id	sid	tid	token	lemma	pos
ejpam-5997	1	1	european	european	PROPN
ejpam-5997	1	2	journal	journal	PROPN
ejpam-5997	1	3	of	of	ADP
ejpam-5997	1	4	pure	pure	ADJ
ejpam-5997	1	5	and	and	CCONJ
ejpam-5997	1	6	applied	applied	ADJ
ejpam-5997	1	7	mathematics	mathematic	NOUN
ejpam-5997	1	8	2025	2025	NUM
ejpam-5997	1	9	,	,	PUNCT
ejpam-5997	1	10	vol	vol	NOUN
ejpam-5997	1	11	.	.	PROPN
ejpam-5997	1	12	18	18	NUM
ejpam-5997	1	13	,	,	PUNCT
ejpam-5997	1	14	issue	issue	NOUN
ejpam-5997	1	15	2	2	NUM
ejpam-5997	1	16	,	,	PUNCT
ejpam-5997	1	17	article	article	NOUN
ejpam-5997	1	18	number	number	NOUN
ejpam-5997	1	19	5997	5997	NUM
ejpam-5997	1	20	issn	issn	PROPN
ejpam-5997	1	21	1307	1307	NUM
ejpam-5997	1	22	-	-	SYM
ejpam-5997	1	23	5543	5543	NUM
ejpam-5997	1	24	–	–	PUNCT
ejpam-5997	1	25	ejpam.com	ejpam.com	X
ejpam-5997	1	26	published	publish	VERB
ejpam-5997	1	27	by	by	ADP
ejpam-5997	1	28	new	new	PROPN
ejpam-5997	1	29	york	york	PROPN
ejpam-5997	1	30	business	business	PROPN
ejpam-5997	1	31	global	global	ADJ
ejpam-5997	1	32	new	new	ADJ
ejpam-5997	1	33	extension	extension	NOUN
ejpam-5997	1	34	of	of	ADP
ejpam-5997	1	35	inequalities	inequality	NOUN
ejpam-5997	1	36	through	through	ADP
ejpam-5997	1	37	extended	extended	ADJ
ejpam-5997	1	38	version	version	NOUN
ejpam-5997	1	39	of	of	ADP
ejpam-5997	1	40	fractional	fractional	ADJ
ejpam-5997	1	41	operators	operator	NOUN
ejpam-5997	1	42	for	for	ADP
ejpam-5997	1	43	s	s	NOUN
ejpam-5997	1	44	-	-	NOUN
ejpam-5997	1	45	convexity	convexity	NOUN
ejpam-5997	1	46	with	with	ADP
ejpam-5997	1	47	applications	application	NOUN
ejpam-5997	1	48	miguel	miguel	PROPN
ejpam-5997	1	49	vivas	vivas	PROPN
ejpam-5997	1	50	-	-	PROPN
ejpam-5997	1	51	cortez1	cortez1	PROPN
ejpam-5997	1	52	,	,	PUNCT
ejpam-5997	1	53	rana	rana	PROPN
ejpam-5997	1	54	safdar	safdar	PROPN
ejpam-5997	1	55	ali2,∗	ali2,∗	PROPN
ejpam-5997	1	56	,	,	PUNCT
ejpam-5997	1	57	naila	naila	PROPN
ejpam-5997	1	58	talib	talib	PROPN
ejpam-5997	1	59	2	2	NUM
ejpam-5997	1	60	,	,	PUNCT
ejpam-5997	1	61	imen	iman	NOUN
ejpam-5997	1	62	kebaili3	kebaili3	PROPN
ejpam-5997	1	63	,	,	PUNCT
ejpam-5997	1	64	imed	imed	PROPN
ejpam-5997	1	65	boukhris3	boukhris3	PROPN
ejpam-5997	1	66	,	,	PUNCT
ejpam-5997	1	67	gauhar	gauhar	PROPN
ejpam-5997	1	68	rahman4	rahman4	NOUN
ejpam-5997	1	69	1	1	NUM
ejpam-5997	1	70	pontificia	pontificia	PROPN
ejpam-5997	1	71	universidad	universidad	PROPN
ejpam-5997	1	72	católica	católica	PROPN
ejpam-5997	1	73	del	del	PROPN
ejpam-5997	1	74	ecuador	ecuador	PROPN
ejpam-5997	1	75	,	,	PUNCT
ejpam-5997	1	76	faculty	faculty	NOUN
ejpam-5997	1	77	of	of	ADP
ejpam-5997	1	78	exact	exact	ADJ
ejpam-5997	1	79	,	,	PUNCT
ejpam-5997	1	80	natural	natural	ADJ
ejpam-5997	1	81	and	and	CCONJ
ejpam-5997	1	82	environmental	environmental	ADJ
ejpam-5997	1	83	sciences	science	NOUN
ejpam-5997	1	84	,	,	PUNCT
ejpam-5997	1	85	fractal	fractal	ADJ
ejpam-5997	1	86	laboratory	laboratory	NOUN
ejpam-5997	1	87	(	(	PUNCT
ejpam-5997	1	88	fractional	fractional	ADJ
ejpam-5997	1	89	research	research	NOUN
ejpam-5997	1	90	in	in	ADP
ejpam-5997	1	91	analysis	analysis	NOUN
ejpam-5997	1	92	,	,	PUNCT
ejpam-5997	1	93	convexity	convexity	NOUN
ejpam-5997	1	94	and	and	CCONJ
ejpam-5997	1	95	their	their	PRON
ejpam-5997	1	96	applications	application	NOUN
ejpam-5997	1	97	laboratory	laboratory	NOUN
ejpam-5997	1	98	,	,	PUNCT
ejpam-5997	1	99	ecuador	ecuador	PROPN
ejpam-5997	1	100	2	2	NUM
ejpam-5997	1	101	department	department	NOUN
ejpam-5997	1	102	of	of	ADP
ejpam-5997	1	103	mathematics	mathematic	NOUN
ejpam-5997	1	104	and	and	CCONJ
ejpam-5997	1	105	statistics	statistic	NOUN
ejpam-5997	1	106	,	,	PUNCT
ejpam-5997	1	107	the	the	DET
ejpam-5997	1	108	university	university	NOUN
ejpam-5997	1	109	of	of	ADP
ejpam-5997	1	110	lahore	lahore	PROPN
ejpam-5997	1	111	,	,	PUNCT
ejpam-5997	1	112	lahore	lahore	PROPN
ejpam-5997	1	113	,	,	PUNCT
ejpam-5997	1	114	pakistan	pakistan	PROPN
ejpam-5997	1	115	3	3	NUM
ejpam-5997	1	116	department	department	PROPN
ejpam-5997	1	117	of	of	ADP
ejpam-5997	1	118	physics	physics	PROPN
ejpam-5997	1	119	,	,	PUNCT
ejpam-5997	1	120	faculty	faculty	NOUN
ejpam-5997	1	121	of	of	ADP
ejpam-5997	1	122	science	science	NOUN
ejpam-5997	1	123	,	,	PUNCT
ejpam-5997	1	124	king	king	PROPN
ejpam-5997	1	125	khalid	khalid	PROPN
ejpam-5997	1	126	university	university	PROPN
ejpam-5997	1	127	,	,	PUNCT
ejpam-5997	1	128	p.o	p.o	PROPN
ejpam-5997	1	129	.	.	PROPN
ejpam-5997	1	130	box	box	PROPN
ejpam-5997	1	131	960	960	NUM
ejpam-5997	1	132	,	,	PUNCT
ejpam-5997	1	133	abha	abha	NOUN
ejpam-5997	1	134	,	,	PUNCT
ejpam-5997	1	135	saudi	saudi	PROPN
ejpam-5997	1	136	arabia	arabia	PROPN
ejpam-5997	1	137	4	4	NUM
ejpam-5997	1	138	department	department	NOUN
ejpam-5997	1	139	of	of	ADP
ejpam-5997	1	140	mathematics	mathematic	NOUN
ejpam-5997	1	141	and	and	CCONJ
ejpam-5997	1	142	statistics	statistic	NOUN
ejpam-5997	1	143	,	,	PUNCT
ejpam-5997	1	144	hazara	hazara	PROPN
ejpam-5997	1	145	university	university	PROPN
ejpam-5997	1	146	mansehra	mansehra	PROPN
ejpam-5997	1	147	21300	21300	NUM
ejpam-5997	1	148	,	,	PUNCT
ejpam-5997	1	149	pakistan	pakistan	PROPN
ejpam-5997	1	150	abstract	abstract	NOUN
ejpam-5997	1	151	.	.	PUNCT
ejpam-5997	2	1	fractional	fractional	ADJ
ejpam-5997	2	2	integral	integral	ADJ
ejpam-5997	2	3	inequalities	inequality	NOUN
ejpam-5997	2	4	play	play	VERB
ejpam-5997	2	5	a	a	DET
ejpam-5997	2	6	significant	significant	ADJ
ejpam-5997	2	7	role	role	NOUN
ejpam-5997	2	8	in	in	ADP
ejpam-5997	2	9	both	both	CCONJ
ejpam-5997	2	10	pure	pure	ADJ
ejpam-5997	2	11	and	and	CCONJ
ejpam-5997	2	12	applied	applied	ADJ
ejpam-5997	2	13	mathematics	mathematic	NOUN
ejpam-5997	2	14	,	,	PUNCT
ejpam-5997	2	15	contributing	contribute	VERB
ejpam-5997	2	16	to	to	ADP
ejpam-5997	2	17	the	the	DET
ejpam-5997	2	18	advancement	advancement	NOUN
ejpam-5997	2	19	and	and	CCONJ
ejpam-5997	2	20	extension	extension	NOUN
ejpam-5997	2	21	of	of	ADP
ejpam-5997	2	22	various	various	ADJ
ejpam-5997	2	23	mathematical	mathematical	ADJ
ejpam-5997	2	24	techniques	technique	NOUN
ejpam-5997	2	25	.	.	PUNCT
ejpam-5997	3	1	an	an	DET
ejpam-5997	3	2	accurate	accurate	ADJ
ejpam-5997	3	3	formulation	formulation	NOUN
ejpam-5997	3	4	of	of	ADP
ejpam-5997	3	5	such	such	ADJ
ejpam-5997	3	6	inequalities	inequality	NOUN
ejpam-5997	3	7	is	be	AUX
ejpam-5997	3	8	essential	essential	ADJ
ejpam-5997	3	9	to	to	PART
ejpam-5997	3	10	establish	establish	VERB
ejpam-5997	3	11	the	the	DET
ejpam-5997	3	12	existence	existence	NOUN
ejpam-5997	3	13	and	and	CCONJ
ejpam-5997	3	14	uniqueness	uniqueness	NOUN
ejpam-5997	3	15	of	of	ADP
ejpam-5997	3	16	fractional	fractional	ADJ
ejpam-5997	3	17	methods	method	NOUN
ejpam-5997	3	18	.	.	PUNCT
ejpam-5997	4	1	additionally	additionally	ADV
ejpam-5997	4	2	,	,	PUNCT
ejpam-5997	4	3	convexity	convexity	NOUN
ejpam-5997	4	4	theory	theory	NOUN
ejpam-5997	4	5	serves	serve	VERB
ejpam-5997	4	6	as	as	ADP
ejpam-5997	4	7	a	a	DET
ejpam-5997	4	8	fundamental	fundamental	ADJ
ejpam-5997	4	9	component	component	NOUN
ejpam-5997	4	10	in	in	ADP
ejpam-5997	4	11	the	the	DET
ejpam-5997	4	12	study	study	NOUN
ejpam-5997	4	13	of	of	ADP
ejpam-5997	4	14	fractional	fractional	ADJ
ejpam-5997	4	15	integral	integral	ADJ
ejpam-5997	4	16	inequalities	inequality	NOUN
ejpam-5997	4	17	due	due	ADP
ejpam-5997	4	18	to	to	ADP
ejpam-5997	4	19	its	its	PRON
ejpam-5997	4	20	defining	define	VERB
ejpam-5997	4	21	characteristics	characteristic	NOUN
ejpam-5997	4	22	and	and	CCONJ
ejpam-5997	4	23	properties	property	NOUN
ejpam-5997	4	24	.	.	PUNCT
ejpam-5997	5	1	moreover	moreover	ADV
ejpam-5997	5	2	,	,	PUNCT
ejpam-5997	5	3	there	there	PRON
ejpam-5997	5	4	is	be	VERB
ejpam-5997	5	5	a	a	DET
ejpam-5997	5	6	strong	strong	ADJ
ejpam-5997	5	7	interconnection	interconnection	NOUN
ejpam-5997	5	8	between	between	ADP
ejpam-5997	5	9	convexity	convexity	NOUN
ejpam-5997	5	10	and	and	CCONJ
ejpam-5997	5	11	symmetric	symmetric	ADJ
ejpam-5997	5	12	theories	theory	NOUN
ejpam-5997	5	13	,	,	PUNCT
ejpam-5997	5	14	allowing	allow	VERB
ejpam-5997	5	15	results	result	NOUN
ejpam-5997	5	16	from	from	ADP
ejpam-5997	5	17	one	one	NUM
ejpam-5997	5	18	to	to	PART
ejpam-5997	5	19	be	be	AUX
ejpam-5997	5	20	effectively	effectively	ADV
ejpam-5997	5	21	applied	apply	VERB
ejpam-5997	5	22	to	to	ADP
ejpam-5997	5	23	the	the	DET
ejpam-5997	5	24	other	other	ADJ
ejpam-5997	5	25	.	.	PUNCT
ejpam-5997	6	1	this	this	DET
ejpam-5997	6	2	correlation	correlation	NOUN
ejpam-5997	6	3	has	have	AUX
ejpam-5997	6	4	become	become	VERB
ejpam-5997	6	5	particularly	particularly	ADV
ejpam-5997	6	6	evident	evident	ADJ
ejpam-5997	6	7	in	in	ADP
ejpam-5997	6	8	recent	recent	ADJ
ejpam-5997	6	9	decades	decade	NOUN
ejpam-5997	6	10	,	,	PUNCT
ejpam-5997	6	11	further	far	ADV
ejpam-5997	6	12	enhancing	enhance	VERB
ejpam-5997	6	13	their	their	PRON
ejpam-5997	6	14	importance	importance	NOUN
ejpam-5997	6	15	in	in	ADP
ejpam-5997	6	16	mathematical	mathematical	ADJ
ejpam-5997	6	17	research	research	NOUN
ejpam-5997	6	18	.	.	PUNCT
ejpam-5997	7	1	this	this	DET
ejpam-5997	7	2	article	article	NOUN
ejpam-5997	7	3	investigate	investigate	VERB
ejpam-5997	7	4	two	two	NUM
ejpam-5997	7	5	innovative	innovative	ADJ
ejpam-5997	7	6	approaches	approach	NOUN
ejpam-5997	7	7	of	of	ADP
ejpam-5997	7	8	differentiable	differentiable	ADJ
ejpam-5997	7	9	functions	function	NOUN
ejpam-5997	7	10	to	to	PART
ejpam-5997	7	11	modify	modify	VERB
ejpam-5997	7	12	hermite	hermite	ADJ
ejpam-5997	7	13	-	-	PUNCT
ejpam-5997	7	14	hadamard	hadamard	ADJ
ejpam-5997	7	15	inequalities	inequality	NOUN
ejpam-5997	7	16	and	and	CCONJ
ejpam-5997	7	17	their	their	PRON
ejpam-5997	7	18	refinements	refinement	NOUN
ejpam-5997	7	19	by	by	ADP
ejpam-5997	7	20	implementation	implementation	NOUN
ejpam-5997	7	21	of	of	ADP
ejpam-5997	7	22	generalized	generalized	ADJ
ejpam-5997	7	23	fractional	fractional	ADJ
ejpam-5997	7	24	operators	operator	NOUN
ejpam-5997	7	25	through	through	ADP
ejpam-5997	7	26	the	the	DET
ejpam-5997	7	27	s	s	NOUN
ejpam-5997	7	28	-	-	PUNCT
ejpam-5997	7	29	convex	convex	ADJ
ejpam-5997	7	30	functions	function	NOUN
ejpam-5997	7	31	.	.	PUNCT
ejpam-5997	8	1	the	the	DET
ejpam-5997	8	2	study	study	NOUN
ejpam-5997	8	3	aims	aim	VERB
ejpam-5997	8	4	to	to	PART
ejpam-5997	8	5	extend	extend	VERB
ejpam-5997	8	6	and	and	CCONJ
ejpam-5997	8	7	refine	refine	VERB
ejpam-5997	8	8	existing	exist	VERB
ejpam-5997	8	9	inequalities	inequality	NOUN
ejpam-5997	8	10	with	with	ADP
ejpam-5997	8	11	a	a	DET
ejpam-5997	8	12	fractional	fractional	ADJ
ejpam-5997	8	13	operator	operator	NOUN
ejpam-5997	8	14	that	that	PRON
ejpam-5997	8	15	has	have	AUX
ejpam-5997	8	16	extended	extend	VERB
ejpam-5997	8	17	the	the	DET
ejpam-5997	8	18	bessel	bessel	NOUN
ejpam-5997	8	19	-	-	PUNCT
ejpam-5997	8	20	maitland	maitland	PROPN
ejpam-5997	8	21	functions	function	NOUN
ejpam-5997	8	22	as	as	ADP
ejpam-5997	8	23	a	a	DET
ejpam-5997	8	24	kernel	kernel	NOUN
ejpam-5997	8	25	,	,	PUNCT
ejpam-5997	8	26	providing	provide	VERB
ejpam-5997	8	27	a	a	DET
ejpam-5997	8	28	more	more	ADV
ejpam-5997	8	29	generalized	generalized	ADJ
ejpam-5997	8	30	framework	framework	NOUN
ejpam-5997	8	31	.	.	PUNCT
ejpam-5997	9	1	by	by	ADP
ejpam-5997	9	2	incorporating	incorporate	VERB
ejpam-5997	9	3	these	these	DET
ejpam-5997	9	4	special	special	ADJ
ejpam-5997	9	5	functions	function	NOUN
ejpam-5997	9	6	,	,	PUNCT
ejpam-5997	9	7	the	the	DET
ejpam-5997	9	8	results	result	NOUN
ejpam-5997	9	9	encompass	encompass	VERB
ejpam-5997	9	10	and	and	CCONJ
ejpam-5997	9	11	improve	improve	VERB
ejpam-5997	9	12	numerous	numerous	ADJ
ejpam-5997	9	13	classical	classical	ADJ
ejpam-5997	9	14	inequalities	inequality	NOUN
ejpam-5997	9	15	found	find	VERB
ejpam-5997	9	16	in	in	ADP
ejpam-5997	9	17	the	the	DET
ejpam-5997	9	18	literature	literature	NOUN
ejpam-5997	9	19	,	,	PUNCT
ejpam-5997	9	20	offering	offer	VERB
ejpam-5997	9	21	deeper	deep	ADJ
ejpam-5997	9	22	insights	insight	NOUN
ejpam-5997	9	23	and	and	CCONJ
ejpam-5997	9	24	broader	broad	ADJ
ejpam-5997	9	25	applicability	applicability	NOUN
ejpam-5997	9	26	in	in	ADP
ejpam-5997	9	27	mathematical	mathematical	ADJ
ejpam-5997	9	28	analysis	analysis	NOUN
ejpam-5997	9	29	.	.	PUNCT
ejpam-5997	10	1	2020	2020	NUM
ejpam-5997	10	2	mathematics	mathematic	NOUN
ejpam-5997	10	3	subject	subject	NOUN
ejpam-5997	10	4	classifications	classification	NOUN
ejpam-5997	10	5	:	:	PUNCT
ejpam-5997	10	6	9b62	9b62	NUM
ejpam-5997	10	7	,	,	PUNCT
ejpam-5997	10	8	33c10	33c10	NUM
ejpam-5997	10	9	,	,	PUNCT
ejpam-5997	10	10	26a33	26a33	NUM
ejpam-5997	10	11	key	key	ADJ
ejpam-5997	10	12	words	word	NOUN
ejpam-5997	10	13	and	and	CCONJ
ejpam-5997	10	14	phrases	phrase	NOUN
ejpam-5997	10	15	:	:	PUNCT
ejpam-5997	10	16	convex	convex	NOUN
ejpam-5997	10	17	function	function	NOUN
ejpam-5997	10	18	,	,	PUNCT
ejpam-5997	10	19	extended	extended	ADJ
ejpam-5997	10	20	bessel	bessel	NOUN
ejpam-5997	10	21	-	-	PUNCT
ejpam-5997	10	22	maitland	maitland	PROPN
ejpam-5997	10	23	function	function	NOUN
ejpam-5997	10	24	;	;	PUNCT
ejpam-5997	10	25	fractional	fractional	ADJ
ejpam-5997	10	26	operators	operator	NOUN
ejpam-5997	10	27	∗corresponding	∗corresponde	VERB
ejpam-5997	10	28	author	author	NOUN
ejpam-5997	10	29	.	.	PUNCT
ejpam-5997	11	1	doi	doi	NOUN
ejpam-5997	11	2	:	:	PUNCT
ejpam-5997	11	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5997	https://doi.org/10.29020/nybg.ejpam.v18i2.5997	ADJ
ejpam-5997	11	4	email	email	NOUN
ejpam-5997	11	5	addresses	address	NOUN
ejpam-5997	11	6	:	:	PUNCT
ejpam-5997	11	7	mjvivas@puce.edu.ec	mjvivas@puce.edu.ec	NOUN
ejpam-5997	11	8	m.	m.	NOUN
ejpam-5997	11	9	v.	v.	ADP
ejpam-5997	11	10	cortez	cortez	PROPN
ejpam-5997	11	11	)	)	PUNCT
ejpam-5997	11	12	,	,	PUNCT
ejpam-5997	11	13	rsafdar0@gmail.com	rsafdar0@gmail.com	X
ejpam-5997	11	14	(	(	PUNCT
ejpam-5997	11	15	r.	r.	PROPN
ejpam-5997	11	16	s.	s.	PROPN
ejpam-5997	11	17	ali),∗	ali),∗	PROPN
ejpam-5997	11	18	,	,	PUNCT
ejpam-5997	11	19	20nailatalib@gmail.com	20nailatalib@gmail.com	PROPN
ejpam-5997	11	20	n.	n.	PROPN
ejpam-5997	11	21	talib	talib	PROPN
ejpam-5997	11	22	)	)	PUNCT
ejpam-5997	11	23	,	,	PUNCT
ejpam-5997	11	24	eqabaeli@kku.edu.sa	eqabaeli@kku.edu.sa	PROPN
ejpam-5997	11	25	(	(	PUNCT
ejpam-5997	11	26	i.	i.	PROPN
ejpam-5997	11	27	kebaili	kebaili	PROPN
ejpam-5997	11	28	)	)	PUNCT
ejpam-5997	11	29	,	,	PUNCT
ejpam-5997	11	30	eakhdar@kku.edu.sa	eakhdar@kku.edu.sa	PROPN
ejpam-5997	11	31	i.	i.	PROPN
ejpam-5997	11	32	boukhris	boukhris	PROPN
ejpam-5997	11	33	)	)	PUNCT
ejpam-5997	11	34	,	,	PUNCT
ejpam-5997	11	35	gauhar55uom@gmail	gauhar55uom@gmail	NOUN
ejpam-5997	11	36	(	(	PUNCT
ejpam-5997	11	37	g.	g.	PROPN
ejpam-5997	11	38	rahman	rahman	PROPN
ejpam-5997	11	39	)	)	PUNCT
ejpam-5997	11	40	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5997	12	1	1	1	NUM
ejpam-5997	12	2	copyright	copyright	NOUN
ejpam-5997	12	3	:	:	PUNCT
ejpam-5997	12	4	©	©	PROPN
ejpam-5997	12	5	2025	2025	NUM
ejpam-5997	12	6	the	the	DET
ejpam-5997	12	7	author(s	author(s	NOUN
ejpam-5997	12	8	)	)	PUNCT
ejpam-5997	12	9	.	.	PUNCT
ejpam-5997	13	1	(	(	PUNCT
ejpam-5997	13	2	cc	cc	NOUN
ejpam-5997	13	3	by	by	ADP
ejpam-5997	13	4	-	-	PUNCT
ejpam-5997	13	5	nc	nc	PROPN
ejpam-5997	13	6	4.0	4.0	NUM
ejpam-5997	13	7	)	)	PUNCT
ejpam-5997	13	8	m.	m.	NOUN
ejpam-5997	13	9	vivas	vivas	PROPN
ejpam-5997	13	10	-	-	PROPN
ejpam-5997	13	11	cortez	cortez	PROPN
ejpam-5997	13	12	et	et	PROPN
ejpam-5997	13	13	al	al	PROPN
ejpam-5997	13	14	.	.	PUNCT
ejpam-5997	13	15	/	/	SYM
ejpam-5997	13	16	eur	eur	PROPN
ejpam-5997	13	17	.	.	PUNCT
ejpam-5997	14	1	j.	j.	PROPN
ejpam-5997	14	2	pure	pure	PROPN
ejpam-5997	14	3	appl	appl	PROPN
ejpam-5997	14	4	.	.	PROPN
ejpam-5997	14	5	math	math	PROPN
ejpam-5997	14	6	,	,	PUNCT
ejpam-5997	14	7	18	18	NUM
ejpam-5997	14	8	(	(	PUNCT
ejpam-5997	14	9	2	2	NUM
ejpam-5997	14	10	)	)	PUNCT
ejpam-5997	14	11	(	(	PUNCT
ejpam-5997	14	12	2025	2025	NUM
ejpam-5997	14	13	)	)	PUNCT
ejpam-5997	14	14	,	,	PUNCT
ejpam-5997	14	15	5997	5997	NUM
ejpam-5997	14	16	2	2	NUM
ejpam-5997	14	17	of	of	ADP
ejpam-5997	14	18	23	23	NUM
ejpam-5997	14	19	1	1	NUM
ejpam-5997	14	20	.	.	PUNCT
ejpam-5997	15	1	introduction	introduction	NOUN
ejpam-5997	15	2	mathematical	mathematical	ADJ
ejpam-5997	15	3	inequalities	inequality	NOUN
ejpam-5997	15	4	are	be	AUX
ejpam-5997	15	5	now	now	ADV
ejpam-5997	15	6	widely	widely	ADV
ejpam-5997	15	7	recognized	recognize	VERB
ejpam-5997	15	8	as	as	ADP
ejpam-5997	15	9	one	one	NUM
ejpam-5997	15	10	of	of	ADP
ejpam-5997	15	11	the	the	DET
ejpam-5997	15	12	most	most	ADV
ejpam-5997	15	13	valuable	valuable	ADJ
ejpam-5997	15	14	and	and	CCONJ
ejpam-5997	15	15	applicable	applicable	ADJ
ejpam-5997	15	16	branches	branch	NOUN
ejpam-5997	15	17	of	of	ADP
ejpam-5997	15	18	mathematics	mathematic	NOUN
ejpam-5997	15	19	.	.	PUNCT
ejpam-5997	16	1	their	their	PRON
ejpam-5997	16	2	versatility	versatility	NOUN
ejpam-5997	16	3	and	and	CCONJ
ejpam-5997	16	4	effectiveness	effectiveness	NOUN
ejpam-5997	16	5	have	have	AUX
ejpam-5997	16	6	been	be	AUX
ejpam-5997	16	7	demonstrated	demonstrate	VERB
ejpam-5997	16	8	in	in	ADP
ejpam-5997	16	9	various	various	ADJ
ejpam-5997	16	10	scientific	scientific	ADJ
ejpam-5997	16	11	and	and	CCONJ
ejpam-5997	16	12	engineering	engineering	NOUN
ejpam-5997	16	13	disciplines	discipline	NOUN
ejpam-5997	16	14	,	,	PUNCT
ejpam-5997	16	15	with	with	ADP
ejpam-5997	16	16	significant	significant	ADJ
ejpam-5997	16	17	applications	application	NOUN
ejpam-5997	16	18	in	in	ADP
ejpam-5997	16	19	information	information	NOUN
ejpam-5997	16	20	theory	theory	NOUN
ejpam-5997	16	21	,	,	PUNCT
ejpam-5997	16	22	economics	economic	NOUN
ejpam-5997	16	23	,	,	PUNCT
ejpam-5997	16	24	finance	finance	NOUN
ejpam-5997	16	25	,	,	PUNCT
ejpam-5997	16	26	and	and	CCONJ
ejpam-5997	16	27	engineering	engineering	NOUN
ejpam-5997	16	28	.	.	PUNCT
ejpam-5997	17	1	the	the	DET
ejpam-5997	17	2	theory	theory	NOUN
ejpam-5997	17	3	of	of	ADP
ejpam-5997	17	4	inequalities	inequality	NOUN
ejpam-5997	17	5	plays	play	VERB
ejpam-5997	17	6	a	a	DET
ejpam-5997	17	7	fundamental	fundamental	ADJ
ejpam-5997	17	8	role	role	NOUN
ejpam-5997	17	9	in	in	ADP
ejpam-5997	17	10	nearly	nearly	ADV
ejpam-5997	17	11	all	all	PRON
ejpam-5997	17	12	areas	area	NOUN
ejpam-5997	17	13	of	of	ADP
ejpam-5997	17	14	pure	pure	ADJ
ejpam-5997	17	15	and	and	CCONJ
ejpam-5997	17	16	applied	applied	ADJ
ejpam-5997	17	17	mathematics	mathematic	NOUN
ejpam-5997	17	18	.	.	PUNCT
ejpam-5997	18	1	the	the	DET
ejpam-5997	18	2	study	study	NOUN
ejpam-5997	18	3	of	of	ADP
ejpam-5997	18	4	convex	convex	NOUN
ejpam-5997	18	5	functions	function	NOUN
ejpam-5997	18	6	has	have	AUX
ejpam-5997	18	7	been	be	AUX
ejpam-5997	18	8	instrumental	instrumental	ADJ
ejpam-5997	18	9	in	in	ADP
ejpam-5997	18	10	advancing	advance	VERB
ejpam-5997	18	11	inequality	inequality	NOUN
ejpam-5997	18	12	theory	theory	NOUN
ejpam-5997	18	13	,	,	PUNCT
ejpam-5997	18	14	tracing	trace	VERB
ejpam-5997	18	15	back	back	ADV
ejpam-5997	18	16	to	to	ADP
ejpam-5997	18	17	the	the	DET
ejpam-5997	18	18	pioneering	pioneering	ADJ
ejpam-5997	18	19	work	work	NOUN
ejpam-5997	18	20	of	of	ADP
ejpam-5997	18	21	jensen	jensen	PROPN
ejpam-5997	18	22	in	in	ADP
ejpam-5997	18	23	1905–1906	1905–1906	NUM
ejpam-5997	18	24	.	.	PUNCT
ejpam-5997	19	1	many	many	ADJ
ejpam-5997	19	2	modern	modern	ADJ
ejpam-5997	19	3	analytical	analytical	ADJ
ejpam-5997	19	4	inequalities	inequality	NOUN
ejpam-5997	19	5	stem	stem	VERB
ejpam-5997	19	6	directly	directly	ADV
ejpam-5997	19	7	from	from	ADP
ejpam-5997	19	8	the	the	DET
ejpam-5997	19	9	properties	property	NOUN
ejpam-5997	19	10	of	of	ADP
ejpam-5997	19	11	convex	convex	NOUN
ejpam-5997	19	12	functions	function	NOUN
ejpam-5997	19	13	.	.	PUNCT
ejpam-5997	20	1	in	in	ADP
ejpam-5997	20	2	addition	addition	NOUN
ejpam-5997	20	3	,	,	PUNCT
ejpam-5997	20	4	convex	convex	NOUN
ejpam-5997	20	5	functions	function	NOUN
ejpam-5997	20	6	and	and	CCONJ
ejpam-5997	20	7	various	various	ADJ
ejpam-5997	20	8	forms	form	NOUN
ejpam-5997	20	9	of	of	ADP
ejpam-5997	20	10	convexity	convexity	NOUN
ejpam-5997	20	11	serve	serve	NOUN
ejpam-5997	20	12	as	as	ADP
ejpam-5997	20	13	powerful	powerful	ADJ
ejpam-5997	20	14	tools	tool	NOUN
ejpam-5997	20	15	to	to	PART
ejpam-5997	20	16	derive	derive	VERB
ejpam-5997	20	17	numerous	numerous	ADJ
ejpam-5997	20	18	important	important	ADJ
ejpam-5997	20	19	and	and	CCONJ
ejpam-5997	20	20	practical	practical	ADJ
ejpam-5997	20	21	inequalities	inequality	NOUN
ejpam-5997	20	22	.	.	PUNCT
ejpam-5997	21	1	due	due	ADP
ejpam-5997	21	2	to	to	ADP
ejpam-5997	21	3	its	its	PRON
ejpam-5997	21	4	expanding	expand	VERB
ejpam-5997	21	5	range	range	NOUN
ejpam-5997	21	6	of	of	ADP
ejpam-5997	21	7	applications	application	NOUN
ejpam-5997	21	8	,	,	PUNCT
ejpam-5997	21	9	the	the	DET
ejpam-5997	21	10	study	study	NOUN
ejpam-5997	21	11	of	of	ADP
ejpam-5997	21	12	inequalities	inequality	NOUN
ejpam-5997	21	13	remains	remain	VERB
ejpam-5997	21	14	one	one	NUM
ejpam-5997	21	15	of	of	ADP
ejpam-5997	21	16	the	the	DET
ejpam-5997	21	17	most	most	ADV
ejpam-5997	21	18	actively	actively	ADV
ejpam-5997	21	19	researched	research	VERB
ejpam-5997	21	20	fields	field	NOUN
ejpam-5997	21	21	in	in	ADP
ejpam-5997	21	22	mathematical	mathematical	ADJ
ejpam-5997	21	23	analysis	analysis	NOUN
ejpam-5997	21	24	.	.	PUNCT
ejpam-5997	22	1	the	the	DET
ejpam-5997	22	2	broad	broad	ADJ
ejpam-5997	22	3	spectrum	spectrum	NOUN
ejpam-5997	22	4	of	of	ADP
ejpam-5997	22	5	applications	application	NOUN
ejpam-5997	22	6	of	of	ADP
ejpam-5997	22	7	fractional	fractional	ADJ
ejpam-5997	22	8	calculus	calculus	NOUN
ejpam-5997	22	9	[	[	X
ejpam-5997	22	10	1	1	NUM
ejpam-5997	22	11	]	]	PUNCT
ejpam-5997	22	12	in	in	ADP
ejpam-5997	22	13	domains	domain	NOUN
ejpam-5997	22	14	such	such	ADJ
ejpam-5997	22	15	as	as	ADP
ejpam-5997	22	16	fluid	fluid	ADJ
ejpam-5997	22	17	dynamics	dynamic	NOUN
ejpam-5997	22	18	,	,	PUNCT
ejpam-5997	22	19	mathematical	mathematical	ADJ
ejpam-5997	22	20	biology	biology	NOUN
ejpam-5997	22	21	,	,	PUNCT
ejpam-5997	22	22	and	and	CCONJ
ejpam-5997	22	23	mathematical	mathematical	ADJ
ejpam-5997	22	24	physics	physics	NOUN
ejpam-5997	22	25	has	have	AUX
ejpam-5997	22	26	made	make	VERB
ejpam-5997	22	27	it	it	PRON
ejpam-5997	22	28	an	an	DET
ejpam-5997	22	29	essential	essential	ADJ
ejpam-5997	22	30	field	field	NOUN
ejpam-5997	22	31	of	of	ADP
ejpam-5997	22	32	ongoing	ongoing	ADJ
ejpam-5997	22	33	research	research	NOUN
ejpam-5997	22	34	[	[	X
ejpam-5997	22	35	2–5	2–5	X
ejpam-5997	22	36	]	]	PUNCT
ejpam-5997	22	37	.	.	PUNCT
ejpam-5997	23	1	in	in	ADP
ejpam-5997	23	2	order	order	NOUN
ejpam-5997	23	3	to	to	PART
ejpam-5997	23	4	validate	validate	VERB
ejpam-5997	23	5	various	various	ADJ
ejpam-5997	23	6	solutions	solution	NOUN
ejpam-5997	23	7	in	in	ADP
ejpam-5997	23	8	theoretical	theoretical	ADJ
ejpam-5997	23	9	and	and	CCONJ
ejpam-5997	23	10	practical	practical	ADJ
ejpam-5997	23	11	contexts	context	NOUN
ejpam-5997	23	12	,	,	PUNCT
ejpam-5997	23	13	numerous	numerous	ADJ
ejpam-5997	23	14	researchers	researcher	NOUN
ejpam-5997	23	15	have	have	AUX
ejpam-5997	23	16	generated	generate	VERB
ejpam-5997	23	17	fractional	fractional	ADJ
ejpam-5997	23	18	integral	integral	ADJ
ejpam-5997	23	19	inequalities	inequality	NOUN
ejpam-5997	23	20	using	use	VERB
ejpam-5997	23	21	fractional	fractional	ADJ
ejpam-5997	23	22	operators	operator	NOUN
ejpam-5997	23	23	[	[	X
ejpam-5997	23	24	6	6	NUM
ejpam-5997	23	25	,	,	PUNCT
ejpam-5997	23	26	7	7	NUM
ejpam-5997	23	27	]	]	PUNCT
ejpam-5997	23	28	.	.	PUNCT
ejpam-5997	24	1	recent	recent	ADJ
ejpam-5997	24	2	research	research	NOUN
ejpam-5997	24	3	has	have	AUX
ejpam-5997	24	4	explored	explore	VERB
ejpam-5997	24	5	fractional	fractional	ADJ
ejpam-5997	24	6	integral	integral	ADJ
ejpam-5997	24	7	inequalities	inequality	NOUN
ejpam-5997	24	8	in	in	ADP
ejpam-5997	24	9	extensive	extensive	ADJ
ejpam-5997	24	10	detail	detail	NOUN
ejpam-5997	24	11	,	,	PUNCT
ejpam-5997	24	12	examining	examine	VERB
ejpam-5997	24	13	their	their	PRON
ejpam-5997	24	14	various	various	ADJ
ejpam-5997	24	15	manifestations	manifestation	NOUN
ejpam-5997	24	16	and	and	CCONJ
ejpam-5997	24	17	possible	possible	ADJ
ejpam-5997	24	18	uses	use	NOUN
ejpam-5997	24	19	.	.	PUNCT
ejpam-5997	25	1	these	these	DET
ejpam-5997	25	2	studies	study	NOUN
ejpam-5997	25	3	have	have	AUX
ejpam-5997	25	4	tremendously	tremendously	ADV
ejpam-5997	25	5	broadened	broaden	VERB
ejpam-5997	25	6	the	the	DET
ejpam-5997	25	7	discipline	discipline	NOUN
ejpam-5997	25	8	and	and	CCONJ
ejpam-5997	25	9	provided	provide	VERB
ejpam-5997	25	10	new	new	ADJ
ejpam-5997	25	11	tools	tool	NOUN
ejpam-5997	25	12	and	and	CCONJ
ejpam-5997	25	13	insights	insight	NOUN
ejpam-5997	25	14	.	.	PUNCT
ejpam-5997	26	1	a	a	DET
ejpam-5997	26	2	notable	notable	ADJ
ejpam-5997	26	3	advancement	advancement	NOUN
ejpam-5997	26	4	in	in	ADP
ejpam-5997	26	5	this	this	DET
ejpam-5997	26	6	field	field	NOUN
ejpam-5997	26	7	is	be	AUX
ejpam-5997	26	8	the	the	DET
ejpam-5997	26	9	formulation	formulation	NOUN
ejpam-5997	26	10	of	of	ADP
ejpam-5997	26	11	integral	integral	ADJ
ejpam-5997	26	12	expressions	expression	NOUN
ejpam-5997	26	13	that	that	PRON
ejpam-5997	26	14	include	include	VERB
ejpam-5997	26	15	special	special	ADJ
ejpam-5997	26	16	functions	function	NOUN
ejpam-5997	26	17	.	.	PUNCT
ejpam-5997	27	1	fractional	fractional	ADJ
ejpam-5997	27	2	integral	integral	ADJ
ejpam-5997	27	3	operators	operator	NOUN
ejpam-5997	27	4	that	that	PRON
ejpam-5997	27	5	utilize	utilize	VERB
ejpam-5997	27	6	particular	particular	ADJ
ejpam-5997	27	7	kernel	kernel	NOUN
ejpam-5997	27	8	functions	function	NOUN
ejpam-5997	27	9	are	be	AUX
ejpam-5997	27	10	essential	essential	ADJ
ejpam-5997	27	11	in	in	ADP
ejpam-5997	27	12	many	many	ADJ
ejpam-5997	27	13	fields	field	NOUN
ejpam-5997	27	14	of	of	ADP
ejpam-5997	27	15	study	study	NOUN
ejpam-5997	27	16	[	[	X
ejpam-5997	27	17	8	8	NUM
ejpam-5997	27	18	,	,	PUNCT
ejpam-5997	27	19	9	9	NUM
ejpam-5997	27	20	]	]	PUNCT
ejpam-5997	27	21	.	.	PUNCT
ejpam-5997	28	1	the	the	DET
ejpam-5997	28	2	bessel	bessel	NOUN
ejpam-5997	28	3	-	-	PUNCT
ejpam-5997	28	4	maitland	maitland	PROPN
ejpam-5997	28	5	function	function	NOUN
ejpam-5997	28	6	,	,	PUNCT
ejpam-5997	28	7	first	first	ADV
ejpam-5997	28	8	proposed	propose	VERB
ejpam-5997	28	9	by	by	ADP
ejpam-5997	28	10	daniel	daniel	PROPN
ejpam-5997	28	11	bernoulli	bernoulli	PROPN
ejpam-5997	28	12	,	,	PUNCT
ejpam-5997	28	13	is	be	AUX
ejpam-5997	28	14	related	relate	VERB
ejpam-5997	28	15	to	to	ADP
ejpam-5997	28	16	the	the	DET
ejpam-5997	28	17	linear	linear	ADJ
ejpam-5997	28	18	differential	differential	NOUN
ejpam-5997	28	19	equation	equation	NOUN
ejpam-5997	28	20	.	.	PUNCT
ejpam-5997	29	1	the	the	DET
ejpam-5997	29	2	fractional	fractional	ADJ
ejpam-5997	29	3	calculus	calculus	NOUN
ejpam-5997	29	4	,	,	PUNCT
ejpam-5997	29	5	with	with	ADP
ejpam-5997	29	6	its	its	PRON
ejpam-5997	29	7	extensive	extensive	ADJ
ejpam-5997	29	8	applications	application	NOUN
ejpam-5997	29	9	,	,	PUNCT
ejpam-5997	29	10	extends	extend	VERB
ejpam-5997	29	11	its	its	PRON
ejpam-5997	29	12	scope	scope	NOUN
ejpam-5997	29	13	.	.	PUNCT
ejpam-5997	30	1	mathematical	mathematical	ADJ
ejpam-5997	30	2	analysis	analysis	NOUN
ejpam-5997	30	3	and	and	CCONJ
ejpam-5997	30	4	fractional	fractional	ADJ
ejpam-5997	30	5	theory	theory	NOUN
ejpam-5997	30	6	have	have	AUX
ejpam-5997	30	7	greatly	greatly	ADV
ejpam-5997	30	8	benefited	benefit	VERB
ejpam-5997	30	9	from	from	ADP
ejpam-5997	30	10	its	its	PRON
ejpam-5997	30	11	extensions	extension	NOUN
ejpam-5997	30	12	.	.	PUNCT
ejpam-5997	31	1	more	more	ADJ
ejpam-5997	31	2	research	research	NOUN
ejpam-5997	31	3	and	and	CCONJ
ejpam-5997	31	4	development	development	NOUN
ejpam-5997	31	5	in	in	ADP
ejpam-5997	31	6	the	the	DET
ejpam-5997	31	7	topic	topic	NOUN
ejpam-5997	31	8	is	be	AUX
ejpam-5997	31	9	being	be	AUX
ejpam-5997	31	10	motivated	motivate	VERB
ejpam-5997	31	11	by	by	ADP
ejpam-5997	31	12	quick	quick	ADJ
ejpam-5997	31	13	developments	development	NOUN
ejpam-5997	31	14	in	in	ADP
ejpam-5997	31	15	fractional	fractional	ADJ
ejpam-5997	31	16	calculus	calculus	NOUN
ejpam-5997	31	17	,	,	PUNCT
ejpam-5997	31	18	which	which	PRON
ejpam-5997	31	19	have	have	AUX
ejpam-5997	31	20	brought	bring	VERB
ejpam-5997	31	21	attention	attention	NOUN
ejpam-5997	31	22	to	to	ADP
ejpam-5997	31	23	the	the	DET
ejpam-5997	31	24	need	need	NOUN
ejpam-5997	31	25	for	for	ADP
ejpam-5997	31	26	creative	creative	ADJ
ejpam-5997	31	27	transformations	transformation	NOUN
ejpam-5997	31	28	and	and	CCONJ
ejpam-5997	31	29	generalized	generalize	VERB
ejpam-5997	31	30	fractional	fractional	ADJ
ejpam-5997	31	31	operators	operator	NOUN
ejpam-5997	31	32	.	.	PUNCT
ejpam-5997	32	1	convex	convex	VERB
ejpam-5997	32	2	analysis	analysis	NOUN
ejpam-5997	32	3	plays	play	VERB
ejpam-5997	32	4	a	a	DET
ejpam-5997	32	5	crucial	crucial	ADJ
ejpam-5997	32	6	role	role	NOUN
ejpam-5997	32	7	in	in	ADP
ejpam-5997	32	8	variational	variational	ADJ
ejpam-5997	32	9	analysis	analysis	NOUN
ejpam-5997	32	10	,	,	PUNCT
ejpam-5997	32	11	as	as	SCONJ
ejpam-5997	32	12	it	it	PRON
ejpam-5997	32	13	encompasses	encompass	VERB
ejpam-5997	32	14	a	a	DET
ejpam-5997	32	15	generalized	generalized	ADJ
ejpam-5997	32	16	differentiation	differentiation	NOUN
ejpam-5997	32	17	theory	theory	NOUN
ejpam-5997	32	18	applicable	applicable	ADJ
ejpam-5997	32	19	to	to	ADP
ejpam-5997	32	20	mathematical	mathematical	ADJ
ejpam-5997	32	21	models	model	NOUN
ejpam-5997	32	22	that	that	PRON
ejpam-5997	32	23	do	do	AUX
ejpam-5997	32	24	not	not	PART
ejpam-5997	32	25	require	require	VERB
ejpam-5997	32	26	differentiability	differentiability	NOUN
ejpam-5997	32	27	assumptions	assumption	NOUN
ejpam-5997	32	28	.	.	PUNCT
ejpam-5997	33	1	convex	convex	NOUN
ejpam-5997	33	2	optimization	optimization	NOUN
ejpam-5997	33	3	is	be	AUX
ejpam-5997	33	4	well	well	ADV
ejpam-5997	33	5	known	known	ADJ
ejpam-5997	33	6	to	to	PART
ejpam-5997	33	7	be	be	AUX
ejpam-5997	33	8	just	just	ADV
ejpam-5997	33	9	one	one	NUM
ejpam-5997	33	10	of	of	ADP
ejpam-5997	33	11	many	many	ADJ
ejpam-5997	33	12	areas	area	NOUN
ejpam-5997	33	13	in	in	ADP
ejpam-5997	33	14	which	which	PRON
ejpam-5997	33	15	convex	convex	NOUN
ejpam-5997	33	16	analysis	analysis	NOUN
ejpam-5997	33	17	has	have	AUX
ejpam-5997	33	18	demonstrated	demonstrate	VERB
ejpam-5997	33	19	its	its	PRON
ejpam-5997	33	20	significance	significance	NOUN
ejpam-5997	33	21	.	.	PUNCT
ejpam-5997	34	1	the	the	DET
ejpam-5997	34	2	convexity	convexity	NOUN
ejpam-5997	34	3	of	of	ADP
ejpam-5997	34	4	a	a	DET
ejpam-5997	34	5	problem	problem	NOUN
ejpam-5997	34	6	allows	allow	VERB
ejpam-5997	34	7	for	for	SCONJ
ejpam-5997	34	8	the	the	DET
ejpam-5997	34	9	development	development	NOUN
ejpam-5997	34	10	of	of	ADP
ejpam-5997	34	11	efficient	efficient	ADJ
ejpam-5997	34	12	numerical	numerical	ADJ
ejpam-5997	34	13	algorithms	algorithm	NOUN
ejpam-5997	34	14	to	to	PART
ejpam-5997	34	15	solve	solve	VERB
ejpam-5997	34	16	convex	convex	NOUN
ejpam-5997	34	17	optimization	optimization	NOUN
ejpam-5997	34	18	problems	problem	NOUN
ejpam-5997	34	19	,	,	PUNCT
ejpam-5997	34	20	even	even	ADV
ejpam-5997	34	21	in	in	ADP
ejpam-5997	34	22	the	the	DET
ejpam-5997	34	23	presence	presence	NOUN
ejpam-5997	34	24	of	of	ADP
ejpam-5997	34	25	non	non	ADJ
ejpam-5997	34	26	-	-	ADJ
ejpam-5997	34	27	differentiable	differentiable	ADJ
ejpam-5997	34	28	data	datum	NOUN
ejpam-5997	34	29	,	,	PUNCT
ejpam-5997	34	30	while	while	SCONJ
ejpam-5997	34	31	also	also	ADV
ejpam-5997	34	32	enabling	enable	VERB
ejpam-5997	34	33	an	an	DET
ejpam-5997	34	34	in	in	ADP
ejpam-5997	34	35	-	-	PUNCT
ejpam-5997	34	36	depth	depth	NOUN
ejpam-5997	34	37	study	study	NOUN
ejpam-5997	34	38	of	of	ADP
ejpam-5997	34	39	the	the	DET
ejpam-5997	34	40	qualitative	qualitative	ADJ
ejpam-5997	34	41	properties	property	NOUN
ejpam-5997	34	42	of	of	ADP
ejpam-5997	34	43	optimal	optimal	ADJ
ejpam-5997	34	44	solutions	solution	NOUN
ejpam-5997	34	45	.	.	PUNCT
ejpam-5997	35	1	the	the	DET
ejpam-5997	35	2	impact	impact	NOUN
ejpam-5997	35	3	of	of	ADP
ejpam-5997	35	4	convex	convex	ADJ
ejpam-5997	35	5	analysis	analysis	NOUN
ejpam-5997	35	6	and	and	CCONJ
ejpam-5997	35	7	optimization	optimization	NOUN
ejpam-5997	35	8	continues	continue	VERB
ejpam-5997	35	9	to	to	PART
ejpam-5997	35	10	expand	expand	VERB
ejpam-5997	35	11	across	across	ADP
ejpam-5997	35	12	various	various	ADJ
ejpam-5997	35	13	mathematical	mathematical	ADJ
ejpam-5997	35	14	disciplines	discipline	NOUN
ejpam-5997	35	15	and	and	CCONJ
ejpam-5997	35	16	practical	practical	ADJ
ejpam-5997	35	17	applications	application	NOUN
ejpam-5997	35	18	,	,	PUNCT
ejpam-5997	35	19	including	include	VERB
ejpam-5997	35	20	estimation	estimation	NOUN
ejpam-5997	35	21	,	,	PUNCT
ejpam-5997	35	22	control	control	NOUN
ejpam-5997	35	23	systems	system	NOUN
ejpam-5997	35	24	,	,	PUNCT
ejpam-5997	35	25	communications	communication	NOUN
ejpam-5997	35	26	,	,	PUNCT
ejpam-5997	35	27	networks	network	NOUN
ejpam-5997	35	28	,	,	PUNCT
ejpam-5997	35	29	signal	signal	ADJ
ejpam-5997	35	30	processing	processing	NOUN
ejpam-5997	35	31	,	,	PUNCT
ejpam-5997	35	32	data	datum	NOUN
ejpam-5997	35	33	analysis	analysis	NOUN
ejpam-5997	35	34	,	,	PUNCT
ejpam-5997	35	35	electrical	electrical	ADJ
ejpam-5997	35	36	circuit	circuit	NOUN
ejpam-5997	35	37	design	design	NOUN
ejpam-5997	35	38	,	,	PUNCT
ejpam-5997	35	39	finance	finance	NOUN
ejpam-5997	35	40	,	,	PUNCT
ejpam-5997	35	41	statistics	statistic	NOUN
ejpam-5997	35	42	,	,	PUNCT
ejpam-5997	35	43	economics	economic	NOUN
ejpam-5997	35	44	,	,	PUNCT
ejpam-5997	35	45	and	and	CCONJ
ejpam-5997	35	46	mathematical	mathematical	ADJ
ejpam-5997	35	47	modeling.inequalities	modeling.inequalitie	NOUN
ejpam-5997	35	48	have	have	VERB
ejpam-5997	35	49	applications	application	NOUN
ejpam-5997	35	50	as	as	ADP
ejpam-5997	35	51	tools	tool	NOUN
ejpam-5997	35	52	in	in	ADP
ejpam-5997	35	53	various	various	ADJ
ejpam-5997	35	54	fields	field	NOUN
ejpam-5997	35	55	of	of	ADP
ejpam-5997	35	56	mathematics	mathematic	NOUN
ejpam-5997	35	57	,	,	PUNCT
ejpam-5997	35	58	such	such	ADJ
ejpam-5997	35	59	as	as	ADP
ejpam-5997	35	60	differential	differential	ADJ
ejpam-5997	35	61	and	and	CCONJ
ejpam-5997	35	62	integral	integral	ADJ
ejpam-5997	35	63	equations	equation	NOUN
ejpam-5997	35	64	,	,	PUNCT
ejpam-5997	35	65	and	and	CCONJ
ejpam-5997	35	66	these	these	DET
ejpam-5997	35	67	ideas	idea	NOUN
ejpam-5997	35	68	serve	serve	VERB
ejpam-5997	35	69	as	as	ADP
ejpam-5997	35	70	a	a	DET
ejpam-5997	35	71	basis	basis	NOUN
ejpam-5997	35	72	for	for	ADP
ejpam-5997	35	73	their	their	PRON
ejpam-5997	35	74	analysis	analysis	NOUN
ejpam-5997	35	75	.	.	PUNCT
ejpam-5997	36	1	one	one	NUM
ejpam-5997	36	2	of	of	ADP
ejpam-5997	36	3	the	the	DET
ejpam-5997	36	4	most	most	ADV
ejpam-5997	36	5	well	well	ADV
ejpam-5997	36	6	-	-	PUNCT
ejpam-5997	36	7	known	know	VERB
ejpam-5997	36	8	inequalities	inequality	NOUN
ejpam-5997	36	9	is	be	AUX
ejpam-5997	36	10	the	the	DET
ejpam-5997	36	11	hermite	hermite	PROPN
ejpam-5997	36	12	-	-	PUNCT
ejpam-5997	36	13	hadamard	hadamard	ADJ
ejpam-5997	36	14	inequality	inequality	NOUN
ejpam-5997	36	15	,	,	PUNCT
ejpam-5997	36	16	which	which	PRON
ejpam-5997	36	17	was	be	AUX
ejpam-5997	36	18	first	first	ADV
ejpam-5997	36	19	introduced	introduce	VERB
ejpam-5997	36	20	by	by	ADP
ejpam-5997	36	21	charles	charle	NOUN
ejpam-5997	36	22	hermite	hermite	PROPN
ejpam-5997	36	23	and	and	CCONJ
ejpam-5997	36	24	jacques	jacques	PROPN
ejpam-5997	36	25	hadamard	hadamard	PROPN
ejpam-5997	36	26	and	and	CCONJ
ejpam-5997	36	27	describes	describe	VERB
ejpam-5997	36	28	how	how	SCONJ
ejpam-5997	36	29	conm	conm	VERB
ejpam-5997	36	30	.	.	PUNCT
ejpam-5997	37	1	vivas	vivas	PROPN
ejpam-5997	37	2	-	-	NOUN
ejpam-5997	37	3	cortez	cortez	PROPN
ejpam-5997	37	4	et	et	PROPN
ejpam-5997	37	5	al	al	PROPN
ejpam-5997	37	6	.	.	PUNCT
ejpam-5997	37	7	/	/	SYM
ejpam-5997	37	8	eur	eur	PROPN
ejpam-5997	37	9	.	.	PUNCT
ejpam-5997	38	1	j.	j.	PROPN
ejpam-5997	38	2	pure	pure	PROPN
ejpam-5997	38	3	appl	appl	PROPN
ejpam-5997	38	4	.	.	PROPN
ejpam-5997	38	5	math	math	PROPN
ejpam-5997	38	6	,	,	PUNCT
ejpam-5997	38	7	18	18	NUM
ejpam-5997	38	8	(	(	PUNCT
ejpam-5997	38	9	2	2	NUM
ejpam-5997	38	10	)	)	PUNCT
ejpam-5997	38	11	(	(	PUNCT
ejpam-5997	38	12	2025	2025	NUM
ejpam-5997	38	13	)	)	PUNCT
ejpam-5997	38	14	,	,	PUNCT
ejpam-5997	38	15	5997	5997	NUM
ejpam-5997	38	16	3	3	NUM
ejpam-5997	38	17	of	of	ADP
ejpam-5997	38	18	23	23	NUM
ejpam-5997	38	19	vex	vex	NOUN
ejpam-5997	38	20	functions	function	NOUN
ejpam-5997	38	21	behave	behave	VERB
ejpam-5997	38	22	and	and	CCONJ
ejpam-5997	38	23	is	be	AUX
ejpam-5997	38	24	used	use	VERB
ejpam-5997	38	25	extensively	extensively	ADV
ejpam-5997	38	26	in	in	ADP
ejpam-5997	38	27	mathematical	mathematical	ADJ
ejpam-5997	38	28	modeling	modeling	NOUN
ejpam-5997	38	29	,	,	PUNCT
ejpam-5997	38	30	optimization	optimization	NOUN
ejpam-5997	38	31	,	,	PUNCT
ejpam-5997	38	32	and	and	CCONJ
ejpam-5997	38	33	numerical	numerical	ADJ
ejpam-5997	38	34	analysis	analysis	NOUN
ejpam-5997	38	35	.	.	PUNCT
ejpam-5997	39	1	in	in	ADP
ejpam-5997	39	2	recent	recent	ADJ
ejpam-5997	39	3	years	year	NOUN
ejpam-5997	39	4	the	the	DET
ejpam-5997	39	5	researchers	researcher	NOUN
ejpam-5997	39	6	have	have	AUX
ejpam-5997	39	7	extended	extend	VERB
ejpam-5997	39	8	the	the	DET
ejpam-5997	39	9	classical	classical	ADJ
ejpam-5997	39	10	convexity	convexity	NOUN
ejpam-5997	39	11	into	into	ADP
ejpam-5997	39	12	h	h	NOUN
ejpam-5997	39	13	-	-	PUNCT
ejpam-5997	39	14	convexity	convexity	NOUN
ejpam-5997	39	15	,	,	PUNCT
ejpam-5997	39	16	h	h	NOUN
ejpam-5997	39	17	-	-	PUNCT
ejpam-5997	39	18	godunova	godunova	ADJ
ejpam-5997	39	19	-	-	PUNCT
ejpam-5997	39	20	levin	levin	PROPN
ejpam-5997	39	21	convexity	convexity	NOUN
ejpam-5997	39	22	,	,	PUNCT
ejpam-5997	39	23	s	s	NOUN
ejpam-5997	39	24	-	-	NOUN
ejpam-5997	39	25	convexity	convexity	NOUN
ejpam-5997	39	26	and	and	CCONJ
ejpam-5997	39	27	(	(	PUNCT
ejpam-5997	39	28	η1	η1	NOUN
ejpam-5997	39	29	,	,	PUNCT
ejpam-5997	39	30	η2	η2	ADJ
ejpam-5997	39	31	)	)	PUNCT
ejpam-5997	39	32	convex	convex	NOUN
ejpam-5997	39	33	functions	function	NOUN
ejpam-5997	39	34	etc	etc	X
ejpam-5997	39	35	.	.	X
ejpam-5997	40	1	for	for	ADP
ejpam-5997	40	2	s	s	NOUN
ejpam-5997	40	3	-	-	PUNCT
ejpam-5997	40	4	convex	convex	NOUN
ejpam-5997	40	5	functions	function	NOUN
ejpam-5997	40	6	,	,	PUNCT
ejpam-5997	40	7	the	the	DET
ejpam-5997	40	8	integral	integral	ADJ
ejpam-5997	40	9	identities	identity	NOUN
ejpam-5997	40	10	linked	link	VERB
ejpam-5997	40	11	to	to	ADP
ejpam-5997	40	12	hermite	hermite	PROPN
ejpam-5997	40	13	-	-	PUNCT
ejpam-5997	40	14	hadamard	hadamard	ADJ
ejpam-5997	40	15	inequality	inequality	NOUN
ejpam-5997	40	16	were	be	AUX
ejpam-5997	40	17	first	first	ADV
ejpam-5997	40	18	presented	present	VERB
ejpam-5997	40	19	by	by	ADP
ejpam-5997	40	20	barsam	barsam	PROPN
ejpam-5997	40	21	et	et	PROPN
ejpam-5997	40	22	al	al	PROPN
ejpam-5997	40	23	.	.	PUNCT
ejpam-5997	41	1	[	[	X
ejpam-5997	41	2	10	10	NUM
ejpam-5997	41	3	]	]	PUNCT
ejpam-5997	41	4	.	.	PUNCT
ejpam-5997	42	1	sattarzadeh	sattarzadeh	PROPN
ejpam-5997	42	2	and	and	CCONJ
ejpam-5997	42	3	barsam	barsam	NOUN
ejpam-5997	43	1	[	[	X
ejpam-5997	43	2	11	11	NUM
ejpam-5997	43	3	]	]	PUNCT
ejpam-5997	43	4	discovered	discover	VERB
ejpam-5997	43	5	the	the	DET
ejpam-5997	43	6	hermite	hermite	PROPN
ejpam-5997	43	7	-	-	PUNCT
ejpam-5997	43	8	hadamard	hadamard	ADJ
ejpam-5997	43	9	type	type	NOUN
ejpam-5997	43	10	problems	problem	NOUN
ejpam-5997	43	11	with	with	ADP
ejpam-5997	43	12	fractional	fractional	ADJ
ejpam-5997	43	13	integrals	integral	NOUN
ejpam-5997	43	14	for	for	ADP
ejpam-5997	43	15	functions	function	NOUN
ejpam-5997	43	16	that	that	PRON
ejpam-5997	43	17	are	be	AUX
ejpam-5997	43	18	uniformly	uniformly	ADV
ejpam-5997	43	19	convex	convex	ADJ
ejpam-5997	43	20	.	.	PUNCT
ejpam-5997	44	1	it	it	PRON
ejpam-5997	44	2	is	be	AUX
ejpam-5997	44	3	meant	mean	VERB
ejpam-5997	44	4	to	to	PART
ejpam-5997	44	5	explore	explore	VERB
ejpam-5997	44	6	the	the	DET
ejpam-5997	44	7	hermitehadamard	hermitehadamard	ADJ
ejpam-5997	44	8	type	type	NOUN
ejpam-5997	44	9	inequalities	inequality	NOUN
ejpam-5997	44	10	involving	involve	VERB
ejpam-5997	44	11	fractional	fractional	ADJ
ejpam-5997	44	12	integrals	integral	NOUN
ejpam-5997	44	13	due	due	ADJ
ejpam-5997	44	14	to	to	ADP
ejpam-5997	44	15	the	the	DET
ejpam-5997	44	16	numerous	numerous	ADJ
