id	sid	tid	token	lemma	pos
ejpam-6159	1	1	european	european	PROPN
ejpam-6159	1	2	journal	journal	PROPN
ejpam-6159	1	3	of	of	ADP
ejpam-6159	1	4	pure	pure	ADJ
ejpam-6159	1	5	and	and	CCONJ
ejpam-6159	1	6	applied	applied	ADJ
ejpam-6159	1	7	mathematics	mathematic	NOUN
ejpam-6159	1	8	2025	2025	NUM
ejpam-6159	1	9	,	,	PUNCT
ejpam-6159	1	10	vol	vol	NOUN
ejpam-6159	1	11	.	.	PROPN
ejpam-6159	1	12	18	18	NUM
ejpam-6159	1	13	,	,	PUNCT
ejpam-6159	1	14	issue	issue	NOUN
ejpam-6159	1	15	3	3	NUM
ejpam-6159	1	16	,	,	PUNCT
ejpam-6159	1	17	article	article	NOUN
ejpam-6159	1	18	number	number	NOUN
ejpam-6159	1	19	6159	6159	NUM
ejpam-6159	1	20	issn	issn	VERB
ejpam-6159	1	21	1307	1307	NUM
ejpam-6159	1	22	-	-	SYM
ejpam-6159	1	23	5543	5543	NUM
ejpam-6159	1	24	–	–	PUNCT
ejpam-6159	1	25	ejpam.com	ejpam.com	X
ejpam-6159	1	26	published	publish	VERB
ejpam-6159	1	27	by	by	ADP
ejpam-6159	1	28	new	new	PROPN
ejpam-6159	1	29	york	york	PROPN
ejpam-6159	1	30	business	business	PROPN
ejpam-6159	1	31	global	global	PROPN
ejpam-6159	1	32	a	a	DET
ejpam-6159	1	33	novel	novel	ADJ
ejpam-6159	1	34	fractional	fractional	ADJ
ejpam-6159	1	35	integral	integral	NOUN
ejpam-6159	1	36	of	of	ADP
ejpam-6159	1	37	a	a	DET
ejpam-6159	1	38	function	function	NOUN
ejpam-6159	1	39	via	via	ADP
ejpam-6159	1	40	polynomial	polynomial	ADJ
ejpam-6159	1	41	n	n	CCONJ
ejpam-6159	1	42	-	-	PUNCT
ejpam-6159	1	43	fractional	fractional	ADJ
ejpam-6159	1	44	s	s	NOUN
ejpam-6159	1	45	-	-	PUNCT
ejpam-6159	1	46	like	like	ADJ
ejpam-6159	1	47	preinvexity	preinvexity	NOUN
ejpam-6159	1	48	jamshed	jamshe	VERB
ejpam-6159	1	49	nasir1	nasir1	PROPN
ejpam-6159	1	50	,	,	PUNCT
ejpam-6159	1	51	hassen	hassen	PROPN
ejpam-6159	1	52	aydi2,3,∗	aydi2,3,∗	PROPN
ejpam-6159	1	53	,	,	PUNCT
ejpam-6159	1	54	saber	saber	NOUN
ejpam-6159	1	55	mansour4	mansour4	PROPN
ejpam-6159	1	56	1	1	NUM
ejpam-6159	1	57	department	department	NOUN
ejpam-6159	1	58	of	of	ADP
ejpam-6159	1	59	mathematics	mathematic	NOUN
ejpam-6159	1	60	and	and	CCONJ
ejpam-6159	1	61	statistics	statistic	NOUN
ejpam-6159	1	62	,	,	PUNCT
ejpam-6159	1	63	virtual	virtual	ADJ
ejpam-6159	1	64	university	university	NOUN
ejpam-6159	1	65	of	of	ADP
ejpam-6159	1	66	pakistan	pakistan	PROPN
ejpam-6159	1	67	,	,	PUNCT
ejpam-6159	1	68	lahore	lahore	NOUN
ejpam-6159	1	69	campus	campus	NOUN
ejpam-6159	1	70	,	,	PUNCT
ejpam-6159	1	71	54000	54000	NUM
ejpam-6159	1	72	,	,	PUNCT
ejpam-6159	1	73	pakistan	pakistan	PROPN
ejpam-6159	1	74	.	.	PUNCT
ejpam-6159	2	1	2	2	NUM
ejpam-6159	2	2	institut	institut	PROPN
ejpam-6159	2	3	supérieur	supérieur	PROPN
ejpam-6159	2	4	d’informatique	d’informatique	PROPN
ejpam-6159	2	5	et	et	NOUN
ejpam-6159	2	6	des	des	X
ejpam-6159	2	7	techniques	techniques	X
ejpam-6159	2	8	de	de	X
ejpam-6159	2	9	communication	communication	NOUN
ejpam-6159	2	10	,	,	PUNCT
ejpam-6159	2	11	université	université	ADJ
ejpam-6159	2	12	de	de	X
ejpam-6159	2	13	sousse	sousse	PROPN
ejpam-6159	2	14	,	,	PUNCT
ejpam-6159	2	15	h.	h.	PROPN
ejpam-6159	2	16	sousse	sousse	PROPN
ejpam-6159	2	17	4000	4000	NUM
ejpam-6159	2	18	,	,	PUNCT
ejpam-6159	2	19	tunisia	tunisia	PROPN
ejpam-6159	2	20	.	.	PUNCT
ejpam-6159	3	1	3	3	NUM
ejpam-6159	3	2	department	department	NOUN
ejpam-6159	3	3	of	of	ADP
ejpam-6159	3	4	mathematics	mathematic	NOUN
ejpam-6159	3	5	and	and	CCONJ
ejpam-6159	3	6	applied	apply	VERB
ejpam-6159	3	7	mathematics	mathematic	NOUN
ejpam-6159	3	8	,	,	PUNCT
ejpam-6159	3	9	sefako	sefako	VERB
ejpam-6159	3	10	makgatho	makgatho	PROPN
ejpam-6159	3	11	health	health	PROPN
ejpam-6159	3	12	sciences	sciences	PROPN
ejpam-6159	3	13	university	university	PROPN
ejpam-6159	3	14	,	,	PUNCT
ejpam-6159	3	15	ga	ga	PROPN
ejpam-6159	3	16	-	-	NOUN
ejpam-6159	3	17	rankuwa	rankuwa	ADJ
ejpam-6159	3	18	,	,	PUNCT
ejpam-6159	3	19	south	south	PROPN
ejpam-6159	3	20	africa	africa	PROPN
ejpam-6159	3	21	.	.	PUNCT
ejpam-6159	4	1	4	4	NUM
ejpam-6159	4	2	department	department	NOUN
ejpam-6159	4	3	of	of	ADP
ejpam-6159	4	4	mathematics	mathematic	NOUN
ejpam-6159	4	5	,	,	PUNCT
ejpam-6159	4	6	umm	umm	INTJ
ejpam-6159	4	7	al	al	PROPN
ejpam-6159	4	8	-	-	PUNCT
ejpam-6159	4	9	qura	qura	PROPN
ejpam-6159	4	10	university	university	NOUN
ejpam-6159	4	11	,	,	PUNCT
ejpam-6159	4	12	faculty	faculty	NOUN
ejpam-6159	4	13	of	of	ADP
ejpam-6159	4	14	sciences	sciences	PROPN
ejpam-6159	4	15	,	,	PUNCT
ejpam-6159	4	16	p.o	p.o	PROPN
ejpam-6159	4	17	.	.	PROPN
ejpam-6159	4	18	box	box	PROPN
ejpam-6159	4	19	14035	14035	NUM
ejpam-6159	4	20	,	,	PUNCT
ejpam-6159	4	21	holy	holy	PROPN
ejpam-6159	4	22	makkah	makkah	PROPN
ejpam-6159	4	23	21955	21955	NUM
ejpam-6159	4	24	,	,	PUNCT
ejpam-6159	4	25	saudi	saudi	PROPN
ejpam-6159	4	26	arabia	arabia	PROPN
ejpam-6159	4	27	.	.	PUNCT
ejpam-6159	5	1	abstract	abstract	ADJ
ejpam-6159	5	2	.	.	PUNCT
ejpam-6159	6	1	in	in	ADP
ejpam-6159	6	2	the	the	DET
ejpam-6159	6	3	following	follow	VERB
ejpam-6159	6	4	numerical	numerical	ADJ
ejpam-6159	6	5	novel	novel	NOUN
ejpam-6159	6	6	,	,	PUNCT
ejpam-6159	6	7	we	we	PRON
ejpam-6159	6	8	develop	develop	VERB
ejpam-6159	6	9	a	a	DET
ejpam-6159	6	10	new	new	ADJ
ejpam-6159	6	11	fractional	fractional	ADJ
ejpam-6159	6	12	integral	integral	ADJ
ejpam-6159	6	13	operator	operator	NOUN
ejpam-6159	6	14	that	that	PRON
ejpam-6159	6	15	incorporates	incorporate	VERB
ejpam-6159	6	16	polynomials	polynomial	NOUN
ejpam-6159	6	17	n	n	CCONJ
ejpam-6159	6	18	-	-	PUNCT
ejpam-6159	6	19	fractional	fractional	ADJ
ejpam-6159	6	20	with	with	ADP
ejpam-6159	6	21	s	s	NOUN
ejpam-6159	6	22	-	-	PUNCT
ejpam-6159	6	23	like	like	ADJ
ejpam-6159	6	24	preinvexity	preinvexity	NOUN
ejpam-6159	6	25	,	,	PUNCT
ejpam-6159	6	26	thus	thus	ADV
ejpam-6159	6	27	expanding	expand	VERB
ejpam-6159	6	28	the	the	DET
ejpam-6159	6	29	notion	notion	NOUN
ejpam-6159	6	30	of	of	ADP
ejpam-6159	6	31	fractional	fractional	ADJ
ejpam-6159	6	32	calculus	calculus	NOUN
ejpam-6159	6	33	.	.	PUNCT
ejpam-6159	7	1	this	this	DET
ejpam-6159	7	2	new	new	ADJ
ejpam-6159	7	3	operator	operator	NOUN
ejpam-6159	7	4	provides	provide	VERB
ejpam-6159	7	5	a	a	DET
ejpam-6159	7	6	more	more	ADV
ejpam-6159	7	7	comprehensive	comprehensive	ADJ
ejpam-6159	7	8	framework	framework	NOUN
ejpam-6159	7	9	for	for	ADP
ejpam-6159	7	10	examining	examine	VERB
ejpam-6159	7	11	the	the	DET
ejpam-6159	7	12	behavior	behavior	NOUN
ejpam-6159	7	13	of	of	ADP
ejpam-6159	7	14	functions	function	NOUN
ejpam-6159	7	15	exhibiting	exhibit	VERB
ejpam-6159	7	16	generalized	generalized	ADJ
ejpam-6159	7	17	preinvexity	preinvexity	NOUN
ejpam-6159	7	18	properties	property	NOUN
ejpam-6159	7	19	which	which	PRON
ejpam-6159	7	20	are	be	AUX
ejpam-6159	7	21	crucial	crucial	ADJ
ejpam-6159	7	22	in	in	ADP
ejpam-6159	7	23	many	many	ADJ
ejpam-6159	7	24	optimization	optimization	NOUN
ejpam-6159	7	25	problems	problem	NOUN
ejpam-6159	7	26	.	.	PUNCT
ejpam-6159	8	1	we	we	PRON
ejpam-6159	8	2	investigate	investigate	VERB
ejpam-6159	8	3	the	the	DET
ejpam-6159	8	4	existence	existence	NOUN
ejpam-6159	8	5	,	,	PUNCT
ejpam-6159	8	6	uniqueness	uniqueness	NOUN
ejpam-6159	8	7	,	,	PUNCT
ejpam-6159	8	8	and	and	CCONJ
ejpam-6159	8	9	stability	stability	NOUN
ejpam-6159	8	10	of	of	ADP
ejpam-6159	8	11	this	this	DET
ejpam-6159	8	12	fractional	fractional	ADJ
ejpam-6159	8	13	integral	integral	ADJ
ejpam-6159	8	14	as	as	ADV
ejpam-6159	8	15	well	well	ADV
ejpam-6159	8	16	as	as	ADP
ejpam-6159	8	17	its	its	PRON
ejpam-6159	8	18	basic	basic	ADJ
ejpam-6159	8	19	characteristics	characteristic	NOUN
ejpam-6159	8	20	.	.	PUNCT
ejpam-6159	9	1	in	in	ADP
ejpam-6159	9	2	addition	addition	NOUN
ejpam-6159	9	3	,	,	PUNCT
ejpam-6159	9	4	we	we	PRON
ejpam-6159	9	5	provide	provide	VERB
ejpam-6159	9	6	a	a	DET
ejpam-6159	9	7	number	number	NOUN
ejpam-6159	9	8	of	of	ADP
ejpam-6159	9	9	inequalities	inequality	NOUN
ejpam-6159	9	10	that	that	PRON
ejpam-6159	9	11	show	show	VERB
ejpam-6159	9	12	how	how	SCONJ
ejpam-6159	9	13	useful	useful	ADJ
ejpam-6159	9	14	this	this	DET
ejpam-6159	9	15	operator	operator	NOUN
ejpam-6159	9	16	is	be	AUX
ejpam-6159	9	17	in	in	ADP
ejpam-6159	9	18	the	the	DET
ejpam-6159	9	19	context	context	NOUN
ejpam-6159	9	20	of	of	ADP
ejpam-6159	9	21	applied	apply	VERB
ejpam-6159	9	22	sciences	science	NOUN
ejpam-6159	9	23	and	and	CCONJ
ejpam-6159	9	24	mathematical	mathematical	ADJ
ejpam-6159	9	25	analysis	analysis	NOUN
ejpam-6159	9	26	.	.	PUNCT
ejpam-6159	10	1	our	our	PRON
ejpam-6159	10	2	results	result	NOUN
ejpam-6159	10	3	not	not	PART
ejpam-6159	10	4	only	only	ADV
ejpam-6159	10	5	advance	advance	VERB
ejpam-6159	10	6	the	the	DET
ejpam-6159	10	7	theory	theory	NOUN
ejpam-6159	10	8	of	of	ADP
ejpam-6159	10	9	fractional	fractional	ADJ
ejpam-6159	10	10	calculus	calculus	NOUN
ejpam-6159	10	11	but	but	CCONJ
ejpam-6159	10	12	also	also	ADV
ejpam-6159	10	13	pave	pave	VERB
ejpam-6159	10	14	the	the	DET
ejpam-6159	10	15	way	way	NOUN
ejpam-6159	10	16	for	for	ADP
ejpam-6159	10	17	future	future	ADJ
ejpam-6159	10	18	investigations	investigation	NOUN
ejpam-6159	10	19	into	into	ADP
ejpam-6159	10	20	integral	integral	ADJ
ejpam-6159	10	21	inequalities	inequality	NOUN
ejpam-6159	10	22	and	and	CCONJ
ejpam-6159	10	23	fractional	fractional	ADJ
ejpam-6159	10	24	optimization	optimization	NOUN
ejpam-6159	10	25	.	.	PUNCT
ejpam-6159	11	1	2020	2020	NUM
ejpam-6159	11	2	mathematics	mathematic	NOUN
ejpam-6159	11	3	subject	subject	NOUN
ejpam-6159	11	4	classifications	classification	NOUN
ejpam-6159	11	5	:	:	PUNCT
ejpam-6159	11	6	26d15	26d15	NUM
ejpam-6159	11	7	,	,	PUNCT
ejpam-6159	11	8	26d51	26d51	NUM
ejpam-6159	11	9	,	,	PUNCT
ejpam-6159	11	10	26d07	26d07	NUM
ejpam-6159	11	11	,	,	PUNCT
ejpam-6159	11	12	26d10	26d10	NUM
ejpam-6159	11	13	key	key	ADJ
ejpam-6159	11	14	words	word	NOUN
ejpam-6159	11	15	and	and	CCONJ
ejpam-6159	11	16	phrases	phrase	NOUN
ejpam-6159	11	17	:	:	PUNCT
ejpam-6159	11	18	preinvex	preinvex	ADJ
ejpam-6159	11	19	function	function	NOUN
ejpam-6159	11	20	,	,	PUNCT
ejpam-6159	11	21	polynomial	polynomial	ADJ
ejpam-6159	11	22	n	n	CCONJ
ejpam-6159	11	23	-	-	PUNCT
ejpam-6159	11	24	fractional	fractional	ADJ
ejpam-6159	11	25	s	s	NOUN
ejpam-6159	11	26	-	-	PUNCT
ejpam-6159	11	27	like	like	ADJ
ejpam-6159	11	28	preinvexity	preinvexity	NOUN
ejpam-6159	11	29	,	,	PUNCT
ejpam-6159	11	30	kfractional	kfractional	ADJ
ejpam-6159	11	31	operator	operator	NOUN
ejpam-6159	11	32	1	1	NUM
ejpam-6159	11	33	.	.	PUNCT
ejpam-6159	12	1	introduction	introduction	NOUN
ejpam-6159	12	2	and	and	CCONJ
ejpam-6159	12	3	preliminaries	preliminary	NOUN
ejpam-6159	12	4	integral	integral	ADJ
ejpam-6159	12	5	inequalities	inequality	NOUN
ejpam-6159	12	6	provide	provide	VERB
ejpam-6159	12	7	significant	significant	ADJ
ejpam-6159	12	8	bounds	bound	NOUN
ejpam-6159	12	9	for	for	ADP
ejpam-6159	12	10	function	function	NOUN
ejpam-6159	12	11	integrals	integral	NOUN
ejpam-6159	12	12	,	,	PUNCT
ejpam-6159	12	13	making	make	VERB
ejpam-6159	12	14	them	they	PRON
ejpam-6159	12	15	indispensable	indispensable	ADJ
ejpam-6159	12	16	tools	tool	NOUN
ejpam-6159	12	17	in	in	ADP
ejpam-6159	12	18	mathematical	mathematical	ADJ
ejpam-6159	12	19	analysis	analysis	NOUN
ejpam-6159	12	20	(	(	PUNCT
ejpam-6159	12	21	see	see	VERB
ejpam-6159	12	22	[	[	X
ejpam-6159	12	23	1	1	NUM
ejpam-6159	12	24	,	,	PUNCT
ejpam-6159	12	25	2	2	NUM
ejpam-6159	12	26	]	]	PUNCT
ejpam-6159	12	27	)	)	PUNCT
ejpam-6159	12	28	.	.	PUNCT
ejpam-6159	13	1	when	when	SCONJ
ejpam-6159	13	2	exact	exact	ADJ
ejpam-6159	13	3	evaluation	evaluation	NOUN
ejpam-6159	13	4	is	be	AUX
ejpam-6159	13	5	challenging	challenge	VERB
ejpam-6159	13	6	or	or	CCONJ
ejpam-6159	13	7	impossible	impossible	ADJ
ejpam-6159	13	8	,	,	PUNCT
ejpam-6159	13	9	these	these	DET
ejpam-6159	13	10	inequalities	inequality	NOUN
ejpam-6159	13	11	can	can	AUX
ejpam-6159	13	12	be	be	AUX
ejpam-6159	13	13	used	use	VERB
ejpam-6159	13	14	to	to	PART
ejpam-6159	13	15	estimate	estimate	VERB
ejpam-6159	13	16	the	the	DET
ejpam-6159	13	17	magnitude	magnitude	NOUN
ejpam-6159	13	18	or	or	CCONJ
ejpam-6159	13	19	behavior	behavior	NOUN
ejpam-6159	13	20	of	of	ADP
ejpam-6159	13	21	a	a	DET
ejpam-6159	13	22	function	function	NOUN
ejpam-6159	13	23	’s	’s	PART
ejpam-6159	13	24	integral	integral	ADJ
ejpam-6159	13	25	.	.	PUNCT
ejpam-6159	14	1	typical	typical	ADJ
ejpam-6159	14	2	instances	instance	NOUN
ejpam-6159	14	3	are	be	AUX
ejpam-6159	14	4	the	the	DET
ejpam-6159	14	5	minkowski	minkowski	ADJ
ejpam-6159	14	6	inequality	inequality	NOUN
ejpam-6159	14	7	,	,	PUNCT
ejpam-6159	14	8	related	relate	VERB
ejpam-6159	14	9	to	to	ADP
ejpam-6159	14	10	lp	lp	NOUN
ejpam-6159	14	11	spaces	space	NOUN
ejpam-6159	14	12	and	and	CCONJ
ejpam-6159	14	13	norms	norm	NOUN
ejpam-6159	14	14	,	,	PUNCT
ejpam-6159	14	15	and	and	CCONJ
ejpam-6159	14	16	hölder	hölder	PROPN
ejpam-6159	14	17	’s	’s	PART
ejpam-6159	14	18	inequality	inequality	NOUN
ejpam-6159	14	19	,	,	PUNCT
ejpam-6159	14	20	which	which	PRON
ejpam-6159	14	21	extends	extend	VERB
ejpam-6159	14	22	the	the	DET
ejpam-6159	14	23	cauchy	cauchy	PROPN
ejpam-6159	14	24	-	-	PUNCT
ejpam-6159	14	25	schwarz	schwarz	PROPN
ejpam-6159	14	26	inequality	inequality	NOUN
ejpam-6159	14	27	∗corresponding	∗corresponde	VERB
ejpam-6159	14	28	author	author	NOUN
ejpam-6159	14	29	.	.	PUNCT
ejpam-6159	15	1	doi	doi	NOUN
ejpam-6159	15	2	:	:	PUNCT
ejpam-6159	15	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6159	https://doi.org/10.29020/nybg.ejpam.v18i3.6159	PRON
ejpam-6159	15	4	email	email	NOUN
ejpam-6159	15	5	addresses	address	NOUN
ejpam-6159	15	6	:	:	PUNCT
ejpam-6159	15	7	jamshed@vu.edu.pk	jamshed@vu.edu.pk	PROPN
ejpam-6159	15	8	(	(	PUNCT
ejpam-6159	15	9	j.	j.	PROPN
ejpam-6159	15	10	nasir	nasir	PROPN
ejpam-6159	15	11	)	)	PUNCT
ejpam-6159	15	12	,	,	PUNCT
ejpam-6159	15	13	hassen.aydi@isima.rnu.tn	hassen.aydi@isima.rnu.tn	PROPN
ejpam-6159	15	14	(	(	PUNCT
ejpam-6159	15	15	h.	h.	PROPN
ejpam-6159	15	16	aydi	aydi	VERB
ejpam-6159	15	17	)	)	PUNCT
ejpam-6159	15	18	,	,	PUNCT
ejpam-6159	15	19	samansour@uqu.edu.sa	samansour@uqu.edu.sa	PROPN
ejpam-6159	15	20	(	(	PUNCT
ejpam-6159	15	21	s.	s.	PROPN
ejpam-6159	15	22	mansour	mansour	PROPN
ejpam-6159	15	23	)	)	PUNCT
ejpam-6159	15	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6159	16	1	1	1	NUM
ejpam-6159	16	2	copyright	copyright	NOUN
ejpam-6159	16	3	:	:	PUNCT
ejpam-6159	16	4	©	©	PROPN
ejpam-6159	16	5	2025	2025	NUM
ejpam-6159	16	6	the	the	DET
ejpam-6159	16	7	author(s	author(s	NOUN
ejpam-6159	16	8	)	)	PUNCT
ejpam-6159	16	9	.	.	PUNCT
ejpam-6159	17	1	(	(	PUNCT
ejpam-6159	17	2	cc	cc	NOUN
ejpam-6159	17	3	by	by	ADP
ejpam-6159	17	4	-	-	PUNCT
ejpam-6159	17	5	nc	nc	PROPN
ejpam-6159	17	6	4.0	4.0	NUM
ejpam-6159	17	7	)	)	PUNCT
ejpam-6159	17	8	j.	j.	PROPN
ejpam-6159	17	9	nasir	nasir	PROPN
ejpam-6159	17	10	et	et	PROPN
ejpam-6159	17	11	al	al	PROPN
ejpam-6159	17	12	.	.	PUNCT
ejpam-6159	17	13	/	/	SYM
ejpam-6159	17	14	eur	eur	PROPN
ejpam-6159	17	15	.	.	PUNCT
ejpam-6159	18	1	j.	j.	PROPN
ejpam-6159	18	2	pure	pure	PROPN
ejpam-6159	18	3	appl	appl	PROPN
ejpam-6159	18	4	.	.	PROPN
ejpam-6159	18	5	math	math	PROPN
ejpam-6159	18	6	,	,	PUNCT
ejpam-6159	18	7	18	18	NUM
ejpam-6159	18	8	(	(	PUNCT
ejpam-6159	18	9	3	3	NUM
ejpam-6159	18	10	)	)	PUNCT
ejpam-6159	18	11	(	(	PUNCT
ejpam-6159	18	12	2025	2025	NUM
ejpam-6159	18	13	)	)	PUNCT
ejpam-6159	18	14	,	,	PUNCT
ejpam-6159	18	15	6159	6159	NUM
ejpam-6159	18	16	2	2	NUM
ejpam-6159	18	17	of	of	ADP
ejpam-6159	18	18	26	26	NUM
ejpam-6159	18	19	to	to	ADP
ejpam-6159	18	20	integrals	integral	NOUN
ejpam-6159	18	21	.	.	PUNCT
ejpam-6159	19	1	in	in	ADP
ejpam-6159	19	2	many	many	ADJ
ejpam-6159	19	3	domains	domain	NOUN
ejpam-6159	19	4	,	,	PUNCT
ejpam-6159	19	5	including	include	VERB
ejpam-6159	19	6	partial	partial	ADJ
ejpam-6159	19	7	differential	differential	ADJ
ejpam-6159	19	8	equations	equation	NOUN
ejpam-6159	19	9	,	,	PUNCT
ejpam-6159	19	10	probability	probability	NOUN
ejpam-6159	19	11	theory	theory	NOUN
ejpam-6159	19	12	,	,	PUNCT
ejpam-6159	19	13	and	and	CCONJ
ejpam-6159	19	14	numerical	numerical	ADJ
ejpam-6159	19	15	analysis	analysis	NOUN
ejpam-6159	19	16	,	,	PUNCT
ejpam-6159	19	17	these	these	DET
ejpam-6159	19	18	inequalities	inequality	NOUN
ejpam-6159	19	19	are	be	AUX
ejpam-6159	19	20	crucial	crucial	ADJ
ejpam-6159	19	21	for	for	ADP
ejpam-6159	19	22	enabling	enable	VERB
ejpam-6159	19	23	the	the	DET
ejpam-6159	19	24	study	study	NOUN
ejpam-6159	19	25	of	of	ADP
ejpam-6159	19	26	function	function	NOUN
ejpam-6159	19	27	spaces	space	NOUN
ejpam-6159	19	28	,	,	PUNCT
ejpam-6159	19	29	the	the	DET
ejpam-6159	19	30	convergence	convergence	NOUN
ejpam-6159	19	31	of	of	ADP
ejpam-6159	19	32	function	function	NOUN
ejpam-6159	19	33	sequences	sequence	NOUN
ejpam-6159	19	34	,	,	PUNCT
ejpam-6159	19	35	and	and	CCONJ
ejpam-6159	19	36	the	the	DET
ejpam-6159	19	37	stability	stability	NOUN
ejpam-6159	19	38	of	of	ADP
ejpam-6159	19	39	differential	differential	ADJ
ejpam-6159	19	40	equation	equation	NOUN
ejpam-6159	19	41	solutions	solution	NOUN
ejpam-6159	19	42	.	.	PUNCT
ejpam-6159	20	1	integral	integral	ADJ
ejpam-6159	20	2	inequalities	inequality	NOUN
ejpam-6159	20	3	are	be	AUX
ejpam-6159	20	4	essential	essential	ADJ
ejpam-6159	20	5	in	in	ADP
ejpam-6159	20	6	optimization	optimization	NOUN
ejpam-6159	20	7	problems	problem	NOUN
ejpam-6159	20	8	and	and	CCONJ
ejpam-6159	20	9	the	the	DET
ejpam-6159	20	10	demonstration	demonstration	NOUN
ejpam-6159	20	11	of	of	ADP
ejpam-6159	20	12	existence	existence	NOUN
ejpam-6159	20	13	and	and	CCONJ
ejpam-6159	20	14	uniqueness	uniqueness	NOUN
ejpam-6159	20	15	because	because	SCONJ
ejpam-6159	20	16	they	they	PRON
ejpam-6159	20	17	set	set	VERB
ejpam-6159	20	18	upper	upper	ADJ
ejpam-6159	20	19	and	and	CCONJ
ejpam-6159	20	20	lower	low	ADJ
ejpam-6159	20	21	bounds	bound	NOUN
ejpam-6159	20	22	.	.	PUNCT
ejpam-6159	21	1	mathematicians	mathematician	NOUN
ejpam-6159	21	2	including	include	VERB
ejpam-6159	21	3	leibniz	leibniz	PROPN
ejpam-6159	21	4	,	,	PUNCT
ejpam-6159	21	5	liouville	liouville	PROPN
ejpam-6159	21	6	,	,	PUNCT
ejpam-6159	21	7	riemann	riemann	PROPN
ejpam-6159	21	8	,	,	PUNCT
ejpam-6159	21	9	and	and	CCONJ
ejpam-6159	21	10	others	other	NOUN
ejpam-6159	21	11	investigated	investigate	VERB
ejpam-6159	21	12	the	the	DET
ejpam-6159	21	13	idea	idea	NOUN
ejpam-6159	21	14	of	of	ADP
ejpam-6159	21	15	extending	extend	VERB
ejpam-6159	21	16	the	the	DET
ejpam-6159	21	17	nth	nth	NOUN
ejpam-6159	21	18	-	-	PUNCT
ejpam-6159	21	19	order	order	NOUN
ejpam-6159	21	20	derivative	derivative	NOUN
ejpam-6159	21	21	to	to	ADP
ejpam-6159	21	22	non	non	ADJ
ejpam-6159	21	23	-	-	ADJ
ejpam-6159	21	24	integer	integer	ADJ
ejpam-6159	21	25	values	value	NOUN
ejpam-6159	21	26	,	,	PUNCT
ejpam-6159	21	27	laying	lay	VERB
ejpam-6159	21	28	the	the	DET
ejpam-6159	21	29	groundwork	groundwork	NOUN
ejpam-6159	21	30	for	for	ADP
ejpam-6159	21	31	fractional	fractional	ADJ
ejpam-6159	21	32	calculus	calculus	NOUN
ejpam-6159	21	33	.	.	PUNCT
ejpam-6159	22	1	the	the	DET
ejpam-6159	22	2	fractional	fractional	ADJ
ejpam-6159	22	3	derivative	derivative	NOUN
ejpam-6159	22	4	,	,	PUNCT
ejpam-6159	22	5	which	which	PRON
ejpam-6159	22	6	has	have	VERB
ejpam-6159	22	7	multiple	multiple	ADJ
ejpam-6159	22	8	definitions	definition	NOUN
ejpam-6159	22	9	(	(	PUNCT
ejpam-6159	22	10	riemannliouville	riemannliouville	NOUN
ejpam-6159	22	11	,	,	PUNCT
ejpam-6159	22	12	caputo	caputo	PROPN
ejpam-6159	22	13	,	,	PUNCT
ejpam-6159	22	14	and	and	CCONJ
ejpam-6159	22	15	grünwald	grünwald	ADJ
ejpam-6159	22	16	-	-	NOUN
ejpam-6159	22	17	letnikov	letnikov	NOUN
ejpam-6159	22	18	)	)	PUNCT
ejpam-6159	22	19	,	,	PUNCT
ejpam-6159	22	20	is	be	AUX
ejpam-6159	22	21	one	one	NUM
ejpam-6159	22	22	of	of	ADP
ejpam-6159	22	23	the	the	DET
ejpam-6159	22	24	fundamental	fundamental	ADJ
ejpam-6159	22	25	ideas	idea	NOUN
ejpam-6159	22	26	in	in	ADP
ejpam-6159	22	27	this	this	DET
ejpam-6159	22	28	discipline	discipline	NOUN
ejpam-6159	22	29	.	.	PUNCT
ejpam-6159	23	1	each	each	DET
ejpam-6159	23	2	definition	definition	NOUN
ejpam-6159	23	3	is	be	AUX
ejpam-6159	23	4	appropriate	appropriate	ADJ
ejpam-6159	23	5	for	for	ADP
ejpam-6159	23	6	a	a	DET
ejpam-6159	23	7	certain	certain	ADJ
ejpam-6159	23	8	set	set	NOUN
ejpam-6159	23	9	of	of	ADP
ejpam-6159	23	10	features	feature	NOUN
ejpam-6159	23	11	and	and	CCONJ
ejpam-6159	23	12	applications	application	NOUN
ejpam-6159	23	13	.	.	PUNCT
ejpam-6159	24	1	convex	convex	NOUN
ejpam-6159	24	2	functions	function	NOUN
ejpam-6159	24	3	were	be	AUX
ejpam-6159	24	4	significantly	significantly	ADV
ejpam-6159	24	5	expanded	expand	VERB
ejpam-6159	24	6	upon	upon	SCONJ
ejpam-6159	24	7	with	with	ADP
ejpam-6159	24	8	the	the	DET
ejpam-6159	24	9	introduction	introduction	NOUN
ejpam-6159	24	10	of	of	ADP
ejpam-6159	24	11	preinvex	preinvex	NOUN
ejpam-6159	24	12	functions	function	NOUN
ejpam-6159	24	13	,	,	PUNCT
ejpam-6159	24	14	which	which	PRON
ejpam-6159	24	15	broadened	broaden	VERB
ejpam-6159	24	16	the	the	DET
ejpam-6159	24	17	meaning	meaning	NOUN
ejpam-6159	24	18	of	of	ADP
ejpam-6159	24	19	convexity	convexity	NOUN
ejpam-6159	24	20	in	in	ADP
ejpam-6159	24	21	optimization	optimization	NOUN
ejpam-6159	24	22	theory	theory	NOUN
ejpam-6159	24	23	(	(	PUNCT
ejpam-6159	24	24	see	see	VERB
ejpam-6159	24	25	[	[	X
ejpam-6159	24	26	3–6	3–6	NUM
ejpam-6159	24	27	]	]	NOUN
ejpam-6159	24	28	)	)	PUNCT
ejpam-6159	24	29	.	.	PUNCT
ejpam-6159	25	1	preinvex	preinvex	NOUN
ejpam-6159	25	2	functions	function	NOUN
ejpam-6159	25	3	reduce	reduce	VERB
ejpam-6159	25	4	this	this	DET
ejpam-6159	25	5	requirement	requirement	NOUN
ejpam-6159	25	6	by	by	ADP
ejpam-6159	25	7	introducing	introduce	VERB
ejpam-6159	25	8	an	an	DET
ejpam-6159	25	9	invex	invex	NOUN
ejpam-6159	25	10	function	function	NOUN
ejpam-6159	25	11	,	,	PUNCT
ejpam-6159	25	12	whereas	whereas	SCONJ
ejpam-6159	25	13	convex	convex	NOUN
ejpam-6159	25	14	functions	function	NOUN
ejpam-6159	25	15	are	be	AUX
ejpam-6159	25	16	defined	define	VERB
ejpam-6159	25	17	by	by	ADP
ejpam-6159	25	18	the	the	DET
ejpam-6159	25	19	fact	fact	NOUN
ejpam-6159	25	20	that	that	SCONJ
ejpam-6159	25	21	any	any	DET
ejpam-6159	25	22	line	line	NOUN
ejpam-6159	25	23	segment	segment	NOUN
ejpam-6159	25	24	connecting	connect	VERB
ejpam-6159	25	25	two	two	NUM
ejpam-6159	25	26	points	point	NOUN
ejpam-6159	25	27	on	on	ADP
ejpam-6159	25	28	the	the	DET
ejpam-6159	25	29	function	function	NOUN
ejpam-6159	25	30	’s	’s	PART
ejpam-6159	25	31	graph	graph	NOUN
ejpam-6159	25	32	lies	lie	VERB
ejpam-6159	25	33	above	above	ADP
ejpam-6159	25	34	the	the	DET
ejpam-6159	25	35	graph	graph	NOUN
ejpam-6159	25	36	.	.	PUNCT
ejpam-6159	26	1	in	in	ADP
ejpam-6159	26	2	particular	particular	ADJ
ejpam-6159	26	3	,	,	PUNCT
ejpam-6159	26	4	an	an	DET
ejpam-6159	26	5	invex	invex	NOUN
ejpam-6159	26	6	function	function	NOUN
ejpam-6159	26	7	serves	serve	VERB
ejpam-6159	26	8	as	as	ADP
ejpam-6159	26	9	a	a	DET
ejpam-6159	26	10	sort	sort	NOUN
ejpam-6159	26	11	of	of	ADP
ejpam-6159	26	12	”	"	PUNCT
ejpam-6159	26	13	generalized	generalized	ADJ
ejpam-6159	26	14	direction	direction	NOUN
ejpam-6159	26	15	”	"	PUNCT
ejpam-6159	26	16	in	in	ADP
ejpam-6159	26	17	the	the	DET
ejpam-6159	26	18	domain	domain	NOUN
ejpam-6159	26	19	of	of	ADP
ejpam-6159	26	20	a	a	DET
ejpam-6159	26	21	function	function	NOUN
ejpam-6159	26	22	,	,	PUNCT
ejpam-6159	26	23	and	and	CCONJ
ejpam-6159	26	24	a	a	DET
ejpam-6159	26	25	function	function	NOUN
ejpam-6159	26	26	is	be	AUX
ejpam-6159	26	27	said	say	VERB
ejpam-6159	26	28	to	to	PART
ejpam-6159	26	29	be	be	AUX
ejpam-6159	26	30	preinvex	preinvex	ADJ
ejpam-6159	26	31	if	if	SCONJ
ejpam-6159	26	32	it	it	PRON
ejpam-6159	26	33	fulfills	fulfill	VERB
ejpam-6159	26	34	a	a	DET
ejpam-6159	26	35	specific	specific	ADJ
ejpam-6159	26	36	inequality	inequality	NOUN
ejpam-6159	26	37	with	with	ADP
ejpam-6159	26	38	regard	regard	NOUN
ejpam-6159	26	39	to	to	ADP
ejpam-6159	26	40	it	it	PRON
ejpam-6159	26	41	.	.	PUNCT
ejpam-6159	27	1	more	more	ADJ
ejpam-6159	27	2	applications	application	NOUN
ejpam-6159	27	3	can	can	AUX
ejpam-6159	27	4	be	be	AUX
ejpam-6159	27	5	made	make	VERB
ejpam-6159	27	6	possible	possible	ADJ
ejpam-6159	27	7	by	by	ADP
ejpam-6159	27	8	this	this	DET
ejpam-6159	27	9	generalization	generalization	NOUN
ejpam-6159	27	10	,	,	PUNCT
ejpam-6159	27	11	especially	especially	ADV
ejpam-6159	27	12	when	when	SCONJ
ejpam-6159	27	13	the	the	DET
ejpam-6159	27	14	standard	standard	ADJ
ejpam-6159	27	15	convexity	convexity	NOUN
ejpam-6159	27	16	requirements	requirement	NOUN
ejpam-6159	27	17	prove	prove	VERB
ejpam-6159	27	18	to	to	PART
ejpam-6159	27	19	be	be	AUX
ejpam-6159	27	20	too	too	ADV
ejpam-6159	27	21	restrictive	restrictive	ADJ
ejpam-6159	27	22	.	.	PUNCT
ejpam-6159	28	1	preinvex	preinvex	NOUN
ejpam-6159	28	2	functions	function	NOUN
ejpam-6159	28	3	are	be	AUX
ejpam-6159	28	4	useful	useful	ADJ
ejpam-6159	28	5	in	in	ADP
ejpam-6159	28	6	tackling	tackle	VERB
ejpam-6159	28	7	complicated	complicated	ADJ
ejpam-6159	28	8	optimization	optimization	NOUN
ejpam-6159	28	9	issues	issue	NOUN
ejpam-6159	28	10	,	,	PUNCT
ejpam-6159	28	11	such	such	ADJ
ejpam-6159	28	12	as	as	ADP
ejpam-6159	28	13	those	those	PRON
ejpam-6159	28	14	found	find	VERB
ejpam-6159	28	15	in	in	ADP
ejpam-6159	28	16	game	game	NOUN
ejpam-6159	28	17	theory	theory	NOUN
ejpam-6159	28	18	,	,	PUNCT
ejpam-6159	28	19	economics	economic	NOUN
ejpam-6159	28	20	,	,	PUNCT
ejpam-6159	28	21	and	and	CCONJ
ejpam-6159	28	22	multi	multi	ADJ
ejpam-6159	28	23	-	-	ADJ
ejpam-6159	28	24	objective	objective	ADJ
ejpam-6159	28	25	optimization	optimization	NOUN
ejpam-6159	28	26	(	(	PUNCT
ejpam-6159	28	27	see	see	VERB
ejpam-6159	28	28	[	[	X
ejpam-6159	28	29	7	7	NUM
ejpam-6159	28	30	–	–	PUNCT
ejpam-6159	28	31	9	9	NUM
ejpam-6159	28	32	]	]	PUNCT
ejpam-6159	28	33	)	)	PUNCT
ejpam-6159	28	34	.	.	PUNCT
ejpam-6159	29	1	they	they	PRON
ejpam-6159	29	2	maintain	maintain	VERB
ejpam-6159	29	3	many	many	ADJ
ejpam-6159	29	4	of	of	ADP
ejpam-6159	29	5	the	the	DET
ejpam-6159	29	6	beneficial	beneficial	ADJ
ejpam-6159	29	7	aspects	aspect	NOUN
ejpam-6159	29	8	of	of	ADP
ejpam-6159	29	9	convex	convex	NOUN
ejpam-6159	29	10	functions	function	NOUN
ejpam-6159	29	11	,	,	PUNCT
ejpam-6159	29	12	such	such	ADJ
ejpam-6159	29	13	as	as	ADP
ejpam-6159	29	14	certain	certain	ADJ
ejpam-6159	29	15	optimality	optimality	NOUN
ejpam-6159	29	16	criteria	criterion	NOUN
ejpam-6159	29	17	.	.	PUNCT
ejpam-6159	30	1	thus	thus	ADV
ejpam-6159	30	2	,	,	PUNCT
ejpam-6159	30	3	the	the	DET
ejpam-6159	30	4	emergence	emergence	NOUN
ejpam-6159	30	5	of	of	ADP
ejpam-6159	30	6	preinvexity	preinvexity	NOUN
ejpam-6159	30	7	has	have	AUX
ejpam-6159	30	8	created	create	VERB
ejpam-6159	30	9	new	new	ADJ
ejpam-6159	30	10	opportunities	opportunity	NOUN
ejpam-6159	30	11	for	for	ADP
ejpam-6159	30	12	study	study	NOUN
ejpam-6159	30	13	and	and	CCONJ
ejpam-6159	30	14	application	application	NOUN
ejpam-6159	30	15	in	in	ADP
ejpam-6159	30	16	fields	field	NOUN
ejpam-6159	30	17	where	where	SCONJ
ejpam-6159	30	18	conventional	conventional	ADJ
ejpam-6159	30	19	convex	convex	NOUN
ejpam-6159	30	20	analysis	analysis	NOUN
ejpam-6159	30	21	would	would	AUX
ejpam-6159	30	22	not	not	PART
ejpam-6159	30	23	be	be	AUX
ejpam-6159	30	24	enough	enough	ADJ
ejpam-6159	30	25	.	.	PUNCT
ejpam-6159	31	1	definition	definition	NOUN
ejpam-6159	31	2	1	1	NUM
ejpam-6159	31	3	.	.	PUNCT
ejpam-6159	32	1	[	[	X
ejpam-6159	32	2	10	10	NUM
ejpam-6159	32	3	]	]	PUNCT
ejpam-6159	32	4	the	the	DET
ejpam-6159	32	5	set	set	NOUN
ejpam-6159	32	6	xo	xo	PROPN
ejpam-6159	33	1	⊂	⊂	PROPN
ejpam-6159	34	1	ℜn	ℜn	PROPN
ejpam-6159	34	2	is	be	AUX
ejpam-6159	34	3	said	say	VERB
ejpam-6159	34	4	to	to	PART
ejpam-6159	34	5	be	be	AUX
ejpam-6159	34	6	invex	invex	NOUN
ejpam-6159	34	7	iwith	iwith	ADP
ejpam-6159	34	8	respect	respect	NOUN
ejpam-6159	34	9	to	to	PART
ejpam-6159	34	10	ς∗(∗	ς∗(∗	VERB
ejpam-6159	34	11	,	,	PUNCT
ejpam-6159	34	12	∗	∗	NOUN
ejpam-6159	34	13	)	)	PUNCT
ejpam-6159	34	14	,	,	PUNCT
ejpam-6159	34	15	if	if	SCONJ
ejpam-6159	34	16	for	for	ADP
ejpam-6159	34	17	every	every	DET
ejpam-6159	34	18	a1	a1	NOUN
ejpam-6159	34	19	,	,	PUNCT
ejpam-6159	34	20	b1	b1	NOUN
ejpam-6159	34	21	∈	∈	PROPN
ejpam-6159	34	22	xo	xo	PROPN
ejpam-6159	34	23	and	and	CCONJ
ejpam-6159	34	24	t	t	PROPN
ejpam-6159	34	25	∈	∈	PROPN
ejpam-6159	35	1	[	[	X
ejpam-6159	35	2	0	0	NUM
ejpam-6159	35	3	,	,	PUNCT
ejpam-6159	35	4	1	1	NUM
ejpam-6159	35	5	]	]	X
ejpam-6159	35	6	a1	a1	NOUN
ejpam-6159	35	7	+	+	CCONJ
ejpam-6159	35	8	tς∗(b1	tς∗(b1	PROPN
ejpam-6159	35	9	,	,	PUNCT
ejpam-6159	35	10	a1	a1	NOUN
ejpam-6159	35	11	)	)	PUNCT
ejpam-6159	35	12	∈	∈	PROPN
ejpam-6159	35	13	xo	xo	PROPN
ejpam-6159	35	14	.	.	PUNCT
ejpam-6159	36	1	in	in	ADP
ejpam-6159	36	2	definition	definition	NOUN
ejpam-6159	36	3	1	1	NUM
ejpam-6159	36	4	,	,	PUNCT
ejpam-6159	36	5	the	the	DET
ejpam-6159	36	6	set	set	NOUN
ejpam-6159	36	7	xo	xo	PROPN
ejpam-6159	36	8	is	be	AUX
ejpam-6159	36	9	also	also	ADV
ejpam-6159	36	10	known	know	VERB
ejpam-6159	36	11	to	to	PART
ejpam-6159	36	12	be	be	AUX
ejpam-6159	36	13	a	a	DET
ejpam-6159	36	14	ς∗−connectediset	ς∗−connectediset	PROPN
ejpam-6159	36	15	.	.	PUNCT
ejpam-6159	37	1	for	for	ADP
ejpam-6159	37	2	every	every	DET
ejpam-6159	37	3	convexiset	convexiset	NOUN
ejpam-6159	37	4	is	be	AUX
ejpam-6159	37	5	invex	invex	NOUN
ejpam-6159	37	6	withirespect	withirespect	ADJ
ejpam-6159	37	7	to	to	ADP
ejpam-6159	37	8	ς∗(b1	ς∗(b1	NOUN
ejpam-6159	37	9	,	,	PUNCT
ejpam-6159	37	10	a1	a1	NOUN
ejpam-6159	37	11	)	)	PUNCT
ejpam-6159	37	12	=	=	SYM
ejpam-6159	37	13	b1	b1	NOUN
ejpam-6159	37	14	−	−	NOUN
ejpam-6159	37	15	a1	a1	NOUN
ejpam-6159	37	16	but	but	CCONJ
ejpam-6159	37	17	there	there	PRON
ejpam-6159	37	18	exist	exist	VERB
ejpam-6159	37	19	invex	invex	NOUN
ejpam-6159	37	20	sets	set	NOUN
ejpam-6159	37	21	which	which	PRON
ejpam-6159	37	22	are	be	AUX
ejpam-6159	37	23	noticonvex	noticonvex	ADJ
ejpam-6159	37	24	(	(	PUNCT
ejpam-6159	37	25	see	see	VERB
ejpam-6159	37	26	[	[	X
ejpam-6159	37	27	11	11	NUM
ejpam-6159	37	28	]	]	NUM
ejpam-6159	37	29	)	)	PUNCT
ejpam-6159	37	30	.	.	PUNCT
ejpam-6159	38	1	definition	definition	NOUN
ejpam-6159	38	2	2	2	NUM
ejpam-6159	38	3	.	.	PUNCT
ejpam-6159	39	1	[	[	X
ejpam-6159	39	2	12	12	NUM
ejpam-6159	39	3	]	]	PUNCT
ejpam-6159	39	4	a	a	DET
ejpam-6159	39	5	mapping	mapping	NOUN
ejpam-6159	39	6	f	f	NOUN
ejpam-6159	39	7	on	on	ADP
ejpam-6159	39	8	the	the	DET
ejpam-6159	39	9	invex	invex	NOUN
ejpam-6159	39	10	set	set	VERB
ejpam-6159	39	11	xo	xo	PROPN
ejpam-6159	39	12	is	be	AUX
ejpam-6159	39	13	called	call	VERB
ejpam-6159	39	14	to	to	PART
ejpam-6159	39	15	be	be	AUX
ejpam-6159	39	16	preinvex	preinvex	ADJ
ejpam-6159	39	17	with	with	ADP
ejpam-6159	39	18	respect	respect	NOUN
ejpam-6159	39	19	(	(	PUNCT
ejpam-6159	39	20	w.r	w.r	PROPN
ejpam-6159	39	21	.	.	PUNCT
ejpam-6159	39	22	)	)	PUNCT
ejpam-6159	39	23	to	to	PART
ejpam-6159	39	24	ς∗	ς∗	VERB
ejpam-6159	39	25	if	if	SCONJ
ejpam-6159	39	26	f	f	PROPN
ejpam-6159	39	27	(	(	PUNCT
ejpam-6159	39	28	a1	a1	NOUN
ejpam-6159	39	29	+	+	CCONJ
ejpam-6159	39	30	tς∗	tς∗	NOUN
ejpam-6159	39	31	(	(	PUNCT
ejpam-6159	39	32	b1	b1	NOUN
ejpam-6159	39	33	,	,	PUNCT
ejpam-6159	39	34	a1	a1	NOUN
ejpam-6159	39	35	)	)	PUNCT
ejpam-6159	39	36	)	)	PUNCT
ejpam-6159	39	37	≤	≤	NOUN
ejpam-6159	39	38	(	(	PUNCT
ejpam-6159	39	39	1−	1−	NUM
ejpam-6159	39	40	t)f	t)f	X
ejpam-6159	39	41	(	(	PUNCT
ejpam-6159	39	42	a1	a1	NOUN
ejpam-6159	39	43	)	)	PUNCT
ejpam-6159	39	44	+	+	CCONJ
ejpam-6159	39	45	tf	tf	PROPN
ejpam-6159	39	46	(	(	PUNCT
ejpam-6159	39	47	b1	b1	PROPN
ejpam-6159	39	48	)	)	PUNCT
ejpam-6159	39	49	;	;	PUNCT
ejpam-6159	39	50	∀a1	∀a1	PROPN
ejpam-6159	39	51	,	,	PUNCT
ejpam-6159	39	52	b1	b1	PROPN
ejpam-6159	39	53	∈	∈	PROPN
ejpam-6159	39	54	xo	xo	PROPN
ejpam-6159	39	55	,	,	PUNCT
ejpam-6159	39	56	t	t	PROPN
ejpam-6159	39	57	∈	∈	PROPN
ejpam-6159	40	1	[	[	X
ejpam-6159	40	2	0	0	NUM
ejpam-6159	40	3	,	,	PUNCT
ejpam-6159	40	4	1	1	NUM
ejpam-6159	40	5	]	]	PUNCT
ejpam-6159	40	6	.	.	PUNCT
ejpam-6159	41	1	(	(	PUNCT
ejpam-6159	41	2	1	1	X
ejpam-6159	41	3	)	)	PUNCT
ejpam-6159	41	4	the	the	DET
ejpam-6159	41	5	function	function	NOUN
ejpam-6159	41	6	−f	−f	NOUN
ejpam-6159	41	7	is	be	AUX
ejpam-6159	41	8	said	say	VERB
ejpam-6159	41	9	to	to	PART
ejpam-6159	41	10	be	be	AUX
ejpam-6159	41	11	preconcave	preconcave	NOUN
ejpam-6159	41	12	if	if	SCONJ
ejpam-6159	41	13	and	and	CCONJ
ejpam-6159	41	14	only	only	ADV
ejpam-6159	41	15	if	if	SCONJ
ejpam-6159	41	16	f	f	PROPN
ejpam-6159	41	17	is	be	AUX
ejpam-6159	41	18	preinvex	preinvex	ADJ
ejpam-6159	41	19	.	.	PUNCT
ejpam-6159	42	1	it	it	PRON
ejpam-6159	42	2	is	be	AUX
ejpam-6159	42	3	necessarily	necessarily	ADV
ejpam-6159	42	4	that	that	SCONJ
ejpam-6159	42	5	each	each	DET
ejpam-6159	42	6	convexity	convexity	NOUN
ejpam-6159	42	7	becomes	become	VERB
ejpam-6159	42	8	preinvexity	preinvexity	NOUN
ejpam-6159	42	9	,	,	PUNCT
ejpam-6159	42	10	but	but	CCONJ
ejpam-6159	42	11	not	not	PART
ejpam-6159	42	12	viceversa	viceversa	ADJ
ejpam-6159	43	1	[	[	X
ejpam-6159	43	2	13	13	NUM
ejpam-6159	43	3	]	]	PUNCT
ejpam-6159	43	4	.	.	PUNCT
ejpam-6159	44	1	for	for	ADP
ejpam-6159	44	2	example	example	NOUN
ejpam-6159	44	3	,	,	PUNCT
ejpam-6159	44	4	f(t	f(t	PROPN
ejpam-6159	44	5	)	)	PUNCT
ejpam-6159	44	6	=	=	SYM
ejpam-6159	45	1	−|t|	−|t|	NOUN
ejpam-6159	45	2	(	(	PUNCT
ejpam-6159	45	3	for	for	ADP
ejpam-6159	45	4	all	all	DET
ejpam-6159	45	5	t	t	NOUN
ejpam-6159	45	6	∈	∈	PROPN
ejpam-6159	45	7	ℜ	ℜ	PROPN
ejpam-6159	45	8	)	)	PUNCT
ejpam-6159	45	9	is	be	AUX
ejpam-6159	45	10	not	not	PART
ejpam-6159	45	11	a	a	DET
ejpam-6159	45	12	iconvex	iconvex	PROPN
ejpam-6159	45	13	mapping	mapping	NOUN
ejpam-6159	45	14	but	but	CCONJ
ejpam-6159	45	15	it	it	PRON
ejpam-6159	45	16	is	be	AUX
ejpam-6159	45	17	apreinvexifunction	apreinvexifunction	NOUN
ejpam-6159	45	18	w.r	w.r	PROPN
ejpam-6159	45	19	.	.	PROPN
ejpam-6159	45	20	to	to	PART
ejpam-6159	45	21	ς∗	ς∗	VERB
ejpam-6159	45	22	(	(	PUNCT
ejpam-6159	45	23	b1	b1	NOUN
ejpam-6159	45	24	,	,	PUNCT
ejpam-6159	45	25	a1	a1	NOUN
ejpam-6159	45	26	)	)	PUNCT
ejpam-6159	45	27	=	=	PRON
ejpam-6159	45	28	{	{	PUNCT
ejpam-6159	45	29	b1	b1	NOUN
ejpam-6159	45	30	−	−	NOUN
ejpam-6159	45	31	a1	a1	NOUN
ejpam-6159	45	32	if	if	SCONJ
ejpam-6159	45	33	a1b1	a1b1	PROPN
ejpam-6159	45	34	>	>	X
ejpam-6159	45	35	0	0	NUM
ejpam-6159	45	36	,	,	PUNCT
ejpam-6159	45	37	a1	a1	NOUN
ejpam-6159	45	38	−	−	PROPN
ejpam-6159	45	39	b1	b1	NOUN
ejpam-6159	45	40	if	if	SCONJ
ejpam-6159	45	41	a1b1	a1b1	PUNCT
ejpam-6159	45	42	<	<	X
ejpam-6159	45	43	0	0	X
ejpam-6159	45	44	.	.	PUNCT
ejpam-6159	46	1	j.	j.	PROPN
ejpam-6159	46	2	nasir	nasir	PROPN
ejpam-6159	46	3	et	et	PROPN
ejpam-6159	46	4	al	al	PROPN
ejpam-6159	46	5	.	.	PUNCT
ejpam-6159	46	6	/	/	SYM
ejpam-6159	46	7	eur	eur	PROPN
ejpam-6159	46	8	.	.	PUNCT
ejpam-6159	47	1	j.	j.	PROPN
ejpam-6159	47	2	pure	pure	PROPN
ejpam-6159	47	3	appl	appl	PROPN
ejpam-6159	47	4	.	.	PROPN
ejpam-6159	47	5	math	math	PROPN
ejpam-6159	47	6	,	,	PUNCT
ejpam-6159	47	7	18	18	NUM
ejpam-6159	47	8	(	(	PUNCT
ejpam-6159	47	9	3	3	NUM
ejpam-6159	47	10	)	)	PUNCT
ejpam-6159	47	11	(	(	PUNCT
ejpam-6159	47	12	2025	2025	NUM
ejpam-6159	47	13	)	)	PUNCT
ejpam-6159	47	14	,	,	PUNCT
ejpam-6159	47	15	6159	6159	NUM
ejpam-6159	47	16	3	3	NUM
ejpam-6159	47	17	of	of	ADP
ejpam-6159	47	18	26	26	NUM
ejpam-6159	47	19	the	the	DET
ejpam-6159	47	20	following	follow	VERB
ejpam-6159	47	21	proposition	proposition	NOUN
ejpam-6159	47	22	regarding	regard	VERB
ejpam-6159	47	23	the	the	DET
ejpam-6159	47	24	mapping	mapping	NOUN
ejpam-6159	47	25	on	on	ADP
ejpam-6159	47	26	ς∗	ς∗	PROPN
ejpam-6159	47	27	is	be	AUX
ejpam-6159	47	28	mentioned	mention	VERB
ejpam-6159	47	29	in	in	ADP
ejpam-6159	47	30	[	[	X
ejpam-6159	47	31	14	14	NUM
ejpam-6159	47	32	]	]	PUNCT
ejpam-6159	47	33	.	.	PUNCT
ejpam-6159	48	1	property−c	property−c	NOUN
ejpam-6159	48	2	:	:	PUNCT
ejpam-6159	48	3	let	let	VERB
ejpam-6159	49	1	xo	xo	PROPN
ejpam-6159	50	1	⊂	⊂	PROPN
ejpam-6159	51	1	ℜn	ℜn	AUX
ejpam-6159	51	2	be	be	AUX
ejpam-6159	51	3	an	an	DET
ejpam-6159	51	4	openiinvex	openiinvex	NOUN
ejpam-6159	51	5	subset	subset	NOUN
ejpam-6159	51	6	w.r	w.r	PROPN
ejpam-6159	51	7	.	.	PROPN
ejpam-6159	51	8	to	to	PART
ejpam-6159	51	9	ς∗	ς∗	VERB
ejpam-6159	51	10	:	:	PUNCT
ejpam-6159	52	1	xo	xo	PROPN
ejpam-6159	52	2	×xo	×xo	PROPN
ejpam-6159	52	3	⊂	⊂	PROPN
ejpam-6159	53	1	ℜn	ℜn	PROPN
ejpam-6159	53	2	.	.	PUNCT
ejpam-6159	54	1	for	for	ADP
ejpam-6159	54	2	any	any	DET
ejpam-6159	54	3	a1	a1	NOUN
ejpam-6159	54	4	,	,	PUNCT
ejpam-6159	54	5	b1	b1	NOUN
ejpam-6159	54	6	∈	∈	PROPN
ejpam-6159	54	7	xo	xo	PROPN
ejpam-6159	54	8	and	and	CCONJ
ejpam-6159	54	9	t	t	PROPN
ejpam-6159	54	10	∈	∈	PROPN
ejpam-6159	55	1	[	[	X
ejpam-6159	55	2	0	0	NUM
ejpam-6159	55	3	,	,	PUNCT
ejpam-6159	55	4	1	1	NUM
ejpam-6159	55	5	]	]	PUNCT
ejpam-6159	55	6	,	,	PUNCT
ejpam-6159	55	7	ς∗	ς∗	PROPN
ejpam-6159	55	8	(	(	PUNCT
ejpam-6159	55	9	b1	b1	NOUN
ejpam-6159	55	10	,	,	PUNCT
ejpam-6159	55	11	b1	b1	NOUN
ejpam-6159	55	12	+	+	CCONJ
ejpam-6159	55	13	tς∗	tς∗	X
ejpam-6159	55	14	(	(	PUNCT
ejpam-6159	55	15	a1	a1	NOUN
ejpam-6159	55	16	,	,	PUNCT
ejpam-6159	55	17	b1	b1	NOUN
ejpam-6159	55	18	)	)	PUNCT
ejpam-6159	55	19	)	)	PUNCT
ejpam-6159	55	20	=	=	SYM
ejpam-6159	55	21	−tς∗	−tς∗	X
ejpam-6159	55	22	(	(	PUNCT
ejpam-6159	55	23	a1	a1	PROPN
ejpam-6159	55	24	,	,	PUNCT
ejpam-6159	55	25	b1	b1	NOUN
ejpam-6159	55	26	)	)	PUNCT
ejpam-6159	55	27	,	,	PUNCT
ejpam-6159	55	28	ς∗	ς∗	PROPN
ejpam-6159	55	29	(	(	PUNCT
ejpam-6159	55	30	a1	a1	NOUN
ejpam-6159	55	31	,	,	PUNCT
ejpam-6159	55	32	b1	b1	NOUN
ejpam-6159	55	33	+	+	CCONJ
ejpam-6159	55	34	tς∗	tς∗	X
ejpam-6159	55	35	(	(	PUNCT
ejpam-6159	55	36	a1	a1	NOUN
ejpam-6159	55	37	,	,	PUNCT
ejpam-6159	55	38	b1	b1	NOUN
ejpam-6159	55	39	)	)	PUNCT
ejpam-6159	55	40	)	)	PUNCT
ejpam-6159	56	1	=	=	PUNCT
ejpam-6159	56	2	(	(	PUNCT
ejpam-6159	56	3	1−	1−	NUM
ejpam-6159	56	4	t	t	NOUN
ejpam-6159	56	5	)	)	PUNCT
ejpam-6159	56	6	ς∗	ς∗	PROPN
ejpam-6159	56	7	(	(	PUNCT
ejpam-6159	56	8	a1	a1	NOUN
ejpam-6159	56	9	,	,	PUNCT
ejpam-6159	56	10	b1	b1	NOUN
ejpam-6159	56	11	)	)	PUNCT
ejpam-6159	56	12	.	.	PUNCT
ejpam-6159	57	1	(	(	PUNCT
ejpam-6159	57	2	2	2	X
ejpam-6159	57	3	)	)	PUNCT
ejpam-6159	57	4	for	for	ADP
ejpam-6159	57	5	any	any	DET
ejpam-6159	57	6	a1	a1	NOUN
ejpam-6159	57	7	,	,	PUNCT
ejpam-6159	57	8	b1	b1	NOUN
ejpam-6159	57	9	∈	∈	PROPN
ejpam-6159	57	10	xo	xo	PROPN
ejpam-6159	57	11	and	and	CCONJ
ejpam-6159	57	12	t1	t1	PROPN
ejpam-6159	57	13	,	,	PUNCT
ejpam-6159	57	14	t2	t2	PROPN
ejpam-6159	57	15	∈	∈	PROPN
ejpam-6159	58	1	[	[	X
ejpam-6159	58	2	0	0	NUM
ejpam-6159	58	3	,	,	PUNCT
ejpam-6159	58	4	1	1	NUM
ejpam-6159	58	5	]	]	PUNCT
ejpam-6159	58	6	from	from	ADP
ejpam-6159	58	7	property−c	property−c	PROPN
ejpam-6159	58	8	,	,	PUNCT
ejpam-6159	58	9	we	we	PRON
ejpam-6159	58	10	have	have	VERB
ejpam-6159	58	11	ς∗	ς∗	NOUN
ejpam-6159	58	12	(	(	PUNCT
ejpam-6159	58	13	b1	b1	NOUN
ejpam-6159	58	14	+	+	CCONJ
ejpam-6159	59	1	t2ς∗	t2ς∗	PROPN
ejpam-6159	59	2	(	(	PUNCT
