id	sid	tid	token	lemma	pos
ejpam-4850	1	1	european	european	PROPN
ejpam-4850	1	2	journal	journal	PROPN
ejpam-4850	1	3	of	of	ADP
ejpam-4850	1	4	pure	pure	ADJ
ejpam-4850	1	5	and	and	CCONJ
ejpam-4850	1	6	applied	apply	VERB
ejpam-4850	1	7	mathematics	mathematic	NOUN
ejpam-4850	1	8	vol	vol	NOUN
ejpam-4850	1	9	.	.	PUNCT
ejpam-4850	2	1	16	16	NUM
ejpam-4850	2	2	,	,	PUNCT
ejpam-4850	2	3	no	no	INTJ
ejpam-4850	2	4	.	.	NOUN
ejpam-4850	2	5	3	3	NUM
ejpam-4850	2	6	,	,	PUNCT
ejpam-4850	2	7	2023	2023	NUM
ejpam-4850	2	8	,	,	PUNCT
ejpam-4850	2	9	1359	1359	NUM
ejpam-4850	2	10	-	-	SYM
ejpam-4850	2	11	1380	1380	NUM
ejpam-4850	3	1	issn	issn	PROPN
ejpam-4850	3	2	1307	1307	NUM
ejpam-4850	3	3	-	-	SYM
ejpam-4850	3	4	5543	5543	NUM
ejpam-4850	3	5	–	–	PUNCT
ejpam-4850	3	6	ejpam.com	ejpam.com	X
ejpam-4850	3	7	published	publish	VERB
ejpam-4850	3	8	by	by	ADP
ejpam-4850	3	9	new	new	PROPN
ejpam-4850	3	10	york	york	PROPN
ejpam-4850	3	11	business	business	PROPN
ejpam-4850	3	12	global	global	PROPN
ejpam-4850	3	13	exploring	explore	VERB
ejpam-4850	3	14	the	the	DET
ejpam-4850	3	15	companion	companion	NOUN
ejpam-4850	3	16	of	of	ADP
ejpam-4850	3	17	ostrowski	ostrowski	PROPN
ejpam-4850	3	18	’s	’s	PART
ejpam-4850	3	19	inequalities	inequality	NOUN
ejpam-4850	3	20	via	via	ADP
ejpam-4850	3	21	local	local	ADJ
ejpam-4850	3	22	fractional	fractional	ADJ
ejpam-4850	3	23	integrals	integral	NOUN
ejpam-4850	3	24	wedad	wedad	PROPN
ejpam-4850	3	25	saleh1,∗	saleh1,∗	PROPN
ejpam-4850	3	26	,	,	PUNCT
ejpam-4850	3	27	badreddine	badreddine	PROPN
ejpam-4850	3	28	meftah2	meftah2	PROPN
ejpam-4850	3	29	,	,	PUNCT
ejpam-4850	3	30	abdelghani	abdelghani	ADJ
ejpam-4850	3	31	lakhdari3	lakhdari3	NOUN
ejpam-4850	3	32	,	,	PUNCT
ejpam-4850	3	33	adem	adem	PROPN
ejpam-4850	3	34	kiliçman4	kiliçman4	PROPN
ejpam-4850	3	35	1	1	NUM
ejpam-4850	3	36	department	department	NOUN
ejpam-4850	3	37	of	of	ADP
ejpam-4850	3	38	mathematics	mathematics	PROPN
ejpam-4850	3	39	,	,	PUNCT
ejpam-4850	3	40	taibah	taibah	PROPN
ejpam-4850	3	41	university	university	PROPN
ejpam-4850	3	42	,	,	PUNCT
ejpam-4850	3	43	almedina	almedina	PROPN
ejpam-4850	3	44	,	,	PUNCT
ejpam-4850	3	45	saudi	saudi	PROPN
ejpam-4850	3	46	arabia	arabia	PROPN
ejpam-4850	3	47	2	2	NUM
ejpam-4850	3	48	department	department	NOUN
ejpam-4850	3	49	of	of	ADP
ejpam-4850	3	50	mathematics	mathematic	NOUN
ejpam-4850	3	51	,	,	PUNCT
ejpam-4850	3	52	university	university	NOUN
ejpam-4850	3	53	8	8	NUM
ejpam-4850	3	54	may	may	PROPN
ejpam-4850	3	55	1945	1945	NUM
ejpam-4850	3	56	,	,	PUNCT
ejpam-4850	3	57	guelma	guelma	ADJ
ejpam-4850	3	58	,	,	PUNCT
ejpam-4850	3	59	algeria	algeria	PROPN
ejpam-4850	3	60	3	3	NUM
ejpam-4850	3	61	national	national	PROPN
ejpam-4850	3	62	higher	high	ADJ
ejpam-4850	3	63	school	school	NOUN
ejpam-4850	3	64	of	of	ADP
ejpam-4850	3	65	technology	technology	NOUN
ejpam-4850	3	66	and	and	CCONJ
ejpam-4850	3	67	engineering	engineering	NOUN
ejpam-4850	3	68	,	,	PUNCT
ejpam-4850	3	69	annaba	annaba	PROPN
ejpam-4850	3	70	,	,	PUNCT
ejpam-4850	3	71	algeria	algeria	PROPN
ejpam-4850	3	72	4	4	NUM
ejpam-4850	3	73	department	department	NOUN
ejpam-4850	3	74	of	of	ADP
ejpam-4850	3	75	mathematics	mathematics	PROPN
ejpam-4850	3	76	and	and	CCONJ
ejpam-4850	3	77	institute	institute	PROPN
ejpam-4850	3	78	for	for	ADP
ejpam-4850	3	79	mathematical	mathematical	ADJ
ejpam-4850	3	80	research	research	NOUN
ejpam-4850	3	81	,	,	PUNCT
ejpam-4850	3	82	university	university	NOUN
ejpam-4850	3	83	putra	putra	PROPN
ejpam-4850	3	84	malaysia	malaysia	PROPN
ejpam-4850	3	85	,	,	PUNCT
ejpam-4850	3	86	43400	43400	NUM
ejpam-4850	3	87	upm	upm	PROPN
ejpam-4850	3	88	serdang	serdang	PROPN
ejpam-4850	3	89	,	,	PUNCT
ejpam-4850	3	90	selangor	selangor	PROPN
ejpam-4850	3	91	,	,	PUNCT
ejpam-4850	3	92	malaysia	malaysia	PROPN
ejpam-4850	3	93	abstract	abstract	NOUN
ejpam-4850	3	94	.	.	PUNCT
ejpam-4850	4	1	this	this	DET
ejpam-4850	4	2	paper	paper	NOUN
ejpam-4850	4	3	investigates	investigate	VERB
ejpam-4850	4	4	the	the	DET
ejpam-4850	4	5	companion	companion	NOUN
ejpam-4850	4	6	of	of	ADP
ejpam-4850	4	7	ostrowski	ostrowski	PROPN
ejpam-4850	4	8	’s	’s	PART
ejpam-4850	4	9	inequality	inequality	NOUN
ejpam-4850	4	10	in	in	ADP
ejpam-4850	4	11	the	the	DET
ejpam-4850	4	12	framework	framework	NOUN
ejpam-4850	4	13	of	of	ADP
ejpam-4850	4	14	fractal	fractal	ADJ
ejpam-4850	4	15	sets	set	NOUN
ejpam-4850	4	16	.	.	PUNCT
ejpam-4850	5	1	first	first	ADV
ejpam-4850	5	2	,	,	PUNCT
ejpam-4850	5	3	a	a	DET
ejpam-4850	5	4	new	new	ADJ
ejpam-4850	5	5	identity	identity	NOUN
ejpam-4850	5	6	related	relate	VERB
ejpam-4850	5	7	to	to	ADP
ejpam-4850	5	8	local	local	ADJ
ejpam-4850	5	9	fractional	fractional	ADJ
ejpam-4850	5	10	integrals	integral	NOUN
ejpam-4850	5	11	is	be	AUX
ejpam-4850	5	12	introduced	introduce	VERB
ejpam-4850	5	13	,	,	PUNCT
ejpam-4850	5	14	serving	serve	VERB
ejpam-4850	5	15	as	as	ADP
ejpam-4850	5	16	the	the	DET
ejpam-4850	5	17	foundation	foundation	NOUN
ejpam-4850	5	18	for	for	ADP
ejpam-4850	5	19	establishing	establish	VERB
ejpam-4850	5	20	a	a	DET
ejpam-4850	5	21	set	set	NOUN
ejpam-4850	5	22	of	of	ADP
ejpam-4850	5	23	inequalities	inequality	NOUN
ejpam-4850	5	24	applicable	applicable	ADJ
ejpam-4850	5	25	to	to	ADP
ejpam-4850	5	26	functions	function	NOUN
ejpam-4850	5	27	with	with	ADP
ejpam-4850	5	28	generalized	generalized	ADJ
ejpam-4850	5	29	sconvex	sconvex	ADJ
ejpam-4850	5	30	and	and	CCONJ
ejpam-4850	5	31	s	s	NOUN
ejpam-4850	5	32	-	-	PUNCT
ejpam-4850	5	33	concave	concave	ADJ
ejpam-4850	5	34	derivatives	derivative	NOUN
ejpam-4850	5	35	.	.	PUNCT
ejpam-4850	6	1	an	an	DET
ejpam-4850	6	2	illustrative	illustrative	ADJ
ejpam-4850	6	3	example	example	NOUN
ejpam-4850	6	4	is	be	AUX
ejpam-4850	6	5	presented	present	VERB
ejpam-4850	6	6	to	to	PART
ejpam-4850	6	7	validate	validate	VERB
ejpam-4850	6	8	the	the	DET
ejpam-4850	6	9	obtained	obtain	VERB
ejpam-4850	6	10	results	result	NOUN
ejpam-4850	6	11	,	,	PUNCT
ejpam-4850	6	12	demonstrating	demonstrate	VERB
ejpam-4850	6	13	their	their	PRON
ejpam-4850	6	14	accuracy	accuracy	NOUN
ejpam-4850	6	15	.	.	PUNCT
ejpam-4850	7	1	additionally	additionally	ADV
ejpam-4850	7	2	,	,	PUNCT
ejpam-4850	7	3	the	the	DET
ejpam-4850	7	4	paper	paper	NOUN
ejpam-4850	7	5	discusses	discuss	VERB
ejpam-4850	7	6	several	several	ADJ
ejpam-4850	7	7	practical	practical	ADJ
ejpam-4850	7	8	applications	application	NOUN
ejpam-4850	7	9	,	,	PUNCT
ejpam-4850	7	10	highlighting	highlight	VERB
ejpam-4850	7	11	the	the	DET
ejpam-4850	7	12	significance	significance	NOUN
ejpam-4850	7	13	of	of	ADP
ejpam-4850	7	14	the	the	DET
ejpam-4850	7	15	established	establish	VERB
ejpam-4850	7	16	inequalities	inequality	NOUN
ejpam-4850	7	17	.	.	PUNCT
ejpam-4850	8	1	the	the	DET
ejpam-4850	8	2	research	research	NOUN
ejpam-4850	8	3	presented	present	VERB
ejpam-4850	8	4	in	in	ADP
ejpam-4850	8	5	this	this	DET
ejpam-4850	8	6	paper	paper	NOUN
ejpam-4850	8	7	contributes	contribute	VERB
ejpam-4850	8	8	to	to	ADP
ejpam-4850	8	9	the	the	DET
ejpam-4850	8	10	growing	grow	VERB
ejpam-4850	8	11	field	field	NOUN
ejpam-4850	8	12	of	of	ADP
ejpam-4850	8	13	studying	study	VERB
ejpam-4850	8	14	functions	function	NOUN
ejpam-4850	8	15	on	on	ADP
ejpam-4850	8	16	fractal	fractal	ADJ
ejpam-4850	8	17	sets	set	NOUN
ejpam-4850	8	18	,	,	PUNCT
ejpam-4850	8	19	which	which	PRON
ejpam-4850	8	20	has	have	AUX
ejpam-4850	8	21	attracted	attract	VERB
ejpam-4850	8	22	considerable	considerable	ADJ
ejpam-4850	8	23	interest	interest	NOUN
ejpam-4850	8	24	from	from	ADP
ejpam-4850	8	25	scientists	scientist	NOUN
ejpam-4850	8	26	and	and	CCONJ
ejpam-4850	8	27	engineers	engineer	NOUN
ejpam-4850	8	28	.	.	PUNCT
ejpam-4850	9	1	2020	2020	NUM
ejpam-4850	9	2	mathematics	mathematics	PROPN
ejpam-4850	9	3	subject	subject	NOUN
ejpam-4850	9	4	classifications	classification	NOUN
ejpam-4850	9	5	:	:	PUNCT
ejpam-4850	9	6	26d10	26d10	NUM
ejpam-4850	9	7	,	,	PUNCT
ejpam-4850	9	8	26d15	26d15	NUM
ejpam-4850	9	9	,	,	PUNCT
ejpam-4850	9	10	26a51	26a51	NUM
ejpam-4850	9	11	key	key	ADJ
ejpam-4850	9	12	words	word	NOUN
ejpam-4850	9	13	and	and	CCONJ
ejpam-4850	9	14	phrases	phrase	NOUN
ejpam-4850	9	15	:	:	PUNCT
ejpam-4850	9	16	tow	tow	NOUN
ejpam-4850	9	17	-	-	PUNCT
ejpam-4850	9	18	point	point	NOUN
ejpam-4850	9	19	newton	newton	PROPN
ejpam-4850	9	20	-	-	PUNCT
ejpam-4850	9	21	cotes	cotes	PROPN
ejpam-4850	9	22	,	,	PUNCT
ejpam-4850	9	23	generalized	generalized	ADJ
ejpam-4850	9	24	s	s	NOUN
ejpam-4850	9	25	-	-	PUNCT
ejpam-4850	9	26	convex	convex	ADJ
ejpam-4850	9	27	functions	function	NOUN
ejpam-4850	9	28	,	,	PUNCT
ejpam-4850	9	29	local	local	ADJ
ejpam-4850	9	30	fractional	fractional	ADJ
ejpam-4850	9	31	integral	integral	ADJ
ejpam-4850	9	32	,	,	PUNCT
ejpam-4850	9	33	fractal	fractal	ADJ
ejpam-4850	9	34	set	set	NOUN
ejpam-4850	9	35	1	1	NUM
ejpam-4850	9	36	.	.	PUNCT
ejpam-4850	9	37	introduction	introduction	NOUN
ejpam-4850	9	38	and	and	CCONJ
ejpam-4850	9	39	preliminaries	preliminary	NOUN
ejpam-4850	9	40	convexity	convexity	NOUN
ejpam-4850	9	41	is	be	AUX
ejpam-4850	9	42	a	a	DET
ejpam-4850	9	43	fundamental	fundamental	ADJ
ejpam-4850	9	44	property	property	NOUN
ejpam-4850	9	45	in	in	ADP
ejpam-4850	9	46	mathematics	mathematic	NOUN
ejpam-4850	9	47	that	that	PRON
ejpam-4850	9	48	appears	appear	VERB
ejpam-4850	9	49	in	in	ADP
ejpam-4850	9	50	various	various	ADJ
ejpam-4850	9	51	fields	field	NOUN
ejpam-4850	9	52	such	such	ADJ
ejpam-4850	9	53	as	as	ADP
ejpam-4850	9	54	optimization	optimization	NOUN
ejpam-4850	9	55	,	,	PUNCT
ejpam-4850	9	56	convex	convex	ADJ
ejpam-4850	9	57	analysis	analysis	NOUN
ejpam-4850	9	58	,	,	PUNCT
ejpam-4850	9	59	geometry	geometry	NOUN
ejpam-4850	9	60	,	,	PUNCT
ejpam-4850	9	61	probability	probability	NOUN
ejpam-4850	9	62	theory	theory	NOUN
ejpam-4850	9	63	,	,	PUNCT
ejpam-4850	9	64	and	and	CCONJ
ejpam-4850	9	65	finance	finance	NOUN
ejpam-4850	9	66	.	.	PUNCT
ejpam-4850	10	1	a	a	DET
ejpam-4850	10	2	function	function	NOUN
ejpam-4850	10	3	j	j	NOUN
ejpam-4850	10	4	:	:	PUNCT
ejpam-4850	11	1	i	i	PRON
ejpam-4850	11	2	→	→	PUNCT
ejpam-4850	11	3	r	r	NOUN
ejpam-4850	11	4	is	be	AUX
ejpam-4850	11	5	said	say	VERB
ejpam-4850	11	6	to	to	PART
ejpam-4850	11	7	be	be	AUX
ejpam-4850	11	8	convex	convex	ADJ
ejpam-4850	11	9	if	if	SCONJ
ejpam-4850	11	10	it	it	PRON
ejpam-4850	11	11	satisfies	satisfy	VERB
ejpam-4850	11	12	the	the	DET
ejpam-4850	11	13	following	follow	VERB
ejpam-4850	11	14	condition	condition	NOUN
ejpam-4850	11	15	j	j	PROPN
ejpam-4850	11	16	(	(	PUNCT
ejpam-4850	11	17	κκ1	κκ1	PROPN
ejpam-4850	11	18	+	+	CCONJ
ejpam-4850	11	19	(	(	PUNCT
ejpam-4850	11	20	1−	1−	NUM
ejpam-4850	11	21	κ)κ2	κ)κ2	PROPN
ejpam-4850	11	22	)	)	PUNCT
ejpam-4850	11	23	≤	≤	NOUN
ejpam-4850	11	24	κj	κj	NOUN
ejpam-4850	11	25	(	(	PUNCT
ejpam-4850	11	26	κ1	κ1	NOUN
ejpam-4850	11	27	)	)	PUNCT
ejpam-4850	11	28	+	+	CCONJ
ejpam-4850	11	29	(	(	PUNCT
ejpam-4850	11	30	1−	1−	NUM
ejpam-4850	11	31	κ)j	κ)j	X
ejpam-4850	11	32	(	(	PUNCT
ejpam-4850	11	33	κ2	κ2	PROPN
ejpam-4850	11	34	)	)	PUNCT
ejpam-4850	11	35	,	,	PUNCT
ejpam-4850	11	36	for	for	ADP
ejpam-4850	11	37	all	all	DET
ejpam-4850	11	38	κ1	κ1	NOUN
ejpam-4850	11	39	,	,	PUNCT
ejpam-4850	11	40	κ2	κ2	NOUN
ejpam-4850	11	41	∈	∈	PROPN
ejpam-4850	12	1	i	i	PRON
ejpam-4850	12	2	and	and	CCONJ
ejpam-4850	12	3	all	all	PRON
ejpam-4850	12	4	κ	κ	PRON
ejpam-4850	12	5	∈	∈	PROPN
ejpam-4850	13	1	[	[	X
ejpam-4850	13	2	0	0	NUM
ejpam-4850	13	3	,	,	PUNCT
ejpam-4850	13	4	1	1	NUM
ejpam-4850	13	5	]	]	PUNCT
ejpam-4850	13	6	.	.	PUNCT
ejpam-4850	14	1	the	the	DET
ejpam-4850	14	2	most	most	ADV
ejpam-4850	14	3	famous	famous	ADJ
ejpam-4850	14	4	result	result	NOUN
ejpam-4850	14	5	connected	connect	VERB
ejpam-4850	14	6	to	to	ADP
ejpam-4850	14	7	this	this	DET
ejpam-4850	14	8	notion	notion	NOUN
ejpam-4850	14	9	is	be	AUX
ejpam-4850	14	10	the	the	DET
ejpam-4850	14	11	one	one	NOUN
ejpam-4850	14	12	called	call	VERB
ejpam-4850	14	13	the	the	DET
ejpam-4850	14	14	hermite	hermite	PROPN
ejpam-4850	14	15	-	-	PUNCT
ejpam-4850	14	16	hadamard	hadamard	ADJ
ejpam-4850	14	17	inequality	inequality	NOUN
ejpam-4850	14	18	,	,	PUNCT
ejpam-4850	14	19	which	which	PRON
ejpam-4850	14	20	can	can	AUX
ejpam-4850	14	21	be	be	AUX
ejpam-4850	14	22	formulated	formulate	VERB
ejpam-4850	14	23	as	as	SCONJ
ejpam-4850	14	24	follows	follow	VERB
ejpam-4850	14	25	(	(	PUNCT
ejpam-4850	14	26	see	see	VERB
ejpam-4850	14	27	[	[	X
ejpam-4850	14	28	22	22	NUM
ejpam-4850	14	29	]	]	PUNCT
ejpam-4850	14	30	):	):	PUNCT
ejpam-4850	14	31	for	for	ADP
ejpam-4850	14	32	a	a	DET
ejpam-4850	14	33	convex	convex	NOUN
ejpam-4850	14	34	function	function	NOUN
ejpam-4850	14	35	j	j	PROPN
ejpam-4850	14	36	defined	define	VERB
ejpam-4850	14	37	on	on	ADP
ejpam-4850	14	38	the	the	DET
ejpam-4850	14	39	interval	interval	NOUN
ejpam-4850	14	40	i	i	PRON
ejpam-4850	15	1	=	=	PUNCT
ejpam-4850	16	1	[	[	X
ejpam-4850	16	2	a	a	X
ejpam-4850	16	3	,	,	PUNCT
ejpam-4850	16	4	b	b	NOUN
ejpam-4850	16	5	]	]	X
ejpam-4850	16	6	,	,	PUNCT
ejpam-4850	16	7	we	we	PRON
ejpam-4850	16	8	have	have	AUX
ejpam-4850	16	9	∗corresponding	∗corresponde	VERB
ejpam-4850	16	10	author	author	NOUN
ejpam-4850	16	11	.	.	PUNCT
ejpam-4850	17	1	doi	doi	NOUN
ejpam-4850	17	2	:	:	PUNCT
ejpam-4850	17	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4850	https://doi.org/10.29020/nybg.ejpam.v16i3.4850	NOUN
ejpam-4850	17	4	email	email	NOUN
ejpam-4850	17	5	addresses	address	VERB
ejpam-4850	17	6	:	:	PUNCT
ejpam-4850	17	7	wlehabi@taibahu.edu.sa	wlehabi@taibahu.edu.sa	PROPN
ejpam-4850	17	8	(	(	PUNCT
ejpam-4850	17	9	w.	w.	PROPN
ejpam-4850	17	10	saleh	saleh	PROPN
ejpam-4850	17	11	)	)	PUNCT
ejpam-4850	17	12	,	,	PUNCT
ejpam-4850	17	13	badrimeftah@yahoo.fr	badrimeftah@yahoo.fr	PROPN
ejpam-4850	17	14	(	(	PUNCT
ejpam-4850	17	15	b.	b.	PROPN
ejpam-4850	17	16	meftah	meftah	PROPN
ejpam-4850	17	17	)	)	PUNCT
ejpam-4850	17	18	,	,	PUNCT
ejpam-4850	17	19	a.lakhdari@esti-annaba.dz	a.lakhdari@esti-annaba.dz	ADV
ejpam-4850	17	20	(	(	PUNCT
ejpam-4850	17	21	a.	a.	NOUN
ejpam-4850	17	22	lakhdari	lakhdari	PROPN
ejpam-4850	17	23	)	)	PUNCT
ejpam-4850	17	24	,	,	PUNCT
ejpam-4850	17	25	akilic@upm.edu.my	akilic@upm.edu.my	PROPN
ejpam-4850	17	26	(	(	PUNCT
ejpam-4850	17	27	a.	a.	NOUN
ejpam-4850	17	28	kiliçman	kiliçman	NOUN
ejpam-4850	17	29	)	)	PUNCT
ejpam-4850	17	30	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4850	17	31	1359	1359	NUM
ejpam-4850	17	32	©	©	PROPN
ejpam-4850	17	33	2023	2023	NUM
ejpam-4850	17	34	ejpam	ejpam	NOUN
ejpam-4850	17	35	all	all	DET
ejpam-4850	17	36	rights	right	NOUN
ejpam-4850	17	37	reserved	reserve	VERB
ejpam-4850	17	38	.	.	PUNCT
ejpam-4850	18	1	w.	w.	PROPN
ejpam-4850	18	2	saleh	saleh	PROPN
ejpam-4850	18	3	et	et	PROPN
ejpam-4850	18	4	al	al	PROPN
ejpam-4850	18	5	.	.	PUNCT
ejpam-4850	18	6	/	/	SYM
ejpam-4850	18	7	eur	eur	PROPN
ejpam-4850	18	8	.	.	PUNCT
ejpam-4850	19	1	j.	j.	PROPN
ejpam-4850	19	2	pure	pure	PROPN
ejpam-4850	19	3	appl	appl	PROPN
ejpam-4850	19	4	.	.	PROPN
ejpam-4850	19	5	math	math	PROPN
ejpam-4850	19	6	,	,	PUNCT
ejpam-4850	19	7	16	16	NUM
ejpam-4850	19	8	(	(	PUNCT
ejpam-4850	19	9	3	3	NUM
ejpam-4850	19	10	)	)	PUNCT
ejpam-4850	19	11	(	(	PUNCT
ejpam-4850	19	12	2023	2023	NUM
ejpam-4850	19	13	)	)	PUNCT
ejpam-4850	19	14	,	,	PUNCT
ejpam-4850	19	15	1359	1359	NUM
ejpam-4850	19	16	-	-	SYM
ejpam-4850	19	17	1380	1380	NUM
ejpam-4850	19	18	1360	1360	NUM
ejpam-4850	19	19	j	j	X
ejpam-4850	19	20	(	(	PUNCT
ejpam-4850	19	21	a+b	a+b	NUM
ejpam-4850	19	22	2	2	NUM
ejpam-4850	19	23	)	)	PUNCT
ejpam-4850	19	24	≤	≤	NOUN
ejpam-4850	19	25	1	1	NUM
ejpam-4850	19	26	b−a	b−a	NOUN
ejpam-4850	19	27	b∫	b∫	PROPN
ejpam-4850	19	28	a	a	DET
ejpam-4850	19	29	j	j	PROPN
ejpam-4850	19	30	(	(	PUNCT
ejpam-4850	19	31	t)dt	t)dt	PROPN
ejpam-4850	19	32	≤	≤	PROPN
ejpam-4850	19	33	j	j	PROPN
ejpam-4850	19	34	(	(	PUNCT
ejpam-4850	19	35	a)+j	a)+j	PROPN
ejpam-4850	19	36	(	(	PUNCT
ejpam-4850	19	37	b	b	NOUN
ejpam-4850	19	38	)	)	PUNCT
ejpam-4850	19	39	2	2	NUM
ejpam-4850	19	40	.	.	PUNCT
ejpam-4850	20	1	(	(	PUNCT
ejpam-4850	20	2	1	1	X
ejpam-4850	20	3	)	)	PUNCT
ejpam-4850	20	4	several	several	ADJ
ejpam-4850	20	5	scientists	scientist	NOUN
ejpam-4850	20	6	have	have	AUX
ejpam-4850	20	7	been	be	AUX
ejpam-4850	20	8	interested	interested	ADJ
ejpam-4850	20	9	in	in	ADP
ejpam-4850	20	10	inequalities	inequality	NOUN
ejpam-4850	20	11	related	relate	VERB
ejpam-4850	20	12	to	to	ADP
ejpam-4850	20	13	(	(	PUNCT
ejpam-4850	20	14	1	1	NUM
ejpam-4850	20	15	)	)	PUNCT
ejpam-4850	20	16	.	.	PUNCT
ejpam-4850	21	1	in	in	ADP
ejpam-4850	21	2	[	[	X
ejpam-4850	21	3	14	14	NUM
ejpam-4850	21	4	]	]	PUNCT
ejpam-4850	21	5	,	,	PUNCT
ejpam-4850	21	6	kirmaci	kirmaci	PROPN
ejpam-4850	21	7	established	establish	VERB
ejpam-4850	21	8	the	the	DET
ejpam-4850	21	9	following	following	ADJ
ejpam-4850	21	10	result	result	NOUN
ejpam-4850	21	11	connected	connect	VERB
ejpam-4850	21	12	to	to	ADP
ejpam-4850	21	13	the	the	DET
ejpam-4850	21	14	left	left	ADJ
ejpam-4850	21	15	part	part	NOUN
ejpam-4850	21	16	of	of	ADP
ejpam-4850	21	17	(	(	PUNCT
ejpam-4850	21	18	1	1	NUM
ejpam-4850	21	19	)	)	PUNCT
ejpam-4850	21	20	for	for	ADP
ejpam-4850	21	21	the	the	DET
ejpam-4850	21	22	class	class	NOUN
ejpam-4850	21	23	of	of	ADP
ejpam-4850	21	24	functions	function	NOUN
ejpam-4850	21	25	whose	whose	DET
ejpam-4850	21	26	first	first	ADJ
ejpam-4850	21	27	derivatives	derivative	NOUN
ejpam-4850	21	28	in	in	ADP
ejpam-4850	21	29	absolute	absolute	ADJ
ejpam-4850	21	30	value	value	NOUN
ejpam-4850	21	31	are	be	AUX
ejpam-4850	21	32	convex	convex	ADJ
ejpam-4850	21	33	,	,	PUNCT
ejpam-4850	21	34	known	know	VERB
ejpam-4850	21	35	as	as	ADP
ejpam-4850	21	36	the	the	DET
ejpam-4850	21	37	midpoint	midpoint	NOUN
ejpam-4850	21	38	inequality.∣∣∣∣∣∣j	inequality.∣∣∣∣∣∣j	PROPN
ejpam-4850	21	39	(	(	PUNCT
ejpam-4850	21	40	a+b	a+b	NUM
ejpam-4850	21	41	2	2	NUM
ejpam-4850	21	42	)	)	PUNCT
ejpam-4850	21	43	−	−	NOUN
ejpam-4850	22	1	1	1	NUM
ejpam-4850	22	2	b−a	b−a	NOUN
ejpam-4850	22	3	b∫	b∫	PROPN
ejpam-4850	22	4	a	a	DET
ejpam-4850	22	5	j	j	PROPN
ejpam-4850	22	6	(	(	PUNCT
ejpam-4850	22	7	t)dt	t)dt	PROPN
ejpam-4850	22	8	∣∣∣∣∣∣	∣∣∣∣∣∣	ADJ
ejpam-4850	22	9	≤	≤	X
ejpam-4850	22	10	b−a	b−a	X
ejpam-4850	22	11	8	8	NUM
ejpam-4850	22	12	(	(	PUNCT
ejpam-4850	22	13	∣∣j	∣∣j	NOUN
ejpam-4850	22	14	′(a	′(a	ADJ
ejpam-4850	22	15	)	)	PUNCT
ejpam-4850	22	16	∣∣+	∣∣+	X
ejpam-4850	22	17	∣∣j	∣∣j	NOUN
ejpam-4850	22	18	′(b	′(b	NOUN
ejpam-4850	22	19	)	)	PUNCT
ejpam-4850	22	20	∣∣	∣∣	X
ejpam-4850	22	21	)	)	PUNCT
ejpam-4850	22	22	.	.	PUNCT
ejpam-4850	23	1	(	(	PUNCT
ejpam-4850	23	2	2	2	X
ejpam-4850	23	3	)	)	PUNCT
ejpam-4850	23	4	this	this	DET
ejpam-4850	23	5	estimate	estimate	NOUN
ejpam-4850	23	6	holds	hold	VERB
ejpam-4850	23	7	even	even	ADV
ejpam-4850	23	8	for	for	ADP
ejpam-4850	23	9	the	the	DET
ejpam-4850	23	10	right	right	ADJ
ejpam-4850	23	11	part	part	NOUN
ejpam-4850	23	12	of	of	ADP
ejpam-4850	23	13	inequality	inequality	NOUN
ejpam-4850	23	14	(	(	PUNCT
ejpam-4850	23	15	1	1	NUM
ejpam-4850	23	16	)	)	PUNCT
ejpam-4850	23	17	,	,	PUNCT
ejpam-4850	23	18	also	also	ADV
ejpam-4850	23	19	known	know	VERB
ejpam-4850	23	20	as	as	ADP
ejpam-4850	23	21	the	the	DET
ejpam-4850	23	22	trapezoid	trapezoid	ADJ
ejpam-4850	23	23	inequality	inequality	NOUN
ejpam-4850	23	24	,	,	PUNCT
ejpam-4850	23	25	as	as	SCONJ
ejpam-4850	23	26	was	be	AUX
ejpam-4850	23	27	proved	prove	VERB
ejpam-4850	23	28	by	by	ADP
ejpam-4850	23	29	dragomir	dragomir	NOUN
ejpam-4850	23	30	and	and	CCONJ
ejpam-4850	23	31	agarwal	agarwal	PROPN
ejpam-4850	23	32	in	in	ADP
ejpam-4850	23	33	[	[	X
ejpam-4850	23	34	6].∣∣∣∣∣∣j	6].∣∣∣∣∣∣j	X
ejpam-4850	23	35	(	(	PUNCT
ejpam-4850	23	36	a)+j	a)+j	PROPN
ejpam-4850	23	37	(	(	PUNCT
ejpam-4850	23	38	b	b	NOUN
ejpam-4850	23	39	)	)	PUNCT
ejpam-4850	23	40	2	2	NUM
ejpam-4850	23	41	−	−	NOUN
ejpam-4850	23	42	1	1	NUM
ejpam-4850	23	43	b−a	b−a	NOUN
ejpam-4850	23	44	b∫	b∫	PROPN
ejpam-4850	23	45	a	a	DET
ejpam-4850	23	46	j	j	PROPN
ejpam-4850	23	47	(	(	PUNCT
ejpam-4850	23	48	t)dt	t)dt	PROPN
ejpam-4850	23	49	∣∣∣∣∣∣	∣∣∣∣∣∣	ADJ
ejpam-4850	23	50	≤	≤	X
ejpam-4850	23	51	b−a	b−a	X
ejpam-4850	23	52	8	8	NUM
ejpam-4850	23	53	(	(	PUNCT
ejpam-4850	23	54	∣∣j	∣∣j	NOUN
ejpam-4850	23	55	′(a	′(a	ADJ
ejpam-4850	23	56	)	)	PUNCT
ejpam-4850	23	57	∣∣+	∣∣+	X
ejpam-4850	23	58	∣∣j	∣∣j	NOUN
ejpam-4850	23	59	′(b	′(b	NOUN
ejpam-4850	23	60	)	)	PUNCT
ejpam-4850	23	61	∣∣	∣∣	X
ejpam-4850	23	62	)	)	PUNCT
ejpam-4850	23	63	.	.	PUNCT
ejpam-4850	24	1	(	(	PUNCT
ejpam-4850	24	2	3	3	X
ejpam-4850	24	3	)	)	PUNCT
ejpam-4850	24	4	in	in	ADP
ejpam-4850	24	5	[	[	X
ejpam-4850	24	6	11	11	NUM
ejpam-4850	24	7	]	]	PUNCT
ejpam-4850	24	8	,	,	PUNCT
ejpam-4850	24	9	alomari	alomari	PROPN
ejpam-4850	24	10	et	et	PROPN
ejpam-4850	24	11	al	al	PROPN
ejpam-4850	24	12	.	.	PROPN
ejpam-4850	24	13	gave	give	VERB
ejpam-4850	24	14	a	a	DET
ejpam-4850	24	15	companion	companion	NOUN
ejpam-4850	24	16	of	of	ADP
ejpam-4850	24	17	ostrowski	ostrowski	ADJ
ejpam-4850	24	18	inequality	inequality	NOUN
ejpam-4850	24	19	for	for	ADP
ejpam-4850	24	20	the	the	DET
ejpam-4850	24	21	same	same	ADJ
ejpam-4850	24	22	classe	classe	NOUN
ejpam-4850	24	23	of	of	ADP
ejpam-4850	24	24	functions	function	NOUN
ejpam-4850	24	25	which	which	PRON
ejpam-4850	24	26	represents	represent	VERB
ejpam-4850	24	27	a	a	DET
ejpam-4850	24	28	generalization	generalization	NOUN
ejpam-4850	24	29	of	of	ADP
ejpam-4850	24	30	the	the	DET
ejpam-4850	24	31	two	two	NUM
ejpam-4850	24	32	previous	previous	ADJ
ejpam-4850	24	33	results	result	NOUN
ejpam-4850	24	34	as	as	SCONJ
ejpam-4850	24	35	follows	follow	VERB
ejpam-4850	24	36	∣∣∣∣∣∣j	∣∣∣∣∣∣j	NOUN
ejpam-4850	24	37	(	(	PUNCT
ejpam-4850	24	38	x)+j	x)+j	PROPN
ejpam-4850	24	39	(	(	PUNCT
ejpam-4850	24	40	a+b−x	a+b−x	PROPN
ejpam-4850	24	41	)	)	PUNCT
ejpam-4850	24	42	2	2	NUM
ejpam-4850	24	43	−	−	PROPN
ejpam-4850	24	44	1	1	NUM
ejpam-4850	24	45	b−a	b−a	NOUN
ejpam-4850	24	46	b∫	b∫	PROPN
ejpam-4850	25	1	a	a	DET
ejpam-4850	25	2	j	j	PROPN
ejpam-4850	25	3	(	(	PUNCT
ejpam-4850	25	4	t)dt	t)dt	PROPN
ejpam-4850	25	5	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4850	25	6	≤	≤	NOUN
ejpam-4850	25	7	(	(	PUNCT
ejpam-4850	25	8	x−a)2	x−a)2	NUM
ejpam-4850	25	9	6(b−a	6(b−a	NOUN
ejpam-4850	25	10	)	)	PUNCT
ejpam-4850	25	11	(	(	PUNCT
ejpam-4850	25	12	∣∣j	∣∣j	NOUN
ejpam-4850	25	13	′(a	′(a	ADV
ejpam-4850	25	14	)	)	PUNCT
ejpam-4850	25	15	∣∣+	∣∣+	X
ejpam-4850	25	16	∣∣j	∣∣j	NOUN
ejpam-4850	25	17	′(b	′(b	NOUN
ejpam-4850	25	18	)	)	PUNCT
ejpam-4850	25	19	∣∣)+	∣∣)+	PROPN
ejpam-4850	25	20	8(x−a)2	8(x−a)2	NUM
ejpam-4850	25	21	+	+	PROPN
ejpam-4850	25	22	3(a+b−2x)2	3(a+b−2x)2	NUM
ejpam-4850	25	23	24(b−a	24(b−a	NUM
ejpam-4850	25	24	)	)	PUNCT
ejpam-4850	25	25	(	(	PUNCT
ejpam-4850	25	26	∣∣j	∣∣j	NOUN
ejpam-4850	25	27	′(x	′(x	NOUN
ejpam-4850	25	28	)	)	PUNCT
ejpam-4850	25	29	∣∣+	∣∣+	NOUN
ejpam-4850	25	30	∣∣j	∣∣j	NOUN
ejpam-4850	25	31	′(a+	′(a+	NOUN
ejpam-4850	25	32	b−	b−	NOUN
ejpam-4850	25	33	x	x	SYM
ejpam-4850	25	34	)	)	PUNCT
ejpam-4850	25	35	∣∣	∣∣	X
ejpam-4850	25	36	)	)	PUNCT
ejpam-4850	25	37	.	.	PUNCT
ejpam-4850	26	1	note	note	VERB
ejpam-4850	26	2	that	that	SCONJ
ejpam-4850	26	3	both	both	DET
ejpam-4850	26	4	inequalities	inequality	NOUN
ejpam-4850	26	5	(	(	PUNCT
ejpam-4850	26	6	2	2	NUM
ejpam-4850	26	7	)	)	PUNCT
ejpam-4850	26	8	and	and	CCONJ
ejpam-4850	26	9	(	(	PUNCT
ejpam-4850	26	10	3	3	X
ejpam-4850	26	11	)	)	PUNCT
ejpam-4850	26	12	can	can	AUX
ejpam-4850	26	13	be	be	AUX
ejpam-4850	26	14	derived	derive	VERB
ejpam-4850	26	15	from	from	ADP
ejpam-4850	26	16	the	the	DET
ejpam-4850	26	17	preceding	precede	VERB
ejpam-4850	26	18	result	result	NOUN
ejpam-4850	26	19	.	.	PUNCT
ejpam-4850	27	1	specifically	specifically	ADV
ejpam-4850	27	2	,	,	PUNCT
ejpam-4850	27	3	the	the	DET
ejpam-4850	27	4	trapezoid	trapezoid	ADJ
ejpam-4850	27	5	type	type	NOUN
ejpam-4850	27	6	inequality	inequality	NOUN
ejpam-4850	27	7	is	be	AUX
ejpam-4850	27	8	obtained	obtain	VERB
ejpam-4850	27	9	for	for	ADP
ejpam-4850	27	10	x	x	X
ejpam-4850	27	11	=	=	PUNCT
ejpam-4850	27	12	a	a	NOUN
ejpam-4850	27	13	,	,	PUNCT
ejpam-4850	27	14	whereas	whereas	SCONJ
ejpam-4850	27	15	midpoint	midpoint	NOUN
ejpam-4850	27	16	inequality	inequality	NOUN
ejpam-4850	27	17	can	can	AUX
ejpam-4850	27	18	be	be	AUX
ejpam-4850	27	19	deduced	deduce	VERB
ejpam-4850	27	20	by	by	ADP
ejpam-4850	27	21	substituting	substitute	VERB
ejpam-4850	27	22	x	x	X
ejpam-4850	27	23	=	=	SYM
ejpam-4850	27	24	a+b	a+b	NUM
ejpam-4850	27	25	2	2	NUM
ejpam-4850	27	26	and	and	CCONJ
ejpam-4850	27	27	utilizing	utilize	VERB
ejpam-4850	27	28	the	the	DET
ejpam-4850	27	29	convexity	convexity	NOUN
ejpam-4850	27	30	of	of	ADP
ejpam-4850	27	31	|j	|j	NOUN
ejpam-4850	27	32	′|	′|	NUM
ejpam-4850	27	33	,	,	PUNCT
ejpam-4850	27	34	i.e.	i.e.	X
ejpam-4850	27	35	,∣∣j	,∣∣j	PUNCT
ejpam-4850	27	36	′	′	NUM
ejpam-4850	27	37	(	(	PUNCT
ejpam-4850	27	38	a+b	a+b	NUM
ejpam-4850	27	39	2	2	NUM
ejpam-4850	27	40	)	)	PUNCT
ejpam-4850	27	41	∣∣	∣∣	PROPN
ejpam-4850	27	42	≤	≤	PROPN
ejpam-4850	27	43	|j	|j	PUNCT
ejpam-4850	27	44	′(a)|+|j	′(a)|+|j	PUNCT
ejpam-4850	28	1	′(b)|	′(b)|	VERB
ejpam-4850	28	2	2	2	NUM
ejpam-4850	28	3	.	.	PUNCT
ejpam-4850	29	1	on	on	ADP
ejpam-4850	29	2	the	the	DET
ejpam-4850	29	3	other	other	ADJ
ejpam-4850	29	4	hand	hand	NOUN
ejpam-4850	29	5	,	,	PUNCT
ejpam-4850	29	6	in	in	ADP
ejpam-4850	29	7	their	their	PRON
ejpam-4850	29	8	paper	paper	NOUN
ejpam-4850	29	9	[	[	X
ejpam-4850	29	10	9	9	NUM
ejpam-4850	29	11	]	]	PUNCT
ejpam-4850	29	12	,	,	PUNCT
ejpam-4850	29	13	hudzik	hudzik	PROPN
ejpam-4850	29	14	and	and	CCONJ
ejpam-4850	29	15	maligranda	maligranda	PROPN
ejpam-4850	29	16	explored	explore	VERB
ejpam-4850	29	17	the	the	DET
ejpam-4850	29	18	class	class	NOUN
ejpam-4850	29	19	of	of	ADP
ejpam-4850	29	20	s	s	NOUN
ejpam-4850	29	21	-	-	ADJ
ejpam-4850	29	22	convex	convex	ADJ
ejpam-4850	29	23	functions	function	NOUN
ejpam-4850	29	24	in	in	ADP
ejpam-4850	29	25	the	the	DET
ejpam-4850	29	26	second	second	ADJ
ejpam-4850	29	27	sense	sense	NOUN
ejpam-4850	29	28	.	.	PUNCT
ejpam-4850	30	1	this	this	DET
ejpam-4850	30	2	class	class	NOUN
ejpam-4850	30	3	is	be	AUX
ejpam-4850	30	4	defined	define	VERB
ejpam-4850	30	5	by	by	ADP
ejpam-4850	30	6	the	the	DET
ejpam-4850	30	7	following	follow	VERB
ejpam-4850	30	8	property	property	NOUN
ejpam-4850	30	9	:	:	PUNCT
ejpam-4850	30	10	a	a	DET
ejpam-4850	30	11	function	function	NOUN
ejpam-4850	30	12	j	j	NOUN
ejpam-4850	30	13	:	:	PUNCT
ejpam-4850	31	1	[	[	X
ejpam-4850	31	2	0,∞	0,∞	NOUN
ejpam-4850	31	3	)	)	PUNCT
ejpam-4850	31	4	→	→	PUNCT
ejpam-4850	31	5	r	r	NOUN
ejpam-4850	31	6	is	be	AUX
ejpam-4850	31	7	said	say	VERB
ejpam-4850	31	8	to	to	PART
ejpam-4850	31	9	be	be	AUX
ejpam-4850	31	10	s	s	NOUN
ejpam-4850	31	11	-	-	NOUN
ejpam-4850	31	12	convex	convex	ADJ
ejpam-4850	31	13	in	in	ADP
ejpam-4850	31	14	the	the	DET
ejpam-4850	31	15	second	second	ADJ
ejpam-4850	31	16	sense	sense	NOUN
ejpam-4850	31	17	if	if	SCONJ
ejpam-4850	31	18	the	the	DET
ejpam-4850	31	19	inequality	inequality	NOUN
ejpam-4850	31	20	j	j	PROPN
ejpam-4850	31	21	(	(	PUNCT
ejpam-4850	31	22	κu+	κu+	PROPN
ejpam-4850	31	23	(	(	PUNCT
ejpam-4850	31	24	1−	1−	NUM
ejpam-4850	31	25	κ	κ	NOUN
ejpam-4850	31	26	)	)	PUNCT
ejpam-4850	31	27	v	v	NOUN
ejpam-4850	31	28	)	)	PUNCT
ejpam-4850	31	29	≤	≤	NOUN
ejpam-4850	31	30	κsj	κsj	NOUN
ejpam-4850	31	31	(	(	PUNCT
ejpam-4850	31	32	u	u	NOUN
ejpam-4850	31	33	)	)	PUNCT
ejpam-4850	31	34	+	+	CCONJ
ejpam-4850	31	35	(	(	PUNCT
ejpam-4850	31	36	1−	1−	NUM
ejpam-4850	31	37	κ)s	κ)s	X
ejpam-4850	31	38	j	j	PROPN
ejpam-4850	31	39	(	(	PUNCT
ejpam-4850	31	40	v	v	NOUN
ejpam-4850	31	41	)	)	PUNCT
ejpam-4850	31	42	holds	hold	VERB
ejpam-4850	31	43	for	for	ADP
ejpam-4850	31	44	all	all	DET
ejpam-4850	31	45	u	u	NOUN
ejpam-4850	31	46	,	,	PUNCT
ejpam-4850	31	47	v	v	NOUN
ejpam-4850	31	48	∈	∈	X
ejpam-4850	32	1	i	i	PRON
ejpam-4850	32	2	,	,	PUNCT
ejpam-4850	32	3	κ	κ	PROPN
ejpam-4850	32	4	∈	∈	PROPN
ejpam-4850	33	1	[	[	X
ejpam-4850	33	2	0	0	NUM
ejpam-4850	33	3	,	,	PUNCT
ejpam-4850	33	4	1	1	NUM
ejpam-4850	33	5	]	]	PUNCT
ejpam-4850	33	6	,	,	PUNCT
ejpam-4850	33	7	and	and	CCONJ
ejpam-4850	33	8	s	s	X
ejpam-4850	33	9	∈	∈	PROPN
ejpam-4850	33	10	(	(	PUNCT
ejpam-4850	33	11	0	0	NUM
ejpam-4850	33	12	,	,	PUNCT
ejpam-4850	33	13	1	1	NUM
ejpam-4850	33	14	]	]	PUNCT
ejpam-4850	33	15	.	.	PUNCT
ejpam-4850	34	1	the	the	DET
ejpam-4850	34	2	counterpart	counterpart	NOUN
ejpam-4850	34	3	of	of	ADP
ejpam-4850	34	4	the	the	DET
ejpam-4850	34	5	hermite	hermite	PROPN
ejpam-4850	34	6	-	-	PUNCT
ejpam-4850	34	7	hadamard	hadamard	ADJ
ejpam-4850	34	8	inequality	inequality	NOUN
ejpam-4850	34	9	for	for	ADP
ejpam-4850	34	10	s	s	NOUN
ejpam-4850	34	11	-	-	PUNCT
ejpam-4850	34	12	convex	convex	ADJ
ejpam-4850	34	13	functions	function	NOUN
ejpam-4850	34	14	was	be	AUX
ejpam-4850	34	15	introduced	introduce	VERB
ejpam-4850	34	16	by	by	ADP
ejpam-4850	34	17	dragomir	dragomir	NOUN
ejpam-4850	34	18	and	and	CCONJ
ejpam-4850	34	19	fitzpatrick	fitzpatrick	NOUN
ejpam-4850	34	20	in	in	ADP
ejpam-4850	34	21	[	[	X
ejpam-4850	34	22	5	5	NUM
ejpam-4850	34	23	]	]	PUNCT
ejpam-4850	34	24	in	in	ADP
ejpam-4850	34	25	the	the	DET
ejpam-4850	34	26	following	following	ADJ
ejpam-4850	34	27	manner	manner	NOUN
ejpam-4850	34	28	.	.	PUNCT
ejpam-4850	35	1	2s−1j	2s−1j	NUM
ejpam-4850	35	2	(	(	PUNCT
ejpam-4850	35	3	a+b	a+b	NUM
ejpam-4850	35	4	2	2	NUM
ejpam-4850	35	5	)	)	PUNCT
ejpam-4850	35	6	≤	≤	NOUN
ejpam-4850	35	7	1	1	NUM
ejpam-4850	35	8	b−a	b−a	NOUN
ejpam-4850	35	9	b∫	b∫	PROPN
ejpam-4850	35	10	a	a	DET
ejpam-4850	35	11	j	j	PROPN
ejpam-4850	35	12	(	(	PUNCT
ejpam-4850	35	13	t)dt	t)dt	PROPN
ejpam-4850	35	14	≤	≤	PROPN
ejpam-4850	35	15	j	j	PROPN
ejpam-4850	35	16	(	(	PUNCT
ejpam-4850	35	17	a)+j	a)+j	PROPN
ejpam-4850	35	18	(	(	PUNCT
ejpam-4850	35	19	b	b	NOUN
ejpam-4850	35	20	)	)	PUNCT
ejpam-4850	35	21	s+1	s+1	NOUN
ejpam-4850	35	22	.	.	PUNCT
ejpam-4850	36	1	(	(	PUNCT
ejpam-4850	36	2	4	4	X
ejpam-4850	36	3	)	)	PUNCT
ejpam-4850	36	4	w.	w.	NOUN
ejpam-4850	36	5	saleh	saleh	PROPN
ejpam-4850	36	6	et	et	PROPN
ejpam-4850	36	7	al	al	PROPN
ejpam-4850	36	8	.	.	PUNCT
ejpam-4850	36	9	/	/	SYM
ejpam-4850	36	10	eur	eur	PROPN
ejpam-4850	36	11	.	.	PUNCT
ejpam-4850	37	1	j.	j.	PROPN
ejpam-4850	37	2	pure	pure	PROPN
ejpam-4850	37	3	appl	appl	PROPN
ejpam-4850	37	4	.	.	PROPN
ejpam-4850	37	5	math	math	PROPN
ejpam-4850	37	6	,	,	PUNCT
ejpam-4850	37	7	16	16	NUM
ejpam-4850	37	8	(	(	PUNCT
ejpam-4850	37	9	3	3	NUM
ejpam-4850	37	10	)	)	PUNCT
ejpam-4850	37	11	(	(	PUNCT
ejpam-4850	37	12	2023	2023	NUM
ejpam-4850	37	13	)	)	PUNCT
ejpam-4850	37	14	,	,	PUNCT
ejpam-4850	37	15	1359	1359	NUM
ejpam-4850	37	16	-	-	SYM
ejpam-4850	37	17	1380	1380	NUM
ejpam-4850	37	18	1361	1361	NUM
ejpam-4850	37	19	recently	recently	ADV
ejpam-4850	37	20	,	,	PUNCT
ejpam-4850	37	21	scientists	scientist	NOUN
ejpam-4850	37	22	and	and	CCONJ
ejpam-4850	37	23	engineers	engineer	NOUN
ejpam-4850	37	24	have	have	AUX
ejpam-4850	37	25	taken	take	VERB
ejpam-4850	37	26	a	a	DET
ejpam-4850	37	27	keen	keen	ADJ
ejpam-4850	37	28	interest	interest	NOUN
ejpam-4850	37	29	in	in	ADP
ejpam-4850	37	30	fractal	fractal	ADJ
ejpam-4850	37	31	sets	set	NOUN
ejpam-4850	37	32	and	and	CCONJ
ejpam-4850	37	33	fractal	fractal	ADJ
ejpam-4850	37	34	theory	theory	NOUN
ejpam-4850	37	35	.	.	PUNCT
ejpam-4850	38	1	according	accord	VERB
ejpam-4850	38	2	to	to	ADP
ejpam-4850	38	3	mandelbrot	mandelbrot	PROPN
ejpam-4850	38	4	[	[	X
ejpam-4850	38	5	8	8	NUM
ejpam-4850	38	6	,	,	PUNCT
ejpam-4850	38	7	15	15	NUM
ejpam-4850	38	8	]	]	PUNCT
ejpam-4850	38	9	,	,	PUNCT
ejpam-4850	38	10	a	a	DET
ejpam-4850	38	11	set	set	NOUN
ejpam-4850	38	12	is	be	AUX
ejpam-4850	38	13	considered	consider	VERB
ejpam-4850	38	14	fractal	fractal	ADJ
ejpam-4850	38	15	when	when	SCONJ
ejpam-4850	38	16	its	its	PRON
ejpam-4850	38	17	hausdorff	hausdorff	NOUN
ejpam-4850	38	18	dimension	dimension	NOUN
ejpam-4850	38	19	exceeds	exceed	VERB
ejpam-4850	38	20	its	its	PRON
ejpam-4850	38	21	topological	topological	ADJ
ejpam-4850	38	22	dimension	dimension	NOUN
ejpam-4850	38	23	.	.	PUNCT
ejpam-4850	39	1	recently	recently	ADV
ejpam-4850	39	2	,	,	PUNCT
ejpam-4850	39	3	several	several	ADJ
ejpam-4850	39	4	studies	study	NOUN
ejpam-4850	39	5	have	have	AUX
ejpam-4850	39	6	been	be	AUX
ejpam-4850	39	7	conducted	conduct	VERB
ejpam-4850	39	8	with	with	ADP
ejpam-4850	39	9	the	the	DET
ejpam-4850	39	10	aim	aim	NOUN
ejpam-4850	39	11	of	of	ADP
ejpam-4850	39	12	extending	extend	VERB
ejpam-4850	39	13	some	some	DET
ejpam-4850	39	14	results	result	NOUN
ejpam-4850	39	15	related	relate	VERB
ejpam-4850	39	16	to	to	ADP
ejpam-4850	39	17	integral	integral	ADJ
ejpam-4850	39	18	inequalities	inequality	NOUN
ejpam-4850	39	19	to	to	ADP
ejpam-4850	39	20	fractal	fractal	ADJ
ejpam-4850	39	21	calculus	calculus	NOUN
ejpam-4850	39	22	,	,	PUNCT
ejpam-4850	39	23	using	use	VERB
ejpam-4850	39	24	various	various	ADJ
ejpam-4850	39	25	forms	form	NOUN
ejpam-4850	39	26	of	of	ADP
ejpam-4850	39	27	generalized	generalized	ADJ
ejpam-4850	39	28	convexity	convexity	NOUN
ejpam-4850	39	29	.	.	PUNCT
ejpam-4850	40	1	here	here	ADV
ejpam-4850	40	2	are	be	AUX
ejpam-4850	40	3	some	some	DET
ejpam-4850	40	4	references	reference	NOUN
ejpam-4850	40	5	[	[	X
ejpam-4850	40	6	1–4	1–4	NOUN
ejpam-4850	40	7	,	,	PUNCT
ejpam-4850	40	8	7	7	NUM
ejpam-4850	40	9	,	,	PUNCT
ejpam-4850	40	10	10	10	NUM
ejpam-4850	40	11	,	,	PUNCT
ejpam-4850	40	12	12	12	NUM
ejpam-4850	40	13	,	,	PUNCT
ejpam-4850	40	14	13	13	NUM
ejpam-4850	40	15	,	,	PUNCT
ejpam-4850	40	16	16–19	16–19	NUM
ejpam-4850	40	17	,	,	PUNCT
ejpam-4850	40	18	23	23	NUM
ejpam-4850	40	19	]	]	PUNCT
ejpam-4850	40	20	.	.	PUNCT
ejpam-4850	41	1	yang	yang	PROPN
ejpam-4850	41	2	’s	’s	PART
ejpam-4850	41	3	research	research	NOUN
ejpam-4850	41	4	in	in	ADP
ejpam-4850	41	5	[	[	X
ejpam-4850	41	6	24	24	NUM
ejpam-4850	41	7	]	]	PUNCT
ejpam-4850	41	8	focuses	focus	VERB
ejpam-4850	41	9	extensively	extensively	ADV
ejpam-4850	41	10	on	on	ADP
ejpam-4850	41	11	investigating	investigate	VERB
ejpam-4850	41	12	and	and	CCONJ
ejpam-4850	41	13	advancing	advance	VERB
ejpam-4850	41	14	local	local	ADJ
ejpam-4850	41	15	fractional	fractional	ADJ
ejpam-4850	41	16	calculus	calculus	NOUN
ejpam-4850	41	17	.	.	PUNCT
ejpam-4850	42	1	in	in	ADP
ejpam-4850	42	2	their	their	PRON
ejpam-4850	42	3	publications	publication	NOUN
ejpam-4850	42	4	[	[	X
ejpam-4850	42	5	24	24	NUM
ejpam-4850	42	6	,	,	PUNCT
ejpam-4850	42	7	25	25	NUM
ejpam-4850	42	8	]	]	PUNCT
ejpam-4850	42	9	,	,	PUNCT
ejpam-4850	42	10	gao	gao	PROPN
ejpam-4850	42	11	-	-	PUNCT
ejpam-4850	42	12	yang	yang	PROPN
ejpam-4850	42	13	-	-	PUNCT
ejpam-4850	42	14	kang	kang	PROPN
ejpam-4850	42	15	proposed	propose	VERB
ejpam-4850	42	16	the	the	DET
ejpam-4850	42	17	concept	concept	NOUN
ejpam-4850	42	18	of	of	ADP
ejpam-4850	42	19	local	local	ADJ
ejpam-4850	42	20	fractional	fractional	ADJ
ejpam-4850	42	21	integral	integral	ADJ
ejpam-4850	42	22	and	and	CCONJ
ejpam-4850	42	23	derivative	derivative	ADJ
ejpam-4850	42	24	.	.	PUNCT
ejpam-4850	43	1	their	their	PRON
ejpam-4850	43	2	definition	definition	NOUN
ejpam-4850	43	3	of	of	ADP
ejpam-4850	43	4	the	the	DET
ejpam-4850	43	5	fractal	fractal	ADJ
ejpam-4850	43	6	set	set	NOUN
ejpam-4850	43	7	of	of	ADP
ejpam-4850	43	8	real	real	ADJ
ejpam-4850	43	9	numbers	number	NOUN
ejpam-4850	43	10	rγ	rγ	PRON
ejpam-4850	43	11	specifies	specify	VERB
ejpam-4850	43	12	the	the	DET
ejpam-4850	43	13	following	follow	VERB
ejpam-4850	43	14	properties	property	NOUN
ejpam-4850	43	15	.	.	PUNCT
ejpam-4850	44	1	if	if	SCONJ
ejpam-4850	44	2	κγ1	κγ1	NOUN
ejpam-4850	44	3	,	,	PUNCT
ejpam-4850	44	4	κ	κ	PROPN
ejpam-4850	44	5	γ	γ	X
ejpam-4850	44	6	2	2	NUM
ejpam-4850	44	7	,	,	PUNCT
ejpam-4850	44	8	and	and	CCONJ
ejpam-4850	44	9	κγ3	κγ3	NOUN
ejpam-4850	44	10	are	be	AUX
ejpam-4850	44	11	within	within	ADP
ejpam-4850	44	12	the	the	DET
ejpam-4850	44	13	set	set	NOUN
ejpam-4850	44	14	rγ	rγ	NOUN
ejpam-4850	44	15	,	,	PUNCT
ejpam-4850	44	16	then	then	ADV
ejpam-4850	44	17	the	the	DET
ejpam-4850	44	18	following	following	ADJ
ejpam-4850	44	19	statements	statement	NOUN
ejpam-4850	44	20	can	can	AUX
ejpam-4850	44	21	be	be	AUX
ejpam-4850	44	22	made	make	VERB
ejpam-4850	44	23	:	:	PUNCT
ejpam-4850	44	24	•	•	NUM
ejpam-4850	44	25	κγ1	κγ1	NOUN
ejpam-4850	44	26	+	+	CCONJ
ejpam-4850	44	27	κγ2	κγ2	NOUN
ejpam-4850	44	28	and	and	CCONJ
ejpam-4850	44	29	κγ1κ	κγ1κ	PROPN
ejpam-4850	44	30	γ	γ	NOUN
ejpam-4850	44	31	2	2	NUM
ejpam-4850	44	32	belongs	belong	VERB
ejpam-4850	44	33	the	the	DET
ejpam-4850	44	34	set	set	NOUN
ejpam-4850	44	35	rγ	rγ	NOUN
ejpam-4850	44	36	,	,	PUNCT
ejpam-4850	44	37	•	•	NUM
ejpam-4850	44	38	κγ1	κγ1	NOUN
ejpam-4850	44	39	+	+	CCONJ
ejpam-4850	44	40	κγ2	κγ2	NOUN
ejpam-4850	44	41	=	=	SYM
ejpam-4850	44	42	κγ2	κγ2	NOUN
ejpam-4850	44	43	+	+	CCONJ
ejpam-4850	44	44	κγ1	κγ1	NOUN
ejpam-4850	44	45	=	=	SYM
ejpam-4850	44	46	(	(	PUNCT
ejpam-4850	44	47	κ1	κ1	NOUN
ejpam-4850	44	48	+	+	CCONJ
ejpam-4850	44	49	κ2	κ2	NOUN
ejpam-4850	44	50	)	)	PUNCT
ejpam-4850	44	51	γ	γ	NOUN
ejpam-4850	44	52	=	=	SYM
ejpam-4850	44	53	(	(	PUNCT
ejpam-4850	44	54	κ2	κ2	PROPN
ejpam-4850	44	55	+	+	CCONJ
ejpam-4850	44	56	κ1	κ1	NOUN
ejpam-4850	44	57	)	)	PUNCT
ejpam-4850	44	58	γ	γ	NOUN
ejpam-4850	44	59	,	,	PUNCT
ejpam-4850	44	60	•	•	NUM
ejpam-4850	44	61	κγ1	κγ1	NOUN
ejpam-4850	44	62	+	+	CCONJ
ejpam-4850	44	63	(	(	PUNCT
ejpam-4850	44	64	κγ2	κγ2	NOUN
ejpam-4850	44	65	+	+	CCONJ
ejpam-4850	44	66	κγ3	κγ3	NOUN
ejpam-4850	44	67	)	)	PUNCT
ejpam-4850	44	68	=	=	PUNCT
ejpam-4850	45	1	(	(	PUNCT
ejpam-4850	45	2	κ1	κ1	NOUN
ejpam-4850	45	3	+	+	CCONJ
ejpam-4850	45	4	κ2	κ2	NOUN
ejpam-4850	45	5	)	)	PUNCT
ejpam-4850	45	6	γ	γ	NOUN
ejpam-4850	45	7	+	+	NUM
ejpam-4850	45	8	κγ3	κγ3	NOUN
ejpam-4850	45	9	,	,	PUNCT
ejpam-4850	45	10	•	•	PROPN
ejpam-4850	45	11	κγ1κ	κγ1κ	PROPN
ejpam-4850	45	12	γ	γ	X
ejpam-4850	45	13	2	2	NUM
ejpam-4850	45	14	=	=	SYM
ejpam-4850	45	15	κγ2κ	κγ2κ	PROPN
ejpam-4850	45	16	γ	γ	X
ejpam-4850	45	17	1	1	NUM
ejpam-4850	45	18	=	=	SYM
ejpam-4850	45	19	(	(	PUNCT
ejpam-4850	45	20	κ1κ2	κ1κ2	NOUN
ejpam-4850	45	21	)	)	PUNCT
ejpam-4850	45	22	γ	γ	X
ejpam-4850	45	23	=	=	SYM
ejpam-4850	45	24	(	(	PUNCT
ejpam-4850	45	25	κ2κ1	κ2κ1	NOUN
ejpam-4850	45	26	)	)	PUNCT
ejpam-4850	45	27	γ	γ	NOUN
ejpam-4850	45	28	,	,	PUNCT
ejpam-4850	45	29	•	•	NUM
ejpam-4850	45	30	κγ1	κγ1	NOUN
ejpam-4850	45	31	(	(	PUNCT
ejpam-4850	45	32	κ	κ	NOUN
ejpam-4850	45	33	γ	γ	X
ejpam-4850	45	34	2κ	2κ	PROPN
ejpam-4850	45	35	γ	γ	NOUN
ejpam-4850	45	36	3	3	NUM
ejpam-4850	45	37	)	)	PUNCT
ejpam-4850	45	38	=	=	SYM
ejpam-4850	46	1	(	(	PUNCT
ejpam-4850	46	2	κγ1κ	κγ1κ	PROPN
ejpam-4850	46	3	γ	γ	PROPN
ejpam-4850	46	4	2)κ	2)κ	NUM
ejpam-4850	46	5	γ	γ	NOUN
ejpam-4850	46	6	3	3	NUM
ejpam-4850	46	7	,	,	PUNCT
ejpam-4850	46	8	•	•	NUM
ejpam-4850	46	9	κγ1	κγ1	NOUN
ejpam-4850	46	10	(	(	PUNCT
ejpam-4850	46	11	κ	κ	NOUN
ejpam-4850	46	12	γ	γ	X
ejpam-4850	46	13	2	2	NUM
ejpam-4850	46	14	+	+	CCONJ
ejpam-4850	46	15	κγ3	κγ3	NOUN
ejpam-4850	46	16	)	)	PUNCT
ejpam-4850	46	17	=	=	SYM
ejpam-4850	46	18	κγ1κ	κγ1κ	PROPN
ejpam-4850	46	19	γ	γ	X
ejpam-4850	46	20	2	2	NUM
ejpam-4850	46	21	+	+	CCONJ
ejpam-4850	46	22	κγ1κ	κγ1κ	PROPN
ejpam-4850	46	23	γ	γ	NOUN
ejpam-4850	46	24	3	3	NUM
ejpam-4850	46	25	,	,	PUNCT
ejpam-4850	46	26	•	•	NOUN
ejpam-4850	46	27	κγ1	κγ1	NOUN
ejpam-4850	46	28	+	+	CCONJ
ejpam-4850	46	29	0γ	0γ	NOUN
ejpam-4850	46	30	=	=	SYM
ejpam-4850	46	31	0γ	0γ	ADJ
ejpam-4850	46	32	+	+	CCONJ
ejpam-4850	46	33	κγ1	κγ1	NOUN
ejpam-4850	46	34	=	=	SYM
ejpam-4850	46	35	κγ1	κγ1	NOUN
ejpam-4850	46	36	and	and	CCONJ
ejpam-4850	46	37	κγ11	κγ11	PROPN
ejpam-4850	46	38	γ	γ	X
ejpam-4850	46	39	=	=	SYM
ejpam-4850	46	40	1γκγ1	1γκγ1	NUM
ejpam-4850	46	41	=	=	NOUN
ejpam-4850	46	42	κγ1	κγ1	NOUN
ejpam-4850	46	43	.	.	PUNCT
ejpam-4850	47	1	lemma	lemma	PROPN
ejpam-4850	47	2	1	1	NUM
ejpam-4850	47	3	(	(	PUNCT
ejpam-4850	47	4	[	[	X
ejpam-4850	47	5	24	24	NUM
ejpam-4850	47	6	]	]	PUNCT
ejpam-4850	47	7	)	)	PUNCT
ejpam-4850	47	8	.	.	PUNCT
ejpam-4850	48	1	let	let	VERB
ejpam-4850	48	2	cγ	cγ	INTJ
ejpam-4850	48	3	(	(	PUNCT
ejpam-4850	48	4	[	[	X
ejpam-4850	48	5	a	a	X
ejpam-4850	48	6	,	,	PUNCT
ejpam-4850	48	7	b	b	NOUN
ejpam-4850	48	8	]	]	X
ejpam-4850	48	9	)	)	PUNCT
ejpam-4850	48	10	be	be	VERB
ejpam-4850	48	11	the	the	DET
ejpam-4850	48	12	set	set	NOUN
ejpam-4850	48	13	of	of	ADP
ejpam-4850	48	14	all	all	DET
ejpam-4850	48	15	local	local	ADJ
ejpam-4850	48	16	fractional	fractional	ADJ
ejpam-4850	48	17	continuous	continuous	ADJ
ejpam-4850	48	18	functions	function	NOUN
ejpam-4850	48	19	on	on	ADP
ejpam-4850	48	20	[	[	X
ejpam-4850	48	21	a	a	X
ejpam-4850	48	22	,	,	PUNCT
ejpam-4850	48	23	b	b	NOUN
ejpam-4850	48	24	]	]	PUNCT
ejpam-4850	48	25	and	and	CCONJ
ejpam-4850	48	26	dγ	dγ	ADP
ejpam-4850	48	27	(	(	PUNCT
ejpam-4850	48	28	[	[	X
ejpam-4850	48	29	a	a	X
ejpam-4850	48	30	,	,	PUNCT
ejpam-4850	48	31	b	b	NOUN
ejpam-4850	48	32	]	]	X
ejpam-4850	48	33	)	)	PUNCT
ejpam-4850	48	34	the	the	DET
ejpam-4850	48	35	set	set	NOUN
ejpam-4850	48	36	of	of	ADP
ejpam-4850	48	37	all	all	DET
ejpam-4850	48	38	local	local	ADJ
ejpam-4850	48	39	fractional	fractional	ADJ
ejpam-4850	48	40	differentiable	differentiable	ADJ
ejpam-4850	48	41	functions	function	NOUN