ejpam-5997	44	17	applications	application	NOUN
ejpam-5997	44	18	of	of	ADP
ejpam-5997	44	19	fractional	fractional	ADJ
ejpam-5997	44	20	calculus	calculus	NOUN
ejpam-5997	44	21	[	[	X
ejpam-5997	44	22	12–16	12–16	NUM
ejpam-5997	44	23	]	]	PUNCT
ejpam-5997	44	24	and	and	CCONJ
ejpam-5997	44	25	hermite	hermite	ADJ
ejpam-5997	44	26	-	-	PUNCT
ejpam-5997	44	27	hadamard	hadamard	ADJ
ejpam-5997	44	28	type	type	NOUN
ejpam-5997	44	29	inequalities	inequality	NOUN
ejpam-5997	44	30	[	[	X
ejpam-5997	44	31	17	17	NUM
ejpam-5997	44	32	–	–	PUNCT
ejpam-5997	44	33	21	21	NUM
ejpam-5997	44	34	]	]	PUNCT
ejpam-5997	44	35	.	.	PUNCT
ejpam-5997	45	1	the	the	DET
ejpam-5997	45	2	inequalities	inequality	NOUN
ejpam-5997	45	3	of	of	ADP
ejpam-5997	45	4	fractional	fractional	ADJ
ejpam-5997	45	5	integral	integral	ADJ
ejpam-5997	45	6	by	by	ADP
ejpam-5997	45	7	convex	convex	NOUN
ejpam-5997	45	8	functions	function	NOUN
ejpam-5997	45	9	with	with	ADP
ejpam-5997	45	10	respect	respect	NOUN
ejpam-5997	45	11	to	to	ADP
ejpam-5997	45	12	increasing	increase	VERB
ejpam-5997	45	13	functions	function	NOUN
ejpam-5997	45	14	was	be	AUX
ejpam-5997	45	15	obtained	obtain	VERB
ejpam-5997	45	16	by	by	ADP
ejpam-5997	45	17	mohammed	mohammed	PROPN
ejpam-5997	46	1	[	[	X
ejpam-5997	46	2	22	22	NUM
ejpam-5997	46	3	]	]	PUNCT
ejpam-5997	46	4	.	.	PUNCT
ejpam-5997	47	1	abdeljawad	abdeljawad	NOUN
ejpam-5997	47	2	et	et	PROPN
ejpam-5997	47	3	al	al	PROPN
ejpam-5997	47	4	.	.	PUNCT
ejpam-5997	48	1	[	[	X
ejpam-5997	48	2	23	23	NUM
ejpam-5997	48	3	]	]	PUNCT
ejpam-5997	48	4	proposed	propose	VERB
ejpam-5997	48	5	new	new	ADJ
ejpam-5997	48	6	simpsontype	simpsontype	NOUN
ejpam-5997	48	7	inequalities	inequality	NOUN
ejpam-5997	48	8	for	for	ADP
ejpam-5997	48	9	(	(	PUNCT
ejpam-5997	48	10	s	s	PROPN
ejpam-5997	48	11	,	,	PUNCT
ejpam-5997	48	12	m)-convex	m)-convex	PUNCT
ejpam-5997	48	13	functions	function	NOUN
ejpam-5997	48	14	.	.	PUNCT
ejpam-5997	49	1	some	some	DET
ejpam-5997	49	2	inequalities	inequality	NOUN
ejpam-5997	49	3	for	for	ADP
ejpam-5997	49	4	s	s	NOUN
ejpam-5997	49	5	-	-	PUNCT
ejpam-5997	49	6	convex	convex	ADJ
ejpam-5997	49	7	functions	function	NOUN
ejpam-5997	49	8	with	with	ADP
ejpam-5997	49	9	fractional	fractional	ADJ
ejpam-5997	49	10	integrals	integral	NOUN
ejpam-5997	49	11	were	be	AUX
ejpam-5997	49	12	presented	present	VERB
ejpam-5997	49	13	by	by	ADP
ejpam-5997	49	14	i̧	i̧	NOUN
ejpam-5997	49	15	scan	scan	NOUN
ejpam-5997	49	16	[	[	X
ejpam-5997	49	17	24	24	NUM
ejpam-5997	49	18	]	]	PUNCT
ejpam-5997	49	19	.	.	PUNCT
ejpam-5997	50	1	trapezoid	trapezoid	ADJ
ejpam-5997	50	2	type	type	NOUN
ejpam-5997	50	3	inequalities	inequality	NOUN
ejpam-5997	50	4	for	for	ADP
ejpam-5997	50	5	sconvex	sconvex	ADJ
ejpam-5997	50	6	functions	function	NOUN
ejpam-5997	50	7	involving	involve	VERB
ejpam-5997	50	8	generalized	generalize	VERB
ejpam-5997	50	9	fractional	fractional	ADJ
ejpam-5997	50	10	operators	operator	NOUN
ejpam-5997	50	11	established	establish	VERB
ejpam-5997	50	12	by	by	ADP
ejpam-5997	50	13	usta	usta	PROPN
ejpam-5997	50	14	et	et	PROPN
ejpam-5997	50	15	al	al	PROPN
ejpam-5997	50	16	.	.	PUNCT
ejpam-5997	51	1	[	[	X
ejpam-5997	51	2	25	25	NUM
ejpam-5997	51	3	]	]	PUNCT
ejpam-5997	51	4	.	.	PUNCT
ejpam-5997	52	1	butt	butt	PROPN
ejpam-5997	52	2	et	et	PROPN
ejpam-5997	52	3	al	al	PROPN
ejpam-5997	52	4	.	.	PUNCT
ejpam-5997	53	1	[	[	X
ejpam-5997	53	2	26	26	NUM
ejpam-5997	53	3	]	]	PUNCT
ejpam-5997	53	4	introduced	introduce	VERB
ejpam-5997	53	5	integral	integral	ADJ
ejpam-5997	53	6	identity	identity	NOUN
ejpam-5997	53	7	;	;	PUNCT
ejpam-5997	53	8	by	by	ADP
ejpam-5997	53	9	using	use	VERB
ejpam-5997	53	10	that	that	DET
ejpam-5997	53	11	identity	identity	NOUN
ejpam-5997	53	12	,	,	PUNCT
ejpam-5997	53	13	new	new	ADJ
ejpam-5997	53	14	inequalities	inequality	NOUN
ejpam-5997	53	15	were	be	AUX
ejpam-5997	53	16	obtained	obtain	VERB
ejpam-5997	53	17	via	via	ADP
ejpam-5997	53	18	a	a	DET
ejpam-5997	53	19	general	general	ADJ
ejpam-5997	53	20	form	form	NOUN
ejpam-5997	53	21	of	of	ADP
ejpam-5997	53	22	fractional	fractional	ADJ
ejpam-5997	53	23	integral	integral	ADJ
ejpam-5997	53	24	operators	operator	NOUN
ejpam-5997	53	25	.	.	PUNCT
ejpam-5997	54	1	agarwal	agarwal	PROPN
ejpam-5997	54	2	et	et	PROPN
ejpam-5997	54	3	al	al	PROPN
ejpam-5997	54	4	.	.	PUNCT
ejpam-5997	55	1	[	[	X
ejpam-5997	55	2	27	27	NUM
ejpam-5997	55	3	]	]	PUNCT
ejpam-5997	55	4	proposed	propose	VERB
ejpam-5997	55	5	hermite	hermite	PROPN
ejpam-5997	55	6	-	-	PUNCT
ejpam-5997	55	7	hadamard	hadamard	ADJ
ejpam-5997	55	8	type	type	NOUN
ejpam-5997	55	9	inequalities	inequality	NOUN
ejpam-5997	55	10	for	for	ADP
ejpam-5997	55	11	generalized	generalized	ADJ
ejpam-5997	55	12	k	k	ADJ
ejpam-5997	55	13	-	-	PUNCT
ejpam-5997	55	14	fractional	fractional	ADJ
ejpam-5997	55	15	integrals	integral	NOUN
ejpam-5997	55	16	.	.	PUNCT
ejpam-5997	56	1	in	in	ADP
ejpam-5997	56	2	our	our	PRON
ejpam-5997	56	3	present	present	ADJ
ejpam-5997	56	4	work	work	NOUN
ejpam-5997	56	5	we	we	PRON
ejpam-5997	56	6	use	use	VERB
ejpam-5997	56	7	the	the	DET
ejpam-5997	56	8	s	s	NOUN
ejpam-5997	56	9	-	-	ADJ
ejpam-5997	56	10	convex	convex	ADJ
ejpam-5997	56	11	function	function	NOUN
ejpam-5997	56	12	for	for	ADP
ejpam-5997	56	13	the	the	DET
ejpam-5997	56	14	class	class	NOUN
ejpam-5997	56	15	of	of	ADP
ejpam-5997	56	16	first	first	ADJ
ejpam-5997	56	17	odder	odd	ADJ
ejpam-5997	56	18	derivatives	derivative	NOUN
ejpam-5997	56	19	and	and	CCONJ
ejpam-5997	56	20	second	second	ADJ
ejpam-5997	56	21	order	order	NOUN
ejpam-5997	56	22	derivatives	derivative	NOUN
ejpam-5997	56	23	and	and	CCONJ
ejpam-5997	56	24	modified	modify	VERB
ejpam-5997	56	25	the	the	DET
ejpam-5997	56	26	hermite	hermite	PROPN
ejpam-5997	56	27	-	-	PUNCT
ejpam-5997	56	28	hadamard	hadamard	ADJ
ejpam-5997	56	29	(	(	PUNCT
ejpam-5997	56	30	h	h	NOUN
ejpam-5997	56	31	-	-	PUNCT
ejpam-5997	56	32	h	h	NOUN
ejpam-5997	56	33	)	)	PUNCT
ejpam-5997	56	34	integral	integral	ADJ
ejpam-5997	56	35	inequalities	inequality	NOUN
ejpam-5997	56	36	by	by	ADP
ejpam-5997	56	37	utilizing	utilize	VERB
ejpam-5997	56	38	the	the	DET
ejpam-5997	56	39	bessel	bessel	NOUN
ejpam-5997	56	40	-	-	PUNCT
ejpam-5997	56	41	maitland	maitland	PROPN
ejpam-5997	56	42	function	function	NOUN
ejpam-5997	56	43	as	as	ADP
ejpam-5997	56	44	its	its	PRON
ejpam-5997	56	45	kernel	kernel	NOUN
ejpam-5997	56	46	.	.	PUNCT
ejpam-5997	57	1	2	2	X
ejpam-5997	57	2	.	.	X
ejpam-5997	57	3	preliminaries	preliminary	NOUN
ejpam-5997	57	4	in	in	ADP
ejpam-5997	57	5	this	this	DET
ejpam-5997	57	6	section	section	NOUN
ejpam-5997	57	7	,	,	PUNCT
ejpam-5997	57	8	we	we	PRON
ejpam-5997	57	9	discuss	discuss	VERB
ejpam-5997	57	10	the	the	DET
ejpam-5997	57	11	basic	basic	ADJ
ejpam-5997	57	12	definitions	definition	NOUN
ejpam-5997	57	13	which	which	PRON
ejpam-5997	57	14	will	will	AUX
ejpam-5997	57	15	help	help	VERB
ejpam-5997	57	16	us	we	PRON
ejpam-5997	57	17	to	to	PART
ejpam-5997	57	18	understand	understand	VERB
ejpam-5997	57	19	our	our	PRON
ejpam-5997	57	20	main	main	ADJ
ejpam-5997	57	21	work	work	NOUN
ejpam-5997	57	22	.	.	PUNCT
ejpam-5997	58	1	definition	definition	NOUN
ejpam-5997	58	2	1	1	NUM
ejpam-5997	58	3	.	.	PUNCT
ejpam-5997	59	1	[	[	X
ejpam-5997	59	2	28	28	NUM
ejpam-5997	59	3	,	,	PUNCT
ejpam-5997	59	4	29	29	NUM
ejpam-5997	59	5	]	]	PUNCT
ejpam-5997	59	6	let	let	VERB
ejpam-5997	59	7	ϕ	ϕ	NOUN
ejpam-5997	59	8	:	:	PUNCT
ejpam-5997	59	9	r	r	NOUN
ejpam-5997	59	10	→	→	SYM
ejpam-5997	59	11	r	r	NOUN
ejpam-5997	59	12	be	be	AUX
ejpam-5997	59	13	real	real	ADV
ejpam-5997	59	14	valued	value	VERB
ejpam-5997	59	15	function	function	NOUN
ejpam-5997	59	16	,	,	PUNCT
ejpam-5997	59	17	is	be	AUX
ejpam-5997	59	18	said	say	VERB
ejpam-5997	59	19	to	to	PART
ejpam-5997	59	20	be	be	AUX
ejpam-5997	59	21	convex	convex	ADJ
ejpam-5997	59	22	if	if	SCONJ
ejpam-5997	59	23	the	the	DET
ejpam-5997	59	24	following	follow	VERB
ejpam-5997	59	25	inequalities	inequality	NOUN
ejpam-5997	59	26	holds	hold	VERB
ejpam-5997	59	27	:	:	PUNCT
ejpam-5997	59	28	ϕ(℘α+	ϕ(℘α+	PROPN
ejpam-5997	59	29	(	(	PUNCT
ejpam-5997	59	30	1−	1−	NUM
ejpam-5997	59	31	℘)ω	℘)ω	NOUN
ejpam-5997	59	32	)	)	PUNCT
ejpam-5997	59	33	≤	≤	NUM
ejpam-5997	59	34	℘ϕ(α	℘ϕ(α	NOUN
ejpam-5997	59	35	)	)	PUNCT
ejpam-5997	60	1	+	+	CCONJ
ejpam-5997	60	2	(	(	PUNCT
ejpam-5997	60	3	1−	1−	NUM
ejpam-5997	60	4	℘)ϕ(ω	℘)ϕ(ω	NOUN
ejpam-5997	60	5	)	)	PUNCT
ejpam-5997	60	6	,	,	PUNCT
ejpam-5997	60	7	(	(	PUNCT
ejpam-5997	60	8	1	1	X
ejpam-5997	60	9	)	)	PUNCT
ejpam-5997	60	10	where	where	SCONJ
ejpam-5997	60	11	℘	℘	VERB
ejpam-5997	60	12	∈	∈	PROPN
ejpam-5997	61	1	[	[	X
ejpam-5997	61	2	0	0	NUM
ejpam-5997	61	3	,	,	PUNCT
ejpam-5997	61	4	1	1	NUM
ejpam-5997	61	5	]	]	PUNCT
ejpam-5997	61	6	and	and	CCONJ
ejpam-5997	61	7	∀	∀	NUM
ejpam-5997	61	8	ω	ω	NOUN
ejpam-5997	61	9	,	,	PUNCT
ejpam-5997	61	10	α	α	PROPN
ejpam-5997	61	11	∈	∈	PROPN
ejpam-5997	61	12	r.	r.	PROPN
ejpam-5997	61	13	definition	definition	NOUN
ejpam-5997	61	14	2	2	NUM
ejpam-5997	61	15	.	.	PUNCT
ejpam-5997	62	1	[	[	X
ejpam-5997	62	2	30	30	NUM
ejpam-5997	62	3	]	]	PUNCT
ejpam-5997	62	4	let	let	VERB
ejpam-5997	62	5	ϕ	ϕ	NOUN
ejpam-5997	62	6	:	:	PUNCT
ejpam-5997	62	7	r	r	NOUN
ejpam-5997	62	8	→	→	SYM
ejpam-5997	62	9	r	r	NOUN
ejpam-5997	62	10	be	be	AUX
ejpam-5997	62	11	real	real	ADV
ejpam-5997	62	12	valued	value	VERB
ejpam-5997	62	13	function	function	NOUN
ejpam-5997	62	14	,	,	PUNCT
ejpam-5997	62	15	is	be	AUX
ejpam-5997	62	16	said	say	VERB
ejpam-5997	62	17	to	to	PART
ejpam-5997	62	18	be	be	AUX
ejpam-5997	62	19	s	s	NOUN
ejpam-5997	62	20	-	-	ADJ
ejpam-5997	62	21	convex	convex	ADJ
ejpam-5997	62	22	function	function	NOUN
ejpam-5997	62	23	,	,	PUNCT
ejpam-5997	62	24	if	if	SCONJ
ejpam-5997	62	25	the	the	DET
ejpam-5997	62	26	following	follow	VERB
ejpam-5997	62	27	relation	relation	NOUN
ejpam-5997	62	28	holds	hold	VERB
ejpam-5997	62	29	:	:	PUNCT
ejpam-5997	62	30	ϕ(℘α+	ϕ(℘α+	PROPN
ejpam-5997	62	31	(	(	PUNCT
ejpam-5997	62	32	1−	1−	NUM
ejpam-5997	62	33	℘)ω	℘)ω	NOUN
ejpam-5997	62	34	)	)	PUNCT
ejpam-5997	62	35	≤	≤	NOUN
ejpam-5997	62	36	℘sϕ(α	℘sϕ(α	PUNCT
ejpam-5997	62	37	)	)	PUNCT
ejpam-5997	63	1	+	+	CCONJ
ejpam-5997	63	2	(	(	PUNCT
ejpam-5997	63	3	1−	1−	NUM
ejpam-5997	63	4	℘)sϕ(ω	℘)sϕ(ω	NOUN
ejpam-5997	63	5	)	)	PUNCT
ejpam-5997	63	6	,	,	PUNCT
ejpam-5997	63	7	(	(	PUNCT
ejpam-5997	63	8	2	2	X
ejpam-5997	63	9	)	)	PUNCT
ejpam-5997	63	10	where	where	SCONJ
ejpam-5997	63	11	α	α	X
ejpam-5997	63	12	,	,	PUNCT
ejpam-5997	63	13	ω	ω	PROPN
ejpam-5997	63	14	∈	∈	PROPN
ejpam-5997	63	15	r	r	NOUN
ejpam-5997	63	16	and	and	CCONJ
ejpam-5997	63	17	℘	℘	PROPN
ejpam-5997	63	18	∈	∈	PROPN
ejpam-5997	63	19	(	(	PUNCT
ejpam-5997	63	20	0	0	NUM
ejpam-5997	63	21	,	,	PUNCT
ejpam-5997	63	22	1	1	NUM
ejpam-5997	63	23	)	)	PUNCT
ejpam-5997	63	24	and	and	CCONJ
ejpam-5997	63	25	s	s	PROPN
ejpam-5997	63	26	∈	∈	PROPN
ejpam-5997	63	27	(	(	PUNCT
ejpam-5997	63	28	0	0	NUM
ejpam-5997	63	29	,	,	PUNCT
ejpam-5997	63	30	1	1	NUM
ejpam-5997	63	31	]	]	PUNCT
ejpam-5997	63	32	.	.	PUNCT
ejpam-5997	64	1	definition	definition	NOUN
ejpam-5997	64	2	3	3	NUM
ejpam-5997	64	3	.	.	PUNCT
ejpam-5997	65	1	[	[	X
ejpam-5997	65	2	29	29	NUM
ejpam-5997	65	3	,	,	PUNCT
ejpam-5997	65	4	31–33	31–33	NUM
ejpam-5997	65	5	]	]	PUNCT
ejpam-5997	65	6	the	the	DET
ejpam-5997	65	7	hermite	hermite	PROPN
ejpam-5997	65	8	-	-	PUNCT
ejpam-5997	65	9	hadamard	hadamard	ADJ
ejpam-5997	65	10	type	type	NOUN
ejpam-5997	65	11	inequality	inequality	NOUN
ejpam-5997	65	12	for	for	ADP
ejpam-5997	65	13	convex	convex	PROPN
ejpam-5997	65	14	function	function	NOUN
ejpam-5997	65	15	ϕ	ϕ	NOUN
ejpam-5997	65	16	:	:	PUNCT
ejpam-5997	65	17	r	r	NOUN
ejpam-5997	65	18	→	→	SYM
ejpam-5997	65	19	r	r	NOUN
ejpam-5997	65	20	,	,	PUNCT
ejpam-5997	65	21	is	be	AUX
ejpam-5997	65	22	defined	define	VERB
ejpam-5997	65	23	as	as	SCONJ
ejpam-5997	65	24	follows	follow	VERB
ejpam-5997	65	25	;	;	PUNCT
ejpam-5997	65	26	ϕ	ϕ	X
ejpam-5997	65	27	(	(	PUNCT
ejpam-5997	65	28	α+	α+	PROPN
ejpam-5997	65	29	ω	ω	PROPN
ejpam-5997	65	30	2	2	NUM
ejpam-5997	65	31	)	)	PUNCT
ejpam-5997	65	32	≤	≤	NOUN
ejpam-5997	65	33	1	1	NUM
ejpam-5997	65	34	ω	ω	NUM
ejpam-5997	65	35	−	−	PROPN
ejpam-5997	66	1	α	α	NOUN
ejpam-5997	66	2	∫	∫	PROPN
ejpam-5997	66	3	ω	ω	PROPN
ejpam-5997	66	4	α	α	PROPN
ejpam-5997	66	5	ϕ(℘)d℘	ϕ(℘)d℘	PROPN
ejpam-5997	66	6	≤	≤	NOUN
ejpam-5997	66	7	ϕ(α	ϕ(α	NUM
ejpam-5997	66	8	)	)	PUNCT
ejpam-5997	67	1	+	+	X
ejpam-5997	67	2	ϕ(ω	ϕ(ω	NOUN
ejpam-5997	67	3	)	)	PUNCT
ejpam-5997	67	4	2	2	NUM
ejpam-5997	67	5	.	.	PUNCT
ejpam-5997	68	1	(	(	PUNCT
ejpam-5997	68	2	3	3	X
ejpam-5997	68	3	)	)	PUNCT
ejpam-5997	68	4	where	where	SCONJ
ejpam-5997	68	5	α	α	X
ejpam-5997	68	6	,	,	PUNCT
ejpam-5997	68	7	ω	ω	PROPN
ejpam-5997	68	8	∈	∈	PROPN
ejpam-5997	68	9	r	r	NOUN
ejpam-5997	68	10	,	,	PUNCT
ejpam-5997	68	11	α	α	X
ejpam-5997	68	12	<	<	X
ejpam-5997	68	13	ω	ω	PROPN
ejpam-5997	68	14	.	.	PUNCT
ejpam-5997	68	15	m.	m.	PROPN
ejpam-5997	68	16	vivas	vivas	PROPN
ejpam-5997	68	17	-	-	PROPN
ejpam-5997	68	18	cortez	cortez	PROPN
ejpam-5997	68	19	et	et	PROPN
ejpam-5997	68	20	al	al	PROPN
ejpam-5997	68	21	.	.	PUNCT
ejpam-5997	68	22	/	/	SYM
ejpam-5997	68	23	eur	eur	PROPN
ejpam-5997	68	24	.	.	PUNCT
ejpam-5997	69	1	j.	j.	PROPN
ejpam-5997	69	2	pure	pure	PROPN
ejpam-5997	69	3	appl	appl	PROPN
ejpam-5997	69	4	.	.	PROPN
ejpam-5997	69	5	math	math	PROPN
ejpam-5997	69	6	,	,	PUNCT
ejpam-5997	69	7	18	18	NUM
ejpam-5997	69	8	(	(	PUNCT
ejpam-5997	69	9	2	2	NUM
ejpam-5997	69	10	)	)	PUNCT
ejpam-5997	69	11	(	(	PUNCT
ejpam-5997	69	12	2025	2025	NUM
ejpam-5997	69	13	)	)	PUNCT
ejpam-5997	69	14	,	,	PUNCT
ejpam-5997	69	15	5997	5997	NUM
ejpam-5997	69	16	4	4	NUM
ejpam-5997	69	17	of	of	ADP
ejpam-5997	69	18	23	23	NUM
ejpam-5997	69	19	definition	definition	NOUN
ejpam-5997	69	20	4	4	NUM
ejpam-5997	69	21	.	.	PUNCT
ejpam-5997	70	1	[	[	X
ejpam-5997	70	2	34	34	NUM
ejpam-5997	70	3	]	]	PUNCT
ejpam-5997	70	4	the	the	DET
ejpam-5997	70	5	gamma	gamma	PROPN
ejpam-5997	70	6	function	function	NOUN
ejpam-5997	70	7	in	in	ADP
ejpam-5997	70	8	integral	integral	ADJ
ejpam-5997	70	9	type	type	NOUN
ejpam-5997	70	10	is	be	AUX
ejpam-5997	70	11	defined	define	VERB
ejpam-5997	70	12	for	for	ADP
ejpam-5997	70	13	ℜ(t	ℜ(t	PRON
ejpam-5997	70	14	)	)	PUNCT
ejpam-5997	70	15	>	>	X
ejpam-5997	70	16	0	0	NUM
ejpam-5997	70	17	,	,	PUNCT
ejpam-5997	70	18	as	as	SCONJ
ejpam-5997	70	19	follows	follow	VERB
ejpam-5997	70	20	γ(t	γ(t	NOUN
ejpam-5997	70	21	)	)	PUNCT
ejpam-5997	70	22	=	=	SYM
ejpam-5997	71	1	∫	∫	PROPN
ejpam-5997	72	1	∞	∞	NUM
ejpam-5997	72	2	0	0	NUM
ejpam-5997	73	1	xt−1e−xdx	xt−1e−xdx	PROPN
ejpam-5997	73	2	.	.	PUNCT
ejpam-5997	74	1	(	(	PUNCT
ejpam-5997	74	2	4	4	X
ejpam-5997	74	3	)	)	PUNCT
ejpam-5997	74	4	definition	definition	NOUN
ejpam-5997	74	5	5	5	NUM
ejpam-5997	74	6	.	.	PUNCT
ejpam-5997	75	1	[	[	X
ejpam-5997	75	2	34	34	NUM
ejpam-5997	75	3	]	]	X
ejpam-5997	75	4	the	the	DET
ejpam-5997	75	5	pochammer	pochammer	NOUN
ejpam-5997	75	6	’s	’s	PART
ejpam-5997	75	7	symbol	symbol	NOUN
ejpam-5997	75	8	is	be	AUX
ejpam-5997	75	9	defined	define	VERB
ejpam-5997	75	10	as	as	SCONJ
ejpam-5997	75	11	follows	follow	VERB
ejpam-5997	75	12	:	:	PUNCT
ejpam-5997	75	13	(	(	PUNCT
ejpam-5997	75	14	ð)η	ð)η	PUNCT
ejpam-5997	76	1	=	=	SYM
ejpam-5997	76	2	{	{	PUNCT
ejpam-5997	76	3	1	1	NUM
ejpam-5997	76	4	,	,	PUNCT
ejpam-5997	76	5	for	for	ADP
ejpam-5997	76	6	η	η	PROPN
ejpam-5997	76	7	=	=	SYM
ejpam-5997	76	8	0	0	PROPN
ejpam-5997	76	9	,	,	PUNCT
ejpam-5997	76	10	ð	ð	PROPN
ejpam-5997	76	11	̸=	̸=	PROPN
ejpam-5997	76	12	0	0	NUM
ejpam-5997	76	13	ð(ð+	ð(ð+	PROPN
ejpam-5997	76	14	1	1	NUM
ejpam-5997	76	15	)	)	PUNCT
ejpam-5997	76	16	·	·	PUNCT
ejpam-5997	76	17	·	·	PUNCT
ejpam-5997	76	18	·	·	PUNCT
ejpam-5997	76	19	(	(	PUNCT
ejpam-5997	76	20	ð+	ð+	PUNCT
ejpam-5997	76	21	η	η	PROPN
ejpam-5997	76	22	−	−	PROPN
ejpam-5997	76	23	1	1	NUM
ejpam-5997	76	24	)	)	PUNCT
ejpam-5997	76	25	,	,	PUNCT
ejpam-5997	76	26	for	for	ADP
ejpam-5997	76	27	η	η	PROPN
ejpam-5997	76	28	≥	≥	PROPN
ejpam-5997	76	29	1	1	NUM
ejpam-5997	76	30	,	,	PUNCT
ejpam-5997	76	31	}	}	PUNCT
ejpam-5997	76	32	(	(	PUNCT
ejpam-5997	76	33	5	5	NUM
ejpam-5997	76	34	)	)	PUNCT
ejpam-5997	76	35	for	for	ADP
ejpam-5997	76	36	η	η	PROPN
ejpam-5997	76	37	∈	∈	PROPN
ejpam-5997	76	38	n	n	PROPN
ejpam-5997	76	39	and	and	CCONJ
ejpam-5997	76	40	ð	ð	PROPN
ejpam-5997	76	41	∈	∈	PROPN
ejpam-5997	76	42	c	c	NOUN
ejpam-5997	76	43	here	here	ADV
ejpam-5997	76	44	,	,	PUNCT
ejpam-5997	76	45	is	be	AUX
ejpam-5997	76	46	some	some	DET
ejpam-5997	76	47	relations	relation	NOUN
ejpam-5997	76	48	of	of	ADP
ejpam-5997	76	49	gamma	gamma	NOUN
ejpam-5997	76	50	functions	function	NOUN
ejpam-5997	76	51	.	.	PUNCT
ejpam-5997	77	1	(	(	PUNCT
ejpam-5997	77	2	℘)n	℘)n	NOUN
ejpam-5997	77	3	=	=	SYM
ejpam-5997	77	4	γ(℘+	γ(℘+	PROPN
ejpam-5997	77	5	n	n	CCONJ
ejpam-5997	77	6	)	)	PUNCT
ejpam-5997	77	7	γ(℘	γ(℘	NOUN
ejpam-5997	77	8	)	)	PUNCT
ejpam-5997	77	9	,	,	PUNCT
ejpam-5997	77	10	(	(	PUNCT
ejpam-5997	77	11	℘)kn	℘)kn	NOUN
ejpam-5997	77	12	=	=	SYM
ejpam-5997	77	13	γ(℘+	γ(℘+	PROPN
ejpam-5997	77	14	kn	kn	PROPN
ejpam-5997	77	15	)	)	PUNCT
ejpam-5997	77	16	γ(℘	γ(℘	PROPN
ejpam-5997	77	17	)	)	PUNCT
ejpam-5997	77	18	.	.	PUNCT
ejpam-5997	78	1	where	where	SCONJ
ejpam-5997	78	2	γ	γ	X
ejpam-5997	78	3	being	be	AUX
ejpam-5997	78	4	the	the	DET
ejpam-5997	78	5	gamma	gamma	NOUN
ejpam-5997	78	6	notation	notation	NOUN
ejpam-5997	78	7	.	.	PUNCT
ejpam-5997	79	1	definition	definition	NOUN
ejpam-5997	79	2	6	6	NUM
ejpam-5997	79	3	.	.	PUNCT
ejpam-5997	80	1	[	[	X
ejpam-5997	80	2	35	35	NUM
ejpam-5997	80	3	]	]	PUNCT
ejpam-5997	80	4	the	the	DET
ejpam-5997	80	5	beta	beta	NOUN
ejpam-5997	80	6	function	function	NOUN
ejpam-5997	80	7	is	be	AUX
ejpam-5997	80	8	defined	define	VERB
ejpam-5997	80	9	for	for	ADP
ejpam-5997	80	10	ℜ(m	ℜ(m	NOUN
ejpam-5997	80	11	)	)	PUNCT
ejpam-5997	80	12	>	>	X
ejpam-5997	80	13	0	0	PUNCT
ejpam-5997	80	14	and	and	CCONJ
ejpam-5997	80	15	ℜ(n	ℜ(n	NOUN
ejpam-5997	80	16	)	)	PUNCT
ejpam-5997	80	17	>	>	X
ejpam-5997	80	18	0	0	PUNCT
ejpam-5997	81	1	as	as	SCONJ
ejpam-5997	81	2	follows	follow	VERB
ejpam-5997	81	3	:	:	PUNCT
ejpam-5997	81	4	b(g	b(g	PROPN
ejpam-5997	81	5	,	,	PUNCT
ejpam-5997	81	6	h	h	NOUN
ejpam-5997	81	7	)	)	PUNCT
ejpam-5997	81	8	=	=	SYM
ejpam-5997	82	1	∫	∫	PROPN
ejpam-5997	83	1	1	1	NUM
ejpam-5997	83	2	0	0	X
ejpam-5997	84	1	ηg−1(1−	ηg−1(1−	PROPN
ejpam-5997	84	2	η)h−1dη	η)h−1dη	NOUN
ejpam-5997	84	3	,	,	PUNCT
ejpam-5997	84	4	=	=	SYM
ejpam-5997	84	5	γ(g)γ(h	γ(g)γ(h	NOUN
ejpam-5997	84	6	)	)	PUNCT
ejpam-5997	84	7	γ(g	γ(g	PROPN
ejpam-5997	85	1	+	+	CCONJ
ejpam-5997	85	2	h	h	NOUN
ejpam-5997	85	3	)	)	PUNCT
ejpam-5997	85	4	.	.	PUNCT
ejpam-5997	86	1	(	(	PUNCT
ejpam-5997	86	2	6	6	X
ejpam-5997	86	3	)	)	PUNCT
ejpam-5997	86	4	definition	definition	NOUN
ejpam-5997	86	5	7	7	NUM
ejpam-5997	86	6	.	.	PUNCT
ejpam-5997	87	1	[	[	X
ejpam-5997	87	2	36	36	NUM
ejpam-5997	87	3	]	]	PUNCT
ejpam-5997	87	4	the	the	DET
ejpam-5997	87	5	extended	extended	ADJ
ejpam-5997	87	6	form	form	NOUN
ejpam-5997	87	7	of	of	ADP
ejpam-5997	87	8	beta	beta	ADJ
ejpam-5997	87	9	function	function	NOUN
ejpam-5997	87	10	is	be	AUX
ejpam-5997	87	11	define	define	VERB
ejpam-5997	87	12	for	for	ADP
ejpam-5997	87	13	ℜ(g	ℜ(g	ADJ
ejpam-5997	87	14	)	)	PUNCT
ejpam-5997	87	15	>	>	X
ejpam-5997	87	16	0	0	NUM
ejpam-5997	87	17	,	,	PUNCT
ejpam-5997	87	18	ℜ(h	ℜ(h	PROPN
ejpam-5997	87	19	)	)	PUNCT
ejpam-5997	87	20	>	>	X
ejpam-5997	87	21	0	0	NUM
ejpam-5997	87	22	,	,	PUNCT
ejpam-5997	87	23	ℜ(p	ℜ(p	PROPN
ejpam-5997	87	24	)	)	PUNCT
ejpam-5997	87	25	>	>	X
ejpam-5997	87	26	0	0	PUNCT
ejpam-5997	88	1	as	as	SCONJ
ejpam-5997	88	2	follows	follow	VERB
ejpam-5997	88	3	bp(g	bp(g	PUNCT
ejpam-5997	88	4	,	,	PUNCT
ejpam-5997	88	5	h	h	NOUN
ejpam-5997	88	6	)	)	PUNCT
ejpam-5997	89	1	=	=	SYM
ejpam-5997	89	2	∫	∫	PROPN
ejpam-5997	89	3	1	1	NUM
ejpam-5997	89	4	0	0	NUM
ejpam-5997	89	5	zg−1(1−	zg−1(1−	PROPN
ejpam-5997	89	6	z)h−1exp	z)h−1exp	PROPN
ejpam-5997	89	7	(	(	PUNCT
ejpam-5997	89	8	−p	−p	ADJ
ejpam-5997	89	9	z(1−	z(1−	X
ejpam-5997	89	10	z	z	NOUN
ejpam-5997	89	11	)	)	PUNCT
ejpam-5997	89	12	)	)	PUNCT
ejpam-5997	90	1	dz	dz	PROPN
ejpam-5997	90	2	.	.	PUNCT
ejpam-5997	91	1	(	(	PUNCT
ejpam-5997	91	2	7	7	X
ejpam-5997	91	3	)	)	PUNCT
ejpam-5997	91	4	taking	take	VERB
ejpam-5997	91	5	the	the	DET
ejpam-5997	91	6	value	value	NOUN
ejpam-5997	91	7	of	of	ADP
ejpam-5997	91	8	p	p	NOUN
ejpam-5997	91	9	=	=	NOUN
ejpam-5997	91	10	1	1	NUM
ejpam-5997	91	11	,	,	PUNCT
ejpam-5997	91	12	the	the	DET
ejpam-5997	91	13	extended	extended	ADJ
ejpam-5997	91	14	beta	beta	NOUN
ejpam-5997	91	15	function	function	NOUN
ejpam-5997	91	16	becomes	become	VERB
ejpam-5997	91	17	the	the	DET
ejpam-5997	91	18	classical	classical	ADJ
ejpam-5997	91	19	beta	beta	NOUN
ejpam-5997	91	20	function	function	NOUN
ejpam-5997	91	21	.	.	PUNCT
ejpam-5997	92	1	definition	definition	NOUN
ejpam-5997	92	2	8	8	NUM
ejpam-5997	92	3	.	.	PUNCT
ejpam-5997	93	1	[	[	X
ejpam-5997	93	2	37	37	NUM
ejpam-5997	93	3	]	]	PUNCT
ejpam-5997	93	4	the	the	DET
ejpam-5997	93	5	bessel	bessel	NOUN
ejpam-5997	93	6	-	-	PUNCT
ejpam-5997	93	7	maitland	maitland	PROPN
ejpam-5997	93	8	function	function	NOUN
ejpam-5997	93	9	is	be	AUX
ejpam-5997	93	10	defined	define	VERB
ejpam-5997	93	11	for	for	ADP
ejpam-5997	93	12	ϕ	ϕ	NOUN
ejpam-5997	93	13	,	,	PUNCT
ejpam-5997	93	14	ψ	ψ	PROPN
ejpam-5997	93	15	,	,	PUNCT
ejpam-5997	93	16	υ	υ	PROPN
ejpam-5997	93	17	,	,	PUNCT
ejpam-5997	93	18	χ,ϖ	χ,ϖ	VERB
ejpam-5997	93	19	∈	∈	PROPN
ejpam-5997	93	20	c	c	PROPN
ejpam-5997	93	21	and	and	CCONJ
ejpam-5997	93	22	ℜ(ϕ	ℜ(ϕ	NUM
ejpam-5997	93	23	)	)	PUNCT
ejpam-5997	94	1	>	>	X
ejpam-5997	94	2	0,ℜ(ξ	0,ℜ(ξ	PROPN
ejpam-5997	94	3	)	)	PUNCT
ejpam-5997	94	4	>	>	X
ejpam-5997	94	5	0,ℜ(υ	0,ℜ(υ	PROPN
ejpam-5997	94	6	)	)	PUNCT
ejpam-5997	94	7	>	>	PUNCT
ejpam-5997	94	8	0,ℜ(χ	0,ℜ(χ	PROPN
ejpam-5997	94	9	)	)	PUNCT
ejpam-5997	94	10	>	>	X
ejpam-5997	94	11	0,ℜ(ϖ	0,ℜ(ϖ	NUM
ejpam-5997	94	12	)	)	PUNCT
ejpam-5997	94	13	>	>	X
ejpam-5997	94	14	0	0	NUM
ejpam-5997	94	15	,	,	PUNCT
ejpam-5997	94	16	ρ	ρ	PROPN
ejpam-5997	94	17	,	,	PUNCT
ejpam-5997	94	18	η	η	PROPN
ejpam-5997	94	19	,	,	PUNCT
ejpam-5997	94	20	m	m	PROPN
ejpam-5997	94	21	≥	≥	NOUN
ejpam-5997	94	22	0	0	NUM
ejpam-5997	94	23	and	and	CCONJ
ejpam-5997	94	24	m	m	PROPN
ejpam-5997	94	25	,	,	PUNCT
ejpam-5997	94	26	η	η	PROPN
ejpam-5997	94	27	>	>	X
ejpam-5997	94	28	ℜ(ϕ	ℜ(ϕ	PROPN
ejpam-5997	94	29	)	)	PUNCT
ejpam-5997	94	30	+	+	CCONJ
ejpam-5997	94	31	η	η	PROPN
ejpam-5997	94	32	;	;	PUNCT
ejpam-5997	94	33	jψ	jψ	PROPN
ejpam-5997	94	34	,	,	PUNCT
ejpam-5997	94	35	υ	υ	NOUN
ejpam-5997	94	36	,	,	PUNCT
ejpam-5997	94	37	χ,ϖϕ,ρ	χ,ϖϕ,ρ	PROPN
ejpam-5997	94	38	,	,	PUNCT
ejpam-5997	94	39	m	m	PROPN
ejpam-5997	94	40	,	,	PUNCT
ejpam-5997	94	41	η	η	PROPN
ejpam-5997	94	42	(	(	PUNCT
ejpam-5997	94	43	y	y	NOUN
ejpam-5997	94	44	)	)	PUNCT
ejpam-5997	94	45	=	=	PUNCT
ejpam-5997	95	1	∞∑	∞∑	NUM
ejpam-5997	95	2	p=0	p=0	PROPN
ejpam-5997	95	3	(	(	PUNCT
ejpam-5997	95	4	υ)ρp(ϖ)ηp(−y)p	υ)ρp(ϖ)ηp(−y)p	NUM
ejpam-5997	95	5	γ(ϕp+	γ(ϕp+	X
ejpam-5997	95	6	ψ	ψ	PROPN
ejpam-5997	95	7	+	+	PROPN
ejpam-5997	95	8	1)(χ)mp	1)(χ)mp	NUM
ejpam-5997	95	9	.	.	PUNCT
ejpam-5997	96	1	(	(	PUNCT
ejpam-5997	96	2	8)	8)	NUM
ejpam-5997	96	3	definition	definition	NOUN
ejpam-5997	96	4	9	9	NUM
ejpam-5997	96	5	.	.	PUNCT
ejpam-5997	97	1	[	[	X
ejpam-5997	97	2	38	38	NUM
ejpam-5997	97	3	]	]	PUNCT
ejpam-5997	97	4	the	the	DET
ejpam-5997	97	5	extended	extended	ADJ
ejpam-5997	97	6	version	version	NOUN
ejpam-5997	97	7	of	of	ADP
ejpam-5997	97	8	bessel	bessel	NOUN
ejpam-5997	97	9	-	-	PUNCT
ejpam-5997	97	10	maitland	maitland	PROPN
ejpam-5997	97	11	is	be	AUX
ejpam-5997	97	12	defined	define	VERB
ejpam-5997	97	13	for	for	ADP
ejpam-5997	97	14	µ	µ	PRON
ejpam-5997	97	15	,	,	PUNCT
ejpam-5997	97	16	ξ	ξ	PROPN
ejpam-5997	97	17	,	,	PUNCT
ejpam-5997	97	18	ζ	ζ	NOUN
ejpam-5997	97	19	,	,	PUNCT
ejpam-5997	97	20	ς	ς	PROPN
ejpam-5997	97	21	,	,	PUNCT
ejpam-5997	97	22	c	c	X
ejpam-5997	97	23	,	,	PUNCT
ejpam-5997	97	24	κ1	κ1	PROPN
ejpam-5997	97	25	∈	∈	PROPN
ejpam-5997	97	26	c,ℜ(µ	c,ℜ(µ	PROPN
ejpam-5997	97	27	)	)	PUNCT
ejpam-5997	97	28	>	>	X
ejpam-5997	97	29	0,ℜ(ξ	0,ℜ(ξ	PROPN
ejpam-5997	97	30	)	)	PUNCT
ejpam-5997	97	31	>	>	X
ejpam-5997	97	32	0,ℜ(ζ	0,ℜ(ζ	PROPN
ejpam-5997	97	33	)	)	PUNCT
ejpam-5997	97	34	>	>	X
ejpam-5997	97	35	0,ℜ(ς	0,ℜ(ς	PROPN
ejpam-5997	97	36	)	)	PUNCT
ejpam-5997	97	37	>	>	X
ejpam-5997	98	1	0,ℜ(κ1	0,ℜ(κ1	PROPN
ejpam-5997	98	2	)	)	PUNCT
ejpam-5997	98	3	>	>	X
ejpam-5997	98	4	0	0	NUM
ejpam-5997	98	5	,	,	PUNCT
ejpam-5997	98	6	ρ	ρ	PROPN
ejpam-5997	98	7	,	,	PUNCT
ejpam-5997	98	8	m	m	PROPN
ejpam-5997	98	9	,	,	PUNCT
ejpam-5997	98	10	η	η	PROPN
ejpam-5997	98	11	≥	≥	X
ejpam-5997	98	12	0	0	NUM
ejpam-5997	98	13	and	and	CCONJ
ejpam-5997	98	14	m	m	PROPN
ejpam-5997	98	15	,	,	PUNCT
ejpam-5997	98	16	ρ	ρ	PROPN
ejpam-5997	98	17	>	>	X
ejpam-5997	98	18	ℜ(µ	ℜ(µ	NOUN
ejpam-5997	98	19	)	)	PUNCT
ejpam-5997	98	20	+	+	CCONJ
ejpam-5997	98	21	η	η	PROPN
ejpam-5997	98	22	,	,	PUNCT
ejpam-5997	98	23	as	as	SCONJ
ejpam-5997	98	24	follows	follow	VERB
ejpam-5997	98	25	jµ,ρ	jµ,ρ	NOUN
ejpam-5997	98	26	,	,	PUNCT
ejpam-5997	98	27	m	m	PROPN
ejpam-5997	98	28	,	,	PUNCT
ejpam-5997	98	29	η	η	PROPN
ejpam-5997	98	30	,	,	PUNCT
ejpam-5997	98	31	cξ	cξ	NOUN
ejpam-5997	98	32	,	,	PUNCT
ejpam-5997	98	33	ζ	ζ	NOUN
ejpam-5997	98	34	,	,	PUNCT
ejpam-5997	98	35	ς	ς	PROPN
ejpam-5997	98	36	,	,	PUNCT
ejpam-5997	98	37	κ1	κ1	NOUN
ejpam-5997	98	38	(	(	PUNCT
ejpam-5997	98	39	κ	κ	NOUN
ejpam-5997	98	40	,	,	PUNCT
ejpam-5997	98	41	p	p	NOUN
ejpam-5997	98	42	)	)	PUNCT
ejpam-5997	98	43	=	=	PUNCT
ejpam-5997	99	1	∞∑	∞∑	NUM
ejpam-5997	99	2	n=0	n=0	NUM
ejpam-5997	99	3	βp(ζ	βp(ζ	PUNCT
ejpam-5997	99	4	+	+	CCONJ
ejpam-5997	99	5	ρn	ρn	INTJ
ejpam-5997	99	6	,	,	PUNCT
ejpam-5997	99	7	c−	c−	NOUN
ejpam-5997	99	8	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	99	9	β(ζ	β(ζ	PROPN
ejpam-5997	99	10	,	,	PUNCT
ejpam-5997	99	11	c−	c−	X
ejpam-5997	99	12	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	99	13	ξ	ξ	X
ejpam-5997	100	1	+	+	NUM
ejpam-5997	100	2	1)(ς)mn	1)(ς)mn	PROPN
ejpam-5997	100	3	(	(	PUNCT
ejpam-5997	100	4	−κ)n	−κ)n	NOUN
ejpam-5997	100	5	.	.	PUNCT
ejpam-5997	101	1	(	(	PUNCT
ejpam-5997	101	2	9	9	X
ejpam-5997	101	3	)	)	PUNCT
ejpam-5997	101	4	m.	m.	NOUN
ejpam-5997	101	5	vivas	vivas	PROPN
ejpam-5997	101	6	-	-	PROPN
ejpam-5997	101	7	cortez	cortez	PROPN
ejpam-5997	101	8	et	et	PROPN
ejpam-5997	101	9	al	al	PROPN
ejpam-5997	101	10	.	.	PUNCT
ejpam-5997	101	11	/	/	SYM
ejpam-5997	101	12	eur	eur	PROPN
ejpam-5997	101	13	.	.	PUNCT
ejpam-5997	102	1	j.	j.	PROPN
ejpam-5997	102	2	pure	pure	PROPN
ejpam-5997	102	3	appl	appl	PROPN
ejpam-5997	102	4	.	.	PROPN
ejpam-5997	102	5	math	math	PROPN
ejpam-5997	102	6	,	,	PUNCT
ejpam-5997	102	7	18	18	NUM
ejpam-5997	102	8	(	(	PUNCT
ejpam-5997	102	9	2	2	NUM
ejpam-5997	102	10	)	)	PUNCT
ejpam-5997	102	11	(	(	PUNCT
ejpam-5997	102	12	2025	2025	NUM
ejpam-5997	102	13	)	)	PUNCT
ejpam-5997	102	14	,	,	PUNCT
ejpam-5997	102	15	5997	5997	NUM
ejpam-5997	102	16	5	5	NUM
ejpam-5997	102	17	of	of	ADP
ejpam-5997	102	18	23	23	NUM
ejpam-5997	102	19	definition	definition	NOUN
ejpam-5997	102	20	10	10	NUM
ejpam-5997	102	21	.	.	PUNCT
ejpam-5997	103	1	[	[	X
ejpam-5997	103	2	39	39	NUM
ejpam-5997	103	3	]	]	PUNCT
ejpam-5997	103	4	the	the	DET
ejpam-5997	103	5	left	left	ADJ
ejpam-5997	103	6	and	and	CCONJ
ejpam-5997	103	7	right	right	ADJ
ejpam-5997	103	8	sided	side	VERB
ejpam-5997	103	9	of	of	ADP
ejpam-5997	103	10	extended	extended	ADJ
ejpam-5997	103	11	version	version	NOUN
ejpam-5997	103	12	of	of	ADP
ejpam-5997	103	13	bessel	bessel	NOUN
ejpam-5997	103	14	-	-	PUNCT
ejpam-5997	103	15	maitland	maitland	PROPN
ejpam-5997	103	16	function	function	NOUN
ejpam-5997	103	17	is	be	AUX
ejpam-5997	103	18	defined	define	VERB
ejpam-5997	103	19	for	for	ADP
ejpam-5997	103	20	the	the	DET
ejpam-5997	103	21	same	same	ADJ
ejpam-5997	103	22	assumption	assumption	NOUN
ejpam-5997	103	23	of	of	ADP
ejpam-5997	103	24	definition	definition	NOUN
ejpam-5997	103	25	(	(	PUNCT
ejpam-5997	103	26	9	9	NUM
ejpam-5997	103	27	)	)	PUNCT
ejpam-5997	103	28	,	,	PUNCT
ejpam-5997	103	29	as	as	SCONJ
ejpam-5997	103	30	follows	follow	VERB
ejpam-5997	103	31	:(	:(	PUNCT
ejpam-5997	103	32	eµ,ρ	eµ,ρ	X
ejpam-5997	103	33	,	,	PUNCT
ejpam-5997	103	34	m	m	PROPN
ejpam-5997	103	35	,	,	PUNCT
ejpam-5997	103	36	η	η	PROPN
ejpam-5997	103	37	,	,	PUNCT
ejpam-5997	103	38	c	c	PROPN
ejpam-5997	103	39	ξ	ξ	PROPN
ejpam-5997	103	40	,	,	PUNCT
ejpam-5997	103	41	ζ	ζ	NOUN
ejpam-5997	103	42	,	,	PUNCT
ejpam-5997	103	43	ς	ς	PROPN
ejpam-5997	103	44	,	,	PUNCT
ejpam-5997	103	45	κ1,p+	κ1,p+	ADJ
ejpam-5997	103	46	f	f	NOUN
ejpam-5997	103	47	)	)	PUNCT
ejpam-5997	103	48	(	(	PUNCT
ejpam-5997	103	49	x	x	X
ejpam-5997	103	50	,	,	PUNCT
ejpam-5997	103	51	r	r	NOUN
ejpam-5997	103	52	)	)	PUNCT
ejpam-5997	103	53	=	=	SYM
ejpam-5997	104	1	∫	∫	PROPN
ejpam-5997	104	2	x	x	X
ejpam-5997	105	1	p	p	X
ejpam-5997	105	2	(	(	PUNCT
ejpam-5997	105	3	x−	x−	PROPN
ejpam-5997	105	4	t)ξjµ,ρ	t)ξjµ,ρ	PROPN
ejpam-5997	105	5	,	,	PUNCT
ejpam-5997	105	6	m	m	PROPN
ejpam-5997	105	7	,	,	PUNCT
ejpam-5997	105	8	ηξ	ηξ	PROPN
ejpam-5997	105	9	,	,	PUNCT
ejpam-5997	105	10	ζ	ζ	PROPN
ejpam-5997	105	11	,	,	PUNCT
ejpam-5997	105	12	ς	ς	PROPN
ejpam-5997	105	13	,	,	PUNCT
ejpam-5997	105	14	κ1	κ1	NOUN
ejpam-5997	105	15	(	(	PUNCT
ejpam-5997	105	16	κ(x−	κ(x−	NOUN
ejpam-5997	105	17	t)µ	t)µ	NOUN
ejpam-5997	105	18	;	;	PUNCT
ejpam-5997	105	19	r)f(t)dt	r)f(t)dt	NOUN
ejpam-5997	105	20	,	,	PUNCT
ejpam-5997	105	21	(	(	PUNCT
ejpam-5997	105	22	10	10	NUM
ejpam-5997	105	23	)	)	PUNCT
ejpam-5997	105	24	(	(	PUNCT
ejpam-5997	105	25	eµ,ρ	eµ,ρ	X
ejpam-5997	105	26	,	,	PUNCT
ejpam-5997	105	27	m	m	PROPN
ejpam-5997	105	28	,	,	PUNCT
ejpam-5997	105	29	η	η	PROPN
ejpam-5997	105	30	,	,	PUNCT
ejpam-5997	105	31	c	c	PROPN
ejpam-5997	105	32	ξ	ξ	PROPN
ejpam-5997	105	33	,	,	PUNCT
ejpam-5997	105	34	ζ	ζ	NOUN
ejpam-5997	105	35	,	,	PUNCT
ejpam-5997	105	36	ς	ς	PROPN
ejpam-5997	105	37	,	,	PUNCT
ejpam-5997	105	38	κ1,q−	κ1,q−	NOUN
ejpam-5997	105	39	f	f	PROPN
ejpam-5997	105	40	)	)	PUNCT
ejpam-5997	105	41	(	(	PUNCT
ejpam-5997	105	42	x	x	X
ejpam-5997	105	43	,	,	PUNCT
ejpam-5997	105	44	r	r	NOUN
ejpam-5997	105	45	)	)	PUNCT
ejpam-5997	105	46	=	=	SYM
ejpam-5997	106	1	∫	∫	PROPN
ejpam-5997	106	2	q	q	NOUN
ejpam-5997	107	1	x	x	X
ejpam-5997	107	2	(	(	PUNCT
ejpam-5997	107	3	t−	t−	PROPN
ejpam-5997	107	4	x)ξjµ,ρ	x)ξjµ,ρ	PROPN
ejpam-5997	107	5	,	,	PUNCT
ejpam-5997	107	6	m	m	PROPN
ejpam-5997	107	7	,	,	PUNCT
ejpam-5997	107	8	ηξ	ηξ	PROPN
ejpam-5997	107	9	,	,	PUNCT
ejpam-5997	107	10	ζ	ζ	PROPN
ejpam-5997	107	11	,	,	PUNCT
ejpam-5997	107	12	ς	ς	PROPN
ejpam-5997	107	13	,	,	PUNCT
ejpam-5997	107	14	κ1	κ1	NOUN
ejpam-5997	107	15	(	(	PUNCT
ejpam-5997	107	16	κ(t−	κ(t−	PROPN
ejpam-5997	107	17	x)µ	x)µ	NOUN
ejpam-5997	107	18	;	;	PUNCT
ejpam-5997	107	19	r)f(t)dt	r)f(t)dt	PROPN
ejpam-5997	107	20	.	.	PUNCT
ejpam-5997	108	1	(	(	PUNCT
ejpam-5997	108	2	11	11	NUM
ejpam-5997	108	3	)	)	PUNCT
ejpam-5997	108	4	remark	remark	NOUN
ejpam-5997	108	5	1	1	NUM
ejpam-5997	108	6	.	.	PUNCT
ejpam-5997	109	1	if	if	SCONJ
ejpam-5997	109	2	we	we	PRON
ejpam-5997	109	3	replace	replace	VERB
ejpam-5997	109	4	r	r	NOUN
ejpam-5997	109	5	=	=	SYM
ejpam-5997	109	6	0	0	NUM
ejpam-5997	109	7	,	,	PUNCT
ejpam-5997	109	8	κ	κ	X
ejpam-5997	109	9	=	=	SYM
ejpam-5997	109	10	0	0	NUM
ejpam-5997	109	11	,	,	PUNCT
ejpam-5997	109	12	and	and	CCONJ
ejpam-5997	109	13	ξ	ξ	X
ejpam-5997	109	14	=	=	SYM
ejpam-5997	109	15	ξ−	ξ−	PROPN
ejpam-5997	109	16	1	1	NUM
ejpam-5997	109	17	in	in	ADP
ejpam-5997	109	18	the	the	DET
ejpam-5997	109	19	definition	definition	NOUN
ejpam-5997	109	20	(	(	PUNCT
ejpam-5997	109	21	10	10	NUM
ejpam-5997	109	22	)	)	PUNCT
ejpam-5997	109	23	,	,	PUNCT
ejpam-5997	109	24	we	we	PRON
ejpam-5997	109	25	obtain	obtain	VERB
ejpam-5997	109	26	the	the	DET
ejpam-5997	109	27	left	left	ADJ
ejpam-5997	109	28	-	-	PUNCT
ejpam-5997	109	29	and	and	CCONJ
ejpam-5997	109	30	right	right	ADV
ejpam-5997	109	31	-	-	PUNCT
ejpam-5997	109	32	sided	sided	ADJ
ejpam-5997	109	33	riemann	riemann	PROPN
ejpam-5997	109	34	fractional	fractional	PROPN
ejpam-5997	109	35	operators	operator	NOUN
ejpam-5997	109	36	.	.	PUNCT
ejpam-5997	110	1	3	3	X
ejpam-5997	110	2	.	.	X
ejpam-5997	110	3	applications	application	NOUN
ejpam-5997	110	4	of	of	ADP
ejpam-5997	110	5	differentiable	differentiable	ADJ
ejpam-5997	110	6	function	function	NOUN
ejpam-5997	110	7	with	with	ADP
ejpam-5997	110	8	the	the	DET
ejpam-5997	110	9	refinements	refinement	NOUN
ejpam-5997	110	10	of	of	ADP
ejpam-5997	110	11	hermite	hermite	PROPN
ejpam-5997	110	12	-	-	PUNCT
ejpam-5997	110	13	hadamard	hadamard	NOUN
ejpam-5997	110	14	(	(	PUNCT
ejpam-5997	110	15	h	h	NOUN
ejpam-5997	110	16	−h	−h	ADJ
ejpam-5997	110	17	)	)	PUNCT
ejpam-5997	110	18	inequalities	inequality	NOUN
ejpam-5997	110	19	here	here	ADV
ejpam-5997	110	20	,	,	PUNCT
ejpam-5997	110	21	we	we	PRON
ejpam-5997	110	22	discuss	discuss	VERB
ejpam-5997	110	23	the	the	DET
ejpam-5997	110	24	refinements	refinement	NOUN
ejpam-5997	110	25	of	of	ADP
ejpam-5997	110	26	hermite	hermite	ADJ
ejpam-5997	110	27	-	-	PUNCT
ejpam-5997	110	28	hadamard	hadamard	ADJ
ejpam-5997	110	29	type	type	NOUN
ejpam-5997	110	30	fractional	fractional	ADJ
ejpam-5997	110	31	inequalities	inequality	NOUN
ejpam-5997	110	32	with	with	ADP
ejpam-5997	110	33	the	the	DET
ejpam-5997	110	34	differentiable	differentiable	ADJ
ejpam-5997	110	35	functions	function	NOUN
ejpam-5997	110	36	by	by	ADP
ejpam-5997	110	37	implementations	implementation	NOUN
ejpam-5997	110	38	of	of	ADP
ejpam-5997	110	39	extended	extended	ADJ
ejpam-5997	110	40	version	version	NOUN
ejpam-5997	110	41	of	of	ADP
ejpam-5997	110	42	fractional	fractional	ADJ
ejpam-5997	110	43	operators	operator	NOUN
ejpam-5997	110	44	for	for	ADP
ejpam-5997	110	45	s	s	NOUN
ejpam-5997	110	46	-	-	NOUN
ejpam-5997	110	47	convexity	convexity	NOUN
ejpam-5997	110	48	.	.	PUNCT
ejpam-5997	111	1	lemma	lemma	PROPN
ejpam-5997	111	2	1	1	X
ejpam-5997	111	3	.	.	PUNCT
ejpam-5997	112	1	let	let	VERB
ejpam-5997	112	2	ϕ	ϕ	NOUN
ejpam-5997	112	3	:	:	PUNCT
ejpam-5997	112	4	i	i	PRON
ejpam-5997	112	5	⊆	⊆	NUM
ejpam-5997	112	6	r	r	NOUN
ejpam-5997	112	7	→	→	SYM
ejpam-5997	112	8	r	r	NOUN
ejpam-5997	112	9	be	be	AUX
ejpam-5997	112	10	a	a	DET
ejpam-5997	112	11	differentiable	differentiable	ADJ
ejpam-5997	112	12	mapping	mapping	NOUN
ejpam-5997	112	13	on	on	ADP
ejpam-5997	112	14	io	io	PROPN
ejpam-5997	112	15	and	and	CCONJ
ejpam-5997	112	16	ω	ω	PROPN
ejpam-5997	112	17	,	,	PUNCT
ejpam-5997	112	18	τ	τ	PROPN
ejpam-5997	112	19	∈	∈	PROPN
ejpam-5997	112	20	io	io	PROPN
ejpam-5997	112	21	with	with	ADP
ejpam-5997	112	22	ω	ω	PROPN
ejpam-5997	112	23	<	<	X
ejpam-5997	112	24	τ	τ	X
ejpam-5997	112	25	.	.	PUNCT
ejpam-5997	113	1	if	if	SCONJ
ejpam-5997	113	2	ϕ	ϕ	NOUN
ejpam-5997	113	3	′	′	NOUN
ejpam-5997	113	4	∈	∈	PROPN
ejpam-5997	113	5	l[ω	l[ω	PROPN
ejpam-5997	113	6	,	,	PUNCT
ejpam-5997	113	7	τ	τ	X
ejpam-5997	113	8	]	]	X
ejpam-5997	113	9	,	,	PUNCT
ejpam-5997	113	10	and	and	CCONJ
ejpam-5997	113	11	µ	µ	NOUN
ejpam-5997	113	12	,	,	PUNCT
ejpam-5997	113	13	ξ	ξ	PROPN
ejpam-5997	113	14	,	,	PUNCT
ejpam-5997	113	15	ζ	ζ	NOUN
ejpam-5997	113	16	,	,	PUNCT
ejpam-5997	113	17	ς	ς	PROPN
ejpam-5997	113	18	,	,	PUNCT
ejpam-5997	113	19	c	c	X
ejpam-5997	113	20	,	,	PUNCT
ejpam-5997	113	21	κ1	κ1	PROPN
ejpam-5997	113	22	∈	∈	PROPN
ejpam-5997	113	23	c,ℜ(µ	c,ℜ(µ	PROPN
ejpam-5997	113	24	)	)	PUNCT
ejpam-5997	113	25	>	>	X
ejpam-5997	113	26	0,ℜ(ξ	0,ℜ(ξ	PROPN
ejpam-5997	113	27	)	)	PUNCT
ejpam-5997	113	28	>	>	X
ejpam-5997	114	1	0,ℜ(ζ	0,ℜ(ζ	PROPN
ejpam-5997	114	2	)	)	PUNCT
ejpam-5997	114	3	>	>	X
ejpam-5997	114	4	0,ℜ(ς	0,ℜ(ς	PROPN
ejpam-5997	114	5	)	)	PUNCT
ejpam-5997	114	6	>	>	X
ejpam-5997	115	1	0,ℜ(κ1	0,ℜ(κ1	PROPN
ejpam-5997	115	2	)	)	PUNCT
ejpam-5997	115	3	>	>	X
ejpam-5997	115	4	0	0	NUM
ejpam-5997	115	5	,	,	PUNCT
ejpam-5997	115	6	ρ	ρ	PROPN
ejpam-5997	115	7	,	,	PUNCT
ejpam-5997	115	8	m	m	PROPN
ejpam-5997	115	9	,	,	PUNCT
ejpam-5997	115	10	η	η	PROPN
ejpam-5997	115	11	≥	≥	X
ejpam-5997	115	12	0	0	NUM
ejpam-5997	115	13	and	and	CCONJ
ejpam-5997	115	14	m	m	PROPN
ejpam-5997	115	15	,	,	PUNCT
ejpam-5997	115	16	ρ	ρ	PROPN
ejpam-5997	115	17	>	>	X
ejpam-5997	115	18	ℜ(µ	ℜ(µ	NOUN
ejpam-5997	115	19	)	)	PUNCT
ejpam-5997	115	20	+	+	CCONJ
ejpam-5997	115	21	η	η	PROPN
ejpam-5997	115	22	,	,	PUNCT
ejpam-5997	115	23	then	then	ADV
ejpam-5997	115	24	following	follow	VERB
ejpam-5997	115	25	integral	integral	ADJ
ejpam-5997	115	26	equality	equality	NOUN
ejpam-5997	115	27	holds	holds	AUX
ejpam-5997	115	28	;	;	PUNCT
ejpam-5997	115	29	ϕ(α)eµ,ρ	ϕ(α)eµ,ρ	NOUN
ejpam-5997	115	30	,	,	PUNCT
ejpam-5997	115	31	m	m	PROPN
ejpam-5997	115	32	,	,	PUNCT
ejpam-5997	115	33	η	η	PROPN
ejpam-5997	115	34	,	,	PUNCT
ejpam-5997	115	35	cξ	cξ	NOUN
ejpam-5997	115	36	,	,	PUNCT
ejpam-5997	115	37	ζ	ζ	NOUN
ejpam-5997	115	38	,	,	PUNCT
ejpam-5997	115	39	ς	ς	PROPN
ejpam-5997	115	40	,	,	PUNCT
ejpam-5997	115	41	κ1	κ1	NOUN
ejpam-5997	115	42	(	(	PUNCT
ejpam-5997	115	43	κ	κ	NOUN
ejpam-5997	115	44	,	,	PUNCT
ejpam-5997	115	45	p	p	NOUN
ejpam-5997	115	46	)	)	PUNCT
ejpam-5997	115	47	[	[	PUNCT
ejpam-5997	115	48	1	1	NUM
ejpam-5997	115	49	α−	α−	ADP
ejpam-5997	115	50	ω	ω	NUM
ejpam-5997	115	51	+	+	CCONJ
ejpam-5997	115	52	1	1	NUM
ejpam-5997	115	53	α−	α−	ADP
ejpam-5997	115	54	τ	τ	X
ejpam-5997	115	55	]	]	X
ejpam-5997	115	56	−	−	PROPN
ejpam-5997	115	57	(	(	PUNCT
ejpam-5997	115	58	ξ	ξ	X
ejpam-5997	115	59	′	′	NUM
ejpam-5997	115	60	+	+	CCONJ
ejpam-5997	115	61	µn	µn	NOUN
ejpam-5997	115	62	)	)	PUNCT
ejpam-5997	115	63	[	[	PUNCT
ejpam-5997	115	64	1	1	NUM
ejpam-5997	115	65	(	(	PUNCT
ejpam-5997	115	66	α−	α−	ADP
ejpam-5997	115	67	ω)ξ	ω)ξ	VERB
ejpam-5997	115	68	′+1	′+1	PROPN
ejpam-5997	115	69	(	(	PUNCT
ejpam-5997	115	70	eµ,ρ	eµ,ρ	X
ejpam-5997	115	71	,	,	PUNCT
ejpam-5997	115	72	m	m	PROPN
ejpam-5997	115	73	,	,	PUNCT
ejpam-5997	115	74	η	η	PROPN
ejpam-5997	115	75	,	,	PUNCT
ejpam-5997	115	76	c	c	PROPN
ejpam-5997	115	77	ξ	ξ	PROPN
ejpam-5997	115	78	,	,	PUNCT
ejpam-5997	115	79	ζ	ζ	NOUN
ejpam-5997	115	80	,	,	PUNCT
ejpam-5997	115	81	ς	ς	NOUN
ejpam-5997	115	82	,	,	PUNCT
ejpam-5997	115	83	κ1,α+ϕ	κ1,α+ϕ	VERB
ejpam-5997	115	84	)	)	PUNCT
ejpam-5997	115	85	(	(	PUNCT
ejpam-5997	115	86	ω	ω	NOUN
ejpam-5997	115	87	,	,	PUNCT
ejpam-5997	115	88	κ1	κ1	NOUN
ejpam-5997	115	89	)	)	PUNCT
ejpam-5997	115	90	+	+	CCONJ
ejpam-5997	115	91	1	1	NUM
ejpam-5997	115	92	(	(	PUNCT
ejpam-5997	115	93	α−	α−	ADP
ejpam-5997	115	94	τ)ξ	τ)ξ	NOUN
ejpam-5997	115	95	′+1	′+1	NOUN
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ejpam-5997	115	98	,	,	PUNCT
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ejpam-5997	115	100	,	,	PUNCT
ejpam-5997	115	101	η	η	PROPN
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ejpam-5997	115	103	c	c	PROPN
ejpam-5997	115	104	ξ	ξ	PROPN
ejpam-5997	115	105	,	,	PUNCT
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ejpam-5997	115	107	,	,	PUNCT
ejpam-5997	115	108	ς	ς	PROPN
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ejpam-5997	115	110	κ1,τ−	κ1,τ−	ADJ
ejpam-5997	115	111	ϕ	ϕ	NOUN
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ejpam-5997	115	113	(	(	PUNCT
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ejpam-5997	115	115	,	,	PUNCT
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ejpam-5997	116	3	1	1	NUM
ejpam-5997	116	4	0	0	NUM
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ejpam-5997	116	6	′	′	NUM
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ejpam-5997	116	8	,	,	PUNCT
ejpam-5997	116	9	m	m	PROPN
ejpam-5997	116	10	,	,	PUNCT
ejpam-5997	116	11	η	η	PROPN
ejpam-5997	116	12	,	,	PUNCT
ejpam-5997	116	13	cξ	cξ	NOUN
ejpam-5997	116	14	,	,	PUNCT
ejpam-5997	116	15	ζ	ζ	NOUN
ejpam-5997	116	16	,	,	PUNCT
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ejpam-5997	116	19	κ1	κ1	NOUN
ejpam-5997	116	20	(	(	PUNCT
ejpam-5997	116	21	κ℘µ	κ℘µ	PROPN
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ejpam-5997	116	24	′	′	NUM
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ejpam-5997	117	2	℘α+	℘α+	NUM
ejpam-5997	117	3	(	(	PUNCT
ejpam-5997	117	4	1−	1−	NUM
ejpam-5997	117	5	℘)ωd℘+	℘)ωd℘+	PROPN
ejpam-5997	117	6	∫	∫	PROPN
ejpam-5997	117	7	1	1	NUM
ejpam-5997	117	8	0	0	NUM
ejpam-5997	117	9	℘ξ	℘ξ	ADJ
ejpam-5997	117	10	′	′	NUM
ejpam-5997	117	11	eµ,ρ	eµ,ρ	NOUN
ejpam-5997	117	12	,	,	PUNCT
ejpam-5997	117	13	m	m	PROPN
ejpam-5997	117	14	,	,	PUNCT
ejpam-5997	117	15	η	η	PROPN
ejpam-5997	117	16	,	,	PUNCT
ejpam-5997	117	17	cξ	cξ	NOUN
ejpam-5997	117	18	,	,	PUNCT
ejpam-5997	117	19	ζ	ζ	NOUN