ejpam-6159	59	3	a1	a1	PROPN
ejpam-6159	59	4	,	,	PUNCT
ejpam-6159	59	5	b1	b1	NOUN
ejpam-6159	59	6	)	)	PUNCT
ejpam-6159	59	7	,	,	PUNCT
ejpam-6159	59	8	b1	b1	NOUN
ejpam-6159	59	9	+	+	CCONJ
ejpam-6159	59	10	t1ς∗	t1ς∗	PROPN
ejpam-6159	59	11	(	(	PUNCT
ejpam-6159	59	12	a1	a1	NOUN
ejpam-6159	59	13	,	,	PUNCT
ejpam-6159	59	14	b1	b1	NOUN
ejpam-6159	59	15	)	)	PUNCT
ejpam-6159	59	16	)	)	PUNCT
ejpam-6159	60	1	=	=	PRON
ejpam-6159	60	2	(	(	PUNCT
ejpam-6159	60	3	t2	t2	PROPN
ejpam-6159	60	4	−	−	PROPN
ejpam-6159	60	5	t1	t1	PROPN
ejpam-6159	60	6	)	)	PUNCT
ejpam-6159	60	7	ς∗	ς∗	PROPN
ejpam-6159	60	8	(	(	PUNCT
ejpam-6159	60	9	a1	a1	NOUN
ejpam-6159	60	10	,	,	PUNCT
ejpam-6159	60	11	b1	b1	NOUN
ejpam-6159	60	12	)	)	PUNCT
ejpam-6159	60	13	.	.	PUNCT
ejpam-6159	61	1	(	(	PUNCT
ejpam-6159	61	2	3	3	X
ejpam-6159	61	3	)	)	PUNCT
ejpam-6159	61	4	if	if	SCONJ
ejpam-6159	61	5	f	f	PROPN
ejpam-6159	61	6	is	be	AUX
ejpam-6159	61	7	a	a	DET
ejpam-6159	61	8	preinvex	preinvex	ADJ
ejpam-6159	61	9	function	function	NOUN
ejpam-6159	61	10	on	on	ADP
ejpam-6159	61	11	ς∗	ς∗	PROPN
ejpam-6159	61	12	(	(	PUNCT
ejpam-6159	61	13	a1	a1	NOUN
ejpam-6159	61	14	,	,	PUNCT
ejpam-6159	61	15	a1	a1	NOUN
ejpam-6159	61	16	+	+	CCONJ
ejpam-6159	61	17	tς∗	tς∗	NOUN
ejpam-6159	61	18	(	(	PUNCT
ejpam-6159	61	19	b1	b1	NOUN
ejpam-6159	61	20	,	,	PUNCT
ejpam-6159	61	21	a1	a1	NOUN
ejpam-6159	61	22	)	)	PUNCT
ejpam-6159	61	23	)	)	PUNCT
ejpam-6159	62	1	and	and	CCONJ
ejpam-6159	62	2	theimapping	theimappe	VERB
ejpam-6159	62	3	ς∗	ς∗	PROPN
ejpam-6159	62	4	satisfies	satisfie	NOUN
ejpam-6159	62	5	property	property	NOUN
ejpam-6159	62	6	–	–	PUNCT
ejpam-6159	62	7	c	c	X
ejpam-6159	62	8	,	,	PUNCT
ejpam-6159	62	9	then	then	ADV
ejpam-6159	62	10	forievery	forievery	PROPN
ejpam-6159	62	11	t	t	PROPN
ejpam-6159	62	12	∈	∈	PROPN
ejpam-6159	63	1	[	[	X
ejpam-6159	63	2	0	0	NUM
ejpam-6159	63	3	,	,	PUNCT
ejpam-6159	63	4	1	1	NUM
ejpam-6159	63	5	]	]	PUNCT
ejpam-6159	63	6	,	,	PUNCT
ejpam-6159	63	7	from	from	ADP
ejpam-6159	63	8	(	(	PUNCT
ejpam-6159	63	9	2	2	NUM
ejpam-6159	63	10	)	)	PUNCT
ejpam-6159	63	11	,	,	PUNCT
ejpam-6159	63	12	it	it	PRON
ejpam-6159	63	13	yields	yield	VERB
ejpam-6159	63	14	that	that	SCONJ
ejpam-6159	63	15	|f	|f	PROPN
ejpam-6159	63	16	(	(	PUNCT
ejpam-6159	63	17	a1	a1	NOUN
ejpam-6159	63	18	+	+	CCONJ
ejpam-6159	63	19	tς∗	tς∗	NOUN
ejpam-6159	63	20	(	(	PUNCT
ejpam-6159	63	21	b1	b1	NOUN
ejpam-6159	63	22	,	,	PUNCT
ejpam-6159	63	23	a1))|	a1))|	PUNCT
ejpam-6159	63	24	=	=	SYM
ejpam-6159	63	25	|f	|f	PROPN
ejpam-6159	63	26	(	(	PUNCT
ejpam-6159	63	27	a1	a1	NOUN
ejpam-6159	63	28	+	+	CCONJ
ejpam-6159	63	29	ς∗	ς∗	PROPN
ejpam-6159	63	30	(	(	PUNCT
ejpam-6159	63	31	b1	b1	NOUN
ejpam-6159	63	32	,	,	PUNCT
ejpam-6159	63	33	a1	a1	NOUN
ejpam-6159	63	34	)	)	PUNCT
ejpam-6159	63	35	)	)	PUNCT
ejpam-6159	64	1	+	+	CCONJ
ejpam-6159	64	2	(	(	PUNCT
ejpam-6159	64	3	1−	1−	NUM
ejpam-6159	64	4	t	t	NOUN
ejpam-6159	64	5	)	)	PUNCT
ejpam-6159	64	6	ς∗	ς∗	PROPN
ejpam-6159	64	7	(	(	PUNCT
ejpam-6159	64	8	a1	a1	NOUN
ejpam-6159	64	9	,	,	PUNCT
ejpam-6159	64	10	a1	a1	NOUN
ejpam-6159	64	11	+	+	CCONJ
ejpam-6159	64	12	ς∗	ς∗	PROPN
ejpam-6159	64	13	(	(	PUNCT
ejpam-6159	64	14	b1	b1	NOUN
ejpam-6159	64	15	,	,	PUNCT
ejpam-6159	64	16	a1))|	a1))|	PROPN
ejpam-6159	64	17	≤	≤	PROPN
ejpam-6159	64	18	t	t	PROPN
ejpam-6159	64	19	|f	|f	PROPN
ejpam-6159	64	20	(	(	PUNCT
ejpam-6159	64	21	a1	a1	NOUN
ejpam-6159	64	22	+	+	CCONJ
ejpam-6159	64	23	ς∗	ς∗	PROPN
ejpam-6159	64	24	(	(	PUNCT
ejpam-6159	64	25	b1	b1	NOUN
ejpam-6159	64	26	,	,	PUNCT
ejpam-6159	64	27	a1))|+	a1))|+	PROPN
ejpam-6159	64	28	(	(	PUNCT
ejpam-6159	64	29	1−	1−	NUM
ejpam-6159	64	30	t	t	PROPN
ejpam-6159	64	31	)	)	PUNCT
ejpam-6159	64	32	|f	|f	PROPN
ejpam-6159	64	33	(	(	PUNCT
ejpam-6159	64	34	a1)|	a1)|	NOUN
ejpam-6159	64	35	and	and	CCONJ
ejpam-6159	64	36	|f	|f	PROPN
ejpam-6159	64	37	(	(	PUNCT
ejpam-6159	64	38	a1	a1	NOUN
ejpam-6159	64	39	+	+	CCONJ
ejpam-6159	64	40	(	(	PUNCT
ejpam-6159	64	41	1−	1−	NUM
ejpam-6159	64	42	t	t	NOUN
ejpam-6159	64	43	)	)	PUNCT
ejpam-6159	64	44	ς∗	ς∗	PROPN
ejpam-6159	64	45	(	(	PUNCT
ejpam-6159	64	46	b1	b1	NOUN
ejpam-6159	64	47	,	,	PUNCT
ejpam-6159	64	48	a1))|	a1))|	PUNCT
ejpam-6159	64	49	=	=	SYM
ejpam-6159	64	50	|f	|f	PROPN
ejpam-6159	64	51	(	(	PUNCT
ejpam-6159	64	52	a1	a1	NOUN
ejpam-6159	64	53	+	+	CCONJ
ejpam-6159	64	54	ς∗	ς∗	PROPN
ejpam-6159	64	55	(	(	PUNCT
ejpam-6159	64	56	b1	b1	NOUN
ejpam-6159	64	57	,	,	PUNCT
ejpam-6159	64	58	a1	a1	NOUN
ejpam-6159	64	59	)	)	PUNCT
ejpam-6159	64	60	)	)	PUNCT
ejpam-6159	65	1	+	+	CCONJ
ejpam-6159	65	2	tς∗	tς∗	X
ejpam-6159	65	3	(	(	PUNCT
ejpam-6159	65	4	a1	a1	NOUN
ejpam-6159	65	5	,	,	PUNCT
ejpam-6159	65	6	a1	a1	NOUN
ejpam-6159	65	7	+	+	CCONJ
ejpam-6159	65	8	ς∗	ς∗	PROPN
ejpam-6159	65	9	(	(	PUNCT
ejpam-6159	65	10	b1	b1	NOUN
ejpam-6159	65	11	,	,	PUNCT
ejpam-6159	65	12	a1))|	a1))|	PROPN
ejpam-6159	65	13	≤	≤	NUM
ejpam-6159	65	14	(	(	PUNCT
ejpam-6159	65	15	1−	1−	NUM
ejpam-6159	65	16	t	t	PROPN
ejpam-6159	65	17	)	)	PUNCT
ejpam-6159	65	18	|f	|f	PROPN
ejpam-6159	66	1	(	(	PUNCT
ejpam-6159	66	2	a1	a1	NOUN
ejpam-6159	66	3	+	+	CCONJ
ejpam-6159	66	4	ς∗	ς∗	PROPN
ejpam-6159	66	5	(	(	PUNCT
ejpam-6159	66	6	b1	b1	PROPN
ejpam-6159	66	7	,	,	PUNCT
ejpam-6159	66	8	a1))|+	a1))|+	PROPN
ejpam-6159	66	9	t	t	PROPN
ejpam-6159	66	10	|f	|f	PROPN
ejpam-6159	66	11	(	(	PUNCT
ejpam-6159	66	12	a1)|	a1)|	PROPN
ejpam-6159	66	13	.	.	PUNCT
ejpam-6159	67	1	in	in	ADP
ejpam-6159	67	2	[	[	X
ejpam-6159	67	3	15	15	NUM
ejpam-6159	67	4	]	]	PUNCT
ejpam-6159	67	5	,	,	PUNCT
ejpam-6159	67	6	the	the	DET
ejpam-6159	67	7	following	follow	VERB
ejpam-6159	67	8	inequalities	inequality	NOUN
ejpam-6159	67	9	of	of	ADP
ejpam-6159	67	10	’	'	PUNCT
ejpam-6159	67	11	h	h	NOUN
ejpam-6159	67	12	–	–	PUNCT
ejpam-6159	67	13	h	h	NOUN
ejpam-6159	67	14	’	'	PUNCT
ejpam-6159	67	15	have	have	AUX
ejpam-6159	67	16	been	be	AUX
ejpam-6159	67	17	proved	prove	VERB
ejpam-6159	67	18	.	.	PUNCT
ejpam-6159	68	1	theorem	theorem	NOUN
ejpam-6159	68	2	1	1	NUM
ejpam-6159	68	3	.	.	PUNCT
ejpam-6159	69	1	[	[	X
ejpam-6159	69	2	10	10	NUM
ejpam-6159	69	3	]	]	PUNCT
ejpam-6159	69	4	suppose	suppose	VERB
ejpam-6159	69	5	f	f	X
ejpam-6159	69	6	:	:	PUNCT
ejpam-6159	69	7	x	x	PUNCT
ejpam-6159	69	8	=	=	PUNCT
ejpam-6159	70	1	[	[	X
ejpam-6159	70	2	a1	a1	NOUN
ejpam-6159	70	3	,	,	PUNCT
ejpam-6159	70	4	a1	a1	NOUN
ejpam-6159	70	5	+	+	CCONJ
ejpam-6159	70	6	ς∗	ς∗	PROPN
ejpam-6159	70	7	(	(	PUNCT
ejpam-6159	70	8	b1	b1	NOUN
ejpam-6159	70	9	,	,	PUNCT
ejpam-6159	70	10	a1	a1	NOUN
ejpam-6159	70	11	)	)	PUNCT
ejpam-6159	70	12	]	]	PUNCT
ejpam-6159	71	1	→	→	X
ejpam-6159	71	2	(	(	PUNCT
ejpam-6159	71	3	0,∞	0,∞	NUM
ejpam-6159	71	4	)	)	PUNCT
ejpam-6159	71	5	is	be	AUX
ejpam-6159	71	6	a	a	DET
ejpam-6159	71	7	ipreinvex	ipreinvex	NOUN
ejpam-6159	71	8	mapping	mapping	NOUN
ejpam-6159	71	9	on	on	ADP
ejpam-6159	71	10	the	the	DET
ejpam-6159	71	11	interval	interval	NOUN
ejpam-6159	71	12	of	of	ADP
ejpam-6159	71	13	realinumbers	realinumber	NOUN
ejpam-6159	71	14	xo	xo	PROPN
ejpam-6159	71	15	with	with	ADP
ejpam-6159	71	16	ς∗	ς∗	PROPN
ejpam-6159	71	17	(	(	PUNCT
ejpam-6159	71	18	b1	b1	NOUN
ejpam-6159	71	19	,	,	PUNCT
ejpam-6159	71	20	a1	a1	PROPN
ejpam-6159	71	21	)	)	PUNCT
ejpam-6159	71	22	>	>	X
ejpam-6159	72	1	0	0	PUNCT
ejpam-6159	72	2	f	f	X
ejpam-6159	72	3	(	(	PUNCT
ejpam-6159	72	4	2a1	2a1	NUM
ejpam-6159	72	5	+	+	CCONJ
ejpam-6159	72	6	ς∗	ς∗	PROPN
ejpam-6159	72	7	(	(	PUNCT
ejpam-6159	72	8	b1	b1	NOUN
ejpam-6159	72	9	,	,	PUNCT
ejpam-6159	72	10	a1	a1	NOUN
ejpam-6159	72	11	)	)	PUNCT
ejpam-6159	72	12	2	2	NUM
ejpam-6159	72	13	)	)	PUNCT
ejpam-6159	72	14	≤	≤	NUM
ejpam-6159	72	15	1	1	NUM
ejpam-6159	72	16	ς∗	ς∗	NOUN
ejpam-6159	72	17	(	(	PUNCT
ejpam-6159	72	18	b1	b1	NOUN
ejpam-6159	72	19	,	,	PUNCT
ejpam-6159	72	20	a1	a1	PROPN
ejpam-6159	72	21	)	)	PUNCT
ejpam-6159	72	22	∫	∫	NOUN
ejpam-6159	72	23	a1+ς∗(b1,a1	a1+ς∗(b1,a1	PROPN
ejpam-6159	72	24	)	)	PUNCT
ejpam-6159	72	25	a1	a1	PROPN
ejpam-6159	72	26	f(x)dx	f(x)dx	VERB
ejpam-6159	72	27	≤	≤	ADJ
ejpam-6159	72	28	f	f	X
ejpam-6159	72	29	(	(	PUNCT
ejpam-6159	72	30	a1	a1	PROPN
ejpam-6159	72	31	)	)	PUNCT
ejpam-6159	72	32	+	+	NUM
ejpam-6159	72	33	f	f	X
ejpam-6159	72	34	(	(	PUNCT
ejpam-6159	72	35	b1	b1	PROPN
ejpam-6159	72	36	)	)	PUNCT
ejpam-6159	72	37	2	2	NUM
ejpam-6159	72	38	.	.	PUNCT
ejpam-6159	73	1	(	(	PUNCT
ejpam-6159	73	2	4	4	X
ejpam-6159	73	3	)	)	PUNCT
ejpam-6159	73	4	suppose	suppose	VERB
ejpam-6159	73	5	x	x	SYM
ejpam-6159	73	6	⊆	⊆	NUM
ejpam-6159	73	7	ℜ	ℜ	PROPN
ejpam-6159	73	8	and	and	CCONJ
ejpam-6159	73	9	f	f	X
ejpam-6159	73	10	:	:	PUNCT
ejpam-6159	73	11	⊆	⊆	NUM
ejpam-6159	73	12	ℜ	ℜ	PROPN
ejpam-6159	73	13	is	be	AUX
ejpam-6159	73	14	a	a	DET
ejpam-6159	73	15	mapping	mapping	NOUN
ejpam-6159	73	16	on	on	ADP
ejpam-6159	73	17	a	a	DET
ejpam-6159	73	18	differentiable	differentiable	NOUN
ejpam-6159	73	19	at	at	ADP
ejpam-6159	73	20	xo(the	xo(the	DET
ejpam-6159	73	21	interior	interior	PROPN
ejpam-6159	73	22	of	of	ADP
ejpam-6159	73	23	x	x	NOUN
ejpam-6159	73	24	)	)	PUNCT
ejpam-6159	73	25	such	such	ADJ
ejpam-6159	73	26	that	that	SCONJ
ejpam-6159	73	27	[	[	X
ejpam-6159	73	28	a1	a1	NOUN
ejpam-6159	73	29	,	,	PUNCT
ejpam-6159	73	30	b1	b1	NOUN
ejpam-6159	73	31	]	]	PUNCT
ejpam-6159	73	32	∈	∈	PROPN
ejpam-6159	73	33	xo	xo	PROPN
ejpam-6159	73	34	with	with	ADP
ejpam-6159	73	35	a1	a1	NOUN
ejpam-6159	73	36	<	<	X
ejpam-6159	73	37	b1	b1	NOUN
ejpam-6159	73	38	.	.	PUNCT
ejpam-6159	74	1	in	in	ADP
ejpam-6159	74	2	this	this	DET
ejpam-6159	74	3	case	case	NOUN
ejpam-6159	74	4	,	,	PUNCT
ejpam-6159	74	5	the	the	DET
ejpam-6159	74	6	famousiostrowski	famousiostrowski	ADJ
ejpam-6159	74	7	inequality	inequality	NOUN
ejpam-6159	74	8	[	[	X
ejpam-6159	74	9	16	16	NUM
ejpam-6159	74	10	]	]	PUNCT
ejpam-6159	74	11	is	be	AUX
ejpam-6159	74	12	stated	state	VERB
ejpam-6159	74	13	as	as	ADP
ejpam-6159	74	14	∣∣∣∣f	∣∣∣∣f	PROPN
ejpam-6159	74	15	(	(	PUNCT
ejpam-6159	74	16	x)−	x)−	PROPN
ejpam-6159	74	17	1	1	NUM
ejpam-6159	74	18	b1	b1	NOUN
ejpam-6159	74	19	−	−	NOUN
ejpam-6159	74	20	a1	a1	NOUN
ejpam-6159	74	21	∫	∫	PROPN
ejpam-6159	74	22	b1	b1	PROPN
ejpam-6159	74	23	a1	a1	NOUN
ejpam-6159	74	24	f(x)dx	f(x)dx	PART
ejpam-6159	74	25	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	74	26	≤	≤	PUNCT
ejpam-6159	74	27	∣∣∣∣∣14	∣∣∣∣∣14	NOUN
ejpam-6159	75	1	+	+	CCONJ
ejpam-6159	75	2	(	(	PUNCT
ejpam-6159	75	3	x−	x−	PROPN
ejpam-6159	75	4	a1+b1	a1+b1	PROPN
ejpam-6159	75	5	2	2	NUM
ejpam-6159	75	6	)	)	SYM
ejpam-6159	75	7	2	2	NUM
ejpam-6159	75	8	(	(	PUNCT
ejpam-6159	75	9	b1	b1	NOUN
ejpam-6159	75	10	−	−	NOUN
ejpam-6159	75	11	a1	a1	NOUN
ejpam-6159	75	12	)	)	PUNCT
ejpam-6159	75	13	2	2	NUM
ejpam-6159	75	14	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6159	75	15	(	(	PUNCT
ejpam-6159	75	16	b1	b1	NOUN
ejpam-6159	75	17	−	−	NOUN
ejpam-6159	75	18	a1)s	a1)s	NOUN
ejpam-6159	75	19	,	,	PUNCT
ejpam-6159	75	20	(	(	PUNCT
ejpam-6159	75	21	5	5	NUM
ejpam-6159	75	22	)	)	PUNCT
ejpam-6159	75	23	for	for	ADP
ejpam-6159	75	24	all	all	PRON
ejpam-6159	75	25	x	x	SYM
ejpam-6159	75	26	∈	∈	PROPN
ejpam-6159	75	27	[	[	X
ejpam-6159	75	28	a1	a1	NOUN
ejpam-6159	75	29	,	,	PUNCT
ejpam-6159	75	30	b1	b1	NOUN
ejpam-6159	75	31	]	]	PUNCT
ejpam-6159	75	32	,	,	PUNCT
ejpam-6159	75	33	if	if	SCONJ
ejpam-6159	75	34	|f′|	|f′|	ADJ
ejpam-6159	75	35	≤	≤	PROPN
ejpam-6159	75	36	s.	s.	PROPN
ejpam-6159	75	37	ostrowski	ostrowski	PROPN
ejpam-6159	75	38	-	-	PUNCT
ejpam-6159	75	39	like	like	ADJ
ejpam-6159	75	40	inequalities	inequality	NOUN
ejpam-6159	75	41	,	,	PUNCT
ejpam-6159	75	42	which	which	PRON
ejpam-6159	75	43	give	give	VERB
ejpam-6159	75	44	estimations	estimation	NOUN
ejpam-6159	75	45	of	of	ADP
ejpam-6159	75	46	error	error	NOUN
ejpam-6159	75	47	for	for	ADP
ejpam-6159	75	48	various	various	ADJ
ejpam-6159	75	49	quadrature	quadrature	NOUN
ejpam-6159	75	50	criteria	criterion	NOUN
ejpam-6159	75	51	,	,	PUNCT
ejpam-6159	75	52	are	be	AUX
ejpam-6159	75	53	widely	widely	ADV
ejpam-6159	75	54	used	use	VERB
ejpam-6159	75	55	in	in	ADP
ejpam-6159	75	56	numericalianalysis	numericalianalysis	NOUN
ejpam-6159	75	57	.	.	PUNCT
ejpam-6159	76	1	these	these	DET
ejpam-6159	76	2	distinctions	distinction	NOUN
ejpam-6159	76	3	have	have	AUX
ejpam-6159	76	4	grown	grow	VERB
ejpam-6159	76	5	and	and	CCONJ
ejpam-6159	76	6	been	be	AUX
ejpam-6159	76	7	applied	apply	VERB
ejpam-6159	76	8	to	to	ADP
ejpam-6159	76	9	more	more	ADJ
ejpam-6159	76	10	fields	field	NOUN
ejpam-6159	76	11	in	in	ADP
ejpam-6159	76	12	recent	recent	ADJ
ejpam-6159	76	13	years	year	NOUN
ejpam-6159	76	14	(	(	PUNCT
ejpam-6159	76	15	see	see	VERB
ejpam-6159	76	16	[	[	X
ejpam-6159	76	17	17–20	17–20	NUM
ejpam-6159	76	18	]	]	PUNCT
ejpam-6159	76	19	)	)	PUNCT
ejpam-6159	76	20	.	.	PUNCT
ejpam-6159	77	1	j.	j.	PROPN
ejpam-6159	77	2	nasir	nasir	PROPN
ejpam-6159	77	3	et	et	PROPN
ejpam-6159	77	4	al	al	PROPN
ejpam-6159	77	5	.	.	PUNCT
ejpam-6159	77	6	/	/	SYM
ejpam-6159	77	7	eur	eur	PROPN
ejpam-6159	77	8	.	.	PUNCT
ejpam-6159	78	1	j.	j.	PROPN
ejpam-6159	78	2	pure	pure	PROPN
ejpam-6159	78	3	appl	appl	PROPN
ejpam-6159	78	4	.	.	PROPN
ejpam-6159	78	5	math	math	PROPN
ejpam-6159	78	6	,	,	PUNCT
ejpam-6159	78	7	18	18	NUM
ejpam-6159	78	8	(	(	PUNCT
ejpam-6159	78	9	3	3	NUM
ejpam-6159	78	10	)	)	PUNCT
ejpam-6159	78	11	(	(	PUNCT
ejpam-6159	78	12	2025	2025	NUM
ejpam-6159	78	13	)	)	PUNCT
ejpam-6159	78	14	,	,	PUNCT
ejpam-6159	78	15	6159	6159	NUM
ejpam-6159	78	16	4	4	NUM
ejpam-6159	78	17	of	of	ADP
ejpam-6159	78	18	26	26	NUM
ejpam-6159	78	19	definition	definition	NOUN
ejpam-6159	78	20	3	3	NUM
ejpam-6159	78	21	.	.	PUNCT
ejpam-6159	79	1	[	[	X
ejpam-6159	79	2	21	21	NUM
ejpam-6159	79	3	,	,	PUNCT
ejpam-6159	79	4	22	22	NUM
ejpam-6159	79	5	]	]	PUNCT
ejpam-6159	79	6	let	let	VERB
ejpam-6159	79	7	s	s	PRON
ejpam-6159	79	8	∈	∈	NOUN
ejpam-6159	80	1	[	[	X
ejpam-6159	80	2	0	0	NUM
ejpam-6159	80	3	,	,	PUNCT
ejpam-6159	80	4	1	1	NUM
ejpam-6159	80	5	]	]	PUNCT
ejpam-6159	80	6	.	.	PUNCT
ejpam-6159	81	1	a	a	DET
ejpam-6159	81	2	real	real	ADV
ejpam-6159	81	3	valued	value	VERB
ejpam-6159	81	4	mapping	mapping	NOUN
ejpam-6159	81	5	xo	xo	NOUN
ejpam-6159	81	6	→	→	PUNCT
ejpam-6159	81	7	ℜ	ℜ	PROPN
ejpam-6159	81	8	is	be	AUX
ejpam-6159	81	9	said	say	VERB
ejpam-6159	81	10	to	to	PART
ejpam-6159	81	11	be	be	AUX
ejpam-6159	81	12	s−like	s−like	ADP
ejpam-6159	81	13	convex	convex	NOUN
ejpam-6159	81	14	on	on	ADP
ejpam-6159	81	15	xo	xo	PROPN
ejpam-6159	81	16	if	if	SCONJ
ejpam-6159	81	17	f	f	PROPN
ejpam-6159	81	18	(	(	PUNCT
ejpam-6159	81	19	µa1	µa1	PROPN
ejpam-6159	81	20	+	+	CCONJ
ejpam-6159	81	21	(	(	PUNCT
ejpam-6159	81	22	1−	1−	NUM
ejpam-6159	81	23	µ	µ	NUM
ejpam-6159	81	24	)	)	PUNCT
ejpam-6159	81	25	b1	b1	NOUN
ejpam-6159	81	26	)	)	PUNCT
ejpam-6159	81	27	≤	≤	NOUN
ejpam-6159	81	28	(	(	PUNCT
ejpam-6159	81	29	1−	1−	NUM
ejpam-6159	81	30	s	s	X
ejpam-6159	81	31	(	(	PUNCT
ejpam-6159	81	32	1−	1−	NUM
ejpam-6159	81	33	µ))f	µ))f	NOUN
ejpam-6159	81	34	(	(	PUNCT
ejpam-6159	81	35	a1	a1	PROPN
ejpam-6159	81	36	)	)	PUNCT
ejpam-6159	81	37	+	+	CCONJ
ejpam-6159	81	38	(	(	PUNCT
ejpam-6159	81	39	1−	1−	NUM
ejpam-6159	81	40	sµ)f	sµ)f	PROPN
ejpam-6159	81	41	(	(	PUNCT
ejpam-6159	81	42	b1	b1	PROPN
ejpam-6159	81	43	)	)	PUNCT
ejpam-6159	81	44	,	,	PUNCT
ejpam-6159	81	45	(	(	PUNCT
ejpam-6159	81	46	6	6	NUM
ejpam-6159	81	47	)	)	PUNCT
ejpam-6159	81	48	for	for	ADP
ejpam-6159	81	49	all	all	DET
ejpam-6159	81	50	a1	a1	NOUN
ejpam-6159	81	51	,	,	PUNCT
ejpam-6159	81	52	b1	b1	NOUN
ejpam-6159	81	53	∈	∈	PROPN
ejpam-6159	81	54	xo	xo	PROPN
ejpam-6159	81	55	and	and	CCONJ
ejpam-6159	81	56	µ	µ	PRON
ejpam-6159	81	57	∈	∈	NOUN
ejpam-6159	82	1	[	[	X
ejpam-6159	82	2	0	0	NUM
ejpam-6159	82	3	,	,	PUNCT
ejpam-6159	82	4	1	1	NUM
ejpam-6159	82	5	]	]	PUNCT
ejpam-6159	82	6	.	.	PUNCT
ejpam-6159	83	1	definition	definition	NOUN
ejpam-6159	83	2	4	4	NUM
ejpam-6159	83	3	.	.	PUNCT
ejpam-6159	84	1	[	[	X
ejpam-6159	84	2	23	23	NUM
ejpam-6159	84	3	]	]	PUNCT
ejpam-6159	84	4	let	let	VERB
ejpam-6159	84	5	x	x	PRON
ejpam-6159	84	6	⊂	⊂	PRON
ejpam-6159	84	7	ℜibe	ℜibe	VERB
ejpam-6159	84	8	a	a	DET
ejpam-6159	84	9	nonempty	nonempty	ADJ
ejpam-6159	84	10	invexiset	invexiset	NOUN
ejpam-6159	84	11	with	with	ADP
ejpam-6159	84	12	respect	respect	NOUN
ejpam-6159	84	13	to	to	PART
ejpam-6159	84	14	ς∗	ς∗	PROPN
ejpam-6159	84	15	:	:	PUNCT
ejpam-6159	84	16	xo	xo	PROPN
ejpam-6159	84	17	×	×	PROPN
ejpam-6159	84	18	xo	xo	PROPN
ejpam-6159	84	19	⊂	⊂	PROPN
ejpam-6159	84	20	ℜ	ℜ	PROPN
ejpam-6159	84	21	→	→	SYM
ejpam-6159	84	22	ℜ.	ℜ.	VERB
ejpam-6159	84	23	ithen	ithen	NOUN
ejpam-6159	84	24	the	the	DET
ejpam-6159	84	25	mapping	mapping	NOUN
ejpam-6159	84	26	ψ	ψ	X
ejpam-6159	84	27	:	:	PUNCT
ejpam-6159	84	28	x	x	SYM
ejpam-6159	84	29	→	→	SYM
ejpam-6159	84	30	ℜ	ℜ	PROPN
ejpam-6159	84	31	is	be	AUX
ejpam-6159	84	32	saidito	saidito	NOUN
ejpam-6159	84	33	be	be	AUX
ejpam-6159	84	34	s−like	s−like	INTJ
ejpam-6159	84	35	preinvex	preinvex	ADJ
ejpam-6159	84	36	,	,	PUNCT
ejpam-6159	84	37	if	if	SCONJ
ejpam-6159	84	38	f	f	PROPN
ejpam-6159	84	39	(	(	PUNCT
ejpam-6159	84	40	b1	b1	NOUN
ejpam-6159	84	41	+	+	CCONJ
ejpam-6159	84	42	µς∗(a1	µς∗(a1	PROPN
ejpam-6159	84	43	,	,	PUNCT
ejpam-6159	84	44	b1	b1	NOUN
ejpam-6159	84	45	)	)	PUNCT
ejpam-6159	84	46	)	)	PUNCT
ejpam-6159	84	47	≤	≤	NOUN
ejpam-6159	84	48	(	(	PUNCT
ejpam-6159	84	49	1−	1−	NUM
ejpam-6159	84	50	s	s	X
ejpam-6159	84	51	(	(	PUNCT
ejpam-6159	84	52	1−	1−	NUM
ejpam-6159	84	53	µ))f	µ))f	NOUN
ejpam-6159	84	54	(	(	PUNCT
ejpam-6159	84	55	a1	a1	PROPN
ejpam-6159	84	56	)	)	PUNCT
ejpam-6159	84	57	+	+	CCONJ
ejpam-6159	84	58	(	(	PUNCT
ejpam-6159	84	59	1−	1−	NUM
ejpam-6159	84	60	sµ)f	sµ)f	PROPN
ejpam-6159	84	61	(	(	PUNCT
ejpam-6159	84	62	b1	b1	PROPN
ejpam-6159	84	63	)	)	PUNCT
ejpam-6159	84	64	.	.	PUNCT
ejpam-6159	85	1	(	(	PUNCT
ejpam-6159	85	2	7	7	X
ejpam-6159	85	3	)	)	PUNCT
ejpam-6159	85	4	in	in	ADP
ejpam-6159	85	5	[	[	X
ejpam-6159	85	6	24	24	NUM
ejpam-6159	85	7	]	]	PUNCT
ejpam-6159	85	8	,	,	PUNCT
ejpam-6159	85	9	i̇şcan	i̇şcan	PROPN
ejpam-6159	85	10	gave	give	VERB
ejpam-6159	85	11	the	the	DET
ejpam-6159	85	12	definition	definition	NOUN
ejpam-6159	85	13	on	on	ADP
ejpam-6159	85	14	n−fractional	n−fractional	ADJ
ejpam-6159	85	15	polynomial	polynomial	ADJ
ejpam-6159	85	16	convexity	convexity	NOUN
ejpam-6159	85	17	as	as	ADP
ejpam-6159	85	18	below	below	ADV
ejpam-6159	85	19	.	.	PUNCT
ejpam-6159	86	1	definition	definition	NOUN
ejpam-6159	86	2	5	5	NUM
ejpam-6159	86	3	.	.	PUNCT
ejpam-6159	87	1	[	[	X
ejpam-6159	87	2	24	24	NUM
ejpam-6159	87	3	]	]	PUNCT
ejpam-6159	87	4	suppose	suppose	VERB
ejpam-6159	87	5	n	n	ADP
ejpam-6159	87	6	∈	∈	PROPN
ejpam-6159	87	7	n	n	NOUN
ejpam-6159	87	8	.	.	PUNCT
ejpam-6159	88	1	a	a	DET
ejpam-6159	88	2	non	non	ADJ
ejpam-6159	88	3	-	-	ADJ
ejpam-6159	88	4	negative	negative	ADJ
ejpam-6159	88	5	mapping	mapping	NOUN
ejpam-6159	88	6	xo	xo	PROPN
ejpam-6159	88	7	⊂	⊂	PROPN
ejpam-6159	88	8	ℜ	ℜ	PROPN
ejpam-6159	88	9	→	→	SYM
ejpam-6159	88	10	ℜ	ℜ	PROPN
ejpam-6159	88	11	is	be	AUX
ejpam-6159	88	12	said	say	VERB
ejpam-6159	88	13	to	to	PART
ejpam-6159	88	14	be	be	AUX
ejpam-6159	88	15	an	an	DET
ejpam-6159	88	16	n−fractional	n−fractional	ADJ
ejpam-6159	88	17	polynomial	polynomial	ADJ
ejpam-6159	88	18	convex(fpc	convex(fpc	NOUN
ejpam-6159	88	19	)	)	PUNCT
ejpam-6159	88	20	mapping	mapping	NOUN
ejpam-6159	88	21	if	if	SCONJ
ejpam-6159	88	22	f	f	PROPN
ejpam-6159	88	23	(	(	PUNCT
ejpam-6159	88	24	µa1	µa1	PROPN
ejpam-6159	88	25	+	+	CCONJ
ejpam-6159	88	26	(	(	PUNCT
ejpam-6159	88	27	1−	1−	NUM
ejpam-6159	88	28	µ	µ	NUM
ejpam-6159	88	29	)	)	PUNCT
ejpam-6159	88	30	b1	b1	NOUN
ejpam-6159	88	31	)	)	PUNCT
ejpam-6159	88	32	≤	≤	NOUN
ejpam-6159	88	33	1	1	NUM
ejpam-6159	88	34	n	n	NUM
ejpam-6159	88	35	n∑	n∑	NOUN
ejpam-6159	88	36	i=1	i=1	PROPN
ejpam-6159	88	37	µ	µ	VERB
ejpam-6159	88	38	1	1	NUM
ejpam-6159	88	39	i	i	NOUN
ejpam-6159	88	40	f	f	PROPN
ejpam-6159	88	41	(	(	PUNCT
ejpam-6159	88	42	a1	a1	PROPN
ejpam-6159	88	43	)	)	PUNCT
ejpam-6159	88	44	+	+	CCONJ
ejpam-6159	88	45	1	1	NUM
ejpam-6159	88	46	n	n	NUM
ejpam-6159	88	47	n∑	n∑	NOUN
ejpam-6159	88	48	i=1	i=1	PROPN
ejpam-6159	88	49	(	(	PUNCT
ejpam-6159	88	50	1−	1−	NUM
ejpam-6159	88	51	µ	µ	NUM
ejpam-6159	88	52	)	)	PUNCT
ejpam-6159	88	53	1	1	NUM
ejpam-6159	89	1	i	i	PRON
ejpam-6159	89	2	f	f	PROPN
ejpam-6159	89	3	(	(	PUNCT
ejpam-6159	89	4	b1	b1	PROPN
ejpam-6159	89	5	)	)	PUNCT
ejpam-6159	89	6	,	,	PUNCT
ejpam-6159	89	7	(	(	PUNCT
ejpam-6159	89	8	8)	8)	NUM
ejpam-6159	89	9	for	for	ADP
ejpam-6159	89	10	all	all	DET
ejpam-6159	89	11	a1	a1	NOUN
ejpam-6159	89	12	,	,	PUNCT
ejpam-6159	89	13	b1	b1	NOUN
ejpam-6159	89	14	∈	∈	PROPN
ejpam-6159	89	15	xo	xo	PROPN
ejpam-6159	89	16	and	and	CCONJ
ejpam-6159	89	17	µ	µ	PRON
ejpam-6159	89	18	∈	∈	NOUN
ejpam-6159	89	19	[	[	X
ejpam-6159	89	20	0	0	NUM
ejpam-6159	89	21	,	,	PUNCT
ejpam-6159	89	22	1	1	NUM
ejpam-6159	89	23	]	]	PUNCT
ejpam-6159	89	24	.	.	PUNCT
ejpam-6159	90	1	definition	definition	NOUN
ejpam-6159	90	2	6	6	NUM
ejpam-6159	90	3	.	.	PUNCT
ejpam-6159	91	1	[	[	X
ejpam-6159	91	2	25	25	NUM
ejpam-6159	91	3	]	]	PUNCT
ejpam-6159	91	4	consider	consider	VERB
ejpam-6159	91	5	f	f	PROPN
ejpam-6159	91	6	∈	∈	PROPN
ejpam-6159	91	7	l[a1	l[a1	PROPN
ejpam-6159	91	8	,	,	PUNCT
ejpam-6159	91	9	b1	b1	PROPN
ejpam-6159	91	10	]	]	PUNCT
ejpam-6159	91	11	.	.	PUNCT
ejpam-6159	92	1	the	the	DET
ejpam-6159	92	2	left	left	ADJ
ejpam-6159	92	3	-	-	PUNCT
ejpam-6159	92	4	right	right	ADJ
ejpam-6159	92	5	-	-	PUNCT
ejpam-6159	92	6	sidediriemann	sidediriemann	NOUN
ejpam-6159	92	7	-	-	PUNCT
ejpam-6159	92	8	liouville(r	liouville(r	NOUN
ejpam-6159	92	9	–	–	PUNCT
ejpam-6159	92	10	l)ifractional	l)ifractional	ADJ
ejpam-6159	92	11	integrals	integral	NOUN
ejpam-6159	92	12	of	of	ADP
ejpam-6159	92	13	order	order	NOUN
ejpam-6159	92	14	ϱ	ϱ	ADP
ejpam-6159	92	15	>	>	X
ejpam-6159	92	16	0	0	NUM
ejpam-6159	92	17	are	be	AUX
ejpam-6159	92	18	defined	define	VERB
ejpam-6159	92	19	by	by	ADP
ejpam-6159	92	20	jϱ	jϱ	ADP
ejpam-6159	92	21	a1−	a1−	PROPN
ejpam-6159	92	22	f	f	PROPN
ejpam-6159	92	23	(	(	PUNCT
ejpam-6159	92	24	x	x	NOUN
ejpam-6159	92	25	)	)	PUNCT
ejpam-6159	92	26	=	=	SYM
ejpam-6159	92	27	1	1	NUM
ejpam-6159	92	28	γ	γ	X
ejpam-6159	92	29	(	(	PUNCT
ejpam-6159	92	30	ϱ	ϱ	PROPN
ejpam-6159	92	31	)	)	PUNCT
ejpam-6159	92	32	∫	∫	NOUN
ejpam-6159	92	33	x	x	PUNCT
ejpam-6159	92	34	a1	a1	PROPN
ejpam-6159	92	35	(	(	PUNCT
ejpam-6159	92	36	x−	x−	PROPN
ejpam-6159	92	37	t)ϱ−1	t)ϱ−1	PROPN
ejpam-6159	92	38	f	f	PROPN
ejpam-6159	92	39	(	(	PUNCT
ejpam-6159	92	40	t	t	PROPN
ejpam-6159	92	41	)	)	PUNCT
ejpam-6159	92	42	dt	dt	PROPN
ejpam-6159	92	43	;	;	PUNCT
ejpam-6159	92	44	a1	a1	VERB
ejpam-6159	92	45	<	<	X
ejpam-6159	92	46	x	x	X
ejpam-6159	92	47	(	(	PUNCT
ejpam-6159	92	48	9	9	NUM
ejpam-6159	92	49	)	)	PUNCT
ejpam-6159	92	50	and	and	CCONJ
ejpam-6159	92	51	jϱ	jϱ	ADP
ejpam-6159	92	52	b1	b1	PROPN
ejpam-6159	92	53	+	+	CCONJ
ejpam-6159	92	54	f	f	X
ejpam-6159	92	55	(	(	PUNCT
ejpam-6159	92	56	x	x	X
ejpam-6159	92	57	)	)	PUNCT
ejpam-6159	92	58	=	=	SYM
ejpam-6159	92	59	1	1	NUM
ejpam-6159	92	60	γ	γ	X
ejpam-6159	92	61	(	(	PUNCT
ejpam-6159	92	62	ϱ	ϱ	PROPN
ejpam-6159	92	63	)	)	PUNCT
ejpam-6159	92	64	∫	∫	PROPN
ejpam-6159	92	65	b1	b1	PROPN
ejpam-6159	92	66	x	x	SYM
ejpam-6159	92	67	(	(	PUNCT
ejpam-6159	92	68	t−	t−	PROPN
ejpam-6159	92	69	x)ϱ−1	x)ϱ−1	PROPN
ejpam-6159	92	70	f	f	PROPN
ejpam-6159	92	71	(	(	PUNCT
ejpam-6159	92	72	t	t	PROPN
ejpam-6159	92	73	)	)	PUNCT
ejpam-6159	92	74	dt	dt	PUNCT
ejpam-6159	92	75	;	;	PUNCT
ejpam-6159	92	76	x	x	X
ejpam-6159	92	77	<	<	X
ejpam-6159	92	78	b1	b1	PROPN
ejpam-6159	92	79	.	.	PUNCT
ejpam-6159	93	1	(	(	PUNCT
ejpam-6159	93	2	10	10	NUM
ejpam-6159	93	3	)	)	PUNCT
ejpam-6159	93	4	gammaifunction	gammaifunction	NOUN
ejpam-6159	93	5	is	be	AUX
ejpam-6159	93	6	defined	define	VERB
ejpam-6159	93	7	as	as	ADP
ejpam-6159	93	8	γ(ϱ	γ(ϱ	NOUN
ejpam-6159	93	9	)	)	PUNCT
ejpam-6159	93	10	=	=	SYM
ejpam-6159	93	11	∫∞	∫∞	NOUN
ejpam-6159	93	12	0	0	NUM
ejpam-6159	93	13	e−uuϱ−1du	e−uuϱ−1du	NOUN
ejpam-6159	93	14	.	.	PUNCT
ejpam-6159	94	1	in	in	ADP
ejpam-6159	94	2	[	[	X
ejpam-6159	94	3	26	26	NUM
ejpam-6159	94	4	]	]	PUNCT
ejpam-6159	94	5	,	,	PUNCT
ejpam-6159	94	6	mubeen	mubeen	PROPN
ejpam-6159	94	7	et	et	PROPN
ejpam-6159	94	8	al	al	PROPN
ejpam-6159	94	9	.	.	PROPN
ejpam-6159	94	10	introduced	introduce	VERB
ejpam-6159	94	11	the	the	DET
ejpam-6159	94	12	following	follow	VERB
ejpam-6159	94	13	class	class	NOUN
ejpam-6159	94	14	of	of	ADP
ejpam-6159	94	15	fractional	fractional	ADJ
ejpam-6159	94	16	integrals	integral	NOUN
ejpam-6159	94	17	.	.	PUNCT
ejpam-6159	95	1	definition	definition	NOUN
ejpam-6159	95	2	7	7	NUM
ejpam-6159	95	3	.	.	PUNCT
ejpam-6159	96	1	[	[	X
ejpam-6159	96	2	26	26	NUM
ejpam-6159	96	3	]	]	PUNCT
ejpam-6159	96	4	suppose	suppose	VERB
ejpam-6159	96	5	that	that	SCONJ
ejpam-6159	96	6	f	f	PROPN
ejpam-6159	96	7	∈	∈	PROPN
ejpam-6159	96	8	l[a1	l[a1	PROPN
ejpam-6159	96	9	,	,	PUNCT
ejpam-6159	96	10	b1	b1	PROPN
ejpam-6159	96	11	]	]	PUNCT
ejpam-6159	96	12	.	.	PUNCT
ejpam-6159	97	1	the	the	DET
ejpam-6159	97	2	k−fractional	k−fractional	ADJ
ejpam-6159	97	3	integrals	integral	NOUN
ejpam-6159	97	4	jϱ,k	jϱ,k	PUNCT
ejpam-6159	98	1	a1−	a1−	PROPN
ejpam-6159	98	2	f	f	X
ejpam-6159	98	3	(	(	PUNCT
ejpam-6159	98	4	x	x	NOUN
ejpam-6159	98	5	)	)	PUNCT
ejpam-6159	98	6	and	and	CCONJ
ejpam-6159	98	7	jϱ,k	jϱ,k	PUNCT
ejpam-6159	98	8	b1	b1	PROPN
ejpam-6159	98	9	+	+	CCONJ
ejpam-6159	98	10	f	f	PROPN
ejpam-6159	98	11	(	(	PUNCT
ejpam-6159	98	12	x	x	NOUN
ejpam-6159	98	13	)	)	PUNCT
ejpam-6159	98	14	order	order	NOUN
ejpam-6159	98	15	ϱ	ϱ	ADP
ejpam-6159	98	16	>	>	X
ejpam-6159	98	17	0,k	0,k	PROPN
ejpam-6159	98	18	>	>	SYM
ejpam-6159	98	19	0	0	NUM
ejpam-6159	98	20	areidefined	areidefine	VERB
ejpam-6159	98	21	as	as	ADP
ejpam-6159	98	22	jϱ,k	jϱ,k	PROPN
ejpam-6159	98	23	a1−	a1−	PROPN
ejpam-6159	98	24	f	f	X
ejpam-6159	98	25	(	(	PUNCT
ejpam-6159	98	26	x	x	NOUN
ejpam-6159	98	27	)	)	PUNCT
ejpam-6159	98	28	=	=	SYM
ejpam-6159	98	29	1	1	NUM
ejpam-6159	98	30	kγk	kγk	NOUN
ejpam-6159	98	31	(	(	PUNCT
ejpam-6159	98	32	ϱ	ϱ	PROPN
ejpam-6159	98	33	)	)	PUNCT
ejpam-6159	98	34	∫	∫	NOUN
ejpam-6159	98	35	x	x	PUNCT
ejpam-6159	98	36	a1	a1	PROPN
ejpam-6159	98	37	(	(	PUNCT
ejpam-6159	98	38	x−	x−	PROPN
ejpam-6159	98	39	t	t	PROPN
ejpam-6159	98	40	)	)	PUNCT
ejpam-6159	98	41	ϱ	ϱ	ADP
ejpam-6159	98	42	k	k	PROPN
ejpam-6159	98	43	−1	−1	NOUN
ejpam-6159	98	44	f	f	PROPN
ejpam-6159	98	45	(	(	PUNCT
ejpam-6159	98	46	t	t	PROPN
ejpam-6159	98	47	)	)	PUNCT
ejpam-6159	98	48	dt	dt	PROPN
ejpam-6159	98	49	;	;	PUNCT
ejpam-6159	98	50	a1	a1	VERB
ejpam-6159	98	51	<	<	X
ejpam-6159	98	52	x	x	X
ejpam-6159	98	53	(	(	PUNCT
ejpam-6159	98	54	11	11	NUM
ejpam-6159	98	55	)	)	PUNCT
ejpam-6159	98	56	and	and	CCONJ
ejpam-6159	98	57	jϱ,k	jϱ,k	PUNCT
ejpam-6159	98	58	b1	b1	PROPN
ejpam-6159	98	59	+	+	CCONJ
ejpam-6159	98	60	f	f	PROPN
ejpam-6159	98	61	(	(	PUNCT
ejpam-6159	98	62	x	x	X
ejpam-6159	98	63	)	)	PUNCT
ejpam-6159	98	64	=	=	SYM
ejpam-6159	98	65	1	1	NUM
ejpam-6159	98	66	kγk	kγk	NOUN
ejpam-6159	98	67	(	(	PUNCT
ejpam-6159	98	68	ϱ	ϱ	PROPN
ejpam-6159	98	69	)	)	PUNCT
ejpam-6159	98	70	∫	∫	PROPN
ejpam-6159	98	71	b1	b1	PROPN
ejpam-6159	98	72	x	x	SYM
ejpam-6159	98	73	(	(	PUNCT
ejpam-6159	98	74	t−	t−	PROPN
ejpam-6159	98	75	x	x	NOUN
ejpam-6159	98	76	)	)	PUNCT
ejpam-6159	98	77	ϱ	ϱ	ADP
ejpam-6159	98	78	k	k	PROPN
ejpam-6159	98	79	−1	−1	NOUN
ejpam-6159	98	80	f	f	PROPN
ejpam-6159	98	81	(	(	PUNCT
ejpam-6159	98	82	t	t	PROPN
ejpam-6159	98	83	)	)	PUNCT
ejpam-6159	98	84	dt	dt	PUNCT
ejpam-6159	98	85	;	;	PUNCT
ejpam-6159	98	86	x	x	X
ejpam-6159	98	87	<	<	X
ejpam-6159	98	88	b1	b1	PROPN
ejpam-6159	98	89	,	,	PUNCT
ejpam-6159	98	90	(	(	PUNCT
ejpam-6159	98	91	12	12	NUM
ejpam-6159	98	92	)	)	PUNCT
ejpam-6159	98	93	respectively	respectively	ADV
ejpam-6159	98	94	,	,	PUNCT
ejpam-6159	98	95	iwhere	iwhere	ADV
ejpam-6159	98	96	k	k	PROPN
ejpam-6159	98	97	>	>	X
ejpam-6159	98	98	0	0	PROPN
ejpam-6159	98	99	and	and	CCONJ
ejpam-6159	98	100	γk(ϱ	γk(ϱ	NUM
ejpam-6159	98	101	)	)	PUNCT
ejpam-6159	98	102	is	be	AUX
ejpam-6159	98	103	the	the	DET
ejpam-6159	98	104	k−gammaifunction	k−gammaifunction	NOUN
ejpam-6159	98	105	is	be	AUX
ejpam-6159	98	106	given	give	VERB
ejpam-6159	98	107	as	as	ADP
ejpam-6159	98	108	γk	γk	PROPN
ejpam-6159	98	109	(	(	PUNCT
ejpam-6159	98	110	ϱ	ϱ	NOUN
ejpam-6159	98	111	)	)	PUNCT
ejpam-6159	98	112	=	=	NOUN
ejpam-6159	98	113	∫∞	∫∞	NOUN
ejpam-6159	98	114	0	0	NUM
ejpam-6159	98	115	tϱ−1e−	tϱ−1e−	NUM
ejpam-6159	98	116	tk	tk	PROPN
ejpam-6159	98	117	k	k	PROPN
ejpam-6159	98	118	dt	dt	PROPN
ejpam-6159	98	119	with	with	ADP
ejpam-6159	98	120	the	the	DET
ejpam-6159	98	121	properties	property	NOUN
ejpam-6159	98	122	γk(ϱ	γk(ϱ	PUNCT
ejpam-6159	99	1	+	+	SYM
ejpam-6159	99	2	k	k	X
ejpam-6159	99	3	)	)	PUNCT
ejpam-6159	99	4	=	=	SYM
ejpam-6159	99	5	ϱγk(ϱ	ϱγk(ϱ	PROPN
ejpam-6159	99	6	)	)	PUNCT
ejpam-6159	99	7	and	and	CCONJ
ejpam-6159	99	8	γk(k	γk(k	NUM
ejpam-6159	99	9	)	)	PUNCT
ejpam-6159	99	10	=	=	SYM
ejpam-6159	100	1	1	1	X
ejpam-6159	100	2	.	.	PUNCT
ejpam-6159	101	1	it	it	PRON
ejpam-6159	101	2	is	be	AUX
ejpam-6159	101	3	noted	note	VERB
ejpam-6159	101	4	that	that	SCONJ
ejpam-6159	101	5	j0,k	j0,k	PROPN
ejpam-6159	101	6	a1−	a1−	PROPN
ejpam-6159	101	7	f	f	PROPN
ejpam-6159	101	8	(	(	PUNCT
ejpam-6159	101	9	x)=j0,k	x)=j0,k	PROPN
ejpam-6159	101	10	b1	b1	PROPN
ejpam-6159	101	11	+	+	CCONJ
ejpam-6159	101	12	f	f	X
ejpam-6159	101	13	(	(	PUNCT
ejpam-6159	101	14	x	x	X
ejpam-6159	101	15	)	)	PUNCT
ejpam-6159	101	16	=	=	SYM
ejpam-6159	101	17	f	f	PROPN
ejpam-6159	101	18	(	(	PUNCT
ejpam-6159	101	19	x	x	NOUN
ejpam-6159	101	20	)	)	PUNCT
ejpam-6159	101	21	.	.	PUNCT
ejpam-6159	102	1	j.	j.	PROPN
ejpam-6159	102	2	nasir	nasir	PROPN
ejpam-6159	102	3	et	et	PROPN
ejpam-6159	102	4	al	al	PROPN
ejpam-6159	102	5	.	.	PUNCT
ejpam-6159	102	6	/	/	SYM
ejpam-6159	102	7	eur	eur	PROPN
ejpam-6159	102	8	.	.	PUNCT
ejpam-6159	103	1	j.	j.	PROPN
ejpam-6159	103	2	pure	pure	PROPN
ejpam-6159	103	3	appl	appl	PROPN
ejpam-6159	103	4	.	.	PROPN
ejpam-6159	103	5	math	math	PROPN
ejpam-6159	103	6	,	,	PUNCT
ejpam-6159	103	7	18	18	NUM
ejpam-6159	103	8	(	(	PUNCT
ejpam-6159	103	9	3	3	NUM
ejpam-6159	103	10	)	)	PUNCT
ejpam-6159	103	11	(	(	PUNCT
ejpam-6159	103	12	2025	2025	NUM
ejpam-6159	103	13	)	)	PUNCT
ejpam-6159	103	14	,	,	PUNCT
ejpam-6159	103	15	6159	6159	NUM
ejpam-6159	103	16	5	5	NUM
ejpam-6159	103	17	of	of	ADP
ejpam-6159	103	18	26	26	NUM
ejpam-6159	103	19	2	2	NUM
ejpam-6159	103	20	.	.	PUNCT
ejpam-6159	103	21	main	main	ADJ
ejpam-6159	103	22	results	result	NOUN
ejpam-6159	103	23	2.1	2.1	NUM
ejpam-6159	103	24	.	.	PUNCT
ejpam-6159	104	1	polynomials	polynomial	NOUN
ejpam-6159	104	2	on	on	ADP
ejpam-6159	104	3	n−fractional	n−fractional	ADJ
ejpam-6159	104	4	s−like	s−like	INTJ
ejpam-6159	104	5	preinvex	preinvex	NOUN
ejpam-6159	104	6	mappings	mapping	NOUN
ejpam-6159	104	7	:	:	PUNCT
ejpam-6159	104	8	this	this	DET
ejpam-6159	104	9	section	section	NOUN
ejpam-6159	104	10	examines	examine	VERB
ejpam-6159	104	11	the	the	DET
ejpam-6159	104	12	basic	basic	ADJ
ejpam-6159	104	13	algebraic	algebraic	ADJ
ejpam-6159	104	14	features	feature	NOUN
ejpam-6159	104	15	of	of	ADP
ejpam-6159	104	16	a	a	DET
ejpam-6159	104	17	novel	novel	ADJ
ejpam-6159	104	18	fractional	fractional	ADJ
ejpam-6159	104	19	integral	integral	ADJ
ejpam-6159	104	20	operator	operator	NOUN
ejpam-6159	104	21	that	that	PRON
ejpam-6159	104	22	incorporates	incorporate	VERB
ejpam-6159	104	23	polynomials	polynomial	NOUN
ejpam-6159	104	24	on	on	ADP
ejpam-6159	104	25	n−fractional	n−fractional	ADJ
ejpam-6159	104	26	with	with	ADP
ejpam-6159	104	27	s−like	s−like	INTJ
ejpam-6159	104	28	preinvex	preinvex	NOUN
ejpam-6159	104	29	mappings	mapping	NOUN
ejpam-6159	104	30	.	.	PUNCT
ejpam-6159	105	1	definition	definition	NOUN
ejpam-6159	105	2	8	8	NUM
ejpam-6159	105	3	.	.	PUNCT
ejpam-6159	106	1	let	let	VERB
ejpam-6159	106	2	us	we	PRON
ejpam-6159	106	3	suppose	suppose	VERB
ejpam-6159	106	4	that	that	SCONJ
ejpam-6159	106	5	s	s	VERB
ejpam-6159	106	6	∈	∈	PROPN
ejpam-6159	107	1	[	[	X
ejpam-6159	107	2	0	0	NUM
ejpam-6159	107	3	,	,	PUNCT
ejpam-6159	107	4	1	1	NUM
ejpam-6159	107	5	]	]	PUNCT
ejpam-6159	107	6	,	,	PUNCT
ejpam-6159	107	7	n	n	PROPN
ejpam-6159	107	8	∈	∈	PROPN
ejpam-6159	107	9	n	n	X
ejpam-6159	107	10	,	,	PUNCT
ejpam-6159	107	11	ai	ai	VERB
ejpam-6159	107	12	≥	≥	NOUN
ejpam-6159	107	13	0	0	NUM
ejpam-6159	107	14	(	(	PUNCT
ejpam-6159	107	15	i	i	PRON
ejpam-6159	107	16	=	=	NOUN
ejpam-6159	107	17	1	1	NUM
ejpam-6159	107	18	,	,	PUNCT
ejpam-6159	107	19	n	n	PROPN
ejpam-6159	107	20	)	)	PUNCT
ejpam-6159	107	21	,	,	PUNCT
ejpam-6159	107	22	such	such	ADJ
ejpam-6159	107	23	that	that	SCONJ
ejpam-6159	107	24	∑n	∑n	PROPN
ejpam-6159	107	25	i=1	i=1	PROPN
ejpam-6159	107	26	ai	ai	VERB
ejpam-6159	107	27	>	>	X
ejpam-6159	107	28	0	0	PROPN
ejpam-6159	107	29	,	,	PUNCT
ejpam-6159	107	30	xo	xo	PROPN
ejpam-6159	107	31	⊂	⊂	PROPN
ejpam-6159	107	32	ℜ	ℜ	PROPN
ejpam-6159	107	33	is	be	AUX
ejpam-6159	107	34	an	an	DET
ejpam-6159	107	35	interval	interval	NOUN
ejpam-6159	107	36	.	.	PUNCT
ejpam-6159	108	1	a	a	DET
ejpam-6159	108	2	non	non	ADJ
ejpam-6159	108	3	-	-	ADJ
ejpam-6159	108	4	negative	negative	ADJ
ejpam-6159	108	5	mapping	mapping	NOUN
ejpam-6159	108	6	xo	xo	PROPN
ejpam-6159	108	7	×	×	PROPN
ejpam-6159	108	8	xo	xo	PROPN
ejpam-6159	108	9	⊂	⊂	PROPN
ejpam-6159	108	10	ℜ	ℜ	PROPN
ejpam-6159	108	11	→	→	SYM
ejpam-6159	108	12	ℜ	ℜ	PROPN
ejpam-6159	108	13	is	be	AUX
ejpam-6159	108	14	said	say	VERB
ejpam-6159	108	15	to	to	PART
ejpam-6159	108	16	be	be	AUX
ejpam-6159	108	17	a	a	DET
ejpam-6159	108	18	polynomial	polynomial	NOUN
ejpam-6159	108	19	on	on	ADP
ejpam-6159	108	20	n−fractional	n−fractional	ADJ
ejpam-6159	108	21	s−like	s−like	INTJ
ejpam-6159	108	22	preinvex	preinvex	NOUN
ejpam-6159	108	23	mapping	mapping	NOUN
ejpam-6159	108	24	if	if	SCONJ
ejpam-6159	108	25	for	for	ADP
ejpam-6159	108	26	every	every	DET
ejpam-6159	108	27	f	f	NOUN
ejpam-6159	108	28	(	(	PUNCT
ejpam-6159	108	29	a1	a1	NOUN
ejpam-6159	108	30	+	+	CCONJ
ejpam-6159	108	31	tς∗	tς∗	NOUN
ejpam-6159	108	32	(	(	PUNCT
ejpam-6159	108	33	b1	b1	NOUN
ejpam-6159	108	34	,	,	PUNCT
ejpam-6159	108	35	a1	a1	NOUN
ejpam-6159	108	36	)	)	PUNCT
ejpam-6159	108	37	)	)	PUNCT
ejpam-6159	108	38	≤	≤	NOUN
ejpam-6159	109	1	∑n	∑n	PROPN
ejpam-6159	110	1	i=1	i=1	PROPN
ejpam-6159	110	2	ai	ai	VERB
ejpam-6159	110	3	(	(	PUNCT
ejpam-6159	110	4	1−	1−	NUM
ejpam-6159	110	5	s	s	X
ejpam-6159	110	6	(	(	PUNCT
ejpam-6159	110	7	1−	1−	NUM
ejpam-6159	110	8	t	t	NOUN
ejpam-6159	110	9	)	)	PUNCT
ejpam-6159	110	10	)	)	PUNCT
ejpam-6159	111	1	1	1	NUM
ejpam-6159	111	2	i∑n	i∑n	PROPN
ejpam-6159	111	3	i=1	i=1	PROPN
ejpam-6159	111	4	ai	ai	VERB
ejpam-6159	111	5	f	f	PROPN
ejpam-6159	111	6	(	(	PUNCT
ejpam-6159	111	7	a1	a1	PROPN
ejpam-6159	111	8	)	)	PUNCT
ejpam-6159	111	9	+	+	CCONJ
ejpam-6159	111	10	∑n	∑n	PROPN
ejpam-6159	111	11	i=1	i=1	PROPN
ejpam-6159	111	12	ai	ai	VERB
ejpam-6159	111	13	(	(	PUNCT
ejpam-6159	111	14	1−	1−	NUM
ejpam-6159	111	15	st	st	NOUN
ejpam-6159	111	16	)	)	PUNCT
ejpam-6159	111	17	1	1	NUM
ejpam-6159	111	18	i∑n	i∑n	PROPN
ejpam-6159	111	19	i=1	i=1	PROPN
ejpam-6159	111	20	ai	ai	VERB
ejpam-6159	111	21	f	f	PROPN
ejpam-6159	111	22	(	(	PUNCT
ejpam-6159	111	23	b1	b1	PROPN
ejpam-6159	111	24	)	)	PUNCT
ejpam-6159	111	25	,	,	PUNCT
ejpam-6159	111	26	(	(	PUNCT
ejpam-6159	111	27	13	13	NUM
ejpam-6159	111	28	)	)	PUNCT
ejpam-6159	111	29	for	for	ADP
ejpam-6159	111	30	all	all	DET
ejpam-6159	111	31	t	t	NOUN
ejpam-6159	111	32	∈	∈	PROPN
ejpam-6159	112	1	[	[	X
ejpam-6159	112	2	0	0	NUM
ejpam-6159	112	3	,	,	PUNCT
ejpam-6159	112	4	1	1	NUM
ejpam-6159	112	5	]	]	PUNCT
ejpam-6159	112	6	,	,	PUNCT
ejpam-6159	112	7	a1	a1	PROPN
ejpam-6159	112	8	,	,	PUNCT
ejpam-6159	112	9	b1	b1	NOUN
ejpam-6159	112	10	∈	∈	PROPN
ejpam-6159	112	11	xo	xo	PROPN
ejpam-6159	112	12	.	.	PROPN
ejpam-6159	112	13	remark	remark	PROPN
ejpam-6159	112	14	1	1	NUM
ejpam-6159	112	15	.	.	NOUN
ejpam-6159	113	1	•	•	NOUN
ejpam-6159	113	2	if	if	SCONJ
ejpam-6159	113	3	we	we	PRON
ejpam-6159	113	4	take	take	VERB
ejpam-6159	113	5	n	n	NOUN
ejpam-6159	113	6	=	=	SYM
ejpam-6159	113	7	1	1	NUM
ejpam-6159	113	8	in	in	ADP
ejpam-6159	113	9	definition	definition	NOUN
ejpam-6159	113	10	(	(	PUNCT
ejpam-6159	113	11	8)	8)	NUM
ejpam-6159	113	12	,	,	PUNCT
ejpam-6159	113	13	we	we	PRON
ejpam-6159	113	14	attain	attain	VERB
ejpam-6159	113	15	[	[	X
ejpam-6159	113	16	21	21	NUM
ejpam-6159	113	17	]	]	PUNCT
ejpam-6159	113	18	.	.	PUNCT
ejpam-6159	114	1	•	•	INTJ
ejpam-6159	114	2	if	if	SCONJ
ejpam-6159	114	3	n	n	NOUN
ejpam-6159	114	4	=	=	SYM
ejpam-6159	114	5	1	1	NUM
ejpam-6159	114	6	and	and	CCONJ
ejpam-6159	114	7	s	s	AUX
ejpam-6159	114	8	=	=	SYM
ejpam-6159	114	9	1	1	NUM
ejpam-6159	114	10	in	in	ADP
ejpam-6159	114	11	definition	definition	NOUN
ejpam-6159	114	12	(	(	PUNCT
ejpam-6159	114	13	8)	8)	NUM
ejpam-6159	114	14	,	,	PUNCT
ejpam-6159	114	15	it	it	PRON
ejpam-6159	114	16	will	will	AUX
ejpam-6159	114	17	be	be	AUX
ejpam-6159	114	18	explored	explore	VERB
ejpam-6159	114	19	by	by	ADP
ejpam-6159	114	20	weiriand	weiriand	NOUN
ejpam-6159	114	21	mond	mond	PROPN
ejpam-6159	115	1	[	[	X
ejpam-6159	115	2	12	12	NUM
ejpam-6159	115	3	]	]	PUNCT
ejpam-6159	115	4	.	.	PUNCT
ejpam-6159	116	1	•	•	NUM
ejpam-6159	116	2	with	with	ADP
ejpam-6159	116	3	taking	take	VERB
ejpam-6159	116	4	n	n	NOUN
ejpam-6159	116	5	=	=	SYM
ejpam-6159	116	6	1	1	NUM
ejpam-6159	116	7	and	and	CCONJ
ejpam-6159	116	8	ς∗	ς∗	PROPN
ejpam-6159	116	9	(	(	PUNCT
ejpam-6159	116	10	b1	b1	NOUN
ejpam-6159	116	11	,	,	PUNCT
ejpam-6159	116	12	a1	a1	NOUN
ejpam-6159	116	13	)	)	PUNCT
ejpam-6159	116	14	=	=	SYM
ejpam-6159	116	15	b1	b1	NOUN
ejpam-6159	116	16	−	−	NOUN
ejpam-6159	116	17	a1	a1	NOUN
ejpam-6159	116	18	in	in	ADP
ejpam-6159	116	19	definition	definition	NOUN
ejpam-6159	116	20	(	(	PUNCT
ejpam-6159	116	21	8)	8)	NUM
ejpam-6159	116	22	,	,	PUNCT
ejpam-6159	116	23	then	then	ADV
ejpam-6159	116	24	it	it	PRON
ejpam-6159	116	25	will	will	AUX
ejpam-6159	116	26	attain	attain	VERB
ejpam-6159	116	27	a	a	DET
ejpam-6159	116	28	published	publish	VERB
ejpam-6159	116	29	definition	definition	NOUN
ejpam-6159	116	30	named	name	VERB
ejpam-6159	116	31	as	as	ADP
ejpam-6159	116	32	s−type	s−type	NOUN
ejpam-6159	116	33	convexity	convexity	NOUN
ejpam-6159	116	34	that	that	PRON
ejpam-6159	116	35	was	be	AUX
ejpam-6159	116	36	explored	explore	VERB
ejpam-6159	116	37	by	by	ADP
ejpam-6159	116	38	i̇.	i̇.	NOUN
ejpam-6159	116	39	i̇şcan	i̇şcan	PROPN
ejpam-6159	116	40	et	et	PROPN
ejpam-6159	116	41	al	al	PROPN
ejpam-6159	116	42	.	.	PUNCT
ejpam-6159	117	1	[	[	X
ejpam-6159	117	2	21	21	NUM
ejpam-6159	117	3	]	]	PUNCT
ejpam-6159	117	4	.	.	PUNCT
ejpam-6159	118	1	we	we	PRON
ejpam-6159	118	2	will	will	AUX
ejpam-6159	118	3	mention	mention	VERB
ejpam-6159	118	4	the	the	DET
ejpam-6159	118	5	nature	nature	NOUN
ejpam-6159	118	6	of	of	ADP
ejpam-6159	118	7	class	class	NOUN
ejpam-6159	118	8	with	with	ADP
ejpam-6159	118	9	some	some	DET
ejpam-6159	118	10	polynomials	polynomial	NOUN
ejpam-6159	118	11	on	on	ADP
