id	sid	tid	token	lemma	pos
ejpam-6979	1	1	european	european	PROPN
ejpam-6979	1	2	journal	journal	PROPN
ejpam-6979	1	3	of	of	ADP
ejpam-6979	1	4	pure	pure	ADJ
ejpam-6979	1	5	and	and	CCONJ
ejpam-6979	1	6	applied	applied	ADJ
ejpam-6979	1	7	mathematics	mathematic	NOUN
ejpam-6979	1	8	2025	2025	NUM
ejpam-6979	1	9	,	,	PUNCT
ejpam-6979	1	10	vol	vol	NOUN
ejpam-6979	1	11	.	.	PROPN
ejpam-6979	1	12	18	18	NUM
ejpam-6979	1	13	,	,	PUNCT
ejpam-6979	1	14	issue	issue	NOUN
ejpam-6979	1	15	4	4	NUM
ejpam-6979	1	16	,	,	PUNCT
ejpam-6979	1	17	article	article	NOUN
ejpam-6979	1	18	number	number	NOUN
ejpam-6979	1	19	6979	6979	NUM
ejpam-6979	1	20	issn	issn	PROPN
ejpam-6979	1	21	1307	1307	NUM
ejpam-6979	1	22	-	-	SYM
ejpam-6979	1	23	5543	5543	NUM
ejpam-6979	1	24	–	–	PUNCT
ejpam-6979	1	25	ejpam.com	ejpam.com	X
ejpam-6979	1	26	published	publish	VERB
ejpam-6979	1	27	by	by	ADP
ejpam-6979	1	28	new	new	PROPN
ejpam-6979	1	29	york	york	PROPN
ejpam-6979	1	30	business	business	PROPN
ejpam-6979	1	31	global	global	VERB
ejpam-6979	1	32	some	some	DET
ejpam-6979	1	33	applications	application	NOUN
ejpam-6979	1	34	of	of	ADP
ejpam-6979	1	35	fuzzy	fuzzy	ADJ
ejpam-6979	1	36	differential	differential	ADJ
ejpam-6979	1	37	subordination	subordination	NOUN
ejpam-6979	1	38	on	on	ADP
ejpam-6979	1	39	analytic	analytic	ADJ
ejpam-6979	1	40	functions	function	NOUN
ejpam-6979	1	41	connected	connect	VERB
ejpam-6979	1	42	with	with	ADP
ejpam-6979	1	43	lommel	lommel	PROPN
ejpam-6979	1	44	function	function	PROPN
ejpam-6979	1	45	ekram	ekram	PROPN
ejpam-6979	1	46	e.	e.	PROPN
ejpam-6979	1	47	ali1	ali1	PROPN
ejpam-6979	1	48	,	,	PUNCT
ejpam-6979	1	49	*	*	PUNCT
ejpam-6979	1	50	,	,	PUNCT
ejpam-6979	1	51	rabha	rabha	ADJ
ejpam-6979	1	52	m.	m.	PROPN
ejpam-6979	1	53	el	el	PROPN
ejpam-6979	1	54	-	-	PROPN
ejpam-6979	1	55	ashwah2	ashwah2	PROPN
ejpam-6979	1	56	,	,	PUNCT
ejpam-6979	1	57	altaf	altaf	PROPN
ejpam-6979	1	58	alshuhail1	alshuhail1	PROPN
ejpam-6979	1	59	,	,	PUNCT
ejpam-6979	1	60	maryam	maryam	PROPN
ejpam-6979	1	61	f.	f.	PROPN
ejpam-6979	1	62	alshammari1	alshammari1	PROPN
ejpam-6979	2	1	1	1	NUM
ejpam-6979	2	2	department	department	NOUN
ejpam-6979	2	3	of	of	ADP
ejpam-6979	2	4	mathematics	mathematic	NOUN
ejpam-6979	2	5	,	,	PUNCT
ejpam-6979	2	6	college	college	NOUN
ejpam-6979	2	7	of	of	ADP
ejpam-6979	2	8	science	science	NOUN
ejpam-6979	2	9	,	,	PUNCT
ejpam-6979	2	10	university	university	NOUN
ejpam-6979	2	11	of	of	ADP
ejpam-6979	2	12	ha’il	ha’il	PROPN
ejpam-6979	2	13	,	,	PUNCT
ejpam-6979	2	14	ha’il	ha’il	PROPN
ejpam-6979	2	15	81451	81451	NUM
ejpam-6979	2	16	,	,	PUNCT
ejpam-6979	2	17	saudi	saudi	PROPN
ejpam-6979	2	18	arabia	arabia	PROPN
ejpam-6979	2	19	2	2	NUM
ejpam-6979	2	20	department	department	NOUN
ejpam-6979	2	21	of	of	ADP
ejpam-6979	2	22	mathematics	mathematic	NOUN
ejpam-6979	2	23	,	,	PUNCT
ejpam-6979	2	24	faculty	faculty	NOUN
ejpam-6979	2	25	of	of	ADP
ejpam-6979	2	26	science	science	NOUN
ejpam-6979	2	27	,	,	PUNCT
ejpam-6979	2	28	damietta	damietta	PROPN
ejpam-6979	2	29	university	university	PROPN
ejpam-6979	2	30	,	,	PUNCT
ejpam-6979	2	31	new	new	PROPN
ejpam-6979	2	32	damietta	damietta	PROPN
ejpam-6979	2	33	34517	34517	NUM
ejpam-6979	2	34	,	,	PUNCT
ejpam-6979	2	35	egypt	egypt	PROPN
ejpam-6979	2	36	abstract	abstract	PROPN
ejpam-6979	2	37	.	.	PUNCT
ejpam-6979	3	1	the	the	DET
ejpam-6979	3	2	findings	finding	NOUN
ejpam-6979	3	3	of	of	ADP
ejpam-6979	3	4	this	this	DET
ejpam-6979	3	5	study	study	NOUN
ejpam-6979	3	6	are	be	AUX
ejpam-6979	3	7	connected	connect	VERB
ejpam-6979	3	8	with	with	ADP
ejpam-6979	3	9	geometric	geometric	ADJ
ejpam-6979	3	10	function	function	NOUN
ejpam-6979	3	11	theory	theory	NOUN
ejpam-6979	3	12	and	and	CCONJ
ejpam-6979	3	13	were	be	AUX
ejpam-6979	3	14	acquired	acquire	VERB
ejpam-6979	3	15	by	by	ADP
ejpam-6979	3	16	using	use	VERB
ejpam-6979	3	17	fuzzy	fuzzy	ADJ
ejpam-6979	3	18	subordination	subordination	NOUN
ejpam-6979	3	19	-	-	PUNCT
ejpam-6979	3	20	based	base	VERB
ejpam-6979	3	21	techniques	technique	NOUN
ejpam-6979	3	22	in	in	ADP
ejpam-6979	3	23	conjunction	conjunction	NOUN
ejpam-6979	3	24	with	with	ADP
ejpam-6979	3	25	the	the	DET
ejpam-6979	3	26	convolution	convolution	NOUN
ejpam-6979	3	27	concept	concept	NOUN
ejpam-6979	3	28	and	and	CCONJ
ejpam-6979	3	29	lommel	lommel	NOUN
ejpam-6979	3	30	function	function	NOUN
ejpam-6979	3	31	lmn	lmn	PROPN
ejpam-6979	3	32	,	,	PUNCT
ejpam-6979	3	33	v.	v.	ADP
ejpam-6979	3	34	the	the	DET
ejpam-6979	3	35	first	first	ADJ
ejpam-6979	3	36	class	class	NOUN
ejpam-6979	3	37	introduced	introduce	VERB
ejpam-6979	3	38	and	and	CCONJ
ejpam-6979	3	39	investigated	investigate	VERB
ejpam-6979	3	40	here	here	ADV
ejpam-6979	3	41	is	be	AUX
ejpam-6979	3	42	a	a	DET
ejpam-6979	3	43	generalized	generalized	ADJ
ejpam-6979	3	44	class	class	NOUN
ejpam-6979	3	45	of	of	ADP
ejpam-6979	3	46	analytic	analytic	ADJ
ejpam-6979	3	47	functions	function	NOUN
ejpam-6979	3	48	.	.	PUNCT
ejpam-6979	4	1	it	it	PRON
ejpam-6979	4	2	is	be	AUX
ejpam-6979	4	3	also	also	ADV
ejpam-6979	4	4	shown	show	VERB
ejpam-6979	4	5	that	that	SCONJ
ejpam-6979	4	6	for	for	ADP
ejpam-6979	4	7	particular	particular	ADJ
ejpam-6979	4	8	choice	choice	NOUN
ejpam-6979	4	9	of	of	ADP
ejpam-6979	4	10	parameters	parameter	NOUN
ejpam-6979	4	11	for	for	ADP
ejpam-6979	4	12	the	the	DET
ejpam-6979	4	13	new	new	ADJ
ejpam-6979	4	14	generalized	generalized	ADJ
ejpam-6979	4	15	class	class	NOUN
ejpam-6979	4	16	,	,	PUNCT
ejpam-6979	4	17	the	the	DET
ejpam-6979	4	18	class	class	NOUN
ejpam-6979	4	19	of	of	ADP
ejpam-6979	4	20	close	close	NOUN
ejpam-6979	4	21	-	-	PUNCT
ejpam-6979	4	22	to	to	ADP
ejpam-6979	4	23	-	-	PUNCT
ejpam-6979	4	24	convex	convex	NOUN
ejpam-6979	4	25	functions	function	NOUN
ejpam-6979	4	26	emerges	emerge	VERB
ejpam-6979	4	27	.	.	PUNCT
ejpam-6979	5	1	using	use	VERB
ejpam-6979	5	2	the	the	DET
ejpam-6979	5	3	properties	property	NOUN
ejpam-6979	5	4	of	of	ADP
ejpam-6979	5	5	the	the	DET
ejpam-6979	5	6	convolution	convolution	NOUN
ejpam-6979	5	7	and	and	CCONJ
ejpam-6979	5	8	subordination	subordination	NOUN
ejpam-6979	5	9	,	,	PUNCT
ejpam-6979	5	10	certain	certain	ADJ
ejpam-6979	5	11	characterization	characterization	NOUN
ejpam-6979	5	12	properties	property	NOUN
ejpam-6979	5	13	of	of	ADP
ejpam-6979	5	14	this	this	DET
ejpam-6979	5	15	class	class	NOUN
ejpam-6979	5	16	are	be	AUX
ejpam-6979	5	17	proved	prove	VERB
ejpam-6979	5	18	involving	involve	VERB
ejpam-6979	5	19	combinations	combination	NOUN
ejpam-6979	5	20	of	of	ADP
ejpam-6979	5	21	the	the	DET
ejpam-6979	5	22	functions	function	NOUN
ejpam-6979	5	23	from	from	ADP
ejpam-6979	5	24	the	the	DET
ejpam-6979	5	25	class	class	NOUN
ejpam-6979	5	26	.	.	PUNCT
ejpam-6979	6	1	further	far	ADV
ejpam-6979	6	2	,	,	PUNCT
ejpam-6979	6	3	three	three	NUM
ejpam-6979	6	4	more	more	ADJ
ejpam-6979	6	5	classes	class	NOUN
ejpam-6979	6	6	are	be	AUX
ejpam-6979	6	7	defined	define	VERB
ejpam-6979	6	8	in	in	ADP
ejpam-6979	6	9	connection	connection	NOUN
ejpam-6979	6	10	to	to	ADP
ejpam-6979	6	11	this	this	DET
ejpam-6979	6	12	first	first	ADJ
ejpam-6979	6	13	class	class	NOUN
ejpam-6979	6	14	,	,	PUNCT
ejpam-6979	6	15	developing	develop	VERB
ejpam-6979	6	16	new	new	ADJ
ejpam-6979	6	17	applications	application	NOUN
ejpam-6979	6	18	of	of	ADP
ejpam-6979	6	19	lommel	lommel	ADJ
ejpam-6979	6	20	function	function	NOUN
ejpam-6979	6	21	by	by	ADP
ejpam-6979	6	22	using	use	VERB
ejpam-6979	6	23	the	the	DET
ejpam-6979	6	24	fuzzy	fuzzy	ADJ
ejpam-6979	6	25	subordination	subordination	NOUN
ejpam-6979	6	26	technique	technique	NOUN
ejpam-6979	6	27	and	and	CCONJ
ejpam-6979	6	28	convolutions	convolution	NOUN
ejpam-6979	6	29	.	.	PUNCT
ejpam-6979	7	1	2020	2020	NUM
ejpam-6979	7	2	mathematics	mathematic	NOUN
ejpam-6979	7	3	subject	subject	NOUN
ejpam-6979	7	4	classifications	classification	NOUN
ejpam-6979	7	5	:	:	PUNCT
ejpam-6979	7	6	30c45	30c45	NUM
ejpam-6979	7	7	,	,	PUNCT
ejpam-6979	7	8	30c80	30c80	NUM
ejpam-6979	7	9	key	key	ADJ
ejpam-6979	7	10	words	word	NOUN
ejpam-6979	7	11	and	and	CCONJ
ejpam-6979	7	12	phrases	phrase	NOUN
ejpam-6979	7	13	:	:	PUNCT
ejpam-6979	7	14	analytic	analytic	ADJ
ejpam-6979	7	15	function	function	NOUN
ejpam-6979	7	16	,	,	PUNCT
ejpam-6979	7	17	fuzzy	fuzzy	ADJ
ejpam-6979	7	18	set	set	NOUN
ejpam-6979	7	19	,	,	PUNCT
ejpam-6979	7	20	differential	differential	ADJ
ejpam-6979	7	21	subordination	subordination	NOUN
ejpam-6979	7	22	,	,	PUNCT
ejpam-6979	7	23	lommel	lommel	PROPN
ejpam-6979	7	24	function	function	NOUN
ejpam-6979	7	25	1	1	NUM
ejpam-6979	7	26	.	.	PUNCT
ejpam-6979	7	27	introduction	introduction	NOUN
ejpam-6979	7	28	lotfi	lotfi	PROPN
ejpam-6979	7	29	a.	a.	PROPN
ejpam-6979	7	30	zadeh	zadeh	PROPN
ejpam-6979	8	1	[	[	X
ejpam-6979	8	2	1	1	X
ejpam-6979	8	3	]	]	PUNCT
ejpam-6979	8	4	established	establish	VERB
ejpam-6979	8	5	the	the	DET
ejpam-6979	8	6	foundations	foundation	NOUN
ejpam-6979	8	7	of	of	ADP
ejpam-6979	8	8	fuzzy	fuzzy	ADJ
ejpam-6979	8	9	set	set	NOUN
ejpam-6979	8	10	theory	theory	NOUN
ejpam-6979	8	11	,	,	PUNCT
ejpam-6979	8	12	which	which	PRON
ejpam-6979	8	13	has	have	AUX
ejpam-6979	8	14	since	since	SCONJ
ejpam-6979	8	15	become	become	VERB
ejpam-6979	8	16	a	a	DET
ejpam-6979	8	17	central	central	ADJ
ejpam-6979	8	18	tool	tool	NOUN
ejpam-6979	8	19	for	for	ADP
ejpam-6979	8	20	handling	handle	VERB
ejpam-6979	8	21	uncertainty	uncertainty	NOUN
ejpam-6979	8	22	in	in	ADP
ejpam-6979	8	23	mathematical	mathematical	ADJ
ejpam-6979	8	24	analysis	analysis	NOUN
ejpam-6979	8	25	.	.	PUNCT
ejpam-6979	9	1	the	the	DET
ejpam-6979	9	2	study	study	NOUN
ejpam-6979	9	3	of	of	ADP
ejpam-6979	9	4	geometric	geometric	ADJ
ejpam-6979	9	5	function	function	NOUN
ejpam-6979	9	6	theory	theory	NOUN
ejpam-6979	9	7	(	(	PUNCT
ejpam-6979	9	8	gft	gft	PROPN
ejpam-6979	9	9	)	)	PUNCT
ejpam-6979	9	10	has	have	AUX
ejpam-6979	9	11	benefited	benefit	VERB
ejpam-6979	9	12	from	from	ADP
ejpam-6979	9	13	the	the	DET
ejpam-6979	9	14	contributions	contribution	NOUN
ejpam-6979	9	15	of	of	ADP
ejpam-6979	9	16	fuzzy	fuzzy	ADJ
ejpam-6979	9	17	set	set	NOUN
ejpam-6979	9	18	theory	theory	NOUN
ejpam-6979	9	19	and	and	CCONJ
ejpam-6979	9	20	complex	complex	ADJ
ejpam-6979	9	21	analysis	analysis	NOUN
ejpam-6979	9	22	since	since	SCONJ
ejpam-6979	9	23	the	the	DET
ejpam-6979	9	24	first	first	ADJ
ejpam-6979	9	25	work	work	NOUN
ejpam-6979	9	26	introducing	introduce	VERB
ejpam-6979	9	27	the	the	DET
ejpam-6979	9	28	idea	idea	NOUN
ejpam-6979	9	29	of	of	ADP
ejpam-6979	9	30	subordination	subordination	NOUN
ejpam-6979	9	31	in	in	ADP
ejpam-6979	9	32	fuzzy	fuzzy	ADJ
ejpam-6979	9	33	set	set	NOUN
ejpam-6979	9	34	theory	theory	NOUN
ejpam-6979	9	35	was	be	AUX
ejpam-6979	9	36	published	publish	VERB
ejpam-6979	9	37	in	in	ADP
ejpam-6979	9	38	2011	2011	NUM
ejpam-6979	10	1	[	[	X
ejpam-6979	10	2	2	2	NUM
ejpam-6979	10	3	]	]	PUNCT
ejpam-6979	10	4	.	.	PUNCT
ejpam-6979	11	1	miller	miller	PROPN
ejpam-6979	11	2	and	and	CCONJ
ejpam-6979	11	3	mocanu	mocanu	PROPN
ejpam-6979	11	4	’s	’s	PART
ejpam-6979	11	5	traditional	traditional	ADJ
ejpam-6979	11	6	qualities	quality	NOUN
ejpam-6979	11	7	of	of	ADP
ejpam-6979	11	8	subordination	subordination	NOUN
ejpam-6979	11	9	[	[	X
ejpam-6979	11	10	3	3	NUM
ejpam-6979	11	11	,	,	PUNCT
ejpam-6979	11	12	4	4	NUM
ejpam-6979	11	13	]	]	PUNCT
ejpam-6979	11	14	served	serve	VERB
ejpam-6979	11	15	as	as	ADP
ejpam-6979	11	16	the	the	DET
ejpam-6979	11	17	inspiration	inspiration	NOUN
ejpam-6979	11	18	for	for	ADP
ejpam-6979	11	19	this	this	DET
ejpam-6979	11	20	concept	concept	NOUN
ejpam-6979	11	21	.	.	PUNCT
ejpam-6979	12	1	later	later	ADJ
ejpam-6979	12	2	papers	paper	NOUN
ejpam-6979	12	3	that	that	PRON
ejpam-6979	12	4	studied	study	VERB
ejpam-6979	12	5	fuzzy	fuzzy	ADJ
ejpam-6979	12	6	differential	differential	NOUN
ejpam-6979	12	7	subordination	subordination	NOUN
ejpam-6979	12	8	,	,	PUNCT
ejpam-6979	12	9	which	which	PRON
ejpam-6979	12	10	included	include	VERB
ejpam-6979	12	11	components	component	NOUN
ejpam-6979	12	12	from	from	ADP
ejpam-6979	12	13	the	the	DET
ejpam-6979	12	14	previously	previously	ADV
ejpam-6979	12	15	established	establish	VERB
ejpam-6979	12	16	theory	theory	NOUN
ejpam-6979	12	17	of	of	ADP
ejpam-6979	12	18	differential	differential	ADJ
ejpam-6979	12	19	subordination	subordination	NOUN
ejpam-6979	13	1	[	[	X
ejpam-6979	13	2	5–7	5–7	NOUN
ejpam-6979	13	3	]	]	PUNCT
ejpam-6979	13	4	,	,	PUNCT
ejpam-6979	13	5	followed	follow	VERB
ejpam-6979	13	6	the	the	DET
ejpam-6979	13	7	study	study	NOUN
ejpam-6979	13	8	path	path	NOUN
ejpam-6979	13	9	laid	lay	VERB
ejpam-6979	13	10	forth	forth	ADP
ejpam-6979	13	11	by	by	ADP
ejpam-6979	13	12	miller	miller	PROPN
ejpam-6979	13	13	and	and	CCONJ
ejpam-6979	13	14	mocanu	mocanu	PROPN
ejpam-6979	13	15	.	.	PUNCT
ejpam-6979	14	1	the	the	DET
ejpam-6979	14	2	idea	idea	NOUN
ejpam-6979	14	3	was	be	AUX
ejpam-6979	14	4	immediately	immediately	ADV
ejpam-6979	14	5	embraced	embrace	VERB
ejpam-6979	14	6	by	by	ADP
ejpam-6979	14	7	gft	gft	PROPN
ejpam-6979	14	8	researchers	researcher	NOUN
ejpam-6979	14	9	,	,	PUNCT
ejpam-6979	14	10	and	and	CCONJ
ejpam-6979	14	11	all	all	PRON
ejpam-6979	14	12	of	of	ADP
ejpam-6979	14	13	the	the	DET
ejpam-6979	14	14	conventional	conventional	ADJ
ejpam-6979	14	15	research	research	NOUN
ejpam-6979	14	16	paths	path	NOUN
ejpam-6979	14	17	in	in	ADP
ejpam-6979	14	18	this	this	DET
ejpam-6979	14	19	area	area	NOUN
ejpam-6979	14	20	were	be	AUX
ejpam-6979	14	21	changed	change	VERB
ejpam-6979	14	22	to	to	PART
ejpam-6979	14	23	account	account	VERB
ejpam-6979	14	24	for	for	ADP
ejpam-6979	14	25	the	the	DET
ejpam-6979	14	26	novel	novel	ADJ
ejpam-6979	14	27	fuzzy	fuzzy	ADJ
ejpam-6979	14	28	properties	property	NOUN
ejpam-6979	14	29	.	.	PUNCT
ejpam-6979	15	1	an	an	DET
ejpam-6979	15	2	essential	essential	ADJ
ejpam-6979	15	3	area	area	NOUN
ejpam-6979	15	4	of	of	ADP
ejpam-6979	15	5	research	research	NOUN
ejpam-6979	15	6	in	in	ADP
ejpam-6979	15	7	gft	gft	PROPN
ejpam-6979	15	8	is	be	AUX
ejpam-6979	15	9	operator	operator	NOUN
ejpam-6979	15	10	-	-	PUNCT
ejpam-6979	15	11	related	relate	VERB
ejpam-6979	15	12	research	research	NOUN
ejpam-6979	15	13	.	.	PUNCT
ejpam-6979	16	1	shortly	shortly	ADV
ejpam-6979	16	2	after	after	SCONJ
ejpam-6979	16	3	the	the	DET
ejpam-6979	16	4	notion	notion	NOUN
ejpam-6979	16	5	was	be	AUX
ejpam-6979	16	6	launched	launch	VERB
ejpam-6979	16	7	,	,	PUNCT
ejpam-6979	16	8	in	in	ADP
ejpam-6979	16	9	2013	2013	NUM
ejpam-6979	16	10	,	,	PUNCT
ejpam-6979	16	11	such	such	ADJ
ejpam-6979	16	12	experiments	experiment	NOUN
ejpam-6979	16	13	were	be	AUX
ejpam-6979	16	14	published	publish	VERB
ejpam-6979	16	15	to	to	PART
ejpam-6979	16	16	acquire	acquire	VERB
ejpam-6979	16	17	new	new	ADJ
ejpam-6979	16	18	fuzzy	fuzzy	ADJ
ejpam-6979	16	19	subordination	subordination	NOUN
ejpam-6979	16	20	results	result	NOUN
ejpam-6979	16	21	[	[	X
ejpam-6979	16	22	8	8	NUM
ejpam-6979	16	23	]	]	PUNCT
ejpam-6979	16	24	.	.	PUNCT
ejpam-6979	17	1	we	we	PRON
ejpam-6979	17	2	only	only	ADV
ejpam-6979	17	3	highlight	highlight	VERB
ejpam-6979	17	4	a	a	DET
ejpam-6979	17	5	few	few	ADJ
ejpam-6979	17	6	of	of	ADP
ejpam-6979	17	7	the	the	DET
ejpam-6979	17	8	numerous	numerous	ADJ
ejpam-6979	17	9	publications	publication	NOUN
ejpam-6979	17	10	that	that	PRON
ejpam-6979	17	11	have	have	AUX
ejpam-6979	17	12	been	be	AUX
ejpam-6979	17	13	published	publish	VERB
ejpam-6979	17	14	in	in	ADP
ejpam-6979	17	15	the	the	DET
ejpam-6979	17	16	∗corresponding	∗corresponding	NOUN
ejpam-6979	17	17	author	author	NOUN
ejpam-6979	17	18	.	.	PUNCT
ejpam-6979	18	1	doi	doi	NOUN
ejpam-6979	18	2	:	:	PUNCT
ejpam-6979	18	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6979	https://doi.org/10.29020/nybg.ejpam.v18i4.6979	NUM
ejpam-6979	18	4	email	email	NOUN
ejpam-6979	18	5	addresses	address	VERB
ejpam-6979	18	6	:	:	PUNCT
ejpam-6979	18	7	e.ahmad@uoh.edu.sa	e.ahmad@uoh.edu.sa	PROPN
ejpam-6979	18	8	(	(	PUNCT
ejpam-6979	18	9	e.	e.	PROPN
ejpam-6979	18	10	e.	e.	PROPN
ejpam-6979	18	11	ali	ali	PROPN
ejpam-6979	18	12	)	)	PUNCT
ejpam-6979	18	13	,	,	PUNCT
ejpam-6979	18	14	r	r	NOUN
ejpam-6979	18	15	elashwah@yahoo.com	elashwah@yahoo.com	X
ejpam-6979	18	16	(	(	PUNCT
ejpam-6979	18	17	r.	r.	PROPN
ejpam-6979	18	18	m.	m.	PROPN
ejpam-6979	18	19	el	el	PROPN
ejpam-6979	18	20	-	-	PUNCT
ejpam-6979	18	21	ashwah	ashwah	NOUN
ejpam-6979	18	22	)	)	PUNCT
ejpam-6979	18	23	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6979	19	1	1	1	NUM
ejpam-6979	19	2	copyright	copyright	NOUN
ejpam-6979	19	3	:	:	PUNCT
ejpam-6979	19	4	©	©	PROPN
ejpam-6979	19	5	2025	2025	NUM
ejpam-6979	19	6	the	the	DET
ejpam-6979	19	7	author(s	author(s	NOUN
ejpam-6979	19	8	)	)	PUNCT
ejpam-6979	19	9	.	.	PUNCT
ejpam-6979	20	1	(	(	PUNCT
ejpam-6979	20	2	cc	cc	NOUN
ejpam-6979	20	3	by	by	ADP
ejpam-6979	20	4	-	-	PUNCT
ejpam-6979	20	5	nc	nc	PROPN
ejpam-6979	20	6	4.0	4.0	NUM
ejpam-6979	20	7	)	)	PUNCT
ejpam-6979	20	8	e.	e.	PROPN
ejpam-6979	20	9	e.	e.	PROPN
ejpam-6979	20	10	ali	ali	PROPN
ejpam-6979	20	11	et	et	PROPN
ejpam-6979	20	12	al	al	PROPN
ejpam-6979	20	13	.	.	PUNCT
ejpam-6979	20	14	/	/	SYM
ejpam-6979	20	15	eur	eur	PROPN
ejpam-6979	20	16	.	.	PUNCT
ejpam-6979	21	1	j.	j.	PROPN
ejpam-6979	21	2	pure	pure	PROPN
ejpam-6979	21	3	appl	appl	PROPN
ejpam-6979	21	4	.	.	PROPN
ejpam-6979	21	5	math	math	PROPN
ejpam-6979	21	6	,	,	PUNCT
ejpam-6979	21	7	18	18	NUM
ejpam-6979	21	8	(	(	PUNCT
ejpam-6979	21	9	4	4	NUM
ejpam-6979	21	10	)	)	PUNCT
ejpam-6979	21	11	(	(	PUNCT
ejpam-6979	21	12	2025	2025	NUM
ejpam-6979	21	13	)	)	PUNCT
ejpam-6979	21	14	,	,	PUNCT
ejpam-6979	21	15	6979	6979	NUM
ejpam-6979	21	16	2	2	NUM
ejpam-6979	21	17	of	of	ADP
ejpam-6979	21	18	18	18	NUM
ejpam-6979	21	19	past	past	ADP
ejpam-6979	21	20	few	few	ADJ
ejpam-6979	21	21	years	year	NOUN
ejpam-6979	21	22	to	to	PART
ejpam-6979	21	23	demonstrate	demonstrate	VERB
ejpam-6979	21	24	how	how	SCONJ
ejpam-6979	21	25	the	the	DET
ejpam-6979	21	26	body	body	NOUN
ejpam-6979	21	27	of	of	ADP
ejpam-6979	21	28	knowledge	knowledge	NOUN
ejpam-6979	21	29	on	on	ADP
ejpam-6979	21	30	this	this	DET
ejpam-6979	21	31	subject	subject	NOUN
ejpam-6979	21	32	is	be	AUX
ejpam-6979	21	33	constantly	constantly	ADV
ejpam-6979	21	34	growing	grow	VERB
ejpam-6979	21	35	[	[	X
ejpam-6979	21	36	9–16	9–16	NOUN
ejpam-6979	21	37	]	]	PUNCT
ejpam-6979	21	38	.	.	PUNCT
ejpam-6979	22	1	in	in	ADP
ejpam-6979	22	2	a	a	DET
ejpam-6979	22	3	related	related	ADJ
ejpam-6979	22	4	study	study	NOUN
ejpam-6979	22	5	,	,	PUNCT
ejpam-6979	22	6	haydar	haydar	PROPN
ejpam-6979	23	1	[	[	X
ejpam-6979	23	2	17	17	NUM
ejpam-6979	23	3	]	]	PUNCT
ejpam-6979	23	4	extended	extend	VERB
ejpam-6979	23	5	these	these	DET
ejpam-6979	23	6	ideas	idea	NOUN
ejpam-6979	23	7	and	and	CCONJ
ejpam-6979	23	8	derived	derive	VERB
ejpam-6979	23	9	new	new	ADJ
ejpam-6979	23	10	results	result	NOUN
ejpam-6979	23	11	for	for	ADP
ejpam-6979	23	12	fuzzy	fuzzy	ADJ
ejpam-6979	23	13	differential	differential	ADJ
ejpam-6979	23	14	subordinations	subordination	NOUN
ejpam-6979	23	15	,	,	PUNCT
ejpam-6979	23	16	highlighting	highlight	VERB
ejpam-6979	23	17	how	how	SCONJ
ejpam-6979	23	18	the	the	DET
ejpam-6979	23	19	use	use	NOUN
ejpam-6979	23	20	of	of	ADP
ejpam-6979	23	21	diverse	diverse	ADJ
ejpam-6979	23	22	operators	operator	NOUN
ejpam-6979	23	23	enriches	enrich	VERB
ejpam-6979	23	24	the	the	DET
ejpam-6979	23	25	subject	subject	NOUN
ejpam-6979	23	26	.	.	PUNCT
ejpam-6979	24	1	a	a	DET
ejpam-6979	24	2	number	number	NOUN
ejpam-6979	24	3	of	of	ADP
ejpam-6979	24	4	researchers	researcher	NOUN
ejpam-6979	24	5	have	have	AUX
ejpam-6979	24	6	since	since	SCONJ
ejpam-6979	24	7	examined	examine	VERB
ejpam-6979	24	8	linear	linear	PROPN
ejpam-6979	24	9	operators	operator	NOUN
ejpam-6979	24	10	in	in	ADP
ejpam-6979	24	11	this	this	DET
ejpam-6979	24	12	setting	setting	NOUN
ejpam-6979	24	13	,	,	PUNCT
ejpam-6979	24	14	producing	produce	VERB
ejpam-6979	24	15	a	a	DET
ejpam-6979	24	16	wide	wide	ADJ
ejpam-6979	24	17	body	body	NOUN
ejpam-6979	24	18	of	of	ADP
ejpam-6979	24	19	work	work	NOUN
ejpam-6979	24	20	on	on	ADP
ejpam-6979	24	21	fuzzy	fuzzy	ADJ
ejpam-6979	24	22	third	third	ADJ
ejpam-6979	24	23	order	order	NOUN
ejpam-6979	24	24	differential	differential	ADJ
ejpam-6979	24	25	subordination	subordination	NOUN
ejpam-6979	24	26	[	[	X
ejpam-6979	24	27	18	18	NUM
ejpam-6979	24	28	,	,	PUNCT
ejpam-6979	24	29	19	19	NUM
ejpam-6979	24	30	]	]	PUNCT
ejpam-6979	24	31	.	.	PUNCT
ejpam-6979	25	1	these	these	DET
ejpam-6979	25	2	contributions	contribution	NOUN
ejpam-6979	25	3	represent	represent	VERB
ejpam-6979	25	4	the	the	DET
ejpam-6979	25	5	first	first	ADJ
ejpam-6979	25	6	systematic	systematic	ADJ
ejpam-6979	25	7	attempts	attempt	NOUN
ejpam-6979	25	8	to	to	PART
ejpam-6979	25	9	employ	employ	VERB
ejpam-6979	25	10	fuzzy	fuzzy	ADJ
ejpam-6979	25	11	sets	set	NOUN
ejpam-6979	25	12	in	in	ADP
ejpam-6979	25	13	the	the	DET
ejpam-6979	25	14	geometric	geometric	ADJ
ejpam-6979	25	15	theory	theory	NOUN
ejpam-6979	25	16	of	of	ADP
ejpam-6979	25	17	analytic	analytic	ADJ
ejpam-6979	25	18	functions	function	NOUN
ejpam-6979	25	19	.	.	PUNCT
ejpam-6979	26	1	let	let	VERB
ejpam-6979	26	2	a	a	DET
ejpam-6979	26	3	denote	denote	NOUN
ejpam-6979	26	4	the	the	DET
ejpam-6979	26	5	class	class	NOUN
ejpam-6979	26	6	of	of	ADP
ejpam-6979	26	7	function	function	NOUN
ejpam-6979	26	8	satisfying	satisfy	VERB
ejpam-6979	26	9	f(0	f(0	NOUN
ejpam-6979	26	10	)	)	PUNCT
ejpam-6979	27	1	=	=	SYM
ejpam-6979	27	2	f	f	X
ejpam-6979	27	3	′	′	NUM
ejpam-6979	27	4	(	(	PUNCT
ejpam-6979	27	5	0	0	NUM
ejpam-6979	27	6	)	)	PUNCT
ejpam-6979	27	7	−	−	NOUN
ejpam-6979	27	8	1	1	NUM
ejpam-6979	27	9	=	=	SYM
ejpam-6979	27	10	0	0	NUM
ejpam-6979	27	11	written	write	VERB
ejpam-6979	27	12	as	as	ADP
ejpam-6979	27	13	:	:	PUNCT
ejpam-6979	27	14	f	f	PROPN
ejpam-6979	27	15	(	(	PUNCT
ejpam-6979	27	16	ξ	ξ	X
ejpam-6979	27	17	)	)	PUNCT
ejpam-6979	27	18	=	=	SYM
ejpam-6979	27	19	ξ	ξ	PROPN
ejpam-6979	27	20	+	+	PUNCT
ejpam-6979	27	21	∞∑	∞∑	NUM
ejpam-6979	27	22	κ=2	κ=2	NUM
ejpam-6979	27	23	aκξκ	aκξκ	NOUN
ejpam-6979	27	24	.	.	PUNCT
ejpam-6979	28	1	(	(	PUNCT
ejpam-6979	28	2	1	1	X
ejpam-6979	28	3	)	)	PUNCT
ejpam-6979	28	4	which	which	PRON
ejpam-6979	28	5	are	be	AUX
ejpam-6979	28	6	analytic	analytic	ADJ
ejpam-6979	28	7	and	and	CCONJ
ejpam-6979	28	8	univalent	univalent	ADJ
ejpam-6979	28	9	in	in	ADP
ejpam-6979	28	10	the	the	DET
ejpam-6979	28	11	open	open	ADJ
ejpam-6979	28	12	unit	unit	NOUN
ejpam-6979	28	13	disc	disc	VERB
ejpam-6979	28	14	u	u	NOUN
ejpam-6979	28	15	=	=	PUNCT
ejpam-6979	28	16	{	{	PUNCT
ejpam-6979	28	17	ξ	ξ	NOUN
ejpam-6979	28	18	:	:	PUNCT
ejpam-6979	28	19	|ξ|	|ξ|	VERB
ejpam-6979	28	20	<	<	X
ejpam-6979	28	21	1	1	NUM
ejpam-6979	28	22	}	}	PUNCT
ejpam-6979	28	23	.	.	PUNCT
ejpam-6979	29	1	if	if	SCONJ
ejpam-6979	29	2	f	f	PROPN
ejpam-6979	29	3	and	and	CCONJ
ejpam-6979	29	4	g	g	PROPN
ejpam-6979	29	5	are	be	AUX
ejpam-6979	29	6	analytic	analytic	ADJ
ejpam-6979	29	7	in	in	ADP
ejpam-6979	29	8	u	u	PROPN
ejpam-6979	29	9	,	,	PUNCT
ejpam-6979	29	10	f	f	PROPN
ejpam-6979	29	11	is	be	AUX
ejpam-6979	29	12	subordinate	subordinate	ADJ
ejpam-6979	29	13	to	to	ADP
ejpam-6979	29	14	g	g	NOUN
ejpam-6979	29	15	,	,	PUNCT
ejpam-6979	29	16	denoted	denote	VERB
ejpam-6979	29	17	f(ξ	f(ξ	NOUN
ejpam-6979	29	18	)	)	PUNCT
ejpam-6979	29	19	≺	≺	NOUN
ejpam-6979	29	20	g(ξ	g(ξ	PROPN
ejpam-6979	29	21	)	)	PUNCT
ejpam-6979	29	22	,	,	PUNCT
ejpam-6979	29	23	if	if	SCONJ
ejpam-6979	29	24	there	there	PRON
ejpam-6979	29	25	exists	exist	VERB
ejpam-6979	29	26	an	an	DET
ejpam-6979	29	27	analytic	analytic	ADJ
ejpam-6979	29	28	function	function	NOUN
ejpam-6979	29	29	ϖ	ϖ	NOUN
ejpam-6979	29	30	,	,	PUNCT
ejpam-6979	29	31	with	with	ADP
ejpam-6979	29	32	ϖ(0	ϖ(0	NOUN
ejpam-6979	29	33	)	)	PUNCT
ejpam-6979	29	34	=	=	SYM
ejpam-6979	29	35	0	0	NUM
ejpam-6979	29	36	and	and	CCONJ
ejpam-6979	29	37	|ϖ(ξ)|	|ϖ(ξ)|	NOUN
ejpam-6979	29	38	<	<	X
ejpam-6979	29	39	1	1	NUM
ejpam-6979	29	40	for	for	ADP
ejpam-6979	29	41	all	all	DET
ejpam-6979	29	42	ξ	ξ	PROPN
ejpam-6979	29	43	∈	∈	PROPN
ejpam-6979	29	44	u	u	NOUN
ejpam-6979	29	45	,	,	PUNCT
ejpam-6979	29	46	such	such	ADJ
ejpam-6979	29	47	that	that	SCONJ
ejpam-6979	29	48	f(ξ	f(ξ	NOUN
ejpam-6979	29	49	)	)	PUNCT
ejpam-6979	29	50	=	=	SYM
ejpam-6979	29	51	g(ϖ(ξ	g(ϖ(ξ	NOUN
ejpam-6979	29	52	)	)	PUNCT
ejpam-6979	29	53	)	)	PUNCT
ejpam-6979	29	54	,	,	PUNCT
ejpam-6979	29	55	ξ	ξ	X
ejpam-6979	29	56	∈	∈	PROPN
ejpam-6979	29	57	u.	u.	VERB
ejpam-6979	29	58	if	if	SCONJ
ejpam-6979	29	59	the	the	DET
ejpam-6979	29	60	function	function	NOUN
ejpam-6979	29	61	g	g	PROPN
ejpam-6979	29	62	is	be	AUX
ejpam-6979	29	63	univalent	univalent	ADJ
ejpam-6979	29	64	inu	inu	NOUN
ejpam-6979	29	65	,	,	PUNCT
ejpam-6979	29	66	f(ξ	f(ξ	PROPN
ejpam-6979	29	67	)	)	PUNCT
ejpam-6979	29	68	≺g(ξ	≺g(ξ	PROPN
ejpam-6979	29	69	)	)	PUNCT
ejpam-6979	29	70	is	be	AUX
ejpam-6979	29	71	given	give	VERB
ejpam-6979	29	72	as	as	ADP
ejpam-6979	29	73	(	(	PUNCT
ejpam-6979	29	74	see	see	VERB
ejpam-6979	29	75	[	[	X
ejpam-6979	29	76	4	4	NUM
ejpam-6979	29	77	,	,	PUNCT
ejpam-6979	29	78	20	20	NUM
ejpam-6979	29	79	,	,	PUNCT
ejpam-6979	29	80	21	21	NUM
ejpam-6979	29	81	]	]	PUNCT
ejpam-6979	29	82	):	):	PUNCT
ejpam-6979	29	83	f	f	PROPN
ejpam-6979	29	84	(	(	PUNCT
ejpam-6979	29	85	0	0	NUM
ejpam-6979	29	86	)	)	PUNCT
ejpam-6979	29	87	=	=	SYM
ejpam-6979	29	88	g(0	g(0	PROPN
ejpam-6979	29	89	)	)	PUNCT
ejpam-6979	29	90	and	and	CCONJ
ejpam-6979	29	91	f	f	PROPN
ejpam-6979	29	92	(	(	PUNCT
ejpam-6979	29	93	u	u	NOUN
ejpam-6979	29	94	)	)	PUNCT
ejpam-6979	29	95	⊂	⊂	PROPN
ejpam-6979	29	96	g(u	g(u	PROPN
ejpam-6979	29	97	)	)	PUNCT
ejpam-6979	29	98	.	.	PUNCT
ejpam-6979	30	1	for	for	ADP
ejpam-6979	30	2	two	two	NUM
ejpam-6979	30	3	functions	function	NOUN
ejpam-6979	30	4	fι(ξ	fι(ξ	PUNCT
ejpam-6979	30	5	)	)	PUNCT
ejpam-6979	30	6	∈	∈	PROPN
ejpam-6979	30	7	a(ι	a(ι	PROPN
ejpam-6979	30	8	=	=	SYM
ejpam-6979	30	9	1	1	NUM
ejpam-6979	30	10	,	,	PUNCT
ejpam-6979	30	11	2	2	NUM
ejpam-6979	30	12	)	)	PUNCT
ejpam-6979	30	13	are	be	AUX
ejpam-6979	30	14	given	give	VERB
ejpam-6979	30	15	by	by	ADP
ejpam-6979	30	16	fι(ξ	fι(ξ	PRON
ejpam-6979	30	17	)	)	PUNCT
ejpam-6979	30	18	=	=	SYM
ejpam-6979	31	1	ξ	ξ	X
ejpam-6979	32	1	+	+	PUNCT
ejpam-6979	33	1	∞∑	∞∑	NUM
ejpam-6979	33	2	κ=2	κ=2	PUNCT
ejpam-6979	33	3	aκ	aκ	INTJ
ejpam-6979	33	4	,	,	PUNCT
ejpam-6979	33	5	ιξκ	ιξκ	INTJ
ejpam-6979	33	6	,	,	PUNCT
ejpam-6979	33	7	we	we	PRON
ejpam-6979	33	8	define	define	VERB
ejpam-6979	33	9	the	the	DET
ejpam-6979	33	10	convolution	convolution	NOUN
ejpam-6979	33	11	of	of	ADP
ejpam-6979	33	12	f1(ξ	f1(ξ	NOUN
ejpam-6979	33	13	)	)	PUNCT
ejpam-6979	33	14	and	and	CCONJ
ejpam-6979	33	15	f2(ξ	f2(ξ	NUM
ejpam-6979	33	16	)	)	PUNCT
ejpam-6979	33	17	as	as	ADP
ejpam-6979	33	18	(	(	PUNCT
ejpam-6979	33	19	f1	f1	PROPN
ejpam-6979	33	20	∗	∗	NOUN
ejpam-6979	33	21	f2)(ξ	f2)(ξ	NOUN
ejpam-6979	33	22	)	)	PUNCT
ejpam-6979	33	23	=	=	SYM
ejpam-6979	34	1	ξ	ξ	PROPN
ejpam-6979	34	2	+	+	PUNCT
ejpam-6979	34	3	∞∑	∞∑	NUM
ejpam-6979	34	4	κ=2	κ=2	NUM
ejpam-6979	34	5	aκ,1aκ,2ξκ	aκ,1aκ,2ξκ	NOUN
ejpam-6979	34	6	=	=	SYM
ejpam-6979	34	7	(	(	PUNCT
ejpam-6979	34	8	f2	f2	X
ejpam-6979	34	9	∗	∗	VERB
ejpam-6979	34	10	f1)(ξ	f1)(ξ	PROPN
ejpam-6979	34	11	)	)	PUNCT
ejpam-6979	34	12	.	.	PUNCT
ejpam-6979	35	1	the	the	DET
ejpam-6979	35	2	lommel	lommel	PROPN
ejpam-6979	35	3	function	function	NOUN
ejpam-6979	35	4	is	be	AUX
ejpam-6979	35	5	a	a	DET
ejpam-6979	35	6	special	special	ADJ
ejpam-6979	35	7	type	type	NOUN
ejpam-6979	35	8	of	of	ADP
ejpam-6979	35	9	mathematical	mathematical	ADJ
ejpam-6979	35	10	function	function	NOUN
ejpam-6979	35	11	that	that	PRON
ejpam-6979	35	12	arises	arise	VERB
ejpam-6979	35	13	in	in	ADP
ejpam-6979	35	14	various	various	ADJ
ejpam-6979	35	15	areas	area	NOUN
ejpam-6979	35	16	of	of	ADP
ejpam-6979	35	17	applied	apply	VERB
ejpam-6979	35	18	mathematics	mathematic	NOUN
ejpam-6979	35	19	and	and	CCONJ
ejpam-6979	35	20	physics	physics	NOUN
ejpam-6979	35	21	.	.	PUNCT
ejpam-6979	36	1	it	it	PRON
ejpam-6979	36	2	is	be	AUX
ejpam-6979	36	3	often	often	ADV
ejpam-6979	36	4	encountered	encounter	VERB
ejpam-6979	36	5	in	in	ADP
ejpam-6979	36	6	problems	problem	NOUN
ejpam-6979	36	7	involving	involve	VERB
ejpam-6979	36	8	wave	wave	NOUN
ejpam-6979	36	9	propagation	propagation	NOUN
ejpam-6979	36	10	,	,	PUNCT
ejpam-6979	36	11	optics	optic	NOUN
ejpam-6979	36	12	,	,	PUNCT
ejpam-6979	36	13	and	and	CCONJ
ejpam-6979	36	14	acoustics	acoustic	NOUN
ejpam-6979	36	15	,	,	PUNCT
ejpam-6979	36	16	particularly	particularly	ADV
ejpam-6979	36	17	when	when	SCONJ
ejpam-6979	36	18	dealing	deal	VERB
ejpam-6979	36	19	with	with	ADP
ejpam-6979	36	20	cylindrical	cylindrical	ADJ
ejpam-6979	36	21	geometries	geometry	NOUN
ejpam-6979	36	22	.	.	PUNCT
ejpam-6979	37	1	the	the	DET
ejpam-6979	37	2	lommel	lommel	PROPN
ejpam-6979	37	3	functions	function	NOUN
ejpam-6979	37	4	are	be	AUX
ejpam-6979	37	5	solutions	solution	NOUN
ejpam-6979	37	6	to	to	ADP
ejpam-6979	37	7	a	a	DET
ejpam-6979	37	8	specific	specific	ADJ
ejpam-6979	37	9	type	type	NOUN
ejpam-6979	37	10	of	of	ADP
ejpam-6979	37	11	differential	differential	ADJ
ejpam-6979	37	12	equation	equation	NOUN
ejpam-6979	37	13	,	,	PUNCT
ejpam-6979	37	14	known	know	VERB
ejpam-6979	37	15	as	as	ADP
ejpam-6979	37	16	bessel	bessel	NOUN
ejpam-6979	37	17	’s	’s	PART
ejpam-6979	37	18	differential	differential	ADJ
ejpam-6979	37	19	equation	equation	NOUN
ejpam-6979	37	20	,	,	PUNCT
ejpam-6979	37	21	which	which	PRON
ejpam-6979	37	22	describes	describe	VERB
ejpam-6979	37	23	the	the	DET
ejpam-6979	37	24	behavior	behavior	NOUN
ejpam-6979	37	25	of	of	ADP
ejpam-6979	37	26	waves	wave	NOUN
ejpam-6979	37	27	in	in	ADP
ejpam-6979	37	28	cylindrical	cylindrical	ADJ
ejpam-6979	37	29	coordinates	coordinate	NOUN
ejpam-6979	37	30	.	.	PUNCT
ejpam-6979	38	1	these	these	DET
ejpam-6979	38	2	functions	function	NOUN
ejpam-6979	38	3	are	be	AUX
ejpam-6979	38	4	particularly	particularly	ADV
ejpam-6979	38	5	valuable	valuable	ADJ
ejpam-6979	38	6	because	because	SCONJ
ejpam-6979	38	7	they	they	PRON
ejpam-6979	38	8	allow	allow	VERB
ejpam-6979	38	9	for	for	ADP
ejpam-6979	38	10	the	the	DET
ejpam-6979	38	11	representation	representation	NOUN
ejpam-6979	38	12	of	of	ADP
ejpam-6979	38	13	waveforms	waveform	NOUN
ejpam-6979	38	14	that	that	PRON
ejpam-6979	38	15	are	be	AUX
ejpam-6979	38	16	not	not	PART
ejpam-6979	38	17	easily	easily	ADV
ejpam-6979	38	18	handled	handle	VERB
ejpam-6979	38	19	by	by	ADP
ejpam-6979	38	20	simpler	simple	ADJ
ejpam-6979	38	21	functions	function	NOUN
ejpam-6979	38	22	,	,	PUNCT
ejpam-6979	38	23	thus	thus	ADV
ejpam-6979	38	24	providing	provide	VERB
ejpam-6979	38	25	more	more	ADV
ejpam-6979	38	26	accurate	accurate	ADJ
ejpam-6979	38	27	models	model	NOUN
ejpam-6979	38	28	in	in	ADP
ejpam-6979	38	29	physical	physical	ADJ
ejpam-6979	38	30	applications	application	NOUN
ejpam-6979	38	31	.	.	PUNCT
ejpam-6979	39	1	geometric	geometric	ADJ
ejpam-6979	39	2	properties	property	NOUN
ejpam-6979	39	3	of	of	ADP
ejpam-6979	39	4	several	several	ADJ
ejpam-6979	39	5	families	family	NOUN
ejpam-6979	39	6	of	of	ADP
ejpam-6979	39	7	special	special	ADJ
