-5407	197	3	τ(κ2	τ(κ2	NOUN
ejpam-5407	197	4	+	+	X
ejpam-5407	197	5	1)−	1)−	NUM
ejpam-5407	197	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	197	7	+	+	NUM
ejpam-5407	197	8	κ2	κ2	NOUN
ejpam-5407	197	9	)	)	PUNCT
ejpam-5407	197	10	]	]	PUNCT
ejpam-5407	197	11	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	197	12	(	(	PUNCT
ejpam-5407	197	13	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	NOUN
ejpam-5407	197	14	rτ	rτ	PROPN
ejpam-5407	197	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5407	197	16	≤	≤	NOUN
ejpam-5407	197	17	∞∑	∞∑	NUM
ejpam-5407	197	18	τ=2	τ=2	PUNCT
ejpam-5407	198	1	[	[	X
ejpam-5407	198	2	(	(	PUNCT
ejpam-5407	198	3	τ2(κ2	τ2(κ2	ADV
ejpam-5407	198	4	+	+	NUM
ejpam-5407	198	5	1	1	X
ejpam-5407	198	6	)	)	PUNCT
ejpam-5407	198	7	−	−	NOUN
ejpam-5407	198	8	τκ3(κ1	τκ3(κ1	NUM
ejpam-5407	199	1	+	+	NUM
ejpam-5407	199	2	κ2	κ2	NOUN
ejpam-5407	199	3	)	)	PUNCT
ejpam-5407	199	4	]	]	PUNCT
ejpam-5407	199	5	(	(	PUNCT
ejpam-5407	199	6	|ℶ1|)τ−1	|ℶ1|)τ−1	PROPN
ejpam-5407	199	7	(	(	PUNCT
ejpam-5407	199	8	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	199	9	(	(	PUNCT
ejpam-5407	199	10	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	199	11	(	(	PUNCT
ejpam-5407	199	12	1)τ−1	1)τ−1	NUM
ejpam-5407	199	13	(	(	PUNCT
ejpam-5407	199	14	υ1)τ−1	υ1)τ−1	PROPN
ejpam-5407	199	15	(	(	PUNCT
ejpam-5407	199	16	1)τ−1	1)τ−1	NUM
ejpam-5407	199	17	≤	≤	NOUN
ejpam-5407	199	18	(	(	PUNCT
ejpam-5407	199	19	κ2	κ2	NOUN
ejpam-5407	199	20	+	+	CCONJ
ejpam-5407	199	21	1	1	X
ejpam-5407	199	22	)	)	PUNCT
ejpam-5407	199	23	∞∑	∞∑	NOUN
ejpam-5407	199	24	τ=2	τ=2	PUNCT
ejpam-5407	199	25	(	(	PUNCT
ejpam-5407	199	26	τ	τ	X
ejpam-5407	199	27	−	−	PROPN
ejpam-5407	199	28	1)(τ	1)(τ	NUM
ejpam-5407	200	1	−	−	NOUN
ejpam-5407	200	2	2	2	NUM
ejpam-5407	200	3	)	)	PUNCT
ejpam-5407	200	4	(	(	PUNCT
ejpam-5407	200	5	|ℶ1|)τ−1	|ℶ1|)τ−1	NOUN
ejpam-5407	200	6	(	(	PUNCT
ejpam-5407	200	7	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	200	8	(	(	PUNCT
ejpam-5407	200	9	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	200	10	(	(	PUNCT
ejpam-5407	200	11	1)τ−1	1)τ−1	NUM
ejpam-5407	200	12	(	(	PUNCT
ejpam-5407	200	13	υ1)τ−1	υ1)τ−1	PROPN
ejpam-5407	200	14	(	(	PUNCT
ejpam-5407	200	15	1)τ−1	1)τ−1	NUM
ejpam-5407	200	16	+	+	ADJ
ejpam-5407	200	17	(	(	PUNCT
ejpam-5407	200	18	3(κ2	3(κ2	NUM
ejpam-5407	200	19	+	+	SYM
ejpam-5407	200	20	1)−	1)−	NUM
ejpam-5407	200	21	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	200	22	+	+	NUM
ejpam-5407	200	23	κ2	κ2	NOUN
ejpam-5407	200	24	)	)	PUNCT
ejpam-5407	200	25	)	)	PUNCT
ejpam-5407	201	1	∞∑	∞∑	NUM
ejpam-5407	201	2	τ=2	τ=2	PUNCT
ejpam-5407	201	3	(	(	PUNCT
ejpam-5407	201	4	τ	τ	X
ejpam-5407	201	5	−	−	PROPN
ejpam-5407	201	6	1	1	NUM
ejpam-5407	201	7	)	)	PUNCT
ejpam-5407	201	8	(	(	PUNCT
ejpam-5407	201	9	|ℶ1|)τ−1	|ℶ1|)τ−1	NOUN
ejpam-5407	201	10	(	(	PUNCT
ejpam-5407	201	11	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	201	12	(	(	PUNCT
ejpam-5407	201	13	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	201	14	(	(	PUNCT
ejpam-5407	201	15	1)τ−1	1)τ−1	NUM
ejpam-5407	201	16	(	(	PUNCT
ejpam-5407	201	17	υ1)τ−1	υ1)τ−1	PROPN
ejpam-5407	201	18	(	(	PUNCT
ejpam-5407	201	19	1)τ−1	1)τ−1	NUM
ejpam-5407	201	20	+	+	ADJ
ejpam-5407	201	21	(	(	PUNCT
ejpam-5407	201	22	κ2	κ2	NOUN
ejpam-5407	201	23	−	−	PROPN
ejpam-5407	201	24	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	201	25	+	+	NUM
ejpam-5407	201	26	κ2	κ2	NOUN
ejpam-5407	201	27	)	)	PUNCT
ejpam-5407	201	28	+	+	CCONJ
ejpam-5407	201	29	1	1	X
ejpam-5407	201	30	)	)	PUNCT
ejpam-5407	201	31	∞∑	∞∑	PROPN
ejpam-5407	201	32	τ=2	τ=2	PUNCT
ejpam-5407	201	33	(	(	PUNCT
ejpam-5407	201	34	|ℶ1|)τ−1	|ℶ1|)τ−1	PROPN
ejpam-5407	201	35	(	(	PUNCT
ejpam-5407	201	36	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	201	37	(	(	PUNCT
ejpam-5407	201	38	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	201	39	(	(	PUNCT
ejpam-5407	201	40	1)τ−1	1)τ−1	NUM
ejpam-5407	201	41	(	(	PUNCT
ejpam-5407	201	42	υ1)τ−1	υ1)τ−1	PROPN
ejpam-5407	201	43	(	(	PUNCT
ejpam-5407	201	44	1)τ−1	1)τ−1	NUM
ejpam-5407	201	45	≤	≤	NOUN
ejpam-5407	201	46	(	(	PUNCT
ejpam-5407	201	47	κ2	κ2	NOUN
ejpam-5407	201	48	+	+	CCONJ
ejpam-5407	201	49	1	1	X
ejpam-5407	201	50	)	)	PUNCT
ejpam-5407	201	51	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	201	52	(	(	PUNCT
ejpam-5407	201	53	|ℶ1|+	|ℶ1|+	X
ejpam-5407	201	54	1	1	NUM
ejpam-5407	201	55	)	)	PUNCT
ejpam-5407	201	56	(	(	PUNCT
ejpam-5407	201	57	|ℶ2|+	|ℶ2|+	X
ejpam-5407	201	58	1	1	NUM
ejpam-5407	201	59	)	)	PUNCT
ejpam-5407	201	60	(	(	PUNCT
ejpam-5407	201	61	υ1	υ1	NOUN
ejpam-5407	201	62	+	+	CCONJ
ejpam-5407	201	63	1)υ1	1)υ1	NUM
ejpam-5407	201	64	ℶ3(ℶ3	ℶ3(ℶ3	NUM
ejpam-5407	201	65	+	+	NOUN
ejpam-5407	201	66	1)(2)1	1)(2)1	NOUN
ejpam-5407	201	67	∞∑	∞∑	NUM
ejpam-5407	201	68	τ=3	τ=3	PUNCT
ejpam-5407	201	69	(	(	PUNCT
ejpam-5407	201	70	|ℶ1|+	|ℶ1|+	X
ejpam-5407	201	71	2)τ−3	2)τ−3	NUM
ejpam-5407	201	72	(	(	PUNCT
ejpam-5407	201	73	|ℶ2|+	|ℶ2|+	X
ejpam-5407	201	74	2)τ−3	2)τ−3	NUM
ejpam-5407	201	75	(	(	PUNCT
ejpam-5407	201	76	υ1	υ1	PROPN
ejpam-5407	201	77	+	+	PROPN
ejpam-5407	201	78	2)τ−3	2)τ−3	NUM
ejpam-5407	201	79	(	(	PUNCT
ejpam-5407	201	80	ℶ3	ℶ3	NOUN
ejpam-5407	201	81	+	+	CCONJ
ejpam-5407	201	82	2)τ−3	2)τ−3	NUM
ejpam-5407	201	83	(	(	PUNCT
ejpam-5407	201	84	1)τ−3(3)τ−3	1)τ−3(3)τ−3	NUM
ejpam-5407	201	85	(	(	PUNCT
ejpam-5407	201	86	3(κ2	3(κ2	NUM
ejpam-5407	201	87	+	+	CCONJ
ejpam-5407	201	88	1)−	1)−	NUM
ejpam-5407	201	89	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	201	90	+	+	NUM
ejpam-5407	201	91	κ2	κ2	NOUN
ejpam-5407	201	92	)	)	PUNCT
ejpam-5407	201	93	)	)	PUNCT
ejpam-5407	202	1	|ℶ1ℶ2|υ1	|ℶ1ℶ2|υ1	NOUN
ejpam-5407	202	2	ℶ3(1)1	ℶ3(1)1	NOUN
ejpam-5407	202	3	∞∑	∞∑	PROPN
ejpam-5407	202	4	τ=2	τ=2	PUNCT
ejpam-5407	202	5	(	(	PUNCT
ejpam-5407	202	6	|ℶ1|+	|ℶ1|+	X
ejpam-5407	202	7	1)τ−2	1)τ−2	NUM
ejpam-5407	202	8	(	(	PUNCT
ejpam-5407	202	9	|ℶ2|+	|ℶ2|+	PROPN
ejpam-5407	202	10	1)τ−2	1)τ−2	NUM
ejpam-5407	202	11	(	(	PUNCT
ejpam-5407	202	12	υ1	υ1	PROPN
ejpam-5407	202	13	+	+	PROPN
ejpam-5407	202	14	1)τ−2	1)τ−2	NUM
ejpam-5407	202	15	(	(	PUNCT
ejpam-5407	202	16	ℶ3	ℶ3	NOUN
ejpam-5407	202	17	+	+	NOUN
ejpam-5407	202	18	1)τ−2	1)τ−2	NUM
ejpam-5407	202	19	(	(	PUNCT
ejpam-5407	202	20	1)τ−2(2)τ−2	1)τ−2(2)τ−2	NUM
ejpam-5407	202	21	+	+	PROPN
ejpam-5407	202	22	(	(	PUNCT
ejpam-5407	202	23	κ2	κ2	NOUN
ejpam-5407	202	24	−	−	PROPN
ejpam-5407	202	25	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	202	26	+	+	NUM
ejpam-5407	202	27	κ2	κ2	NOUN
ejpam-5407	202	28	)	)	PUNCT
ejpam-5407	202	29	+	+	CCONJ
ejpam-5407	202	30	1	1	X
ejpam-5407	202	31	)	)	PUNCT
ejpam-5407	202	32	∞∑	∞∑	PROPN
ejpam-5407	202	33	τ=2	τ=2	PUNCT
ejpam-5407	202	34	(	(	PUNCT
ejpam-5407	202	35	|ℶ1|)τ−1	|ℶ1|)τ−1	PROPN
ejpam-5407	202	36	(	(	PUNCT
ejpam-5407	202	37	|ℶ2|)τ−1	|ℶ2|)τ−1	PROPN
ejpam-5407	202	38	(	(	PUNCT
ejpam-5407	202	39	υ1)τ−1	υ1)τ−1	PROPN
ejpam-5407	202	40	(	(	PUNCT
ejpam-5407	202	41	ℶ3)τ−1	ℶ3)τ−1	PROPN
ejpam-5407	202	42	(	(	PUNCT
ejpam-5407	202	43	1)τ−1(1)τ−1	1)τ−1(1)τ−1	NUM
ejpam-5407	202	44	.	.	PUNCT
ejpam-5407	203	1	by	by	ADP
ejpam-5407	203	2	gauss	gauss	ADJ
ejpam-5407	203	3	summation	summation	NOUN
ejpam-5407	203	4	theorem	theorem	PROPN
ejpam-5407	203	5	,	,	PUNCT
ejpam-5407	203	6	we	we	PRON
ejpam-5407	203	7	can	can	AUX
ejpam-5407	203	8	write	write	VERB
ejpam-5407	203	9	∞∑	∞∑	NUM
ejpam-5407	203	10	τ=2	τ=2	PUNCT
ejpam-5407	203	11	τ	τ	PROPN
ejpam-5407	204	1	[	[	X
ejpam-5407	204	2	(	(	PUNCT
ejpam-5407	204	3	τ(κ2	τ(κ2	NOUN
ejpam-5407	204	4	+	+	X
ejpam-5407	204	5	1)−	1)−	NUM
ejpam-5407	204	6	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	204	7	+	+	NUM
ejpam-5407	204	8	κ2	κ2	NOUN
ejpam-5407	204	9	)	)	PUNCT
ejpam-5407	204	10	]	]	PUNCT
ejpam-5407	204	11	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	∣∣∣∣(ℶ1)τ−1(ℶ2)τ−1	X
ejpam-5407	204	12	(	(	PUNCT
ejpam-5407	204	13	ℶ3)τ−1(1)τ−1	ℶ3)τ−1(1)τ−1	PROPN
ejpam-5407	204	14	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5407	204	15	≤	≤	NOUN
ejpam-5407	204	16	(	(	PUNCT
ejpam-5407	204	17	κ2	κ2	NOUN
ejpam-5407	204	18	+	+	CCONJ
ejpam-5407	204	19	1	1	X
ejpam-5407	204	20	)	)	PUNCT
ejpam-5407	204	21	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	204	22	(	(	PUNCT
ejpam-5407	204	23	|ℶ1|+	|ℶ1|+	X
ejpam-5407	204	24	1	1	NUM
ejpam-5407	204	25	)	)	PUNCT
ejpam-5407	204	26	(	(	PUNCT
ejpam-5407	204	27	|ℶ2|+	|ℶ2|+	X
ejpam-5407	204	28	1	1	NUM
ejpam-5407	204	29	)	)	PUNCT
ejpam-5407	204	30	(	(	PUNCT
ejpam-5407	204	31	υ1	υ1	NOUN
ejpam-5407	204	32	+	+	CCONJ
ejpam-5407	204	33	1)υ1	1)υ1	NUM
ejpam-5407	204	34	ℶ3(ℶ3	ℶ3(ℶ3	NUM
ejpam-5407	204	35	+	+	NOUN
ejpam-5407	204	36	1)(2)1	1)(2)1	PROPN
ejpam-5407	204	37	g3,2(|ℶ1|+	g3,2(|ℶ1|+	NOUN
ejpam-5407	204	38	2	2	NUM
ejpam-5407	204	39	,	,	PUNCT
ejpam-5407	204	40	|ℶ2|+	|ℶ2|+	PROPN
ejpam-5407	204	41	2,υ1	2,υ1	NUM
ejpam-5407	204	42	+	+	NUM
ejpam-5407	204	43	2;ℶ3	2;ℶ3	NUM
ejpam-5407	204	44	+	+	CCONJ
ejpam-5407	204	45	2	2	NUM
ejpam-5407	204	46	,	,	PUNCT
ejpam-5407	204	47	3	3	NUM