ejpam-4850	48	42	on	on	ADP
ejpam-4850	48	43	[	[	X
ejpam-4850	48	44	a	a	X
ejpam-4850	48	45	,	,	PUNCT
ejpam-4850	48	46	b	b	NOUN
ejpam-4850	48	47	]	]	X
ejpam-4850	48	48	.	.	PUNCT
ejpam-4850	49	1	it	it	PRON
ejpam-4850	49	2	can	can	AUX
ejpam-4850	49	3	then	then	ADV
ejpam-4850	49	4	be	be	AUX
ejpam-4850	49	5	stated	state	VERB
ejpam-4850	49	6	that	that	SCONJ
ejpam-4850	49	7	:	:	PUNCT
ejpam-4850	49	8	(	(	PUNCT
ejpam-4850	49	9	i	i	NOUN
ejpam-4850	49	10	)	)	PUNCT
ejpam-4850	49	11	suppose	suppose	VERB
ejpam-4850	49	12	that	that	SCONJ
ejpam-4850	49	13	j	j	PROPN
ejpam-4850	49	14	(	(	PUNCT
ejpam-4850	49	15	t	t	PROPN
ejpam-4850	49	16	)	)	PUNCT
ejpam-4850	49	17	=	=	SYM
ejpam-4850	49	18	q(γ	q(γ	PROPN
ejpam-4850	49	19	)	)	PUNCT
ejpam-4850	49	20	(	(	PUNCT
ejpam-4850	49	21	t	t	X
ejpam-4850	49	22	)	)	PUNCT
ejpam-4850	49	23	∈	∈	PROPN
ejpam-4850	49	24	cγ	cγ	NOUN
ejpam-4850	49	25	[	[	X
ejpam-4850	49	26	a	a	X
ejpam-4850	49	27	,	,	PUNCT
ejpam-4850	49	28	b	b	NOUN
ejpam-4850	49	29	]	]	PUNCT
ejpam-4850	49	30	,	,	PUNCT
ejpam-4850	49	31	then	then	ADV
ejpam-4850	49	32	we	we	PRON
ejpam-4850	49	33	have	have	AUX
ejpam-4850	49	34	ai	ai	VERB
ejpam-4850	49	35	γ	γ	PROPN
ejpam-4850	49	36	b	b	PROPN
ejpam-4850	49	37	j	j	PROPN
ejpam-4850	49	38	(	(	PUNCT
ejpam-4850	49	39	t	t	PROPN
ejpam-4850	49	40	)	)	PUNCT
ejpam-4850	49	41	=	=	SYM
ejpam-4850	50	1	q	q	X
ejpam-4850	51	1	(	(	PUNCT
ejpam-4850	51	2	b)−q	b)−q	X
ejpam-4850	51	3	(	(	PUNCT
ejpam-4850	51	4	a	a	NOUN
ejpam-4850	51	5	)	)	PUNCT
ejpam-4850	51	6	.	.	PUNCT
ejpam-4850	52	1	(	(	PUNCT
ejpam-4850	52	2	ii	ii	NOUN
ejpam-4850	52	3	)	)	PUNCT
ejpam-4850	52	4	suppose	suppose	VERB
ejpam-4850	52	5	that	that	SCONJ
ejpam-4850	52	6	j	j	PROPN
ejpam-4850	52	7	,	,	PUNCT
ejpam-4850	52	8	q	q	PROPN
ejpam-4850	52	9	∈	∈	NOUN
ejpam-4850	52	10	dγ	dγ	ADP
ejpam-4850	52	11	[	[	X
ejpam-4850	52	12	a	a	X
ejpam-4850	52	13	,	,	PUNCT
ejpam-4850	52	14	b	b	NOUN
ejpam-4850	52	15	]	]	X
ejpam-4850	52	16	and	and	CCONJ
ejpam-4850	52	17	j	j	PROPN
ejpam-4850	52	18	(	(	PUNCT
ejpam-4850	52	19	γ	γ	PROPN
ejpam-4850	52	20	)	)	PUNCT
ejpam-4850	52	21	(	(	PUNCT
ejpam-4850	52	22	t	t	PROPN
ejpam-4850	52	23	)	)	PUNCT
ejpam-4850	52	24	,	,	PUNCT
ejpam-4850	52	25	q(γ	q(γ	PROPN
ejpam-4850	52	26	)	)	PUNCT
ejpam-4850	52	27	(	(	PUNCT
ejpam-4850	52	28	t	t	X
ejpam-4850	52	29	)	)	PUNCT
ejpam-4850	52	30	∈	∈	PROPN
ejpam-4850	52	31	cγ	cγ	NOUN
ejpam-4850	52	32	[	[	X
ejpam-4850	52	33	a	a	X
ejpam-4850	52	34	,	,	PUNCT
ejpam-4850	52	35	b	b	NOUN
ejpam-4850	52	36	]	]	X
ejpam-4850	52	37	,	,	PUNCT
ejpam-4850	52	38	then	then	ADV
ejpam-4850	52	39	we	we	PRON
ejpam-4850	52	40	have	have	AUX
ejpam-4850	52	41	ai	ai	VERB
ejpam-4850	52	42	γ	γ	PROPN
ejpam-4850	52	43	b	b	PROPN
ejpam-4850	52	44	j	j	PROPN
ejpam-4850	52	45	(	(	PUNCT
ejpam-4850	52	46	t)q(γ	t)q(γ	PROPN
ejpam-4850	52	47	)	)	PUNCT
ejpam-4850	52	48	(	(	PUNCT
ejpam-4850	52	49	t	t	NOUN
ejpam-4850	52	50	)	)	PUNCT
ejpam-4850	52	51	=	=	SYM
ejpam-4850	52	52	j	j	PROPN
ejpam-4850	52	53	(	(	PUNCT
ejpam-4850	52	54	t)q	t)q	X
ejpam-4850	52	55	(	(	PUNCT
ejpam-4850	52	56	t)|	t)|	NOUN
ejpam-4850	52	57	b	b	PROPN
ejpam-4850	52	58	a	a	PRON
ejpam-4850	52	59	−	−	NOUN
ejpam-4850	52	60	ai	ai	NOUN
ejpam-4850	52	61	γ	γ	PROPN
ejpam-4850	52	62	b	b	PROPN
ejpam-4850	52	63	j	j	PROPN
ejpam-4850	52	64	(	(	PUNCT
ejpam-4850	52	65	γ	γ	PROPN
ejpam-4850	52	66	)	)	PUNCT
ejpam-4850	52	67	(	(	PUNCT
ejpam-4850	52	68	t)q	t)q	X
ejpam-4850	52	69	(	(	PUNCT
ejpam-4850	52	70	t	t	PROPN
ejpam-4850	52	71	)	)	PUNCT
ejpam-4850	52	72	.	.	PUNCT
ejpam-4850	53	1	lemma	lemma	PROPN
ejpam-4850	53	2	2	2	NUM
ejpam-4850	53	3	(	(	PUNCT
ejpam-4850	53	4	[	[	X
ejpam-4850	53	5	24	24	NUM
ejpam-4850	53	6	]	]	PUNCT
ejpam-4850	53	7	)	)	PUNCT
ejpam-4850	53	8	.	.	PUNCT
ejpam-4850	54	1	for	for	ADP
ejpam-4850	54	2	j	j	PROPN
ejpam-4850	54	3	(	(	PUNCT
ejpam-4850	54	4	t	t	PROPN
ejpam-4850	54	5	)	)	PUNCT
ejpam-4850	54	6	=	=	NOUN
ejpam-4850	55	1	tkγ	tkγ	INTJ
ejpam-4850	55	2	,	,	PUNCT
ejpam-4850	55	3	we	we	PRON
ejpam-4850	55	4	have	have	AUX
ejpam-4850	55	5	following	follow	VERB
ejpam-4850	55	6	equations	equation	NOUN
ejpam-4850	55	7	dγtkγ	dγtkγ	VERB
ejpam-4850	55	8	dtγ	dtγ	X
ejpam-4850	55	9	=	=	SYM
ejpam-4850	55	10	γ(1+kγ	γ(1+kγ	PROPN
ejpam-4850	55	11	)	)	PUNCT
ejpam-4850	55	12	γ(1+(k−1)γ	γ(1+(k−1)γ	PROPN
ejpam-4850	55	13	)	)	PUNCT
ejpam-4850	55	14	t	t	PROPN
ejpam-4850	55	15	(	(	PUNCT
ejpam-4850	55	16	k−1)γ	k−1)γ	PROPN
ejpam-4850	55	17	,	,	PUNCT
ejpam-4850	55	18	1	1	NUM
ejpam-4850	55	19	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	55	20	)	)	PUNCT
ejpam-4850	55	21	b∫	b∫	PROPN
ejpam-4850	55	22	a	a	DET
ejpam-4850	55	23	tkγ	tkγ	NOUN
ejpam-4850	55	24	(	(	PUNCT
ejpam-4850	55	25	dt)γ	dt)γ	PROPN
ejpam-4850	55	26	=	=	SYM
ejpam-4850	55	27	γ(1+kγ	γ(1+kγ	PROPN
ejpam-4850	55	28	)	)	PUNCT
ejpam-4850	55	29	γ(1+(k+1)γ	γ(1+(k+1)γ	PROPN
ejpam-4850	55	30	)	)	PUNCT
ejpam-4850	55	31	(	(	PUNCT
ejpam-4850	55	32	b(k+1)γ	b(k+1)γ	PROPN
ejpam-4850	55	33	−	−	PROPN
ejpam-4850	55	34	a(k+1)γ	a(k+1)γ	PROPN
ejpam-4850	55	35	)	)	PUNCT
ejpam-4850	55	36	,	,	PUNCT
ejpam-4850	56	1	k	k	PROPN
ejpam-4850	56	2	∈	∈	PROPN
ejpam-4850	56	3	r.	r.	PROPN
ejpam-4850	56	4	w.	w.	PROPN
ejpam-4850	56	5	saleh	saleh	PROPN
ejpam-4850	56	6	et	et	PROPN
ejpam-4850	56	7	al	al	PROPN
ejpam-4850	56	8	.	.	PUNCT
ejpam-4850	56	9	/	/	SYM
ejpam-4850	56	10	eur	eur	PROPN
ejpam-4850	56	11	.	.	PUNCT
ejpam-4850	57	1	j.	j.	PROPN
ejpam-4850	57	2	pure	pure	PROPN
ejpam-4850	57	3	appl	appl	PROPN
ejpam-4850	57	4	.	.	PROPN
ejpam-4850	57	5	math	math	PROPN
ejpam-4850	57	6	,	,	PUNCT
ejpam-4850	57	7	16	16	NUM
ejpam-4850	57	8	(	(	PUNCT
ejpam-4850	57	9	3	3	NUM
ejpam-4850	57	10	)	)	PUNCT
ejpam-4850	57	11	(	(	PUNCT
ejpam-4850	57	12	2023	2023	NUM
ejpam-4850	57	13	)	)	PUNCT
ejpam-4850	57	14	,	,	PUNCT
ejpam-4850	57	15	1359	1359	NUM
ejpam-4850	57	16	-	-	SYM
ejpam-4850	57	17	1380	1380	NUM
ejpam-4850	57	18	1362	1362	NUM
ejpam-4850	57	19	lemma	lemma	PROPN
ejpam-4850	57	20	3	3	NUM
ejpam-4850	57	21	(	(	PUNCT
ejpam-4850	57	22	generalized	generalized	ADJ
ejpam-4850	57	23	hölder	hölder	NOUN
ejpam-4850	57	24	’s	’s	PART
ejpam-4850	57	25	inequality	inequality	NOUN
ejpam-4850	57	26	[	[	X
ejpam-4850	57	27	4	4	NUM
ejpam-4850	57	28	]	]	NUM
ejpam-4850	57	29	)	)	PUNCT
ejpam-4850	57	30	.	.	PUNCT
ejpam-4850	58	1	let	let	VERB
ejpam-4850	58	2	j	j	PROPN
ejpam-4850	58	3	,	,	PUNCT
ejpam-4850	58	4	q	q	PROPN
ejpam-4850	58	5	∈	∈	PROPN
ejpam-4850	58	6	cγ	cγ	NOUN
ejpam-4850	58	7	[	[	X
ejpam-4850	58	8	a	a	X
ejpam-4850	58	9	,	,	PUNCT
ejpam-4850	58	10	b	b	NOUN
ejpam-4850	58	11	]	]	X
ejpam-4850	58	12	,	,	PUNCT
ejpam-4850	58	13	p	p	X
ejpam-4850	58	14	,	,	PUNCT
ejpam-4850	58	15	q	q	X
ejpam-4850	58	16	>	>	X
ejpam-4850	58	17	1	1	NUM
ejpam-4850	58	18	with	with	ADP
ejpam-4850	58	19	1	1	NUM
ejpam-4850	58	20	p+	p+	NOUN
ejpam-4850	58	21	1	1	NUM
ejpam-4850	58	22	q	q	NOUN
ejpam-4850	58	23	=	=	SYM
ejpam-4850	58	24	1	1	NUM
ejpam-4850	58	25	,	,	PUNCT
ejpam-4850	58	26	then	then	ADV
ejpam-4850	58	27	1	1	NUM
ejpam-4850	58	28	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	58	29	)	)	PUNCT
ejpam-4850	58	30	b∫	b∫	PROPN
ejpam-4850	58	31	a	a	PROPN
ejpam-4850	58	32	|j	|j	NOUN
ejpam-4850	58	33	(	(	PUNCT
ejpam-4850	58	34	t)q	t)q	X
ejpam-4850	58	35	(	(	PUNCT
ejpam-4850	58	36	t)|	t)|	INTJ
ejpam-4850	58	37	(	(	PUNCT
ejpam-4850	58	38	dt)γ	dt)γ	PROPN
ejpam-4850	58	39	=	=	SYM
ejpam-4850	58	40			PROPN
ejpam-4850	58	41	1	1	NUM
ejpam-4850	58	42	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	58	43	)	)	PUNCT
ejpam-4850	58	44	b∫	b∫	PROPN
ejpam-4850	58	45	a	a	PROPN
ejpam-4850	58	46	|j	|j	NOUN
ejpam-4850	58	47	(	(	PUNCT
ejpam-4850	58	48	t)|p	t)|p	NOUN
ejpam-4850	58	49	(	(	PUNCT
ejpam-4850	58	50	dt)γ	dt)γ	PROPN
ejpam-4850	58	51			PROPN
ejpam-4850	59	1	1	1	NUM
ejpam-4850	59	2	p	p	NOUN
ejpam-4850	59	3			PROPN
ejpam-4850	59	4	1	1	NUM
ejpam-4850	59	5	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	59	6	)	)	PUNCT
ejpam-4850	59	7	b∫	b∫	NOUN
ejpam-4850	59	8	a	a	DET
ejpam-4850	59	9	|q	|q	NOUN
ejpam-4850	59	10	(	(	PUNCT
ejpam-4850	59	11	t)|q	t)|q	NOUN
ejpam-4850	59	12	(	(	PUNCT
ejpam-4850	59	13	dt)γ	dt)γ	PROPN
ejpam-4850	59	14			PROPN
ejpam-4850	59	15	1	1	NUM
ejpam-4850	59	16	q	q	NOUN
ejpam-4850	59	17	.	.	PUNCT
ejpam-4850	60	1	definition	definition	NOUN
ejpam-4850	60	2	1	1	NUM
ejpam-4850	60	3	(	(	PUNCT
ejpam-4850	60	4	[	[	X
ejpam-4850	60	5	24	24	NUM
ejpam-4850	60	6	]	]	PUNCT
ejpam-4850	60	7	)	)	PUNCT
ejpam-4850	60	8	.	.	PUNCT
ejpam-4850	61	1	let	let	VERB
ejpam-4850	62	1	j	j	NOUN
ejpam-4850	62	2	:	:	PUNCT
ejpam-4850	62	3	i	i	PRON
ejpam-4850	62	4	⊆	⊆	NUM
ejpam-4850	62	5	r	r	NOUN
ejpam-4850	62	6	→	→	SYM
ejpam-4850	62	7	rγ	rγ	NOUN
ejpam-4850	62	8	.	.	PUNCT
ejpam-4850	63	1	for	for	ADP
ejpam-4850	63	2	any	any	DET
ejpam-4850	63	3	κ1	κ1	NOUN
ejpam-4850	63	4	,	,	PUNCT
ejpam-4850	63	5	κ2	κ2	NOUN
ejpam-4850	63	6	∈	∈	PROPN
ejpam-4850	64	1	i	i	PRON
ejpam-4850	64	2	and	and	CCONJ
ejpam-4850	64	3	κ	κ	PRON
ejpam-4850	64	4	∈	∈	PROPN
ejpam-4850	65	1	[	[	X
ejpam-4850	65	2	0	0	NUM
ejpam-4850	65	3	,	,	PUNCT
ejpam-4850	65	4	1	1	NUM
ejpam-4850	65	5	]	]	PUNCT
ejpam-4850	65	6	,	,	PUNCT
ejpam-4850	65	7	if	if	SCONJ
ejpam-4850	65	8	j	j	PROPN
ejpam-4850	65	9	(	(	PUNCT
ejpam-4850	65	10	κκ1	κκ1	PROPN
ejpam-4850	65	11	+	+	CCONJ
ejpam-4850	65	12	(	(	PUNCT
ejpam-4850	65	13	1−	1−	NUM
ejpam-4850	65	14	κ)κ2	κ)κ2	PROPN
ejpam-4850	65	15	)	)	PUNCT
ejpam-4850	65	16	≤	≤	PUNCT
ejpam-4850	65	17	κγj	κγj	ADJ
ejpam-4850	65	18	(	(	PUNCT
ejpam-4850	65	19	κ1	κ1	NOUN
ejpam-4850	65	20	)	)	PUNCT
ejpam-4850	65	21	+	+	CCONJ
ejpam-4850	65	22	(	(	PUNCT
ejpam-4850	65	23	1−	1−	NUM
ejpam-4850	65	24	κ)γ	κ)γ	X
ejpam-4850	65	25	j	j	PROPN
ejpam-4850	65	26	(	(	PUNCT
ejpam-4850	65	27	κ2	κ2	PROPN
ejpam-4850	65	28	)	)	PUNCT
ejpam-4850	65	29	holds	hold	VERB
ejpam-4850	65	30	,	,	PUNCT
ejpam-4850	65	31	then	then	ADV
ejpam-4850	65	32	j	j	PROPN
ejpam-4850	65	33	is	be	AUX
ejpam-4850	65	34	a	a	DET
ejpam-4850	65	35	generalized	generalized	ADJ
ejpam-4850	65	36	convex	convex	NOUN
ejpam-4850	65	37	function	function	NOUN
ejpam-4850	65	38	on	on	ADP
ejpam-4850	65	39	i.	i.	PROPN
ejpam-4850	65	40	more	more	ADJ
ejpam-4850	65	41	scientists	scientist	NOUN
ejpam-4850	65	42	have	have	AUX
ejpam-4850	65	43	made	make	VERB
ejpam-4850	65	44	efforts	effort	NOUN
ejpam-4850	65	45	to	to	PART
ejpam-4850	65	46	extend	extend	VERB
ejpam-4850	65	47	the	the	DET
ejpam-4850	65	48	notion	notion	NOUN
ejpam-4850	65	49	of	of	ADP
ejpam-4850	65	50	convexity	convexity	NOUN
ejpam-4850	65	51	in	in	ADP
ejpam-4850	65	52	order	order	NOUN
ejpam-4850	65	53	to	to	PART
ejpam-4850	65	54	cover	cover	VERB
ejpam-4850	65	55	a	a	DET
ejpam-4850	65	56	wider	wide	ADJ
ejpam-4850	65	57	class	class	NOUN
ejpam-4850	65	58	of	of	ADP
ejpam-4850	65	59	functions	function	NOUN
ejpam-4850	65	60	.	.	PUNCT
ejpam-4850	66	1	one	one	NUM
ejpam-4850	66	2	of	of	ADP
ejpam-4850	66	3	the	the	DET
ejpam-4850	66	4	most	most	ADV
ejpam-4850	66	5	interesting	interesting	ADJ
ejpam-4850	66	6	extensions	extension	NOUN
ejpam-4850	66	7	that	that	PRON
ejpam-4850	66	8	has	have	AUX
ejpam-4850	66	9	emerged	emerge	VERB
ejpam-4850	66	10	is	be	AUX
ejpam-4850	66	11	the	the	DET
ejpam-4850	66	12	generalized	generalized	ADJ
ejpam-4850	66	13	s	s	NOUN
ejpam-4850	66	14	-	-	PUNCT
ejpam-4850	66	15	convexity	convexity	NOUN
ejpam-4850	66	16	introduced	introduce	VERB
ejpam-4850	66	17	in	in	ADP
ejpam-4850	66	18	[	[	X
ejpam-4850	66	19	20	20	NUM
ejpam-4850	66	20	]	]	PUNCT
ejpam-4850	66	21	.	.	PUNCT
ejpam-4850	67	1	definition	definition	NOUN
ejpam-4850	67	2	2	2	NUM
ejpam-4850	67	3	.	.	PUNCT
ejpam-4850	68	1	let	let	VERB
ejpam-4850	68	2	j	j	NOUN
ejpam-4850	68	3	:	:	PUNCT
ejpam-4850	68	4	i	i	PRON
ejpam-4850	68	5	⊆	⊆	NUM
ejpam-4850	68	6	r	r	NOUN
ejpam-4850	68	7	→	→	SYM
ejpam-4850	68	8	rγ	rγ	NOUN
ejpam-4850	68	9	.	.	PUNCT
ejpam-4850	69	1	for	for	ADP
ejpam-4850	69	2	any	any	DET
ejpam-4850	69	3	κ1	κ1	NOUN
ejpam-4850	69	4	,	,	PUNCT
ejpam-4850	69	5	κ2	κ2	NOUN
ejpam-4850	69	6	∈	∈	PROPN
ejpam-4850	70	1	i	i	PRON
ejpam-4850	70	2	and	and	CCONJ
ejpam-4850	70	3	κ	κ	PRON
ejpam-4850	70	4	∈	∈	PROPN
ejpam-4850	71	1	[	[	X
ejpam-4850	71	2	0	0	NUM
ejpam-4850	71	3	,	,	PUNCT
ejpam-4850	71	4	1	1	NUM
ejpam-4850	71	5	]	]	PUNCT
ejpam-4850	71	6	,	,	PUNCT
ejpam-4850	71	7	if	if	SCONJ
ejpam-4850	71	8	j	j	PROPN
ejpam-4850	71	9	(	(	PUNCT
ejpam-4850	71	10	κκ1	κκ1	PROPN
ejpam-4850	71	11	+	+	CCONJ
ejpam-4850	71	12	(	(	PUNCT
ejpam-4850	71	13	1−	1−	NUM
ejpam-4850	71	14	κ)κ2	κ)κ2	PROPN
ejpam-4850	71	15	)	)	PUNCT
ejpam-4850	71	16	≤	≤	NOUN
ejpam-4850	71	17	κsγj	κsγj	NOUN
ejpam-4850	71	18	(	(	PUNCT
ejpam-4850	71	19	κ1	κ1	NOUN
ejpam-4850	71	20	)	)	PUNCT
ejpam-4850	71	21	+	+	CCONJ
ejpam-4850	71	22	(	(	PUNCT
ejpam-4850	71	23	1−	1−	NUM
ejpam-4850	71	24	κ)sγ	κ)sγ	PROPN
ejpam-4850	71	25	j	j	PROPN
ejpam-4850	71	26	(	(	PUNCT
ejpam-4850	71	27	κ2	κ2	PROPN
ejpam-4850	71	28	)	)	PUNCT
ejpam-4850	71	29	holds	hold	VERB
ejpam-4850	71	30	for	for	ADP
ejpam-4850	71	31	some	some	DET
ejpam-4850	71	32	fixed	fix	VERB
ejpam-4850	71	33	s	s	X
ejpam-4850	71	34	∈	∈	NOUN
ejpam-4850	71	35	(	(	PUNCT
ejpam-4850	71	36	0	0	NUM
ejpam-4850	71	37	,	,	PUNCT
ejpam-4850	71	38	1	1	NUM
ejpam-4850	71	39	]	]	PUNCT
ejpam-4850	71	40	,	,	PUNCT
ejpam-4850	71	41	then	then	ADV
ejpam-4850	71	42	j	j	PROPN
ejpam-4850	71	43	is	be	AUX
ejpam-4850	71	44	a	a	DET
ejpam-4850	71	45	generalized	generalized	ADJ
ejpam-4850	71	46	s	s	NOUN
ejpam-4850	71	47	-	-	ADJ
ejpam-4850	71	48	convex	convex	ADJ
ejpam-4850	71	49	function	function	NOUN
ejpam-4850	71	50	in	in	ADP
ejpam-4850	71	51	the	the	DET
ejpam-4850	71	52	second	second	ADJ
ejpam-4850	71	53	sense	sense	NOUN
ejpam-4850	71	54	on	on	ADP
ejpam-4850	71	55	i.	i.	NOUN
ejpam-4850	71	56	in	in	ADP
ejpam-4850	71	57	[	[	X
ejpam-4850	71	58	21	21	NUM
ejpam-4850	71	59	]	]	PUNCT
ejpam-4850	71	60	,	,	PUNCT
ejpam-4850	71	61	the	the	DET
ejpam-4850	71	62	authors	author	NOUN
ejpam-4850	71	63	gave	give	VERB
ejpam-4850	71	64	the	the	DET
ejpam-4850	71	65	analogue	analogue	NOUN
ejpam-4850	71	66	of	of	ADP
ejpam-4850	71	67	inequality	inequality	NOUN
ejpam-4850	71	68	(	(	PUNCT
ejpam-4850	71	69	1	1	NUM
ejpam-4850	71	70	)	)	PUNCT
ejpam-4850	71	71	for	for	ADP
ejpam-4850	71	72	generalized	generalized	ADJ
ejpam-4850	71	73	s	s	NOUN
ejpam-4850	71	74	-	-	ADJ
ejpam-4850	71	75	convex	convex	ADJ
ejpam-4850	71	76	functions	function	NOUN
ejpam-4850	71	77	on	on	ADP
ejpam-4850	71	78	fractal	fractal	ADJ
ejpam-4850	71	79	set	set	NOUN
ejpam-4850	71	80	as	as	SCONJ
ejpam-4850	71	81	follows	follow	VERB
ejpam-4850	71	82	2(s−1)γ	2(s−1)γ	NUM
ejpam-4850	71	83	γ(1+γ)j	γ(1+γ)j	NOUN
ejpam-4850	71	84	(	(	PUNCT
ejpam-4850	71	85	a+b	a+b	NUM
ejpam-4850	71	86	2	2	NUM
ejpam-4850	71	87	)	)	PUNCT
ejpam-4850	71	88	≤	≤	NOUN
ejpam-4850	71	89	ai	ai	VERB
ejpam-4850	71	90	γ	γ	PROPN
ejpam-4850	71	91	b	b	PROPN
ejpam-4850	71	92	j	j	PROPN
ejpam-4850	71	93	(	(	PUNCT
ejpam-4850	71	94	t	t	PROPN
ejpam-4850	71	95	)	)	PUNCT
ejpam-4850	71	96	(	(	PUNCT
ejpam-4850	71	97	b−a)γ	b−a)γ	VERB
ejpam-4850	71	98	≤	≤	ADJ
ejpam-4850	71	99	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	71	100	)	)	PUNCT
ejpam-4850	71	101	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	71	102	)	)	PUNCT
ejpam-4850	71	103	(	(	PUNCT
ejpam-4850	71	104	j	j	X
ejpam-4850	71	105	(	(	PUNCT
ejpam-4850	71	106	a	a	NOUN
ejpam-4850	71	107	)	)	PUNCT
ejpam-4850	71	108	+	+	PROPN
ejpam-4850	71	109	j	j	PROPN
ejpam-4850	71	110	(	(	PUNCT
ejpam-4850	71	111	b	b	NOUN
ejpam-4850	71	112	)	)	PUNCT
ejpam-4850	71	113	)	)	PUNCT
ejpam-4850	71	114	,	,	PUNCT
ejpam-4850	71	115	0	0	PUNCT
ejpam-4850	72	1	<	<	X
ejpam-4850	72	2	s	s	X
ejpam-4850	72	3	≤	≤	ADJ
ejpam-4850	72	4	1	1	NUM
ejpam-4850	72	5	.	.	PUNCT
ejpam-4850	73	1	(	(	PUNCT
ejpam-4850	73	2	5	5	X
ejpam-4850	73	3	)	)	PUNCT
ejpam-4850	73	4	this	this	DET
ejpam-4850	73	5	paper	paper	NOUN
ejpam-4850	73	6	examines	examine	VERB
ejpam-4850	73	7	the	the	DET
ejpam-4850	73	8	companion	companion	NOUN
ejpam-4850	73	9	of	of	ADP
ejpam-4850	73	10	ostrowski	ostrowski	PROPN
ejpam-4850	73	11	’s	’s	PART
ejpam-4850	73	12	inequality	inequality	NOUN
ejpam-4850	73	13	,	,	PUNCT
ejpam-4850	73	14	as	as	SCONJ
ejpam-4850	73	15	studied	study	VERB
ejpam-4850	73	16	by	by	ADP
ejpam-4850	73	17	the	the	DET
ejpam-4850	73	18	authors	author	NOUN
ejpam-4850	73	19	in	in	ADP
ejpam-4850	73	20	[	[	X
ejpam-4850	73	21	11	11	NUM
ejpam-4850	73	22	]	]	PUNCT
ejpam-4850	73	23	,	,	PUNCT
ejpam-4850	73	24	within	within	ADP
ejpam-4850	73	25	the	the	DET
ejpam-4850	73	26	context	context	NOUN
ejpam-4850	73	27	of	of	ADP
ejpam-4850	73	28	fractal	fractal	ADJ
ejpam-4850	73	29	sets	set	NOUN
ejpam-4850	73	30	.	.	PUNCT
ejpam-4850	74	1	we	we	PRON
ejpam-4850	74	2	start	start	VERB
ejpam-4850	74	3	by	by	ADP
ejpam-4850	74	4	introducing	introduce	VERB
ejpam-4850	74	5	a	a	DET
ejpam-4850	74	6	new	new	ADJ
ejpam-4850	74	7	identity	identity	NOUN
ejpam-4850	74	8	related	relate	VERB
ejpam-4850	74	9	to	to	ADP
ejpam-4850	74	10	local	local	ADJ
ejpam-4850	74	11	fractional	fractional	ADJ
ejpam-4850	74	12	integrals	integral	NOUN
ejpam-4850	74	13	,	,	PUNCT
ejpam-4850	74	14	on	on	ADP
ejpam-4850	74	15	the	the	DET
ejpam-4850	74	16	basis	basis	NOUN
ejpam-4850	74	17	of	of	ADP
ejpam-4850	74	18	which	which	PRON
ejpam-4850	74	19	we	we	PRON
ejpam-4850	74	20	establish	establish	VERB
ejpam-4850	74	21	several	several	ADJ
ejpam-4850	74	22	inequalities	inequality	NOUN
ejpam-4850	74	23	for	for	ADP
ejpam-4850	74	24	functions	function	NOUN
ejpam-4850	74	25	possessing	possess	VERB
ejpam-4850	74	26	generalized	generalize	VERB
ejpam-4850	74	27	s	s	NOUN
ejpam-4850	74	28	-	-	NOUN
ejpam-4850	74	29	convex	convex	ADJ
ejpam-4850	74	30	and	and	CCONJ
ejpam-4850	74	31	s	s	NOUN
ejpam-4850	74	32	-	-	ADJ
ejpam-4850	74	33	concave	concave	ADJ
ejpam-4850	74	34	derivatives	derivative	NOUN
ejpam-4850	74	35	.	.	PUNCT
ejpam-4850	75	1	the	the	DET
ejpam-4850	75	2	study	study	NOUN
ejpam-4850	75	3	is	be	AUX
ejpam-4850	75	4	concluded	conclude	VERB
ejpam-4850	75	5	with	with	ADP
ejpam-4850	75	6	an	an	DET
ejpam-4850	75	7	example	example	NOUN
ejpam-4850	75	8	that	that	PRON
ejpam-4850	75	9	justifies	justify	VERB
ejpam-4850	75	10	the	the	DET
ejpam-4850	75	11	correctness	correctness	NOUN
ejpam-4850	75	12	of	of	ADP
ejpam-4850	75	13	the	the	DET
ejpam-4850	75	14	obtained	obtain	VERB
ejpam-4850	75	15	results	result	NOUN
ejpam-4850	75	16	,	,	PUNCT
ejpam-4850	75	17	as	as	ADV
ejpam-4850	75	18	well	well	ADV
ejpam-4850	75	19	as	as	ADP
ejpam-4850	75	20	a	a	DET
ejpam-4850	75	21	few	few	ADJ
ejpam-4850	75	22	applications	application	NOUN
ejpam-4850	75	23	.	.	PUNCT
ejpam-4850	76	1	2	2	X
ejpam-4850	76	2	.	.	X
ejpam-4850	76	3	main	main	ADJ
ejpam-4850	76	4	results	result	NOUN
ejpam-4850	76	5	in	in	ADP
ejpam-4850	76	6	order	order	NOUN
ejpam-4850	76	7	to	to	PART
ejpam-4850	76	8	demonstrate	demonstrate	VERB
ejpam-4850	76	9	our	our	PRON
ejpam-4850	76	10	results	result	NOUN
ejpam-4850	76	11	,	,	PUNCT
ejpam-4850	76	12	it	it	PRON
ejpam-4850	76	13	is	be	AUX
ejpam-4850	76	14	necessary	necessary	ADJ
ejpam-4850	76	15	to	to	PART
ejpam-4850	76	16	present	present	VERB
ejpam-4850	76	17	the	the	DET
ejpam-4850	76	18	following	follow	VERB
ejpam-4850	76	19	lemma	lemma	PROPN
ejpam-4850	76	20	.	.	PUNCT
ejpam-4850	77	1	lemma	lemma	PROPN
ejpam-4850	77	2	4	4	X
ejpam-4850	77	3	.	.	PUNCT
ejpam-4850	77	4	suppose	suppose	VERB
ejpam-4850	78	1	j	j	NOUN
ejpam-4850	78	2	:	:	PUNCT
ejpam-4850	78	3	i	i	PRON
ejpam-4850	78	4	=	=	PUNCT
ejpam-4850	79	1	[	[	X
ejpam-4850	79	2	a	a	X
ejpam-4850	79	3	,	,	PUNCT
ejpam-4850	79	4	b	b	NOUN
ejpam-4850	79	5	]	]	X
ejpam-4850	79	6	→	→	PUNCT
ejpam-4850	79	7	rγ	rγ	PRON
ejpam-4850	79	8	is	be	AUX
ejpam-4850	79	9	a	a	DET
ejpam-4850	79	10	differentiable	differentiable	ADJ
ejpam-4850	79	11	function	function	NOUN
ejpam-4850	79	12	on	on	ADP
ejpam-4850	79	13	i	i	PRON
ejpam-4850	79	14	with	with	ADP
ejpam-4850	79	15	a	a	DET
ejpam-4850	79	16	<	<	X
ejpam-4850	79	17	b	b	NOUN
ejpam-4850	79	18	,	,	PUNCT
ejpam-4850	79	19	and	and	CCONJ
ejpam-4850	79	20	j	j	PROPN
ejpam-4850	79	21	(	(	PUNCT
ejpam-4850	79	22	γ	γ	PROPN
ejpam-4850	79	23	)	)	PUNCT
ejpam-4850	79	24	∈	∈	NOUN
ejpam-4850	79	25	cγ	cγ	NOUN
ejpam-4850	79	26	[	[	X
ejpam-4850	79	27	a	a	X
ejpam-4850	79	28	,	,	PUNCT
ejpam-4850	79	29	b	b	NOUN
ejpam-4850	79	30	]	]	X
ejpam-4850	79	31	.	.	PUNCT
ejpam-4850	80	1	then	then	ADV
ejpam-4850	80	2	,	,	PUNCT
ejpam-4850	80	3	for	for	ADP
ejpam-4850	80	4	all	all	DET
ejpam-4850	80	5	x	x	SYM
ejpam-4850	80	6	∈	∈	PROPN
ejpam-4850	81	1	[	[	X
ejpam-4850	81	2	a	a	X
ejpam-4850	81	3	,	,	PUNCT
ejpam-4850	81	4	a+b	a+b	NUM
ejpam-4850	81	5	2	2	NUM
ejpam-4850	81	6	]	]	PUNCT
ejpam-4850	81	7	,	,	PUNCT
ejpam-4850	81	8	the	the	DET
ejpam-4850	81	9	following	follow	VERB
ejpam-4850	81	10	equation	equation	NOUN
ejpam-4850	81	11	is	be	AUX
ejpam-4850	81	12	satisfied	satisfied	ADJ
ejpam-4850	81	13	j	j	PROPN
ejpam-4850	81	14	(	(	PUNCT
ejpam-4850	81	15	x)+j	x)+j	PROPN
ejpam-4850	81	16	(	(	PUNCT
ejpam-4850	81	17	a+b−x	a+b−x	PROPN
ejpam-4850	81	18	)	)	PUNCT
ejpam-4850	81	19	2γ	2γ	NOUN
ejpam-4850	81	20	−	−	PROPN
ejpam-4850	81	21	γ(γ+1	γ(γ+1	NUM
ejpam-4850	81	22	)	)	PUNCT
ejpam-4850	81	23	(	(	PUNCT
ejpam-4850	81	24	b−a)γ	b−a)γ	NOUN
ejpam-4850	81	25	ai	ai	VERB
ejpam-4850	81	26	γ	γ	PROPN
ejpam-4850	81	27	b	b	PROPN
ejpam-4850	81	28	j	j	PROPN
ejpam-4850	81	29	(	(	PUNCT
ejpam-4850	81	30	t	t	PROPN
ejpam-4850	81	31	)	)	PUNCT
ejpam-4850	81	32	=	=	SYM
ejpam-4850	82	1	(	(	PUNCT
ejpam-4850	82	2	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	82	3	(	(	PUNCT
ejpam-4850	82	4	b−a)γ	b−a)γ	NOUN
ejpam-4850	82	5			PROPN
ejpam-4850	82	6	1	1	NUM
ejpam-4850	82	7	γ(γ+1	γ(γ+1	NUM
ejpam-4850	82	8	)	)	PUNCT
ejpam-4850	83	1	1∫	1∫	NUM
ejpam-4850	83	2	0	0	NUM
ejpam-4850	83	3	ηγj	ηγj	NOUN
ejpam-4850	83	4	(	(	PUNCT
ejpam-4850	83	5	γ	γ	X
ejpam-4850	83	6	)	)	PUNCT
ejpam-4850	83	7	(	(	PUNCT
ejpam-4850	83	8	(	(	PUNCT
ejpam-4850	83	9	1−	1−	NUM
ejpam-4850	83	10	η	η	NOUN
ejpam-4850	83	11	)	)	PUNCT
ejpam-4850	83	12	a+	a+	PUNCT
ejpam-4850	83	13	ηx	ηx	NOUN
ejpam-4850	83	14	)	)	PUNCT
ejpam-4850	83	15	(	(	PUNCT
ejpam-4850	83	16	dη)γ	dη)γ	PROPN
ejpam-4850	83	17	w.	w.	PROPN
ejpam-4850	83	18	saleh	saleh	PROPN
ejpam-4850	83	19	et	et	PROPN
ejpam-4850	83	20	al	al	PROPN
ejpam-4850	83	21	.	.	PUNCT
ejpam-4850	83	22	/	/	SYM
ejpam-4850	83	23	eur	eur	PROPN
ejpam-4850	83	24	.	.	PUNCT
ejpam-4850	84	1	j.	j.	PROPN
ejpam-4850	84	2	pure	pure	PROPN
ejpam-4850	84	3	appl	appl	PROPN
ejpam-4850	84	4	.	.	PROPN
ejpam-4850	84	5	math	math	PROPN
ejpam-4850	84	6	,	,	PUNCT
ejpam-4850	84	7	16	16	NUM
ejpam-4850	84	8	(	(	PUNCT
ejpam-4850	84	9	3	3	NUM
ejpam-4850	84	10	)	)	PUNCT
ejpam-4850	84	11	(	(	PUNCT
ejpam-4850	84	12	2023	2023	NUM
ejpam-4850	84	13	)	)	PUNCT
ejpam-4850	84	14	,	,	PUNCT
ejpam-4850	84	15	1359	1359	NUM
ejpam-4850	84	16	-	-	SYM
ejpam-4850	84	17	1380	1380	NUM
ejpam-4850	84	18	1363	1363	NUM
ejpam-4850	84	19	+	+	CCONJ
ejpam-4850	84	20	1	1	NUM
ejpam-4850	84	21	γ(γ+1	γ(γ+1	NUM
ejpam-4850	84	22	)	)	PUNCT
ejpam-4850	85	1	1∫	1∫	NUM
ejpam-4850	85	2	0	0	NUM
ejpam-4850	85	3	(	(	PUNCT
ejpam-4850	85	4	η	η	PROPN
ejpam-4850	85	5	−	−	PROPN
ejpam-4850	85	6	1)γ	1)γ	PROPN
ejpam-4850	85	7	j	j	PROPN
ejpam-4850	85	8	(	(	PUNCT
ejpam-4850	85	9	γ	γ	PROPN
ejpam-4850	85	10	)	)	PUNCT
ejpam-4850	85	11	(	(	PUNCT
ejpam-4850	85	12	(	(	PUNCT
ejpam-4850	85	13	1−	1−	NUM
ejpam-4850	85	14	η	η	NOUN
ejpam-4850	85	15	)	)	PUNCT
ejpam-4850	85	16	(	(	PUNCT
ejpam-4850	85	17	a+	a+	PUNCT
ejpam-4850	85	18	b−	b−	PROPN
ejpam-4850	85	19	x	x	PROPN
ejpam-4850	85	20	)	)	PUNCT
ejpam-4850	85	21	+	+	CCONJ
ejpam-4850	85	22	ηb	ηb	X
ejpam-4850	85	23	)	)	PUNCT
ejpam-4850	85	24	(	(	PUNCT
ejpam-4850	85	25	dη)γ	dη)γ	PROPN
ejpam-4850	85	26			PROPN
ejpam-4850	85	27	+	+	CCONJ
ejpam-4850	85	28	(	(	PUNCT
ejpam-4850	85	29	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	85	30	4γ(b−a)γ	4γ(b−a)γ	PROPN
ejpam-4850	85	31			PROPN
ejpam-4850	85	32	1	1	NUM
ejpam-4850	85	33	γ(γ+1	γ(γ+1	NUM
ejpam-4850	85	34	)	)	PUNCT
ejpam-4850	86	1	1∫	1∫	NUM
ejpam-4850	86	2	0	0	NUM
ejpam-4850	86	3	(	(	PUNCT
ejpam-4850	86	4	η	η	PROPN
ejpam-4850	86	5	−	−	PROPN
ejpam-4850	86	6	1)γ	1)γ	PROPN
ejpam-4850	86	7	j	j	PROPN
ejpam-4850	86	8	(	(	PUNCT
ejpam-4850	86	9	γ	γ	PROPN
ejpam-4850	86	10	)	)	PUNCT
ejpam-4850	86	11	(	(	PUNCT
ejpam-4850	86	12	(	(	PUNCT
ejpam-4850	86	13	1−	1−	NUM
ejpam-4850	86	14	η)x+	η)x+	NUM
ejpam-4850	86	15	η	η	PROPN
ejpam-4850	86	16	a+b	a+b	NUM
ejpam-4850	86	17	2	2	NUM
ejpam-4850	86	18	)	)	PUNCT
ejpam-4850	86	19	(	(	PUNCT
ejpam-4850	86	20	dη)γ	dη)γ	PROPN
ejpam-4850	86	21	+	+	NUM
ejpam-4850	86	22	1	1	NUM
ejpam-4850	86	23	γ(γ+1	γ(γ+1	NUM
ejpam-4850	86	24	)	)	PUNCT
ejpam-4850	87	1	1∫	1∫	NUM
ejpam-4850	87	2	0	0	NUM
ejpam-4850	87	3	ηγj	ηγj	NOUN
ejpam-4850	87	4	(	(	PUNCT
ejpam-4850	87	5	γ	γ	X
ejpam-4850	87	6	)	)	PUNCT
ejpam-4850	87	7	(	(	PUNCT
ejpam-4850	87	8	(	(	PUNCT
ejpam-4850	87	9	1−	1−	NUM
ejpam-4850	87	10	η	η	NOUN
ejpam-4850	87	11	)	)	PUNCT
ejpam-4850	87	12	a+b	a+b	NUM
ejpam-4850	87	13	2	2	NUM
ejpam-4850	87	14	+	+	SYM
ejpam-4850	87	15	η	η	PROPN
ejpam-4850	87	16	(	(	PUNCT
ejpam-4850	87	17	a+	a+	PUNCT
ejpam-4850	87	18	b−	b−	PROPN
ejpam-4850	87	19	x	x	PROPN
ejpam-4850	87	20	)	)	PUNCT
ejpam-4850	87	21	)	)	PUNCT
ejpam-4850	88	1	(	(	PUNCT
ejpam-4850	88	2	dη)γ	dη)γ	PROPN
ejpam-4850	88	3			PROPN
ejpam-4850	88	4	.	.	PUNCT
ejpam-4850	89	1	proof	proof	NOUN
ejpam-4850	89	2	.	.	PUNCT
ejpam-4850	90	1	let	let	VERB
ejpam-4850	90	2	i	i	PRON
ejpam-4850	90	3	=	=	PUNCT
ejpam-4850	90	4	(	(	PUNCT
ejpam-4850	90	5	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	90	6	(	(	PUNCT
ejpam-4850	90	7	b−a)γ	b−a)γ	PROPN
ejpam-4850	90	8	i1	i1	PROPN
ejpam-4850	90	9	+	+	CCONJ
ejpam-4850	91	1	(	(	PUNCT
ejpam-4850	91	2	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	91	3	4γ(b−a)γ	4γ(b−a)γ	PROPN
ejpam-4850	91	4	i2	i2	PROPN
ejpam-4850	91	5	+	+	CCONJ
ejpam-4850	92	1	(	(	PUNCT
ejpam-4850	92	2	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	92	3	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	92	4	i3	i3	NOUN
ejpam-4850	92	5	+	+	CCONJ
ejpam-4850	92	6	(	(	PUNCT
ejpam-4850	92	7	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	92	8	(	(	PUNCT
ejpam-4850	92	9	b−a)γ	b−a)γ	PROPN
ejpam-4850	92	10	i4	i4	PROPN
ejpam-4850	92	11	,	,	PUNCT
ejpam-4850	92	12	(	(	PUNCT
ejpam-4850	92	13	6	6	NUM
ejpam-4850	92	14	)	)	PUNCT
ejpam-4850	93	1	where	where	SCONJ
ejpam-4850	93	2	i1	i1	PROPN
ejpam-4850	93	3	=	=	PROPN
ejpam-4850	93	4	1	1	NUM
ejpam-4850	93	5	γ(γ+1	γ(γ+1	NUM
ejpam-4850	93	6	)	)	PUNCT
ejpam-4850	94	1	1∫	1∫	NUM
ejpam-4850	94	2	0	0	NUM
ejpam-4850	94	3	ηγj	ηγj	NOUN
ejpam-4850	94	4	(	(	PUNCT
ejpam-4850	94	5	γ	γ	X
ejpam-4850	94	6	)	)	PUNCT
ejpam-4850	94	7	(	(	PUNCT
ejpam-4850	94	8	(	(	PUNCT
ejpam-4850	94	9	1−	1−	NUM
ejpam-4850	94	10	η	η	NOUN
ejpam-4850	94	11	)	)	PUNCT
ejpam-4850	94	12	a+	a+	PUNCT
ejpam-4850	94	13	ηx	ηx	NOUN
ejpam-4850	94	14	)	)	PUNCT
ejpam-4850	94	15	(	(	PUNCT
ejpam-4850	94	16	dη)γ	dη)γ	PROPN
ejpam-4850	94	17	,	,	PUNCT
ejpam-4850	94	18	i2	i2	PROPN
ejpam-4850	94	19	=	=	PROPN
ejpam-4850	94	20	1	1	NUM
ejpam-4850	94	21	γ(γ+1	γ(γ+1	NUM
ejpam-4850	94	22	)	)	PUNCT
ejpam-4850	95	1	1∫	1∫	NUM
ejpam-4850	95	2	0	0	NUM
ejpam-4850	95	3	(	(	PUNCT
ejpam-4850	95	4	η	η	PROPN
ejpam-4850	95	5	−	−	PROPN
ejpam-4850	95	6	1)γ	1)γ	PROPN
ejpam-4850	95	7	j	j	PROPN
ejpam-4850	95	8	(	(	PUNCT
ejpam-4850	95	9	γ	γ	PROPN
ejpam-4850	95	10	)	)	PUNCT
ejpam-4850	95	11	(	(	PUNCT
ejpam-4850	95	12	(	(	PUNCT
ejpam-4850	95	13	1−	1−	NUM
ejpam-4850	95	14	η)x+	η)x+	NUM
ejpam-4850	95	15	η	η	PROPN
ejpam-4850	95	16	a+b	a+b	NUM
ejpam-4850	95	17	2	2	NUM
ejpam-4850	95	18	)	)	PUNCT
ejpam-4850	95	19	(	(	PUNCT
ejpam-4850	95	20	dη)γ	dη)γ	PROPN
ejpam-4850	95	21	,	,	PUNCT
ejpam-4850	95	22	i3	i3	NOUN
ejpam-4850	95	23	=	=	SYM
ejpam-4850	95	24	1	1	NUM
ejpam-4850	95	25	γ(γ+1	γ(γ+1	NUM
ejpam-4850	95	26	)	)	PUNCT
ejpam-4850	96	1	1∫	1∫	NUM
ejpam-4850	96	2	0	0	NUM
ejpam-4850	96	3	ηγj	ηγj	NOUN
ejpam-4850	96	4	(	(	PUNCT
ejpam-4850	96	5	γ	γ	X
ejpam-4850	96	6	)	)	PUNCT
ejpam-4850	96	7	(	(	PUNCT
ejpam-4850	96	8	(	(	PUNCT
ejpam-4850	96	9	1−	1−	NUM
ejpam-4850	96	10	η	η	NOUN
ejpam-4850	96	11	)	)	PUNCT
ejpam-4850	96	12	a+b	a+b	NUM
ejpam-4850	96	13	2	2	NUM
ejpam-4850	96	14	+	+	SYM
ejpam-4850	96	15	η	η	PROPN
ejpam-4850	96	16	(	(	PUNCT
ejpam-4850	96	17	a+	a+	PUNCT
ejpam-4850	96	18	b−	b−	PROPN
ejpam-4850	96	19	x	x	PROPN
ejpam-4850	96	20	)	)	PUNCT
ejpam-4850	96	21	)	)	PUNCT
ejpam-4850	97	1	(	(	PUNCT
ejpam-4850	97	2	dη)γ	dη)γ	PROPN
ejpam-4850	97	3	and	and	CCONJ
ejpam-4850	97	4	i4	i4	PROPN
ejpam-4850	97	5	=	=	PROPN
ejpam-4850	97	6	1	1	NUM
ejpam-4850	97	7	γ(γ+1	γ(γ+1	NUM
ejpam-4850	97	8	)	)	PUNCT
ejpam-4850	98	1	1∫	1∫	NUM
ejpam-4850	98	2	0	0	NUM
ejpam-4850	98	3	(	(	PUNCT
ejpam-4850	98	4	η	η	PROPN
ejpam-4850	98	5	−	−	PROPN
ejpam-4850	98	6	1)γ	1)γ	PROPN
ejpam-4850	98	7	j	j	PROPN
ejpam-4850	98	8	(	(	PUNCT
ejpam-4850	98	9	γ	γ	PROPN
ejpam-4850	98	10	)	)	PUNCT
ejpam-4850	98	11	(	(	PUNCT
ejpam-4850	98	12	(	(	PUNCT
ejpam-4850	98	13	1−	1−	NUM
ejpam-4850	98	14	η	η	NOUN
ejpam-4850	98	15	)	)	PUNCT
ejpam-4850	98	16	(	(	PUNCT
ejpam-4850	98	17	a+	a+	PUNCT
ejpam-4850	98	18	b−	b−	PROPN
ejpam-4850	98	19	x	x	PROPN
ejpam-4850	98	20	)	)	PUNCT
ejpam-4850	98	21	+	+	CCONJ
ejpam-4850	98	22	ηb	ηb	X
ejpam-4850	98	23	)	)	PUNCT
ejpam-4850	98	24	(	(	PUNCT
ejpam-4850	98	25	dη)γ	dη)γ	PROPN
ejpam-4850	98	26	.	.	PUNCT
ejpam-4850	99	1	using	use	VERB
ejpam-4850	99	2	lemmas	lemmas	PROPN
ejpam-4850	99	3	1	1	NUM
ejpam-4850	99	4	and	and	CCONJ
ejpam-4850	99	5	2	2	NUM
ejpam-4850	99	6	,	,	PUNCT
ejpam-4850	99	7	we	we	PRON
ejpam-4850	99	8	get	get	VERB
ejpam-4850	99	9	i1	i1	PROPN
ejpam-4850	99	10	=	=	PUNCT
ejpam-4850	99	11	1γ	1γ	NUM
ejpam-4850	99	12	(	(	PUNCT
ejpam-4850	99	13	x−a)γ	x−a)γ	PROPN
ejpam-4850	99	14	ηγj	ηγj	VERB
ejpam-4850	99	15	(	(	PUNCT
ejpam-4850	99	16	(	(	PUNCT
ejpam-4850	99	17	1−	1−	NUM
ejpam-4850	99	18	η	η	NOUN
ejpam-4850	99	19	)	)	PUNCT
ejpam-4850	99	20	a+	a+	PRON
ejpam-4850	99	21	ηx	ηx	NOUN
ejpam-4850	99	22	)	)	PUNCT
ejpam-4850	99	23	∣∣∣η=1	∣∣∣η=1	X
ejpam-4850	100	1	η=0	η=0	PRON
ejpam-4850	100	2	(	(	PUNCT
ejpam-4850	100	3	7	7	NUM
ejpam-4850	100	4	)	)	PUNCT
ejpam-4850	100	5	−	−	PROPN
ejpam-4850	100	6	1γ	1γ	NUM
ejpam-4850	100	7	(	(	PUNCT
ejpam-4850	100	8	x−a)γγ(γ+1	x−a)γγ(γ+1	NUM
ejpam-4850	100	9	)	)	PUNCT
ejpam-4850	101	1	1∫	1∫	NUM
ejpam-4850	101	2	0	0	NUM
ejpam-4850	101	3	γ	γ	X
ejpam-4850	101	4	(	(	PUNCT
ejpam-4850	101	5	γ	γ	X
ejpam-4850	101	6	+	+	X
ejpam-4850	101	7	1)j	1)j	NUM
ejpam-4850	101	8	(	(	PUNCT
ejpam-4850	101	9	(	(	PUNCT
ejpam-4850	101	10	1−	1−	NUM
ejpam-4850	101	11	η	η	NOUN
ejpam-4850	101	12	)	)	PUNCT
ejpam-4850	101	13	a+	a+	PUNCT
ejpam-4850	101	14	ηx	ηx	NOUN
ejpam-4850	101	15	)	)	PUNCT
ejpam-4850	101	16	(	(	PUNCT
ejpam-4850	101	17	dη)γ	dη)γ	PROPN
ejpam-4850	101	18	=	=	SYM
ejpam-4850	101	19	1γ	1γ	NUM
ejpam-4850	101	20	(	(	PUNCT
ejpam-4850	101	21	x−a)γ	x−a)γ	PROPN
ejpam-4850	101	22	j	j	PROPN
ejpam-4850	101	23	(	(	PUNCT
ejpam-4850	101	24	x)−	x)−	PROPN
ejpam-4850	101	25	1γ	1γ	PROPN
ejpam-4850	101	26	(	(	PUNCT
ejpam-4850	101	27	x−a)γ	x−a)γ	PROPN
ejpam-4850	101	28	1∫	1∫	NUM
ejpam-4850	101	29	0	0	NUM
ejpam-4850	101	30	j	j	NOUN
ejpam-4850	101	31	(	(	PUNCT
ejpam-4850	101	32	(	(	PUNCT
ejpam-4850	101	33	1−	1−	NUM
ejpam-4850	101	34	η	η	NOUN
ejpam-4850	101	35	)	)	PUNCT
ejpam-4850	101	36	a+	a+	PUNCT
ejpam-4850	101	37	ηx	ηx	NOUN
ejpam-4850	101	38	)	)	PUNCT
ejpam-4850	101	39	(	(	PUNCT
ejpam-4850	101	40	dκ)γ	dκ)γ	NOUN
ejpam-4850	101	41	=	=	SYM
ejpam-4850	101	42	1γ	1γ	NUM
ejpam-4850	101	43	(	(	PUNCT
ejpam-4850	101	44	x−a)γ	x−a)γ	PROPN
ejpam-4850	101	45	j	j	PROPN
ejpam-4850	101	46	(	(	PUNCT
ejpam-4850	101	47	x)−	x)−	PROPN
ejpam-4850	101	48	1γ	1γ	NUM
ejpam-4850	101	49	(	(	PUNCT
ejpam-4850	101	50	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	101	51	x∫	x∫	PROPN
ejpam-4850	101	52	a	a	DET
ejpam-4850	101	53	j	j	PROPN
ejpam-4850	101	54	(	(	PUNCT
ejpam-4850	101	55	ϖ	ϖ	NOUN
ejpam-4850	101	56	)	)	PUNCT
ejpam-4850	101	57	(	(	PUNCT
ejpam-4850	101	58	dϖ)γ	dϖ)γ	NOUN
ejpam-4850	101	59	.	.	PUNCT
ejpam-4850	102	1	w.	w.	PROPN
ejpam-4850	102	2	saleh	saleh	PROPN
ejpam-4850	102	3	et	et	PROPN
ejpam-4850	102	4	al	al	PROPN
ejpam-4850	102	5	.	.	PUNCT
ejpam-4850	102	6	/	/	SYM
ejpam-4850	102	7	eur	eur	PROPN
ejpam-4850	102	8	.	.	PUNCT
ejpam-4850	103	1	j.	j.	PROPN
ejpam-4850	103	2	pure	pure	PROPN
ejpam-4850	103	3	appl	appl	PROPN
ejpam-4850	103	4	.	.	PROPN
ejpam-4850	103	5	math	math	PROPN
ejpam-4850	103	6	,	,	PUNCT
ejpam-4850	103	7	16	16	NUM
ejpam-4850	103	8	(	(	PUNCT
ejpam-4850	103	9	3	3	NUM
ejpam-4850	103	10	)	)	PUNCT
ejpam-4850	103	11	(	(	PUNCT
ejpam-4850	103	12	2023	2023	NUM
ejpam-4850	103	13	)	)	PUNCT
ejpam-4850	103	14	,	,	PUNCT
ejpam-4850	103	15	1359	1359	NUM
ejpam-4850	103	16	-	-	SYM
ejpam-4850	103	17	1380	1380	NUM
ejpam-4850	103	18	1364	1364	NUM
ejpam-4850	103	19	similarly	similarly	ADV
ejpam-4850	103	20	,	,	PUNCT
ejpam-4850	103	21	we	we	PRON
ejpam-4850	103	22	obtain	obtain	VERB
ejpam-4850	103	23	i2	i2	NOUN
ejpam-4850	103	24	=	=	NOUN
ejpam-4850	103	25	2γ	2γ	NOUN
ejpam-4850	103	26	(	(	PUNCT
ejpam-4850	103	27	a+b−2x)γ	a+b−2x)γ	NOUN
ejpam-4850	103	28	(	(	PUNCT
ejpam-4850	103	29	η	η	PROPN
ejpam-4850	103	30	−	−	PROPN
ejpam-4850	103	31	1)γ	1)γ	PROPN
ejpam-4850	103	32	j	j	PROPN
ejpam-4850	103	33	(	(	PUNCT
ejpam-4850	103	34	(	(	PUNCT
ejpam-4850	103	35	1−	1−	NUM
ejpam-4850	103	36	η)x+	η)x+	NUM
ejpam-4850	103	37	η	η	PROPN
ejpam-4850	103	38	a+b	a+b	NUM
ejpam-4850	103	39	2	2	NUM
ejpam-4850	103	40	)	)	PUNCT
ejpam-4850	103	41	∣∣∣η=1	∣∣∣η=1	X
ejpam-4850	104	1	η=0	η=0	PROPN
ejpam-4850	104	2	(	(	PUNCT
ejpam-4850	104	3	8)	8)	NUM
ejpam-4850	104	4	−	−	NOUN
ejpam-4850	104	5	2γ	2γ	NOUN
ejpam-4850	104	6	(	(	PUNCT
ejpam-4850	104	7	a+b−2x)γγ(γ+1	a+b−2x)γγ(γ+1	NOUN
ejpam-4850	104	8	)	)	PUNCT
ejpam-4850	105	1	1∫	1∫	NUM
ejpam-4850	105	2	0	0	NUM
ejpam-4850	105	3	γ	γ	X
ejpam-4850	105	4	(	(	PUNCT
ejpam-4850	105	5	γ	γ	X
ejpam-4850	105	6	+	+	X
ejpam-4850	105	7	1)j	1)j	NUM
ejpam-4850	105	8	(	(	PUNCT
ejpam-4850	105	9	(	(	PUNCT
ejpam-4850	105	10	1−	1−	NUM
ejpam-4850	105	11	η)x+	η)x+	NUM
ejpam-4850	105	12	η	η	PROPN
ejpam-4850	105	13	a+b	a+b	NUM
ejpam-4850	105	14	2	2	NUM
ejpam-4850	105	15	)	)	PUNCT
ejpam-4850	105	16	(	(	PUNCT
ejpam-4850	105	17	dη)γ	dη)γ	PROPN
ejpam-4850	105	18	=	=	SYM
ejpam-4850	105	19	2γ	2γ	NOUN
ejpam-4850	105	20	(	(	PUNCT
ejpam-4850	105	21	a+b−2x)γ	a+b−2x)γ	NOUN
ejpam-4850	105	22	j	j	PROPN
ejpam-4850	105	23	(	(	PUNCT
ejpam-4850	105	24	x)−	x)−	PROPN
ejpam-4850	105	25	4γ	4γ	PROPN
ejpam-4850	105	26	(	(	PUNCT
ejpam-4850	105	27	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	105	28	a+b	a+b	NUM
ejpam-4850	105	29	2∫	2∫	NUM
ejpam-4850	105	30	x	x	SYM
ejpam-4850	105	31	j	j	PROPN
ejpam-4850	105	32	(	(	PUNCT
ejpam-4850	105	33	ϖ	ϖ	NOUN
ejpam-4850	105	34	)	)	PUNCT
ejpam-4850	105	35	(	(	PUNCT
ejpam-4850	105	36	dϖ)γ	dϖ)γ	NOUN
ejpam-4850	105	37	,	,	PUNCT
ejpam-4850	105	38	i3	i3	NOUN
ejpam-4850	105	39	=	=	SYM
ejpam-4850	105	40	2γ	2γ	NOUN
ejpam-4850	105	41	(	(	PUNCT
ejpam-4850	105	42	a+b−2x)γ	a+b−2x)γ	NOUN
ejpam-4850	105	43	ηγj	ηγj	NOUN
ejpam-4850	105	44	(	(	PUNCT
ejpam-4850	105	45	(	(	PUNCT
ejpam-4850	105	46	1−	1−	NUM
ejpam-4850	105	47	η	η	NOUN
ejpam-4850	105	48	)	)	PUNCT
ejpam-4850	105	49	a+b	a+b	NUM
ejpam-4850	105	50	2	2	NUM
ejpam-4850	105	51	+	+	SYM
ejpam-4850	105	52	η	η	PROPN
ejpam-4850	105	53	(	(	PUNCT
ejpam-4850	105	54	a+	a+	PUNCT
ejpam-4850	105	55	b−	b−	PROPN
ejpam-4850	105	56	x	x	PROPN
ejpam-4850	105	57	)	)	PUNCT
ejpam-4850	105	58	)	)	PUNCT
ejpam-4850	105	59	∣∣∣η=1	∣∣∣η=1	X
ejpam-4850	106	1	η=0	η=0	PRON
ejpam-4850	106	2	(	(	PUNCT
ejpam-4850	106	3	9	9	NUM
ejpam-4850	106	4	)	)	PUNCT
ejpam-4850	106	5	−	−	NOUN
ejpam-4850	106	6	2γ	2γ	NOUN
ejpam-4850	106	7	(	(	PUNCT
ejpam-4850	106	8	a+b−2x)γγ(γ+1	a+b−2x)γγ(γ+1	NOUN
ejpam-4850	106	9	)	)	PUNCT
ejpam-4850	107	1	1∫	1∫	NUM
ejpam-4850	107	2	0	0	NUM
ejpam-4850	107	3	γ	γ	X
ejpam-4850	107	4	(	(	PUNCT
ejpam-4850	107	5	γ	γ	X
ejpam-4850	107	6	+	+	X
ejpam-4850	107	7	1)j	1)j	NUM
ejpam-4850	107	8	(	(	PUNCT
ejpam-4850	107	9	(	(	PUNCT
ejpam-4850	107	10	1−	1−	NUM
ejpam-4850	107	11	η	η	NOUN
ejpam-4850	107	12	)	)	PUNCT
ejpam-4850	107	13	a+b	a+b	NUM
ejpam-4850	107	14	2	2	NUM
ejpam-4850	107	15	+	+	SYM
ejpam-4850	107	16	η	η	PROPN
ejpam-4850	107	17	(	(	PUNCT
ejpam-4850	107	18	a+	a+	PUNCT
ejpam-4850	107	19	b−	b−	PROPN
ejpam-4850	107	20	x	x	PROPN
ejpam-4850	107	21	)	)	PUNCT
ejpam-4850	107	22	)	)	PUNCT
ejpam-4850	108	1	(	(	PUNCT
ejpam-4850	108	2	dη)γ	dη)γ	PROPN
ejpam-4850	108	3	=	=	SYM
ejpam-4850	108	4	2γ	2γ	NOUN
ejpam-4850	108	5	(	(	PUNCT
ejpam-4850	108	6	a+b−2x)γ	a+b−2x)γ	NOUN
ejpam-4850	108	7	j	j	PROPN
ejpam-4850	108	8	(	(	PUNCT
ejpam-4850	108	9	a+	a+	PUNCT
ejpam-4850	108	10	b−	b−	PROPN
ejpam-4850	108	11	x)−	x)−	PROPN
ejpam-4850	108	12	(	(	PUNCT
ejpam-4850	108	13	4)γ	4)γ	PART
ejpam-4850	108	14	(	(	PUNCT
ejpam-4850	108	15	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	108	16	a+b−x∫	a+b−x∫	PROPN
ejpam-4850	108	17	a+b	a+b	NUM
ejpam-4850	108	18	2	2	NUM
ejpam-4850	108	19	j	j	NOUN
ejpam-4850	108	20	(	(	PUNCT
ejpam-4850	108	21	ϖ	ϖ	NOUN
ejpam-4850	108	22	)	)	PUNCT
ejpam-4850	108	23	(	(	PUNCT
ejpam-4850	108	24	dϖ)γ	dϖ)γ	NOUN
ejpam-4850	108	25	and	and	CCONJ
ejpam-4850	108	26	i4	i4	PROPN
ejpam-4850	108	27	=	=	SYM
ejpam-4850	108	28	1γ	1γ	PROPN
ejpam-4850	108	29	(	(	PUNCT
ejpam-4850	108	30	x−a)γ	x−a)γ	PROPN
ejpam-4850	108	31	(	(	PUNCT
ejpam-4850	108	32	η	η	PROPN
ejpam-4850	108	33	−	−	PROPN
ejpam-4850	108	34	1)γ	1)γ	PROPN
ejpam-4850	108	35	j	j	PROPN
ejpam-4850	108	36	(	(	PUNCT
ejpam-4850	108	37	(	(	PUNCT
ejpam-4850	108	38	1−	1−	NUM
ejpam-4850	108	39	η	η	NOUN
ejpam-4850	108	40	)	)	PUNCT
ejpam-4850	108	41	(	(	PUNCT
ejpam-4850	108	42	a+	a+	PUNCT
ejpam-4850	108	43	b−	b−	PROPN
ejpam-4850	108	44	x	x	PROPN
ejpam-4850	108	45	)	)	PUNCT
ejpam-4850	108	46	+	+	CCONJ
ejpam-4850	108	47	ηb	ηb	X
ejpam-4850	108	48	)	)	PUNCT
ejpam-4850	108	49	∣∣∣η=1	∣∣∣η=1	X
ejpam-4850	109	1	η=0	η=0	PRON
ejpam-4850	109	2	(	(	PUNCT
ejpam-4850	109	3	10	10	NUM
ejpam-4850	109	4	)	)	PUNCT
ejpam-4850	109	5	−	−	PROPN
ejpam-4850	109	6	1γ	1γ	NUM
ejpam-4850	109	7	(	(	PUNCT
ejpam-4850	109	8	x−a)γγ(γ+1	x−a)γγ(γ+1	NUM
ejpam-4850	109	9	)	)	PUNCT
ejpam-4850	110	1	1∫	1∫	NUM
ejpam-4850	110	2	0	0	NUM
ejpam-4850	110	3	γ	γ	X
ejpam-4850	110	4	(	(	PUNCT
ejpam-4850	110	5	γ	γ	X
ejpam-4850	110	6	+	+	X
ejpam-4850	110	7	1)j	1)j	NUM
ejpam-4850	110	8	(	(	PUNCT
ejpam-4850	110	9	(	(	PUNCT
ejpam-4850	110	10	1−	1−	NUM
ejpam-4850	110	11	η	η	NOUN
ejpam-4850	110	12	)	)	PUNCT
ejpam-4850	110	13	(	(	PUNCT
ejpam-4850	110	14	a+	a+	PUNCT
ejpam-4850	110	15	b−	b−	PROPN
ejpam-4850	110	16	x	x	PROPN
ejpam-4850	110	17	)	)	PUNCT
ejpam-4850	110	18	+	+	CCONJ
ejpam-4850	110	19	ηb	ηb	X
ejpam-4850	110	20	)	)	PUNCT
ejpam-4850	110	21	(	(	PUNCT
ejpam-4850	110	22	dη)γ	dη)γ	PROPN
ejpam-4850	110	23	=	=	SYM
ejpam-4850	110	24	1γ	1γ	NUM
ejpam-4850	110	25	(	(	PUNCT
ejpam-4850	110	26	x−a)γ	x−a)γ	PROPN
ejpam-4850	110	27	j	j	PROPN
ejpam-4850	110	28	(	(	PUNCT
ejpam-4850	110	29	a+	a+	PUNCT
ejpam-4850	110	30	b−	b−	PROPN
ejpam-4850	110	31	x)−	x)−	PROPN
ejpam-4850	110	32	1γ	1γ	PROPN
ejpam-4850	110	33	(	(	PUNCT
ejpam-4850	110	34	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	110	35	b∫	b∫	PROPN
ejpam-4850	110	36	a+b−x	a+b−x	PROPN
ejpam-4850	110	37	j	j	PROPN
ejpam-4850	110	38	(	(	PUNCT
ejpam-4850	110	39	ϖ	ϖ	NOUN
ejpam-4850	110	40	)	)	PUNCT
ejpam-4850	110	41	(	(	PUNCT
ejpam-4850	110	42	dϖ)γ	dϖ)γ	NOUN
ejpam-4850	110	43	.	.	PUNCT
ejpam-4850	111	1	after	after	ADP
ejpam-4850	111	2	substituting	substitute	VERB
ejpam-4850	111	3	equations	equation	NOUN
ejpam-4850	111	4	(	(	PUNCT
ejpam-4850	111	5	7)-(10	7)-(10	NOUN
ejpam-4850	111	6	)	)	PUNCT
ejpam-4850	111	7	into	into	ADP
ejpam-4850	111	8	equation	equation	NOUN
ejpam-4850	111	9	(	(	PUNCT
ejpam-4850	111	10	6	6	NUM
ejpam-4850	111	11	)	)	PUNCT
ejpam-4850	111	12	,	,	PUNCT
ejpam-4850	111	13	we	we	PRON
ejpam-4850	111	14	multiply	multiply	VERB
ejpam-4850	111	15	and	and	CCONJ
ejpam-4850	111	16	divide	divide	VERB
ejpam-4850	111	17	the	the	DET
ejpam-4850	111	18	resulting	result	VERB
ejpam-4850	111	19	equation	equation	NOUN
ejpam-4850	111	20	by	by	ADP
ejpam-4850	111	21	γ(γ	γ(γ	NOUN
ejpam-4850	111	22	+	+	CCONJ
ejpam-4850	111	23	1	1	X
ejpam-4850	111	24	)	)	PUNCT
ejpam-4850	111	25	to	to	PART
ejpam-4850	111	26	obtain	obtain	VERB
ejpam-4850	111	27	the	the	DET
ejpam-4850	111	28	desired	desire	VERB
ejpam-4850	111	29	result	result	NOUN
ejpam-4850	111	30	.	.	PUNCT
ejpam-4850	112	1	theorem	theorem	NOUN
ejpam-4850	112	2	1	1	X
ejpam-4850	112	3	.	.	PUNCT
ejpam-4850	112	4	suppose	suppose	VERB
ejpam-4850	113	1	j	j	NOUN
ejpam-4850	113	2	:	:	PUNCT
ejpam-4850	114	1	[	[	X
ejpam-4850	114	2	a	a	X
ejpam-4850	114	3	,	,	PUNCT
ejpam-4850	114	4	b	b	NOUN
ejpam-4850	114	5	]	]	X
ejpam-4850	114	6	→	→	PUNCT
ejpam-4850	114	7	rγ	rγ	PRON
ejpam-4850	114	8	is	be	AUX
ejpam-4850	114	9	a	a	DET
ejpam-4850	114	10	differentiable	differentiable	ADJ
ejpam-4850	114	11	function	function	NOUN