ejpam-6979	39	8	functions	function	NOUN
ejpam-6979	39	9	are	be	AUX
ejpam-6979	39	10	discussed	discuss	VERB
ejpam-6979	39	11	in	in	ADP
ejpam-6979	39	12	many	many	ADJ
ejpam-6979	39	13	articles	article	NOUN
ejpam-6979	39	14	,	,	PUNCT
ejpam-6979	39	15	especially	especially	ADV
ejpam-6979	39	16	the	the	DET
ejpam-6979	39	17	bessel	bessel	ADJ
ejpam-6979	39	18	functions	function	NOUN
ejpam-6979	39	19	(	(	PUNCT
ejpam-6979	39	20	see	see	VERB
ejpam-6979	39	21	[	[	X
ejpam-6979	39	22	22–25	22–25	NUM
ejpam-6979	39	23	]	]	PUNCT
ejpam-6979	39	24	)	)	PUNCT
ejpam-6979	39	25	and	and	CCONJ
ejpam-6979	39	26	the	the	DET
ejpam-6979	39	27	generalized	generalized	ADJ
ejpam-6979	39	28	hypergeometric	hypergeometric	ADJ
ejpam-6979	39	29	functions	function	NOUN
ejpam-6979	39	30	(	(	PUNCT
ejpam-6979	39	31	see	see	VERB
ejpam-6979	39	32	[	[	X
ejpam-6979	39	33	26–29	26–29	NOUN
ejpam-6979	39	34	]	]	X
ejpam-6979	39	35	)	)	PUNCT
ejpam-6979	39	36	.	.	PUNCT
ejpam-6979	40	1	the	the	DET
ejpam-6979	40	2	theory	theory	NOUN
ejpam-6979	40	3	of	of	ADP
ejpam-6979	40	4	bessel	bessel	NOUN
ejpam-6979	40	5	functions	function	NOUN
ejpam-6979	40	6	contains	contain	VERB
ejpam-6979	40	7	the	the	DET
ejpam-6979	40	8	first	first	ADJ
ejpam-6979	40	9	and	and	CCONJ
ejpam-6979	40	10	second	second	ADJ
ejpam-6979	40	11	class	class	NOUN
ejpam-6979	40	12	lommel	lommel	NOUN
ejpam-6979	40	13	functions	function	NOUN
ejpam-6979	40	14	as	as	ADP
ejpam-6979	40	15	specific	specific	ADJ
ejpam-6979	40	16	solutions	solution	NOUN
ejpam-6979	40	17	of	of	ADP
ejpam-6979	40	18	certain	certain	ADJ
ejpam-6979	40	19	second	second	ADJ
ejpam-6979	40	20	-	-	PUNCT
ejpam-6979	40	21	order	order	NOUN
ejpam-6979	40	22	differential	differential	ADJ
ejpam-6979	40	23	equations	equation	NOUN
ejpam-6979	41	1	[	[	X
ejpam-6979	41	2	30–32	30–32	NUM
ejpam-6979	41	3	]	]	PUNCT
ejpam-6979	41	4	.	.	PUNCT
ejpam-6979	42	1	we	we	PRON
ejpam-6979	42	2	now	now	ADV
ejpam-6979	42	3	review	review	VERB
ejpam-6979	42	4	the	the	DET
ejpam-6979	42	5	lommel	lommel	PROPN
ejpam-6979	42	6	function	function	NOUN
ejpam-6979	42	7	,	,	PUNCT
ejpam-6979	42	8	which	which	PRON
ejpam-6979	42	9	is	be	AUX
ejpam-6979	42	10	represented	represent	VERB
ejpam-6979	42	11	by	by	ADP
ejpam-6979	42	12	lρ	lρ	INTJ
ejpam-6979	42	13	,	,	PUNCT
ejpam-6979	42	14	ν(ξ	ν(ξ	PROPN
ejpam-6979	42	15	)	)	PUNCT
ejpam-6979	42	16	and	and	CCONJ
ejpam-6979	42	17	provided	provide	VERB
ejpam-6979	42	18	by	by	ADP
ejpam-6979	42	19	lρ	lρ	INTJ
ejpam-6979	42	20	,	,	PUNCT
ejpam-6979	42	21	ν(ξ	ν(ξ	PROPN
ejpam-6979	42	22	)	)	PUNCT
ejpam-6979	42	23	=	=	SYM
ejpam-6979	43	1	ξρ+1	ξρ+1	NUM
ejpam-6979	43	2	4	4	NUM
ejpam-6979	43	3	∞∑	∞∑	NUM
ejpam-6979	43	4	κ=0	κ=0	ADJ
ejpam-6979	43	5	(	(	PUNCT
ejpam-6979	43	6	−1)κ	−1)κ	X
ejpam-6979	43	7	γ	γ	X
ejpam-6979	43	8	(	(	PUNCT
ejpam-6979	43	9	ρ−ν+1	ρ−ν+1	PROPN
ejpam-6979	43	10	2	2	NUM
ejpam-6979	43	11	)	)	PUNCT
ejpam-6979	43	12	γ	γ	NOUN
ejpam-6979	43	13	(	(	PUNCT
ejpam-6979	43	14	ρ+ν+1	ρ+ν+1	NOUN
ejpam-6979	43	15	2	2	NUM
ejpam-6979	43	16	)	)	PUNCT
ejpam-6979	43	17	γ	γ	X
ejpam-6979	43	18	(	(	PUNCT
ejpam-6979	43	19	ρ−ν+3	ρ−ν+3	PROPN
ejpam-6979	43	20	2	2	NUM
ejpam-6979	43	21	+	+	CCONJ
ejpam-6979	43	22	κ	κ	X
ejpam-6979	43	23	)	)	PUNCT
ejpam-6979	43	24	γ	γ	PROPN
ejpam-6979	43	25	(	(	PUNCT
ejpam-6979	43	26	ρ+ν+3	ρ+ν+3	PROPN
ejpam-6979	43	27	2	2	NUM
ejpam-6979	43	28	+	+	SYM
ejpam-6979	43	29	κ	κ	NOUN
ejpam-6979	43	30	)	)	PUNCT
ejpam-6979	43	31	(	(	PUNCT
ejpam-6979	43	32	ξ	ξ	PROPN
ejpam-6979	43	33	2	2	NUM
ejpam-6979	43	34	)	)	PUNCT
ejpam-6979	43	35	2κ	2κ	NOUN
ejpam-6979	43	36	(	(	PUNCT
ejpam-6979	43	37	2	2	NUM
ejpam-6979	43	38	)	)	PUNCT
ejpam-6979	43	39	e.	e.	PROPN
ejpam-6979	43	40	e.	e.	PROPN
ejpam-6979	43	41	ali	ali	PROPN
ejpam-6979	43	42	et	et	PROPN
ejpam-6979	43	43	al	al	PROPN
ejpam-6979	43	44	.	.	PUNCT
ejpam-6979	43	45	/	/	SYM
ejpam-6979	43	46	eur	eur	PROPN
ejpam-6979	43	47	.	.	PUNCT
ejpam-6979	44	1	j.	j.	PROPN
ejpam-6979	44	2	pure	pure	PROPN
ejpam-6979	44	3	appl	appl	PROPN
ejpam-6979	44	4	.	.	PROPN
ejpam-6979	44	5	math	math	PROPN
ejpam-6979	44	6	,	,	PUNCT
ejpam-6979	44	7	18	18	NUM
ejpam-6979	44	8	(	(	PUNCT
ejpam-6979	44	9	4	4	NUM
ejpam-6979	44	10	)	)	PUNCT
ejpam-6979	44	11	(	(	PUNCT
ejpam-6979	44	12	2025	2025	NUM
ejpam-6979	44	13	)	)	PUNCT
ejpam-6979	44	14	,	,	PUNCT
ejpam-6979	44	15	6979	6979	NUM
ejpam-6979	44	16	3	3	NUM
ejpam-6979	44	17	of	of	ADP
ejpam-6979	44	18	18	18	NUM
ejpam-6979	44	19	which	which	PRON
ejpam-6979	44	20	is	be	AUX
ejpam-6979	44	21	a	a	DET
ejpam-6979	44	22	particular	particular	ADJ
ejpam-6979	44	23	solution	solution	NOUN
ejpam-6979	44	24	of	of	ADP
ejpam-6979	44	25	the	the	DET
ejpam-6979	44	26	nonhomogeneous	nonhomogeneous	ADJ
ejpam-6979	44	27	bessel	bessel	ADJ
ejpam-6979	44	28	differential	differential	NOUN
ejpam-6979	44	29	equation	equation	NOUN
ejpam-6979	44	30	ξ2w′′(ξ	ξ2w′′(ξ	NOUN
ejpam-6979	44	31	)	)	PUNCT
ejpam-6979	45	1	+	+	CCONJ
ejpam-6979	45	2	ξw′(ξ	ξw′(ξ	NOUN
ejpam-6979	45	3	)	)	PUNCT
ejpam-6979	46	1	+	+	CCONJ
ejpam-6979	46	2	[	[	PUNCT
ejpam-6979	46	3	ξ2	ξ2	NOUN
ejpam-6979	46	4	−	−	PROPN
ejpam-6979	46	5	ν2	ν2	NOUN
ejpam-6979	46	6	]	]	PUNCT
ejpam-6979	46	7	w(ξ	w(ξ	NOUN
ejpam-6979	46	8	)	)	PUNCT
ejpam-6979	46	9	=	=	PUNCT
ejpam-6979	46	10	ξρ+1	ξρ+1	X
ejpam-6979	46	11	,	,	PUNCT
ejpam-6979	46	12	(	(	PUNCT
ejpam-6979	46	13	3	3	X
ejpam-6979	46	14	)	)	PUNCT
ejpam-6979	46	15	where	where	SCONJ
ejpam-6979	46	16	ρ−ν+1	ρ−ν+1	NOUN
ejpam-6979	46	17	2	2	NUM
ejpam-6979	46	18	,	,	PUNCT
ejpam-6979	46	19	ρ+ν+1	ρ+ν+1	NOUN
ejpam-6979	46	20	2	2	NUM
ejpam-6979	46	21	∈	∈	NOUN
ejpam-6979	46	22	c\z−;z−={−1,−2	c\z−;z−={−1,−2	VERB
ejpam-6979	46	23	,	,	PUNCT
ejpam-6979	46	24	...	...	PUNCT
ejpam-6979	46	25	}	}	PUNCT
ejpam-6979	46	26	and	and	CCONJ
ejpam-6979	46	27	γ	γ	PROPN
ejpam-6979	46	28	stands	stand	VERB
ejpam-6979	46	29	for	for	ADP
ejpam-6979	46	30	euler	euler	PROPN
ejpam-6979	46	31	gamma	gamma	PROPN
ejpam-6979	46	32	function	function	PROPN
ejpam-6979	46	33	,	,	PUNCT
ejpam-6979	46	34	it	it	PRON
ejpam-6979	46	35	is	be	AUX
ejpam-6979	46	36	clear	clear	ADJ
ejpam-6979	46	37	that	that	SCONJ
ejpam-6979	46	38	the	the	DET
ejpam-6979	46	39	function	function	NOUN
ejpam-6979	46	40	lρ	lρ	INTJ
ejpam-6979	46	41	,	,	PUNCT
ejpam-6979	46	42	ν	ν	NOUN
ejpam-6979	46	43	is	be	AUX
ejpam-6979	46	44	analytic	analytic	ADJ
ejpam-6979	46	45	for	for	ADP
ejpam-6979	46	46	all	all	DET
ejpam-6979	46	47	ξ	ξ	PROPN
ejpam-6979	46	48	∈	∈	PROPN
ejpam-6979	46	49	c.	c.	NOUN
ejpam-6979	46	50	now	now	ADV
ejpam-6979	46	51	,	,	PUNCT
ejpam-6979	46	52	we	we	PRON
ejpam-6979	46	53	define	define	VERB
ejpam-6979	46	54	lρ	lρ	ADP
ejpam-6979	46	55	,	,	PUNCT
ejpam-6979	46	56	ν(ξ	ν(ξ	PROPN
ejpam-6979	46	57	)	)	PUNCT
ejpam-6979	46	58	as	as	SCONJ
ejpam-6979	46	59	follows	follow	VERB
ejpam-6979	46	60	:	:	PUNCT
ejpam-6979	46	61	lρ	lρ	ADJ
ejpam-6979	46	62	,	,	PUNCT
ejpam-6979	46	63	ν(ξ	ν(ξ	PROPN
ejpam-6979	46	64	)	)	PUNCT
ejpam-6979	46	65	=	=	SYM
ejpam-6979	46	66	4	4	NUM
ejpam-6979	46	67	(	(	PUNCT
ejpam-6979	46	68	ρ−ν+1	ρ−ν+1	NOUN
ejpam-6979	46	69	2	2	NUM
ejpam-6979	46	70	)	)	PUNCT
ejpam-6979	46	71	(	(	PUNCT
ejpam-6979	46	72	ρ+ν+1	ρ+ν+1	NOUN
ejpam-6979	46	73	2	2	NUM
ejpam-6979	46	74	)	)	PUNCT
ejpam-6979	46	75	ξ	ξ	PROPN
ejpam-6979	46	76	1−ρ	1−ρ	NUM
ejpam-6979	46	77	2	2	NUM
ejpam-6979	46	78	lρ	lρ	NOUN
ejpam-6979	46	79	,	,	PUNCT
ejpam-6979	46	80	ν	ν	X
ejpam-6979	46	81	(	(	PUNCT
ejpam-6979	46	82	√	√	NUM
ejpam-6979	46	83	ξ	ξ	NUM
ejpam-6979	46	84	)	)	PUNCT
ejpam-6979	46	85	,	,	PUNCT
ejpam-6979	46	86	(	(	PUNCT
ejpam-6979	46	87	4	4	NUM
ejpam-6979	46	88	)	)	PUNCT
ejpam-6979	46	89	and	and	CCONJ
ejpam-6979	46	90	using	use	VERB
ejpam-6979	46	91	the	the	DET
ejpam-6979	46	92	shifted	shift	VERB
ejpam-6979	46	93	factorial	factorial	NOUN
ejpam-6979	46	94	(	(	PUNCT
ejpam-6979	46	95	y)n	y)n	CCONJ
ejpam-6979	46	96	defined	define	VERB
ejpam-6979	46	97	as	as	ADP
ejpam-6979	46	98	(	(	PUNCT
ejpam-6979	46	99	y)n	y)n	VERB
ejpam-6979	46	100	=	=	SYM
ejpam-6979	46	101	γ	γ	X
ejpam-6979	46	102	(	(	PUNCT
ejpam-6979	46	103	y	y	PROPN
ejpam-6979	46	104	+	+	CCONJ
ejpam-6979	46	105	n	n	CCONJ
ejpam-6979	46	106	)	)	PUNCT
ejpam-6979	46	107	γ	γ	PROPN
ejpam-6979	46	108	(	(	PUNCT
ejpam-6979	46	109	y	y	NOUN
ejpam-6979	46	110	)	)	PUNCT
ejpam-6979	46	111	=	=	NOUN
ejpam-6979	46	112	{	{	PUNCT
ejpam-6979	46	113	1	1	NUM
ejpam-6979	46	114	,	,	PUNCT
ejpam-6979	46	115	(	(	PUNCT
ejpam-6979	46	116	n	n	X
ejpam-6979	46	117	=	=	SYM
ejpam-6979	46	118	0	0	NUM
ejpam-6979	46	119	,	,	PUNCT
ejpam-6979	46	120	y	y	PROPN
ejpam-6979	46	121	∈	∈	PROPN
ejpam-6979	46	122	c\	c\	PROPN
ejpam-6979	46	123	{	{	PUNCT
ejpam-6979	46	124	0	0	NUM
ejpam-6979	46	125	}	}	PUNCT
ejpam-6979	46	126	)	)	PUNCT
ejpam-6979	46	127	,	,	PUNCT
ejpam-6979	46	128	y	y	PROPN
ejpam-6979	46	129	(	(	PUNCT
ejpam-6979	46	130	y	y	PROPN
ejpam-6979	46	131	+	+	PROPN
ejpam-6979	46	132	1	1	NUM
ejpam-6979	46	133	)	)	PUNCT
ejpam-6979	46	134	...	...	PUNCT
ejpam-6979	47	1	(	(	PUNCT
ejpam-6979	47	2	y	y	NOUN
ejpam-6979	47	3	+	+	CCONJ
ejpam-6979	47	4	n	n	CCONJ
ejpam-6979	47	5	−	−	PROPN
ejpam-6979	47	6	1	1	NUM
ejpam-6979	47	7	)	)	PUNCT
ejpam-6979	47	8	,	,	PUNCT
ejpam-6979	47	9	(	(	PUNCT
ejpam-6979	47	10	n	n	X
ejpam-6979	47	11	∈	∈	PROPN
ejpam-6979	47	12	n	n	CCONJ
ejpam-6979	47	13	,	,	PUNCT
ejpam-6979	47	14	y	y	PROPN
ejpam-6979	47	15	∈	∈	PROPN
ejpam-6979	47	16	c	c	PROPN
ejpam-6979	47	17	)	)	PUNCT
ejpam-6979	47	18	,	,	PUNCT
ejpam-6979	47	19	then	then	ADV
ejpam-6979	47	20	lρ	lρ	PRON
ejpam-6979	47	21	,	,	PUNCT
ejpam-6979	47	22	ν(ξ	ν(ξ	PROPN
ejpam-6979	47	23	)	)	PUNCT
ejpam-6979	47	24	can	can	AUX
ejpam-6979	47	25	be	be	AUX
ejpam-6979	47	26	represented	represent	VERB
ejpam-6979	47	27	by	by	ADP
ejpam-6979	47	28	the	the	DET
ejpam-6979	47	29	following	follow	VERB
ejpam-6979	47	30	series	series	PROPN
ejpam-6979	47	31	representation	representation	PROPN
ejpam-6979	47	32	lρ	lρ	ADP
ejpam-6979	47	33	,	,	PUNCT
ejpam-6979	47	34	ν(ξ	ν(ξ	PROPN
ejpam-6979	47	35	)	)	PUNCT
ejpam-6979	47	36	=	=	SYM
ejpam-6979	48	1	ξ	ξ	PROPN
ejpam-6979	49	1	+	+	PUNCT
ejpam-6979	49	2	∞∑	∞∑	NUM
ejpam-6979	49	3	κ=2	κ=2	SYM
ejpam-6979	49	4	(	(	PUNCT
ejpam-6979	49	5	−1)κ−1	−1)κ−1	PROPN
ejpam-6979	49	6	4κ−1	4κ−1	PROPN
ejpam-6979	49	7	(	(	PUNCT
ejpam-6979	49	8	ρ−ν+1	ρ−ν+1	PROPN
ejpam-6979	49	9	2	2	NUM
ejpam-6979	49	10	+	+	CCONJ
ejpam-6979	49	11	1	1	NUM
ejpam-6979	49	12	)	)	PUNCT
ejpam-6979	49	13	κ−1	κ−1	PROPN
ejpam-6979	49	14	(	(	PUNCT
ejpam-6979	49	15	ρ+ν+1	ρ+ν+1	NOUN
ejpam-6979	49	16	2	2	NUM
ejpam-6979	49	17	+	+	SYM
ejpam-6979	49	18	1	1	NUM
ejpam-6979	49	19	)	)	PUNCT
ejpam-6979	49	20	κ−1	κ−1	PROPN
ejpam-6979	49	21	ξκ	ξκ	PROPN
ejpam-6979	49	22	,	,	PUNCT
ejpam-6979	49	23	(	(	PUNCT
ejpam-6979	49	24	5	5	NUM
ejpam-6979	49	25	)	)	PUNCT
ejpam-6979	49	26	for	for	ADP
ejpam-6979	49	27	simplicity	simplicity	NOUN
ejpam-6979	49	28	,	,	PUNCT
ejpam-6979	49	29	let	let	VERB
ejpam-6979	49	30	n	n	NOUN
ejpam-6979	49	31	=	=	SYM
ejpam-6979	49	32	ρ−ν+3	ρ−ν+3	NUM
ejpam-6979	49	33	2	2	NUM
ejpam-6979	49	34	and	and	CCONJ
ejpam-6979	49	35	v	v	NOUN
ejpam-6979	49	36	=	=	SYM
ejpam-6979	49	37	ρ+ν+3	ρ+ν+3	NOUN
ejpam-6979	49	38	2	2	NUM
ejpam-6979	49	39	.	.	PUNCT
ejpam-6979	50	1	thus	thus	ADV
ejpam-6979	50	2	the	the	DET
ejpam-6979	50	3	function	function	NOUN
ejpam-6979	50	4	ln	ln	PROPN
ejpam-6979	50	5	,	,	PUNCT
ejpam-6979	50	6	v	v	NOUN
ejpam-6979	50	7	can	can	AUX
ejpam-6979	50	8	be	be	AUX
ejpam-6979	50	9	defined	define	VERB
ejpam-6979	50	10	as	as	ADP
ejpam-6979	50	11	following	follow	VERB
ejpam-6979	50	12	:	:	PUNCT
ejpam-6979	50	13	ln	ln	ADJ
ejpam-6979	50	14	,	,	PUNCT
ejpam-6979	50	15	v(ξ	v(ξ	NOUN
ejpam-6979	50	16	)	)	PUNCT
ejpam-6979	50	17	=	=	SYM
ejpam-6979	51	1	ξ	ξ	PROPN
ejpam-6979	52	1	+	+	PUNCT
ejpam-6979	52	2	∞∑	∞∑	NUM
ejpam-6979	52	3	κ=2	κ=2	SYM
ejpam-6979	52	4	(	(	PUNCT
ejpam-6979	52	5	−1)κ−1	−1)κ−1	PROPN
ejpam-6979	52	6	4κ−1	4κ−1	PROPN
ejpam-6979	52	7	(	(	PUNCT
ejpam-6979	52	8	n)κ−1	n)κ−1	PROPN
ejpam-6979	52	9	(	(	PUNCT
ejpam-6979	52	10	v)κ−1	v)κ−1	PROPN
ejpam-6979	52	11	ξκ	ξκ	PROPN
ejpam-6979	52	12	,	,	PUNCT
ejpam-6979	52	13	(	(	PUNCT
ejpam-6979	52	14	6	6	NUM
ejpam-6979	52	15	)	)	PUNCT
ejpam-6979	52	16	the	the	DET
ejpam-6979	52	17	function	function	NOUN
ejpam-6979	52	18	ln	ln	ADP
ejpam-6979	52	19	,	,	PUNCT
ejpam-6979	52	20	v(ξ	v(ξ	NOUN
ejpam-6979	52	21	)	)	PUNCT
ejpam-6979	52	22	is	be	AUX
ejpam-6979	52	23	analytic	analytic	ADJ
ejpam-6979	52	24	for	for	ADP
ejpam-6979	52	25	all	all	DET
ejpam-6979	52	26	ξ	ξ	PROPN
ejpam-6979	52	27	∈	∈	PROPN
ejpam-6979	52	28	c	c	NOUN
ejpam-6979	52	29	and	and	CCONJ
ejpam-6979	52	30	n	n	CCONJ
ejpam-6979	52	31	,	,	PUNCT
ejpam-6979	52	32	v	v	X
ejpam-6979	52	33	∈	∈	PROPN
ejpam-6979	52	34	c\z−0	c\z−0	NOUN
ejpam-6979	52	35	,	,	PUNCT
ejpam-6979	52	36	it	it	PRON
ejpam-6979	52	37	is	be	AUX
ejpam-6979	52	38	clear	clear	ADJ
ejpam-6979	52	39	that	that	SCONJ
ejpam-6979	52	40	ln	ln	ADJ
ejpam-6979	52	41	,	,	PUNCT
ejpam-6979	52	42	v(ξ	v(ξ	NOUN
ejpam-6979	52	43	)	)	PUNCT
ejpam-6979	52	44	∈	∈	PROPN
ejpam-6979	52	45	a	a	DET
ejpam-6979	52	46	now	now	ADV
ejpam-6979	52	47	,	,	PUNCT
ejpam-6979	52	48	we	we	PRON
ejpam-6979	52	49	define	define	VERB
ejpam-6979	52	50	the	the	DET
ejpam-6979	52	51	new	new	ADJ
ejpam-6979	52	52	operator	operator	NOUN
ejpam-6979	52	53	lmn	lmn	NOUN
ejpam-6979	52	54	,	,	PUNCT
ejpam-6979	52	55	v	v	NOUN
ejpam-6979	52	56	:	:	PUNCT
ejpam-6979	52	57	a	a	DET
ejpam-6979	52	58	−→	−→	NOUN
ejpam-6979	52	59	a	a	PRON
ejpam-6979	52	60	,	,	PUNCT
ejpam-6979	52	61	by	by	ADP
ejpam-6979	52	62	means	mean	NOUN
ejpam-6979	52	63	of	of	ADP
ejpam-6979	52	64	hadamard	hadamard	ADJ
ejpam-6979	52	65	product	product	NOUN
ejpam-6979	52	66	as	as	ADP
ejpam-6979	52	67	following	follow	VERB
ejpam-6979	52	68	:	:	PUNCT
ejpam-6979	52	69	lmn	lmn	NOUN
ejpam-6979	52	70	,	,	PUNCT
ejpam-6979	52	71	vf(ξ	vf(ξ	NUM
ejpam-6979	52	72	)	)	PUNCT
ejpam-6979	52	73	:	:	PUNCT
ejpam-6979	53	1	=	=	SYM
ejpam-6979	53	2	(	(	PUNCT
ejpam-6979	53	3	ln	ln	ADJ
ejpam-6979	53	4	,	,	PUNCT
ejpam-6979	53	5	v	v	NOUN
ejpam-6979	53	6	∗	∗	X
ejpam-6979	53	7	f	f	NOUN
ejpam-6979	53	8	)	)	PUNCT
ejpam-6979	53	9	(	(	PUNCT
ejpam-6979	53	10	ξ	ξ	X
ejpam-6979	53	11	)	)	PUNCT
ejpam-6979	53	12	=	=	SYM
ejpam-6979	54	1	ξ	ξ	PROPN
ejpam-6979	55	1	+	+	PUNCT
ejpam-6979	55	2	∞∑	∞∑	NUM
ejpam-6979	55	3	κ=2	κ=2	SYM
ejpam-6979	55	4	(	(	PUNCT
ejpam-6979	55	5	−1)κ−1	−1)κ−1	PROPN
ejpam-6979	55	6	4κ−1	4κ−1	PROPN
ejpam-6979	55	7	(	(	PUNCT
ejpam-6979	55	8	n)κ−1	n)κ−1	PROPN
ejpam-6979	55	9	(	(	PUNCT
ejpam-6979	55	10	v)κ−1	v)κ−1	PROPN
ejpam-6979	55	11	aκξκ	aκξκ	NOUN
ejpam-6979	55	12	.	.	PUNCT
ejpam-6979	56	1	(	(	PUNCT
ejpam-6979	56	2	7	7	X
ejpam-6979	56	3	)	)	PUNCT
ejpam-6979	56	4	remark	remark	NOUN
ejpam-6979	56	5	1	1	NUM
ejpam-6979	56	6	.	.	PUNCT
ejpam-6979	57	1	we	we	PRON
ejpam-6979	57	2	note	note	VERB
ejpam-6979	57	3	that	that	SCONJ
ejpam-6979	57	4	by	by	ADP
ejpam-6979	57	5	taking	take	VERB
ejpam-6979	57	6	v	v	NOUN
ejpam-6979	57	7	=	=	SYM
ejpam-6979	57	8	1	1	NUM
ejpam-6979	57	9	in	in	ADP
ejpam-6979	57	10	(	(	PUNCT
ejpam-6979	57	11	7	7	NUM
ejpam-6979	57	12	)	)	PUNCT
ejpam-6979	57	13	,	,	PUNCT
ejpam-6979	57	14	then	then	ADV
ejpam-6979	57	15	we	we	PRON
ejpam-6979	57	16	get	get	VERB
ejpam-6979	57	17	the	the	DET
ejpam-6979	57	18	operator	operator	NOUN
ejpam-6979	57	19	lmn	lmn	NOUN
ejpam-6979	57	20	defined	define	VERB
ejpam-6979	57	21	as	as	ADP
ejpam-6979	57	22	following	follow	VERB
ejpam-6979	57	23	:	:	PUNCT
ejpam-6979	57	24	lmn	lmn	NOUN
ejpam-6979	57	25	,	,	PUNCT
ejpam-6979	57	26	vf(ξ	vf(ξ	NUM
ejpam-6979	57	27	)	)	PUNCT
ejpam-6979	57	28	=	=	SYM
ejpam-6979	58	1	ξ	ξ	PROPN
ejpam-6979	59	1	+	+	PUNCT
ejpam-6979	59	2	∞∑	∞∑	NUM
ejpam-6979	59	3	κ=2	κ=2	SYM
ejpam-6979	59	4	(	(	PUNCT
ejpam-6979	59	5	−1)κ−1	−1)κ−1	PROPN
ejpam-6979	59	6	4κ−1	4κ−1	PROPN
ejpam-6979	59	7	(	(	PUNCT
ejpam-6979	59	8	n)κ−1	n)κ−1	PROPN
ejpam-6979	59	9	(	(	PUNCT
ejpam-6979	59	10	κ	κ	NOUN
ejpam-6979	59	11	−	−	PROPN
ejpam-6979	59	12	1	1	NUM
ejpam-6979	59	13	)	)	PUNCT
ejpam-6979	59	14	!	!	PUNCT
ejpam-6979	60	1	aκξκ	aκξκ	PROPN
ejpam-6979	60	2	.	.	PUNCT
ejpam-6979	61	1	which	which	PRON
ejpam-6979	61	2	is	be	AUX
ejpam-6979	61	3	related	relate	VERB
ejpam-6979	61	4	to	to	ADP
ejpam-6979	61	5	bessel	bessel	ADJ
ejpam-6979	61	6	functions	function	NOUN
ejpam-6979	61	7	of	of	ADP
ejpam-6979	61	8	the	the	DET
ejpam-6979	61	9	first	first	ADJ
ejpam-6979	61	10	kind	kind	NOUN
ejpam-6979	61	11	(	(	PUNCT
ejpam-6979	61	12	see	see	VERB
ejpam-6979	61	13	[	[	X
ejpam-6979	61	14	24	24	NUM
ejpam-6979	61	15	]	]	PUNCT
ejpam-6979	61	16	)	)	PUNCT
ejpam-6979	61	17	.	.	PUNCT
ejpam-6979	62	1	the	the	DET
ejpam-6979	62	2	operator	operator	NOUN
ejpam-6979	62	3	lmn	lmn	NOUN
ejpam-6979	62	4	,	,	PUNCT
ejpam-6979	62	5	vf(ξ	vf(ξ	NUM
ejpam-6979	62	6	)	)	PUNCT
ejpam-6979	62	7	,	,	PUNCT
ejpam-6979	62	8	satisfying	satisfy	VERB
ejpam-6979	62	9	ξ	ξ	PROPN
ejpam-6979	62	10	(	(	PUNCT
ejpam-6979	62	11	lmn+1,vf(ξ	lmn+1,vf(ξ	PROPN
ejpam-6979	62	12	)	)	PUNCT
ejpam-6979	62	13	)	)	PUNCT
ejpam-6979	63	1	′	′	NUM
ejpam-6979	63	2	=	=	PUNCT
ejpam-6979	63	3	nlmn	nlmn	NOUN
ejpam-6979	63	4	,	,	PUNCT
ejpam-6979	63	5	vf(ξ	vf(ξ	NUM
ejpam-6979	63	6	)	)	PUNCT
ejpam-6979	63	7	−	−	PROPN
ejpam-6979	63	8	(	(	PUNCT
ejpam-6979	63	9	n	n	CCONJ
ejpam-6979	63	10	−	−	PROPN
ejpam-6979	63	11	1)lmn+1,vf(ξ	1)lmn+1,vf(ξ	NUM
ejpam-6979	63	12	)	)	PUNCT
ejpam-6979	63	13	(	(	PUNCT
ejpam-6979	63	14	8)	8)	NUM
ejpam-6979	63	15	and	and	CCONJ
ejpam-6979	63	16	ξ	ξ	PROPN
ejpam-6979	63	17	(	(	PUNCT
ejpam-6979	63	18	lmn	lmn	PROPN
ejpam-6979	63	19	,	,	PUNCT
ejpam-6979	63	20	v+1f(ξ	v+1f(ξ	NUM
ejpam-6979	63	21	)	)	PUNCT
ejpam-6979	63	22	)	)	PUNCT
ejpam-6979	63	23	′	′	NUM
ejpam-6979	64	1	=	=	PUNCT
ejpam-6979	64	2	vlmn	vlmn	NOUN
ejpam-6979	64	3	,	,	PUNCT
ejpam-6979	64	4	vf(ξ	vf(ξ	NUM
ejpam-6979	64	5	)	)	PUNCT
ejpam-6979	64	6	−	−	PROPN
ejpam-6979	65	1	(	(	PUNCT
ejpam-6979	65	2	v	v	NOUN
ejpam-6979	65	3	−	−	NOUN
ejpam-6979	65	4	1)lmn	1)lmn	NUM
ejpam-6979	65	5	,	,	PUNCT
ejpam-6979	65	6	v+1f(ξ	v+1f(ξ	X
ejpam-6979	65	7	)	)	PUNCT
ejpam-6979	65	8	(	(	PUNCT
ejpam-6979	65	9	9	9	NUM
ejpam-6979	65	10	)	)	PUNCT
ejpam-6979	65	11	.	.	PUNCT
ejpam-6979	66	1	e.	e.	PROPN
ejpam-6979	66	2	e.	e.	PROPN
ejpam-6979	66	3	ali	ali	PROPN
ejpam-6979	66	4	et	et	PROPN
ejpam-6979	66	5	al	al	PROPN
ejpam-6979	66	6	.	.	PUNCT
ejpam-6979	66	7	/	/	SYM
ejpam-6979	66	8	eur	eur	PROPN
ejpam-6979	66	9	.	.	PUNCT
ejpam-6979	67	1	j.	j.	PROPN
ejpam-6979	67	2	pure	pure	PROPN
ejpam-6979	67	3	appl	appl	PROPN
ejpam-6979	67	4	.	.	PROPN
ejpam-6979	67	5	math	math	PROPN
ejpam-6979	67	6	,	,	PUNCT
ejpam-6979	67	7	18	18	NUM
ejpam-6979	67	8	(	(	PUNCT
ejpam-6979	67	9	4	4	NUM
ejpam-6979	67	10	)	)	PUNCT
ejpam-6979	67	11	(	(	PUNCT
ejpam-6979	67	12	2025	2025	NUM
ejpam-6979	67	13	)	)	PUNCT
ejpam-6979	67	14	,	,	PUNCT
ejpam-6979	67	15	6979	6979	NUM
ejpam-6979	67	16	4	4	NUM
ejpam-6979	67	17	of	of	ADP
ejpam-6979	67	18	18	18	NUM
ejpam-6979	67	19	2	2	NUM
ejpam-6979	67	20	.	.	PUNCT
ejpam-6979	68	1	definitions	definition	NOUN
ejpam-6979	68	2	and	and	CCONJ
ejpam-6979	68	3	preliminaries	preliminary	NOUN
ejpam-6979	68	4	definition	definition	NOUN
ejpam-6979	68	5	1	1	NUM
ejpam-6979	68	6	.	.	PUNCT
ejpam-6979	69	1	[	[	X
ejpam-6979	69	2	2	2	X
ejpam-6979	69	3	]	]	PUNCT
ejpam-6979	69	4	a	a	DET
ejpam-6979	69	5	fuzzy	fuzzy	ADJ
ejpam-6979	69	6	set	set	NOUN
ejpam-6979	69	7	is	be	AUX
ejpam-6979	69	8	pair	pair	NOUN
ejpam-6979	69	9	(	(	PUNCT
ejpam-6979	69	10	s	s	NOUN
ejpam-6979	69	11	,	,	PUNCT
ejpam-6979	69	12	f	f	PROPN
ejpam-6979	69	13	)	)	PUNCT
ejpam-6979	69	14	,	,	PUNCT
ejpam-6979	69	15	where	where	SCONJ
ejpam-6979	69	16	s	s	NOUN
ejpam-6979	69	17	is	be	AUX
ejpam-6979	69	18	a	a	DET
ejpam-6979	69	19	set	set	NOUN
ejpam-6979	69	20	,	,	PUNCT
ejpam-6979	69	21	s	s	PART
ejpam-6979	69	22	,	,	PUNCT
ejpam-6979	69	23	ϕ	ϕ	PROPN
ejpam-6979	69	24	and	and	CCONJ
ejpam-6979	69	25	f	f	PROPN
ejpam-6979	69	26	:	:	PUNCT
ejpam-6979	69	27	s	s	X
ejpam-6979	69	28	→	→	SYM
ejpam-6979	69	29	[	[	X
ejpam-6979	69	30	0	0	NUM
ejpam-6979	69	31	,	,	PUNCT
ejpam-6979	69	32	1	1	NUM
ejpam-6979	69	33	]	]	PUNCT
ejpam-6979	69	34	a	a	DET
ejpam-6979	69	35	membership	membership	NOUN
ejpam-6979	69	36	function	function	NOUN
ejpam-6979	69	37	.	.	PUNCT
ejpam-6979	70	1	the	the	DET
ejpam-6979	70	2	fuzzy	fuzzy	ADJ
ejpam-6979	70	3	subset	subset	NOUN
ejpam-6979	70	4	is	be	AUX
ejpam-6979	70	5	likewise	likewise	ADV
ejpam-6979	70	6	covered	cover	VERB
ejpam-6979	70	7	by	by	ADP
ejpam-6979	70	8	the	the	DET
ejpam-6979	70	9	following	follow	VERB
ejpam-6979	70	10	idea	idea	NOUN
ejpam-6979	70	11	.	.	PUNCT
ejpam-6979	71	1	definition	definition	NOUN
ejpam-6979	71	2	2	2	NUM
ejpam-6979	71	3	.	.	PUNCT
ejpam-6979	72	1	[	[	X
ejpam-6979	72	2	2	2	X
ejpam-6979	72	3	]	]	PUNCT
ejpam-6979	72	4	a	a	DET
ejpam-6979	72	5	fuzzy	fuzzy	ADJ
ejpam-6979	72	6	subset	subset	NOUN
ejpam-6979	72	7	of	of	ADP
ejpam-6979	72	8	s	s	PROPN
ejpam-6979	72	9	is	be	AUX
ejpam-6979	72	10	a	a	DET
ejpam-6979	72	11	pair	pair	NOUN
ejpam-6979	72	12	(	(	PUNCT
ejpam-6979	72	13	ℓ	ℓ	INTJ
ejpam-6979	72	14	,	,	PUNCT
ejpam-6979	72	15	fℓ	fℓ	NOUN
ejpam-6979	72	16	)	)	PUNCT
ejpam-6979	72	17	,	,	PUNCT
ejpam-6979	72	18	where	where	SCONJ
ejpam-6979	72	19	the	the	DET
ejpam-6979	72	20	support	support	NOUN
ejpam-6979	72	21	of	of	ADP
ejpam-6979	72	22	the	the	DET
ejpam-6979	72	23	fuzzy	fuzzy	ADJ
ejpam-6979	72	24	set	set	NOUN
ejpam-6979	72	25	(	(	PUNCT
ejpam-6979	72	26	ℓ	ℓ	INTJ
ejpam-6979	72	27	,	,	PUNCT
ejpam-6979	72	28	fℓ	fℓ	CCONJ
ejpam-6979	72	29	)	)	PUNCT
ejpam-6979	72	30	is	be	AUX
ejpam-6979	72	31	defined	define	VERB
ejpam-6979	72	32	as	as	ADP
ejpam-6979	72	33	ℓ	ℓ	X
ejpam-6979	72	34	=	=	PRON
ejpam-6979	72	35	{	{	PUNCT
ejpam-6979	72	36	x	x	PUNCT
ejpam-6979	72	37	∈	∈	PROPN
ejpam-6979	72	38	s	s	PART
ejpam-6979	72	39	:	:	PUNCT
ejpam-6979	72	40	0	0	NUM
ejpam-6979	72	41	<	<	X
ejpam-6979	72	42	fℓ(x	fℓ(x	NOUN
ejpam-6979	72	43	)	)	PUNCT
ejpam-6979	72	44	≤	≤	NUM
ejpam-6979	72	45	1	1	NUM
ejpam-6979	72	46	}	}	PUNCT
ejpam-6979	72	47	=	=	SYM
ejpam-6979	72	48	sup	sup	NOUN
ejpam-6979	72	49	(	(	PUNCT
ejpam-6979	72	50	ℓ	ℓ	INTJ
ejpam-6979	72	51	,	,	PUNCT
ejpam-6979	72	52	fℓ	fℓ	NOUN
ejpam-6979	72	53	)	)	PUNCT
ejpam-6979	72	54	and	and	CCONJ
ejpam-6979	72	55	fℓ	fℓ	INTJ
ejpam-6979	72	56	:	:	PUNCT
ejpam-6979	72	57	s	s	X
ejpam-6979	72	58	→	→	SYM
ejpam-6979	72	59	[	[	X
ejpam-6979	72	60	0	0	NUM
ejpam-6979	72	61	,	,	PUNCT
ejpam-6979	72	62	1	1	NUM
ejpam-6979	72	63	]	]	PUNCT
ejpam-6979	72	64	is	be	AUX
ejpam-6979	72	65	belongs	belong	VERB
ejpam-6979	72	66	to	to	ADP
ejpam-6979	72	67	(	(	PUNCT
ejpam-6979	72	68	ℓ	ℓ	INTJ
ejpam-6979	72	69	,	,	PUNCT
ejpam-6979	72	70	fℓ	fℓ	NOUN
ejpam-6979	72	71	)	)	PUNCT
ejpam-6979	72	72	.	.	PUNCT
ejpam-6979	73	1	definition	definition	NOUN
ejpam-6979	73	2	3	3	NUM
ejpam-6979	73	3	.	.	PUNCT
ejpam-6979	74	1	[	[	X
ejpam-6979	74	2	2	2	NUM
ejpam-6979	74	3	]	]	X
ejpam-6979	74	4	fuzzy	fuzzy	ADJ
ejpam-6979	74	5	subsets	subset	NOUN
ejpam-6979	74	6	(	(	PUNCT
ejpam-6979	74	7	y1	y1	INTJ
ejpam-6979	74	8	,	,	PUNCT
ejpam-6979	74	9	fy1	fy1	NOUN
ejpam-6979	74	10	)	)	PUNCT
ejpam-6979	74	11	and	and	CCONJ
ejpam-6979	74	12	(	(	PUNCT
ejpam-6979	74	13	y2	y2	PROPN
ejpam-6979	74	14	,	,	PUNCT
ejpam-6979	74	15	fy2	fy2	NOUN
ejpam-6979	74	16	)	)	PUNCT
ejpam-6979	74	17	of	of	ADP
ejpam-6979	74	18	s	s	NOUN
ejpam-6979	74	19	are	be	AUX
ejpam-6979	74	20	equal	equal	ADJ
ejpam-6979	74	21	iff	iff	PROPN
ejpam-6979	74	22	y1	y1	PROPN
ejpam-6979	74	23	=	=	PUNCT
ejpam-6979	74	24	y2	y2	PROPN
ejpam-6979	74	25	,	,	PUNCT
ejpam-6979	74	26	whereas	whereas	SCONJ
ejpam-6979	74	27	(	(	PUNCT
ejpam-6979	74	28	y1	y1	NOUN
ejpam-6979	74	29	,	,	PUNCT
ejpam-6979	74	30	fy1	fy1	NOUN
ejpam-6979	74	31	)	)	PUNCT
ejpam-6979	74	32	⊆	⊆	NUM
ejpam-6979	74	33	(	(	PUNCT
ejpam-6979	74	34	y2	y2	PROPN
ejpam-6979	74	35	,	,	PUNCT
ejpam-6979	74	36	fy2	fy2	NOUN
ejpam-6979	74	37	)	)	PUNCT
ejpam-6979	74	38	iff	iff	PROPN
ejpam-6979	74	39	fy1	fy1	PROPN
ejpam-6979	74	40	(	(	PUNCT
ejpam-6979	74	41	η	η	NOUN
ejpam-6979	74	42	)	)	PUNCT
ejpam-6979	74	43	≤	≤	NOUN
ejpam-6979	74	44	fy2	fy2	PROPN
ejpam-6979	74	45	(	(	PUNCT
ejpam-6979	74	46	η	η	PROPN
ejpam-6979	74	47	)	)	PUNCT
ejpam-6979	74	48	,	,	PUNCT
ejpam-6979	74	49	η	η	PROPN
ejpam-6979	74	50	∈	∈	PROPN
ejpam-6979	74	51	s	s	PART
ejpam-6979	74	52	.	.	PUNCT
ejpam-6979	75	1	definition	definition	NOUN
ejpam-6979	75	2	4	4	NUM
ejpam-6979	75	3	.	.	PUNCT
ejpam-6979	76	1	[	[	X
ejpam-6979	76	2	2	2	NUM
ejpam-6979	76	3	]	]	PUNCT
ejpam-6979	76	4	letu	letu	VERB
ejpam-6979	76	5	⊂	⊂	PROPN
ejpam-6979	76	6	c	c	PROPN
ejpam-6979	76	7	and	and	CCONJ
ejpam-6979	76	8	ξ0	ξ0	PROPN
ejpam-6979	76	9	are	be	AUX
ejpam-6979	76	10	a	a	DET
ejpam-6979	76	11	fixed	fix	VERB
ejpam-6979	76	12	point	point	NOUN
ejpam-6979	76	13	inu	inu	NOUN
ejpam-6979	76	14	and	and	CCONJ
ejpam-6979	76	15	let	let	VERB
ejpam-6979	76	16	the	the	DET
ejpam-6979	76	17	functions	function	NOUN
ejpam-6979	76	18	f	f	X
ejpam-6979	76	19	,	,	PUNCT
ejpam-6979	76	20	µ	µ	PROPN
ejpam-6979	76	21	∈	∈	PROPN
ejpam-6979	76	22	h(u	h(u	PROPN
ejpam-6979	76	23	)	)	PUNCT
ejpam-6979	76	24	.	.	PUNCT
ejpam-6979	77	1	f	f	PROPN
ejpam-6979	77	2	is	be	AUX
ejpam-6979	77	3	said	say	VERB
ejpam-6979	77	4	to	to	PART
ejpam-6979	77	5	be	be	AUX
ejpam-6979	77	6	fuzzy	fuzzy	ADJ
ejpam-6979	77	7	subordinate	subordinate	ADJ
ejpam-6979	77	8	to	to	ADP
ejpam-6979	77	9	µ	µ	PROPN
ejpam-6979	77	10	and	and	CCONJ
ejpam-6979	77	11	write	write	VERB
ejpam-6979	77	12	f	f	PROPN
ejpam-6979	77	13	≺f	≺f	PROPN
ejpam-6979	77	14	µ	µ	PROPN
ejpam-6979	77	15	or	or	CCONJ
ejpam-6979	77	16	f(ξ	f(ξ	NUM
ejpam-6979	77	17	)	)	PUNCT
ejpam-6979	78	1	≺f	≺f	PROPN
ejpam-6979	78	2	µ(ξ	µ(ξ	X
ejpam-6979	78	3	)	)	PUNCT
ejpam-6979	78	4	if	if	SCONJ
ejpam-6979	78	5	f(ξ0	f(ξ0	ADJ
ejpam-6979	78	6	)	)	PUNCT
ejpam-6979	78	7	=	=	SYM
ejpam-6979	78	8	µ(ξ0	µ(ξ0	NOUN
ejpam-6979	78	9	)	)	PUNCT
ejpam-6979	78	10	and	and	CCONJ
ejpam-6979	78	11	ff(u	ff(u	NOUN
ejpam-6979	78	12	)	)	PUNCT
ejpam-6979	78	13	(	(	PUNCT
ejpam-6979	78	14	f	f	X
ejpam-6979	78	15	(	(	PUNCT
ejpam-6979	78	16	ξ	ξ	NOUN
ejpam-6979	78	17	)	)	PUNCT
ejpam-6979	78	18	)	)	PUNCT
ejpam-6979	78	19	≤	≤	NOUN
ejpam-6979	78	20	fµ(u	fµ(u	NOUN
ejpam-6979	78	21	)	)	PUNCT
ejpam-6979	78	22	(	(	PUNCT
ejpam-6979	78	23	µ	µ	X
ejpam-6979	78	24	(	(	PUNCT
ejpam-6979	78	25	ξ	ξ	NOUN
ejpam-6979	78	26	)	)	PUNCT
ejpam-6979	78	27	)	)	PUNCT
ejpam-6979	78	28	,	,	PUNCT
ejpam-6979	78	29	ξ	ξ	PROPN
ejpam-6979	78	30	∈	∈	PROPN
ejpam-6979	78	31	u	u	NOUN
ejpam-6979	78	32	,	,	PUNCT
ejpam-6979	78	33	where	where	SCONJ
ejpam-6979	78	34	f(u	f(u	PROPN
ejpam-6979	78	35	)	)	PUNCT
ejpam-6979	78	36	=	=	SYM
ejpam-6979	78	37	sup(f(u	sup(f(u	ADJ
ejpam-6979	78	38	)	)	PUNCT
ejpam-6979	78	39	,	,	PUNCT
ejpam-6979	78	40	ff(u	ff(u	NOUN
ejpam-6979	78	41	)	)	PUNCT
ejpam-6979	78	42	)	)	PUNCT
ejpam-6979	79	1	=	=	PRON
ejpam-6979	79	2	{	{	PUNCT
ejpam-6979	79	3	f	f	X
ejpam-6979	79	4	(	(	PUNCT
ejpam-6979	79	5	ξ	ξ	PROPN
ejpam-6979	79	6	)	)	PUNCT
ejpam-6979	79	7	:	:	PUNCT
ejpam-6979	79	8	0	0	PUNCT
ejpam-6979	79	9	<	<	X
ejpam-6979	79	10	ff(u)(f	ff(u)(f	PROPN
ejpam-6979	79	11	(	(	PUNCT
ejpam-6979	79	12	ξ	ξ	NOUN
ejpam-6979	79	13	)	)	PUNCT
ejpam-6979	79	14	)	)	PUNCT
ejpam-6979	79	15	≤	≤	NUM
ejpam-6979	79	16	1	1	NUM
ejpam-6979	79	17	,	,	PUNCT
ejpam-6979	79	18	ξ	ξ	PROPN
ejpam-6979	79	19	∈	∈	PROPN
ejpam-6979	79	20	u	u	NOUN
ejpam-6979	79	21	and	and	CCONJ
ejpam-6979	79	22	µ(u	µ(u	NOUN
ejpam-6979	79	23	)	)	PUNCT
ejpam-6979	79	24	=	=	SYM
ejpam-6979	79	25	sup(µ(u	sup(µ(u	PROPN
ejpam-6979	79	26	)	)	PUNCT
ejpam-6979	79	27	,	,	PUNCT
ejpam-6979	79	28	fµ(u	fµ(u	NOUN
ejpam-6979	79	29	)	)	PUNCT
ejpam-6979	79	30	)	)	PUNCT
ejpam-6979	79	31	=	=	PRON
ejpam-6979	79	32	{	{	PUNCT
ejpam-6979	79	33	µ	µ	X
ejpam-6979	79	34	(	(	PUNCT
ejpam-6979	79	35	ξ	ξ	NOUN
ejpam-6979	79	36	)	)	PUNCT
ejpam-6979	79	37	:	:	PUNCT
ejpam-6979	79	38	0	0	NUM
ejpam-6979	79	39	<	<	X
ejpam-6979	79	40	fµ(u)(µ	fµ(u)(µ	X
ejpam-6979	79	41	(	(	PUNCT
ejpam-6979	79	42	ξ	ξ	NOUN
ejpam-6979	79	43	)	)	PUNCT
ejpam-6979	79	44	)	)	PUNCT
ejpam-6979	79	45	≤	≤	NUM
ejpam-6979	79	46	1	1	NUM
ejpam-6979	79	47	,	,	PUNCT
ejpam-6979	79	48	ξ	ξ	X
ejpam-6979	79	49	∈	∈	PROPN
ejpam-6979	79	50	u.	u.	VERB
ejpam-6979	79	51	the	the	DET
ejpam-6979	79	52	following	follow	VERB
ejpam-6979	79	53	lemma	lemma	PROPN
ejpam-6979	79	54	is	be	AUX
ejpam-6979	79	55	necessary	necessary	ADJ
ejpam-6979	79	56	to	to	PART
ejpam-6979	79	57	validate	validate	VERB
ejpam-6979	79	58	our	our	PRON
ejpam-6979	79	59	research	research	NOUN
ejpam-6979	79	60	.	.	PUNCT
ejpam-6979	80	1	lemma	lemma	PROPN
ejpam-6979	80	2	1	1	NUM
ejpam-6979	80	3	.	.	PUNCT
ejpam-6979	81	1	[	[	X
ejpam-6979	81	2	6	6	NUM
ejpam-6979	81	3	]	]	PUNCT
ejpam-6979	81	4	let	let	VERB
ejpam-6979	81	5	β	β	X
ejpam-6979	81	6	,	,	PUNCT
ejpam-6979	81	7	γ	γ	PROPN
ejpam-6979	81	8	∈	∈	PROPN
ejpam-6979	81	9	c.	c.	NOUN
ejpam-6979	81	10	also	also	ADV
ejpam-6979	81	11	let	let	VERB
ejpam-6979	81	12	µ	µ	X
ejpam-6979	81	13	∈	∈	NOUN
ejpam-6979	81	14	a	a	DET
ejpam-6979	81	15	be	be	AUX
ejpam-6979	81	16	convex	convex	ADJ
ejpam-6979	81	17	univalent	univalent	ADJ
ejpam-6979	81	18	inu	inu	NOUN
ejpam-6979	81	19	with	with	ADP
ejpam-6979	81	20	re[βµ(ξ	re[βµ(ξ	PROPN
ejpam-6979	81	21	)	)	PUNCT
ejpam-6979	81	22	+	+	CCONJ
ejpam-6979	81	23	γ	γ	X
ejpam-6979	81	24	]	]	X
ejpam-6979	81	25	>	>	X
ejpam-6979	81	26	0	0	PUNCT
ejpam-6979	81	27	(	(	PUNCT
ejpam-6979	81	28	ξ	ξ	PROPN
ejpam-6979	81	29	∈	∈	PROPN
ejpam-6979	81	30	u	u	NOUN
ejpam-6979	81	31	)	)	PUNCT
ejpam-6979	81	32	,	,	PUNCT
ejpam-6979	81	33	µ(0	µ(0	NOUN
ejpam-6979	81	34	)	)	PUNCT
ejpam-6979	81	35	=	=	SYM
ejpam-6979	81	36	1	1	NUM
ejpam-6979	81	37	and	and	CCONJ
ejpam-6979	81	38	p(ξ	p(ξ	ADJ
ejpam-6979	81	39	)	)	PUNCT
ejpam-6979	81	40	∈	∈	PROPN
ejpam-6979	81	41	a	a	PRON
ejpam-6979	81	42	with	with	ADP
ejpam-6979	81	43	p(ξ	p(ξ	NOUN
ejpam-6979	81	44	)	)	PUNCT
ejpam-6979	81	45	=	=	SYM
ejpam-6979	82	1	1	1	NUM
ejpam-6979	82	2	+	+	NUM
ejpam-6979	82	3	p1ξ	p1ξ	NOUN
ejpam-6979	82	4	+	+	CCONJ
ejpam-6979	82	5	p2ξ	p2ξ	NUM
ejpam-6979	82	6	2	2	NUM
ejpam-6979	82	7	+	+	CCONJ
ejpam-6979	82	8	....	....	PUNCT
ejpam-6979	82	9	is	be	AUX
ejpam-6979	82	10	analytic	analytic	ADJ
ejpam-6979	82	11	inu	inu	NOUN
ejpam-6979	82	12	.	.	PUNCT
ejpam-6979	83	1	if	if	SCONJ
ejpam-6979	83	2	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	83	3	)	)	PUNCT
ejpam-6979	83	4	[	[	PUNCT
ejpam-6979	83	5	p(ξ	p(ξ	NOUN
ejpam-6979	83	6	)	)	PUNCT
ejpam-6979	84	1	+	+	CCONJ
ejpam-6979	84	2	ξp	ξp	NUM
ejpam-6979	84	3	′	′	NUM
ejpam-6979	84	4	(	(	PUNCT
ejpam-6979	84	5	ξ	ξ	NOUN
ejpam-6979	84	6	)	)	PUNCT
ejpam-6979	84	7	βp(ξ	βp(ξ	PUNCT
ejpam-6979	84	8	)	)	PUNCT
ejpam-6979	85	1	+	+	CCONJ
ejpam-6979	85	2	γ	γ	X
ejpam-6979	85	3	]	]	PUNCT
ejpam-6979	85	4	≤	≤	NUM
ejpam-6979	85	5	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	85	6	)	)	PUNCT
ejpam-6979	85	7	,	,	PUNCT
ejpam-6979	85	8	implies	imply	VERB
ejpam-6979	85	9	fp(u	fp(u	NOUN
ejpam-6979	85	10	)	)	PUNCT
ejpam-6979	85	11	p(ξ	p(ξ	NOUN
ejpam-6979	85	12	)	)	PUNCT
ejpam-6979	85	13	≤	≤	NUM
ejpam-6979	85	14	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	85	15	)	)	PUNCT
ejpam-6979	85	16	,	,	PUNCT