ejpam-5407	204	48	;	;	PUNCT
ejpam-5407	204	49	1	1	NUM
ejpam-5407	204	50	)	)	PUNCT
ejpam-5407	204	51	+	+	CCONJ
ejpam-5407	204	52	(	(	PUNCT
ejpam-5407	204	53	3(κ2	3(κ2	NUM
ejpam-5407	204	54	+	+	SYM
ejpam-5407	204	55	1)−	1)−	NUM
ejpam-5407	204	56	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	204	57	+	+	NUM
ejpam-5407	204	58	κ2	κ2	NOUN
ejpam-5407	204	59	)	)	PUNCT
ejpam-5407	204	60	)	)	PUNCT
ejpam-5407	205	1	|ℶ1ℶ2|υ1	|ℶ1ℶ2|υ1	NOUN
ejpam-5407	205	2	ℶ3(1)1	ℶ3(1)1	PROPN
ejpam-5407	205	3	g3,2(|ℶ1|+	g3,2(|ℶ1|+	PROPN
ejpam-5407	205	4	1	1	NUM
ejpam-5407	205	5	,	,	PUNCT
ejpam-5407	205	6	|ℶ2|+	|ℶ2|+	X
ejpam-5407	206	1	1,υ1	1,υ1	NUM
ejpam-5407	206	2	+	+	NUM
ejpam-5407	206	3	1;ℶ3	1;ℶ3	NUM
ejpam-5407	206	4	+	+	CCONJ
ejpam-5407	206	5	1	1	NUM
ejpam-5407	206	6	,	,	PUNCT
ejpam-5407	206	7	2	2	NUM
ejpam-5407	206	8	;	;	PUNCT
ejpam-5407	206	9	1	1	NUM
ejpam-5407	206	10	)	)	PUNCT
ejpam-5407	206	11	+	+	CCONJ
ejpam-5407	206	12	(	(	PUNCT
ejpam-5407	206	13	κ2	κ2	NOUN
ejpam-5407	206	14	−	−	PROPN
ejpam-5407	206	15	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	206	16	+	+	NUM
ejpam-5407	206	17	κ2	κ2	NOUN
ejpam-5407	206	18	)	)	PUNCT
ejpam-5407	207	1	+	+	CCONJ
ejpam-5407	208	1	1	1	X
ejpam-5407	208	2	)	)	PUNCT
ejpam-5407	208	3	[	[	X
ejpam-5407	208	4	g3,2(|ℶ1|	g3,2(|ℶ1|	NOUN
ejpam-5407	208	5	,	,	PUNCT
ejpam-5407	208	6	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	208	7	,	,	PUNCT
ejpam-5407	208	8	υ1;ℶ3	υ1;ℶ3	PROPN
ejpam-5407	208	9	,	,	PUNCT
ejpam-5407	208	10	1	1	NUM
ejpam-5407	208	11	;	;	PUNCT
ejpam-5407	208	12	1)−	1)−	PROPN
ejpam-5407	208	13	1	1	NUM
ejpam-5407	208	14	]	]	PUNCT
ejpam-5407	208	15	.	.	PUNCT
ejpam-5407	209	1	(	(	PUNCT
ejpam-5407	209	2	13	13	NUM
ejpam-5407	209	3	)	)	PUNCT
ejpam-5407	209	4	but	but	CCONJ
ejpam-5407	209	5	the	the	DET
ejpam-5407	209	6	expression	expression	NOUN
ejpam-5407	209	7	(	(	PUNCT
ejpam-5407	209	8	13	13	NUM
ejpam-5407	209	9	)	)	PUNCT
ejpam-5407	209	10	is	be	AUX
ejpam-5407	209	11	bounded	bound	VERB
ejpam-5407	209	12	above	above	ADV
ejpam-5407	209	13	by	by	ADP
ejpam-5407	209	14	1−	1−	NUM
ejpam-5407	209	15	κ1	κ1	NOUN
ejpam-5407	209	16	,	,	PUNCT
ejpam-5407	209	17	thus	thus	ADV
ejpam-5407	209	18	the	the	DET
ejpam-5407	209	19	proof	proof	NOUN
ejpam-5407	209	20	is	be	AUX
ejpam-5407	209	21	completed	complete	VERB
ejpam-5407	209	22	.	.	PUNCT
ejpam-5407	210	1	using	use	VERB
ejpam-5407	210	2	the	the	DET
ejpam-5407	210	3	same	same	ADJ
ejpam-5407	210	4	proceeding	proceeding	NOUN
ejpam-5407	210	5	used	use	VERB
ejpam-5407	210	6	to	to	PART
ejpam-5407	210	7	prove	prove	VERB
ejpam-5407	210	8	theorem	theorem	ADJ
ejpam-5407	210	9	1	1	NUM
ejpam-5407	210	10	,	,	PUNCT
ejpam-5407	210	11	theorem	theorem	VERB
ejpam-5407	210	12	2	2	NUM
ejpam-5407	210	13	and	and	CCONJ
ejpam-5407	210	14	theorem	theorem	VERB
ejpam-5407	210	15	4	4	NUM
ejpam-5407	210	16	,	,	PUNCT
ejpam-5407	210	17	we	we	PRON
ejpam-5407	210	18	get	get	VERB
ejpam-5407	210	19	the	the	DET
ejpam-5407	210	20	following	follow	VERB
ejpam-5407	210	21	theorems	theorem	NOUN
ejpam-5407	210	22	for	for	ADP
ejpam-5407	210	23	subfamily	subfamily	ADV
ejpam-5407	210	24	s∗κ3(κ1	s∗κ3(κ1	ADJ
ejpam-5407	210	25	,	,	PUNCT
ejpam-5407	210	26	κ2	κ2	NOUN
ejpam-5407	210	27	)	)	PUNCT
ejpam-5407	210	28	,	,	PUNCT
ejpam-5407	210	29	respictivlly	respictivlly	ADV
ejpam-5407	210	30	.	.	PUNCT
ejpam-5407	211	1	t.	t.	PROPN
ejpam-5407	211	2	al	al	PROPN
ejpam-5407	211	3	-	-	PUNCT
ejpam-5407	211	4	hawary	hawary	PROPN
ejpam-5407	211	5	,	,	PUNCT
ejpam-5407	211	6	m.	m.	NOUN
ejpam-5407	211	7	o.	o.	PROPN
ejpam-5407	211	8	massa’deh	massa’deh	PROPN
ejpam-5407	211	9	,	,	PUNCT
ejpam-5407	211	10	a.	a.	NOUN
ejpam-5407	211	11	o	o	X
ejpam-5407	211	12	fallatah	fallatah	PROPN
ejpam-5407	211	13	/	/	SYM
ejpam-5407	211	14	eur	eur	PROPN
ejpam-5407	211	15	.	.	PUNCT
ejpam-5407	212	1	j.	j.	PROPN
ejpam-5407	212	2	pure	pure	PROPN
ejpam-5407	212	3	appl	appl	PROPN
ejpam-5407	212	4	.	.	PROPN
ejpam-5407	212	5	math	math	PROPN
ejpam-5407	212	6	,	,	PUNCT
ejpam-5407	212	7	17	17	NUM
ejpam-5407	212	8	(	(	PUNCT
ejpam-5407	212	9	4	4	NUM
ejpam-5407	212	10	)	)	PUNCT
ejpam-5407	212	11	(	(	PUNCT
ejpam-5407	212	12	2024	2024	NUM
ejpam-5407	212	13	)	)	PUNCT
ejpam-5407	212	14	,	,	PUNCT
ejpam-5407	212	15	3386	3386	NUM
ejpam-5407	212	16	-	-	SYM
ejpam-5407	212	17	3398	3398	NUM
ejpam-5407	212	18	3395	3395	NUM
ejpam-5407	212	19	theorem	theorem	NOUN
ejpam-5407	212	20	5	5	NUM
ejpam-5407	212	21	.	.	PUNCT
ejpam-5407	213	1	if	if	SCONJ
ejpam-5407	213	2	l	l	PROPN
ejpam-5407	213	3	∈	∈	PROPN
ejpam-5407	213	4	st	st	PROPN
ejpam-5407	213	5	and	and	CCONJ
ejpam-5407	213	6	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	213	7	∈	∈	PROPN
ejpam-5407	213	8	c−{0	c−{0	ADV
ejpam-5407	213	9	}	}	PUNCT
ejpam-5407	213	10	,	,	PUNCT
ejpam-5407	213	11	ℶ3	ℶ3	PROPN
ejpam-5407	213	12	∈	∈	PROPN
ejpam-5407	213	13	r	r	NOUN
ejpam-5407	213	14	,	,	PUNCT
ejpam-5407	213	15	then	then	ADV
ejpam-5407	213	16	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	213	17	)	)	PUNCT
ejpam-5407	213	18	∈	∈	PROPN
ejpam-5407	213	19	s∗κ3(κ1	s∗κ3(κ1	NOUN
ejpam-5407	213	20	,	,	PUNCT
ejpam-5407	213	21	κ2	κ2	NOUN
ejpam-5407	213	22	)	)	PUNCT
ejpam-5407	213	23	if	if	SCONJ
ejpam-5407	213	24	the	the	DET
ejpam-5407	213	25	following	follow	VERB
ejpam-5407	213	26	condition	condition	NOUN
ejpam-5407	213	27	is	be	AUX
ejpam-5407	213	28	satisfied	satisfied	ADJ
ejpam-5407	213	29	:	:	PUNCT
ejpam-5407	213	30	(	(	PUNCT
ejpam-5407	213	31	κ2	κ2	NOUN
ejpam-5407	213	32	+	+	CCONJ
ejpam-5407	213	33	1	1	X
ejpam-5407	213	34	)	)	PUNCT
ejpam-5407	213	35	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	213	36	(	(	PUNCT
ejpam-5407	213	37	|ℶ1|+	|ℶ1|+	X
ejpam-5407	213	38	1	1	NUM
ejpam-5407	213	39	)	)	PUNCT
ejpam-5407	213	40	(	(	PUNCT
ejpam-5407	213	41	|ℶ2|+	|ℶ2|+	X
ejpam-5407	213	42	1	1	NUM
ejpam-5407	213	43	)	)	PUNCT
ejpam-5407	213	44	ℶ3(ℶ3	ℶ3(ℶ3	VERB
ejpam-5407	213	45	+	+	NOUN
ejpam-5407	213	46	1	1	NUM
ejpam-5407	213	47	)	)	PUNCT
ejpam-5407	213	48	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	213	49	2	2	NUM
ejpam-5407	213	50	,	,	PUNCT
ejpam-5407	213	51	|ℶ2|+	|ℶ2|+	X
ejpam-5407	213	52	2;ℶ3	2;ℶ3	NUM
ejpam-5407	213	53	+	+	CCONJ
ejpam-5407	213	54	2	2	NUM
ejpam-5407	213	55	,	,	PUNCT
ejpam-5407	213	56	1	1	NUM
ejpam-5407	213	57	)	)	PUNCT
ejpam-5407	213	58	+	+	CCONJ
ejpam-5407	213	59	(	(	PUNCT
ejpam-5407	213	60	3(κ2	3(κ2	NUM
ejpam-5407	213	61	+	+	SYM
ejpam-5407	213	62	1)−	1)−	NUM
ejpam-5407	213	63	κ3(κ1	κ3(κ1	ADJ
ejpam-5407	213	64	+	+	NUM
ejpam-5407	213	65	κ2	κ2	NOUN
ejpam-5407	213	66	)	)	PUNCT
ejpam-5407	213	67	)	)	PUNCT
ejpam-5407	213	68	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	213	69	ℶ3	ℶ3	PROPN
ejpam-5407	213	70	g2,1(|ℶ1|+	g2,1(|ℶ1|+	PROPN
ejpam-5407	213	71	1	1	NUM
ejpam-5407	213	72	,	,	PUNCT
ejpam-5407	213	73	|ℶ2|+	|ℶ2|+	X
ejpam-5407	213	74	1;ℶ3	1;ℶ3	NUM
ejpam-5407	213	75	+	+	SYM
ejpam-5407	213	76	1	1	NUM
ejpam-5407	213	77	,	,	PUNCT
ejpam-5407	213	78	1	1	NUM
ejpam-5407	213	79	)	)	PUNCT
ejpam-5407	213	80	+	+	CCONJ
ejpam-5407	213	81	(	(	PUNCT
ejpam-5407	213	82	κ2	κ2	NOUN
ejpam-5407	213	83	−	−	PROPN
ejpam-5407	213	84	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	213	85	+	+	NUM
ejpam-5407	213	86	κ2	κ2	NOUN
ejpam-5407	213	87	)	)	PUNCT
ejpam-5407	213	88	+	+	CCONJ
ejpam-5407	213	89	1	1	X
ejpam-5407	213	90	)	)	PUNCT
ejpam-5407	214	1	[	[	X
ejpam-5407	214	2	g2,1(|ℶ1|	g2,1(|ℶ1|	NOUN
ejpam-5407	214	3	,	,	PUNCT
ejpam-5407	214	4	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	214	5	;	;	PUNCT
ejpam-5407	214	6	ℶ3	ℶ3	PROPN
ejpam-5407	214	7	,	,	PUNCT
ejpam-5407	214	8	1)−	1)−	PROPN
ejpam-5407	214	9	1	1	NUM
ejpam-5407	214	10	]	]	PUNCT
ejpam-5407	214	11	≤	≤	NUM
ejpam-5407	214	12	1−	1−	NUM
ejpam-5407	214	13	κ1	κ1	NOUN
ejpam-5407	214	14	.	.	PUNCT
ejpam-5407	215	1	theorem	theorem	VERB
ejpam-5407	215	2	6	6	NUM
ejpam-5407	215	3	.	.	PUNCT
ejpam-5407	216	1	if	if	SCONJ
ejpam-5407	216	2	l	l	PROPN
ejpam-5407	216	3	∈	∈	PROPN
ejpam-5407	216	4	cv	cv	PROPN
ejpam-5407	216	5	and	and	CCONJ
ejpam-5407	216	6	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	216	7	∈	∈	PROPN
ejpam-5407	216	8	c−{0	c−{0	ADV
ejpam-5407	216	9	}	}	PUNCT
ejpam-5407	216	10	,	,	PUNCT
ejpam-5407	216	11	ℶ3	ℶ3	PROPN
ejpam-5407	216	12	∈	∈	PROPN
ejpam-5407	216	13	r	r	NOUN
ejpam-5407	216	14	,	,	PUNCT
ejpam-5407	216	15	then	then	ADV
ejpam-5407	216	16	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	216	17	)	)	PUNCT
ejpam-5407	216	18	∈	∈	PROPN
ejpam-5407	216	19	s∗κ3(κ1	s∗κ3(κ1	NOUN
ejpam-5407	216	20	,	,	PUNCT
ejpam-5407	216	21	κ2	κ2	NOUN
ejpam-5407	216	22	)	)	PUNCT
ejpam-5407	216	23	if	if	SCONJ
ejpam-5407	216	24	the	the	DET
ejpam-5407	216	25	following	follow	VERB
ejpam-5407	216	26	condition	condition	NOUN
ejpam-5407	216	27	is	be	AUX
ejpam-5407	216	28	satisfied	satisfied	ADJ
ejpam-5407	216	29	:	:	PUNCT
ejpam-5407	216	30	(	(	PUNCT
ejpam-5407	216	31	κ2	κ2	NOUN
ejpam-5407	216	32	+	+	CCONJ
ejpam-5407	216	33	1	1	X
ejpam-5407	216	34	)	)	PUNCT
