id	sid	tid	token	lemma	pos
ejpam-6413	1	1	european	european	PROPN
ejpam-6413	1	2	journal	journal	PROPN
ejpam-6413	1	3	of	of	ADP
ejpam-6413	1	4	pure	pure	ADJ
ejpam-6413	1	5	and	and	CCONJ
ejpam-6413	1	6	applied	applied	ADJ
ejpam-6413	1	7	mathematics	mathematic	NOUN
ejpam-6413	1	8	2025	2025	NUM
ejpam-6413	1	9	,	,	PUNCT
ejpam-6413	1	10	vol	vol	NOUN
ejpam-6413	1	11	.	.	PROPN
ejpam-6413	1	12	18	18	NUM
ejpam-6413	1	13	,	,	PUNCT
ejpam-6413	1	14	issue	issue	NOUN
ejpam-6413	1	15	3	3	NUM
ejpam-6413	1	16	,	,	PUNCT
ejpam-6413	1	17	article	article	NOUN
ejpam-6413	1	18	number	number	NOUN
ejpam-6413	1	19	6413	6413	NUM
ejpam-6413	1	20	issn	issn	VERB
ejpam-6413	1	21	1307	1307	NUM
ejpam-6413	1	22	-	-	SYM
ejpam-6413	1	23	5543	5543	NUM
ejpam-6413	1	24	–	–	PUNCT
ejpam-6413	1	25	ejpam.com	ejpam.com	X
ejpam-6413	1	26	published	publish	VERB
ejpam-6413	1	27	by	by	ADP
ejpam-6413	1	28	new	new	PROPN
ejpam-6413	1	29	york	york	PROPN
ejpam-6413	1	30	business	business	PROPN
ejpam-6413	1	31	global	global	ADJ
ejpam-6413	1	32	hermite	hermite	PROPN
ejpam-6413	1	33	-	-	PUNCT
ejpam-6413	1	34	hadamard	hadamard	ADJ
ejpam-6413	1	35	inequalities	inequality	NOUN
ejpam-6413	1	36	via	via	ADP
ejpam-6413	1	37	riemann	riemann	PROPN
ejpam-6413	1	38	-	-	PUNCT
ejpam-6413	1	39	liouville	liouville	VERB
ejpam-6413	1	40	fractional	fractional	ADJ
ejpam-6413	1	41	integrals	integral	NOUN
ejpam-6413	1	42	with	with	ADP
ejpam-6413	1	43	generalized	generalized	ADJ
ejpam-6413	1	44	convex	convex	NOUN
ejpam-6413	1	45	functions	function	NOUN
ejpam-6413	1	46	muhammad	muhammad	PROPN
ejpam-6413	1	47	samraiz1	samraiz1	PROPN
ejpam-6413	1	48	,	,	PUNCT
ejpam-6413	1	49	tahira	tahira	PROPN
ejpam-6413	1	50	atta1	atta1	PROPN
ejpam-6413	1	51	,	,	PUNCT
ejpam-6413	1	52	saima	saima	PROPN
ejpam-6413	1	53	naheed1	naheed1	PROPN
ejpam-6413	1	54	,	,	PUNCT
ejpam-6413	1	55	gauhar	gauhar	PROPN
ejpam-6413	1	56	rahman2	rahman2	PROPN
ejpam-6413	1	57	,	,	PUNCT
ejpam-6413	1	58	miguel	miguel	PROPN
ejpam-6413	1	59	vivas	vivas	PROPN
ejpam-6413	1	60	-	-	PROPN
ejpam-6413	1	61	cortez3,∗	cortez3,∗	ADJ
ejpam-6413	1	62	1	1	NUM
ejpam-6413	1	63	department	department	NOUN
ejpam-6413	1	64	of	of	ADP
ejpam-6413	1	65	mathematics	mathematic	NOUN
ejpam-6413	1	66	,	,	PUNCT
ejpam-6413	1	67	university	university	PROPN
ejpam-6413	1	68	of	of	ADP
ejpam-6413	1	69	sargodha	sargodha	PROPN
ejpam-6413	1	70	,	,	PUNCT
ejpam-6413	1	71	sargodha	sargodha	PROPN
ejpam-6413	1	72	40100	40100	NUM
ejpam-6413	1	73	,	,	PUNCT
ejpam-6413	1	74	pakistan	pakistan	PROPN
ejpam-6413	1	75	.	.	PUNCT
ejpam-6413	2	1	2	2	NUM
ejpam-6413	2	2	department	department	NOUN
ejpam-6413	2	3	of	of	ADP
ejpam-6413	2	4	mathematics	mathematics	PROPN
ejpam-6413	2	5	&	&	CCONJ
ejpam-6413	2	6	statistics	statistics	PROPN
ejpam-6413	2	7	,	,	PUNCT
ejpam-6413	2	8	hazara	hazara	PROPN
ejpam-6413	2	9	university	university	PROPN
ejpam-6413	2	10	,	,	PUNCT
ejpam-6413	2	11	mansehra	mansehra	PROPN
ejpam-6413	2	12	21300	21300	NUM
ejpam-6413	2	13	,	,	PUNCT
ejpam-6413	2	14	pakistan	pakistan	PROPN
ejpam-6413	2	15	.	.	PUNCT
ejpam-6413	3	1	3	3	NUM
ejpam-6413	3	2	pontificia	pontificia	PROPN
ejpam-6413	3	3	universidad	universidad	PROPN
ejpam-6413	3	4	católica	católica	PROPN
ejpam-6413	3	5	del	del	PROPN
ejpam-6413	3	6	ecuador	ecuador	PROPN
ejpam-6413	3	7	,	,	PUNCT
ejpam-6413	3	8	faculty	faculty	NOUN
ejpam-6413	3	9	of	of	ADP
ejpam-6413	3	10	exact	exact	ADJ
ejpam-6413	3	11	,	,	PUNCT
ejpam-6413	3	12	natural	natural	ADJ
ejpam-6413	3	13	and	and	CCONJ
ejpam-6413	3	14	environmental	environmental	ADJ
ejpam-6413	3	15	sciences	science	NOUN
ejpam-6413	3	16	,	,	PUNCT
ejpam-6413	3	17	fractal	fractal	ADJ
ejpam-6413	3	18	laboratory	laboratory	NOUN
ejpam-6413	3	19	(	(	PUNCT
ejpam-6413	3	20	fractional	fractional	ADJ
ejpam-6413	3	21	research	research	NOUN
ejpam-6413	3	22	in	in	ADP
ejpam-6413	3	23	analysis	analysis	NOUN
ejpam-6413	3	24	,	,	PUNCT
ejpam-6413	3	25	convexity	convexity	NOUN
ejpam-6413	3	26	and	and	CCONJ
ejpam-6413	3	27	their	their	PRON
ejpam-6413	3	28	applications	application	NOUN
ejpam-6413	3	29	laboratory	laboratory	NOUN
ejpam-6413	3	30	)	)	PUNCT
ejpam-6413	3	31	,	,	PUNCT
ejpam-6413	3	32	ecuador	ecuador	NOUN
ejpam-6413	3	33	.	.	PUNCT
ejpam-6413	4	1	abstract	abstract	ADJ
ejpam-6413	4	2	.	.	PUNCT
ejpam-6413	5	1	in	in	ADP
ejpam-6413	5	2	this	this	DET
ejpam-6413	5	3	study	study	NOUN
ejpam-6413	5	4	,	,	PUNCT
ejpam-6413	5	5	novel	novel	ADJ
ejpam-6413	5	6	fractional	fractional	ADJ
ejpam-6413	5	7	integral	integral	ADJ
ejpam-6413	5	8	inequalities	inequality	NOUN
ejpam-6413	5	9	for	for	ADP
ejpam-6413	5	10	twice	twice	ADV
ejpam-6413	5	11	-	-	PUNCT
ejpam-6413	5	12	differentiable	differentiable	NOUN
ejpam-6413	5	13	geometrically	geometrically	ADV
ejpam-6413	5	14	arithmetically	arithmetically	ADV
ejpam-6413	5	15	(	(	PUNCT
ejpam-6413	5	16	α	α	NOUN
ejpam-6413	5	17	,	,	PUNCT
ejpam-6413	5	18	m)-convex	m)-convex	PUNCT
ejpam-6413	5	19	functions	function	NOUN
ejpam-6413	5	20	are	be	AUX
ejpam-6413	5	21	presented	present	VERB
ejpam-6413	5	22	.	.	PUNCT
ejpam-6413	6	1	the	the	DET
ejpam-6413	6	2	classical	classical	ADJ
ejpam-6413	6	3	riemann	riemann	PROPN
ejpam-6413	6	4	-	-	PUNCT
ejpam-6413	6	5	liouville	liouville	VERB
ejpam-6413	6	6	fractional	fractional	ADJ
ejpam-6413	6	7	integrals	integral	NOUN
ejpam-6413	6	8	are	be	AUX
ejpam-6413	6	9	used	use	VERB
ejpam-6413	6	10	to	to	PART
ejpam-6413	6	11	obtain	obtain	VERB
ejpam-6413	6	12	several	several	ADJ
ejpam-6413	6	13	new	new	ADJ
ejpam-6413	6	14	identities	identity	NOUN
ejpam-6413	6	15	.	.	PUNCT
ejpam-6413	7	1	by	by	ADP
ejpam-6413	7	2	employing	employ	VERB
ejpam-6413	7	3	the	the	DET
ejpam-6413	7	4	above	above	ADJ
ejpam-6413	7	5	convexity	convexity	NOUN
ejpam-6413	7	6	,	,	PUNCT
ejpam-6413	7	7	hermitehadamard	hermitehadamard	ADJ
ejpam-6413	7	8	type	type	NOUN
ejpam-6413	7	9	inequalities	inequality	NOUN
ejpam-6413	7	10	are	be	AUX
ejpam-6413	7	11	investigated	investigate	VERB
ejpam-6413	7	12	using	use	VERB
ejpam-6413	7	13	these	these	DET
ejpam-6413	7	14	identities	identity	NOUN
ejpam-6413	7	15	.	.	PUNCT
ejpam-6413	8	1	the	the	DET
ejpam-6413	8	2	main	main	ADJ
ejpam-6413	8	3	findings	finding	NOUN
ejpam-6413	8	4	of	of	ADP
ejpam-6413	8	5	this	this	DET
ejpam-6413	8	6	work	work	NOUN
ejpam-6413	8	7	extend	extend	VERB
ejpam-6413	8	8	the	the	DET
ejpam-6413	8	9	existing	exist	VERB
ejpam-6413	8	10	literature	literature	NOUN
ejpam-6413	8	11	and	and	CCONJ
ejpam-6413	8	12	are	be	AUX
ejpam-6413	8	13	derived	derive	VERB
ejpam-6413	8	14	as	as	ADP
ejpam-6413	8	15	special	special	ADJ
ejpam-6413	8	16	cases	case	NOUN
ejpam-6413	8	17	.	.	PUNCT
ejpam-6413	9	1	2020	2020	NUM
ejpam-6413	9	2	mathematics	mathematic	NOUN
ejpam-6413	9	3	subject	subject	NOUN
ejpam-6413	9	4	classifications	classification	NOUN
ejpam-6413	9	5	:	:	PUNCT
ejpam-6413	9	6	26a51	26a51	NUM
ejpam-6413	9	7	,	,	PUNCT
ejpam-6413	9	8	26a33	26a33	NUM
ejpam-6413	9	9	,	,	PUNCT
ejpam-6413	9	10	26d15	26d15	DET
ejpam-6413	9	11	key	key	ADJ
ejpam-6413	9	12	words	word	NOUN
ejpam-6413	9	13	and	and	CCONJ
ejpam-6413	9	14	phrases	phrase	NOUN
ejpam-6413	9	15	:	:	PUNCT
ejpam-6413	9	16	geometrically	geometrically	ADV
ejpam-6413	9	17	arithmetically	arithmetically	ADV
ejpam-6413	9	18	(	(	PUNCT
ejpam-6413	9	19	α	α	NOUN
ejpam-6413	9	20	,	,	PUNCT
ejpam-6413	9	21	m)-convex	m)-convex	ADJ
ejpam-6413	9	22	,	,	PUNCT
ejpam-6413	9	23	hermite	hermite	ADJ
ejpam-6413	9	24	-	-	PUNCT
ejpam-6413	9	25	hadamard	hadamard	ADJ
ejpam-6413	9	26	type	type	NOUN
ejpam-6413	9	27	inequalities	inequality	NOUN
ejpam-6413	9	28	,	,	PUNCT
ejpam-6413	9	29	hölder	hölder	PROPN
ejpam-6413	9	30	’s	’s	PART
ejpam-6413	9	31	inequality	inequality	NOUN
ejpam-6413	9	32	,	,	PUNCT
ejpam-6413	9	33	fractional	fractional	ADJ
ejpam-6413	9	34	integrals	integral	NOUN
ejpam-6413	9	35	1	1	NUM
ejpam-6413	9	36	.	.	PUNCT
ejpam-6413	9	37	introduction	introduction	NOUN
ejpam-6413	9	38	and	and	CCONJ
ejpam-6413	9	39	preliminaries	preliminary	NOUN
ejpam-6413	9	40	fractional	fractional	ADJ
ejpam-6413	9	41	calculus	calculus	NOUN
ejpam-6413	9	42	explores	explore	VERB
ejpam-6413	9	43	the	the	DET
ejpam-6413	9	44	integrals	integral	NOUN
ejpam-6413	9	45	and	and	CCONJ
ejpam-6413	9	46	derivatives	derivative	NOUN
ejpam-6413	9	47	of	of	ADP
ejpam-6413	9	48	arbitrary	arbitrary	ADJ
ejpam-6413	9	49	real	real	ADJ
ejpam-6413	9	50	or	or	CCONJ
ejpam-6413	9	51	complex	complex	ADJ
ejpam-6413	9	52	orders	order	NOUN
ejpam-6413	9	53	.	.	PUNCT
ejpam-6413	10	1	it	it	PRON
ejpam-6413	10	2	provides	provide	VERB
ejpam-6413	10	3	a	a	DET
ejpam-6413	10	4	range	range	NOUN
ejpam-6413	10	5	of	of	ADP
ejpam-6413	10	6	tools	tool	NOUN
ejpam-6413	10	7	that	that	PRON
ejpam-6413	10	8	can	can	AUX
ejpam-6413	10	9	be	be	AUX
ejpam-6413	10	10	used	use	VERB
ejpam-6413	10	11	to	to	PART
ejpam-6413	10	12	solve	solve	VERB
ejpam-6413	10	13	differential	differential	ADJ
ejpam-6413	10	14	equations	equation	NOUN
ejpam-6413	10	15	,	,	PUNCT
ejpam-6413	10	16	integral	integral	ADJ
ejpam-6413	10	17	equations	equation	NOUN
ejpam-6413	10	18	,	,	PUNCT
ejpam-6413	10	19	mathematical	mathematical	ADJ
ejpam-6413	10	20	physics	physics	NOUN
ejpam-6413	10	21	,	,	PUNCT
ejpam-6413	10	22	engineering	engineering	NOUN
ejpam-6413	10	23	and	and	CCONJ
ejpam-6413	10	24	machine	machine	NOUN
ejpam-6413	10	25	learning	learning	NOUN
ejpam-6413	10	26	problems	problem	NOUN
ejpam-6413	10	27	.	.	PUNCT
ejpam-6413	11	1	within	within	ADP
ejpam-6413	11	2	the	the	DET
ejpam-6413	11	3	context	context	NOUN
ejpam-6413	11	4	of	of	ADP
ejpam-6413	11	5	riemann	riemann	PROPN
ejpam-6413	11	6	-	-	PUNCT
ejpam-6413	11	7	liouville	liouville	VERB
ejpam-6413	11	8	fractional	fractional	ADJ
ejpam-6413	11	9	calculus	calculus	NOUN
ejpam-6413	11	10	,	,	PUNCT
ejpam-6413	11	11	this	this	DET
ejpam-6413	11	12	discussion	discussion	NOUN
ejpam-6413	11	13	focuses	focus	VERB
ejpam-6413	11	14	on	on	ADP
ejpam-6413	11	15	the	the	DET
ejpam-6413	11	16	linear	linear	PROPN
ejpam-6413	11	17	operators	operator	NOUN
ejpam-6413	11	18	of	of	ADP
ejpam-6413	11	19	fractional	fractional	ADJ
ejpam-6413	11	20	integration	integration	NOUN
ejpam-6413	11	21	and	and	CCONJ
ejpam-6413	11	22	differentiation	differentiation	NOUN
ejpam-6413	11	23	[	[	X
ejpam-6413	11	24	1	1	NUM
ejpam-6413	11	25	,	,	PUNCT
ejpam-6413	11	26	2	2	NUM
ejpam-6413	11	27	]	]	PUNCT
ejpam-6413	11	28	.	.	PUNCT
ejpam-6413	12	1	it	it	PRON
ejpam-6413	12	2	also	also	ADV
ejpam-6413	12	3	addresses	address	VERB
ejpam-6413	12	4	the	the	DET
ejpam-6413	12	5	existence	existence	NOUN
ejpam-6413	12	6	of	of	ADP
ejpam-6413	12	7	mild	mild	ADJ
ejpam-6413	12	8	solutions	solution	NOUN
ejpam-6413	12	9	for	for	ADP
ejpam-6413	12	10	fractional	fractional	ADJ
ejpam-6413	12	11	-	-	PUNCT
ejpam-6413	12	12	order	order	NOUN
ejpam-6413	12	13	caputo	caputo	NOUN
ejpam-6413	12	14	derivatives	derivative	NOUN
ejpam-6413	12	15	in	in	ADP
ejpam-6413	12	16	banach	banach	NOUN
ejpam-6413	12	17	spaces	space	NOUN
ejpam-6413	12	18	.	.	PUNCT
ejpam-6413	13	1	moreover	moreover	ADV
ejpam-6413	13	2	,	,	PUNCT
ejpam-6413	13	3	it	it	PRON
ejpam-6413	13	4	delves	delve	VERB
ejpam-6413	13	5	into	into	ADP
ejpam-6413	13	6	the	the	DET
ejpam-6413	13	7	existence	existence	NOUN
ejpam-6413	13	8	of	of	ADP
ejpam-6413	13	9	mild	mild	ADJ
ejpam-6413	13	10	solutions	solution	NOUN
ejpam-6413	13	11	for	for	ADP
ejpam-6413	13	12	nonlocal	nonlocal	ADJ
ejpam-6413	13	13	impulsive	impulsive	ADJ
ejpam-6413	13	14	differential	differential	ADJ
ejpam-6413	13	15	inclusions	inclusion	NOUN
ejpam-6413	13	16	[	[	X
ejpam-6413	13	17	3	3	NUM
ejpam-6413	13	18	,	,	PUNCT
ejpam-6413	13	19	4	4	NUM
ejpam-6413	13	20	]	]	PUNCT
ejpam-6413	13	21	,	,	PUNCT
ejpam-6413	13	22	considering	consider	VERB
ejpam-6413	13	23	neumann	neumann	PROPN
ejpam-6413	13	24	boundary	boundary	ADJ
ejpam-6413	13	25	conditions	condition	NOUN
ejpam-6413	13	26	in	in	ADP
ejpam-6413	13	27	the	the	DET
ejpam-6413	13	28	form	form	NOUN
ejpam-6413	13	29	where	where	SCONJ
ejpam-6413	13	30	u	u	NOUN
ejpam-6413	13	31	and	and	CCONJ
ejpam-6413	13	32	v	v	NOUN
ejpam-6413	13	33	represent	represent	VERB
ejpam-6413	13	34	∗corresponding	∗corresponde	VERB
ejpam-6413	13	35	author	author	NOUN
ejpam-6413	13	36	.	.	PUNCT
ejpam-6413	14	1	doi	doi	NOUN
ejpam-6413	14	2	:	:	PUNCT
ejpam-6413	14	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6413	https://doi.org/10.29020/nybg.ejpam.v18i3.6413	PROPN
ejpam-6413	14	4	email	email	NOUN
ejpam-6413	14	5	addresses	address	NOUN
ejpam-6413	14	6	:	:	PUNCT
ejpam-6413	14	7	muhammad.samraiz@uos.edu.pk	muhammad.samraiz@uos.edu.pk	PROPN
ejpam-6413	14	8	(	(	PUNCT
ejpam-6413	14	9	m.	m.	NOUN
ejpam-6413	14	10	samraiz	samraiz	PROPN
ejpam-6413	14	11	)	)	PUNCT
ejpam-6413	14	12	,	,	PUNCT
ejpam-6413	14	13	tahiraatta55@gmail.com	tahiraatta55@gmail.com	X
ejpam-6413	14	14	(	(	PUNCT
ejpam-6413	14	15	t.	t.	NOUN
ejpam-6413	14	16	atta	atta	PROPN
ejpam-6413	14	17	)	)	PUNCT
ejpam-6413	14	18	,	,	PUNCT
ejpam-6413	14	19	saima.naheed@uos.edu.pk	saima.naheed@uos.edu.pk	PROPN
ejpam-6413	14	20	(	(	PUNCT
ejpam-6413	14	21	s.	s.	PROPN
ejpam-6413	14	22	naheed	naheed	PROPN
ejpam-6413	14	23	)	)	PUNCT
ejpam-6413	14	24	,	,	PUNCT
ejpam-6413	14	25	drgauhar.rahman@hu.edu.pk	drgauhar.rahman@hu.edu.pk	PROPN
ejpam-6413	14	26	,	,	PUNCT
ejpam-6413	14	27	gauhar55uom@gmail.com	gauhar55uom@gmail.com	X
ejpam-6413	14	28	(	(	PUNCT
ejpam-6413	14	29	g.	g.	PROPN
ejpam-6413	14	30	rahman	rahman	PROPN
ejpam-6413	14	31	)	)	PUNCT
ejpam-6413	14	32	,	,	PUNCT
ejpam-6413	14	33	mjvivas@puce.edu.ec	mjvivas@puce.edu.ec	NOUN
ejpam-6413	14	34	(	(	PUNCT
ejpam-6413	14	35	m.	m.	PROPN
ejpam-6413	14	36	vivas	vivas	PROPN
ejpam-6413	14	37	-	-	NOUN
ejpam-6413	14	38	cortez	cortez	PROPN
ejpam-6413	14	39	)	)	PUNCT
ejpam-6413	14	40	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6413	14	41	1	1	NUM
ejpam-6413	14	42	copyright	copyright	NOUN
ejpam-6413	14	43	:	:	PUNCT
ejpam-6413	15	1	©	©	PROPN
ejpam-6413	15	2	2025	2025	NUM
ejpam-6413	15	3	the	the	DET
ejpam-6413	15	4	author(s	author(s	NOUN
ejpam-6413	15	5	)	)	PUNCT
ejpam-6413	15	6	.	.	PUNCT
ejpam-6413	16	1	(	(	PUNCT
ejpam-6413	16	2	cc	cc	NOUN
ejpam-6413	16	3	by	by	ADP
ejpam-6413	16	4	-	-	PUNCT
ejpam-6413	16	5	nc	nc	PROPN
ejpam-6413	16	6	4.0	4.0	NUM
ejpam-6413	16	7	)	)	PUNCT
ejpam-6413	16	8	m.	m.	NOUN
ejpam-6413	16	9	samraiz	samraiz	PROPN
ejpam-6413	16	10	et	et	PROPN
ejpam-6413	16	11	al	al	PROPN
ejpam-6413	16	12	.	.	PUNCT
ejpam-6413	16	13	/	/	SYM
ejpam-6413	16	14	eur	eur	PROPN
ejpam-6413	16	15	.	.	PUNCT
ejpam-6413	17	1	j.	j.	PROPN
ejpam-6413	17	2	pure	pure	PROPN
ejpam-6413	17	3	appl	appl	PROPN
ejpam-6413	17	4	.	.	PROPN
ejpam-6413	17	5	math	math	PROPN
ejpam-6413	17	6	,	,	PUNCT
ejpam-6413	17	7	18	18	NUM
ejpam-6413	17	8	(	(	PUNCT
ejpam-6413	17	9	3	3	NUM
ejpam-6413	17	10	)	)	PUNCT
ejpam-6413	17	11	(	(	PUNCT
ejpam-6413	17	12	2025	2025	NUM
ejpam-6413	17	13	)	)	PUNCT
ejpam-6413	17	14	,	,	PUNCT
ejpam-6413	17	15	6413	6413	NUM
ejpam-6413	17	16	2	2	NUM
ejpam-6413	17	17	of	of	ADP
ejpam-6413	17	18	26	26	NUM
ejpam-6413	17	19	typical	typical	ADJ
ejpam-6413	17	20	caputo	caputo	PROPN
ejpam-6413	17	21	fractional	fractional	ADJ
ejpam-6413	17	22	derivatives	derivative	NOUN
ejpam-6413	17	23	[	[	X
ejpam-6413	17	24	5	5	NUM
ejpam-6413	17	25	]	]	PUNCT
ejpam-6413	17	26	.	.	PUNCT
ejpam-6413	18	1	the	the	DET
ejpam-6413	18	2	investigation	investigation	NOUN
ejpam-6413	18	3	further	far	ADV
ejpam-6413	18	4	encompasses	encompass	VERB
ejpam-6413	18	5	fractionalorder	fractionalorder	PROPN
ejpam-6413	18	6	delay	delay	NOUN
ejpam-6413	18	7	differential	differential	ADJ
ejpam-6413	18	8	equations	equation	NOUN
ejpam-6413	19	1	[	[	X
ejpam-6413	19	2	6	6	NUM
ejpam-6413	19	3	]	]	PUNCT
ejpam-6413	19	4	,	,	PUNCT
ejpam-6413	19	5	while	while	SCONJ
ejpam-6413	19	6	volterra	volterra	NOUN
ejpam-6413	19	7	-	-	PUNCT
ejpam-6413	19	8	fredholm	fredholm	NOUN
ejpam-6413	19	9	integral	integral	ADJ
ejpam-6413	19	10	equations	equation	NOUN
ejpam-6413	19	11	involving	involve	VERB
ejpam-6413	19	12	the	the	DET
ejpam-6413	19	13	erdlyi	erdlyi	NOUN
ejpam-6413	19	14	-	-	PUNCT
ejpam-6413	19	15	kober	kober	NOUN
ejpam-6413	19	16	fractional	fractional	ADJ
ejpam-6413	19	17	integral	integral	ADJ
ejpam-6413	19	18	operator	operator	NOUN
ejpam-6413	19	19	are	be	AUX
ejpam-6413	19	20	discussed	discuss	VERB
ejpam-6413	19	21	in	in	ADP
ejpam-6413	19	22	[	[	X
ejpam-6413	19	23	7	7	NUM
ejpam-6413	19	24	]	]	PUNCT
ejpam-6413	19	25	.	.	PUNCT
ejpam-6413	20	1	the	the	DET
ejpam-6413	20	2	ulam	ulam	PROPN
ejpam-6413	20	3	-	-	PUNCT
ejpam-6413	20	4	hyers	hyer	NOUN
ejpam-6413	20	5	type	type	NOUN
ejpam-6413	20	6	stability	stability	NOUN
ejpam-6413	20	7	for	for	ADP
ejpam-6413	20	8	certain	certain	ADJ
ejpam-6413	20	9	nonlinear	nonlinear	ADJ
ejpam-6413	20	10	differential	differential	ADJ
ejpam-6413	20	11	equations	equation	NOUN
ejpam-6413	20	12	are	be	AUX
ejpam-6413	20	13	discussed	discuss	VERB
ejpam-6413	20	14	in	in	ADP
ejpam-6413	20	15	[	[	X
ejpam-6413	20	16	8	8	NUM
ejpam-6413	20	17	]	]	PUNCT
ejpam-6413	20	18	.	.	PUNCT
ejpam-6413	21	1	this	this	DET
ejpam-6413	21	2	study	study	NOUN
ejpam-6413	21	3	also	also	ADV
ejpam-6413	21	4	derives	derive	VERB
ejpam-6413	21	5	several	several	ADJ
ejpam-6413	21	6	tensorial	tensorial	ADJ
ejpam-6413	21	7	trapezoid	trapezoid	ADJ
ejpam-6413	21	8	-	-	PUNCT
ejpam-6413	21	9	type	type	NOUN
ejpam-6413	21	10	inequalities	inequality	NOUN
ejpam-6413	21	11	in	in	ADP
ejpam-6413	21	12	hilbert	hilbert	PROPN
ejpam-6413	21	13	spaces	space	NOUN
ejpam-6413	21	14	by	by	ADP
ejpam-6413	21	15	employing	employ	VERB
ejpam-6413	21	16	classical	classical	ADJ
ejpam-6413	21	17	analytical	analytical	ADJ
ejpam-6413	21	18	identities	identity	NOUN
ejpam-6413	21	19	and	and	CCONJ
ejpam-6413	21	20	exploring	explore	VERB
ejpam-6413	21	21	the	the	DET
ejpam-6413	21	22	convexity	convexity	NOUN
ejpam-6413	21	23	properties	property	NOUN
ejpam-6413	21	24	of	of	ADP
ejpam-6413	21	25	functions	function	NOUN
ejpam-6413	21	26	involving	involve	VERB
ejpam-6413	21	27	selfadjoint	selfadjoint	NOUN
ejpam-6413	21	28	operators	operator	NOUN
ejpam-6413	21	29	[	[	X
ejpam-6413	21	30	9	9	NUM
ejpam-6413	21	31	]	]	PUNCT
ejpam-6413	21	32	.	.	PUNCT
ejpam-6413	22	1	the	the	DET
ejpam-6413	22	2	applications	application	NOUN
ejpam-6413	22	3	of	of	ADP
ejpam-6413	22	4	non	non	ADJ
ejpam-6413	22	5	-	-	ADJ
ejpam-6413	22	6	integer	integer	ADJ
ejpam-6413	22	7	order	order	NOUN
ejpam-6413	22	8	derivatives	derivative	NOUN
ejpam-6413	22	9	can	can	AUX
ejpam-6413	22	10	be	be	AUX
ejpam-6413	22	11	studied	study	VERB
ejpam-6413	22	12	in	in	ADP
ejpam-6413	22	13	[	[	X
ejpam-6413	22	14	10	10	NUM
ejpam-6413	22	15	]	]	PUNCT
ejpam-6413	22	16	and	and	CCONJ
ejpam-6413	22	17	numerical	numerical	ADJ
ejpam-6413	22	18	solutions	solution	NOUN
ejpam-6413	22	19	for	for	ADP
ejpam-6413	22	20	various	various	ADJ
ejpam-6413	22	21	types	type	NOUN
ejpam-6413	22	22	of	of	ADP
ejpam-6413	22	23	fractional	fractional	ADJ
ejpam-6413	22	24	diffusion	diffusion	NOUN
ejpam-6413	22	25	equations	equation	NOUN
ejpam-6413	22	26	in	in	ADP
ejpam-6413	22	27	[	[	X
ejpam-6413	22	28	11	11	NUM
ejpam-6413	22	29	]	]	PUNCT
ejpam-6413	22	30	.	.	PUNCT
ejpam-6413	23	1	additionally	additionally	ADV
ejpam-6413	23	2	,	,	PUNCT
ejpam-6413	23	3	the	the	DET
ejpam-6413	23	4	applications	application	NOUN
ejpam-6413	23	5	in	in	ADP
ejpam-6413	23	6	the	the	DET
ejpam-6413	23	7	dynamics	dynamic	NOUN
ejpam-6413	23	8	of	of	ADP
ejpam-6413	23	9	particles	particle	NOUN
ejpam-6413	23	10	,	,	PUNCT
ejpam-6413	23	11	fields	field	NOUN
ejpam-6413	23	12	and	and	CCONJ
ejpam-6413	23	13	media	medium	NOUN
ejpam-6413	23	14	can	can	AUX
ejpam-6413	23	15	be	be	AUX
ejpam-6413	23	16	explored	explore	VERB
ejpam-6413	23	17	in	in	ADP
ejpam-6413	23	18	the	the	DET
ejpam-6413	23	19	book	book	NOUN
ejpam-6413	23	20	[	[	X
ejpam-6413	23	21	12	12	NUM
ejpam-6413	23	22	]	]	PUNCT
ejpam-6413	23	23	.	.	PUNCT
ejpam-6413	24	1	the	the	DET
ejpam-6413	24	2	theory	theory	NOUN
ejpam-6413	24	3	of	of	ADP
ejpam-6413	24	4	convex	convex	NOUN
ejpam-6413	24	5	functions	function	NOUN
ejpam-6413	24	6	has	have	AUX
ejpam-6413	24	7	experienced	experience	VERB
ejpam-6413	24	8	rapid	rapid	ADJ
ejpam-6413	24	9	development	development	NOUN
ejpam-6413	24	10	.	.	PUNCT
ejpam-6413	25	1	there	there	PRON
ejpam-6413	25	2	are	be	VERB
ejpam-6413	25	3	several	several	ADJ
ejpam-6413	25	4	reasons	reason	NOUN
ejpam-6413	25	5	to	to	PART
ejpam-6413	25	6	study	study	VERB
ejpam-6413	25	7	this	this	DET
ejpam-6413	25	8	concept	concept	NOUN
ejpam-6413	25	9	.	.	PUNCT
ejpam-6413	26	1	firstly	firstly	ADV
ejpam-6413	26	2	,	,	PUNCT
ejpam-6413	26	3	modern	modern	ADJ
ejpam-6413	26	4	analysis	analysis	NOUN
ejpam-6413	26	5	involve	involve	VERB
ejpam-6413	26	6	applications	application	NOUN
ejpam-6413	26	7	of	of	ADP
ejpam-6413	26	8	convex	convex	NOUN
ejpam-6413	26	9	functions	function	NOUN
ejpam-6413	26	10	directly	directly	ADV
ejpam-6413	26	11	or	or	CCONJ
ejpam-6413	26	12	indirectly	indirectly	ADV
ejpam-6413	26	13	.	.	PUNCT
ejpam-6413	27	1	secondly	secondly	ADV
ejpam-6413	27	2	,	,	PUNCT
ejpam-6413	27	3	this	this	DET
ejpam-6413	27	4	theory	theory	NOUN
ejpam-6413	27	5	plays	play	VERB
ejpam-6413	27	6	a	a	DET
ejpam-6413	27	7	significant	significant	ADJ
ejpam-6413	27	8	role	role	NOUN
ejpam-6413	27	9	in	in	ADP
ejpam-6413	27	10	the	the	DET
ejpam-6413	27	11	construction	construction	NOUN
ejpam-6413	27	12	of	of	ADP
ejpam-6413	27	13	many	many	ADJ
ejpam-6413	27	14	existing	exist	VERB
ejpam-6413	27	15	inequalities	inequality	NOUN
ejpam-6413	27	16	,	,	PUNCT
ejpam-6413	27	17	which	which	PRON
ejpam-6413	27	18	play	play	VERB
ejpam-6413	27	19	a	a	DET
ejpam-6413	27	20	major	major	ADJ
ejpam-6413	27	21	role	role	NOUN
ejpam-6413	27	22	in	in	ADP
ejpam-6413	27	23	optimization	optimization	NOUN
ejpam-6413	27	24	theory	theory	NOUN
ejpam-6413	27	25	.	.	PUNCT
ejpam-6413	28	1	it	it	PRON
ejpam-6413	28	2	has	have	AUX
ejpam-6413	28	3	been	be	AUX
ejpam-6413	28	4	demonstrated	demonstrate	VERB
ejpam-6413	28	5	that	that	SCONJ
ejpam-6413	28	6	fractional	fractional	ADJ
ejpam-6413	28	7	integral	integral	ADJ
ejpam-6413	28	8	inequalities	inequality	NOUN
ejpam-6413	28	9	are	be	AUX
ejpam-6413	28	10	one	one	NUM
ejpam-6413	28	11	of	of	ADP
ejpam-6413	28	12	the	the	DET
ejpam-6413	28	13	best	good	ADJ
ejpam-6413	28	14	tools	tool	NOUN
ejpam-6413	28	15	for	for	ADP
ejpam-6413	28	16	the	the	DET
ejpam-6413	28	17	growth	growth	NOUN
ejpam-6413	28	18	of	of	ADP
ejpam-6413	28	19	many	many	ADJ
ejpam-6413	28	20	fields	field	NOUN
ejpam-6413	28	21	of	of	ADP
ejpam-6413	28	22	pure	pure	ADJ
ejpam-6413	28	23	and	and	CCONJ
ejpam-6413	28	24	applied	applied	ADJ
ejpam-6413	28	25	mathematics	mathematic	NOUN
ejpam-6413	28	26	.	.	PUNCT
ejpam-6413	29	1	research	research	NOUN
ejpam-6413	29	2	on	on	ADP
ejpam-6413	29	3	hermite	hermite	PROPN
ejpam-6413	29	4	-	-	PUNCT
ejpam-6413	29	5	hadamard	hadamard	ADJ
ejpam-6413	29	6	inequality	inequality	NOUN
ejpam-6413	29	7	has	have	AUX
ejpam-6413	29	8	been	be	AUX
ejpam-6413	29	9	ongoing	ongoing	ADJ
ejpam-6413	29	10	since	since	SCONJ
ejpam-6413	29	11	its	its	PRON
ejpam-6413	29	12	introduction	introduction	NOUN
ejpam-6413	29	13	in	in	ADP
ejpam-6413	29	14	1893	1893	NUM
ejpam-6413	29	15	.	.	PUNCT
ejpam-6413	30	1	the	the	DET
ejpam-6413	30	2	hermite	hermite	PROPN
ejpam-6413	30	3	-	-	PUNCT
ejpam-6413	30	4	hadamard	hadamard	ADJ
ejpam-6413	30	5	inequality	inequality	NOUN
ejpam-6413	30	6	for	for	ADP
ejpam-6413	30	7	fractional	fractional	ADJ
ejpam-6413	30	8	integrals	integral	NOUN
ejpam-6413	30	9	was	be	AUX
ejpam-6413	30	10	initially	initially	ADV
ejpam-6413	30	11	formulated	formulate	VERB
ejpam-6413	30	12	by	by	ADP
ejpam-6413	30	13	sarikaya	sarikaya	PROPN
ejpam-6413	30	14	et	et	PROPN
ejpam-6413	30	15	al	al	PROPN
ejpam-6413	30	16	.	.	PUNCT
ejpam-6413	31	1	in	in	ADP
ejpam-6413	31	2	[	[	X
ejpam-6413	31	3	13	13	NUM
ejpam-6413	31	4	]	]	PUNCT
ejpam-6413	31	5	.	.	PUNCT
ejpam-6413	32	1	such	such	ADJ
ejpam-6413	32	2	inequalities	inequality	NOUN
ejpam-6413	32	3	were	be	AUX
ejpam-6413	32	4	further	far	ADV
ejpam-6413	32	5	studied	study	VERB
ejpam-6413	32	6	by	by	ADP
ejpam-6413	32	7	shuang	shuang	PROPN
ejpam-6413	32	8	et	et	PROPN
ejpam-6413	32	9	al	al	PROPN
ejpam-6413	32	10	.	.	PROPN
ejpam-6413	32	11	for	for	ADP
ejpam-6413	32	12	geometrically	geometrically	ADV
ejpam-6413	32	13	arithmetically	arithmetically	ADV
ejpam-6413	32	14	(	(	PUNCT
ejpam-6413	32	15	ga	ga	NOUN
ejpam-6413	32	16	)	)	PUNCT
ejpam-6413	32	17	s	s	NOUN
ejpam-6413	32	18	-	-	PUNCT
ejpam-6413	32	19	convex	convex	NOUN
ejpam-6413	32	20	functions	function	NOUN
ejpam-6413	32	21	in	in	ADP
ejpam-6413	32	22	[	[	X
ejpam-6413	32	23	14	14	NUM
ejpam-6413	32	24	]	]	PUNCT
ejpam-6413	32	25	.	.	PUNCT
ejpam-6413	33	1	the	the	DET
ejpam-6413	33	2	riemann	riemann	PROPN
ejpam-6413	33	3	-	-	PUNCT
ejpam-6413	33	4	liouville	liouville	VERB
ejpam-6413	33	5	fractional	fractional	ADJ
ejpam-6413	33	6	hermite	hermite	PROPN
ejpam-6413	33	7	-	-	PUNCT
ejpam-6413	33	8	hadamard	hadamard	ADJ
ejpam-6413	33	9	inequalities	inequality	NOUN
ejpam-6413	33	10	for	for	ADP
ejpam-6413	33	11	twice	twice	ADV
ejpam-6413	33	12	differentiable	differentiable	ADJ
ejpam-6413	33	13	geometrically	geometrically	ADV
ejpam-6413	33	14	and	and	CCONJ
ejpam-6413	33	15	arithmetically	arithmetically	ADV
ejpam-6413	33	16	s	s	NOUN
ejpam-6413	33	17	-	-	PUNCT
ejpam-6413	33	18	convex	convex	ADJ
ejpam-6413	33	19	functions	function	NOUN
ejpam-6413	33	20	,	,	PUNCT
ejpam-6413	33	21	along	along	ADP
ejpam-6413	33	22	with	with	ADP
ejpam-6413	33	23	precise	precise	ADJ
ejpam-6413	33	24	error	error	NOUN
ejpam-6413	33	25	estimates	estimate	NOUN
ejpam-6413	33	26	presented	present	VERB
ejpam-6413	33	27	in	in	ADP
ejpam-6413	33	28	[	[	X
ejpam-6413	33	29	15	15	NUM
ejpam-6413	33	30	,	,	PUNCT
ejpam-6413	33	31	16	16	NUM
ejpam-6413	33	32	]	]	PUNCT
ejpam-6413	33	33	highlighting	highlight	VERB
ejpam-6413	33	34	the	the	DET
ejpam-6413	33	35	significance	significance	NOUN
ejpam-6413	33	36	of	of	ADP
ejpam-6413	33	37	hermite	hermite	PROPN
ejpam-6413	33	38	-	-	PUNCT
ejpam-6413	33	39	hadamard	hadamard	NOUN
ejpam-6413	33	40	.	.	PUNCT
ejpam-6413	34	1	the	the	DET
ejpam-6413	34	2	inequality	inequality	NOUN
ejpam-6413	34	3	provides	provide	VERB
ejpam-6413	34	4	bounds	bound	NOUN
ejpam-6413	34	5	on	on	ADP
ejpam-6413	34	6	the	the	DET
ejpam-6413	34	7	mean	mean	ADJ
ejpam-6413	34	8	function	function	NOUN
ejpam-6413	34	9	,	,	PUNCT
ejpam-6413	34	10	assisting	assist	VERB
ejpam-6413	34	11	in	in	ADP
ejpam-6413	34	12	error	error	NOUN
ejpam-6413	34	13	estimation	estimation	NOUN
ejpam-6413	34	14	for	for	ADP
ejpam-6413	34	15	trapezoid	trapezoid	ADJ
ejpam-6413	34	16	formulas	formula	NOUN
ejpam-6413	34	17	and	and	CCONJ
ejpam-6413	34	18	the	the	DET
ejpam-6413	34	19	construction	construction	NOUN
ejpam-6413	34	20	of	of	ADP
ejpam-6413	34	21	generalized	generalized	ADJ
ejpam-6413	34	22	means	mean	NOUN
ejpam-6413	34	23	.	.	PUNCT
ejpam-6413	35	1	fractional	fractional	ADJ
ejpam-6413	35	2	hermite	hermite	PROPN
ejpam-6413	35	3	-	-	PUNCT
ejpam-6413	35	4	hadamard	hadamard	ADJ
ejpam-6413	35	5	inequalities	inequality	NOUN
ejpam-6413	35	6	involving	involve	VERB
ejpam-6413	35	7	different	different	ADJ
ejpam-6413	35	8	types	type	NOUN
ejpam-6413	35	9	of	of	ADP
ejpam-6413	35	10	fractional	fractional	ADJ
ejpam-6413	35	11	integrals	integral	NOUN
ejpam-6413	35	12	and	and	CCONJ
ejpam-6413	35	13	various	various	ADJ
ejpam-6413	35	14	classes	class	NOUN
ejpam-6413	35	15	of	of	ADP
ejpam-6413	35	16	convex	convex	NOUN
ejpam-6413	35	17	functions	function	NOUN
ejpam-6413	35	18	have	have	AUX
ejpam-6413	35	19	attracted	attract	VERB
ejpam-6413	35	20	significant	significant	ADJ
ejpam-6413	35	21	attention	attention	NOUN
ejpam-6413	35	22	of	of	ADP
ejpam-6413	35	23	the	the	DET
ejpam-6413	35	24	scientists	scientist	NOUN
ejpam-6413	35	25	.	.	PUNCT
ejpam-6413	36	1	applications	application	NOUN
ejpam-6413	36	2	to	to	ADP
ejpam-6413	36	3	special	special	ADJ
ejpam-6413	36	4	means	mean	NOUN
ejpam-6413	36	5	,	,	PUNCT
ejpam-6413	36	6	fractional	fractional	ADJ
ejpam-6413	36	7	integral	integral	ADJ
ejpam-6413	36	8	inequalities	inequality	NOUN
ejpam-6413	36	9	for	for	ADP
ejpam-6413	36	10	differentiable	differentiable	ADJ
ejpam-6413	36	11	convex	convex	NOUN
ejpam-6413	36	12	maps	map	NOUN
ejpam-6413	36	13	and	and	CCONJ
ejpam-6413	36	14	midpoint	midpoint	NOUN
ejpam-6413	36	15	formulas	formula	NOUN
ejpam-6413	36	16	were	be	AUX
ejpam-6413	36	17	explored	explore	VERB
ejpam-6413	36	18	in	in	ADP
ejpam-6413	36	19	[	[	X
ejpam-6413	36	20	17	17	NUM
ejpam-6413	36	21	]	]	PUNCT
ejpam-6413	36	22	,	,	PUNCT
ejpam-6413	36	23	while	while	SCONJ
ejpam-6413	36	24	the	the	DET
ejpam-6413	36	25	integral	integral	ADJ
ejpam-6413	36	26	inequality	inequality	NOUN
ejpam-6413	36	27	of	of	ADP
ejpam-6413	36	28	the	the	DET
ejpam-6413	36	29	ostrowski	ostrowski	NOUN
ejpam-6413	36	30	’s	’s	PART
ejpam-6413	36	31	type	type	NOUN
ejpam-6413	36	32	and	and	CCONJ
ejpam-6413	36	33	hermite	hermite	ADJ
ejpam-6413	36	34	-	-	PUNCT
ejpam-6413	36	35	hadamard	hadamard	ADJ
ejpam-6413	36	36	integral	integral	ADJ
ejpam-6413	36	37	inequality	inequality	NOUN
ejpam-6413	36	38	were	be	AUX
ejpam-6413	36	39	investigated	investigate	VERB
ejpam-6413	36	40	in	in	ADP
ejpam-6413	36	41	[	[	X
ejpam-6413	36	42	18	18	NUM
ejpam-6413	36	43	,	,	PUNCT
ejpam-6413	36	44	19	19	NUM
ejpam-6413	36	45	]	]	PUNCT
ejpam-6413	36	46	.	.	PUNCT
ejpam-6413	37	1	references	reference	NOUN
ejpam-6413	37	2	such	such	ADJ
ejpam-6413	37	3	as	as	ADP
ejpam-6413	37	4	[	[	X
ejpam-6413	37	5	20–23	20–23	NOUN
ejpam-6413	37	6	]	]	PUNCT
ejpam-6413	37	7	provide	provide	VERB
ejpam-6413	37	8	insights	insight	NOUN
ejpam-6413	37	9	into	into	ADP
ejpam-6413	37	10	convex	convex	NOUN
ejpam-6413	37	11	functions	function	NOUN
ejpam-6413	37	12	,	,	PUNCT
ejpam-6413	37	13	s	s	NOUN
ejpam-6413	37	14	-	-	PUNCT
ejpam-6413	37	15	convex	convex	ADJ
ejpam-6413	37	16	functions	function	NOUN
ejpam-6413	37	17	,	,	PUNCT
ejpam-6413	37	18	r	r	NOUN
ejpam-6413	37	19	-	-	PUNCT
ejpam-6413	37	20	convex	convex	NOUN
ejpam-6413	37	21	functions	function	NOUN
ejpam-6413	37	22	,	,	PUNCT
ejpam-6413	37	23	(	(	PUNCT
ejpam-6413	37	24	s	s	X
ejpam-6413	37	25	,	,	PUNCT
ejpam-6413	37	26	m)-convex	m)-convex	PUNCT
ejpam-6413	37	27	,	,	PUNCT
ejpam-6413	37	28	and	and	CCONJ
ejpam-6413	37	29	(	(	PUNCT
ejpam-6413	37	30	s	s	X
ejpam-6413	37	31	,	,	PUNCT
ejpam-6413	37	32	m	m	NOUN
ejpam-6413	37	33	)	)	PUNCT
ejpam-6413	37	34	logarithmical	logarithmical	ADJ
ejpam-6413	37	35	functions	function	NOUN
ejpam-6413	37	36	,	,	PUNCT
ejpam-6413	37	37	respectively	respectively	ADV
ejpam-6413	37	38	.	.	PUNCT
ejpam-6413	38	1	two	two	NUM
ejpam-6413	38	2	classes	class	NOUN
ejpam-6413	38	3	of	of	ADP
ejpam-6413	38	4	new	new	ADJ
ejpam-6413	38	5	hermite	hermite	ADJ
ejpam-6413	38	6	-	-	PUNCT
ejpam-6413	38	7	hadamard	hadamard	ADJ
ejpam-6413	38	8	type	type	NOUN
ejpam-6413	38	9	inequalities	inequality	NOUN
ejpam-6413	38	10	,	,	PUNCT
ejpam-6413	38	11	requiring	require	VERB
ejpam-6413	38	12	riemannliouville	riemannliouville	NOUN
ejpam-6413	38	13	fractional	fractional	ADJ
ejpam-6413	38	14	integrals	integral	NOUN
ejpam-6413	38	15	,	,	PUNCT
ejpam-6413	38	16	were	be	AUX
ejpam-6413	38	17	constructed	construct	VERB
ejpam-6413	38	18	for	for	ADP
ejpam-6413	38	19	once	once	ADV
ejpam-6413	38	20	differentiable	differentiable	ADJ
ejpam-6413	38	21	and	and	CCONJ
ejpam-6413	38	22	twice	twice	ADV
ejpam-6413	38	23	differentiable	differentiable	ADJ
ejpam-6413	38	24	(	(	PUNCT
ejpam-6413	38	25	s	s	X
ejpam-6413	38	26	,	,	PUNCT
ejpam-6413	38	27	m	m	NOUN
ejpam-6413	38	28	)	)	PUNCT
ejpam-6413	38	29	and	and	CCONJ
ejpam-6413	38	30	(	(	PUNCT
ejpam-6413	38	31	α	α	NOUN
ejpam-6413	38	32	,	,	PUNCT
ejpam-6413	38	33	m)-lgorithmically	m)-lgorithmically	ADV
ejpam-6413	38	34	convex	convex	NOUN
ejpam-6413	38	35	functions	function	NOUN
ejpam-6413	38	36	in	in	ADP
ejpam-6413	38	37	[	[	X
ejpam-6413	38	38	24	24	NUM
ejpam-6413	38	39	,	,	PUNCT
ejpam-6413	38	40	25	25	NUM
ejpam-6413	38	41	]	]	PUNCT
ejpam-6413	38	42	.	.	PUNCT
ejpam-6413	39	1	hermite	hermite	PROPN
ejpam-6413	39	2	-	-	PUNCT
ejpam-6413	39	3	hadamard	hadamard	ADJ
ejpam-6413	39	4	inequalities	inequality	NOUN
ejpam-6413	39	5	for	for	ADP
ejpam-6413	39	6	functions	function	NOUN
ejpam-6413	39	7	satisfying	satisfy	VERB
ejpam-6413	39	8	the	the	DET
ejpam-6413	39	9	s−	s−	PROPN
ejpam-6413	39	10	e	e	NOUN
ejpam-6413	39	11	-	-	NOUN
ejpam-6413	39	12	condition	condition	NOUN
ejpam-6413	39	13	and	and	CCONJ
ejpam-6413	39	14	along	along	ADP
ejpam-6413	39	15	with	with	ADP
ejpam-6413	39	16	a	a	DET
ejpam-6413	39	17	method	method	NOUN
ejpam-6413	39	18	for	for	ADP
ejpam-6413	39	19	solving	solve	VERB
ejpam-6413	39	20	nonlinear	nonlinear	ADJ
ejpam-6413	39	21	integral	integral	ADJ
ejpam-6413	39	22	equations	equation	NOUN
ejpam-6413	39	23	through	through	ADP
ejpam-6413	39	24	the	the	DET
ejpam-6413	39	25	riemann	riemann	PROPN
ejpam-6413	39	26	-	-	PUNCT
ejpam-6413	39	27	liouville	liouville	VERB
ejpam-6413	39	28	fractional	fractional	ADJ
ejpam-6413	39	29	operator	operator	NOUN
ejpam-6413	39	30	were	be	AUX
ejpam-6413	39	31	studied	study	VERB
ejpam-6413	39	32	in	in	ADP
ejpam-6413	39	33	[	[	X
ejpam-6413	39	34	26	26	NUM
ejpam-6413	39	35	]	]	PUNCT
ejpam-6413	39	36	.	.	PUNCT
ejpam-6413	40	1	researchers	researcher	NOUN
ejpam-6413	40	2	have	have	AUX
ejpam-6413	40	3	also	also	ADV
ejpam-6413	40	4	explored	explore	VERB
ejpam-6413	40	5	inequalities	inequality	NOUN
ejpam-6413	40	6	using	use	VERB
ejpam-6413	40	7	fractional	fractional	ADJ
ejpam-6413	40	8	continuities	continuity	NOUN
ejpam-6413	40	9	and	and	CCONJ
ejpam-6413	40	10	differences	difference	NOUN
ejpam-6413	40	11	.	.	PUNCT
ejpam-6413	41	1	hermite	hermite	PROPN
ejpam-6413	41	2	-	-	PUNCT
ejpam-6413	41	3	hadamard	hadamard	ADJ
ejpam-6413	41	4	type	type	NOUN
ejpam-6413	41	5	integral	integral	ADJ
ejpam-6413	41	6	inequalities	inequality	NOUN
ejpam-6413	41	7	involving	involve	VERB
ejpam-6413	41	8	the	the	DET
ejpam-6413	41	9	k	k	ADJ
ejpam-6413	41	10	-	-	ADJ
ejpam-6413	41	11	riemannliouville	riemannliouville	ADJ
ejpam-6413	41	12	fractional	fractional	ADJ
ejpam-6413	41	13	operator	operator	NOUN
ejpam-6413	41	14	for	for	ADP
ejpam-6413	41	15	twice	twice	ADV
ejpam-6413	41	16	-	-	PUNCT
ejpam-6413	41	17	differentiable	differentiable	ADJ
ejpam-6413	41	18	h	h	NOUN
ejpam-6413	41	19	-	-	PUNCT
ejpam-6413	41	20	convex	convex	NOUN
ejpam-6413	41	21	functions	function	NOUN
ejpam-6413	41	22	are	be	AUX
ejpam-6413	41	23	investigated	investigate	VERB
ejpam-6413	41	24	in	in	ADP
ejpam-6413	41	25	[	[	X
ejpam-6413	41	26	27	27	NUM
ejpam-6413	41	27	]	]	SYM
ejpam-6413	41	28	.	.	PUNCT
ejpam-6413	42	1	hermite	hermite	PROPN
ejpam-6413	42	2	-	-	PUNCT
ejpam-6413	42	3	hadamard	hadamard	ADJ
ejpam-6413	42	4	type	type	NOUN
ejpam-6413	42	5	inequalities	inequality	NOUN
ejpam-6413	42	6	for	for	ADP
ejpam-6413	42	7	h	h	NOUN
ejpam-6413	42	8	-	-	PUNCT
ejpam-6413	42	9	convex	convex	ADJ
ejpam-6413	42	10	function	function	NOUN
ejpam-6413	42	11	,	,	PUNCT
ejpam-6413	42	12	as	as	ADV
ejpam-6413	42	13	well	well	ADV
ejpam-6413	42	14	as	as	ADP
ejpam-6413	42	15	those	those	PRON
ejpam-6413	42	16	involving	involve	VERB
ejpam-6413	42	17	(	(	PUNCT
ejpam-6413	42	18	k	k	NOUN
ejpam-6413	42	19	−	−	PROPN
ejpam-6413	42	20	p)-operator	p)-operator	NOUN
ejpam-6413	42	21	with	with	ADP
ejpam-6413	42	22	(	(	PUNCT
ejpam-6413	42	23	α	α	NOUN
ejpam-6413	42	24	,	,	PUNCT
ejpam-6413	42	25	h	h	NOUN
ejpam-6413	42	26	-	-	PUNCT
ejpam-6413	42	27	m)-p	m)-p	ADV
ejpam-6413	42	28	convexity	convexity	NOUN
ejpam-6413	42	29	are	be	AUX
ejpam-6413	42	30	discussed	discuss	VERB
ejpam-6413	42	31	in	in	ADP
ejpam-6413	42	32	[	[	X
ejpam-6413	42	33	28	28	NUM
ejpam-6413	42	34	]	]	PUNCT
ejpam-6413	42	35	.	.	PUNCT
ejpam-6413	43	1	iqbal	iqbal	PROPN
ejpam-6413	43	2	et	et	PROPN
ejpam-6413	43	3	al	al	PROPN
ejpam-6413	43	4	.	.	PROPN
ejpam-6413	43	5	investigated	investigate	VERB
ejpam-6413	43	6	grüss	grüss	PROPN
ejpam-6413	43	7	inequalities	inequality	NOUN
ejpam-6413	43	8	in	in	ADP
ejpam-6413	43	9	[	[	X
ejpam-6413	43	10	29	29	NUM
ejpam-6413	43	11	]	]	PUNCT
ejpam-6413	43	12	by	by	ADP
ejpam-6413	43	13	considering	consider	VERB
ejpam-6413	43	14	the	the	DET
ejpam-6413	43	15	notion	notion	NOUN
ejpam-6413	43	16	of	of	ADP
ejpam-6413	43	17	generalized	generalized	ADJ
ejpam-6413	43	18	fractional	fractional	ADJ
ejpam-6413	43	19	derivative	derivative	NOUN
ejpam-6413	43	20	and	and	CCONJ
ejpam-6413	43	21	samraiz	samraiz	PROPN
ejpam-6413	43	22	et	et	PROPN
ejpam-6413	43	23	al	al	PROPN
ejpam-6413	43	24	.	.	PROPN
ejpam-6413	43	25	examined	examine	VERB
ejpam-6413	43	26	hermite	hermite	PROPN
ejpam-6413	43	27	-	-	PUNCT
ejpam-6413	43	28	hadamard	hadamard	ADJ
ejpam-6413	43	29	inequalities	inequality	NOUN
ejpam-6413	43	30	for	for	ADP
ejpam-6413	43	31	differentiable	differentiable	ADJ
ejpam-6413	43	32	functions	function	NOUN
ejpam-6413	43	33	m.	m.	NOUN
ejpam-6413	43	34	samraiz	samraiz	PROPN
ejpam-6413	43	35	et	et	PROPN
ejpam-6413	43	36	al	al	PROPN
ejpam-6413	43	37	.	.	PUNCT
ejpam-6413	43	38	/	/	SYM
ejpam-6413	43	39	eur	eur	PROPN
ejpam-6413	43	40	.	.	PUNCT
ejpam-6413	44	1	j.	j.	PROPN
ejpam-6413	44	2	pure	pure	PROPN
ejpam-6413	44	3	appl	appl	PROPN
ejpam-6413	44	4	.	.	PROPN
ejpam-6413	44	5	math	math	PROPN
ejpam-6413	44	6	,	,	PUNCT
ejpam-6413	44	7	18	18	NUM
ejpam-6413	44	8	(	(	PUNCT
ejpam-6413	44	9	3	3	NUM
ejpam-6413	44	10	)	)	PUNCT
ejpam-6413	44	11	(	(	PUNCT
ejpam-6413	44	12	2025	2025	NUM
ejpam-6413	44	13	)	)	PUNCT
ejpam-6413	44	14	,	,	PUNCT
ejpam-6413	44	15	6413	6413	NUM
ejpam-6413	44	16	3	3	NUM
ejpam-6413	44	17	of	of	ADP
ejpam-6413	44	18	26	26	NUM
ejpam-6413	44	19	in	in	ADP
ejpam-6413	44	20	[	[	X
ejpam-6413	44	21	30	30	NUM
ejpam-6413	44	22	]	]	PUNCT
ejpam-6413	44	23	.	.	PUNCT
ejpam-6413	45	1	convex	convex	NOUN
ejpam-6413	45	2	functions	function	NOUN
ejpam-6413	45	3	in	in	ADP
ejpam-6413	45	4	the	the	DET
ejpam-6413	45	5	second	second	ADJ
ejpam-6413	45	6	sense	sense	NOUN
ejpam-6413	45	7	were	be	AUX
ejpam-6413	45	8	studied	study	VERB
ejpam-6413	45	9	in	in	ADP
ejpam-6413	45	10	[	[	X
ejpam-6413	45	11	31	31	NUM
ejpam-6413	45	12	]	]	PUNCT
ejpam-6413	45	13	and	and	CCONJ
ejpam-6413	45	14	the	the	DET
ejpam-6413	45	15	fractional	fractional	ADJ
ejpam-6413	45	16	hermite	hermite	ADJ
ejpam-6413	45	17	-	-	PUNCT
ejpam-6413	45	18	hadamard	hadamard	ADJ
ejpam-6413	45	19	inequalities	inequality	NOUN
ejpam-6413	45	20	in	in	ADP
ejpam-6413	45	21	the	the	DET
ejpam-6413	45	22	second	second	ADJ
ejpam-6413	45	23	sense	sense	NOUN
ejpam-6413	45	24	were	be	AUX
ejpam-6413	45	25	investigated	investigate	VERB
ejpam-6413	45	26	in	in	ADP
ejpam-6413	45	27	[	[	X
ejpam-6413	45	28	32	32	NUM
ejpam-6413	45	29	]	]	PUNCT
ejpam-6413	45	30	.	.	PUNCT
ejpam-6413	46	1	2	2	X
ejpam-6413	46	2	.	.	X
ejpam-6413	46	3	preliminaries	preliminary	NOUN
ejpam-6413	46	4	this	this	DET
ejpam-6413	46	5	section	section	NOUN
ejpam-6413	46	6	contains	contain	VERB
ejpam-6413	46	7	basic	basic	ADJ
ejpam-6413	46	8	definitions	definition	NOUN
ejpam-6413	46	9	and	and	CCONJ
ejpam-6413	46	10	introductory	introductory	ADJ
ejpam-6413	46	11	information	information	NOUN
ejpam-6413	46	12	need	need	VERB
ejpam-6413	46	13	to	to	PART
ejpam-6413	46	14	explore	explore	VERB
ejpam-6413	46	15	the	the	DET
ejpam-6413	46	16	main	main	ADJ
ejpam-6413	46	17	results	result	NOUN
ejpam-6413	46	18	.	.	PUNCT
ejpam-6413	47	1	one	one	NUM
ejpam-6413	47	2	of	of	ADP
ejpam-6413	47	3	the	the	DET
ejpam-6413	47	4	early	early	ADJ
ejpam-6413	47	5	mathematicians	mathematician	NOUN
ejpam-6413	47	6	to	to	PART
ejpam-6413	47	7	investigate	investigate	VERB
ejpam-6413	47	8	the	the	DET
ejpam-6413	47	9	gamma	gamma	NOUN
ejpam-6413	47	10	function	function	NOUN
ejpam-6413	47	11	was	be	AUX
ejpam-6413	47	12	leonhard	leonhard	PROPN
ejpam-6413	47	13	euler	euler	NOUN
ejpam-6413	47	14	in	in	ADP
ejpam-6413	47	15	1729	1729	NUM
ejpam-6413	47	16	,	,	PUNCT
ejpam-6413	47	17	as	as	SCONJ
ejpam-6413	47	18	documented	document	VERB
ejpam-6413	47	19	in	in	ADP
ejpam-6413	47	20	[	[	X
ejpam-6413	47	21	33	33	NUM
ejpam-6413	47	22	]	]	PUNCT
ejpam-6413	47	23	.	.	PUNCT
ejpam-6413	48	1	the	the	DET
ejpam-6413	48	2	gamma	gamma	PROPN
ejpam-6413	48	3	function	function	NOUN
ejpam-6413	48	4	,	,	PUNCT
ejpam-6413	48	5	as	as	SCONJ
ejpam-6413	48	6	defined	define	VERB
ejpam-6413	48	7	in	in	ADP
ejpam-6413	48	8	[	[	PUNCT
ejpam-6413	48	9	34	34	NUM
ejpam-6413	48	10	]	]	PUNCT
ejpam-6413	48	11	,	,	PUNCT
ejpam-6413	48	12	can	can	AUX
ejpam-6413	48	13	be	be	AUX
ejpam-6413	48	14	expressed	express	VERB
ejpam-6413	48	15	using	use	VERB
ejpam-6413	48	16	the	the	DET
ejpam-6413	48	17	following	follow	VERB
ejpam-6413	48	18	definition	definition	NOUN
ejpam-6413	48	19	.	.	PUNCT
ejpam-6413	49	1	definition	definition	NOUN
ejpam-6413	49	2	1	1	NUM
ejpam-6413	49	3	.	.	PUNCT
ejpam-6413	50	1	the	the	DET
ejpam-6413	50	2	gamma	gamma	PROPN
ejpam-6413	50	3	function	function	NOUN
ejpam-6413	50	4	,	,	PUNCT
ejpam-6413	50	5	for	for	ADP
ejpam-6413	50	6	r(λ	r(λ	NOUN
ejpam-6413	50	7	)	)	PUNCT
ejpam-6413	50	8	>	>	X
ejpam-6413	50	9	0	0	NUM
ejpam-6413	50	10	,	,	PUNCT
ejpam-6413	50	11	is	be	AUX
ejpam-6413	50	12	defined	define	VERB
ejpam-6413	50	13	by	by	ADP
ejpam-6413	50	14	the	the	DET
ejpam-6413	50	15	relation	relation	NOUN
ejpam-6413	50	16	:	:	PUNCT
ejpam-6413	50	17	γ(λ	γ(λ	VERB
ejpam-6413	50	18	)	)	PUNCT
ejpam-6413	50	19	=	=	SYM
ejpam-6413	51	1	∫	∫	PROPN
ejpam-6413	52	1	+	+	NUM
ejpam-6413	52	2	∞	∞	NOUN
ejpam-6413	52	3	0	0	PUNCT
ejpam-6413	52	4	⊺λ−1e−⊺d	⊺λ−1e−⊺d	PROPN
ejpam-6413	52	5	⊺	⊺	NUM
ejpam-6413	52	6	.	.	PUNCT
ejpam-6413	53	1	the	the	DET
ejpam-6413	53	2	expression	expression	NOUN
ejpam-6413	53	3	below	below	ADP
ejpam-6413	53	4	that	that	PRON
ejpam-6413	53	5	defines	define	VERB
ejpam-6413	53	6	the	the	DET
ejpam-6413	53	7	complete	complete	ADJ
ejpam-6413	53	8	beta	beta	ADJ
ejpam-6413	53	9	function	function	NOUN
ejpam-6413	53	10	as	as	SCONJ
ejpam-6413	53	11	presented	present	VERB
ejpam-6413	53	12	in	in	ADP
ejpam-6413	53	13	reference	reference	NOUN
ejpam-6413	53	14	[	[	X
ejpam-6413	53	15	35	35	NUM
ejpam-6413	53	16	]	]	PUNCT
ejpam-6413	53	17	.	.	PUNCT
ejpam-6413	54	1	definition	definition	NOUN
ejpam-6413	54	2	2	2	NUM
ejpam-6413	54	3	.	.	PUNCT
ejpam-6413	55	1	the	the	DET
ejpam-6413	55	2	complete	complete	ADJ
ejpam-6413	55	3	beta	beta	NOUN
ejpam-6413	55	4	function	function	NOUN
ejpam-6413	55	5	defined	define	VERB
ejpam-6413	55	6	for	for	ADP
ejpam-6413	55	7	positive	positive	ADJ
ejpam-6413	55	8	real	real	ADJ
ejpam-6413	55	9	numbers	number	NOUN
ejpam-6413	55	10	ā	ā	ADJ
ejpam-6413	55	11	and	and	CCONJ
ejpam-6413	55	12	b̄	b̄	PROPN
ejpam-6413	55	13	,	,	PUNCT
ejpam-6413	55	14	where	where	SCONJ
ejpam-6413	55	15	r(ā	r(ā	NOUN
ejpam-6413	55	16	)	)	PUNCT
ejpam-6413	55	17	>	>	X
ejpam-6413	55	18	0	0	PROPN
ejpam-6413	55	19	and	and	CCONJ
ejpam-6413	55	20	r(b̄	r(b̄	PROPN
ejpam-6413	55	21	)	)	PUNCT
ejpam-6413	55	22	>	>	X
ejpam-6413	55	23	0	0	X
ejpam-6413	55	24	.	.	PUNCT
ejpam-6413	55	25	b(ā	b(ā	PROPN
ejpam-6413	55	26	,	,	PUNCT
ejpam-6413	55	27	b̄	b̄	NOUN
ejpam-6413	55	28	)	)	PUNCT
ejpam-6413	56	1	=	=	PUNCT
ejpam-6413	56	2	∫	∫	PROPN
ejpam-6413	57	1	1	1	NUM
ejpam-6413	57	2	0	0	X
ejpam-6413	57	3	⊺ā−1(1−	⊺ā−1(1−	PROPN
ejpam-6413	57	4	⊺)b̄−1d	⊺)b̄−1d	NOUN
ejpam-6413	57	5	⊺	⊺	NUM
ejpam-6413	57	6	.	.	PUNCT
ejpam-6413	58	1	the	the	DET
ejpam-6413	58	2	incomplete	incomplete	ADJ
ejpam-6413	58	3	beta	beta	NOUN
ejpam-6413	58	4	function	function	NOUN
ejpam-6413	58	5	,	,	PUNCT
ejpam-6413	58	6	defined	define	VERB
ejpam-6413	58	7	in	in	ADP
ejpam-6413	58	8	reference	reference	NOUN
ejpam-6413	58	9	[	[	X
ejpam-6413	58	10	36	36	NUM
ejpam-6413	58	11	]	]	PUNCT