ejpam-6159	118	12	n−fractional	n−fractional	ADJ
ejpam-6159	118	13	s−like	s−like	INTJ
ejpam-6159	118	14	preinvex	preinvex	NOUN
ejpam-6159	118	15	mappings	mapping	NOUN
ejpam-6159	118	16	by	by	ADP
ejpam-6159	118	17	gfpp−s	gfpp−s	PROPN
ejpam-6159	118	18	.	.	PUNCT
ejpam-6159	118	19	example	example	NOUN
ejpam-6159	119	1	1	1	NUM
ejpam-6159	119	2	.	.	X
ejpam-6159	119	3	consider	consider	VERB
ejpam-6159	119	4	a	a	DET
ejpam-6159	119	5	mapping	mapping	NOUN
ejpam-6159	119	6	f(x	f(x	NOUN
ejpam-6159	119	7	)	)	PUNCT
ejpam-6159	120	1	=	=	SYM
ejpam-6159	120	2	x2	x2	PROPN
ejpam-6159	120	3	,	,	PUNCT
ejpam-6159	120	4	and	and	CCONJ
ejpam-6159	120	5	with	with	ADP
ejpam-6159	120	6	some	some	DET
ejpam-6159	120	7	substitutions	substitution	NOUN
ejpam-6159	120	8	as	as	ADP
ejpam-6159	120	9	s	s	NOUN
ejpam-6159	120	10	=	=	NOUN
ejpam-6159	120	11	0.4	0.4	NUM
ejpam-6159	120	12	,	,	PUNCT
ejpam-6159	120	13	n	n	NOUN
ejpam-6159	120	14	=	=	SYM
ejpam-6159	120	15	2	2	NUM
ejpam-6159	120	16	,	,	PUNCT
ejpam-6159	120	17	a1	a1	NOUN
ejpam-6159	120	18	=	=	SYM
ejpam-6159	120	19	1	1	NUM
ejpam-6159	120	20	,	,	PUNCT
ejpam-6159	120	21	b1	b1	NOUN
ejpam-6159	120	22	=	=	SYM
ejpam-6159	120	23	2	2	NUM
ejpam-6159	120	24	and	and	CCONJ
ejpam-6159	120	25	t	t	NOUN
ejpam-6159	120	26	=	=	NUM
ejpam-6159	120	27	0.4	0.4	NUM
ejpam-6159	120	28	.	.	PUNCT
ejpam-6159	121	1	according	accord	VERB
ejpam-6159	121	2	to	to	ADP
ejpam-6159	121	3	(	(	PUNCT
ejpam-6159	121	4	13	13	NUM
ejpam-6159	121	5	)	)	PUNCT
ejpam-6159	121	6	,	,	PUNCT
ejpam-6159	121	7	one	one	PRON
ejpam-6159	121	8	writes	write	VERB
ejpam-6159	121	9	f	f	PROPN
ejpam-6159	121	10	(	(	PUNCT
ejpam-6159	121	11	a1	a1	NOUN
ejpam-6159	121	12	+	+	CCONJ
ejpam-6159	121	13	tς∗	tς∗	NOUN
ejpam-6159	121	14	(	(	PUNCT
ejpam-6159	121	15	b1	b1	NOUN
ejpam-6159	121	16	,	,	PUNCT
ejpam-6159	121	17	a1	a1	NOUN
ejpam-6159	121	18	)	)	PUNCT
ejpam-6159	121	19	)	)	PUNCT
ejpam-6159	121	20	≤	≤	NOUN
ejpam-6159	122	1	∑n	∑n	PROPN
ejpam-6159	123	1	i=1	i=1	PROPN
ejpam-6159	123	2	ai	ai	VERB
ejpam-6159	123	3	(	(	PUNCT
ejpam-6159	123	4	1−	1−	NUM
ejpam-6159	123	5	s	s	X
ejpam-6159	123	6	(	(	PUNCT
ejpam-6159	123	7	1−	1−	NUM
ejpam-6159	123	8	t	t	NOUN
ejpam-6159	123	9	)	)	PUNCT
ejpam-6159	123	10	)	)	PUNCT
ejpam-6159	124	1	1	1	NUM
ejpam-6159	124	2	i∑n	i∑n	PROPN
ejpam-6159	124	3	i=1	i=1	PROPN
ejpam-6159	124	4	ai	ai	VERB
ejpam-6159	124	5	f	f	PROPN
ejpam-6159	124	6	(	(	PUNCT
ejpam-6159	124	7	a1	a1	PROPN
ejpam-6159	124	8	)	)	PUNCT
ejpam-6159	124	9	+	+	CCONJ
ejpam-6159	124	10	∑n	∑n	PROPN
ejpam-6159	124	11	i=1	i=1	PROPN
ejpam-6159	124	12	ai	ai	VERB
ejpam-6159	124	13	(	(	PUNCT
ejpam-6159	124	14	1−	1−	NUM
ejpam-6159	124	15	st	st	NOUN
ejpam-6159	124	16	)	)	PUNCT
ejpam-6159	124	17	1	1	NUM
ejpam-6159	124	18	i∑n	i∑n	PROPN
ejpam-6159	124	19	i=1	i=1	PROPN
ejpam-6159	124	20	ai	ai	VERB
ejpam-6159	124	21	f	f	PROPN
ejpam-6159	124	22	(	(	PUNCT
ejpam-6159	124	23	b1	b1	PROPN
ejpam-6159	124	24	)	)	PUNCT
ejpam-6159	124	25	.	.	PUNCT
ejpam-6159	125	1	for	for	ADP
ejpam-6159	125	2	a1	a1	NOUN
ejpam-6159	125	3	=	=	SYM
ejpam-6159	125	4	1	1	NUM
ejpam-6159	125	5	and	and	CCONJ
ejpam-6159	125	6	b1	b1	NOUN
ejpam-6159	125	7	=	=	SYM
ejpam-6159	125	8	3	3	NUM
ejpam-6159	125	9	,	,	PUNCT
ejpam-6159	125	10	we	we	PRON
ejpam-6159	125	11	have	have	VERB
ejpam-6159	125	12	f	f	X
ejpam-6159	125	13	(	(	PUNCT
ejpam-6159	125	14	1	1	NUM
ejpam-6159	125	15	+	+	NUM
ejpam-6159	125	16	0.4ς∗	0.4ς∗	NUM
ejpam-6159	125	17	(	(	PUNCT
ejpam-6159	125	18	3	3	NUM
ejpam-6159	125	19	,	,	PUNCT
ejpam-6159	125	20	1	1	NUM
ejpam-6159	125	21	)	)	PUNCT
ejpam-6159	125	22	)	)	PUNCT
ejpam-6159	126	1	=	=	SYM
ejpam-6159	126	2	f(1.8	f(1.8	PROPN
ejpam-6159	126	3	)	)	PUNCT
ejpam-6159	126	4	=	=	PUNCT
ejpam-6159	127	1	1.82	1.82	NUM
ejpam-6159	127	2	=	=	SYM
ejpam-6159	127	3	3.24	3.24	NUM
ejpam-6159	127	4	and	and	CCONJ
ejpam-6159	127	5	the	the	DET
ejpam-6159	127	6	other	other	ADJ
ejpam-6159	127	7	side	side	NOUN
ejpam-6159	127	8	will	will	AUX
ejpam-6159	127	9	be	be	AUX
ejpam-6159	127	10	1	1	NUM
ejpam-6159	127	11	.	.	PUNCT
ejpam-6159	128	1	(	(	PUNCT
ejpam-6159	128	2	1−	1−	NUM
ejpam-6159	128	3	0.4	0.4	NUM
ejpam-6159	128	4	(	(	PUNCT
ejpam-6159	128	5	0.6	0.6	NUM
ejpam-6159	128	6	)	)	PUNCT
ejpam-6159	128	7	)	)	PUNCT
ejpam-6159	129	1	1	1	NUM
ejpam-6159	129	2	1	1	NUM
ejpam-6159	129	3	+	+	NUM
ejpam-6159	129	4	2	2	NUM
ejpam-6159	129	5	.	.	PUNCT
ejpam-6159	129	6	(	(	PUNCT
ejpam-6159	129	7	1−	1−	NUM
ejpam-6159	129	8	0.4	0.4	NUM
ejpam-6159	129	9	(	(	PUNCT
ejpam-6159	129	10	0.6	0.6	NUM
ejpam-6159	129	11	)	)	PUNCT
ejpam-6159	129	12	)	)	PUNCT
ejpam-6159	129	13	1	1	NUM
ejpam-6159	129	14	2	2	NUM
ejpam-6159	129	15	3	3	NUM
ejpam-6159	129	16	12	12	NUM
ejpam-6159	129	17	+	+	CCONJ
ejpam-6159	129	18	1	1	NUM
ejpam-6159	129	19	.	.	PUNCT
ejpam-6159	129	20	(	(	PUNCT
ejpam-6159	129	21	1−	1−	NUM
ejpam-6159	129	22	0.4	0.4	NUM
ejpam-6159	129	23	(	(	PUNCT
ejpam-6159	129	24	0.6	0.6	NUM
ejpam-6159	129	25	)	)	PUNCT
ejpam-6159	129	26	)	)	PUNCT
ejpam-6159	129	27	1	1	NUM
ejpam-6159	129	28	1	1	NUM
ejpam-6159	129	29	+	+	NUM
ejpam-6159	129	30	2	2	NUM
ejpam-6159	129	31	.	.	PUNCT
ejpam-6159	129	32	(	(	PUNCT
ejpam-6159	129	33	1−	1−	NUM
ejpam-6159	129	34	0.4	0.4	NUM
ejpam-6159	129	35	(	(	PUNCT
ejpam-6159	129	36	0.6	0.6	NUM
ejpam-6159	129	37	)	)	PUNCT
ejpam-6159	129	38	)	)	PUNCT
ejpam-6159	129	39	1	1	NUM
ejpam-6159	129	40	2	2	NUM
ejpam-6159	129	41	3	3	NUM
ejpam-6159	129	42	32	32	NUM
ejpam-6159	129	43	=	=	SYM
ejpam-6159	129	44	8.35	8.35	NUM
ejpam-6159	129	45	so	so	SCONJ
ejpam-6159	129	46	that	that	SCONJ
ejpam-6159	129	47	3.24	3.24	NUM
ejpam-6159	129	48	≤	≤	NUM
ejpam-6159	129	49	8.35	8.35	NUM
ejpam-6159	129	50	.	.	PUNCT
ejpam-6159	129	51	.	.	PUNCT
ejpam-6159	130	1	j.	j.	PROPN
ejpam-6159	130	2	nasir	nasir	PROPN
ejpam-6159	130	3	et	et	PROPN
ejpam-6159	130	4	al	al	PROPN
ejpam-6159	130	5	.	.	PUNCT
ejpam-6159	130	6	/	/	SYM
ejpam-6159	130	7	eur	eur	PROPN
ejpam-6159	130	8	.	.	PUNCT
ejpam-6159	131	1	j.	j.	PROPN
ejpam-6159	131	2	pure	pure	PROPN
ejpam-6159	131	3	appl	appl	PROPN
ejpam-6159	131	4	.	.	PROPN
ejpam-6159	131	5	math	math	PROPN
ejpam-6159	131	6	,	,	PUNCT
ejpam-6159	131	7	18	18	NUM
ejpam-6159	131	8	(	(	PUNCT
ejpam-6159	131	9	3	3	NUM
ejpam-6159	131	10	)	)	PUNCT
ejpam-6159	131	11	(	(	PUNCT
ejpam-6159	131	12	2025	2025	NUM
ejpam-6159	131	13	)	)	PUNCT
ejpam-6159	131	14	,	,	PUNCT
ejpam-6159	131	15	6159	6159	NUM
ejpam-6159	131	16	6	6	NUM
ejpam-6159	131	17	of	of	ADP
ejpam-6159	131	18	26	26	NUM
ejpam-6159	131	19	2.2	2.2	NUM
ejpam-6159	131	20	.	.	PUNCT
ejpam-6159	132	1	polynomials	polynomial	NOUN
ejpam-6159	132	2	on	on	ADP
ejpam-6159	132	3	n−fractional	n−fractional	ADJ
ejpam-6159	132	4	s−like	s−like	INTJ
ejpam-6159	132	5	preinvex	preinvex	NOUN
ejpam-6159	132	6	mapping	mapping	NOUN
ejpam-6159	132	7	as	as	ADP
ejpam-6159	132	8	new	new	ADJ
ejpam-6159	132	9	extensions	extension	NOUN
ejpam-6159	132	10	of	of	ADP
ejpam-6159	132	11	h	h	NOUN
ejpam-6159	132	12	–	–	PUNCT
ejpam-6159	132	13	h	h	NOUN
ejpam-6159	132	14	like	like	ADP
ejpam-6159	132	15	inequalities	inequality	NOUN
ejpam-6159	132	16	now	now	ADV
ejpam-6159	132	17	,	,	PUNCT
ejpam-6159	132	18	we	we	PRON
ejpam-6159	132	19	will	will	AUX
ejpam-6159	132	20	attain	attain	VERB
ejpam-6159	132	21	a	a	DET
ejpam-6159	132	22	new	new	ADJ
ejpam-6159	132	23	generalization	generalization	NOUN
ejpam-6159	132	24	ofih	ofih	NOUN
ejpam-6159	132	25	–	–	PUNCT
ejpam-6159	132	26	h	h	NOUN
ejpam-6159	132	27	inequality	inequality	NOUN
ejpam-6159	132	28	for	for	ADP
ejpam-6159	132	29	the	the	DET
ejpam-6159	132	30	gfpp−s	gfpp−s	PROPN
ejpam-6159	132	31	function	function	NOUN
ejpam-6159	132	32	f.	f.	PROPN
ejpam-6159	132	33	theorem	theorem	VERB
ejpam-6159	132	34	2	2	X
ejpam-6159	132	35	.	.	PUNCT
ejpam-6159	133	1	let	let	VERB
ejpam-6159	133	2	xo	xo	PROPN
ejpam-6159	133	3	⊆	⊆	PROPN
ejpam-6159	133	4	ℜ	ℜ	PROPN
ejpam-6159	133	5	ibe	ibe	VERB
ejpam-6159	133	6	an	an	DET
ejpam-6159	133	7	open	open	ADJ
ejpam-6159	133	8	invexisubset	invexisubset	NOUN
ejpam-6159	133	9	with	with	ADP
ejpam-6159	133	10	respectito	respectito	ADJ
ejpam-6159	133	11	ς∗	ς∗	NOUN
ejpam-6159	133	12	:	:	PUNCT
ejpam-6159	133	13	xo×xo	xo×xo	PROPN
ejpam-6159	133	14	→	→	SYM
ejpam-6159	133	15	ℜ	ℜ	PROPN
ejpam-6159	133	16	and	and	CCONJ
ejpam-6159	133	17	a1	a1	NOUN
ejpam-6159	133	18	,	,	PUNCT
ejpam-6159	133	19	b1	b1	NOUN
ejpam-6159	133	20	∈	∈	PROPN
ejpam-6159	133	21	xo	xo	PROPN
ejpam-6159	133	22	with	with	ADP
ejpam-6159	133	23	b1	b1	NOUN
ejpam-6159	133	24	+	+	CCONJ
ejpam-6159	133	25	ς∗	ς∗	PROPN
ejpam-6159	133	26	(	(	PUNCT
ejpam-6159	133	27	a1	a1	NOUN
ejpam-6159	133	28	,	,	PUNCT
ejpam-6159	133	29	b1	b1	NOUN
ejpam-6159	133	30	)	)	PUNCT
ejpam-6159	133	31	≤	≤	NUM
ejpam-6159	133	32	b1	b1	NOUN
ejpam-6159	133	33	.	.	PUNCT
ejpam-6159	134	1	suppose	suppose	VERB
ejpam-6159	134	2	that	that	SCONJ
ejpam-6159	134	3	f	f	X
ejpam-6159	134	4	:	:	PUNCT
ejpam-6159	135	1	[	[	X
ejpam-6159	135	2	b1	b1	NOUN
ejpam-6159	135	3	+	+	CCONJ
ejpam-6159	135	4	ς∗	ς∗	PROPN
ejpam-6159	135	5	(	(	PUNCT
ejpam-6159	135	6	a1	a1	NOUN
ejpam-6159	135	7	,	,	PUNCT
ejpam-6159	135	8	b1	b1	NOUN
ejpam-6159	135	9	)	)	PUNCT
ejpam-6159	135	10	,	,	PUNCT
ejpam-6159	135	11	b1	b1	PROPN
ejpam-6159	135	12	]	]	PUNCT
ejpam-6159	135	13	and	and	CCONJ
ejpam-6159	135	14	satisfies	satisfy	VERB
ejpam-6159	135	15	propertyc	propertyc	NOUN
ejpam-6159	135	16	with	with	ADP
ejpam-6159	135	17	n	n	PRON
ejpam-6159	135	18	∈	∈	PROPN
ejpam-6159	135	19	n	n	NOUN
ejpam-6159	135	20	,	,	PUNCT
ejpam-6159	135	21	ai	ai	VERB
ejpam-6159	135	22	≥	≥	NOUN
ejpam-6159	135	23	0	0	NUM
ejpam-6159	135	24	(	(	PUNCT
ejpam-6159	135	25	i	i	PRON
ejpam-6159	135	26	=	=	NOUN
ejpam-6159	135	27	1	1	NUM
ejpam-6159	135	28	,	,	PUNCT
ejpam-6159	135	29	n	n	PROPN
ejpam-6159	135	30	)	)	PUNCT
ejpam-6159	135	31	,	,	PUNCT
ejpam-6159	135	32	such	such	ADJ
ejpam-6159	135	33	that	that	SCONJ
ejpam-6159	135	34	∑n	∑n	PROPN
ejpam-6159	135	35	i=1	i=1	PROPN
ejpam-6159	135	36	ai	ai	AUX
ejpam-6159	135	37	>	>	X
ejpam-6159	135	38	0	0	NUM
ejpam-6159	135	39	,	,	PUNCT
ejpam-6159	135	40	s	s	VERB
ejpam-6159	135	41	∈	∈	PROPN
ejpam-6159	136	1	[	[	X
ejpam-6159	136	2	0	0	NUM
ejpam-6159	136	3	,	,	PUNCT
ejpam-6159	136	4	1	1	NUM
ejpam-6159	136	5	]	]	PUNCT
ejpam-6159	136	6	,	,	PUNCT
ejpam-6159	136	7	ϱ	ϱ	PROPN
ejpam-6159	136	8	∈	∈	PROPN
ejpam-6159	137	1	[	[	X
ejpam-6159	137	2	0	0	NUM
ejpam-6159	137	3	,	,	PUNCT
ejpam-6159	137	4	1	1	NUM
ejpam-6159	137	5	]	]	PUNCT
ejpam-6159	137	6	,	,	PUNCT
ejpam-6159	137	7	k	k	X
ejpam-6159	137	8	>	>	X
ejpam-6159	137	9	0	0	X
ejpam-6159	137	10	.	.	PUNCT
ejpam-6159	138	1	then	then	ADV
ejpam-6159	138	2	∑n	∑n	PROPN
ejpam-6159	138	3	i=1	i=1	PROPN
ejpam-6159	138	4	ai∑n	ai∑n	PROPN
ejpam-6159	139	1	i=1	i=1	X
ejpam-6159	139	2	ai	ai	VERB
ejpam-6159	139	3	(	(	PUNCT
ejpam-6159	139	4	1−	1−	NUM
ejpam-6159	139	5	s	s	NOUN
ejpam-6159	139	6	2	2	NUM
ejpam-6159	139	7	)	)	PUNCT
ejpam-6159	139	8	1	1	NUM
ejpam-6159	139	9	i	i	PRON
ejpam-6159	139	10	f	f	PROPN
ejpam-6159	139	11	(	(	PUNCT
ejpam-6159	139	12	2a1	2a1	NUM
ejpam-6159	139	13	+	+	CCONJ
ejpam-6159	139	14	ς∗	ς∗	PROPN
ejpam-6159	139	15	(	(	PUNCT
ejpam-6159	139	16	b1	b1	NOUN
ejpam-6159	139	17	,	,	PUNCT
ejpam-6159	139	18	a1	a1	NOUN
ejpam-6159	139	19	)	)	PUNCT
ejpam-6159	139	20	2	2	NUM
ejpam-6159	139	21	)	)	PUNCT
ejpam-6159	139	22	≤	≤	NUM
ejpam-6159	139	23	γk	γk	X
ejpam-6159	139	24	(	(	PUNCT
ejpam-6159	139	25	ϱ+	ϱ+	X
ejpam-6159	139	26	k	k	NOUN
ejpam-6159	139	27	)	)	PUNCT
ejpam-6159	139	28	ς	ς	PROPN
ejpam-6159	139	29	ϱ	ϱ	PROPN
ejpam-6159	139	30	k	k	PROPN
ejpam-6159	139	31	∗	∗	X
ejpam-6159	139	32	(	(	PUNCT
ejpam-6159	139	33	b1	b1	NOUN
ejpam-6159	139	34	,	,	PUNCT
ejpam-6159	139	35	a1	a1	NOUN
ejpam-6159	139	36	)	)	PUNCT
ejpam-6159	139	37	{	{	PUNCT
ejpam-6159	139	38	jϱ,k	jϱ,k	X
ejpam-6159	139	39	a1	a1	PROPN
ejpam-6159	139	40	+	+	X
ejpam-6159	139	41	f	f	X
ejpam-6159	139	42	(	(	PUNCT
ejpam-6159	139	43	a1	a1	NOUN
ejpam-6159	139	44	+	+	CCONJ
ejpam-6159	139	45	ς∗	ς∗	PROPN
ejpam-6159	139	46	(	(	PUNCT
ejpam-6159	139	47	b1	b1	NOUN
ejpam-6159	139	48	,	,	PUNCT
ejpam-6159	139	49	a1	a1	NOUN
ejpam-6159	139	50	)	)	PUNCT
ejpam-6159	139	51	)	)	PUNCT
ejpam-6159	140	1	+	+	CCONJ
ejpam-6159	140	2	jϱ,k	jϱ,k	X
ejpam-6159	140	3	(	(	PUNCT
ejpam-6159	140	4	a1+ς∗(b1,a1	a1+ς∗(b1,a1	PROPN
ejpam-6159	140	5	)	)	PUNCT
ejpam-6159	140	6	)	)	PUNCT
ejpam-6159	141	1	−	−	PROPN
ejpam-6159	141	2	f	f	X
ejpam-6159	141	3	(	(	PUNCT
ejpam-6159	141	4	a1	a1	PROPN
ejpam-6159	141	5	)	)	PUNCT
ejpam-6159	141	6	}	}	PUNCT
ejpam-6159	141	7	≤	≤	NOUN
ejpam-6159	142	1	[	[	X
ejpam-6159	142	2	f	f	X
ejpam-6159	142	3	(	(	PUNCT
ejpam-6159	142	4	a1	a1	PROPN
ejpam-6159	142	5	)	)	PUNCT
ejpam-6159	143	1	+	+	NUM
ejpam-6159	143	2	f	f	X
ejpam-6159	143	3	(	(	PUNCT
ejpam-6159	143	4	a1	a1	NOUN
ejpam-6159	143	5	+	+	CCONJ
ejpam-6159	143	6	ς∗	ς∗	PROPN
ejpam-6159	143	7	(	(	PUNCT
ejpam-6159	143	8	b1	b1	NOUN
ejpam-6159	143	9	,	,	PUNCT
ejpam-6159	143	10	a1	a1	NOUN
ejpam-6159	143	11	)	)	PUNCT
ejpam-6159	143	12	)	)	PUNCT
ejpam-6159	143	13	]	]	PUNCT
ejpam-6159	144	1	×	×	NOUN
ejpam-6159	144	2	∫	∫	PROPN
ejpam-6159	144	3	1	1	NUM
ejpam-6159	144	4	0	0	NUM
ejpam-6159	144	5	t	t	PROPN
ejpam-6159	144	6	ϱ	ϱ	PROPN
ejpam-6159	144	7	k	k	X
ejpam-6159	144	8	−1	−1	NOUN
ejpam-6159	144	9	{	{	PUNCT
ejpam-6159	144	10	∑n	∑n	PROPN
ejpam-6159	144	11	i=1	i=1	PROPN
ejpam-6159	144	12	ai	ai	VERB
ejpam-6159	144	13	(	(	PUNCT
ejpam-6159	144	14	1−	1−	NUM
ejpam-6159	144	15	st	st	NOUN
ejpam-6159	144	16	)	)	PUNCT
ejpam-6159	144	17	1	1	NUM
ejpam-6159	144	18	i∑n	i∑n	PROPN
ejpam-6159	144	19	i=1	i=1	PROPN
ejpam-6159	144	20	ai	ai	VERB
ejpam-6159	145	1	+	+	ADJ
ejpam-6159	145	2	∑n	∑n	PROPN
ejpam-6159	145	3	i=1	i=1	PROPN
ejpam-6159	145	4	ai	ai	VERB
ejpam-6159	145	5	(	(	PUNCT
ejpam-6159	145	6	1−	1−	NUM
ejpam-6159	145	7	s	s	X
ejpam-6159	145	8	(	(	PUNCT
ejpam-6159	145	9	1−	1−	NUM
ejpam-6159	145	10	t	t	NOUN
ejpam-6159	145	11	)	)	PUNCT
ejpam-6159	145	12	)	)	PUNCT
ejpam-6159	145	13	1	1	NUM
ejpam-6159	145	14	i∑n	i∑n	NOUN
ejpam-6159	145	15	i=1	i=1	PROPN
ejpam-6159	145	16	ai	ai	VERB
ejpam-6159	145	17	}	}	PUNCT
ejpam-6159	145	18	dt	dt	PROPN
ejpam-6159	145	19	..	..	PUNCT
ejpam-6159	145	20	(	(	PUNCT
ejpam-6159	145	21	14	14	NUM
ejpam-6159	145	22	)	)	PUNCT
ejpam-6159	145	23	proof	proof	NOUN
ejpam-6159	145	24	.	.	PUNCT
ejpam-6159	146	1	from	from	ADP
ejpam-6159	146	2	the	the	DET
ejpam-6159	146	3	definition	definition	NOUN
ejpam-6159	146	4	of	of	ADP
ejpam-6159	146	5	the	the	DET
ejpam-6159	146	6	gfpp−s	gfpp−s	PROPN
ejpam-6159	146	7	function	function	NOUN
ejpam-6159	146	8	f	f	PROPN
ejpam-6159	146	9	,	,	PUNCT
ejpam-6159	146	10	one	one	NOUN
ejpam-6159	146	11	obtains	obtain	VERB
ejpam-6159	146	12	f	f	PROPN
ejpam-6159	146	13	(	(	PUNCT
ejpam-6159	146	14	x+	x+	X
ejpam-6159	146	15	ς∗	ς∗	PROPN
ejpam-6159	146	16	(	(	PUNCT
ejpam-6159	146	17	y	y	PROPN
ejpam-6159	146	18	,	,	PUNCT
ejpam-6159	146	19	x	x	NOUN
ejpam-6159	146	20	)	)	PUNCT
ejpam-6159	146	21	2	2	NUM
ejpam-6159	146	22	)	)	PUNCT
ejpam-6159	146	23	≤	≤	NOUN
ejpam-6159	147	1	∑n	∑n	PROPN
ejpam-6159	148	1	i=1	i=1	PROPN
ejpam-6159	148	2	ai	ai	VERB
ejpam-6159	148	3	(	(	PUNCT
ejpam-6159	148	4	1−	1−	NUM
ejpam-6159	148	5	s	s	NOUN
ejpam-6159	148	6	2	2	NUM
ejpam-6159	148	7	)	)	PUNCT
ejpam-6159	148	8	1	1	NUM
ejpam-6159	148	9	i∑n	i∑n	PROPN
ejpam-6159	148	10	i=1	i=1	PROPN
ejpam-6159	149	1	ai	ai	VERB
ejpam-6159	149	2	f	f	PROPN
ejpam-6159	149	3	(	(	PUNCT
ejpam-6159	149	4	x	x	X
ejpam-6159	149	5	)	)	PUNCT
ejpam-6159	150	1	+	+	CCONJ
ejpam-6159	151	1	∑n	∑n	PROPN
ejpam-6159	151	2	i=1	i=1	PROPN
ejpam-6159	151	3	ai	ai	VERB
ejpam-6159	151	4	(	(	PUNCT
ejpam-6159	151	5	1−	1−	NUM
ejpam-6159	151	6	s	s	NOUN
ejpam-6159	151	7	2	2	NUM
ejpam-6159	151	8	)	)	PUNCT
ejpam-6159	151	9	1	1	NUM
ejpam-6159	151	10	i∑n	i∑n	PROPN
ejpam-6159	151	11	i=1	i=1	PROPN
ejpam-6159	151	12	ai	ai	VERB
ejpam-6159	151	13	f	f	PROPN
ejpam-6159	151	14	(	(	PUNCT
ejpam-6159	151	15	y	y	PROPN
ejpam-6159	151	16	)	)	PUNCT
ejpam-6159	151	17	f	f	NOUN
ejpam-6159	151	18	(	(	PUNCT
ejpam-6159	151	19	x+	x+	X
ejpam-6159	151	20	ς∗	ς∗	PROPN
ejpam-6159	151	21	(	(	PUNCT
ejpam-6159	151	22	y	y	PROPN
ejpam-6159	151	23	,	,	PUNCT
ejpam-6159	151	24	x	x	NOUN
ejpam-6159	151	25	)	)	PUNCT
ejpam-6159	151	26	2	2	NUM
ejpam-6159	151	27	)	)	PUNCT
ejpam-6159	151	28	≤	≤	NOUN
ejpam-6159	152	1	∑n	∑n	PROPN
ejpam-6159	153	1	i=1	i=1	PROPN
ejpam-6159	153	2	ai	ai	VERB
ejpam-6159	153	3	(	(	PUNCT
ejpam-6159	153	4	1−	1−	NUM
ejpam-6159	153	5	s	s	NOUN
ejpam-6159	153	6	2	2	NUM
ejpam-6159	153	7	)	)	PUNCT
ejpam-6159	153	8	1	1	NUM
ejpam-6159	153	9	i∑n	i∑n	NOUN
ejpam-6159	153	10	i=1	i=1	PRON
ejpam-6159	153	11	ai	ai	VERB
ejpam-6159	154	1	[	[	X
ejpam-6159	154	2	f	f	X
ejpam-6159	154	3	(	(	PUNCT
ejpam-6159	154	4	x	x	X
ejpam-6159	154	5	)	)	PUNCT
ejpam-6159	154	6	+	+	NUM
ejpam-6159	154	7	f	f	X
ejpam-6159	154	8	(	(	PUNCT
ejpam-6159	154	9	y	y	PROPN
ejpam-6159	154	10	)	)	PUNCT
ejpam-6159	154	11	]	]	PUNCT
ejpam-6159	154	12	.	.	PUNCT
ejpam-6159	155	1	(	(	PUNCT
ejpam-6159	155	2	15	15	NUM
ejpam-6159	155	3	)	)	PUNCT
ejpam-6159	155	4	with	with	ADP
ejpam-6159	155	5	substituting	substitute	VERB
ejpam-6159	155	6	the	the	DET
ejpam-6159	155	7	x	x	NOUN
ejpam-6159	155	8	=	=	SYM
ejpam-6159	155	9	a1	a1	NOUN
ejpam-6159	155	10	+	+	CCONJ
ejpam-6159	155	11	(	(	PUNCT
ejpam-6159	155	12	1−	1−	NUM
ejpam-6159	155	13	t	t	NOUN
ejpam-6159	155	14	)	)	PUNCT
ejpam-6159	155	15	ς∗	ς∗	PROPN
ejpam-6159	155	16	(	(	PUNCT
ejpam-6159	155	17	b1	b1	NOUN
ejpam-6159	155	18	,	,	PUNCT
ejpam-6159	155	19	a1	a1	NOUN
ejpam-6159	155	20	)	)	PUNCT
ejpam-6159	155	21	and	and	CCONJ
ejpam-6159	155	22	y	y	NOUN
ejpam-6159	155	23	=	=	NOUN
ejpam-6159	155	24	a1	a1	PROPN
ejpam-6159	155	25	+	+	CCONJ
ejpam-6159	155	26	tς∗	tς∗	X
ejpam-6159	155	27	(	(	PUNCT
ejpam-6159	155	28	b1	b1	NOUN
ejpam-6159	155	29	,	,	PUNCT
ejpam-6159	155	30	a1	a1	NOUN
ejpam-6159	155	31	)	)	PUNCT
ejpam-6159	155	32	in	in	ADP
ejpam-6159	155	33	(	(	PUNCT
ejpam-6159	155	34	15	15	NUM
ejpam-6159	155	35	)	)	PUNCT
ejpam-6159	155	36	,	,	PUNCT
ejpam-6159	155	37	we	we	PRON
ejpam-6159	155	38	get	get	VERB
ejpam-6159	155	39	f	f	NOUN
ejpam-6159	155	40	(	(	PUNCT
ejpam-6159	155	41	a1	a1	NOUN
ejpam-6159	155	42	+	+	CCONJ
ejpam-6159	155	43	(	(	PUNCT
ejpam-6159	155	44	1−	1−	NUM
ejpam-6159	155	45	t	t	NOUN
ejpam-6159	155	46	)	)	PUNCT
ejpam-6159	155	47	ς∗	ς∗	PROPN
ejpam-6159	155	48	(	(	PUNCT
ejpam-6159	155	49	b1	b1	NOUN
ejpam-6159	155	50	,	,	PUNCT
ejpam-6159	155	51	a1	a1	NOUN
ejpam-6159	155	52	)	)	PUNCT
ejpam-6159	156	1	+	+	NUM
ejpam-6159	156	2	ς∗	ς∗	NOUN
ejpam-6159	156	3	(	(	PUNCT
ejpam-6159	156	4	a1	a1	NOUN
ejpam-6159	156	5	+	+	CCONJ
ejpam-6159	156	6	tς∗	tς∗	NOUN
ejpam-6159	156	7	(	(	PUNCT
ejpam-6159	156	8	b1	b1	NOUN
ejpam-6159	156	9	,	,	PUNCT
ejpam-6159	156	10	a1	a1	NOUN
ejpam-6159	156	11	)	)	PUNCT
ejpam-6159	156	12	,	,	PUNCT
ejpam-6159	156	13	a1	a1	NOUN
ejpam-6159	156	14	+	+	CCONJ
ejpam-6159	156	15	(	(	PUNCT
ejpam-6159	156	16	1−	1−	NUM
ejpam-6159	156	17	t	t	NOUN
ejpam-6159	156	18	)	)	PUNCT
ejpam-6159	156	19	ς∗	ς∗	PROPN
ejpam-6159	156	20	(	(	PUNCT
ejpam-6159	156	21	b1	b1	NOUN
ejpam-6159	156	22	,	,	PUNCT
ejpam-6159	156	23	a1	a1	NOUN
ejpam-6159	156	24	)	)	PUNCT
ejpam-6159	156	25	)	)	PUNCT
ejpam-6159	156	26	2	2	NUM
ejpam-6159	156	27	)	)	PUNCT
ejpam-6159	156	28	≤	≤	NOUN
ejpam-6159	157	1	∑n	∑n	PROPN
ejpam-6159	158	1	i=1	i=1	PROPN
ejpam-6159	158	2	ai	ai	VERB
ejpam-6159	158	3	(	(	PUNCT
ejpam-6159	158	4	1−	1−	NUM
ejpam-6159	158	5	s	s	NOUN
ejpam-6159	158	6	2	2	NUM
ejpam-6159	158	7	)	)	PUNCT
ejpam-6159	158	8	1	1	NUM
ejpam-6159	158	9	i∑n	i∑n	NOUN
ejpam-6159	158	10	i=1	i=1	PRON
ejpam-6159	158	11	ai	ai	VERB
ejpam-6159	159	1	[	[	X
ejpam-6159	159	2	f	f	X
ejpam-6159	159	3	(	(	PUNCT
ejpam-6159	159	4	a1	a1	NOUN
ejpam-6159	159	5	+	+	CCONJ
ejpam-6159	159	6	(	(	PUNCT
ejpam-6159	159	7	1−	1−	NUM
ejpam-6159	159	8	t	t	NOUN
ejpam-6159	159	9	)	)	PUNCT
ejpam-6159	159	10	ς∗	ς∗	PROPN
ejpam-6159	159	11	(	(	PUNCT
ejpam-6159	159	12	b1	b1	NOUN
ejpam-6159	159	13	,	,	PUNCT
ejpam-6159	159	14	a1	a1	NOUN
ejpam-6159	159	15	)	)	PUNCT
ejpam-6159	159	16	)	)	PUNCT
ejpam-6159	160	1	+	+	CCONJ
ejpam-6159	160	2	f	f	X
ejpam-6159	160	3	(	(	PUNCT
ejpam-6159	160	4	a1	a1	NOUN
ejpam-6159	160	5	+	+	CCONJ
ejpam-6159	160	6	tς∗	tς∗	NOUN
ejpam-6159	160	7	(	(	PUNCT
ejpam-6159	160	8	b1	b1	NOUN
ejpam-6159	160	9	,	,	PUNCT
ejpam-6159	160	10	a1	a1	NOUN
ejpam-6159	160	11	)	)	PUNCT
ejpam-6159	160	12	)	)	PUNCT
ejpam-6159	160	13	]	]	PUNCT
ejpam-6159	160	14	.	.	PUNCT
ejpam-6159	161	1	(	(	PUNCT
ejpam-6159	161	2	16	16	NUM
ejpam-6159	161	3	)	)	PUNCT
ejpam-6159	161	4	by	by	ADP
ejpam-6159	161	5	taking	take	VERB
ejpam-6159	161	6	product	product	NOUN
ejpam-6159	161	7	with	with	ADP
ejpam-6159	161	8	the	the	DET
ejpam-6159	161	9	term	term	NOUN
ejpam-6159	161	10	t	t	PROPN
ejpam-6159	161	11	ϱ	ϱ	VERB
ejpam-6159	161	12	k	k	X
ejpam-6159	161	13	−1	−1	NOUN
ejpam-6159	161	14	and	and	CCONJ
ejpam-6159	161	15	antiderivative	antiderivative	ADJ
ejpam-6159	161	16	with	with	ADP
ejpam-6159	161	17	respect	respect	NOUN
ejpam-6159	161	18	to	to	ADP
ejpam-6159	161	19	t	t	PROPN
ejpam-6159	161	20	∈	∈	PROPN
ejpam-6159	162	1	[	[	X
ejpam-6159	162	2	0	0	NUM
ejpam-6159	162	3	,	,	PUNCT
ejpam-6159	162	4	1	1	NUM
ejpam-6159	162	5	]	]	PUNCT
ejpam-6159	162	6	,	,	PUNCT
ejpam-6159	162	7	one	one	PRON
ejpam-6159	162	8	gets	get	VERB
ejpam-6159	162	9	1	1	NUM
ejpam-6159	162	10	ϱ	ϱ	ADP
ejpam-6159	162	11	k	k	PROPN
ejpam-6159	162	12	f	f	PROPN
ejpam-6159	162	13	(	(	PUNCT
ejpam-6159	162	14	2a1	2a1	NUM
ejpam-6159	162	15	+	+	CCONJ
ejpam-6159	162	16	ς∗	ς∗	PROPN
ejpam-6159	162	17	(	(	PUNCT
ejpam-6159	162	18	b1	b1	NOUN
ejpam-6159	162	19	,	,	PUNCT
ejpam-6159	162	20	a1	a1	NOUN
ejpam-6159	162	21	)	)	PUNCT
ejpam-6159	162	22	2	2	NUM
ejpam-6159	162	23	)	)	PUNCT
ejpam-6159	162	24	≤	≤	NOUN
ejpam-6159	163	1	∑n	∑n	PROPN
ejpam-6159	164	1	i=1	i=1	PROPN
ejpam-6159	164	2	ai	ai	VERB
ejpam-6159	164	3	(	(	PUNCT
ejpam-6159	164	4	1−	1−	NUM
ejpam-6159	164	5	s	s	NOUN
ejpam-6159	164	6	2	2	NUM
ejpam-6159	164	7	)	)	PUNCT
ejpam-6159	164	8	1	1	NUM
ejpam-6159	164	9	i∑n	i∑n	PROPN
ejpam-6159	164	10	i=1	i=1	PROPN
ejpam-6159	164	11	ai	ai	VERB
ejpam-6159	164	12	j.	j.	PROPN
ejpam-6159	164	13	nasir	nasir	PROPN
ejpam-6159	164	14	et	et	PROPN
ejpam-6159	164	15	al	al	PROPN
ejpam-6159	164	16	.	.	PUNCT
ejpam-6159	164	17	/	/	SYM
ejpam-6159	164	18	eur	eur	PROPN
ejpam-6159	164	19	.	.	PUNCT
ejpam-6159	165	1	j.	j.	PROPN
ejpam-6159	165	2	pure	pure	PROPN
ejpam-6159	165	3	appl	appl	PROPN
ejpam-6159	165	4	.	.	PROPN
ejpam-6159	165	5	math	math	PROPN
ejpam-6159	165	6	,	,	PUNCT
ejpam-6159	165	7	18	18	NUM
ejpam-6159	165	8	(	(	PUNCT
ejpam-6159	165	9	3	3	NUM
ejpam-6159	165	10	)	)	PUNCT
ejpam-6159	165	11	(	(	PUNCT
ejpam-6159	165	12	2025	2025	NUM
ejpam-6159	165	13	)	)	PUNCT
ejpam-6159	165	14	,	,	PUNCT
ejpam-6159	165	15	6159	6159	NUM
ejpam-6159	165	16	7	7	NUM
ejpam-6159	165	17	of	of	ADP
ejpam-6159	165	18	26	26	NUM
ejpam-6159	165	19	×	×	NOUN
ejpam-6159	165	20	[	[	PUNCT
ejpam-6159	165	21	∫	∫	PROPN
ejpam-6159	165	22	1	1	NUM
ejpam-6159	165	23	0	0	NUM
ejpam-6159	165	24	t	t	PROPN
ejpam-6159	165	25	ϱ	ϱ	PROPN
ejpam-6159	165	26	k	k	PROPN
ejpam-6159	165	27	−1f	−1f	PROPN
ejpam-6159	165	28	(	(	PUNCT
ejpam-6159	165	29	a1	a1	NOUN
ejpam-6159	165	30	+	+	CCONJ
ejpam-6159	165	31	(	(	PUNCT
ejpam-6159	165	32	1−	1−	NUM
ejpam-6159	165	33	t	t	NOUN
ejpam-6159	165	34	)	)	PUNCT
ejpam-6159	165	35	ς∗	ς∗	PROPN
ejpam-6159	165	36	(	(	PUNCT
ejpam-6159	165	37	b1	b1	NOUN
ejpam-6159	165	38	,	,	PUNCT
ejpam-6159	165	39	a1	a1	NOUN
ejpam-6159	165	40	)	)	PUNCT
ejpam-6159	165	41	)	)	PUNCT
ejpam-6159	166	1	dt+	dt+	NOUN
ejpam-6159	166	2	∫	∫	NOUN
ejpam-6159	166	3	1	1	NUM
ejpam-6159	166	4	0	0	NUM
ejpam-6159	166	5	t	t	PROPN
ejpam-6159	166	6	ϱ	ϱ	PROPN
ejpam-6159	166	7	k	k	PROPN
ejpam-6159	166	8	−1f	−1f	PROPN
ejpam-6159	166	9	(	(	PUNCT
ejpam-6159	166	10	a1	a1	NOUN
ejpam-6159	166	11	+	+	CCONJ
ejpam-6159	166	12	tς∗	tς∗	X
ejpam-6159	166	13	(	(	PUNCT
ejpam-6159	166	14	b1	b1	NOUN
ejpam-6159	166	15	,	,	PUNCT
ejpam-6159	166	16	a1	a1	NOUN
ejpam-6159	166	17	)	)	PUNCT
ejpam-6159	166	18	)	)	PUNCT
ejpam-6159	167	1	dt	dt	PUNCT
ejpam-6159	167	2	]	]	PUNCT
ejpam-6159	168	1	1	1	NUM
ejpam-6159	168	2	ϱ	ϱ	VERB
ejpam-6159	168	3	k	k	PROPN
ejpam-6159	168	4	f	f	PROPN
ejpam-6159	168	5	(	(	PUNCT
ejpam-6159	168	6	2a1	2a1	NUM
ejpam-6159	168	7	+	+	CCONJ
ejpam-6159	168	8	ς∗	ς∗	PROPN
ejpam-6159	168	9	(	(	PUNCT
ejpam-6159	168	10	b1	b1	NOUN
ejpam-6159	168	11	,	,	PUNCT
ejpam-6159	168	12	a1	a1	NOUN
ejpam-6159	168	13	)	)	PUNCT
ejpam-6159	168	14	2	2	NUM
ejpam-6159	168	15	)	)	PUNCT
ejpam-6159	168	16	≤	≤	NOUN
ejpam-6159	169	1	∑n	∑n	PROPN
ejpam-6159	170	1	i=1	i=1	PROPN
ejpam-6159	170	2	ai	ai	VERB
ejpam-6159	170	3	(	(	PUNCT
ejpam-6159	170	4	1−	1−	NUM
ejpam-6159	170	5	s	s	NOUN
ejpam-6159	170	6	2	2	NUM
ejpam-6159	170	7	)	)	PUNCT
ejpam-6159	170	8	1	1	NUM
ejpam-6159	170	9	i∑n	i∑n	PROPN
ejpam-6159	170	10	i=1	i=1	PROPN
ejpam-6159	170	11	ai	ai	VERB
ejpam-6159	170	12	×	×	PROPN
ejpam-6159	170	13	[	[	PUNCT
ejpam-6159	170	14	kγk	kγk	X
ejpam-6159	170	15	(	(	PUNCT
ejpam-6159	170	16	ϱ	ϱ	NOUN
ejpam-6159	170	17	)	)	PUNCT
ejpam-6159	170	18	ς	ς	PROPN
ejpam-6159	170	19	ϱ	ϱ	PROPN
ejpam-6159	170	20	k	k	PROPN
ejpam-6159	170	21	∗	∗	X
ejpam-6159	170	22	(	(	PUNCT
ejpam-6159	170	23	b1	b1	NOUN
ejpam-6159	170	24	,	,	PUNCT
ejpam-6159	170	25	a1	a1	NOUN
ejpam-6159	170	26	)	)	PUNCT
ejpam-6159	170	27	{	{	PUNCT
ejpam-6159	170	28	jϱ,k	jϱ,k	X
ejpam-6159	170	29	a1	a1	PROPN
ejpam-6159	170	30	+	+	X
ejpam-6159	170	31	f	f	X
ejpam-6159	170	32	(	(	PUNCT
ejpam-6159	170	33	a1	a1	NOUN
ejpam-6159	170	34	+	+	CCONJ
ejpam-6159	170	35	ς∗	ς∗	PROPN
ejpam-6159	170	36	(	(	PUNCT
ejpam-6159	170	37	b1	b1	NOUN
ejpam-6159	170	38	,	,	PUNCT
ejpam-6159	170	39	a1	a1	NOUN
ejpam-6159	170	40	)	)	PUNCT
ejpam-6159	170	41	)	)	PUNCT
ejpam-6159	171	1	+	+	CCONJ
ejpam-6159	171	2	jϱ,k	jϱ,k	X
ejpam-6159	171	3	(	(	PUNCT
ejpam-6159	171	4	a1+ς∗(b1,a1	a1+ς∗(b1,a1	PROPN
ejpam-6159	171	5	)	)	PUNCT
ejpam-6159	171	6	)	)	PUNCT
ejpam-6159	172	1	−	−	PROPN
ejpam-6159	172	2	f	f	X
ejpam-6159	172	3	(	(	PUNCT
ejpam-6159	172	4	a1	a1	PROPN
ejpam-6159	172	5	)	)	PUNCT
ejpam-6159	172	6	}	}	PUNCT
ejpam-6159	172	7	]	]	PUNCT
ejpam-6159	172	8	,	,	PUNCT
ejpam-6159	172	9	(	(	PUNCT
ejpam-6159	172	10	17	17	NUM
ejpam-6159	172	11	)	)	PUNCT
ejpam-6159	172	12	which	which	PRON
ejpam-6159	172	13	completes	complete	VERB
ejpam-6159	172	14	the	the	DET
ejpam-6159	172	15	leftihand	leftihand	ADJ
ejpam-6159	172	16	side	side	NOUN
ejpam-6159	172	17	of	of	ADP
ejpam-6159	172	18	(	(	PUNCT
ejpam-6159	172	19	14	14	NUM
ejpam-6159	172	20	)	)	PUNCT
ejpam-6159	172	21	.	.	PUNCT
ejpam-6159	173	1	for	for	ADP
ejpam-6159	173	2	theiproof	theiproof	NOUN
ejpam-6159	173	3	of	of	ADP
ejpam-6159	173	4	the	the	DET
ejpam-6159	173	5	secondiinequality	secondiinequality	NOUN
ejpam-6159	173	6	in	in	ADP
ejpam-6159	173	7	(	(	PUNCT
ejpam-6159	173	8	14	14	NUM
ejpam-6159	173	9	)	)	PUNCT
ejpam-6159	173	10	,	,	PUNCT
ejpam-6159	173	11	we	we	PRON
ejpam-6159	173	12	first	first	ADV
ejpam-6159	173	13	note	note	VERB
ejpam-6159	173	14	that	that	SCONJ
ejpam-6159	173	15	if	if	SCONJ
ejpam-6159	173	16	f	f	PROPN
ejpam-6159	173	17	is	be	AUX
ejpam-6159	173	18	n−polynomial	n−polynomial	DET
ejpam-6159	173	19	s−like	s−like	ADJ
ejpam-6159	173	20	preinvexity	preinvexity	NOUN
ejpam-6159	173	21	on	on	ADP
ejpam-6159	173	22	[	[	X
ejpam-6159	173	23	a1	a1	NOUN
ejpam-6159	173	24	,	,	PUNCT
ejpam-6159	173	25	a1	a1	NOUN
ejpam-6159	173	26	+	+	CCONJ
ejpam-6159	173	27	ς∗	ς∗	PROPN
ejpam-6159	173	28	(	(	PUNCT
ejpam-6159	173	29	b1	b1	NOUN
ejpam-6159	173	30	,	,	PUNCT
ejpam-6159	173	31	a1	a1	NOUN
ejpam-6159	173	32	)	)	PUNCT
ejpam-6159	173	33	]	]	PUNCT
ejpam-6159	173	34	and	and	CCONJ
ejpam-6159	173	35	the	the	DET
ejpam-6159	173	36	mapping	mapping	NOUN
ejpam-6159	173	37	ς∗	ς∗	NOUN
ejpam-6159	173	38	satisfies	satisfy	VERB
ejpam-6159	173	39	the	the	DET
ejpam-6159	173	40	property	property	NOUN
ejpam-6159	173	41	-	-	PUNCT
ejpam-6159	173	42	c	c	NOUN
ejpam-6159	173	43	,	,	PUNCT
ejpam-6159	173	44	then	then	ADV
ejpam-6159	173	45	for	for	ADP
ejpam-6159	173	46	ievery	ievery	NOUN
ejpam-6159	173	47	t	t	X
ejpam-6159	173	48	∈	∈	PROPN
ejpam-6159	174	1	[	[	X
ejpam-6159	174	2	0	0	NUM
ejpam-6159	174	3	,	,	PUNCT
ejpam-6159	174	4	1	1	NUM
ejpam-6159	174	5	]	]	PUNCT
ejpam-6159	174	6	,	,	PUNCT
ejpam-6159	174	7	it	it	PRON
ejpam-6159	174	8	yields	yield	VERB
ejpam-6159	174	9	that	that	SCONJ
ejpam-6159	174	10	f	f	PROPN
ejpam-6159	174	11	(	(	PUNCT
ejpam-6159	174	12	a1	a1	NOUN
ejpam-6159	174	13	+	+	CCONJ
ejpam-6159	174	14	(	(	PUNCT
ejpam-6159	174	15	1−	1−	NUM
ejpam-6159	174	16	t	t	NOUN
ejpam-6159	174	17	)	)	PUNCT
ejpam-6159	174	18	ς∗	ς∗	PROPN
ejpam-6159	174	19	(	(	PUNCT
ejpam-6159	174	20	b1	b1	NOUN
ejpam-6159	174	21	,	,	PUNCT
ejpam-6159	174	22	a1	a1	NOUN
ejpam-6159	174	23	)	)	PUNCT
ejpam-6159	174	24	)	)	PUNCT
ejpam-6159	174	25	≤	≤	NOUN
ejpam-6159	175	1	∑n	∑n	PROPN
ejpam-6159	176	1	i=1	i=1	PROPN
ejpam-6159	176	2	ai	ai	VERB
ejpam-6159	176	3	(	(	PUNCT
ejpam-6159	176	4	1−	1−	NUM
ejpam-6159	176	5	s	s	X
ejpam-6159	176	6	(	(	PUNCT
ejpam-6159	176	7	1−	1−	NUM
ejpam-6159	176	8	t	t	NOUN
ejpam-6159	176	9	)	)	PUNCT
ejpam-6159	176	10	)	)	PUNCT
ejpam-6159	177	1	1	1	NUM
ejpam-6159	177	2	i∑n	i∑n	PROPN
ejpam-6159	177	3	i=1	i=1	PROPN
ejpam-6159	177	4	ai	ai	VERB
ejpam-6159	177	5	f	f	PROPN
ejpam-6159	177	6	(	(	PUNCT
ejpam-6159	177	7	a1	a1	NOUN
ejpam-6159	177	8	+	+	CCONJ
ejpam-6159	177	9	ς∗	ς∗	PROPN
ejpam-6159	177	10	(	(	PUNCT
ejpam-6159	177	11	b1	b1	NOUN
ejpam-6159	177	12	,	,	PUNCT
ejpam-6159	177	13	a1	a1	NOUN
ejpam-6159	177	14	)	)	PUNCT
ejpam-6159	177	15	)	)	PUNCT
ejpam-6159	178	1	+	+	CCONJ
ejpam-6159	179	1	∑n	∑n	NOUN
ejpam-6159	179	2	i=1	i=1	PROPN
ejpam-6159	179	3	ai	ai	VERB
ejpam-6159	179	4	(	(	PUNCT
ejpam-6159	179	5	1−	1−	NUM
ejpam-6159	179	6	st	st	NOUN
ejpam-6159	179	7	)	)	PUNCT
ejpam-6159	179	8	1	1	NUM
ejpam-6159	179	9	i∑n	i∑n	PROPN
ejpam-6159	179	10	i=1	i=1	PROPN
ejpam-6159	179	11	ai	ai	VERB
ejpam-6159	179	12	f	f	PROPN
ejpam-6159	179	13	(	(	PUNCT
ejpam-6159	179	14	a1	a1	PROPN
ejpam-6159	179	15	)	)	PUNCT
ejpam-6159	179	16	f	f	NOUN
ejpam-6159	179	17	(	(	PUNCT
ejpam-6159	179	18	a1	a1	NOUN
ejpam-6159	179	19	+	+	CCONJ
ejpam-6159	179	20	tς∗	tς∗	NOUN
ejpam-6159	179	21	(	(	PUNCT
ejpam-6159	179	22	b1	b1	NOUN
ejpam-6159	179	23	,	,	PUNCT
ejpam-6159	179	24	a1	a1	NOUN
ejpam-6159	179	25	)	)	PUNCT
ejpam-6159	179	26	)	)	PUNCT
ejpam-6159	179	27	≤	≤	NOUN
ejpam-6159	180	1	∑n	∑n	PROPN
ejpam-6159	181	1	i=1	i=1	PROPN
ejpam-6159	181	2	ai	ai	PROPN
ejpam-6159	181	3	(	(	PUNCT
ejpam-6159	181	4	1−	1−	NUM
ejpam-6159	181	5	st	st	NOUN
ejpam-6159	181	6	)	)	PUNCT
ejpam-6159	181	7	1	1	NUM
ejpam-6159	181	8	i∑n	i∑n	PROPN
ejpam-6159	181	9	i=1	i=1	PROPN
ejpam-6159	181	10	ai	ai	VERB
ejpam-6159	181	11	f	f	PROPN
ejpam-6159	181	12	(	(	PUNCT
ejpam-6159	181	13	a1	a1	NOUN
ejpam-6159	181	14	+	+	CCONJ
ejpam-6159	181	15	ς∗	ς∗	PROPN
ejpam-6159	181	16	(	(	PUNCT
ejpam-6159	181	17	b1	b1	NOUN
ejpam-6159	181	18	,	,	PUNCT
ejpam-6159	181	19	a1	a1	NOUN
ejpam-6159	181	20	)	)	PUNCT
ejpam-6159	181	21	)	)	PUNCT
ejpam-6159	182	1	+	+	CCONJ
ejpam-6159	183	1	∑n	∑n	NOUN
ejpam-6159	183	2	i=1	i=1	PROPN
ejpam-6159	183	3	ai	ai	VERB
ejpam-6159	183	4	(	(	PUNCT
ejpam-6159	183	5	1−	1−	NUM
ejpam-6159	183	6	s	s	X
ejpam-6159	183	7	(	(	PUNCT
ejpam-6159	183	8	1−	1−	NUM
ejpam-6159	183	9	t	t	NOUN
ejpam-6159	183	10	)	)	PUNCT
ejpam-6159	183	11	)	)	PUNCT
ejpam-6159	184	1	1	1	NUM
ejpam-6159	184	2	i∑n	i∑n	PROPN
ejpam-6159	184	3	i=1	i=1	PROPN
ejpam-6159	184	4	ai	ai	VERB
ejpam-6159	184	5	f	f	PROPN
ejpam-6159	184	6	(	(	PUNCT
ejpam-6159	184	7	a1	a1	PROPN
ejpam-6159	184	8	)	)	PUNCT
ejpam-6159	184	9	.	.	PUNCT
ejpam-6159	185	1	(	(	PUNCT
ejpam-6159	185	2	18	18	NUM
ejpam-6159	185	3	)	)	PUNCT
ejpam-6159	185	4	by	by	ADP
ejpam-6159	185	5	adding	add	VERB
ejpam-6159	185	6	above	above	ADP
ejpam-6159	185	7	two	two	NUM
ejpam-6159	185	8	inequalities	inequality	NOUN
ejpam-6159	185	9	,	,	PUNCT
ejpam-6159	185	10	one	one	PRON
ejpam-6159	185	11	gets	get	VERB
ejpam-6159	185	12	f	f	NOUN
ejpam-6159	185	13	(	(	PUNCT
ejpam-6159	185	14	a1	a1	NOUN
ejpam-6159	185	15	+	+	CCONJ
ejpam-6159	185	16	(	(	PUNCT
ejpam-6159	185	17	1−	1−	NUM
ejpam-6159	185	18	t	t	NOUN
ejpam-6159	185	19	)	)	PUNCT
ejpam-6159	185	20	ς∗	ς∗	PROPN
ejpam-6159	185	21	(	(	PUNCT
ejpam-6159	185	22	b1	b1	NOUN
ejpam-6159	185	23	,	,	PUNCT
ejpam-6159	185	24	a1	a1	NOUN
ejpam-6159	185	25	)	)	PUNCT
ejpam-6159	185	26	)	)	PUNCT
ejpam-6159	186	1	+	+	CCONJ
ejpam-6159	187	1	f	f	X
ejpam-6159	187	2	(	(	PUNCT
ejpam-6159	187	3	a1	a1	NOUN
ejpam-6159	187	4	+	+	CCONJ
ejpam-6159	187	5	tς∗	tς∗	NOUN
ejpam-6159	187	6	(	(	PUNCT
ejpam-6159	187	7	b1	b1	NOUN
ejpam-6159	187	8	,	,	PUNCT
ejpam-6159	187	9	a1	a1	NOUN
ejpam-6159	187	10	)	)	PUNCT
ejpam-6159	187	11	)	)	PUNCT
ejpam-6159	187	12	≤	≤	NOUN
ejpam-6159	187	13	{	{	PUNCT
ejpam-6159	187	14	∑n	∑n	PROPN
ejpam-6159	187	15	i=1	i=1	PROPN
ejpam-6159	187	16	ai	ai	VERB
ejpam-6159	187	17	(	(	PUNCT
ejpam-6159	187	18	1−	1−	NUM
ejpam-6159	187	19	s	s	X
ejpam-6159	187	20	(	(	PUNCT
ejpam-6159	187	21	1−	1−	NUM
ejpam-6159	187	22	t	t	NOUN
ejpam-6159	187	23	)	)	PUNCT
ejpam-6159	187	24	)	)	PUNCT
ejpam-6159	187	25	1	1	NUM
ejpam-6159	187	26	i∑n	i∑n	PROPN
ejpam-6159	187	27	i=1	i=1	PROPN
ejpam-6159	187	28	ai	ai	VERB
ejpam-6159	187	29	+	+	ADJ
ejpam-6159	188	1	∑n	∑n	PROPN
ejpam-6159	188	2	i=1	i=1	PROPN
ejpam-6159	188	3	ai	ai	VERB
ejpam-6159	188	4	(	(	PUNCT
ejpam-6159	188	5	1−	1−	NUM
ejpam-6159	188	6	st	st	NOUN
ejpam-6159	188	7	)	)	PUNCT
ejpam-6159	188	8	1	1	NUM
ejpam-6159	188	9	i∑n	i∑n	PROPN
ejpam-6159	188	10	i=1	i=1	PROPN
ejpam-6159	188	11	ai	ai	VERB
ejpam-6159	188	12	}	}	PUNCT
ejpam-6159	189	1	[	[	X
ejpam-6159	189	2	f	f	X
ejpam-6159	189	3	(	(	PUNCT
ejpam-6159	189	4	a1	a1	PROPN
ejpam-6159	189	5	)	)	PUNCT
ejpam-6159	190	1	+	+	NUM
ejpam-6159	190	2	f	f	X
ejpam-6159	190	3	(	(	PUNCT
ejpam-6159	190	4	a1	a1	NOUN
ejpam-6159	190	5	+	+	CCONJ
ejpam-6159	190	6	ς∗	ς∗	PROPN
ejpam-6159	190	7	(	(	PUNCT
ejpam-6159	190	8	b1	b1	NOUN
ejpam-6159	190	9	,	,	PUNCT
ejpam-6159	190	10	a1	a1	NOUN
ejpam-6159	190	11	)	)	PUNCT
ejpam-6159	190	12	)	)	PUNCT
ejpam-6159	190	13	]	]	PUNCT
ejpam-6159	190	14	.	.	PUNCT
ejpam-6159	191	1	(	(	PUNCT
ejpam-6159	191	2	19	19	NUM
ejpam-6159	191	3	)	)	PUNCT
ejpam-6159	191	4	by	by	ADP
ejpam-6159	191	5	taking	take	VERB
ejpam-6159	191	6	product	product	NOUN
ejpam-6159	191	7	with	with	ADP
ejpam-6159	191	8	the	the	DET
ejpam-6159	191	9	term	term	NOUN
ejpam-6159	191	10	t	t	PROPN
ejpam-6159	191	11	ϱ	ϱ	VERB
ejpam-6159	191	12	k	k	X
ejpam-6159	191	13	−1	−1	NOUN
ejpam-6159	191	14	and	and	CCONJ
ejpam-6159	191	15	antiderivative	antiderivative	ADJ
ejpam-6159	191	16	with	with	ADP
ejpam-6159	191	17	respect	respect	NOUN
ejpam-6159	191	18	to	to	ADP
ejpam-6159	191	19	t	t	PROPN
ejpam-6159	191	20	∈	∈	PROPN
ejpam-6159	192	1	[	[	X
ejpam-6159	192	2	0	0	NUM
ejpam-6159	192	3	,	,	PUNCT
ejpam-6159	192	4	1	1	NUM
ejpam-6159	192	5	]	]	PUNCT
ejpam-6159	192	6	,	,	PUNCT
ejpam-6159	192	7	one	one	PRON
ejpam-6159	192	8	gets	get	VERB
ejpam-6159	192	9	f	f	NOUN
ejpam-6159	192	10	(	(	PUNCT
ejpam-6159	192	11	a1	a1	NOUN
ejpam-6159	192	12	+	+	CCONJ
ejpam-6159	192	13	(	(	PUNCT
ejpam-6159	192	14	1−	1−	NUM
ejpam-6159	192	15	t	t	NOUN
ejpam-6159	192	16	)	)	PUNCT
ejpam-6159	192	17	ς∗	ς∗	PROPN
ejpam-6159	192	18	(	(	PUNCT
ejpam-6159	192	19	b1	b1	NOUN
ejpam-6159	192	20	,	,	PUNCT
ejpam-6159	192	21	a1	a1	NOUN
ejpam-6159	192	22	)	)	PUNCT
ejpam-6159	192	23	)	)	PUNCT
ejpam-6159	193	1	+	+	CCONJ
ejpam-6159	194	1	f	f	X
ejpam-6159	194	2	(	(	PUNCT
ejpam-6159	194	3	a1	a1	NOUN
ejpam-6159	194	4	+	+	CCONJ
ejpam-6159	194	5	tς∗	tς∗	NOUN
ejpam-6159	194	6	(	(	PUNCT
ejpam-6159	194	7	b1	b1	NOUN
ejpam-6159	194	8	,	,	PUNCT
ejpam-6159	194	9	a1	a1	NOUN
ejpam-6159	194	10	)	)	PUNCT
ejpam-6159	194	11	)	)	PUNCT
ejpam-6159	194	12	≤	≤	NOUN
ejpam-6159	194	13	{	{	PUNCT
ejpam-6159	194	14	∑n	∑n	PROPN
ejpam-6159	194	15	i=1	i=1	PROPN
ejpam-6159	194	16	ai	ai	VERB
ejpam-6159	194	17	(	(	PUNCT
ejpam-6159	194	18	1−	1−	NUM
ejpam-6159	194	19	s	s	X
ejpam-6159	194	20	(	(	PUNCT
ejpam-6159	194	21	1−	1−	NUM
ejpam-6159	194	22	t	t	NOUN
ejpam-6159	194	23	)	)	PUNCT
ejpam-6159	194	24	)	)	PUNCT
ejpam-6159	194	25	1	1	NUM
ejpam-6159	194	26	i∑n	i∑n	PROPN
ejpam-6159	194	27	i=1	i=1	PROPN
ejpam-6159	194	28	ai	ai	VERB
ejpam-6159	194	29	+	+	ADJ
ejpam-6159	195	1	∑n	∑n	PROPN
ejpam-6159	195	2	i=1	i=1	PROPN
ejpam-6159	195	3	ai	ai	VERB
ejpam-6159	195	4	(	(	PUNCT
ejpam-6159	195	5	1−	1−	NUM
ejpam-6159	195	6	st	st	NOUN
ejpam-6159	195	7	)	)	PUNCT
ejpam-6159	195	8	1	1	NUM
ejpam-6159	195	9	i∑n	i∑n	PROPN
ejpam-6159	195	10	i=1	i=1	PROPN
ejpam-6159	195	11	ai	ai	VERB
ejpam-6159	195	12	}	}	PUNCT
ejpam-6159	196	1	[	[	X
ejpam-6159	196	2	f	f	X
ejpam-6159	196	3	(	(	PUNCT
ejpam-6159	196	4	a1	a1	PROPN
ejpam-6159	196	5	)	)	PUNCT
ejpam-6159	197	1	+	+	NUM
ejpam-6159	197	2	f	f	X
ejpam-6159	197	3	(	(	PUNCT
ejpam-6159	197	4	a1	a1	NOUN
ejpam-6159	197	5	+	+	CCONJ
ejpam-6159	197	6	ς∗	ς∗	PROPN
ejpam-6159	197	7	(	(	PUNCT
ejpam-6159	197	8	b1	b1	NOUN
ejpam-6159	197	9	,	,	PUNCT
ejpam-6159	197	10	a1	a1	NOUN
ejpam-6159	197	11	)	)	PUNCT
ejpam-6159	197	12	)	)	PUNCT
ejpam-6159	197	13	]	]	PUNCT
ejpam-6159	198	1	(	(	PUNCT
ejpam-6159	198	2	20	20	NUM
ejpam-6159	198	3	)	)	PUNCT
ejpam-6159	198	4	∫	∫	PROPN
ejpam-6159	198	5	1	1	NUM
ejpam-6159	198	6	0	0	NUM
ejpam-6159	198	7	t	t	PROPN
ejpam-6159	198	8	ϱ	ϱ	PROPN
ejpam-6159	198	9	k	k	PROPN
ejpam-6159	198	10	−1f	−1f	PROPN
ejpam-6159	198	11	(	(	PUNCT
ejpam-6159	198	12	a1	a1	NOUN
ejpam-6159	198	13	+	+	CCONJ
ejpam-6159	198	14	(	(	PUNCT
ejpam-6159	198	15	1−	1−	NUM
ejpam-6159	198	16	t	t	NOUN
ejpam-6159	198	17	)	)	PUNCT
ejpam-6159	198	18	ς∗	ς∗	PROPN
ejpam-6159	198	19	(	(	PUNCT
ejpam-6159	198	20	b1	b1	NOUN
ejpam-6159	198	21	,	,	PUNCT
ejpam-6159	198	22	a1	a1	NOUN
ejpam-6159	198	23	)	)	PUNCT
ejpam-6159	198	24	)	)	PUNCT
ejpam-6159	199	1	dt+	dt+	NOUN
ejpam-6159	199	2	∫	∫	NOUN
ejpam-6159	199	3	1	1	NUM
ejpam-6159	199	4	0	0	NUM
ejpam-6159	199	5	t	t	PROPN
ejpam-6159	199	6	ϱ	ϱ	PROPN
ejpam-6159	199	7	k	k	PROPN
ejpam-6159	199	8	−1	−1	NOUN
ejpam-6159	199	9	f	f	PROPN
ejpam-6159	199	10	(	(	PUNCT
ejpam-6159	199	11	a1	a1	NOUN
ejpam-6159	199	12	+	+	CCONJ
ejpam-6159	199	13	tς∗	tς∗	NOUN
ejpam-6159	199	14	(	(	PUNCT
ejpam-6159	199	15	b1	b1	NOUN
ejpam-6159	199	16	,	,	PUNCT
ejpam-6159	199	17	a1	a1	NOUN
ejpam-6159	199	18	)	)	PUNCT
ejpam-6159	199	19	)	)	PUNCT
ejpam-6159	199	20	dt	dt	ADP
ejpam-6159	199	21	≤	≤	NOUN
ejpam-6159	200	1	[	[	X
ejpam-6159	200	2	f	f	X
ejpam-6159	200	3	(	(	PUNCT
ejpam-6159	200	4	a1	a1	PROPN
ejpam-6159	200	5	)	)	PUNCT
ejpam-6159	201	1	+	+	NUM
ejpam-6159	201	2	f	f	X
ejpam-6159	201	3	(	(	PUNCT
ejpam-6159	201	4	a1	a1	NOUN
ejpam-6159	201	5	+	+	CCONJ
ejpam-6159	201	6	ς∗	ς∗	PROPN
ejpam-6159	201	7	(	(	PUNCT
ejpam-6159	201	8	b1	b1	NOUN
ejpam-6159	201	9	,	,	PUNCT
ejpam-6159	201	10	a1	a1	NOUN
ejpam-6159	201	11	)	)	PUNCT
ejpam-6159	201	12	)	)	PUNCT