ejpam-5407	216	35	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	216	36	ℶ3	ℶ3	PROPN
ejpam-5407	216	37	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	216	38	1	1	NUM
ejpam-5407	216	39	,	,	PUNCT
ejpam-5407	216	40	|ℶ2|+	|ℶ2|+	X
ejpam-5407	216	41	1;ℶ3	1;ℶ3	NUM
ejpam-5407	216	42	+	+	SYM
ejpam-5407	216	43	1	1	NUM
ejpam-5407	216	44	,	,	PUNCT
ejpam-5407	216	45	1	1	NUM
ejpam-5407	216	46	)	)	PUNCT
ejpam-5407	216	47	+	+	CCONJ
ejpam-5407	216	48	(	(	PUNCT
ejpam-5407	216	49	κ2	κ2	NOUN
ejpam-5407	216	50	−	−	PROPN
ejpam-5407	216	51	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	216	52	+	+	NUM
ejpam-5407	216	53	κ2	κ2	NOUN
ejpam-5407	216	54	)	)	PUNCT
ejpam-5407	216	55	+	+	CCONJ
ejpam-5407	216	56	1	1	X
ejpam-5407	216	57	)	)	PUNCT
ejpam-5407	217	1	[	[	X
ejpam-5407	217	2	g2,1(|ℶ1|	g2,1(|ℶ1|	NOUN
ejpam-5407	217	3	,	,	PUNCT
ejpam-5407	217	4	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	217	5	;	;	PUNCT
ejpam-5407	217	6	ℶ3	ℶ3	PROPN
ejpam-5407	217	7	,	,	PUNCT
ejpam-5407	217	8	1)−	1)−	PROPN
ejpam-5407	217	9	1	1	NUM
ejpam-5407	217	10	]	]	PUNCT
ejpam-5407	217	11	≤	≤	NUM
ejpam-5407	217	12	1−	1−	NUM
ejpam-5407	217	13	κ1	κ1	NOUN
ejpam-5407	217	14	.	.	PUNCT
ejpam-5407	218	1	theorem	theorem	VERB
ejpam-5407	218	2	7	7	NUM
ejpam-5407	218	3	.	.	PUNCT
ejpam-5407	219	1	let	let	VERB
ejpam-5407	219	2	υ1	υ1	PROPN
ejpam-5407	219	3	given	give	VERB
ejpam-5407	219	4	by	by	ADP
ejpam-5407	219	5	(	(	PUNCT
ejpam-5407	219	6	3	3	NUM
ejpam-5407	219	7	)	)	PUNCT
ejpam-5407	219	8	and	and	CCONJ
ejpam-5407	219	9	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	219	10	∈	∈	PROPN
ejpam-5407	219	11	c−{0	c−{0	ADV
ejpam-5407	219	12	}	}	PUNCT
ejpam-5407	219	13	,	,	PUNCT
ejpam-5407	219	14	ℶ3	ℶ3	PROPN
ejpam-5407	219	15	∈	∈	PROPN
ejpam-5407	219	16	r.	r.	PROPN
ejpam-5407	219	17	if	if	SCONJ
ejpam-5407	219	18	l	l	PROPN
ejpam-5407	219	19	∈	∈	PROPN
ejpam-5407	219	20	ξ−st	ξ−st	NOUN
ejpam-5407	219	21	for	for	ADP
ejpam-5407	219	22	some	some	DET
ejpam-5407	219	23	ξ(0	ξ(0	SYM
ejpam-5407	219	24	≤	≤	PUNCT
ejpam-5407	220	1	ξ	ξ	X
ejpam-5407	220	2	<	<	X
ejpam-5407	220	3	∞	∞	NUM
ejpam-5407	220	4	)	)	PUNCT
ejpam-5407	220	5	and	and	CCONJ
ejpam-5407	220	6	satisfies	satisfy	VERB
ejpam-5407	220	7	the	the	DET
ejpam-5407	220	8	inequality	inequality	NOUN
ejpam-5407	220	9	(	(	PUNCT
ejpam-5407	220	10	κ2	κ2	NOUN
ejpam-5407	220	11	+	+	CCONJ
ejpam-5407	220	12	1	1	X
ejpam-5407	220	13	)	)	PUNCT
ejpam-5407	220	14	|ℶ1ℶ2|υ1	|ℶ1ℶ2|υ1	NOUN
ejpam-5407	220	15	ℶ3(1)1	ℶ3(1)1	PROPN
ejpam-5407	220	16	g3,2(|ℶ1|+	g3,2(|ℶ1|+	PROPN
ejpam-5407	220	17	1	1	NUM
ejpam-5407	220	18	,	,	PUNCT
ejpam-5407	220	19	|ℶ2|+	|ℶ2|+	X
ejpam-5407	221	1	1,υ1	1,υ1	NUM
ejpam-5407	221	2	+	+	NUM
ejpam-5407	221	3	1;ℶ3	1;ℶ3	NUM
ejpam-5407	221	4	+	+	CCONJ
ejpam-5407	221	5	1	1	NUM
ejpam-5407	221	6	,	,	PUNCT
ejpam-5407	221	7	2	2	NUM
ejpam-5407	221	8	;	;	PUNCT
ejpam-5407	221	9	1	1	NUM
ejpam-5407	221	10	)	)	PUNCT
ejpam-5407	221	11	+	+	CCONJ
ejpam-5407	221	12	(	(	PUNCT
ejpam-5407	221	13	κ2	κ2	NOUN
ejpam-5407	221	14	−	−	PROPN
ejpam-5407	221	15	κ3(κ1	κ3(κ1	NOUN
ejpam-5407	221	16	+	+	NUM
ejpam-5407	221	17	κ2	κ2	NOUN
ejpam-5407	221	18	)	)	PUNCT
ejpam-5407	222	1	+	+	CCONJ
ejpam-5407	223	1	1	1	X
ejpam-5407	223	2	)	)	PUNCT
ejpam-5407	224	1	[	[	X
ejpam-5407	224	2	g3,2(|ℶ1|	g3,2(|ℶ1|	NOUN
ejpam-5407	224	3	,	,	PUNCT
ejpam-5407	224	4	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	224	5	,	,	PUNCT
ejpam-5407	224	6	υ1;ℶ3	υ1;ℶ3	PROPN
ejpam-5407	224	7	,	,	PUNCT
ejpam-5407	224	8	1	1	NUM
ejpam-5407	224	9	;	;	PUNCT
ejpam-5407	224	10	1)−	1)−	PROPN
ejpam-5407	224	11	1	1	NUM
ejpam-5407	224	12	]	]	PUNCT
ejpam-5407	224	13	≤	≤	NUM
ejpam-5407	224	14	1−	1−	NUM
ejpam-5407	224	15	κ1	κ1	NOUN
ejpam-5407	224	16	,	,	PUNCT
ejpam-5407	224	17	then	then	ADV
ejpam-5407	224	18	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	224	19	)	)	PUNCT
ejpam-5407	224	20	∈	∈	PROPN
ejpam-5407	224	21	s∗κ3(κ1	s∗κ3(κ1	NOUN
ejpam-5407	224	22	,	,	PUNCT
ejpam-5407	224	23	κ2	κ2	NOUN
ejpam-5407	224	24	)	)	PUNCT
ejpam-5407	224	25	.	.	PUNCT
ejpam-5407	225	1	3	3	X
ejpam-5407	225	2	.	.	X
ejpam-5407	226	1	some	some	DET
ejpam-5407	226	2	corollaries	corollary	NOUN
ejpam-5407	226	3	in	in	ADP
ejpam-5407	226	4	this	this	DET
ejpam-5407	226	5	section	section	NOUN
ejpam-5407	226	6	,	,	PUNCT
ejpam-5407	226	7	by	by	ADP
ejpam-5407	226	8	suitable	suitable	ADJ
ejpam-5407	226	9	choices	choice	NOUN
ejpam-5407	226	10	for	for	ADP
ejpam-5407	226	11	parameters	parameter	NOUN
ejpam-5407	226	12	ℶ1	ℶ1	PROPN
ejpam-5407	226	13	,	,	PUNCT
ejpam-5407	226	14	ℶ2	ℶ2	PROPN
ejpam-5407	226	15	and	and	CCONJ
ejpam-5407	226	16	ℶ3	ℶ3	NUM
ejpam-5407	226	17	,	,	PUNCT
ejpam-5407	226	18	we	we	PRON
ejpam-5407	226	19	can	can	AUX
ejpam-5407	226	20	conclude	conclude	VERB
ejpam-5407	226	21	many	many	ADJ
ejpam-5407	226	22	subresults	subresult	NOUN
ejpam-5407	226	23	from	from	ADP
ejpam-5407	226	24	our	our	PRON
ejpam-5407	226	25	main	main	ADJ
ejpam-5407	226	26	results	result	NOUN
ejpam-5407	226	27	related	relate	VERB
ejpam-5407	226	28	to	to	ADP
ejpam-5407	226	29	bernardi	bernardi	PROPN
ejpam-5407	226	30	operator	operator	NOUN
ejpam-5407	226	31	ho1,α+1,α+2(l	ho1,α+1,α+2(l	NOUN
ejpam-5407	226	32	)	)	PUNCT
ejpam-5407	226	33	,	,	PUNCT
ejpam-5407	226	34	alexander	alexander	NOUN
ejpam-5407	226	35	operator	operator	NOUN
ejpam-5407	226	36	ho1,1,2(l	ho1,1,2(l	NOUN
ejpam-5407	226	37	)	)	PUNCT
ejpam-5407	226	38	and	and	CCONJ
ejpam-5407	226	39	libera	libera	NOUN
ejpam-5407	226	40	operator	operator	NOUN
ejpam-5407	226	41	ho1,2,3(l	ho1,2,3(l	NOUN
ejpam-5407	226	42	)	)	PUNCT
ejpam-5407	226	43	.	.	PUNCT
ejpam-5407	227	1	also	also	ADV
ejpam-5407	227	2	,	,	PUNCT
ejpam-5407	227	3	by	by	ADP
ejpam-5407	227	4	suitable	suitable	ADJ
ejpam-5407	227	5	choices	choice	NOUN
ejpam-5407	227	6	for	for	ADP
ejpam-5407	227	7	parameters	parameter	NOUN
ejpam-5407	227	8	κ1	κ1	NOUN
ejpam-5407	227	9	,	,	PUNCT
ejpam-5407	227	10	κ2	κ2	PROPN
ejpam-5407	227	11	and	and	CCONJ
ejpam-5407	227	12	κ3	κ3	PROPN
ejpam-5407	227	13	,	,	PUNCT
ejpam-5407	227	14	we	we	PRON
ejpam-5407	227	15	have	have	VERB
ejpam-5407	227	16	many	many	ADJ
ejpam-5407	227	17	subresults	subresult	NOUN
ejpam-5407	227	18	.	.	PUNCT
ejpam-5407	228	1	for	for	ADP
ejpam-5407	228	2	example	example	NOUN
ejpam-5407	228	3	,	,	PUNCT
ejpam-5407	228	4	if	if	SCONJ
ejpam-5407	228	5	we	we	PRON
ejpam-5407	228	6	set	set	VERB
ejpam-5407	228	7	κ2	κ2	NOUN
ejpam-5407	228	8	=	=	SYM
ejpam-5407	228	9	0	0	PUNCT
ejpam-5407	228	10	and	and	CCONJ
ejpam-5407	228	11	κ3	κ3	PROPN
ejpam-5407	228	12	=	=	SYM
ejpam-5407	228	13	1	1	NUM
ejpam-5407	228	14	in	in	ADP
ejpam-5407	228	15	our	our	PRON
ejpam-5407	228	16	main	main	ADJ
ejpam-5407	228	17	results	result	NOUN
ejpam-5407	228	18	,	,	PUNCT
ejpam-5407	228	19	we	we	PRON
ejpam-5407	228	20	get	get	VERB
ejpam-5407	228	21	the	the	DET
ejpam-5407	228	22	following	follow	VERB
ejpam-5407	228	23	corollaries	corollary	NOUN
ejpam-5407	228	24	for	for	ADP
ejpam-5407	228	25	subfamilies	subfamily	NOUN
ejpam-5407	228	26	cv(κ1	cv(κ1	VERB
ejpam-5407	228	27	)	)	PUNCT
ejpam-5407	228	28	and	and	CCONJ
ejpam-5407	228	29	st	st	PROPN
ejpam-5407	228	30	(	(	PUNCT
ejpam-5407	228	31	κ1	κ1	PROPN
ejpam-5407	228	32	)	)	PUNCT
ejpam-5407	228	33	.	.	PUNCT
ejpam-5407	229	1	corollary	corollary	ADJ
ejpam-5407	229	2	1	1	NUM
ejpam-5407	229	3	.	.	PUNCT
ejpam-5407	230	1	if	if	SCONJ
ejpam-5407	230	2	l	l	PROPN
ejpam-5407	230	3	∈	∈	PROPN
ejpam-5407	230	4	st	st	PROPN
ejpam-5407	230	5	and	and	CCONJ
ejpam-5407	230	6	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	230	7	∈	∈	PROPN
ejpam-5407	230	8	c−	c−	NOUN
ejpam-5407	230	9	{	{	PUNCT
ejpam-5407	230	10	0	0	NUM
ejpam-5407	230	11	}	}	PUNCT
ejpam-5407	230	12	,	,	PUNCT
ejpam-5407	230	13	ℶ3	ℶ3	PROPN
ejpam-5407	230	14	∈	∈	PROPN
ejpam-5407	230	15	r	r	NOUN
ejpam-5407	230	16	,	,	PUNCT
ejpam-5407	230	17	then	then	ADV
ejpam-5407	230	18	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	230	19	)	)	PUNCT
ejpam-5407	230	20	∈	∈	PROPN
ejpam-5407	230	21	cv(κ1	cv(κ1	NOUN
ejpam-5407	230	22	)	)	PUNCT
ejpam-5407	230	23	if	if	SCONJ
ejpam-5407	230	24	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	230	25	(	(	PUNCT
ejpam-5407	230	26	|ℶ1|+	|ℶ1|+	X
ejpam-5407	230	27	1	1	NUM
ejpam-5407	230	28	)	)	PUNCT
ejpam-5407	230	29	(	(	PUNCT
ejpam-5407	230	30	|ℶ2|+	|ℶ2|+	X
ejpam-5407	230	31	1	1	NUM
ejpam-5407	230	32	)	)	PUNCT
ejpam-5407	230	33	(	(	PUNCT
ejpam-5407	230	34	|ℶ1|+	|ℶ1|+	X
ejpam-5407	230	35	2	2	NUM
ejpam-5407	230	36	)	)	PUNCT
ejpam-5407	230	37	(	(	PUNCT
ejpam-5407	230	38	|ℶ2|+	|ℶ2|+	X
ejpam-5407	230	39	2	2	NUM
ejpam-5407	230	40	)	)	PUNCT
ejpam-5407	230	41	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	231	1	+	+	CCONJ
ejpam-5407	231	2	1)(ℶ3	1)(ℶ3	NUM
ejpam-5407	231	3	+	+	CCONJ
ejpam-5407	231	4	2	2	X
ejpam-5407	231	5	)	)	PUNCT
ejpam-5407	231	6	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	231	7	3	3	NUM
ejpam-5407	231	8	,	,	PUNCT
ejpam-5407	231	9	|ℶ2|+	|ℶ2|+	X
ejpam-5407	231	10	3;ℶ3	3;ℶ3	NUM
ejpam-5407	231	11	+	+	SYM
ejpam-5407	231	12	3,1	3,1	NUM