ejpam-4850	114	12	on	on	ADP
ejpam-4850	114	13	[	[	X
ejpam-4850	114	14	a	a	X
ejpam-4850	114	15	,	,	PUNCT
ejpam-4850	114	16	b	b	NOUN
ejpam-4850	114	17	]	]	X
ejpam-4850	114	18	such	such	ADJ
ejpam-4850	114	19	that	that	SCONJ
ejpam-4850	114	20	j	j	PROPN
ejpam-4850	114	21	∈	∈	PROPN
ejpam-4850	114	22	dγ	dγ	ADP
ejpam-4850	114	23	[	[	X
ejpam-4850	114	24	a	a	X
ejpam-4850	114	25	,	,	PUNCT
ejpam-4850	114	26	b	b	NOUN
ejpam-4850	114	27	]	]	X
ejpam-4850	114	28	and	and	CCONJ
ejpam-4850	114	29	j	j	PROPN
ejpam-4850	114	30	(	(	PUNCT
ejpam-4850	114	31	γ	γ	PROPN
ejpam-4850	114	32	)	)	PUNCT
ejpam-4850	114	33	∈	∈	NOUN
ejpam-4850	114	34	cγ	cγ	NOUN
ejpam-4850	114	35	[	[	X
ejpam-4850	114	36	a	a	X
ejpam-4850	114	37	,	,	PUNCT
ejpam-4850	114	38	b	b	NOUN
ejpam-4850	114	39	]	]	X
ejpam-4850	114	40	with	with	ADP
ejpam-4850	114	41	0	0	NUM
ejpam-4850	114	42	≤	≤	NOUN
ejpam-4850	114	43	a	a	DET
ejpam-4850	114	44	<	<	X
ejpam-4850	114	45	b.	b.	NOUN
ejpam-4850	114	46	if	if	SCONJ
ejpam-4850	114	47	∣∣j	∣∣j	X
ejpam-4850	114	48	(	(	PUNCT
ejpam-4850	114	49	γ	γ	NOUN
ejpam-4850	114	50	)	)	PUNCT
ejpam-4850	114	51	∣∣	∣∣	NUM
ejpam-4850	114	52	is	be	AUX
ejpam-4850	114	53	generalized	generalize	VERB
ejpam-4850	114	54	s	s	NOUN
ejpam-4850	114	55	-	-	NOUN
ejpam-4850	114	56	convex	convex	NOUN
ejpam-4850	114	57	in	in	ADP
ejpam-4850	114	58	the	the	DET
ejpam-4850	114	59	second	second	ADJ
ejpam-4850	114	60	sense	sense	NOUN
ejpam-4850	114	61	on	on	ADP
ejpam-4850	114	62	[	[	X
ejpam-4850	114	63	a	a	X
ejpam-4850	114	64	,	,	PUNCT
ejpam-4850	114	65	b	b	NOUN
ejpam-4850	114	66	]	]	X
ejpam-4850	114	67	,	,	PUNCT
ejpam-4850	114	68	then	then	ADV
ejpam-4850	114	69	the	the	DET
ejpam-4850	114	70	following	follow	VERB
ejpam-4850	114	71	inequality	inequality	NOUN
ejpam-4850	114	72	holds∣∣∣j	holds∣∣∣j	PROPN
ejpam-4850	114	73	(	(	PUNCT
ejpam-4850	114	74	x)+j	x)+j	PROPN
ejpam-4850	114	75	(	(	PUNCT
ejpam-4850	114	76	a+b−x	a+b−x	PROPN
ejpam-4850	114	77	)	)	PUNCT
ejpam-4850	114	78	2γ	2γ	NOUN
ejpam-4850	114	79	−	−	PROPN
ejpam-4850	114	80	γ(γ+1	γ(γ+1	NUM
ejpam-4850	114	81	)	)	PUNCT
ejpam-4850	114	82	(	(	PUNCT
ejpam-4850	114	83	b−a)γ	b−a)γ	NOUN
ejpam-4850	114	84	ai	ai	VERB
ejpam-4850	114	85	γ	γ	PROPN
ejpam-4850	114	86	b	b	PROPN
ejpam-4850	114	87	j	j	PROPN
ejpam-4850	114	88	(	(	PUNCT
ejpam-4850	114	89	t	t	PROPN
ejpam-4850	114	90	)	)	PUNCT
ejpam-4850	114	91	∣∣∣	∣∣∣	NOUN
ejpam-4850	114	92	≤	≤	NUM
ejpam-4850	114	93	(	(	PUNCT
ejpam-4850	114	94	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	114	95	(	(	PUNCT
ejpam-4850	114	96	b−a)γ	b−a)γ	PROPN
ejpam-4850	114	97	(	(	PUNCT
ejpam-4850	114	98	(	(	PUNCT
ejpam-4850	114	99	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	114	100	)	)	PUNCT
ejpam-4850	114	101	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	114	102	)	)	PUNCT
ejpam-4850	114	103	−	−	PROPN
ejpam-4850	114	104	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	114	105	)	)	PUNCT
ejpam-4850	114	106	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	114	107	)	)	PUNCT
ejpam-4850	114	108	)	)	PUNCT
ejpam-4850	115	1	(	(	PUNCT
ejpam-4850	115	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	115	3	(	(	PUNCT
ejpam-4850	115	4	γ	γ	PROPN
ejpam-4850	115	5	)	)	PUNCT
ejpam-4850	115	6	(	(	PUNCT
ejpam-4850	115	7	a	a	NOUN
ejpam-4850	115	8	)	)	PUNCT
ejpam-4850	115	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	115	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	115	11	(	(	PUNCT
ejpam-4850	115	12	γ	γ	PROPN
ejpam-4850	115	13	)	)	PUNCT
ejpam-4850	115	14	(	(	PUNCT
ejpam-4850	115	15	b	b	NOUN
ejpam-4850	115	16	)	)	PUNCT
ejpam-4850	115	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	115	18	)	)	PUNCT
ejpam-4850	115	19	w.	w.	PROPN
ejpam-4850	115	20	saleh	saleh	PROPN
ejpam-4850	115	21	et	et	PROPN
ejpam-4850	115	22	al	al	PROPN
ejpam-4850	115	23	.	.	PUNCT
ejpam-4850	115	24	/	/	SYM
ejpam-4850	115	25	eur	eur	PROPN
ejpam-4850	115	26	.	.	PUNCT
ejpam-4850	116	1	j.	j.	PROPN
ejpam-4850	116	2	pure	pure	PROPN
ejpam-4850	116	3	appl	appl	PROPN
ejpam-4850	116	4	.	.	PROPN
ejpam-4850	116	5	math	math	PROPN
ejpam-4850	116	6	,	,	PUNCT
ejpam-4850	116	7	16	16	NUM
ejpam-4850	116	8	(	(	PUNCT
ejpam-4850	116	9	3	3	NUM
ejpam-4850	116	10	)	)	PUNCT
ejpam-4850	116	11	(	(	PUNCT
ejpam-4850	116	12	2023	2023	NUM
ejpam-4850	116	13	)	)	PUNCT
ejpam-4850	116	14	,	,	PUNCT
ejpam-4850	116	15	1359	1359	NUM
ejpam-4850	116	16	-	-	SYM
ejpam-4850	116	17	1380	1380	NUM
ejpam-4850	116	18	1365	1365	NUM
ejpam-4850	116	19	+	+	CCONJ
ejpam-4850	116	20	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	116	21	)	)	PUNCT
ejpam-4850	116	22	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	116	23	)	)	PUNCT
ejpam-4850	116	24	(	(	PUNCT
ejpam-4850	116	25	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	116	26	(	(	PUNCT
ejpam-4850	116	27	γ	γ	PROPN
ejpam-4850	116	28	)	)	PUNCT
ejpam-4850	116	29	(	(	PUNCT
ejpam-4850	116	30	x	x	X
ejpam-4850	116	31	)	)	PUNCT
ejpam-4850	116	32	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	116	33	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	116	34	(	(	PUNCT
ejpam-4850	116	35	γ	γ	PROPN
ejpam-4850	116	36	)	)	PUNCT
ejpam-4850	116	37	(	(	PUNCT
ejpam-4850	116	38	a+	a+	PUNCT
ejpam-4850	116	39	b−	b−	PROPN
ejpam-4850	116	40	x	x	NOUN
ejpam-4850	116	41	)	)	PUNCT
ejpam-4850	116	42	∣∣∣	∣∣∣	ADJ
ejpam-4850	116	43	)	)	PUNCT
ejpam-4850	116	44	)	)	PUNCT
ejpam-4850	117	1	+	+	CCONJ
ejpam-4850	117	2	(	(	PUNCT
ejpam-4850	117	3	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	117	4	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	117	5	(	(	PUNCT
ejpam-4850	117	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	117	7	)	)	PUNCT
ejpam-4850	117	8	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	117	9	)	)	PUNCT
ejpam-4850	117	10	(	(	PUNCT
ejpam-4850	117	11	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	117	12	(	(	PUNCT
ejpam-4850	117	13	γ	γ	PROPN
ejpam-4850	117	14	)	)	PUNCT
ejpam-4850	117	15	(	(	PUNCT
ejpam-4850	117	16	x	x	X
ejpam-4850	117	17	)	)	PUNCT
ejpam-4850	117	18	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	117	19	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	117	20	(	(	PUNCT
ejpam-4850	117	21	γ	γ	PROPN
ejpam-4850	117	22	)	)	PUNCT
ejpam-4850	117	23	(	(	PUNCT
ejpam-4850	117	24	a+	a+	PUNCT
ejpam-4850	117	25	b−	b−	PROPN
ejpam-4850	117	26	x	x	NOUN
ejpam-4850	117	27	)	)	PUNCT
ejpam-4850	117	28	∣∣∣	∣∣∣	ADJ
ejpam-4850	117	29	)	)	PUNCT
ejpam-4850	118	1	+	+	CCONJ
ejpam-4850	118	2	2γ	2γ	NOUN
ejpam-4850	118	3	(	(	PUNCT
ejpam-4850	118	4	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	118	5	)	)	PUNCT
ejpam-4850	118	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	118	7	)	)	PUNCT
ejpam-4850	118	8	−	−	PROPN
ejpam-4850	118	9	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	118	10	)	)	PUNCT
ejpam-4850	118	11	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	118	12	)	)	PUNCT
ejpam-4850	118	13	)	)	PUNCT
ejpam-4850	119	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	119	2	(	(	PUNCT
ejpam-4850	119	3	γ	γ	PROPN
ejpam-4850	119	4	)	)	PUNCT
ejpam-4850	119	5	(	(	PUNCT
ejpam-4850	119	6	a+b	a+b	NUM
ejpam-4850	119	7	2	2	NUM
ejpam-4850	119	8	)	)	PUNCT
ejpam-4850	119	9	∣∣∣	∣∣∣	ADJ
ejpam-4850	119	10	)	)	PUNCT
ejpam-4850	119	11	.	.	PUNCT
ejpam-4850	120	1	proof	proof	NOUN
ejpam-4850	120	2	.	.	PUNCT
ejpam-4850	121	1	using	use	VERB
ejpam-4850	121	2	lemma	lemma	PROPN
ejpam-4850	121	3	4	4	NUM
ejpam-4850	121	4	,	,	PUNCT
ejpam-4850	121	5	properties	property	NOUN
ejpam-4850	121	6	of	of	ADP
ejpam-4850	121	7	modulus	modulus	NOUN
ejpam-4850	121	8	,	,	PUNCT
ejpam-4850	121	9	and	and	CCONJ
ejpam-4850	121	10	the	the	DET
ejpam-4850	121	11	generalized	generalized	ADJ
ejpam-4850	121	12	s	s	PROPN
ejpam-4850	121	13	-	-	PUNCT
ejpam-4850	121	14	convexity	convexity	NOUN
ejpam-4850	121	15	of∣∣j	of∣∣j	NOUN
ejpam-4850	121	16	(	(	PUNCT
ejpam-4850	121	17	γ	γ	X
ejpam-4850	121	18	)	)	PUNCT
ejpam-4850	121	19	∣∣	∣∣	ADJ
ejpam-4850	121	20	,	,	PUNCT
ejpam-4850	121	21	we	we	PRON
ejpam-4850	121	22	can	can	AUX
ejpam-4850	121	23	conclude	conclude	VERB
ejpam-4850	121	24	that∣∣∣j	that∣∣∣j	NOUN
ejpam-4850	121	25	(	(	PUNCT
ejpam-4850	121	26	x)+j	x)+j	PROPN
ejpam-4850	121	27	(	(	PUNCT
ejpam-4850	121	28	a+b−x	a+b−x	PROPN
ejpam-4850	121	29	)	)	PUNCT
ejpam-4850	121	30	2γ	2γ	NOUN
ejpam-4850	121	31	−	−	PROPN
ejpam-4850	121	32	γ(γ+1	γ(γ+1	NUM
ejpam-4850	121	33	)	)	PUNCT
ejpam-4850	121	34	(	(	PUNCT
ejpam-4850	121	35	b−a)γ	b−a)γ	NOUN
ejpam-4850	121	36	ai	ai	VERB
ejpam-4850	121	37	γ	γ	PROPN
ejpam-4850	121	38	b	b	PROPN
ejpam-4850	121	39	j	j	PROPN
ejpam-4850	121	40	(	(	PUNCT
ejpam-4850	121	41	t	t	PROPN
ejpam-4850	121	42	)	)	PUNCT
ejpam-4850	121	43	∣∣∣	∣∣∣	NOUN
ejpam-4850	121	44	≤	≤	NUM
ejpam-4850	121	45	(	(	PUNCT
ejpam-4850	121	46	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	121	47	(	(	PUNCT
ejpam-4850	121	48	b−a)γ	b−a)γ	NOUN
ejpam-4850	121	49			PROPN
ejpam-4850	121	50	1	1	NUM
ejpam-4850	121	51	γ(γ+1	γ(γ+1	NUM
ejpam-4850	121	52	)	)	PUNCT
ejpam-4850	122	1	1∫	1∫	NUM
ejpam-4850	122	2	0	0	NUM
ejpam-4850	122	3	ηγ	ηγ	PROPN
ejpam-4850	122	4	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	122	5	(	(	PUNCT
ejpam-4850	122	6	γ	γ	PROPN
ejpam-4850	122	7	)	)	PUNCT
ejpam-4850	122	8	(	(	PUNCT
ejpam-4850	122	9	(	(	PUNCT
ejpam-4850	122	10	1−	1−	NUM
ejpam-4850	122	11	η	η	NOUN
ejpam-4850	122	12	)	)	PUNCT
ejpam-4850	122	13	a+	a+	PUNCT
ejpam-4850	122	14	ηx	ηx	NOUN
ejpam-4850	122	15	)	)	PUNCT
ejpam-4850	122	16	∣∣∣	∣∣∣	NOUN
ejpam-4850	122	17	(	(	PUNCT
ejpam-4850	122	18	dη)γ	dη)γ	PROPN
ejpam-4850	122	19	+	+	NUM
ejpam-4850	122	20	1	1	NUM
ejpam-4850	122	21	γ(γ+1	γ(γ+1	NUM
ejpam-4850	122	22	)	)	PUNCT
ejpam-4850	123	1	1∫	1∫	NUM
ejpam-4850	123	2	0	0	NUM
ejpam-4850	123	3	(	(	PUNCT
ejpam-4850	123	4	1−	1−	NUM
ejpam-4850	123	5	η)γ	η)γ	PROPN
ejpam-4850	123	6	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	123	7	(	(	PUNCT
ejpam-4850	123	8	γ	γ	PROPN
ejpam-4850	123	9	)	)	PUNCT
ejpam-4850	123	10	(	(	PUNCT
ejpam-4850	123	11	(	(	PUNCT
ejpam-4850	123	12	1−	1−	NUM
ejpam-4850	123	13	η	η	NOUN
ejpam-4850	123	14	)	)	PUNCT
ejpam-4850	123	15	(	(	PUNCT
ejpam-4850	123	16	a+	a+	PUNCT
ejpam-4850	123	17	b−	b−	PROPN
ejpam-4850	123	18	x	x	PROPN
ejpam-4850	123	19	)	)	PUNCT
ejpam-4850	123	20	+	+	CCONJ
ejpam-4850	123	21	ηb	ηb	X
ejpam-4850	123	22	)	)	PUNCT
ejpam-4850	123	23	∣∣∣	∣∣∣	NOUN
ejpam-4850	123	24	(	(	PUNCT
ejpam-4850	123	25	dη)γ	dη)γ	PROPN
ejpam-4850	123	26			PROPN
ejpam-4850	123	27	+	+	CCONJ
ejpam-4850	123	28	(	(	PUNCT
ejpam-4850	123	29	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	123	30	4γ(b−a)γ	4γ(b−a)γ	PROPN
ejpam-4850	123	31			PROPN
ejpam-4850	123	32	1	1	NUM
ejpam-4850	123	33	γ(γ+1	γ(γ+1	NUM
ejpam-4850	123	34	)	)	PUNCT
ejpam-4850	124	1	1∫	1∫	NUM
ejpam-4850	124	2	0	0	NUM
ejpam-4850	124	3	(	(	PUNCT
ejpam-4850	124	4	1−	1−	NUM
ejpam-4850	124	5	η)γ	η)γ	PROPN
ejpam-4850	124	6	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	124	7	(	(	PUNCT
ejpam-4850	124	8	γ	γ	PROPN
ejpam-4850	124	9	)	)	PUNCT
ejpam-4850	124	10	(	(	PUNCT
ejpam-4850	124	11	(	(	PUNCT
ejpam-4850	124	12	1−	1−	NUM
ejpam-4850	124	13	η)x+	η)x+	NUM
ejpam-4850	124	14	η	η	PROPN
ejpam-4850	124	15	a+b	a+b	NUM
ejpam-4850	124	16	2	2	NUM
ejpam-4850	124	17	)	)	PUNCT
ejpam-4850	124	18	∣∣∣	∣∣∣	NOUN
ejpam-4850	124	19	(	(	PUNCT
ejpam-4850	124	20	dη)γ	dη)γ	PROPN
ejpam-4850	124	21	+	+	NUM
ejpam-4850	124	22	1	1	NUM
ejpam-4850	124	23	γ(γ+1	γ(γ+1	NUM
ejpam-4850	124	24	)	)	PUNCT
ejpam-4850	125	1	1∫	1∫	NUM
ejpam-4850	125	2	0	0	NUM
ejpam-4850	125	3	ηγ	ηγ	PROPN
ejpam-4850	125	4	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	125	5	(	(	PUNCT
ejpam-4850	125	6	γ	γ	PROPN
ejpam-4850	125	7	)	)	PUNCT
ejpam-4850	125	8	(	(	PUNCT
ejpam-4850	125	9	(	(	PUNCT
ejpam-4850	125	10	1−	1−	NUM
ejpam-4850	125	11	η	η	NOUN
ejpam-4850	125	12	)	)	PUNCT
ejpam-4850	125	13	a+b	a+b	NUM
ejpam-4850	125	14	2	2	NUM
ejpam-4850	125	15	+	+	SYM
ejpam-4850	125	16	η	η	PROPN
ejpam-4850	125	17	(	(	PUNCT
ejpam-4850	125	18	a+	a+	PUNCT
ejpam-4850	125	19	b−	b−	PROPN
ejpam-4850	125	20	x	x	NOUN
ejpam-4850	125	21	)	)	PUNCT
ejpam-4850	125	22	)	)	PUNCT
ejpam-4850	125	23	∣∣∣	∣∣∣	NOUN
ejpam-4850	125	24	(	(	PUNCT
ejpam-4850	125	25	dη)γ	dη)γ	PROPN
ejpam-4850	125	26			PROPN
ejpam-4850	125	27	≤	≤	X
ejpam-4850	125	28	(	(	PUNCT
ejpam-4850	125	29	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	125	30	(	(	PUNCT
ejpam-4850	125	31	b−a)γ	b−a)γ	NOUN
ejpam-4850	125	32			PROPN
ejpam-4850	125	33	1	1	NUM
ejpam-4850	125	34	γ(γ+1	γ(γ+1	NUM
ejpam-4850	125	35	)	)	PUNCT
ejpam-4850	126	1	1∫	1∫	NUM
ejpam-4850	126	2	0	0	NUM
ejpam-4850	126	3	ηγ	ηγ	INTJ
ejpam-4850	126	4	(	(	PUNCT
ejpam-4850	126	5	(	(	PUNCT
ejpam-4850	126	6	1−	1−	NUM
ejpam-4850	126	7	η)sγ	η)sγ	PROPN
ejpam-4850	126	8	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	126	9	(	(	PUNCT
ejpam-4850	126	10	γ	γ	PROPN
ejpam-4850	126	11	)	)	PUNCT
ejpam-4850	126	12	(	(	PUNCT
ejpam-4850	126	13	a	a	X
ejpam-4850	126	14	)	)	PUNCT
ejpam-4850	126	15	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	126	16	ηsγ	ηsγ	ADV
ejpam-4850	126	17	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	126	18	(	(	PUNCT
ejpam-4850	126	19	γ	γ	PROPN
ejpam-4850	126	20	)	)	PUNCT
ejpam-4850	126	21	(	(	PUNCT
ejpam-4850	126	22	x	x	NOUN
ejpam-4850	126	23	)	)	PUNCT
ejpam-4850	126	24	∣∣∣	∣∣∣	ADJ
ejpam-4850	126	25	)	)	PUNCT
ejpam-4850	126	26	(	(	PUNCT
ejpam-4850	126	27	dη)γ	dη)γ	PROPN
ejpam-4850	126	28	+	+	NUM
ejpam-4850	126	29	1	1	NUM
ejpam-4850	126	30	γ(γ+1	γ(γ+1	NUM
ejpam-4850	126	31	)	)	PUNCT
ejpam-4850	127	1	1∫	1∫	NUM
ejpam-4850	127	2	0	0	NUM
ejpam-4850	127	3	(	(	PUNCT
ejpam-4850	127	4	1−	1−	NUM
ejpam-4850	127	5	η)γ	η)γ	NUM
ejpam-4850	127	6	(	(	PUNCT
ejpam-4850	127	7	(	(	PUNCT
ejpam-4850	127	8	1−	1−	NUM
ejpam-4850	127	9	η)sγ	η)sγ	PROPN
ejpam-4850	127	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	127	11	(	(	PUNCT
ejpam-4850	127	12	γ	γ	PROPN
ejpam-4850	127	13	)	)	PUNCT
ejpam-4850	127	14	(	(	PUNCT
ejpam-4850	127	15	a+	a+	PUNCT
ejpam-4850	127	16	b−	b−	PROPN
ejpam-4850	127	17	x	x	SYM
ejpam-4850	127	18	)	)	PUNCT
ejpam-4850	127	19	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	127	20	ηsγ	ηsγ	ADV
ejpam-4850	127	21	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	127	22	(	(	PUNCT
ejpam-4850	127	23	γ	γ	PROPN
ejpam-4850	127	24	)	)	PUNCT
ejpam-4850	127	25	(	(	PUNCT
ejpam-4850	127	26	b	b	NOUN
ejpam-4850	127	27	)	)	PUNCT
ejpam-4850	127	28	∣∣∣	∣∣∣	ADJ
ejpam-4850	127	29	)	)	PUNCT
ejpam-4850	127	30	(	(	PUNCT
ejpam-4850	127	31	dη)γ	dη)γ	PROPN
ejpam-4850	127	32			PROPN
ejpam-4850	128	1	+	+	CCONJ
ejpam-4850	128	2	(	(	PUNCT
ejpam-4850	128	3	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	128	4	4γ(b−a)γ	4γ(b−a)γ	PROPN
ejpam-4850	128	5			PROPN
ejpam-4850	128	6	1	1	NUM
ejpam-4850	128	7	γ(γ+1	γ(γ+1	NUM
ejpam-4850	128	8	)	)	PUNCT
ejpam-4850	129	1	1∫	1∫	NUM
ejpam-4850	129	2	0	0	NUM
ejpam-4850	129	3	(	(	PUNCT
ejpam-4850	129	4	1−	1−	NUM
ejpam-4850	129	5	η)γ	η)γ	NUM
ejpam-4850	129	6	(	(	PUNCT
ejpam-4850	129	7	(	(	PUNCT
ejpam-4850	129	8	1−	1−	NUM
ejpam-4850	129	9	η)sγ	η)sγ	PROPN
ejpam-4850	129	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	129	11	(	(	PUNCT
ejpam-4850	129	12	γ	γ	PROPN
ejpam-4850	129	13	)	)	PUNCT
ejpam-4850	129	14	(	(	PUNCT
ejpam-4850	129	15	x	x	X
ejpam-4850	129	16	)	)	PUNCT
ejpam-4850	129	17	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	129	18	ηsγ	ηsγ	ADV
ejpam-4850	129	19	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	129	20	(	(	PUNCT
ejpam-4850	129	21	γ	γ	PROPN
ejpam-4850	129	22	)	)	PUNCT
ejpam-4850	129	23	(	(	PUNCT
ejpam-4850	129	24	a+b	a+b	NUM
ejpam-4850	129	25	2	2	NUM
ejpam-4850	129	26	)	)	PUNCT
ejpam-4850	129	27	∣∣∣	∣∣∣	NOUN
ejpam-4850	129	28	)	)	PUNCT
ejpam-4850	129	29	(	(	PUNCT
ejpam-4850	129	30	dη)γ	dη)γ	PROPN
ejpam-4850	129	31	+	+	NUM
ejpam-4850	129	32	1	1	NUM
ejpam-4850	129	33	γ(γ+1	γ(γ+1	NUM
ejpam-4850	129	34	)	)	PUNCT
ejpam-4850	130	1	1∫	1∫	NUM
ejpam-4850	130	2	0	0	NUM
ejpam-4850	130	3	ηγ	ηγ	INTJ
ejpam-4850	130	4	(	(	PUNCT
ejpam-4850	130	5	(	(	PUNCT
ejpam-4850	130	6	1−	1−	NUM
ejpam-4850	130	7	η)sγ	η)sγ	PROPN
ejpam-4850	130	8	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	130	9	(	(	PUNCT
ejpam-4850	130	10	γ	γ	PROPN
ejpam-4850	130	11	)	)	PUNCT
ejpam-4850	130	12	(	(	PUNCT
ejpam-4850	130	13	a+b	a+b	NUM
ejpam-4850	130	14	2	2	NUM
ejpam-4850	130	15	)	)	PUNCT
ejpam-4850	130	16	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	130	17	ηsγ	ηsγ	PART
ejpam-4850	130	18	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	130	19	(	(	PUNCT
ejpam-4850	130	20	γ	γ	PROPN
ejpam-4850	130	21	)	)	PUNCT
ejpam-4850	130	22	(	(	PUNCT
ejpam-4850	130	23	a+	a+	PUNCT
ejpam-4850	130	24	b−	b−	PROPN
ejpam-4850	130	25	x	x	NOUN
ejpam-4850	130	26	)	)	PUNCT
ejpam-4850	130	27	∣∣∣	∣∣∣	ADJ
ejpam-4850	130	28	)	)	PUNCT
ejpam-4850	130	29	(	(	PUNCT
ejpam-4850	130	30	dη)γ	dη)γ	PROPN
ejpam-4850	130	31			PROPN
ejpam-4850	130	32	=	=	SYM
ejpam-4850	130	33	(	(	PUNCT
ejpam-4850	130	34	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	130	35	(	(	PUNCT
ejpam-4850	130	36	b−a)γ	b−a)γ	VERB
ejpam-4850	130	37			PROPN
ejpam-4850	130	38	1	1	NUM
ejpam-4850	130	39	γ(γ+1	γ(γ+1	NUM
ejpam-4850	130	40	)	)	PUNCT
ejpam-4850	131	1	1∫	1∫	NUM
ejpam-4850	131	2	0	0	NUM
ejpam-4850	131	3	ηγ	ηγ	INTJ
ejpam-4850	131	4	(	(	PUNCT
ejpam-4850	131	5	1−	1−	NUM
ejpam-4850	131	6	η)sγ	η)sγ	PROPN
ejpam-4850	131	7	(	(	PUNCT
ejpam-4850	131	8	dη)γ	dη)γ	PROPN
ejpam-4850	131	9	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	131	10	(	(	PUNCT
ejpam-4850	131	11	γ	γ	PROPN
ejpam-4850	131	12	)	)	PUNCT
ejpam-4850	131	13	(	(	PUNCT
ejpam-4850	131	14	a	a	NOUN
ejpam-4850	131	15	)	)	PUNCT
ejpam-4850	131	16	∣∣∣	∣∣∣	NOUN
ejpam-4850	132	1	+	+	CCONJ
ejpam-4850	132	2			PROPN
ejpam-4850	132	3	1	1	NUM
ejpam-4850	132	4	γ(γ+1	γ(γ+1	NUM
ejpam-4850	132	5	)	)	PUNCT
ejpam-4850	132	6	1∫	1∫	NUM
ejpam-4850	132	7	0	0	NUM
ejpam-4850	132	8	η(s+1)γ	η(s+1)γ	PROPN
ejpam-4850	132	9	(	(	PUNCT
ejpam-4850	132	10	dη)γ	dη)γ	PROPN
ejpam-4850	132	11	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	132	12	(	(	PUNCT
ejpam-4850	132	13	γ	γ	NOUN
ejpam-4850	132	14	)	)	PUNCT
ejpam-4850	132	15	(	(	PUNCT
ejpam-4850	132	16	x	x	NOUN
ejpam-4850	132	17	)	)	PUNCT
ejpam-4850	132	18	∣∣∣	∣∣∣	NOUN
ejpam-4850	133	1	+	+	CCONJ
ejpam-4850	133	2			PROPN
ejpam-4850	133	3	1	1	NUM
ejpam-4850	133	4	γ(γ+1	γ(γ+1	NUM
ejpam-4850	133	5	)	)	PUNCT
ejpam-4850	134	1	1∫	1∫	NUM
ejpam-4850	134	2	0	0	NUM
ejpam-4850	134	3	(	(	PUNCT
ejpam-4850	134	4	1−	1−	NUM
ejpam-4850	134	5	η)(s+1)γ	η)(s+1)γ	PROPN
ejpam-4850	134	6	(	(	PUNCT
ejpam-4850	134	7	dη)γ	dη)γ	PROPN
ejpam-4850	134	8	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	134	9	(	(	PUNCT
ejpam-4850	134	10	γ	γ	NOUN
ejpam-4850	134	11	)	)	PUNCT
ejpam-4850	134	12	(	(	PUNCT
ejpam-4850	134	13	a+	a+	PUNCT
ejpam-4850	134	14	b−	b−	PROPN
ejpam-4850	134	15	x	x	NOUN
ejpam-4850	134	16	)	)	PUNCT
ejpam-4850	134	17	∣∣∣	∣∣∣	PROPN
ejpam-4850	134	18	w.	w.	PROPN
ejpam-4850	134	19	saleh	saleh	PROPN
ejpam-4850	134	20	et	et	PROPN
ejpam-4850	134	21	al	al	PROPN
ejpam-4850	134	22	.	.	PUNCT
ejpam-4850	134	23	/	/	SYM
ejpam-4850	134	24	eur	eur	PROPN
ejpam-4850	134	25	.	.	PUNCT
ejpam-4850	135	1	j.	j.	PROPN
ejpam-4850	135	2	pure	pure	PROPN
ejpam-4850	135	3	appl	appl	PROPN
ejpam-4850	135	4	.	.	PROPN
ejpam-4850	135	5	math	math	PROPN
ejpam-4850	135	6	,	,	PUNCT
ejpam-4850	135	7	16	16	NUM
ejpam-4850	135	8	(	(	PUNCT
ejpam-4850	135	9	3	3	NUM
ejpam-4850	135	10	)	)	PUNCT
ejpam-4850	135	11	(	(	PUNCT
ejpam-4850	135	12	2023	2023	NUM
ejpam-4850	135	13	)	)	PUNCT
ejpam-4850	135	14	,	,	PUNCT
ejpam-4850	135	15	1359	1359	NUM
ejpam-4850	135	16	-	-	SYM
ejpam-4850	135	17	1380	1380	NUM
ejpam-4850	135	18	1366	1366	NUM
ejpam-4850	135	19	+	+	CCONJ
ejpam-4850	136	1			PROPN
ejpam-4850	136	2	1	1	NUM
ejpam-4850	136	3	γ(γ+1	γ(γ+1	NUM
ejpam-4850	136	4	)	)	PUNCT
ejpam-4850	137	1	1∫	1∫	NUM
ejpam-4850	137	2	0	0	NUM
ejpam-4850	137	3	(	(	PUNCT
ejpam-4850	137	4	1−	1−	NUM
ejpam-4850	137	5	η)γ	η)γ	PROPN
ejpam-4850	137	6	ηsγ	ηsγ	PART
ejpam-4850	137	7	(	(	PUNCT
ejpam-4850	137	8	dη)γ	dη)γ	PROPN
ejpam-4850	137	9	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	137	10	(	(	PUNCT
ejpam-4850	137	11	γ	γ	NOUN
ejpam-4850	137	12	)	)	PUNCT
ejpam-4850	137	13	(	(	PUNCT
ejpam-4850	137	14	b	b	NOUN
ejpam-4850	137	15	)	)	PUNCT
ejpam-4850	137	16	∣∣∣	∣∣∣	NOUN
ejpam-4850	137	17			PROPN
ejpam-4850	137	18	+	+	CCONJ
ejpam-4850	137	19	(	(	PUNCT
ejpam-4850	137	20	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	137	21	4γ(b−a)γ	4γ(b−a)γ	PROPN
ejpam-4850	137	22			PROPN
ejpam-4850	137	23	1	1	NUM
ejpam-4850	137	24	γ(γ+1	γ(γ+1	NUM
ejpam-4850	137	25	)	)	PUNCT
ejpam-4850	138	1	1∫	1∫	NUM
ejpam-4850	138	2	0	0	NUM
ejpam-4850	138	3	(	(	PUNCT
ejpam-4850	138	4	1−	1−	NUM
ejpam-4850	138	5	η)(s+1)γ	η)(s+1)γ	PROPN
ejpam-4850	138	6	(	(	PUNCT
ejpam-4850	138	7	dη)γ	dη)γ	PROPN
ejpam-4850	138	8	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	138	9	(	(	PUNCT
ejpam-4850	138	10	γ	γ	NOUN
ejpam-4850	138	11	)	)	PUNCT
ejpam-4850	138	12	(	(	PUNCT
ejpam-4850	138	13	x	x	NOUN
ejpam-4850	138	14	)	)	PUNCT
ejpam-4850	138	15	∣∣∣	∣∣∣	NOUN
ejpam-4850	139	1	+	+	CCONJ
ejpam-4850	139	2			PROPN
ejpam-4850	139	3	1	1	NUM
ejpam-4850	139	4	γ(γ+1	γ(γ+1	NUM
ejpam-4850	139	5	)	)	PUNCT
ejpam-4850	140	1	1∫	1∫	NUM
ejpam-4850	140	2	0	0	NUM
ejpam-4850	140	3	(	(	PUNCT
ejpam-4850	140	4	1−	1−	NUM
ejpam-4850	140	5	η)γ	η)γ	PROPN
ejpam-4850	140	6	ηsγ	ηsγ	X
ejpam-4850	140	7	(	(	PUNCT
ejpam-4850	140	8	dη)γ	dη)γ	PROPN
ejpam-4850	140	9	+	+	NUM
ejpam-4850	140	10	1	1	NUM
ejpam-4850	140	11	γ(γ+1	γ(γ+1	NUM
ejpam-4850	140	12	)	)	PUNCT
ejpam-4850	141	1	1∫	1∫	NUM
ejpam-4850	141	2	0	0	NUM
ejpam-4850	141	3	ηγ	ηγ	INTJ
ejpam-4850	141	4	(	(	PUNCT
ejpam-4850	141	5	1−	1−	NUM
ejpam-4850	141	6	η)sγ	η)sγ	PROPN
ejpam-4850	141	7	(	(	PUNCT
ejpam-4850	141	8	dη)γ	dη)γ	PROPN
ejpam-4850	141	9	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	141	10	(	(	PUNCT
ejpam-4850	141	11	γ	γ	NOUN
ejpam-4850	141	12	)	)	PUNCT
ejpam-4850	141	13	(	(	PUNCT
ejpam-4850	141	14	a+b	a+b	NUM
ejpam-4850	141	15	2	2	NUM
ejpam-4850	141	16	)	)	PUNCT
ejpam-4850	141	17	∣∣∣	∣∣∣	NOUN
ejpam-4850	142	1	+	+	CCONJ
ejpam-4850	142	2			PROPN
ejpam-4850	142	3	1	1	NUM
ejpam-4850	142	4	γ(γ+1	γ(γ+1	NUM
ejpam-4850	142	5	)	)	PUNCT
ejpam-4850	142	6	1∫	1∫	NUM
ejpam-4850	142	7	0	0	NUM
ejpam-4850	142	8	η(s+1)γ	η(s+1)γ	PROPN
ejpam-4850	142	9	(	(	PUNCT
ejpam-4850	142	10	dη)γ	dη)γ	PROPN
ejpam-4850	142	11	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	142	12	(	(	PUNCT
ejpam-4850	142	13	γ	γ	NOUN
ejpam-4850	142	14	)	)	PUNCT
ejpam-4850	142	15	(	(	PUNCT
ejpam-4850	142	16	a+	a+	PUNCT
ejpam-4850	142	17	b−	b−	PROPN
ejpam-4850	142	18	x	x	NOUN
ejpam-4850	142	19	)	)	PUNCT
ejpam-4850	142	20	∣∣∣	∣∣∣	NOUN
ejpam-4850	142	21			PROPN
ejpam-4850	142	22	=	=	SYM
ejpam-4850	142	23	(	(	PUNCT
ejpam-4850	142	24	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	142	25	(	(	PUNCT
ejpam-4850	142	26	b−a)γ	b−a)γ	PROPN
ejpam-4850	142	27	(	(	PUNCT
ejpam-4850	142	28	(	(	PUNCT
ejpam-4850	142	29	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	142	30	)	)	PUNCT
ejpam-4850	142	31	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	142	32	)	)	PUNCT
ejpam-4850	142	33	−	−	PROPN
ejpam-4850	142	34	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	142	35	)	)	PUNCT
ejpam-4850	142	36	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	142	37	)	)	PUNCT
ejpam-4850	142	38	)	)	PUNCT
ejpam-4850	143	1	(	(	PUNCT
ejpam-4850	143	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	143	3	(	(	PUNCT
ejpam-4850	143	4	γ	γ	PROPN
ejpam-4850	143	5	)	)	PUNCT
ejpam-4850	143	6	(	(	PUNCT
ejpam-4850	143	7	a	a	NOUN
ejpam-4850	143	8	)	)	PUNCT
ejpam-4850	143	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	143	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	143	11	(	(	PUNCT
ejpam-4850	143	12	γ	γ	PROPN
ejpam-4850	143	13	)	)	PUNCT
ejpam-4850	143	14	(	(	PUNCT
ejpam-4850	143	15	b	b	NOUN
ejpam-4850	143	16	)	)	PUNCT
ejpam-4850	143	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	143	18	)	)	PUNCT
ejpam-4850	143	19	+	+	CCONJ
ejpam-4850	143	20	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	143	21	)	)	PUNCT
ejpam-4850	143	22	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	143	23	)	)	PUNCT
ejpam-4850	143	24	(	(	PUNCT
ejpam-4850	143	25	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	143	26	(	(	PUNCT
ejpam-4850	143	27	γ	γ	PROPN
ejpam-4850	143	28	)	)	PUNCT
ejpam-4850	143	29	(	(	PUNCT
ejpam-4850	143	30	x	x	X
ejpam-4850	143	31	)	)	PUNCT
ejpam-4850	143	32	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	143	33	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	143	34	(	(	PUNCT
ejpam-4850	143	35	γ	γ	PROPN
ejpam-4850	143	36	)	)	PUNCT
ejpam-4850	143	37	(	(	PUNCT
ejpam-4850	143	38	a+	a+	PUNCT
ejpam-4850	143	39	b−	b−	PROPN
ejpam-4850	143	40	x	x	NOUN
ejpam-4850	143	41	)	)	PUNCT
ejpam-4850	143	42	∣∣∣	∣∣∣	ADJ
ejpam-4850	143	43	)	)	PUNCT
ejpam-4850	143	44	)	)	PUNCT
ejpam-4850	144	1	+	+	CCONJ
ejpam-4850	144	2	(	(	PUNCT
ejpam-4850	144	3	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	144	4	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	144	5	(	(	PUNCT
ejpam-4850	144	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	144	7	)	)	PUNCT
ejpam-4850	144	8	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	144	9	)	)	PUNCT
ejpam-4850	144	10	(	(	PUNCT
ejpam-4850	144	11	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	144	12	(	(	PUNCT
ejpam-4850	144	13	γ	γ	PROPN
ejpam-4850	144	14	)	)	PUNCT
ejpam-4850	144	15	(	(	PUNCT
ejpam-4850	144	16	x	x	X
ejpam-4850	144	17	)	)	PUNCT
ejpam-4850	144	18	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	144	19	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	144	20	(	(	PUNCT
ejpam-4850	144	21	γ	γ	PROPN
ejpam-4850	144	22	)	)	PUNCT
ejpam-4850	144	23	(	(	PUNCT
ejpam-4850	144	24	a+	a+	PUNCT
ejpam-4850	144	25	b−	b−	PROPN
ejpam-4850	144	26	x	x	NOUN
ejpam-4850	144	27	)	)	PUNCT
ejpam-4850	144	28	∣∣∣	∣∣∣	ADJ
ejpam-4850	144	29	)	)	PUNCT
ejpam-4850	145	1	+	+	CCONJ
ejpam-4850	145	2	2γ	2γ	NOUN
ejpam-4850	145	3	(	(	PUNCT
ejpam-4850	145	4	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	145	5	)	)	PUNCT
ejpam-4850	145	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	145	7	)	)	PUNCT
ejpam-4850	145	8	−	−	PROPN
ejpam-4850	145	9	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	145	10	)	)	PUNCT
ejpam-4850	145	11	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	145	12	)	)	PUNCT
ejpam-4850	145	13	)	)	PUNCT
ejpam-4850	146	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	146	2	(	(	PUNCT
ejpam-4850	146	3	γ	γ	PROPN
ejpam-4850	146	4	)	)	PUNCT
ejpam-4850	146	5	(	(	PUNCT
ejpam-4850	146	6	a+b	a+b	NUM
ejpam-4850	146	7	2	2	NUM
ejpam-4850	146	8	)	)	PUNCT
ejpam-4850	146	9	∣∣∣	∣∣∣	NOUN
ejpam-4850	146	10	)	)	PUNCT
ejpam-4850	146	11	,	,	PUNCT
ejpam-4850	146	12	where	where	SCONJ
ejpam-4850	146	13	we	we	PRON
ejpam-4850	146	14	have	have	AUX
ejpam-4850	146	15	used	use	VERB
ejpam-4850	146	16	the	the	DET
ejpam-4850	146	17	facts	fact	NOUN
ejpam-4850	146	18	that	that	SCONJ
ejpam-4850	146	19	1	1	NUM
ejpam-4850	146	20	γ(γ+1	γ(γ+1	NUM
ejpam-4850	146	21	)	)	PUNCT
ejpam-4850	147	1	1∫	1∫	NUM
ejpam-4850	147	2	0	0	NUM
ejpam-4850	147	3	ηγ	ηγ	INTJ
ejpam-4850	147	4	(	(	PUNCT
ejpam-4850	147	5	1−	1−	NUM
ejpam-4850	147	6	η)sγ	η)sγ	PROPN
ejpam-4850	147	7	(	(	PUNCT
ejpam-4850	147	8	dη)γ	dη)γ	PROPN
ejpam-4850	147	9	=	=	SYM
ejpam-4850	147	10	1	1	NUM
ejpam-4850	147	11	γ(γ+1	γ(γ+1	NUM
ejpam-4850	147	12	)	)	PUNCT
ejpam-4850	148	1	1∫	1∫	NUM
ejpam-4850	148	2	0	0	NUM
ejpam-4850	148	3	(	(	PUNCT
ejpam-4850	148	4	1−	1−	NUM
ejpam-4850	148	5	η)γ	η)γ	PROPN
ejpam-4850	148	6	ηsγ	ηsγ	PART
ejpam-4850	148	7	(	(	PUNCT
ejpam-4850	148	8	dη)γ	dη)γ	PROPN
ejpam-4850	148	9	=	=	SYM
ejpam-4850	148	10	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	148	11	)	)	PUNCT
ejpam-4850	148	12	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	148	13	)	)	PUNCT
ejpam-4850	148	14	−	−	PROPN
ejpam-4850	148	15	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	148	16	)	)	PUNCT
ejpam-4850	148	17	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	148	18	)	)	PUNCT
ejpam-4850	148	19	(	(	PUNCT
ejpam-4850	148	20	11	11	NUM
ejpam-4850	148	21	)	)	PUNCT
ejpam-4850	148	22	and	and	CCONJ
ejpam-4850	148	23	1	1	NUM
ejpam-4850	148	24	γ(γ+1	γ(γ+1	NUM
ejpam-4850	148	25	)	)	PUNCT
ejpam-4850	149	1	1∫	1∫	NUM
ejpam-4850	149	2	0	0	NUM
ejpam-4850	149	3	η(s+1)γ	η(s+1)γ	PROPN
ejpam-4850	149	4	(	(	PUNCT
ejpam-4850	149	5	dη)γ	dη)γ	PROPN
ejpam-4850	149	6	=	=	SYM
ejpam-4850	149	7	1	1	NUM
ejpam-4850	149	8	γ(γ+1	γ(γ+1	NUM
ejpam-4850	149	9	)	)	PUNCT
ejpam-4850	150	1	1∫	1∫	NUM
ejpam-4850	150	2	0	0	NUM
ejpam-4850	150	3	(	(	PUNCT
ejpam-4850	150	4	1−	1−	NUM
ejpam-4850	150	5	η)(s+1)γ	η)(s+1)γ	PROPN
ejpam-4850	150	6	(	(	PUNCT
ejpam-4850	150	7	dη)γ	dη)γ	PROPN
ejpam-4850	150	8	=	=	SYM
ejpam-4850	150	9	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	150	10	)	)	PUNCT
ejpam-4850	150	11	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	150	12	)	)	PUNCT
ejpam-4850	150	13	.	.	PUNCT
ejpam-4850	151	1	(	(	PUNCT
ejpam-4850	151	2	12	12	NUM
ejpam-4850	151	3	)	)	PUNCT
ejpam-4850	151	4	the	the	DET
ejpam-4850	151	5	proof	proof	NOUN
ejpam-4850	151	6	is	be	AUX
ejpam-4850	151	7	completed	complete	VERB
ejpam-4850	151	8	.	.	PUNCT
ejpam-4850	152	1	corollary	corollary	ADJ
ejpam-4850	152	2	1	1	NUM
ejpam-4850	152	3	.	.	PUNCT
ejpam-4850	153	1	in	in	ADP
ejpam-4850	153	2	theorem	theorem	NOUN
ejpam-4850	153	3	1	1	NUM
ejpam-4850	153	4	,	,	PUNCT
ejpam-4850	153	5	if	if	SCONJ
ejpam-4850	153	6	we	we	PRON
ejpam-4850	153	7	take	take	VERB
ejpam-4850	153	8	s	s	NOUN
ejpam-4850	153	9	=	=	SYM
ejpam-4850	153	10	1	1	NUM
ejpam-4850	153	11	,	,	PUNCT
ejpam-4850	153	12	we	we	PRON
ejpam-4850	153	13	obtain∣∣∣j	obtain∣∣∣j	VERB
ejpam-4850	153	14	(	(	PUNCT
ejpam-4850	153	15	x)+j	x)+j	PROPN
ejpam-4850	153	16	(	(	PUNCT
ejpam-4850	153	17	a+b−x	a+b−x	PROPN
ejpam-4850	153	18	)	)	PUNCT
ejpam-4850	153	19	2γ	2γ	NOUN
ejpam-4850	153	20	−	−	PROPN
ejpam-4850	153	21	γ(γ+1	γ(γ+1	NUM
ejpam-4850	153	22	)	)	PUNCT
ejpam-4850	153	23	(	(	PUNCT
ejpam-4850	153	24	b−a)γ	b−a)γ	NOUN
ejpam-4850	153	25	ai	ai	VERB
ejpam-4850	153	26	γ	γ	PROPN
ejpam-4850	153	27	b	b	PROPN
ejpam-4850	153	28	j	j	PROPN
ejpam-4850	153	29	(	(	PUNCT
ejpam-4850	153	30	t	t	PROPN
ejpam-4850	153	31	)	)	PUNCT
ejpam-4850	153	32	∣∣∣	∣∣∣	NOUN
ejpam-4850	153	33	≤	≤	NUM
ejpam-4850	153	34	(	(	PUNCT
ejpam-4850	153	35	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	153	36	(	(	PUNCT
ejpam-4850	153	37	b−a)γ	b−a)γ	PROPN
ejpam-4850	153	38	(	(	PUNCT
ejpam-4850	153	39	(	(	PUNCT
ejpam-4850	153	40	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	153	41	)	)	PUNCT
ejpam-4850	154	1	γ(1	γ(1	ADP
ejpam-4850	154	2	+	+	NOUN
ejpam-4850	154	3	2γ	2γ	NOUN
ejpam-4850	154	4	)	)	PUNCT
ejpam-4850	154	5	−	−	PROPN
ejpam-4850	155	1	γ(1	γ(1	PROPN
ejpam-4850	155	2	+	+	NOUN
ejpam-4850	155	3	2γ	2γ	NOUN
ejpam-4850	155	4	)	)	PUNCT
ejpam-4850	156	1	γ(1	γ(1	PROPN
ejpam-4850	156	2	+	+	NOUN
ejpam-4850	156	3	3γ	3γ	NUM
ejpam-4850	156	4	)	)	PUNCT
ejpam-4850	156	5	)	)	PUNCT
ejpam-4850	157	1	(	(	PUNCT
ejpam-4850	157	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	157	3	(	(	PUNCT
ejpam-4850	157	4	γ	γ	PROPN
ejpam-4850	157	5	)	)	PUNCT
ejpam-4850	157	6	(	(	PUNCT
ejpam-4850	157	7	a	a	NOUN
ejpam-4850	157	8	)	)	PUNCT
ejpam-4850	157	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	157	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	157	11	(	(	PUNCT
ejpam-4850	157	12	γ	γ	PROPN
ejpam-4850	157	13	)	)	PUNCT
ejpam-4850	157	14	(	(	PUNCT
ejpam-4850	157	15	b	b	NOUN
ejpam-4850	157	16	)	)	PUNCT
ejpam-4850	157	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	157	18	)	)	PUNCT
ejpam-4850	157	19	+	+	CCONJ
ejpam-4850	158	1	γ(1	γ(1	PROPN
ejpam-4850	158	2	+	+	NOUN
ejpam-4850	158	3	2γ	2γ	NOUN
ejpam-4850	158	4	)	)	PUNCT
ejpam-4850	159	1	γ(1	γ(1	PROPN
ejpam-4850	159	2	+	+	NOUN
ejpam-4850	159	3	3γ	3γ	NUM
ejpam-4850	159	4	)	)	PUNCT
ejpam-4850	159	5	(	(	PUNCT
ejpam-4850	159	6	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	159	7	(	(	PUNCT
ejpam-4850	159	8	γ	γ	PROPN
ejpam-4850	159	9	)	)	PUNCT
ejpam-4850	159	10	(	(	PUNCT
ejpam-4850	159	11	x	x	X
ejpam-4850	159	12	)	)	PUNCT
ejpam-4850	159	13	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	159	14	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	159	15	(	(	PUNCT
ejpam-4850	159	16	γ	γ	PROPN
ejpam-4850	159	17	)	)	PUNCT
ejpam-4850	159	18	(	(	PUNCT
ejpam-4850	159	19	a+	a+	PUNCT
ejpam-4850	159	20	b−	b−	PROPN
ejpam-4850	159	21	x	x	NOUN
ejpam-4850	159	22	)	)	PUNCT
ejpam-4850	159	23	∣∣∣	∣∣∣	ADJ
ejpam-4850	159	24	)	)	PUNCT
ejpam-4850	159	25	)	)	PUNCT
ejpam-4850	160	1	+	+	CCONJ
ejpam-4850	160	2	(	(	PUNCT
ejpam-4850	160	3	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	160	4	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	160	5	(	(	PUNCT
ejpam-4850	160	6	γ(1	γ(1	PROPN
ejpam-4850	160	7	+	+	NOUN
ejpam-4850	160	8	2γ	2γ	NOUN
ejpam-4850	160	9	)	)	PUNCT
ejpam-4850	161	1	γ(1	γ(1	PROPN
ejpam-4850	161	2	+	+	NOUN
ejpam-4850	161	3	3γ	3γ	NUM
ejpam-4850	161	4	)	)	PUNCT
ejpam-4850	161	5	(	(	PUNCT
ejpam-4850	161	6	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	161	7	(	(	PUNCT
ejpam-4850	161	8	γ	γ	PROPN
ejpam-4850	161	9	)	)	PUNCT
ejpam-4850	161	10	(	(	PUNCT
ejpam-4850	161	11	x	x	X
ejpam-4850	161	12	)	)	PUNCT
ejpam-4850	161	13	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	161	14	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	161	15	(	(	PUNCT
ejpam-4850	161	16	γ	γ	PROPN
ejpam-4850	161	17	)	)	PUNCT
ejpam-4850	161	18	(	(	PUNCT
ejpam-4850	161	19	a+	a+	PUNCT
ejpam-4850	161	20	b−	b−	PROPN
ejpam-4850	161	21	x	x	NOUN
ejpam-4850	161	22	)	)	PUNCT
ejpam-4850	161	23	∣∣∣	∣∣∣	ADJ
ejpam-4850	161	24	)	)	PUNCT
ejpam-4850	162	1	+	+	CCONJ
ejpam-4850	162	2	2γ	2γ	NOUN
ejpam-4850	162	3	(	(	PUNCT
ejpam-4850	162	4	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	162	5	)	)	PUNCT
ejpam-4850	163	1	γ(1	γ(1	ADP
ejpam-4850	164	1	+	+	NOUN
ejpam-4850	165	1	2γ	2γ	NOUN
ejpam-4850	165	2	)	)	PUNCT
ejpam-4850	166	1	−	−	PROPN
ejpam-4850	167	1	γ(1	γ(1	PROPN
ejpam-4850	167	2	+	+	NOUN
ejpam-4850	167	3	2γ	2γ	NOUN
ejpam-4850	167	4	)	)	PUNCT
ejpam-4850	168	1	γ(1	γ(1	PROPN
ejpam-4850	168	2	+	+	NOUN
ejpam-4850	168	3	3γ	3γ	NUM
ejpam-4850	168	4	)	)	PUNCT
ejpam-4850	168	5	)	)	PUNCT
ejpam-4850	169	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	169	2	(	(	PUNCT
ejpam-4850	169	3	γ	γ	PROPN
ejpam-4850	169	4	)	)	PUNCT
ejpam-4850	169	5	(	(	PUNCT
ejpam-4850	169	6	a+b	a+b	NUM
ejpam-4850	169	7	2	2	NUM
ejpam-4850	169	8	)	)	PUNCT
ejpam-4850	169	9	∣∣∣	∣∣∣	ADJ
ejpam-4850	169	10	)	)	PUNCT
ejpam-4850	169	11	.	.	PUNCT
ejpam-4850	170	1	w.	w.	PROPN
ejpam-4850	170	2	saleh	saleh	PROPN
ejpam-4850	170	3	et	et	PROPN
ejpam-4850	170	4	al	al	PROPN
ejpam-4850	170	5	.	.	PUNCT
ejpam-4850	170	6	/	/	SYM
ejpam-4850	170	7	eur	eur	PROPN
ejpam-4850	170	8	.	.	PUNCT
ejpam-4850	171	1	j.	j.	PROPN
ejpam-4850	171	2	pure	pure	PROPN
ejpam-4850	171	3	appl	appl	PROPN
ejpam-4850	171	4	.	.	PROPN
ejpam-4850	171	5	math	math	PROPN
ejpam-4850	171	6	,	,	PUNCT
ejpam-4850	171	7	16	16	NUM
ejpam-4850	171	8	(	(	PUNCT
ejpam-4850	171	9	3	3	NUM
ejpam-4850	171	10	)	)	PUNCT
ejpam-4850	171	11	(	(	PUNCT
ejpam-4850	171	12	2023	2023	NUM
ejpam-4850	171	13	)	)	PUNCT
ejpam-4850	171	14	,	,	PUNCT
ejpam-4850	171	15	1359	1359	NUM
ejpam-4850	171	16	-	-	SYM
ejpam-4850	171	17	1380	1380	NUM
ejpam-4850	171	18	1367	1367	NUM
ejpam-4850	171	19	corollary	corollary	NOUN
ejpam-4850	171	20	2	2	NUM
ejpam-4850	171	21	.	.	PUNCT
ejpam-4850	172	1	in	in	ADP
ejpam-4850	172	2	theorem	theorem	NOUN
ejpam-4850	172	3	1	1	NUM
ejpam-4850	172	4	applying	apply	VERB
ejpam-4850	172	5	the	the	DET
ejpam-4850	172	6	generalized	generalize	VERB
ejpam-4850	172	7	s	s	NOUN
ejpam-4850	172	8	-	-	NOUN
ejpam-4850	172	9	convexity	convexity	NOUN
ejpam-4850	172	10	of	of	ADP
ejpam-4850	172	11	∣∣j	∣∣j	NOUN
ejpam-4850	172	12	(	(	PUNCT
ejpam-4850	172	13	γ	γ	NOUN
ejpam-4850	172	14	)	)	PUNCT
ejpam-4850	172	15	∣∣	∣∣	NOUN
ejpam-4850	172	16	,	,	PUNCT
ejpam-4850	172	17	i.e∣∣∣j	i.e∣∣∣j	X
ejpam-4850	172	18	(	(	PUNCT
ejpam-4850	172	19	γ	γ	X
ejpam-4850	172	20	)	)	PUNCT
ejpam-4850	172	21	(	(	PUNCT
ejpam-4850	172	22	a+b	a+b	NUM
ejpam-4850	172	23	2	2	NUM
ejpam-4850	172	24	)	)	PUNCT
ejpam-4850	172	25	∣∣∣	∣∣∣	NOUN
ejpam-4850	172	26	≤	≤	NUM
ejpam-4850	172	27	2(1−s)γ	2(1−s)γ	NUM
ejpam-4850	172	28	γ(1+sγ)γ(1+γ	γ(1+sγ)γ(1+γ	ADJ
ejpam-4850	172	29	)	)	PUNCT
ejpam-4850	172	30	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	172	31	)	)	PUNCT
ejpam-4850	172	32	(	(	PUNCT
ejpam-4850	172	33	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	172	34	(	(	PUNCT
ejpam-4850	172	35	γ	γ	PROPN
ejpam-4850	172	36	)	)	PUNCT
ejpam-4850	172	37	(	(	PUNCT
ejpam-4850	172	38	x	x	X
ejpam-4850	172	39	)	)	PUNCT
ejpam-4850	172	40	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	172	41	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	172	42	(	(	PUNCT
ejpam-4850	172	43	γ	γ	PROPN
ejpam-4850	172	44	)	)	PUNCT
ejpam-4850	172	45	(	(	PUNCT
ejpam-4850	172	46	a+	a+	PUNCT
ejpam-4850	172	47	b−	b−	PROPN
ejpam-4850	172	48	x	x	NOUN
ejpam-4850	172	49	)	)	PUNCT
ejpam-4850	172	50	∣∣∣	∣∣∣	NUM
ejpam-4850	172	51	)	)	PUNCT
ejpam-4850	172	52	,	,	PUNCT
ejpam-4850	172	53	we	we	PRON
ejpam-4850	172	54	obtain	obtain	VERB
ejpam-4850	172	55	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	172	56	(	(	PUNCT
ejpam-4850	172	57	x)+j	x)+j	PROPN
ejpam-4850	172	58	(	(	PUNCT
ejpam-4850	172	59	a+b−x	a+b−x	PROPN
ejpam-4850	172	60	)	)	PUNCT
ejpam-4850	172	61	2γ	2γ	NOUN
ejpam-4850	172	62	−	−	PROPN
ejpam-4850	172	63	γ(γ+1	γ(γ+1	NUM
ejpam-4850	172	64	)	)	PUNCT
ejpam-4850	173	1	(	(	PUNCT
ejpam-4850	173	2	b−a)γ	b−a)γ	NOUN
ejpam-4850	173	3	ai	ai	VERB
ejpam-4850	173	4	γ	γ	PROPN
ejpam-4850	173	5	b	b	PROPN
ejpam-4850	173	6	j	j	PROPN
ejpam-4850	173	7	(	(	PUNCT
ejpam-4850	173	8	t	t	PROPN
ejpam-4850	173	9	)	)	PUNCT
ejpam-4850	173	10	∣∣∣	∣∣∣	NOUN
ejpam-4850	173	11	≤	≤	NUM
ejpam-4850	173	12	(	(	PUNCT
ejpam-4850	173	13	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	173	14	(	(	PUNCT
ejpam-4850	173	15	b−a)γ	b−a)γ	PROPN
ejpam-4850	173	16	(	(	PUNCT
ejpam-4850	173	17	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	173	18	)	)	PUNCT
ejpam-4850	173	19	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	173	20	)	)	PUNCT
ejpam-4850	173	21	−	−	PROPN
ejpam-4850	173	22	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	173	23	)	)	PUNCT
ejpam-4850	173	24	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	173	25	)	)	PUNCT
ejpam-4850	173	26	)	)	PUNCT
ejpam-4850	174	1	(	(	PUNCT
ejpam-4850	174	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	174	3	(	(	PUNCT
ejpam-4850	174	4	γ	γ	PROPN
ejpam-4850	174	5	)	)	PUNCT
ejpam-4850	174	6	(	(	PUNCT
ejpam-4850	174	7	a	a	NOUN
ejpam-4850	174	8	)	)	PUNCT
ejpam-4850	174	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	174	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	174	11	(	(	PUNCT
ejpam-4850	174	12	γ	γ	PROPN
ejpam-4850	174	13	)	)	PUNCT
ejpam-4850	174	14	(	(	PUNCT
ejpam-4850	174	15	b	b	NOUN
ejpam-4850	174	16	)	)	PUNCT
ejpam-4850	174	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	174	18	)	)	PUNCT
ejpam-4850	175	1	+	+	CCONJ
ejpam-4850	175	2	(	(	PUNCT
ejpam-4850	175	3	(	(	PUNCT
ejpam-4850	175	4	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	175	5	(	(	PUNCT
ejpam-4850	175	6	b−a)γ	b−a)γ	PROPN
ejpam-4850	175	7	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	175	8	)	)	PUNCT
ejpam-4850	175	9	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	175	10	)	)	PUNCT
ejpam-4850	176	1	+	+	CCONJ
ejpam-4850	176	2	(	(	PUNCT
ejpam-4850	176	3	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	176	4	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	176	5	(	(	PUNCT
ejpam-4850	176	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	176	7	)	)	PUNCT
ejpam-4850	176	8	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	176	9	)	)	PUNCT
ejpam-4850	177	1	−	−	PROPN
ejpam-4850	177	2	2(2−s)γγ(1+γ)γ(1+sγ	2(2−s)γγ(1+γ)γ(1+sγ	NUM
ejpam-4850	177	3	)	)	PUNCT
ejpam-4850	177	4	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	177	5	)	)	PUNCT
ejpam-4850	178	1	+	+	CCONJ
ejpam-4850	178	2	2(2−s)γγ	2(2−s)γγ	NUM
ejpam-4850	178	3	(	(	PUNCT
ejpam-4850	178	4	1	1	NUM
ejpam-4850	178	5	+	+	CCONJ
ejpam-4850	178	6	γ	γ	X
ejpam-4850	178	7	)	)	PUNCT
ejpam-4850	178	8	(	(	PUNCT
ejpam-4850	178	9	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	178	10	)	)	PUNCT
ejpam-4850	178	11	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	178	12	)	)	PUNCT
ejpam-4850	178	13	)	)	PUNCT
ejpam-4850	179	1	2γ))(∣∣∣j	2γ))(∣∣∣j	PROPN
ejpam-4850	179	2	(	(	PUNCT
ejpam-4850	179	3	γ	γ	X
ejpam-4850	179	4	)	)	PUNCT
ejpam-4850	179	5	(	(	PUNCT
ejpam-4850	179	6	x	x	X
ejpam-4850	179	7	)	)	PUNCT