ejpam-6413	58	12	,	,	PUNCT
ejpam-6413	58	13	given	give	VERB
ejpam-6413	58	14	by	by	ADP
ejpam-6413	58	15	the	the	DET
ejpam-6413	58	16	the	the	DET
ejpam-6413	58	17	following	follow	VERB
ejpam-6413	58	18	definition	definition	NOUN
ejpam-6413	58	19	.	.	PUNCT
ejpam-6413	59	1	definition	definition	NOUN
ejpam-6413	59	2	3	3	X
ejpam-6413	59	3	.	.	PUNCT
ejpam-6413	60	1	let	let	VERB
ejpam-6413	60	2	λ	λ	X
ejpam-6413	60	3	∈	∈	PROPN
ejpam-6413	61	1	[	[	X
ejpam-6413	61	2	0	0	NUM
ejpam-6413	61	3	,	,	PUNCT
ejpam-6413	61	4	1	1	NUM
ejpam-6413	61	5	]	]	PUNCT
ejpam-6413	61	6	and	and	CCONJ
ejpam-6413	61	7	ā	ā	VERB
ejpam-6413	61	8	,	,	PUNCT
ejpam-6413	61	9	b̄	b̄	VERB
ejpam-6413	61	10	>	>	X
ejpam-6413	61	11	0	0	X
ejpam-6413	61	12	.	.	PUNCT
ejpam-6413	62	1	then	then	ADV
ejpam-6413	62	2	,	,	PUNCT
ejpam-6413	62	3	the	the	DET
ejpam-6413	62	4	incomplete	incomplete	ADJ
ejpam-6413	62	5	beta	beta	NOUN
ejpam-6413	62	6	function	function	NOUN
ejpam-6413	62	7	is	be	AUX
ejpam-6413	62	8	defined	define	VERB
ejpam-6413	62	9	by	by	ADP
ejpam-6413	62	10	bλ(ā	bλ(ā	PROPN
ejpam-6413	62	11	,	,	PUNCT
ejpam-6413	62	12	b̄	b̄	NOUN
ejpam-6413	62	13	)	)	PUNCT
ejpam-6413	63	1	=	=	SYM
ejpam-6413	64	1	∫	∫	PROPN
ejpam-6413	64	2	λ	λ	X
ejpam-6413	64	3	0	0	SYM
ejpam-6413	64	4	⊺ā−1(1−	⊺ā−1(1−	PROPN
ejpam-6413	64	5	⊺)b̄−1d	⊺)b̄−1d	NOUN
ejpam-6413	64	6	⊺	⊺	NUM
ejpam-6413	64	7	.	.	PUNCT
ejpam-6413	65	1	the	the	DET
ejpam-6413	65	2	beta	beta	ADJ
ejpam-6413	65	3	function	function	NOUN
ejpam-6413	65	4	is	be	AUX
ejpam-6413	65	5	also	also	ADV
ejpam-6413	65	6	related	relate	VERB
ejpam-6413	65	7	to	to	ADP
ejpam-6413	65	8	the	the	DET
ejpam-6413	65	9	gamma	gamma	NOUN
ejpam-6413	65	10	function	function	NOUN
ejpam-6413	65	11	through	through	ADP
ejpam-6413	65	12	the	the	DET
ejpam-6413	65	13	following	follow	VERB
ejpam-6413	65	14	relationship	relationship	NOUN
ejpam-6413	65	15	:	:	PUNCT
ejpam-6413	65	16	bλ(ā	bλ(ā	NOUN
ejpam-6413	65	17	,	,	PUNCT
ejpam-6413	65	18	b̄	b̄	NOUN
ejpam-6413	65	19	)	)	PUNCT
ejpam-6413	65	20	=	=	SYM
ejpam-6413	65	21	bλ(b̄	bλ(b̄	PROPN
ejpam-6413	65	22	,	,	PUNCT
ejpam-6413	65	23	ā	ā	NOUN
ejpam-6413	65	24	)	)	PUNCT
ejpam-6413	65	25	=	=	SYM
ejpam-6413	65	26	γ(ā)γ(b̄	γ(ā)γ(b̄	PROPN
ejpam-6413	65	27	)	)	PUNCT
ejpam-6413	65	28	γ(ā+	γ(ā+	PROPN
ejpam-6413	65	29	b̄	b̄	PROPN
ejpam-6413	65	30	)	)	PUNCT
ejpam-6413	65	31	.	.	PUNCT
ejpam-6413	66	1	the	the	DET
ejpam-6413	66	2	(	(	PUNCT
ejpam-6413	66	3	α	α	NOUN
ejpam-6413	66	4	,	,	PUNCT
ejpam-6413	66	5	m)-convexity	m)-convexity	NOUN
ejpam-6413	66	6	presented	present	VERB
ejpam-6413	66	7	in	in	ADP
ejpam-6413	66	8	[	[	X
ejpam-6413	66	9	37	37	NUM
ejpam-6413	66	10	]	]	PUNCT
ejpam-6413	66	11	can	can	AUX
ejpam-6413	66	12	be	be	AUX
ejpam-6413	66	13	considered	consider	VERB
ejpam-6413	66	14	as	as	ADP
ejpam-6413	66	15	a	a	DET
ejpam-6413	66	16	generalization	generalization	NOUN
ejpam-6413	66	17	of	of	ADP
ejpam-6413	66	18	ordinary	ordinary	ADJ
ejpam-6413	66	19	convexity	convexity	NOUN
ejpam-6413	66	20	and	and	CCONJ
ejpam-6413	66	21	is	be	AUX
ejpam-6413	66	22	defined	define	VERB
ejpam-6413	66	23	by	by	ADP
ejpam-6413	66	24	the	the	DET
ejpam-6413	66	25	following	following	NOUN
ejpam-6413	66	26	:	:	PUNCT
ejpam-6413	66	27	definition	definition	NOUN
ejpam-6413	66	28	4	4	NUM
ejpam-6413	66	29	.	.	PUNCT
ejpam-6413	67	1	let	let	VERB
ejpam-6413	67	2	a	a	DET
ejpam-6413	67	3	function	function	NOUN
ejpam-6413	67	4	𭟋	𭟋	ADP
ejpam-6413	67	5	:	:	PUNCT
ejpam-6413	68	1	[	[	X
ejpam-6413	68	2	0	0	NUM
ejpam-6413	68	3	,	,	PUNCT
ejpam-6413	68	4	b̄	b̄	X
ejpam-6413	68	5	]	]	PUNCT
ejpam-6413	68	6	→	→	SYM
ejpam-6413	68	7	r	r	NOUN
ejpam-6413	68	8	,	,	PUNCT
ejpam-6413	68	9	and	and	CCONJ
ejpam-6413	68	10	(	(	PUNCT
ejpam-6413	68	11	α	α	NOUN
ejpam-6413	68	12	,	,	PUNCT
ejpam-6413	68	13	m	m	NOUN
ejpam-6413	68	14	)	)	PUNCT
ejpam-6413	68	15	∈	∈	PROPN
ejpam-6413	68	16	(	(	PUNCT
ejpam-6413	68	17	0	0	NUM
ejpam-6413	68	18	,	,	PUNCT
ejpam-6413	68	19	1]2	1]2	NUM
ejpam-6413	68	20	if	if	SCONJ
ejpam-6413	68	21	,	,	PUNCT
ejpam-6413	68	22	𭟋(⊺ā+m(1−	𭟋(⊺ā+m(1−	ADJ
ejpam-6413	68	23	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	68	24	)	)	PUNCT
ejpam-6413	68	25	≤	≤	NUM
ejpam-6413	68	26	⊺α𭟋(ā	⊺α𭟋(ā	NOUN
ejpam-6413	68	27	)	)	PUNCT
ejpam-6413	69	1	+	+	ADJ
ejpam-6413	69	2	m(1−	m(1−	PROPN
ejpam-6413	69	3	⊺α)𭟋(b̄	⊺α)𭟋(b̄	PROPN
ejpam-6413	69	4	)	)	PUNCT
ejpam-6413	69	5	.	.	PUNCT
ejpam-6413	70	1	(	(	PUNCT
ejpam-6413	70	2	1	1	X
ejpam-6413	70	3	)	)	PUNCT
ejpam-6413	70	4	is	be	AUX
ejpam-6413	70	5	valid	valid	ADJ
ejpam-6413	70	6	for	for	ADP
ejpam-6413	70	7	all	all	DET
ejpam-6413	70	8	ā	ā	NOUN
ejpam-6413	70	9	,	,	PUNCT
ejpam-6413	70	10	b̄	b̄	PROPN
ejpam-6413	70	11	∈	∈	PROPN
ejpam-6413	71	1	[	[	X
ejpam-6413	71	2	0	0	NUM
ejpam-6413	71	3	,	,	PUNCT
ejpam-6413	71	4	b̄	b̄	NOUN
ejpam-6413	71	5	]	]	PUNCT
ejpam-6413	71	6	and	and	CCONJ
ejpam-6413	71	7	⊺	⊺	PUNCT
ejpam-6413	71	8	∈	∈	PROPN
ejpam-6413	72	1	[	[	X
ejpam-6413	72	2	0	0	NUM
ejpam-6413	72	3	,	,	PUNCT
ejpam-6413	72	4	1	1	NUM
ejpam-6413	72	5	]	]	PUNCT
ejpam-6413	72	6	,	,	PUNCT
ejpam-6413	72	7	then	then	ADV
ejpam-6413	72	8	we	we	PRON
ejpam-6413	72	9	say	say	VERB
ejpam-6413	72	10	𭟋	𭟋	NOUN
ejpam-6413	72	11	is	be	AUX
ejpam-6413	72	12	(	(	PUNCT
ejpam-6413	72	13	α	α	NOUN
ejpam-6413	72	14	,	,	PUNCT
ejpam-6413	72	15	m)-convex	m)-convex	PUNCT
ejpam-6413	72	16	on	on	ADP
ejpam-6413	72	17	[	[	X
ejpam-6413	72	18	0	0	NUM
ejpam-6413	72	19	,	,	PUNCT
ejpam-6413	72	20	b̄	b̄	NOUN
ejpam-6413	72	21	]	]	PUNCT
ejpam-6413	72	22	.	.	PUNCT
ejpam-6413	73	1	this	this	DET
ejpam-6413	73	2	definition	definition	NOUN
ejpam-6413	73	3	generalized	generalize	VERB
ejpam-6413	73	4	the	the	DET
ejpam-6413	73	5	following	follow	VERB
ejpam-6413	73	6	convexities	convexity	NOUN
ejpam-6413	73	7	(	(	PUNCT
ejpam-6413	73	8	i	i	NOUN
ejpam-6413	73	9	)	)	PUNCT
ejpam-6413	73	10	if	if	SCONJ
ejpam-6413	73	11	we	we	PRON
ejpam-6413	73	12	substitute	substitute	VERB
ejpam-6413	73	13	m	m	VERB
ejpam-6413	73	14	=	=	SYM
ejpam-6413	73	15	1	1	NUM
ejpam-6413	73	16	in	in	ADP
ejpam-6413	73	17	(	(	PUNCT
ejpam-6413	73	18	1	1	NUM
ejpam-6413	73	19	)	)	PUNCT
ejpam-6413	73	20	,	,	PUNCT
ejpam-6413	73	21	then	then	ADV
ejpam-6413	73	22	we	we	PRON
ejpam-6413	73	23	get	get	VERB
ejpam-6413	73	24	α	α	PRON
ejpam-6413	73	25	-	-	ADJ
ejpam-6413	73	26	convex	convex	ADJ
ejpam-6413	73	27	function	function	NOUN
ejpam-6413	73	28	.	.	PUNCT
ejpam-6413	74	1	𭟋(⊺αā+	𭟋(⊺αā+	PROPN
ejpam-6413	74	2	(	(	PUNCT
ejpam-6413	74	3	1−	1−	NUM
ejpam-6413	74	4	⊺α)b̄	⊺α)b̄	NOUN
ejpam-6413	74	5	)	)	PUNCT
ejpam-6413	74	6	≤	≤	NUM
ejpam-6413	74	7	⊺α𭟋(ā	⊺α𭟋(ā	ADJ
ejpam-6413	74	8	)	)	PUNCT
ejpam-6413	75	1	+	+	CCONJ
ejpam-6413	75	2	(	(	PUNCT
ejpam-6413	75	3	1−	1−	NUM
ejpam-6413	75	4	⊺α)𭟋(b̄	⊺α)𭟋(b̄	NOUN
ejpam-6413	75	5	)	)	PUNCT
ejpam-6413	75	6	.	.	PUNCT
ejpam-6413	76	1	m.	m.	NOUN
ejpam-6413	76	2	samraiz	samraiz	PROPN
ejpam-6413	76	3	et	et	PROPN
ejpam-6413	76	4	al	al	PROPN
ejpam-6413	76	5	.	.	PUNCT
ejpam-6413	76	6	/	/	SYM
ejpam-6413	76	7	eur	eur	PROPN
ejpam-6413	76	8	.	.	PUNCT
ejpam-6413	77	1	j.	j.	PROPN
ejpam-6413	77	2	pure	pure	PROPN
ejpam-6413	77	3	appl	appl	PROPN
ejpam-6413	77	4	.	.	PROPN
ejpam-6413	77	5	math	math	PROPN
ejpam-6413	77	6	,	,	PUNCT
ejpam-6413	77	7	18	18	NUM
ejpam-6413	77	8	(	(	PUNCT
ejpam-6413	77	9	3	3	NUM
ejpam-6413	77	10	)	)	PUNCT
ejpam-6413	77	11	(	(	PUNCT
ejpam-6413	77	12	2025	2025	NUM
ejpam-6413	77	13	)	)	PUNCT
ejpam-6413	77	14	,	,	PUNCT
ejpam-6413	77	15	6413	6413	NUM
ejpam-6413	77	16	4	4	NUM
ejpam-6413	77	17	of	of	ADP
ejpam-6413	77	18	26	26	NUM
ejpam-6413	77	19	(	(	PUNCT
ejpam-6413	77	20	ii	ii	NOUN
ejpam-6413	77	21	)	)	PUNCT
ejpam-6413	77	22	if	if	SCONJ
ejpam-6413	77	23	we	we	PRON
ejpam-6413	77	24	substitute	substitute	VERB
ejpam-6413	77	25	α	α	NOUN
ejpam-6413	77	26	=	=	SYM
ejpam-6413	77	27	1	1	NUM
ejpam-6413	77	28	in	in	ADP
ejpam-6413	77	29	(	(	PUNCT
ejpam-6413	77	30	1	1	NUM
ejpam-6413	77	31	)	)	PUNCT
ejpam-6413	77	32	,	,	PUNCT
ejpam-6413	77	33	then	then	ADV
ejpam-6413	77	34	we	we	PRON
ejpam-6413	77	35	get	get	VERB
ejpam-6413	77	36	m	m	ADJ
ejpam-6413	77	37	-	-	ADJ
ejpam-6413	77	38	convex	convex	ADJ
ejpam-6413	77	39	function	function	NOUN
ejpam-6413	77	40	.	.	PUNCT
ejpam-6413	78	1	𭟋(⊺ā+m(1−	𭟋(⊺ā+m(1−	ADJ
ejpam-6413	78	2	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	78	3	)	)	PUNCT
ejpam-6413	78	4	≤	≤	NUM
ejpam-6413	78	5	⊺𭟋(ā	⊺𭟋(ā	PROPN
ejpam-6413	78	6	)	)	PUNCT
ejpam-6413	79	1	+	+	ADJ
ejpam-6413	79	2	m(1−	m(1−	PROPN
ejpam-6413	79	3	⊺)𭟋(b̄	⊺)𭟋(b̄	NOUN
ejpam-6413	79	4	)	)	PUNCT
ejpam-6413	79	5	.	.	PUNCT
ejpam-6413	80	1	(	(	PUNCT
ejpam-6413	80	2	iii	iii	X
ejpam-6413	80	3	)	)	PUNCT
ejpam-6413	80	4	if	if	SCONJ
ejpam-6413	80	5	we	we	PRON
ejpam-6413	80	6	substitute	substitute	VERB
ejpam-6413	80	7	α	α	NOUN
ejpam-6413	80	8	=	=	SYM
ejpam-6413	80	9	1	1	NUM
ejpam-6413	80	10	and	and	CCONJ
ejpam-6413	80	11	m	m	VERB
ejpam-6413	80	12	=	=	ADJ
ejpam-6413	80	13	1	1	NUM
ejpam-6413	80	14	in	in	ADP
ejpam-6413	80	15	(	(	PUNCT
ejpam-6413	80	16	1	1	NUM
ejpam-6413	80	17	)	)	PUNCT
ejpam-6413	80	18	,	,	PUNCT
ejpam-6413	80	19	then	then	ADV
ejpam-6413	80	20	we	we	PRON
ejpam-6413	80	21	get	get	VERB
ejpam-6413	80	22	convex	convex	ADJ
ejpam-6413	80	23	function	function	NOUN
ejpam-6413	80	24	.	.	PUNCT
ejpam-6413	81	1	𭟋(⊺ā+	𭟋(⊺ā+	PROPN
ejpam-6413	81	2	(	(	PUNCT
ejpam-6413	81	3	1−	1−	NUM
ejpam-6413	81	4	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	81	5	)	)	PUNCT
ejpam-6413	81	6	≤	≤	NUM
ejpam-6413	81	7	⊺𭟋(ā	⊺𭟋(ā	PROPN
ejpam-6413	81	8	)	)	PUNCT
ejpam-6413	82	1	+	+	CCONJ
ejpam-6413	82	2	(	(	PUNCT
ejpam-6413	82	3	1−	1−	NUM
ejpam-6413	82	4	⊺)𭟋(b̄	⊺)𭟋(b̄	NOUN
ejpam-6413	82	5	)	)	PUNCT
ejpam-6413	82	6	.	.	PUNCT
ejpam-6413	83	1	the	the	DET
ejpam-6413	83	2	information	information	NOUN
ejpam-6413	83	3	related	relate	VERB
ejpam-6413	83	4	to	to	ADP
ejpam-6413	83	5	riemann	riemann	PROPN
ejpam-6413	83	6	-	-	PUNCT
ejpam-6413	83	7	liouville	liouville	VERB
ejpam-6413	83	8	fractional	fractional	ADJ
ejpam-6413	83	9	integrals	integral	NOUN
ejpam-6413	83	10	provided	provide	VERB
ejpam-6413	83	11	in	in	ADP
ejpam-6413	83	12	[	[	X
ejpam-6413	83	13	1	1	NUM
ejpam-6413	83	14	]	]	PUNCT
ejpam-6413	83	15	and	and	CCONJ
ejpam-6413	83	16	[	[	X
ejpam-6413	83	17	2	2	NUM
ejpam-6413	83	18	]	]	PUNCT
ejpam-6413	83	19	can	can	AUX
ejpam-6413	83	20	be	be	AUX
ejpam-6413	83	21	summarized	summarize	VERB
ejpam-6413	83	22	as	as	SCONJ
ejpam-6413	83	23	follows	follow	VERB
ejpam-6413	83	24	:	:	PUNCT
ejpam-6413	83	25	definition	definition	NOUN
ejpam-6413	83	26	5	5	NUM
ejpam-6413	83	27	.	.	PUNCT
ejpam-6413	84	1	if	if	SCONJ
ejpam-6413	84	2	𭟋	𭟋	PROPN
ejpam-6413	84	3	∈	∈	PROPN
ejpam-6413	84	4	l[ā	l[ā	PROPN
ejpam-6413	84	5	,	,	PUNCT
ejpam-6413	84	6	b̄	b̄	NOUN
ejpam-6413	84	7	]	]	PUNCT
ejpam-6413	84	8	,	,	PUNCT
ejpam-6413	84	9	then	then	ADV
ejpam-6413	84	10	the	the	DET
ejpam-6413	84	11	riemann	riemann	PROPN
ejpam-6413	84	12	-	-	PUNCT
ejpam-6413	84	13	liouville	liouville	VERB
ejpam-6413	84	14	fractional	fractional	ADJ
ejpam-6413	84	15	integrals	integral	NOUN
ejpam-6413	84	16	of	of	ADP
ejpam-6413	84	17	order	order	NOUN
ejpam-6413	84	18	θ	θ	PROPN
ejpam-6413	84	19	∈	∈	PROPN
ejpam-6413	84	20	r+	r+	X
ejpam-6413	84	21	,	,	PUNCT
ejpam-6413	84	22	denoted	denote	VERB
ejpam-6413	84	23	by	by	ADP
ejpam-6413	84	24	χθ	χθ	INTJ
ejpam-6413	84	25	ā+𭟋	ā+𭟋	PROPN
ejpam-6413	84	26	and	and	CCONJ
ejpam-6413	84	27	χθ	χθ	ADJ
ejpam-6413	84	28	ā−𭟋	ā−𭟋	ADV
ejpam-6413	84	29	,	,	PUNCT
ejpam-6413	84	30	represent	represent	VERB
ejpam-6413	84	31	the	the	DET
ejpam-6413	84	32	left	left	ADJ
ejpam-6413	84	33	and	and	CCONJ
ejpam-6413	84	34	right	right	ADJ
ejpam-6413	84	35	sided	sided	ADJ
ejpam-6413	84	36	integrals	integral	NOUN
ejpam-6413	84	37	,	,	PUNCT
ejpam-6413	84	38	respectively	respectively	ADV
ejpam-6413	84	39	i.e.	i.e.	X
ejpam-6413	84	40	,	,	PUNCT
ejpam-6413	84	41	(	(	PUNCT
ejpam-6413	84	42	χθ	χθ	X
ejpam-6413	84	43	ā+𭟋)(λ	ā+𭟋)(λ	NOUN
ejpam-6413	84	44	)	)	PUNCT
ejpam-6413	84	45	=	=	SYM
ejpam-6413	84	46	1	1	NUM
ejpam-6413	84	47	γ(θ	γ(θ	PROPN
ejpam-6413	84	48	)	)	PUNCT
ejpam-6413	85	1	λ∫	λ∫	ADJ
ejpam-6413	85	2	ā	ā	NOUN
ejpam-6413	85	3	(	(	PUNCT
ejpam-6413	85	4	λ−	λ−	PROPN
ejpam-6413	85	5	⊺)θ−1𭟋(⊺)d⊺	⊺)θ−1𭟋(⊺)d⊺	PROPN
ejpam-6413	85	6	,	,	PUNCT
ejpam-6413	85	7	(	(	PUNCT
ejpam-6413	85	8	0	0	NUM
ejpam-6413	85	9	≤	≤	NUM
ejpam-6413	85	10	ā	ā	NOUN
ejpam-6413	85	11	<	<	X
ejpam-6413	85	12	λ	λ	X
ejpam-6413	85	13	)	)	PUNCT
ejpam-6413	85	14	and	and	CCONJ
ejpam-6413	85	15	(	(	PUNCT
ejpam-6413	85	16	χθ	χθ	X
ejpam-6413	85	17	b̄−𭟋)(λ	b̄−𭟋)(λ	NOUN
ejpam-6413	85	18	)	)	PUNCT
ejpam-6413	85	19	=	=	SYM
ejpam-6413	85	20	1	1	NUM
ejpam-6413	85	21	γ(θ	γ(θ	PROPN
ejpam-6413	85	22	)	)	PUNCT
ejpam-6413	85	23	b̄∫	b̄∫	PROPN
ejpam-6413	85	24	λ	λ	X
ejpam-6413	85	25	(	(	PUNCT
ejpam-6413	85	26	⊺−	⊺−	PROPN
ejpam-6413	85	27	λ)θ−1𭟋(⊺)d⊺	λ)θ−1𭟋(⊺)d⊺	NOUN
ejpam-6413	85	28	,	,	PUNCT
ejpam-6413	85	29	(	(	PUNCT
ejpam-6413	85	30	0	0	NUM
ejpam-6413	85	31	≤	≤	NUM
ejpam-6413	85	32	λ	λ	PROPN
ejpam-6413	85	33	<	<	X
ejpam-6413	85	34	b̄	b̄	PROPN
ejpam-6413	85	35	)	)	PUNCT
ejpam-6413	85	36	.	.	PUNCT
ejpam-6413	86	1	in	in	ADP
ejpam-6413	86	2	[	[	X
ejpam-6413	86	3	24	24	NUM
ejpam-6413	86	4	]	]	PUNCT
ejpam-6413	86	5	,	,	PUNCT
ejpam-6413	86	6	the	the	DET
ejpam-6413	86	7	following	follow	VERB
ejpam-6413	86	8	lemma	lemma	PROPN
ejpam-6413	86	9	discussed	discuss	VERB
ejpam-6413	86	10	.	.	PUNCT
ejpam-6413	87	1	lemma	lemma	PROPN
ejpam-6413	87	2	1	1	NUM
ejpam-6413	87	3	.	.	PUNCT
ejpam-6413	88	1	for	for	ADP
ejpam-6413	88	2	⊺	⊺	NUM
ejpam-6413	88	3	∈	∈	PROPN
ejpam-6413	88	4	[	[	X
ejpam-6413	88	5	0	0	NUM
ejpam-6413	88	6	,	,	PUNCT
ejpam-6413	88	7	1	1	NUM
ejpam-6413	88	8	]	]	PUNCT
ejpam-6413	88	9	,	,	PUNCT
ejpam-6413	88	10	we	we	PRON
ejpam-6413	88	11	obtain	obtain	VERB
ejpam-6413	88	12	the	the	DET
ejpam-6413	88	13	following	follow	VERB
ejpam-6413	88	14	(	(	PUNCT
ejpam-6413	88	15	1−	1−	NUM
ejpam-6413	88	16	⊺)ω	⊺)ω	NUM
ejpam-6413	88	17	≤	≤	NOUN
ejpam-6413	88	18	21−ω	21−ω	NUM
ejpam-6413	88	19	−	−	NOUN
ejpam-6413	88	20	⊺ω	⊺ω	VERB
ejpam-6413	88	21	,	,	PUNCT
ejpam-6413	88	22	for	for	ADP
ejpam-6413	88	23	ω	ω	PROPN
ejpam-6413	88	24	∈	∈	PROPN
ejpam-6413	89	1	[	[	X
ejpam-6413	89	2	0	0	NUM
ejpam-6413	89	3	,	,	PUNCT
ejpam-6413	89	4	1	1	NUM
ejpam-6413	89	5	]	]	PUNCT
ejpam-6413	89	6	,	,	PUNCT
ejpam-6413	89	7	(	(	PUNCT
ejpam-6413	89	8	1−	1−	NUM
ejpam-6413	89	9	⊺)ω	⊺)ω	NUM
ejpam-6413	89	10	≥	≥	NOUN
ejpam-6413	89	11	21−ω	21−ω	NUM
ejpam-6413	89	12	−	−	NOUN
ejpam-6413	89	13	⊺ω	⊺ω	VERB
ejpam-6413	89	14	,	,	PUNCT
ejpam-6413	89	15	for	for	ADP
ejpam-6413	89	16	ω	ω	PROPN
ejpam-6413	89	17	∈	∈	PROPN
ejpam-6413	90	1	[	[	X
ejpam-6413	90	2	1,+∞	1,+∞	NUM
ejpam-6413	90	3	)	)	PUNCT
ejpam-6413	90	4	.	.	PUNCT
ejpam-6413	91	1	the	the	DET
ejpam-6413	91	2	following	follow	VERB
ejpam-6413	91	3	lemma	lemma	PROPN
ejpam-6413	91	4	presented	present	VERB
ejpam-6413	91	5	in	in	ADP
ejpam-6413	91	6	[	[	X
ejpam-6413	91	7	38	38	NUM
ejpam-6413	91	8	]	]	PUNCT
ejpam-6413	91	9	stated	state	VERB
ejpam-6413	91	10	as	as	SCONJ
ejpam-6413	91	11	follows	follow	VERB
ejpam-6413	91	12	:	:	PUNCT
ejpam-6413	91	13	lemma	lemma	PROPN
ejpam-6413	91	14	2	2	X
ejpam-6413	91	15	.	.	PUNCT
ejpam-6413	92	1	let	let	VERB
ejpam-6413	92	2	𭟋	𭟋	VERB
ejpam-6413	92	3	:	:	PUNCT
ejpam-6413	92	4	[	[	X
ejpam-6413	92	5	0	0	NUM
ejpam-6413	92	6	,	,	PUNCT
ejpam-6413	92	7	b̄	b̄	X
ejpam-6413	92	8	]	]	PUNCT
ejpam-6413	92	9	→	→	SYM
ejpam-6413	92	10	r	r	NOUN
ejpam-6413	92	11	and	and	CCONJ
ejpam-6413	92	12	(	(	PUNCT
ejpam-6413	92	13	α	α	NOUN
ejpam-6413	92	14	,	,	PUNCT
ejpam-6413	92	15	m	m	NOUN
ejpam-6413	92	16	)	)	PUNCT
ejpam-6413	92	17	∈	∈	PROPN
ejpam-6413	92	18	(	(	PUNCT
ejpam-6413	92	19	0	0	NUM
ejpam-6413	92	20	,	,	PUNCT
ejpam-6413	92	21	1]2	1]2	NUM
ejpam-6413	92	22	.	.	PUNCT
ejpam-6413	93	1	if	if	SCONJ
ejpam-6413	93	2	𭟋(ā⊺b̄m(1−⊺	𭟋(ā⊺b̄m(1−⊺	NOUN
ejpam-6413	93	3	)	)	PUNCT
ejpam-6413	93	4	)	)	PUNCT
ejpam-6413	94	1	≤	≤	NUM
ejpam-6413	94	2	⊺α𭟋(ā	⊺α𭟋(ā	ADJ
ejpam-6413	94	3	)	)	PUNCT
ejpam-6413	94	4	+	+	ADJ
ejpam-6413	94	5	m(1−	m(1−	PROPN
ejpam-6413	94	6	⊺α)𭟋(b̄	⊺α)𭟋(b̄	PROPN
ejpam-6413	94	7	)	)	PUNCT
ejpam-6413	94	8	.	.	PUNCT
ejpam-6413	95	1	is	be	AUX
ejpam-6413	95	2	valid	valid	ADJ
ejpam-6413	95	3	for	for	ADP
ejpam-6413	95	4	all	all	DET
ejpam-6413	95	5	ā	ā	NOUN
ejpam-6413	95	6	,	,	PUNCT
ejpam-6413	95	7	b̄	b̄	PROPN
ejpam-6413	95	8	∈	∈	PROPN
ejpam-6413	96	1	[	[	X
ejpam-6413	96	2	0	0	NUM
ejpam-6413	96	3	,	,	PUNCT
ejpam-6413	96	4	b̄	b̄	NOUN
ejpam-6413	96	5	]	]	PUNCT
ejpam-6413	96	6	and	and	CCONJ
ejpam-6413	96	7	⊺	⊺	PUNCT
ejpam-6413	96	8	∈	∈	PROPN
ejpam-6413	97	1	[	[	X
ejpam-6413	97	2	0	0	NUM
ejpam-6413	97	3	,	,	PUNCT
ejpam-6413	97	4	1	1	NUM
ejpam-6413	97	5	]	]	PUNCT
ejpam-6413	97	6	,	,	PUNCT
ejpam-6413	97	7	then	then	ADV
ejpam-6413	97	8	we	we	PRON
ejpam-6413	97	9	say	say	VERB
ejpam-6413	97	10	𭟋	𭟋	PROPN
ejpam-6413	97	11	is	be	AUX
ejpam-6413	97	12	ga	ga	PROPN
ejpam-6413	97	13	(	(	PUNCT
ejpam-6413	97	14	α	α	NOUN
ejpam-6413	97	15	,	,	PUNCT
ejpam-6413	97	16	m)-convex	m)-convex	PUNCT
ejpam-6413	97	17	function	function	VERB
ejpam-6413	97	18	on	on	ADP
ejpam-6413	97	19	[	[	X
ejpam-6413	97	20	0	0	NUM
ejpam-6413	97	21	,	,	PUNCT
ejpam-6413	97	22	b̄	b̄	NOUN
ejpam-6413	97	23	]	]	PUNCT
ejpam-6413	97	24	.	.	PUNCT
ejpam-6413	98	1	mathematicians	mathematician	NOUN
ejpam-6413	98	2	are	be	AUX
ejpam-6413	98	3	exploring	explore	VERB
ejpam-6413	98	4	fascinating	fascinating	ADJ
ejpam-6413	98	5	inequalities	inequality	NOUN
ejpam-6413	98	6	and	and	CCONJ
ejpam-6413	98	7	extending	extend	VERB
ejpam-6413	98	8	their	their	PRON
ejpam-6413	98	9	reach	reach	NOUN
ejpam-6413	98	10	through	through	ADP
ejpam-6413	98	11	various	various	ADJ
ejpam-6413	98	12	convexities	convexity	NOUN
ejpam-6413	98	13	.	.	PUNCT
ejpam-6413	99	1	generalizations	generalization	NOUN
ejpam-6413	99	2	in	in	ADP
ejpam-6413	99	3	inequalities	inequality	NOUN
ejpam-6413	99	4	through	through	ADP
ejpam-6413	99	5	different	different	ADJ
ejpam-6413	99	6	convexities	convexity	NOUN
ejpam-6413	99	7	showcase	showcase	VERB
ejpam-6413	99	8	the	the	DET
ejpam-6413	99	9	versatility	versatility	NOUN
ejpam-6413	99	10	and	and	CCONJ
ejpam-6413	99	11	depth	depth	NOUN
ejpam-6413	99	12	of	of	ADP
ejpam-6413	99	13	the	the	DET
ejpam-6413	99	14	mathematical	mathematical	ADJ
ejpam-6413	99	15	approach	approach	NOUN
ejpam-6413	99	16	.	.	PUNCT
ejpam-6413	100	1	mathematicians	mathematician	NOUN
ejpam-6413	100	2	not	not	PART
ejpam-6413	100	3	only	only	ADV
ejpam-6413	100	4	refine	refine	VERB
ejpam-6413	100	5	existing	exist	VERB
ejpam-6413	100	6	inequalities	inequality	NOUN
ejpam-6413	100	7	but	but	CCONJ
ejpam-6413	100	8	also	also	ADV
ejpam-6413	100	9	explore	explore	VERB
ejpam-6413	100	10	new	new	ADJ
ejpam-6413	100	11	insights	insight	NOUN
ejpam-6413	100	12	into	into	ADP
ejpam-6413	100	13	the	the	DET
ejpam-6413	100	14	relationships	relationship	NOUN
ejpam-6413	100	15	between	between	ADP
ejpam-6413	100	16	mathematical	mathematical	ADJ
ejpam-6413	100	17	entities	entity	NOUN
ejpam-6413	100	18	.	.	PUNCT
ejpam-6413	101	1	these	these	DET
ejpam-6413	101	2	generalizations	generalization	NOUN
ejpam-6413	101	3	provide	provide	VERB
ejpam-6413	101	4	a	a	DET
ejpam-6413	101	5	broader	broad	ADJ
ejpam-6413	101	6	understanding	understanding	NOUN
ejpam-6413	101	7	of	of	ADP
ejpam-6413	101	8	mathematical	mathematical	ADJ
ejpam-6413	101	9	structures	structure	NOUN
ejpam-6413	101	10	,	,	PUNCT
ejpam-6413	101	11	enriching	enrich	VERB
ejpam-6413	101	12	the	the	DET
ejpam-6413	101	13	field	field	NOUN
ejpam-6413	101	14	with	with	ADP
ejpam-6413	101	15	powerful	powerful	ADJ
ejpam-6413	101	16	tools	tool	NOUN
ejpam-6413	101	17	for	for	ADP
ejpam-6413	101	18	analysis	analysis	NOUN
ejpam-6413	101	19	and	and	CCONJ
ejpam-6413	101	20	applications	application	NOUN
ejpam-6413	101	21	across	across	ADP
ejpam-6413	101	22	various	various	ADJ
ejpam-6413	101	23	domains	domain	NOUN
ejpam-6413	101	24	.	.	PUNCT
ejpam-6413	102	1	the	the	DET
ejpam-6413	102	2	extensions	extension	NOUN
ejpam-6413	102	3	and	and	CCONJ
ejpam-6413	102	4	generalizations	generalization	NOUN
ejpam-6413	102	5	of	of	ADP
ejpam-6413	102	6	inequalities	inequality	NOUN
ejpam-6413	102	7	via	via	ADP
ejpam-6413	102	8	different	different	ADJ
ejpam-6413	102	9	convexities	convexity	NOUN
ejpam-6413	102	10	m.	m.	NOUN
ejpam-6413	102	11	samraiz	samraiz	PROPN
ejpam-6413	102	12	et	et	PROPN
ejpam-6413	102	13	al	al	PROPN
ejpam-6413	102	14	.	.	PUNCT
ejpam-6413	102	15	/	/	SYM
ejpam-6413	102	16	eur	eur	PROPN
ejpam-6413	102	17	.	.	PUNCT
ejpam-6413	103	1	j.	j.	PROPN
ejpam-6413	103	2	pure	pure	PROPN
ejpam-6413	103	3	appl	appl	PROPN
ejpam-6413	103	4	.	.	PROPN
ejpam-6413	103	5	math	math	PROPN
ejpam-6413	103	6	,	,	PUNCT
ejpam-6413	103	7	18	18	NUM
ejpam-6413	103	8	(	(	PUNCT
ejpam-6413	103	9	3	3	NUM
ejpam-6413	103	10	)	)	PUNCT
ejpam-6413	103	11	(	(	PUNCT
ejpam-6413	103	12	2025	2025	NUM
ejpam-6413	103	13	)	)	PUNCT
ejpam-6413	103	14	,	,	PUNCT
ejpam-6413	103	15	6413	6413	NUM
ejpam-6413	103	16	5	5	NUM
ejpam-6413	103	17	of	of	ADP
ejpam-6413	103	18	26	26	NUM
ejpam-6413	103	19	reflect	reflect	VERB
ejpam-6413	103	20	the	the	DET
ejpam-6413	103	21	dynamic	dynamic	ADJ
ejpam-6413	103	22	and	and	CCONJ
ejpam-6413	103	23	evolving	evolve	VERB
ejpam-6413	103	24	nature	nature	NOUN
ejpam-6413	103	25	of	of	ADP
ejpam-6413	103	26	mathematics	mathematic	NOUN
ejpam-6413	103	27	,	,	PUNCT
ejpam-6413	103	28	leading	lead	VERB
ejpam-6413	103	29	to	to	ADP
ejpam-6413	103	30	a	a	DET
ejpam-6413	103	31	deeper	deep	ADJ
ejpam-6413	103	32	comprehension	comprehension	NOUN
ejpam-6413	103	33	of	of	ADP
ejpam-6413	103	34	fundamental	fundamental	ADJ
ejpam-6413	103	35	mathematical	mathematical	ADJ
ejpam-6413	103	36	principles	principle	NOUN
ejpam-6413	103	37	.	.	PUNCT
ejpam-6413	104	1	the	the	DET
ejpam-6413	104	2	main	main	ADJ
ejpam-6413	104	3	objective	objective	NOUN
ejpam-6413	104	4	of	of	ADP
ejpam-6413	104	5	the	the	DET
ejpam-6413	104	6	present	present	ADJ
ejpam-6413	104	7	work	work	NOUN
ejpam-6413	104	8	is	be	AUX
ejpam-6413	104	9	to	to	PART
ejpam-6413	104	10	establish	establish	VERB
ejpam-6413	104	11	more	more	ADJ
ejpam-6413	104	12	generalized	generalized	ADJ
ejpam-6413	104	13	forms	form	NOUN
ejpam-6413	104	14	of	of	ADP
ejpam-6413	104	15	hermite	hermite	ADJ
ejpam-6413	104	16	-	-	PUNCT
ejpam-6413	104	17	hadamard	hadamard	ADJ
ejpam-6413	104	18	inequalities	inequality	NOUN
ejpam-6413	104	19	by	by	ADP
ejpam-6413	104	20	using	use	VERB
ejpam-6413	104	21	ga	ga	PROPN
ejpam-6413	104	22	(	(	PUNCT
ejpam-6413	104	23	α	α	NOUN
ejpam-6413	104	24	,	,	PUNCT
ejpam-6413	104	25	m)-convex	m)-convex	NOUN
ejpam-6413	104	26	functions	function	NOUN
ejpam-6413	104	27	.	.	PUNCT
ejpam-6413	105	1	it	it	PRON
ejpam-6413	105	2	is	be	AUX
ejpam-6413	105	3	important	important	ADJ
ejpam-6413	105	4	to	to	PART
ejpam-6413	105	5	mention	mention	VERB
ejpam-6413	105	6	here	here	ADV
ejpam-6413	105	7	that	that	SCONJ
ejpam-6413	105	8	it	it	PRON
ejpam-6413	105	9	is	be	AUX
ejpam-6413	105	10	not	not	PART
ejpam-6413	105	11	easy	easy	ADJ
ejpam-6413	105	12	and	and	CCONJ
ejpam-6413	105	13	not	not	PART
ejpam-6413	105	14	always	always	ADV
ejpam-6413	105	15	possible	possible	ADJ
ejpam-6413	105	16	to	to	PART
ejpam-6413	105	17	introduce	introduce	VERB
ejpam-6413	105	18	inequalities	inequality	NOUN
ejpam-6413	105	19	by	by	ADP
ejpam-6413	105	20	only	only	ADV
ejpam-6413	105	21	changing	change	VERB
ejpam-6413	105	22	the	the	DET
ejpam-6413	105	23	convexity	convexity	NOUN
ejpam-6413	105	24	.	.	PUNCT
ejpam-6413	106	1	sometimes	sometimes	ADV
ejpam-6413	106	2	,	,	PUNCT
ejpam-6413	106	3	it	it	PRON
ejpam-6413	106	4	is	be	AUX
ejpam-6413	106	5	a	a	DET
ejpam-6413	106	6	complex	complex	ADJ
ejpam-6413	106	7	procedure	procedure	NOUN
ejpam-6413	106	8	to	to	PART
ejpam-6413	106	9	investigate	investigate	VERB
ejpam-6413	106	10	predicted	predict	VERB
ejpam-6413	106	11	results	result	NOUN
ejpam-6413	106	12	by	by	ADP
ejpam-6413	106	13	using	use	VERB
ejpam-6413	106	14	a	a	DET
ejpam-6413	106	15	convexity	convexity	NOUN
ejpam-6413	106	16	involving	involve	VERB
ejpam-6413	106	17	new	new	ADJ
ejpam-6413	106	18	parameters	parameter	NOUN
ejpam-6413	106	19	,	,	PUNCT
ejpam-6413	106	20	as	as	ADP
ejpam-6413	106	21	in	in	ADP
ejpam-6413	106	22	our	our	PRON
ejpam-6413	106	23	work	work	NOUN
ejpam-6413	106	24	.	.	PUNCT
ejpam-6413	107	1	we	we	PRON
ejpam-6413	107	2	hope	hope	VERB
ejpam-6413	107	3	this	this	DET
ejpam-6413	107	4	idea	idea	NOUN
ejpam-6413	107	5	motivates	motivate	VERB
ejpam-6413	107	6	researchers	researcher	NOUN
ejpam-6413	107	7	to	to	PART
ejpam-6413	107	8	explore	explore	VERB
ejpam-6413	107	9	more	more	ADJ
ejpam-6413	107	10	generalized	generalized	ADJ
ejpam-6413	107	11	inequalities	inequality	NOUN
ejpam-6413	107	12	by	by	ADP
ejpam-6413	107	13	using	use	VERB
ejpam-6413	107	14	appropriate	appropriate	ADJ
ejpam-6413	107	15	convexities	convexity	NOUN
ejpam-6413	107	16	.	.	PUNCT
ejpam-6413	108	1	3	3	X
ejpam-6413	108	2	.	.	X
ejpam-6413	108	3	fractional	fractional	ADJ
ejpam-6413	108	4	integral	integral	ADJ
ejpam-6413	108	5	inequalities	inequality	NOUN
ejpam-6413	108	6	for	for	ADP
ejpam-6413	108	7	geometrically	geometrically	ADV
ejpam-6413	108	8	-	-	PUNCT
ejpam-6413	108	9	arithmetically	arithmetically	ADV
ejpam-6413	108	10	(	(	PUNCT
ejpam-6413	108	11	α	α	NOUN
ejpam-6413	108	12	,	,	PUNCT
ejpam-6413	108	13	m)-convex	m)-convex	PUNCT
ejpam-6413	108	14	functions	function	NOUN
ejpam-6413	108	15	in	in	ADP
ejpam-6413	108	16	this	this	DET
ejpam-6413	108	17	section	section	NOUN
ejpam-6413	108	18	,	,	PUNCT
ejpam-6413	108	19	we	we	PRON
ejpam-6413	108	20	derive	derive	VERB
ejpam-6413	108	21	fundamental	fundamental	ADJ
ejpam-6413	108	22	identities	identity	NOUN
ejpam-6413	108	23	to	to	PART
ejpam-6413	108	24	explore	explore	VERB
ejpam-6413	108	25	the	the	DET
ejpam-6413	108	26	hermite	hermite	PROPN
ejpam-6413	108	27	-	-	PUNCT
ejpam-6413	108	28	hadamard	hadamard	ADJ
ejpam-6413	108	29	inequalities	inequality	NOUN
ejpam-6413	108	30	.	.	PUNCT
ejpam-6413	109	1	the	the	DET
ejpam-6413	109	2	first	first	ADJ
ejpam-6413	109	3	lemma	lemma	PROPN
ejpam-6413	109	4	is	be	AUX
ejpam-6413	109	5	presented	present	VERB
ejpam-6413	109	6	as	as	SCONJ
ejpam-6413	109	7	follows	follow	VERB
ejpam-6413	109	8	:	:	PUNCT
ejpam-6413	109	9	lemma	lemma	PROPN
ejpam-6413	109	10	3	3	X
ejpam-6413	109	11	.	.	PUNCT
ejpam-6413	110	1	let	let	VERB
ejpam-6413	110	2	𭟋	𭟋	VERB
ejpam-6413	110	3	:	:	PUNCT
ejpam-6413	110	4	[	[	X
ejpam-6413	110	5	ā	ā	X
ejpam-6413	110	6	,	,	PUNCT
ejpam-6413	110	7	b̄	b̄	PROPN
ejpam-6413	110	8	]	]	PUNCT
ejpam-6413	110	9	→	→	PUNCT
ejpam-6413	110	10	r	r	NOUN
ejpam-6413	110	11	be	be	AUX
ejpam-6413	110	12	a	a	DET
ejpam-6413	110	13	differentiable	differentiable	ADJ
ejpam-6413	110	14	mapping	mapping	NOUN
ejpam-6413	110	15	on	on	ADP
ejpam-6413	110	16	(	(	PUNCT
ejpam-6413	110	17	ā	ā	ADJ
ejpam-6413	110	18	,	,	PUNCT
ejpam-6413	110	19	b̄	b̄	PROPN
ejpam-6413	110	20	)	)	PUNCT
ejpam-6413	110	21	where	where	SCONJ
ejpam-6413	110	22	ā	ā	NOUN
ejpam-6413	110	23	<	<	X
ejpam-6413	110	24	mb̄	mb̄	NOUN
ejpam-6413	110	25	≤	≤	NUM
ejpam-6413	110	26	b̄	b̄	NOUN
ejpam-6413	110	27	,	,	PUNCT
ejpam-6413	110	28	mb̄	mb̄	VERB
ejpam-6413	110	29	=	=	SYM
ejpam-6413	110	30	µ	µ	X
ejpam-6413	110	31	and	and	CCONJ
ejpam-6413	110	32	µ	µ	PRON
ejpam-6413	110	33	∈	∈	PROPN
ejpam-6413	110	34	(	(	PUNCT
ejpam-6413	110	35	ā	ā	NOUN
ejpam-6413	110	36	,	,	PUNCT
ejpam-6413	110	37	b̄	b̄	PROPN
ejpam-6413	110	38	]	]	PUNCT
ejpam-6413	110	39	.	.	PUNCT
ejpam-6413	111	1	if	if	SCONJ
ejpam-6413	111	2	𭟋′	𭟋′	PROPN
ejpam-6413	111	3	∈	∈	PROPN
ejpam-6413	111	4	l[ā	l[ā	PROPN
ejpam-6413	111	5	,	,	PUNCT
ejpam-6413	111	6	b̄	b̄	NOUN
ejpam-6413	111	7	]	]	PUNCT
ejpam-6413	111	8	,	,	PUNCT
ejpam-6413	111	9	then	then	ADV
ejpam-6413	111	10	the	the	DET
ejpam-6413	111	11	following	follow	VERB
ejpam-6413	111	12	equality	equality	NOUN
ejpam-6413	111	13	for	for	ADP
ejpam-6413	111	14	fractional	fractional	ADJ
ejpam-6413	111	15	integrals	integral	NOUN
ejpam-6413	111	16	holds	hold	VERB
ejpam-6413	111	17	.	.	PUNCT
ejpam-6413	111	18	𭟋(ā	𭟋(ā	VERB
ejpam-6413	111	19	)	)	PUNCT
ejpam-6413	112	1	+	+	NOUN
ejpam-6413	112	2	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	112	3	)	)	PUNCT
ejpam-6413	112	4	2	2	NUM
ejpam-6413	112	5	−	−	NOUN
ejpam-6413	112	6	γ(θ	γ(θ	PROPN
ejpam-6413	112	7	+	+	CCONJ
ejpam-6413	112	8	1	1	X
ejpam-6413	112	9	)	)	PUNCT
ejpam-6413	112	10	2(µ−	2(µ−	NUM
ejpam-6413	112	11	ā)θ	ā)θ	NOUN
ejpam-6413	112	12	[	[	PUNCT
ejpam-6413	112	13	χθ	χθ	X
ejpam-6413	112	14	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	112	15	)	)	PUNCT
ejpam-6413	113	1	+	+	CCONJ
ejpam-6413	113	2	χθ	χθ	X
ejpam-6413	113	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	113	4	)	)	PUNCT
ejpam-6413	113	5	]	]	PUNCT
ejpam-6413	114	1	=	=	PUNCT
ejpam-6413	114	2	µ−	µ−	PROPN
ejpam-6413	114	3	ā	ā	NOUN
ejpam-6413	114	4	2	2	NUM
ejpam-6413	114	5	∫	∫	NOUN
ejpam-6413	114	6	1	1	NUM
ejpam-6413	114	7	0	0	NUM
ejpam-6413	115	1	[	[	X
ejpam-6413	115	2	(	(	PUNCT
ejpam-6413	115	3	1−	1−	NUM
ejpam-6413	115	4	⊺)θ	⊺)θ	NUM
ejpam-6413	115	5	−	−	PROPN
ejpam-6413	115	6	⊺θ]𭟋′	⊺θ]𭟋′	PROPN
ejpam-6413	115	7	(	(	PUNCT
ejpam-6413	115	8	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	115	9	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	115	10	)	)	PUNCT
ejpam-6413	115	11	d	d	NOUN
ejpam-6413	115	12	⊺	⊺	NUM
ejpam-6413	115	13	.	.	PUNCT
ejpam-6413	116	1	(	(	PUNCT
ejpam-6413	116	2	2	2	X
ejpam-6413	116	3	)	)	PUNCT
ejpam-6413	116	4	proof	proof	NOUN
ejpam-6413	116	5	.	.	PUNCT
ejpam-6413	117	1	consider	consider	VERB
ejpam-6413	117	2	i	i	PRON
ejpam-6413	117	3	=	=	PUNCT
ejpam-6413	117	4	∫	∫	PROPN
ejpam-6413	118	1	1	1	NUM
ejpam-6413	118	2	0	0	NUM
ejpam-6413	119	1	[	[	X
ejpam-6413	119	2	(	(	PUNCT
ejpam-6413	119	3	1−	1−	NUM
ejpam-6413	119	4	⊺)θ	⊺)θ	NUM
ejpam-6413	119	5	−	−	PROPN
ejpam-6413	119	6	⊺θ]𭟋′	⊺θ]𭟋′	PROPN
ejpam-6413	119	7	(	(	PUNCT
ejpam-6413	119	8	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	119	9	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	119	10	)	)	PUNCT
ejpam-6413	119	11	d⊺	d⊺	PROPN
ejpam-6413	119	12	=	=	PUNCT
ejpam-6413	120	1	[	[	X
ejpam-6413	120	2	∫	∫	PROPN
ejpam-6413	120	3	1	1	NUM
ejpam-6413	120	4	0	0	NUM
ejpam-6413	120	5	(	(	PUNCT
ejpam-6413	120	6	1−	1−	NUM
ejpam-6413	120	7	⊺)θ𭟋′	⊺)θ𭟋′	PROPN
ejpam-6413	120	8	(	(	PUNCT
ejpam-6413	120	9	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	120	10	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	120	11	)	)	PUNCT
ejpam-6413	120	12	d⊺	d⊺	PROPN
ejpam-6413	120	13	]	]	PUNCT
ejpam-6413	121	1	+	+	CCONJ
ejpam-6413	121	2	[	[	PUNCT
ejpam-6413	121	3	−	−	NUM
ejpam-6413	121	4	∫	∫	PROPN
ejpam-6413	121	5	1	1	NUM
ejpam-6413	121	6	0	0	PROPN
ejpam-6413	121	7	⊺θ𭟋′	⊺θ𭟋′	NOUN
ejpam-6413	121	8	(	(	PUNCT
ejpam-6413	121	9	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	121	10	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	121	11	)	)	PUNCT
ejpam-6413	121	12	d⊺	d⊺	PROPN
ejpam-6413	121	13	]	]	PUNCT
ejpam-6413	121	14	=	=	PUNCT
ejpam-6413	121	15	i1	i1	PROPN
ejpam-6413	121	16	+	+	CCONJ
ejpam-6413	121	17	i2	i2	PROPN
ejpam-6413	121	18	.	.	PUNCT
ejpam-6413	122	1	(	(	PUNCT
ejpam-6413	122	2	3	3	X
ejpam-6413	122	3	)	)	PUNCT
ejpam-6413	122	4	applying	apply	VERB
ejpam-6413	122	5	integration	integration	NOUN
ejpam-6413	122	6	by	by	ADP
ejpam-6413	122	7	parts	part	NOUN
ejpam-6413	122	8	i1	i1	NOUN
ejpam-6413	122	9	=	=	PUNCT
ejpam-6413	122	10	∫	∫	PROPN
ejpam-6413	123	1	1	1	NUM
ejpam-6413	123	2	0	0	NUM
ejpam-6413	123	3	(	(	PUNCT
ejpam-6413	123	4	1−	1−	NUM
ejpam-6413	123	5	⊺)θ𭟋′	⊺)θ𭟋′	PROPN
ejpam-6413	123	6	(	(	PUNCT
ejpam-6413	123	7	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	123	8	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	123	9	)	)	PUNCT
ejpam-6413	123	10	d⊺	d⊺	PROPN
ejpam-6413	123	11	=	=	SYM
ejpam-6413	123	12	𭟋(µ	𭟋(µ	PROPN
ejpam-6413	123	13	)	)	PUNCT
ejpam-6413	123	14	µ−	µ−	PROPN
ejpam-6413	123	15	ā	ā	NOUN
ejpam-6413	123	16	−	−	PROPN
ejpam-6413	123	17	γ(θ	γ(θ	PROPN
ejpam-6413	123	18	+	+	PROPN
ejpam-6413	123	19	1	1	X
ejpam-6413	123	20	)	)	PUNCT
ejpam-6413	123	21	(	(	PUNCT
ejpam-6413	123	22	µ−	µ−	PROPN
ejpam-6413	123	23	ā)θ+1	ā)θ+1	PROPN
ejpam-6413	123	24	χθ	χθ	PROPN
ejpam-6413	123	25	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	123	26	)	)	PUNCT
ejpam-6413	123	27	.	.	PUNCT
ejpam-6413	124	1	(	(	PUNCT
ejpam-6413	124	2	4	4	X
ejpam-6413	124	3	)	)	PUNCT
ejpam-6413	124	4	similarly	similarly	ADV
ejpam-6413	124	5	i2	i2	NOUN
ejpam-6413	124	6	=	=	PUNCT
ejpam-6413	124	7	−	−	PROPN
ejpam-6413	125	1	[	[	X
ejpam-6413	125	2	∫	∫	PROPN
ejpam-6413	125	3	1	1	NUM
ejpam-6413	125	4	0	0	PROPN
ejpam-6413	125	5	⊺θ𭟋′	⊺θ𭟋′	NOUN
ejpam-6413	125	6	(	(	PUNCT
ejpam-6413	125	7	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	125	8	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	125	9	)	)	PUNCT
ejpam-6413	125	10	d⊺	d⊺	PROPN
ejpam-6413	125	11	]	]	PUNCT
ejpam-6413	125	12	=	=	SYM
ejpam-6413	125	13	𭟋(ā	𭟋(ā	VERB
ejpam-6413	125	14	)	)	PUNCT
ejpam-6413	125	15	µ−	µ−	PROPN
ejpam-6413	125	16	ā	ā	NOUN
ejpam-6413	125	17	−	−	PROPN
ejpam-6413	125	18	γ(θ	γ(θ	PROPN
ejpam-6413	125	19	+	+	PROPN
ejpam-6413	125	20	1	1	X
ejpam-6413	125	21	)	)	PUNCT
ejpam-6413	125	22	(	(	PUNCT
ejpam-6413	125	23	µ−	µ−	PROPN
ejpam-6413	125	24	ā)θ+1	ā)θ+1	PROPN
ejpam-6413	125	25	χθ	χθ	NUM
ejpam-6413	125	26	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	125	27	)	)	PUNCT
ejpam-6413	125	28	.	.	PUNCT
ejpam-6413	126	1	(	(	PUNCT
ejpam-6413	126	2	5	5	X
ejpam-6413	126	3	)	)	PUNCT
ejpam-6413	126	4	m.	m.	NOUN
ejpam-6413	126	5	samraiz	samraiz	PROPN
ejpam-6413	126	6	et	et	PROPN
ejpam-6413	126	7	al	al	PROPN
ejpam-6413	126	8	.	.	PUNCT
ejpam-6413	126	9	/	/	SYM
ejpam-6413	126	10	eur	eur	PROPN
ejpam-6413	126	11	.	.	PUNCT
ejpam-6413	127	1	j.	j.	PROPN
ejpam-6413	127	2	pure	pure	PROPN
ejpam-6413	127	3	appl	appl	PROPN
ejpam-6413	127	4	.	.	PROPN
ejpam-6413	127	5	math	math	PROPN
ejpam-6413	127	6	,	,	PUNCT
ejpam-6413	127	7	18	18	NUM
ejpam-6413	127	8	(	(	PUNCT
ejpam-6413	127	9	3	3	NUM
ejpam-6413	127	10	)	)	PUNCT
ejpam-6413	127	11	(	(	PUNCT
ejpam-6413	127	12	2025	2025	NUM
ejpam-6413	127	13	)	)	PUNCT
ejpam-6413	127	14	,	,	PUNCT
ejpam-6413	127	15	6413	6413	NUM
ejpam-6413	127	16	6	6	NUM
ejpam-6413	127	17	of	of	ADP
ejpam-6413	127	18	26	26	NUM
ejpam-6413	127	19	using	use	VERB
ejpam-6413	127	20	(	(	PUNCT
ejpam-6413	127	21	4	4	NUM
ejpam-6413	127	22	)	)	PUNCT
ejpam-6413	127	23	and	and	CCONJ
ejpam-6413	127	24	(	(	PUNCT
ejpam-6413	127	25	5	5	NUM
ejpam-6413	127	26	)	)	PUNCT
ejpam-6413	127	27	in	in	ADP
ejpam-6413	127	28	(	(	PUNCT
ejpam-6413	127	29	3	3	NUM
ejpam-6413	127	30	)	)	PUNCT
ejpam-6413	128	1	,	,	PUNCT
ejpam-6413	128	2	it	it	PRON
ejpam-6413	128	3	follows	follow	VERB
ejpam-6413	128	4	that	that	SCONJ
ejpam-6413	128	5	i	i	PRON
ejpam-6413	128	6	=	=	SYM
ejpam-6413	128	7	𭟋(ā	𭟋(ā	VERB
ejpam-6413	128	8	)	)	PUNCT
ejpam-6413	128	9	+	+	NOUN
ejpam-6413	128	10	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	128	11	)	)	PUNCT
ejpam-6413	128	12	µ−	µ−	PROPN
ejpam-6413	128	13	ā	ā	NOUN
ejpam-6413	128	14	−	−	PROPN
ejpam-6413	128	15	γ(θ	γ(θ	PROPN
ejpam-6413	129	1	+	+	PROPN
ejpam-6413	129	2	1	1	X
ejpam-6413	129	3	)	)	PUNCT
ejpam-6413	129	4	(	(	PUNCT
ejpam-6413	129	5	µ−	µ−	PROPN
ejpam-6413	129	6	ā)θ+1	ā)θ+1	PROPN
ejpam-6413	129	7	[	[	X
ejpam-6413	129	8	χθ	χθ	NUM
ejpam-6413	129	9	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	129	10	)	)	PUNCT
ejpam-6413	130	1	+	+	CCONJ
ejpam-6413	130	2	χθ	χθ	X
ejpam-6413	130	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	130	4	)	)	PUNCT
ejpam-6413	130	5	]	]	PUNCT
ejpam-6413	130	6	.	.	PUNCT
ejpam-6413	131	1	(	(	PUNCT
ejpam-6413	131	2	6	6	NUM
ejpam-6413	131	3	)	)	PUNCT
ejpam-6413	131	4	thus	thus	ADV
ejpam-6413	131	5	,	,	PUNCT
ejpam-6413	131	6	by	by	ADP
ejpam-6413	131	7	multiplying	multiply	VERB
ejpam-6413	131	8	both	both	DET
ejpam-6413	131	9	sides	side	NOUN
ejpam-6413	131	10	of	of	ADP
ejpam-6413	131	11	(	(	PUNCT
ejpam-6413	131	12	6	6	NUM
ejpam-6413	131	13	)	)	PUNCT
ejpam-6413	131	14	by	by	ADP
ejpam-6413	131	15	(	(	PUNCT
ejpam-6413	131	16	µ−ā	µ−ā	NOUN
ejpam-6413	131	17	)	)	PUNCT
ejpam-6413	131	18	2	2	NUM
ejpam-6413	131	19	,	,	PUNCT
ejpam-6413	131	20	we	we	PRON
ejpam-6413	131	21	obtain	obtain	VERB
ejpam-6413	131	22	the	the	DET
ejpam-6413	131	23	required	require	VERB
ejpam-6413	131	24	result	result	NOUN
ejpam-6413	131	25	.	.	PUNCT
ejpam-6413	132	1	remark	remark	NOUN
ejpam-6413	132	2	1	1	NUM
ejpam-6413	132	3	.	.	PUNCT
ejpam-6413	133	1	by	by	ADP
ejpam-6413	133	2	substituting	substitute	VERB
ejpam-6413	133	3	m	m	PROPN
ejpam-6413	133	4	=	=	SYM
ejpam-6413	133	5	1	1	NUM
ejpam-6413	133	6	in	in	ADP
ejpam-6413	133	7	lemma	lemma	PROPN
ejpam-6413	133	8	3	3	NUM
ejpam-6413	133	9	,	,	PUNCT
ejpam-6413	133	10	we	we	PRON
ejpam-6413	133	11	arrive	arrive	VERB
ejpam-6413	133	12	at	at	ADP
ejpam-6413	133	13	[	[	X
ejpam-6413	133	14	20	20	NUM
ejpam-6413	133	15	,	,	PUNCT
ejpam-6413	133	16	lemma	lemma	PROPN
ejpam-6413	133	17	1.5	1.5	NUM
ejpam-6413	133	18	]	]	PUNCT
ejpam-6413	133	19	i.e.	i.e.	X
ejpam-6413	133	20	,	,	PUNCT
ejpam-6413	133	21	𭟋(ā	𭟋(ā	NUM
ejpam-6413	133	22	)	)	PUNCT
ejpam-6413	133	23	+	+	NOUN
ejpam-6413	133	24	𭟋(b̄	𭟋(b̄	NOUN
ejpam-6413	133	25	)	)	PUNCT
ejpam-6413	133	26	2	2	NUM
ejpam-6413	133	27	−	−	NOUN
ejpam-6413	133	28	γ(θ	γ(θ	PROPN
ejpam-6413	134	1	+	+	CCONJ
ejpam-6413	134	2	1	1	X
ejpam-6413	134	3	)	)	PUNCT
ejpam-6413	134	4	2(b̄−	2(b̄−	NUM
ejpam-6413	134	5	ā)θ	ā)θ	NOUN
ejpam-6413	134	6	[	[	PUNCT
ejpam-6413	134	7	χθ	χθ	X
ejpam-6413	134	8	ā+𭟋(b̄	ā+𭟋(b̄	NUM
ejpam-6413	134	9	)	)	PUNCT
ejpam-6413	135	1	+	+	CCONJ
ejpam-6413	135	2	χθ	χθ	X
ejpam-6413	135	3	b̄−𭟋(ā	b̄−𭟋(ā	NOUN
ejpam-6413	135	4	)	)	PUNCT
ejpam-6413	135	5	]	]	PUNCT
ejpam-6413	136	1	=	=	PUNCT
ejpam-6413	136	2	b̄−	b̄−	PROPN
ejpam-6413	136	3	ā	ā	NOUN
ejpam-6413	136	4	2	2	NUM
ejpam-6413	136	5	∫	∫	NOUN
ejpam-6413	136	6	1	1	NUM
ejpam-6413	136	7	0	0	NUM
ejpam-6413	137	1	[	[	X
ejpam-6413	137	2	(	(	PUNCT
ejpam-6413	137	3	1−	1−	NUM
ejpam-6413	137	4	⊺)θ	⊺)θ	NUM
ejpam-6413	137	5	−	−	PROPN
ejpam-6413	137	6	⊺θ]𭟋′	⊺θ]𭟋′	PROPN
ejpam-6413	137	7	(	(	PUNCT
ejpam-6413	137	8	⊺ā+	⊺ā+	PROPN
ejpam-6413	137	9	(	(	PUNCT
ejpam-6413	137	10	1−	1−	NUM
ejpam-6413	137	11	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	137	12	)	)	PUNCT
ejpam-6413	137	13	d	d	NOUN
ejpam-6413	137	14	⊺	⊺	NUM
ejpam-6413	137	15	.	.	PUNCT
ejpam-6413	138	1	lemma	lemma	PROPN
ejpam-6413	138	2	4	4	X
ejpam-6413	138	3	.	.	PUNCT
ejpam-6413	139	1	let	let	VERB
ejpam-6413	139	2	𭟋	𭟋	VERB
ejpam-6413	139	3	:	:	PUNCT
ejpam-6413	139	4	[	[	X
ejpam-6413	139	5	ā	ā	X
ejpam-6413	139	6	,	,	PUNCT
ejpam-6413	139	7	b̄	b̄	PROPN
ejpam-6413	139	8	]	]	PUNCT
ejpam-6413	139	9	→	→	PUNCT
ejpam-6413	139	10	r	r	NOUN
ejpam-6413	139	11	be	be	AUX
ejpam-6413	139	12	a	a	DET
ejpam-6413	139	13	twice	twice	ADV
ejpam-6413	139	14	differentiable	differentiable	ADJ
ejpam-6413	139	15	mapping	mapping	NOUN
ejpam-6413	139	16	on	on	ADP
ejpam-6413	139	17	(	(	PUNCT
ejpam-6413	139	18	ā	ā	ADJ
ejpam-6413	139	19	,	,	PUNCT
ejpam-6413	139	20	b̄	b̄	PROPN
ejpam-6413	139	21	)	)	PUNCT
ejpam-6413	139	22	with	with	ADP
ejpam-6413	139	23	ā	ā	PROPN
ejpam-6413	139	24	<	<	X
ejpam-6413	139	25	b̄.	b̄.	PUNCT
ejpam-6413	139	26	if	if	SCONJ
ejpam-6413	139	27	𭟋′′	𭟋′′	PROPN
ejpam-6413	139	28	∈	∈	PROPN
ejpam-6413	139	29	l[ā	l[ā	PROPN
ejpam-6413	139	30	,	,	PUNCT
ejpam-6413	139	31	b̄	b̄	NOUN
ejpam-6413	139	32	]	]	PUNCT
ejpam-6413	139	33	,	,	PUNCT
ejpam-6413	139	34	then	then	ADV
ejpam-6413	139	35	the	the	DET
ejpam-6413	139	36	following	follow	VERB
ejpam-6413	139	37	fractional	fractional	ADJ
ejpam-6413	139	38	integral	integral	ADJ
ejpam-6413	139	39	equality	equality	NOUN
ejpam-6413	139	40	is	be	AUX
ejpam-6413	139	41	true	true	ADJ
ejpam-6413	139	42	.	.	PUNCT
ejpam-6413	140	1	𭟋(ā	𭟋(ā	VERB
ejpam-6413	140	2	)	)	PUNCT
ejpam-6413	141	1	+	+	NOUN
ejpam-6413	141	2	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	141	3	)	)	PUNCT
ejpam-6413	141	4	2	2	NUM
ejpam-6413	141	5	−	−	NOUN
ejpam-6413	141	6	γ(θ	γ(θ	PROPN
ejpam-6413	141	7	+	+	CCONJ
ejpam-6413	141	8	1	1	X
ejpam-6413	141	9	)	)	PUNCT
ejpam-6413	141	10	2(µ−	2(µ−	NUM
ejpam-6413	141	11	ā)θ	ā)θ	NOUN
ejpam-6413	141	12	[	[	PUNCT
ejpam-6413	141	13	χθ	χθ	X
ejpam-6413	141	14	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	141	15	)	)	PUNCT
ejpam-6413	142	1	+	+	CCONJ
ejpam-6413	142	2	χθ	χθ	X
ejpam-6413	142	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	142	4	)	)	PUNCT
ejpam-6413	142	5	]	]	PUNCT
ejpam-6413	143	1	=	=	PUNCT
ejpam-6413	143	2	(	(	PUNCT
ejpam-6413	143	3	µ−	µ−	PROPN
ejpam-6413	143	4	ā)2	ā)2	VERB
ejpam-6413	143	5	2	2	NUM
ejpam-6413	143	6	∫	∫	NOUN
ejpam-6413	143	7	1	1	NUM
ejpam-6413	143	8	0	0	NUM
ejpam-6413	143	9	1−	1−	NUM
ejpam-6413	143	10	(	(	PUNCT
ejpam-6413	143	11	1−	1−	NUM
ejpam-6413	143	12	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	143	13	−	−	PROPN
ejpam-6413	143	14	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	143	15	θ	θ	PROPN
ejpam-6413	143	16	+	+	PUNCT
ejpam-6413	143	17	1	1	NUM
ejpam-6413	143	18	𭟋′′	𭟋′′	NOUN
ejpam-6413	143	19	(	(	PUNCT
ejpam-6413	143	20	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	143	21	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	143	22	)	)	PUNCT
ejpam-6413	144	1	d	d	NOUN
ejpam-6413	144	2	⊺	⊺	NUM
ejpam-6413	144	3	.	.	PUNCT
ejpam-6413	145	1	(	(	PUNCT
ejpam-6413	145	2	7	7	X
ejpam-6413	145	3	)	)	PUNCT
ejpam-6413	145	4	proof	proof	NOUN
ejpam-6413	145	5	.	.	PUNCT
ejpam-6413	146	1	by	by	ADP
ejpam-6413	146	2	comparing	compare	VERB
ejpam-6413	146	3	lemma	lemma	PROPN
ejpam-6413	146	4	3	3	NUM
ejpam-6413	146	5	and	and	CCONJ
ejpam-6413	146	6	(	(	PUNCT
ejpam-6413	146	7	7	7	NUM
ejpam-6413	146	8	)	)	PUNCT
ejpam-6413	146	9	,	,	PUNCT
ejpam-6413	146	10	we	we	PRON
ejpam-6413	146	11	can	can	AUX
ejpam-6413	146	12	write	write	VERB
ejpam-6413	146	13	(	(	PUNCT
ejpam-6413	146	14	µ−	µ−	PROPN
ejpam-6413	146	15	ā	ā	NOUN
ejpam-6413	146	16	)	)	PUNCT
ejpam-6413	146	17	2	2	NUM
ejpam-6413	146	18	∫	∫	NOUN
ejpam-6413	146	19	1	1	NUM
ejpam-6413	146	20	0	0	NUM
ejpam-6413	147	1	[	[	X
ejpam-6413	147	2	(	(	PUNCT
ejpam-6413	147	3	1−	1−	NUM
ejpam-6413	147	4	⊺)θ	⊺)θ	NUM
ejpam-6413	147	5	−	−	PROPN
ejpam-6413	147	6	⊺θ]𭟋′	⊺θ]𭟋′	PROPN
ejpam-6413	147	7	(	(	PUNCT
ejpam-6413	147	8	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	147	9	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	147	10	)	)	PUNCT
ejpam-6413	147	11	d⊺	d⊺	PROPN
ejpam-6413	147	12	=	=	PUNCT
ejpam-6413	147	13	(	(	PUNCT
ejpam-6413	147	14	µ−	µ−	PROPN
ejpam-6413	147	15	ā)2	ā)2	VERB
ejpam-6413	147	16	2	2	NUM
ejpam-6413	147	17	∫	∫	NOUN
ejpam-6413	147	18	1	1	NUM
ejpam-6413	147	19	0	0	NUM
ejpam-6413	147	20	1−	1−	NUM
ejpam-6413	147	21	(	(	PUNCT
ejpam-6413	147	22	1−	1−	NUM
ejpam-6413	147	23	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	147	24	−	−	PROPN
ejpam-6413	147	25	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	147	26	θ	θ	PROPN
ejpam-6413	147	27	+	+	PUNCT
ejpam-6413	147	28	1	1	NUM
ejpam-6413	147	29	𭟋′′	𭟋′′	NOUN
ejpam-6413	147	30	(	(	PUNCT
ejpam-6413	147	31	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	147	32	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	147	33	)	)	PUNCT
ejpam-6413	147	34	d	d	NOUN
ejpam-6413	147	35	⊺	⊺	NUM
ejpam-6413	147	36	.	.	PUNCT
ejpam-6413	148	1	(	(	PUNCT
ejpam-6413	148	2	8)	8)	NUM
ejpam-6413	148	3	to	to	PART
ejpam-6413	148	4	prove	prove	VERB
ejpam-6413	148	5	the	the	DET
ejpam-6413	148	6	required	require	VERB
ejpam-6413	148	7	result	result	NOUN
ejpam-6413	148	8	,	,	PUNCT
ejpam-6413	148	9	we	we	PRON
ejpam-6413	148	10	are	be	AUX
ejpam-6413	148	11	to	to	PART
ejpam-6413	148	12	prove	prove	VERB
ejpam-6413	148	13	(	(	PUNCT
ejpam-6413	148	14	8)	8)	NUM