ejpam-6159	201	13	]	]	PUNCT
ejpam-6159	202	1	∫	∫	PROPN
ejpam-6159	202	2	1	1	NUM
ejpam-6159	202	3	0	0	NUM
ejpam-6159	202	4	t	t	PROPN
ejpam-6159	202	5	ϱ	ϱ	PROPN
ejpam-6159	202	6	k	k	PROPN
ejpam-6159	202	7	−1	−1	NOUN
ejpam-6159	202	8	j.	j.	PROPN
ejpam-6159	202	9	nasir	nasir	PROPN
ejpam-6159	202	10	et	et	PROPN
ejpam-6159	202	11	al	al	PROPN
ejpam-6159	202	12	.	.	PUNCT
ejpam-6159	202	13	/	/	SYM
ejpam-6159	202	14	eur	eur	PROPN
ejpam-6159	202	15	.	.	PUNCT
ejpam-6159	203	1	j.	j.	PROPN
ejpam-6159	203	2	pure	pure	PROPN
ejpam-6159	203	3	appl	appl	PROPN
ejpam-6159	203	4	.	.	PROPN
ejpam-6159	203	5	math	math	PROPN
ejpam-6159	203	6	,	,	PUNCT
ejpam-6159	203	7	18	18	NUM
ejpam-6159	203	8	(	(	PUNCT
ejpam-6159	203	9	3	3	NUM
ejpam-6159	203	10	)	)	PUNCT
ejpam-6159	203	11	(	(	PUNCT
ejpam-6159	203	12	2025	2025	NUM
ejpam-6159	203	13	)	)	PUNCT
ejpam-6159	203	14	,	,	PUNCT
ejpam-6159	203	15	6159	6159	NUM
ejpam-6159	203	16	8	8	NUM
ejpam-6159	203	17	of	of	ADP
ejpam-6159	203	18	26	26	NUM
ejpam-6159	203	19	×	×	NOUN
ejpam-6159	203	20	{	{	PUNCT
ejpam-6159	203	21	∑n	∑n	PROPN
ejpam-6159	203	22	i=1	i=1	PROPN
ejpam-6159	203	23	ai	ai	VERB
ejpam-6159	203	24	(	(	PUNCT
ejpam-6159	203	25	1−	1−	NUM
ejpam-6159	203	26	s	s	X
ejpam-6159	203	27	(	(	PUNCT
ejpam-6159	203	28	1−	1−	NUM
ejpam-6159	203	29	t	t	NOUN
ejpam-6159	203	30	)	)	PUNCT
ejpam-6159	203	31	)	)	PUNCT
ejpam-6159	203	32	1	1	NUM
ejpam-6159	203	33	i∑n	i∑n	PROPN
ejpam-6159	203	34	i=1	i=1	PROPN
ejpam-6159	203	35	ai	ai	VERB
ejpam-6159	203	36	+	+	ADJ
ejpam-6159	204	1	∑n	∑n	PROPN
ejpam-6159	204	2	i=1	i=1	PROPN
ejpam-6159	204	3	ai	ai	VERB
ejpam-6159	204	4	(	(	PUNCT
ejpam-6159	204	5	1−	1−	NUM
ejpam-6159	204	6	st	st	NOUN
ejpam-6159	204	7	)	)	PUNCT
ejpam-6159	204	8	1	1	NUM
ejpam-6159	204	9	i∑n	i∑n	PROPN
ejpam-6159	204	10	i=1	i=1	PROPN
ejpam-6159	204	11	ai	ai	VERB
ejpam-6159	204	12	}	}	PUNCT
ejpam-6159	204	13	dt	dt	PROPN
ejpam-6159	204	14	(	(	PUNCT
ejpam-6159	204	15	21	21	NUM
ejpam-6159	204	16	)	)	PUNCT
ejpam-6159	204	17	kγk	kγk	NOUN
ejpam-6159	204	18	(	(	PUNCT
ejpam-6159	204	19	ϱ	ϱ	NOUN
ejpam-6159	204	20	)	)	PUNCT
ejpam-6159	204	21	ς	ς	PROPN
ejpam-6159	204	22	ϱ	ϱ	PROPN
ejpam-6159	204	23	k	k	PROPN
ejpam-6159	204	24	∗	∗	X
ejpam-6159	204	25	(	(	PUNCT
ejpam-6159	204	26	b1	b1	NOUN
ejpam-6159	204	27	,	,	PUNCT
ejpam-6159	204	28	a1	a1	NOUN
ejpam-6159	204	29	)	)	PUNCT
ejpam-6159	204	30	{	{	PUNCT
ejpam-6159	204	31	jϱ,k	jϱ,k	X
ejpam-6159	204	32	a1	a1	PROPN
ejpam-6159	204	33	+	+	X
ejpam-6159	204	34	f	f	X
ejpam-6159	204	35	(	(	PUNCT
ejpam-6159	204	36	a1	a1	NOUN
ejpam-6159	204	37	+	+	CCONJ
ejpam-6159	204	38	ς∗	ς∗	PROPN
ejpam-6159	204	39	(	(	PUNCT
ejpam-6159	204	40	b1	b1	NOUN
ejpam-6159	204	41	,	,	PUNCT
ejpam-6159	204	42	a1	a1	NOUN
ejpam-6159	204	43	)	)	PUNCT
ejpam-6159	204	44	)	)	PUNCT
ejpam-6159	205	1	+	+	CCONJ
ejpam-6159	205	2	jϱ,k	jϱ,k	X
ejpam-6159	205	3	(	(	PUNCT
ejpam-6159	205	4	a1+ς∗(b1,a1	a1+ς∗(b1,a1	PROPN
ejpam-6159	205	5	)	)	PUNCT
ejpam-6159	205	6	)	)	PUNCT
ejpam-6159	206	1	−	−	PROPN
ejpam-6159	206	2	f	f	X
ejpam-6159	206	3	(	(	PUNCT
ejpam-6159	206	4	a1	a1	PROPN
ejpam-6159	206	5	)	)	PUNCT
ejpam-6159	206	6	}	}	PUNCT
ejpam-6159	206	7	≤	≤	NOUN
ejpam-6159	207	1	[	[	X
ejpam-6159	207	2	f	f	X
ejpam-6159	207	3	(	(	PUNCT
ejpam-6159	207	4	a1	a1	PROPN
ejpam-6159	207	5	)	)	PUNCT
ejpam-6159	208	1	+	+	NUM
ejpam-6159	208	2	f	f	X
ejpam-6159	208	3	(	(	PUNCT
ejpam-6159	208	4	a1	a1	NOUN
ejpam-6159	208	5	+	+	CCONJ
ejpam-6159	208	6	ς∗	ς∗	PROPN
ejpam-6159	208	7	(	(	PUNCT
ejpam-6159	208	8	b1	b1	NOUN
ejpam-6159	208	9	,	,	PUNCT
ejpam-6159	208	10	a1	a1	NOUN
ejpam-6159	208	11	)	)	PUNCT
ejpam-6159	208	12	)	)	PUNCT
ejpam-6159	208	13	]	]	PUNCT
ejpam-6159	209	1	∫	∫	PROPN
ejpam-6159	209	2	1	1	NUM
ejpam-6159	209	3	0	0	NUM
ejpam-6159	209	4	t	t	PROPN
ejpam-6159	209	5	ϱ	ϱ	PROPN
ejpam-6159	209	6	k	k	X
ejpam-6159	209	7	−1	−1	NOUN
ejpam-6159	209	8	×	×	NOUN
ejpam-6159	209	9	{	{	PUNCT
ejpam-6159	209	10	∑n	∑n	PROPN
ejpam-6159	209	11	i=1	i=1	PROPN
ejpam-6159	209	12	ai	ai	VERB
ejpam-6159	209	13	(	(	PUNCT
ejpam-6159	209	14	1−	1−	NUM
ejpam-6159	209	15	s	s	X
ejpam-6159	209	16	(	(	PUNCT
ejpam-6159	209	17	1−	1−	NUM
ejpam-6159	209	18	t	t	NOUN
ejpam-6159	209	19	)	)	PUNCT
ejpam-6159	209	20	)	)	PUNCT
ejpam-6159	209	21	1	1	NUM
ejpam-6159	209	22	i∑n	i∑n	PROPN
ejpam-6159	209	23	i=1	i=1	PROPN
ejpam-6159	209	24	ai	ai	VERB
ejpam-6159	209	25	+	+	ADJ
ejpam-6159	210	1	∑n	∑n	PROPN
ejpam-6159	210	2	i=1	i=1	PROPN
ejpam-6159	210	3	ai	ai	VERB
ejpam-6159	210	4	(	(	PUNCT
ejpam-6159	210	5	1−	1−	NUM
ejpam-6159	210	6	st	st	NOUN
ejpam-6159	210	7	)	)	PUNCT
ejpam-6159	210	8	1	1	NUM
ejpam-6159	210	9	i∑n	i∑n	PROPN
ejpam-6159	210	10	i=1	i=1	PROPN
ejpam-6159	210	11	ai	ai	VERB
ejpam-6159	210	12	}	}	PUNCT
ejpam-6159	210	13	dt	dt	PROPN
ejpam-6159	210	14	.	.	PUNCT
ejpam-6159	211	1	(	(	PUNCT
ejpam-6159	211	2	22	22	NUM
ejpam-6159	211	3	)	)	PUNCT
ejpam-6159	211	4	by	by	ADP
ejpam-6159	211	5	combining	combine	VERB
ejpam-6159	211	6	the	the	DET
ejpam-6159	211	7	inequalities	inequality	NOUN
ejpam-6159	211	8	(	(	PUNCT
ejpam-6159	211	9	17	17	NUM
ejpam-6159	211	10	)	)	PUNCT
ejpam-6159	211	11	and	and	CCONJ
ejpam-6159	211	12	(	(	PUNCT
ejpam-6159	211	13	22	22	NUM
ejpam-6159	211	14	)	)	PUNCT
ejpam-6159	211	15	,	,	PUNCT
ejpam-6159	211	16	we	we	PRON
ejpam-6159	211	17	can	can	AUX
ejpam-6159	211	18	get	get	VERB
ejpam-6159	211	19	(	(	PUNCT
ejpam-6159	211	20	14	14	NUM
ejpam-6159	211	21	)	)	PUNCT
ejpam-6159	211	22	.	.	PUNCT
ejpam-6159	212	1	corollary	corollary	ADJ
ejpam-6159	212	2	1	1	NUM
ejpam-6159	212	3	.	.	PUNCT
ejpam-6159	213	1	if	if	SCONJ
ejpam-6159	213	2	we	we	PRON
ejpam-6159	213	3	judge	judge	VERB
ejpam-6159	213	4	the	the	DET
ejpam-6159	213	5	value	value	NOUN
ejpam-6159	213	6	s	s	PART
ejpam-6159	213	7	=	=	SYM
ejpam-6159	213	8	1	1	NUM
ejpam-6159	213	9	in	in	ADP
ejpam-6159	213	10	theorem	theorem	NOUN
ejpam-6159	213	11	2	2	NUM
ejpam-6159	213	12	,	,	PUNCT
ejpam-6159	213	13	then	then	ADV
ejpam-6159	213	14	the	the	DET
ejpam-6159	213	15	following	follow	VERB
ejpam-6159	213	16	inequalities	inequality	NOUN
ejpam-6159	213	17	for	for	ADP
ejpam-6159	213	18	gfpp	gfpp	NOUN
ejpam-6159	213	19	function	function	NOUN
ejpam-6159	213	20	with	with	ADP
ejpam-6159	213	21	k−fractionaliintegral	k−fractionaliintegral	ADJ
ejpam-6159	213	22	operators:∑n	operators:∑n	PROPN
ejpam-6159	213	23	i=1	i=1	PROPN
ejpam-6159	213	24	ai∑n	ai∑n	PROPN
ejpam-6159	214	1	i=1	i=1	PRON
ejpam-6159	214	2	ai	ai	VERB
ejpam-6159	214	3	(	(	PUNCT
ejpam-6159	214	4	1	1	NUM
ejpam-6159	214	5	2	2	NUM
ejpam-6159	214	6	)	)	PUNCT
ejpam-6159	214	7	1	1	NUM
ejpam-6159	215	1	i	i	PRON
ejpam-6159	215	2	f	f	PROPN
ejpam-6159	215	3	(	(	PUNCT
ejpam-6159	215	4	2a1	2a1	NUM
ejpam-6159	215	5	+	+	CCONJ
ejpam-6159	215	6	ς∗	ς∗	PROPN
ejpam-6159	215	7	(	(	PUNCT
ejpam-6159	215	8	b1	b1	NOUN
ejpam-6159	215	9	,	,	PUNCT
ejpam-6159	215	10	a1	a1	NOUN
ejpam-6159	215	11	)	)	PUNCT
ejpam-6159	215	12	2	2	NUM
ejpam-6159	215	13	)	)	PUNCT
ejpam-6159	215	14	≤	≤	NUM
ejpam-6159	215	15	γk	γk	X
ejpam-6159	215	16	(	(	PUNCT
ejpam-6159	215	17	ϱ+	ϱ+	X
ejpam-6159	215	18	k	k	NOUN
ejpam-6159	215	19	)	)	PUNCT
ejpam-6159	215	20	ς	ς	PROPN
ejpam-6159	215	21	ϱ	ϱ	PROPN
ejpam-6159	215	22	k	k	PROPN
ejpam-6159	215	23	∗	∗	X
ejpam-6159	215	24	(	(	PUNCT
ejpam-6159	215	25	b1	b1	NOUN
ejpam-6159	215	26	,	,	PUNCT
ejpam-6159	215	27	a1	a1	NOUN
ejpam-6159	215	28	)	)	PUNCT
ejpam-6159	215	29	{	{	PUNCT
ejpam-6159	215	30	jϱ,k	jϱ,k	X
ejpam-6159	215	31	a1	a1	PROPN
ejpam-6159	215	32	+	+	X
ejpam-6159	215	33	f	f	X
ejpam-6159	215	34	(	(	PUNCT
ejpam-6159	215	35	a1	a1	NOUN
ejpam-6159	215	36	+	+	CCONJ
ejpam-6159	215	37	ς∗	ς∗	PROPN
ejpam-6159	215	38	(	(	PUNCT
ejpam-6159	215	39	b1	b1	NOUN
ejpam-6159	215	40	,	,	PUNCT
ejpam-6159	215	41	a1	a1	NOUN
ejpam-6159	215	42	)	)	PUNCT
ejpam-6159	215	43	)	)	PUNCT
ejpam-6159	216	1	+	+	CCONJ
ejpam-6159	216	2	jϱ,k	jϱ,k	X
ejpam-6159	216	3	(	(	PUNCT
ejpam-6159	216	4	a1+ς∗(b1,a1	a1+ς∗(b1,a1	PROPN
ejpam-6159	216	5	)	)	PUNCT
ejpam-6159	216	6	)	)	PUNCT
ejpam-6159	217	1	−	−	PROPN
ejpam-6159	217	2	f	f	X
ejpam-6159	217	3	(	(	PUNCT
ejpam-6159	217	4	a1	a1	PROPN
ejpam-6159	217	5	)	)	PUNCT
ejpam-6159	217	6	}	}	PUNCT
ejpam-6159	217	7	≤	≤	NOUN
ejpam-6159	218	1	[	[	X
ejpam-6159	218	2	f	f	X
ejpam-6159	218	3	(	(	PUNCT
ejpam-6159	218	4	a1	a1	PROPN
ejpam-6159	218	5	)	)	PUNCT
ejpam-6159	219	1	+	+	NUM
ejpam-6159	219	2	f	f	X
ejpam-6159	219	3	(	(	PUNCT
ejpam-6159	219	4	a1	a1	NOUN
ejpam-6159	219	5	+	+	CCONJ
ejpam-6159	219	6	ς∗	ς∗	PROPN
ejpam-6159	219	7	(	(	PUNCT
ejpam-6159	219	8	b1	b1	NOUN
ejpam-6159	219	9	,	,	PUNCT
ejpam-6159	219	10	a1))]∑n	a1))]∑n	PROPN
ejpam-6159	219	11	i=1	i=1	PROPN
ejpam-6159	220	1	ai	ai	VERB
ejpam-6159	220	2	×	×	PROPN
ejpam-6159	220	3	∫	∫	PROPN
ejpam-6159	220	4	1	1	NUM
ejpam-6159	220	5	0	0	NUM
ejpam-6159	221	1	n∑	n∑	NOUN
ejpam-6159	221	2	i=1	i=1	PROPN
ejpam-6159	221	3	ait	ait	VERB
ejpam-6159	221	4	ϱ	ϱ	PROPN
ejpam-6159	221	5	k	k	PROPN
ejpam-6159	221	6	−1{(1−	−1{(1−	PROPN
ejpam-6159	221	7	t	t	PROPN
ejpam-6159	221	8	)	)	PUNCT
ejpam-6159	221	9	1	1	NUM
ejpam-6159	222	1	i	i	PRON
ejpam-6159	222	2	+	+	CCONJ
ejpam-6159	222	3	(	(	PUNCT
ejpam-6159	222	4	t	t	NOUN
ejpam-6159	222	5	)	)	PUNCT
ejpam-6159	222	6	1	1	NUM
ejpam-6159	222	7	i	i	NOUN
ejpam-6159	222	8	}	}	PUNCT
ejpam-6159	222	9	dt	dt	PROPN
ejpam-6159	222	10	.	.	PUNCT
ejpam-6159	223	1	(	(	PUNCT
ejpam-6159	223	2	23	23	NUM
ejpam-6159	223	3	)	)	PUNCT
ejpam-6159	223	4	corollary	corollary	ADJ
ejpam-6159	223	5	2	2	NUM
ejpam-6159	223	6	.	.	PUNCT
ejpam-6159	224	1	if	if	SCONJ
ejpam-6159	224	2	we	we	PRON
ejpam-6159	224	3	judge	judge	VERB
ejpam-6159	224	4	the	the	DET
ejpam-6159	224	5	value	value	NOUN
ejpam-6159	224	6	k	k	PROPN
ejpam-6159	224	7	=	=	SYM
ejpam-6159	224	8	1	1	NUM
ejpam-6159	224	9	in	in	ADP
ejpam-6159	224	10	corollary	corollary	ADJ
ejpam-6159	224	11	1	1	NUM
ejpam-6159	224	12	,	,	PUNCT
ejpam-6159	224	13	then	then	ADV
ejpam-6159	224	14	we	we	PRON
ejpam-6159	224	15	get	get	VERB
ejpam-6159	224	16	the	the	DET
ejpam-6159	224	17	following	follow	VERB
ejpam-6159	224	18	inequalities	inequality	NOUN
ejpam-6159	224	19	for	for	ADP
ejpam-6159	224	20	gfpp	gfpp	NOUN
ejpam-6159	224	21	function	function	NOUN
ejpam-6159	224	22	with	with	ADP
ejpam-6159	224	23	rl−fractionaliintegral	rl−fractionaliintegral	ADJ
ejpam-6159	224	24	operators:∑n	operators:∑n	PROPN
ejpam-6159	224	25	i=1	i=1	PROPN
ejpam-6159	224	26	ai∑n	ai∑n	PROPN
ejpam-6159	225	1	i=1	i=1	PRON
ejpam-6159	225	2	ai	ai	VERB
ejpam-6159	225	3	(	(	PUNCT
ejpam-6159	225	4	1	1	NUM
ejpam-6159	225	5	2	2	NUM
ejpam-6159	225	6	)	)	PUNCT
ejpam-6159	225	7	1	1	NUM
ejpam-6159	226	1	i	i	PRON
ejpam-6159	226	2	f	f	PROPN
ejpam-6159	226	3	(	(	PUNCT
ejpam-6159	226	4	2a1	2a1	NUM
ejpam-6159	226	5	+	+	CCONJ
ejpam-6159	226	6	ς∗	ς∗	PROPN
ejpam-6159	226	7	(	(	PUNCT
ejpam-6159	226	8	b1	b1	NOUN
ejpam-6159	226	9	,	,	PUNCT
ejpam-6159	226	10	a1	a1	NOUN
ejpam-6159	226	11	)	)	PUNCT
ejpam-6159	226	12	2	2	NUM
ejpam-6159	226	13	)	)	PUNCT
ejpam-6159	226	14	≤	≤	NOUN
ejpam-6159	226	15	γ	γ	X
ejpam-6159	226	16	(	(	PUNCT
ejpam-6159	226	17	ϱ+	ϱ+	NOUN
ejpam-6159	226	18	1	1	NUM
ejpam-6159	226	19	)	)	PUNCT
ejpam-6159	226	20	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	226	21	(	(	PUNCT
ejpam-6159	226	22	b1	b1	NOUN
ejpam-6159	226	23	,	,	PUNCT
ejpam-6159	226	24	a1	a1	NOUN
ejpam-6159	226	25	)	)	PUNCT
ejpam-6159	226	26	{	{	PUNCT
ejpam-6159	226	27	jϱ	jϱ	PART
ejpam-6159	226	28	a1	a1	PROPN
ejpam-6159	226	29	+	+	X
ejpam-6159	226	30	f	f	X
ejpam-6159	226	31	(	(	PUNCT
ejpam-6159	226	32	a1	a1	NOUN
ejpam-6159	226	33	+	+	CCONJ
ejpam-6159	226	34	ς∗	ς∗	PROPN
ejpam-6159	226	35	(	(	PUNCT
ejpam-6159	226	36	b1	b1	NOUN
ejpam-6159	226	37	,	,	PUNCT
ejpam-6159	226	38	a1	a1	NOUN
ejpam-6159	226	39	)	)	PUNCT
ejpam-6159	226	40	)	)	PUNCT
ejpam-6159	227	1	+	+	CCONJ
ejpam-6159	227	2	jϱ	jϱ	X
ejpam-6159	227	3	(	(	PUNCT
ejpam-6159	227	4	a1+ς∗(b1,a1	a1+ς∗(b1,a1	PROPN
ejpam-6159	227	5	)	)	PUNCT
ejpam-6159	227	6	)	)	PUNCT
ejpam-6159	228	1	−	−	PROPN
ejpam-6159	228	2	f	f	X
ejpam-6159	228	3	(	(	PUNCT
ejpam-6159	228	4	a1	a1	PROPN
ejpam-6159	228	5	)	)	PUNCT
ejpam-6159	228	6	}	}	PUNCT
ejpam-6159	228	7	≤	≤	NOUN
ejpam-6159	229	1	[	[	X
ejpam-6159	229	2	f	f	X
ejpam-6159	229	3	(	(	PUNCT
ejpam-6159	229	4	a1	a1	PROPN
ejpam-6159	229	5	)	)	PUNCT
ejpam-6159	230	1	+	+	NUM
ejpam-6159	230	2	f	f	X
ejpam-6159	230	3	(	(	PUNCT
ejpam-6159	230	4	a1	a1	NOUN
ejpam-6159	230	5	+	+	CCONJ
ejpam-6159	230	6	ς∗	ς∗	PROPN
ejpam-6159	230	7	(	(	PUNCT
ejpam-6159	230	8	b1	b1	NOUN
ejpam-6159	230	9	,	,	PUNCT
ejpam-6159	230	10	a1))]∑n	a1))]∑n	PROPN
ejpam-6159	230	11	i=1	i=1	PROPN
ejpam-6159	231	1	ai	ai	VERB
ejpam-6159	231	2	×	×	PROPN
ejpam-6159	231	3	∫	∫	PROPN
ejpam-6159	231	4	1	1	NUM
ejpam-6159	231	5	0	0	NUM
ejpam-6159	232	1	n∑	n∑	NOUN
ejpam-6159	232	2	i=1	i=1	PROPN
ejpam-6159	232	3	ait	ait	ADJ
ejpam-6159	232	4	ϱ−1{(1−	ϱ−1{(1−	PROPN
ejpam-6159	232	5	t	t	PROPN
ejpam-6159	232	6	)	)	PUNCT
ejpam-6159	232	7	1	1	NUM
ejpam-6159	233	1	i	i	PRON
ejpam-6159	233	2	+	+	CCONJ
ejpam-6159	233	3	(	(	PUNCT
ejpam-6159	233	4	t	t	NOUN
ejpam-6159	233	5	)	)	PUNCT
ejpam-6159	233	6	1	1	NUM
ejpam-6159	233	7	i	i	NOUN
ejpam-6159	233	8	}	}	PUNCT
ejpam-6159	233	9	dt	dt	PROPN
ejpam-6159	233	10	.	.	PUNCT
ejpam-6159	234	1	(	(	PUNCT
ejpam-6159	234	2	24	24	NUM
ejpam-6159	234	3	)	)	PUNCT
ejpam-6159	234	4	remark	remark	NOUN
ejpam-6159	234	5	2	2	NUM
ejpam-6159	234	6	.	.	PUNCT
ejpam-6159	235	1	if	if	SCONJ
ejpam-6159	235	2	we	we	PRON
ejpam-6159	235	3	take	take	VERB
ejpam-6159	235	4	ϱ	ϱ	NOUN
ejpam-6159	235	5	=	=	SYM
ejpam-6159	235	6	1	1	NUM
ejpam-6159	235	7	andin	andin	NOUN
ejpam-6159	235	8	=	=	SYM
ejpam-6159	235	9	1	1	NUM
ejpam-6159	235	10	,	,	PUNCT
ejpam-6159	235	11	in	in	ADP
ejpam-6159	235	12	corollary	corollary	ADJ
ejpam-6159	235	13	2	2	NUM
ejpam-6159	235	14	,	,	PUNCT
ejpam-6159	235	15	then	then	ADV
ejpam-6159	235	16	one	one	PRON
ejpam-6159	235	17	can	can	AUX
ejpam-6159	235	18	get	get	VERB
ejpam-6159	235	19	the	the	DET
ejpam-6159	235	20	inequalities	inequality	NOUN
ejpam-6159	235	21	(	(	PUNCT
ejpam-6159	235	22	4	4	NUM
ejpam-6159	235	23	)	)	PUNCT
ejpam-6159	235	24	.	.	PUNCT
ejpam-6159	236	1	through	through	ADP
ejpam-6159	236	2	out	out	ADP
ejpam-6159	236	3	the	the	DET
ejpam-6159	236	4	article	article	NOUN
ejpam-6159	236	5	,	,	PUNCT
ejpam-6159	236	6	we	we	PRON
ejpam-6159	236	7	take	take	VERB
ejpam-6159	236	8	u∗	u∗	ADV
ejpam-6159	236	9	=	=	PUNCT
ejpam-6159	236	10	let	let	VERB
ejpam-6159	236	11	us	we	PRON
ejpam-6159	236	12	suppose	suppose	VERB
ejpam-6159	236	13	that	that	SCONJ
ejpam-6159	236	14	n	n	PROPN
ejpam-6159	236	15	∈	∈	PROPN
ejpam-6159	236	16	n	n	NOUN
ejpam-6159	236	17	,	,	PUNCT
ejpam-6159	236	18	ai	ai	VERB
ejpam-6159	236	19	≥	≥	NOUN
ejpam-6159	236	20	0	0	NUM
ejpam-6159	236	21	(	(	PUNCT
ejpam-6159	236	22	i	i	PRON
ejpam-6159	236	23	=	=	NOUN
ejpam-6159	236	24	1	1	NUM
ejpam-6159	236	25	,	,	PUNCT
ejpam-6159	236	26	n	n	PROPN
ejpam-6159	236	27	)	)	PUNCT
ejpam-6159	236	28	,	,	PUNCT
ejpam-6159	237	1	such	such	ADJ
ejpam-6159	237	2	that	that	SCONJ
ejpam-6159	237	3	∑n	∑n	PROPN
ejpam-6159	237	4	i=1	i=1	PROPN
ejpam-6159	237	5	ai	ai	AUX
ejpam-6159	237	6	>	>	X
ejpam-6159	237	7	0	0	NUM
ejpam-6159	237	8	,	,	PUNCT
ejpam-6159	237	9	s	s	VERB
ejpam-6159	237	10	∈	∈	PROPN
ejpam-6159	238	1	[	[	X
ejpam-6159	238	2	0	0	NUM
ejpam-6159	238	3	,	,	PUNCT
ejpam-6159	238	4	1	1	NUM
ejpam-6159	238	5	]	]	PUNCT
ejpam-6159	238	6	,	,	PUNCT
ejpam-6159	238	7	a1	a1	NOUN
ejpam-6159	238	8	<	<	X
ejpam-6159	238	9	a1	a1	NOUN
ejpam-6159	238	10	+	+	CCONJ
ejpam-6159	238	11	ς∗	ς∗	PROPN
ejpam-6159	238	12	(	(	PUNCT
ejpam-6159	238	13	b1	b1	NOUN
ejpam-6159	238	14	,	,	PUNCT
ejpam-6159	238	15	a1	a1	NOUN
ejpam-6159	238	16	)	)	PUNCT
ejpam-6159	238	17	and	and	CCONJ
ejpam-6159	238	18	ϱ,k	ϱ,k	X
ejpam-6159	238	19	>	>	X
ejpam-6159	238	20	0	0	X
ejpam-6159	238	21	.	.	PUNCT
ejpam-6159	239	1	j.	j.	PROPN
ejpam-6159	239	2	nasir	nasir	PROPN
ejpam-6159	239	3	et	et	PROPN
ejpam-6159	239	4	al	al	PROPN
ejpam-6159	239	5	.	.	PUNCT
ejpam-6159	239	6	/	/	SYM
ejpam-6159	239	7	eur	eur	PROPN
ejpam-6159	239	8	.	.	PUNCT
ejpam-6159	240	1	j.	j.	PROPN
ejpam-6159	240	2	pure	pure	PROPN
ejpam-6159	240	3	appl	appl	PROPN
ejpam-6159	240	4	.	.	PROPN
ejpam-6159	240	5	math	math	PROPN
ejpam-6159	240	6	,	,	PUNCT
ejpam-6159	240	7	18	18	NUM
ejpam-6159	240	8	(	(	PUNCT
ejpam-6159	240	9	3	3	NUM
ejpam-6159	240	10	)	)	PUNCT
ejpam-6159	240	11	(	(	PUNCT
ejpam-6159	240	12	2025	2025	NUM
ejpam-6159	240	13	)	)	PUNCT
ejpam-6159	240	14	,	,	PUNCT
ejpam-6159	240	15	6159	6159	NUM
ejpam-6159	240	16	9	9	NUM
ejpam-6159	240	17	of	of	ADP
ejpam-6159	240	18	26	26	NUM
ejpam-6159	240	19	2.3	2.3	NUM
ejpam-6159	240	20	.	.	PUNCT
ejpam-6159	241	1	new	new	ADJ
ejpam-6159	241	2	generalizations	generalization	NOUN
ejpam-6159	241	3	of	of	ADP
ejpam-6159	241	4	ostrowski	ostrowski	ADJ
ejpam-6159	241	5	type	type	NOUN
ejpam-6159	241	6	inequalities	inequality	NOUN
ejpam-6159	241	7	using	use	VERB
ejpam-6159	241	8	polynomial	polynomial	ADJ
ejpam-6159	241	9	n−fractional	n−fractional	ADJ
ejpam-6159	241	10	s−like	s−like	INTJ
ejpam-6159	241	11	preinvex	preinvex	NOUN
ejpam-6159	241	12	functions	function	NOUN
ejpam-6159	241	13	this	this	DET
ejpam-6159	241	14	portion	portion	NOUN
ejpam-6159	241	15	explores	explore	VERB
ejpam-6159	241	16	the	the	DET
ejpam-6159	241	17	new	new	ADJ
ejpam-6159	241	18	inequalities	inequality	NOUN
ejpam-6159	241	19	for	for	ADP
ejpam-6159	241	20	the	the	DET
ejpam-6159	241	21	derivatives	derivative	NOUN
ejpam-6159	241	22	of	of	ADP
ejpam-6159	241	23	first	first	ADJ
ejpam-6159	241	24	and	and	CCONJ
ejpam-6159	241	25	second	second	ADJ
ejpam-6159	241	26	with	with	ADP
ejpam-6159	241	27	the	the	DET
ejpam-6159	241	28	gfpp−s	gfpp−s	PROPN
ejpam-6159	241	29	function	function	NOUN
ejpam-6159	241	30	.	.	PUNCT
ejpam-6159	242	1	in	in	ADP
ejpam-6159	242	2	the	the	DET
ejpam-6159	242	3	mean	mean	ADJ
ejpam-6159	242	4	while	while	NOUN
ejpam-6159	242	5	,	,	PUNCT
ejpam-6159	242	6	we	we	PRON
ejpam-6159	242	7	will	will	AUX
ejpam-6159	242	8	develop	develop	VERB
ejpam-6159	242	9	a	a	DET
ejpam-6159	242	10	following	follow	VERB
ejpam-6159	242	11	new	new	ADJ
ejpam-6159	242	12	lemma	lemma	PROPN
ejpam-6159	242	13	.	.	PUNCT
ejpam-6159	243	1	lemma	lemma	PROPN
ejpam-6159	243	2	1	1	X
ejpam-6159	243	3	.	.	PUNCT
ejpam-6159	243	4	suppose	suppose	VERB
ejpam-6159	244	1	f	f	X
ejpam-6159	244	2	:	:	PUNCT
ejpam-6159	244	3	[	[	X
ejpam-6159	244	4	a1	a1	NOUN
ejpam-6159	244	5	,	,	PUNCT
ejpam-6159	244	6	a1	a1	NOUN
ejpam-6159	244	7	+	+	CCONJ
ejpam-6159	244	8	ς∗	ς∗	PROPN
ejpam-6159	244	9	(	(	PUNCT
ejpam-6159	244	10	b1	b1	NOUN
ejpam-6159	244	11	,	,	PUNCT
ejpam-6159	244	12	a1	a1	NOUN
ejpam-6159	244	13	)	)	PUNCT
ejpam-6159	244	14	]	]	PUNCT
ejpam-6159	245	1	→	→	PUNCT
ejpam-6159	245	2	ℜ	ℜ	PROPN
ejpam-6159	245	3	is	be	AUX
ejpam-6159	245	4	a	a	DET
ejpam-6159	245	5	differentiable	differentiable	ADJ
ejpam-6159	245	6	mapping	mapping	NOUN
ejpam-6159	245	7	on	on	ADP
ejpam-6159	245	8	(	(	PUNCT
ejpam-6159	245	9	a1	a1	NOUN
ejpam-6159	245	10	,	,	PUNCT
ejpam-6159	245	11	a1	a1	NOUN
ejpam-6159	245	12	+	+	CCONJ
ejpam-6159	245	13	ς∗	ς∗	PROPN
ejpam-6159	245	14	(	(	PUNCT
ejpam-6159	245	15	b1	b1	NOUN
ejpam-6159	245	16	,	,	PUNCT
ejpam-6159	245	17	a1	a1	NOUN
ejpam-6159	245	18	)	)	PUNCT
ejpam-6159	245	19	)	)	PUNCT
ejpam-6159	245	20	with	with	ADP
ejpam-6159	245	21	a1	a1	NOUN
ejpam-6159	245	22	<	<	X
ejpam-6159	245	23	a1	a1	NOUN
ejpam-6159	245	24	+	+	CCONJ
ejpam-6159	245	25	ς∗	ς∗	PROPN
ejpam-6159	245	26	(	(	PUNCT
ejpam-6159	245	27	b1	b1	NOUN
ejpam-6159	245	28	,	,	PUNCT
ejpam-6159	245	29	a1	a1	NOUN
ejpam-6159	245	30	)	)	PUNCT
ejpam-6159	245	31	.	.	PUNCT
ejpam-6159	246	1	if	if	SCONJ
ejpam-6159	246	2	f	f	PROPN
ejpam-6159	246	3	′	′	NOUN
ejpam-6159	246	4	∈	∈	PROPN
ejpam-6159	246	5	l[a1	l[a1	ADV
ejpam-6159	246	6	,	,	PUNCT
ejpam-6159	246	7	a1	a1	NOUN
ejpam-6159	246	8	+	+	CCONJ
ejpam-6159	246	9	ς∗	ς∗	PROPN
ejpam-6159	246	10	(	(	PUNCT
ejpam-6159	246	11	b1	b1	NOUN
ejpam-6159	246	12	,	,	PUNCT
ejpam-6159	246	13	a1	a1	NOUN
ejpam-6159	246	14	)	)	PUNCT
ejpam-6159	246	15	]	]	PUNCT
ejpam-6159	246	16	,	,	PUNCT
ejpam-6159	246	17	ϱ	ϱ	ADP
ejpam-6159	246	18	>	>	X
ejpam-6159	246	19	0,k	0,k	PROPN
ejpam-6159	246	20	>	>	PUNCT
ejpam-6159	246	21	0	0	NUM
ejpam-6159	246	22	,	,	PUNCT
ejpam-6159	246	23	then	then	ADV
ejpam-6159	246	24	the	the	DET
ejpam-6159	246	25	followingiequality	followingiequality	NOUN
ejpam-6159	246	26	for	for	ADP
ejpam-6159	246	27	k−fractional	k−fractional	ADJ
ejpam-6159	246	28	integral	integral	ADJ
ejpam-6159	246	29	operator	operator	NOUN
ejpam-6159	246	30	is	be	AUX
ejpam-6159	246	31	as	as	SCONJ
ejpam-6159	246	32	follows	follow	VERB
ejpam-6159	246	33	ς	ς	PROPN
ejpam-6159	246	34	ϱ	ϱ	PROPN
ejpam-6159	246	35	k	k	PROPN
ejpam-6159	246	36	∗	∗	X
ejpam-6159	246	37	(	(	PUNCT
ejpam-6159	246	38	x	x	NOUN
ejpam-6159	246	39	,	,	PUNCT
ejpam-6159	246	40	a1	a1	NOUN
ejpam-6159	246	41	)	)	PUNCT
ejpam-6159	246	42	+	+	CCONJ
ejpam-6159	247	1	ς	ς	PROPN
ejpam-6159	247	2	ϱ	ϱ	PROPN
ejpam-6159	247	3	k	k	PROPN
ejpam-6159	247	4	∗	∗	X
ejpam-6159	247	5	(	(	PUNCT
ejpam-6159	247	6	x	x	NOUN
ejpam-6159	247	7	,	,	PUNCT
ejpam-6159	247	8	b1	b1	NOUN
ejpam-6159	247	9	)	)	PUNCT
ejpam-6159	247	10	ς∗	ς∗	PROPN
ejpam-6159	247	11	(	(	PUNCT
ejpam-6159	247	12	b1	b1	NOUN
ejpam-6159	247	13	,	,	PUNCT
ejpam-6159	247	14	a1	a1	PROPN
ejpam-6159	247	15	)	)	PUNCT
ejpam-6159	247	16	f	f	NOUN
ejpam-6159	247	17	(	(	PUNCT
ejpam-6159	247	18	x)−	x)−	PROPN
ejpam-6159	247	19	γk	γk	PROPN
ejpam-6159	247	20	(	(	PUNCT
ejpam-6159	247	21	ϱ+	ϱ+	X
ejpam-6159	247	22	k	k	NOUN
ejpam-6159	247	23	)	)	PUNCT
ejpam-6159	247	24	ς	ς	PROPN
ejpam-6159	247	25	ϱ	ϱ	PROPN
ejpam-6159	247	26	k	k	PROPN
ejpam-6159	247	27	∗	∗	X
ejpam-6159	247	28	(	(	PUNCT
ejpam-6159	247	29	b1	b1	NOUN
ejpam-6159	247	30	,	,	PUNCT
ejpam-6159	247	31	a1	a1	PROPN
ejpam-6159	247	32	)	)	PUNCT
ejpam-6159	247	33	×	×	NOUN
ejpam-6159	247	34	{	{	PUNCT
ejpam-6159	247	35	jϱ,k	jϱ,k	X
ejpam-6159	247	36	(	(	PUNCT
ejpam-6159	247	37	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	247	38	,	,	PUNCT
ejpam-6159	247	39	a1	a1	NOUN
ejpam-6159	247	40	)	)	PUNCT
ejpam-6159	247	41	)	)	PUNCT
ejpam-6159	248	1	−	−	PROPN
ejpam-6159	248	2	f	f	X
ejpam-6159	248	3	(	(	PUNCT
ejpam-6159	248	4	a1	a1	PROPN
ejpam-6159	248	5	)	)	PUNCT
ejpam-6159	248	6	+	+	NUM
ejpam-6159	248	7	jϱ,k	jϱ,k	X
ejpam-6159	248	8	(	(	PUNCT
ejpam-6159	248	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	248	10	,	,	PUNCT
ejpam-6159	248	11	b1	b1	NOUN
ejpam-6159	248	12	)	)	PUNCT
ejpam-6159	248	13	)	)	PUNCT
ejpam-6159	249	1	+	+	CCONJ
ejpam-6159	249	2	f	f	X
ejpam-6159	249	3	(	(	PUNCT
ejpam-6159	249	4	a1	a1	NOUN
ejpam-6159	249	5	+	+	CCONJ
ejpam-6159	249	6	ς∗	ς∗	PROPN
ejpam-6159	249	7	(	(	PUNCT
ejpam-6159	249	8	b1	b1	NOUN
ejpam-6159	249	9	,	,	PUNCT
ejpam-6159	249	10	a1	a1	NOUN
ejpam-6159	249	11	)	)	PUNCT
ejpam-6159	249	12	)	)	PUNCT
ejpam-6159	249	13	}	}	PUNCT
ejpam-6159	250	1	=	=	PUNCT
ejpam-6159	250	2	ς	ς	X
ejpam-6159	250	3	ϱ	ϱ	X
ejpam-6159	250	4	k	k	PROPN
ejpam-6159	250	5	+1	+1	PROPN
ejpam-6159	250	6	∗	∗	NOUN
ejpam-6159	250	7	(	(	PUNCT
ejpam-6159	250	8	x	x	NOUN
ejpam-6159	250	9	,	,	PUNCT
ejpam-6159	250	10	a1	a1	NOUN
ejpam-6159	250	11	)	)	PUNCT
ejpam-6159	250	12	ς∗	ς∗	NOUN
ejpam-6159	250	13	(	(	PUNCT
ejpam-6159	250	14	b1	b1	NOUN
ejpam-6159	250	15	,	,	PUNCT
ejpam-6159	250	16	a1	a1	PROPN
ejpam-6159	250	17	)	)	PUNCT
ejpam-6159	250	18	∫	∫	NOUN
ejpam-6159	250	19	1	1	NUM
ejpam-6159	250	20	0	0	NUM
ejpam-6159	250	21	t	t	PROPN
ejpam-6159	250	22	ϱ	ϱ	PROPN
ejpam-6159	250	23	kf	kf	PROPN
ejpam-6159	250	24	(	(	PUNCT
ejpam-6159	250	25	a1	a1	NOUN
ejpam-6159	250	26	+	+	CCONJ
ejpam-6159	250	27	tς∗	tς∗	X
ejpam-6159	250	28	(	(	PUNCT
ejpam-6159	250	29	x	x	NOUN
ejpam-6159	250	30	,	,	PUNCT
ejpam-6159	250	31	a1	a1	NOUN
ejpam-6159	250	32	)	)	PUNCT
ejpam-6159	250	33	)	)	PUNCT
ejpam-6159	250	34	dt+	dt+	NOUN
ejpam-6159	250	35	ς	ς	PROPN
ejpam-6159	250	36	ϱ	ϱ	PROPN
ejpam-6159	250	37	k	k	PROPN
ejpam-6159	250	38	+1	+1	PROPN
ejpam-6159	250	39	∗	∗	NOUN
ejpam-6159	250	40	(	(	PUNCT
ejpam-6159	250	41	x	x	NOUN
ejpam-6159	250	42	,	,	PUNCT
ejpam-6159	250	43	b1	b1	NOUN
ejpam-6159	250	44	)	)	PUNCT
ejpam-6159	250	45	ς∗	ς∗	PROPN
ejpam-6159	250	46	(	(	PUNCT
ejpam-6159	250	47	b1	b1	NOUN
ejpam-6159	250	48	,	,	PUNCT
ejpam-6159	250	49	a1	a1	PROPN
ejpam-6159	250	50	)	)	PUNCT
ejpam-6159	250	51	∫	∫	NOUN
ejpam-6159	250	52	1	1	NUM
ejpam-6159	250	53	0	0	NUM
ejpam-6159	250	54	t	t	PROPN
ejpam-6159	250	55	ϱ	ϱ	PROPN
ejpam-6159	250	56	kf	kf	PROPN
ejpam-6159	250	57	(	(	PUNCT
ejpam-6159	250	58	b1	b1	NOUN
ejpam-6159	250	59	+	+	CCONJ
ejpam-6159	250	60	tς∗	tς∗	X
ejpam-6159	250	61	(	(	PUNCT
ejpam-6159	250	62	x	x	NOUN
ejpam-6159	250	63	,	,	PUNCT
ejpam-6159	250	64	b1	b1	NOUN
ejpam-6159	250	65	)	)	PUNCT
ejpam-6159	250	66	)	)	PUNCT
ejpam-6159	251	1	dt	dt	X
ejpam-6159	251	2	.	.	PUNCT
ejpam-6159	252	1	(	(	PUNCT
ejpam-6159	252	2	25	25	NUM
ejpam-6159	252	3	)	)	PUNCT
ejpam-6159	252	4	proof	proof	NOUN
ejpam-6159	252	5	.	.	PUNCT
ejpam-6159	253	1	let	let	VERB
ejpam-6159	253	2	us	we	PRON
ejpam-6159	253	3	assume	assume	VERB
ejpam-6159	253	4	that	that	SCONJ
ejpam-6159	253	5	ς	ς	PROPN
ejpam-6159	253	6	ϱ	ϱ	PROPN
ejpam-6159	253	7	k	k	PROPN
ejpam-6159	253	8	+1	+1	PROPN
ejpam-6159	253	9	∗	∗	NOUN
ejpam-6159	253	10	(	(	PUNCT
ejpam-6159	253	11	x	x	NOUN
ejpam-6159	253	12	,	,	PUNCT
ejpam-6159	253	13	a1	a1	NOUN
ejpam-6159	253	14	)	)	PUNCT
ejpam-6159	253	15	ς∗	ς∗	NOUN
ejpam-6159	253	16	(	(	PUNCT
ejpam-6159	253	17	b1	b1	NOUN
ejpam-6159	253	18	,	,	PUNCT
ejpam-6159	253	19	a1	a1	PROPN
ejpam-6159	253	20	)	)	PUNCT
ejpam-6159	253	21	∫	∫	NOUN
ejpam-6159	253	22	1	1	NUM
ejpam-6159	253	23	0	0	NUM
ejpam-6159	253	24	t	t	PROPN
ejpam-6159	253	25	ϱ	ϱ	PROPN
ejpam-6159	253	26	kf	kf	PROPN
ejpam-6159	253	27	(	(	PUNCT
ejpam-6159	253	28	a1	a1	NOUN
ejpam-6159	253	29	+	+	CCONJ
ejpam-6159	253	30	tς∗	tς∗	X
ejpam-6159	253	31	(	(	PUNCT
ejpam-6159	253	32	x	x	NOUN
ejpam-6159	253	33	,	,	PUNCT
ejpam-6159	253	34	a1	a1	NOUN
ejpam-6159	253	35	)	)	PUNCT
ejpam-6159	253	36	)	)	PUNCT
ejpam-6159	253	37	dt+	dt+	NOUN
ejpam-6159	253	38	ς	ς	PROPN
ejpam-6159	253	39	ϱ	ϱ	PROPN
ejpam-6159	253	40	k	k	PROPN
ejpam-6159	253	41	+1	+1	PROPN
ejpam-6159	253	42	∗	∗	NOUN
ejpam-6159	253	43	(	(	PUNCT
ejpam-6159	253	44	x	x	NOUN
ejpam-6159	253	45	,	,	PUNCT
ejpam-6159	253	46	b1	b1	NOUN
ejpam-6159	253	47	)	)	PUNCT
ejpam-6159	253	48	ς∗	ς∗	PROPN
ejpam-6159	253	49	(	(	PUNCT
ejpam-6159	253	50	b1	b1	NOUN
ejpam-6159	253	51	,	,	PUNCT
ejpam-6159	253	52	a1	a1	PROPN
ejpam-6159	253	53	)	)	PUNCT
ejpam-6159	253	54	∫	∫	NOUN
ejpam-6159	253	55	1	1	NUM
ejpam-6159	253	56	0	0	NUM
ejpam-6159	253	57	t	t	PROPN
ejpam-6159	253	58	ϱ	ϱ	PROPN
ejpam-6159	253	59	kf	kf	PROPN
ejpam-6159	253	60	(	(	PUNCT
ejpam-6159	253	61	b1	b1	NOUN
ejpam-6159	253	62	+	+	CCONJ
ejpam-6159	253	63	tς∗	tς∗	X
ejpam-6159	253	64	(	(	PUNCT
ejpam-6159	253	65	x	x	NOUN
ejpam-6159	253	66	,	,	PUNCT
ejpam-6159	253	67	b1	b1	NOUN
ejpam-6159	253	68	)	)	PUNCT
ejpam-6159	253	69	)	)	PUNCT
ejpam-6159	254	1	dt	dt	X
ejpam-6159	254	2	.	.	PUNCT
ejpam-6159	255	1	(	(	PUNCT
ejpam-6159	255	2	26	26	NUM
ejpam-6159	255	3	)	)	PUNCT
ejpam-6159	255	4	by	by	ADP
ejpam-6159	255	5	using	use	VERB
ejpam-6159	255	6	integrationiby	integrationiby	PROPN
ejpam-6159	255	7	parts	part	NOUN
ejpam-6159	255	8	and	and	CCONJ
ejpam-6159	255	9	suitable	suitable	ADJ
ejpam-6159	255	10	substitution	substitution	NOUN
ejpam-6159	255	11	,	,	PUNCT
ejpam-6159	255	12	we	we	PRON
ejpam-6159	255	13	get	get	VERB
ejpam-6159	255	14	i1	i1	PROPN
ejpam-6159	255	15	=	=	PUNCT
ejpam-6159	256	1	∫	∫	PROPN
ejpam-6159	256	2	1	1	NUM
ejpam-6159	256	3	0	0	NUM
ejpam-6159	256	4	t	t	PROPN
ejpam-6159	256	5	ϱ	ϱ	PROPN
ejpam-6159	256	6	kf	kf	PROPN
ejpam-6159	256	7	(	(	PUNCT
ejpam-6159	256	8	a1	a1	NOUN
ejpam-6159	256	9	+	+	CCONJ
ejpam-6159	256	10	tς∗	tς∗	X
ejpam-6159	256	11	(	(	PUNCT
ejpam-6159	256	12	x	x	NOUN
ejpam-6159	256	13	,	,	PUNCT
ejpam-6159	256	14	a1	a1	NOUN
ejpam-6159	256	15	)	)	PUNCT
ejpam-6159	256	16	)	)	PUNCT
ejpam-6159	257	1	dt	dt	NOUN
ejpam-6159	258	1	=	=	SYM
ejpam-6159	258	2	f	f	PROPN
ejpam-6159	258	3	(	(	PUNCT
ejpam-6159	258	4	a1	a1	NOUN
ejpam-6159	258	5	+	+	CCONJ
ejpam-6159	258	6	ς∗	ς∗	PROPN
ejpam-6159	258	7	(	(	PUNCT
ejpam-6159	258	8	x	x	NOUN
ejpam-6159	258	9	,	,	PUNCT
ejpam-6159	258	10	a1	a1	NOUN
ejpam-6159	258	11	)	)	PUNCT
ejpam-6159	258	12	)	)	PUNCT
ejpam-6159	258	13	ς∗	ς∗	NOUN
ejpam-6159	258	14	(	(	PUNCT
ejpam-6159	258	15	x	x	NOUN
ejpam-6159	258	16	,	,	PUNCT
ejpam-6159	258	17	a1	a1	PROPN
ejpam-6159	258	18	)	)	PUNCT
ejpam-6159	258	19	−	−	PROPN
ejpam-6159	258	20	γk	γk	NOUN
ejpam-6159	258	21	(	(	PUNCT
ejpam-6159	258	22	ϱ+	ϱ+	X
ejpam-6159	258	23	k	k	NOUN
ejpam-6159	258	24	)	)	PUNCT
ejpam-6159	258	25	ς	ς	PROPN
ejpam-6159	258	26	ϱ	ϱ	PROPN
ejpam-6159	258	27	k	k	X
ejpam-6159	258	28	+1	+1	PROPN
ejpam-6159	258	29	∗	∗	NOUN
ejpam-6159	258	30	(	(	PUNCT
ejpam-6159	258	31	x	x	NOUN
ejpam-6159	258	32	,	,	PUNCT
ejpam-6159	258	33	a1	a1	PROPN
ejpam-6159	258	34	)	)	PUNCT
ejpam-6159	258	35	.jϱ,k	.jϱ,k	PUNCT
ejpam-6159	259	1	(	(	PUNCT
ejpam-6159	259	2	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	259	3	,	,	PUNCT
ejpam-6159	259	4	a1	a1	NOUN
ejpam-6159	259	5	)	)	PUNCT
ejpam-6159	259	6	)	)	PUNCT
ejpam-6159	260	1	−	−	PROPN
ejpam-6159	260	2	f	f	X
ejpam-6159	260	3	(	(	PUNCT
ejpam-6159	260	4	a1	a1	PROPN
ejpam-6159	260	5	)	)	PUNCT
ejpam-6159	260	6	.	.	PUNCT
ejpam-6159	261	1	(	(	PUNCT
ejpam-6159	261	2	27	27	NUM
ejpam-6159	261	3	)	)	PUNCT
ejpam-6159	261	4	similarly	similarly	ADV
ejpam-6159	261	5	,	,	PUNCT
ejpam-6159	261	6	we	we	PRON
ejpam-6159	261	7	can	can	AUX
ejpam-6159	261	8	find	find	VERB
ejpam-6159	261	9	i2	i2	PROPN
ejpam-6159	261	10	=	=	SYM
ejpam-6159	262	1	∫	∫	PROPN
ejpam-6159	262	2	1	1	NUM
ejpam-6159	262	3	0	0	NUM
ejpam-6159	262	4	t	t	PROPN
ejpam-6159	262	5	ϱ	ϱ	PROPN
ejpam-6159	262	6	kf	kf	PROPN
ejpam-6159	262	7	(	(	PUNCT
ejpam-6159	262	8	b1	b1	NOUN
ejpam-6159	262	9	+	+	CCONJ
ejpam-6159	262	10	tς∗	tς∗	X
ejpam-6159	262	11	(	(	PUNCT
ejpam-6159	262	12	x	x	NOUN
ejpam-6159	262	13	,	,	PUNCT
ejpam-6159	262	14	b1	b1	NOUN
ejpam-6159	262	15	)	)	PUNCT
ejpam-6159	262	16	)	)	PUNCT
ejpam-6159	263	1	dt	dt	NOUN
ejpam-6159	264	1	=	=	SYM
ejpam-6159	264	2	f	f	PROPN
ejpam-6159	264	3	(	(	PUNCT
ejpam-6159	264	4	b1	b1	NOUN
ejpam-6159	264	5	+	+	CCONJ
ejpam-6159	264	6	ς∗	ς∗	PROPN
ejpam-6159	264	7	(	(	PUNCT
ejpam-6159	264	8	x	x	NOUN
ejpam-6159	264	9	,	,	PUNCT
ejpam-6159	264	10	b1	b1	NOUN
ejpam-6159	264	11	)	)	PUNCT
ejpam-6159	264	12	)	)	PUNCT
ejpam-6159	264	13	ς∗	ς∗	PROPN
ejpam-6159	264	14	(	(	PUNCT
ejpam-6159	264	15	x	x	NOUN
ejpam-6159	264	16	,	,	PUNCT
ejpam-6159	264	17	b1	b1	NOUN
ejpam-6159	264	18	)	)	PUNCT
ejpam-6159	264	19	−	−	PROPN
ejpam-6159	264	20	γk	γk	NOUN
ejpam-6159	264	21	(	(	PUNCT
ejpam-6159	264	22	ϱ+	ϱ+	X
ejpam-6159	264	23	k	k	NOUN
ejpam-6159	264	24	)	)	PUNCT
ejpam-6159	264	25	ς	ς	PROPN
ejpam-6159	264	26	ϱ	ϱ	PROPN
ejpam-6159	264	27	k	k	X
ejpam-6159	264	28	+1	+1	PROPN
ejpam-6159	264	29	∗	∗	NOUN
ejpam-6159	264	30	(	(	PUNCT
ejpam-6159	264	31	x	x	NOUN
ejpam-6159	264	32	,	,	PUNCT
ejpam-6159	264	33	b1	b1	NOUN
ejpam-6159	264	34	)	)	PUNCT
ejpam-6159	264	35	.jϱ,k	.jϱ,k	PUNCT
ejpam-6159	264	36	(	(	PUNCT
ejpam-6159	264	37	b1+ς∗(x	b1+ς∗(x	X
ejpam-6159	264	38	,	,	PUNCT
ejpam-6159	264	39	b1	b1	NOUN
ejpam-6159	264	40	)	)	PUNCT
ejpam-6159	264	41	)	)	PUNCT
ejpam-6159	265	1	+	+	CCONJ
ejpam-6159	265	2	f	f	X
ejpam-6159	265	3	(	(	PUNCT
ejpam-6159	265	4	a1	a1	NOUN
ejpam-6159	265	5	+	+	CCONJ
ejpam-6159	265	6	ς∗	ς∗	PROPN
ejpam-6159	265	7	(	(	PUNCT
ejpam-6159	265	8	b1	b1	NOUN
ejpam-6159	265	9	,	,	PUNCT
ejpam-6159	265	10	a1	a1	NOUN
ejpam-6159	265	11	)	)	PUNCT
ejpam-6159	265	12	)	)	PUNCT
ejpam-6159	265	13	.	.	PUNCT
ejpam-6159	266	1	(	(	PUNCT
ejpam-6159	266	2	28	28	X
ejpam-6159	266	3	)	)	PUNCT
ejpam-6159	266	4	substituting	substitute	VERB
ejpam-6159	266	5	the	the	DET
ejpam-6159	266	6	values	value	NOUN
ejpam-6159	266	7	of	of	ADP
ejpam-6159	266	8	i1	i1	PROPN
ejpam-6159	266	9	and	and	CCONJ
ejpam-6159	266	10	i2	i2	PROPN
ejpam-6159	266	11	in	in	ADP
ejpam-6159	266	12	(	(	PUNCT
ejpam-6159	266	13	26	26	NUM
ejpam-6159	266	14	)	)	PUNCT
ejpam-6159	266	15	,	,	PUNCT
ejpam-6159	266	16	we	we	PRON
ejpam-6159	266	17	can	can	AUX
ejpam-6159	266	18	get	get	VERB
ejpam-6159	266	19	(	(	PUNCT
ejpam-6159	266	20	25	25	NUM
ejpam-6159	266	21	)	)	PUNCT
ejpam-6159	266	22	.	.	PUNCT
ejpam-6159	267	1	j.	j.	PROPN
ejpam-6159	267	2	nasir	nasir	PROPN
ejpam-6159	267	3	et	et	PROPN
ejpam-6159	267	4	al	al	PROPN
ejpam-6159	267	5	.	.	PUNCT
ejpam-6159	267	6	/	/	SYM
ejpam-6159	267	7	eur	eur	PROPN
ejpam-6159	267	8	.	.	PUNCT
ejpam-6159	268	1	j.	j.	PROPN
ejpam-6159	268	2	pure	pure	PROPN
ejpam-6159	268	3	appl	appl	PROPN
ejpam-6159	268	4	.	.	PROPN
ejpam-6159	268	5	math	math	PROPN
ejpam-6159	268	6	,	,	PUNCT
ejpam-6159	268	7	18	18	NUM
ejpam-6159	268	8	(	(	PUNCT
ejpam-6159	268	9	3	3	NUM
ejpam-6159	268	10	)	)	PUNCT
ejpam-6159	268	11	(	(	PUNCT
ejpam-6159	268	12	2025	2025	NUM
ejpam-6159	268	13	)	)	PUNCT
ejpam-6159	268	14	,	,	PUNCT
ejpam-6159	268	15	6159	6159	NUM
ejpam-6159	268	16	10	10	NUM
ejpam-6159	268	17	of	of	ADP
ejpam-6159	268	18	26	26	NUM
ejpam-6159	268	19	theorem	theorem	NOUN
ejpam-6159	268	20	3	3	X
ejpam-6159	268	21	.	.	PUNCT
ejpam-6159	268	22	suppose	suppose	VERB
ejpam-6159	268	23	f	f	X
ejpam-6159	268	24	:	:	PUNCT
ejpam-6159	268	25	x	x	PUNCT
ejpam-6159	268	26	=	=	PUNCT
ejpam-6159	269	1	[	[	X
ejpam-6159	269	2	a1	a1	NOUN
ejpam-6159	269	3	,	,	PUNCT
ejpam-6159	269	4	a1	a1	NOUN
ejpam-6159	269	5	+	+	CCONJ
ejpam-6159	269	6	ς∗	ς∗	PROPN
ejpam-6159	269	7	(	(	PUNCT
ejpam-6159	269	8	b1	b1	NOUN
ejpam-6159	269	9	,	,	PUNCT
ejpam-6159	269	10	a1	a1	NOUN
ejpam-6159	269	11	)	)	PUNCT
ejpam-6159	269	12	]	]	PUNCT
ejpam-6159	270	1	→	→	PUNCT
ejpam-6159	270	2	ℜ	ℜ	PROPN
ejpam-6159	270	3	is	be	AUX
ejpam-6159	270	4	a	a	DET
ejpam-6159	270	5	differentiable	differentiable	ADJ
ejpam-6159	270	6	function	function	NOUN
ejpam-6159	270	7	on	on	ADP
ejpam-6159	270	8	xo	xo	PROPN
ejpam-6159	270	9	such	such	ADJ
ejpam-6159	270	10	that	that	SCONJ
ejpam-6159	270	11	f′	f′	PROPN
ejpam-6159	270	12	∈	∈	PROPN
ejpam-6159	270	13	l[a1	l[a1	NOUN
ejpam-6159	270	14	,	,	PUNCT
ejpam-6159	270	15	a1	a1	NOUN
ejpam-6159	270	16	+	+	CCONJ
ejpam-6159	270	17	ς∗	ς∗	PROPN
ejpam-6159	270	18	(	(	PUNCT
ejpam-6159	270	19	b1	b1	NOUN
ejpam-6159	270	20	,	,	PUNCT
ejpam-6159	270	21	a1	a1	NOUN
ejpam-6159	270	22	)	)	PUNCT
ejpam-6159	270	23	]	]	PUNCT
ejpam-6159	270	24	and	and	CCONJ
ejpam-6159	270	25	consideration	consideration	NOUN
ejpam-6159	270	26	with	with	ADP
ejpam-6159	270	27	u∗.	u∗.	PROPN
ejpam-6159	270	28	let	let	VERB
ejpam-6159	270	29	|f′|	|f′|	PROPN
ejpam-6159	270	30	be	be	AUX
ejpam-6159	270	31	a	a	DET
ejpam-6159	270	32	gfpp−s	gfpp−s	NOUN
ejpam-6159	270	33	function	function	NOUN
ejpam-6159	270	34	on	on	ADP
ejpam-6159	270	35	x	x	PUNCT
ejpam-6159	270	36	with	with	ADP
ejpam-6159	270	37	|f′|	|f′|	ADJ
ejpam-6159	270	38	≤	≤	NOUN
ejpam-6159	270	39	s	s	NOUN
ejpam-6159	270	40	,	,	PUNCT
ejpam-6159	270	41	for	for	ADP
ejpam-6159	270	42	all	all	DET
ejpam-6159	270	43	x	x	SYM
ejpam-6159	270	44	∈	∈	PROPN
ejpam-6159	270	45	[	[	X
ejpam-6159	270	46	a1	a1	NOUN
ejpam-6159	270	47	,	,	PUNCT
ejpam-6159	270	48	a1	a1	NOUN
ejpam-6159	270	49	+	+	CCONJ
ejpam-6159	270	50	ς∗	ς∗	PROPN
ejpam-6159	270	51	(	(	PUNCT
ejpam-6159	270	52	b1	b1	NOUN
ejpam-6159	270	53	,	,	PUNCT
ejpam-6159	270	54	a1	a1	NOUN
ejpam-6159	270	55	)	)	PUNCT
ejpam-6159	270	56	]	]	PUNCT
ejpam-6159	270	57	.	.	PUNCT
ejpam-6159	271	1	then	then	ADV
ejpam-6159	271	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	271	3	ς	ς	PROPN
ejpam-6159	271	4	ϱ	ϱ	PROPN
ejpam-6159	271	5	k	k	PROPN
ejpam-6159	271	6	∗	∗	X
ejpam-6159	271	7	(	(	PUNCT
ejpam-6159	271	8	x	x	NOUN
ejpam-6159	271	9	,	,	PUNCT
ejpam-6159	271	10	a1	a1	NOUN
ejpam-6159	271	11	)	)	PUNCT
ejpam-6159	271	12	+	+	CCONJ
ejpam-6159	271	13	ς	ς	PROPN
ejpam-6159	271	14	ϱ	ϱ	PROPN
ejpam-6159	271	15	k	k	PROPN
ejpam-6159	271	16	∗	∗	X
ejpam-6159	271	17	(	(	PUNCT
ejpam-6159	271	18	x	x	NOUN
ejpam-6159	271	19	,	,	PUNCT
ejpam-6159	271	20	b1	b1	NOUN
ejpam-6159	271	21	)	)	PUNCT
ejpam-6159	271	22	ς∗	ς∗	PROPN
ejpam-6159	271	23	(	(	PUNCT
ejpam-6159	271	24	b1	b1	NOUN
ejpam-6159	271	25	,	,	PUNCT
ejpam-6159	271	26	a1	a1	PROPN
ejpam-6159	271	27	)	)	PUNCT
ejpam-6159	271	28	f	f	NOUN
ejpam-6159	271	29	(	(	PUNCT
ejpam-6159	271	30	x)−	x)−	PROPN
ejpam-6159	271	31	γk	γk	PROPN
ejpam-6159	271	32	(	(	PUNCT
ejpam-6159	271	33	ϱ+	ϱ+	X
ejpam-6159	271	34	k	k	NOUN
ejpam-6159	271	35	)	)	PUNCT
ejpam-6159	271	36	ς	ς	PROPN
ejpam-6159	271	37	ϱ	ϱ	PROPN
ejpam-6159	271	38	k	k	PROPN
ejpam-6159	271	39	∗	∗	X
ejpam-6159	271	40	(	(	PUNCT
ejpam-6159	271	41	b1	b1	NOUN
ejpam-6159	271	42	,	,	PUNCT
ejpam-6159	271	43	a1	a1	PROPN
ejpam-6159	271	44	)	)	PUNCT
ejpam-6159	271	45	×	×	NOUN
ejpam-6159	271	46	{	{	PUNCT
ejpam-6159	271	47	jϱ,k	jϱ,k	X
ejpam-6159	271	48	(	(	PUNCT
ejpam-6159	271	49	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	271	50	,	,	PUNCT
ejpam-6159	271	51	a1	a1	NOUN
ejpam-6159	271	52	)	)	PUNCT
ejpam-6159	271	53	)	)	PUNCT
ejpam-6159	272	1	−	−	PROPN
ejpam-6159	272	2	f	f	X
ejpam-6159	272	3	(	(	PUNCT
ejpam-6159	272	4	a1	a1	PROPN
ejpam-6159	272	5	)	)	PUNCT
ejpam-6159	272	6	+	+	NUM
ejpam-6159	272	7	jϱ,k	jϱ,k	X
ejpam-6159	272	8	(	(	PUNCT
ejpam-6159	272	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	272	10	,	,	PUNCT
ejpam-6159	272	11	b1	b1	NOUN
ejpam-6159	272	12	)	)	PUNCT
ejpam-6159	272	13	)	)	PUNCT
ejpam-6159	273	1	+	+	CCONJ
ejpam-6159	273	2	f	f	X
ejpam-6159	273	3	(	(	PUNCT
ejpam-6159	273	4	a1	a1	NOUN
ejpam-6159	273	5	+	+	CCONJ
ejpam-6159	273	6	ς∗	ς∗	PROPN
ejpam-6159	273	7	(	(	PUNCT
ejpam-6159	273	8	b1	b1	NOUN
ejpam-6159	273	9	,	,	PUNCT
ejpam-6159	273	10	a1	a1	NOUN
ejpam-6159	273	11	)	)	PUNCT
ejpam-6159	273	12	)	)	PUNCT
ejpam-6159	273	13	}	}	PUNCT
ejpam-6159	273	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	273	15	≤	≤	NOUN
ejpam-6159	273	16	(	(	PUNCT
ejpam-6159	273	17	ς	ς	PROPN
ejpam-6159	273	18	ϱ	ϱ	PROPN
ejpam-6159	273	19	k	k	PROPN
ejpam-6159	273	20	+1	+1	PROPN
ejpam-6159	273	21	∗	∗	NOUN
ejpam-6159	273	22	(	(	PUNCT
ejpam-6159	273	23	x	x	NOUN
ejpam-6159	273	24	,	,	PUNCT
ejpam-6159	273	25	a1	a1	NOUN
ejpam-6159	273	26	)	)	PUNCT
ejpam-6159	273	27	+	+	CCONJ
ejpam-6159	273	28	ς	ς	PROPN
ejpam-6159	273	29	ϱ	ϱ	PROPN
ejpam-6159	273	30	k	k	PROPN
ejpam-6159	273	31	+1	+1	PROPN
ejpam-6159	273	32	∗	∗	NOUN
ejpam-6159	273	33	(	(	PUNCT
ejpam-6159	273	34	x	x	NOUN
ejpam-6159	273	35	,	,	PUNCT
ejpam-6159	273	36	b1	b1	NOUN
ejpam-6159	273	37	)	)	PUNCT
ejpam-6159	273	38	ς∗	ς∗	PROPN
ejpam-6159	273	39	(	(	PUNCT
ejpam-6159	273	40	b1	b1	NOUN
ejpam-6159	273	41	,	,	PUNCT
ejpam-6159	273	42	a1	a1	NOUN
ejpam-6159	273	43	)	)	PUNCT
ejpam-6159	273	44	)	)	PUNCT
ejpam-6159	274	1	×	×	PROPN
ejpam-6159	274	2	s∑n	s∑n	NOUN
ejpam-6159	274	3	i=1	i=1	PRON
ejpam-6159	274	4	ai	ai	VERB