ejpam-4850	179	8	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	179	9	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	179	10	(	(	PUNCT
ejpam-4850	179	11	γ	γ	PROPN
ejpam-4850	179	12	)	)	PUNCT
ejpam-4850	179	13	(	(	PUNCT
ejpam-4850	179	14	a+	a+	PUNCT
ejpam-4850	179	15	b−	b−	PROPN
ejpam-4850	179	16	x	x	NOUN
ejpam-4850	179	17	)	)	PUNCT
ejpam-4850	179	18	∣∣∣	∣∣∣	ADJ
ejpam-4850	179	19	)	)	PUNCT
ejpam-4850	179	20	.	.	PUNCT
ejpam-4850	180	1	corollary	corollary	ADJ
ejpam-4850	180	2	3	3	X
ejpam-4850	180	3	.	.	PUNCT
ejpam-4850	181	1	in	in	ADP
ejpam-4850	181	2	corollary	corollary	ADJ
ejpam-4850	181	3	2	2	NUM
ejpam-4850	181	4	,	,	PUNCT
ejpam-4850	181	5	taking	take	VERB
ejpam-4850	181	6	s	s	PART
ejpam-4850	181	7	=	=	SYM
ejpam-4850	181	8	1	1	NUM
ejpam-4850	181	9	we	we	PRON
ejpam-4850	181	10	obtain∣∣∣j	obtain∣∣∣j	VERB
ejpam-4850	181	11	(	(	PUNCT
ejpam-4850	181	12	x)+j	x)+j	PROPN
ejpam-4850	181	13	(	(	PUNCT
ejpam-4850	181	14	a+b−x	a+b−x	PROPN
ejpam-4850	181	15	)	)	PUNCT
ejpam-4850	181	16	2γ	2γ	NOUN
ejpam-4850	181	17	−	−	PROPN
ejpam-4850	181	18	γ(γ+1	γ(γ+1	NUM
ejpam-4850	181	19	)	)	PUNCT
ejpam-4850	181	20	(	(	PUNCT
ejpam-4850	181	21	b−a)γ	b−a)γ	NOUN
ejpam-4850	181	22	ai	ai	VERB
ejpam-4850	181	23	γ	γ	PROPN
ejpam-4850	181	24	b	b	PROPN
ejpam-4850	181	25	j	j	PROPN
ejpam-4850	181	26	(	(	PUNCT
ejpam-4850	181	27	t	t	PROPN
ejpam-4850	181	28	)	)	PUNCT
ejpam-4850	181	29	∣∣∣	∣∣∣	NOUN
ejpam-4850	181	30	≤	≤	NUM
ejpam-4850	181	31	(	(	PUNCT
ejpam-4850	181	32	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	181	33	(	(	PUNCT
ejpam-4850	181	34	b−a)γ	b−a)γ	PROPN
ejpam-4850	181	35	(	(	PUNCT
ejpam-4850	181	36	γ(1+γ	γ(1+γ	PROPN
ejpam-4850	181	37	)	)	PUNCT
ejpam-4850	182	1	γ(1	γ(1	ADP
ejpam-4850	183	1	+	+	NOUN
ejpam-4850	184	1	2γ	2γ	NOUN
ejpam-4850	184	2	)	)	PUNCT
ejpam-4850	185	1	−	−	PROPN
ejpam-4850	186	1	γ(1	γ(1	PROPN
ejpam-4850	186	2	+	+	NOUN
ejpam-4850	186	3	2γ	2γ	NOUN
ejpam-4850	186	4	)	)	PUNCT
ejpam-4850	187	1	γ(1	γ(1	PROPN
ejpam-4850	187	2	+	+	NOUN
ejpam-4850	187	3	3γ	3γ	NUM
ejpam-4850	187	4	)	)	PUNCT
ejpam-4850	187	5	)	)	PUNCT
ejpam-4850	188	1	(	(	PUNCT
ejpam-4850	188	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	188	3	(	(	PUNCT
ejpam-4850	188	4	γ	γ	PROPN
ejpam-4850	188	5	)	)	PUNCT
ejpam-4850	188	6	(	(	PUNCT
ejpam-4850	188	7	a	a	NOUN
ejpam-4850	188	8	)	)	PUNCT
ejpam-4850	188	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	188	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	188	11	(	(	PUNCT
ejpam-4850	188	12	γ	γ	PROPN
ejpam-4850	188	13	)	)	PUNCT
ejpam-4850	188	14	(	(	PUNCT
ejpam-4850	188	15	b	b	NOUN
ejpam-4850	188	16	)	)	PUNCT
ejpam-4850	188	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	188	18	)	)	PUNCT
ejpam-4850	189	1	+	+	CCONJ
ejpam-4850	189	2	(	(	PUNCT
ejpam-4850	189	3	(	(	PUNCT
ejpam-4850	189	4	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	189	5	(	(	PUNCT
ejpam-4850	189	6	b−a)γ	b−a)γ	PROPN
ejpam-4850	189	7	γ(1	γ(1	PROPN
ejpam-4850	189	8	+	+	NOUN
ejpam-4850	189	9	2γ	2γ	NOUN
ejpam-4850	189	10	)	)	PUNCT
ejpam-4850	190	1	γ(1	γ(1	PROPN
ejpam-4850	190	2	+	+	NOUN
ejpam-4850	190	3	3γ	3γ	NUM
ejpam-4850	190	4	)	)	PUNCT
ejpam-4850	191	1	+	+	CCONJ
ejpam-4850	191	2	(	(	PUNCT
ejpam-4850	191	3	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	191	4	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	191	5	(	(	PUNCT
ejpam-4850	191	6	γ(1	γ(1	PROPN
ejpam-4850	191	7	+	+	NOUN
ejpam-4850	191	8	2γ	2γ	NOUN
ejpam-4850	191	9	)	)	PUNCT
ejpam-4850	192	1	γ(1	γ(1	PROPN
ejpam-4850	192	2	+	+	NOUN
ejpam-4850	192	3	3γ	3γ	NUM
ejpam-4850	192	4	)	)	PUNCT
ejpam-4850	192	5	−	−	PROPN
ejpam-4850	193	1	2γ(γ(1+γ))2γ	2γ(γ(1+γ))2γ	NUM
ejpam-4850	193	2	γ(1	γ(1	SYM
ejpam-4850	193	3	+	+	NOUN
ejpam-4850	193	4	3γ	3γ	NUM
ejpam-4850	193	5	)	)	PUNCT
ejpam-4850	194	1	+	+	CCONJ
ejpam-4850	194	2	2γγ	2γγ	ADJ
ejpam-4850	194	3	(	(	PUNCT
ejpam-4850	194	4	1	1	NUM
ejpam-4850	194	5	+	+	CCONJ
ejpam-4850	194	6	γ	γ	X
ejpam-4850	194	7	)	)	PUNCT
ejpam-4850	194	8	(	(	PUNCT
ejpam-4850	194	9	γ(1+γ	γ(1+γ	PROPN
ejpam-4850	194	10	)	)	PUNCT
ejpam-4850	195	1	γ(1	γ(1	ADP
ejpam-4850	195	2	+	+	NOUN
ejpam-4850	195	3	2γ	2γ	NOUN
ejpam-4850	195	4	)	)	PUNCT
ejpam-4850	195	5	)	)	PUNCT
ejpam-4850	195	6	2γ))(∣∣∣j	2γ))(∣∣∣j	PROPN
ejpam-4850	195	7	(	(	PUNCT
ejpam-4850	195	8	γ	γ	X
ejpam-4850	195	9	)	)	PUNCT
ejpam-4850	195	10	(	(	PUNCT
ejpam-4850	195	11	x	x	X
ejpam-4850	195	12	)	)	PUNCT
ejpam-4850	195	13	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	195	14	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	195	15	(	(	PUNCT
ejpam-4850	195	16	γ	γ	PROPN
ejpam-4850	195	17	)	)	PUNCT
ejpam-4850	195	18	(	(	PUNCT
ejpam-4850	195	19	a+	a+	PUNCT
ejpam-4850	195	20	b−	b−	PROPN
ejpam-4850	195	21	x	x	NOUN
ejpam-4850	195	22	)	)	PUNCT
ejpam-4850	195	23	∣∣∣	∣∣∣	ADJ
ejpam-4850	195	24	)	)	PUNCT
ejpam-4850	195	25	.	.	PUNCT
ejpam-4850	196	1	remark	remark	NOUN
ejpam-4850	196	2	1	1	NUM
ejpam-4850	196	3	.	.	PUNCT
ejpam-4850	196	4	for	for	ADP
ejpam-4850	196	5	γ	γ	X
ejpam-4850	196	6	=	=	SYM
ejpam-4850	196	7	1	1	NUM
ejpam-4850	196	8	,	,	PUNCT
ejpam-4850	196	9	corollary	corollary	ADJ
ejpam-4850	196	10	3	3	NUM
ejpam-4850	196	11	will	will	AUX
ejpam-4850	196	12	be	be	AUX
ejpam-4850	196	13	reduces	reduce	VERB
ejpam-4850	196	14	to	to	PART
ejpam-4850	196	15	theorem	theorem	VERB
ejpam-4850	196	16	5	5	NUM
ejpam-4850	196	17	from	from	ADP
ejpam-4850	196	18	[	[	X
ejpam-4850	196	19	11	11	NUM
ejpam-4850	196	20	]	]	PUNCT
ejpam-4850	196	21	.	.	PUNCT
ejpam-4850	197	1	corollary	corollary	ADJ
ejpam-4850	197	2	4	4	NUM
ejpam-4850	197	3	.	.	PUNCT
ejpam-4850	197	4	in	in	ADP
ejpam-4850	197	5	theorem	theorem	NOUN
ejpam-4850	197	6	1	1	NUM
ejpam-4850	197	7	,	,	PUNCT
ejpam-4850	197	8	taking	take	VERB
ejpam-4850	197	9	x	x	X
ejpam-4850	197	10	=	=	PUNCT
ejpam-4850	197	11	a	a	DET
ejpam-4850	197	12	we	we	PRON
ejpam-4850	197	13	get∣∣∣j	get∣∣∣j	NOUN
ejpam-4850	197	14	(	(	PUNCT
ejpam-4850	197	15	a)+j	a)+j	PROPN
ejpam-4850	197	16	(	(	PUNCT
ejpam-4850	197	17	b	b	NOUN
ejpam-4850	197	18	)	)	PUNCT
ejpam-4850	197	19	2γ	2γ	NOUN
ejpam-4850	197	20	−	−	PROPN
ejpam-4850	197	21	γ(γ+1	γ(γ+1	NUM
ejpam-4850	197	22	)	)	PUNCT
ejpam-4850	197	23	(	(	PUNCT
ejpam-4850	197	24	b−a)γ	b−a)γ	NOUN
ejpam-4850	197	25	ai	ai	VERB
ejpam-4850	197	26	γ	γ	PROPN
ejpam-4850	197	27	b	b	PROPN
ejpam-4850	197	28	j	j	PROPN
ejpam-4850	197	29	(	(	PUNCT
ejpam-4850	197	30	t	t	PROPN
ejpam-4850	197	31	)	)	PUNCT
ejpam-4850	197	32	∣∣∣	∣∣∣	NOUN
ejpam-4850	197	33	≤	≤	NOUN
ejpam-4850	197	34	(	(	PUNCT
ejpam-4850	197	35	b−a)γ	b−a)γ	NOUN
ejpam-4850	197	36	4γ	4γ	NOUN
ejpam-4850	197	37	(	(	PUNCT
ejpam-4850	197	38	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	197	39	)	)	PUNCT
ejpam-4850	197	40	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	197	41	)	)	PUNCT
ejpam-4850	197	42	(	(	PUNCT
ejpam-4850	197	43	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	197	44	(	(	PUNCT
ejpam-4850	197	45	γ	γ	PROPN
ejpam-4850	197	46	)	)	PUNCT
ejpam-4850	197	47	(	(	PUNCT
ejpam-4850	197	48	a	a	NOUN
ejpam-4850	197	49	)	)	PUNCT
ejpam-4850	197	50	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	197	51	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	197	52	(	(	PUNCT
ejpam-4850	197	53	γ	γ	PROPN
ejpam-4850	197	54	)	)	PUNCT
ejpam-4850	197	55	(	(	PUNCT
ejpam-4850	197	56	b	b	NOUN
ejpam-4850	197	57	)	)	PUNCT
ejpam-4850	197	58	∣∣∣	∣∣∣	ADJ
ejpam-4850	197	59	)	)	PUNCT
ejpam-4850	198	1	+2γ	+2γ	NUM
ejpam-4850	198	2	(	(	PUNCT
ejpam-4850	198	3	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	198	4	)	)	PUNCT
ejpam-4850	198	5	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	198	6	)	)	PUNCT
ejpam-4850	198	7	−	−	PROPN
ejpam-4850	198	8	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	198	9	)	)	PUNCT
ejpam-4850	198	10	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	198	11	)	)	PUNCT
ejpam-4850	198	12	)	)	PUNCT
ejpam-4850	199	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	199	2	(	(	PUNCT
ejpam-4850	199	3	γ	γ	PROPN
ejpam-4850	199	4	)	)	PUNCT
ejpam-4850	199	5	(	(	PUNCT
ejpam-4850	199	6	a+b	a+b	NUM
ejpam-4850	199	7	2	2	NUM
ejpam-4850	199	8	)	)	PUNCT
ejpam-4850	199	9	∣∣∣	∣∣∣	ADJ
ejpam-4850	199	10	)	)	PUNCT
ejpam-4850	199	11	.	.	PUNCT
ejpam-4850	200	1	corollary	corollary	ADJ
ejpam-4850	200	2	5	5	NUM
ejpam-4850	200	3	.	.	PUNCT
ejpam-4850	201	1	in	in	ADP
ejpam-4850	201	2	corollary	corollary	ADJ
ejpam-4850	201	3	4	4	NUM
ejpam-4850	201	4	using	use	VERB
ejpam-4850	201	5	the	the	DET
ejpam-4850	201	6	generalized	generalized	ADJ
ejpam-4850	201	7	s	s	NOUN
ejpam-4850	201	8	-	-	NOUN
ejpam-4850	201	9	convexity	convexity	NOUN
ejpam-4850	201	10	of	of	ADP
ejpam-4850	201	11	∣∣j	∣∣j	NOUN
ejpam-4850	201	12	(	(	PUNCT
ejpam-4850	201	13	γ	γ	NOUN
ejpam-4850	201	14	)	)	PUNCT
ejpam-4850	201	15	∣∣	∣∣	NUM
ejpam-4850	201	16	i.e.∣∣∣j	i.e.∣∣∣j	X
ejpam-4850	201	17	(	(	PUNCT
ejpam-4850	201	18	γ	γ	X
ejpam-4850	201	19	)	)	PUNCT
ejpam-4850	201	20	(	(	PUNCT
ejpam-4850	201	21	a+b	a+b	NUM
ejpam-4850	201	22	2	2	NUM
ejpam-4850	201	23	)	)	PUNCT
ejpam-4850	201	24	∣∣∣	∣∣∣	NOUN
ejpam-4850	201	25	≤	≤	NUM
ejpam-4850	201	26	2(1−s)γ	2(1−s)γ	NUM
ejpam-4850	201	27	γ(1+sγ)γ(1+γ	γ(1+sγ)γ(1+γ	ADJ
ejpam-4850	201	28	)	)	PUNCT
ejpam-4850	201	29	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	201	30	)	)	PUNCT
ejpam-4850	201	31	(	(	PUNCT
ejpam-4850	201	32	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	201	33	(	(	PUNCT
ejpam-4850	201	34	γ	γ	PROPN
ejpam-4850	201	35	)	)	PUNCT
ejpam-4850	201	36	(	(	PUNCT
ejpam-4850	201	37	a	a	NOUN
ejpam-4850	201	38	)	)	PUNCT
ejpam-4850	201	39	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	201	40	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	201	41	(	(	PUNCT
ejpam-4850	201	42	γ	γ	PROPN
ejpam-4850	201	43	)	)	PUNCT
ejpam-4850	201	44	(	(	PUNCT
ejpam-4850	201	45	b	b	NOUN
ejpam-4850	201	46	)	)	PUNCT
ejpam-4850	201	47	∣∣∣	∣∣∣	ADJ
ejpam-4850	201	48	)	)	PUNCT
ejpam-4850	201	49	,	,	PUNCT
ejpam-4850	201	50	we	we	PRON
ejpam-4850	201	51	obtain	obtain	VERB
ejpam-4850	201	52	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	201	53	(	(	PUNCT
ejpam-4850	201	54	a)+j	a)+j	PROPN
ejpam-4850	201	55	(	(	PUNCT
ejpam-4850	201	56	b	b	NOUN
ejpam-4850	201	57	)	)	PUNCT
ejpam-4850	201	58	2γ	2γ	NOUN
ejpam-4850	201	59	−	−	PROPN
ejpam-4850	201	60	γ(γ+1	γ(γ+1	NUM
ejpam-4850	201	61	)	)	PUNCT
ejpam-4850	201	62	(	(	PUNCT
ejpam-4850	201	63	b−a)γ	b−a)γ	NOUN
ejpam-4850	201	64	ai	ai	VERB
ejpam-4850	201	65	γ	γ	PROPN
ejpam-4850	201	66	b	b	PROPN
ejpam-4850	201	67	j	j	PROPN
ejpam-4850	201	68	(	(	PUNCT
ejpam-4850	201	69	t	t	PROPN
ejpam-4850	201	70	)	)	PUNCT
ejpam-4850	201	71	∣∣∣	∣∣∣	NOUN
ejpam-4850	201	72	≤	≤	NOUN
ejpam-4850	201	73	(	(	PUNCT
ejpam-4850	201	74	b−a)γ	b−a)γ	NOUN
ejpam-4850	201	75	4γ	4γ	NOUN
ejpam-4850	201	76	(	(	PUNCT
ejpam-4850	201	77	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	201	78	)	)	PUNCT
ejpam-4850	201	79	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	201	80	)	)	PUNCT
ejpam-4850	202	1	+	+	CCONJ
ejpam-4850	202	2	2(2−s)γ	2(2−s)γ	NUM
ejpam-4850	202	3	(	(	PUNCT
ejpam-4850	202	4	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	202	5	)	)	PUNCT
ejpam-4850	202	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	202	7	)	)	PUNCT
ejpam-4850	202	8	)	)	PUNCT
ejpam-4850	203	1	2γ	2γ	VERB
ejpam-4850	203	2	γ	γ	X
ejpam-4850	203	3	(	(	PUNCT
ejpam-4850	203	4	1	1	NUM
ejpam-4850	203	5	+	+	CCONJ
ejpam-4850	203	6	γ	γ	X
ejpam-4850	203	7	)	)	PUNCT
ejpam-4850	203	8	−	−	PROPN
ejpam-4850	203	9	2(2−s)γ	2(2−s)γ	NUM
ejpam-4850	203	10	γ(1+sγ)γ(1+γ	γ(1+sγ)γ(1+γ	NOUN
ejpam-4850	203	11	)	)	PUNCT
ejpam-4850	203	12	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	203	13	)	)	PUNCT
ejpam-4850	203	14	)	)	PUNCT
ejpam-4850	204	1	(	(	PUNCT
ejpam-4850	204	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	204	3	(	(	PUNCT
ejpam-4850	204	4	γ	γ	PROPN
ejpam-4850	204	5	)	)	PUNCT
ejpam-4850	204	6	(	(	PUNCT
ejpam-4850	204	7	a	a	NOUN
ejpam-4850	204	8	)	)	PUNCT
ejpam-4850	204	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	204	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	204	11	(	(	PUNCT
ejpam-4850	204	12	γ	γ	PROPN
ejpam-4850	204	13	)	)	PUNCT
ejpam-4850	204	14	(	(	PUNCT
ejpam-4850	204	15	b	b	NOUN
ejpam-4850	204	16	)	)	PUNCT
ejpam-4850	204	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	204	18	)	)	PUNCT
ejpam-4850	204	19	.	.	PUNCT
ejpam-4850	205	1	w.	w.	PROPN
ejpam-4850	205	2	saleh	saleh	PROPN
ejpam-4850	205	3	et	et	PROPN
ejpam-4850	205	4	al	al	PROPN
ejpam-4850	205	5	.	.	PUNCT
ejpam-4850	205	6	/	/	SYM
ejpam-4850	205	7	eur	eur	PROPN
ejpam-4850	205	8	.	.	PUNCT
ejpam-4850	206	1	j.	j.	PROPN
ejpam-4850	206	2	pure	pure	PROPN
ejpam-4850	206	3	appl	appl	PROPN
ejpam-4850	206	4	.	.	PROPN
ejpam-4850	206	5	math	math	PROPN
ejpam-4850	206	6	,	,	PUNCT
ejpam-4850	206	7	16	16	NUM
ejpam-4850	206	8	(	(	PUNCT
ejpam-4850	206	9	3	3	NUM
ejpam-4850	206	10	)	)	PUNCT
ejpam-4850	206	11	(	(	PUNCT
ejpam-4850	206	12	2023	2023	NUM
ejpam-4850	206	13	)	)	PUNCT
ejpam-4850	206	14	,	,	PUNCT
ejpam-4850	206	15	1359	1359	NUM
ejpam-4850	206	16	-	-	SYM
ejpam-4850	206	17	1380	1380	NUM
ejpam-4850	206	18	1368	1368	NUM
ejpam-4850	206	19	corollary	corollary	NOUN
ejpam-4850	206	20	6	6	NUM
ejpam-4850	206	21	.	.	PUNCT
ejpam-4850	207	1	in	in	ADP
ejpam-4850	207	2	corollary	corollary	ADJ
ejpam-4850	207	3	5	5	NUM
ejpam-4850	207	4	,	,	PUNCT
ejpam-4850	207	5	taking	take	VERB
ejpam-4850	207	6	s	s	PART
ejpam-4850	207	7	=	=	SYM
ejpam-4850	207	8	1	1	NUM
ejpam-4850	207	9	,	,	PUNCT
ejpam-4850	207	10	we	we	PRON
ejpam-4850	207	11	obtain∣∣∣j	obtain∣∣∣j	VERB
ejpam-4850	207	12	(	(	PUNCT
ejpam-4850	207	13	a)+j	a)+j	PROPN
ejpam-4850	207	14	(	(	PUNCT
ejpam-4850	207	15	b	b	NOUN
ejpam-4850	207	16	)	)	PUNCT
ejpam-4850	207	17	2γ	2γ	NOUN
ejpam-4850	207	18	−	−	PROPN
ejpam-4850	207	19	γ(γ+1	γ(γ+1	NUM
ejpam-4850	207	20	)	)	PUNCT
ejpam-4850	207	21	(	(	PUNCT
ejpam-4850	207	22	b−a)γ	b−a)γ	NOUN
ejpam-4850	207	23	ai	ai	VERB
ejpam-4850	207	24	γ	γ	PROPN
ejpam-4850	207	25	b	b	PROPN
ejpam-4850	207	26	j	j	PROPN
ejpam-4850	207	27	(	(	PUNCT
ejpam-4850	207	28	t	t	PROPN
ejpam-4850	207	29	)	)	PUNCT
ejpam-4850	207	30	∣∣∣	∣∣∣	NOUN
ejpam-4850	207	31	≤	≤	NOUN
ejpam-4850	207	32	(	(	PUNCT
ejpam-4850	207	33	b−a)γ	b−a)γ	NOUN
ejpam-4850	207	34	4γ	4γ	NOUN
ejpam-4850	207	35	(	(	PUNCT
ejpam-4850	208	1	γ(1	γ(1	ADP
ejpam-4850	208	2	+	+	NOUN
ejpam-4850	208	3	2γ	2γ	NOUN
ejpam-4850	208	4	)	)	PUNCT
ejpam-4850	209	1	γ(1	γ(1	PROPN
ejpam-4850	209	2	+	+	NOUN
ejpam-4850	209	3	3γ	3γ	NUM
ejpam-4850	209	4	)	)	PUNCT
ejpam-4850	210	1	+	+	CCONJ
ejpam-4850	210	2	2γ	2γ	NOUN
ejpam-4850	210	3	(	(	PUNCT
ejpam-4850	210	4	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	210	5	)	)	PUNCT
ejpam-4850	211	1	γ(1	γ(1	ADP
ejpam-4850	211	2	+	+	NOUN
ejpam-4850	211	3	2γ	2γ	NOUN
ejpam-4850	211	4	)	)	PUNCT
ejpam-4850	211	5	)	)	PUNCT
ejpam-4850	211	6	2γ	2γ	VERB
ejpam-4850	211	7	γ	γ	X
ejpam-4850	211	8	(	(	PUNCT
ejpam-4850	211	9	1	1	NUM
ejpam-4850	211	10	+	+	CCONJ
ejpam-4850	211	11	γ)−	γ)−	PROPN
ejpam-4850	211	12	2γ	2γ	NOUN
ejpam-4850	211	13	(	(	PUNCT
ejpam-4850	211	14	γ(1+γ))2γ	γ(1+γ))2γ	PROPN
ejpam-4850	211	15	γ(1	γ(1	PROPN
ejpam-4850	211	16	+	+	NOUN
ejpam-4850	211	17	3γ	3γ	NUM
ejpam-4850	211	18	)	)	PUNCT
ejpam-4850	211	19	)	)	PUNCT
ejpam-4850	212	1	(	(	PUNCT
ejpam-4850	212	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	212	3	(	(	PUNCT
ejpam-4850	212	4	γ	γ	PROPN
ejpam-4850	212	5	)	)	PUNCT
ejpam-4850	212	6	(	(	PUNCT
ejpam-4850	212	7	a	a	NOUN
ejpam-4850	212	8	)	)	PUNCT
ejpam-4850	212	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	212	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	212	11	(	(	PUNCT
ejpam-4850	212	12	γ	γ	PROPN
ejpam-4850	212	13	)	)	PUNCT
ejpam-4850	212	14	(	(	PUNCT
ejpam-4850	212	15	b	b	NOUN
ejpam-4850	212	16	)	)	PUNCT
ejpam-4850	212	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	212	18	)	)	PUNCT
ejpam-4850	212	19	.	.	PUNCT
ejpam-4850	213	1	remark	remark	NOUN
ejpam-4850	213	2	2	2	NUM
ejpam-4850	213	3	.	.	PUNCT
ejpam-4850	213	4	for	for	ADP
ejpam-4850	213	5	γ	γ	X
ejpam-4850	213	6	=	=	SYM
ejpam-4850	213	7	1	1	NUM
ejpam-4850	213	8	,	,	PUNCT
ejpam-4850	213	9	corollary	corollary	ADJ
ejpam-4850	213	10	6	6	NUM
ejpam-4850	213	11	will	will	AUX
ejpam-4850	213	12	be	be	AUX
ejpam-4850	213	13	reduces	reduce	VERB
ejpam-4850	213	14	to	to	PART
ejpam-4850	213	15	theorem	theorem	VERB
ejpam-4850	213	16	2.2	2.2	NUM
ejpam-4850	213	17	from	from	ADP
ejpam-4850	213	18	[	[	X
ejpam-4850	213	19	6	6	NUM
ejpam-4850	213	20	]	]	PUNCT
ejpam-4850	213	21	.	.	PUNCT
ejpam-4850	214	1	corollary	corollary	ADJ
ejpam-4850	214	2	7	7	NUM
ejpam-4850	214	3	.	.	PUNCT
ejpam-4850	214	4	in	in	ADP
ejpam-4850	214	5	theorem	theorem	NOUN
ejpam-4850	214	6	1	1	NUM
ejpam-4850	214	7	,	,	PUNCT
ejpam-4850	214	8	taking	take	VERB
ejpam-4850	214	9	x	x	X
ejpam-4850	214	10	=	=	SYM
ejpam-4850	214	11	a+b	a+b	NUM
ejpam-4850	214	12	2	2	NUM
ejpam-4850	214	13	we	we	PRON
ejpam-4850	214	14	get∣∣∣j	get∣∣∣j	NOUN
ejpam-4850	214	15	(	(	PUNCT
ejpam-4850	214	16	a+b	a+b	NUM
ejpam-4850	214	17	2	2	NUM
ejpam-4850	214	18	)	)	PUNCT
ejpam-4850	214	19	−	−	PROPN
ejpam-4850	214	20	γ(γ+1	γ(γ+1	NUM
ejpam-4850	214	21	)	)	PUNCT
ejpam-4850	214	22	(	(	PUNCT
ejpam-4850	214	23	b−a)γ	b−a)γ	NOUN
ejpam-4850	214	24	ai	ai	VERB
ejpam-4850	214	25	γ	γ	PROPN
ejpam-4850	214	26	b	b	PROPN
ejpam-4850	214	27	j	j	PROPN
ejpam-4850	214	28	(	(	PUNCT
ejpam-4850	214	29	t	t	PROPN
ejpam-4850	214	30	)	)	PUNCT
ejpam-4850	214	31	∣∣∣	∣∣∣	NOUN
ejpam-4850	214	32	≤	≤	NOUN
ejpam-4850	214	33	(	(	PUNCT
ejpam-4850	214	34	b−a)γ	b−a)γ	NOUN
ejpam-4850	214	35	4γ	4γ	NOUN
ejpam-4850	214	36	(	(	PUNCT
ejpam-4850	214	37	(	(	PUNCT
ejpam-4850	214	38	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	214	39	)	)	PUNCT
ejpam-4850	214	40	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	214	41	)	)	PUNCT
ejpam-4850	214	42	−	−	PROPN
ejpam-4850	214	43	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	214	44	)	)	PUNCT
ejpam-4850	214	45	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	214	46	)	)	PUNCT
ejpam-4850	214	47	)	)	PUNCT
ejpam-4850	215	1	(	(	PUNCT
ejpam-4850	215	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	215	3	(	(	PUNCT
ejpam-4850	215	4	γ	γ	PROPN
ejpam-4850	215	5	)	)	PUNCT
ejpam-4850	215	6	(	(	PUNCT
ejpam-4850	215	7	a	a	NOUN
ejpam-4850	215	8	)	)	PUNCT
ejpam-4850	215	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	215	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	215	11	(	(	PUNCT
ejpam-4850	215	12	γ	γ	PROPN
ejpam-4850	215	13	)	)	PUNCT
ejpam-4850	215	14	(	(	PUNCT
ejpam-4850	215	15	b	b	NOUN
ejpam-4850	215	16	)	)	PUNCT
ejpam-4850	215	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	215	18	)	)	PUNCT
ejpam-4850	215	19	+2γ	+2γ	PROPN
ejpam-4850	215	20	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	215	21	)	)	PUNCT
ejpam-4850	215	22	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	215	23	)	)	PUNCT
ejpam-4850	215	24	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	215	25	(	(	PUNCT
ejpam-4850	215	26	γ	γ	PROPN
ejpam-4850	215	27	)	)	PUNCT
ejpam-4850	215	28	(	(	PUNCT
ejpam-4850	215	29	a+b	a+b	NUM
ejpam-4850	215	30	2	2	NUM
ejpam-4850	215	31	)	)	PUNCT
ejpam-4850	215	32	∣∣∣	∣∣∣	ADJ
ejpam-4850	215	33	)	)	PUNCT
ejpam-4850	215	34	.	.	PUNCT
ejpam-4850	216	1	corollary	corollary	ADJ
ejpam-4850	216	2	8	8	NUM
ejpam-4850	216	3	.	.	PUNCT
ejpam-4850	217	1	in	in	ADP
ejpam-4850	217	2	corollary	corollary	ADJ
ejpam-4850	217	3	7	7	NUM
ejpam-4850	217	4	using	use	VERB
ejpam-4850	217	5	the	the	DET
ejpam-4850	217	6	generalized	generalized	ADJ
ejpam-4850	217	7	s	s	NOUN
ejpam-4850	217	8	-	-	NOUN
ejpam-4850	217	9	convexity	convexity	NOUN
ejpam-4850	217	10	of	of	ADP
ejpam-4850	217	11	∣∣j	∣∣j	NOUN
ejpam-4850	217	12	(	(	PUNCT
ejpam-4850	217	13	γ	γ	NOUN
ejpam-4850	217	14	)	)	PUNCT
ejpam-4850	217	15	∣∣∣∣∣j	∣∣∣∣∣j	NOUN
ejpam-4850	217	16	(	(	PUNCT
ejpam-4850	217	17	a+b	a+b	NUM
ejpam-4850	217	18	2	2	NUM
ejpam-4850	217	19	)	)	PUNCT
ejpam-4850	217	20	−	−	PROPN
ejpam-4850	217	21	γ(γ+1	γ(γ+1	NUM
ejpam-4850	217	22	)	)	PUNCT
ejpam-4850	217	23	(	(	PUNCT
ejpam-4850	217	24	b−a)γ	b−a)γ	NOUN
ejpam-4850	217	25	ai	ai	VERB
ejpam-4850	217	26	γ	γ	PROPN
ejpam-4850	217	27	b	b	PROPN
ejpam-4850	217	28	j	j	PROPN
ejpam-4850	217	29	(	(	PUNCT
ejpam-4850	217	30	t	t	PROPN
ejpam-4850	217	31	)	)	PUNCT
ejpam-4850	217	32	∣∣∣	∣∣∣	NOUN
ejpam-4850	217	33	≤	≤	NOUN
ejpam-4850	217	34	(	(	PUNCT
ejpam-4850	217	35	b−a)γ	b−a)γ	NOUN
ejpam-4850	217	36	4γ	4γ	NOUN
ejpam-4850	217	37	(	(	PUNCT
ejpam-4850	217	38	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	217	39	)	)	PUNCT
ejpam-4850	217	40	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	217	41	)	)	PUNCT
ejpam-4850	217	42	−	−	PROPN
ejpam-4850	217	43	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	217	44	)	)	PUNCT
ejpam-4850	217	45	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	217	46	)	)	PUNCT
ejpam-4850	218	1	+	+	CCONJ
ejpam-4850	218	2	2(2−s)γ	2(2−s)γ	NUM
ejpam-4850	218	3	γ(1+sγ)γ(1+γ	γ(1+sγ)γ(1+γ	ADV
ejpam-4850	218	4	)	)	PUNCT
ejpam-4850	218	5	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	218	6	)	)	PUNCT
ejpam-4850	218	7	)	)	PUNCT
ejpam-4850	219	1	(	(	PUNCT
ejpam-4850	219	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	219	3	(	(	PUNCT
ejpam-4850	219	4	γ	γ	PROPN
ejpam-4850	219	5	)	)	PUNCT
ejpam-4850	219	6	(	(	PUNCT
ejpam-4850	219	7	a	a	NOUN
ejpam-4850	219	8	)	)	PUNCT
ejpam-4850	219	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	219	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	219	11	(	(	PUNCT
ejpam-4850	219	12	γ	γ	PROPN
ejpam-4850	219	13	)	)	PUNCT
ejpam-4850	219	14	(	(	PUNCT
ejpam-4850	219	15	b	b	NOUN
ejpam-4850	219	16	)	)	PUNCT
ejpam-4850	219	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	219	18	)	)	PUNCT
ejpam-4850	219	19	.	.	PUNCT
ejpam-4850	220	1	corollary	corollary	ADJ
ejpam-4850	220	2	9	9	NUM
ejpam-4850	220	3	.	.	PUNCT
ejpam-4850	221	1	in	in	ADP
ejpam-4850	221	2	corollary	corollary	ADJ
ejpam-4850	221	3	8	8	NUM
ejpam-4850	221	4	if	if	SCONJ
ejpam-4850	221	5	we	we	PRON
ejpam-4850	221	6	take	take	VERB
ejpam-4850	221	7	s	s	VERB
ejpam-4850	221	8	=	=	SYM
ejpam-4850	221	9	1	1	NUM
ejpam-4850	221	10	we	we	PRON
ejpam-4850	221	11	obtain∣∣∣j	obtain∣∣∣j	VERB
ejpam-4850	221	12	(	(	PUNCT
ejpam-4850	221	13	a+b	a+b	NUM
ejpam-4850	221	14	2	2	NUM
ejpam-4850	221	15	)	)	PUNCT
ejpam-4850	221	16	−	−	PROPN
ejpam-4850	221	17	γ(γ+1	γ(γ+1	NUM
ejpam-4850	221	18	)	)	PUNCT
ejpam-4850	221	19	(	(	PUNCT
ejpam-4850	221	20	b−a)γ	b−a)γ	NOUN
ejpam-4850	221	21	ai	ai	VERB
ejpam-4850	221	22	γ	γ	PROPN
ejpam-4850	221	23	b	b	PROPN
ejpam-4850	221	24	j	j	PROPN
ejpam-4850	221	25	(	(	PUNCT
ejpam-4850	221	26	t	t	PROPN
ejpam-4850	221	27	)	)	PUNCT
ejpam-4850	221	28	∣∣∣	∣∣∣	NOUN
ejpam-4850	221	29	≤	≤	NOUN
ejpam-4850	221	30	(	(	PUNCT
ejpam-4850	221	31	b−a)γ	b−a)γ	NOUN
ejpam-4850	221	32	4γ	4γ	NOUN
ejpam-4850	221	33	(	(	PUNCT
ejpam-4850	221	34	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	221	35	)	)	PUNCT
ejpam-4850	222	1	γ(1	γ(1	ADP
ejpam-4850	222	2	+	+	NOUN
ejpam-4850	222	3	2γ	2γ	NOUN
ejpam-4850	222	4	)	)	PUNCT
ejpam-4850	222	5	−	−	PROPN
ejpam-4850	223	1	γ(1	γ(1	PROPN
ejpam-4850	223	2	+	+	NOUN
ejpam-4850	223	3	2γ	2γ	NOUN
ejpam-4850	223	4	)	)	PUNCT
ejpam-4850	224	1	γ(1	γ(1	PROPN
ejpam-4850	224	2	+	+	NOUN
ejpam-4850	224	3	3γ	3γ	NUM
ejpam-4850	224	4	)	)	PUNCT
ejpam-4850	225	1	+	+	CCONJ
ejpam-4850	225	2	2γ	2γ	NOUN
ejpam-4850	225	3	(	(	PUNCT
ejpam-4850	225	4	γ(1+γ))2γ	γ(1+γ))2γ	PROPN
ejpam-4850	225	5	γ(1	γ(1	PROPN
ejpam-4850	225	6	+	+	NOUN
ejpam-4850	225	7	3γ	3γ	NUM
ejpam-4850	225	8	)	)	PUNCT
ejpam-4850	225	9	)	)	PUNCT
ejpam-4850	226	1	(	(	PUNCT
ejpam-4850	226	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	226	3	(	(	PUNCT
ejpam-4850	226	4	γ	γ	PROPN
ejpam-4850	226	5	)	)	PUNCT
ejpam-4850	226	6	(	(	PUNCT
ejpam-4850	226	7	a	a	NOUN
ejpam-4850	226	8	)	)	PUNCT
ejpam-4850	226	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	226	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	226	11	(	(	PUNCT
ejpam-4850	226	12	γ	γ	PROPN
ejpam-4850	226	13	)	)	PUNCT
ejpam-4850	226	14	(	(	PUNCT
ejpam-4850	226	15	b	b	NOUN
ejpam-4850	226	16	)	)	PUNCT
ejpam-4850	226	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	226	18	)	)	PUNCT
ejpam-4850	226	19	.	.	PUNCT
ejpam-4850	227	1	remark	remark	NOUN
ejpam-4850	227	2	3	3	NUM
ejpam-4850	227	3	.	.	PUNCT
ejpam-4850	227	4	for	for	ADP
ejpam-4850	227	5	γ	γ	X
ejpam-4850	227	6	=	=	SYM
ejpam-4850	227	7	1	1	NUM
ejpam-4850	227	8	,	,	PUNCT
ejpam-4850	227	9	corollary	corollary	ADJ
ejpam-4850	227	10	9	9	NUM
ejpam-4850	227	11	will	will	AUX
ejpam-4850	227	12	be	be	AUX
ejpam-4850	227	13	reduces	reduce	VERB
ejpam-4850	227	14	to	to	PART
ejpam-4850	227	15	theorem	theorem	VERB
ejpam-4850	227	16	2.2	2.2	NUM
ejpam-4850	227	17	from	from	ADP
ejpam-4850	227	18	[	[	X
ejpam-4850	227	19	14	14	NUM
ejpam-4850	227	20	]	]	PUNCT
ejpam-4850	227	21	.	.	PUNCT
ejpam-4850	228	1	theorem	theorem	NOUN
ejpam-4850	228	2	2	2	NUM
ejpam-4850	228	3	.	.	PUNCT
ejpam-4850	228	4	suppose	suppose	VERB
ejpam-4850	229	1	j	j	NOUN
ejpam-4850	229	2	:	:	PUNCT
ejpam-4850	230	1	[	[	X
ejpam-4850	230	2	a	a	X
ejpam-4850	230	3	,	,	PUNCT
ejpam-4850	230	4	b	b	NOUN
ejpam-4850	230	5	]	]	X
ejpam-4850	230	6	→	→	PUNCT
ejpam-4850	230	7	rγ	rγ	PRON
ejpam-4850	230	8	is	be	AUX
ejpam-4850	230	9	a	a	DET
ejpam-4850	230	10	differentiable	differentiable	ADJ
ejpam-4850	230	11	function	function	NOUN
ejpam-4850	230	12	on	on	ADP
ejpam-4850	230	13	[	[	X
ejpam-4850	230	14	a	a	X
ejpam-4850	230	15	,	,	PUNCT
ejpam-4850	230	16	b	b	NOUN
ejpam-4850	230	17	]	]	X
ejpam-4850	230	18	such	such	ADJ
ejpam-4850	230	19	that	that	SCONJ
ejpam-4850	230	20	j	j	PROPN
ejpam-4850	230	21	∈	∈	PROPN
ejpam-4850	230	22	dγ	dγ	ADP
ejpam-4850	230	23	[	[	X
ejpam-4850	230	24	a	a	X
ejpam-4850	230	25	,	,	PUNCT
ejpam-4850	230	26	b	b	NOUN
ejpam-4850	230	27	]	]	X
ejpam-4850	230	28	and	and	CCONJ
ejpam-4850	230	29	j	j	PROPN
ejpam-4850	230	30	(	(	PUNCT
ejpam-4850	230	31	γ	γ	PROPN
ejpam-4850	230	32	)	)	PUNCT
ejpam-4850	230	33	∈	∈	NOUN
ejpam-4850	230	34	cγ	cγ	NOUN
ejpam-4850	230	35	[	[	X
ejpam-4850	230	36	a	a	X
ejpam-4850	230	37	,	,	PUNCT
ejpam-4850	230	38	b	b	NOUN
ejpam-4850	230	39	]	]	X
ejpam-4850	230	40	with	with	ADP
ejpam-4850	230	41	0	0	NUM
ejpam-4850	230	42	≤	≤	NOUN
ejpam-4850	230	43	a	a	DET
ejpam-4850	230	44	<	<	X
ejpam-4850	230	45	b.	b.	NOUN
ejpam-4850	230	46	if	if	SCONJ
ejpam-4850	230	47	∣∣j	∣∣j	X
ejpam-4850	230	48	(	(	PUNCT
ejpam-4850	230	49	γ	γ	NOUN
ejpam-4850	230	50	)	)	PUNCT
ejpam-4850	230	51	∣∣q	∣∣q	NUM
ejpam-4850	230	52	is	be	AUX
ejpam-4850	230	53	generalized	generalize	VERB
ejpam-4850	230	54	s	s	NOUN
ejpam-4850	230	55	-	-	NOUN
ejpam-4850	230	56	convex	convex	NOUN
ejpam-4850	230	57	on	on	ADP
ejpam-4850	230	58	[	[	X
ejpam-4850	230	59	a	a	X
ejpam-4850	230	60	,	,	PUNCT
ejpam-4850	230	61	b	b	NOUN
ejpam-4850	230	62	]	]	X
ejpam-4850	230	63	,	,	PUNCT
ejpam-4850	230	64	where	where	SCONJ
ejpam-4850	230	65	q	q	PUNCT
ejpam-4850	230	66	>	>	X
ejpam-4850	230	67	1	1	NUM
ejpam-4850	230	68	with	with	ADP
ejpam-4850	230	69	1	1	NUM
ejpam-4850	230	70	p	p	NOUN
ejpam-4850	231	1	+	+	NOUN
ejpam-4850	231	2	1	1	NUM
ejpam-4850	231	3	q	q	NOUN
ejpam-4850	231	4	=	=	SYM
ejpam-4850	231	5	1	1	NUM
ejpam-4850	231	6	,	,	PUNCT
ejpam-4850	231	7	then	then	ADV
ejpam-4850	231	8	we	we	PRON
ejpam-4850	231	9	have∣∣∣j	have∣∣∣j	VERB
ejpam-4850	231	10	(	(	PUNCT
ejpam-4850	231	11	x)+j	x)+j	PROPN
ejpam-4850	231	12	(	(	PUNCT
ejpam-4850	231	13	a+b−x	a+b−x	PROPN
ejpam-4850	231	14	)	)	PUNCT
ejpam-4850	231	15	2γ	2γ	NOUN
ejpam-4850	231	16	−	−	PROPN
ejpam-4850	231	17	γ(γ+1	γ(γ+1	NUM
ejpam-4850	231	18	)	)	PUNCT
ejpam-4850	231	19	(	(	PUNCT
ejpam-4850	231	20	b−a)γ	b−a)γ	NOUN
ejpam-4850	231	21	ai	ai	VERB
ejpam-4850	231	22	γ	γ	PROPN
ejpam-4850	231	23	b	b	PROPN
ejpam-4850	231	24	j	j	PROPN
ejpam-4850	231	25	(	(	PUNCT
ejpam-4850	231	26	t	t	PROPN
ejpam-4850	231	27	)	)	PUNCT
ejpam-4850	231	28	∣∣∣	∣∣∣	NOUN
ejpam-4850	231	29	≤	≤	PROPN
ejpam-4850	231	30	(	(	PUNCT
ejpam-4850	231	31	γ(1+pγ	γ(1+pγ	NUM
ejpam-4850	231	32	)	)	PUNCT
ejpam-4850	231	33	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	231	34	)	)	PUNCT
ejpam-4850	231	35	)	)	PUNCT
ejpam-4850	231	36	1	1	NUM
ejpam-4850	231	37	p	p	NOUN
ejpam-4850	231	38	(	(	PUNCT
ejpam-4850	231	39	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	231	40	)	)	PUNCT
ejpam-4850	231	41	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	231	42	)	)	PUNCT
ejpam-4850	231	43	)	)	PUNCT
ejpam-4850	231	44	1	1	NUM
ejpam-4850	231	45	q	q	NOUN
ejpam-4850	231	46	×	×	NOUN
ejpam-4850	231	47	(	(	PUNCT
ejpam-4850	231	48	(	(	PUNCT
ejpam-4850	231	49	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	231	50	(	(	PUNCT
ejpam-4850	231	51	b−a)γ	b−a)γ	PROPN
ejpam-4850	231	52	(	(	PUNCT
ejpam-4850	231	53	(	(	PUNCT
ejpam-4850	231	54	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	231	55	(	(	PUNCT
ejpam-4850	231	56	γ	γ	PROPN
ejpam-4850	231	57	)	)	PUNCT
ejpam-4850	231	58	(	(	PUNCT
ejpam-4850	231	59	a	a	X
ejpam-4850	231	60	)	)	PUNCT
ejpam-4850	231	61	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	231	62	+	+	CCONJ
ejpam-4850	231	63	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	231	64	(	(	PUNCT
ejpam-4850	231	65	γ	γ	PROPN
ejpam-4850	231	66	)	)	PUNCT
ejpam-4850	231	67	(	(	PUNCT
ejpam-4850	231	68	x	x	X
ejpam-4850	231	69	)	)	PUNCT
ejpam-4850	231	70	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	231	71	q	q	PROPN
ejpam-4850	232	1	+	+	CCONJ
ejpam-4850	232	2	(	(	PUNCT
ejpam-4850	232	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	232	4	(	(	PUNCT
ejpam-4850	232	5	γ	γ	PROPN
ejpam-4850	232	6	)	)	PUNCT
ejpam-4850	232	7	(	(	PUNCT
ejpam-4850	232	8	a+	a+	PUNCT
ejpam-4850	232	9	b−	b−	PROPN
ejpam-4850	232	10	x	x	SYM
ejpam-4850	232	11	)	)	PUNCT
ejpam-4850	232	12	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	233	1	+	+	CCONJ
ejpam-4850	233	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	233	3	(	(	PUNCT
ejpam-4850	233	4	γ	γ	PROPN
ejpam-4850	233	5	)	)	PUNCT
ejpam-4850	233	6	(	(	PUNCT
ejpam-4850	233	7	b	b	X
ejpam-4850	233	8	)	)	PUNCT
ejpam-4850	233	9	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	233	10	q	q	PROPN
ejpam-4850	233	11	)	)	PUNCT
ejpam-4850	234	1	+	+	CCONJ
ejpam-4850	234	2	(	(	PUNCT
ejpam-4850	234	3	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	234	4	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	234	5	(	(	PUNCT
ejpam-4850	234	6	(	(	PUNCT
ejpam-4850	234	7	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	234	8	(	(	PUNCT
ejpam-4850	234	9	γ	γ	PROPN
ejpam-4850	234	10	)	)	PUNCT
ejpam-4850	234	11	(	(	PUNCT
ejpam-4850	234	12	x	x	X
ejpam-4850	234	13	)	)	PUNCT
ejpam-4850	234	14	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	235	1	+	+	CCONJ
ejpam-4850	235	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	235	3	(	(	PUNCT
ejpam-4850	235	4	γ	γ	PROPN
ejpam-4850	235	5	)	)	PUNCT
ejpam-4850	235	6	(	(	PUNCT
ejpam-4850	235	7	a+b	a+b	NUM
ejpam-4850	235	8	2	2	NUM
ejpam-4850	235	9	)	)	PUNCT
ejpam-4850	235	10	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	235	11	q	q	PROPN
ejpam-4850	236	1	+	+	CCONJ
ejpam-4850	236	2	(	(	PUNCT
ejpam-4850	236	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	236	4	(	(	PUNCT
ejpam-4850	236	5	γ	γ	PROPN
ejpam-4850	236	6	)	)	PUNCT
ejpam-4850	236	7	(	(	PUNCT
ejpam-4850	236	8	a+b	a+b	NUM
ejpam-4850	236	9	2	2	NUM
ejpam-4850	236	10	)	)	PUNCT
ejpam-4850	236	11	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	237	1	+	+	CCONJ
ejpam-4850	237	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	237	3	(	(	PUNCT
ejpam-4850	237	4	γ	γ	PROPN
ejpam-4850	237	5	)	)	PUNCT
ejpam-4850	237	6	(	(	PUNCT
ejpam-4850	237	7	a+	a+	PUNCT
ejpam-4850	237	8	b−	b−	PROPN
ejpam-4850	237	9	x	x	SYM
ejpam-4850	237	10	)	)	PUNCT
ejpam-4850	237	11	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	237	12	q	q	PROPN
ejpam-4850	237	13	)	)	PUNCT
ejpam-4850	237	14	)	)	PUNCT
ejpam-4850	237	15	.	.	PUNCT
ejpam-4850	238	1	w.	w.	PROPN
ejpam-4850	238	2	saleh	saleh	PROPN
ejpam-4850	238	3	et	et	PROPN
ejpam-4850	238	4	al	al	PROPN
ejpam-4850	238	5	.	.	PUNCT
ejpam-4850	238	6	/	/	SYM
ejpam-4850	238	7	eur	eur	PROPN
ejpam-4850	238	8	.	.	PUNCT
ejpam-4850	239	1	j.	j.	PROPN
ejpam-4850	239	2	pure	pure	PROPN
ejpam-4850	239	3	appl	appl	PROPN
ejpam-4850	239	4	.	.	PROPN
ejpam-4850	239	5	math	math	PROPN
ejpam-4850	239	6	,	,	PUNCT
ejpam-4850	239	7	16	16	NUM
ejpam-4850	239	8	(	(	PUNCT
ejpam-4850	239	9	3	3	NUM
ejpam-4850	239	10	)	)	PUNCT
ejpam-4850	239	11	(	(	PUNCT
ejpam-4850	239	12	2023	2023	NUM
ejpam-4850	239	13	)	)	PUNCT
ejpam-4850	239	14	,	,	PUNCT
ejpam-4850	239	15	1359	1359	NUM
ejpam-4850	239	16	-	-	SYM
ejpam-4850	239	17	1380	1380	NUM
ejpam-4850	239	18	1369	1369	NUM
ejpam-4850	239	19	proof	proof	NOUN
ejpam-4850	239	20	.	.	PUNCT
ejpam-4850	240	1	using	use	VERB
ejpam-4850	240	2	lemma	lemma	PROPN
ejpam-4850	240	3	4	4	NUM
ejpam-4850	240	4	as	as	ADV
ejpam-4850	240	5	well	well	ADV
ejpam-4850	240	6	as	as	ADP
ejpam-4850	240	7	the	the	DET
ejpam-4850	240	8	generalized	generalized	ADJ
ejpam-4850	240	9	hölder	hölder	NOUN
ejpam-4850	240	10	inequality	inequality	NOUN
ejpam-4850	240	11	,	,	PUNCT
ejpam-4850	240	12	properties	property	NOUN
ejpam-4850	240	13	of	of	ADP
ejpam-4850	240	14	modulus	modulus	NOUN
ejpam-4850	240	15	,	,	PUNCT
ejpam-4850	240	16	and	and	CCONJ
ejpam-4850	240	17	the	the	DET
ejpam-4850	240	18	generalized	generalized	ADJ
ejpam-4850	240	19	s	s	NOUN
ejpam-4850	240	20	-	-	NOUN
ejpam-4850	240	21	convexity	convexity	NOUN
ejpam-4850	240	22	of	of	ADP
ejpam-4850	240	23	∣∣j	∣∣j	NOUN
ejpam-4850	240	24	(	(	PUNCT
ejpam-4850	240	25	γ	γ	NOUN
ejpam-4850	240	26	)	)	PUNCT
ejpam-4850	240	27	∣∣q	∣∣q	NUM
ejpam-4850	240	28	,	,	PUNCT
ejpam-4850	240	29	we	we	PRON
ejpam-4850	240	30	can	can	AUX
ejpam-4850	240	31	conclude	conclude	VERB
ejpam-4850	240	32	that∣∣∣j	that∣∣∣j	NOUN
ejpam-4850	240	33	(	(	PUNCT
ejpam-4850	240	34	x)+j	x)+j	PROPN
ejpam-4850	240	35	(	(	PUNCT
ejpam-4850	240	36	a+b−x	a+b−x	PROPN
ejpam-4850	240	37	)	)	PUNCT
ejpam-4850	240	38	2γ	2γ	NOUN
ejpam-4850	240	39	−	−	PROPN
ejpam-4850	240	40	γ(γ+1	γ(γ+1	NUM
ejpam-4850	240	41	)	)	PUNCT
ejpam-4850	240	42	(	(	PUNCT
ejpam-4850	240	43	b−a)γ	b−a)γ	NOUN
ejpam-4850	240	44	ai	ai	VERB
ejpam-4850	240	45	γ	γ	PROPN
ejpam-4850	240	46	b	b	PROPN
ejpam-4850	240	47	j	j	PROPN
ejpam-4850	240	48	(	(	PUNCT
ejpam-4850	240	49	t	t	PROPN
ejpam-4850	240	50	)	)	PUNCT
ejpam-4850	240	51	∣∣∣	∣∣∣	NOUN
ejpam-4850	240	52	≤	≤	NUM
ejpam-4850	240	53	(	(	PUNCT
ejpam-4850	240	54	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	240	55	(	(	PUNCT
ejpam-4850	240	56	b−a)γ	b−a)γ	PROPN
ejpam-4850	241	1			PROPN
ejpam-4850	241	2			PROPN
ejpam-4850	241	3	1	1	NUM
ejpam-4850	241	4	γ(γ+1	γ(γ+1	NUM
ejpam-4850	241	5	)	)	PUNCT
ejpam-4850	242	1	1∫	1∫	NUM
ejpam-4850	242	2	0	0	NUM
ejpam-4850	242	3	ηpγ	ηpγ	NOUN
ejpam-4850	242	4	(	(	PUNCT
ejpam-4850	242	5	dη)γ	dη)γ	PROPN
ejpam-4850	242	6			PROPN
ejpam-4850	242	7	1	1	NUM
ejpam-4850	242	8	p	p	NOUN
ejpam-4850	242	9			PROPN
ejpam-4850	242	10	1	1	NUM
ejpam-4850	242	11	γ(γ+1	γ(γ+1	NUM
ejpam-4850	242	12	)	)	PUNCT
ejpam-4850	243	1	1∫	1∫	NUM
ejpam-4850	243	2	0	0	NUM
ejpam-4850	243	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	243	4	(	(	PUNCT
ejpam-4850	243	5	γ	γ	PROPN
ejpam-4850	243	6	)	)	PUNCT
ejpam-4850	243	7	(	(	PUNCT
ejpam-4850	243	8	(	(	PUNCT
ejpam-4850	243	9	1−	1−	NUM
ejpam-4850	243	10	η	η	NOUN
ejpam-4850	243	11	)	)	PUNCT
ejpam-4850	243	12	a+	a+	PUNCT
ejpam-4850	243	13	ηx	ηx	PROPN
ejpam-4850	243	14	)	)	PUNCT
ejpam-4850	243	15	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	243	16	(	(	PUNCT
ejpam-4850	243	17	dη)γ	dη)γ	PROPN
ejpam-4850	243	18			PROPN
ejpam-4850	243	19	1	1	NUM
ejpam-4850	243	20	q	q	NOUN
ejpam-4850	243	21	+	+	CCONJ
ejpam-4850	243	22			PROPN
ejpam-4850	243	23	1	1	NUM
ejpam-4850	243	24	γ(γ+1	γ(γ+1	NUM
ejpam-4850	243	25	)	)	PUNCT
ejpam-4850	244	1	1∫	1∫	NUM
ejpam-4850	244	2	0	0	NUM
ejpam-4850	244	3	(	(	PUNCT
ejpam-4850	244	4	1−	1−	NUM
ejpam-4850	244	5	η)pγ	η)pγ	PROPN
ejpam-4850	244	6	(	(	PUNCT
ejpam-4850	244	7	dη)γ	dη)γ	PROPN
ejpam-4850	244	8			PROPN
ejpam-4850	244	9	1	1	NUM
ejpam-4850	244	10	p	p	NOUN
ejpam-4850	244	11			PROPN
ejpam-4850	244	12	1	1	NUM
ejpam-4850	244	13	γ(γ+1	γ(γ+1	NUM
ejpam-4850	244	14	)	)	PUNCT
ejpam-4850	245	1	1∫	1∫	NUM
ejpam-4850	245	2	0	0	NUM
ejpam-4850	245	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	245	4	(	(	PUNCT
ejpam-4850	245	5	γ	γ	PROPN
ejpam-4850	245	6	)	)	PUNCT
ejpam-4850	245	7	(	(	PUNCT
ejpam-4850	245	8	(	(	PUNCT
ejpam-4850	245	9	1−	1−	NUM
ejpam-4850	245	10	η	η	NOUN
ejpam-4850	245	11	)	)	PUNCT
ejpam-4850	245	12	(	(	PUNCT
ejpam-4850	245	13	a+	a+	PUNCT
ejpam-4850	245	14	b−	b−	PROPN
ejpam-4850	245	15	x	x	PROPN
ejpam-4850	245	16	)	)	PUNCT
ejpam-4850	245	17	+	+	CCONJ
ejpam-4850	245	18	ηb	ηb	X
ejpam-4850	245	19	)	)	PUNCT
ejpam-4850	245	20	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	245	21	(	(	PUNCT
ejpam-4850	245	22	dη)γ	dη)γ	PROPN
ejpam-4850	245	23			PROPN
ejpam-4850	245	24	1	1	NUM
ejpam-4850	245	25	q	q	NOUN
ejpam-4850	245	26			NOUN
ejpam-4850	245	27	+	+	CCONJ
ejpam-4850	245	28	(	(	PUNCT
ejpam-4850	245	29	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	245	30	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	245	31			PROPN
ejpam-4850	245	32			PROPN
ejpam-4850	245	33	1	1	NUM
ejpam-4850	245	34	γ(γ+1	γ(γ+1	NUM
ejpam-4850	245	35	)	)	PUNCT
ejpam-4850	246	1	1∫	1∫	NUM
ejpam-4850	246	2	0	0	NUM
ejpam-4850	246	3	(	(	PUNCT
ejpam-4850	246	4	1−	1−	NUM
ejpam-4850	246	5	η)pγ	η)pγ	PROPN
ejpam-4850	246	6	(	(	PUNCT
ejpam-4850	246	7	dη)γ	dη)γ	PROPN
ejpam-4850	246	8			PROPN
ejpam-4850	246	9	1	1	NUM
ejpam-4850	246	10	p	p	NOUN
ejpam-4850	246	11			PROPN
ejpam-4850	246	12	1	1	NUM
ejpam-4850	246	13	γ(γ+1	γ(γ+1	NUM
ejpam-4850	246	14	)	)	PUNCT
ejpam-4850	247	1	1∫	1∫	NUM
ejpam-4850	247	2	0	0	NUM
ejpam-4850	247	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	247	4	(	(	PUNCT
ejpam-4850	247	5	γ	γ	PROPN
ejpam-4850	247	6	)	)	PUNCT
ejpam-4850	247	7	(	(	PUNCT
ejpam-4850	247	8	(	(	PUNCT
ejpam-4850	247	9	1−	1−	NUM
ejpam-4850	247	10	η)x+	η)x+	NUM
ejpam-4850	247	11	η	η	PROPN
ejpam-4850	247	12	a+b	a+b	NUM
ejpam-4850	247	13	2	2	NUM
ejpam-4850	247	14	)	)	PUNCT
ejpam-4850	247	15	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	247	16	(	(	PUNCT
ejpam-4850	247	17	dη)γ	dη)γ	PROPN
ejpam-4850	247	18			PROPN
ejpam-4850	247	19	1	1	NUM
ejpam-4850	247	20	q	q	NOUN
ejpam-4850	247	21	+	+	CCONJ
ejpam-4850	247	22			PROPN
ejpam-4850	247	23	1	1	NUM
ejpam-4850	247	24	γ(γ+1	γ(γ+1	NUM
ejpam-4850	247	25	)	)	PUNCT
ejpam-4850	247	26	1∫	1∫	NUM
ejpam-4850	247	27	0	0	NUM
ejpam-4850	247	28	ηpγ	ηpγ	NOUN
ejpam-4850	247	29	(	(	PUNCT
ejpam-4850	247	30	dη)γ	dη)γ	PROPN
ejpam-4850	247	31			PROPN
ejpam-4850	247	32	1	1	NUM
ejpam-4850	247	33	p	p	NOUN
ejpam-4850	247	34			PROPN
ejpam-4850	247	35	1	1	NUM
ejpam-4850	247	36	γ(γ+1	γ(γ+1	NUM
ejpam-4850	247	37	)	)	PUNCT
ejpam-4850	248	1	1∫	1∫	NUM
ejpam-4850	248	2	0	0	NUM
ejpam-4850	248	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	248	4	(	(	PUNCT
ejpam-4850	248	5	γ	γ	PROPN
ejpam-4850	248	6	)	)	PUNCT
ejpam-4850	248	7	(	(	PUNCT
ejpam-4850	248	8	(	(	PUNCT
ejpam-4850	248	9	1−	1−	NUM
ejpam-4850	248	10	η	η	NOUN
ejpam-4850	248	11	)	)	PUNCT
ejpam-4850	248	12	a+b	a+b	NUM
ejpam-4850	248	13	2	2	NUM
ejpam-4850	248	14	+	+	SYM
ejpam-4850	248	15	η	η	PROPN
ejpam-4850	248	16	(	(	PUNCT
ejpam-4850	248	17	a+	a+	PUNCT
ejpam-4850	248	18	b−	b−	PROPN
ejpam-4850	248	19	x	x	PROPN
ejpam-4850	248	20	)	)	PUNCT
ejpam-4850	248	21	)	)	PUNCT
ejpam-4850	248	22	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	248	23	(	(	PUNCT
ejpam-4850	248	24	dη)γ	dη)γ	PROPN
ejpam-4850	248	25			PROPN
ejpam-4850	248	26	1	1	NUM
ejpam-4850	248	27	q	q	NOUN
ejpam-4850	248	28			NOUN
ejpam-4850	248	29	≤	≤	NUM
ejpam-4850	248	30	(	(	PUNCT
ejpam-4850	248	31	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	248	32	(	(	PUNCT
ejpam-4850	248	33	b−a)γ	b−a)γ	PROPN
ejpam-4850	248	34	(	(	PUNCT
ejpam-4850	248	35	γ(1+pγ	γ(1+pγ	NUM
ejpam-4850	248	36	)	)	PUNCT
ejpam-4850	248	37	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	248	38	)	)	PUNCT
ejpam-4850	248	39	)	)	PUNCT
ejpam-4850	248	40	1	1	NUM
ejpam-4850	248	41	p	p	NOUN
ejpam-4850	248	42			PROPN
ejpam-4850	248	43			PROPN
ejpam-4850	248	44	1	1	NUM
ejpam-4850	248	45	γ(γ+1	γ(γ+1	NUM
ejpam-4850	248	46	)	)	PUNCT
ejpam-4850	249	1	1∫	1∫	NUM
ejpam-4850	249	2	0	0	NUM
ejpam-4850	249	3	(	(	PUNCT
ejpam-4850	249	4	(	(	PUNCT
ejpam-4850	249	5	1−	1−	NUM
ejpam-4850	249	6	η)sγ	η)sγ	PROPN
ejpam-4850	249	7	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	249	8	(	(	PUNCT
ejpam-4850	249	9	γ	γ	PROPN
ejpam-4850	249	10	)	)	PUNCT
ejpam-4850	249	11	(	(	PUNCT
ejpam-4850	249	12	a	a	X
ejpam-4850	249	13	)	)	PUNCT
ejpam-4850	249	14	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	250	1	+	+	NUM
ejpam-4850	250	2	ηsγ	ηsγ	PROPN