ejpam-6979	85	17	ξ	ξ	PROPN
ejpam-6979	85	18	∈	∈	PROPN
ejpam-6979	85	19	u.	u.	PROPN
ejpam-6979	85	20	lemma	lemma	PROPN
ejpam-6979	85	21	2	2	X
ejpam-6979	85	22	.	.	PUNCT
ejpam-6979	86	1	[	[	X
ejpam-6979	86	2	6	6	NUM
ejpam-6979	86	3	]	]	PUNCT
ejpam-6979	86	4	let	let	VERB
ejpam-6979	86	5	β	β	PRON
ejpam-6979	86	6	,	,	PUNCT
ejpam-6979	86	7	y	y	PROPN
ejpam-6979	86	8	∈	∈	PROPN
ejpam-6979	86	9	c.	c.	PROPN
ejpam-6979	86	10	also	also	ADV
ejpam-6979	86	11	let	let	VERB
ejpam-6979	86	12	µ	µ	X
ejpam-6979	86	13	∈	∈	NOUN
ejpam-6979	86	14	a	a	DET
ejpam-6979	86	15	be	be	AUX
ejpam-6979	86	16	convex	convex	ADJ
ejpam-6979	86	17	univalent	univalent	ADJ
ejpam-6979	86	18	inu	inu	NOUN
ejpam-6979	86	19	with	with	ADP
ejpam-6979	86	20	µ(0	µ(0	NOUN
ejpam-6979	86	21	)	)	PUNCT
ejpam-6979	86	22	=	=	SYM
ejpam-6979	86	23	1	1	NUM
ejpam-6979	86	24	and	and	CCONJ
ejpam-6979	86	25	re[βµ(ξ)+	re[βµ(ξ)+	PROPN
ejpam-6979	86	26	y	y	PROPN
ejpam-6979	86	27	]	]	X
ejpam-6979	86	28	>	>	X
ejpam-6979	86	29	0	0	PUNCT
ejpam-6979	87	1	(	(	PUNCT
ejpam-6979	87	2	ξ	ξ	PROPN
ejpam-6979	87	3	∈	∈	PROPN
ejpam-6979	87	4	u	u	NOUN
ejpam-6979	87	5	)	)	PUNCT
ejpam-6979	87	6	,	,	PUNCT
ejpam-6979	87	7	and	and	CCONJ
ejpam-6979	87	8	q(ξ	q(ξ	NUM
ejpam-6979	87	9	)	)	PUNCT
ejpam-6979	87	10	∈	∈	PROPN
ejpam-6979	87	11	a	a	DET
ejpam-6979	87	12	with	with	ADP
ejpam-6979	87	13	q(0	q(0	PROPN
ejpam-6979	87	14	)	)	PUNCT
ejpam-6979	87	15	=	=	NOUN
ejpam-6979	87	16	1	1	NUM
ejpam-6979	87	17	and	and	CCONJ
ejpam-6979	87	18	q(ξ	q(ξ	ADJ
ejpam-6979	87	19	)	)	PUNCT
ejpam-6979	87	20	≺	≺	NOUN
ejpam-6979	87	21	µ(ξ	µ(ξ	NOUN
ejpam-6979	87	22	)	)	PUNCT
ejpam-6979	87	23	(	(	PUNCT
ejpam-6979	87	24	ξ	ξ	PROPN
ejpam-6979	87	25	∈	∈	PROPN
ejpam-6979	87	26	u	u	NOUN
ejpam-6979	87	27	)	)	PUNCT
ejpam-6979	87	28	.	.	PUNCT
ejpam-6979	88	1	if	if	SCONJ
ejpam-6979	88	2	p(ξ	p(ξ	NOUN
ejpam-6979	88	3	)	)	PUNCT
ejpam-6979	88	4	=	=	SYM
ejpam-6979	88	5	1	1	NUM
ejpam-6979	88	6	+	+	NUM
ejpam-6979	88	7	p1ξ	p1ξ	NOUN
ejpam-6979	88	8	+	+	CCONJ
ejpam-6979	88	9	p2ξ	p2ξ	NUM
ejpam-6979	88	10	2	2	NUM
ejpam-6979	88	11	+	+	CCONJ
ejpam-6979	88	12	...	...	PUNCT
ejpam-6979	88	13	is	be	AUX
ejpam-6979	88	14	analytic	analytic	ADJ
ejpam-6979	88	15	inu	inu	NOUN
ejpam-6979	88	16	,	,	PUNCT
ejpam-6979	88	17	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	88	18	)	)	PUNCT
ejpam-6979	88	19	[	[	PUNCT
ejpam-6979	88	20	p(ξ	p(ξ	NOUN
ejpam-6979	88	21	)	)	PUNCT
ejpam-6979	88	22	+	+	CCONJ
ejpam-6979	88	23	ξp	ξp	NUM
ejpam-6979	88	24	′	′	NUM
ejpam-6979	88	25	(	(	PUNCT
ejpam-6979	88	26	ξ	ξ	NOUN
ejpam-6979	88	27	)	)	PUNCT
ejpam-6979	88	28	βq(ξ	βq(ξ	PUNCT
ejpam-6979	88	29	)	)	PUNCT
ejpam-6979	89	1	+	+	CCONJ
ejpam-6979	89	2	y	y	X
ejpam-6979	89	3	]	]	PUNCT
ejpam-6979	89	4	≤	≤	NUM
ejpam-6979	89	5	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	89	6	)	)	PUNCT
ejpam-6979	89	7	(	(	PUNCT
ejpam-6979	89	8	ξ	ξ	PROPN
ejpam-6979	89	9	∈	∈	PROPN
ejpam-6979	89	10	u	u	NOUN
ejpam-6979	89	11	)	)	PUNCT
ejpam-6979	89	12	,	,	PUNCT
ejpam-6979	89	13	then	then	ADV
ejpam-6979	89	14	fp(u	fp(u	X
ejpam-6979	89	15	)	)	PUNCT
ejpam-6979	89	16	p(ξ	p(ξ	NOUN
ejpam-6979	89	17	)	)	PUNCT
ejpam-6979	89	18	≤	≤	NUM
ejpam-6979	89	19	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	89	20	)	)	PUNCT
ejpam-6979	89	21	.	.	PUNCT
ejpam-6979	90	1	where	where	SCONJ
ejpam-6979	90	2	f	f	X
ejpam-6979	90	3	:	:	PUNCT
ejpam-6979	90	4	u→	u→	PUNCT
ejpam-6979	91	1	[	[	X
ejpam-6979	91	2	0	0	NUM
ejpam-6979	91	3	,	,	PUNCT
ejpam-6979	91	4	1	1	NUM
ejpam-6979	91	5	]	]	PUNCT
ejpam-6979	91	6	.	.	PUNCT
ejpam-6979	92	1	e.	e.	PROPN
ejpam-6979	92	2	e.	e.	PROPN
ejpam-6979	92	3	ali	ali	PROPN
ejpam-6979	92	4	et	et	PROPN
ejpam-6979	92	5	al	al	PROPN
ejpam-6979	92	6	.	.	PUNCT
ejpam-6979	92	7	/	/	SYM
ejpam-6979	92	8	eur	eur	PROPN
ejpam-6979	92	9	.	.	PUNCT
ejpam-6979	93	1	j.	j.	PROPN
ejpam-6979	93	2	pure	pure	PROPN
ejpam-6979	93	3	appl	appl	PROPN
ejpam-6979	93	4	.	.	PROPN
ejpam-6979	93	5	math	math	PROPN
ejpam-6979	93	6	,	,	PUNCT
ejpam-6979	93	7	18	18	NUM
ejpam-6979	93	8	(	(	PUNCT
ejpam-6979	93	9	4	4	NUM
ejpam-6979	93	10	)	)	PUNCT
ejpam-6979	93	11	(	(	PUNCT
ejpam-6979	93	12	2025	2025	NUM
ejpam-6979	93	13	)	)	PUNCT
ejpam-6979	93	14	,	,	PUNCT
ejpam-6979	93	15	6979	6979	NUM
ejpam-6979	93	16	5	5	NUM
ejpam-6979	93	17	of	of	ADP
ejpam-6979	93	18	18	18	NUM
ejpam-6979	93	19	using	use	VERB
ejpam-6979	93	20	the	the	DET
ejpam-6979	93	21	operator	operator	NOUN
ejpam-6979	93	22	lmn	lmn	NOUN
ejpam-6979	93	23	,	,	PUNCT
ejpam-6979	93	24	vf(ξ	vf(ξ	NUM
ejpam-6979	93	25	)	)	PUNCT
ejpam-6979	94	1	,	,	PUNCT
ejpam-6979	94	2	we	we	PRON
ejpam-6979	94	3	introduce	introduce	VERB
ejpam-6979	94	4	the	the	DET
ejpam-6979	94	5	class	class	NOUN
ejpam-6979	94	6	fℜn	fℜn	NOUN
ejpam-6979	94	7	,	,	PUNCT
ejpam-6979	94	8	v(ϑ	v(ϑ	NOUN
ejpam-6979	94	9	;	;	PUNCT
ejpam-6979	94	10	µ	µ	X
ejpam-6979	94	11	)	)	PUNCT
ejpam-6979	94	12	,	,	PUNCT
ejpam-6979	94	13	of	of	ADP
ejpam-6979	94	14	analytic	analytic	ADJ
ejpam-6979	94	15	functions	function	NOUN
ejpam-6979	94	16	f	f	X
ejpam-6979	94	17	=	=	NOUN
ejpam-6979	94	18	{	{	PUNCT
ejpam-6979	94	19	f1	f1	NOUN
ejpam-6979	94	20	,	,	PUNCT
ejpam-6979	94	21	f2	f2	PROPN
ejpam-6979	94	22	,	,	PUNCT
ejpam-6979	94	23	...	...	PUNCT
ejpam-6979	94	24	,	,	PUNCT
ejpam-6979	94	25	fϑ	fϑ	ADP
ejpam-6979	94	26	}	}	PUNCT
ejpam-6979	94	27	on	on	ADP
ejpam-6979	94	28	open	open	ADJ
ejpam-6979	94	29	unit	unit	NOUN
ejpam-6979	94	30	discu	discu	NOUN
ejpam-6979	94	31	satisfying	satisfy	VERB
ejpam-6979	94	32	ξ(lmn+1,vfi(ξ	ξ(lmn+1,vfi(ξ	PROPN
ejpam-6979	94	33	)	)	PUNCT
ejpam-6979	94	34	)	)	PUNCT
ejpam-6979	95	1	′	′	NUM
ejpam-6979	95	2	1	1	NUM
ejpam-6979	95	3	ϑ	ϑ	X
ejpam-6979	95	4	ϑ∑	ϑ∑	X
ejpam-6979	95	5	j=1	j=1	PROPN
ejpam-6979	95	6	lmn+1,vf	lmn+1,vf	X
ejpam-6979	95	7	j(ξ	j(ξ	PROPN
ejpam-6979	95	8	)	)	PUNCT
ejpam-6979	95	9	≺f	≺f	PROPN
ejpam-6979	95	10	µ(ξ)(fi	µ(ξ)(fi	ADJ
ejpam-6979	95	11	∈	∈	PROPN
ejpam-6979	95	12	a	a	PRON
ejpam-6979	95	13	,	,	PUNCT
ejpam-6979	95	14	i	i	NOUN
ejpam-6979	95	15	=	=	NOUN
ejpam-6979	95	16	1	1	NUM
ejpam-6979	95	17	,	,	PUNCT
ejpam-6979	95	18	2	2	NUM
ejpam-6979	95	19	,	,	PUNCT
ejpam-6979	95	20	...	...	PUNCT
ejpam-6979	95	21	,	,	PUNCT
ejpam-6979	95	22	ϑ	ϑ	X
ejpam-6979	95	23	,	,	PUNCT
ejpam-6979	95	24	ξ	ξ	PROPN
ejpam-6979	95	25	∈	∈	PROPN
ejpam-6979	95	26	u	u	NOUN
ejpam-6979	95	27	)	)	PUNCT
ejpam-6979	95	28	,	,	PUNCT
ejpam-6979	95	29	where	where	SCONJ
ejpam-6979	95	30	ξ−1	ξ−1	PROPN
ejpam-6979	95	31	ϑ∑	ϑ∑	PROPN
ejpam-6979	95	32	j=1	j=1	PROPN
ejpam-6979	95	33	lmn+1,vf	lmn+1,vf	X
ejpam-6979	95	34	j(ξ	j(ξ	PROPN
ejpam-6979	95	35	)	)	PUNCT
ejpam-6979	95	36	,	,	PUNCT
ejpam-6979	95	37	0	0	NUM
ejpam-6979	95	38	and	and	CCONJ
ejpam-6979	95	39	µ	µ	NOUN
ejpam-6979	95	40	is	be	AUX
ejpam-6979	95	41	convex	convex	ADJ
ejpam-6979	95	42	univalent	univalent	ADJ
ejpam-6979	95	43	in	in	ADP
ejpam-6979	95	44	u	u	NOUN
ejpam-6979	95	45	with	with	ADP
ejpam-6979	95	46	µ(0	µ(0	NOUN
ejpam-6979	95	47	)	)	PUNCT
ejpam-6979	95	48	=	=	SYM
ejpam-6979	95	49	1	1	X
ejpam-6979	95	50	.	.	X
ejpam-6979	95	51	also	also	ADV
ejpam-6979	95	52	we	we	PRON
ejpam-6979	95	53	describe	describe	VERB
ejpam-6979	95	54	f	f	NOUN
ejpam-6979	95	55	=	=	PRON
ejpam-6979	95	56	{	{	PUNCT
ejpam-6979	95	57	f1,f2	f1,f2	PROPN
ejpam-6979	95	58	,	,	PUNCT
ejpam-6979	95	59	...	...	PUNCT
ejpam-6979	95	60	,	,	PUNCT
ejpam-6979	95	61	fϑ	fϑ	ADP
ejpam-6979	95	62	}	}	PUNCT
ejpam-6979	95	63	where	where	SCONJ
ejpam-6979	95	64	fi(ξ	fi(ξ	NOUN
ejpam-6979	95	65	)	)	PUNCT
ejpam-6979	95	66	=	=	SYM
ejpam-6979	96	1	ς+1	ς+1	NUM
ejpam-6979	96	2	ξς	ξς	NUM
ejpam-6979	96	3	ξ∫	ξ∫	PROPN
ejpam-6979	96	4	0	0	NUM
ejpam-6979	97	1	tς−1fi(t)dt	tς−1fi(t)dt	NOUN
ejpam-6979	98	1	(	(	PUNCT
ejpam-6979	98	2	ς	ς	PROPN
ejpam-6979	98	3	∈	∈	PROPN
ejpam-6979	98	4	c	c	X
ejpam-6979	98	5	;	;	PUNCT
ejpam-6979	98	6	re(ς	re(ς	NUM
ejpam-6979	98	7	)	)	PUNCT
ejpam-6979	98	8	>	>	X
ejpam-6979	99	1	0	0	NUM
ejpam-6979	99	2	;	;	PUNCT
ejpam-6979	99	3	i	i	PRON
ejpam-6979	99	4	=	=	NOUN
ejpam-6979	99	5	1	1	NUM
ejpam-6979	99	6	,	,	PUNCT
ejpam-6979	99	7	2	2	NUM
ejpam-6979	99	8	,	,	PUNCT
ejpam-6979	99	9	...	...	PUNCT
ejpam-6979	99	10	,	,	PUNCT
ejpam-6979	99	11	ϑ	ϑ	NOUN
ejpam-6979	99	12	)	)	PUNCT
ejpam-6979	99	13	.	.	PUNCT
ejpam-6979	100	1	and	and	CCONJ
ejpam-6979	100	2	proved	prove	VERB
ejpam-6979	100	3	that	that	SCONJ
ejpam-6979	100	4	f	f	PROPN
ejpam-6979	100	5	∈	∈	PROPN
ejpam-6979	100	6	fℜn	fℜn	PROPN
ejpam-6979	100	7	,	,	PUNCT
ejpam-6979	100	8	v(ϑ	v(ϑ	NOUN
ejpam-6979	100	9	;	;	PUNCT
ejpam-6979	100	10	µ	µ	X
ejpam-6979	100	11	)	)	PUNCT
ejpam-6979	100	12	,	,	PUNCT
ejpam-6979	100	13	whenever	whenever	SCONJ
ejpam-6979	100	14	f	f	PROPN
ejpam-6979	100	15	∈	∈	PROPN
ejpam-6979	100	16	fℜn	fℜn	PROPN
ejpam-6979	100	17	,	,	PUNCT
ejpam-6979	100	18	v(ϑ	v(ϑ	NOUN
ejpam-6979	100	19	;	;	PUNCT
ejpam-6979	100	20	µ	µ	NUM
ejpam-6979	100	21	)	)	PUNCT
ejpam-6979	100	22	.	.	PUNCT
ejpam-6979	101	1	there	there	ADV
ejpam-6979	101	2	more	more	ADV
ejpam-6979	101	3	such	such	ADJ
ejpam-6979	101	4	classes	class	NOUN
ejpam-6979	101	5	denoted	denote	VERB
ejpam-6979	101	6	by	by	ADP
ejpam-6979	101	7	fℵn	fℵn	PROPN
ejpam-6979	101	8	,	,	PUNCT
ejpam-6979	101	9	v(ϑ	v(ϑ	NOUN
ejpam-6979	101	10	;	;	PUNCT
ejpam-6979	101	11	µ	µ	NUM
ejpam-6979	101	12	)	)	PUNCT
ejpam-6979	101	13	,	,	PUNCT
ejpam-6979	101	14	f℘n	f℘n	PROPN
ejpam-6979	101	15	,	,	PUNCT
ejpam-6979	101	16	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	101	17	,	,	PUNCT
ejpam-6979	101	18	µ	µ	NOUN
ejpam-6979	101	19	)	)	PUNCT
ejpam-6979	101	20	and	and	CCONJ
ejpam-6979	101	21	fℜn	fℜn	PROPN
ejpam-6979	101	22	,	,	PUNCT
ejpam-6979	101	23	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	101	24	,	,	PUNCT
ejpam-6979	101	25	µ	µ	X
ejpam-6979	101	26	)	)	PUNCT
ejpam-6979	101	27	are	be	AUX
ejpam-6979	101	28	introduced	introduce	VERB
ejpam-6979	101	29	and	and	CCONJ
ejpam-6979	101	30	studied	study	VERB
ejpam-6979	101	31	here	here	ADV
ejpam-6979	101	32	by	by	ADP
ejpam-6979	101	33	fuzzy	fuzzy	ADJ
ejpam-6979	101	34	subordination	subordination	NOUN
ejpam-6979	101	35	method	method	NOUN
ejpam-6979	101	36	and	and	CCONJ
ejpam-6979	101	37	convolutions	convolution	NOUN
ejpam-6979	101	38	.	.	PUNCT
ejpam-6979	102	1	3	3	X
ejpam-6979	102	2	.	.	X
ejpam-6979	102	3	main	main	ADJ
ejpam-6979	102	4	results	result	NOUN
ejpam-6979	102	5	throughout	throughout	ADP
ejpam-6979	102	6	this	this	DET
ejpam-6979	102	7	paper	paper	NOUN
ejpam-6979	102	8	,	,	PUNCT
ejpam-6979	102	9	unless	unless	SCONJ
ejpam-6979	102	10	otherwise	otherwise	ADV
ejpam-6979	102	11	mentioned	mention	VERB
ejpam-6979	102	12	,	,	PUNCT
ejpam-6979	102	13	we	we	PRON
ejpam-6979	102	14	set	set	VERB
ejpam-6979	102	15	n	n	CCONJ
ejpam-6979	102	16	,	,	PUNCT
ejpam-6979	102	17	v	v	X
ejpam-6979	102	18	>	>	X
ejpam-6979	102	19	1	1	NUM
ejpam-6979	102	20	.	.	NOUN
ejpam-6979	102	21	3.1	3.1	NUM
ejpam-6979	102	22	.	.	PUNCT
ejpam-6979	103	1	the	the	DET
ejpam-6979	103	2	class	class	PROPN
ejpam-6979	103	3	fℜn	fℜn	PROPN
ejpam-6979	103	4	,	,	PUNCT
ejpam-6979	103	5	v(ϑ	v(ϑ	NOUN
ejpam-6979	103	6	;	;	PUNCT
ejpam-6979	103	7	µ	µ	X
ejpam-6979	103	8	)	)	PUNCT
ejpam-6979	103	9	definition	definition	NOUN
ejpam-6979	103	10	5	5	NUM
ejpam-6979	103	11	.	.	PUNCT
ejpam-6979	104	1	let	let	VERB
ejpam-6979	104	2	f	f	PROPN
ejpam-6979	104	3	=	=	PRON
ejpam-6979	104	4	{	{	PUNCT
ejpam-6979	104	5	f1,f2	f1,f2	PROPN
ejpam-6979	104	6	,	,	PUNCT
ejpam-6979	104	7	...	...	PUNCT
ejpam-6979	104	8	,	,	PUNCT
ejpam-6979	104	9	fϑ	fϑ	ADJ
ejpam-6979	104	10	}	}	PUNCT
ejpam-6979	104	11	,	,	PUNCT
ejpam-6979	104	12	fi	fi	NOUN
ejpam-6979	104	13	∈	∈	PROPN
ejpam-6979	104	14	a	a	DET
ejpam-6979	104	15	,	,	PUNCT
ejpam-6979	104	16	1	1	NUM
ejpam-6979	104	17	≤	≤	NUM
ejpam-6979	104	18	i	i	PRON
ejpam-6979	104	19	≤	≤	NOUN
ejpam-6979	104	20	ϑ	ϑ	AUX
ejpam-6979	104	21	be	be	VERB
ejpam-6979	104	22	such	such	ADJ
ejpam-6979	104	23	that	that	DET
ejpam-6979	104	24	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	104	25	)	)	PUNCT
ejpam-6979	104	26			NOUN
ejpam-6979	105	1	ξ	ξ	X
ejpam-6979	105	2	(	(	PUNCT
ejpam-6979	105	3	lmn+1,vfi(ξ	lmn+1,vfi(ξ	NOUN
ejpam-6979	105	4	)	)	PUNCT
ejpam-6979	105	5	)	)	PUNCT
ejpam-6979	106	1	′	′	NOUN
ejpam-6979	106	2	1	1	NUM
ejpam-6979	106	3	ϑ	ϑ	X
ejpam-6979	106	4	ϑ∑	ϑ∑	X
ejpam-6979	106	5	j=1	j=1	PROPN
ejpam-6979	106	6	lmn+1,vf	lmn+1,vf	X
ejpam-6979	106	7	j(ξ	j(ξ	PROPN
ejpam-6979	106	8	)	)	PUNCT
ejpam-6979	106	9			VERB
ejpam-6979	106	10	≤	≤	NUM
ejpam-6979	106	11	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	106	12	)	)	PUNCT
ejpam-6979	106	13	(	(	PUNCT
ejpam-6979	106	14	ξ	ξ	PROPN
ejpam-6979	106	15	∈	∈	PROPN
ejpam-6979	106	16	u	u	NOUN
ejpam-6979	106	17	;	;	PUNCT
ejpam-6979	106	18	i	i	NOUN
ejpam-6979	106	19	=	=	NOUN
ejpam-6979	106	20	1	1	NUM
ejpam-6979	106	21	,	,	PUNCT
ejpam-6979	106	22	2	2	NUM
ejpam-6979	106	23	,	,	PUNCT
ejpam-6979	106	24	...	...	PUNCT
ejpam-6979	106	25	,	,	PUNCT
ejpam-6979	106	26	ϑ	ϑ	X
ejpam-6979	106	27	)	)	PUNCT
ejpam-6979	106	28	,	,	PUNCT
ejpam-6979	106	29	where	where	SCONJ
ejpam-6979	106	30	ξ−1	ξ−1	PROPN
ejpam-6979	106	31	ϑ∑	ϑ∑	PROPN
ejpam-6979	106	32	j=1	j=1	PROPN
ejpam-6979	106	33	lmn+1,vf	lmn+1,vf	X
ejpam-6979	106	34	j(ξ	j(ξ	PROPN
ejpam-6979	106	35	)	)	PUNCT
ejpam-6979	106	36	,	,	PUNCT
ejpam-6979	106	37	0	0	NUM
ejpam-6979	106	38	in	in	ADP
ejpam-6979	106	39	u	u	PROPN
ejpam-6979	106	40	,	,	PUNCT
ejpam-6979	106	41	µ	µ	PRON
ejpam-6979	106	42	is	be	AUX
ejpam-6979	106	43	convex	convex	ADJ
ejpam-6979	106	44	univalent	univalent	ADJ
ejpam-6979	106	45	in	in	ADP
ejpam-6979	106	46	u	u	NOUN
ejpam-6979	106	47	with	with	ADP
ejpam-6979	106	48	µ(0	µ(0	NOUN
ejpam-6979	106	49	)	)	PUNCT
ejpam-6979	106	50	=	=	SYM
ejpam-6979	107	1	1	1	X
ejpam-6979	107	2	.	.	PUNCT
ejpam-6979	107	3	then	then	ADV
ejpam-6979	107	4	we	we	PRON
ejpam-6979	107	5	say	say	VERB
ejpam-6979	107	6	that	that	SCONJ
ejpam-6979	107	7	f	f	PROPN
ejpam-6979	107	8	=	=	PRON
ejpam-6979	107	9	{	{	PUNCT
ejpam-6979	107	10	f1	f1	NOUN
ejpam-6979	107	11	,	,	PUNCT
ejpam-6979	107	12	f2	f2	PROPN
ejpam-6979	107	13	,	,	PUNCT
ejpam-6979	107	14	....	....	PUNCT
ejpam-6979	107	15	,	,	PUNCT
ejpam-6979	107	16	fϑ	fϑ	ADJ
ejpam-6979	107	17	}	}	PUNCT
ejpam-6979	107	18	∈	∈	PROPN
ejpam-6979	107	19	fℜn	fℜn	NOUN
ejpam-6979	107	20	,	,	PUNCT
ejpam-6979	107	21	v(ϑ	v(ϑ	NOUN
ejpam-6979	107	22	;	;	PUNCT
ejpam-6979	107	23	µ	µ	NUM
ejpam-6979	107	24	)	)	PUNCT
ejpam-6979	107	25	.	.	PUNCT
ejpam-6979	108	1	theorem	theorem	NOUN
ejpam-6979	108	2	1	1	NUM
ejpam-6979	108	3	.	.	PUNCT
ejpam-6979	109	1	let	let	VERB
ejpam-6979	109	2	f	f	PROPN
ejpam-6979	109	3	=	=	PRON
ejpam-6979	109	4	{	{	PUNCT
ejpam-6979	109	5	f1	f1	NOUN
ejpam-6979	109	6	,	,	PUNCT
ejpam-6979	109	7	f2	f2	PROPN
ejpam-6979	109	8	,	,	PUNCT
ejpam-6979	109	9	...	...	PUNCT
ejpam-6979	109	10	,	,	PUNCT
ejpam-6979	109	11	fϑ	fϑ	ADJ
ejpam-6979	109	12	}	}	PUNCT
ejpam-6979	109	13	∈	∈	PROPN
ejpam-6979	109	14	fℜn	fℜn	NOUN
ejpam-6979	109	15	,	,	PUNCT
ejpam-6979	109	16	v(ϑ	v(ϑ	NOUN
ejpam-6979	109	17	;	;	PUNCT
ejpam-6979	109	18	µ	µ	X
ejpam-6979	109	19	)	)	PUNCT
ejpam-6979	109	20	and	and	CCONJ
ejpam-6979	109	21	f	f	PROPN
ejpam-6979	109	22	(	(	PUNCT
ejpam-6979	109	23	ξ	ξ	NOUN
ejpam-6979	109	24	)	)	PUNCT
ejpam-6979	109	25	=	=	SYM
ejpam-6979	109	26	1	1	NUM
ejpam-6979	109	27	ϑ	ϑ	VERB
ejpam-6979	109	28	ϑ∑	ϑ∑	X
ejpam-6979	109	29	i=1	i=1	PRON
ejpam-6979	109	30	fi(ξ	fi(ξ	NOUN
ejpam-6979	109	31	)	)	PUNCT
ejpam-6979	109	32	.	.	PUNCT
ejpam-6979	110	1	then	then	ADV
ejpam-6979	110	2	f	f	PROPN
ejpam-6979	110	3	(	(	PUNCT
ejpam-6979	110	4	ξ	ξ	NOUN
ejpam-6979	110	5	)	)	PUNCT
ejpam-6979	110	6	satisfies	satisfie	NOUN
ejpam-6979	110	7	:	:	PUNCT
ejpam-6979	110	8	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	110	9	)	)	PUNCT
ejpam-6979	110	10	ξ	ξ	PUNCT
ejpam-6979	110	11	(	(	PUNCT
ejpam-6979	110	12	lmn+1,vf	lmn+1,vf	X
ejpam-6979	110	13	(	(	PUNCT
ejpam-6979	110	14	ξ	ξ	NOUN
ejpam-6979	110	15	)	)	PUNCT
ejpam-6979	110	16	)	)	PUNCT
ejpam-6979	111	1	′	′	NUM
ejpam-6979	111	2	lmn+1,vf	lmn+1,vf	NUM
ejpam-6979	111	3	(	(	PUNCT
ejpam-6979	111	4	ξ	ξ	NOUN
ejpam-6979	111	5	)	)	PUNCT
ejpam-6979	111	6			VERB
ejpam-6979	111	7	≤	≤	ADJ
ejpam-6979	111	8	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	111	9	)	)	PUNCT
ejpam-6979	111	10	(	(	PUNCT
ejpam-6979	111	11	ξ	ξ	PROPN
ejpam-6979	111	12	∈	∈	PROPN
ejpam-6979	111	13	u	u	NOUN
ejpam-6979	111	14	)	)	PUNCT
ejpam-6979	111	15	(	(	PUNCT
ejpam-6979	111	16	10	10	X
ejpam-6979	111	17	)	)	PUNCT
ejpam-6979	111	18	proof	proof	NOUN
ejpam-6979	111	19	.	.	PUNCT
ejpam-6979	112	1	let	let	VERB
ejpam-6979	112	2	f	f	NOUN
ejpam-6979	112	3	=	=	PRON
ejpam-6979	112	4	{	{	PUNCT
ejpam-6979	112	5	f1	f1	NOUN
ejpam-6979	112	6	,	,	PUNCT
ejpam-6979	112	7	f2	f2	PROPN
ejpam-6979	112	8	,	,	PUNCT
ejpam-6979	112	9	...	...	PUNCT
ejpam-6979	112	10	,	,	PUNCT
ejpam-6979	112	11	fϑ	fϑ	ADJ
ejpam-6979	112	12	}	}	PUNCT
ejpam-6979	112	13	∈	∈	PROPN
ejpam-6979	112	14	fℜn	fℜn	NOUN
ejpam-6979	112	15	,	,	PUNCT
ejpam-6979	112	16	v(ϑ	v(ϑ	NOUN
ejpam-6979	112	17	;	;	PUNCT
ejpam-6979	112	18	µ).then	µ).then	PROPN
ejpam-6979	112	19	for	for	ADP
ejpam-6979	112	20	any	any	DET
ejpam-6979	112	21	ξ0	ξ0	PROPN
ejpam-6979	112	22	∈	∈	PROPN
ejpam-6979	112	23	u	u	NOUN
ejpam-6979	112	24	,	,	PUNCT
ejpam-6979	112	25	we	we	PRON
ejpam-6979	112	26	have	have	VERB
ejpam-6979	112	27	ξ0	ξ0	PROPN
ejpam-6979	112	28	(	(	PUNCT
ejpam-6979	112	29	lmn+1,vfi(ξ0	lmn+1,vfi(ξ0	PROPN
ejpam-6979	112	30	)	)	PUNCT
ejpam-6979	112	31	)	)	PUNCT
ejpam-6979	113	1	′	′	NOUN
ejpam-6979	113	2	1	1	NUM
ejpam-6979	113	3	ϑ	ϑ	X
ejpam-6979	113	4	ϑ∑	ϑ∑	X
ejpam-6979	113	5	j=1	j=1	PROPN
ejpam-6979	113	6	lmn+1,vf	lmn+1,vf	X
ejpam-6979	113	7	j(ξ0	j(ξ0	NOUN
ejpam-6979	113	8	)	)	PUNCT
ejpam-6979	113	9	≺f	≺f	PROPN
ejpam-6979	113	10	µ(ξ	µ(ξ	X
ejpam-6979	113	11	)	)	PUNCT
ejpam-6979	113	12	and	and	CCONJ
ejpam-6979	113	13	hence	hence	ADV
ejpam-6979	113	14	equals	equal	VERB
ejpam-6979	113	15	to	to	ADP
ejpam-6979	113	16	µ(wi)(say	µ(wi)(say	NOUN
ejpam-6979	113	17	)	)	PUNCT
ejpam-6979	113	18	for	for	ADP
ejpam-6979	113	19	some	some	DET
ejpam-6979	113	20	wi	wi	PROPN
ejpam-6979	113	21	∈	∈	PROPN
ejpam-6979	113	22	u	u	PROPN
ejpam-6979	113	23	,	,	PUNCT
ejpam-6979	113	24	i	i	PRON
ejpam-6979	113	25	=	=	NOUN
ejpam-6979	113	26	1	1	NUM
ejpam-6979	113	27	,	,	PUNCT
ejpam-6979	113	28	2	2	NUM
ejpam-6979	113	29	,	,	PUNCT
ejpam-6979	113	30	...	...	PUNCT
ejpam-6979	113	31	,	,	PUNCT
ejpam-6979	113	32	ϑ.	ϑ.	NOUN
ejpam-6979	113	33	then	then	ADV
ejpam-6979	113	34	ϑ∑	ϑ∑	PROPN
ejpam-6979	113	35	i=1	i=1	PROPN
ejpam-6979	113	36	ξ0	ξ0	PROPN
ejpam-6979	113	37	(	(	PUNCT
ejpam-6979	113	38	lmn+1,vfi(ξ0	lmn+1,vfi(ξ0	PROPN
ejpam-6979	113	39	)	)	PUNCT
ejpam-6979	113	40	)	)	PUNCT
ejpam-6979	114	1	′	′	NUM
ejpam-6979	114	2	1	1	NUM
ejpam-6979	114	3	ϑ	ϑ	X
ejpam-6979	114	4	ϑ∑	ϑ∑	X
ejpam-6979	114	5	j=1	j=1	PROPN
ejpam-6979	114	6	lmn+1,vf	lmn+1,vf	X
ejpam-6979	114	7	j(ξ0	j(ξ0	NOUN
ejpam-6979	114	8	)	)	PUNCT
ejpam-6979	114	9	=	=	PUNCT
ejpam-6979	114	10	ϑ∑	ϑ∑	X
ejpam-6979	114	11	i=1	i=1	PRON
ejpam-6979	114	12	µ(wi	µ(wi	ADV
ejpam-6979	114	13	)	)	PUNCT
ejpam-6979	114	14	.	.	PUNCT
ejpam-6979	115	1	e.	e.	PROPN
ejpam-6979	115	2	e.	e.	PROPN
ejpam-6979	115	3	ali	ali	PROPN
ejpam-6979	115	4	et	et	PROPN
ejpam-6979	115	5	al	al	PROPN
ejpam-6979	115	6	.	.	PUNCT
ejpam-6979	115	7	/	/	SYM
ejpam-6979	115	8	eur	eur	PROPN
ejpam-6979	115	9	.	.	PUNCT
ejpam-6979	116	1	j.	j.	PROPN
ejpam-6979	116	2	pure	pure	PROPN
ejpam-6979	116	3	appl	appl	PROPN
ejpam-6979	116	4	.	.	PROPN
ejpam-6979	116	5	math	math	PROPN
ejpam-6979	116	6	,	,	PUNCT
ejpam-6979	116	7	18	18	NUM
ejpam-6979	116	8	(	(	PUNCT
ejpam-6979	116	9	4	4	NUM
ejpam-6979	116	10	)	)	PUNCT
ejpam-6979	116	11	(	(	PUNCT
ejpam-6979	116	12	2025	2025	NUM
ejpam-6979	116	13	)	)	PUNCT
ejpam-6979	116	14	,	,	PUNCT
ejpam-6979	116	15	6979	6979	NUM
ejpam-6979	116	16	6	6	NUM
ejpam-6979	116	17	of	of	ADP
ejpam-6979	116	18	18	18	NUM
ejpam-6979	116	19	let	let	VERB
ejpam-6979	116	20	f(ξ	f(ξ	NOUN
ejpam-6979	116	21	)	)	PUNCT
ejpam-6979	116	22	=	=	SYM
ejpam-6979	117	1	ξ	ξ	PROPN
ejpam-6979	117	2	+	+	PUNCT
ejpam-6979	117	3	∞∑	∞∑	NUM
ejpam-6979	117	4	κ=2	κ=2	NUM
ejpam-6979	117	5	aκξκ	aκξκ	NOUN
ejpam-6979	117	6	.	.	PUNCT
ejpam-6979	118	1	then	then	ADV
ejpam-6979	118	2	,	,	PUNCT
ejpam-6979	118	3	from	from	ADP
ejpam-6979	118	4	(	(	PUNCT
ejpam-6979	118	5	7	7	NUM
ejpam-6979	118	6	)	)	PUNCT
ejpam-6979	118	7	,	,	PUNCT
ejpam-6979	118	8	we	we	PRON
ejpam-6979	118	9	see	see	VERB
ejpam-6979	118	10	that	that	SCONJ
ejpam-6979	118	11	lmn	lmn	NOUN
ejpam-6979	118	12	,	,	PUNCT
ejpam-6979	118	13	vf(ξ	vf(ξ	NUM
ejpam-6979	118	14	)	)	PUNCT
ejpam-6979	118	15	=	=	SYM
ejpam-6979	118	16	f(ξ	f(ξ	X
ejpam-6979	118	17	)	)	PUNCT
ejpam-6979	118	18	∗	∗	NOUN
ejpam-6979	118	19	{	{	PUNCT
ejpam-6979	118	20	ξ	ξ	X
ejpam-6979	118	21	+	+	PROPN
ejpam-6979	118	22	∞κ=2	∞κ=2	NOUN
ejpam-6979	118	23	(	(	PUNCT
ejpam-6979	118	24	−1)κ−1	−1)κ−1	PROPN
ejpam-6979	118	25	4κ−1	4κ−1	PROPN
ejpam-6979	118	26	(	(	PUNCT
ejpam-6979	118	27	n)κ−1	n)κ−1	PROPN
ejpam-6979	118	28	(	(	PUNCT
ejpam-6979	118	29	v)κ−1	v)κ−1	NOUN
ejpam-6979	118	30	ξk	ξk	ADP
ejpam-6979	118	31	}	}	PUNCT
ejpam-6979	118	32	=	=	SYM
ejpam-6979	118	33	(	(	PUNCT
ejpam-6979	118	34	ln	ln	ADJ
ejpam-6979	118	35	,	,	PUNCT
ejpam-6979	118	36	v	v	NOUN
ejpam-6979	118	37	∗	∗	X
ejpam-6979	118	38	f	f	NOUN
ejpam-6979	118	39	)	)	PUNCT
ejpam-6979	118	40	(	(	PUNCT
ejpam-6979	118	41	ξ	ξ	NOUN
ejpam-6979	118	42	)	)	PUNCT
ejpam-6979	118	43	,	,	PUNCT
ejpam-6979	118	44	where	where	SCONJ
ejpam-6979	118	45	ln	ln	ADJ
ejpam-6979	118	46	,	,	PUNCT
ejpam-6979	118	47	v(ξ	v(ξ	NOUN
ejpam-6979	118	48	)	)	PUNCT
ejpam-6979	118	49	=	=	SYM
ejpam-6979	119	1	ξ	ξ	PROPN
ejpam-6979	120	1	+	+	PUNCT
ejpam-6979	121	1	∞∑	∞∑	NUM
ejpam-6979	121	2	κ=2	κ=2	SYM
ejpam-6979	121	3	(	(	PUNCT
ejpam-6979	121	4	−1)κ−1	−1)κ−1	PROPN
ejpam-6979	121	5	4κ−1	4κ−1	PROPN
ejpam-6979	121	6	(	(	PUNCT
ejpam-6979	121	7	n)κ−1	n)κ−1	PROPN
ejpam-6979	121	8	(	(	PUNCT
ejpam-6979	121	9	v)κ−1	v)κ−1	PROPN
ejpam-6979	121	10	ξk	ξk	PROPN
ejpam-6979	121	11	.	.	PUNCT
ejpam-6979	122	1	(	(	PUNCT
ejpam-6979	122	2	11	11	NUM
ejpam-6979	122	3	)	)	PUNCT
ejpam-6979	122	4	hence	hence	ADV
ejpam-6979	122	5	ξ0	ξ0	NOUN
ejpam-6979	122	6	(	(	PUNCT
ejpam-6979	122	7	lmn+1,vf	lmn+1,vf	X
ejpam-6979	122	8	(	(	PUNCT
ejpam-6979	122	9	ξ0	ξ0	NOUN
ejpam-6979	122	10	)	)	PUNCT
ejpam-6979	122	11	)	)	PUNCT
ejpam-6979	123	1	′	′	NUM
ejpam-6979	123	2	lmn+1,vf	lmn+1,vf	NUM
ejpam-6979	123	3	(	(	PUNCT
ejpam-6979	123	4	ξ0	ξ0	NOUN
ejpam-6979	123	5	)	)	PUNCT
ejpam-6979	123	6	=	=	SYM
ejpam-6979	124	1	ξ0[ln	ξ0[ln	NOUN
ejpam-6979	124	2	,	,	PUNCT
ejpam-6979	124	3	v(ξ	v(ξ	NOUN
ejpam-6979	124	4	)	)	PUNCT
ejpam-6979	124	5	∗	∗	NOUN
ejpam-6979	124	6	ϑ∑	ϑ∑	X
ejpam-6979	124	7	i=1	i=1	PROPN
ejpam-6979	124	8	fi(ξ0	fi(ξ0	PROPN
ejpam-6979	124	9	)	)	PUNCT
ejpam-6979	124	10	]	]	PUNCT
ejpam-6979	125	1	′	′	NUM
ejpam-6979	125	2	ln	ln	ADJ
ejpam-6979	125	3	,	,	PUNCT
ejpam-6979	125	4	v(ξ	v(ξ	NOUN
ejpam-6979	125	5	)	)	PUNCT
ejpam-6979	125	6	∗	∗	NOUN
ejpam-6979	125	7	ϑ∑	ϑ∑	X
ejpam-6979	125	8	j=1	j=1	PROPN
ejpam-6979	125	9	f	f	PROPN
ejpam-6979	125	10	j(ξ0	j(ξ0	PROPN
ejpam-6979	125	11	)	)	PUNCT
ejpam-6979	125	12	.	.	PUNCT
ejpam-6979	126	1	since	since	SCONJ
ejpam-6979	126	2	lmn+1,v	lmn+1,v	PROPN
ejpam-6979	126	3	ϑ∑	ϑ∑	NOUN
ejpam-6979	126	4	j=1	j=1	PROPN
ejpam-6979	126	5	f	f	PROPN
ejpam-6979	126	6	j(ξ	j(ξ	PROPN
ejpam-6979	126	7	)	)	PUNCT
ejpam-6979	126	8	=	=	PUNCT
ejpam-6979	126	9	ϑ∑	ϑ∑	PROPN
ejpam-6979	126	10	j=1	j=1	PROPN
ejpam-6979	126	11	lmn+1,vf	lmn+1,vf	X
ejpam-6979	126	12	j(ξ	j(ξ	PROPN
ejpam-6979	126	13	)	)	PUNCT
ejpam-6979	126	14	,	,	PUNCT
ejpam-6979	126	15	we	we	PRON
ejpam-6979	126	16	have	have	VERB
ejpam-6979	126	17	ξ0	ξ0	NOUN
ejpam-6979	126	18	(	(	PUNCT
ejpam-6979	126	19	lmn+1,vf	lmn+1,vf	X
ejpam-6979	126	20	(	(	PUNCT
ejpam-6979	126	21	ξ0	ξ0	NOUN
ejpam-6979	126	22	)	)	PUNCT
ejpam-6979	126	23	)	)	PUNCT
ejpam-6979	127	1	′	′	NUM
ejpam-6979	128	1	lmn+1,vf	lmn+1,vf	NUM
ejpam-6979	128	2	(	(	PUNCT
ejpam-6979	128	3	ξ0	ξ0	PROPN
ejpam-6979	128	4	)	)	PUNCT
ejpam-6979	128	5	=	=	SYM
ejpam-6979	129	1	1	1	NUM
ejpam-6979	129	2	ϑ	ϑ	X
ejpam-6979	129	3			NOUN
ejpam-6979	129	4	ξ0	ξ0	ADJ
ejpam-6979	129	5	ϑ∑	ϑ∑	NOUN
ejpam-6979	129	6	i=1	i=1	PROPN
ejpam-6979	129	7	(	(	PUNCT
ejpam-6979	129	8	lmn+1,vfi(ξ0	lmn+1,vfi(ξ0	PROPN
ejpam-6979	129	9	)	)	PUNCT
ejpam-6979	129	10	)	)	PUNCT
ejpam-6979	130	1	′	′	NOUN
ejpam-6979	130	2	1	1	NUM
ejpam-6979	130	3	ϑ	ϑ	X
ejpam-6979	130	4	ϑ∑	ϑ∑	X
ejpam-6979	130	5	j=1	j=1	PROPN
ejpam-6979	130	6	lmn+1,vf	lmn+1,vf	X
ejpam-6979	130	7	j(ξ0	j(ξ0	NOUN
ejpam-6979	130	8	)	)	PUNCT
ejpam-6979	130	9			PUNCT
ejpam-6979	130	10	=	=	SYM
ejpam-6979	130	11	1	1	NUM
ejpam-6979	130	12	ϑ	ϑ	PROPN
ejpam-6979	130	13	ϑ∑	ϑ∑	X
ejpam-6979	130	14	i=1	i=1	PRON
ejpam-6979	130	15	µ(wi	µ(wi	ADV
ejpam-6979	130	16	)	)	PUNCT
ejpam-6979	130	17	=	=	SYM
ejpam-6979	130	18	µ(w0	µ(w0	NOUN
ejpam-6979	130	19	)	)	PUNCT
ejpam-6979	130	20	,	,	PUNCT
ejpam-6979	130	21	for	for	ADP
ejpam-6979	130	22	some	some	DET
ejpam-6979	130	23	w0	w0	PROPN
ejpam-6979	130	24	∈	∈	PROPN
ejpam-6979	130	25	u	u	NOUN
ejpam-6979	130	26	,	,	PUNCT
ejpam-6979	130	27	since	since	SCONJ
ejpam-6979	130	28	µ	µ	NOUN
ejpam-6979	130	29	is	be	AUX
ejpam-6979	130	30	convex	convex	PROPN
ejpam-6979	130	31	inu	inu	PROPN
ejpam-6979	130	32	.	.	PUNCT
ejpam-6979	131	1	theorem	theorem	PROPN
ejpam-6979	131	2	2	2	NUM
ejpam-6979	131	3	.	.	PUNCT
ejpam-6979	131	4	suppose	suppose	VERB
ejpam-6979	131	5	f	f	X
ejpam-6979	131	6	=	=	NOUN
ejpam-6979	131	7	{	{	PUNCT
ejpam-6979	131	8	f1	f1	NOUN
ejpam-6979	131	9	,	,	PUNCT
ejpam-6979	131	10	f2	f2	PROPN
ejpam-6979	131	11	,	,	PUNCT
ejpam-6979	131	12	...	...	PUNCT
ejpam-6979	131	13	,	,	PUNCT
ejpam-6979	131	14	fϑ	fϑ	ADJ
ejpam-6979	131	15	}	}	PUNCT
ejpam-6979	131	16	∈	∈	PROPN
ejpam-6979	131	17	fℜn	fℜn	NOUN
ejpam-6979	131	18	,	,	PUNCT
ejpam-6979	131	19	v(ϑ	v(ϑ	NOUN
ejpam-6979	131	20	;	;	PUNCT
ejpam-6979	131	21	µ	µ	NUM
ejpam-6979	131	22	)	)	PUNCT
ejpam-6979	131	23	.	.	PUNCT
ejpam-6979	132	1	define	define	VERB
ejpam-6979	132	2	fi(ξ	fi(ξ	NOUN
ejpam-6979	132	3	)	)	PUNCT
ejpam-6979	132	4	=	=	SYM
ejpam-6979	133	1	ς	ς	PROPN
ejpam-6979	134	1	+	+	NUM
ejpam-6979	134	2	1	1	NUM
ejpam-6979	134	3	ξς	ξς	NUM
ejpam-6979	134	4	ξ∫	ξ∫	NUM
ejpam-6979	134	5	0	0	PUNCT
ejpam-6979	135	1	tς−1	tς−1	PROPN
ejpam-6979	135	2	fi(t)dt	fi(t)dt	NOUN
ejpam-6979	135	3	(	(	PUNCT
ejpam-6979	135	4	ς	ς	PROPN
ejpam-6979	135	5	∈	∈	PROPN
ejpam-6979	135	6	c	c	X
ejpam-6979	135	7	;	;	PUNCT
ejpam-6979	135	8	re(ς	re(ς	NUM
ejpam-6979	135	9	)	)	PUNCT
ejpam-6979	135	10	>	>	X
ejpam-6979	135	11	0	0	NUM
ejpam-6979	135	12	;	;	PUNCT
ejpam-6979	135	13	i	i	PRON
ejpam-6979	135	14	=	=	NOUN
ejpam-6979	135	15	1	1	NUM
ejpam-6979	135	16	,	,	PUNCT
ejpam-6979	135	17	2	2	NUM
ejpam-6979	135	18	,	,	PUNCT
ejpam-6979	135	19	...	...	PUNCT
ejpam-6979	135	20	,	,	PUNCT
ejpam-6979	135	21	ϑ	ϑ	NOUN
ejpam-6979	135	22	)	)	PUNCT
ejpam-6979	135	23	.	.	PUNCT
ejpam-6979	136	1	if	if	SCONJ
ejpam-6979	136	2	µ	µ	NOUN
ejpam-6979	136	3	is	be	AUX
ejpam-6979	136	4	bounded	bound	VERB
ejpam-6979	136	5	inu	inu	NOUN
ejpam-6979	136	6	and	and	CCONJ
ejpam-6979	136	7	re{µ(ξ	re{µ(ξ	NOUN
ejpam-6979	136	8	)	)	PUNCT
ejpam-6979	136	9	+	+	CCONJ
ejpam-6979	136	10	ς	ς	X
ejpam-6979	136	11	}	}	PUNCT
ejpam-6979	136	12	>	>	X
ejpam-6979	136	13	0	0	NUM
ejpam-6979	136	14	,	,	PUNCT
ejpam-6979	136	15	then	then	ADV
ejpam-6979	136	16	f	f	PROPN
ejpam-6979	136	17	=	=	PRON
ejpam-6979	136	18	{	{	PUNCT
ejpam-6979	136	19	f1,f2	f1,f2	PROPN
ejpam-6979	136	20	,	,	PUNCT
ejpam-6979	136	21	...	...	PUNCT
ejpam-6979	136	22	,	,	PUNCT
ejpam-6979	136	23	fϑ	fϑ	ADJ
ejpam-6979	136	24	}	}	PUNCT
ejpam-6979	136	25	∈	∈	PROPN
ejpam-6979	136	26	fℜn	fℜn	NOUN
ejpam-6979	136	27	,	,	PUNCT
ejpam-6979	136	28	v(ϑ	v(ϑ	NOUN
ejpam-6979	136	29	;	;	PUNCT
ejpam-6979	136	30	µ	µ	NUM
ejpam-6979	136	31	)	)	PUNCT
ejpam-6979	136	32	.	.	PUNCT
ejpam-6979	137	1	proof	proof	NOUN
ejpam-6979	137	2	.	.	PUNCT
ejpam-6979	138	1	from	from	ADP
ejpam-6979	138	2	the	the	DET
ejpam-6979	138	3	definition	definition	NOUN
ejpam-6979	138	4	of	of	ADP
ejpam-6979	138	5	fi(ξ	fi(ξ	NOUN
ejpam-6979	138	6	)	)	PUNCT
ejpam-6979	138	7	,	,	PUNCT
ejpam-6979	138	8	it	it	PRON
ejpam-6979	138	9	follows	follow	VERB
ejpam-6979	138	10	that	that	SCONJ
ejpam-6979	138	11	ξf	ξf	ADP
ejpam-6979	139	1	′	′	NUM
ejpam-6979	139	2	i	i	NOUN
ejpam-6979	139	3	(	(	PUNCT
ejpam-6979	139	4	ξ	ξ	NOUN
ejpam-6979	139	5	)	)	PUNCT
ejpam-6979	139	6	+	+	SYM
ejpam-6979	139	7	ςfi(ξ	ςfi(ξ	X
ejpam-6979	139	8	)	)	PUNCT
ejpam-6979	139	9	=	=	SYM
ejpam-6979	139	10	(	(	PUNCT
ejpam-6979	139	11	ς	ς	PROPN
ejpam-6979	139	12	+	+	PROPN
ejpam-6979	139	13	1)fi(ξ	1)fi(ξ	NUM
ejpam-6979	139	14	)	)	PUNCT
ejpam-6979	139	15	,	,	PUNCT
ejpam-6979	139	16	and	and	CCONJ
ejpam-6979	139	17	on	on	ADP
ejpam-6979	139	18	taking	take	VERB
ejpam-6979	139	19	convolution	convolution	NOUN
ejpam-6979	139	20	with	with	ADP
ejpam-6979	139	21	ln	ln	ADJ
ejpam-6979	139	22	,	,	PUNCT
ejpam-6979	139	23	v	v	NOUN
ejpam-6979	139	24	given	give	VERB
ejpam-6979	139	25	by	by	ADP
ejpam-6979	139	26	(	(	PUNCT
ejpam-6979	139	27	11	11	NUM
ejpam-6979	139	28	)	)	PUNCT
ejpam-6979	139	29	,	,	PUNCT
ejpam-6979	139	30	we	we	PRON
ejpam-6979	139	31	obtain	obtain	VERB
ejpam-6979	139	32	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	139	33	,	,	PUNCT
ejpam-6979	139	34	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	139	35	)	)	PUNCT
ejpam-6979	139	36	]	]	PUNCT
ejpam-6979	140	1	′	′	NOUN
ejpam-6979	141	1	+	+	CCONJ
ejpam-6979	141	2	ςlmn	ςlmn	NOUN
ejpam-6979	141	3	,	,	PUNCT
ejpam-6979	141	4	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	141	5	)	)	PUNCT
ejpam-6979	141	6	=	=	SYM
ejpam-6979	141	7	(	(	PUNCT
ejpam-6979	141	8	ς	ς	PROPN
ejpam-6979	141	9	+	+	SYM
ejpam-6979	141	10	1)lmn	1)lmn	NUM
ejpam-6979	141	11	,	,	PUNCT
ejpam-6979	141	12	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	141	13	)	)	PUNCT
ejpam-6979	141	14	,	,	PUNCT
ejpam-6979	141	15	i	i	PRON
ejpam-6979	141	16	=	=	NOUN
ejpam-6979	141	17	1	1	NUM
ejpam-6979	141	18	,	,	PUNCT
ejpam-6979	141	19	2	2	NUM
ejpam-6979	141	20	,	,	PUNCT
ejpam-6979	141	21	...	...	PUNCT
ejpam-6979	141	22	,	,	PUNCT
ejpam-6979	141	23	ϑ.	ϑ.	NOUN
ejpam-6979	141	24	(	(	PUNCT
ejpam-6979	141	25	12	12	X
ejpam-6979	141	26	)	)	PUNCT
ejpam-6979	141	27	e.	e.	PROPN
ejpam-6979	141	28	e.	e.	PROPN
ejpam-6979	141	29	ali	ali	PROPN
ejpam-6979	141	30	et	et	PROPN
ejpam-6979	141	31	al	al	PROPN
ejpam-6979	141	32	.	.	PUNCT
ejpam-6979	141	33	/	/	SYM
ejpam-6979	141	34	eur	eur	PROPN
ejpam-6979	141	35	.	.	PUNCT
ejpam-6979	142	1	j.	j.	PROPN
ejpam-6979	142	2	pure	pure	PROPN
ejpam-6979	142	3	appl	appl	PROPN
ejpam-6979	142	4	.	.	PROPN
ejpam-6979	142	5	math	math	PROPN
ejpam-6979	142	6	,	,	PUNCT
ejpam-6979	142	7	18	18	NUM
ejpam-6979	142	8	(	(	PUNCT
ejpam-6979	142	9	4	4	NUM
ejpam-6979	142	10	)	)	PUNCT
ejpam-6979	142	11	(	(	PUNCT
ejpam-6979	142	12	2025	2025	NUM
ejpam-6979	142	13	)	)	PUNCT
ejpam-6979	142	14	,	,	PUNCT
ejpam-6979	142	15	6979	6979	NUM
ejpam-6979	142	16	7	7	NUM
ejpam-6979	142	17	of	of	ADP
ejpam-6979	142	18	18	18	NUM
ejpam-6979	142	19	let	let	VERB