ejpam-6159	274	5	.	.	PUNCT
ejpam-6159	275	1	n∑	n∑	INTJ
ejpam-6159	276	1	i=1	i=1	PROPN
ejpam-6159	276	2	ai	ai	VERB
ejpam-6159	276	3	[	[	PUNCT
ejpam-6159	276	4	∫	∫	PROPN
ejpam-6159	276	5	1	1	NUM
ejpam-6159	276	6	0	0	NUM
ejpam-6159	276	7	t	t	PROPN
ejpam-6159	276	8	ϱ	ϱ	PROPN
ejpam-6159	276	9	k	k	X
ejpam-6159	276	10	(	(	PUNCT
ejpam-6159	276	11	(	(	PUNCT
ejpam-6159	276	12	1−	1−	NUM
ejpam-6159	276	13	s	s	X
ejpam-6159	276	14	(	(	PUNCT
ejpam-6159	276	15	1−	1−	NUM
ejpam-6159	276	16	t	t	NOUN
ejpam-6159	276	17	)	)	PUNCT
ejpam-6159	276	18	)	)	PUNCT
ejpam-6159	276	19	1	1	NUM
ejpam-6159	276	20	i	i	NOUN
ejpam-6159	276	21	)	)	PUNCT
ejpam-6159	277	1	dt+	dt+	NOUN
ejpam-6159	277	2	∫	∫	PROPN
ejpam-6159	277	3	1	1	NUM
ejpam-6159	277	4	0	0	NUM
ejpam-6159	277	5	t	t	PROPN
ejpam-6159	277	6	ϱ	ϱ	PROPN
ejpam-6159	277	7	k	k	X
ejpam-6159	277	8	(	(	PUNCT
ejpam-6159	277	9	1−	1−	NUM
ejpam-6159	277	10	st	st	NOUN
ejpam-6159	277	11	)	)	PUNCT
ejpam-6159	277	12	1	1	NUM
ejpam-6159	278	1	i	i	PRON
ejpam-6159	278	2	dt	dt	X
ejpam-6159	278	3	]	]	PUNCT
ejpam-6159	278	4	.	.	PUNCT
ejpam-6159	279	1	(	(	PUNCT
ejpam-6159	279	2	29	29	NUM
ejpam-6159	279	3	)	)	PUNCT
ejpam-6159	279	4	proof	proof	NOUN
ejpam-6159	279	5	.	.	PUNCT
ejpam-6159	280	1	from	from	ADP
ejpam-6159	280	2	lemma	lemma	PROPN
ejpam-6159	280	3	1	1	NUM
ejpam-6159	280	4	and	and	CCONJ
ejpam-6159	280	5	a	a	DET
ejpam-6159	280	6	modulus	modulus	ADJ
ejpam-6159	280	7	property	property	NOUN
ejpam-6159	280	8	of	of	ADP
ejpam-6159	280	9	the	the	DET
ejpam-6159	280	10	gfpp−s	gfpp−s	PROPN
ejpam-6159	280	11	function	function	NOUN
ejpam-6159	280	12	|f′|	|f′|	PROPN
ejpam-6159	280	13	,	,	PUNCT
ejpam-6159	280	14	one	one	PRON
ejpam-6159	280	15	has	have	VERB
ejpam-6159	280	16	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	280	17	ς	ς	PROPN
ejpam-6159	280	18	ϱ	ϱ	PROPN
ejpam-6159	280	19	k	k	PROPN
ejpam-6159	280	20	∗	∗	X
ejpam-6159	280	21	(	(	PUNCT
ejpam-6159	280	22	x	x	NOUN
ejpam-6159	280	23	,	,	PUNCT
ejpam-6159	280	24	a1	a1	NOUN
ejpam-6159	280	25	)	)	PUNCT
ejpam-6159	280	26	+	+	CCONJ
ejpam-6159	281	1	ς	ς	PROPN
ejpam-6159	281	2	ϱ	ϱ	PROPN
ejpam-6159	281	3	k	k	PROPN
ejpam-6159	281	4	∗	∗	X
ejpam-6159	281	5	(	(	PUNCT
ejpam-6159	281	6	x	x	NOUN
ejpam-6159	281	7	,	,	PUNCT
ejpam-6159	281	8	b1	b1	NOUN
ejpam-6159	281	9	)	)	PUNCT
ejpam-6159	281	10	ς∗	ς∗	PROPN
ejpam-6159	281	11	(	(	PUNCT
ejpam-6159	281	12	b1	b1	NOUN
ejpam-6159	281	13	,	,	PUNCT
ejpam-6159	281	14	a1	a1	PROPN
ejpam-6159	281	15	)	)	PUNCT
ejpam-6159	281	16	f	f	NOUN
ejpam-6159	281	17	(	(	PUNCT
ejpam-6159	281	18	x)−	x)−	PROPN
ejpam-6159	281	19	γk	γk	PROPN
ejpam-6159	281	20	(	(	PUNCT
ejpam-6159	281	21	ϱ+	ϱ+	X
ejpam-6159	281	22	k	k	NOUN
ejpam-6159	281	23	)	)	PUNCT
ejpam-6159	281	24	ς	ς	PROPN
ejpam-6159	281	25	ϱ	ϱ	PROPN
ejpam-6159	281	26	k	k	PROPN
ejpam-6159	281	27	∗	∗	X
ejpam-6159	281	28	(	(	PUNCT
ejpam-6159	281	29	b1	b1	NOUN
ejpam-6159	281	30	,	,	PUNCT
ejpam-6159	281	31	a1	a1	PROPN
ejpam-6159	281	32	)	)	PUNCT
ejpam-6159	281	33	×	×	NOUN
ejpam-6159	281	34	{	{	PUNCT
ejpam-6159	281	35	jϱ,k	jϱ,k	X
ejpam-6159	281	36	(	(	PUNCT
ejpam-6159	281	37	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	281	38	,	,	PUNCT
ejpam-6159	281	39	a1	a1	NOUN
ejpam-6159	281	40	)	)	PUNCT
ejpam-6159	281	41	)	)	PUNCT
ejpam-6159	282	1	−	−	PROPN
ejpam-6159	282	2	f	f	X
ejpam-6159	282	3	(	(	PUNCT
ejpam-6159	282	4	a1	a1	PROPN
ejpam-6159	282	5	)	)	PUNCT
ejpam-6159	282	6	+	+	NUM
ejpam-6159	282	7	jϱ,k	jϱ,k	X
ejpam-6159	282	8	(	(	PUNCT
ejpam-6159	282	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	282	10	,	,	PUNCT
ejpam-6159	282	11	b1	b1	NOUN
ejpam-6159	282	12	)	)	PUNCT
ejpam-6159	282	13	)	)	PUNCT
ejpam-6159	283	1	+	+	CCONJ
ejpam-6159	283	2	f	f	X
ejpam-6159	283	3	(	(	PUNCT
ejpam-6159	283	4	a1	a1	NOUN
ejpam-6159	283	5	+	+	CCONJ
ejpam-6159	283	6	ς∗	ς∗	PROPN
ejpam-6159	283	7	(	(	PUNCT
ejpam-6159	283	8	b1	b1	NOUN
ejpam-6159	283	9	,	,	PUNCT
ejpam-6159	283	10	a1	a1	NOUN
ejpam-6159	283	11	)	)	PUNCT
ejpam-6159	283	12	)	)	PUNCT
ejpam-6159	283	13	}	}	PUNCT
ejpam-6159	283	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	283	15	≤	≤	NUM
ejpam-6159	283	16	ς	ς	PROPN
ejpam-6159	283	17	ϱ	ϱ	PROPN
ejpam-6159	283	18	k	k	PROPN
ejpam-6159	283	19	+1	+1	PROPN
ejpam-6159	283	20	∗	∗	NOUN
ejpam-6159	283	21	(	(	PUNCT
ejpam-6159	283	22	x	x	NOUN
ejpam-6159	283	23	,	,	PUNCT
ejpam-6159	283	24	a1	a1	NOUN
ejpam-6159	283	25	)	)	PUNCT
ejpam-6159	283	26	ς∗	ς∗	NOUN
ejpam-6159	283	27	(	(	PUNCT
ejpam-6159	283	28	b1	b1	NOUN
ejpam-6159	283	29	,	,	PUNCT
ejpam-6159	283	30	a1	a1	PROPN
ejpam-6159	283	31	)	)	PUNCT
ejpam-6159	283	32	∫	∫	NOUN
ejpam-6159	283	33	1	1	NUM
ejpam-6159	283	34	0	0	NUM
ejpam-6159	283	35	t	t	PROPN
ejpam-6159	283	36	ϱ	ϱ	ADP
ejpam-6159	283	37	k	k	PROPN
ejpam-6159	283	38	∣∣f′	∣∣f′	PROPN
ejpam-6159	283	39	(	(	PUNCT
ejpam-6159	283	40	a1	a1	NOUN
ejpam-6159	283	41	+	+	CCONJ
ejpam-6159	283	42	tς∗	tς∗	X
ejpam-6159	283	43	(	(	PUNCT
ejpam-6159	283	44	x	x	NOUN
ejpam-6159	283	45	,	,	PUNCT
ejpam-6159	283	46	a1	a1	NOUN
ejpam-6159	283	47	)	)	PUNCT
ejpam-6159	283	48	)	)	PUNCT
ejpam-6159	284	1	∣∣dt+	∣∣dt+	PROPN
ejpam-6159	284	2	ς	ς	PROPN
ejpam-6159	284	3	ϱ	ϱ	PROPN
ejpam-6159	284	4	k	k	PROPN
ejpam-6159	284	5	+1	+1	PROPN
ejpam-6159	284	6	∗	∗	NOUN
ejpam-6159	284	7	(	(	PUNCT
ejpam-6159	284	8	x	x	NOUN
ejpam-6159	284	9	,	,	PUNCT
ejpam-6159	284	10	b1	b1	NOUN
ejpam-6159	284	11	)	)	PUNCT
ejpam-6159	284	12	ς∗	ς∗	PROPN
ejpam-6159	284	13	(	(	PUNCT
ejpam-6159	284	14	b1	b1	NOUN
ejpam-6159	284	15	,	,	PUNCT
ejpam-6159	284	16	a1	a1	PROPN
ejpam-6159	284	17	)	)	PUNCT
ejpam-6159	284	18	∫	∫	NOUN
ejpam-6159	284	19	1	1	NUM
ejpam-6159	284	20	0	0	NUM
ejpam-6159	284	21	t	t	PROPN
ejpam-6159	284	22	ϱ	ϱ	ADP
ejpam-6159	284	23	k	k	PROPN
ejpam-6159	284	24	∣∣f′	∣∣f′	PROPN
ejpam-6159	284	25	(	(	PUNCT
ejpam-6159	284	26	b1	b1	NOUN
ejpam-6159	284	27	+	+	CCONJ
ejpam-6159	284	28	tς∗	tς∗	X
ejpam-6159	284	29	(	(	PUNCT
ejpam-6159	284	30	x	x	NOUN
ejpam-6159	284	31	,	,	PUNCT
ejpam-6159	284	32	b1	b1	NOUN
ejpam-6159	284	33	)	)	PUNCT
ejpam-6159	284	34	)	)	PUNCT
ejpam-6159	285	1	∣∣dt	∣∣dt	PROPN
ejpam-6159	285	2	≤	≤	ADV
ejpam-6159	285	3	ς	ς	PROPN
ejpam-6159	285	4	ϱ	ϱ	PROPN
ejpam-6159	285	5	k	k	PROPN
ejpam-6159	285	6	+1	+1	PROPN
ejpam-6159	285	7	∗	∗	NOUN
ejpam-6159	285	8	(	(	PUNCT
ejpam-6159	285	9	x	x	NOUN
ejpam-6159	285	10	,	,	PUNCT
ejpam-6159	285	11	a1	a1	NOUN
ejpam-6159	285	12	)	)	PUNCT
ejpam-6159	285	13	ς∗	ς∗	NOUN
ejpam-6159	285	14	(	(	PUNCT
ejpam-6159	285	15	b1	b1	NOUN
ejpam-6159	285	16	,	,	PUNCT
ejpam-6159	285	17	a1	a1	PROPN
ejpam-6159	285	18	)	)	PUNCT
ejpam-6159	285	19	∫	∫	NOUN
ejpam-6159	285	20	1	1	NUM
ejpam-6159	285	21	0	0	NUM
ejpam-6159	285	22	t	t	PROPN
ejpam-6159	285	23	ϱ	ϱ	PROPN
ejpam-6159	285	24	k	k	PROPN
ejpam-6159	286	1	[	[	X
ejpam-6159	286	2	∑n	∑n	NOUN
ejpam-6159	286	3	i=1	i=1	PROPN
ejpam-6159	286	4	ai	ai	VERB
ejpam-6159	286	5	(	(	PUNCT
ejpam-6159	286	6	1−	1−	NUM
ejpam-6159	286	7	s	s	X
ejpam-6159	286	8	(	(	PUNCT
ejpam-6159	286	9	1−	1−	NUM
ejpam-6159	286	10	t	t	NOUN
ejpam-6159	286	11	)	)	PUNCT
ejpam-6159	286	12	)	)	PUNCT
ejpam-6159	286	13	1	1	NUM
ejpam-6159	286	14	i∑n	i∑n	PROPN
ejpam-6159	286	15	i=1	i=1	PROPN
ejpam-6159	286	16	ai	ai	VERB
ejpam-6159	286	17	∣∣f′	∣∣f′	NOUN
ejpam-6159	286	18	(	(	PUNCT
ejpam-6159	286	19	x	x	NOUN
ejpam-6159	286	20	)	)	PUNCT
ejpam-6159	286	21	∣∣+	∣∣+	PROPN
ejpam-6159	287	1	∑n	∑n	PROPN
ejpam-6159	287	2	i=1	i=1	PROPN
ejpam-6159	287	3	ai	ai	VERB
ejpam-6159	287	4	(	(	PUNCT
ejpam-6159	287	5	1−	1−	NUM
ejpam-6159	287	6	st	st	NOUN
ejpam-6159	287	7	)	)	PUNCT
ejpam-6159	287	8	1	1	NUM
ejpam-6159	287	9	i∑n	i∑n	PROPN
ejpam-6159	287	10	i=1	i=1	PROPN
ejpam-6159	287	11	ai	ai	VERB
ejpam-6159	287	12	∣∣f′	∣∣f′	NOUN
ejpam-6159	287	13	(	(	PUNCT
ejpam-6159	287	14	a1	a1	NOUN
ejpam-6159	287	15	)	)	PUNCT
ejpam-6159	287	16	∣∣	∣∣	X
ejpam-6159	287	17	]	]	PUNCT
ejpam-6159	287	18	dt	dt	X
ejpam-6159	288	1	+	+	CCONJ
ejpam-6159	288	2	ς	ς	PROPN
ejpam-6159	288	3	ϱ	ϱ	PROPN
ejpam-6159	288	4	k	k	PROPN
ejpam-6159	288	5	+1	+1	PROPN
ejpam-6159	288	6	∗	∗	NOUN
ejpam-6159	288	7	(	(	PUNCT
ejpam-6159	288	8	x	x	NOUN
ejpam-6159	288	9	,	,	PUNCT
ejpam-6159	288	10	b1	b1	NOUN
ejpam-6159	288	11	)	)	PUNCT
ejpam-6159	288	12	ς∗	ς∗	PROPN
ejpam-6159	288	13	(	(	PUNCT
ejpam-6159	288	14	b1	b1	NOUN
ejpam-6159	288	15	,	,	PUNCT
ejpam-6159	288	16	a1	a1	PROPN
ejpam-6159	288	17	)	)	PUNCT
ejpam-6159	288	18	∫	∫	NOUN
ejpam-6159	289	1	1	1	NUM
ejpam-6159	289	2	0	0	NUM
ejpam-6159	289	3	t	t	PROPN
ejpam-6159	289	4	ϱ	ϱ	PROPN
ejpam-6159	289	5	k	k	PROPN
ejpam-6159	290	1	[	[	X
ejpam-6159	290	2	∑n	∑n	NOUN
ejpam-6159	290	3	i=1	i=1	PROPN
ejpam-6159	290	4	ai	ai	VERB
ejpam-6159	290	5	(	(	PUNCT
ejpam-6159	290	6	1−	1−	NUM
ejpam-6159	290	7	s	s	X
ejpam-6159	290	8	(	(	PUNCT
ejpam-6159	290	9	1−	1−	NUM
ejpam-6159	290	10	t	t	NOUN
ejpam-6159	290	11	)	)	PUNCT
ejpam-6159	290	12	)	)	PUNCT
ejpam-6159	290	13	1	1	NUM
ejpam-6159	290	14	i∑n	i∑n	PROPN
ejpam-6159	290	15	i=1	i=1	PROPN
ejpam-6159	290	16	ai	ai	VERB
ejpam-6159	290	17	∣∣f′	∣∣f′	NOUN
ejpam-6159	290	18	(	(	PUNCT
ejpam-6159	290	19	x	x	NOUN
ejpam-6159	290	20	)	)	PUNCT
ejpam-6159	290	21	∣∣+	∣∣+	PROPN
ejpam-6159	291	1	∑n	∑n	PROPN
ejpam-6159	291	2	i=1	i=1	PROPN
ejpam-6159	291	3	ai	ai	VERB
ejpam-6159	291	4	(	(	PUNCT
ejpam-6159	291	5	1−	1−	NUM
ejpam-6159	291	6	st	st	NOUN
ejpam-6159	291	7	)	)	PUNCT
ejpam-6159	291	8	1	1	NUM
ejpam-6159	291	9	i∑n	i∑n	PROPN
ejpam-6159	291	10	i=1	i=1	PROPN
ejpam-6159	291	11	ai	ai	VERB
ejpam-6159	291	12	∣∣f′	∣∣f′	NOUN
ejpam-6159	291	13	(	(	PUNCT
ejpam-6159	291	14	b1	b1	NOUN
ejpam-6159	291	15	)	)	PUNCT
ejpam-6159	291	16	∣∣	∣∣	X
ejpam-6159	292	1	]	]	PUNCT
ejpam-6159	292	2	dt	dt	X
ejpam-6159	292	3	≤	≤	NUM
ejpam-6159	292	4	(	(	PUNCT
ejpam-6159	292	5	ς	ς	PROPN
ejpam-6159	292	6	ϱ	ϱ	PROPN
ejpam-6159	292	7	k	k	PROPN
ejpam-6159	292	8	+1	+1	PROPN
ejpam-6159	292	9	∗	∗	NOUN
ejpam-6159	292	10	(	(	PUNCT
ejpam-6159	292	11	x	x	NOUN
ejpam-6159	292	12	,	,	PUNCT
ejpam-6159	292	13	a1	a1	NOUN
ejpam-6159	292	14	)	)	PUNCT
ejpam-6159	292	15	+	+	CCONJ
ejpam-6159	292	16	ς	ς	PROPN
ejpam-6159	292	17	ϱ	ϱ	PROPN
ejpam-6159	292	18	k	k	PROPN
ejpam-6159	292	19	+1	+1	PROPN
ejpam-6159	292	20	∗	∗	NOUN
ejpam-6159	292	21	(	(	PUNCT
ejpam-6159	292	22	x	x	NOUN
ejpam-6159	292	23	,	,	PUNCT
ejpam-6159	292	24	b1	b1	NOUN
ejpam-6159	292	25	)	)	PUNCT
ejpam-6159	292	26	ς∗	ς∗	PROPN
ejpam-6159	292	27	(	(	PUNCT
ejpam-6159	292	28	b1	b1	NOUN
ejpam-6159	292	29	,	,	PUNCT
ejpam-6159	292	30	a1	a1	NOUN
ejpam-6159	292	31	)	)	PUNCT
ejpam-6159	292	32	)	)	PUNCT
ejpam-6159	293	1	×	×	PROPN
ejpam-6159	293	2	s∑n	s∑n	NOUN
ejpam-6159	293	3	i=1	i=1	PRON
ejpam-6159	293	4	ai	ai	VERB
ejpam-6159	293	5	.	.	PUNCT
ejpam-6159	294	1	n∑	n∑	INTJ
ejpam-6159	295	1	i=1	i=1	PROPN
ejpam-6159	295	2	ai	ai	VERB
ejpam-6159	295	3	[	[	PUNCT
ejpam-6159	295	4	∫	∫	PROPN
ejpam-6159	295	5	1	1	NUM
ejpam-6159	295	6	0	0	NUM
ejpam-6159	295	7	t	t	PROPN
ejpam-6159	295	8	ϱ	ϱ	PROPN
ejpam-6159	295	9	k	k	X
ejpam-6159	295	10	(	(	PUNCT
ejpam-6159	295	11	(	(	PUNCT
ejpam-6159	295	12	1−	1−	NUM
ejpam-6159	295	13	s	s	X
ejpam-6159	295	14	(	(	PUNCT
ejpam-6159	295	15	1−	1−	NUM
ejpam-6159	295	16	t	t	NOUN
ejpam-6159	295	17	)	)	PUNCT
ejpam-6159	295	18	)	)	PUNCT
ejpam-6159	295	19	1	1	NUM
ejpam-6159	295	20	i	i	NOUN
ejpam-6159	295	21	)	)	PUNCT
ejpam-6159	296	1	dt+	dt+	NOUN
ejpam-6159	296	2	∫	∫	PROPN
ejpam-6159	296	3	1	1	NUM
ejpam-6159	296	4	0	0	NUM
ejpam-6159	296	5	t	t	PROPN
ejpam-6159	296	6	ϱ	ϱ	PROPN
ejpam-6159	296	7	k	k	X
ejpam-6159	296	8	(	(	PUNCT
ejpam-6159	296	9	1−	1−	NUM
ejpam-6159	296	10	st	st	NOUN
ejpam-6159	296	11	)	)	PUNCT
ejpam-6159	296	12	1	1	NUM
ejpam-6159	297	1	i	i	PRON
ejpam-6159	297	2	dt	dt	X
ejpam-6159	297	3	]	]	PUNCT
ejpam-6159	297	4	.	.	PUNCT
ejpam-6159	298	1	(	(	PUNCT
ejpam-6159	298	2	30	30	NUM
ejpam-6159	298	3	)	)	PUNCT
ejpam-6159	298	4	corollary	corollary	NOUN
ejpam-6159	298	5	3	3	NUM
ejpam-6159	298	6	.	.	PUNCT
ejpam-6159	299	1	if	if	SCONJ
ejpam-6159	299	2	we	we	PRON
ejpam-6159	299	3	judge	judge	VERB
ejpam-6159	299	4	the	the	DET
ejpam-6159	299	5	value	value	NOUN
ejpam-6159	299	6	s	s	PART
ejpam-6159	299	7	=	=	SYM
ejpam-6159	299	8	1	1	NUM
ejpam-6159	299	9	initheorem	initheorem	VERB
ejpam-6159	299	10	3	3	NUM
ejpam-6159	299	11	,	,	PUNCT
ejpam-6159	299	12	then	then	ADV
ejpam-6159	299	13	we	we	PRON
ejpam-6159	299	14	have	have	VERB
ejpam-6159	299	15	the	the	DET
ejpam-6159	299	16	followingiinequalities	followingiinequalitie	NOUN
ejpam-6159	299	17	for	for	ADP
ejpam-6159	299	18	gfpp	gfpp	NOUN
ejpam-6159	299	19	function	function	NOUN
ejpam-6159	299	20	with	with	ADP
ejpam-6159	299	21	k−fractionaliintegral	k−fractionaliintegral	PROPN
ejpam-6159	299	22	operators:∣∣∣∣	operators:∣∣∣∣	PROPN
ejpam-6159	299	23	ς	ς	PROPN
ejpam-6159	299	24	ϱ	ϱ	PROPN
ejpam-6159	299	25	k	k	PROPN
ejpam-6159	299	26	∗	∗	X
ejpam-6159	299	27	(	(	PUNCT
ejpam-6159	299	28	x	x	NOUN
ejpam-6159	299	29	,	,	PUNCT
ejpam-6159	299	30	a1	a1	NOUN
ejpam-6159	299	31	)	)	PUNCT
ejpam-6159	299	32	+	+	CCONJ
ejpam-6159	300	1	ς	ς	PROPN
ejpam-6159	300	2	ϱ	ϱ	PROPN
ejpam-6159	300	3	k	k	PROPN
ejpam-6159	300	4	∗	∗	X
ejpam-6159	300	5	(	(	PUNCT
ejpam-6159	300	6	x	x	NOUN
ejpam-6159	300	7	,	,	PUNCT
ejpam-6159	300	8	b1	b1	NOUN
ejpam-6159	300	9	)	)	PUNCT
ejpam-6159	300	10	ς∗	ς∗	PROPN
ejpam-6159	300	11	(	(	PUNCT
ejpam-6159	300	12	b1	b1	NOUN
ejpam-6159	300	13	,	,	PUNCT
ejpam-6159	300	14	a1	a1	PROPN
ejpam-6159	300	15	)	)	PUNCT
ejpam-6159	300	16	f	f	NOUN
ejpam-6159	300	17	(	(	PUNCT
ejpam-6159	300	18	x)−	x)−	PROPN
ejpam-6159	300	19	γk	γk	PROPN
ejpam-6159	300	20	(	(	PUNCT
ejpam-6159	300	21	ϱ+	ϱ+	X
ejpam-6159	300	22	k	k	NOUN
ejpam-6159	300	23	)	)	PUNCT
ejpam-6159	300	24	ς	ς	PROPN
ejpam-6159	300	25	ϱ	ϱ	PROPN
ejpam-6159	300	26	k	k	PROPN
ejpam-6159	300	27	∗	∗	X
ejpam-6159	300	28	(	(	PUNCT
ejpam-6159	300	29	b1	b1	NOUN
ejpam-6159	300	30	,	,	PUNCT
ejpam-6159	300	31	a1	a1	PROPN
ejpam-6159	300	32	)	)	PUNCT
ejpam-6159	300	33	j.	j.	PROPN
ejpam-6159	300	34	nasir	nasir	PROPN
ejpam-6159	300	35	et	et	PROPN
ejpam-6159	300	36	al	al	PROPN
ejpam-6159	300	37	.	.	PUNCT
ejpam-6159	300	38	/	/	SYM
ejpam-6159	300	39	eur	eur	PROPN
ejpam-6159	300	40	.	.	PUNCT
ejpam-6159	301	1	j.	j.	PROPN
ejpam-6159	301	2	pure	pure	PROPN
ejpam-6159	301	3	appl	appl	PROPN
ejpam-6159	301	4	.	.	PROPN
ejpam-6159	301	5	math	math	PROPN
ejpam-6159	301	6	,	,	PUNCT
ejpam-6159	301	7	18	18	NUM
ejpam-6159	301	8	(	(	PUNCT
ejpam-6159	301	9	3	3	NUM
ejpam-6159	301	10	)	)	PUNCT
ejpam-6159	301	11	(	(	PUNCT
ejpam-6159	301	12	2025	2025	NUM
ejpam-6159	301	13	)	)	PUNCT
ejpam-6159	301	14	,	,	PUNCT
ejpam-6159	301	15	6159	6159	NUM
ejpam-6159	301	16	11	11	NUM
ejpam-6159	301	17	of	of	ADP
ejpam-6159	301	18	26	26	NUM
ejpam-6159	301	19	×	×	NOUN
ejpam-6159	301	20	{	{	PUNCT
ejpam-6159	301	21	jϱ,k	jϱ,k	X
ejpam-6159	301	22	(	(	PUNCT
ejpam-6159	301	23	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	301	24	,	,	PUNCT
ejpam-6159	301	25	a1	a1	NOUN
ejpam-6159	301	26	)	)	PUNCT
ejpam-6159	301	27	)	)	PUNCT
ejpam-6159	302	1	−	−	PROPN
ejpam-6159	302	2	f	f	X
ejpam-6159	302	3	(	(	PUNCT
ejpam-6159	302	4	a1	a1	PROPN
ejpam-6159	302	5	)	)	PUNCT
ejpam-6159	302	6	+	+	NUM
ejpam-6159	302	7	jϱ,k	jϱ,k	X
ejpam-6159	302	8	(	(	PUNCT
ejpam-6159	302	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	302	10	,	,	PUNCT
ejpam-6159	302	11	b1	b1	NOUN
ejpam-6159	302	12	)	)	PUNCT
ejpam-6159	302	13	)	)	PUNCT
ejpam-6159	303	1	+	+	CCONJ
ejpam-6159	303	2	f	f	X
ejpam-6159	303	3	(	(	PUNCT
ejpam-6159	303	4	a1	a1	NOUN
ejpam-6159	303	5	+	+	CCONJ
ejpam-6159	303	6	ς∗	ς∗	PROPN
ejpam-6159	303	7	(	(	PUNCT
ejpam-6159	303	8	b1	b1	NOUN
ejpam-6159	303	9	,	,	PUNCT
ejpam-6159	303	10	a1	a1	NOUN
ejpam-6159	303	11	)	)	PUNCT
ejpam-6159	303	12	)	)	PUNCT
ejpam-6159	303	13	}	}	PUNCT
ejpam-6159	303	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	303	15	≤	≤	NOUN
ejpam-6159	303	16	(	(	PUNCT
ejpam-6159	303	17	ς	ς	PROPN
ejpam-6159	303	18	ϱ	ϱ	PROPN
ejpam-6159	303	19	k	k	PROPN
ejpam-6159	303	20	+1	+1	PROPN
ejpam-6159	303	21	∗	∗	NOUN
ejpam-6159	303	22	(	(	PUNCT
ejpam-6159	303	23	x	x	NOUN
ejpam-6159	303	24	,	,	PUNCT
ejpam-6159	303	25	a1	a1	NOUN
ejpam-6159	303	26	)	)	PUNCT
ejpam-6159	303	27	+	+	CCONJ
ejpam-6159	303	28	ς	ς	PROPN
ejpam-6159	303	29	ϱ	ϱ	PROPN
ejpam-6159	303	30	k	k	PROPN
ejpam-6159	303	31	+1	+1	PROPN
ejpam-6159	303	32	∗	∗	NOUN
ejpam-6159	303	33	(	(	PUNCT
ejpam-6159	303	34	x	x	NOUN
ejpam-6159	303	35	,	,	PUNCT
ejpam-6159	303	36	b1	b1	NOUN
ejpam-6159	303	37	)	)	PUNCT
ejpam-6159	303	38	ς∗	ς∗	PROPN
ejpam-6159	303	39	(	(	PUNCT
ejpam-6159	303	40	b1	b1	NOUN
ejpam-6159	303	41	,	,	PUNCT
ejpam-6159	303	42	a1	a1	NOUN
ejpam-6159	303	43	)	)	PUNCT
ejpam-6159	303	44	)	)	PUNCT
ejpam-6159	304	1	s∑n	s∑n	NOUN
ejpam-6159	304	2	i=1	i=1	PRON
ejpam-6159	304	3	ai	ai	VERB
ejpam-6159	304	4	.	.	PUNCT
ejpam-6159	305	1	n∑	n∑	INTJ
ejpam-6159	306	1	i=1	i=1	PROPN
ejpam-6159	306	2	ai	ai	VERB
ejpam-6159	306	3	[	[	PUNCT
ejpam-6159	306	4	∫	∫	PROPN
ejpam-6159	306	5	1	1	NUM
ejpam-6159	306	6	0	0	NUM
ejpam-6159	306	7	t	t	PROPN
ejpam-6159	306	8	ϱ	ϱ	PROPN
ejpam-6159	306	9	k	k	PROPN
ejpam-6159	306	10	t	t	PROPN
ejpam-6159	306	11	1	1	NUM
ejpam-6159	306	12	i	i	PRON
ejpam-6159	306	13	dt+	dt+	NOUN
ejpam-6159	306	14	∫	∫	PROPN
ejpam-6159	306	15	1	1	NUM
ejpam-6159	306	16	0	0	NUM
ejpam-6159	306	17	t	t	PROPN
ejpam-6159	306	18	ϱ	ϱ	PROPN
ejpam-6159	306	19	k	k	X
ejpam-6159	306	20	(	(	PUNCT
ejpam-6159	306	21	1−	1−	NUM
ejpam-6159	306	22	t	t	NOUN
ejpam-6159	306	23	)	)	PUNCT
ejpam-6159	306	24	1	1	NUM
ejpam-6159	307	1	i	i	PRON
ejpam-6159	307	2	dt	dt	X
ejpam-6159	307	3	]	]	PUNCT
ejpam-6159	307	4	.	.	PUNCT
ejpam-6159	308	1	corollary	corollary	ADJ
ejpam-6159	308	2	4	4	NUM
ejpam-6159	308	3	.	.	PUNCT
ejpam-6159	309	1	if	if	SCONJ
ejpam-6159	309	2	we	we	PRON
ejpam-6159	309	3	judge	judge	VERB
ejpam-6159	309	4	the	the	DET
ejpam-6159	309	5	value	value	NOUN
ejpam-6159	309	6	k	k	PROPN
ejpam-6159	309	7	=	=	SYM
ejpam-6159	309	8	1	1	NUM
ejpam-6159	309	9	in	in	ADP
ejpam-6159	309	10	corollary	corollary	ADJ
ejpam-6159	309	11	3	3	NUM
ejpam-6159	309	12	,	,	PUNCT
ejpam-6159	309	13	then	then	ADV
ejpam-6159	309	14	we	we	PRON
ejpam-6159	309	15	have	have	VERB
ejpam-6159	309	16	the	the	DET
ejpam-6159	309	17	following	follow	VERB
ejpam-6159	309	18	inequalities	inequality	NOUN
ejpam-6159	309	19	for	for	ADP
ejpam-6159	309	20	gfpp	gfpp	NOUN
ejpam-6159	309	21	function	function	NOUN
ejpam-6159	309	22	with	with	ADP
ejpam-6159	309	23	rl−fractionaliintegral	rl−fractionaliintegral	PROPN
ejpam-6159	309	24	operators:∣∣∣∣	operators:∣∣∣∣	ADJ
ejpam-6159	309	25	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	309	26	(	(	PUNCT
ejpam-6159	309	27	x	x	NOUN
ejpam-6159	309	28	,	,	PUNCT
ejpam-6159	309	29	a1	a1	PROPN
ejpam-6159	309	30	)	)	PUNCT
ejpam-6159	309	31	+	+	NUM
ejpam-6159	309	32	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	309	33	(	(	PUNCT
ejpam-6159	309	34	x	x	NOUN
ejpam-6159	309	35	,	,	PUNCT
ejpam-6159	309	36	b1	b1	NOUN
ejpam-6159	309	37	)	)	PUNCT
ejpam-6159	309	38	ς∗	ς∗	PROPN
ejpam-6159	309	39	(	(	PUNCT
ejpam-6159	309	40	b1	b1	NOUN
ejpam-6159	309	41	,	,	PUNCT
ejpam-6159	309	42	a1	a1	PROPN
ejpam-6159	309	43	)	)	PUNCT
ejpam-6159	309	44	f	f	NOUN
ejpam-6159	309	45	(	(	PUNCT
ejpam-6159	309	46	x)−	x)−	PROPN
ejpam-6159	309	47	γ	γ	PROPN
ejpam-6159	309	48	(	(	PUNCT
ejpam-6159	309	49	ϱ+	ϱ+	NOUN
ejpam-6159	309	50	1	1	NUM
ejpam-6159	309	51	)	)	PUNCT
ejpam-6159	309	52	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	309	53	(	(	PUNCT
ejpam-6159	309	54	b1	b1	NOUN
ejpam-6159	309	55	,	,	PUNCT
ejpam-6159	309	56	a1	a1	PROPN
ejpam-6159	309	57	)	)	PUNCT
ejpam-6159	309	58	×	×	NOUN
ejpam-6159	309	59	{	{	PUNCT
ejpam-6159	309	60	jϱ	jϱ	NOUN
ejpam-6159	309	61	(	(	PUNCT
ejpam-6159	309	62	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	309	63	,	,	PUNCT
ejpam-6159	309	64	a1	a1	NOUN
ejpam-6159	309	65	)	)	PUNCT
ejpam-6159	309	66	)	)	PUNCT
ejpam-6159	310	1	−	−	PROPN
ejpam-6159	310	2	f	f	X
ejpam-6159	310	3	(	(	PUNCT
ejpam-6159	310	4	a1	a1	PROPN
ejpam-6159	310	5	)	)	PUNCT
ejpam-6159	310	6	+	+	NUM
ejpam-6159	310	7	jϱ	jϱ	ADJ
ejpam-6159	310	8	(	(	PUNCT
ejpam-6159	310	9	b1+ς∗(x	b1+ς∗(x	PROPN
ejpam-6159	310	10	,	,	PUNCT
ejpam-6159	310	11	b1	b1	NOUN
ejpam-6159	310	12	)	)	PUNCT
ejpam-6159	310	13	)	)	PUNCT
ejpam-6159	311	1	+	+	CCONJ
ejpam-6159	311	2	f	f	X
ejpam-6159	311	3	(	(	PUNCT
ejpam-6159	311	4	a1	a1	NOUN
ejpam-6159	311	5	+	+	CCONJ
ejpam-6159	311	6	ς∗	ς∗	PROPN
ejpam-6159	311	7	(	(	PUNCT
ejpam-6159	311	8	b1	b1	NOUN
ejpam-6159	311	9	,	,	PUNCT
ejpam-6159	311	10	a1	a1	NOUN
ejpam-6159	311	11	)	)	PUNCT
ejpam-6159	311	12	)	)	PUNCT
ejpam-6159	311	13	}	}	PUNCT
ejpam-6159	311	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	311	15	≤	≤	NOUN
ejpam-6159	311	16	(	(	PUNCT
ejpam-6159	311	17	ςϱ+1	ςϱ+1	ADV
ejpam-6159	311	18	∗	∗	NOUN
ejpam-6159	311	19	(	(	PUNCT
ejpam-6159	311	20	x	x	NOUN
ejpam-6159	311	21	,	,	PUNCT
ejpam-6159	311	22	a1	a1	NOUN
ejpam-6159	311	23	)	)	PUNCT
ejpam-6159	311	24	+	+	CCONJ
ejpam-6159	311	25	ςϱ+1	ςϱ+1	ADV
ejpam-6159	311	26	∗	∗	NOUN
ejpam-6159	311	27	(	(	PUNCT
ejpam-6159	311	28	x	x	NOUN
ejpam-6159	311	29	,	,	PUNCT
ejpam-6159	311	30	b1	b1	NOUN
ejpam-6159	311	31	)	)	PUNCT
ejpam-6159	311	32	ς∗	ς∗	PROPN
ejpam-6159	311	33	(	(	PUNCT
ejpam-6159	311	34	b1	b1	NOUN
ejpam-6159	311	35	,	,	PUNCT
ejpam-6159	311	36	a1	a1	NOUN
ejpam-6159	311	37	)	)	PUNCT
ejpam-6159	311	38	)	)	PUNCT
ejpam-6159	312	1	s∑n	s∑n	NOUN
ejpam-6159	312	2	i=1	i=1	PRON
ejpam-6159	312	3	ai	ai	VERB
ejpam-6159	312	4	.	.	PUNCT
ejpam-6159	313	1	n∑	n∑	INTJ
ejpam-6159	314	1	i=1	i=1	PROPN
ejpam-6159	314	2	ai	ai	VERB
ejpam-6159	314	3	[	[	PUNCT
ejpam-6159	314	4	∫	∫	PROPN
ejpam-6159	314	5	1	1	NUM
ejpam-6159	314	6	0	0	NUM
ejpam-6159	314	7	tϱt	tϱt	NUM
ejpam-6159	314	8	1	1	NUM
ejpam-6159	314	9	i	i	PRON
ejpam-6159	314	10	dt+	dt+	NOUN
ejpam-6159	314	11	∫	∫	PROPN
ejpam-6159	315	1	1	1	NUM
ejpam-6159	315	2	0	0	NUM
ejpam-6159	315	3	tϱ	tϱ	PRON
ejpam-6159	315	4	(	(	PUNCT
ejpam-6159	315	5	1−	1−	NUM
ejpam-6159	315	6	t	t	NOUN
ejpam-6159	315	7	)	)	PUNCT
ejpam-6159	315	8	1	1	NUM
ejpam-6159	316	1	i	i	PRON
ejpam-6159	316	2	dt	dt	X
ejpam-6159	316	3	]	]	PUNCT
ejpam-6159	316	4	.	.	PUNCT
ejpam-6159	317	1	remark	remark	PROPN
ejpam-6159	317	2	3	3	NUM
ejpam-6159	317	3	.	.	PUNCT
ejpam-6159	318	1	if	if	SCONJ
ejpam-6159	318	2	we	we	PRON
ejpam-6159	318	3	take	take	VERB
ejpam-6159	318	4	ϱ	ϱ	NOUN
ejpam-6159	318	5	=	=	SYM
ejpam-6159	318	6	1	1	NUM
ejpam-6159	318	7	and	and	CCONJ
ejpam-6159	318	8	n	n	CCONJ
ejpam-6159	318	9	=	=	SYM
ejpam-6159	318	10	1	1	NUM
ejpam-6159	318	11	and	and	CCONJ
ejpam-6159	318	12	ς∗(b1	ς∗(b1	NOUN
ejpam-6159	318	13	,	,	PUNCT
ejpam-6159	318	14	a1	a1	NOUN
ejpam-6159	318	15	)	)	PUNCT
ejpam-6159	318	16	=	=	SYM
ejpam-6159	318	17	b1	b1	NOUN
ejpam-6159	318	18	−	−	NOUN
ejpam-6159	318	19	a1	a1	NOUN
ejpam-6159	318	20	,	,	PUNCT
ejpam-6159	318	21	in	in	ADP
ejpam-6159	318	22	corollary	corollary	ADJ
ejpam-6159	318	23	4	4	NUM
ejpam-6159	318	24	,	,	PUNCT
ejpam-6159	318	25	then	then	ADV
ejpam-6159	318	26	one	one	PRON
ejpam-6159	318	27	can	can	AUX
ejpam-6159	318	28	get	get	VERB
ejpam-6159	318	29	the	the	DET
ejpam-6159	318	30	inequalities	inequality	NOUN
ejpam-6159	318	31	(	(	PUNCT
ejpam-6159	318	32	5	5	NUM
ejpam-6159	318	33	)	)	PUNCT
ejpam-6159	318	34	.	.	PUNCT
ejpam-6159	319	1	theorem	theorem	ADJ
ejpam-6159	319	2	4	4	NUM
ejpam-6159	319	3	.	.	PUNCT
ejpam-6159	320	1	suppose	suppose	VERB
ejpam-6159	320	2	f	f	X
ejpam-6159	320	3	:	:	PUNCT
ejpam-6159	320	4	x	x	PUNCT
ejpam-6159	321	1	=	=	NOUN
ejpam-6159	321	2	:	:	PUNCT
ejpam-6159	321	3	[	[	X
ejpam-6159	321	4	a1	a1	NOUN
ejpam-6159	321	5	,	,	PUNCT
ejpam-6159	321	6	a1+ς∗	a1+ς∗	PROPN
ejpam-6159	321	7	(	(	PUNCT
ejpam-6159	321	8	b1	b1	NOUN
ejpam-6159	321	9	,	,	PUNCT
ejpam-6159	321	10	a1	a1	NOUN
ejpam-6159	321	11	)	)	PUNCT
ejpam-6159	321	12	]	]	PUNCT
ejpam-6159	321	13	→	→	PUNCT
ejpam-6159	321	14	ℜ	ℜ	PROPN
ejpam-6159	321	15	is	be	AUX
ejpam-6159	321	16	a	a	DET
ejpam-6159	321	17	differentiable	differentiable	ADJ
ejpam-6159	321	18	function	function	NOUN
ejpam-6159	321	19	function	function	NOUN
ejpam-6159	321	20	on	on	ADP
ejpam-6159	321	21	xo	xo	PROPN
ejpam-6159	321	22	such	such	ADJ
ejpam-6159	321	23	that	that	SCONJ
ejpam-6159	321	24	f′	f′	PROPN
ejpam-6159	321	25	∈	∈	PROPN
ejpam-6159	321	26	l[a1	l[a1	NOUN
ejpam-6159	321	27	,	,	PUNCT
ejpam-6159	321	28	a1	a1	NOUN
ejpam-6159	321	29	+	+	CCONJ
ejpam-6159	321	30	ς∗	ς∗	PROPN
ejpam-6159	321	31	(	(	PUNCT
ejpam-6159	321	32	b1	b1	NOUN
ejpam-6159	321	33	,	,	PUNCT
ejpam-6159	321	34	a1	a1	NOUN
ejpam-6159	321	35	)	)	PUNCT
ejpam-6159	321	36	]	]	PUNCT
ejpam-6159	321	37	and	and	CCONJ
ejpam-6159	321	38	consideration	consideration	NOUN
ejpam-6159	321	39	with	with	ADP
ejpam-6159	321	40	u∗.	u∗.	PROPN
ejpam-6159	321	41	let	let	VERB
ejpam-6159	321	42	for	for	ADP
ejpam-6159	321	43	some	some	PRON
ejpam-6159	321	44	q	q	NOUN
ejpam-6159	321	45	>	>	X
ejpam-6159	321	46	1	1	NUM
ejpam-6159	321	47	,	,	PUNCT
ejpam-6159	321	48	|f′|q	|f′|q	VERB
ejpam-6159	321	49	be	be	AUX
ejpam-6159	321	50	a	a	DET
ejpam-6159	321	51	gfpp−s	gfpp−s	NOUN
ejpam-6159	321	52	function	function	NOUN
ejpam-6159	321	53	on	on	ADP
ejpam-6159	321	54	x	x	PUNCT
ejpam-6159	321	55	with	with	ADP
ejpam-6159	321	56	|f′|	|f′|	ADJ
ejpam-6159	321	57	≤	≤	NOUN
ejpam-6159	321	58	s	s	NOUN
ejpam-6159	321	59	,	,	PUNCT
ejpam-6159	321	60	for	for	ADP
ejpam-6159	321	61	all	all	DET
ejpam-6159	321	62	x	x	SYM
ejpam-6159	321	63	∈	∈	PROPN
ejpam-6159	321	64	[	[	X
ejpam-6159	321	65	a1	a1	NOUN
ejpam-6159	321	66	,	,	PUNCT
ejpam-6159	321	67	a1	a1	NOUN
ejpam-6159	321	68	+	+	CCONJ
ejpam-6159	321	69	ς∗	ς∗	PROPN
ejpam-6159	321	70	(	(	PUNCT
ejpam-6159	321	71	b1	b1	NOUN
ejpam-6159	321	72	,	,	PUNCT
ejpam-6159	321	73	a1	a1	NOUN
ejpam-6159	321	74	)	)	PUNCT
ejpam-6159	321	75	]	]	PUNCT
ejpam-6159	321	76	.	.	PUNCT
ejpam-6159	322	1	then	then	ADV
ejpam-6159	322	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	322	3	ς	ς	PROPN
ejpam-6159	322	4	ϱ	ϱ	PROPN
ejpam-6159	322	5	k	k	PROPN
ejpam-6159	322	6	∗	∗	X
ejpam-6159	322	7	(	(	PUNCT
ejpam-6159	322	8	x	x	NOUN
ejpam-6159	322	9	,	,	PUNCT
ejpam-6159	322	10	a1	a1	NOUN
ejpam-6159	322	11	)	)	PUNCT
ejpam-6159	322	12	+	+	CCONJ
ejpam-6159	322	13	ς	ς	PROPN
ejpam-6159	322	14	ϱ	ϱ	PROPN
ejpam-6159	322	15	k	k	PROPN
ejpam-6159	322	16	∗	∗	X
ejpam-6159	322	17	(	(	PUNCT
ejpam-6159	322	18	x	x	NOUN
ejpam-6159	322	19	,	,	PUNCT
ejpam-6159	322	20	b1	b1	NOUN
ejpam-6159	322	21	)	)	PUNCT
ejpam-6159	322	22	ς∗	ς∗	PROPN
ejpam-6159	322	23	(	(	PUNCT
ejpam-6159	322	24	b1	b1	NOUN
ejpam-6159	322	25	,	,	PUNCT
ejpam-6159	322	26	a1	a1	PROPN
ejpam-6159	322	27	)	)	PUNCT
ejpam-6159	322	28	f	f	NOUN
ejpam-6159	322	29	(	(	PUNCT
ejpam-6159	322	30	x)−	x)−	PROPN
ejpam-6159	322	31	γk	γk	PROPN
ejpam-6159	322	32	(	(	PUNCT
ejpam-6159	322	33	ϱ+	ϱ+	X
ejpam-6159	322	34	k	k	NOUN
ejpam-6159	322	35	)	)	PUNCT
ejpam-6159	322	36	ς	ς	PROPN
ejpam-6159	322	37	ϱ	ϱ	PROPN
ejpam-6159	322	38	k	k	PROPN
ejpam-6159	322	39	∗	∗	X
ejpam-6159	322	40	(	(	PUNCT
ejpam-6159	322	41	b1	b1	NOUN
ejpam-6159	322	42	,	,	PUNCT
ejpam-6159	322	43	a1	a1	PROPN
ejpam-6159	322	44	)	)	PUNCT
ejpam-6159	322	45	×	×	NOUN
ejpam-6159	322	46	{	{	PUNCT
ejpam-6159	322	47	jϱ,k	jϱ,k	X
ejpam-6159	322	48	(	(	PUNCT
ejpam-6159	322	49	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	322	50	,	,	PUNCT
ejpam-6159	322	51	a1	a1	NOUN
ejpam-6159	322	52	)	)	PUNCT
ejpam-6159	322	53	)	)	PUNCT
ejpam-6159	323	1	−	−	PROPN
ejpam-6159	323	2	f	f	X
ejpam-6159	323	3	(	(	PUNCT
ejpam-6159	323	4	a1	a1	PROPN
ejpam-6159	323	5	)	)	PUNCT
ejpam-6159	323	6	+	+	NUM
ejpam-6159	323	7	jϱ,k	jϱ,k	X
ejpam-6159	323	8	(	(	PUNCT
ejpam-6159	323	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	323	10	,	,	PUNCT
ejpam-6159	323	11	b1	b1	NOUN
ejpam-6159	323	12	)	)	PUNCT
ejpam-6159	323	13	)	)	PUNCT
ejpam-6159	324	1	+	+	CCONJ
ejpam-6159	324	2	f	f	X
ejpam-6159	324	3	(	(	PUNCT
ejpam-6159	324	4	a1	a1	NOUN
ejpam-6159	324	5	+	+	CCONJ
ejpam-6159	324	6	ς∗	ς∗	PROPN
ejpam-6159	324	7	(	(	PUNCT
ejpam-6159	324	8	b1	b1	NOUN
ejpam-6159	324	9	,	,	PUNCT
ejpam-6159	324	10	a1	a1	NOUN
ejpam-6159	324	11	)	)	PUNCT
ejpam-6159	324	12	)	)	PUNCT
ejpam-6159	324	13	}	}	PUNCT
ejpam-6159	324	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	324	15	≤	≤	NOUN
ejpam-6159	324	16	(	(	PUNCT
ejpam-6159	324	17	k	k	X
ejpam-6159	324	18	k+	k+	NOUN
ejpam-6159	324	19	ϱ	ϱ	PROPN
ejpam-6159	324	20	)	)	PUNCT
ejpam-6159	324	21	1−	1−	NUM
ejpam-6159	324	22	1	1	NUM
ejpam-6159	324	23	q	q	NOUN
ejpam-6159	324	24	(	(	PUNCT
ejpam-6159	324	25	ς	ς	PROPN
ejpam-6159	324	26	ϱ	ϱ	PROPN
ejpam-6159	324	27	k	k	PROPN
ejpam-6159	324	28	+1	+1	PROPN
ejpam-6159	324	29	∗	∗	NOUN
ejpam-6159	324	30	(	(	PUNCT
ejpam-6159	324	31	x	x	NOUN
ejpam-6159	324	32	,	,	PUNCT
ejpam-6159	324	33	a1	a1	NOUN
ejpam-6159	324	34	)	)	PUNCT
ejpam-6159	324	35	+	+	CCONJ
ejpam-6159	324	36	ς	ς	PROPN
ejpam-6159	324	37	ϱ	ϱ	PROPN
ejpam-6159	324	38	k	k	PROPN
ejpam-6159	324	39	+1	+1	PROPN
ejpam-6159	324	40	∗	∗	NOUN
ejpam-6159	324	41	(	(	PUNCT
ejpam-6159	324	42	x	x	NOUN
ejpam-6159	324	43	,	,	PUNCT
ejpam-6159	324	44	b1	b1	NOUN
ejpam-6159	324	45	)	)	PUNCT
ejpam-6159	324	46	ς∗	ς∗	PROPN
ejpam-6159	324	47	(	(	PUNCT
ejpam-6159	324	48	b1	b1	NOUN
ejpam-6159	324	49	,	,	PUNCT
ejpam-6159	324	50	a1	a1	NOUN
ejpam-6159	324	51	)	)	PUNCT
ejpam-6159	324	52	)	)	PUNCT
ejpam-6159	325	1	×	×	NOUN
ejpam-6159	325	2	sq∑n	sq∑n	NUM
ejpam-6159	325	3	i=1	i=1	ADP
ejpam-6159	325	4	ai	ai	VERB
ejpam-6159	325	5	.	.	PUNCT
ejpam-6159	326	1	n∑	n∑	INTJ
ejpam-6159	327	1	i=1	i=1	PROPN
ejpam-6159	327	2	ai	ai	VERB
ejpam-6159	327	3	[	[	PUNCT
ejpam-6159	327	4	∫	∫	PROPN
ejpam-6159	327	5	1	1	NUM
ejpam-6159	327	6	0	0	NUM
ejpam-6159	327	7	t	t	PROPN
ejpam-6159	327	8	ϱ	ϱ	PROPN
ejpam-6159	327	9	k	k	X
ejpam-6159	327	10	(	(	PUNCT
ejpam-6159	327	11	(	(	PUNCT
ejpam-6159	327	12	1−	1−	NUM
ejpam-6159	327	13	s	s	X
ejpam-6159	327	14	(	(	PUNCT
ejpam-6159	327	15	1−	1−	NUM
ejpam-6159	327	16	t	t	NOUN
ejpam-6159	327	17	)	)	PUNCT
ejpam-6159	327	18	)	)	PUNCT
ejpam-6159	327	19	1	1	NUM
ejpam-6159	327	20	i	i	NOUN
ejpam-6159	327	21	)	)	PUNCT
ejpam-6159	328	1	dt+	dt+	NOUN
ejpam-6159	328	2	∫	∫	PROPN
ejpam-6159	328	3	1	1	NUM
ejpam-6159	328	4	0	0	NUM
ejpam-6159	328	5	t	t	PROPN
ejpam-6159	328	6	ϱ	ϱ	PROPN
ejpam-6159	328	7	k	k	X
ejpam-6159	328	8	(	(	PUNCT
ejpam-6159	328	9	1−	1−	NUM
ejpam-6159	328	10	st	st	NOUN
ejpam-6159	328	11	)	)	PUNCT
ejpam-6159	328	12	1	1	NUM
ejpam-6159	329	1	i	i	PRON
ejpam-6159	329	2	dt	dt	X
ejpam-6159	329	3	]	]	PUNCT
ejpam-6159	329	4	1	1	NUM
ejpam-6159	329	5	q	q	NOUN
ejpam-6159	329	6	.	.	PUNCT
ejpam-6159	330	1	(	(	PUNCT
ejpam-6159	330	2	31	31	NUM
ejpam-6159	330	3	)	)	PUNCT
ejpam-6159	330	4	proof	proof	NOUN
ejpam-6159	330	5	.	.	PUNCT
ejpam-6159	331	1	from	from	ADP
ejpam-6159	331	2	lemma	lemma	PROPN
ejpam-6159	331	3	1	1	NUM
ejpam-6159	331	4	and	and	CCONJ
ejpam-6159	331	5	a	a	DET
ejpam-6159	331	6	propertyiof	propertyiof	NOUN
ejpam-6159	331	7	the	the	DET
ejpam-6159	331	8	gfpp−s	gfpp−s	PROPN
ejpam-6159	331	9	function	function	NOUN
ejpam-6159	331	10	|f′|q	|f′|q	NOUN
ejpam-6159	331	11	,	,	PUNCT
ejpam-6159	331	12	and	and	CCONJ
ejpam-6159	331	13	the	the	DET
ejpam-6159	331	14	power	power	NOUN
ejpam-6159	331	15	meaniinequality	meaniinequality	NOUN
ejpam-6159	331	16	,	,	PUNCT
ejpam-6159	331	17	one	one	PRON
ejpam-6159	331	18	has	have	VERB
ejpam-6159	331	19	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	331	20	ς	ς	PROPN
ejpam-6159	331	21	ϱ	ϱ	PROPN
ejpam-6159	331	22	k	k	PROPN
ejpam-6159	331	23	∗	∗	X
ejpam-6159	331	24	(	(	PUNCT
ejpam-6159	331	25	x	x	NOUN
ejpam-6159	331	26	,	,	PUNCT
ejpam-6159	331	27	a1	a1	NOUN
ejpam-6159	331	28	)	)	PUNCT
ejpam-6159	331	29	+	+	CCONJ
ejpam-6159	332	1	ς	ς	PROPN
ejpam-6159	332	2	ϱ	ϱ	PROPN
ejpam-6159	332	3	k	k	PROPN
ejpam-6159	332	4	∗	∗	X
ejpam-6159	332	5	(	(	PUNCT
ejpam-6159	332	6	x	x	NOUN
ejpam-6159	332	7	,	,	PUNCT
ejpam-6159	332	8	b1	b1	NOUN
ejpam-6159	332	9	)	)	PUNCT
ejpam-6159	332	10	ς∗	ς∗	PROPN
ejpam-6159	332	11	(	(	PUNCT
ejpam-6159	332	12	b1	b1	NOUN
ejpam-6159	332	13	,	,	PUNCT
ejpam-6159	332	14	a1	a1	PROPN
ejpam-6159	332	15	)	)	PUNCT
ejpam-6159	332	16	f	f	NOUN
ejpam-6159	332	17	(	(	PUNCT
ejpam-6159	332	18	x)−	x)−	PROPN
ejpam-6159	332	19	γk	γk	PROPN
ejpam-6159	332	20	(	(	PUNCT
ejpam-6159	332	21	ϱ+	ϱ+	X
ejpam-6159	332	22	k	k	NOUN
ejpam-6159	332	23	)	)	PUNCT
ejpam-6159	332	24	ς	ς	PROPN
ejpam-6159	332	25	ϱ	ϱ	PROPN
ejpam-6159	332	26	k	k	PROPN
ejpam-6159	332	27	∗	∗	X
ejpam-6159	332	28	(	(	PUNCT
ejpam-6159	332	29	b1	b1	NOUN
ejpam-6159	332	30	,	,	PUNCT
ejpam-6159	332	31	a1	a1	PROPN
ejpam-6159	332	32	)	)	PUNCT
ejpam-6159	332	33	×	×	NOUN
ejpam-6159	332	34	{	{	PUNCT
ejpam-6159	332	35	jϱ,k	jϱ,k	X
ejpam-6159	332	36	(	(	PUNCT
ejpam-6159	332	37	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	332	38	,	,	PUNCT
ejpam-6159	332	39	a1	a1	NOUN
ejpam-6159	332	40	)	)	PUNCT
ejpam-6159	332	41	)	)	PUNCT
ejpam-6159	333	1	−	−	PROPN
ejpam-6159	333	2	f	f	X
ejpam-6159	333	3	(	(	PUNCT
ejpam-6159	333	4	a1	a1	PROPN
ejpam-6159	333	5	)	)	PUNCT
ejpam-6159	333	6	+	+	NUM
ejpam-6159	333	7	jϱ,k	jϱ,k	X
ejpam-6159	333	8	(	(	PUNCT
ejpam-6159	333	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	333	10	,	,	PUNCT
ejpam-6159	333	11	b1	b1	NOUN
ejpam-6159	333	12	)	)	PUNCT
ejpam-6159	333	13	)	)	PUNCT
ejpam-6159	334	1	+	+	CCONJ
ejpam-6159	334	2	f	f	X
ejpam-6159	334	3	(	(	PUNCT
ejpam-6159	334	4	a1	a1	NOUN
ejpam-6159	334	5	+	+	CCONJ
ejpam-6159	334	6	ς∗	ς∗	PROPN
ejpam-6159	334	7	(	(	PUNCT
ejpam-6159	334	8	b1	b1	NOUN
ejpam-6159	334	9	,	,	PUNCT
ejpam-6159	334	10	a1	a1	NOUN
ejpam-6159	334	11	)	)	PUNCT
ejpam-6159	334	12	)	)	PUNCT
ejpam-6159	334	13	}	}	PUNCT
ejpam-6159	334	14	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	334	15	j.	j.	PROPN
ejpam-6159	334	16	nasir	nasir	PROPN
ejpam-6159	334	17	et	et	PROPN
ejpam-6159	334	18	al	al	PROPN
ejpam-6159	334	19	.	.	PUNCT
ejpam-6159	334	20	/	/	SYM
ejpam-6159	334	21	eur	eur	PROPN
ejpam-6159	334	22	.	.	PUNCT
ejpam-6159	335	1	j.	j.	PROPN
ejpam-6159	335	2	pure	pure	PROPN
ejpam-6159	335	3	appl	appl	PROPN
ejpam-6159	335	4	.	.	PROPN
ejpam-6159	335	5	math	math	PROPN
ejpam-6159	335	6	,	,	PUNCT
ejpam-6159	335	7	18	18	NUM
ejpam-6159	335	8	(	(	PUNCT
ejpam-6159	335	9	3	3	NUM
ejpam-6159	335	10	)	)	PUNCT
ejpam-6159	335	11	(	(	PUNCT
ejpam-6159	335	12	2025	2025	NUM
ejpam-6159	335	13	)	)	PUNCT
ejpam-6159	335	14	,	,	PUNCT
ejpam-6159	335	15	6159	6159	NUM
ejpam-6159	335	16	12	12	NUM
ejpam-6159	335	17	of	of	ADP
ejpam-6159	335	18	26	26	NUM
ejpam-6159	335	19	≤	≤	NUM
ejpam-6159	335	20	ς	ς	PROPN
ejpam-6159	335	21	ϱ	ϱ	PROPN
ejpam-6159	335	22	k	k	PROPN
ejpam-6159	335	23	+1	+1	PROPN
ejpam-6159	335	24	∗	∗	NOUN
ejpam-6159	335	25	(	(	PUNCT
ejpam-6159	335	26	x	x	NOUN
ejpam-6159	335	27	,	,	PUNCT
ejpam-6159	335	28	a1	a1	NOUN
ejpam-6159	335	29	)	)	PUNCT
ejpam-6159	335	30	ς∗	ς∗	NOUN
ejpam-6159	335	31	(	(	PUNCT
ejpam-6159	335	32	b1	b1	NOUN
ejpam-6159	335	33	,	,	PUNCT
ejpam-6159	335	34	a1	a1	PROPN
ejpam-6159	335	35	)	)	PUNCT
ejpam-6159	335	36	∫	∫	NOUN
ejpam-6159	335	37	1	1	NUM
ejpam-6159	335	38	0	0	NUM
ejpam-6159	335	39	t	t	PROPN
ejpam-6159	335	40	ϱ	ϱ	ADP
ejpam-6159	335	41	k	k	PROPN
ejpam-6159	335	42	∣∣f′	∣∣f′	PROPN
ejpam-6159	335	43	(	(	PUNCT
ejpam-6159	335	44	a1	a1	NOUN
ejpam-6159	335	45	+	+	CCONJ
ejpam-6159	335	46	tς∗	tς∗	X
ejpam-6159	335	47	(	(	PUNCT
ejpam-6159	335	48	x	x	NOUN
ejpam-6159	335	49	,	,	PUNCT
ejpam-6159	335	50	a1	a1	NOUN
ejpam-6159	335	51	)	)	PUNCT
ejpam-6159	335	52	)	)	PUNCT
ejpam-6159	336	1	∣∣dt	∣∣dt	PROPN
ejpam-6159	337	1	+	+	CCONJ
ejpam-6159	337	2	ς	ς	PROPN
ejpam-6159	337	3	ϱ	ϱ	PROPN
ejpam-6159	337	4	k	k	PROPN
ejpam-6159	337	5	+1	+1	PROPN
ejpam-6159	337	6	∗	∗	NOUN
ejpam-6159	337	7	(	(	PUNCT
ejpam-6159	337	8	x	x	NOUN
ejpam-6159	337	9	,	,	PUNCT
ejpam-6159	337	10	b1	b1	NOUN
ejpam-6159	337	11	)	)	PUNCT
ejpam-6159	337	12	ς∗	ς∗	PROPN
ejpam-6159	337	13	(	(	PUNCT
ejpam-6159	337	14	b1	b1	NOUN
ejpam-6159	337	15	,	,	PUNCT
ejpam-6159	337	16	a1	a1	PROPN
ejpam-6159	337	17	)	)	PUNCT
ejpam-6159	337	18	∫	∫	NOUN
ejpam-6159	338	1	1	1	NUM
ejpam-6159	338	2	0	0	NUM
ejpam-6159	338	3	t	t	PROPN
ejpam-6159	338	4	ϱ	ϱ	ADP
ejpam-6159	338	5	k	k	PROPN
ejpam-6159	338	6	∣∣f′	∣∣f′	PROPN
ejpam-6159	338	7	(	(	PUNCT
ejpam-6159	338	8	b1	b1	NOUN
ejpam-6159	338	9	+	+	CCONJ
ejpam-6159	338	10	tς∗	tς∗	X
ejpam-6159	338	11	(	(	PUNCT
ejpam-6159	338	12	x	x	NOUN
ejpam-6159	338	13	,	,	PUNCT
ejpam-6159	338	14	b1	b1	NOUN
ejpam-6159	338	15	)	)	PUNCT
ejpam-6159	338	16	)	)	PUNCT
ejpam-6159	339	1	∣∣dt	∣∣dt	PROPN
ejpam-6159	339	2	(	(	PUNCT
ejpam-6159	339	3	32	32	NUM
ejpam-6159	339	4	)	)	PUNCT
ejpam-6159	339	5	≤	≤	NOUN
ejpam-6159	339	6	ς	ς	PROPN
ejpam-6159	339	7	ϱ	ϱ	PROPN
ejpam-6159	339	8	k	k	PROPN
ejpam-6159	339	9	+1	+1	PROPN
ejpam-6159	339	10	∗	∗	NOUN
ejpam-6159	339	11	(	(	PUNCT
ejpam-6159	339	12	x	x	NOUN
ejpam-6159	339	13	,	,	PUNCT
ejpam-6159	339	14	a1	a1	NOUN
ejpam-6159	339	15	)	)	PUNCT
ejpam-6159	339	16	ς∗	ς∗	NOUN
ejpam-6159	339	17	(	(	PUNCT
ejpam-6159	339	18	b1	b1	NOUN
ejpam-6159	339	19	,	,	PUNCT
ejpam-6159	339	20	a1	a1	PROPN
ejpam-6159	339	21	)	)	PUNCT
ejpam-6159	339	22	(	(	PUNCT
ejpam-6159	339	23	∫	∫	PROPN
ejpam-6159	339	24	1	1	NUM
ejpam-6159	339	25	0	0	NUM
ejpam-6159	339	26	t	t	NOUN
ejpam-6159	339	27	ϱ	ϱ	ADP
ejpam-6159	339	28	kdt	kdt	PROPN
ejpam-6159	339	29	)	)	PUNCT
ejpam-6159	339	30	1−	1−	PROPN
ejpam-6159	339	31	1	1	NUM
ejpam-6159	339	32	q	q	NOUN
ejpam-6159	339	33	(	(	PUNCT
ejpam-6159	339	34	∫	∫	PROPN
ejpam-6159	339	35	1	1	NUM
ejpam-6159	339	36	0	0	NUM
ejpam-6159	339	37	t	t	PROPN
ejpam-6159	339	38	ϱ	ϱ	ADP
ejpam-6159	339	39	k	k	PROPN
ejpam-6159	339	40	∣∣f′	∣∣f′	PROPN
ejpam-6159	339	41	(	(	PUNCT
ejpam-6159	339	42	a1	a1	NOUN
ejpam-6159	339	43	+	+	CCONJ
ejpam-6159	339	44	tς∗	tς∗	X
ejpam-6159	339	45	(	(	PUNCT
ejpam-6159	339	46	x	x	NOUN
ejpam-6159	339	47	,	,	PUNCT
ejpam-6159	339	48	a1	a1	NOUN
ejpam-6159	339	49	)	)	PUNCT
ejpam-6159	339	50	)	)	PUNCT
ejpam-6159	339	51	∣∣qdt	∣∣qdt	NOUN
ejpam-6159	339	52	)	)	PUNCT
ejpam-6159	339	53	1	1	NUM
ejpam-6159	339	54	q	q	NOUN
ejpam-6159	340	1	+	+	CCONJ
ejpam-6159	340	2	ς	ς	PROPN
ejpam-6159	340	3	ϱ	ϱ	PROPN
ejpam-6159	340	4	k	k	PROPN
ejpam-6159	340	5	+1	+1	PROPN
ejpam-6159	340	6	∗	∗	NOUN
ejpam-6159	340	7	(	(	PUNCT
ejpam-6159	340	8	x	x	NOUN
ejpam-6159	340	9	,	,	PUNCT
ejpam-6159	340	10	b1	b1	NOUN
ejpam-6159	340	11	)	)	PUNCT
ejpam-6159	340	12	ς∗	ς∗	PROPN
ejpam-6159	340	13	(	(	PUNCT
ejpam-6159	340	14	b1	b1	NOUN
ejpam-6159	340	15	,	,	PUNCT
ejpam-6159	340	16	a1	a1	PROPN
ejpam-6159	340	17	)	)	PUNCT
ejpam-6159	340	18	(	(	PUNCT
ejpam-6159	340	19	∫	∫	PROPN
ejpam-6159	340	20	1	1	NUM
ejpam-6159	340	21	0	0	NUM
ejpam-6159	340	22	t	t	NOUN
ejpam-6159	340	23	ϱ	ϱ	ADP
ejpam-6159	340	24	kdt	kdt	PROPN
ejpam-6159	340	25	)	)	PUNCT
ejpam-6159	340	26	1−	1−	PROPN
ejpam-6159	340	27	1	1	NUM
ejpam-6159	340	28	q	q	NOUN
ejpam-6159	340	29	(	(	PUNCT
ejpam-6159	340	30	∫	∫	PROPN
ejpam-6159	340	31	1	1	NUM
ejpam-6159	340	32	0	0	NUM