ejpam-4850	250	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	250	4	(	(	PUNCT
ejpam-4850	250	5	γ	γ	PROPN
ejpam-4850	250	6	)	)	PUNCT
ejpam-4850	250	7	(	(	PUNCT
ejpam-4850	250	8	x	x	X
ejpam-4850	250	9	)	)	PUNCT
ejpam-4850	250	10	∣∣∣q	∣∣∣q	NUM
ejpam-4850	250	11	)	)	PUNCT
ejpam-4850	250	12	(	(	PUNCT
ejpam-4850	250	13	dη)γ	dη)γ	PROPN
ejpam-4850	250	14			PROPN
ejpam-4850	250	15	1	1	NUM
ejpam-4850	250	16	q	q	NOUN
ejpam-4850	251	1	+	+	CCONJ
ejpam-4850	251	2			PROPN
ejpam-4850	251	3	1	1	NUM
ejpam-4850	251	4	γ(γ+1	γ(γ+1	NUM
ejpam-4850	251	5	)	)	PUNCT
ejpam-4850	252	1	1∫	1∫	NUM
ejpam-4850	252	2	0	0	NUM
ejpam-4850	252	3	(	(	PUNCT
ejpam-4850	252	4	(	(	PUNCT
ejpam-4850	252	5	1−	1−	NUM
ejpam-4850	252	6	η)sγ	η)sγ	PROPN
ejpam-4850	252	7	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	252	8	(	(	PUNCT
ejpam-4850	252	9	γ	γ	PROPN
ejpam-4850	252	10	)	)	PUNCT
ejpam-4850	252	11	(	(	PUNCT
ejpam-4850	252	12	a+	a+	PUNCT
ejpam-4850	252	13	b−	b−	PROPN
ejpam-4850	252	14	x	x	SYM
ejpam-4850	252	15	)	)	PUNCT
ejpam-4850	252	16	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	253	1	+	+	NUM
ejpam-4850	253	2	ηsγ	ηsγ	PROPN
ejpam-4850	253	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	253	4	(	(	PUNCT
ejpam-4850	253	5	γ	γ	PROPN
ejpam-4850	253	6	)	)	PUNCT
ejpam-4850	253	7	(	(	PUNCT
ejpam-4850	253	8	b	b	X
ejpam-4850	253	9	)	)	PUNCT
ejpam-4850	253	10	∣∣∣q	∣∣∣q	NUM
ejpam-4850	253	11	)	)	PUNCT
ejpam-4850	253	12	(	(	PUNCT
ejpam-4850	253	13	dη)γ	dη)γ	PROPN
ejpam-4850	253	14			PROPN
ejpam-4850	253	15	1	1	NUM
ejpam-4850	253	16	q	q	NOUN
ejpam-4850	253	17			NOUN
ejpam-4850	253	18	+	+	CCONJ
ejpam-4850	253	19	(	(	PUNCT
ejpam-4850	253	20	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	253	21	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	253	22			PROPN
ejpam-4850	253	23			PROPN
ejpam-4850	253	24	1	1	NUM
ejpam-4850	253	25	γ(γ+1	γ(γ+1	NUM
ejpam-4850	253	26	)	)	PUNCT
ejpam-4850	254	1	1∫	1∫	NUM
ejpam-4850	254	2	0	0	NUM
ejpam-4850	254	3	(	(	PUNCT
ejpam-4850	254	4	1−	1−	NUM
ejpam-4850	254	5	η)pγ	η)pγ	PROPN
ejpam-4850	254	6	(	(	PUNCT
ejpam-4850	254	7	dη)γ	dη)γ	PROPN
ejpam-4850	254	8			PROPN
ejpam-4850	254	9	1	1	NUM
ejpam-4850	254	10	p	p	NOUN
ejpam-4850	254	11	×	×	NOUN
ejpam-4850	254	12			PROPN
ejpam-4850	254	13	1	1	NUM
ejpam-4850	254	14	γ(γ+1	γ(γ+1	NUM
ejpam-4850	254	15	)	)	PUNCT
ejpam-4850	255	1	1∫	1∫	NUM
ejpam-4850	255	2	0	0	NUM
ejpam-4850	255	3	(	(	PUNCT
ejpam-4850	255	4	(	(	PUNCT
ejpam-4850	255	5	1−	1−	NUM
ejpam-4850	255	6	η)sγ	η)sγ	PROPN
ejpam-4850	255	7	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	255	8	(	(	PUNCT
ejpam-4850	255	9	γ	γ	PROPN
ejpam-4850	255	10	)	)	PUNCT
ejpam-4850	255	11	(	(	PUNCT
ejpam-4850	255	12	x	x	X
ejpam-4850	255	13	)	)	PUNCT
ejpam-4850	255	14	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	256	1	+	+	NUM
ejpam-4850	256	2	ηsγ	ηsγ	PROPN
ejpam-4850	256	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	256	4	(	(	PUNCT
ejpam-4850	256	5	γ	γ	PROPN
ejpam-4850	256	6	)	)	PUNCT
ejpam-4850	256	7	(	(	PUNCT
ejpam-4850	256	8	a+b	a+b	NUM
ejpam-4850	256	9	2	2	NUM
ejpam-4850	256	10	)	)	PUNCT
ejpam-4850	256	11	∣∣∣q	∣∣∣q	NUM
ejpam-4850	256	12	)	)	PUNCT
ejpam-4850	256	13	(	(	PUNCT
ejpam-4850	256	14	dη)γ	dη)γ	PROPN
ejpam-4850	256	15			PROPN
ejpam-4850	256	16	1	1	NUM
ejpam-4850	256	17	q	q	NOUN
ejpam-4850	257	1	+	+	CCONJ
ejpam-4850	258	1			PROPN
ejpam-4850	258	2	1	1	NUM
ejpam-4850	258	3	γ(γ+1	γ(γ+1	NUM
ejpam-4850	258	4	)	)	PUNCT
ejpam-4850	258	5	1∫	1∫	NUM
ejpam-4850	258	6	0	0	NUM
ejpam-4850	258	7	ηpγ	ηpγ	NOUN
ejpam-4850	258	8	(	(	PUNCT
ejpam-4850	258	9	dη)γ	dη)γ	PROPN
ejpam-4850	258	10			PROPN
ejpam-4850	258	11	1	1	NUM
ejpam-4850	258	12	p	p	NOUN
ejpam-4850	258	13	w.	w.	PROPN
ejpam-4850	258	14	saleh	saleh	PROPN
ejpam-4850	258	15	et	et	PROPN
ejpam-4850	258	16	al	al	PROPN
ejpam-4850	258	17	.	.	PUNCT
ejpam-4850	258	18	/	/	SYM
ejpam-4850	258	19	eur	eur	PROPN
ejpam-4850	258	20	.	.	PUNCT
ejpam-4850	259	1	j.	j.	PROPN
ejpam-4850	259	2	pure	pure	PROPN
ejpam-4850	259	3	appl	appl	PROPN
ejpam-4850	259	4	.	.	PROPN
ejpam-4850	259	5	math	math	PROPN
ejpam-4850	259	6	,	,	PUNCT
ejpam-4850	259	7	16	16	NUM
ejpam-4850	259	8	(	(	PUNCT
ejpam-4850	259	9	3	3	NUM
ejpam-4850	259	10	)	)	PUNCT
ejpam-4850	259	11	(	(	PUNCT
ejpam-4850	259	12	2023	2023	NUM
ejpam-4850	259	13	)	)	PUNCT
ejpam-4850	259	14	,	,	PUNCT
ejpam-4850	259	15	1359	1359	NUM
ejpam-4850	259	16	-	-	SYM
ejpam-4850	259	17	1380	1380	NUM
ejpam-4850	259	18	1370	1370	NUM
ejpam-4850	259	19	×	×	NOUN
ejpam-4850	259	20			PROPN
ejpam-4850	259	21	1	1	NUM
ejpam-4850	259	22	γ(γ+1	γ(γ+1	NUM
ejpam-4850	259	23	)	)	PUNCT
ejpam-4850	260	1	1∫	1∫	NUM
ejpam-4850	260	2	0	0	NUM
ejpam-4850	260	3	(	(	PUNCT
ejpam-4850	260	4	(	(	PUNCT
ejpam-4850	260	5	1−	1−	NUM
ejpam-4850	260	6	η)sγ	η)sγ	PROPN
ejpam-4850	260	7	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	260	8	(	(	PUNCT
ejpam-4850	260	9	γ	γ	PROPN
ejpam-4850	260	10	)	)	PUNCT
ejpam-4850	260	11	(	(	PUNCT
ejpam-4850	260	12	a+b	a+b	NUM
ejpam-4850	260	13	2	2	NUM
ejpam-4850	260	14	)	)	PUNCT
ejpam-4850	260	15	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	261	1	+	+	NUM
ejpam-4850	261	2	ηsγ	ηsγ	PROPN
ejpam-4850	261	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	261	4	(	(	PUNCT
ejpam-4850	261	5	γ	γ	PROPN
ejpam-4850	261	6	)	)	PUNCT
ejpam-4850	261	7	(	(	PUNCT
ejpam-4850	261	8	a+	a+	PUNCT
ejpam-4850	261	9	b−	b−	PROPN
ejpam-4850	261	10	x	x	SYM
ejpam-4850	261	11	)	)	PUNCT
ejpam-4850	261	12	∣∣∣q	∣∣∣q	NUM
ejpam-4850	261	13	)	)	PUNCT
ejpam-4850	261	14	(	(	PUNCT
ejpam-4850	261	15	dη)γ	dη)γ	PROPN
ejpam-4850	261	16			PROPN
ejpam-4850	261	17	1	1	NUM
ejpam-4850	261	18	q	q	NOUN
ejpam-4850	261	19			NOUN
ejpam-4850	261	20	=	=	SYM
ejpam-4850	261	21	(	(	PUNCT
ejpam-4850	261	22	γ(1+pγ	γ(1+pγ	NUM
ejpam-4850	261	23	)	)	PUNCT
ejpam-4850	261	24	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	261	25	)	)	PUNCT
ejpam-4850	261	26	)	)	PUNCT
ejpam-4850	261	27	1	1	NUM
ejpam-4850	261	28	p	p	NOUN
ejpam-4850	261	29	(	(	PUNCT
ejpam-4850	261	30	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	261	31	)	)	PUNCT
ejpam-4850	261	32	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	261	33	)	)	PUNCT
ejpam-4850	261	34	)	)	PUNCT
ejpam-4850	261	35	1	1	NUM
ejpam-4850	261	36	q	q	NOUN
ejpam-4850	261	37	×	×	NOUN
ejpam-4850	261	38	(	(	PUNCT
ejpam-4850	261	39	(	(	PUNCT
ejpam-4850	261	40	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	261	41	(	(	PUNCT
ejpam-4850	261	42	b−a)γ	b−a)γ	PROPN
ejpam-4850	261	43	(	(	PUNCT
ejpam-4850	261	44	(	(	PUNCT
ejpam-4850	261	45	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	261	46	(	(	PUNCT
ejpam-4850	261	47	γ	γ	PROPN
ejpam-4850	261	48	)	)	PUNCT
ejpam-4850	261	49	(	(	PUNCT
ejpam-4850	261	50	a	a	X
ejpam-4850	261	51	)	)	PUNCT
ejpam-4850	261	52	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	261	53	+	+	CCONJ
ejpam-4850	261	54	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	261	55	(	(	PUNCT
ejpam-4850	261	56	γ	γ	PROPN
ejpam-4850	261	57	)	)	PUNCT
ejpam-4850	261	58	(	(	PUNCT
ejpam-4850	261	59	x	x	X
ejpam-4850	261	60	)	)	PUNCT
ejpam-4850	261	61	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	261	62	q	q	PROPN
ejpam-4850	262	1	+	+	CCONJ
ejpam-4850	262	2	(	(	PUNCT
ejpam-4850	262	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	262	4	(	(	PUNCT
ejpam-4850	262	5	γ	γ	PROPN
ejpam-4850	262	6	)	)	PUNCT
ejpam-4850	262	7	(	(	PUNCT
ejpam-4850	262	8	a+	a+	PUNCT
ejpam-4850	262	9	b−	b−	PROPN
ejpam-4850	262	10	x	x	SYM
ejpam-4850	262	11	)	)	PUNCT
ejpam-4850	262	12	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	263	1	+	+	CCONJ
ejpam-4850	263	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	263	3	(	(	PUNCT
ejpam-4850	263	4	γ	γ	PROPN
ejpam-4850	263	5	)	)	PUNCT
ejpam-4850	263	6	(	(	PUNCT
ejpam-4850	263	7	b	b	X
ejpam-4850	263	8	)	)	PUNCT
ejpam-4850	263	9	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	263	10	q	q	PROPN
ejpam-4850	263	11	)	)	PUNCT
ejpam-4850	264	1	+	+	CCONJ
ejpam-4850	264	2	(	(	PUNCT
ejpam-4850	264	3	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	264	4	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	264	5	(	(	PUNCT
ejpam-4850	264	6	(	(	PUNCT
ejpam-4850	264	7	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	264	8	(	(	PUNCT
ejpam-4850	264	9	γ	γ	PROPN
ejpam-4850	264	10	)	)	PUNCT
ejpam-4850	264	11	(	(	PUNCT
ejpam-4850	264	12	x	x	X
ejpam-4850	264	13	)	)	PUNCT
ejpam-4850	264	14	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	265	1	+	+	CCONJ
ejpam-4850	265	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	265	3	(	(	PUNCT
ejpam-4850	265	4	γ	γ	PROPN
ejpam-4850	265	5	)	)	PUNCT
ejpam-4850	265	6	(	(	PUNCT
ejpam-4850	265	7	a+b	a+b	NUM
ejpam-4850	265	8	2	2	NUM
ejpam-4850	265	9	)	)	PUNCT
ejpam-4850	265	10	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	265	11	q	q	PROPN
ejpam-4850	266	1	+	+	CCONJ
ejpam-4850	266	2	(	(	PUNCT
ejpam-4850	266	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	266	4	(	(	PUNCT
ejpam-4850	266	5	γ	γ	PROPN
ejpam-4850	266	6	)	)	PUNCT
ejpam-4850	266	7	(	(	PUNCT
ejpam-4850	266	8	a+b	a+b	NUM
ejpam-4850	266	9	2	2	NUM
ejpam-4850	266	10	)	)	PUNCT
ejpam-4850	266	11	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	267	1	+	+	CCONJ
ejpam-4850	267	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	267	3	(	(	PUNCT
ejpam-4850	267	4	γ	γ	PROPN
ejpam-4850	267	5	)	)	PUNCT
ejpam-4850	267	6	(	(	PUNCT
ejpam-4850	267	7	a+	a+	PUNCT
ejpam-4850	267	8	b−	b−	PROPN
ejpam-4850	267	9	x	x	SYM
ejpam-4850	267	10	)	)	PUNCT
ejpam-4850	267	11	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	267	12	q	q	PROPN
ejpam-4850	267	13	)	)	PUNCT
ejpam-4850	267	14	)	)	PUNCT
ejpam-4850	267	15	,	,	PUNCT
ejpam-4850	267	16	where	where	SCONJ
ejpam-4850	267	17	we	we	PRON
ejpam-4850	267	18	have	have	AUX
ejpam-4850	267	19	used	use	VERB
ejpam-4850	267	20	the	the	DET
ejpam-4850	267	21	fact	fact	NOUN
ejpam-4850	267	22	that	that	SCONJ
ejpam-4850	267	23	1	1	NUM
ejpam-4850	267	24	γ(γ+1	γ(γ+1	NUM
ejpam-4850	267	25	)	)	PUNCT
ejpam-4850	268	1	1∫	1∫	NUM
ejpam-4850	268	2	0	0	NUM
ejpam-4850	268	3	ηpγ	ηpγ	NOUN
ejpam-4850	268	4	(	(	PUNCT
ejpam-4850	268	5	dη)γ	dη)γ	PROPN
ejpam-4850	268	6	=	=	SYM
ejpam-4850	268	7	1	1	NUM
ejpam-4850	268	8	γ(γ+1	γ(γ+1	NUM
ejpam-4850	268	9	)	)	PUNCT
ejpam-4850	269	1	1∫	1∫	NUM
ejpam-4850	269	2	0	0	NUM
ejpam-4850	269	3	(	(	PUNCT
ejpam-4850	269	4	1−	1−	NUM
ejpam-4850	269	5	η)pγ	η)pγ	PROPN
ejpam-4850	269	6	(	(	PUNCT
ejpam-4850	269	7	dη)γ	dη)γ	PROPN
ejpam-4850	269	8	=	=	SYM
ejpam-4850	269	9	γ(1+pγ	γ(1+pγ	PROPN
ejpam-4850	269	10	)	)	PUNCT
ejpam-4850	269	11	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	269	12	)	)	PUNCT
ejpam-4850	269	13	.	.	PUNCT
ejpam-4850	270	1	the	the	DET
ejpam-4850	270	2	proof	proof	NOUN
ejpam-4850	270	3	is	be	AUX
ejpam-4850	270	4	completed	complete	VERB
ejpam-4850	270	5	.	.	PUNCT
ejpam-4850	271	1	corollary	corollary	ADJ
ejpam-4850	271	2	10	10	NUM
ejpam-4850	271	3	.	.	PUNCT
ejpam-4850	272	1	in	in	ADP
ejpam-4850	272	2	theorem	theorem	NOUN
ejpam-4850	272	3	2	2	NUM
ejpam-4850	272	4	,	,	PUNCT
ejpam-4850	272	5	taking	take	VERB
ejpam-4850	272	6	x	x	X
ejpam-4850	272	7	=	=	PUNCT
ejpam-4850	272	8	a	a	PRON
ejpam-4850	272	9	,	,	PUNCT
ejpam-4850	272	10	we	we	PRON
ejpam-4850	272	11	obtain∣∣∣j	obtain∣∣∣j	VERB
ejpam-4850	272	12	(	(	PUNCT
ejpam-4850	272	13	a)+j	a)+j	PROPN
ejpam-4850	272	14	(	(	PUNCT
ejpam-4850	272	15	b	b	NOUN
ejpam-4850	272	16	)	)	PUNCT
ejpam-4850	272	17	2γ	2γ	NOUN
ejpam-4850	272	18	−	−	PROPN
ejpam-4850	272	19	γ(γ+1	γ(γ+1	NUM
ejpam-4850	272	20	)	)	PUNCT
ejpam-4850	272	21	(	(	PUNCT
ejpam-4850	272	22	b−a)γ	b−a)γ	NOUN
ejpam-4850	272	23	ai	ai	VERB
ejpam-4850	272	24	γ	γ	PROPN
ejpam-4850	272	25	b	b	PROPN
ejpam-4850	272	26	j	j	PROPN
ejpam-4850	272	27	(	(	PUNCT
ejpam-4850	272	28	t	t	PROPN
ejpam-4850	272	29	)	)	PUNCT
ejpam-4850	272	30	∣∣∣	∣∣∣	NOUN
ejpam-4850	272	31	≤	≤	NOUN
ejpam-4850	272	32	(	(	PUNCT
ejpam-4850	272	33	b−a)γ	b−a)γ	NOUN
ejpam-4850	272	34	4γ	4γ	NOUN
ejpam-4850	272	35	(	(	PUNCT
ejpam-4850	272	36	γ(1+pγ	γ(1+pγ	NUM
ejpam-4850	272	37	)	)	PUNCT
ejpam-4850	272	38	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	272	39	)	)	PUNCT
ejpam-4850	272	40	)	)	PUNCT
ejpam-4850	272	41	1	1	NUM
ejpam-4850	272	42	p	p	NOUN
ejpam-4850	272	43	(	(	PUNCT
ejpam-4850	272	44	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	272	45	)	)	PUNCT
ejpam-4850	272	46	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	272	47	)	)	PUNCT
ejpam-4850	272	48	)	)	PUNCT
ejpam-4850	272	49	1	1	NUM
ejpam-4850	272	50	q	q	NOUN
ejpam-4850	272	51	×	×	NOUN
ejpam-4850	272	52	(	(	PUNCT
ejpam-4850	272	53	(	(	PUNCT
ejpam-4850	272	54	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	272	55	(	(	PUNCT
ejpam-4850	272	56	γ	γ	PROPN
ejpam-4850	272	57	)	)	PUNCT
ejpam-4850	272	58	(	(	PUNCT
ejpam-4850	272	59	a	a	X
ejpam-4850	272	60	)	)	PUNCT
ejpam-4850	272	61	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	273	1	+	+	CCONJ
ejpam-4850	273	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	273	3	(	(	PUNCT
ejpam-4850	273	4	γ	γ	PROPN
ejpam-4850	273	5	)	)	PUNCT
ejpam-4850	273	6	(	(	PUNCT
ejpam-4850	273	7	a+b	a+b	NUM
ejpam-4850	273	8	2	2	NUM
ejpam-4850	273	9	)	)	PUNCT
ejpam-4850	273	10	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	273	11	q	q	PROPN
ejpam-4850	274	1	+	+	CCONJ
ejpam-4850	274	2	(	(	PUNCT
ejpam-4850	274	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	274	4	(	(	PUNCT
ejpam-4850	274	5	γ	γ	PROPN
ejpam-4850	274	6	)	)	PUNCT
ejpam-4850	274	7	(	(	PUNCT
ejpam-4850	274	8	a+b	a+b	NUM
ejpam-4850	274	9	2	2	NUM
ejpam-4850	274	10	)	)	PUNCT
ejpam-4850	274	11	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	275	1	+	+	CCONJ
ejpam-4850	275	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	275	3	(	(	PUNCT
ejpam-4850	275	4	γ	γ	PROPN
ejpam-4850	275	5	)	)	PUNCT
ejpam-4850	275	6	(	(	PUNCT
ejpam-4850	275	7	b	b	X
ejpam-4850	275	8	)	)	PUNCT
ejpam-4850	275	9	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	275	10	q	q	PROPN
ejpam-4850	275	11	)	)	PUNCT
ejpam-4850	275	12	.	.	PUNCT
ejpam-4850	276	1	corollary	corollary	ADJ
ejpam-4850	276	2	11	11	NUM
ejpam-4850	276	3	.	.	PUNCT
ejpam-4850	277	1	in	in	ADP
ejpam-4850	277	2	theorem	theorem	NOUN
ejpam-4850	277	3	2	2	NUM
ejpam-4850	277	4	,	,	PUNCT
ejpam-4850	277	5	taking	take	VERB
ejpam-4850	277	6	x	x	X
ejpam-4850	277	7	=	=	SYM
ejpam-4850	277	8	a+b	a+b	NUM
ejpam-4850	277	9	2	2	NUM
ejpam-4850	277	10	,	,	PUNCT
ejpam-4850	277	11	we	we	PRON
ejpam-4850	277	12	obtain∣∣∣j	obtain∣∣∣j	VERB
ejpam-4850	277	13	(	(	PUNCT
ejpam-4850	277	14	a+b	a+b	NUM
ejpam-4850	277	15	2	2	NUM
ejpam-4850	277	16	)	)	PUNCT
ejpam-4850	277	17	−	−	PROPN
ejpam-4850	277	18	γ(γ+1	γ(γ+1	NUM
ejpam-4850	277	19	)	)	PUNCT
ejpam-4850	277	20	(	(	PUNCT
ejpam-4850	277	21	b−a)γ	b−a)γ	NOUN
ejpam-4850	277	22	ai	ai	VERB
ejpam-4850	277	23	γ	γ	PROPN
ejpam-4850	277	24	b	b	PROPN
ejpam-4850	277	25	j	j	PROPN
ejpam-4850	277	26	(	(	PUNCT
ejpam-4850	277	27	t	t	PROPN
ejpam-4850	277	28	)	)	PUNCT
ejpam-4850	277	29	∣∣∣	∣∣∣	NOUN
ejpam-4850	277	30	≤	≤	NOUN
ejpam-4850	277	31	(	(	PUNCT
ejpam-4850	277	32	b−a)γ	b−a)γ	NOUN
ejpam-4850	277	33	4γ	4γ	NOUN
ejpam-4850	277	34	(	(	PUNCT
ejpam-4850	277	35	γ(1+pγ	γ(1+pγ	NUM
ejpam-4850	277	36	)	)	PUNCT
ejpam-4850	277	37	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	277	38	)	)	PUNCT
ejpam-4850	277	39	)	)	PUNCT
ejpam-4850	277	40	1	1	NUM
ejpam-4850	277	41	p	p	NOUN
ejpam-4850	277	42	(	(	PUNCT
ejpam-4850	277	43	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	277	44	)	)	PUNCT
ejpam-4850	277	45	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	277	46	)	)	PUNCT
ejpam-4850	277	47	)	)	PUNCT
ejpam-4850	277	48	1	1	NUM
ejpam-4850	277	49	q	q	NOUN
ejpam-4850	277	50	×	×	NOUN
ejpam-4850	277	51	(	(	PUNCT
ejpam-4850	277	52	(	(	PUNCT
ejpam-4850	277	53	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	277	54	(	(	PUNCT
ejpam-4850	277	55	γ	γ	PROPN
ejpam-4850	277	56	)	)	PUNCT
ejpam-4850	277	57	(	(	PUNCT
ejpam-4850	277	58	a	a	X
ejpam-4850	277	59	)	)	PUNCT
ejpam-4850	277	60	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	278	1	+	+	CCONJ
ejpam-4850	278	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	278	3	(	(	PUNCT
ejpam-4850	278	4	γ	γ	PROPN
ejpam-4850	278	5	)	)	PUNCT
ejpam-4850	278	6	(	(	PUNCT
ejpam-4850	278	7	a+b	a+b	NUM
ejpam-4850	278	8	2	2	NUM
ejpam-4850	278	9	)	)	PUNCT
ejpam-4850	278	10	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	278	11	q	q	PROPN
ejpam-4850	279	1	+	+	CCONJ
ejpam-4850	279	2	(	(	PUNCT
ejpam-4850	279	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	279	4	(	(	PUNCT
ejpam-4850	279	5	γ	γ	PROPN
ejpam-4850	279	6	)	)	PUNCT
ejpam-4850	279	7	(	(	PUNCT
ejpam-4850	279	8	a+b	a+b	NUM
ejpam-4850	279	9	2	2	NUM
ejpam-4850	279	10	)	)	PUNCT
ejpam-4850	279	11	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	280	1	+	+	CCONJ
ejpam-4850	280	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	280	3	(	(	PUNCT
ejpam-4850	280	4	γ	γ	PROPN
ejpam-4850	280	5	)	)	PUNCT
ejpam-4850	280	6	(	(	PUNCT
ejpam-4850	280	7	b	b	X
ejpam-4850	280	8	)	)	PUNCT
ejpam-4850	280	9	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	280	10	q	q	PROPN
ejpam-4850	280	11	)	)	PUNCT
ejpam-4850	280	12	.	.	PUNCT
ejpam-4850	281	1	theorem	theorem	NOUN
ejpam-4850	281	2	3	3	X
ejpam-4850	281	3	.	.	PUNCT
ejpam-4850	281	4	suppose	suppose	VERB
ejpam-4850	282	1	j	j	NOUN
ejpam-4850	282	2	:	:	PUNCT
ejpam-4850	283	1	[	[	X
ejpam-4850	283	2	a	a	X
ejpam-4850	283	3	,	,	PUNCT
ejpam-4850	283	4	b	b	NOUN
ejpam-4850	283	5	]	]	X
ejpam-4850	283	6	→	→	PUNCT
ejpam-4850	283	7	rγ	rγ	PRON
ejpam-4850	283	8	is	be	AUX
ejpam-4850	283	9	a	a	DET
ejpam-4850	283	10	differentiable	differentiable	ADJ
ejpam-4850	283	11	function	function	NOUN
ejpam-4850	283	12	on	on	ADP
ejpam-4850	283	13	[	[	X
ejpam-4850	283	14	a	a	X
ejpam-4850	283	15	,	,	PUNCT
ejpam-4850	283	16	b	b	NOUN
ejpam-4850	283	17	]	]	X
ejpam-4850	283	18	such	such	ADJ
ejpam-4850	283	19	that	that	SCONJ
ejpam-4850	283	20	j	j	PROPN
ejpam-4850	283	21	∈	∈	PROPN
ejpam-4850	283	22	dγ	dγ	ADP
ejpam-4850	283	23	[	[	X
ejpam-4850	283	24	a	a	X
ejpam-4850	283	25	,	,	PUNCT
ejpam-4850	283	26	b	b	NOUN
ejpam-4850	283	27	]	]	X
ejpam-4850	283	28	and	and	CCONJ
ejpam-4850	283	29	j	j	PROPN
ejpam-4850	283	30	(	(	PUNCT
ejpam-4850	283	31	γ	γ	PROPN
ejpam-4850	283	32	)	)	PUNCT
ejpam-4850	283	33	∈	∈	NOUN
ejpam-4850	283	34	cγ	cγ	NOUN
ejpam-4850	283	35	[	[	X
ejpam-4850	283	36	a	a	X
ejpam-4850	283	37	,	,	PUNCT
ejpam-4850	283	38	b	b	NOUN
ejpam-4850	283	39	]	]	X
ejpam-4850	283	40	with	with	ADP
ejpam-4850	283	41	0	0	NUM
ejpam-4850	283	42	≤	≤	NOUN
ejpam-4850	283	43	a	a	DET
ejpam-4850	283	44	<	<	X
ejpam-4850	283	45	b.	b.	NOUN
ejpam-4850	283	46	if	if	SCONJ
ejpam-4850	283	47	∣∣j	∣∣j	X
ejpam-4850	283	48	(	(	PUNCT
ejpam-4850	283	49	γ	γ	NOUN
ejpam-4850	283	50	)	)	PUNCT
ejpam-4850	283	51	∣∣q	∣∣q	NUM
ejpam-4850	283	52	is	be	AUX
ejpam-4850	283	53	generalized	generalize	VERB
ejpam-4850	283	54	s	s	NOUN
ejpam-4850	283	55	-	-	NOUN
ejpam-4850	283	56	convex	convex	NOUN
ejpam-4850	283	57	on	on	ADP
ejpam-4850	283	58	[	[	X
ejpam-4850	283	59	a	a	X
ejpam-4850	283	60	,	,	PUNCT
ejpam-4850	283	61	b	b	NOUN
ejpam-4850	283	62	]	]	X
ejpam-4850	283	63	,	,	PUNCT
ejpam-4850	283	64	where	where	SCONJ
ejpam-4850	283	65	q	q	PUNCT
ejpam-4850	283	66	>	>	X
ejpam-4850	283	67	1	1	NUM
ejpam-4850	283	68	,	,	PUNCT
ejpam-4850	283	69	then	then	ADV
ejpam-4850	283	70	we	we	PRON
ejpam-4850	283	71	have∣∣∣j	have∣∣∣j	VERB
ejpam-4850	283	72	(	(	PUNCT
ejpam-4850	283	73	x)+j	x)+j	PROPN
ejpam-4850	283	74	(	(	PUNCT
ejpam-4850	283	75	a+b−x	a+b−x	PROPN
ejpam-4850	283	76	)	)	PUNCT
ejpam-4850	283	77	2γ	2γ	NOUN
ejpam-4850	283	78	−	−	PROPN
ejpam-4850	283	79	γ(γ+1	γ(γ+1	NUM
ejpam-4850	283	80	)	)	PUNCT
ejpam-4850	283	81	(	(	PUNCT
ejpam-4850	283	82	b−a)γ	b−a)γ	NOUN
ejpam-4850	283	83	ai	ai	VERB
ejpam-4850	283	84	γ	γ	PROPN
ejpam-4850	283	85	b	b	PROPN
ejpam-4850	283	86	j	j	PROPN
ejpam-4850	283	87	(	(	PUNCT
ejpam-4850	283	88	t	t	PROPN
ejpam-4850	283	89	)	)	PUNCT
ejpam-4850	283	90	∣∣∣	∣∣∣	NOUN
ejpam-4850	283	91	w.	w.	PROPN
ejpam-4850	283	92	saleh	saleh	PROPN
ejpam-4850	283	93	et	et	PROPN
ejpam-4850	283	94	al	al	PROPN
ejpam-4850	283	95	.	.	PUNCT
ejpam-4850	283	96	/	/	SYM
ejpam-4850	283	97	eur	eur	PROPN
ejpam-4850	283	98	.	.	PUNCT
ejpam-4850	284	1	j.	j.	PROPN
ejpam-4850	284	2	pure	pure	PROPN
ejpam-4850	284	3	appl	appl	PROPN
ejpam-4850	284	4	.	.	PROPN
ejpam-4850	284	5	math	math	PROPN
ejpam-4850	284	6	,	,	PUNCT
ejpam-4850	284	7	16	16	NUM
ejpam-4850	284	8	(	(	PUNCT
ejpam-4850	284	9	3	3	NUM
ejpam-4850	284	10	)	)	PUNCT
ejpam-4850	284	11	(	(	PUNCT
ejpam-4850	284	12	2023	2023	NUM
ejpam-4850	284	13	)	)	PUNCT
ejpam-4850	284	14	,	,	PUNCT
ejpam-4850	284	15	1359	1359	NUM
ejpam-4850	284	16	-	-	SYM
ejpam-4850	284	17	1380	1380	NUM
ejpam-4850	284	18	1371	1371	NUM
ejpam-4850	284	19	≤	≤	NOUN
ejpam-4850	284	20	(	(	PUNCT
ejpam-4850	284	21	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	284	22	)	)	PUNCT
ejpam-4850	285	1	γ(1	γ(1	PROPN
ejpam-4850	285	2	+	+	NOUN
ejpam-4850	285	3	2γ	2γ	NOUN
ejpam-4850	285	4	)	)	PUNCT
ejpam-4850	285	5	)	)	PUNCT
ejpam-4850	286	1	1−1	1−1	NUM
ejpam-4850	286	2	q	q	NOUN
ejpam-4850	286	3	×	×	NOUN
ejpam-4850	286	4	(	(	PUNCT
ejpam-4850	286	5	(	(	PUNCT
ejpam-4850	286	6	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	286	7	(	(	PUNCT
ejpam-4850	286	8	b−a)γ	b−a)γ	PROPN
ejpam-4850	286	9	(	(	PUNCT
ejpam-4850	286	10	(	(	PUNCT
ejpam-4850	286	11	(	(	PUNCT
ejpam-4850	286	12	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	286	13	)	)	PUNCT
ejpam-4850	286	14	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	286	15	)	)	PUNCT
ejpam-4850	286	16	−	−	PROPN
ejpam-4850	286	17	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	286	18	)	)	PUNCT
ejpam-4850	286	19	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	286	20	)	)	PUNCT
ejpam-4850	286	21	)	)	PUNCT
ejpam-4850	286	22	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	286	23	(	(	PUNCT
ejpam-4850	286	24	γ	γ	PROPN
ejpam-4850	286	25	)	)	PUNCT
ejpam-4850	286	26	(	(	PUNCT
ejpam-4850	286	27	a	a	X
ejpam-4850	286	28	)	)	PUNCT
ejpam-4850	286	29	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	286	30	+	+	CCONJ
ejpam-4850	286	31	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	286	32	)	)	PUNCT
ejpam-4850	286	33	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	286	34	)	)	PUNCT
ejpam-4850	286	35	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	286	36	(	(	PUNCT
ejpam-4850	286	37	γ	γ	PROPN
ejpam-4850	286	38	)	)	PUNCT
ejpam-4850	286	39	(	(	PUNCT
ejpam-4850	286	40	x	x	X
ejpam-4850	286	41	)	)	PUNCT
ejpam-4850	286	42	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	286	43	q	q	PROPN
ejpam-4850	287	1	+	+	CCONJ
ejpam-4850	287	2	(	(	PUNCT
ejpam-4850	287	3	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	287	4	)	)	PUNCT
ejpam-4850	287	5	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	287	6	)	)	PUNCT
ejpam-4850	287	7	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	287	8	(	(	PUNCT
ejpam-4850	287	9	γ	γ	PROPN
ejpam-4850	287	10	)	)	PUNCT
ejpam-4850	287	11	(	(	PUNCT
ejpam-4850	287	12	a+	a+	PUNCT
ejpam-4850	287	13	b−	b−	PROPN
ejpam-4850	287	14	x	x	SYM
ejpam-4850	287	15	)	)	PUNCT
ejpam-4850	287	16	∣∣∣q	∣∣∣q	NUM
ejpam-4850	288	1	+	+	CCONJ
ejpam-4850	288	2	(	(	PUNCT
ejpam-4850	288	3	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	288	4	)	)	PUNCT
ejpam-4850	288	5	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	288	6	)	)	PUNCT
ejpam-4850	288	7	−	−	PROPN
ejpam-4850	288	8	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	288	9	)	)	PUNCT
ejpam-4850	288	10	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	288	11	)	)	PUNCT
ejpam-4850	288	12	)	)	PUNCT
ejpam-4850	289	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	289	2	(	(	PUNCT
ejpam-4850	289	3	γ	γ	PROPN
ejpam-4850	289	4	)	)	PUNCT
ejpam-4850	289	5	(	(	PUNCT
ejpam-4850	289	6	b	b	X
ejpam-4850	289	7	)	)	PUNCT
ejpam-4850	289	8	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	289	9	q	q	PROPN
ejpam-4850	289	10	)	)	PUNCT
ejpam-4850	290	1	+	+	CCONJ
ejpam-4850	290	2	(	(	PUNCT
ejpam-4850	290	3	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	290	4	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	290	5	(	(	PUNCT
ejpam-4850	290	6	(	(	PUNCT
ejpam-4850	290	7	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	290	8	)	)	PUNCT
ejpam-4850	290	9	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	290	10	)	)	PUNCT
ejpam-4850	290	11	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	290	12	(	(	PUNCT
ejpam-4850	290	13	γ	γ	PROPN
ejpam-4850	290	14	)	)	PUNCT
ejpam-4850	290	15	(	(	PUNCT
ejpam-4850	290	16	x	x	X
ejpam-4850	290	17	)	)	PUNCT
ejpam-4850	290	18	∣∣∣q	∣∣∣q	NUM
ejpam-4850	291	1	+	+	CCONJ
ejpam-4850	291	2	(	(	PUNCT
ejpam-4850	291	3	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	291	4	)	)	PUNCT
ejpam-4850	291	5	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	291	6	)	)	PUNCT
ejpam-4850	291	7	−	−	PROPN
ejpam-4850	291	8	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	291	9	)	)	PUNCT
ejpam-4850	291	10	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	291	11	)	)	PUNCT
ejpam-4850	291	12	)	)	PUNCT
ejpam-4850	292	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	292	2	(	(	PUNCT
ejpam-4850	292	3	γ	γ	PROPN
ejpam-4850	292	4	)	)	PUNCT
ejpam-4850	292	5	(	(	PUNCT
ejpam-4850	292	6	a+b	a+b	NUM
ejpam-4850	292	7	2	2	NUM
ejpam-4850	292	8	)	)	PUNCT
ejpam-4850	292	9	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	292	10	q	q	PROPN
ejpam-4850	293	1	+	+	CCONJ
ejpam-4850	293	2	(	(	PUNCT
ejpam-4850	293	3	(	(	PUNCT
ejpam-4850	293	4	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	293	5	)	)	PUNCT
ejpam-4850	293	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	293	7	)	)	PUNCT
ejpam-4850	293	8	−	−	PROPN
ejpam-4850	293	9	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	293	10	)	)	PUNCT
ejpam-4850	293	11	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	293	12	)	)	PUNCT
ejpam-4850	293	13	)	)	PUNCT
ejpam-4850	294	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	294	2	(	(	PUNCT
ejpam-4850	294	3	γ	γ	PROPN
ejpam-4850	294	4	)	)	PUNCT
ejpam-4850	294	5	(	(	PUNCT
ejpam-4850	294	6	a+b	a+b	NUM
ejpam-4850	294	7	2	2	NUM
ejpam-4850	294	8	)	)	PUNCT
ejpam-4850	294	9	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	295	1	+	+	CCONJ
ejpam-4850	295	2	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	295	3	)	)	PUNCT
ejpam-4850	295	4	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	295	5	)	)	PUNCT
ejpam-4850	295	6	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	295	7	(	(	PUNCT
ejpam-4850	295	8	γ	γ	PROPN
ejpam-4850	295	9	)	)	PUNCT
ejpam-4850	295	10	(	(	PUNCT
ejpam-4850	295	11	a+	a+	PUNCT
ejpam-4850	295	12	b−	b−	PROPN
ejpam-4850	295	13	x	x	SYM
ejpam-4850	295	14	)	)	PUNCT
ejpam-4850	295	15	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	295	16	q	q	PROPN
ejpam-4850	295	17	)	)	PUNCT
ejpam-4850	295	18	)	)	PUNCT
ejpam-4850	295	19	.	.	PUNCT
ejpam-4850	296	1	proof	proof	NOUN
ejpam-4850	296	2	.	.	PUNCT
ejpam-4850	297	1	using	use	VERB
ejpam-4850	297	2	lemma	lemma	PROPN
ejpam-4850	297	3	4	4	NUM
ejpam-4850	297	4	as	as	ADV
ejpam-4850	297	5	well	well	ADV
ejpam-4850	297	6	as	as	ADP
ejpam-4850	297	7	the	the	DET
ejpam-4850	297	8	generalized	generalized	ADJ
ejpam-4850	297	9	power	power	NOUN
ejpam-4850	297	10	mean	mean	NOUN
ejpam-4850	297	11	inequality	inequality	NOUN
ejpam-4850	297	12	,	,	PUNCT
ejpam-4850	297	13	properties	property	NOUN
ejpam-4850	297	14	of	of	ADP
ejpam-4850	297	15	modulus	modulus	NOUN
ejpam-4850	297	16	,	,	PUNCT
ejpam-4850	297	17	and	and	CCONJ
ejpam-4850	297	18	the	the	DET
ejpam-4850	297	19	generalized	generalized	ADJ
ejpam-4850	297	20	s	s	NOUN
ejpam-4850	297	21	-	-	NOUN
ejpam-4850	297	22	convexity	convexity	NOUN
ejpam-4850	297	23	of	of	ADP
ejpam-4850	297	24	∣∣j	∣∣j	NOUN
ejpam-4850	297	25	(	(	PUNCT
ejpam-4850	297	26	γ	γ	NOUN
ejpam-4850	297	27	)	)	PUNCT
ejpam-4850	297	28	∣∣q	∣∣q	NUM
ejpam-4850	297	29	,	,	PUNCT
ejpam-4850	297	30	we	we	PRON
ejpam-4850	297	31	can	can	AUX
ejpam-4850	297	32	conclude	conclude	VERB
ejpam-4850	297	33	that∣∣∣j	that∣∣∣j	NOUN
ejpam-4850	297	34	(	(	PUNCT
ejpam-4850	297	35	x)+j	x)+j	PROPN
ejpam-4850	297	36	(	(	PUNCT
ejpam-4850	297	37	a+b−x	a+b−x	PROPN
ejpam-4850	297	38	)	)	PUNCT
ejpam-4850	297	39	2γ	2γ	NOUN
ejpam-4850	297	40	−	−	PROPN
ejpam-4850	297	41	γ(γ+1	γ(γ+1	NUM
ejpam-4850	297	42	)	)	PUNCT
ejpam-4850	297	43	(	(	PUNCT
ejpam-4850	297	44	b−a)γ	b−a)γ	NOUN
ejpam-4850	297	45	ai	ai	VERB
ejpam-4850	297	46	γ	γ	PROPN
ejpam-4850	297	47	b	b	PROPN
ejpam-4850	297	48	j	j	PROPN
ejpam-4850	297	49	(	(	PUNCT
ejpam-4850	297	50	t	t	PROPN
ejpam-4850	297	51	)	)	PUNCT
ejpam-4850	297	52	∣∣∣	∣∣∣	NOUN
ejpam-4850	297	53	≤	≤	NUM
ejpam-4850	297	54	(	(	PUNCT
ejpam-4850	297	55	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	297	56	(	(	PUNCT
ejpam-4850	297	57	b−a)γ	b−a)γ	PROPN
ejpam-4850	298	1			PROPN
ejpam-4850	298	2			PROPN
ejpam-4850	298	3	1	1	NUM
ejpam-4850	298	4	γ(γ+1	γ(γ+1	NUM
ejpam-4850	298	5	)	)	PUNCT
ejpam-4850	299	1	1∫	1∫	NUM
ejpam-4850	299	2	0	0	NUM
ejpam-4850	299	3	ηγ	ηγ	INTJ
ejpam-4850	299	4	(	(	PUNCT
ejpam-4850	299	5	dη)γ	dη)γ	PROPN
ejpam-4850	299	6	1−1	1−1	PROPN
ejpam-4850	299	7	q	q	PUNCT
ejpam-4850	299	8			PROPN
ejpam-4850	299	9	1	1	NUM
ejpam-4850	299	10	γ(γ+1	γ(γ+1	NUM
ejpam-4850	299	11	)	)	PUNCT
ejpam-4850	300	1	1∫	1∫	NUM
ejpam-4850	300	2	0	0	NUM
ejpam-4850	300	3	ηγ	ηγ	PROPN
ejpam-4850	300	4	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	300	5	(	(	PUNCT
ejpam-4850	300	6	γ	γ	PROPN
ejpam-4850	300	7	)	)	PUNCT
ejpam-4850	300	8	(	(	PUNCT
ejpam-4850	300	9	(	(	PUNCT
ejpam-4850	300	10	1−	1−	NUM
ejpam-4850	300	11	η	η	NOUN
ejpam-4850	300	12	)	)	PUNCT
ejpam-4850	300	13	a+	a+	PUNCT
ejpam-4850	300	14	ηx	ηx	PROPN
ejpam-4850	300	15	)	)	PUNCT
ejpam-4850	300	16	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	300	17	(	(	PUNCT
ejpam-4850	300	18	dη)γ	dη)γ	PROPN
ejpam-4850	300	19			PROPN
ejpam-4850	300	20	1	1	NUM
ejpam-4850	300	21	q	q	NOUN
ejpam-4850	300	22	+	+	CCONJ
ejpam-4850	300	23			PROPN
ejpam-4850	300	24	1	1	NUM
ejpam-4850	300	25	γ(γ+1	γ(γ+1	NUM
ejpam-4850	300	26	)	)	PUNCT
ejpam-4850	301	1	1∫	1∫	NUM
ejpam-4850	301	2	0	0	NUM
ejpam-4850	301	3	(	(	PUNCT
ejpam-4850	301	4	1−	1−	NUM
ejpam-4850	301	5	η)γ	η)γ	X
ejpam-4850	301	6	(	(	PUNCT
ejpam-4850	301	7	dη)γ	dη)γ	PROPN
ejpam-4850	301	8	1−1	1−1	PROPN
ejpam-4850	301	9	q	q	NOUN
ejpam-4850	301	10	×	×	NOUN
ejpam-4850	301	11			PROPN
ejpam-4850	301	12	1	1	NUM
ejpam-4850	301	13	γ(γ+1	γ(γ+1	NUM
ejpam-4850	301	14	)	)	PUNCT
ejpam-4850	302	1	1∫	1∫	NUM
ejpam-4850	302	2	0	0	NUM
ejpam-4850	302	3	(	(	PUNCT
ejpam-4850	302	4	1−	1−	NUM
ejpam-4850	302	5	η)γ	η)γ	PROPN
ejpam-4850	302	6	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	302	7	(	(	PUNCT
ejpam-4850	302	8	γ	γ	PROPN
ejpam-4850	302	9	)	)	PUNCT
ejpam-4850	302	10	(	(	PUNCT
ejpam-4850	302	11	(	(	PUNCT
ejpam-4850	302	12	1−	1−	NUM
ejpam-4850	302	13	η	η	NOUN
ejpam-4850	302	14	)	)	PUNCT
ejpam-4850	302	15	(	(	PUNCT
ejpam-4850	302	16	a+	a+	PUNCT
ejpam-4850	302	17	b−	b−	PROPN
ejpam-4850	302	18	x	x	PROPN
ejpam-4850	302	19	)	)	PUNCT
ejpam-4850	302	20	+	+	CCONJ
ejpam-4850	302	21	ηb	ηb	X
ejpam-4850	302	22	)	)	PUNCT
ejpam-4850	302	23	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	302	24	(	(	PUNCT
ejpam-4850	302	25	dη)γ	dη)γ	PROPN
ejpam-4850	302	26			PROPN
ejpam-4850	302	27	1	1	NUM
ejpam-4850	302	28	q	q	NOUN
ejpam-4850	302	29			NOUN
ejpam-4850	302	30	+	+	CCONJ
ejpam-4850	302	31	(	(	PUNCT
ejpam-4850	302	32	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	302	33	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	302	34			PROPN
ejpam-4850	302	35			PROPN
ejpam-4850	302	36	1	1	NUM
ejpam-4850	302	37	γ(γ+1	γ(γ+1	NUM
ejpam-4850	302	38	)	)	PUNCT
ejpam-4850	303	1	1∫	1∫	NUM
ejpam-4850	303	2	0	0	NUM
ejpam-4850	303	3	(	(	PUNCT
ejpam-4850	303	4	1−	1−	NUM
ejpam-4850	303	5	η)γ	η)γ	X
ejpam-4850	303	6	(	(	PUNCT
ejpam-4850	303	7	dη)γ	dη)γ	PROPN
ejpam-4850	303	8	1−1	1−1	PROPN
ejpam-4850	303	9	q	q	NOUN
ejpam-4850	303	10	×	×	NOUN
ejpam-4850	303	11			PROPN
ejpam-4850	303	12	1	1	NUM
ejpam-4850	303	13	γ(γ+1	γ(γ+1	NUM
ejpam-4850	303	14	)	)	PUNCT
ejpam-4850	304	1	1∫	1∫	NUM
ejpam-4850	304	2	0	0	NUM
ejpam-4850	304	3	(	(	PUNCT
ejpam-4850	304	4	1−	1−	NUM
ejpam-4850	304	5	η)γ	η)γ	PROPN
ejpam-4850	304	6	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	304	7	(	(	PUNCT
ejpam-4850	304	8	γ	γ	PROPN
ejpam-4850	304	9	)	)	PUNCT
ejpam-4850	304	10	(	(	PUNCT
ejpam-4850	304	11	(	(	PUNCT
ejpam-4850	304	12	1−	1−	NUM
ejpam-4850	304	13	η)x+	η)x+	NUM
ejpam-4850	304	14	η	η	PROPN
ejpam-4850	304	15	a+b	a+b	NUM
ejpam-4850	304	16	2	2	NUM
ejpam-4850	304	17	)	)	PUNCT
ejpam-4850	304	18	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	304	19	(	(	PUNCT
ejpam-4850	304	20	dη)γ	dη)γ	PROPN
ejpam-4850	304	21			PROPN
ejpam-4850	304	22	1	1	NUM
ejpam-4850	304	23	q	q	NOUN
ejpam-4850	305	1	+	+	CCONJ
ejpam-4850	305	2			PROPN
ejpam-4850	305	3	1	1	NUM
ejpam-4850	305	4	γ(γ+1	γ(γ+1	NUM
ejpam-4850	305	5	)	)	PUNCT
ejpam-4850	306	1	1∫	1∫	NUM
ejpam-4850	306	2	0	0	NUM
ejpam-4850	306	3	ηγ	ηγ	INTJ
ejpam-4850	306	4	(	(	PUNCT
ejpam-4850	306	5	dη)γ	dη)γ	PROPN
ejpam-4850	306	6	1−1	1−1	PROPN
ejpam-4850	306	7	q	q	PUNCT
ejpam-4850	306	8			PROPN
ejpam-4850	306	9	1	1	NUM
ejpam-4850	306	10	γ(γ+1	γ(γ+1	NUM
ejpam-4850	306	11	)	)	PUNCT
ejpam-4850	307	1	1∫	1∫	NUM
ejpam-4850	307	2	0	0	NUM
ejpam-4850	307	3	ηγ	ηγ	PROPN
ejpam-4850	307	4	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	307	5	(	(	PUNCT
ejpam-4850	307	6	γ	γ	PROPN
ejpam-4850	307	7	)	)	PUNCT
ejpam-4850	307	8	(	(	PUNCT
ejpam-4850	307	9	(	(	PUNCT
ejpam-4850	307	10	1−	1−	NUM
ejpam-4850	307	11	η	η	NOUN
ejpam-4850	307	12	)	)	PUNCT
ejpam-4850	307	13	a+b	a+b	NUM
ejpam-4850	307	14	2	2	NUM
ejpam-4850	307	15	+	+	SYM
ejpam-4850	307	16	η	η	PROPN
ejpam-4850	307	17	(	(	PUNCT
ejpam-4850	307	18	a+	a+	PUNCT
ejpam-4850	307	19	b−	b−	PROPN
ejpam-4850	307	20	x	x	PROPN
ejpam-4850	307	21	)	)	PUNCT
ejpam-4850	307	22	)	)	PUNCT
ejpam-4850	307	23	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	307	24	(	(	PUNCT
ejpam-4850	307	25	dη)γ	dη)γ	PROPN
ejpam-4850	307	26			PROPN
ejpam-4850	307	27	1	1	NUM
ejpam-4850	307	28	q	q	NOUN
ejpam-4850	307	29			NOUN
ejpam-4850	307	30	w.	w.	PROPN
ejpam-4850	307	31	saleh	saleh	PROPN
ejpam-4850	307	32	et	et	PROPN
ejpam-4850	307	33	al	al	PROPN
ejpam-4850	307	34	.	.	PUNCT
ejpam-4850	307	35	/	/	SYM
ejpam-4850	307	36	eur	eur	PROPN
ejpam-4850	307	37	.	.	PUNCT
ejpam-4850	308	1	j.	j.	PROPN
ejpam-4850	308	2	pure	pure	PROPN
ejpam-4850	308	3	appl	appl	PROPN
ejpam-4850	308	4	.	.	PROPN
ejpam-4850	308	5	math	math	PROPN
ejpam-4850	308	6	,	,	PUNCT
ejpam-4850	308	7	16	16	NUM
ejpam-4850	308	8	(	(	PUNCT
ejpam-4850	308	9	3	3	NUM
ejpam-4850	308	10	)	)	PUNCT
ejpam-4850	308	11	(	(	PUNCT
ejpam-4850	308	12	2023	2023	NUM
ejpam-4850	308	13	)	)	PUNCT
ejpam-4850	308	14	,	,	PUNCT
ejpam-4850	308	15	1359	1359	NUM
ejpam-4850	308	16	-	-	SYM
ejpam-4850	308	17	1380	1380	NUM
ejpam-4850	308	18	1372	1372	NUM
ejpam-4850	308	19	≤	≤	NOUN
ejpam-4850	308	20	(	(	PUNCT
ejpam-4850	308	21	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	308	22	)	)	PUNCT
ejpam-4850	309	1	γ(1	γ(1	PROPN
ejpam-4850	309	2	+	+	NOUN
ejpam-4850	309	3	2γ	2γ	NOUN
ejpam-4850	309	4	)	)	PUNCT
ejpam-4850	309	5	)	)	PUNCT
ejpam-4850	310	1	1−1	1−1	NUM
ejpam-4850	310	2	q	q	NOUN
ejpam-4850	310	3			PROPN
ejpam-4850	310	4	(	(	PUNCT
ejpam-4850	310	5	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	310	6	(	(	PUNCT
ejpam-4850	310	7	b−a)γ	b−a)γ	PROPN
ejpam-4850	310	8			PROPN
ejpam-4850	310	9			PROPN
ejpam-4850	310	10	1	1	NUM
ejpam-4850	310	11	γ(γ+1	γ(γ+1	NUM
ejpam-4850	310	12	)	)	PUNCT
ejpam-4850	311	1	1∫	1∫	NUM
ejpam-4850	311	2	0	0	NUM
ejpam-4850	311	3	ηγ	ηγ	INTJ
ejpam-4850	311	4	(	(	PUNCT
ejpam-4850	311	5	(	(	PUNCT
ejpam-4850	311	6	1−	1−	NUM
ejpam-4850	311	7	η)sγ	η)sγ	PROPN
ejpam-4850	311	8	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	311	9	(	(	PUNCT
ejpam-4850	311	10	γ	γ	PROPN
ejpam-4850	311	11	)	)	PUNCT
ejpam-4850	311	12	(	(	PUNCT
ejpam-4850	311	13	a	a	X
ejpam-4850	311	14	)	)	PUNCT
ejpam-4850	311	15	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	312	1	+	+	NUM
ejpam-4850	312	2	ηsγ	ηsγ	PROPN
ejpam-4850	312	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	312	4	(	(	PUNCT
ejpam-4850	312	5	γ	γ	PROPN
ejpam-4850	312	6	)	)	PUNCT
ejpam-4850	312	7	(	(	PUNCT
ejpam-4850	312	8	x	x	X
ejpam-4850	312	9	)	)	PUNCT
ejpam-4850	312	10	∣∣∣q	∣∣∣q	NUM
ejpam-4850	312	11	)	)	PUNCT
ejpam-4850	312	12	(	(	PUNCT
ejpam-4850	312	13	dη)γ	dη)γ	PROPN
ejpam-4850	312	14			PROPN
ejpam-4850	312	15	1	1	NUM
ejpam-4850	312	16	q	q	NOUN
ejpam-4850	313	1	+	+	CCONJ
ejpam-4850	313	2			PROPN
ejpam-4850	313	3	1	1	NUM
ejpam-4850	313	4	γ(γ+1	γ(γ+1	NUM
ejpam-4850	313	5	)	)	PUNCT
ejpam-4850	314	1	1∫	1∫	NUM
ejpam-4850	314	2	0	0	NUM
ejpam-4850	314	3	(	(	PUNCT
ejpam-4850	314	4	1−	1−	NUM
ejpam-4850	314	5	η)γ	η)γ	NUM
ejpam-4850	314	6	(	(	PUNCT
ejpam-4850	314	7	(	(	PUNCT
ejpam-4850	314	8	1−	1−	NUM
ejpam-4850	314	9	η)sγ	η)sγ	PROPN
ejpam-4850	314	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	314	11	(	(	PUNCT
ejpam-4850	314	12	γ	γ	PROPN
ejpam-4850	314	13	)	)	PUNCT
ejpam-4850	314	14	(	(	PUNCT
ejpam-4850	314	15	a+	a+	PUNCT
ejpam-4850	314	16	b−	b−	PROPN
ejpam-4850	314	17	x	x	SYM
ejpam-4850	314	18	)	)	PUNCT
ejpam-4850	314	19	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	315	1	+	+	NUM
ejpam-4850	315	2	ηsγ	ηsγ	PROPN
ejpam-4850	315	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	315	4	(	(	PUNCT
ejpam-4850	315	5	γ	γ	PROPN
ejpam-4850	315	6	)	)	PUNCT
ejpam-4850	315	7	(	(	PUNCT
ejpam-4850	315	8	b	b	X
ejpam-4850	315	9	)	)	PUNCT
ejpam-4850	315	10	∣∣∣q	∣∣∣q	NUM
ejpam-4850	315	11	)	)	PUNCT
ejpam-4850	315	12	(	(	PUNCT
ejpam-4850	315	13	dη)γ	dη)γ	PROPN
ejpam-4850	315	14			PROPN
ejpam-4850	315	15	1	1	NUM
ejpam-4850	315	16	q	q	NOUN
ejpam-4850	315	17			NOUN
ejpam-4850	315	18	+	+	CCONJ
ejpam-4850	315	19	(	(	PUNCT
ejpam-4850	315	20	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	315	21	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	315	22			PROPN
ejpam-4850	315	23			PROPN
ejpam-4850	315	24	1	1	NUM
ejpam-4850	315	25	γ(γ+1	γ(γ+1	NUM
ejpam-4850	315	26	)	)	PUNCT
ejpam-4850	316	1	1∫	1∫	NUM
ejpam-4850	316	2	0	0	NUM
ejpam-4850	316	3	(	(	PUNCT
ejpam-4850	316	4	1−	1−	NUM
ejpam-4850	316	5	η)γ	η)γ	NUM
ejpam-4850	316	6	(	(	PUNCT
ejpam-4850	316	7	(	(	PUNCT
ejpam-4850	316	8	1−	1−	NUM
ejpam-4850	316	9	η)sγ	η)sγ	PROPN
ejpam-4850	316	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	316	11	(	(	PUNCT
ejpam-4850	316	12	γ	γ	PROPN
ejpam-4850	316	13	)	)	PUNCT
ejpam-4850	316	14	(	(	PUNCT
ejpam-4850	316	15	x	x	X
ejpam-4850	316	16	)	)	PUNCT
ejpam-4850	316	17	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	316	18	+	+	NUM
ejpam-4850	316	19	ηsγ	ηsγ	PROPN
ejpam-4850	316	20	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	316	21	(	(	PUNCT
ejpam-4850	316	22	γ	γ	PROPN
ejpam-4850	316	23	)	)	PUNCT
ejpam-4850	316	24	(	(	PUNCT
ejpam-4850	316	25	a+b	a+b	NUM
ejpam-4850	316	26	2	2	NUM
ejpam-4850	316	27	)	)	PUNCT
ejpam-4850	316	28	∣∣∣q	∣∣∣q	NUM
ejpam-4850	316	29	)	)	PUNCT
ejpam-4850	316	30	(	(	PUNCT
ejpam-4850	316	31	dη)γ	dη)γ	PROPN
ejpam-4850	316	32			PROPN
ejpam-4850	316	33	1	1	NUM
ejpam-4850	316	34	q	q	NOUN
ejpam-4850	317	1	+	+	CCONJ
ejpam-4850	317	2			PROPN
ejpam-4850	317	3	1	1	NUM
ejpam-4850	317	4	γ(γ+1	γ(γ+1	NUM
ejpam-4850	317	5	)	)	PUNCT
ejpam-4850	318	1	1∫	1∫	NUM
ejpam-4850	318	2	0	0	NUM
ejpam-4850	318	3	ηγ	ηγ	INTJ
ejpam-4850	318	4	(	(	PUNCT
ejpam-4850	318	5	(	(	PUNCT
ejpam-4850	318	6	1−	1−	NUM
ejpam-4850	318	7	η)sγ	η)sγ	PROPN
ejpam-4850	318	8	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	318	9	(	(	PUNCT
ejpam-4850	318	10	γ	γ	PROPN
ejpam-4850	318	11	)	)	PUNCT
ejpam-4850	318	12	(	(	PUNCT
ejpam-4850	318	13	a+b	a+b	NUM
ejpam-4850	318	14	2	2	NUM
ejpam-4850	318	15	)	)	PUNCT
ejpam-4850	318	16	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	319	1	+	+	NUM
ejpam-4850	319	2	ηsγ	ηsγ	PROPN
ejpam-4850	319	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	319	4	(	(	PUNCT
ejpam-4850	319	5	γ	γ	PROPN
ejpam-4850	319	6	)	)	PUNCT
ejpam-4850	319	7	(	(	PUNCT
ejpam-4850	319	8	a+	a+	PUNCT
ejpam-4850	319	9	b−	b−	PROPN
ejpam-4850	319	10	x	x	SYM
ejpam-4850	319	11	)	)	PUNCT
ejpam-4850	319	12	∣∣∣q	∣∣∣q	NUM
ejpam-4850	319	13	)	)	PUNCT
ejpam-4850	319	14	(	(	PUNCT
ejpam-4850	319	15	dη)γ	dη)γ	PROPN
ejpam-4850	319	16			PROPN
ejpam-4850	319	17	1	1	NUM
ejpam-4850	319	18	q	q	NOUN
ejpam-4850	319	19			NOUN
ejpam-4850	319	20			NOUN
ejpam-4850	319	21	=	=	PUNCT
ejpam-4850	319	22	(	(	PUNCT
ejpam-4850	319	23	γ(1+γ	γ(1+γ	PROPN
ejpam-4850	319	24	)	)	PUNCT
ejpam-4850	320	1	γ(1	γ(1	PROPN
ejpam-4850	320	2	+	+	NOUN
ejpam-4850	320	3	2γ	2γ	NOUN
ejpam-4850	320	4	)	)	PUNCT
ejpam-4850	320	5	)	)	PUNCT