ejpam-5997	117	20	,	,	PUNCT
ejpam-5997	117	21	ς	ς	PROPN
ejpam-5997	117	22	,	,	PUNCT
ejpam-5997	117	23	κ1	κ1	NOUN
ejpam-5997	117	24	(	(	PUNCT
ejpam-5997	117	25	κ℘µ	κ℘µ	PROPN
ejpam-5997	117	26	;	;	PUNCT
ejpam-5997	117	27	p)ϕ	p)ϕ	X
ejpam-5997	117	28	′	′	NUM
ejpam-5997	118	1	(	(	PUNCT
ejpam-5997	118	2	℘α+	℘α+	NUM
ejpam-5997	118	3	(	(	PUNCT
ejpam-5997	118	4	1−	1−	NUM
ejpam-5997	118	5	℘)τd℘.	℘)τd℘.	NOUN
ejpam-5997	118	6	proof	proof	NOUN
ejpam-5997	118	7	.	.	PUNCT
ejpam-5997	119	1	consider	consider	VERB
ejpam-5997	119	2	the	the	DET
ejpam-5997	119	3	integral	integral	ADJ
ejpam-5997	119	4	i1	i1	PROPN
ejpam-5997	119	5	=	=	PUNCT
ejpam-5997	119	6	∫	∫	PROPN
ejpam-5997	119	7	1	1	NUM
ejpam-5997	119	8	0	0	NUM
ejpam-5997	119	9	℘ξ	℘ξ	ADJ
ejpam-5997	119	10	′	′	NUM
ejpam-5997	119	11	eµ,ρ	eµ,ρ	NOUN
ejpam-5997	119	12	,	,	PUNCT
ejpam-5997	119	13	m	m	PROPN
ejpam-5997	119	14	,	,	PUNCT
ejpam-5997	119	15	η	η	PROPN
ejpam-5997	119	16	,	,	PUNCT
ejpam-5997	119	17	cξ	cξ	NOUN
ejpam-5997	119	18	,	,	PUNCT
ejpam-5997	119	19	ζ	ζ	NOUN
ejpam-5997	119	20	,	,	PUNCT
ejpam-5997	119	21	ς	ς	PROPN
ejpam-5997	119	22	,	,	PUNCT
ejpam-5997	119	23	κ1	κ1	NOUN
ejpam-5997	119	24	(	(	PUNCT
ejpam-5997	119	25	κ℘µ	κ℘µ	PROPN
ejpam-5997	119	26	;	;	PUNCT
ejpam-5997	119	27	p)ϕ	p)ϕ	X
ejpam-5997	119	28	′	′	NUM
ejpam-5997	120	1	(	(	PUNCT
ejpam-5997	120	2	℘α+	℘α+	NUM
ejpam-5997	120	3	(	(	PUNCT
ejpam-5997	120	4	1−	1−	NUM
ejpam-5997	120	5	℘)ωd℘	℘)ωd℘	NOUN
ejpam-5997	120	6	=	=	PUNCT
ejpam-5997	120	7	∞∑	∞∑	PROPN
ejpam-5997	120	8	n=0	n=0	NUM
ejpam-5997	120	9	βp(ζ	βp(ζ	PUNCT
ejpam-5997	121	1	+	+	CCONJ
ejpam-5997	121	2	ρn	ρn	INTJ
ejpam-5997	121	3	,	,	PUNCT
ejpam-5997	121	4	c−	c−	NOUN
ejpam-5997	121	5	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	121	6	β(ζ	β(ζ	PROPN
ejpam-5997	121	7	,	,	PUNCT
ejpam-5997	121	8	c−	c−	X
ejpam-5997	121	9	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	121	10	ξ	ξ	X
ejpam-5997	122	1	+	+	NUM
ejpam-5997	122	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	122	3	(	(	PUNCT
ejpam-5997	122	4	−κ)n	−κ)n	NOUN
ejpam-5997	122	5	∫	∫	PROPN
ejpam-5997	122	6	1	1	NUM
ejpam-5997	122	7	0	0	NUM
ejpam-5997	122	8	℘ξ	℘ξ	NOUN
ejpam-5997	122	9	′	′	NUM
ejpam-5997	123	1	+	+	CCONJ
ejpam-5997	123	2	µnϕ	µnϕ	NOUN
ejpam-5997	123	3	′	′	NUM
ejpam-5997	123	4	(	(	PUNCT
ejpam-5997	123	5	℘α+	℘α+	NUM
ejpam-5997	123	6	(	(	PUNCT
ejpam-5997	123	7	1−	1−	NUM
ejpam-5997	123	8	℘)ωd℘	℘)ωd℘	NOUN
ejpam-5997	123	9	=	=	PUNCT
ejpam-5997	124	1	∞∑	∞∑	PROPN
ejpam-5997	124	2	n=0	n=0	NUM
ejpam-5997	124	3	βp(ζ	βp(ζ	PUNCT
ejpam-5997	125	1	+	+	CCONJ
ejpam-5997	125	2	ρn	ρn	INTJ
ejpam-5997	125	3	,	,	PUNCT
ejpam-5997	125	4	c−	c−	NOUN
ejpam-5997	125	5	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	125	6	β(ζ	β(ζ	PROPN
ejpam-5997	125	7	,	,	PUNCT
ejpam-5997	125	8	c−	c−	X
ejpam-5997	125	9	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	125	10	ξ	ξ	X
ejpam-5997	126	1	+	+	NUM
ejpam-5997	126	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	126	3	(	(	PUNCT
ejpam-5997	126	4	−κ)n	−κ)n	NOUN
ejpam-5997	126	5	[	[	PUNCT
ejpam-5997	126	6	∫	∫	PROPN
ejpam-5997	126	7	1	1	NUM
ejpam-5997	126	8	0	0	NUM
ejpam-5997	126	9	℘ξ	℘ξ	NOUN
ejpam-5997	126	10	′	′	NUM
ejpam-5997	127	1	+	+	PUNCT
ejpam-5997	127	2	µn	µn	NOUN
ejpam-5997	127	3	α−	α−	ADP
ejpam-5997	127	4	ω	ω	NUM
ejpam-5997	127	5	ϕ(℘α+	ϕ(℘α+	NOUN
ejpam-5997	127	6	(	(	PUNCT
ejpam-5997	127	7	1−	1−	NUM
ejpam-5997	127	8	℘)ω	℘)ω	VERB
ejpam-5997	127	9	∣∣1	∣∣1	NUM
ejpam-5997	127	10	0	0	NUM
ejpam-5997	128	1	−	−	NUM
ejpam-5997	128	2	∫	∫	PROPN
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ejpam-5997	128	7	+	+	CCONJ
ejpam-5997	128	8	µn	µn	PROPN
ejpam-5997	128	9	α−	α−	ADP
ejpam-5997	128	10	ω	ω	NUM
ejpam-5997	128	11	℘ξ	℘ξ	NOUN
ejpam-5997	128	12	′	′	PUNCT
ejpam-5997	129	1	+	+	ADJ
ejpam-5997	129	2	µn−1ϕ(℘α+	µn−1ϕ(℘α+	PROPN
ejpam-5997	129	3	(	(	PUNCT
ejpam-5997	129	4	1−	1−	NUM
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ejpam-5997	131	1	+	+	NUM
ejpam-5997	131	2	1)(ς)mn	1)(ς)mn	NUM
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ejpam-5997	131	4	−κ)n	−κ)n	NOUN
ejpam-5997	131	5	[	[	PUNCT
ejpam-5997	131	6	ϕ(α	ϕ(α	PROPN
ejpam-5997	131	7	)	)	PUNCT
ejpam-5997	131	8	α−	α−	ADP
ejpam-5997	131	9	ω	ω	NUM
ejpam-5997	131	10	−	−	PROPN
ejpam-5997	132	1	ξ	ξ	X
ejpam-5997	132	2	′	′	NUM
ejpam-5997	133	1	+	+	CCONJ
ejpam-5997	133	2	µn	µn	PROPN
ejpam-5997	133	3	α−	α−	ADP
ejpam-5997	133	4	ω	ω	NUM
ejpam-5997	133	5	∫	∫	PROPN
ejpam-5997	133	6	1	1	NUM
ejpam-5997	133	7	0	0	NUM
ejpam-5997	133	8	℘ξ	℘ξ	NOUN
ejpam-5997	133	9	′	′	NUM
ejpam-5997	134	1	+	+	ADJ
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ejpam-5997	134	3	(	(	PUNCT
ejpam-5997	134	4	1−	1−	NUM
ejpam-5997	134	5	℘)ωd℘	℘)ωd℘	PROPN
ejpam-5997	134	6	]	]	PUNCT
ejpam-5997	134	7	.(12	.(12	X
ejpam-5997	134	8	)	)	PUNCT
ejpam-5997	134	9	m.	m.	NOUN
ejpam-5997	134	10	vivas	vivas	PROPN
ejpam-5997	134	11	-	-	PROPN
ejpam-5997	134	12	cortez	cortez	PROPN
ejpam-5997	134	13	et	et	PROPN
ejpam-5997	134	14	al	al	PROPN
ejpam-5997	134	15	.	.	PUNCT
ejpam-5997	134	16	/	/	SYM
ejpam-5997	134	17	eur	eur	PROPN
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ejpam-5997	135	2	pure	pure	PROPN
ejpam-5997	135	3	appl	appl	PROPN
ejpam-5997	135	4	.	.	PROPN
ejpam-5997	135	5	math	math	PROPN
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ejpam-5997	135	9	2	2	NUM
ejpam-5997	135	10	)	)	PUNCT
ejpam-5997	135	11	(	(	PUNCT
ejpam-5997	135	12	2025	2025	NUM
ejpam-5997	135	13	)	)	PUNCT
ejpam-5997	135	14	,	,	PUNCT
ejpam-5997	135	15	5997	5997	NUM
ejpam-5997	135	16	6	6	NUM
ejpam-5997	135	17	of	of	ADP
ejpam-5997	135	18	23	23	NUM
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ejpam-5997	135	20	substitution	substitution	NOUN
ejpam-5997	135	21	℘α+	℘α+	PROPN
ejpam-5997	135	22	(	(	PUNCT
ejpam-5997	135	23	1−	1−	NUM
ejpam-5997	135	24	℘)ω	℘)ω	NOUN
ejpam-5997	135	25	=	=	PROPN
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ejpam-5997	136	2	in	in	ADP
ejpam-5997	136	3	equation	equation	NOUN
ejpam-5997	136	4	(	(	PUNCT
ejpam-5997	136	5	12	12	NUM
ejpam-5997	136	6	)	)	PUNCT
ejpam-5997	136	7	,	,	PUNCT
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ejpam-5997	136	18	m	m	PROPN
ejpam-5997	136	19	,	,	PUNCT
ejpam-5997	136	20	η	η	PROPN
ejpam-5997	136	21	,	,	PUNCT
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ejpam-5997	136	23	,	,	PUNCT
ejpam-5997	136	24	ζ	ζ	NOUN
ejpam-5997	136	25	,	,	PUNCT
ejpam-5997	136	26	ς	ς	PROPN
ejpam-5997	136	27	,	,	PUNCT
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ejpam-5997	136	29	(	(	PUNCT
ejpam-5997	136	30	κ	κ	NOUN
ejpam-5997	136	31	,	,	PUNCT
ejpam-5997	136	32	p)−	p)−	PROPN
ejpam-5997	136	33	ξ	ξ	PROPN
ejpam-5997	137	1	′	′	NUM
ejpam-5997	138	1	+	+	CCONJ
ejpam-5997	138	2	µn	µn	PROPN
ejpam-5997	138	3	(	(	PUNCT
ejpam-5997	138	4	α−	α−	ADP
ejpam-5997	138	5	ω)ξ	ω)ξ	VERB
ejpam-5997	138	6	′+1	′+1	PROPN
ejpam-5997	138	7	(	(	PUNCT
ejpam-5997	138	8	eµ,ρ	eµ,ρ	X
ejpam-5997	138	9	,	,	PUNCT
ejpam-5997	138	10	m	m	PROPN
ejpam-5997	138	11	,	,	PUNCT
ejpam-5997	138	12	η	η	PROPN
ejpam-5997	138	13	,	,	PUNCT
ejpam-5997	138	14	c	c	PROPN
ejpam-5997	138	15	ξ	ξ	PROPN
ejpam-5997	138	16	,	,	PUNCT
ejpam-5997	138	17	ζ	ζ	NOUN
ejpam-5997	138	18	,	,	PUNCT
ejpam-5997	138	19	ς	ς	NOUN
ejpam-5997	138	20	,	,	PUNCT
ejpam-5997	138	21	κ1,α+ϕ	κ1,α+ϕ	VERB
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ejpam-5997	138	23	(	(	PUNCT
ejpam-5997	138	24	ω	ω	PROPN
ejpam-5997	138	25	,	,	PUNCT
ejpam-5997	138	26	κ	κ	NOUN
ejpam-5997	138	27	)	)	PUNCT
ejpam-5997	138	28	.	.	PUNCT
ejpam-5997	139	1	(	(	PUNCT
ejpam-5997	139	2	13	13	NUM
ejpam-5997	139	3	)	)	PUNCT
ejpam-5997	139	4	now	now	ADV
ejpam-5997	139	5	,	,	PUNCT
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ejpam-5997	139	7	the	the	DET
ejpam-5997	139	8	integral	integral	ADJ
ejpam-5997	139	9	i2	i2	NOUN
ejpam-5997	139	10	,	,	PUNCT
ejpam-5997	139	11	we	we	PRON
ejpam-5997	139	12	have	have	VERB
ejpam-5997	139	13	i2	i2	PROPN
ejpam-5997	139	14	=	=	SYM
ejpam-5997	140	1	∫	∫	PROPN
ejpam-5997	140	2	1	1	NUM
ejpam-5997	140	3	0	0	NUM
ejpam-5997	140	4	℘ξ	℘ξ	ADJ
ejpam-5997	140	5	′	′	NUM
ejpam-5997	140	6	eµ,ρ	eµ,ρ	NOUN
ejpam-5997	140	7	,	,	PUNCT
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ejpam-5997	140	9	,	,	PUNCT
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ejpam-5997	140	11	,	,	PUNCT
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ejpam-5997	140	13	,	,	PUNCT
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ejpam-5997	140	16	ς	ς	PROPN
ejpam-5997	140	17	,	,	PUNCT
ejpam-5997	140	18	κ1	κ1	NOUN
ejpam-5997	140	19	(	(	PUNCT
ejpam-5997	140	20	κ℘µ	κ℘µ	PROPN
ejpam-5997	140	21	;	;	PUNCT
ejpam-5997	140	22	p)ϕ	p)ϕ	X
ejpam-5997	140	23	′	′	NUM
ejpam-5997	140	24	(	(	PUNCT
ejpam-5997	140	25	℘α+	℘α+	NUM
ejpam-5997	140	26	(	(	PUNCT
ejpam-5997	140	27	1−	1−	NUM
ejpam-5997	140	28	℘)τd℘.	℘)τd℘.	PROPN
ejpam-5997	140	29	proceeding	proceeding	NOUN
ejpam-5997	140	30	same	same	ADJ
ejpam-5997	140	31	as	as	ADP
ejpam-5997	140	32	i1	i1	PROPN
ejpam-5997	140	33	and	and	CCONJ
ejpam-5997	140	34	we	we	PRON
ejpam-5997	140	35	get	get	VERB
ejpam-5997	140	36	the	the	DET
ejpam-5997	140	37	result	result	NOUN
ejpam-5997	140	38	,	,	PUNCT
ejpam-5997	140	39	i2	i2	PROPN
ejpam-5997	140	40	=	=	SYM
ejpam-5997	140	41	ϕ(α	ϕ(α	PROPN
ejpam-5997	140	42	)	)	PUNCT
ejpam-5997	140	43	α−	α−	ADP
ejpam-5997	140	44	τ	τ	PROPN
ejpam-5997	140	45	jµ,ρ	jµ,ρ	X
ejpam-5997	140	46	,	,	PUNCT
ejpam-5997	140	47	m	m	PROPN
ejpam-5997	140	48	,	,	PUNCT
ejpam-5997	140	49	η	η	PROPN
ejpam-5997	140	50	,	,	PUNCT
ejpam-5997	140	51	cξ	cξ	NOUN
ejpam-5997	140	52	,	,	PUNCT
ejpam-5997	140	53	ζ	ζ	NOUN
ejpam-5997	140	54	,	,	PUNCT
ejpam-5997	140	55	ς	ς	PROPN
ejpam-5997	140	56	,	,	PUNCT
ejpam-5997	140	57	κ1	κ1	NOUN
ejpam-5997	140	58	(	(	PUNCT
ejpam-5997	140	59	κ	κ	NOUN
ejpam-5997	140	60	,	,	PUNCT
ejpam-5997	140	61	p)−	p)−	PROPN
ejpam-5997	140	62	ξ	ξ	PROPN
ejpam-5997	140	63	′	′	NUM
ejpam-5997	141	1	+	+	CCONJ
ejpam-5997	141	2	µn	µn	PROPN
ejpam-5997	141	3	(	(	PUNCT
ejpam-5997	141	4	α−	α−	ADP
ejpam-5997	141	5	τ)ξ	τ)ξ	NOUN
ejpam-5997	141	6	′+1	′+1	NOUN
ejpam-5997	141	7	(	(	PUNCT
ejpam-5997	141	8	eµ,ρ	eµ,ρ	X
ejpam-5997	141	9	,	,	PUNCT
ejpam-5997	141	10	m	m	PROPN
ejpam-5997	141	11	,	,	PUNCT
ejpam-5997	141	12	η	η	PROPN
ejpam-5997	141	13	,	,	PUNCT
ejpam-5997	141	14	c	c	PROPN
ejpam-5997	141	15	ξ	ξ	PROPN
ejpam-5997	141	16	,	,	PUNCT
ejpam-5997	141	17	ζ	ζ	NOUN
ejpam-5997	141	18	,	,	PUNCT
ejpam-5997	141	19	ς	ς	PROPN
ejpam-5997	141	20	,	,	PUNCT
ejpam-5997	141	21	κ1,τ−	κ1,τ−	ADJ
ejpam-5997	141	22	ϕ	ϕ	NOUN
ejpam-5997	141	23	)	)	PUNCT
ejpam-5997	141	24	(	(	PUNCT
ejpam-5997	141	25	ω	ω	PROPN
ejpam-5997	141	26	,	,	PUNCT
ejpam-5997	141	27	κ	κ	NOUN
ejpam-5997	141	28	)	)	PUNCT
ejpam-5997	141	29	.	.	PUNCT
ejpam-5997	142	1	(	(	PUNCT
ejpam-5997	142	2	14	14	NUM
ejpam-5997	142	3	)	)	PUNCT
ejpam-5997	142	4	by	by	ADP
ejpam-5997	142	5	combining	combine	VERB
ejpam-5997	142	6	equation	equation	NOUN
ejpam-5997	142	7	(	(	PUNCT
ejpam-5997	142	8	13	13	NUM
ejpam-5997	142	9	)	)	PUNCT
ejpam-5997	142	10	and	and	CCONJ
ejpam-5997	142	11	(	(	PUNCT
ejpam-5997	142	12	14	14	NUM
ejpam-5997	142	13	)	)	PUNCT
ejpam-5997	142	14	we	we	PRON
ejpam-5997	142	15	get	get	VERB
ejpam-5997	142	16	the	the	DET
ejpam-5997	142	17	required	require	VERB
ejpam-5997	142	18	result	result	NOUN
ejpam-5997	142	19	.	.	PUNCT
ejpam-5997	143	1	corollary	corollary	ADJ
ejpam-5997	143	2	1	1	NUM
ejpam-5997	143	3	.	.	PUNCT
ejpam-5997	144	1	if	if	SCONJ
ejpam-5997	144	2	we	we	PRON
ejpam-5997	144	3	replace	replace	VERB
ejpam-5997	144	4	p	p	NOUN
ejpam-5997	144	5	=	=	NOUN
ejpam-5997	144	6	0	0	NUM
ejpam-5997	144	7	,	,	PUNCT
ejpam-5997	144	8	κ	κ	X
ejpam-5997	144	9	=	=	SYM
ejpam-5997	144	10	0	0	NUM
ejpam-5997	144	11	,	,	PUNCT
ejpam-5997	144	12	and	and	CCONJ
ejpam-5997	144	13	ξ	ξ	X
ejpam-5997	144	14	=	=	SYM
ejpam-5997	144	15	ξ	ξ	PROPN
ejpam-5997	144	16	−	−	PROPN
ejpam-5997	144	17	1	1	NUM
ejpam-5997	144	18	in	in	ADP
ejpam-5997	144	19	the	the	DET
ejpam-5997	144	20	lemma	lemma	PROPN
ejpam-5997	144	21	(	(	PUNCT
ejpam-5997	144	22	1	1	NUM
ejpam-5997	144	23	)	)	PUNCT
ejpam-5997	144	24	,	,	PUNCT
ejpam-5997	144	25	we	we	PRON
ejpam-5997	144	26	have	have	VERB
ejpam-5997	144	27	a	a	DET
ejpam-5997	144	28	result	result	NOUN
ejpam-5997	144	29	[	[	X
ejpam-5997	144	30	19	19	NUM
ejpam-5997	144	31	]	]	PUNCT
ejpam-5997	144	32	.	.	PUNCT
ejpam-5997	145	1	theorem	theorem	NOUN
ejpam-5997	145	2	1	1	X
ejpam-5997	145	3	.	.	PUNCT
ejpam-5997	146	1	let	let	VERB
ejpam-5997	146	2	ϕ	ϕ	NOUN
ejpam-5997	146	3	:	:	PUNCT
ejpam-5997	146	4	[	[	X
ejpam-5997	146	5	ω	ω	PROPN
ejpam-5997	146	6	,	,	PUNCT
ejpam-5997	146	7	τ	τ	X
ejpam-5997	146	8	]	]	PUNCT
ejpam-5997	146	9	→	→	PUNCT
ejpam-5997	146	10	r	r	NOUN
ejpam-5997	146	11	be	be	AUX
ejpam-5997	146	12	a	a	DET
ejpam-5997	146	13	positive	positive	ADJ
ejpam-5997	146	14	function	function	NOUN
ejpam-5997	146	15	with	with	ADP
ejpam-5997	146	16	0	0	NUM
ejpam-5997	146	17	≤	≤	NUM
ejpam-5997	146	18	ω	ω	PROPN
ejpam-5997	146	19	<	<	X
ejpam-5997	146	20	α	α	X
ejpam-5997	146	21	<	<	X
ejpam-5997	146	22	τ	τ	PROPN
ejpam-5997	146	23	and	and	CCONJ
ejpam-5997	146	24	ϕ	ϕ	PROPN
ejpam-5997	146	25	∈	∈	PROPN
ejpam-5997	146	26	l[ω	l[ω	PROPN
ejpam-5997	146	27	,	,	PUNCT
ejpam-5997	146	28	τ	τ	X
ejpam-5997	146	29	]	]	X
ejpam-5997	146	30	.	.	PUNCT
ejpam-5997	147	1	if	if	SCONJ
ejpam-5997	147	2	ϕ	ϕ	NOUN
ejpam-5997	147	3	is	be	AUX
ejpam-5997	147	4	s	s	NOUN
ejpam-5997	147	5	-	-	ADJ
ejpam-5997	147	6	convex	convex	ADJ
ejpam-5997	147	7	function	function	NOUN
ejpam-5997	147	8	on	on	ADP
ejpam-5997	147	9	[	[	X
ejpam-5997	147	10	ω	ω	PROPN
ejpam-5997	147	11	,	,	PUNCT
ejpam-5997	147	12	τ	τ	X
ejpam-5997	147	13	]	]	X
ejpam-5997	147	14	,	,	PUNCT
ejpam-5997	147	15	and	and	CCONJ
ejpam-5997	147	16	µ	µ	NOUN
ejpam-5997	147	17	,	,	PUNCT
ejpam-5997	147	18	ξ	ξ	PROPN
ejpam-5997	147	19	,	,	PUNCT
ejpam-5997	147	20	ζ	ζ	NOUN
ejpam-5997	147	21	,	,	PUNCT
ejpam-5997	147	22	ς	ς	PROPN
ejpam-5997	147	23	,	,	PUNCT
ejpam-5997	147	24	c	c	X
ejpam-5997	147	25	,	,	PUNCT
ejpam-5997	147	26	κ1	κ1	PROPN
ejpam-5997	147	27	∈	∈	PROPN
ejpam-5997	147	28	c,ℜ(µ	c,ℜ(µ	PROPN
ejpam-5997	147	29	)	)	PUNCT
ejpam-5997	147	30	>	>	X
ejpam-5997	147	31	0,ℜ(ξ	0,ℜ(ξ	PROPN
ejpam-5997	147	32	)	)	PUNCT
ejpam-5997	147	33	>	>	X
ejpam-5997	147	34	0,ℜ(ζ	0,ℜ(ζ	PROPN
ejpam-5997	147	35	)	)	PUNCT
ejpam-5997	147	36	>	>	X
ejpam-5997	147	37	0,ℜ(ς	0,ℜ(ς	PROPN
ejpam-5997	147	38	)	)	PUNCT
ejpam-5997	147	39	>	>	X
ejpam-5997	148	1	0,ℜ(κ1	0,ℜ(κ1	PROPN
ejpam-5997	148	2	)	)	PUNCT
ejpam-5997	148	3	>	>	X
ejpam-5997	148	4	0	0	NUM
ejpam-5997	148	5	,	,	PUNCT
ejpam-5997	148	6	ρ	ρ	PROPN
ejpam-5997	148	7	,	,	PUNCT
ejpam-5997	148	8	m	m	PROPN
ejpam-5997	148	9	,	,	PUNCT
ejpam-5997	148	10	η	η	PROPN
ejpam-5997	148	11	≥	≥	X
ejpam-5997	148	12	0	0	NUM
ejpam-5997	148	13	and	and	CCONJ
ejpam-5997	148	14	m	m	PROPN
ejpam-5997	148	15	,	,	PUNCT
ejpam-5997	148	16	ρ	ρ	PROPN
ejpam-5997	148	17	>	>	X
ejpam-5997	148	18	ℜ(µ	ℜ(µ	NOUN
ejpam-5997	148	19	)	)	PUNCT
ejpam-5997	148	20	+	+	CCONJ
ejpam-5997	148	21	η	η	PROPN
ejpam-5997	148	22	,	,	PUNCT
ejpam-5997	148	23	then	then	ADV
ejpam-5997	148	24	we	we	PRON
ejpam-5997	148	25	get	get	VERB
ejpam-5997	148	26	the	the	DET
ejpam-5997	148	27	following	follow	VERB
ejpam-5997	148	28	inequality	inequality	NOUN
ejpam-5997	148	29	(	(	PUNCT
ejpam-5997	148	30	eµ,ρ	eµ,ρ	X
ejpam-5997	148	31	,	,	PUNCT
ejpam-5997	148	32	m	m	PROPN
ejpam-5997	148	33	,	,	PUNCT
ejpam-5997	148	34	η	η	PROPN
ejpam-5997	148	35	,	,	PUNCT
ejpam-5997	148	36	c	c	PROPN
ejpam-5997	148	37	ξ	ξ	PROPN
ejpam-5997	148	38	,	,	PUNCT
ejpam-5997	148	39	ζ	ζ	NOUN
ejpam-5997	148	40	,	,	PUNCT
ejpam-5997	148	41	ς	ς	NOUN
ejpam-5997	148	42	,	,	PUNCT
ejpam-5997	148	43	κ1,α+ϕ	κ1,α+ϕ	VERB
ejpam-5997	148	44	)	)	PUNCT
ejpam-5997	148	45	(	(	PUNCT
ejpam-5997	148	46	ω	ω	PROPN
ejpam-5997	148	47	,	,	PUNCT
ejpam-5997	148	48	κ	κ	NOUN
ejpam-5997	148	49	)	)	PUNCT
ejpam-5997	148	50	(	(	PUNCT
ejpam-5997	148	51	α−	α−	ADP
ejpam-5997	148	52	ω)ξ′+µn+1	ω)ξ′+µn+1	NUM
ejpam-5997	148	53	+	+	CCONJ
ejpam-5997	148	54	(	(	PUNCT
ejpam-5997	148	55	eµ,ρ	eµ,ρ	X
ejpam-5997	148	56	,	,	PUNCT
ejpam-5997	148	57	m	m	PROPN
ejpam-5997	148	58	,	,	PUNCT
ejpam-5997	148	59	η	η	PROPN
ejpam-5997	148	60	,	,	PUNCT
ejpam-5997	148	61	c	c	PROPN
ejpam-5997	148	62	ξ	ξ	PROPN
ejpam-5997	148	63	,	,	PUNCT
ejpam-5997	148	64	ζ	ζ	NOUN
ejpam-5997	148	65	,	,	PUNCT
ejpam-5997	148	66	ς	ς	PROPN
ejpam-5997	148	67	,	,	PUNCT
ejpam-5997	148	68	κ1,τ−	κ1,τ−	ADJ
ejpam-5997	148	69	ϕ	ϕ	NOUN
ejpam-5997	148	70	)	)	PUNCT
ejpam-5997	148	71	(	(	PUNCT
ejpam-5997	148	72	ω	ω	PROPN
ejpam-5997	148	73	,	,	PUNCT
ejpam-5997	148	74	κ	κ	NOUN
ejpam-5997	148	75	)	)	PUNCT
ejpam-5997	148	76	(	(	PUNCT
ejpam-5997	148	77	α−	α−	X
ejpam-5997	148	78	τ)ξ′+µn+1	τ)ξ′+µn+1	PUNCT
ejpam-5997	148	79	≤	≤	NUM
ejpam-5997	148	80	ϕ(α)jµ,ρ	ϕ(α)jµ,ρ	NUM
ejpam-5997	148	81	,	,	PUNCT
ejpam-5997	148	82	m	m	PROPN
ejpam-5997	148	83	,	,	PUNCT
ejpam-5997	148	84	η	η	PROPN
ejpam-5997	148	85	,	,	PUNCT
ejpam-5997	148	86	cξ	cξ	NOUN
ejpam-5997	148	87	,	,	PUNCT
ejpam-5997	148	88	ζ	ζ	NOUN
ejpam-5997	148	89	,	,	PUNCT
ejpam-5997	148	90	ς	ς	PROPN
ejpam-5997	148	91	,	,	PUNCT
ejpam-5997	148	92	κ1	κ1	NOUN
ejpam-5997	148	93	(	(	PUNCT
ejpam-5997	148	94	κ	κ	NOUN
ejpam-5997	148	95	,	,	PUNCT
ejpam-5997	148	96	p	p	NOUN
ejpam-5997	148	97	)	)	PUNCT
ejpam-5997	148	98	[	[	PUNCT
ejpam-5997	148	99	β(ξ	β(ξ	PROPN
ejpam-5997	148	100	′	′	NOUN
ejpam-5997	148	101	+	+	CCONJ
ejpam-5997	148	102	µn+	µn+	ADV
ejpam-5997	148	103	s+	s+	ADP
ejpam-5997	148	104	1	1	NUM
ejpam-5997	148	105	,	,	PUNCT
ejpam-5997	148	106	1	1	NUM
ejpam-5997	148	107	)	)	PUNCT
ejpam-5997	149	1	+	+	CCONJ
ejpam-5997	149	2	β(ξ	β(ξ	PROPN
ejpam-5997	149	3	′	′	NOUN
ejpam-5997	149	4	+	+	CCONJ
ejpam-5997	149	5	s	s	X
ejpam-5997	149	6	,	,	PUNCT
ejpam-5997	149	7	1	1	NUM
ejpam-5997	149	8	)	)	PUNCT
ejpam-5997	149	9	]	]	PUNCT
ejpam-5997	150	1	+	+	CCONJ
ejpam-5997	150	2	[	[	PUNCT
ejpam-5997	150	3	ϕ(ω	ϕ(ω	NOUN
ejpam-5997	150	4	)	)	PUNCT
ejpam-5997	150	5	+	+	CCONJ
ejpam-5997	150	6	ϕ(τ	ϕ(τ	PROPN
ejpam-5997	150	7	)	)	PUNCT
ejpam-5997	150	8	]	]	PUNCT
ejpam-5997	150	9	jµ,ρ	jµ,ρ	PROPN
ejpam-5997	150	10	,	,	PUNCT
ejpam-5997	150	11	m	m	PROPN
ejpam-5997	150	12	,	,	PUNCT
ejpam-5997	150	13	η	η	PROPN
ejpam-5997	150	14	,	,	PUNCT
ejpam-5997	150	15	cξ	cξ	NOUN
ejpam-5997	150	16	,	,	PUNCT
ejpam-5997	150	17	ζ	ζ	NOUN
ejpam-5997	150	18	,	,	PUNCT
ejpam-5997	150	19	ς	ς	PROPN
ejpam-5997	150	20	,	,	PUNCT
ejpam-5997	150	21	κ1	κ1	NOUN
ejpam-5997	150	22	(	(	PUNCT
ejpam-5997	150	23	κ	κ	NOUN
ejpam-5997	150	24	,	,	PUNCT
ejpam-5997	150	25	p)β(ξ	p)β(ξ	PRON
ejpam-5997	150	26	′	′	VERB
ejpam-5997	151	1	+	+	CCONJ
ejpam-5997	151	2	1	1	NUM
ejpam-5997	151	3	,	,	PUNCT
ejpam-5997	151	4	s+	s+	X
ejpam-5997	151	5	1	1	NUM
ejpam-5997	151	6	)	)	PUNCT
ejpam-5997	151	7	.	.	PUNCT
ejpam-5997	152	1	proof	proof	NOUN
ejpam-5997	152	2	.	.	PUNCT
ejpam-5997	153	1	from	from	ADP
ejpam-5997	153	2	definition	definition	NOUN
ejpam-5997	153	3	of	of	ADP
ejpam-5997	153	4	s	s	NOUN
ejpam-5997	153	5	-	-	NOUN
ejpam-5997	153	6	convexity	convexity	NOUN
ejpam-5997	153	7	of	of	ADP
ejpam-5997	153	8	ϕ	ϕ	NOUN
ejpam-5997	153	9	,	,	PUNCT
ejpam-5997	153	10	ϕ(℘α+	ϕ(℘α+	PROPN
ejpam-5997	153	11	(	(	PUNCT
ejpam-5997	153	12	1−	1−	NUM
ejpam-5997	153	13	℘)ω	℘)ω	NOUN
ejpam-5997	153	14	)	)	PUNCT
ejpam-5997	154	1	+	+	CCONJ
ejpam-5997	154	2	ϕ(℘α+	ϕ(℘α+	PRON
ejpam-5997	154	3	(	(	PUNCT
ejpam-5997	154	4	1−	1−	NUM
ejpam-5997	154	5	℘)τ	℘)τ	NOUN
ejpam-5997	154	6	)	)	PUNCT
ejpam-5997	154	7	≤	≤	NOUN
ejpam-5997	154	8	℘sϕ(α	℘sϕ(α	PUNCT
ejpam-5997	154	9	)	)	PUNCT
ejpam-5997	155	1	+	+	CCONJ
ejpam-5997	155	2	(	(	PUNCT
ejpam-5997	155	3	1−	1−	NUM
ejpam-5997	155	4	℘)sϕ(ω	℘)sϕ(ω	NOUN
ejpam-5997	155	5	)	)	PUNCT
ejpam-5997	155	6	+	+	CCONJ
ejpam-5997	155	7	℘sϕ(α	℘sϕ(α	X
ejpam-5997	155	8	)	)	PUNCT
ejpam-5997	155	9	+	+	CCONJ
ejpam-5997	155	10	(	(	PUNCT
ejpam-5997	155	11	1−	1−	NUM
ejpam-5997	155	12	℘)sϕ(τ	℘)sϕ(τ	NOUN
ejpam-5997	155	13	)	)	PUNCT
ejpam-5997	155	14	multiplying	multiply	VERB
ejpam-5997	155	15	both	both	DET
ejpam-5997	155	16	sides	side	NOUN
ejpam-5997	155	17	with	with	ADP
ejpam-5997	155	18	℘ξ	℘ξ	ADJ
ejpam-5997	155	19	′	′	NUM
ejpam-5997	155	20	eµ,ρ	eµ,ρ	NOUN
ejpam-5997	155	21	,	,	PUNCT
ejpam-5997	155	22	m	m	PROPN
ejpam-5997	155	23	,	,	PUNCT
ejpam-5997	155	24	η	η	PROPN
ejpam-5997	155	25	,	,	PUNCT
ejpam-5997	155	26	cξ	cξ	NOUN
ejpam-5997	155	27	,	,	PUNCT
ejpam-5997	155	28	ζ	ζ	NOUN
ejpam-5997	155	29	,	,	PUNCT
ejpam-5997	155	30	ς	ς	PROPN
ejpam-5997	155	31	,	,	PUNCT
ejpam-5997	155	32	κ1	κ1	NOUN
ejpam-5997	155	33	(	(	PUNCT
ejpam-5997	155	34	κ℘µ	κ℘µ	PROPN
ejpam-5997	155	35	;	;	PUNCT
ejpam-5997	155	36	p	p	X
ejpam-5997	155	37	)	)	PUNCT
ejpam-5997	155	38	and	and	CCONJ
ejpam-5997	155	39	integrate	integrate	VERB
ejpam-5997	155	40	w.r.t	w.r.t	ADJ
ejpam-5997	155	41	℘	℘	PROPN
ejpam-5997	155	42	on	on	ADP
ejpam-5997	155	43	[	[	X
ejpam-5997	155	44	0	0	NUM
ejpam-5997	155	45	,	,	PUNCT
ejpam-5997	155	46	1]∫	1]∫	NOUN
ejpam-5997	155	47	1	1	NUM
ejpam-5997	155	48	0	0	NUM
ejpam-5997	155	49	℘ξ	℘ξ	ADJ
ejpam-5997	155	50	′	′	NUM
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ejpam-5997	155	69	1−	1−	NUM
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ejpam-5997	156	6	′	′	NUM
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ejpam-5997	156	8	,	,	PUNCT
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ejpam-5997	156	21	κ℘µ	κ℘µ	PROPN
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ejpam-5997	156	23	p)ϕ(℘α+	p)ϕ(℘α+	PROPN
ejpam-5997	156	24	(	(	PUNCT
ejpam-5997	156	25	1−	1−	NUM
ejpam-5997	156	26	℘)τ	℘)τ	NOUN
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ejpam-5997	157	1	+	+	NOUN
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ejpam-5997	158	4	0	0	NUM
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ejpam-5997	158	6	′	′	NUM
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ejpam-5997	158	8	,	,	PUNCT
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ejpam-5997	158	21	κ℘µ	κ℘µ	PROPN
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ejpam-5997	158	23	p)(1−	p)(1−	PROPN
ejpam-5997	158	24	℘)sϕ(ω	℘)sϕ(ω	NOUN
ejpam-5997	158	25	)	)	PUNCT
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ejpam-5997	159	3	1	1	NUM
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ejpam-5997	159	6	′	′	NUM
ejpam-5997	160	1	+	+	NOUN
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ejpam-5997	160	3	,	,	PUNCT
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ejpam-5997	160	16	κ℘µ	κ℘µ	PROPN
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ejpam-5997	160	18	p)ϕ(α	p)ϕ(α	NOUN
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ejpam-5997	161	1	+	+	CCONJ
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ejpam-5997	162	18	p)ϕ(α	p)ϕ(α	NOUN
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ejpam-5997	164	8	c−	c−	X
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ejpam-5997	165	1	+	+	NUM
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ejpam-5997	166	1	+	+	NOUN
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ejpam-5997	167	12	2025	2025	NUM
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ejpam-5997	170	2	16	16	NUM
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ejpam-5997	171	1	+	+	CCONJ
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ejpam-5997	171	3	1	1	NUM
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ejpam-5997	171	6	1	1	X
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ejpam-5997	171	10	)	)	PUNCT
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ejpam-5997	171	13	0	0	NUM
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ejpam-5997	172	1	+	+	NOUN
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ejpam-5997	173	17	p)β(ξ	p)β(ξ	PRON
ejpam-5997	173	18	′	′	VERB
ejpam-5997	174	1	+	+	CCONJ
ejpam-5997	174	2	µn+	µn+	ADJ
ejpam-5997	174	3	s	s	NOUN
ejpam-5997	174	4	,	,	PUNCT
ejpam-5997	174	5	1	1	NUM
ejpam-5997	174	6	)	)	PUNCT
ejpam-5997	174	7	(	(	PUNCT
ejpam-5997	174	8	18	18	NUM
ejpam-5997	174	9	)	)	PUNCT
ejpam-5997	174	10	∫	∫	PROPN
ejpam-5997	174	11	1	1	NUM
ejpam-5997	174	12	0	0	NUM
ejpam-5997	174	13	℘ξ	℘ξ	ADJ
ejpam-5997	174	14	′	′	NUM
ejpam-5997	174	15	eµ,ρ	eµ,ρ	NOUN
ejpam-5997	174	16	,	,	PUNCT
ejpam-5997	174	17	m	m	PROPN
ejpam-5997	174	18	,	,	PUNCT
ejpam-5997	174	19	η	η	PROPN
ejpam-5997	174	20	,	,	PUNCT
ejpam-5997	174	21	cξ	cξ	NOUN
ejpam-5997	174	22	,	,	PUNCT
ejpam-5997	174	23	ζ	ζ	NOUN
ejpam-5997	174	24	,	,	PUNCT
ejpam-5997	174	25	ς	ς	PROPN
ejpam-5997	174	26	,	,	PUNCT
ejpam-5997	174	27	κ1	κ1	NOUN
ejpam-5997	174	28	(	(	PUNCT
ejpam-5997	174	29	κ℘µ	κ℘µ	PROPN
ejpam-5997	174	30	;	;	PUNCT
ejpam-5997	174	31	p)(1−	p)(1−	ADJ
ejpam-5997	174	32	℘)sϕ(τ	℘)sϕ(τ	NOUN
ejpam-5997	174	33	)	)	PUNCT
ejpam-5997	175	1	=	=	SYM
ejpam-5997	175	2	ϕ(τ)jµ,ρ	ϕ(τ)jµ,ρ	PROPN
ejpam-5997	175	3	,	,	PUNCT
ejpam-5997	175	4	m	m	PROPN
ejpam-5997	175	5	,	,	PUNCT
ejpam-5997	175	6	η	η	PROPN
ejpam-5997	175	7	,	,	PUNCT
ejpam-5997	175	8	cξ	cξ	NOUN
ejpam-5997	175	9	,	,	PUNCT
ejpam-5997	175	10	ζ	ζ	NOUN
ejpam-5997	175	11	,	,	PUNCT
ejpam-5997	175	12	ς	ς	PROPN
ejpam-5997	175	13	,	,	PUNCT
ejpam-5997	175	14	κ1	κ1	NOUN
ejpam-5997	175	15	(	(	PUNCT
ejpam-5997	175	16	κ	κ	NOUN
ejpam-5997	175	17	,	,	PUNCT
ejpam-5997	175	18	p)β(ξ	p)β(ξ	PRON
ejpam-5997	175	19	′	′	VERB
ejpam-5997	176	1	+	+	CCONJ
ejpam-5997	176	2	µn+	µn+	ADJ
ejpam-5997	176	3	1	1	NUM
ejpam-5997	176	4	,	,	PUNCT
ejpam-5997	176	5	s+	s+	X
ejpam-5997	176	6	1	1	X
ejpam-5997	176	7	)	)	PUNCT
ejpam-5997	176	8	(	(	PUNCT
ejpam-5997	176	9	19	19	NUM
ejpam-5997	176	10	)	)	PUNCT
ejpam-5997	176	11	putting	put	VERB
ejpam-5997	176	12	the	the	DET
ejpam-5997	176	13	values	value	NOUN
ejpam-5997	176	14	(	(	PUNCT
ejpam-5997	176	15	16	16	NUM
ejpam-5997	176	16	)	)	PUNCT
ejpam-5997	176	17	,	,	PUNCT
ejpam-5997	176	18	(	(	PUNCT
ejpam-5997	176	19	17	17	NUM
ejpam-5997	176	20	)	)	PUNCT
ejpam-5997	176	21	,	,	PUNCT
ejpam-5997	176	22	(	(	PUNCT
ejpam-5997	176	23	18	18	NUM
ejpam-5997	176	24	)	)	PUNCT
ejpam-5997	176	25	and	and	CCONJ
ejpam-5997	176	26	(	(	PUNCT
ejpam-5997	176	27	19	19	NUM
ejpam-5997	176	28	)	)	PUNCT
ejpam-5997	176	29	in	in	ADP
ejpam-5997	176	30	equation	equation	NOUN
ejpam-5997	176	31	(	(	PUNCT
ejpam-5997	176	32	15	15	NUM
ejpam-5997	176	33	)	)	PUNCT
ejpam-5997	176	34	,	,	PUNCT
ejpam-5997	176	35	we	we	PRON
ejpam-5997	176	36	have∫	have∫	VERB
ejpam-5997	176	37	1	1	NUM
ejpam-5997	176	38	0	0	NUM
ejpam-5997	176	39	℘ξ	℘ξ	ADJ
ejpam-5997	176	40	′	′	NUM
ejpam-5997	176	41	eµ,ρ	eµ,ρ	NOUN
ejpam-5997	176	42	,	,	PUNCT
ejpam-5997	176	43	m	m	PROPN
ejpam-5997	176	44	,	,	PUNCT
ejpam-5997	176	45	η	η	PROPN
ejpam-5997	176	46	,	,	PUNCT
ejpam-5997	176	47	cξ	cξ	NOUN
ejpam-5997	176	48	,	,	PUNCT
ejpam-5997	176	49	ζ	ζ	NOUN
ejpam-5997	176	50	,	,	PUNCT
ejpam-5997	176	51	ς	ς	PROPN
ejpam-5997	176	52	,	,	PUNCT
ejpam-5997	176	53	κ1	κ1	NOUN
ejpam-5997	176	54	(	(	PUNCT
ejpam-5997	176	55	κ℘µ	κ℘µ	PROPN
ejpam-5997	176	56	;	;	PUNCT
ejpam-5997	176	57	p)ϕ(℘α+	p)ϕ(℘α+	PROPN
ejpam-5997	176	58	(	(	PUNCT
ejpam-5997	176	59	1−	1−	NUM
ejpam-5997	176	60	℘)ω	℘)ω	NOUN
ejpam-5997	176	61	)	)	PUNCT
ejpam-5997	177	1	+	+	CCONJ
ejpam-5997	177	2	∫	∫	PROPN
ejpam-5997	177	3	1	1	NUM
ejpam-5997	177	4	0	0	NUM
ejpam-5997	177	5	℘ξ	℘ξ	ADJ
ejpam-5997	177	6	′	′	NUM
ejpam-5997	177	7	eµ,ρ	eµ,ρ	NOUN
ejpam-5997	177	8	,	,	PUNCT
ejpam-5997	177	9	m	m	PROPN
ejpam-5997	177	10	,	,	PUNCT
ejpam-5997	177	11	η	η	PROPN
ejpam-5997	177	12	,	,	PUNCT
ejpam-5997	177	13	cξ	cξ	NOUN
ejpam-5997	177	14	,	,	PUNCT
ejpam-5997	177	15	ζ	ζ	NOUN
ejpam-5997	177	16	,	,	PUNCT
ejpam-5997	177	17	ς	ς	PROPN
ejpam-5997	177	18	,	,	PUNCT
ejpam-5997	177	19	κ1	κ1	NOUN
ejpam-5997	177	20	(	(	PUNCT
ejpam-5997	177	21	κ℘µ	κ℘µ	PROPN
ejpam-5997	177	22	;	;	PUNCT
ejpam-5997	177	23	p)ϕ(℘α+	p)ϕ(℘α+	PROPN
ejpam-5997	177	24	(	(	PUNCT
ejpam-5997	177	25	1−	1−	NUM
ejpam-5997	177	26	℘)τ	℘)τ	NOUN
ejpam-5997	177	27	)	)	PUNCT
ejpam-5997	177	28	≤	≤	NUM
ejpam-5997	177	29	ϕ(α)jµ,ρ	ϕ(α)jµ,ρ	NUM
ejpam-5997	177	30	,	,	PUNCT
ejpam-5997	177	31	m	m	PROPN
ejpam-5997	177	32	,	,	PUNCT
ejpam-5997	177	33	η	η	PROPN
ejpam-5997	177	34	,	,	PUNCT
ejpam-5997	177	35	cξ	cξ	NOUN
ejpam-5997	177	36	,	,	PUNCT
ejpam-5997	177	37	ζ	ζ	NOUN
ejpam-5997	177	38	,	,	PUNCT
ejpam-5997	177	39	ς	ς	PROPN
ejpam-5997	177	40	,	,	PUNCT
ejpam-5997	177	41	κ1	κ1	NOUN
ejpam-5997	177	42	(	(	PUNCT
ejpam-5997	177	43	κ	κ	NOUN
ejpam-5997	177	44	,	,	PUNCT
ejpam-5997	177	45	p	p	NOUN
ejpam-5997	177	46	)	)	PUNCT
ejpam-5997	177	47	[	[	PUNCT
ejpam-5997	177	48	β(ξ	β(ξ	PROPN
ejpam-5997	177	49	′	′	NOUN
ejpam-5997	177	50	+	+	CCONJ
ejpam-5997	177	51	µn+	µn+	ADV
ejpam-5997	177	52	s+	s+	ADP
ejpam-5997	177	53	1	1	NUM
ejpam-5997	177	54	,	,	PUNCT
ejpam-5997	177	55	1	1	NUM
ejpam-5997	177	56	)	)	PUNCT
ejpam-5997	177	57	+	+	CCONJ
ejpam-5997	177	58	β(ξ	β(ξ	PROPN
ejpam-5997	177	59	′	′	NOUN
ejpam-5997	177	60	+	+	CCONJ
ejpam-5997	177	61	µn+	µn+	ADJ
ejpam-5997	177	62	s	s	NOUN
ejpam-5997	177	63	,	,	PUNCT
ejpam-5997	177	64	1	1	NUM
ejpam-5997	177	65	)	)	PUNCT
ejpam-5997	177	66	]	]	PUNCT
ejpam-5997	178	1	+	+	PROPN
ejpam-5997	178	2	[	[	PUNCT
ejpam-5997	178	3	ϕ(ω	ϕ(ω	NOUN
ejpam-5997	178	4	)	)	PUNCT
ejpam-5997	178	5	+	+	CCONJ
ejpam-5997	178	6	ϕ(τ	ϕ(τ	PROPN
ejpam-5997	178	7	)	)	PUNCT
ejpam-5997	178	8	]	]	PUNCT
ejpam-5997	178	9	jµ,ρ	jµ,ρ	PROPN
ejpam-5997	178	10	,	,	PUNCT
ejpam-5997	178	11	m	m	PROPN
ejpam-5997	178	12	,	,	PUNCT
ejpam-5997	178	13	η	η	PROPN
ejpam-5997	178	14	,	,	PUNCT
ejpam-5997	178	15	cξ	cξ	NOUN
ejpam-5997	178	16	,	,	PUNCT
ejpam-5997	178	17	ζ	ζ	NOUN
ejpam-5997	178	18	,	,	PUNCT
ejpam-5997	178	19	ς	ς	PROPN
ejpam-5997	178	20	,	,	PUNCT
ejpam-5997	178	21	κ1	κ1	NOUN
ejpam-5997	178	22	(	(	PUNCT
ejpam-5997	178	23	κ	κ	NOUN
ejpam-5997	178	24	,	,	PUNCT
ejpam-5997	178	25	p)β(ξ	p)β(ξ	PRON
ejpam-5997	178	26	′	′	VERB
ejpam-5997	178	27	+	+	CCONJ
ejpam-5997	178	28	µn+	µn+	ADJ
ejpam-5997	178	29	1	1	NUM
ejpam-5997	178	30	,	,	PUNCT
ejpam-5997	178	31	s+	s+	X
ejpam-5997	178	32	1	1	NUM
ejpam-5997	178	33	)	)	PUNCT
ejpam-5997	178	34	.	.	PUNCT
ejpam-5997	179	1	(	(	PUNCT
ejpam-5997	179	2	20	20	NUM
ejpam-5997	179	3	)	)	PUNCT
ejpam-5997	179	4	by	by	ADP
ejpam-5997	179	5	substitution	substitution	NOUN
ejpam-5997	179	6	℘α	℘α	NOUN
ejpam-5997	179	7	+	+	CCONJ
ejpam-5997	179	8	(	(	PUNCT
ejpam-5997	179	9	1	1	NUM
ejpam-5997	179	10	−	−	NOUN
ejpam-5997	179	11	℘)ω	℘)ω	NOUN
ejpam-5997	179	12	=	=	SYM
ejpam-5997	179	13	x	x	NOUN
ejpam-5997	179	14	,	,	PUNCT
ejpam-5997	179	15	and	and	CCONJ
ejpam-5997	179	16	℘α	℘α	NOUN
ejpam-5997	179	17	+	+	CCONJ
ejpam-5997	179	18	(	(	PUNCT
ejpam-5997	179	19	1	1	NUM
ejpam-5997	179	20	−	−	NOUN
ejpam-5997	179	21	℘)τ	℘)τ	NOUN
ejpam-5997	179	22	=	=	SYM
ejpam-5997	179	23	ℓ	ℓ	PROPN
ejpam-5997	179	24	in	in	ADP
ejpam-5997	179	25	left	left	ADJ
ejpam-5997	179	26	side	side	NOUN
ejpam-5997	179	27	of	of	ADP
ejpam-5997	179	28	equation	equation	NOUN
ejpam-5997	179	29	(	(	PUNCT
ejpam-5997	179	30	20	20	NUM
ejpam-5997	179	31	)	)	PUNCT
ejpam-5997	179	32	,	,	PUNCT
ejpam-5997	179	33	and	and	CCONJ
ejpam-5997	179	34	then	then	ADV
ejpam-5997	179	35	simplify	simplify	VERB
ejpam-5997	179	36	,	,	PUNCT
ejpam-5997	179	37	we	we	PRON
ejpam-5997	179	38	have	have	VERB
ejpam-5997	179	39	the	the	DET
ejpam-5997	179	40	required	require	VERB
ejpam-5997	179	41	result	result	NOUN
ejpam-5997	179	42	.	.	PUNCT
ejpam-5997	180	1	corollary	corollary	ADJ
ejpam-5997	180	2	2	2	NUM
ejpam-5997	180	3	.	.	PUNCT
ejpam-5997	181	1	if	if	SCONJ
ejpam-5997	181	2	we	we	PRON
ejpam-5997	181	3	replace	replace	VERB
ejpam-5997	181	4	p	p	NOUN
ejpam-5997	181	5	=	=	NOUN
ejpam-5997	181	6	0	0	NUM
ejpam-5997	181	7	,	,	PUNCT
ejpam-5997	181	8	κ	κ	X
ejpam-5997	181	9	=	=	SYM
ejpam-5997	181	10	0	0	NUM
ejpam-5997	181	11	,	,	PUNCT
ejpam-5997	181	12	and	and	CCONJ
ejpam-5997	181	13	ξ	ξ	X
ejpam-5997	181	14	=	=	SYM
ejpam-5997	181	15	ξ	ξ	PROPN
ejpam-5997	181	16	−	−	PROPN
ejpam-5997	181	17	1	1	NUM
ejpam-5997	181	18	in	in	ADP
ejpam-5997	181	19	the	the	DET
ejpam-5997	181	20	theorem	theorem	NOUN
ejpam-5997	181	21	(	(	PUNCT
ejpam-5997	181	22	1	1	NUM
ejpam-5997	181	23	)	)	PUNCT
ejpam-5997	181	24	,	,	PUNCT
ejpam-5997	181	25	we	we	PRON
ejpam-5997	181	26	have	have	VERB
ejpam-5997	181	27	a	a	DET
ejpam-5997	181	28	result	result	NOUN
ejpam-5997	181	29	[	[	X
ejpam-5997	181	30	19	19	NUM
ejpam-5997	181	31	]	]	PUNCT
ejpam-5997	181	32	.	.	PUNCT
ejpam-5997	182	1	theorem	theorem	NOUN
ejpam-5997	182	2	2	2	NUM
ejpam-5997	182	3	.	.	PUNCT
ejpam-5997	183	1	let	let	VERB
ejpam-5997	183	2	ϕ	ϕ	NOUN
ejpam-5997	183	3	:	:	PUNCT
ejpam-5997	183	4	i	i	PRON
ejpam-5997	183	5	⊆	⊆	NUM
ejpam-5997	183	6	r	r	NOUN
ejpam-5997	183	7	→	→	SYM
ejpam-5997	183	8	r	r	NOUN
ejpam-5997	183	9	be	be	AUX
ejpam-5997	183	10	a	a	DET
ejpam-5997	183	11	differentiable	differentiable	ADJ
ejpam-5997	183	12	mapping	mapping	NOUN
ejpam-5997	183	13	on	on	ADP
ejpam-5997	183	14	io	io	PROPN
ejpam-5997	183	15	and	and	CCONJ
ejpam-5997	183	16	ω	ω	PROPN
ejpam-5997	183	17	,	,	PUNCT
ejpam-5997	183	18	τ	τ	PROPN
ejpam-5997	183	19	∈	∈	PROPN
ejpam-5997	183	20	io	io	X
ejpam-5997	183	21	with	with	ADP
ejpam-5997	183	22	ω	ω	PROPN
ejpam-5997	183	23	<	<	X
ejpam-5997	183	24	α	α	X
ejpam-5997	183	25	<	<	X
ejpam-5997	183	26	τ	τ	PROPN
ejpam-5997	183	27	such	such	ADJ
ejpam-5997	183	28	that	that	SCONJ
ejpam-5997	183	29	ϕ	ϕ	PROPN
ejpam-5997	183	30	′	′	NUM
ejpam-5997	183	31	∈	∈	PROPN
ejpam-5997	183	32	l[ω	l[ω	PROPN
ejpam-5997	183	33	,	,	PUNCT
ejpam-5997	183	34	τ	τ	X
ejpam-5997	183	35	]	]	X
ejpam-5997	183	36	.	.	PUNCT
ejpam-5997	184	1	if	if	SCONJ
ejpam-5997	184	2	|ϕ′	|ϕ′	PROPN
ejpam-5997	184	3	|	|	ADV
ejpam-5997	184	4	is	be	AUX
ejpam-5997	184	5	s	s	NOUN
ejpam-5997	184	6	-	-	ADJ
ejpam-5997	184	7	convex	convex	ADJ
ejpam-5997	184	8	function	function	NOUN
ejpam-5997	184	9	on	on	ADP
ejpam-5997	184	10	[	[	X
ejpam-5997	184	11	ω	ω	PROPN
ejpam-5997	184	12	,	,	PUNCT
ejpam-5997	184	13	τ	τ	X
ejpam-5997	184	14	]	]	X
ejpam-5997	184	15	,	,	PUNCT
ejpam-5997	184	16	and	and	CCONJ
ejpam-5997	184	17	µ	µ	NOUN
ejpam-5997	184	18	,	,	PUNCT
ejpam-5997	184	19	ξ	ξ	PROPN
ejpam-5997	184	20	,	,	PUNCT
ejpam-5997	184	21	ζ	ζ	NOUN
ejpam-5997	184	22	,	,	PUNCT
ejpam-5997	184	23	ς	ς	PROPN
ejpam-5997	184	24	,	,	PUNCT
ejpam-5997	184	25	c	c	X
ejpam-5997	184	26	,	,	PUNCT
ejpam-5997	184	27	κ1	κ1	PROPN
ejpam-5997	184	28	∈	∈	PROPN
ejpam-5997	184	29	c,ℜ(µ	c,ℜ(µ	PROPN
ejpam-5997	184	30	)	)	PUNCT
ejpam-5997	184	31	>	>	X
ejpam-5997	184	32	0,ℜ(ξ	0,ℜ(ξ	PROPN
ejpam-5997	184	33	)	)	PUNCT
ejpam-5997	184	34	>	>	X
ejpam-5997	184	35	0,ℜ(ζ	0,ℜ(ζ	PROPN
ejpam-5997	184	36	)	)	PUNCT
ejpam-5997	184	37	>	>	X
ejpam-5997	184	38	0,ℜ(ς	0,ℜ(ς	PROPN
ejpam-5997	184	39	)	)	PUNCT
ejpam-5997	184	40	>	>	X
ejpam-5997	185	1	0,ℜ(κ1	0,ℜ(κ1	PROPN
ejpam-5997	185	2	)	)	PUNCT
ejpam-5997	185	3	>	>	X
ejpam-5997	185	4	0	0	NUM
ejpam-5997	185	5	,	,	PUNCT
ejpam-5997	185	6	ρ	ρ	PROPN
ejpam-5997	185	7	,	,	PUNCT
ejpam-5997	185	8	m	m	PROPN
ejpam-5997	185	9	,	,	PUNCT
ejpam-5997	185	10	η	η	PROPN
ejpam-5997	185	11	≥	≥	X
ejpam-5997	185	12	0	0	NUM
ejpam-5997	185	13	and	and	CCONJ
ejpam-5997	185	14	m	m	PROPN
ejpam-5997	185	15	,	,	PUNCT
ejpam-5997	185	16	ρ	ρ	PROPN
ejpam-5997	185	17	>	>	X
ejpam-5997	185	18	ℜ(µ	ℜ(µ	NOUN
ejpam-5997	185	19	)	)	PUNCT
ejpam-5997	185	20	+	+	CCONJ
ejpam-5997	185	21	η	η	PROPN
ejpam-5997	185	22	,	,	PUNCT
ejpam-5997	185	23	then	then	ADV
ejpam-5997	185	24	we	we	PRON
ejpam-5997	185	25	have	have	VERB
ejpam-5997	185	26	the	the	DET
ejpam-5997	185	27	following	follow	VERB
ejpam-5997	185	28	integral	integral	ADJ
ejpam-5997	185	29	inequality	inequality	NOUN
ejpam-5997	185	30	in	in	ADP
ejpam-5997	185	31	result∣∣∣∣ϕ(α)eµ,ρ	result∣∣∣∣ϕ(α)eµ,ρ	PROPN
ejpam-5997	185	32	,	,	PUNCT
ejpam-5997	185	33	m	m	PROPN
ejpam-5997	185	34	,	,	PUNCT
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ejpam-5997	198	4	]	]	PUNCT
ejpam-5997	199	1	+	+	CCONJ
ejpam-5997	199	2	∞∑	∞∑	NUM
ejpam-5997	199	3	n=0	n=0	NUM
ejpam-5997	199	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	199	5	βp(ζ	βp(ζ	NUM
ejpam-5997	199	6	+	+	CCONJ
ejpam-5997	199	7	ρn	ρn	INTJ
ejpam-5997	199	8	,	,	PUNCT
ejpam-5997	199	9	c−	c−	NOUN
ejpam-5997	199	10	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	199	11	β(ζ	β(ζ	PROPN
ejpam-5997	199	12	,	,	PUNCT
ejpam-5997	199	13	c−	c−	X
ejpam-5997	199	14	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	199	15	ξ	ξ	X
ejpam-5997	200	1	+	+	NUM
ejpam-5997	200	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	200	3	(	(	PUNCT
ejpam-5997	200	4	−κ)n	−κ)n	NOUN
ejpam-5997	200	5	∣∣∣∣[∣∣ϕ′	∣∣∣∣[∣∣ϕ′	PROPN
ejpam-5997	200	6	(	(	PUNCT
ejpam-5997	200	7	α	α	NOUN
ejpam-5997	200	8	)	)	PUNCT
ejpam-5997	200	9	∣∣	∣∣	NUM
ejpam-5997	200	10	∫	∫	PROPN
ejpam-5997	200	11	1	1	NUM
ejpam-5997	200	12	0	0	NUM
ejpam-5997	200	13	℘ξ	℘ξ	NOUN
ejpam-5997	200	14	′	′	NUM
ejpam-5997	201	1	+	+	ADP
ejpam-5997	201	2	µn+sd℘+	µn+sd℘+	PROPN
ejpam-5997	201	3	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	201	4	(	(	PUNCT
ejpam-5997	201	5	τ	τ	X
ejpam-5997	201	6	)	)	PUNCT
ejpam-5997	201	7	∣∣	∣∣	NUM
ejpam-5997	201	8	∫	∫	PROPN
ejpam-5997	201	9	1	1	NUM
ejpam-5997	201	10	0	0	NUM
ejpam-5997	201	11	℘ξ	℘ξ	NOUN
ejpam-5997	201	12	′	′	NUM
ejpam-5997	202	1	+	+	ADJ
ejpam-5997	202	2	µn(1−	µn(1−	NOUN
ejpam-5997	202	3	℘)sd℘	℘)sd℘	ADP
ejpam-5997	202	4	]	]	PUNCT
ejpam-5997	202	5	≤	≤	NUM
ejpam-5997	202	6	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	202	7	(	(	PUNCT
ejpam-5997	202	8	α	α	NOUN
ejpam-5997	202	9	)	)	PUNCT
ejpam-5997	202	10	∣∣jµ,ρ	∣∣jµ,ρ	PROPN
ejpam-5997	202	11	,	,	PUNCT
ejpam-5997	202	12	m	m	PROPN
ejpam-5997	202	13	,	,	PUNCT
ejpam-5997	202	14	η	η	PROPN
ejpam-5997	202	15	,	,	PUNCT
ejpam-5997	202	16	cξ	cξ	NOUN
ejpam-5997	202	17	,	,	PUNCT
ejpam-5997	202	18	ζ	ζ	NOUN
ejpam-5997	202	19	,	,	PUNCT
ejpam-5997	202	20	ς	ς	PROPN
ejpam-5997	202	21	,	,	PUNCT
ejpam-5997	202	22	κ1	κ1	NOUN
ejpam-5997	202	23	(	(	PUNCT
ejpam-5997	202	24	κ	κ	NOUN
ejpam-5997	202	25	,	,	PUNCT
ejpam-5997	202	26	p)β(ξ	p)β(ξ	PROPN
ejpam-5997	202	27	′	′	VERB
ejpam-5997	202	28	+	+	CCONJ
ejpam-5997	202	29	µn+	µn+	ADV
ejpam-5997	202	30	s+	s+	ADP
ejpam-5997	202	31	1	1	NUM
ejpam-5997	202	32	,	,	PUNCT
ejpam-5997	202	33	1	1	NUM
ejpam-5997	202	34	)	)	PUNCT
ejpam-5997	202	35	+	+	CCONJ
ejpam-5997	202	36	∣∣ϕ′	∣∣ϕ′	X
ejpam-5997	202	37	(	(	PUNCT
ejpam-5997	202	38	ω	ω	NOUN
ejpam-5997	202	39	)	)	PUNCT
ejpam-5997	202	40	∣∣jµ,ρ	∣∣jµ,ρ	PROPN
ejpam-5997	202	41	,	,	PUNCT
ejpam-5997	202	42	m	m	PROPN
ejpam-5997	202	43	,	,	PUNCT
ejpam-5997	202	44	η	η	PROPN
ejpam-5997	202	45	,	,	PUNCT
ejpam-5997	202	46	cξ	cξ	NOUN
ejpam-5997	202	47	,	,	PUNCT
ejpam-5997	202	48	ζ	ζ	NOUN
ejpam-5997	202	49	,	,	PUNCT
ejpam-5997	202	50	ς	ς	PROPN
ejpam-5997	202	51	,	,	PUNCT
ejpam-5997	202	52	κ1	κ1	NOUN
ejpam-5997	202	53	(	(	PUNCT
ejpam-5997	202	54	κ	κ	NOUN
ejpam-5997	202	55	,	,	PUNCT
ejpam-5997	202	56	p)β(ξ	p)β(ξ	PRON
ejpam-5997	202	57	′	′	VERB
ejpam-5997	202	58	+	+	CCONJ
ejpam-5997	202	59	µn+	µn+	ADJ
ejpam-5997	202	60	1	1	NUM
ejpam-5997	202	61	,	,	PUNCT
ejpam-5997	202	62	s+	s+	X
ejpam-5997	202	63	1	1	X
ejpam-5997	202	64	)	)	PUNCT
ejpam-5997	203	1	+	+	NOUN
ejpam-5997	203	2	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	203	3	(	(	PUNCT
ejpam-5997	203	4	α	α	NOUN
ejpam-5997	203	5	)	)	PUNCT
ejpam-5997	203	6	∣∣jµ,ρ	∣∣jµ,ρ	PROPN
ejpam-5997	203	7	,	,	PUNCT
ejpam-5997	203	8	m	m	PROPN
ejpam-5997	203	9	,	,	PUNCT
ejpam-5997	203	10	η	η	PROPN
ejpam-5997	203	11	,	,	PUNCT
ejpam-5997	203	12	cξ	cξ	NOUN
ejpam-5997	203	13	,	,	PUNCT
ejpam-5997	203	14	ζ	ζ	NOUN
ejpam-5997	203	15	,	,	PUNCT
ejpam-5997	203	16	ς	ς	PROPN
ejpam-5997	203	17	,	,	PUNCT
ejpam-5997	203	18	κ1	κ1	NOUN
ejpam-5997	203	19	(	(	PUNCT
ejpam-5997	203	20	κ	κ	NOUN
ejpam-5997	203	21	,	,	PUNCT
ejpam-5997	203	22	p)β(ξ	p)β(ξ	PRON
ejpam-5997	203	23	′	′	VERB
ejpam-5997	204	1	+	+	CCONJ
ejpam-5997	204	2	µn+	µn+	ADJ
ejpam-5997	204	3	s	s	NOUN
ejpam-5997	204	4	,	,	PUNCT
ejpam-5997	204	5	1	1	NUM
ejpam-5997	204	6	)	)	PUNCT
ejpam-5997	204	7	+	+	NUM
ejpam-5997	204	8	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	204	9	(	(	PUNCT
ejpam-5997	204	10	τ	τ	NOUN
ejpam-5997	204	11	)	)	PUNCT
ejpam-5997	204	12	∣∣jµ,ρ	∣∣jµ,ρ	PROPN
ejpam-5997	204	13	,	,	PUNCT
ejpam-5997	204	14	m	m	PROPN
ejpam-5997	204	15	,	,	PUNCT
ejpam-5997	204	16	η	η	PROPN
ejpam-5997	204	17	,	,	PUNCT
ejpam-5997	204	18	cξ	cξ	NOUN
ejpam-5997	204	19	,	,	PUNCT
ejpam-5997	204	20	ζ	ζ	NOUN
ejpam-5997	204	21	,	,	PUNCT
ejpam-5997	204	22	ς	ς	PROPN
ejpam-5997	204	23	,	,	PUNCT
ejpam-5997	204	24	κ1	κ1	NOUN