ejpam-6159	340	33	t	t	PROPN
ejpam-6159	340	34	ϱ	ϱ	ADP
ejpam-6159	340	35	k	k	PROPN
ejpam-6159	340	36	∣∣f′	∣∣f′	PROPN
ejpam-6159	340	37	(	(	PUNCT
ejpam-6159	340	38	b1	b1	NOUN
ejpam-6159	340	39	+	+	CCONJ
ejpam-6159	340	40	tς∗	tς∗	X
ejpam-6159	340	41	(	(	PUNCT
ejpam-6159	340	42	x	x	NOUN
ejpam-6159	340	43	,	,	PUNCT
ejpam-6159	340	44	b1	b1	NOUN
ejpam-6159	340	45	)	)	PUNCT
ejpam-6159	340	46	)	)	PUNCT
ejpam-6159	341	1	∣∣qdt	∣∣qdt	NOUN
ejpam-6159	341	2	)	)	PUNCT
ejpam-6159	341	3	1	1	NUM
ejpam-6159	341	4	q	q	NOUN
ejpam-6159	341	5	≤	≤	NUM
ejpam-6159	341	6	(	(	PUNCT
ejpam-6159	341	7	k	k	X
ejpam-6159	341	8	k+	k+	NOUN
ejpam-6159	341	9	ϱ	ϱ	PROPN
ejpam-6159	341	10	)	)	PUNCT
ejpam-6159	341	11	1−	1−	PROPN
ejpam-6159	341	12	1	1	NUM
ejpam-6159	341	13	q	q	NOUN
ejpam-6159	341	14	[	[	PUNCT
ejpam-6159	341	15	ς	ς	PROPN
ejpam-6159	341	16	ϱ	ϱ	X
ejpam-6159	341	17	k	k	PROPN
ejpam-6159	341	18	+1	+1	PROPN
ejpam-6159	341	19	∗	∗	NOUN
ejpam-6159	341	20	(	(	PUNCT
ejpam-6159	341	21	x	x	NOUN
ejpam-6159	341	22	,	,	PUNCT
ejpam-6159	341	23	a1	a1	NOUN
ejpam-6159	341	24	)	)	PUNCT
ejpam-6159	341	25	ς∗	ς∗	NOUN
ejpam-6159	341	26	(	(	PUNCT
ejpam-6159	341	27	b1	b1	NOUN
ejpam-6159	341	28	,	,	PUNCT
ejpam-6159	341	29	a1	a1	NOUN
ejpam-6159	341	30	)	)	PUNCT
ejpam-6159	341	31	{	{	PUNCT
ejpam-6159	342	1	∑n	∑n	PROPN
ejpam-6159	342	2	i=1	i=1	PROPN
ejpam-6159	342	3	ai	ai	VERB
ejpam-6159	342	4	∫	∫	PROPN
ejpam-6159	342	5	1	1	NUM
ejpam-6159	342	6	0	0	NUM
ejpam-6159	342	7	t	t	PROPN
ejpam-6159	342	8	ϱ	ϱ	PROPN
ejpam-6159	342	9	k	k	X
ejpam-6159	342	10	(	(	PUNCT
ejpam-6159	342	11	(	(	PUNCT
ejpam-6159	342	12	1−	1−	NUM
ejpam-6159	342	13	s	s	X
ejpam-6159	342	14	(	(	PUNCT
ejpam-6159	342	15	1−	1−	NUM
ejpam-6159	342	16	t	t	NOUN
ejpam-6159	342	17	)	)	PUNCT
ejpam-6159	342	18	)	)	PUNCT
ejpam-6159	342	19	1	1	NUM
ejpam-6159	342	20	i	i	NOUN
ejpam-6159	342	21	)	)	PUNCT
ejpam-6159	343	1	∑n	∑n	PROPN
ejpam-6159	343	2	i=1	i=1	PROPN
ejpam-6159	343	3	ai	ai	VERB
ejpam-6159	343	4	∣∣f′	∣∣f′	NOUN
ejpam-6159	343	5	(	(	PUNCT
ejpam-6159	343	6	x	x	X
ejpam-6159	343	7	)	)	PUNCT
ejpam-6159	343	8	∣∣q	∣∣q	NUM
ejpam-6159	343	9	dt	dt	NOUN
ejpam-6159	344	1	+	+	CCONJ
ejpam-6159	344	2	∑n	∑n	PROPN
ejpam-6159	345	1	i=1	i=1	PROPN
ejpam-6159	345	2	ai	ai	VERB
ejpam-6159	345	3	∫	∫	PROPN
ejpam-6159	345	4	1	1	NUM
ejpam-6159	345	5	0	0	NUM
ejpam-6159	345	6	t	t	PROPN
ejpam-6159	345	7	ϱ	ϱ	PROPN
ejpam-6159	345	8	k	k	X
ejpam-6159	345	9	(	(	PUNCT
ejpam-6159	345	10	(	(	PUNCT
ejpam-6159	345	11	1−	1−	NUM
ejpam-6159	345	12	st	st	NOUN
ejpam-6159	345	13	)	)	PUNCT
ejpam-6159	345	14	1	1	NUM
ejpam-6159	345	15	i	i	NOUN
ejpam-6159	345	16	)	)	PUNCT
ejpam-6159	346	1	∑n	∑n	PROPN
ejpam-6159	346	2	i=1	i=1	PROPN
ejpam-6159	346	3	ai	ai	VERB
ejpam-6159	346	4	∣∣f′	∣∣f′	NOUN
ejpam-6159	346	5	(	(	PUNCT
ejpam-6159	346	6	a1	a1	NOUN
ejpam-6159	346	7	)	)	PUNCT
ejpam-6159	346	8	∣∣q	∣∣q	NUM
ejpam-6159	346	9	dt	dt	NOUN
ejpam-6159	346	10	}	}	PUNCT
ejpam-6159	346	11	1	1	NUM
ejpam-6159	346	12	q	q	NOUN
ejpam-6159	347	1	+	+	NUM
ejpam-6159	347	2	ς	ς	PROPN
ejpam-6159	347	3	ϱ	ϱ	PROPN
ejpam-6159	347	4	k	k	PROPN
ejpam-6159	347	5	+1	+1	PROPN
ejpam-6159	347	6	∗	∗	NOUN
ejpam-6159	347	7	(	(	PUNCT
ejpam-6159	347	8	x	x	NOUN
ejpam-6159	347	9	,	,	PUNCT
ejpam-6159	347	10	b1	b1	NOUN
ejpam-6159	347	11	)	)	PUNCT
ejpam-6159	347	12	ς∗	ς∗	PROPN
ejpam-6159	347	13	(	(	PUNCT
ejpam-6159	347	14	b1	b1	NOUN
ejpam-6159	347	15	,	,	PUNCT
ejpam-6159	347	16	a1	a1	NOUN
ejpam-6159	347	17	)	)	PUNCT
ejpam-6159	347	18	{	{	PUNCT
ejpam-6159	348	1	∑n	∑n	PROPN
ejpam-6159	348	2	i=1	i=1	PROPN
ejpam-6159	348	3	ai	ai	VERB
ejpam-6159	348	4	∫	∫	PROPN
ejpam-6159	348	5	1	1	NUM
ejpam-6159	348	6	0	0	NUM
ejpam-6159	348	7	t	t	PROPN
ejpam-6159	348	8	ϱ	ϱ	PROPN
ejpam-6159	348	9	k	k	X
ejpam-6159	348	10	(	(	PUNCT
ejpam-6159	348	11	(	(	PUNCT
ejpam-6159	348	12	1−	1−	NUM
ejpam-6159	348	13	s	s	X
ejpam-6159	348	14	(	(	PUNCT
ejpam-6159	348	15	1−	1−	NUM
ejpam-6159	348	16	t	t	NOUN
ejpam-6159	348	17	)	)	PUNCT
ejpam-6159	348	18	)	)	PUNCT
ejpam-6159	348	19	1	1	NUM
ejpam-6159	348	20	i	i	NOUN
ejpam-6159	348	21	)	)	PUNCT
ejpam-6159	349	1	∑n	∑n	PROPN
ejpam-6159	349	2	i=1	i=1	PROPN
ejpam-6159	349	3	ai	ai	VERB
ejpam-6159	349	4	∣∣f′	∣∣f′	NOUN
ejpam-6159	349	5	(	(	PUNCT
ejpam-6159	349	6	x	x	X
ejpam-6159	349	7	)	)	PUNCT
ejpam-6159	349	8	∣∣q	∣∣q	NUM
ejpam-6159	349	9	dt	dt	NOUN
ejpam-6159	350	1	+	+	CCONJ
ejpam-6159	350	2	∑n	∑n	PROPN
ejpam-6159	351	1	i=1	i=1	PROPN
ejpam-6159	351	2	ai	ai	VERB
ejpam-6159	351	3	∫	∫	PROPN
ejpam-6159	351	4	1	1	NUM
ejpam-6159	351	5	0	0	NUM
ejpam-6159	351	6	t	t	PROPN
ejpam-6159	351	7	ϱ	ϱ	PROPN
ejpam-6159	351	8	k	k	X
ejpam-6159	351	9	(	(	PUNCT
ejpam-6159	351	10	(	(	PUNCT
ejpam-6159	351	11	1−	1−	NUM
ejpam-6159	351	12	st	st	NOUN
ejpam-6159	351	13	)	)	PUNCT
ejpam-6159	351	14	1	1	NUM
ejpam-6159	351	15	i	i	NOUN
ejpam-6159	351	16	)	)	PUNCT
ejpam-6159	352	1	∑n	∑n	PROPN
ejpam-6159	352	2	i=1	i=1	PROPN
ejpam-6159	352	3	ai	ai	VERB
ejpam-6159	352	4	∣∣f′	∣∣f′	NOUN
ejpam-6159	352	5	(	(	PUNCT
ejpam-6159	352	6	b1	b1	NOUN
ejpam-6159	352	7	)	)	PUNCT
ejpam-6159	352	8	∣∣q	∣∣q	NUM
ejpam-6159	352	9	dt	dt	NOUN
ejpam-6159	352	10	}	}	PUNCT
ejpam-6159	352	11	1	1	NUM
ejpam-6159	352	12	q	q	NOUN
ejpam-6159	352	13	]	]	PUNCT
ejpam-6159	352	14	≤	≤	NUM
ejpam-6159	352	15	(	(	PUNCT
ejpam-6159	352	16	k	k	X
ejpam-6159	352	17	k+	k+	NOUN
ejpam-6159	352	18	ϱ	ϱ	PROPN
ejpam-6159	352	19	)	)	PUNCT
ejpam-6159	352	20	1−	1−	NUM
ejpam-6159	352	21	1	1	NUM
ejpam-6159	352	22	q	q	NOUN
ejpam-6159	352	23	(	(	PUNCT
ejpam-6159	352	24	ς	ς	PROPN
ejpam-6159	352	25	ϱ	ϱ	PROPN
ejpam-6159	352	26	k	k	PROPN
ejpam-6159	352	27	+1	+1	PROPN
ejpam-6159	352	28	∗	∗	NOUN
ejpam-6159	352	29	(	(	PUNCT
ejpam-6159	352	30	x	x	NOUN
ejpam-6159	352	31	,	,	PUNCT
ejpam-6159	352	32	a1	a1	NOUN
ejpam-6159	352	33	)	)	PUNCT
ejpam-6159	352	34	+	+	CCONJ
ejpam-6159	352	35	ς	ς	PROPN
ejpam-6159	352	36	ϱ	ϱ	PROPN
ejpam-6159	352	37	k	k	PROPN
ejpam-6159	352	38	+1	+1	PROPN
ejpam-6159	352	39	∗	∗	NOUN
ejpam-6159	352	40	(	(	PUNCT
ejpam-6159	352	41	x	x	NOUN
ejpam-6159	352	42	,	,	PUNCT
ejpam-6159	352	43	b1	b1	NOUN
ejpam-6159	352	44	)	)	PUNCT
ejpam-6159	352	45	ς∗	ς∗	PROPN
ejpam-6159	352	46	(	(	PUNCT
ejpam-6159	352	47	b1	b1	NOUN
ejpam-6159	352	48	,	,	PUNCT
ejpam-6159	352	49	a1	a1	NOUN
ejpam-6159	352	50	)	)	PUNCT
ejpam-6159	352	51	)	)	PUNCT
ejpam-6159	353	1	×	×	NOUN
ejpam-6159	353	2	sq∑n	sq∑n	NUM
ejpam-6159	353	3	i=1	i=1	ADP
ejpam-6159	353	4	ai	ai	VERB
ejpam-6159	353	5	.	.	PUNCT
ejpam-6159	354	1	n∑	n∑	INTJ
ejpam-6159	355	1	i=1	i=1	PROPN
ejpam-6159	355	2	ai	ai	VERB
ejpam-6159	355	3	[	[	PUNCT
ejpam-6159	355	4	∫	∫	PROPN
ejpam-6159	355	5	1	1	NUM
ejpam-6159	355	6	0	0	NUM
ejpam-6159	355	7	t	t	PROPN
ejpam-6159	355	8	ϱ	ϱ	PROPN
ejpam-6159	355	9	k	k	X
ejpam-6159	355	10	(	(	PUNCT
ejpam-6159	355	11	(	(	PUNCT
ejpam-6159	355	12	1−	1−	NUM
ejpam-6159	355	13	s	s	X
ejpam-6159	355	14	(	(	PUNCT
ejpam-6159	355	15	1−	1−	NUM
ejpam-6159	355	16	t	t	NOUN
ejpam-6159	355	17	)	)	PUNCT
ejpam-6159	355	18	)	)	PUNCT
ejpam-6159	355	19	1	1	NUM
ejpam-6159	355	20	i	i	NOUN
ejpam-6159	355	21	)	)	PUNCT
ejpam-6159	356	1	dt+	dt+	NOUN
ejpam-6159	356	2	∫	∫	PROPN
ejpam-6159	356	3	1	1	NUM
ejpam-6159	356	4	0	0	NUM
ejpam-6159	356	5	t	t	PROPN
ejpam-6159	356	6	ϱ	ϱ	PROPN
ejpam-6159	356	7	k	k	X
ejpam-6159	356	8	(	(	PUNCT
ejpam-6159	356	9	1−	1−	NUM
ejpam-6159	356	10	st	st	NOUN
ejpam-6159	356	11	)	)	PUNCT
ejpam-6159	356	12	1	1	NUM
ejpam-6159	357	1	i	i	PRON
ejpam-6159	357	2	dt	dt	X
ejpam-6159	357	3	]	]	PUNCT
ejpam-6159	357	4	1	1	NUM
ejpam-6159	357	5	q	q	NOUN
ejpam-6159	357	6	.	.	PUNCT
ejpam-6159	358	1	(	(	PUNCT
ejpam-6159	358	2	33	33	NUM
ejpam-6159	358	3	)	)	PUNCT
ejpam-6159	358	4	corollary	corollary	NOUN
ejpam-6159	358	5	5	5	NUM
ejpam-6159	358	6	.	.	PUNCT
ejpam-6159	359	1	if	if	SCONJ
ejpam-6159	359	2	one	one	PRON
ejpam-6159	359	3	can	can	AUX
ejpam-6159	359	4	take	take	VERB
ejpam-6159	359	5	s	s	PART
ejpam-6159	359	6	=	=	SYM
ejpam-6159	359	7	1	1	NUM
ejpam-6159	359	8	initheorem	initheorem	VERB
ejpam-6159	359	9	4	4	NUM
ejpam-6159	359	10	,	,	PUNCT
ejpam-6159	359	11	then	then	ADV
ejpam-6159	359	12	we	we	PRON
ejpam-6159	359	13	have	have	VERB
ejpam-6159	359	14	the	the	DET
ejpam-6159	359	15	followingiinequalities	followingiinequalitie	NOUN
ejpam-6159	359	16	for	for	ADP
ejpam-6159	359	17	gfpp	gfpp	NOUN
ejpam-6159	359	18	function	function	NOUN
ejpam-6159	359	19	with	with	ADP
ejpam-6159	359	20	k−fractionaliintegral	k−fractionaliintegral	PROPN
ejpam-6159	359	21	operators:∣∣∣∣	operators:∣∣∣∣	PROPN
ejpam-6159	359	22	ς	ς	PROPN
ejpam-6159	359	23	ϱ	ϱ	PROPN
ejpam-6159	359	24	k	k	PROPN
ejpam-6159	359	25	∗	∗	X
ejpam-6159	359	26	(	(	PUNCT
ejpam-6159	359	27	x	x	NOUN
ejpam-6159	359	28	,	,	PUNCT
ejpam-6159	359	29	a1	a1	NOUN
ejpam-6159	359	30	)	)	PUNCT
ejpam-6159	359	31	+	+	CCONJ
ejpam-6159	360	1	ς	ς	PROPN
ejpam-6159	360	2	ϱ	ϱ	PROPN
ejpam-6159	360	3	k	k	PROPN
ejpam-6159	360	4	∗	∗	X
ejpam-6159	360	5	(	(	PUNCT
ejpam-6159	360	6	x	x	NOUN
ejpam-6159	360	7	,	,	PUNCT
ejpam-6159	360	8	b1	b1	NOUN
ejpam-6159	360	9	)	)	PUNCT
ejpam-6159	360	10	ς∗	ς∗	PROPN
ejpam-6159	360	11	(	(	PUNCT
ejpam-6159	360	12	b1	b1	NOUN
ejpam-6159	360	13	,	,	PUNCT
ejpam-6159	360	14	a1	a1	PROPN
ejpam-6159	360	15	)	)	PUNCT
ejpam-6159	360	16	f	f	NOUN
ejpam-6159	360	17	(	(	PUNCT
ejpam-6159	360	18	x)−	x)−	PROPN
ejpam-6159	360	19	γk	γk	PROPN
ejpam-6159	360	20	(	(	PUNCT
ejpam-6159	360	21	ϱ+	ϱ+	X
ejpam-6159	360	22	k	k	NOUN
ejpam-6159	360	23	)	)	PUNCT
ejpam-6159	360	24	ς	ς	PROPN
ejpam-6159	360	25	ϱ	ϱ	PROPN
ejpam-6159	360	26	k	k	PROPN
ejpam-6159	360	27	∗	∗	X
ejpam-6159	360	28	(	(	PUNCT
ejpam-6159	360	29	b1	b1	NOUN
ejpam-6159	360	30	,	,	PUNCT
ejpam-6159	360	31	a1	a1	PROPN
ejpam-6159	360	32	)	)	PUNCT
ejpam-6159	360	33	×	×	NOUN
ejpam-6159	360	34	{	{	PUNCT
ejpam-6159	360	35	jϱ,k	jϱ,k	X
ejpam-6159	360	36	(	(	PUNCT
ejpam-6159	360	37	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	360	38	,	,	PUNCT
ejpam-6159	360	39	a1	a1	NOUN
ejpam-6159	360	40	)	)	PUNCT
ejpam-6159	360	41	)	)	PUNCT
ejpam-6159	361	1	−	−	PROPN
ejpam-6159	361	2	f	f	X
ejpam-6159	361	3	(	(	PUNCT
ejpam-6159	361	4	a1	a1	PROPN
ejpam-6159	361	5	)	)	PUNCT
ejpam-6159	361	6	+	+	NUM
ejpam-6159	361	7	jϱ,k	jϱ,k	X
ejpam-6159	361	8	(	(	PUNCT
ejpam-6159	361	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	361	10	,	,	PUNCT
ejpam-6159	361	11	b1	b1	NOUN
ejpam-6159	361	12	)	)	PUNCT
ejpam-6159	361	13	)	)	PUNCT
ejpam-6159	362	1	+	+	CCONJ
ejpam-6159	362	2	f	f	X
ejpam-6159	362	3	(	(	PUNCT
ejpam-6159	362	4	a1	a1	NOUN
ejpam-6159	362	5	+	+	CCONJ
ejpam-6159	362	6	ς∗	ς∗	PROPN
ejpam-6159	362	7	(	(	PUNCT
ejpam-6159	362	8	b	b	NOUN
ejpam-6159	362	9	,	,	PUNCT
ejpam-6159	362	10	a1	a1	NOUN
ejpam-6159	362	11	)	)	PUNCT
ejpam-6159	362	12	)	)	PUNCT
ejpam-6159	362	13	}	}	PUNCT
ejpam-6159	362	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	362	15	≤	≤	NOUN
ejpam-6159	362	16	(	(	PUNCT
ejpam-6159	362	17	k	k	X
ejpam-6159	362	18	k+	k+	NOUN
ejpam-6159	362	19	ϱ	ϱ	PROPN
ejpam-6159	362	20	)	)	PUNCT
ejpam-6159	362	21	1−	1−	NUM
ejpam-6159	362	22	1	1	NUM
ejpam-6159	362	23	q	q	NOUN
ejpam-6159	362	24	(	(	PUNCT
ejpam-6159	362	25	ς	ς	PROPN
ejpam-6159	362	26	ϱ	ϱ	PROPN
ejpam-6159	362	27	k	k	PROPN
ejpam-6159	362	28	+1	+1	PROPN
ejpam-6159	362	29	∗	∗	NOUN
ejpam-6159	362	30	(	(	PUNCT
ejpam-6159	362	31	x	x	NOUN
ejpam-6159	362	32	,	,	PUNCT
ejpam-6159	362	33	a1	a1	NOUN
ejpam-6159	362	34	)	)	PUNCT
ejpam-6159	362	35	+	+	CCONJ
ejpam-6159	362	36	ς	ς	PROPN
ejpam-6159	362	37	ϱ	ϱ	PROPN
ejpam-6159	362	38	k	k	PROPN
ejpam-6159	362	39	+1	+1	PROPN
ejpam-6159	362	40	∗	∗	NOUN
ejpam-6159	362	41	(	(	PUNCT
ejpam-6159	362	42	x	x	NOUN
ejpam-6159	362	43	,	,	PUNCT
ejpam-6159	362	44	b1	b1	NOUN
ejpam-6159	362	45	)	)	PUNCT
ejpam-6159	362	46	ς∗	ς∗	PROPN
ejpam-6159	362	47	(	(	PUNCT
ejpam-6159	362	48	b1	b1	NOUN
ejpam-6159	362	49	,	,	PUNCT
ejpam-6159	362	50	a1	a1	NOUN
ejpam-6159	362	51	)	)	PUNCT
ejpam-6159	362	52	)	)	PUNCT
ejpam-6159	363	1	×	×	NOUN
ejpam-6159	363	2	sq∑n	sq∑n	NUM
ejpam-6159	363	3	i=1	i=1	ADP
ejpam-6159	363	4	ai	ai	VERB
ejpam-6159	363	5	.	.	PUNCT
ejpam-6159	364	1	n∑	n∑	INTJ
ejpam-6159	365	1	i=1	i=1	PROPN
ejpam-6159	365	2	ai	ai	VERB
ejpam-6159	365	3	[	[	PUNCT
ejpam-6159	365	4	∫	∫	PROPN
ejpam-6159	365	5	1	1	NUM
ejpam-6159	365	6	0	0	NUM
ejpam-6159	365	7	t	t	PROPN
ejpam-6159	365	8	ϱ	ϱ	PROPN
ejpam-6159	365	9	k	k	PROPN
ejpam-6159	365	10	t	t	PROPN
ejpam-6159	365	11	1	1	NUM
ejpam-6159	365	12	i	i	PRON
ejpam-6159	365	13	dt+	dt+	NOUN
ejpam-6159	365	14	∫	∫	PROPN
ejpam-6159	365	15	1	1	NUM
ejpam-6159	365	16	0	0	NUM
ejpam-6159	365	17	t	t	PROPN
ejpam-6159	365	18	ϱ	ϱ	PROPN
ejpam-6159	365	19	k	k	X
ejpam-6159	365	20	(	(	PUNCT
ejpam-6159	365	21	1−	1−	NUM
ejpam-6159	365	22	t	t	NOUN
ejpam-6159	365	23	)	)	PUNCT
ejpam-6159	365	24	1	1	NUM
ejpam-6159	366	1	i	i	PRON
ejpam-6159	366	2	dt	dt	X
ejpam-6159	366	3	]	]	PUNCT
ejpam-6159	366	4	1	1	NUM
ejpam-6159	366	5	q	q	NOUN
ejpam-6159	366	6	.	.	PUNCT
ejpam-6159	367	1	j.	j.	PROPN
ejpam-6159	367	2	nasir	nasir	PROPN
ejpam-6159	367	3	et	et	PROPN
ejpam-6159	367	4	al	al	PROPN
ejpam-6159	367	5	.	.	PUNCT
ejpam-6159	367	6	/	/	SYM
ejpam-6159	367	7	eur	eur	PROPN
ejpam-6159	367	8	.	.	PUNCT
ejpam-6159	368	1	j.	j.	PROPN
ejpam-6159	368	2	pure	pure	PROPN
ejpam-6159	368	3	appl	appl	PROPN
ejpam-6159	368	4	.	.	PROPN
ejpam-6159	368	5	math	math	PROPN
ejpam-6159	368	6	,	,	PUNCT
ejpam-6159	368	7	18	18	NUM
ejpam-6159	368	8	(	(	PUNCT
ejpam-6159	368	9	3	3	NUM
ejpam-6159	368	10	)	)	PUNCT
ejpam-6159	368	11	(	(	PUNCT
ejpam-6159	368	12	2025	2025	NUM
ejpam-6159	368	13	)	)	PUNCT
ejpam-6159	368	14	,	,	PUNCT
ejpam-6159	368	15	6159	6159	NUM
ejpam-6159	368	16	13	13	NUM
ejpam-6159	368	17	of	of	ADP
ejpam-6159	368	18	26	26	NUM
ejpam-6159	368	19	corollary	corollary	ADJ
ejpam-6159	368	20	6	6	NUM
ejpam-6159	368	21	.	.	PUNCT
ejpam-6159	369	1	if	if	SCONJ
ejpam-6159	369	2	one	one	PRON
ejpam-6159	369	3	can	can	AUX
ejpam-6159	369	4	takes	take	VERB
ejpam-6159	369	5	k	k	NOUN
ejpam-6159	369	6	=	=	SYM
ejpam-6159	369	7	1	1	NUM
ejpam-6159	369	8	in	in	ADP
ejpam-6159	369	9	corollary	corollary	ADJ
ejpam-6159	369	10	5	5	NUM
ejpam-6159	369	11	,	,	PUNCT
ejpam-6159	369	12	then	then	ADV
ejpam-6159	369	13	we	we	PRON
ejpam-6159	369	14	have	have	VERB
ejpam-6159	369	15	the	the	DET
ejpam-6159	369	16	following	follow	VERB
ejpam-6159	369	17	inequalities	inequality	NOUN
ejpam-6159	369	18	for	for	ADP
ejpam-6159	369	19	gfpp	gfpp	NOUN
ejpam-6159	369	20	function	function	NOUN
ejpam-6159	369	21	with	with	ADP
ejpam-6159	369	22	rl−fractional	rl−fractional	ADJ
ejpam-6159	369	23	integral	integral	ADJ
ejpam-6159	369	24	operators:∣∣∣∣	operators:∣∣∣∣	ADJ
ejpam-6159	369	25	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	369	26	(	(	PUNCT
ejpam-6159	369	27	x	x	NOUN
ejpam-6159	369	28	,	,	PUNCT
ejpam-6159	369	29	a1	a1	PROPN
ejpam-6159	369	30	)	)	PUNCT
ejpam-6159	369	31	+	+	NUM
ejpam-6159	369	32	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	369	33	(	(	PUNCT
ejpam-6159	369	34	x	x	NOUN
ejpam-6159	369	35	,	,	PUNCT
ejpam-6159	369	36	b1	b1	NOUN
ejpam-6159	369	37	)	)	PUNCT
ejpam-6159	369	38	ς∗	ς∗	PROPN
ejpam-6159	369	39	(	(	PUNCT
ejpam-6159	369	40	b1	b1	NOUN
ejpam-6159	369	41	,	,	PUNCT
ejpam-6159	369	42	a1	a1	PROPN
ejpam-6159	369	43	)	)	PUNCT
ejpam-6159	369	44	f	f	NOUN
ejpam-6159	369	45	(	(	PUNCT
ejpam-6159	369	46	x)−	x)−	PROPN
ejpam-6159	369	47	γ	γ	PROPN
ejpam-6159	369	48	(	(	PUNCT
ejpam-6159	369	49	ϱ+	ϱ+	NOUN
ejpam-6159	369	50	1	1	NUM
ejpam-6159	369	51	)	)	PUNCT
ejpam-6159	369	52	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	369	53	(	(	PUNCT
ejpam-6159	369	54	b1	b1	NOUN
ejpam-6159	369	55	,	,	PUNCT
ejpam-6159	369	56	a1	a1	PROPN
ejpam-6159	369	57	)	)	PUNCT
ejpam-6159	369	58	×	×	NOUN
ejpam-6159	369	59	{	{	PUNCT
ejpam-6159	369	60	jϱ	jϱ	NOUN
ejpam-6159	369	61	(	(	PUNCT
ejpam-6159	369	62	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	369	63	,	,	PUNCT
ejpam-6159	369	64	a1	a1	NOUN
ejpam-6159	369	65	)	)	PUNCT
ejpam-6159	369	66	)	)	PUNCT
ejpam-6159	370	1	−	−	PROPN
ejpam-6159	370	2	f	f	X
ejpam-6159	370	3	(	(	PUNCT
ejpam-6159	370	4	a1	a1	PROPN
ejpam-6159	370	5	)	)	PUNCT
ejpam-6159	370	6	+	+	NUM
ejpam-6159	370	7	jϱ	jϱ	ADJ
ejpam-6159	370	8	(	(	PUNCT
ejpam-6159	370	9	b1+ς∗(x	b1+ς∗(x	PROPN
ejpam-6159	370	10	,	,	PUNCT
ejpam-6159	370	11	b1	b1	NOUN
ejpam-6159	370	12	)	)	PUNCT
ejpam-6159	370	13	)	)	PUNCT
ejpam-6159	371	1	+	+	CCONJ
ejpam-6159	371	2	f	f	X
ejpam-6159	371	3	(	(	PUNCT
ejpam-6159	371	4	a1	a1	NOUN
ejpam-6159	371	5	+	+	CCONJ
ejpam-6159	371	6	ς∗	ς∗	PROPN
ejpam-6159	371	7	(	(	PUNCT
ejpam-6159	371	8	b1	b1	NOUN
ejpam-6159	371	9	,	,	PUNCT
ejpam-6159	371	10	a1	a1	NOUN
ejpam-6159	371	11	)	)	PUNCT
ejpam-6159	371	12	)	)	PUNCT
ejpam-6159	371	13	}	}	PUNCT
ejpam-6159	371	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	371	15	≤	≤	NOUN
ejpam-6159	371	16	(	(	PUNCT
ejpam-6159	371	17	1	1	NUM
ejpam-6159	371	18	1	1	NUM
ejpam-6159	371	19	+	+	NUM
ejpam-6159	371	20	ϱ	ϱ	NOUN
ejpam-6159	371	21	)	)	PUNCT
ejpam-6159	371	22	1−	1−	NUM
ejpam-6159	371	23	1	1	NUM
ejpam-6159	371	24	q	q	NOUN
ejpam-6159	371	25	(	(	PUNCT
ejpam-6159	371	26	ςϱ+1	ςϱ+1	ADV
ejpam-6159	371	27	∗	∗	NOUN
ejpam-6159	371	28	(	(	PUNCT
ejpam-6159	371	29	x	x	NOUN
ejpam-6159	371	30	,	,	PUNCT
ejpam-6159	371	31	a1	a1	NOUN
ejpam-6159	371	32	)	)	PUNCT
ejpam-6159	371	33	+	+	CCONJ
ejpam-6159	371	34	ςϱ+1	ςϱ+1	ADV
ejpam-6159	371	35	∗	∗	NOUN
ejpam-6159	371	36	(	(	PUNCT
ejpam-6159	371	37	x	x	NOUN
ejpam-6159	371	38	,	,	PUNCT
ejpam-6159	371	39	b1	b1	NOUN
ejpam-6159	371	40	)	)	PUNCT
ejpam-6159	371	41	ς∗	ς∗	PROPN
ejpam-6159	371	42	(	(	PUNCT
ejpam-6159	371	43	b1	b1	NOUN
ejpam-6159	371	44	,	,	PUNCT
ejpam-6159	371	45	a1	a1	NOUN
ejpam-6159	371	46	)	)	PUNCT
ejpam-6159	371	47	)	)	PUNCT
ejpam-6159	372	1	×	×	NOUN
ejpam-6159	372	2	sq∑n	sq∑n	NUM
ejpam-6159	372	3	i=1	i=1	ADP
ejpam-6159	372	4	ai	ai	VERB
ejpam-6159	372	5	.	.	PUNCT
ejpam-6159	373	1	n∑	n∑	INTJ
ejpam-6159	374	1	i=1	i=1	PROPN
ejpam-6159	374	2	ai	ai	VERB
ejpam-6159	374	3	[	[	PUNCT
ejpam-6159	374	4	∫	∫	PROPN
ejpam-6159	374	5	1	1	NUM
ejpam-6159	374	6	0	0	NUM
ejpam-6159	374	7	tϱt	tϱt	NUM
ejpam-6159	374	8	1	1	NUM
ejpam-6159	374	9	i	i	PRON
ejpam-6159	374	10	dt+	dt+	NOUN
ejpam-6159	374	11	∫	∫	PROPN
ejpam-6159	375	1	1	1	NUM
ejpam-6159	375	2	0	0	NUM
ejpam-6159	375	3	tϱ	tϱ	PRON
ejpam-6159	375	4	(	(	PUNCT
ejpam-6159	375	5	1−	1−	NUM
ejpam-6159	375	6	t	t	NOUN
ejpam-6159	375	7	)	)	PUNCT
ejpam-6159	375	8	1	1	NUM
ejpam-6159	376	1	i	i	PRON
ejpam-6159	376	2	dt	dt	X
ejpam-6159	376	3	]	]	PUNCT
ejpam-6159	376	4	1	1	NUM
ejpam-6159	376	5	q	q	NOUN
ejpam-6159	376	6	.	.	PUNCT
ejpam-6159	377	1	theorem	theorem	NOUN
ejpam-6159	377	2	5	5	NUM
ejpam-6159	377	3	.	.	PUNCT
ejpam-6159	377	4	suppose	suppose	VERB
ejpam-6159	377	5	f	f	X
ejpam-6159	377	6	:	:	PUNCT
ejpam-6159	377	7	x	x	PUNCT
ejpam-6159	377	8	=	=	PUNCT
ejpam-6159	378	1	[	[	X
ejpam-6159	378	2	a1	a1	NOUN
ejpam-6159	378	3	,	,	PUNCT
ejpam-6159	378	4	a1+ς∗	a1+ς∗	PROPN
ejpam-6159	378	5	(	(	PUNCT
ejpam-6159	378	6	b1	b1	NOUN
ejpam-6159	378	7	,	,	PUNCT
ejpam-6159	378	8	a1	a1	NOUN
ejpam-6159	378	9	)	)	PUNCT
ejpam-6159	378	10	]	]	PUNCT
ejpam-6159	379	1	→	→	PUNCT
ejpam-6159	379	2	ℜ	ℜ	PROPN
ejpam-6159	379	3	is	be	AUX
ejpam-6159	379	4	a	a	DET
ejpam-6159	379	5	differentiableifunction	differentiableifunction	NOUN
ejpam-6159	379	6	function	function	NOUN
ejpam-6159	379	7	on	on	ADP
ejpam-6159	379	8	xo	xo	PROPN
ejpam-6159	379	9	such	such	ADJ
ejpam-6159	379	10	that	that	SCONJ
ejpam-6159	379	11	f′	f′	PROPN
ejpam-6159	379	12	∈	∈	PROPN
ejpam-6159	379	13	l[a1	l[a1	NOUN
ejpam-6159	379	14	,	,	PUNCT
ejpam-6159	379	15	a1	a1	NOUN
ejpam-6159	379	16	+	+	CCONJ
ejpam-6159	379	17	ς∗	ς∗	PROPN
ejpam-6159	379	18	(	(	PUNCT
ejpam-6159	379	19	b1	b1	NOUN
ejpam-6159	379	20	,	,	PUNCT
ejpam-6159	379	21	a1	a1	NOUN
ejpam-6159	379	22	)	)	PUNCT
ejpam-6159	379	23	]	]	PUNCT
ejpam-6159	379	24	and	and	CCONJ
ejpam-6159	379	25	consideration	consideration	NOUN
ejpam-6159	379	26	with	with	ADP
ejpam-6159	379	27	u∗.	u∗.	PROPN
ejpam-6159	379	28	let	let	VERB
ejpam-6159	379	29	for	for	ADP
ejpam-6159	379	30	some	some	DET
ejpam-6159	379	31	p	p	NOUN
ejpam-6159	379	32	,	,	PUNCT
ejpam-6159	379	33	q	q	ADJ
ejpam-6159	379	34	>	>	X
ejpam-6159	379	35	1	1	NUM
ejpam-6159	379	36	,	,	PUNCT
ejpam-6159	379	37	with	with	ADP
ejpam-6159	379	38	1	1	NUM
ejpam-6159	379	39	p	p	NOUN
ejpam-6159	380	1	+	+	NOUN
ejpam-6159	380	2	1	1	NUM
ejpam-6159	380	3	q	q	NOUN
ejpam-6159	380	4	=	=	SYM
ejpam-6159	380	5	1	1	NUM
ejpam-6159	380	6	,	,	PUNCT
ejpam-6159	380	7	|f′|q	|f′|q	VERB
ejpam-6159	380	8	be	be	AUX
ejpam-6159	380	9	a	a	DET
ejpam-6159	380	10	gfpp−s	gfpp−s	NOUN
ejpam-6159	380	11	function	function	NOUN
ejpam-6159	380	12	on	on	ADP
ejpam-6159	380	13	x	x	PUNCT
ejpam-6159	380	14	with	with	ADP
ejpam-6159	380	15	|f′|	|f′|	ADJ
ejpam-6159	380	16	≤	≤	NOUN
ejpam-6159	380	17	s	s	NOUN
ejpam-6159	380	18	,	,	PUNCT
ejpam-6159	380	19	for	for	ADP
ejpam-6159	380	20	all	all	DET
ejpam-6159	380	21	x	x	SYM
ejpam-6159	380	22	∈	∈	PROPN
ejpam-6159	380	23	[	[	X
ejpam-6159	380	24	a1	a1	NOUN
ejpam-6159	380	25	,	,	PUNCT
ejpam-6159	380	26	a1	a1	NOUN
ejpam-6159	380	27	+	+	CCONJ
ejpam-6159	380	28	ς∗	ς∗	PROPN
ejpam-6159	380	29	(	(	PUNCT
ejpam-6159	380	30	b1	b1	NOUN
ejpam-6159	380	31	,	,	PUNCT
ejpam-6159	380	32	a1	a1	NOUN
ejpam-6159	380	33	)	)	PUNCT
ejpam-6159	380	34	]	]	PUNCT
ejpam-6159	380	35	.	.	PUNCT
ejpam-6159	381	1	then	then	ADV
ejpam-6159	381	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	381	3	ς	ς	PROPN
ejpam-6159	381	4	ϱ	ϱ	PROPN
ejpam-6159	381	5	k	k	PROPN
ejpam-6159	381	6	∗	∗	X
ejpam-6159	381	7	(	(	PUNCT
ejpam-6159	381	8	x	x	NOUN
ejpam-6159	381	9	,	,	PUNCT
ejpam-6159	381	10	a1	a1	NOUN
ejpam-6159	381	11	)	)	PUNCT
ejpam-6159	381	12	+	+	CCONJ
ejpam-6159	381	13	ς	ς	PROPN
ejpam-6159	381	14	ϱ	ϱ	PROPN
ejpam-6159	381	15	k	k	PROPN
ejpam-6159	381	16	∗	∗	X
ejpam-6159	381	17	(	(	PUNCT
ejpam-6159	381	18	x	x	NOUN
ejpam-6159	381	19	,	,	PUNCT
ejpam-6159	381	20	b1	b1	NOUN
ejpam-6159	381	21	)	)	PUNCT
ejpam-6159	381	22	ς∗	ς∗	PROPN
ejpam-6159	381	23	(	(	PUNCT
ejpam-6159	381	24	b1	b1	NOUN
ejpam-6159	381	25	,	,	PUNCT
ejpam-6159	381	26	a1	a1	PROPN
ejpam-6159	381	27	)	)	PUNCT
ejpam-6159	381	28	f	f	NOUN
ejpam-6159	381	29	(	(	PUNCT
ejpam-6159	381	30	x)−	x)−	PROPN
ejpam-6159	381	31	γk	γk	PROPN
ejpam-6159	381	32	(	(	PUNCT
ejpam-6159	381	33	ϱ+	ϱ+	X
ejpam-6159	381	34	k	k	NOUN
ejpam-6159	381	35	)	)	PUNCT
ejpam-6159	381	36	ς	ς	PROPN
ejpam-6159	381	37	ϱ	ϱ	PROPN
ejpam-6159	381	38	k	k	PROPN
ejpam-6159	381	39	∗	∗	X
ejpam-6159	381	40	(	(	PUNCT
ejpam-6159	381	41	b1	b1	NOUN
ejpam-6159	381	42	,	,	PUNCT
ejpam-6159	381	43	a1	a1	PROPN
ejpam-6159	381	44	)	)	PUNCT
ejpam-6159	381	45	×	×	NOUN
ejpam-6159	381	46	{	{	PUNCT
ejpam-6159	381	47	jϱ,k	jϱ,k	X
ejpam-6159	381	48	(	(	PUNCT
ejpam-6159	381	49	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	381	50	,	,	PUNCT
ejpam-6159	381	51	a1	a1	NOUN
ejpam-6159	381	52	)	)	PUNCT
ejpam-6159	381	53	)	)	PUNCT
ejpam-6159	382	1	−	−	PROPN
ejpam-6159	382	2	f	f	X
ejpam-6159	382	3	(	(	PUNCT
ejpam-6159	382	4	a1	a1	PROPN
ejpam-6159	382	5	)	)	PUNCT
ejpam-6159	382	6	+	+	NUM
ejpam-6159	382	7	jϱ,k	jϱ,k	X
ejpam-6159	382	8	(	(	PUNCT
ejpam-6159	382	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	382	10	,	,	PUNCT
ejpam-6159	382	11	b1	b1	NOUN
ejpam-6159	382	12	)	)	PUNCT
ejpam-6159	382	13	)	)	PUNCT
ejpam-6159	383	1	+	+	CCONJ
ejpam-6159	384	1	f	f	X
ejpam-6159	384	2	(	(	PUNCT
ejpam-6159	384	3	a1	a1	NOUN
ejpam-6159	384	4	+	+	CCONJ
ejpam-6159	384	5	ς∗	ς∗	PROPN
ejpam-6159	384	6	(	(	PUNCT
ejpam-6159	384	7	b1	b1	NOUN
ejpam-6159	384	8	,	,	PUNCT
ejpam-6159	384	9	a1	a1	NOUN
ejpam-6159	384	10	)	)	PUNCT
ejpam-6159	384	11	)	)	PUNCT
ejpam-6159	384	12	}	}	PUNCT
ejpam-6159	384	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	384	14	≤	≤	NOUN
ejpam-6159	384	15	(	(	PUNCT
ejpam-6159	384	16	k	k	X
ejpam-6159	384	17	k+	k+	PROPN
ejpam-6159	384	18	pϱ	pϱ	PROPN
ejpam-6159	384	19	)	)	PUNCT
ejpam-6159	384	20	1	1	NUM
ejpam-6159	384	21	p	p	NOUN
ejpam-6159	384	22	(	(	PUNCT
ejpam-6159	384	23	ς	ς	PROPN
ejpam-6159	384	24	ϱ	ϱ	PROPN
ejpam-6159	384	25	k	k	PROPN
ejpam-6159	384	26	+1	+1	PROPN
ejpam-6159	384	27	∗	∗	NOUN
ejpam-6159	384	28	(	(	PUNCT
ejpam-6159	384	29	x	x	NOUN
ejpam-6159	384	30	,	,	PUNCT
ejpam-6159	384	31	a1	a1	NOUN
ejpam-6159	384	32	)	)	PUNCT
ejpam-6159	384	33	+	+	CCONJ
ejpam-6159	384	34	ς	ς	PROPN
ejpam-6159	384	35	ϱ	ϱ	PROPN
ejpam-6159	384	36	k	k	PROPN
ejpam-6159	384	37	+1	+1	PROPN
ejpam-6159	384	38	∗	∗	NOUN
ejpam-6159	384	39	(	(	PUNCT
ejpam-6159	384	40	x	x	NOUN
ejpam-6159	384	41	,	,	PUNCT
ejpam-6159	384	42	b1	b1	NOUN
ejpam-6159	384	43	)	)	PUNCT
ejpam-6159	384	44	ς∗	ς∗	PROPN
ejpam-6159	384	45	(	(	PUNCT
ejpam-6159	384	46	b1	b1	NOUN
ejpam-6159	384	47	,	,	PUNCT
ejpam-6159	384	48	a1	a1	NOUN
ejpam-6159	384	49	)	)	PUNCT
ejpam-6159	384	50	)	)	PUNCT
ejpam-6159	384	51	×	×	NOUN
ejpam-6159	384	52	sq∑n	sq∑n	NUM
ejpam-6159	385	1	i=1	i=1	ADP
ejpam-6159	385	2	ai	ai	VERB
ejpam-6159	385	3	.	.	PUNCT
ejpam-6159	386	1	n∑	n∑	INTJ
ejpam-6159	387	1	i=1	i=1	PROPN
ejpam-6159	387	2	ai	ai	VERB
ejpam-6159	387	3	[	[	PUNCT
ejpam-6159	387	4	∫	∫	PROPN
ejpam-6159	387	5	1	1	NUM
ejpam-6159	387	6	0	0	NUM
ejpam-6159	387	7	(	(	PUNCT
ejpam-6159	387	8	(	(	PUNCT
ejpam-6159	387	9	1−	1−	NUM
ejpam-6159	387	10	s	s	X
ejpam-6159	387	11	(	(	PUNCT
ejpam-6159	387	12	1−	1−	NUM
ejpam-6159	387	13	t	t	NOUN
ejpam-6159	387	14	)	)	PUNCT
ejpam-6159	387	15	)	)	PUNCT
ejpam-6159	387	16	1	1	NUM
ejpam-6159	387	17	i	i	NOUN
ejpam-6159	387	18	)	)	PUNCT
ejpam-6159	388	1	dt+	dt+	NOUN
ejpam-6159	388	2	∫	∫	PROPN
ejpam-6159	388	3	1	1	NUM
ejpam-6159	388	4	0	0	NUM
ejpam-6159	388	5	(	(	PUNCT
ejpam-6159	388	6	1−	1−	NUM
ejpam-6159	388	7	st	st	NOUN
ejpam-6159	388	8	)	)	PUNCT
ejpam-6159	388	9	1	1	NUM
ejpam-6159	389	1	i	i	PRON
ejpam-6159	389	2	dt	dt	X
ejpam-6159	389	3	]	]	PUNCT
ejpam-6159	389	4	1	1	NUM
ejpam-6159	389	5	q	q	NOUN
ejpam-6159	389	6	.	.	PUNCT
ejpam-6159	390	1	(	(	PUNCT
ejpam-6159	390	2	34	34	NUM
ejpam-6159	390	3	)	)	PUNCT
ejpam-6159	390	4	proof	proof	NOUN
ejpam-6159	390	5	.	.	PUNCT
ejpam-6159	391	1	from	from	ADP
ejpam-6159	391	2	lemma	lemma	PROPN
ejpam-6159	391	3	1	1	NUM
ejpam-6159	391	4	and	and	CCONJ
ejpam-6159	391	5	a	a	DET
ejpam-6159	391	6	propertyiof	propertyiof	NOUN
ejpam-6159	391	7	the	the	DET
ejpam-6159	391	8	gfpp−s	gfpp−s	PROPN
ejpam-6159	391	9	function	function	NOUN
ejpam-6159	391	10	|f′|q	|f′|q	NOUN
ejpam-6159	391	11	,	,	PUNCT
ejpam-6159	391	12	and	and	CCONJ
ejpam-6159	391	13	the	the	DET
ejpam-6159	391	14	hölder	hölder	NOUN
ejpam-6159	391	15	inequality	inequality	NOUN
ejpam-6159	391	16	,	,	PUNCT
ejpam-6159	391	17	one	one	PRON
ejpam-6159	391	18	has	have	VERB
ejpam-6159	391	19	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	391	20	ς	ς	PROPN
ejpam-6159	391	21	ϱ	ϱ	PROPN
ejpam-6159	391	22	k	k	PROPN
ejpam-6159	391	23	∗	∗	X
ejpam-6159	391	24	(	(	PUNCT
ejpam-6159	391	25	x	x	NOUN
ejpam-6159	391	26	,	,	PUNCT
ejpam-6159	391	27	a1	a1	NOUN
ejpam-6159	391	28	)	)	PUNCT
ejpam-6159	391	29	+	+	CCONJ
ejpam-6159	392	1	ς	ς	PROPN
ejpam-6159	392	2	ϱ	ϱ	PROPN
ejpam-6159	392	3	k	k	PROPN
ejpam-6159	392	4	∗	∗	X
ejpam-6159	392	5	(	(	PUNCT
ejpam-6159	392	6	x	x	NOUN
ejpam-6159	392	7	,	,	PUNCT
ejpam-6159	392	8	b1	b1	NOUN
ejpam-6159	392	9	)	)	PUNCT
ejpam-6159	392	10	ς∗	ς∗	PROPN
ejpam-6159	392	11	(	(	PUNCT
ejpam-6159	392	12	b1	b1	NOUN
ejpam-6159	392	13	,	,	PUNCT
ejpam-6159	392	14	a1	a1	PROPN
ejpam-6159	392	15	)	)	PUNCT
ejpam-6159	392	16	f	f	NOUN
ejpam-6159	392	17	(	(	PUNCT
ejpam-6159	392	18	x)−	x)−	PROPN
ejpam-6159	392	19	γk	γk	PROPN
ejpam-6159	392	20	(	(	PUNCT
ejpam-6159	392	21	ϱ+	ϱ+	X
ejpam-6159	392	22	k	k	NOUN
ejpam-6159	392	23	)	)	PUNCT
ejpam-6159	392	24	ς	ς	PROPN
ejpam-6159	392	25	ϱ	ϱ	PROPN
ejpam-6159	392	26	k	k	PROPN
ejpam-6159	392	27	∗	∗	X
ejpam-6159	392	28	(	(	PUNCT
ejpam-6159	392	29	b1	b1	NOUN
ejpam-6159	392	30	,	,	PUNCT
ejpam-6159	392	31	a1	a1	PROPN
ejpam-6159	392	32	)	)	PUNCT
ejpam-6159	392	33	×	×	NOUN
ejpam-6159	392	34	{	{	PUNCT
ejpam-6159	392	35	jϱ,k	jϱ,k	X
ejpam-6159	392	36	(	(	PUNCT
ejpam-6159	392	37	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	392	38	,	,	PUNCT
ejpam-6159	392	39	a1	a1	NOUN
ejpam-6159	392	40	)	)	PUNCT
ejpam-6159	392	41	)	)	PUNCT
ejpam-6159	393	1	−	−	PROPN
ejpam-6159	393	2	f	f	X
ejpam-6159	393	3	(	(	PUNCT
ejpam-6159	393	4	a1	a1	PROPN
ejpam-6159	393	5	)	)	PUNCT
ejpam-6159	393	6	+	+	NUM
ejpam-6159	393	7	jϱ,k	jϱ,k	X
ejpam-6159	393	8	(	(	PUNCT
ejpam-6159	393	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	393	10	,	,	PUNCT
ejpam-6159	393	11	b1	b1	NOUN
ejpam-6159	393	12	)	)	PUNCT
ejpam-6159	393	13	)	)	PUNCT
ejpam-6159	394	1	+	+	CCONJ
ejpam-6159	394	2	f	f	X
ejpam-6159	394	3	(	(	PUNCT
ejpam-6159	394	4	a1	a1	NOUN
ejpam-6159	394	5	+	+	CCONJ
ejpam-6159	394	6	ς∗	ς∗	PROPN
ejpam-6159	394	7	(	(	PUNCT
ejpam-6159	394	8	b1	b1	NOUN
ejpam-6159	394	9	,	,	PUNCT
ejpam-6159	394	10	a1	a1	NOUN
ejpam-6159	394	11	)	)	PUNCT
ejpam-6159	394	12	)	)	PUNCT
ejpam-6159	394	13	}	}	PUNCT
ejpam-6159	394	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	394	15	≤	≤	NUM
ejpam-6159	394	16	ς	ς	PROPN
ejpam-6159	394	17	ϱ	ϱ	PROPN
ejpam-6159	394	18	k	k	PROPN
ejpam-6159	394	19	+1	+1	PROPN
ejpam-6159	394	20	∗	∗	NOUN
ejpam-6159	394	21	(	(	PUNCT
ejpam-6159	394	22	x	x	NOUN
ejpam-6159	394	23	,	,	PUNCT
ejpam-6159	394	24	a1	a1	NOUN
ejpam-6159	394	25	)	)	PUNCT
ejpam-6159	394	26	ς∗	ς∗	NOUN
ejpam-6159	394	27	(	(	PUNCT
ejpam-6159	394	28	b1	b1	NOUN
ejpam-6159	394	29	,	,	PUNCT
ejpam-6159	394	30	a1	a1	PROPN
ejpam-6159	394	31	)	)	PUNCT
ejpam-6159	394	32	∫	∫	NOUN
ejpam-6159	394	33	1	1	NUM
ejpam-6159	394	34	0	0	NUM
ejpam-6159	394	35	t	t	PROPN
ejpam-6159	394	36	ϱ	ϱ	ADP
ejpam-6159	394	37	k	k	PROPN
ejpam-6159	394	38	∣∣f′	∣∣f′	PROPN
ejpam-6159	394	39	(	(	PUNCT
ejpam-6159	394	40	a1	a1	NOUN
ejpam-6159	394	41	+	+	CCONJ
ejpam-6159	394	42	tς∗	tς∗	X
ejpam-6159	394	43	(	(	PUNCT
ejpam-6159	394	44	x	x	NOUN
ejpam-6159	394	45	,	,	PUNCT
ejpam-6159	394	46	a1	a1	NOUN
ejpam-6159	394	47	)	)	PUNCT
ejpam-6159	394	48	)	)	PUNCT
ejpam-6159	395	1	∣∣dt	∣∣dt	PROPN
ejpam-6159	396	1	+	+	CCONJ
ejpam-6159	396	2	ς	ς	PROPN
ejpam-6159	396	3	ϱ	ϱ	PROPN
ejpam-6159	396	4	k	k	PROPN
ejpam-6159	396	5	+1	+1	PROPN
ejpam-6159	396	6	∗	∗	NOUN
ejpam-6159	396	7	(	(	PUNCT
ejpam-6159	396	8	x	x	NOUN
ejpam-6159	396	9	,	,	PUNCT
ejpam-6159	396	10	b1	b1	NOUN
ejpam-6159	396	11	)	)	PUNCT
ejpam-6159	396	12	ς∗	ς∗	PROPN
ejpam-6159	396	13	(	(	PUNCT
ejpam-6159	396	14	b1	b1	NOUN
ejpam-6159	396	15	,	,	PUNCT
ejpam-6159	396	16	a1	a1	PROPN
ejpam-6159	396	17	)	)	PUNCT
ejpam-6159	396	18	∫	∫	NOUN
ejpam-6159	397	1	1	1	NUM
ejpam-6159	397	2	0	0	NUM
ejpam-6159	397	3	t	t	PROPN
ejpam-6159	397	4	ϱ	ϱ	ADP
ejpam-6159	397	5	k	k	PROPN
ejpam-6159	397	6	∣∣f′	∣∣f′	PROPN
ejpam-6159	397	7	(	(	PUNCT
ejpam-6159	397	8	b1	b1	NOUN
ejpam-6159	397	9	+	+	CCONJ
ejpam-6159	397	10	tς∗	tς∗	X
ejpam-6159	397	11	(	(	PUNCT
ejpam-6159	397	12	x	x	NOUN
ejpam-6159	397	13	,	,	PUNCT
ejpam-6159	397	14	b1	b1	NOUN
ejpam-6159	397	15	)	)	PUNCT
ejpam-6159	397	16	)	)	PUNCT
ejpam-6159	398	1	∣∣dt	∣∣dt	PROPN
ejpam-6159	398	2	j.	j.	PROPN
ejpam-6159	398	3	nasir	nasir	PROPN
ejpam-6159	398	4	et	et	PROPN
ejpam-6159	398	5	al	al	PROPN
ejpam-6159	398	6	.	.	PUNCT
ejpam-6159	398	7	/	/	SYM
ejpam-6159	398	8	eur	eur	PROPN
ejpam-6159	398	9	.	.	PUNCT
ejpam-6159	399	1	j.	j.	PROPN
ejpam-6159	399	2	pure	pure	PROPN
ejpam-6159	399	3	appl	appl	PROPN
ejpam-6159	399	4	.	.	PROPN
ejpam-6159	399	5	math	math	PROPN
ejpam-6159	399	6	,	,	PUNCT
ejpam-6159	399	7	18	18	NUM
ejpam-6159	399	8	(	(	PUNCT
ejpam-6159	399	9	3	3	NUM
ejpam-6159	399	10	)	)	PUNCT
ejpam-6159	399	11	(	(	PUNCT
ejpam-6159	399	12	2025	2025	NUM
ejpam-6159	399	13	)	)	PUNCT
ejpam-6159	399	14	,	,	PUNCT
ejpam-6159	399	15	6159	6159	NUM
ejpam-6159	399	16	14	14	NUM
ejpam-6159	399	17	of	of	ADP
ejpam-6159	399	18	26	26	NUM
ejpam-6159	399	19	≤	≤	NUM
ejpam-6159	399	20	ς	ς	PROPN
ejpam-6159	399	21	ϱ	ϱ	PROPN
ejpam-6159	399	22	k	k	PROPN
ejpam-6159	399	23	+1	+1	PROPN
ejpam-6159	399	24	∗	∗	NOUN
ejpam-6159	399	25	(	(	PUNCT
ejpam-6159	399	26	x	x	NOUN
ejpam-6159	399	27	,	,	PUNCT
ejpam-6159	399	28	a1	a1	NOUN
ejpam-6159	399	29	)	)	PUNCT
ejpam-6159	399	30	ς∗	ς∗	NOUN
ejpam-6159	399	31	(	(	PUNCT
ejpam-6159	399	32	b1	b1	NOUN
ejpam-6159	399	33	,	,	PUNCT
ejpam-6159	399	34	a1	a1	PROPN
ejpam-6159	399	35	)	)	PUNCT
ejpam-6159	399	36	(	(	PUNCT
ejpam-6159	399	37	∫	∫	PROPN
ejpam-6159	399	38	1	1	NUM
ejpam-6159	399	39	0	0	NUM
ejpam-6159	399	40	t	t	NOUN
ejpam-6159	399	41	ϱ	ϱ	X
ejpam-6159	399	42	kdt	kdt	PROPN
ejpam-6159	399	43	)	)	PUNCT
ejpam-6159	399	44	1	1	NUM
ejpam-6159	399	45	p	p	NOUN
ejpam-6159	399	46	(	(	PUNCT
ejpam-6159	399	47	∫	∫	PROPN
ejpam-6159	399	48	1	1	NUM
ejpam-6159	399	49	0	0	NUM
ejpam-6159	399	50	∣∣f′	∣∣f′	NOUN
ejpam-6159	399	51	(	(	PUNCT
ejpam-6159	399	52	a1	a1	NOUN
ejpam-6159	399	53	+	+	CCONJ
ejpam-6159	399	54	tς∗	tς∗	X
ejpam-6159	399	55	(	(	PUNCT
ejpam-6159	399	56	x	x	NOUN
ejpam-6159	399	57	,	,	PUNCT
ejpam-6159	399	58	a1	a1	NOUN
ejpam-6159	399	59	)	)	PUNCT
ejpam-6159	399	60	)	)	PUNCT
ejpam-6159	400	1	∣∣qdt	∣∣qdt	NOUN
ejpam-6159	400	2	)	)	PUNCT
ejpam-6159	400	3	1	1	NUM
ejpam-6159	400	4	q	q	NOUN
ejpam-6159	401	1	+	+	CCONJ
ejpam-6159	401	2	ς	ς	PROPN
ejpam-6159	401	3	ϱ	ϱ	PROPN
ejpam-6159	401	4	k	k	PROPN
ejpam-6159	401	5	+1	+1	PROPN
ejpam-6159	401	6	∗	∗	NOUN
ejpam-6159	401	7	(	(	PUNCT
ejpam-6159	401	8	x	x	NOUN
ejpam-6159	401	9	,	,	PUNCT
ejpam-6159	401	10	b1	b1	NOUN
ejpam-6159	401	11	)	)	PUNCT
ejpam-6159	401	12	ς∗	ς∗	PROPN
ejpam-6159	401	13	(	(	PUNCT
ejpam-6159	401	14	b1	b1	NOUN
ejpam-6159	401	15	,	,	PUNCT
ejpam-6159	401	16	a1	a1	PROPN
ejpam-6159	401	17	)	)	PUNCT
ejpam-6159	401	18	(	(	PUNCT
ejpam-6159	401	19	∫	∫	PROPN
ejpam-6159	401	20	1	1	NUM
ejpam-6159	401	21	0	0	NUM
ejpam-6159	401	22	t	t	NOUN
ejpam-6159	401	23	ϱ	ϱ	X
ejpam-6159	401	24	kdt	kdt	PROPN
ejpam-6159	401	25	)	)	PUNCT
ejpam-6159	401	26	1	1	NUM
ejpam-6159	401	27	p	p	NOUN
ejpam-6159	401	28	(	(	PUNCT
ejpam-6159	401	29	∫	∫	PROPN
ejpam-6159	401	30	1	1	NUM
ejpam-6159	401	31	0	0	NUM
ejpam-6159	401	32	∣∣f′	∣∣f′	NOUN
ejpam-6159	401	33	(	(	PUNCT
ejpam-6159	401	34	b1	b1	NOUN
ejpam-6159	401	35	+	+	CCONJ
ejpam-6159	401	36	tς∗	tς∗	X
ejpam-6159	401	37	(	(	PUNCT
ejpam-6159	401	38	x	x	NOUN
ejpam-6159	401	39	,	,	PUNCT
ejpam-6159	401	40	b1	b1	NOUN
ejpam-6159	401	41	)	)	PUNCT
ejpam-6159	401	42	)	)	PUNCT
ejpam-6159	402	1	∣∣qdt	∣∣qdt	NOUN
ejpam-6159	402	2	)	)	PUNCT
ejpam-6159	402	3	1	1	NUM
ejpam-6159	402	4	q	q	NOUN
ejpam-6159	402	5	≤	≤	NUM
ejpam-6159	402	6	(	(	PUNCT
ejpam-6159	402	7	k	k	X
ejpam-6159	402	8	k+	k+	PROPN
ejpam-6159	402	9	pϱ	pϱ	PROPN
ejpam-6159	402	10	)	)	PUNCT
ejpam-6159	403	1	1	1	NUM
ejpam-6159	403	2	p	p	NOUN
ejpam-6159	403	3	[	[	PUNCT
ejpam-6159	403	4	ς	ς	PROPN
ejpam-6159	403	5	ϱ	ϱ	PROPN
ejpam-6159	403	6	k	k	PROPN
ejpam-6159	403	7	+1	+1	PROPN
ejpam-6159	403	8	∗	∗	NOUN
ejpam-6159	403	9	(	(	PUNCT
ejpam-6159	403	10	x	x	NOUN
ejpam-6159	403	11	,	,	PUNCT
ejpam-6159	403	12	a1	a1	NOUN
ejpam-6159	403	13	)	)	PUNCT
ejpam-6159	403	14	ς∗	ς∗	NOUN
ejpam-6159	403	15	(	(	PUNCT
ejpam-6159	403	16	b1	b1	NOUN
ejpam-6159	403	17	,	,	PUNCT
ejpam-6159	403	18	a1	a1	NOUN
ejpam-6159	403	19	)	)	PUNCT
ejpam-6159	403	20	{	{	PUNCT
ejpam-6159	403	21	∑n	∑n	PROPN
ejpam-6159	403	22	i=1	i=1	PROPN
ejpam-6159	403	23	ai	ai	VERB
ejpam-6159	403	24	∫	∫	PROPN
ejpam-6159	403	25	1	1	NUM
ejpam-6159	403	26	0	0	NUM
ejpam-6159	403	27	(	(	PUNCT
ejpam-6159	403	28	(	(	PUNCT
ejpam-6159	403	29	1−	1−	NUM
ejpam-6159	403	30	s	s	X
ejpam-6159	403	31	(	(	PUNCT
ejpam-6159	403	32	1−	1−	NUM
ejpam-6159	403	33	t	t	NOUN
ejpam-6159	403	34	)	)	PUNCT
ejpam-6159	403	35	)	)	PUNCT
ejpam-6159	403	36	1	1	NUM
ejpam-6159	403	37	i	i	NOUN
ejpam-6159	403	38	)	)	PUNCT
ejpam-6159	404	1	∑n	∑n	PROPN
ejpam-6159	404	2	i=1	i=1	PROPN
ejpam-6159	404	3	ai	ai	VERB
ejpam-6159	404	4	∣∣f′	∣∣f′	NOUN
ejpam-6159	404	5	(	(	PUNCT
ejpam-6159	404	6	x	x	X
ejpam-6159	404	7	)	)	PUNCT
ejpam-6159	404	8	∣∣q	∣∣q	NUM
ejpam-6159	404	9	dt	dt	NOUN
ejpam-6159	405	1	+	+	CCONJ
ejpam-6159	405	2	∑n	∑n	PROPN
ejpam-6159	406	1	i=1	i=1	PROPN
ejpam-6159	406	2	ai	ai	VERB
ejpam-6159	406	3	∫	∫	PROPN
ejpam-6159	406	4	1	1	NUM
ejpam-6159	406	5	0	0	NUM
ejpam-6159	406	6	(	(	PUNCT
ejpam-6159	406	7	(	(	PUNCT
ejpam-6159	406	8	1−	1−	NUM
ejpam-6159	406	9	st	st	NOUN
ejpam-6159	406	10	)	)	PUNCT
ejpam-6159	406	11	1	1	NUM
ejpam-6159	406	12	i	i	NOUN
ejpam-6159	406	13	)	)	PUNCT
ejpam-6159	407	1	∑n	∑n	PROPN
ejpam-6159	407	2	i=1	i=1	PROPN
ejpam-6159	407	3	ai	ai	VERB
ejpam-6159	407	4	∣∣f′	∣∣f′	NOUN
ejpam-6159	407	5	(	(	PUNCT
ejpam-6159	407	6	a1	a1	NOUN
ejpam-6159	407	7	)	)	PUNCT
ejpam-6159	407	8	∣∣q	∣∣q	NUM
ejpam-6159	407	9	dt	dt	NOUN
ejpam-6159	407	10	}	}	PUNCT
ejpam-6159	407	11	1	1	NUM
ejpam-6159	407	12	q	q	NOUN
ejpam-6159	408	1	+	+	NUM
ejpam-6159	408	2	ς	ς	PROPN
ejpam-6159	408	3	ϱ	ϱ	PROPN
ejpam-6159	408	4	k	k	PROPN
ejpam-6159	408	5	+1	+1	PROPN
ejpam-6159	408	6	∗	∗	NOUN
ejpam-6159	408	7	(	(	PUNCT
ejpam-6159	408	8	x	x	NOUN
ejpam-6159	408	9	,	,	PUNCT
ejpam-6159	408	10	b1	b1	NOUN
ejpam-6159	408	11	)	)	PUNCT
ejpam-6159	408	12	ς∗	ς∗	PROPN
ejpam-6159	408	13	(	(	PUNCT
ejpam-6159	408	14	b1	b1	NOUN
ejpam-6159	408	15	,	,	PUNCT
ejpam-6159	408	16	a1	a1	NOUN
ejpam-6159	408	17	)	)	PUNCT
ejpam-6159	408	18	{	{	PUNCT
ejpam-6159	409	1	∑n	∑n	PROPN
ejpam-6159	409	2	i=1	i=1	PROPN
ejpam-6159	409	3	ai	ai	VERB
ejpam-6159	409	4	∫	∫	PROPN
ejpam-6159	409	5	1	1	NUM
ejpam-6159	409	6	0	0	NUM
ejpam-6159	409	7	(	(	PUNCT
ejpam-6159	409	8	(	(	PUNCT
ejpam-6159	409	9	1−	1−	NUM
ejpam-6159	409	10	s	s	X
ejpam-6159	409	11	(	(	PUNCT
ejpam-6159	409	12	1−	1−	NUM
ejpam-6159	409	13	t	t	NOUN
ejpam-6159	409	14	)	)	PUNCT
ejpam-6159	409	15	)	)	PUNCT
ejpam-6159	409	16	1	1	NUM
ejpam-6159	409	17	i	i	NOUN
ejpam-6159	409	18	)	)	PUNCT
ejpam-6159	410	1	∑n	∑n	PROPN
ejpam-6159	410	2	i=1	i=1	PROPN
ejpam-6159	410	3	ai	ai	VERB
ejpam-6159	410	4	∣∣f′	∣∣f′	NOUN
ejpam-6159	410	5	(	(	PUNCT
ejpam-6159	410	6	x	x	X
ejpam-6159	410	7	)	)	PUNCT
ejpam-6159	410	8	∣∣q	∣∣q	NUM
ejpam-6159	410	9	dt	dt	NOUN
ejpam-6159	411	1	+	+	CCONJ
ejpam-6159	411	2	∑n	∑n	PROPN
ejpam-6159	412	1	i=1	i=1	PROPN
ejpam-6159	412	2	ai	ai	VERB
ejpam-6159	412	3	∫	∫	PROPN
ejpam-6159	412	4	1	1	NUM
ejpam-6159	412	5	0	0	NUM
ejpam-6159	412	6	(	(	PUNCT
ejpam-6159	412	7	(	(	PUNCT
ejpam-6159	412	8	1−	1−	NUM
ejpam-6159	412	9	st	st	NOUN
ejpam-6159	412	10	)	)	PUNCT
ejpam-6159	412	11	1	1	NUM
ejpam-6159	412	12	i	i	NOUN
ejpam-6159	412	13	)	)	PUNCT
ejpam-6159	413	1	∑n	∑n	PROPN
ejpam-6159	413	2	i=1	i=1	PROPN
ejpam-6159	413	3	ai	ai	VERB
ejpam-6159	413	4	∣∣f′	∣∣f′	NOUN
ejpam-6159	413	5	(	(	PUNCT
ejpam-6159	413	6	b1	b1	NOUN
ejpam-6159	413	7	)	)	PUNCT
ejpam-6159	413	8	∣∣q	∣∣q	NUM
ejpam-6159	413	9	dt	dt	NOUN
ejpam-6159	413	10	}	}	PUNCT
ejpam-6159	413	11	1	1	NUM
ejpam-6159	413	12	q	q	NOUN
ejpam-6159	413	13	]	]	PUNCT
ejpam-6159	413	14	≤	≤	X
ejpam-6159	413	15	(	(	PUNCT
ejpam-6159	413	16	k	k	X
ejpam-6159	413	17	k+	k+	PROPN
ejpam-6159	413	18	pϱ	pϱ	PROPN