ejpam-5407	231	13	)	)	PUNCT
ejpam-5407	232	1	+	+	CCONJ
ejpam-5407	232	2	(	(	PUNCT
ejpam-5407	232	3	6−	6−	NUM
ejpam-5407	232	4	κ1	κ1	NOUN
ejpam-5407	232	5	)	)	PUNCT
ejpam-5407	232	6	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	232	7	(	(	PUNCT
ejpam-5407	232	8	|ℶ1|+	|ℶ1|+	X
ejpam-5407	232	9	1	1	NUM
ejpam-5407	232	10	)	)	PUNCT
ejpam-5407	232	11	(	(	PUNCT
ejpam-5407	232	12	|ℶ2|+	|ℶ2|+	X
ejpam-5407	232	13	1	1	NUM
ejpam-5407	232	14	)	)	PUNCT
ejpam-5407	232	15	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	232	16	+	+	NOUN
ejpam-5407	232	17	1	1	X
ejpam-5407	232	18	)	)	PUNCT
ejpam-5407	232	19	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	232	20	2	2	NUM
ejpam-5407	232	21	,	,	PUNCT
ejpam-5407	232	22	|ℶ2|+	|ℶ2|+	X
ejpam-5407	232	23	2;ℶ3	2;ℶ3	NUM
ejpam-5407	232	24	+	+	NUM
ejpam-5407	232	25	2,1	2,1	NUM
ejpam-5407	232	26	)	)	PUNCT
ejpam-5407	233	1	+	+	CCONJ
ejpam-5407	233	2	(	(	PUNCT
ejpam-5407	233	3	7−	7−	NUM
ejpam-5407	233	4	3κ1	3κ1	NUM
ejpam-5407	233	5	)	)	PUNCT
ejpam-5407	233	6	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	233	7	ℶ3	ℶ3	PROPN
ejpam-5407	233	8	g2,1(|ℶ1|+	g2,1(|ℶ1|+	PROPN
ejpam-5407	233	9	1	1	NUM
ejpam-5407	233	10	,	,	PUNCT
ejpam-5407	233	11	|ℶ2|+	|ℶ2|+	X
ejpam-5407	233	12	1;ℶ3	1;ℶ3	NUM
ejpam-5407	233	13	+	+	SYM
ejpam-5407	233	14	1,1	1,1	NUM
ejpam-5407	233	15	)	)	PUNCT
ejpam-5407	233	16	+	+	CCONJ
ejpam-5407	233	17	(	(	PUNCT
ejpam-5407	233	18	1−κ1	1−κ1	NUM
ejpam-5407	233	19	)	)	PUNCT
ejpam-5407	234	1	[	[	X
ejpam-5407	234	2	g2,1	g2,1	ADJ
ejpam-5407	234	3	|ℶ1|	|ℶ1|	NOUN
ejpam-5407	234	4	,	,	PUNCT
ejpam-5407	234	5	|ℶ2|	|ℶ2|	ADJ
ejpam-5407	234	6	;	;	PUNCT
ejpam-5407	234	7	ℶ3,1)−	ℶ3,1)−	PROPN
ejpam-5407	234	8	1	1	NUM
ejpam-5407	234	9	]	]	PUNCT
ejpam-5407	234	10	≤	≤	NUM
ejpam-5407	234	11	1−	1−	NUM
ejpam-5407	234	12	κ1	κ1	NOUN
ejpam-5407	234	13	.	.	PUNCT
ejpam-5407	235	1	t.	t.	PROPN
ejpam-5407	235	2	al	al	PROPN
ejpam-5407	235	3	-	-	PUNCT
ejpam-5407	235	4	hawary	hawary	PROPN
ejpam-5407	235	5	,	,	PUNCT
ejpam-5407	235	6	m.	m.	NOUN
ejpam-5407	235	7	o.	o.	PROPN
ejpam-5407	235	8	massa’deh	massa’deh	PROPN
ejpam-5407	235	9	,	,	PUNCT
ejpam-5407	235	10	a.	a.	NOUN
ejpam-5407	235	11	o	o	X
ejpam-5407	235	12	fallatah	fallatah	PROPN
ejpam-5407	235	13	/	/	SYM
ejpam-5407	235	14	eur	eur	PROPN
ejpam-5407	235	15	.	.	PUNCT
ejpam-5407	236	1	j.	j.	PROPN
ejpam-5407	236	2	pure	pure	PROPN
ejpam-5407	236	3	appl	appl	PROPN
ejpam-5407	236	4	.	.	PROPN
ejpam-5407	236	5	math	math	PROPN
ejpam-5407	236	6	,	,	PUNCT
ejpam-5407	236	7	17	17	NUM
ejpam-5407	236	8	(	(	PUNCT
ejpam-5407	236	9	4	4	NUM
ejpam-5407	236	10	)	)	PUNCT
ejpam-5407	236	11	(	(	PUNCT
ejpam-5407	236	12	2024	2024	NUM
ejpam-5407	236	13	)	)	PUNCT
ejpam-5407	236	14	,	,	PUNCT
ejpam-5407	236	15	3386	3386	NUM
ejpam-5407	236	16	-	-	SYM
ejpam-5407	236	17	3398	3398	NUM
ejpam-5407	236	18	3396	3396	NUM
ejpam-5407	236	19	corollary	corollary	ADJ
ejpam-5407	236	20	2	2	NUM
ejpam-5407	236	21	.	.	PUNCT
ejpam-5407	237	1	if	if	SCONJ
ejpam-5407	237	2	l	l	PROPN
ejpam-5407	237	3	∈	∈	PROPN
ejpam-5407	237	4	cv	cv	PROPN
ejpam-5407	237	5	and	and	CCONJ
ejpam-5407	237	6	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	237	7	∈	∈	PROPN
ejpam-5407	237	8	c−	c−	NOUN
ejpam-5407	237	9	{	{	PUNCT
ejpam-5407	237	10	0	0	NUM
ejpam-5407	237	11	}	}	PUNCT
ejpam-5407	237	12	,	,	PUNCT
ejpam-5407	237	13	ℶ3	ℶ3	PROPN
ejpam-5407	237	14	∈	∈	PROPN
ejpam-5407	237	15	r	r	NOUN
ejpam-5407	237	16	,	,	PUNCT
ejpam-5407	237	17	then	then	ADV
ejpam-5407	237	18	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	237	19	)	)	PUNCT
ejpam-5407	237	20	∈	∈	PROPN
ejpam-5407	237	21	cv(κ1	cv(κ1	NOUN
ejpam-5407	237	22	)	)	PUNCT
ejpam-5407	237	23	if	if	SCONJ
ejpam-5407	237	24	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	237	25	(	(	PUNCT
ejpam-5407	237	26	|ℶ1|+	|ℶ1|+	X
ejpam-5407	237	27	1	1	NUM
ejpam-5407	237	28	)	)	PUNCT
ejpam-5407	237	29	(	(	PUNCT
ejpam-5407	237	30	|ℶ2|+	|ℶ2|+	X
ejpam-5407	237	31	1	1	NUM
ejpam-5407	237	32	)	)	PUNCT
ejpam-5407	237	33	ℶ3(ℶ3	ℶ3(ℶ3	NOUN
ejpam-5407	237	34	+	+	NOUN
ejpam-5407	237	35	1	1	X
ejpam-5407	237	36	)	)	PUNCT
ejpam-5407	237	37	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	237	38	2	2	NUM
ejpam-5407	237	39	,	,	PUNCT
ejpam-5407	237	40	|ℶ2|+	|ℶ2|+	X
ejpam-5407	237	41	2;ℶ3	2;ℶ3	NUM
ejpam-5407	237	42	+	+	NUM
ejpam-5407	237	43	2,1	2,1	NUM
ejpam-5407	237	44	)	)	PUNCT
ejpam-5407	237	45	+	+	CCONJ
ejpam-5407	237	46	(	(	PUNCT
ejpam-5407	237	47	3−	3−	NUM
ejpam-5407	237	48	κ1	κ1	NOUN
ejpam-5407	237	49	)	)	PUNCT
ejpam-5407	237	50	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	237	51	ℶ3	ℶ3	PROPN
ejpam-5407	237	52	g2,1(|ℶ1|+	g2,1(|ℶ1|+	PROPN
ejpam-5407	237	53	1	1	NUM
ejpam-5407	237	54	,	,	PUNCT
ejpam-5407	237	55	|ℶ2|+	|ℶ2|+	X
ejpam-5407	237	56	1;ℶ3	1;ℶ3	NUM
ejpam-5407	237	57	+	+	SYM
ejpam-5407	237	58	1,1	1,1	NUM
ejpam-5407	237	59	)	)	PUNCT
ejpam-5407	238	1	+	+	CCONJ
ejpam-5407	238	2	(	(	PUNCT
ejpam-5407	238	3	1−κ1	1−κ1	NUM
ejpam-5407	238	4	)	)	PUNCT
ejpam-5407	239	1	[	[	X
ejpam-5407	239	2	g2,1(|ℶ1|	g2,1(|ℶ1|	NOUN
ejpam-5407	239	3	,	,	PUNCT
ejpam-5407	239	4	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	239	5	;	;	PUNCT
ejpam-5407	239	6	ℶ3,1)−	ℶ3,1)−	PROPN
ejpam-5407	239	7	1	1	NUM
ejpam-5407	239	8	]	]	PUNCT
ejpam-5407	239	9	≤	≤	NUM
ejpam-5407	239	10	1−	1−	NUM
ejpam-5407	239	11	κ1	κ1	NOUN
ejpam-5407	239	12	.	.	PUNCT
ejpam-5407	240	1	corollary	corollary	ADJ
ejpam-5407	240	2	3	3	NUM
ejpam-5407	240	3	.	.	PUNCT
ejpam-5407	241	1	let	let	VERB
ejpam-5407	241	2	υ1	υ1	PROPN
ejpam-5407	241	3	given	give	VERB
ejpam-5407	241	4	by	by	ADP
ejpam-5407	241	5	(	(	PUNCT
ejpam-5407	241	6	3	3	NUM
ejpam-5407	241	7	)	)	PUNCT
ejpam-5407	241	8	and	and	CCONJ
ejpam-5407	241	9	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	241	10	∈	∈	PROPN
ejpam-5407	241	11	c	c	NOUN
ejpam-5407	241	12	−	−	NOUN
ejpam-5407	242	1	{	{	PUNCT
ejpam-5407	242	2	0	0	NUM
ejpam-5407	242	3	}	}	PUNCT
ejpam-5407	242	4	,	,	PUNCT
ejpam-5407	242	5	ℶ3	ℶ3	PROPN
ejpam-5407	242	6	∈	∈	PROPN
ejpam-5407	242	7	r.	r.	PROPN
ejpam-5407	242	8	if	if	SCONJ
ejpam-5407	242	9	l	l	PROPN
ejpam-5407	242	10	∈	∈	PROPN
ejpam-5407	242	11	ξ	ξ	X
ejpam-5407	242	12	−	−	PROPN
ejpam-5407	242	13	ucv	ucv	NOUN
ejpam-5407	242	14	for	for	ADP
ejpam-5407	242	15	some	some	DET
ejpam-5407	242	16	ξ(0	ξ(0	SYM
ejpam-5407	242	17	≤	≤	PUNCT
ejpam-5407	242	18	ξ	ξ	X
ejpam-5407	242	19	<	<	X
ejpam-5407	242	20	∞	∞	NUM
ejpam-5407	242	21	)	)	PUNCT
ejpam-5407	242	22	and	and	CCONJ
ejpam-5407	242	23	satisfies	satisfy	VERB
ejpam-5407	242	24	|ℶ1ℶ2|υ1	|ℶ1ℶ2|υ1	PROPN
ejpam-5407	242	25	ℶ3(1)1	ℶ3(1)1	PROPN
ejpam-5407	242	26	g3,2(|ℶ1|+	g3,2(|ℶ1|+	PROPN
ejpam-5407	242	27	1	1	NUM
ejpam-5407	242	28	,	,	PUNCT
ejpam-5407	242	29	|ℶ2|+	|ℶ2|+	X
ejpam-5407	243	1	1,υ1	1,υ1	NUM
ejpam-5407	243	2	+	+	NUM
ejpam-5407	243	3	1;ℶ3	1;ℶ3	NUM
ejpam-5407	243	4	+	+	CCONJ
ejpam-5407	243	5	1	1	NUM
ejpam-5407	243	6	,	,	PUNCT
ejpam-5407	243	7	2	2	NUM
ejpam-5407	243	8	;	;	PUNCT
ejpam-5407	243	9	1	1	NUM
ejpam-5407	243	10	)	)	PUNCT
ejpam-5407	243	11	+	+	CCONJ
ejpam-5407	243	12	(	(	PUNCT
ejpam-5407	243	13	1−κ1	1−κ1	NUM
ejpam-5407	243	14	)	)	PUNCT
ejpam-5407	244	1	[	[	X
ejpam-5407	244	2	g3,2(|ℶ1|	g3,2(|ℶ1|	NOUN
ejpam-5407	244	3	,	,	PUNCT
ejpam-5407	244	4	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	244	5	,	,	PUNCT
ejpam-5407	244	6	υ1;ℶ3	υ1;ℶ3	PROPN
ejpam-5407	244	7	,	,	PUNCT
ejpam-5407	244	8	1	1	NUM
ejpam-5407	244	9	;	;	PUNCT
ejpam-5407	244	10	1)−	1)−	PROPN
ejpam-5407	244	11	1	1	NUM
ejpam-5407	244	12	]	]	PUNCT
ejpam-5407	244	13	≤	≤	NUM
ejpam-5407	244	14	1−	1−	NUM
ejpam-5407	244	15	κ1	κ1	NOUN
ejpam-5407	244	16	,	,	PUNCT
ejpam-5407	244	17	then	then	ADV
ejpam-5407	244	18	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	244	19	)	)	PUNCT
ejpam-5407	244	20	∈	∈	PROPN
ejpam-5407	244	21	k(κ1	k(κ1	NOUN
ejpam-5407	244	22	)	)	PUNCT
ejpam-5407	244	23	.	.	PUNCT
ejpam-5407	245	1	corollary	corollary	ADJ
ejpam-5407	245	2	4	4	NUM
ejpam-5407	245	3	.	.	PUNCT
ejpam-5407	246	1	let	let	VERB
ejpam-5407	246	2	υ1	υ1	PROPN
ejpam-5407	246	3	given	give	VERB
ejpam-5407	246	4	by	by	ADP
ejpam-5407	246	5	(	(	PUNCT
ejpam-5407	246	6	3	3	NUM
ejpam-5407	246	7	)	)	PUNCT
ejpam-5407	246	8	and	and	CCONJ
ejpam-5407	246	9	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	246	10	∈	∈	PROPN
ejpam-5407	246	11	c−{0	c−{0	ADV
ejpam-5407	246	12	}	}	PUNCT
ejpam-5407	246	13	,	,	PUNCT
ejpam-5407	246	14	ℶ3	ℶ3	PROPN
ejpam-5407	246	15	∈	∈	PROPN
ejpam-5407	246	16	r.	r.	PROPN
ejpam-5407	246	17	if	if	SCONJ
ejpam-5407	246	18	l	l	PROPN
ejpam-5407	246	19	∈	∈	PROPN
ejpam-5407	246	20	ξ−st	ξ−st	NOUN
ejpam-5407	246	21	for	for	ADP
ejpam-5407	246	22	some	some	DET
ejpam-5407	246	23	ξ(0	ξ(0	SYM
ejpam-5407	246	24	≤	≤	PUNCT
ejpam-5407	247	1	ξ	ξ	X
ejpam-5407	247	2	<	<	X
ejpam-5407	247	3	∞	∞	NUM
ejpam-5407	247	4	)	)	PUNCT
ejpam-5407	247	5	and	and	CCONJ
ejpam-5407	247	6	satisfies	satisfie	NOUN
ejpam-5407	247	7	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	247	8	(	(	PUNCT