ejpam-5997	204	25	(	(	PUNCT
ejpam-5997	204	26	κ	κ	NOUN
ejpam-5997	204	27	,	,	PUNCT
ejpam-5997	204	28	p)β(ξ	p)β(ξ	PRON
ejpam-5997	204	29	′	′	VERB
ejpam-5997	205	1	+	+	CCONJ
ejpam-5997	205	2	µn+	µn+	ADJ
ejpam-5997	205	3	1	1	NUM
ejpam-5997	205	4	,	,	PUNCT
ejpam-5997	205	5	s+	s+	X
ejpam-5997	205	6	1	1	X
ejpam-5997	205	7	)	)	PUNCT
ejpam-5997	205	8	≤	≤	NOUN
ejpam-5997	205	9	2	2	NUM
ejpam-5997	205	10	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	205	11	(	(	PUNCT
ejpam-5997	205	12	α	α	NOUN
ejpam-5997	205	13	)	)	PUNCT
ejpam-5997	205	14	∣∣jµ,ρ	∣∣jµ,ρ	PROPN
ejpam-5997	205	15	,	,	PUNCT
ejpam-5997	205	16	m	m	PROPN
ejpam-5997	205	17	,	,	PUNCT
ejpam-5997	205	18	η	η	PROPN
ejpam-5997	205	19	,	,	PUNCT
ejpam-5997	205	20	cξ	cξ	NOUN
ejpam-5997	205	21	,	,	PUNCT
ejpam-5997	205	22	ζ	ζ	NOUN
ejpam-5997	205	23	,	,	PUNCT
ejpam-5997	205	24	ς	ς	PROPN
ejpam-5997	205	25	,	,	PUNCT
ejpam-5997	205	26	κ1	κ1	NOUN
ejpam-5997	205	27	(	(	PUNCT
ejpam-5997	205	28	κ	κ	NOUN
ejpam-5997	205	29	,	,	PUNCT
ejpam-5997	205	30	p)β(ξ	p)β(ξ	PROPN
ejpam-5997	205	31	′	′	VERB
ejpam-5997	206	1	+	+	CCONJ
ejpam-5997	206	2	µn+	µn+	ADV
ejpam-5997	206	3	s+	s+	ADP
ejpam-5997	206	4	1	1	NUM
ejpam-5997	206	5	,	,	PUNCT
ejpam-5997	206	6	1	1	NUM
ejpam-5997	206	7	)	)	PUNCT
ejpam-5997	207	1	+	+	CCONJ
ejpam-5997	208	1	[	[	X
ejpam-5997	208	2	∣∣ϕ′	∣∣ϕ′	X
ejpam-5997	208	3	(	(	PUNCT
ejpam-5997	208	4	ω	ω	NOUN
ejpam-5997	208	5	)	)	PUNCT
ejpam-5997	208	6	∣∣+	∣∣+	PROPN
ejpam-5997	208	7	∣∣ϕ′	∣∣ϕ′	PROPN
ejpam-5997	208	8	(	(	PUNCT
ejpam-5997	208	9	τ	τ	NOUN
ejpam-5997	208	10	)	)	PUNCT
ejpam-5997	208	11	∣∣]jµ,ρ	∣∣]jµ,ρ	PROPN
ejpam-5997	208	12	,	,	PUNCT
ejpam-5997	208	13	m	m	PROPN
ejpam-5997	208	14	,	,	PUNCT
ejpam-5997	208	15	η	η	PROPN
ejpam-5997	208	16	,	,	PUNCT
ejpam-5997	208	17	cξ	cξ	NOUN
ejpam-5997	208	18	,	,	PUNCT
ejpam-5997	208	19	ζ	ζ	NOUN
ejpam-5997	208	20	,	,	PUNCT
ejpam-5997	208	21	ς	ς	PROPN
ejpam-5997	208	22	,	,	PUNCT
ejpam-5997	208	23	κ1	κ1	NOUN
ejpam-5997	208	24	(	(	PUNCT
ejpam-5997	208	25	κ	κ	NOUN
ejpam-5997	208	26	,	,	PUNCT
ejpam-5997	208	27	p)β(ξ	p)β(ξ	PRON
ejpam-5997	208	28	′	′	VERB
ejpam-5997	208	29	+	+	CCONJ
ejpam-5997	208	30	µn+	µn+	ADJ
ejpam-5997	208	31	1	1	NUM
ejpam-5997	208	32	,	,	PUNCT
ejpam-5997	208	33	s+	s+	X
ejpam-5997	208	34	1	1	X
ejpam-5997	208	35	)	)	PUNCT
ejpam-5997	208	36	the	the	DET
ejpam-5997	208	37	proof	proof	NOUN
ejpam-5997	208	38	is	be	AUX
ejpam-5997	208	39	completed	complete	VERB
ejpam-5997	208	40	.	.	PUNCT
ejpam-5997	209	1	corollary	corollary	ADJ
ejpam-5997	209	2	3	3	X
ejpam-5997	209	3	.	.	PUNCT
ejpam-5997	210	1	if	if	SCONJ
ejpam-5997	210	2	we	we	PRON
ejpam-5997	210	3	replace	replace	VERB
ejpam-5997	210	4	p	p	NOUN
ejpam-5997	210	5	=	=	NOUN
ejpam-5997	210	6	0	0	NUM
ejpam-5997	210	7	,	,	PUNCT
ejpam-5997	210	8	κ	κ	X
ejpam-5997	210	9	=	=	SYM
ejpam-5997	210	10	0	0	NUM
ejpam-5997	210	11	,	,	PUNCT
ejpam-5997	210	12	and	and	CCONJ
ejpam-5997	210	13	ξ	ξ	X
ejpam-5997	210	14	=	=	SYM
ejpam-5997	210	15	ξ	ξ	PROPN
ejpam-5997	210	16	−	−	PROPN
ejpam-5997	210	17	1	1	NUM
ejpam-5997	210	18	in	in	ADP
ejpam-5997	210	19	the	the	DET
ejpam-5997	210	20	theorem	theorem	NOUN
ejpam-5997	210	21	(	(	PUNCT
ejpam-5997	210	22	2	2	NUM
ejpam-5997	210	23	)	)	PUNCT
ejpam-5997	210	24	,	,	PUNCT
ejpam-5997	210	25	we	we	PRON
ejpam-5997	210	26	have	have	VERB
ejpam-5997	210	27	a	a	DET
ejpam-5997	210	28	result	result	NOUN
ejpam-5997	210	29	[	[	X
ejpam-5997	210	30	19	19	NUM
ejpam-5997	210	31	]	]	PUNCT
ejpam-5997	210	32	.	.	PUNCT
ejpam-5997	211	1	theorem	theorem	NOUN
ejpam-5997	211	2	3	3	X
ejpam-5997	211	3	.	.	PUNCT
ejpam-5997	212	1	let	let	VERB
ejpam-5997	212	2	ϕ	ϕ	NOUN
ejpam-5997	212	3	:	:	PUNCT
ejpam-5997	212	4	i	i	PRON
ejpam-5997	212	5	⊆	⊆	NUM
ejpam-5997	212	6	r	r	NOUN
ejpam-5997	212	7	→	→	SYM
ejpam-5997	212	8	r	r	NOUN
ejpam-5997	212	9	be	be	AUX
ejpam-5997	212	10	a	a	DET
ejpam-5997	212	11	differentiable	differentiable	ADJ
ejpam-5997	212	12	mapping	mapping	NOUN
ejpam-5997	212	13	on	on	ADP
ejpam-5997	212	14	io	io	PROPN
ejpam-5997	212	15	and	and	CCONJ
ejpam-5997	212	16	ω	ω	PROPN
ejpam-5997	212	17	,	,	PUNCT
ejpam-5997	212	18	τ	τ	PROPN
ejpam-5997	212	19	∈	∈	PROPN
ejpam-5997	212	20	io	io	X
ejpam-5997	212	21	with	with	ADP
ejpam-5997	212	22	ω	ω	PROPN
ejpam-5997	212	23	<	<	X
ejpam-5997	212	24	α	α	X
ejpam-5997	212	25	<	<	X
ejpam-5997	212	26	τ	τ	PROPN
ejpam-5997	212	27	such	such	ADJ
ejpam-5997	212	28	that	that	SCONJ
ejpam-5997	212	29	ϕ	ϕ	PROPN
ejpam-5997	212	30	′	′	NUM
ejpam-5997	212	31	∈	∈	PROPN
ejpam-5997	212	32	l[ω	l[ω	PROPN
ejpam-5997	212	33	,	,	PUNCT
ejpam-5997	212	34	τ	τ	X
ejpam-5997	212	35	]	]	X
ejpam-5997	212	36	.	.	PUNCT
ejpam-5997	213	1	if	if	SCONJ
ejpam-5997	213	2	|ϕ′	|ϕ′	PROPN
ejpam-5997	213	3	|q(q	|q(q	PROPN
ejpam-5997	213	4	>	>	X
ejpam-5997	213	5	0	0	NUM
ejpam-5997	213	6	)	)	PUNCT
ejpam-5997	213	7	is	be	AUX
ejpam-5997	213	8	s	s	NOUN
ejpam-5997	213	9	-	-	ADJ
ejpam-5997	213	10	convex	convex	ADJ
ejpam-5997	213	11	function	function	NOUN
ejpam-5997	213	12	on	on	ADP
ejpam-5997	213	13	[	[	X
ejpam-5997	213	14	ω	ω	PROPN
ejpam-5997	213	15	,	,	PUNCT
ejpam-5997	213	16	τ	τ	X
ejpam-5997	213	17	]	]	X
ejpam-5997	213	18	,	,	PUNCT
ejpam-5997	213	19	and	and	CCONJ
ejpam-5997	213	20	µ	µ	NOUN
ejpam-5997	213	21	,	,	PUNCT
ejpam-5997	213	22	ξ	ξ	PROPN
ejpam-5997	213	23	,	,	PUNCT
ejpam-5997	213	24	ζ	ζ	NOUN
ejpam-5997	213	25	,	,	PUNCT
ejpam-5997	213	26	ς	ς	PROPN
ejpam-5997	213	27	,	,	PUNCT
ejpam-5997	213	28	c	c	X
ejpam-5997	213	29	,	,	PUNCT
ejpam-5997	213	30	κ1	κ1	PROPN
ejpam-5997	213	31	∈	∈	PROPN
ejpam-5997	213	32	c,ℜ(µ	c,ℜ(µ	PROPN
ejpam-5997	213	33	)	)	PUNCT
ejpam-5997	213	34	>	>	X
ejpam-5997	213	35	0,ℜ(ξ	0,ℜ(ξ	PROPN
ejpam-5997	213	36	)	)	PUNCT
ejpam-5997	213	37	>	>	X
ejpam-5997	213	38	0,ℜ(ζ	0,ℜ(ζ	PROPN
ejpam-5997	213	39	)	)	PUNCT
ejpam-5997	213	40	>	>	X
ejpam-5997	213	41	0,ℜ(ς	0,ℜ(ς	PROPN
ejpam-5997	213	42	)	)	PUNCT
ejpam-5997	213	43	>	>	X
ejpam-5997	214	1	0,ℜ(κ1	0,ℜ(κ1	PROPN
ejpam-5997	214	2	)	)	PUNCT
ejpam-5997	214	3	>	>	X
ejpam-5997	214	4	0	0	NUM
ejpam-5997	214	5	,	,	PUNCT
ejpam-5997	214	6	ρ	ρ	PROPN
ejpam-5997	214	7	,	,	PUNCT
ejpam-5997	214	8	m	m	PROPN
ejpam-5997	214	9	,	,	PUNCT
ejpam-5997	214	10	η	η	PROPN
ejpam-5997	214	11	≥	≥	X
ejpam-5997	214	12	0	0	NUM
ejpam-5997	214	13	and	and	CCONJ
ejpam-5997	214	14	m	m	PROPN
ejpam-5997	214	15	,	,	PUNCT
ejpam-5997	214	16	ρ	ρ	PROPN
ejpam-5997	214	17	>	>	X
ejpam-5997	214	18	ℜ(µ	ℜ(µ	NOUN
ejpam-5997	214	19	)	)	PUNCT
ejpam-5997	214	20	+	+	CCONJ
ejpam-5997	214	21	η	η	PROPN
ejpam-5997	214	22	,	,	PUNCT
ejpam-5997	214	23	then	then	ADV
ejpam-5997	214	24	we	we	PRON
ejpam-5997	214	25	have	have	VERB
ejpam-5997	214	26	the	the	DET
ejpam-5997	214	27	following	follow	VERB
ejpam-5997	214	28	integral	integral	ADJ
ejpam-5997	214	29	inequality	inequality	NOUN
ejpam-5997	214	30	in	in	ADP
ejpam-5997	214	31	result;∣∣∣∣ϕ(α)eµ,ρ	result;∣∣∣∣ϕ(α)eµ,ρ	PROPN
ejpam-5997	214	32	,	,	PUNCT
ejpam-5997	214	33	m	m	PROPN
ejpam-5997	214	34	,	,	PUNCT
ejpam-5997	214	35	η	η	PROPN
ejpam-5997	214	36	,	,	PUNCT
ejpam-5997	214	37	cξ	cξ	NOUN
ejpam-5997	214	38	,	,	PUNCT
ejpam-5997	214	39	ζ	ζ	NOUN
ejpam-5997	214	40	,	,	PUNCT
ejpam-5997	214	41	ς	ς	PROPN
ejpam-5997	214	42	,	,	PUNCT
ejpam-5997	214	43	κ1	κ1	NOUN
ejpam-5997	214	44	(	(	PUNCT
ejpam-5997	214	45	κ	κ	NOUN
ejpam-5997	214	46	,	,	PUNCT
ejpam-5997	214	47	p	p	NOUN
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ejpam-5997	214	49	[	[	PUNCT
ejpam-5997	214	50	1	1	NUM
ejpam-5997	214	51	α−	α−	ADP
ejpam-5997	214	52	ω	ω	NUM
ejpam-5997	214	53	+	+	CCONJ
ejpam-5997	214	54	1	1	NUM
ejpam-5997	214	55	α−	α−	ADP
ejpam-5997	214	56	τ	τ	X
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ejpam-5997	215	1	−	−	PROPN
ejpam-5997	215	2	(	(	PUNCT
ejpam-5997	215	3	ξ	ξ	X
ejpam-5997	215	4	′	′	NUM
ejpam-5997	215	5	+	+	CCONJ
ejpam-5997	215	6	µn	µn	X
ejpam-5997	215	7	)	)	PUNCT
ejpam-5997	215	8	[	[	PUNCT
ejpam-5997	215	9	1	1	NUM
ejpam-5997	215	10	(	(	PUNCT
ejpam-5997	215	11	α−	α−	ADP
ejpam-5997	215	12	ω)ξ	ω)ξ	VERB
ejpam-5997	215	13	′+1	′+1	PROPN
ejpam-5997	215	14	(	(	PUNCT
ejpam-5997	215	15	eµ,ρ	eµ,ρ	X
ejpam-5997	215	16	,	,	PUNCT
ejpam-5997	215	17	m	m	PROPN
ejpam-5997	215	18	,	,	PUNCT
ejpam-5997	215	19	η	η	PROPN
ejpam-5997	215	20	,	,	PUNCT
ejpam-5997	215	21	c	c	PROPN
ejpam-5997	215	22	ξ	ξ	PROPN
ejpam-5997	215	23	,	,	PUNCT
ejpam-5997	215	24	ζ	ζ	NOUN
ejpam-5997	215	25	,	,	PUNCT
ejpam-5997	215	26	ς	ς	NOUN
ejpam-5997	215	27	,	,	PUNCT
ejpam-5997	215	28	κ1,α+ϕ	κ1,α+ϕ	VERB
ejpam-5997	215	29	)	)	PUNCT
ejpam-5997	215	30	(	(	PUNCT
ejpam-5997	215	31	ω	ω	NOUN
ejpam-5997	215	32	,	,	PUNCT
ejpam-5997	215	33	κ	κ	NOUN
ejpam-5997	215	34	)	)	PUNCT
ejpam-5997	215	35	+	+	CCONJ
ejpam-5997	215	36	1	1	NUM
ejpam-5997	215	37	(	(	PUNCT
ejpam-5997	215	38	α−	α−	ADP
ejpam-5997	215	39	τ)ξ	τ)ξ	NOUN
ejpam-5997	215	40	′+1	′+1	NOUN
ejpam-5997	215	41	(	(	PUNCT
ejpam-5997	215	42	eµ,ρ	eµ,ρ	X
ejpam-5997	215	43	,	,	PUNCT
ejpam-5997	215	44	m	m	PROPN
ejpam-5997	215	45	,	,	PUNCT
ejpam-5997	215	46	η	η	PROPN
ejpam-5997	215	47	,	,	PUNCT
ejpam-5997	215	48	c	c	PROPN
ejpam-5997	215	49	ξ	ξ	PROPN
ejpam-5997	215	50	,	,	PUNCT
ejpam-5997	215	51	ζ	ζ	NOUN
ejpam-5997	215	52	,	,	PUNCT
ejpam-5997	215	53	ς	ς	PROPN
ejpam-5997	215	54	,	,	PUNCT
ejpam-5997	215	55	κ1,τ−	κ1,τ−	ADJ
ejpam-5997	215	56	ϕ	ϕ	NOUN
ejpam-5997	215	57	)	)	PUNCT
ejpam-5997	215	58	(	(	PUNCT
ejpam-5997	215	59	ω	ω	PROPN
ejpam-5997	215	60	,	,	PUNCT
ejpam-5997	215	61	κ	κ	NOUN
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ejpam-5997	215	64	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	215	65	≤	≤	NUM
ejpam-5997	215	66	jµ,ρ	jµ,ρ	NOUN
ejpam-5997	215	67	,	,	PUNCT
ejpam-5997	215	68	m	m	PROPN
ejpam-5997	215	69	,	,	PUNCT
ejpam-5997	215	70	η	η	PROPN
ejpam-5997	215	71	,	,	PUNCT
ejpam-5997	215	72	cξ	cξ	NOUN
ejpam-5997	215	73	,	,	PUNCT
ejpam-5997	215	74	ζ	ζ	NOUN
ejpam-5997	215	75	,	,	PUNCT
ejpam-5997	215	76	ς	ς	PROPN
ejpam-5997	215	77	,	,	PUNCT
ejpam-5997	215	78	κ1	κ1	NOUN
ejpam-5997	215	79	(	(	PUNCT
ejpam-5997	215	80	κ	κ	NOUN
ejpam-5997	215	81	,	,	PUNCT
ejpam-5997	215	82	p	p	NOUN
ejpam-5997	215	83	)	)	PUNCT
ejpam-5997	215	84	(	(	PUNCT
ejpam-5997	215	85	1	1	NUM
ejpam-5997	215	86	ξ′	ξ′	NOUN
ejpam-5997	215	87	+	+	CCONJ
ejpam-5997	215	88	µn+	µn+	ADJ
ejpam-5997	215	89	1	1	NUM
ejpam-5997	215	90	)	)	PUNCT
ejpam-5997	215	91	1−	1−	NUM
ejpam-5997	216	1	1	1	NUM
ejpam-5997	216	2	q	q	NOUN
ejpam-5997	216	3	[	[	X
ejpam-5997	216	4	(	(	PUNCT
ejpam-5997	216	5	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	216	6	(	(	PUNCT
ejpam-5997	216	7	α	α	NOUN
ejpam-5997	216	8	)	)	PUNCT
ejpam-5997	216	9	∣∣q	∣∣q	NUM
ejpam-5997	216	10	ξ′	ξ′	NOUN
ejpam-5997	216	11	+	+	CCONJ
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ejpam-5997	216	13	s+	s+	PUNCT
ejpam-5997	216	14	1	1	NUM
ejpam-5997	216	15	+	+	CCONJ
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ejpam-5997	216	17	(	(	PUNCT
ejpam-5997	216	18	ω	ω	NOUN
ejpam-5997	216	19	)	)	PUNCT
ejpam-5997	216	20	∣∣qβ(ξ′	∣∣qβ(ξ′	PROPN
ejpam-5997	216	21	+	+	CCONJ
ejpam-5997	216	22	µn+	µn+	ADV
ejpam-5997	216	23	s+	s+	ADP
ejpam-5997	216	24	1	1	NUM
ejpam-5997	216	25	,	,	PUNCT
ejpam-5997	216	26	1	1	NUM
ejpam-5997	216	27	)	)	PUNCT
ejpam-5997	216	28	)	)	PUNCT
ejpam-5997	216	29	1	1	NUM
ejpam-5997	217	1	q	q	NOUN
ejpam-5997	217	2	+	+	ADJ
ejpam-5997	217	3	(	(	PUNCT
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ejpam-5997	217	5	(	(	PUNCT
ejpam-5997	217	6	α	α	NOUN
ejpam-5997	217	7	)	)	PUNCT
ejpam-5997	217	8	∣∣q	∣∣q	NUM
ejpam-5997	217	9	ξ′	ξ′	NOUN
ejpam-5997	217	10	+	+	CCONJ
ejpam-5997	217	11	µn+	µn+	ADV
ejpam-5997	217	12	s+	s+	PUNCT
ejpam-5997	217	13	1	1	NUM
ejpam-5997	217	14	+	+	CCONJ
ejpam-5997	217	15	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	217	16	(	(	PUNCT
ejpam-5997	217	17	τ	τ	NOUN
ejpam-5997	217	18	)	)	PUNCT
ejpam-5997	217	19	∣∣qβ(ξ′	∣∣qβ(ξ′	PROPN
ejpam-5997	217	20	+	+	CCONJ
ejpam-5997	217	21	µn+	µn+	ADV
ejpam-5997	217	22	s+	s+	ADP
ejpam-5997	217	23	1	1	NUM
ejpam-5997	217	24	,	,	PUNCT
ejpam-5997	217	25	1	1	NUM
ejpam-5997	217	26	)	)	PUNCT
ejpam-5997	217	27	)	)	PUNCT
ejpam-5997	217	28	1	1	NUM
ejpam-5997	217	29	q	q	NOUN
ejpam-5997	217	30	]	]	PUNCT
ejpam-5997	217	31	.	.	PUNCT
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ejpam-5997	219	6	:	:	PUNCT
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ejpam-5997	219	9	,	,	PUNCT
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ejpam-5997	219	13	,	,	PUNCT
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ejpam-5997	219	15	,	,	PUNCT
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ejpam-5997	219	17	,	,	PUNCT
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ejpam-5997	219	19	,	,	PUNCT
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ejpam-5997	219	21	(	(	PUNCT
ejpam-5997	219	22	κ	κ	NOUN
ejpam-5997	219	23	,	,	PUNCT
ejpam-5997	219	24	p	p	NOUN
ejpam-5997	219	25	)	)	PUNCT
ejpam-5997	219	26	[	[	PUNCT
ejpam-5997	219	27	1	1	NUM
ejpam-5997	219	28	α−ω	α−ω	NOUN
ejpam-5997	219	29	+	+	CCONJ
ejpam-5997	219	30	1	1	NUM
ejpam-5997	219	31	α−τ	α−τ	X
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ejpam-5997	219	33	−	−	PROPN
ejpam-5997	219	34	(	(	PUNCT
ejpam-5997	219	35	ξ	ξ	X
ejpam-5997	219	36	′	′	NUM
ejpam-5997	219	37	+	+	CCONJ
ejpam-5997	219	38	µn	µn	X
ejpam-5997	219	39	)	)	PUNCT
ejpam-5997	219	40	[	[	PUNCT
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ejpam-5997	219	42	(	(	PUNCT
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ejpam-5997	219	47	,	,	PUNCT
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ejpam-5997	219	53	ξ	ξ	PROPN
ejpam-5997	219	54	,	,	PUNCT
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ejpam-5997	219	60	)	)	PUNCT
ejpam-5997	219	61	(	(	PUNCT
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ejpam-5997	219	63	,	,	PUNCT
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ejpam-5997	219	66	+	+	CCONJ
ejpam-5997	219	67	1	1	X
ejpam-5997	219	68	(	(	PUNCT
ejpam-5997	219	69	α−τ)ξ	α−τ)ξ	PROPN
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ejpam-5997	219	72	eµ,ρ	eµ,ρ	X
ejpam-5997	219	73	,	,	PUNCT
ejpam-5997	219	74	m	m	PROPN
ejpam-5997	219	75	,	,	PUNCT
ejpam-5997	219	76	η	η	PROPN
ejpam-5997	219	77	,	,	PUNCT
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ejpam-5997	219	79	ξ	ξ	PROPN
ejpam-5997	219	80	,	,	PUNCT
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ejpam-5997	219	86	ϕ	ϕ	NOUN
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ejpam-5997	219	88	(	(	PUNCT
ejpam-5997	219	89	ω	ω	PROPN
ejpam-5997	219	90	,	,	PUNCT
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ejpam-5997	219	97	1	1	NUM
ejpam-5997	219	98	0	0	NUM
ejpam-5997	219	99	℘	℘	PROPN
ejpam-5997	219	100	ξ	ξ	PROPN
ejpam-5997	219	101	′	′	NUM
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ejpam-5997	219	109	,	,	PUNCT
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ejpam-5997	219	111	,	,	PUNCT
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ejpam-5997	219	118	p	p	X
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ejpam-5997	219	122	℘α+	℘α+	NUM
ejpam-5997	219	123	(	(	PUNCT
ejpam-5997	219	124	1−	1−	NUM
ejpam-5997	219	125	℘)ω	℘)ω	PROPN
ejpam-5997	219	126	∣∣d℘+	∣∣d℘+	VERB
ejpam-5997	219	127	∫	∫	PROPN
ejpam-5997	219	128	1	1	NUM
ejpam-5997	219	129	0	0	NUM
ejpam-5997	219	130	℘	℘	PROPN
ejpam-5997	219	131	ξ	ξ	PROPN
ejpam-5997	219	132	′	′	NUM
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ejpam-5997	219	147	κ℘µ	κ℘µ	PROPN
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ejpam-5997	219	149	p	p	X
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ejpam-5997	219	151	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	219	152	(	(	PUNCT
ejpam-5997	219	153	℘α+	℘α+	NUM
ejpam-5997	219	154	(	(	PUNCT
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ejpam-5997	219	156	℘)τ	℘)τ	PROPN
ejpam-5997	219	157	∣∣d℘	∣∣d℘	PROPN
ejpam-5997	219	158	m.	m.	PROPN
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ejpam-5997	220	3	appl	appl	PROPN
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ejpam-5997	220	6	,	,	PUNCT
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ejpam-5997	220	8	(	(	PUNCT
ejpam-5997	220	9	2	2	NUM
ejpam-5997	220	10	)	)	PUNCT
ejpam-5997	220	11	(	(	PUNCT
ejpam-5997	220	12	2025	2025	NUM
ejpam-5997	220	13	)	)	PUNCT
ejpam-5997	220	14	,	,	PUNCT
ejpam-5997	220	15	5997	5997	NUM
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ejpam-5997	220	18	23	23	NUM
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ejpam-5997	220	20	power	power	NOUN
ejpam-5997	220	21	mean	mean	VERB
ejpam-5997	220	22	inequality	inequality	NOUN
ejpam-5997	220	23	;	;	PUNCT
ejpam-5997	220	24	ℵ	ℵ	X
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ejpam-5997	221	4	βp(ζ	βp(ζ	NUM
ejpam-5997	221	5	+	+	CCONJ
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ejpam-5997	221	9	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	221	10	β(ζ	β(ζ	PROPN
ejpam-5997	221	11	,	,	PUNCT
ejpam-5997	221	12	c−	c−	X
ejpam-5997	221	13	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	221	14	ξ	ξ	X
ejpam-5997	222	1	+	+	NUM
ejpam-5997	222	2	1)(ς)mn	1)(ς)mn	NUM
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ejpam-5997	222	5	∣∣∣∣[(∫	∣∣∣∣[(∫	PROPN
ejpam-5997	222	6	1	1	NUM
ejpam-5997	222	7	0	0	NUM
ejpam-5997	222	8	℘ξ	℘ξ	NOUN
ejpam-5997	222	9	′	′	NUM
ejpam-5997	223	1	+	+	CCONJ
ejpam-5997	223	2	µnd℘	µnd℘	X
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ejpam-5997	223	4	1−	1−	PROPN
ejpam-5997	223	5	1	1	NUM
ejpam-5997	223	6	q	q	NOUN
ejpam-5997	223	7	(	(	PUNCT
ejpam-5997	223	8	∫	∫	PROPN
ejpam-5997	223	9	1	1	NUM
ejpam-5997	223	10	0	0	NUM
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ejpam-5997	224	1	+	+	PUNCT
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ejpam-5997	224	9	∣∣qd℘	∣∣qd℘	PROPN
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ejpam-5997	224	11	1	1	NUM
ejpam-5997	224	12	q	q	NOUN
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ejpam-5997	224	18	βp(ζ	βp(ζ	NUM
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ejpam-5997	224	26	c−	c−	X
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ejpam-5997	226	12	′	′	NUM
ejpam-5997	227	1	+	+	PUNCT
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ejpam-5997	227	8	℘)τ	℘)τ	PROPN
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ejpam-5997	227	11	1	1	NUM
ejpam-5997	227	12	q	q	NOUN
ejpam-5997	227	13	]	]	PUNCT
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ejpam-5997	227	19	convex	convex	ADJ
ejpam-5997	227	20	function	function	NOUN
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ejpam-5997	228	3	1	1	NUM
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ejpam-5997	228	8	)	)	PUNCT
ejpam-5997	228	9	1−	1−	NUM
ejpam-5997	228	10	1	1	NUM
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ejpam-5997	228	14	(	(	PUNCT
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ejpam-5997	228	22	′	′	NUM
ejpam-5997	229	1	+	+	ADP
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ejpam-5997	236	9	1−	1−	NUM
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ejpam-5997	236	14	(	(	PUNCT
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ejpam-5997	238	9	1−	1−	NUM
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ejpam-5997	240	29	1	1	NUM
ejpam-5997	241	1	q	q	NOUN
ejpam-5997	241	2	+	+	CCONJ
ejpam-5997	241	3	(	(	PUNCT
ejpam-5997	241	4	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	241	5	(	(	PUNCT
ejpam-5997	241	6	α	α	NOUN
ejpam-5997	241	7	)	)	PUNCT
ejpam-5997	241	8	∣∣q	∣∣q	NUM
ejpam-5997	241	9	ξ′	ξ′	NOUN
ejpam-5997	241	10	+	+	CCONJ
ejpam-5997	241	11	µn+	µn+	ADV
ejpam-5997	241	12	s+	s+	PUNCT
ejpam-5997	241	13	1	1	NUM
ejpam-5997	241	14	+	+	CCONJ
ejpam-5997	241	15	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	241	16	(	(	PUNCT
ejpam-5997	241	17	τ	τ	NOUN
ejpam-5997	241	18	)	)	PUNCT
ejpam-5997	241	19	∣∣qβ(ξ′	∣∣qβ(ξ′	PROPN
ejpam-5997	241	20	+	+	CCONJ
ejpam-5997	241	21	µn+	µn+	ADV
ejpam-5997	241	22	s+	s+	ADP
ejpam-5997	241	23	1	1	NUM
ejpam-5997	241	24	,	,	PUNCT
ejpam-5997	241	25	1	1	NUM
ejpam-5997	241	26	)	)	PUNCT
ejpam-5997	241	27	)	)	PUNCT
ejpam-5997	241	28	1	1	NUM
ejpam-5997	241	29	q	q	NOUN
ejpam-5997	241	30	]	]	PUNCT
ejpam-5997	241	31	.	.	PUNCT
ejpam-5997	242	1	corollary	corollary	ADJ
ejpam-5997	242	2	4	4	NUM
ejpam-5997	242	3	.	.	PUNCT
ejpam-5997	243	1	if	if	SCONJ
ejpam-5997	243	2	we	we	PRON
ejpam-5997	243	3	replace	replace	VERB
ejpam-5997	243	4	p	p	NOUN
ejpam-5997	243	5	=	=	NOUN
ejpam-5997	243	6	0	0	NUM
ejpam-5997	243	7	,	,	PUNCT
ejpam-5997	243	8	κ	κ	X
ejpam-5997	243	9	=	=	SYM
ejpam-5997	243	10	0	0	NUM
ejpam-5997	243	11	,	,	PUNCT
ejpam-5997	243	12	and	and	CCONJ
ejpam-5997	243	13	ξ	ξ	X
ejpam-5997	243	14	=	=	SYM
ejpam-5997	243	15	ξ	ξ	PROPN
ejpam-5997	243	16	−	−	PROPN
ejpam-5997	243	17	1	1	NUM
ejpam-5997	243	18	in	in	ADP
ejpam-5997	243	19	theorem	theorem	NOUN
ejpam-5997	243	20	(	(	PUNCT
ejpam-5997	243	21	3	3	NUM
ejpam-5997	243	22	)	)	PUNCT
ejpam-5997	243	23	,	,	PUNCT
ejpam-5997	243	24	we	we	PRON
ejpam-5997	243	25	have	have	VERB
ejpam-5997	243	26	a	a	DET
ejpam-5997	243	27	result	result	NOUN
ejpam-5997	243	28	[	[	X
ejpam-5997	243	29	19	19	NUM
ejpam-5997	243	30	]	]	PUNCT
ejpam-5997	243	31	.	.	PUNCT
ejpam-5997	244	1	theorem	theorem	ADJ
ejpam-5997	244	2	4	4	NUM
ejpam-5997	244	3	.	.	PUNCT
ejpam-5997	245	1	let	let	VERB
ejpam-5997	245	2	ϕ	ϕ	NOUN
ejpam-5997	245	3	:	:	PUNCT
ejpam-5997	245	4	i	i	PRON
ejpam-5997	245	5	⊆	⊆	NUM
ejpam-5997	245	6	r	r	NOUN
ejpam-5997	245	7	→	→	SYM
ejpam-5997	245	8	r	r	NOUN
ejpam-5997	245	9	be	be	AUX
ejpam-5997	245	10	a	a	DET
ejpam-5997	245	11	differentiable	differentiable	ADJ
ejpam-5997	245	12	mapping	mapping	NOUN
ejpam-5997	245	13	on	on	ADP
ejpam-5997	245	14	io	io	PROPN
ejpam-5997	245	15	and	and	CCONJ
ejpam-5997	245	16	ω	ω	PROPN
ejpam-5997	245	17	,	,	PUNCT
ejpam-5997	245	18	τ	τ	PROPN
ejpam-5997	245	19	∈	∈	PROPN
ejpam-5997	245	20	io	io	X
ejpam-5997	245	21	with	with	ADP
ejpam-5997	245	22	ω	ω	PROPN
ejpam-5997	245	23	<	<	X
ejpam-5997	245	24	α	α	X
ejpam-5997	245	25	<	<	X
ejpam-5997	245	26	τ	τ	PROPN
ejpam-5997	245	27	such	such	ADJ
ejpam-5997	245	28	that	that	SCONJ
ejpam-5997	245	29	ϕ	ϕ	PROPN
ejpam-5997	245	30	′	′	NUM
ejpam-5997	245	31	∈	∈	PROPN
ejpam-5997	245	32	l[ω	l[ω	PROPN
ejpam-5997	245	33	,	,	PUNCT
ejpam-5997	245	34	τ	τ	X
ejpam-5997	245	35	]	]	X
ejpam-5997	245	36	.	.	PUNCT
ejpam-5997	246	1	if	if	SCONJ
ejpam-5997	246	2	|ϕ′	|ϕ′	PROPN
ejpam-5997	246	3	|q	|q	NOUN
ejpam-5997	246	4	is	be	AUX
ejpam-5997	246	5	s	s	NOUN
ejpam-5997	246	6	-	-	ADJ
ejpam-5997	246	7	convex	convex	ADJ
ejpam-5997	246	8	function	function	NOUN
ejpam-5997	246	9	on	on	ADP
ejpam-5997	246	10	[	[	X
ejpam-5997	246	11	ω	ω	PROPN
ejpam-5997	246	12	,	,	PUNCT
ejpam-5997	246	13	τ	τ	X
ejpam-5997	246	14	]	]	X
ejpam-5997	246	15	,	,	PUNCT
ejpam-5997	246	16	and	and	CCONJ
ejpam-5997	246	17	µ	µ	NOUN
ejpam-5997	246	18	,	,	PUNCT
ejpam-5997	246	19	ξ	ξ	PROPN
ejpam-5997	246	20	,	,	PUNCT
ejpam-5997	246	21	ζ	ζ	NOUN
ejpam-5997	246	22	,	,	PUNCT
ejpam-5997	246	23	ς	ς	PROPN
ejpam-5997	246	24	,	,	PUNCT
ejpam-5997	246	25	c	c	X
ejpam-5997	246	26	,	,	PUNCT
ejpam-5997	246	27	κ1	κ1	PROPN
ejpam-5997	246	28	∈	∈	PROPN
ejpam-5997	246	29	c,ℜ(µ	c,ℜ(µ	PROPN
ejpam-5997	246	30	)	)	PUNCT
ejpam-5997	246	31	>	>	X
ejpam-5997	246	32	0,ℜ(ξ	0,ℜ(ξ	PROPN
ejpam-5997	246	33	)	)	PUNCT
ejpam-5997	246	34	>	>	X
ejpam-5997	246	35	0,ℜ(ζ	0,ℜ(ζ	PROPN
ejpam-5997	246	36	)	)	PUNCT
ejpam-5997	246	37	>	>	X
ejpam-5997	246	38	0,ℜ(ς	0,ℜ(ς	PROPN
ejpam-5997	246	39	)	)	PUNCT
ejpam-5997	246	40	>	>	X
ejpam-5997	247	1	0,ℜ(κ1	0,ℜ(κ1	PROPN
ejpam-5997	247	2	)	)	PUNCT
ejpam-5997	247	3	>	>	X
ejpam-5997	247	4	0	0	NUM
ejpam-5997	247	5	,	,	PUNCT
ejpam-5997	247	6	ρ	ρ	PROPN
ejpam-5997	247	7	,	,	PUNCT
ejpam-5997	247	8	m	m	PROPN
ejpam-5997	247	9	,	,	PUNCT
ejpam-5997	247	10	η	η	PROPN
ejpam-5997	247	11	≥	≥	X
ejpam-5997	247	12	0	0	NUM
ejpam-5997	247	13	and	and	CCONJ
ejpam-5997	247	14	m	m	PROPN
ejpam-5997	247	15	,	,	PUNCT
ejpam-5997	247	16	ρ	ρ	PROPN
ejpam-5997	247	17	>	>	X
ejpam-5997	247	18	ℜ(µ	ℜ(µ	NOUN
ejpam-5997	247	19	)	)	PUNCT
ejpam-5997	247	20	+	+	CCONJ
ejpam-5997	247	21	η	η	PROPN
ejpam-5997	247	22	,	,	PUNCT
ejpam-5997	247	23	then	then	ADV
ejpam-5997	247	24	following	follow	VERB
ejpam-5997	247	25	fractional	fractional	ADJ
ejpam-5997	247	26	integral	integral	ADJ
ejpam-5997	247	27	inequality	inequality	NOUN
ejpam-5997	247	28	holds	holds	AUX
ejpam-5997	247	29	;	;	PUNCT
ejpam-5997	247	30	m.	m.	NOUN
ejpam-5997	247	31	vivas	vivas	PROPN
ejpam-5997	247	32	-	-	PROPN
ejpam-5997	247	33	cortez	cortez	PROPN
ejpam-5997	247	34	et	et	PROPN
ejpam-5997	247	35	al	al	PROPN
ejpam-5997	247	36	.	.	PUNCT
ejpam-5997	247	37	/	/	SYM
ejpam-5997	247	38	eur	eur	PROPN
ejpam-5997	247	39	.	.	PUNCT
ejpam-5997	248	1	j.	j.	PROPN
ejpam-5997	248	2	pure	pure	PROPN
ejpam-5997	248	3	appl	appl	PROPN
ejpam-5997	248	4	.	.	PROPN
ejpam-5997	248	5	math	math	PROPN
ejpam-5997	248	6	,	,	PUNCT
ejpam-5997	248	7	18	18	NUM
ejpam-5997	248	8	(	(	PUNCT
ejpam-5997	248	9	2	2	NUM
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ejpam-5997	248	11	(	(	PUNCT
ejpam-5997	248	12	2025	2025	NUM
ejpam-5997	248	13	)	)	PUNCT
ejpam-5997	248	14	,	,	PUNCT
ejpam-5997	248	15	5997	5997	NUM
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ejpam-5997	248	18	23	23	NUM
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ejpam-5997	248	20	,	,	PUNCT
ejpam-5997	248	21	m	m	PROPN
ejpam-5997	248	22	,	,	PUNCT
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ejpam-5997	248	24	,	,	PUNCT
ejpam-5997	248	25	cξ	cξ	NOUN
ejpam-5997	248	26	,	,	PUNCT
ejpam-5997	248	27	ζ	ζ	NOUN
ejpam-5997	248	28	,	,	PUNCT
ejpam-5997	248	29	ς	ς	PROPN
ejpam-5997	248	30	,	,	PUNCT
ejpam-5997	248	31	κ1	κ1	NOUN
ejpam-5997	248	32	(	(	PUNCT
ejpam-5997	248	33	κ	κ	NOUN
ejpam-5997	248	34	,	,	PUNCT
ejpam-5997	248	35	p	p	NOUN
ejpam-5997	248	36	)	)	PUNCT
ejpam-5997	248	37	[	[	PUNCT
ejpam-5997	248	38	1	1	NUM
ejpam-5997	248	39	α−	α−	ADP
ejpam-5997	248	40	ω	ω	NUM
ejpam-5997	248	41	+	+	CCONJ
ejpam-5997	248	42	1	1	NUM
ejpam-5997	248	43	α−	α−	ADP
ejpam-5997	248	44	τ	τ	X
ejpam-5997	248	45	]	]	X
ejpam-5997	248	46	−	−	PROPN
ejpam-5997	248	47	(	(	PUNCT
ejpam-5997	248	48	ξ	ξ	X
ejpam-5997	248	49	′	′	NUM
ejpam-5997	248	50	+	+	CCONJ
ejpam-5997	248	51	µn	µn	X
ejpam-5997	248	52	)	)	PUNCT
ejpam-5997	248	53	[	[	PUNCT
ejpam-5997	248	54	1	1	NUM
ejpam-5997	248	55	(	(	PUNCT
ejpam-5997	248	56	α−	α−	ADP
ejpam-5997	248	57	ω)ξ	ω)ξ	VERB
ejpam-5997	248	58	′+1	′+1	PROPN
ejpam-5997	248	59	(	(	PUNCT
ejpam-5997	248	60	eµ,ρ	eµ,ρ	X
ejpam-5997	248	61	,	,	PUNCT
ejpam-5997	248	62	m	m	PROPN
ejpam-5997	248	63	,	,	PUNCT
ejpam-5997	248	64	η	η	PROPN
ejpam-5997	248	65	,	,	PUNCT
ejpam-5997	248	66	c	c	PROPN
ejpam-5997	248	67	ξ	ξ	PROPN
ejpam-5997	248	68	,	,	PUNCT
ejpam-5997	248	69	ζ	ζ	NOUN
ejpam-5997	248	70	,	,	PUNCT
ejpam-5997	248	71	ς	ς	NOUN
ejpam-5997	248	72	,	,	PUNCT
ejpam-5997	248	73	κ1,α+ϕ	κ1,α+ϕ	VERB
ejpam-5997	248	74	)	)	PUNCT
ejpam-5997	248	75	(	(	PUNCT
ejpam-5997	248	76	ω	ω	NOUN
ejpam-5997	248	77	,	,	PUNCT
ejpam-5997	248	78	κ	κ	NOUN
ejpam-5997	248	79	)	)	PUNCT
ejpam-5997	248	80	+	+	CCONJ
ejpam-5997	248	81	1	1	NUM
ejpam-5997	248	82	(	(	PUNCT
ejpam-5997	248	83	α−	α−	ADP
ejpam-5997	248	84	τ)ξ	τ)ξ	NOUN
ejpam-5997	248	85	′+1	′+1	NOUN
ejpam-5997	248	86	(	(	PUNCT
ejpam-5997	248	87	eµ,ρ	eµ,ρ	X
ejpam-5997	248	88	,	,	PUNCT
ejpam-5997	248	89	m	m	PROPN
ejpam-5997	248	90	,	,	PUNCT
ejpam-5997	248	91	η	η	PROPN
ejpam-5997	248	92	,	,	PUNCT
ejpam-5997	248	93	c	c	PROPN
ejpam-5997	248	94	ξ	ξ	PROPN
ejpam-5997	248	95	,	,	PUNCT
ejpam-5997	248	96	ζ	ζ	NOUN
ejpam-5997	248	97	,	,	PUNCT
ejpam-5997	248	98	ς	ς	PROPN
ejpam-5997	248	99	,	,	PUNCT
ejpam-5997	248	100	κ1,τ−	κ1,τ−	ADJ
ejpam-5997	248	101	ϕ	ϕ	NOUN
ejpam-5997	248	102	)	)	PUNCT
ejpam-5997	248	103	(	(	PUNCT
ejpam-5997	248	104	ω	ω	PROPN
ejpam-5997	248	105	,	,	PUNCT
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ejpam-5997	248	108	]	]	PUNCT
ejpam-5997	248	109	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	248	110	≤	≤	NUM
ejpam-5997	248	111	jµ,ρ	jµ,ρ	NOUN
ejpam-5997	248	112	,	,	PUNCT
ejpam-5997	248	113	m	m	PROPN
ejpam-5997	248	114	,	,	PUNCT
ejpam-5997	248	115	η	η	PROPN
ejpam-5997	248	116	,	,	PUNCT
ejpam-5997	248	117	cξ	cξ	NOUN
ejpam-5997	248	118	,	,	PUNCT
ejpam-5997	248	119	ζ	ζ	NOUN
ejpam-5997	248	120	,	,	PUNCT
ejpam-5997	248	121	ς	ς	PROPN
ejpam-5997	248	122	,	,	PUNCT
ejpam-5997	248	123	κ1	κ1	NOUN
ejpam-5997	248	124	(	(	PUNCT
ejpam-5997	248	125	κ	κ	NOUN
ejpam-5997	248	126	,	,	PUNCT
ejpam-5997	248	127	p	p	NOUN
ejpam-5997	248	128	)	)	PUNCT
ejpam-5997	248	129	(	(	PUNCT
ejpam-5997	248	130	1	1	NUM
ejpam-5997	248	131	pξ′	pξ′	NOUN
ejpam-5997	248	132	+	+	X
ejpam-5997	248	133	pµn+	pµn+	CCONJ
ejpam-5997	248	134	1	1	NUM
ejpam-5997	248	135	)	)	PUNCT
ejpam-5997	248	136	1	1	NUM
ejpam-5997	249	1	p	p	NOUN
ejpam-5997	249	2	[	[	X
ejpam-5997	249	3	(	(	PUNCT
ejpam-5997	249	4	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	249	5	(	(	PUNCT
ejpam-5997	249	6	α	α	NOUN
ejpam-5997	249	7	)	)	PUNCT
ejpam-5997	249	8	∣∣q	∣∣q	NUM
ejpam-5997	249	9	1	1	NUM
ejpam-5997	249	10	s+	s+	ADP
ejpam-5997	249	11	1	1	NUM
ejpam-5997	249	12	+	+	CCONJ
ejpam-5997	249	13	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	249	14	(	(	PUNCT
ejpam-5997	249	15	ω	ω	NOUN
ejpam-5997	249	16	)	)	PUNCT
ejpam-5997	249	17	∣∣q	∣∣q	NUM
ejpam-5997	249	18	1	1	NUM
ejpam-5997	249	19	s+	s+	ADP
ejpam-5997	249	20	1	1	NUM
ejpam-5997	249	21	)	)	PUNCT
ejpam-5997	249	22	1	1	NUM
ejpam-5997	249	23	q	q	NOUN
ejpam-5997	249	24	+	+	CCONJ
ejpam-5997	249	25	(	(	PUNCT
ejpam-5997	249	26	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	249	27	(	(	PUNCT
ejpam-5997	249	28	α	α	NOUN
ejpam-5997	249	29	)	)	PUNCT
ejpam-5997	249	30	∣∣q	∣∣q	NUM
ejpam-5997	249	31	1	1	NUM
ejpam-5997	249	32	s+	s+	ADP
ejpam-5997	249	33	1	1	NUM
ejpam-5997	249	34	+	+	CCONJ
ejpam-5997	249	35	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	249	36	(	(	PUNCT
ejpam-5997	249	37	τ	τ	NOUN
ejpam-5997	249	38	)	)	PUNCT
ejpam-5997	249	39	∣∣q	∣∣q	NUM
ejpam-5997	249	40	1	1	NUM
ejpam-5997	249	41	s+	s+	ADP
ejpam-5997	249	42	1	1	NUM
ejpam-5997	249	43	)	)	PUNCT
ejpam-5997	249	44	1	1	NUM
ejpam-5997	249	45	q	q	NOUN
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ejpam-5997	249	47	.	.	PUNCT
ejpam-5997	250	1	proof	proof	NOUN
ejpam-5997	250	2	.	.	PUNCT
ejpam-5997	251	1	according	accord	VERB
ejpam-5997	251	2	to	to	ADP
ejpam-5997	251	3	lemma	lemma	PROPN
ejpam-5997	251	4	1	1	NUM
ejpam-5997	251	5	ℵ	ℵ	NOUN
ejpam-5997	251	6	=	=	SYM
ejpam-5997	251	7	∣∣∣∣ϕ(α)eµ,ρ	∣∣∣∣ϕ(α)eµ,ρ	PROPN
ejpam-5997	251	8	,	,	PUNCT
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ejpam-5997	251	10	,	,	PUNCT
ejpam-5997	251	11	η	η	PROPN
ejpam-5997	251	12	,	,	PUNCT
ejpam-5997	251	13	cξ	cξ	NOUN
ejpam-5997	251	14	,	,	PUNCT
ejpam-5997	251	15	ζ	ζ	NOUN
ejpam-5997	251	16	,	,	PUNCT
ejpam-5997	251	17	ς	ς	PROPN
ejpam-5997	251	18	,	,	PUNCT
ejpam-5997	251	19	κ1	κ1	NOUN
ejpam-5997	251	20	(	(	PUNCT
ejpam-5997	251	21	κ	κ	NOUN
ejpam-5997	251	22	,	,	PUNCT
ejpam-5997	251	23	p	p	NOUN
ejpam-5997	251	24	)	)	PUNCT
ejpam-5997	251	25	[	[	PUNCT
ejpam-5997	251	26	1	1	NUM
ejpam-5997	251	27	α−	α−	ADP
ejpam-5997	251	28	ω	ω	NUM
ejpam-5997	251	29	+	+	CCONJ
ejpam-5997	251	30	1	1	NUM
ejpam-5997	251	31	α−	α−	ADP
ejpam-5997	251	32	τ	τ	X
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ejpam-5997	262	12	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	262	13	(	(	PUNCT
ejpam-5997	262	14	ω	ω	NOUN
ejpam-5997	262	15	)	)	PUNCT
ejpam-5997	262	16	∣∣q	∣∣q	NUM
ejpam-5997	262	17	1	1	NUM
ejpam-5997	262	18	s+	s+	ADP
ejpam-5997	262	19	1	1	NUM
ejpam-5997	262	20	]	]	SYM
ejpam-5997	262	21	1	1	NUM
ejpam-5997	262	22	q	q	NOUN
ejpam-5997	262	23	+	+	NUM
ejpam-5997	262	24	m.	m.	NOUN
ejpam-5997	262	25	vivas	vivas	PROPN
ejpam-5997	262	26	-	-	PROPN
ejpam-5997	262	27	cortez	cortez	PROPN
ejpam-5997	262	28	et	et	PROPN
ejpam-5997	262	29	al	al	PROPN
ejpam-5997	262	30	.	.	PUNCT
ejpam-5997	262	31	/	/	SYM
ejpam-5997	262	32	eur	eur	PROPN
ejpam-5997	262	33	.	.	PUNCT
ejpam-5997	263	1	j.	j.	PROPN
ejpam-5997	263	2	pure	pure	PROPN
ejpam-5997	263	3	appl	appl	PROPN
ejpam-5997	263	4	.	.	PROPN
ejpam-5997	263	5	math	math	PROPN
ejpam-5997	263	6	,	,	PUNCT
ejpam-5997	263	7	18	18	NUM
ejpam-5997	263	8	(	(	PUNCT
ejpam-5997	263	9	2	2	NUM
ejpam-5997	263	10	)	)	PUNCT
ejpam-5997	263	11	(	(	PUNCT
ejpam-5997	263	12	2025	2025	NUM
ejpam-5997	263	13	)	)	PUNCT
ejpam-5997	263	14	,	,	PUNCT
ejpam-5997	263	15	5997	5997	NUM
ejpam-5997	263	16	11	11	NUM
ejpam-5997	263	17	of	of	ADP
ejpam-5997	263	18	23	23	NUM
ejpam-5997	263	19	jµ,ρ	jµ,ρ	NOUN
ejpam-5997	263	20	,	,	PUNCT
ejpam-5997	263	21	m	m	PROPN
ejpam-5997	263	22	,	,	PUNCT
ejpam-5997	263	23	η	η	PROPN
ejpam-5997	263	24	,	,	PUNCT
ejpam-5997	263	25	cξ	cξ	NOUN
ejpam-5997	263	26	,	,	PUNCT
ejpam-5997	263	27	ζ	ζ	NOUN
ejpam-5997	263	28	,	,	PUNCT
ejpam-5997	263	29	ς	ς	PROPN
ejpam-5997	263	30	,	,	PUNCT
ejpam-5997	263	31	κ1	κ1	NOUN
ejpam-5997	263	32	(	(	PUNCT
ejpam-5997	263	33	κ	κ	NOUN
ejpam-5997	263	34	,	,	PUNCT
ejpam-5997	263	35	p	p	NOUN
ejpam-5997	263	36	)	)	PUNCT
ejpam-5997	263	37	(	(	PUNCT
ejpam-5997	263	38	1	1	NUM
ejpam-5997	263	39	pξ′	pξ′	NOUN
ejpam-5997	263	40	+	+	X
ejpam-5997	263	41	pµn+	pµn+	CCONJ
ejpam-5997	263	42	1	1	NUM
ejpam-5997	263	43	)	)	PUNCT
ejpam-5997	263	44	1	1	NUM
ejpam-5997	264	1	p	p	NOUN
ejpam-5997	264	2	[	[	X
ejpam-5997	264	3	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	264	4	(	(	PUNCT
ejpam-5997	264	5	α	α	NOUN
ejpam-5997	264	6	)	)	PUNCT
ejpam-5997	264	7	∣∣q	∣∣q	NUM
ejpam-5997	264	8	1	1	NUM
ejpam-5997	264	9	s+	s+	ADP
ejpam-5997	264	10	1	1	NUM
ejpam-5997	264	11	+	+	CCONJ
ejpam-5997	264	12	∣∣ϕ′	∣∣ϕ′	NOUN
ejpam-5997	264	13	(	(	PUNCT
ejpam-5997	264	14	τ	τ	NOUN
ejpam-5997	264	15	)	)	PUNCT
ejpam-5997	264	16	∣∣q	∣∣q	NUM
ejpam-5997	264	17	1	1	NUM
ejpam-5997	264	18	s+	s+	ADP
ejpam-5997	264	19	1	1	NUM
ejpam-5997	264	20	]	]	SYM
ejpam-5997	264	21	1	1	NUM
ejpam-5997	264	22	q	q	NOUN
ejpam-5997	264	23	the	the	DET
ejpam-5997	264	24	proof	proof	NOUN
ejpam-5997	264	25	is	be	AUX
ejpam-5997	264	26	completed	complete	VERB
ejpam-5997	264	27	.	.	PUNCT
ejpam-5997	265	1	corollary	corollary	ADJ
ejpam-5997	265	2	5	5	NUM
ejpam-5997	265	3	.	.	PUNCT
ejpam-5997	266	1	if	if	SCONJ
ejpam-5997	266	2	we	we	PRON
ejpam-5997	266	3	replace	replace	VERB
ejpam-5997	266	4	p	p	NOUN
ejpam-5997	266	5	=	=	NOUN
ejpam-5997	266	6	0	0	NUM
ejpam-5997	266	7	,	,	PUNCT
ejpam-5997	266	8	κ	κ	X
ejpam-5997	266	9	=	=	SYM
ejpam-5997	266	10	0	0	NUM
ejpam-5997	266	11	,	,	PUNCT
ejpam-5997	266	12	and	and	CCONJ
ejpam-5997	266	13	ξ	ξ	X
ejpam-5997	266	14	=	=	SYM
ejpam-5997	266	15	ξ	ξ	PROPN
ejpam-5997	266	16	−	−	PROPN
ejpam-5997	266	17	1	1	NUM
ejpam-5997	266	18	in	in	ADP
ejpam-5997	266	19	theorem	theorem	NOUN
ejpam-5997	266	20	(	(	PUNCT
ejpam-5997	266	21	4	4	NUM
ejpam-5997	266	22	)	)	PUNCT
ejpam-5997	266	23	,	,	PUNCT
ejpam-5997	266	24	we	we	PRON
ejpam-5997	266	25	have	have	VERB
ejpam-5997	266	26	an	an	DET
ejpam-5997	266	27	inequality	inequality	NOUN
ejpam-5997	266	28	[	[	X
ejpam-5997	266	29	19	19	NUM
ejpam-5997	266	30	]	]	PUNCT
ejpam-5997	266	31	.	.	PUNCT
ejpam-5997	267	1	4	4	X
ejpam-5997	267	2	.	.	X
ejpam-5997	267	3	behavior	behavior	NOUN
ejpam-5997	267	4	of	of	ADP
ejpam-5997	267	5	hermite	hermite	PROPN
ejpam-5997	267	6	-	-	PUNCT
ejpam-5997	267	7	hadamard	hadamard	ADJ
ejpam-5997	267	8	type	type	NOUN
ejpam-5997	267	9	fractional	fractional	ADJ
ejpam-5997	267	10	integral	integral	ADJ
ejpam-5997	267	11	inequalities	inequality	NOUN
ejpam-5997	267	12	for	for	ADP
ejpam-5997	267	13	the	the	DET
ejpam-5997	267	14	class	class	NOUN
ejpam-5997	267	15	of	of	ADP
ejpam-5997	267	16	twice	twice	ADJ
ejpam-5997	267	17	differentiable	differentiable	ADJ
ejpam-5997	267	18	function	function	NOUN
ejpam-5997	267	19	in	in	ADP
ejpam-5997	267	20	this	this	DET
ejpam-5997	267	21	section	section	NOUN
ejpam-5997	267	22	,	,	PUNCT
ejpam-5997	267	23	we	we	PRON
ejpam-5997	267	24	develop	develop	VERB
ejpam-5997	267	25	the	the	DET
ejpam-5997	267	26	lemma	lemma	PROPN
ejpam-5997	267	27	for	for	ADP
ejpam-5997	267	28	twice	twice	ADJ
ejpam-5997	267	29	differentiable	differentiable	ADJ
ejpam-5997	267	30	s	s	NOUN
ejpam-5997	267	31	-	-	ADJ
ejpam-5997	267	32	convex	convex	ADJ
ejpam-5997	267	33	function	function	NOUN
ejpam-5997	267	34	with	with	ADP
ejpam-5997	267	35	extended	extended	ADJ
ejpam-5997	267	36	bessel	bessel	NOUN
ejpam-5997	267	37	-	-	PUNCT
ejpam-5997	267	38	maitland	maitland	NOUN
ejpam-5997	267	39	function	function	NOUN
ejpam-5997	267	40	as	as	ADP
ejpam-5997	267	41	a	a	DET
ejpam-5997	267	42	kernel	kernel	NOUN
ejpam-5997	267	43	which	which	PRON
ejpam-5997	267	44	is	be	AUX
ejpam-5997	267	45	helpful	helpful	ADJ
ejpam-5997	267	46	to	to	PART
ejpam-5997	267	47	prove	prove	VERB
ejpam-5997	267	48	our	our	PRON
ejpam-5997	267	49	main	main	ADJ
ejpam-5997	267	50	results	result	NOUN
ejpam-5997	267	51	.	.	PUNCT
ejpam-5997	268	1	lemma	lemma	PROPN
ejpam-5997	268	2	2	2	X
ejpam-5997	268	3	.	.	PUNCT
ejpam-5997	269	1	let	let	VERB
ejpam-5997	269	2	ϕ	ϕ	NOUN
ejpam-5997	269	3	:	:	PUNCT
ejpam-5997	269	4	i	i	PRON
ejpam-5997	269	5	⊆	⊆	NUM
ejpam-5997	269	6	r	r	NOUN
ejpam-5997	269	7	→	→	SYM
ejpam-5997	269	8	r	r	NOUN
ejpam-5997	269	9	be	be	VERB
ejpam-5997	269	10	twice	twice	ADV
ejpam-5997	269	11	differentiable	differentiable	ADJ
ejpam-5997	269	12	mapping	mapping	NOUN
ejpam-5997	269	13	on	on	ADP
ejpam-5997	269	14	io	io	PROPN
ejpam-5997	269	15	and	and	CCONJ
ejpam-5997	269	16	let	let	VERB
ejpam-5997	269	17	,	,	PUNCT
ejpam-5997	269	18	if	if	SCONJ
ejpam-5997	269	19	ω	ω	PROPN
ejpam-5997	269	20	,	,	PUNCT
ejpam-5997	269	21	τ	τ	PROPN
ejpam-5997	269	22	∈	∈	PROPN
ejpam-5997	269	23	io	io	X
ejpam-5997	269	24	with	with	ADP
ejpam-5997	269	25	ω	ω	PROPN
ejpam-5997	269	26	<	<	X
ejpam-5997	269	27	α	α	X
ejpam-5997	269	28	<	<	X
ejpam-5997	269	29	τ	τ	PROPN
ejpam-5997	269	30	such	such	ADJ
ejpam-5997	269	31	that	that	SCONJ
ejpam-5997	269	32	ϕ	ϕ	NOUN
ejpam-5997	269	33	′′	′′	PROPN
ejpam-5997	269	34	∈	∈	PROPN
ejpam-5997	269	35	l[ω	l[ω	PROPN
ejpam-5997	269	36	,	,	PUNCT
ejpam-5997	269	37	τ	τ	X
ejpam-5997	269	38	]	]	X
ejpam-5997	269	39	,	,	PUNCT
ejpam-5997	269	40	and	and	CCONJ
ejpam-5997	269	41	µ	µ	NOUN
ejpam-5997	269	42	,	,	PUNCT
ejpam-5997	269	43	ξ	ξ	PROPN
ejpam-5997	269	44	,	,	PUNCT
ejpam-5997	269	45	ζ	ζ	NOUN
ejpam-5997	269	46	,	,	PUNCT
ejpam-5997	269	47	ς	ς	PROPN
ejpam-5997	269	48	,	,	PUNCT
ejpam-5997	269	49	c	c	X
ejpam-5997	269	50	,	,	PUNCT
ejpam-5997	269	51	κ1	κ1	PROPN
ejpam-5997	269	52	∈	∈	PROPN
ejpam-5997	269	53	c,ℜ(µ	c,ℜ(µ	PROPN
ejpam-5997	269	54	)	)	PUNCT
ejpam-5997	269	55	>	>	X
ejpam-5997	269	56	0,ℜ(ξ	0,ℜ(ξ	PROPN
ejpam-5997	269	57	)	)	PUNCT
ejpam-5997	269	58	>	>	X
ejpam-5997	269	59	0,ℜ(ζ	0,ℜ(ζ	PROPN
ejpam-5997	269	60	)	)	PUNCT
ejpam-5997	269	61	>	>	X
ejpam-5997	269	62	0,ℜ(ς	0,ℜ(ς	PROPN
ejpam-5997	269	63	)	)	PUNCT
ejpam-5997	269	64	>	>	X
ejpam-5997	270	1	0,ℜ(κ1	0,ℜ(κ1	PROPN
ejpam-5997	270	2	)	)	PUNCT
ejpam-5997	270	3	>	>	X
ejpam-5997	270	4	0	0	NUM
ejpam-5997	270	5	,	,	PUNCT
ejpam-5997	270	6	ρ	ρ	PROPN
ejpam-5997	270	7	,	,	PUNCT
ejpam-5997	270	8	m	m	PROPN
ejpam-5997	270	9	,	,	PUNCT
ejpam-5997	270	10	η	η	PROPN
ejpam-5997	270	11	≥	≥	X
ejpam-5997	270	12	0	0	NUM
ejpam-5997	270	13	and	and	CCONJ
ejpam-5997	270	14	m	m	PROPN
ejpam-5997	270	15	,	,	PUNCT
ejpam-5997	270	16	ρ	ρ	PROPN
ejpam-5997	270	17	>	>	X
ejpam-5997	270	18	ℜ(µ	ℜ(µ	NOUN
ejpam-5997	270	19	)	)	PUNCT
ejpam-5997	270	20	+	+	CCONJ
ejpam-5997	270	21	η	η	PROPN
ejpam-5997	270	22	,	,	PUNCT
ejpam-5997	270	23	then	then	ADV
ejpam-5997	270	24	we	we	PRON
ejpam-5997	270	25	get	get	VERB
ejpam-5997	270	26	the	the	DET
ejpam-5997	270	27	following	follow	VERB
ejpam-5997	270	28	result	result	NOUN
ejpam-5997	270	29	;	;	PUNCT
ejpam-5997	270	30	(	(	PUNCT
ejpam-5997	270	31	ξ	ξ	PROPN
ejpam-5997	270	32	′	′	NUM
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ejpam-5997	270	34	jµ,ρ	jµ,ρ	NOUN
ejpam-5997	270	35	,	,	PUNCT
ejpam-5997	270	36	m	m	PROPN
ejpam-5997	270	37	,	,	PUNCT
ejpam-5997	270	38	η	η	PROPN
ejpam-5997	270	39	,	,	PUNCT
ejpam-5997	270	40	cξ	cξ	NOUN
ejpam-5997	270	41	,	,	PUNCT
ejpam-5997	270	42	ζ	ζ	NOUN
ejpam-5997	270	43	,	,	PUNCT
ejpam-5997	270	44	ς	ς	PROPN
ejpam-5997	270	45	,	,	PUNCT
ejpam-5997	270	46	κ1	κ1	NOUN
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ejpam-5997	270	48	κ	κ	NOUN
ejpam-5997	270	49	,	,	PUNCT
ejpam-5997	270	50	p	p	NOUN