ejpam-4850	321	1	1−1	1−1	NUM
ejpam-4850	321	2	q	q	NOUN
ejpam-4850	321	3	×	×	NOUN
ejpam-4850	321	4	(	(	PUNCT
ejpam-4850	321	5	(	(	PUNCT
ejpam-4850	321	6	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	321	7	(	(	PUNCT
ejpam-4850	321	8	b−a)γ	b−a)γ	PROPN
ejpam-4850	321	9	(	(	PUNCT
ejpam-4850	321	10	(	(	PUNCT
ejpam-4850	321	11	(	(	PUNCT
ejpam-4850	321	12	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	321	13	)	)	PUNCT
ejpam-4850	321	14	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	321	15	)	)	PUNCT
ejpam-4850	321	16	−	−	PROPN
ejpam-4850	321	17	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	321	18	)	)	PUNCT
ejpam-4850	321	19	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	321	20	)	)	PUNCT
ejpam-4850	321	21	)	)	PUNCT
ejpam-4850	321	22	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	321	23	(	(	PUNCT
ejpam-4850	321	24	γ	γ	PROPN
ejpam-4850	321	25	)	)	PUNCT
ejpam-4850	321	26	(	(	PUNCT
ejpam-4850	321	27	a	a	X
ejpam-4850	321	28	)	)	PUNCT
ejpam-4850	321	29	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	321	30	+	+	CCONJ
ejpam-4850	321	31	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	321	32	)	)	PUNCT
ejpam-4850	321	33	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	321	34	)	)	PUNCT
ejpam-4850	321	35	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	321	36	(	(	PUNCT
ejpam-4850	321	37	γ	γ	PROPN
ejpam-4850	321	38	)	)	PUNCT
ejpam-4850	321	39	(	(	PUNCT
ejpam-4850	321	40	x	x	X
ejpam-4850	321	41	)	)	PUNCT
ejpam-4850	321	42	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	321	43	q	q	PROPN
ejpam-4850	322	1	+	+	CCONJ
ejpam-4850	322	2	(	(	PUNCT
ejpam-4850	322	3	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	322	4	)	)	PUNCT
ejpam-4850	322	5	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	322	6	)	)	PUNCT
ejpam-4850	322	7	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	322	8	(	(	PUNCT
ejpam-4850	322	9	γ	γ	PROPN
ejpam-4850	322	10	)	)	PUNCT
ejpam-4850	322	11	(	(	PUNCT
ejpam-4850	322	12	a+	a+	PUNCT
ejpam-4850	322	13	b−	b−	PROPN
ejpam-4850	322	14	x	x	SYM
ejpam-4850	322	15	)	)	PUNCT
ejpam-4850	322	16	∣∣∣q	∣∣∣q	NUM
ejpam-4850	323	1	+	+	CCONJ
ejpam-4850	323	2	(	(	PUNCT
ejpam-4850	323	3	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	323	4	)	)	PUNCT
ejpam-4850	323	5	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	323	6	)	)	PUNCT
ejpam-4850	323	7	−	−	PROPN
ejpam-4850	323	8	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	323	9	)	)	PUNCT
ejpam-4850	323	10	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	323	11	)	)	PUNCT
ejpam-4850	323	12	)	)	PUNCT
ejpam-4850	324	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	324	2	(	(	PUNCT
ejpam-4850	324	3	γ	γ	PROPN
ejpam-4850	324	4	)	)	PUNCT
ejpam-4850	324	5	(	(	PUNCT
ejpam-4850	324	6	b	b	X
ejpam-4850	324	7	)	)	PUNCT
ejpam-4850	324	8	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	324	9	q	q	PROPN
ejpam-4850	324	10	)	)	PUNCT
ejpam-4850	325	1	+	+	CCONJ
ejpam-4850	325	2	(	(	PUNCT
ejpam-4850	325	3	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	325	4	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	325	5	(	(	PUNCT
ejpam-4850	325	6	(	(	PUNCT
ejpam-4850	325	7	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	325	8	)	)	PUNCT
ejpam-4850	325	9	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	325	10	)	)	PUNCT
ejpam-4850	325	11	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	325	12	(	(	PUNCT
ejpam-4850	325	13	γ	γ	PROPN
ejpam-4850	325	14	)	)	PUNCT
ejpam-4850	325	15	(	(	PUNCT
ejpam-4850	325	16	x	x	X
ejpam-4850	325	17	)	)	PUNCT
ejpam-4850	325	18	∣∣∣q	∣∣∣q	NUM
ejpam-4850	326	1	+	+	CCONJ
ejpam-4850	326	2	(	(	PUNCT
ejpam-4850	326	3	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	326	4	)	)	PUNCT
ejpam-4850	326	5	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	326	6	)	)	PUNCT
ejpam-4850	326	7	−	−	PROPN
ejpam-4850	326	8	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	326	9	)	)	PUNCT
ejpam-4850	326	10	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	326	11	)	)	PUNCT
ejpam-4850	326	12	)	)	PUNCT
ejpam-4850	327	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	327	2	(	(	PUNCT
ejpam-4850	327	3	γ	γ	PROPN
ejpam-4850	327	4	)	)	PUNCT
ejpam-4850	327	5	(	(	PUNCT
ejpam-4850	327	6	a+b	a+b	NUM
ejpam-4850	327	7	2	2	NUM
ejpam-4850	327	8	)	)	PUNCT
ejpam-4850	327	9	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	327	10	q	q	PROPN
ejpam-4850	328	1	+	+	CCONJ
ejpam-4850	328	2	(	(	PUNCT
ejpam-4850	328	3	(	(	PUNCT
ejpam-4850	328	4	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	328	5	)	)	PUNCT
ejpam-4850	328	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	328	7	)	)	PUNCT
ejpam-4850	328	8	−	−	PROPN
ejpam-4850	328	9	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	328	10	)	)	PUNCT
ejpam-4850	328	11	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	328	12	)	)	PUNCT
ejpam-4850	328	13	)	)	PUNCT
ejpam-4850	329	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	329	2	(	(	PUNCT
ejpam-4850	329	3	γ	γ	PROPN
ejpam-4850	329	4	)	)	PUNCT
ejpam-4850	329	5	(	(	PUNCT
ejpam-4850	329	6	a+b	a+b	NUM
ejpam-4850	329	7	2	2	NUM
ejpam-4850	329	8	)	)	PUNCT
ejpam-4850	329	9	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	330	1	+	+	CCONJ
ejpam-4850	330	2	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	330	3	)	)	PUNCT
ejpam-4850	330	4	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	330	5	)	)	PUNCT
ejpam-4850	330	6	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	330	7	(	(	PUNCT
ejpam-4850	330	8	γ	γ	PROPN
ejpam-4850	330	9	)	)	PUNCT
ejpam-4850	330	10	(	(	PUNCT
ejpam-4850	330	11	a+	a+	PUNCT
ejpam-4850	330	12	b−	b−	PROPN
ejpam-4850	330	13	x	x	SYM
ejpam-4850	330	14	)	)	PUNCT
ejpam-4850	330	15	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	330	16	q	q	PROPN
ejpam-4850	330	17	)	)	PUNCT
ejpam-4850	330	18	)	)	PUNCT
ejpam-4850	330	19	,	,	PUNCT
ejpam-4850	330	20	where	where	SCONJ
ejpam-4850	330	21	we	we	PRON
ejpam-4850	330	22	have	have	AUX
ejpam-4850	330	23	used	use	VERB
ejpam-4850	330	24	(	(	PUNCT
ejpam-4850	330	25	11	11	NUM
ejpam-4850	330	26	)	)	PUNCT
ejpam-4850	330	27	and	and	CCONJ
ejpam-4850	330	28	(	(	PUNCT
ejpam-4850	330	29	12	12	NUM
ejpam-4850	330	30	)	)	PUNCT
ejpam-4850	330	31	.	.	PUNCT
ejpam-4850	331	1	the	the	DET
ejpam-4850	331	2	proof	proof	NOUN
ejpam-4850	331	3	is	be	AUX
ejpam-4850	331	4	completed	complete	VERB
ejpam-4850	331	5	.	.	PUNCT
ejpam-4850	332	1	corollary	corollary	ADJ
ejpam-4850	332	2	12	12	NUM
ejpam-4850	332	3	.	.	PUNCT
ejpam-4850	333	1	in	in	ADP
ejpam-4850	333	2	theorem	theorem	NOUN
ejpam-4850	333	3	3	3	NUM
ejpam-4850	333	4	,	,	PUNCT
ejpam-4850	333	5	taking	take	VERB
ejpam-4850	333	6	x	x	X
ejpam-4850	333	7	=	=	PUNCT
ejpam-4850	333	8	a	a	PRON
ejpam-4850	333	9	,	,	PUNCT
ejpam-4850	333	10	we	we	PRON
ejpam-4850	333	11	obtain∣∣∣j	obtain∣∣∣j	VERB
ejpam-4850	333	12	(	(	PUNCT
ejpam-4850	333	13	a)+j	a)+j	PROPN
ejpam-4850	333	14	(	(	PUNCT
ejpam-4850	333	15	b	b	NOUN
ejpam-4850	333	16	)	)	PUNCT
ejpam-4850	333	17	2γ	2γ	NOUN
ejpam-4850	333	18	−	−	PROPN
ejpam-4850	333	19	γ(γ+1	γ(γ+1	NUM
ejpam-4850	333	20	)	)	PUNCT
ejpam-4850	333	21	(	(	PUNCT
ejpam-4850	333	22	b−a)γ	b−a)γ	NOUN
ejpam-4850	333	23	ai	ai	VERB
ejpam-4850	333	24	γ	γ	PROPN
ejpam-4850	333	25	b	b	PROPN
ejpam-4850	333	26	j	j	PROPN
ejpam-4850	333	27	(	(	PUNCT
ejpam-4850	333	28	t	t	PROPN
ejpam-4850	333	29	)	)	PUNCT
ejpam-4850	333	30	∣∣∣	∣∣∣	NOUN
ejpam-4850	333	31	≤	≤	NOUN
ejpam-4850	333	32	(	(	PUNCT
ejpam-4850	333	33	b−a)γ	b−a)γ	NOUN
ejpam-4850	333	34	4γ	4γ	NOUN
ejpam-4850	333	35	(	(	PUNCT
ejpam-4850	333	36	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	333	37	)	)	PUNCT
ejpam-4850	334	1	γ(1	γ(1	ADP
ejpam-4850	334	2	+	+	NOUN
ejpam-4850	334	3	2γ	2γ	NOUN
ejpam-4850	334	4	)	)	PUNCT
ejpam-4850	334	5	)	)	PUNCT
ejpam-4850	335	1	1−1	1−1	NUM
ejpam-4850	335	2	q	q	NOUN
ejpam-4850	335	3	×	×	NOUN
ejpam-4850	335	4	(	(	PUNCT
ejpam-4850	335	5	(	(	PUNCT
ejpam-4850	335	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	335	7	)	)	PUNCT
ejpam-4850	335	8	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	335	9	)	)	PUNCT
ejpam-4850	335	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	335	11	(	(	PUNCT
ejpam-4850	335	12	γ	γ	PROPN
ejpam-4850	335	13	)	)	PUNCT
ejpam-4850	335	14	(	(	PUNCT
ejpam-4850	335	15	a	a	X
ejpam-4850	335	16	)	)	PUNCT
ejpam-4850	335	17	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	335	18	+	+	CCONJ
ejpam-4850	335	19	(	(	PUNCT
ejpam-4850	335	20	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	335	21	)	)	PUNCT
ejpam-4850	335	22	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	335	23	)	)	PUNCT
ejpam-4850	335	24	−	−	PROPN
ejpam-4850	335	25	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	335	26	)	)	PUNCT
ejpam-4850	335	27	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	335	28	)	)	PUNCT
ejpam-4850	335	29	)	)	PUNCT
ejpam-4850	335	30	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	335	31	(	(	PUNCT
ejpam-4850	335	32	γ	γ	PROPN
ejpam-4850	335	33	)	)	PUNCT
ejpam-4850	335	34	(	(	PUNCT
ejpam-4850	335	35	a+b	a+b	NUM
ejpam-4850	335	36	2	2	NUM
ejpam-4850	335	37	)	)	PUNCT
ejpam-4850	335	38	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	335	39	q	q	PROPN
ejpam-4850	336	1	+	+	CCONJ
ejpam-4850	336	2	(	(	PUNCT
ejpam-4850	336	3	(	(	PUNCT
ejpam-4850	336	4	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	336	5	)	)	PUNCT
ejpam-4850	336	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	336	7	)	)	PUNCT
ejpam-4850	336	8	−	−	PROPN
ejpam-4850	336	9	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	336	10	)	)	PUNCT
ejpam-4850	336	11	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	336	12	)	)	PUNCT
ejpam-4850	336	13	)	)	PUNCT
ejpam-4850	337	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	337	2	(	(	PUNCT
ejpam-4850	337	3	γ	γ	PROPN
ejpam-4850	337	4	)	)	PUNCT
ejpam-4850	337	5	(	(	PUNCT
ejpam-4850	337	6	a+b	a+b	NUM
ejpam-4850	337	7	2	2	NUM
ejpam-4850	337	8	)	)	PUNCT
ejpam-4850	337	9	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	338	1	+	+	CCONJ
ejpam-4850	338	2	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	338	3	)	)	PUNCT
ejpam-4850	338	4	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	338	5	)	)	PUNCT
ejpam-4850	338	6	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	338	7	(	(	PUNCT
ejpam-4850	338	8	γ	γ	PROPN
ejpam-4850	338	9	)	)	PUNCT
ejpam-4850	338	10	(	(	PUNCT
ejpam-4850	338	11	b	b	X
ejpam-4850	338	12	)	)	PUNCT
ejpam-4850	338	13	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	338	14	q	q	PROPN
ejpam-4850	338	15	)	)	PUNCT
ejpam-4850	338	16	.	.	PUNCT
ejpam-4850	339	1	w.	w.	PROPN
ejpam-4850	339	2	saleh	saleh	PROPN
ejpam-4850	339	3	et	et	PROPN
ejpam-4850	339	4	al	al	PROPN
ejpam-4850	339	5	.	.	PUNCT
ejpam-4850	339	6	/	/	SYM
ejpam-4850	339	7	eur	eur	PROPN
ejpam-4850	339	8	.	.	PUNCT
ejpam-4850	340	1	j.	j.	PROPN
ejpam-4850	340	2	pure	pure	PROPN
ejpam-4850	340	3	appl	appl	PROPN
ejpam-4850	340	4	.	.	PROPN
ejpam-4850	340	5	math	math	PROPN
ejpam-4850	340	6	,	,	PUNCT
ejpam-4850	340	7	16	16	NUM
ejpam-4850	340	8	(	(	PUNCT
ejpam-4850	340	9	3	3	NUM
ejpam-4850	340	10	)	)	PUNCT
ejpam-4850	340	11	(	(	PUNCT
ejpam-4850	340	12	2023	2023	NUM
ejpam-4850	340	13	)	)	PUNCT
ejpam-4850	340	14	,	,	PUNCT
ejpam-4850	340	15	1359	1359	NUM
ejpam-4850	340	16	-	-	SYM
ejpam-4850	340	17	1380	1380	NUM
ejpam-4850	340	18	1373	1373	NUM
ejpam-4850	340	19	corollary	corollary	NOUN
ejpam-4850	340	20	13	13	NUM
ejpam-4850	340	21	.	.	PUNCT
ejpam-4850	341	1	in	in	ADP
ejpam-4850	341	2	theorem	theorem	NOUN
ejpam-4850	341	3	3	3	NUM
ejpam-4850	341	4	,	,	PUNCT
ejpam-4850	341	5	taking	take	VERB
ejpam-4850	341	6	x	x	X
ejpam-4850	341	7	=	=	SYM
ejpam-4850	341	8	a+b	a+b	NUM
ejpam-4850	341	9	2	2	NUM
ejpam-4850	341	10	,	,	PUNCT
ejpam-4850	341	11	we	we	PRON
ejpam-4850	341	12	obtain∣∣∣j	obtain∣∣∣j	VERB
ejpam-4850	341	13	(	(	PUNCT
ejpam-4850	341	14	a+b	a+b	NUM
ejpam-4850	341	15	2	2	NUM
ejpam-4850	341	16	)	)	PUNCT
ejpam-4850	341	17	−	−	PROPN
ejpam-4850	341	18	γ(γ+1	γ(γ+1	NUM
ejpam-4850	341	19	)	)	PUNCT
ejpam-4850	341	20	(	(	PUNCT
ejpam-4850	341	21	b−a)γ	b−a)γ	NOUN
ejpam-4850	341	22	ai	ai	VERB
ejpam-4850	341	23	γ	γ	PROPN
ejpam-4850	341	24	b	b	PROPN
ejpam-4850	341	25	j	j	PROPN
ejpam-4850	341	26	(	(	PUNCT
ejpam-4850	341	27	t	t	PROPN
ejpam-4850	341	28	)	)	PUNCT
ejpam-4850	341	29	∣∣∣	∣∣∣	NOUN
ejpam-4850	341	30	≤	≤	NOUN
ejpam-4850	341	31	(	(	PUNCT
ejpam-4850	341	32	b−a)γ	b−a)γ	NOUN
ejpam-4850	341	33	4γ	4γ	NOUN
ejpam-4850	341	34	(	(	PUNCT
ejpam-4850	341	35	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	341	36	)	)	PUNCT
ejpam-4850	342	1	γ(1	γ(1	ADP
ejpam-4850	342	2	+	+	NOUN
ejpam-4850	342	3	2γ	2γ	NOUN
ejpam-4850	342	4	)	)	PUNCT
ejpam-4850	342	5	)	)	PUNCT
ejpam-4850	343	1	1−1	1−1	NUM
ejpam-4850	343	2	q	q	NOUN
ejpam-4850	343	3	×	×	NOUN
ejpam-4850	343	4	(	(	PUNCT
ejpam-4850	343	5	(	(	PUNCT
ejpam-4850	343	6	(	(	PUNCT
ejpam-4850	343	7	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	343	8	)	)	PUNCT
ejpam-4850	343	9	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	343	10	)	)	PUNCT
ejpam-4850	343	11	−	−	PROPN
ejpam-4850	343	12	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	343	13	)	)	PUNCT
ejpam-4850	343	14	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	343	15	)	)	PUNCT
ejpam-4850	343	16	)	)	PUNCT
ejpam-4850	343	17	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	343	18	(	(	PUNCT
ejpam-4850	343	19	γ	γ	PROPN
ejpam-4850	343	20	)	)	PUNCT
ejpam-4850	343	21	(	(	PUNCT
ejpam-4850	343	22	a	a	X
ejpam-4850	343	23	)	)	PUNCT
ejpam-4850	343	24	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	343	25	+	+	CCONJ
ejpam-4850	343	26	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	343	27	)	)	PUNCT
ejpam-4850	343	28	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	343	29	)	)	PUNCT
ejpam-4850	343	30	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	343	31	(	(	PUNCT
ejpam-4850	343	32	γ	γ	PROPN
ejpam-4850	343	33	)	)	PUNCT
ejpam-4850	343	34	(	(	PUNCT
ejpam-4850	343	35	a+b	a+b	NUM
ejpam-4850	343	36	2	2	NUM
ejpam-4850	343	37	)	)	PUNCT
ejpam-4850	343	38	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	343	39	q	q	PROPN
ejpam-4850	344	1	+	+	CCONJ
ejpam-4850	344	2	(	(	PUNCT
ejpam-4850	344	3	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	344	4	)	)	PUNCT
ejpam-4850	344	5	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	344	6	)	)	PUNCT
ejpam-4850	344	7	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	344	8	(	(	PUNCT
ejpam-4850	344	9	γ	γ	PROPN
ejpam-4850	344	10	)	)	PUNCT
ejpam-4850	344	11	(	(	PUNCT
ejpam-4850	344	12	a+b	a+b	NUM
ejpam-4850	344	13	2	2	NUM
ejpam-4850	344	14	)	)	PUNCT
ejpam-4850	344	15	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	345	1	+	+	CCONJ
ejpam-4850	345	2	(	(	PUNCT
ejpam-4850	345	3	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	345	4	)	)	PUNCT
ejpam-4850	345	5	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	345	6	)	)	PUNCT
ejpam-4850	345	7	−	−	PROPN
ejpam-4850	345	8	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	345	9	)	)	PUNCT
ejpam-4850	345	10	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	345	11	)	)	PUNCT
ejpam-4850	345	12	)	)	PUNCT
ejpam-4850	346	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	346	2	(	(	PUNCT
ejpam-4850	346	3	γ	γ	PROPN
ejpam-4850	346	4	)	)	PUNCT
ejpam-4850	346	5	(	(	PUNCT
ejpam-4850	346	6	b	b	X
ejpam-4850	346	7	)	)	PUNCT
ejpam-4850	346	8	∣∣∣q)1	∣∣∣q)1	PROPN
ejpam-4850	346	9	q	q	PROPN
ejpam-4850	346	10	)	)	PUNCT
ejpam-4850	346	11	.	.	PUNCT
ejpam-4850	347	1	theorem	theorem	ADJ
ejpam-4850	347	2	4	4	NUM
ejpam-4850	347	3	.	.	PUNCT
ejpam-4850	347	4	suppose	suppose	VERB
ejpam-4850	348	1	j	j	NOUN
ejpam-4850	348	2	:	:	PUNCT
ejpam-4850	349	1	[	[	X
ejpam-4850	349	2	a	a	X
ejpam-4850	349	3	,	,	PUNCT
ejpam-4850	349	4	b	b	NOUN
ejpam-4850	349	5	]	]	X
ejpam-4850	349	6	→	→	PUNCT
ejpam-4850	349	7	rγ	rγ	PRON
ejpam-4850	349	8	is	be	AUX
ejpam-4850	349	9	a	a	DET
ejpam-4850	349	10	differentiable	differentiable	ADJ
ejpam-4850	349	11	function	function	NOUN
ejpam-4850	349	12	on	on	ADP
ejpam-4850	349	13	[	[	X
ejpam-4850	349	14	a	a	X
ejpam-4850	349	15	,	,	PUNCT
ejpam-4850	349	16	b	b	NOUN
ejpam-4850	349	17	]	]	X
ejpam-4850	349	18	such	such	ADJ
ejpam-4850	349	19	that	that	SCONJ
ejpam-4850	349	20	j	j	PROPN
ejpam-4850	349	21	∈	∈	PROPN
ejpam-4850	349	22	dγ	dγ	ADP
ejpam-4850	349	23	[	[	X
ejpam-4850	349	24	a	a	X
ejpam-4850	349	25	,	,	PUNCT
ejpam-4850	349	26	b	b	NOUN
ejpam-4850	349	27	]	]	X
ejpam-4850	349	28	and	and	CCONJ
ejpam-4850	349	29	j	j	PROPN
ejpam-4850	349	30	(	(	PUNCT
ejpam-4850	349	31	γ	γ	PROPN
ejpam-4850	349	32	)	)	PUNCT
ejpam-4850	349	33	∈	∈	NOUN
ejpam-4850	349	34	cγ	cγ	NOUN
ejpam-4850	349	35	[	[	X
ejpam-4850	349	36	a	a	X
ejpam-4850	349	37	,	,	PUNCT
ejpam-4850	349	38	b	b	NOUN
ejpam-4850	349	39	]	]	X
ejpam-4850	349	40	with	with	ADP
ejpam-4850	349	41	0	0	NUM
ejpam-4850	349	42	≤	≤	NOUN
ejpam-4850	349	43	a	a	DET
ejpam-4850	349	44	<	<	X
ejpam-4850	349	45	b.	b.	NOUN
ejpam-4850	349	46	if	if	SCONJ
ejpam-4850	349	47	∣∣j	∣∣j	X
ejpam-4850	349	48	(	(	PUNCT
ejpam-4850	349	49	γ	γ	NOUN
ejpam-4850	349	50	)	)	PUNCT
ejpam-4850	349	51	∣∣q	∣∣q	NUM
ejpam-4850	349	52	is	be	AUX
ejpam-4850	349	53	generalized	generalize	VERB
ejpam-4850	349	54	s	s	NOUN
ejpam-4850	349	55	-	-	PUNCT
ejpam-4850	349	56	concave	concave	NOUN
ejpam-4850	349	57	on	on	ADP
ejpam-4850	349	58	[	[	X
ejpam-4850	349	59	a	a	X
ejpam-4850	349	60	,	,	PUNCT
ejpam-4850	349	61	b	b	NOUN
ejpam-4850	349	62	]	]	X
ejpam-4850	349	63	,	,	PUNCT
ejpam-4850	349	64	where	where	SCONJ
ejpam-4850	349	65	q	q	PUNCT
ejpam-4850	349	66	>	>	X
ejpam-4850	349	67	1	1	NUM
ejpam-4850	349	68	with	with	ADP
ejpam-4850	349	69	1	1	NUM
ejpam-4850	349	70	p	p	NOUN
ejpam-4850	349	71	+	+	NOUN
ejpam-4850	349	72	1	1	NUM
ejpam-4850	349	73	q	q	NOUN
ejpam-4850	349	74	=	=	SYM
ejpam-4850	349	75	1	1	NUM
ejpam-4850	349	76	,	,	PUNCT
ejpam-4850	349	77	then	then	ADV
ejpam-4850	349	78	we	we	PRON
ejpam-4850	349	79	have∣∣∣j	have∣∣∣j	VERB
ejpam-4850	349	80	(	(	PUNCT
ejpam-4850	349	81	x)+j	x)+j	PROPN
ejpam-4850	349	82	(	(	PUNCT
ejpam-4850	349	83	a+b−x	a+b−x	PROPN
ejpam-4850	349	84	)	)	PUNCT
ejpam-4850	349	85	2γ	2γ	NOUN
ejpam-4850	349	86	−	−	PROPN
ejpam-4850	349	87	γ(γ+1	γ(γ+1	NUM
ejpam-4850	349	88	)	)	PUNCT
ejpam-4850	349	89	(	(	PUNCT
ejpam-4850	349	90	b−a)γ	b−a)γ	NOUN
ejpam-4850	349	91	ai	ai	VERB
ejpam-4850	349	92	γ	γ	PROPN
ejpam-4850	349	93	b	b	PROPN
ejpam-4850	349	94	j	j	PROPN
ejpam-4850	349	95	(	(	PUNCT
ejpam-4850	349	96	t	t	PROPN
ejpam-4850	349	97	)	)	PUNCT
ejpam-4850	349	98	∣∣∣	∣∣∣	NOUN
ejpam-4850	349	99	≤	≤	PROPN
ejpam-4850	349	100	(	(	PUNCT
ejpam-4850	349	101	γ(1+pγ	γ(1+pγ	NUM
ejpam-4850	349	102	)	)	PUNCT
ejpam-4850	349	103	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	349	104	)	)	PUNCT
ejpam-4850	349	105	)	)	PUNCT
ejpam-4850	349	106	1	1	NUM
ejpam-4850	349	107	p	p	NOUN
ejpam-4850	349	108	(	(	PUNCT
ejpam-4850	349	109	(	(	PUNCT
ejpam-4850	349	110	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	349	111	(	(	PUNCT
ejpam-4850	349	112	b−a)γ	b−a)γ	PROPN
ejpam-4850	349	113	(	(	PUNCT
ejpam-4850	349	114	(	(	PUNCT
ejpam-4850	349	115	x−a)γ2(s−1)γ	x−a)γ2(s−1)γ	PROPN
ejpam-4850	349	116	γ(1+γ	γ(1+γ	PROPN
ejpam-4850	349	117	)	)	PUNCT
ejpam-4850	349	118	)	)	PUNCT
ejpam-4850	349	119	1	1	NUM
ejpam-4850	349	120	q	q	NOUN
ejpam-4850	349	121	(	(	PUNCT
ejpam-4850	349	122	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	349	123	(	(	PUNCT
ejpam-4850	349	124	γ	γ	PROPN
ejpam-4850	349	125	)	)	PUNCT
ejpam-4850	349	126	(	(	PUNCT
ejpam-4850	349	127	a+x	a+x	ADP
ejpam-4850	349	128	2	2	NUM
ejpam-4850	349	129	)	)	PUNCT
ejpam-4850	349	130	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	349	131	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	349	132	(	(	PUNCT
ejpam-4850	349	133	γ	γ	PROPN
ejpam-4850	349	134	)	)	PUNCT
ejpam-4850	349	135	(	(	PUNCT
ejpam-4850	349	136	a+2b−x	a+2b−x	ADV
ejpam-4850	349	137	2	2	NUM
ejpam-4850	349	138	)	)	PUNCT
ejpam-4850	349	139	∣∣∣	∣∣∣	NOUN
ejpam-4850	349	140	)	)	PUNCT
ejpam-4850	350	1	+	+	CCONJ
ejpam-4850	350	2	(	(	PUNCT
ejpam-4850	350	3	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	350	4	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	350	5	(	(	PUNCT
ejpam-4850	350	6	(	(	PUNCT
ejpam-4850	350	7	a+b−2x)γ2(s−1)γ	a+b−2x)γ2(s−1)γ	PROPN
ejpam-4850	350	8	2γγ(1+γ	2γγ(1+γ	NUM
ejpam-4850	350	9	)	)	PUNCT
ejpam-4850	350	10	)	)	PUNCT
ejpam-4850	350	11	1	1	NUM
ejpam-4850	350	12	q	q	NOUN
ejpam-4850	350	13	(	(	PUNCT
ejpam-4850	350	14	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	350	15	(	(	PUNCT
ejpam-4850	350	16	γ	γ	PROPN
ejpam-4850	350	17	)	)	PUNCT
ejpam-4850	350	18	(	(	PUNCT
ejpam-4850	350	19	a+b+2x	a+b+2x	X
ejpam-4850	350	20	4	4	NUM
ejpam-4850	350	21	)	)	PUNCT
ejpam-4850	350	22	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	350	23	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	350	24	(	(	PUNCT
ejpam-4850	350	25	γ	γ	PROPN
ejpam-4850	350	26	)	)	PUNCT
ejpam-4850	350	27	(	(	PUNCT
ejpam-4850	350	28	3a+3b−2x	3a+3b−2x	NOUN
ejpam-4850	350	29	4	4	NUM
ejpam-4850	350	30	)	)	PUNCT
ejpam-4850	350	31	∣∣∣	∣∣∣	NOUN
ejpam-4850	350	32	)	)	PUNCT
ejpam-4850	350	33	)	)	PUNCT
ejpam-4850	350	34	.	.	PUNCT
ejpam-4850	351	1	proof	proof	NOUN
ejpam-4850	351	2	.	.	PUNCT
ejpam-4850	352	1	by	by	ADP
ejpam-4850	352	2	utilizing	utilize	VERB
ejpam-4850	352	3	lemma	lemma	PROPN
ejpam-4850	352	4	4	4	NUM
ejpam-4850	352	5	,	,	PUNCT
ejpam-4850	352	6	as	as	ADV
ejpam-4850	352	7	well	well	ADV
ejpam-4850	352	8	as	as	ADP
ejpam-4850	352	9	the	the	DET
ejpam-4850	352	10	generalized	generalized	ADJ
ejpam-4850	352	11	hölder	hölder	NOUN
ejpam-4850	352	12	’s	’s	PART
ejpam-4850	352	13	inequality	inequality	NOUN
ejpam-4850	352	14	,	,	PUNCT
ejpam-4850	352	15	properties	property	NOUN
ejpam-4850	352	16	of	of	ADP
ejpam-4850	352	17	the	the	DET
ejpam-4850	352	18	modulus	modulus	ADJ
ejpam-4850	352	19	function	function	NOUN
ejpam-4850	352	20	,	,	PUNCT
ejpam-4850	352	21	and	and	CCONJ
ejpam-4850	352	22	the	the	DET
ejpam-4850	352	23	generalized	generalize	VERB
ejpam-4850	352	24	s	s	NOUN
ejpam-4850	352	25	-	-	PUNCT
ejpam-4850	352	26	concavity	concavity	NOUN
ejpam-4850	352	27	of	of	ADP
ejpam-4850	352	28	∣∣j	∣∣j	NOUN
ejpam-4850	352	29	(	(	PUNCT
ejpam-4850	352	30	γ	γ	NOUN
ejpam-4850	352	31	)	)	PUNCT
ejpam-4850	352	32	∣∣q	∣∣q	NUM
ejpam-4850	352	33	,	,	PUNCT
ejpam-4850	352	34	we	we	PRON
ejpam-4850	352	35	have∣∣∣j	have∣∣∣j	VERB
ejpam-4850	352	36	(	(	PUNCT
ejpam-4850	352	37	x)+j	x)+j	PROPN
ejpam-4850	352	38	(	(	PUNCT
ejpam-4850	352	39	a+b−x	a+b−x	PROPN
ejpam-4850	352	40	)	)	PUNCT
ejpam-4850	352	41	2γ	2γ	NOUN
ejpam-4850	352	42	−	−	PROPN
ejpam-4850	352	43	γ(γ+1	γ(γ+1	NUM
ejpam-4850	352	44	)	)	PUNCT
ejpam-4850	352	45	(	(	PUNCT
ejpam-4850	352	46	b−a)γ	b−a)γ	NOUN
ejpam-4850	352	47	ai	ai	VERB
ejpam-4850	352	48	γ	γ	PROPN
ejpam-4850	352	49	b	b	PROPN
ejpam-4850	352	50	j	j	PROPN
ejpam-4850	352	51	(	(	PUNCT
ejpam-4850	352	52	t	t	PROPN
ejpam-4850	352	53	)	)	PUNCT
ejpam-4850	352	54	∣∣∣	∣∣∣	NOUN
ejpam-4850	352	55	≤	≤	NUM
ejpam-4850	352	56	(	(	PUNCT
ejpam-4850	352	57	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	352	58	(	(	PUNCT
ejpam-4850	352	59	b−a)γ	b−a)γ	PROPN
ejpam-4850	353	1			PROPN
ejpam-4850	353	2			PROPN
ejpam-4850	353	3	1	1	NUM
ejpam-4850	353	4	γ(γ+1	γ(γ+1	NUM
ejpam-4850	353	5	)	)	PUNCT
ejpam-4850	354	1	1∫	1∫	NUM
ejpam-4850	354	2	0	0	NUM
ejpam-4850	354	3	ηpγ	ηpγ	NOUN
ejpam-4850	354	4	(	(	PUNCT
ejpam-4850	354	5	dη)γ	dη)γ	PROPN
ejpam-4850	354	6			PROPN
ejpam-4850	354	7	1	1	NUM
ejpam-4850	354	8	p	p	NOUN
ejpam-4850	354	9			PROPN
ejpam-4850	354	10	1	1	NUM
ejpam-4850	354	11	γ(γ+1	γ(γ+1	NUM
ejpam-4850	354	12	)	)	PUNCT
ejpam-4850	355	1	1∫	1∫	NUM
ejpam-4850	355	2	0	0	NUM
ejpam-4850	355	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	355	4	(	(	PUNCT
ejpam-4850	355	5	γ	γ	PROPN
ejpam-4850	355	6	)	)	PUNCT
ejpam-4850	355	7	(	(	PUNCT
ejpam-4850	355	8	(	(	PUNCT
ejpam-4850	355	9	1−	1−	NUM
ejpam-4850	355	10	η	η	NOUN
ejpam-4850	355	11	)	)	PUNCT
ejpam-4850	355	12	a+	a+	PUNCT
ejpam-4850	355	13	ηx	ηx	PROPN
ejpam-4850	355	14	)	)	PUNCT
ejpam-4850	355	15	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	355	16	(	(	PUNCT
ejpam-4850	355	17	dη)γ	dη)γ	PROPN
ejpam-4850	355	18			PROPN
ejpam-4850	355	19	1	1	NUM
ejpam-4850	355	20	q	q	NOUN
ejpam-4850	355	21	+	+	CCONJ
ejpam-4850	355	22			PROPN
ejpam-4850	355	23	1	1	NUM
ejpam-4850	355	24	γ(γ+1	γ(γ+1	NUM
ejpam-4850	355	25	)	)	PUNCT
ejpam-4850	356	1	1∫	1∫	NUM
ejpam-4850	356	2	0	0	NUM
ejpam-4850	356	3	(	(	PUNCT
ejpam-4850	356	4	1−	1−	NUM
ejpam-4850	356	5	η)pγ	η)pγ	PROPN
ejpam-4850	356	6	(	(	PUNCT
ejpam-4850	356	7	dη)γ	dη)γ	PROPN
ejpam-4850	356	8			PROPN
ejpam-4850	356	9	1	1	NUM
ejpam-4850	356	10	p	p	NOUN
ejpam-4850	356	11			PROPN
ejpam-4850	356	12	1	1	NUM
ejpam-4850	356	13	γ(γ+1	γ(γ+1	NUM
ejpam-4850	356	14	)	)	PUNCT
ejpam-4850	357	1	1∫	1∫	NUM
ejpam-4850	357	2	0	0	NUM
ejpam-4850	357	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	357	4	(	(	PUNCT
ejpam-4850	357	5	γ	γ	PROPN
ejpam-4850	357	6	)	)	PUNCT
ejpam-4850	357	7	(	(	PUNCT
ejpam-4850	357	8	(	(	PUNCT
ejpam-4850	357	9	1−	1−	NUM
ejpam-4850	357	10	η	η	NOUN
ejpam-4850	357	11	)	)	PUNCT
ejpam-4850	357	12	(	(	PUNCT
ejpam-4850	357	13	a+	a+	PUNCT
ejpam-4850	357	14	b−	b−	PROPN
ejpam-4850	357	15	x	x	PROPN
ejpam-4850	357	16	)	)	PUNCT
ejpam-4850	357	17	+	+	CCONJ
ejpam-4850	357	18	ηb	ηb	X
ejpam-4850	357	19	)	)	PUNCT
ejpam-4850	357	20	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	357	21	(	(	PUNCT
ejpam-4850	357	22	dη)γ	dη)γ	PROPN
ejpam-4850	357	23			PROPN
ejpam-4850	357	24	1	1	NUM
ejpam-4850	357	25	q	q	NOUN
ejpam-4850	357	26			NOUN
ejpam-4850	357	27	+	+	CCONJ
ejpam-4850	357	28	(	(	PUNCT
ejpam-4850	357	29	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	357	30	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	357	31			PROPN
ejpam-4850	357	32			PROPN
ejpam-4850	357	33	1	1	NUM
ejpam-4850	357	34	γ(γ+1	γ(γ+1	NUM
ejpam-4850	357	35	)	)	PUNCT
ejpam-4850	358	1	1∫	1∫	NUM
ejpam-4850	358	2	0	0	NUM
ejpam-4850	358	3	(	(	PUNCT
ejpam-4850	358	4	1−	1−	NUM
ejpam-4850	358	5	η)pγ	η)pγ	PROPN
ejpam-4850	358	6	(	(	PUNCT
ejpam-4850	358	7	dη)γ	dη)γ	PROPN
ejpam-4850	358	8			PROPN
ejpam-4850	358	9	1	1	NUM
ejpam-4850	358	10	p	p	NOUN
ejpam-4850	358	11	×	×	NOUN
ejpam-4850	358	12			PROPN
ejpam-4850	358	13	1	1	NUM
ejpam-4850	358	14	γ(γ+1	γ(γ+1	NUM
ejpam-4850	358	15	)	)	PUNCT
ejpam-4850	359	1	1∫	1∫	NUM
ejpam-4850	359	2	0	0	NUM
ejpam-4850	359	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	359	4	(	(	PUNCT
ejpam-4850	359	5	γ	γ	PROPN
ejpam-4850	359	6	)	)	PUNCT
ejpam-4850	359	7	(	(	PUNCT
ejpam-4850	359	8	(	(	PUNCT
ejpam-4850	359	9	1−	1−	NUM
ejpam-4850	359	10	η)x+	η)x+	NUM
ejpam-4850	359	11	η	η	PROPN
ejpam-4850	359	12	a+b	a+b	NUM
ejpam-4850	359	13	2	2	NUM
ejpam-4850	359	14	)	)	PUNCT
ejpam-4850	359	15	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	359	16	(	(	PUNCT
ejpam-4850	359	17	dη)γ	dη)γ	PROPN
ejpam-4850	359	18			PROPN
ejpam-4850	359	19	1	1	NUM
ejpam-4850	359	20	q	q	NOUN
ejpam-4850	359	21	w.	w.	PROPN
ejpam-4850	359	22	saleh	saleh	PROPN
ejpam-4850	359	23	et	et	PROPN
ejpam-4850	359	24	al	al	PROPN
ejpam-4850	359	25	.	.	PUNCT
ejpam-4850	359	26	/	/	SYM
ejpam-4850	359	27	eur	eur	PROPN
ejpam-4850	359	28	.	.	PUNCT
ejpam-4850	360	1	j.	j.	PROPN
ejpam-4850	360	2	pure	pure	PROPN
ejpam-4850	360	3	appl	appl	PROPN
ejpam-4850	360	4	.	.	PROPN
ejpam-4850	360	5	math	math	PROPN
ejpam-4850	360	6	,	,	PUNCT
ejpam-4850	360	7	16	16	NUM
ejpam-4850	360	8	(	(	PUNCT
ejpam-4850	360	9	3	3	NUM
ejpam-4850	360	10	)	)	PUNCT
ejpam-4850	360	11	(	(	PUNCT
ejpam-4850	360	12	2023	2023	NUM
ejpam-4850	360	13	)	)	PUNCT
ejpam-4850	360	14	,	,	PUNCT
ejpam-4850	360	15	1359	1359	NUM
ejpam-4850	360	16	-	-	SYM
ejpam-4850	360	17	1380	1380	NUM
ejpam-4850	360	18	1374	1374	NUM
ejpam-4850	360	19	+	+	CCONJ
ejpam-4850	361	1			PROPN
ejpam-4850	361	2	1	1	NUM
ejpam-4850	361	3	γ(γ+1	γ(γ+1	NUM
ejpam-4850	361	4	)	)	PUNCT
ejpam-4850	362	1	1∫	1∫	NUM
ejpam-4850	362	2	0	0	NUM
ejpam-4850	362	3	ηpγ	ηpγ	NOUN
ejpam-4850	362	4	(	(	PUNCT
ejpam-4850	362	5	dη)γ	dη)γ	PROPN
ejpam-4850	362	6			PROPN
ejpam-4850	362	7	1	1	NUM
ejpam-4850	362	8	p	p	NOUN
ejpam-4850	362	9			PROPN
ejpam-4850	362	10	1	1	NUM
ejpam-4850	362	11	γ(γ+1	γ(γ+1	NUM
ejpam-4850	362	12	)	)	PUNCT
ejpam-4850	363	1	1∫	1∫	NUM
ejpam-4850	363	2	0	0	NUM
ejpam-4850	363	3	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	363	4	(	(	PUNCT
ejpam-4850	363	5	γ	γ	PROPN
ejpam-4850	363	6	)	)	PUNCT
ejpam-4850	363	7	(	(	PUNCT
ejpam-4850	363	8	(	(	PUNCT
ejpam-4850	363	9	1−	1−	NUM
ejpam-4850	363	10	η	η	NOUN
ejpam-4850	363	11	)	)	PUNCT
ejpam-4850	363	12	a+b	a+b	NUM
ejpam-4850	363	13	2	2	NUM
ejpam-4850	363	14	+	+	SYM
ejpam-4850	363	15	η	η	PROPN
ejpam-4850	363	16	(	(	PUNCT
ejpam-4850	363	17	a+	a+	PUNCT
ejpam-4850	363	18	b−	b−	PROPN
ejpam-4850	363	19	x	x	PROPN
ejpam-4850	363	20	)	)	PUNCT
ejpam-4850	363	21	)	)	PUNCT
ejpam-4850	363	22	∣∣∣q	∣∣∣q	PROPN
ejpam-4850	363	23	(	(	PUNCT
ejpam-4850	363	24	dη)γ	dη)γ	PROPN
ejpam-4850	363	25			PROPN
ejpam-4850	363	26	1	1	NUM
ejpam-4850	363	27	q	q	NOUN
ejpam-4850	363	28			NOUN
ejpam-4850	363	29	≤	≤	NOUN
ejpam-4850	363	30	(	(	PUNCT
ejpam-4850	363	31	γ(1+pγ	γ(1+pγ	NUM
ejpam-4850	363	32	)	)	PUNCT
ejpam-4850	363	33	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	363	34	)	)	PUNCT
ejpam-4850	363	35	)	)	PUNCT
ejpam-4850	363	36	1	1	NUM
ejpam-4850	363	37	p	p	NOUN
ejpam-4850	363	38	(	(	PUNCT
ejpam-4850	363	39	(	(	PUNCT
ejpam-4850	363	40	x−a)2γ	x−a)2γ	PROPN
ejpam-4850	363	41	(	(	PUNCT
ejpam-4850	363	42	b−a)γ	b−a)γ	PROPN
ejpam-4850	363	43	(	(	PUNCT
ejpam-4850	363	44	(	(	PUNCT
ejpam-4850	363	45	x−a)γ2(s−1)γ	x−a)γ2(s−1)γ	PROPN
ejpam-4850	363	46	γ(1+γ	γ(1+γ	PROPN
ejpam-4850	363	47	)	)	PUNCT
ejpam-4850	363	48	)	)	PUNCT
ejpam-4850	363	49	1	1	NUM
ejpam-4850	363	50	q	q	NOUN
ejpam-4850	363	51	(	(	PUNCT
ejpam-4850	363	52	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	363	53	(	(	PUNCT
ejpam-4850	363	54	γ	γ	PROPN
ejpam-4850	363	55	)	)	PUNCT
ejpam-4850	363	56	(	(	PUNCT
ejpam-4850	363	57	a+x	a+x	ADP
ejpam-4850	363	58	2	2	NUM
ejpam-4850	363	59	)	)	PUNCT
ejpam-4850	363	60	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	363	61	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	363	62	(	(	PUNCT
ejpam-4850	363	63	γ	γ	PROPN
ejpam-4850	363	64	)	)	PUNCT
ejpam-4850	363	65	(	(	PUNCT
ejpam-4850	363	66	a+2b−x	a+2b−x	ADV
ejpam-4850	363	67	2	2	NUM
ejpam-4850	363	68	)	)	PUNCT
ejpam-4850	363	69	∣∣∣	∣∣∣	NOUN
ejpam-4850	363	70	)	)	PUNCT
ejpam-4850	363	71	+	+	CCONJ
ejpam-4850	363	72	(	(	PUNCT
ejpam-4850	363	73	a+b−2x)2γ	a+b−2x)2γ	PROPN
ejpam-4850	363	74	4γ(b−a)γ	4γ(b−a)γ	NUM
ejpam-4850	363	75	(	(	PUNCT
ejpam-4850	363	76	(	(	PUNCT
ejpam-4850	363	77	(	(	PUNCT
ejpam-4850	363	78	a+b−2x)γ2(s−1)γ	a+b−2x)γ2(s−1)γ	PROPN
ejpam-4850	363	79	2γγ(1+γ	2γγ(1+γ	NUM
ejpam-4850	363	80	)	)	PUNCT
ejpam-4850	363	81	)	)	PUNCT
ejpam-4850	363	82	1	1	NUM
ejpam-4850	363	83	q	q	NOUN
ejpam-4850	363	84	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	363	85	(	(	PUNCT
ejpam-4850	363	86	γ	γ	PROPN
ejpam-4850	363	87	)	)	PUNCT
ejpam-4850	363	88	(	(	PUNCT
ejpam-4850	363	89	a+b+2x	a+b+2x	X
ejpam-4850	363	90	4	4	NUM
ejpam-4850	363	91	)	)	PUNCT
ejpam-4850	363	92	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	363	93	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	363	94	(	(	PUNCT
ejpam-4850	363	95	γ	γ	PROPN
ejpam-4850	363	96	)	)	PUNCT
ejpam-4850	363	97	(	(	PUNCT
ejpam-4850	363	98	3a+3b−2x	3a+3b−2x	NOUN
ejpam-4850	363	99	4	4	NUM
ejpam-4850	363	100	)	)	PUNCT
ejpam-4850	363	101	∣∣∣	∣∣∣	NOUN
ejpam-4850	363	102	)	)	PUNCT
ejpam-4850	363	103	)	)	PUNCT
ejpam-4850	363	104	.	.	PUNCT
ejpam-4850	364	1	the	the	DET
ejpam-4850	364	2	proof	proof	NOUN
ejpam-4850	364	3	is	be	AUX
ejpam-4850	364	4	completed	complete	VERB
ejpam-4850	364	5	.	.	PUNCT
ejpam-4850	365	1	corollary	corollary	ADJ
ejpam-4850	365	2	14	14	NUM
ejpam-4850	365	3	.	.	PUNCT
ejpam-4850	366	1	in	in	ADP
ejpam-4850	366	2	theorem	theorem	NOUN
ejpam-4850	366	3	4	4	NUM
ejpam-4850	366	4	,	,	PUNCT
ejpam-4850	366	5	taking	take	VERB
ejpam-4850	366	6	x	x	X
ejpam-4850	366	7	=	=	PUNCT
ejpam-4850	366	8	a	a	PRON
ejpam-4850	366	9	,	,	PUNCT
ejpam-4850	366	10	we	we	PRON
ejpam-4850	366	11	obtain∣∣∣j	obtain∣∣∣j	VERB
ejpam-4850	366	12	(	(	PUNCT
ejpam-4850	366	13	x)+j	x)+j	PROPN
ejpam-4850	366	14	(	(	PUNCT
ejpam-4850	366	15	a+b−x	a+b−x	PROPN
ejpam-4850	366	16	)	)	PUNCT
ejpam-4850	366	17	2γ	2γ	NOUN
ejpam-4850	366	18	−	−	PROPN
ejpam-4850	366	19	γ(γ+1	γ(γ+1	NUM
ejpam-4850	366	20	)	)	PUNCT
ejpam-4850	366	21	(	(	PUNCT
ejpam-4850	366	22	b−a)γ	b−a)γ	NOUN
ejpam-4850	366	23	ai	ai	VERB
ejpam-4850	366	24	γ	γ	PROPN
ejpam-4850	366	25	b	b	PROPN
ejpam-4850	366	26	j	j	PROPN
ejpam-4850	366	27	(	(	PUNCT
ejpam-4850	366	28	t	t	PROPN
ejpam-4850	366	29	)	)	PUNCT
ejpam-4850	366	30	∣∣∣	∣∣∣	NOUN
ejpam-4850	366	31	≤	≤	NOUN
ejpam-4850	366	32	(	(	PUNCT
ejpam-4850	366	33	b−a)γ	b−a)γ	NOUN
ejpam-4850	366	34	4γ	4γ	NOUN
ejpam-4850	366	35	(	(	PUNCT
ejpam-4850	366	36	γ(1+pγ	γ(1+pγ	NUM
ejpam-4850	366	37	)	)	PUNCT
ejpam-4850	366	38	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	366	39	)	)	PUNCT
ejpam-4850	366	40	)	)	PUNCT
ejpam-4850	366	41	1	1	NUM
ejpam-4850	366	42	p	p	NOUN
ejpam-4850	366	43	(	(	PUNCT
ejpam-4850	366	44	(	(	PUNCT
ejpam-4850	366	45	b−a)γ	b−a)γ	NOUN
ejpam-4850	366	46	2(2−s)γγ(1+γ	2(2−s)γγ(1+γ	NOUN
ejpam-4850	366	47	)	)	PUNCT
ejpam-4850	366	48	)	)	PUNCT
ejpam-4850	366	49	1	1	NUM
ejpam-4850	366	50	q	q	NOUN
ejpam-4850	366	51	(	(	PUNCT
ejpam-4850	366	52	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	366	53	(	(	PUNCT
ejpam-4850	366	54	γ	γ	PROPN
ejpam-4850	366	55	)	)	PUNCT
ejpam-4850	366	56	(	(	PUNCT
ejpam-4850	366	57	3a+b	3a+b	NUM
ejpam-4850	366	58	4	4	NUM
ejpam-4850	366	59	)	)	PUNCT
ejpam-4850	366	60	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	366	61	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	366	62	(	(	PUNCT
ejpam-4850	366	63	γ	γ	PROPN
ejpam-4850	366	64	)	)	PUNCT
ejpam-4850	366	65	(	(	PUNCT
ejpam-4850	366	66	a+3b	a+3b	PROPN
ejpam-4850	366	67	4	4	NUM
ejpam-4850	366	68	)	)	PUNCT
ejpam-4850	366	69	∣∣∣	∣∣∣	ADJ
ejpam-4850	366	70	)	)	PUNCT
ejpam-4850	366	71	.	.	PUNCT
ejpam-4850	367	1	corollary	corollary	ADJ
ejpam-4850	367	2	15	15	NUM
ejpam-4850	367	3	.	.	PUNCT
ejpam-4850	368	1	in	in	ADP
ejpam-4850	368	2	theorem	theorem	NOUN
ejpam-4850	368	3	4	4	NUM
ejpam-4850	368	4	,	,	PUNCT
ejpam-4850	368	5	taking	take	VERB
ejpam-4850	368	6	x	x	X
ejpam-4850	368	7	=	=	SYM
ejpam-4850	368	8	a+b	a+b	NUM
ejpam-4850	368	9	2	2	NUM
ejpam-4850	368	10	,	,	PUNCT
ejpam-4850	368	11	we	we	PRON
ejpam-4850	368	12	obtain∣∣∣j	obtain∣∣∣j	VERB
ejpam-4850	368	13	(	(	PUNCT
ejpam-4850	368	14	x)+j	x)+j	PROPN
ejpam-4850	368	15	(	(	PUNCT
ejpam-4850	368	16	a+b−x	a+b−x	PROPN
ejpam-4850	368	17	)	)	PUNCT
ejpam-4850	368	18	2γ	2γ	NOUN
ejpam-4850	368	19	−	−	PROPN
ejpam-4850	368	20	γ(γ+1	γ(γ+1	NUM
ejpam-4850	368	21	)	)	PUNCT
ejpam-4850	368	22	(	(	PUNCT
ejpam-4850	368	23	b−a)γ	b−a)γ	NOUN
ejpam-4850	368	24	ai	ai	VERB
ejpam-4850	368	25	γ	γ	PROPN
ejpam-4850	368	26	b	b	PROPN
ejpam-4850	368	27	j	j	PROPN
ejpam-4850	368	28	(	(	PUNCT
ejpam-4850	368	29	t	t	PROPN
ejpam-4850	368	30	)	)	PUNCT
ejpam-4850	368	31	∣∣∣	∣∣∣	NOUN
ejpam-4850	368	32	≤	≤	NOUN
ejpam-4850	368	33	(	(	PUNCT
ejpam-4850	368	34	b−a)γ	b−a)γ	NOUN
ejpam-4850	368	35	4γ	4γ	NOUN
ejpam-4850	368	36	(	(	PUNCT
ejpam-4850	368	37	γ(1+pγ	γ(1+pγ	NUM
ejpam-4850	368	38	)	)	PUNCT
ejpam-4850	368	39	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	368	40	)	)	PUNCT
ejpam-4850	368	41	)	)	PUNCT
ejpam-4850	368	42	1	1	NUM
ejpam-4850	368	43	p	p	NOUN
ejpam-4850	368	44	(	(	PUNCT
ejpam-4850	368	45	(	(	PUNCT
ejpam-4850	368	46	b−a)γ	b−a)γ	NOUN
ejpam-4850	368	47	2(2−s)γγ(1+γ	2(2−s)γγ(1+γ	NOUN
ejpam-4850	368	48	)	)	PUNCT
ejpam-4850	368	49	)	)	PUNCT
ejpam-4850	368	50	1	1	NUM
ejpam-4850	368	51	q	q	NOUN
ejpam-4850	368	52	(	(	PUNCT
ejpam-4850	368	53	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	368	54	(	(	PUNCT
ejpam-4850	368	55	γ	γ	PROPN
ejpam-4850	368	56	)	)	PUNCT
ejpam-4850	368	57	(	(	PUNCT
ejpam-4850	368	58	a+x	a+x	ADP
ejpam-4850	368	59	2	2	NUM
ejpam-4850	368	60	)	)	PUNCT
ejpam-4850	368	61	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	368	62	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	368	63	(	(	PUNCT
ejpam-4850	368	64	γ	γ	PROPN
ejpam-4850	368	65	)	)	PUNCT
ejpam-4850	368	66	(	(	PUNCT
ejpam-4850	368	67	a+2b−x	a+2b−x	ADV
ejpam-4850	368	68	2	2	NUM
ejpam-4850	368	69	)	)	PUNCT
ejpam-4850	368	70	∣∣∣	∣∣∣	ADJ
ejpam-4850	368	71	)	)	PUNCT
ejpam-4850	368	72	.	.	PUNCT
ejpam-4850	369	1	3	3	X
ejpam-4850	369	2	.	.	NOUN
ejpam-4850	369	3	example	example	NOUN
ejpam-4850	369	4	and	and	CCONJ
ejpam-4850	369	5	applications	application	NOUN
ejpam-4850	369	6	the	the	DET
ejpam-4850	369	7	purpose	purpose	NOUN
ejpam-4850	369	8	of	of	ADP
ejpam-4850	369	9	this	this	DET
ejpam-4850	369	10	section	section	NOUN
ejpam-4850	369	11	is	be	AUX
ejpam-4850	369	12	to	to	PART
ejpam-4850	369	13	verify	verify	VERB
ejpam-4850	369	14	the	the	DET
ejpam-4850	369	15	correctness	correctness	NOUN
ejpam-4850	369	16	and	and	CCONJ
ejpam-4850	369	17	effectiveness	effectiveness	NOUN
ejpam-4850	369	18	of	of	ADP
ejpam-4850	369	19	the	the	DET
ejpam-4850	369	20	results	result	NOUN
ejpam-4850	369	21	obtained	obtain	VERB
ejpam-4850	369	22	.	.	PUNCT
ejpam-4850	370	1	to	to	PART
ejpam-4850	370	2	achieve	achieve	VERB
ejpam-4850	370	3	this	this	PRON
ejpam-4850	370	4	,	,	PUNCT
ejpam-4850	370	5	we	we	PRON
ejpam-4850	370	6	start	start	VERB
ejpam-4850	370	7	with	with	ADP
ejpam-4850	370	8	an	an	DET
ejpam-4850	370	9	example	example	NOUN
ejpam-4850	370	10	that	that	PRON
ejpam-4850	370	11	includes	include	VERB
ejpam-4850	370	12	a	a	DET
ejpam-4850	370	13	graphical	graphical	ADJ
ejpam-4850	370	14	representations	representation	NOUN
ejpam-4850	370	15	to	to	PART
ejpam-4850	370	16	demonstrate	demonstrate	VERB
ejpam-4850	370	17	the	the	DET
ejpam-4850	370	18	accuracy	accuracy	NOUN
ejpam-4850	370	19	of	of	ADP
ejpam-4850	370	20	our	our	PRON
ejpam-4850	370	21	results	result	NOUN
ejpam-4850	370	22	.	.	PUNCT
ejpam-4850	371	1	we	we	PRON
ejpam-4850	371	2	then	then	ADV
ejpam-4850	371	3	provide	provide	VERB
ejpam-4850	371	4	a	a	DET
ejpam-4850	371	5	few	few	ADJ
ejpam-4850	371	6	applications	application	NOUN
ejpam-4850	371	7	for	for	ADP
ejpam-4850	371	8	estimating	estimate	VERB
ejpam-4850	371	9	the	the	DET
ejpam-4850	371	10	error	error	NOUN
ejpam-4850	371	11	of	of	ADP
ejpam-4850	371	12	a	a	DET
ejpam-4850	371	13	given	give	VERB
ejpam-4850	371	14	quadrature	quadrature	NOUN
ejpam-4850	371	15	formula	formula	NOUN
ejpam-4850	371	16	.	.	PUNCT
ejpam-4850	372	1	3.1	3.1	NUM
ejpam-4850	372	2	.	.	PUNCT
ejpam-4850	372	3	example	example	NOUN
ejpam-4850	372	4	supporting	support	VERB
ejpam-4850	372	5	our	our	PRON
ejpam-4850	372	6	findings	finding	NOUN
ejpam-4850	372	7	in	in	ADP
ejpam-4850	372	8	an	an	DET
ejpam-4850	372	9	effort	effort	NOUN
ejpam-4850	372	10	to	to	PART
ejpam-4850	372	11	provide	provide	VERB
ejpam-4850	372	12	additional	additional	ADJ
ejpam-4850	372	13	support	support	NOUN
ejpam-4850	372	14	and	and	CCONJ
ejpam-4850	372	15	substantiation	substantiation	NOUN
ejpam-4850	372	16	for	for	ADP
ejpam-4850	372	17	the	the	DET
ejpam-4850	372	18	results	result	NOUN
ejpam-4850	372	19	derived	derive	VERB
ejpam-4850	372	20	in	in	ADP
ejpam-4850	372	21	this	this	DET
ejpam-4850	372	22	study	study	NOUN
ejpam-4850	372	23	,	,	PUNCT
ejpam-4850	372	24	we	we	PRON
ejpam-4850	372	25	present	present	VERB
ejpam-4850	372	26	an	an	DET
ejpam-4850	372	27	illustrative	illustrative	ADJ
ejpam-4850	372	28	example	example	NOUN
ejpam-4850	372	29	that	that	PRON
ejpam-4850	372	30	encompasses	encompass	VERB
ejpam-4850	372	31	various	various	ADJ
ejpam-4850	372	32	cases	case	NOUN
ejpam-4850	372	33	and	and	CCONJ
ejpam-4850	372	34	incorporates	incorporate	VERB
ejpam-4850	372	35	2d	2d	NUM
ejpam-4850	372	36	and	and	CCONJ
ejpam-4850	372	37	3d	3d	NUM
ejpam-4850	372	38	graphical	graphical	ADJ
ejpam-4850	372	39	depictions	depiction	NOUN
ejpam-4850	372	40	.	.	PUNCT
ejpam-4850	373	1	the	the	DET
ejpam-4850	373	2	purpose	purpose	NOUN
ejpam-4850	373	3	of	of	ADP
ejpam-4850	373	4	this	this	DET
ejpam-4850	373	5	example	example	NOUN
ejpam-4850	373	6	is	be	AUX
ejpam-4850	373	7	to	to	PART
ejpam-4850	373	8	demonstrate	demonstrate	VERB
ejpam-4850	373	9	the	the	DET
ejpam-4850	373	10	effectiveness	effectiveness	NOUN
ejpam-4850	373	11	and	and	CCONJ
ejpam-4850	373	12	accuracy	accuracy	NOUN
ejpam-4850	373	13	of	of	ADP
ejpam-4850	373	14	our	our	PRON
ejpam-4850	373	15	findings	finding	NOUN
ejpam-4850	373	16	.	.	PUNCT
ejpam-4850	374	1	it	it	PRON
ejpam-4850	374	2	is	be	AUX
ejpam-4850	374	3	important	important	ADJ
ejpam-4850	374	4	to	to	PART
ejpam-4850	374	5	note	note	VERB