ejpam-6979	142	20	pi(ξ	pi(ξ	PUNCT
ejpam-6979	142	21	)	)	PUNCT
ejpam-6979	142	22	=	=	SYM
ejpam-6979	142	23	ϑξ[lmn	ϑξ[lmn	ADJ
ejpam-6979	142	24	,	,	PUNCT
ejpam-6979	142	25	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	142	26	)	)	PUNCT
ejpam-6979	142	27	]	]	PUNCT
ejpam-6979	143	1	′	′	NUM
ejpam-6979	143	2	ϑ∑	ϑ∑	NOUN
ejpam-6979	143	3	j=1	j=1	PROPN
ejpam-6979	143	4	lmn	lmn	PROPN
ejpam-6979	143	5	,	,	PUNCT
ejpam-6979	143	6	vf	vf	PROPN
ejpam-6979	143	7	j(ξ	j(ξ	PROPN
ejpam-6979	143	8	)	)	PUNCT
ejpam-6979	143	9	.	.	PUNCT
ejpam-6979	144	1	(	(	PUNCT
ejpam-6979	144	2	13	13	NUM
ejpam-6979	144	3	)	)	PUNCT
ejpam-6979	144	4	from	from	ADP
ejpam-6979	144	5	(	(	PUNCT
ejpam-6979	144	6	12	12	NUM
ejpam-6979	144	7	)	)	PUNCT
ejpam-6979	144	8	,	,	PUNCT
ejpam-6979	144	9	we	we	PRON
ejpam-6979	144	10	have	have	VERB
ejpam-6979	144	11	pi(ξ	pi(ξ	NOUN
ejpam-6979	144	12	)	)	PUNCT
ejpam-6979	144	13	ϑ	ϑ	ADP
ejpam-6979	144	14	ϑ∑	ϑ∑	X
ejpam-6979	144	15	j=1	j=1	PROPN
ejpam-6979	144	16	lmn	lmn	PROPN
ejpam-6979	144	17	,	,	PUNCT
ejpam-6979	144	18	vf	vf	PROPN
ejpam-6979	144	19	j(ξ	j(ξ	PROPN
ejpam-6979	144	20	)	)	PUNCT
ejpam-6979	145	1	+	+	CCONJ
ejpam-6979	145	2	ςlmn	ςlmn	NOUN
ejpam-6979	145	3	,	,	PUNCT
ejpam-6979	145	4	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	145	5	)	)	PUNCT
ejpam-6979	145	6	=	=	SYM
ejpam-6979	145	7	(	(	PUNCT
ejpam-6979	145	8	ς	ς	PROPN
ejpam-6979	145	9	+	+	SYM
ejpam-6979	145	10	1)lmn	1)lmn	NUM
ejpam-6979	145	11	,	,	PUNCT
ejpam-6979	145	12	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	145	13	)	)	PUNCT
ejpam-6979	145	14	.	.	PUNCT
ejpam-6979	146	1	(	(	PUNCT
ejpam-6979	146	2	14	14	X
ejpam-6979	146	3	)	)	PUNCT
ejpam-6979	146	4	differentiating	differentiate	VERB
ejpam-6979	146	5	(	(	PUNCT
ejpam-6979	146	6	14	14	NUM
ejpam-6979	146	7	)	)	PUNCT
ejpam-6979	146	8	with	with	ADP
ejpam-6979	146	9	respect	respect	NOUN
ejpam-6979	146	10	to	to	ADP
ejpam-6979	146	11	ξ	ξ	PROPN
ejpam-6979	146	12	,	,	PUNCT
ejpam-6979	146	13	we	we	PRON
ejpam-6979	146	14	obtain	obtain	VERB
ejpam-6979	146	15	p	p	NOUN
ejpam-6979	146	16	′	′	NUM
ejpam-6979	146	17	i(ξ	i(ξ	PROPN
ejpam-6979	146	18	)	)	PUNCT
ejpam-6979	146	19	ϑ	ϑ	ADP
ejpam-6979	146	20	ϑ∑	ϑ∑	X
ejpam-6979	146	21	j=1	j=1	PROPN
ejpam-6979	146	22	lmn	lmn	PROPN
ejpam-6979	146	23	,	,	PUNCT
ejpam-6979	146	24	vf	vf	PROPN
ejpam-6979	146	25	j(ξ	j(ξ	PROPN
ejpam-6979	146	26	)	)	PUNCT
ejpam-6979	146	27	+	+	NUM
ejpam-6979	146	28	pi(ξ	pi(ξ	NOUN
ejpam-6979	146	29	)	)	PUNCT
ejpam-6979	146	30	ϑ	ϑ	X
ejpam-6979	146	31	ϑ∑	ϑ∑	X
ejpam-6979	146	32	j=1	j=1	PUNCT
ejpam-6979	147	1	[	[	X
ejpam-6979	147	2	lmn	lmn	PROPN
ejpam-6979	147	3	,	,	PUNCT
ejpam-6979	147	4	vf	vf	PROPN
ejpam-6979	147	5	j(ξ	j(ξ	PROPN
ejpam-6979	147	6	)	)	PUNCT
ejpam-6979	147	7	]	]	PUNCT
ejpam-6979	147	8	′	′	NUM
ejpam-6979	148	1	+	+	CCONJ
ejpam-6979	148	2	ς[lmn	ς[lmn	NOUN
ejpam-6979	148	3	,	,	PUNCT
ejpam-6979	148	4	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	148	5	)	)	PUNCT
ejpam-6979	148	6	]	]	PUNCT
ejpam-6979	149	1	′	′	NOUN
ejpam-6979	149	2	=	=	PUNCT
ejpam-6979	149	3	(	(	PUNCT
ejpam-6979	149	4	ς	ς	PROPN
ejpam-6979	149	5	+	+	PROPN
ejpam-6979	149	6	1)[lmn	1)[lmn	NUM
ejpam-6979	149	7	,	,	PUNCT
ejpam-6979	149	8	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	149	9	)	)	PUNCT
ejpam-6979	149	10	]	]	PUNCT
ejpam-6979	150	1	′	′	X
ejpam-6979	150	2	.	.	PUNCT
ejpam-6979	151	1	from	from	ADP
ejpam-6979	151	2	(	(	PUNCT
ejpam-6979	151	3	13	13	NUM
ejpam-6979	151	4	)	)	PUNCT
ejpam-6979	151	5	,	,	PUNCT
ejpam-6979	151	6	we	we	PRON
ejpam-6979	151	7	have	have	VERB
ejpam-6979	151	8	p	p	X
ejpam-6979	151	9	′	′	NUM
ejpam-6979	151	10	i(ξ	i(ξ	NOUN
ejpam-6979	151	11	)	)	PUNCT
ejpam-6979	151	12	ϑ∑	ϑ∑	X
ejpam-6979	151	13	j=1	j=1	PROPN
ejpam-6979	151	14	lmn	lmn	PROPN
ejpam-6979	151	15	,	,	PUNCT
ejpam-6979	151	16	vf	vf	PROPN
ejpam-6979	151	17	j(ξ	j(ξ	PROPN
ejpam-6979	151	18	)	)	PUNCT
ejpam-6979	152	1	ϑ	ϑ	X
ejpam-6979	152	2	+	+	X
ejpam-6979	152	3	pi(ξ	pi(ξ	NOUN
ejpam-6979	152	4	)	)	PUNCT
ejpam-6979	152	5	ϑ	ϑ	ADP
ejpam-6979	152	6	ϑ∑	ϑ∑	X
ejpam-6979	152	7	i=1	i=1	PRON
ejpam-6979	152	8	pi(ξ	pi(ξ	NOUN
ejpam-6979	152	9	)	)	PUNCT
ejpam-6979	152	10	ϑ∑	ϑ∑	VERB
ejpam-6979	152	11	j=1	j=1	PROPN
ejpam-6979	152	12	lmn	lmn	PROPN
ejpam-6979	152	13	,	,	PUNCT
ejpam-6979	152	14	vf	vf	PROPN
ejpam-6979	152	15	j(ξ	j(ξ	PROPN
ejpam-6979	152	16	)	)	PUNCT
ejpam-6979	152	17	ϑξ	ϑξ	PROPN
ejpam-6979	153	1	+	+	CCONJ
ejpam-6979	153	2	ς	ς	PROPN
ejpam-6979	153	3	pi(ξ	pi(ξ	X
ejpam-6979	153	4	)	)	PUNCT
ejpam-6979	153	5	ϑ∑	ϑ∑	VERB
ejpam-6979	153	6	j=1	j=1	PROPN
ejpam-6979	153	7	lmn	lmn	PROPN
ejpam-6979	153	8	,	,	PUNCT
ejpam-6979	153	9	vf	vf	PROPN
ejpam-6979	153	10	j(ξ	j(ξ	PROPN
ejpam-6979	153	11	)	)	PUNCT
ejpam-6979	153	12	ϑξ	ϑξ	PROPN
ejpam-6979	154	1	=	=	PUNCT
ejpam-6979	154	2	(	(	PUNCT
ejpam-6979	154	3	ς	ς	PROPN
ejpam-6979	154	4	+	+	PROPN
ejpam-6979	154	5	1)[lmn	1)[lmn	NUM
ejpam-6979	154	6	,	,	PUNCT
ejpam-6979	154	7	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	154	8	)	)	PUNCT
ejpam-6979	154	9	]	]	PUNCT
ejpam-6979	154	10	′	′	X
ejpam-6979	154	11	.	.	PUNCT
ejpam-6979	155	1	hence	hence	ADV
ejpam-6979	155	2	p	p	X
ejpam-6979	155	3	′	′	NUM
ejpam-6979	155	4	i(ξ	i(ξ	PROPN
ejpam-6979	155	5	)	)	PUNCT
ejpam-6979	156	1	+	+	NUM
ejpam-6979	156	2	pi(ξ	pi(ξ	NOUN
ejpam-6979	156	3	)	)	PUNCT
ejpam-6979	156	4	ϑξ	ϑξ	PROPN
ejpam-6979	156	5	ϑ∑	ϑ∑	NOUN
ejpam-6979	156	6	i=1	i=1	PRON
ejpam-6979	156	7	pi(ξ	pi(ξ	PUNCT
ejpam-6979	156	8	)	)	PUNCT
ejpam-6979	157	1	+	+	CCONJ
ejpam-6979	157	2	ς	ς	PROPN
ejpam-6979	157	3	pi(ξ	pi(ξ	X
ejpam-6979	157	4	)	)	PUNCT
ejpam-6979	158	1	ξ	ξ	X
ejpam-6979	158	2	=	=	SYM
ejpam-6979	158	3	(	(	PUNCT
ejpam-6979	158	4	ς	ς	PROPN
ejpam-6979	158	5	+	+	PROPN
ejpam-6979	158	6	1)[lmn	1)[lmn	NUM
ejpam-6979	158	7	,	,	PUNCT
ejpam-6979	158	8	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	158	9	)	)	PUNCT
ejpam-6979	158	10	]	]	PUNCT
ejpam-6979	159	1	′	′	NOUN
ejpam-6979	159	2	1	1	NUM
ejpam-6979	159	3	ϑ	ϑ	X
ejpam-6979	159	4	ϑ∑	ϑ∑	X
ejpam-6979	159	5	j=1	j=1	PROPN
ejpam-6979	159	6	lmn	lmn	PROPN
ejpam-6979	159	7	,	,	PUNCT
ejpam-6979	159	8	vf	vf	PROPN
ejpam-6979	159	9	j(ξ	j(ξ	PROPN
ejpam-6979	159	10	)	)	PUNCT
ejpam-6979	159	11	.	.	PUNCT
ejpam-6979	160	1	then	then	ADV
ejpam-6979	160	2	ξp	ξp	AUX
ejpam-6979	160	3	′	′	NUM
ejpam-6979	160	4	i(ξ	i(ξ	PROPN
ejpam-6979	160	5	)	)	PUNCT
ejpam-6979	160	6	1	1	NUM
ejpam-6979	160	7	ϑ	ϑ	PROPN
ejpam-6979	160	8	ϑ∑	ϑ∑	X
ejpam-6979	160	9	i=1	i=1	PRON
ejpam-6979	160	10	pi(ξ	pi(ξ	PUNCT
ejpam-6979	160	11	)	)	PUNCT
ejpam-6979	161	1	+	+	CCONJ
ejpam-6979	161	2	ς	ς	PROPN
ejpam-6979	161	3	+	+	CCONJ
ejpam-6979	161	4	pi(ξ	pi(ξ	X
ejpam-6979	161	5	)	)	PUNCT
ejpam-6979	161	6	=	=	SYM
ejpam-6979	161	7	(	(	PUNCT
ejpam-6979	161	8	ς	ς	PROPN
ejpam-6979	161	9	+	+	SYM
ejpam-6979	161	10	1)ξ[lmn	1)ξ[lmn	NUM
ejpam-6979	161	11	,	,	PUNCT
ejpam-6979	161	12	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	161	13	)	)	PUNCT
ejpam-6979	161	14	]	]	PUNCT
ejpam-6979	162	1	′	′	NOUN
ejpam-6979	162	2	1	1	NUM
ejpam-6979	162	3	ϑ	ϑ	X
ejpam-6979	162	4	ϑ∑	ϑ∑	X
ejpam-6979	162	5	j=1	j=1	PROPN
ejpam-6979	162	6	lmn	lmn	PROPN
ejpam-6979	162	7	,	,	PUNCT
ejpam-6979	162	8	vf	vf	PROPN
ejpam-6979	162	9	j(ξ	j(ξ	PROPN
ejpam-6979	162	10	)	)	PUNCT
ejpam-6979	162	11	.	.	PUNCT
ejpam-6979	163	1	1	1	NUM
ejpam-6979	163	2	1	1	NUM
ejpam-6979	163	3	ϑ	ϑ	VERB
ejpam-6979	163	4	ϑ∑	ϑ∑	X
ejpam-6979	163	5	i=1	i=1	PRON
ejpam-6979	163	6	pi(ξ	pi(ξ	PUNCT
ejpam-6979	163	7	)	)	PUNCT
ejpam-6979	164	1	+	+	CCONJ
ejpam-6979	164	2	ς	ς	PROPN
ejpam-6979	164	3	=	=	PUNCT
ejpam-6979	164	4	(	(	PUNCT
ejpam-6979	164	5	ς	ς	PROPN
ejpam-6979	164	6	+	+	SYM
ejpam-6979	164	7	1)ξ[lmn	1)ξ[lmn	NUM
ejpam-6979	164	8	,	,	PUNCT
ejpam-6979	164	9	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	164	10	)	)	PUNCT
ejpam-6979	164	11	]	]	PUNCT
ejpam-6979	165	1	′	′	NOUN
ejpam-6979	165	2	1	1	NUM
ejpam-6979	165	3	ϑ	ϑ	X
ejpam-6979	165	4	{	{	PUNCT
ejpam-6979	165	5	1	1	NUM
ejpam-6979	165	6	ϑ	ϑ	X
ejpam-6979	165	7	ϑ∑	ϑ∑	X
ejpam-6979	165	8	j=1	j=1	PROPN
ejpam-6979	165	9	lmn	lmn	PROPN
ejpam-6979	165	10	,	,	PUNCT
ejpam-6979	165	11	vf	vf	PROPN
ejpam-6979	165	12	j(ξ	j(ξ	PROPN
ejpam-6979	165	13	)	)	PUNCT
ejpam-6979	165	14	.	.	PUNCT
ejpam-6979	166	1	ϑ∑	ϑ∑	X
ejpam-6979	166	2	i=1	i=1	PRON
ejpam-6979	166	3	pi(ξ	pi(ξ	PUNCT
ejpam-6979	166	4	)	)	PUNCT
ejpam-6979	167	1	+	+	CCONJ
ejpam-6979	167	2	ς	ς	PROPN
ejpam-6979	167	3	ϑ∑	ϑ∑	PROPN
ejpam-6979	167	4	j=1	j=1	PROPN
ejpam-6979	167	5	lmn	lmn	PROPN
ejpam-6979	167	6	,	,	PUNCT
ejpam-6979	167	7	vf	vf	PROPN
ejpam-6979	167	8	j(ξ	j(ξ	PROPN
ejpam-6979	167	9	)	)	PUNCT
ejpam-6979	167	10	}	}	PUNCT
ejpam-6979	167	11	.	.	PUNCT
ejpam-6979	168	1	from	from	ADP
ejpam-6979	168	2	(	(	PUNCT
ejpam-6979	168	3	14	14	NUM
ejpam-6979	168	4	)	)	PUNCT
ejpam-6979	168	5	,	,	PUNCT
ejpam-6979	168	6	we	we	PRON
ejpam-6979	168	7	have	have	VERB
ejpam-6979	168	8	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	168	9	)	)	PUNCT
ejpam-6979	168	10			NOUN
ejpam-6979	168	11	ξp	ξp	ADP
ejpam-6979	168	12	′	′	NUM
ejpam-6979	168	13	i(ξ	i(ξ	PROPN
ejpam-6979	168	14	)	)	PUNCT
ejpam-6979	168	15	1	1	NUM
ejpam-6979	168	16	ϑ	ϑ	PROPN
ejpam-6979	168	17	ϑ∑	ϑ∑	X
ejpam-6979	168	18	i=1	i=1	PRON
ejpam-6979	168	19	pi(ξ	pi(ξ	PUNCT
ejpam-6979	168	20	)	)	PUNCT
ejpam-6979	169	1	+	+	CCONJ
ejpam-6979	169	2	ς	ς	PROPN
ejpam-6979	169	3	+	+	ADJ
ejpam-6979	169	4	pi(ξ	pi(ξ	X
ejpam-6979	169	5	)	)	PUNCT
ejpam-6979	169	6			PART
ejpam-6979	169	7	=	=	NOUN
ejpam-6979	169	8	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	169	9	)	)	PUNCT
ejpam-6979	169	10			NOUN
ejpam-6979	169	11	(	(	PUNCT
ejpam-6979	169	12	ς	ς	PROPN
ejpam-6979	169	13	+	+	SYM
ejpam-6979	169	14	1)ξ[lmn	1)ξ[lmn	NUM
ejpam-6979	169	15	,	,	PUNCT
ejpam-6979	169	16	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	169	17	)	)	PUNCT
ejpam-6979	169	18	]	]	PUNCT
ejpam-6979	170	1	′	′	NOUN
ejpam-6979	170	2	1	1	NUM
ejpam-6979	170	3	ϑ	ϑ	X
ejpam-6979	170	4	(	(	PUNCT
ejpam-6979	170	5	ς	ς	PROPN
ejpam-6979	170	6	+	+	PROPN
ejpam-6979	170	7	1	1	NUM
ejpam-6979	170	8	)	)	PUNCT
ejpam-6979	170	9	ϑ∑	ϑ∑	NOUN
ejpam-6979	170	10	i=1	i=1	PROPN
ejpam-6979	170	11	lmn	lmn	PROPN
ejpam-6979	170	12	,	,	PUNCT
ejpam-6979	170	13	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	170	14	)	)	PUNCT
ejpam-6979	170	15			PART
ejpam-6979	170	16	≤	≤	NUM
ejpam-6979	170	17	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	170	18	)	)	PUNCT
ejpam-6979	170	19	,	,	PUNCT
ejpam-6979	170	20	(	(	PUNCT
ejpam-6979	170	21	15	15	NUM
ejpam-6979	170	22	)	)	PUNCT
ejpam-6979	170	23	since	since	SCONJ
ejpam-6979	170	24	f	f	PROPN
ejpam-6979	170	25	=	=	SYM
ejpam-6979	170	26	{	{	PUNCT
ejpam-6979	170	27	f1	f1	NOUN
ejpam-6979	170	28	,	,	PUNCT
ejpam-6979	170	29	f2	f2	PROPN
ejpam-6979	170	30	,	,	PUNCT
ejpam-6979	170	31	....	....	PUNCT
ejpam-6979	170	32	,	,	PUNCT
ejpam-6979	170	33	fϑ	fϑ	ADJ
ejpam-6979	170	34	}	}	PUNCT
ejpam-6979	170	35	∈	∈	PROPN
ejpam-6979	170	36	fℜn	fℜn	NOUN
ejpam-6979	170	37	,	,	PUNCT
ejpam-6979	170	38	v(ϑ	v(ϑ	NOUN
ejpam-6979	170	39	;	;	PUNCT
ejpam-6979	170	40	µ	µ	NUM
ejpam-6979	170	41	)	)	PUNCT
ejpam-6979	170	42	.	.	PUNCT
ejpam-6979	171	1	now	now	ADV
ejpam-6979	171	2	we	we	PRON
ejpam-6979	171	3	can	can	AUX
ejpam-6979	171	4	write	write	VERB
ejpam-6979	171	5	for	for	ADP
ejpam-6979	171	6	any	any	DET
ejpam-6979	171	7	ξ0	ξ0	PROPN
ejpam-6979	171	8	∈	∈	PROPN
ejpam-6979	171	9	u	u	NOUN
ejpam-6979	171	10	,	,	PUNCT
ejpam-6979	171	11	1	1	NUM
ejpam-6979	171	12	ϑξ0	ϑξ0	VERB
ejpam-6979	171	13	p	p	ADJ
ejpam-6979	171	14	′	′	NUM
ejpam-6979	171	15	i(ξ0	i(ξ0	NOUN
ejpam-6979	171	16	)	)	PUNCT
ejpam-6979	171	17	1	1	NUM
ejpam-6979	171	18	ϑ	ϑ	X
ejpam-6979	171	19	ϑ∑	ϑ∑	X
ejpam-6979	171	20	j=1	j=1	PROPN
ejpam-6979	172	1	p	p	PROPN
ejpam-6979	172	2	j(ξ0	j(ξ0	NOUN
ejpam-6979	172	3	)	)	PUNCT
ejpam-6979	173	1	+	+	CCONJ
ejpam-6979	174	1	ς	ς	PROPN
ejpam-6979	174	2	+	+	PROPN
ejpam-6979	174	3	1	1	NUM
ejpam-6979	174	4	ϑ	ϑ	NOUN
ejpam-6979	174	5	pi(ξ0	pi(ξ0	NOUN
ejpam-6979	174	6	)	)	PUNCT
ejpam-6979	174	7	=	=	SYM
ejpam-6979	174	8	1	1	NUM
ejpam-6979	174	9	ϑ	ϑ	X
ejpam-6979	174	10	µ(wi	µ(wi	ADV
ejpam-6979	174	11	)	)	PUNCT
ejpam-6979	174	12	,	,	PUNCT
ejpam-6979	174	13	e.	e.	PROPN
ejpam-6979	174	14	e.	e.	PROPN
ejpam-6979	174	15	ali	ali	PROPN
ejpam-6979	174	16	et	et	PROPN
ejpam-6979	174	17	al	al	PROPN
ejpam-6979	174	18	.	.	PUNCT
ejpam-6979	174	19	/	/	SYM
ejpam-6979	174	20	eur	eur	PROPN
ejpam-6979	174	21	.	.	PUNCT
ejpam-6979	175	1	j.	j.	PROPN
ejpam-6979	175	2	pure	pure	PROPN
ejpam-6979	175	3	appl	appl	PROPN
ejpam-6979	175	4	.	.	PROPN
ejpam-6979	175	5	math	math	PROPN
ejpam-6979	175	6	,	,	PUNCT
ejpam-6979	175	7	18	18	NUM
ejpam-6979	175	8	(	(	PUNCT
ejpam-6979	175	9	4	4	NUM
ejpam-6979	175	10	)	)	PUNCT
ejpam-6979	175	11	(	(	PUNCT
ejpam-6979	175	12	2025	2025	NUM
ejpam-6979	175	13	)	)	PUNCT
ejpam-6979	175	14	,	,	PUNCT
ejpam-6979	175	15	6979	6979	NUM
ejpam-6979	175	16	8	8	NUM
ejpam-6979	175	17	of	of	ADP
ejpam-6979	175	18	18	18	NUM
ejpam-6979	175	19	for	for	ADP
ejpam-6979	175	20	some	some	DET
ejpam-6979	175	21	wi	wi	PROPN
ejpam-6979	175	22	∈	∈	PROPN
ejpam-6979	175	23	u.	u.	NOUN
ejpam-6979	175	24	this	this	PRON
ejpam-6979	175	25	is	be	AUX
ejpam-6979	175	26	true	true	ADJ
ejpam-6979	175	27	for	for	ADP
ejpam-6979	175	28	i	i	PROPN
ejpam-6979	175	29	=	=	NOUN
ejpam-6979	175	30	1	1	NUM
ejpam-6979	175	31	,	,	PUNCT
ejpam-6979	175	32	2	2	NUM
ejpam-6979	175	33	,	,	PUNCT
ejpam-6979	175	34	...	...	PUNCT
ejpam-6979	175	35	,	,	PUNCT
ejpam-6979	175	36	ϑ.	ϑ.	NOUN
ejpam-6979	175	37	since	since	SCONJ
ejpam-6979	175	38	µ	µ	NOUN
ejpam-6979	175	39	is	be	AUX
ejpam-6979	175	40	convex	convex	ADJ
ejpam-6979	175	41	,	,	PUNCT
ejpam-6979	175	42	there	there	PRON
ejpam-6979	175	43	exists	exist	VERB
ejpam-6979	175	44	a	a	DET
ejpam-6979	175	45	w0	w0	PROPN
ejpam-6979	175	46	∈	∈	PROPN
ejpam-6979	175	47	u	u	NOUN
ejpam-6979	175	48	such	such	ADJ
ejpam-6979	175	49	that	that	SCONJ
ejpam-6979	175	50	ξ0q	ξ0q	PRON
ejpam-6979	175	51	′	′	NUM
ejpam-6979	175	52	(	(	PUNCT
ejpam-6979	175	53	ξ0	ξ0	PROPN
ejpam-6979	175	54	)	)	PUNCT
ejpam-6979	175	55	q(ξ0	q(ξ0	NOUN
ejpam-6979	175	56	)	)	PUNCT
ejpam-6979	176	1	+	+	CCONJ
ejpam-6979	176	2	ς	ς	PROPN
ejpam-6979	176	3	+	+	NUM
ejpam-6979	176	4	q(ξ0	q(ξ0	NOUN
ejpam-6979	176	5	)	)	PUNCT
ejpam-6979	176	6	=	=	SYM
ejpam-6979	176	7	µ(w0	µ(w0	NOUN
ejpam-6979	176	8	)	)	PUNCT
ejpam-6979	176	9	,	,	PUNCT
ejpam-6979	176	10	where	where	SCONJ
ejpam-6979	176	11	q(ξ	q(ξ	ADV
ejpam-6979	176	12	)	)	PUNCT
ejpam-6979	176	13	=	=	SYM
ejpam-6979	177	1	1	1	NUM
ejpam-6979	177	2	ϑ	ϑ	VERB
ejpam-6979	177	3	ϑ∑	ϑ∑	X
ejpam-6979	177	4	i=1	i=1	PRON
ejpam-6979	177	5	pi(ξ	pi(ξ	ADJ
ejpam-6979	177	6	)	)	PUNCT
ejpam-6979	177	7	.	.	PUNCT
ejpam-6979	178	1	hence	hence	ADV
ejpam-6979	178	2	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	178	3	)	)	PUNCT
ejpam-6979	179	1	[	[	PUNCT
ejpam-6979	179	2	ξq	ξq	INTJ
ejpam-6979	179	3	′	′	NUM
ejpam-6979	179	4	(	(	PUNCT
ejpam-6979	179	5	ξ	ξ	NOUN
ejpam-6979	179	6	)	)	PUNCT
ejpam-6979	179	7	q(ξ	q(ξ	ADV
ejpam-6979	179	8	)	)	PUNCT
ejpam-6979	180	1	+	+	CCONJ
ejpam-6979	181	1	ς	ς	PROPN
ejpam-6979	181	2	+	+	NOUN
ejpam-6979	181	3	q(ξ	q(ξ	ADJ
ejpam-6979	181	4	)	)	PUNCT
ejpam-6979	181	5	]	]	PUNCT
ejpam-6979	181	6	≤	≤	NUM
ejpam-6979	181	7	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	181	8	)	)	PUNCT
ejpam-6979	181	9	.	.	PUNCT
ejpam-6979	182	1	since	since	SCONJ
ejpam-6979	182	2	re{µ	re{µ	PROPN
ejpam-6979	182	3	}	}	PUNCT
ejpam-6979	182	4	is	be	AUX
ejpam-6979	182	5	bounded	bound	VERB
ejpam-6979	182	6	and	and	CCONJ
ejpam-6979	182	7	re{µ(ξ	re{µ(ξ	X
ejpam-6979	182	8	)	)	PUNCT
ejpam-6979	183	1	+	+	CCONJ
ejpam-6979	183	2	ς	ς	X
ejpam-6979	183	3	}	}	PUNCT
ejpam-6979	183	4	>	>	X
ejpam-6979	183	5	0	0	NUM
ejpam-6979	183	6	,	,	PUNCT
ejpam-6979	183	7	it	it	PRON
ejpam-6979	183	8	follows	follow	VERB
ejpam-6979	183	9	from	from	ADP
ejpam-6979	183	10	lemma	lemma	PROPN
ejpam-6979	183	11	1	1	NUM
ejpam-6979	183	12	that	that	SCONJ
ejpam-6979	183	13	q(ξ	q(ξ	ADV
ejpam-6979	183	14	)	)	PUNCT
ejpam-6979	183	15	≺f	≺f	PROPN
ejpam-6979	183	16	µ(ξ	µ(ξ	X
ejpam-6979	183	17	)	)	PUNCT
ejpam-6979	183	18	(	(	PUNCT
ejpam-6979	183	19	ξ	ξ	PROPN
ejpam-6979	183	20	∈	∈	PROPN
ejpam-6979	183	21	u	u	NOUN
ejpam-6979	183	22	)	)	PUNCT
ejpam-6979	183	23	.	.	PUNCT
ejpam-6979	184	1	from	from	ADP
ejpam-6979	184	2	(	(	PUNCT
ejpam-6979	184	3	15	15	NUM
ejpam-6979	184	4	)	)	PUNCT
ejpam-6979	184	5	,	,	PUNCT
ejpam-6979	184	6	we	we	PRON
ejpam-6979	184	7	have	have	VERB
ejpam-6979	184	8	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	184	9	)	)	PUNCT
ejpam-6979	184	10			NOUN
ejpam-6979	184	11	ξp	ξp	NOUN
ejpam-6979	184	12	′	′	NUM
ejpam-6979	184	13	i(ξ	i(ξ	PROPN
ejpam-6979	184	14	)	)	PUNCT
ejpam-6979	184	15	q(ξ	q(ξ	ADV
ejpam-6979	184	16	)	)	PUNCT
ejpam-6979	185	1	+	+	CCONJ
ejpam-6979	185	2	ς	ς	PROPN
ejpam-6979	185	3	+	+	CCONJ
ejpam-6979	185	4	pi(ξ	pi(ξ	PROPN
ejpam-6979	185	5	)	)	PUNCT
ejpam-6979	185	6			VERB
ejpam-6979	185	7	≤	≤	ADJ
ejpam-6979	185	8	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	185	9	)	)	PUNCT
ejpam-6979	185	10	,	,	PUNCT
ejpam-6979	185	11	where	where	SCONJ
ejpam-6979	185	12	q(ξ	q(ξ	ADV
ejpam-6979	185	13	)	)	PUNCT
ejpam-6979	186	1	≺f	≺f	PROPN
ejpam-6979	186	2	µ(ξ	µ(ξ	NOUN
ejpam-6979	186	3	)	)	PUNCT
ejpam-6979	186	4	.	.	PUNCT
ejpam-6979	187	1	lemma	lemma	PROPN
ejpam-6979	187	2	2	2	PROPN
ejpam-6979	187	3	gives	give	VERB
ejpam-6979	187	4	pi(ξ	pi(ξ	NOUN
ejpam-6979	187	5	)	)	PUNCT
ejpam-6979	188	1	≺f	≺f	PROPN
ejpam-6979	188	2	µ(ξ	µ(ξ	X
ejpam-6979	188	3	)	)	PUNCT
ejpam-6979	188	4	(	(	PUNCT
ejpam-6979	188	5	ξ	ξ	PROPN
ejpam-6979	188	6	∈	∈	PROPN
ejpam-6979	188	7	u	u	NOUN
ejpam-6979	188	8	)	)	PUNCT
ejpam-6979	188	9	,	,	PUNCT
ejpam-6979	188	10	i	i	PRON
ejpam-6979	188	11	=	=	NOUN
ejpam-6979	188	12	1	1	NUM
ejpam-6979	188	13	,	,	PUNCT
ejpam-6979	188	14	2	2	NUM
ejpam-6979	188	15	,	,	PUNCT
ejpam-6979	188	16	...	...	PUNCT
ejpam-6979	188	17	,	,	PUNCT
ejpam-6979	188	18	ϑ	ϑ	X
ejpam-6979	188	19	,	,	PUNCT
ejpam-6979	188	20	that	that	PRON
ejpam-6979	188	21	is	be	AUX
ejpam-6979	188	22	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	188	23	)	)	PUNCT
ejpam-6979	188	24			NOUN
ejpam-6979	188	25	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	188	26	,	,	PUNCT
ejpam-6979	188	27	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	188	28	)	)	PUNCT
ejpam-6979	188	29	]	]	PUNCT
ejpam-6979	189	1	′	′	NOUN
ejpam-6979	189	2	1	1	NUM
ejpam-6979	189	3	ϑ	ϑ	X
ejpam-6979	189	4	ϑ∑	ϑ∑	X
ejpam-6979	189	5	j=1	j=1	PROPN
ejpam-6979	189	6	lmn	lmn	PROPN
ejpam-6979	189	7	,	,	PUNCT
ejpam-6979	189	8	vf	vf	PROPN
ejpam-6979	189	9	j(ξ	j(ξ	PROPN
ejpam-6979	189	10	)	)	PUNCT
ejpam-6979	189	11			VERB
ejpam-6979	189	12	≤	≤	NUM
ejpam-6979	189	13	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	189	14	)	)	PUNCT
ejpam-6979	189	15	.	.	PUNCT
ejpam-6979	190	1	now	now	ADV
ejpam-6979	190	2	fi(ξ	fi(ξ	VERB
ejpam-6979	190	3	)	)	PUNCT
ejpam-6979	190	4	=	=	SYM
ejpam-6979	191	1	ς	ς	PROPN
ejpam-6979	192	1	+	+	NUM
ejpam-6979	192	2	1	1	NUM
ejpam-6979	192	3	ξς	ξς	NUM
ejpam-6979	192	4	ξ∫	ξ∫	NUM
ejpam-6979	192	5	0	0	NUM
ejpam-6979	193	1	tς−1	tς−1	PROPN
ejpam-6979	193	2	fi(t)dt	fi(t)dt	PROPN
ejpam-6979	193	3	,	,	PUNCT
ejpam-6979	193	4	ς	ς	PROPN
ejpam-6979	193	5	∈	∈	PROPN
ejpam-6979	193	6	c	c	PROPN
ejpam-6979	193	7	,	,	PUNCT
ejpam-6979	193	8	reς	reς	X
ejpam-6979	193	9	>	>	X
ejpam-6979	193	10	0	0	X
ejpam-6979	193	11	.	.	PUNCT
ejpam-6979	194	1	it	it	PRON
ejpam-6979	194	2	can	can	AUX
ejpam-6979	194	3	be	be	AUX
ejpam-6979	194	4	proved	prove	VERB
ejpam-6979	194	5	,	,	PUNCT
ejpam-6979	194	6	easily	easily	ADV
ejpam-6979	194	7	,	,	PUNCT
ejpam-6979	194	8	that	that	SCONJ
ejpam-6979	194	9	,	,	PUNCT
ejpam-6979	194	10	for	for	ADP
ejpam-6979	194	11	every	every	DET
ejpam-6979	194	12	i	i	NOUN
ejpam-6979	194	13	,	,	PUNCT
ejpam-6979	194	14	1	1	NUM
ejpam-6979	194	15	≤	≤	NUM
ejpam-6979	194	16	i	i	PRON
ejpam-6979	194	17	≤	≤	PROPN
ejpam-6979	194	18	ϑ	ϑ	VERB
ejpam-6979	194	19	,	,	PUNCT
ejpam-6979	194	20	lmn	lmn	PROPN
ejpam-6979	194	21	,	,	PUNCT
ejpam-6979	194	22	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	194	23	)	)	PUNCT
ejpam-6979	195	1	=	=	PUNCT
ejpam-6979	195	2	ς	ς	PROPN
ejpam-6979	196	1	+	+	NUM
ejpam-6979	196	2	1	1	NUM
ejpam-6979	196	3	ξς	ξς	NUM
ejpam-6979	196	4	ξ∫	ξ∫	NUM
ejpam-6979	196	5	0	0	NUM
ejpam-6979	197	1	tς−1	tς−1	PROPN
ejpam-6979	197	2	lmn	lmn	PROPN
ejpam-6979	197	3	,	,	PUNCT
ejpam-6979	197	4	vfi(t)dt	vfi(t)dt	NOUN
ejpam-6979	197	5	,	,	PUNCT
ejpam-6979	197	6	and	and	CCONJ
ejpam-6979	197	7	hence	hence	ADV
ejpam-6979	197	8	ϑ∑	ϑ∑	NUM
ejpam-6979	197	9	i=1	i=1	PROPN
ejpam-6979	197	10	lmn	lmn	PROPN
ejpam-6979	197	11	,	,	PUNCT
ejpam-6979	197	12	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	197	13	)	)	PUNCT
ejpam-6979	197	14	=	=	PUNCT
ejpam-6979	198	1	ς	ς	PROPN
ejpam-6979	199	1	+	+	NUM
ejpam-6979	199	2	1	1	NUM
ejpam-6979	199	3	ξς	ξς	NUM
ejpam-6979	199	4	ξ∫	ξ∫	NUM
ejpam-6979	199	5	0	0	NUM
ejpam-6979	200	1	tς−1	tς−1	PROPN
ejpam-6979	200	2	ϑ∑	ϑ∑	NOUN
ejpam-6979	200	3	i=1	i=1	PROPN
ejpam-6979	200	4	lmn	lmn	PROPN
ejpam-6979	200	5	,	,	PUNCT
ejpam-6979	200	6	vfi(t)dt	vfi(t)dt	NUM
ejpam-6979	200	7	=	=	SYM
ejpam-6979	200	8	ς	ς	PROPN
ejpam-6979	200	9	+	+	NUM
ejpam-6979	200	10	1	1	NUM
ejpam-6979	200	11	ξς	ξς	NUM
ejpam-6979	200	12	ϑ∫	ϑ∫	NOUN
ejpam-6979	200	13	0	0	NUM
ejpam-6979	201	1	tςg(t)dt	tςg(t)dt	ADP
ejpam-6979	201	2	,	,	PUNCT
ejpam-6979	201	3	where	where	SCONJ
ejpam-6979	201	4	g(t	g(t	NOUN
ejpam-6979	201	5	)	)	PUNCT
ejpam-6979	202	1	=	=	SYM
ejpam-6979	202	2	t−1	t−1	PROPN
ejpam-6979	202	3	ϑ∑	ϑ∑	NOUN
ejpam-6979	202	4	i=1	i=1	PROPN
ejpam-6979	203	1	lmn	lmn	PROPN
ejpam-6979	203	2	,	,	PUNCT
ejpam-6979	203	3	vfi(t	vfi(t	PROPN
ejpam-6979	203	4	)	)	PUNCT
ejpam-6979	203	5	,	,	PUNCT
ejpam-6979	203	6	0	0	NUM
ejpam-6979	203	7	,	,	PUNCT
ejpam-6979	203	8	for	for	SCONJ
ejpam-6979	203	9	ξ	ξ	PROPN
ejpam-6979	203	10	∈	∈	PROPN
ejpam-6979	203	11	u.	u.	NOUN
ejpam-6979	203	12	now	now	ADV
ejpam-6979	203	13	define	define	VERB
ejpam-6979	203	14	ω(ξ	ω(ξ	NOUN
ejpam-6979	203	15	)	)	PUNCT
ejpam-6979	204	1	=	=	NOUN
ejpam-6979	205	1	∞∑	∞∑	NUM
ejpam-6979	205	2	k=1	k=1	PUNCT
ejpam-6979	205	3	ς	ς	PROPN
ejpam-6979	206	1	+	+	PROPN
ejpam-6979	206	2	1	1	NUM
ejpam-6979	206	3	ς	ς	PROPN
ejpam-6979	206	4	+	+	PROPN
ejpam-6979	206	5	k	k	PROPN
ejpam-6979	206	6	ξk−1	ξk−1	PROPN
ejpam-6979	206	7	,	,	PUNCT
ejpam-6979	206	8	re(ς	re(ς	NUM
ejpam-6979	206	9	)	)	PUNCT
ejpam-6979	206	10	>	>	X
ejpam-6979	206	11	0	0	X
ejpam-6979	206	12	.	.	PUNCT
ejpam-6979	207	1	e.	e.	PROPN
ejpam-6979	207	2	e.	e.	PROPN
ejpam-6979	207	3	ali	ali	PROPN
ejpam-6979	207	4	et	et	PROPN
ejpam-6979	207	5	al	al	PROPN
ejpam-6979	207	6	.	.	PUNCT
ejpam-6979	207	7	/	/	SYM
ejpam-6979	207	8	eur	eur	PROPN
ejpam-6979	207	9	.	.	PUNCT
ejpam-6979	208	1	j.	j.	PROPN
ejpam-6979	208	2	pure	pure	PROPN
ejpam-6979	208	3	appl	appl	PROPN
ejpam-6979	208	4	.	.	PROPN
ejpam-6979	208	5	math	math	PROPN
ejpam-6979	208	6	,	,	PUNCT
ejpam-6979	208	7	18	18	NUM
ejpam-6979	208	8	(	(	PUNCT
ejpam-6979	208	9	4	4	NUM
ejpam-6979	208	10	)	)	PUNCT
ejpam-6979	208	11	(	(	PUNCT
ejpam-6979	208	12	2025	2025	NUM
ejpam-6979	208	13	)	)	PUNCT
ejpam-6979	208	14	,	,	PUNCT
ejpam-6979	208	15	6979	6979	NUM
ejpam-6979	208	16	9	9	NUM
ejpam-6979	208	17	of	of	ADP
ejpam-6979	208	18	18	18	NUM
ejpam-6979	208	19	then	then	ADV
ejpam-6979	208	20	an	an	DET
ejpam-6979	208	21	easy	easy	ADJ
ejpam-6979	208	22	calculations	calculation	NOUN
ejpam-6979	208	23	show	show	VERB
ejpam-6979	208	24	that	that	SCONJ
ejpam-6979	208	25	ξ−1	ξ−1	PROPN
ejpam-6979	208	26	ϑ∑	ϑ∑	NOUN
ejpam-6979	208	27	i=1	i=1	PROPN
ejpam-6979	208	28	lmn	lmn	PROPN
ejpam-6979	208	29	,	,	PUNCT
ejpam-6979	208	30	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	208	31	)	)	PUNCT
ejpam-6979	208	32	=	=	SYM
ejpam-6979	208	33	(	(	PUNCT
ejpam-6979	208	34	ω	ω	NOUN
ejpam-6979	208	35	∗	∗	NOUN
ejpam-6979	208	36	g)(ξ	g)(ξ	PROPN
ejpam-6979	208	37	)	)	PUNCT
ejpam-6979	208	38	,	,	PUNCT
ejpam-6979	208	39	0	0	X
ejpam-6979	208	40	.	.	PUNCT
ejpam-6979	209	1	thus	thus	ADV
ejpam-6979	209	2	f	f	X
ejpam-6979	209	3	=	=	PRON
ejpam-6979	209	4	{	{	PUNCT
ejpam-6979	209	5	f1,f2	f1,f2	PROPN
ejpam-6979	209	6	,	,	PUNCT
ejpam-6979	209	7	...	...	PUNCT
ejpam-6979	209	8	,	,	PUNCT
ejpam-6979	209	9	fϑ	fϑ	ADJ
ejpam-6979	209	10	}	}	PUNCT
ejpam-6979	209	11	∈	∈	PROPN
ejpam-6979	209	12	fℜn	fℜn	NOUN
ejpam-6979	209	13	,	,	PUNCT
ejpam-6979	209	14	v(ϑ	v(ϑ	NOUN
ejpam-6979	209	15	;	;	PUNCT
ejpam-6979	209	16	µ	µ	NUM
ejpam-6979	209	17	)	)	PUNCT
ejpam-6979	209	18	.	.	PUNCT
ejpam-6979	210	1	theorem	theorem	NOUN
ejpam-6979	210	2	3	3	NUM
ejpam-6979	210	3	.	.	PUNCT
ejpam-6979	211	1	if	if	SCONJ
ejpam-6979	211	2	f	f	PROPN
ejpam-6979	211	3	=	=	PRON
ejpam-6979	211	4	{	{	PUNCT
ejpam-6979	211	5	f1,f2	f1,f2	PROPN
ejpam-6979	211	6	,	,	PUNCT
ejpam-6979	211	7	...	...	PUNCT
ejpam-6979	211	8	,	,	PUNCT
ejpam-6979	211	9	fϑ	fϑ	ADJ
ejpam-6979	211	10	}	}	PUNCT
ejpam-6979	211	11	∈	∈	PROPN
ejpam-6979	211	12	fℜn	fℜn	NOUN
ejpam-6979	211	13	,	,	PUNCT
ejpam-6979	211	14	v(ϑ	v(ϑ	NOUN
ejpam-6979	211	15	;	;	PUNCT
ejpam-6979	211	16	µ	µ	NUM
ejpam-6979	211	17	)	)	PUNCT
ejpam-6979	211	18	,	,	PUNCT
ejpam-6979	211	19	and	and	CCONJ
ejpam-6979	211	20	re{µ	re{µ	PROPN
ejpam-6979	211	21	}	}	PUNCT
ejpam-6979	211	22	is	be	AUX
ejpam-6979	211	23	bounded	bound	VERB
ejpam-6979	211	24	in	in	ADP
ejpam-6979	211	25	u	u	NOUN
ejpam-6979	211	26	,	,	PUNCT
ejpam-6979	211	27	then	then	ADV
ejpam-6979	211	28	f	f	PROPN
ejpam-6979	211	29	=	=	PRON
ejpam-6979	211	30	{	{	PUNCT
ejpam-6979	211	31	f1,f2	f1,f2	PROPN
ejpam-6979	211	32	,	,	PUNCT
ejpam-6979	211	33	...	...	PUNCT
ejpam-6979	211	34	,	,	PUNCT
ejpam-6979	211	35	fϑ	fϑ	ADJ
ejpam-6979	211	36	}	}	PUNCT
ejpam-6979	211	37	∈	∈	NOUN
ejpam-6979	211	38	fℜn+1,v(ϑ	fℜn+1,v(ϑ	NOUN
ejpam-6979	211	39	;	;	PUNCT
ejpam-6979	211	40	µ	µ	X
ejpam-6979	211	41	)	)	PUNCT
ejpam-6979	211	42	holds	hold	VERB
ejpam-6979	211	43	for	for	ADP
ejpam-6979	211	44	re{µ(ξ	re{µ(ξ	NOUN
ejpam-6979	211	45	)	)	PUNCT
ejpam-6979	211	46	+	+	CCONJ
ejpam-6979	211	47	(	(	PUNCT
ejpam-6979	211	48	n	n	CCONJ
ejpam-6979	211	49	−	−	PROPN
ejpam-6979	211	50	1	1	NUM
ejpam-6979	211	51	)	)	PUNCT
ejpam-6979	211	52	}	}	PUNCT
ejpam-6979	211	53	>	>	X
ejpam-6979	211	54	0	0	NUM
ejpam-6979	211	55	inu	inu	PROPN
ejpam-6979	211	56	.	.	PUNCT
ejpam-6979	212	1	proof	proof	NOUN
ejpam-6979	212	2	.	.	PUNCT
ejpam-6979	213	1	let	let	VERB
ejpam-6979	213	2	pi(ξ	pi(ξ	PUNCT
ejpam-6979	213	3	)	)	PUNCT
ejpam-6979	213	4	=	=	SYM
ejpam-6979	213	5	ϑξ[lmn+1,vfi(ξ	ϑξ[lmn+1,vfi(ξ	ADJ
ejpam-6979	213	6	)	)	PUNCT
ejpam-6979	213	7	]	]	PUNCT
ejpam-6979	214	1	′	′	NUM
ejpam-6979	214	2	ϑ∑	ϑ∑	NOUN
ejpam-6979	215	1	j=1	j=1	PROPN
ejpam-6979	215	2	lmn+1,vf	lmn+1,vf	X
ejpam-6979	215	3	j(ξ	j(ξ	PROPN
ejpam-6979	215	4	)	)	PUNCT
ejpam-6979	215	5	(	(	PUNCT
ejpam-6979	215	6	ξ	ξ	X
ejpam-6979	215	7	∈	∈	PROPN
ejpam-6979	215	8	u	u	NOUN
ejpam-6979	215	9	;	;	PUNCT
ejpam-6979	215	10	i	i	NOUN
ejpam-6979	215	11	=	=	NOUN
ejpam-6979	215	12	1	1	NUM
ejpam-6979	215	13	,	,	PUNCT
ejpam-6979	215	14	2	2	NUM
ejpam-6979	215	15	,	,	PUNCT
ejpam-6979	215	16	...	...	PUNCT
ejpam-6979	215	17	,	,	PUNCT
ejpam-6979	215	18	ϑ	ϑ	NOUN
ejpam-6979	215	19	)	)	PUNCT
ejpam-6979	215	20	.	.	PUNCT
ejpam-6979	216	1	(	(	PUNCT
ejpam-6979	216	2	16	16	NUM
ejpam-6979	216	3	)	)	PUNCT
ejpam-6979	216	4	from	from	ADP
ejpam-6979	216	5	(	(	PUNCT
ejpam-6979	216	6	8)	8)	NUM
ejpam-6979	216	7	and	and	CCONJ
ejpam-6979	216	8	(	(	PUNCT
ejpam-6979	216	9	16	16	NUM
ejpam-6979	216	10	)	)	PUNCT
ejpam-6979	216	11	,	,	PUNCT
ejpam-6979	216	12	we	we	PRON
ejpam-6979	216	13	have	have	VERB
ejpam-6979	216	14	1	1	NUM
ejpam-6979	216	15	ϑ	ϑ	X
ejpam-6979	216	16	pi(ξ	pi(ξ	X
ejpam-6979	216	17	)	)	PUNCT
ejpam-6979	216	18	ϑ∑	ϑ∑	NOUN
ejpam-6979	217	1	j=1	j=1	PROPN
ejpam-6979	217	2	lmn+1,vf	lmn+1,vf	X
ejpam-6979	217	3	j(ξ	j(ξ	PROPN
ejpam-6979	217	4	)	)	PUNCT
ejpam-6979	218	1	=	=	SYM
ejpam-6979	218	2	nlmn	nlmn	PROPN
ejpam-6979	218	3	,	,	PUNCT
ejpam-6979	218	4	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	218	5	)	)	PUNCT
ejpam-6979	218	6	−	−	PROPN
ejpam-6979	218	7	(	(	PUNCT
ejpam-6979	218	8	n	n	CCONJ
ejpam-6979	218	9	−	−	PROPN
ejpam-6979	218	10	1)lmn+1,vfi(ξ	1)lmn+1,vfi(ξ	NUM
ejpam-6979	218	11	)	)	PUNCT
ejpam-6979	218	12	.	.	PUNCT
ejpam-6979	219	1	(	(	PUNCT
ejpam-6979	219	2	17	17	NUM
ejpam-6979	219	3	)	)	PUNCT
ejpam-6979	219	4	differentiating	differentiate	VERB
ejpam-6979	219	5	(	(	PUNCT
ejpam-6979	219	6	17	17	NUM
ejpam-6979	219	7	)	)	PUNCT
ejpam-6979	219	8	with	with	ADP
ejpam-6979	219	9	respect	respect	NOUN
ejpam-6979	219	10	to	to	ADP
ejpam-6979	219	11	ξ	ξ	PROPN
ejpam-6979	219	12	,	,	PUNCT
ejpam-6979	219	13	we	we	PRON
ejpam-6979	219	14	get	get	VERB
ejpam-6979	219	15	ξ	ξ	PRON
ejpam-6979	219	16	ϑ	ϑ	X
ejpam-6979	219	17	p	p	X
ejpam-6979	219	18	′	′	NUM
ejpam-6979	219	19	i(ξ	i(ξ	NOUN
ejpam-6979	219	20	)	)	PUNCT
ejpam-6979	219	21	ϑ∑	ϑ∑	PROPN
ejpam-6979	220	1	j=1	j=1	PROPN
ejpam-6979	220	2	lmn+1,vf	lmn+1,vf	X
ejpam-6979	220	3	j(ξ	j(ξ	PROPN
ejpam-6979	220	4	)	)	PUNCT
ejpam-6979	221	1	+	+	CCONJ
ejpam-6979	221	2	ξ	ξ	DET
ejpam-6979	221	3	ϑ	ϑ	X
ejpam-6979	221	4	pi(ξ	pi(ξ	X
ejpam-6979	221	5	)	)	PUNCT
ejpam-6979	221	6	ϑ∑	ϑ∑	X
ejpam-6979	221	7	j=1	j=1	PUNCT
ejpam-6979	222	1	[	[	X
ejpam-6979	222	2	lmn+1,vf	lmn+1,vf	X
ejpam-6979	222	3	j(ξ	j(ξ	PROPN
ejpam-6979	222	4	)	)	PUNCT
ejpam-6979	222	5	]	]	PUNCT
ejpam-6979	222	6	′	′	NOUN
ejpam-6979	222	7	=	=	PUNCT
ejpam-6979	222	8	nξ[lmn	nξ[lmn	NOUN
ejpam-6979	222	9	,	,	PUNCT
ejpam-6979	222	10	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	222	11	)	)	PUNCT
ejpam-6979	222	12	]	]	PUNCT
ejpam-6979	223	1	′	′	NUM
ejpam-6979	223	2	−	−	PROPN
ejpam-6979	224	1	(	(	PUNCT
ejpam-6979	224	2	n	n	CCONJ
ejpam-6979	224	3	−	−	PROPN
ejpam-6979	224	4	1)ξ[lmn+1,vfi(ξ	1)ξ[lmn+1,vfi(ξ	NUM
ejpam-6979	224	5	)	)	PUNCT
ejpam-6979	224	6	]	]	PUNCT
ejpam-6979	225	1	′	′	X
ejpam-6979	225	2	.	.	PUNCT
ejpam-6979	226	1	using	use	VERB
ejpam-6979	226	2	(	(	PUNCT
ejpam-6979	226	3	16	16	NUM
ejpam-6979	226	4	)	)	PUNCT
ejpam-6979	226	5	,	,	PUNCT
ejpam-6979	226	6	we	we	PRON
ejpam-6979	226	7	obtain	obtain	VERB
ejpam-6979	226	8	ξ	ξ	X
ejpam-6979	226	9	ϑ	ϑ	X
ejpam-6979	226	10	p	p	X
ejpam-6979	226	11	′	′	NUM
ejpam-6979	226	12	i(ξ	i(ξ	NOUN
ejpam-6979	226	13	)	)	PUNCT
ejpam-6979	226	14	ϑ∑	ϑ∑	PROPN
ejpam-6979	227	1	j=1	j=1	PROPN
ejpam-6979	227	2	lmn+1,vf	lmn+1,vf	X
ejpam-6979	227	3	j(ξ	j(ξ	PROPN
ejpam-6979	227	4	)	)	PUNCT
ejpam-6979	228	1	+	+	NUM
ejpam-6979	228	2	pi(ξ	pi(ξ	X
ejpam-6979	228	3	)	)	PUNCT
ejpam-6979	228	4			NOUN
ejpam-6979	228	5	ξϑ	ξϑ	PROPN
ejpam-6979	228	6	ϑ∑	ϑ∑	NOUN
ejpam-6979	228	7	j=1	j=1	PUNCT
ejpam-6979	229	1	[	[	X
ejpam-6979	229	2	lmn+1,vf	lmn+1,vf	X
ejpam-6979	229	3	j(ξ	j(ξ	PROPN
ejpam-6979	229	4	)	)	PUNCT
ejpam-6979	229	5	]	]	PUNCT
ejpam-6979	230	1	′	′	NUM
ejpam-6979	231	1	+	+	CCONJ
ejpam-6979	231	2	(	(	PUNCT
ejpam-6979	231	3	n	n	CCONJ
ejpam-6979	231	4	−	−	PROPN
ejpam-6979	231	5	1	1	NUM
ejpam-6979	231	6	)	)	PUNCT
ejpam-6979	231	7	ϑ	ϑ	X
ejpam-6979	231	8	ϑ∑	ϑ∑	PROPN
ejpam-6979	231	9	j=1	j=1	PROPN