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ejpam-5997	271	1	[	[	X
ejpam-5997	271	2	ϕ(α	ϕ(α	NUM
ejpam-5997	271	3	)	)	PUNCT
ejpam-5997	271	4	+	+	SYM
ejpam-5997	271	5	ϕ(ω	ϕ(ω	NOUN
ejpam-5997	271	6	)	)	PUNCT
ejpam-5997	271	7	2	2	NUM
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ejpam-5997	272	1	+	+	CCONJ
ejpam-5997	272	2	[	[	PUNCT
ejpam-5997	272	3	(	(	PUNCT
ejpam-5997	272	4	µn+	µn+	ADJ
ejpam-5997	272	5	1)(µn	1)(µn	NUM
ejpam-5997	272	6	)	)	PUNCT
ejpam-5997	272	7	2(α−	2(α−	NUM
ejpam-5997	273	1	ω)µn	ω)µn	PROPN
ejpam-5997	273	2	−	−	PROPN
ejpam-5997	273	3	(	(	PUNCT
ejpam-5997	273	4	ξ	ξ	X
ejpam-5997	273	5	′	′	NOUN
ejpam-5997	274	1	+	+	CCONJ
ejpam-5997	274	2	µn+	µn+	ADJ
ejpam-5997	274	3	1)(ξ	1)(ξ	NUM
ejpam-5997	274	4	′	′	NUM
ejpam-5997	274	5	+	+	CCONJ
ejpam-5997	274	6	µn	µn	X
ejpam-5997	274	7	)	)	PUNCT
ejpam-5997	274	8	2(α−	2(α−	NUM
ejpam-5997	274	9	ω)ξ	ω)ξ	NOUN
ejpam-5997	274	10	′+µn	′+µn	PROPN
ejpam-5997	274	11	]	]	PUNCT
ejpam-5997	274	12	×	×	PROPN
ejpam-5997	274	13	[	[	X
ejpam-5997	274	14	(	(	PUNCT
ejpam-5997	274	15	eµ,ρ	eµ,ρ	X
ejpam-5997	274	16	,	,	PUNCT
ejpam-5997	274	17	m	m	PROPN
ejpam-5997	274	18	,	,	PUNCT
ejpam-5997	274	19	η	η	PROPN
ejpam-5997	274	20	,	,	PUNCT
ejpam-5997	274	21	c	c	PROPN
ejpam-5997	274	22	ξ	ξ	PROPN
ejpam-5997	274	23	,	,	PUNCT
ejpam-5997	274	24	ζ	ζ	NOUN
ejpam-5997	274	25	,	,	PUNCT
ejpam-5997	274	26	ς	ς	PROPN
ejpam-5997	274	27	,	,	PUNCT
ejpam-5997	274	28	κ1,ω+ϕ	κ1,ω+ϕ	PROPN
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ejpam-5997	274	30	(	(	PUNCT
ejpam-5997	274	31	α	α	X
ejpam-5997	274	32	,	,	PUNCT
ejpam-5997	274	33	κ	κ	NOUN
ejpam-5997	274	34	)	)	PUNCT
ejpam-5997	274	35	+	+	CCONJ
ejpam-5997	274	36	(	(	PUNCT
ejpam-5997	274	37	eµ,ρ	eµ,ρ	X
ejpam-5997	274	38	,	,	PUNCT
ejpam-5997	274	39	m	m	PROPN
ejpam-5997	274	40	,	,	PUNCT
ejpam-5997	274	41	η	η	PROPN
ejpam-5997	274	42	,	,	PUNCT
ejpam-5997	274	43	c	c	PROPN
ejpam-5997	274	44	ξ	ξ	PROPN
ejpam-5997	274	45	,	,	PUNCT
ejpam-5997	274	46	ζ	ζ	NOUN
ejpam-5997	274	47	,	,	PUNCT
ejpam-5997	274	48	ς	ς	PROPN
ejpam-5997	274	49	,	,	PUNCT
ejpam-5997	274	50	κ1,α−ϕ	κ1,α−ϕ	NOUN
ejpam-5997	274	51	)	)	PUNCT
ejpam-5997	274	52	(	(	PUNCT
ejpam-5997	274	53	ω	ω	NOUN
ejpam-5997	274	54	,	,	PUNCT
ejpam-5997	274	55	κ	κ	NOUN
ejpam-5997	274	56	)	)	PUNCT
ejpam-5997	274	57	]	]	PUNCT
ejpam-5997	275	1	=	=	PUNCT
ejpam-5997	275	2	(	(	PUNCT
ejpam-5997	275	3	α−	α−	ADP
ejpam-5997	275	4	ω)2	ω)2	NOUN
ejpam-5997	275	5	2	2	NUM
ejpam-5997	275	6	∫	∫	NOUN
ejpam-5997	275	7	1	1	NUM
ejpam-5997	275	8	0	0	NUM
ejpam-5997	275	9	℘(1−	℘(1−	PROPN
ejpam-5997	275	10	℘ξ	℘ξ	NOUN
ejpam-5997	275	11	′	′	NUM
ejpam-5997	275	12	)	)	PUNCT
ejpam-5997	275	13	eµ,ρ	eµ,ρ	X
ejpam-5997	275	14	,	,	PUNCT
ejpam-5997	275	15	m	m	PROPN
ejpam-5997	275	16	,	,	PUNCT
ejpam-5997	275	17	η	η	PROPN
ejpam-5997	275	18	,	,	PUNCT
ejpam-5997	275	19	cξ	cξ	NOUN
ejpam-5997	275	20	,	,	PUNCT
ejpam-5997	275	21	ζ	ζ	NOUN
ejpam-5997	275	22	,	,	PUNCT
ejpam-5997	275	23	ς	ς	PROPN
ejpam-5997	275	24	,	,	PUNCT
ejpam-5997	275	25	κ1	κ1	NOUN
ejpam-5997	275	26	(	(	PUNCT
ejpam-5997	275	27	κ℘µ	κ℘µ	PROPN
ejpam-5997	275	28	;	;	PUNCT
ejpam-5997	275	29	p	p	X
ejpam-5997	275	30	)	)	PUNCT
ejpam-5997	275	31	[	[	PUNCT
ejpam-5997	275	32	ϕ	ϕ	PROPN
ejpam-5997	275	33	′′	′′	PROPN
ejpam-5997	275	34	(	(	PUNCT
ejpam-5997	275	35	℘ω	℘ω	NOUN
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ejpam-5997	275	42	(	(	PUNCT
ejpam-5997	275	43	(	(	PUNCT
ejpam-5997	275	44	1−	1−	NUM
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ejpam-5997	275	46	+	+	CCONJ
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ejpam-5997	275	49	]	]	PUNCT
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ejpam-5997	276	8	0	0	NUM
ejpam-5997	276	9	℘(1−	℘(1−	PROPN
ejpam-5997	276	10	℘ξ	℘ξ	NOUN
ejpam-5997	276	11	′	′	NUM
ejpam-5997	276	12	)	)	PUNCT
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ejpam-5997	276	33	′′	′′	PROPN
ejpam-5997	276	34	(	(	PUNCT
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ejpam-5997	276	36	+	+	CCONJ
ejpam-5997	276	37	(	(	PUNCT
ejpam-5997	276	38	1−	1−	NUM
ejpam-5997	276	39	℘)α+	℘)α+	PROPN
ejpam-5997	276	40	ϕ	ϕ	PROPN
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ejpam-5997	276	42	(	(	PUNCT
ejpam-5997	276	43	(	(	PUNCT
ejpam-5997	276	44	1−	1−	NUM
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ejpam-5997	276	46	+	+	CCONJ
ejpam-5997	276	47	℘α	℘α	NOUN
ejpam-5997	276	48	)	)	PUNCT
ejpam-5997	276	49	]	]	PUNCT
ejpam-5997	277	1	d℘	d℘	PROPN
ejpam-5997	277	2	i	i	NOUN
ejpam-5997	277	3	=	=	PUNCT
ejpam-5997	277	4	∫	∫	PROPN
ejpam-5997	277	5	1	1	NUM
ejpam-5997	277	6	0	0	NUM
ejpam-5997	277	7	℘(1−	℘(1−	PROPN
ejpam-5997	277	8	℘ξ	℘ξ	NOUN
ejpam-5997	277	9	′	′	NUM
ejpam-5997	277	10	)	)	PUNCT
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ejpam-5997	277	16	,	,	PUNCT
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ejpam-5997	277	21	ς	ς	PROPN
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ejpam-5997	277	25	κ℘µ	κ℘µ	PROPN
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ejpam-5997	278	6	1−	1−	NUM
ejpam-5997	278	7	℘)α	℘)α	NOUN
ejpam-5997	278	8	)	)	PUNCT
ejpam-5997	278	9	d℘	d℘	VERB
ejpam-5997	278	10	+	+	CCONJ
ejpam-5997	278	11	∫	∫	PROPN
ejpam-5997	278	12	1	1	NUM
ejpam-5997	278	13	0	0	NUM
ejpam-5997	278	14	℘(1−	℘(1−	PROPN
ejpam-5997	278	15	℘ξ	℘ξ	NOUN
ejpam-5997	278	16	′	′	NUM
ejpam-5997	278	17	)	)	PUNCT
ejpam-5997	278	18	eµ,ρ	eµ,ρ	X
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ejpam-5997	278	21	,	,	PUNCT
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ejpam-5997	278	23	,	,	PUNCT
ejpam-5997	278	24	cξ	cξ	NOUN
ejpam-5997	278	25	,	,	PUNCT
ejpam-5997	278	26	ζ	ζ	NOUN
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ejpam-5997	278	28	ς	ς	PROPN
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ejpam-5997	278	32	κ℘µ	κ℘µ	PROPN
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ejpam-5997	278	36	(	(	PUNCT
ejpam-5997	278	37	(	(	PUNCT
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ejpam-5997	278	40	+	+	CCONJ
ejpam-5997	278	41	℘α	℘α	PROPN
ejpam-5997	278	42	)	)	PUNCT
ejpam-5997	278	43	d℘	d℘	PROPN
ejpam-5997	278	44	(	(	PUNCT
ejpam-5997	278	45	21	21	NUM
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ejpam-5997	278	47	i	i	PROPN
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ejpam-5997	278	49	i1	i1	PROPN
ejpam-5997	278	50	+	+	CCONJ
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ejpam-5997	279	1	consider	consider	VERB
ejpam-5997	279	2	the	the	DET
ejpam-5997	279	3	integral	integral	ADJ
ejpam-5997	279	4	i1	i1	PROPN
ejpam-5997	279	5	i1	i1	PROPN
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ejpam-5997	280	2	∫	∫	PROPN
ejpam-5997	280	3	1	1	NUM
ejpam-5997	280	4	0	0	NUM
ejpam-5997	280	5	℘(1−	℘(1−	PROPN
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ejpam-5997	281	4	+	+	CCONJ
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ejpam-5997	281	9	d℘	d℘	PROPN
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ejpam-5997	282	11	c−	c−	X
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ejpam-5997	283	1	+	+	NUM
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ejpam-5997	285	9	2	2	NUM
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ejpam-5997	285	11	(	(	PUNCT
ejpam-5997	285	12	2025	2025	NUM
ejpam-5997	285	13	)	)	PUNCT
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ejpam-5997	301	10	℘)α	℘)α	NOUN
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ejpam-5997	303	1	+	+	CCONJ
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ejpam-5997	303	7	,	,	PUNCT
ejpam-5997	303	8	c−	c−	X
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ejpam-5997	304	10	µn+	µn+	ADJ
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ejpam-5997	304	14	ω	ω	NUM
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ejpam-5997	305	1	+	+	CCONJ
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ejpam-5997	305	3	′	′	NOUN
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ejpam-5997	306	2	22	22	X
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ejpam-5997	306	5	=	=	SYM
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ejpam-5997	306	8	i4	i4	PROPN
ejpam-5997	306	9	taking	take	VERB
ejpam-5997	306	10	i3	i3	NOUN
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ejpam-5997	306	12	above	above	ADP
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ejpam-5997	322	11	α−	α−	ADP
ejpam-5997	322	12	ω)2	ω)2	NOUN
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ejpam-5997	322	22	℘)α	℘)α	NOUN
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ejpam-5997	322	24	d℘	d℘	PROPN
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ejpam-5997	322	27	substitution	substitution	NOUN
ejpam-5997	322	28	℘ω+(1−℘)α	℘ω+(1−℘)α	ADP
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ejpam-5997	322	30	ℓ	ℓ	PROPN
ejpam-5997	322	31	in	in	ADP
ejpam-5997	322	32	above	above	ADP
ejpam-5997	322	33	equation	equation	NOUN
ejpam-5997	322	34	and	and	CCONJ
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ejpam-5997	323	33	m.	m.	NOUN
ejpam-5997	323	34	vivas	vivas	PROPN
ejpam-5997	323	35	-	-	PROPN
ejpam-5997	323	36	cortez	cortez	PROPN
ejpam-5997	323	37	et	et	PROPN
ejpam-5997	323	38	al	al	PROPN
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ejpam-5997	323	40	/	/	SYM
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ejpam-5997	323	42	.	.	PUNCT
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ejpam-5997	324	2	pure	pure	PROPN
ejpam-5997	324	3	appl	appl	PROPN
ejpam-5997	324	4	.	.	PROPN
ejpam-5997	324	5	math	math	PROPN
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ejpam-5997	324	9	2	2	NUM
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ejpam-5997	324	11	(	(	PUNCT
ejpam-5997	324	12	2025	2025	NUM
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ejpam-5997	324	14	,	,	PUNCT
ejpam-5997	324	15	5997	5997	NUM
ejpam-5997	324	16	13	13	NUM
ejpam-5997	324	17	of	of	ADP
ejpam-5997	324	18	23	23	NUM
ejpam-5997	324	19	now	now	ADV
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ejpam-5997	324	22	i4	i4	PROPN
ejpam-5997	324	23	from	from	ADP
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ejpam-5997	324	28	i4	i4	NOUN
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ejpam-5997	326	8	c−	c−	X
ejpam-5997	326	9	ζ)γ(µn+	ζ)γ(µn+	NOUN
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ejpam-5997	327	2	1)(ς)mn	1)(ς)mn	NUM
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ejpam-5997	327	6	(	(	PUNCT
ejpam-5997	327	7	ξ	ξ	X
ejpam-5997	327	8	′	′	NOUN
ejpam-5997	327	9	+	+	CCONJ
ejpam-5997	327	10	µn+	µn+	ADJ
ejpam-5997	327	11	1	1	NUM
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ejpam-5997	327	14	ω	ω	NUM
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ejpam-5997	328	1	+	+	CCONJ
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ejpam-5997	328	9	℘)α	℘)α	NOUN
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ejpam-5997	328	11	d℘	d℘	VERB
ejpam-5997	328	12	]	]	PUNCT
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ejpam-5997	329	5	+	+	CCONJ
ejpam-5997	329	6	ρn	ρn	INTJ
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ejpam-5997	329	13	ζ)γ(µn+	ζ)γ(µn+	NOUN
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ejpam-5997	330	17	′	′	NUM
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ejpam-5997	331	3	(	(	PUNCT
ejpam-5997	331	4	℘ω	℘ω	NOUN
ejpam-5997	331	5	+	+	CCONJ
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ejpam-5997	331	8	℘)α	℘)α	NOUN
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ejpam-5997	332	3	α	α	NOUN
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ejpam-5997	333	2	∫	∫	PROPN
ejpam-5997	333	3	1	1	NUM
ejpam-5997	333	4	0	0	NUM
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ejpam-5997	333	6	ξ	ξ	X
ejpam-5997	333	7	′	′	NOUN
ejpam-5997	334	1	+	+	CCONJ
ejpam-5997	334	2	µn)℘ξ	µn)℘ξ	VERB
ejpam-5997	334	3	′	′	NUM
ejpam-5997	335	1	+	+	PUNCT
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ejpam-5997	335	4	℘ω	℘ω	NOUN
ejpam-5997	335	5	+	+	CCONJ
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ejpam-5997	337	5	+	+	CCONJ
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ejpam-5997	337	12	c−	c−	X
ejpam-5997	337	13	ζ)γ(µn+	ζ)γ(µn+	NOUN
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ejpam-5997	338	1	+	+	NUM
ejpam-5997	338	2	1)(ς)mn	1)(ς)mn	NUM
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ejpam-5997	338	13	α−	α−	ADP
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ejpam-5997	338	17	ϕ(ω	ϕ(ω	NOUN
ejpam-5997	338	18	)	)	PUNCT
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ejpam-5997	338	20	ω	ω	PROPN
ejpam-5997	339	1	+	+	CCONJ
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ejpam-5997	339	6	ξ	ξ	X
ejpam-5997	339	7	′	′	NOUN
ejpam-5997	340	1	+	+	CCONJ
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ejpam-5997	341	1	+	+	PUNCT
ejpam-5997	341	2	µn−1ϕ	µn−1ϕ	NOUN
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ejpam-5997	346	3	1)(ξ	1)(ξ	NUM
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ejpam-5997	347	1	+	+	PUNCT
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ejpam-5997	347	5	+	+	CCONJ
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ejpam-5997	347	8	℘)α	℘)α	NOUN
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ejpam-5997	347	10	d℘	d℘	PROPN
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ejpam-5997	347	12	use	use	VERB
ejpam-5997	347	13	substitution	substitution	NOUN
ejpam-5997	347	14	℘ω+(1−℘)α	℘ω+(1−℘)α	ADP
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ejpam-5997	347	18	above	above	ADP
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ejpam-5997	347	20	and	and	CCONJ
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ejpam-5997	347	62	ϕ(ω	ϕ(ω	NOUN
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ejpam-5997	348	1	+	+	CCONJ
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ejpam-5997	348	5	+	+	CCONJ
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ejpam-5997	348	7	1)(ξ	1)(ξ	NUM
ejpam-5997	348	8	′	′	NUM
ejpam-5997	348	9	+	+	CCONJ
ejpam-5997	348	10	µn	µn	X
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ejpam-5997	348	12	(	(	PUNCT
ejpam-5997	348	13	α−	α−	ADP
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ejpam-5997	348	37	using	use	VERB
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ejpam-5997	348	43	(	(	PUNCT
ejpam-5997	348	44	24	24	NUM
ejpam-5997	348	45	)	)	PUNCT
ejpam-5997	348	46	in	in	ADP
ejpam-5997	348	47	(	(	PUNCT
ejpam-5997	348	48	22	22	NUM
ejpam-5997	348	49	)	)	PUNCT
ejpam-5997	348	50	,	,	PUNCT
ejpam-5997	348	51	we	we	PRON
ejpam-5997	348	52	have	have	VERB
ejpam-5997	348	53	i1	i1	PROPN
ejpam-5997	348	54	=	=	PUNCT
ejpam-5997	348	55	(	(	PUNCT
ejpam-5997	348	56	ξ	ξ	X
ejpam-5997	348	57	′	′	NUM
ejpam-5997	348	58	(	(	PUNCT
ejpam-5997	348	59	α−	α−	ADP
ejpam-5997	348	60	ω)2	ω)2	NOUN
ejpam-5997	348	61	)	)	PUNCT
ejpam-5997	348	62	jµ,ρ	jµ,ρ	PROPN
ejpam-5997	348	63	,	,	PUNCT
ejpam-5997	348	64	m	m	PROPN
ejpam-5997	348	65	,	,	PUNCT
ejpam-5997	348	66	η	η	PROPN
ejpam-5997	348	67	,	,	PUNCT
ejpam-5997	348	68	cξ	cξ	NOUN
ejpam-5997	348	69	,	,	PUNCT
ejpam-5997	348	70	ζ	ζ	NOUN
ejpam-5997	348	71	,	,	PUNCT
ejpam-5997	348	72	ς	ς	PROPN
ejpam-5997	348	73	,	,	PUNCT
ejpam-5997	348	74	κ1	κ1	NOUN
ejpam-5997	348	75	(	(	PUNCT
ejpam-5997	348	76	κ	κ	NOUN
ejpam-5997	348	77	,	,	PUNCT
ejpam-5997	348	78	p)[ϕ(ω	p)[ϕ(ω	NOUN
ejpam-5997	348	79	)	)	PUNCT
ejpam-5997	348	80	]	]	PUNCT
ejpam-5997	349	1	+	+	CCONJ
ejpam-5997	349	2	(	(	PUNCT
ejpam-5997	349	3	eµ,ρ	eµ,ρ	X
ejpam-5997	349	4	,	,	PUNCT
ejpam-5997	349	5	m	m	PROPN
ejpam-5997	349	6	,	,	PUNCT
ejpam-5997	349	7	η	η	PROPN
ejpam-5997	349	8	,	,	PUNCT
ejpam-5997	349	9	c	c	PROPN
ejpam-5997	349	10	ξ	ξ	PROPN
ejpam-5997	349	11	,	,	PUNCT
ejpam-5997	349	12	ζ	ζ	NOUN
ejpam-5997	349	13	,	,	PUNCT
ejpam-5997	349	14	ς	ς	PROPN
ejpam-5997	349	15	,	,	PUNCT
ejpam-5997	349	16	κ1,ω+ϕ	κ1,ω+ϕ	PROPN
ejpam-5997	349	17	)	)	PUNCT
ejpam-5997	349	18	(	(	PUNCT
ejpam-5997	349	19	α	α	NOUN
ejpam-5997	349	20	,	,	PUNCT
ejpam-5997	349	21	κ1	κ1	NOUN
ejpam-5997	349	22	)	)	PUNCT
ejpam-5997	349	23	[	[	PUNCT
ejpam-5997	349	24	(	(	PUNCT
ejpam-5997	349	25	µn+	µn+	ADJ
ejpam-5997	349	26	1)(µn	1)(µn	NUM
ejpam-5997	349	27	)	)	PUNCT
ejpam-5997	349	28	(	(	PUNCT
ejpam-5997	349	29	α−	α−	ADP
ejpam-5997	349	30	ω)2+µn	ω)2+µn	PROPN
ejpam-5997	349	31	−	−	X
ejpam-5997	349	32	(	(	PUNCT
ejpam-5997	349	33	ξ	ξ	X
ejpam-5997	349	34	′	′	NOUN
ejpam-5997	349	35	+	+	CCONJ
ejpam-5997	349	36	µn+	µn+	ADJ
ejpam-5997	349	37	1)(ξ	1)(ξ	NUM
ejpam-5997	349	38	′	′	NUM
ejpam-5997	349	39	+	+	CCONJ
ejpam-5997	349	40	µn	µn	X
ejpam-5997	349	41	)	)	PUNCT
ejpam-5997	349	42	(	(	PUNCT
ejpam-5997	349	43	α−	α−	ADP
ejpam-5997	349	44	ω)2+ξ	ω)2+ξ	NUM
ejpam-5997	349	45	′+µn	′+µn	PROPN
ejpam-5997	349	46	]	]	PUNCT
ejpam-5997	349	47	.(25	.(25	X
ejpam-5997	349	48	)	)	PUNCT
ejpam-5997	349	49	similarly	similarly	ADV
ejpam-5997	349	50	,	,	PUNCT
ejpam-5997	349	51	we	we	PRON
ejpam-5997	349	52	solve	solve	VERB
ejpam-5997	349	53	i2	i2	PROPN
ejpam-5997	349	54	and	and	CCONJ
ejpam-5997	349	55	get	get	VERB
ejpam-5997	349	56	the	the	DET
ejpam-5997	349	57	result	result	NOUN
ejpam-5997	349	58	;	;	PUNCT
ejpam-5997	349	59	i2	i2	PROPN
ejpam-5997	349	60	=	=	PUNCT
ejpam-5997	349	61	(	(	PUNCT
ejpam-5997	349	62	ξ	ξ	X
ejpam-5997	349	63	′	′	NUM
ejpam-5997	349	64	(	(	PUNCT
ejpam-5997	349	65	α−	α−	ADP
ejpam-5997	349	66	ω)2	ω)2	NOUN
ejpam-5997	349	67	)	)	PUNCT
ejpam-5997	349	68	jµ,ρ	jµ,ρ	PROPN
ejpam-5997	349	69	,	,	PUNCT
ejpam-5997	349	70	m	m	PROPN
ejpam-5997	349	71	,	,	PUNCT
ejpam-5997	349	72	η	η	PROPN
ejpam-5997	349	73	,	,	PUNCT
ejpam-5997	349	74	cξ	cξ	NOUN
ejpam-5997	349	75	,	,	PUNCT
ejpam-5997	349	76	ζ	ζ	NOUN
ejpam-5997	349	77	,	,	PUNCT
ejpam-5997	349	78	ς	ς	PROPN
ejpam-5997	349	79	,	,	PUNCT
ejpam-5997	349	80	κ1	κ1	NOUN
ejpam-5997	349	81	(	(	PUNCT
ejpam-5997	349	82	κ	κ	NOUN
ejpam-5997	349	83	,	,	PUNCT
ejpam-5997	349	84	p)[ϕ(α	p)[ϕ(α	NOUN
ejpam-5997	349	85	)	)	PUNCT
ejpam-5997	349	86	]	]	PUNCT
ejpam-5997	350	1	+	+	CCONJ
ejpam-5997	350	2	(	(	PUNCT
ejpam-5997	350	3	eµ,ρ	eµ,ρ	X
ejpam-5997	350	4	,	,	PUNCT
ejpam-5997	350	5	m	m	PROPN
ejpam-5997	350	6	,	,	PUNCT
ejpam-5997	350	7	η	η	PROPN
ejpam-5997	350	8	,	,	PUNCT
ejpam-5997	350	9	c	c	PROPN
ejpam-5997	350	10	ξ	ξ	PROPN
ejpam-5997	350	11	,	,	PUNCT
ejpam-5997	350	12	ζ	ζ	NOUN
ejpam-5997	350	13	,	,	PUNCT
ejpam-5997	350	14	ς	ς	PROPN
ejpam-5997	350	15	,	,	PUNCT
ejpam-5997	350	16	κ1,α−ϕ	κ1,α−ϕ	NOUN
ejpam-5997	350	17	)	)	PUNCT
ejpam-5997	350	18	(	(	PUNCT
ejpam-5997	350	19	ω	ω	NOUN
ejpam-5997	350	20	,	,	PUNCT
ejpam-5997	350	21	κ	κ	NOUN
ejpam-5997	350	22	)	)	PUNCT
ejpam-5997	350	23	[	[	PUNCT
ejpam-5997	350	24	(	(	PUNCT
ejpam-5997	350	25	µn+	µn+	ADJ
ejpam-5997	350	26	1)(µn	1)(µn	NUM
ejpam-5997	350	27	)	)	PUNCT
ejpam-5997	350	28	(	(	PUNCT
ejpam-5997	350	29	α−	α−	ADP
ejpam-5997	350	30	ω)2+µn	ω)2+µn	PROPN
ejpam-5997	350	31	−	−	X
ejpam-5997	350	32	(	(	PUNCT
ejpam-5997	350	33	ξ	ξ	X
ejpam-5997	350	34	′	′	NOUN
ejpam-5997	350	35	+	+	CCONJ
ejpam-5997	350	36	µn+	µn+	ADJ
ejpam-5997	350	37	1)(ξ	1)(ξ	NUM
ejpam-5997	350	38	′	′	NUM
ejpam-5997	350	39	+	+	CCONJ
ejpam-5997	350	40	µn	µn	X
ejpam-5997	350	41	)	)	PUNCT
ejpam-5997	350	42	(	(	PUNCT
ejpam-5997	350	43	α−	α−	ADP
ejpam-5997	350	44	ω)2+ξ	ω)2+ξ	DET
ejpam-5997	350	45	′+µn	′+µn	PROPN
ejpam-5997	350	46	]	]	PUNCT
ejpam-5997	350	47	(	(	PUNCT
ejpam-5997	350	48	26	26	NUM
ejpam-5997	350	49	)	)	PUNCT
ejpam-5997	350	50	combining	combine	VERB
ejpam-5997	350	51	equations	equation	NOUN
ejpam-5997	350	52	(	(	PUNCT
ejpam-5997	350	53	25	25	NUM
ejpam-5997	350	54	)	)	PUNCT
ejpam-5997	350	55	and	and	CCONJ
ejpam-5997	350	56	(	(	PUNCT
ejpam-5997	350	57	26	26	NUM
ejpam-5997	350	58	)	)	PUNCT
ejpam-5997	350	59	,	,	PUNCT
ejpam-5997	350	60	then	then	ADV
ejpam-5997	350	61	simplify	simplify	VERB
ejpam-5997	350	62	,	,	PUNCT
ejpam-5997	350	63	we	we	PRON
ejpam-5997	350	64	have	have	VERB
ejpam-5997	350	65	i	i	PRON
ejpam-5997	350	66	=	=	SYM
ejpam-5997	350	67	(	(	PUNCT
ejpam-5997	350	68	ξ	ξ	PROPN
ejpam-5997	350	69	′	′	NUM
ejpam-5997	350	70	)	)	PUNCT
ejpam-5997	350	71	jµ,ρ	jµ,ρ	NOUN
ejpam-5997	350	72	,	,	PUNCT
ejpam-5997	350	73	m	m	PROPN
ejpam-5997	350	74	,	,	PUNCT
ejpam-5997	350	75	η	η	PROPN
ejpam-5997	350	76	,	,	PUNCT
ejpam-5997	350	77	cξ	cξ	NOUN
ejpam-5997	350	78	,	,	PUNCT
ejpam-5997	350	79	ζ	ζ	NOUN
ejpam-5997	350	80	,	,	PUNCT
ejpam-5997	350	81	ς	ς	PROPN
ejpam-5997	350	82	,	,	PUNCT
ejpam-5997	350	83	κ1	κ1	NOUN
ejpam-5997	350	84	(	(	PUNCT
ejpam-5997	350	85	κ	κ	NOUN
ejpam-5997	350	86	,	,	PUNCT
ejpam-5997	350	87	p	p	NOUN
ejpam-5997	350	88	)	)	PUNCT
ejpam-5997	351	1	[	[	X
ejpam-5997	351	2	ϕ(α	ϕ(α	NUM
ejpam-5997	351	3	)	)	PUNCT
ejpam-5997	351	4	+	+	SYM
ejpam-5997	351	5	ϕ(ω	ϕ(ω	NOUN
ejpam-5997	351	6	)	)	PUNCT
ejpam-5997	351	7	2	2	NUM
ejpam-5997	351	8	]	]	PUNCT
ejpam-5997	352	1	+	+	CCONJ
ejpam-5997	352	2	[	[	PUNCT
ejpam-5997	352	3	(	(	PUNCT
ejpam-5997	352	4	µn+	µn+	ADJ
ejpam-5997	352	5	1)(µn	1)(µn	NUM
ejpam-5997	352	6	)	)	PUNCT
ejpam-5997	352	7	2(α−	2(α−	NUM
ejpam-5997	353	1	ω)µn	ω)µn	PROPN
ejpam-5997	353	2	−	−	PROPN
ejpam-5997	353	3	(	(	PUNCT
ejpam-5997	353	4	ξ	ξ	X
ejpam-5997	353	5	′	′	NOUN
ejpam-5997	354	1	+	+	CCONJ
ejpam-5997	354	2	µn+	µn+	ADJ
ejpam-5997	354	3	1)(ξ	1)(ξ	NUM
ejpam-5997	354	4	′	′	NUM
ejpam-5997	354	5	+	+	CCONJ
ejpam-5997	354	6	µn	µn	X
ejpam-5997	354	7	)	)	PUNCT
ejpam-5997	354	8	2(α−	2(α−	NUM
ejpam-5997	354	9	ω)ξ	ω)ξ	NOUN
ejpam-5997	354	10	′+µn	′+µn	PROPN
ejpam-5997	354	11	]	]	PUNCT
ejpam-5997	354	12	×	×	PROPN
ejpam-5997	354	13	[	[	X
ejpam-5997	354	14	(	(	PUNCT
ejpam-5997	354	15	eµ,ρ	eµ,ρ	X
ejpam-5997	354	16	,	,	PUNCT
ejpam-5997	354	17	m	m	PROPN
ejpam-5997	354	18	,	,	PUNCT
ejpam-5997	354	19	η	η	PROPN
ejpam-5997	354	20	,	,	PUNCT
ejpam-5997	354	21	c	c	PROPN
ejpam-5997	354	22	ξ	ξ	PROPN
ejpam-5997	354	23	,	,	PUNCT
ejpam-5997	354	24	ζ	ζ	NOUN
ejpam-5997	354	25	,	,	PUNCT
ejpam-5997	354	26	ς	ς	PROPN
ejpam-5997	354	27	,	,	PUNCT
ejpam-5997	354	28	κ1,ω+ϕ	κ1,ω+ϕ	PROPN
ejpam-5997	354	29	)	)	PUNCT
ejpam-5997	354	30	(	(	PUNCT
ejpam-5997	354	31	α	α	X
ejpam-5997	354	32	,	,	PUNCT
ejpam-5997	354	33	κ	κ	NOUN
ejpam-5997	354	34	)	)	PUNCT
ejpam-5997	354	35	+	+	CCONJ
ejpam-5997	354	36	(	(	PUNCT
ejpam-5997	354	37	eµ,ρ	eµ,ρ	X
ejpam-5997	354	38	,	,	PUNCT
ejpam-5997	354	39	m	m	PROPN
ejpam-5997	354	40	,	,	PUNCT
ejpam-5997	354	41	η	η	PROPN
ejpam-5997	354	42	,	,	PUNCT
ejpam-5997	354	43	c	c	PROPN
ejpam-5997	354	44	ξ	ξ	PROPN
ejpam-5997	354	45	,	,	PUNCT
ejpam-5997	354	46	ζ	ζ	NOUN
ejpam-5997	354	47	,	,	PUNCT
ejpam-5997	354	48	ς	ς	PROPN
ejpam-5997	354	49	,	,	PUNCT
ejpam-5997	354	50	κ1,α−ϕ	κ1,α−ϕ	NOUN
ejpam-5997	354	51	)	)	PUNCT
ejpam-5997	354	52	(	(	PUNCT
ejpam-5997	354	53	ω	ω	NOUN
ejpam-5997	354	54	,	,	PUNCT
ejpam-5997	354	55	κ	κ	NOUN
ejpam-5997	354	56	)	)	PUNCT
ejpam-5997	354	57	]	]	PUNCT
ejpam-5997	354	58	.	.	PUNCT
ejpam-5997	355	1	hence	hence	ADV
ejpam-5997	355	2	the	the	DET
ejpam-5997	355	3	required	require	VERB
ejpam-5997	355	4	result	result	NOUN
ejpam-5997	355	5	is	be	AUX
ejpam-5997	355	6	proved	prove	VERB
ejpam-5997	355	7	.	.	PUNCT
ejpam-5997	356	1	m.	m.	NOUN
ejpam-5997	356	2	vivas	vivas	PROPN
ejpam-5997	356	3	-	-	PROPN
ejpam-5997	356	4	cortez	cortez	PROPN
ejpam-5997	356	5	et	et	PROPN
ejpam-5997	356	6	al	al	PROPN
ejpam-5997	356	7	.	.	PUNCT
ejpam-5997	356	8	/	/	SYM
ejpam-5997	356	9	eur	eur	PROPN
ejpam-5997	356	10	.	.	PUNCT
ejpam-5997	357	1	j.	j.	PROPN
ejpam-5997	357	2	pure	pure	PROPN
ejpam-5997	357	3	appl	appl	PROPN
ejpam-5997	357	4	.	.	PROPN
ejpam-5997	357	5	math	math	PROPN
ejpam-5997	357	6	,	,	PUNCT
ejpam-5997	357	7	18	18	NUM
ejpam-5997	357	8	(	(	PUNCT
ejpam-5997	357	9	2	2	NUM
ejpam-5997	357	10	)	)	PUNCT
ejpam-5997	357	11	(	(	PUNCT
ejpam-5997	357	12	2025	2025	NUM
ejpam-5997	357	13	)	)	PUNCT
ejpam-5997	357	14	,	,	PUNCT
ejpam-5997	357	15	5997	5997	NUM
ejpam-5997	357	16	14	14	NUM
ejpam-5997	357	17	of	of	ADP
ejpam-5997	357	18	23	23	NUM
ejpam-5997	357	19	corollary	corollary	ADJ
ejpam-5997	357	20	6	6	NUM
ejpam-5997	357	21	.	.	PUNCT
ejpam-5997	358	1	if	if	SCONJ
ejpam-5997	358	2	we	we	PRON
ejpam-5997	358	3	replace	replace	VERB
ejpam-5997	358	4	p	p	NOUN
ejpam-5997	358	5	=	=	NOUN
ejpam-5997	358	6	0	0	NUM
ejpam-5997	358	7	,	,	PUNCT
ejpam-5997	358	8	κ	κ	X
ejpam-5997	358	9	=	=	SYM
ejpam-5997	358	10	0	0	NUM
ejpam-5997	358	11	,	,	PUNCT
ejpam-5997	358	12	and	and	CCONJ
ejpam-5997	358	13	ξ	ξ	X
ejpam-5997	358	14	=	=	SYM
ejpam-5997	358	15	ξ	ξ	PROPN
ejpam-5997	358	16	−	−	PROPN
ejpam-5997	358	17	1	1	NUM
ejpam-5997	358	18	in	in	ADP
ejpam-5997	358	19	the	the	DET
ejpam-5997	358	20	lamma	lamma	PROPN
ejpam-5997	358	21	(	(	PUNCT
ejpam-5997	358	22	2	2	NUM
ejpam-5997	358	23	)	)	PUNCT
ejpam-5997	358	24	,	,	PUNCT
ejpam-5997	358	25	we	we	PRON
ejpam-5997	358	26	have	have	VERB
ejpam-5997	358	27	a	a	DET
ejpam-5997	358	28	result	result	NOUN
ejpam-5997	358	29	[	[	X
ejpam-5997	358	30	19	19	NUM
ejpam-5997	358	31	]	]	PUNCT
ejpam-5997	358	32	.	.	PUNCT
ejpam-5997	359	1	theorem	theorem	NOUN
ejpam-5997	359	2	5	5	NUM
ejpam-5997	359	3	.	.	PUNCT
ejpam-5997	360	1	let	let	VERB
ejpam-5997	360	2	ϕ	ϕ	NOUN
ejpam-5997	360	3	:	:	PUNCT
ejpam-5997	360	4	i	i	PRON
ejpam-5997	360	5	⊆	⊆	NUM
ejpam-5997	360	6	r	r	NOUN
ejpam-5997	360	7	→	→	SYM
ejpam-5997	360	8	r	r	NOUN
ejpam-5997	360	9	be	be	VERB
ejpam-5997	360	10	twice	twice	ADV
ejpam-5997	360	11	differentiable	differentiable	ADJ
ejpam-5997	360	12	mapping	mapping	NOUN
ejpam-5997	360	13	on	on	ADP
ejpam-5997	360	14	io	io	PROPN
ejpam-5997	360	15	and	and	CCONJ
ejpam-5997	360	16	ω	ω	PROPN
ejpam-5997	360	17	,	,	PUNCT
ejpam-5997	360	18	τ	τ	PROPN
ejpam-5997	360	19	∈	∈	PROPN
ejpam-5997	360	20	io	io	X
ejpam-5997	360	21	with	with	ADP
ejpam-5997	360	22	ω	ω	PROPN
ejpam-5997	360	23	<	<	X
ejpam-5997	360	24	α	α	X
ejpam-5997	360	25	<	<	X
ejpam-5997	360	26	τ	τ	PROPN
ejpam-5997	360	27	such	such	ADJ
ejpam-5997	360	28	that	that	SCONJ
ejpam-5997	360	29	ϕ	ϕ	NOUN
ejpam-5997	360	30	′′	′′	PROPN
ejpam-5997	360	31	∈	∈	PROPN
ejpam-5997	360	32	l[ω	l[ω	PROPN
ejpam-5997	360	33	,	,	PUNCT
ejpam-5997	360	34	τ	τ	X
ejpam-5997	360	35	]	]	PUNCT
ejpam-5997	360	36	.	.	PUNCT
ejpam-5997	361	1	if	if	SCONJ
ejpam-5997	361	2	|ϕ′′	|ϕ′′	PRON
ejpam-5997	361	3	|	|	ADV
ejpam-5997	361	4	is	be	AUX
ejpam-5997	361	5	s	s	NOUN
ejpam-5997	361	6	-	-	ADJ
ejpam-5997	361	7	convex	convex	ADJ
ejpam-5997	361	8	function	function	NOUN
ejpam-5997	361	9	on	on	ADP
ejpam-5997	361	10	i	i	PROPN
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ejpam-5997	361	12	and	and	CCONJ
ejpam-5997	361	13	µ	µ	NOUN
ejpam-5997	361	14	,	,	PUNCT
ejpam-5997	361	15	ξ	ξ	PROPN
ejpam-5997	361	16	,	,	PUNCT
ejpam-5997	361	17	ζ	ζ	NOUN
ejpam-5997	361	18	,	,	PUNCT
ejpam-5997	361	19	ς	ς	PROPN
ejpam-5997	361	20	,	,	PUNCT
ejpam-5997	361	21	c	c	X
ejpam-5997	361	22	,	,	PUNCT
ejpam-5997	361	23	κ1	κ1	PROPN
ejpam-5997	361	24	∈	∈	PROPN
ejpam-5997	361	25	c,ℜ(µ	c,ℜ(µ	PROPN
ejpam-5997	361	26	)	)	PUNCT
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ejpam-5997	361	28	0,ℜ(ξ	0,ℜ(ξ	PROPN
ejpam-5997	361	29	)	)	PUNCT
ejpam-5997	361	30	>	>	X
ejpam-5997	361	31	0,ℜ(ζ	0,ℜ(ζ	PROPN
ejpam-5997	361	32	)	)	PUNCT
ejpam-5997	361	33	>	>	X
ejpam-5997	361	34	0,ℜ(ς	0,ℜ(ς	PROPN
ejpam-5997	361	35	)	)	PUNCT
ejpam-5997	361	36	>	>	X
ejpam-5997	362	1	0,ℜ(κ1	0,ℜ(κ1	PROPN
ejpam-5997	362	2	)	)	PUNCT
ejpam-5997	362	3	>	>	X
ejpam-5997	362	4	0	0	NUM
ejpam-5997	362	5	,	,	PUNCT
ejpam-5997	362	6	ρ	ρ	PROPN
ejpam-5997	362	7	,	,	PUNCT
ejpam-5997	362	8	m	m	PROPN
ejpam-5997	362	9	,	,	PUNCT
ejpam-5997	362	10	η	η	PROPN
ejpam-5997	362	11	≥	≥	X
ejpam-5997	362	12	0	0	NUM
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ejpam-5997	362	14	m	m	PROPN
ejpam-5997	362	15	,	,	PUNCT
ejpam-5997	362	16	ρ	ρ	PROPN
ejpam-5997	362	17	>	>	X
ejpam-5997	362	18	ℜ(µ	ℜ(µ	NOUN
ejpam-5997	362	19	)	)	PUNCT
ejpam-5997	362	20	+	+	CCONJ
ejpam-5997	362	21	η	η	PROPN
ejpam-5997	362	22	,	,	PUNCT
ejpam-5997	362	23	then	then	ADV
ejpam-5997	362	24	following	follow	VERB
ejpam-5997	362	25	fractional	fractional	ADJ
ejpam-5997	362	26	integral	integral	ADJ
ejpam-5997	362	27	inequality	inequality	NOUN
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ejpam-5997	362	42	κ	κ	NOUN
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ejpam-5997	363	1	[	[	X
ejpam-5997	363	2	ϕ(α	ϕ(α	NUM
ejpam-5997	363	3	)	)	PUNCT
ejpam-5997	363	4	+	+	SYM
ejpam-5997	363	5	ϕ(ω	ϕ(ω	NOUN
ejpam-5997	363	6	)	)	PUNCT
ejpam-5997	363	7	2	2	NUM
ejpam-5997	363	8	]	]	PUNCT
ejpam-5997	364	1	+	+	CCONJ
ejpam-5997	364	2	[	[	PUNCT
ejpam-5997	364	3	(	(	PUNCT
ejpam-5997	364	4	µn+	µn+	ADJ
ejpam-5997	364	5	1)(µn	1)(µn	NUM
ejpam-5997	364	6	)	)	PUNCT
ejpam-5997	364	7	2(α−	2(α−	NUM
ejpam-5997	365	1	ω)µn	ω)µn	PROPN
ejpam-5997	365	2	−	−	PROPN
ejpam-5997	365	3	(	(	PUNCT
ejpam-5997	365	4	ξ	ξ	X
ejpam-5997	365	5	′	′	NOUN
ejpam-5997	366	1	+	+	CCONJ
ejpam-5997	366	2	µn+	µn+	ADJ
ejpam-5997	366	3	1)(ξ	1)(ξ	NUM
ejpam-5997	366	4	′	′	NUM
ejpam-5997	366	5	+	+	CCONJ
ejpam-5997	366	6	µn	µn	X
ejpam-5997	366	7	)	)	PUNCT
ejpam-5997	366	8	2(α−	2(α−	NUM
ejpam-5997	366	9	ω)ξ	ω)ξ	NOUN
ejpam-5997	366	10	′+µn	′+µn	PROPN
ejpam-5997	366	11	]	]	PUNCT
ejpam-5997	366	12	×	×	PROPN
ejpam-5997	366	13	[	[	X
ejpam-5997	366	14	(	(	PUNCT
ejpam-5997	366	15	eµ,ρ	eµ,ρ	X
ejpam-5997	366	16	,	,	PUNCT
ejpam-5997	366	17	m	m	PROPN
ejpam-5997	366	18	,	,	PUNCT
ejpam-5997	366	19	η	η	PROPN
ejpam-5997	366	20	,	,	PUNCT
ejpam-5997	366	21	c	c	PROPN
ejpam-5997	366	22	ξ	ξ	PROPN
ejpam-5997	366	23	,	,	PUNCT
ejpam-5997	366	24	ζ	ζ	NOUN
ejpam-5997	366	25	,	,	PUNCT
ejpam-5997	366	26	ς	ς	PROPN
ejpam-5997	366	27	,	,	PUNCT
ejpam-5997	366	28	κ1,ω+ϕ	κ1,ω+ϕ	PROPN
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ejpam-5997	366	30	(	(	PUNCT
ejpam-5997	366	31	α	α	X
ejpam-5997	366	32	,	,	PUNCT
ejpam-5997	366	33	κ	κ	NOUN
ejpam-5997	366	34	)	)	PUNCT
ejpam-5997	366	35	+	+	CCONJ
ejpam-5997	366	36	(	(	PUNCT
ejpam-5997	366	37	eµ,ρ	eµ,ρ	X
ejpam-5997	366	38	,	,	PUNCT
ejpam-5997	366	39	m	m	PROPN
ejpam-5997	366	40	,	,	PUNCT
ejpam-5997	366	41	η	η	PROPN
ejpam-5997	366	42	,	,	PUNCT
ejpam-5997	366	43	c	c	PROPN
ejpam-5997	366	44	ξ	ξ	PROPN
ejpam-5997	366	45	,	,	PUNCT
ejpam-5997	366	46	ζ	ζ	NOUN
ejpam-5997	366	47	,	,	PUNCT
ejpam-5997	366	48	ς	ς	PROPN
ejpam-5997	366	49	,	,	PUNCT
ejpam-5997	366	50	κ1,α−ϕ	κ1,α−ϕ	NOUN
ejpam-5997	366	51	)	)	PUNCT
ejpam-5997	366	52	(	(	PUNCT
ejpam-5997	366	53	ω	ω	NOUN
ejpam-5997	366	54	,	,	PUNCT
ejpam-5997	366	55	κ	κ	NOUN
ejpam-5997	366	56	)	)	PUNCT
ejpam-5997	366	57	]	]	PUNCT
ejpam-5997	366	58	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	366	59	≤	≤	NOUN
ejpam-5997	366	60	∞∑	∞∑	NUM
ejpam-5997	366	61	n=0	n=0	NUM
ejpam-5997	366	62	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	366	63	βp(ζ	βp(ζ	NUM
ejpam-5997	366	64	+	+	CCONJ
ejpam-5997	366	65	ρn	ρn	INTJ
ejpam-5997	366	66	,	,	PUNCT
ejpam-5997	366	67	c−	c−	NOUN
ejpam-5997	366	68	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	366	69	β(ζ	β(ζ	PROPN
ejpam-5997	366	70	,	,	PUNCT
ejpam-5997	366	71	c−	c−	X
ejpam-5997	366	72	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	366	73	ξ	ξ	X
ejpam-5997	367	1	+	+	NUM
ejpam-5997	367	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	367	3	(	(	PUNCT
ejpam-5997	367	4	−κ)n	−κ)n	VERB
ejpam-5997	367	5	∣∣∣∣(α−	∣∣∣∣(α−	PROPN
ejpam-5997	367	6	ω)2	ω)2	X
ejpam-5997	367	7	2	2	NUM
ejpam-5997	367	8	[	[	X
ejpam-5997	367	9	(	(	PUNCT
ejpam-5997	367	10	|ϕ′′	|ϕ′′	PUNCT
ejpam-5997	367	11	(	(	PUNCT
ejpam-5997	367	12	ω	ω	NOUN
ejpam-5997	367	13	)	)	PUNCT
ejpam-5997	368	1	+	+	CCONJ
ejpam-5997	368	2	|ϕ′′	|ϕ′′	PRON
ejpam-5997	368	3	(	(	PUNCT
ejpam-5997	368	4	α)|	α)|	VERB
ejpam-5997	368	5	)	)	PUNCT
ejpam-5997	368	6	[	[	PUNCT
ejpam-5997	368	7	β(µn+	β(µn+	ADP
ejpam-5997	368	8	2	2	NUM
ejpam-5997	368	9	+	+	SYM
ejpam-5997	368	10	s	s	X
ejpam-5997	368	11	,	,	PUNCT
ejpam-5997	368	12	ξ	ξ	NOUN
ejpam-5997	368	13	′	′	NUM
ejpam-5997	369	1	+	+	CCONJ
ejpam-5997	369	2	1	1	X
ejpam-5997	369	3	)	)	PUNCT
ejpam-5997	369	4	+	+	NOUN
ejpam-5997	369	5	β(µn+	β(µn+	PROPN
ejpam-5997	369	6	2	2	NUM
ejpam-5997	369	7	,	,	PUNCT
ejpam-5997	369	8	ξ	ξ	NOUN
ejpam-5997	369	9	′	′	NUM
ejpam-5997	370	1	+	+	CCONJ
ejpam-5997	370	2	s+	s+	NUM
ejpam-5997	370	3	1	1	NUM
ejpam-5997	370	4	)	)	PUNCT
ejpam-5997	370	5	]	]	PUNCT
ejpam-5997	370	6	]	]	PUNCT
ejpam-5997	370	7	.	.	PUNCT
ejpam-5997	371	1	proof	proof	NOUN
ejpam-5997	371	2	.	.	PUNCT
ejpam-5997	372	1	by	by	ADP
ejpam-5997	372	2	using	use	VERB
ejpam-5997	372	3	lemma	lemma	PROPN
ejpam-5997	372	4	2	2	NUM
ejpam-5997	372	5	ℶ	ℶ	NOUN
ejpam-5997	372	6	:	:	PUNCT
ejpam-5997	372	7	=	=	SYM
ejpam-5997	372	8	∣∣∣∣(ξ′)jµ,ρ	∣∣∣∣(ξ′)jµ,ρ	NOUN
ejpam-5997	372	9	,	,	PUNCT
ejpam-5997	372	10	m	m	PROPN
ejpam-5997	372	11	,	,	PUNCT
ejpam-5997	372	12	η	η	PROPN
ejpam-5997	372	13	,	,	PUNCT
ejpam-5997	372	14	cξ	cξ	NOUN
ejpam-5997	372	15	,	,	PUNCT
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ejpam-5997	372	17	,	,	PUNCT
ejpam-5997	372	18	ς	ς	PROPN
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ejpam-5997	372	20	κ1	κ1	NOUN
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ejpam-5997	372	22	κ	κ	NOUN
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ejpam-5997	372	24	p	p	NOUN
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ejpam-5997	372	26	[	[	X
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ejpam-5997	372	28	)	)	PUNCT
ejpam-5997	372	29	+	+	SYM
ejpam-5997	372	30	ϕ(ω	ϕ(ω	NOUN
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ejpam-5997	372	32	2	2	NUM
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ejpam-5997	373	1	+	+	CCONJ
ejpam-5997	373	2	[	[	PUNCT
ejpam-5997	373	3	(	(	PUNCT
ejpam-5997	373	4	µn+	µn+	ADJ
ejpam-5997	373	5	1)(µn	1)(µn	NUM
ejpam-5997	373	6	)	)	PUNCT
ejpam-5997	373	7	2(α−	2(α−	NUM
ejpam-5997	374	1	ω)µn	ω)µn	PROPN
ejpam-5997	374	2	−	−	PROPN
ejpam-5997	374	3	(	(	PUNCT
ejpam-5997	374	4	ξ	ξ	X
ejpam-5997	374	5	′	′	NOUN
ejpam-5997	375	1	+	+	CCONJ
ejpam-5997	375	2	µn+	µn+	ADJ
ejpam-5997	375	3	1)(ξ	1)(ξ	NUM
ejpam-5997	375	4	′	′	NUM
ejpam-5997	375	5	+	+	CCONJ
ejpam-5997	375	6	µn	µn	X
ejpam-5997	375	7	)	)	PUNCT
ejpam-5997	375	8	2(α−	2(α−	NUM
ejpam-5997	375	9	ω)ξ	ω)ξ	NUM
ejpam-5997	375	10	′	′	NUM
ejpam-5997	376	1	+	+	PUNCT
ejpam-5997	376	2	µn	µn	X
ejpam-5997	376	3	]	]	PUNCT
ejpam-5997	376	4	×	×	NOUN
ejpam-5997	376	5	[	[	X
ejpam-5997	376	6	(	(	PUNCT
ejpam-5997	376	7	eµ,ρ	eµ,ρ	X
ejpam-5997	376	8	,	,	PUNCT
ejpam-5997	376	9	m	m	PROPN
ejpam-5997	376	10	,	,	PUNCT
ejpam-5997	376	11	η	η	PROPN
ejpam-5997	376	12	,	,	PUNCT
ejpam-5997	376	13	c	c	PROPN
ejpam-5997	376	14	ξ	ξ	PROPN
ejpam-5997	376	15	,	,	PUNCT
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ejpam-5997	376	17	,	,	PUNCT
ejpam-5997	376	18	ς	ς	PROPN
ejpam-5997	376	19	,	,	PUNCT
ejpam-5997	376	20	κ1,ω+ϕ	κ1,ω+ϕ	PROPN
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ejpam-5997	376	22	(	(	PUNCT
ejpam-5997	376	23	α	α	X
ejpam-5997	376	24	,	,	PUNCT
ejpam-5997	376	25	κ	κ	NOUN
ejpam-5997	376	26	)	)	PUNCT
ejpam-5997	376	27	+	+	CCONJ
ejpam-5997	376	28	(	(	PUNCT
ejpam-5997	376	29	eµ,ρ	eµ,ρ	X
ejpam-5997	376	30	,	,	PUNCT
ejpam-5997	376	31	m	m	PROPN
ejpam-5997	376	32	,	,	PUNCT
ejpam-5997	376	33	η	η	PROPN
ejpam-5997	376	34	,	,	PUNCT
ejpam-5997	376	35	c	c	PROPN
ejpam-5997	376	36	ξ	ξ	PROPN
ejpam-5997	376	37	,	,	PUNCT
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ejpam-5997	376	44	(	(	PUNCT
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ejpam-5997	376	47	κ	κ	NOUN
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ejpam-5997	376	53	α−	α−	ADP
ejpam-5997	376	54	ω)2	ω)2	NOUN
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ejpam-5997	376	57	1	1	NUM
ejpam-5997	376	58	0	0	NUM
ejpam-5997	376	59	℘(1−	℘(1−	PROPN
ejpam-5997	376	60	℘ξ	℘ξ	NOUN
ejpam-5997	376	61	′	′	NUM
ejpam-5997	376	62	)	)	PUNCT
ejpam-5997	376	63	eµ,ρ	eµ,ρ	X
ejpam-5997	376	64	,	,	PUNCT
ejpam-5997	376	65	m	m	PROPN
ejpam-5997	376	66	,	,	PUNCT
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ejpam-5997	376	68	,	,	PUNCT
ejpam-5997	376	69	cξ	cξ	NOUN
ejpam-5997	376	70	,	,	PUNCT
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ejpam-5997	376	72	,	,	PUNCT
ejpam-5997	376	73	ς	ς	PROPN
ejpam-5997	376	74	,	,	PUNCT
ejpam-5997	376	75	κ1	κ1	NOUN
ejpam-5997	376	76	(	(	PUNCT
ejpam-5997	376	77	κ℘µ	κ℘µ	PROPN
ejpam-5997	376	78	;	;	PUNCT
ejpam-5997	376	79	p	p	X
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ejpam-5997	376	81	∣∣[ϕ′′	∣∣[ϕ′′	NOUN
ejpam-5997	376	82	(	(	PUNCT
ejpam-5997	376	83	℘ω	℘ω	NOUN
ejpam-5997	376	84	+	+	CCONJ
ejpam-5997	376	85	(	(	PUNCT
ejpam-5997	376	86	1−	1−	NUM
ejpam-5997	376	87	℘)α+	℘)α+	PROPN
ejpam-5997	376	88	ϕ	ϕ	PROPN
ejpam-5997	376	89	′′	′′	PROPN
ejpam-5997	376	90	(	(	PUNCT
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ejpam-5997	376	92	1−	1−	NUM
ejpam-5997	376	93	℘)ω	℘)ω	NOUN
ejpam-5997	376	94	+	+	CCONJ
ejpam-5997	376	95	℘α	℘α	NOUN
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ejpam-5997	376	98	∣∣d℘	∣∣d℘	PROPN
ejpam-5997	376	99	ℵ	ℵ	X
ejpam-5997	376	100	≤	≤	NUM
ejpam-5997	377	1	∞∑	∞∑	NUM
ejpam-5997	377	2	n=0	n=0	NUM
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ejpam-5997	377	4	βp(ζ	βp(ζ	NUM
ejpam-5997	377	5	+	+	CCONJ
ejpam-5997	377	6	ρn	ρn	INTJ
ejpam-5997	377	7	,	,	PUNCT
ejpam-5997	377	8	c−	c−	NOUN
ejpam-5997	377	9	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	377	10	β(ζ	β(ζ	PROPN
ejpam-5997	377	11	,	,	PUNCT
ejpam-5997	377	12	c−	c−	X
ejpam-5997	377	13	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	377	14	ξ	ξ	X
ejpam-5997	378	1	+	+	NUM
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ejpam-5997	378	3	(	(	PUNCT
ejpam-5997	378	4	−κ)n	−κ)n	VERB
ejpam-5997	378	5	∣∣∣∣(α−	∣∣∣∣(α−	PROPN
ejpam-5997	378	6	ω)2	ω)2	PROPN
ejpam-5997	378	7	2	2	NUM
ejpam-5997	378	8	×	×	NOUN
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ejpam-5997	380	33	)	)	PUNCT
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ejpam-5997	380	35	(	(	PUNCT
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ejpam-5997	380	48	-	-	ADJ
ejpam-5997	380	49	convex	convex	ADJ
ejpam-5997	380	50	function	function	NOUN
ejpam-5997	380	51	;	;	PUNCT
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ejpam-5997	381	5	+	+	CCONJ
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ejpam-5997	381	11	,	,	PUNCT
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ejpam-5997	382	13	et	et	PROPN
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ejpam-5997	382	15	.	.	PUNCT
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ejpam-5997	383	29	ω)|+	ω)|+	NOUN
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ejpam-5997	384	3	(	(	PUNCT
ejpam-5997	384	4	ω)|+	ω)|+	NOUN
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ejpam-5997	384	7	α)|	α)|	VERB
ejpam-5997	384	8	]	]	X
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ejpam-5997	390	5	ω)|	ω)|	ADJ
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ejpam-5997	391	5	α)|	α)|	VERB
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ejpam-5997	393	11	ω)|β(µn+	ω)|β(µn+	PROPN
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ejpam-5997	397	4	α)|β(µn+	α)|β(µn+	ADV
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ejpam-5997	398	9	,	,	PUNCT
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ejpam-5997	398	12	β(ζ	β(ζ	PROPN
ejpam-5997	398	13	,	,	PUNCT
ejpam-5997	398	14	c−	c−	X
ejpam-5997	398	15	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	398	16	ξ	ξ	X
ejpam-5997	399	1	+	+	NUM
ejpam-5997	399	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	399	3	(	(	PUNCT
ejpam-5997	399	4	−κ)n	−κ)n	VERB
ejpam-5997	399	5	∣∣∣∣(α−	∣∣∣∣(α−	PROPN
ejpam-5997	399	6	ω)2	ω)2	X
ejpam-5997	399	7	2	2	NUM
ejpam-5997	399	8	[	[	X
ejpam-5997	399	9	(	(	PUNCT
ejpam-5997	399	10	|ϕ′′	|ϕ′′	PUNCT
ejpam-5997	399	11	(	(	PUNCT
ejpam-5997	399	12	ω	ω	NOUN
ejpam-5997	399	13	)	)	PUNCT
ejpam-5997	400	1	+	+	CCONJ
ejpam-5997	400	2	|ϕ′′	|ϕ′′	PRON
ejpam-5997	400	3	(	(	PUNCT
ejpam-5997	400	4	α)|	α)|	VERB
ejpam-5997	400	5	)	)	PUNCT
ejpam-5997	400	6	[	[	PUNCT
ejpam-5997	400	7	β(µn+	β(µn+	ADP
ejpam-5997	400	8	2	2	NUM
ejpam-5997	400	9	+	+	SYM
ejpam-5997	400	10	s	s	X
ejpam-5997	400	11	,	,	PUNCT
ejpam-5997	400	12	ξ	ξ	NOUN
ejpam-5997	400	13	′	′	NUM
ejpam-5997	401	1	+	+	CCONJ
ejpam-5997	401	2	1	1	X
ejpam-5997	401	3	)	)	PUNCT
ejpam-5997	401	4	+	+	NOUN
ejpam-5997	401	5	β(µn+	β(µn+	PROPN
ejpam-5997	401	6	2	2	NUM
ejpam-5997	401	7	,	,	PUNCT
ejpam-5997	401	8	ξ	ξ	NOUN