ejpam-6159	413	19	)	)	PUNCT
ejpam-6159	413	20	1	1	NUM
ejpam-6159	413	21	p	p	NOUN
ejpam-6159	413	22	(	(	PUNCT
ejpam-6159	413	23	ς	ς	PROPN
ejpam-6159	413	24	ϱ	ϱ	PROPN
ejpam-6159	413	25	k	k	PROPN
ejpam-6159	413	26	+1	+1	PROPN
ejpam-6159	413	27	∗	∗	NOUN
ejpam-6159	413	28	(	(	PUNCT
ejpam-6159	413	29	x	x	NOUN
ejpam-6159	413	30	,	,	PUNCT
ejpam-6159	413	31	a1	a1	NOUN
ejpam-6159	413	32	)	)	PUNCT
ejpam-6159	413	33	+	+	CCONJ
ejpam-6159	413	34	ς	ς	PROPN
ejpam-6159	413	35	ϱ	ϱ	PROPN
ejpam-6159	413	36	k	k	PROPN
ejpam-6159	413	37	+1	+1	PROPN
ejpam-6159	413	38	∗	∗	NOUN
ejpam-6159	413	39	(	(	PUNCT
ejpam-6159	413	40	x	x	NOUN
ejpam-6159	413	41	,	,	PUNCT
ejpam-6159	413	42	b1	b1	NOUN
ejpam-6159	413	43	)	)	PUNCT
ejpam-6159	413	44	ς∗	ς∗	PROPN
ejpam-6159	413	45	(	(	PUNCT
ejpam-6159	413	46	b1	b1	NOUN
ejpam-6159	413	47	,	,	PUNCT
ejpam-6159	413	48	a1	a1	NOUN
ejpam-6159	413	49	)	)	PUNCT
ejpam-6159	413	50	)	)	PUNCT
ejpam-6159	414	1	×	×	NOUN
ejpam-6159	414	2	sq∑n	sq∑n	NUM
ejpam-6159	414	3	i=1	i=1	ADP
ejpam-6159	414	4	ai	ai	VERB
ejpam-6159	414	5	.	.	PUNCT
ejpam-6159	415	1	n∑	n∑	INTJ
ejpam-6159	416	1	i=1	i=1	PROPN
ejpam-6159	416	2	ai	ai	VERB
ejpam-6159	416	3	[	[	PUNCT
ejpam-6159	416	4	∫	∫	PROPN
ejpam-6159	416	5	1	1	NUM
ejpam-6159	416	6	0	0	NUM
ejpam-6159	416	7	(	(	PUNCT
ejpam-6159	416	8	(	(	PUNCT
ejpam-6159	416	9	1−	1−	NUM
ejpam-6159	416	10	s	s	X
ejpam-6159	416	11	(	(	PUNCT
ejpam-6159	416	12	1−	1−	NUM
ejpam-6159	416	13	t	t	NOUN
ejpam-6159	416	14	)	)	PUNCT
ejpam-6159	416	15	)	)	PUNCT
ejpam-6159	416	16	1	1	NUM
ejpam-6159	416	17	i	i	NOUN
ejpam-6159	416	18	)	)	PUNCT
ejpam-6159	417	1	dt+	dt+	NOUN
ejpam-6159	417	2	∫	∫	PROPN
ejpam-6159	417	3	1	1	NUM
ejpam-6159	417	4	0	0	NUM
ejpam-6159	417	5	(	(	PUNCT
ejpam-6159	417	6	1−	1−	NUM
ejpam-6159	417	7	st	st	NOUN
ejpam-6159	417	8	)	)	PUNCT
ejpam-6159	417	9	1	1	NUM
ejpam-6159	418	1	i	i	PRON
ejpam-6159	418	2	dt	dt	X
ejpam-6159	418	3	]	]	PUNCT
ejpam-6159	418	4	1	1	NUM
ejpam-6159	418	5	q	q	NOUN
ejpam-6159	418	6	.	.	PUNCT
ejpam-6159	419	1	(	(	PUNCT
ejpam-6159	419	2	35	35	NUM
ejpam-6159	419	3	)	)	PUNCT
ejpam-6159	419	4	corollary	corollary	NOUN
ejpam-6159	419	5	7	7	NUM
ejpam-6159	419	6	.	.	PUNCT
ejpam-6159	420	1	if	if	SCONJ
ejpam-6159	420	2	one	one	PRON
ejpam-6159	420	3	can	can	AUX
ejpam-6159	420	4	take	take	VERB
ejpam-6159	420	5	s	s	PART
ejpam-6159	420	6	=	=	SYM
ejpam-6159	420	7	1	1	NUM
ejpam-6159	420	8	initheorem	initheorem	VERB
ejpam-6159	420	9	5	5	NUM
ejpam-6159	420	10	,	,	PUNCT
ejpam-6159	420	11	then	then	ADV
ejpam-6159	420	12	we	we	PRON
ejpam-6159	420	13	have	have	VERB
ejpam-6159	420	14	the	the	DET
ejpam-6159	420	15	following	follow	VERB
ejpam-6159	420	16	inequalities	inequality	NOUN
ejpam-6159	420	17	for	for	ADP
ejpam-6159	420	18	a	a	DET
ejpam-6159	420	19	gfpp	gfpp	NOUN
ejpam-6159	420	20	function	function	NOUN
ejpam-6159	420	21	with	with	ADP
ejpam-6159	420	22	k−fractional	k−fractional	PROPN
ejpam-6159	420	23	integral	integral	ADJ
ejpam-6159	420	24	operators:∣∣∣∣	operators:∣∣∣∣	ADJ
ejpam-6159	420	25	ς	ς	PROPN
ejpam-6159	420	26	ϱ	ϱ	PROPN
ejpam-6159	420	27	k	k	PROPN
ejpam-6159	420	28	∗	∗	X
ejpam-6159	420	29	(	(	PUNCT
ejpam-6159	420	30	x	x	NOUN
ejpam-6159	420	31	,	,	PUNCT
ejpam-6159	420	32	a1	a1	NOUN
ejpam-6159	420	33	)	)	PUNCT
ejpam-6159	420	34	+	+	CCONJ
ejpam-6159	421	1	ς	ς	PROPN
ejpam-6159	421	2	ϱ	ϱ	PROPN
ejpam-6159	421	3	k	k	PROPN
ejpam-6159	421	4	∗	∗	X
ejpam-6159	421	5	(	(	PUNCT
ejpam-6159	421	6	x	x	NOUN
ejpam-6159	421	7	,	,	PUNCT
ejpam-6159	421	8	b1	b1	NOUN
ejpam-6159	421	9	)	)	PUNCT
ejpam-6159	421	10	ς∗	ς∗	PROPN
ejpam-6159	421	11	(	(	PUNCT
ejpam-6159	421	12	b1	b1	NOUN
ejpam-6159	421	13	,	,	PUNCT
ejpam-6159	421	14	a1	a1	PROPN
ejpam-6159	421	15	)	)	PUNCT
ejpam-6159	421	16	f	f	NOUN
ejpam-6159	421	17	(	(	PUNCT
ejpam-6159	421	18	x)−	x)−	PROPN
ejpam-6159	421	19	γk	γk	PROPN
ejpam-6159	421	20	(	(	PUNCT
ejpam-6159	421	21	ϱ+	ϱ+	X
ejpam-6159	421	22	k	k	NOUN
ejpam-6159	421	23	)	)	PUNCT
ejpam-6159	421	24	ς	ς	PROPN
ejpam-6159	421	25	ϱ	ϱ	PROPN
ejpam-6159	421	26	k	k	PROPN
ejpam-6159	421	27	∗	∗	X
ejpam-6159	421	28	(	(	PUNCT
ejpam-6159	421	29	b1	b1	NOUN
ejpam-6159	421	30	,	,	PUNCT
ejpam-6159	421	31	a1	a1	PROPN
ejpam-6159	421	32	)	)	PUNCT
ejpam-6159	421	33	×	×	NOUN
ejpam-6159	421	34	{	{	PUNCT
ejpam-6159	421	35	jϱ,k	jϱ,k	X
ejpam-6159	421	36	(	(	PUNCT
ejpam-6159	421	37	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	421	38	,	,	PUNCT
ejpam-6159	421	39	a1	a1	NOUN
ejpam-6159	421	40	)	)	PUNCT
ejpam-6159	421	41	)	)	PUNCT
ejpam-6159	422	1	−	−	PROPN
ejpam-6159	422	2	f	f	X
ejpam-6159	422	3	(	(	PUNCT
ejpam-6159	422	4	a1	a1	PROPN
ejpam-6159	422	5	)	)	PUNCT
ejpam-6159	422	6	+	+	NUM
ejpam-6159	422	7	jϱ,k	jϱ,k	X
ejpam-6159	422	8	(	(	PUNCT
ejpam-6159	422	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	422	10	,	,	PUNCT
ejpam-6159	422	11	b1	b1	NOUN
ejpam-6159	422	12	)	)	PUNCT
ejpam-6159	422	13	)	)	PUNCT
ejpam-6159	423	1	+	+	CCONJ
ejpam-6159	424	1	f	f	X
ejpam-6159	424	2	(	(	PUNCT
ejpam-6159	424	3	a1	a1	NOUN
ejpam-6159	424	4	+	+	CCONJ
ejpam-6159	424	5	ς∗	ς∗	PROPN
ejpam-6159	424	6	(	(	PUNCT
ejpam-6159	424	7	b1	b1	NOUN
ejpam-6159	424	8	,	,	PUNCT
ejpam-6159	424	9	a1	a1	NOUN
ejpam-6159	424	10	)	)	PUNCT
ejpam-6159	424	11	)	)	PUNCT
ejpam-6159	424	12	}	}	PUNCT
ejpam-6159	424	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	424	14	≤	≤	NOUN
ejpam-6159	424	15	(	(	PUNCT
ejpam-6159	424	16	k	k	X
ejpam-6159	424	17	k+	k+	PROPN
ejpam-6159	424	18	pϱ	pϱ	PROPN
ejpam-6159	424	19	)	)	PUNCT
ejpam-6159	424	20	1	1	NUM
ejpam-6159	424	21	p	p	NOUN
ejpam-6159	424	22	(	(	PUNCT
ejpam-6159	424	23	ς	ς	PROPN
ejpam-6159	424	24	ϱ	ϱ	PROPN
ejpam-6159	424	25	k	k	PROPN
ejpam-6159	424	26	+1	+1	PROPN
ejpam-6159	424	27	∗	∗	NOUN
ejpam-6159	424	28	(	(	PUNCT
ejpam-6159	424	29	x	x	NOUN
ejpam-6159	424	30	,	,	PUNCT
ejpam-6159	424	31	a1	a1	NOUN
ejpam-6159	424	32	)	)	PUNCT
ejpam-6159	424	33	+	+	CCONJ
ejpam-6159	424	34	ς	ς	PROPN
ejpam-6159	424	35	ϱ	ϱ	PROPN
ejpam-6159	424	36	k	k	PROPN
ejpam-6159	424	37	+1	+1	PROPN
ejpam-6159	424	38	∗	∗	NOUN
ejpam-6159	424	39	(	(	PUNCT
ejpam-6159	424	40	x	x	NOUN
ejpam-6159	424	41	,	,	PUNCT
ejpam-6159	424	42	b1	b1	NOUN
ejpam-6159	424	43	)	)	PUNCT
ejpam-6159	424	44	ς∗	ς∗	PROPN
ejpam-6159	424	45	(	(	PUNCT
ejpam-6159	424	46	b1	b1	NOUN
ejpam-6159	424	47	,	,	PUNCT
ejpam-6159	424	48	a1	a1	NOUN
ejpam-6159	424	49	)	)	PUNCT
ejpam-6159	424	50	)	)	PUNCT
ejpam-6159	425	1	[	[	PUNCT
ejpam-6159	425	2	sq∑n	sq∑n	VERB
ejpam-6159	425	3	i=1	i=1	ADP
ejpam-6159	425	4	ai	ai	VERB
ejpam-6159	425	5	.	.	PUNCT
ejpam-6159	426	1	n∑	n∑	INTJ
ejpam-6159	427	1	i=1	i=1	PROPN
ejpam-6159	427	2	ai	ai	VERB
ejpam-6159	427	3	(	(	PUNCT
ejpam-6159	427	4	2i	2i	NUM
ejpam-6159	427	5	i+	i+	NOUN
ejpam-6159	427	6	1	1	NUM
ejpam-6159	427	7	)	)	PUNCT
ejpam-6159	427	8	]	]	PUNCT
ejpam-6159	427	9	1	1	NUM
ejpam-6159	427	10	q	q	NOUN
ejpam-6159	427	11	.	.	PUNCT
ejpam-6159	428	1	corollary	corollary	ADJ
ejpam-6159	428	2	8	8	NUM
ejpam-6159	428	3	.	.	PUNCT
ejpam-6159	429	1	if	if	SCONJ
ejpam-6159	429	2	one	one	PRON
ejpam-6159	429	3	can	can	AUX
ejpam-6159	429	4	take	take	VERB
ejpam-6159	429	5	k	k	NOUN
ejpam-6159	429	6	=	=	PUNCT
ejpam-6159	429	7	1	1	NUM
ejpam-6159	429	8	in	in	ADP
ejpam-6159	429	9	corollary	corollary	ADJ
ejpam-6159	429	10	7	7	NUM
ejpam-6159	429	11	,	,	PUNCT
ejpam-6159	429	12	then	then	ADV
ejpam-6159	429	13	we	we	PRON
ejpam-6159	429	14	have	have	VERB
ejpam-6159	429	15	the	the	DET
ejpam-6159	429	16	following	follow	VERB
ejpam-6159	429	17	inequalities	inequality	NOUN
ejpam-6159	429	18	for	for	ADP
ejpam-6159	429	19	a	a	DET
ejpam-6159	429	20	gfpp	gfpp	NOUN
ejpam-6159	429	21	function	function	NOUN
ejpam-6159	429	22	with	with	ADP
ejpam-6159	429	23	rl−fractional	rl−fractional	ADJ
ejpam-6159	429	24	integral	integral	ADJ
ejpam-6159	429	25	operators:∣∣∣∣	operators:∣∣∣∣	ADJ
ejpam-6159	429	26	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	429	27	(	(	PUNCT
ejpam-6159	429	28	x	x	NOUN
ejpam-6159	429	29	,	,	PUNCT
ejpam-6159	429	30	a1	a1	PROPN
ejpam-6159	429	31	)	)	PUNCT
ejpam-6159	429	32	+	+	NUM
ejpam-6159	429	33	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	429	34	(	(	PUNCT
ejpam-6159	429	35	x	x	NOUN
ejpam-6159	429	36	,	,	PUNCT
ejpam-6159	429	37	b1	b1	NOUN
ejpam-6159	429	38	)	)	PUNCT
ejpam-6159	429	39	ς∗	ς∗	PROPN
ejpam-6159	429	40	(	(	PUNCT
ejpam-6159	429	41	b1	b1	NOUN
ejpam-6159	429	42	,	,	PUNCT
ejpam-6159	429	43	a1	a1	PROPN
ejpam-6159	429	44	)	)	PUNCT
ejpam-6159	429	45	f	f	NOUN
ejpam-6159	429	46	(	(	PUNCT
ejpam-6159	429	47	x)−	x)−	PROPN
ejpam-6159	429	48	γ	γ	PROPN
ejpam-6159	429	49	(	(	PUNCT
ejpam-6159	429	50	ϱ+	ϱ+	NOUN
ejpam-6159	429	51	1	1	NUM
ejpam-6159	429	52	)	)	PUNCT
ejpam-6159	429	53	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	429	54	(	(	PUNCT
ejpam-6159	429	55	b1	b1	NOUN
ejpam-6159	429	56	,	,	PUNCT
ejpam-6159	429	57	a1	a1	PROPN
ejpam-6159	429	58	)	)	PUNCT
ejpam-6159	429	59	×	×	NOUN
ejpam-6159	429	60	{	{	PUNCT
ejpam-6159	429	61	jϱ	jϱ	NOUN
ejpam-6159	429	62	(	(	PUNCT
ejpam-6159	429	63	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	429	64	,	,	PUNCT
ejpam-6159	429	65	a1	a1	NOUN
ejpam-6159	429	66	)	)	PUNCT
ejpam-6159	429	67	)	)	PUNCT
ejpam-6159	430	1	−	−	PROPN
ejpam-6159	430	2	f	f	X
ejpam-6159	430	3	(	(	PUNCT
ejpam-6159	430	4	a1	a1	PROPN
ejpam-6159	430	5	)	)	PUNCT
ejpam-6159	430	6	+	+	NUM
ejpam-6159	430	7	jϱ	jϱ	ADJ
ejpam-6159	430	8	(	(	PUNCT
ejpam-6159	430	9	b1+ς∗(x	b1+ς∗(x	PROPN
ejpam-6159	430	10	,	,	PUNCT
ejpam-6159	430	11	b1	b1	NOUN
ejpam-6159	430	12	)	)	PUNCT
ejpam-6159	430	13	)	)	PUNCT
ejpam-6159	431	1	+	+	CCONJ
ejpam-6159	431	2	f	f	X
ejpam-6159	431	3	(	(	PUNCT
ejpam-6159	431	4	a1	a1	NOUN
ejpam-6159	431	5	+	+	CCONJ
ejpam-6159	431	6	ς∗	ς∗	PROPN
ejpam-6159	431	7	(	(	PUNCT
ejpam-6159	431	8	b1	b1	NOUN
ejpam-6159	431	9	,	,	PUNCT
ejpam-6159	431	10	a1	a1	NOUN
ejpam-6159	431	11	)	)	PUNCT
ejpam-6159	431	12	)	)	PUNCT
ejpam-6159	431	13	}	}	PUNCT
ejpam-6159	431	14	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	431	15	≤	≤	NOUN
ejpam-6159	431	16	(	(	PUNCT
ejpam-6159	431	17	1	1	NUM
ejpam-6159	431	18	1	1	NUM
ejpam-6159	431	19	+	+	NUM
ejpam-6159	431	20	pϱ	pϱ	PROPN
ejpam-6159	431	21	)	)	PUNCT
ejpam-6159	431	22	1	1	NUM
ejpam-6159	431	23	p	p	NOUN
ejpam-6159	431	24	(	(	PUNCT
ejpam-6159	431	25	ςϱ+1	ςϱ+1	ADV
ejpam-6159	431	26	∗	∗	NOUN
ejpam-6159	431	27	(	(	PUNCT
ejpam-6159	431	28	x	x	NOUN
ejpam-6159	431	29	,	,	PUNCT
ejpam-6159	431	30	a1	a1	NOUN
ejpam-6159	431	31	)	)	PUNCT
ejpam-6159	431	32	+	+	CCONJ
ejpam-6159	431	33	ςϱ+1	ςϱ+1	ADV
ejpam-6159	431	34	∗	∗	NOUN
ejpam-6159	431	35	(	(	PUNCT
ejpam-6159	431	36	x	x	NOUN
ejpam-6159	431	37	,	,	PUNCT
ejpam-6159	431	38	b1	b1	NOUN
ejpam-6159	431	39	)	)	PUNCT
ejpam-6159	431	40	ς∗	ς∗	PROPN
ejpam-6159	431	41	(	(	PUNCT
ejpam-6159	431	42	b1	b1	NOUN
ejpam-6159	431	43	,	,	PUNCT
ejpam-6159	431	44	a1	a1	NOUN
ejpam-6159	431	45	)	)	PUNCT
ejpam-6159	431	46	)	)	PUNCT
ejpam-6159	432	1	[	[	PUNCT
ejpam-6159	432	2	sq∑n	sq∑n	VERB
ejpam-6159	432	3	i=1	i=1	ADP
ejpam-6159	432	4	ai	ai	VERB
ejpam-6159	432	5	.	.	PUNCT
ejpam-6159	433	1	n∑	n∑	INTJ
ejpam-6159	434	1	i=1	i=1	PROPN
ejpam-6159	434	2	ai	ai	VERB
ejpam-6159	434	3	(	(	PUNCT
ejpam-6159	434	4	2i	2i	NUM
ejpam-6159	434	5	i+	i+	NOUN
ejpam-6159	434	6	1	1	NUM
ejpam-6159	434	7	)	)	PUNCT
ejpam-6159	434	8	]	]	PUNCT
ejpam-6159	434	9	1	1	NUM
ejpam-6159	434	10	q	q	NOUN
ejpam-6159	434	11	.	.	PUNCT
ejpam-6159	435	1	j.	j.	PROPN
ejpam-6159	435	2	nasir	nasir	PROPN
ejpam-6159	435	3	et	et	PROPN
ejpam-6159	435	4	al	al	PROPN
ejpam-6159	435	5	.	.	PUNCT
ejpam-6159	435	6	/	/	SYM
ejpam-6159	435	7	eur	eur	PROPN
ejpam-6159	435	8	.	.	PUNCT
ejpam-6159	436	1	j.	j.	PROPN
ejpam-6159	436	2	pure	pure	PROPN
ejpam-6159	436	3	appl	appl	PROPN
ejpam-6159	436	4	.	.	PROPN
ejpam-6159	436	5	math	math	PROPN
ejpam-6159	436	6	,	,	PUNCT
ejpam-6159	436	7	18	18	NUM
ejpam-6159	436	8	(	(	PUNCT
ejpam-6159	436	9	3	3	NUM
ejpam-6159	436	10	)	)	PUNCT
ejpam-6159	436	11	(	(	PUNCT
ejpam-6159	436	12	2025	2025	NUM
ejpam-6159	436	13	)	)	PUNCT
ejpam-6159	436	14	,	,	PUNCT
ejpam-6159	436	15	6159	6159	NUM
ejpam-6159	436	16	15	15	NUM
ejpam-6159	436	17	of	of	ADP
ejpam-6159	436	18	26	26	NUM
ejpam-6159	436	19	now	now	ADV
ejpam-6159	436	20	,	,	PUNCT
ejpam-6159	436	21	we	we	PRON
ejpam-6159	436	22	develop	develop	VERB
ejpam-6159	436	23	some	some	DET
ejpam-6159	436	24	new	new	ADJ
ejpam-6159	436	25	ostrowskiitype	ostrowskiitype	NOUN
ejpam-6159	436	26	inequalities	inequality	NOUN
ejpam-6159	436	27	for	for	ADP
ejpam-6159	436	28	twiceidifferentiable	twiceidifferentiable	ADJ
ejpam-6159	436	29	functions	function	NOUN
ejpam-6159	436	30	.	.	PUNCT
ejpam-6159	437	1	first	first	ADV
ejpam-6159	437	2	,	,	PUNCT
ejpam-6159	437	3	we	we	PRON
ejpam-6159	437	4	will	will	AUX
ejpam-6159	437	5	give	give	VERB
ejpam-6159	437	6	the	the	DET
ejpam-6159	437	7	new	new	ADJ
ejpam-6159	437	8	following	follow	VERB
ejpam-6159	437	9	lemma	lemma	PROPN
ejpam-6159	437	10	:	:	PUNCT
ejpam-6159	437	11	lemma	lemma	PROPN
ejpam-6159	437	12	2	2	X
ejpam-6159	437	13	.	.	PUNCT
ejpam-6159	437	14	suppose	suppose	VERB
ejpam-6159	437	15	f	f	X
ejpam-6159	438	1	:	:	PUNCT
ejpam-6159	438	2	[	[	X
ejpam-6159	438	3	a1	a1	NOUN
ejpam-6159	438	4	,	,	PUNCT
ejpam-6159	438	5	a1+ς∗	a1+ς∗	PROPN
ejpam-6159	438	6	(	(	PUNCT
ejpam-6159	438	7	b1	b1	NOUN
ejpam-6159	438	8	,	,	PUNCT
ejpam-6159	438	9	a1	a1	NOUN
ejpam-6159	438	10	)	)	PUNCT
ejpam-6159	438	11	]	]	PUNCT
ejpam-6159	439	1	→	→	PUNCT
ejpam-6159	439	2	ℜ	ℜ	PROPN
ejpam-6159	439	3	is	be	AUX
ejpam-6159	439	4	twice	twice	ADV
ejpam-6159	439	5	differentiable	differentiable	ADJ
ejpam-6159	439	6	mapping	mapping	NOUN
ejpam-6159	439	7	on	on	ADP
ejpam-6159	439	8	(	(	PUNCT
ejpam-6159	439	9	a1	a1	NOUN
ejpam-6159	439	10	,	,	PUNCT
ejpam-6159	439	11	a1	a1	NOUN
ejpam-6159	439	12	+	+	CCONJ
ejpam-6159	439	13	ς∗	ς∗	NOUN
ejpam-6159	439	14	(	(	PUNCT
ejpam-6159	439	15	b1	b1	NOUN
ejpam-6159	439	16	,	,	PUNCT
ejpam-6159	439	17	a1	a1	NOUN
ejpam-6159	439	18	)	)	PUNCT
ejpam-6159	439	19	)	)	PUNCT
ejpam-6159	439	20	with	with	ADP
ejpam-6159	439	21	a1	a1	NOUN
ejpam-6159	439	22	<	<	X
ejpam-6159	439	23	a1	a1	NOUN
ejpam-6159	439	24	+	+	CCONJ
ejpam-6159	439	25	ς∗	ς∗	PROPN
ejpam-6159	439	26	(	(	PUNCT
ejpam-6159	439	27	b1	b1	NOUN
ejpam-6159	439	28	,	,	PUNCT
ejpam-6159	439	29	a1	a1	NOUN
ejpam-6159	439	30	)	)	PUNCT
ejpam-6159	439	31	.	.	PUNCT
ejpam-6159	440	1	if	if	SCONJ
ejpam-6159	440	2	f	f	NUM
ejpam-6159	440	3	′′	′′	PROPN
ejpam-6159	440	4	∈	∈	PROPN
ejpam-6159	440	5	l[a1	l[a1	VERB
ejpam-6159	440	6	,	,	PUNCT
ejpam-6159	440	7	a1	a1	NOUN
ejpam-6159	440	8	+	+	CCONJ
ejpam-6159	440	9	ς∗	ς∗	PROPN
ejpam-6159	440	10	(	(	PUNCT
ejpam-6159	440	11	b1	b1	NOUN
ejpam-6159	440	12	,	,	PUNCT
ejpam-6159	440	13	a1	a1	NOUN
ejpam-6159	440	14	)	)	PUNCT
ejpam-6159	440	15	]	]	PUNCT
ejpam-6159	440	16	,	,	PUNCT
ejpam-6159	440	17	ϱ	ϱ	ADP
ejpam-6159	440	18	>	>	X
ejpam-6159	440	19	0,k	0,k	PROPN
ejpam-6159	440	20	>	>	PUNCT
ejpam-6159	440	21	0	0	NUM
ejpam-6159	440	22	,	,	PUNCT
ejpam-6159	440	23	then	then	ADV
ejpam-6159	440	24	we	we	PRON
ejpam-6159	440	25	have	have	VERB
ejpam-6159	440	26	the	the	DET
ejpam-6159	440	27	followingiequality	followingiequality	NOUN
ejpam-6159	440	28	for	for	ADP
ejpam-6159	440	29	k−fractional	k−fractional	ADJ
ejpam-6159	440	30	integral	integral	ADJ
ejpam-6159	440	31	operator	operator	NOUN
ejpam-6159	440	32	(	(	PUNCT
ejpam-6159	440	33	1−	1−	NUM
ejpam-6159	440	34	λ	λ	NOUN
ejpam-6159	440	35	)	)	PUNCT
ejpam-6159	440	36	[	[	PUNCT
ejpam-6159	440	37	ς	ς	X
ejpam-6159	440	38	ϱ	ϱ	PROPN
ejpam-6159	440	39	k	k	PROPN
ejpam-6159	440	40	∗	∗	X
ejpam-6159	440	41	(	(	PUNCT
ejpam-6159	440	42	b1	b1	NOUN
ejpam-6159	440	43	,	,	PUNCT
ejpam-6159	440	44	x)−	x)−	PROPN
ejpam-6159	440	45	ς	ς	PROPN
ejpam-6159	440	46	ϱ	ϱ	PROPN
ejpam-6159	440	47	k	k	PROPN
ejpam-6159	440	48	∗	∗	X
ejpam-6159	440	49	(	(	PUNCT
ejpam-6159	440	50	x	x	NOUN
ejpam-6159	440	51	,	,	PUNCT
ejpam-6159	440	52	a1	a1	NOUN
ejpam-6159	440	53	)	)	PUNCT
ejpam-6159	440	54	ς∗	ς∗	NOUN
ejpam-6159	440	55	(	(	PUNCT
ejpam-6159	440	56	b1	b1	NOUN
ejpam-6159	440	57	,	,	PUNCT
ejpam-6159	440	58	a1	a1	PROPN
ejpam-6159	440	59	)	)	PUNCT
ejpam-6159	440	60	]	]	PUNCT
ejpam-6159	440	61	f′	f′	PROPN
ejpam-6159	440	62	(	(	PUNCT
ejpam-6159	440	63	x	x	X
ejpam-6159	440	64	)	)	PUNCT
ejpam-6159	441	1	+	+	CCONJ
ejpam-6159	441	2	(	(	PUNCT
ejpam-6159	441	3	1	1	NUM
ejpam-6159	441	4	+	+	CCONJ
ejpam-6159	441	5	ϱ	ϱ	ADP
ejpam-6159	441	6	k	k	X
ejpam-6159	441	7	−	−	PROPN
ejpam-6159	441	8	λ	λ	PROPN
ejpam-6159	441	9	)	)	PUNCT
ejpam-6159	441	10	[	[	PUNCT
ejpam-6159	441	11	ς	ς	PROPN
ejpam-6159	441	12	ϱ	ϱ	PROPN
ejpam-6159	441	13	k	k	PROPN
ejpam-6159	441	14	∗	∗	X
ejpam-6159	441	15	(	(	PUNCT
ejpam-6159	441	16	b1	b1	NOUN
ejpam-6159	441	17	,	,	PUNCT
ejpam-6159	441	18	x	x	X
ejpam-6159	441	19	)	)	PUNCT
ejpam-6159	441	20	+	+	CCONJ
ejpam-6159	441	21	ς	ς	PROPN
ejpam-6159	441	22	ϱ	ϱ	PROPN
ejpam-6159	441	23	k	k	PROPN
ejpam-6159	441	24	∗	∗	X
ejpam-6159	441	25	(	(	PUNCT
ejpam-6159	441	26	x	x	NOUN
ejpam-6159	441	27	,	,	PUNCT
ejpam-6159	441	28	a1	a1	NOUN
ejpam-6159	441	29	)	)	PUNCT
ejpam-6159	441	30	ς∗	ς∗	NOUN
ejpam-6159	441	31	(	(	PUNCT
ejpam-6159	441	32	b1	b1	NOUN
ejpam-6159	441	33	,	,	PUNCT
ejpam-6159	441	34	a1	a1	PROPN
ejpam-6159	441	35	)	)	PUNCT
ejpam-6159	441	36	]	]	PUNCT
ejpam-6159	442	1	f	f	PROPN
ejpam-6159	442	2	(	(	PUNCT
ejpam-6159	442	3	x	x	X
ejpam-6159	442	4	)	)	PUNCT
ejpam-6159	443	1	+	+	NUM
ejpam-6159	443	2	λ	λ	X
ejpam-6159	443	3	[	[	PUNCT
ejpam-6159	443	4	ς	ς	PROPN
ejpam-6159	443	5	ϱ	ϱ	PROPN
ejpam-6159	443	6	k	k	PROPN
ejpam-6159	443	7	∗	∗	X
ejpam-6159	443	8	(	(	PUNCT
ejpam-6159	443	9	b1	b1	NOUN
ejpam-6159	443	10	,	,	PUNCT
ejpam-6159	443	11	x)f	x)f	X
ejpam-6159	443	12	(	(	PUNCT
ejpam-6159	443	13	b1	b1	NOUN
ejpam-6159	443	14	)	)	PUNCT
ejpam-6159	443	15	+	+	CCONJ
ejpam-6159	443	16	ς	ς	PROPN
ejpam-6159	443	17	ϱ	ϱ	PROPN
ejpam-6159	443	18	k	k	PROPN
ejpam-6159	443	19	∗	∗	X
ejpam-6159	443	20	(	(	PUNCT
ejpam-6159	443	21	x	x	X
ejpam-6159	443	22	,	,	PUNCT
ejpam-6159	443	23	a1)f	a1)f	PROPN
ejpam-6159	443	24	(	(	PUNCT
ejpam-6159	443	25	a1	a1	PROPN
ejpam-6159	443	26	)	)	PUNCT
ejpam-6159	443	27	ς∗	ς∗	NOUN
ejpam-6159	443	28	(	(	PUNCT
ejpam-6159	443	29	b1	b1	NOUN
ejpam-6159	443	30	,	,	PUNCT
ejpam-6159	443	31	a1	a1	PROPN
ejpam-6159	443	32	)	)	PUNCT
ejpam-6159	443	33	]	]	PUNCT
ejpam-6159	444	1	−	−	PROPN
ejpam-6159	444	2	γk	γk	X
ejpam-6159	444	3	(	(	PUNCT
ejpam-6159	444	4	ϱ+	ϱ+	NOUN
ejpam-6159	444	5	2k	2k	NUM
ejpam-6159	444	6	)	)	PUNCT
ejpam-6159	444	7	ς∗	ς∗	PROPN
ejpam-6159	444	8	(	(	PUNCT
ejpam-6159	444	9	b1	b1	NOUN
ejpam-6159	444	10	,	,	PUNCT
ejpam-6159	444	11	a1	a1	NOUN
ejpam-6159	444	12	)	)	PUNCT
ejpam-6159	444	13	{	{	PUNCT
ejpam-6159	444	14	jϱ,k	jϱ,k	X
ejpam-6159	444	15	(	(	PUNCT
ejpam-6159	444	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	444	17	,	,	PUNCT
ejpam-6159	444	18	a1	a1	NOUN
ejpam-6159	444	19	)	)	PUNCT
ejpam-6159	444	20	)	)	PUNCT
ejpam-6159	445	1	−	−	PROPN
ejpam-6159	445	2	f	f	X
ejpam-6159	445	3	(	(	PUNCT
ejpam-6159	445	4	a1	a1	PROPN
ejpam-6159	445	5	)	)	PUNCT
ejpam-6159	445	6	+	+	NUM
ejpam-6159	445	7	jϱ,k	jϱ,k	X
ejpam-6159	445	8	(	(	PUNCT
ejpam-6159	445	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	445	10	,	,	PUNCT
ejpam-6159	445	11	b1	b1	NOUN
ejpam-6159	445	12	)	)	PUNCT
ejpam-6159	445	13	)	)	PUNCT
ejpam-6159	446	1	+	+	CCONJ
ejpam-6159	446	2	f	f	X
ejpam-6159	446	3	(	(	PUNCT
ejpam-6159	446	4	b1	b1	PROPN
ejpam-6159	446	5	)	)	PUNCT
ejpam-6159	446	6	}	}	PUNCT
ejpam-6159	447	1	=	=	PUNCT
ejpam-6159	447	2	ς	ς	PROPN
ejpam-6159	447	3	ϱ	ϱ	X
ejpam-6159	447	4	k	k	PROPN
ejpam-6159	447	5	+2	+2	PROPN
ejpam-6159	447	6	∗	∗	NOUN
ejpam-6159	447	7	(	(	PUNCT
ejpam-6159	447	8	x	x	NOUN
ejpam-6159	447	9	,	,	PUNCT
ejpam-6159	447	10	a1	a1	NOUN
ejpam-6159	447	11	)	)	PUNCT
ejpam-6159	447	12	ς∗	ς∗	NOUN
ejpam-6159	447	13	(	(	PUNCT
ejpam-6159	447	14	b1	b1	NOUN
ejpam-6159	447	15	,	,	PUNCT
ejpam-6159	447	16	a1	a1	PROPN
ejpam-6159	447	17	)	)	PUNCT
ejpam-6159	447	18	∫	∫	NOUN
ejpam-6159	448	1	1	1	NUM
ejpam-6159	448	2	0	0	NUM
ejpam-6159	448	3	t	t	PROPN
ejpam-6159	448	4	(	(	PUNCT
ejpam-6159	448	5	λ−	λ−	PROPN
ejpam-6159	448	6	t	t	PROPN
ejpam-6159	448	7	ϱ	ϱ	PROPN
ejpam-6159	448	8	k	k	PROPN
ejpam-6159	448	9	)	)	PUNCT
ejpam-6159	448	10	f′′	f′′	NOUN
ejpam-6159	448	11	(	(	PUNCT
ejpam-6159	448	12	a1	a1	NOUN
ejpam-6159	448	13	+	+	CCONJ
ejpam-6159	448	14	tς∗	tς∗	X
ejpam-6159	448	15	(	(	PUNCT
ejpam-6159	448	16	x	x	NOUN
ejpam-6159	448	17	,	,	PUNCT
ejpam-6159	448	18	a1	a1	NOUN
ejpam-6159	448	19	)	)	PUNCT
ejpam-6159	448	20	)	)	PUNCT
ejpam-6159	448	21	dt	dt	PUNCT
ejpam-6159	449	1	+	+	CCONJ
ejpam-6159	449	2	ς	ς	X
ejpam-6159	449	3	ϱ	ϱ	ADP
ejpam-6159	449	4	k	k	PROPN
ejpam-6159	449	5	+2	+2	PROPN
ejpam-6159	449	6	∗	∗	NOUN
ejpam-6159	449	7	(	(	PUNCT
ejpam-6159	449	8	b1	b1	NOUN
ejpam-6159	449	9	,	,	PUNCT
ejpam-6159	449	10	x	x	NOUN
ejpam-6159	449	11	)	)	PUNCT
ejpam-6159	449	12	ς∗	ς∗	PROPN
ejpam-6159	449	13	(	(	PUNCT
ejpam-6159	449	14	b1	b1	NOUN
ejpam-6159	449	15	,	,	PUNCT
ejpam-6159	449	16	a1	a1	PROPN
ejpam-6159	449	17	)	)	PUNCT
ejpam-6159	449	18	∫	∫	NOUN
ejpam-6159	449	19	1	1	NUM
ejpam-6159	449	20	0	0	NUM
ejpam-6159	449	21	t	t	PROPN
ejpam-6159	449	22	(	(	PUNCT
ejpam-6159	449	23	λ−	λ−	PROPN
ejpam-6159	449	24	t	t	PROPN
ejpam-6159	449	25	ϱ	ϱ	PROPN
ejpam-6159	449	26	k	k	PROPN
ejpam-6159	449	27	)	)	PUNCT
ejpam-6159	449	28	f′′	f′′	NOUN
ejpam-6159	449	29	(	(	PUNCT
ejpam-6159	449	30	b1	b1	NOUN
ejpam-6159	449	31	+	+	CCONJ
ejpam-6159	449	32	tς∗	tς∗	X
ejpam-6159	449	33	(	(	PUNCT
ejpam-6159	449	34	x	x	NOUN
ejpam-6159	449	35	,	,	PUNCT
ejpam-6159	449	36	b1	b1	NOUN
ejpam-6159	449	37	)	)	PUNCT
ejpam-6159	449	38	)	)	PUNCT
ejpam-6159	450	1	dt	dt	PROPN
ejpam-6159	450	2	,	,	PUNCT
ejpam-6159	450	3	holds	hold	VERB
ejpam-6159	450	4	forall	forall	NOUN
ejpam-6159	450	5	x	x	SYM
ejpam-6159	450	6	∈	∈	PROPN
ejpam-6159	451	1	[	[	X
ejpam-6159	451	2	a1	a1	NOUN
ejpam-6159	451	3	,	,	PUNCT
ejpam-6159	451	4	+	+	CCONJ
ejpam-6159	451	5	ς∗	ς∗	PROPN
ejpam-6159	451	6	(	(	PUNCT
ejpam-6159	451	7	b1	b1	NOUN
ejpam-6159	451	8	,	,	PUNCT
ejpam-6159	451	9	a1	a1	NOUN
ejpam-6159	451	10	)	)	PUNCT
ejpam-6159	451	11	]	]	PUNCT
ejpam-6159	451	12	,	,	PUNCT
ejpam-6159	451	13	λ	λ	X
ejpam-6159	451	14	∈	∈	PROPN
ejpam-6159	452	1	[	[	X
ejpam-6159	452	2	0	0	NUM
ejpam-6159	452	3	,	,	PUNCT
ejpam-6159	452	4	1	1	NUM
ejpam-6159	452	5	]	]	PUNCT
ejpam-6159	452	6	.	.	PUNCT
ejpam-6159	453	1	(	(	PUNCT
ejpam-6159	453	2	36	36	NUM
ejpam-6159	453	3	)	)	PUNCT
ejpam-6159	453	4	proof	proof	NOUN
ejpam-6159	453	5	.	.	PUNCT
ejpam-6159	454	1	it	it	PRON
ejpam-6159	454	2	can	can	AUX
ejpam-6159	454	3	easily	easily	ADV
ejpam-6159	454	4	be	be	AUX
ejpam-6159	454	5	proved	prove	VERB
ejpam-6159	454	6	as	as	ADP
ejpam-6159	454	7	similar	similar	ADJ
ejpam-6159	454	8	lemma	lemma	PROPN
ejpam-6159	454	9	1	1	NUM
ejpam-6159	454	10	.	.	PUNCT
ejpam-6159	454	11	theorem	theorem	NOUN
ejpam-6159	454	12	6	6	NUM
ejpam-6159	454	13	.	.	PUNCT
ejpam-6159	454	14	suppose	suppose	VERB
ejpam-6159	454	15	f	f	X
ejpam-6159	455	1	:	:	PUNCT
ejpam-6159	455	2	x	x	PUNCT
ejpam-6159	455	3	=	=	PUNCT
ejpam-6159	456	1	[	[	X
ejpam-6159	456	2	a1	a1	NOUN
ejpam-6159	456	3	,	,	PUNCT
ejpam-6159	456	4	a1	a1	NOUN
ejpam-6159	456	5	+	+	CCONJ
ejpam-6159	456	6	ς∗	ς∗	PROPN
ejpam-6159	456	7	(	(	PUNCT
ejpam-6159	456	8	b1	b1	NOUN
ejpam-6159	456	9	,	,	PUNCT
ejpam-6159	456	10	a1	a1	NOUN
ejpam-6159	456	11	)	)	PUNCT
ejpam-6159	456	12	]	]	PUNCT
ejpam-6159	457	1	→	→	PUNCT
ejpam-6159	457	2	ℜ	ℜ	PROPN
ejpam-6159	457	3	is	be	AUX
ejpam-6159	457	4	a	a	DET
ejpam-6159	457	5	twice	twice	ADV
ejpam-6159	457	6	differentiable	differentiable	ADJ
ejpam-6159	457	7	function	function	NOUN
ejpam-6159	457	8	on	on	ADP
ejpam-6159	457	9	xo	xo	PROPN
ejpam-6159	457	10	such	such	ADJ
ejpam-6159	457	11	that	that	SCONJ
ejpam-6159	457	12	f′′	f′′	NOUN
ejpam-6159	457	13	∈	∈	NOUN
ejpam-6159	457	14	l[a1	l[a1	NOUN
ejpam-6159	457	15	,	,	PUNCT
ejpam-6159	457	16	a1	a1	NOUN
ejpam-6159	457	17	+	+	CCONJ
ejpam-6159	457	18	ς∗	ς∗	PROPN
ejpam-6159	457	19	(	(	PUNCT
ejpam-6159	457	20	b1	b1	NOUN
ejpam-6159	457	21	,	,	PUNCT
ejpam-6159	457	22	a1	a1	NOUN
ejpam-6159	457	23	)	)	PUNCT
ejpam-6159	457	24	]	]	PUNCT
ejpam-6159	457	25	and	and	CCONJ
ejpam-6159	457	26	consideration	consideration	NOUN
ejpam-6159	457	27	with	with	ADP
ejpam-6159	457	28	u∗.	u∗.	PROPN
ejpam-6159	457	29	let	let	VERB
ejpam-6159	457	30	|f′′(x)|	|f′′(x)|	PRON
ejpam-6159	457	31	be	be	AUX
ejpam-6159	457	32	a	a	DET
ejpam-6159	457	33	gfpp−s	gfpp−s	NOUN
ejpam-6159	457	34	function	function	NOUN
ejpam-6159	457	35	on	on	ADP
ejpam-6159	457	36	x.	x.	NOUN
ejpam-6159	457	37	then	then	ADV
ejpam-6159	457	38	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	457	39	(	(	PUNCT
ejpam-6159	457	40	1−	1−	NUM
ejpam-6159	457	41	λ	λ	NOUN
ejpam-6159	457	42	)	)	PUNCT
ejpam-6159	457	43	[	[	PUNCT
ejpam-6159	457	44	ς	ς	X
ejpam-6159	457	45	ϱ	ϱ	PROPN
ejpam-6159	457	46	k	k	PROPN
ejpam-6159	457	47	∗	∗	X
ejpam-6159	457	48	(	(	PUNCT
ejpam-6159	457	49	b1	b1	NOUN
ejpam-6159	457	50	,	,	PUNCT
ejpam-6159	457	51	x)−	x)−	PROPN
ejpam-6159	457	52	ς	ς	PROPN
ejpam-6159	457	53	ϱ	ϱ	PROPN
ejpam-6159	457	54	k	k	PROPN
ejpam-6159	457	55	∗	∗	X
ejpam-6159	457	56	(	(	PUNCT
ejpam-6159	457	57	x	x	NOUN
ejpam-6159	457	58	,	,	PUNCT
ejpam-6159	457	59	a1	a1	NOUN
ejpam-6159	457	60	)	)	PUNCT
ejpam-6159	457	61	ς∗	ς∗	NOUN
ejpam-6159	457	62	(	(	PUNCT
ejpam-6159	457	63	b1	b1	NOUN
ejpam-6159	457	64	,	,	PUNCT
ejpam-6159	457	65	a1	a1	PROPN
ejpam-6159	457	66	)	)	PUNCT
ejpam-6159	457	67	]	]	PUNCT
ejpam-6159	457	68	f′	f′	PROPN
ejpam-6159	457	69	(	(	PUNCT
ejpam-6159	457	70	x	x	X
ejpam-6159	457	71	)	)	PUNCT
ejpam-6159	458	1	+	+	CCONJ
ejpam-6159	458	2	(	(	PUNCT
ejpam-6159	458	3	1	1	NUM
ejpam-6159	458	4	+	+	CCONJ
ejpam-6159	458	5	ϱ	ϱ	ADP
ejpam-6159	458	6	k	k	X
ejpam-6159	458	7	−	−	PROPN
ejpam-6159	458	8	λ	λ	PROPN
ejpam-6159	458	9	)	)	PUNCT
ejpam-6159	458	10	[	[	PUNCT
ejpam-6159	458	11	ς	ς	PROPN
ejpam-6159	458	12	ϱ	ϱ	PROPN
ejpam-6159	458	13	k	k	PROPN
ejpam-6159	458	14	∗	∗	X
ejpam-6159	458	15	(	(	PUNCT
ejpam-6159	458	16	b1	b1	NOUN
ejpam-6159	458	17	,	,	PUNCT
ejpam-6159	458	18	x	x	X
ejpam-6159	458	19	)	)	PUNCT
ejpam-6159	458	20	+	+	CCONJ
ejpam-6159	458	21	ς	ς	PROPN
ejpam-6159	458	22	ϱ	ϱ	PROPN
ejpam-6159	458	23	k	k	PROPN
ejpam-6159	458	24	∗	∗	X
ejpam-6159	458	25	(	(	PUNCT
ejpam-6159	458	26	x	x	NOUN
ejpam-6159	458	27	,	,	PUNCT
ejpam-6159	458	28	a1	a1	NOUN
ejpam-6159	458	29	)	)	PUNCT
ejpam-6159	458	30	ς∗	ς∗	NOUN
ejpam-6159	458	31	(	(	PUNCT
ejpam-6159	458	32	b1	b1	NOUN
ejpam-6159	458	33	,	,	PUNCT
ejpam-6159	458	34	a1	a1	PROPN
ejpam-6159	458	35	)	)	PUNCT
ejpam-6159	458	36	]	]	PUNCT
ejpam-6159	459	1	f	f	PROPN
ejpam-6159	459	2	(	(	PUNCT
ejpam-6159	459	3	x	x	X
ejpam-6159	459	4	)	)	PUNCT
ejpam-6159	460	1	+	+	NUM
ejpam-6159	460	2	λ	λ	X
ejpam-6159	460	3	[	[	PUNCT
ejpam-6159	460	4	ς	ς	PROPN
ejpam-6159	460	5	ϱ	ϱ	PROPN
ejpam-6159	460	6	k	k	PROPN
ejpam-6159	460	7	∗	∗	X
ejpam-6159	460	8	(	(	PUNCT
ejpam-6159	460	9	b1	b1	NOUN
ejpam-6159	460	10	,	,	PUNCT
ejpam-6159	460	11	x)f	x)f	X
ejpam-6159	460	12	(	(	PUNCT
ejpam-6159	460	13	b1	b1	NOUN
ejpam-6159	460	14	)	)	PUNCT
ejpam-6159	460	15	+	+	CCONJ
ejpam-6159	460	16	ς	ς	PROPN
ejpam-6159	460	17	ϱ	ϱ	PROPN
ejpam-6159	460	18	k	k	PROPN
ejpam-6159	460	19	∗	∗	X
ejpam-6159	460	20	(	(	PUNCT
ejpam-6159	460	21	x	x	X
ejpam-6159	460	22	,	,	PUNCT
ejpam-6159	460	23	a1)f	a1)f	PROPN
ejpam-6159	460	24	(	(	PUNCT
ejpam-6159	460	25	a1	a1	PROPN
ejpam-6159	460	26	)	)	PUNCT
ejpam-6159	460	27	ς∗	ς∗	NOUN
ejpam-6159	460	28	(	(	PUNCT
ejpam-6159	460	29	b1	b1	NOUN
ejpam-6159	460	30	,	,	PUNCT
ejpam-6159	460	31	a1	a1	PROPN
ejpam-6159	460	32	)	)	PUNCT
ejpam-6159	460	33	]	]	PUNCT
ejpam-6159	461	1	−	−	PROPN
ejpam-6159	461	2	γk	γk	X
ejpam-6159	461	3	(	(	PUNCT
ejpam-6159	461	4	ϱ+	ϱ+	NOUN
ejpam-6159	461	5	2k	2k	NUM
ejpam-6159	461	6	)	)	PUNCT
ejpam-6159	461	7	ς∗	ς∗	PROPN
ejpam-6159	461	8	(	(	PUNCT
ejpam-6159	461	9	b1	b1	NOUN
ejpam-6159	461	10	,	,	PUNCT
ejpam-6159	461	11	a1	a1	NOUN
ejpam-6159	461	12	)	)	PUNCT
ejpam-6159	461	13	{	{	PUNCT
ejpam-6159	461	14	jϱ,k	jϱ,k	X
ejpam-6159	461	15	(	(	PUNCT
ejpam-6159	461	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	461	17	,	,	PUNCT
ejpam-6159	461	18	a1	a1	NOUN
ejpam-6159	461	19	)	)	PUNCT
ejpam-6159	461	20	)	)	PUNCT
ejpam-6159	462	1	−	−	PROPN
ejpam-6159	462	2	f	f	X
ejpam-6159	462	3	(	(	PUNCT
ejpam-6159	462	4	a1	a1	PROPN
ejpam-6159	462	5	)	)	PUNCT
ejpam-6159	462	6	+	+	NUM
ejpam-6159	462	7	jϱ,k	jϱ,k	X
ejpam-6159	462	8	(	(	PUNCT
ejpam-6159	462	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	462	10	,	,	PUNCT
ejpam-6159	462	11	b1	b1	NOUN
ejpam-6159	462	12	)	)	PUNCT
ejpam-6159	462	13	)	)	PUNCT
ejpam-6159	463	1	+	+	CCONJ
ejpam-6159	463	2	f	f	X
ejpam-6159	463	3	(	(	PUNCT
ejpam-6159	463	4	b1	b1	PROPN
ejpam-6159	463	5	)	)	PUNCT
ejpam-6159	463	6	}	}	PUNCT
ejpam-6159	463	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	463	8	≤	≤	NOUN
ejpam-6159	463	9	[	[	PUNCT
ejpam-6159	463	10	ς	ς	X
ejpam-6159	463	11	ϱ	ϱ	ADP
ejpam-6159	463	12	k	k	PROPN
ejpam-6159	463	13	+2	+2	PROPN
ejpam-6159	463	14	∗	∗	NOUN
ejpam-6159	463	15	(	(	PUNCT
ejpam-6159	463	16	x	x	NOUN
ejpam-6159	463	17	,	,	PUNCT
ejpam-6159	463	18	a1	a1	PROPN
ejpam-6159	463	19	)	)	PUNCT
ejpam-6159	463	20	|f′′	|f′′	NUM
ejpam-6159	463	21	(	(	PUNCT
ejpam-6159	463	22	a1)|+	a1)|+	VERB
ejpam-6159	463	23	ς	ς	PROPN
ejpam-6159	463	24	ϱ	ϱ	PROPN
ejpam-6159	463	25	k	k	PROPN
ejpam-6159	463	26	+2	+2	PROPN
ejpam-6159	463	27	∗	∗	NOUN
ejpam-6159	463	28	(	(	PUNCT
ejpam-6159	463	29	b1	b1	NOUN
ejpam-6159	463	30	,	,	PUNCT
ejpam-6159	463	31	x	x	NOUN
ejpam-6159	463	32	)	)	PUNCT
ejpam-6159	463	33	|f′′	|f′′	NUM
ejpam-6159	464	1	(	(	PUNCT
ejpam-6159	464	2	b1)|	b1)|	PROPN
ejpam-6159	464	3	ς∗	ς∗	PROPN
ejpam-6159	464	4	(	(	PUNCT
ejpam-6159	464	5	b1	b1	NOUN
ejpam-6159	464	6	,	,	PUNCT
ejpam-6159	464	7	a1	a1	PROPN
ejpam-6159	464	8	)	)	PUNCT
ejpam-6159	464	9	]	]	PUNCT
ejpam-6159	465	1	1∑n	1∑n	X
ejpam-6159	465	2	i=1	i=1	PROPN
ejpam-6159	465	3	ai	ai	VERB
ejpam-6159	466	1	n∑	n∑	PROPN
ejpam-6159	466	2	i=1	i=1	PROPN
ejpam-6159	467	1	ai	ai	INTJ
ejpam-6159	467	2	∫	∫	PROPN
ejpam-6159	467	3	1	1	NUM
ejpam-6159	467	4	0	0	NUM
ejpam-6159	467	5	t	t	PROPN
ejpam-6159	467	6	(	(	PUNCT
ejpam-6159	467	7	λ−	λ−	PROPN
ejpam-6159	467	8	t	t	PROPN
ejpam-6159	467	9	ϱ	ϱ	PROPN
ejpam-6159	467	10	k	k	PROPN
ejpam-6159	467	11	)	)	PUNCT
ejpam-6159	467	12	(	(	PUNCT
ejpam-6159	467	13	1−	1−	NUM
ejpam-6159	467	14	st	st	NOUN
ejpam-6159	467	15	)	)	PUNCT
ejpam-6159	467	16	1	1	NUM
ejpam-6159	468	1	i	i	PRON
ejpam-6159	468	2	dt	dt	X
ejpam-6159	468	3	(	(	PUNCT
ejpam-6159	468	4	37	37	NUM
ejpam-6159	468	5	)	)	PUNCT
ejpam-6159	469	1	+	+	CCONJ
ejpam-6159	469	2	ς	ς	PROPN
ejpam-6159	469	3	ϱ	ϱ	ADP
ejpam-6159	469	4	k	k	PROPN
ejpam-6159	469	5	+2	+2	PROPN
ejpam-6159	469	6	∗	∗	NOUN
ejpam-6159	469	7	(	(	PUNCT
ejpam-6159	469	8	x	x	NOUN
ejpam-6159	469	9	,	,	PUNCT
ejpam-6159	469	10	a1	a1	NOUN
ejpam-6159	469	11	)	)	PUNCT
ejpam-6159	469	12	+	+	CCONJ
ejpam-6159	469	13	ς	ς	PROPN
ejpam-6159	469	14	ϱ	ϱ	ADP
ejpam-6159	469	15	k	k	PROPN
ejpam-6159	469	16	+2	+2	PROPN
ejpam-6159	469	17	∗	∗	NOUN
ejpam-6159	469	18	(	(	PUNCT
ejpam-6159	469	19	b1	b1	NOUN
ejpam-6159	469	20	,	,	PUNCT
ejpam-6159	469	21	x)∑n	x)∑n	PUNCT
ejpam-6159	470	1	i=1	i=1	PROPN
ejpam-6159	471	1	ai	ai	VERB
ejpam-6159	471	2	ς∗	ς∗	PROPN
ejpam-6159	471	3	(	(	PUNCT
ejpam-6159	471	4	b1	b1	NOUN
ejpam-6159	471	5	,	,	PUNCT
ejpam-6159	471	6	a1	a1	NOUN
ejpam-6159	471	7	)	)	PUNCT
ejpam-6159	471	8	∣∣f′′	∣∣f′′	NOUN
ejpam-6159	471	9	(	(	PUNCT
ejpam-6159	471	10	x	x	X
ejpam-6159	471	11	)	)	PUNCT
ejpam-6159	471	12	∣∣	∣∣	PROPN
ejpam-6159	472	1	n∑	n∑	PROPN
ejpam-6159	472	2	i=1	i=1	PROPN
ejpam-6159	473	1	ai	ai	INTJ
ejpam-6159	473	2	∫	∫	PROPN
ejpam-6159	473	3	1	1	NUM
ejpam-6159	473	4	0	0	NUM
ejpam-6159	473	5	t	t	PROPN
ejpam-6159	473	6	(	(	PUNCT
ejpam-6159	473	7	λ−	λ−	PROPN
ejpam-6159	473	8	t	t	PROPN
ejpam-6159	473	9	ϱ	ϱ	PROPN
ejpam-6159	473	10	k	k	PROPN
ejpam-6159	473	11	)	)	PUNCT
ejpam-6159	473	12	(	(	PUNCT
ejpam-6159	473	13	1−	1−	NUM
ejpam-6159	473	14	s	s	X
ejpam-6159	473	15	(	(	PUNCT
ejpam-6159	473	16	1−	1−	NUM
ejpam-6159	473	17	t	t	NOUN
ejpam-6159	473	18	)	)	PUNCT
ejpam-6159	473	19	)	)	PUNCT
ejpam-6159	474	1	1	1	NUM
ejpam-6159	475	1	i	i	PRON
ejpam-6159	475	2	dt	dt	VERB
ejpam-6159	475	3	holds	hold	VERB
ejpam-6159	475	4	∀	∀	X
ejpam-6159	475	5	∈	∈	PROPN
ejpam-6159	475	6	[	[	X
ejpam-6159	475	7	a1	a1	NOUN
ejpam-6159	475	8	,	,	PUNCT
ejpam-6159	475	9	b1	b1	NOUN
ejpam-6159	475	10	]	]	PUNCT
ejpam-6159	475	11	and	and	CCONJ
ejpam-6159	475	12	λ	λ	X
ejpam-6159	475	13	∈	∈	PROPN
ejpam-6159	476	1	[	[	X
ejpam-6159	476	2	0	0	NUM
ejpam-6159	476	3	,	,	PUNCT
ejpam-6159	476	4	1	1	NUM
ejpam-6159	476	5	]	]	PUNCT
ejpam-6159	476	6	.	.	PUNCT
ejpam-6159	477	1	j.	j.	PROPN
ejpam-6159	477	2	nasir	nasir	PROPN
ejpam-6159	477	3	et	et	PROPN
ejpam-6159	477	4	al	al	PROPN
ejpam-6159	477	5	.	.	PUNCT
ejpam-6159	477	6	/	/	SYM
ejpam-6159	477	7	eur	eur	PROPN
ejpam-6159	477	8	.	.	PUNCT
ejpam-6159	478	1	j.	j.	PROPN
ejpam-6159	478	2	pure	pure	PROPN
ejpam-6159	478	3	appl	appl	PROPN
ejpam-6159	478	4	.	.	PROPN
ejpam-6159	478	5	math	math	PROPN
ejpam-6159	478	6	,	,	PUNCT
ejpam-6159	478	7	18	18	NUM
ejpam-6159	478	8	(	(	PUNCT
ejpam-6159	478	9	3	3	NUM
ejpam-6159	478	10	)	)	PUNCT
ejpam-6159	478	11	(	(	PUNCT
ejpam-6159	478	12	2025	2025	NUM
ejpam-6159	478	13	)	)	PUNCT
ejpam-6159	478	14	,	,	PUNCT
ejpam-6159	478	15	6159	6159	NUM
ejpam-6159	478	16	16	16	NUM
ejpam-6159	478	17	of	of	ADP
ejpam-6159	478	18	26	26	NUM
ejpam-6159	478	19	proof	proof	NOUN
ejpam-6159	478	20	.	.	PUNCT
ejpam-6159	479	1	from	from	ADP
ejpam-6159	479	2	lemma	lemma	PROPN
ejpam-6159	479	3	2	2	NUM
ejpam-6159	479	4	and	and	CCONJ
ejpam-6159	479	5	a	a	DET
ejpam-6159	479	6	modulus	modulus	ADJ
ejpam-6159	479	7	property	property	NOUN
ejpam-6159	479	8	of	of	ADP
ejpam-6159	479	9	the	the	DET
ejpam-6159	479	10	gfpp−s	gfpp−s	PROPN
ejpam-6159	479	11	function	function	NOUN
ejpam-6159	479	12	|f′′|	|f′′|	PROPN
ejpam-6159	479	13	,	,	PUNCT
ejpam-6159	479	14	one	one	NUM
ejpam-6159	479	15	has∣∣∣∣	has∣∣∣∣	ADJ
ejpam-6159	479	16	(	(	PUNCT
ejpam-6159	479	17	1−	1−	NUM
ejpam-6159	479	18	λ	λ	NOUN
ejpam-6159	479	19	)	)	PUNCT
ejpam-6159	479	20	[	[	PUNCT
ejpam-6159	479	21	ς	ς	X
ejpam-6159	479	22	ϱ	ϱ	PROPN
ejpam-6159	479	23	k	k	PROPN
ejpam-6159	479	24	∗	∗	X
ejpam-6159	479	25	(	(	PUNCT
ejpam-6159	479	26	b1	b1	NOUN
ejpam-6159	479	27	,	,	PUNCT
ejpam-6159	479	28	x)−	x)−	PROPN
ejpam-6159	479	29	ς	ς	PROPN
ejpam-6159	479	30	ϱ	ϱ	PROPN
ejpam-6159	479	31	k	k	PROPN
ejpam-6159	479	32	∗	∗	X
ejpam-6159	479	33	(	(	PUNCT
ejpam-6159	479	34	x	x	NOUN
ejpam-6159	479	35	,	,	PUNCT
ejpam-6159	479	36	a1	a1	NOUN
ejpam-6159	479	37	)	)	PUNCT
ejpam-6159	479	38	ς∗	ς∗	NOUN
ejpam-6159	479	39	(	(	PUNCT
ejpam-6159	479	40	b1	b1	NOUN
ejpam-6159	479	41	,	,	PUNCT
ejpam-6159	479	42	a1	a1	PROPN
ejpam-6159	479	43	)	)	PUNCT
ejpam-6159	479	44	]	]	PUNCT
ejpam-6159	479	45	f′	f′	PROPN
ejpam-6159	479	46	(	(	PUNCT
ejpam-6159	479	47	x	x	X
ejpam-6159	479	48	)	)	PUNCT
ejpam-6159	480	1	+	+	CCONJ
ejpam-6159	480	2	(	(	PUNCT
ejpam-6159	480	3	1	1	NUM
ejpam-6159	480	4	+	+	CCONJ
ejpam-6159	480	5	ϱ	ϱ	ADP
ejpam-6159	480	6	k	k	X
ejpam-6159	480	7	−	−	PROPN
ejpam-6159	480	8	λ	λ	PROPN
ejpam-6159	480	9	)	)	PUNCT
ejpam-6159	480	10	[	[	PUNCT
ejpam-6159	480	11	ς	ς	PROPN
ejpam-6159	480	12	ϱ	ϱ	PROPN
ejpam-6159	480	13	k	k	PROPN
ejpam-6159	480	14	∗	∗	X
ejpam-6159	480	15	(	(	PUNCT
ejpam-6159	480	16	b1	b1	NOUN
ejpam-6159	480	17	,	,	PUNCT
ejpam-6159	480	18	x	x	X
ejpam-6159	480	19	)	)	PUNCT
ejpam-6159	480	20	+	+	CCONJ
ejpam-6159	480	21	ς	ς	PROPN
ejpam-6159	480	22	ϱ	ϱ	PROPN
ejpam-6159	480	23	k	k	PROPN
ejpam-6159	480	24	∗	∗	X
ejpam-6159	480	25	(	(	PUNCT
ejpam-6159	480	26	x	x	NOUN
ejpam-6159	480	27	,	,	PUNCT
ejpam-6159	480	28	a1	a1	NOUN
ejpam-6159	480	29	)	)	PUNCT
ejpam-6159	480	30	ς∗	ς∗	NOUN
ejpam-6159	480	31	(	(	PUNCT
ejpam-6159	480	32	b1	b1	NOUN
ejpam-6159	480	33	,	,	PUNCT
ejpam-6159	480	34	a1	a1	PROPN
ejpam-6159	480	35	)	)	PUNCT
ejpam-6159	480	36	]	]	PUNCT
ejpam-6159	481	1	f	f	PROPN
ejpam-6159	481	2	(	(	PUNCT
ejpam-6159	481	3	x	x	X
ejpam-6159	481	4	)	)	PUNCT
ejpam-6159	482	1	+	+	NUM
ejpam-6159	482	2	λ	λ	X
ejpam-6159	482	3	[	[	PUNCT
ejpam-6159	482	4	ς	ς	PROPN
ejpam-6159	482	5	ϱ	ϱ	PROPN
ejpam-6159	482	6	k	k	PROPN
ejpam-6159	482	7	∗	∗	X
ejpam-6159	482	8	(	(	PUNCT
ejpam-6159	482	9	b1	b1	NOUN
ejpam-6159	482	10	,	,	PUNCT
ejpam-6159	482	11	x)f	x)f	X
ejpam-6159	482	12	(	(	PUNCT
ejpam-6159	482	13	b1	b1	NOUN
ejpam-6159	482	14	)	)	PUNCT
ejpam-6159	482	15	+	+	CCONJ
ejpam-6159	482	16	ς	ς	PROPN
ejpam-6159	482	17	ϱ	ϱ	PROPN
ejpam-6159	482	18	k	k	PROPN
ejpam-6159	482	19	∗	∗	X
ejpam-6159	482	20	(	(	PUNCT
ejpam-6159	482	21	x	x	X
ejpam-6159	482	22	,	,	PUNCT
ejpam-6159	482	23	a1)f	a1)f	PROPN
ejpam-6159	482	24	(	(	PUNCT
ejpam-6159	482	25	a1	a1	PROPN
ejpam-6159	482	26	)	)	PUNCT
ejpam-6159	482	27	ς∗	ς∗	NOUN
ejpam-6159	482	28	(	(	PUNCT
ejpam-6159	482	29	b1	b1	NOUN
ejpam-6159	482	30	,	,	PUNCT
ejpam-6159	482	31	a1	a1	PROPN
ejpam-6159	482	32	)	)	PUNCT
ejpam-6159	482	33	]	]	PUNCT
ejpam-6159	483	1	−	−	PROPN
ejpam-6159	483	2	γk	γk	X
ejpam-6159	483	3	(	(	PUNCT
ejpam-6159	483	4	ϱ+	ϱ+	NOUN
ejpam-6159	483	5	2k	2k	NUM
ejpam-6159	483	6	)	)	PUNCT
ejpam-6159	483	7	ς∗	ς∗	PROPN
ejpam-6159	483	8	(	(	PUNCT
ejpam-6159	483	9	b1	b1	NOUN
ejpam-6159	483	10	,	,	PUNCT
ejpam-6159	483	11	a1	a1	NOUN
ejpam-6159	483	12	)	)	PUNCT
ejpam-6159	483	13	{	{	PUNCT
ejpam-6159	483	14	jϱ,k	jϱ,k	X
ejpam-6159	483	15	(	(	PUNCT
ejpam-6159	483	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	483	17	,	,	PUNCT
ejpam-6159	483	18	a1	a1	NOUN
ejpam-6159	483	19	)	)	PUNCT
ejpam-6159	483	20	)	)	PUNCT
ejpam-6159	484	1	−	−	PROPN
ejpam-6159	484	2	f	f	X
ejpam-6159	484	3	(	(	PUNCT
ejpam-6159	484	4	a1	a1	PROPN
ejpam-6159	484	5	)	)	PUNCT
ejpam-6159	484	6	+	+	NUM
ejpam-6159	484	7	jϱ,k	jϱ,k	X
ejpam-6159	484	8	(	(	PUNCT
ejpam-6159	484	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	484	10	,	,	PUNCT
ejpam-6159	484	11	b1	b1	NOUN
ejpam-6159	484	12	)	)	PUNCT
ejpam-6159	484	13	)	)	PUNCT
ejpam-6159	485	1	+	+	CCONJ
ejpam-6159	485	2	f	f	X
ejpam-6159	485	3	(	(	PUNCT
ejpam-6159	485	4	b1	b1	PROPN
ejpam-6159	485	5	)	)	PUNCT
ejpam-6159	485	6	}	}	PUNCT
ejpam-6159	485	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	485	8	≤	≤	NUM
ejpam-6159	485	9	ς	ς	PROPN
ejpam-6159	485	10	ϱ	ϱ	PROPN
ejpam-6159	485	11	k	k	PROPN
ejpam-6159	485	12	+2	+2	PROPN
ejpam-6159	485	13	∗	∗	NOUN
ejpam-6159	485	14	(	(	PUNCT
ejpam-6159	485	15	x	x	NOUN
ejpam-6159	485	16	,	,	PUNCT
ejpam-6159	485	17	a1	a1	NOUN
ejpam-6159	485	18	)	)	PUNCT
ejpam-6159	485	19	ς∗	ς∗	NOUN
ejpam-6159	485	20	(	(	PUNCT
ejpam-6159	485	21	b1	b1	NOUN
ejpam-6159	485	22	,	,	PUNCT
ejpam-6159	485	23	a1	a1	PROPN
ejpam-6159	485	24	)	)	PUNCT
ejpam-6159	485	25	∫	∫	NOUN
ejpam-6159	486	1	1	1	NUM
ejpam-6159	486	2	0	0	NUM