ejpam-6413	148	15	.	.	PUNCT
ejpam-6413	149	1	for	for	ADP
ejpam-6413	149	2	this	this	DET
ejpam-6413	149	3	purpose	purpose	NOUN
ejpam-6413	149	4	,	,	PUNCT
ejpam-6413	149	5	consider	consider	VERB
ejpam-6413	149	6	(	(	PUNCT
ejpam-6413	149	7	µ−	µ−	NOUN
ejpam-6413	149	8	ā	ā	NOUN
ejpam-6413	149	9	)	)	PUNCT
ejpam-6413	149	10	2	2	NUM
ejpam-6413	149	11	∫	∫	NOUN
ejpam-6413	149	12	1	1	NUM
ejpam-6413	149	13	0	0	NUM
ejpam-6413	150	1	[	[	X
ejpam-6413	150	2	(	(	PUNCT
ejpam-6413	150	3	1−	1−	NUM
ejpam-6413	150	4	⊺)θ	⊺)θ	NUM
ejpam-6413	150	5	−	−	PROPN
ejpam-6413	150	6	⊺θ]𭟋′	⊺θ]𭟋′	PROPN
ejpam-6413	150	7	(	(	PUNCT
ejpam-6413	150	8	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	150	9	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	150	10	)	)	PUNCT
ejpam-6413	150	11	d	d	NOUN
ejpam-6413	150	12	⊺	⊺	NUM
ejpam-6413	150	13	.	.	PUNCT
ejpam-6413	151	1	integrating	integrate	VERB
ejpam-6413	151	2	by	by	ADP
ejpam-6413	151	3	parts	part	NOUN
ejpam-6413	151	4	the	the	DET
ejpam-6413	151	5	following	following	NOUN
ejpam-6413	151	6	,	,	PUNCT
ejpam-6413	151	7	we	we	PRON
ejpam-6413	151	8	have∫	have∫	VERB
ejpam-6413	151	9	1	1	NUM
ejpam-6413	151	10	0	0	NUM
ejpam-6413	152	1	[	[	X
ejpam-6413	152	2	(	(	PUNCT
ejpam-6413	152	3	1−	1−	NUM
ejpam-6413	152	4	⊺)θ	⊺)θ	NUM
ejpam-6413	152	5	−	−	PROPN
ejpam-6413	152	6	⊺θ]𭟋′	⊺θ]𭟋′	PROPN
ejpam-6413	152	7	(	(	PUNCT
ejpam-6413	152	8	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	152	9	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	152	10	)	)	PUNCT
ejpam-6413	152	11	d⊺	d⊺	PROPN
ejpam-6413	152	12	=	=	SYM
ejpam-6413	152	13	−𭟋′(ā	−𭟋′(ā	X
ejpam-6413	152	14	)	)	PUNCT
ejpam-6413	152	15	+	+	ADJ
ejpam-6413	152	16	𭟋′(µ	𭟋′(µ	NOUN
ejpam-6413	152	17	)	)	PUNCT
ejpam-6413	152	18	θ	θ	NOUN
ejpam-6413	153	1	+	+	PUNCT
ejpam-6413	153	2	1	1	NUM
ejpam-6413	153	3	−	−	NOUN
ejpam-6413	153	4	(	(	PUNCT
ejpam-6413	153	5	µ−	µ−	PROPN
ejpam-6413	153	6	ā	ā	NOUN
ejpam-6413	153	7	)	)	PUNCT
ejpam-6413	153	8	∫	∫	PROPN
ejpam-6413	153	9	1	1	NUM
ejpam-6413	153	10	0	0	NUM
ejpam-6413	153	11	(	(	PUNCT
ejpam-6413	153	12	1−	1−	NUM
ejpam-6413	153	13	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	153	14	+	+	CCONJ
ejpam-6413	153	15	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	153	16	θ	θ	NOUN
ejpam-6413	153	17	+	+	CCONJ
ejpam-6413	153	18	1	1	NUM
ejpam-6413	153	19	𭟋′′	𭟋′′	NOUN
ejpam-6413	153	20	(	(	PUNCT
ejpam-6413	153	21	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	153	22	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	153	23	)	)	PUNCT
ejpam-6413	153	24	d	d	NOUN
ejpam-6413	153	25	⊺	⊺	NUM
ejpam-6413	153	26	.	.	PUNCT
ejpam-6413	154	1	(	(	PUNCT
ejpam-6413	154	2	9	9	X
ejpam-6413	154	3	)	)	PUNCT
ejpam-6413	154	4	note	note	NOUN
ejpam-6413	154	5	that	that	SCONJ
ejpam-6413	154	6	𭟋′(µ)−𭟋′(ā	𭟋′(µ)−𭟋′(ā	NOUN
ejpam-6413	154	7	)	)	PUNCT
ejpam-6413	154	8	=	=	SYM
ejpam-6413	155	1	∫	∫	PROPN
ejpam-6413	155	2	µ	µ	PRON
ejpam-6413	155	3	ā	ā	PROPN
ejpam-6413	155	4	𭟋′′(λ)dλ	𭟋′′(λ)dλ	PROPN
ejpam-6413	155	5	.	.	PUNCT
ejpam-6413	156	1	(	(	PUNCT
ejpam-6413	156	2	10	10	NUM
ejpam-6413	156	3	)	)	PUNCT
ejpam-6413	156	4	m.	m.	NOUN
ejpam-6413	156	5	samraiz	samraiz	PROPN
ejpam-6413	156	6	et	et	PROPN
ejpam-6413	156	7	al	al	PROPN
ejpam-6413	156	8	.	.	PUNCT
ejpam-6413	156	9	/	/	SYM
ejpam-6413	156	10	eur	eur	PROPN
ejpam-6413	156	11	.	.	PUNCT
ejpam-6413	157	1	j.	j.	PROPN
ejpam-6413	157	2	pure	pure	PROPN
ejpam-6413	157	3	appl	appl	PROPN
ejpam-6413	157	4	.	.	PROPN
ejpam-6413	157	5	math	math	PROPN
ejpam-6413	157	6	,	,	PUNCT
ejpam-6413	157	7	18	18	NUM
ejpam-6413	157	8	(	(	PUNCT
ejpam-6413	157	9	3	3	NUM
ejpam-6413	157	10	)	)	PUNCT
ejpam-6413	157	11	(	(	PUNCT
ejpam-6413	157	12	2025	2025	NUM
ejpam-6413	157	13	)	)	PUNCT
ejpam-6413	157	14	,	,	PUNCT
ejpam-6413	157	15	6413	6413	NUM
ejpam-6413	157	16	7	7	NUM
ejpam-6413	157	17	of	of	ADP
ejpam-6413	157	18	26	26	NUM
ejpam-6413	157	19	substituting	substitute	VERB
ejpam-6413	157	20	λ	λ	NOUN
ejpam-6413	157	21	=	=	SYM
ejpam-6413	157	22	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	157	23	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	157	24	,	,	PUNCT
ejpam-6413	157	25	we	we	PRON
ejpam-6413	157	26	can	can	AUX
ejpam-6413	157	27	write	write	VERB
ejpam-6413	157	28	𭟋′(µ)−𭟋′(ā	𭟋′(µ)−𭟋′(ā	NUM
ejpam-6413	157	29	)	)	PUNCT
ejpam-6413	157	30	=	=	SYM
ejpam-6413	158	1	∫	∫	PROPN
ejpam-6413	158	2	1	1	NUM
ejpam-6413	158	3	0	0	NUM
ejpam-6413	158	4	𭟋′′(⊺ā+m(1−	𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	158	5	⊺)b̄)(µ−	⊺)b̄)(µ−	NOUN
ejpam-6413	158	6	ā)d	ā)d	NOUN
ejpam-6413	158	7	⊺	⊺	NUM
ejpam-6413	158	8	.	.	PUNCT
ejpam-6413	159	1	(	(	PUNCT
ejpam-6413	159	2	11	11	X
ejpam-6413	159	3	)	)	PUNCT
ejpam-6413	159	4	submitting	submit	VERB
ejpam-6413	159	5	(	(	PUNCT
ejpam-6413	159	6	11	11	NUM
ejpam-6413	159	7	)	)	PUNCT
ejpam-6413	159	8	in	in	ADP
ejpam-6413	159	9	(	(	PUNCT
ejpam-6413	159	10	9	9	NUM
ejpam-6413	159	11	)	)	PUNCT
ejpam-6413	159	12	,	,	PUNCT
ejpam-6413	159	13	we	we	PRON
ejpam-6413	159	14	have∫	have∫	VERB
ejpam-6413	159	15	1	1	NUM
ejpam-6413	159	16	0	0	NUM
ejpam-6413	160	1	[	[	X
ejpam-6413	160	2	(	(	PUNCT
ejpam-6413	160	3	1−	1−	NUM
ejpam-6413	160	4	⊺)θ	⊺)θ	NUM
ejpam-6413	160	5	−	−	PROPN
ejpam-6413	160	6	⊺θ]𭟋′	⊺θ]𭟋′	PROPN
ejpam-6413	160	7	(	(	PUNCT
ejpam-6413	160	8	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	160	9	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	160	10	)	)	PUNCT
ejpam-6413	160	11	d⊺	d⊺	PROPN
ejpam-6413	160	12	=	=	NUM
ejpam-6413	160	13	1	1	NUM
ejpam-6413	160	14	θ	θ	NOUN
ejpam-6413	160	15	+	+	NOUN
ejpam-6413	160	16	1	1	NUM
ejpam-6413	160	17	∫	∫	NOUN
ejpam-6413	160	18	1	1	NUM
ejpam-6413	160	19	0	0	NUM
ejpam-6413	160	20	𭟋′′(⊺ā+m(1−	𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	160	21	⊺)b̄)(µ−	⊺)b̄)(µ−	NOUN
ejpam-6413	160	22	ā)d⊺	ā)d⊺	VERB
ejpam-6413	160	23	−	−	PROPN
ejpam-6413	160	24	(	(	PUNCT
ejpam-6413	160	25	µ−	µ−	PROPN
ejpam-6413	160	26	ā	ā	NOUN
ejpam-6413	160	27	)	)	PUNCT
ejpam-6413	160	28	∫	∫	PROPN
ejpam-6413	160	29	1	1	NUM
ejpam-6413	160	30	0	0	NUM
ejpam-6413	160	31	(	(	PUNCT
ejpam-6413	160	32	1−	1−	NUM
ejpam-6413	160	33	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	160	34	+	+	CCONJ
ejpam-6413	160	35	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	160	36	θ	θ	NOUN
ejpam-6413	160	37	+	+	CCONJ
ejpam-6413	160	38	1	1	NUM
ejpam-6413	160	39	𭟋′′	𭟋′′	NOUN
ejpam-6413	160	40	(	(	PUNCT
ejpam-6413	160	41	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	160	42	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	160	43	)	)	PUNCT
ejpam-6413	160	44	d	d	NOUN
ejpam-6413	160	45	⊺	⊺	NUM
ejpam-6413	160	46	.	.	PUNCT
ejpam-6413	161	1	multiplying	multiply	VERB
ejpam-6413	161	2	by	by	ADP
ejpam-6413	161	3	µ−ā	µ−ā	NOUN
ejpam-6413	161	4	2	2	NUM
ejpam-6413	161	5	,	,	PUNCT
ejpam-6413	161	6	we	we	PRON
ejpam-6413	161	7	obtain	obtain	VERB
ejpam-6413	161	8	µ−	µ−	PROPN
ejpam-6413	161	9	ā	ā	NOUN
ejpam-6413	161	10	2	2	NUM
ejpam-6413	161	11	∫	∫	NOUN
ejpam-6413	161	12	1	1	NUM
ejpam-6413	161	13	0	0	NUM
ejpam-6413	162	1	[	[	X
ejpam-6413	162	2	(	(	PUNCT
ejpam-6413	162	3	1−	1−	NUM
ejpam-6413	162	4	⊺)θ	⊺)θ	NUM
ejpam-6413	162	5	−	−	PROPN
ejpam-6413	162	6	⊺θ]𭟋′	⊺θ]𭟋′	PROPN
ejpam-6413	162	7	(	(	PUNCT
ejpam-6413	162	8	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	162	9	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	162	10	)	)	PUNCT
ejpam-6413	162	11	d⊺	d⊺	PROPN
ejpam-6413	162	12	=	=	PUNCT
ejpam-6413	162	13	(	(	PUNCT
ejpam-6413	162	14	µ−	µ−	PROPN
ejpam-6413	162	15	ā)2	ā)2	VERB
ejpam-6413	162	16	2	2	NUM
ejpam-6413	162	17	∫	∫	NOUN
ejpam-6413	162	18	1	1	NUM
ejpam-6413	162	19	0	0	NUM
ejpam-6413	162	20	1−	1−	NUM
ejpam-6413	162	21	(	(	PUNCT
ejpam-6413	162	22	1−	1−	NUM
ejpam-6413	162	23	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	162	24	−	−	PROPN
ejpam-6413	162	25	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	162	26	θ	θ	PROPN
ejpam-6413	162	27	+	+	PUNCT
ejpam-6413	162	28	1	1	NUM
ejpam-6413	162	29	𭟋′′	𭟋′′	NOUN
ejpam-6413	162	30	(	(	PUNCT
ejpam-6413	162	31	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	162	32	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	162	33	)	)	PUNCT
ejpam-6413	162	34	d	d	NOUN
ejpam-6413	162	35	⊺	⊺	NUM
ejpam-6413	162	36	.	.	PUNCT
ejpam-6413	163	1	hence	hence	ADV
ejpam-6413	163	2	,	,	PUNCT
ejpam-6413	163	3	the	the	DET
ejpam-6413	163	4	proof	proof	NOUN
ejpam-6413	163	5	is	be	AUX
ejpam-6413	163	6	done	do	VERB
ejpam-6413	163	7	.	.	PUNCT
ejpam-6413	164	1	remark	remark	NOUN
ejpam-6413	164	2	2	2	NUM
ejpam-6413	164	3	.	.	PUNCT
ejpam-6413	165	1	by	by	ADP
ejpam-6413	165	2	substituting	substitute	VERB
ejpam-6413	165	3	m	m	PROPN
ejpam-6413	165	4	=	=	SYM
ejpam-6413	165	5	1	1	NUM
ejpam-6413	165	6	in	in	ADP
ejpam-6413	165	7	lemma	lemma	PROPN
ejpam-6413	165	8	4	4	NUM
ejpam-6413	165	9	,	,	PUNCT
ejpam-6413	165	10	we	we	PRON
ejpam-6413	165	11	arrive	arrive	VERB
ejpam-6413	165	12	at	at	ADP
ejpam-6413	165	13	[	[	X
ejpam-6413	165	14	?	?	PUNCT
ejpam-6413	165	15	,	,	PUNCT
ejpam-6413	165	16	lemma	lemma	PROPN
ejpam-6413	165	17	2	2	NUM
ejpam-6413	165	18	]	]	PUNCT
ejpam-6413	165	19	i.e.	i.e.	X
ejpam-6413	165	20	,	,	PUNCT
ejpam-6413	165	21	𭟋(ā	𭟋(ā	NUM
ejpam-6413	165	22	)	)	PUNCT
ejpam-6413	165	23	+	+	NOUN
ejpam-6413	165	24	𭟋(b̄	𭟋(b̄	NOUN
ejpam-6413	165	25	)	)	PUNCT
ejpam-6413	165	26	2	2	NUM
ejpam-6413	165	27	−	−	NOUN
ejpam-6413	165	28	γ(θ	γ(θ	PROPN
ejpam-6413	165	29	+	+	CCONJ
ejpam-6413	165	30	1	1	X
ejpam-6413	165	31	)	)	PUNCT
ejpam-6413	165	32	2(b̄−	2(b̄−	NUM
ejpam-6413	165	33	ā)θ	ā)θ	NOUN
ejpam-6413	165	34	[	[	PUNCT
ejpam-6413	165	35	χθ	χθ	X
ejpam-6413	165	36	ā+𭟋(b̄	ā+𭟋(b̄	NUM
ejpam-6413	165	37	)	)	PUNCT
ejpam-6413	166	1	+	+	CCONJ
ejpam-6413	166	2	χθ	χθ	X
ejpam-6413	166	3	b̄−𭟋(ā	b̄−𭟋(ā	NOUN
ejpam-6413	166	4	)	)	PUNCT
ejpam-6413	166	5	]	]	PUNCT
ejpam-6413	167	1	=	=	PUNCT
ejpam-6413	167	2	(	(	PUNCT
ejpam-6413	167	3	b̄−	b̄−	PROPN
ejpam-6413	167	4	ā)2	ā)2	ADJ
ejpam-6413	167	5	2	2	NUM
ejpam-6413	167	6	∫	∫	NOUN
ejpam-6413	167	7	1	1	NUM
ejpam-6413	167	8	0	0	NUM
ejpam-6413	167	9	1−	1−	NUM
ejpam-6413	167	10	(	(	PUNCT
ejpam-6413	167	11	1−	1−	NUM
ejpam-6413	167	12	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	167	13	−	−	PROPN
ejpam-6413	167	14	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	167	15	θ	θ	PROPN
ejpam-6413	167	16	+	+	PUNCT
ejpam-6413	167	17	1	1	NUM
ejpam-6413	167	18	𭟋′′	𭟋′′	NOUN
ejpam-6413	167	19	(	(	PUNCT
ejpam-6413	167	20	⊺ā+	⊺ā+	PROPN
ejpam-6413	167	21	(	(	PUNCT
ejpam-6413	167	22	1−	1−	NUM
ejpam-6413	167	23	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	167	24	)	)	PUNCT
ejpam-6413	167	25	d	d	NOUN
ejpam-6413	167	26	⊺	⊺	NUM
ejpam-6413	167	27	.	.	PUNCT
ejpam-6413	168	1	lemma	lemma	PROPN
ejpam-6413	168	2	5	5	X
ejpam-6413	168	3	.	.	PUNCT
ejpam-6413	169	1	let	let	VERB
ejpam-6413	169	2	𭟋	𭟋	VERB
ejpam-6413	169	3	:	:	PUNCT
ejpam-6413	169	4	[	[	X
ejpam-6413	169	5	ā	ā	X
ejpam-6413	169	6	,	,	PUNCT
ejpam-6413	169	7	b̄	b̄	PROPN
ejpam-6413	169	8	]	]	PUNCT
ejpam-6413	169	9	→	→	PUNCT
ejpam-6413	169	10	r	r	NOUN
ejpam-6413	169	11	be	be	AUX
ejpam-6413	169	12	a	a	DET
ejpam-6413	169	13	twice	twice	ADV
ejpam-6413	169	14	differentiable	differentiable	ADJ
ejpam-6413	169	15	mapping	mapping	NOUN
ejpam-6413	169	16	on	on	ADP
ejpam-6413	169	17	(	(	PUNCT
ejpam-6413	169	18	ā	ā	ADJ
ejpam-6413	169	19	,	,	PUNCT
ejpam-6413	169	20	b̄	b̄	PROPN
ejpam-6413	169	21	)	)	PUNCT
ejpam-6413	169	22	with	with	ADP
ejpam-6413	169	23	ā	ā	PROPN
ejpam-6413	169	24	<	<	X
ejpam-6413	169	25	b̄.	b̄.	PUNCT
ejpam-6413	169	26	if	if	SCONJ
ejpam-6413	169	27	𭟋′′	𭟋′′	PROPN
ejpam-6413	169	28	∈	∈	PROPN
ejpam-6413	169	29	l[ā	l[ā	PROPN
ejpam-6413	169	30	,	,	PUNCT
ejpam-6413	169	31	b̄	b̄	NOUN
ejpam-6413	169	32	]	]	PUNCT
ejpam-6413	169	33	,	,	PUNCT
ejpam-6413	169	34	then	then	ADV
ejpam-6413	169	35	γ(θ	γ(θ	PROPN
ejpam-6413	170	1	+	+	CCONJ
ejpam-6413	170	2	1	1	X
ejpam-6413	170	3	)	)	PUNCT
ejpam-6413	170	4	2(µ−	2(µ−	NUM
ejpam-6413	170	5	ā)θ	ā)θ	NOUN
ejpam-6413	170	6	[	[	PUNCT
ejpam-6413	170	7	χθ	χθ	X
ejpam-6413	170	8	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	170	9	)	)	PUNCT
ejpam-6413	171	1	+	+	CCONJ
ejpam-6413	171	2	χθ	χθ	X
ejpam-6413	171	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	171	4	)	)	PUNCT
ejpam-6413	171	5	]	]	PUNCT
ejpam-6413	172	1	−𭟋	−𭟋	INTJ
ejpam-6413	172	2	(	(	PUNCT
ejpam-6413	172	3	ā+	ā+	PUNCT
ejpam-6413	172	4	µ	µ	X
ejpam-6413	172	5	2	2	NUM
ejpam-6413	172	6	)	)	PUNCT
ejpam-6413	172	7	=	=	PUNCT
ejpam-6413	172	8	(	(	PUNCT
ejpam-6413	172	9	µ−	µ−	PROPN
ejpam-6413	172	10	ā)2	ā)2	VERB
ejpam-6413	172	11	2	2	NUM
ejpam-6413	172	12	∫	∫	NOUN
ejpam-6413	172	13	1	1	NUM
ejpam-6413	172	14	0	0	NUM
ejpam-6413	172	15	p0(⊺)𭟋′′	p0(⊺)𭟋′′	NOUN
ejpam-6413	172	16	(	(	PUNCT
ejpam-6413	172	17	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	172	18	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	172	19	)	)	PUNCT
ejpam-6413	172	20	d⊺	d⊺	PROPN
ejpam-6413	172	21	,	,	PUNCT
ejpam-6413	172	22	where	where	SCONJ
ejpam-6413	172	23	p0(⊺	p0(⊺	NOUN
ejpam-6413	172	24	)	)	PUNCT
ejpam-6413	172	25	=	=	PRON
ejpam-6413	172	26	{	{	PUNCT
ejpam-6413	172	27	⊺−	⊺−	PROPN
ejpam-6413	172	28	1−(1−⊺)θ+1−⊺θ+1	1−(1−⊺)θ+1−⊺θ+1	PROPN
ejpam-6413	172	29	θ+1	θ+1	NUM
ejpam-6413	172	30	,	,	PUNCT
ejpam-6413	172	31	⊺	⊺	PUNCT
ejpam-6413	172	32	∈	∈	PROPN
ejpam-6413	173	1	[	[	X
ejpam-6413	173	2	0	0	NUM
ejpam-6413	173	3	,	,	PUNCT
ejpam-6413	173	4	12	12	NUM
ejpam-6413	173	5	)	)	PUNCT
ejpam-6413	173	6	,	,	PUNCT
ejpam-6413	173	7	1−	1−	NUM
ejpam-6413	173	8	⊺−	⊺−	PROPN
ejpam-6413	173	9	1−(1−⊺)θ+1−⊺θ+1	1−(1−⊺)θ+1−⊺θ+1	PROPN
ejpam-6413	173	10	θ+1	θ+1	NUM
ejpam-6413	173	11	,	,	PUNCT
ejpam-6413	173	12	⊺	⊺	PUNCT
ejpam-6413	173	13	∈	∈	PROPN
ejpam-6413	173	14	[	[	X
ejpam-6413	173	15	12	12	NUM
ejpam-6413	173	16	,	,	PUNCT
ejpam-6413	173	17	1	1	NUM
ejpam-6413	173	18	)	)	PUNCT
ejpam-6413	173	19	.	.	PUNCT
ejpam-6413	174	1	m.	m.	NOUN
ejpam-6413	174	2	samraiz	samraiz	PROPN
ejpam-6413	174	3	et	et	PROPN
ejpam-6413	174	4	al	al	PROPN
ejpam-6413	174	5	.	.	PUNCT
ejpam-6413	174	6	/	/	SYM
ejpam-6413	174	7	eur	eur	PROPN
ejpam-6413	174	8	.	.	PUNCT
ejpam-6413	175	1	j.	j.	PROPN
ejpam-6413	175	2	pure	pure	PROPN
ejpam-6413	175	3	appl	appl	PROPN
ejpam-6413	175	4	.	.	PROPN
ejpam-6413	175	5	math	math	PROPN
ejpam-6413	175	6	,	,	PUNCT
ejpam-6413	175	7	18	18	NUM
ejpam-6413	175	8	(	(	PUNCT
ejpam-6413	175	9	3	3	NUM
ejpam-6413	175	10	)	)	PUNCT
ejpam-6413	175	11	(	(	PUNCT
ejpam-6413	175	12	2025	2025	NUM
ejpam-6413	175	13	)	)	PUNCT
ejpam-6413	175	14	,	,	PUNCT
ejpam-6413	175	15	6413	6413	NUM
ejpam-6413	175	16	8	8	NUM
ejpam-6413	175	17	of	of	ADP
ejpam-6413	175	18	26	26	NUM
ejpam-6413	175	19	proof	proof	NOUN
ejpam-6413	175	20	.	.	PUNCT
ejpam-6413	176	1	consider∫	consider∫	NOUN
ejpam-6413	176	2	1	1	NUM
ejpam-6413	176	3	0	0	NUM
ejpam-6413	176	4	p0(⊺)𭟋′′	p0(⊺)𭟋′′	NOUN
ejpam-6413	176	5	(	(	PUNCT
ejpam-6413	176	6	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	176	7	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	176	8	)	)	PUNCT
ejpam-6413	176	9	d⊺	d⊺	PROPN
ejpam-6413	176	10	=	=	PUNCT
ejpam-6413	177	1	[	[	X
ejpam-6413	177	2	∫	∫	X
ejpam-6413	177	3	1	1	NUM
ejpam-6413	177	4	2	2	NUM
ejpam-6413	177	5	0	0	NUM
ejpam-6413	177	6	(	(	PUNCT
ejpam-6413	177	7	⊺−	⊺−	PROPN
ejpam-6413	177	8	1−	1−	NUM
ejpam-6413	177	9	(	(	PUNCT
ejpam-6413	177	10	1−	1−	NUM
ejpam-6413	177	11	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	177	12	−	−	PROPN
ejpam-6413	177	13	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	177	14	θ	θ	PROPN
ejpam-6413	177	15	+	+	CCONJ
ejpam-6413	177	16	1	1	X
ejpam-6413	177	17	)	)	PUNCT
ejpam-6413	177	18	𭟋′′(⊺ā+m(1−	𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	177	19	⊺)b̄)d⊺	⊺)b̄)d⊺	PROPN
ejpam-6413	177	20	∫	∫	NOUN
ejpam-6413	177	21	1	1	NUM
ejpam-6413	177	22	1	1	NUM
ejpam-6413	177	23	2	2	NUM
ejpam-6413	177	24	(	(	PUNCT
ejpam-6413	177	25	1−	1−	NUM
ejpam-6413	177	26	⊺−	⊺−	PROPN
ejpam-6413	177	27	1−	1−	NUM
ejpam-6413	177	28	(	(	PUNCT
ejpam-6413	177	29	1−	1−	NUM
ejpam-6413	177	30	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	177	31	−	−	PROPN
ejpam-6413	177	32	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	177	33	θ	θ	PROPN
ejpam-6413	178	1	+	+	CCONJ
ejpam-6413	178	2	1	1	X
ejpam-6413	178	3	)	)	PUNCT
ejpam-6413	178	4	𭟋′′(⊺ā+m(1−	𭟋′′(⊺ā+m(1−	VERB
ejpam-6413	178	5	⊺)b̄)d⊺	⊺)b̄)d⊺	NOUN
ejpam-6413	178	6	]	]	PUNCT
ejpam-6413	179	1	=	=	PUNCT
ejpam-6413	179	2	[	[	X
ejpam-6413	179	3	(	(	PUNCT
ejpam-6413	179	4	∫	∫	PROPN
ejpam-6413	179	5	1	1	NUM
ejpam-6413	179	6	2	2	NUM
ejpam-6413	179	7	0	0	NUM
ejpam-6413	179	8	⊺𭟋′′(⊺ā+m(1−	⊺𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	179	9	⊺)b̄)d	⊺)b̄)d	PROPN
ejpam-6413	179	10	⊺+	⊺+	NOUN
ejpam-6413	179	11	∫	∫	NOUN
ejpam-6413	179	12	1	1	NUM
ejpam-6413	179	13	1	1	NUM
ejpam-6413	179	14	2	2	NUM
ejpam-6413	179	15	(	(	PUNCT
ejpam-6413	179	16	1−	1−	NUM
ejpam-6413	179	17	⊺)𭟋′′(⊺ā+m(1−	⊺)𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	179	18	⊺)b̄)d⊺	⊺)b̄)d⊺	PROPN
ejpam-6413	179	19	)	)	PUNCT
ejpam-6413	180	1	−	−	NOUN
ejpam-6413	181	1	∫	∫	NOUN
ejpam-6413	181	2	1	1	NUM
ejpam-6413	181	3	0	0	NUM
ejpam-6413	181	4	1−	1−	NUM
ejpam-6413	181	5	(	(	PUNCT
ejpam-6413	181	6	1−	1−	NUM
ejpam-6413	181	7	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	181	8	−	−	PROPN
ejpam-6413	181	9	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	181	10	θ	θ	PROPN
ejpam-6413	181	11	+	+	CCONJ
ejpam-6413	181	12	1	1	NUM
ejpam-6413	181	13	𭟋′′(⊺ā+m(1−	𭟋′′(⊺ā+m(1−	NOUN
ejpam-6413	181	14	⊺)b̄)d⊺	⊺)b̄)d⊺	NOUN
ejpam-6413	181	15	]	]	PUNCT
ejpam-6413	181	16	.	.	PUNCT
ejpam-6413	182	1	(	(	PUNCT
ejpam-6413	182	2	12	12	NUM
ejpam-6413	182	3	)	)	PUNCT
ejpam-6413	182	4	let	let	VERB
ejpam-6413	182	5	i	i	PRON
ejpam-6413	182	6	=	=	PUNCT
ejpam-6413	183	1	∫	∫	PROPN
ejpam-6413	183	2	1	1	NUM
ejpam-6413	183	3	2	2	NUM
ejpam-6413	183	4	0	0	NUM
ejpam-6413	183	5	⊺𭟋′′	⊺𭟋′′	NOUN
ejpam-6413	183	6	(	(	PUNCT
ejpam-6413	183	7	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	183	8	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	183	9	)	)	PUNCT
ejpam-6413	184	1	d	d	X
ejpam-6413	184	2	⊺+	⊺+	PROPN
ejpam-6413	184	3	∫	∫	PROPN
ejpam-6413	184	4	1	1	NUM
ejpam-6413	184	5	1	1	NUM
ejpam-6413	184	6	2	2	NUM
ejpam-6413	184	7	(	(	PUNCT
ejpam-6413	184	8	1−	1−	NUM
ejpam-6413	184	9	⊺)𭟋′′	⊺)𭟋′′	NOUN
ejpam-6413	184	10	(	(	PUNCT
ejpam-6413	184	11	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	184	12	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	184	13	)	)	PUNCT
ejpam-6413	184	14	d⊺	d⊺	PROPN
ejpam-6413	184	15	=	=	SYM
ejpam-6413	184	16	i1	i1	PROPN
ejpam-6413	184	17	+	+	CCONJ
ejpam-6413	184	18	i2	i2	PROPN
ejpam-6413	184	19	.	.	PUNCT
ejpam-6413	185	1	(	(	PUNCT
ejpam-6413	185	2	13	13	NUM
ejpam-6413	185	3	)	)	PUNCT
ejpam-6413	185	4	integrating	integrating	NOUN
ejpam-6413	185	5	by	by	ADP
ejpam-6413	185	6	parts	part	NOUN
ejpam-6413	185	7	,	,	PUNCT
ejpam-6413	185	8	we	we	PRON
ejpam-6413	185	9	have	have	VERB
ejpam-6413	185	10	i1	i1	PROPN
ejpam-6413	185	11	=	=	SYM
ejpam-6413	185	12	∫	∫	PROPN
ejpam-6413	185	13	1	1	NUM
ejpam-6413	185	14	2	2	NUM
ejpam-6413	185	15	0	0	NUM
ejpam-6413	185	16	⊺𭟋′′	⊺𭟋′′	NOUN
ejpam-6413	185	17	(	(	PUNCT
ejpam-6413	185	18	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	185	19	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	185	20	)	)	PUNCT
ejpam-6413	186	1	d⊺	d⊺	PROPN
ejpam-6413	186	2	=	=	NOUN
ejpam-6413	186	3	1	1	NUM
ejpam-6413	186	4	2(ā−	2(ā−	NUM
ejpam-6413	186	5	µ	µ	NUM
ejpam-6413	186	6	)	)	PUNCT
ejpam-6413	186	7	𭟋′	𭟋′	PROPN
ejpam-6413	186	8	(	(	PUNCT
ejpam-6413	186	9	ā+	ā+	PUNCT
ejpam-6413	186	10	µ	µ	X
ejpam-6413	186	11	2	2	NUM
ejpam-6413	186	12	)	)	PUNCT
ejpam-6413	186	13	−	−	NOUN
ejpam-6413	186	14	1	1	NUM
ejpam-6413	186	15	(	(	PUNCT
ejpam-6413	186	16	ā−	ā−	PROPN
ejpam-6413	186	17	µ	µ	NUM
ejpam-6413	186	18	)	)	PUNCT
ejpam-6413	186	19	[	[	PUNCT
ejpam-6413	186	20	𭟋	𭟋	X
ejpam-6413	186	21	(	(	PUNCT
ejpam-6413	186	22	ā+	ā+	PUNCT
ejpam-6413	186	23	µ	µ	X
ejpam-6413	186	24	2	2	NUM
ejpam-6413	186	25	)	)	PUNCT
ejpam-6413	186	26	−𭟋(µ	−𭟋(µ	PROPN
ejpam-6413	186	27	)	)	PUNCT
ejpam-6413	186	28	]	]	PUNCT
ejpam-6413	186	29	,	,	PUNCT
ejpam-6413	186	30	(	(	PUNCT
ejpam-6413	186	31	14	14	NUM
ejpam-6413	186	32	)	)	PUNCT
ejpam-6413	186	33	and	and	CCONJ
ejpam-6413	186	34	i2	i2	PROPN
ejpam-6413	186	35	=	=	SYM
ejpam-6413	186	36	∫	∫	PROPN
ejpam-6413	186	37	1	1	NUM
ejpam-6413	186	38	1	1	NUM
ejpam-6413	186	39	2	2	NUM
ejpam-6413	186	40	(	(	PUNCT
ejpam-6413	186	41	1−	1−	NUM
ejpam-6413	186	42	⊺)𭟋′′	⊺)𭟋′′	NOUN
ejpam-6413	186	43	(	(	PUNCT
ejpam-6413	186	44	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	186	45	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	186	46	)	)	PUNCT
ejpam-6413	186	47	d⊺	d⊺	PROPN
ejpam-6413	187	1	=	=	PUNCT
ejpam-6413	188	1	−	−	PROPN
ejpam-6413	188	2	1	1	NUM
ejpam-6413	188	3	2(ā−	2(ā−	NUM
ejpam-6413	188	4	µ	µ	NUM
ejpam-6413	188	5	)	)	PUNCT
ejpam-6413	188	6	𭟋′	𭟋′	PROPN
ejpam-6413	188	7	(	(	PUNCT
ejpam-6413	188	8	ā+	ā+	PUNCT
ejpam-6413	188	9	µ	µ	X
ejpam-6413	188	10	2	2	NUM
ejpam-6413	188	11	)	)	PUNCT
ejpam-6413	188	12	−	−	NOUN
ejpam-6413	188	13	1	1	NUM
ejpam-6413	188	14	(	(	PUNCT
ejpam-6413	188	15	ā−	ā−	PROPN
ejpam-6413	188	16	µ	µ	NUM
ejpam-6413	188	17	)	)	PUNCT
ejpam-6413	188	18	[	[	PUNCT
ejpam-6413	188	19	𭟋(ā)−𭟋	𭟋(ā)−𭟋	NOUN
ejpam-6413	188	20	(	(	PUNCT
ejpam-6413	188	21	ā+	ā+	PUNCT
ejpam-6413	188	22	µ	µ	X
ejpam-6413	188	23	2	2	NUM
ejpam-6413	188	24	)	)	PUNCT
ejpam-6413	188	25	]	]	PUNCT
ejpam-6413	188	26	.	.	PUNCT
ejpam-6413	189	1	(	(	PUNCT
ejpam-6413	189	2	15	15	X
ejpam-6413	189	3	)	)	PUNCT
ejpam-6413	189	4	substituting	substituting	NOUN
ejpam-6413	189	5	(	(	PUNCT
ejpam-6413	189	6	14	14	NUM
ejpam-6413	189	7	)	)	PUNCT
ejpam-6413	189	8	and	and	CCONJ
ejpam-6413	189	9	(	(	PUNCT
ejpam-6413	189	10	15	15	NUM
ejpam-6413	189	11	)	)	PUNCT
ejpam-6413	189	12	in	in	ADP
ejpam-6413	189	13	(	(	PUNCT
ejpam-6413	189	14	13	13	NUM
ejpam-6413	189	15	)	)	PUNCT
ejpam-6413	189	16	,	,	PUNCT
ejpam-6413	189	17	it	it	PRON
ejpam-6413	189	18	follows	follow	VERB
ejpam-6413	189	19	that	that	SCONJ
ejpam-6413	189	20	i	i	PRON
ejpam-6413	189	21	=	=	SYM
ejpam-6413	189	22	𭟋(ā	𭟋(ā	VERB
ejpam-6413	189	23	)	)	PUNCT
ejpam-6413	189	24	+	+	NOUN
ejpam-6413	189	25	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	189	26	)	)	PUNCT
ejpam-6413	189	27	(	(	PUNCT
ejpam-6413	189	28	µ−	µ−	PROPN
ejpam-6413	189	29	ā)2	ā)2	NOUN
ejpam-6413	189	30	−	−	PROPN
ejpam-6413	189	31	2	2	NUM
ejpam-6413	189	32	(	(	PUNCT
ejpam-6413	189	33	µ−	µ−	PROPN
ejpam-6413	189	34	ā)2	ā)2	NOUN
ejpam-6413	189	35	𭟋	𭟋	PROPN
ejpam-6413	189	36	(	(	PUNCT
ejpam-6413	189	37	ā+	ā+	PUNCT
ejpam-6413	189	38	µ	µ	X
ejpam-6413	189	39	2	2	NUM
ejpam-6413	189	40	)	)	PUNCT
ejpam-6413	189	41	.	.	PUNCT
ejpam-6413	190	1	(	(	PUNCT
ejpam-6413	190	2	16	16	NUM
ejpam-6413	190	3	)	)	PUNCT
ejpam-6413	190	4	from	from	ADP
ejpam-6413	190	5	(	(	PUNCT
ejpam-6413	190	6	12	12	NUM
ejpam-6413	190	7	)	)	PUNCT
ejpam-6413	190	8	,	,	PUNCT
ejpam-6413	190	9	we	we	PRON
ejpam-6413	190	10	obtain∫	obtain∫	VERB
ejpam-6413	190	11	1	1	NUM
ejpam-6413	190	12	0	0	NUM
ejpam-6413	190	13	p0(⊺)𭟋′′	p0(⊺)𭟋′′	NOUN
ejpam-6413	190	14	(	(	PUNCT
ejpam-6413	190	15	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	190	16	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	190	17	)	)	PUNCT
ejpam-6413	191	1	d⊺	d⊺	PROPN
ejpam-6413	191	2	m.	m.	NOUN
ejpam-6413	191	3	samraiz	samraiz	PROPN
ejpam-6413	191	4	et	et	PROPN
ejpam-6413	191	5	al	al	PROPN
ejpam-6413	191	6	.	.	PUNCT
ejpam-6413	191	7	/	/	SYM
ejpam-6413	191	8	eur	eur	PROPN
ejpam-6413	191	9	.	.	PUNCT
ejpam-6413	192	1	j.	j.	PROPN
ejpam-6413	192	2	pure	pure	PROPN
ejpam-6413	192	3	appl	appl	PROPN
ejpam-6413	192	4	.	.	PROPN
ejpam-6413	192	5	math	math	PROPN
ejpam-6413	192	6	,	,	PUNCT
ejpam-6413	192	7	18	18	NUM
ejpam-6413	192	8	(	(	PUNCT
ejpam-6413	192	9	3	3	NUM
ejpam-6413	192	10	)	)	PUNCT
ejpam-6413	192	11	(	(	PUNCT
ejpam-6413	192	12	2025	2025	NUM
ejpam-6413	192	13	)	)	PUNCT
ejpam-6413	192	14	,	,	PUNCT
ejpam-6413	192	15	6413	6413	NUM
ejpam-6413	192	16	9	9	NUM
ejpam-6413	192	17	of	of	ADP
ejpam-6413	192	18	26	26	NUM
ejpam-6413	192	19	=	=	SYM
ejpam-6413	192	20	𭟋(ā	𭟋(ā	PROPN
ejpam-6413	192	21	)	)	PUNCT
ejpam-6413	192	22	+	+	NOUN
ejpam-6413	192	23	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	192	24	)	)	PUNCT
ejpam-6413	192	25	(	(	PUNCT
ejpam-6413	192	26	µ−	µ−	PROPN
ejpam-6413	192	27	ā)2	ā)2	NOUN
ejpam-6413	192	28	−	−	PROPN
ejpam-6413	192	29	2	2	NUM
ejpam-6413	192	30	(	(	PUNCT
ejpam-6413	192	31	µ−	µ−	PROPN
ejpam-6413	192	32	ā)2	ā)2	NOUN
ejpam-6413	192	33	𭟋	𭟋	PROPN
ejpam-6413	192	34	(	(	PUNCT
ejpam-6413	192	35	ā+	ā+	PUNCT
ejpam-6413	192	36	µ	µ	X
ejpam-6413	192	37	2	2	NUM
ejpam-6413	192	38	)	)	PUNCT
ejpam-6413	192	39	−	−	NOUN
ejpam-6413	193	1	∫	∫	PROPN
ejpam-6413	193	2	1	1	NUM
ejpam-6413	193	3	0	0	NUM
ejpam-6413	193	4	1−	1−	NUM
ejpam-6413	193	5	(	(	PUNCT
ejpam-6413	193	6	1−	1−	NUM
ejpam-6413	193	7	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	193	8	−	−	PROPN
ejpam-6413	193	9	⊺θ+1	⊺θ+1	NOUN
ejpam-6413	193	10	⋎(θ	⋎(θ	NOUN
ejpam-6413	193	11	+	+	NOUN
ejpam-6413	193	12	1	1	X
ejpam-6413	193	13	)	)	PUNCT
ejpam-6413	193	14	𭟋′′(⊺ā+m(1−	𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	193	15	⊺)b̄)d	⊺)b̄)d	NOUN
ejpam-6413	193	16	⊺	⊺	NUM
ejpam-6413	193	17	.	.	PUNCT
ejpam-6413	194	1	(	(	PUNCT
ejpam-6413	194	2	17	17	NUM
ejpam-6413	194	3	)	)	PUNCT
ejpam-6413	194	4	thus	thus	ADV
ejpam-6413	194	5	,	,	PUNCT
ejpam-6413	194	6	by	by	ADP
ejpam-6413	194	7	multiplying	multiply	VERB
ejpam-6413	194	8	both	both	DET
ejpam-6413	194	9	sides	side	NOUN
ejpam-6413	194	10	of	of	ADP
ejpam-6413	194	11	(	(	PUNCT
ejpam-6413	194	12	17	17	NUM
ejpam-6413	194	13	)	)	PUNCT
ejpam-6413	194	14	by	by	ADP
ejpam-6413	194	15	(	(	PUNCT
ejpam-6413	194	16	µ−ā)2	µ−ā)2	PROPN
ejpam-6413	194	17	2	2	NUM
ejpam-6413	194	18	,	,	PUNCT
ejpam-6413	194	19	we	we	PRON
ejpam-6413	194	20	have	have	AUX
ejpam-6413	194	21	(	(	PUNCT
ejpam-6413	194	22	µ−	µ−	PROPN
ejpam-6413	194	23	ā)2	ā)2	NOUN
ejpam-6413	194	24	2	2	NUM
ejpam-6413	194	25	∫	∫	NOUN
ejpam-6413	194	26	1	1	NUM
ejpam-6413	194	27	0	0	NUM
ejpam-6413	194	28	p0(⊺)𭟋′′	p0(⊺)𭟋′′	NOUN
ejpam-6413	194	29	(	(	PUNCT
ejpam-6413	194	30	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	194	31	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	194	32	)	)	PUNCT
ejpam-6413	194	33	d⊺	d⊺	PROPN
ejpam-6413	194	34	=	=	SYM
ejpam-6413	194	35	𭟋(ā	𭟋(ā	VERB
ejpam-6413	194	36	)	)	PUNCT
ejpam-6413	194	37	+	+	NOUN
ejpam-6413	194	38	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	194	39	)	)	PUNCT
ejpam-6413	194	40	2	2	NUM
ejpam-6413	194	41	−𭟋	−𭟋	NOUN
ejpam-6413	194	42	(	(	PUNCT
ejpam-6413	194	43	ā+	ā+	PUNCT
ejpam-6413	194	44	µ	µ	X
ejpam-6413	194	45	2	2	NUM
ejpam-6413	194	46	)	)	PUNCT
ejpam-6413	194	47	−	−	PROPN
ejpam-6413	195	1	(	(	PUNCT
ejpam-6413	195	2	µ−	µ−	PROPN
ejpam-6413	195	3	ā)2	ā)2	NOUN
ejpam-6413	195	4	2	2	NUM
ejpam-6413	195	5	∫	∫	NOUN
ejpam-6413	195	6	1	1	NUM
ejpam-6413	195	7	0	0	NUM
ejpam-6413	195	8	1−	1−	NUM
ejpam-6413	195	9	(	(	PUNCT
ejpam-6413	195	10	1−	1−	NUM
ejpam-6413	195	11	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	195	12	−	−	PROPN
ejpam-6413	195	13	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	195	14	θ	θ	PROPN
ejpam-6413	195	15	+	+	PUNCT
ejpam-6413	196	1	1	1	NUM
ejpam-6413	196	2	𭟋′′	𭟋′′	NOUN
ejpam-6413	196	3	(	(	PUNCT
ejpam-6413	196	4	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	196	5	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	196	6	)	)	PUNCT
ejpam-6413	196	7	d	d	NOUN
ejpam-6413	196	8	⊺	⊺	NUM
ejpam-6413	196	9	.	.	PUNCT
ejpam-6413	197	1	(	(	PUNCT
ejpam-6413	197	2	18	18	NUM
ejpam-6413	197	3	)	)	PUNCT
ejpam-6413	197	4	on	on	ADP
ejpam-6413	197	5	the	the	DET
ejpam-6413	197	6	other	other	ADJ
ejpam-6413	197	7	hand	hand	NOUN
ejpam-6413	197	8	,	,	PUNCT
ejpam-6413	197	9	by	by	ADP
ejpam-6413	197	10	(	(	PUNCT
ejpam-6413	197	11	7	7	NUM
ejpam-6413	197	12	)	)	PUNCT
ejpam-6413	197	13	,	,	PUNCT
ejpam-6413	197	14	we	we	PRON
ejpam-6413	197	15	obtain	obtain	VERB
ejpam-6413	197	16	𭟋(ā	𭟋(ā	NUM
ejpam-6413	197	17	)	)	PUNCT
ejpam-6413	198	1	+	+	NOUN
ejpam-6413	198	2	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	198	3	)	)	PUNCT
ejpam-6413	198	4	2	2	NUM
ejpam-6413	198	5	−	−	NOUN
ejpam-6413	198	6	γ(θ	γ(θ	PROPN
ejpam-6413	199	1	+	+	CCONJ
ejpam-6413	199	2	1	1	X
ejpam-6413	199	3	)	)	PUNCT
ejpam-6413	199	4	2(µ−	2(µ−	NUM
ejpam-6413	199	5	ā)θ	ā)θ	NOUN
ejpam-6413	199	6	[	[	PUNCT
ejpam-6413	199	7	χθ	χθ	X
ejpam-6413	199	8	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	199	9	)	)	PUNCT
ejpam-6413	200	1	+	+	CCONJ
ejpam-6413	200	2	χθ	χθ	X
ejpam-6413	200	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	200	4	)	)	PUNCT
ejpam-6413	200	5	]	]	PUNCT
ejpam-6413	201	1	=	=	PUNCT
ejpam-6413	201	2	(	(	PUNCT
ejpam-6413	201	3	µ−	µ−	PROPN
ejpam-6413	201	4	ā)2	ā)2	VERB
ejpam-6413	201	5	2	2	NUM
ejpam-6413	201	6	∫	∫	NOUN
ejpam-6413	201	7	1	1	NUM
ejpam-6413	201	8	0	0	NUM
ejpam-6413	201	9	1−	1−	NUM
ejpam-6413	201	10	(	(	PUNCT
ejpam-6413	201	11	1−	1−	NUM
ejpam-6413	201	12	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	201	13	−	−	PROPN
ejpam-6413	201	14	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	201	15	θ	θ	PROPN
ejpam-6413	201	16	+	+	PUNCT
ejpam-6413	201	17	1	1	NUM
ejpam-6413	201	18	𭟋′′	𭟋′′	NOUN
ejpam-6413	201	19	(	(	PUNCT
ejpam-6413	201	20	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	201	21	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	201	22	)	)	PUNCT
ejpam-6413	202	1	d	d	NOUN
ejpam-6413	202	2	⊺	⊺	NUM
ejpam-6413	202	3	.	.	PUNCT
ejpam-6413	203	1	(	(	PUNCT
ejpam-6413	203	2	19	19	NUM
ejpam-6413	203	3	)	)	PUNCT
ejpam-6413	203	4	combining	combine	VERB
ejpam-6413	203	5	(	(	PUNCT
ejpam-6413	203	6	18	18	NUM
ejpam-6413	203	7	)	)	PUNCT
ejpam-6413	203	8	and	and	CCONJ
ejpam-6413	203	9	(	(	PUNCT
ejpam-6413	203	10	19	19	NUM
ejpam-6413	203	11	)	)	PUNCT
ejpam-6413	203	12	,	,	PUNCT
ejpam-6413	203	13	we	we	PRON
ejpam-6413	203	14	have	have	AUX
ejpam-6413	203	15	obtained	obtain	VERB
ejpam-6413	203	16	the	the	DET
ejpam-6413	203	17	conclusion	conclusion	NOUN
ejpam-6413	203	18	of	of	ADP
ejpam-6413	203	19	the	the	DET
ejpam-6413	203	20	proof	proof	NOUN
ejpam-6413	203	21	.	.	PUNCT
ejpam-6413	204	1	remark	remark	VERB
ejpam-6413	204	2	3	3	NUM
ejpam-6413	204	3	.	.	PUNCT
ejpam-6413	205	1	by	by	ADP
ejpam-6413	205	2	substituting	substitute	VERB
ejpam-6413	205	3	m	m	PROPN
ejpam-6413	205	4	=	=	SYM
ejpam-6413	205	5	1	1	NUM
ejpam-6413	205	6	in	in	ADP
ejpam-6413	205	7	lemma	lemma	PROPN
ejpam-6413	205	8	5	5	NUM
ejpam-6413	205	9	,	,	PUNCT
ejpam-6413	205	10	we	we	PRON
ejpam-6413	205	11	arrive	arrive	VERB
ejpam-6413	205	12	at	at	ADP
ejpam-6413	205	13	[	[	X
ejpam-6413	205	14	20	20	NUM
ejpam-6413	205	15	,	,	PUNCT
ejpam-6413	205	16	lemma	lemma	PROPN
ejpam-6413	205	17	2.1	2.1	NUM
ejpam-6413	205	18	]	]	PUNCT
ejpam-6413	205	19	i.e.	i.e.	X
ejpam-6413	205	20	,	,	PUNCT
ejpam-6413	205	21	γ(θ	γ(θ	PROPN
ejpam-6413	205	22	+	+	CCONJ
ejpam-6413	206	1	1	1	X
ejpam-6413	206	2	)	)	PUNCT
ejpam-6413	206	3	2(b̄−	2(b̄−	NUM
ejpam-6413	206	4	ā)θ	ā)θ	NOUN
ejpam-6413	206	5	[	[	PUNCT
ejpam-6413	206	6	χθ	χθ	X
ejpam-6413	206	7	ā+𭟋(b̄	ā+𭟋(b̄	NUM
ejpam-6413	206	8	)	)	PUNCT
ejpam-6413	207	1	+	+	CCONJ
ejpam-6413	207	2	χθ	χθ	X
ejpam-6413	207	3	b̄−𭟋(ā	b̄−𭟋(ā	NOUN
ejpam-6413	207	4	)	)	PUNCT
ejpam-6413	207	5	]	]	PUNCT
ejpam-6413	208	1	−𭟋	−𭟋	INTJ
ejpam-6413	208	2	(	(	PUNCT
ejpam-6413	208	3	ā+	ā+	PUNCT
ejpam-6413	208	4	b̄	b̄	VERB
ejpam-6413	208	5	2	2	NUM
ejpam-6413	208	6	)	)	PUNCT
ejpam-6413	208	7	=	=	SYM
ejpam-6413	208	8	(	(	PUNCT
ejpam-6413	208	9	b̄−	b̄−	PROPN
ejpam-6413	208	10	ā)2	ā)2	ADJ
ejpam-6413	208	11	2	2	NUM
ejpam-6413	208	12	∫	∫	NOUN
ejpam-6413	208	13	1	1	NUM
ejpam-6413	208	14	0	0	NUM
ejpam-6413	208	15	p0(⊺)𭟋′′	p0(⊺)𭟋′′	NOUN
ejpam-6413	208	16	(	(	PUNCT
ejpam-6413	208	17	⊺ā+	⊺ā+	PROPN
ejpam-6413	208	18	(	(	PUNCT
ejpam-6413	208	19	1−	1−	NUM
ejpam-6413	208	20	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	208	21	)	)	PUNCT
ejpam-6413	208	22	d	d	NOUN
ejpam-6413	208	23	⊺	⊺	NUM
ejpam-6413	208	24	.	.	PUNCT
ejpam-6413	209	1	lemma	lemma	PROPN
ejpam-6413	209	2	6	6	NUM
ejpam-6413	209	3	.	.	PUNCT
ejpam-6413	210	1	let	let	VERB
ejpam-6413	210	2	𭟋	𭟋	VERB
ejpam-6413	210	3	:	:	PUNCT
ejpam-6413	210	4	[	[	X
ejpam-6413	210	5	ā	ā	X
ejpam-6413	210	6	,	,	PUNCT
ejpam-6413	210	7	b̄	b̄	PROPN
ejpam-6413	210	8	]	]	PUNCT
ejpam-6413	210	9	→	→	PUNCT
ejpam-6413	210	10	r	r	NOUN
ejpam-6413	210	11	be	be	AUX
ejpam-6413	210	12	a	a	DET
ejpam-6413	210	13	twice	twice	ADV
ejpam-6413	210	14	differentiable	differentiable	ADJ
ejpam-6413	210	15	mapping	mapping	NOUN
ejpam-6413	210	16	on	on	ADP
ejpam-6413	210	17	(	(	PUNCT
ejpam-6413	210	18	ā	ā	ADJ
ejpam-6413	210	19	,	,	PUNCT
ejpam-6413	210	20	b̄	b̄	PROPN
ejpam-6413	210	21	)	)	PUNCT
ejpam-6413	210	22	with	with	ADP
ejpam-6413	210	23	ā	ā	PROPN
ejpam-6413	210	24	<	<	X
ejpam-6413	210	25	b̄.	b̄.	PUNCT
ejpam-6413	210	26	if	if	SCONJ
ejpam-6413	210	27	⋎	⋎	NOUN
ejpam-6413	210	28	>	>	X
ejpam-6413	210	29	0	0	NUM
ejpam-6413	210	30	,	,	PUNCT
ejpam-6413	210	31	𭟋′′	𭟋′′	NOUN
ejpam-6413	210	32	∈	∈	PROPN
ejpam-6413	210	33	l[ā	l[ā	PROPN
ejpam-6413	210	34	,	,	PUNCT
ejpam-6413	210	35	b̄	b̄	NOUN
ejpam-6413	210	36	]	]	PUNCT
ejpam-6413	210	37	,	,	PUNCT
ejpam-6413	210	38	then	then	ADV
ejpam-6413	210	39	𭟋(ā	𭟋(ā	VERB
ejpam-6413	210	40	)	)	PUNCT
ejpam-6413	211	1	+	+	NOUN
ejpam-6413	211	2	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	211	3	)	)	PUNCT
ejpam-6413	211	4	⋎(⋎+	⋎(⋎+	VERB
ejpam-6413	211	5	1	1	NUM
ejpam-6413	211	6	)	)	PUNCT
ejpam-6413	212	1	+	+	CCONJ
ejpam-6413	212	2	2	2	NUM
ejpam-6413	212	3	⋎+	⋎+	DET
ejpam-6413	212	4	1	1	NUM
ejpam-6413	212	5	𭟋	𭟋	PROPN
ejpam-6413	212	6	(	(	PUNCT
ejpam-6413	212	7	ā+	ā+	PUNCT
ejpam-6413	212	8	µ	µ	X
ejpam-6413	212	9	2	2	NUM
ejpam-6413	212	10	)	)	PUNCT
ejpam-6413	212	11	−	−	PROPN
ejpam-6413	213	1	γ(θ	γ(θ	PROPN
ejpam-6413	214	1	+	+	CCONJ
ejpam-6413	214	2	1	1	X
ejpam-6413	214	3	)	)	PUNCT
ejpam-6413	214	4	⋎(µ−	⋎(µ−	NOUN
ejpam-6413	214	5	ā)θ	ā)θ	NOUN
ejpam-6413	214	6	[	[	PUNCT
ejpam-6413	214	7	χθ	χθ	X
ejpam-6413	214	8	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	214	9	)	)	PUNCT
ejpam-6413	215	1	+	+	CCONJ
ejpam-6413	215	2	χθ	χθ	X
ejpam-6413	215	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	215	4	)	)	PUNCT
ejpam-6413	215	5	]	]	PUNCT
ejpam-6413	216	1	=	=	PUNCT
ejpam-6413	216	2	(	(	PUNCT
ejpam-6413	216	3	µ−	µ−	PROPN
ejpam-6413	216	4	ā)2	ā)2	PROPN
ejpam-6413	216	5	∫	∫	PROPN
ejpam-6413	216	6	1	1	NUM
ejpam-6413	216	7	0	0	NUM
ejpam-6413	216	8	q0(⊺)𭟋′′	q0(⊺)𭟋′′	PROPN
ejpam-6413	216	9	(	(	PUNCT
ejpam-6413	216	10	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	216	11	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	216	12	)	)	PUNCT
ejpam-6413	216	13	d⊺	d⊺	PROPN
ejpam-6413	216	14	,	,	PUNCT
ejpam-6413	216	15	where	where	SCONJ
ejpam-6413	216	16	q0(⊺	q0(⊺	VERB
ejpam-6413	216	17	)	)	PUNCT
ejpam-6413	216	18	=	=	PUNCT
ejpam-6413	216	19			PROPN
ejpam-6413	216	20	1−(1−⊺)θ+1−⊺θ+1	1−(1−⊺)θ+1−⊺θ+1	PROPN
ejpam-6413	216	21	⋎(θ+1	⋎(θ+1	PROPN
ejpam-6413	216	22	)	)	PUNCT
ejpam-6413	216	23	−	−	NOUN
ejpam-6413	216	24	⊺	⊺	PUNCT
ejpam-6413	216	25	⋎+1	⋎+1	ADJ
ejpam-6413	216	26	,	,	PUNCT
ejpam-6413	216	27	⊺	⊺	PUNCT
ejpam-6413	216	28	∈	∈	PROPN
ejpam-6413	217	1	[	[	X
ejpam-6413	217	2	0	0	NUM
ejpam-6413	217	3	,	,	PUNCT
ejpam-6413	217	4	12	12	NUM
ejpam-6413	217	5	)	)	PUNCT
ejpam-6413	217	6	,	,	PUNCT
ejpam-6413	217	7	1−(1−⊺)θ+1−⊺θ+1	1−(1−⊺)θ+1−⊺θ+1	PROPN
ejpam-6413	217	8	⋎(θ+1	⋎(θ+1	PROPN
ejpam-6413	217	9	)	)	PUNCT
ejpam-6413	217	10	−	−	PROPN
ejpam-6413	217	11	1−⊺	1−⊺	NUM
ejpam-6413	217	12	⋎+1	⋎+1	NOUN
ejpam-6413	217	13	,	,	PUNCT
ejpam-6413	217	14	⊺	⊺	PUNCT
ejpam-6413	217	15	∈	∈	PROPN
ejpam-6413	217	16	[	[	X
ejpam-6413	217	17	12	12	NUM
ejpam-6413	217	18	,	,	PUNCT
ejpam-6413	217	19	1	1	NUM
ejpam-6413	217	20	)	)	PUNCT
ejpam-6413	217	21	.	.	PUNCT
ejpam-6413	218	1	m.	m.	NOUN
ejpam-6413	218	2	samraiz	samraiz	PROPN
ejpam-6413	218	3	et	et	PROPN
ejpam-6413	218	4	al	al	PROPN
ejpam-6413	218	5	.	.	PUNCT
ejpam-6413	218	6	/	/	SYM
ejpam-6413	218	7	eur	eur	PROPN
ejpam-6413	218	8	.	.	PUNCT
ejpam-6413	219	1	j.	j.	PROPN
ejpam-6413	219	2	pure	pure	PROPN
ejpam-6413	219	3	appl	appl	PROPN
ejpam-6413	219	4	.	.	PROPN
ejpam-6413	219	5	math	math	PROPN
ejpam-6413	219	6	,	,	PUNCT
ejpam-6413	219	7	18	18	NUM
ejpam-6413	219	8	(	(	PUNCT
ejpam-6413	219	9	3	3	NUM
ejpam-6413	219	10	)	)	PUNCT
ejpam-6413	219	11	(	(	PUNCT
ejpam-6413	219	12	2025	2025	NUM
ejpam-6413	219	13	)	)	PUNCT
ejpam-6413	219	14	,	,	PUNCT
ejpam-6413	219	15	6413	6413	NUM
ejpam-6413	219	16	10	10	NUM
ejpam-6413	219	17	of	of	ADP
ejpam-6413	219	18	26	26	NUM
ejpam-6413	219	19	proof	proof	NOUN
ejpam-6413	219	20	.	.	PUNCT
ejpam-6413	220	1	consider∫	consider∫	NOUN
ejpam-6413	220	2	1	1	NUM
ejpam-6413	220	3	0	0	NUM
ejpam-6413	220	4	q0(⊺)𭟋′′	q0(⊺)𭟋′′	NOUN
ejpam-6413	220	5	(	(	PUNCT
ejpam-6413	220	6	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	220	7	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	220	8	)	)	PUNCT
ejpam-6413	220	9	d⊺	d⊺	PROPN
ejpam-6413	221	1	=	=	PUNCT
ejpam-6413	222	1	[	[	X
ejpam-6413	222	2	∫	∫	X
ejpam-6413	222	3	1	1	NUM
ejpam-6413	222	4	2	2	NUM
ejpam-6413	222	5	0	0	NUM
ejpam-6413	222	6	(	(	PUNCT
ejpam-6413	222	7	1−	1−	NUM
ejpam-6413	222	8	(	(	PUNCT
ejpam-6413	222	9	1−	1−	NUM
ejpam-6413	222	10	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	222	11	−	−	PROPN
ejpam-6413	222	12	⊺θ+1	⊺θ+1	NOUN
ejpam-6413	222	13	⋎(θ	⋎(θ	NOUN
ejpam-6413	222	14	+	+	NOUN
ejpam-6413	222	15	1	1	NUM
ejpam-6413	222	16	)	)	PUNCT
ejpam-6413	222	17	−	−	NOUN
ejpam-6413	222	18	⊺	⊺	NUM
ejpam-6413	222	19	⋎+	⋎+	PRON
ejpam-6413	222	20	1	1	X
ejpam-6413	222	21	)	)	PUNCT
ejpam-6413	222	22	𭟋′′(⊺ā+m(1−	𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	222	23	⊺)b̄)d⊺	⊺)b̄)d⊺	PROPN
ejpam-6413	222	24	∫	∫	NOUN
ejpam-6413	222	25	1	1	NUM
ejpam-6413	222	26	1	1	NUM
ejpam-6413	222	27	2	2	NUM
ejpam-6413	222	28	(	(	PUNCT
ejpam-6413	222	29	1−	1−	NUM
ejpam-6413	222	30	(	(	PUNCT
ejpam-6413	222	31	1−	1−	NUM
ejpam-6413	222	32	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	222	33	−	−	PROPN
ejpam-6413	222	34	⊺θ+1	⊺θ+1	NOUN
ejpam-6413	222	35	⋎(θ	⋎(θ	NOUN
ejpam-6413	222	36	+	+	NOUN
ejpam-6413	222	37	1	1	NUM
ejpam-6413	222	38	)	)	PUNCT
ejpam-6413	222	39	−	−	PROPN
ejpam-6413	222	40	1−	1−	NUM
ejpam-6413	222	41	⊺	⊺	NUM
ejpam-6413	222	42	⋎+	⋎+	PRON
ejpam-6413	222	43	1	1	X
ejpam-6413	222	44	)	)	PUNCT
ejpam-6413	222	45	𭟋′′(⊺ā+m(1−	𭟋′′(⊺ā+m(1−	VERB
ejpam-6413	222	46	⊺)b̄)d⊺	⊺)b̄)d⊺	NOUN
ejpam-6413	222	47	]	]	PUNCT
ejpam-6413	222	48	=	=	PUNCT
ejpam-6413	223	1	[	[	X
ejpam-6413	223	2	∫	∫	PROPN
ejpam-6413	223	3	1	1	NUM
ejpam-6413	223	4	0	0	NUM
ejpam-6413	223	5	1−	1−	NUM
ejpam-6413	223	6	(	(	PUNCT
ejpam-6413	223	7	1−	1−	NUM
ejpam-6413	223	8	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	223	9	−	−	PROPN
ejpam-6413	223	10	⊺θ+1	⊺θ+1	NOUN
ejpam-6413	223	11	⋎(θ	⋎(θ	NOUN
ejpam-6413	223	12	+	+	NOUN
ejpam-6413	223	13	1	1	X
ejpam-6413	223	14	)	)	PUNCT
ejpam-6413	223	15	𭟋′′(⊺ā+m(1−	𭟋′′(⊺ā+m(1−	VERB
ejpam-6413	223	16	⊺)b̄)d⊺	⊺)b̄)d⊺	NOUN
ejpam-6413	223	17	−	−	NOUN
ejpam-6413	223	18	1	1	NUM
ejpam-6413	223	19	⋎+	⋎+	DET
ejpam-6413	223	20	1	1	NUM
ejpam-6413	223	21	(	(	PUNCT
ejpam-6413	223	22	∫	∫	PROPN
ejpam-6413	223	23	1	1	NUM
ejpam-6413	223	24	2	2	NUM
ejpam-6413	223	25	0	0	NUM
ejpam-6413	223	26	⊺𭟋′′(⊺ā+m(1−	⊺𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	223	27	⊺)b̄)d	⊺)b̄)d	PROPN
ejpam-6413	223	28	⊺+	⊺+	NOUN
ejpam-6413	223	29	∫	∫	NOUN
ejpam-6413	223	30	1	1	NUM
ejpam-6413	223	31	1	1	NUM
ejpam-6413	223	32	2	2	NUM
ejpam-6413	223	33	(	(	PUNCT
ejpam-6413	223	34	1−	1−	NUM
ejpam-6413	223	35	⊺)𭟋′′(⊺ā+m(1−	⊺)𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	223	36	⊺)b̄)d⊺	⊺)b̄)d⊺	PROPN
ejpam-6413	223	37	)	)	PUNCT
ejpam-6413	223	38	]	]	PUNCT
ejpam-6413	223	39	.	.	PUNCT
ejpam-6413	224	1	(	(	PUNCT
ejpam-6413	224	2	20	20	NUM
ejpam-6413	224	3	)	)	PUNCT
ejpam-6413	224	4	by	by	ADP
ejpam-6413	224	5	using	use	VERB
ejpam-6413	224	6	(	(	PUNCT
ejpam-6413	224	7	16	16	NUM
ejpam-6413	224	8	)	)	PUNCT
ejpam-6413	224	9	,	,	PUNCT
ejpam-6413	224	10	we	we	PRON
ejpam-6413	224	11	obtain∫	obtain∫	VERB
ejpam-6413	224	12	1	1	NUM
ejpam-6413	224	13	0	0	NUM
ejpam-6413	224	14	q0(⊺)𭟋′′	q0(⊺)𭟋′′	NOUN
ejpam-6413	224	15	(	(	PUNCT
ejpam-6413	224	16	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	224	17	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	224	18	)	)	PUNCT
ejpam-6413	224	19	d⊺	d⊺	PROPN
ejpam-6413	224	20	=	=	SYM
ejpam-6413	225	1	∫	∫	PROPN
ejpam-6413	225	2	1	1	NUM
ejpam-6413	225	3	0	0	NUM
ejpam-6413	225	4	1−	1−	NUM
ejpam-6413	225	5	(	(	PUNCT
ejpam-6413	225	6	1−	1−	NUM
ejpam-6413	225	7	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	225	8	−	−	PROPN
ejpam-6413	225	9	⊺θ+1	⊺θ+1	NOUN
ejpam-6413	225	10	⋎(θ	⋎(θ	NOUN
ejpam-6413	225	11	+	+	NOUN
ejpam-6413	225	12	1	1	X
ejpam-6413	225	13	)	)	PUNCT
ejpam-6413	225	14	𭟋′′(⊺ā+m(1−	𭟋′′(⊺ā+m(1−	VERB
ejpam-6413	225	15	⊺)b̄)d⊺	⊺)b̄)d⊺	NOUN
ejpam-6413	226	1	−	−	NOUN
ejpam-6413	226	2	1	1	NUM
ejpam-6413	226	3	⋎+	⋎+	PRON
ejpam-6413	226	4	1	1	NUM
ejpam-6413	226	5	(	(	PUNCT
ejpam-6413	226	6	𭟋(ā	𭟋(ā	NOUN
ejpam-6413	226	7	)	)	PUNCT
ejpam-6413	226	8	+	+	NOUN
ejpam-6413	226	9	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	226	10	)	)	PUNCT
ejpam-6413	226	11	(	(	PUNCT
ejpam-6413	226	12	µ−	µ−	PROPN
ejpam-6413	226	13	ā)2	ā)2	NOUN
ejpam-6413	226	14	−	−	PROPN
ejpam-6413	226	15	2	2	NUM
ejpam-6413	226	16	(	(	PUNCT
ejpam-6413	226	17	µ−	µ−	PROPN
ejpam-6413	226	18	ā)2	ā)2	NOUN
ejpam-6413	226	19	𭟋	𭟋	PROPN
ejpam-6413	226	20	(	(	PUNCT
ejpam-6413	226	21	ā+	ā+	PUNCT
ejpam-6413	226	22	µ	µ	X
ejpam-6413	226	23	2	2	NUM
ejpam-6413	226	24	)	)	PUNCT
ejpam-6413	226	25	)	)	PUNCT
ejpam-6413	226	26	.	.	PUNCT
ejpam-6413	227	1	(	(	PUNCT
ejpam-6413	227	2	21	21	NUM
ejpam-6413	227	3	)	)	PUNCT
ejpam-6413	227	4	multiplying	multiply	VERB
ejpam-6413	227	5	both	both	DET
ejpam-6413	227	6	sides	side	NOUN
ejpam-6413	227	7	of	of	ADP
ejpam-6413	227	8	(	(	PUNCT
ejpam-6413	227	9	21	21	NUM
ejpam-6413	227	10	)	)	PUNCT
ejpam-6413	227	11	by	by	ADP
ejpam-6413	227	12	(	(	PUNCT
ejpam-6413	227	13	µ−	µ−	PROPN
ejpam-6413	227	14	ā)2	ā)2	NOUN
ejpam-6413	227	15	,	,	PUNCT
ejpam-6413	227	16	we	we	PRON
ejpam-6413	227	17	get	get	VERB
ejpam-6413	227	18	(	(	PUNCT
ejpam-6413	227	19	µ−	µ−	PROPN
ejpam-6413	227	20	ā)2	ā)2	PROPN
ejpam-6413	227	21	∫	∫	PROPN
ejpam-6413	227	22	1	1	NUM
ejpam-6413	227	23	0	0	NUM
ejpam-6413	227	24	q0(⊺)𭟋′′	q0(⊺)𭟋′′	PROPN
ejpam-6413	227	25	(	(	PUNCT
ejpam-6413	227	26	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	227	27	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	227	28	)	)	PUNCT
ejpam-6413	227	29	d⊺	d⊺	PROPN
ejpam-6413	227	30	=	=	PUNCT
ejpam-6413	228	1	(	(	PUNCT
ejpam-6413	228	2	µ−	µ−	PROPN
ejpam-6413	228	3	ā)2	ā)2	PROPN
ejpam-6413	228	4	∫	∫	PROPN
ejpam-6413	228	5	1	1	NUM
ejpam-6413	228	6	0	0	NUM
ejpam-6413	228	7	1−	1−	NUM
ejpam-6413	228	8	(	(	PUNCT
ejpam-6413	228	9	1−	1−	NUM
ejpam-6413	228	10	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	228	11	−	−	PROPN
ejpam-6413	228	12	⊺θ+1	⊺θ+1	NOUN
ejpam-6413	228	13	⋎(θ	⋎(θ	NOUN
ejpam-6413	228	14	+	+	NOUN
ejpam-6413	228	15	1	1	X
ejpam-6413	228	16	)	)	PUNCT
ejpam-6413	228	17	𭟋′′(⊺ā+m(1−	𭟋′′(⊺ā+m(1−	VERB
ejpam-6413	228	18	⊺)b̄)d⊺	⊺)b̄)d⊺	PROPN
ejpam-6413	228	19	−	−	NOUN
ejpam-6413	228	20	𭟋(ā	𭟋(ā	NOUN
ejpam-6413	228	21	)	)	PUNCT
ejpam-6413	229	1	+	+	NOUN
ejpam-6413	229	2	𭟋(µ	𭟋(µ	X
ejpam-6413	229	3	)	)	PUNCT
ejpam-6413	229	4	(	(	PUNCT
ejpam-6413	229	5	⋎+	⋎+	DET
ejpam-6413	229	6	1	1	X
ejpam-6413	229	7	)	)	PUNCT
ejpam-6413	230	1	+	+	CCONJ
ejpam-6413	230	2	2	2	NUM