ejpam-5997	401	9	′	′	NUM
ejpam-5997	402	1	+	+	CCONJ
ejpam-5997	402	2	s+	s+	NUM
ejpam-5997	402	3	1	1	NUM
ejpam-5997	402	4	)	)	PUNCT
ejpam-5997	403	1	]	]	PUNCT
ejpam-5997	403	2	]	]	X
ejpam-5997	403	3	corollary	corollary	ADJ
ejpam-5997	403	4	7	7	X
ejpam-5997	403	5	.	.	PUNCT
ejpam-5997	404	1	if	if	SCONJ
ejpam-5997	404	2	we	we	PRON
ejpam-5997	404	3	replace	replace	VERB
ejpam-5997	404	4	p	p	NOUN
ejpam-5997	404	5	=	=	NOUN
ejpam-5997	404	6	0	0	NUM
ejpam-5997	404	7	,	,	PUNCT
ejpam-5997	404	8	κ	κ	X
ejpam-5997	404	9	=	=	SYM
ejpam-5997	404	10	0	0	NUM
ejpam-5997	404	11	,	,	PUNCT
ejpam-5997	404	12	and	and	CCONJ
ejpam-5997	404	13	ξ	ξ	X
ejpam-5997	404	14	=	=	SYM
ejpam-5997	404	15	ξ	ξ	PROPN
ejpam-5997	404	16	−	−	PROPN
ejpam-5997	404	17	1	1	NUM
ejpam-5997	404	18	in	in	ADP
ejpam-5997	404	19	theorem	theorem	NOUN
ejpam-5997	404	20	(	(	PUNCT
ejpam-5997	404	21	5	5	NUM
ejpam-5997	404	22	)	)	PUNCT
ejpam-5997	404	23	,	,	PUNCT
ejpam-5997	404	24	we	we	PRON
ejpam-5997	404	25	have	have	VERB
ejpam-5997	404	26	a	a	DET
ejpam-5997	404	27	result	result	NOUN
ejpam-5997	404	28	[	[	X
ejpam-5997	404	29	19	19	NUM
ejpam-5997	404	30	]	]	PUNCT
ejpam-5997	404	31	.	.	PUNCT
ejpam-5997	405	1	theorem	theorem	ADJ
ejpam-5997	405	2	6	6	NUM
ejpam-5997	405	3	.	.	PUNCT
ejpam-5997	406	1	let	let	VERB
ejpam-5997	406	2	ϕ	ϕ	NOUN
ejpam-5997	406	3	:	:	PUNCT
ejpam-5997	406	4	i	i	PRON
ejpam-5997	406	5	⊆	⊆	NUM
ejpam-5997	406	6	r	r	NOUN
ejpam-5997	406	7	→	→	SYM
ejpam-5997	406	8	r	r	NOUN
ejpam-5997	406	9	be	be	VERB
ejpam-5997	406	10	twice	twice	ADV
ejpam-5997	406	11	differentiable	differentiable	ADJ
ejpam-5997	406	12	mapping	mapping	NOUN
ejpam-5997	406	13	on	on	ADP
ejpam-5997	406	14	io	io	PROPN
ejpam-5997	406	15	and	and	CCONJ
ejpam-5997	406	16	ω	ω	PROPN
ejpam-5997	406	17	,	,	PUNCT
ejpam-5997	406	18	τ	τ	PROPN
ejpam-5997	406	19	∈	∈	PROPN
ejpam-5997	406	20	io	io	X
ejpam-5997	406	21	with	with	ADP
ejpam-5997	406	22	ω	ω	PROPN
ejpam-5997	406	23	<	<	X
ejpam-5997	406	24	α	α	X
ejpam-5997	406	25	<	<	X
ejpam-5997	406	26	τ	τ	PROPN
ejpam-5997	406	27	such	such	ADJ
ejpam-5997	406	28	that	that	SCONJ
ejpam-5997	406	29	ϕ	ϕ	NOUN
ejpam-5997	406	30	′′	′′	PROPN
ejpam-5997	406	31	∈	∈	PROPN
ejpam-5997	406	32	l[ω	l[ω	PROPN
ejpam-5997	406	33	,	,	PUNCT
ejpam-5997	406	34	τ	τ	X
ejpam-5997	406	35	]	]	PUNCT
ejpam-5997	406	36	.	.	PUNCT
ejpam-5997	407	1	if	if	SCONJ
ejpam-5997	407	2	|ϕ′′	|ϕ′′	PRON
ejpam-5997	407	3	|q(q	|q(q	PROPN
ejpam-5997	407	4	>	>	SYM
ejpam-5997	407	5	1	1	NUM
ejpam-5997	407	6	)	)	PUNCT
ejpam-5997	407	7	is	be	AUX
ejpam-5997	407	8	s	s	NOUN
ejpam-5997	407	9	-	-	ADJ
ejpam-5997	407	10	convex	convex	ADJ
ejpam-5997	407	11	function	function	NOUN
ejpam-5997	407	12	on	on	ADP
ejpam-5997	407	13	i	i	PROPN
ejpam-5997	407	14	,	,	PUNCT
ejpam-5997	407	15	and	and	CCONJ
ejpam-5997	407	16	µ	µ	NOUN
ejpam-5997	407	17	,	,	PUNCT
ejpam-5997	407	18	ξ	ξ	PROPN
ejpam-5997	407	19	,	,	PUNCT
ejpam-5997	407	20	ζ	ζ	NOUN
ejpam-5997	407	21	,	,	PUNCT
ejpam-5997	407	22	ς	ς	PROPN
ejpam-5997	407	23	,	,	PUNCT
ejpam-5997	407	24	c	c	X
ejpam-5997	407	25	,	,	PUNCT
ejpam-5997	407	26	κ1	κ1	PROPN
ejpam-5997	407	27	∈	∈	PROPN
ejpam-5997	407	28	c,ℜ(µ	c,ℜ(µ	PROPN
ejpam-5997	407	29	)	)	PUNCT
ejpam-5997	407	30	>	>	X
ejpam-5997	407	31	0,ℜ(ξ	0,ℜ(ξ	PROPN
ejpam-5997	407	32	)	)	PUNCT
ejpam-5997	407	33	>	>	X
ejpam-5997	407	34	0,ℜ(ζ	0,ℜ(ζ	PROPN
ejpam-5997	407	35	)	)	PUNCT
ejpam-5997	407	36	>	>	X
ejpam-5997	407	37	0,ℜ(ς	0,ℜ(ς	PROPN
ejpam-5997	407	38	)	)	PUNCT
ejpam-5997	407	39	>	>	X
ejpam-5997	408	1	0,ℜ(κ1	0,ℜ(κ1	PROPN
ejpam-5997	408	2	)	)	PUNCT
ejpam-5997	408	3	>	>	X
ejpam-5997	408	4	0	0	NUM
ejpam-5997	408	5	,	,	PUNCT
ejpam-5997	408	6	ρ	ρ	PROPN
ejpam-5997	408	7	,	,	PUNCT
ejpam-5997	408	8	m	m	PROPN
ejpam-5997	408	9	,	,	PUNCT
ejpam-5997	408	10	η	η	PROPN
ejpam-5997	408	11	≥	≥	X
ejpam-5997	408	12	0	0	NUM
ejpam-5997	408	13	and	and	CCONJ
ejpam-5997	408	14	m	m	PROPN
ejpam-5997	408	15	,	,	PUNCT
ejpam-5997	408	16	ρ	ρ	PROPN
ejpam-5997	408	17	>	>	X
ejpam-5997	408	18	ℜ(µ	ℜ(µ	NOUN
ejpam-5997	408	19	)	)	PUNCT
ejpam-5997	408	20	+	+	CCONJ
ejpam-5997	408	21	η	η	PROPN
ejpam-5997	408	22	,	,	PUNCT
ejpam-5997	408	23	then	then	ADV
ejpam-5997	408	24	we	we	PRON
ejpam-5997	408	25	have	have	VERB
ejpam-5997	408	26	the	the	DET
ejpam-5997	408	27	following	follow	VERB
ejpam-5997	408	28	fractional	fractional	ADJ
ejpam-5997	408	29	inequality	inequality	NOUN
ejpam-5997	408	30	∣∣∣∣(ξ′)jµ,ρ	∣∣∣∣(ξ′)jµ,ρ	NOUN
ejpam-5997	408	31	,	,	PUNCT
ejpam-5997	408	32	m	m	PROPN
ejpam-5997	408	33	,	,	PUNCT
ejpam-5997	408	34	η	η	PROPN
ejpam-5997	408	35	,	,	PUNCT
ejpam-5997	408	36	cξ	cξ	NOUN
ejpam-5997	408	37	,	,	PUNCT
ejpam-5997	408	38	ζ	ζ	NOUN
ejpam-5997	408	39	,	,	PUNCT
ejpam-5997	408	40	ς	ς	PROPN
ejpam-5997	408	41	,	,	PUNCT
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ejpam-5997	408	43	(	(	PUNCT
ejpam-5997	408	44	κ	κ	NOUN
ejpam-5997	408	45	,	,	PUNCT
ejpam-5997	408	46	p	p	NOUN
ejpam-5997	408	47	)	)	PUNCT
ejpam-5997	409	1	[	[	X
ejpam-5997	409	2	ϕ(α	ϕ(α	NUM
ejpam-5997	409	3	)	)	PUNCT
ejpam-5997	409	4	+	+	SYM
ejpam-5997	409	5	ϕ(ω	ϕ(ω	NOUN
ejpam-5997	409	6	)	)	PUNCT
ejpam-5997	409	7	2	2	NUM
ejpam-5997	409	8	]	]	PUNCT
ejpam-5997	410	1	+	+	CCONJ
ejpam-5997	410	2	[	[	PUNCT
ejpam-5997	410	3	(	(	PUNCT
ejpam-5997	410	4	µn+	µn+	ADJ
ejpam-5997	410	5	1)(µn	1)(µn	NUM
ejpam-5997	410	6	)	)	PUNCT
ejpam-5997	410	7	2(α−	2(α−	NUM
ejpam-5997	411	1	ω)µn	ω)µn	PROPN
ejpam-5997	411	2	−	−	PROPN
ejpam-5997	411	3	(	(	PUNCT
ejpam-5997	411	4	ξ	ξ	X
ejpam-5997	411	5	′	′	NOUN
ejpam-5997	412	1	+	+	CCONJ
ejpam-5997	412	2	µn+	µn+	ADJ
ejpam-5997	412	3	1)(ξ	1)(ξ	NUM
ejpam-5997	412	4	′	′	NUM
ejpam-5997	412	5	+	+	CCONJ
ejpam-5997	412	6	µn	µn	X
ejpam-5997	412	7	)	)	PUNCT
ejpam-5997	412	8	2(α−	2(α−	NUM
ejpam-5997	412	9	ω)ξ	ω)ξ	NOUN
ejpam-5997	412	10	′+µn	′+µn	PROPN
ejpam-5997	412	11	]	]	PUNCT
ejpam-5997	412	12	×	×	PROPN
ejpam-5997	412	13	[	[	X
ejpam-5997	412	14	(	(	PUNCT
ejpam-5997	412	15	eµ,ρ	eµ,ρ	X
ejpam-5997	412	16	,	,	PUNCT
ejpam-5997	412	17	m	m	PROPN
ejpam-5997	412	18	,	,	PUNCT
ejpam-5997	412	19	η	η	PROPN
ejpam-5997	412	20	,	,	PUNCT
ejpam-5997	412	21	c	c	PROPN
ejpam-5997	412	22	ξ	ξ	PROPN
ejpam-5997	412	23	,	,	PUNCT
ejpam-5997	412	24	ζ	ζ	NOUN
ejpam-5997	412	25	,	,	PUNCT
ejpam-5997	412	26	ς	ς	PROPN
ejpam-5997	412	27	,	,	PUNCT
ejpam-5997	412	28	κ1,ω+ϕ	κ1,ω+ϕ	PROPN
ejpam-5997	412	29	)	)	PUNCT
ejpam-5997	412	30	(	(	PUNCT
ejpam-5997	412	31	α	α	X
ejpam-5997	412	32	,	,	PUNCT
ejpam-5997	412	33	κ	κ	NOUN
ejpam-5997	412	34	)	)	PUNCT
ejpam-5997	412	35	+	+	CCONJ
ejpam-5997	412	36	(	(	PUNCT
ejpam-5997	412	37	eµ,ρ	eµ,ρ	X
ejpam-5997	412	38	,	,	PUNCT
ejpam-5997	412	39	m	m	PROPN
ejpam-5997	412	40	,	,	PUNCT
ejpam-5997	412	41	η	η	PROPN
ejpam-5997	412	42	,	,	PUNCT
ejpam-5997	412	43	c	c	PROPN
ejpam-5997	412	44	ξ	ξ	PROPN
ejpam-5997	412	45	,	,	PUNCT
ejpam-5997	412	46	ζ	ζ	NOUN
ejpam-5997	412	47	,	,	PUNCT
ejpam-5997	412	48	ς	ς	PROPN
ejpam-5997	412	49	,	,	PUNCT
ejpam-5997	412	50	κ1,α−ϕ	κ1,α−ϕ	NOUN
ejpam-5997	412	51	)	)	PUNCT
ejpam-5997	412	52	(	(	PUNCT
ejpam-5997	412	53	ω	ω	NOUN
ejpam-5997	412	54	,	,	PUNCT
ejpam-5997	412	55	κ	κ	NOUN
ejpam-5997	412	56	)	)	PUNCT
ejpam-5997	412	57	]	]	PUNCT
ejpam-5997	412	58	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	412	59	≤	≤	NOUN
ejpam-5997	412	60	∞∑	∞∑	NUM
ejpam-5997	412	61	n=0	n=0	NUM
ejpam-5997	412	62	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	412	63	βp(ζ	βp(ζ	NUM
ejpam-5997	412	64	+	+	CCONJ
ejpam-5997	412	65	ρn	ρn	INTJ
ejpam-5997	412	66	,	,	PUNCT
ejpam-5997	412	67	c−	c−	NOUN
ejpam-5997	412	68	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	412	69	β(ζ	β(ζ	PROPN
ejpam-5997	412	70	,	,	PUNCT
ejpam-5997	412	71	c−	c−	X
ejpam-5997	412	72	ζ)γ(µn+	ζ)γ(µn+	NOUN
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ejpam-5997	413	2	1)(ς)mn	1)(ς)mn	NUM
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ejpam-5997	413	4	−κ)n	−κ)n	VERB
ejpam-5997	413	5	∣∣∣∣(α−	∣∣∣∣(α−	PROPN
ejpam-5997	413	6	ω)2	ω)2	VERB
ejpam-5997	413	7	×	×	NOUN
ejpam-5997	414	1	[	[	X
ejpam-5997	414	2	(	(	PUNCT
ejpam-5997	414	3	β(µnp+	β(µnp+	ADJ
ejpam-5997	414	4	p+	p+	NOUN
ejpam-5997	414	5	1	1	NUM
ejpam-5997	414	6	,	,	PUNCT
ejpam-5997	414	7	ξ	ξ	PROPN
ejpam-5997	414	8	′	′	NOUN
ejpam-5997	414	9	p+	p+	NOUN
ejpam-5997	414	10	1	1	NUM
ejpam-5997	414	11	)	)	PUNCT
ejpam-5997	414	12	)	)	PUNCT
ejpam-5997	414	13	1	1	NUM
ejpam-5997	414	14	p	p	NOUN
ejpam-5997	414	15	(	(	PUNCT
ejpam-5997	414	16	|ϕ′′	|ϕ′′	X
ejpam-5997	414	17	(	(	PUNCT
ejpam-5997	414	18	ω)|q	ω)|q	VERB
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ejpam-5997	414	24	1	1	X
ejpam-5997	414	25	)	)	PUNCT
ejpam-5997	414	26	1	1	NUM
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ejpam-5997	414	28	]	]	PUNCT
ejpam-5997	414	29	.	.	PUNCT
ejpam-5997	415	1	(	(	PUNCT
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ejpam-5997	415	3	)	)	PUNCT
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ejpam-5997	415	5	vivas	vivas	PROPN
ejpam-5997	415	6	-	-	PROPN
ejpam-5997	415	7	cortez	cortez	PROPN
ejpam-5997	415	8	et	et	PROPN
ejpam-5997	415	9	al	al	PROPN
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ejpam-5997	415	11	/	/	SYM
ejpam-5997	415	12	eur	eur	PROPN
ejpam-5997	415	13	.	.	PUNCT
ejpam-5997	416	1	j.	j.	PROPN
ejpam-5997	416	2	pure	pure	PROPN
ejpam-5997	416	3	appl	appl	PROPN
ejpam-5997	416	4	.	.	PROPN
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ejpam-5997	416	7	18	18	NUM
ejpam-5997	416	8	(	(	PUNCT
ejpam-5997	416	9	2	2	NUM
ejpam-5997	416	10	)	)	PUNCT
ejpam-5997	416	11	(	(	PUNCT
ejpam-5997	416	12	2025	2025	NUM
ejpam-5997	416	13	)	)	PUNCT
ejpam-5997	416	14	,	,	PUNCT
ejpam-5997	416	15	5997	5997	NUM
ejpam-5997	416	16	16	16	NUM
ejpam-5997	416	17	of	of	ADP
ejpam-5997	416	18	23	23	NUM
ejpam-5997	416	19	proof	proof	NOUN
ejpam-5997	416	20	.	.	PUNCT
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ejpam-5997	417	2	using	use	VERB
ejpam-5997	417	3	lemma	lemma	PROPN
ejpam-5997	417	4	2	2	NUM
ejpam-5997	417	5	ℶ	ℶ	PROPN
ejpam-5997	417	6	=	=	SYM
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ejpam-5997	417	8	,	,	PUNCT
ejpam-5997	417	9	m	m	PROPN
ejpam-5997	417	10	,	,	PUNCT
ejpam-5997	417	11	η	η	PROPN
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ejpam-5997	417	14	,	,	PUNCT
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ejpam-5997	417	16	,	,	PUNCT
ejpam-5997	417	17	ς	ς	PROPN
ejpam-5997	417	18	,	,	PUNCT
ejpam-5997	417	19	κ1	κ1	NOUN
ejpam-5997	417	20	(	(	PUNCT
ejpam-5997	417	21	κ	κ	NOUN
ejpam-5997	417	22	,	,	PUNCT
ejpam-5997	417	23	p	p	NOUN
ejpam-5997	417	24	)	)	PUNCT
ejpam-5997	417	25	[	[	X
ejpam-5997	417	26	ϕ(α	ϕ(α	NUM
ejpam-5997	417	27	)	)	PUNCT
ejpam-5997	417	28	+	+	SYM
ejpam-5997	417	29	ϕ(ω	ϕ(ω	NOUN
ejpam-5997	417	30	)	)	PUNCT
ejpam-5997	417	31	2	2	NUM
ejpam-5997	417	32	]	]	PUNCT
ejpam-5997	418	1	+	+	CCONJ
ejpam-5997	418	2	[	[	PUNCT
ejpam-5997	418	3	(	(	PUNCT
ejpam-5997	418	4	µn+	µn+	ADJ
ejpam-5997	418	5	1)(µn	1)(µn	NUM
ejpam-5997	418	6	)	)	PUNCT
ejpam-5997	418	7	2(α−	2(α−	NUM
ejpam-5997	419	1	ω)µn	ω)µn	PROPN
ejpam-5997	419	2	−	−	PROPN
ejpam-5997	419	3	(	(	PUNCT
ejpam-5997	419	4	ξ	ξ	X
ejpam-5997	419	5	′	′	NOUN
ejpam-5997	420	1	+	+	CCONJ
ejpam-5997	420	2	µn+	µn+	ADJ
ejpam-5997	420	3	1)(ξ	1)(ξ	NUM
ejpam-5997	420	4	′	′	NUM
ejpam-5997	420	5	+	+	CCONJ
ejpam-5997	420	6	µn	µn	X
ejpam-5997	420	7	)	)	PUNCT
ejpam-5997	420	8	2(α−	2(α−	NUM
ejpam-5997	420	9	ω)ξ	ω)ξ	NOUN
ejpam-5997	420	10	′+µn	′+µn	PROPN
ejpam-5997	420	11	]	]	PUNCT
ejpam-5997	420	12	×	×	PROPN
ejpam-5997	420	13	[	[	X
ejpam-5997	420	14	(	(	PUNCT
ejpam-5997	420	15	eµ,ρ	eµ,ρ	X
ejpam-5997	420	16	,	,	PUNCT
ejpam-5997	420	17	m	m	PROPN
ejpam-5997	420	18	,	,	PUNCT
ejpam-5997	420	19	η	η	PROPN
ejpam-5997	420	20	,	,	PUNCT
ejpam-5997	420	21	c	c	PROPN
ejpam-5997	420	22	ξ	ξ	PROPN
ejpam-5997	420	23	,	,	PUNCT
ejpam-5997	420	24	ζ	ζ	NOUN
ejpam-5997	420	25	,	,	PUNCT
ejpam-5997	420	26	ς	ς	PROPN
ejpam-5997	420	27	,	,	PUNCT
ejpam-5997	420	28	κ1,ω+ϕ	κ1,ω+ϕ	PROPN
ejpam-5997	420	29	)	)	PUNCT
ejpam-5997	420	30	(	(	PUNCT
ejpam-5997	420	31	α	α	X
ejpam-5997	420	32	,	,	PUNCT
ejpam-5997	420	33	κ	κ	NOUN
ejpam-5997	420	34	)	)	PUNCT
ejpam-5997	420	35	+	+	CCONJ
ejpam-5997	420	36	(	(	PUNCT
ejpam-5997	420	37	eµ,ρ	eµ,ρ	X
ejpam-5997	420	38	,	,	PUNCT
ejpam-5997	420	39	m	m	PROPN
ejpam-5997	420	40	,	,	PUNCT
ejpam-5997	420	41	η	η	PROPN
ejpam-5997	420	42	,	,	PUNCT
ejpam-5997	420	43	c	c	PROPN
ejpam-5997	420	44	ξ	ξ	PROPN
ejpam-5997	420	45	,	,	PUNCT
ejpam-5997	420	46	ζ	ζ	NOUN
ejpam-5997	420	47	,	,	PUNCT
ejpam-5997	420	48	ς	ς	PROPN
ejpam-5997	420	49	,	,	PUNCT
ejpam-5997	420	50	κ1,α−ϕ	κ1,α−ϕ	NOUN
ejpam-5997	420	51	)	)	PUNCT
ejpam-5997	420	52	(	(	PUNCT
ejpam-5997	420	53	ω	ω	NOUN
ejpam-5997	420	54	,	,	PUNCT
ejpam-5997	420	55	κ	κ	NOUN
ejpam-5997	420	56	)	)	PUNCT
ejpam-5997	420	57	]	]	PUNCT
ejpam-5997	420	58	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	420	59	≤	≤	NOUN
ejpam-5997	420	60	(	(	PUNCT
ejpam-5997	420	61	α−	α−	ADP
ejpam-5997	420	62	ω)2	ω)2	NOUN
ejpam-5997	420	63	2	2	NUM
ejpam-5997	420	64	∫	∫	NOUN
ejpam-5997	420	65	1	1	NUM
ejpam-5997	420	66	0	0	NUM
ejpam-5997	420	67	℘(1−	℘(1−	PROPN
ejpam-5997	420	68	℘ξ	℘ξ	NOUN
ejpam-5997	420	69	′	′	NUM
ejpam-5997	420	70	)	)	PUNCT
ejpam-5997	420	71	eµ,ρ	eµ,ρ	X
ejpam-5997	420	72	,	,	PUNCT
ejpam-5997	420	73	m	m	PROPN
ejpam-5997	420	74	,	,	PUNCT
ejpam-5997	420	75	η	η	PROPN
ejpam-5997	420	76	,	,	PUNCT
ejpam-5997	420	77	cξ	cξ	NOUN
ejpam-5997	420	78	,	,	PUNCT
ejpam-5997	420	79	ζ	ζ	NOUN
ejpam-5997	420	80	,	,	PUNCT
ejpam-5997	420	81	ς	ς	PROPN
ejpam-5997	420	82	,	,	PUNCT
ejpam-5997	420	83	κ1	κ1	NOUN
ejpam-5997	420	84	(	(	PUNCT
ejpam-5997	420	85	κ℘µ	κ℘µ	PROPN
ejpam-5997	420	86	;	;	PUNCT
ejpam-5997	420	87	p	p	X
ejpam-5997	420	88	)	)	PUNCT
ejpam-5997	420	89	∣∣[ϕ′′	∣∣[ϕ′′	NOUN
ejpam-5997	420	90	(	(	PUNCT
ejpam-5997	420	91	℘ω	℘ω	NOUN
ejpam-5997	420	92	+	+	CCONJ
ejpam-5997	420	93	(	(	PUNCT
ejpam-5997	420	94	1−	1−	NUM
ejpam-5997	420	95	℘)α+	℘)α+	PROPN
ejpam-5997	420	96	ϕ	ϕ	PROPN
ejpam-5997	420	97	′′	′′	PROPN
ejpam-5997	420	98	(	(	PUNCT
ejpam-5997	420	99	(	(	PUNCT
ejpam-5997	420	100	1−	1−	NUM
ejpam-5997	420	101	℘)ω	℘)ω	NOUN
ejpam-5997	420	102	+	+	CCONJ
ejpam-5997	420	103	℘α	℘α	NOUN
ejpam-5997	420	104	)	)	PUNCT
ejpam-5997	420	105	]	]	PUNCT
ejpam-5997	420	106	∣∣d℘	∣∣d℘	VERB
ejpam-5997	420	107	ℶ	ℶ	PROPN
ejpam-5997	420	108	≤	≤	NOUN
ejpam-5997	421	1	∞∑	∞∑	NUM
ejpam-5997	421	2	n=0	n=0	NUM
ejpam-5997	421	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	421	4	βp(ζ	βp(ζ	NUM
ejpam-5997	421	5	+	+	CCONJ
ejpam-5997	421	6	ρn	ρn	INTJ
ejpam-5997	421	7	,	,	PUNCT
ejpam-5997	421	8	c−	c−	NOUN
ejpam-5997	421	9	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	421	10	β(ζ	β(ζ	PROPN
ejpam-5997	421	11	,	,	PUNCT
ejpam-5997	421	12	c−	c−	X
ejpam-5997	421	13	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	421	14	ξ	ξ	X
ejpam-5997	422	1	+	+	NUM
ejpam-5997	422	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	422	3	(	(	PUNCT
ejpam-5997	422	4	−κ)n	−κ)n	VERB
ejpam-5997	422	5	∣∣∣∣(α−	∣∣∣∣(α−	PROPN
ejpam-5997	422	6	ω)2	ω)2	PROPN
ejpam-5997	422	7	2	2	NUM
ejpam-5997	422	8	×	×	NOUN
ejpam-5997	422	9	[	[	PUNCT
ejpam-5997	422	10	∫	∫	PROPN
ejpam-5997	422	11	1	1	NUM
ejpam-5997	422	12	0	0	X
ejpam-5997	422	13	℘µn+1(1−	℘µn+1(1−	ADJ
ejpam-5997	422	14	℘ξ	℘ξ	ADJ
ejpam-5997	422	15	′	′	NOUN
ejpam-5997	422	16	)	)	PUNCT
ejpam-5997	422	17	∣∣[ϕ′′	∣∣[ϕ′′	NOUN
ejpam-5997	422	18	(	(	PUNCT
ejpam-5997	422	19	℘ω	℘ω	NOUN
ejpam-5997	422	20	+	+	CCONJ
ejpam-5997	422	21	(	(	PUNCT
ejpam-5997	422	22	1−	1−	NUM
ejpam-5997	422	23	℘)α+	℘)α+	PROPN
ejpam-5997	422	24	ϕ	ϕ	PROPN
ejpam-5997	422	25	′′	′′	PROPN
ejpam-5997	422	26	(	(	PUNCT
ejpam-5997	422	27	(	(	PUNCT
ejpam-5997	422	28	1−	1−	NUM
ejpam-5997	422	29	℘)ω	℘)ω	NOUN
ejpam-5997	422	30	+	+	CCONJ
ejpam-5997	422	31	℘α	℘α	NOUN
ejpam-5997	422	32	)	)	PUNCT
ejpam-5997	422	33	]	]	PUNCT
ejpam-5997	422	34	∣∣]d℘	∣∣]d℘	X
ejpam-5997	422	35	ℶ	ℶ	X
ejpam-5997	422	36	≤	≤	NOUN
ejpam-5997	423	1	∞∑	∞∑	NUM
ejpam-5997	423	2	n=0	n=0	NUM
ejpam-5997	423	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	423	4	βp(ζ	βp(ζ	NUM
ejpam-5997	423	5	+	+	CCONJ
ejpam-5997	423	6	ρn	ρn	INTJ
ejpam-5997	423	7	,	,	PUNCT
ejpam-5997	423	8	c−	c−	NOUN
ejpam-5997	423	9	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	423	10	β(ζ	β(ζ	PROPN
ejpam-5997	423	11	,	,	PUNCT
ejpam-5997	423	12	c−	c−	X
ejpam-5997	423	13	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	423	14	ξ	ξ	X
ejpam-5997	424	1	+	+	NUM
ejpam-5997	424	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	424	3	(	(	PUNCT
ejpam-5997	424	4	−κ)n	−κ)n	VERB
ejpam-5997	424	5	∣∣∣∣(α−	∣∣∣∣(α−	PROPN
ejpam-5997	424	6	ω)2	ω)2	PROPN
ejpam-5997	424	7	2	2	NUM
ejpam-5997	424	8	×	×	NOUN
ejpam-5997	424	9	[	[	PUNCT
ejpam-5997	424	10	∫	∫	PROPN
ejpam-5997	424	11	1	1	NUM
ejpam-5997	424	12	0	0	X
ejpam-5997	424	13	℘µn+1(1−	℘µn+1(1−	ADJ
ejpam-5997	424	14	℘ξ	℘ξ	ADJ
ejpam-5997	424	15	′	′	NOUN
ejpam-5997	424	16	)	)	PUNCT
ejpam-5997	424	17	∣∣[ϕ′′	∣∣[ϕ′′	NOUN
ejpam-5997	424	18	(	(	PUNCT
ejpam-5997	424	19	℘ω	℘ω	NOUN
ejpam-5997	424	20	+	+	CCONJ
ejpam-5997	424	21	(	(	PUNCT
ejpam-5997	424	22	1−	1−	NUM
ejpam-5997	424	23	℘)α	℘)α	NOUN
ejpam-5997	424	24	)	)	PUNCT
ejpam-5997	424	25	]	]	PUNCT
ejpam-5997	424	26	∣∣d℘+	∣∣d℘+	X
ejpam-5997	424	27	∫	∫	PROPN
ejpam-5997	424	28	1	1	NUM
ejpam-5997	424	29	0	0	PUNCT
ejpam-5997	424	30	℘µn+1(1−	℘µn+1(1−	ADJ
ejpam-5997	424	31	℘ξ	℘ξ	ADJ
ejpam-5997	424	32	′	′	NOUN
ejpam-5997	424	33	)	)	PUNCT
ejpam-5997	424	34	∣∣[ϕ′′	∣∣[ϕ′′	NOUN
ejpam-5997	424	35	(	(	PUNCT
ejpam-5997	424	36	(	(	PUNCT
ejpam-5997	424	37	1−	1−	NUM
ejpam-5997	424	38	℘)ω	℘)ω	NOUN
ejpam-5997	424	39	+	+	CCONJ
ejpam-5997	424	40	℘α	℘α	NOUN
ejpam-5997	424	41	)	)	PUNCT
ejpam-5997	424	42	]	]	PUNCT
ejpam-5997	424	43	∣∣]d℘.	∣∣]d℘.	NOUN
ejpam-5997	424	44	using	use	VERB
ejpam-5997	424	45	holder	holder	NOUN
ejpam-5997	424	46	inequality	inequality	NOUN
ejpam-5997	424	47	,	,	PUNCT
ejpam-5997	424	48	ℶ	ℶ	NOUN
ejpam-5997	424	49	≤	≤	NOUN
ejpam-5997	425	1	∞∑	∞∑	NUM
ejpam-5997	425	2	n=0	n=0	NUM
ejpam-5997	425	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	425	4	βp(ζ	βp(ζ	NUM
ejpam-5997	425	5	+	+	CCONJ
ejpam-5997	425	6	ρn	ρn	INTJ
ejpam-5997	425	7	,	,	PUNCT
ejpam-5997	425	8	c−	c−	NOUN
ejpam-5997	425	9	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	425	10	β(ζ	β(ζ	PROPN
ejpam-5997	425	11	,	,	PUNCT
ejpam-5997	425	12	c−	c−	X
ejpam-5997	425	13	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	425	14	ξ	ξ	X
ejpam-5997	426	1	+	+	NUM
ejpam-5997	426	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	426	3	(	(	PUNCT
ejpam-5997	426	4	−κ)n	−κ)n	VERB
ejpam-5997	426	5	∣∣∣∣(α−	∣∣∣∣(α−	PROPN
ejpam-5997	426	6	ω)2	ω)2	VERB
ejpam-5997	426	7	2	2	NUM
ejpam-5997	426	8	×	×	NOUN
ejpam-5997	426	9	[	[	X
ejpam-5997	426	10	(	(	PUNCT
ejpam-5997	426	11	∫	∫	PROPN
ejpam-5997	426	12	1	1	NUM
ejpam-5997	426	13	0	0	NUM
ejpam-5997	426	14	℘µnp+p(1−	℘µnp+p(1−	NUM
ejpam-5997	426	15	℘ξ	℘ξ	ADJ
ejpam-5997	426	16	′	′	NUM
ejpam-5997	426	17	)	)	PUNCT
ejpam-5997	427	1	p	p	X
ejpam-5997	427	2	)	)	PUNCT
ejpam-5997	427	3	1	1	NUM
ejpam-5997	427	4	p	p	NOUN
ejpam-5997	427	5	(	(	PUNCT
ejpam-5997	427	6	∫	∫	PROPN
ejpam-5997	427	7	1	1	NUM
ejpam-5997	427	8	0	0	NUM
ejpam-5997	427	9	∣∣[ϕ′′	∣∣[ϕ′′	NOUN
ejpam-5997	427	10	(	(	PUNCT
ejpam-5997	427	11	℘ω	℘ω	NOUN
ejpam-5997	427	12	+	+	CCONJ
ejpam-5997	427	13	(	(	PUNCT
ejpam-5997	427	14	1−	1−	NUM
ejpam-5997	427	15	℘)α	℘)α	NOUN
ejpam-5997	427	16	)	)	PUNCT
ejpam-5997	427	17	]	]	X
ejpam-5997	427	18	∣∣q	∣∣q	NUM
ejpam-5997	427	19	)	)	PUNCT
ejpam-5997	427	20	1	1	NUM
ejpam-5997	427	21	q	q	NOUN
ejpam-5997	427	22	d℘+(∫	d℘+(∫	VERB
ejpam-5997	427	23	1	1	NUM
ejpam-5997	427	24	0	0	NUM
ejpam-5997	427	25	℘µnp+p(1−	℘µnp+p(1−	NUM
ejpam-5997	427	26	℘ξ	℘ξ	ADJ
ejpam-5997	427	27	′	′	NUM
ejpam-5997	427	28	)	)	PUNCT
ejpam-5997	428	1	p	p	X
ejpam-5997	428	2	)	)	PUNCT
ejpam-5997	428	3	1	1	NUM
ejpam-5997	428	4	p	p	NOUN
ejpam-5997	428	5	(	(	PUNCT
ejpam-5997	428	6	∫	∫	PROPN
ejpam-5997	428	7	1	1	NUM
ejpam-5997	428	8	0	0	NUM
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ejpam-5997	428	10	(	(	PUNCT
ejpam-5997	428	11	(	(	PUNCT
ejpam-5997	428	12	1−	1−	NUM
ejpam-5997	428	13	℘)ω	℘)ω	NOUN
ejpam-5997	428	14	+	+	CCONJ
ejpam-5997	428	15	℘α	℘α	NOUN
ejpam-5997	428	16	)	)	PUNCT
ejpam-5997	428	17	]	]	SYM
ejpam-5997	428	18	∣∣q	∣∣q	NUM
ejpam-5997	428	19	)	)	PUNCT
ejpam-5997	428	20	1	1	NUM
ejpam-5997	428	21	q	q	NOUN
ejpam-5997	428	22	d℘	d℘	NUM
ejpam-5997	428	23	]	]	PUNCT
ejpam-5997	428	24	d℘	d℘	PROPN
ejpam-5997	428	25	(	(	PUNCT
ejpam-5997	428	26	28	28	NUM
ejpam-5997	428	27	)	)	PUNCT
ejpam-5997	428	28	since	since	SCONJ
ejpam-5997	428	29	,	,	PUNCT
ejpam-5997	428	30	℘ξ	℘ξ	ADJ
ejpam-5997	428	31	′	′	NUM
ejpam-5997	428	32	≥	≥	NOUN
ejpam-5997	428	33	℘	℘	NOUN
ejpam-5997	428	34	,	,	PUNCT
ejpam-5997	428	35	ξ	ξ	PROPN
ejpam-5997	428	36	′	′	NUM
ejpam-5997	428	37	∈	∈	NOUN
ejpam-5997	428	38	(	(	PUNCT
ejpam-5997	428	39	0	0	NUM
ejpam-5997	428	40	,	,	PUNCT
ejpam-5997	428	41	1	1	NUM
ejpam-5997	428	42	]	]	PUNCT
ejpam-5997	428	43	and	and	CCONJ
ejpam-5997	428	44	℘	℘	PROPN
ejpam-5997	428	45	∈	∈	PROPN
ejpam-5997	429	1	[	[	X
ejpam-5997	429	2	0	0	NUM
ejpam-5997	429	3	,	,	PUNCT
ejpam-5997	429	4	1	1	NUM
ejpam-5997	429	5	]	]	PUNCT
ejpam-5997	429	6	,	,	PUNCT
ejpam-5997	429	7	we	we	PRON
ejpam-5997	429	8	have	have	VERB
ejpam-5997	429	9	−℘ξ	−℘ξ	NOUN
ejpam-5997	429	10	′	′	ADJ
ejpam-5997	429	11	≤	≤	ADJ
ejpam-5997	429	12	℘⇒	℘⇒	NOUN
ejpam-5997	429	13	1−	1−	NUM
ejpam-5997	429	14	℘ξ	℘ξ	ADJ
ejpam-5997	429	15	′	′	NUM
ejpam-5997	429	16	≤	≤	NOUN
ejpam-5997	429	17	1−	1−	NUM
ejpam-5997	429	18	℘	℘	PROPN
ejpam-5997	429	19	≤	≤	NUM
ejpam-5997	429	20	(	(	PUNCT
ejpam-5997	429	21	1−	1−	NUM
ejpam-5997	429	22	℘)ξ	℘)ξ	NOUN
ejpam-5997	430	1	′	′	NUM
ejpam-5997	430	2	ℶ	ℶ	NOUN
ejpam-5997	430	3	≤	≤	NOUN
ejpam-5997	431	1	∞∑	∞∑	NUM
ejpam-5997	431	2	n=0	n=0	NUM
ejpam-5997	431	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	431	4	βp(ζ	βp(ζ	NUM
ejpam-5997	431	5	+	+	CCONJ
ejpam-5997	431	6	ρn	ρn	INTJ
ejpam-5997	431	7	,	,	PUNCT
ejpam-5997	431	8	c−	c−	NOUN
ejpam-5997	431	9	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	431	10	β(ζ	β(ζ	PROPN
ejpam-5997	431	11	,	,	PUNCT
ejpam-5997	431	12	c−	c−	X
ejpam-5997	431	13	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	431	14	ξ	ξ	X
ejpam-5997	432	1	+	+	NUM
ejpam-5997	432	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	432	3	(	(	PUNCT
ejpam-5997	432	4	−κ)n	−κ)n	VERB
ejpam-5997	432	5	∣∣∣∣(α−	∣∣∣∣(α−	PROPN
ejpam-5997	432	6	ω)2	ω)2	VERB
ejpam-5997	432	7	2	2	NUM
ejpam-5997	432	8	×	×	NOUN
ejpam-5997	433	1	[	[	X
ejpam-5997	433	2	(	(	PUNCT
ejpam-5997	433	3	∫	∫	PROPN
ejpam-5997	433	4	1	1	NUM
ejpam-5997	433	5	0	0	NUM
ejpam-5997	433	6	℘µnp+p(1−	℘µnp+p(1−	NUM
ejpam-5997	433	7	℘)ξ	℘)ξ	NOUN
ejpam-5997	433	8	′	′	NOUN
ejpam-5997	433	9	p	p	NOUN
ejpam-5997	433	10	)	)	PUNCT
ejpam-5997	433	11	1	1	NUM
ejpam-5997	433	12	p	p	NOUN
ejpam-5997	433	13	{	{	PUNCT
ejpam-5997	433	14	(	(	PUNCT
ejpam-5997	433	15	∫	∫	PROPN
ejpam-5997	433	16	1	1	NUM
ejpam-5997	433	17	0	0	NUM
ejpam-5997	433	18	∣∣[ϕ′′	∣∣[ϕ′′	NOUN
ejpam-5997	433	19	(	(	PUNCT
ejpam-5997	433	20	℘ω	℘ω	NOUN
ejpam-5997	433	21	+	+	CCONJ
ejpam-5997	433	22	(	(	PUNCT
ejpam-5997	433	23	1−	1−	NUM
ejpam-5997	433	24	℘)α	℘)α	NOUN
ejpam-5997	433	25	)	)	PUNCT
ejpam-5997	433	26	]	]	X
ejpam-5997	433	27	∣∣q	∣∣q	NUM
ejpam-5997	433	28	)	)	PUNCT
ejpam-5997	433	29	1	1	NUM
ejpam-5997	433	30	q	q	NOUN
ejpam-5997	433	31	d℘+(∫	d℘+(∫	VERB
ejpam-5997	433	32	1	1	NUM
ejpam-5997	433	33	0	0	NUM
ejpam-5997	433	34	∣∣[ϕ′′	∣∣[ϕ′′	NOUN
ejpam-5997	433	35	(	(	PUNCT
ejpam-5997	433	36	(	(	PUNCT
ejpam-5997	433	37	1−	1−	NUM
ejpam-5997	433	38	℘)ω	℘)ω	NOUN
ejpam-5997	433	39	+	+	CCONJ
ejpam-5997	433	40	℘α	℘α	NOUN
ejpam-5997	433	41	)	)	PUNCT
ejpam-5997	433	42	]	]	SYM
ejpam-5997	433	43	∣∣q	∣∣q	NUM
ejpam-5997	433	44	)	)	PUNCT
ejpam-5997	433	45	1	1	NUM
ejpam-5997	433	46	q	q	NOUN
ejpam-5997	433	47	d℘	d℘	NUM
ejpam-5997	433	48	}	}	PUNCT
ejpam-5997	433	49	]	]	PUNCT
ejpam-5997	433	50	(	(	PUNCT
ejpam-5997	433	51	29	29	NUM
ejpam-5997	433	52	)	)	PUNCT
ejpam-5997	433	53	as	as	SCONJ
ejpam-5997	433	54	∣∣ϕ′′∣∣q	∣∣ϕ′′∣∣q	PROPN
ejpam-5997	433	55	is	be	AUX
ejpam-5997	433	56	s	s	NOUN
ejpam-5997	433	57	-	-	ADJ
ejpam-5997	433	58	convex	convex	ADJ
ejpam-5997	433	59	function;∫	function;∫	NOUN
ejpam-5997	433	60	1	1	NUM
ejpam-5997	433	61	0	0	NUM
ejpam-5997	433	62	∣∣[ϕ′′	∣∣[ϕ′′	NOUN
ejpam-5997	433	63	(	(	PUNCT
ejpam-5997	433	64	℘ω	℘ω	NOUN
ejpam-5997	433	65	+	+	CCONJ
ejpam-5997	433	66	(	(	PUNCT
ejpam-5997	433	67	1−	1−	NUM
ejpam-5997	433	68	℘)α	℘)α	NOUN
ejpam-5997	433	69	)	)	PUNCT
ejpam-5997	433	70	]	]	PUNCT
ejpam-5997	433	71	∣∣qd℘	∣∣qd℘	PROPN
ejpam-5997	433	72	≤	≤	ADJ
ejpam-5997	433	73	|ϕ′′	|ϕ′′	PRON
ejpam-5997	433	74	(	(	PUNCT
ejpam-5997	433	75	ω)|q	ω)|q	PROPN
ejpam-5997	433	76	∫	∫	PROPN
ejpam-5997	433	77	1	1	NUM
ejpam-5997	433	78	0	0	NUM
ejpam-5997	433	79	℘sd℘+	℘sd℘+	PROPN
ejpam-5997	433	80	|ϕ′′	|ϕ′′	PRON
ejpam-5997	433	81	(	(	PUNCT
ejpam-5997	433	82	α)|q	α)|q	NOUN
ejpam-5997	433	83	∫	∫	PROPN
ejpam-5997	433	84	1	1	NUM
ejpam-5997	433	85	0	0	NUM
ejpam-5997	433	86	(	(	PUNCT
ejpam-5997	433	87	1−	1−	NUM
ejpam-5997	433	88	℘)sd℘	℘)sd℘	PROPN
ejpam-5997	433	89	m.	m.	PROPN
ejpam-5997	433	90	vivas	vivas	PROPN
ejpam-5997	433	91	-	-	PROPN
ejpam-5997	433	92	cortez	cortez	PROPN
ejpam-5997	433	93	et	et	PROPN
ejpam-5997	433	94	al	al	PROPN
ejpam-5997	433	95	.	.	PUNCT
ejpam-5997	433	96	/	/	SYM
ejpam-5997	433	97	eur	eur	PROPN
ejpam-5997	433	98	.	.	PUNCT
ejpam-5997	434	1	j.	j.	PROPN
ejpam-5997	434	2	pure	pure	PROPN
ejpam-5997	434	3	appl	appl	PROPN
ejpam-5997	434	4	.	.	PROPN
ejpam-5997	434	5	math	math	PROPN
ejpam-5997	434	6	,	,	PUNCT
ejpam-5997	434	7	18	18	NUM
ejpam-5997	434	8	(	(	PUNCT
ejpam-5997	434	9	2	2	NUM
ejpam-5997	434	10	)	)	PUNCT
ejpam-5997	434	11	(	(	PUNCT
ejpam-5997	434	12	2025	2025	NUM
ejpam-5997	434	13	)	)	PUNCT
ejpam-5997	434	14	,	,	PUNCT
ejpam-5997	434	15	5997	5997	NUM
ejpam-5997	434	16	17	17	NUM
ejpam-5997	434	17	of	of	ADP
ejpam-5997	434	18	23	23	NUM
ejpam-5997	434	19	=	=	SYM
ejpam-5997	434	20	|ϕ′′	|ϕ′′	PUNCT
ejpam-5997	434	21	(	(	PUNCT
ejpam-5997	434	22	ω)|q	ω)|q	VERB
ejpam-5997	434	23	+	+	PRON
ejpam-5997	434	24	|ϕ′′	|ϕ′′	PRON
ejpam-5997	434	25	(	(	PUNCT
ejpam-5997	434	26	α)|q	α)|q	NOUN
ejpam-5997	434	27	s+	s+	NUM
ejpam-5997	434	28	1	1	NUM
ejpam-5997	434	29	(	(	PUNCT
ejpam-5997	434	30	30	30	NUM
ejpam-5997	434	31	)	)	PUNCT
ejpam-5997	434	32	∫	∫	PROPN
ejpam-5997	434	33	1	1	NUM
ejpam-5997	434	34	0	0	NUM
ejpam-5997	434	35	∣∣[ϕ′′	∣∣[ϕ′′	NOUN
ejpam-5997	434	36	(	(	PUNCT
ejpam-5997	434	37	(	(	PUNCT
ejpam-5997	434	38	1−	1−	NUM
ejpam-5997	434	39	℘)ω	℘)ω	NOUN
ejpam-5997	434	40	+	+	CCONJ
ejpam-5997	434	41	℘α	℘α	NOUN
ejpam-5997	434	42	)	)	PUNCT
ejpam-5997	434	43	]	]	PUNCT
ejpam-5997	434	44	∣∣qd℘	∣∣qd℘	PROPN
ejpam-5997	434	45	≤	≤	PROPN
ejpam-5997	435	1	ϕ	ϕ	PROPN
ejpam-5997	436	1	′′	′′	PROPN
ejpam-5997	436	2	(	(	PUNCT
ejpam-5997	436	3	ω)|q	ω)|q	PROPN
ejpam-5997	436	4	∫	∫	PROPN
ejpam-5997	436	5	1	1	NUM
ejpam-5997	436	6	0	0	NUM
ejpam-5997	436	7	(	(	PUNCT
ejpam-5997	436	8	1−	1−	NUM
ejpam-5997	436	9	℘)sd℘+	℘)sd℘+	NUM
ejpam-5997	436	10	|ϕ′′	|ϕ′′	PRON
ejpam-5997	436	11	(	(	PUNCT
ejpam-5997	436	12	α)|q	α)|q	NOUN
ejpam-5997	436	13	∫	∫	PROPN
ejpam-5997	436	14	1	1	NUM
ejpam-5997	436	15	0	0	NUM
ejpam-5997	436	16	℘sd℘	℘sd℘	NUM
ejpam-5997	436	17	=	=	PRON
ejpam-5997	436	18	|ϕ′′	|ϕ′′	PUNCT
ejpam-5997	436	19	(	(	PUNCT
ejpam-5997	436	20	ω)|q	ω)|q	VERB
ejpam-5997	436	21	+	+	PRON
ejpam-5997	436	22	|ϕ′′	|ϕ′′	PRON
ejpam-5997	436	23	(	(	PUNCT
ejpam-5997	436	24	α)|q	α)|q	NOUN
ejpam-5997	436	25	s+	s+	NUM
ejpam-5997	436	26	1	1	NUM
ejpam-5997	436	27	(	(	PUNCT
ejpam-5997	436	28	31	31	NUM
ejpam-5997	436	29	)	)	PUNCT
ejpam-5997	436	30	β(µnp+	β(µnp+	X
ejpam-5997	436	31	p+	p+	VERB
ejpam-5997	436	32	1	1	NUM
ejpam-5997	436	33	,	,	PUNCT
ejpam-5997	436	34	ξ	ξ	PROPN
ejpam-5997	436	35	′	′	NOUN
ejpam-5997	436	36	p+	p+	NOUN
ejpam-5997	436	37	1	1	NUM
ejpam-5997	436	38	)	)	PUNCT
ejpam-5997	436	39	=	=	SYM
ejpam-5997	437	1	∫	∫	PROPN
ejpam-5997	438	1	1	1	NUM
ejpam-5997	438	2	0	0	NUM
ejpam-5997	438	3	℘µnp+p(1−	℘µnp+p(1−	NUM
ejpam-5997	438	4	℘)ξ	℘)ξ	NOUN
ejpam-5997	438	5	′	′	NUM
ejpam-5997	438	6	pd℘	pd℘	PROPN
ejpam-5997	438	7	(	(	PUNCT
ejpam-5997	438	8	32	32	NUM
ejpam-5997	438	9	)	)	PUNCT
ejpam-5997	438	10	substitute	substitute	NOUN
ejpam-5997	438	11	equations	equation	NOUN
ejpam-5997	438	12	(	(	PUNCT
ejpam-5997	438	13	30	30	NUM
ejpam-5997	438	14	)	)	PUNCT
ejpam-5997	438	15	,	,	PUNCT
ejpam-5997	438	16	(	(	PUNCT
ejpam-5997	438	17	31),(32	31),(32	NOUN
ejpam-5997	438	18	)	)	PUNCT
ejpam-5997	438	19	in	in	ADP
ejpam-5997	438	20	equation	equation	NOUN
ejpam-5997	438	21	(	(	PUNCT
ejpam-5997	438	22	29	29	NUM
ejpam-5997	438	23	)	)	PUNCT
ejpam-5997	439	1	,	,	PUNCT
ejpam-5997	439	2	then	then	ADV
ejpam-5997	439	3	we	we	PRON
ejpam-5997	439	4	get	get	VERB
ejpam-5997	439	5	ℶ	ℶ	DET
ejpam-5997	439	6	≤	≤	NOUN
ejpam-5997	440	1	∞∑	∞∑	DET
ejpam-5997	440	2	n=0	n=0	NUM
ejpam-5997	440	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	440	4	βp(ζ	βp(ζ	NUM
ejpam-5997	440	5	+	+	CCONJ
ejpam-5997	440	6	ρn	ρn	INTJ
ejpam-5997	440	7	,	,	PUNCT
ejpam-5997	440	8	c−	c−	NOUN
ejpam-5997	440	9	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	440	10	β(ζ	β(ζ	PROPN
ejpam-5997	440	11	,	,	PUNCT
ejpam-5997	440	12	c−	c−	X
ejpam-5997	440	13	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	440	14	ξ	ξ	X
ejpam-5997	441	1	+	+	NUM
ejpam-5997	441	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	441	3	(	(	PUNCT
ejpam-5997	441	4	−κ)n	−κ)n	VERB
ejpam-5997	441	5	∣∣∣∣(α−	∣∣∣∣(α−	PROPN
ejpam-5997	441	6	ω)2	ω)2	VERB
ejpam-5997	441	7	2	2	NUM
ejpam-5997	441	8	×	×	NOUN
ejpam-5997	442	1	[	[	X
ejpam-5997	442	2	(	(	PUNCT
ejpam-5997	442	3	β(µnp+	β(µnp+	ADJ
ejpam-5997	442	4	p+	p+	NOUN
ejpam-5997	442	5	1	1	NUM
ejpam-5997	442	6	,	,	PUNCT
ejpam-5997	442	7	ξ	ξ	PROPN
ejpam-5997	442	8	′	′	NOUN
ejpam-5997	442	9	p+	p+	NOUN
ejpam-5997	442	10	1	1	NUM
ejpam-5997	442	11	)	)	PUNCT
ejpam-5997	442	12	)	)	PUNCT
ejpam-5997	442	13	1	1	NUM
ejpam-5997	442	14	p	p	NOUN
ejpam-5997	442	15	{	{	PUNCT
ejpam-5997	442	16	(	(	PUNCT
ejpam-5997	442	17	|ϕ′′	|ϕ′′	X
ejpam-5997	442	18	(	(	PUNCT
ejpam-5997	442	19	ω)|q	ω)|q	VERB
ejpam-5997	442	20	+	+	PRON
ejpam-5997	442	21	|ϕ′′	|ϕ′′	PRON
ejpam-5997	442	22	(	(	PUNCT
ejpam-5997	442	23	α)|q	α)|q	NOUN
ejpam-5997	442	24	s+	s+	PUNCT
ejpam-5997	442	25	1	1	X
ejpam-5997	442	26	)	)	PUNCT
ejpam-5997	442	27	1	1	NUM
ejpam-5997	442	28	q	q	NOUN
ejpam-5997	443	1	+	+	CCONJ
ejpam-5997	443	2	(	(	PUNCT
ejpam-5997	443	3	|ϕ′′	|ϕ′′	PRON
ejpam-5997	443	4	(	(	PUNCT
ejpam-5997	443	5	ω)|q	ω)|q	VERB
ejpam-5997	443	6	+	+	PRON
ejpam-5997	443	7	|ϕ′′	|ϕ′′	PRON
ejpam-5997	443	8	(	(	PUNCT
ejpam-5997	443	9	α)|q	α)|q	NOUN
ejpam-5997	443	10	s+	s+	PUNCT
ejpam-5997	443	11	1	1	X
ejpam-5997	443	12	)	)	PUNCT
ejpam-5997	443	13	1	1	NUM
ejpam-5997	443	14	q	q	NOUN
ejpam-5997	443	15	}	}	PUNCT
ejpam-5997	443	16	]	]	PUNCT
ejpam-5997	443	17	the	the	DET
ejpam-5997	443	18	proof	proof	NOUN
ejpam-5997	443	19	is	be	AUX
ejpam-5997	443	20	completed	complete	VERB
ejpam-5997	443	21	.	.	PUNCT
ejpam-5997	444	1	corollary	corollary	ADJ
ejpam-5997	444	2	8	8	NUM
ejpam-5997	444	3	.	.	PUNCT
ejpam-5997	445	1	if	if	SCONJ
ejpam-5997	445	2	we	we	PRON
ejpam-5997	445	3	replace	replace	VERB
ejpam-5997	445	4	p	p	NOUN
ejpam-5997	445	5	=	=	NOUN
ejpam-5997	445	6	0	0	NUM
ejpam-5997	445	7	,	,	PUNCT
ejpam-5997	445	8	κ	κ	X
ejpam-5997	445	9	=	=	SYM
ejpam-5997	445	10	0	0	NUM
ejpam-5997	445	11	,	,	PUNCT
ejpam-5997	445	12	and	and	CCONJ
ejpam-5997	445	13	ξ	ξ	X
ejpam-5997	445	14	=	=	SYM
ejpam-5997	445	15	ξ	ξ	PROPN
ejpam-5997	445	16	−	−	PROPN
ejpam-5997	445	17	1	1	NUM
ejpam-5997	445	18	in	in	ADP
ejpam-5997	445	19	theorem	theorem	NOUN
ejpam-5997	445	20	(	(	PUNCT
ejpam-5997	445	21	6	6	NUM
ejpam-5997	445	22	)	)	PUNCT
ejpam-5997	445	23	,	,	PUNCT
ejpam-5997	445	24	we	we	PRON
ejpam-5997	445	25	have	have	VERB
ejpam-5997	445	26	a	a	DET
ejpam-5997	445	27	result	result	NOUN
ejpam-5997	445	28	[	[	X
ejpam-5997	445	29	19	19	NUM
ejpam-5997	445	30	]	]	PUNCT
ejpam-5997	445	31	.	.	PUNCT
ejpam-5997	446	1	theorem	theorem	ADJ
ejpam-5997	446	2	7	7	NUM
ejpam-5997	446	3	.	.	PUNCT
ejpam-5997	447	1	let	let	VERB
ejpam-5997	447	2	ϕ	ϕ	NOUN
ejpam-5997	447	3	:	:	PUNCT
ejpam-5997	447	4	i	i	PRON
ejpam-5997	447	5	⊆	⊆	NUM
ejpam-5997	447	6	r	r	NOUN
ejpam-5997	447	7	→	→	SYM
ejpam-5997	447	8	r	r	NOUN
ejpam-5997	447	9	be	be	VERB
ejpam-5997	447	10	twice	twice	ADV
ejpam-5997	447	11	differentiable	differentiable	ADJ
ejpam-5997	447	12	mapping	mapping	NOUN
ejpam-5997	447	13	on	on	ADP
ejpam-5997	447	14	io	io	PROPN
ejpam-5997	447	15	and	and	CCONJ
ejpam-5997	447	16	ω	ω	PROPN
ejpam-5997	447	17	,	,	PUNCT
ejpam-5997	447	18	τ	τ	PROPN
ejpam-5997	447	19	∈	∈	PROPN
ejpam-5997	447	20	io	io	X
ejpam-5997	447	21	with	with	ADP
ejpam-5997	447	22	ω	ω	PROPN
ejpam-5997	447	23	<	<	X
ejpam-5997	447	24	α	α	X
ejpam-5997	447	25	<	<	X
ejpam-5997	447	26	τ	τ	PROPN
ejpam-5997	447	27	such	such	ADJ
ejpam-5997	447	28	that	that	SCONJ
ejpam-5997	447	29	ϕ	ϕ	NOUN
ejpam-5997	447	30	′′	′′	PROPN
ejpam-5997	447	31	∈	∈	PROPN
ejpam-5997	447	32	l[ω	l[ω	PROPN
ejpam-5997	447	33	,	,	PUNCT
ejpam-5997	447	34	τ	τ	X
ejpam-5997	447	35	]	]	PUNCT
ejpam-5997	447	36	.	.	PUNCT
ejpam-5997	448	1	if	if	SCONJ
ejpam-5997	448	2	|ϕ′′	|ϕ′′	PRON
ejpam-5997	448	3	|q(q	|q(q	NOUN
ejpam-5997	448	4	≥	≥	NOUN
ejpam-5997	448	5	1	1	NUM
ejpam-5997	448	6	)	)	PUNCT
ejpam-5997	448	7	is	be	AUX
ejpam-5997	448	8	s	s	NOUN
ejpam-5997	448	9	-	-	ADJ
ejpam-5997	448	10	convex	convex	ADJ
ejpam-5997	448	11	function	function	NOUN
ejpam-5997	448	12	on	on	ADP
ejpam-5997	448	13	i	i	PROPN
ejpam-5997	448	14	,	,	PUNCT
ejpam-5997	448	15	and	and	CCONJ
ejpam-5997	448	16	µ	µ	NOUN
ejpam-5997	448	17	,	,	PUNCT
ejpam-5997	448	18	ξ	ξ	PROPN
ejpam-5997	448	19	,	,	PUNCT
ejpam-5997	448	20	ζ	ζ	NOUN
ejpam-5997	448	21	,	,	PUNCT
ejpam-5997	448	22	ς	ς	PROPN
ejpam-5997	448	23	,	,	PUNCT
ejpam-5997	448	24	c	c	X
ejpam-5997	448	25	,	,	PUNCT
ejpam-5997	448	26	κ1	κ1	PROPN
ejpam-5997	448	27	∈	∈	PROPN
ejpam-5997	448	28	c,ℜ(µ	c,ℜ(µ	PROPN
ejpam-5997	448	29	)	)	PUNCT
ejpam-5997	448	30	>	>	X
ejpam-5997	448	31	0,ℜ(ξ	0,ℜ(ξ	PROPN
ejpam-5997	448	32	)	)	PUNCT
ejpam-5997	448	33	>	>	X
ejpam-5997	448	34	0,ℜ(ζ	0,ℜ(ζ	PROPN
ejpam-5997	448	35	)	)	PUNCT
ejpam-5997	448	36	>	>	X
ejpam-5997	448	37	0,ℜ(ς	0,ℜ(ς	PROPN
ejpam-5997	448	38	)	)	PUNCT
ejpam-5997	448	39	>	>	X
ejpam-5997	449	1	0,ℜ(κ1	0,ℜ(κ1	PROPN
ejpam-5997	449	2	)	)	PUNCT
ejpam-5997	449	3	>	>	X
ejpam-5997	449	4	0	0	NUM
ejpam-5997	449	5	,	,	PUNCT
ejpam-5997	449	6	ρ	ρ	PROPN
ejpam-5997	449	7	,	,	PUNCT
ejpam-5997	449	8	m	m	PROPN
ejpam-5997	449	9	,	,	PUNCT
ejpam-5997	449	10	η	η	PROPN
ejpam-5997	449	11	≥	≥	X
ejpam-5997	449	12	0	0	NUM
ejpam-5997	449	13	and	and	CCONJ
ejpam-5997	449	14	m	m	PROPN
ejpam-5997	449	15	,	,	PUNCT
ejpam-5997	449	16	ρ	ρ	PROPN
ejpam-5997	449	17	>	>	X
ejpam-5997	449	18	ℜ(µ	ℜ(µ	NOUN
ejpam-5997	449	19	)	)	PUNCT
ejpam-5997	449	20	+	+	CCONJ
ejpam-5997	449	21	η	η	PROPN
ejpam-5997	449	22	,	,	PUNCT
ejpam-5997	449	23	then	then	ADV
ejpam-5997	449	24	following	follow	VERB
ejpam-5997	449	25	integral	integral	ADJ
ejpam-5997	449	26	inequality	inequality	NOUN
ejpam-5997	449	27	holds	hold	VERB
ejpam-5997	449	28	as	as	ADP
ejpam-5997	449	29	a	a	DET
ejpam-5997	449	30	result	result	NOUN
ejpam-5997	449	31	;	;	PUNCT
ejpam-5997	449	32	∣∣∣∣(ξ′)jµ,ρ	∣∣∣∣(ξ′)jµ,ρ	X
ejpam-5997	449	33	,	,	PUNCT
ejpam-5997	449	34	m	m	PROPN
ejpam-5997	449	35	,	,	PUNCT
ejpam-5997	449	36	η	η	PROPN
ejpam-5997	449	37	,	,	PUNCT
ejpam-5997	449	38	cξ	cξ	NOUN
ejpam-5997	449	39	,	,	PUNCT
ejpam-5997	449	40	ζ	ζ	NOUN
ejpam-5997	449	41	,	,	PUNCT
ejpam-5997	449	42	ς	ς	PROPN
ejpam-5997	449	43	,	,	PUNCT
ejpam-5997	449	44	κ1	κ1	NOUN
ejpam-5997	449	45	(	(	PUNCT
ejpam-5997	449	46	κ	κ	NOUN
ejpam-5997	449	47	,	,	PUNCT
ejpam-5997	449	48	p	p	NOUN
ejpam-5997	449	49	)	)	PUNCT
ejpam-5997	450	1	[	[	X
ejpam-5997	450	2	ϕ(α	ϕ(α	NUM
ejpam-5997	450	3	)	)	PUNCT
ejpam-5997	450	4	+	+	SYM
ejpam-5997	450	5	ϕ(ω	ϕ(ω	NOUN
ejpam-5997	450	6	)	)	PUNCT
ejpam-5997	450	7	2	2	NUM
ejpam-5997	450	8	]	]	PUNCT
ejpam-5997	451	1	+	+	CCONJ
ejpam-5997	451	2	[	[	PUNCT
ejpam-5997	451	3	(	(	PUNCT
ejpam-5997	451	4	µn+	µn+	ADJ
ejpam-5997	451	5	1)(µn	1)(µn	NUM
ejpam-5997	451	6	)	)	PUNCT
ejpam-5997	451	7	2(α−	2(α−	NUM
ejpam-5997	452	1	ω)µn	ω)µn	PROPN
ejpam-5997	452	2	−	−	PROPN
ejpam-5997	452	3	(	(	PUNCT
ejpam-5997	452	4	ξ	ξ	X
ejpam-5997	452	5	′	′	NOUN
ejpam-5997	453	1	+	+	CCONJ
ejpam-5997	453	2	µn+	µn+	ADJ
ejpam-5997	453	3	1)(ξ	1)(ξ	NUM
ejpam-5997	453	4	′	′	NUM
ejpam-5997	453	5	+	+	CCONJ
ejpam-5997	453	6	µn	µn	X
ejpam-5997	453	7	)	)	PUNCT
ejpam-5997	453	8	2(α−	2(α−	NUM
ejpam-5997	453	9	ω)ξ	ω)ξ	NOUN
ejpam-5997	453	10	′+µn	′+µn	PROPN
ejpam-5997	453	11	]	]	PUNCT
ejpam-5997	453	12	×	×	PROPN
ejpam-5997	453	13	[	[	X
ejpam-5997	453	14	(	(	PUNCT
ejpam-5997	453	15	eµ,ρ	eµ,ρ	X
ejpam-5997	453	16	,	,	PUNCT
ejpam-5997	453	17	m	m	PROPN
ejpam-5997	453	18	,	,	PUNCT
ejpam-5997	453	19	η	η	PROPN
ejpam-5997	453	20	,	,	PUNCT
ejpam-5997	453	21	c	c	PROPN
ejpam-5997	453	22	ξ	ξ	PROPN
ejpam-5997	453	23	,	,	PUNCT
ejpam-5997	453	24	ζ	ζ	NOUN
ejpam-5997	453	25	,	,	PUNCT
ejpam-5997	453	26	ς	ς	PROPN
ejpam-5997	453	27	,	,	PUNCT
ejpam-5997	453	28	κ1,ω+ϕ	κ1,ω+ϕ	PROPN
ejpam-5997	453	29	)	)	PUNCT
ejpam-5997	453	30	(	(	PUNCT
ejpam-5997	453	31	α	α	X
ejpam-5997	453	32	,	,	PUNCT
ejpam-5997	453	33	κ	κ	NOUN
ejpam-5997	453	34	)	)	PUNCT
ejpam-5997	453	35	+	+	CCONJ
ejpam-5997	453	36	(	(	PUNCT
ejpam-5997	453	37	eµ,ρ	eµ,ρ	X
ejpam-5997	453	38	,	,	PUNCT
ejpam-5997	453	39	m	m	PROPN
ejpam-5997	453	40	,	,	PUNCT
ejpam-5997	453	41	η	η	PROPN
ejpam-5997	453	42	,	,	PUNCT
ejpam-5997	453	43	c	c	PROPN
ejpam-5997	453	44	ξ	ξ	PROPN
ejpam-5997	453	45	,	,	PUNCT
ejpam-5997	453	46	ζ	ζ	NOUN
ejpam-5997	453	47	,	,	PUNCT
ejpam-5997	453	48	ς	ς	PROPN
ejpam-5997	453	49	,	,	PUNCT
ejpam-5997	453	50	κ1,α−ϕ	κ1,α−ϕ	NOUN
ejpam-5997	453	51	)	)	PUNCT
ejpam-5997	453	52	(	(	PUNCT
ejpam-5997	453	53	ω	ω	NOUN
ejpam-5997	453	54	,	,	PUNCT
ejpam-5997	453	55	κ	κ	NOUN
ejpam-5997	453	56	)	)	PUNCT
ejpam-5997	453	57	]	]	PUNCT
ejpam-5997	453	58	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	453	59	≤	≤	NOUN
ejpam-5997	453	60	∞∑	∞∑	NUM
ejpam-5997	453	61	n=0	n=0	NUM
ejpam-5997	453	62	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	453	63	βp(ζ	βp(ζ	NUM
ejpam-5997	453	64	+	+	CCONJ
ejpam-5997	453	65	ρn	ρn	INTJ
ejpam-5997	453	66	,	,	PUNCT
ejpam-5997	453	67	c−	c−	NOUN
ejpam-5997	453	68	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	453	69	β(ζ	β(ζ	PROPN
ejpam-5997	453	70	,	,	PUNCT
ejpam-5997	453	71	c−	c−	X
ejpam-5997	453	72	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	453	73	ξ	ξ	X
ejpam-5997	454	1	+	+	NUM
ejpam-5997	454	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	454	3	(	(	PUNCT
ejpam-5997	454	4	−κ)n	−κ)n	VERB
ejpam-5997	454	5	∣∣∣∣(α−	∣∣∣∣(α−	PROPN
ejpam-5997	454	6	ω)2	ω)2	X
ejpam-5997	454	7	2	2	NUM
ejpam-5997	454	8	[	[	X
ejpam-5997	454	9	(	(	PUNCT
ejpam-5997	454	10	ξ	ξ	NOUN
ejpam-5997	454	11	′	′	NUM
ejpam-5997	454	12	(	(	PUNCT
ejpam-5997	454	13	µn+	µn+	ADJ
ejpam-5997	454	14	2)(ξ′	2)(ξ′	NUM
ejpam-5997	454	15	+	+	CCONJ
ejpam-5997	454	16	µn+	µn+	ADJ
ejpam-5997	454	17	2	2	NUM
ejpam-5997	454	18	)	)	PUNCT
ejpam-5997	454	19	)	)	PUNCT
ejpam-5997	455	1	1−	1−	NUM
ejpam-5997	455	2	1	1	NUM
ejpam-5997	455	3	q	q	NOUN
ejpam-5997	455	4	×	×	NOUN
ejpam-5997	455	5	{	{	PUNCT
ejpam-5997	455	6	(	(	PUNCT
ejpam-5997	455	7	|ϕ′′	|ϕ′′	X
ejpam-5997	455	8	(	(	PUNCT
ejpam-5997	455	9	ω)|qβ(µn+	ω)|qβ(µn+	NOUN
ejpam-5997	455	10	s+	s+	PUNCT
ejpam-5997	455	11	2	2	NUM
ejpam-5997	455	12	,	,	PUNCT
ejpam-5997	455	13	ξ	ξ	NOUN
ejpam-5997	455	14	′	′	NUM
ejpam-5997	456	1	+	+	CCONJ
ejpam-5997	456	2	1	1	X
ejpam-5997	456	3	)	)	PUNCT
ejpam-5997	456	4	+	+	CCONJ
ejpam-5997	456	5	|ϕ′′	|ϕ′′	PRON
ejpam-5997	456	6	|q(α)β(µn+	|q(α)β(µn+	ADV
ejpam-5997	456	7	2	2	NUM
ejpam-5997	456	8	,	,	PUNCT
ejpam-5997	456	9	ξ	ξ	NOUN
ejpam-5997	456	10	′	′	NUM
ejpam-5997	457	1	+	+	CCONJ
ejpam-5997	457	2	s+	s+	NUM
ejpam-5997	457	3	1	1	NUM
ejpam-5997	457	4	)	)	PUNCT
ejpam-5997	457	5	)	)	PUNCT
ejpam-5997	458	1	1	1	NUM
ejpam-5997	458	2	q	q	NOUN
ejpam-5997	458	3	+	+	PROPN
ejpam-5997	458	4	(	(	PUNCT
ejpam-5997	458	5	|ϕ′′	|ϕ′′	PUNCT
ejpam-5997	458	6	(	(	PUNCT
ejpam-5997	458	7	ω)|qβ(µn+	ω)|qβ(µn+	PROPN
ejpam-5997	458	8	2	2	NUM
ejpam-5997	458	9	,	,	PUNCT