ejpam-6979	231	10	lmn+1,vf	lmn+1,vf	X
ejpam-6979	231	11	j(ξ	j(ξ	PROPN
ejpam-6979	231	12	)	)	PUNCT
ejpam-6979	231	13			VERB
ejpam-6979	231	14	=	=	NOUN
ejpam-6979	231	15	nξ[lmn	nξ[lmn	NOUN
ejpam-6979	231	16	,	,	PUNCT
ejpam-6979	231	17	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	231	18	)	)	PUNCT
ejpam-6979	231	19	]	]	PUNCT
ejpam-6979	232	1	′	′	X
ejpam-6979	232	2	.	.	PUNCT
ejpam-6979	233	1	then	then	ADV
ejpam-6979	233	2	ξ	ξ	X
ejpam-6979	233	3	ϑ	ϑ	X
ejpam-6979	233	4	p	p	X
ejpam-6979	233	5	′	′	NUM
ejpam-6979	233	6	i(ξ	i(ξ	NOUN
ejpam-6979	233	7	)	)	PUNCT
ejpam-6979	234	1	ϑ∑	ϑ∑	PROPN
ejpam-6979	234	2	j=1	j=1	PROPN
ejpam-6979	234	3	lmn+1,vf	lmn+1,vf	X
ejpam-6979	234	4	j(ξ	j(ξ	PROPN
ejpam-6979	234	5	)	)	PUNCT
ejpam-6979	235	1	ξ	ξ	PROPN
ejpam-6979	235	2	ϑ	ϑ	X
ejpam-6979	235	3	ϑ∑	ϑ∑	X
ejpam-6979	235	4	j=1	j=1	PUNCT
ejpam-6979	236	1	[	[	X
ejpam-6979	236	2	lmn+1,vf	lmn+1,vf	X
ejpam-6979	236	3	j(ξ	j(ξ	PROPN
ejpam-6979	236	4	)	)	PUNCT
ejpam-6979	236	5	]	]	PUNCT
ejpam-6979	237	1	′	′	NUM
ejpam-6979	238	1	+	+	CCONJ
ejpam-6979	238	2	(	(	PUNCT
ejpam-6979	238	3	n−1	n−1	PROPN
ejpam-6979	238	4	)	)	PUNCT
ejpam-6979	238	5	ϑ	ϑ	X
ejpam-6979	238	6	ϑ∑	ϑ∑	X
ejpam-6979	238	7	j=1	j=1	PROPN
ejpam-6979	238	8	lmn+1,vf	lmn+1,vf	X
ejpam-6979	238	9	j(ξ	j(ξ	PROPN
ejpam-6979	238	10	)	)	PUNCT
ejpam-6979	238	11	+	+	NUM
ejpam-6979	239	1	pi(ξ	pi(ξ	X
ejpam-6979	239	2	)	)	PUNCT
ejpam-6979	239	3	=	=	SYM
ejpam-6979	239	4	nξ[lmn	nξ[lmn	NOUN
ejpam-6979	239	5	,	,	PUNCT
ejpam-6979	239	6	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	239	7	)	)	PUNCT
ejpam-6979	239	8	]	]	PUNCT
ejpam-6979	240	1	′	′	NUM
ejpam-6979	240	2	ξ	ξ	X
ejpam-6979	240	3	ϑ	ϑ	X
ejpam-6979	240	4	ϑ∑	ϑ∑	X
ejpam-6979	240	5	j=1	j=1	PUNCT
ejpam-6979	241	1	[	[	X
ejpam-6979	241	2	lmn+1,vf	lmn+1,vf	X
ejpam-6979	241	3	j(ξ	j(ξ	PROPN
ejpam-6979	241	4	)	)	PUNCT
ejpam-6979	241	5	]	]	PUNCT
ejpam-6979	242	1	′	′	NUM
ejpam-6979	243	1	+	+	CCONJ
ejpam-6979	243	2	(	(	PUNCT
ejpam-6979	243	3	n	n	CCONJ
ejpam-6979	243	4	−	−	PROPN
ejpam-6979	243	5	1	1	NUM
ejpam-6979	243	6	)	)	PUNCT
ejpam-6979	243	7	ϑ	ϑ	X
ejpam-6979	243	8	ϑ∑	ϑ∑	PROPN
ejpam-6979	243	9	j=1	j=1	PROPN
ejpam-6979	243	10	lmn+1,vf	lmn+1,vf	X
ejpam-6979	243	11	j(ξ	j(ξ	PROPN
ejpam-6979	243	12	)	)	PUNCT
ejpam-6979	243	13	.	.	PUNCT
ejpam-6979	244	1	using	use	VERB
ejpam-6979	244	2	(	(	PUNCT
ejpam-6979	244	3	8)	8)	NUM
ejpam-6979	244	4	,	,	PUNCT
ejpam-6979	244	5	we	we	PRON
ejpam-6979	244	6	have	have	VERB
ejpam-6979	244	7	ξ	ξ	X
ejpam-6979	244	8	ϑ	ϑ	X
ejpam-6979	244	9	p	p	X
ejpam-6979	244	10	′	′	NUM
ejpam-6979	244	11	i(ξ	i(ξ	NOUN
ejpam-6979	244	12	)	)	PUNCT
ejpam-6979	244	13	ϑ∑	ϑ∑	PROPN
ejpam-6979	245	1	j=1	j=1	PROPN
ejpam-6979	245	2	lmn+1,vf	lmn+1,vf	X
ejpam-6979	245	3	j(ξ	j(ξ	PROPN
ejpam-6979	245	4	)	)	PUNCT
ejpam-6979	246	1	ξ	ξ	PROPN
ejpam-6979	246	2	ϑ	ϑ	X
ejpam-6979	246	3	ϑ∑	ϑ∑	X
ejpam-6979	246	4	j=1	j=1	PUNCT
ejpam-6979	247	1	[	[	X
ejpam-6979	247	2	lmn+1,vf	lmn+1,vf	X
ejpam-6979	247	3	j(ξ	j(ξ	PROPN
ejpam-6979	247	4	)	)	PUNCT
ejpam-6979	247	5	]	]	PUNCT
ejpam-6979	248	1	′	′	NUM
ejpam-6979	249	1	+	+	CCONJ
ejpam-6979	249	2	(	(	PUNCT
ejpam-6979	249	3	n−1	n−1	PROPN
ejpam-6979	249	4	)	)	PUNCT
ejpam-6979	249	5	ϑ	ϑ	X
ejpam-6979	249	6	ϑ∑	ϑ∑	X
ejpam-6979	249	7	j=1	j=1	PROPN
ejpam-6979	249	8	lmn+1,vf	lmn+1,vf	X
ejpam-6979	249	9	j(ξ	j(ξ	PROPN
ejpam-6979	249	10	)	)	PUNCT
ejpam-6979	249	11	+	+	NUM
ejpam-6979	249	12	pi(ξ	pi(ξ	X
ejpam-6979	249	13	)	)	PUNCT
ejpam-6979	249	14	=	=	SYM
ejpam-6979	249	15	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	249	16	,	,	PUNCT
ejpam-6979	249	17	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	249	18	)	)	PUNCT
ejpam-6979	249	19	]	]	PUNCT
ejpam-6979	250	1	′	′	NOUN
ejpam-6979	250	2	1	1	NUM
ejpam-6979	250	3	ϑ	ϑ	X
ejpam-6979	250	4	ϑ∑	ϑ∑	X
ejpam-6979	250	5	j=1	j=1	PROPN
ejpam-6979	250	6	lmn	lmn	PROPN
ejpam-6979	250	7	,	,	PUNCT
ejpam-6979	250	8	vf	vf	PROPN
ejpam-6979	250	9	j(ξ	j(ξ	PROPN
ejpam-6979	250	10	)	)	PUNCT
ejpam-6979	250	11	.	.	PUNCT
ejpam-6979	251	1	(	(	PUNCT
ejpam-6979	251	2	18	18	NUM
ejpam-6979	251	3	)	)	PUNCT
ejpam-6979	251	4	e.	e.	PROPN
ejpam-6979	251	5	e.	e.	PROPN
ejpam-6979	251	6	ali	ali	PROPN
ejpam-6979	251	7	et	et	PROPN
ejpam-6979	251	8	al	al	PROPN
ejpam-6979	251	9	.	.	PUNCT
ejpam-6979	251	10	/	/	SYM
ejpam-6979	251	11	eur	eur	PROPN
ejpam-6979	251	12	.	.	PUNCT
ejpam-6979	252	1	j.	j.	PROPN
ejpam-6979	252	2	pure	pure	PROPN
ejpam-6979	252	3	appl	appl	PROPN
ejpam-6979	252	4	.	.	PROPN
ejpam-6979	252	5	math	math	PROPN
ejpam-6979	252	6	,	,	PUNCT
ejpam-6979	252	7	18	18	NUM
ejpam-6979	252	8	(	(	PUNCT
ejpam-6979	252	9	4	4	NUM
ejpam-6979	252	10	)	)	PUNCT
ejpam-6979	252	11	(	(	PUNCT
ejpam-6979	252	12	2025	2025	NUM
ejpam-6979	252	13	)	)	PUNCT
ejpam-6979	252	14	,	,	PUNCT
ejpam-6979	252	15	6979	6979	NUM
ejpam-6979	252	16	10	10	NUM
ejpam-6979	252	17	of	of	ADP
ejpam-6979	252	18	18	18	NUM
ejpam-6979	252	19	on	on	ADP
ejpam-6979	252	20	the	the	DET
ejpam-6979	252	21	left	left	ADJ
ejpam-6979	252	22	side	side	NOUN
ejpam-6979	252	23	of	of	ADP
ejpam-6979	252	24	(	(	PUNCT
ejpam-6979	252	25	18	18	NUM
ejpam-6979	252	26	)	)	PUNCT
ejpam-6979	252	27	,	,	PUNCT
ejpam-6979	252	28	by	by	ADP
ejpam-6979	252	29	using	use	VERB
ejpam-6979	252	30	(	(	PUNCT
ejpam-6979	252	31	16	16	NUM
ejpam-6979	252	32	)	)	PUNCT
ejpam-6979	253	1	,	,	PUNCT
ejpam-6979	253	2	we	we	PRON
ejpam-6979	253	3	’ve	’ve	VERB
ejpam-6979	253	4	ξp	ξp	NUM
ejpam-6979	253	5	′	′	NUM
ejpam-6979	253	6	i(ξ	i(ξ	PROPN
ejpam-6979	253	7	)	)	PUNCT
ejpam-6979	253	8	1	1	NUM
ejpam-6979	253	9	ϑ	ϑ	X
ejpam-6979	253	10	ϑ∑	ϑ∑	X
ejpam-6979	253	11	j=1	j=1	PROPN
ejpam-6979	254	1	p	p	PROPN
ejpam-6979	254	2	j(ξ	j(ξ	PROPN
ejpam-6979	254	3	)	)	PUNCT
ejpam-6979	255	1	+	+	CCONJ
ejpam-6979	255	2	(	(	PUNCT
ejpam-6979	255	3	n	n	CCONJ
ejpam-6979	255	4	−	−	PROPN
ejpam-6979	255	5	1	1	NUM
ejpam-6979	255	6	)	)	PUNCT
ejpam-6979	255	7	+	+	NUM
ejpam-6979	255	8	pi(ξ	pi(ξ	X
ejpam-6979	255	9	)	)	PUNCT
ejpam-6979	255	10	=	=	SYM
ejpam-6979	255	11	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	255	12	,	,	PUNCT
ejpam-6979	255	13	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	255	14	)	)	PUNCT
ejpam-6979	255	15	]	]	PUNCT
ejpam-6979	256	1	′	′	NOUN
ejpam-6979	256	2	1	1	NUM
ejpam-6979	256	3	ϑ	ϑ	X
ejpam-6979	256	4	ϑ∑	ϑ∑	X
ejpam-6979	256	5	j=1	j=1	PROPN
ejpam-6979	256	6	lmn	lmn	PROPN
ejpam-6979	256	7	,	,	PUNCT
ejpam-6979	256	8	vf	vf	PROPN
ejpam-6979	256	9	j(ξ	j(ξ	PROPN
ejpam-6979	256	10	)	)	PUNCT
ejpam-6979	256	11	.	.	PUNCT
ejpam-6979	257	1	since	since	SCONJ
ejpam-6979	257	2	f	f	PROPN
ejpam-6979	257	3	=	=	PRON
ejpam-6979	257	4	{	{	PUNCT
ejpam-6979	257	5	f1,f2	f1,f2	PROPN
ejpam-6979	257	6	,	,	PUNCT
ejpam-6979	257	7	...	...	PUNCT
ejpam-6979	257	8	,	,	PUNCT
ejpam-6979	257	9	fϑ	fϑ	ADJ
ejpam-6979	257	10	}	}	PUNCT
ejpam-6979	257	11	∈	∈	PROPN
ejpam-6979	257	12	fℜn	fℜn	NOUN
ejpam-6979	257	13	,	,	PUNCT
ejpam-6979	257	14	v(ϑ	v(ϑ	NOUN
ejpam-6979	257	15	;	;	PUNCT
ejpam-6979	257	16	µ	µ	X
ejpam-6979	257	17	)	)	PUNCT
ejpam-6979	257	18	,	,	PUNCT
ejpam-6979	257	19	then	then	ADV
ejpam-6979	257	20	we	we	PRON
ejpam-6979	257	21	’ve	’ve	VERB
ejpam-6979	257	22	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	257	23	)	)	PUNCT
ejpam-6979	257	24			NOUN
ejpam-6979	257	25	ξp′i(ξ	ξp′i(ξ	NOUN
ejpam-6979	257	26	)	)	PUNCT
ejpam-6979	257	27	1	1	NUM
ejpam-6979	257	28	ϑ	ϑ	X
ejpam-6979	257	29	ϑ∑	ϑ∑	X
ejpam-6979	257	30	j=1	j=1	PROPN
ejpam-6979	257	31	p	p	PROPN
ejpam-6979	257	32	j(ξ	j(ξ	PROPN
ejpam-6979	257	33	)	)	PUNCT
ejpam-6979	258	1	+	+	CCONJ
ejpam-6979	258	2	(	(	PUNCT
ejpam-6979	258	3	n	n	CCONJ
ejpam-6979	258	4	−	−	PROPN
ejpam-6979	258	5	1	1	NUM
ejpam-6979	258	6	)	)	PUNCT
ejpam-6979	258	7	+	+	NUM
ejpam-6979	258	8	pi(ξ	pi(ξ	NOUN
ejpam-6979	258	9	)	)	PUNCT
ejpam-6979	258	10			NUM
ejpam-6979	258	11	=	=	SYM
ejpam-6979	258	12	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	258	13	)	)	PUNCT
ejpam-6979	258	14			NOUN
ejpam-6979	259	1	ξ	ξ	X
ejpam-6979	259	2	[	[	X
ejpam-6979	259	3	lmn	lmn	NOUN
ejpam-6979	259	4	,	,	PUNCT
ejpam-6979	259	5	vfi(ξ)]′	vfi(ξ)]′	NOUN
ejpam-6979	259	6	1	1	NUM
ejpam-6979	259	7	ϑ	ϑ	PROPN
ejpam-6979	259	8	ϑ∑	ϑ∑	X
ejpam-6979	259	9	j=1	j=1	PROPN
ejpam-6979	259	10	lmn	lmn	PROPN
ejpam-6979	259	11	,	,	PUNCT
ejpam-6979	259	12	vf	vf	PROPN
ejpam-6979	259	13	j(ξ	j(ξ	PROPN
ejpam-6979	259	14	)	)	PUNCT
ejpam-6979	259	15			VERB
ejpam-6979	259	16	≤	≤	NUM
ejpam-6979	259	17	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	259	18	)	)	PUNCT
ejpam-6979	259	19	,	,	PUNCT
ejpam-6979	259	20	i	i	PRON
ejpam-6979	259	21	=	=	NOUN
ejpam-6979	259	22	1	1	NUM
ejpam-6979	259	23	,	,	PUNCT
ejpam-6979	259	24	2	2	NUM
ejpam-6979	259	25	,	,	PUNCT
ejpam-6979	259	26	.	.	PUNCT
ejpam-6979	259	27	.	.	PUNCT
ejpam-6979	259	28	.	.	PUNCT
ejpam-6979	260	1	,	,	PUNCT
ejpam-6979	260	2	ϑ.	ϑ.	NOUN
ejpam-6979	260	3	(	(	PUNCT
ejpam-6979	260	4	19	19	NUM
ejpam-6979	260	5	)	)	PUNCT
ejpam-6979	260	6	therefore	therefore	ADV
ejpam-6979	260	7	for	for	ADP
ejpam-6979	260	8	any	any	DET
ejpam-6979	260	9	ξ0	ξ0	PROPN
ejpam-6979	260	10	∈	∈	PROPN
ejpam-6979	260	11	u	u	NOUN
ejpam-6979	260	12	,	,	PUNCT
ejpam-6979	260	13	we	we	PRON
ejpam-6979	260	14	have	have	VERB
ejpam-6979	260	15	ξ0	ξ0	PROPN
ejpam-6979	260	16	p	p	NOUN
ejpam-6979	260	17	′	′	NUM
ejpam-6979	260	18	i(ξ0	i(ξ0	NOUN
ejpam-6979	260	19	)	)	PUNCT
ejpam-6979	260	20	1	1	NUM
ejpam-6979	260	21	ϑ	ϑ	X
ejpam-6979	260	22	ϑ∑	ϑ∑	X
ejpam-6979	260	23	j=1	j=1	PROPN
ejpam-6979	261	1	p	p	PROPN
ejpam-6979	261	2	j(ξ0	j(ξ0	NOUN
ejpam-6979	261	3	)	)	PUNCT
ejpam-6979	262	1	+	+	CCONJ
ejpam-6979	262	2	(	(	PUNCT
ejpam-6979	262	3	n	n	CCONJ
ejpam-6979	262	4	−	−	PROPN
ejpam-6979	262	5	1	1	NUM
ejpam-6979	262	6	)	)	PUNCT
ejpam-6979	262	7	+	+	NUM
ejpam-6979	262	8	pi(ξ0	pi(ξ0	X
ejpam-6979	262	9	)	)	PUNCT
ejpam-6979	262	10	=	=	SYM
ejpam-6979	263	1	1	1	NUM
ejpam-6979	263	2	ϑ	ϑ	X
ejpam-6979	263	3	µ(wi	µ(wi	ADV
ejpam-6979	263	4	)	)	PUNCT
ejpam-6979	263	5	for	for	ADP
ejpam-6979	263	6	some	some	DET
ejpam-6979	263	7	w0	w0	PROPN
ejpam-6979	263	8	∈	∈	PROPN
ejpam-6979	263	9	u.	u.	PROPN
ejpam-6979	263	10	since	since	SCONJ
ejpam-6979	263	11	µ	µ	NOUN
ejpam-6979	263	12	is	be	AUX
ejpam-6979	263	13	convex	convex	ADJ
ejpam-6979	263	14	,	,	PUNCT
ejpam-6979	263	15	there	there	PRON
ejpam-6979	263	16	exists	exist	VERB
ejpam-6979	263	17	a	a	DET
ejpam-6979	263	18	wi	wi	PROPN
ejpam-6979	263	19	∈	∈	PROPN
ejpam-6979	263	20	u	u	PROPN
ejpam-6979	263	21	,	,	PUNCT
ejpam-6979	263	22	such	such	ADJ
ejpam-6979	263	23	that	that	SCONJ
ejpam-6979	263	24	ξ0	ξ0	PROPN
ejpam-6979	263	25	ϑ	ϑ	PROPN
ejpam-6979	263	26	n∑	n∑	NOUN
ejpam-6979	263	27	i=1	i=1	PROPN
ejpam-6979	263	28	p	p	X
ejpam-6979	263	29	′	′	NUM
ejpam-6979	263	30	i(ξ0	i(ξ0	NOUN
ejpam-6979	263	31	)	)	PUNCT
ejpam-6979	263	32	1	1	NUM
ejpam-6979	263	33	ϑ	ϑ	X
ejpam-6979	263	34	ϑ∑	ϑ∑	X
ejpam-6979	263	35	j=1	j=1	PROPN
ejpam-6979	264	1	p	p	PROPN
ejpam-6979	264	2	j(ξ0	j(ξ0	NOUN
ejpam-6979	264	3	)	)	PUNCT
ejpam-6979	265	1	+	+	CCONJ
ejpam-6979	265	2	(	(	PUNCT
ejpam-6979	265	3	n	n	CCONJ
ejpam-6979	265	4	−	−	PROPN
ejpam-6979	265	5	1	1	NUM
ejpam-6979	265	6	)	)	PUNCT
ejpam-6979	265	7	+	+	CCONJ
ejpam-6979	265	8	1	1	NUM
ejpam-6979	265	9	ϑ	ϑ	X
ejpam-6979	265	10	ϑ∑	ϑ∑	NOUN
ejpam-6979	265	11	j=1	j=1	PROPN
ejpam-6979	266	1	p	p	PROPN
ejpam-6979	266	2	j(ξ0	j(ξ0	NOUN
ejpam-6979	266	3	)	)	PUNCT
ejpam-6979	266	4	=	=	SYM
ejpam-6979	267	1	1	1	NUM
ejpam-6979	267	2	ϑ	ϑ	VERB
ejpam-6979	267	3	ϑ∑	ϑ∑	X
ejpam-6979	267	4	i=1	i=1	PRON
ejpam-6979	267	5	µ(wi	µ(wi	ADV
ejpam-6979	267	6	)	)	PUNCT
ejpam-6979	267	7	=	=	SYM
ejpam-6979	267	8	µ(w0	µ(w0	NOUN
ejpam-6979	267	9	)	)	PUNCT
ejpam-6979	267	10	.	.	PUNCT
ejpam-6979	268	1	setting	set	VERB
ejpam-6979	268	2	q(ξ	q(ξ	ADV
ejpam-6979	268	3	)	)	PUNCT
ejpam-6979	268	4	=	=	SYM
ejpam-6979	269	1	1	1	NUM
ejpam-6979	269	2	ϑ	ϑ	VERB
ejpam-6979	269	3	ϑ∑	ϑ∑	X
ejpam-6979	269	4	i=1	i=1	PRON
ejpam-6979	269	5	pi(ξ	pi(ξ	PROPN
ejpam-6979	269	6	)	)	PUNCT
ejpam-6979	269	7	,	,	PUNCT
ejpam-6979	269	8	we	we	PRON
ejpam-6979	269	9	have	have	VERB
ejpam-6979	269	10	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	269	11	)	)	PUNCT
ejpam-6979	270	1	[	[	PUNCT
ejpam-6979	270	2	ξq	ξq	INTJ
ejpam-6979	270	3	′	′	NUM
ejpam-6979	270	4	(	(	PUNCT
ejpam-6979	270	5	ξ	ξ	NOUN
ejpam-6979	270	6	)	)	PUNCT
ejpam-6979	270	7	q(ξ	q(ξ	ADV
ejpam-6979	270	8	)	)	PUNCT
ejpam-6979	271	1	+	+	CCONJ
ejpam-6979	271	2	(	(	PUNCT
ejpam-6979	271	3	n	n	CCONJ
ejpam-6979	271	4	−	−	PROPN
ejpam-6979	271	5	1	1	NUM
ejpam-6979	271	6	)	)	PUNCT
ejpam-6979	271	7	+	+	CCONJ
ejpam-6979	271	8	q(ξ	q(ξ	ADJ
ejpam-6979	271	9	)	)	PUNCT
ejpam-6979	271	10	]	]	PUNCT
ejpam-6979	272	1	≤	≤	NUM
ejpam-6979	272	2	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	272	3	)	)	PUNCT
ejpam-6979	272	4	,	,	PUNCT
ejpam-6979	272	5	which	which	PRON
ejpam-6979	272	6	by	by	ADP
ejpam-6979	272	7	lemma	lemma	PROPN
ejpam-6979	272	8	1	1	NUM
ejpam-6979	272	9	,	,	PUNCT
ejpam-6979	272	10	implies	imply	VERB
ejpam-6979	272	11	that	that	SCONJ
ejpam-6979	272	12	q(ξ	q(ξ	ADJ
ejpam-6979	272	13	)	)	PUNCT
ejpam-6979	272	14	≺	≺	NOUN
ejpam-6979	272	15	µ(ξ	µ(ξ	NOUN
ejpam-6979	272	16	)	)	PUNCT
ejpam-6979	272	17	.	.	PUNCT
ejpam-6979	273	1	from	from	ADP
ejpam-6979	273	2	(	(	PUNCT
ejpam-6979	273	3	19	19	NUM
ejpam-6979	273	4	)	)	PUNCT
ejpam-6979	273	5	,	,	PUNCT
ejpam-6979	273	6	we	we	PRON
ejpam-6979	273	7	’ve	’ve	VERB
ejpam-6979	273	8	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	273	9	)	)	PUNCT
ejpam-6979	273	10			NOUN
ejpam-6979	273	11	ξp	ξp	NOUN
ejpam-6979	273	12	′	′	NUM
ejpam-6979	273	13	i(ξ	i(ξ	PROPN
ejpam-6979	273	14	)	)	PUNCT
ejpam-6979	273	15	q(ξ	q(ξ	ADV
ejpam-6979	273	16	)	)	PUNCT
ejpam-6979	274	1	+	+	CCONJ
ejpam-6979	274	2	(	(	PUNCT
ejpam-6979	274	3	n	n	CCONJ
ejpam-6979	274	4	−	−	PROPN
ejpam-6979	274	5	1	1	NUM
ejpam-6979	274	6	)	)	PUNCT
ejpam-6979	274	7	+	+	NUM
ejpam-6979	274	8	pi(ξ	pi(ξ	NOUN
ejpam-6979	274	9	)	)	PUNCT
ejpam-6979	274	10			VERB
ejpam-6979	274	11	≤	≤	ADJ
ejpam-6979	274	12	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	274	13	)	)	PUNCT
ejpam-6979	274	14	,	,	PUNCT
ejpam-6979	274	15	where	where	SCONJ
ejpam-6979	274	16	q(ξ	q(ξ	ADV
ejpam-6979	274	17	)	)	PUNCT
ejpam-6979	275	1	≺f	≺f	PROPN
ejpam-6979	275	2	µ(ξ	µ(ξ	NOUN
ejpam-6979	275	3	)	)	PUNCT
ejpam-6979	275	4	.	.	PUNCT
ejpam-6979	276	1	the	the	DET
ejpam-6979	276	2	using	using	NOUN
ejpam-6979	276	3	of	of	ADP
ejpam-6979	276	4	lemma	lemma	PROPN
ejpam-6979	276	5	2	2	NUM
ejpam-6979	276	6	gives	give	NOUN
ejpam-6979	276	7	pi(ξ	pi(ξ	NOUN
ejpam-6979	276	8	)	)	PUNCT
ejpam-6979	276	9	≺f	≺f	PROPN
ejpam-6979	276	10	µ(ξ),which	µ(ξ),which	PRON
ejpam-6979	276	11	implies	imply	VERB
ejpam-6979	276	12	that	that	SCONJ
ejpam-6979	276	13	f	f	PROPN
ejpam-6979	276	14	=	=	PRON
ejpam-6979	276	15	{	{	PUNCT
ejpam-6979	276	16	f1	f1	NOUN
ejpam-6979	276	17	,	,	PUNCT
ejpam-6979	276	18	f2	f2	PROPN
ejpam-6979	276	19	,	,	PUNCT
ejpam-6979	276	20	...	...	PUNCT
ejpam-6979	276	21	,	,	PUNCT
ejpam-6979	276	22	fϑ	fϑ	ADJ
ejpam-6979	276	23	}	}	PUNCT
ejpam-6979	276	24	∈	∈	NOUN
ejpam-6979	276	25	fℜn+1,v(ϑ	fℜn+1,v(ϑ	NOUN
ejpam-6979	276	26	;	;	PUNCT
ejpam-6979	276	27	µ	µ	X
ejpam-6979	276	28	)	)	PUNCT
ejpam-6979	276	29	.	.	PUNCT
ejpam-6979	277	1	e.	e.	PROPN
ejpam-6979	277	2	e.	e.	PROPN
ejpam-6979	277	3	ali	ali	PROPN
ejpam-6979	277	4	et	et	PROPN
ejpam-6979	277	5	al	al	PROPN
ejpam-6979	277	6	.	.	PUNCT
ejpam-6979	277	7	/	/	SYM
ejpam-6979	277	8	eur	eur	PROPN
ejpam-6979	277	9	.	.	PUNCT
ejpam-6979	278	1	j.	j.	PROPN
ejpam-6979	278	2	pure	pure	PROPN
ejpam-6979	278	3	appl	appl	PROPN
ejpam-6979	278	4	.	.	PROPN
ejpam-6979	278	5	math	math	PROPN
ejpam-6979	278	6	,	,	PUNCT
ejpam-6979	278	7	18	18	NUM
ejpam-6979	278	8	(	(	PUNCT
ejpam-6979	278	9	4	4	NUM
ejpam-6979	278	10	)	)	PUNCT
ejpam-6979	278	11	(	(	PUNCT
ejpam-6979	278	12	2025	2025	NUM
ejpam-6979	278	13	)	)	PUNCT
ejpam-6979	278	14	,	,	PUNCT
ejpam-6979	278	15	6979	6979	NUM
ejpam-6979	278	16	11	11	NUM
ejpam-6979	278	17	of	of	ADP
ejpam-6979	278	18	18	18	NUM
ejpam-6979	278	19	3.2	3.2	NUM
ejpam-6979	278	20	.	.	PUNCT
ejpam-6979	279	1	the	the	DET
ejpam-6979	279	2	class	class	PROPN
ejpam-6979	279	3	fℵn	fℵn	PROPN
ejpam-6979	279	4	,	,	PUNCT
ejpam-6979	279	5	v(ϑ	v(ϑ	NOUN
ejpam-6979	279	6	;	;	PUNCT
ejpam-6979	279	7	µ	µ	X
ejpam-6979	279	8	)	)	PUNCT
ejpam-6979	279	9	definition	definition	NOUN
ejpam-6979	279	10	6	6	NUM
ejpam-6979	279	11	.	.	PUNCT
ejpam-6979	280	1	let	let	AUX
ejpam-6979	280	2	fℵn	fℵn	VERB
ejpam-6979	280	3	,	,	PUNCT
ejpam-6979	280	4	v(ϑ	v(ϑ	NOUN
ejpam-6979	280	5	;	;	PUNCT
ejpam-6979	280	6	µ	µ	X
ejpam-6979	280	7	)	)	PUNCT
ejpam-6979	280	8	denote	denote	VERB
ejpam-6979	280	9	the	the	DET
ejpam-6979	280	10	class	class	NOUN
ejpam-6979	280	11	of	of	ADP
ejpam-6979	280	12	functions	function	NOUN
ejpam-6979	280	13	f	f	PROPN
ejpam-6979	280	14	∈	∈	PROPN
ejpam-6979	280	15	a	a	DET
ejpam-6979	280	16	which	which	PRON
ejpam-6979	280	17	satisfies	satisfy	VERB
ejpam-6979	280	18	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	280	19	)	)	PUNCT
ejpam-6979	280	20			NOUN
ejpam-6979	280	21	ξ[lmn+1,vf(ξ	ξ[lmn+1,vf(ξ	PROPN
ejpam-6979	280	22	)	)	PUNCT
ejpam-6979	280	23	]	]	PUNCT
ejpam-6979	281	1	′	′	NOUN
ejpam-6979	281	2	1	1	NUM
ejpam-6979	281	3	ϑ	ϑ	X
ejpam-6979	281	4	ϑ∑	ϑ∑	X
ejpam-6979	281	5	j=1	j=1	PROPN
ejpam-6979	281	6	lmn+1,vg	lmn+1,vg	PROPN
ejpam-6979	281	7	j(ξ	j(ξ	PROPN
ejpam-6979	281	8	)	)	PUNCT
ejpam-6979	281	9			VERB
ejpam-6979	281	10	≤	≤	NUM
ejpam-6979	281	11	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	281	12	)	)	PUNCT
ejpam-6979	281	13	(	(	PUNCT
ejpam-6979	281	14	ξ	ξ	PROPN
ejpam-6979	281	15	∈	∈	PROPN
ejpam-6979	281	16	u	u	NOUN
ejpam-6979	281	17	)	)	PUNCT
ejpam-6979	281	18	,	,	PUNCT
ejpam-6979	281	19	where	where	SCONJ
ejpam-6979	281	20	g	g	NOUN
ejpam-6979	281	21	=	=	SYM
ejpam-6979	281	22	{	{	PUNCT
ejpam-6979	281	23	g1	g1	PROPN
ejpam-6979	281	24	,	,	PUNCT
ejpam-6979	281	25	g2	g2	PROPN
ejpam-6979	281	26	,	,	PUNCT
ejpam-6979	281	27	...	...	PUNCT
ejpam-6979	281	28	,	,	PUNCT
ejpam-6979	281	29	gϑ	gϑ	ADP
ejpam-6979	281	30	}	}	PUNCT
ejpam-6979	281	31	∈	∈	PROPN
ejpam-6979	281	32	fℜn	fℜn	NOUN
ejpam-6979	281	33	,	,	PUNCT
ejpam-6979	281	34	v(ϑ	v(ϑ	NOUN
ejpam-6979	281	35	;	;	PUNCT
ejpam-6979	281	36	µ	µ	X
ejpam-6979	281	37	)	)	PUNCT
ejpam-6979	281	38	,	,	PUNCT
ejpam-6979	281	39	µ	µ	PROPN
ejpam-6979	281	40	is	be	AUX
ejpam-6979	281	41	convex	convex	ADJ
ejpam-6979	281	42	univalent	univalent	ADJ
ejpam-6979	281	43	inu	inu	NOUN
ejpam-6979	281	44	with	with	ADP
ejpam-6979	281	45	µ(0	µ(0	NOUN
ejpam-6979	281	46	)	)	PUNCT
ejpam-6979	281	47	=	=	SYM
ejpam-6979	281	48	1	1	X
ejpam-6979	281	49	.	.	X
ejpam-6979	281	50	theorem	theorem	NOUN
ejpam-6979	281	51	4	4	NUM
ejpam-6979	281	52	.	.	PUNCT
ejpam-6979	282	1	let	let	VERB
ejpam-6979	282	2	f	f	PROPN
ejpam-6979	282	3	∈	∈	PROPN
ejpam-6979	282	4	fℵn	fℵn	PROPN
ejpam-6979	282	5	,	,	PUNCT
ejpam-6979	282	6	v(ϑ	v(ϑ	NOUN
ejpam-6979	282	7	;	;	PUNCT
ejpam-6979	282	8	µ	µ	NUM
ejpam-6979	282	9	)	)	PUNCT
ejpam-6979	282	10	.	.	PUNCT
ejpam-6979	283	1	if	if	SCONJ
ejpam-6979	283	2	re(µ	re(µ	NUM
ejpam-6979	283	3	)	)	PUNCT
ejpam-6979	283	4	is	be	AUX
ejpam-6979	283	5	bounded	bound	VERB
ejpam-6979	283	6	inu	inu	NOUN
ejpam-6979	283	7	and	and	CCONJ
ejpam-6979	283	8	re{µ(ξ	re{µ(ξ	NOUN
ejpam-6979	283	9	)	)	PUNCT
ejpam-6979	284	1	+	+	CCONJ
ejpam-6979	284	2	τ	τ	X
ejpam-6979	284	3	}	}	PUNCT
ejpam-6979	284	4	>	>	X
ejpam-6979	284	5	0	0	NUM
ejpam-6979	284	6	,	,	PUNCT
ejpam-6979	284	7	then	then	ADV
ejpam-6979	284	8	f	f	X
ejpam-6979	284	9	(	(	PUNCT
ejpam-6979	284	10	ξ	ξ	PROPN
ejpam-6979	284	11	)	)	PUNCT
ejpam-6979	284	12	=	=	SYM
ejpam-6979	284	13	τ	τ	PROPN
ejpam-6979	285	1	+	+	NOUN
ejpam-6979	285	2	1	1	NUM
ejpam-6979	285	3	ξτ	ξτ	ADP
ejpam-6979	285	4	ξ∫	ξ∫	NUM
ejpam-6979	285	5	0	0	NUM
ejpam-6979	285	6	tτ−1	tτ−1	NOUN
ejpam-6979	285	7	f(t)dt	f(t)dt	NOUN
ejpam-6979	285	8	(	(	PUNCT
ejpam-6979	285	9	ξ	ξ	PROPN
ejpam-6979	285	10	∈	∈	PROPN
ejpam-6979	285	11	u	u	NOUN
ejpam-6979	285	12	;	;	PUNCT
ejpam-6979	285	13	τ	τ	PROPN
ejpam-6979	285	14	∈	∈	PROPN
ejpam-6979	285	15	c	c	PROPN
ejpam-6979	285	16	,	,	PUNCT
ejpam-6979	285	17	re(τ	re(τ	NOUN
ejpam-6979	285	18	)	)	PUNCT
ejpam-6979	285	19	>	>	X
ejpam-6979	285	20	0	0	NUM
ejpam-6979	285	21	)	)	PUNCT
ejpam-6979	285	22	,	,	PUNCT
ejpam-6979	285	23	also	also	ADV
ejpam-6979	285	24	belongs	belong	VERB
ejpam-6979	285	25	to	to	ADP
ejpam-6979	285	26	fℵn	fℵn	PROPN
ejpam-6979	285	27	,	,	PUNCT
ejpam-6979	285	28	v(ϑ	v(ϑ	NOUN
ejpam-6979	285	29	;	;	PUNCT
ejpam-6979	285	30	µ	µ	NUM
ejpam-6979	285	31	)	)	PUNCT
ejpam-6979	285	32	.	.	PUNCT
ejpam-6979	286	1	proof	proof	NOUN
ejpam-6979	286	2	.	.	PUNCT
ejpam-6979	287	1	since	since	SCONJ
ejpam-6979	287	2	f	f	PROPN
ejpam-6979	287	3	∈	∈	PROPN
ejpam-6979	287	4	fℵn	fℵn	PROPN
ejpam-6979	287	5	,	,	PUNCT
ejpam-6979	287	6	v(ϑ	v(ϑ	NOUN
ejpam-6979	287	7	;	;	PUNCT
ejpam-6979	287	8	µ	µ	X
ejpam-6979	287	9	)	)	PUNCT
ejpam-6979	287	10	,	,	PUNCT
ejpam-6979	287	11	then	then	ADV
ejpam-6979	287	12	there	there	PRON
ejpam-6979	287	13	exists	exist	VERB
ejpam-6979	287	14	g	g	PROPN
ejpam-6979	287	15	=	=	SYM
ejpam-6979	287	16	{	{	PUNCT
ejpam-6979	287	17	g1	g1	PROPN
ejpam-6979	287	18	,	,	PUNCT
ejpam-6979	287	19	g2	g2	PROPN
ejpam-6979	287	20	,	,	PUNCT
ejpam-6979	287	21	...	...	PUNCT
ejpam-6979	287	22	,	,	PUNCT
ejpam-6979	287	23	gϑ	gϑ	ADP
ejpam-6979	287	24	}	}	PUNCT
ejpam-6979	287	25	∈	∈	PROPN
ejpam-6979	287	26	fℜn	fℜn	NOUN
ejpam-6979	287	27	,	,	PUNCT
ejpam-6979	287	28	v(ϑ	v(ϑ	NOUN
ejpam-6979	287	29	;	;	PUNCT
ejpam-6979	287	30	µ	µ	X
ejpam-6979	287	31	)	)	PUNCT
ejpam-6979	287	32	,	,	PUNCT
ejpam-6979	287	33	such	such	ADJ
ejpam-6979	287	34	that	that	DET
ejpam-6979	287	35	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	287	36	)	)	PUNCT
ejpam-6979	287	37			NOUN
ejpam-6979	287	38	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	287	39	,	,	PUNCT
ejpam-6979	287	40	vf(ξ	vf(ξ	NUM
ejpam-6979	287	41	)	)	PUNCT
ejpam-6979	287	42	]	]	PUNCT
ejpam-6979	288	1	′	′	NOUN
ejpam-6979	288	2	1	1	NUM
ejpam-6979	288	3	ϑ	ϑ	X
ejpam-6979	288	4	ϑ∑	ϑ∑	X
ejpam-6979	288	5	j=1	j=1	PROPN
ejpam-6979	288	6	lmn	lmn	PROPN
ejpam-6979	288	7	,	,	PUNCT
ejpam-6979	288	8	vg	vg	PROPN
ejpam-6979	288	9	j(ξ	j(ξ	PROPN
ejpam-6979	288	10	)	)	PUNCT
ejpam-6979	288	11			VERB
ejpam-6979	288	12	≤	≤	NUM
ejpam-6979	288	13	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	288	14	)	)	PUNCT
ejpam-6979	288	15	(	(	PUNCT
ejpam-6979	288	16	ξ	ξ	PROPN
ejpam-6979	288	17	∈	∈	PROPN
ejpam-6979	288	18	u	u	NOUN
ejpam-6979	288	19	)	)	PUNCT
ejpam-6979	288	20	.	.	PUNCT
ejpam-6979	289	1	let	let	VERB
ejpam-6979	289	2	gi(ξ	gi(ξ	PUNCT
ejpam-6979	289	3	)	)	PUNCT
ejpam-6979	289	4	=	=	SYM
ejpam-6979	290	1	τ	τ	PROPN
ejpam-6979	291	1	+	+	NOUN
ejpam-6979	291	2	1	1	NUM
ejpam-6979	291	3	ξτ	ξτ	ADP
ejpam-6979	291	4	ξ∫	ξ∫	NUM
ejpam-6979	291	5	0	0	NUM
ejpam-6979	291	6	tτ−1	tτ−1	NOUN
ejpam-6979	291	7	gi(t)dt	gi(t)dt	NOUN
ejpam-6979	291	8	(	(	PUNCT
ejpam-6979	291	9	reτ	reτ	NOUN
ejpam-6979	291	10	>	>	X
ejpam-6979	291	11	0	0	NUM
ejpam-6979	291	12	)	)	PUNCT
ejpam-6979	291	13	.	.	PUNCT
ejpam-6979	292	1	then	then	ADV
ejpam-6979	292	2	by	by	ADP
ejpam-6979	292	3	theorem	theorem	NOUN
ejpam-6979	292	4	2	2	NUM
ejpam-6979	292	5	,	,	PUNCT
ejpam-6979	292	6	we	we	PRON
ejpam-6979	292	7	have	have	VERB
ejpam-6979	292	8	g	g	NOUN
ejpam-6979	292	9	=	=	SYM
ejpam-6979	292	10	{	{	PUNCT
ejpam-6979	292	11	g1,g2	g1,g2	PROPN
ejpam-6979	292	12	,	,	PUNCT
ejpam-6979	292	13	...	...	PUNCT
ejpam-6979	292	14	,	,	PUNCT
ejpam-6979	292	15	gϑ	gϑ	INTJ
ejpam-6979	292	16	}	}	PUNCT
ejpam-6979	292	17	∈	∈	PROPN
ejpam-6979	292	18	fℜn	fℜn	NOUN
ejpam-6979	292	19	,	,	PUNCT
ejpam-6979	292	20	v(ϑ	v(ϑ	NOUN
ejpam-6979	292	21	;	;	PUNCT
ejpam-6979	292	22	µ	µ	NUM
ejpam-6979	292	23	)	)	PUNCT
ejpam-6979	292	24	.	.	PUNCT
ejpam-6979	293	1	also	also	ADV
ejpam-6979	293	2	let	let	VERB
ejpam-6979	293	3	p(ξ	p(ξ	NOUN
ejpam-6979	293	4	)	)	PUNCT
ejpam-6979	293	5	=	=	SYM
ejpam-6979	293	6	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	293	7	,	,	PUNCT
ejpam-6979	293	8	vf	vf	X
ejpam-6979	293	9	(	(	PUNCT
ejpam-6979	293	10	ξ	ξ	NOUN
ejpam-6979	293	11	)	)	PUNCT
ejpam-6979	293	12	]	]	PUNCT
ejpam-6979	294	1	′	′	NOUN
ejpam-6979	294	2	1	1	NUM
ejpam-6979	294	3	ϑ	ϑ	X
ejpam-6979	294	4	ϑ∑	ϑ∑	X
ejpam-6979	294	5	j=1	j=1	PROPN
ejpam-6979	294	6	lmn	lmn	PROPN
ejpam-6979	294	7	,	,	PUNCT
ejpam-6979	294	8	vg	vg	PROPN
ejpam-6979	294	9	j(ξ	j(ξ	PROPN
ejpam-6979	294	10	)	)	PUNCT
ejpam-6979	294	11	(	(	PUNCT
ejpam-6979	294	12	ξ	ξ	PROPN
ejpam-6979	294	13	∈	∈	PROPN
ejpam-6979	294	14	u	u	NOUN
ejpam-6979	294	15	)	)	PUNCT
ejpam-6979	294	16	.	.	PUNCT
ejpam-6979	295	1	(	(	PUNCT
ejpam-6979	295	2	20	20	NUM
ejpam-6979	295	3	)	)	PUNCT
ejpam-6979	295	4	now	now	ADV
ejpam-6979	295	5	,	,	PUNCT
ejpam-6979	295	6	from	from	ADP
ejpam-6979	295	7	the	the	DET
ejpam-6979	295	8	definitions	definition	NOUN
ejpam-6979	295	9	of	of	ADP
ejpam-6979	295	10	gi	gi	NOUN
ejpam-6979	295	11	and	and	CCONJ
ejpam-6979	295	12	f	f	PROPN
ejpam-6979	295	13	,	,	PUNCT
ejpam-6979	295	14	we	we	PRON
ejpam-6979	295	15	have	have	VERB
ejpam-6979	295	16	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	295	17	,	,	PUNCT
ejpam-6979	295	18	vgi(ξ	vgi(ξ	PROPN
ejpam-6979	295	19	)	)	PUNCT
ejpam-6979	295	20	]	]	PUNCT
ejpam-6979	296	1	′	′	NUM
ejpam-6979	297	1	+	+	CCONJ
ejpam-6979	297	2	τlmn	τlmn	ADJ
ejpam-6979	297	3	,	,	PUNCT
ejpam-6979	297	4	vgi(ξ	vgi(ξ	NOUN
ejpam-6979	297	5	)	)	PUNCT
ejpam-6979	298	1	=	=	SYM
ejpam-6979	298	2	(	(	PUNCT
ejpam-6979	298	3	τ	τ	X
ejpam-6979	298	4	+	+	NOUN
ejpam-6979	298	5	1)lmn	1)lmn	NUM
ejpam-6979	298	6	,	,	PUNCT
ejpam-6979	298	7	vgi(ξ	vgi(ξ	NOUN
ejpam-6979	298	8	)	)	PUNCT
ejpam-6979	298	9	,	,	PUNCT
ejpam-6979	298	10	(	(	PUNCT
ejpam-6979	298	11	21	21	NUM
ejpam-6979	298	12	)	)	PUNCT
ejpam-6979	298	13	and	and	CCONJ
ejpam-6979	298	14	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	298	15	,	,	PUNCT
ejpam-6979	298	16	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	298	17	)	)	PUNCT
ejpam-6979	298	18	]	]	PUNCT
ejpam-6979	299	1	′	′	NUM
ejpam-6979	300	1	+	+	CCONJ
ejpam-6979	300	2	τlmn	τlmn	ADJ
ejpam-6979	300	3	,	,	PUNCT
ejpam-6979	300	4	vf	vf	X
ejpam-6979	300	5	(	(	PUNCT
ejpam-6979	300	6	ξ	ξ	NOUN
ejpam-6979	300	7	)	)	PUNCT
ejpam-6979	300	8	=	=	SYM
ejpam-6979	300	9	(	(	PUNCT
ejpam-6979	300	10	τ	τ	X
ejpam-6979	300	11	+	+	NOUN
ejpam-6979	300	12	1)lmn	1)lmn	NUM
ejpam-6979	300	13	,	,	PUNCT
ejpam-6979	300	14	vf(ξ	vf(ξ	NUM
ejpam-6979	300	15	)	)	PUNCT
ejpam-6979	300	16	.	.	PUNCT
ejpam-6979	301	1	(	(	PUNCT
ejpam-6979	301	2	22	22	NUM
ejpam-6979	301	3	)	)	PUNCT
ejpam-6979	301	4	from	from	ADP
ejpam-6979	301	5	(	(	PUNCT
ejpam-6979	301	6	20	20	NUM
ejpam-6979	301	7	)	)	PUNCT
ejpam-6979	301	8	,	,	PUNCT
ejpam-6979	301	9	(	(	PUNCT
ejpam-6979	301	10	21	21	NUM
ejpam-6979	301	11	)	)	PUNCT
ejpam-6979	301	12	and	and	CCONJ
ejpam-6979	301	13	(	(	PUNCT
ejpam-6979	301	14	22	22	NUM
ejpam-6979	301	15	)	)	PUNCT
ejpam-6979	301	16	,	,	PUNCT
ejpam-6979	301	17	we	we	PRON
ejpam-6979	301	18	have	have	VERB
ejpam-6979	301	19	1	1	NUM
ejpam-6979	301	20	ϑ	ϑ	PRON
ejpam-6979	301	21	p(ξ	p(ξ	NOUN
ejpam-6979	301	22	)	)	PUNCT
ejpam-6979	301	23	ϑ∑	ϑ∑	NOUN
ejpam-6979	301	24	j=1	j=1	PROPN
ejpam-6979	301	25	lmn	lmn	PROPN
ejpam-6979	301	26	,	,	PUNCT
ejpam-6979	301	27	vg	vg	PROPN
ejpam-6979	301	28	j(ξ	j(ξ	PROPN
ejpam-6979	301	29	)	)	PUNCT
ejpam-6979	302	1	+	+	NUM
ejpam-6979	302	2	τlmn	τlmn	ADJ
ejpam-6979	302	3	,	,	PUNCT
ejpam-6979	302	4	vf	vf	X
ejpam-6979	302	5	(	(	PUNCT
ejpam-6979	302	6	ξ	ξ	NOUN
ejpam-6979	302	7	)	)	PUNCT
ejpam-6979	302	8	=	=	SYM
ejpam-6979	302	9	(	(	PUNCT
ejpam-6979	302	10	τ	τ	X
ejpam-6979	302	11	+	+	NOUN
ejpam-6979	302	12	1)lmn	1)lmn	NUM
ejpam-6979	302	13	,	,	PUNCT
ejpam-6979	302	14	vf(ξ	vf(ξ	NUM
ejpam-6979	302	15	)	)	PUNCT
ejpam-6979	302	16	.	.	PUNCT
ejpam-6979	303	1	(	(	PUNCT
ejpam-6979	303	2	23	23	NUM
ejpam-6979	303	3	)	)	PUNCT
ejpam-6979	303	4	e.	e.	PROPN
ejpam-6979	303	5	e.	e.	PROPN
ejpam-6979	303	6	ali	ali	PROPN
ejpam-6979	303	7	et	et	PROPN
ejpam-6979	303	8	al	al	PROPN
ejpam-6979	303	9	.	.	PUNCT
ejpam-6979	303	10	/	/	SYM
ejpam-6979	303	11	eur	eur	PROPN
ejpam-6979	303	12	.	.	PUNCT
ejpam-6979	304	1	j.	j.	PROPN
ejpam-6979	304	2	pure	pure	PROPN
ejpam-6979	304	3	appl	appl	PROPN
ejpam-6979	304	4	.	.	PROPN
ejpam-6979	304	5	math	math	PROPN
ejpam-6979	304	6	,	,	PUNCT
ejpam-6979	304	7	18	18	NUM
ejpam-6979	304	8	(	(	PUNCT
ejpam-6979	304	9	4	4	NUM
ejpam-6979	304	10	)	)	PUNCT
ejpam-6979	304	11	(	(	PUNCT
ejpam-6979	304	12	2025	2025	NUM
ejpam-6979	304	13	)	)	PUNCT
ejpam-6979	304	14	,	,	PUNCT
ejpam-6979	304	15	6979	6979	NUM
ejpam-6979	304	16	12	12	NUM
ejpam-6979	304	17	of	of	ADP
ejpam-6979	304	18	18	18	NUM
ejpam-6979	304	19	differentiating	differentiate	VERB
ejpam-6979	304	20	(	(	PUNCT
ejpam-6979	304	21	23	23	NUM
ejpam-6979	304	22	)	)	PUNCT
ejpam-6979	304	23	with	with	ADP
ejpam-6979	304	24	respect	respect	NOUN
ejpam-6979	304	25	to	to	ADP
ejpam-6979	304	26	ξ	ξ	NUM
ejpam-6979	304	27	,	,	PUNCT
ejpam-6979	304	28	and	and	CCONJ
ejpam-6979	304	29	multiplying	multiply	VERB
ejpam-6979	304	30	the	the	DET
ejpam-6979	304	31	resulting	result	VERB
ejpam-6979	304	32	equation	equation	NOUN
ejpam-6979	304	33	by	by	ADP
ejpam-6979	304	34	ξ	ξ	PROPN
ejpam-6979	304	35	,	,	PUNCT
ejpam-6979	304	36	we	we	PRON
ejpam-6979	304	37	have	have	VERB
ejpam-6979	304	38	ξ	ξ	X
ejpam-6979	304	39	ϑ	ϑ	X
ejpam-6979	304	40	p	p	X
ejpam-6979	304	41	′	′	NUM
ejpam-6979	304	42	(	(	PUNCT
ejpam-6979	304	43	ξ	ξ	NOUN
ejpam-6979	304	44	)	)	PUNCT
ejpam-6979	304	45	ϑ∑	ϑ∑	NOUN
ejpam-6979	304	46	j=1	j=1	PROPN
ejpam-6979	304	47	lmn	lmn	PROPN
ejpam-6979	304	48	,	,	PUNCT
ejpam-6979	304	49	vg	vg	ADP
ejpam-6979	304	50	j(ξ)+	j(ξ)+	PROPN
ejpam-6979	304	51	ξ	ξ	X
ejpam-6979	304	52	ϑ	ϑ	X
ejpam-6979	304	53	p(ξ	p(ξ	NOUN
ejpam-6979	304	54	)	)	PUNCT
ejpam-6979	304	55	ϑ∑	ϑ∑	NOUN
ejpam-6979	304	56	j=1	j=1	PUNCT
ejpam-6979	305	1	[	[	X
ejpam-6979	305	2	lmn	lmn	NOUN
ejpam-6979	305	3	,	,	PUNCT
ejpam-6979	305	4	vg	vg	ADP
ejpam-6979	305	5	j(ξ	j(ξ	PROPN
ejpam-6979	305	6	)	)	PUNCT
ejpam-6979	305	7	]	]	PUNCT
ejpam-6979	305	8	′	′	NUM
ejpam-6979	306	1	+	+	NUM
ejpam-6979	306	2	τξ[lmn	τξ[lmn	NOUN
ejpam-6979	306	3	,	,	PUNCT
ejpam-6979	306	4	vf	vf	X
ejpam-6979	306	5	(	(	PUNCT
ejpam-6979	306	6	ξ	ξ	NOUN
ejpam-6979	306	7	)	)	PUNCT
ejpam-6979	306	8	]	]	PUNCT
ejpam-6979	306	9	′	′	NOUN
ejpam-6979	306	10	=	=	SYM
ejpam-6979	306	11	(	(	PUNCT
ejpam-6979	306	12	τ+1)ξ[lmn	τ+1)ξ[lmn	NOUN
ejpam-6979	306	13	,	,	PUNCT
ejpam-6979	306	14	vf(ξ	vf(ξ	NUM
ejpam-6979	306	15	)	)	PUNCT
ejpam-6979	306	16	]	]	PUNCT
ejpam-6979	307	1	′	′	X
ejpam-6979	307	2	.	.	PUNCT
ejpam-6979	308	1	(	(	PUNCT
ejpam-6979	308	2	24	24	NUM
ejpam-6979	308	3	)	)	PUNCT
ejpam-6979	308	4	from	from	ADP
ejpam-6979	308	5	(	(	PUNCT
ejpam-6979	308	6	20	20	NUM
ejpam-6979	308	7	)	)	PUNCT
ejpam-6979	308	8	into	into	ADP
ejpam-6979	308	9	(	(	PUNCT
ejpam-6979	308	10	24	24	NUM
ejpam-6979	308	11	)	)	PUNCT
ejpam-6979	308	12	,	,	PUNCT
ejpam-6979	308	13	we	we	PRON
ejpam-6979	308	14	have	have	VERB
ejpam-6979	308	15	ξ	ξ	X
ejpam-6979	308	16	ϑ	ϑ	X
ejpam-6979	308	17	p	p	X
ejpam-6979	308	18	′	′	NUM