ejpam-6413	230	3	⋎+	⋎+	DET
ejpam-6413	230	4	1	1	NUM
ejpam-6413	230	5	𭟋	𭟋	PROPN
ejpam-6413	230	6	(	(	PUNCT
ejpam-6413	230	7	ā+	ā+	PUNCT
ejpam-6413	230	8	µ	µ	X
ejpam-6413	230	9	2	2	NUM
ejpam-6413	230	10	)	)	PUNCT
ejpam-6413	230	11	.	.	PUNCT
ejpam-6413	231	1	(	(	PUNCT
ejpam-6413	231	2	22	22	NUM
ejpam-6413	231	3	)	)	PUNCT
ejpam-6413	231	4	by	by	ADP
ejpam-6413	231	5	multiplying	multiply	VERB
ejpam-6413	231	6	1	1	NUM
ejpam-6413	231	7	⋎	⋎	NOUN
ejpam-6413	231	8	on	on	ADP
ejpam-6413	231	9	both	both	DET
ejpam-6413	231	10	sides	side	NOUN
ejpam-6413	231	11	of	of	ADP
ejpam-6413	231	12	lemma	lemma	PROPN
ejpam-6413	231	13	4	4	NUM
ejpam-6413	231	14	,	,	PUNCT
ejpam-6413	231	15	we	we	PRON
ejpam-6413	231	16	can	can	AUX
ejpam-6413	231	17	write	write	VERB
ejpam-6413	231	18	𭟋(ā	𭟋(ā	NUM
ejpam-6413	231	19	)	)	PUNCT
ejpam-6413	232	1	+	+	NOUN
ejpam-6413	232	2	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	232	3	)	)	PUNCT
ejpam-6413	232	4	⋎	⋎	NOUN
ejpam-6413	232	5	−	−	PROPN
ejpam-6413	232	6	γ(θ	γ(θ	PROPN
ejpam-6413	233	1	+	+	CCONJ
ejpam-6413	233	2	1	1	X
ejpam-6413	233	3	)	)	PUNCT
ejpam-6413	233	4	⋎(µ−	⋎(µ−	NOUN
ejpam-6413	233	5	ā)θ	ā)θ	NOUN
ejpam-6413	233	6	[	[	PUNCT
ejpam-6413	233	7	χθ	χθ	X
ejpam-6413	233	8	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	233	9	)	)	PUNCT
ejpam-6413	234	1	+	+	CCONJ
ejpam-6413	234	2	χθ	χθ	X
ejpam-6413	234	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	234	4	)	)	PUNCT
ejpam-6413	234	5	]	]	PUNCT
ejpam-6413	235	1	=	=	PUNCT
ejpam-6413	235	2	(	(	PUNCT
ejpam-6413	235	3	µ−	µ−	PROPN
ejpam-6413	235	4	ā)2	ā)2	PROPN
ejpam-6413	235	5	∫	∫	PROPN
ejpam-6413	235	6	1	1	NUM
ejpam-6413	235	7	0	0	NUM
ejpam-6413	235	8	1−	1−	NUM
ejpam-6413	235	9	(	(	PUNCT
ejpam-6413	235	10	1−	1−	NUM
ejpam-6413	235	11	⊺)θ	⊺)θ	NUM
ejpam-6413	235	12	−	−	NOUN
ejpam-6413	235	13	⊺θ	⊺θ	PROPN
ejpam-6413	235	14	⋎(θ	⋎(θ	NOUN
ejpam-6413	235	15	+	+	CCONJ
ejpam-6413	235	16	1	1	X
ejpam-6413	235	17	)	)	PUNCT
ejpam-6413	235	18	𭟋′	𭟋′	PROPN
ejpam-6413	235	19	(	(	PUNCT
ejpam-6413	235	20	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	235	21	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	235	22	)	)	PUNCT
ejpam-6413	235	23	d	d	NOUN
ejpam-6413	235	24	⊺	⊺	NUM
ejpam-6413	235	25	.	.	PUNCT
ejpam-6413	236	1	(	(	PUNCT
ejpam-6413	236	2	23	23	X
ejpam-6413	236	3	)	)	PUNCT
ejpam-6413	236	4	combining	combine	VERB
ejpam-6413	236	5	(	(	PUNCT
ejpam-6413	236	6	22	22	NUM
ejpam-6413	236	7	)	)	PUNCT
ejpam-6413	236	8	and	and	CCONJ
ejpam-6413	236	9	(	(	PUNCT
ejpam-6413	236	10	23	23	NUM
ejpam-6413	236	11	)	)	PUNCT
ejpam-6413	236	12	,	,	PUNCT
ejpam-6413	236	13	we	we	PRON
ejpam-6413	236	14	have	have	AUX
ejpam-6413	236	15	obtained	obtain	VERB
ejpam-6413	236	16	the	the	DET
ejpam-6413	236	17	conclusion	conclusion	NOUN
ejpam-6413	236	18	of	of	ADP
ejpam-6413	236	19	the	the	DET
ejpam-6413	236	20	proof	proof	NOUN
ejpam-6413	236	21	.	.	PUNCT
ejpam-6413	237	1	m.	m.	NOUN
ejpam-6413	237	2	samraiz	samraiz	PROPN
ejpam-6413	237	3	et	et	PROPN
ejpam-6413	237	4	al	al	PROPN
ejpam-6413	237	5	.	.	PUNCT
ejpam-6413	237	6	/	/	SYM
ejpam-6413	237	7	eur	eur	PROPN
ejpam-6413	237	8	.	.	PUNCT
ejpam-6413	238	1	j.	j.	PROPN
ejpam-6413	238	2	pure	pure	PROPN
ejpam-6413	238	3	appl	appl	PROPN
ejpam-6413	238	4	.	.	PROPN
ejpam-6413	238	5	math	math	PROPN
ejpam-6413	238	6	,	,	PUNCT
ejpam-6413	238	7	18	18	NUM
ejpam-6413	238	8	(	(	PUNCT
ejpam-6413	238	9	3	3	NUM
ejpam-6413	238	10	)	)	PUNCT
ejpam-6413	238	11	(	(	PUNCT
ejpam-6413	238	12	2025	2025	NUM
ejpam-6413	238	13	)	)	PUNCT
ejpam-6413	238	14	,	,	PUNCT
ejpam-6413	238	15	6413	6413	NUM
ejpam-6413	238	16	11	11	NUM
ejpam-6413	238	17	of	of	ADP
ejpam-6413	238	18	26	26	NUM
ejpam-6413	238	19	remark	remark	NOUN
ejpam-6413	238	20	4	4	NUM
ejpam-6413	238	21	.	.	PUNCT
ejpam-6413	239	1	by	by	ADP
ejpam-6413	239	2	substituting	substitute	VERB
ejpam-6413	239	3	m	m	PROPN
ejpam-6413	239	4	=	=	SYM
ejpam-6413	239	5	1	1	NUM
ejpam-6413	239	6	in	in	ADP
ejpam-6413	239	7	lemma	lemma	PROPN
ejpam-6413	239	8	6	6	NUM
ejpam-6413	239	9	,	,	PUNCT
ejpam-6413	239	10	we	we	PRON
ejpam-6413	239	11	arrive	arrive	VERB
ejpam-6413	239	12	at	at	ADP
ejpam-6413	239	13	[	[	X
ejpam-6413	239	14	20	20	NUM
ejpam-6413	239	15	,	,	PUNCT
ejpam-6413	239	16	lemma	lemma	PROPN
ejpam-6413	239	17	2.2	2.2	NUM
ejpam-6413	239	18	]	]	PUNCT
ejpam-6413	239	19	i.e.	i.e.	X
ejpam-6413	239	20	,	,	PUNCT
ejpam-6413	239	21	𭟋(ā	𭟋(ā	NUM
ejpam-6413	239	22	)	)	PUNCT
ejpam-6413	240	1	+	+	NOUN
ejpam-6413	240	2	𭟋(b̄	𭟋(b̄	NOUN
ejpam-6413	240	3	)	)	PUNCT
ejpam-6413	240	4	⋎(⋎+	⋎(⋎+	VERB
ejpam-6413	240	5	1	1	NUM
ejpam-6413	240	6	)	)	PUNCT
ejpam-6413	240	7	+	+	CCONJ
ejpam-6413	240	8	2	2	NUM
ejpam-6413	240	9	⋎+	⋎+	DET
ejpam-6413	240	10	1	1	NUM
ejpam-6413	240	11	𭟋	𭟋	PROPN
ejpam-6413	240	12	(	(	PUNCT
ejpam-6413	240	13	ā+	ā+	PUNCT
ejpam-6413	240	14	b̄	b̄	VERB
ejpam-6413	240	15	2	2	NUM
ejpam-6413	240	16	)	)	PUNCT
ejpam-6413	240	17	−	−	PROPN
ejpam-6413	241	1	γ(θ	γ(θ	PROPN
ejpam-6413	241	2	+	+	CCONJ
ejpam-6413	241	3	1	1	X
ejpam-6413	241	4	)	)	PUNCT
ejpam-6413	241	5	⋎(b̄−	⋎(b̄−	ADJ
ejpam-6413	241	6	ā)θ	ā)θ	NOUN
ejpam-6413	241	7	[	[	PUNCT
ejpam-6413	241	8	χθ	χθ	X
ejpam-6413	241	9	ā+𭟋(ā	ā+𭟋(ā	NOUN
ejpam-6413	241	10	)	)	PUNCT
ejpam-6413	242	1	+	+	CCONJ
ejpam-6413	242	2	χθ	χθ	ADJ
ejpam-6413	242	3	b̄−𭟋(b̄	b̄−𭟋(b̄	NOUN
ejpam-6413	242	4	)	)	PUNCT
ejpam-6413	242	5	]	]	PUNCT
ejpam-6413	243	1	=	=	PUNCT
ejpam-6413	243	2	(	(	PUNCT
ejpam-6413	243	3	b̄−	b̄−	PROPN
ejpam-6413	243	4	ā)2	ā)2	NOUN
ejpam-6413	243	5	∫	∫	PROPN
ejpam-6413	243	6	1	1	NUM
ejpam-6413	243	7	0	0	NUM
ejpam-6413	243	8	q0(⊺)𭟋′′	q0(⊺)𭟋′′	PROPN
ejpam-6413	243	9	(	(	PUNCT
ejpam-6413	243	10	⊺ā+	⊺ā+	PROPN
ejpam-6413	243	11	(	(	PUNCT
ejpam-6413	243	12	1−	1−	NUM
ejpam-6413	243	13	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	243	14	)	)	PUNCT
ejpam-6413	244	1	d	d	NOUN
ejpam-6413	244	2	⊺	⊺	NOUN
ejpam-6413	244	3	.	.	PUNCT
ejpam-6413	245	1	4	4	X
ejpam-6413	245	2	.	.	X
ejpam-6413	245	3	hermite	hermite	PROPN
ejpam-6413	245	4	-	-	PUNCT
ejpam-6413	245	5	hadamard	hadamard	ADJ
ejpam-6413	245	6	inequalities	inequality	NOUN
ejpam-6413	245	7	for	for	ADP
ejpam-6413	245	8	ga	ga	PROPN
ejpam-6413	245	9	(	(	PUNCT
ejpam-6413	245	10	α	α	NOUN
ejpam-6413	245	11	,	,	PUNCT
ejpam-6413	245	12	m)-convex	m)-convex	PUNCT
ejpam-6413	245	13	functions	function	NOUN
ejpam-6413	245	14	this	this	DET
ejpam-6413	245	15	section	section	NOUN
ejpam-6413	245	16	is	be	AUX
ejpam-6413	245	17	dedicated	dedicate	VERB
ejpam-6413	245	18	to	to	PART
ejpam-6413	245	19	explore	explore	VERB
ejpam-6413	245	20	hermite	hermite	ADJ
ejpam-6413	245	21	-	-	PUNCT
ejpam-6413	245	22	hadamard	hadamard	ADJ
ejpam-6413	245	23	type	type	NOUN
ejpam-6413	245	24	inequalities	inequality	NOUN
ejpam-6413	245	25	by	by	ADP
ejpam-6413	245	26	using	use	VERB
ejpam-6413	245	27	the	the	DET
ejpam-6413	245	28	results	result	NOUN
ejpam-6413	245	29	proved	prove	VERB
ejpam-6413	245	30	in	in	ADP
ejpam-6413	245	31	the	the	DET
ejpam-6413	245	32	previous	previous	ADJ
ejpam-6413	245	33	section	section	NOUN
ejpam-6413	245	34	.	.	PUNCT
ejpam-6413	246	1	to	to	PART
ejpam-6413	246	2	establish	establish	VERB
ejpam-6413	246	3	the	the	DET
ejpam-6413	246	4	inequalities	inequality	NOUN
ejpam-6413	246	5	,	,	PUNCT
ejpam-6413	246	6	we	we	PRON
ejpam-6413	246	7	need	need	VERB
ejpam-6413	246	8	the	the	DET
ejpam-6413	246	9	following	follow	VERB
ejpam-6413	246	10	lemma	lemma	PROPN
ejpam-6413	246	11	.	.	PUNCT
ejpam-6413	247	1	lemma	lemma	PROPN
ejpam-6413	247	2	7	7	NUM
ejpam-6413	247	3	.	.	PUNCT
ejpam-6413	248	1	for	for	ADP
ejpam-6413	248	2	⊺	⊺	NUM
ejpam-6413	248	3	∈	∈	PROPN
ejpam-6413	248	4	[	[	X
ejpam-6413	248	5	0	0	NUM
ejpam-6413	248	6	,	,	PUNCT
ejpam-6413	248	7	1	1	NUM
ejpam-6413	248	8	]	]	PUNCT
ejpam-6413	248	9	,	,	PUNCT
ejpam-6413	248	10	ā	ā	PROPN
ejpam-6413	248	11	,	,	PUNCT
ejpam-6413	248	12	b̄	b̄	VERB
ejpam-6413	248	13	>	>	X
ejpam-6413	248	14	0	0	NUM
ejpam-6413	248	15	,	,	PUNCT
ejpam-6413	248	16	we	we	PRON
ejpam-6413	248	17	have	have	VERB
ejpam-6413	248	18	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	248	19	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	248	20	≤	≤	NOUN
ejpam-6413	248	21	(	(	PUNCT
ejpam-6413	248	22	ā⊺b̄m(1−⊺	ā⊺b̄m(1−⊺	NOUN
ejpam-6413	248	23	)	)	PUNCT
ejpam-6413	248	24	)	)	PUNCT
ejpam-6413	248	25	.	.	PUNCT
ejpam-6413	249	1	theorem	theorem	NOUN
ejpam-6413	249	2	1	1	X
ejpam-6413	249	3	.	.	PUNCT
ejpam-6413	250	1	let	let	VERB
ejpam-6413	250	2	𭟋	𭟋	VERB
ejpam-6413	250	3	:	:	PUNCT
ejpam-6413	250	4	[	[	X
ejpam-6413	250	5	ā	ā	X
ejpam-6413	250	6	,	,	PUNCT
ejpam-6413	250	7	b̄	b̄	PROPN
ejpam-6413	250	8	]	]	PUNCT
ejpam-6413	250	9	−→	−→	NOUN
ejpam-6413	250	10	r	r	NOUN
ejpam-6413	250	11	be	be	VERB
ejpam-6413	250	12	a	a	DET
ejpam-6413	250	13	twice	twice	ADV
ejpam-6413	250	14	differentiable	differentiable	ADJ
ejpam-6413	250	15	function	function	NOUN
ejpam-6413	250	16	such	such	ADJ
ejpam-6413	250	17	that	that	DET
ejpam-6413	250	18	|𭟋′′|	|𭟋′′|	PROPN
ejpam-6413	250	19	is	be	AUX
ejpam-6413	250	20	lebesgue	lebesgue	NOUN
ejpam-6413	250	21	integerable	integerable	ADJ
ejpam-6413	250	22	,	,	PUNCT
ejpam-6413	250	23	increasing	increase	VERB
ejpam-6413	250	24	and	and	CCONJ
ejpam-6413	250	25	ga	ga	PROPN
ejpam-6413	250	26	(	(	PUNCT
ejpam-6413	250	27	α	α	NOUN
ejpam-6413	250	28	,	,	PUNCT
ejpam-6413	250	29	m)-convex	m)-convex	PUNCT
ejpam-6413	250	30	function	function	VERB
ejpam-6413	250	31	on	on	ADP
ejpam-6413	250	32	[	[	X
ejpam-6413	250	33	ā	ā	X
ejpam-6413	250	34	,	,	PUNCT
ejpam-6413	250	35	b̄	b̄	PROPN
ejpam-6413	250	36	]	]	PUNCT
ejpam-6413	250	37	.	.	PUNCT
ejpam-6413	251	1	then	then	ADV
ejpam-6413	251	2	for	for	ADP
ejpam-6413	251	3	given	give	VERB
ejpam-6413	251	4	parameters	parameter	NOUN
ejpam-6413	251	5	θ	θ	PROPN
ejpam-6413	251	6	∈	∈	PROPN
ejpam-6413	251	7	(	(	PUNCT
ejpam-6413	251	8	0,+∞	0,+∞	NUM
ejpam-6413	251	9	)	)	PUNCT
ejpam-6413	251	10	and	and	CCONJ
ejpam-6413	251	11	(	(	PUNCT
ejpam-6413	251	12	α	α	NOUN
ejpam-6413	251	13	,	,	PUNCT
ejpam-6413	251	14	m	m	NOUN
ejpam-6413	251	15	)	)	PUNCT
ejpam-6413	251	16	∈	∈	PROPN
ejpam-6413	251	17	(	(	PUNCT
ejpam-6413	251	18	0	0	NUM
ejpam-6413	251	19	,	,	PUNCT
ejpam-6413	251	20	1]2	1]2	NUM
ejpam-6413	251	21	,	,	PUNCT
ejpam-6413	251	22	where	where	SCONJ
ejpam-6413	251	23	0	0	NUM
ejpam-6413	251	24	≤	≤	NUM
ejpam-6413	251	25	ā	ā	NOUN
ejpam-6413	251	26	<	<	X
ejpam-6413	251	27	b̄	b̄	VERB
ejpam-6413	251	28	the	the	DET
ejpam-6413	251	29	following	follow	VERB
ejpam-6413	251	30	inequality∣∣∣∣𭟋(ā	inequality∣∣∣∣𭟋(ā	NOUN
ejpam-6413	251	31	)	)	PUNCT
ejpam-6413	251	32	+	+	NOUN
ejpam-6413	251	33	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	251	34	)	)	PUNCT
ejpam-6413	251	35	2	2	NUM
ejpam-6413	251	36	−	−	NOUN
ejpam-6413	251	37	γ(θ	γ(θ	PROPN
ejpam-6413	252	1	+	+	CCONJ
ejpam-6413	252	2	1	1	X
ejpam-6413	252	3	)	)	PUNCT
ejpam-6413	252	4	2(µ−	2(µ−	NUM
ejpam-6413	252	5	ā)θ	ā)θ	NOUN
ejpam-6413	252	6	[	[	PUNCT
ejpam-6413	252	7	χθ	χθ	X
ejpam-6413	252	8	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	252	9	)	)	PUNCT
ejpam-6413	253	1	+	+	CCONJ
ejpam-6413	253	2	χθ	χθ	X
ejpam-6413	253	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	253	4	)	)	PUNCT
ejpam-6413	253	5	]	]	PUNCT
ejpam-6413	253	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	253	7	≤	≤	NOUN
ejpam-6413	253	8	(	(	PUNCT
ejpam-6413	253	9	µ−	µ−	PROPN
ejpam-6413	253	10	ā)2	ā)2	VERB
ejpam-6413	253	11	2(θ	2(θ	NUM
ejpam-6413	253	12	+	+	CCONJ
ejpam-6413	253	13	1	1	X
ejpam-6413	253	14	)	)	PUNCT
ejpam-6413	253	15	[	[	PUNCT
ejpam-6413	253	16	|𭟋′′(ā)|	|𭟋′′(ā)|	PROPN
ejpam-6413	253	17	(	(	PUNCT
ejpam-6413	253	18	1	1	NUM
ejpam-6413	253	19	α+	α+	SYM
ejpam-6413	253	20	1	1	NUM
ejpam-6413	253	21	−	−	NUM
ejpam-6413	253	22	1	1	NUM
ejpam-6413	253	23	θ	θ	NOUN
ejpam-6413	253	24	+	+	PUNCT
ejpam-6413	253	25	α+	α+	PUNCT
ejpam-6413	253	26	2	2	NUM
ejpam-6413	253	27	)	)	PUNCT
ejpam-6413	254	1	+	+	X
ejpam-6413	254	2	m|𭟋′′(b̄)|	m|𭟋′′(b̄)|	PROPN
ejpam-6413	254	3	(	(	PUNCT
ejpam-6413	254	4	α	α	X
ejpam-6413	254	5	α+	α+	X
ejpam-6413	254	6	1	1	NUM
ejpam-6413	254	7	+	+	SYM
ejpam-6413	254	8	1	1	NUM
ejpam-6413	254	9	θ	θ	NOUN
ejpam-6413	254	10	+	+	PUNCT
ejpam-6413	254	11	α+	α+	PUNCT
ejpam-6413	254	12	2	2	NUM
ejpam-6413	254	13	)	)	PUNCT
ejpam-6413	254	14	]	]	PUNCT
ejpam-6413	254	15	(	(	PUNCT
ejpam-6413	254	16	24	24	NUM
ejpam-6413	254	17	)	)	PUNCT
ejpam-6413	254	18	holds	hold	VERB
ejpam-6413	254	19	true	true	ADJ
ejpam-6413	254	20	.	.	PUNCT
ejpam-6413	255	1	proof	proof	NOUN
ejpam-6413	255	2	.	.	PUNCT
ejpam-6413	256	1	by	by	ADP
ejpam-6413	256	2	using	use	VERB
ejpam-6413	256	3	lemma	lemma	PROPN
ejpam-6413	256	4	2	2	NUM
ejpam-6413	256	5	,	,	PUNCT
ejpam-6413	256	6	lemma	lemma	PROPN
ejpam-6413	256	7	4	4	NUM
ejpam-6413	256	8	and	and	CCONJ
ejpam-6413	256	9	lemma	lemma	PROPN
ejpam-6413	256	10	7	7	NUM
ejpam-6413	256	11	,	,	PUNCT
ejpam-6413	256	12	we	we	PRON
ejpam-6413	256	13	have∣∣∣∣𭟋(ā	have∣∣∣∣𭟋(ā	NOUN
ejpam-6413	256	14	)	)	PUNCT
ejpam-6413	256	15	+	+	NOUN
ejpam-6413	256	16	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	256	17	)	)	PUNCT
ejpam-6413	256	18	2	2	NUM
ejpam-6413	256	19	−	−	NOUN
ejpam-6413	256	20	γ(θ	γ(θ	PROPN
ejpam-6413	256	21	+	+	CCONJ
ejpam-6413	256	22	1	1	X
ejpam-6413	256	23	)	)	PUNCT
ejpam-6413	256	24	2(µ−	2(µ−	NUM
ejpam-6413	256	25	ā)θ	ā)θ	NOUN
ejpam-6413	256	26	[	[	PUNCT
ejpam-6413	256	27	χθ	χθ	X
ejpam-6413	256	28	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	256	29	)	)	PUNCT
ejpam-6413	257	1	+	+	CCONJ
ejpam-6413	257	2	χθ	χθ	X
ejpam-6413	257	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	257	4	)	)	PUNCT
ejpam-6413	257	5	]	]	PUNCT
ejpam-6413	257	6	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	257	7	≤	≤	NOUN
ejpam-6413	257	8	(	(	PUNCT
ejpam-6413	257	9	µ−	µ−	PROPN
ejpam-6413	257	10	ā)2	ā)2	NOUN
ejpam-6413	257	11	2	2	NUM
ejpam-6413	257	12	∫	∫	NOUN
ejpam-6413	257	13	1	1	NUM
ejpam-6413	257	14	0	0	NUM
ejpam-6413	257	15	∣∣∣∣1−	∣∣∣∣1−	NOUN
ejpam-6413	257	16	(	(	PUNCT
ejpam-6413	257	17	1−	1−	NUM
ejpam-6413	257	18	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	257	19	−	−	PROPN
ejpam-6413	257	20	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	257	21	θ	θ	PROPN
ejpam-6413	257	22	+	+	CCONJ
ejpam-6413	257	23	1	1	NUM
ejpam-6413	257	24	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	257	25	∣∣𭟋′′	∣∣𭟋′′	NOUN
ejpam-6413	257	26	(	(	PUNCT
ejpam-6413	257	27	⊺ā+m(1−	⊺ā+m(1−	ADJ
ejpam-6413	257	28	⊺)b̄	⊺)b̄	NOUN
ejpam-6413	257	29	)	)	PUNCT
ejpam-6413	257	30	∣∣	∣∣	X
ejpam-6413	257	31	d⊺	d⊺	PROPN
ejpam-6413	257	32	≤	≤	NUM
ejpam-6413	257	33	(	(	PUNCT
ejpam-6413	257	34	µ−	µ−	PROPN
ejpam-6413	257	35	ā)2	ā)2	NOUN
ejpam-6413	257	36	2	2	NUM
ejpam-6413	257	37	∫	∫	NOUN
ejpam-6413	257	38	1	1	NUM
ejpam-6413	257	39	0	0	NUM
ejpam-6413	257	40	∣∣∣∣1−	∣∣∣∣1−	NOUN
ejpam-6413	257	41	(	(	PUNCT
ejpam-6413	257	42	1−	1−	NUM
ejpam-6413	257	43	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	257	44	−	−	PROPN
ejpam-6413	257	45	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	257	46	θ	θ	PROPN
ejpam-6413	258	1	+	+	CCONJ
ejpam-6413	258	2	1	1	NUM
ejpam-6413	258	3	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	258	4	∣∣∣𭟋′′	∣∣∣𭟋′′	PROPN
ejpam-6413	258	5	(	(	PUNCT
ejpam-6413	258	6	ā⊺b̄m(1−⊺	ā⊺b̄m(1−⊺	PROPN
ejpam-6413	258	7	)	)	PUNCT
ejpam-6413	258	8	)	)	PUNCT
ejpam-6413	258	9	∣∣∣	∣∣∣	ADP
ejpam-6413	258	10	d⊺	d⊺	PROPN
ejpam-6413	258	11	≤	≤	NUM
ejpam-6413	258	12	(	(	PUNCT
ejpam-6413	258	13	µ−	µ−	PROPN
ejpam-6413	258	14	ā)2	ā)2	VERB
ejpam-6413	258	15	2(θ	2(θ	NUM
ejpam-6413	258	16	+	+	CCONJ
ejpam-6413	258	17	1	1	X
ejpam-6413	258	18	)	)	PUNCT
ejpam-6413	258	19	∫	∫	NOUN
ejpam-6413	258	20	1	1	NUM
ejpam-6413	258	21	0	0	NUM
ejpam-6413	258	22	∣∣∣1−	∣∣∣1−	NUM
ejpam-6413	258	23	(	(	PUNCT
ejpam-6413	258	24	1−	1−	NUM
ejpam-6413	258	25	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	258	26	−	−	PROPN
ejpam-6413	258	27	⊺θ+1	⊺θ+1	ADJ
ejpam-6413	258	28	∣∣∣	∣∣∣	NOUN
ejpam-6413	258	29	[	[	X
ejpam-6413	258	30	⊺α	⊺α	PROPN
ejpam-6413	258	31	∣∣𭟋′′(ā	∣∣𭟋′′(ā	NOUN
ejpam-6413	258	32	)	)	PUNCT
ejpam-6413	258	33	∣∣+m(1−	∣∣+m(1−	PROPN
ejpam-6413	258	34	⊺α	⊺α	ADJ
ejpam-6413	258	35	)	)	PUNCT
ejpam-6413	258	36	∣∣𭟋′′(b̄	∣∣𭟋′′(b̄	PROPN
ejpam-6413	258	37	)	)	PUNCT
ejpam-6413	259	1	∣∣	∣∣	X
ejpam-6413	259	2	]	]	X
ejpam-6413	259	3	d⊺	d⊺	PROPN
ejpam-6413	259	4	≤	≤	NUM
ejpam-6413	259	5	(	(	PUNCT
ejpam-6413	259	6	µ−	µ−	PROPN
ejpam-6413	259	7	ā)2	ā)2	VERB
ejpam-6413	259	8	2(θ	2(θ	NUM
ejpam-6413	259	9	+	+	CCONJ
ejpam-6413	259	10	1	1	X
ejpam-6413	259	11	)	)	PUNCT
ejpam-6413	259	12	[	[	PUNCT
ejpam-6413	259	13	|𭟋′′(ā)|	|𭟋′′(ā)|	PROPN
ejpam-6413	259	14	(	(	PUNCT
ejpam-6413	259	15	1	1	NUM
ejpam-6413	259	16	α+	α+	SYM
ejpam-6413	259	17	1	1	NUM
ejpam-6413	259	18	−	−	NUM
ejpam-6413	259	19	1	1	NUM
ejpam-6413	259	20	θ	θ	NOUN
ejpam-6413	259	21	+	+	PUNCT
ejpam-6413	259	22	α+	α+	PUNCT
ejpam-6413	259	23	2	2	NUM
ejpam-6413	259	24	)	)	PUNCT
ejpam-6413	260	1	+	+	X
ejpam-6413	260	2	m|𭟋′′(b̄)|	m|𭟋′′(b̄)|	PROPN
ejpam-6413	260	3	(	(	PUNCT
ejpam-6413	260	4	α	α	X
ejpam-6413	260	5	α+	α+	X
ejpam-6413	260	6	1	1	NUM
ejpam-6413	260	7	+	+	SYM
ejpam-6413	260	8	1	1	NUM
ejpam-6413	260	9	θ	θ	NOUN
ejpam-6413	260	10	+	+	PUNCT
ejpam-6413	260	11	α+	α+	PUNCT
ejpam-6413	260	12	2	2	NUM
ejpam-6413	260	13	)	)	PUNCT
ejpam-6413	260	14	]	]	PUNCT
ejpam-6413	260	15	.	.	PUNCT
ejpam-6413	261	1	hence	hence	ADV
ejpam-6413	261	2	,	,	PUNCT
ejpam-6413	261	3	the	the	DET
ejpam-6413	261	4	proof	proof	NOUN
ejpam-6413	261	5	is	be	AUX
ejpam-6413	261	6	done	do	VERB
ejpam-6413	261	7	.	.	PUNCT
ejpam-6413	262	1	example	example	NOUN
ejpam-6413	263	1	1	1	NUM
ejpam-6413	263	2	.	.	PUNCT
ejpam-6413	263	3	let	let	VERB
ejpam-6413	263	4	𭟋(⊺	𭟋(⊺	PRON
ejpam-6413	263	5	)	)	PUNCT
ejpam-6413	263	6	=	=	SYM
ejpam-6413	263	7	⊺3	⊺3	PROPN
ejpam-6413	263	8	and	and	CCONJ
ejpam-6413	263	9	by	by	ADP
ejpam-6413	263	10	taking	take	VERB
ejpam-6413	263	11	the	the	DET
ejpam-6413	263	12	values	value	NOUN
ejpam-6413	263	13	of	of	ADP
ejpam-6413	263	14	the	the	DET
ejpam-6413	263	15	parameters	parameter	NOUN
ejpam-6413	264	1	m.	m.	PROPN
ejpam-6413	264	2	samraiz	samraiz	PROPN
ejpam-6413	264	3	et	et	PROPN
ejpam-6413	264	4	al	al	PROPN
ejpam-6413	264	5	.	.	PUNCT
ejpam-6413	264	6	/	/	SYM
ejpam-6413	264	7	eur	eur	PROPN
ejpam-6413	264	8	.	.	PUNCT
ejpam-6413	265	1	j.	j.	PROPN
ejpam-6413	265	2	pure	pure	PROPN
ejpam-6413	265	3	appl	appl	PROPN
ejpam-6413	265	4	.	.	PROPN
ejpam-6413	265	5	math	math	PROPN
ejpam-6413	265	6	,	,	PUNCT
ejpam-6413	265	7	18	18	NUM
ejpam-6413	265	8	(	(	PUNCT
ejpam-6413	265	9	3	3	NUM
ejpam-6413	265	10	)	)	PUNCT
ejpam-6413	265	11	(	(	PUNCT
ejpam-6413	265	12	2025	2025	NUM
ejpam-6413	265	13	)	)	PUNCT
ejpam-6413	265	14	,	,	PUNCT
ejpam-6413	265	15	6413	6413	NUM
ejpam-6413	265	16	12	12	NUM
ejpam-6413	265	17	of	of	ADP
ejpam-6413	265	18	26	26	NUM
ejpam-6413	265	19	•	•	NOUN
ejpam-6413	265	20	ā	ā	NOUN
ejpam-6413	265	21	=	=	SYM
ejpam-6413	265	22	0	0	NUM
ejpam-6413	265	23	,	,	PUNCT
ejpam-6413	265	24	µ	µ	X
ejpam-6413	265	25	=	=	SYM
ejpam-6413	265	26	1	1	NUM
ejpam-6413	265	27	and	and	CCONJ
ejpam-6413	265	28	b̄	b̄	AUX
ejpam-6413	265	29	=	=	SYM
ejpam-6413	265	30	2	2	NUM
ejpam-6413	265	31	•	•	NUM
ejpam-6413	265	32	α	α	NOUN
ejpam-6413	265	33	=	=	PUNCT
ejpam-6413	265	34	0.5,m	0.5,m	NOUN
ejpam-6413	266	1	=	=	SYM
ejpam-6413	266	2	0.5	0.5	NUM
ejpam-6413	266	3	and	and	CCONJ
ejpam-6413	266	4	θ	θ	NOUN
ejpam-6413	266	5	=	=	SYM
ejpam-6413	266	6	1	1	NUM
ejpam-6413	266	7	the	the	DET
ejpam-6413	266	8	lhs	lhs	NOUN
ejpam-6413	266	9	of	of	ADP
ejpam-6413	266	10	the	the	DET
ejpam-6413	266	11	inequality∣∣∣∣𭟋(ā	inequality∣∣∣∣𭟋(ā	NOUN
ejpam-6413	266	12	)	)	PUNCT
ejpam-6413	266	13	+	+	NOUN
ejpam-6413	266	14	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	266	15	)	)	PUNCT
ejpam-6413	266	16	2	2	NUM
ejpam-6413	266	17	−	−	NOUN
ejpam-6413	266	18	γ(θ	γ(θ	PROPN
ejpam-6413	266	19	+	+	CCONJ
ejpam-6413	266	20	1	1	X
ejpam-6413	266	21	)	)	PUNCT
ejpam-6413	266	22	2(µ−	2(µ−	NUM
ejpam-6413	266	23	ā)θ	ā)θ	NOUN
ejpam-6413	266	24	[	[	PUNCT
ejpam-6413	266	25	χθ	χθ	X
ejpam-6413	266	26	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	266	27	)	)	PUNCT
ejpam-6413	267	1	+	+	CCONJ
ejpam-6413	267	2	χθ	χθ	X
ejpam-6413	267	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	267	4	)	)	PUNCT
ejpam-6413	267	5	]	]	PUNCT
ejpam-6413	267	6	∣∣∣∣∣∣∣∣(0)3	∣∣∣∣∣∣∣∣(0)3	X
ejpam-6413	268	1	+	+	CCONJ
ejpam-6413	268	2	(	(	PUNCT
ejpam-6413	268	3	1)3	1)3	PROPN
ejpam-6413	268	4	2	2	NUM
ejpam-6413	268	5	−	−	NOUN
ejpam-6413	268	6	γ(1	γ(1	NOUN
ejpam-6413	268	7	+	+	CCONJ
ejpam-6413	268	8	1	1	NUM
ejpam-6413	268	9	)	)	PUNCT
ejpam-6413	268	10	2(1−	2(1−	NUM
ejpam-6413	269	1	0)1	0)1	PROPN
ejpam-6413	269	2	[	[	PUNCT
ejpam-6413	269	3	χ1	χ1	NOUN
ejpam-6413	269	4	0+𭟋(1	0+𭟋(1	NOUN
ejpam-6413	269	5	)	)	PUNCT
ejpam-6413	270	1	+	+	NUM
ejpam-6413	270	2	χ1	χ1	NOUN
ejpam-6413	270	3	1−𭟋(0	1−𭟋(0	NUM
ejpam-6413	270	4	)	)	PUNCT
ejpam-6413	270	5	]	]	PUNCT
ejpam-6413	270	6	∣∣∣∣∣∣∣∣∣∣(0	∣∣∣∣∣∣∣∣∣∣(0	X
ejpam-6413	270	7	)	)	PUNCT
ejpam-6413	270	8	3	3	NUM
ejpam-6413	271	1	+	+	CCONJ
ejpam-6413	271	2	(	(	PUNCT
ejpam-6413	271	3	1)3	1)3	PROPN
ejpam-6413	271	4	2	2	NUM
ejpam-6413	271	5	−	−	NOUN
ejpam-6413	271	6	γ(1	γ(1	NOUN
ejpam-6413	271	7	+	+	CCONJ
ejpam-6413	271	8	1	1	NUM
ejpam-6413	271	9	)	)	PUNCT
ejpam-6413	271	10	2(1−	2(1−	NUM
ejpam-6413	271	11	0)1	0)1	NUM
ejpam-6413	271	12			NOUN
ejpam-6413	271	13	1	1	NUM
ejpam-6413	271	14	γ(1	γ(1	PROPN
ejpam-6413	271	15	)	)	PUNCT
ejpam-6413	272	1	1∫	1∫	NUM
ejpam-6413	272	2	0	0	NUM
ejpam-6413	272	3	(	(	PUNCT
ejpam-6413	272	4	1−	1−	NUM
ejpam-6413	272	5	⊺)1−1(⊺)3d	⊺)1−1(⊺)3d	PROPN
ejpam-6413	272	6	⊺+	⊺+	VERB
ejpam-6413	272	7	1	1	NUM
ejpam-6413	272	8	γ(1	γ(1	PROPN
ejpam-6413	272	9	)	)	PUNCT
ejpam-6413	272	10	2∫	2∫	NUM
ejpam-6413	272	11	1	1	NUM
ejpam-6413	272	12	(	(	PUNCT
ejpam-6413	272	13	⊺−	⊺−	PROPN
ejpam-6413	272	14	0)1−1(0)3d⊺	0)1−1(0)3d⊺	PROPN
ejpam-6413	272	15	∣∣∣∣∣∣∣∣∣∣∣12	∣∣∣∣∣∣∣∣∣∣∣12	PROPN
ejpam-6413	272	16	−	−	PROPN
ejpam-6413	272	17	γ(2	γ(2	PROPN
ejpam-6413	272	18	)	)	PUNCT
ejpam-6413	272	19	2	2	NUM
ejpam-6413	272	20	[	[	PUNCT
ejpam-6413	272	21	1	1	NUM
ejpam-6413	272	22	γ(1	γ(1	PROPN
ejpam-6413	272	23	)	)	PUNCT
ejpam-6413	272	24	[	[	PUNCT
ejpam-6413	272	25	⊺4	⊺4	NOUN
ejpam-6413	272	26	4	4	NUM
ejpam-6413	272	27	]	]	SYM
ejpam-6413	272	28	1	1	NUM
ejpam-6413	272	29	0	0	NUM
ejpam-6413	273	1	+	+	CCONJ
ejpam-6413	273	2	0	0	NUM
ejpam-6413	273	3	]	]	X
ejpam-6413	273	4	∣∣∣∣∣∣∣∣∣12	∣∣∣∣∣∣∣∣∣12	ADJ
ejpam-6413	273	5	−	−	NUM
ejpam-6413	273	6	1	1	NUM
ejpam-6413	273	7	2	2	NUM
ejpam-6413	273	8	×	×	NOUN
ejpam-6413	273	9	1	1	NUM
ejpam-6413	273	10	4	4	NUM
ejpam-6413	273	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	273	12	|0.5−	|0.5−	PUNCT
ejpam-6413	273	13	0.125|	0.125|	NUM
ejpam-6413	273	14	=	=	SYM
ejpam-6413	273	15	0.375	0.375	NUM
ejpam-6413	273	16	.	.	PUNCT
ejpam-6413	274	1	the	the	DET
ejpam-6413	274	2	rhs	rhs	PROPN
ejpam-6413	274	3	of	of	ADP
ejpam-6413	274	4	the	the	DET
ejpam-6413	274	5	inequality	inequality	NOUN
ejpam-6413	274	6	(	(	PUNCT
ejpam-6413	274	7	µ−	µ−	PROPN
ejpam-6413	274	8	ā)2	ā)2	VERB
ejpam-6413	274	9	2(θ	2(θ	NUM
ejpam-6413	274	10	+	+	CCONJ
ejpam-6413	274	11	1	1	X
ejpam-6413	274	12	)	)	PUNCT
ejpam-6413	274	13	[	[	PUNCT
ejpam-6413	274	14	|𭟋′′(ā)|	|𭟋′′(ā)|	PROPN
ejpam-6413	274	15	(	(	PUNCT
ejpam-6413	274	16	1	1	NUM
ejpam-6413	274	17	α+	α+	SYM
ejpam-6413	274	18	1	1	NUM
ejpam-6413	274	19	−	−	NUM
ejpam-6413	274	20	1	1	NUM
ejpam-6413	274	21	θ	θ	NOUN
ejpam-6413	274	22	+	+	PUNCT
ejpam-6413	274	23	α+	α+	PUNCT
ejpam-6413	274	24	2	2	NUM
ejpam-6413	274	25	)	)	PUNCT
ejpam-6413	275	1	+	+	X
ejpam-6413	275	2	m|𭟋′′(b̄)|	m|𭟋′′(b̄)|	PROPN
ejpam-6413	275	3	(	(	PUNCT
ejpam-6413	275	4	α	α	X
ejpam-6413	275	5	α+	α+	X
ejpam-6413	275	6	1	1	NUM
ejpam-6413	275	7	+	+	SYM
ejpam-6413	275	8	1	1	NUM
ejpam-6413	275	9	θ	θ	NOUN
ejpam-6413	275	10	+	+	PUNCT
ejpam-6413	275	11	α+	α+	PUNCT
ejpam-6413	275	12	2	2	NUM
ejpam-6413	275	13	)	)	PUNCT
ejpam-6413	275	14	]	]	PUNCT
ejpam-6413	275	15	(	(	PUNCT
ejpam-6413	275	16	1−	1−	NUM
ejpam-6413	275	17	0)2	0)2	NUM
ejpam-6413	275	18	2(1	2(1	NUM
ejpam-6413	275	19	+	+	CCONJ
ejpam-6413	275	20	1	1	X
ejpam-6413	275	21	)	)	PUNCT
ejpam-6413	275	22	[	[	PUNCT
ejpam-6413	275	23	|6(0)|	|6(0)|	NOUN
ejpam-6413	275	24	(	(	PUNCT
ejpam-6413	275	25	1	1	NUM
ejpam-6413	275	26	0.5	0.5	NUM
ejpam-6413	275	27	+	+	CCONJ
ejpam-6413	275	28	1	1	NUM
ejpam-6413	275	29	−	−	NUM
ejpam-6413	275	30	1	1	NUM
ejpam-6413	275	31	1	1	NUM
ejpam-6413	275	32	+	+	NUM
ejpam-6413	275	33	0.5	0.5	NUM
ejpam-6413	275	34	+	+	CCONJ
ejpam-6413	275	35	2	2	NUM
ejpam-6413	275	36	)	)	PUNCT
ejpam-6413	275	37	+	+	NUM
ejpam-6413	275	38	0.5|6(2)|	0.5|6(2)|	NOUN
ejpam-6413	275	39	(	(	PUNCT
ejpam-6413	275	40	0.5	0.5	NUM
ejpam-6413	275	41	0.5	0.5	NUM
ejpam-6413	275	42	+	+	CCONJ
ejpam-6413	275	43	1	1	NUM
ejpam-6413	275	44	+	+	CCONJ
ejpam-6413	275	45	1	1	NUM
ejpam-6413	275	46	1	1	NUM
ejpam-6413	275	47	+	+	NUM
ejpam-6413	275	48	0.5	0.5	NUM
ejpam-6413	275	49	+	+	CCONJ
ejpam-6413	275	50	2	2	NUM
ejpam-6413	275	51	)	)	PUNCT
ejpam-6413	275	52	]	]	PUNCT
ejpam-6413	275	53	.	.	PUNCT
ejpam-6413	276	1	to	to	PART
ejpam-6413	276	2	simplify	simplify	VERB
ejpam-6413	276	3	,	,	PUNCT
ejpam-6413	276	4	0.5	0.5	NUM
ejpam-6413	276	5	1.5	1.5	NUM
ejpam-6413	276	6	=	=	SYM
ejpam-6413	276	7	1	1	NUM
ejpam-6413	276	8	3	3	NUM
ejpam-6413	276	9	,	,	PUNCT
ejpam-6413	276	10	1	1	NUM
ejpam-6413	276	11	0.5	0.5	NUM
ejpam-6413	276	12	=	=	SYM
ejpam-6413	276	13	1	1	NUM
ejpam-6413	276	14	2	2	NUM
ejpam-6413	276	15	and	and	CCONJ
ejpam-6413	276	16	1	1	NUM
ejpam-6413	276	17	3.5	3.5	NUM
ejpam-6413	276	18	=	=	SYM
ejpam-6413	276	19	2	2	NUM
ejpam-6413	276	20	7	7	NUM
ejpam-6413	276	21	1	1	NUM
ejpam-6413	276	22	4	4	NUM
ejpam-6413	276	23	[	[	PUNCT
ejpam-6413	276	24	0.5(12	0.5(12	NUM
ejpam-6413	276	25	)	)	PUNCT
ejpam-6413	276	26	(	(	PUNCT
ejpam-6413	276	27	0.5	0.5	NUM
ejpam-6413	276	28	1.5	1.5	NUM
ejpam-6413	276	29	+	+	CCONJ
ejpam-6413	276	30	1	1	NUM
ejpam-6413	276	31	3.5	3.5	NUM
ejpam-6413	276	32	)	)	PUNCT
ejpam-6413	276	33	]	]	PUNCT
ejpam-6413	277	1	≈	≈	PROPN
ejpam-6413	277	2	0.9286	0.9286	NUM
ejpam-6413	277	3	hence	hence	ADV
ejpam-6413	277	4	,	,	PUNCT
ejpam-6413	277	5	the	the	DET
ejpam-6413	277	6	chosen	choose	VERB
ejpam-6413	277	7	values	value	NOUN
ejpam-6413	277	8	satisfy	satisfy	VERB
ejpam-6413	277	9	the	the	DET
ejpam-6413	277	10	inequality	inequality	NOUN
ejpam-6413	277	11	0.375	0.375	NUM
ejpam-6413	277	12	≤	≤	NUM
ejpam-6413	277	13	0.9286	0.9286	NUM
ejpam-6413	277	14	.	.	PUNCT
ejpam-6413	278	1	this	this	DET
ejpam-6413	278	2	example	example	NOUN
ejpam-6413	278	3	confirms	confirm	VERB
ejpam-6413	278	4	the	the	DET
ejpam-6413	278	5	validity	validity	NOUN
ejpam-6413	278	6	of	of	ADP
ejpam-6413	278	7	the	the	DET
ejpam-6413	278	8	fractional	fractional	ADJ
ejpam-6413	278	9	hermite	hermite	ADJ
ejpam-6413	278	10	-	-	PUNCT
ejpam-6413	278	11	hadamard	hadamard	ADJ
ejpam-6413	278	12	-	-	PUNCT
ejpam-6413	278	13	type	type	NOUN
ejpam-6413	278	14	inequality	inequality	NOUN
ejpam-6413	278	15	and	and	CCONJ
ejpam-6413	278	16	demonstrates	demonstrate	VERB
ejpam-6413	278	17	its	its	PRON
ejpam-6413	278	18	usefulness	usefulness	NOUN
ejpam-6413	278	19	in	in	ADP
ejpam-6413	278	20	numerical	numerical	ADJ
ejpam-6413	278	21	analysis	analysis	NOUN
ejpam-6413	278	22	for	for	ADP
ejpam-6413	278	23	estimating	estimate	VERB
ejpam-6413	278	24	error	error	NOUN
ejpam-6413	278	25	bounds	bound	NOUN
ejpam-6413	278	26	in	in	ADP
ejpam-6413	278	27	numerical	numerical	ADJ
ejpam-6413	278	28	integration	integration	NOUN
ejpam-6413	278	29	,	,	PUNCT
ejpam-6413	278	30	as	as	ADV
ejpam-6413	278	31	well	well	ADV
ejpam-6413	278	32	as	as	ADP
ejpam-6413	278	33	in	in	ADP
ejpam-6413	278	34	inequality	inequality	NOUN
ejpam-6413	278	35	theory	theory	NOUN
ejpam-6413	278	36	,	,	PUNCT
ejpam-6413	278	37	fractional	fractional	ADJ
ejpam-6413	278	38	differential	differential	ADJ
ejpam-6413	278	39	equations	equation	NOUN
ejpam-6413	278	40	and	and	CCONJ
ejpam-6413	278	41	mathematical	mathematical	ADJ
ejpam-6413	278	42	modeling	modeling	NOUN
ejpam-6413	278	43	.	.	PUNCT
ejpam-6413	279	1	theorem	theorem	NOUN
ejpam-6413	279	2	2	2	NUM
ejpam-6413	279	3	.	.	PUNCT
ejpam-6413	280	1	let	let	VERB
ejpam-6413	280	2	𭟋	𭟋	VERB
ejpam-6413	280	3	:	:	PUNCT
ejpam-6413	280	4	[	[	X
ejpam-6413	280	5	ā	ā	X
ejpam-6413	280	6	,	,	PUNCT
ejpam-6413	280	7	b̄	b̄	PROPN
ejpam-6413	280	8	]	]	PUNCT
ejpam-6413	280	9	−→	−→	NOUN
ejpam-6413	280	10	r	r	NOUN
ejpam-6413	280	11	be	be	VERB
ejpam-6413	280	12	a	a	DET
ejpam-6413	280	13	twice	twice	ADV
ejpam-6413	280	14	differentiable	differentiable	ADJ
ejpam-6413	280	15	function	function	NOUN
ejpam-6413	280	16	on	on	ADP
ejpam-6413	280	17	[	[	X
ejpam-6413	280	18	ā	ā	X
ejpam-6413	280	19	,	,	PUNCT
ejpam-6413	280	20	b̄	b̄	PROPN
ejpam-6413	280	21	]	]	PUNCT
ejpam-6413	280	22	and	and	CCONJ
ejpam-6413	280	23	1	1	NUM
ejpam-6413	280	24	<	<	X
ejpam-6413	280	25	⋋2	⋋2	NOUN
ejpam-6413	280	26	<	<	X
ejpam-6413	280	27	+	+	X
ejpam-6413	280	28	∞.	∞.	PROPN
ejpam-6413	280	29	if	if	SCONJ
ejpam-6413	280	30	|𭟋′′|⋋2	|𭟋′′|⋋2	NUM
ejpam-6413	280	31	is	be	AUX
ejpam-6413	280	32	lebesgue	lebesgue	NOUN
ejpam-6413	280	33	integerable	integerable	ADJ
ejpam-6413	280	34	,	,	PUNCT
ejpam-6413	280	35	increasing	increase	VERB
ejpam-6413	280	36	and	and	CCONJ
ejpam-6413	280	37	ga	ga	PROPN
ejpam-6413	280	38	(	(	PUNCT
ejpam-6413	280	39	α	α	NOUN
ejpam-6413	280	40	,	,	PUNCT
ejpam-6413	280	41	m)-convex	m)-convex	PUNCT
ejpam-6413	280	42	on	on	ADP
ejpam-6413	280	43	[	[	X
ejpam-6413	280	44	ā	ā	X
ejpam-6413	280	45	,	,	PUNCT
ejpam-6413	280	46	b̄	b̄	PROPN
ejpam-6413	280	47	]	]	PUNCT
ejpam-6413	280	48	.	.	PUNCT
ejpam-6413	281	1	then	then	ADV
ejpam-6413	281	2	for	for	ADP
ejpam-6413	281	3	given	give	VERB
ejpam-6413	281	4	parameters	parameter	NOUN
ejpam-6413	281	5	θ	θ	PROPN
ejpam-6413	281	6	∈	∈	PROPN
ejpam-6413	281	7	(	(	PUNCT
ejpam-6413	281	8	0,+∞	0,+∞	NUM
ejpam-6413	281	9	)	)	PUNCT
ejpam-6413	281	10	and	and	CCONJ
ejpam-6413	281	11	(	(	PUNCT
ejpam-6413	281	12	α	α	NOUN
ejpam-6413	281	13	,	,	PUNCT
ejpam-6413	281	14	m	m	NOUN
ejpam-6413	281	15	)	)	PUNCT
ejpam-6413	281	16	∈	∈	PROPN
ejpam-6413	281	17	(	(	PUNCT
ejpam-6413	281	18	0	0	NUM
ejpam-6413	281	19	,	,	PUNCT
ejpam-6413	281	20	1]2	1]2	NUM
ejpam-6413	281	21	,	,	PUNCT
ejpam-6413	281	22	where	where	SCONJ
ejpam-6413	281	23	0	0	NUM
ejpam-6413	281	24	≤	≤	NUM
ejpam-6413	281	25	ā	ā	NOUN
ejpam-6413	281	26	<	<	X
ejpam-6413	281	27	b̄	b̄	VERB
ejpam-6413	281	28	the	the	DET
ejpam-6413	281	29	following	follow	VERB
ejpam-6413	281	30	inequality	inequality	NOUN
ejpam-6413	281	31	∣∣∣∣𭟋(ā	∣∣∣∣𭟋(ā	PUNCT
ejpam-6413	281	32	)	)	PUNCT
ejpam-6413	281	33	+	+	NOUN
ejpam-6413	281	34	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	281	35	)	)	PUNCT
ejpam-6413	281	36	2	2	NUM
ejpam-6413	281	37	−	−	NOUN
ejpam-6413	281	38	γ(θ	γ(θ	PROPN
ejpam-6413	281	39	+	+	CCONJ
ejpam-6413	281	40	1	1	X
ejpam-6413	281	41	)	)	PUNCT
ejpam-6413	281	42	2(µ−	2(µ−	NUM
ejpam-6413	281	43	ā)θ	ā)θ	NOUN
ejpam-6413	281	44	[	[	PUNCT
ejpam-6413	281	45	χθ	χθ	X
ejpam-6413	281	46	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	281	47	)	)	PUNCT
ejpam-6413	282	1	+	+	CCONJ
ejpam-6413	282	2	χθ	χθ	X
ejpam-6413	282	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	282	4	)	)	PUNCT
ejpam-6413	282	5	]	]	PUNCT
ejpam-6413	282	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6413	282	7	m.	m.	NOUN
ejpam-6413	282	8	samraiz	samraiz	PROPN
ejpam-6413	282	9	et	et	PROPN
ejpam-6413	282	10	al	al	PROPN
ejpam-6413	282	11	.	.	PUNCT
ejpam-6413	282	12	/	/	SYM
ejpam-6413	282	13	eur	eur	PROPN
ejpam-6413	282	14	.	.	PUNCT
ejpam-6413	283	1	j.	j.	PROPN
ejpam-6413	283	2	pure	pure	PROPN
ejpam-6413	283	3	appl	appl	PROPN
ejpam-6413	283	4	.	.	PROPN
ejpam-6413	283	5	math	math	PROPN
ejpam-6413	283	6	,	,	PUNCT
ejpam-6413	283	7	18	18	NUM
ejpam-6413	283	8	(	(	PUNCT
ejpam-6413	283	9	3	3	NUM
ejpam-6413	283	10	)	)	PUNCT
ejpam-6413	283	11	(	(	PUNCT
ejpam-6413	283	12	2025	2025	NUM
ejpam-6413	283	13	)	)	PUNCT
ejpam-6413	283	14	,	,	PUNCT
ejpam-6413	283	15	6413	6413	NUM
ejpam-6413	283	16	13	13	NUM
ejpam-6413	283	17	of	of	ADP
ejpam-6413	283	18	26	26	NUM
ejpam-6413	283	19	≤	≤	NOUN
ejpam-6413	283	20	(	(	PUNCT
ejpam-6413	283	21	µ−	µ−	PROPN
ejpam-6413	283	22	ā)2max(1−	ā)2max(1−	PUNCT
ejpam-6413	283	23	21−θ	21−θ	NUM
ejpam-6413	283	24	,	,	PUNCT
ejpam-6413	283	25	21−θ	21−θ	NUM
ejpam-6413	283	26	−	−	NOUN
ejpam-6413	283	27	1	1	NUM
ejpam-6413	283	28	)	)	PUNCT
ejpam-6413	283	29	2(θ	2(θ	NUM
ejpam-6413	284	1	+	+	CCONJ
ejpam-6413	284	2	1	1	X
ejpam-6413	284	3	)	)	PUNCT
ejpam-6413	284	4	(	(	PUNCT
ejpam-6413	284	5	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	284	6	+	+	X
ejpam-6413	284	7	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	284	8	α+	α+	PUNCT
ejpam-6413	284	9	1	1	NUM
ejpam-6413	284	10	)	)	SYM
ejpam-6413	284	11	1	1	NUM
ejpam-6413	284	12	⋋2	⋋2	NOUN
ejpam-6413	284	13	(	(	PUNCT
ejpam-6413	284	14	25	25	NUM
ejpam-6413	284	15	)	)	PUNCT
ejpam-6413	284	16	holds	hold	VERB
ejpam-6413	284	17	true	true	ADJ
ejpam-6413	284	18	.	.	PUNCT
ejpam-6413	285	1	proof	proof	NOUN
ejpam-6413	285	2	.	.	PUNCT
ejpam-6413	286	1	the	the	DET
ejpam-6413	286	2	proof	proof	NOUN
ejpam-6413	286	3	of	of	ADP
ejpam-6413	286	4	this	this	DET
ejpam-6413	286	5	result	result	NOUN
ejpam-6413	286	6	is	be	AUX
ejpam-6413	286	7	split	split	VERB
ejpam-6413	286	8	into	into	ADP
ejpam-6413	286	9	two	two	NUM
ejpam-6413	286	10	situations	situation	NOUN
ejpam-6413	286	11	presented	present	VERB
ejpam-6413	286	12	as	as	SCONJ
ejpam-6413	286	13	follows	follow	VERB
ejpam-6413	286	14	.	.	PUNCT
ejpam-6413	287	1	case(i	case(i	PROPN
ejpam-6413	287	2	)	)	PUNCT
ejpam-6413	287	3	let	let	VERB
ejpam-6413	287	4	θ	θ	PROPN
ejpam-6413	287	5	∈	∈	PROPN
ejpam-6413	287	6	(	(	PUNCT
ejpam-6413	287	7	0	0	NUM
ejpam-6413	287	8	,	,	PUNCT
ejpam-6413	287	9	1	1	NUM
ejpam-6413	287	10	)	)	PUNCT
ejpam-6413	287	11	.	.	PUNCT
ejpam-6413	288	1	by	by	ADP
ejpam-6413	288	2	utilizing	utilize	VERB
ejpam-6413	288	3	lemma	lemma	PROPN
ejpam-6413	288	4	1	1	NUM
ejpam-6413	288	5	,	,	PUNCT
ejpam-6413	288	6	2	2	NUM
ejpam-6413	288	7	,	,	PUNCT
ejpam-6413	288	8	4	4	NUM
ejpam-6413	288	9	,	,	PUNCT
ejpam-6413	288	10	7	7	NUM
ejpam-6413	288	11	and	and	CCONJ
ejpam-6413	288	12	applying	apply	VERB
ejpam-6413	288	13	hölder	hölder	NOUN
ejpam-6413	288	14	’s	’s	PART
ejpam-6413	288	15	inequality	inequality	NOUN
ejpam-6413	288	16	,	,	PUNCT
ejpam-6413	288	17	we	we	PRON
ejpam-6413	288	18	have	have	VERB
ejpam-6413	288	19	∣∣∣∣𭟋(ā	∣∣∣∣𭟋(ā	VERB
ejpam-6413	288	20	)	)	PUNCT
ejpam-6413	288	21	+	+	NOUN
ejpam-6413	288	22	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	288	23	)	)	PUNCT
ejpam-6413	288	24	2	2	NUM
ejpam-6413	288	25	−	−	NOUN
ejpam-6413	288	26	γ(θ	γ(θ	PROPN
ejpam-6413	289	1	+	+	CCONJ
ejpam-6413	289	2	1	1	X
ejpam-6413	289	3	)	)	PUNCT
ejpam-6413	289	4	2(µ−	2(µ−	NUM
ejpam-6413	289	5	ā)θ	ā)θ	NOUN
ejpam-6413	289	6	[	[	PUNCT
ejpam-6413	289	7	χθ	χθ	X
ejpam-6413	289	8	ā+𭟋(b̄	ā+𭟋(b̄	NUM
ejpam-6413	289	9	)	)	PUNCT
ejpam-6413	290	1	+	+	CCONJ
ejpam-6413	290	2	χθ	χθ	X
ejpam-6413	290	3	b̄−𭟋(ā	b̄−𭟋(ā	NOUN
ejpam-6413	290	4	)	)	PUNCT
ejpam-6413	291	1	]	]	PUNCT
ejpam-6413	291	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	291	3	≤	≤	NOUN
ejpam-6413	291	4	(	(	PUNCT
ejpam-6413	291	5	µ−	µ−	PROPN
ejpam-6413	291	6	ā)2	ā)2	NOUN
ejpam-6413	291	7	2	2	NUM
ejpam-6413	291	8	∫	∫	NOUN
ejpam-6413	291	9	1	1	NUM
ejpam-6413	291	10	0	0	NUM
ejpam-6413	291	11	∣∣∣∣1−	∣∣∣∣1−	NOUN
ejpam-6413	291	12	(	(	PUNCT
ejpam-6413	291	13	1−	1−	NUM
ejpam-6413	291	14	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	291	15	−	−	PROPN
ejpam-6413	291	16	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	291	17	θ	θ	PROPN
ejpam-6413	291	18	+	+	PUNCT
ejpam-6413	291	19	1	1	NUM
ejpam-6413	291	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	291	21	|𭟋′′(⊺ā+	|𭟋′′(⊺ā+	PROPN
ejpam-6413	291	22	(	(	PUNCT
ejpam-6413	291	23	1−	1−	NUM
ejpam-6413	291	24	⊺)b̄)|d⊺	⊺)b̄)|d⊺	NUM
ejpam-6413	291	25	≤	≤	PROPN
ejpam-6413	291	26	(	(	PUNCT
ejpam-6413	291	27	µ−	µ−	PROPN
ejpam-6413	291	28	ā)2	ā)2	NOUN
ejpam-6413	291	29	2	2	NUM
ejpam-6413	291	30	(	(	PUNCT
ejpam-6413	291	31	∫	∫	PROPN
ejpam-6413	291	32	1	1	NUM
ejpam-6413	291	33	0	0	NUM
ejpam-6413	291	34	∣∣∣∣1−	∣∣∣∣1−	NOUN
ejpam-6413	291	35	(	(	PUNCT
ejpam-6413	291	36	1−	1−	NUM
ejpam-6413	291	37	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	291	38	−	−	PROPN
ejpam-6413	291	39	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	291	40	θ	θ	PROPN
ejpam-6413	291	41	+	+	CCONJ
ejpam-6413	291	42	1	1	NUM
ejpam-6413	291	43	∣∣∣∣⋋1	∣∣∣∣⋋1	PROPN
ejpam-6413	291	44	d⊺	d⊺	PROPN
ejpam-6413	291	45	)	)	PUNCT
ejpam-6413	291	46	1	1	NUM
ejpam-6413	291	47	⋋1	⋋1	NUM
ejpam-6413	291	48	×	×	NOUN
ejpam-6413	291	49	(	(	PUNCT
ejpam-6413	291	50	∫	∫	PROPN
ejpam-6413	291	51	1	1	NUM
ejpam-6413	291	52	0	0	NUM
ejpam-6413	291	53	|𭟋′′(⊺ā+m(1−	|𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	291	54	⊺)b̄)|⋋2d⊺	⊺)b̄)|⋋2d⊺	NOUN
ejpam-6413	291	55	)	)	PUNCT
ejpam-6413	291	56	1	1	NUM
ejpam-6413	291	57	⋋2	⋋2	NOUN
ejpam-6413	291	58	≤	≤	NOUN
ejpam-6413	291	59	(	(	PUNCT
ejpam-6413	291	60	µ−	µ−	PROPN
ejpam-6413	291	61	ā)2	ā)2	VERB
ejpam-6413	291	62	2(θ	2(θ	NUM
ejpam-6413	291	63	+	+	CCONJ
ejpam-6413	291	64	1	1	NUM
ejpam-6413	291	65	)	)	PUNCT
ejpam-6413	291	66	(	(	PUNCT
ejpam-6413	291	67	∫	∫	PROPN
ejpam-6413	291	68	1	1	NUM
ejpam-6413	291	69	0	0	NUM
ejpam-6413	291	70	∣∣∣1−	∣∣∣1−	NUM
ejpam-6413	291	71	(	(	PUNCT
ejpam-6413	291	72	1−	1−	NUM
ejpam-6413	291	73	⊺)θ	⊺)θ	NUM
ejpam-6413	291	74	−	−	NOUN
ejpam-6413	291	75	⊺θ	⊺θ	PROPN
ejpam-6413	291	76	∣∣∣⋋1	∣∣∣⋋1	PROPN
ejpam-6413	291	77	d⊺	d⊺	PROPN
ejpam-6413	291	78	)	)	PUNCT
ejpam-6413	291	79	1	1	NUM
ejpam-6413	291	80	⋋1	⋋1	NUM
ejpam-6413	291	81	(	(	PUNCT
ejpam-6413	291	82	∫	∫	PROPN
ejpam-6413	291	83	1	1	NUM
ejpam-6413	291	84	0	0	NUM
ejpam-6413	291	85	|𭟋′′(ā⊺b̄m(1−⊺))|⋋2d⊺	|𭟋′′(ā⊺b̄m(1−⊺))|⋋2d⊺	PROPN
ejpam-6413	291	86	)	)	PUNCT
ejpam-6413	291	87	1	1	NUM
ejpam-6413	291	88	⋋2	⋋2	NOUN
ejpam-6413	291	89	≤	≤	NOUN
ejpam-6413	291	90	(	(	PUNCT
ejpam-6413	291	91	µ−	µ−	PROPN
ejpam-6413	291	92	ā)2	ā)2	VERB
ejpam-6413	291	93	2(θ	2(θ	NUM
ejpam-6413	291	94	+	+	CCONJ
ejpam-6413	291	95	1	1	NUM
ejpam-6413	291	96	)	)	PUNCT
ejpam-6413	291	97	(	(	PUNCT
ejpam-6413	291	98	∫	∫	PROPN
ejpam-6413	291	99	1	1	NUM
ejpam-6413	291	100	0	0	NUM
ejpam-6413	291	101	|1−	|1−	X
ejpam-6413	291	102	(	(	PUNCT
ejpam-6413	291	103	1−	1−	NUM
ejpam-6413	291	104	⊺)θ	⊺)θ	NUM
ejpam-6413	291	105	−	−	PROPN
ejpam-6413	291	106	⊺θ|⋋1d⊺	⊺θ|⋋1d⊺	PROPN
ejpam-6413	291	107	)	)	PUNCT
ejpam-6413	291	108	1	1	NUM
ejpam-6413	291	109	⋋1	⋋1	NUM
ejpam-6413	291	110	×	×	NOUN
ejpam-6413	291	111	(	(	PUNCT
ejpam-6413	291	112	∫	∫	PROPN
ejpam-6413	291	113	1	1	NUM
ejpam-6413	291	114	0	0	NUM
ejpam-6413	291	115	(	(	PUNCT
ejpam-6413	291	116	⊺α|𭟋′′(ā)|⋋2	⊺α|𭟋′′(ā)|⋋2	PROPN
ejpam-6413	291	117	+	+	ADJ
ejpam-6413	291	118	m(1−	m(1−	ADJ
ejpam-6413	291	119	⊺α)|𭟋′′(b̄)|⋋2)d⊺	⊺α)|𭟋′′(b̄)|⋋2)d⊺	NOUN
ejpam-6413	291	120	)	)	PUNCT
ejpam-6413	291	121	1	1	NUM
ejpam-6413	291	122	⋋2	⋋2	PROPN
ejpam-6413	291	123	≤	≤	NOUN
ejpam-6413	291	124	(	(	PUNCT
ejpam-6413	291	125	µ−	µ−	PROPN
ejpam-6413	291	126	ā)2	ā)2	VERB
ejpam-6413	291	127	2(θ	2(θ	NUM
ejpam-6413	291	128	+	+	CCONJ
ejpam-6413	291	129	1	1	X
ejpam-6413	291	130	)	)	PUNCT
ejpam-6413	291	131	(	(	PUNCT
ejpam-6413	291	132	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	292	1	+	+	X
ejpam-6413	292	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	292	3	α+	α+	PUNCT
ejpam-6413	292	4	1	1	NUM
ejpam-6413	292	5	)	)	SYM
ejpam-6413	292	6	1	1	NUM
ejpam-6413	292	7	⋋2	⋋2	NOUN
ejpam-6413	292	8	(	(	PUNCT
ejpam-6413	292	9	∫	∫	PROPN
ejpam-6413	292	10	1	1	NUM
ejpam-6413	292	11	0	0	NUM
ejpam-6413	292	12	∣∣∣1−	∣∣∣1−	NUM
ejpam-6413	292	13	(	(	PUNCT
ejpam-6413	292	14	1−	1−	NUM
ejpam-6413	292	15	⊺)θ	⊺)θ	NUM
ejpam-6413	292	16	−	−	NOUN
ejpam-6413	292	17	⊺θ	⊺θ	PROPN
ejpam-6413	292	18	∣∣∣⋋1	∣∣∣⋋1	PROPN
ejpam-6413	292	19	)	)	PUNCT
ejpam-6413	292	20	1	1	NUM
ejpam-6413	292	21	⋋1	⋋1	NUM
ejpam-6413	292	22	≤	≤	NOUN
ejpam-6413	292	23	(	(	PUNCT
ejpam-6413	292	24	µ−	µ−	PROPN
ejpam-6413	292	25	ā)2	ā)2	VERB
ejpam-6413	292	26	2(θ	2(θ	NUM
ejpam-6413	292	27	+	+	CCONJ
ejpam-6413	292	28	1	1	X
ejpam-6413	292	29	)	)	PUNCT
ejpam-6413	292	30	(	(	PUNCT
ejpam-6413	292	31	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	293	1	+	+	X
ejpam-6413	293	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	293	3	α+	α+	PUNCT
ejpam-6413	293	4	1	1	NUM
ejpam-6413	293	5	)	)	SYM
ejpam-6413	293	6	1	1	NUM
ejpam-6413	293	7	⋋2	⋋2	NOUN
ejpam-6413	293	8	(	(	PUNCT
ejpam-6413	293	9	∫	∫	PROPN
ejpam-6413	293	10	1	1	NUM
ejpam-6413	293	11	0	0	NUM
ejpam-6413	294	1	[	[	X
ejpam-6413	294	2	(	(	PUNCT
ejpam-6413	294	3	1−	1−	NUM
ejpam-6413	294	4	⊺)θ	⊺)θ	NUM
ejpam-6413	294	5	+	+	CCONJ
ejpam-6413	294	6	⊺θ	⊺θ	PROPN
ejpam-6413	294	7	−	−	NUM
ejpam-6413	294	8	1]⋋1	1]⋋1	NUM
ejpam-6413	294	9	)	)	PUNCT
ejpam-6413	294	10	1	1	NUM
ejpam-6413	294	11	⋋1	⋋1	NUM
ejpam-6413	294	12	≤	≤	NOUN
ejpam-6413	294	13	(	(	PUNCT
ejpam-6413	294	14	µ−	µ−	PROPN
ejpam-6413	294	15	ā)2(21−θ	ā)2(21−θ	NOUN
ejpam-6413	294	16	−	−	PROPN
ejpam-6413	294	17	1	1	NUM
ejpam-6413	294	18	)	)	PUNCT
ejpam-6413	294	19	2(θ	2(θ	NUM
ejpam-6413	295	1	+	+	CCONJ
ejpam-6413	295	2	1	1	X
ejpam-6413	295	3	)	)	PUNCT
ejpam-6413	295	4	(	(	PUNCT
ejpam-6413	295	5	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	296	1	+	+	X
ejpam-6413	296	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	296	3	α+	α+	PUNCT
ejpam-6413	296	4	1	1	NUM
ejpam-6413	296	5	)	)	PUNCT
ejpam-6413	296	6	1	1	NUM
ejpam-6413	296	7	⋋2	⋋2	NOUN
ejpam-6413	296	8	,	,	PUNCT
ejpam-6413	296	9	(	(	PUNCT
ejpam-6413	296	10	26	26	NUM
ejpam-6413	296	11	)	)	PUNCT
ejpam-6413	297	1	where	where	SCONJ
ejpam-6413	297	2	1	1	NUM
ejpam-6413	297	3	⋋1	⋋1	NUM
ejpam-6413	297	4	+	+	SYM
ejpam-6413	297	5	1	1	NUM
ejpam-6413	297	6	⋋2	⋋2	NOUN
ejpam-6413	297	7	=	=	SYM
ejpam-6413	297	8	1	1	X
ejpam-6413	297	9	.	.	PUNCT
ejpam-6413	297	10	case(ii	case(ii	ADJ
ejpam-6413	297	11	):	):	PUNCT
ejpam-6413	297	12	let	let	VERB
ejpam-6413	297	13	θ	θ	PROPN
ejpam-6413	297	14	∈	∈	PROPN
ejpam-6413	298	1	[	[	X
ejpam-6413	298	2	1,+∞	1,+∞	NUM
ejpam-6413	298	3	)	)	PUNCT
ejpam-6413	298	4	.	.	PUNCT
ejpam-6413	299	1	by	by	ADP
ejpam-6413	299	2	utilizing	utilize	VERB
ejpam-6413	299	3	lemma	lemma	PROPN
ejpam-6413	299	4	1	1	NUM
ejpam-6413	299	5	,	,	PUNCT
ejpam-6413	299	6	2	2	NUM
ejpam-6413	299	7	,	,	PUNCT
ejpam-6413	299	8	3	3	NUM
ejpam-6413	299	9	,	,	PUNCT
ejpam-6413	299	10	7	7	NUM
ejpam-6413	299	11	and	and	CCONJ
ejpam-6413	299	12	applying	apply	VERB
ejpam-6413	299	13	hölder	hölder	NOUN
ejpam-6413	299	14	’s	’s	PART
ejpam-6413	299	15	inequality	inequality	NOUN
ejpam-6413	299	16	,	,	PUNCT
ejpam-6413	299	17	we	we	PRON
ejpam-6413	299	18	have	have	VERB
ejpam-6413	299	19	∣∣∣∣𭟋(ā	∣∣∣∣𭟋(ā	VERB
ejpam-6413	299	20	)	)	PUNCT
ejpam-6413	299	21	+	+	NOUN
ejpam-6413	299	22	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	299	23	)	)	PUNCT
ejpam-6413	299	24	2	2	NUM
ejpam-6413	299	25	−	−	NOUN
ejpam-6413	299	26	γ(θ	γ(θ	PROPN
ejpam-6413	300	1	+	+	CCONJ
ejpam-6413	300	2	1	1	X
ejpam-6413	300	3	)	)	PUNCT
ejpam-6413	300	4	2(µ−	2(µ−	NUM
ejpam-6413	300	5	ā)θ	ā)θ	NOUN
ejpam-6413	300	6	[	[	PUNCT
ejpam-6413	300	7	χθ	χθ	X
ejpam-6413	300	8	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	300	9	)	)	PUNCT
ejpam-6413	301	1	+	+	CCONJ
ejpam-6413	301	2	χθ	χθ	X
ejpam-6413	301	3	b̄−𭟋(ā	b̄−𭟋(ā	NOUN
ejpam-6413	301	4	)	)	PUNCT
ejpam-6413	302	1	]	]	PUNCT
ejpam-6413	302	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	302	3	≤	≤	NOUN
ejpam-6413	302	4	(	(	PUNCT
ejpam-6413	302	5	µ−	µ−	PROPN
ejpam-6413	302	6	ā)2	ā)2	VERB
ejpam-6413	302	7	2(θ	2(θ	NUM