ejpam-5997	458	10	ξ	ξ	PROPN
ejpam-5997	458	11	′	′	NUM
ejpam-5997	459	1	+	+	CCONJ
ejpam-5997	459	2	s+	s+	NUM
ejpam-5997	459	3	1	1	X
ejpam-5997	459	4	)	)	PUNCT
ejpam-5997	460	1	+	+	NUM
ejpam-5997	460	2	|ϕ′′	|ϕ′′	PUNCT
ejpam-5997	460	3	|qβ(µn+	|qβ(µn+	CCONJ
ejpam-5997	460	4	s+	s+	X
ejpam-5997	460	5	2	2	NUM
ejpam-5997	460	6	,	,	PUNCT
ejpam-5997	460	7	ξ	ξ	NOUN
ejpam-5997	460	8	′	′	NUM
ejpam-5997	461	1	+	+	CCONJ
ejpam-5997	461	2	1	1	NUM
ejpam-5997	461	3	)	)	PUNCT
ejpam-5997	461	4	)	)	PUNCT
ejpam-5997	461	5	1	1	NUM
ejpam-5997	461	6	q	q	NOUN
ejpam-5997	461	7	}	}	PUNCT
ejpam-5997	461	8	]	]	PUNCT
ejpam-5997	461	9	m.	m.	NOUN
ejpam-5997	461	10	vivas	vivas	PROPN
ejpam-5997	461	11	-	-	PROPN
ejpam-5997	461	12	cortez	cortez	PROPN
ejpam-5997	461	13	et	et	PROPN
ejpam-5997	461	14	al	al	PROPN
ejpam-5997	461	15	.	.	PUNCT
ejpam-5997	461	16	/	/	SYM
ejpam-5997	461	17	eur	eur	PROPN
ejpam-5997	461	18	.	.	PUNCT
ejpam-5997	462	1	j.	j.	PROPN
ejpam-5997	462	2	pure	pure	PROPN
ejpam-5997	462	3	appl	appl	PROPN
ejpam-5997	462	4	.	.	PROPN
ejpam-5997	462	5	math	math	PROPN
ejpam-5997	462	6	,	,	PUNCT
ejpam-5997	462	7	18	18	NUM
ejpam-5997	462	8	(	(	PUNCT
ejpam-5997	462	9	2	2	NUM
ejpam-5997	462	10	)	)	PUNCT
ejpam-5997	462	11	(	(	PUNCT
ejpam-5997	462	12	2025	2025	NUM
ejpam-5997	462	13	)	)	PUNCT
ejpam-5997	462	14	,	,	PUNCT
ejpam-5997	462	15	5997	5997	NUM
ejpam-5997	462	16	18	18	NUM
ejpam-5997	462	17	of	of	ADP
ejpam-5997	462	18	23	23	NUM
ejpam-5997	462	19	proof	proof	NOUN
ejpam-5997	462	20	.	.	PUNCT
ejpam-5997	463	1	by	by	ADP
ejpam-5997	463	2	using	use	VERB
ejpam-5997	463	3	lemma	lemma	PROPN
ejpam-5997	463	4	2	2	NUM
ejpam-5997	463	5	,	,	PUNCT
ejpam-5997	463	6	we	we	PRON
ejpam-5997	463	7	have	have	VERB
ejpam-5997	463	8	ℶ	ℶ	PROPN
ejpam-5997	463	9	=	=	SYM
ejpam-5997	463	10	∣∣∣∣(ξ′)jµ,ρ	∣∣∣∣(ξ′)jµ,ρ	PROPN
ejpam-5997	463	11	,	,	PUNCT
ejpam-5997	463	12	m	m	PROPN
ejpam-5997	463	13	,	,	PUNCT
ejpam-5997	463	14	η	η	PROPN
ejpam-5997	463	15	,	,	PUNCT
ejpam-5997	463	16	cξ	cξ	NOUN
ejpam-5997	463	17	,	,	PUNCT
ejpam-5997	463	18	ζ	ζ	NOUN
ejpam-5997	463	19	,	,	PUNCT
ejpam-5997	463	20	ς	ς	PROPN
ejpam-5997	463	21	,	,	PUNCT
ejpam-5997	463	22	κ1	κ1	NOUN
ejpam-5997	463	23	(	(	PUNCT
ejpam-5997	463	24	κ	κ	NOUN
ejpam-5997	463	25	,	,	PUNCT
ejpam-5997	463	26	p	p	NOUN
ejpam-5997	463	27	)	)	PUNCT
ejpam-5997	464	1	[	[	X
ejpam-5997	464	2	ϕ(α	ϕ(α	NUM
ejpam-5997	464	3	)	)	PUNCT
ejpam-5997	464	4	+	+	SYM
ejpam-5997	464	5	ϕ(ω	ϕ(ω	NOUN
ejpam-5997	464	6	)	)	PUNCT
ejpam-5997	464	7	2	2	NUM
ejpam-5997	464	8	]	]	PUNCT
ejpam-5997	465	1	+	+	CCONJ
ejpam-5997	465	2	[	[	PUNCT
ejpam-5997	465	3	(	(	PUNCT
ejpam-5997	465	4	µn+	µn+	ADJ
ejpam-5997	465	5	1)(µn	1)(µn	NUM
ejpam-5997	465	6	)	)	PUNCT
ejpam-5997	465	7	2(α−	2(α−	NUM
ejpam-5997	466	1	ω)µn	ω)µn	PROPN
ejpam-5997	466	2	−	−	PROPN
ejpam-5997	466	3	(	(	PUNCT
ejpam-5997	466	4	ξ	ξ	X
ejpam-5997	466	5	′	′	NOUN
ejpam-5997	467	1	+	+	CCONJ
ejpam-5997	467	2	µn+	µn+	ADJ
ejpam-5997	467	3	1)(ξ	1)(ξ	NUM
ejpam-5997	467	4	′	′	NUM
ejpam-5997	467	5	+	+	CCONJ
ejpam-5997	467	6	µn	µn	X
ejpam-5997	467	7	)	)	PUNCT
ejpam-5997	467	8	2(α−	2(α−	NUM
ejpam-5997	467	9	ω)ξ	ω)ξ	NOUN
ejpam-5997	467	10	′+µn	′+µn	PROPN
ejpam-5997	467	11	]	]	PUNCT
ejpam-5997	467	12	×	×	PROPN
ejpam-5997	467	13	[	[	X
ejpam-5997	467	14	(	(	PUNCT
ejpam-5997	467	15	eµ,ρ	eµ,ρ	X
ejpam-5997	467	16	,	,	PUNCT
ejpam-5997	467	17	m	m	PROPN
ejpam-5997	467	18	,	,	PUNCT
ejpam-5997	467	19	η	η	PROPN
ejpam-5997	467	20	,	,	PUNCT
ejpam-5997	467	21	c	c	PROPN
ejpam-5997	467	22	ξ	ξ	PROPN
ejpam-5997	467	23	,	,	PUNCT
ejpam-5997	467	24	ζ	ζ	NOUN
ejpam-5997	467	25	,	,	PUNCT
ejpam-5997	467	26	ς	ς	PROPN
ejpam-5997	467	27	,	,	PUNCT
ejpam-5997	467	28	κ1,ω+ϕ	κ1,ω+ϕ	PROPN
ejpam-5997	467	29	)	)	PUNCT
ejpam-5997	467	30	(	(	PUNCT
ejpam-5997	467	31	α	α	X
ejpam-5997	467	32	,	,	PUNCT
ejpam-5997	467	33	κ	κ	NOUN
ejpam-5997	467	34	)	)	PUNCT
ejpam-5997	467	35	+	+	CCONJ
ejpam-5997	467	36	(	(	PUNCT
ejpam-5997	467	37	eµ,ρ	eµ,ρ	X
ejpam-5997	467	38	,	,	PUNCT
ejpam-5997	467	39	m	m	PROPN
ejpam-5997	467	40	,	,	PUNCT
ejpam-5997	467	41	η	η	PROPN
ejpam-5997	467	42	,	,	PUNCT
ejpam-5997	467	43	c	c	PROPN
ejpam-5997	467	44	ξ	ξ	PROPN
ejpam-5997	467	45	,	,	PUNCT
ejpam-5997	467	46	ζ	ζ	NOUN
ejpam-5997	467	47	,	,	PUNCT
ejpam-5997	467	48	ς	ς	PROPN
ejpam-5997	467	49	,	,	PUNCT
ejpam-5997	467	50	κ1,α−ϕ	κ1,α−ϕ	NOUN
ejpam-5997	467	51	)	)	PUNCT
ejpam-5997	467	52	(	(	PUNCT
ejpam-5997	467	53	ω	ω	NOUN
ejpam-5997	467	54	,	,	PUNCT
ejpam-5997	467	55	κ	κ	NOUN
ejpam-5997	467	56	)	)	PUNCT
ejpam-5997	467	57	]	]	PUNCT
ejpam-5997	467	58	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	467	59	≤	≤	NOUN
ejpam-5997	467	60	(	(	PUNCT
ejpam-5997	467	61	α−	α−	ADP
ejpam-5997	467	62	ω)2	ω)2	NOUN
ejpam-5997	467	63	2	2	NUM
ejpam-5997	467	64	∫	∫	NOUN
ejpam-5997	467	65	1	1	NUM
ejpam-5997	467	66	0	0	NUM
ejpam-5997	467	67	℘(1−	℘(1−	PROPN
ejpam-5997	467	68	℘ξ	℘ξ	NOUN
ejpam-5997	467	69	′	′	NUM
ejpam-5997	467	70	)	)	PUNCT
ejpam-5997	467	71	eµ,ρ	eµ,ρ	X
ejpam-5997	467	72	,	,	PUNCT
ejpam-5997	467	73	m	m	PROPN
ejpam-5997	467	74	,	,	PUNCT
ejpam-5997	467	75	η	η	PROPN
ejpam-5997	467	76	,	,	PUNCT
ejpam-5997	467	77	cξ	cξ	NOUN
ejpam-5997	467	78	,	,	PUNCT
ejpam-5997	467	79	ζ	ζ	NOUN
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ejpam-5997	483	12	/	/	SYM
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ejpam-5997	483	14	.	.	PUNCT
ejpam-5997	484	1	j.	j.	PROPN
ejpam-5997	484	2	pure	pure	PROPN
ejpam-5997	484	3	appl	appl	PROPN
ejpam-5997	484	4	.	.	PROPN
ejpam-5997	484	5	math	math	PROPN
ejpam-5997	484	6	,	,	PUNCT
ejpam-5997	484	7	18	18	NUM
ejpam-5997	484	8	(	(	PUNCT
ejpam-5997	484	9	2	2	NUM
ejpam-5997	484	10	)	)	PUNCT
ejpam-5997	484	11	(	(	PUNCT
ejpam-5997	484	12	2025	2025	NUM
ejpam-5997	484	13	)	)	PUNCT
ejpam-5997	484	14	,	,	PUNCT
ejpam-5997	484	15	5997	5997	NUM
ejpam-5997	484	16	19	19	NUM
ejpam-5997	484	17	of	of	ADP
ejpam-5997	484	18	23{(∫	23{(∫	NUM
ejpam-5997	484	19	1	1	NUM
ejpam-5997	484	20	0	0	PUNCT
ejpam-5997	484	21	℘µn+1(1−	℘µn+1(1−	ADJ
ejpam-5997	484	22	℘ξ	℘ξ	NOUN
ejpam-5997	484	23	′	′	NUM
ejpam-5997	484	24	)	)	PUNCT
ejpam-5997	485	1	[	[	X
ejpam-5997	485	2	|ϕ′′	|ϕ′′	X
ejpam-5997	485	3	(	(	PUNCT
ejpam-5997	485	4	ω)|q℘s	ω)|q℘s	PROPN
ejpam-5997	485	5	+	+	NUM
ejpam-5997	485	6	|ϕ′′	|ϕ′′	PRON
ejpam-5997	485	7	(	(	PUNCT
ejpam-5997	485	8	α)|q(1−	α)|q(1−	ADJ
ejpam-5997	485	9	℘)s]d℘	℘)s]d℘	PROPN
ejpam-5997	485	10	)	)	PUNCT
ejpam-5997	485	11	1	1	NUM
ejpam-5997	485	12	q	q	NOUN
ejpam-5997	485	13	+	+	NOUN
ejpam-5997	485	14	(	(	PUNCT
ejpam-5997	485	15	∫	∫	PROPN
ejpam-5997	485	16	1	1	NUM
ejpam-5997	485	17	0	0	X
ejpam-5997	485	18	℘µn+1(1−	℘µn+1(1−	ADJ
ejpam-5997	485	19	℘ξ	℘ξ	NOUN
ejpam-5997	485	20	′	′	NUM
ejpam-5997	485	21	)	)	PUNCT
ejpam-5997	486	1	[	[	X
ejpam-5997	486	2	|ϕ′′	|ϕ′′	X
ejpam-5997	486	3	(	(	PUNCT
ejpam-5997	486	4	ω)|q(1−	ω)|q(1−	ADJ
ejpam-5997	486	5	℘)s	℘)s	NOUN
ejpam-5997	486	6	+	+	CCONJ
ejpam-5997	486	7	|ϕ′′	|ϕ′′	PRON
ejpam-5997	486	8	(	(	PUNCT
ejpam-5997	486	9	α)|q℘s]d℘	α)|q℘s]d℘	NOUN
ejpam-5997	486	10	)	)	PUNCT
ejpam-5997	486	11	1	1	NUM
ejpam-5997	486	12	q	q	NOUN
ejpam-5997	486	13	}	}	PUNCT
ejpam-5997	486	14	]	]	PUNCT
ejpam-5997	486	15	(	(	PUNCT
ejpam-5997	486	16	36	36	NUM
ejpam-5997	486	17	)	)	PUNCT
ejpam-5997	486	18	since	since	SCONJ
ejpam-5997	486	19	℘ξ	℘ξ	ADJ
ejpam-5997	486	20	′	′	NUM
ejpam-5997	486	21	≥	≥	NOUN
ejpam-5997	486	22	℘	℘	NOUN
ejpam-5997	486	23	,	,	PUNCT
ejpam-5997	486	24	ξ	ξ	PROPN
ejpam-5997	486	25	′	′	NUM
ejpam-5997	486	26	∈	∈	NOUN
ejpam-5997	486	27	(	(	PUNCT
ejpam-5997	486	28	0	0	NUM
ejpam-5997	486	29	,	,	PUNCT
ejpam-5997	486	30	1	1	NUM
ejpam-5997	486	31	]	]	PUNCT
ejpam-5997	486	32	and	and	CCONJ
ejpam-5997	486	33	℘	℘	PROPN
ejpam-5997	486	34	∈	∈	PROPN
ejpam-5997	486	35	[	[	X
ejpam-5997	486	36	0	0	NUM
ejpam-5997	486	37	,	,	PUNCT
ejpam-5997	486	38	1	1	NUM
ejpam-5997	486	39	]	]	PUNCT
ejpam-5997	486	40	,	,	PUNCT
ejpam-5997	486	41	we	we	PRON
ejpam-5997	486	42	have	have	VERB
ejpam-5997	486	43	−℘ξ	−℘ξ	NOUN
ejpam-5997	486	44	′	′	ADJ
ejpam-5997	486	45	≤	≤	ADJ
ejpam-5997	486	46	℘⇒	℘⇒	NOUN
ejpam-5997	486	47	1−	1−	NUM
ejpam-5997	486	48	℘ξ	℘ξ	ADJ
ejpam-5997	486	49	′	′	NUM
ejpam-5997	486	50	≤	≤	NOUN
ejpam-5997	486	51	1−	1−	NUM
ejpam-5997	486	52	℘	℘	PROPN
ejpam-5997	486	53	≤	≤	NUM
ejpam-5997	486	54	(	(	PUNCT
ejpam-5997	486	55	1−	1−	NUM
ejpam-5997	486	56	℘)ξ	℘)ξ	NOUN
ejpam-5997	486	57	′	′	NOUN
ejpam-5997	486	58	simplify	simplify	NOUN
ejpam-5997	486	59	;	;	PUNCT
ejpam-5997	486	60	∫	∫	PROPN
ejpam-5997	486	61	1	1	NUM
ejpam-5997	486	62	0	0	X
ejpam-5997	486	63	℘µn+1(1−	℘µn+1(1−	ADJ
ejpam-5997	486	64	℘)ξ	℘)ξ	NOUN
ejpam-5997	486	65	′	′	NOUN
ejpam-5997	487	1	[	[	X
ejpam-5997	487	2	|ϕ′′	|ϕ′′	X
ejpam-5997	487	3	(	(	PUNCT
ejpam-5997	487	4	ω)|q℘s	ω)|q℘s	PROPN
ejpam-5997	487	5	+	+	NUM
ejpam-5997	487	6	|ϕ′′	|ϕ′′	PRON
ejpam-5997	487	7	(	(	PUNCT
ejpam-5997	487	8	α)|q(1−	α)|q(1−	ADJ
ejpam-5997	487	9	℘)s]d℘	℘)s]d℘	X
ejpam-5997	487	10	=	=	PRON
ejpam-5997	487	11	|ϕ′′	|ϕ′′	X
ejpam-5997	487	12	(	(	PUNCT
ejpam-5997	487	13	ω)|q	ω)|q	PROPN
ejpam-5997	487	14	∫	∫	PROPN
ejpam-5997	487	15	1	1	NUM
ejpam-5997	487	16	0	0	NUM
ejpam-5997	487	17	℘µn+s+1(1−	℘µn+s+1(1−	ADJ
ejpam-5997	487	18	℘)ξ	℘)ξ	NOUN
ejpam-5997	487	19	′	′	NUM
ejpam-5997	487	20	d℘+	d℘+	NOUN
ejpam-5997	487	21	|ϕ′′	|ϕ′′	PRON
ejpam-5997	487	22	(	(	PUNCT
ejpam-5997	487	23	α)|q	α)|q	NOUN
ejpam-5997	487	24	∫	∫	PROPN
ejpam-5997	487	25	1	1	NUM
ejpam-5997	487	26	0	0	PUNCT
ejpam-5997	487	27	℘µn+1(1−	℘µn+1(1−	ADJ
ejpam-5997	487	28	℘)ξ	℘)ξ	NOUN
ejpam-5997	487	29	′	′	NOUN
ejpam-5997	488	1	+	+	PROPN
ejpam-5997	488	2	s	s	NOUN
ejpam-5997	488	3	=	=	X
ejpam-5997	488	4	|ϕ′′	|ϕ′′	PUNCT
ejpam-5997	488	5	(	(	PUNCT
ejpam-5997	488	6	ω)|qβ(µn+	ω)|qβ(µn+	NOUN
ejpam-5997	488	7	s+	s+	PUNCT
ejpam-5997	488	8	2	2	NUM
ejpam-5997	488	9	,	,	PUNCT
ejpam-5997	488	10	ξ	ξ	NOUN
ejpam-5997	488	11	′	′	NUM
ejpam-5997	489	1	+	+	CCONJ
ejpam-5997	489	2	1	1	X
ejpam-5997	489	3	)	)	PUNCT
ejpam-5997	489	4	+	+	CCONJ
ejpam-5997	489	5	|ϕ′′	|ϕ′′	PRON
ejpam-5997	489	6	|q(α)β(µn+	|q(α)β(µn+	ADV
ejpam-5997	489	7	2	2	NUM
ejpam-5997	489	8	,	,	PUNCT
ejpam-5997	489	9	ξ	ξ	NOUN
ejpam-5997	489	10	′	′	NUM
ejpam-5997	490	1	+	+	CCONJ
ejpam-5997	490	2	s+	s+	NUM
ejpam-5997	490	3	1	1	NUM
ejpam-5997	490	4	)	)	PUNCT
ejpam-5997	490	5	.	.	PUNCT
ejpam-5997	491	1	(	(	PUNCT
ejpam-5997	491	2	37	37	NUM
ejpam-5997	491	3	)	)	PUNCT
ejpam-5997	491	4	consider	consider	VERB
ejpam-5997	491	5	the	the	DET
ejpam-5997	491	6	integral∫	integral∫	NOUN
ejpam-5997	491	7	1	1	NUM
ejpam-5997	491	8	0	0	NUM
ejpam-5997	491	9	℘µn+1(1−	℘µn+1(1−	PROPN
ejpam-5997	491	10	℘)ξ	℘)ξ	NOUN
ejpam-5997	491	11	′	′	NOUN
ejpam-5997	492	1	[	[	X
ejpam-5997	492	2	|ϕ′′	|ϕ′′	X
ejpam-5997	492	3	(	(	PUNCT
ejpam-5997	492	4	ω)|q(1−	ω)|q(1−	ADJ
ejpam-5997	492	5	℘)s	℘)s	NOUN
ejpam-5997	492	6	+	+	CCONJ
ejpam-5997	492	7	|ϕ′′	|ϕ′′	PRON
ejpam-5997	492	8	(	(	PUNCT
ejpam-5997	492	9	α)|q℘s]d℘	α)|q℘s]d℘	NOUN
ejpam-5997	492	10	=	=	PRON
ejpam-5997	492	11	|ϕ′′	|ϕ′′	X
ejpam-5997	492	12	(	(	PUNCT
ejpam-5997	492	13	ω)|q	ω)|q	NOUN
ejpam-5997	492	14	∫	∫	PROPN
ejpam-5997	492	15	1	1	NUM
ejpam-5997	492	16	0	0	PUNCT
ejpam-5997	492	17	℘µn+1(1−	℘µn+1(1−	PROPN
ejpam-5997	492	18	℘)ξ	℘)ξ	NOUN
ejpam-5997	492	19	′	′	NOUN
ejpam-5997	493	1	+	+	NOUN
ejpam-5997	493	2	sd℘+	sd℘+	X
ejpam-5997	493	3	|ϕ′′	|ϕ′′	PRON
ejpam-5997	493	4	(	(	PUNCT
ejpam-5997	493	5	α)|q	α)|q	NOUN
ejpam-5997	493	6	∫	∫	PROPN
ejpam-5997	493	7	1	1	NUM
ejpam-5997	493	8	0	0	NUM
ejpam-5997	493	9	℘µn+s+1(1−	℘µn+s+1(1−	ADJ
ejpam-5997	493	10	℘)ξ	℘)ξ	NOUN
ejpam-5997	493	11	′	′	NOUN
ejpam-5997	493	12	d℘	d℘	NUM
ejpam-5997	493	13	=	=	SYM
ejpam-5997	493	14	|ϕ′′	|ϕ′′	X
ejpam-5997	493	15	(	(	PUNCT
ejpam-5997	493	16	ω)|qβ(µn+	ω)|qβ(µn+	PROPN
ejpam-5997	493	17	2	2	NUM
ejpam-5997	493	18	,	,	PUNCT
ejpam-5997	493	19	ξ	ξ	PROPN
ejpam-5997	493	20	′	′	NUM
ejpam-5997	493	21	+	+	CCONJ
ejpam-5997	493	22	s+	s+	NUM
ejpam-5997	493	23	1	1	X
ejpam-5997	493	24	)	)	PUNCT
ejpam-5997	494	1	+	+	NUM
ejpam-5997	494	2	|ϕ′′	|ϕ′′	PUNCT
ejpam-5997	494	3	|qβ(µn+	|qβ(µn+	CCONJ
ejpam-5997	494	4	s+	s+	X
ejpam-5997	494	5	2	2	NUM
ejpam-5997	494	6	,	,	PUNCT
ejpam-5997	494	7	ξ	ξ	NOUN
ejpam-5997	494	8	′	′	NUM
ejpam-5997	495	1	+	+	CCONJ
ejpam-5997	495	2	1	1	X
ejpam-5997	495	3	)	)	PUNCT
ejpam-5997	495	4	(	(	PUNCT
ejpam-5997	495	5	38	38	NUM
ejpam-5997	495	6	)	)	PUNCT
ejpam-5997	495	7	use	use	NOUN
ejpam-5997	495	8	equations	equation	NOUN
ejpam-5997	495	9	(	(	PUNCT
ejpam-5997	495	10	37	37	NUM
ejpam-5997	495	11	)	)	PUNCT
ejpam-5997	495	12	and	and	CCONJ
ejpam-5997	495	13	(	(	PUNCT
ejpam-5997	495	14	38	38	NUM
ejpam-5997	495	15	)	)	PUNCT
ejpam-5997	495	16	in	in	ADP
ejpam-5997	495	17	(	(	PUNCT
ejpam-5997	495	18	36	36	NUM
ejpam-5997	495	19	)	)	PUNCT
ejpam-5997	495	20	then	then	ADV
ejpam-5997	495	21	we	we	PRON
ejpam-5997	495	22	get	get	VERB
ejpam-5997	495	23	;	;	PUNCT
ejpam-5997	495	24	ℶ	ℶ	X
ejpam-5997	495	25	≤	≤	NOUN
ejpam-5997	496	1	∞∑	∞∑	NUM
ejpam-5997	496	2	n=0	n=0	NUM
ejpam-5997	496	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5997	496	4	βp(ζ	βp(ζ	NUM
ejpam-5997	496	5	+	+	CCONJ
ejpam-5997	496	6	ρn	ρn	INTJ
ejpam-5997	496	7	,	,	PUNCT
ejpam-5997	496	8	c−	c−	NOUN
ejpam-5997	496	9	ζ)(cρn)(κ1)ηn	ζ)(cρn)(κ1)ηn	PROPN
ejpam-5997	496	10	β(ζ	β(ζ	PROPN
ejpam-5997	496	11	,	,	PUNCT
ejpam-5997	496	12	c−	c−	X
ejpam-5997	496	13	ζ)γ(µn+	ζ)γ(µn+	NOUN
ejpam-5997	496	14	ξ	ξ	X
ejpam-5997	497	1	+	+	NUM
ejpam-5997	497	2	1)(ς)mn	1)(ς)mn	NUM
ejpam-5997	497	3	(	(	PUNCT
ejpam-5997	497	4	−κ)n	−κ)n	VERB
ejpam-5997	497	5	∣∣∣∣(α−	∣∣∣∣(α−	PROPN
ejpam-5997	497	6	ω)2	ω)2	X
ejpam-5997	497	7	2	2	NUM
ejpam-5997	497	8	[	[	X
ejpam-5997	497	9	(	(	PUNCT
ejpam-5997	497	10	ξ	ξ	NOUN
ejpam-5997	497	11	′	′	NUM
ejpam-5997	497	12	(	(	PUNCT
ejpam-5997	497	13	µn+	µn+	ADJ
ejpam-5997	497	14	2)(ξ′	2)(ξ′	NUM
ejpam-5997	497	15	+	+	CCONJ
ejpam-5997	497	16	µn+	µn+	ADJ
ejpam-5997	497	17	2	2	NUM
ejpam-5997	497	18	)	)	PUNCT
ejpam-5997	497	19	)	)	PUNCT
ejpam-5997	498	1	1−	1−	NUM
ejpam-5997	498	2	1	1	NUM
ejpam-5997	498	3	q	q	NOUN
ejpam-5997	498	4	×	×	NOUN
ejpam-5997	498	5	{	{	PUNCT
ejpam-5997	498	6	(	(	PUNCT
ejpam-5997	498	7	|ϕ′′	|ϕ′′	X
ejpam-5997	498	8	(	(	PUNCT
ejpam-5997	498	9	ω)|qβ(µn+	ω)|qβ(µn+	NOUN
ejpam-5997	498	10	s+	s+	PUNCT
ejpam-5997	498	11	2	2	NUM
ejpam-5997	498	12	,	,	PUNCT
ejpam-5997	498	13	ξ	ξ	NOUN
ejpam-5997	498	14	′	′	NUM
ejpam-5997	499	1	+	+	CCONJ
ejpam-5997	499	2	1	1	X
ejpam-5997	499	3	)	)	PUNCT
ejpam-5997	499	4	+	+	CCONJ
ejpam-5997	499	5	|ϕ′′	|ϕ′′	PRON
ejpam-5997	499	6	|q(α)β(µn+	|q(α)β(µn+	ADV
ejpam-5997	499	7	2	2	NUM
ejpam-5997	499	8	,	,	PUNCT
ejpam-5997	499	9	ξ	ξ	NOUN
ejpam-5997	499	10	′	′	NUM
ejpam-5997	500	1	+	+	CCONJ
ejpam-5997	500	2	s+	s+	NUM
ejpam-5997	500	3	1	1	NUM
ejpam-5997	500	4	)	)	PUNCT
ejpam-5997	500	5	)	)	PUNCT
ejpam-5997	501	1	1	1	NUM
ejpam-5997	501	2	q	q	NOUN
ejpam-5997	501	3	+	+	PROPN
ejpam-5997	501	4	(	(	PUNCT
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ejpam-5997	501	6	(	(	PUNCT
ejpam-5997	501	7	ω)|qβ(µn+	ω)|qβ(µn+	PROPN
ejpam-5997	501	8	2	2	NUM
ejpam-5997	501	9	,	,	PUNCT
ejpam-5997	501	10	ξ	ξ	PROPN
ejpam-5997	501	11	′	′	NUM
ejpam-5997	502	1	+	+	CCONJ
ejpam-5997	502	2	s+	s+	NUM
ejpam-5997	502	3	1	1	X
ejpam-5997	502	4	)	)	PUNCT
ejpam-5997	503	1	+	+	NUM
ejpam-5997	503	2	|ϕ′′	|ϕ′′	PUNCT
ejpam-5997	503	3	|qβ(µn+	|qβ(µn+	CCONJ
ejpam-5997	503	4	s+	s+	X
ejpam-5997	503	5	2	2	NUM
ejpam-5997	503	6	,	,	PUNCT
ejpam-5997	503	7	ξ	ξ	NOUN
ejpam-5997	503	8	′	′	NUM
ejpam-5997	504	1	+	+	CCONJ
ejpam-5997	504	2	1	1	NUM
ejpam-5997	504	3	)	)	PUNCT
ejpam-5997	504	4	)	)	PUNCT
ejpam-5997	505	1	1	1	NUM
ejpam-5997	505	2	q	q	NOUN
ejpam-5997	505	3	}	}	PUNCT
ejpam-5997	505	4	]	]	PUNCT
ejpam-5997	505	5	the	the	DET
ejpam-5997	505	6	proof	proof	NOUN
ejpam-5997	505	7	is	be	AUX
ejpam-5997	505	8	completed	complete	VERB
ejpam-5997	505	9	.	.	PUNCT
ejpam-5997	506	1	corollary	corollary	ADJ
ejpam-5997	506	2	9	9	NUM
ejpam-5997	506	3	.	.	PUNCT
ejpam-5997	507	1	if	if	SCONJ
ejpam-5997	507	2	we	we	PRON
ejpam-5997	507	3	replace	replace	VERB
ejpam-5997	507	4	p	p	NOUN
ejpam-5997	507	5	=	=	NOUN
ejpam-5997	507	6	0	0	NUM
ejpam-5997	507	7	,	,	PUNCT
ejpam-5997	507	8	κ	κ	X
ejpam-5997	507	9	=	=	SYM
ejpam-5997	507	10	0	0	NUM
ejpam-5997	507	11	,	,	PUNCT
ejpam-5997	507	12	and	and	CCONJ
ejpam-5997	507	13	ξ	ξ	X
ejpam-5997	507	14	=	=	SYM
ejpam-5997	507	15	ξ	ξ	PROPN
ejpam-5997	507	16	−	−	PROPN
ejpam-5997	507	17	1	1	NUM
ejpam-5997	507	18	in	in	ADP
ejpam-5997	507	19	theorem	theorem	NOUN
ejpam-5997	507	20	(	(	PUNCT
ejpam-5997	507	21	7	7	NUM
ejpam-5997	507	22	)	)	PUNCT
ejpam-5997	507	23	,	,	PUNCT
ejpam-5997	507	24	we	we	PRON
ejpam-5997	507	25	have	have	VERB
ejpam-5997	507	26	a	a	DET
ejpam-5997	507	27	result	result	NOUN
ejpam-5997	507	28	[	[	X
ejpam-5997	507	29	19	19	NUM
ejpam-5997	507	30	]	]	PUNCT
ejpam-5997	507	31	.	.	PUNCT
ejpam-5997	508	1	5	5	X
ejpam-5997	508	2	.	.	X
ejpam-5997	508	3	conclusion	conclusion	NOUN
ejpam-5997	508	4	this	this	DET
ejpam-5997	508	5	study	study	NOUN
ejpam-5997	508	6	introduced	introduce	VERB
ejpam-5997	508	7	two	two	NUM
ejpam-5997	508	8	innovative	innovative	ADJ
ejpam-5997	508	9	approaches	approach	NOUN
ejpam-5997	508	10	to	to	ADP
ejpam-5997	508	11	proving	prove	VERB
ejpam-5997	508	12	hermite	hermite	ADJ
ejpam-5997	508	13	-	-	PUNCT
ejpam-5997	508	14	hadamard	hadamard	ADJ
ejpam-5997	508	15	type	type	NOUN
ejpam-5997	508	16	inequalities	inequality	NOUN
ejpam-5997	508	17	using	use	VERB
ejpam-5997	508	18	the	the	DET
ejpam-5997	508	19	extended	extended	ADJ
ejpam-5997	508	20	bessel	bessel	NOUN
ejpam-5997	508	21	-	-	PUNCT
ejpam-5997	508	22	maitland	maitland	NOUN
ejpam-5997	508	23	function	function	NOUN
ejpam-5997	508	24	as	as	ADP
ejpam-5997	508	25	a	a	DET
ejpam-5997	508	26	kernel	kernel	NOUN
ejpam-5997	508	27	within	within	ADP
ejpam-5997	508	28	the	the	DET
ejpam-5997	508	29	framework	framework	NOUN
ejpam-5997	508	30	of	of	ADP
ejpam-5997	508	31	s	s	NOUN
ejpam-5997	508	32	-	-	PUNCT
ejpam-5997	508	33	convex	convex	NOUN
ejpam-5997	508	34	functions	function	NOUN
ejpam-5997	508	35	.	.	PUNCT
ejpam-5997	509	1	the	the	DET
ejpam-5997	509	2	first	first	ADJ
ejpam-5997	509	3	approach	approach	NOUN
ejpam-5997	509	4	used	use	VERB
ejpam-5997	509	5	differentiable	differentiable	ADJ
ejpam-5997	509	6	functions	function	NOUN
ejpam-5997	509	7	and	and	CCONJ
ejpam-5997	509	8	their	their	PRON
ejpam-5997	509	9	m.	m.	NOUN
ejpam-5997	509	10	vivas	vivas	PROPN
ejpam-5997	509	11	-	-	PROPN
ejpam-5997	509	12	cortez	cortez	PROPN
ejpam-5997	509	13	et	et	PROPN
ejpam-5997	509	14	al	al	PROPN
ejpam-5997	509	15	.	.	PUNCT
ejpam-5997	509	16	/	/	SYM
ejpam-5997	509	17	eur	eur	PROPN
ejpam-5997	509	18	.	.	PUNCT
ejpam-5997	510	1	j.	j.	PROPN
ejpam-5997	510	2	pure	pure	PROPN
ejpam-5997	510	3	appl	appl	PROPN
ejpam-5997	510	4	.	.	PROPN
ejpam-5997	510	5	math	math	PROPN
ejpam-5997	510	6	,	,	PUNCT
ejpam-5997	510	7	18	18	NUM
ejpam-5997	510	8	(	(	PUNCT
ejpam-5997	510	9	2	2	NUM
ejpam-5997	510	10	)	)	PUNCT
ejpam-5997	510	11	(	(	PUNCT
ejpam-5997	510	12	2025	2025	NUM
ejpam-5997	510	13	)	)	PUNCT
ejpam-5997	510	14	,	,	PUNCT
ejpam-5997	510	15	5997	5997	NUM
ejpam-5997	510	16	20	20	NUM
ejpam-5997	510	17	of	of	ADP
ejpam-5997	510	18	23	23	NUM
ejpam-5997	510	19	first	first	ADJ
ejpam-5997	510	20	derivatives	derivative	NOUN
ejpam-5997	510	21	to	to	PART
ejpam-5997	510	22	derive	derive	VERB
ejpam-5997	510	23	a	a	DET
ejpam-5997	510	24	key	key	ADJ
ejpam-5997	510	25	identity	identity	NOUN
ejpam-5997	510	26	that	that	PRON
ejpam-5997	510	27	serves	serve	VERB
ejpam-5997	510	28	as	as	ADP
ejpam-5997	510	29	the	the	DET
ejpam-5997	510	30	basis	basis	NOUN
ejpam-5997	510	31	for	for	ADP
ejpam-5997	510	32	establishing	establish	VERB
ejpam-5997	510	33	these	these	DET
ejpam-5997	510	34	inequalities	inequality	NOUN
ejpam-5997	510	35	.	.	PUNCT
ejpam-5997	511	1	taking	take	VERB
ejpam-5997	511	2	a	a	DET
ejpam-5997	511	3	more	more	ADV
ejpam-5997	511	4	comprehensive	comprehensive	ADJ
ejpam-5997	511	5	perspective	perspective	NOUN
ejpam-5997	511	6	,	,	PUNCT
ejpam-5997	511	7	the	the	DET
ejpam-5997	511	8	second	second	ADJ
ejpam-5997	511	9	approach	approach	NOUN
ejpam-5997	511	10	employs	employ	VERB
ejpam-5997	511	11	the	the	DET
ejpam-5997	511	12	integral	integral	NOUN
ejpam-5997	511	13	of	of	ADP
ejpam-5997	511	14	a	a	DET
ejpam-5997	511	15	second	second	ADJ
ejpam-5997	511	16	derivative	derivative	NOUN
ejpam-5997	511	17	as	as	ADP
ejpam-5997	511	18	an	an	DET
ejpam-5997	511	19	alternative	alternative	NOUN
ejpam-5997	511	20	,	,	PUNCT
ejpam-5997	511	21	yet	yet	CCONJ
ejpam-5997	511	22	equally	equally	ADV
ejpam-5997	511	23	effective	effective	ADJ
ejpam-5997	511	24	,	,	PUNCT
ejpam-5997	511	25	way	way	NOUN
ejpam-5997	511	26	to	to	PART
ejpam-5997	511	27	establish	establish	VERB
ejpam-5997	511	28	the	the	DET
ejpam-5997	511	29	fundamental	fundamental	ADJ
ejpam-5997	511	30	identity	identity	NOUN
ejpam-5997	511	31	.	.	PUNCT
ejpam-5997	512	1	beyond	beyond	ADP
ejpam-5997	512	2	proving	prove	VERB
ejpam-5997	512	3	these	these	DET
ejpam-5997	512	4	inequalities	inequality	NOUN
ejpam-5997	512	5	,	,	PUNCT
ejpam-5997	512	6	we	we	PRON
ejpam-5997	512	7	explore	explore	VERB
ejpam-5997	512	8	various	various	ADJ
ejpam-5997	512	9	applications	application	NOUN
ejpam-5997	512	10	,	,	PUNCT
ejpam-5997	512	11	particularly	particularly	ADV
ejpam-5997	512	12	in	in	ADP
ejpam-5997	512	13	relation	relation	NOUN
ejpam-5997	512	14	to	to	ADP
ejpam-5997	512	15	different	different	ADJ
ejpam-5997	512	16	types	type	NOUN
ejpam-5997	512	17	of	of	ADP
ejpam-5997	512	18	means	mean	NOUN
ejpam-5997	512	19	.	.	PUNCT
ejpam-5997	513	1	furthermore	furthermore	ADV
ejpam-5997	513	2	,	,	PUNCT
ejpam-5997	513	3	this	this	DET
ejpam-5997	513	4	approach	approach	NOUN
ejpam-5997	513	5	can	can	AUX
ejpam-5997	513	6	be	be	AUX
ejpam-5997	513	7	extended	extend	VERB
ejpam-5997	513	8	to	to	ADP
ejpam-5997	513	9	other	other	ADJ
ejpam-5997	513	10	classes	class	NOUN
ejpam-5997	513	11	of	of	ADP
ejpam-5997	513	12	convex	convex	NOUN
ejpam-5997	513	13	functions	function	NOUN
ejpam-5997	513	14	,	,	PUNCT
ejpam-5997	513	15	which	which	PRON
ejpam-5997	513	16	enhances	enhance	VERB
ejpam-5997	513	17	its	its	PRON
ejpam-5997	513	18	broader	broad	ADJ
ejpam-5997	513	19	mathematical	mathematical	ADJ
ejpam-5997	513	20	significance	significance	NOUN
ejpam-5997	513	21	.	.	PUNCT
ejpam-5997	514	1	ultimately	ultimately	ADV
ejpam-5997	514	2	,	,	PUNCT
ejpam-5997	514	3	this	this	DET
ejpam-5997	514	4	study	study	NOUN
ejpam-5997	514	5	deepens	deepen	VERB
ejpam-5997	514	6	the	the	DET
ejpam-5997	514	7	understanding	understanding	NOUN
ejpam-5997	514	8	of	of	ADP
ejpam-5997	514	9	convexity	convexity	NOUN
ejpam-5997	514	10	-	-	PUNCT
ejpam-5997	514	11	based	base	VERB
ejpam-5997	514	12	inequalities	inequality	NOUN
ejpam-5997	514	13	and	and	CCONJ
ejpam-5997	514	14	paves	pave	VERB
ejpam-5997	514	15	the	the	DET
ejpam-5997	514	16	way	way	NOUN
ejpam-5997	514	17	for	for	ADP
ejpam-5997	514	18	further	further	ADJ
ejpam-5997	514	19	research	research	NOUN
ejpam-5997	514	20	in	in	ADP
ejpam-5997	514	21	mathematical	mathematical	ADJ
ejpam-5997	514	22	analysis	analysis	NOUN
ejpam-5997	514	23	.	.	PUNCT
ejpam-5997	515	1	acknowledgements	acknowledgement	NOUN
ejpam-5997	515	2	the	the	DET
ejpam-5997	515	3	authors	author	NOUN
ejpam-5997	515	4	extend	extend	VERB
ejpam-5997	515	5	their	their	PRON
ejpam-5997	515	6	appreciation	appreciation	NOUN
ejpam-5997	515	7	to	to	ADP
ejpam-5997	515	8	the	the	DET
ejpam-5997	515	9	deanship	deanship	NOUN
ejpam-5997	515	10	of	of	ADP
ejpam-5997	515	11	research	research	NOUN
ejpam-5997	515	12	and	and	CCONJ
ejpam-5997	515	13	graduate	graduate	NOUN
ejpam-5997	515	14	studies	study	NOUN
ejpam-5997	515	15	at	at	ADP
ejpam-5997	515	16	king	king	PROPN
ejpam-5997	515	17	khalid	khalid	PROPN
ejpam-5997	515	18	university	university	PROPN
ejpam-5997	515	19	,	,	PUNCT
ejpam-5997	515	20	saudi	saudi	PROPN
ejpam-5997	515	21	arabia	arabia	PROPN
ejpam-5997	515	22	for	for	ADP
ejpam-5997	515	23	funding	fund	VERB
ejpam-5997	515	24	this	this	DET
ejpam-5997	515	25	work	work	NOUN
ejpam-5997	515	26	through	through	ADP
ejpam-5997	515	27	large	large	ADJ
ejpam-5997	515	28	groups	group	NOUN
ejpam-5997	515	29	project	project	NOUN
ejpam-5997	515	30	under	under	ADP
ejpam-5997	515	31	grant	grant	NOUN
ejpam-5997	515	32	number	number	NOUN
ejpam-5997	515	33	r.g.p2/76/46	r.g.p2/76/46	PROPN
ejpam-5997	515	34	.	.	PUNCT
ejpam-5997	516	1	availability	availability	NOUN
ejpam-5997	516	2	of	of	ADP
ejpam-5997	516	3	data	datum	NOUN
ejpam-5997	516	4	and	and	CCONJ
ejpam-5997	516	5	material	material	NOUN
ejpam-5997	516	6	data	datum	NOUN
ejpam-5997	516	7	sharing	sharing	NOUN
ejpam-5997	516	8	is	be	AUX
ejpam-5997	516	9	not	not	PART
ejpam-5997	516	10	applicable	applicable	ADJ
ejpam-5997	516	11	to	to	ADP
ejpam-5997	516	12	this	this	DET
ejpam-5997	516	13	paper	paper	NOUN
ejpam-5997	516	14	as	as	SCONJ
ejpam-5997	516	15	no	no	DET
ejpam-5997	516	16	datasets	dataset	NOUN
ejpam-5997	516	17	were	be	AUX
ejpam-5997	516	18	generated	generate	VERB
ejpam-5997	516	19	or	or	CCONJ
ejpam-5997	516	20	analyzed	analyze	VERB
ejpam-5997	516	21	during	during	ADP
ejpam-5997	516	22	218	218	NUM
ejpam-5997	516	23	the	the	DET
ejpam-5997	516	24	current	current	ADJ
ejpam-5997	516	25	study	study	NOUN
ejpam-5997	516	26	.	.	PUNCT
ejpam-5997	517	1	competing	compete	VERB
ejpam-5997	517	2	interests	interest	NOUN
ejpam-5997	517	3	the	the	DET
ejpam-5997	517	4	authors	author	NOUN
ejpam-5997	517	5	declare	declare	VERB
ejpam-5997	517	6	that	that	SCONJ
ejpam-5997	517	7	there	there	PRON
ejpam-5997	517	8	is	be	VERB
ejpam-5997	517	9	no	no	DET
ejpam-5997	517	10	conflict	conflict	NOUN
ejpam-5997	517	11	of	of	ADP
ejpam-5997	517	12	interest	interest	NOUN
ejpam-5997	517	13	regarding	regard	VERB
ejpam-5997	517	14	the	the	DET
ejpam-5997	517	15	publication	publication	NOUN
ejpam-5997	517	16	of	of	ADP
ejpam-5997	517	17	this	this	DET
ejpam-5997	517	18	article	article	NOUN
ejpam-5997	517	19	.	.	PUNCT
ejpam-5997	518	1	author	author	PROPN
ejpam-5997	518	2	’s	’s	PART
ejpam-5997	518	3	contributions	contribution	NOUN
ejpam-5997	518	4	all	all	DET
ejpam-5997	518	5	authors	author	NOUN
ejpam-5997	518	6	contributed	contribute	VERB
ejpam-5997	518	7	equally	equally	ADV
ejpam-5997	518	8	to	to	ADP
ejpam-5997	518	9	this	this	DET
ejpam-5997	518	10	manuscript	manuscript	NOUN
ejpam-5997	518	11	.	.	PUNCT
ejpam-5997	519	1	all	all	DET
ejpam-5997	519	2	authors	author	NOUN
ejpam-5997	519	3	read	read	VERB
ejpam-5997	519	4	and	and	CCONJ
ejpam-5997	519	5	approved	approve	VERB
ejpam-5997	519	6	the	the	DET
ejpam-5997	519	7	final	final	ADJ
ejpam-5997	519	8	manuscript	manuscript	NOUN
ejpam-5997	519	9	.	.	PUNCT
ejpam-5997	520	1	references	reference	NOUN
ejpam-5997	520	2	[	[	X
ejpam-5997	520	3	1	1	NUM
ejpam-5997	520	4	]	]	PUNCT
ejpam-5997	520	5	rudolf	rudolf	NOUN
ejpam-5997	520	6	gorenflo	gorenflo	NOUN
ejpam-5997	520	7	and	and	CCONJ
ejpam-5997	520	8	francesco	francesco	PROPN
ejpam-5997	520	9	mainardi	mainardi	PROPN
ejpam-5997	520	10	.	.	PUNCT
ejpam-5997	521	1	fractional	fractional	ADJ
ejpam-5997	521	2	calculus	calculus	NOUN
ejpam-5997	521	3	:	:	PUNCT
ejpam-5997	521	4	integral	integral	ADJ
ejpam-5997	521	5	and	and	CCONJ
ejpam-5997	521	6	differential	differential	ADJ
ejpam-5997	521	7	equations	equation	NOUN
ejpam-5997	521	8	of	of	ADP
ejpam-5997	521	9	fractional	fractional	ADJ
ejpam-5997	521	10	order	order	NOUN
ejpam-5997	521	11	.	.	PUNCT
ejpam-5997	522	1	springer	springer	NOUN
ejpam-5997	522	2	,	,	PUNCT
ejpam-5997	522	3	1997	1997	NUM
ejpam-5997	522	4	.	.	PUNCT
ejpam-5997	523	1	[	[	X
ejpam-5997	523	2	2	2	NUM
ejpam-5997	523	3	]	]	PUNCT
ejpam-5997	523	4	sunil	sunil	PROPN
ejpam-5997	523	5	kumar	kumar	PROPN
ejpam-5997	523	6	,	,	PUNCT
ejpam-5997	523	7	kottakkaran	kottakkaran	VERB
ejpam-5997	523	8	sooppy	sooppy	ADJ
ejpam-5997	523	9	nisar	nisar	PROPN
ejpam-5997	523	10	,	,	PUNCT
ejpam-5997	523	11	ranbir	ranbir	PROPN
ejpam-5997	523	12	kumar	kumar	PROPN
ejpam-5997	523	13	,	,	PUNCT
ejpam-5997	523	14	carlo	carlo	PROPN
ejpam-5997	523	15	cattani	cattani	PROPN
ejpam-5997	523	16	,	,	PUNCT
ejpam-5997	523	17	and	and	CCONJ
ejpam-5997	523	18	bessem	bessem	NOUN
ejpam-5997	523	19	samet	samet	NOUN
ejpam-5997	523	20	.	.	PUNCT
ejpam-5997	524	1	a	a	DET
ejpam-5997	524	2	new	new	ADJ
ejpam-5997	524	3	rabotnov	rabotnov	NOUN
ejpam-5997	524	4	fractional	fractional	ADJ
ejpam-5997	524	5	-	-	PUNCT
ejpam-5997	524	6	exponential	exponential	ADJ
ejpam-5997	524	7	function	function	NOUN
ejpam-5997	524	8	-	-	PUNCT
ejpam-5997	524	9	based	base	VERB
ejpam-5997	524	10	fractional	fractional	ADJ
ejpam-5997	524	11	derivative	derivative	NOUN
ejpam-5997	524	12	for	for	ADP
ejpam-5997	524	13	diffusion	diffusion	NOUN
ejpam-5997	524	14	equation	equation	NOUN
ejpam-5997	524	15	under	under	ADP
ejpam-5997	524	16	external	external	ADJ
ejpam-5997	524	17	force	force	NOUN
ejpam-5997	524	18	.	.	PUNCT
ejpam-5997	525	1	mathematical	mathematical	ADJ
ejpam-5997	525	2	methods	method	NOUN
ejpam-5997	525	3	in	in	ADP
ejpam-5997	525	4	the	the	DET
ejpam-5997	525	5	applied	apply	VERB
ejpam-5997	525	6	sciences	science	NOUN
ejpam-5997	525	7	,	,	PUNCT
ejpam-5997	525	8	43(7):4460–4471	43(7):4460–4471	NUM
ejpam-5997	525	9	,	,	PUNCT
ejpam-5997	525	10	2020	2020	NUM
ejpam-5997	525	11	.	.	PUNCT
ejpam-5997	526	1	[	[	X
ejpam-5997	526	2	3	3	NUM
ejpam-5997	526	3	]	]	X
ejpam-5997	526	4	behzad	behzad	PROPN
ejpam-5997	526	5	ghanbari	ghanbari	PROPN
ejpam-5997	526	6	,	,	PUNCT
ejpam-5997	526	7	sunil	sunil	PROPN
ejpam-5997	526	8	kumar	kumar	PROPN
ejpam-5997	526	9	,	,	PUNCT
ejpam-5997	526	10	and	and	CCONJ
ejpam-5997	526	11	ranbir	ranbir	PROPN
ejpam-5997	526	12	kumar	kumar	PROPN
ejpam-5997	526	13	.	.	PUNCT
ejpam-5997	527	1	a	a	DET
ejpam-5997	527	2	study	study	NOUN
ejpam-5997	527	3	of	of	ADP
ejpam-5997	527	4	behaviour	behaviour	NOUN
ejpam-5997	527	5	for	for	ADP
ejpam-5997	527	6	immune	immune	ADJ
ejpam-5997	527	7	and	and	CCONJ
ejpam-5997	527	8	tumor	tumor	NOUN
ejpam-5997	527	9	cells	cell	NOUN
ejpam-5997	527	10	in	in	ADP
ejpam-5997	527	11	immunogenetic	immunogenetic	ADJ
ejpam-5997	527	12	tumour	tumour	NOUN
ejpam-5997	527	13	model	model	NOUN
ejpam-5997	527	14	with	with	ADP
ejpam-5997	527	15	non	non	ADJ
ejpam-5997	527	16	-	-	ADJ
ejpam-5997	527	17	singular	singular	ADJ
ejpam-5997	527	18	fractional	fractional	ADJ
ejpam-5997	527	19	derivative	derivative	NOUN
ejpam-5997	527	20	.	.	PUNCT
ejpam-5997	528	1	chaos	chaos	NOUN
ejpam-5997	528	2	,	,	PUNCT
ejpam-5997	528	3	solitons	soliton	NOUN
ejpam-5997	528	4	&	&	CCONJ
ejpam-5997	528	5	fractals	fractal	NOUN
ejpam-5997	528	6	,	,	PUNCT
ejpam-5997	528	7	133:109619	133:109619	NUM
ejpam-5997	528	8	,	,	PUNCT
ejpam-5997	528	9	2020	2020	NUM
ejpam-5997	528	10	.	.	PUNCT
ejpam-5997	529	1	m.	m.	NOUN
ejpam-5997	529	2	vivas	vivas	PROPN
ejpam-5997	529	3	-	-	PROPN
ejpam-5997	529	4	cortez	cortez	PROPN
ejpam-5997	529	5	et	et	PROPN
ejpam-5997	529	6	al	al	PROPN
ejpam-5997	529	7	.	.	PUNCT
ejpam-5997	529	8	/	/	SYM
ejpam-5997	529	9	eur	eur	PROPN
ejpam-5997	529	10	.	.	PUNCT
ejpam-5997	530	1	j.	j.	PROPN
ejpam-5997	530	2	pure	pure	PROPN
ejpam-5997	530	3	appl	appl	PROPN
ejpam-5997	530	4	.	.	PROPN
ejpam-5997	530	5	math	math	PROPN
ejpam-5997	530	6	,	,	PUNCT
ejpam-5997	530	7	18	18	NUM
ejpam-5997	530	8	(	(	PUNCT
ejpam-5997	530	9	2	2	NUM
ejpam-5997	530	10	)	)	PUNCT
ejpam-5997	530	11	(	(	PUNCT
ejpam-5997	530	12	2025	2025	NUM
ejpam-5997	530	13	)	)	PUNCT
ejpam-5997	530	14	,	,	PUNCT
ejpam-5997	530	15	5997	5997	NUM
ejpam-5997	530	16	21	21	NUM
ejpam-5997	530	17	of	of	ADP
ejpam-5997	530	18	23	23	NUM
ejpam-5997	531	1	[	[	SYM
ejpam-5997	531	2	4	4	NUM
ejpam-5997	531	3	]	]	X
ejpam-5997	531	4	khalid	khalid	PROPN
ejpam-5997	531	5	k	k	PROPN
ejpam-5997	531	6	ali	ali	PROPN
ejpam-5997	531	7	,	,	PUNCT
ejpam-5997	531	8	mohamed	mohame	VERB
ejpam-5997	531	9	a	a	DET
ejpam-5997	531	10	abd	abd	PROPN
ejpam-5997	531	11	el	el	PROPN
ejpam-5997	531	12	salam	salam	PROPN
ejpam-5997	531	13	,	,	PUNCT
ejpam-5997	531	14	emad	emad	PROPN
ejpam-5997	531	15	mh	mh	PROPN
ejpam-5997	531	16	mohamed	mohamed	PROPN
ejpam-5997	531	17	,	,	PUNCT
ejpam-5997	531	18	bessem	bessem	NOUN
ejpam-5997	531	19	samet	samet	NOUN
ejpam-5997	531	20	,	,	PUNCT
ejpam-5997	531	21	sunil	sunil	PROPN
ejpam-5997	531	22	kumar	kumar	PROPN
ejpam-5997	531	23	,	,	PUNCT
ejpam-5997	531	24	and	and	CCONJ
ejpam-5997	531	25	ms	ms	PROPN
ejpam-5997	531	26	osman	osman	PROPN
ejpam-5997	531	27	.	.	PUNCT
ejpam-5997	532	1	numerical	numerical	ADJ
ejpam-5997	532	2	solution	solution	NOUN
ejpam-5997	532	3	for	for	ADP
ejpam-5997	532	4	generalized	generalized	ADJ
ejpam-5997	532	5	nonlinear	nonlinear	ADJ
ejpam-5997	532	6	fractional	fractional	ADJ
ejpam-5997	532	7	integro	integro	ADJ
ejpam-5997	532	8	-	-	PUNCT
ejpam-5997	532	9	differential	differential	NOUN
ejpam-5997	532	10	equations	equation	NOUN
ejpam-5997	532	11	with	with	ADP
ejpam-5997	532	12	linear	linear	ADJ
ejpam-5997	532	13	functional	functional	ADJ
ejpam-5997	532	14	arguments	argument	NOUN
ejpam-5997	532	15	using	use	VERB
ejpam-5997	532	16	chebyshev	chebyshev	PROPN
ejpam-5997	532	17	series	series	NOUN
ejpam-5997	532	18	.	.	PUNCT
ejpam-5997	533	1	advances	advance	NOUN
ejpam-5997	533	2	in	in	ADP
ejpam-5997	533	3	difference	difference	NOUN
ejpam-5997	533	4	equations	equation	NOUN
ejpam-5997	533	5	,	,	PUNCT
ejpam-5997	533	6	2020:1–23	2020:1–23	NUM
ejpam-5997	533	7	,	,	PUNCT
ejpam-5997	533	8	2020	2020	NUM
ejpam-5997	533	9	.	.	PUNCT
ejpam-5997	534	1	[	[	X
ejpam-5997	534	2	5	5	NUM
ejpam-5997	534	3	]	]	PUNCT
ejpam-5997	534	4	sunil	sunil	PROPN
ejpam-5997	534	5	kumar	kumar	PROPN
ejpam-5997	534	6	,	,	PUNCT
ejpam-5997	534	7	surath	surath	PROPN
ejpam-5997	534	8	ghosh	ghosh	PROPN
ejpam-5997	534	9	,	,	PUNCT
ejpam-5997	534	10	mansour	mansour	PROPN
ejpam-5997	534	11	sm	sm	PROPN
ejpam-5997	534	12	lotayif	lotayif	PROPN
ejpam-5997	534	13	,	,	PUNCT
ejpam-5997	534	14	and	and	CCONJ
ejpam-5997	534	15	bessem	bessem	NOUN
ejpam-5997	534	16	samet	samet	NOUN
ejpam-5997	534	17	.	.	PUNCT
ejpam-5997	535	1	a	a	DET
ejpam-5997	535	2	model	model	NOUN
ejpam-5997	535	3	for	for	ADP
ejpam-5997	535	4	describing	describe	VERB
ejpam-5997	535	5	the	the	DET
ejpam-5997	535	6	velocity	velocity	NOUN
ejpam-5997	535	7	of	of	ADP
ejpam-5997	535	8	a	a	DET
ejpam-5997	535	9	particle	particle	NOUN
ejpam-5997	535	10	in	in	ADP
ejpam-5997	535	11	brownian	brownian	ADJ
ejpam-5997	535	12	motion	motion	NOUN
ejpam-5997	535	13	by	by	ADP
ejpam-5997	535	14	robotnov	robotnov	PROPN
ejpam-5997	535	15	function	function	PROPN
ejpam-5997	535	16	based	base	VERB
ejpam-5997	535	17	fractional	fractional	ADJ
ejpam-5997	535	18	operator	operator	NOUN
ejpam-5997	535	19	.	.	PUNCT
ejpam-5997	536	1	alexandria	alexandria	PROPN
ejpam-5997	536	2	engineering	engineering	PROPN
ejpam-5997	536	3	journal	journal	PROPN
ejpam-5997	536	4	,	,	PUNCT
ejpam-5997	536	5	59(3):1435–1449	59(3):1435–1449	PROPN
ejpam-5997	536	6	,	,	PUNCT
ejpam-5997	536	7	2020	2020	NUM
ejpam-5997	536	8	.	.	PUNCT
ejpam-5997	537	1	[	[	X
ejpam-5997	537	2	6	6	X
ejpam-5997	537	3	]	]	X
ejpam-5997	537	4	gauhar	gauhar	PROPN
ejpam-5997	537	5	rahman	rahman	PROPN
ejpam-5997	537	6	,	,	PUNCT
ejpam-5997	537	7	kottakkaran	kottakkaran	VERB
ejpam-5997	537	8	sooppy	sooppy	ADJ
ejpam-5997	537	9	nisar	nisar	PROPN
ejpam-5997	537	10	,	,	PUNCT
ejpam-5997	537	11	thabet	thabet	ADJ
ejpam-5997	537	12	abdeljawad	abdeljawad	NOUN
ejpam-5997	537	13	,	,	PUNCT
ejpam-5997	537	14	and	and	CCONJ
ejpam-5997	537	15	muhammad	muhammad	PROPN
ejpam-5997	537	16	samraiz	samraiz	PROPN
ejpam-5997	537	17	.	.	PUNCT
ejpam-5997	538	1	some	some	DET
ejpam-5997	538	2	new	new	ADJ
ejpam-5997	538	3	tempered	temper	VERB
ejpam-5997	538	4	fractional	fractional	ADJ
ejpam-5997	538	5	pólya	pólya	ADV
ejpam-5997	538	6	-	-	PUNCT
ejpam-5997	538	7	szegö	szegö	VERB
ejpam-5997	538	8	and	and	CCONJ
ejpam-5997	538	9	chebyshev	chebyshev	NOUN
ejpam-5997	538	10	-	-	PUNCT
ejpam-5997	538	11	type	type	NOUN
ejpam-5997	538	12	inequalities	inequality	NOUN
ejpam-5997	538	13	with	with	ADP
ejpam-5997	538	14	respect	respect	NOUN
ejpam-5997	538	15	to	to	ADP
ejpam-5997	538	16	another	another	DET
ejpam-5997	538	17	function	function	NOUN
ejpam-5997	538	18	.	.	PUNCT
ejpam-5997	539	1	journal	journal	NOUN
ejpam-5997	539	2	of	of	ADP
ejpam-5997	539	3	mathematics	mathematic	NOUN
ejpam-5997	539	4	,	,	PUNCT
ejpam-5997	539	5	2020(1):9858671	2020(1):9858671	NUM
ejpam-5997	539	6	,	,	PUNCT
ejpam-5997	539	7	2020	2020	NUM
ejpam-5997	539	8	.	.	PUNCT
ejpam-5997	540	1	[	[	X
ejpam-5997	540	2	7	7	X
ejpam-5997	540	3	]	]	X
ejpam-5997	540	4	muhammad	muhammad	PROPN
ejpam-5997	540	5	samraiz	samraiz	PROPN
ejpam-5997	540	6	,	,	PUNCT
ejpam-5997	540	7	fakhra	fakhra	ADJ
ejpam-5997	540	8	nawaz	nawaz	NOUN
ejpam-5997	540	9	,	,	PUNCT
ejpam-5997	540	10	sajid	sajid	PROPN
ejpam-5997	540	11	iqbal	iqbal	PROPN
ejpam-5997	540	12	,	,	PUNCT
ejpam-5997	540	13	thabet	thabet	ADJ
ejpam-5997	540	14	abdeljawad	abdeljawad	NOUN
ejpam-5997	540	15	,	,	PUNCT
ejpam-5997	540	16	gauhar	gauhar	PROPN
ejpam-5997	540	17	rahman	rahman	PROPN
ejpam-5997	540	18	,	,	PUNCT
ejpam-5997	540	19	and	and	CCONJ
ejpam-5997	540	20	kottakkaran	kottakkaran	VERB
ejpam-5997	540	21	sooppy	sooppy	ADJ
ejpam-5997	540	22	nisar	nisar	PROPN
ejpam-5997	540	23	.	.	PUNCT
ejpam-5997	541	1	certain	certain	ADJ
ejpam-5997	541	2	mean	mean	ADJ
ejpam-5997	541	3	-	-	PUNCT
ejpam-5997	541	4	type	type	NOUN
ejpam-5997	541	5	fractional	fractional	ADJ
ejpam-5997	541	6	integral	integral	ADJ
ejpam-5997	541	7	inequalities	inequality	NOUN
ejpam-5997	541	8	via	via	ADP
ejpam-5997	541	9	different	different	ADJ
ejpam-5997	541	10	convexities	convexity	NOUN
ejpam-5997	541	11	with	with	ADP
ejpam-5997	541	12	applications	application	NOUN
ejpam-5997	541	13	.	.	PUNCT
ejpam-5997	542	1	journal	journal	PROPN
ejpam-5997	542	2	of	of	ADP
ejpam-5997	542	3	inequalities	inequality	NOUN
ejpam-5997	542	4	and	and	CCONJ
ejpam-5997	542	5	applications	application	NOUN
ejpam-5997	542	6	,	,	PUNCT
ejpam-5997	542	7	2020(1):208	2020(1):208	NUM
ejpam-5997	542	8	,	,	PUNCT
ejpam-5997	542	9	2020	2020	NUM
ejpam-5997	542	10	.	.	PUNCT
ejpam-5997	543	1	[	[	X
ejpam-5997	543	2	8	8	NUM
ejpam-5997	543	3	]	]	X
ejpam-5997	543	4	miguel	miguel	PROPN
ejpam-5997	543	5	vivas	vivas	PROPN
ejpam-5997	543	6	-	-	PROPN
ejpam-5997	543	7	cortez	cortez	PROPN
ejpam-5997	543	8	,	,	PUNCT
ejpam-5997	543	9	muhammad	muhammad	PROPN
ejpam-5997	543	10	aamir	aamir	PROPN
ejpam-5997	543	11	ali	ali	PROPN
ejpam-5997	543	12	,	,	PUNCT
ejpam-5997	543	13	artion	artion	NOUN
ejpam-5997	543	14	kashuri	kashuri	PROPN
ejpam-5997	543	15	,	,	PUNCT
ejpam-5997	543	16	and	and	CCONJ
ejpam-5997	543	17	hüseyin	hüseyin	PROPN
ejpam-5997	543	18	budak	budak	PROPN
ejpam-5997	543	19	.	.	PUNCT
ejpam-5997	544	1	generalizations	generalization	NOUN
ejpam-5997	544	2	of	of	ADP
ejpam-5997	544	3	fractional	fractional	ADJ
ejpam-5997	544	4	hermite	hermite	ADJ
ejpam-5997	544	5	-	-	PUNCT
ejpam-5997	544	6	hadamard	hadamard	NOUN
ejpam-5997	544	7	-	-	PUNCT
ejpam-5997	544	8	mercer	mercer	NOUN
ejpam-5997	544	9	like	like	ADP
ejpam-5997	544	10	inequalities	inequality	NOUN
ejpam-5997	544	11	for	for	ADP
ejpam-5997	544	12	convex	convex	NOUN
ejpam-5997	544	13	functions	function	NOUN
ejpam-5997	544	14	.	.	PUNCT
ejpam-5997	545	1	aims	aim	VERB
ejpam-5997	545	2	math	math	NOUN
ejpam-5997	545	3	,	,	PUNCT
ejpam-5997	545	4	6(9):9397–9421	6(9):9397–9421	PROPN
ejpam-5997	545	5	,	,	PUNCT
ejpam-5997	545	6	2021	2021	NUM
ejpam-5997	545	7	.	.	PUNCT
ejpam-5997	546	1	[	[	X
ejpam-5997	546	2	9	9	NUM
ejpam-5997	546	3	]	]	PUNCT
ejpam-5997	546	4	tilak	tilak	PROPN
ejpam-5997	546	5	raj	raj	PROPN
ejpam-5997	546	6	prabhakar	prabhakar	PROPN
ejpam-5997	546	7	.	.	PUNCT
ejpam-5997	547	1	a	a	DET
ejpam-5997	547	2	singular	singular	ADJ
ejpam-5997	547	3	integral	integral	ADJ
ejpam-5997	547	4	equation	equation	NOUN
ejpam-5997	547	5	with	with	ADP
ejpam-5997	547	6	a	a	DET
ejpam-5997	547	7	generalized	generalize	VERB
ejpam-5997	547	8	mittag	mittag	ADJ
ejpam-5997	547	9	leffler	leffl	ADJ
ejpam-5997	547	10	function	function	NOUN
ejpam-5997	547	11	in	in	ADP
ejpam-5997	547	12	the	the	DET
ejpam-5997	547	13	kernel	kernel	NOUN
ejpam-5997	547	14	.	.	PUNCT
ejpam-5997	548	1	yokohama	yokohama	PROPN
ejpam-5997	548	2	mathematical	mathematical	PROPN
ejpam-5997	548	3	journal=	journal=	NUM
ejpam-5997	548	4	.	.	PUNCT
ejpam-5997	549	1	d	d	X
ejpam-5997	549	2	,	,	PUNCT