ejpam-6979	308	19	(	(	PUNCT
ejpam-6979	308	20	ξ	ξ	NOUN
ejpam-6979	308	21	)	)	PUNCT
ejpam-6979	308	22	ϑ∑	ϑ∑	NOUN
ejpam-6979	308	23	j=1	j=1	PROPN
ejpam-6979	308	24	lmn	lmn	PROPN
ejpam-6979	308	25	,	,	PUNCT
ejpam-6979	308	26	vg	vg	PROPN
ejpam-6979	308	27	j(ξ	j(ξ	PROPN
ejpam-6979	308	28	)	)	PUNCT
ejpam-6979	309	1	+	+	CCONJ
ejpam-6979	309	2	ξ	ξ	X
ejpam-6979	309	3	ϑ	ϑ	X
ejpam-6979	309	4	p(ξ	p(ξ	NOUN
ejpam-6979	309	5	)	)	PUNCT
ejpam-6979	309	6	ϑ∑	ϑ∑	NOUN
ejpam-6979	309	7	j=1	j=1	PUNCT
ejpam-6979	310	1	[	[	X
ejpam-6979	310	2	lmn	lmn	NOUN
ejpam-6979	310	3	,	,	PUNCT
ejpam-6979	310	4	vg	vg	ADP
ejpam-6979	310	5	j(ξ	j(ξ	PROPN
ejpam-6979	310	6	)	)	PUNCT
ejpam-6979	310	7	]	]	PUNCT
ejpam-6979	311	1	′	′	NUM
ejpam-6979	312	1	+	+	CCONJ
ejpam-6979	312	2	τ	τ	X
ejpam-6979	312	3	p(ξ	p(ξ	NOUN
ejpam-6979	312	4	)	)	PUNCT
ejpam-6979	312	5	ϑ	ϑ	X
ejpam-6979	312	6	ϑ∑	ϑ∑	X
ejpam-6979	312	7	j=1	j=1	PROPN
ejpam-6979	312	8	lmn	lmn	PROPN
ejpam-6979	312	9	,	,	PUNCT
ejpam-6979	312	10	vg	vg	PROPN
ejpam-6979	312	11	j(ξ	j(ξ	PROPN
ejpam-6979	312	12	)	)	PUNCT
ejpam-6979	312	13	=	=	PUNCT
ejpam-6979	312	14	(	(	PUNCT
ejpam-6979	312	15	τ	τ	PROPN
ejpam-6979	312	16	+	+	NUM
ejpam-6979	312	17	1)ξ[lmn	1)ξ[lmn	NUM
ejpam-6979	312	18	,	,	PUNCT
ejpam-6979	312	19	vf(ξ	vf(ξ	NUM
ejpam-6979	312	20	)	)	PUNCT
ejpam-6979	312	21	]	]	PUNCT
ejpam-6979	313	1	′	′	X
ejpam-6979	313	2	.	.	PUNCT
ejpam-6979	314	1	hence	hence	ADV
ejpam-6979	314	2	,	,	PUNCT
ejpam-6979	314	3	we	we	PRON
ejpam-6979	314	4	get	get	VERB
ejpam-6979	314	5	ξ	ξ	PRON
ejpam-6979	314	6	ϑ	ϑ	X
ejpam-6979	314	7	p	p	X
ejpam-6979	314	8	′	′	NUM
ejpam-6979	314	9	(	(	PUNCT
ejpam-6979	314	10	ξ	ξ	NOUN
ejpam-6979	314	11	)	)	PUNCT
ejpam-6979	314	12	ϑ∑	ϑ∑	NOUN
ejpam-6979	314	13	j=1	j=1	PROPN
ejpam-6979	314	14	lmn	lmn	PROPN
ejpam-6979	314	15	,	,	PUNCT
ejpam-6979	314	16	vg	vg	PROPN
ejpam-6979	314	17	j(ξ	j(ξ	PROPN
ejpam-6979	314	18	)	)	PUNCT
ejpam-6979	315	1	ξ	ξ	PROPN
ejpam-6979	315	2	ϑ	ϑ	X
ejpam-6979	315	3	ϑ∑	ϑ∑	X
ejpam-6979	315	4	j=1	j=1	PUNCT
ejpam-6979	316	1	[	[	X
ejpam-6979	316	2	lmn	lmn	NOUN
ejpam-6979	316	3	,	,	PUNCT
ejpam-6979	316	4	vg	vg	ADP
ejpam-6979	316	5	j(ξ	j(ξ	PROPN
ejpam-6979	316	6	)	)	PUNCT
ejpam-6979	316	7	]	]	PUNCT
ejpam-6979	317	1	′	′	NUM
ejpam-6979	318	1	+	+	CCONJ
ejpam-6979	318	2	τ	τ	X
ejpam-6979	318	3	ϑ	ϑ	X
ejpam-6979	318	4	ϑ∑	ϑ∑	X
ejpam-6979	318	5	j=1	j=1	PROPN
ejpam-6979	318	6	lmn	lmn	PROPN
ejpam-6979	318	7	,	,	PUNCT
ejpam-6979	318	8	vg	vg	PROPN
ejpam-6979	318	9	j(ξ	j(ξ	PROPN
ejpam-6979	318	10	)	)	PUNCT
ejpam-6979	319	1	+	+	CCONJ
ejpam-6979	319	2	p(ξ	p(ξ	NOUN
ejpam-6979	319	3	)	)	PUNCT
ejpam-6979	319	4	=	=	SYM
ejpam-6979	319	5	(	(	PUNCT
ejpam-6979	320	1	τ	τ	PROPN
ejpam-6979	320	2	+	+	NUM
ejpam-6979	320	3	1)ξ[lmn	1)ξ[lmn	NUM
ejpam-6979	320	4	,	,	PUNCT
ejpam-6979	320	5	vf(ξ	vf(ξ	NUM
ejpam-6979	320	6	)	)	PUNCT
ejpam-6979	320	7	]	]	PUNCT
ejpam-6979	321	1	′	′	NUM
ejpam-6979	322	1	ξ	ξ	X
ejpam-6979	322	2	ϑ	ϑ	X
ejpam-6979	322	3	ϑ∑	ϑ∑	X
ejpam-6979	322	4	j=1	j=1	PUNCT
ejpam-6979	323	1	[	[	X
ejpam-6979	323	2	lmn	lmn	NOUN
ejpam-6979	323	3	,	,	PUNCT
ejpam-6979	323	4	vg	vg	ADP
ejpam-6979	323	5	j(ξ	j(ξ	PROPN
ejpam-6979	323	6	)	)	PUNCT
ejpam-6979	323	7	]	]	PUNCT
ejpam-6979	324	1	′	′	NUM
ejpam-6979	325	1	+	+	CCONJ
ejpam-6979	325	2	τ	τ	X
ejpam-6979	325	3	ϑ	ϑ	X
ejpam-6979	325	4	ϑ∑	ϑ∑	X
ejpam-6979	325	5	j=1	j=1	PROPN
ejpam-6979	325	6	lmn	lmn	PROPN
ejpam-6979	325	7	,	,	PUNCT
ejpam-6979	325	8	vg	vg	PROPN
ejpam-6979	325	9	j(ξ	j(ξ	PROPN
ejpam-6979	325	10	)	)	PUNCT
ejpam-6979	326	1	=	=	SYM
ejpam-6979	326	2	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	326	3	,	,	PUNCT
ejpam-6979	326	4	vf(ξ	vf(ξ	NUM
ejpam-6979	326	5	)	)	PUNCT
ejpam-6979	326	6	]	]	PUNCT
ejpam-6979	327	1	′	′	NOUN
ejpam-6979	327	2	1	1	NUM
ejpam-6979	327	3	ϑ	ϑ	X
ejpam-6979	327	4	ϑ∑	ϑ∑	X
ejpam-6979	327	5	j=1	j=1	PROPN
ejpam-6979	327	6	lmn	lmn	PROPN
ejpam-6979	327	7	,	,	PUNCT
ejpam-6979	327	8	vg	vg	PROPN
ejpam-6979	327	9	j(ξ	j(ξ	PROPN
ejpam-6979	327	10	)	)	PUNCT
ejpam-6979	327	11	(	(	PUNCT
ejpam-6979	327	12	by	by	ADP
ejpam-6979	327	13	using	use	VERB
ejpam-6979	327	14	(	(	PUNCT
ejpam-6979	327	15	21	21	NUM
ejpam-6979	327	16	)	)	PUNCT
ejpam-6979	327	17	)	)	PUNCT
ejpam-6979	327	18	.	.	PUNCT
ejpam-6979	328	1	from	from	ADP
ejpam-6979	328	2	the	the	DET
ejpam-6979	328	3	above	above	NOUN
ejpam-6979	328	4	,	,	PUNCT
ejpam-6979	328	5	we	we	PRON
ejpam-6979	328	6	have	have	VERB
ejpam-6979	328	7	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	328	8	)	)	PUNCT
ejpam-6979	328	9			NOUN
ejpam-6979	329	1	ξp	ξp	ADP
ejpam-6979	329	2	′	′	NUM
ejpam-6979	329	3	(	(	PUNCT
ejpam-6979	329	4	ξ	ξ	X
ejpam-6979	329	5	)	)	PUNCT
ejpam-6979	329	6	1	1	NUM
ejpam-6979	329	7	ϑ	ϑ	X
ejpam-6979	329	8	ϑ∑	ϑ∑	X
ejpam-6979	329	9	j=1	j=1	PROPN
ejpam-6979	329	10	q	q	PROPN
ejpam-6979	329	11	j(ξ	j(ξ	PROPN
ejpam-6979	329	12	)	)	PUNCT
ejpam-6979	330	1	+	+	CCONJ
ejpam-6979	330	2	τ	τ	PROPN
ejpam-6979	330	3	+	+	CCONJ
ejpam-6979	330	4	p(ξ	p(ξ	NOUN
ejpam-6979	330	5	)	)	PUNCT
ejpam-6979	330	6			NUM
ejpam-6979	330	7	=	=	SYM
ejpam-6979	330	8	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	330	9	)	)	PUNCT
ejpam-6979	330	10			NOUN
ejpam-6979	330	11	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	330	12	,	,	PUNCT
ejpam-6979	330	13	vf(ξ	vf(ξ	NUM
ejpam-6979	330	14	)	)	PUNCT
ejpam-6979	330	15	]	]	PUNCT
ejpam-6979	331	1	′	′	NOUN
ejpam-6979	331	2	1	1	NUM
ejpam-6979	331	3	ϑ	ϑ	X
ejpam-6979	331	4	ϑ∑	ϑ∑	X
ejpam-6979	331	5	j=1	j=1	PROPN
ejpam-6979	331	6	lmn	lmn	PROPN
ejpam-6979	331	7	,	,	PUNCT
ejpam-6979	331	8	vg	vg	PROPN
ejpam-6979	331	9	j(ξ	j(ξ	PROPN
ejpam-6979	331	10	)	)	PUNCT
ejpam-6979	331	11			VERB
ejpam-6979	331	12	≤	≤	NUM
ejpam-6979	331	13	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	331	14	)	)	PUNCT
ejpam-6979	331	15	,	,	PUNCT
ejpam-6979	331	16	where	where	SCONJ
ejpam-6979	331	17	q	q	PROPN
ejpam-6979	331	18	j(ξ	j(ξ	PROPN
ejpam-6979	331	19	)	)	PUNCT
ejpam-6979	331	20	=	=	SYM
ejpam-6979	331	21	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	331	22	,	,	PUNCT
ejpam-6979	331	23	vg	vg	ADP
ejpam-6979	331	24	j(ξ	j(ξ	PROPN
ejpam-6979	331	25	)	)	PUNCT
ejpam-6979	331	26	]	]	PUNCT
ejpam-6979	332	1	′	′	NOUN
ejpam-6979	332	2	1	1	NUM
ejpam-6979	332	3	ϑ	ϑ	X
ejpam-6979	332	4	ϑ∑	ϑ∑	X
ejpam-6979	332	5	j=1	j=1	PROPN
ejpam-6979	332	6	lmn	lmn	PROPN
ejpam-6979	332	7	,	,	PUNCT
ejpam-6979	332	8	vg	vg	ADP
ejpam-6979	332	9	j(ξ	j(ξ	PROPN
ejpam-6979	332	10	)	)	PUNCT
ejpam-6979	332	11	.now	.now	PUNCT
ejpam-6979	333	1	q	q	PROPN
ejpam-6979	333	2	j(ξ	j(ξ	PROPN
ejpam-6979	333	3	)	)	PUNCT
ejpam-6979	334	1	≺f	≺f	PROPN
ejpam-6979	334	2	µ(ξ	µ(ξ	PROPN
ejpam-6979	334	3	)	)	PUNCT
ejpam-6979	334	4	,	,	PUNCT
ejpam-6979	334	5	j	j	PROPN
ejpam-6979	334	6	=	=	SYM
ejpam-6979	334	7	1	1	NUM
ejpam-6979	334	8	,	,	PUNCT
ejpam-6979	334	9	2	2	NUM
ejpam-6979	334	10	,	,	PUNCT
ejpam-6979	334	11	...	...	PUNCT
ejpam-6979	334	12	,	,	PUNCT
ejpam-6979	334	13	ϑ	ϑ	X
ejpam-6979	334	14	,	,	PUNCT
ejpam-6979	334	15	since	since	SCONJ
ejpam-6979	334	16	g	g	PROPN
ejpam-6979	334	17	=	=	SYM
ejpam-6979	334	18	{	{	PUNCT
ejpam-6979	334	19	g1,g2	g1,g2	PROPN
ejpam-6979	334	20	,	,	PUNCT
ejpam-6979	334	21	...	...	PUNCT
ejpam-6979	334	22	,	,	PUNCT
ejpam-6979	334	23	gϑ	gϑ	INTJ
ejpam-6979	334	24	}	}	PUNCT
ejpam-6979	334	25	∈	∈	PROPN
ejpam-6979	334	26	fℜn	fℜn	NOUN
ejpam-6979	334	27	,	,	PUNCT
ejpam-6979	334	28	v(ϑ	v(ϑ	NOUN
ejpam-6979	334	29	;	;	PUNCT
ejpam-6979	334	30	µ	µ	X
ejpam-6979	334	31	)	)	PUNCT
ejpam-6979	334	32	and	and	CCONJ
ejpam-6979	334	33	µ	µ	X
ejpam-6979	334	34	is	be	AUX
ejpam-6979	334	35	a	a	DET
ejpam-6979	334	36	convex	convex	NOUN
ejpam-6979	334	37	univalent	univalent	ADJ
ejpam-6979	334	38	.	.	PUNCT
ejpam-6979	335	1	since	since	SCONJ
ejpam-6979	335	2	re{µ(ξ)+τ	re{µ(ξ)+τ	NOUN
ejpam-6979	335	3	}	}	PUNCT
ejpam-6979	335	4	>	>	X
ejpam-6979	335	5	0	0	PROPN
ejpam-6979	335	6	,	,	PUNCT
ejpam-6979	335	7	an	an	DET
ejpam-6979	335	8	application	application	NOUN
ejpam-6979	335	9	of	of	ADP
ejpam-6979	335	10	lemma	lemma	PROPN
ejpam-6979	335	11	2	2	NUM
ejpam-6979	335	12	implies	imply	VERB
ejpam-6979	335	13	that	that	SCONJ
ejpam-6979	335	14	p(ξ	p(ξ	NOUN
ejpam-6979	335	15	)	)	PUNCT
ejpam-6979	335	16	≺f	≺f	PROPN
ejpam-6979	335	17	µ(ξ	µ(ξ	NOUN
ejpam-6979	335	18	)	)	PUNCT
ejpam-6979	335	19	,	,	PUNCT
ejpam-6979	335	20	hence	hence	ADV
ejpam-6979	335	21	f	f	PROPN
ejpam-6979	335	22	∈	∈	PROPN
ejpam-6979	335	23	fℵn	fℵn	PROPN
ejpam-6979	335	24	,	,	PUNCT
ejpam-6979	335	25	v(ϑ	v(ϑ	NOUN
ejpam-6979	335	26	;	;	PUNCT
ejpam-6979	335	27	µ	µ	NUM
ejpam-6979	335	28	)	)	PUNCT
ejpam-6979	335	29	.	.	PUNCT
ejpam-6979	336	1	this	this	PRON
ejpam-6979	336	2	complete	complete	ADJ
ejpam-6979	336	3	the	the	DET
ejpam-6979	336	4	proof	proof	NOUN
ejpam-6979	336	5	.	.	PUNCT
ejpam-6979	337	1	theorem	theorem	ADJ
ejpam-6979	337	2	5	5	NUM
ejpam-6979	337	3	.	.	PUNCT
ejpam-6979	338	1	if	if	SCONJ
ejpam-6979	338	2	f	f	PROPN
ejpam-6979	338	3	∈	∈	PROPN
ejpam-6979	338	4	fℵn	fℵn	PROPN
ejpam-6979	338	5	,	,	PUNCT
ejpam-6979	338	6	v(ϑ	v(ϑ	NOUN
ejpam-6979	338	7	;	;	PUNCT
ejpam-6979	338	8	µ	µ	X
ejpam-6979	338	9	)	)	PUNCT
ejpam-6979	338	10	and	and	CCONJ
ejpam-6979	338	11	re(µ	re(µ	NUM
ejpam-6979	338	12	)	)	PUNCT
ejpam-6979	338	13	is	be	AUX
ejpam-6979	338	14	bounded	bound	VERB
ejpam-6979	338	15	inu	inu	PROPN
ejpam-6979	338	16	,	,	PUNCT
ejpam-6979	338	17	then	then	ADV
ejpam-6979	338	18	f	f	PROPN
ejpam-6979	338	19	∈	∈	PROPN
ejpam-6979	338	20	fℵn	fℵn	PROPN
ejpam-6979	338	21	,	,	PUNCT
ejpam-6979	338	22	v(ϑ	v(ϑ	NOUN
ejpam-6979	338	23	;	;	PUNCT
ejpam-6979	338	24	µ	µ	X
ejpam-6979	338	25	)	)	PUNCT
ejpam-6979	338	26	holds	hold	VERB
ejpam-6979	338	27	for	for	ADP
ejpam-6979	338	28	re(µ(ξ)+	re(µ(ξ)+	NOUN
ejpam-6979	338	29	(	(	PUNCT
ejpam-6979	338	30	n	n	CCONJ
ejpam-6979	338	31	−	−	PROPN
ejpam-6979	338	32	1	1	NUM
ejpam-6979	338	33	)	)	PUNCT
ejpam-6979	338	34	)	)	PUNCT
ejpam-6979	338	35	>	>	X
ejpam-6979	338	36	0	0	NUM
ejpam-6979	338	37	inu	inu	PROPN
ejpam-6979	338	38	.	.	PUNCT
ejpam-6979	339	1	proof	proof	NOUN
ejpam-6979	339	2	.	.	PUNCT
ejpam-6979	340	1	this	this	DET
ejpam-6979	340	2	theorem	theorem	VERB
ejpam-6979	340	3	’s	’s	PART
ejpam-6979	340	4	proof	proof	NOUN
ejpam-6979	340	5	is	be	AUX
ejpam-6979	340	6	removed	remove	VERB
ejpam-6979	340	7	since	since	SCONJ
ejpam-6979	340	8	it	it	PRON
ejpam-6979	340	9	is	be	AUX
ejpam-6979	340	10	similar	similar	ADJ
ejpam-6979	340	11	to	to	ADP
ejpam-6979	340	12	that	that	PRON
ejpam-6979	340	13	of	of	ADP
ejpam-6979	340	14	theorem	theorem	ADJ
ejpam-6979	340	15	3	3	NUM
ejpam-6979	340	16	.	.	NOUN
ejpam-6979	340	17	3.3	3.3	NUM
ejpam-6979	340	18	.	.	PUNCT
ejpam-6979	341	1	the	the	DET
ejpam-6979	341	2	class	class	NOUN
ejpam-6979	341	3	f℘n	f℘n	PROPN
ejpam-6979	341	4	,	,	PUNCT
ejpam-6979	341	5	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	341	6	,	,	PUNCT
ejpam-6979	341	7	µ	µ	NOUN
ejpam-6979	341	8	)	)	PUNCT
ejpam-6979	341	9	definition	definition	NOUN
ejpam-6979	341	10	7	7	NUM
ejpam-6979	341	11	.	.	PUNCT
ejpam-6979	342	1	let	let	VERB
ejpam-6979	342	2	f℘n	f℘n	NOUN
ejpam-6979	342	3	,	,	PUNCT
ejpam-6979	342	4	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	342	5	,	,	PUNCT
ejpam-6979	342	6	µ	µ	NOUN
ejpam-6979	342	7	)	)	PUNCT
ejpam-6979	342	8	,	,	PUNCT
ejpam-6979	342	9	α	α	PRON
ejpam-6979	342	10	≥	≥	NOUN
ejpam-6979	342	11	0	0	NUM
ejpam-6979	342	12	,	,	PUNCT
ejpam-6979	342	13	denote	denote	VERB
ejpam-6979	342	14	the	the	DET
ejpam-6979	342	15	class	class	NOUN
ejpam-6979	342	16	of	of	ADP
ejpam-6979	342	17	functions	function	NOUN
ejpam-6979	342	18	f	f	PROPN
ejpam-6979	342	19	∈	∈	PROPN
ejpam-6979	342	20	a	a	DET
ejpam-6979	342	21	satisfying	satisfying	NOUN
ejpam-6979	342	22	the	the	DET
ejpam-6979	342	23	condition	condition	NOUN
ejpam-6979	342	24	e.	e.	PROPN
ejpam-6979	342	25	e.	e.	PROPN
ejpam-6979	342	26	ali	ali	PROPN
ejpam-6979	342	27	et	et	PROPN
ejpam-6979	342	28	al	al	PROPN
ejpam-6979	342	29	.	.	PUNCT
ejpam-6979	342	30	/	/	SYM
ejpam-6979	342	31	eur	eur	PROPN
ejpam-6979	342	32	.	.	PUNCT
ejpam-6979	343	1	j.	j.	PROPN
ejpam-6979	343	2	pure	pure	PROPN
ejpam-6979	343	3	appl	appl	PROPN
ejpam-6979	343	4	.	.	PROPN
ejpam-6979	343	5	math	math	PROPN
ejpam-6979	343	6	,	,	PUNCT
ejpam-6979	343	7	18	18	NUM
ejpam-6979	343	8	(	(	PUNCT
ejpam-6979	343	9	4	4	NUM
ejpam-6979	343	10	)	)	PUNCT
ejpam-6979	343	11	(	(	PUNCT
ejpam-6979	343	12	2025	2025	NUM
ejpam-6979	343	13	)	)	PUNCT
ejpam-6979	343	14	,	,	PUNCT
ejpam-6979	343	15	6979	6979	NUM
ejpam-6979	343	16	13	13	NUM
ejpam-6979	343	17	of	of	ADP
ejpam-6979	343	18	18	18	NUM
ejpam-6979	343	19	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	343	20	)	)	PUNCT
ejpam-6979	343	21	[	[	PUNCT
ejpam-6979	343	22	j(α	j(α	PROPN
ejpam-6979	343	23	;	;	PUNCT
ejpam-6979	343	24	f	f	X
ejpam-6979	343	25	;	;	PUNCT
ejpam-6979	343	26	g1	g1	NOUN
ejpam-6979	343	27	,	,	PUNCT
ejpam-6979	343	28	g2	g2	PROPN
ejpam-6979	343	29	,	,	PUNCT
ejpam-6979	343	30	...	...	PUNCT
ejpam-6979	343	31	,	,	PUNCT
ejpam-6979	343	32	gϑ)(ξ	gϑ)(ξ	PROPN
ejpam-6979	343	33	)	)	PUNCT
ejpam-6979	343	34	]	]	PUNCT
ejpam-6979	344	1	=	=	PUNCT
ejpam-6979	344	2	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	344	3	)	)	PUNCT
ejpam-6979	344	4	α	α	PROPN
ejpam-6979	344	5	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	344	6	,	,	PUNCT
ejpam-6979	344	7	vf(ξ	vf(ξ	NUM
ejpam-6979	344	8	)	)	PUNCT
ejpam-6979	344	9	]	]	PUNCT
ejpam-6979	345	1	′	′	NOUN
ejpam-6979	345	2	1	1	NUM
ejpam-6979	345	3	ϑ	ϑ	X
ejpam-6979	345	4	ϑ∑	ϑ∑	X
ejpam-6979	345	5	j=1	j=1	PROPN
ejpam-6979	345	6	lmn	lmn	PROPN
ejpam-6979	345	7	,	,	PUNCT
ejpam-6979	345	8	vg	vg	PROPN
ejpam-6979	345	9	j(ξ	j(ξ	PROPN
ejpam-6979	345	10	)	)	PUNCT
ejpam-6979	346	1	+	+	CCONJ
ejpam-6979	346	2	(	(	PUNCT
ejpam-6979	346	3	1	1	NUM
ejpam-6979	346	4	−	−	PROPN
ejpam-6979	346	5	α	α	X
ejpam-6979	346	6	)	)	PUNCT
ejpam-6979	346	7	ξ[lmn+1,vf(ξ	ξ[lmn+1,vf(ξ	PROPN
ejpam-6979	346	8	)	)	PUNCT
ejpam-6979	346	9	]	]	PUNCT
ejpam-6979	347	1	′	′	NOUN
ejpam-6979	347	2	1	1	NUM
ejpam-6979	347	3	ϑ	ϑ	X
ejpam-6979	347	4	ϑ∑	ϑ∑	X
ejpam-6979	347	5	j=1	j=1	PROPN
ejpam-6979	347	6	lmn+1,vg	lmn+1,vg	PROPN
ejpam-6979	347	7	j(ξ	j(ξ	PROPN
ejpam-6979	347	8	)	)	PUNCT
ejpam-6979	347	9			ADJ
ejpam-6979	347	10	≤	≤	NUM
ejpam-6979	347	11	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	347	12	)	)	PUNCT
ejpam-6979	347	13	(	(	PUNCT
ejpam-6979	347	14	ξ	ξ	PROPN
ejpam-6979	347	15	∈	∈	PROPN
ejpam-6979	347	16	u	u	NOUN
ejpam-6979	347	17	)	)	PUNCT
ejpam-6979	347	18	,	,	PUNCT
ejpam-6979	347	19	where	where	SCONJ
ejpam-6979	347	20	g	g	NOUN
ejpam-6979	347	21	=	=	SYM
ejpam-6979	347	22	{	{	PUNCT
ejpam-6979	347	23	g1	g1	PROPN
ejpam-6979	347	24	,	,	PUNCT
ejpam-6979	347	25	g2,	g2,	NOUN
ejpam-6979	347	26	...	...	PUNCT
ejpam-6979	347	27	,gϑ	,gϑ	PUNCT
ejpam-6979	347	28	}	}	PUNCT
ejpam-6979	347	29	∈	∈	PROPN
ejpam-6979	347	30	fℜn	fℜn	NOUN
ejpam-6979	347	31	,	,	PUNCT
ejpam-6979	347	32	v(ϑ	v(ϑ	NOUN
ejpam-6979	347	33	;	;	PUNCT
ejpam-6979	347	34	µ	µ	X
ejpam-6979	347	35	)	)	PUNCT
ejpam-6979	347	36	,	,	PUNCT
ejpam-6979	347	37	ξ−1	ξ−1	PROPN
ejpam-6979	347	38	ϑ∑	ϑ∑	NUM
ejpam-6979	347	39	j=1	j=1	PROPN
ejpam-6979	347	40	lmn	lmn	PROPN
ejpam-6979	347	41	,	,	PUNCT
ejpam-6979	347	42	vg	vg	PROPN
ejpam-6979	347	43	j(ξ	j(ξ	PROPN
ejpam-6979	347	44	)	)	PUNCT
ejpam-6979	347	45	,	,	PUNCT
ejpam-6979	347	46	0	0	NUM
ejpam-6979	347	47	in	in	ADP
ejpam-6979	347	48	u	u	PROPN
ejpam-6979	347	49	,	,	PUNCT
ejpam-6979	347	50	µ	µ	PRON
ejpam-6979	347	51	is	be	AUX
ejpam-6979	347	52	convex	convex	ADJ
ejpam-6979	347	53	univalent	univalent	ADJ
ejpam-6979	347	54	in	in	ADP
ejpam-6979	347	55	u	u	NOUN
ejpam-6979	347	56	with	with	ADP
ejpam-6979	347	57	µ(0	µ(0	NOUN
ejpam-6979	347	58	)	)	PUNCT
ejpam-6979	347	59	=	=	SYM
ejpam-6979	347	60	1	1	X
ejpam-6979	347	61	.	.	NOUN
ejpam-6979	347	62	remark	remark	NOUN
ejpam-6979	347	63	2	2	NUM
ejpam-6979	347	64	.	.	PUNCT
ejpam-6979	348	1	we	we	PRON
ejpam-6979	348	2	note	note	VERB
ejpam-6979	348	3	that	that	SCONJ
ejpam-6979	348	4	f℘n	f℘n	NOUN
ejpam-6979	348	5	,	,	PUNCT
ejpam-6979	348	6	v(ϑ	v(ϑ	NOUN
ejpam-6979	348	7	;	;	PUNCT
ejpam-6979	348	8	0	0	NUM
ejpam-6979	348	9	,	,	PUNCT
ejpam-6979	348	10	µ	µ	NOUN
ejpam-6979	348	11	)	)	PUNCT
ejpam-6979	348	12	=	=	SYM
ejpam-6979	348	13	fℵn	fℵn	PROPN
ejpam-6979	348	14	,	,	PUNCT
ejpam-6979	348	15	v(ϑ	v(ϑ	NOUN
ejpam-6979	348	16	;	;	PUNCT
ejpam-6979	348	17	µ	µ	NUM
ejpam-6979	348	18	)	)	PUNCT
ejpam-6979	348	19	.	.	PUNCT
ejpam-6979	349	1	theorem	theorem	VERB
ejpam-6979	349	2	6	6	NUM
ejpam-6979	349	3	.	.	PUNCT
ejpam-6979	350	1	if	if	SCONJ
ejpam-6979	350	2	f	f	PROPN
ejpam-6979	350	3	∈	∈	PROPN
ejpam-6979	350	4	f℘n	f℘n	PROPN
ejpam-6979	350	5	,	,	PUNCT
ejpam-6979	350	6	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	350	7	,	,	PUNCT
ejpam-6979	350	8	µ	µ	NOUN
ejpam-6979	350	9	)	)	PUNCT
ejpam-6979	350	10	and	and	CCONJ
ejpam-6979	350	11	re{µ	re{µ	PROPN
ejpam-6979	350	12	}	}	PUNCT
ejpam-6979	350	13	is	be	AUX
ejpam-6979	350	14	bounded	bounded	ADJ
ejpam-6979	350	15	inu	inu	PROPN
ejpam-6979	350	16	,	,	PUNCT
ejpam-6979	350	17	then	then	ADV
ejpam-6979	350	18	f	f	PROPN
ejpam-6979	350	19	∈	∈	PROPN
ejpam-6979	350	20	f℘n	f℘n	PROPN
ejpam-6979	350	21	,	,	PUNCT
ejpam-6979	350	22	v(ϑ	v(ϑ	NOUN
ejpam-6979	350	23	;	;	PUNCT
ejpam-6979	350	24	0	0	NUM
ejpam-6979	350	25	,	,	PUNCT
ejpam-6979	350	26	µ	µ	NOUN
ejpam-6979	350	27	)	)	PUNCT
ejpam-6979	350	28	=	=	SYM
ejpam-6979	350	29	fℵn	fℵn	PROPN
ejpam-6979	350	30	,	,	PUNCT
ejpam-6979	350	31	v(ϑ	v(ϑ	NOUN
ejpam-6979	350	32	;	;	PUNCT
ejpam-6979	350	33	µ	µ	X
ejpam-6979	350	34	)	)	PUNCT
ejpam-6979	350	35	hold	hold	NOUN
ejpam-6979	350	36	for	for	ADP
ejpam-6979	350	37	re{µ(ξ	re{µ(ξ	NOUN
ejpam-6979	350	38	)	)	PUNCT
ejpam-6979	350	39	+	+	CCONJ
ejpam-6979	350	40	(	(	PUNCT
ejpam-6979	350	41	n	n	CCONJ
ejpam-6979	350	42	−	−	PROPN
ejpam-6979	350	43	1	1	NUM
ejpam-6979	350	44	)	)	PUNCT
ejpam-6979	350	45	}	}	PUNCT
ejpam-6979	350	46	≥	≥	NOUN
ejpam-6979	350	47	0	0	NUM
ejpam-6979	350	48	.	.	PUNCT
ejpam-6979	351	1	proof	proof	NOUN
ejpam-6979	351	2	.	.	PUNCT
ejpam-6979	352	1	for	for	ADP
ejpam-6979	352	2	α	α	NOUN
ejpam-6979	352	3	=	=	SYM
ejpam-6979	352	4	0	0	NUM
ejpam-6979	352	5	,	,	PUNCT
ejpam-6979	352	6	the	the	DET
ejpam-6979	352	7	theorem	theorem	NOUN
ejpam-6979	352	8	is	be	AUX
ejpam-6979	352	9	trivial	trivial	ADJ
ejpam-6979	352	10	and	and	CCONJ
ejpam-6979	352	11	hence	hence	ADV
ejpam-6979	352	12	we	we	PRON
ejpam-6979	352	13	can	can	AUX
ejpam-6979	352	14	assume	assume	VERB
ejpam-6979	352	15	that	that	SCONJ
ejpam-6979	352	16	α	α	NOUN
ejpam-6979	352	17	,	,	PUNCT
ejpam-6979	352	18	0	0	X
ejpam-6979	352	19	.	.	PUNCT
ejpam-6979	352	20	let	let	VERB
ejpam-6979	352	21	p(ξ	p(ξ	NOUN
ejpam-6979	352	22	)	)	PUNCT
ejpam-6979	353	1	=	=	SYM
ejpam-6979	353	2	ξ[lmn+1,vf(ξ	ξ[lmn+1,vf(ξ	PROPN
ejpam-6979	353	3	)	)	PUNCT
ejpam-6979	353	4	]	]	PUNCT
ejpam-6979	354	1	′	′	NOUN
ejpam-6979	354	2	1	1	NUM
ejpam-6979	354	3	ϑ	ϑ	X
ejpam-6979	354	4	ϑ∑	ϑ∑	X
ejpam-6979	354	5	j=1	j=1	PROPN
ejpam-6979	354	6	lmn+1,vg	lmn+1,vg	PROPN
ejpam-6979	354	7	j(ξ	j(ξ	PROPN
ejpam-6979	354	8	)	)	PUNCT
ejpam-6979	354	9	(	(	PUNCT
ejpam-6979	354	10	ξ	ξ	PROPN
ejpam-6979	354	11	∈	∈	PROPN
ejpam-6979	354	12	u	u	NOUN
ejpam-6979	354	13	)	)	PUNCT
ejpam-6979	354	14	.	.	PUNCT
ejpam-6979	355	1	then	then	ADV
ejpam-6979	355	2	,	,	PUNCT
ejpam-6979	355	3	a	a	DET
ejpam-6979	355	4	simple	simple	ADJ
ejpam-6979	355	5	calculation	calculation	NOUN
ejpam-6979	355	6	reveals	reveal	VERB
ejpam-6979	355	7	that	that	SCONJ
ejpam-6979	355	8	ξp	ξp	PART
ejpam-6979	355	9	′	′	NUM
ejpam-6979	355	10	(	(	PUNCT
ejpam-6979	355	11	ξ	ξ	X
ejpam-6979	355	12	)	)	PUNCT
ejpam-6979	355	13	1	1	NUM
ejpam-6979	355	14	ϑ	ϑ	X
ejpam-6979	355	15	ϑ∑	ϑ∑	X
ejpam-6979	355	16	j=1	j=1	PROPN
ejpam-6979	355	17	q	q	PROPN
ejpam-6979	355	18	j(ξ	j(ξ	PROPN
ejpam-6979	355	19	)	)	PUNCT
ejpam-6979	356	1	+	+	CCONJ
ejpam-6979	356	2	(	(	PUNCT
ejpam-6979	356	3	n	n	CCONJ
ejpam-6979	356	4	−	−	PROPN
ejpam-6979	356	5	1	1	NUM
ejpam-6979	356	6	)	)	PUNCT
ejpam-6979	356	7	+	+	CCONJ
ejpam-6979	356	8	p(ξ	p(ξ	X
ejpam-6979	356	9	)	)	PUNCT
ejpam-6979	356	10	=	=	NOUN
ejpam-6979	356	11	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	356	12	,	,	PUNCT
ejpam-6979	356	13	vf(ξ	vf(ξ	NUM
ejpam-6979	356	14	)	)	PUNCT
ejpam-6979	356	15	]	]	PUNCT
ejpam-6979	357	1	′	′	NOUN
ejpam-6979	357	2	1	1	NUM
ejpam-6979	357	3	ϑ	ϑ	X
ejpam-6979	357	4	ϑ∑	ϑ∑	X
ejpam-6979	357	5	j=1	j=1	PROPN
ejpam-6979	357	6	lmn	lmn	PROPN
ejpam-6979	357	7	,	,	PUNCT
ejpam-6979	357	8	vg	vg	PROPN
ejpam-6979	357	9	j(ξ	j(ξ	PROPN
ejpam-6979	357	10	)	)	PUNCT
ejpam-6979	357	11	,	,	PUNCT
ejpam-6979	357	12	where	where	SCONJ
ejpam-6979	357	13	q	q	PROPN
ejpam-6979	357	14	j(ξ	j(ξ	PROPN
ejpam-6979	357	15	)	)	PUNCT
ejpam-6979	357	16	=	=	SYM
ejpam-6979	357	17	ξ[lmn+1,vgi(ξ	ξ[lmn+1,vgi(ξ	NOUN
ejpam-6979	357	18	)	)	PUNCT
ejpam-6979	357	19	]	]	PUNCT
ejpam-6979	357	20	′	′	NOUN
ejpam-6979	358	1	1	1	NUM
ejpam-6979	358	2	ϑ	ϑ	X
ejpam-6979	358	3	ϑ∑	ϑ∑	X
ejpam-6979	358	4	j=1	j=1	PROPN
ejpam-6979	358	5	lmn+1,vg	lmn+1,vg	PROPN
ejpam-6979	358	6	j(ξ	j(ξ	PROPN
ejpam-6979	358	7	)	)	PUNCT
ejpam-6979	358	8	.	.	PUNCT
ejpam-6979	359	1	also	also	ADV
ejpam-6979	359	2	1	1	NUM
ejpam-6979	359	3	ϑ	ϑ	X
ejpam-6979	359	4	ϑ∑	ϑ∑	X
ejpam-6979	359	5	j=1	j=1	PROPN
ejpam-6979	359	6	q	q	PROPN
ejpam-6979	359	7	j(ξ	j(ξ	PROPN
ejpam-6979	359	8	)	)	PUNCT
ejpam-6979	360	1	≺f	≺f	PROPN
ejpam-6979	360	2	µ(ξ	µ(ξ	NOUN
ejpam-6979	360	3	)	)	PUNCT
ejpam-6979	360	4	.	.	PUNCT
ejpam-6979	361	1	since	since	SCONJ
ejpam-6979	361	2	f	f	PROPN
ejpam-6979	361	3	∈	∈	PROPN
ejpam-6979	361	4	f℘n	f℘n	PROPN
ejpam-6979	361	5	,	,	PUNCT
ejpam-6979	361	6	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	361	7	,	,	PUNCT
ejpam-6979	361	8	µ	µ	NOUN
ejpam-6979	361	9	)	)	PUNCT
ejpam-6979	361	10	,	,	PUNCT
ejpam-6979	361	11	we	we	PRON
ejpam-6979	361	12	have	have	VERB
ejpam-6979	361	13	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	361	14	)	)	PUNCT
ejpam-6979	361	15	[	[	PUNCT
ejpam-6979	361	16	j(α	j(α	PROPN
ejpam-6979	361	17	;	;	PUNCT
ejpam-6979	361	18	f	f	X
ejpam-6979	361	19	;	;	PUNCT
ejpam-6979	361	20	g1	g1	NOUN
ejpam-6979	361	21	,	,	PUNCT
ejpam-6979	361	22	g2	g2	PROPN
ejpam-6979	361	23	,	,	PUNCT
ejpam-6979	361	24	...	...	PUNCT
ejpam-6979	361	25	,	,	PUNCT
ejpam-6979	361	26	gϑ)(ξ	gϑ)(ξ	PROPN
ejpam-6979	361	27	)	)	PUNCT
ejpam-6979	361	28	]	]	PUNCT
ejpam-6979	362	1	=	=	PUNCT
ejpam-6979	362	2	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	362	3	)	)	PUNCT
ejpam-6979	362	4			NOUN
ejpam-6979	362	5	αξp	αξp	NOUN
ejpam-6979	362	6	′	′	NUM
ejpam-6979	362	7	(	(	PUNCT
ejpam-6979	362	8	ξ	ξ	NOUN
ejpam-6979	362	9	)	)	PUNCT
ejpam-6979	362	10	1	1	NUM
ejpam-6979	362	11	ϑ	ϑ	X
ejpam-6979	362	12	ϑ∑	ϑ∑	X
ejpam-6979	362	13	j=1	j=1	PROPN
ejpam-6979	362	14	q	q	PROPN
ejpam-6979	362	15	j(ξ	j(ξ	PROPN
ejpam-6979	362	16	)	)	PUNCT
ejpam-6979	363	1	+	+	CCONJ
ejpam-6979	363	2	(	(	PUNCT
ejpam-6979	363	3	n	n	CCONJ
ejpam-6979	363	4	−	−	PROPN
ejpam-6979	363	5	1	1	NUM
ejpam-6979	363	6	)	)	PUNCT
ejpam-6979	363	7	+	+	CCONJ
ejpam-6979	363	8	p(ξ	p(ξ	NOUN
ejpam-6979	363	9	)	)	PUNCT
ejpam-6979	363	10			VERB
ejpam-6979	363	11	≤	≤	NUM
ejpam-6979	363	12	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	363	13	)	)	PUNCT
ejpam-6979	363	14	.	.	PUNCT
ejpam-6979	364	1	now	now	ADV
ejpam-6979	364	2	an	an	DET
ejpam-6979	364	3	application	application	NOUN
ejpam-6979	364	4	of	of	ADP
ejpam-6979	364	5	lemma	lemma	PROPN
ejpam-6979	364	6	2	2	PROPN
ejpam-6979	364	7	gives	give	VERB
ejpam-6979	364	8	p(ξ	p(ξ	NOUN
ejpam-6979	364	9	)	)	PUNCT
ejpam-6979	364	10	≺f	≺f	PROPN
ejpam-6979	364	11	µ(ξ	µ(ξ	NOUN
ejpam-6979	364	12	)	)	PUNCT
ejpam-6979	364	13	which	which	PRON
ejpam-6979	364	14	implies	imply	VERB
ejpam-6979	364	15	f	f	PROPN
ejpam-6979	364	16	∈	∈	PROPN
ejpam-6979	364	17	fℵn	fℵn	PROPN
ejpam-6979	364	18	,	,	PUNCT
ejpam-6979	364	19	v(ϑ	v(ϑ	NOUN
ejpam-6979	364	20	;	;	PUNCT
ejpam-6979	364	21	µ	µ	NUM
ejpam-6979	364	22	)	)	PUNCT
ejpam-6979	364	23	.	.	PUNCT
ejpam-6979	365	1	this	this	PRON
ejpam-6979	365	2	completes	complete	VERB
ejpam-6979	365	3	the	the	DET
ejpam-6979	365	4	proof	proof	NOUN
ejpam-6979	365	5	.	.	PUNCT
ejpam-6979	366	1	theorem	theorem	ADJ
ejpam-6979	366	2	7	7	NUM
ejpam-6979	366	3	.	.	PUNCT
ejpam-6979	367	1	forα	forα	PROPN
ejpam-6979	367	2	>	>	PUNCT
ejpam-6979	367	3	β	β	X
ejpam-6979	367	4	≥	≥	NOUN
ejpam-6979	367	5	0	0	NUM
ejpam-6979	367	6	,	,	PUNCT
ejpam-6979	367	7	and	and	CCONJ
ejpam-6979	367	8	reµ(ξ	reµ(ξ	NOUN
ejpam-6979	367	9	)	)	PUNCT
ejpam-6979	368	1	is	be	AUX
ejpam-6979	368	2	bounded	bound	VERB
ejpam-6979	368	3	inu	inu	PROPN
ejpam-6979	368	4	,	,	PUNCT
ejpam-6979	368	5	then	then	ADV
ejpam-6979	368	6	f℘n	f℘n	PROPN
ejpam-6979	368	7	,	,	PUNCT
ejpam-6979	368	8	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	368	9	,	,	PUNCT
ejpam-6979	368	10	µ	µ	NOUN
ejpam-6979	368	11	)	)	PUNCT
ejpam-6979	368	12	⊂	⊂	PROPN
ejpam-6979	368	13	f℘n	f℘n	PROPN
ejpam-6979	368	14	,	,	PUNCT
ejpam-6979	368	15	v(ϑ	v(ϑ	NOUN
ejpam-6979	368	16	;	;	PUNCT
ejpam-6979	368	17	β	β	X
ejpam-6979	368	18	,	,	PUNCT
ejpam-6979	368	19	µ	µ	NOUN
ejpam-6979	368	20	)	)	PUNCT
ejpam-6979	368	21	.	.	PUNCT
ejpam-6979	369	1	e.	e.	PROPN
ejpam-6979	369	2	e.	e.	PROPN
ejpam-6979	369	3	ali	ali	PROPN
ejpam-6979	369	4	et	et	PROPN
ejpam-6979	369	5	al	al	PROPN
ejpam-6979	369	6	.	.	PUNCT
ejpam-6979	369	7	/	/	SYM
ejpam-6979	369	8	eur	eur	PROPN
ejpam-6979	369	9	.	.	PUNCT
ejpam-6979	370	1	j.	j.	PROPN
ejpam-6979	370	2	pure	pure	PROPN
ejpam-6979	370	3	appl	appl	PROPN
ejpam-6979	370	4	.	.	PROPN
ejpam-6979	370	5	math	math	PROPN
ejpam-6979	370	6	,	,	PUNCT
ejpam-6979	370	7	18	18	NUM
ejpam-6979	370	8	(	(	PUNCT
ejpam-6979	370	9	4	4	NUM
ejpam-6979	370	10	)	)	PUNCT
ejpam-6979	370	11	(	(	PUNCT
ejpam-6979	370	12	2025	2025	NUM
ejpam-6979	370	13	)	)	PUNCT
ejpam-6979	370	14	,	,	PUNCT
ejpam-6979	370	15	6979	6979	NUM
ejpam-6979	370	16	14	14	NUM
ejpam-6979	370	17	of	of	ADP
ejpam-6979	370	18	18	18	NUM
ejpam-6979	370	19	proof	proof	NOUN
ejpam-6979	370	20	.	.	PUNCT
ejpam-6979	371	1	the	the	DET
ejpam-6979	371	2	case	case	NOUN
ejpam-6979	371	3	β	β	X
ejpam-6979	371	4	=	=	SYM
ejpam-6979	371	5	0	0	NUM
ejpam-6979	371	6	was	be	AUX
ejpam-6979	371	7	treated	treat	VERB
ejpam-6979	371	8	in	in	ADP
ejpam-6979	371	9	the	the	DET
ejpam-6979	371	10	previous	previous	ADJ
ejpam-6979	371	11	theorem	theorem	NOUN
ejpam-6979	371	12	.	.	PUNCT
ejpam-6979	372	1	hence	hence	ADV
ejpam-6979	372	2	we	we	PRON
ejpam-6979	372	3	assume	assume	VERB
ejpam-6979	372	4	that	that	SCONJ
ejpam-6979	372	5	β	β	NOUN
ejpam-6979	372	6	,	,	PUNCT
ejpam-6979	372	7	0	0	X
ejpam-6979	372	8	.	.	PUNCT
ejpam-6979	372	9	suppose	suppose	VERB
ejpam-6979	372	10	that	that	SCONJ
ejpam-6979	372	11	f	f	PROPN
ejpam-6979	372	12	∈	∈	PROPN
ejpam-6979	372	13	f℘n	f℘n	PROPN
ejpam-6979	372	14	,	,	PUNCT
ejpam-6979	372	15	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	372	16	,	,	PUNCT
ejpam-6979	372	17	µ	µ	NOUN
ejpam-6979	372	18	)	)	PUNCT
ejpam-6979	372	19	.	.	PUNCT
ejpam-6979	373	1	then	then	ADV
ejpam-6979	373	2	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	373	3	)	)	PUNCT
ejpam-6979	374	1	[	[	PUNCT
ejpam-6979	374	2	j(α	j(α	PROPN
ejpam-6979	374	3	;	;	PUNCT
ejpam-6979	374	4	f	f	X
ejpam-6979	374	5	;	;	PUNCT
ejpam-6979	374	6	g1	g1	NOUN
ejpam-6979	374	7	,	,	PUNCT
ejpam-6979	374	8	g2	g2	PROPN
ejpam-6979	374	9	,	,	PUNCT
ejpam-6979	374	10	...	...	PUNCT
ejpam-6979	374	11	,	,	PUNCT
ejpam-6979	374	12	gϑ)(ξ	gϑ)(ξ	PROPN
ejpam-6979	374	13	)	)	PUNCT
ejpam-6979	374	14	]	]	PUNCT
ejpam-6979	374	15	≤	≤	NUM
ejpam-6979	374	16	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	374	17	)	)	PUNCT
ejpam-6979	374	18	.	.	PUNCT
ejpam-6979	375	1	(	(	PUNCT
ejpam-6979	375	2	25	25	NUM
ejpam-6979	375	3	)	)	PUNCT
ejpam-6979	375	4	let	let	VERB
ejpam-6979	375	5	ξ1	ξ1	NOUN
ejpam-6979	375	6	be	be	AUX
ejpam-6979	375	7	any	any	DET
ejpam-6979	375	8	arbitrary	arbitrary	ADJ
ejpam-6979	375	9	point	point	NOUN
ejpam-6979	375	10	inu	inu	NOUN
ejpam-6979	375	11	.	.	PUNCT
ejpam-6979	376	1	then	then	ADV
ejpam-6979	376	2	j(α	j(α	PROPN
ejpam-6979	376	3	;	;	PUNCT
ejpam-6979	376	4	f	f	X
ejpam-6979	376	5	;	;	PUNCT
ejpam-6979	376	6	g1	g1	NOUN
ejpam-6979	376	7	,	,	PUNCT
ejpam-6979	376	8	g2	g2	PROPN
ejpam-6979	376	9	,	,	PUNCT
ejpam-6979	376	10	...	...	PUNCT
ejpam-6979	376	11	,	,	PUNCT
ejpam-6979	376	12	gϑ)(ξ1	gϑ)(ξ1	NOUN
ejpam-6979	376	13	)	)	PUNCT
ejpam-6979	376	14	∈	∈	PROPN
ejpam-6979	376	15	µ(u	µ(u	NOUN
ejpam-6979	376	16	)	)	PUNCT
ejpam-6979	376	17	.	.	PUNCT
ejpam-6979	377	1	from	from	ADP
ejpam-6979	377	2	theorem	theorem	ADJ
ejpam-6979	377	3	6	6	NUM
ejpam-6979	377	4	,	,	PUNCT
ejpam-6979	377	5	we	we	PRON
ejpam-6979	377	6	have	have	VERB
ejpam-6979	377	7	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	377	8	)	)	PUNCT
ejpam-6979	377	9			NOUN
ejpam-6979	377	10	ξ[lmn+1,vf(ξ	ξ[lmn+1,vf(ξ	PROPN
ejpam-6979	377	11	)	)	PUNCT
ejpam-6979	377	12	]	]	PUNCT
ejpam-6979	378	1	′	′	NOUN
ejpam-6979	378	2	1	1	NUM
ejpam-6979	378	3	ϑ	ϑ	X
ejpam-6979	378	4	ϑ∑	ϑ∑	X
ejpam-6979	378	5	j=1	j=1	PROPN
ejpam-6979	378	6	lmn+1,vg	lmn+1,vg	PROPN
ejpam-6979	378	7	j(ξ	j(ξ	PROPN
ejpam-6979	378	8	)	)	PUNCT
ejpam-6979	378	9			VERB
ejpam-6979	378	10	≤	≤	NUM
ejpam-6979	378	11	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	378	12	)	)	PUNCT
ejpam-6979	378	13	.	.	PUNCT
ejpam-6979	379	1	(	(	PUNCT
ejpam-6979	379	2	26	26	NUM
ejpam-6979	379	3	)	)	PUNCT
ejpam-6979	379	4	now	now	ADV
ejpam-6979	379	5	j(β	j(β	VERB
ejpam-6979	379	6	;	;	PUNCT
ejpam-6979	379	7	f	f	X
ejpam-6979	379	8	;	;	PUNCT
ejpam-6979	379	9	g1	g1	NOUN
ejpam-6979	379	10	,	,	PUNCT
ejpam-6979	379	11	g2	g2	PROPN
ejpam-6979	379	12	,	,	PUNCT
ejpam-6979	379	13	...	...	PUNCT
ejpam-6979	379	14	,	,	PUNCT
ejpam-6979	379	15	gϑ)(ξ	gϑ)(ξ	PROPN
ejpam-6979	379	16	)	)	PUNCT
ejpam-6979	380	1	=	=	PRON
ejpam-6979	380	2	(	(	PUNCT
ejpam-6979	380	3	1	1	NUM
ejpam-6979	380	4	−	−	PROPN
ejpam-6979	380	5	β	β	X
ejpam-6979	380	6	α	α	NOUN
ejpam-6979	380	7	)	)	PUNCT
ejpam-6979	380	8	ξ[lmn+1,vf(ξ	ξ[lmn+1,vf(ξ	PROPN
ejpam-6979	380	9	)	)	PUNCT
ejpam-6979	380	10	]	]	PUNCT
ejpam-6979	381	1	′	′	NOUN
ejpam-6979	381	2	1	1	NUM
ejpam-6979	381	3	ϑ	ϑ	X
ejpam-6979	381	4	ϑ∑	ϑ∑	X
ejpam-6979	381	5	j=1	j=1	PROPN
ejpam-6979	381	6	lmn+1,vg	lmn+1,vg	PROPN
ejpam-6979	381	7	j(ξ	j(ξ	PROPN
ejpam-6979	381	8	)	)	PUNCT
ejpam-6979	382	1	+	+	CCONJ
ejpam-6979	382	2	β	β	X
ejpam-6979	382	3	α	α	PRON
ejpam-6979	382	4	j(α	j(α	PROPN
ejpam-6979	382	5	;	;	PUNCT
ejpam-6979	382	6	f	f	X
ejpam-6979	382	7	;	;	PUNCT
ejpam-6979	382	8	g1	g1	NOUN
ejpam-6979	382	9	,	,	PUNCT
ejpam-6979	382	10	g2	g2	PROPN
ejpam-6979	382	11	,	,	PUNCT
ejpam-6979	382	12	...	...	PUNCT
ejpam-6979	382	13	,	,	PUNCT
ejpam-6979	382	14	gϑ)(ξ	gϑ)(ξ	PROPN
ejpam-6979	382	15	)	)	PUNCT
ejpam-6979	382	16	.	.	PUNCT
ejpam-6979	383	1	from	from	ADP
ejpam-6979	383	2	(	(	PUNCT
ejpam-6979	383	3	25	25	NUM
ejpam-6979	383	4	)	)	PUNCT
ejpam-6979	383	5	and	and	CCONJ
ejpam-6979	383	6	(	(	PUNCT
ejpam-6979	383	7	26	26	NUM
ejpam-6979	383	8	)	)	PUNCT
ejpam-6979	383	9	it	it	PRON
ejpam-6979	383	10	follows	follow	VERB
ejpam-6979	383	11	that	that	SCONJ