ejpam-6413	302	8	+	+	CCONJ
ejpam-6413	302	9	1	1	X
ejpam-6413	302	10	)	)	PUNCT
ejpam-6413	302	11	(	(	PUNCT
ejpam-6413	302	12	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	303	1	+	+	X
ejpam-6413	303	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	303	3	α+	α+	PUNCT
ejpam-6413	303	4	1	1	NUM
ejpam-6413	303	5	)	)	SYM
ejpam-6413	303	6	1	1	NUM
ejpam-6413	303	7	⋋2	⋋2	NOUN
ejpam-6413	303	8	(	(	PUNCT
ejpam-6413	303	9	∫	∫	PROPN
ejpam-6413	303	10	1	1	NUM
ejpam-6413	303	11	0	0	NUM
ejpam-6413	304	1	[	[	X
ejpam-6413	304	2	1−	1−	NUM
ejpam-6413	304	3	(	(	PUNCT
ejpam-6413	304	4	1−	1−	NUM
ejpam-6413	304	5	⊺)θ	⊺)θ	NUM
ejpam-6413	304	6	−	−	NOUN
ejpam-6413	304	7	⊺θ]⋋1d⊺	⊺θ]⋋1d⊺	NOUN
ejpam-6413	304	8	)	)	PUNCT
ejpam-6413	304	9	1	1	NUM
ejpam-6413	304	10	⋋1	⋋1	NUM
ejpam-6413	304	11	m.	m.	NOUN
ejpam-6413	304	12	samraiz	samraiz	PROPN
ejpam-6413	304	13	et	et	PROPN
ejpam-6413	304	14	al	al	PROPN
ejpam-6413	304	15	.	.	PUNCT
ejpam-6413	304	16	/	/	SYM
ejpam-6413	304	17	eur	eur	PROPN
ejpam-6413	304	18	.	.	PUNCT
ejpam-6413	305	1	j.	j.	PROPN
ejpam-6413	305	2	pure	pure	PROPN
ejpam-6413	305	3	appl	appl	PROPN
ejpam-6413	305	4	.	.	PROPN
ejpam-6413	305	5	math	math	PROPN
ejpam-6413	305	6	,	,	PUNCT
ejpam-6413	305	7	18	18	NUM
ejpam-6413	305	8	(	(	PUNCT
ejpam-6413	305	9	3	3	NUM
ejpam-6413	305	10	)	)	PUNCT
ejpam-6413	305	11	(	(	PUNCT
ejpam-6413	305	12	2025	2025	NUM
ejpam-6413	305	13	)	)	PUNCT
ejpam-6413	305	14	,	,	PUNCT
ejpam-6413	305	15	6413	6413	NUM
ejpam-6413	305	16	14	14	NUM
ejpam-6413	305	17	of	of	ADP
ejpam-6413	305	18	26	26	NUM
ejpam-6413	305	19	≤	≤	NOUN
ejpam-6413	305	20	(	(	PUNCT
ejpam-6413	305	21	µ−	µ−	PROPN
ejpam-6413	305	22	ā)2(1−	ā)2(1−	PROPN
ejpam-6413	305	23	21−θ	21−θ	NUM
ejpam-6413	305	24	)	)	PUNCT
ejpam-6413	305	25	2(θ	2(θ	NUM
ejpam-6413	306	1	+	+	CCONJ
ejpam-6413	306	2	1	1	X
ejpam-6413	306	3	)	)	PUNCT
ejpam-6413	306	4	(	(	PUNCT
ejpam-6413	306	5	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	307	1	+	+	X
ejpam-6413	307	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	307	3	α+	α+	PUNCT
ejpam-6413	307	4	1	1	NUM
ejpam-6413	307	5	)	)	PUNCT
ejpam-6413	307	6	1	1	NUM
ejpam-6413	307	7	⋋2	⋋2	NOUN
ejpam-6413	307	8	.	.	PUNCT
ejpam-6413	308	1	(	(	PUNCT
ejpam-6413	308	2	27	27	NUM
ejpam-6413	308	3	)	)	PUNCT
ejpam-6413	308	4	from	from	ADP
ejpam-6413	308	5	(	(	PUNCT
ejpam-6413	308	6	26	26	NUM
ejpam-6413	308	7	)	)	PUNCT
ejpam-6413	308	8	and	and	CCONJ
ejpam-6413	308	9	(	(	PUNCT
ejpam-6413	308	10	27	27	NUM
ejpam-6413	308	11	)	)	PUNCT
ejpam-6413	308	12	,	,	PUNCT
ejpam-6413	308	13	we	we	PRON
ejpam-6413	308	14	have	have	AUX
ejpam-6413	308	15	obtained	obtain	VERB
ejpam-6413	308	16	the	the	DET
ejpam-6413	308	17	required	require	VERB
ejpam-6413	308	18	result	result	NOUN
ejpam-6413	308	19	.	.	PUNCT
ejpam-6413	309	1	remark	remark	NOUN
ejpam-6413	309	2	5	5	NUM
ejpam-6413	309	3	.	.	PUNCT
ejpam-6413	310	1	in	in	ADP
ejpam-6413	310	2	accordance	accordance	NOUN
ejpam-6413	310	3	with	with	ADP
ejpam-6413	310	4	the	the	DET
ejpam-6413	310	5	selection	selection	NOUN
ejpam-6413	310	6	of	of	ADP
ejpam-6413	310	7	parameters	parameter	NOUN
ejpam-6413	310	8	α	α	X
ejpam-6413	310	9	=	=	SYM
ejpam-6413	310	10	1	1	NUM
ejpam-6413	310	11	and	and	CCONJ
ejpam-6413	310	12	m	m	VERB
ejpam-6413	310	13	=	=	ADJ
ejpam-6413	310	14	1	1	NUM
ejpam-6413	310	15	in	in	ADP
ejpam-6413	310	16	theorem	theorem	NOUN
ejpam-6413	310	17	2	2	NUM
ejpam-6413	310	18	and	and	CCONJ
ejpam-6413	310	19	s	s	NOUN
ejpam-6413	310	20	=	=	SYM
ejpam-6413	310	21	1	1	NUM
ejpam-6413	310	22	in	in	ADP
ejpam-6413	310	23	[	[	PUNCT
ejpam-6413	310	24	2	2	NUM
ejpam-6413	310	25	,	,	PUNCT
ejpam-6413	310	26	theorem	theorem	VERB
ejpam-6413	310	27	3.2	3.2	NUM
ejpam-6413	310	28	]	]	PUNCT
ejpam-6413	310	29	,	,	PUNCT
ejpam-6413	310	30	we	we	PRON
ejpam-6413	310	31	get∣∣∣∣𭟋(ā	get∣∣∣∣𭟋(ā	X
ejpam-6413	310	32	)	)	PUNCT
ejpam-6413	311	1	+	+	NOUN
ejpam-6413	311	2	𭟋(b̄	𭟋(b̄	NOUN
ejpam-6413	311	3	)	)	PUNCT
ejpam-6413	311	4	2	2	NUM
ejpam-6413	311	5	−	−	NOUN
ejpam-6413	311	6	γ(θ	γ(θ	PROPN
ejpam-6413	311	7	+	+	CCONJ
ejpam-6413	311	8	1	1	X
ejpam-6413	311	9	)	)	PUNCT
ejpam-6413	311	10	2(b̄−	2(b̄−	NUM
ejpam-6413	311	11	ā)θ	ā)θ	NOUN
ejpam-6413	311	12	[	[	PUNCT
ejpam-6413	311	13	χθ	χθ	X
ejpam-6413	311	14	ā+𭟋(b̄	ā+𭟋(b̄	NUM
ejpam-6413	311	15	)	)	PUNCT
ejpam-6413	312	1	+	+	CCONJ
ejpam-6413	312	2	χθ	χθ	X
ejpam-6413	312	3	b̄−𭟋(ā	b̄−𭟋(ā	NOUN
ejpam-6413	312	4	)	)	PUNCT
ejpam-6413	313	1	]	]	PUNCT
ejpam-6413	313	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	313	3	≤	≤	NOUN
ejpam-6413	313	4	(	(	PUNCT
ejpam-6413	313	5	b̄−	b̄−	ADJ
ejpam-6413	313	6	ā)2max(1−	ā)2max(1−	PUNCT
ejpam-6413	313	7	21−θ	21−θ	NUM
ejpam-6413	313	8	,	,	PUNCT
ejpam-6413	313	9	21−θ	21−θ	NUM
ejpam-6413	313	10	−	−	NOUN
ejpam-6413	313	11	1	1	NUM
ejpam-6413	313	12	)	)	PUNCT
ejpam-6413	313	13	2(θ	2(θ	NUM
ejpam-6413	314	1	+	+	CCONJ
ejpam-6413	314	2	1	1	X
ejpam-6413	314	3	)	)	PUNCT
ejpam-6413	314	4	(	(	PUNCT
ejpam-6413	314	5	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	PROPN
ejpam-6413	314	6	+	+	CCONJ
ejpam-6413	314	7	|𭟋′′(b̄)|⋋2	|𭟋′′(b̄)|⋋2	NUM
ejpam-6413	314	8	2	2	NUM
ejpam-6413	314	9	)	)	PUNCT
ejpam-6413	314	10	1	1	NUM
ejpam-6413	314	11	⋋2	⋋2	NOUN
ejpam-6413	314	12	.	.	PUNCT
ejpam-6413	315	1	the	the	DET
ejpam-6413	315	2	following	follow	VERB
ejpam-6413	315	3	main	main	ADJ
ejpam-6413	315	4	result	result	NOUN
ejpam-6413	315	5	is	be	AUX
ejpam-6413	315	6	based	base	VERB
ejpam-6413	315	7	on	on	ADP
ejpam-6413	315	8	utilization	utilization	NOUN
ejpam-6413	315	9	of	of	ADP
ejpam-6413	315	10	lemma	lemma	PROPN
ejpam-6413	315	11	5	5	NUM
ejpam-6413	315	12	.	.	PUNCT
ejpam-6413	315	13	theorem	theorem	NOUN
ejpam-6413	315	14	3	3	X
ejpam-6413	315	15	.	.	PUNCT
ejpam-6413	316	1	let	let	VERB
ejpam-6413	316	2	𭟋	𭟋	VERB
ejpam-6413	316	3	:	:	PUNCT
ejpam-6413	316	4	[	[	X
ejpam-6413	316	5	ā	ā	X
ejpam-6413	316	6	,	,	PUNCT
ejpam-6413	316	7	b̄	b̄	PROPN
ejpam-6413	316	8	]	]	PUNCT
ejpam-6413	316	9	−→	−→	NOUN
ejpam-6413	316	10	r	r	NOUN
ejpam-6413	316	11	be	be	VERB
ejpam-6413	316	12	a	a	DET
ejpam-6413	316	13	twice	twice	ADV
ejpam-6413	316	14	differentiable	differentiable	ADJ
ejpam-6413	316	15	function	function	NOUN
ejpam-6413	316	16	such	such	ADJ
ejpam-6413	316	17	that	that	DET
ejpam-6413	316	18	|𭟋′′|	|𭟋′′|	PROPN
ejpam-6413	316	19	is	be	AUX
ejpam-6413	316	20	lebesgue	lebesgue	NOUN
ejpam-6413	316	21	integerable	integerable	ADJ
ejpam-6413	316	22	,	,	PUNCT
ejpam-6413	316	23	increasing	increase	VERB
ejpam-6413	316	24	and	and	CCONJ
ejpam-6413	316	25	ga	ga	PROPN
ejpam-6413	316	26	(	(	PUNCT
ejpam-6413	316	27	α	α	NOUN
ejpam-6413	316	28	,	,	PUNCT
ejpam-6413	316	29	m)-convex	m)-convex	PUNCT
ejpam-6413	316	30	function	function	VERB
ejpam-6413	316	31	on	on	ADP
ejpam-6413	316	32	[	[	X
ejpam-6413	316	33	ā	ā	X
ejpam-6413	316	34	,	,	PUNCT
ejpam-6413	316	35	b̄	b̄	PROPN
ejpam-6413	316	36	]	]	PUNCT
ejpam-6413	316	37	.	.	PUNCT
ejpam-6413	317	1	then	then	ADV
ejpam-6413	317	2	for	for	ADP
ejpam-6413	317	3	given	give	VERB
ejpam-6413	317	4	parameters	parameter	NOUN
ejpam-6413	317	5	θ	θ	PROPN
ejpam-6413	317	6	∈	∈	PROPN
ejpam-6413	317	7	(	(	PUNCT
ejpam-6413	317	8	0,+∞	0,+∞	NUM
ejpam-6413	317	9	)	)	PUNCT
ejpam-6413	317	10	and	and	CCONJ
ejpam-6413	317	11	(	(	PUNCT
ejpam-6413	317	12	α	α	NOUN
ejpam-6413	317	13	,	,	PUNCT
ejpam-6413	317	14	m	m	NOUN
ejpam-6413	317	15	)	)	PUNCT
ejpam-6413	317	16	∈	∈	PROPN
ejpam-6413	317	17	(	(	PUNCT
ejpam-6413	317	18	0	0	NUM
ejpam-6413	317	19	,	,	PUNCT
ejpam-6413	317	20	1]2	1]2	NUM
ejpam-6413	317	21	,	,	PUNCT
ejpam-6413	317	22	where	where	SCONJ
ejpam-6413	317	23	0	0	NUM
ejpam-6413	317	24	≤	≤	NUM
ejpam-6413	317	25	ā	ā	NOUN
ejpam-6413	317	26	<	<	X
ejpam-6413	317	27	b̄	b̄	VERB
ejpam-6413	317	28	the	the	DET
ejpam-6413	317	29	following	follow	VERB
ejpam-6413	317	30	inequality∣∣∣∣	inequality∣∣∣∣	PROPN
ejpam-6413	317	31	γ(θ	γ(θ	PROPN
ejpam-6413	318	1	+	+	CCONJ
ejpam-6413	319	1	1	1	X
ejpam-6413	319	2	)	)	PUNCT
ejpam-6413	319	3	2(b̄−	2(b̄−	NUM
ejpam-6413	319	4	ā)θ	ā)θ	NOUN
ejpam-6413	319	5	[	[	PUNCT
ejpam-6413	319	6	χθ	χθ	X
ejpam-6413	319	7	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	319	8	)	)	PUNCT
ejpam-6413	320	1	+	+	CCONJ
ejpam-6413	320	2	χθ	χθ	X
ejpam-6413	320	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	320	4	)	)	PUNCT
ejpam-6413	320	5	]	]	PUNCT
ejpam-6413	321	1	−𭟋	−𭟋	INTJ
ejpam-6413	321	2	(	(	PUNCT
ejpam-6413	321	3	ā+	ā+	PUNCT
ejpam-6413	321	4	µ	µ	X
ejpam-6413	321	5	2	2	NUM
ejpam-6413	321	6	)	)	PUNCT
ejpam-6413	321	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	321	8	≤	≤	NOUN
ejpam-6413	321	9	(	(	PUNCT
ejpam-6413	321	10	µ−	µ−	PROPN
ejpam-6413	321	11	ā)2	ā)2	VERB
ejpam-6413	321	12	2(θ	2(θ	NUM
ejpam-6413	321	13	+	+	CCONJ
ejpam-6413	321	14	1	1	X
ejpam-6413	321	15	)	)	PUNCT
ejpam-6413	321	16	[	[	PUNCT
ejpam-6413	321	17	|𭟋′′(ā)|	|𭟋′′(ā)|	PROPN
ejpam-6413	321	18	(	(	PUNCT
ejpam-6413	321	19	θ	θ	NOUN
ejpam-6413	321	20	−	−	PROPN
ejpam-6413	322	1	θ2−α−1	θ2−α−1	PROPN
ejpam-6413	322	2	−	−	PROPN
ejpam-6413	322	3	2−α−1	2−α−1	NUM
ejpam-6413	322	4	α+	α+	PUNCT
ejpam-6413	322	5	1	1	NUM
ejpam-6413	322	6	−	−	NUM
ejpam-6413	322	7	θ	θ	NOUN
ejpam-6413	323	1	+	+	CCONJ
ejpam-6413	323	2	1	1	NUM
ejpam-6413	323	3	α+	α+	SYM
ejpam-6413	323	4	2	2	NUM
ejpam-6413	323	5	+	+	SYM
ejpam-6413	323	6	1	1	NUM
ejpam-6413	323	7	θ	θ	NOUN
ejpam-6413	323	8	+	+	PUNCT
ejpam-6413	323	9	α+	α+	PUNCT
ejpam-6413	323	10	2	2	NUM
ejpam-6413	323	11	+	+	NUM
ejpam-6413	323	12	2b0.5(θ	2b0.5(θ	NUM
ejpam-6413	323	13	+	+	CCONJ
ejpam-6413	323	14	2	2	NUM
ejpam-6413	323	15	,	,	PUNCT
ejpam-6413	323	16	α+	α+	DET
ejpam-6413	323	17	1	1	NUM
ejpam-6413	323	18	)	)	PUNCT
ejpam-6413	323	19	)	)	PUNCT
ejpam-6413	324	1	+	+	PUNCT
ejpam-6413	324	2	m|𭟋′′(b̄)|	m|𭟋′′(b̄)|	PROPN
ejpam-6413	324	3	(	(	PUNCT
ejpam-6413	324	4	θ	θ	NOUN
ejpam-6413	324	5	−	−	PROPN
ejpam-6413	324	6	3	3	NUM
ejpam-6413	324	7	4	4	NUM
ejpam-6413	324	8	+	+	SYM
ejpam-6413	324	9	1	1	NUM
ejpam-6413	324	10	θ	θ	NOUN
ejpam-6413	324	11	+	+	NOUN
ejpam-6413	324	12	2	2	NUM
ejpam-6413	324	13	−	−	NUM
ejpam-6413	324	14	θ	θ	NOUN
ejpam-6413	324	15	−	−	PROPN
ejpam-6413	325	1	θ2−α−1	θ2−α−1	PROPN
ejpam-6413	325	2	−	−	PROPN
ejpam-6413	325	3	2−α−1	2−α−1	NUM
ejpam-6413	325	4	α+	α+	PUNCT
ejpam-6413	325	5	1	1	NUM
ejpam-6413	325	6	−	−	NUM
ejpam-6413	325	7	θ	θ	NOUN
ejpam-6413	325	8	+	+	PROPN
ejpam-6413	325	9	1(1−	1(1−	NUM
ejpam-6413	325	10	2−α	2−α	NUM
ejpam-6413	325	11	)	)	PUNCT
ejpam-6413	325	12	α+	α+	PUNCT
ejpam-6413	325	13	2	2	NUM
ejpam-6413	325	14	−	−	NUM
ejpam-6413	325	15	1	1	NUM
ejpam-6413	325	16	θ	θ	NOUN
ejpam-6413	325	17	+	+	PUNCT
ejpam-6413	325	18	α+	α+	PUNCT
ejpam-6413	325	19	2	2	NUM
ejpam-6413	325	20	−	−	NOUN
ejpam-6413	325	21	2b0.5(α+	2b0.5(α+	NUM
ejpam-6413	325	22	1	1	NUM
ejpam-6413	325	23	,	,	PUNCT
ejpam-6413	325	24	θ	θ	PROPN
ejpam-6413	325	25	+	+	PROPN
ejpam-6413	325	26	2	2	NUM
ejpam-6413	325	27	)	)	PUNCT
ejpam-6413	325	28	)	)	PUNCT
ejpam-6413	325	29	]	]	PUNCT
ejpam-6413	325	30	holds	hold	VERB
ejpam-6413	325	31	true	true	ADJ
ejpam-6413	325	32	.	.	PUNCT
ejpam-6413	326	1	proof	proof	NOUN
ejpam-6413	326	2	.	.	PUNCT
ejpam-6413	327	1	by	by	ADP
ejpam-6413	327	2	using	use	VERB
ejpam-6413	327	3	lemma	lemma	PROPN
ejpam-6413	327	4	2	2	NUM
ejpam-6413	327	5	,	,	PUNCT
ejpam-6413	327	6	5	5	NUM
ejpam-6413	327	7	and	and	CCONJ
ejpam-6413	327	8	7	7	NUM
ejpam-6413	327	9	we	we	PRON
ejpam-6413	327	10	have∣∣∣∣	have∣∣∣∣	VERB
ejpam-6413	327	11	γ(θ	γ(θ	PROPN
ejpam-6413	327	12	+	+	PROPN
ejpam-6413	327	13	1	1	X
ejpam-6413	327	14	)	)	PUNCT
ejpam-6413	327	15	2(µ−	2(µ−	NUM
ejpam-6413	327	16	ā)θ	ā)θ	NOUN
ejpam-6413	327	17	[	[	X
ejpam-6413	327	18	χθ	χθ	X
ejpam-6413	327	19	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	327	20	)	)	PUNCT
ejpam-6413	328	1	+	+	CCONJ
ejpam-6413	328	2	χθ	χθ	X
ejpam-6413	328	3	µ−𭟋(ā)]−𭟋	µ−𭟋(ā)]−𭟋	NOUN
ejpam-6413	328	4	(	(	PUNCT
ejpam-6413	328	5	ā+	ā+	PUNCT
ejpam-6413	328	6	µ	µ	X
ejpam-6413	328	7	2	2	NUM
ejpam-6413	328	8	)	)	PUNCT
ejpam-6413	328	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	328	10	≤	≤	NOUN
ejpam-6413	328	11	(	(	PUNCT
ejpam-6413	328	12	µ−	µ−	PROPN
ejpam-6413	328	13	ā)2	ā)2	NOUN
ejpam-6413	328	14	2	2	NUM
ejpam-6413	328	15	∫	∫	NOUN
ejpam-6413	328	16	1	1	NUM
ejpam-6413	328	17	0	0	X
ejpam-6413	328	18	|p0(⊺)||𭟋′′(⊺ā+m(1−	|p0(⊺)||𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	328	19	⊺)b̄)|d⊺	⊺)b̄)|d⊺	NOUN
ejpam-6413	328	20	≤	≤	NOUN
ejpam-6413	328	21	(	(	PUNCT
ejpam-6413	328	22	µ−	µ−	PROPN
ejpam-6413	328	23	ā)2	ā)2	NOUN
ejpam-6413	328	24	2	2	NUM
ejpam-6413	328	25	∫	∫	NOUN
ejpam-6413	328	26	1	1	NUM
ejpam-6413	328	27	0	0	NUM
ejpam-6413	328	28	|p0(⊺)||𭟋′′(ā⊺b̄m(1−⊺)|d⊺	|p0(⊺)||𭟋′′(ā⊺b̄m(1−⊺)|d⊺	NUM
ejpam-6413	328	29	≤	≤	NOUN
ejpam-6413	328	30	(	(	PUNCT
ejpam-6413	328	31	µ−	µ−	PROPN
ejpam-6413	328	32	ā)2	ā)2	NOUN
ejpam-6413	328	33	2	2	NUM
ejpam-6413	328	34	∫	∫	NOUN
ejpam-6413	328	35	1	1	NUM
ejpam-6413	328	36	0	0	NUM
ejpam-6413	328	37	|p0(⊺)|(⊺α|𭟋′′(ā)|+m(1−	|p0(⊺)|(⊺α|𭟋′′(ā)|+m(1−	PROPN
ejpam-6413	328	38	⊺α)|𭟋′′(b̄)|)d⊺	⊺α)|𭟋′′(b̄)|)d⊺	PROPN
ejpam-6413	328	39	m.	m.	NOUN
ejpam-6413	328	40	samraiz	samraiz	PROPN
ejpam-6413	328	41	et	et	PROPN
ejpam-6413	328	42	al	al	PROPN
ejpam-6413	328	43	.	.	PUNCT
ejpam-6413	328	44	/	/	SYM
ejpam-6413	328	45	eur	eur	PROPN
ejpam-6413	328	46	.	.	PUNCT
ejpam-6413	329	1	j.	j.	PROPN
ejpam-6413	329	2	pure	pure	PROPN
ejpam-6413	329	3	appl	appl	PROPN
ejpam-6413	329	4	.	.	PROPN
ejpam-6413	329	5	math	math	PROPN
ejpam-6413	329	6	,	,	PUNCT
ejpam-6413	329	7	18	18	NUM
ejpam-6413	329	8	(	(	PUNCT
ejpam-6413	329	9	3	3	NUM
ejpam-6413	329	10	)	)	PUNCT
ejpam-6413	329	11	(	(	PUNCT
ejpam-6413	329	12	2025	2025	NUM
ejpam-6413	329	13	)	)	PUNCT
ejpam-6413	329	14	,	,	PUNCT
ejpam-6413	329	15	6413	6413	NUM
ejpam-6413	329	16	15	15	NUM
ejpam-6413	329	17	of	of	ADP
ejpam-6413	329	18	26	26	NUM
ejpam-6413	329	19	≤	≤	NOUN
ejpam-6413	329	20	(	(	PUNCT
ejpam-6413	329	21	µ−	µ−	NOUN
ejpam-6413	329	22	ā)2	ā)2	VERB
ejpam-6413	329	23	2	2	NUM
ejpam-6413	330	1	[	[	X
ejpam-6413	330	2	∫	∫	PROPN
ejpam-6413	330	3	1	1	NUM
ejpam-6413	330	4	2	2	NUM
ejpam-6413	330	5	0	0	NUM
ejpam-6413	330	6	∣∣∣∣⊺−	∣∣∣∣⊺−	NOUN
ejpam-6413	330	7	1−	1−	NUM
ejpam-6413	330	8	(	(	PUNCT
ejpam-6413	330	9	1−	1−	NUM
ejpam-6413	330	10	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	330	11	−	−	PROPN
ejpam-6413	330	12	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	330	13	θ	θ	PROPN
ejpam-6413	330	14	+	+	CCONJ
ejpam-6413	330	15	1	1	NUM
ejpam-6413	330	16	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	330	17	×	×	NOUN
ejpam-6413	330	18	(	(	PUNCT
ejpam-6413	330	19	⊺α|𭟋′′(ā)|+m(1−	⊺α|𭟋′′(ā)|+m(1−	NOUN
ejpam-6413	330	20	⊺α)|𭟋′′(b̄)|	⊺α)|𭟋′′(b̄)|	PROPN
ejpam-6413	330	21	)	)	PUNCT
ejpam-6413	331	1	d⊺	d⊺	PROPN
ejpam-6413	331	2	+	+	CCONJ
ejpam-6413	331	3	∫	∫	PROPN
ejpam-6413	331	4	1	1	NUM
ejpam-6413	331	5	1	1	NUM
ejpam-6413	331	6	2	2	NUM
ejpam-6413	331	7	∣∣∣∣1−	∣∣∣∣1−	NUM
ejpam-6413	331	8	⊺−	⊺−	PROPN
ejpam-6413	331	9	1−	1−	NUM
ejpam-6413	331	10	(	(	PUNCT
ejpam-6413	331	11	1−	1−	NUM
ejpam-6413	331	12	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	331	13	−	−	PROPN
ejpam-6413	331	14	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	331	15	θ	θ	PROPN
ejpam-6413	331	16	+	+	CCONJ
ejpam-6413	331	17	1	1	NUM
ejpam-6413	331	18	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	331	19	(	(	PUNCT
ejpam-6413	331	20	⊺α|𭟋′′(ā)|+m(1−	⊺α|𭟋′′(ā)|+m(1−	NOUN
ejpam-6413	331	21	⊺α)|𭟋′′(b̄)|)d⊺	⊺α)|𭟋′′(b̄)|)d⊺	NOUN
ejpam-6413	331	22	]	]	PUNCT
ejpam-6413	331	23	≤	≤	NUM
ejpam-6413	331	24	(	(	PUNCT
ejpam-6413	331	25	µ−	µ−	PROPN
ejpam-6413	331	26	ā)2	ā)2	VERB
ejpam-6413	331	27	2(θ	2(θ	NUM
ejpam-6413	331	28	+	+	CCONJ
ejpam-6413	331	29	1	1	X
ejpam-6413	331	30	)	)	PUNCT
ejpam-6413	332	1	[	[	X
ejpam-6413	332	2	∫	∫	X
ejpam-6413	332	3	1	1	NUM
ejpam-6413	332	4	2	2	NUM
ejpam-6413	332	5	0	0	NUM
ejpam-6413	332	6	∣∣∣⊺(θ	∣∣∣⊺(θ	NOUN
ejpam-6413	332	7	+	+	X
ejpam-6413	333	1	1)−	1)−	NUM
ejpam-6413	333	2	1	1	NUM
ejpam-6413	333	3	+	+	CCONJ
ejpam-6413	333	4	(	(	PUNCT
ejpam-6413	333	5	1−	1−	NUM
ejpam-6413	333	6	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	333	7	+	+	CCONJ
ejpam-6413	333	8	⊺θ+1	⊺θ+1	ADJ
ejpam-6413	333	9	∣∣∣	∣∣∣	ADJ
ejpam-6413	333	10	×(⊺α|𭟋′′(ā)|+m(1−	×(⊺α|𭟋′′(ā)|+m(1−	NOUN
ejpam-6413	333	11	⊺α)|𭟋′′(b̄)|)d⊺	⊺α)|𭟋′′(b̄)|)d⊺	PROPN
ejpam-6413	333	12	+	+	CCONJ
ejpam-6413	333	13	∫	∫	PROPN
ejpam-6413	333	14	1	1	NUM
ejpam-6413	333	15	1	1	NUM
ejpam-6413	333	16	2	2	NUM
ejpam-6413	333	17	∣∣∣θ	∣∣∣θ	NOUN
ejpam-6413	333	18	−	−	NOUN
ejpam-6413	333	19	⊺(θ	⊺(θ	NOUN
ejpam-6413	333	20	+	+	CCONJ
ejpam-6413	333	21	1	1	NUM
ejpam-6413	333	22	)	)	PUNCT
ejpam-6413	333	23	+	+	CCONJ
ejpam-6413	333	24	(	(	PUNCT
ejpam-6413	333	25	1−	1−	NUM
ejpam-6413	333	26	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	333	27	+	+	CCONJ
ejpam-6413	333	28	⊺θ+1	⊺θ+1	ADJ
ejpam-6413	333	29	∣∣∣	∣∣∣	ADJ
ejpam-6413	333	30	(	(	PUNCT
ejpam-6413	333	31	⊺α|𭟋′′(ā)|+m(1−	⊺α|𭟋′′(ā)|+m(1−	NOUN
ejpam-6413	333	32	⊺α)|𭟋′′(b̄)|)d⊺	⊺α)|𭟋′′(b̄)|)d⊺	NOUN
ejpam-6413	333	33	]	]	PUNCT
ejpam-6413	333	34	.	.	PUNCT
ejpam-6413	334	1	(	(	PUNCT
ejpam-6413	334	2	28	28	NUM
ejpam-6413	334	3	)	)	PUNCT
ejpam-6413	334	4	consider∫	consider∫	NOUN
ejpam-6413	334	5	1	1	NUM
ejpam-6413	334	6	2	2	NUM
ejpam-6413	334	7	0	0	NUM
ejpam-6413	334	8	∣∣∣⊺(θ	∣∣∣⊺(θ	NOUN
ejpam-6413	334	9	+	+	X
ejpam-6413	335	1	1)−	1)−	NUM
ejpam-6413	335	2	1	1	NUM
ejpam-6413	335	3	+	+	CCONJ
ejpam-6413	335	4	(	(	PUNCT
ejpam-6413	335	5	1−	1−	NUM
ejpam-6413	335	6	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	335	7	+	+	CCONJ
ejpam-6413	335	8	⊺θ+1	⊺θ+1	ADJ
ejpam-6413	335	9	∣∣∣	∣∣∣	ADJ
ejpam-6413	335	10	(	(	PUNCT
ejpam-6413	335	11	⊺α|𭟋′′(ā)|+m(1−	⊺α|𭟋′′(ā)|+m(1−	ADJ
ejpam-6413	335	12	⊺α)|𭟋′′(µ)|)d⊺	⊺α)|𭟋′′(µ)|)d⊺	ADJ
ejpam-6413	335	13	≤	≤	NOUN
ejpam-6413	335	14	|𭟋′′(ā)|	|𭟋′′(ā)|	PUNCT
ejpam-6413	336	1	(	(	PUNCT
ejpam-6413	336	2	(	(	PUNCT
ejpam-6413	336	3	θ	θ	NOUN
ejpam-6413	336	4	+	+	NOUN
ejpam-6413	336	5	1	1	NUM
ejpam-6413	336	6	)	)	PUNCT
ejpam-6413	336	7	(	(	PUNCT
ejpam-6413	336	8	12	12	NUM
ejpam-6413	336	9	)	)	PUNCT
ejpam-6413	336	10	α+2	α+2	NUM
ejpam-6413	336	11	α+	α+	PUNCT
ejpam-6413	336	12	2	2	NUM
ejpam-6413	336	13	−	−	NOUN
ejpam-6413	336	14	(	(	PUNCT
ejpam-6413	336	15	12	12	NUM
ejpam-6413	336	16	)	)	PUNCT
ejpam-6413	336	17	α+1	α+1	NUM
ejpam-6413	336	18	α+	α+	SYM
ejpam-6413	336	19	1	1	NUM
ejpam-6413	336	20	+	+	NOUN
ejpam-6413	336	21	b0.5(α+	b0.5(α+	NOUN
ejpam-6413	336	22	1	1	NUM
ejpam-6413	336	23	,	,	PUNCT
ejpam-6413	336	24	θ	θ	PROPN
ejpam-6413	336	25	+	+	PROPN
ejpam-6413	336	26	2	2	NUM
ejpam-6413	336	27	)	)	PUNCT
ejpam-6413	336	28	+	+	CCONJ
ejpam-6413	336	29	(	(	PUNCT
ejpam-6413	336	30	12	12	NUM
ejpam-6413	336	31	)	)	PUNCT
ejpam-6413	336	32	θ+α+2	θ+α+2	VERB
ejpam-6413	336	33	θ	θ	X
ejpam-6413	336	34	+	+	CCONJ
ejpam-6413	336	35	α+	α+	PUNCT
ejpam-6413	336	36	2	2	NUM
ejpam-6413	336	37	)	)	PUNCT
ejpam-6413	336	38	+	+	NOUN
ejpam-6413	336	39	m|𭟋′′(b̄	m|𭟋′′(b̄	NOUN
ejpam-6413	336	40	)	)	PUNCT
ejpam-6413	336	41	(	(	PUNCT
ejpam-6413	336	42	θ	θ	NOUN
ejpam-6413	336	43	−	−	PROPN
ejpam-6413	336	44	3	3	NUM
ejpam-6413	336	45	8	8	NUM
ejpam-6413	336	46	+	+	SYM
ejpam-6413	336	47	2−α−1	2−α−1	NUM
ejpam-6413	336	48	α+	α+	PRON
ejpam-6413	336	49	1	1	NUM
ejpam-6413	336	50	−	−	PROPN
ejpam-6413	336	51	(	(	PUNCT
ejpam-6413	336	52	θ	θ	X
ejpam-6413	336	53	+	+	PUNCT
ejpam-6413	337	1	1)2−α−2	1)2−α−2	NUM
ejpam-6413	337	2	α+	α+	PUNCT
ejpam-6413	337	3	2	2	NUM
ejpam-6413	337	4	−	−	PROPN
ejpam-6413	337	5	2−θ−α−2	2−θ−α−2	NUM
ejpam-6413	337	6	θ	θ	NOUN
ejpam-6413	338	1	+	+	PUNCT
ejpam-6413	338	2	α+	α+	PUNCT
ejpam-6413	338	3	2	2	NUM
ejpam-6413	338	4	−b0.5(α+	−b0.5(α+	PROPN
ejpam-6413	338	5	1	1	NUM
ejpam-6413	338	6	,	,	PUNCT
ejpam-6413	338	7	θ	θ	PROPN
ejpam-6413	338	8	+	+	PROPN
ejpam-6413	338	9	2	2	NUM
ejpam-6413	338	10	)	)	PUNCT
ejpam-6413	338	11	)	)	PUNCT
ejpam-6413	338	12	.	.	PUNCT
ejpam-6413	339	1	(	(	PUNCT
ejpam-6413	339	2	29	29	NUM
ejpam-6413	339	3	)	)	PUNCT
ejpam-6413	339	4	also	also	ADV
ejpam-6413	339	5	,	,	PUNCT
ejpam-6413	339	6	consider∫	consider∫	NOUN
ejpam-6413	339	7	1	1	NUM
ejpam-6413	339	8	1	1	NUM
ejpam-6413	339	9	2	2	NUM
ejpam-6413	339	10	∣∣∣θ	∣∣∣θ	NOUN
ejpam-6413	339	11	−	−	NOUN
ejpam-6413	339	12	⊺(θ	⊺(θ	NOUN
ejpam-6413	339	13	+	+	CCONJ
ejpam-6413	339	14	1	1	NUM
ejpam-6413	339	15	)	)	PUNCT
ejpam-6413	339	16	+	+	CCONJ
ejpam-6413	339	17	(	(	PUNCT
ejpam-6413	339	18	1−	1−	NUM
ejpam-6413	339	19	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	339	20	+	+	CCONJ
ejpam-6413	339	21	⊺θ+1	⊺θ+1	ADJ
ejpam-6413	339	22	∣∣∣	∣∣∣	ADJ
ejpam-6413	339	23	(	(	PUNCT
ejpam-6413	339	24	⊺α|𭟋′′(ā)|+m(1−	⊺α|𭟋′′(ā)|+m(1−	DET
ejpam-6413	339	25	⊺α)|𭟋′′(b̄)|)d⊺	⊺α)|𭟋′′(b̄)|)d⊺	PROPN
ejpam-6413	339	26	≤	≤	NUM
ejpam-6413	339	27	|𭟋′′(ā)|	|𭟋′′(ā)|	PUNCT
ejpam-6413	340	1	(	(	PUNCT
ejpam-6413	340	2	θ	θ	PROPN
ejpam-6413	340	3	1−	1−	NUM
ejpam-6413	340	4	(	(	PUNCT
ejpam-6413	340	5	12	12	NUM
ejpam-6413	340	6	)	)	PUNCT
ejpam-6413	340	7	α+1	α+1	NUM
ejpam-6413	340	8	α+	α+	PRON
ejpam-6413	340	9	1	1	NUM
ejpam-6413	340	10	−	−	NOUN
ejpam-6413	340	11	(	(	PUNCT
ejpam-6413	340	12	θ	θ	NOUN
ejpam-6413	340	13	+	+	PROPN
ejpam-6413	340	14	1	1	NUM
ejpam-6413	340	15	)	)	PUNCT
ejpam-6413	340	16	1−	1−	NUM
ejpam-6413	340	17	(	(	PUNCT
ejpam-6413	340	18	12	12	NUM
ejpam-6413	340	19	)	)	PUNCT
ejpam-6413	340	20	α+2	α+2	NUM
ejpam-6413	340	21	α+	α+	PUNCT
ejpam-6413	340	22	2	2	NUM
ejpam-6413	340	23	+	+	NOUN
ejpam-6413	340	24	b0.5(α+	b0.5(α+	NOUN
ejpam-6413	340	25	1	1	NUM
ejpam-6413	340	26	,	,	PUNCT
ejpam-6413	340	27	θ	θ	PROPN
ejpam-6413	340	28	+	+	PROPN
ejpam-6413	340	29	2	2	NUM
ejpam-6413	340	30	)	)	PUNCT
ejpam-6413	340	31	+	+	NUM
ejpam-6413	340	32	1−	1−	NUM
ejpam-6413	340	33	(	(	PUNCT
ejpam-6413	340	34	12	12	NUM
ejpam-6413	340	35	)	)	PUNCT
ejpam-6413	340	36	θ+α+2	θ+α+2	VERB
ejpam-6413	340	37	θ	θ	X
ejpam-6413	341	1	+	+	CCONJ
ejpam-6413	341	2	α+	α+	PUNCT
ejpam-6413	341	3	2	2	NUM
ejpam-6413	341	4	)	)	PUNCT
ejpam-6413	342	1	+	+	X
ejpam-6413	342	2	m|𭟋′′(b̄)|	m|𭟋′′(b̄)|	PROPN
ejpam-6413	342	3	(	(	PUNCT
ejpam-6413	342	4	θ	θ	NOUN
ejpam-6413	342	5	−	−	PROPN
ejpam-6413	342	6	3	3	NUM
ejpam-6413	342	7	8	8	NUM
ejpam-6413	342	8	+	+	SYM
ejpam-6413	342	9	1	1	NUM
ejpam-6413	342	10	θ	θ	NOUN
ejpam-6413	342	11	+	+	NOUN
ejpam-6413	342	12	2	2	NUM
ejpam-6413	342	13	−	−	NUM
ejpam-6413	342	14	θ	θ	NOUN
ejpam-6413	342	15	−	−	PROPN
ejpam-6413	343	1	θ2−α−1	θ2−α−1	PROPN
ejpam-6413	343	2	α+	α+	PUNCT
ejpam-6413	343	3	1	1	NUM
ejpam-6413	343	4	+	+	CCONJ
ejpam-6413	343	5	(	(	PUNCT
ejpam-6413	343	6	θ	θ	X
ejpam-6413	343	7	+	+	CCONJ
ejpam-6413	343	8	1)(1−	1)(1−	NUM
ejpam-6413	343	9	2−α−2	2−α−2	NUM
ejpam-6413	343	10	)	)	PUNCT
ejpam-6413	343	11	α+	α+	PUNCT
ejpam-6413	343	12	2	2	NUM
ejpam-6413	343	13	−	−	NOUN
ejpam-6413	343	14	1−	1−	NUM
ejpam-6413	343	15	2−θ−α−2	2−θ−α−2	NUM
ejpam-6413	343	16	θ	θ	X
ejpam-6413	344	1	+	+	PUNCT
ejpam-6413	344	2	α+	α+	PUNCT
ejpam-6413	344	3	2	2	NUM
ejpam-6413	344	4	−b0.5(α+	−b0.5(α+	PROPN
ejpam-6413	344	5	1	1	NUM
ejpam-6413	344	6	,	,	PUNCT
ejpam-6413	344	7	θ	θ	PROPN
ejpam-6413	344	8	+	+	PROPN
ejpam-6413	344	9	2	2	NUM
ejpam-6413	344	10	)	)	PUNCT
ejpam-6413	344	11	)	)	PUNCT
ejpam-6413	344	12	.	.	PUNCT
ejpam-6413	345	1	(	(	PUNCT
ejpam-6413	345	2	30	30	X
ejpam-6413	345	3	)	)	PUNCT
ejpam-6413	345	4	m.	m.	NOUN
ejpam-6413	345	5	samraiz	samraiz	PROPN
ejpam-6413	345	6	et	et	PROPN
ejpam-6413	345	7	al	al	PROPN
ejpam-6413	345	8	.	.	PUNCT
ejpam-6413	345	9	/	/	SYM
ejpam-6413	345	10	eur	eur	PROPN
ejpam-6413	345	11	.	.	PUNCT
ejpam-6413	346	1	j.	j.	PROPN
ejpam-6413	346	2	pure	pure	PROPN
ejpam-6413	346	3	appl	appl	PROPN
ejpam-6413	346	4	.	.	PROPN
ejpam-6413	346	5	math	math	PROPN
ejpam-6413	346	6	,	,	PUNCT
ejpam-6413	346	7	18	18	NUM
ejpam-6413	346	8	(	(	PUNCT
ejpam-6413	346	9	3	3	NUM
ejpam-6413	346	10	)	)	PUNCT
ejpam-6413	346	11	(	(	PUNCT
ejpam-6413	346	12	2025	2025	NUM
ejpam-6413	346	13	)	)	PUNCT
ejpam-6413	346	14	,	,	PUNCT
ejpam-6413	346	15	6413	6413	NUM
ejpam-6413	346	16	16	16	NUM
ejpam-6413	346	17	of	of	ADP
ejpam-6413	346	18	26	26	NUM
ejpam-6413	346	19	substituting	substitute	VERB
ejpam-6413	346	20	values	value	NOUN
ejpam-6413	346	21	of	of	ADP
ejpam-6413	346	22	(	(	PUNCT
ejpam-6413	346	23	29	29	NUM
ejpam-6413	346	24	)	)	PUNCT
ejpam-6413	346	25	and	and	CCONJ
ejpam-6413	346	26	(	(	PUNCT
ejpam-6413	346	27	30	30	NUM
ejpam-6413	346	28	)	)	PUNCT
ejpam-6413	346	29	in	in	ADP
ejpam-6413	346	30	(	(	PUNCT
ejpam-6413	346	31	28	28	NUM
ejpam-6413	346	32	)	)	PUNCT
ejpam-6413	346	33	,	,	PUNCT
ejpam-6413	346	34	we	we	PRON
ejpam-6413	346	35	obtain∣∣∣∣	obtain∣∣∣∣	ADJ
ejpam-6413	346	36	γ(θ	γ(θ	PROPN
ejpam-6413	346	37	+	+	CCONJ
ejpam-6413	346	38	1	1	X
ejpam-6413	346	39	)	)	PUNCT
ejpam-6413	346	40	2(µ−	2(µ−	NUM
ejpam-6413	346	41	ā)θ	ā)θ	NOUN
ejpam-6413	346	42	[	[	X
ejpam-6413	346	43	χθ	χθ	X
ejpam-6413	346	44	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	346	45	)	)	PUNCT
ejpam-6413	347	1	+	+	CCONJ
ejpam-6413	348	1	χθ	χθ	X
ejpam-6413	348	2	µ−𭟋(ā)]−𭟋	µ−𭟋(ā)]−𭟋	NOUN
ejpam-6413	348	3	(	(	PUNCT
ejpam-6413	348	4	ā+	ā+	PUNCT
ejpam-6413	348	5	µ	µ	X
ejpam-6413	348	6	2	2	NUM
ejpam-6413	348	7	)	)	PUNCT
ejpam-6413	348	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	348	9	≤	≤	NOUN
ejpam-6413	348	10	(	(	PUNCT
ejpam-6413	348	11	µ−	µ−	PROPN
ejpam-6413	348	12	ā)2	ā)2	VERB
ejpam-6413	348	13	2(θ	2(θ	NUM
ejpam-6413	348	14	+	+	CCONJ
ejpam-6413	348	15	1	1	X
ejpam-6413	348	16	)	)	PUNCT
ejpam-6413	348	17	|𭟋′′(ā)|	|𭟋′′(ā)|	PROPN
ejpam-6413	348	18	(	(	PUNCT
ejpam-6413	348	19	(	(	PUNCT
ejpam-6413	348	20	θ	θ	NOUN
ejpam-6413	348	21	+	+	NOUN
ejpam-6413	348	22	1	1	NUM
ejpam-6413	348	23	)	)	PUNCT
ejpam-6413	348	24	(	(	PUNCT
ejpam-6413	348	25	12	12	NUM
ejpam-6413	348	26	)	)	PUNCT
ejpam-6413	348	27	α+2	α+2	NUM
ejpam-6413	348	28	α+	α+	PUNCT
ejpam-6413	348	29	2	2	NUM
ejpam-6413	348	30	−	−	NOUN
ejpam-6413	348	31	(	(	PUNCT
ejpam-6413	348	32	12	12	NUM
ejpam-6413	348	33	)	)	PUNCT
ejpam-6413	348	34	α+1	α+1	NUM
ejpam-6413	348	35	α+	α+	SYM
ejpam-6413	348	36	1	1	NUM
ejpam-6413	348	37	+	+	NOUN
ejpam-6413	348	38	b0.5(α+	b0.5(α+	NOUN
ejpam-6413	348	39	1	1	NUM
ejpam-6413	348	40	,	,	PUNCT
ejpam-6413	348	41	θ	θ	PROPN
ejpam-6413	348	42	+	+	PROPN
ejpam-6413	348	43	2	2	NUM
ejpam-6413	348	44	)	)	PUNCT
ejpam-6413	348	45	+	+	CCONJ
ejpam-6413	348	46	(	(	PUNCT
ejpam-6413	348	47	12	12	NUM
ejpam-6413	348	48	)	)	PUNCT
ejpam-6413	348	49	θ+α+2	θ+α+2	VERB
ejpam-6413	348	50	θ	θ	X
ejpam-6413	348	51	+	+	CCONJ
ejpam-6413	348	52	α+	α+	PUNCT
ejpam-6413	348	53	2	2	NUM
ejpam-6413	348	54	)	)	PUNCT
ejpam-6413	349	1	+	+	CCONJ
ejpam-6413	349	2	(	(	PUNCT
ejpam-6413	349	3	µ−	µ−	PROPN
ejpam-6413	349	4	ā)2	ā)2	VERB
ejpam-6413	349	5	2(θ	2(θ	NUM
ejpam-6413	350	1	+	+	CCONJ
ejpam-6413	350	2	1	1	X
ejpam-6413	350	3	)	)	PUNCT
ejpam-6413	350	4	m|𭟋′′(b̄	m|𭟋′′(b̄	NOUN
ejpam-6413	350	5	)	)	PUNCT
ejpam-6413	351	1	(	(	PUNCT
ejpam-6413	351	2	θ	θ	NOUN
ejpam-6413	351	3	−	−	PROPN
ejpam-6413	351	4	3	3	NUM
ejpam-6413	351	5	8	8	NUM
ejpam-6413	351	6	+	+	CCONJ
ejpam-6413	351	7	(	(	PUNCT
ejpam-6413	351	8	12	12	NUM
ejpam-6413	351	9	)	)	PUNCT
ejpam-6413	351	10	α+1	α+1	NUM
ejpam-6413	351	11	α+	α+	PRON
ejpam-6413	351	12	1	1	NUM
ejpam-6413	351	13	−	−	PROPN
ejpam-6413	351	14	(	(	PUNCT
ejpam-6413	351	15	θ	θ	PROPN
ejpam-6413	351	16	+	+	NOUN
ejpam-6413	351	17	1)(12	1)(12	NUM
ejpam-6413	351	18	)	)	PUNCT
ejpam-6413	351	19	α+2	α+2	NUM
ejpam-6413	351	20	α+	α+	PUNCT
ejpam-6413	351	21	2	2	NUM
ejpam-6413	351	22	−	−	NOUN
ejpam-6413	351	23	(	(	PUNCT
ejpam-6413	351	24	12	12	NUM
ejpam-6413	351	25	)	)	PUNCT
ejpam-6413	351	26	θ+α+2	θ+α+2	VERB
ejpam-6413	351	27	θ	θ	X
ejpam-6413	352	1	+	+	CCONJ
ejpam-6413	352	2	α+	α+	PUNCT
ejpam-6413	352	3	2	2	NUM
ejpam-6413	352	4	−b0.5(α+	−b0.5(α+	PROPN
ejpam-6413	352	5	1	1	NUM
ejpam-6413	352	6	,	,	PUNCT
ejpam-6413	352	7	θ	θ	PROPN
ejpam-6413	352	8	+	+	PROPN
ejpam-6413	352	9	2	2	NUM
ejpam-6413	352	10	)	)	PUNCT
ejpam-6413	352	11	)	)	PUNCT
ejpam-6413	353	1	+	+	CCONJ
ejpam-6413	353	2	(	(	PUNCT
ejpam-6413	353	3	µ−	µ−	PROPN
ejpam-6413	353	4	ā)2	ā)2	VERB
ejpam-6413	353	5	2(θ	2(θ	NUM
ejpam-6413	354	1	+	+	CCONJ
ejpam-6413	354	2	1	1	X
ejpam-6413	354	3	)	)	PUNCT
ejpam-6413	354	4	|𭟋′′(ā)|	|𭟋′′(ā)|	PROPN
ejpam-6413	355	1	(	(	PUNCT
ejpam-6413	355	2	θ	θ	PROPN
ejpam-6413	355	3	1−	1−	NUM
ejpam-6413	355	4	(	(	PUNCT
ejpam-6413	355	5	12	12	NUM
ejpam-6413	355	6	)	)	PUNCT
ejpam-6413	355	7	α+1	α+1	NUM
ejpam-6413	355	8	α+	α+	PRON
ejpam-6413	355	9	1	1	NUM
ejpam-6413	355	10	−	−	NOUN
ejpam-6413	355	11	(	(	PUNCT
ejpam-6413	355	12	θ	θ	NOUN
ejpam-6413	355	13	+	+	PROPN
ejpam-6413	355	14	1	1	NUM
ejpam-6413	355	15	)	)	PUNCT
ejpam-6413	355	16	1−	1−	NUM
ejpam-6413	355	17	(	(	PUNCT
ejpam-6413	355	18	12	12	NUM
ejpam-6413	355	19	)	)	PUNCT
ejpam-6413	355	20	α+2	α+2	NUM
ejpam-6413	355	21	α+	α+	PUNCT
ejpam-6413	355	22	2	2	NUM
ejpam-6413	355	23	+	+	NOUN
ejpam-6413	355	24	b(α+	b(α+	NOUN
ejpam-6413	355	25	1	1	NUM
ejpam-6413	355	26	,	,	PUNCT
ejpam-6413	355	27	θ	θ	PROPN
ejpam-6413	355	28	+	+	PROPN
ejpam-6413	355	29	2	2	NUM
ejpam-6413	355	30	)	)	PUNCT
ejpam-6413	355	31	+	+	NUM
ejpam-6413	355	32	1−	1−	NUM
ejpam-6413	355	33	(	(	PUNCT
ejpam-6413	355	34	12	12	NUM
ejpam-6413	355	35	)	)	PUNCT
ejpam-6413	355	36	θ+α+2	θ+α+2	VERB
ejpam-6413	355	37	θ	θ	X
ejpam-6413	356	1	+	+	CCONJ
ejpam-6413	356	2	α+	α+	PUNCT
ejpam-6413	356	3	2	2	NUM
ejpam-6413	356	4	)	)	PUNCT
ejpam-6413	356	5	+	+	CCONJ
ejpam-6413	356	6	(	(	PUNCT
ejpam-6413	356	7	µ−	µ−	PROPN
ejpam-6413	356	8	ā)2	ā)2	VERB
ejpam-6413	356	9	2(θ	2(θ	NUM
ejpam-6413	357	1	+	+	CCONJ
ejpam-6413	357	2	1	1	X
ejpam-6413	357	3	)	)	PUNCT
ejpam-6413	357	4	m|𭟋′′(b̄)|	m|𭟋′′(b̄)|	PROPN
ejpam-6413	357	5	(	(	PUNCT
ejpam-6413	357	6	θ	θ	NOUN
ejpam-6413	357	7	−	−	PROPN
ejpam-6413	357	8	3	3	NUM
ejpam-6413	357	9	8	8	NUM
ejpam-6413	357	10	+	+	SYM
ejpam-6413	357	11	1	1	NUM
ejpam-6413	357	12	θ	θ	NOUN
ejpam-6413	357	13	+	+	NOUN
ejpam-6413	357	14	2	2	NUM
ejpam-6413	357	15	−	−	NUM
ejpam-6413	357	16	θ	θ	NOUN
ejpam-6413	358	1	−	−	PROPN
ejpam-6413	358	2	θ2−α−1	θ2−α−1	PROPN
ejpam-6413	358	3	α+	α+	PUNCT
ejpam-6413	358	4	1	1	NUM
ejpam-6413	358	5	+	+	CCONJ
ejpam-6413	358	6	(	(	PUNCT
ejpam-6413	358	7	θ	θ	X
ejpam-6413	358	8	+	+	CCONJ
ejpam-6413	358	9	1)(1−	1)(1−	NUM
ejpam-6413	358	10	2−α−2	2−α−2	NUM
ejpam-6413	358	11	)	)	PUNCT
ejpam-6413	358	12	α+	α+	PUNCT
ejpam-6413	358	13	2	2	NUM
ejpam-6413	358	14	−	−	NOUN
ejpam-6413	358	15	1−	1−	NUM
ejpam-6413	358	16	2−θ−α−2	2−θ−α−2	NUM
ejpam-6413	358	17	θ	θ	X
ejpam-6413	359	1	+	+	PUNCT
ejpam-6413	359	2	α+	α+	PUNCT
ejpam-6413	359	3	2	2	NUM
ejpam-6413	359	4	−b0.5(α+	−b0.5(α+	PROPN
ejpam-6413	359	5	1	1	NUM
ejpam-6413	359	6	,	,	PUNCT
ejpam-6413	359	7	θ	θ	PROPN
ejpam-6413	359	8	+	+	PROPN
ejpam-6413	359	9	2	2	NUM
ejpam-6413	359	10	)	)	PUNCT
ejpam-6413	359	11	)	)	PUNCT
ejpam-6413	359	12	.	.	PUNCT
ejpam-6413	360	1	hence	hence	ADV
ejpam-6413	360	2	,	,	PUNCT
ejpam-6413	360	3	the	the	DET
ejpam-6413	360	4	proof	proof	NOUN
ejpam-6413	360	5	is	be	AUX
ejpam-6413	360	6	done	do	VERB
ejpam-6413	360	7	.	.	PUNCT
ejpam-6413	361	1	theorem	theorem	ADJ
ejpam-6413	361	2	4	4	NUM
ejpam-6413	361	3	.	.	PUNCT
ejpam-6413	362	1	let	let	VERB
ejpam-6413	362	2	𭟋	𭟋	VERB
ejpam-6413	362	3	:	:	PUNCT
ejpam-6413	362	4	[	[	X
ejpam-6413	362	5	ā	ā	X
ejpam-6413	362	6	,	,	PUNCT
ejpam-6413	362	7	b̄	b̄	PROPN
ejpam-6413	362	8	]	]	PUNCT
ejpam-6413	362	9	−→	−→	NOUN
ejpam-6413	362	10	r	r	NOUN
ejpam-6413	362	11	be	be	VERB
ejpam-6413	362	12	a	a	DET
ejpam-6413	362	13	twice	twice	ADV
ejpam-6413	362	14	differentiable	differentiable	ADJ
ejpam-6413	362	15	function	function	NOUN
ejpam-6413	362	16	such	such	ADJ
ejpam-6413	362	17	that	that	DET
ejpam-6413	362	18	|𭟋′′|	|𭟋′′|	PROPN
ejpam-6413	362	19	is	be	AUX
ejpam-6413	362	20	lebesgue	lebesgue	NOUN
ejpam-6413	362	21	integerable	integerable	ADJ
ejpam-6413	362	22	,	,	PUNCT
ejpam-6413	362	23	increasing	increase	VERB
ejpam-6413	362	24	and	and	CCONJ
ejpam-6413	362	25	ga	ga	PROPN
ejpam-6413	362	26	(	(	PUNCT
ejpam-6413	362	27	α	α	NOUN
ejpam-6413	362	28	,	,	PUNCT
ejpam-6413	362	29	m)-convex	m)-convex	PUNCT
ejpam-6413	362	30	function	function	VERB
ejpam-6413	362	31	on	on	ADP
ejpam-6413	362	32	[	[	X
ejpam-6413	362	33	ā	ā	X
ejpam-6413	362	34	,	,	PUNCT
ejpam-6413	362	35	b̄	b̄	PROPN
ejpam-6413	362	36	]	]	PUNCT
ejpam-6413	362	37	.	.	PUNCT
ejpam-6413	363	1	then	then	ADV
ejpam-6413	363	2	for	for	ADP
ejpam-6413	363	3	given	give	VERB
ejpam-6413	363	4	parameters	parameter	NOUN
ejpam-6413	363	5	θ	θ	PROPN
ejpam-6413	363	6	∈	∈	PROPN
ejpam-6413	363	7	(	(	PUNCT
ejpam-6413	363	8	0,+∞	0,+∞	NUM
ejpam-6413	363	9	)	)	PUNCT
ejpam-6413	363	10	and	and	CCONJ
ejpam-6413	363	11	(	(	PUNCT
ejpam-6413	363	12	α	α	NOUN
ejpam-6413	363	13	,	,	PUNCT
ejpam-6413	363	14	m	m	NOUN
ejpam-6413	363	15	)	)	PUNCT
ejpam-6413	363	16	∈	∈	PROPN
ejpam-6413	363	17	(	(	PUNCT
ejpam-6413	363	18	0	0	NUM
ejpam-6413	363	19	,	,	PUNCT
ejpam-6413	363	20	1]2	1]2	NUM
ejpam-6413	363	21	,	,	PUNCT
ejpam-6413	363	22	where	where	SCONJ
ejpam-6413	363	23	0	0	NUM
ejpam-6413	363	24	≤	≤	NUM
ejpam-6413	363	25	ā	ā	NOUN
ejpam-6413	363	26	<	<	X
ejpam-6413	363	27	b̄.	b̄.	PUNCT
ejpam-6413	363	28	thus	thus	ADV
ejpam-6413	363	29	,	,	PUNCT
ejpam-6413	363	30	let	let	VERB
ejpam-6413	363	31	1	1	NUM
ejpam-6413	363	32	<	<	X
ejpam-6413	363	33	⋋2	⋋2	NOUN
ejpam-6413	363	34	<	<	X
ejpam-6413	364	1	+	+	PROPN
ejpam-6413	364	2	∞	∞	PROPN
ejpam-6413	364	3	the	the	DET
ejpam-6413	364	4	following	follow	VERB
ejpam-6413	364	5	inequality∣∣∣∣	inequality∣∣∣∣	PROPN
ejpam-6413	364	6	γ(θ	γ(θ	PROPN
ejpam-6413	364	7	+	+	CCONJ
ejpam-6413	364	8	1	1	X
ejpam-6413	364	9	)	)	PUNCT
ejpam-6413	364	10	2(µ−	2(µ−	NUM
ejpam-6413	364	11	ā)θ	ā)θ	NOUN
ejpam-6413	364	12	[	[	PUNCT
ejpam-6413	364	13	χθ	χθ	X
ejpam-6413	364	14	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	364	15	)	)	PUNCT
ejpam-6413	365	1	+	+	CCONJ
ejpam-6413	365	2	χθ	χθ	X
ejpam-6413	365	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	365	4	)	)	PUNCT
ejpam-6413	365	5	]	]	PUNCT
ejpam-6413	366	1	−𭟋	−𭟋	INTJ
ejpam-6413	366	2	(	(	PUNCT
ejpam-6413	366	3	ā+	ā+	PUNCT
ejpam-6413	366	4	µ	µ	X
ejpam-6413	366	5	2	2	NUM
ejpam-6413	366	6	)	)	PUNCT
ejpam-6413	366	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	366	8	≤	≤	NOUN
ejpam-6413	366	9	(	(	PUNCT
ejpam-6413	366	10	µ−	µ−	PROPN
ejpam-6413	366	11	ā)2	ā)2	VERB
ejpam-6413	366	12	2(θ	2(θ	NUM
ejpam-6413	366	13	+	+	CCONJ
ejpam-6413	366	14	1	1	X
ejpam-6413	366	15	)	)	PUNCT
ejpam-6413	366	16	(	(	PUNCT
ejpam-6413	366	17	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	366	18	+	+	X
ejpam-6413	366	19	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	366	20	α+	α+	PUNCT
ejpam-6413	366	21	1	1	NUM
ejpam-6413	366	22	)	)	PUNCT
ejpam-6413	366	23	1	1	NUM
ejpam-6413	366	24	⋋2	⋋2	PROPN
ejpam-6413	366	25	×	×	NOUN
ejpam-6413	366	26	(	(	PUNCT
ejpam-6413	366	27	(	(	PUNCT
ejpam-6413	366	28	θ	θ	NOUN
ejpam-6413	366	29	+	+	PUNCT
ejpam-6413	366	30	1)2−⋋1−1	1)2−⋋1−1	NUM
ejpam-6413	366	31	+	+	CCONJ
ejpam-6413	366	32	(	(	PUNCT
ejpam-6413	366	33	θ	θ	NOUN
ejpam-6413	366	34	+	+	PUNCT
ejpam-6413	366	35	0.5)⋋1	0.5)⋋1	ADJ
ejpam-6413	366	36	+	+	ADJ
ejpam-6413	366	37	1	1	NUM
ejpam-6413	366	38	−	−	ADP
ejpam-6413	366	39	θ⋋1	θ⋋1	NOUN
ejpam-6413	366	40	+	+	PROPN
ejpam-6413	366	41	1	1	NUM
ejpam-6413	366	42	⋋1	⋋1	NUM
ejpam-6413	366	43	+	+	CCONJ
ejpam-6413	366	44	1	1	NUM
ejpam-6413	366	45	)	)	PUNCT
ejpam-6413	366	46	1	1	NUM
ejpam-6413	366	47	⋋1	⋋1	NUM
ejpam-6413	366	48	holds	hold	VERB
ejpam-6413	366	49	true	true	ADJ
ejpam-6413	366	50	,	,	PUNCT
ejpam-6413	366	51	where	where	SCONJ
ejpam-6413	366	52	1	1	NUM
ejpam-6413	366	53	⋋1	⋋1	NUM
ejpam-6413	366	54	+	+	SYM
ejpam-6413	366	55	1	1	NUM
ejpam-6413	366	56	⋋2	⋋2	NOUN
ejpam-6413	366	57	=	=	SYM
ejpam-6413	366	58	1	1	X
ejpam-6413	366	59	.	.	X
ejpam-6413	366	60	m.	m.	NOUN
ejpam-6413	366	61	samraiz	samraiz	PROPN
ejpam-6413	366	62	et	et	PROPN
ejpam-6413	366	63	al	al	PROPN
ejpam-6413	366	64	.	.	PUNCT
ejpam-6413	366	65	/	/	SYM
ejpam-6413	366	66	eur	eur	PROPN
ejpam-6413	366	67	.	.	PUNCT
ejpam-6413	367	1	j.	j.	PROPN
ejpam-6413	367	2	pure	pure	PROPN
ejpam-6413	367	3	appl	appl	PROPN
ejpam-6413	367	4	.	.	PROPN
ejpam-6413	367	5	math	math	PROPN
ejpam-6413	367	6	,	,	PUNCT
ejpam-6413	367	7	18	18	NUM
ejpam-6413	367	8	(	(	PUNCT
ejpam-6413	367	9	3	3	NUM
ejpam-6413	367	10	)	)	PUNCT
ejpam-6413	367	11	(	(	PUNCT
ejpam-6413	367	12	2025	2025	NUM
ejpam-6413	367	13	)	)	PUNCT
ejpam-6413	367	14	,	,	PUNCT
ejpam-6413	367	15	6413	6413	NUM
ejpam-6413	367	16	17	17	NUM
ejpam-6413	367	17	of	of	ADP
ejpam-6413	367	18	26	26	NUM
ejpam-6413	367	19	proof	proof	NOUN
ejpam-6413	367	20	.	.	PUNCT
ejpam-6413	368	1	by	by	ADP
ejpam-6413	368	2	utilizing	utilize	VERB
ejpam-6413	368	3	lemma	lemma	PROPN
ejpam-6413	368	4	5	5	NUM
ejpam-6413	368	5	,	,	PUNCT
ejpam-6413	368	6	7	7	NUM
ejpam-6413	368	7	and	and	CCONJ
ejpam-6413	368	8	applying	apply	VERB
ejpam-6413	368	9	hölder	hölder	NOUN
ejpam-6413	368	10	’s	’s	PART
ejpam-6413	368	11	inequality	inequality	NOUN
ejpam-6413	368	12	,	,	PUNCT
ejpam-6413	368	13	we	we	PRON
ejpam-6413	368	14	have∣∣∣∣	have∣∣∣∣	VERB
ejpam-6413	368	15	γ(θ	γ(θ	PROPN
ejpam-6413	368	16	+	+	PROPN
ejpam-6413	368	17	1	1	X
ejpam-6413	368	18	)	)	PUNCT
ejpam-6413	368	19	2(µ−	2(µ−	NUM
ejpam-6413	368	20	ā)θ	ā)θ	NOUN
ejpam-6413	368	21	[	[	X
ejpam-6413	368	22	χθ	χθ	X
ejpam-6413	368	23	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	368	24	)	)	PUNCT
ejpam-6413	369	1	+	+	CCONJ
ejpam-6413	369	2	χθ	χθ	X
ejpam-6413	369	3	µ−𭟋(ā)]−𭟋	µ−𭟋(ā)]−𭟋	NOUN
ejpam-6413	369	4	(	(	PUNCT
ejpam-6413	369	5	ā+	ā+	PUNCT
ejpam-6413	369	6	µ	µ	X
ejpam-6413	369	7	2	2	NUM
ejpam-6413	369	8	)	)	PUNCT
ejpam-6413	369	9	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	369	10	≤	≤	NOUN
ejpam-6413	369	11	(	(	PUNCT
ejpam-6413	369	12	µ−	µ−	PROPN
ejpam-6413	369	13	ā)2	ā)2	NOUN
ejpam-6413	369	14	2	2	NUM
ejpam-6413	369	15	∫	∫	NOUN
ejpam-6413	369	16	1	1	NUM
ejpam-6413	369	17	0	0	X
ejpam-6413	369	18	|p0(⊺)||𭟋′′(⊺ā+m(1−	|p0(⊺)||𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	369	19	⊺)b̄)|d⊺	⊺)b̄)|d⊺	NOUN
ejpam-6413	369	20	≤	≤	NOUN
ejpam-6413	369	21	(	(	PUNCT
ejpam-6413	369	22	µ−	µ−	PROPN
ejpam-6413	369	23	ā)2	ā)2	NOUN
ejpam-6413	369	24	2	2	NUM
ejpam-6413	369	25	∫	∫	NOUN
ejpam-6413	369	26	1	1	NUM
ejpam-6413	369	27	0	0	NUM
ejpam-6413	369	28	|p0(⊺)||𭟋′′(ā⊺b̄m(1−⊺)|d⊺	|p0(⊺)||𭟋′′(ā⊺b̄m(1−⊺)|d⊺	NUM
ejpam-6413	369	29	≤	≤	NOUN
ejpam-6413	369	30	(	(	PUNCT
ejpam-6413	369	31	µ−	µ−	PROPN
ejpam-6413	369	32	ā)2	ā)2	NOUN
ejpam-6413	369	33	2	2	NUM
ejpam-6413	369	34	∫	∫	NOUN
ejpam-6413	369	35	1	1	NUM
ejpam-6413	369	36	0	0	NUM
ejpam-6413	369	37	|p0(⊺)|⊺α|𭟋′′(ā)|+m(1−	|p0(⊺)|⊺α|𭟋′′(ā)|+m(1−	NOUN
ejpam-6413	369	38	⊺α)|𭟋′′(b̄)|d⊺	⊺α)|𭟋′′(b̄)|d⊺	VERB
ejpam-6413	369	39	≤	≤	NOUN
ejpam-6413	369	40	(	(	PUNCT
ejpam-6413	369	41	µ−	µ−	PROPN
ejpam-6413	369	42	ā)2	ā)2	NOUN
ejpam-6413	369	43	2	2	NUM
ejpam-6413	369	44	∫	∫	NOUN
ejpam-6413	369	45	1	1	NUM
ejpam-6413	369	46	0	0	NUM
ejpam-6413	369	47	(	(	PUNCT
ejpam-6413	369	48	|(p0(⊺))⋋1	|(p0(⊺))⋋1	PROPN
ejpam-6413	369	49	|	|	CCONJ
ejpam-6413	369	50	)	)	PUNCT
ejpam-6413	369	51	1	1	NUM
ejpam-6413	369	52	⋋1	⋋1	NUM
ejpam-6413	369	53	(	(	PUNCT
ejpam-6413	369	54	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	PROPN
ejpam-6413	369	55	∫	∫	PROPN
ejpam-6413	369	56	1	1	NUM
ejpam-6413	369	57	0	0	NUM
ejpam-6413	369	58	⊺αd	⊺αd	PROPN
ejpam-6413	369	59	⊺+m|𭟋′′(b̄)|⋋2	⊺+m|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	369	60	∫	∫	PROPN
ejpam-6413	369	61	1	1	NUM
ejpam-6413	369	62	0	0	NUM
ejpam-6413	369	63	(	(	PUNCT
ejpam-6413	369	64	1−	1−	NUM
ejpam-6413	369	65	⊺α)d⊺	⊺α)d⊺	ADJ
ejpam-6413	369	66	)	)	PUNCT
ejpam-6413	369	67	1	1	NUM
ejpam-6413	369	68	⋋2	⋋2	PROPN
ejpam-6413	369	69	≤	≤	NOUN
ejpam-6413	369	70	(	(	PUNCT
ejpam-6413	369	71	µ−	µ−	PROPN
ejpam-6413	369	72	ā)2	ā)2	NOUN
ejpam-6413	369	73	2	2	NUM
ejpam-6413	369	74	∫	∫	NOUN
ejpam-6413	369	75	1	1	NUM
ejpam-6413	369	76	0	0	NUM
ejpam-6413	369	77	(	(	PUNCT
ejpam-6413	369	78	|(p0(⊺))⋋1	|(p0(⊺))⋋1	PROPN
ejpam-6413	369	79	|	|	CCONJ
ejpam-6413	369	80	)	)	PUNCT
ejpam-6413	369	81	1	1	NUM
ejpam-6413	369	82	⋋1	⋋1	NUM
ejpam-6413	369	83	(	(	PUNCT
ejpam-6413	369	84	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	PROPN
ejpam-6413	369	85	1	1	NUM
ejpam-6413	369	86	α+	α+	SYM
ejpam-6413	369	87	1	1	NUM
ejpam-6413	370	1	+	+	NOUN
ejpam-6413	370	2	m|𭟋′′(b̄)|⋋2	m|𭟋′′(b̄)|⋋2	ADJ
ejpam-6413	370	3	α	α	NOUN
ejpam-6413	370	4	α+	α+	PUNCT
ejpam-6413	370	5	1	1	NUM
ejpam-6413	370	6	)	)	PUNCT
ejpam-6413	370	7	1	1	NUM
ejpam-6413	370	8	⋋2	⋋2	NOUN
ejpam-6413	370	9	substituting	substitute	VERB
ejpam-6413	370	10	the	the	DET
ejpam-6413	370	11	value	value	NOUN
ejpam-6413	370	12	p0(⊺	p0(⊺	PROPN
ejpam-6413	370	13	)	)	PUNCT
ejpam-6413	370	14	of	of	ADP
ejpam-6413	370	15	lemma	lemma	PROPN
ejpam-6413	370	16	4	4	NUM
ejpam-6413	370	17	.	.	PUNCT
ejpam-6413	370	18	≤	≤	NUM
ejpam-6413	370	19	(	(	PUNCT
ejpam-6413	370	20	µ−	µ−	PROPN
ejpam-6413	370	21	ā)2	ā)2	NOUN
ejpam-6413	370	22	2	2	NUM
ejpam-6413	370	23	(	(	PUNCT
ejpam-6413	370	24	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	370	25	+	+	NOUN
ejpam-6413	370	26	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	370	27	α+	α+	PUNCT
ejpam-6413	370	28	1	1	NUM
ejpam-6413	370	29	)	)	SYM
ejpam-6413	370	30	1	1	NUM
ejpam-6413	370	31	⋋2	⋋2	NOUN
ejpam-6413	370	32	(	(	PUNCT
ejpam-6413	370	33	∫	∫	PROPN
ejpam-6413	370	34	1	1	NUM
ejpam-6413	370	35	2	2	NUM
ejpam-6413	370	36	0	0	NUM
ejpam-6413	370	37	∣∣∣∣⊺−	∣∣∣∣⊺−	NOUN
ejpam-6413	370	38	1−	1−	NUM
ejpam-6413	370	39	(	(	PUNCT
ejpam-6413	370	40	1−	1−	NUM
ejpam-6413	370	41	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	370	42	−	−	PROPN
ejpam-6413	370	43	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	370	44	θ	θ	PROPN
ejpam-6413	370	45	+	+	CCONJ
ejpam-6413	370	46	1	1	NUM
ejpam-6413	370	47	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	370	48	d⊺	d⊺	PROPN
ejpam-6413	370	49	+	+	CCONJ
ejpam-6413	370	50	∫	∫	PROPN
ejpam-6413	370	51	1	1	NUM
ejpam-6413	370	52	1	1	NUM
ejpam-6413	370	53	2	2	NUM
ejpam-6413	370	54	∣∣∣∣1−	∣∣∣∣1−	NUM
ejpam-6413	370	55	⊺−	⊺−	PROPN
ejpam-6413	370	56	1−	1−	NUM
ejpam-6413	370	57	(	(	PUNCT
ejpam-6413	370	58	1−	1−	NUM
ejpam-6413	370	59	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	370	60	−	−	PROPN
ejpam-6413	370	61	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	370	62	θ	θ	PROPN
ejpam-6413	370	63	+	+	CCONJ
ejpam-6413	370	64	1	1	NUM
ejpam-6413	370	65	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	370	66	d⊺	d⊺	PROPN
ejpam-6413	370	67	)	)	PUNCT
ejpam-6413	371	1	1	1	NUM
ejpam-6413	371	2	⋋1	⋋1	NUM
ejpam-6413	371	3	≤	≤	NOUN
ejpam-6413	371	4	(	(	PUNCT
ejpam-6413	371	5	µ−	µ−	PROPN
ejpam-6413	371	6	ā)2	ā)2	VERB
ejpam-6413	371	7	2(θ	2(θ	NUM
ejpam-6413	371	8	+	+	CCONJ
ejpam-6413	371	9	1	1	X
ejpam-6413	371	10	)	)	PUNCT
ejpam-6413	371	11	(	(	PUNCT
ejpam-6413	371	12	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	372	1	+	+	X
ejpam-6413	372	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	372	3	α+	α+	PUNCT
ejpam-6413	372	4	1	1	NUM
ejpam-6413	372	5	)	)	PUNCT
ejpam-6413	372	6	1	1	NUM
ejpam-6413	372	7	⋋2	⋋2	PROPN
ejpam-6413	372	8	×	×	NOUN
ejpam-6413	372	9	(	(	PUNCT
ejpam-6413	372	10	∫	∫	PROPN
ejpam-6413	372	11	1	1	NUM
ejpam-6413	372	12	2	2	NUM
ejpam-6413	372	13	0	0	NUM
ejpam-6413	372	14	∣∣∣θ(⊺	∣∣∣θ(⊺	NOUN
ejpam-6413	372	15	)	)	PUNCT
ejpam-6413	373	1	+	+	CCONJ
ejpam-6413	373	2	⊺−	⊺−	PROPN
ejpam-6413	373	3	1	1	NUM
ejpam-6413	373	4	+	+	CCONJ
ejpam-6413	373	5	(	(	PUNCT
ejpam-6413	373	6	1−	1−	NUM
ejpam-6413	373	7	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	373	8	+	+	CCONJ
ejpam-6413	373	9	⊺θ+1	⊺θ+1	ADJ
ejpam-6413	373	10	∣∣∣⋋1	∣∣∣⋋1	ADJ
ejpam-6413	373	11	d⊺	d⊺	PROPN
ejpam-6413	373	12	+	+	CCONJ
ejpam-6413	373	13	∫	∫	PROPN