ejpam-5997	549	3	,	,	PUNCT
ejpam-5997	549	4	19(1):7–15	19(1):7–15	NUM
ejpam-5997	549	5	,	,	PUNCT
ejpam-5997	549	6	1971	1971	NUM
ejpam-5997	549	7	.	.	PUNCT
ejpam-5997	550	1	[	[	X
ejpam-5997	550	2	10	10	NUM
ejpam-5997	550	3	]	]	X
ejpam-5997	550	4	hasan	hasan	PROPN
ejpam-5997	550	5	barsam	barsam	PROPN
ejpam-5997	550	6	,	,	PUNCT
ejpam-5997	550	7	sayyed	sayyed	PROPN
ejpam-5997	550	8	mehrab	mehrab	PROPN
ejpam-5997	550	9	ramezani	ramezani	PROPN
ejpam-5997	550	10	,	,	PUNCT
ejpam-5997	550	11	and	and	CCONJ
ejpam-5997	550	12	yamin	yamin	PROPN
ejpam-5997	550	13	sayyari	sayyari	PROPN
ejpam-5997	550	14	.	.	PUNCT
ejpam-5997	551	1	on	on	ADP
ejpam-5997	551	2	the	the	DET
ejpam-5997	551	3	new	new	ADJ
ejpam-5997	551	4	hermite	hermite	PROPN
ejpam-5997	551	5	–	–	PUNCT
ejpam-5997	551	6	hadamard	hadamard	ADJ
ejpam-5997	551	7	type	type	NOUN
ejpam-5997	551	8	inequalities	inequality	NOUN
ejpam-5997	551	9	for	for	ADP
ejpam-5997	551	10	s	s	NOUN
ejpam-5997	551	11	-	-	PUNCT
ejpam-5997	551	12	convex	convex	NOUN
ejpam-5997	551	13	functions	function	NOUN
ejpam-5997	551	14	.	.	PUNCT
ejpam-5997	552	1	afrika	afrika	PROPN
ejpam-5997	552	2	matematika	matematika	PROPN
ejpam-5997	552	3	,	,	PUNCT
ejpam-5997	552	4	32(7):1355	32(7):1355	NUM
ejpam-5997	552	5	–	–	PUNCT
ejpam-5997	552	6	1367	1367	NUM
ejpam-5997	552	7	,	,	PUNCT
ejpam-5997	552	8	2021	2021	NUM
ejpam-5997	552	9	.	.	PUNCT
ejpam-5997	553	1	[	[	X
ejpam-5997	553	2	11	11	NUM
ejpam-5997	553	3	]	]	PUNCT
ejpam-5997	553	4	h	h	NOUN
ejpam-5997	553	5	barsam	barsam	NOUN
ejpam-5997	553	6	and	and	CCONJ
ejpam-5997	553	7	ar	ar	PROPN
ejpam-5997	553	8	sattarzadeh	sattarzadeh	PROPN
ejpam-5997	553	9	.	.	PUNCT
ejpam-5997	554	1	hermite	hermite	PROPN
ejpam-5997	554	2	-	-	PUNCT
ejpam-5997	554	3	hadamard	hadamard	ADJ
ejpam-5997	554	4	inequalities	inequality	NOUN
ejpam-5997	554	5	for	for	ADP
ejpam-5997	554	6	uniformly	uniformly	ADV
ejpam-5997	554	7	convex	convex	NOUN
ejpam-5997	554	8	functions	function	NOUN
ejpam-5997	554	9	and	and	CCONJ
ejpam-5997	554	10	its	its	PRON
ejpam-5997	554	11	applications	application	NOUN
ejpam-5997	554	12	in	in	ADP
ejpam-5997	554	13	means	mean	NOUN
ejpam-5997	554	14	.	.	PUNCT
ejpam-5997	555	1	miskolc	miskolc	ADJ
ejpam-5997	555	2	mathematical	mathematical	ADJ
ejpam-5997	555	3	notes	note	NOUN
ejpam-5997	555	4	,	,	PUNCT
ejpam-5997	555	5	21(2):621–630	21(2):621–630	PROPN
ejpam-5997	555	6	,	,	PUNCT
ejpam-5997	555	7	2020	2020	NUM
ejpam-5997	555	8	.	.	PUNCT
ejpam-5997	556	1	[	[	X
ejpam-5997	556	2	12	12	NUM
ejpam-5997	556	3	]	]	X
ejpam-5997	556	4	chun	chun	PROPN
ejpam-5997	556	5	zhu	zhu	PROPN
ejpam-5997	556	6	,	,	PUNCT
ejpam-5997	556	7	michal	michal	PROPN
ejpam-5997	556	8	feckan	feckan	PROPN
ejpam-5997	556	9	,	,	PUNCT
ejpam-5997	556	10	and	and	CCONJ
ejpam-5997	556	11	jinrong	jinrong	PROPN
ejpam-5997	556	12	wang	wang	PROPN
ejpam-5997	556	13	.	.	PUNCT
ejpam-5997	557	1	fractional	fractional	ADJ
ejpam-5997	557	2	integral	integral	ADJ
ejpam-5997	557	3	inequalities	inequality	NOUN
ejpam-5997	557	4	for	for	ADP
ejpam-5997	557	5	differentiable	differentiable	ADJ
ejpam-5997	557	6	convex	convex	NOUN
ejpam-5997	557	7	mappings	mapping	NOUN
ejpam-5997	557	8	and	and	CCONJ
ejpam-5997	557	9	applications	application	NOUN
ejpam-5997	557	10	to	to	ADP
ejpam-5997	557	11	special	special	ADJ
ejpam-5997	557	12	means	mean	NOUN
ejpam-5997	557	13	and	and	CCONJ
ejpam-5997	557	14	a	a	DET
ejpam-5997	557	15	midpoint	midpoint	NOUN
ejpam-5997	557	16	formula	formula	NOUN
ejpam-5997	557	17	.	.	PUNCT
ejpam-5997	558	1	journal	journal	NOUN
ejpam-5997	558	2	of	of	ADP
ejpam-5997	558	3	applied	apply	VERB
ejpam-5997	558	4	mathematics	mathematic	NOUN
ejpam-5997	558	5	,	,	PUNCT
ejpam-5997	558	6	statistics	statistic	NOUN
ejpam-5997	558	7	and	and	CCONJ
ejpam-5997	558	8	informatic	informatic	ADJ
ejpam-5997	558	9	,	,	PUNCT
ejpam-5997	558	10	8(2	8(2	NUM
ejpam-5997	558	11	)	)	PUNCT
ejpam-5997	558	12	,	,	PUNCT
ejpam-5997	558	13	2012	2012	NUM
ejpam-5997	558	14	.	.	PUNCT
ejpam-5997	559	1	[	[	X
ejpam-5997	559	2	13	13	NUM
ejpam-5997	559	3	]	]	SYM
ejpam-5997	559	4	pshtiwan	pshtiwan	PROPN
ejpam-5997	559	5	othman	othman	PROPN
ejpam-5997	559	6	mohammed	mohammed	PROPN
ejpam-5997	559	7	and	and	CCONJ
ejpam-5997	559	8	mehmet	mehmet	PROPN
ejpam-5997	559	9	zeki	zeki	PROPN
ejpam-5997	559	10	sarikaya	sarikaya	PROPN
ejpam-5997	559	11	.	.	PUNCT
ejpam-5997	560	1	hermite	hermite	PROPN
ejpam-5997	560	2	–	–	PUNCT
ejpam-5997	560	3	hadamard	hadamard	ADJ
ejpam-5997	560	4	type	type	NOUN
ejpam-5997	560	5	inequalities	inequality	NOUN
ejpam-5997	560	6	for	for	ADP
ejpam-5997	560	7	f	f	NOUN
ejpam-5997	560	8	-	-	PUNCT
ejpam-5997	560	9	convex	convex	ADJ
ejpam-5997	560	10	function	function	NOUN
ejpam-5997	560	11	involving	involve	VERB
ejpam-5997	560	12	fractional	fractional	ADJ
ejpam-5997	560	13	integrals	integral	NOUN
ejpam-5997	560	14	.	.	PUNCT
ejpam-5997	561	1	journal	journal	PROPN
ejpam-5997	561	2	of	of	ADP
ejpam-5997	561	3	inequalities	inequality	NOUN
ejpam-5997	561	4	and	and	CCONJ
ejpam-5997	561	5	applications	application	NOUN
ejpam-5997	561	6	,	,	PUNCT
ejpam-5997	561	7	2018:1–33	2018:1–33	PROPN
ejpam-5997	561	8	,	,	PUNCT
ejpam-5997	561	9	2018	2018	NUM
ejpam-5997	561	10	.	.	PUNCT
ejpam-5997	562	1	[	[	X
ejpam-5997	562	2	14	14	NUM
ejpam-5997	562	3	]	]	X
ejpam-5997	562	4	tieyan	tieyan	PROPN
ejpam-5997	562	5	lian	lian	PROPN
ejpam-5997	562	6	,	,	PUNCT
ejpam-5997	562	7	wei	wei	PROPN
ejpam-5997	562	8	tang	tang	PROPN
ejpam-5997	562	9	,	,	PUNCT
ejpam-5997	562	10	and	and	CCONJ
ejpam-5997	562	11	rui	rui	PROPN
ejpam-5997	562	12	zhou	zhou	PROPN
ejpam-5997	562	13	.	.	PUNCT
ejpam-5997	563	1	fractional	fractional	ADJ
ejpam-5997	563	2	hermite	hermite	PROPN
ejpam-5997	563	3	–	–	PUNCT
ejpam-5997	563	4	hadamard	hadamard	ADJ
ejpam-5997	563	5	inequalities	inequality	NOUN
ejpam-5997	563	6	for	for	ADP
ejpam-5997	563	7	(	(	PUNCT
ejpam-5997	563	8	s	s	X
ejpam-5997	563	9	,	,	PUNCT
ejpam-5997	563	10	m)-convex	m)-convex	PUNCT
ejpam-5997	563	11	or	or	CCONJ
ejpam-5997	563	12	s	s	NOUN
ejpam-5997	563	13	-	-	PUNCT
ejpam-5997	563	14	concave	concave	ADJ
ejpam-5997	563	15	functions	function	NOUN
ejpam-5997	563	16	.	.	PUNCT
ejpam-5997	564	1	journal	journal	PROPN
ejpam-5997	564	2	of	of	ADP
ejpam-5997	564	3	inequalities	inequality	NOUN
ejpam-5997	564	4	and	and	CCONJ
ejpam-5997	564	5	applications	application	NOUN
ejpam-5997	564	6	,	,	PUNCT
ejpam-5997	564	7	2018(1):240	2018(1):240	NUM
ejpam-5997	564	8	,	,	PUNCT
ejpam-5997	564	9	2018	2018	NUM
ejpam-5997	564	10	.	.	PUNCT
ejpam-5997	565	1	[	[	X
ejpam-5997	565	2	15	15	NUM
ejpam-5997	565	3	]	]	X
ejpam-5997	565	4	yousaf	yousaf	PROPN
ejpam-5997	565	5	khurshid	khurshid	PROPN
ejpam-5997	565	6	,	,	PUNCT
ejpam-5997	565	7	m	m	PROPN
ejpam-5997	565	8	adil	adil	PROPN
ejpam-5997	565	9	khan	khan	PROPN
ejpam-5997	565	10	,	,	PUNCT
ejpam-5997	565	11	and	and	CCONJ
ejpam-5997	565	12	yu	yu	PROPN
ejpam-5997	565	13	-	-	PUNCT
ejpam-5997	565	14	ming	ming	PROPN
ejpam-5997	565	15	chu	chu	PROPN
ejpam-5997	565	16	.	.	PUNCT
ejpam-5997	566	1	conformable	conformable	ADJ
ejpam-5997	566	2	fractional	fractional	ADJ
ejpam-5997	566	3	integral	integral	ADJ
ejpam-5997	566	4	inequalities	inequality	NOUN
ejpam-5997	566	5	for	for	ADP
ejpam-5997	566	6	gg	gg	PROPN
ejpam-5997	566	7	-	-	PUNCT
ejpam-5997	566	8	and	and	CCONJ
ejpam-5997	566	9	ga	ga	NOUN
ejpam-5997	566	10	-	-	ADJ
ejpam-5997	566	11	convex	convex	NOUN
ejpam-5997	566	12	function	function	NOUN
ejpam-5997	566	13	.	.	PUNCT
ejpam-5997	567	1	aims	aim	VERB
ejpam-5997	567	2	math	math	NOUN
ejpam-5997	567	3	,	,	PUNCT
ejpam-5997	567	4	5(5):5012–5030	5(5):5012–5030	NUM
ejpam-5997	567	5	,	,	PUNCT
ejpam-5997	567	6	2020	2020	NUM
ejpam-5997	567	7	.	.	PUNCT
ejpam-5997	568	1	[	[	X
ejpam-5997	568	2	16	16	NUM
ejpam-5997	568	3	]	]	X
ejpam-5997	568	4	shahid	shahid	PROPN
ejpam-5997	568	5	qaisar	qaisar	PROPN
ejpam-5997	568	6	,	,	PUNCT
ejpam-5997	568	7	jamshed	jamshed	PROPN
ejpam-5997	568	8	nasir	nasir	PROPN
ejpam-5997	568	9	,	,	PUNCT
ejpam-5997	568	10	saad	saad	PROPN
ejpam-5997	568	11	ihsan	ihsan	PROPN
ejpam-5997	568	12	butt	butt	PROPN
ejpam-5997	568	13	,	,	PUNCT
ejpam-5997	568	14	and	and	CCONJ
ejpam-5997	568	15	sabir	sabir	PROPN
ejpam-5997	568	16	hussain	hussain	PROPN
ejpam-5997	568	17	.	.	PUNCT
ejpam-5997	569	1	on	on	ADP
ejpam-5997	569	2	some	some	DET
ejpam-5997	569	3	fractional	fractional	ADJ
ejpam-5997	569	4	integral	integral	ADJ
ejpam-5997	569	5	inequalities	inequality	NOUN
ejpam-5997	569	6	of	of	ADP
ejpam-5997	569	7	hermite	hermite	PROPN
ejpam-5997	569	8	-	-	PUNCT
ejpam-5997	569	9	hadamard	hadamard	PROPN
ejpam-5997	569	10	’s	’s	PART
ejpam-5997	569	11	type	type	NOUN
ejpam-5997	569	12	through	through	ADP
ejpam-5997	569	13	convexity	convexity	NOUN
ejpam-5997	569	14	.	.	PUNCT
ejpam-5997	569	15	symmetry	symmetry	NOUN
ejpam-5997	569	16	,	,	PUNCT
ejpam-5997	569	17	11(2):137	11(2):137	NUM
ejpam-5997	569	18	,	,	PUNCT
ejpam-5997	569	19	2019	2019	NUM
ejpam-5997	569	20	.	.	PUNCT
ejpam-5997	570	1	[	[	X
ejpam-5997	570	2	17	17	NUM
ejpam-5997	570	3	]	]	X
ejpam-5997	570	4	m	m	PROPN
ejpam-5997	570	5	emin	emin	PROPN
ejpam-5997	570	6	ozdemir	ozdemir	PROPN
ejpam-5997	570	7	,	,	PUNCT
ejpam-5997	570	8	saad	saad	PROPN
ejpam-5997	570	9	i	i	PROPN
ejpam-5997	570	10	butt	butt	PROPN
ejpam-5997	570	11	,	,	PUNCT
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ejpam-5997	570	13	bayraktar	bayraktar	NOUN
ejpam-5997	570	14	,	,	PUNCT
ejpam-5997	570	15	and	and	CCONJ
ejpam-5997	570	16	jamshed	jamshed	PROPN
ejpam-5997	570	17	nasir	nasir	PROPN
ejpam-5997	570	18	.	.	PUNCT
ejpam-5997	571	1	several	several	ADJ
ejpam-5997	571	2	integral	integral	ADJ
ejpam-5997	571	3	inequalities	inequality	NOUN
ejpam-5997	571	4	for	for	ADP
ejpam-5997	571	5	(	(	PUNCT
ejpam-5997	571	6	α	α	X
ejpam-5997	571	7	,	,	PUNCT
ejpam-5997	571	8	s	s	PROPN
ejpam-5997	571	9	,	,	PUNCT
ejpam-5997	571	10	m)-convex	m)-convex	PUNCT
ejpam-5997	571	11	functions	function	NOUN
ejpam-5997	571	12	.	.	PUNCT
ejpam-5997	572	1	aims	aim	VERB
ejpam-5997	572	2	mathematics	mathematic	NOUN
ejpam-5997	572	3	,	,	PUNCT
ejpam-5997	572	4	5(4):3906	5(4):3906	NUM
ejpam-5997	572	5	–	–	PUNCT
ejpam-5997	572	6	3921	3921	NUM
ejpam-5997	572	7	,	,	PUNCT
ejpam-5997	572	8	2020	2020	NUM
ejpam-5997	572	9	.	.	PUNCT
ejpam-5997	573	1	[	[	X
ejpam-5997	573	2	18	18	NUM
ejpam-5997	573	3	]	]	X
ejpam-5997	573	4	hasan	hasan	PROPN
ejpam-5997	573	5	barsam	barsam	PROPN
ejpam-5997	573	6	and	and	CCONJ
ejpam-5997	573	7	ali	ali	PROPN
ejpam-5997	573	8	sattarzadeh	sattarzadeh	PROPN
ejpam-5997	573	9	.	.	PUNCT
ejpam-5997	574	1	some	some	DET
ejpam-5997	574	2	results	result	NOUN
ejpam-5997	574	3	on	on	ADP
ejpam-5997	574	4	hermite	hermite	ADJ
ejpam-5997	574	5	-	-	PUNCT
ejpam-5997	574	6	hadamard	hadamard	ADJ
ejpam-5997	574	7	inequalities	inequality	NOUN
ejpam-5997	574	8	.	.	PUNCT
ejpam-5997	575	1	m.	m.	PROPN
ejpam-5997	575	2	vivas	vivas	PROPN
ejpam-5997	575	3	-	-	PROPN
ejpam-5997	575	4	cortez	cortez	PROPN
ejpam-5997	575	5	et	et	PROPN
ejpam-5997	575	6	al	al	PROPN
ejpam-5997	575	7	.	.	PUNCT
ejpam-5997	575	8	/	/	SYM
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ejpam-5997	575	10	.	.	PUNCT
ejpam-5997	576	1	j.	j.	PROPN
ejpam-5997	576	2	pure	pure	PROPN
ejpam-5997	576	3	appl	appl	PROPN
ejpam-5997	576	4	.	.	PROPN
ejpam-5997	576	5	math	math	PROPN
ejpam-5997	576	6	,	,	PUNCT
ejpam-5997	576	7	18	18	NUM
ejpam-5997	576	8	(	(	PUNCT
ejpam-5997	576	9	2	2	NUM
ejpam-5997	576	10	)	)	PUNCT
ejpam-5997	576	11	(	(	PUNCT
ejpam-5997	576	12	2025	2025	NUM
ejpam-5997	576	13	)	)	PUNCT
ejpam-5997	576	14	,	,	PUNCT
ejpam-5997	576	15	5997	5997	NUM
ejpam-5997	576	16	22	22	NUM
ejpam-5997	576	17	of	of	ADP
ejpam-5997	576	18	23	23	NUM
ejpam-5997	576	19	journal	journal	NOUN
ejpam-5997	576	20	of	of	ADP
ejpam-5997	576	21	mahani	mahani	PROPN
ejpam-5997	576	22	mathematical	mathematical	PROPN
ejpam-5997	576	23	research	research	NOUN
ejpam-5997	576	24	,	,	PUNCT
ejpam-5997	576	25	9(2):79–86	9(2):79–86	NUM
ejpam-5997	576	26	,	,	PUNCT
ejpam-5997	576	27	2020	2020	NUM
ejpam-5997	576	28	.	.	PUNCT
ejpam-5997	577	1	[	[	X
ejpam-5997	577	2	19	19	NUM
ejpam-5997	577	3	]	]	X
ejpam-5997	577	4	khuram	khuram	PROPN
ejpam-5997	577	5	ali	ali	PROPN
ejpam-5997	577	6	khan	khan	PROPN
ejpam-5997	577	7	,	,	PUNCT
ejpam-5997	577	8	saeeda	saeeda	NOUN
ejpam-5997	577	9	fatima	fatima	PROPN
ejpam-5997	577	10	,	,	PUNCT
ejpam-5997	577	11	ammara	ammara	ADV
ejpam-5997	577	12	nosheen	nosheen	ADJ
ejpam-5997	577	13	,	,	PUNCT
ejpam-5997	577	14	and	and	CCONJ
ejpam-5997	577	15	rostin	rostin	VERB
ejpam-5997	577	16	matendo	matendo	PROPN
ejpam-5997	577	17	mabela	mabela	PROPN
ejpam-5997	577	18	.	.	PUNCT
ejpam-5997	578	1	new	new	ADJ
ejpam-5997	578	2	developments	development	NOUN
ejpam-5997	578	3	of	of	ADP
ejpam-5997	578	4	hermite	hermite	ADJ
ejpam-5997	578	5	–	–	PUNCT
ejpam-5997	578	6	hadamard	hadamard	ADJ
ejpam-5997	578	7	type	type	NOUN
ejpam-5997	578	8	inequalities	inequality	NOUN
ejpam-5997	578	9	via	via	ADP
ejpam-5997	578	10	s	s	NOUN
ejpam-5997	578	11	-	-	PUNCT
ejpam-5997	578	12	convexity	convexity	NOUN
ejpam-5997	578	13	and	and	CCONJ
ejpam-5997	578	14	fractional	fractional	ADJ
ejpam-5997	578	15	integrals	integral	NOUN
ejpam-5997	578	16	.	.	PUNCT
ejpam-5997	579	1	journal	journal	NOUN
ejpam-5997	579	2	of	of	ADP
ejpam-5997	579	3	mathematics	mathematic	NOUN
ejpam-5997	579	4	,	,	PUNCT
ejpam-5997	579	5	2024(1):1997549	2024(1):1997549	NUM
ejpam-5997	579	6	,	,	PUNCT
ejpam-5997	579	7	2024	2024	NUM
ejpam-5997	579	8	.	.	PUNCT
ejpam-5997	580	1	[	[	X
ejpam-5997	580	2	20	20	NUM
ejpam-5997	580	3	]	]	X
ejpam-5997	580	4	bo	bo	PROPN
ejpam-5997	580	5	-	-	PUNCT
ejpam-5997	580	6	yan	yan	PROPN
ejpam-5997	580	7	xi	xi	PROPN
ejpam-5997	580	8	,	,	PUNCT
ejpam-5997	580	9	dan	dan	PROPN
ejpam-5997	580	10	-	-	PUNCT
ejpam-5997	580	11	dan	dan	PROPN
ejpam-5997	580	12	gao	gao	PROPN
ejpam-5997	580	13	,	,	PUNCT
ejpam-5997	580	14	and	and	CCONJ
ejpam-5997	580	15	feng	feng	PROPN
ejpam-5997	580	16	qi	qi	PROPN
ejpam-5997	580	17	.	.	PUNCT
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ejpam-5997	580	19	inequalities	inequality	NOUN
ejpam-5997	580	20	of	of	ADP
ejpam-5997	580	21	hermite	hermite	ADJ
ejpam-5997	580	22	–	–	PUNCT
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ejpam-5997	580	24	type	type	NOUN
ejpam-5997	580	25	for	for	ADP
ejpam-5997	580	26	(	(	PUNCT
ejpam-5997	580	27	\alpha	\alpha	PROPN
ejpam-5997	580	28	,	,	PUNCT
ejpam-5997	580	29	s	s	PART
ejpam-5997	580	30	)	)	PUNCT
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ejpam-5997	580	32	,	,	PUNCT
ejpam-5997	580	33	s	s	X
ejpam-5997	580	34	,	,	PUNCT
ejpam-5997	580	35	m	m	NOUN
ejpam-5997	580	36	)	)	PUNCT
ejpam-5997	580	37	−convexfunctions	−convexfunction	NOUN
ejpam-5997	580	38	.	.	PUNCT
ejpam-5997	581	1	italianjournalofpureandappliedmathematics	italianjournalofpureandappliedmathematic	NOUN
ejpam-5997	581	2	,	,	PUNCT
ejpam-5997	581	3	(	(	PUNCT
ejpam-5997	581	4	44	44	NUM
ejpam-5997	581	5	)	)	PUNCT
ejpam-5997	581	6	:	:	PUNCT
ejpam-5997	581	7	499−−510	499−−510	NUM
ejpam-5997	581	8	,	,	PUNCT
ejpam-5997	581	9	2020	2020	NUM
ejpam-5997	581	10	.	.	PUNCT
ejpam-5997	582	1	[	[	X
ejpam-5997	582	2	21	21	NUM
ejpam-5997	582	3	]	]	X
ejpam-5997	582	4	muhammad	muhammad	PROPN
ejpam-5997	582	5	adil	adil	PROPN
ejpam-5997	582	6	khan	khan	PROPN
ejpam-5997	582	7	,	,	PUNCT
ejpam-5997	582	8	yuming	yuming	PROPN
ejpam-5997	582	9	chu	chu	PROPN
ejpam-5997	582	10	,	,	PUNCT
ejpam-5997	582	11	tahir	tahir	PROPN
ejpam-5997	582	12	ullah	ullah	PROPN
ejpam-5997	582	13	khan	khan	PROPN
ejpam-5997	582	14	,	,	PUNCT
ejpam-5997	582	15	and	and	CCONJ
ejpam-5997	582	16	jamroz	jamroz	PROPN
ejpam-5997	582	17	khan	khan	PROPN
ejpam-5997	582	18	.	.	PUNCT
ejpam-5997	583	1	some	some	DET
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ejpam-5997	583	4	of	of	ADP
ejpam-5997	583	5	hermite	hermite	ADJ
ejpam-5997	583	6	-	-	PUNCT
ejpam-5997	583	7	hadamard	hadamard	ADJ
ejpam-5997	583	8	type	type	NOUN
ejpam-5997	583	9	for	for	ADP
ejpam-5997	583	10	s	s	NOUN
ejpam-5997	583	11	-	-	PUNCT
ejpam-5997	583	12	convex	convex	ADJ
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ejpam-5997	583	14	with	with	ADP
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ejpam-5997	583	16	.	.	PUNCT
ejpam-5997	584	1	open	open	ADJ
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ejpam-5997	584	3	,	,	PUNCT
ejpam-5997	584	4	15(1):1414–1430	15(1):1414–1430	NUM
ejpam-5997	584	5	,	,	PUNCT
ejpam-5997	584	6	2017	2017	NUM
ejpam-5997	584	7	.	.	PUNCT
ejpam-5997	585	1	[	[	X
ejpam-5997	585	2	22	22	NUM
ejpam-5997	585	3	]	]	X
ejpam-5997	585	4	pshtiwan	pshtiwan	PROPN
ejpam-5997	585	5	othman	othman	PROPN
ejpam-5997	585	6	mohammed	mohammed	PROPN
ejpam-5997	585	7	.	.	PUNCT
ejpam-5997	586	1	hermite	hermite	PROPN
ejpam-5997	586	2	-	-	PUNCT
ejpam-5997	586	3	hadamard	hadamard	ADJ
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ejpam-5997	586	5	for	for	ADP
ejpam-5997	586	6	riemann	riemann	PROPN
ejpam-5997	586	7	-	-	PUNCT
ejpam-5997	586	8	liouville	liouville	VERB
ejpam-5997	586	9	fractional	fractional	ADJ
ejpam-5997	586	10	integrals	integral	NOUN
ejpam-5997	586	11	of	of	ADP
ejpam-5997	586	12	a	a	DET
ejpam-5997	586	13	convex	convex	NOUN
ejpam-5997	586	14	function	function	NOUN
ejpam-5997	586	15	with	with	ADP
ejpam-5997	586	16	respect	respect	NOUN
ejpam-5997	586	17	to	to	ADP
ejpam-5997	586	18	a	a	DET
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ejpam-5997	586	20	function	function	NOUN
ejpam-5997	586	21	.	.	PUNCT
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ejpam-5997	587	6	sciences	science	NOUN
ejpam-5997	587	7	,	,	PUNCT
ejpam-5997	587	8	44(3):2314–2324	44(3):2314–2324	NUM
ejpam-5997	587	9	,	,	PUNCT
ejpam-5997	587	10	2021	2021	NUM
ejpam-5997	587	11	.	.	PUNCT
ejpam-5997	588	1	[	[	X
ejpam-5997	588	2	23	23	NUM
ejpam-5997	588	3	]	]	X
ejpam-5997	588	4	thabet	thabet	ADJ
ejpam-5997	588	5	abdeljawad	abdeljawad	NOUN
ejpam-5997	588	6	,	,	PUNCT
ejpam-5997	588	7	saima	saima	PROPN
ejpam-5997	588	8	rashid	rashid	PROPN
ejpam-5997	588	9	,	,	PUNCT
ejpam-5997	588	10	zakia	zakia	NOUN
ejpam-5997	588	11	hammouch	hammouch	NOUN
ejpam-5997	588	12	,	,	PUNCT
ejpam-5997	588	13	and	and	CCONJ
ejpam-5997	588	14	yu	yu	PROPN
ejpam-5997	588	15	-	-	PUNCT
ejpam-5997	588	16	ming	ming	PROPN
ejpam-5997	588	17	chu	chu	PROPN
ejpam-5997	588	18	.	.	PUNCT
ejpam-5997	589	1	some	some	DET
ejpam-5997	589	2	new	new	ADJ
ejpam-5997	589	3	local	local	ADJ
ejpam-5997	589	4	fractional	fractional	ADJ
ejpam-5997	589	5	inequalities	inequality	NOUN
ejpam-5997	589	6	associated	associate	VERB
ejpam-5997	589	7	with	with	ADP
ejpam-5997	589	8	generalized	generalized	ADJ
ejpam-5997	589	9	(	(	PUNCT
ejpam-5997	589	10	s	s	NOUN
ejpam-5997	589	11	,	,	PUNCT
ejpam-5997	589	12	m)-convex	m)-convex	PUNCT
ejpam-5997	589	13	functions	function	NOUN
ejpam-5997	589	14	and	and	CCONJ
ejpam-5997	589	15	applications	application	NOUN
ejpam-5997	589	16	.	.	PUNCT
ejpam-5997	590	1	advances	advance	NOUN
ejpam-5997	590	2	in	in	ADP
ejpam-5997	590	3	difference	difference	NOUN
ejpam-5997	590	4	equations	equation	NOUN
ejpam-5997	590	5	,	,	PUNCT
ejpam-5997	590	6	2020(1):406	2020(1):406	NUM
ejpam-5997	590	7	,	,	PUNCT
ejpam-5997	590	8	2020	2020	NUM
ejpam-5997	590	9	.	.	PUNCT
ejpam-5997	591	1	[	[	X
ejpam-5997	591	2	24	24	NUM
ejpam-5997	591	3	]	]	PUNCT
ejpam-5997	591	4	i̇mdat	i̇mdat	PRON
ejpam-5997	591	5	i̇şcan	i̇şcan	PROPN
ejpam-5997	591	6	.	.	PUNCT
ejpam-5997	592	1	generalization	generalization	NOUN
ejpam-5997	592	2	of	of	ADP
ejpam-5997	592	3	different	different	ADJ
ejpam-5997	592	4	type	type	NOUN
ejpam-5997	592	5	integral	integral	ADJ
ejpam-5997	592	6	inequalities	inequality	NOUN
ejpam-5997	592	7	for	for	ADP
ejpam-5997	592	8	s	s	NOUN
ejpam-5997	592	9	-	-	PUNCT
ejpam-5997	592	10	convex	convex	ADJ
ejpam-5997	592	11	functions	function	NOUN
ejpam-5997	592	12	via	via	ADP
ejpam-5997	592	13	fractional	fractional	ADJ
ejpam-5997	592	14	integrals	integral	NOUN
ejpam-5997	592	15	.	.	PUNCT
ejpam-5997	593	1	applicable	applicable	ADJ
ejpam-5997	593	2	analysis	analysis	NOUN
ejpam-5997	593	3	,	,	PUNCT
ejpam-5997	593	4	93(9):1846–1862	93(9):1846–1862	NUM
ejpam-5997	593	5	,	,	PUNCT
ejpam-5997	593	6	2014	2014	NUM
ejpam-5997	593	7	.	.	PUNCT
ejpam-5997	594	1	[	[	X
ejpam-5997	594	2	25	25	NUM
ejpam-5997	594	3	]	]	X
ejpam-5997	594	4	fuat	fuat	PROPN
ejpam-5997	594	5	usta	usta	PROPN
ejpam-5997	594	6	,	,	PUNCT
ejpam-5997	594	7	hüseyin	hüseyin	PROPN
ejpam-5997	594	8	budak	budak	PROPN
ejpam-5997	594	9	,	,	PUNCT
ejpam-5997	594	10	mehmet	mehmet	PROPN
ejpam-5997	594	11	zeki	zeki	PROPN
ejpam-5997	594	12	sarikaya	sarikaya	PROPN
ejpam-5997	594	13	,	,	PUNCT
ejpam-5997	594	14	and	and	CCONJ
ejpam-5997	594	15	erhan	erhan	SCONJ
ejpam-5997	594	16	set	set	VERB
ejpam-5997	594	17	.	.	PUNCT
ejpam-5997	595	1	on	on	ADP
ejpam-5997	595	2	generalization	generalization	NOUN
ejpam-5997	595	3	of	of	ADP
ejpam-5997	595	4	trapezoid	trapezoid	ADJ
ejpam-5997	595	5	type	type	NOUN
ejpam-5997	595	6	inequalities	inequality	NOUN
ejpam-5997	595	7	for	for	ADP
ejpam-5997	595	8	s	s	NOUN
ejpam-5997	595	9	-	-	PUNCT
ejpam-5997	595	10	convex	convex	ADJ
ejpam-5997	595	11	functions	function	NOUN
ejpam-5997	595	12	with	with	ADP
ejpam-5997	595	13	generalized	generalized	ADJ
ejpam-5997	595	14	fractional	fractional	ADJ
ejpam-5997	595	15	integral	integral	ADJ
ejpam-5997	595	16	operators	operator	NOUN
ejpam-5997	595	17	.	.	PUNCT
ejpam-5997	596	1	filomat	filomat	NOUN
ejpam-5997	596	2	,	,	PUNCT
ejpam-5997	596	3	32(6):2153–2171	32(6):2153–2171	NUM
ejpam-5997	596	4	,	,	PUNCT
ejpam-5997	596	5	2018	2018	NUM
ejpam-5997	596	6	.	.	PUNCT
ejpam-5997	597	1	[	[	X
ejpam-5997	597	2	26	26	NUM
ejpam-5997	597	3	]	]	X
ejpam-5997	597	4	saad	saad	PROPN
ejpam-5997	597	5	ihsan	ihsan	PROPN
ejpam-5997	597	6	butt	butt	PROPN
ejpam-5997	597	7	,	,	PUNCT
ejpam-5997	597	8	saba	saba	PROPN
ejpam-5997	597	9	yousaf	yousaf	PROPN
ejpam-5997	597	10	,	,	PUNCT
ejpam-5997	597	11	ahmet	ahmet	PROPN
ejpam-5997	597	12	ocak	ocak	PROPN
ejpam-5997	597	13	akdemir	akdemir	NOUN
ejpam-5997	597	14	,	,	PUNCT
ejpam-5997	597	15	and	and	CCONJ
ejpam-5997	597	16	mustafa	mustafa	PROPN
ejpam-5997	597	17	ali	ali	PROPN
ejpam-5997	597	18	dokuyucu	dokuyucu	PROPN
ejpam-5997	597	19	.	.	PUNCT
ejpam-5997	598	1	new	new	ADJ
ejpam-5997	598	2	hadamard	hadamard	ADJ
ejpam-5997	598	3	-	-	PUNCT
ejpam-5997	598	4	type	type	NOUN
ejpam-5997	598	5	integral	integral	ADJ
ejpam-5997	598	6	inequalities	inequality	NOUN
ejpam-5997	598	7	via	via	ADP
ejpam-5997	598	8	a	a	DET
ejpam-5997	598	9	general	general	ADJ
ejpam-5997	598	10	form	form	NOUN
ejpam-5997	598	11	of	of	ADP
ejpam-5997	598	12	fractional	fractional	ADJ
ejpam-5997	598	13	integral	integral	ADJ
ejpam-5997	598	14	operators	operator	NOUN
ejpam-5997	598	15	.	.	PUNCT
ejpam-5997	599	1	chaos	chaos	NOUN
ejpam-5997	599	2	,	,	PUNCT
ejpam-5997	599	3	solitons	soliton	NOUN
ejpam-5997	599	4	&	&	CCONJ
ejpam-5997	599	5	fractals	fractal	NOUN
ejpam-5997	599	6	,	,	PUNCT
ejpam-5997	599	7	148:111025	148:111025	NUM
ejpam-5997	599	8	,	,	PUNCT
ejpam-5997	599	9	2021	2021	NUM
ejpam-5997	599	10	.	.	PUNCT
ejpam-5997	600	1	[	[	X
ejpam-5997	600	2	27	27	NUM
ejpam-5997	600	3	]	]	X
ejpam-5997	600	4	praveen	praveen	PROPN
ejpam-5997	600	5	agarwal	agarwal	PROPN
ejpam-5997	600	6	,	,	PUNCT
ejpam-5997	600	7	mohamed	mohamed	PROPN
ejpam-5997	600	8	jleli	jleli	PROPN
ejpam-5997	600	9	,	,	PUNCT
ejpam-5997	600	10	and	and	CCONJ
ejpam-5997	600	11	muharrem	muharrem	ADJ
ejpam-5997	600	12	tomar	tomar	NOUN
ejpam-5997	600	13	.	.	PUNCT
ejpam-5997	601	1	certain	certain	ADJ
ejpam-5997	601	2	hermite	hermite	ADJ
ejpam-5997	601	3	-	-	PUNCT
ejpam-5997	601	4	hadamard	hadamard	ADJ
ejpam-5997	601	5	type	type	NOUN
ejpam-5997	601	6	inequalities	inequality	NOUN
ejpam-5997	601	7	via	via	ADP
ejpam-5997	601	8	generalized	generalized	ADJ
ejpam-5997	601	9	k	k	ADJ
ejpam-5997	601	10	-	-	PUNCT
ejpam-5997	601	11	fractional	fractional	ADJ
ejpam-5997	601	12	integrals	integral	NOUN
ejpam-5997	601	13	.	.	PUNCT
ejpam-5997	602	1	journal	journal	NOUN
ejpam-5997	602	2	of	of	ADP
ejpam-5997	602	3	inequalities	inequality	NOUN
ejpam-5997	602	4	and	and	CCONJ
ejpam-5997	602	5	applications	application	NOUN
ejpam-5997	602	6	,	,	PUNCT
ejpam-5997	602	7	2017:1–10	2017:1–10	NUM
ejpam-5997	602	8	,	,	PUNCT
ejpam-5997	602	9	2017	2017	NUM
ejpam-5997	602	10	.	.	PUNCT
ejpam-5997	603	1	[	[	X
ejpam-5997	603	2	28	28	NUM
ejpam-5997	603	3	]	]	X
ejpam-5997	603	4	gheorghe	gheorghe	NOUN
ejpam-5997	603	5	toader	toader	NOUN
ejpam-5997	603	6	.	.	PUNCT
ejpam-5997	604	1	some	some	DET
ejpam-5997	604	2	generalizations	generalization	NOUN
ejpam-5997	604	3	of	of	ADP
ejpam-5997	604	4	the	the	DET
ejpam-5997	604	5	convexity	convexity	NOUN
ejpam-5997	604	6	.	.	PUNCT
ejpam-5997	605	1	in	in	ADP
ejpam-5997	605	2	proceedings	proceeding	NOUN
ejpam-5997	605	3	of	of	ADP
ejpam-5997	605	4	the	the	DET
ejpam-5997	605	5	colloquium	colloquium	NOUN
ejpam-5997	605	6	on	on	ADP
ejpam-5997	605	7	approximation	approximation	NOUN
ejpam-5997	605	8	and	and	CCONJ
ejpam-5997	605	9	optimization	optimization	NOUN
ejpam-5997	605	10	,	,	PUNCT
ejpam-5997	605	11	volume	volume	NOUN
ejpam-5997	605	12	329	329	NUM
ejpam-5997	605	13	,	,	PUNCT
ejpam-5997	605	14	page	page	NOUN
ejpam-5997	605	15	338	338	NUM
ejpam-5997	605	16	.	.	PUNCT
ejpam-5997	606	1	university	university	NOUN
ejpam-5997	606	2	of	of	ADP
ejpam-5997	606	3	cluj	cluj	PROPN
ejpam-5997	606	4	-	-	PUNCT
ejpam-5997	606	5	napoca	napoca	NOUN
ejpam-5997	606	6	cluj	cluj	PROPN
ejpam-5997	606	7	-	-	PUNCT
ejpam-5997	606	8	napoca	napoca	PROPN
ejpam-5997	606	9	,	,	PUNCT
ejpam-5997	606	10	romania	romania	PROPN
ejpam-5997	606	11	,	,	PUNCT
ejpam-5997	606	12	1984	1984	NUM
ejpam-5997	606	13	.	.	PUNCT
ejpam-5997	607	1	[	[	X
ejpam-5997	607	2	29	29	NUM
ejpam-5997	607	3	]	]	X
ejpam-5997	607	4	xiaoli	xiaoli	PROPN
ejpam-5997	607	5	qiang	qiang	PROPN
ejpam-5997	607	6	,	,	PUNCT
ejpam-5997	607	7	ghulam	ghulam	PROPN
ejpam-5997	607	8	farid	farid	PROPN
ejpam-5997	607	9	,	,	PUNCT
ejpam-5997	607	10	muhammad	muhammad	PROPN
ejpam-5997	607	11	yussouf	yussouf	PROPN
ejpam-5997	607	12	,	,	PUNCT
ejpam-5997	607	13	khuram	khuram	PROPN
ejpam-5997	607	14	ali	ali	PROPN
ejpam-5997	607	15	khan	khan	PROPN
ejpam-5997	607	16	,	,	PUNCT
ejpam-5997	607	17	and	and	CCONJ
ejpam-5997	607	18	atiq	atiq	VERB
ejpam-5997	607	19	ur	ur	INTJ
ejpam-5997	607	20	rahman	rahman	PROPN
ejpam-5997	607	21	.	.	PUNCT
ejpam-5997	608	1	new	new	ADJ
ejpam-5997	608	2	generalized	generalize	VERB
ejpam-5997	608	3	fractional	fractional	ADJ
ejpam-5997	608	4	versions	version	NOUN
ejpam-5997	608	5	of	of	ADP
ejpam-5997	608	6	hadamard	hadamard	ADJ
ejpam-5997	608	7	and	and	CCONJ
ejpam-5997	608	8	fejér	fejér	NOUN
ejpam-5997	608	9	inequalities	inequality	NOUN
ejpam-5997	608	10	for	for	ADP
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ejpam-5997	608	12	convex	convex	ADJ
ejpam-5997	608	13	functions	function	NOUN
ejpam-5997	608	14	.	.	PUNCT
ejpam-5997	609	1	journal	journal	NOUN
ejpam-5997	609	2	of	of	ADP
ejpam-5997	609	3	inequalities	inequality	NOUN
ejpam-5997	609	4	and	and	CCONJ
ejpam-5997	609	5	applications	application	NOUN
ejpam-5997	609	6	,	,	PUNCT
ejpam-5997	609	7	2020:1–13	2020:1–13	NUM
ejpam-5997	609	8	,	,	PUNCT
ejpam-5997	609	9	2020	2020	NUM
ejpam-5997	609	10	.	.	PUNCT
ejpam-5997	610	1	[	[	X
ejpam-5997	610	2	30	30	NUM
ejpam-5997	610	3	]	]	X
ejpam-5997	610	4	muhamet	muhamet	PROPN
ejpam-5997	610	5	emin	emin	PROPN
ejpam-5997	610	6	özdemir	özdemir	PROPN
ejpam-5997	610	7	,	,	PUNCT
ejpam-5997	610	8	çetin	çetin	PROPN
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ejpam-5997	610	10	,	,	PUNCT
ejpam-5997	610	11	ahmet	ahmet	PROPN
ejpam-5997	610	12	ocak	ocak	PROPN
ejpam-5997	610	13	akdemir	akdemir	NOUN
ejpam-5997	610	14	,	,	PUNCT
ejpam-5997	610	15	and	and	CCONJ
ejpam-5997	610	16	erhan	erhan	SCONJ
ejpam-5997	610	17	set	set	VERB
ejpam-5997	610	18	.	.	PUNCT
ejpam-5997	611	1	on	on	ADP
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ejpam-5997	611	4	for	for	ADP
ejpam-5997	611	5	s	s	NOUN
ejpam-5997	611	6	-	-	PUNCT
ejpam-5997	611	7	convex	convex	ADJ
ejpam-5997	611	8	functions	function	NOUN
ejpam-5997	611	9	and	and	CCONJ
ejpam-5997	611	10	applications	application	NOUN
ejpam-5997	611	11	.	.	PUNCT
ejpam-5997	612	1	journal	journal	PROPN
ejpam-5997	612	2	of	of	ADP
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ejpam-5997	612	4	and	and	CCONJ
ejpam-5997	612	5	applications	application	NOUN
ejpam-5997	612	6	,	,	PUNCT
ejpam-5997	612	7	2013:1–11	2013:1–11	ADP
ejpam-5997	612	8	,	,	PUNCT
ejpam-5997	612	9	2013	2013	NUM
ejpam-5997	612	10	.	.	PUNCT
ejpam-5997	613	1	[	[	X
ejpam-5997	613	2	31	31	NUM
ejpam-5997	613	3	]	]	PUNCT
ejpam-5997	613	4	josip	josip	PROPN
ejpam-5997	613	5	e	e	PROPN
ejpam-5997	613	6	peajcariaac	peajcariaac	PROPN
ejpam-5997	613	7	and	and	CCONJ
ejpam-5997	613	8	yung	yung	PROPN
ejpam-5997	613	9	liang	liang	PROPN
ejpam-5997	613	10	tong	tong	PROPN
ejpam-5997	613	11	.	.	PUNCT
ejpam-5997	614	1	convex	convex	PROPN
ejpam-5997	614	2	functions	function	NOUN
ejpam-5997	614	3	,	,	PUNCT
ejpam-5997	614	4	partial	partial	ADJ
ejpam-5997	614	5	orderings	ordering	NOUN
ejpam-5997	614	6	,	,	PUNCT
ejpam-5997	614	7	and	and	CCONJ
ejpam-5997	614	8	statistical	statistical	ADJ
ejpam-5997	614	9	applications	application	NOUN
ejpam-5997	614	10	.	.	PUNCT
ejpam-5997	615	1	academic	academic	ADJ
ejpam-5997	615	2	press	press	NOUN
ejpam-5997	615	3	,	,	PUNCT
ejpam-5997	615	4	1992	1992	NUM
ejpam-5997	615	5	.	.	PUNCT
ejpam-5997	616	1	[	[	X
ejpam-5997	616	2	32	32	NUM
ejpam-5997	616	3	]	]	PUNCT
ejpam-5997	616	4	i̇mdat	i̇mdat	PRON
ejpam-5997	616	5	i̇şcan	i̇şcan	PROPN
ejpam-5997	616	6	and	and	CCONJ
ejpam-5997	616	7	shanhe	shanhe	VERB
ejpam-5997	616	8	wu	wu	PROPN
ejpam-5997	616	9	.	.	PUNCT
ejpam-5997	617	1	hermite	hermite	PROPN
ejpam-5997	617	2	–	–	PUNCT
ejpam-5997	617	3	hadamard	hadamard	ADJ
ejpam-5997	617	4	type	type	NOUN
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ejpam-5997	617	6	for	for	ADP
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ejpam-5997	617	8	convex	convex	ADJ
ejpam-5997	617	9	functions	function	NOUN
ejpam-5997	617	10	via	via	ADP
ejpam-5997	617	11	fractional	fractional	ADJ
ejpam-5997	617	12	integrals	integral	NOUN
ejpam-5997	617	13	.	.	PUNCT
ejpam-5997	618	1	applied	apply	VERB
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ejpam-5997	618	4	computation	computation	NOUN
ejpam-5997	618	5	,	,	PUNCT
ejpam-5997	618	6	238:237–244	238:237–244	NUM
ejpam-5997	618	7	,	,	PUNCT
ejpam-5997	618	8	2014	2014	NUM
ejpam-5997	618	9	.	.	PUNCT
ejpam-5997	619	1	[	[	X
ejpam-5997	619	2	33	33	NUM
ejpam-5997	619	3	]	]	X
ejpam-5997	619	4	daniel	daniel	PROPN
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ejpam-5997	619	7	.	.	PUNCT
ejpam-5997	620	1	some	some	DET
ejpam-5997	620	2	estimates	estimate	NOUN
ejpam-5997	620	3	on	on	ADP
ejpam-5997	620	4	the	the	DET
ejpam-5997	620	5	hermite	hermite	PROPN
ejpam-5997	620	6	-	-	PUNCT
ejpam-5997	620	7	hadamard	hadamard	ADJ
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ejpam-5997	620	9	through	through	ADP
ejpam-5997	620	10	quasim	quasim	NOUN
ejpam-5997	620	11	.	.	PUNCT
ejpam-5997	621	1	vivas	vivas	PROPN
ejpam-5997	621	2	-	-	NOUN
ejpam-5997	621	3	cortez	cortez	PROPN
ejpam-5997	621	4	et	et	PROPN
ejpam-5997	621	5	al	al	PROPN
ejpam-5997	621	6	.	.	PUNCT
ejpam-5997	621	7	/	/	SYM
ejpam-5997	621	8	eur	eur	PROPN
ejpam-5997	621	9	.	.	PUNCT
ejpam-5997	622	1	j.	j.	PROPN
ejpam-5997	622	2	pure	pure	PROPN
ejpam-5997	622	3	appl	appl	PROPN
ejpam-5997	622	4	.	.	PROPN
ejpam-5997	622	5	math	math	PROPN
ejpam-5997	622	6	,	,	PUNCT
ejpam-5997	622	7	18	18	NUM
ejpam-5997	622	8	(	(	PUNCT
ejpam-5997	622	9	2	2	NUM
ejpam-5997	622	10	)	)	PUNCT
ejpam-5997	622	11	(	(	PUNCT
ejpam-5997	622	12	2025	2025	NUM
ejpam-5997	622	13	)	)	PUNCT
ejpam-5997	622	14	,	,	PUNCT
ejpam-5997	622	15	5997	5997	NUM
ejpam-5997	622	16	23	23	NUM
ejpam-5997	622	17	of	of	ADP
ejpam-5997	622	18	23	23	NUM
ejpam-5997	622	19	convex	convex	NOUN
ejpam-5997	622	20	functions	function	NOUN
ejpam-5997	622	21	.	.	PUNCT
ejpam-5997	623	1	annals	annal	NOUN
ejpam-5997	623	2	of	of	ADP
ejpam-5997	623	3	the	the	DET
ejpam-5997	623	4	university	university	NOUN
ejpam-5997	623	5	of	of	ADP
ejpam-5997	623	6	craiova	craiova	PROPN
ejpam-5997	623	7	-	-	PUNCT
ejpam-5997	623	8	mathematics	mathematic	NOUN
ejpam-5997	623	9	and	and	CCONJ
ejpam-5997	623	10	computer	computer	NOUN
ejpam-5997	623	11	science	science	NOUN
ejpam-5997	623	12	series	series	NOUN
ejpam-5997	623	13	,	,	PUNCT
ejpam-5997	623	14	34:82–87	34:82–87	NUM
ejpam-5997	623	15	,	,	PUNCT
ejpam-5997	623	16	2007	2007	NUM
ejpam-5997	623	17	.	.	PUNCT
ejpam-5997	624	1	[	[	X
ejpam-5997	624	2	34	34	NUM
ejpam-5997	624	3	]	]	SYM
ejpam-5997	624	4	ed	ed	NOUN
ejpam-5997	624	5	rainville	rainville	NOUN
ejpam-5997	624	6	.	.	PUNCT
ejpam-5997	625	1	special	special	ADJ
ejpam-5997	625	2	functions	function	NOUN
ejpam-5997	625	3	,	,	PUNCT
ejpam-5997	625	4	chelsea	chelsea	PROPN
ejpam-5997	625	5	publ	publ	PROPN
ejpam-5997	625	6	.	.	PUNCT
ejpam-5997	626	1	co.	co.	PROPN
ejpam-5997	626	2	,	,	PUNCT
ejpam-5997	626	3	bronx	bronx	PROPN
ejpam-5997	626	4	,	,	PUNCT
ejpam-5997	626	5	new	new	PROPN
ejpam-5997	626	6	york	york	PROPN
ejpam-5997	626	7	,	,	PUNCT
ejpam-5997	626	8	1971	1971	NUM
ejpam-5997	626	9	.	.	PUNCT
ejpam-5997	627	1	[	[	X
ejpam-5997	627	2	35	35	NUM
ejpam-5997	627	3	]	]	PUNCT
ejpam-5997	627	4	aleksandar	aleksandar	PROPN
ejpam-5997	627	5	petojevic	petojevic	VERB
ejpam-5997	627	6	.	.	PUNCT
ejpam-5997	628	1	a	a	DET
ejpam-5997	628	2	note	note	NOUN
ejpam-5997	628	3	about	about	ADP
ejpam-5997	628	4	the	the	DET
ejpam-5997	628	5	pochhammer	pochhammer	NOUN
ejpam-5997	628	6	symbol	symbol	NOUN
ejpam-5997	628	7	.	.	PUNCT
ejpam-5997	629	1	mathematica	mathematica	PROPN
ejpam-5997	629	2	moravica	moravica	PROPN
ejpam-5997	629	3	,	,	PUNCT
ejpam-5997	629	4	12(1):37–42	12(1):37–42	NUM
ejpam-5997	629	5	,	,	PUNCT
ejpam-5997	629	6	2008	2008	NUM
ejpam-5997	629	7	.	.	PUNCT
ejpam-5997	630	1	[	[	X
ejpam-5997	630	2	36	36	NUM
ejpam-5997	630	3	]	]	X
ejpam-5997	630	4	shahid	shahid	PROPN
ejpam-5997	630	5	mubeen	mubeen	PROPN
ejpam-5997	630	6	,	,	PUNCT
ejpam-5997	630	7	rana	rana	PROPN
ejpam-5997	630	8	safdar	safdar	PROPN
ejpam-5997	630	9	ali	ali	PROPN
ejpam-5997	630	10	,	,	PUNCT
ejpam-5997	630	11	iqra	iqra	PROPN
ejpam-5997	630	12	nayab	nayab	PROPN
ejpam-5997	630	13	,	,	PUNCT
ejpam-5997	630	14	gauhar	gauhar	PROPN
ejpam-5997	630	15	rahman	rahman	PROPN
ejpam-5997	630	16	,	,	PUNCT
ejpam-5997	630	17	thabet	thabet	ADJ
ejpam-5997	630	18	abdeljawad	abdeljawad	NOUN
ejpam-5997	630	19	,	,	PUNCT
ejpam-5997	630	20	and	and	CCONJ
ejpam-5997	630	21	kottakkaran	kottakkaran	VERB
ejpam-5997	630	22	sooppy	sooppy	ADJ
ejpam-5997	630	23	nisar	nisar	PROPN
ejpam-5997	630	24	.	.	PUNCT
ejpam-5997	631	1	integral	integral	ADJ
ejpam-5997	631	2	transforms	transform	NOUN
ejpam-5997	631	3	of	of	ADP
ejpam-5997	631	4	an	an	DET
ejpam-5997	631	5	extended	extended	ADJ
ejpam-5997	631	6	generalized	generalize	VERB
ejpam-5997	631	7	multi	multi	ADJ
ejpam-5997	631	8	-	-	ADJ
ejpam-5997	631	9	index	index	ADJ
ejpam-5997	631	10	bessel	bessel	NOUN
ejpam-5997	631	11	function	function	NOUN
ejpam-5997	631	12	.	.	PUNCT
ejpam-5997	632	1	aims	aim	VERB
ejpam-5997	632	2	mathematics	mathematic	NOUN
ejpam-5997	632	3	,	,	PUNCT
ejpam-5997	632	4	5(6):7531–7546	5(6):7531–7546	PROPN
ejpam-5997	632	5	,	,	PUNCT
ejpam-5997	632	6	2020	2020	NUM
ejpam-5997	632	7	.	.	PUNCT
ejpam-5997	633	1	[	[	X
ejpam-5997	633	2	37	37	NUM
ejpam-5997	633	3	]	]	X
ejpam-5997	633	4	rana	rana	PROPN
ejpam-5997	633	5	safdar	safdar	PROPN
ejpam-5997	633	6	ali	ali	PROPN
ejpam-5997	633	7	,	,	PUNCT
ejpam-5997	633	8	shahid	shahid	PROPN
ejpam-5997	633	9	mubeen	mubeen	PROPN
ejpam-5997	633	10	,	,	PUNCT
ejpam-5997	633	11	iqra	iqra	NOUN
ejpam-5997	633	12	nayab	nayab	PROPN
ejpam-5997	633	13	,	,	PUNCT
ejpam-5997	633	14	serkan	serkan	ADJ
ejpam-5997	633	15	araci	araci	PROPN
ejpam-5997	633	16	,	,	PUNCT
ejpam-5997	633	17	gauhar	gauhar	PROPN
ejpam-5997	633	18	rahman	rahman	PROPN
ejpam-5997	633	19	,	,	PUNCT
ejpam-5997	633	20	and	and	CCONJ
ejpam-5997	633	21	kottakkaran	kottakkaran	VERB
ejpam-5997	633	22	sooppy	sooppy	ADJ
ejpam-5997	633	23	nisar	nisar	PROPN
ejpam-5997	633	24	.	.	PUNCT
ejpam-5997	634	1	some	some	DET
ejpam-5997	634	2	fractional	fractional	ADJ
ejpam-5997	634	3	operators	operator	NOUN
ejpam-5997	634	4	with	with	ADP
ejpam-5997	634	5	the	the	DET
ejpam-5997	634	6	generalized	generalize	VERB
ejpam-5997	634	7	bessel	bessel	NOUN
ejpam-5997	634	8	–	–	PUNCT
ejpam-5997	634	9	maitland	maitland	PROPN
ejpam-5997	634	10	function	function	NOUN
ejpam-5997	634	11	.	.	PUNCT
ejpam-5997	635	1	discrete	discrete	ADJ
ejpam-5997	635	2	dynamics	dynamic	NOUN
ejpam-5997	635	3	in	in	ADP
ejpam-5997	635	4	nature	nature	NOUN
ejpam-5997	635	5	and	and	CCONJ
ejpam-5997	635	6	society	society	NOUN
ejpam-5997	635	7	,	,	PUNCT
ejpam-5997	635	8	2020(1):1378457	2020(1):1378457	NUM
ejpam-5997	635	9	,	,	PUNCT
ejpam-5997	635	10	2020	2020	NUM
ejpam-5997	635	11	.	.	PUNCT
ejpam-5997	636	1	[	[	X
ejpam-5997	636	2	38	38	NUM
ejpam-5997	636	3	]	]	PUNCT
ejpam-5997	636	4	sabila	sabila	PROPN
ejpam-5997	636	5	ali	ali	PROPN
ejpam-5997	636	6	,	,	PUNCT
ejpam-5997	636	7	shahid	shahid	PROPN
ejpam-5997	636	8	mubeen	mubeen	PROPN
ejpam-5997	636	9	,	,	PUNCT
ejpam-5997	636	10	rana	rana	PROPN
ejpam-5997	636	11	safdar	safdar	PROPN
ejpam-5997	636	12	ali	ali	PROPN
ejpam-5997	636	13	,	,	PUNCT
ejpam-5997	636	14	gauhar	gauhar	PROPN
ejpam-5997	636	15	rahman	rahman	PROPN
ejpam-5997	636	16	,	,	PUNCT
ejpam-5997	636	17	ahmed	ahmed	PROPN
ejpam-5997	636	18	morsy	morsy	PROPN
ejpam-5997	636	19	,	,	PUNCT
ejpam-5997	636	20	kottakkaran	kottakkaran	VERB
ejpam-5997	636	21	sooppy	sooppy	ADJ
ejpam-5997	636	22	nisar	nisar	PROPN
ejpam-5997	636	23	,	,	PUNCT
ejpam-5997	636	24	sunil	sunil	PROPN
ejpam-5997	636	25	dutt	dutt	PROPN
ejpam-5997	636	26	purohit	purohit	PROPN
ejpam-5997	636	27	,	,	PUNCT
ejpam-5997	636	28	and	and	CCONJ
ejpam-5997	636	29	m	m	VERB
ejpam-5997	636	30	zakarya	zakarya	ADJ
ejpam-5997	636	31	.	.	PUNCT
ejpam-5997	637	1	dynamical	dynamical	ADJ
ejpam-5997	637	2	significance	significance	NOUN
ejpam-5997	637	3	of	of	ADP
ejpam-5997	637	4	generalized	generalized	ADJ
ejpam-5997	637	5	fractional	fractional	ADJ
ejpam-5997	637	6	integral	integral	ADJ
ejpam-5997	637	7	inequalities	inequality	NOUN
ejpam-5997	637	8	via	via	ADP
ejpam-5997	637	9	convexity	convexity	NOUN
ejpam-5997	637	10	.	.	PUNCT
ejpam-5997	638	1	aims	aim	VERB
ejpam-5997	638	2	math	math	NOUN
ejpam-5997	638	3	,	,	PUNCT
ejpam-5997	638	4	6(9):9705–9730	6(9):9705–9730	NUM
ejpam-5997	638	5	,	,	PUNCT
ejpam-5997	638	6	2021	2021	NUM
ejpam-5997	638	7	.	.	PUNCT
ejpam-5997	639	1	[	[	X
ejpam-5997	639	2	39	39	NUM
ejpam-5997	639	3	]	]	PUNCT
ejpam-5997	639	4	shahid	shahid	PROPN
ejpam-5997	639	5	mubeen	mubeen	PROPN
ejpam-5997	639	6	,	,	PUNCT
ejpam-5997	639	7	rana	rana	PROPN
ejpam-5997	639	8	safdar	safdar	PROPN
ejpam-5997	639	9	ali	ali	PROPN
ejpam-5997	639	10	,	,	PUNCT
ejpam-5997	639	11	yasser	yasser	PROPN
ejpam-5997	639	12	elmasry	elmasry	PROPN
ejpam-5997	639	13	,	,	PUNCT
ejpam-5997	639	14	ebenezer	ebenezer	PROPN
ejpam-5997	639	15	bonyah	bonyah	PROPN
ejpam-5997	639	16	,	,	PUNCT
ejpam-5997	639	17	artion	artion	NOUN
ejpam-5997	639	18	kashuri	kashuri	PROPN
ejpam-5997	639	19	,	,	PUNCT
ejpam-5997	639	20	gauhar	gauhar	PROPN
ejpam-5997	639	21	rahman	rahman	PROPN
ejpam-5997	639	22	,	,	PUNCT
ejpam-5997	639	23	and	and	CCONJ
ejpam-5997	639	24	çetin	çetin	PROPN
ejpam-5997	639	25	yildiz	yildiz	NOUN
ejpam-5997	639	26	.	.	PUNCT
ejpam-5997	640	1	on	on	ADP
ejpam-5997	640	2	novel	novel	ADJ
ejpam-5997	640	3	fractional	fractional	ADJ
ejpam-5997	640	4	integral	integral	ADJ
ejpam-5997	640	5	and	and	CCONJ
ejpam-5997	640	6	differential	differential	ADJ
ejpam-5997	640	7	operators	operator	NOUN
ejpam-5997	640	8	and	and	CCONJ
ejpam-5997	640	9	their	their	PRON
ejpam-5997	640	10	properties	property	NOUN
ejpam-5997	640	11	.	.	PUNCT
ejpam-5997	641	1	journal	journal	NOUN
ejpam-5997	641	2	of	of	ADP
ejpam-5997	641	3	mathematics	mathematic	NOUN
ejpam-5997	641	4	,	,	PUNCT
ejpam-5997	641	5	2023(1):4165363	2023(1):4165363	NOUN
ejpam-5997	641	6	,	,	PUNCT
ejpam-5997	641	7	2023	2023	NUM
ejpam-5997	641	8	.	.	PUNCT