ejpam-5407	247	9	|ℶ1|+	|ℶ1|+	X
ejpam-5407	247	10	1	1	NUM
ejpam-5407	247	11	)	)	PUNCT
ejpam-5407	247	12	(	(	PUNCT
ejpam-5407	247	13	|ℶ2|+	|ℶ2|+	X
ejpam-5407	247	14	1	1	NUM
ejpam-5407	247	15	)	)	PUNCT
ejpam-5407	247	16	(	(	PUNCT
ejpam-5407	247	17	υ1	υ1	NOUN
ejpam-5407	247	18	+	+	CCONJ
ejpam-5407	247	19	1)υ1	1)υ1	NUM
ejpam-5407	247	20	ℶ3(ℶ3	ℶ3(ℶ3	NUM
ejpam-5407	247	21	+	+	NOUN
ejpam-5407	247	22	1)(2)1	1)(2)1	PROPN
ejpam-5407	247	23	g3,2(|ℶ1|+	g3,2(|ℶ1|+	NOUN
ejpam-5407	247	24	2	2	NUM
ejpam-5407	247	25	,	,	PUNCT
ejpam-5407	247	26	|ℶ2|+	|ℶ2|+	PROPN
ejpam-5407	247	27	2,υ1	2,υ1	NUM
ejpam-5407	247	28	+	+	NUM
ejpam-5407	247	29	2;ℶ3	2;ℶ3	NUM
ejpam-5407	247	30	+	+	CCONJ
ejpam-5407	247	31	2	2	NUM
ejpam-5407	247	32	,	,	PUNCT
ejpam-5407	247	33	3	3	NUM
ejpam-5407	247	34	;	;	PUNCT
ejpam-5407	247	35	1	1	NUM
ejpam-5407	247	36	)	)	PUNCT
ejpam-5407	247	37	+	+	CCONJ
ejpam-5407	247	38	(	(	PUNCT
ejpam-5407	247	39	3−	3−	NUM
ejpam-5407	247	40	κ1	κ1	NOUN
ejpam-5407	247	41	)	)	PUNCT
ejpam-5407	247	42	|ℶ1ℶ2|υ1	|ℶ1ℶ2|υ1	NOUN
ejpam-5407	247	43	ℶ3(1)1	ℶ3(1)1	PROPN
ejpam-5407	247	44	g3,2(|ℶ1|+	g3,2(|ℶ1|+	PROPN
ejpam-5407	247	45	1	1	NUM
ejpam-5407	247	46	,	,	PUNCT
ejpam-5407	247	47	|ℶ2|+	|ℶ2|+	X
ejpam-5407	248	1	1,υ1	1,υ1	NUM
ejpam-5407	248	2	+	+	NUM
ejpam-5407	248	3	1;ℶ3	1;ℶ3	NUM
ejpam-5407	248	4	+	+	CCONJ
ejpam-5407	248	5	1	1	NUM
ejpam-5407	248	6	,	,	PUNCT
ejpam-5407	248	7	2	2	NUM
ejpam-5407	248	8	;	;	PUNCT
ejpam-5407	248	9	1	1	NUM
ejpam-5407	248	10	)	)	PUNCT
ejpam-5407	248	11	+	+	CCONJ
ejpam-5407	248	12	(	(	PUNCT
ejpam-5407	248	13	1−	1−	NUM
ejpam-5407	248	14	κ1	κ1	NOUN
ejpam-5407	248	15	)	)	PUNCT
ejpam-5407	249	1	[	[	X
ejpam-5407	249	2	g3,2(|ℶ1|	g3,2(|ℶ1|	PROPN
ejpam-5407	249	3	,	,	PUNCT
ejpam-5407	249	4	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	249	5	,	,	PUNCT
ejpam-5407	249	6	υ1;ℶ3	υ1;ℶ3	PROPN
ejpam-5407	249	7	,	,	PUNCT
ejpam-5407	249	8	1	1	NUM
ejpam-5407	249	9	;	;	PUNCT
ejpam-5407	249	10	1)−	1)−	PROPN
ejpam-5407	249	11	1	1	NUM
ejpam-5407	249	12	]	]	PUNCT
ejpam-5407	249	13	≤	≤	NUM
ejpam-5407	249	14	1−	1−	NUM
ejpam-5407	249	15	κ1	κ1	NOUN
ejpam-5407	249	16	,	,	PUNCT
ejpam-5407	249	17	then	then	ADV
ejpam-5407	249	18	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	249	19	)	)	PUNCT
ejpam-5407	249	20	∈	∈	PROPN
ejpam-5407	249	21	cv(κ1	cv(κ1	NOUN
ejpam-5407	249	22	)	)	PUNCT
ejpam-5407	249	23	.	.	PUNCT
ejpam-5407	250	1	corollary	corollary	ADJ
ejpam-5407	250	2	5	5	NUM
ejpam-5407	250	3	.	.	PUNCT
ejpam-5407	251	1	if	if	SCONJ
ejpam-5407	251	2	l	l	PROPN
ejpam-5407	251	3	∈	∈	PROPN
ejpam-5407	251	4	st	st	PROPN
ejpam-5407	251	5	and	and	CCONJ
ejpam-5407	251	6	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	251	7	∈	∈	PROPN
ejpam-5407	251	8	c−{0	c−{0	ADV
ejpam-5407	251	9	}	}	PUNCT
ejpam-5407	251	10	,	,	PUNCT
ejpam-5407	251	11	ℶ3	ℶ3	PROPN
ejpam-5407	251	12	∈	∈	PROPN
ejpam-5407	251	13	r	r	NOUN
ejpam-5407	251	14	,	,	PUNCT
ejpam-5407	251	15	then	then	ADV
ejpam-5407	251	16	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	251	17	)	)	PUNCT
ejpam-5407	251	18	∈	∈	PROPN
ejpam-5407	251	19	st	st	PROPN
ejpam-5407	251	20	(	(	PUNCT
ejpam-5407	251	21	κ1	κ1	NOUN
ejpam-5407	251	22	)	)	PUNCT
ejpam-5407	251	23	if	if	SCONJ
ejpam-5407	251	24	|ℶ1ℶ2|	|ℶ1ℶ2|	X
ejpam-5407	251	25	(	(	PUNCT
ejpam-5407	251	26	|ℶ1|+	|ℶ1|+	X
ejpam-5407	251	27	1	1	NUM
ejpam-5407	251	28	)	)	PUNCT
ejpam-5407	251	29	(	(	PUNCT
ejpam-5407	251	30	|ℶ2|+	|ℶ2|+	X
ejpam-5407	251	31	1	1	NUM
ejpam-5407	251	32	)	)	PUNCT
ejpam-5407	251	33	ℶ3(ℶ3	ℶ3(ℶ3	VERB
ejpam-5407	251	34	+	+	NOUN
ejpam-5407	251	35	1	1	NUM
ejpam-5407	251	36	)	)	PUNCT
ejpam-5407	251	37	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	251	38	2	2	NUM
ejpam-5407	251	39	,	,	PUNCT
ejpam-5407	251	40	|ℶ2|+	|ℶ2|+	X
ejpam-5407	251	41	2;ℶ3	2;ℶ3	NUM
ejpam-5407	251	42	+	+	CCONJ
ejpam-5407	251	43	2	2	NUM
ejpam-5407	251	44	,	,	PUNCT
ejpam-5407	251	45	1	1	NUM
ejpam-5407	251	46	)	)	PUNCT
ejpam-5407	251	47	+	+	CCONJ
ejpam-5407	251	48	(	(	PUNCT
ejpam-5407	251	49	3−	3−	NUM
ejpam-5407	251	50	κ1	κ1	NOUN
ejpam-5407	251	51	)	)	PUNCT
ejpam-5407	251	52	|ℶ1ℶ2|	|ℶ1ℶ2|	NOUN
ejpam-5407	251	53	ℶ3	ℶ3	PROPN
ejpam-5407	251	54	g2,1(|ℶ1|+	g2,1(|ℶ1|+	PROPN
ejpam-5407	251	55	1	1	NUM
ejpam-5407	251	56	,	,	PUNCT
ejpam-5407	251	57	|ℶ2|+	|ℶ2|+	X
ejpam-5407	251	58	1;ℶ3	1;ℶ3	NUM
ejpam-5407	251	59	+	+	SYM
ejpam-5407	251	60	1	1	NUM
ejpam-5407	251	61	,	,	PUNCT
ejpam-5407	251	62	1	1	NUM
ejpam-5407	251	63	)	)	PUNCT
ejpam-5407	251	64	+	+	CCONJ
ejpam-5407	251	65	(	(	PUNCT
ejpam-5407	251	66	1−κ1	1−κ1	NUM
ejpam-5407	251	67	)	)	PUNCT
ejpam-5407	252	1	[	[	X
ejpam-5407	252	2	g2,1(|ℶ1|	g2,1(|ℶ1|	NOUN
ejpam-5407	252	3	,	,	PUNCT
ejpam-5407	252	4	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	252	5	;	;	PUNCT
ejpam-5407	252	6	ℶ3	ℶ3	PROPN
ejpam-5407	252	7	,	,	PUNCT
ejpam-5407	252	8	1)−	1)−	PROPN
ejpam-5407	252	9	1	1	NUM
ejpam-5407	252	10	]	]	PUNCT
ejpam-5407	252	11	≤	≤	NUM
ejpam-5407	252	12	1−	1−	NUM
ejpam-5407	252	13	κ1	κ1	NOUN
ejpam-5407	252	14	.	.	PUNCT
ejpam-5407	253	1	corollary	corollary	ADJ
ejpam-5407	253	2	6	6	NUM
ejpam-5407	253	3	.	.	PUNCT
ejpam-5407	254	1	iif	iif	PROPN
ejpam-5407	254	2	l	l	PROPN
ejpam-5407	254	3	∈	∈	PROPN
ejpam-5407	254	4	cv	cv	PROPN
ejpam-5407	254	5	and	and	CCONJ
ejpam-5407	254	6	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	254	7	∈	∈	PROPN
ejpam-5407	254	8	c−{0	c−{0	ADV
ejpam-5407	254	9	}	}	PUNCT
ejpam-5407	254	10	,	,	PUNCT
ejpam-5407	254	11	ℶ3	ℶ3	PROPN
ejpam-5407	254	12	∈	∈	PROPN
ejpam-5407	254	13	r	r	NOUN
ejpam-5407	254	14	,	,	PUNCT
ejpam-5407	254	15	then	then	ADV
ejpam-5407	254	16	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	254	17	)	)	PUNCT
ejpam-5407	254	18	∈	∈	PROPN
ejpam-5407	254	19	st	st	PROPN
ejpam-5407	254	20	(	(	PUNCT
ejpam-5407	254	21	κ1	κ1	NOUN
ejpam-5407	254	22	)	)	PUNCT
ejpam-5407	254	23	if	if	SCONJ
ejpam-5407	254	24	|ℶ1ℶ2|	|ℶ1ℶ2|	ADJ
ejpam-5407	254	25	ℶ3	ℶ3	PROPN
ejpam-5407	254	26	g2,1(|ℶ1|+	g2,1(|ℶ1|+	NOUN
ejpam-5407	254	27	1	1	NUM
ejpam-5407	254	28	,	,	PUNCT
ejpam-5407	254	29	|ℶ2|+	|ℶ2|+	X
ejpam-5407	254	30	1;ℶ3	1;ℶ3	NUM
ejpam-5407	254	31	+	+	SYM
ejpam-5407	254	32	1	1	NUM
ejpam-5407	254	33	,	,	PUNCT
ejpam-5407	254	34	1	1	NUM
ejpam-5407	254	35	)	)	PUNCT
ejpam-5407	254	36	+	+	CCONJ
ejpam-5407	254	37	(	(	PUNCT
ejpam-5407	254	38	1−κ1	1−κ1	NUM
ejpam-5407	254	39	)	)	PUNCT
ejpam-5407	255	1	[	[	X
ejpam-5407	255	2	g2,1(|ℶ1|	g2,1(|ℶ1|	NOUN
ejpam-5407	255	3	,	,	PUNCT
ejpam-5407	255	4	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	255	5	;	;	PUNCT
ejpam-5407	255	6	ℶ3	ℶ3	PROPN
ejpam-5407	255	7	,	,	PUNCT
ejpam-5407	255	8	1)−	1)−	PROPN
ejpam-5407	255	9	1	1	NUM
ejpam-5407	255	10	]	]	PUNCT
ejpam-5407	255	11	≤	≤	NUM
ejpam-5407	255	12	1−	1−	NUM
ejpam-5407	255	13	κ1	κ1	NOUN
ejpam-5407	255	14	.	.	PUNCT
ejpam-5407	256	1	corollary	corollary	ADJ
ejpam-5407	256	2	7	7	NUM
ejpam-5407	256	3	.	.	PUNCT
ejpam-5407	257	1	let	let	VERB
ejpam-5407	257	2	υ1	υ1	PROPN
ejpam-5407	257	3	given	give	VERB
ejpam-5407	257	4	by	by	ADP
ejpam-5407	257	5	(	(	PUNCT
ejpam-5407	257	6	3	3	NUM
ejpam-5407	257	7	)	)	PUNCT
ejpam-5407	257	8	and	and	CCONJ
ejpam-5407	257	9	ℶ1,ℶ2	ℶ1,ℶ2	PROPN
ejpam-5407	257	10	∈	∈	PROPN
ejpam-5407	257	11	c−{0	c−{0	ADV
ejpam-5407	257	12	}	}	PUNCT
ejpam-5407	257	13	,	,	PUNCT
ejpam-5407	257	14	ℶ3	ℶ3	PROPN
ejpam-5407	257	15	∈	∈	PROPN
ejpam-5407	257	16	r.	r.	PROPN
ejpam-5407	258	1	if	if	SCONJ
ejpam-5407	258	2	l	l	PROPN
ejpam-5407	258	3	∈	∈	PROPN
ejpam-5407	258	4	ξ−st	ξ−st	NOUN
ejpam-5407	258	5	for	for	ADP
ejpam-5407	258	6	some	some	DET
ejpam-5407	258	7	ξ(0	ξ(0	SYM
ejpam-5407	258	8	≤	≤	PUNCT
ejpam-5407	258	9	ξ	ξ	X
ejpam-5407	258	10	<	<	X
ejpam-5407	258	11	∞	∞	NUM
ejpam-5407	258	12	)	)	PUNCT
ejpam-5407	258	13	and	and	CCONJ
ejpam-5407	258	14	satisfies	satisfy	VERB
ejpam-5407	258	15	|ℶ1ℶ2|υ1	|ℶ1ℶ2|υ1	PROPN
ejpam-5407	258	16	ℶ3(1)1	ℶ3(1)1	PROPN
ejpam-5407	258	17	g3,2(|ℶ1|+	g3,2(|ℶ1|+	PROPN
ejpam-5407	258	18	1	1	NUM
ejpam-5407	258	19	,	,	PUNCT
ejpam-5407	258	20	|ℶ2|+	|ℶ2|+	X
ejpam-5407	259	1	1,υ1	1,υ1	NUM
ejpam-5407	259	2	+	+	NUM
ejpam-5407	259	3	1;ℶ3	1;ℶ3	NUM
ejpam-5407	259	4	+	+	CCONJ
ejpam-5407	259	5	1	1	NUM
ejpam-5407	259	6	,	,	PUNCT
ejpam-5407	259	7	2	2	NUM
ejpam-5407	259	8	;	;	PUNCT
ejpam-5407	259	9	1	1	NUM
ejpam-5407	259	10	)	)	PUNCT
ejpam-5407	259	11	+	+	CCONJ
ejpam-5407	259	12	(	(	PUNCT
ejpam-5407	259	13	1−κ1	1−κ1	NUM
ejpam-5407	259	14	)	)	PUNCT
ejpam-5407	260	1	[	[	X
ejpam-5407	260	2	g3,2(|ℶ1|	g3,2(|ℶ1|	NOUN
ejpam-5407	260	3	,	,	PUNCT
ejpam-5407	260	4	|ℶ2|	|ℶ2|	NOUN
ejpam-5407	260	5	,	,	PUNCT
ejpam-5407	260	6	υ1;ℶ3	υ1;ℶ3	PROPN
ejpam-5407	260	7	,	,	PUNCT
ejpam-5407	260	8	1	1	NUM
ejpam-5407	260	9	;	;	PUNCT
ejpam-5407	260	10	1)−	1)−	PROPN
ejpam-5407	260	11	1	1	NUM
ejpam-5407	260	12	]	]	PUNCT
ejpam-5407	260	13	≤	≤	NUM
ejpam-5407	260	14	1−	1−	NUM
ejpam-5407	260	15	κ1	κ1	NOUN
ejpam-5407	260	16	,	,	PUNCT
ejpam-5407	260	17	then	then	ADV
ejpam-5407	260	18	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	PROPN
ejpam-5407	260	19	)	)	PUNCT
ejpam-5407	260	20	∈	∈	PROPN