ejpam-6413	373	14	1	1	NUM
ejpam-6413	373	15	1	1	NUM
ejpam-6413	373	16	2	2	NUM
ejpam-6413	373	17	∣∣∣θ	∣∣∣θ	PROPN
ejpam-6413	373	18	−	−	PROPN
ejpam-6413	373	19	⊺+	⊺+	NOUN
ejpam-6413	373	20	(	(	PUNCT
ejpam-6413	373	21	1−	1−	NUM
ejpam-6413	373	22	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	373	23	+	+	CCONJ
ejpam-6413	373	24	⊺θ+1	⊺θ+1	ADJ
ejpam-6413	373	25	∣∣∣⋋1	∣∣∣⋋1	ADJ
ejpam-6413	373	26	d⊺	d⊺	PROPN
ejpam-6413	373	27	)	)	PUNCT
ejpam-6413	373	28	1	1	NUM
ejpam-6413	373	29	⋋1	⋋1	NUM
ejpam-6413	373	30	≤	≤	NOUN
ejpam-6413	373	31	(	(	PUNCT
ejpam-6413	373	32	µ−	µ−	PROPN
ejpam-6413	373	33	ā)2	ā)2	VERB
ejpam-6413	373	34	2(θ	2(θ	NUM
ejpam-6413	373	35	+	+	CCONJ
ejpam-6413	373	36	1	1	X
ejpam-6413	373	37	)	)	PUNCT
ejpam-6413	373	38	(	(	PUNCT
ejpam-6413	373	39	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	374	1	+	+	X
ejpam-6413	374	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	374	3	α+	α+	PUNCT
ejpam-6413	374	4	1	1	NUM
ejpam-6413	374	5	)	)	PUNCT
ejpam-6413	374	6	1	1	NUM
ejpam-6413	374	7	⋋2	⋋2	PROPN
ejpam-6413	374	8	×	×	NOUN
ejpam-6413	374	9	(	(	PUNCT
ejpam-6413	374	10	(	(	PUNCT
ejpam-6413	374	11	θ	θ	NOUN
ejpam-6413	374	12	+	+	NOUN
ejpam-6413	374	13	1	1	X
ejpam-6413	374	14	)	)	PUNCT
ejpam-6413	374	15	∫	∫	NOUN
ejpam-6413	374	16	1	1	NUM
ejpam-6413	374	17	2	2	NUM
ejpam-6413	374	18	0	0	NUM
ejpam-6413	374	19	⊺⋋1d	⊺⋋1d	PROPN
ejpam-6413	374	20	⊺+	⊺+	PROPN
ejpam-6413	374	21	∫	∫	PROPN
ejpam-6413	374	22	1	1	NUM
ejpam-6413	374	23	1	1	NUM
ejpam-6413	374	24	2	2	NUM
ejpam-6413	374	25	(	(	PUNCT
ejpam-6413	374	26	θ	θ	NOUN
ejpam-6413	374	27	−	−	PROPN
ejpam-6413	374	28	⊺+	⊺+	PROPN
ejpam-6413	374	29	1)⋋1d⊺	1)⋋1d⊺	NUM
ejpam-6413	374	30	)	)	PUNCT
ejpam-6413	374	31	1	1	NUM
ejpam-6413	374	32	⋋1	⋋1	NUM
ejpam-6413	374	33	≤	≤	NOUN
ejpam-6413	374	34	(	(	PUNCT
ejpam-6413	374	35	µ−	µ−	PROPN
ejpam-6413	374	36	ā)2	ā)2	VERB
ejpam-6413	374	37	2(θ	2(θ	NUM
ejpam-6413	374	38	+	+	CCONJ
ejpam-6413	374	39	1	1	X
ejpam-6413	374	40	)	)	PUNCT
ejpam-6413	374	41	(	(	PUNCT
ejpam-6413	374	42	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	375	1	+	+	X
ejpam-6413	375	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	375	3	α+	α+	PUNCT
ejpam-6413	375	4	1	1	NUM
ejpam-6413	375	5	)	)	PUNCT
ejpam-6413	375	6	1	1	NUM
ejpam-6413	375	7	⋋2	⋋2	NOUN
ejpam-6413	375	8	(	(	PUNCT
ejpam-6413	375	9	(	(	PUNCT
ejpam-6413	375	10	θ	θ	NOUN
ejpam-6413	375	11	+	+	NOUN
ejpam-6413	375	12	1	1	NUM
ejpam-6413	375	13	)	)	PUNCT
ejpam-6413	375	14	(	(	PUNCT
ejpam-6413	375	15	12	12	NUM
ejpam-6413	375	16	)	)	PUNCT
ejpam-6413	375	17	⋋1	⋋1	NUM
ejpam-6413	375	18	+	+	PROPN
ejpam-6413	375	19	1	1	NUM
ejpam-6413	375	20	⋋1	⋋1	NUM
ejpam-6413	375	21	+	+	SYM
ejpam-6413	375	22	1	1	NUM
ejpam-6413	375	23	−	−	NOUN
ejpam-6413	375	24	(	(	PUNCT
ejpam-6413	375	25	θ)⋋1	θ)⋋1	NOUN
ejpam-6413	375	26	+	+	PROPN
ejpam-6413	375	27	1	1	NUM
ejpam-6413	375	28	⋋1	⋋1	NUM
ejpam-6413	375	29	+	+	SYM
ejpam-6413	375	30	1	1	NUM
ejpam-6413	375	31	+	+	CCONJ
ejpam-6413	375	32	(	(	PUNCT
ejpam-6413	375	33	θ	θ	NOUN
ejpam-6413	375	34	+	+	NOUN
ejpam-6413	375	35	1	1	NUM
ejpam-6413	375	36	2	2	NUM
ejpam-6413	375	37	)	)	PUNCT
ejpam-6413	375	38	⋋1	⋋1	NUM
ejpam-6413	375	39	+	+	PROPN
ejpam-6413	375	40	1	1	NUM
ejpam-6413	375	41	⋋1	⋋1	NUM
ejpam-6413	375	42	+	+	CCONJ
ejpam-6413	375	43	1	1	NUM
ejpam-6413	375	44	)	)	PUNCT
ejpam-6413	375	45	1	1	NUM
ejpam-6413	375	46	⋋1	⋋1	PROPN
ejpam-6413	375	47	m.	m.	NOUN
ejpam-6413	375	48	samraiz	samraiz	PROPN
ejpam-6413	375	49	et	et	PROPN
ejpam-6413	375	50	al	al	PROPN
ejpam-6413	375	51	.	.	PUNCT
ejpam-6413	375	52	/	/	SYM
ejpam-6413	375	53	eur	eur	PROPN
ejpam-6413	375	54	.	.	PUNCT
ejpam-6413	376	1	j.	j.	PROPN
ejpam-6413	376	2	pure	pure	PROPN
ejpam-6413	376	3	appl	appl	PROPN
ejpam-6413	376	4	.	.	PROPN
ejpam-6413	376	5	math	math	PROPN
ejpam-6413	376	6	,	,	PUNCT
ejpam-6413	376	7	18	18	NUM
ejpam-6413	376	8	(	(	PUNCT
ejpam-6413	376	9	3	3	NUM
ejpam-6413	376	10	)	)	PUNCT
ejpam-6413	376	11	(	(	PUNCT
ejpam-6413	376	12	2025	2025	NUM
ejpam-6413	376	13	)	)	PUNCT
ejpam-6413	376	14	,	,	PUNCT
ejpam-6413	376	15	6413	6413	NUM
ejpam-6413	376	16	18	18	NUM
ejpam-6413	376	17	of	of	ADP
ejpam-6413	376	18	26	26	NUM
ejpam-6413	376	19	≤	≤	NOUN
ejpam-6413	376	20	(	(	PUNCT
ejpam-6413	376	21	µ−	µ−	PROPN
ejpam-6413	376	22	ā)2	ā)2	VERB
ejpam-6413	376	23	2(θ	2(θ	NUM
ejpam-6413	376	24	+	+	CCONJ
ejpam-6413	376	25	1	1	X
ejpam-6413	376	26	)	)	PUNCT
ejpam-6413	376	27	(	(	PUNCT
ejpam-6413	376	28	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	377	1	+	+	X
ejpam-6413	377	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	377	3	α+	α+	PUNCT
ejpam-6413	377	4	1	1	NUM
ejpam-6413	377	5	)	)	PUNCT
ejpam-6413	377	6	1	1	NUM
ejpam-6413	377	7	⋋2	⋋2	PROPN
ejpam-6413	377	8	×	×	NOUN
ejpam-6413	377	9	(	(	PUNCT
ejpam-6413	377	10	(	(	PUNCT
ejpam-6413	377	11	θ	θ	NOUN
ejpam-6413	377	12	+	+	PUNCT
ejpam-6413	377	13	1)2−⋋1−1	1)2−⋋1−1	NUM
ejpam-6413	377	14	−	−	PRON
ejpam-6413	377	15	θ⋋1	θ⋋1	X
ejpam-6413	377	16	+	+	PROPN
ejpam-6413	377	17	1	1	NUM
ejpam-6413	377	18	+	+	CCONJ
ejpam-6413	377	19	(	(	PUNCT
ejpam-6413	377	20	θ	θ	NOUN
ejpam-6413	377	21	+	+	NOUN
ejpam-6413	377	22	0.5)⋋1	0.5)⋋1	ADJ
ejpam-6413	377	23	+	+	ADJ
ejpam-6413	377	24	1	1	NUM
ejpam-6413	377	25	⋋1	⋋1	NUM
ejpam-6413	377	26	+	+	CCONJ
ejpam-6413	377	27	1	1	NUM
ejpam-6413	377	28	)	)	PUNCT
ejpam-6413	377	29	1	1	NUM
ejpam-6413	377	30	⋋1	⋋1	NUM
ejpam-6413	377	31	.	.	PUNCT
ejpam-6413	378	1	hence	hence	ADV
ejpam-6413	378	2	,	,	PUNCT
ejpam-6413	378	3	the	the	DET
ejpam-6413	378	4	proof	proof	NOUN
ejpam-6413	378	5	is	be	AUX
ejpam-6413	378	6	done	do	VERB
ejpam-6413	378	7	.	.	PUNCT
ejpam-6413	379	1	remark	remark	VERB
ejpam-6413	379	2	6	6	NUM
ejpam-6413	379	3	.	.	PUNCT
ejpam-6413	380	1	in	in	ADP
ejpam-6413	380	2	accordance	accordance	NOUN
ejpam-6413	380	3	with	with	ADP
ejpam-6413	380	4	the	the	DET
ejpam-6413	380	5	selection	selection	NOUN
ejpam-6413	380	6	of	of	ADP
ejpam-6413	380	7	parameters	parameter	NOUN
ejpam-6413	380	8	α	α	X
ejpam-6413	380	9	=	=	SYM
ejpam-6413	380	10	1	1	NUM
ejpam-6413	380	11	and	and	CCONJ
ejpam-6413	380	12	m	m	VERB
ejpam-6413	380	13	=	=	ADJ
ejpam-6413	380	14	1	1	NUM
ejpam-6413	380	15	in	in	ADP
ejpam-6413	380	16	theorem	theorem	NOUN
ejpam-6413	380	17	4	4	NUM
ejpam-6413	380	18	and	and	CCONJ
ejpam-6413	380	19	s	s	NOUN
ejpam-6413	380	20	=	=	SYM
ejpam-6413	380	21	1	1	NUM
ejpam-6413	380	22	in	in	ADP
ejpam-6413	380	23	[	[	PUNCT
ejpam-6413	380	24	2	2	NUM
ejpam-6413	380	25	,	,	PUNCT
ejpam-6413	380	26	theorem	theorem	VERB
ejpam-6413	380	27	4.2	4.2	NUM
ejpam-6413	380	28	]	]	PUNCT
ejpam-6413	380	29	,	,	PUNCT
ejpam-6413	380	30	we	we	PRON
ejpam-6413	380	31	get∣∣∣∣	get∣∣∣∣	VERB
ejpam-6413	380	32	γ(θ	γ(θ	PUNCT
ejpam-6413	381	1	+	+	CCONJ
ejpam-6413	381	2	1	1	X
ejpam-6413	381	3	)	)	PUNCT
ejpam-6413	381	4	2(b̄−	2(b̄−	NUM
ejpam-6413	381	5	ā)θ	ā)θ	NOUN
ejpam-6413	381	6	[	[	X
ejpam-6413	381	7	χθ	χθ	X
ejpam-6413	381	8	ā+𭟋(b̄	ā+𭟋(b̄	NUM
ejpam-6413	381	9	)	)	PUNCT
ejpam-6413	382	1	+	+	CCONJ
ejpam-6413	383	1	χθ	χθ	X
ejpam-6413	383	2	b̄−𭟋(ā)]−𭟋	b̄−𭟋(ā)]−𭟋	NOUN
ejpam-6413	383	3	(	(	PUNCT
ejpam-6413	383	4	ā+	ā+	PUNCT
ejpam-6413	383	5	b̄	b̄	VERB
ejpam-6413	383	6	2	2	NUM
ejpam-6413	383	7	)	)	PUNCT
ejpam-6413	383	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	383	9	≤	≤	NOUN
ejpam-6413	383	10	(	(	PUNCT
ejpam-6413	383	11	b̄−	b̄−	ADJ
ejpam-6413	383	12	ā)2	ā)2	NOUN
ejpam-6413	383	13	2(θ	2(θ	NUM
ejpam-6413	384	1	+	+	CCONJ
ejpam-6413	384	2	1	1	X
ejpam-6413	384	3	)	)	PUNCT
ejpam-6413	384	4	(	(	PUNCT
ejpam-6413	384	5	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	PROPN
ejpam-6413	384	6	+	+	CCONJ
ejpam-6413	384	7	|𭟋′′(b̄)|⋋2	|𭟋′′(b̄)|⋋2	NUM
ejpam-6413	384	8	2	2	NUM
ejpam-6413	384	9	)	)	PUNCT
ejpam-6413	384	10	1	1	NUM
ejpam-6413	384	11	⋋2	⋋2	PROPN
ejpam-6413	384	12	×	×	NOUN
ejpam-6413	384	13	(	(	PUNCT
ejpam-6413	384	14	(	(	PUNCT
ejpam-6413	384	15	θ	θ	NOUN
ejpam-6413	384	16	+	+	PUNCT
ejpam-6413	384	17	1)2−⋋1−1	1)2−⋋1−1	NUM
ejpam-6413	384	18	+	+	CCONJ
ejpam-6413	384	19	(	(	PUNCT
ejpam-6413	384	20	θ	θ	NOUN
ejpam-6413	384	21	+	+	PUNCT
ejpam-6413	384	22	0.5)⋋1	0.5)⋋1	ADJ
ejpam-6413	384	23	+	+	ADJ
ejpam-6413	384	24	1	1	NUM
ejpam-6413	384	25	−	−	ADP
ejpam-6413	384	26	θ⋋1	θ⋋1	NOUN
ejpam-6413	384	27	+	+	PROPN
ejpam-6413	384	28	1	1	NUM
ejpam-6413	384	29	⋋1	⋋1	NUM
ejpam-6413	384	30	+	+	CCONJ
ejpam-6413	384	31	1	1	NUM
ejpam-6413	384	32	)	)	PUNCT
ejpam-6413	384	33	1	1	NUM
ejpam-6413	384	34	⋋1	⋋1	NUM
ejpam-6413	384	35	.	.	PUNCT
ejpam-6413	385	1	in	in	ADP
ejpam-6413	385	2	the	the	DET
ejpam-6413	385	3	following	follow	VERB
ejpam-6413	385	4	result	result	NOUN
ejpam-6413	385	5	,	,	PUNCT
ejpam-6413	385	6	we	we	PRON
ejpam-6413	385	7	utilize	utilize	VERB
ejpam-6413	385	8	lemma	lemma	PROPN
ejpam-6413	385	9	6	6	NUM
ejpam-6413	385	10	.	.	PUNCT
ejpam-6413	385	11	theorem	theorem	NOUN
ejpam-6413	385	12	5	5	NUM
ejpam-6413	385	13	.	.	PUNCT
ejpam-6413	386	1	let	let	VERB
ejpam-6413	386	2	𭟋	𭟋	VERB
ejpam-6413	386	3	:	:	PUNCT
ejpam-6413	386	4	[	[	X
ejpam-6413	386	5	ā	ā	X
ejpam-6413	386	6	,	,	PUNCT
ejpam-6413	386	7	b̄	b̄	PROPN
ejpam-6413	386	8	]	]	PUNCT
ejpam-6413	386	9	−→	−→	NOUN
ejpam-6413	386	10	r	r	NOUN
ejpam-6413	386	11	be	be	VERB
ejpam-6413	386	12	a	a	DET
ejpam-6413	386	13	twice	twice	ADV
ejpam-6413	386	14	differentiable	differentiable	ADJ
ejpam-6413	386	15	function	function	NOUN
ejpam-6413	386	16	such	such	ADJ
ejpam-6413	386	17	that	that	DET
ejpam-6413	386	18	|𭟋′′|	|𭟋′′|	PROPN
ejpam-6413	386	19	is	be	AUX
ejpam-6413	386	20	lebesgue	lebesgue	NOUN
ejpam-6413	386	21	integerable	integerable	ADJ
ejpam-6413	386	22	,	,	PUNCT
ejpam-6413	386	23	increasing	increase	VERB
ejpam-6413	386	24	and	and	CCONJ
ejpam-6413	386	25	ga	ga	PROPN
ejpam-6413	386	26	(	(	PUNCT
ejpam-6413	386	27	α	α	NOUN
ejpam-6413	386	28	,	,	PUNCT
ejpam-6413	386	29	m)-convex	m)-convex	PUNCT
ejpam-6413	386	30	function	function	VERB
ejpam-6413	386	31	on	on	ADP
ejpam-6413	386	32	[	[	X
ejpam-6413	386	33	ā	ā	X
ejpam-6413	386	34	,	,	PUNCT
ejpam-6413	386	35	b̄	b̄	PROPN
ejpam-6413	386	36	]	]	PUNCT
ejpam-6413	386	37	.	.	PUNCT
ejpam-6413	387	1	then	then	ADV
ejpam-6413	387	2	for	for	ADP
ejpam-6413	387	3	some	some	DET
ejpam-6413	387	4	given	give	VERB
ejpam-6413	387	5	parameters	parameter	NOUN
ejpam-6413	387	6	θ	θ	PROPN
ejpam-6413	387	7	∈	∈	PROPN
ejpam-6413	387	8	(	(	PUNCT
ejpam-6413	387	9	0,+∞	0,+∞	NUM
ejpam-6413	387	10	)	)	PUNCT
ejpam-6413	387	11	and	and	CCONJ
ejpam-6413	387	12	(	(	PUNCT
ejpam-6413	387	13	α	α	NOUN
ejpam-6413	387	14	,	,	PUNCT
ejpam-6413	387	15	m	m	NOUN
ejpam-6413	387	16	)	)	PUNCT
ejpam-6413	387	17	∈	∈	PROPN
ejpam-6413	387	18	(	(	PUNCT
ejpam-6413	387	19	0	0	NUM
ejpam-6413	387	20	,	,	PUNCT
ejpam-6413	387	21	1]2	1]2	NUM
ejpam-6413	387	22	,	,	PUNCT
ejpam-6413	387	23	where	where	SCONJ
ejpam-6413	387	24	0	0	NUM
ejpam-6413	387	25	≤	≤	NUM
ejpam-6413	387	26	ā	ā	NOUN
ejpam-6413	387	27	<	<	X
ejpam-6413	387	28	b̄	b̄	VERB
ejpam-6413	387	29	the	the	DET
ejpam-6413	387	30	following	follow	VERB
ejpam-6413	387	31	inequality∣∣∣∣𭟋(ā	inequality∣∣∣∣𭟋(ā	NOUN
ejpam-6413	387	32	)	)	PUNCT
ejpam-6413	387	33	+	+	NOUN
ejpam-6413	387	34	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	387	35	)	)	PUNCT
ejpam-6413	387	36	⋎(⋎+	⋎(⋎+	VERB
ejpam-6413	387	37	1	1	NUM
ejpam-6413	387	38	)	)	PUNCT
ejpam-6413	388	1	+	+	CCONJ
ejpam-6413	388	2	2	2	NUM
ejpam-6413	388	3	⋎+	⋎+	DET
ejpam-6413	388	4	1	1	NUM
ejpam-6413	388	5	𭟋	𭟋	PROPN
ejpam-6413	388	6	(	(	PUNCT
ejpam-6413	388	7	ā+	ā+	PUNCT
ejpam-6413	388	8	µ	µ	X
ejpam-6413	388	9	2	2	NUM
ejpam-6413	388	10	)	)	PUNCT
ejpam-6413	388	11	−	−	PROPN
ejpam-6413	389	1	γ(θ	γ(θ	PROPN
ejpam-6413	390	1	+	+	CCONJ
ejpam-6413	390	2	1	1	X
ejpam-6413	390	3	)	)	PUNCT
ejpam-6413	390	4	⋎(µ−	⋎(µ−	NOUN
ejpam-6413	390	5	ā)θ	ā)θ	NOUN
ejpam-6413	391	1	[	[	X
ejpam-6413	391	2	χθ	χθ	X
ejpam-6413	391	3	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	391	4	)	)	PUNCT
ejpam-6413	392	1	+	+	CCONJ
ejpam-6413	392	2	χθ	χθ	X
ejpam-6413	392	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	392	4	)	)	PUNCT
ejpam-6413	392	5	]	]	PUNCT
ejpam-6413	393	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	393	2	≤	≤	NOUN
ejpam-6413	393	3	(	(	PUNCT
ejpam-6413	393	4	µ−	µ−	PROPN
ejpam-6413	393	5	ā)2	ā)2	VERB
ejpam-6413	393	6	⋎(θ	⋎(θ	NOUN
ejpam-6413	393	7	+	+	X
ejpam-6413	393	8	1)(⋎+	1)(⋎+	NUM
ejpam-6413	393	9	1	1	NUM
ejpam-6413	393	10	)	)	PUNCT
ejpam-6413	393	11	max	max	NOUN
ejpam-6413	394	1	[	[	PUNCT
ejpam-6413	394	2	[	[	X
ejpam-6413	394	3	(	(	PUNCT
ejpam-6413	394	4	⋎+	⋎+	PROPN
ejpam-6413	394	5	1)−	1)−	PROPN
ejpam-6413	394	6	(	(	PUNCT
ejpam-6413	394	7	⋎+	⋎+	DET
ejpam-6413	394	8	1)2−θ	1)2−θ	ADJ
ejpam-6413	394	9	]	]	X
ejpam-6413	394	10	×	×	PROPN
ejpam-6413	394	11	(	(	PUNCT
ejpam-6413	394	12	2−α|𭟋′′(ā	2−α|𭟋′′(ā	NUM
ejpam-6413	394	13	)	)	PUNCT
ejpam-6413	394	14	+	+	CCONJ
ejpam-6413	394	15	(	(	PUNCT
ejpam-6413	394	16	α+	α+	X
ejpam-6413	394	17	1−	1−	NUM
ejpam-6413	394	18	2−α)m|𭟋′′(b̄	2−α)m|𭟋′′(b̄	NUM
ejpam-6413	394	19	)	)	PUNCT
ejpam-6413	394	20	2(α+	2(α+	NUM
ejpam-6413	394	21	1	1	NUM
ejpam-6413	394	22	)	)	PUNCT
ejpam-6413	394	23	)	)	PUNCT
ejpam-6413	394	24	−⋎	−⋎	NOUN
ejpam-6413	394	25	(	(	PUNCT
ejpam-6413	394	26	θ	θ	NOUN
ejpam-6413	394	27	+	+	NOUN
ejpam-6413	394	28	1	1	X
ejpam-6413	394	29	)	)	PUNCT
ejpam-6413	394	30	(	(	PUNCT
ejpam-6413	394	31	2−α+1|𭟋′′(ā)|+	2−α+1|𭟋′′(ā)|+	NUM
ejpam-6413	394	32	(	(	PUNCT
ejpam-6413	394	33	α+	α+	PROPN
ejpam-6413	394	34	2−	2−	NUM
ejpam-6413	394	35	2−α+1)m|𭟋′′(b̄)|	2−α+1)m|𭟋′′(b̄)|	NUM
ejpam-6413	394	36	8(α+	8(α+	NUM
ejpam-6413	394	37	2	2	NUM
ejpam-6413	394	38	)	)	PUNCT
ejpam-6413	394	39	)	)	PUNCT
ejpam-6413	394	40	,	,	PUNCT
ejpam-6413	394	41	⋎(θ	⋎(θ	NOUN
ejpam-6413	394	42	+	+	NOUN
ejpam-6413	394	43	1	1	NUM
ejpam-6413	394	44	)	)	PUNCT
ejpam-6413	394	45	(	(	PUNCT
ejpam-6413	394	46	2−α+1|𭟋′′(ā)|+	2−α+1|𭟋′′(ā)|+	NUM
ejpam-6413	394	47	(	(	PUNCT
ejpam-6413	394	48	α+	α+	PROPN
ejpam-6413	394	49	2−	2−	NUM
ejpam-6413	394	50	2−α+1)m|𭟋′′(b̄)|	2−α+1)m|𭟋′′(b̄)|	NUM
ejpam-6413	394	51	8(α+	8(α+	NUM
ejpam-6413	394	52	2	2	NUM
ejpam-6413	394	53	)	)	PUNCT
ejpam-6413	394	54	)	)	PUNCT
ejpam-6413	394	55	]	]	PUNCT
ejpam-6413	395	1	+	+	CCONJ
ejpam-6413	395	2	(	(	PUNCT
ejpam-6413	395	3	µ−	µ−	PROPN
ejpam-6413	395	4	ā)2	ā)2	VERB
ejpam-6413	395	5	⋎(θ	⋎(θ	NOUN
ejpam-6413	395	6	+	+	X
ejpam-6413	395	7	1)(⋎+	1)(⋎+	NUM
ejpam-6413	395	8	1	1	NUM
ejpam-6413	395	9	)	)	PUNCT
ejpam-6413	395	10	max	max	NOUN
ejpam-6413	396	1	[	[	PUNCT
ejpam-6413	396	2	[	[	X
ejpam-6413	396	3	(	(	PUNCT
ejpam-6413	396	4	⋎+	⋎+	PROPN
ejpam-6413	396	5	1)−	1)−	PROPN
ejpam-6413	396	6	(	(	PUNCT
ejpam-6413	396	7	⋎+	⋎+	DET
ejpam-6413	396	8	1)2−θ	1)2−θ	NUM
ejpam-6413	396	9	−⋎(θ	−⋎(θ	NOUN
ejpam-6413	396	10	+	+	NOUN
ejpam-6413	396	11	1	1	NUM
ejpam-6413	396	12	)	)	PUNCT
ejpam-6413	396	13	]	]	PUNCT
ejpam-6413	396	14	×	×	NOUN
ejpam-6413	396	15	(	(	PUNCT
ejpam-6413	396	16	(	(	PUNCT
ejpam-6413	396	17	2−	2−	NUM
ejpam-6413	396	18	2−α)|𭟋′′(ā)|+	2−α)|𭟋′′(ā)|+	NUM
ejpam-6413	396	19	(	(	PUNCT
ejpam-6413	396	20	α−	α−	ADP
ejpam-6413	396	21	1	1	NUM
ejpam-6413	396	22	+	+	NUM
ejpam-6413	396	23	2−α)m|𭟋′′(b̄)|	2−α)m|𭟋′′(b̄)|	NUM
ejpam-6413	396	24	2(α+	2(α+	NUM
ejpam-6413	396	25	1	1	NUM
ejpam-6413	396	26	)	)	PUNCT
ejpam-6413	396	27	)	)	PUNCT
ejpam-6413	397	1	+	+	PUNCT
ejpam-6413	397	2	⋎	⋎	NOUN
ejpam-6413	397	3	(	(	PUNCT
ejpam-6413	397	4	θ	θ	NOUN
ejpam-6413	397	5	+	+	NOUN
ejpam-6413	397	6	1	1	X
ejpam-6413	397	7	)	)	PUNCT
ejpam-6413	397	8	(	(	PUNCT
ejpam-6413	397	9	(	(	PUNCT
ejpam-6413	397	10	8−	8−	NUM
ejpam-6413	397	11	2−α+1)|𭟋′′(ā)|+	2−α+1)|𭟋′′(ā)|+	NUM
ejpam-6413	397	12	(	(	PUNCT
ejpam-6413	397	13	3α−	3α−	PROPN
ejpam-6413	397	14	2	2	NUM
ejpam-6413	397	15	+	+	CCONJ
ejpam-6413	397	16	2−α+1)m|𭟋′′(b̄)|	2−α+1)m|𭟋′′(b̄)|	NUM
ejpam-6413	397	17	8(α+	8(α+	NUM
ejpam-6413	397	18	2	2	NUM
ejpam-6413	397	19	)	)	PUNCT
ejpam-6413	397	20	)	)	PUNCT
ejpam-6413	397	21	,	,	PUNCT
ejpam-6413	397	22	⋎(θ	⋎(θ	NOUN
ejpam-6413	397	23	+	+	NOUN
ejpam-6413	397	24	1	1	NUM
ejpam-6413	397	25	)	)	PUNCT
ejpam-6413	397	26	(	(	PUNCT
ejpam-6413	397	27	(	(	PUNCT
ejpam-6413	397	28	2−	2−	NUM
ejpam-6413	397	29	2−α)|𭟋′′(ā)|+	2−α)|𭟋′′(ā)|+	NUM
ejpam-6413	397	30	(	(	PUNCT
ejpam-6413	397	31	α−	α−	ADP
ejpam-6413	397	32	1	1	NUM
ejpam-6413	397	33	+	+	NUM
ejpam-6413	397	34	2−α)m|𭟋′′(b̄)|	2−α)m|𭟋′′(b̄)|	NUM
ejpam-6413	397	35	2(α+	2(α+	NUM
ejpam-6413	397	36	1	1	NUM
ejpam-6413	397	37	)	)	PUNCT
ejpam-6413	397	38	m.	m.	NOUN
ejpam-6413	397	39	samraiz	samraiz	PROPN
ejpam-6413	397	40	et	et	PROPN
ejpam-6413	397	41	al	al	PROPN
ejpam-6413	397	42	.	.	PUNCT
ejpam-6413	397	43	/	/	SYM
ejpam-6413	397	44	eur	eur	PROPN
ejpam-6413	397	45	.	.	PUNCT
ejpam-6413	398	1	j.	j.	PROPN
ejpam-6413	398	2	pure	pure	PROPN
ejpam-6413	398	3	appl	appl	PROPN
ejpam-6413	398	4	.	.	PROPN
ejpam-6413	398	5	math	math	PROPN
ejpam-6413	398	6	,	,	PUNCT
ejpam-6413	398	7	18	18	NUM
ejpam-6413	398	8	(	(	PUNCT
ejpam-6413	398	9	3	3	NUM
ejpam-6413	398	10	)	)	PUNCT
ejpam-6413	398	11	(	(	PUNCT
ejpam-6413	398	12	2025	2025	NUM
ejpam-6413	398	13	)	)	PUNCT
ejpam-6413	398	14	,	,	PUNCT
ejpam-6413	398	15	6413	6413	NUM
ejpam-6413	398	16	19	19	NUM
ejpam-6413	398	17	of	of	ADP
ejpam-6413	398	18	26	26	NUM
ejpam-6413	398	19	−(8−	−(8−	NOUN
ejpam-6413	398	20	2−α+1)|𭟋′′(ā)|+	2−α+1)|𭟋′′(ā)|+	NUM
ejpam-6413	398	21	(	(	PUNCT
ejpam-6413	398	22	3α−	3α−	PROPN
ejpam-6413	398	23	2	2	NUM
ejpam-6413	398	24	+	+	SYM
ejpam-6413	398	25	2−α+1)m|𭟋′′(b̄	2−α+1)m|𭟋′′(b̄	NUM
ejpam-6413	398	26	)	)	PUNCT
ejpam-6413	398	27	8(α+	8(α+	NUM
ejpam-6413	398	28	2	2	NUM
ejpam-6413	398	29	)	)	PUNCT
ejpam-6413	398	30	)	)	PUNCT
ejpam-6413	398	31	]	]	PUNCT
ejpam-6413	398	32	holds	hold	VERB
ejpam-6413	398	33	true	true	ADJ
ejpam-6413	398	34	.	.	PUNCT
ejpam-6413	399	1	proof	proof	NOUN
ejpam-6413	399	2	.	.	PUNCT
ejpam-6413	400	1	by	by	ADP
ejpam-6413	400	2	using	use	VERB
ejpam-6413	400	3	lemma	lemma	PROPN
ejpam-6413	400	4	2	2	NUM
ejpam-6413	400	5	,	,	PUNCT
ejpam-6413	400	6	6	6	NUM
ejpam-6413	400	7	and	and	CCONJ
ejpam-6413	400	8	7	7	NUM
ejpam-6413	400	9	,	,	PUNCT
ejpam-6413	400	10	we	we	PRON
ejpam-6413	400	11	have∣∣∣∣𭟋(ā	have∣∣∣∣𭟋(ā	NOUN
ejpam-6413	400	12	)	)	PUNCT
ejpam-6413	400	13	+	+	NOUN
ejpam-6413	400	14	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	400	15	)	)	PUNCT
ejpam-6413	400	16	⋎(⋎+	⋎(⋎+	VERB
ejpam-6413	400	17	1	1	NUM
ejpam-6413	400	18	)	)	PUNCT
ejpam-6413	400	19	+	+	CCONJ
ejpam-6413	400	20	2	2	NUM
ejpam-6413	400	21	⋎+	⋎+	DET
ejpam-6413	400	22	1	1	NUM
ejpam-6413	400	23	𭟋	𭟋	PROPN
ejpam-6413	400	24	(	(	PUNCT
ejpam-6413	400	25	ā+	ā+	PUNCT
ejpam-6413	400	26	µ	µ	X
ejpam-6413	400	27	2	2	NUM
ejpam-6413	400	28	)	)	PUNCT
ejpam-6413	400	29	−	−	PROPN
ejpam-6413	400	30	γ(θ	γ(θ	PROPN
ejpam-6413	401	1	+	+	CCONJ
ejpam-6413	401	2	1	1	X
ejpam-6413	401	3	)	)	PUNCT
ejpam-6413	401	4	⋎(µ−	⋎(µ−	NOUN
ejpam-6413	401	5	ā)θ	ā)θ	NOUN
ejpam-6413	402	1	[	[	X
ejpam-6413	402	2	χθ	χθ	X
ejpam-6413	402	3	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	402	4	)	)	PUNCT
ejpam-6413	403	1	+	+	CCONJ
ejpam-6413	403	2	χθ	χθ	X
ejpam-6413	403	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	403	4	)	)	PUNCT
ejpam-6413	403	5	]	]	PUNCT
ejpam-6413	404	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	404	2	≤	≤	NOUN
ejpam-6413	404	3	(	(	PUNCT
ejpam-6413	404	4	µ−	µ−	PROPN
ejpam-6413	404	5	ā)2	ā)2	PROPN
ejpam-6413	404	6	∫	∫	PROPN
ejpam-6413	404	7	1	1	NUM
ejpam-6413	404	8	0	0	NUM
ejpam-6413	404	9	|q0(⊺)||𭟋′′(⊺ā+m(1−	|q0(⊺)||𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	404	10	⊺)b̄)|d⊺	⊺)b̄)|d⊺	PROPN
ejpam-6413	404	11	≤	≤	NOUN
ejpam-6413	404	12	(	(	PUNCT
ejpam-6413	404	13	µ−	µ−	PROPN
ejpam-6413	404	14	ā)2	ā)2	PROPN
ejpam-6413	404	15	∫	∫	PROPN
ejpam-6413	404	16	1	1	NUM
ejpam-6413	404	17	0	0	NUM
ejpam-6413	404	18	|q0(⊺)||𭟋′′(ā⊺b̄m(1−⊺)|d⊺	|q0(⊺)||𭟋′′(ā⊺b̄m(1−⊺)|d⊺	X
ejpam-6413	404	19	≤	≤	NOUN
ejpam-6413	404	20	(	(	PUNCT
ejpam-6413	404	21	µ−	µ−	PROPN
ejpam-6413	404	22	ā)2	ā)2	NOUN
ejpam-6413	404	23	2	2	NUM
ejpam-6413	404	24	∫	∫	NOUN
ejpam-6413	404	25	1	1	NUM
ejpam-6413	404	26	0	0	NUM
ejpam-6413	404	27	|q0(⊺)|[⊺α|𭟋′′(ā)|+m(1−	|q0(⊺)|[⊺α|𭟋′′(ā)|+m(1−	NOUN
ejpam-6413	404	28	⊺α)|𭟋′′(b̄)|]d⊺	⊺α)|𭟋′′(b̄)|]d⊺	PROPN
ejpam-6413	404	29	≤	≤	NOUN
ejpam-6413	404	30	(	(	PUNCT
ejpam-6413	404	31	µ−	µ−	PROPN
ejpam-6413	404	32	ā)2	ā)2	NOUN
ejpam-6413	404	33	2	2	NUM
ejpam-6413	404	34	(	(	PUNCT
ejpam-6413	404	35	∫	∫	PROPN
ejpam-6413	404	36	1	1	NUM
ejpam-6413	404	37	2	2	NUM
ejpam-6413	404	38	0	0	NUM
ejpam-6413	404	39	∣∣∣∣1−	∣∣∣∣1−	NOUN
ejpam-6413	404	40	(	(	PUNCT
ejpam-6413	404	41	1−	1−	NUM
ejpam-6413	404	42	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	404	43	−	−	PROPN
ejpam-6413	404	44	⊺θ+1	⊺θ+1	NOUN
ejpam-6413	404	45	⋎(θ	⋎(θ	NOUN
ejpam-6413	404	46	+	+	NOUN
ejpam-6413	404	47	1	1	NUM
ejpam-6413	404	48	)	)	PUNCT
ejpam-6413	404	49	−	−	NOUN
ejpam-6413	404	50	⊺	⊺	NUM
ejpam-6413	404	51	⋎+	⋎+	DET
ejpam-6413	404	52	1	1	NUM
ejpam-6413	404	53	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	404	54	×[⊺α|𭟋′′(ā)|+m(1−	×[⊺α|𭟋′′(ā)|+m(1−	NOUN
ejpam-6413	404	55	⊺α)|𭟋′′(b̄)|]d⊺	⊺α)|𭟋′′(b̄)|]d⊺	PROPN
ejpam-6413	404	56	+	+	NUM
ejpam-6413	404	57	∫	∫	PROPN
ejpam-6413	404	58	1	1	NUM
ejpam-6413	404	59	1	1	NUM
ejpam-6413	404	60	2	2	NUM
ejpam-6413	404	61	∣∣∣∣1−	∣∣∣∣1−	NOUN
ejpam-6413	404	62	(	(	PUNCT
ejpam-6413	404	63	1−	1−	NUM
ejpam-6413	404	64	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	404	65	−	−	PROPN
ejpam-6413	404	66	⊺θ+1	⊺θ+1	NOUN
ejpam-6413	404	67	⋎(θ	⋎(θ	NOUN
ejpam-6413	404	68	+	+	NOUN
ejpam-6413	404	69	1	1	NUM
ejpam-6413	404	70	)	)	PUNCT
ejpam-6413	404	71	−	−	PROPN
ejpam-6413	404	72	1−	1−	NUM
ejpam-6413	404	73	⊺	⊺	NUM
ejpam-6413	404	74	⋎+	⋎+	DET
ejpam-6413	404	75	1	1	NUM
ejpam-6413	404	76	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	404	77	[	[	X
ejpam-6413	404	78	⊺α|𭟋′′(ā)|+m(1−	⊺α|𭟋′′(ā)|+m(1−	X
ejpam-6413	404	79	⊺α)|𭟋′′(b̄)|]d⊺	⊺α)|𭟋′′(b̄)|]d⊺	NOUN
ejpam-6413	404	80	)	)	PUNCT
ejpam-6413	404	81	≤	≤	NOUN
ejpam-6413	404	82	(	(	PUNCT
ejpam-6413	404	83	µ−	µ−	PROPN
ejpam-6413	404	84	ā)2	ā)2	VERB
ejpam-6413	404	85	2(θ	2(θ	NUM
ejpam-6413	404	86	+	+	CCONJ
ejpam-6413	404	87	1)(⋎+	1)(⋎+	NUM
ejpam-6413	404	88	1	1	NUM
ejpam-6413	404	89	)	)	PUNCT
ejpam-6413	404	90	×	×	NOUN
ejpam-6413	404	91	(	(	PUNCT
ejpam-6413	404	92	∫	∫	PROPN
ejpam-6413	404	93	1	1	NUM
ejpam-6413	404	94	2	2	NUM
ejpam-6413	404	95	0	0	NUM
ejpam-6413	405	1	[	[	X
ejpam-6413	405	2	(	(	PUNCT
ejpam-6413	405	3	⋎+	⋎+	PROPN
ejpam-6413	405	4	1)−	1)−	PROPN
ejpam-6413	405	5	(	(	PUNCT
ejpam-6413	405	6	⋎+	⋎+	PROPN
ejpam-6413	405	7	1)(1−	1)(1−	NUM
ejpam-6413	405	8	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	405	9	−	−	PROPN
ejpam-6413	405	10	(	(	PUNCT
ejpam-6413	405	11	⋎+	⋎+	DET
ejpam-6413	405	12	1	1	X
ejpam-6413	405	13	)	)	PUNCT
ejpam-6413	405	14	⊺θ+1	⊺θ+1	NOUN
ejpam-6413	405	15	−	−	NOUN
ejpam-6413	405	16	⊺	⊺	PUNCT
ejpam-6413	405	17	⋎(θ	⋎(θ	NOUN
ejpam-6413	405	18	+	+	NOUN
ejpam-6413	405	19	1	1	NUM
ejpam-6413	405	20	)	)	PUNCT
ejpam-6413	405	21	]	]	PUNCT
ejpam-6413	405	22	×(⊺α|𭟋′′(ā)|+m(1−	×(⊺α|𭟋′′(ā)|+m(1−	PROPN
ejpam-6413	405	23	⊺α)|𭟋′′(b̄)|)d⊺	⊺α)|𭟋′′(b̄)|)d⊺	PROPN
ejpam-6413	405	24	+	+	CCONJ
ejpam-6413	405	25	∫	∫	PROPN
ejpam-6413	405	26	1	1	NUM
ejpam-6413	405	27	1	1	NUM
ejpam-6413	405	28	2	2	NUM
ejpam-6413	405	29	[	[	X
ejpam-6413	405	30	(	(	PUNCT
ejpam-6413	405	31	⋎+	⋎+	PROPN
ejpam-6413	405	32	1)−	1)−	PROPN
ejpam-6413	405	33	(	(	PUNCT
ejpam-6413	405	34	⋎+	⋎+	PROPN
ejpam-6413	405	35	1)(1−	1)(1−	NUM
ejpam-6413	405	36	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	405	37	−	−	PROPN
ejpam-6413	405	38	(	(	PUNCT
ejpam-6413	405	39	⋎+	⋎+	DET
ejpam-6413	405	40	1	1	X
ejpam-6413	405	41	)	)	PUNCT
ejpam-6413	405	42	⊺θ+1	⊺θ+1	ADJ
ejpam-6413	405	43	−⋎	−⋎	NOUN
ejpam-6413	405	44	(	(	PUNCT
ejpam-6413	405	45	θ	θ	X
ejpam-6413	405	46	+	+	CCONJ
ejpam-6413	405	47	1)(1−	1)(1−	NUM
ejpam-6413	405	48	⊺	⊺	NOUN
ejpam-6413	405	49	)	)	PUNCT
ejpam-6413	405	50	]	]	PUNCT
ejpam-6413	405	51	×[⊺α|𭟋′′(ā)|+m(1−	×[⊺α|𭟋′′(ā)|+m(1−	PROPN
ejpam-6413	405	52	⊺α)|𭟋′′(b̄)|d⊺	⊺α)|𭟋′′(b̄)|d⊺	X
ejpam-6413	405	53	]	]	PUNCT
ejpam-6413	405	54	)	)	PUNCT
ejpam-6413	405	55	.	.	PUNCT
ejpam-6413	406	1	(	(	PUNCT
ejpam-6413	406	2	31	31	NUM
ejpam-6413	406	3	)	)	PUNCT
ejpam-6413	406	4	let	let	VERB
ejpam-6413	406	5	us	we	PRON
ejpam-6413	406	6	consider∫	consider∫	VERB
ejpam-6413	406	7	1	1	NUM
ejpam-6413	406	8	2	2	NUM
ejpam-6413	406	9	0	0	NUM
ejpam-6413	407	1	[	[	X
ejpam-6413	407	2	⋎+	⋎+	PRON
ejpam-6413	407	3	1−	1−	NUM
ejpam-6413	407	4	(	(	PUNCT
ejpam-6413	407	5	⋎+	⋎+	DET
ejpam-6413	407	6	1)[(1−	1)[(1−	NUM
ejpam-6413	407	7	⊺)θ+1	⊺)θ+1	NOUN
ejpam-6413	407	8	+	+	CCONJ
ejpam-6413	407	9	⊺θ+1]−	⊺θ+1]−	DET
ejpam-6413	407	10	⊺	⊺	VERB
ejpam-6413	407	11	⋎	⋎	NOUN
ejpam-6413	407	12	(	(	PUNCT
ejpam-6413	407	13	θ	θ	NOUN
ejpam-6413	407	14	+	+	NOUN
ejpam-6413	407	15	1	1	NUM
ejpam-6413	407	16	)	)	PUNCT
ejpam-6413	407	17	]	]	PUNCT
ejpam-6413	408	1	×	×	NOUN
ejpam-6413	409	1	[	[	X
ejpam-6413	409	2	⊺α|𭟋′′(ā)|+m(1−	⊺α|𭟋′′(ā)|+m(1−	X
ejpam-6413	409	3	⊺α)|𭟋′′(b̄)|]d⊺	⊺α)|𭟋′′(b̄)|]d⊺	NOUN
ejpam-6413	409	4	≤	≤	NOUN
ejpam-6413	409	5	[	[	X
ejpam-6413	409	6	(	(	PUNCT
ejpam-6413	409	7	⋎+	⋎+	PROPN
ejpam-6413	409	8	1)−	1)−	PROPN
ejpam-6413	409	9	(	(	PUNCT
ejpam-6413	409	10	⋎+	⋎+	PRON
ejpam-6413	409	11	1)2−θ	1)2−θ	NUM
ejpam-6413	409	12	]	]	X
ejpam-6413	409	13	(	(	PUNCT
ejpam-6413	409	14	|𭟋′′(ā)|	|𭟋′′(ā)|	NUM
ejpam-6413	409	15	∫	∫	PROPN
ejpam-6413	409	16	1	1	NUM
ejpam-6413	409	17	2	2	NUM
ejpam-6413	409	18	0	0	NUM
ejpam-6413	409	19	⊺αd	⊺αd	NOUN
ejpam-6413	409	20	⊺+m|𭟋′′(b̄)|	⊺+m|𭟋′′(b̄)|	PROPN
ejpam-6413	409	21	∫	∫	PROPN
ejpam-6413	409	22	1	1	NUM
ejpam-6413	409	23	2	2	NUM
ejpam-6413	409	24	0	0	NUM
ejpam-6413	409	25	(	(	PUNCT
ejpam-6413	409	26	1−	1−	NUM
ejpam-6413	409	27	⊺α)d⊺	⊺α)d⊺	ADJ
ejpam-6413	409	28	)	)	PUNCT
ejpam-6413	409	29	−	−	NOUN
ejpam-6413	409	30	⊺	⊺	NUM
ejpam-6413	409	31	⋎	⋎	NOUN
ejpam-6413	409	32	(	(	PUNCT
ejpam-6413	409	33	θ	θ	NOUN
ejpam-6413	409	34	+	+	PROPN
ejpam-6413	409	35	1	1	X
ejpam-6413	409	36	)	)	PUNCT
ejpam-6413	409	37	(	(	PUNCT
ejpam-6413	409	38	|𭟋′′(ā)|	|𭟋′′(ā)|	NUM
ejpam-6413	409	39	∫	∫	PROPN
ejpam-6413	409	40	1	1	NUM
ejpam-6413	409	41	2	2	NUM
ejpam-6413	409	42	0	0	NUM
ejpam-6413	409	43	⊺αd	⊺αd	NOUN
ejpam-6413	409	44	⊺+m|𭟋′′(b̄)|	⊺+m|𭟋′′(b̄)|	PROPN
ejpam-6413	409	45	∫	∫	PROPN
ejpam-6413	409	46	1	1	NUM
ejpam-6413	409	47	2	2	NUM
ejpam-6413	409	48	0	0	NUM
ejpam-6413	409	49	(	(	PUNCT
ejpam-6413	409	50	1−	1−	NUM
ejpam-6413	409	51	⊺α)d⊺	⊺α)d⊺	ADJ
ejpam-6413	409	52	)	)	PUNCT
ejpam-6413	409	53	m.	m.	NOUN
ejpam-6413	409	54	samraiz	samraiz	PROPN
ejpam-6413	409	55	et	et	PROPN
ejpam-6413	409	56	al	al	PROPN
ejpam-6413	409	57	.	.	PUNCT
ejpam-6413	409	58	/	/	SYM
ejpam-6413	409	59	eur	eur	PROPN
ejpam-6413	409	60	.	.	PUNCT
ejpam-6413	410	1	j.	j.	PROPN
ejpam-6413	410	2	pure	pure	PROPN
ejpam-6413	410	3	appl	appl	PROPN
ejpam-6413	410	4	.	.	PROPN
ejpam-6413	410	5	math	math	PROPN
ejpam-6413	410	6	,	,	PUNCT
ejpam-6413	410	7	18	18	NUM
ejpam-6413	410	8	(	(	PUNCT
ejpam-6413	410	9	3	3	NUM
ejpam-6413	410	10	)	)	PUNCT
ejpam-6413	410	11	(	(	PUNCT
ejpam-6413	410	12	2025	2025	NUM
ejpam-6413	410	13	)	)	PUNCT
ejpam-6413	410	14	,	,	PUNCT
ejpam-6413	410	15	6413	6413	NUM
ejpam-6413	410	16	20	20	NUM
ejpam-6413	410	17	of	of	ADP
ejpam-6413	410	18	26	26	NUM
ejpam-6413	410	19	≤	≤	NOUN
ejpam-6413	411	1	[	[	X
ejpam-6413	411	2	(	(	PUNCT
ejpam-6413	411	3	⋎+	⋎+	PROPN
ejpam-6413	411	4	1)−	1)−	PROPN
ejpam-6413	411	5	(	(	PUNCT
ejpam-6413	411	6	⋎+	⋎+	PRON
ejpam-6413	411	7	1)2−θ	1)2−θ	NUM
ejpam-6413	411	8	]	]	X
ejpam-6413	411	9	(	(	PUNCT
ejpam-6413	411	10	|𭟋′′(ā)2−α	|𭟋′′(ā)2−α	PUNCT
ejpam-6413	411	11	+	+	NOUN
ejpam-6413	411	12	m|𭟋′′(b̄)(α+	m|𭟋′′(b̄)(α+	NOUN
ejpam-6413	411	13	1−	1−	NUM
ejpam-6413	411	14	2−α	2−α	NUM
ejpam-6413	411	15	)	)	PUNCT
ejpam-6413	411	16	2(α+	2(α+	NUM
ejpam-6413	411	17	1	1	NUM
ejpam-6413	411	18	)	)	PUNCT
ejpam-6413	411	19	)	)	PUNCT
ejpam-6413	412	1	−⋎(θ	−⋎(θ	NOUN
ejpam-6413	412	2	+	+	NOUN
ejpam-6413	412	3	1	1	NUM
ejpam-6413	412	4	)	)	PUNCT
ejpam-6413	412	5	(	(	PUNCT
ejpam-6413	412	6	|𭟋′′(ā)|2−α+1	|𭟋′′(ā)|2−α+1	PROPN
ejpam-6413	412	7	+	+	NOUN
ejpam-6413	412	8	m|𭟋′′(b̄)(α+	m|𭟋′′(b̄)(α+	NOUN
ejpam-6413	412	9	2−	2−	NUM
ejpam-6413	412	10	2−α+1	2−α+1	NOUN
ejpam-6413	412	11	)	)	PUNCT
ejpam-6413	412	12	8(α+	8(α+	NUM
ejpam-6413	412	13	2	2	NUM
ejpam-6413	412	14	)	)	PUNCT
ejpam-6413	412	15	)	)	PUNCT
ejpam-6413	412	16	,	,	PUNCT
ejpam-6413	412	17	(	(	PUNCT
ejpam-6413	412	18	32	32	NUM
ejpam-6413	412	19	)	)	PUNCT
ejpam-6413	412	20	and	and	CCONJ
ejpam-6413	412	21	∫	∫	PROPN
ejpam-6413	412	22	1	1	NUM
ejpam-6413	412	23	2	2	NUM
ejpam-6413	412	24	0	0	NUM
ejpam-6413	413	1	[	[	X
ejpam-6413	413	2	−⋎−1	−⋎−1	X
ejpam-6413	413	3	+	+	X
ejpam-6413	413	4	(	(	PUNCT
ejpam-6413	413	5	⋎+	⋎+	DET
ejpam-6413	413	6	1)2−θ	1)2−θ	NUM
ejpam-6413	413	7	+	+	NOUN
ejpam-6413	413	8	⊺	⊺	NUM
ejpam-6413	413	9	⋎	⋎	NOUN
ejpam-6413	413	10	(	(	PUNCT
ejpam-6413	413	11	θ	θ	NOUN
ejpam-6413	413	12	+	+	NOUN
ejpam-6413	413	13	1	1	NUM
ejpam-6413	413	14	)	)	PUNCT
ejpam-6413	413	15	]	]	PUNCT
ejpam-6413	414	1	[	[	PUNCT
ejpam-6413	414	2	|𭟋′′(ā)|	|𭟋′′(ā)|	PROPN
ejpam-6413	414	3	⊺α	⊺α	ADJ
ejpam-6413	414	4	+	+	PROPN
ejpam-6413	414	5	m|𭟋′′(b̄)|(1−	m|𭟋′′(b̄)|(1−	PROPN
ejpam-6413	414	6	⊺α	⊺α	ADJ
ejpam-6413	414	7	)	)	PUNCT
ejpam-6413	414	8	]	]	PUNCT
ejpam-6413	415	1	d⊺	d⊺	PROPN
ejpam-6413	415	2	≤	≤	X
ejpam-6413	416	1	[	[	X
ejpam-6413	416	2	−⋎−1	−⋎−1	X
ejpam-6413	416	3	+	+	X
ejpam-6413	416	4	(	(	PUNCT
ejpam-6413	416	5	⋎+	⋎+	DET
ejpam-6413	416	6	1)2−θ	1)2−θ	NUM
ejpam-6413	416	7	]	]	X
ejpam-6413	416	8	∫	∫	PROPN
ejpam-6413	416	9	1	1	NUM
ejpam-6413	416	10	2	2	NUM
ejpam-6413	416	11	0	0	NUM
ejpam-6413	416	12	[	[	PUNCT
ejpam-6413	416	13	|𭟋′′(ā)|	|𭟋′′(ā)|	PROPN
ejpam-6413	416	14	⊺α	⊺α	ADJ
ejpam-6413	416	15	+	+	PROPN
ejpam-6413	416	16	m|𭟋′′(b̄)|(1−	m|𭟋′′(b̄)|(1−	PROPN
ejpam-6413	416	17	⊺α	⊺α	ADJ
ejpam-6413	416	18	)	)	PUNCT
ejpam-6413	416	19	]	]	PUNCT
ejpam-6413	417	1	d⊺	d⊺	PROPN
ejpam-6413	418	1	+	+	NOUN
ejpam-6413	418	2	⋎(θ	⋎(θ	NOUN
ejpam-6413	418	3	+	+	NOUN
ejpam-6413	418	4	1	1	NUM
ejpam-6413	418	5	)	)	PUNCT
ejpam-6413	418	6	∫	∫	NOUN
ejpam-6413	418	7	1	1	NUM
ejpam-6413	418	8	2	2	NUM
ejpam-6413	418	9	0	0	NUM
ejpam-6413	418	10	[	[	PUNCT
ejpam-6413	418	11	|𭟋′′(ā)|	|𭟋′′(ā)|	PROPN
ejpam-6413	418	12	⊺α+1	⊺α+1	PROPN
ejpam-6413	419	1	+	+	ADJ
ejpam-6413	419	2	m|𭟋′′(b̄)|	m|𭟋′′(b̄)|	ADJ
ejpam-6413	419	3	⊺	⊺	NUM
ejpam-6413	419	4	(	(	PUNCT
ejpam-6413	419	5	1−	1−	NUM
ejpam-6413	419	6	⊺)α	⊺)α	PROPN
ejpam-6413	419	7	]	]	PUNCT
ejpam-6413	419	8	d⊺	d⊺	PROPN
ejpam-6413	419	9	≤	≤	PUNCT
ejpam-6413	419	10	⋎(θ	⋎(θ	NOUN
ejpam-6413	419	11	+	+	NOUN
ejpam-6413	419	12	1	1	NUM
ejpam-6413	419	13	)	)	PUNCT
ejpam-6413	419	14	(	(	PUNCT
ejpam-6413	419	15	|𭟋′′(ā)|2−α+1	|𭟋′′(ā)|2−α+1	PROPN
ejpam-6413	419	16	+	+	NOUN
ejpam-6413	419	17	m|𭟋′′(b̄)(α+	m|𭟋′′(b̄)(α+	NOUN
ejpam-6413	419	18	2−	2−	NUM
ejpam-6413	419	19	2−α+1	2−α+1	NOUN
ejpam-6413	419	20	)	)	PUNCT
ejpam-6413	419	21	8(α+	8(α+	NUM
ejpam-6413	419	22	2	2	NUM
ejpam-6413	419	23	)	)	PUNCT
ejpam-6413	419	24	)	)	PUNCT
ejpam-6413	419	25	,	,	PUNCT
ejpam-6413	419	26	(	(	PUNCT
ejpam-6413	419	27	33	33	NUM
ejpam-6413	419	28	)	)	PUNCT
ejpam-6413	419	29	and∫	and∫	NOUN
ejpam-6413	419	30	1	1	NUM
ejpam-6413	419	31	1	1	NUM
ejpam-6413	419	32	2	2	NUM
ejpam-6413	419	33	[	[	PUNCT
ejpam-6413	419	34	(	(	PUNCT
ejpam-6413	419	35	⋎+	⋎+	PROPN
ejpam-6413	419	36	1)−	1)−	PROPN
ejpam-6413	419	37	(	(	PUNCT
ejpam-6413	419	38	⋎+	⋎+	PRON
ejpam-6413	419	39	1)2−θ	1)2−θ	NUM
ejpam-6413	419	40	+	+	NOUN
ejpam-6413	419	41	⊺	⊺	NUM
ejpam-6413	419	42	⋎	⋎	NOUN
ejpam-6413	419	43	(	(	PUNCT
ejpam-6413	419	44	θ	θ	NOUN
ejpam-6413	419	45	+	+	CCONJ
ejpam-6413	419	46	1)−⋎(θ	1)−⋎(θ	NUM
ejpam-6413	419	47	+	+	CCONJ
ejpam-6413	419	48	1	1	NUM
ejpam-6413	419	49	)	)	PUNCT
ejpam-6413	419	50	]	]	PUNCT
ejpam-6413	419	51	×	×	PROPN
ejpam-6413	419	52	(	(	PUNCT
ejpam-6413	419	53	|𭟋′′(ā)|	|𭟋′′(ā)|	PROPN
ejpam-6413	419	54	⊺α	⊺α	PROPN
ejpam-6413	419	55	d	d	X
ejpam-6413	419	56	⊺+m|𭟋′′(b̄)|(1−	⊺+m|𭟋′′(b̄)|(1−	NOUN
ejpam-6413	419	57	⊺α)d⊺	⊺α)d⊺	ADJ
ejpam-6413	419	58	)	)	PUNCT
ejpam-6413	419	59	≤	≤	PUNCT
ejpam-6413	420	1	[	[	X
ejpam-6413	420	2	(	(	PUNCT
ejpam-6413	420	3	⋎+	⋎+	PROPN
ejpam-6413	420	4	1)−	1)−	PROPN
ejpam-6413	420	5	(	(	PUNCT
ejpam-6413	420	6	⋎+	⋎+	DET
ejpam-6413	420	7	1)2−θ	1)2−θ	NUM
ejpam-6413	420	8	−⋎(θ	−⋎(θ	NOUN
ejpam-6413	420	9	+	+	NOUN
ejpam-6413	420	10	1	1	NUM
ejpam-6413	420	11	)	)	PUNCT
ejpam-6413	420	12	]	]	PUNCT
ejpam-6413	420	13	(	(	PUNCT
ejpam-6413	420	14	|𭟋′′(ā)|	|𭟋′′(ā)|	NUM
ejpam-6413	420	15	∫	∫	PROPN
ejpam-6413	420	16	1	1	NUM
ejpam-6413	420	17	1	1	NUM
ejpam-6413	420	18	2	2	NUM
ejpam-6413	420	19	⊺αd	⊺αd	NOUN
ejpam-6413	420	20	⊺+m|𭟋′′(b̄)|	⊺+m|𭟋′′(b̄)|	PROPN
ejpam-6413	420	21	∫	∫	PROPN
ejpam-6413	420	22	1	1	NUM
ejpam-6413	420	23	1	1	NUM
ejpam-6413	420	24	2	2	NUM
ejpam-6413	420	25	(	(	PUNCT
ejpam-6413	420	26	1−	1−	NUM
ejpam-6413	420	27	⊺α)d⊺	⊺α)d⊺	ADJ
ejpam-6413	420	28	)	)	PUNCT
ejpam-6413	421	1	+	+	ADP
ejpam-6413	421	2	⋎(θ	⋎(θ	NOUN
ejpam-6413	421	3	+	+	NOUN
ejpam-6413	421	4	1	1	NUM
ejpam-6413	421	5	)	)	PUNCT
ejpam-6413	421	6	(	(	PUNCT
ejpam-6413	421	7	|𭟋′′(ā)|	|𭟋′′(ā)|	NUM
ejpam-6413	421	8	∫	∫	PROPN
ejpam-6413	421	9	1	1	NUM
ejpam-6413	421	10	1	1	NUM
ejpam-6413	421	11	2	2	NUM
ejpam-6413	421	12	⊺α+1d	⊺α+1d	NOUN
ejpam-6413	421	13	⊺+m|𭟋′′(b̄)|	⊺+m|𭟋′′(b̄)|	PROPN
ejpam-6413	421	14	∫	∫	PROPN
ejpam-6413	421	15	1	1	NUM
ejpam-6413	421	16	1	1	NUM
ejpam-6413	421	17	2	2	NUM
ejpam-6413	421	18	⊺(1−	⊺(1−	NOUN
ejpam-6413	421	19	⊺α)d⊺	⊺α)d⊺	ADJ
ejpam-6413	421	20	)	)	PUNCT
ejpam-6413	421	21	≤	≤	PUNCT
ejpam-6413	422	1	[	[	X
ejpam-6413	422	2	(	(	PUNCT
ejpam-6413	422	3	⋎+	⋎+	PROPN
ejpam-6413	422	4	1)−	1)−	PROPN
ejpam-6413	422	5	(	(	PUNCT
ejpam-6413	422	6	⋎+	⋎+	DET
ejpam-6413	422	7	1)2−θ	1)2−θ	NUM
ejpam-6413	422	8	−⋎(θ	−⋎(θ	NOUN
ejpam-6413	422	9	+	+	NOUN
ejpam-6413	422	10	1	1	NUM
ejpam-6413	422	11	)	)	PUNCT
ejpam-6413	422	12	]	]	PUNCT
ejpam-6413	422	13	(	(	PUNCT
ejpam-6413	422	14	(	(	PUNCT
ejpam-6413	422	15	2−	2−	NUM
ejpam-6413	422	16	2−α)|𭟋′′(ā)|+	2−α)|𭟋′′(ā)|+	NUM
ejpam-6413	422	17	(	(	PUNCT
ejpam-6413	422	18	α−	α−	ADP
ejpam-6413	422	19	1	1	NUM
ejpam-6413	422	20	+	+	NUM
ejpam-6413	422	21	2−α)m|𭟋′′(b̄)|	2−α)m|𭟋′′(b̄)|	NUM
ejpam-6413	422	22	2(α+	2(α+	NUM
ejpam-6413	422	23	1	1	NUM
ejpam-6413	422	24	)	)	PUNCT
ejpam-6413	422	25	)	)	PUNCT
ejpam-6413	423	1	+	+	ADP
ejpam-6413	423	2	⋎(θ	⋎(θ	NOUN
ejpam-6413	423	3	+	+	NOUN
ejpam-6413	423	4	1	1	NUM
ejpam-6413	423	5	)	)	PUNCT
ejpam-6413	423	6	(	(	PUNCT
ejpam-6413	423	7	(	(	PUNCT
ejpam-6413	423	8	8−	8−	NUM
ejpam-6413	423	9	2−α+1)|𭟋′′(ā)|+	2−α+1)|𭟋′′(ā)|+	NUM
ejpam-6413	423	10	(	(	PUNCT
ejpam-6413	423	11	3α−	3α−	PROPN
ejpam-6413	423	12	2	2	NUM
ejpam-6413	423	13	+	+	SYM
ejpam-6413	423	14	2−α+1)m|𭟋′′(b̄)|	2−α+1)m|𭟋′′(b̄)|	X
ejpam-6413	423	15	)	)	PUNCT
ejpam-6413	423	16	8(α+	8(α+	NUM
ejpam-6413	423	17	2	2	NUM
ejpam-6413	423	18	)	)	PUNCT
ejpam-6413	423	19	)	)	PUNCT
ejpam-6413	423	20	,	,	PUNCT
ejpam-6413	423	21	(	(	PUNCT
ejpam-6413	423	22	34	34	NUM
ejpam-6413	423	23	)	)	PUNCT
ejpam-6413	423	24	and	and	CCONJ
ejpam-6413	423	25	∫	∫	PROPN
ejpam-6413	423	26	1	1	NUM
ejpam-6413	423	27	1	1	NUM
ejpam-6413	423	28	2	2	NUM
ejpam-6413	423	29	[	[	X
ejpam-6413	423	30	−⋎−1	−⋎−1	X
ejpam-6413	423	31	+	+	X
ejpam-6413	423	32	(	(	PUNCT
ejpam-6413	423	33	⋎+	⋎+	DET
ejpam-6413	423	34	1)2−θ	1)2−θ	NUM
ejpam-6413	423	35	−	−	NOUN
ejpam-6413	423	36	⊺	⊺	NUM
ejpam-6413	423	37	⋎	⋎	NOUN
ejpam-6413	423	38	(	(	PUNCT
ejpam-6413	423	39	θ	θ	NOUN
ejpam-6413	423	40	+	+	NOUN
ejpam-6413	423	41	1	1	X
ejpam-6413	423	42	)	)	PUNCT
ejpam-6413	424	1	+	+	ADP
ejpam-6413	424	2	⋎(θ	⋎(θ	NOUN
ejpam-6413	424	3	+	+	NOUN
ejpam-6413	424	4	1	1	NUM
ejpam-6413	424	5	)	)	PUNCT
ejpam-6413	424	6	]	]	PUNCT
ejpam-6413	424	7	(	(	PUNCT
ejpam-6413	424	8	|𭟋′′(ā)|	|𭟋′′(ā)|	PROPN
ejpam-6413	424	9	⊺α	⊺α	PROPN
ejpam-6413	424	10	d	d	X
ejpam-6413	424	11	⊺+m|𭟋′′(b̄)|(1−	⊺+m|𭟋′′(b̄)|(1−	NOUN
ejpam-6413	424	12	⊺α)d⊺	⊺α)d⊺	ADJ
ejpam-6413	424	13	)	)	PUNCT
ejpam-6413	424	14	≤	≤	NOUN
ejpam-6413	425	1	[	[	X
ejpam-6413	425	2	−⋎−1	−⋎−1	X
ejpam-6413	425	3	+	+	X
ejpam-6413	425	4	(	(	PUNCT
ejpam-6413	425	5	⋎+	⋎+	DET
ejpam-6413	425	6	1	1	X
ejpam-6413	425	7	)	)	PUNCT
ejpam-6413	426	1	+	+	ADP
ejpam-6413	426	2	⋎(θ	⋎(θ	NOUN
ejpam-6413	426	3	+	+	NOUN
ejpam-6413	426	4	1	1	NUM
ejpam-6413	426	5	)	)	PUNCT
ejpam-6413	426	6	]	]	PUNCT
ejpam-6413	426	7	(	(	PUNCT
ejpam-6413	426	8	|𭟋′′(ā)|	|𭟋′′(ā)|	NUM
ejpam-6413	426	9	∫	∫	PROPN
ejpam-6413	426	10	1	1	NUM
ejpam-6413	426	11	1	1	NUM
ejpam-6413	426	12	2	2	NUM
ejpam-6413	426	13	⊺αd	⊺αd	NOUN
ejpam-6413	426	14	⊺−m|𭟋′′(b̄)|	⊺−m|𭟋′′(b̄)|	NOUN
ejpam-6413	426	15	∫	∫	PROPN
ejpam-6413	426	16	1	1	NUM
ejpam-6413	426	17	1	1	NUM
ejpam-6413	426	18	2	2	NUM
ejpam-6413	426	19	(	(	PUNCT
ejpam-6413	426	20	1−	1−	NUM
ejpam-6413	426	21	⊺α)d⊺	⊺α)d⊺	ADJ
ejpam-6413	426	22	)	)	PUNCT
ejpam-6413	427	1	+	+	ADP
ejpam-6413	427	2	⋎(θ	⋎(θ	NOUN
ejpam-6413	427	3	+	+	NOUN
ejpam-6413	427	4	1	1	NUM
ejpam-6413	427	5	)	)	PUNCT
ejpam-6413	427	6	(	(	PUNCT
ejpam-6413	427	7	|𭟋′′(ā)|	|𭟋′′(ā)|	NUM
ejpam-6413	427	8	∫	∫	PROPN
ejpam-6413	427	9	1	1	NUM
ejpam-6413	427	10	1	1	NUM
ejpam-6413	427	11	2	2	NUM
ejpam-6413	427	12	⊺α+1d	⊺α+1d	NOUN
ejpam-6413	427	13	⊺+m|𭟋′′(b̄)|	⊺+m|𭟋′′(b̄)|	PROPN
ejpam-6413	427	14	∫	∫	PROPN
ejpam-6413	427	15	1	1	NUM
ejpam-6413	427	16	1	1	NUM
ejpam-6413	427	17	2	2	NUM
ejpam-6413	427	18	⊺(1−	⊺(1−	NOUN
ejpam-6413	427	19	⊺α)d⊺	⊺α)d⊺	ADJ
ejpam-6413	427	20	)	)	PUNCT
ejpam-6413	427	21	m.	m.	NOUN
ejpam-6413	427	22	samraiz	samraiz	PROPN
ejpam-6413	427	23	et	et	PROPN
ejpam-6413	427	24	al	al	PROPN
ejpam-6413	427	25	.	.	PUNCT
ejpam-6413	427	26	/	/	SYM
ejpam-6413	427	27	eur	eur	PROPN
ejpam-6413	427	28	.	.	PUNCT
ejpam-6413	428	1	j.	j.	PROPN
ejpam-6413	428	2	pure	pure	PROPN
ejpam-6413	428	3	appl	appl	PROPN
ejpam-6413	428	4	.	.	PROPN
ejpam-6413	428	5	math	math	PROPN
ejpam-6413	428	6	,	,	PUNCT
ejpam-6413	428	7	18	18	NUM
ejpam-6413	428	8	(	(	PUNCT
ejpam-6413	428	9	3	3	NUM
ejpam-6413	428	10	)	)	PUNCT
ejpam-6413	428	11	(	(	PUNCT
ejpam-6413	428	12	2025	2025	NUM
ejpam-6413	428	13	)	)	PUNCT
ejpam-6413	428	14	,	,	PUNCT
ejpam-6413	428	15	6413	6413	NUM
ejpam-6413	428	16	21	21	NUM
ejpam-6413	428	17	of	of	ADP
ejpam-6413	428	18	26	26	NUM
ejpam-6413	428	19	≤	≤	NOUN
ejpam-6413	428	20	⋎(θ	⋎(θ	NOUN
ejpam-6413	428	21	+	+	NOUN
ejpam-6413	428	22	1	1	NUM
ejpam-6413	428	23	)	)	PUNCT
ejpam-6413	428	24	(	(	PUNCT
ejpam-6413	428	25	(	(	PUNCT
ejpam-6413	428	26	2−	2−	NUM
ejpam-6413	428	27	2−α)|𭟋′′(ā)|(α−	2−α)|𭟋′′(ā)|(α−	NUM
ejpam-6413	428	28	1	1	NUM
ejpam-6413	428	29	+	+	NUM
ejpam-6413	428	30	2−α)m|𭟋′′(b̄)|	2−α)m|𭟋′′(b̄)|	NUM
ejpam-6413	428	31	)	)	PUNCT
ejpam-6413	428	32	2(α+	2(α+	NUM
ejpam-6413	428	33	1	1	NUM
ejpam-6413	428	34	)	)	PUNCT
ejpam-6413	428	35	−(8−	−(8−	NOUN
ejpam-6413	428	36	2−α+1)|𭟋′′(ā)|+	2−α+1)|𭟋′′(ā)|+	NUM
ejpam-6413	428	37	(	(	PUNCT
ejpam-6413	428	38	3α−	3α−	PROPN
ejpam-6413	428	39	2	2	NUM
ejpam-6413	428	40	+	+	SYM
ejpam-6413	428	41	2−α+1)m|𭟋′′(b̄	2−α+1)m|𭟋′′(b̄	NUM
ejpam-6413	428	42	)	)	PUNCT
ejpam-6413	428	43	8(α+	8(α+	NUM
ejpam-6413	428	44	2	2	NUM
ejpam-6413	428	45	)	)	PUNCT
ejpam-6413	428	46	)	)	PUNCT
ejpam-6413	428	47	.	.	PUNCT
ejpam-6413	429	1	(	(	PUNCT
ejpam-6413	429	2	35	35	NUM
ejpam-6413	429	3	)	)	PUNCT
ejpam-6413	429	4	substituting	substitute	VERB
ejpam-6413	429	5	the	the	DET
ejpam-6413	429	6	values	value	NOUN
ejpam-6413	429	7	of	of	ADP
ejpam-6413	429	8	(	(	PUNCT
ejpam-6413	429	9	32	32	NUM
ejpam-6413	429	10	)	)	PUNCT
ejpam-6413	429	11	,	,	PUNCT
ejpam-6413	429	12	(	(	PUNCT
ejpam-6413	429	13	33	33	NUM
ejpam-6413	429	14	)	)	PUNCT
ejpam-6413	429	15	,	,	PUNCT
ejpam-6413	429	16	(	(	PUNCT
ejpam-6413	429	17	34	34	NUM
ejpam-6413	429	18	)	)	PUNCT
ejpam-6413	429	19	and	and	CCONJ
ejpam-6413	429	20	(	(	PUNCT
ejpam-6413	429	21	35	35	NUM
ejpam-6413	429	22	)	)	PUNCT
ejpam-6413	429	23	in	in	ADP
ejpam-6413	429	24	(	(	PUNCT
ejpam-6413	429	25	31	31	NUM
ejpam-6413	429	26	)	)	PUNCT
ejpam-6413	429	27	,	,	PUNCT
ejpam-6413	429	28	we	we	PRON
ejpam-6413	429	29	obtained	obtain	VERB
ejpam-6413	429	30	the	the	DET
ejpam-6413	429	31	required	require	VERB
ejpam-6413	429	32	result	result	NOUN
ejpam-6413	429	33	.	.	PUNCT
ejpam-6413	430	1	theorem	theorem	ADJ
ejpam-6413	430	2	6	6	NUM
ejpam-6413	430	3	.	.	PUNCT
ejpam-6413	431	1	let	let	VERB
ejpam-6413	431	2	𭟋	𭟋	VERB
ejpam-6413	431	3	:	:	PUNCT
ejpam-6413	431	4	[	[	X
ejpam-6413	431	5	ā	ā	X
ejpam-6413	431	6	,	,	PUNCT
ejpam-6413	431	7	b̄	b̄	PROPN
ejpam-6413	431	8	]	]	PUNCT
ejpam-6413	431	9	−→	−→	NOUN
ejpam-6413	431	10	r	r	NOUN
ejpam-6413	431	11	be	be	VERB
ejpam-6413	431	12	a	a	DET
ejpam-6413	431	13	twice	twice	ADV
ejpam-6413	431	14	differentiable	differentiable	ADJ
ejpam-6413	431	15	function	function	NOUN
ejpam-6413	431	16	such	such	ADJ
ejpam-6413	431	17	that	that	DET
ejpam-6413	431	18	|𭟋′′|	|𭟋′′|	PROPN
ejpam-6413	431	19	is	be	AUX
ejpam-6413	431	20	lebesgue	lebesgue	NOUN
ejpam-6413	431	21	integrable	integrable	ADJ
ejpam-6413	431	22	,	,	PUNCT
ejpam-6413	431	23	increasing	increase	VERB
ejpam-6413	431	24	and	and	CCONJ
ejpam-6413	431	25	ga	ga	PROPN
ejpam-6413	431	26	(	(	PUNCT
ejpam-6413	431	27	α	α	NOUN
ejpam-6413	431	28	,	,	PUNCT
ejpam-6413	431	29	m)-convex	m)-convex	PUNCT
ejpam-6413	431	30	function	function	VERB
ejpam-6413	431	31	on	on	ADP
ejpam-6413	431	32	[	[	X
ejpam-6413	431	33	ā	ā	X
ejpam-6413	431	34	,	,	PUNCT
ejpam-6413	431	35	b̄	b̄	PROPN
ejpam-6413	431	36	]	]	PUNCT
ejpam-6413	431	37	.	.	PUNCT
ejpam-6413	432	1	then	then	ADV
ejpam-6413	432	2	for	for	ADP
ejpam-6413	432	3	given	give	VERB
ejpam-6413	432	4	parameters	parameter	NOUN
ejpam-6413	432	5	θ	θ	PROPN
ejpam-6413	432	6	∈	∈	PROPN
ejpam-6413	432	7	(	(	PUNCT
ejpam-6413	432	8	0,+∞	0,+∞	NUM
ejpam-6413	432	9	]	]	PUNCT
ejpam-6413	432	10	and	and	CCONJ
ejpam-6413	432	11	(	(	PUNCT
ejpam-6413	432	12	α	α	NOUN
ejpam-6413	432	13	,	,	PUNCT
ejpam-6413	432	14	m	m	NOUN
ejpam-6413	432	15	)	)	PUNCT
ejpam-6413	432	16	∈	∈	PROPN
ejpam-6413	432	17	(	(	PUNCT
ejpam-6413	432	18	0	0	NUM
ejpam-6413	432	19	,	,	PUNCT
ejpam-6413	432	20	1]2	1]2	NUM
ejpam-6413	432	21	,	,	PUNCT
ejpam-6413	432	22	where	where	SCONJ
ejpam-6413	432	23	0	0	NUM
ejpam-6413	432	24	≤	≤	NUM
ejpam-6413	432	25	ā	ā	NOUN
ejpam-6413	432	26	<	<	X
ejpam-6413	432	27	b̄.	b̄.	PUNCT
ejpam-6413	432	28	thus	thus	ADV
ejpam-6413	432	29	,	,	PUNCT
ejpam-6413	432	30	let	let	VERB
ejpam-6413	432	31	1	1	NUM
ejpam-6413	432	32	<	<	X
ejpam-6413	432	33	⋋2	⋋2	NOUN
ejpam-6413	432	34	<	<	X
ejpam-6413	433	1	+	+	NOUN
ejpam-6413	433	2	∞	∞	PROPN
ejpam-6413	433	3	then	then	ADV
ejpam-6413	433	4	,	,	PUNCT
ejpam-6413	433	5	the	the	DET
ejpam-6413	433	6	following	follow	VERB
ejpam-6413	433	7	inequality∣∣∣∣𭟋(ā	inequality∣∣∣∣𭟋(ā	NOUN
ejpam-6413	433	8	)	)	PUNCT
ejpam-6413	433	9	+	+	NOUN
ejpam-6413	433	10	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	433	11	)	)	PUNCT
ejpam-6413	433	12	⋎(⋎+	⋎(⋎+	VERB
ejpam-6413	433	13	1	1	NUM
ejpam-6413	433	14	)	)	PUNCT
ejpam-6413	434	1	+	+	CCONJ
ejpam-6413	434	2	2	2	NUM
ejpam-6413	434	3	⋎+	⋎+	DET
ejpam-6413	434	4	1	1	NUM
ejpam-6413	434	5	𭟋	𭟋	PROPN
ejpam-6413	434	6	(	(	PUNCT
ejpam-6413	434	7	ā+	ā+	PUNCT
ejpam-6413	434	8	µ	µ	X
ejpam-6413	434	9	2	2	NUM
ejpam-6413	434	10	)	)	PUNCT
ejpam-6413	434	11	−	−	PROPN
ejpam-6413	435	1	γ(θ	γ(θ	PROPN
ejpam-6413	436	1	+	+	CCONJ
ejpam-6413	436	2	1	1	X
ejpam-6413	436	3	)	)	PUNCT
ejpam-6413	436	4	⋎(µ−	⋎(µ−	NOUN
ejpam-6413	436	5	ā)θ	ā)θ	NOUN
ejpam-6413	437	1	[	[	X
ejpam-6413	437	2	χθ	χθ	X
ejpam-6413	437	3	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	437	4	)	)	PUNCT
ejpam-6413	438	1	+	+	CCONJ
ejpam-6413	438	2	χθ	χθ	X
ejpam-6413	438	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	438	4	)	)	PUNCT
ejpam-6413	438	5	]	]	PUNCT
ejpam-6413	439	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	439	2	≤	≤	NOUN