ejpam-6979	383	12	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	383	13	)	)	PUNCT
ejpam-6979	383	14			NOUN
ejpam-6979	383	15	ξ1[lmn+1,vf(ξ1	ξ1[lmn+1,vf(ξ1	NUM
ejpam-6979	383	16	)	)	PUNCT
ejpam-6979	383	17	]	]	PUNCT
ejpam-6979	384	1	′	′	NOUN
ejpam-6979	384	2	1	1	NUM
ejpam-6979	384	3	ϑ	ϑ	X
ejpam-6979	384	4	ϑ∑	ϑ∑	X
ejpam-6979	384	5	j=1	j=1	PROPN
ejpam-6979	384	6	lmn+1,vg	lmn+1,vg	X
ejpam-6979	384	7	j(ξ1	j(ξ1	ADV
ejpam-6979	384	8	)	)	PUNCT
ejpam-6979	384	9			VERB
ejpam-6979	384	10	≤	≤	NUM
ejpam-6979	384	11	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	384	12	)	)	PUNCT
ejpam-6979	384	13	and	and	CCONJ
ejpam-6979	384	14	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	384	15	)	)	PUNCT
ejpam-6979	384	16	α	α	X
ejpam-6979	385	1	ξ1[lmn	ξ1[lmn	PROPN
ejpam-6979	385	2	,	,	PUNCT
ejpam-6979	385	3	vf(ξ1	vf(ξ1	NOUN
ejpam-6979	385	4	)	)	PUNCT
ejpam-6979	385	5	]	]	PUNCT
ejpam-6979	386	1	′	′	NOUN
ejpam-6979	386	2	1	1	NUM
ejpam-6979	387	1	ϑ	ϑ	X
ejpam-6979	387	2	ϑ∑	ϑ∑	X
ejpam-6979	387	3	j=1	j=1	PROPN
ejpam-6979	387	4	lmn	lmn	PROPN
ejpam-6979	387	5	,	,	PUNCT
ejpam-6979	387	6	vg	vg	NOUN
ejpam-6979	387	7	j(ξ1	j(ξ1	NUM
ejpam-6979	387	8	)	)	PUNCT
ejpam-6979	388	1	+	+	CCONJ
ejpam-6979	388	2	(	(	PUNCT
ejpam-6979	388	3	1	1	NUM
ejpam-6979	388	4	−	−	PROPN
ejpam-6979	388	5	α	α	NUM
ejpam-6979	388	6	)	)	PUNCT
ejpam-6979	388	7	ξ1[lmn+1,vf(ξ1	ξ1[lmn+1,vf(ξ1	NUM
ejpam-6979	388	8	)	)	PUNCT
ejpam-6979	388	9	]	]	PUNCT
ejpam-6979	389	1	′	′	NOUN
ejpam-6979	389	2	1	1	NUM
ejpam-6979	389	3	ϑ	ϑ	X
ejpam-6979	389	4	ϑ∑	ϑ∑	X
ejpam-6979	389	5	j=1	j=1	PROPN
ejpam-6979	389	6	lmn+1,vg	lmn+1,vg	X
ejpam-6979	389	7	j(ξ1	j(ξ1	ADV
ejpam-6979	389	8	)	)	PUNCT
ejpam-6979	389	9			VERB
ejpam-6979	389	10	≤	≤	NUM
ejpam-6979	389	11	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	389	12	)	)	PUNCT
ejpam-6979	389	13	.	.	PUNCT
ejpam-6979	390	1	now	now	ADV
ejpam-6979	390	2	µ(u	µ(u	NOUN
ejpam-6979	390	3	)	)	PUNCT
ejpam-6979	390	4	is	be	AUX
ejpam-6979	390	5	convex	convex	ADJ
ejpam-6979	390	6	and	and	CCONJ
ejpam-6979	390	7	β	β	X
ejpam-6979	390	8	α	α	X
ejpam-6979	390	9	<	<	X
ejpam-6979	390	10	1	1	NUM
ejpam-6979	390	11	,	,	PUNCT
ejpam-6979	390	12	hence	hence	ADV
ejpam-6979	390	13	we	we	PRON
ejpam-6979	390	14	have	have	VERB
ejpam-6979	390	15	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	390	16	)	)	PUNCT
ejpam-6979	391	1	[	[	PUNCT
ejpam-6979	391	2	j(β	j(β	NOUN
ejpam-6979	391	3	;	;	PUNCT
ejpam-6979	391	4	f	f	X
ejpam-6979	391	5	;	;	PUNCT
ejpam-6979	391	6	g1	g1	NOUN
ejpam-6979	391	7	,	,	PUNCT
ejpam-6979	391	8	g2	g2	PROPN
ejpam-6979	391	9	,	,	PUNCT
ejpam-6979	391	10	...	...	PUNCT
ejpam-6979	391	11	,	,	PUNCT
ejpam-6979	391	12	gϑ)(ξ	gϑ)(ξ	PROPN
ejpam-6979	391	13	)	)	PUNCT
ejpam-6979	391	14	]	]	PUNCT
ejpam-6979	391	15	≤	≤	NUM
ejpam-6979	391	16	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	391	17	)	)	PUNCT
ejpam-6979	391	18	.	.	PUNCT
ejpam-6979	392	1	showing	show	VERB
ejpam-6979	392	2	that	that	SCONJ
ejpam-6979	392	3	f	f	PROPN
ejpam-6979	392	4	∈	∈	PROPN
ejpam-6979	392	5	f℘n	f℘n	PROPN
ejpam-6979	392	6	,	,	PUNCT
ejpam-6979	392	7	v(ϑ	v(ϑ	NOUN
ejpam-6979	392	8	;	;	PUNCT
ejpam-6979	392	9	β	β	X
ejpam-6979	392	10	,	,	PUNCT
ejpam-6979	392	11	µ	µ	NOUN
ejpam-6979	392	12	)	)	PUNCT
ejpam-6979	392	13	.	.	PUNCT
ejpam-6979	393	1	this	this	PRON
ejpam-6979	393	2	completes	complete	VERB
ejpam-6979	393	3	the	the	DET
ejpam-6979	393	4	proof	proof	NOUN
ejpam-6979	393	5	.	.	PUNCT
ejpam-6979	394	1	e.	e.	PROPN
ejpam-6979	394	2	e.	e.	PROPN
ejpam-6979	394	3	ali	ali	PROPN
ejpam-6979	394	4	et	et	PROPN
ejpam-6979	394	5	al	al	PROPN
ejpam-6979	394	6	.	.	PUNCT
ejpam-6979	394	7	/	/	SYM
ejpam-6979	394	8	eur	eur	PROPN
ejpam-6979	394	9	.	.	PUNCT
ejpam-6979	395	1	j.	j.	PROPN
ejpam-6979	395	2	pure	pure	PROPN
ejpam-6979	395	3	appl	appl	PROPN
ejpam-6979	395	4	.	.	PROPN
ejpam-6979	395	5	math	math	PROPN
ejpam-6979	395	6	,	,	PUNCT
ejpam-6979	395	7	18	18	NUM
ejpam-6979	395	8	(	(	PUNCT
ejpam-6979	395	9	4	4	NUM
ejpam-6979	395	10	)	)	PUNCT
ejpam-6979	395	11	(	(	PUNCT
ejpam-6979	395	12	2025	2025	NUM
ejpam-6979	395	13	)	)	PUNCT
ejpam-6979	395	14	,	,	PUNCT
ejpam-6979	395	15	6979	6979	NUM
ejpam-6979	395	16	15	15	NUM
ejpam-6979	395	17	of	of	ADP
ejpam-6979	395	18	18	18	NUM
ejpam-6979	395	19	3.4	3.4	NUM
ejpam-6979	395	20	.	.	PUNCT
ejpam-6979	396	1	the	the	DET
ejpam-6979	396	2	class	class	PROPN
ejpam-6979	396	3	fℜn	fℜn	PROPN
ejpam-6979	396	4	,	,	PUNCT
ejpam-6979	396	5	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	396	6	,	,	PUNCT
ejpam-6979	396	7	µ	µ	NOUN
ejpam-6979	396	8	)	)	PUNCT
ejpam-6979	396	9	definition	definition	NOUN
ejpam-6979	396	10	8	8	NUM
ejpam-6979	396	11	.	.	PUNCT
ejpam-6979	397	1	let	let	AUX
ejpam-6979	397	2	fℜn	fℜn	PROPN
ejpam-6979	397	3	,	,	PUNCT
ejpam-6979	397	4	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	397	5	,	,	PUNCT
ejpam-6979	397	6	µ	µ	NOUN
ejpam-6979	397	7	)	)	PUNCT
ejpam-6979	397	8	,	,	PUNCT
ejpam-6979	397	9	α	α	PRON
ejpam-6979	397	10	≥	≥	NOUN
ejpam-6979	397	11	0	0	NUM
ejpam-6979	397	12	,	,	PUNCT
ejpam-6979	397	13	denote	denote	VERB
ejpam-6979	397	14	the	the	DET
ejpam-6979	397	15	class	class	NOUN
ejpam-6979	397	16	of	of	ADP
ejpam-6979	397	17	functions	function	NOUN
ejpam-6979	397	18	f	f	PROPN
ejpam-6979	397	19	∈	∈	PROPN
ejpam-6979	397	20	a	a	DET
ejpam-6979	397	21	satisfying	satisfying	ADJ
ejpam-6979	397	22	fψ(c2×u	fψ(c2×u	NOUN
ejpam-6979	397	23	)	)	PUNCT
ejpam-6979	397	24	[	[	PUNCT
ejpam-6979	397	25	j(α	j(α	PROPN
ejpam-6979	397	26	;	;	PUNCT
ejpam-6979	397	27	f	f	X
ejpam-6979	397	28	;	;	PUNCT
ejpam-6979	397	29	f1	f1	NOUN
ejpam-6979	397	30	,	,	PUNCT
ejpam-6979	397	31	f2	f2	PROPN
ejpam-6979	397	32	,	,	PUNCT
ejpam-6979	397	33	...	...	PUNCT
ejpam-6979	397	34	,	,	PUNCT
ejpam-6979	397	35	fϑ)(ξ	fϑ)(ξ	PROPN
ejpam-6979	397	36	)	)	PUNCT
ejpam-6979	397	37	]	]	PUNCT
ejpam-6979	398	1	=	=	PUNCT
ejpam-6979	398	2	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	398	3	)	)	PUNCT
ejpam-6979	398	4	α	α	PROPN
ejpam-6979	398	5	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	398	6	,	,	PUNCT
ejpam-6979	398	7	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	398	8	)	)	PUNCT
ejpam-6979	398	9	]	]	PUNCT
ejpam-6979	399	1	′	′	NOUN
ejpam-6979	399	2	1	1	NUM
ejpam-6979	399	3	ϑ	ϑ	X
ejpam-6979	399	4	ϑ∑	ϑ∑	X
ejpam-6979	399	5	j=1	j=1	PROPN
ejpam-6979	399	6	lmn	lmn	PROPN
ejpam-6979	399	7	,	,	PUNCT
ejpam-6979	399	8	vf	vf	PROPN
ejpam-6979	399	9	j(ξ	j(ξ	PROPN
ejpam-6979	399	10	)	)	PUNCT
ejpam-6979	400	1	+	+	CCONJ
ejpam-6979	400	2	(	(	PUNCT
ejpam-6979	400	3	1	1	NUM
ejpam-6979	400	4	−	−	PROPN
ejpam-6979	400	5	α	α	NUM
ejpam-6979	400	6	)	)	PUNCT
ejpam-6979	400	7	ξ[lmn+1,vfi(ξ	ξ[lmn+1,vfi(ξ	PROPN
ejpam-6979	400	8	)	)	PUNCT
ejpam-6979	400	9	]	]	PUNCT
ejpam-6979	401	1	′	′	NOUN
ejpam-6979	401	2	1	1	NUM
ejpam-6979	401	3	ϑ	ϑ	X
ejpam-6979	401	4	ϑ∑	ϑ∑	X
ejpam-6979	401	5	j=1	j=1	PROPN
ejpam-6979	401	6	lmn+1,vf	lmn+1,vf	X
ejpam-6979	401	7	j(ξ	j(ξ	PROPN
ejpam-6979	401	8	)	)	PUNCT
ejpam-6979	401	9			ADJ
ejpam-6979	401	10	≤	≤	NUM
ejpam-6979	401	11	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	401	12	)	)	PUNCT
ejpam-6979	401	13	.	.	PUNCT
ejpam-6979	402	1	(	(	PUNCT
ejpam-6979	402	2	ξ	ξ	X
ejpam-6979	402	3	∈	∈	PROPN
ejpam-6979	402	4	u	u	NOUN
ejpam-6979	402	5	)	)	PUNCT
ejpam-6979	402	6	,	,	PUNCT
ejpam-6979	402	7	where	where	SCONJ
ejpam-6979	402	8	f	f	PROPN
ejpam-6979	402	9	=	=	PRON
ejpam-6979	402	10	{	{	PUNCT
ejpam-6979	402	11	f1,f2,	f1,f2,	PROPN
ejpam-6979	402	12	...	...	PUNCT
ejpam-6979	402	13	,fϑ	,fϑ	PUNCT
ejpam-6979	402	14	}	}	PUNCT
ejpam-6979	402	15	∈	∈	PROPN
ejpam-6979	402	16	fℜn	fℜn	NOUN
ejpam-6979	402	17	,	,	PUNCT
ejpam-6979	402	18	v(ϑ	v(ϑ	NOUN
ejpam-6979	402	19	;	;	PUNCT
ejpam-6979	402	20	µ	µ	X
ejpam-6979	402	21	)	)	PUNCT
ejpam-6979	402	22	and	and	CCONJ
ejpam-6979	402	23	ξ−1	ξ−1	PROPN
ejpam-6979	402	24	ϑ∑	ϑ∑	NOUN
ejpam-6979	402	25	j=1	j=1	PROPN
ejpam-6979	402	26	lmn	lmn	PROPN
ejpam-6979	402	27	,	,	PUNCT
ejpam-6979	402	28	vf	vf	PROPN
ejpam-6979	402	29	j(ξ	j(ξ	PROPN
ejpam-6979	402	30	)	)	PUNCT
ejpam-6979	402	31	,	,	PUNCT
ejpam-6979	402	32	0	0	NUM
ejpam-6979	402	33	in	in	ADP
ejpam-6979	402	34	u	u	PROPN
ejpam-6979	402	35	,	,	PUNCT
ejpam-6979	402	36	µ	µ	PRON
ejpam-6979	402	37	is	be	AUX
ejpam-6979	402	38	convex	convex	ADJ
ejpam-6979	402	39	univalent	univalent	ADJ
ejpam-6979	402	40	in	in	ADP
ejpam-6979	402	41	u	u	NOUN
ejpam-6979	402	42	with	with	ADP
ejpam-6979	402	43	µ(0	µ(0	NOUN
ejpam-6979	402	44	)	)	PUNCT
ejpam-6979	402	45	=	=	SYM
ejpam-6979	402	46	1	1	X
ejpam-6979	402	47	.	.	NOUN
ejpam-6979	402	48	remark	remark	NOUN
ejpam-6979	402	49	3	3	NUM
ejpam-6979	402	50	.	.	PUNCT
ejpam-6979	403	1	we	we	PRON
ejpam-6979	403	2	note	note	VERB
ejpam-6979	403	3	that	that	SCONJ
ejpam-6979	403	4	fℜn	fℜn	NOUN
ejpam-6979	403	5	,	,	PUNCT
ejpam-6979	403	6	v(ϑ	v(ϑ	NOUN
ejpam-6979	403	7	;	;	PUNCT
ejpam-6979	403	8	0	0	NUM
ejpam-6979	403	9	;	;	PUNCT
ejpam-6979	403	10	µ	µ	X
ejpam-6979	403	11	)	)	PUNCT
ejpam-6979	403	12	=	=	SYM
ejpam-6979	403	13	fℜn	fℜn	PROPN
ejpam-6979	403	14	,	,	PUNCT
ejpam-6979	403	15	v(ϑ	v(ϑ	NOUN
ejpam-6979	403	16	;	;	PUNCT
ejpam-6979	403	17	µ	µ	NUM
ejpam-6979	403	18	)	)	PUNCT
ejpam-6979	403	19	.	.	PUNCT
ejpam-6979	404	1	theorem	theorem	ADJ
ejpam-6979	404	2	8	8	NUM
ejpam-6979	404	3	.	.	PUNCT
ejpam-6979	405	1	if	if	SCONJ
ejpam-6979	405	2	f	f	PROPN
ejpam-6979	405	3	∈	∈	PROPN
ejpam-6979	405	4	fℜn	fℜn	PROPN
ejpam-6979	405	5	,	,	PUNCT
ejpam-6979	405	6	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	405	7	;	;	PUNCT
ejpam-6979	405	8	µ	µ	X
ejpam-6979	405	9	)	)	PUNCT
ejpam-6979	405	10	and	and	CCONJ
ejpam-6979	405	11	re{µ	re{µ	PROPN
ejpam-6979	405	12	}	}	PUNCT
ejpam-6979	405	13	is	be	AUX
ejpam-6979	405	14	bounded	bounded	ADJ
ejpam-6979	405	15	inu	inu	PROPN
ejpam-6979	405	16	,	,	PUNCT
ejpam-6979	405	17	then	then	ADV
ejpam-6979	405	18	f	f	PROPN
ejpam-6979	405	19	∈	∈	PROPN
ejpam-6979	405	20	fℜn	fℜn	PROPN
ejpam-6979	405	21	,	,	PUNCT
ejpam-6979	405	22	v(ϑ	v(ϑ	NOUN
ejpam-6979	405	23	;	;	PUNCT
ejpam-6979	405	24	0	0	NUM
ejpam-6979	405	25	;	;	PUNCT
ejpam-6979	405	26	µ	µ	X
ejpam-6979	405	27	)	)	PUNCT
ejpam-6979	405	28	=	=	SYM
ejpam-6979	405	29	fℜn	fℜn	PROPN
ejpam-6979	405	30	,	,	PUNCT
ejpam-6979	405	31	v(ϑ	v(ϑ	NOUN
ejpam-6979	405	32	;	;	PUNCT
ejpam-6979	405	33	µ	µ	X
ejpam-6979	405	34	)	)	PUNCT
ejpam-6979	405	35	hold	hold	NOUN
ejpam-6979	405	36	for	for	ADP
ejpam-6979	405	37	re{µ(ξ	re{µ(ξ	NOUN
ejpam-6979	405	38	)	)	PUNCT
ejpam-6979	405	39	+	+	CCONJ
ejpam-6979	405	40	(	(	PUNCT
ejpam-6979	405	41	n	n	CCONJ
ejpam-6979	405	42	−	−	PROPN
ejpam-6979	405	43	1	1	NUM
ejpam-6979	405	44	)	)	PUNCT
ejpam-6979	405	45	}	}	PUNCT
ejpam-6979	405	46	≥	≥	NOUN
ejpam-6979	405	47	0	0	NUM
ejpam-6979	405	48	.	.	PUNCT
ejpam-6979	406	1	proof	proof	NOUN
ejpam-6979	406	2	.	.	PUNCT
ejpam-6979	407	1	for	for	ADP
ejpam-6979	407	2	α	α	NOUN
ejpam-6979	407	3	=	=	SYM
ejpam-6979	407	4	0	0	NUM
ejpam-6979	407	5	,	,	PUNCT
ejpam-6979	407	6	the	the	DET
ejpam-6979	407	7	theorem	theorem	NOUN
ejpam-6979	407	8	is	be	AUX
ejpam-6979	407	9	trivial	trivial	ADJ
ejpam-6979	407	10	and	and	CCONJ
ejpam-6979	407	11	hence	hence	ADV
ejpam-6979	407	12	we	we	PRON
ejpam-6979	407	13	can	can	AUX
ejpam-6979	407	14	assume	assume	VERB
ejpam-6979	407	15	that	that	SCONJ
ejpam-6979	407	16	α	α	NOUN
ejpam-6979	407	17	,	,	PUNCT
ejpam-6979	407	18	0	0	X
ejpam-6979	407	19	.	.	PUNCT
ejpam-6979	407	20	let	let	VERB
ejpam-6979	407	21	p(ξ	p(ξ	NOUN
ejpam-6979	408	1	)	)	PUNCT
ejpam-6979	408	2	=	=	SYM
ejpam-6979	408	3	ξ[lmn+1,vfi(ξ	ξ[lmn+1,vfi(ξ	NOUN
ejpam-6979	408	4	)	)	PUNCT
ejpam-6979	408	5	]	]	PUNCT
ejpam-6979	409	1	′	′	NOUN
ejpam-6979	409	2	1	1	NUM
ejpam-6979	409	3	ϑ	ϑ	X
ejpam-6979	409	4	ϑ∑	ϑ∑	X
ejpam-6979	409	5	j=1	j=1	PROPN
ejpam-6979	409	6	lmn+1,vf	lmn+1,vf	X
ejpam-6979	409	7	j(ξ	j(ξ	PROPN
ejpam-6979	409	8	)	)	PUNCT
ejpam-6979	409	9	(	(	PUNCT
ejpam-6979	409	10	ξ	ξ	PROPN
ejpam-6979	409	11	∈	∈	PROPN
ejpam-6979	409	12	u	u	NOUN
ejpam-6979	409	13	)	)	PUNCT
ejpam-6979	409	14	.	.	PUNCT
ejpam-6979	410	1	a	a	DET
ejpam-6979	410	2	quick	quick	ADJ
ejpam-6979	410	3	calculation	calculation	NOUN
ejpam-6979	410	4	then	then	ADV
ejpam-6979	410	5	reveals	reveal	VERB
ejpam-6979	410	6	that	that	SCONJ
ejpam-6979	410	7	ξp	ξp	PART
ejpam-6979	410	8	′	′	NUM
ejpam-6979	410	9	(	(	PUNCT
ejpam-6979	410	10	ξ	ξ	X
ejpam-6979	410	11	)	)	PUNCT
ejpam-6979	410	12	1	1	NUM
ejpam-6979	410	13	ϑ	ϑ	X
ejpam-6979	410	14	ϑ∑	ϑ∑	X
ejpam-6979	410	15	j=1	j=1	PROPN
ejpam-6979	410	16	q	q	PROPN
ejpam-6979	410	17	j(ξ	j(ξ	PROPN
ejpam-6979	410	18	)	)	PUNCT
ejpam-6979	411	1	+	+	CCONJ
ejpam-6979	411	2	(	(	PUNCT
ejpam-6979	411	3	n	n	CCONJ
ejpam-6979	411	4	−	−	PROPN
ejpam-6979	411	5	1	1	NUM
ejpam-6979	411	6	)	)	PUNCT
ejpam-6979	411	7	+	+	CCONJ
ejpam-6979	411	8	p(ξ	p(ξ	X
ejpam-6979	411	9	)	)	PUNCT
ejpam-6979	411	10	=	=	NOUN
ejpam-6979	411	11	ξ[lmn	ξ[lmn	NOUN
ejpam-6979	411	12	,	,	PUNCT
ejpam-6979	411	13	vfi(ξ	vfi(ξ	PROPN
ejpam-6979	411	14	)	)	PUNCT
ejpam-6979	411	15	]	]	PUNCT
ejpam-6979	412	1	′	′	NOUN
ejpam-6979	412	2	1	1	NUM
ejpam-6979	412	3	ϑ	ϑ	X
ejpam-6979	412	4	ϑ∑	ϑ∑	X
ejpam-6979	412	5	j=1	j=1	PROPN
ejpam-6979	412	6	lmn	lmn	PROPN
ejpam-6979	412	7	,	,	PUNCT
ejpam-6979	412	8	vf	vf	PROPN
ejpam-6979	412	9	j(ξ	j(ξ	PROPN
ejpam-6979	412	10	)	)	PUNCT
ejpam-6979	412	11	,	,	PUNCT
ejpam-6979	412	12	where	where	SCONJ
ejpam-6979	412	13	q	q	PROPN
ejpam-6979	412	14	j(ξ	j(ξ	PROPN
ejpam-6979	412	15	)	)	PUNCT
ejpam-6979	412	16	=	=	SYM
ejpam-6979	412	17	ξ[lmn+1,vfi(ξ	ξ[lmn+1,vfi(ξ	PROPN
ejpam-6979	412	18	)	)	PUNCT
ejpam-6979	412	19	]	]	PUNCT
ejpam-6979	413	1	′	′	NOUN
ejpam-6979	413	2	1	1	NUM
ejpam-6979	413	3	ϑ	ϑ	X
ejpam-6979	413	4	ϑ∑	ϑ∑	X
ejpam-6979	413	5	j=1	j=1	PROPN
ejpam-6979	413	6	lmn+1,vf	lmn+1,vf	X
ejpam-6979	413	7	j(ξ	j(ξ	PROPN
ejpam-6979	413	8	)	)	PUNCT
ejpam-6979	413	9	.	.	PUNCT
ejpam-6979	414	1	also	also	ADV
ejpam-6979	414	2	1	1	NUM
ejpam-6979	414	3	ϑ	ϑ	X
ejpam-6979	414	4	ϑ∑	ϑ∑	X
ejpam-6979	414	5	j=1	j=1	PROPN
ejpam-6979	414	6	q	q	PROPN
ejpam-6979	414	7	j(ξ	j(ξ	PROPN
ejpam-6979	414	8	)	)	PUNCT
ejpam-6979	415	1	≺f	≺f	PROPN
ejpam-6979	415	2	µ(ξ	µ(ξ	NOUN
ejpam-6979	415	3	)	)	PUNCT
ejpam-6979	415	4	.	.	PUNCT
ejpam-6979	416	1	since	since	SCONJ
ejpam-6979	416	2	f(ξ	f(ξ	NUM
ejpam-6979	416	3	)	)	PUNCT
ejpam-6979	416	4	∈	∈	PROPN
ejpam-6979	416	5	fℜn	fℜn	PROPN
ejpam-6979	416	6	,	,	PUNCT
ejpam-6979	416	7	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	416	8	;	;	PUNCT
ejpam-6979	416	9	µ	µ	X
ejpam-6979	416	10	)	)	PUNCT
ejpam-6979	416	11	,	,	PUNCT
ejpam-6979	416	12	we	we	PRON
ejpam-6979	416	13	have	have	VERB
ejpam-6979	416	14	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	416	15	)	)	PUNCT
ejpam-6979	416	16	[	[	PUNCT
ejpam-6979	416	17	j(α	j(α	PROPN
ejpam-6979	416	18	;	;	PUNCT
ejpam-6979	416	19	f	f	X
ejpam-6979	416	20	;	;	PUNCT
ejpam-6979	416	21	f1	f1	NOUN
ejpam-6979	416	22	,	,	PUNCT
ejpam-6979	416	23	f2	f2	PROPN
ejpam-6979	416	24	,	,	PUNCT
ejpam-6979	416	25	...	...	PUNCT
ejpam-6979	416	26	,	,	PUNCT
ejpam-6979	416	27	fϑ)(ξ	fϑ)(ξ	PROPN
ejpam-6979	416	28	)	)	PUNCT
ejpam-6979	416	29	]	]	PUNCT
ejpam-6979	417	1	=	=	PUNCT
ejpam-6979	417	2	fψ(c2×u	fψ(c2×u	PROPN
ejpam-6979	417	3	)	)	PUNCT
ejpam-6979	417	4			NOUN
ejpam-6979	417	5	αξp	αξp	NOUN
ejpam-6979	417	6	′	′	NUM
ejpam-6979	417	7	(	(	PUNCT
ejpam-6979	417	8	ξ	ξ	NOUN
ejpam-6979	417	9	)	)	PUNCT
ejpam-6979	417	10	1	1	NUM
ejpam-6979	417	11	ϑ	ϑ	X
ejpam-6979	417	12	ϑ∑	ϑ∑	X
ejpam-6979	417	13	j=1	j=1	PROPN
ejpam-6979	417	14	q	q	PROPN
ejpam-6979	417	15	j(ξ	j(ξ	PROPN
ejpam-6979	417	16	)	)	PUNCT
ejpam-6979	418	1	+	+	CCONJ
ejpam-6979	418	2	(	(	PUNCT
ejpam-6979	418	3	n	n	CCONJ
ejpam-6979	418	4	−	−	PROPN
ejpam-6979	418	5	1	1	NUM
ejpam-6979	418	6	)	)	PUNCT
ejpam-6979	418	7	+	+	CCONJ
ejpam-6979	418	8	p(ξ	p(ξ	NOUN
ejpam-6979	418	9	)	)	PUNCT
ejpam-6979	418	10			VERB
ejpam-6979	418	11	≤	≤	NUM
ejpam-6979	418	12	fµ(u)µ(ξ	fµ(u)µ(ξ	NOUN
ejpam-6979	418	13	)	)	PUNCT
ejpam-6979	418	14	.	.	PUNCT
ejpam-6979	419	1	now	now	ADV
ejpam-6979	419	2	an	an	DET
ejpam-6979	419	3	application	application	NOUN
ejpam-6979	419	4	of	of	ADP
ejpam-6979	419	5	lemma	lemma	PROPN
ejpam-6979	419	6	2	2	PROPN
ejpam-6979	419	7	gives	give	VERB
ejpam-6979	419	8	p(ξ	p(ξ	NOUN
ejpam-6979	419	9	)	)	PUNCT
ejpam-6979	419	10	≺f	≺f	PROPN
ejpam-6979	419	11	µ(ξ	µ(ξ	NOUN
ejpam-6979	419	12	)	)	PUNCT
ejpam-6979	419	13	which	which	PRON
ejpam-6979	419	14	implies	imply	VERB
ejpam-6979	419	15	f	f	PROPN
ejpam-6979	419	16	∈	∈	PROPN
ejpam-6979	419	17	fℜn	fℜn	PROPN
ejpam-6979	419	18	,	,	PUNCT
ejpam-6979	419	19	v(ϑ	v(ϑ	NOUN
ejpam-6979	419	20	;	;	PUNCT
ejpam-6979	419	21	µ	µ	NUM
ejpam-6979	419	22	)	)	PUNCT
ejpam-6979	419	23	.	.	PUNCT
ejpam-6979	420	1	this	this	PRON
ejpam-6979	420	2	completes	complete	VERB
ejpam-6979	420	3	the	the	DET
ejpam-6979	420	4	proof	proof	NOUN
ejpam-6979	420	5	.	.	PUNCT
ejpam-6979	421	1	theorem	theorem	VERB
ejpam-6979	421	2	9	9	NUM
ejpam-6979	421	3	.	.	PUNCT
ejpam-6979	421	4	for	for	ADP
ejpam-6979	421	5	α	α	PROPN
ejpam-6979	421	6	>	>	X
ejpam-6979	421	7	β	β	X
ejpam-6979	421	8	≥	≥	NOUN
ejpam-6979	421	9	0	0	NUM
ejpam-6979	421	10	,	,	PUNCT
ejpam-6979	421	11	and	and	CCONJ
ejpam-6979	421	12	re{µ	re{µ	NOUN
ejpam-6979	421	13	}	}	PUNCT
ejpam-6979	421	14	is	be	AUX
ejpam-6979	421	15	bounded	bounded	ADJ
ejpam-6979	421	16	inu	inu	PROPN
ejpam-6979	421	17	,	,	PUNCT
ejpam-6979	421	18	then	then	ADV
ejpam-6979	421	19	fℜn	fℜn	PROPN
ejpam-6979	421	20	,	,	PUNCT
ejpam-6979	421	21	v(ϑ;α	v(ϑ;α	PROPN
ejpam-6979	421	22	;	;	PUNCT
ejpam-6979	421	23	µ	µ	X
ejpam-6979	421	24	)	)	PUNCT
ejpam-6979	421	25	⊂	⊂	PROPN
ejpam-6979	421	26	fℜn	fℜn	PROPN
ejpam-6979	421	27	,	,	PUNCT
ejpam-6979	421	28	v(ϑ	v(ϑ	NOUN
ejpam-6979	421	29	;	;	PUNCT
ejpam-6979	421	30	β	β	X
ejpam-6979	421	31	;	;	PUNCT
ejpam-6979	421	32	µ	µ	NUM
ejpam-6979	421	33	)	)	PUNCT
ejpam-6979	421	34	.	.	PUNCT
ejpam-6979	422	1	proof	proof	NOUN
ejpam-6979	422	2	.	.	PUNCT
ejpam-6979	423	1	this	this	DET
ejpam-6979	423	2	theorem	theorem	VERB
ejpam-6979	423	3	’s	’s	PART
ejpam-6979	423	4	proof	proof	NOUN
ejpam-6979	423	5	is	be	AUX
ejpam-6979	423	6	removed	remove	VERB
ejpam-6979	423	7	since	since	SCONJ
ejpam-6979	423	8	it	it	PRON
ejpam-6979	423	9	is	be	AUX
ejpam-6979	423	10	similar	similar	ADJ
ejpam-6979	423	11	to	to	ADP
ejpam-6979	423	12	that	that	PRON
ejpam-6979	423	13	of	of	ADP
ejpam-6979	423	14	theorem	theorem	ADJ
ejpam-6979	423	15	7	7	NUM
ejpam-6979	423	16	.	.	NOUN
ejpam-6979	423	17	remark	remark	NOUN
ejpam-6979	423	18	4	4	NUM
ejpam-6979	423	19	.	.	PUNCT
ejpam-6979	424	1	we	we	PRON
ejpam-6979	424	2	can	can	AUX
ejpam-6979	424	3	get	get	VERB
ejpam-6979	424	4	the	the	DET
ejpam-6979	424	5	same	same	ADJ
ejpam-6979	424	6	results	result	NOUN
ejpam-6979	424	7	if	if	SCONJ
ejpam-6979	424	8	we	we	PRON
ejpam-6979	424	9	used	use	VERB
ejpam-6979	424	10	equation	equation	NOUN
ejpam-6979	424	11	(	(	PUNCT
ejpam-6979	424	12	9	9	NUM
ejpam-6979	424	13	)	)	PUNCT
ejpam-6979	424	14	.	.	PUNCT
ejpam-6979	425	1	e.	e.	PROPN
ejpam-6979	425	2	e.	e.	PROPN
ejpam-6979	425	3	ali	ali	PROPN
ejpam-6979	425	4	et	et	PROPN
ejpam-6979	425	5	al	al	PROPN
ejpam-6979	425	6	.	.	PUNCT
ejpam-6979	425	7	/	/	SYM
ejpam-6979	425	8	eur	eur	PROPN
ejpam-6979	425	9	.	.	PUNCT
ejpam-6979	426	1	j.	j.	PROPN
ejpam-6979	426	2	pure	pure	PROPN
ejpam-6979	426	3	appl	appl	PROPN
ejpam-6979	426	4	.	.	PROPN
ejpam-6979	426	5	math	math	PROPN
ejpam-6979	426	6	,	,	PUNCT
ejpam-6979	426	7	18	18	NUM
ejpam-6979	426	8	(	(	PUNCT
ejpam-6979	426	9	4	4	NUM
ejpam-6979	426	10	)	)	PUNCT
ejpam-6979	426	11	(	(	PUNCT
ejpam-6979	426	12	2025	2025	NUM
ejpam-6979	426	13	)	)	PUNCT
ejpam-6979	426	14	,	,	PUNCT
ejpam-6979	426	15	6979	6979	NUM
ejpam-6979	426	16	16	16	NUM
ejpam-6979	426	17	of	of	ADP
ejpam-6979	426	18	18	18	NUM
ejpam-6979	426	19	4	4	NUM
ejpam-6979	426	20	.	.	PUNCT
ejpam-6979	426	21	conclusion	conclusion	NOUN
ejpam-6979	426	22	the	the	DET
ejpam-6979	426	23	new	new	ADJ
ejpam-6979	426	24	findings	finding	NOUN
ejpam-6979	426	25	of	of	ADP
ejpam-6979	426	26	this	this	DET
ejpam-6979	426	27	work	work	NOUN
ejpam-6979	426	28	are	be	AUX
ejpam-6979	426	29	related	relate	VERB
ejpam-6979	426	30	to	to	ADP
ejpam-6979	426	31	new	new	ADJ
ejpam-6979	426	32	classes	class	NOUN
ejpam-6979	426	33	of	of	ADP
ejpam-6979	426	34	analytic	analytic	ADJ
ejpam-6979	426	35	normalized	normalize	VERB
ejpam-6979	426	36	functions	function	NOUN
ejpam-6979	426	37	inu	inu	PROPN
ejpam-6979	426	38	.	.	PUNCT
ejpam-6979	427	1	the	the	DET
ejpam-6979	427	2	novel	novel	NOUN
ejpam-6979	427	3	results	result	VERB
ejpam-6979	427	4	from	from	ADP
ejpam-6979	427	5	the	the	DET
ejpam-6979	427	6	investigation	investigation	NOUN
ejpam-6979	427	7	reported	report	VERB
ejpam-6979	427	8	in	in	ADP
ejpam-6979	427	9	this	this	DET
ejpam-6979	427	10	work	work	NOUN
ejpam-6979	427	11	lead	lead	NOUN
ejpam-6979	427	12	to	to	ADP
ejpam-6979	427	13	an	an	DET
ejpam-6979	427	14	advancement	advancement	NOUN
ejpam-6979	427	15	in	in	ADP
ejpam-6979	427	16	the	the	DET
ejpam-6979	427	17	theory	theory	NOUN
ejpam-6979	427	18	of	of	ADP
ejpam-6979	427	19	fuzzy	fuzzy	ADJ
ejpam-6979	427	20	differential	differential	ADJ
ejpam-6979	427	21	subordination	subordination	NOUN
ejpam-6979	427	22	to	to	PART
ejpam-6979	427	23	introduce	introduce	VERB
ejpam-6979	427	24	some	some	DET
ejpam-6979	427	25	classes	class	NOUN
ejpam-6979	427	26	of	of	ADP
ejpam-6979	427	27	univalent	univalent	ADJ
ejpam-6979	427	28	functions	function	NOUN
ejpam-6979	427	29	.	.	PUNCT
ejpam-6979	428	1	the	the	DET
ejpam-6979	428	2	introduction	introduction	NOUN
ejpam-6979	428	3	in	in	ADP
ejpam-6979	428	4	section	section	NOUN
ejpam-6979	428	5	1	1	NUM
ejpam-6979	428	6	covers	cover	VERB
ejpam-6979	428	7	the	the	DET
ejpam-6979	428	8	lommel	lommel	PROPN
ejpam-6979	428	9	function	function	NOUN
ejpam-6979	428	10	lmn	lmn	NOUN
ejpam-6979	428	11	,	,	PUNCT
ejpam-6979	428	12	vf(ξ	vf(ξ	NUM
ejpam-6979	428	13	)	)	PUNCT
ejpam-6979	428	14	,	,	PUNCT
ejpam-6979	428	15	the	the	DET
ejpam-6979	428	16	fundamental	fundamental	ADJ
ejpam-6979	428	17	ideas	idea	NOUN
ejpam-6979	428	18	required	require	VERB
ejpam-6979	428	19	for	for	ADP
ejpam-6979	428	20	the	the	DET
ejpam-6979	428	21	study	study	NOUN
ejpam-6979	428	22	,	,	PUNCT
ejpam-6979	428	23	and	and	CCONJ
ejpam-6979	428	24	the	the	DET
ejpam-6979	428	25	rationale	rationale	NOUN
ejpam-6979	428	26	behind	behind	ADP
ejpam-6979	428	27	the	the	DET
ejpam-6979	428	28	topic	topic	NOUN
ejpam-6979	428	29	’s	’s	PART
ejpam-6979	428	30	investigation	investigation	NOUN
ejpam-6979	428	31	.	.	PUNCT
ejpam-6979	429	1	the	the	DET
ejpam-6979	429	2	main	main	ADJ
ejpam-6979	429	3	finding	finding	NOUN
ejpam-6979	429	4	is	be	AUX
ejpam-6979	429	5	presented	present	VERB
ejpam-6979	429	6	in	in	ADP
ejpam-6979	429	7	section	section	NOUN
ejpam-6979	429	8	2	2	NUM
ejpam-6979	429	9	.	.	PUNCT
ejpam-6979	430	1	the	the	DET
ejpam-6979	430	2	current	current	ADJ
ejpam-6979	430	3	effort	effort	NOUN
ejpam-6979	430	4	offers	offer	VERB
ejpam-6979	430	5	valuable	valuable	ADJ
ejpam-6979	430	6	information	information	NOUN
ejpam-6979	430	7	to	to	PART
ejpam-6979	430	8	advance	advance	VERB
ejpam-6979	430	9	the	the	DET
ejpam-6979	430	10	recently	recently	ADV
ejpam-6979	430	11	initiated	initiate	VERB
ejpam-6979	430	12	research	research	NOUN
ejpam-6979	430	13	avenues	avenue	NOUN
ejpam-6979	430	14	.	.	PUNCT
ejpam-6979	431	1	the	the	DET
ejpam-6979	431	2	outcome	outcome	NOUN
ejpam-6979	431	3	of	of	ADP
ejpam-6979	431	4	the	the	DET
ejpam-6979	431	5	present	present	ADJ
ejpam-6979	431	6	investigation	investigation	NOUN
ejpam-6979	431	7	could	could	AUX
ejpam-6979	431	8	inspire	inspire	VERB
ejpam-6979	431	9	the	the	DET
ejpam-6979	431	10	use	use	NOUN
ejpam-6979	431	11	of	of	ADP
ejpam-6979	431	12	this	this	DET
ejpam-6979	431	13	operator	operator	NOUN
ejpam-6979	431	14	for	for	ADP
ejpam-6979	431	15	introducing	introduce	VERB
ejpam-6979	431	16	other	other	ADJ
ejpam-6979	431	17	new	new	ADJ
ejpam-6979	431	18	classes	class	NOUN
ejpam-6979	431	19	of	of	ADP
ejpam-6979	431	20	analytic	analytic	ADJ
ejpam-6979	431	21	functions	function	NOUN
ejpam-6979	431	22	.	.	PUNCT
ejpam-6979	432	1	in	in	ADP
ejpam-6979	432	2	addition	addition	NOUN
ejpam-6979	432	3	to	to	ADP
ejpam-6979	432	4	their	their	PRON
ejpam-6979	432	5	theoretical	theoretical	ADJ
ejpam-6979	432	6	significance	significance	NOUN
ejpam-6979	432	7	,	,	PUNCT
ejpam-6979	432	8	lommel	lommel	NOUN
ejpam-6979	432	9	functions	function	NOUN
ejpam-6979	432	10	are	be	AUX
ejpam-6979	432	11	computationally	computationally	ADV
ejpam-6979	432	12	relevant	relevant	ADJ
ejpam-6979	432	13	.	.	PUNCT
ejpam-6979	433	1	numerical	numerical	ADJ
ejpam-6979	433	2	methods	method	NOUN
ejpam-6979	433	3	for	for	ADP
ejpam-6979	433	4	evaluating	evaluate	VERB
ejpam-6979	433	5	these	these	DET
ejpam-6979	433	6	functions	function	NOUN
ejpam-6979	433	7	have	have	AUX
ejpam-6979	433	8	been	be	AUX
ejpam-6979	433	9	developed	develop	VERB
ejpam-6979	433	10	,	,	PUNCT
ejpam-6979	433	11	allowing	allow	VERB
ejpam-6979	433	12	researchers	researcher	NOUN
ejpam-6979	433	13	and	and	CCONJ
ejpam-6979	433	14	engineers	engineer	NOUN
ejpam-6979	433	15	to	to	PART
ejpam-6979	433	16	apply	apply	VERB
ejpam-6979	433	17	them	they	PRON
ejpam-6979	433	18	effectively	effectively	ADV
ejpam-6979	433	19	in	in	ADP
ejpam-6979	433	20	simulations	simulation	NOUN
ejpam-6979	433	21	and	and	CCONJ
ejpam-6979	433	22	predictive	predictive	ADJ
ejpam-6979	433	23	models	model	NOUN
ejpam-6979	433	24	.	.	PUNCT
ejpam-6979	434	1	the	the	DET
ejpam-6979	434	2	development	development	NOUN
ejpam-6979	434	3	of	of	ADP
ejpam-6979	434	4	algorithms	algorithm	NOUN
ejpam-6979	434	5	and	and	CCONJ
ejpam-6979	434	6	software	software	NOUN
ejpam-6979	434	7	libraries	library	NOUN
ejpam-6979	434	8	that	that	PRON
ejpam-6979	434	9	incorporate	incorporate	VERB
ejpam-6979	434	10	the	the	DET
ejpam-6979	434	11	computation	computation	NOUN
ejpam-6979	434	12	of	of	ADP
ejpam-6979	434	13	lommel	lommel	NOUN
ejpam-6979	434	14	functions	function	NOUN
ejpam-6979	434	15	has	have	AUX
ejpam-6979	434	16	greatly	greatly	ADV
ejpam-6979	434	17	enhanced	enhance	VERB
ejpam-6979	434	18	our	our	PRON
ejpam-6979	434	19	ability	ability	NOUN
ejpam-6979	434	20	to	to	PART
ejpam-6979	434	21	analyze	analyze	VERB
ejpam-6979	434	22	complex	complex	ADJ
ejpam-6979	434	23	systems	system	NOUN
ejpam-6979	434	24	featuring	feature	VERB
ejpam-6979	434	25	cylindrical	cylindrical	ADJ
ejpam-6979	434	26	symmetry	symmetry	NOUN
ejpam-6979	434	27	.	.	PUNCT
ejpam-6979	435	1	consequently	consequently	ADV
ejpam-6979	435	2	,	,	PUNCT
ejpam-6979	435	3	the	the	DET
ejpam-6979	435	4	lommel	lommel	PROPN
ejpam-6979	435	5	function	function	NOUN
ejpam-6979	435	6	stands	stand	VERB
ejpam-6979	435	7	out	out	ADP
ejpam-6979	435	8	as	as	ADP
ejpam-6979	435	9	a	a	DET
ejpam-6979	435	10	rich	rich	ADJ
ejpam-6979	435	11	area	area	NOUN
ejpam-6979	435	12	of	of	ADP
ejpam-6979	435	13	study	study	NOUN
ejpam-6979	435	14	,	,	PUNCT
ejpam-6979	435	15	interlinking	interlink	VERB
ejpam-6979	435	16	pure	pure	ADJ
ejpam-6979	435	17	mathematics	mathematic	NOUN
ejpam-6979	435	18	with	with	ADP
ejpam-6979	435	19	practical	practical	ADJ
ejpam-6979	435	20	technological	technological	ADJ
ejpam-6979	435	21	applications	application	NOUN
ejpam-6979	435	22	,	,	PUNCT
ejpam-6979	435	23	offering	offer	VERB
ejpam-6979	435	24	insights	insight	NOUN
ejpam-6979	435	25	that	that	PRON
ejpam-6979	435	26	could	could	AUX
ejpam-6979	435	27	lead	lead	VERB
ejpam-6979	435	28	to	to	ADP
ejpam-6979	435	29	advancements	advancement	NOUN
ejpam-6979	435	30	in	in	ADP
ejpam-6979	435	31	fields	field	NOUN
ejpam-6979	435	32	ranging	range	VERB
ejpam-6979	435	33	from	from	ADP
ejpam-6979	435	34	telecommunications	telecommunication	NOUN
ejpam-6979	435	35	to	to	ADP
ejpam-6979	435	36	structural	structural	ADJ
ejpam-6979	435	37	engineering	engineering	NOUN
ejpam-6979	435	38	.	.	PUNCT
ejpam-6979	436	1	acknowledgements	acknowledgement	NOUN
ejpam-6979	436	2	this	this	DET
ejpam-6979	436	3	research	research	NOUN
ejpam-6979	436	4	has	have	AUX
ejpam-6979	436	5	been	be	AUX
ejpam-6979	436	6	funded	fund	VERB
ejpam-6979	436	7	by	by	ADP
ejpam-6979	436	8	scientific	scientific	ADJ
ejpam-6979	436	9	research	research	NOUN
ejpam-6979	436	10	deanship	deanship	NOUN
ejpam-6979	436	11	at	at	ADP
ejpam-6979	436	12	university	university	NOUN
ejpam-6979	436	13	of	of	ADP
ejpam-6979	436	14	hail	hail	NOUN
ejpam-6979	436	15	-	-	PUNCT
ejpam-6979	436	16	saudi	saudi	PROPN
ejpam-6979	436	17	arabia	arabia	PROPN
ejpam-6979	436	18	through	through	ADP
ejpam-6979	436	19	project	project	NOUN
ejpam-6979	436	20	number	number	NOUN
ejpam-6979	436	21	rg-25006	rg-25006	NOUN
ejpam-6979	436	22	.	.	PUNCT
ejpam-6979	437	1	references	reference	NOUN
ejpam-6979	437	2	[	[	X
ejpam-6979	437	3	1	1	NUM
ejpam-6979	437	4	]	]	PUNCT
ejpam-6979	437	5	l.	l.	PROPN
ejpam-6979	437	6	a.	a.	PROPN
ejpam-6979	437	7	zadeh	zadeh	PROPN
ejpam-6979	437	8	.	.	PUNCT
ejpam-6979	438	1	fuzzy	fuzzy	ADJ
ejpam-6979	438	2	sets	set	NOUN
ejpam-6979	438	3	.	.	PUNCT
ejpam-6979	439	1	information	information	NOUN
ejpam-6979	439	2	and	and	CCONJ
ejpam-6979	439	3	control	control	NOUN
ejpam-6979	439	4	,	,	PUNCT
ejpam-6979	439	5	8(3):338–353	8(3):338–353	NUM
ejpam-6979	439	6	,	,	PUNCT
ejpam-6979	439	7	1965	1965	NUM
ejpam-6979	439	8	.	.	PUNCT
ejpam-6979	440	1	[	[	X
ejpam-6979	440	2	2	2	X
ejpam-6979	440	3	]	]	X
ejpam-6979	440	4	g.	g.	PROPN
ejpam-6979	440	5	i.	i.	PROPN
ejpam-6979	440	6	oros	oros	PROPN
ejpam-6979	440	7	and	and	CCONJ
ejpam-6979	440	8	g.	g.	PROPN
ejpam-6979	440	9	oros	oros	PROPN
ejpam-6979	440	10	.	.	PUNCT
ejpam-6979	441	1	the	the	DET
ejpam-6979	441	2	notion	notion	NOUN
ejpam-6979	441	3	of	of	ADP
ejpam-6979	441	4	subordination	subordination	NOUN
ejpam-6979	441	5	in	in	ADP
ejpam-6979	441	6	fuzzy	fuzzy	ADJ
ejpam-6979	441	7	sets	set	NOUN
ejpam-6979	441	8	theory	theory	NOUN
ejpam-6979	441	9	.	.	PUNCT
ejpam-6979	442	1	general	general	ADJ
ejpam-6979	442	2	mathematics	mathematics	PROPN
ejpam-6979	442	3	,	,	PUNCT
ejpam-6979	442	4	19:97–103	19:97–103	NUM
ejpam-6979	442	5	,	,	PUNCT
ejpam-6979	442	6	2011	2011	NUM
ejpam-6979	442	7	.	.	PUNCT
ejpam-6979	443	1	[	[	X
ejpam-6979	443	2	3	3	X
ejpam-6979	443	3	]	]	PUNCT
ejpam-6979	443	4	s.	s.	PROPN
ejpam-6979	443	5	s.	s.	PROPN
ejpam-6979	443	6	miller	miller	PROPN
ejpam-6979	443	7	and	and	CCONJ
ejpam-6979	443	8	p.	p.	PROPN
ejpam-6979	443	9	t.	t.	PROPN
ejpam-6979	443	10	mocanu	mocanu	PROPN
ejpam-6979	443	11	.	.	PUNCT
ejpam-6979	444	1	second	second	ADJ
ejpam-6979	444	2	order	order	NOUN
ejpam-6979	444	3	-	-	PUNCT
ejpam-6979	444	4	differential	differential	NOUN
ejpam-6979	444	5	inequalities	inequality	NOUN
ejpam-6979	444	6	in	in	ADP
ejpam-6979	444	7	the	the	DET
ejpam-6979	444	8	complex	complex	ADJ
ejpam-6979	444	9	plane	plane	NOUN
ejpam-6979	444	10	.	.	PUNCT
ejpam-6979	445	1	journal	journal	PROPN
ejpam-6979	445	2	of	of	ADP
ejpam-6979	445	3	mathematical	mathematical	ADJ
ejpam-6979	445	4	analysis	analysis	NOUN
ejpam-6979	445	5	and	and	CCONJ
ejpam-6979	445	6	applications	application	NOUN