ejpam-4850	374	6	that	that	SCONJ
ejpam-4850	374	7	the	the	DET
ejpam-4850	374	8	figures	figure	NOUN
ejpam-4850	374	9	presented	present	VERB
ejpam-4850	374	10	herein	herein	NOUN
ejpam-4850	374	11	were	be	AUX
ejpam-4850	374	12	generated	generate	VERB
ejpam-4850	374	13	utilizing	utilize	VERB
ejpam-4850	374	14	matlab	matlab	PROPN
ejpam-4850	374	15	,	,	PUNCT
ejpam-4850	374	16	where	where	SCONJ
ejpam-4850	374	17	the	the	DET
ejpam-4850	374	18	color	color	NOUN
ejpam-4850	374	19	green	green	ADJ
ejpam-4850	374	20	denotes	denote	VERB
ejpam-4850	374	21	the	the	DET
ejpam-4850	374	22	right	right	ADJ
ejpam-4850	374	23	hand	hand	NOUN
ejpam-4850	374	24	side	side	NOUN
ejpam-4850	374	25	(	(	PUNCT
ejpam-4850	374	26	rhs	rhs	PROPN
ejpam-4850	374	27	)	)	PUNCT
ejpam-4850	374	28	and	and	CCONJ
ejpam-4850	374	29	red	red	ADJ
ejpam-4850	374	30	signifies	signifie	NOUN
ejpam-4850	374	31	the	the	DET
ejpam-4850	374	32	left	left	ADJ
ejpam-4850	374	33	hand	hand	NOUN
ejpam-4850	374	34	side	side	NOUN
ejpam-4850	374	35	(	(	PUNCT
ejpam-4850	374	36	lhs	lhs	PROPN
ejpam-4850	374	37	)	)	PUNCT
ejpam-4850	374	38	of	of	ADP
ejpam-4850	374	39	their	their	PRON
ejpam-4850	374	40	respective	respective	ADJ
ejpam-4850	374	41	inequalities	inequality	NOUN
ejpam-4850	374	42	.	.	PUNCT
ejpam-4850	374	43	example	example	NOUN
ejpam-4850	375	1	1	1	NUM
ejpam-4850	375	2	.	.	X
ejpam-4850	375	3	we	we	PRON
ejpam-4850	375	4	present	present	VERB
ejpam-4850	375	5	the	the	DET
ejpam-4850	375	6	function	function	NOUN
ejpam-4850	375	7	j	j	NOUN
ejpam-4850	375	8	:	:	PUNCT
ejpam-4850	376	1	[	[	X
ejpam-4850	376	2	0	0	NUM
ejpam-4850	376	3	,	,	PUNCT
ejpam-4850	376	4	1	1	NUM
ejpam-4850	376	5	]	]	PUNCT
ejpam-4850	376	6	→	→	SYM
ejpam-4850	376	7	rγ	rγ	NOUN
ejpam-4850	376	8	,	,	PUNCT
ejpam-4850	376	9	which	which	PRON
ejpam-4850	376	10	is	be	AUX
ejpam-4850	376	11	defined	define	VERB
ejpam-4850	376	12	for	for	ADP
ejpam-4850	376	13	a	a	DET
ejpam-4850	376	14	fixed	fix	VERB
ejpam-4850	376	15	value	value	NOUN
ejpam-4850	376	16	s	s	X
ejpam-4850	376	17	∈	∈	NOUN
ejpam-4850	376	18	(	(	PUNCT
ejpam-4850	376	19	0	0	NUM
ejpam-4850	376	20	,	,	PUNCT
ejpam-4850	376	21	1	1	NUM
ejpam-4850	376	22	]	]	PUNCT
ejpam-4850	376	23	as	as	ADP
ejpam-4850	376	24	j	j	PROPN
ejpam-4850	376	25	(	(	PUNCT
ejpam-4850	376	26	t	t	PROPN
ejpam-4850	376	27	)	)	PUNCT
ejpam-4850	376	28	=	=	SYM
ejpam-4850	376	29	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	376	30	)	)	PUNCT
ejpam-4850	376	31	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	376	32	)	)	PUNCT
ejpam-4850	376	33	t	t	PROPN
ejpam-4850	376	34	(	(	PUNCT
ejpam-4850	376	35	s+1)γ	s+1)γ	PROPN
ejpam-4850	376	36	.	.	PUNCT
ejpam-4850	377	1	the	the	DET
ejpam-4850	377	2	crucial	crucial	ADJ
ejpam-4850	377	3	aspect	aspect	NOUN
ejpam-4850	377	4	of	of	ADP
ejpam-4850	377	5	this	this	DET
ejpam-4850	377	6	function	function	NOUN
ejpam-4850	377	7	,	,	PUNCT
ejpam-4850	377	8	which	which	PRON
ejpam-4850	377	9	underpins	underpin	VERB
ejpam-4850	377	10	our	our	PRON
ejpam-4850	377	11	investigation	investigation	NOUN
ejpam-4850	377	12	,	,	PUNCT
ejpam-4850	377	13	is	be	AUX
ejpam-4850	377	14	that	that	SCONJ
ejpam-4850	377	15	its	its	PRON
ejpam-4850	377	16	derivative	derivative	ADJ
ejpam-4850	377	17	∣∣j	∣∣j	NOUN
ejpam-4850	377	18	(	(	PUNCT
ejpam-4850	377	19	γ	γ	NOUN
ejpam-4850	377	20	)	)	PUNCT
ejpam-4850	377	21	∣∣	∣∣	X
ejpam-4850	377	22	=	=	PUNCT
ejpam-4850	377	23	tsγ	tsγ	NOUN
ejpam-4850	377	24	is	be	AUX
ejpam-4850	377	25	a	a	DET
ejpam-4850	377	26	generalized	generalized	ADJ
ejpam-4850	377	27	s	s	NOUN
ejpam-4850	377	28	-	-	ADJ
ejpam-4850	377	29	convex	convex	ADJ
ejpam-4850	377	30	function	function	NOUN
ejpam-4850	377	31	.	.	PUNCT
ejpam-4850	378	1	w.	w.	PROPN
ejpam-4850	378	2	saleh	saleh	PROPN
ejpam-4850	378	3	et	et	PROPN
ejpam-4850	378	4	al	al	PROPN
ejpam-4850	378	5	.	.	PUNCT
ejpam-4850	378	6	/	/	SYM
ejpam-4850	378	7	eur	eur	PROPN
ejpam-4850	378	8	.	.	PUNCT
ejpam-4850	379	1	j.	j.	PROPN
ejpam-4850	379	2	pure	pure	PROPN
ejpam-4850	379	3	appl	appl	PROPN
ejpam-4850	379	4	.	.	PROPN
ejpam-4850	379	5	math	math	PROPN
ejpam-4850	379	6	,	,	PUNCT
ejpam-4850	379	7	16	16	NUM
ejpam-4850	379	8	(	(	PUNCT
ejpam-4850	379	9	3	3	NUM
ejpam-4850	379	10	)	)	PUNCT
ejpam-4850	379	11	(	(	PUNCT
ejpam-4850	379	12	2023	2023	NUM
ejpam-4850	379	13	)	)	PUNCT
ejpam-4850	379	14	,	,	PUNCT
ejpam-4850	379	15	1359	1359	NUM
ejpam-4850	379	16	-	-	SYM
ejpam-4850	379	17	1380	1380	NUM
ejpam-4850	379	18	1375	1375	NUM
ejpam-4850	379	19	in	in	ADP
ejpam-4850	379	20	the	the	DET
ejpam-4850	379	21	ensuing	ensue	VERB
ejpam-4850	379	22	discussion	discussion	NOUN
ejpam-4850	380	1	,	,	PUNCT
ejpam-4850	380	2	we	we	PRON
ejpam-4850	380	3	will	will	AUX
ejpam-4850	380	4	set	set	VERB
ejpam-4850	380	5	γ	γ	X
ejpam-4850	380	6	=	=	SYM
ejpam-4850	380	7	1	1	NUM
ejpam-4850	380	8	and	and	CCONJ
ejpam-4850	380	9	subsequently	subsequently	ADV
ejpam-4850	380	10	present	present	VERB
ejpam-4850	380	11	the	the	DET
ejpam-4850	380	12	different	different	ADJ
ejpam-4850	380	13	cases	case	NOUN
ejpam-4850	380	14	in	in	ADP
ejpam-4850	380	15	the	the	DET
ejpam-4850	380	16	following	following	ADJ
ejpam-4850	380	17	manner	manner	NOUN
ejpam-4850	380	18	.	.	PUNCT
ejpam-4850	381	1	case	case	NOUN
ejpam-4850	381	2	1	1	NUM
ejpam-4850	381	3	.	.	PUNCT
ejpam-4850	381	4	applying	apply	VERB
ejpam-4850	381	5	theorem	theorem	NOUN
ejpam-4850	381	6	1	1	NUM
ejpam-4850	381	7	to	to	ADP
ejpam-4850	381	8	the	the	DET
ejpam-4850	381	9	function	function	NOUN
ejpam-4850	381	10	under	under	ADP
ejpam-4850	381	11	consideration	consideration	NOUN
ejpam-4850	381	12	yields	yield	NOUN
ejpam-4850	381	13	the	the	DET
ejpam-4850	381	14	following	following	ADJ
ejpam-4850	381	15	result	result	NOUN
ejpam-4850	381	16	depicted	depict	VERB
ejpam-4850	381	17	in	in	ADP
ejpam-4850	381	18	figure	figure	NOUN
ejpam-4850	381	19	1	1	NUM
ejpam-4850	381	20	for	for	ADP
ejpam-4850	381	21	x	x	PROPN
ejpam-4850	381	22	∈	∈	PROPN
ejpam-4850	381	23	[	[	PUNCT
ejpam-4850	381	24	0	0	NUM
ejpam-4850	381	25	,	,	PUNCT
ejpam-4850	381	26	12	12	NUM
ejpam-4850	381	27	]	]	PUNCT
ejpam-4850	381	28	and	and	CCONJ
ejpam-4850	381	29	s	s	PROPN
ejpam-4850	381	30	∈	∈	PROPN
ejpam-4850	381	31	(	(	PUNCT
ejpam-4850	381	32	0	0	NUM
ejpam-4850	381	33	,	,	PUNCT
ejpam-4850	381	34	1	1	NUM
ejpam-4850	381	35	]	]	PUNCT
ejpam-4850	381	36	.	.	PUNCT
ejpam-4850	382	1	∣∣∣	∣∣∣	NOUN
ejpam-4850	382	2	1	1	NUM
ejpam-4850	382	3	s+1	s+1	PROPN
ejpam-4850	382	4	(	(	PUNCT
ejpam-4850	382	5	xs+1+(1−x)s+1	xs+1+(1−x)s+1	PROPN
ejpam-4850	382	6	2	2	NUM
ejpam-4850	382	7	−	−	PROPN
ejpam-4850	382	8	1	1	NUM
ejpam-4850	382	9	s+2	s+2	NUM
ejpam-4850	382	10	)	)	PUNCT
ejpam-4850	382	11	∣∣∣	∣∣∣	NOUN
ejpam-4850	382	12	≤x2	≤x2	X
ejpam-4850	382	13	(	(	PUNCT
ejpam-4850	382	14	1	1	NUM
ejpam-4850	382	15	(	(	PUNCT
ejpam-4850	382	16	s+1)(s+2	s+1)(s+2	NOUN
ejpam-4850	382	17	)	)	PUNCT
ejpam-4850	382	18	+	+	CCONJ
ejpam-4850	382	19	1	1	NUM
ejpam-4850	382	20	s+2	s+2	NUM
ejpam-4850	382	21	(	(	PUNCT
ejpam-4850	382	22	x	x	SYM
ejpam-4850	382	23	s	s	X
ejpam-4850	382	24	+	+	X
ejpam-4850	382	25	(	(	PUNCT
ejpam-4850	382	26	1−	1−	NUM
ejpam-4850	382	27	x)s	x)s	NUM
ejpam-4850	382	28	)	)	PUNCT
ejpam-4850	382	29	)	)	PUNCT
ejpam-4850	383	1	+	+	CCONJ
ejpam-4850	383	2	(	(	PUNCT
ejpam-4850	383	3	1−2x)2	1−2x)2	NUM
ejpam-4850	383	4	4	4	NUM
ejpam-4850	383	5	(	(	PUNCT
ejpam-4850	383	6	1	1	NUM
ejpam-4850	383	7	s+2	s+2	NUM
ejpam-4850	383	8	(	(	PUNCT
ejpam-4850	383	9	x	x	SYM
ejpam-4850	383	10	s	s	X
ejpam-4850	383	11	+	+	X
ejpam-4850	383	12	(	(	PUNCT
ejpam-4850	383	13	1−	1−	NUM
ejpam-4850	383	14	x)s	x)s	NUM
ejpam-4850	383	15	)	)	PUNCT
ejpam-4850	384	1	+	+	CCONJ
ejpam-4850	384	2	21−s	21−s	NUM
ejpam-4850	384	3	(	(	PUNCT
ejpam-4850	384	4	s+1)(s+2	s+1)(s+2	NOUN
ejpam-4850	384	5	)	)	PUNCT
ejpam-4850	384	6	)	)	PUNCT
ejpam-4850	384	7	.	.	PUNCT
ejpam-4850	385	1	case	case	NOUN
ejpam-4850	385	2	2	2	X
ejpam-4850	385	3	.	.	X
ejpam-4850	385	4	fixing	fix	VERB
ejpam-4850	385	5	s	s	PART
ejpam-4850	385	6	=	=	SYM
ejpam-4850	385	7	1	1	NUM
ejpam-4850	385	8	2	2	NUM
ejpam-4850	385	9	,	,	PUNCT
ejpam-4850	385	10	we	we	PRON
ejpam-4850	385	11	obtain	obtain	VERB
ejpam-4850	385	12	the	the	DET
ejpam-4850	385	13	following	following	ADJ
ejpam-4850	385	14	result	result	NOUN
ejpam-4850	385	15	for	for	ADP
ejpam-4850	385	16	x	x	SYM
ejpam-4850	385	17	as	as	SCONJ
ejpam-4850	385	18	shown	show	VERB
ejpam-4850	385	19	in	in	ADP
ejpam-4850	385	20	figure	figure	NOUN
ejpam-4850	385	21	2	2	NUM
ejpam-4850	385	22	.	.	NOUN
ejpam-4850	385	23	0	0	NUM
ejpam-4850	385	24	0.1	0.1	NUM
ejpam-4850	385	25	0.2	0.2	NUM
ejpam-4850	385	26	0.3	0.3	NUM
ejpam-4850	385	27	0.4	0.4	NUM
ejpam-4850	385	28	0.5	0.5	NUM
ejpam-4850	385	29	0	0	NUM
ejpam-4850	385	30	0.5	0.5	NUM
ejpam-4850	385	31	1	1	NUM
ejpam-4850	385	32	0	0	NUM
ejpam-4850	385	33	0.1	0.1	NUM
ejpam-4850	385	34	0.2	0.2	NUM
ejpam-4850	385	35	0.3	0.3	NUM
ejpam-4850	385	36	0.4	0.4	NUM
ejpam-4850	385	37	0.5	0.5	NUM
ejpam-4850	385	38	parameter	parameter	NOUN
ejpam-4850	385	39	xparameter	xparameter	PROPN
ejpam-4850	385	40	s	s	PART
ejpam-4850	385	41	(	(	PUNCT
ejpam-4850	385	42	a	a	NOUN
ejpam-4850	385	43	)	)	PUNCT
ejpam-4850	385	44	view.1	view.1	ADP
ejpam-4850	385	45	0	0	NUM
ejpam-4850	385	46	0.1	0.1	NUM
ejpam-4850	385	47	0.2	0.2	NUM
ejpam-4850	385	48	0.3	0.3	NUM
ejpam-4850	385	49	0.4	0.4	NUM
ejpam-4850	385	50	0.5	0.5	NUM
ejpam-4850	385	51	0	0	NUM
ejpam-4850	385	52	0.2	0.2	NUM
ejpam-4850	385	53	0.4	0.4	NUM
ejpam-4850	385	54	0.6	0.6	NUM
ejpam-4850	385	55	0.8	0.8	NUM
ejpam-4850	385	56	1	1	NUM
ejpam-4850	385	57	0	0	NUM
ejpam-4850	385	58	0.1	0.1	NUM
ejpam-4850	385	59	0.2	0.2	NUM
ejpam-4850	385	60	0.3	0.3	NUM
ejpam-4850	385	61	0.4	0.4	NUM
ejpam-4850	385	62	0.5	0.5	NUM
ejpam-4850	385	63	parameter	parameter	NOUN
ejpam-4850	385	64	s	s	PART
ejpam-4850	385	65	parameter	parameter	NOUN
ejpam-4850	385	66	x	x	X
ejpam-4850	385	67	(	(	PUNCT
ejpam-4850	385	68	b	b	NOUN
ejpam-4850	385	69	)	)	PUNCT
ejpam-4850	386	1	view.2	view.2	PRON
ejpam-4850	386	2	figure	figure	NOUN
ejpam-4850	386	3	1	1	NUM
ejpam-4850	386	4	:	:	PUNCT
ejpam-4850	386	5	case	case	NOUN
ejpam-4850	386	6	1	1	NUM
ejpam-4850	386	7	.	.	PUNCT
ejpam-4850	387	1	x	x	SYM
ejpam-4850	387	2	∈	∈	PROPN
ejpam-4850	387	3	[	[	PUNCT
ejpam-4850	387	4	0	0	NUM
ejpam-4850	387	5	,	,	PUNCT
ejpam-4850	387	6	12	12	NUM
ejpam-4850	387	7	]	]	PUNCT
ejpam-4850	387	8	and	and	CCONJ
ejpam-4850	387	9	s	s	PROPN
ejpam-4850	387	10	∈	∈	PROPN
ejpam-4850	387	11	(	(	PUNCT
ejpam-4850	387	12	0	0	NUM
ejpam-4850	387	13	,	,	PUNCT
ejpam-4850	387	14	1	1	NUM
ejpam-4850	387	15	]	]	PUNCT
ejpam-4850	387	16	∣∣∣∣∣23	∣∣∣∣∣23	PROPN
ejpam-4850	387	17	(	(	PUNCT
ejpam-4850	387	18	x	x	SYM
ejpam-4850	387	19	3	3	NUM
ejpam-4850	387	20	2	2	NUM
ejpam-4850	387	21	+	+	ADJ
ejpam-4850	387	22	(	(	PUNCT
ejpam-4850	387	23	1−x	1−x	NUM
ejpam-4850	387	24	)	)	PUNCT
ejpam-4850	387	25	3	3	NUM
ejpam-4850	387	26	2	2	NUM
ejpam-4850	387	27	2	2	NUM
ejpam-4850	387	28	−	−	NUM
ejpam-4850	387	29	2	2	NUM
ejpam-4850	387	30	5	5	NUM
ejpam-4850	387	31	)	)	PUNCT
ejpam-4850	387	32	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-4850	387	33	≤x2	≤x2	NOUN
ejpam-4850	387	34	(	(	PUNCT
ejpam-4850	387	35	4	4	NUM
ejpam-4850	387	36	15	15	NUM
ejpam-4850	387	37	+	+	CCONJ
ejpam-4850	387	38	2	2	NUM
ejpam-4850	387	39	5	5	NUM
ejpam-4850	387	40	(	(	PUNCT
ejpam-4850	387	41	√	√	ADV
ejpam-4850	387	42	x+	x+	NUM
ejpam-4850	387	43	√	√	PROPN
ejpam-4850	387	44	1−	1−	NUM
ejpam-4850	387	45	x	x	NOUN
ejpam-4850	387	46	)	)	PUNCT
ejpam-4850	387	47	)	)	PUNCT
ejpam-4850	388	1	+	+	CCONJ
ejpam-4850	388	2	(	(	PUNCT
ejpam-4850	388	3	1−2x)2	1−2x)2	NUM
ejpam-4850	388	4	4	4	NUM
ejpam-4850	388	5	(	(	PUNCT
ejpam-4850	388	6	2	2	NUM
ejpam-4850	388	7	5	5	NUM
ejpam-4850	388	8	(	(	PUNCT
ejpam-4850	388	9	√	√	ADV
ejpam-4850	388	10	x+	x+	NUM
ejpam-4850	388	11	√	√	NUM
ejpam-4850	388	12	1−	1−	NUM
ejpam-4850	388	13	x	x	SYM
ejpam-4850	388	14	)	)	PUNCT
ejpam-4850	389	1	+	+	CCONJ
ejpam-4850	389	2	4	4	NUM
ejpam-4850	389	3	√	√	NUM
ejpam-4850	389	4	2	2	NUM
ejpam-4850	389	5	15	15	NUM
ejpam-4850	389	6	)	)	PUNCT
ejpam-4850	389	7	.	.	PUNCT
ejpam-4850	390	1	0	0	NUM
ejpam-4850	390	2	0.1	0.1	NUM
ejpam-4850	390	3	0.2	0.2	NUM
ejpam-4850	390	4	0.3	0.3	NUM
ejpam-4850	390	5	0.4	0.4	NUM
ejpam-4850	390	6	0.5	0.5	NUM
ejpam-4850	390	7	0	0	NUM
ejpam-4850	390	8	0.05	0.05	NUM
ejpam-4850	390	9	0.1	0.1	NUM
ejpam-4850	390	10	0.15	0.15	NUM
ejpam-4850	390	11	0.2	0.2	NUM
ejpam-4850	390	12	0.25	0.25	NUM
ejpam-4850	390	13	parameter	parameter	NOUN
ejpam-4850	390	14	x	x	PUNCT
ejpam-4850	390	15	figure	figure	NOUN
ejpam-4850	390	16	2	2	NUM
ejpam-4850	390	17	:	:	PUNCT
ejpam-4850	390	18	case	case	NOUN
ejpam-4850	390	19	2	2	NUM
ejpam-4850	390	20	.	.	X
ejpam-4850	390	21	s	s	PART
ejpam-4850	391	1	=	=	SYM
ejpam-4850	391	2	1	1	NUM
ejpam-4850	391	3	2	2	NUM
ejpam-4850	391	4	and	and	CCONJ
ejpam-4850	391	5	x	x	NOUN
ejpam-4850	391	6	∈	∈	PROPN
ejpam-4850	391	7	[	[	PUNCT
ejpam-4850	391	8	0	0	NUM
ejpam-4850	391	9	,	,	PUNCT
ejpam-4850	391	10	12	12	NUM
ejpam-4850	391	11	]	]	PUNCT
ejpam-4850	391	12	case	case	NOUN
ejpam-4850	391	13	3	3	X
ejpam-4850	391	14	.	.	PUNCT
ejpam-4850	392	1	lastly	lastly	ADV
ejpam-4850	392	2	,	,	PUNCT
ejpam-4850	392	3	we	we	PRON
ejpam-4850	392	4	present	present	VERB
ejpam-4850	392	5	with	with	ADP
ejpam-4850	392	6	respect	respect	NOUN
ejpam-4850	392	7	to	to	ADP
ejpam-4850	392	8	s	s	PRON
ejpam-4850	392	9	the	the	DET
ejpam-4850	392	10	result	result	NOUN
ejpam-4850	392	11	obtained	obtain	VERB
ejpam-4850	392	12	by	by	ADP
ejpam-4850	392	13	fixing	fix	VERB
ejpam-4850	392	14	x	x	X
ejpam-4850	392	15	=	=	SYM
ejpam-4850	392	16	0	0	NUM
ejpam-4850	392	17	,	,	PUNCT
ejpam-4850	392	18	as	as	SCONJ
ejpam-4850	392	19	depicted	depict	VERB
ejpam-4850	392	20	in	in	ADP
ejpam-4850	392	21	figure	figure	NOUN
ejpam-4850	392	22	3	3	NUM
ejpam-4850	392	23	.	.	PUNCT
ejpam-4850	392	24	w.	w.	PROPN
ejpam-4850	392	25	saleh	saleh	PROPN
ejpam-4850	392	26	et	et	PROPN
ejpam-4850	392	27	al	al	PROPN
ejpam-4850	392	28	.	.	PUNCT
ejpam-4850	392	29	/	/	SYM
ejpam-4850	392	30	eur	eur	PROPN
ejpam-4850	392	31	.	.	PUNCT
ejpam-4850	393	1	j.	j.	PROPN
ejpam-4850	393	2	pure	pure	PROPN
ejpam-4850	393	3	appl	appl	PROPN
ejpam-4850	393	4	.	.	PROPN
ejpam-4850	393	5	math	math	PROPN
ejpam-4850	393	6	,	,	PUNCT
ejpam-4850	393	7	16	16	NUM
ejpam-4850	393	8	(	(	PUNCT
ejpam-4850	393	9	3	3	NUM
ejpam-4850	393	10	)	)	PUNCT
ejpam-4850	393	11	(	(	PUNCT
ejpam-4850	393	12	2023	2023	NUM
ejpam-4850	393	13	)	)	PUNCT
ejpam-4850	393	14	,	,	PUNCT
ejpam-4850	393	15	1359	1359	NUM
ejpam-4850	393	16	-	-	SYM
ejpam-4850	393	17	1380	1380	NUM
ejpam-4850	393	18	1376	1376	NUM
ejpam-4850	393	19	∣∣∣	∣∣∣	NOUN
ejpam-4850	393	20	1	1	NUM
ejpam-4850	393	21	s+1	s+1	PROPN
ejpam-4850	393	22	(	(	PUNCT
ejpam-4850	393	23	1	1	NUM
ejpam-4850	393	24	2	2	NUM
ejpam-4850	393	25	−	−	NUM
ejpam-4850	393	26	1	1	NUM
ejpam-4850	393	27	s+2	s+2	NUM
ejpam-4850	393	28	)	)	PUNCT
ejpam-4850	393	29	∣∣∣	∣∣∣	NOUN
ejpam-4850	394	1	≤1	≤1	PROPN
ejpam-4850	394	2	4	4	NUM
ejpam-4850	394	3	(	(	PUNCT
ejpam-4850	394	4	1	1	NUM
ejpam-4850	394	5	s+2	s+2	NUM
ejpam-4850	394	6	+	+	CCONJ
ejpam-4850	394	7	21−s	21−s	NUM
ejpam-4850	394	8	(	(	PUNCT
ejpam-4850	394	9	s+1)(s+2	s+1)(s+2	NOUN
ejpam-4850	394	10	)	)	PUNCT
ejpam-4850	394	11	)	)	PUNCT
ejpam-4850	394	12	.	.	PUNCT
ejpam-4850	395	1	0	0	NUM
ejpam-4850	395	2	0.2	0.2	NUM
ejpam-4850	395	3	0.4	0.4	NUM
ejpam-4850	395	4	0.6	0.6	NUM
ejpam-4850	395	5	0.8	0.8	NUM
ejpam-4850	395	6	1	1	NUM
ejpam-4850	395	7	0	0	NUM
ejpam-4850	395	8	0.05	0.05	NUM
ejpam-4850	395	9	0.1	0.1	NUM
ejpam-4850	395	10	0.15	0.15	NUM
ejpam-4850	395	11	0.2	0.2	NUM
ejpam-4850	395	12	0.25	0.25	NUM
ejpam-4850	395	13	0.3	0.3	NUM
ejpam-4850	395	14	0.35	0.35	NUM
ejpam-4850	395	15	0.4	0.4	NUM
ejpam-4850	395	16	parameter	parameter	NOUN
ejpam-4850	395	17	s	s	PART
ejpam-4850	395	18	figure	figure	NOUN
ejpam-4850	395	19	3	3	NUM
ejpam-4850	395	20	:	:	PUNCT
ejpam-4850	395	21	case	case	NOUN
ejpam-4850	395	22	3	3	NUM
ejpam-4850	395	23	.	.	PUNCT
ejpam-4850	395	24	x	x	X
ejpam-4850	396	1	=	=	SYM
ejpam-4850	396	2	0	0	NUM
ejpam-4850	396	3	and	and	CCONJ
ejpam-4850	396	4	s	s	PROPN
ejpam-4850	396	5	∈	∈	PROPN
ejpam-4850	396	6	(	(	PUNCT
ejpam-4850	396	7	0	0	NUM
ejpam-4850	396	8	,	,	PUNCT
ejpam-4850	396	9	1	1	NUM
ejpam-4850	396	10	]	]	SYM
ejpam-4850	396	11	3.2	3.2	NUM
ejpam-4850	396	12	.	.	PUNCT
ejpam-4850	396	13	applications	application	NOUN
ejpam-4850	396	14	to	to	ADP
ejpam-4850	396	15	quadrature	quadrature	NOUN
ejpam-4850	396	16	formula	formula	NOUN
ejpam-4850	396	17	let	let	VERB
ejpam-4850	396	18	λ	λ	NOUN
ejpam-4850	396	19	be	be	AUX
ejpam-4850	396	20	the	the	DET
ejpam-4850	396	21	partition	partition	NOUN
ejpam-4850	396	22	of	of	ADP
ejpam-4850	396	23	the	the	DET
ejpam-4850	396	24	interval	interval	NOUN
ejpam-4850	396	25	[	[	X
ejpam-4850	396	26	a	a	X
ejpam-4850	396	27	,	,	PUNCT
ejpam-4850	396	28	b	b	NOUN
ejpam-4850	396	29	]	]	X
ejpam-4850	396	30	,	,	PUNCT
ejpam-4850	396	31	a	a	DET
ejpam-4850	396	32	=	=	SYM
ejpam-4850	396	33	y0	y0	NOUN
ejpam-4850	396	34	<	<	X
ejpam-4850	396	35	y1	y1	X
ejpam-4850	396	36	<	<	X
ejpam-4850	396	37	...	...	PUNCT
ejpam-4850	396	38	<	<	X
ejpam-4850	396	39	yn	yn	X
ejpam-4850	396	40	=	=	PUNCT
ejpam-4850	396	41	b.	b.	PROPN
ejpam-4850	396	42	we	we	PRON
ejpam-4850	396	43	consider	consider	VERB
ejpam-4850	396	44	the	the	DET
ejpam-4850	396	45	following	follow	VERB
ejpam-4850	396	46	quadrature	quadrature	NOUN
ejpam-4850	396	47	rule	rule	NOUN
ejpam-4850	396	48	1	1	NUM
ejpam-4850	396	49	γ(γ+1	γ(γ+1	NUM
ejpam-4850	396	50	)	)	PUNCT
ejpam-4850	396	51	b∫	b∫	PROPN
ejpam-4850	396	52	a	a	DET
ejpam-4850	396	53	j	j	PROPN
ejpam-4850	396	54	(	(	PUNCT
ejpam-4850	396	55	u	u	NOUN
ejpam-4850	396	56	)	)	PUNCT
ejpam-4850	396	57	(	(	PUNCT
ejpam-4850	396	58	du)γ	du)γ	PROPN
ejpam-4850	396	59	=	=	SYM
ejpam-4850	396	60	t	t	PROPN
ejpam-4850	396	61	(	(	PUNCT
ejpam-4850	396	62	j	j	PROPN
ejpam-4850	396	63	,	,	PUNCT
ejpam-4850	396	64	λ	λ	PROPN
ejpam-4850	396	65	)	)	PUNCT
ejpam-4850	397	1	+	+	NOUN
ejpam-4850	397	2	r	r	NOUN
ejpam-4850	397	3	(	(	PUNCT
ejpam-4850	397	4	j	j	PROPN
ejpam-4850	397	5	,	,	PUNCT
ejpam-4850	397	6	λ	λ	PROPN
ejpam-4850	397	7	)	)	PUNCT
ejpam-4850	397	8	,	,	PUNCT
ejpam-4850	397	9	where	where	SCONJ
ejpam-4850	397	10	t	t	PROPN
ejpam-4850	397	11	(	(	PUNCT
ejpam-4850	397	12	j	j	PROPN
ejpam-4850	397	13	,	,	PUNCT
ejpam-4850	397	14	λ	λ	PROPN
ejpam-4850	397	15	)	)	PUNCT
ejpam-4850	397	16	=	=	SYM
ejpam-4850	397	17	m−1∑	m−1∑	PROPN
ejpam-4850	397	18	k=0	k=0	X
ejpam-4850	397	19	(	(	PUNCT
ejpam-4850	397	20	yk+1−yk	yk+1−yk	PROPN
ejpam-4850	397	21	)	)	PUNCT
ejpam-4850	397	22	γ	γ	NOUN
ejpam-4850	397	23	γ(γ+1	γ(γ+1	NUM
ejpam-4850	397	24	)	)	PUNCT
ejpam-4850	397	25	(	(	PUNCT
ejpam-4850	397	26	j	j	PROPN
ejpam-4850	397	27	(	(	PUNCT
ejpam-4850	397	28	x)+j	x)+j	PROPN
ejpam-4850	397	29	(	(	PUNCT
ejpam-4850	397	30	yk+yk+1−x	yk+yk+1−x	NOUN
ejpam-4850	397	31	)	)	PUNCT
ejpam-4850	397	32	2γ	2γ	NOUN
ejpam-4850	397	33	)	)	PUNCT
ejpam-4850	397	34	and	and	CCONJ
ejpam-4850	397	35	r	r	NOUN
ejpam-4850	397	36	(	(	PUNCT
ejpam-4850	397	37	j	j	PROPN
ejpam-4850	397	38	,	,	PUNCT
ejpam-4850	397	39	λ	λ	PROPN
ejpam-4850	397	40	)	)	PUNCT
ejpam-4850	397	41	denotes	denote	VERB
ejpam-4850	397	42	the	the	DET
ejpam-4850	397	43	associated	associated	ADJ
ejpam-4850	397	44	approximation	approximation	NOUN
ejpam-4850	397	45	error	error	NOUN
ejpam-4850	397	46	.	.	PUNCT
ejpam-4850	398	1	proposition	proposition	NOUN
ejpam-4850	398	2	1	1	NUM
ejpam-4850	398	3	.	.	PUNCT
ejpam-4850	398	4	suppose	suppose	VERB
ejpam-4850	398	5	m	m	VERB
ejpam-4850	398	6	∈	∈	PROPN
ejpam-4850	398	7	n	n	PROPN
ejpam-4850	398	8	and	and	CCONJ
ejpam-4850	398	9	j	j	NOUN
ejpam-4850	398	10	:	:	PUNCT
ejpam-4850	399	1	[	[	X
ejpam-4850	399	2	a	a	X
ejpam-4850	399	3	,	,	PUNCT
ejpam-4850	399	4	b	b	NOUN
ejpam-4850	399	5	]	]	X
ejpam-4850	399	6	→	→	PUNCT
ejpam-4850	399	7	rγ	rγ	PRON
ejpam-4850	399	8	is	be	AUX
ejpam-4850	399	9	a	a	DET
ejpam-4850	399	10	differentiable	differentiable	ADJ
ejpam-4850	399	11	function	function	NOUN
ejpam-4850	399	12	on	on	ADP
ejpam-4850	399	13	[	[	X
ejpam-4850	399	14	a	a	X
ejpam-4850	399	15	,	,	PUNCT
ejpam-4850	399	16	b	b	NOUN
ejpam-4850	399	17	]	]	X
ejpam-4850	399	18	,	,	PUNCT
ejpam-4850	399	19	where	where	SCONJ
ejpam-4850	399	20	0	0	NUM
ejpam-4850	399	21	≤	≤	NOUN
ejpam-4850	399	22	a	a	DET
ejpam-4850	399	23	<	<	X
ejpam-4850	399	24	b	b	PROPN
ejpam-4850	399	25	and	and	CCONJ
ejpam-4850	399	26	j	j	PROPN
ejpam-4850	399	27	(	(	PUNCT
ejpam-4850	399	28	γ	γ	PROPN
ejpam-4850	399	29	)	)	PUNCT
ejpam-4850	399	30	∈	∈	NOUN
ejpam-4850	399	31	cγ	cγ	NOUN
ejpam-4850	399	32	[	[	X
ejpam-4850	399	33	a	a	X
ejpam-4850	399	34	,	,	PUNCT
ejpam-4850	399	35	b	b	NOUN
ejpam-4850	399	36	]	]	X
ejpam-4850	399	37	.	.	PUNCT
ejpam-4850	400	1	if	if	SCONJ
ejpam-4850	400	2	∣∣j	∣∣j	NOUN
ejpam-4850	400	3	(	(	PUNCT
ejpam-4850	400	4	γ	γ	NOUN
ejpam-4850	400	5	)	)	PUNCT
ejpam-4850	400	6	∣∣	∣∣	NUM
ejpam-4850	400	7	is	be	AUX
ejpam-4850	400	8	a	a	DET
ejpam-4850	400	9	generalized	generalized	ADJ
ejpam-4850	400	10	s	s	NOUN
ejpam-4850	400	11	-	-	ADJ
ejpam-4850	400	12	convex	convex	ADJ
ejpam-4850	400	13	function	function	NOUN
ejpam-4850	400	14	,	,	PUNCT
ejpam-4850	400	15	then	then	ADV
ejpam-4850	400	16	we	we	PRON
ejpam-4850	400	17	have	have	VERB
ejpam-4850	400	18	|r	|r	PROPN
ejpam-4850	400	19	(	(	PUNCT
ejpam-4850	400	20	j	j	PROPN
ejpam-4850	400	21	,	,	PUNCT
ejpam-4850	400	22	λ)|	λ)|	PROPN
ejpam-4850	400	23	≤	≤	NOUN
ejpam-4850	400	24	m−1∑	m−1∑	NUM
ejpam-4850	400	25	k=0	k=0	PROPN
ejpam-4850	400	26	(	(	PUNCT
ejpam-4850	400	27	x−yk	x−yk	PROPN
ejpam-4850	400	28	)	)	PUNCT
ejpam-4850	400	29	2γ	2γ	NUM
ejpam-4850	400	30	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	400	31	)	)	PUNCT
ejpam-4850	400	32	(	(	PUNCT
ejpam-4850	400	33	(	(	PUNCT
ejpam-4850	400	34	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	400	35	)	)	PUNCT
ejpam-4850	400	36	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	400	37	)	)	PUNCT
ejpam-4850	400	38	−	−	PROPN
ejpam-4850	400	39	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	400	40	)	)	PUNCT
ejpam-4850	400	41	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	400	42	)	)	PUNCT
ejpam-4850	400	43	)	)	PUNCT
ejpam-4850	401	1	(	(	PUNCT
ejpam-4850	401	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	401	3	(	(	PUNCT
ejpam-4850	401	4	γ	γ	PROPN
ejpam-4850	401	5	)	)	PUNCT
ejpam-4850	401	6	(	(	PUNCT
ejpam-4850	401	7	yk	yk	PROPN
ejpam-4850	401	8	)	)	PUNCT
ejpam-4850	401	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	401	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	401	11	(	(	PUNCT
ejpam-4850	401	12	γ	γ	PROPN
ejpam-4850	401	13	)	)	PUNCT
ejpam-4850	401	14	(	(	PUNCT
ejpam-4850	401	15	yk+1	yk+1	NOUN
ejpam-4850	401	16	)	)	PUNCT
ejpam-4850	401	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	401	18	)	)	PUNCT
ejpam-4850	402	1	+	+	CCONJ
ejpam-4850	402	2	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	402	3	)	)	PUNCT
ejpam-4850	402	4	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	402	5	)	)	PUNCT
ejpam-4850	402	6	(	(	PUNCT
ejpam-4850	402	7	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	402	8	(	(	PUNCT
ejpam-4850	402	9	γ	γ	PROPN
ejpam-4850	402	10	)	)	PUNCT
ejpam-4850	402	11	(	(	PUNCT
ejpam-4850	402	12	x	x	X
ejpam-4850	402	13	)	)	PUNCT
ejpam-4850	402	14	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	402	15	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	402	16	(	(	PUNCT
ejpam-4850	402	17	γ	γ	PROPN
ejpam-4850	402	18	)	)	PUNCT
ejpam-4850	402	19	(	(	PUNCT
ejpam-4850	402	20	yk	yk	NOUN
ejpam-4850	402	21	+	+	PROPN
ejpam-4850	402	22	yk+1	yk+1	NUM
ejpam-4850	402	23	−	−	NOUN
ejpam-4850	402	24	x	x	NOUN
ejpam-4850	402	25	)	)	PUNCT
ejpam-4850	402	26	∣∣∣	∣∣∣	ADJ
ejpam-4850	402	27	)	)	PUNCT
ejpam-4850	402	28	)	)	PUNCT
ejpam-4850	403	1	+	+	CCONJ
ejpam-4850	403	2	(	(	PUNCT
ejpam-4850	403	3	yk+yk+1−2x)2γ	yk+yk+1−2x)2γ	NUM
ejpam-4850	403	4	4γγ(1+γ	4γγ(1+γ	NUM
ejpam-4850	403	5	)	)	PUNCT
ejpam-4850	403	6	(	(	PUNCT
ejpam-4850	403	7	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	403	8	)	)	PUNCT
ejpam-4850	403	9	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	403	10	)	)	PUNCT
ejpam-4850	403	11	(	(	PUNCT
ejpam-4850	403	12	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	403	13	(	(	PUNCT
ejpam-4850	403	14	γ	γ	PROPN
ejpam-4850	403	15	)	)	PUNCT
ejpam-4850	403	16	(	(	PUNCT
ejpam-4850	403	17	x	x	X
ejpam-4850	403	18	)	)	PUNCT
ejpam-4850	403	19	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	403	20	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	403	21	(	(	PUNCT
ejpam-4850	403	22	γ	γ	PROPN
ejpam-4850	403	23	)	)	PUNCT
ejpam-4850	403	24	(	(	PUNCT
ejpam-4850	403	25	yk	yk	NOUN
ejpam-4850	403	26	+	+	PROPN
ejpam-4850	403	27	yk+1	yk+1	NUM
ejpam-4850	403	28	−	−	NOUN
ejpam-4850	403	29	x	x	NOUN
ejpam-4850	403	30	)	)	PUNCT
ejpam-4850	403	31	∣∣∣	∣∣∣	ADJ
ejpam-4850	403	32	)	)	PUNCT
ejpam-4850	404	1	+	+	CCONJ
ejpam-4850	404	2	2γ	2γ	NOUN
ejpam-4850	404	3	(	(	PUNCT
ejpam-4850	404	4	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	404	5	)	)	PUNCT
ejpam-4850	404	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	404	7	)	)	PUNCT
ejpam-4850	404	8	−	−	PROPN
ejpam-4850	404	9	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	404	10	)	)	PUNCT
ejpam-4850	404	11	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	404	12	)	)	PUNCT
ejpam-4850	404	13	)	)	PUNCT
ejpam-4850	405	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	405	2	(	(	PUNCT
ejpam-4850	405	3	γ	γ	PROPN
ejpam-4850	405	4	)	)	PUNCT
ejpam-4850	405	5	(	(	PUNCT
ejpam-4850	405	6	yk+yk+1	yk+yk+1	ADP
ejpam-4850	405	7	2	2	NUM
ejpam-4850	405	8	)	)	PUNCT
ejpam-4850	405	9	∣∣∣	∣∣∣	NOUN
ejpam-4850	405	10	)	)	PUNCT
ejpam-4850	405	11	.	.	PUNCT
ejpam-4850	406	1	w.	w.	PROPN
ejpam-4850	406	2	saleh	saleh	PROPN
ejpam-4850	406	3	et	et	PROPN
ejpam-4850	406	4	al	al	PROPN
ejpam-4850	406	5	.	.	PUNCT
ejpam-4850	406	6	/	/	SYM
ejpam-4850	406	7	eur	eur	PROPN
ejpam-4850	406	8	.	.	PUNCT
ejpam-4850	407	1	j.	j.	PROPN
ejpam-4850	407	2	pure	pure	PROPN
ejpam-4850	407	3	appl	appl	PROPN
ejpam-4850	407	4	.	.	PROPN
ejpam-4850	407	5	math	math	PROPN
ejpam-4850	407	6	,	,	PUNCT
ejpam-4850	407	7	16	16	NUM
ejpam-4850	407	8	(	(	PUNCT
ejpam-4850	407	9	3	3	NUM
ejpam-4850	407	10	)	)	PUNCT
ejpam-4850	407	11	(	(	PUNCT
ejpam-4850	407	12	2023	2023	NUM
ejpam-4850	407	13	)	)	PUNCT
ejpam-4850	407	14	,	,	PUNCT
ejpam-4850	407	15	1359	1359	NUM
ejpam-4850	407	16	-	-	SYM
ejpam-4850	407	17	1380	1380	NUM
ejpam-4850	407	18	1377	1377	NUM
ejpam-4850	407	19	proof	proof	NOUN
ejpam-4850	407	20	.	.	PUNCT
ejpam-4850	408	1	applying	apply	VERB
ejpam-4850	408	2	theorem	theorem	NOUN
ejpam-4850	408	3	1	1	NUM
ejpam-4850	408	4	on	on	ADP
ejpam-4850	408	5	the	the	DET
ejpam-4850	408	6	subintervals	subinterval	NOUN
ejpam-4850	408	7	[	[	X
ejpam-4850	408	8	yk	yk	PROPN
ejpam-4850	408	9	,	,	PUNCT
ejpam-4850	408	10	yk+1	yk+1	NOUN
ejpam-4850	408	11	]	]	X
ejpam-4850	408	12	,	,	PUNCT
ejpam-4850	408	13	(	(	PUNCT
ejpam-4850	408	14	k	k	NOUN
ejpam-4850	408	15	=	=	SYM
ejpam-4850	408	16	0	0	NUM
ejpam-4850	408	17	,	,	PUNCT
ejpam-4850	408	18	1	1	NUM
ejpam-4850	408	19	,	,	PUNCT
ejpam-4850	408	20	...	...	PUNCT
ejpam-4850	408	21	,	,	PUNCT
ejpam-4850	408	22	m−	m−	PROPN
ejpam-4850	408	23	1	1	NUM
ejpam-4850	408	24	)	)	PUNCT
ejpam-4850	408	25	of	of	ADP
ejpam-4850	408	26	the	the	DET
ejpam-4850	408	27	partition	partition	NOUN
ejpam-4850	408	28	λ	λ	PROPN
ejpam-4850	408	29	,	,	PUNCT
ejpam-4850	408	30	we	we	PRON
ejpam-4850	408	31	get∣∣∣j	get∣∣∣j	VERB
ejpam-4850	408	32	(	(	PUNCT
ejpam-4850	408	33	x)+j	x)+j	NOUN
ejpam-4850	408	34	(	(	PUNCT
ejpam-4850	408	35	yk+yk+1−x	yk+yk+1−x	NOUN
ejpam-4850	408	36	)	)	PUNCT
ejpam-4850	408	37	2γ	2γ	NOUN
ejpam-4850	408	38	−	−	PROPN
ejpam-4850	408	39	γ(γ+1	γ(γ+1	NUM
ejpam-4850	408	40	)	)	PUNCT
ejpam-4850	408	41	(	(	PUNCT
ejpam-4850	408	42	yk+1−yk	yk+1−yk	PROPN
ejpam-4850	408	43	)	)	PUNCT
ejpam-4850	408	44	γ	γ	NOUN
ejpam-4850	408	45	yki	yki	NOUN
ejpam-4850	408	46	γ	γ	X
ejpam-4850	408	47	yk+1	yk+1	PRON
ejpam-4850	408	48	j	j	PROPN
ejpam-4850	408	49	(	(	PUNCT
ejpam-4850	408	50	t	t	PROPN
ejpam-4850	408	51	)	)	PUNCT
ejpam-4850	408	52	∣∣∣	∣∣∣	NOUN
ejpam-4850	408	53	≤	≤	PROPN
ejpam-4850	408	54	(	(	PUNCT
ejpam-4850	408	55	x−yk	x−yk	NOUN
ejpam-4850	408	56	)	)	PUNCT
ejpam-4850	408	57	2γ	2γ	NOUN
ejpam-4850	408	58	(	(	PUNCT
ejpam-4850	408	59	yk+1−yk	yk+1−yk	ADJ
ejpam-4850	408	60	)	)	PUNCT
ejpam-4850	408	61	γ	γ	X
ejpam-4850	408	62	(	(	PUNCT
ejpam-4850	408	63	(	(	PUNCT
ejpam-4850	408	64	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	408	65	)	)	PUNCT
ejpam-4850	408	66	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	408	67	)	)	PUNCT
ejpam-4850	408	68	−	−	PROPN
ejpam-4850	408	69	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	408	70	)	)	PUNCT
ejpam-4850	408	71	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	408	72	)	)	PUNCT
ejpam-4850	408	73	)	)	PUNCT
ejpam-4850	409	1	(	(	PUNCT
ejpam-4850	409	2	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	409	3	(	(	PUNCT
ejpam-4850	409	4	γ	γ	PROPN
ejpam-4850	409	5	)	)	PUNCT
ejpam-4850	409	6	(	(	PUNCT
ejpam-4850	409	7	yk	yk	PROPN
ejpam-4850	409	8	)	)	PUNCT
ejpam-4850	409	9	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	409	10	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	409	11	(	(	PUNCT
ejpam-4850	409	12	γ	γ	PROPN
ejpam-4850	409	13	)	)	PUNCT
ejpam-4850	409	14	(	(	PUNCT
ejpam-4850	409	15	yk+1	yk+1	NOUN
ejpam-4850	409	16	)	)	PUNCT
ejpam-4850	409	17	∣∣∣	∣∣∣	ADJ
ejpam-4850	409	18	)	)	PUNCT
ejpam-4850	410	1	+	+	CCONJ
ejpam-4850	410	2	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	410	3	)	)	PUNCT
ejpam-4850	410	4	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	410	5	)	)	PUNCT
ejpam-4850	410	6	(	(	PUNCT
ejpam-4850	410	7	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	410	8	(	(	PUNCT
ejpam-4850	410	9	γ	γ	PROPN
ejpam-4850	410	10	)	)	PUNCT
ejpam-4850	410	11	(	(	PUNCT
ejpam-4850	410	12	x	x	X
ejpam-4850	410	13	)	)	PUNCT
ejpam-4850	410	14	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	410	15	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	410	16	(	(	PUNCT
ejpam-4850	410	17	γ	γ	PROPN
ejpam-4850	410	18	)	)	PUNCT
ejpam-4850	410	19	(	(	PUNCT
ejpam-4850	410	20	yk	yk	NOUN
ejpam-4850	410	21	+	+	PROPN
ejpam-4850	410	22	yk+1	yk+1	NUM
ejpam-4850	410	23	−	−	NOUN
ejpam-4850	410	24	x	x	NOUN
ejpam-4850	410	25	)	)	PUNCT
ejpam-4850	410	26	∣∣∣	∣∣∣	ADJ
ejpam-4850	410	27	)	)	PUNCT
ejpam-4850	410	28	)	)	PUNCT
ejpam-4850	411	1	+	+	CCONJ
ejpam-4850	411	2	(	(	PUNCT
ejpam-4850	411	3	yk+yk+1−2x)2γ	yk+yk+1−2x)2γ	NUM
ejpam-4850	411	4	4γ(yk+1−yk	4γ(yk+1−yk	NUM
ejpam-4850	411	5	)	)	PUNCT
ejpam-4850	411	6	γ	γ	PROPN
ejpam-4850	411	7	(	(	PUNCT
ejpam-4850	411	8	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	411	9	)	)	PUNCT
ejpam-4850	411	10	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	411	11	)	)	PUNCT
ejpam-4850	411	12	(	(	PUNCT
ejpam-4850	411	13	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	411	14	(	(	PUNCT
ejpam-4850	411	15	γ	γ	PROPN
ejpam-4850	411	16	)	)	PUNCT
ejpam-4850	411	17	(	(	PUNCT
ejpam-4850	411	18	x	x	X
ejpam-4850	411	19	)	)	PUNCT
ejpam-4850	411	20	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	411	21	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	411	22	(	(	PUNCT
ejpam-4850	411	23	γ	γ	PROPN
ejpam-4850	411	24	)	)	PUNCT
ejpam-4850	411	25	(	(	PUNCT
ejpam-4850	411	26	yk	yk	NOUN
ejpam-4850	411	27	+	+	PROPN
ejpam-4850	411	28	yk+1	yk+1	NUM
ejpam-4850	411	29	−	−	NOUN
ejpam-4850	411	30	x	x	NOUN
ejpam-4850	411	31	)	)	PUNCT
ejpam-4850	411	32	∣∣∣	∣∣∣	ADJ
ejpam-4850	411	33	)	)	PUNCT
ejpam-4850	412	1	+	+	CCONJ
ejpam-4850	412	2	2γ	2γ	NOUN
ejpam-4850	412	3	(	(	PUNCT
ejpam-4850	412	4	γ(1+sγ	γ(1+sγ	PROPN
ejpam-4850	412	5	)	)	PUNCT
ejpam-4850	412	6	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	412	7	)	)	PUNCT
ejpam-4850	412	8	−	−	PROPN
ejpam-4850	412	9	γ(1+(s+1)γ	γ(1+(s+1)γ	PROPN
ejpam-4850	412	10	)	)	PUNCT
ejpam-4850	412	11	γ(1+(s+2)γ	γ(1+(s+2)γ	PROPN
ejpam-4850	412	12	)	)	PUNCT
ejpam-4850	412	13	)	)	PUNCT
ejpam-4850	413	1	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	413	2	(	(	PUNCT
ejpam-4850	413	3	γ	γ	PROPN
ejpam-4850	413	4	)	)	PUNCT
ejpam-4850	413	5	(	(	PUNCT
ejpam-4850	413	6	yk+yk+1	yk+yk+1	ADP
ejpam-4850	413	7	2	2	NUM
ejpam-4850	413	8	)	)	PUNCT
ejpam-4850	413	9	∣∣∣	∣∣∣	NOUN
ejpam-4850	413	10	)	)	PUNCT
ejpam-4850	413	11	.	.	PUNCT
ejpam-4850	414	1	we	we	PRON
ejpam-4850	414	2	can	can	AUX
ejpam-4850	414	3	obtain	obtain	VERB
ejpam-4850	414	4	the	the	DET
ejpam-4850	414	5	desired	desire	VERB
ejpam-4850	414	6	result	result	NOUN
ejpam-4850	414	7	by	by	ADP
ejpam-4850	414	8	multiplying	multiply	VERB
ejpam-4850	414	9	both	both	DET
ejpam-4850	414	10	sides	side	NOUN
ejpam-4850	414	11	of	of	ADP
ejpam-4850	414	12	the	the	DET
ejpam-4850	414	13	inequality	inequality	NOUN
ejpam-4850	414	14	above	above	ADV
ejpam-4850	414	15	by	by	ADP
ejpam-4850	414	16	(	(	PUNCT
ejpam-4850	414	17	yk+1−yk	yk+1−yk	PROPN
ejpam-4850	414	18	)	)	PUNCT
ejpam-4850	414	19	γ	γ	PROPN
ejpam-4850	414	20	γ(1+γ	γ(1+γ	PROPN
ejpam-4850	414	21	)	)	PUNCT
ejpam-4850	414	22	,	,	PUNCT
ejpam-4850	414	23	summing	sum	VERB
ejpam-4850	414	24	the	the	DET
ejpam-4850	414	25	resulting	result	VERB
ejpam-4850	414	26	inequalities	inequality	NOUN
ejpam-4850	414	27	for	for	ADP
ejpam-4850	414	28	all	all	PRON
ejpam-4850	414	29	k	k	NOUN
ejpam-4850	414	30	=	=	SYM
ejpam-4850	414	31	0	0	NUM
ejpam-4850	414	32	,	,	PUNCT
ejpam-4850	414	33	1	1	NUM
ejpam-4850	414	34	,	,	PUNCT
ejpam-4850	414	35	...	...	PUNCT
ejpam-4850	414	36	,	,	PUNCT
ejpam-4850	414	37	m−	m−	PROPN
ejpam-4850	414	38	1	1	NUM
ejpam-4850	414	39	,	,	PUNCT
ejpam-4850	414	40	and	and	CCONJ
ejpam-4850	414	41	then	then	ADV
ejpam-4850	414	42	applying	apply	VERB
ejpam-4850	414	43	the	the	DET
ejpam-4850	414	44	triangular	triangular	NOUN
ejpam-4850	414	45	inequality	inequality	NOUN
ejpam-4850	414	46	.	.	PUNCT
ejpam-4850	415	1	proposition	proposition	NOUN
ejpam-4850	415	2	2	2	NUM
ejpam-4850	415	3	.	.	PUNCT
ejpam-4850	415	4	suppose	suppose	VERB
ejpam-4850	415	5	m	m	VERB
ejpam-4850	415	6	∈	∈	PROPN
ejpam-4850	415	7	n	n	PROPN
ejpam-4850	415	8	and	and	CCONJ
ejpam-4850	415	9	j	j	NOUN
ejpam-4850	415	10	:	:	PUNCT
ejpam-4850	416	1	[	[	X
ejpam-4850	416	2	a	a	X
ejpam-4850	416	3	,	,	PUNCT
ejpam-4850	416	4	b	b	NOUN
ejpam-4850	416	5	]	]	X
ejpam-4850	416	6	→	→	PUNCT
ejpam-4850	416	7	rγ	rγ	PRON
ejpam-4850	416	8	is	be	AUX
ejpam-4850	416	9	a	a	DET
ejpam-4850	416	10	differentiable	differentiable	ADJ
ejpam-4850	416	11	function	function	NOUN
ejpam-4850	416	12	on	on	ADP
ejpam-4850	416	13	[	[	X
ejpam-4850	416	14	a	a	X
ejpam-4850	416	15	,	,	PUNCT
ejpam-4850	416	16	b	b	NOUN
ejpam-4850	416	17	]	]	X
ejpam-4850	416	18	,	,	PUNCT
ejpam-4850	416	19	where	where	SCONJ
ejpam-4850	416	20	0	0	NUM
ejpam-4850	416	21	≤	≤	NOUN
ejpam-4850	416	22	a	a	DET
ejpam-4850	416	23	<	<	X
ejpam-4850	416	24	b	b	PROPN
ejpam-4850	416	25	and	and	CCONJ
ejpam-4850	416	26	j	j	PROPN
ejpam-4850	416	27	(	(	PUNCT
ejpam-4850	416	28	γ	γ	PROPN
ejpam-4850	416	29	)	)	PUNCT
ejpam-4850	416	30	∈	∈	NOUN
ejpam-4850	416	31	cγ	cγ	NOUN
ejpam-4850	416	32	[	[	X
ejpam-4850	416	33	a	a	X
ejpam-4850	416	34	,	,	PUNCT
ejpam-4850	416	35	b	b	NOUN
ejpam-4850	416	36	]	]	X
ejpam-4850	416	37	.	.	PUNCT
ejpam-4850	417	1	if	if	SCONJ
ejpam-4850	417	2	∣∣j	∣∣j	NOUN
ejpam-4850	417	3	(	(	PUNCT
ejpam-4850	417	4	γ	γ	NOUN
ejpam-4850	417	5	)	)	PUNCT
ejpam-4850	417	6	∣∣q	∣∣q	NUM
ejpam-4850	417	7	is	be	AUX
ejpam-4850	417	8	a	a	DET
ejpam-4850	417	9	generalized	generalized	ADJ
ejpam-4850	417	10	s	s	NOUN
ejpam-4850	417	11	-	-	PUNCT
ejpam-4850	417	12	concave	concave	ADJ
ejpam-4850	417	13	,	,	PUNCT
ejpam-4850	417	14	where	where	SCONJ
ejpam-4850	417	15	q	q	X
ejpam-4850	417	16	>	>	X
ejpam-4850	417	17	1	1	NUM
ejpam-4850	417	18	with	with	ADP
ejpam-4850	417	19	1	1	NUM
ejpam-4850	417	20	p	p	NOUN
ejpam-4850	417	21	+	+	NOUN
ejpam-4850	417	22	1	1	NUM
ejpam-4850	417	23	q	q	NOUN
ejpam-4850	417	24	=	=	SYM
ejpam-4850	417	25	1	1	NUM
ejpam-4850	417	26	,	,	PUNCT
ejpam-4850	417	27	then	then	ADV
ejpam-4850	417	28	we	we	PRON
ejpam-4850	417	29	have	have	VERB
ejpam-4850	417	30	|r	|r	PROPN
ejpam-4850	417	31	(	(	PUNCT
ejpam-4850	417	32	j	j	PROPN
ejpam-4850	417	33	,	,	PUNCT
ejpam-4850	417	34	λ)|	λ)|	PROPN
ejpam-4850	417	35	≤	≤	NOUN
ejpam-4850	417	36	m−1∑	m−1∑	NUM
ejpam-4850	417	37	k=0	k=0	PROPN
ejpam-4850	417	38	(	(	PUNCT
ejpam-4850	417	39	γ(1+pγ	γ(1+pγ	NUM
ejpam-4850	417	40	)	)	PUNCT
ejpam-4850	417	41	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	417	42	)	)	PUNCT
ejpam-4850	417	43	)	)	PUNCT
ejpam-4850	417	44	1	1	NUM
ejpam-4850	417	45	p	p	NOUN
ejpam-4850	417	46	(	(	PUNCT
ejpam-4850	417	47	(	(	PUNCT
ejpam-4850	417	48	x−yk	x−yk	PROPN
ejpam-4850	417	49	)	)	PUNCT
ejpam-4850	417	50	2γ	2γ	NUM
ejpam-4850	417	51	γ(1+γ	γ(1+γ	NOUN
ejpam-4850	417	52	)	)	PUNCT
ejpam-4850	417	53	(	(	PUNCT
ejpam-4850	417	54	(	(	PUNCT
ejpam-4850	417	55	x−yk	x−yk	PROPN
ejpam-4850	417	56	)	)	PUNCT
ejpam-4850	417	57	γ2(s−1)γ	γ2(s−1)γ	PROPN
ejpam-4850	417	58	γ(1+γ	γ(1+γ	PROPN
ejpam-4850	417	59	)	)	PUNCT
ejpam-4850	417	60	)	)	PUNCT
ejpam-4850	417	61	1	1	NUM
ejpam-4850	417	62	q	q	NOUN
ejpam-4850	417	63	(	(	PUNCT
ejpam-4850	417	64	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	417	65	(	(	PUNCT
ejpam-4850	417	66	γ	γ	PROPN
ejpam-4850	417	67	)	)	PUNCT
ejpam-4850	417	68	(	(	PUNCT
ejpam-4850	417	69	yk+x	yk+x	PROPN
ejpam-4850	417	70	2	2	NUM
ejpam-4850	417	71	)	)	PUNCT
ejpam-4850	417	72	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	417	73	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	417	74	(	(	PUNCT
ejpam-4850	417	75	γ	γ	PROPN
ejpam-4850	417	76	)	)	PUNCT
ejpam-4850	417	77	(	(	PUNCT
ejpam-4850	417	78	yk+2yk+1−x	yk+2yk+1−x	NOUN
ejpam-4850	417	79	2	2	NUM
ejpam-4850	417	80	)	)	PUNCT
ejpam-4850	417	81	∣∣∣	∣∣∣	ADJ
ejpam-4850	417	82	)	)	PUNCT
ejpam-4850	417	83	+	+	CCONJ
ejpam-4850	417	84	(	(	PUNCT
ejpam-4850	417	85	yk+yk+1−2x)2γ	yk+yk+1−2x)2γ	NUM
ejpam-4850	417	86	4γγ(1+γ	4γγ(1+γ	NUM
ejpam-4850	417	87	)	)	PUNCT
ejpam-4850	417	88	(	(	PUNCT
ejpam-4850	417	89	(	(	PUNCT
ejpam-4850	417	90	yk+yk+1−2x)γ2(s−1)γ	yk+yk+1−2x)γ2(s−1)γ	PROPN
ejpam-4850	417	91	2γγ(1+γ	2γγ(1+γ	NUM
ejpam-4850	417	92	)	)	PUNCT
ejpam-4850	417	93	)	)	PUNCT
ejpam-4850	417	94	1	1	NUM
ejpam-4850	417	95	q	q	NOUN
ejpam-4850	417	96	(	(	PUNCT
ejpam-4850	417	97	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	417	98	(	(	PUNCT
ejpam-4850	417	99	γ	γ	PROPN
ejpam-4850	417	100	)	)	PUNCT
ejpam-4850	417	101	(	(	PUNCT
ejpam-4850	417	102	yk+yk+1	yk+yk+1	ADP
ejpam-4850	417	103	+	+	ADJ
ejpam-4850	417	104	2x	2x	NUM
ejpam-4850	417	105	4	4	NUM
ejpam-4850	417	106	)	)	PUNCT
ejpam-4850	417	107	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	417	108	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	417	109	(	(	PUNCT
ejpam-4850	417	110	γ	γ	PROPN
ejpam-4850	417	111	)	)	PUNCT
ejpam-4850	417	112	(	(	PUNCT
ejpam-4850	417	113	3yk+3yk+1−2x	3yk+3yk+1−2x	NOUN
ejpam-4850	417	114	4	4	NUM
ejpam-4850	417	115	)	)	PUNCT
ejpam-4850	417	116	∣∣∣	∣∣∣	NOUN
ejpam-4850	417	117	)	)	PUNCT
ejpam-4850	417	118	)	)	PUNCT
ejpam-4850	417	119	.	.	PUNCT
ejpam-4850	418	1	proof	proof	NOUN
ejpam-4850	418	2	.	.	PUNCT
ejpam-4850	419	1	applying	apply	VERB
ejpam-4850	419	2	theorem	theorem	NOUN
ejpam-4850	419	3	4	4	NUM
ejpam-4850	419	4	on	on	ADP
ejpam-4850	419	5	the	the	DET
ejpam-4850	419	6	subintervals	subinterval	NOUN
ejpam-4850	420	1	[	[	X
ejpam-4850	420	2	yk	yk	PROPN
ejpam-4850	420	3	,	,	PUNCT
ejpam-4850	420	4	yk+1	yk+1	NOUN
ejpam-4850	420	5	]	]	X
ejpam-4850	420	6	,	,	PUNCT
ejpam-4850	420	7	(	(	PUNCT
ejpam-4850	420	8	k	k	NOUN
ejpam-4850	420	9	=	=	SYM
ejpam-4850	420	10	0	0	NUM
ejpam-4850	420	11	,	,	PUNCT
ejpam-4850	420	12	1	1	NUM
ejpam-4850	420	13	,	,	PUNCT
ejpam-4850	420	14	...	...	PUNCT
ejpam-4850	420	15	,	,	PUNCT
ejpam-4850	420	16	m−	m−	PROPN
ejpam-4850	420	17	1	1	NUM
ejpam-4850	420	18	)	)	PUNCT
ejpam-4850	420	19	of	of	ADP
ejpam-4850	420	20	the	the	DET
ejpam-4850	420	21	partition	partition	NOUN
ejpam-4850	420	22	λ	λ	PROPN
ejpam-4850	420	23	,	,	PUNCT
ejpam-4850	420	24	we	we	PRON
ejpam-4850	420	25	get∣∣∣j	get∣∣∣j	VERB
ejpam-4850	420	26	(	(	PUNCT
ejpam-4850	420	27	x)+j	x)+j	NOUN
ejpam-4850	420	28	(	(	PUNCT
ejpam-4850	420	29	yk+yk+1−x	yk+yk+1−x	NOUN
ejpam-4850	420	30	)	)	PUNCT
ejpam-4850	420	31	2γ	2γ	NOUN
ejpam-4850	420	32	−	−	PROPN
ejpam-4850	420	33	γ(γ+1	γ(γ+1	NUM
ejpam-4850	420	34	)	)	PUNCT
ejpam-4850	420	35	(	(	PUNCT
ejpam-4850	420	36	yk+1−yk	yk+1−yk	PROPN
ejpam-4850	420	37	)	)	PUNCT
ejpam-4850	420	38	γ	γ	NOUN
ejpam-4850	420	39	yki	yki	NOUN
ejpam-4850	420	40	γ	γ	X
ejpam-4850	420	41	yk+1	yk+1	PRON
ejpam-4850	420	42	j	j	PROPN
ejpam-4850	420	43	(	(	PUNCT
ejpam-4850	420	44	t	t	PROPN
ejpam-4850	420	45	)	)	PUNCT
ejpam-4850	420	46	∣∣∣	∣∣∣	NOUN
ejpam-4850	420	47	≤	≤	PROPN