ejpam-6413	439	3	(	(	PUNCT
ejpam-6413	439	4	µ−	µ−	PROPN
ejpam-6413	439	5	ā)2	ā)2	NOUN
ejpam-6413	439	6	[	[	X
ejpam-6413	439	7	⋎(θ	⋎(θ	NOUN
ejpam-6413	439	8	+	+	NOUN
ejpam-6413	439	9	1)(⋎+	1)(⋎+	NUM
ejpam-6413	439	10	1)]1+⋋−1	1)]1+⋋−1	NUM
ejpam-6413	439	11	1	1	NUM
ejpam-6413	439	12	(	(	PUNCT
ejpam-6413	439	13	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	440	1	+	+	NOUN
ejpam-6413	440	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	440	3	α+	α+	PUNCT
ejpam-6413	440	4	1	1	NUM
ejpam-6413	440	5	)	)	PUNCT
ejpam-6413	440	6	1	1	NUM
ejpam-6413	440	7	⋋2	⋋2	PROPN
ejpam-6413	440	8	×	×	NOUN
ejpam-6413	440	9	[	[	PUNCT
ejpam-6413	440	10	max	max	PROPN
ejpam-6413	440	11	(	(	PUNCT
ejpam-6413	440	12	(	(	PUNCT
ejpam-6413	440	13	⋎+	⋎+	PRON
ejpam-6413	440	14	1−	1−	NUM
ejpam-6413	440	15	(	(	PUNCT
ejpam-6413	440	16	⋎+	⋎+	DET
ejpam-6413	440	17	1)2−θ	1)2−θ	NUM
ejpam-6413	440	18	)	)	PUNCT
ejpam-6413	440	19	⋋1	⋋1	PROPN
ejpam-6413	440	20	+	+	PROPN
ejpam-6413	440	21	1	1	NUM
ejpam-6413	440	22	−	−	NOUN
ejpam-6413	440	23	(	(	PUNCT
ejpam-6413	440	24	1	1	NUM
ejpam-6413	440	25	+	+	NUM
ejpam-6413	440	26	0.5⋎	0.5⋎	NUM
ejpam-6413	440	27	(	(	PUNCT
ejpam-6413	440	28	1−	1−	NUM
ejpam-6413	440	29	θ)−	θ)−	PROPN
ejpam-6413	440	30	(	(	PUNCT
ejpam-6413	440	31	1	1	NUM
ejpam-6413	440	32	+	+	NOUN
ejpam-6413	440	33	⋎)2−θ	⋎)2−θ	NOUN
ejpam-6413	440	34	)	)	PUNCT
ejpam-6413	440	35	⋋1	⋋1	PROPN
ejpam-6413	440	36	+	+	PROPN
ejpam-6413	440	37	1	1	NUM
ejpam-6413	440	38	,	,	PUNCT
ejpam-6413	440	39	(	(	PUNCT
ejpam-6413	440	40	⋎(θ	⋎(θ	NOUN
ejpam-6413	440	41	+	+	NOUN
ejpam-6413	440	42	1))⋋1	1))⋋1	NUM
ejpam-6413	440	43	+	+	ADJ
ejpam-6413	440	44	1	1	NUM
ejpam-6413	440	45	2−⋋1−1	2−⋋1−1	NUM
ejpam-6413	440	46	)	)	PUNCT
ejpam-6413	441	1	+	+	X
ejpam-6413	441	2	max	max	PROPN
ejpam-6413	441	3	(	(	PUNCT
ejpam-6413	441	4	(	(	PUNCT
ejpam-6413	441	5	⋎+	⋎+	PRON
ejpam-6413	441	6	1−	1−	NUM
ejpam-6413	441	7	(	(	PUNCT
ejpam-6413	441	8	⋎+	⋎+	DET
ejpam-6413	441	9	1)2−θ	1)2−θ	NUM
ejpam-6413	441	10	)	)	PUNCT
ejpam-6413	441	11	⋋1	⋋1	PROPN
ejpam-6413	441	12	+	+	PROPN
ejpam-6413	441	13	1	1	NUM
ejpam-6413	441	14	−	−	NOUN
ejpam-6413	441	15	(	(	PUNCT
ejpam-6413	441	16	1	1	NUM
ejpam-6413	441	17	+	+	NUM
ejpam-6413	441	18	0.5⋎	0.5⋎	NUM
ejpam-6413	441	19	(	(	PUNCT
ejpam-6413	441	20	1−	1−	NUM
ejpam-6413	441	21	θ)−	θ)−	PROPN
ejpam-6413	441	22	(	(	PUNCT
ejpam-6413	441	23	1	1	NUM
ejpam-6413	441	24	+	+	NOUN
ejpam-6413	441	25	⋎)2−θ	⋎)2−θ	NOUN
ejpam-6413	441	26	)	)	PUNCT
ejpam-6413	441	27	⋋1	⋋1	PROPN
ejpam-6413	441	28	+	+	PROPN
ejpam-6413	441	29	1	1	NUM
ejpam-6413	441	30	,	,	PUNCT
ejpam-6413	441	31	0.5⋎	0.5⋎	NUM
ejpam-6413	441	32	(	(	PUNCT
ejpam-6413	441	33	θ	θ	PROPN
ejpam-6413	441	34	+	+	NOUN
ejpam-6413	441	35	1)⋋1	1)⋋1	NUM
ejpam-6413	441	36	+	+	SYM
ejpam-6413	441	37	1	1	NUM
ejpam-6413	441	38	)	)	PUNCT
ejpam-6413	441	39	)	)	PUNCT
ejpam-6413	441	40	1	1	NUM
ejpam-6413	441	41	⋋1	⋋1	NUM
ejpam-6413	441	42	)	)	PUNCT
ejpam-6413	441	43	]	]	PUNCT
ejpam-6413	441	44	holds	hold	VERB
ejpam-6413	441	45	true	true	ADJ
ejpam-6413	441	46	,	,	PUNCT
ejpam-6413	441	47	where	where	SCONJ
ejpam-6413	441	48	1	1	NUM
ejpam-6413	441	49	⋋1	⋋1	NUM
ejpam-6413	441	50	+	+	SYM
ejpam-6413	441	51	1	1	NUM
ejpam-6413	441	52	⋋2	⋋2	NOUN
ejpam-6413	441	53	=	=	SYM
ejpam-6413	441	54	1	1	X
ejpam-6413	441	55	.	.	PUNCT
ejpam-6413	441	56	proof	proof	NOUN
ejpam-6413	441	57	.	.	PUNCT
ejpam-6413	442	1	by	by	ADP
ejpam-6413	442	2	utilizing	utilize	VERB
ejpam-6413	442	3	definitions	definition	NOUN
ejpam-6413	442	4	2	2	NUM
ejpam-6413	442	5	,	,	PUNCT
ejpam-6413	442	6	4	4	NUM
ejpam-6413	442	7	,	,	PUNCT
ejpam-6413	442	8	lemma	lemma	PROPN
ejpam-6413	442	9	2	2	NUM
ejpam-6413	442	10	,	,	PUNCT
ejpam-6413	442	11	6	6	NUM
ejpam-6413	442	12	,	,	PUNCT
ejpam-6413	442	13	7	7	NUM
ejpam-6413	442	14	and	and	CCONJ
ejpam-6413	442	15	applying	apply	VERB
ejpam-6413	442	16	hölder	hölder	NOUN
ejpam-6413	442	17	’s	’s	PART
ejpam-6413	442	18	inequality	inequality	NOUN
ejpam-6413	442	19	,	,	PUNCT
ejpam-6413	442	20	we	we	PRON
ejpam-6413	442	21	have∣∣∣∣𭟋(ā	have∣∣∣∣𭟋(ā	NOUN
ejpam-6413	442	22	)	)	PUNCT
ejpam-6413	442	23	+	+	NOUN
ejpam-6413	442	24	𭟋(µ	𭟋(µ	NOUN
ejpam-6413	442	25	)	)	PUNCT
ejpam-6413	442	26	⋎(⋎+	⋎(⋎+	VERB
ejpam-6413	442	27	1	1	NUM
ejpam-6413	442	28	)	)	PUNCT
ejpam-6413	443	1	+	+	CCONJ
ejpam-6413	443	2	2	2	NUM
ejpam-6413	443	3	⋎+	⋎+	DET
ejpam-6413	443	4	1	1	NUM
ejpam-6413	443	5	𭟋	𭟋	PROPN
ejpam-6413	443	6	(	(	PUNCT
ejpam-6413	443	7	ā+	ā+	PUNCT
ejpam-6413	443	8	µ	µ	X
ejpam-6413	443	9	2	2	NUM
ejpam-6413	443	10	)	)	PUNCT
ejpam-6413	443	11	−	−	PROPN
ejpam-6413	444	1	γ(θ	γ(θ	PROPN
ejpam-6413	445	1	+	+	CCONJ
ejpam-6413	445	2	1	1	X
ejpam-6413	445	3	)	)	PUNCT
ejpam-6413	445	4	⋎(µ−	⋎(µ−	NOUN
ejpam-6413	445	5	ā)θ	ā)θ	NOUN
ejpam-6413	446	1	[	[	X
ejpam-6413	446	2	χθ	χθ	X
ejpam-6413	446	3	ā+𭟋(µ	ā+𭟋(µ	NUM
ejpam-6413	446	4	)	)	PUNCT
ejpam-6413	447	1	+	+	CCONJ
ejpam-6413	447	2	χθ	χθ	X
ejpam-6413	447	3	µ−𭟋(ā	µ−𭟋(ā	PROPN
ejpam-6413	447	4	)	)	PUNCT
ejpam-6413	447	5	]	]	PUNCT
ejpam-6413	448	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	448	2	≤	≤	NOUN
ejpam-6413	448	3	(	(	PUNCT
ejpam-6413	448	4	µ−	µ−	PROPN
ejpam-6413	448	5	ā)2	ā)2	PROPN
ejpam-6413	448	6	∫	∫	PROPN
ejpam-6413	448	7	1	1	NUM
ejpam-6413	448	8	0	0	NUM
ejpam-6413	448	9	|q0(⊺)||𭟋′′(⊺ā+m(1−	|q0(⊺)||𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	448	10	⊺)b̄)|d⊺	⊺)b̄)|d⊺	PROPN
ejpam-6413	448	11	≤	≤	NOUN
ejpam-6413	448	12	(	(	PUNCT
ejpam-6413	448	13	µ−	µ−	PROPN
ejpam-6413	448	14	ā)2	ā)2	NOUN
ejpam-6413	448	15	(	(	PUNCT
ejpam-6413	448	16	∫	∫	PROPN
ejpam-6413	448	17	1	1	NUM
ejpam-6413	448	18	0	0	NUM
ejpam-6413	448	19	|q0(⊺)|⋋1	|q0(⊺)|⋋1	NOUN
ejpam-6413	448	20	)	)	PUNCT
ejpam-6413	448	21	1	1	NUM
ejpam-6413	448	22	⋋1	⋋1	NUM
ejpam-6413	448	23	(	(	PUNCT
ejpam-6413	448	24	∫	∫	PROPN
ejpam-6413	448	25	1	1	NUM
ejpam-6413	448	26	0	0	NUM
ejpam-6413	448	27	|𭟋′′(⊺ā+m(1−	|𭟋′′(⊺ā+m(1−	PROPN
ejpam-6413	448	28	⊺)b̄)|⋋2d⊺	⊺)b̄)|⋋2d⊺	NOUN
ejpam-6413	448	29	)	)	PUNCT
ejpam-6413	448	30	1	1	NUM
ejpam-6413	448	31	⋋2	⋋2	NOUN
ejpam-6413	448	32	≤	≤	NOUN
ejpam-6413	448	33	(	(	PUNCT
ejpam-6413	448	34	µ−	µ−	PROPN
ejpam-6413	448	35	ā)2	ā)2	NOUN
ejpam-6413	448	36	(	(	PUNCT
ejpam-6413	448	37	∫	∫	PROPN
ejpam-6413	448	38	1	1	NUM
ejpam-6413	448	39	0	0	NUM
ejpam-6413	448	40	|q0(⊺)|⋋1	|q0(⊺)|⋋1	NOUN
ejpam-6413	448	41	)	)	PUNCT
ejpam-6413	448	42	1	1	NUM
ejpam-6413	448	43	⋋1	⋋1	NUM
ejpam-6413	448	44	(	(	PUNCT
ejpam-6413	448	45	∫	∫	PROPN
ejpam-6413	448	46	1	1	NUM
ejpam-6413	448	47	0	0	NUM
ejpam-6413	448	48	|𭟋′′(ā⊺b̄m(1−⊺)|⋋2d⊺	|𭟋′′(ā⊺b̄m(1−⊺)|⋋2d⊺	NOUN
ejpam-6413	448	49	)	)	PUNCT
ejpam-6413	448	50	1	1	NUM
ejpam-6413	448	51	⋋2	⋋2	NOUN
ejpam-6413	448	52	≤	≤	NOUN
ejpam-6413	448	53	(	(	PUNCT
ejpam-6413	448	54	µ−	µ−	PROPN
ejpam-6413	448	55	ā)2	ā)2	NOUN
ejpam-6413	448	56	(	(	PUNCT
ejpam-6413	448	57	∫	∫	PROPN
ejpam-6413	448	58	1	1	NUM
ejpam-6413	448	59	0	0	NUM
ejpam-6413	448	60	|q0(⊺)|⋋1	|q0(⊺)|⋋1	NOUN
ejpam-6413	448	61	)	)	PUNCT
ejpam-6413	448	62	1	1	NUM
ejpam-6413	448	63	⋋1	⋋1	NUM
ejpam-6413	448	64	(	(	PUNCT
ejpam-6413	448	65	∫	∫	PROPN
ejpam-6413	448	66	1	1	NUM
ejpam-6413	448	67	0	0	NUM
ejpam-6413	448	68	⊺α|𭟋′′(ā)|⋋2	⊺α|𭟋′′(ā)|⋋2	PROPN
ejpam-6413	449	1	+	+	SYM
ejpam-6413	449	2	m(1−	m(1−	PROPN
ejpam-6413	449	3	⊺α)|𭟋′′(b̄)|⋋2	⊺α)|𭟋′′(b̄)|⋋2	NUM
ejpam-6413	449	4	)	)	PUNCT
ejpam-6413	449	5	1	1	NUM
ejpam-6413	449	6	⋋2	⋋2	PROPN
ejpam-6413	449	7	m.	m.	NOUN
ejpam-6413	449	8	samraiz	samraiz	PROPN
ejpam-6413	449	9	et	et	PROPN
ejpam-6413	449	10	al	al	PROPN
ejpam-6413	449	11	.	.	PUNCT
ejpam-6413	449	12	/	/	SYM
ejpam-6413	449	13	eur	eur	PROPN
ejpam-6413	449	14	.	.	PUNCT
ejpam-6413	450	1	j.	j.	PROPN
ejpam-6413	450	2	pure	pure	PROPN
ejpam-6413	450	3	appl	appl	PROPN
ejpam-6413	450	4	.	.	PROPN
ejpam-6413	450	5	math	math	PROPN
ejpam-6413	450	6	,	,	PUNCT
ejpam-6413	450	7	18	18	NUM
ejpam-6413	450	8	(	(	PUNCT
ejpam-6413	450	9	3	3	NUM
ejpam-6413	450	10	)	)	PUNCT
ejpam-6413	450	11	(	(	PUNCT
ejpam-6413	450	12	2025	2025	NUM
ejpam-6413	450	13	)	)	PUNCT
ejpam-6413	450	14	,	,	PUNCT
ejpam-6413	450	15	6413	6413	NUM
ejpam-6413	450	16	22	22	NUM
ejpam-6413	450	17	of	of	ADP
ejpam-6413	450	18	26	26	NUM
ejpam-6413	450	19	≤	≤	NOUN
ejpam-6413	450	20	(	(	PUNCT
ejpam-6413	450	21	µ−	µ−	PROPN
ejpam-6413	450	22	ā)2	ā)2	NOUN
ejpam-6413	450	23	(	(	PUNCT
ejpam-6413	450	24	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	PROPN
ejpam-6413	451	1	+	+	NOUN
ejpam-6413	451	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	451	3	α+	α+	PUNCT
ejpam-6413	451	4	1	1	NUM
ejpam-6413	451	5	)	)	SYM
ejpam-6413	451	6	1	1	NUM
ejpam-6413	451	7	⋋2	⋋2	NOUN
ejpam-6413	451	8	(	(	PUNCT
ejpam-6413	451	9	∫	∫	PROPN
ejpam-6413	451	10	1	1	NUM
ejpam-6413	451	11	0	0	NUM
ejpam-6413	451	12	|q0(⊺)|⋋1	|q0(⊺)|⋋1	NOUN
ejpam-6413	451	13	)	)	PUNCT
ejpam-6413	451	14	1	1	NUM
ejpam-6413	451	15	⋋1	⋋1	NUM
ejpam-6413	451	16	≤	≤	NOUN
ejpam-6413	451	17	(	(	PUNCT
ejpam-6413	451	18	µ−	µ−	PROPN
ejpam-6413	451	19	ā)2	ā)2	NOUN
ejpam-6413	451	20	(	(	PUNCT
ejpam-6413	451	21	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	PROPN
ejpam-6413	451	22	+	+	NOUN
ejpam-6413	451	23	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	451	24	α+	α+	PUNCT
ejpam-6413	451	25	1	1	NUM
ejpam-6413	451	26	)	)	PUNCT
ejpam-6413	451	27	1	1	NUM
ejpam-6413	451	28	⋋2	⋋2	PROPN
ejpam-6413	451	29	×	×	NOUN
ejpam-6413	451	30	(	(	PUNCT
ejpam-6413	451	31	∫	∫	PROPN
ejpam-6413	451	32	1	1	NUM
ejpam-6413	451	33	2	2	NUM
ejpam-6413	451	34	0	0	NUM
ejpam-6413	451	35	∣∣∣∣1−	∣∣∣∣1−	NOUN
ejpam-6413	451	36	(	(	PUNCT
ejpam-6413	451	37	1−	1−	NUM
ejpam-6413	451	38	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	451	39	−	−	PROPN
ejpam-6413	451	40	⊺θ+1	⊺θ+1	NOUN
ejpam-6413	451	41	⋎(θ	⋎(θ	NOUN
ejpam-6413	451	42	+	+	NOUN
ejpam-6413	451	43	1	1	NUM
ejpam-6413	451	44	)	)	PUNCT
ejpam-6413	451	45	−	−	NOUN
ejpam-6413	451	46	⊺	⊺	NOUN
ejpam-6413	451	47	⋎+	⋎+	DET
ejpam-6413	451	48	1	1	NUM
ejpam-6413	451	49	∣∣∣∣⋋1	∣∣∣∣⋋1	PROPN
ejpam-6413	451	50	d⊺	d⊺	PROPN
ejpam-6413	451	51	+	+	CCONJ
ejpam-6413	451	52	∫	∫	PROPN
ejpam-6413	451	53	1	1	NUM
ejpam-6413	451	54	1	1	NUM
ejpam-6413	451	55	2	2	NUM
ejpam-6413	451	56	∣∣∣∣1−	∣∣∣∣1−	NOUN
ejpam-6413	451	57	(	(	PUNCT
ejpam-6413	451	58	1−	1−	NUM
ejpam-6413	451	59	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	451	60	−	−	PROPN
ejpam-6413	451	61	⊺θ+1	⊺θ+1	NOUN
ejpam-6413	451	62	⋎(θ	⋎(θ	NOUN
ejpam-6413	451	63	+	+	NOUN
ejpam-6413	451	64	1	1	NUM
ejpam-6413	451	65	)	)	PUNCT
ejpam-6413	451	66	−	−	PROPN
ejpam-6413	451	67	1−	1−	NUM
ejpam-6413	451	68	⊺	⊺	NUM
ejpam-6413	451	69	⋎+	⋎+	DET
ejpam-6413	451	70	1	1	NUM
ejpam-6413	451	71	∣∣∣∣⋋1	∣∣∣∣⋋1	PROPN
ejpam-6413	451	72	d⊺	d⊺	PROPN
ejpam-6413	451	73	)	)	PUNCT
ejpam-6413	451	74	1	1	NUM
ejpam-6413	451	75	⋋1	⋋1	NUM
ejpam-6413	451	76	≤	≤	NOUN
ejpam-6413	451	77	(	(	PUNCT
ejpam-6413	451	78	µ−	µ−	PROPN
ejpam-6413	451	79	ā)2	ā)2	PROPN
ejpam-6413	451	80	⋎(⋎+	⋎(⋎+	NUM
ejpam-6413	451	81	1)(θ	1)(θ	NUM
ejpam-6413	451	82	+	+	CCONJ
ejpam-6413	451	83	1	1	NUM
ejpam-6413	451	84	)	)	PUNCT
ejpam-6413	451	85	(	(	PUNCT
ejpam-6413	451	86	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	VERB
ejpam-6413	452	1	+	+	X
ejpam-6413	452	2	mα|𭟋′′(b̄)|⋋2	mα|𭟋′′(b̄)|⋋2	NOUN
ejpam-6413	452	3	α+	α+	PUNCT
ejpam-6413	452	4	1	1	NUM
ejpam-6413	452	5	)	)	PUNCT
ejpam-6413	452	6	1	1	NUM
ejpam-6413	452	7	⋋2	⋋2	PROPN
ejpam-6413	452	8	×	×	NOUN
ejpam-6413	452	9	(	(	PUNCT
ejpam-6413	452	10	∫	∫	PROPN
ejpam-6413	452	11	1	1	NUM
ejpam-6413	452	12	2	2	NUM
ejpam-6413	452	13	0	0	NUM
ejpam-6413	452	14	∣∣∣(⋎+	∣∣∣(⋎+	PROPN
ejpam-6413	452	15	1)−	1)−	PROPN
ejpam-6413	452	16	(	(	PUNCT
ejpam-6413	452	17	⋎+	⋎+	PRON
ejpam-6413	452	18	1)[(1	1)[(1	NOUN
ejpam-6413	452	19	+	+	CCONJ
ejpam-6413	452	20	⊺)θ+1	⊺)θ+1	NOUN
ejpam-6413	452	21	+	+	CCONJ
ejpam-6413	452	22	⊺θ+1]−	⊺θ+1]−	PRON
ejpam-6413	452	23	⊺	⊺	VERB
ejpam-6413	452	24	⋎	⋎	NOUN
ejpam-6413	452	25	(	(	PUNCT
ejpam-6413	452	26	θ	θ	NOUN
ejpam-6413	452	27	+	+	NOUN
ejpam-6413	452	28	1	1	X
ejpam-6413	452	29	)	)	PUNCT
ejpam-6413	452	30	∣∣∣⋋1	∣∣∣⋋1	NOUN
ejpam-6413	452	31	d⊺	d⊺	PROPN
ejpam-6413	452	32	+	+	CCONJ
ejpam-6413	452	33	∫	∫	PROPN
ejpam-6413	452	34	1	1	NUM
ejpam-6413	452	35	1	1	NUM
ejpam-6413	452	36	2	2	NUM
ejpam-6413	452	37	∣∣∣(⋎+	∣∣∣(⋎+	PROPN
ejpam-6413	452	38	1)−	1)−	PROPN
ejpam-6413	452	39	(	(	PUNCT
ejpam-6413	452	40	⋎+	⋎+	PRON
ejpam-6413	452	41	1)[(1	1)[(1	NOUN
ejpam-6413	452	42	+	+	CCONJ
ejpam-6413	452	43	⊺)θ+1	⊺)θ+1	NOUN
ejpam-6413	452	44	+	+	CCONJ
ejpam-6413	452	45	⊺θ+1]−⋎(θ	⊺θ+1]−⋎(θ	NOUN
ejpam-6413	452	46	+	+	CCONJ
ejpam-6413	452	47	1)(1−	1)(1−	NUM
ejpam-6413	452	48	⊺	⊺	NOUN
ejpam-6413	452	49	)	)	PUNCT
ejpam-6413	452	50	∣∣∣⋋1	∣∣∣⋋1	PROPN
ejpam-6413	452	51	d⊺	d⊺	PROPN
ejpam-6413	452	52	)	)	PUNCT
ejpam-6413	452	53	1	1	NUM
ejpam-6413	452	54	⋋1	⋋1	NUM
ejpam-6413	452	55	.	.	PUNCT
ejpam-6413	453	1	(	(	PUNCT
ejpam-6413	453	2	36	36	NUM
ejpam-6413	453	3	)	)	PUNCT
ejpam-6413	453	4	let	let	VERB
ejpam-6413	453	5	us	we	PRON
ejpam-6413	453	6	consider∫	consider∫	VERB
ejpam-6413	453	7	1	1	NUM
ejpam-6413	453	8	2	2	NUM
ejpam-6413	453	9	0	0	NUM
ejpam-6413	453	10	[	[	PUNCT
ejpam-6413	453	11	(	(	PUNCT
ejpam-6413	453	12	⋎+	⋎+	PROPN
ejpam-6413	453	13	1)−	1)−	PROPN
ejpam-6413	453	14	(	(	PUNCT
ejpam-6413	453	15	⋎+	⋎+	PRON
ejpam-6413	453	16	1)[(1	1)[(1	NOUN
ejpam-6413	454	1	+	+	CCONJ
ejpam-6413	454	2	⊺)θ+1	⊺)θ+1	NOUN
ejpam-6413	454	3	+	+	CCONJ
ejpam-6413	454	4	⊺θ+1]−	⊺θ+1]−	PRON
ejpam-6413	454	5	⊺	⊺	VERB
ejpam-6413	454	6	⋎	⋎	NOUN
ejpam-6413	454	7	(	(	PUNCT
ejpam-6413	454	8	θ	θ	NOUN
ejpam-6413	454	9	+	+	PROPN
ejpam-6413	454	10	1	1	NUM
ejpam-6413	454	11	)	)	PUNCT
ejpam-6413	454	12	]	]	PUNCT
ejpam-6413	454	13	⋋1	⋋1	NUM
ejpam-6413	454	14	d⊺	d⊺	PROPN
ejpam-6413	454	15	≤	≤	NUM
ejpam-6413	454	16	−	−	ADP
ejpam-6413	454	17	1	1	NUM
ejpam-6413	454	18	⋎(θ	⋎(θ	NOUN
ejpam-6413	454	19	+	+	NOUN
ejpam-6413	454	20	1	1	NUM
ejpam-6413	454	21	)	)	PUNCT
ejpam-6413	454	22	[	[	PUNCT
ejpam-6413	454	23	[	[	X
ejpam-6413	454	24	(	(	PUNCT
ejpam-6413	454	25	⋎+	⋎+	PROPN
ejpam-6413	454	26	1)−	1)−	PROPN
ejpam-6413	454	27	(	(	PUNCT
ejpam-6413	454	28	⋎+	⋎+	PRON
ejpam-6413	454	29	1)2−θ	1)2−θ	NUM
ejpam-6413	454	30	−	−	NOUN
ejpam-6413	454	31	⊺	⊺	NUM
ejpam-6413	454	32	⋎	⋎	NOUN
ejpam-6413	454	33	(	(	PUNCT
ejpam-6413	454	34	θ	θ	NOUN
ejpam-6413	454	35	+	+	NOUN
ejpam-6413	454	36	1)]⋋1	1)]⋋1	NUM
ejpam-6413	454	37	+	+	SYM
ejpam-6413	454	38	1	1	NUM
ejpam-6413	454	39	⋋1	⋋1	NUM
ejpam-6413	454	40	+	+	SYM
ejpam-6413	454	41	1	1	NUM
ejpam-6413	454	42	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	454	43	1	1	NUM
ejpam-6413	454	44	2	2	NUM
ejpam-6413	454	45	0	0	NUM
ejpam-6413	454	46	]	]	PUNCT
ejpam-6413	454	47	≤	≤	NUM
ejpam-6413	455	1	[	[	X
ejpam-6413	455	2	(	(	PUNCT
ejpam-6413	455	3	⋎+	⋎+	PROPN
ejpam-6413	455	4	1)−	1)−	PROPN
ejpam-6413	455	5	(	(	PUNCT
ejpam-6413	455	6	⋎+	⋎+	PRON
ejpam-6413	455	7	1)2−θ]⋋1	1)2−θ]⋋1	NUM
ejpam-6413	455	8	+	+	NOUN
ejpam-6413	455	9	1	1	NUM
ejpam-6413	455	10	−	−	NOUN
ejpam-6413	456	1	[	[	X
ejpam-6413	456	2	1	1	NUM
ejpam-6413	456	3	+	+	NUM
ejpam-6413	456	4	0.5⋎	0.5⋎	NUM
ejpam-6413	456	5	(	(	PUNCT
ejpam-6413	456	6	1−	1−	NUM
ejpam-6413	456	7	θ)−	θ)−	PROPN
ejpam-6413	456	8	(	(	PUNCT
ejpam-6413	456	9	1	1	NUM
ejpam-6413	456	10	+	+	NOUN
ejpam-6413	456	11	⋎)2−θ]⋋1	⋎)2−θ]⋋1	ADJ
ejpam-6413	456	12	+	+	ADJ
ejpam-6413	456	13	1	1	NUM
ejpam-6413	456	14	⋎(θ	⋎(θ	NOUN
ejpam-6413	456	15	+	+	CCONJ
ejpam-6413	456	16	1)(⋋1	1)(⋋1	NUM
ejpam-6413	456	17	+	+	NUM
ejpam-6413	456	18	1	1	NUM
ejpam-6413	456	19	)	)	PUNCT
ejpam-6413	456	20	,	,	PUNCT
ejpam-6413	456	21	(	(	PUNCT
ejpam-6413	456	22	37	37	NUM
ejpam-6413	456	23	)	)	PUNCT
ejpam-6413	456	24	and	and	CCONJ
ejpam-6413	456	25	∫	∫	PROPN
ejpam-6413	456	26	1	1	NUM
ejpam-6413	456	27	2	2	NUM
ejpam-6413	456	28	0	0	NUM
ejpam-6413	456	29	[	[	PUNCT
ejpam-6413	456	30	−(⋎+	−(⋎+	NUM
ejpam-6413	456	31	1	1	NUM
ejpam-6413	456	32	)	)	PUNCT
ejpam-6413	457	1	+	+	CCONJ
ejpam-6413	457	2	(	(	PUNCT
ejpam-6413	457	3	⋎+	⋎+	PRON
ejpam-6413	457	4	1)[(1	1)[(1	NOUN
ejpam-6413	457	5	+	+	CCONJ
ejpam-6413	457	6	⊺)θ+1	⊺)θ+1	PROPN
ejpam-6413	457	7	+	+	CCONJ
ejpam-6413	457	8	⊺θ+1	⊺θ+1	PROPN
ejpam-6413	457	9	]	]	X
ejpam-6413	457	10	+	+	CCONJ
ejpam-6413	457	11	⊺	⊺	NUM
ejpam-6413	457	12	⋎	⋎	NOUN
ejpam-6413	457	13	(	(	PUNCT
ejpam-6413	457	14	θ	θ	NOUN
ejpam-6413	457	15	+	+	PROPN
ejpam-6413	457	16	1	1	NUM
ejpam-6413	457	17	)	)	PUNCT
ejpam-6413	457	18	]	]	PUNCT
ejpam-6413	457	19	⋋1	⋋1	NUM
ejpam-6413	457	20	d⊺	d⊺	PROPN
ejpam-6413	457	21	≤	≤	NUM
ejpam-6413	457	22	1	1	NUM
ejpam-6413	457	23	⋎(θ	⋎(θ	NOUN
ejpam-6413	457	24	+	+	NOUN
ejpam-6413	457	25	1	1	NUM
ejpam-6413	457	26	)	)	PUNCT
ejpam-6413	457	27	[	[	PUNCT
ejpam-6413	457	28	[	[	X
ejpam-6413	457	29	−⋎−1	−⋎−1	X
ejpam-6413	457	30	+	+	X
ejpam-6413	457	31	(	(	PUNCT
ejpam-6413	457	32	⋎+	⋎+	DET
ejpam-6413	457	33	1)2−θ	1)2−θ	NUM
ejpam-6413	457	34	+	+	NOUN
ejpam-6413	457	35	⋎(θ	⋎(θ	NOUN
ejpam-6413	457	36	+	+	NOUN
ejpam-6413	457	37	1)⊺]⋋1	1)⊺]⋋1	NUM
ejpam-6413	457	38	+	+	SYM
ejpam-6413	457	39	1	1	NUM
ejpam-6413	457	40	⋋1	⋋1	NUM
ejpam-6413	457	41	+	+	SYM
ejpam-6413	457	42	1	1	NUM
ejpam-6413	457	43	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	457	44	1	1	NUM
ejpam-6413	457	45	2	2	NUM
ejpam-6413	457	46	0	0	NUM
ejpam-6413	457	47	]	]	PUNCT
ejpam-6413	457	48	≤	≤	NOUN
ejpam-6413	458	1	[	[	X
ejpam-6413	458	2	⋎(θ	⋎(θ	NOUN
ejpam-6413	458	3	+	+	NOUN
ejpam-6413	458	4	1)]⋋1	1)]⋋1	NUM
ejpam-6413	458	5	+	+	NOUN
ejpam-6413	458	6	12−⋋1−1	12−⋋1−1	NUM
ejpam-6413	458	7	⋎(θ	⋎(θ	NOUN
ejpam-6413	458	8	+	+	CCONJ
ejpam-6413	458	9	1)(⋋1	1)(⋋1	NUM
ejpam-6413	458	10	+	+	NUM
ejpam-6413	458	11	1	1	NUM
ejpam-6413	458	12	)	)	PUNCT
ejpam-6413	458	13	,	,	PUNCT
ejpam-6413	458	14	(	(	PUNCT
ejpam-6413	458	15	38	38	NUM
ejpam-6413	458	16	)	)	PUNCT
ejpam-6413	458	17	and	and	CCONJ
ejpam-6413	458	18	∫	∫	PROPN
ejpam-6413	458	19	1	1	NUM
ejpam-6413	458	20	1	1	NUM
ejpam-6413	458	21	2	2	NUM
ejpam-6413	458	22	[	[	PUNCT
ejpam-6413	458	23	(	(	PUNCT
ejpam-6413	458	24	⋎+	⋎+	PROPN
ejpam-6413	458	25	1)−	1)−	PROPN
ejpam-6413	458	26	(	(	PUNCT
ejpam-6413	458	27	⋎+	⋎+	PRON
ejpam-6413	458	28	1)[(1	1)[(1	NOUN
ejpam-6413	459	1	+	+	CCONJ
ejpam-6413	459	2	⊺)θ+1	⊺)θ+1	NOUN
ejpam-6413	459	3	+	+	CCONJ
ejpam-6413	459	4	⊺θ+1]−⋎(θ	⊺θ+1]−⋎(θ	NOUN
ejpam-6413	459	5	+	+	NUM
ejpam-6413	459	6	1)(1−	1)(1−	NUM
ejpam-6413	459	7	⊺	⊺	NOUN
ejpam-6413	459	8	)	)	PUNCT
ejpam-6413	459	9	]	]	PUNCT
ejpam-6413	459	10	⋋1	⋋1	NUM
ejpam-6413	459	11	d⊺	d⊺	PROPN
ejpam-6413	459	12	m.	m.	NOUN
ejpam-6413	459	13	samraiz	samraiz	PROPN
ejpam-6413	459	14	et	et	PROPN
ejpam-6413	459	15	al	al	PROPN
ejpam-6413	459	16	.	.	PUNCT
ejpam-6413	459	17	/	/	SYM
ejpam-6413	459	18	eur	eur	PROPN
ejpam-6413	459	19	.	.	PUNCT
ejpam-6413	460	1	j.	j.	PROPN
ejpam-6413	460	2	pure	pure	PROPN
ejpam-6413	460	3	appl	appl	PROPN
ejpam-6413	460	4	.	.	PROPN
ejpam-6413	460	5	math	math	PROPN
ejpam-6413	460	6	,	,	PUNCT
ejpam-6413	460	7	18	18	NUM
ejpam-6413	460	8	(	(	PUNCT
ejpam-6413	460	9	3	3	NUM
ejpam-6413	460	10	)	)	PUNCT
ejpam-6413	460	11	(	(	PUNCT
ejpam-6413	460	12	2025	2025	NUM
ejpam-6413	460	13	)	)	PUNCT
ejpam-6413	460	14	,	,	PUNCT
ejpam-6413	460	15	6413	6413	NUM
ejpam-6413	460	16	23	23	NUM
ejpam-6413	460	17	of	of	ADP
ejpam-6413	460	18	26	26	NUM
ejpam-6413	460	19	≤	≤	NUM
ejpam-6413	460	20	−	−	ADP
ejpam-6413	460	21	1	1	NUM
ejpam-6413	460	22	⋎(θ	⋎(θ	NOUN
ejpam-6413	460	23	+	+	NOUN
ejpam-6413	460	24	1	1	NUM
ejpam-6413	460	25	)	)	PUNCT
ejpam-6413	460	26	[	[	PUNCT
ejpam-6413	460	27	[	[	X
ejpam-6413	460	28	(	(	PUNCT
ejpam-6413	460	29	⋎+	⋎+	PROPN
ejpam-6413	460	30	1)−	1)−	PROPN
ejpam-6413	460	31	(	(	PUNCT
ejpam-6413	460	32	⋎+	⋎+	DET
ejpam-6413	460	33	1)2−θ	1)2−θ	NUM
ejpam-6413	460	34	−⋎(θ	−⋎(θ	NOUN
ejpam-6413	460	35	+	+	NOUN
ejpam-6413	460	36	1)(1−	1)(1−	NUM
ejpam-6413	460	37	⊺)]⋋1	⊺)]⋋1	X
ejpam-6413	460	38	+	+	PROPN
ejpam-6413	460	39	1	1	NUM
ejpam-6413	460	40	⋋1	⋋1	NUM
ejpam-6413	460	41	+	+	SYM
ejpam-6413	460	42	1	1	NUM
ejpam-6413	460	43	∣∣∣∣1	∣∣∣∣1	NOUN
ejpam-6413	460	44	1	1	NUM
ejpam-6413	460	45	2	2	NUM
ejpam-6413	460	46	]	]	PUNCT
ejpam-6413	460	47	≤	≤	NOUN
ejpam-6413	461	1	[	[	X
ejpam-6413	461	2	(	(	PUNCT
ejpam-6413	461	3	(	(	PUNCT
ejpam-6413	461	4	⋎+	⋎+	PROPN
ejpam-6413	461	5	1)−	1)−	PROPN
ejpam-6413	461	6	(	(	PUNCT
ejpam-6413	461	7	⋎+	⋎+	PRON
ejpam-6413	461	8	1)2−θ)−	1)2−θ)−	NUM
ejpam-6413	461	9	(	(	PUNCT
ejpam-6413	461	10	1	1	NUM
ejpam-6413	461	11	+	+	NUM
ejpam-6413	461	12	0.5⋎	0.5⋎	NUM
ejpam-6413	461	13	(	(	PUNCT
ejpam-6413	461	14	1−	1−	NUM
ejpam-6413	461	15	θ	θ	NOUN
ejpam-6413	461	16	)	)	PUNCT
ejpam-6413	462	1	+	+	CCONJ
ejpam-6413	462	2	(	(	PUNCT
ejpam-6413	462	3	⋎+	⋎+	PRON
ejpam-6413	462	4	1)2−θ)]⋋1	1)2−θ)]⋋1	NUM
ejpam-6413	462	5	+	+	ADJ
ejpam-6413	462	6	1	1	NUM
ejpam-6413	462	7	⋎(θ	⋎(θ	NOUN
ejpam-6413	462	8	+	+	NOUN
ejpam-6413	462	9	1)(⋋1	1)(⋋1	NUM
ejpam-6413	462	10	+	+	NUM
ejpam-6413	462	11	1	1	NUM
ejpam-6413	462	12	)	)	PUNCT
ejpam-6413	462	13	,	,	PUNCT
ejpam-6413	462	14	(	(	PUNCT
ejpam-6413	462	15	39	39	NUM
ejpam-6413	462	16	)	)	PUNCT
ejpam-6413	462	17	and	and	CCONJ
ejpam-6413	462	18	∫	∫	PROPN
ejpam-6413	462	19	1	1	NUM
ejpam-6413	462	20	1	1	NUM
ejpam-6413	462	21	2	2	NUM
ejpam-6413	462	22	[	[	PUNCT
ejpam-6413	462	23	(	(	PUNCT
ejpam-6413	462	24	−⋎−1	−⋎−1	PROPN
ejpam-6413	462	25	+	+	NUM
ejpam-6413	462	26	(	(	PUNCT
ejpam-6413	462	27	⋎+	⋎+	DET
ejpam-6413	462	28	1)2−θ	1)2−θ	NUM
ejpam-6413	462	29	+	+	NOUN
ejpam-6413	462	30	⋎(θ	⋎(θ	NOUN
ejpam-6413	462	31	+	+	NOUN
ejpam-6413	462	32	1)(1−	1)(1−	NUM
ejpam-6413	462	33	⊺))d⊺	⊺))d⊺	ADJ
ejpam-6413	462	34	]	]	X
ejpam-6413	462	35	⋋1	⋋1	NUM
ejpam-6413	462	36	≤	≤	NOUN
ejpam-6413	463	1	[	[	X
ejpam-6413	463	2	⋎(θ	⋎(θ	NOUN
ejpam-6413	463	3	+	+	NOUN
ejpam-6413	463	4	1)]⋋1	1)]⋋1	NUM
ejpam-6413	463	5	+	+	NOUN
ejpam-6413	463	6	12−⋋1−1	12−⋋1−1	NUM
ejpam-6413	463	7	⋎(θ	⋎(θ	NOUN
ejpam-6413	463	8	+	+	CCONJ
ejpam-6413	463	9	1)(⋋1	1)(⋋1	NUM
ejpam-6413	463	10	+	+	NUM
ejpam-6413	463	11	1	1	NUM
ejpam-6413	463	12	)	)	PUNCT
ejpam-6413	463	13	.	.	PUNCT
ejpam-6413	464	1	(	(	PUNCT
ejpam-6413	464	2	40	40	NUM
ejpam-6413	464	3	)	)	PUNCT
ejpam-6413	464	4	substituting	substitute	VERB
ejpam-6413	464	5	(	(	PUNCT
ejpam-6413	464	6	37	37	NUM
ejpam-6413	464	7	)	)	PUNCT
ejpam-6413	464	8	,	,	PUNCT
ejpam-6413	464	9	(	(	PUNCT
ejpam-6413	464	10	38	38	NUM
ejpam-6413	464	11	)	)	PUNCT
ejpam-6413	464	12	,	,	PUNCT
ejpam-6413	464	13	(	(	PUNCT
ejpam-6413	464	14	39	39	NUM
ejpam-6413	464	15	)	)	PUNCT
ejpam-6413	464	16	and	and	CCONJ
ejpam-6413	464	17	(	(	PUNCT
ejpam-6413	464	18	40	40	NUM
ejpam-6413	464	19	)	)	PUNCT
ejpam-6413	464	20	in	in	ADP
ejpam-6413	464	21	(	(	PUNCT
ejpam-6413	464	22	36	36	NUM
ejpam-6413	464	23	)	)	PUNCT
ejpam-6413	464	24	,	,	PUNCT
ejpam-6413	464	25	we	we	PRON
ejpam-6413	464	26	obtained	obtain	VERB
ejpam-6413	464	27	the	the	DET
ejpam-6413	464	28	required	require	VERB
ejpam-6413	464	29	result	result	NOUN
ejpam-6413	464	30	.	.	PUNCT
ejpam-6413	465	1	remark	remark	VERB
ejpam-6413	465	2	7	7	NUM
ejpam-6413	465	3	.	.	PUNCT
ejpam-6413	466	1	in	in	ADP
ejpam-6413	466	2	accordance	accordance	NOUN
ejpam-6413	466	3	with	with	ADP
ejpam-6413	466	4	the	the	DET
ejpam-6413	466	5	selection	selection	NOUN
ejpam-6413	466	6	of	of	ADP
ejpam-6413	466	7	parameters	parameter	NOUN
ejpam-6413	466	8	α	α	X
ejpam-6413	466	9	=	=	SYM
ejpam-6413	466	10	1	1	NUM
ejpam-6413	466	11	and	and	CCONJ
ejpam-6413	466	12	m	m	VERB
ejpam-6413	466	13	=	=	ADJ
ejpam-6413	466	14	1	1	NUM
ejpam-6413	466	15	in	in	ADP
ejpam-6413	466	16	theorem	theorem	NOUN
ejpam-6413	466	17	6	6	NUM
ejpam-6413	466	18	and	and	CCONJ
ejpam-6413	466	19	s	s	NOUN
ejpam-6413	466	20	=	=	SYM
ejpam-6413	466	21	1	1	NUM
ejpam-6413	466	22	in	in	ADP
ejpam-6413	466	23	[	[	PUNCT
ejpam-6413	466	24	2	2	NUM
ejpam-6413	466	25	,	,	PUNCT
ejpam-6413	466	26	theorem	theorem	VERB
ejpam-6413	466	27	5.2	5.2	NUM
ejpam-6413	466	28	]	]	PUNCT
ejpam-6413	466	29	,	,	PUNCT
ejpam-6413	466	30	we	we	PRON
ejpam-6413	466	31	obtained	obtain	VERB
ejpam-6413	466	32	the	the	DET
ejpam-6413	466	33	same	same	ADJ
ejpam-6413	466	34	result	result	NOUN
ejpam-6413	466	35	i.e.	i.e.	X
ejpam-6413	466	36	,∣∣∣∣𭟋(ā	,∣∣∣∣𭟋(ā	PUNCT
ejpam-6413	466	37	)	)	PUNCT
ejpam-6413	467	1	+	+	NOUN
ejpam-6413	467	2	𭟋(b̄	𭟋(b̄	X
ejpam-6413	467	3	)	)	PUNCT
ejpam-6413	467	4	⋎(⋎+	⋎(⋎+	VERB
ejpam-6413	467	5	1	1	NUM
ejpam-6413	467	6	)	)	PUNCT
ejpam-6413	467	7	+	+	CCONJ
ejpam-6413	467	8	2	2	NUM
ejpam-6413	467	9	⋎+	⋎+	DET
ejpam-6413	467	10	1	1	NUM
ejpam-6413	467	11	𭟋	𭟋	PROPN
ejpam-6413	467	12	(	(	PUNCT
ejpam-6413	467	13	ā+	ā+	PUNCT
ejpam-6413	467	14	b̄	b̄	VERB
ejpam-6413	467	15	2	2	NUM
ejpam-6413	467	16	)	)	PUNCT
ejpam-6413	467	17	−	−	PROPN
ejpam-6413	468	1	γ(θ	γ(θ	PROPN
ejpam-6413	468	2	+	+	CCONJ
ejpam-6413	468	3	1	1	X
ejpam-6413	468	4	)	)	PUNCT
ejpam-6413	468	5	⋎(b̄−	⋎(b̄−	NUM
ejpam-6413	468	6	ā)θ	ā)θ	NOUN
ejpam-6413	468	7	[	[	X
ejpam-6413	468	8	χθ	χθ	X
ejpam-6413	468	9	ā+𭟋(b̄	ā+𭟋(b̄	NUM
ejpam-6413	468	10	)	)	PUNCT
ejpam-6413	469	1	+	+	CCONJ
ejpam-6413	469	2	χθ	χθ	X
ejpam-6413	469	3	b̄−𭟋(ā	b̄−𭟋(ā	NOUN
ejpam-6413	469	4	)	)	PUNCT
ejpam-6413	469	5	]	]	PUNCT
ejpam-6413	470	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6413	470	2	≤	≤	NOUN
ejpam-6413	470	3	(	(	PUNCT
ejpam-6413	470	4	b̄−	b̄−	ADJ
ejpam-6413	470	5	ā)2	ā)2	NOUN
ejpam-6413	471	1	[	[	X
ejpam-6413	471	2	⋎(θ	⋎(θ	NOUN
ejpam-6413	471	3	+	+	NOUN
ejpam-6413	471	4	1)(⋎+	1)(⋎+	NUM
ejpam-6413	471	5	1)]1+⋋−1	1)]1+⋋−1	NUM
ejpam-6413	471	6	1	1	NUM
ejpam-6413	471	7	(	(	PUNCT
ejpam-6413	471	8	|𭟋′′(ā)|⋋2	|𭟋′′(ā)|⋋2	PROPN
ejpam-6413	471	9	+	+	CCONJ
ejpam-6413	471	10	|𭟋′′(b̄)|⋋2	|𭟋′′(b̄)|⋋2	PROPN
ejpam-6413	471	11	2	2	NUM
ejpam-6413	471	12	)	)	PUNCT
ejpam-6413	471	13	1	1	NUM
ejpam-6413	471	14	⋋2	⋋2	PROPN
ejpam-6413	471	15	×	×	NOUN
ejpam-6413	471	16	[	[	PUNCT
ejpam-6413	471	17	max	max	PROPN
ejpam-6413	471	18	(	(	PUNCT
ejpam-6413	471	19	(	(	PUNCT
ejpam-6413	471	20	⋎+	⋎+	PRON
ejpam-6413	471	21	1−	1−	NUM
ejpam-6413	471	22	(	(	PUNCT
ejpam-6413	471	23	⋎+	⋎+	DET
ejpam-6413	471	24	1)2−θ	1)2−θ	NUM
ejpam-6413	471	25	)	)	PUNCT
ejpam-6413	471	26	⋋1	⋋1	PROPN
ejpam-6413	471	27	+	+	PROPN
ejpam-6413	471	28	1	1	NUM
ejpam-6413	471	29	−	−	NOUN
ejpam-6413	471	30	(	(	PUNCT
ejpam-6413	471	31	1	1	NUM
ejpam-6413	471	32	+	+	NUM
ejpam-6413	471	33	0.5⋎	0.5⋎	NUM
ejpam-6413	471	34	(	(	PUNCT
ejpam-6413	471	35	1−	1−	NUM
ejpam-6413	471	36	θ)−	θ)−	PROPN
ejpam-6413	471	37	(	(	PUNCT
ejpam-6413	471	38	1	1	NUM
ejpam-6413	471	39	+	+	NOUN
ejpam-6413	471	40	⋎)2−θ	⋎)2−θ	NOUN
ejpam-6413	471	41	)	)	PUNCT
ejpam-6413	472	1	⋋1	⋋1	PROPN
ejpam-6413	473	1	+	+	PROPN
ejpam-6413	473	2	1	1	NUM
ejpam-6413	473	3	,	,	PUNCT
ejpam-6413	473	4	(	(	PUNCT
ejpam-6413	473	5	⋎(θ	⋎(θ	NOUN
ejpam-6413	473	6	+	+	NOUN
ejpam-6413	473	7	1))⋋1	1))⋋1	NUM
ejpam-6413	473	8	+	+	ADJ
ejpam-6413	473	9	1	1	NUM
ejpam-6413	473	10	2−⋋1−1	2−⋋1−1	NUM
ejpam-6413	473	11	)	)	PUNCT
ejpam-6413	474	1	+	+	X
ejpam-6413	474	2	max	max	PROPN
ejpam-6413	474	3	(	(	PUNCT
ejpam-6413	474	4	(	(	PUNCT
ejpam-6413	474	5	⋎+	⋎+	PRON
ejpam-6413	474	6	1−	1−	NUM
ejpam-6413	474	7	(	(	PUNCT
ejpam-6413	474	8	⋎+	⋎+	DET
ejpam-6413	474	9	1)2−θ	1)2−θ	NUM
ejpam-6413	474	10	)	)	PUNCT
ejpam-6413	474	11	⋋1	⋋1	PROPN
ejpam-6413	474	12	+	+	PROPN
ejpam-6413	474	13	1	1	NUM
ejpam-6413	474	14	−	−	NOUN
ejpam-6413	474	15	(	(	PUNCT
ejpam-6413	474	16	1	1	NUM
ejpam-6413	474	17	+	+	NUM
ejpam-6413	474	18	0.5⋎	0.5⋎	NUM
ejpam-6413	474	19	(	(	PUNCT
ejpam-6413	474	20	1−	1−	NUM
ejpam-6413	474	21	θ)−	θ)−	PROPN
ejpam-6413	474	22	(	(	PUNCT
ejpam-6413	474	23	1	1	NUM
ejpam-6413	474	24	+	+	NOUN
ejpam-6413	474	25	⋎)2−θ	⋎)2−θ	NOUN
ejpam-6413	474	26	)	)	PUNCT
ejpam-6413	474	27	⋋1	⋋1	PROPN
ejpam-6413	474	28	+	+	PROPN
ejpam-6413	474	29	1	1	NUM
ejpam-6413	474	30	,	,	PUNCT
ejpam-6413	474	31	0.5⋎	0.5⋎	NUM
ejpam-6413	474	32	(	(	PUNCT
ejpam-6413	474	33	θ	θ	PROPN
ejpam-6413	474	34	+	+	NOUN
ejpam-6413	474	35	1)⋋1	1)⋋1	NUM
ejpam-6413	474	36	+	+	SYM
ejpam-6413	474	37	1	1	NUM
ejpam-6413	474	38	)	)	PUNCT
ejpam-6413	474	39	)	)	PUNCT
ejpam-6413	474	40	1	1	NUM
ejpam-6413	474	41	⋋1	⋋1	NUM
ejpam-6413	474	42	)	)	PUNCT
ejpam-6413	474	43	]	]	PUNCT
ejpam-6413	474	44	.	.	PUNCT
ejpam-6413	475	1	5	5	X
ejpam-6413	475	2	.	.	X
ejpam-6413	475	3	conclusions	conclusion	NOUN
ejpam-6413	475	4	the	the	DET
ejpam-6413	475	5	importance	importance	NOUN
ejpam-6413	475	6	of	of	ADP
ejpam-6413	475	7	convexity	convexity	NOUN
ejpam-6413	475	8	and	and	CCONJ
ejpam-6413	475	9	fractional	fractional	ADJ
ejpam-6413	475	10	calculus	calculus	NOUN
ejpam-6413	475	11	in	in	ADP
ejpam-6413	475	12	real	real	ADJ
ejpam-6413	475	13	-	-	PUNCT
ejpam-6413	475	14	life	life	NOUN
ejpam-6413	475	15	implications	implication	NOUN
ejpam-6413	475	16	is	be	AUX
ejpam-6413	475	17	unavoidable	unavoidable	ADJ
ejpam-6413	475	18	.	.	PUNCT
ejpam-6413	476	1	both	both	DET
ejpam-6413	476	2	concepts	concept	NOUN
ejpam-6413	476	3	represent	represent	VERB
ejpam-6413	476	4	nature	nature	NOUN
ejpam-6413	476	5	well	well	ADV
ejpam-6413	476	6	.	.	PUNCT
ejpam-6413	477	1	in	in	ADP
ejpam-6413	477	2	the	the	DET
ejpam-6413	477	3	presented	present	VERB
ejpam-6413	477	4	work	work	NOUN
ejpam-6413	477	5	,	,	PUNCT
ejpam-6413	477	6	we	we	PRON
ejpam-6413	477	7	utilized	utilize	VERB
ejpam-6413	477	8	both	both	DET
ejpam-6413	477	9	concepts	concept	NOUN
ejpam-6413	477	10	and	and	CCONJ
ejpam-6413	477	11	obtained	obtain	VERB
ejpam-6413	477	12	some	some	DET
ejpam-6413	477	13	good	good	ADJ
ejpam-6413	477	14	results	result	NOUN
ejpam-6413	477	15	.	.	PUNCT
ejpam-6413	478	1	this	this	DET
ejpam-6413	478	2	paper	paper	NOUN
ejpam-6413	478	3	introduces	introduce	VERB
ejpam-6413	478	4	new	new	ADJ
ejpam-6413	478	5	fractional	fractional	ADJ
ejpam-6413	478	6	integral	integral	ADJ
ejpam-6413	478	7	inequalities	inequality	NOUN
ejpam-6413	478	8	that	that	PRON
ejpam-6413	478	9	are	be	AUX
ejpam-6413	478	10	applicable	applicable	ADJ
ejpam-6413	478	11	to	to	ADP
ejpam-6413	478	12	twice	twice	ADV
ejpam-6413	478	13	-	-	PUNCT
ejpam-6413	478	14	differentiable	differentiable	NOUN
ejpam-6413	478	15	geometrically	geometrically	ADV
ejpam-6413	478	16	arithmetically	arithmetically	ADV
ejpam-6413	478	17	(	(	PUNCT
ejpam-6413	478	18	α	α	NOUN
ejpam-6413	478	19	,	,	PUNCT
ejpam-6413	478	20	m)-convex	m)-convex	NOUN
ejpam-6413	478	21	functions	function	NOUN
ejpam-6413	478	22	.	.	PUNCT
ejpam-6413	479	1	the	the	DET
ejpam-6413	479	2	utilization	utilization	NOUN
ejpam-6413	479	3	of	of	ADP
ejpam-6413	479	4	classical	classical	ADJ
ejpam-6413	479	5	riemann	riemann	PROPN
ejpam-6413	479	6	-	-	PUNCT
ejpam-6413	479	7	liouville	liouville	VERB
ejpam-6413	479	8	fractional	fractional	ADJ
ejpam-6413	479	9	integrals	integral	NOUN
ejpam-6413	479	10	leads	lead	VERB
ejpam-6413	479	11	to	to	ADP
ejpam-6413	479	12	the	the	DET
ejpam-6413	479	13	derivation	derivation	NOUN
ejpam-6413	479	14	of	of	ADP
ejpam-6413	479	15	new	new	ADJ
ejpam-6413	479	16	identities	identity	NOUN
ejpam-6413	479	17	.	.	PUNCT
ejpam-6413	480	1	consequently	consequently	ADV
ejpam-6413	480	2	,	,	PUNCT
ejpam-6413	480	3	we	we	PRON
ejpam-6413	480	4	are	be	AUX
ejpam-6413	480	5	able	able	ADJ
ejpam-6413	480	6	to	to	PART
ejpam-6413	480	7	explore	explore	VERB
ejpam-6413	480	8	the	the	DET
ejpam-6413	480	9	hermite	hermite	ADJ
ejpam-6413	480	10	-	-	PUNCT
ejpam-6413	480	11	hadamard	hadamard	ADJ
ejpam-6413	480	12	type	type	NOUN
ejpam-6413	480	13	inequalities	inequality	NOUN
ejpam-6413	480	14	based	base	VERB
ejpam-6413	480	15	on	on	ADP
ejpam-6413	480	16	the	the	DET
ejpam-6413	480	17	mentioned	mention	VERB
ejpam-6413	480	18	convexity	convexity	NOUN
ejpam-6413	480	19	.	.	PUNCT
ejpam-6413	481	1	hölder	hölder	PROPN
ejpam-6413	481	2	’s	’s	PART
ejpam-6413	481	3	inequality	inequality	NOUN
ejpam-6413	481	4	is	be	AUX
ejpam-6413	481	5	employed	employ	VERB
ejpam-6413	481	6	to	to	PART
ejpam-6413	481	7	investigate	investigate	VERB
ejpam-6413	481	8	the	the	DET
ejpam-6413	481	9	mean	mean	ADJ
ejpam-6413	481	10	inequalities	inequality	NOUN
ejpam-6413	481	11	,	,	PUNCT
ejpam-6413	481	12	which	which	PRON
ejpam-6413	481	13	have	have	VERB
ejpam-6413	481	14	strong	strong	ADJ
ejpam-6413	481	15	applicability	applicability	NOUN
ejpam-6413	481	16	in	in	ADP
ejpam-6413	481	17	optimization	optimization	NOUN
ejpam-6413	481	18	theory	theory	NOUN
ejpam-6413	481	19	.	.	PUNCT
ejpam-6413	482	1	these	these	DET
ejpam-6413	482	2	findings	finding	NOUN
ejpam-6413	482	3	significantly	significantly	ADV
ejpam-6413	482	4	extend	extend	VERB
ejpam-6413	482	5	the	the	DET
ejpam-6413	482	6	existing	exist	VERB
ejpam-6413	482	7	literature	literature	NOUN
ejpam-6413	482	8	,	,	PUNCT
ejpam-6413	482	9	presenting	present	VERB
ejpam-6413	482	10	them	they	PRON
ejpam-6413	482	11	as	as	ADP
ejpam-6413	482	12	special	special	ADJ
ejpam-6413	482	13	cases	case	NOUN
ejpam-6413	482	14	m.	m.	NOUN
ejpam-6413	482	15	samraiz	samraiz	PROPN
ejpam-6413	482	16	et	et	PROPN
ejpam-6413	482	17	al	al	PROPN
ejpam-6413	482	18	.	.	PUNCT
ejpam-6413	482	19	/	/	SYM
ejpam-6413	482	20	eur	eur	PROPN
ejpam-6413	482	21	.	.	PUNCT
ejpam-6413	483	1	j.	j.	PROPN
ejpam-6413	483	2	pure	pure	PROPN
ejpam-6413	483	3	appl	appl	PROPN
ejpam-6413	483	4	.	.	PROPN
ejpam-6413	483	5	math	math	PROPN
ejpam-6413	483	6	,	,	PUNCT
ejpam-6413	483	7	18	18	NUM
ejpam-6413	483	8	(	(	PUNCT
ejpam-6413	483	9	3	3	NUM
ejpam-6413	483	10	)	)	PUNCT
ejpam-6413	483	11	(	(	PUNCT
ejpam-6413	483	12	2025	2025	NUM
ejpam-6413	483	13	)	)	PUNCT
ejpam-6413	483	14	,	,	PUNCT
ejpam-6413	483	15	6413	6413	NUM
ejpam-6413	483	16	24	24	NUM
ejpam-6413	483	17	of	of	ADP
ejpam-6413	483	18	26	26	NUM
ejpam-6413	483	19	of	of	ADP
ejpam-6413	483	20	our	our	PRON
ejpam-6413	483	21	newly	newly	ADV
ejpam-6413	483	22	established	establish	VERB
ejpam-6413	483	23	consequences	consequence	NOUN
ejpam-6413	483	24	.	.	PUNCT
ejpam-6413	484	1	this	this	DET
ejpam-6413	484	2	work	work	NOUN
ejpam-6413	484	3	contributes	contribute	VERB
ejpam-6413	484	4	to	to	ADP
ejpam-6413	484	5	a	a	DET
ejpam-6413	484	6	deeper	deep	ADJ
ejpam-6413	484	7	understanding	understanding	NOUN
ejpam-6413	484	8	of	of	ADP
ejpam-6413	484	9	the	the	DET
ejpam-6413	484	10	properties	property	NOUN
ejpam-6413	484	11	and	and	CCONJ
ejpam-6413	484	12	applications	application	NOUN
ejpam-6413	484	13	of	of	ADP
ejpam-6413	484	14	ga	ga	PROPN
ejpam-6413	484	15	(	(	PUNCT
ejpam-6413	484	16	α	α	X
ejpam-6413	484	17	,	,	PUNCT
ejpam-6413	484	18	m)-convex	m)-convex	PUNCT
ejpam-6413	484	19	functions	function	NOUN
ejpam-6413	484	20	in	in	ADP
ejpam-6413	484	21	the	the	DET
ejpam-6413	484	22	context	context	NOUN
ejpam-6413	484	23	of	of	ADP
ejpam-6413	484	24	fractional	fractional	ADJ
ejpam-6413	484	25	integral	integral	ADJ
ejpam-6413	484	26	inequalities	inequality	NOUN
ejpam-6413	484	27	.	.	PUNCT
ejpam-6413	485	1	the	the	DET
ejpam-6413	485	2	presented	present	VERB
ejpam-6413	485	3	work	work	NOUN
ejpam-6413	485	4	opens	open	VERB
ejpam-6413	485	5	avenues	avenue	NOUN
ejpam-6413	485	6	for	for	ADP
ejpam-6413	485	7	further	further	ADJ
ejpam-6413	485	8	exploration	exploration	NOUN
ejpam-6413	485	9	and	and	CCONJ
ejpam-6413	485	10	expansion	expansion	NOUN
ejpam-6413	485	11	of	of	ADP
ejpam-6413	485	12	inequalities	inequality	NOUN
ejpam-6413	485	13	applicable	applicable	ADJ
ejpam-6413	485	14	in	in	ADP
ejpam-6413	485	15	optimization	optimization	NOUN
ejpam-6413	485	16	theory	theory	NOUN
ejpam-6413	485	17	.	.	PUNCT
ejpam-6413	486	1	the	the	DET
ejpam-6413	486	2	mathematicians	mathematician	NOUN
ejpam-6413	486	3	can	can	AUX
ejpam-6413	486	4	compare	compare	VERB
ejpam-6413	486	5	the	the	DET
ejpam-6413	486	6	proposed	propose	VERB
ejpam-6413	486	7	approach	approach	NOUN
ejpam-6413	486	8	with	with	ADP
ejpam-6413	486	9	alternative	alternative	ADJ
ejpam-6413	486	10	methods	method	NOUN
ejpam-6413	486	11	or	or	CCONJ
ejpam-6413	486	12	convexities	convexity	NOUN
ejpam-6413	486	13	to	to	PART
ejpam-6413	486	14	evaluate	evaluate	VERB
ejpam-6413	486	15	its	its	PRON
ejpam-6413	486	16	efficiency	efficiency	NOUN
ejpam-6413	486	17	and	and	CCONJ
ejpam-6413	486	18	uniqueness	uniqueness	NOUN
ejpam-6413	486	19	in	in	ADP
ejpam-6413	486	20	handling	handle	VERB
ejpam-6413	486	21	similar	similar	ADJ
ejpam-6413	486	22	mathematical	mathematical	ADJ
ejpam-6413	486	23	problems	problem	NOUN
ejpam-6413	486	24	.	.	PUNCT
ejpam-6413	487	1	acknowledgements	acknowledgement	NOUN
ejpam-6413	487	2	researchers	researcher	NOUN
ejpam-6413	487	3	supporting	support	VERB
ejpam-6413	487	4	project	project	NOUN
ejpam-6413	487	5	number	number	NOUN
ejpam-6413	487	6	(	(	PUNCT
ejpam-6413	487	7	rspd2024r1060	rspd2024r1060	NOUN
ejpam-6413	487	8	)	)	PUNCT
ejpam-6413	487	9	,	,	PUNCT
ejpam-6413	487	10	king	king	PROPN
ejpam-6413	487	11	saud	saud	PROPN
ejpam-6413	487	12	university	university	PROPN
ejpam-6413	487	13	,	,	PUNCT
ejpam-6413	487	14	riyadh	riyadh	PROPN
ejpam-6413	487	15	,	,	PUNCT
ejpam-6413	487	16	saudi	saudi	PROPN
ejpam-6413	487	17	arabia	arabia	PROPN
ejpam-6413	487	18	.	.	PUNCT
ejpam-6413	488	1	declarations	declaration	NOUN
ejpam-6413	488	2	availability	availability	NOUN
ejpam-6413	488	3	of	of	ADP
ejpam-6413	488	4	data	datum	NOUN
ejpam-6413	488	5	and	and	CCONJ
ejpam-6413	488	6	material	material	NOUN
ejpam-6413	488	7	no	no	DET
ejpam-6413	488	8	data	datum	NOUN
ejpam-6413	488	9	were	be	AUX
ejpam-6413	488	10	used	use	VERB
ejpam-6413	488	11	to	to	PART
ejpam-6413	488	12	support	support	VERB
ejpam-6413	488	13	this	this	DET
ejpam-6413	488	14	study	study	NOUN
ejpam-6413	488	15	.	.	PUNCT
ejpam-6413	489	1	ethical	ethical	ADJ
ejpam-6413	489	2	approval	approval	NOUN
ejpam-6413	489	3	not	not	PART
ejpam-6413	489	4	applicable	applicable	ADJ
ejpam-6413	489	5	.	.	PUNCT
ejpam-6413	490	1	competing	compete	VERB
ejpam-6413	490	2	interests	interest	NOUN
ejpam-6413	490	3	the	the	DET
ejpam-6413	490	4	authors	author	NOUN
ejpam-6413	490	5	declare	declare	VERB
ejpam-6413	490	6	that	that	SCONJ
ejpam-6413	490	7	they	they	PRON
ejpam-6413	490	8	have	have	VERB
ejpam-6413	490	9	no	no	DET
ejpam-6413	490	10	competing	compete	VERB
ejpam-6413	490	11	interests	interest	NOUN
ejpam-6413	490	12	.	.	PUNCT
ejpam-6413	491	1	funding	fund	VERB
ejpam-6413	491	2	this	this	DET
ejpam-6413	491	3	project	project	NOUN
ejpam-6413	491	4	is	be	AUX
ejpam-6413	491	5	funded	fund	VERB
ejpam-6413	491	6	by	by	ADP
ejpam-6413	491	7	king	king	PROPN
ejpam-6413	491	8	saud	saud	PROPN
ejpam-6413	491	9	university	university	PROPN
ejpam-6413	491	10	,	,	PUNCT
ejpam-6413	491	11	riyadh	riyadh	PROPN
ejpam-6413	491	12	,	,	PUNCT
ejpam-6413	491	13	saudi	saudi	PROPN
ejpam-6413	491	14	arabia	arabia	PROPN
ejpam-6413	491	15	.	.	PUNCT
ejpam-6413	492	1	authors	author	NOUN
ejpam-6413	492	2	’	'	PUNCT
ejpam-6413	492	3	contributions	contribution	NOUN
ejpam-6413	492	4	all	all	DET
ejpam-6413	492	5	authors	author	NOUN
ejpam-6413	492	6	contributed	contribute	VERB
ejpam-6413	492	7	equally	equally	ADV
ejpam-6413	492	8	to	to	ADP
ejpam-6413	492	9	the	the	DET
ejpam-6413	492	10	writing	writing	NOUN
ejpam-6413	492	11	of	of	ADP
ejpam-6413	492	12	this	this	DET
ejpam-6413	492	13	paper	paper	NOUN
ejpam-6413	492	14	.	.	PUNCT
ejpam-6413	493	1	all	all	DET
ejpam-6413	493	2	authors	author	NOUN
ejpam-6413	493	3	read	read	VERB
ejpam-6413	493	4	and	and	CCONJ
ejpam-6413	493	5	approved	approve	VERB
ejpam-6413	493	6	the	the	DET
ejpam-6413	493	7	final	final	ADJ
ejpam-6413	493	8	manuscript	manuscript	NOUN
ejpam-6413	493	9	.	.	PUNCT
ejpam-6413	494	1	references	reference	NOUN
ejpam-6413	494	2	[	[	X
ejpam-6413	494	3	1	1	NUM
ejpam-6413	494	4	]	]	PUNCT
ejpam-6413	494	5	r.	r.	PROPN
ejpam-6413	494	6	gorenflo	gorenflo	PROPN
ejpam-6413	494	7	and	and	CCONJ
ejpam-6413	494	8	f.	f.	PROPN
ejpam-6413	494	9	mainardi	mainardi	PROPN
ejpam-6413	494	10	.	.	PUNCT
ejpam-6413	495	1	fractional	fractional	ADJ
ejpam-6413	495	2	calculus	calculus	NOUN
ejpam-6413	495	3	:	:	PUNCT
ejpam-6413	495	4	integral	integral	ADJ
ejpam-6413	495	5	and	and	CCONJ
ejpam-6413	495	6	differential	differential	ADJ
ejpam-6413	495	7	equations	equation	NOUN
ejpam-6413	495	8	of	of	ADP
ejpam-6413	495	9	fractional	fractional	ADJ
ejpam-6413	495	10	order	order	NOUN
ejpam-6413	495	11	,	,	PUNCT
ejpam-6413	495	12	volume	volume	NOUN
ejpam-6413	495	13	378	378	NUM
ejpam-6413	495	14	.	.	PUNCT
ejpam-6413	496	1	springer	springer	NOUN
ejpam-6413	496	2	,	,	PUNCT
ejpam-6413	496	3	vienna	vienna	PROPN
ejpam-6413	496	4	,	,	PUNCT
ejpam-6413	496	5	1997	1997	NUM
ejpam-6413	496	6	.	.	PUNCT
ejpam-6413	497	1	[	[	X
ejpam-6413	497	2	2	2	NUM
ejpam-6413	497	3	]	]	PUNCT
ejpam-6413	497	4	a.	a.	NOUN
ejpam-6413	497	5	a.	a.	NOUN
ejpam-6413	497	6	kilbas	kilbas	PROPN
ejpam-6413	497	7	,	,	PUNCT
ejpam-6413	497	8	h.	h.	PROPN
ejpam-6413	497	9	m.	m.	PROPN
ejpam-6413	497	10	srivastava	srivastava	PROPN
ejpam-6413	497	11	,	,	PUNCT
ejpam-6413	497	12	and	and	CCONJ
ejpam-6413	497	13	j.	j.	PROPN
ejpam-6413	497	14	j.	j.	PROPN
ejpam-6413	497	15	trujillo	trujillo	PROPN
ejpam-6413	497	16	.	.	PUNCT
ejpam-6413	497	17	theory	theory	NOUN
ejpam-6413	497	18	and	and	CCONJ
ejpam-6413	497	19	applications	application	NOUN
ejpam-6413	497	20	of	of	ADP
ejpam-6413	497	21	fractional	fractional	ADJ
ejpam-6413	497	22	differential	differential	ADJ
ejpam-6413	497	23	equations	equation	NOUN
ejpam-6413	497	24	,	,	PUNCT
ejpam-6413	497	25	volume	volume	NOUN
ejpam-6413	497	26	204	204	NUM
ejpam-6413	497	27	.	.	PUNCT
ejpam-6413	498	1	elsevier	elsevier	NOUN
ejpam-6413	498	2	,	,	PUNCT
ejpam-6413	498	3	2006	2006	NUM
ejpam-6413	498	4	.	.	PUNCT
ejpam-6413	499	1	[	[	X
ejpam-6413	499	2	3	3	X
ejpam-6413	499	3	]	]	X
ejpam-6413	499	4	d.	d.	PROPN
ejpam-6413	499	5	baleanu	baleanu	PROPN
ejpam-6413	499	6	,	,	PUNCT
ejpam-6413	499	7	a.	a.	PROPN
ejpam-6413	499	8	c.	c.	PROPN
ejpam-6413	499	9	j.	j.	PROPN
ejpam-6413	499	10	luo	luo	PROPN
ejpam-6413	499	11	,	,	PUNCT
ejpam-6413	499	12	and	and	CCONJ
ejpam-6413	499	13	j.	j.	PROPN
ejpam-6413	499	14	a.	a.	PROPN
ejpam-6413	499	15	t.	t.	PROPN
ejpam-6413	499	16	machado	machado	PROPN
ejpam-6413	499	17	.	.	PUNCT
ejpam-6413	500	1	fractional	fractional	ADJ
ejpam-6413	500	2	dynamics	dynamic	NOUN
ejpam-6413	500	3	and	and	CCONJ
ejpam-6413	500	4	control	control	NOUN
ejpam-6413	500	5	.	.	PUNCT
ejpam-6413	501	1	springer	springer	NOUN
ejpam-6413	501	2	,	,	PUNCT
ejpam-6413	501	3	new	new	PROPN
ejpam-6413	501	4	york	york	PROPN
ejpam-6413	501	5	,	,	PUNCT
ejpam-6413	501	6	2020	2020	NUM
ejpam-6413	501	7	.	.	PUNCT
ejpam-6413	502	1	[	[	X
ejpam-6413	502	2	4	4	NUM
ejpam-6413	502	3	]	]	PUNCT
ejpam-6413	502	4	k.	k.	PROPN
ejpam-6413	502	5	diethelm	diethelm	PROPN
ejpam-6413	502	6	.	.	PUNCT
ejpam-6413	503	1	the	the	DET
ejpam-6413	503	2	analysis	analysis	NOUN
ejpam-6413	503	3	of	of	ADP
ejpam-6413	503	4	fractional	fractional	ADJ
ejpam-6413	503	5	differential	differential	ADJ
ejpam-6413	503	6	equations	equation	NOUN
ejpam-6413	503	7	,	,	PUNCT
ejpam-6413	503	8	volume	volume	NOUN
ejpam-6413	503	9	2004	2004	NUM
ejpam-6413	503	10	of	of	ADP
ejpam-6413	503	11	lecture	lecture	NOUN
ejpam-6413	503	12	notes	note	NOUN
ejpam-6413	503	13	in	in	ADP
ejpam-6413	503	14	mathematics	mathematic	NOUN
ejpam-6413	503	15	.	.	PUNCT
ejpam-6413	503	16	springer	springer	NOUN
ejpam-6413	503	17	,	,	PUNCT
ejpam-6413	503	18	2010	2010	NUM
ejpam-6413	503	19	.	.	PUNCT
ejpam-6413	504	1	[	[	X
ejpam-6413	504	2	5	5	X
ejpam-6413	504	3	]	]	PUNCT
ejpam-6413	504	4	v.	v.	CCONJ
ejpam-6413	504	5	lakshmikantham	lakshmikantham	PROPN
ejpam-6413	504	6	,	,	PUNCT
ejpam-6413	504	7	s.	s.	PROPN
ejpam-6413	504	8	leela	leela	PROPN
ejpam-6413	504	9	,	,	PUNCT
ejpam-6413	504	10	and	and	CCONJ
ejpam-6413	504	11	j.	j.	PROPN
ejpam-6413	504	12	v.	v.	PROPN
ejpam-6413	504	13	devi	devi	PROPN
ejpam-6413	504	14	.	.	PUNCT
ejpam-6413	505	1	theory	theory	NOUN
ejpam-6413	505	2	of	of	ADP
ejpam-6413	505	3	fractional	fractional	ADJ
ejpam-6413	505	4	dynamic	dynamic	ADJ