ejpam-6979	445	7	,	,	PUNCT
ejpam-6979	445	8	65:298–305	65:298–305	NOUN
ejpam-6979	445	9	,	,	PUNCT
ejpam-6979	445	10	1978	1978	NUM
ejpam-6979	445	11	.	.	PUNCT
ejpam-6979	446	1	[	[	X
ejpam-6979	446	2	4	4	X
ejpam-6979	446	3	]	]	PUNCT
ejpam-6979	446	4	s.	s.	PROPN
ejpam-6979	446	5	s.	s.	PROPN
ejpam-6979	446	6	miller	miller	PROPN
ejpam-6979	446	7	and	and	CCONJ
ejpam-6979	446	8	p.	p.	PROPN
ejpam-6979	446	9	t.	t.	PROPN
ejpam-6979	446	10	mocanu	mocanu	PROPN
ejpam-6979	446	11	.	.	PUNCT
ejpam-6979	447	1	differential	differential	ADJ
ejpam-6979	447	2	subordinations	subordination	NOUN
ejpam-6979	447	3	and	and	CCONJ
ejpam-6979	447	4	univalent	univalent	ADJ
ejpam-6979	447	5	functions	function	NOUN
ejpam-6979	447	6	.	.	PUNCT
ejpam-6979	448	1	michigan	michigan	PROPN
ejpam-6979	448	2	mathematical	mathematical	PROPN
ejpam-6979	448	3	journal	journal	PROPN
ejpam-6979	448	4	,	,	PUNCT
ejpam-6979	448	5	28:157–171	28:157–171	PROPN
ejpam-6979	448	6	,	,	PUNCT
ejpam-6979	448	7	1981	1981	NUM
ejpam-6979	448	8	.	.	PUNCT
ejpam-6979	449	1	[	[	X
ejpam-6979	449	2	5	5	X
ejpam-6979	449	3	]	]	PUNCT
ejpam-6979	449	4	g.	g.	PROPN
ejpam-6979	449	5	i.	i.	PROPN
ejpam-6979	449	6	oros	oros	PROPN
ejpam-6979	449	7	and	and	CCONJ
ejpam-6979	449	8	g.	g.	PROPN
ejpam-6979	449	9	oros	oros	PROPN
ejpam-6979	449	10	.	.	PUNCT
ejpam-6979	450	1	fuzzy	fuzzy	ADJ
ejpam-6979	450	2	differential	differential	ADJ
ejpam-6979	450	3	subordination	subordination	NOUN
ejpam-6979	450	4	.	.	PUNCT
ejpam-6979	451	1	acta	acta	PROPN
ejpam-6979	451	2	universitatis	universitatis	PROPN
ejpam-6979	451	3	apulensis	apulensis	NOUN
ejpam-6979	451	4	,	,	PUNCT
ejpam-6979	451	5	3:55–64	3:55–64	NUM
ejpam-6979	451	6	,	,	PUNCT
ejpam-6979	451	7	2012	2012	NUM
ejpam-6979	451	8	.	.	PUNCT
ejpam-6979	452	1	[	[	X
ejpam-6979	452	2	6	6	NUM
ejpam-6979	452	3	]	]	PUNCT
ejpam-6979	452	4	g.	g.	PROPN
ejpam-6979	452	5	i.	i.	PROPN
ejpam-6979	452	6	oros	oros	PROPN
ejpam-6979	452	7	and	and	CCONJ
ejpam-6979	452	8	g.	g.	PROPN
ejpam-6979	452	9	oros	oros	PROPN
ejpam-6979	452	10	.	.	PUNCT
ejpam-6979	453	1	dominants	dominant	NOUN
ejpam-6979	453	2	and	and	CCONJ
ejpam-6979	453	3	best	good	ADJ
ejpam-6979	453	4	dominants	dominant	NOUN
ejpam-6979	453	5	in	in	ADP
ejpam-6979	453	6	fuzzy	fuzzy	ADJ
ejpam-6979	453	7	differential	differential	ADJ
ejpam-6979	453	8	subordinations	subordination	NOUN
ejpam-6979	453	9	.	.	PUNCT
ejpam-6979	454	1	studia	studia	PROPN
ejpam-6979	454	2	universitatis	universitatis	PROPN
ejpam-6979	454	3	babeş-bolyai	babeş-bolyai	PROPN
ejpam-6979	454	4	mathematica	mathematica	PROPN
ejpam-6979	454	5	,	,	PUNCT
ejpam-6979	454	6	57:239–248	57:239–248	PROPN
ejpam-6979	454	7	,	,	PUNCT
ejpam-6979	454	8	2012	2012	NUM
ejpam-6979	454	9	.	.	PUNCT
ejpam-6979	455	1	[	[	X
ejpam-6979	455	2	7	7	X
ejpam-6979	455	3	]	]	X
ejpam-6979	455	4	g.	g.	PROPN
ejpam-6979	455	5	i.	i.	PROPN
ejpam-6979	455	6	oros	oros	PROPN
ejpam-6979	455	7	and	and	CCONJ
ejpam-6979	455	8	g.	g.	PROPN
ejpam-6979	455	9	oros	oros	PROPN
ejpam-6979	455	10	.	.	PUNCT
ejpam-6979	456	1	briot	briot	NOUN
ejpam-6979	456	2	–	–	PUNCT
ejpam-6979	456	3	bouquet	bouquet	NOUN
ejpam-6979	456	4	fuzzy	fuzzy	ADJ
ejpam-6979	456	5	differential	differential	ADJ
ejpam-6979	456	6	subordination	subordination	NOUN
ejpam-6979	456	7	.	.	PUNCT
ejpam-6979	457	1	analele	analele	PROPN
ejpam-6979	457	2	universităţii	universităţii	VERB
ejpam-6979	457	3	oradea	oradea	PROPN
ejpam-6979	457	4	fascicula	fascicula	PROPN
ejpam-6979	457	5	matematică	matematică	PROPN
ejpam-6979	457	6	,	,	PUNCT
ejpam-6979	457	7	19:83–87	19:83–87	NUM
ejpam-6979	457	8	,	,	PUNCT
ejpam-6979	457	9	2012	2012	NUM
ejpam-6979	457	10	.	.	PUNCT
ejpam-6979	458	1	[	[	X
ejpam-6979	458	2	8	8	NUM
ejpam-6979	458	3	]	]	X
ejpam-6979	458	4	a.	a.	NOUN
ejpam-6979	458	5	alb	alb	PROPN
ejpam-6979	458	6	lupaş.	lupaş.	PROPN
ejpam-6979	458	7	a	a	DET
ejpam-6979	458	8	note	note	NOUN
ejpam-6979	458	9	on	on	ADP
ejpam-6979	458	10	special	special	ADJ
ejpam-6979	458	11	fuzzy	fuzzy	ADJ
ejpam-6979	458	12	differential	differential	NOUN
ejpam-6979	458	13	subordinations	subordination	NOUN
ejpam-6979	458	14	using	use	VERB
ejpam-6979	458	15	generalized	generalized	ADJ
ejpam-6979	458	16	sălăgean	sălăgean	ADJ
ejpam-6979	458	17	operator	operator	NOUN
ejpam-6979	458	18	and	and	CCONJ
ejpam-6979	458	19	ruscheweyh	ruscheweyh	NOUN
ejpam-6979	458	20	derivative	derivative	PROPN
ejpam-6979	458	21	.	.	PUNCT
ejpam-6979	459	1	journal	journal	PROPN
ejpam-6979	459	2	of	of	ADP
ejpam-6979	459	3	computational	computational	ADJ
ejpam-6979	459	4	analysis	analysis	NOUN
ejpam-6979	459	5	and	and	CCONJ
ejpam-6979	459	6	applications	application	NOUN
ejpam-6979	459	7	,	,	PUNCT
ejpam-6979	459	8	15:1476–1483	15:1476–1483	NUM
ejpam-6979	459	9	,	,	PUNCT
ejpam-6979	459	10	2013	2013	NUM
ejpam-6979	459	11	.	.	PUNCT
ejpam-6979	460	1	[	[	X
ejpam-6979	460	2	9	9	NUM
ejpam-6979	460	3	]	]	PUNCT
ejpam-6979	460	4	a.	a.	NOUN
ejpam-6979	460	5	alb	alb	PROPN
ejpam-6979	460	6	lupaş	lupaş	PROPN
ejpam-6979	460	7	and	and	CCONJ
ejpam-6979	460	8	g.	g.	PROPN
ejpam-6979	460	9	oros	oros	PROPN
ejpam-6979	460	10	.	.	PUNCT
ejpam-6979	461	1	on	on	ADP
ejpam-6979	461	2	special	special	ADJ
ejpam-6979	461	3	fuzzy	fuzzy	ADJ
ejpam-6979	461	4	differential	differential	NOUN
ejpam-6979	461	5	subordinations	subordination	NOUN
ejpam-6979	461	6	using	use	VERB
ejpam-6979	461	7	sălăgean	sălăgean	NOUN
ejpam-6979	461	8	and	and	CCONJ
ejpam-6979	461	9	ruscheweyh	ruscheweyh	NOUN
ejpam-6979	461	10	operators	operator	NOUN
ejpam-6979	461	11	.	.	PUNCT
ejpam-6979	462	1	applied	apply	VERB
ejpam-6979	462	2	mathematics	mathematic	NOUN
ejpam-6979	462	3	and	and	CCONJ
ejpam-6979	462	4	computation	computation	NOUN
ejpam-6979	462	5	,	,	PUNCT
ejpam-6979	462	6	261:119–127	261:119–127	NUM
ejpam-6979	462	7	,	,	PUNCT
ejpam-6979	462	8	2015	2015	NUM
ejpam-6979	462	9	.	.	PUNCT
ejpam-6979	463	1	e.	e.	PROPN
ejpam-6979	463	2	e.	e.	PROPN
ejpam-6979	463	3	ali	ali	PROPN
ejpam-6979	463	4	et	et	PROPN
ejpam-6979	463	5	al	al	PROPN
ejpam-6979	463	6	.	.	PUNCT
ejpam-6979	463	7	/	/	SYM
ejpam-6979	463	8	eur	eur	PROPN
ejpam-6979	463	9	.	.	PUNCT
ejpam-6979	464	1	j.	j.	PROPN
ejpam-6979	464	2	pure	pure	PROPN
ejpam-6979	464	3	appl	appl	PROPN
ejpam-6979	464	4	.	.	PROPN
ejpam-6979	464	5	math	math	PROPN
ejpam-6979	464	6	,	,	PUNCT
ejpam-6979	464	7	18	18	NUM
ejpam-6979	464	8	(	(	PUNCT
ejpam-6979	464	9	4	4	NUM
ejpam-6979	464	10	)	)	PUNCT
ejpam-6979	464	11	(	(	PUNCT
ejpam-6979	464	12	2025	2025	NUM
ejpam-6979	464	13	)	)	PUNCT
ejpam-6979	464	14	,	,	PUNCT
ejpam-6979	464	15	6979	6979	NUM
ejpam-6979	464	16	17	17	NUM
ejpam-6979	464	17	of	of	ADP
ejpam-6979	464	18	18	18	NUM
ejpam-6979	464	19	[	[	SYM
ejpam-6979	464	20	10	10	NUM
ejpam-6979	464	21	]	]	PUNCT
ejpam-6979	464	22	a.	a.	NOUN
ejpam-6979	464	23	o.	o.	NOUN
ejpam-6979	464	24	venter	venter	PROPN
ejpam-6979	464	25	.	.	PUNCT
ejpam-6979	465	1	on	on	ADP
ejpam-6979	465	2	special	special	ADJ
ejpam-6979	465	3	fuzzy	fuzzy	ADJ
ejpam-6979	465	4	differential	differential	NOUN
ejpam-6979	465	5	subordination	subordination	NOUN
ejpam-6979	465	6	using	use	VERB
ejpam-6979	465	7	ruscheweyh	ruscheweyh	NOUN
ejpam-6979	465	8	operator	operator	NOUN
ejpam-6979	465	9	.	.	PUNCT
ejpam-6979	466	1	analele	analele	PROPN
ejpam-6979	466	2	universităţii	universităţii	VERB
ejpam-6979	466	3	oradea	oradea	PROPN
ejpam-6979	466	4	fascicula	fascicula	PROPN
ejpam-6979	466	5	matematică	matematică	PROPN
ejpam-6979	466	6	,	,	PUNCT
ejpam-6979	466	7	22:167–176	22:167–176	PROPN
ejpam-6979	466	8	,	,	PUNCT
ejpam-6979	466	9	2015	2015	NUM
ejpam-6979	466	10	.	.	PUNCT
ejpam-6979	467	1	[	[	X
ejpam-6979	467	2	11	11	NUM
ejpam-6979	467	3	]	]	PUNCT
ejpam-6979	467	4	a.	a.	NOUN
ejpam-6979	467	5	h.	h.	PROPN
ejpam-6979	467	6	es	es	PROPN
ejpam-6979	467	7	.	.	PROPN
ejpam-6979	468	1	on	on	ADP
ejpam-6979	468	2	fuzzy	fuzzy	ADJ
ejpam-6979	468	3	differential	differential	ADJ
ejpam-6979	468	4	subordination	subordination	NOUN
ejpam-6979	468	5	.	.	PUNCT
ejpam-6979	469	1	mathematica	mathematica	PROPN
ejpam-6979	469	2	moravica	moravica	PROPN
ejpam-6979	469	3	,	,	PUNCT
ejpam-6979	469	4	19:123–129	19:123–129	NUM
ejpam-6979	469	5	,	,	PUNCT
ejpam-6979	469	6	2015	2015	NUM
ejpam-6979	469	7	.	.	PUNCT
ejpam-6979	470	1	[	[	X
ejpam-6979	470	2	12	12	NUM
ejpam-6979	470	3	]	]	PUNCT
ejpam-6979	470	4	a.	a.	PROPN
ejpam-6979	470	5	h.	h.	PROPN
ejpam-6979	470	6	majeed	majeed	PROPN
ejpam-6979	470	7	.	.	PUNCT
ejpam-6979	471	1	fuzzy	fuzzy	ADJ
ejpam-6979	471	2	differential	differential	ADJ
ejpam-6979	471	3	subordinations	subordination	NOUN
ejpam-6979	471	4	properties	property	NOUN
ejpam-6979	471	5	of	of	ADP
ejpam-6979	471	6	analytic	analytic	ADJ
ejpam-6979	471	7	functions	function	NOUN
ejpam-6979	471	8	involving	involve	VERB
ejpam-6979	471	9	generalized	generalized	ADJ
ejpam-6979	471	10	differential	differential	ADJ
ejpam-6979	471	11	operator	operator	NOUN
ejpam-6979	471	12	.	.	PUNCT
ejpam-6979	472	1	science	science	PROPN
ejpam-6979	472	2	international	international	PROPN
ejpam-6979	472	3	(	(	PUNCT
ejpam-6979	472	4	lahore	lahore	PROPN
ejpam-6979	472	5	)	)	PUNCT
ejpam-6979	472	6	,	,	PUNCT
ejpam-6979	472	7	30:297–302	30:297–302	PROPN
ejpam-6979	472	8	,	,	PUNCT
ejpam-6979	472	9	2018	2018	NUM
ejpam-6979	472	10	.	.	PUNCT
ejpam-6979	473	1	[	[	X
ejpam-6979	473	2	13	13	NUM
ejpam-6979	473	3	]	]	X
ejpam-6979	473	4	e.	e.	PROPN
ejpam-6979	473	5	e.	e.	PROPN
ejpam-6979	473	6	ali	ali	PROPN
ejpam-6979	473	7	,	,	PUNCT
ejpam-6979	473	8	m.	m.	PROPN
ejpam-6979	473	9	v.	v.	ADP
ejpam-6979	473	10	cortez	cortez	PROPN
ejpam-6979	473	11	,	,	PUNCT
ejpam-6979	473	12	r.	r.	PROPN
ejpam-6979	473	13	m.	m.	PROPN
ejpam-6979	473	14	el	el	PROPN
ejpam-6979	473	15	-	-	PUNCT
ejpam-6979	473	16	ashwah	ashwah	NOUN
ejpam-6979	473	17	,	,	PUNCT
ejpam-6979	473	18	and	and	CCONJ
ejpam-6979	473	19	a.	a.	NOUN
ejpam-6979	473	20	m.	m.	NOUN
ejpam-6979	473	21	albalahi	albalahi	PROPN
ejpam-6979	473	22	.	.	PUNCT
ejpam-6979	474	1	fuzzy	fuzzy	ADJ
ejpam-6979	474	2	subordination	subordination	NOUN
ejpam-6979	474	3	results	result	NOUN
ejpam-6979	474	4	for	for	ADP
ejpam-6979	474	5	meromorphic	meromorphic	ADJ
ejpam-6979	474	6	functions	function	NOUN
ejpam-6979	474	7	connected	connect	VERB
ejpam-6979	474	8	with	with	ADP
ejpam-6979	474	9	a	a	DET
ejpam-6979	474	10	linear	linear	ADJ
ejpam-6979	474	11	operator	operator	NOUN
ejpam-6979	474	12	.	.	PUNCT
ejpam-6979	475	1	fractal	fractal	PROPN
ejpam-6979	475	2	and	and	CCONJ
ejpam-6979	475	3	fractional	fractional	ADJ
ejpam-6979	475	4	,	,	PUNCT
ejpam-6979	475	5	8:308	8:308	NUM
ejpam-6979	475	6	,	,	PUNCT
ejpam-6979	475	7	2024	2024	NUM
ejpam-6979	475	8	.	.	PUNCT
ejpam-6979	476	1	[	[	X
ejpam-6979	476	2	14	14	NUM
ejpam-6979	476	3	]	]	X
ejpam-6979	476	4	e.	e.	PROPN
ejpam-6979	476	5	e.	e.	PROPN
ejpam-6979	476	6	ali	ali	PROPN
ejpam-6979	476	7	,	,	PUNCT
ejpam-6979	476	8	m.	m.	NOUN
ejpam-6979	476	9	v.	v.	ADP
ejpam-6979	476	10	cortez	cortez	PROPN
ejpam-6979	476	11	,	,	PUNCT
ejpam-6979	476	12	and	and	CCONJ
ejpam-6979	476	13	r.	r.	PROPN
ejpam-6979	476	14	m.	m.	PROPN
ejpam-6979	476	15	el	el	PROPN
ejpam-6979	476	16	-	-	PUNCT
ejpam-6979	476	17	ashwah	ashwah	NOUN
ejpam-6979	476	18	.	.	PUNCT
ejpam-6979	477	1	fuzzy	fuzzy	ADJ
ejpam-6979	477	2	differential	differential	ADJ
ejpam-6979	477	3	subordination	subordination	NOUN
ejpam-6979	477	4	for	for	ADP
ejpam-6979	477	5	classes	class	NOUN
ejpam-6979	477	6	of	of	ADP
ejpam-6979	477	7	admissible	admissible	ADJ
ejpam-6979	477	8	functions	function	NOUN
ejpam-6979	477	9	defined	define	VERB
ejpam-6979	477	10	by	by	ADP
ejpam-6979	477	11	a	a	DET
ejpam-6979	477	12	class	class	NOUN
ejpam-6979	477	13	of	of	ADP
ejpam-6979	477	14	operators	operator	NOUN
ejpam-6979	477	15	.	.	PUNCT
ejpam-6979	478	1	fractal	fractal	ADJ
ejpam-6979	478	2	and	and	CCONJ
ejpam-6979	478	3	fractional	fractional	ADJ
ejpam-6979	478	4	,	,	PUNCT
ejpam-6979	478	5	8:405	8:405	NUM
ejpam-6979	478	6	,	,	PUNCT
ejpam-6979	478	7	2024	2024	NUM
ejpam-6979	478	8	.	.	PUNCT
ejpam-6979	479	1	[	[	X
ejpam-6979	479	2	15	15	NUM
ejpam-6979	479	3	]	]	X
ejpam-6979	479	4	e.	e.	PROPN
ejpam-6979	479	5	e.	e.	PROPN
ejpam-6979	479	6	ali	ali	PROPN
ejpam-6979	479	7	,	,	PUNCT
ejpam-6979	479	8	m.	m.	NOUN
ejpam-6979	479	9	v.	v.	ADP
ejpam-6979	479	10	cortez	cortez	PROPN
ejpam-6979	479	11	,	,	PUNCT
ejpam-6979	479	12	and	and	CCONJ
ejpam-6979	479	13	r.	r.	PROPN
ejpam-6979	479	14	m.	m.	PROPN
ejpam-6979	479	15	el	el	PROPN
ejpam-6979	479	16	-	-	PUNCT
ejpam-6979	479	17	ashwah	ashwah	NOUN
ejpam-6979	479	18	.	.	PUNCT
ejpam-6979	480	1	new	new	ADJ
ejpam-6979	480	2	results	result	NOUN
ejpam-6979	480	3	about	about	ADP
ejpam-6979	480	4	fuzzy	fuzzy	ADJ
ejpam-6979	480	5	γ	γ	X
ejpam-6979	480	6	-	-	ADJ
ejpam-6979	480	7	convex	convex	ADJ
ejpam-6979	480	8	functions	function	NOUN
ejpam-6979	480	9	connected	connect	VERB
ejpam-6979	480	10	with	with	ADP
ejpam-6979	480	11	the	the	DET
ejpam-6979	480	12	q	q	ADJ
ejpam-6979	480	13	-	-	PUNCT
ejpam-6979	480	14	analogue	analogue	NOUN
ejpam-6979	480	15	multiplier	multipli	ADJ
ejpam-6979	480	16	-	-	PUNCT
ejpam-6979	480	17	noor	noor	ADJ
ejpam-6979	480	18	integral	integral	ADJ
ejpam-6979	480	19	operator	operator	NOUN
ejpam-6979	480	20	.	.	PUNCT
ejpam-6979	481	1	aims	aim	VERB
ejpam-6979	481	2	mathematics	mathematic	NOUN
ejpam-6979	481	3	,	,	PUNCT
ejpam-6979	481	4	9(3):5451–5465	9(3):5451–5465	NUM
ejpam-6979	481	5	,	,	PUNCT
ejpam-6979	481	6	2024	2024	NUM
ejpam-6979	481	7	.	.	PUNCT
ejpam-6979	482	1	[	[	X
ejpam-6979	482	2	16	16	NUM
ejpam-6979	482	3	]	]	X
ejpam-6979	482	4	e.	e.	PROPN
ejpam-6979	482	5	e.	e.	PROPN
ejpam-6979	482	6	ali	ali	PROPN
ejpam-6979	482	7	,	,	PUNCT
ejpam-6979	482	8	g.	g.	PROPN
ejpam-6979	482	9	i.	i.	PROPN
ejpam-6979	482	10	oros	oros	PROPN
ejpam-6979	482	11	,	,	PUNCT
ejpam-6979	482	12	r.	r.	PROPN
ejpam-6979	482	13	m.	m.	PROPN
ejpam-6979	482	14	el	el	PROPN
ejpam-6979	482	15	-	-	PUNCT
ejpam-6979	482	16	ashwah	ashwah	NOUN
ejpam-6979	482	17	,	,	PUNCT
ejpam-6979	482	18	and	and	CCONJ
ejpam-6979	482	19	a.	a.	NOUN
ejpam-6979	482	20	m.	m.	NOUN
ejpam-6979	482	21	albalahi	albalahi	PROPN
ejpam-6979	482	22	.	.	PUNCT
ejpam-6979	483	1	application	application	NOUN
ejpam-6979	483	2	on	on	ADP
ejpam-6979	483	3	fuzzy	fuzzy	ADJ
ejpam-6979	483	4	third	third	ADJ
ejpam-6979	483	5	-	-	PUNCT
ejpam-6979	483	6	order	order	NOUN
ejpam-6979	483	7	subordination	subordination	NOUN
ejpam-6979	483	8	and	and	CCONJ
ejpam-6979	483	9	superordination	superordination	NOUN
ejpam-6979	483	10	connected	connect	VERB
ejpam-6979	483	11	with	with	ADP
ejpam-6979	483	12	lommel	lommel	PROPN
ejpam-6979	483	13	function	function	NOUN
ejpam-6979	483	14	.	.	PUNCT
ejpam-6979	484	1	mathematics	mathematic	NOUN
ejpam-6979	484	2	,	,	PUNCT
ejpam-6979	484	3	13:1917	13:1917	NUM
ejpam-6979	484	4	,	,	PUNCT
ejpam-6979	484	5	2025	2025	NUM
ejpam-6979	484	6	.	.	PUNCT
ejpam-6979	485	1	[	[	X
ejpam-6979	485	2	17	17	NUM
ejpam-6979	485	3	]	]	X
ejpam-6979	485	4	e.	e.	PROPN
ejpam-6979	485	5	a.	a.	PROPN
ejpam-6979	485	6	haydar	haydar	PROPN
ejpam-6979	485	7	.	.	PUNCT
ejpam-6979	486	1	on	on	ADP
ejpam-6979	486	2	fuzzy	fuzzy	ADJ
ejpam-6979	486	3	differential	differential	ADJ
ejpam-6979	486	4	subordination	subordination	NOUN
ejpam-6979	486	5	.	.	PUNCT
ejpam-6979	487	1	mathematica	mathematica	PROPN
ejpam-6979	487	2	moravica	moravica	PROPN
ejpam-6979	487	3	,	,	PUNCT
ejpam-6979	487	4	19:123–129	19:123–129	NUM
ejpam-6979	487	5	,	,	PUNCT
ejpam-6979	487	6	2015	2015	NUM
ejpam-6979	487	7	.	.	PUNCT
ejpam-6979	488	1	[	[	X
ejpam-6979	488	2	18	18	NUM
ejpam-6979	488	3	]	]	X
ejpam-6979	488	4	g.	g.	PROPN
ejpam-6979	488	5	i.	i.	PROPN
ejpam-6979	488	6	oros	oros	PROPN
ejpam-6979	488	7	,	,	PUNCT
ejpam-6979	488	8	s.	s.	PROPN
ejpam-6979	488	9	dzitac	dzitac	PROPN
ejpam-6979	488	10	,	,	PUNCT
ejpam-6979	488	11	and	and	CCONJ
ejpam-6979	488	12	d.	d.	PROPN
ejpam-6979	488	13	a.	a.	PROPN
ejpam-6979	488	14	bardac	bardac	PROPN
ejpam-6979	488	15	-	-	PUNCT
ejpam-6979	488	16	vlada	vlada	PROPN
ejpam-6979	488	17	.	.	PUNCT
ejpam-6979	489	1	introduction	introduction	NOUN
ejpam-6979	489	2	in	in	ADP
ejpam-6979	489	3	third	third	ADJ
ejpam-6979	489	4	-	-	PUNCT
ejpam-6979	489	5	order	order	NOUN
ejpam-6979	489	6	fuzzy	fuzzy	ADJ
ejpam-6979	489	7	differential	differential	ADJ
ejpam-6979	489	8	subordination	subordination	NOUN
ejpam-6979	489	9	.	.	PUNCT
ejpam-6979	490	1	hacettepe	hacettepe	PROPN
ejpam-6979	490	2	journal	journal	PROPN
ejpam-6979	490	3	of	of	ADP
ejpam-6979	490	4	mathematics	mathematic	NOUN
ejpam-6979	490	5	and	and	CCONJ
ejpam-6979	490	6	statistics	statistic	NOUN
ejpam-6979	490	7	,	,	PUNCT
ejpam-6979	490	8	12:1–15	12:1–15	NUM
ejpam-6979	490	9	,	,	PUNCT
ejpam-6979	490	10	2024	2024	NUM
ejpam-6979	490	11	.	.	PUNCT
ejpam-6979	491	1	[	[	X
ejpam-6979	491	2	19	19	NUM
ejpam-6979	491	3	]	]	X
ejpam-6979	491	4	g.	g.	PROPN
ejpam-6979	491	5	i.	i.	PROPN
ejpam-6979	491	6	oros	oros	PROPN
ejpam-6979	491	7	,	,	PUNCT
ejpam-6979	491	8	s.	s.	PROPN
ejpam-6979	491	9	dzitac	dzitac	PROPN
ejpam-6979	491	10	,	,	PUNCT
ejpam-6979	491	11	and	and	CCONJ
ejpam-6979	491	12	d.	d.	PROPN
ejpam-6979	491	13	a.	a.	PROPN
ejpam-6979	491	14	bardac	bardac	PROPN
ejpam-6979	491	15	-	-	PUNCT
ejpam-6979	491	16	vlada	vlada	PROPN
ejpam-6979	491	17	.	.	PUNCT
ejpam-6979	492	1	introducing	introduce	VERB
ejpam-6979	492	2	the	the	DET
ejpam-6979	492	3	third	third	ADJ
ejpam-6979	492	4	-	-	PUNCT
ejpam-6979	492	5	order	order	NOUN
ejpam-6979	492	6	fuzzy	fuzzy	ADJ
ejpam-6979	492	7	superordination	superordination	NOUN
ejpam-6979	492	8	concept	concept	NOUN
ejpam-6979	492	9	and	and	CCONJ
ejpam-6979	492	10	related	related	ADJ
ejpam-6979	492	11	results	result	NOUN
ejpam-6979	492	12	.	.	PUNCT
ejpam-6979	493	1	mathematics	mathematic	NOUN
ejpam-6979	493	2	,	,	PUNCT
ejpam-6979	493	3	12:3095	12:3095	NOUN
ejpam-6979	493	4	,	,	PUNCT
ejpam-6979	493	5	2024	2024	NUM
ejpam-6979	493	6	.	.	PUNCT
ejpam-6979	494	1	[	[	X
ejpam-6979	494	2	20	20	NUM
ejpam-6979	494	3	]	]	PUNCT
ejpam-6979	494	4	s.	s.	PROPN
ejpam-6979	494	5	s.	s.	PROPN
ejpam-6979	494	6	miller	miller	PROPN
ejpam-6979	494	7	and	and	CCONJ
ejpam-6979	494	8	p.	p.	PROPN
ejpam-6979	494	9	t.	t.	PROPN
ejpam-6979	494	10	mocanu	mocanu	PROPN
ejpam-6979	494	11	.	.	PUNCT
ejpam-6979	495	1	differential	differential	ADJ
ejpam-6979	495	2	subordinations	subordination	NOUN
ejpam-6979	495	3	:	:	PUNCT
ejpam-6979	495	4	theory	theory	NOUN
ejpam-6979	495	5	and	and	CCONJ
ejpam-6979	495	6	applications	application	NOUN
ejpam-6979	495	7	,	,	PUNCT
ejpam-6979	495	8	volume	volume	NOUN
ejpam-6979	495	9	225	225	NUM
ejpam-6979	495	10	of	of	ADP
ejpam-6979	495	11	monographs	monograph	NOUN
ejpam-6979	495	12	and	and	CCONJ
ejpam-6979	495	13	textbooks	textbook	NOUN
ejpam-6979	495	14	in	in	ADP
ejpam-6979	495	15	pure	pure	ADJ
ejpam-6979	495	16	and	and	CCONJ
ejpam-6979	495	17	applied	applied	ADJ
ejpam-6979	495	18	mathematics	mathematic	NOUN
ejpam-6979	495	19	.	.	PUNCT
ejpam-6979	496	1	marcel	marcel	PROPN
ejpam-6979	496	2	dekker	dekker	PROPN
ejpam-6979	496	3	,	,	PUNCT
ejpam-6979	496	4	new	new	PROPN
ejpam-6979	496	5	york	york	PROPN
ejpam-6979	496	6	,	,	PUNCT
ejpam-6979	496	7	ny	ny	PROPN
ejpam-6979	496	8	,	,	PUNCT
ejpam-6979	496	9	usa	usa	PROPN
ejpam-6979	496	10	;	;	PUNCT
ejpam-6979	496	11	basel	basel	PROPN
ejpam-6979	496	12	,	,	PUNCT
ejpam-6979	496	13	switzerland	switzerland	PROPN
ejpam-6979	496	14	,	,	PUNCT
ejpam-6979	496	15	2000	2000	NUM
ejpam-6979	496	16	.	.	PUNCT
ejpam-6979	497	1	[	[	X
ejpam-6979	497	2	21	21	NUM
ejpam-6979	497	3	]	]	PUNCT
ejpam-6979	497	4	t.	t.	NOUN
ejpam-6979	497	5	bulboacă.	bulboacă.	PROPN
ejpam-6979	497	6	differential	differential	VERB
ejpam-6979	497	7	subordinations	subordination	NOUN
ejpam-6979	497	8	and	and	CCONJ
ejpam-6979	497	9	superordinations	superordination	NOUN
ejpam-6979	497	10	,	,	PUNCT
ejpam-6979	497	11	recent	recent	ADJ
ejpam-6979	497	12	results	result	NOUN
ejpam-6979	497	13	.	.	PUNCT
ejpam-6979	498	1	house	house	NOUN
ejpam-6979	498	2	of	of	ADP
ejpam-6979	498	3	scientific	scientific	ADJ
ejpam-6979	498	4	book	book	NOUN
ejpam-6979	498	5	publication	publication	NOUN
ejpam-6979	498	6	,	,	PUNCT
ejpam-6979	498	7	cluj	cluj	NOUN
ejpam-6979	498	8	-	-	PUNCT
ejpam-6979	498	9	napoca	napoca	PROPN
ejpam-6979	498	10	,	,	PUNCT
ejpam-6979	498	11	romania	romania	PROPN
ejpam-6979	498	12	,	,	PUNCT
ejpam-6979	498	13	2005	2005	NUM
ejpam-6979	498	14	.	.	PUNCT
ejpam-6979	499	1	[	[	X
ejpam-6979	499	2	22	22	NUM
ejpam-6979	499	3	]	]	PUNCT
ejpam-6979	499	4	á.	á.	X
ejpam-6979	499	5	baricz	baricz	NOUN
ejpam-6979	499	6	.	.	PUNCT
ejpam-6979	500	1	geometric	geometric	ADJ
ejpam-6979	500	2	properties	property	NOUN
ejpam-6979	500	3	of	of	ADP
ejpam-6979	500	4	generalized	generalized	ADJ
ejpam-6979	500	5	bessel	bessel	ADJ
ejpam-6979	500	6	functions	function	NOUN
ejpam-6979	500	7	of	of	ADP
ejpam-6979	500	8	complex	complex	ADJ
ejpam-6979	500	9	order	order	NOUN
ejpam-6979	500	10	.	.	PUNCT
ejpam-6979	501	1	mathematica	mathematica	PROPN
ejpam-6979	501	2	,	,	PUNCT
ejpam-6979	501	3	48(376):13–18	48(376):13–18	NOUN
ejpam-6979	501	4	,	,	PUNCT
ejpam-6979	501	5	2006	2006	NUM
ejpam-6979	501	6	.	.	PUNCT
ejpam-6979	502	1	[	[	X
ejpam-6979	502	2	23	23	NUM
ejpam-6979	502	3	]	]	PUNCT
ejpam-6979	502	4	á.	á.	X
ejpam-6979	502	5	baricz	baricz	NOUN
ejpam-6979	502	6	.	.	PUNCT
ejpam-6979	503	1	geometric	geometric	ADJ
ejpam-6979	503	2	properties	property	NOUN
ejpam-6979	503	3	of	of	ADP
ejpam-6979	503	4	generalized	generalized	ADJ
ejpam-6979	503	5	bessel	bessel	NOUN
ejpam-6979	503	6	functions	function	NOUN
ejpam-6979	503	7	.	.	PUNCT
ejpam-6979	504	1	publicationes	publicatione	NOUN
ejpam-6979	504	2	mathematicae	mathematicae	PROPN
ejpam-6979	504	3	debrecen	debrecen	PROPN
ejpam-6979	504	4	,	,	PUNCT
ejpam-6979	504	5	73:155–178	73:155–178	NUM
ejpam-6979	504	6	,	,	PUNCT
ejpam-6979	504	7	2008	2008	NUM
ejpam-6979	504	8	.	.	PUNCT
ejpam-6979	505	1	[	[	X
ejpam-6979	505	2	24	24	NUM
ejpam-6979	505	3	]	]	PUNCT
ejpam-6979	505	4	á.	á.	X
ejpam-6979	505	5	baricz	baricz	NOUN
ejpam-6979	505	6	.	.	PUNCT
ejpam-6979	506	1	generalized	generalized	ADJ
ejpam-6979	506	2	bessel	bessel	NOUN
ejpam-6979	506	3	functions	function	NOUN
ejpam-6979	506	4	of	of	ADP
ejpam-6979	506	5	the	the	DET
ejpam-6979	506	6	first	first	ADJ
ejpam-6979	506	7	kind	kind	NOUN
ejpam-6979	506	8	,	,	PUNCT
ejpam-6979	506	9	volume	volume	NOUN
ejpam-6979	506	10	1994	1994	NUM
ejpam-6979	506	11	of	of	ADP
ejpam-6979	506	12	lecture	lecture	NOUN
ejpam-6979	506	13	notes	note	NOUN
ejpam-6979	506	14	in	in	ADP
ejpam-6979	506	15	mathematics	mathematic	NOUN
ejpam-6979	506	16	.	.	PUNCT
ejpam-6979	507	1	springer	springer	PROPN
ejpam-6979	507	2	verlag	verlag	PROPN
ejpam-6979	507	3	,	,	PUNCT
ejpam-6979	507	4	berlin	berlin	PROPN
ejpam-6979	507	5	,	,	PUNCT
ejpam-6979	507	6	2010	2010	NUM
ejpam-6979	507	7	.	.	PUNCT
ejpam-6979	508	1	[	[	X
ejpam-6979	508	2	25	25	NUM
ejpam-6979	508	3	]	]	X
ejpam-6979	508	4	s.	s.	PROPN
ejpam-6979	508	5	r.	r.	PROPN
ejpam-6979	508	6	mondal	mondal	PROPN
ejpam-6979	508	7	and	and	CCONJ
ejpam-6979	508	8	a.	a.	NOUN
ejpam-6979	508	9	swaminathan	swaminathan	ADV
ejpam-6979	508	10	.	.	PUNCT
ejpam-6979	509	1	geometric	geometric	ADJ
ejpam-6979	509	2	properties	property	NOUN
ejpam-6979	509	3	of	of	ADP
ejpam-6979	509	4	generalized	generalized	ADJ
ejpam-6979	509	5	bessel	bessel	NOUN
ejpam-6979	509	6	functions	function	NOUN
ejpam-6979	509	7	.	.	PUNCT
ejpam-6979	510	1	bulletin	bulletin	NOUN
ejpam-6979	510	2	of	of	ADP
ejpam-6979	510	3	the	the	DET
ejpam-6979	510	4	malaysian	malaysian	PROPN
ejpam-6979	510	5	mathematical	mathematical	PROPN
ejpam-6979	510	6	sciences	sciences	PROPN
ejpam-6979	510	7	society	society	NOUN
ejpam-6979	510	8	,	,	PUNCT
ejpam-6979	510	9	35:179–194	35:179–194	PROPN
ejpam-6979	510	10	,	,	PUNCT
ejpam-6979	510	11	2012	2012	NUM
ejpam-6979	510	12	.	.	PUNCT
ejpam-6979	511	1	[	[	X
ejpam-6979	511	2	26	26	NUM
ejpam-6979	511	3	]	]	X
ejpam-6979	511	4	n.	n.	PROPN
ejpam-6979	511	5	e.	e.	PROPN
ejpam-6979	511	6	cho	cho	PROPN
ejpam-6979	511	7	,	,	PUNCT
ejpam-6979	511	8	s.	s.	PROPN
ejpam-6979	511	9	y.	y.	PROPN
ejpam-6979	511	10	woo	woo	PROPN
ejpam-6979	511	11	,	,	PUNCT
ejpam-6979	511	12	and	and	CCONJ
ejpam-6979	511	13	s.	s.	PROPN
ejpam-6979	511	14	owa	owa	PROPN
ejpam-6979	511	15	.	.	PROPN
ejpam-6979	511	16	uniform	uniform	PROPN
ejpam-6979	511	17	convexity	convexity	NOUN
ejpam-6979	511	18	properties	property	NOUN
ejpam-6979	511	19	for	for	ADP
ejpam-6979	511	20	hypergeometric	hypergeometric	ADJ
ejpam-6979	511	21	functions	function	NOUN
ejpam-6979	511	22	.	.	PUNCT
ejpam-6979	512	1	fractional	fractional	ADJ
ejpam-6979	512	2	calculus	calculus	NOUN
ejpam-6979	512	3	and	and	CCONJ
ejpam-6979	512	4	applied	apply	VERB
ejpam-6979	512	5	analysis	analysis	NOUN
ejpam-6979	512	6	,	,	PUNCT
ejpam-6979	512	7	5:303–313	5:303–313	NUM
ejpam-6979	512	8	,	,	PUNCT
ejpam-6979	512	9	2002	2002	NUM
ejpam-6979	512	10	.	.	PUNCT
ejpam-6979	513	1	[	[	X
ejpam-6979	513	2	27	27	NUM
ejpam-6979	513	3	]	]	PUNCT
ejpam-6979	513	4	e.	e.	PROPN
ejpam-6979	513	5	p.	p.	PROPN
ejpam-6979	513	6	merkes	merke	NOUN
ejpam-6979	513	7	and	and	CCONJ
ejpam-6979	513	8	w.	w.	PROPN
ejpam-6979	513	9	p.	p.	PROPN
ejpam-6979	513	10	scott	scott	PROPN
ejpam-6979	513	11	.	.	PUNCT
ejpam-6979	514	1	starlike	starlike	ADJ
ejpam-6979	514	2	hypergeometric	hypergeometric	ADJ
ejpam-6979	514	3	functions	function	NOUN
ejpam-6979	514	4	.	.	PUNCT
ejpam-6979	515	1	proceedings	proceeding	NOUN
ejpam-6979	515	2	of	of	ADP
ejpam-6979	515	3	the	the	DET
ejpam-6979	515	4	american	american	PROPN
ejpam-6979	515	5	mathematical	mathematical	PROPN
ejpam-6979	515	6	society	society	NOUN
ejpam-6979	515	7	,	,	PUNCT
ejpam-6979	515	8	12:885–888	12:885–888	NUM
ejpam-6979	515	9	,	,	PUNCT
ejpam-6979	515	10	1961	1961	NUM
ejpam-6979	515	11	.	.	PUNCT
ejpam-6979	516	1	[	[	X
ejpam-6979	516	2	28	28	NUM
ejpam-6979	516	3	]	]	X
ejpam-6979	516	4	s.	s.	PROPN
ejpam-6979	516	5	owa	owa	PROPN
ejpam-6979	516	6	and	and	CCONJ
ejpam-6979	516	7	h.	h.	PROPN
ejpam-6979	516	8	m.	m.	PROPN
ejpam-6979	516	9	srivastava	srivastava	PROPN
ejpam-6979	516	10	.	.	PUNCT
ejpam-6979	517	1	univalent	univalent	ADJ
ejpam-6979	517	2	and	and	CCONJ
ejpam-6979	517	3	starlike	starlike	ADJ
ejpam-6979	517	4	generalized	generalize	VERB
ejpam-6979	517	5	hypergeometric	hypergeometric	ADJ
ejpam-6979	517	6	functions	function	NOUN
ejpam-6979	517	7	.	.	PUNCT
ejpam-6979	518	1	canadian	canadian	ADJ
ejpam-6979	518	2	journal	journal	PROPN
ejpam-6979	518	3	of	of	ADP
ejpam-6979	518	4	mathematics	mathematic	NOUN
ejpam-6979	518	5	,	,	PUNCT
ejpam-6979	518	6	39:1057–1077	39:1057–1077	NUM
ejpam-6979	518	7	,	,	PUNCT
ejpam-6979	518	8	1987	1987	NUM
ejpam-6979	518	9	.	.	PUNCT
ejpam-6979	519	1	[	[	X
ejpam-6979	519	2	29	29	NUM
ejpam-6979	519	3	]	]	X
ejpam-6979	519	4	h.	h.	PROPN
ejpam-6979	519	5	silverman	silverman	PROPN
ejpam-6979	519	6	.	.	PUNCT
ejpam-6979	520	1	starlike	starlike	PROPN
ejpam-6979	520	2	and	and	CCONJ
ejpam-6979	520	3	convexity	convexity	NOUN
ejpam-6979	520	4	properties	property	NOUN
ejpam-6979	520	5	for	for	ADP
ejpam-6979	520	6	hypergeometric	hypergeometric	ADJ
ejpam-6979	520	7	functions	function	NOUN
ejpam-6979	520	8	.	.	PUNCT
ejpam-6979	521	1	journal	journal	NOUN
ejpam-6979	521	2	of	of	ADP
ejpam-6979	521	3	mathematical	mathematical	ADJ
ejpam-6979	521	4	analysis	analysis	NOUN
ejpam-6979	521	5	and	and	CCONJ
ejpam-6979	521	6	applications	application	NOUN
ejpam-6979	521	7	,	,	PUNCT
ejpam-6979	521	8	172:574–581	172:574–581	NUM
ejpam-6979	521	9	,	,	PUNCT
ejpam-6979	521	10	1993	1993	NUM
ejpam-6979	521	11	.	.	PUNCT
ejpam-6979	522	1	e.	e.	PROPN
ejpam-6979	522	2	e.	e.	PROPN
ejpam-6979	522	3	ali	ali	PROPN
ejpam-6979	522	4	et	et	PROPN
ejpam-6979	522	5	al	al	PROPN
ejpam-6979	522	6	.	.	PUNCT
ejpam-6979	522	7	/	/	SYM
ejpam-6979	522	8	eur	eur	PROPN
ejpam-6979	522	9	.	.	PUNCT
ejpam-6979	523	1	j.	j.	PROPN
ejpam-6979	523	2	pure	pure	PROPN
ejpam-6979	523	3	appl	appl	PROPN
ejpam-6979	523	4	.	.	PROPN
ejpam-6979	523	5	math	math	PROPN
ejpam-6979	523	6	,	,	PUNCT
ejpam-6979	523	7	18	18	NUM
ejpam-6979	523	8	(	(	PUNCT
ejpam-6979	523	9	4	4	NUM
ejpam-6979	523	10	)	)	PUNCT
ejpam-6979	523	11	(	(	PUNCT
ejpam-6979	523	12	2025	2025	NUM
ejpam-6979	523	13	)	)	PUNCT
ejpam-6979	523	14	,	,	PUNCT
ejpam-6979	523	15	6979	6979	NUM
ejpam-6979	523	16	18	18	NUM
ejpam-6979	523	17	of	of	ADP
ejpam-6979	523	18	18	18	NUM
ejpam-6979	523	19	[	[	SYM
ejpam-6979	523	20	30	30	NUM
ejpam-6979	523	21	]	]	PUNCT
ejpam-6979	523	22	á.	á.	VERB
ejpam-6979	523	23	baricz	baricz	NOUN
ejpam-6979	523	24	and	and	CCONJ
ejpam-6979	523	25	s.	s.	PROPN
ejpam-6979	523	26	koumandos	koumandos	PROPN
ejpam-6979	523	27	.	.	PUNCT
ejpam-6979	524	1	turn	turn	VERB
ejpam-6979	524	2	type	type	NOUN
ejpam-6979	524	3	inequalities	inequality	NOUN
ejpam-6979	524	4	for	for	ADP
ejpam-6979	524	5	some	some	DET
ejpam-6979	524	6	lommel	lommel	ADJ
ejpam-6979	524	7	functions	function	NOUN
ejpam-6979	524	8	of	of	ADP
ejpam-6979	524	9	the	the	DET
ejpam-6979	524	10	first	first	ADJ
ejpam-6979	524	11	kind	kind	NOUN
ejpam-6979	524	12	.	.	PUNCT
ejpam-6979	525	1	2013	2013	NUM
ejpam-6979	525	2	.	.	PUNCT
ejpam-6979	525	3	arxiv:1308.6477	arxiv:1308.6477	NOUN
ejpam-6979	525	4	.	.	PUNCT
ejpam-6979	526	1	[	[	X
ejpam-6979	526	2	31	31	NUM
ejpam-6979	526	3	]	]	PUNCT
ejpam-6979	526	4	s.	s.	PROPN
ejpam-6979	526	5	koumandos	koumandos	PROPN
ejpam-6979	526	6	and	and	CCONJ
ejpam-6979	526	7	m.	m.	NOUN
ejpam-6979	526	8	lamprecht	lamprecht	PROPN
ejpam-6979	526	9	.	.	PUNCT
ejpam-6979	527	1	the	the	DET
ejpam-6979	527	2	zeros	zero	NOUN
ejpam-6979	527	3	of	of	ADP
ejpam-6979	527	4	certain	certain	ADJ
ejpam-6979	527	5	lommel	lommel	ADJ
ejpam-6979	527	6	functions	function	NOUN
ejpam-6979	527	7	.	.	PUNCT
ejpam-6979	528	1	proceedings	proceeding	NOUN
ejpam-6979	528	2	of	of	ADP
ejpam-6979	528	3	the	the	DET
ejpam-6979	528	4	american	american	PROPN
ejpam-6979	528	5	mathematical	mathematical	PROPN
ejpam-6979	528	6	society	society	NOUN
ejpam-6979	528	7	,	,	PUNCT
ejpam-6979	528	8	140(9):3091–3100	140(9):3091–3100	NUM
ejpam-6979	528	9	,	,	PUNCT
ejpam-6979	528	10	2012	2012	NUM
ejpam-6979	528	11	.	.	PUNCT
ejpam-6979	529	1	[	[	X
ejpam-6979	529	2	32	32	NUM
ejpam-6979	529	3	]	]	PUNCT
ejpam-6979	529	4	m.	m.	NOUN
ejpam-6979	529	5	çağlar	çağlar	PROPN
ejpam-6979	529	6	and	and	CCONJ
ejpam-6979	529	7	e.	e.	PROPN
ejpam-6979	529	8	deniz	deniz	PROPN
ejpam-6979	529	9	.	.	PUNCT
ejpam-6979	530	1	partial	partial	ADJ
ejpam-6979	530	2	sums	sum	NOUN
ejpam-6979	530	3	of	of	ADP
ejpam-6979	530	4	the	the	DET
ejpam-6979	530	5	normalized	normalize	VERB
ejpam-6979	530	6	lommel	lommel	ADJ
ejpam-6979	530	7	functions	function	NOUN
ejpam-6979	530	8	.	.	PUNCT
ejpam-6979	531	1	mathematical	mathematical	ADJ
ejpam-6979	531	2	inequalities	inequality	NOUN
ejpam-6979	531	3	&	&	CCONJ
ejpam-6979	531	4	applications	application	NOUN
ejpam-6979	531	5	,	,	PUNCT
ejpam-6979	531	6	18(3):1189–1199	18(3):1189–1199	NUM
ejpam-6979	531	7	,	,	PUNCT
ejpam-6979	531	8	2015	2015	NUM
ejpam-6979	531	9	.	.	PUNCT