ejpam-5407	260	21	st	st	PROPN
ejpam-5407	260	22	(	(	PUNCT
ejpam-5407	260	23	κ1	κ1	PROPN
ejpam-5407	260	24	)	)	PUNCT
ejpam-5407	260	25	.	.	PUNCT
ejpam-5407	261	1	references	reference	NOUN
ejpam-5407	261	2	3397	3397	NUM
ejpam-5407	261	3	4	4	NUM
ejpam-5407	261	4	.	.	PUNCT
ejpam-5407	262	1	conclusions	conclusion	NOUN
ejpam-5407	262	2	using	use	VERB
ejpam-5407	262	3	of	of	ADP
ejpam-5407	262	4	the	the	DET
ejpam-5407	262	5	hohlov	hohlov	NOUN
ejpam-5407	262	6	operator	operator	NOUN
ejpam-5407	262	7	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	VERB
ejpam-5407	262	8	)	)	PUNCT
ejpam-5407	262	9	,	,	PUNCT
ejpam-5407	262	10	we	we	PRON
ejpam-5407	262	11	find	find	VERB
ejpam-5407	262	12	necessary	necessary	ADJ
ejpam-5407	262	13	condition	condition	NOUN
ejpam-5407	262	14	for	for	SCONJ
ejpam-5407	262	15	this	this	DET
ejpam-5407	262	16	operator	operator	NOUN
ejpam-5407	262	17	to	to	PART
ejpam-5407	262	18	be	be	AUX
ejpam-5407	262	19	in	in	ADP
ejpam-5407	262	20	the	the	DET
ejpam-5407	262	21	subfamilies	subfamily	NOUN
ejpam-5407	262	22	cκ3(κ1	cκ3(κ1	NOUN
ejpam-5407	262	23	,	,	PUNCT
ejpam-5407	262	24	κ2	κ2	NOUN
ejpam-5407	262	25	)	)	PUNCT
ejpam-5407	262	26	and	and	CCONJ
ejpam-5407	262	27	s∗κ3(κ1	s∗κ3(κ1	ADJ
ejpam-5407	262	28	,	,	PUNCT
ejpam-5407	262	29	κ2	κ2	NOUN
ejpam-5407	262	30	)	)	PUNCT
ejpam-5407	262	31	of	of	ADP
ejpam-5407	262	32	analytic	analytic	ADJ
ejpam-5407	262	33	functions	function	NOUN
ejpam-5407	262	34	with	with	ADP
ejpam-5407	262	35	negative	negative	ADJ
ejpam-5407	262	36	coefficients	coefficient	NOUN
ejpam-5407	262	37	.	.	PUNCT
ejpam-5407	263	1	furthermore	furthermore	ADV
ejpam-5407	263	2	,	,	PUNCT
ejpam-5407	263	3	we	we	PRON
ejpam-5407	263	4	investigate	investigate	VERB
ejpam-5407	263	5	several	several	ADJ
ejpam-5407	263	6	inclusion	inclusion	NOUN
ejpam-5407	263	7	properties	property	NOUN
ejpam-5407	263	8	for	for	ADP
ejpam-5407	263	9	these	these	DET
ejpam-5407	263	10	subfamilies	subfamily	NOUN
ejpam-5407	263	11	.	.	PUNCT
ejpam-5407	264	1	also	also	ADV
ejpam-5407	264	2	,	,	PUNCT
ejpam-5407	264	3	our	our	PRON
ejpam-5407	264	4	results	result	NOUN
ejpam-5407	264	5	will	will	AUX
ejpam-5407	264	6	imply	imply	VERB
ejpam-5407	264	7	a	a	DET
ejpam-5407	264	8	number	number	NOUN
ejpam-5407	264	9	of	of	ADP
ejpam-5407	264	10	corollaries	corollary	NOUN
ejpam-5407	264	11	.	.	PUNCT
ejpam-5407	265	1	hohlov	hohlov	NOUN
ejpam-5407	265	2	operator	operator	NOUN
ejpam-5407	265	3	hoℶ1,ℶ2,ℶ3(l	hoℶ1,ℶ2,ℶ3(l	NOUN
ejpam-5407	265	4	)	)	PUNCT
ejpam-5407	265	5	can	can	AUX
ejpam-5407	265	6	be	be	AUX
ejpam-5407	265	7	used	use	VERB
ejpam-5407	265	8	to	to	PART
ejpam-5407	265	9	derive	derive	VERB
ejpam-5407	265	10	new	new	ADJ
ejpam-5407	265	11	necessary	necessary	ADJ
ejpam-5407	265	12	and	and	CCONJ
ejpam-5407	265	13	sufficient	sufficient	ADJ
ejpam-5407	265	14	condition	condition	NOUN
ejpam-5407	265	15	for	for	ADP
ejpam-5407	265	16	analytic	analytic	ADJ
ejpam-5407	265	17	functions	function	NOUN
ejpam-5407	265	18	in	in	ADP
ejpam-5407	265	19	various	various	ADJ
ejpam-5407	265	20	subfamilies	subfamily	NOUN
ejpam-5407	265	21	in	in	ADP
ejpam-5407	265	22	the	the	DET
ejpam-5407	265	23	open	open	ADJ
ejpam-5407	265	24	unit	unit	NOUN
ejpam-5407	265	25	disk	disk	NOUN
ejpam-5407	265	26	.	.	PUNCT
ejpam-5407	266	1	references	reference	NOUN
ejpam-5407	266	2	[	[	X
ejpam-5407	266	3	1	1	NUM
ejpam-5407	266	4	]	]	X
ejpam-5407	266	5	b	b	NOUN
ejpam-5407	266	6	a	a	DET
ejpam-5407	266	7	frasin	frasin	NOUN
ejpam-5407	266	8	g	g	PROPN
ejpam-5407	266	9	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-5407	266	10	a	a	DET
ejpam-5407	266	11	amourah	amourah	NOUN
ejpam-5407	266	12	and	and	CCONJ
ejpam-5407	266	13	t	t	PROPN
ejpam-5407	266	14	al	al	PROPN
ejpam-5407	266	15	-	-	PUNCT
ejpam-5407	266	16	hawary	hawary	PROPN
ejpam-5407	266	17	.	.	PUNCT
ejpam-5407	267	1	bi	bi	ADJ
ejpam-5407	267	2	-	-	ADJ
ejpam-5407	267	3	bazilevič	bazilevič	NOUN
ejpam-5407	267	4	functions	function	NOUN
ejpam-5407	267	5	of	of	ADP
ejpam-5407	267	6	order	order	NOUN
ejpam-5407	268	1	+	+	ADV
ejpam-5407	268	2	i	i	PRON
ejpam-5407	268	3	associated	associate	VERB
ejpam-5407	268	4	with	with	ADP
ejpam-5407	268	5	(	(	PUNCT
ejpam-5407	268	6	p	p	X
ejpam-5407	268	7	,	,	PUNCT
ejpam-5407	268	8	q)-lucas	q)-lucas	DET
ejpam-5407	268	9	polynomials	polynomial	NOUN
ejpam-5407	268	10	.	.	PUNCT
ejpam-5407	269	1	aims	aim	VERB
ejpam-5407	269	2	mathematics	mathematic	NOUN
ejpam-5407	269	3	,	,	PUNCT
ejpam-5407	269	4	6.5:4296–4305	6.5:4296–4305	NOUN
ejpam-5407	269	5	,	,	PUNCT
ejpam-5407	269	6	2021	2021	NUM
ejpam-5407	269	7	.	.	PUNCT
ejpam-5407	270	1	[	[	X
ejpam-5407	270	2	2	2	NUM
ejpam-5407	270	3	]	]	PUNCT
ejpam-5407	270	4	t	t	PROPN
ejpam-5407	270	5	al	al	PROPN
ejpam-5407	270	6	-	-	PUNCT
ejpam-5407	270	7	hawary	hawary	PROPN
ejpam-5407	270	8	,	,	PUNCT
ejpam-5407	270	9	i	i	PRON
ejpam-5407	270	10	aldawish	aldawish	VERB
ejpam-5407	270	11	,	,	PUNCT
ejpam-5407	270	12	b	b	PROPN
ejpam-5407	270	13	a	a	DET
ejpam-5407	270	14	frasin	frasin	NOUN
ejpam-5407	270	15	,	,	PUNCT
ejpam-5407	270	16	o	o	PROPN
ejpam-5407	270	17	alkam	alkam	ADV
ejpam-5407	270	18	,	,	PUNCT
ejpam-5407	270	19	and	and	CCONJ
ejpam-5407	270	20	f	f	PROPN
ejpam-5407	270	21	yousef	yousef	PROPN
ejpam-5407	270	22	.	.	PROPN
ejpam-5407	271	1	necessary	necessary	ADJ
ejpam-5407	271	2	and	and	CCONJ
ejpam-5407	271	3	sufficient	sufficient	ADJ
ejpam-5407	271	4	conditions	condition	NOUN
ejpam-5407	271	5	for	for	SCONJ
ejpam-5407	271	6	normalized	normalize	VERB
ejpam-5407	271	7	wright	wright	PROPN
ejpam-5407	271	8	functions	function	NOUN
ejpam-5407	271	9	to	to	PART
ejpam-5407	271	10	be	be	AUX
ejpam-5407	271	11	in	in	ADP
ejpam-5407	271	12	certain	certain	ADJ
ejpam-5407	271	13	classes	class	NOUN
ejpam-5407	271	14	of	of	ADP
ejpam-5407	271	15	analytic	analytic	ADJ
ejpam-5407	271	16	functions	function	NOUN
ejpam-5407	271	17	.	.	PUNCT
ejpam-5407	272	1	mathematics	mathematic	NOUN
ejpam-5407	272	2	,	,	PUNCT
ejpam-5407	272	3	10(24):1–11	10(24):1–11	NUM
ejpam-5407	272	4	,	,	PUNCT
ejpam-5407	272	5	2022	2022	NUM
ejpam-5407	272	6	.	.	PUNCT
ejpam-5407	273	1	[	[	X
ejpam-5407	273	2	3	3	X
ejpam-5407	273	3	]	]	X
ejpam-5407	273	4	j	j	PROPN
ejpam-5407	273	5	w	w	PROPN
ejpam-5407	273	6	alexander	alexander	PROPN
ejpam-5407	273	7	.	.	PUNCT
ejpam-5407	273	8	functions	function	NOUN
ejpam-5407	273	9	which	which	PRON
ejpam-5407	273	10	map	map	VERB
ejpam-5407	273	11	the	the	DET
ejpam-5407	273	12	interior	interior	NOUN
ejpam-5407	273	13	of	of	ADP
ejpam-5407	273	14	the	the	DET
ejpam-5407	273	15	unit	unit	NOUN
ejpam-5407	273	16	circle	circle	NOUN
ejpam-5407	273	17	upon	upon	SCONJ
ejpam-5407	273	18	simple	simple	ADJ
ejpam-5407	273	19	regions	region	NOUN
ejpam-5407	273	20	.	.	PUNCT
ejpam-5407	274	1	ann	ann	PROPN
ejpam-5407	274	2	.	.	PROPN
ejpam-5407	274	3	of	of	ADP
ejpam-5407	274	4	math	math	NOUN
ejpam-5407	274	5	.	.	PUNCT
ejpam-5407	274	6	,	,	PUNCT
ejpam-5407	274	7	second	second	ADJ
ejpam-5407	274	8	series	series	NOUN
ejpam-5407	274	9	,	,	PUNCT
ejpam-5407	274	10	17:12–22	17:12–22	NUM
ejpam-5407	274	11	,	,	PUNCT
ejpam-5407	274	12	1915	1915	NUM
ejpam-5407	274	13	.	.	PUNCT
ejpam-5407	275	1	[	[	X
ejpam-5407	275	2	4	4	X
ejpam-5407	275	3	]	]	PUNCT
ejpam-5407	275	4	t	t	PROPN
ejpam-5407	275	5	al	al	PROPN
ejpam-5407	275	6	-	-	PUNCT
ejpam-5407	275	7	hawary	hawary	PROPN
ejpam-5407	275	8	b	b	PROPN
ejpam-5407	275	9	a	a	DET
ejpam-5407	275	10	frasin	frasin	NOUN
ejpam-5407	275	11	,	,	PUNCT
ejpam-5407	275	12	f	f	PROPN
ejpam-5407	275	13	yousef	yousef	PROPN
ejpam-5407	275	14	and	and	CCONJ
ejpam-5407	275	15	i	i	PRON
ejpam-5407	275	16	aldawish	aldawish	VERB
ejpam-5407	275	17	.	.	PUNCT
ejpam-5407	276	1	application	application	NOUN
ejpam-5407	276	2	of	of	ADP
ejpam-5407	276	3	generalized	generalized	ADJ
ejpam-5407	276	4	bessel	bessel	NOUN
ejpam-5407	276	5	functions	function	NOUN
ejpam-5407	276	6	to	to	ADP
ejpam-5407	276	7	classes	class	NOUN
ejpam-5407	276	8	of	of	ADP
ejpam-5407	276	9	analytic	analytic	ADJ
ejpam-5407	276	10	functions	function	NOUN
ejpam-5407	276	11	.	.	PUNCT
ejpam-5407	277	1	afrika	afrika	ADJ
ejpam-5407	277	2	matematika	matematika	PROPN
ejpam-5407	277	3	,	,	PUNCT
ejpam-5407	277	4	32:431–439	32:431–439	PROPN
ejpam-5407	277	5	,	,	PUNCT
ejpam-5407	277	6	2021	2021	NUM
ejpam-5407	277	7	.	.	PUNCT
ejpam-5407	278	1	[	[	X
ejpam-5407	278	2	5	5	X
ejpam-5407	278	3	]	]	PUNCT
ejpam-5407	278	4	tareq	tareq	PROPN
ejpam-5407	278	5	al	al	PROPN
ejpam-5407	278	6	-	-	PUNCT
ejpam-5407	278	7	hawary	hawary	PROPN
ejpam-5407	278	8	f	f	PROPN
ejpam-5407	278	9	yousef	yousef	PROPN
ejpam-5407	278	10	b	b	PROPN
ejpam-5407	278	11	a	a	DET
ejpam-5407	278	12	frasin	frasin	NOUN
ejpam-5407	278	13	and	and	CCONJ
ejpam-5407	278	14	i	i	PRON
ejpam-5407	278	15	aldawish	aldawish	VERB
ejpam-5407	278	16	.	.	PUNCT
ejpam-5407	279	1	on	on	ADP
ejpam-5407	279	2	subclasses	subclass	NOUN
ejpam-5407	279	3	of	of	ADP
ejpam-5407	279	4	analytic	analytic	ADJ
ejpam-5407	279	5	functions	function	NOUN