ejpam-4850	420	48	(	(	PUNCT
ejpam-4850	420	49	γ(1+pγ	γ(1+pγ	NUM
ejpam-4850	420	50	)	)	PUNCT
ejpam-4850	420	51	γ(1+(p+1)γ	γ(1+(p+1)γ	PROPN
ejpam-4850	420	52	)	)	PUNCT
ejpam-4850	420	53	)	)	PUNCT
ejpam-4850	420	54	1	1	NUM
ejpam-4850	420	55	p	p	NOUN
ejpam-4850	420	56	(	(	PUNCT
ejpam-4850	420	57	(	(	PUNCT
ejpam-4850	420	58	x−yk	x−yk	NOUN
ejpam-4850	420	59	)	)	PUNCT
ejpam-4850	420	60	2γ	2γ	NOUN
ejpam-4850	420	61	(	(	PUNCT
ejpam-4850	420	62	yk+1−yk	yk+1−yk	ADJ
ejpam-4850	420	63	)	)	PUNCT
ejpam-4850	420	64	γ	γ	X
ejpam-4850	420	65	(	(	PUNCT
ejpam-4850	420	66	(	(	PUNCT
ejpam-4850	420	67	x−yk	x−yk	PROPN
ejpam-4850	420	68	)	)	PUNCT
ejpam-4850	420	69	γ2(s−1)γ	γ2(s−1)γ	PROPN
ejpam-4850	420	70	γ(1+γ	γ(1+γ	PROPN
ejpam-4850	420	71	)	)	PUNCT
ejpam-4850	420	72	)	)	PUNCT
ejpam-4850	420	73	1	1	NUM
ejpam-4850	420	74	q	q	NOUN
ejpam-4850	420	75	(	(	PUNCT
ejpam-4850	420	76	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	420	77	(	(	PUNCT
ejpam-4850	420	78	γ	γ	PROPN
ejpam-4850	420	79	)	)	PUNCT
ejpam-4850	420	80	(	(	PUNCT
ejpam-4850	420	81	yk+x	yk+x	PROPN
ejpam-4850	420	82	2	2	NUM
ejpam-4850	420	83	)	)	PUNCT
ejpam-4850	420	84	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	420	85	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	420	86	(	(	PUNCT
ejpam-4850	420	87	γ	γ	PROPN
ejpam-4850	420	88	)	)	PUNCT
ejpam-4850	420	89	(	(	PUNCT
ejpam-4850	420	90	yk+2yk+1−x	yk+2yk+1−x	NOUN
ejpam-4850	420	91	2	2	NUM
ejpam-4850	420	92	)	)	PUNCT
ejpam-4850	420	93	∣∣∣	∣∣∣	ADJ
ejpam-4850	420	94	)	)	PUNCT
ejpam-4850	421	1	+	+	CCONJ
ejpam-4850	421	2	(	(	PUNCT
ejpam-4850	421	3	yk+yk+1−2x)2γ	yk+yk+1−2x)2γ	NUM
ejpam-4850	421	4	4γ(yk+1−yk	4γ(yk+1−yk	NUM
ejpam-4850	421	5	)	)	PUNCT
ejpam-4850	421	6	γ	γ	X
ejpam-4850	421	7	(	(	PUNCT
ejpam-4850	421	8	(	(	PUNCT
ejpam-4850	421	9	yk+yk+1−2x)γ2(s−1)γ	yk+yk+1−2x)γ2(s−1)γ	PROPN
ejpam-4850	421	10	2γγ(1+γ	2γγ(1+γ	NUM
ejpam-4850	421	11	)	)	PUNCT
ejpam-4850	421	12	)	)	PUNCT
ejpam-4850	421	13	1	1	NUM
ejpam-4850	421	14	q	q	NOUN
ejpam-4850	421	15	(	(	PUNCT
ejpam-4850	421	16	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	421	17	(	(	PUNCT
ejpam-4850	421	18	γ	γ	PROPN
ejpam-4850	421	19	)	)	PUNCT
ejpam-4850	421	20	(	(	PUNCT
ejpam-4850	421	21	yk+yk+1	yk+yk+1	ADP
ejpam-4850	421	22	+	+	ADJ
ejpam-4850	421	23	2x	2x	NUM
ejpam-4850	421	24	4	4	NUM
ejpam-4850	421	25	)	)	PUNCT
ejpam-4850	421	26	∣∣∣+	∣∣∣+	PROPN
ejpam-4850	421	27	∣∣∣j	∣∣∣j	PROPN
ejpam-4850	421	28	(	(	PUNCT
ejpam-4850	421	29	γ	γ	PROPN
ejpam-4850	421	30	)	)	PUNCT
ejpam-4850	421	31	(	(	PUNCT
ejpam-4850	421	32	3yk+3yk+1−2x	3yk+3yk+1−2x	NOUN
ejpam-4850	421	33	4	4	NUM
ejpam-4850	421	34	)	)	PUNCT
ejpam-4850	421	35	∣∣∣	∣∣∣	NOUN
ejpam-4850	421	36	)	)	PUNCT
ejpam-4850	421	37	)	)	PUNCT
ejpam-4850	421	38	.	.	PUNCT
ejpam-4850	422	1	we	we	PRON
ejpam-4850	422	2	can	can	AUX
ejpam-4850	422	3	obtain	obtain	VERB
ejpam-4850	422	4	the	the	DET
ejpam-4850	422	5	desired	desire	VERB
ejpam-4850	422	6	result	result	NOUN
ejpam-4850	422	7	by	by	ADP
ejpam-4850	422	8	multiplying	multiply	VERB
ejpam-4850	422	9	both	both	DET
ejpam-4850	422	10	sides	side	NOUN
ejpam-4850	422	11	of	of	ADP
ejpam-4850	422	12	the	the	DET
ejpam-4850	422	13	inequality	inequality	NOUN
ejpam-4850	422	14	above	above	ADV
ejpam-4850	422	15	by	by	ADP
ejpam-4850	422	16	(	(	PUNCT
ejpam-4850	422	17	yk+1−yk	yk+1−yk	PROPN
ejpam-4850	422	18	)	)	PUNCT
ejpam-4850	422	19	γ	γ	PROPN
ejpam-4850	422	20	γ(1+γ	γ(1+γ	PROPN
ejpam-4850	422	21	)	)	PUNCT
ejpam-4850	422	22	,	,	PUNCT
ejpam-4850	422	23	summing	sum	VERB
ejpam-4850	422	24	the	the	DET
ejpam-4850	422	25	resulting	result	VERB
ejpam-4850	422	26	inequalities	inequality	NOUN
ejpam-4850	422	27	for	for	ADP
ejpam-4850	422	28	all	all	PRON
ejpam-4850	422	29	k	k	NOUN
ejpam-4850	422	30	=	=	SYM
ejpam-4850	422	31	0	0	NUM
ejpam-4850	422	32	,	,	PUNCT
ejpam-4850	422	33	1	1	NUM
ejpam-4850	422	34	,	,	PUNCT
ejpam-4850	422	35	...	...	PUNCT
ejpam-4850	422	36	,	,	PUNCT
ejpam-4850	422	37	m−	m−	PROPN
ejpam-4850	422	38	1	1	NUM
ejpam-4850	422	39	,	,	PUNCT
ejpam-4850	422	40	and	and	CCONJ
ejpam-4850	422	41	then	then	ADV
ejpam-4850	422	42	applying	apply	VERB
ejpam-4850	422	43	the	the	DET
ejpam-4850	422	44	triangular	triangular	NOUN
ejpam-4850	422	45	inequality	inequality	NOUN
ejpam-4850	422	46	.	.	PUNCT
ejpam-4850	423	1	references	reference	NOUN
ejpam-4850	423	2	1378	1378	NUM
ejpam-4850	423	3	4	4	NUM
ejpam-4850	423	4	.	.	PUNCT
ejpam-4850	423	5	conclusion	conclusion	NOUN
ejpam-4850	423	6	in	in	ADP
ejpam-4850	423	7	conclusion	conclusion	NOUN
ejpam-4850	423	8	,	,	PUNCT
ejpam-4850	423	9	fractal	fractal	ADJ
ejpam-4850	423	10	sets	set	NOUN
ejpam-4850	423	11	and	and	CCONJ
ejpam-4850	423	12	fractal	fractal	ADJ
ejpam-4850	423	13	theory	theory	NOUN
ejpam-4850	423	14	have	have	AUX
ejpam-4850	423	15	generated	generate	VERB
ejpam-4850	423	16	significant	significant	ADJ
ejpam-4850	423	17	interest	interest	NOUN
ejpam-4850	423	18	among	among	ADP
ejpam-4850	423	19	scientists	scientist	NOUN
ejpam-4850	423	20	and	and	CCONJ
ejpam-4850	423	21	engineers	engineer	NOUN
ejpam-4850	423	22	,	,	PUNCT
ejpam-4850	423	23	particularly	particularly	ADV
ejpam-4850	423	24	with	with	ADP
ejpam-4850	423	25	regards	regard	NOUN
ejpam-4850	423	26	to	to	ADP
ejpam-4850	423	27	studying	study	VERB
ejpam-4850	423	28	the	the	DET
ejpam-4850	423	29	properties	property	NOUN
ejpam-4850	423	30	of	of	ADP
ejpam-4850	423	31	functions	function	NOUN
ejpam-4850	423	32	operating	operate	VERB
ejpam-4850	423	33	on	on	ADP
ejpam-4850	423	34	these	these	DET
ejpam-4850	423	35	sets	set	NOUN
ejpam-4850	423	36	using	use	VERB
ejpam-4850	423	37	techniques	technique	NOUN
ejpam-4850	423	38	of	of	ADP
ejpam-4850	423	39	fractional	fractional	ADJ
ejpam-4850	423	40	calculus	calculus	NOUN
ejpam-4850	423	41	.	.	PUNCT
ejpam-4850	424	1	this	this	DET
ejpam-4850	424	2	paper	paper	NOUN
ejpam-4850	424	3	contributes	contribute	VERB
ejpam-4850	424	4	to	to	ADP
ejpam-4850	424	5	this	this	DET
ejpam-4850	424	6	area	area	NOUN
ejpam-4850	424	7	of	of	ADP
ejpam-4850	424	8	research	research	NOUN
ejpam-4850	424	9	by	by	ADP
ejpam-4850	424	10	examining	examine	VERB
ejpam-4850	424	11	the	the	DET
ejpam-4850	424	12	companion	companion	NOUN
ejpam-4850	424	13	of	of	ADP
ejpam-4850	424	14	ostrowski	ostrowski	PROPN
ejpam-4850	424	15	’s	’s	PART
ejpam-4850	424	16	inequality	inequality	NOUN
ejpam-4850	424	17	within	within	ADP
ejpam-4850	424	18	the	the	DET
ejpam-4850	424	19	framework	framework	NOUN
ejpam-4850	424	20	of	of	ADP
ejpam-4850	424	21	fractal	fractal	ADJ
ejpam-4850	424	22	sets	set	NOUN
ejpam-4850	424	23	.	.	PUNCT
ejpam-4850	425	1	the	the	DET
ejpam-4850	425	2	introduction	introduction	NOUN
ejpam-4850	425	3	of	of	ADP
ejpam-4850	425	4	a	a	DET
ejpam-4850	425	5	new	new	ADJ
ejpam-4850	425	6	identity	identity	NOUN
ejpam-4850	425	7	related	relate	VERB
ejpam-4850	425	8	to	to	ADP
ejpam-4850	425	9	local	local	ADJ
ejpam-4850	425	10	fractional	fractional	ADJ
ejpam-4850	425	11	integrals	integral	NOUN
ejpam-4850	425	12	allows	allow	VERB
ejpam-4850	425	13	us	we	PRON
ejpam-4850	425	14	to	to	PART
ejpam-4850	425	15	establish	establish	VERB
ejpam-4850	425	16	several	several	ADJ
ejpam-4850	425	17	inequalities	inequality	NOUN
ejpam-4850	425	18	for	for	ADP
ejpam-4850	425	19	functions	function	NOUN
ejpam-4850	425	20	with	with	ADP
ejpam-4850	425	21	generalized	generalized	ADJ
ejpam-4850	425	22	s	s	NOUN
ejpam-4850	425	23	-	-	ADJ
ejpam-4850	425	24	convex	convex	ADJ
ejpam-4850	425	25	derivatives	derivative	NOUN
ejpam-4850	425	26	and	and	CCONJ
ejpam-4850	425	27	s	s	NOUN
ejpam-4850	425	28	-	-	PUNCT
ejpam-4850	425	29	concave	concave	ADJ
ejpam-4850	425	30	derivatives	derivative	NOUN
ejpam-4850	425	31	.	.	PUNCT
ejpam-4850	426	1	the	the	DET
ejpam-4850	426	2	correctness	correctness	NOUN
ejpam-4850	426	3	of	of	ADP
ejpam-4850	426	4	the	the	DET
ejpam-4850	426	5	results	result	NOUN
ejpam-4850	426	6	is	be	AUX
ejpam-4850	426	7	justified	justify	VERB
ejpam-4850	426	8	through	through	ADP
ejpam-4850	426	9	an	an	DET
ejpam-4850	426	10	example	example	NOUN
ejpam-4850	426	11	,	,	PUNCT
ejpam-4850	426	12	and	and	CCONJ
ejpam-4850	426	13	a	a	DET
ejpam-4850	426	14	few	few	ADJ
ejpam-4850	426	15	applications	application	NOUN
ejpam-4850	426	16	are	be	AUX
ejpam-4850	426	17	discussed	discuss	VERB
ejpam-4850	426	18	.	.	PUNCT
ejpam-4850	427	1	this	this	DET
ejpam-4850	427	2	work	work	NOUN
ejpam-4850	427	3	also	also	ADV
ejpam-4850	427	4	opens	open	VERB
ejpam-4850	427	5	up	up	ADP
ejpam-4850	427	6	new	new	ADJ
ejpam-4850	427	7	horizons	horizon	NOUN
ejpam-4850	427	8	for	for	ADP
ejpam-4850	427	9	the	the	DET
ejpam-4850	427	10	study	study	NOUN
ejpam-4850	427	11	of	of	ADP
ejpam-4850	427	12	integral	integral	ADJ
ejpam-4850	427	13	inequalities	inequality	NOUN
ejpam-4850	427	14	via	via	ADP
ejpam-4850	427	15	other	other	ADJ
ejpam-4850	427	16	types	type	NOUN
ejpam-4850	427	17	of	of	ADP
ejpam-4850	427	18	convexity	convexity	NOUN
ejpam-4850	427	19	and	and	CCONJ
ejpam-4850	427	20	for	for	ADP
ejpam-4850	427	21	functions	function	NOUN
ejpam-4850	427	22	of	of	ADP
ejpam-4850	427	23	two	two	NUM
ejpam-4850	427	24	variables	variable	NOUN
ejpam-4850	427	25	.	.	PUNCT
ejpam-4850	428	1	these	these	DET
ejpam-4850	428	2	future	future	ADJ
ejpam-4850	428	3	developments	development	NOUN
ejpam-4850	428	4	can	can	AUX
ejpam-4850	428	5	contribute	contribute	VERB
ejpam-4850	428	6	to	to	ADP
ejpam-4850	428	7	a	a	DET
ejpam-4850	428	8	deeper	deep	ADJ
ejpam-4850	428	9	understanding	understanding	NOUN
ejpam-4850	428	10	of	of	ADP
ejpam-4850	428	11	the	the	DET
ejpam-4850	428	12	properties	property	NOUN
ejpam-4850	428	13	of	of	ADP
ejpam-4850	428	14	fractal	fractal	ADJ
ejpam-4850	428	15	sets	set	NOUN
ejpam-4850	428	16	and	and	CCONJ
ejpam-4850	428	17	the	the	DET
ejpam-4850	428	18	functions	function	NOUN
ejpam-4850	428	19	that	that	PRON
ejpam-4850	428	20	operate	operate	VERB
ejpam-4850	428	21	on	on	ADP
ejpam-4850	428	22	them	they	PRON
ejpam-4850	428	23	.	.	PUNCT
ejpam-4850	429	1	acknowledgements	acknowledgement	VERB
ejpam-4850	429	2	the	the	DET
ejpam-4850	429	3	work	work	NOUN
ejpam-4850	429	4	of	of	ADP
ejpam-4850	429	5	the	the	DET
ejpam-4850	429	6	third	third	ADJ
ejpam-4850	429	7	author	author	NOUN
ejpam-4850	429	8	was	be	AUX
ejpam-4850	429	9	supported	support	VERB
ejpam-4850	429	10	by	by	ADP
ejpam-4850	429	11	dgrsdt	dgrsdt	NOUN
ejpam-4850	429	12	,	,	PUNCT
ejpam-4850	429	13	mesrs	mesrs	NOUN
ejpam-4850	429	14	of	of	ADP
ejpam-4850	429	15	algeria	algeria	PROPN
ejpam-4850	429	16	.	.	PUNCT
ejpam-4850	430	1	(	(	PUNCT
ejpam-4850	430	2	prfu	prfu	ADJ
ejpam-4850	430	3	project	project	NOUN
ejpam-4850	430	4	a14n01ep230220230001	a14n01ep230220230001	PROPN
ejpam-4850	430	5	)	)	PUNCT
ejpam-4850	430	6	.	.	PUNCT
ejpam-4850	431	1	references	reference	NOUN
ejpam-4850	431	2	[	[	X
ejpam-4850	431	3	1	1	NUM
ejpam-4850	431	4	]	]	X
ejpam-4850	431	5	thabet	thabet	ADJ
ejpam-4850	431	6	abdeljawad	abdeljawad	NOUN
ejpam-4850	431	7	,	,	PUNCT
ejpam-4850	431	8	saima	saima	PROPN
ejpam-4850	431	9	rashid	rashid	PROPN
ejpam-4850	431	10	,	,	PUNCT
ejpam-4850	431	11	zakia	zakia	NOUN
ejpam-4850	431	12	hammouch	hammouch	NOUN
ejpam-4850	431	13	,	,	PUNCT
ejpam-4850	431	14	and	and	CCONJ
ejpam-4850	431	15	yu	yu	PROPN
ejpam-4850	431	16	-	-	PUNCT
ejpam-4850	431	17	ming	ming	PROPN
ejpam-4850	431	18	chu	chu	PROPN
ejpam-4850	431	19	.	.	PUNCT
ejpam-4850	432	1	some	some	DET
ejpam-4850	432	2	new	new	ADJ
ejpam-4850	432	3	local	local	ADJ
ejpam-4850	432	4	fractional	fractional	ADJ
ejpam-4850	432	5	inequalities	inequality	NOUN
ejpam-4850	432	6	associated	associate	VERB
ejpam-4850	432	7	with	with	ADP
ejpam-4850	432	8	generalized	generalized	ADJ
ejpam-4850	432	9	(	(	PUNCT
ejpam-4850	432	10	s	s	NOUN
ejpam-4850	432	11	,	,	PUNCT
ejpam-4850	432	12	m)-convex	m)-convex	PUNCT
ejpam-4850	432	13	functions	function	NOUN
ejpam-4850	432	14	and	and	CCONJ
ejpam-4850	432	15	applications	application	NOUN
ejpam-4850	432	16	.	.	PUNCT
ejpam-4850	433	1	advances	advance	NOUN
ejpam-4850	433	2	in	in	ADP
ejpam-4850	433	3	difference	difference	NOUN
ejpam-4850	433	4	equations	equation	NOUN
ejpam-4850	433	5	,	,	PUNCT
ejpam-4850	433	6	2020(1):1–27	2020(1):1–27	NOUN
ejpam-4850	433	7	,	,	PUNCT
ejpam-4850	433	8	2020	2020	NUM
ejpam-4850	433	9	.	.	PUNCT
ejpam-4850	434	1	[	[	X
ejpam-4850	434	2	2	2	X
ejpam-4850	434	3	]	]	PUNCT
ejpam-4850	434	4	maysaa	maysaa	PROPN
ejpam-4850	434	5	al	al	PROPN
ejpam-4850	434	6	qurashi	qurashi	PROPN
ejpam-4850	434	7	,	,	PUNCT
ejpam-4850	434	8	saima	saima	PROPN
ejpam-4850	434	9	rashid	rashid	PROPN
ejpam-4850	434	10	,	,	PUNCT
ejpam-4850	434	11	aasma	aasma	PROPN
ejpam-4850	434	12	khalid	khalid	PROPN
ejpam-4850	434	13	,	,	PUNCT
ejpam-4850	434	14	yeliz	yeliz	PROPN
ejpam-4850	434	15	karaca	karaca	PROPN
ejpam-4850	434	16	,	,	PUNCT
ejpam-4850	434	17	and	and	CCONJ
ejpam-4850	434	18	yu	yu	PROPN
ejpam-4850	434	19	-	-	PROPN
ejpam-4850	434	20	ming	ming	PROPN
ejpam-4850	434	21	chu	chu	PROPN
ejpam-4850	434	22	.	.	PUNCT
ejpam-4850	435	1	new	new	ADJ
ejpam-4850	435	2	computations	computation	NOUN
ejpam-4850	435	3	of	of	ADP
ejpam-4850	435	4	ostrowski	ostrowski	ADJ
ejpam-4850	435	5	-	-	PUNCT
ejpam-4850	435	6	type	type	NOUN
ejpam-4850	435	7	inequality	inequality	NOUN
ejpam-4850	435	8	pertaining	pertain	VERB
ejpam-4850	435	9	to	to	ADP
ejpam-4850	435	10	fractal	fractal	ADJ
ejpam-4850	435	11	style	style	NOUN
ejpam-4850	435	12	with	with	ADP
ejpam-4850	435	13	applications	application	NOUN
ejpam-4850	435	14	.	.	PUNCT
ejpam-4850	436	1	fractals	fractal	NOUN
ejpam-4850	436	2	,	,	PUNCT
ejpam-4850	436	3	29(05):2140026	29(05):2140026	NUM
ejpam-4850	436	4	,	,	PUNCT
ejpam-4850	436	5	2021	2021	NUM
ejpam-4850	436	6	.	.	PUNCT
ejpam-4850	437	1	[	[	X
ejpam-4850	437	2	3	3	X
ejpam-4850	437	3	]	]	X
ejpam-4850	437	4	hüseyin	hüseyin	PROPN
ejpam-4850	437	5	budak	budak	PROPN
ejpam-4850	437	6	,	,	PUNCT
ejpam-4850	437	7	mehmet	mehmet	PROPN
ejpam-4850	437	8	zeki	zeki	PROPN
ejpam-4850	437	9	sarikaya	sarikaya	PROPN
ejpam-4850	437	10	,	,	PUNCT
ejpam-4850	437	11	and	and	CCONJ
ejpam-4850	437	12	erhan	erhan	SCONJ
ejpam-4850	437	13	set	set	VERB
ejpam-4850	437	14	.	.	PUNCT
ejpam-4850	438	1	generalized	generalized	ADJ
ejpam-4850	438	2	ostrowski	ostrowski	ADJ
ejpam-4850	438	3	type	type	NOUN
ejpam-4850	438	4	inequalities	inequality	NOUN
ejpam-4850	438	5	for	for	ADP
ejpam-4850	438	6	functions	function	NOUN
ejpam-4850	438	7	whose	whose	DET
ejpam-4850	438	8	local	local	ADJ
ejpam-4850	438	9	fractional	fractional	ADJ
ejpam-4850	438	10	derivatives	derivative	NOUN
ejpam-4850	438	11	are	be	AUX
ejpam-4850	438	12	generalized	generalize	VERB
ejpam-4850	438	13	s	s	NOUN
ejpam-4850	438	14	-	-	NOUN
ejpam-4850	438	15	convex	convex	NOUN
ejpam-4850	438	16	in	in	ADP
ejpam-4850	438	17	the	the	DET
ejpam-4850	438	18	second	second	ADJ
ejpam-4850	438	19	sense	sense	NOUN
ejpam-4850	438	20	.	.	PUNCT
ejpam-4850	439	1	journal	journal	PROPN
ejpam-4850	439	2	of	of	ADP
ejpam-4850	439	3	applied	apply	VERB
ejpam-4850	439	4	mathematics	mathematic	NOUN
ejpam-4850	439	5	and	and	CCONJ
ejpam-4850	439	6	computational	computational	ADJ
ejpam-4850	439	7	mechanics	mechanic	NOUN
ejpam-4850	439	8	,	,	PUNCT
ejpam-4850	439	9	15(4):11–21	15(4):11–21	NUM
ejpam-4850	439	10	,	,	PUNCT
ejpam-4850	439	11	2016	2016	NUM
ejpam-4850	439	12	.	.	PUNCT
ejpam-4850	440	1	[	[	X
ejpam-4850	440	2	4	4	NUM
ejpam-4850	440	3	]	]	X
ejpam-4850	440	4	guang	guang	PROPN
ejpam-4850	440	5	-	-	PUNCT
ejpam-4850	440	6	sheng	sheng	PROPN
ejpam-4850	440	7	chen	chen	PROPN
ejpam-4850	440	8	.	.	PUNCT
ejpam-4850	441	1	generalizations	generalization	NOUN
ejpam-4850	441	2	of	of	ADP
ejpam-4850	441	3	hölder	hölder	NOUN
ejpam-4850	441	4	’s	’s	PART
ejpam-4850	441	5	and	and	CCONJ
ejpam-4850	441	6	some	some	DET
ejpam-4850	441	7	related	relate	VERB
ejpam-4850	441	8	integral	integral	ADJ
ejpam-4850	441	9	inequalities	inequality	NOUN
ejpam-4850	441	10	on	on	ADP
ejpam-4850	441	11	fractal	fractal	ADJ
ejpam-4850	441	12	space	space	NOUN
ejpam-4850	441	13	.	.	PUNCT
ejpam-4850	442	1	journal	journal	PROPN
ejpam-4850	442	2	of	of	ADP
ejpam-4850	442	3	function	function	NOUN
ejpam-4850	442	4	spaces	space	NOUN
ejpam-4850	442	5	and	and	CCONJ
ejpam-4850	442	6	applications	application	NOUN
ejpam-4850	442	7	,	,	PUNCT
ejpam-4850	442	8	2013	2013	NUM
ejpam-4850	442	9	,	,	PUNCT
ejpam-4850	442	10	2013	2013	NUM
ejpam-4850	442	11	.	.	PUNCT
ejpam-4850	443	1	[	[	X
ejpam-4850	443	2	5	5	X
ejpam-4850	443	3	]	]	X
ejpam-4850	443	4	sever	sever	PROPN
ejpam-4850	443	5	s	s	PRON
ejpam-4850	443	6	dragomir	dragomir	ADJ
ejpam-4850	443	7	and	and	CCONJ
ejpam-4850	443	8	simon	simon	PROPN
ejpam-4850	443	9	fitzpatrick	fitzpatrick	PROPN
ejpam-4850	443	10	.	.	PUNCT
ejpam-4850	444	1	the	the	DET
ejpam-4850	444	2	hadamard	hadamard	ADJ
ejpam-4850	444	3	inequalities	inequality	NOUN
ejpam-4850	444	4	for	for	ADP
ejpam-4850	444	5	s	s	NOUN
ejpam-4850	444	6	-	-	PUNCT
ejpam-4850	444	7	convex	convex	ADJ
ejpam-4850	444	8	functions	function	NOUN
ejpam-4850	444	9	in	in	ADP
ejpam-4850	444	10	the	the	DET
ejpam-4850	444	11	second	second	ADJ
ejpam-4850	444	12	sense	sense	NOUN
ejpam-4850	444	13	.	.	PUNCT
ejpam-4850	445	1	demonstratio	demonstratio	PROPN
ejpam-4850	445	2	mathematica	mathematica	PROPN
ejpam-4850	445	3	,	,	PUNCT
ejpam-4850	445	4	32(4):687–696	32(4):687–696	NUM
ejpam-4850	445	5	,	,	PUNCT
ejpam-4850	445	6	1999	1999	NUM
ejpam-4850	445	7	.	.	PUNCT
ejpam-4850	446	1	[	[	X
ejpam-4850	446	2	6	6	NUM
ejpam-4850	446	3	]	]	PUNCT
ejpam-4850	446	4	ss	ss	NOUN
ejpam-4850	446	5	dragomir	dragomir	NOUN
ejpam-4850	446	6	and	and	CCONJ
ejpam-4850	446	7	rp	rp	NOUN
ejpam-4850	446	8	agarwal	agarwal	PROPN
ejpam-4850	446	9	.	.	PUNCT
ejpam-4850	447	1	two	two	NUM
ejpam-4850	447	2	inequalities	inequality	NOUN
ejpam-4850	447	3	for	for	ADP
ejpam-4850	447	4	differentiable	differentiable	ADJ
ejpam-4850	447	5	mappings	mapping	NOUN
ejpam-4850	447	6	and	and	CCONJ
ejpam-4850	447	7	applications	application	NOUN
ejpam-4850	447	8	to	to	ADP
ejpam-4850	447	9	special	special	ADJ
ejpam-4850	447	10	means	mean	NOUN
ejpam-4850	447	11	of	of	ADP
ejpam-4850	447	12	real	real	ADJ
ejpam-4850	447	13	numbers	number	NOUN
ejpam-4850	447	14	and	and	CCONJ
ejpam-4850	447	15	to	to	ADP
ejpam-4850	447	16	trapezoidal	trapezoidal	ADJ
ejpam-4850	447	17	formula	formula	NOUN
ejpam-4850	447	18	.	.	PUNCT
ejpam-4850	448	1	applied	apply	VERB
ejpam-4850	448	2	mathematics	mathematics	NOUN
ejpam-4850	448	3	letters	letter	NOUN
ejpam-4850	448	4	,	,	PUNCT
ejpam-4850	448	5	11(5):91–95	11(5):91–95	NUM
ejpam-4850	448	6	,	,	PUNCT
ejpam-4850	448	7	1998	1998	NUM
ejpam-4850	448	8	.	.	PUNCT
ejpam-4850	449	1	references	reference	NOUN
ejpam-4850	449	2	1379	1379	NUM
ejpam-4850	449	3	[	[	X
ejpam-4850	449	4	7	7	NUM
ejpam-4850	449	5	]	]	PUNCT
ejpam-4850	449	6	tingsong	tingsong	PROPN
ejpam-4850	449	7	du	du	PROPN
ejpam-4850	449	8	,	,	PUNCT
ejpam-4850	449	9	hao	hao	PROPN
ejpam-4850	449	10	wang	wang	PROPN
ejpam-4850	449	11	,	,	PUNCT
ejpam-4850	449	12	muhammad	muhammad	PROPN
ejpam-4850	449	13	adil	adil	PROPN
ejpam-4850	449	14	khan	khan	PROPN
ejpam-4850	449	15	,	,	PUNCT
ejpam-4850	449	16	and	and	CCONJ
ejpam-4850	449	17	yao	yao	PROPN
ejpam-4850	449	18	zhang	zhang	PROPN
ejpam-4850	449	19	.	.	PUNCT
ejpam-4850	450	1	certain	certain	ADJ
ejpam-4850	450	2	integral	integral	ADJ
ejpam-4850	450	3	inequalities	inequality	NOUN
ejpam-4850	450	4	considering	consider	VERB
ejpam-4850	450	5	generalized	generalized	ADJ
ejpam-4850	450	6	m	m	NOUN
ejpam-4850	450	7	-	-	NOUN
ejpam-4850	450	8	convexity	convexity	NOUN
ejpam-4850	450	9	on	on	ADP
ejpam-4850	450	10	fractal	fractal	ADJ
ejpam-4850	450	11	sets	set	NOUN
ejpam-4850	450	12	and	and	CCONJ
ejpam-4850	450	13	their	their	PRON
ejpam-4850	450	14	applications	application	NOUN
ejpam-4850	450	15	.	.	PUNCT
ejpam-4850	451	1	fractals	fractal	NOUN
ejpam-4850	451	2	,	,	PUNCT
ejpam-4850	451	3	27(07):1950117	27(07):1950117	NUM
ejpam-4850	451	4	,	,	PUNCT
ejpam-4850	451	5	2019	2019	NUM
ejpam-4850	451	6	.	.	PUNCT
ejpam-4850	452	1	[	[	X
ejpam-4850	452	2	8	8	NUM
ejpam-4850	452	3	]	]	X
ejpam-4850	452	4	g.	g.	PROPN
ejpam-4850	452	5	a.	a.	PROPN
ejpam-4850	452	6	edgar	edgar	PROPN
ejpam-4850	452	7	.	.	PUNCT
ejpam-4850	453	1	integral	integral	ADJ
ejpam-4850	453	2	,	,	PUNCT
ejpam-4850	453	3	probability	probability	NOUN
ejpam-4850	453	4	,	,	PUNCT
ejpam-4850	453	5	and	and	CCONJ
ejpam-4850	453	6	fractal	fractal	ADJ
ejpam-4850	453	7	measures	measure	NOUN
ejpam-4850	453	8	.	.	PUNCT
ejpam-4850	454	1	springer	springer	NOUN
ejpam-4850	454	2	,	,	PUNCT
ejpam-4850	454	3	new	new	PROPN
ejpam-4850	454	4	york	york	PROPN
ejpam-4850	454	5	,	,	PUNCT
ejpam-4850	454	6	ny	ny	PROPN
ejpam-4850	454	7	,	,	PUNCT
ejpam-4850	454	8	usa	usa	PROPN
ejpam-4850	454	9	,	,	PUNCT
ejpam-4850	454	10	1988	1988	NUM
ejpam-4850	454	11	.	.	PUNCT
ejpam-4850	455	1	[	[	X
ejpam-4850	455	2	9	9	NUM
ejpam-4850	455	3	]	]	X
ejpam-4850	455	4	henryk	henryk	ADV
ejpam-4850	455	5	hudzik	hudzik	ADV
ejpam-4850	455	6	and	and	CCONJ
ejpam-4850	455	7	lech	lech	PROPN
ejpam-4850	455	8	maligranda	maligranda	PROPN
ejpam-4850	455	9	.	.	PUNCT
ejpam-4850	456	1	some	some	DET
ejpam-4850	456	2	remarks	remark	NOUN
ejpam-4850	456	3	on	on	ADP
ejpam-4850	456	4	s	s	NOUN
ejpam-4850	456	5	-	-	PUNCT
ejpam-4850	456	6	convex	convex	ADJ
ejpam-4850	456	7	functions	function	NOUN
ejpam-4850	456	8	.	.	PUNCT
ejpam-4850	457	1	aequationes	aequatione	NOUN
ejpam-4850	457	2	mathematicae	mathematicae	PROPN
ejpam-4850	457	3	,	,	PUNCT
ejpam-4850	457	4	48:100–111	48:100–111	PROPN
ejpam-4850	457	5	,	,	PUNCT
ejpam-4850	457	6	1994	1994	NUM
ejpam-4850	457	7	.	.	PUNCT
ejpam-4850	458	1	[	[	X
ejpam-4850	458	2	10	10	NUM
ejpam-4850	458	3	]	]	X
ejpam-4850	458	4	sabah	sabah	PROPN
ejpam-4850	458	5	iftikhar	iftikhar	PROPN
ejpam-4850	458	6	,	,	PUNCT
ejpam-4850	458	7	poom	poom	NOUN
ejpam-4850	458	8	kumam	kumam	NOUN
ejpam-4850	458	9	,	,	PUNCT
ejpam-4850	458	10	and	and	CCONJ
ejpam-4850	458	11	samet	samet	PROPN
ejpam-4850	458	12	erden	erden	PROPN
ejpam-4850	458	13	.	.	PUNCT
ejpam-4850	459	1	newton’s	newton’s	NOUN
ejpam-4850	459	2	-	-	PUNCT
ejpam-4850	459	3	type	type	NOUN
ejpam-4850	459	4	integral	integral	ADJ
ejpam-4850	459	5	inequalities	inequality	NOUN
ejpam-4850	459	6	via	via	ADP
ejpam-4850	459	7	local	local	ADJ
ejpam-4850	459	8	fractional	fractional	ADJ
ejpam-4850	459	9	integrals	integral	NOUN
ejpam-4850	459	10	.	.	PUNCT
ejpam-4850	460	1	fractals	fractal	NOUN
ejpam-4850	460	2	,	,	PUNCT
ejpam-4850	460	3	28(03):2050037	28(03):2050037	NUM
ejpam-4850	460	4	,	,	PUNCT
ejpam-4850	460	5	2020	2020	NUM
ejpam-4850	460	6	.	.	PUNCT
ejpam-4850	461	1	[	[	X
ejpam-4850	461	2	11	11	NUM
ejpam-4850	461	3	]	]	PUNCT
ejpam-4850	461	4	havva	havva	NOUN
ejpam-4850	461	5	kavurmaci	kavurmaci	NOUN
ejpam-4850	461	6	,	,	PUNCT
ejpam-4850	461	7	mohammad	mohammad	PROPN
ejpam-4850	461	8	w	w	PROPN
ejpam-4850	461	9	alomari	alomari	PROPN
ejpam-4850	461	10	,	,	PUNCT
ejpam-4850	461	11	and	and	CCONJ
ejpam-4850	461	12	m	m	PROPN
ejpam-4850	461	13	emin	emin	PROPN
ejpam-4850	461	14	özdemir	özdemir	PROPN
ejpam-4850	461	15	.	.	PUNCT
ejpam-4850	462	1	on	on	ADP
ejpam-4850	462	2	companion	companion	NOUN
ejpam-4850	462	3	of	of	ADP
ejpam-4850	462	4	ostrowski	ostrowski	ADJ
ejpam-4850	462	5	inequality	inequality	NOUN
ejpam-4850	462	6	for	for	ADP
ejpam-4850	462	7	mappings	mapping	NOUN
ejpam-4850	462	8	whose	whose	DET
ejpam-4850	462	9	first	first	ADJ
ejpam-4850	462	10	derivatives	derivative	NOUN
ejpam-4850	462	11	absolute	absolute	ADJ
ejpam-4850	462	12	value	value	NOUN
ejpam-4850	462	13	are	be	AUX
ejpam-4850	462	14	convex	convex	ADJ
ejpam-4850	462	15	with	with	ADP
ejpam-4850	462	16	applications	application	NOUN
ejpam-4850	462	17	.	.	PUNCT
ejpam-4850	463	1	miskolc	miskolc	ADJ
ejpam-4850	463	2	mathematical	mathematical	ADJ
ejpam-4850	463	3	notes	note	NOUN
ejpam-4850	463	4	,	,	PUNCT
ejpam-4850	463	5	13(2):233–248	13(2):233–248	PROPN
ejpam-4850	463	6	,	,	PUNCT
ejpam-4850	463	7	2012	2012	NUM
ejpam-4850	463	8	.	.	PUNCT
ejpam-4850	464	1	[	[	X
ejpam-4850	464	2	12	12	NUM
ejpam-4850	464	3	]	]	PUNCT
ejpam-4850	464	4	zareen	zareen	X
ejpam-4850	464	5	a	a	DET
ejpam-4850	464	6	khan	khan	PROPN
ejpam-4850	464	7	,	,	PUNCT
ejpam-4850	464	8	saima	saima	PROPN
ejpam-4850	464	9	rashid	rashid	PROPN
ejpam-4850	464	10	,	,	PUNCT
ejpam-4850	464	11	rehana	rehana	PROPN
ejpam-4850	464	12	ashraf	ashraf	PROPN
ejpam-4850	464	13	,	,	PUNCT
ejpam-4850	464	14	dumitru	dumitru	PROPN
ejpam-4850	464	15	baleanu	baleanu	NOUN
ejpam-4850	464	16	,	,	PUNCT
ejpam-4850	464	17	and	and	CCONJ
ejpam-4850	464	18	yu	yu	PROPN
ejpam-4850	464	19	-	-	PROPN
ejpam-4850	464	20	ming	ming	PROPN
ejpam-4850	464	21	chu	chu	PROPN
ejpam-4850	464	22	.	.	PUNCT
ejpam-4850	465	1	generalized	generalize	VERB
ejpam-4850	465	2	trapezium	trapezium	NOUN
ejpam-4850	465	3	-	-	PUNCT
ejpam-4850	465	4	type	type	NOUN
ejpam-4850	465	5	inequalities	inequality	NOUN
ejpam-4850	465	6	in	in	ADP
ejpam-4850	465	7	the	the	DET
ejpam-4850	465	8	settings	setting	NOUN
ejpam-4850	465	9	of	of	ADP
ejpam-4850	465	10	fractal	fractal	ADJ
ejpam-4850	465	11	sets	set	NOUN
ejpam-4850	465	12	for	for	ADP
ejpam-4850	465	13	functions	function	NOUN
ejpam-4850	465	14	having	have	VERB
ejpam-4850	465	15	generalized	generalize	VERB
ejpam-4850	465	16	convexity	convexity	NOUN
ejpam-4850	465	17	property	property	NOUN
ejpam-4850	465	18	.	.	PUNCT
ejpam-4850	466	1	advances	advance	NOUN
ejpam-4850	466	2	in	in	ADP
ejpam-4850	466	3	difference	difference	NOUN
ejpam-4850	466	4	equations	equation	NOUN
ejpam-4850	466	5	,	,	PUNCT
ejpam-4850	466	6	2020(1):1	2020(1):1	PROPN
ejpam-4850	466	7	–	–	PUNCT
ejpam-4850	466	8	24	24	NUM
ejpam-4850	466	9	,	,	PUNCT
ejpam-4850	466	10	2020	2020	NUM
ejpam-4850	466	11	.	.	PUNCT
ejpam-4850	467	1	[	[	X
ejpam-4850	467	2	13	13	NUM
ejpam-4850	467	3	]	]	PUNCT
ejpam-4850	467	4	yousaf	yousaf	PROPN
ejpam-4850	467	5	khurshid	khurshid	PROPN
ejpam-4850	467	6	,	,	PUNCT
ejpam-4850	467	7	muhammad	muhammad	PROPN
ejpam-4850	467	8	adil	adil	PROPN
ejpam-4850	467	9	khan	khan	PROPN
ejpam-4850	467	10	,	,	PUNCT
ejpam-4850	467	11	and	and	CCONJ
ejpam-4850	467	12	yu	yu	PROPN
ejpam-4850	467	13	-	-	PROPN
ejpam-4850	467	14	ming	ming	PROPN
ejpam-4850	467	15	chu	chu	PROPN
ejpam-4850	467	16	.	.	PROPN
ejpam-4850	467	17	ostrowski	ostrowski	ADJ
ejpam-4850	467	18	type	type	NOUN
ejpam-4850	467	19	inequalities	inequality	NOUN
ejpam-4850	467	20	involving	involve	VERB
ejpam-4850	467	21	conformable	conformable	ADJ
ejpam-4850	467	22	integrals	integral	NOUN
ejpam-4850	467	23	via	via	ADP
ejpam-4850	467	24	preinvex	preinvex	NOUN
ejpam-4850	467	25	functions	function	NOUN
ejpam-4850	467	26	.	.	PUNCT
ejpam-4850	468	1	aip	aip	PROPN
ejpam-4850	468	2	advances	advance	NOUN
ejpam-4850	468	3	,	,	PUNCT
ejpam-4850	468	4	10(5):055204	10(5):055204	NUM
ejpam-4850	468	5	,	,	PUNCT
ejpam-4850	468	6	2020	2020	NUM
ejpam-4850	468	7	.	.	PUNCT
ejpam-4850	469	1	[	[	X
ejpam-4850	469	2	14	14	NUM
ejpam-4850	469	3	]	]	X
ejpam-4850	470	1	uǧur	uǧur	NOUN
ejpam-4850	470	2	s	s	PART
ejpam-4850	470	3	kirmaci	kirmaci	NOUN
ejpam-4850	470	4	.	.	PUNCT
ejpam-4850	471	1	inequalities	inequality	NOUN
ejpam-4850	471	2	for	for	ADP
ejpam-4850	471	3	differentiable	differentiable	ADJ
ejpam-4850	471	4	mappings	mapping	NOUN
ejpam-4850	471	5	and	and	CCONJ
ejpam-4850	471	6	applications	application	NOUN
ejpam-4850	471	7	to	to	ADP
ejpam-4850	471	8	special	special	ADJ
ejpam-4850	471	9	means	mean	NOUN
ejpam-4850	471	10	of	of	ADP
ejpam-4850	471	11	real	real	ADJ
ejpam-4850	471	12	numbers	number	NOUN
ejpam-4850	471	13	and	and	CCONJ
ejpam-4850	471	14	to	to	PART
ejpam-4850	471	15	midpoint	midpoint	NOUN
ejpam-4850	471	16	formula	formula	NOUN
ejpam-4850	471	17	.	.	PUNCT
ejpam-4850	472	1	applied	apply	VERB
ejpam-4850	472	2	mathematics	mathematic	NOUN
ejpam-4850	472	3	and	and	CCONJ
ejpam-4850	472	4	computation	computation	NOUN
ejpam-4850	472	5	,	,	PUNCT
ejpam-4850	472	6	147(1):137–146	147(1):137–146	NUM
ejpam-4850	472	7	,	,	PUNCT
ejpam-4850	472	8	2004	2004	NUM
ejpam-4850	472	9	.	.	PUNCT
ejpam-4850	473	1	[	[	X
ejpam-4850	473	2	15	15	NUM
ejpam-4850	473	3	]	]	X
ejpam-4850	473	4	kiran	kiran	PROPN
ejpam-4850	473	5	m	m	PROPN
ejpam-4850	473	6	kolwankar	kolwankar	PROPN
ejpam-4850	473	7	and	and	CCONJ
ejpam-4850	473	8	anil	anil	PROPN
ejpam-4850	473	9	d	d	PROPN
ejpam-4850	473	10	gangal	gangal	PROPN
ejpam-4850	473	11	.	.	PUNCT
ejpam-4850	474	1	local	local	ADJ
ejpam-4850	474	2	fractional	fractional	ADJ
ejpam-4850	474	3	calculus	calculus	NOUN
ejpam-4850	474	4	:	:	PUNCT
ejpam-4850	474	5	a	a	DET
ejpam-4850	474	6	calculus	calculus	NOUN
ejpam-4850	474	7	for	for	ADP
ejpam-4850	474	8	fractal	fractal	ADJ
ejpam-4850	474	9	space	space	NOUN
ejpam-4850	474	10	-	-	PUNCT
ejpam-4850	474	11	time	time	NOUN
ejpam-4850	474	12	.	.	PUNCT
ejpam-4850	475	1	in	in	ADP
ejpam-4850	475	2	fractals	fractal	NOUN
ejpam-4850	475	3	:	:	PUNCT
ejpam-4850	475	4	theory	theory	NOUN
ejpam-4850	475	5	and	and	CCONJ
ejpam-4850	475	6	applications	application	NOUN
ejpam-4850	475	7	in	in	ADP
ejpam-4850	475	8	engineering	engineering	NOUN
ejpam-4850	475	9	,	,	PUNCT
ejpam-4850	475	10	pages	page	NOUN
ejpam-4850	475	11	171	171	NUM
ejpam-4850	475	12	–	–	PUNCT
ejpam-4850	475	13	181	181	NUM
ejpam-4850	475	14	.	.	PUNCT
ejpam-4850	475	15	springer	springer	NOUN
ejpam-4850	475	16	,	,	PUNCT
ejpam-4850	475	17	1999	1999	NUM
ejpam-4850	475	18	.	.	PUNCT
ejpam-4850	476	1	[	[	X
ejpam-4850	476	2	16	16	NUM
ejpam-4850	476	3	]	]	PUNCT
ejpam-4850	476	4	abdelghani	abdelghani	ADJ
ejpam-4850	476	5	lakhdari	lakhdari	PROPN
ejpam-4850	476	6	,	,	PUNCT
ejpam-4850	476	7	wedad	wedad	PROPN
ejpam-4850	476	8	saleh	saleh	PROPN
ejpam-4850	476	9	,	,	PUNCT
ejpam-4850	476	10	badreddine	badreddine	PROPN
ejpam-4850	476	11	meftah	meftah	NOUN
ejpam-4850	476	12	,	,	PUNCT
ejpam-4850	476	13	and	and	CCONJ
ejpam-4850	476	14	akhlad	akhlad	PROPN
ejpam-4850	476	15	iqbal	iqbal	PROPN
ejpam-4850	476	16	.	.	PUNCT
ejpam-4850	476	17	corrected	correct	VERB
ejpam-4850	476	18	dual	dual	ADJ
ejpam-4850	476	19	-	-	PUNCT
ejpam-4850	476	20	simpson	simpson	NOUN
ejpam-4850	476	21	-	-	PUNCT
ejpam-4850	476	22	type	type	NOUN
ejpam-4850	476	23	inequalities	inequality	NOUN
ejpam-4850	476	24	for	for	ADP
ejpam-4850	476	25	differentiable	differentiable	ADJ
ejpam-4850	476	26	generalized	generalize	VERB
ejpam-4850	476	27	convex	convex	NOUN
ejpam-4850	476	28	functions	function	NOUN
ejpam-4850	476	29	on	on	ADP
ejpam-4850	476	30	fractal	fractal	ADJ
ejpam-4850	476	31	set	set	PROPN
ejpam-4850	476	32	.	.	PUNCT
ejpam-4850	477	1	fractal	fractal	PROPN
ejpam-4850	477	2	and	and	CCONJ
ejpam-4850	477	3	fractional	fractional	ADJ
ejpam-4850	477	4	,	,	PUNCT
ejpam-4850	477	5	6(12):710	6(12):710	NUM
ejpam-4850	477	6	,	,	PUNCT
ejpam-4850	477	7	2022	2022	NUM
ejpam-4850	477	8	.	.	PUNCT
ejpam-4850	478	1	[	[	X
ejpam-4850	478	2	17	17	NUM
ejpam-4850	478	3	]	]	PUNCT
ejpam-4850	478	4	chunyan	chunyan	PROPN
ejpam-4850	478	5	luo	luo	PROPN
ejpam-4850	478	6	,	,	PUNCT
ejpam-4850	478	7	hao	hao	PROPN
ejpam-4850	478	8	wang	wang	PROPN
ejpam-4850	478	9	,	,	PUNCT
ejpam-4850	478	10	and	and	CCONJ
ejpam-4850	478	11	tingsong	tingsong	PROPN
ejpam-4850	478	12	du	du	PROPN
ejpam-4850	478	13	.	.	PUNCT
ejpam-4850	479	1	fejér	fejér	NOUN
ejpam-4850	479	2	–	–	PUNCT
ejpam-4850	479	3	hermite	hermite	ADJ
ejpam-4850	479	4	–	–	PUNCT
ejpam-4850	479	5	hadamard	hadamard	ADJ
ejpam-4850	479	6	type	type	NOUN
ejpam-4850	479	7	inequalities	inequality	NOUN
ejpam-4850	479	8	involving	involve	VERB
ejpam-4850	479	9	generalized	generalized	ADJ
ejpam-4850	479	10	h	h	NOUN
ejpam-4850	479	11	-	-	PUNCT
ejpam-4850	479	12	convexity	convexity	NOUN
ejpam-4850	479	13	on	on	ADP
ejpam-4850	479	14	fractal	fractal	ADJ
ejpam-4850	479	15	sets	set	NOUN
ejpam-4850	479	16	and	and	CCONJ
ejpam-4850	479	17	their	their	PRON
ejpam-4850	479	18	applications	application	NOUN
ejpam-4850	479	19	.	.	PUNCT
ejpam-4850	480	1	chaos	chaos	NOUN
ejpam-4850	480	2	,	,	PUNCT
ejpam-4850	480	3	solitons	soliton	NOUN
ejpam-4850	480	4	&	&	CCONJ
ejpam-4850	480	5	fractals	fractal	NOUN
ejpam-4850	480	6	,	,	PUNCT
ejpam-4850	480	7	131:109547	131:109547	NUM
ejpam-4850	480	8	,	,	PUNCT
ejpam-4850	480	9	2020	2020	NUM
ejpam-4850	480	10	.	.	PUNCT
ejpam-4850	481	1	[	[	X
ejpam-4850	481	2	18	18	NUM
ejpam-4850	481	3	]	]	SYM
ejpam-4850	481	4	b	b	NOUN
ejpam-4850	481	5	meftah	meftah	NOUN
ejpam-4850	481	6	,	,	PUNCT
ejpam-4850	481	7	a	a	DET
ejpam-4850	481	8	souahi	souahi	NOUN
ejpam-4850	481	9	,	,	PUNCT
ejpam-4850	481	10	and	and	CCONJ
ejpam-4850	481	11	m	m	PROPN
ejpam-4850	481	12	merad	merad	NOUN
ejpam-4850	481	13	.	.	PUNCT
ejpam-4850	482	1	some	some	DET
ejpam-4850	482	2	local	local	ADJ
ejpam-4850	482	3	fractional	fractional	ADJ
ejpam-4850	482	4	maclaurin	maclaurin	NOUN
ejpam-4850	482	5	type	type	NOUN
ejpam-4850	482	6	inequalities	inequality	NOUN
ejpam-4850	482	7	for	for	ADP
ejpam-4850	482	8	generalized	generalized	ADJ
ejpam-4850	482	9	convex	convex	NOUN
ejpam-4850	482	10	functions	function	NOUN
ejpam-4850	482	11	and	and	CCONJ
ejpam-4850	482	12	their	their	PRON
ejpam-4850	482	13	applications	application	NOUN
ejpam-4850	482	14	.	.	PUNCT
ejpam-4850	483	1	chaos	chaos	NOUN
ejpam-4850	483	2	,	,	PUNCT
ejpam-4850	483	3	solitons	soliton	NOUN
ejpam-4850	483	4	&	&	CCONJ
ejpam-4850	483	5	fractals	fractal	NOUN
ejpam-4850	483	6	,	,	PUNCT
ejpam-4850	483	7	162:112504	162:112504	NUM
ejpam-4850	483	8	,	,	PUNCT
ejpam-4850	483	9	2022	2022	NUM
ejpam-4850	483	10	.	.	PUNCT
ejpam-4850	484	1	references	reference	NOUN
ejpam-4850	484	2	1380	1380	NUM
ejpam-4850	484	3	[	[	X
ejpam-4850	484	4	19	19	NUM
ejpam-4850	484	5	]	]	X
ejpam-4850	484	6	badreddine	badreddine	PROPN
ejpam-4850	484	7	meftah	meftah	NOUN
ejpam-4850	484	8	,	,	PUNCT
ejpam-4850	484	9	abdelghani	abdelghani	ADJ
ejpam-4850	484	10	lakhdari	lakhdari	PROPN
ejpam-4850	484	11	,	,	PUNCT
ejpam-4850	484	12	wedad	wedad	PROPN
ejpam-4850	484	13	saleh	saleh	PROPN
ejpam-4850	484	14	,	,	PUNCT
ejpam-4850	484	15	and	and	CCONJ
ejpam-4850	484	16	adem	adem	PROPN
ejpam-4850	484	17	kiliçman	kiliçman	PROPN
ejpam-4850	484	18	.	.	PUNCT
ejpam-4850	485	1	some	some	DET
ejpam-4850	485	2	new	new	ADJ
ejpam-4850	485	3	fractal	fractal	ADJ
ejpam-4850	485	4	milne	milne	NOUN
ejpam-4850	485	5	-	-	PUNCT
ejpam-4850	485	6	type	type	NOUN
ejpam-4850	485	7	integral	integral	ADJ
ejpam-4850	485	8	inequalities	inequality	NOUN
ejpam-4850	485	9	via	via	ADP
ejpam-4850	485	10	generalized	generalized	ADJ
ejpam-4850	485	11	convexity	convexity	NOUN
ejpam-4850	485	12	with	with	ADP
ejpam-4850	485	13	applications	application	NOUN
ejpam-4850	485	14	.	.	PUNCT
ejpam-4850	486	1	fractal	fractal	ADJ
ejpam-4850	486	2	and	and	CCONJ
ejpam-4850	486	3	fractional	fractional	ADJ
ejpam-4850	486	4	,	,	PUNCT
ejpam-4850	486	5	7(2):166	7(2):166	NUM
ejpam-4850	486	6	,	,	PUNCT
ejpam-4850	486	7	2023	2023	NUM
ejpam-4850	486	8	.	.	PUNCT
ejpam-4850	487	1	[	[	X
ejpam-4850	487	2	20	20	NUM
ejpam-4850	487	3	]	]	X
ejpam-4850	487	4	huixia	huixia	NOUN
ejpam-4850	487	5	mo	mo	PROPN
ejpam-4850	487	6	and	and	CCONJ
ejpam-4850	487	7	xin	xin	PROPN
ejpam-4850	487	8	sui	sui	PROPN
ejpam-4850	487	9	.	.	PUNCT
ejpam-4850	487	10	generalized	generalize	VERB
ejpam-4850	487	11	-	-	PUNCT
ejpam-4850	487	12	convex	convex	NOUN
ejpam-4850	487	13	functions	function	NOUN
ejpam-4850	487	14	on	on	ADP
ejpam-4850	487	15	fractal	fractal	ADJ
ejpam-4850	487	16	sets	set	NOUN
ejpam-4850	487	17	.	.	PUNCT
ejpam-4850	488	1	in	in	ADP
ejpam-4850	488	2	abstract	abstract	ADJ
ejpam-4850	488	3	and	and	CCONJ
ejpam-4850	488	4	applied	apply	VERB
ejpam-4850	488	5	analysis	analysis	NOUN
ejpam-4850	488	6	,	,	PUNCT
ejpam-4850	488	7	volume	volume	NOUN
ejpam-4850	488	8	2014	2014	NUM
ejpam-4850	488	9	.	.	PUNCT
ejpam-4850	489	1	hindawi	hindawi	ADJ
ejpam-4850	489	2	,	,	PUNCT
ejpam-4850	489	3	2014	2014	NUM
ejpam-4850	489	4	.	.	PUNCT
ejpam-4850	490	1	[	[	X
ejpam-4850	490	2	21	21	NUM
ejpam-4850	490	3	]	]	X
ejpam-4850	490	4	huixia	huixia	NOUN
ejpam-4850	490	5	mo	mo	PROPN
ejpam-4850	490	6	and	and	CCONJ
ejpam-4850	490	7	xin	xin	PROPN
ejpam-4850	490	8	sui	sui	PROPN
ejpam-4850	490	9	.	.	PUNCT
ejpam-4850	491	1	hermite	hermite	PROPN
ejpam-4850	491	2	–	–	PUNCT
ejpam-4850	491	3	hadamard	hadamard	ADJ
ejpam-4850	491	4	-	-	PUNCT
ejpam-4850	491	5	type	type	NOUN
ejpam-4850	491	6	inequalities	inequality	NOUN
ejpam-4850	491	7	for	for	ADP
ejpam-4850	491	8	generalized	generalized	ADJ
ejpam-4850	491	9	s	s	NOUN
ejpam-4850	491	10	-	-	ADJ
ejpam-4850	491	11	convex	convex	ADJ
ejpam-4850	491	12	functions	function	NOUN
ejpam-4850	491	13	on	on	ADP
ejpam-4850	491	14	real	real	ADJ
ejpam-4850	491	15	linear	linear	ADJ
ejpam-4850	491	16	fractal	fractal	NOUN
ejpam-4850	491	17	set	set	VERB
ejpam-4850	491	18	rγ	rγ	NOUN
ejpam-4850	491	19	(	(	PUNCT
ejpam-4850	491	20	0	0	PUNCT
ejpam-4850	491	21	<	<	X
ejpam-4850	491	22	γ	γ	X
ejpam-4850	491	23	<	<	X
ejpam-4850	491	24	1	1	NUM
ejpam-4850	491	25	)	)	PUNCT
ejpam-4850	491	26	.	.	PUNCT
ejpam-4850	492	1	mathematical	mathematical	ADJ
ejpam-4850	492	2	sciences	sciences	PROPN
ejpam-4850	492	3	,	,	PUNCT
ejpam-4850	492	4	11:241–246	11:241–246	NUM
ejpam-4850	492	5	,	,	PUNCT
ejpam-4850	492	6	2017	2017	NUM
ejpam-4850	492	7	.	.	PUNCT
ejpam-4850	493	1	[	[	X
ejpam-4850	493	2	22	22	NUM
ejpam-4850	493	3	]	]	X
ejpam-4850	493	4	josip	josip	PROPN
ejpam-4850	493	5	e	e	PROPN
ejpam-4850	493	6	peajcariaac	peajcariaac	PROPN
ejpam-4850	493	7	and	and	CCONJ
ejpam-4850	493	8	yung	yung	PROPN
ejpam-4850	493	9	liang	liang	PROPN
ejpam-4850	493	10	tong	tong	PROPN
ejpam-4850	493	11	.	.	PUNCT
ejpam-4850	494	1	convex	convex	PROPN
ejpam-4850	494	2	functions	function	NOUN
ejpam-4850	494	3	,	,	PUNCT
ejpam-4850	494	4	partial	partial	ADJ
ejpam-4850	494	5	orderings	ordering	NOUN
ejpam-4850	494	6	,	,	PUNCT
ejpam-4850	494	7	and	and	CCONJ
ejpam-4850	494	8	statistical	statistical	ADJ
ejpam-4850	494	9	applications	application	NOUN
ejpam-4850	494	10	.	.	PUNCT
ejpam-4850	495	1	academic	academic	ADJ
ejpam-4850	495	2	press	press	NOUN
ejpam-4850	495	3	,	,	PUNCT
ejpam-4850	495	4	1992	1992	NUM
ejpam-4850	495	5	.	.	PUNCT
ejpam-4850	496	1	[	[	X
ejpam-4850	496	2	23	23	NUM
ejpam-4850	496	3	]	]	X
ejpam-4850	496	4	mehmet	mehmet	PROPN
ejpam-4850	496	5	sarikaya	sarikaya	PROPN
ejpam-4850	496	6	and	and	CCONJ
ejpam-4850	496	7	hüseyin	hüseyin	PROPN
ejpam-4850	496	8	budak	budak	PROPN
ejpam-4850	496	9	.	.	PUNCT
ejpam-4850	497	1	generalized	generalized	ADJ
ejpam-4850	497	2	ostrowski	ostrowski	ADJ
ejpam-4850	497	3	type	type	NOUN
ejpam-4850	497	4	inequalities	inequality	NOUN
ejpam-4850	497	5	for	for	ADP
ejpam-4850	497	6	local	local	ADJ
ejpam-4850	497	7	fractional	fractional	ADJ
ejpam-4850	497	8	integrals	integral	NOUN
ejpam-4850	497	9	.	.	PUNCT
ejpam-4850	498	1	proceedings	proceeding	NOUN
ejpam-4850	498	2	of	of	ADP
ejpam-4850	498	3	the	the	DET
ejpam-4850	498	4	american	american	PROPN
ejpam-4850	498	5	mathematical	mathematical	PROPN
ejpam-4850	498	6	society	society	NOUN
ejpam-4850	498	7	,	,	PUNCT
ejpam-4850	498	8	145(4):1527–1538	145(4):1527–1538	NUM
ejpam-4850	498	9	,	,	PUNCT
ejpam-4850	498	10	2017	2017	NUM
ejpam-4850	498	11	.	.	PUNCT
ejpam-4850	499	1	[	[	X
ejpam-4850	499	2	24	24	NUM
ejpam-4850	499	3	]	]	X
ejpam-4850	499	4	xiao	xiao	PROPN
ejpam-4850	499	5	-	-	PUNCT
ejpam-4850	499	6	jun	jun	PROPN
ejpam-4850	499	7	yang	yang	PROPN
ejpam-4850	499	8	.	.	PUNCT
ejpam-4850	500	1	advanced	advanced	ADJ
ejpam-4850	500	2	local	local	ADJ
ejpam-4850	500	3	fractional	fractional	ADJ
ejpam-4850	500	4	calculus	calculus	NOUN
ejpam-4850	500	5	and	and	CCONJ
ejpam-4850	500	6	its	its	PRON
ejpam-4850	500	7	applications	application	NOUN
ejpam-4850	500	8	,	,	PUNCT
ejpam-4850	500	9	2012	2012	NUM
ejpam-4850	500	10	.	.	PUNCT
ejpam-4850	501	1	[	[	X
ejpam-4850	501	2	25	25	NUM
ejpam-4850	501	3	]	]	X
ejpam-4850	501	4	yong	yong	PROPN
ejpam-4850	501	5	-	-	PUNCT
ejpam-4850	501	6	ju	ju	PROPN
ejpam-4850	501	7	yang	yang	PROPN
ejpam-4850	501	8	,	,	PUNCT
ejpam-4850	501	9	dumitru	dumitru	PROPN
ejpam-4850	501	10	baleanu	baleanu	NOUN
ejpam-4850	501	11	,	,	PUNCT
ejpam-4850	501	12	and	and	CCONJ
ejpam-4850	501	13	xiao	xiao	PROPN
ejpam-4850	501	14	-	-	PUNCT
ejpam-4850	501	15	jun	jun	PROPN
ejpam-4850	501	16	yang	yang	PROPN
ejpam-4850	501	17	.	.	PUNCT
ejpam-4850	502	1	analysis	analysis	NOUN
ejpam-4850	502	2	of	of	ADP
ejpam-4850	502	3	fractal	fractal	ADJ
ejpam-4850	502	4	wave	wave	NOUN
ejpam-4850	502	5	equations	equation	NOUN
ejpam-4850	502	6	by	by	ADP
ejpam-4850	502	7	local	local	ADJ
ejpam-4850	502	8	fractional	fractional	ADJ
ejpam-4850	502	9	fourier	fourier	NOUN
ejpam-4850	502	10	series	series	NOUN
ejpam-4850	502	11	method	method	PROPN
ejpam-4850	502	12	.	.	PUNCT
ejpam-4850	503	1	advances	advance	NOUN
ejpam-4850	503	2	in	in	ADP
ejpam-4850	503	3	mathematical	mathematical	ADJ
ejpam-4850	503	4	physics	physics	NOUN
ejpam-4850	503	5	,	,	PUNCT
ejpam-4850	503	6	2013	2013	NUM
ejpam-4850	503	7	,	,	PUNCT
ejpam-4850	503	8	2013	2013	NUM
ejpam-4850	503	9	.	.	PUNCT