ejpam-6413	505	5	systems	system	NOUN
ejpam-6413	505	6	.	.	PUNCT
ejpam-6413	506	1	cambridge	cambridge	PROPN
ejpam-6413	506	2	science	science	NOUN
ejpam-6413	506	3	publishers	publisher	NOUN
ejpam-6413	506	4	,	,	PUNCT
ejpam-6413	506	5	2009	2009	NUM
ejpam-6413	506	6	.	.	PUNCT
ejpam-6413	507	1	[	[	X
ejpam-6413	507	2	6	6	NUM
ejpam-6413	507	3	]	]	PUNCT
ejpam-6413	507	4	k.	k.	PROPN
ejpam-6413	507	5	s.	s.	PROPN
ejpam-6413	507	6	miller	miller	PROPN
ejpam-6413	507	7	and	and	CCONJ
ejpam-6413	507	8	b.	b.	PROPN
ejpam-6413	507	9	ross	ross	PROPN
ejpam-6413	507	10	.	.	PUNCT
ejpam-6413	508	1	an	an	DET
ejpam-6413	508	2	introduction	introduction	NOUN
ejpam-6413	508	3	to	to	ADP
ejpam-6413	508	4	the	the	DET
ejpam-6413	508	5	fractional	fractional	ADJ
ejpam-6413	508	6	calculus	calculus	NOUN
ejpam-6413	508	7	and	and	CCONJ
ejpam-6413	508	8	fractional	fractional	ADJ
ejpam-6413	508	9	differential	differential	ADJ
ejpam-6413	508	10	equations	equation	NOUN
ejpam-6413	508	11	.	.	PUNCT
ejpam-6413	509	1	wiley	wiley	PROPN
ejpam-6413	509	2	,	,	PUNCT
ejpam-6413	509	3	1993	1993	NUM
ejpam-6413	509	4	.	.	PUNCT
ejpam-6413	510	1	[	[	X
ejpam-6413	510	2	7	7	X
ejpam-6413	510	3	]	]	PUNCT
ejpam-6413	510	4	s.	s.	PROPN
ejpam-6413	510	5	k.	k.	PROPN
ejpam-6413	510	6	paul	paul	PROPN
ejpam-6413	510	7	,	,	PUNCT
ejpam-6413	510	8	l.	l.	PROPN
ejpam-6413	510	9	n.	n.	PROPN
ejpam-6413	510	10	mishra	mishra	PROPN
ejpam-6413	510	11	,	,	PUNCT
ejpam-6413	510	12	v.	v.	PROPN
ejpam-6413	510	13	n.	n.	PROPN
ejpam-6413	510	14	mishra	mishra	PROPN
ejpam-6413	510	15	,	,	PUNCT
ejpam-6413	510	16	and	and	CCONJ
ejpam-6413	510	17	d.	d.	PROPN
ejpam-6413	510	18	baleanu	baleanu	PROPN
ejpam-6413	510	19	.	.	PUNCT
ejpam-6413	511	1	analysis	analysis	NOUN
ejpam-6413	511	2	of	of	ADP
ejpam-6413	511	3	mixed	mixed	ADJ
ejpam-6413	511	4	type	type	NOUN
ejpam-6413	511	5	nonlinear	nonlinear	PROPN
ejpam-6413	511	6	volterra	volterra	NOUN
ejpam-6413	511	7	-	-	PUNCT
ejpam-6413	511	8	fredholm	fredholm	NOUN
ejpam-6413	511	9	integral	integral	ADJ
ejpam-6413	511	10	equations	equation	NOUN
ejpam-6413	511	11	involving	involve	VERB
ejpam-6413	511	12	the	the	DET
ejpam-6413	511	13	erdélyi	erdélyi	PROPN
ejpam-6413	511	14	-	-	PUNCT
ejpam-6413	511	15	kober	kober	NOUN
ejpam-6413	511	16	fractional	fractional	ADJ
ejpam-6413	511	17	operator	operator	NOUN
ejpam-6413	511	18	.	.	PUNCT
ejpam-6413	512	1	journal	journal	PROPN
ejpam-6413	512	2	of	of	ADP
ejpam-6413	512	3	king	king	PROPN
ejpam-6413	512	4	saud	saud	PROPN
ejpam-6413	512	5	university	university	PROPN
ejpam-6413	512	6	-	-	PUNCT
ejpam-6413	512	7	science	science	NOUN
ejpam-6413	512	8	,	,	PUNCT
ejpam-6413	512	9	35(10):102949	35(10):102949	NUM
ejpam-6413	512	10	,	,	PUNCT
ejpam-6413	512	11	2023	2023	NUM
ejpam-6413	512	12	.	.	PUNCT
ejpam-6413	513	1	m.	m.	NOUN
ejpam-6413	513	2	samraiz	samraiz	PROPN
ejpam-6413	513	3	et	et	PROPN
ejpam-6413	513	4	al	al	PROPN
ejpam-6413	513	5	.	.	PUNCT
ejpam-6413	513	6	/	/	SYM
ejpam-6413	513	7	eur	eur	PROPN
ejpam-6413	513	8	.	.	PUNCT
ejpam-6413	514	1	j.	j.	PROPN
ejpam-6413	514	2	pure	pure	PROPN
ejpam-6413	514	3	appl	appl	PROPN
ejpam-6413	514	4	.	.	PROPN
ejpam-6413	514	5	math	math	PROPN
ejpam-6413	514	6	,	,	PUNCT
ejpam-6413	514	7	18	18	NUM
ejpam-6413	514	8	(	(	PUNCT
ejpam-6413	514	9	3	3	NUM
ejpam-6413	514	10	)	)	PUNCT
ejpam-6413	514	11	(	(	PUNCT
ejpam-6413	514	12	2025	2025	NUM
ejpam-6413	514	13	)	)	PUNCT
ejpam-6413	514	14	,	,	PUNCT
ejpam-6413	514	15	6413	6413	NUM
ejpam-6413	514	16	25	25	NUM
ejpam-6413	514	17	of	of	ADP
ejpam-6413	514	18	26	26	NUM
ejpam-6413	514	19	[	[	SYM
ejpam-6413	514	20	8	8	NUM
ejpam-6413	514	21	]	]	PUNCT
ejpam-6413	514	22	l.	l.	PROPN
ejpam-6413	514	23	p.	p.	PROPN
ejpam-6413	514	24	castro	castro	PROPN
ejpam-6413	514	25	and	and	CCONJ
ejpam-6413	514	26	a.	a.	NOUN
ejpam-6413	514	27	m.	m.	PROPN
ejpam-6413	514	28	simoes	simoes	PROPN
ejpam-6413	514	29	.	.	PUNCT
ejpam-6413	515	1	stabilities	stability	NOUN
ejpam-6413	515	2	of	of	ADP
ejpam-6413	515	3	ulam	ulam	NOUN
ejpam-6413	515	4	-	-	PUNCT
ejpam-6413	515	5	hyers	hyer	NOUN
ejpam-6413	515	6	type	type	NOUN
ejpam-6413	515	7	for	for	ADP
ejpam-6413	515	8	a	a	DET
ejpam-6413	515	9	class	class	NOUN
ejpam-6413	515	10	of	of	ADP
ejpam-6413	515	11	nonlinear	nonlinear	ADJ
ejpam-6413	515	12	fractional	fractional	ADJ
ejpam-6413	515	13	differential	differential	ADJ
ejpam-6413	515	14	equations	equation	NOUN
ejpam-6413	515	15	with	with	ADP
ejpam-6413	515	16	integral	integral	ADJ
ejpam-6413	515	17	boundary	boundary	ADJ
ejpam-6413	515	18	conditions	condition	NOUN
ejpam-6413	515	19	in	in	ADP
ejpam-6413	515	20	banach	banach	NOUN
ejpam-6413	515	21	spaces	space	NOUN
ejpam-6413	515	22	.	.	PUNCT
ejpam-6413	516	1	filomat	filomat	NOUN
ejpam-6413	516	2	,	,	PUNCT
ejpam-6413	516	3	39(2):617–628	39(2):617–628	PROPN
ejpam-6413	516	4	,	,	PUNCT
ejpam-6413	516	5	2025	2025	NUM
ejpam-6413	516	6	.	.	PUNCT
ejpam-6413	517	1	[	[	X
ejpam-6413	517	2	9	9	NUM
ejpam-6413	517	3	]	]	PUNCT
ejpam-6413	517	4	v.	v.	CCONJ
ejpam-6413	517	5	stojiljkovic	stojiljkovic	ADJ
ejpam-6413	517	6	,	,	PUNCT
ejpam-6413	517	7	n.	n.	NOUN
ejpam-6413	517	8	mirkov	mirkov	PROPN
ejpam-6413	517	9	,	,	PUNCT
ejpam-6413	517	10	and	and	CCONJ
ejpam-6413	517	11	s.	s.	PROPN
ejpam-6413	517	12	radenovic	radenovic	PROPN
ejpam-6413	517	13	.	.	PUNCT
ejpam-6413	518	1	variations	variation	NOUN
ejpam-6413	518	2	in	in	ADP
ejpam-6413	518	3	the	the	DET
ejpam-6413	518	4	tensorial	tensorial	ADJ
ejpam-6413	518	5	trapezoid	trapezoid	ADJ
ejpam-6413	518	6	type	type	NOUN
ejpam-6413	518	7	inequalities	inequality	NOUN
ejpam-6413	518	8	for	for	ADP
ejpam-6413	518	9	convex	convex	NOUN
ejpam-6413	518	10	functions	function	NOUN
ejpam-6413	518	11	of	of	ADP
ejpam-6413	518	12	self	self	NOUN
ejpam-6413	518	13	-	-	PUNCT
ejpam-6413	518	14	adjoint	adjoint	NOUN
ejpam-6413	518	15	operators	operator	NOUN
ejpam-6413	518	16	in	in	ADP
ejpam-6413	518	17	hilbert	hilbert	PROPN
ejpam-6413	518	18	spaces	space	NOUN
ejpam-6413	518	19	.	.	PUNCT
ejpam-6413	519	1	symmetry	symmetry	NOUN
ejpam-6413	519	2	,	,	PUNCT
ejpam-6413	519	3	16(1):121	16(1):121	NUM
ejpam-6413	519	4	,	,	PUNCT
ejpam-6413	519	5	2024	2024	NUM
ejpam-6413	519	6	.	.	PUNCT
ejpam-6413	520	1	[	[	X
ejpam-6413	520	2	10	10	NUM
ejpam-6413	520	3	]	]	PUNCT
ejpam-6413	520	4	m.	m.	NOUN
ejpam-6413	520	5	w.	w.	PROPN
ejpam-6413	520	6	michalski	michalski	PROPN
ejpam-6413	520	7	.	.	PUNCT
ejpam-6413	521	1	derivatives	derivative	NOUN
ejpam-6413	521	2	of	of	ADP
ejpam-6413	521	3	non	non	ADJ
ejpam-6413	521	4	-	-	ADJ
ejpam-6413	521	5	integer	integer	ADJ
ejpam-6413	521	6	order	order	NOUN
ejpam-6413	521	7	and	and	CCONJ
ejpam-6413	521	8	their	their	PRON
ejpam-6413	521	9	application	application	NOUN
ejpam-6413	521	10	.	.	PUNCT
ejpam-6413	522	1	1993	1993	NUM
ejpam-6413	522	2	.	.	PUNCT
ejpam-6413	523	1	[	[	X
ejpam-6413	523	2	11	11	NUM
ejpam-6413	523	3	]	]	PUNCT
ejpam-6413	523	4	i.	i.	NOUN
ejpam-6413	523	5	podlubny	podlubny	PROPN
ejpam-6413	523	6	,	,	PUNCT
ejpam-6413	523	7	a.	a.	NOUN
ejpam-6413	523	8	chechkin	chechkin	NOUN
ejpam-6413	523	9	,	,	PUNCT
ejpam-6413	523	10	t.	t.	PROPN
ejpam-6413	523	11	skovranek	skovranek	NOUN
ejpam-6413	523	12	,	,	PUNCT
ejpam-6413	523	13	y.	y.	PROPN
ejpam-6413	523	14	chen	chen	PROPN
ejpam-6413	523	15	,	,	PUNCT
ejpam-6413	523	16	and	and	CCONJ
ejpam-6413	523	17	b.	b.	PROPN
ejpam-6413	523	18	m.	m.	PROPN
ejpam-6413	523	19	v.	v.	PROPN
ejpam-6413	523	20	jara	jara	PROPN
ejpam-6413	523	21	.	.	PUNCT
ejpam-6413	523	22	matrix	matrix	NOUN
ejpam-6413	523	23	approach	approach	NOUN
ejpam-6413	523	24	to	to	PART
ejpam-6413	523	25	discrete	discrete	VERB
ejpam-6413	523	26	fractional	fractional	ADJ
ejpam-6413	523	27	calculus	calculus	NOUN
ejpam-6413	523	28	ii	ii	PROPN
ejpam-6413	523	29	:	:	PUNCT
ejpam-6413	523	30	partial	partial	ADJ
ejpam-6413	523	31	fractional	fractional	ADJ
ejpam-6413	523	32	differential	differential	ADJ
ejpam-6413	523	33	equations	equation	NOUN
ejpam-6413	523	34	.	.	PUNCT
ejpam-6413	524	1	journal	journal	NOUN
ejpam-6413	524	2	of	of	ADP
ejpam-6413	524	3	computational	computational	ADJ
ejpam-6413	524	4	physics	physic	NOUN
ejpam-6413	524	5	,	,	PUNCT
ejpam-6413	524	6	228(8):3137–3153	228(8):3137–3153	NUM
ejpam-6413	524	7	,	,	PUNCT
ejpam-6413	524	8	2009	2009	NUM
ejpam-6413	524	9	.	.	PUNCT
ejpam-6413	525	1	[	[	X
ejpam-6413	525	2	12	12	NUM
ejpam-6413	525	3	]	]	X
ejpam-6413	525	4	v.	v.	PROPN
ejpam-6413	525	5	e.	e.	PROPN
ejpam-6413	525	6	tarasov	tarasov	PROPN
ejpam-6413	525	7	.	.	PUNCT
ejpam-6413	526	1	fractional	fractional	ADJ
ejpam-6413	526	2	dynamics	dynamic	NOUN
ejpam-6413	526	3	:	:	PUNCT
ejpam-6413	526	4	applications	application	NOUN
ejpam-6413	526	5	of	of	ADP
ejpam-6413	526	6	fractional	fractional	ADJ
ejpam-6413	526	7	calculus	calculus	NOUN
ejpam-6413	526	8	to	to	ADP
ejpam-6413	526	9	dynamics	dynamic	NOUN
ejpam-6413	526	10	of	of	ADP
ejpam-6413	526	11	particles	particle	NOUN
ejpam-6413	526	12	,	,	PUNCT
ejpam-6413	526	13	fields	field	NOUN
ejpam-6413	526	14	and	and	CCONJ
ejpam-6413	526	15	media	medium	NOUN
ejpam-6413	526	16	.	.	PUNCT
ejpam-6413	527	1	springer	springer	NOUN
ejpam-6413	527	2	science	science	PROPN
ejpam-6413	527	3	and	and	CCONJ
ejpam-6413	527	4	business	business	NOUN
ejpam-6413	527	5	media	medium	NOUN
ejpam-6413	527	6	,	,	PUNCT
ejpam-6413	527	7	2011	2011	NUM
ejpam-6413	527	8	.	.	PUNCT
ejpam-6413	528	1	[	[	X
ejpam-6413	528	2	13	13	NUM
ejpam-6413	528	3	]	]	PUNCT
ejpam-6413	528	4	m.	m.	NOUN
ejpam-6413	528	5	z.	z.	PROPN
ejpam-6413	528	6	sarikaya	sarikaya	PROPN
ejpam-6413	528	7	,	,	PUNCT
ejpam-6413	528	8	e.	e.	PROPN
ejpam-6413	528	9	set	set	PROPN
ejpam-6413	528	10	,	,	PUNCT
ejpam-6413	528	11	h.	h.	PROPN
ejpam-6413	528	12	yaldiz	yaldiz	PROPN
ejpam-6413	528	13	,	,	PUNCT
ejpam-6413	528	14	and	and	CCONJ
ejpam-6413	528	15	n.	n.	PROPN
ejpam-6413	528	16	basak	basak	PROPN
ejpam-6413	528	17	.	.	PUNCT
ejpam-6413	529	1	hermite	hermite	PROPN
ejpam-6413	529	2	-	-	PUNCT
ejpam-6413	529	3	hadamard	hadamard	PROPN
ejpam-6413	529	4	’s	’s	PART
ejpam-6413	529	5	inequalities	inequality	NOUN
ejpam-6413	529	6	for	for	ADP
ejpam-6413	529	7	fractional	fractional	ADJ
ejpam-6413	529	8	integrals	integral	NOUN
ejpam-6413	529	9	and	and	CCONJ
ejpam-6413	529	10	related	relate	VERB
ejpam-6413	529	11	fractional	fractional	ADJ
ejpam-6413	529	12	inequalities	inequality	NOUN
ejpam-6413	529	13	.	.	PUNCT
ejpam-6413	530	1	mathematical	mathematical	ADJ
ejpam-6413	530	2	and	and	CCONJ
ejpam-6413	530	3	computer	computer	NOUN
ejpam-6413	530	4	modelling	modelling	NOUN
ejpam-6413	530	5	,	,	PUNCT
ejpam-6413	530	6	57(9	57(9	NOUN
ejpam-6413	530	7	-	-	SYM
ejpam-6413	530	8	10):2403–2407	10):2403–2407	NOUN
ejpam-6413	530	9	,	,	PUNCT
ejpam-6413	530	10	2013	2013	NUM
ejpam-6413	530	11	.	.	PUNCT
ejpam-6413	531	1	[	[	X
ejpam-6413	531	2	14	14	NUM
ejpam-6413	531	3	]	]	X
ejpam-6413	531	4	y.	y.	PROPN
ejpam-6413	531	5	shuang	shuang	PROPN
ejpam-6413	531	6	,	,	PUNCT
ejpam-6413	531	7	h.	h.	PROPN
ejpam-6413	531	8	p.	p.	PROPN
ejpam-6413	531	9	yin	yin	PROPN
ejpam-6413	531	10	,	,	PUNCT
ejpam-6413	531	11	and	and	CCONJ
ejpam-6413	531	12	f.	f.	PROPN
ejpam-6413	531	13	qi	qi	PROPN
ejpam-6413	531	14	.	.	PUNCT
ejpam-6413	532	1	hermite	hermite	PROPN
ejpam-6413	532	2	-	-	PUNCT
ejpam-6413	532	3	hadamard	hadamard	ADJ
ejpam-6413	532	4	type	type	NOUN
ejpam-6413	532	5	integral	integral	ADJ
ejpam-6413	532	6	inequalities	inequality	NOUN
ejpam-6413	532	7	for	for	ADP
ejpam-6413	532	8	geometric	geometric	NOUN
ejpam-6413	532	9	-	-	PUNCT
ejpam-6413	532	10	arithmetically	arithmetically	ADV
ejpam-6413	532	11	s	s	NOUN
ejpam-6413	532	12	-	-	PUNCT
ejpam-6413	532	13	convex	convex	ADJ
ejpam-6413	532	14	functions	function	NOUN
ejpam-6413	532	15	.	.	PUNCT
ejpam-6413	533	1	analysis	analysis	NOUN
ejpam-6413	533	2	,	,	PUNCT
ejpam-6413	533	3	33(2):197–208	33(2):197–208	NUM
ejpam-6413	533	4	,	,	PUNCT
ejpam-6413	533	5	2013	2013	NUM
ejpam-6413	533	6	.	.	PUNCT
ejpam-6413	534	1	[	[	X
ejpam-6413	534	2	15	15	NUM
ejpam-6413	534	3	]	]	X
ejpam-6413	534	4	y.	y.	PROPN
ejpam-6413	534	5	liao	liao	PROPN
ejpam-6413	534	6	,	,	PUNCT
ejpam-6413	534	7	j.	j.	PROPN
ejpam-6413	534	8	deng	deng	PROPN
ejpam-6413	534	9	,	,	PUNCT
ejpam-6413	534	10	and	and	CCONJ
ejpam-6413	534	11	j.	j.	PROPN
ejpam-6413	534	12	wang	wang	PROPN
ejpam-6413	534	13	.	.	PUNCT
ejpam-6413	535	1	riemann	riemann	PROPN
ejpam-6413	535	2	-	-	PUNCT
ejpam-6413	535	3	liouville	liouville	VERB
ejpam-6413	535	4	fractional	fractional	ADJ
ejpam-6413	535	5	hermite	hermite	PROPN
ejpam-6413	535	6	-	-	PUNCT
ejpam-6413	535	7	hadamard	hadamard	ADJ
ejpam-6413	535	8	inequalities	inequality	NOUN
ejpam-6413	535	9	.	.	PUNCT
ejpam-6413	536	1	part	part	PROPN
ejpam-6413	536	2	ii	ii	PROPN
ejpam-6413	536	3	:	:	PUNCT
ejpam-6413	536	4	for	for	ADP
ejpam-6413	536	5	twice	twice	ADV
ejpam-6413	536	6	differentiable	differentiable	ADJ
ejpam-6413	536	7	geometric	geometric	NOUN
ejpam-6413	536	8	-	-	PUNCT
ejpam-6413	536	9	arithmetically	arithmetically	ADV
ejpam-6413	536	10	s	s	NOUN
ejpam-6413	536	11	-	-	PUNCT
ejpam-6413	536	12	convex	convex	ADJ
ejpam-6413	536	13	functions	function	NOUN
ejpam-6413	536	14	.	.	PUNCT
ejpam-6413	537	1	journal	journal	NOUN
ejpam-6413	537	2	of	of	ADP
ejpam-6413	537	3	inequalities	inequality	NOUN
ejpam-6413	537	4	and	and	CCONJ
ejpam-6413	537	5	applications	application	NOUN
ejpam-6413	537	6	,	,	PUNCT
ejpam-6413	537	7	2013(517):1–13	2013(517):1–13	NUM
ejpam-6413	537	8	,	,	PUNCT
ejpam-6413	537	9	2013	2013	NUM
ejpam-6413	537	10	.	.	PUNCT
ejpam-6413	538	1	[	[	X
ejpam-6413	538	2	16	16	NUM
ejpam-6413	538	3	]	]	X
ejpam-6413	538	4	h.	h.	PROPN
ejpam-6413	538	5	kavurmaci	kavurmaci	PROPN
ejpam-6413	538	6	,	,	PUNCT
ejpam-6413	538	7	m.	m.	NOUN
ejpam-6413	538	8	avci	avci	PROPN
ejpam-6413	538	9	,	,	PUNCT
ejpam-6413	538	10	and	and	CCONJ
ejpam-6413	538	11	m.	m.	PROPN
ejpam-6413	538	12	e.	e.	PROPN
ejpam-6413	538	13	özdemir	özdemir	PROPN
ejpam-6413	538	14	.	.	PUNCT
ejpam-6413	539	1	new	new	ADJ
ejpam-6413	539	2	inequalities	inequality	NOUN
ejpam-6413	539	3	of	of	ADP
ejpam-6413	539	4	hermite	hermite	ADJ
ejpam-6413	539	5	-	-	PUNCT
ejpam-6413	539	6	hadamard	hadamard	ADJ
ejpam-6413	539	7	type	type	NOUN
ejpam-6413	539	8	for	for	ADP
ejpam-6413	539	9	convex	convex	NOUN
ejpam-6413	539	10	functions	function	NOUN
ejpam-6413	539	11	with	with	ADP
ejpam-6413	539	12	applications	application	NOUN
ejpam-6413	539	13	.	.	PUNCT
ejpam-6413	540	1	journal	journal	PROPN
ejpam-6413	540	2	of	of	ADP
ejpam-6413	540	3	inequalities	inequality	NOUN
ejpam-6413	540	4	and	and	CCONJ
ejpam-6413	540	5	applications	application	NOUN
ejpam-6413	540	6	,	,	PUNCT
ejpam-6413	540	7	2011(86):1–11	2011(86):1–11	PROPN
ejpam-6413	540	8	,	,	PUNCT
ejpam-6413	540	9	2011	2011	NUM
ejpam-6413	540	10	.	.	PUNCT
ejpam-6413	541	1	[	[	X
ejpam-6413	541	2	17	17	NUM
ejpam-6413	541	3	]	]	X
ejpam-6413	541	4	c.	c.	PROPN
ejpam-6413	541	5	zhu	zhu	PROPN
ejpam-6413	541	6	,	,	PUNCT
ejpam-6413	541	7	m.	m.	NOUN
ejpam-6413	541	8	feckan	feckan	PROPN
ejpam-6413	541	9	,	,	PUNCT
ejpam-6413	541	10	and	and	CCONJ
ejpam-6413	541	11	j.	j.	PROPN
ejpam-6413	541	12	wang	wang	PROPN
ejpam-6413	541	13	.	.	PUNCT
ejpam-6413	542	1	fractional	fractional	ADJ
ejpam-6413	542	2	integral	integral	ADJ
ejpam-6413	542	3	inequalities	inequality	NOUN
ejpam-6413	542	4	for	for	ADP
ejpam-6413	542	5	differentiable	differentiable	ADJ
ejpam-6413	542	6	convex	convex	NOUN
ejpam-6413	542	7	mappings	mapping	NOUN
ejpam-6413	542	8	and	and	CCONJ
ejpam-6413	542	9	applications	application	NOUN
ejpam-6413	542	10	to	to	ADP
ejpam-6413	542	11	special	special	ADJ
ejpam-6413	542	12	means	mean	NOUN
ejpam-6413	542	13	and	and	CCONJ
ejpam-6413	542	14	a	a	DET
ejpam-6413	542	15	midpoint	midpoint	NOUN
ejpam-6413	542	16	formula	formula	NOUN
ejpam-6413	542	17	.	.	PUNCT
ejpam-6413	543	1	journal	journal	NOUN
ejpam-6413	543	2	of	of	ADP
ejpam-6413	543	3	applied	apply	VERB
ejpam-6413	543	4	mathematics	mathematic	NOUN
ejpam-6413	543	5	,	,	PUNCT
ejpam-6413	543	6	statistics	statistic	NOUN
ejpam-6413	543	7	and	and	CCONJ
ejpam-6413	543	8	informatics	informatic	NOUN
ejpam-6413	543	9	,	,	PUNCT
ejpam-6413	543	10	8(2):21–28	8(2):21–28	NUM
ejpam-6413	543	11	,	,	PUNCT
ejpam-6413	543	12	2012	2012	NUM
ejpam-6413	543	13	.	.	PUNCT
ejpam-6413	544	1	[	[	X
ejpam-6413	544	2	18	18	NUM
ejpam-6413	544	3	]	]	PUNCT
ejpam-6413	544	4	m.	m.	NOUN
ejpam-6413	544	5	a.	a.	PROPN
ejpam-6413	544	6	latif	latif	PROPN
ejpam-6413	544	7	,	,	PUNCT
ejpam-6413	544	8	s.	s.	PROPN
ejpam-6413	544	9	s.	s.	PROPN
ejpam-6413	544	10	dragomir	dragomir	PROPN
ejpam-6413	544	11	,	,	PUNCT
ejpam-6413	544	12	and	and	CCONJ
ejpam-6413	544	13	a.	a.	PROPN
ejpam-6413	544	14	e.	e.	PROPN
ejpam-6413	544	15	matouk	matouk	PROPN
ejpam-6413	544	16	.	.	PUNCT
ejpam-6413	545	1	new	new	ADJ
ejpam-6413	545	2	inequalities	inequality	NOUN
ejpam-6413	545	3	of	of	ADP
ejpam-6413	545	4	ostrowski	ostrowski	ADJ
ejpam-6413	545	5	type	type	NOUN
ejpam-6413	545	6	for	for	ADP
ejpam-6413	545	7	co	co	VERB
ejpam-6413	545	8	-	-	ADJ
ejpam-6413	545	9	ordinated	ordinated	ADJ
ejpam-6413	545	10	convex	convex	NOUN
ejpam-6413	545	11	functions	function	NOUN
ejpam-6413	545	12	via	via	ADP
ejpam-6413	545	13	fractional	fractional	ADJ
ejpam-6413	545	14	integrals	integral	NOUN
ejpam-6413	545	15	.	.	PUNCT
ejpam-6413	546	1	journal	journal	NOUN
ejpam-6413	546	2	of	of	ADP
ejpam-6413	546	3	fractional	fractional	ADJ
ejpam-6413	546	4	calculus	calculus	NOUN
ejpam-6413	546	5	and	and	CCONJ
ejpam-6413	546	6	its	its	PRON
ejpam-6413	546	7	application	application	NOUN
ejpam-6413	546	8	,	,	PUNCT
ejpam-6413	546	9	2(1):1–15	2(1):1–15	NUM
ejpam-6413	546	10	,	,	PUNCT
ejpam-6413	546	11	2012	2012	NUM
ejpam-6413	546	12	.	.	PUNCT
ejpam-6413	547	1	[	[	X
ejpam-6413	547	2	19	19	NUM
ejpam-6413	547	3	]	]	PUNCT
ejpam-6413	547	4	j.	j.	PROPN
ejpam-6413	547	5	wang	wang	PROPN
ejpam-6413	547	6	,	,	PUNCT
ejpam-6413	547	7	x.	x.	PROPN
ejpam-6413	547	8	li	li	PROPN
ejpam-6413	547	9	,	,	PUNCT
ejpam-6413	547	10	and	and	CCONJ
ejpam-6413	547	11	c.	c.	PROPN
ejpam-6413	547	12	zhu	zhu	PROPN
ejpam-6413	547	13	.	.	PUNCT
ejpam-6413	548	1	refinements	refinement	NOUN
ejpam-6413	548	2	of	of	ADP
ejpam-6413	548	3	hermite	hermite	ADJ
ejpam-6413	548	4	-	-	PUNCT
ejpam-6413	548	5	hadamard	hadamard	ADJ
ejpam-6413	548	6	type	type	NOUN
ejpam-6413	548	7	inequalities	inequality	NOUN
ejpam-6413	548	8	involving	involve	VERB
ejpam-6413	548	9	fractional	fractional	ADJ
ejpam-6413	548	10	integrals	integral	NOUN
ejpam-6413	548	11	.	.	PUNCT
ejpam-6413	549	1	bulletin	bulletin	NOUN
ejpam-6413	549	2	of	of	ADP
ejpam-6413	549	3	the	the	DET
ejpam-6413	549	4	belgian	belgian	ADJ
ejpam-6413	549	5	mathematical	mathematical	ADJ
ejpam-6413	549	6	society	society	NOUN
ejpam-6413	549	7	-	-	PUNCT
ejpam-6413	549	8	simon	simon	PROPN
ejpam-6413	549	9	stevin	stevin	NOUN
ejpam-6413	549	10	,	,	PUNCT
ejpam-6413	549	11	20(4):655–666	20(4):655–666	PROPN
ejpam-6413	549	12	,	,	PUNCT
ejpam-6413	549	13	2013	2013	NUM
ejpam-6413	549	14	.	.	PUNCT
ejpam-6413	550	1	[	[	X
ejpam-6413	550	2	20	20	NUM
ejpam-6413	550	3	]	]	X
ejpam-6413	550	4	y.	y.	PROPN
ejpam-6413	550	5	zhang	zhang	PROPN
ejpam-6413	550	6	and	and	CCONJ
ejpam-6413	550	7	j.	j.	PROPN
ejpam-6413	550	8	wang	wang	PROPN
ejpam-6413	550	9	.	.	PUNCT
ejpam-6413	551	1	on	on	ADP
ejpam-6413	551	2	some	some	DET
ejpam-6413	551	3	new	new	ADJ
ejpam-6413	551	4	hermite	hermite	ADJ
ejpam-6413	551	5	-	-	PUNCT
ejpam-6413	551	6	hadamard	hadamard	ADJ
ejpam-6413	551	7	inequalities	inequality	NOUN
ejpam-6413	551	8	involving	involve	VERB
ejpam-6413	551	9	riemann	riemann	PROPN
ejpam-6413	551	10	-	-	PUNCT
ejpam-6413	551	11	liouville	liouville	VERB
ejpam-6413	551	12	fractional	fractional	ADJ
ejpam-6413	551	13	integrals	integral	NOUN
ejpam-6413	551	14	.	.	PUNCT
ejpam-6413	552	1	journal	journal	PROPN
ejpam-6413	552	2	of	of	ADP
ejpam-6413	552	3	inequalities	inequality	NOUN
ejpam-6413	552	4	and	and	CCONJ
ejpam-6413	552	5	applications	application	NOUN
ejpam-6413	552	6	,	,	PUNCT
ejpam-6413	552	7	2013(220):1–27	2013(220):1–27	NUM
ejpam-6413	552	8	,	,	PUNCT
ejpam-6413	552	9	2013	2013	NUM
ejpam-6413	552	10	.	.	PUNCT
ejpam-6413	553	1	[	[	X
ejpam-6413	553	2	21	21	NUM
ejpam-6413	553	3	]	]	X
ejpam-6413	553	4	e.	e.	PROPN
ejpam-6413	553	5	set	set	PROPN
ejpam-6413	553	6	.	.	PUNCT
ejpam-6413	554	1	new	new	ADJ
ejpam-6413	554	2	inequalities	inequality	NOUN
ejpam-6413	554	3	of	of	ADP
ejpam-6413	554	4	ostrowski	ostrowski	ADJ
ejpam-6413	554	5	type	type	NOUN
ejpam-6413	554	6	for	for	ADP
ejpam-6413	554	7	mappings	mapping	NOUN
ejpam-6413	554	8	whose	whose	DET
ejpam-6413	554	9	derivatives	derivative	NOUN
ejpam-6413	554	10	are	be	AUX
ejpam-6413	554	11	sconvex	sconvex	ADJ
ejpam-6413	554	12	in	in	ADP
ejpam-6413	554	13	the	the	DET
ejpam-6413	554	14	second	second	ADJ
ejpam-6413	554	15	sense	sense	NOUN
ejpam-6413	554	16	via	via	ADP
ejpam-6413	554	17	fractional	fractional	ADJ
ejpam-6413	554	18	integrals	integral	NOUN
ejpam-6413	554	19	.	.	PUNCT
ejpam-6413	555	1	computers	computer	NOUN
ejpam-6413	555	2	and	and	CCONJ
ejpam-6413	555	3	mathematics	mathematic	NOUN
ejpam-6413	555	4	with	with	ADP
ejpam-6413	555	5	applications	application	NOUN
ejpam-6413	555	6	,	,	PUNCT
ejpam-6413	555	7	63(7):1147–1154	63(7):1147–1154	NUM
ejpam-6413	555	8	,	,	PUNCT
ejpam-6413	555	9	2012	2012	NUM
ejpam-6413	555	10	.	.	PUNCT
ejpam-6413	556	1	[	[	X
ejpam-6413	556	2	22	22	NUM
ejpam-6413	556	3	]	]	PUNCT
ejpam-6413	556	4	j.	j.	PROPN
ejpam-6413	556	5	wang	wang	PROPN
ejpam-6413	556	6	,	,	PUNCT
ejpam-6413	556	7	j.	j.	PROPN
ejpam-6413	556	8	deng	deng	PROPN
ejpam-6413	556	9	,	,	PUNCT
ejpam-6413	556	10	and	and	CCONJ
ejpam-6413	556	11	m.	m.	NOUN
ejpam-6413	556	12	feckan	feckan	PROPN
ejpam-6413	556	13	.	.	PUNCT
ejpam-6413	557	1	hermite	hermite	PROPN
ejpam-6413	557	2	-	-	PUNCT
ejpam-6413	557	3	hadamard	hadamard	ADJ
ejpam-6413	557	4	-	-	PUNCT
ejpam-6413	557	5	type	type	NOUN
ejpam-6413	557	6	inequalities	inequality	NOUN
ejpam-6413	557	7	for	for	ADP
ejpam-6413	557	8	r	r	NOUN
ejpam-6413	557	9	-	-	PUNCT
ejpam-6413	557	10	convex	convex	NOUN
ejpam-6413	557	11	functions	function	NOUN
ejpam-6413	557	12	based	base	VERB
ejpam-6413	557	13	on	on	ADP
ejpam-6413	557	14	the	the	DET
ejpam-6413	557	15	use	use	NOUN
ejpam-6413	557	16	of	of	ADP
ejpam-6413	557	17	riemann	riemann	PROPN
ejpam-6413	557	18	-	-	PUNCT
ejpam-6413	557	19	liouville	liouville	VERB
ejpam-6413	557	20	fractional	fractional	ADJ
ejpam-6413	557	21	integrals	integral	NOUN
ejpam-6413	557	22	.	.	PUNCT
ejpam-6413	558	1	ukrains’kyi	ukrains’kyi	PROPN
ejpam-6413	558	2	matematychnyi	matematychnyi	PROPN
ejpam-6413	558	3	zhurnal	zhurnal	PROPN
ejpam-6413	558	4	,	,	PUNCT
ejpam-6413	558	5	65(2):175–191	65(2):175–191	PROPN
ejpam-6413	558	6	,	,	PUNCT
ejpam-6413	558	7	2013	2013	NUM
ejpam-6413	558	8	.	.	PUNCT
ejpam-6413	559	1	[	[	X
ejpam-6413	559	2	23	23	NUM
ejpam-6413	559	3	]	]	PUNCT
ejpam-6413	559	4	j.	j.	PROPN
ejpam-6413	559	5	wang	wang	PROPN
ejpam-6413	559	6	,	,	PUNCT
ejpam-6413	559	7	x.	x.	PROPN
ejpam-6413	559	8	li	li	PROPN
ejpam-6413	559	9	,	,	PUNCT
ejpam-6413	559	10	m.	m.	NOUN
ejpam-6413	559	11	fekan	fekan	PROPN
ejpam-6413	559	12	,	,	PUNCT
ejpam-6413	559	13	and	and	CCONJ
ejpam-6413	559	14	y.	y.	PROPN
ejpam-6413	559	15	zhou	zhou	PROPN
ejpam-6413	559	16	.	.	PUNCT
ejpam-6413	560	1	hermite	hermite	PROPN
ejpam-6413	560	2	-	-	PUNCT
ejpam-6413	560	3	hadamard	hadamard	ADJ
ejpam-6413	560	4	-	-	PUNCT
ejpam-6413	560	5	type	type	NOUN
ejpam-6413	560	6	inequalities	inequality	NOUN
ejpam-6413	560	7	for	for	ADP
ejpam-6413	560	8	riemann	riemann	PROPN
ejpam-6413	560	9	-	-	PUNCT
ejpam-6413	560	10	liouville	liouville	VERB
ejpam-6413	560	11	fractional	fractional	ADJ
ejpam-6413	560	12	integrals	integral	NOUN
ejpam-6413	560	13	via	via	ADP
ejpam-6413	560	14	two	two	NUM
ejpam-6413	560	15	kinds	kind	NOUN
ejpam-6413	560	16	of	of	ADP
ejpam-6413	560	17	convexity	convexity	NOUN
ejpam-6413	560	18	.	.	PUNCT
ejpam-6413	561	1	applicable	applicable	ADJ
ejpam-6413	561	2	analysis	analysis	NOUN
ejpam-6413	561	3	,	,	PUNCT
ejpam-6413	561	4	m.	m.	NOUN
ejpam-6413	561	5	samraiz	samraiz	PROPN
ejpam-6413	561	6	et	et	PROPN
ejpam-6413	561	7	al	al	PROPN
ejpam-6413	561	8	.	.	PUNCT
ejpam-6413	561	9	/	/	SYM
ejpam-6413	561	10	eur	eur	PROPN
ejpam-6413	561	11	.	.	PUNCT
ejpam-6413	562	1	j.	j.	PROPN
ejpam-6413	562	2	pure	pure	PROPN
ejpam-6413	562	3	appl	appl	PROPN
ejpam-6413	562	4	.	.	PROPN
ejpam-6413	562	5	math	math	PROPN
ejpam-6413	562	6	,	,	PUNCT
ejpam-6413	562	7	18	18	NUM
ejpam-6413	562	8	(	(	PUNCT
ejpam-6413	562	9	3	3	NUM
ejpam-6413	562	10	)	)	PUNCT
ejpam-6413	562	11	(	(	PUNCT
ejpam-6413	562	12	2025	2025	NUM
ejpam-6413	562	13	)	)	PUNCT
ejpam-6413	562	14	,	,	PUNCT
ejpam-6413	562	15	6413	6413	NUM
ejpam-6413	562	16	26	26	NUM
ejpam-6413	562	17	of	of	ADP
ejpam-6413	562	18	26	26	NUM
ejpam-6413	562	19	92(11):2241–2253	92(11):2241–2253	NUM
ejpam-6413	562	20	,	,	PUNCT
ejpam-6413	562	21	2013	2013	NUM
ejpam-6413	562	22	.	.	PUNCT
ejpam-6413	563	1	[	[	X
ejpam-6413	563	2	24	24	NUM
ejpam-6413	563	3	]	]	X
ejpam-6413	563	4	g.	g.	PROPN
ejpam-6413	563	5	farid	farid	PROPN
ejpam-6413	563	6	,	,	PUNCT
ejpam-6413	563	7	s.	s.	PROPN
ejpam-6413	563	8	bibi	bibi	PROPN
ejpam-6413	563	9	,	,	PUNCT
ejpam-6413	563	10	l.	l.	PROPN
ejpam-6413	563	11	rathour	rathour	PROPN
ejpam-6413	563	12	,	,	PUNCT
ejpam-6413	563	13	l.	l.	PROPN
ejpam-6413	563	14	n.	n.	PROPN
ejpam-6413	563	15	mishra	mishra	PROPN
ejpam-6413	563	16	,	,	PUNCT
ejpam-6413	563	17	and	and	CCONJ
ejpam-6413	563	18	v.	v.	ADP
ejpam-6413	563	19	n.	n.	PROPN
ejpam-6413	563	20	mishra	mishra	PROPN
ejpam-6413	563	21	.	.	PROPN
ejpam-6413	563	22	fractional	fractional	ADJ
ejpam-6413	563	23	versions	version	NOUN
ejpam-6413	563	24	of	of	ADP
ejpam-6413	563	25	hadamard	hadamard	ADJ
ejpam-6413	563	26	inequalities	inequality	NOUN
ejpam-6413	563	27	for	for	ADP
ejpam-6413	563	28	strongly	strongly	ADV
ejpam-6413	563	29	(	(	PUNCT
ejpam-6413	563	30	s	s	X
ejpam-6413	563	31	,	,	PUNCT
ejpam-6413	563	32	m)-convex	m)-convex	PUNCT
ejpam-6413	563	33	functions	function	NOUN
ejpam-6413	563	34	via	via	ADP
ejpam-6413	563	35	caputo	caputo	PROPN
ejpam-6413	563	36	fractional	fractional	ADJ
ejpam-6413	563	37	derivatives	derivative	NOUN
ejpam-6413	563	38	.	.	PUNCT
ejpam-6413	564	1	korean	korean	ADJ
ejpam-6413	564	2	journal	journal	PROPN
ejpam-6413	564	3	of	of	ADP
ejpam-6413	564	4	mathematics	mathematic	NOUN
ejpam-6413	564	5	,	,	PUNCT
ejpam-6413	564	6	31(1):75–94	31(1):75–94	NUM
ejpam-6413	564	7	,	,	PUNCT
ejpam-6413	564	8	2023	2023	NUM
ejpam-6413	564	9	.	.	PUNCT
ejpam-6413	565	1	[	[	X
ejpam-6413	565	2	25	25	NUM
ejpam-6413	565	3	]	]	PUNCT
ejpam-6413	565	4	j.	j.	PROPN
ejpam-6413	565	5	deng	deng	PROPN
ejpam-6413	565	6	and	and	CCONJ
ejpam-6413	565	7	j.	j.	PROPN
ejpam-6413	565	8	wang	wang	PROPN
ejpam-6413	565	9	.	.	PUNCT
ejpam-6413	566	1	fractional	fractional	ADJ
ejpam-6413	566	2	hermite	hermite	PROPN
ejpam-6413	566	3	-	-	PUNCT
ejpam-6413	566	4	hadamard	hadamard	ADJ
ejpam-6413	566	5	inequalities	inequality	NOUN
ejpam-6413	566	6	for	for	ADP
ejpam-6413	566	7	(	(	PUNCT
ejpam-6413	566	8	α	α	NOUN
ejpam-6413	566	9	,	,	PUNCT
ejpam-6413	566	10	m)logarithmically	m)logarithmically	ADV
ejpam-6413	566	11	convex	convex	NOUN
ejpam-6413	566	12	functions	function	NOUN
ejpam-6413	566	13	.	.	PUNCT
ejpam-6413	567	1	journal	journal	PROPN
ejpam-6413	567	2	of	of	ADP
ejpam-6413	567	3	inequalities	inequality	NOUN
ejpam-6413	567	4	and	and	CCONJ
ejpam-6413	567	5	applications	application	NOUN
ejpam-6413	567	6	,	,	PUNCT
ejpam-6413	567	7	pages	page	NOUN
ejpam-6413	567	8	1–11	1–11	PROPN
ejpam-6413	567	9	,	,	PUNCT
ejpam-6413	567	10	2013	2013	NUM
ejpam-6413	567	11	.	.	PUNCT
ejpam-6413	568	1	[	[	X
ejpam-6413	568	2	26	26	NUM
ejpam-6413	568	3	]	]	PUNCT
ejpam-6413	568	4	j.	j.	PROPN
ejpam-6413	568	5	wang	wang	PROPN
ejpam-6413	568	6	,	,	PUNCT
ejpam-6413	568	7	j.	j.	PROPN
ejpam-6413	568	8	deng	deng	PROPN
ejpam-6413	568	9	,	,	PUNCT
ejpam-6413	568	10	and	and	CCONJ
ejpam-6413	568	11	m.	m.	NOUN
ejpam-6413	568	12	feckan	feckan	PROPN
ejpam-6413	568	13	.	.	PUNCT
ejpam-6413	569	1	exploring	explore	VERB
ejpam-6413	569	2	s−e	s−e	NOUN
ejpam-6413	569	3	-	-	PUNCT
ejpam-6413	569	4	conditions	condition	NOUN
ejpam-6413	569	5	and	and	CCONJ
ejpam-6413	569	6	applications	application	NOUN
ejpam-6413	569	7	to	to	ADP
ejpam-6413	569	8	some	some	DET
ejpam-6413	569	9	ostrowski	ostrowski	ADJ
ejpam-6413	569	10	type	type	NOUN
ejpam-6413	569	11	inequalities	inequality	NOUN
ejpam-6413	569	12	via	via	ADP
ejpam-6413	569	13	riemann	riemann	PROPN
ejpam-6413	569	14	-	-	PUNCT
ejpam-6413	569	15	liouville	liouville	VERB
ejpam-6413	569	16	fractional	fractional	ADJ
ejpam-6413	569	17	integrals	integral	NOUN
ejpam-6413	569	18	.	.	PUNCT
ejpam-6413	570	1	mathematica	mathematica	PROPN
ejpam-6413	570	2	slovaca	slovaca	PROPN
ejpam-6413	570	3	,	,	PUNCT
ejpam-6413	570	4	64(6):1381–1396	64(6):1381–1396	NUM
ejpam-6413	570	5	,	,	PUNCT
ejpam-6413	570	6	2014	2014	NUM
ejpam-6413	570	7	.	.	PUNCT
ejpam-6413	571	1	[	[	X
ejpam-6413	571	2	27	27	NUM
ejpam-6413	571	3	]	]	PUNCT
ejpam-6413	571	4	s.	s.	PROPN
ejpam-6413	571	5	s.	s.	PROPN
ejpam-6413	571	6	dragomir	dragomir	PROPN
ejpam-6413	571	7	.	.	PUNCT
ejpam-6413	572	1	hermite	hermite	PROPN
ejpam-6413	572	2	-	-	PUNCT
ejpam-6413	572	3	hadamard	hadamard	ADJ
ejpam-6413	572	4	type	type	NOUN
ejpam-6413	572	5	inequalities	inequality	NOUN
ejpam-6413	572	6	for	for	ADP
ejpam-6413	572	7	generalized	generalized	ADJ
ejpam-6413	572	8	riemann	riemann	PROPN
ejpam-6413	572	9	-	-	PUNCT
ejpam-6413	572	10	liouville	liouville	VERB
ejpam-6413	572	11	fractional	fractional	ADJ
ejpam-6413	572	12	integrals	integral	NOUN
ejpam-6413	572	13	of	of	ADP
ejpam-6413	572	14	h	h	NOUN
ejpam-6413	572	15	-	-	PUNCT
ejpam-6413	572	16	convex	convex	NOUN
ejpam-6413	572	17	functions	function	NOUN
ejpam-6413	572	18	.	.	PUNCT
ejpam-6413	573	1	mathematical	mathematical	ADJ
ejpam-6413	573	2	methods	method	NOUN
ejpam-6413	573	3	in	in	ADP
ejpam-6413	573	4	the	the	DET
ejpam-6413	573	5	applied	apply	VERB
ejpam-6413	573	6	sciences	science	NOUN
ejpam-6413	573	7	,	,	PUNCT
ejpam-6413	573	8	44(3):2364–2380	44(3):2364–2380	NOUN
ejpam-6413	573	9	,	,	PUNCT
ejpam-6413	573	10	2021	2021	NUM
ejpam-6413	573	11	.	.	PUNCT
ejpam-6413	574	1	[	[	X
ejpam-6413	574	2	28	28	NUM
ejpam-6413	574	3	]	]	X
ejpam-6413	574	4	v.	v.	CCONJ
ejpam-6413	574	5	stojiljkovic	stojiljkovic	VERB
ejpam-6413	574	6	.	.	PUNCT
ejpam-6413	575	1	hermite	hermite	PROPN
ejpam-6413	575	2	-	-	PUNCT
ejpam-6413	575	3	hadamard	hadamard	ADJ
ejpam-6413	575	4	type	type	NOUN
ejpam-6413	575	5	inequalities	inequality	NOUN
ejpam-6413	575	6	involving	involve	VERB
ejpam-6413	575	7	kp	kp	PROPN
ejpam-6413	575	8	fractional	fractional	ADJ
ejpam-6413	575	9	operator	operator	NOUN
ejpam-6413	575	10	with	with	ADP
ejpam-6413	575	11	(	(	PUNCT
ejpam-6413	575	12	a	a	PRON
ejpam-6413	575	13	,	,	PUNCT
ejpam-6413	575	14	h	h	NOUN
ejpam-6413	575	15	−m	−m	NOUN
ejpam-6413	575	16	)	)	PUNCT
ejpam-6413	576	1	−	−	PROPN
ejpam-6413	577	1	p	p	PRON
ejpam-6413	577	2	convexity	convexity	NOUN
ejpam-6413	577	3	.	.	PUNCT
ejpam-6413	578	1	european	european	PROPN
ejpam-6413	578	2	journal	journal	PROPN
ejpam-6413	578	3	of	of	ADP
ejpam-6413	578	4	pure	pure	ADJ
ejpam-6413	578	5	and	and	CCONJ
ejpam-6413	578	6	applied	applied	ADJ
ejpam-6413	578	7	mathematics	mathematic	NOUN
ejpam-6413	578	8	,	,	PUNCT
ejpam-6413	578	9	16(1):503–522	16(1):503–522	NUM
ejpam-6413	578	10	,	,	PUNCT
ejpam-6413	578	11	2023	2023	NUM
ejpam-6413	578	12	.	.	PUNCT
ejpam-6413	579	1	[	[	X
ejpam-6413	579	2	29	29	NUM
ejpam-6413	579	3	]	]	PUNCT
ejpam-6413	579	4	s.	s.	PROPN
ejpam-6413	579	5	iqbal	iqbal	PROPN
ejpam-6413	579	6	,	,	PUNCT
ejpam-6413	579	7	m.	m.	PROPN
ejpam-6413	579	8	samraiz	samraiz	PROPN
ejpam-6413	579	9	,	,	PUNCT
ejpam-6413	579	10	g.	g.	PROPN
ejpam-6413	579	11	rahman	rahman	PROPN
ejpam-6413	579	12	,	,	PUNCT
ejpam-6413	579	13	k.	k.	PROPN
ejpam-6413	579	14	s.	s.	PROPN
ejpam-6413	579	15	nisar	nisar	PROPN
ejpam-6413	579	16	,	,	PUNCT
ejpam-6413	579	17	and	and	CCONJ
ejpam-6413	579	18	t.	t.	NOUN
ejpam-6413	579	19	abdeljawad	abdeljawad	NOUN
ejpam-6413	579	20	.	.	PUNCT
ejpam-6413	580	1	some	some	DET
ejpam-6413	580	2	new	new	ADJ
ejpam-6413	580	3	grüss	grüss	PROPN
ejpam-6413	580	4	inequalities	inequality	NOUN
ejpam-6413	580	5	associated	associate	VERB
ejpam-6413	580	6	with	with	ADP
ejpam-6413	580	7	generalized	generalized	ADJ
ejpam-6413	580	8	fractional	fractional	ADJ
ejpam-6413	580	9	derivative	derivative	NOUN
ejpam-6413	580	10	.	.	PUNCT
ejpam-6413	581	1	aims	aim	VERB
ejpam-6413	581	2	mathematics	mathematic	NOUN
ejpam-6413	581	3	,	,	PUNCT
ejpam-6413	581	4	8(1):213–227	8(1):213–227	NUM
ejpam-6413	581	5	,	,	PUNCT
ejpam-6413	581	6	2023	2023	NUM
ejpam-6413	581	7	.	.	PUNCT
ejpam-6413	582	1	article	article	NOUN
ejpam-6413	582	2	i	i	PROPN
ejpam-6413	582	3	d	d	PROPN
ejpam-6413	582	4	2023010	2023010	NUM
ejpam-6413	582	5	.	.	PUNCT
ejpam-6413	583	1	[	[	X
ejpam-6413	583	2	30	30	NUM
ejpam-6413	583	3	]	]	X
ejpam-6413	583	4	m.	m.	NOUN
ejpam-6413	583	5	samraiz	samraiz	PROPN
ejpam-6413	583	6	,	,	PUNCT
ejpam-6413	583	7	z.	z.	PROPN
ejpam-6413	583	8	perveen	perveen	PROPN
ejpam-6413	583	9	,	,	PUNCT
ejpam-6413	583	10	g.	g.	PROPN
ejpam-6413	583	11	rahman	rahman	PROPN
ejpam-6413	583	12	,	,	PUNCT
ejpam-6413	583	13	m.	m.	PROPN
ejpam-6413	583	14	adil	adil	PROPN
ejpam-6413	583	15	khan	khan	PROPN
ejpam-6413	583	16	,	,	PUNCT
ejpam-6413	583	17	and	and	CCONJ
ejpam-6413	583	18	k.	k.	PROPN
ejpam-6413	583	19	s.	s.	PROPN
ejpam-6413	583	20	nisar	nisar	PROPN
ejpam-6413	583	21	.	.	PUNCT
ejpam-6413	584	1	hermitehadamard	hermitehadamard	ADJ
ejpam-6413	584	2	fractional	fractional	ADJ
ejpam-6413	584	3	inequalities	inequality	NOUN
ejpam-6413	584	4	for	for	ADP
ejpam-6413	584	5	differentiable	differentiable	ADJ
ejpam-6413	584	6	functions	function	NOUN
ejpam-6413	584	7	.	.	PUNCT
ejpam-6413	585	1	fractal	fractal	ADJ
ejpam-6413	585	2	and	and	CCONJ
ejpam-6413	585	3	fractional	fractional	ADJ
ejpam-6413	585	4	,	,	PUNCT
ejpam-6413	585	5	6(2):60	6(2):60	NUM
ejpam-6413	585	6	,	,	PUNCT
ejpam-6413	585	7	2022	2022	NUM
ejpam-6413	585	8	.	.	PUNCT
ejpam-6413	586	1	[	[	X
ejpam-6413	586	2	31	31	NUM
ejpam-6413	586	3	]	]	PUNCT
ejpam-6413	586	4	s.	s.	PROPN
ejpam-6413	586	5	s.	s.	PROPN
ejpam-6413	586	6	dragomir	dragomir	PROPN
ejpam-6413	586	7	and	and	CCONJ
ejpam-6413	586	8	c.	c.	PROPN
ejpam-6413	586	9	e.	e.	PROPN
ejpam-6413	586	10	m.	m.	PROPN
ejpam-6413	586	11	pearce	pearce	PROPN
ejpam-6413	586	12	.	.	PUNCT
ejpam-6413	587	1	selected	select	VERB
ejpam-6413	587	2	topics	topic	NOUN
ejpam-6413	587	3	on	on	ADP
ejpam-6413	587	4	hermite	hermite	ADJ
ejpam-6413	587	5	-	-	PUNCT
ejpam-6413	587	6	hadamard	hadamard	ADJ
ejpam-6413	587	7	inequalities	inequality	NOUN
ejpam-6413	587	8	and	and	CCONJ
ejpam-6413	587	9	applications	application	NOUN
ejpam-6413	587	10	.	.	PUNCT
ejpam-6413	588	1	science	science	NOUN
ejpam-6413	588	2	direct	direct	ADJ
ejpam-6413	588	3	working	working	NOUN
ejpam-6413	588	4	paper	paper	NOUN
ejpam-6413	588	5	,	,	PUNCT
ejpam-6413	588	6	s1574	s1574	NOUN
ejpam-6413	588	7	-	-	PUNCT
ejpam-6413	588	8	0358(4	0358(4	NUM
ejpam-6413	588	9	)	)	PUNCT
ejpam-6413	588	10	,	,	PUNCT
ejpam-6413	588	11	2003	2003	NUM
ejpam-6413	588	12	.	.	PUNCT
ejpam-6413	589	1	[	[	X
ejpam-6413	589	2	32	32	NUM
ejpam-6413	589	3	]	]	PUNCT
ejpam-6413	589	4	m.	m.	NOUN
ejpam-6413	589	5	z.	z.	PROPN
ejpam-6413	589	6	sarikaya	sarikaya	PROPN
ejpam-6413	589	7	,	,	PUNCT
ejpam-6413	589	8	e.	e.	PROPN
ejpam-6413	589	9	set	set	PROPN
ejpam-6413	589	10	,	,	PUNCT
ejpam-6413	589	11	h.	h.	PROPN
ejpam-6413	589	12	yaldiz	yaldiz	PROPN
ejpam-6413	589	13	,	,	PUNCT
ejpam-6413	589	14	and	and	CCONJ
ejpam-6413	589	15	n.	n.	PROPN
ejpam-6413	589	16	basak	basak	PROPN
ejpam-6413	589	17	.	.	PUNCT
ejpam-6413	590	1	hermite	hermite	PROPN
ejpam-6413	590	2	-	-	PUNCT
ejpam-6413	590	3	hadamard	hadamard	PROPN
ejpam-6413	590	4	’s	’s	PART
ejpam-6413	590	5	inequalities	inequality	NOUN
ejpam-6413	590	6	for	for	ADP
ejpam-6413	590	7	fractional	fractional	ADJ
ejpam-6413	590	8	integrals	integral	NOUN
ejpam-6413	590	9	and	and	CCONJ
ejpam-6413	590	10	related	relate	VERB
ejpam-6413	590	11	fractional	fractional	ADJ
ejpam-6413	590	12	inequalities	inequality	NOUN
ejpam-6413	590	13	.	.	PUNCT
ejpam-6413	591	1	mathematical	mathematical	ADJ
ejpam-6413	591	2	and	and	CCONJ
ejpam-6413	591	3	computer	computer	NOUN
ejpam-6413	591	4	modelling	modelling	NOUN
ejpam-6413	591	5	,	,	PUNCT
ejpam-6413	591	6	57(9–10):2403–2407	57(9–10):2403–2407	NUM
ejpam-6413	591	7	,	,	PUNCT
ejpam-6413	591	8	2013	2013	NUM
ejpam-6413	591	9	.	.	PUNCT
ejpam-6413	592	1	[	[	X
ejpam-6413	592	2	33	33	NUM
ejpam-6413	592	3	]	]	PUNCT
ejpam-6413	592	4	p.	p.	PROPN
ejpam-6413	592	5	j.	j.	PROPN
ejpam-6413	592	6	davis	davis	PROPN
ejpam-6413	592	7	.	.	PUNCT
ejpam-6413	593	1	leonhard	leonhard	PROPN
ejpam-6413	593	2	euler	euler	PROPN
ejpam-6413	593	3	’s	’s	PART
ejpam-6413	593	4	integral	integral	ADJ
ejpam-6413	593	5	:	:	PUNCT
ejpam-6413	593	6	a	a	DET
ejpam-6413	593	7	historical	historical	ADJ
ejpam-6413	593	8	profile	profile	NOUN
ejpam-6413	593	9	of	of	ADP
ejpam-6413	593	10	the	the	DET
ejpam-6413	593	11	gamma	gamma	NOUN
ejpam-6413	593	12	function	function	NOUN
ejpam-6413	593	13	:	:	PUNCT
ejpam-6413	593	14	in	in	ADP
ejpam-6413	593	15	memoriam	memoriam	PROPN
ejpam-6413	593	16	:	:	PUNCT
ejpam-6413	593	17	milton	milton	PROPN
ejpam-6413	593	18	abramowitz	abramowitz	PROPN
ejpam-6413	593	19	.	.	PUNCT
ejpam-6413	594	1	the	the	DET
ejpam-6413	594	2	american	american	PROPN
ejpam-6413	594	3	mathematical	mathematical	PROPN
ejpam-6413	594	4	monthly	monthly	ADV
ejpam-6413	594	5	,	,	PUNCT
ejpam-6413	594	6	66(10):849	66(10):849	NUM
ejpam-6413	594	7	–	–	PUNCT
ejpam-6413	594	8	869	869	NUM
ejpam-6413	594	9	,	,	PUNCT
ejpam-6413	594	10	1959	1959	NUM
ejpam-6413	594	11	.	.	PUNCT
ejpam-6413	595	1	[	[	X
ejpam-6413	595	2	34	34	NUM
ejpam-6413	595	3	]	]	X
ejpam-6413	595	4	r.	r.	PROPN
ejpam-6413	595	5	a.	a.	PROPN
ejpam-6413	595	6	askey	askey	PROPN
ejpam-6413	595	7	and	and	CCONJ
ejpam-6413	595	8	r.	r.	PROPN
ejpam-6413	595	9	roy	roy	PROPN
ejpam-6413	595	10	.	.	PROPN
ejpam-6413	595	11	nist	nist	PROPN
ejpam-6413	595	12	handbook	handbook	PROPN
ejpam-6413	595	13	of	of	ADP
ejpam-6413	595	14	mathematical	mathematical	ADJ
ejpam-6413	595	15	functions	function	NOUN
ejpam-6413	595	16	.	.	PUNCT
ejpam-6413	596	1	cambridge	cambridge	PROPN
ejpam-6413	596	2	university	university	PROPN
ejpam-6413	596	3	press	press	PROPN
ejpam-6413	596	4	,	,	PUNCT
ejpam-6413	596	5	new	new	PROPN
ejpam-6413	596	6	york	york	PROPN
ejpam-6413	596	7	,	,	PUNCT
ejpam-6413	596	8	2010	2010	NUM
ejpam-6413	596	9	.	.	PUNCT
ejpam-6413	597	1	[	[	X
ejpam-6413	597	2	35	35	NUM
ejpam-6413	597	3	]	]	X
ejpam-6413	597	4	m.	m.	NOUN
ejpam-6413	597	5	a.	a.	PROPN
ejpam-6413	597	6	chaudhry	chaudhry	PROPN
ejpam-6413	597	7	,	,	PUNCT
ejpam-6413	597	8	a.	a.	PROPN
ejpam-6413	597	9	qadir	qadir	PROPN
ejpam-6413	597	10	,	,	PUNCT
ejpam-6413	597	11	m.	m.	NOUN
ejpam-6413	597	12	rafique	rafique	PROPN
ejpam-6413	597	13	,	,	PUNCT
ejpam-6413	597	14	and	and	CCONJ
ejpam-6413	597	15	s.	s.	PROPN
ejpam-6413	597	16	m.	m.	PROPN
ejpam-6413	597	17	zubair	zubair	PROPN
ejpam-6413	597	18	.	.	PUNCT
ejpam-6413	598	1	extension	extension	NOUN
ejpam-6413	598	2	of	of	ADP
ejpam-6413	598	3	euler	euler	PROPN
ejpam-6413	598	4	’s	’s	PART
ejpam-6413	598	5	beta	beta	NOUN
ejpam-6413	598	6	function	function	NOUN
ejpam-6413	598	7	.	.	PUNCT
ejpam-6413	599	1	journal	journal	NOUN
ejpam-6413	599	2	of	of	ADP
ejpam-6413	599	3	computational	computational	ADJ
ejpam-6413	599	4	and	and	CCONJ
ejpam-6413	599	5	applied	applied	ADJ
ejpam-6413	599	6	mathematics	mathematic	NOUN
ejpam-6413	599	7	,	,	PUNCT
ejpam-6413	599	8	78(1):19–32	78(1):19–32	NUM
ejpam-6413	599	9	,	,	PUNCT
ejpam-6413	599	10	1997	1997	NUM
ejpam-6413	599	11	.	.	PUNCT
ejpam-6413	600	1	[	[	X
ejpam-6413	600	2	36	36	NUM
ejpam-6413	600	3	]	]	PUNCT
ejpam-6413	600	4	a.	a.	PROPN
ejpam-6413	600	5	r.	r.	PROPN
ejpam-6413	600	6	didonato	didonato	PROPN
ejpam-6413	600	7	and	and	CCONJ
ejpam-6413	600	8	m.	m.	NOUN
ejpam-6413	600	9	p.	p.	NOUN
ejpam-6413	600	10	jarnagin	jarnagin	NOUN
ejpam-6413	600	11	.	.	PUNCT
ejpam-6413	601	1	the	the	DET
ejpam-6413	601	2	efficient	efficient	ADJ
ejpam-6413	601	3	calculation	calculation	NOUN
ejpam-6413	601	4	of	of	ADP
ejpam-6413	601	5	the	the	DET
ejpam-6413	601	6	incomplete	incomplete	ADJ
ejpam-6413	601	7	betafunction	betafunction	NOUN
ejpam-6413	601	8	ratio	ratio	NOUN
ejpam-6413	601	9	for	for	ADP
ejpam-6413	601	10	half	half	ADJ
ejpam-6413	601	11	-	-	PUNCT
ejpam-6413	601	12	integer	integer	NOUN
ejpam-6413	601	13	values	value	NOUN
ejpam-6413	601	14	of	of	ADP
ejpam-6413	601	15	the	the	DET
ejpam-6413	601	16	parameters	parameter	NOUN
ejpam-6413	601	17	.	.	PUNCT
ejpam-6413	602	1	mathematics	mathematic	NOUN
ejpam-6413	602	2	of	of	ADP
ejpam-6413	602	3	computation	computation	NOUN
ejpam-6413	602	4	,	,	PUNCT
ejpam-6413	602	5	21(100):652–662	21(100):652–662	PROPN
ejpam-6413	602	6	,	,	PUNCT
ejpam-6413	602	7	1967	1967	NUM
ejpam-6413	602	8	.	.	PUNCT
ejpam-6413	603	1	[	[	X
ejpam-6413	603	2	37	37	NUM
ejpam-6413	603	3	]	]	PUNCT
ejpam-6413	603	4	s.	s.	PROPN
ejpam-6413	603	5	özcan	özcan	PROPN
ejpam-6413	603	6	.	.	PUNCT
ejpam-6413	604	1	hermite	hermite	PROPN
ejpam-6413	604	2	-	-	PUNCT
ejpam-6413	604	3	hadamard	hadamard	ADJ
ejpam-6413	604	4	type	type	NOUN
ejpam-6413	604	5	inequalities	inequality	NOUN
ejpam-6413	604	6	for	for	ADP
ejpam-6413	604	7	m	m	NOUN
ejpam-6413	604	8	-	-	NOUN
ejpam-6413	604	9	convex	convex	ADJ
ejpam-6413	604	10	and	and	CCONJ
ejpam-6413	604	11	(	(	PUNCT
ejpam-6413	604	12	α	α	NOUN
ejpam-6413	604	13	,	,	PUNCT
ejpam-6413	604	14	m)-convex	m)-convex	NOUN
ejpam-6413	604	15	functions	function	NOUN
ejpam-6413	604	16	.	.	PUNCT
ejpam-6413	605	1	journal	journal	PROPN
ejpam-6413	605	2	of	of	ADP
ejpam-6413	605	3	inequalities	inequality	NOUN
ejpam-6413	605	4	and	and	CCONJ
ejpam-6413	605	5	applications	application	NOUN
ejpam-6413	605	6	,	,	PUNCT
ejpam-6413	605	7	2020(1	2020(1	NUM
ejpam-6413	605	8	)	)	PUNCT
ejpam-6413	605	9	,	,	PUNCT
ejpam-6413	605	10	2020	2020	NUM
ejpam-6413	605	11	.	.	PUNCT
ejpam-6413	606	1	[	[	X
ejpam-6413	606	2	38	38	NUM
ejpam-6413	606	3	]	]	PUNCT
ejpam-6413	606	4	j.-y	j.-y	NOUN
ejpam-6413	606	5	.	.	PUNCT
ejpam-6413	607	1	wang	wang	PROPN
ejpam-6413	607	2	,	,	PUNCT
ejpam-6413	607	3	h.-p	h.-p	PROPN
ejpam-6413	607	4	.	.	PUNCT
ejpam-6413	608	1	yin	yin	PROPN
ejpam-6413	608	2	,	,	PUNCT
ejpam-6413	608	3	w.-l	w.-l	PROPN
ejpam-6413	608	4	.	.	PUNCT
ejpam-6413	609	1	sun	sun	PROPN
ejpam-6413	609	2	,	,	PUNCT
ejpam-6413	609	3	and	and	CCONJ
ejpam-6413	609	4	b.-n	b.-n	PROPN
ejpam-6413	609	5	.	.	PUNCT
ejpam-6413	610	1	guo	guo	PROPN
ejpam-6413	610	2	.	.	PUNCT
ejpam-6413	611	1	hermite	hermite	PROPN
ejpam-6413	611	2	-	-	PUNCT
ejpam-6413	611	3	hadamard	hadamard	ADJ
ejpam-6413	611	4	integral	integral	ADJ
ejpam-6413	611	5	inequalities	inequality	NOUN
ejpam-6413	611	6	of	of	ADP
ejpam-6413	611	7	(	(	PUNCT
ejpam-6413	611	8	α	α	NOUN
ejpam-6413	611	9	,	,	PUNCT
ejpam-6413	611	10	s)-ga	s)-ga	NOUN
ejpam-6413	611	11	and	and	CCONJ
ejpam-6413	611	12	(	(	PUNCT
ejpam-6413	611	13	α	α	NOUN
ejpam-6413	611	14	,	,	PUNCT
ejpam-6413	611	15	s	s	PROPN
ejpam-6413	611	16	,	,	PUNCT
ejpam-6413	611	17	m)-ga	m)-ga	ADJ
ejpam-6413	611	18	-	-	PUNCT
ejpam-6413	611	19	convex	convex	NOUN
ejpam-6413	611	20	functions	function	NOUN
ejpam-6413	611	21	.	.	PUNCT
ejpam-6413	612	1	axioms	axiom	NOUN
ejpam-6413	612	2	,	,	PUNCT
ejpam-6413	612	3	11(11):616	11(11):616	NUM
ejpam-6413	612	4	,	,	PUNCT
ejpam-6413	612	5	2022	2022	NUM
ejpam-6413	612	6	.	.	PUNCT