ejpam-5407	279	6	associated	associate	VERB
ejpam-5407	279	7	with	with	ADP
ejpam-5407	279	8	struve	struve	PROPN
ejpam-5407	279	9	functions	function	NOUN
ejpam-5407	279	10	.	.	PUNCT
ejpam-5407	280	1	nonlinear	nonlinear	ADJ
ejpam-5407	280	2	functional	functional	ADJ
ejpam-5407	280	3	analysis	analysis	NOUN
ejpam-5407	280	4	and	and	CCONJ
ejpam-5407	280	5	applications	application	NOUN
ejpam-5407	280	6	,	,	PUNCT
ejpam-5407	280	7	27(1):99–110	27(1):99–110	NUM
ejpam-5407	280	8	,	,	PUNCT
ejpam-5407	280	9	2022	2022	NUM
ejpam-5407	280	10	.	.	PUNCT
ejpam-5407	281	1	[	[	X
ejpam-5407	281	2	6	6	NUM
ejpam-5407	281	3	]	]	PUNCT
ejpam-5407	281	4	a	a	DET
ejpam-5407	281	5	baricz	baricz	NOUN
ejpam-5407	281	6	and	and	CCONJ
ejpam-5407	281	7	s	s	NOUN
ejpam-5407	281	8	ponnusamy	ponnusamy	NOUN
ejpam-5407	281	9	.	.	PUNCT
ejpam-5407	282	1	starlikeness	starlikeness	NOUN
ejpam-5407	282	2	and	and	CCONJ
ejpam-5407	282	3	convexity	convexity	NOUN
ejpam-5407	282	4	of	of	ADP
ejpam-5407	282	5	generalized	generalized	ADJ
ejpam-5407	282	6	bessel	bessel	NOUN
ejpam-5407	282	7	functions	function	NOUN
ejpam-5407	282	8	.	.	PUNCT
ejpam-5407	283	1	integral	integral	ADJ
ejpam-5407	283	2	transforms	transform	VERB
ejpam-5407	283	3	spec	spec	NOUN
ejpam-5407	283	4	.	.	PUNCT
ejpam-5407	284	1	funct	funct	PROPN
ejpam-5407	284	2	.	.	PROPN
ejpam-5407	284	3	,	,	PUNCT
ejpam-5407	285	1	21:641–653	21:641–653	PROPN
ejpam-5407	285	2	,	,	PUNCT
ejpam-5407	285	3	2010	2010	NUM
ejpam-5407	285	4	.	.	PUNCT
ejpam-5407	286	1	[	[	X
ejpam-5407	286	2	7	7	NUM
ejpam-5407	286	3	]	]	SYM
ejpam-5407	286	4	s	s	PROPN
ejpam-5407	286	5	d	d	X
ejpam-5407	286	6	bernardi	bernardi	PROPN
ejpam-5407	286	7	.	.	PUNCT
ejpam-5407	287	1	convex	convex	PROPN
ejpam-5407	287	2	and	and	CCONJ
ejpam-5407	287	3	starlike	starlike	NOUN
ejpam-5407	287	4	univalent	univalent	ADJ
ejpam-5407	287	5	functions	function	NOUN
ejpam-5407	287	6	.	.	PUNCT
ejpam-5407	288	1	transactions	transaction	NOUN
ejpam-5407	288	2	of	of	ADP
ejpam-5407	288	3	the	the	DET
ejpam-5407	288	4	american	american	PROPN
ejpam-5407	288	5	mathematical	mathematical	PROPN
ejpam-5407	288	6	society	society	NOUN
ejpam-5407	288	7	,	,	PUNCT
ejpam-5407	288	8	135:429–446	135:429–446	NUM
ejpam-5407	288	9	,	,	PUNCT
ejpam-5407	288	10	1969	1969	NUM
ejpam-5407	288	11	.	.	PUNCT
ejpam-5407	289	1	[	[	X
ejpam-5407	289	2	8	8	NUM
ejpam-5407	289	3	]	]	X
ejpam-5407	289	4	d	d	PROPN
ejpam-5407	289	5	eric	eric	PROPN
ejpam-5407	289	6	feigelson	feigelson	PROPN
ejpam-5407	289	7	and	and	CCONJ
ejpam-5407	289	8	g	g	PROPN
ejpam-5407	289	9	jogesh	jogesh	PROPN
ejpam-5407	289	10	babu	babu	PROPN
ejpam-5407	289	11	.	.	PUNCT
ejpam-5407	290	1	statistical	statistical	ADJ
ejpam-5407	290	2	methods	method	NOUN
ejpam-5407	290	3	for	for	ADP
ejpam-5407	290	4	astronomy	astronomy	NOUN
ejpam-5407	290	5	.	.	PUNCT
ejpam-5407	291	1	springer	springer	NOUN
ejpam-5407	291	2	natherlands	natherland	NOUN
ejpam-5407	291	3	,	,	PUNCT
ejpam-5407	291	4	pages	page	NOUN
ejpam-5407	291	5	445–480	445–480	NUM
ejpam-5407	291	6	,	,	PUNCT
ejpam-5407	291	7	2013	2013	NUM
ejpam-5407	291	8	.	.	PUNCT
ejpam-5407	292	1	[	[	X
ejpam-5407	292	2	9	9	NUM
ejpam-5407	292	3	]	]	X
ejpam-5407	292	4	b.a	b.a	PROPN
ejpam-5407	292	5	.	.	PROPN
ejpam-5407	292	6	frasin	frasin	PROPN
ejpam-5407	292	7	.	.	PUNCT
ejpam-5407	293	1	subordinations	subordination	NOUN
ejpam-5407	293	2	results	result	VERB
ejpam-5407	293	3	for	for	ADP
ejpam-5407	293	4	a	a	DET
ejpam-5407	293	5	class	class	NOUN
ejpam-5407	293	6	of	of	ADP
ejpam-5407	293	7	analytic	analytic	ADJ
ejpam-5407	293	8	functions	function	NOUN
ejpam-5407	293	9	defined	define	VERB
ejpam-5407	293	10	by	by	ADP
ejpam-5407	293	11	linear	linear	ADJ
ejpam-5407	293	12	operator	operator	NOUN
ejpam-5407	293	13	.	.	PUNCT
ejpam-5407	294	1	j.	j.	PROPN
ejpam-5407	294	2	ineq	ineq	PROPN
ejpam-5407	294	3	.	.	PUNCT
ejpam-5407	295	1	pure	pure	ADJ
ejpam-5407	295	2	appl	appl	PROPN
ejpam-5407	295	3	.	.	PUNCT
ejpam-5407	295	4	math	math	PROPN
ejpam-5407	295	5	.	.	PUNCT
ejpam-5407	295	6	,	,	PUNCT
ejpam-5407	295	7	7(4):article	7(4):article	NUM
ejpam-5407	295	8	134	134	NUM
ejpam-5407	295	9	,	,	PUNCT
ejpam-5407	295	10	2006	2006	NUM
ejpam-5407	295	11	.	.	PUNCT
ejpam-5407	296	1	[	[	X
ejpam-5407	296	2	10	10	NUM
ejpam-5407	296	3	]	]	X
ejpam-5407	296	4	a	a	DET
ejpam-5407	296	5	w	w	PROPN
ejpam-5407	296	6	goodman	goodman	PROPN
ejpam-5407	296	7	.	.	PUNCT
ejpam-5407	297	1	on	on	ADP
ejpam-5407	297	2	uniformly	uniformly	ADV
ejpam-5407	297	3	convex	convex	NOUN
ejpam-5407	297	4	functions	function	NOUN
ejpam-5407	297	5	.	.	PUNCT
ejpam-5407	298	1	ann	ann	PROPN
ejpam-5407	298	2	.	.	PUNCT
ejpam-5407	298	3	polon	polon	PROPN
ejpam-5407	298	4	.	.	PUNCT
ejpam-5407	299	1	math	math	NOUN
ejpam-5407	299	2	.	.	PUNCT
ejpam-5407	299	3	,	,	PUNCT
ejpam-5407	300	1	56:87–92	56:87–92	PROPN
ejpam-5407	300	2	,	,	PUNCT
ejpam-5407	300	3	1991	1991	NUM
ejpam-5407	300	4	.	.	PUNCT
ejpam-5407	301	1	[	[	X
ejpam-5407	301	2	11	11	NUM
ejpam-5407	301	3	]	]	X
ejpam-5407	301	4	y	y	PROPN
ejpam-5407	301	5	e	e	NOUN
ejpam-5407	301	6	hohlov	hohlov	NOUN
ejpam-5407	301	7	.	.	PUNCT
ejpam-5407	302	1	operators	operator	NOUN
ejpam-5407	302	2	and	and	CCONJ
ejpam-5407	302	3	operations	operation	NOUN
ejpam-5407	302	4	on	on	ADP
ejpam-5407	302	5	the	the	DET
ejpam-5407	302	6	class	class	NOUN
ejpam-5407	302	7	of	of	ADP
ejpam-5407	302	8	univalent	univalent	ADJ
ejpam-5407	302	9	functions	function	NOUN
ejpam-5407	302	10	.	.	PUNCT
ejpam-5407	303	1	izv	izv	PROPN
ejpam-5407	303	2	.	.	PUNCT
ejpam-5407	304	1	vysš.	vysš.	ADJ
ejpam-5407	304	2	učebn	učebn	PROPN
ejpam-5407	304	3	.	.	PUNCT
ejpam-5407	305	1	zaved	zave	VERB
ejpam-5407	305	2	.	.	PUNCT
ejpam-5407	306	1	matematika	matematika	PROPN
ejpam-5407	306	2	,	,	PUNCT
ejpam-5407	306	3	10:83–89	10:83–89	NUM
ejpam-5407	306	4	,	,	PUNCT
ejpam-5407	306	5	1978	1978	NUM
ejpam-5407	306	6	.	.	PUNCT
ejpam-5407	307	1	[	[	X
ejpam-5407	307	2	12	12	NUM
ejpam-5407	307	3	]	]	X
ejpam-5407	307	4	p	p	X
ejpam-5407	307	5	balasubrahmanyam	balasubrahmanyam	NOUN
ejpam-5407	307	6	k	k	PROPN
ejpam-5407	307	7	g	g	PROPN
ejpam-5407	307	8	subramanian	subramanian	PROPN
ejpam-5407	307	9	,	,	PUNCT
ejpam-5407	307	10	t	t	PROPN
ejpam-5407	307	11	v	v	X
ejpam-5407	307	12	sudharsan	sudharsan	NOUN
ejpam-5407	307	13	and	and	CCONJ
ejpam-5407	307	14	h	h	NOUN
ejpam-5407	307	15	silverman	silverman	NOUN
ejpam-5407	307	16	.	.	PUNCT
ejpam-5407	308	1	classes	class	NOUN
ejpam-5407	308	2	of	of	ADP
ejpam-5407	308	3	uniformly	uniformly	ADJ
ejpam-5407	308	4	starlike	starlike	NOUN
ejpam-5407	308	5	functions	function	NOUN
ejpam-5407	308	6	.	.	PUNCT
ejpam-5407	309	1	publ	publ	NOUN
ejpam-5407	309	2	.	.	PUNCT
ejpam-5407	310	1	math	math	NOUN
ejpam-5407	310	2	.	.	PUNCT
ejpam-5407	311	1	debrecen	debrecen	PROPN
ejpam-5407	311	2	,	,	PUNCT
ejpam-5407	311	3	3	3	PROPN
ejpam-5407	311	4	-	-	SYM
ejpam-5407	311	5	4:309–315	4:309–315	NUM
ejpam-5407	311	6	,	,	PUNCT
ejpam-5407	311	7	1998	1998	NUM
ejpam-5407	311	8	.	.	PUNCT
ejpam-5407	312	1	references	reference	NOUN
ejpam-5407	312	2	3398	3398	NUM
ejpam-5407	313	1	[	[	X
ejpam-5407	313	2	13	13	NUM
ejpam-5407	313	3	]	]	SYM
ejpam-5407	313	4	s	s	X
ejpam-5407	313	5	kanas	kanas	PROPN
ejpam-5407	313	6	and	and	CCONJ
ejpam-5407	313	7	a	a	DET
ejpam-5407	313	8	wi	wi	PROPN
ejpam-5407	313	9	sniowska	sniowska	PROPN
ejpam-5407	313	10	.	.	PUNCT
ejpam-5407	314	1	conic	conic	ADJ
ejpam-5407	314	2	regions	region	NOUN
ejpam-5407	314	3	and	and	CCONJ
ejpam-5407	314	4	k	k	ADJ
ejpam-5407	314	5	-	-	PUNCT
ejpam-5407	314	6	uniform	uniform	ADJ
ejpam-5407	314	7	convexity	convexity	NOUN
ejpam-5407	314	8	.	.	PUNCT
ejpam-5407	315	1	j.	j.	PROPN
ejpam-5407	315	2	comput	comput	PROPN
ejpam-5407	315	3	.	.	PUNCT
ejpam-5407	316	1	appl	appl	PROPN
ejpam-5407	316	2	.	.	PROPN
ejpam-5407	316	3	math	math	PROPN
ejpam-5407	316	4	.	.	PUNCT
ejpam-5407	316	5	,	,	PUNCT
ejpam-5407	316	6	105:327–336	105:327–336	NUM
ejpam-5407	316	7	,	,	PUNCT
ejpam-5407	316	8	1999	1999	NUM
ejpam-5407	316	9	.	.	PUNCT
ejpam-5407	317	1	[	[	X
ejpam-5407	317	2	14	14	NUM
ejpam-5407	317	3	]	]	SYM
ejpam-5407	317	4	s	s	X
ejpam-5407	317	5	kanas	kanas	PROPN
ejpam-5407	317	6	and	and	CCONJ
ejpam-5407	317	7	a	a	DET
ejpam-5407	317	8	wi	wi	PROPN
ejpam-5407	317	9	sniowska	sniowska	PROPN
ejpam-5407	317	10	.	.	PUNCT
ejpam-5407	318	1	conic	conic	ADJ
ejpam-5407	318	2	regions	region	NOUN
ejpam-5407	318	3	and	and	CCONJ
ejpam-5407	318	4	k	k	ADJ
ejpam-5407	318	5	-	-	PUNCT
ejpam-5407	318	6	starlike	starlike	ADJ
ejpam-5407	318	7	functions	function	NOUN
ejpam-5407	318	8	.	.	PUNCT
ejpam-5407	319	1	roumaine	roumaine	VERB
ejpam-5407	319	2	math	math	NOUN
ejpam-5407	319	3	.	.	PUNCT
ejpam-5407	320	1	pures	pure	NOUN
ejpam-5407	320	2	appl	appl	PROPN
ejpam-5407	320	3	.	.	PROPN
ejpam-5407	320	4	,	,	PUNCT
ejpam-5407	320	5	45:647–657	45:647–657	PROPN
ejpam-5407	320	6	,	,	PUNCT
ejpam-5407	320	7	2000	2000	NUM
ejpam-5407	320	8	.	.	PUNCT
ejpam-5407	321	1	[	[	X
ejpam-5407	321	2	15	15	NUM
ejpam-5407	321	3	]	]	X
ejpam-5407	321	4	m	m	VERB
ejpam-5407	321	5	kasthuri	kasthuri	PROPN
ejpam-5407	321	6	and	and	CCONJ
ejpam-5407	321	7	k	k	PROPN
ejpam-5407	321	8	vijaya	vijaya	PROPN
ejpam-5407	321	9	.	.	PUNCT
ejpam-5407	322	1	some	some	DET
ejpam-5407	322	2	inclusion	inclusion	NOUN
ejpam-5407	322	3	properties	property	NOUN
ejpam-5407	322	4	of	of	ADP
ejpam-5407	322	5	starlike	starlike	NOUN
ejpam-5407	322	6	and	and	CCONJ
ejpam-5407	322	7	convex	convex	NOUN
ejpam-5407	322	8	functions	function	NOUN
ejpam-5407	322	9	associated	associate	VERB
ejpam-5407	322	10	with	with	ADP
ejpam-5407	322	11	hohlov	hohlov	NOUN
ejpam-5407	322	12	operator	operator	NOUN
ejpam-5407	322	13	.	.	PUNCT
ejpam-5407	323	1	international	international	ADJ
ejpam-5407	323	2	journal	journal	PROPN
ejpam-5407	323	3	of	of	ADP
ejpam-5407	323	4	mathematical	mathematical	ADJ
ejpam-5407	323	5	analysis	analysis	NOUN
ejpam-5407	323	6	,	,	PUNCT
ejpam-5407	323	7	20(9):985–992	20(9):985–992	NUM
ejpam-5407	323	8	,	,	PUNCT
ejpam-5407	323	9	2015	2015	NUM
ejpam-5407	323	10	.	.	PUNCT
ejpam-5407	324	1	[	[	X
ejpam-5407	324	2	16	16	NUM
ejpam-5407	324	3	]	]	X
ejpam-5407	324	4	r	r	NOUN
ejpam-5407	324	5	j	j	PROPN
ejpam-5407	324	6	libera	libera	NOUN
ejpam-5407	324	7	.	.	PUNCT
ejpam-5407	325	1	some	some	DET
ejpam-5407	325	2	classes	class	NOUN
ejpam-5407	325	3	of	of	ADP
ejpam-5407	325	4	regular	regular	ADJ
ejpam-5407	325	5	uni	uni	ADJ
ejpam-5407	325	6	alent	alent	NOUN
ejpam-5407	325	7	functions	function	NOUN
ejpam-5407	325	8	.	.	PUNCT
ejpam-5407	326	1	proceedings	proceeding	NOUN
ejpam-5407	326	2	of	of	ADP
ejpam-5407	326	3	the	the	DET
ejpam-5407	326	4	american	american	PROPN
ejpam-5407	326	5	mathematical	mathematical	PROPN
ejpam-5407	326	6	society	society	NOUN
ejpam-5407	326	7	,	,	PUNCT
ejpam-5407	326	8	16:755–758	16:755–758	NUM
ejpam-5407	326	9	,	,	PUNCT
ejpam-5407	326	10	1965	1965	NUM
ejpam-5407	326	11	.	.	PUNCT
ejpam-5407	327	1	[	[	X
ejpam-5407	327	2	17	17	NUM
ejpam-5407	327	3	]	]	X
ejpam-5407	327	4	g	g	PROPN
ejpam-5407	327	5	murugusundaramoorthy	murugusundaramoorthy	PROPN
ejpam-5407	327	6	m	m	VERB
ejpam-5407	327	7	ahmad	ahmad	PROPN
ejpam-5407	327	8	,	,	PUNCT
ejpam-5407	327	9	b	b	X
ejpam-5407	327	10	frasin	frasin	NOUN
ejpam-5407	327	11	and	and	CCONJ
ejpam-5407	327	12	a	a	DET
ejpam-5407	327	13	al	al	PROPN
ejpam-5407	327	14	-	-	PUNCT
ejpam-5407	327	15	khazaleh	khazaleh	NOUN
ejpam-5407	327	16	.	.	PUNCT
ejpam-5407	328	1	an	an	DET
ejpam-5407	328	2	application	application	NOUN
ejpam-5407	328	3	of	of	ADP
ejpam-5407	328	4	mittag	mittag	ADJ
ejpam-5407	328	5	–	–	PUNCT
ejpam-5407	328	6	leffler	leffler	NOUN
ejpam-5407	328	7	-	-	PUNCT
ejpam-5407	328	8	type	type	NOUN
ejpam-5407	328	9	poisson	poisson	NOUN
ejpam-5407	328	10	distribution	distribution	NOUN
ejpam-5407	328	11	on	on	ADP
ejpam-5407	328	12	certain	certain	ADJ
ejpam-5407	328	13	subclasses	subclass	NOUN
ejpam-5407	328	14	of	of	ADP
ejpam-5407	328	15	analytic	analytic	ADJ
ejpam-5407	328	16	functions	function	NOUN
ejpam-5407	328	17	associated	associate	VERB
ejpam-5407	328	18	with	with	ADP
ejpam-5407	328	19	conic	conic	ADJ
ejpam-5407	328	20	domains	domain	NOUN
ejpam-5407	328	21	.	.	PUNCT
ejpam-5407	329	1	heliyon	heliyon	NOUN
ejpam-5407	329	2	,	,	PUNCT
ejpam-5407	329	3	7(10):e08109	7(10):e08109	NUM
ejpam-5407	329	4	,	,	PUNCT
ejpam-5407	329	5	2021	2021	NUM
ejpam-5407	329	6	.	.	PUNCT
ejpam-5407	330	1	[	[	X
ejpam-5407	330	2	18	18	NUM
ejpam-5407	330	3	]	]	X
ejpam-5407	330	4	g	g	NOUN
ejpam-5407	330	5	murugusundaramoorthy	murugusundaramoorthy	ADJ
ejpam-5407	330	6	,	,	PUNCT
ejpam-5407	330	7	k	k	PROPN
ejpam-5407	330	8	vijaya	vijaya	PROPN
ejpam-5407	330	9	,	,	PUNCT
ejpam-5407	330	10	and	and	CCONJ
ejpam-5407	330	11	k	k	PROPN
ejpam-5407	330	12	uma	uma	PROPN
ejpam-5407	330	13	.	.	PROPN
ejpam-5407	330	14	subordination	subordination	NOUN
ejpam-5407	330	15	results	result	VERB
ejpam-5407	330	16	for	for	ADP
ejpam-5407	330	17	a	a	DET
ejpam-5407	330	18	class	class	NOUN
ejpam-5407	330	19	of	of	ADP
ejpam-5407	330	20	analytic	analytic	ADJ
ejpam-5407	330	21	functions	function	NOUN
ejpam-5407	330	22	involving	involve	VERB
ejpam-5407	330	23	the	the	DET
ejpam-5407	330	24	hurwitz	hurwitz	PROPN
ejpam-5407	330	25	-	-	PUNCT
ejpam-5407	330	26	lerch	lerch	PROPN
ejpam-5407	330	27	zeta	zeta	PROPN
ejpam-5407	330	28	function	function	PROPN
ejpam-5407	330	29	.	.	PUNCT
ejpam-5407	331	1	international	international	ADJ
ejpam-5407	331	2	journal	journal	PROPN
ejpam-5407	331	3	of	of	ADP
ejpam-5407	331	4	nonlinear	nonlinear	ADJ
ejpam-5407	331	5	science	science	NOUN
ejpam-5407	331	6	,	,	PUNCT
ejpam-5407	331	7	4(10):430–437	4(10):430–437	NUM
ejpam-5407	331	8	,	,	PUNCT
ejpam-5407	331	9	2010	2010	NUM
ejpam-5407	331	10	.	.	PUNCT
ejpam-5407	332	1	[	[	X
ejpam-5407	332	2	19	19	NUM
ejpam-5407	332	3	]	]	SYM
ejpam-5407	332	4	r	r	NOUN
ejpam-5407	332	5	parvatham	parvatham	ADJ
ejpam-5407	332	6	r	r	NOUN
ejpam-5407	332	7	bharati	bharati	NOUN
ejpam-5407	332	8	and	and	CCONJ
ejpam-5407	332	9	a	a	DET
ejpam-5407	332	10	swaminathan	swaminathan	NOUN
ejpam-5407	332	11	.	.	PUNCT
ejpam-5407	333	1	on	on	ADP
ejpam-5407	333	2	subclasses	subclass	NOUN
ejpam-5407	333	3	of	of	ADP
ejpam-5407	333	4	uniformly	uniformly	ADJ
ejpam-5407	333	5	convex	convex	NOUN
ejpam-5407	333	6	functions	function	NOUN
ejpam-5407	333	7	and	and	CCONJ
ejpam-5407	333	8	corresponding	correspond	VERB
ejpam-5407	333	9	class	class	NOUN
ejpam-5407	333	10	of	of	ADP
ejpam-5407	333	11	starlike	starlike	NOUN
ejpam-5407	333	12	functions	function	NOUN
ejpam-5407	333	13	.	.	PUNCT
ejpam-5407	334	1	tamkang	tamkang	PROPN
ejpam-5407	334	2	j.	j.	PROPN
ejpam-5407	334	3	math	math	PROPN
ejpam-5407	334	4	.	.	PROPN
ejpam-5407	334	5	,	,	PUNCT
ejpam-5407	334	6	1(26):17	1(26):17	NUM
ejpam-5407	334	7	–	–	PUNCT
ejpam-5407	334	8	32	32	NUM
ejpam-5407	334	9	,	,	PUNCT
ejpam-5407	334	10	1997	1997	NUM
ejpam-5407	334	11	.	.	PUNCT
ejpam-5407	335	1	[	[	X
ejpam-5407	335	2	20	20	NUM
ejpam-5407	335	3	]	]	SYM
ejpam-5407	335	4	v	v	NOUN
ejpam-5407	335	5	ravichandran	ravichandran	NOUN
ejpam-5407	335	6	r	r	NOUN
ejpam-5407	335	7	m	m	NOUN
ejpam-5407	335	8	ali	ali	PROPN
ejpam-5407	335	9	,	,	PUNCT
ejpam-5407	335	10	k	k	PROPN
ejpam-5407	335	11	g	g	PROPN
ejpam-5407	335	12	subramanian	subramanian	PROPN
ejpam-5407	335	13	and	and	CCONJ
ejpam-5407	335	14	om	om	PROPN
ejpam-5407	335	15	p	p	PROPN
ejpam-5407	335	16	ahuja	ahuja	PROPN
ejpam-5407	335	17	.	.	PUNCT
ejpam-5407	336	1	neighborhoods	neighborhood	NOUN
ejpam-5407	336	2	of	of	ADP
ejpam-5407	336	3	starlike	starlike	NOUN
ejpam-5407	336	4	and	and	CCONJ
ejpam-5407	336	5	convex	convex	NOUN
ejpam-5407	336	6	functions	function	NOUN
ejpam-5407	336	7	associated	associate	VERB
ejpam-5407	336	8	with	with	ADP
ejpam-5407	336	9	parabola	parabola	PROPN
ejpam-5407	336	10	.	.	PUNCT
ejpam-5407	337	1	journal	journal	PROPN
ejpam-5407	337	2	of	of	ADP
ejpam-5407	337	3	inequalities	inequality	NOUN
ejpam-5407	337	4	and	and	CCONJ
ejpam-5407	337	5	applications	application	NOUN
ejpam-5407	337	6	,	,	PUNCT
ejpam-5407	337	7	i	i	PROPN
ejpam-5407	337	8	d	d	PROPN
ejpam-5407	337	9	346279:9	346279:9	NUM
ejpam-5407	337	10	pages	page	NOUN
ejpam-5407	337	11	,	,	PUNCT
ejpam-5407	337	12	2021	2021	NUM
ejpam-5407	337	13	.	.	PUNCT
ejpam-5407	338	1	[	[	X
ejpam-5407	338	2	21	21	NUM
ejpam-5407	338	3	]	]	X
ejpam-5407	338	4	h	h	PROPN
ejpam-5407	338	5	silverman	silverman	NOUN
ejpam-5407	338	6	.	.	PUNCT
ejpam-5407	339	1	univalent	univalent	ADJ
ejpam-5407	339	2	functions	function	NOUN
ejpam-5407	339	3	with	with	ADP
ejpam-5407	339	4	negative	negative	ADJ
ejpam-5407	339	5	coefficients	coefficient	NOUN
ejpam-5407	339	6	.	.	PUNCT
ejpam-5407	340	1	proc	proc	NOUN
ejpam-5407	340	2	.	.	PUNCT
ejpam-5407	341	1	amer	amer	PROPN
ejpam-5407	341	2	.	.	PUNCT
ejpam-5407	341	3	math	math	PROPN
ejpam-5407	341	4	.	.	PUNCT
ejpam-5407	342	1	soc	soc	PROPN
ejpam-5407	342	2	.	.	PUNCT
ejpam-5407	342	3	,	,	PUNCT
ejpam-5407	343	1	51:109–116	51:109–116	PROPN
ejpam-5407	343	2	,	,	PUNCT
ejpam-5407	343	3	1975	1975	NUM
ejpam-5407	343	4	.	.	PUNCT
ejpam-5407	344	1	[	[	X
ejpam-5407	344	2	22	22	NUM
ejpam-5407	344	3	]	]	PUNCT
ejpam-5407	344	4	a	a	DET
ejpam-5407	344	5	swaminathan	swaminathan	NOUN
ejpam-5407	344	6	.	.	PUNCT
ejpam-5407	345	1	certain	certain	ADJ
ejpam-5407	345	2	sufficient	sufficient	ADJ
ejpam-5407	345	3	conditions	condition	NOUN
ejpam-5407	345	4	on	on	ADP
ejpam-5407	345	5	gaussian	gaussian	ADJ
ejpam-5407	345	6	hypergeometric	hypergeometric	ADJ
ejpam-5407	345	7	functions	function	NOUN
ejpam-5407	345	8	.	.	PUNCT
ejpam-5407	346	1	journal	journal	PROPN
ejpam-5407	346	2	of	of	ADP
ejpam-5407	346	3	inequalities	inequality	NOUN
ejpam-5407	346	4	in	in	ADP
ejpam-5407	346	5	pure	pure	ADJ
ejpam-5407	346	6	and	and	CCONJ
ejpam-5407	346	7	applied	applied	ADJ
ejpam-5407	346	8	mathematics	mathematic	NOUN
ejpam-5407	346	9	,	,	PUNCT
ejpam-5407	346	10	4(5):1–10	4(5):1–10	NUM
ejpam-5407	346	11	,	,	PUNCT
ejpam-5407	346	12	2004	2004	NUM
ejpam-5407	346	13	.	.	PUNCT