ejpam-6159	486	3	t	t	PROPN
ejpam-6159	486	4	(	(	PUNCT
ejpam-6159	486	5	λ−	λ−	PROPN
ejpam-6159	486	6	t	t	PROPN
ejpam-6159	486	7	ϱ	ϱ	PROPN
ejpam-6159	486	8	k	k	PROPN
ejpam-6159	486	9	)	)	PUNCT
ejpam-6159	486	10	|f′′	|f′′	NUM
ejpam-6159	486	11	(	(	PUNCT
ejpam-6159	486	12	a1	a1	NOUN
ejpam-6159	486	13	+	+	CCONJ
ejpam-6159	486	14	tς∗	tς∗	X
ejpam-6159	486	15	(	(	PUNCT
ejpam-6159	486	16	x	x	NOUN
ejpam-6159	486	17	,	,	PUNCT
ejpam-6159	486	18	a1	a1	NOUN
ejpam-6159	486	19	)	)	PUNCT
ejpam-6159	486	20	)	)	PUNCT
ejpam-6159	487	1	|dt	|dt	PROPN
ejpam-6159	488	1	+	+	X
ejpam-6159	488	2	ς	ς	PROPN
ejpam-6159	488	3	ϱ	ϱ	ADP
ejpam-6159	488	4	k	k	PROPN
ejpam-6159	488	5	+2	+2	PROPN
ejpam-6159	488	6	∗	∗	NOUN
ejpam-6159	488	7	(	(	PUNCT
ejpam-6159	488	8	b1	b1	NOUN
ejpam-6159	488	9	,	,	PUNCT
ejpam-6159	488	10	x	x	NOUN
ejpam-6159	488	11	)	)	PUNCT
ejpam-6159	488	12	ς∗	ς∗	PROPN
ejpam-6159	488	13	(	(	PUNCT
ejpam-6159	488	14	b1	b1	NOUN
ejpam-6159	488	15	,	,	PUNCT
ejpam-6159	488	16	a1	a1	PROPN
ejpam-6159	488	17	)	)	PUNCT
ejpam-6159	488	18	∫	∫	NOUN
ejpam-6159	488	19	1	1	NUM
ejpam-6159	488	20	0	0	NUM
ejpam-6159	488	21	t	t	PROPN
ejpam-6159	488	22	(	(	PUNCT
ejpam-6159	488	23	λ−	λ−	PROPN
ejpam-6159	488	24	t	t	PROPN
ejpam-6159	488	25	ϱ	ϱ	PROPN
ejpam-6159	488	26	k	k	PROPN
ejpam-6159	488	27	)	)	PUNCT
ejpam-6159	488	28	|f′′	|f′′	NUM
ejpam-6159	488	29	(	(	PUNCT
ejpam-6159	488	30	b1	b1	NOUN
ejpam-6159	488	31	+	+	CCONJ
ejpam-6159	488	32	tς∗	tς∗	X
ejpam-6159	488	33	(	(	PUNCT
ejpam-6159	488	34	x	x	NOUN
ejpam-6159	488	35	,	,	PUNCT
ejpam-6159	488	36	b1	b1	NOUN
ejpam-6159	488	37	)	)	PUNCT
ejpam-6159	488	38	)	)	PUNCT
ejpam-6159	489	1	|dt	|dt	X
ejpam-6159	489	2	≤	≤	NUM
ejpam-6159	489	3	ς	ς	PROPN
ejpam-6159	489	4	ϱ	ϱ	PROPN
ejpam-6159	489	5	k	k	PROPN
ejpam-6159	489	6	+2	+2	PROPN
ejpam-6159	489	7	∗	∗	NOUN
ejpam-6159	489	8	(	(	PUNCT
ejpam-6159	489	9	x	x	NOUN
ejpam-6159	489	10	,	,	PUNCT
ejpam-6159	489	11	a1	a1	NOUN
ejpam-6159	489	12	)	)	PUNCT
ejpam-6159	489	13	ς∗	ς∗	NOUN
ejpam-6159	489	14	(	(	PUNCT
ejpam-6159	489	15	b1	b1	NOUN
ejpam-6159	489	16	,	,	PUNCT
ejpam-6159	489	17	a1	a1	PROPN
ejpam-6159	489	18	)	)	PUNCT
ejpam-6159	489	19	∫	∫	NOUN
ejpam-6159	490	1	1	1	NUM
ejpam-6159	490	2	0	0	NUM
ejpam-6159	490	3	t	t	PROPN
ejpam-6159	490	4	(	(	PUNCT
ejpam-6159	490	5	λ−	λ−	PROPN
ejpam-6159	490	6	t	t	PROPN
ejpam-6159	490	7	ϱ	ϱ	PROPN
ejpam-6159	490	8	k	k	X
ejpam-6159	490	9	)	)	PUNCT
ejpam-6159	490	10	×[∑n	×[∑n	NOUN
ejpam-6159	490	11	i=1	i=1	X
ejpam-6159	490	12	ai	ai	VERB
ejpam-6159	490	13	(	(	PUNCT
ejpam-6159	490	14	1−	1−	NUM
ejpam-6159	490	15	s	s	X
ejpam-6159	490	16	(	(	PUNCT
ejpam-6159	490	17	1−	1−	NUM
ejpam-6159	490	18	t	t	NOUN
ejpam-6159	490	19	)	)	PUNCT
ejpam-6159	490	20	)	)	PUNCT
ejpam-6159	490	21	1	1	NUM
ejpam-6159	490	22	i∑n	i∑n	PROPN
ejpam-6159	490	23	i=1	i=1	PROPN
ejpam-6159	490	24	ai	ai	VERB
ejpam-6159	490	25	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	490	26	(	(	PUNCT
ejpam-6159	490	27	x	x	NOUN
ejpam-6159	490	28	)	)	PUNCT
ejpam-6159	490	29	∣∣+	∣∣+	PROPN
ejpam-6159	491	1	∑n	∑n	PROPN
ejpam-6159	491	2	i=1	i=1	PROPN
ejpam-6159	491	3	ai	ai	VERB
ejpam-6159	491	4	(	(	PUNCT
ejpam-6159	491	5	1−	1−	NUM
ejpam-6159	491	6	st	st	NOUN
ejpam-6159	491	7	)	)	PUNCT
ejpam-6159	491	8	1	1	NUM
ejpam-6159	491	9	i∑n	i∑n	PROPN
ejpam-6159	491	10	i=1	i=1	PROPN
ejpam-6159	491	11	ai	ai	VERB
ejpam-6159	491	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	491	13	(	(	PUNCT
ejpam-6159	491	14	a1	a1	PROPN
ejpam-6159	491	15	)	)	PUNCT
ejpam-6159	491	16	∣∣	∣∣	X
ejpam-6159	491	17	]	]	PUNCT
ejpam-6159	491	18	dt	dt	X
ejpam-6159	492	1	+	+	CCONJ
ejpam-6159	492	2	ς	ς	PROPN
ejpam-6159	492	3	ϱ	ϱ	ADP
ejpam-6159	492	4	k	k	PROPN
ejpam-6159	492	5	+2	+2	PROPN
ejpam-6159	492	6	∗	∗	NOUN
ejpam-6159	492	7	(	(	PUNCT
ejpam-6159	492	8	b1	b1	NOUN
ejpam-6159	492	9	,	,	PUNCT
ejpam-6159	492	10	x	x	NOUN
ejpam-6159	492	11	)	)	PUNCT
ejpam-6159	492	12	ς∗	ς∗	PROPN
ejpam-6159	492	13	(	(	PUNCT
ejpam-6159	492	14	b1	b1	NOUN
ejpam-6159	492	15	,	,	PUNCT
ejpam-6159	492	16	a1	a1	PROPN
ejpam-6159	492	17	)	)	PUNCT
ejpam-6159	492	18	∫	∫	NOUN
ejpam-6159	492	19	1	1	NUM
ejpam-6159	492	20	0	0	NUM
ejpam-6159	492	21	t	t	PROPN
ejpam-6159	492	22	(	(	PUNCT
ejpam-6159	492	23	λ−	λ−	PROPN
ejpam-6159	492	24	t	t	PROPN
ejpam-6159	492	25	ϱ	ϱ	PROPN
ejpam-6159	492	26	k	k	X
ejpam-6159	492	27	)	)	PUNCT
ejpam-6159	492	28	×[∑n	×[∑n	NOUN
ejpam-6159	493	1	i=1	i=1	X
ejpam-6159	493	2	ai	ai	VERB
ejpam-6159	493	3	(	(	PUNCT
ejpam-6159	493	4	1−	1−	NUM
ejpam-6159	493	5	s	s	X
ejpam-6159	493	6	(	(	PUNCT
ejpam-6159	493	7	1−	1−	NUM
ejpam-6159	493	8	t	t	NOUN
ejpam-6159	493	9	)	)	PUNCT
ejpam-6159	493	10	)	)	PUNCT
ejpam-6159	493	11	1	1	NUM
ejpam-6159	493	12	i∑n	i∑n	PROPN
ejpam-6159	493	13	i=1	i=1	PROPN
ejpam-6159	493	14	ai	ai	VERB
ejpam-6159	493	15	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	493	16	(	(	PUNCT
ejpam-6159	493	17	x	x	NOUN
ejpam-6159	493	18	)	)	PUNCT
ejpam-6159	493	19	∣∣+	∣∣+	PROPN
ejpam-6159	494	1	∑n	∑n	PROPN
ejpam-6159	494	2	i=1	i=1	PROPN
ejpam-6159	494	3	ai	ai	VERB
ejpam-6159	494	4	(	(	PUNCT
ejpam-6159	494	5	1−	1−	NUM
ejpam-6159	494	6	st	st	NOUN
ejpam-6159	494	7	)	)	PUNCT
ejpam-6159	494	8	1	1	NUM
ejpam-6159	494	9	i∑n	i∑n	PROPN
ejpam-6159	494	10	i=1	i=1	PROPN
ejpam-6159	494	11	ai	ai	VERB
ejpam-6159	494	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	494	13	(	(	PUNCT
ejpam-6159	494	14	b1	b1	NOUN
ejpam-6159	494	15	)	)	PUNCT
ejpam-6159	494	16	∣∣	∣∣	X
ejpam-6159	495	1	]	]	PUNCT
ejpam-6159	495	2	dt	dt	X
ejpam-6159	495	3	≤	≤	X
ejpam-6159	495	4	[	[	PUNCT
ejpam-6159	495	5	ς	ς	X
ejpam-6159	495	6	ϱ	ϱ	ADP
ejpam-6159	495	7	k	k	PROPN
ejpam-6159	495	8	+2	+2	PROPN
ejpam-6159	495	9	∗	∗	NOUN
ejpam-6159	495	10	(	(	PUNCT
ejpam-6159	495	11	x	x	NOUN
ejpam-6159	495	12	,	,	PUNCT
ejpam-6159	495	13	a1	a1	PROPN
ejpam-6159	495	14	)	)	PUNCT
ejpam-6159	495	15	|f′′	|f′′	NUM
ejpam-6159	495	16	(	(	PUNCT
ejpam-6159	495	17	a1)|+	a1)|+	VERB
ejpam-6159	495	18	ς	ς	PROPN
ejpam-6159	495	19	ϱ	ϱ	PROPN
ejpam-6159	495	20	k	k	PROPN
ejpam-6159	495	21	+2	+2	PROPN
ejpam-6159	495	22	∗	∗	NOUN
ejpam-6159	495	23	(	(	PUNCT
ejpam-6159	495	24	b1	b1	NOUN
ejpam-6159	495	25	,	,	PUNCT
ejpam-6159	495	26	x	x	NOUN
ejpam-6159	495	27	)	)	PUNCT
ejpam-6159	495	28	|f′′	|f′′	NUM
ejpam-6159	495	29	(	(	PUNCT
ejpam-6159	495	30	b1)|	b1)|	PROPN
ejpam-6159	495	31	ς∗	ς∗	PROPN
ejpam-6159	495	32	(	(	PUNCT
ejpam-6159	495	33	b1	b1	NOUN
ejpam-6159	495	34	,	,	PUNCT
ejpam-6159	495	35	a1	a1	PROPN
ejpam-6159	495	36	)	)	PUNCT
ejpam-6159	495	37	]	]	PUNCT
ejpam-6159	496	1	1∑n	1∑n	X
ejpam-6159	496	2	i=1	i=1	PROPN
ejpam-6159	496	3	ai	ai	VERB
ejpam-6159	497	1	n∑	n∑	PROPN
ejpam-6159	497	2	i=1	i=1	PROPN
ejpam-6159	498	1	ai	ai	INTJ
ejpam-6159	498	2	∫	∫	PROPN
ejpam-6159	498	3	1	1	NUM
ejpam-6159	498	4	0	0	NUM
ejpam-6159	498	5	t	t	PROPN
ejpam-6159	498	6	(	(	PUNCT
ejpam-6159	498	7	λ−	λ−	PROPN
ejpam-6159	498	8	t	t	PROPN
ejpam-6159	498	9	ϱ	ϱ	PROPN
ejpam-6159	498	10	k	k	PROPN
ejpam-6159	498	11	)	)	PUNCT
ejpam-6159	498	12	(	(	PUNCT
ejpam-6159	498	13	1−	1−	NUM
ejpam-6159	498	14	st	st	NOUN
ejpam-6159	498	15	)	)	PUNCT
ejpam-6159	498	16	1	1	NUM
ejpam-6159	499	1	i	i	PRON
ejpam-6159	499	2	dt	dt	VERB
ejpam-6159	500	1	+	+	CCONJ
ejpam-6159	500	2	ς	ς	X
ejpam-6159	500	3	ϱ	ϱ	ADP
ejpam-6159	500	4	k	k	PROPN
ejpam-6159	500	5	+2	+2	PROPN
ejpam-6159	500	6	∗	∗	NOUN
ejpam-6159	500	7	(	(	PUNCT
ejpam-6159	500	8	x	x	NOUN
ejpam-6159	500	9	,	,	PUNCT
ejpam-6159	500	10	a1	a1	NOUN
ejpam-6159	500	11	)	)	PUNCT
ejpam-6159	500	12	+	+	CCONJ
ejpam-6159	500	13	ς	ς	PROPN
ejpam-6159	500	14	ϱ	ϱ	ADP
ejpam-6159	500	15	k	k	PROPN
ejpam-6159	500	16	+2	+2	PROPN
ejpam-6159	500	17	∗	∗	NOUN
ejpam-6159	500	18	(	(	PUNCT
ejpam-6159	500	19	b1	b1	NOUN
ejpam-6159	500	20	,	,	PUNCT
ejpam-6159	500	21	x)∑n	x)∑n	PUNCT
ejpam-6159	501	1	i=1	i=1	PROPN
ejpam-6159	502	1	ai	ai	VERB
ejpam-6159	502	2	ς∗	ς∗	PROPN
ejpam-6159	502	3	(	(	PUNCT
ejpam-6159	502	4	b1	b1	NOUN
ejpam-6159	502	5	,	,	PUNCT
ejpam-6159	502	6	a1	a1	NOUN
ejpam-6159	502	7	)	)	PUNCT
ejpam-6159	502	8	∣∣f′′	∣∣f′′	NOUN
ejpam-6159	502	9	(	(	PUNCT
ejpam-6159	502	10	x	x	X
ejpam-6159	502	11	)	)	PUNCT
ejpam-6159	502	12	∣∣	∣∣	PROPN
ejpam-6159	503	1	n∑	n∑	PROPN
ejpam-6159	503	2	i=1	i=1	PROPN
ejpam-6159	504	1	ai	ai	INTJ
ejpam-6159	504	2	∫	∫	PROPN
ejpam-6159	504	3	1	1	NUM
ejpam-6159	504	4	0	0	NUM
ejpam-6159	504	5	t	t	PROPN
ejpam-6159	504	6	(	(	PUNCT
ejpam-6159	504	7	λ−	λ−	PROPN
ejpam-6159	504	8	t	t	PROPN
ejpam-6159	504	9	ϱ	ϱ	PROPN
ejpam-6159	504	10	k	k	PROPN
ejpam-6159	504	11	)	)	PUNCT
ejpam-6159	504	12	(	(	PUNCT
ejpam-6159	504	13	1−	1−	NUM
ejpam-6159	504	14	s	s	X
ejpam-6159	504	15	(	(	PUNCT
ejpam-6159	504	16	1−	1−	NUM
ejpam-6159	504	17	t	t	NOUN
ejpam-6159	504	18	)	)	PUNCT
ejpam-6159	504	19	)	)	PUNCT
ejpam-6159	505	1	1	1	NUM
ejpam-6159	505	2	i	i	PRON
ejpam-6159	505	3	dt	dt	X
ejpam-6159	505	4	.	.	PUNCT
ejpam-6159	506	1	(	(	PUNCT
ejpam-6159	506	2	38	38	NUM
ejpam-6159	506	3	)	)	PUNCT
ejpam-6159	506	4	corollary	corollary	ADJ
ejpam-6159	506	5	9	9	NUM
ejpam-6159	506	6	.	.	PUNCT
ejpam-6159	507	1	if	if	SCONJ
ejpam-6159	507	2	one	one	PRON
ejpam-6159	507	3	can	can	AUX
ejpam-6159	507	4	take	take	VERB
ejpam-6159	507	5	s	s	PART
ejpam-6159	507	6	=	=	SYM
ejpam-6159	507	7	1	1	NUM
ejpam-6159	507	8	in	in	ADP
ejpam-6159	507	9	theorem	theorem	NOUN
ejpam-6159	507	10	6	6	NUM
ejpam-6159	507	11	,	,	PUNCT
ejpam-6159	507	12	then	then	ADV
ejpam-6159	507	13	we	we	PRON
ejpam-6159	507	14	have	have	VERB
ejpam-6159	507	15	the	the	DET
ejpam-6159	507	16	followingiinequalities	followingiinequalitie	NOUN
ejpam-6159	507	17	for	for	ADP
ejpam-6159	507	18	gfpp	gfpp	NOUN
ejpam-6159	507	19	function	function	NOUN
ejpam-6159	507	20	with	with	ADP
ejpam-6159	507	21	k−fractional	k−fractional	ADJ
ejpam-6159	507	22	integral	integral	ADJ
ejpam-6159	507	23	operators:∣∣∣∣	operators:∣∣∣∣	ADJ
ejpam-6159	507	24	(	(	PUNCT
ejpam-6159	507	25	1−	1−	NUM
ejpam-6159	507	26	λ	λ	NOUN
ejpam-6159	507	27	)	)	PUNCT
ejpam-6159	507	28	[	[	PUNCT
ejpam-6159	507	29	ς	ς	X
ejpam-6159	507	30	ϱ	ϱ	PROPN
ejpam-6159	507	31	k	k	PROPN
ejpam-6159	507	32	∗	∗	X
ejpam-6159	507	33	(	(	PUNCT
ejpam-6159	507	34	b1	b1	NOUN
ejpam-6159	507	35	,	,	PUNCT
ejpam-6159	507	36	x)−	x)−	PROPN
ejpam-6159	507	37	ς	ς	PROPN
ejpam-6159	507	38	ϱ	ϱ	PROPN
ejpam-6159	507	39	k	k	PROPN
ejpam-6159	507	40	∗	∗	X
ejpam-6159	507	41	(	(	PUNCT
ejpam-6159	507	42	x	x	NOUN
ejpam-6159	507	43	,	,	PUNCT
ejpam-6159	507	44	a1	a1	NOUN
ejpam-6159	507	45	)	)	PUNCT
ejpam-6159	507	46	ς∗	ς∗	NOUN
ejpam-6159	507	47	(	(	PUNCT
ejpam-6159	507	48	b1	b1	NOUN
ejpam-6159	507	49	,	,	PUNCT
ejpam-6159	507	50	a1	a1	PROPN
ejpam-6159	507	51	)	)	PUNCT
ejpam-6159	507	52	]	]	PUNCT
ejpam-6159	507	53	f′	f′	PROPN
ejpam-6159	507	54	(	(	PUNCT
ejpam-6159	507	55	x	x	X
ejpam-6159	507	56	)	)	PUNCT
ejpam-6159	508	1	+	+	CCONJ
ejpam-6159	508	2	(	(	PUNCT
ejpam-6159	508	3	1	1	NUM
ejpam-6159	508	4	+	+	CCONJ
ejpam-6159	508	5	ϱ	ϱ	ADP
ejpam-6159	508	6	k	k	X
ejpam-6159	508	7	−	−	PROPN
ejpam-6159	508	8	λ	λ	PROPN
ejpam-6159	508	9	)	)	PUNCT
ejpam-6159	508	10	[	[	PUNCT
ejpam-6159	508	11	ς	ς	PROPN
ejpam-6159	508	12	ϱ	ϱ	PROPN
ejpam-6159	508	13	k	k	PROPN
ejpam-6159	508	14	∗	∗	X
ejpam-6159	508	15	(	(	PUNCT
ejpam-6159	508	16	b1	b1	NOUN
ejpam-6159	508	17	,	,	PUNCT
ejpam-6159	508	18	x	x	X
ejpam-6159	508	19	)	)	PUNCT
ejpam-6159	508	20	+	+	CCONJ
ejpam-6159	508	21	ς	ς	PROPN
ejpam-6159	508	22	ϱ	ϱ	PROPN
ejpam-6159	508	23	k	k	PROPN
ejpam-6159	508	24	∗	∗	X
ejpam-6159	508	25	(	(	PUNCT
ejpam-6159	508	26	x	x	NOUN
ejpam-6159	508	27	,	,	PUNCT
ejpam-6159	508	28	a1	a1	NOUN
ejpam-6159	508	29	)	)	PUNCT
ejpam-6159	508	30	ς∗	ς∗	NOUN
ejpam-6159	508	31	(	(	PUNCT
ejpam-6159	508	32	b1	b1	NOUN
ejpam-6159	508	33	,	,	PUNCT
ejpam-6159	508	34	a1	a1	PROPN
ejpam-6159	508	35	)	)	PUNCT
ejpam-6159	508	36	]	]	PUNCT
ejpam-6159	509	1	f	f	PROPN
ejpam-6159	509	2	(	(	PUNCT
ejpam-6159	509	3	x	x	X
ejpam-6159	509	4	)	)	PUNCT
ejpam-6159	510	1	+	+	NUM
ejpam-6159	510	2	λ	λ	X
ejpam-6159	510	3	[	[	PUNCT
ejpam-6159	510	4	ς	ς	PROPN
ejpam-6159	510	5	ϱ	ϱ	PROPN
ejpam-6159	510	6	k	k	PROPN
ejpam-6159	510	7	∗	∗	X
ejpam-6159	510	8	(	(	PUNCT
ejpam-6159	510	9	b1	b1	NOUN
ejpam-6159	510	10	,	,	PUNCT
ejpam-6159	510	11	x)f	x)f	X
ejpam-6159	510	12	(	(	PUNCT
ejpam-6159	510	13	b1	b1	NOUN
ejpam-6159	510	14	)	)	PUNCT
ejpam-6159	510	15	+	+	CCONJ
ejpam-6159	510	16	ς	ς	PROPN
ejpam-6159	510	17	ϱ	ϱ	PROPN
ejpam-6159	510	18	k	k	PROPN
ejpam-6159	510	19	∗	∗	X
ejpam-6159	510	20	(	(	PUNCT
ejpam-6159	510	21	x	x	X
ejpam-6159	510	22	,	,	PUNCT
ejpam-6159	510	23	a1)f	a1)f	PROPN
ejpam-6159	510	24	(	(	PUNCT
ejpam-6159	510	25	a1	a1	PROPN
ejpam-6159	510	26	)	)	PUNCT
ejpam-6159	510	27	ς∗	ς∗	NOUN
ejpam-6159	510	28	(	(	PUNCT
ejpam-6159	510	29	b1	b1	NOUN
ejpam-6159	510	30	,	,	PUNCT
ejpam-6159	510	31	a1	a1	PROPN
ejpam-6159	510	32	)	)	PUNCT
ejpam-6159	510	33	]	]	PUNCT
ejpam-6159	511	1	−	−	PROPN
ejpam-6159	511	2	γk	γk	X
ejpam-6159	511	3	(	(	PUNCT
ejpam-6159	511	4	ϱ+	ϱ+	NOUN
ejpam-6159	511	5	2k	2k	NUM
ejpam-6159	511	6	)	)	PUNCT
ejpam-6159	511	7	ς∗	ς∗	PROPN
ejpam-6159	511	8	(	(	PUNCT
ejpam-6159	511	9	b1	b1	NOUN
ejpam-6159	511	10	,	,	PUNCT
ejpam-6159	511	11	a1	a1	NOUN
ejpam-6159	511	12	)	)	PUNCT
ejpam-6159	511	13	{	{	PUNCT
ejpam-6159	511	14	jϱ,k	jϱ,k	X
ejpam-6159	511	15	(	(	PUNCT
ejpam-6159	511	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	511	17	,	,	PUNCT
ejpam-6159	511	18	a1	a1	NOUN
ejpam-6159	511	19	)	)	PUNCT
ejpam-6159	511	20	)	)	PUNCT
ejpam-6159	512	1	−	−	PROPN
ejpam-6159	512	2	f	f	X
ejpam-6159	512	3	(	(	PUNCT
ejpam-6159	512	4	a1	a1	PROPN
ejpam-6159	512	5	)	)	PUNCT
ejpam-6159	512	6	+	+	NUM
ejpam-6159	512	7	jϱ,k	jϱ,k	X
ejpam-6159	512	8	(	(	PUNCT
ejpam-6159	512	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	512	10	,	,	PUNCT
ejpam-6159	512	11	b1	b1	NOUN
ejpam-6159	512	12	)	)	PUNCT
ejpam-6159	512	13	)	)	PUNCT
ejpam-6159	513	1	+	+	CCONJ
ejpam-6159	513	2	f	f	X
ejpam-6159	513	3	(	(	PUNCT
ejpam-6159	513	4	b1	b1	PROPN
ejpam-6159	513	5	)	)	PUNCT
ejpam-6159	513	6	}	}	PUNCT
ejpam-6159	513	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	513	8	≤	≤	NOUN
ejpam-6159	513	9	[	[	PUNCT
ejpam-6159	513	10	ς	ς	X
ejpam-6159	513	11	ϱ	ϱ	ADP
ejpam-6159	513	12	k	k	PROPN
ejpam-6159	513	13	+2	+2	PROPN
ejpam-6159	513	14	∗	∗	NOUN
ejpam-6159	513	15	(	(	PUNCT
ejpam-6159	513	16	x	x	NOUN
ejpam-6159	513	17	,	,	PUNCT
ejpam-6159	513	18	a1	a1	PROPN
ejpam-6159	513	19	)	)	PUNCT
ejpam-6159	513	20	|f′′	|f′′	NUM
ejpam-6159	513	21	(	(	PUNCT
ejpam-6159	513	22	a1)|+	a1)|+	VERB
ejpam-6159	513	23	ς	ς	PROPN
ejpam-6159	513	24	ϱ	ϱ	PROPN
ejpam-6159	513	25	k	k	PROPN
ejpam-6159	513	26	+2	+2	PROPN
ejpam-6159	513	27	∗	∗	NOUN
ejpam-6159	513	28	(	(	PUNCT
ejpam-6159	513	29	b1	b1	NOUN
ejpam-6159	513	30	,	,	PUNCT
ejpam-6159	513	31	x	x	NOUN
ejpam-6159	513	32	)	)	PUNCT
ejpam-6159	513	33	|f′′	|f′′	NUM
ejpam-6159	514	1	(	(	PUNCT
ejpam-6159	514	2	b1)|	b1)|	PROPN
ejpam-6159	514	3	ς∗	ς∗	PROPN
ejpam-6159	514	4	(	(	PUNCT
ejpam-6159	514	5	b1	b1	NOUN
ejpam-6159	514	6	,	,	PUNCT
ejpam-6159	514	7	a1	a1	PROPN
ejpam-6159	514	8	)	)	PUNCT
ejpam-6159	514	9	]	]	PUNCT
ejpam-6159	515	1	1∑n	1∑n	X
ejpam-6159	515	2	i=1	i=1	PROPN
ejpam-6159	515	3	ai	ai	VERB
ejpam-6159	516	1	n∑	n∑	PROPN
ejpam-6159	516	2	i=1	i=1	PROPN
ejpam-6159	517	1	ai	ai	INTJ
ejpam-6159	517	2	∫	∫	PROPN
ejpam-6159	517	3	1	1	NUM
ejpam-6159	517	4	0	0	NUM
ejpam-6159	517	5	t	t	PROPN
ejpam-6159	517	6	(	(	PUNCT
ejpam-6159	517	7	λ−	λ−	PROPN
ejpam-6159	517	8	t	t	PROPN
ejpam-6159	517	9	ϱ	ϱ	PROPN
ejpam-6159	517	10	k	k	PROPN
ejpam-6159	517	11	)	)	PUNCT
ejpam-6159	517	12	(	(	PUNCT
ejpam-6159	517	13	1−	1−	NUM
ejpam-6159	517	14	t	t	NOUN
ejpam-6159	517	15	)	)	PUNCT
ejpam-6159	517	16	1	1	NUM
ejpam-6159	518	1	i	i	PRON
ejpam-6159	518	2	dt	dt	PROPN
ejpam-6159	518	3	j.	j.	PROPN
ejpam-6159	518	4	nasir	nasir	PROPN
ejpam-6159	518	5	et	et	PROPN
ejpam-6159	518	6	al	al	PROPN
ejpam-6159	518	7	.	.	PUNCT
ejpam-6159	518	8	/	/	SYM
ejpam-6159	518	9	eur	eur	PROPN
ejpam-6159	518	10	.	.	PUNCT
ejpam-6159	519	1	j.	j.	PROPN
ejpam-6159	519	2	pure	pure	PROPN
ejpam-6159	519	3	appl	appl	PROPN
ejpam-6159	519	4	.	.	PROPN
ejpam-6159	519	5	math	math	PROPN
ejpam-6159	519	6	,	,	PUNCT
ejpam-6159	519	7	18	18	NUM
ejpam-6159	519	8	(	(	PUNCT
ejpam-6159	519	9	3	3	NUM
ejpam-6159	519	10	)	)	PUNCT
ejpam-6159	519	11	(	(	PUNCT
ejpam-6159	519	12	2025	2025	NUM
ejpam-6159	519	13	)	)	PUNCT
ejpam-6159	519	14	,	,	PUNCT
ejpam-6159	519	15	6159	6159	NUM
ejpam-6159	519	16	17	17	NUM
ejpam-6159	519	17	of	of	ADP
ejpam-6159	519	18	26	26	NUM
ejpam-6159	519	19	+	+	CCONJ
ejpam-6159	519	20	ς	ς	PROPN
ejpam-6159	519	21	ϱ	ϱ	ADP
ejpam-6159	519	22	k	k	PROPN
ejpam-6159	519	23	+2	+2	PROPN
ejpam-6159	519	24	∗	∗	NOUN
ejpam-6159	519	25	(	(	PUNCT
ejpam-6159	519	26	x	x	NOUN
ejpam-6159	519	27	,	,	PUNCT
ejpam-6159	519	28	a1	a1	NOUN
ejpam-6159	519	29	)	)	PUNCT
ejpam-6159	519	30	+	+	CCONJ
ejpam-6159	519	31	ς	ς	PROPN
ejpam-6159	519	32	ϱ	ϱ	ADP
ejpam-6159	519	33	k	k	PROPN
ejpam-6159	519	34	+2	+2	PROPN
ejpam-6159	519	35	∗	∗	NOUN
ejpam-6159	519	36	(	(	PUNCT
ejpam-6159	519	37	b1	b1	NOUN
ejpam-6159	519	38	,	,	PUNCT
ejpam-6159	519	39	x)∑n	x)∑n	PUNCT
ejpam-6159	520	1	i=1	i=1	PROPN
ejpam-6159	521	1	ai	ai	VERB
ejpam-6159	521	2	ς∗	ς∗	PROPN
ejpam-6159	521	3	(	(	PUNCT
ejpam-6159	521	4	b1	b1	NOUN
ejpam-6159	521	5	,	,	PUNCT
ejpam-6159	521	6	a1	a1	NOUN
ejpam-6159	521	7	)	)	PUNCT
ejpam-6159	521	8	∣∣f′′	∣∣f′′	NOUN
ejpam-6159	521	9	(	(	PUNCT
ejpam-6159	521	10	x	x	X
ejpam-6159	521	11	)	)	PUNCT
ejpam-6159	521	12	∣∣	∣∣	PROPN
ejpam-6159	522	1	n∑	n∑	PROPN
ejpam-6159	522	2	i=1	i=1	PROPN
ejpam-6159	523	1	ai	ai	INTJ
ejpam-6159	523	2	∫	∫	PROPN
ejpam-6159	523	3	1	1	NUM
ejpam-6159	523	4	0	0	NUM
ejpam-6159	523	5	(	(	PUNCT
ejpam-6159	523	6	λ−	λ−	PROPN
ejpam-6159	523	7	t	t	PROPN
ejpam-6159	523	8	ϱ	ϱ	PROPN
ejpam-6159	523	9	k	k	PROPN
ejpam-6159	523	10	)	)	PUNCT
ejpam-6159	523	11	(	(	PUNCT
ejpam-6159	523	12	t	t	X
ejpam-6159	523	13	)	)	PUNCT
ejpam-6159	523	14	1	1	NUM
ejpam-6159	524	1	i	i	PRON
ejpam-6159	524	2	+1	+1	PRON
ejpam-6159	524	3	dt	dt	X
ejpam-6159	524	4	.	.	PUNCT
ejpam-6159	525	1	corollary	corollary	ADJ
ejpam-6159	525	2	10	10	NUM
ejpam-6159	525	3	.	.	PUNCT
ejpam-6159	526	1	if	if	SCONJ
ejpam-6159	526	2	one	one	PRON
ejpam-6159	526	3	can	can	AUX
ejpam-6159	526	4	take	take	VERB
ejpam-6159	526	5	k	k	NOUN
ejpam-6159	526	6	=	=	PUNCT
ejpam-6159	526	7	1	1	NUM
ejpam-6159	526	8	in	in	ADP
ejpam-6159	526	9	corollary	corollary	ADJ
ejpam-6159	526	10	9	9	NUM
ejpam-6159	526	11	,	,	PUNCT
ejpam-6159	526	12	then	then	ADV
ejpam-6159	526	13	we	we	PRON
ejpam-6159	526	14	have	have	VERB
ejpam-6159	526	15	the	the	DET
ejpam-6159	526	16	following	follow	VERB
ejpam-6159	526	17	inequalities	inequality	NOUN
ejpam-6159	526	18	for	for	ADP
ejpam-6159	526	19	a	a	DET
ejpam-6159	526	20	gfpp	gfpp	NOUN
ejpam-6159	526	21	function	function	NOUN
ejpam-6159	526	22	with	with	ADP
ejpam-6159	526	23	rl−fractional	rl−fractional	ADJ
ejpam-6159	526	24	integral	integral	ADJ
ejpam-6159	526	25	operators:∣∣∣∣	operators:∣∣∣∣	ADJ
ejpam-6159	526	26	(	(	PUNCT
ejpam-6159	526	27	1−	1−	NUM
ejpam-6159	526	28	λ	λ	NOUN
ejpam-6159	526	29	)	)	PUNCT
ejpam-6159	526	30	[	[	PUNCT
ejpam-6159	526	31	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	526	32	(	(	PUNCT
ejpam-6159	526	33	b1	b1	NOUN
ejpam-6159	526	34	,	,	PUNCT
ejpam-6159	526	35	x)−	x)−	PROPN
ejpam-6159	526	36	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	526	37	(	(	PUNCT
ejpam-6159	526	38	x	x	NOUN
ejpam-6159	526	39	,	,	PUNCT
ejpam-6159	526	40	a1	a1	NOUN
ejpam-6159	526	41	)	)	PUNCT
ejpam-6159	526	42	ς∗	ς∗	NOUN
ejpam-6159	526	43	(	(	PUNCT
ejpam-6159	526	44	b1	b1	NOUN
ejpam-6159	526	45	,	,	PUNCT
ejpam-6159	526	46	a1	a1	PROPN
ejpam-6159	526	47	)	)	PUNCT
ejpam-6159	526	48	]	]	PUNCT
ejpam-6159	526	49	f′	f′	PROPN
ejpam-6159	526	50	(	(	PUNCT
ejpam-6159	526	51	x	x	X
ejpam-6159	526	52	)	)	PUNCT
ejpam-6159	527	1	+	+	CCONJ
ejpam-6159	527	2	(	(	PUNCT
ejpam-6159	527	3	1	1	NUM
ejpam-6159	527	4	+	+	NUM
ejpam-6159	527	5	ϱ−	ϱ−	NOUN
ejpam-6159	527	6	λ	λ	NOUN
ejpam-6159	527	7	)	)	PUNCT
ejpam-6159	527	8	[	[	PUNCT
ejpam-6159	527	9	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	527	10	(	(	PUNCT
ejpam-6159	527	11	b1	b1	NOUN
ejpam-6159	527	12	,	,	PUNCT
ejpam-6159	527	13	x	x	X
ejpam-6159	527	14	)	)	PUNCT
ejpam-6159	528	1	+	+	NUM
ejpam-6159	528	2	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	528	3	(	(	PUNCT
ejpam-6159	528	4	x	x	NOUN
ejpam-6159	528	5	,	,	PUNCT
ejpam-6159	528	6	a1	a1	NOUN
ejpam-6159	528	7	)	)	PUNCT
ejpam-6159	528	8	ς∗	ς∗	NOUN
ejpam-6159	528	9	(	(	PUNCT
ejpam-6159	528	10	b1	b1	NOUN
ejpam-6159	528	11	,	,	PUNCT
ejpam-6159	528	12	a1	a1	PROPN
ejpam-6159	528	13	)	)	PUNCT
ejpam-6159	528	14	]	]	PUNCT
ejpam-6159	529	1	f	f	PROPN
ejpam-6159	529	2	(	(	PUNCT
ejpam-6159	529	3	x	x	X
ejpam-6159	529	4	)	)	PUNCT
ejpam-6159	530	1	+	+	NUM
ejpam-6159	530	2	λ	λ	X
ejpam-6159	530	3	[	[	PUNCT
ejpam-6159	530	4	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	530	5	(	(	PUNCT
ejpam-6159	530	6	b1	b1	NOUN
ejpam-6159	530	7	,	,	PUNCT
ejpam-6159	530	8	x)f	x)f	X
ejpam-6159	530	9	(	(	PUNCT
ejpam-6159	530	10	b1	b1	NOUN
ejpam-6159	530	11	)	)	PUNCT
ejpam-6159	531	1	+	+	NUM
ejpam-6159	531	2	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	531	3	(	(	PUNCT
ejpam-6159	531	4	x	x	X
ejpam-6159	531	5	,	,	PUNCT
ejpam-6159	531	6	a1)f	a1)f	PROPN
ejpam-6159	531	7	(	(	PUNCT
ejpam-6159	531	8	a1	a1	PROPN
ejpam-6159	531	9	)	)	PUNCT
ejpam-6159	531	10	ς∗	ς∗	NOUN
ejpam-6159	531	11	(	(	PUNCT
ejpam-6159	531	12	b1	b1	NOUN
ejpam-6159	531	13	,	,	PUNCT
ejpam-6159	531	14	a1	a1	PROPN
ejpam-6159	531	15	)	)	PUNCT
ejpam-6159	531	16	]	]	PUNCT
ejpam-6159	532	1	−	−	PROPN
ejpam-6159	532	2	γ	γ	X
ejpam-6159	532	3	(	(	PUNCT
ejpam-6159	532	4	ϱ+	ϱ+	X
ejpam-6159	532	5	2	2	X
ejpam-6159	532	6	)	)	PUNCT
ejpam-6159	532	7	ς∗	ς∗	NOUN
ejpam-6159	532	8	(	(	PUNCT
ejpam-6159	532	9	b1	b1	NOUN
ejpam-6159	532	10	,	,	PUNCT
ejpam-6159	532	11	a1	a1	NOUN
ejpam-6159	532	12	)	)	PUNCT
ejpam-6159	532	13	{	{	PUNCT
ejpam-6159	532	14	jϱ	jϱ	NOUN
ejpam-6159	532	15	(	(	PUNCT
ejpam-6159	532	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	532	17	,	,	PUNCT
ejpam-6159	532	18	a1	a1	NOUN
ejpam-6159	532	19	)	)	PUNCT
ejpam-6159	532	20	)	)	PUNCT
ejpam-6159	533	1	−	−	PROPN
ejpam-6159	534	1	f	f	X
ejpam-6159	534	2	(	(	PUNCT
ejpam-6159	534	3	a1	a1	PROPN
ejpam-6159	534	4	)	)	PUNCT
ejpam-6159	534	5	+	+	NUM
ejpam-6159	534	6	jϱ	jϱ	ADJ
ejpam-6159	534	7	(	(	PUNCT
ejpam-6159	534	8	b1+ς∗(x	b1+ς∗(x	PROPN
ejpam-6159	534	9	,	,	PUNCT
ejpam-6159	534	10	b1	b1	NOUN
ejpam-6159	534	11	)	)	PUNCT
ejpam-6159	534	12	)	)	PUNCT
ejpam-6159	535	1	+	+	CCONJ
ejpam-6159	535	2	f	f	X
ejpam-6159	535	3	(	(	PUNCT
ejpam-6159	535	4	b1	b1	PROPN
ejpam-6159	535	5	)	)	PUNCT
ejpam-6159	535	6	}	}	PUNCT
ejpam-6159	535	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	535	8	≤	≤	NOUN
ejpam-6159	535	9	[	[	PUNCT
ejpam-6159	535	10	ςϱ+2	ςϱ+2	NUM
ejpam-6159	535	11	∗	∗	NOUN
ejpam-6159	535	12	(	(	PUNCT
ejpam-6159	535	13	x	x	NOUN
ejpam-6159	535	14	,	,	PUNCT
ejpam-6159	535	15	a1	a1	PROPN
ejpam-6159	535	16	)	)	PUNCT
ejpam-6159	535	17	|f′′	|f′′	NUM
ejpam-6159	535	18	(	(	PUNCT
ejpam-6159	535	19	a1)|+	a1)|+	ADP
ejpam-6159	535	20	ςϱ+2	ςϱ+2	NUM
ejpam-6159	535	21	∗	∗	NOUN
ejpam-6159	535	22	(	(	PUNCT
ejpam-6159	535	23	b1	b1	NOUN
ejpam-6159	535	24	,	,	PUNCT
ejpam-6159	535	25	x	x	NOUN
ejpam-6159	535	26	)	)	PUNCT
ejpam-6159	535	27	|f′′	|f′′	NUM
ejpam-6159	536	1	(	(	PUNCT
ejpam-6159	536	2	b1)|	b1)|	PROPN
ejpam-6159	536	3	ς∗	ς∗	PROPN
ejpam-6159	536	4	(	(	PUNCT
ejpam-6159	536	5	b1	b1	NOUN
ejpam-6159	536	6	,	,	PUNCT
ejpam-6159	536	7	a1	a1	PROPN
ejpam-6159	536	8	)	)	PUNCT
ejpam-6159	536	9	]	]	PUNCT
ejpam-6159	537	1	1∑n	1∑n	X
ejpam-6159	537	2	i=1	i=1	PROPN
ejpam-6159	537	3	ai	ai	VERB
ejpam-6159	538	1	n∑	n∑	PROPN
ejpam-6159	538	2	i=1	i=1	PROPN
ejpam-6159	539	1	ai	ai	INTJ
ejpam-6159	539	2	∫	∫	PROPN
ejpam-6159	539	3	1	1	NUM
ejpam-6159	539	4	0	0	NUM
ejpam-6159	539	5	t	t	PROPN
ejpam-6159	539	6	(	(	PUNCT
ejpam-6159	539	7	λ−	λ−	PROPN
ejpam-6159	539	8	tϱ	tϱ	X
ejpam-6159	539	9	)	)	PUNCT
ejpam-6159	539	10	(	(	PUNCT
ejpam-6159	539	11	1−	1−	NUM
ejpam-6159	539	12	t	t	NOUN
ejpam-6159	539	13	)	)	PUNCT
ejpam-6159	539	14	1	1	NUM
ejpam-6159	540	1	i	i	PRON
ejpam-6159	540	2	dt	dt	VERB
ejpam-6159	541	1	+	+	CCONJ
ejpam-6159	541	2	ςϱ+2	ςϱ+2	NUM
ejpam-6159	541	3	∗	∗	NOUN
ejpam-6159	541	4	(	(	PUNCT
ejpam-6159	541	5	x	x	NOUN
ejpam-6159	541	6	,	,	PUNCT
ejpam-6159	541	7	a1	a1	NOUN
ejpam-6159	541	8	)	)	PUNCT
ejpam-6159	541	9	+	+	CCONJ
ejpam-6159	541	10	ςϱ+2	ςϱ+2	NUM
ejpam-6159	541	11	∗	∗	NOUN
ejpam-6159	541	12	(	(	PUNCT
ejpam-6159	541	13	b1	b1	NOUN
ejpam-6159	541	14	,	,	PUNCT
ejpam-6159	541	15	x)∑n	x)∑n	PUNCT
ejpam-6159	542	1	i=1	i=1	PROPN
ejpam-6159	543	1	ai	ai	VERB
ejpam-6159	543	2	ς∗	ς∗	PROPN
ejpam-6159	543	3	(	(	PUNCT
ejpam-6159	543	4	b1	b1	NOUN
ejpam-6159	543	5	,	,	PUNCT
ejpam-6159	543	6	a1	a1	NOUN
ejpam-6159	543	7	)	)	PUNCT
ejpam-6159	543	8	∣∣f′′	∣∣f′′	NOUN
ejpam-6159	543	9	(	(	PUNCT
ejpam-6159	543	10	x	x	X
ejpam-6159	543	11	)	)	PUNCT
ejpam-6159	543	12	∣∣	∣∣	PROPN
ejpam-6159	544	1	n∑	n∑	PROPN
ejpam-6159	544	2	i=1	i=1	PROPN
ejpam-6159	545	1	ai	ai	INTJ
ejpam-6159	545	2	∫	∫	PROPN
ejpam-6159	545	3	1	1	NUM
ejpam-6159	545	4	0	0	NUM
ejpam-6159	545	5	(	(	PUNCT
ejpam-6159	545	6	λ−	λ−	PROPN
ejpam-6159	545	7	tϱ	tϱ	X
ejpam-6159	545	8	)	)	PUNCT
ejpam-6159	545	9	(	(	PUNCT
ejpam-6159	545	10	t	t	NOUN
ejpam-6159	545	11	)	)	PUNCT
ejpam-6159	545	12	1	1	NUM
ejpam-6159	546	1	i	i	PRON
ejpam-6159	546	2	+1	+1	PRON
ejpam-6159	546	3	dt	dt	PROPN
ejpam-6159	546	4	.	.	PUNCT
ejpam-6159	547	1	theorem	theorem	ADJ
ejpam-6159	547	2	7	7	NUM
ejpam-6159	547	3	.	.	PUNCT
ejpam-6159	548	1	suppose	suppose	VERB
ejpam-6159	548	2	f	f	X
ejpam-6159	548	3	:	:	PUNCT
ejpam-6159	548	4	x	x	PUNCT
ejpam-6159	549	1	=	=	NOUN
ejpam-6159	549	2	:	:	PUNCT
ejpam-6159	549	3	[	[	X
ejpam-6159	549	4	a1	a1	NOUN
ejpam-6159	549	5	,	,	PUNCT
ejpam-6159	549	6	a1	a1	NOUN
ejpam-6159	549	7	+	+	CCONJ
ejpam-6159	549	8	ς∗	ς∗	PROPN
ejpam-6159	549	9	(	(	PUNCT
ejpam-6159	549	10	b1	b1	NOUN
ejpam-6159	549	11	,	,	PUNCT
ejpam-6159	549	12	a1	a1	NOUN
ejpam-6159	549	13	)	)	PUNCT
ejpam-6159	549	14	]	]	PUNCT
ejpam-6159	549	15	→	→	PUNCT
ejpam-6159	549	16	ℜ	ℜ	PROPN
ejpam-6159	549	17	is	be	AUX
ejpam-6159	549	18	twice	twice	ADV
ejpam-6159	549	19	differentiable	differentiable	ADJ
ejpam-6159	549	20	function	function	NOUN
ejpam-6159	549	21	function	function	NOUN
ejpam-6159	549	22	on	on	ADP
ejpam-6159	549	23	xo	xo	PROPN
ejpam-6159	549	24	such	such	ADJ
ejpam-6159	549	25	that	that	SCONJ
ejpam-6159	549	26	f′′	f′′	NOUN
ejpam-6159	549	27	∈	∈	NOUN
ejpam-6159	549	28	l[a1	l[a1	NOUN
ejpam-6159	549	29	,	,	PUNCT
ejpam-6159	549	30	a1	a1	NOUN
ejpam-6159	549	31	+	+	CCONJ
ejpam-6159	549	32	ς∗	ς∗	PROPN
ejpam-6159	549	33	(	(	PUNCT
ejpam-6159	549	34	b1	b1	NOUN
ejpam-6159	549	35	,	,	PUNCT
ejpam-6159	549	36	a1	a1	NOUN
ejpam-6159	549	37	)	)	PUNCT
ejpam-6159	549	38	]	]	PUNCT
ejpam-6159	549	39	and	and	CCONJ
ejpam-6159	549	40	consideration	consideration	NOUN
ejpam-6159	549	41	with	with	ADP
ejpam-6159	549	42	u∗.	u∗.	PROPN
ejpam-6159	549	43	let	let	VERB
ejpam-6159	549	44	for	for	ADP
ejpam-6159	549	45	some	some	DET
ejpam-6159	549	46	q	q	NOUN
ejpam-6159	549	47	>	>	X
ejpam-6159	549	48	1	1	NUM
ejpam-6159	549	49	,	,	PUNCT
ejpam-6159	549	50	|f′′(x)|q	|f′′(x)|q	PROPN
ejpam-6159	549	51	be	be	VERB
ejpam-6159	549	52	a	a	DET
ejpam-6159	549	53	gfpp−s	gfpp−s	NOUN
ejpam-6159	549	54	function	function	NOUN
ejpam-6159	549	55	on	on	ADP
ejpam-6159	549	56	x	x	PRON
ejpam-6159	549	57	,	,	PUNCT
ejpam-6159	549	58	for	for	ADP
ejpam-6159	549	59	all	all	DET
ejpam-6159	549	60	x	x	SYM
ejpam-6159	549	61	∈	∈	PROPN
ejpam-6159	549	62	[	[	X
ejpam-6159	549	63	a1	a1	NOUN
ejpam-6159	549	64	,	,	PUNCT
ejpam-6159	549	65	a1	a1	NOUN
ejpam-6159	549	66	+	+	CCONJ
ejpam-6159	549	67	ς∗	ς∗	PROPN
ejpam-6159	549	68	(	(	PUNCT
ejpam-6159	549	69	b1	b1	NOUN
ejpam-6159	549	70	,	,	PUNCT
ejpam-6159	549	71	a1	a1	NOUN
ejpam-6159	549	72	)	)	PUNCT
ejpam-6159	549	73	]	]	PUNCT
ejpam-6159	549	74	.	.	PUNCT
ejpam-6159	550	1	then∣∣∣∣	then∣∣∣∣	PROPN
ejpam-6159	550	2	(	(	PUNCT
ejpam-6159	550	3	1−	1−	NUM
ejpam-6159	550	4	λ	λ	NOUN
ejpam-6159	550	5	)	)	PUNCT
ejpam-6159	550	6	[	[	PUNCT
ejpam-6159	550	7	ς	ς	X
ejpam-6159	550	8	ϱ	ϱ	PROPN
ejpam-6159	550	9	k	k	PROPN
ejpam-6159	550	10	∗	∗	X
ejpam-6159	550	11	(	(	PUNCT
ejpam-6159	550	12	b1	b1	NOUN
ejpam-6159	550	13	,	,	PUNCT
ejpam-6159	550	14	x)−	x)−	PROPN
ejpam-6159	550	15	ς	ς	PROPN
ejpam-6159	550	16	ϱ	ϱ	PROPN
ejpam-6159	550	17	k	k	PROPN
ejpam-6159	550	18	∗	∗	X
ejpam-6159	550	19	(	(	PUNCT
ejpam-6159	550	20	x	x	NOUN
ejpam-6159	550	21	,	,	PUNCT
ejpam-6159	550	22	a1	a1	NOUN
ejpam-6159	550	23	)	)	PUNCT
ejpam-6159	550	24	ς∗	ς∗	NOUN
ejpam-6159	550	25	(	(	PUNCT
ejpam-6159	550	26	b1	b1	NOUN
ejpam-6159	550	27	,	,	PUNCT
ejpam-6159	550	28	a1	a1	PROPN
ejpam-6159	550	29	)	)	PUNCT
ejpam-6159	550	30	]	]	PUNCT
ejpam-6159	550	31	f′	f′	PROPN
ejpam-6159	550	32	(	(	PUNCT
ejpam-6159	550	33	x	x	X
ejpam-6159	550	34	)	)	PUNCT
ejpam-6159	551	1	+	+	CCONJ
ejpam-6159	551	2	(	(	PUNCT
ejpam-6159	551	3	1	1	NUM
ejpam-6159	551	4	+	+	CCONJ
ejpam-6159	551	5	ϱ	ϱ	ADP
ejpam-6159	551	6	k	k	X
ejpam-6159	551	7	−	−	PROPN
ejpam-6159	551	8	λ	λ	PROPN
ejpam-6159	551	9	)	)	PUNCT
ejpam-6159	551	10	[	[	PUNCT
ejpam-6159	551	11	ς	ς	PROPN
ejpam-6159	551	12	ϱ	ϱ	PROPN
ejpam-6159	551	13	k	k	PROPN
ejpam-6159	551	14	∗	∗	X
ejpam-6159	551	15	(	(	PUNCT
ejpam-6159	551	16	b1	b1	NOUN
ejpam-6159	551	17	,	,	PUNCT
ejpam-6159	551	18	x	x	X
ejpam-6159	551	19	)	)	PUNCT
ejpam-6159	551	20	+	+	CCONJ
ejpam-6159	551	21	ς	ς	PROPN
ejpam-6159	551	22	ϱ	ϱ	PROPN
ejpam-6159	551	23	k	k	PROPN
ejpam-6159	551	24	∗	∗	X
ejpam-6159	551	25	(	(	PUNCT
ejpam-6159	551	26	x	x	NOUN
ejpam-6159	551	27	,	,	PUNCT
ejpam-6159	551	28	a1	a1	NOUN
ejpam-6159	551	29	)	)	PUNCT
ejpam-6159	551	30	ς∗	ς∗	NOUN
ejpam-6159	551	31	(	(	PUNCT
ejpam-6159	551	32	b1	b1	NOUN
ejpam-6159	551	33	,	,	PUNCT
ejpam-6159	551	34	a1	a1	PROPN
ejpam-6159	551	35	)	)	PUNCT
ejpam-6159	551	36	]	]	PUNCT
ejpam-6159	552	1	f	f	PROPN
ejpam-6159	552	2	(	(	PUNCT
ejpam-6159	552	3	x	x	X
ejpam-6159	552	4	)	)	PUNCT
ejpam-6159	553	1	+	+	NUM
ejpam-6159	553	2	λ	λ	X
ejpam-6159	553	3	[	[	PUNCT
ejpam-6159	553	4	ς	ς	PROPN
ejpam-6159	553	5	ϱ	ϱ	PROPN
ejpam-6159	553	6	k	k	PROPN
ejpam-6159	553	7	∗	∗	X
ejpam-6159	553	8	(	(	PUNCT
ejpam-6159	553	9	b1	b1	NOUN
ejpam-6159	553	10	,	,	PUNCT
ejpam-6159	553	11	x)f	x)f	X
ejpam-6159	553	12	(	(	PUNCT
ejpam-6159	553	13	b1	b1	NOUN
ejpam-6159	553	14	)	)	PUNCT
ejpam-6159	553	15	+	+	CCONJ
ejpam-6159	553	16	ς	ς	PROPN
ejpam-6159	553	17	ϱ	ϱ	PROPN
ejpam-6159	553	18	k	k	PROPN
ejpam-6159	553	19	∗	∗	X
ejpam-6159	553	20	(	(	PUNCT
ejpam-6159	553	21	x	x	X
ejpam-6159	553	22	,	,	PUNCT
ejpam-6159	553	23	a1)f	a1)f	PROPN
ejpam-6159	553	24	(	(	PUNCT
ejpam-6159	553	25	a1	a1	PROPN
ejpam-6159	553	26	)	)	PUNCT
ejpam-6159	553	27	ς∗	ς∗	NOUN
ejpam-6159	553	28	(	(	PUNCT
ejpam-6159	553	29	b1	b1	NOUN
ejpam-6159	553	30	,	,	PUNCT
ejpam-6159	553	31	a1	a1	PROPN
ejpam-6159	553	32	)	)	PUNCT
ejpam-6159	553	33	]	]	PUNCT
ejpam-6159	554	1	−	−	PROPN
ejpam-6159	554	2	γk	γk	X
ejpam-6159	554	3	(	(	PUNCT
ejpam-6159	554	4	ϱ+	ϱ+	NOUN
ejpam-6159	554	5	2k	2k	NUM
ejpam-6159	554	6	)	)	PUNCT
ejpam-6159	554	7	ς∗	ς∗	PROPN
ejpam-6159	554	8	(	(	PUNCT
ejpam-6159	554	9	b1	b1	NOUN
ejpam-6159	554	10	,	,	PUNCT
ejpam-6159	554	11	a1	a1	NOUN
ejpam-6159	554	12	)	)	PUNCT
ejpam-6159	554	13	{	{	PUNCT
ejpam-6159	554	14	jϱ,k	jϱ,k	X
ejpam-6159	554	15	(	(	PUNCT
ejpam-6159	554	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	554	17	,	,	PUNCT
ejpam-6159	554	18	a1	a1	NOUN
ejpam-6159	554	19	)	)	PUNCT
ejpam-6159	554	20	)	)	PUNCT
ejpam-6159	555	1	−	−	PROPN
ejpam-6159	555	2	f	f	X
ejpam-6159	555	3	(	(	PUNCT
ejpam-6159	555	4	a1	a1	PROPN
ejpam-6159	555	5	)	)	PUNCT
ejpam-6159	555	6	+	+	NUM
ejpam-6159	555	7	jϱ,k	jϱ,k	X
ejpam-6159	555	8	(	(	PUNCT
ejpam-6159	555	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	555	10	,	,	PUNCT
ejpam-6159	555	11	b1	b1	NOUN
ejpam-6159	555	12	)	)	PUNCT
ejpam-6159	555	13	)	)	PUNCT
ejpam-6159	556	1	+	+	CCONJ
ejpam-6159	556	2	f	f	X
ejpam-6159	556	3	(	(	PUNCT
ejpam-6159	556	4	b1	b1	PROPN
ejpam-6159	556	5	)	)	PUNCT
ejpam-6159	556	6	}	}	PUNCT
ejpam-6159	556	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	556	8	≤	≤	NUM
ejpam-6159	556	9	m	m	VERB
ejpam-6159	556	10	1−	1−	NUM
ejpam-6159	556	11	1	1	NUM
ejpam-6159	556	12	q	q	NOUN
ejpam-6159	556	13	(	(	PUNCT
ejpam-6159	556	14	ϱ,k	ϱ,k	PROPN
ejpam-6159	556	15	,	,	PUNCT
ejpam-6159	556	16	λ	λ	NOUN
ejpam-6159	556	17	)	)	PUNCT
ejpam-6159	556	18	×	×	NOUN
ejpam-6159	556	19	[	[	PUNCT
ejpam-6159	556	20	ς	ς	PROPN
ejpam-6159	556	21	ϱ	ϱ	ADP
ejpam-6159	556	22	k	k	PROPN
ejpam-6159	556	23	+2	+2	PROPN
ejpam-6159	556	24	∗	∗	NOUN
ejpam-6159	556	25	(	(	PUNCT
ejpam-6159	556	26	x	x	NOUN
ejpam-6159	556	27	,	,	PUNCT
ejpam-6159	556	28	a1	a1	NOUN
ejpam-6159	556	29	)	)	PUNCT
ejpam-6159	556	30	ς∗	ς∗	NOUN
ejpam-6159	556	31	(	(	PUNCT
ejpam-6159	556	32	b1	b1	NOUN
ejpam-6159	556	33	,	,	PUNCT
ejpam-6159	556	34	a1	a1	PROPN
ejpam-6159	556	35	)	)	PUNCT
ejpam-6159	556	36	{	{	PUNCT
ejpam-6159	556	37	∫	∫	PROPN
ejpam-6159	556	38	1	1	NUM
ejpam-6159	556	39	0	0	NUM
ejpam-6159	556	40	t	t	PROPN
ejpam-6159	556	41	(	(	PUNCT
ejpam-6159	556	42	λ−	λ−	PROPN
ejpam-6159	556	43	t	t	PROPN
ejpam-6159	556	44	ϱ	ϱ	PROPN
ejpam-6159	556	45	k	k	PROPN
ejpam-6159	556	46	)	)	PUNCT
ejpam-6159	556	47	{	{	PUNCT
ejpam-6159	557	1	∑n	∑n	PROPN
ejpam-6159	557	2	i=1	i=1	PROPN
ejpam-6159	557	3	ai	ai	VERB
ejpam-6159	557	4	(	(	PUNCT
ejpam-6159	557	5	1−	1−	NUM
ejpam-6159	557	6	st	st	NOUN
ejpam-6159	557	7	)	)	PUNCT
ejpam-6159	557	8	1	1	NUM
ejpam-6159	557	9	i∑n	i∑n	PROPN
ejpam-6159	557	10	i=1	i=1	PROPN
ejpam-6159	557	11	ai	ai	VERB
ejpam-6159	557	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	557	13	(	(	PUNCT
ejpam-6159	557	14	a1	a1	PROPN
ejpam-6159	557	15	)	)	PUNCT
ejpam-6159	557	16	∣∣q	∣∣q	NUM
ejpam-6159	558	1	+	+	NUM
ejpam-6159	558	2	∑n	∑n	PROPN
ejpam-6159	558	3	i=1	i=1	PROPN
ejpam-6159	558	4	ai	ai	VERB
ejpam-6159	558	5	(	(	PUNCT
ejpam-6159	558	6	1−	1−	NUM
ejpam-6159	558	7	s	s	X
ejpam-6159	558	8	(	(	PUNCT
ejpam-6159	558	9	1−	1−	NUM
ejpam-6159	558	10	t	t	NOUN
ejpam-6159	558	11	)	)	PUNCT
ejpam-6159	558	12	)	)	PUNCT
ejpam-6159	558	13	1	1	NUM
ejpam-6159	558	14	i∑n	i∑n	PROPN
ejpam-6159	558	15	i=1	i=1	PROPN
ejpam-6159	558	16	ai	ai	VERB
ejpam-6159	558	17	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	558	18	(	(	PUNCT
ejpam-6159	558	19	x	x	NOUN
ejpam-6159	558	20	)	)	PUNCT
ejpam-6159	558	21	∣∣q	∣∣q	NUM
ejpam-6159	558	22	}	}	PUNCT
ejpam-6159	558	23	dt	dt	PROPN
ejpam-6159	558	24	}	}	PUNCT
ejpam-6159	558	25	1	1	NUM
ejpam-6159	558	26	q	q	NOUN
ejpam-6159	559	1	+	+	NUM
ejpam-6159	559	2	ς	ς	PROPN
ejpam-6159	559	3	ϱ	ϱ	ADP
ejpam-6159	559	4	k	k	PROPN
ejpam-6159	559	5	+2	+2	PROPN
ejpam-6159	559	6	∗	∗	NOUN
ejpam-6159	559	7	(	(	PUNCT
ejpam-6159	559	8	b1	b1	NOUN
ejpam-6159	559	9	,	,	PUNCT
ejpam-6159	559	10	x	x	NOUN
ejpam-6159	559	11	)	)	PUNCT
ejpam-6159	559	12	ς∗	ς∗	PROPN
ejpam-6159	559	13	(	(	PUNCT
ejpam-6159	559	14	b1	b1	NOUN
ejpam-6159	559	15	,	,	PUNCT
ejpam-6159	559	16	a1	a1	PROPN
ejpam-6159	559	17	)	)	PUNCT
ejpam-6159	559	18	{	{	PUNCT
ejpam-6159	559	19	∫	∫	PROPN
ejpam-6159	559	20	1	1	NUM
ejpam-6159	559	21	0	0	NUM
ejpam-6159	559	22	t	t	PROPN
ejpam-6159	559	23	(	(	PUNCT
ejpam-6159	559	24	λ−	λ−	PROPN
ejpam-6159	559	25	t	t	PROPN
ejpam-6159	559	26	ϱ	ϱ	PROPN
ejpam-6159	559	27	k	k	PROPN
ejpam-6159	559	28	)	)	PUNCT
ejpam-6159	559	29	{	{	PUNCT
ejpam-6159	560	1	∑n	∑n	PROPN
ejpam-6159	560	2	i=1	i=1	PROPN
ejpam-6159	560	3	ai	ai	VERB
ejpam-6159	560	4	(	(	PUNCT
ejpam-6159	560	5	1−	1−	NUM
ejpam-6159	560	6	st	st	NOUN
ejpam-6159	560	7	)	)	PUNCT
ejpam-6159	560	8	1	1	NUM
ejpam-6159	560	9	i∑n	i∑n	PROPN
ejpam-6159	560	10	i=1	i=1	PROPN
ejpam-6159	560	11	ai	ai	VERB
ejpam-6159	560	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	560	13	(	(	PUNCT
ejpam-6159	560	14	b1	b1	PROPN
ejpam-6159	560	15	)	)	PUNCT
ejpam-6159	560	16	∣∣q	∣∣q	NUM
ejpam-6159	561	1	+	+	NUM
ejpam-6159	561	2	∑n	∑n	PROPN
ejpam-6159	561	3	i=1	i=1	PROPN
ejpam-6159	561	4	ai	ai	VERB
ejpam-6159	561	5	(	(	PUNCT
ejpam-6159	561	6	1−	1−	NUM
ejpam-6159	561	7	s	s	X
ejpam-6159	561	8	(	(	PUNCT
ejpam-6159	561	9	1−	1−	NUM
ejpam-6159	561	10	t	t	NOUN
ejpam-6159	561	11	)	)	PUNCT
ejpam-6159	561	12	)	)	PUNCT
ejpam-6159	561	13	1	1	NUM
ejpam-6159	561	14	i∑n	i∑n	PROPN
ejpam-6159	561	15	i=1	i=1	PROPN
ejpam-6159	561	16	ai	ai	VERB
ejpam-6159	561	17	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	561	18	(	(	PUNCT
ejpam-6159	561	19	x	x	NOUN
ejpam-6159	561	20	)	)	PUNCT
ejpam-6159	561	21	∣∣q	∣∣q	NUM
ejpam-6159	561	22	}	}	PUNCT
ejpam-6159	561	23	dt	dt	PROPN
ejpam-6159	561	24	}	}	PUNCT
ejpam-6159	561	25	1	1	NUM
ejpam-6159	561	26	q	q	NOUN
ejpam-6159	561	27	]	]	PUNCT
ejpam-6159	561	28	,	,	PUNCT
ejpam-6159	561	29	where	where	SCONJ
ejpam-6159	561	30	m	m	VERB
ejpam-6159	561	31	(	(	PUNCT
ejpam-6159	561	32	ϱ,k	ϱ,k	PROPN
ejpam-6159	561	33	,	,	PUNCT
ejpam-6159	561	34	λ	λ	NOUN
ejpam-6159	561	35	)	)	PUNCT
ejpam-6159	561	36	=	=	SYM
ejpam-6159	562	1	∫	∫	PROPN
ejpam-6159	562	2	1	1	NUM
ejpam-6159	562	3	0	0	NUM
ejpam-6159	563	1	[	[	X
ejpam-6159	563	2	t	t	X
ejpam-6159	563	3	(	(	PUNCT
ejpam-6159	563	4	λ−	λ−	PROPN
ejpam-6159	563	5	t	t	PROPN
ejpam-6159	563	6	ϱ	ϱ	PROPN
ejpam-6159	563	7	k	k	PROPN
ejpam-6159	563	8	)	)	PUNCT
ejpam-6159	563	9	]	]	X
ejpam-6159	563	10	qdt	qdt	X
ejpam-6159	563	11	j.	j.	PROPN
ejpam-6159	563	12	nasir	nasir	PROPN
ejpam-6159	563	13	et	et	PROPN
ejpam-6159	563	14	al	al	PROPN
ejpam-6159	563	15	.	.	PUNCT
ejpam-6159	563	16	/	/	SYM
ejpam-6159	563	17	eur	eur	PROPN
ejpam-6159	563	18	.	.	PUNCT
ejpam-6159	564	1	j.	j.	PROPN
ejpam-6159	564	2	pure	pure	PROPN
ejpam-6159	564	3	appl	appl	PROPN
ejpam-6159	564	4	.	.	PROPN
ejpam-6159	564	5	math	math	PROPN
ejpam-6159	564	6	,	,	PUNCT
ejpam-6159	564	7	18	18	NUM
ejpam-6159	564	8	(	(	PUNCT
ejpam-6159	564	9	3	3	NUM
ejpam-6159	564	10	)	)	PUNCT
ejpam-6159	564	11	(	(	PUNCT
ejpam-6159	564	12	2025	2025	NUM
ejpam-6159	564	13	)	)	PUNCT
ejpam-6159	564	14	,	,	PUNCT
ejpam-6159	564	15	6159	6159	NUM
ejpam-6159	564	16	18	18	NUM
ejpam-6159	564	17	of	of	ADP
ejpam-6159	564	18	26	26	NUM
ejpam-6159	564	19	=	=	SYM
ejpam-6159	564	20	k	k	PROPN
ejpam-6159	564	21	λ	λ	PROPN
ejpam-6159	564	22	k(1+q)+ϱq	k(1+q)+ϱq	PROPN
ejpam-6159	564	23	q	q	PROPN
ejpam-6159	564	24	ϱ	ϱ	PROPN
ejpam-6159	564	25	[	[	PUNCT
ejpam-6159	564	26	γ	γ	X
ejpam-6159	564	27	(	(	PUNCT
ejpam-6159	564	28	1	1	NUM
ejpam-6159	564	29	+	+	CCONJ
ejpam-6159	564	30	q	q	X
ejpam-6159	564	31	)	)	PUNCT
ejpam-6159	564	32	γ	γ	NOUN
ejpam-6159	564	33	(	(	PUNCT
ejpam-6159	564	34	k	k	X
ejpam-6159	564	35	(	(	PUNCT
ejpam-6159	564	36	1	1	NUM
ejpam-6159	564	37	+	+	CCONJ
ejpam-6159	564	38	q	q	X
ejpam-6159	564	39	)	)	PUNCT
ejpam-6159	565	1	+	+	CCONJ
ejpam-6159	565	2	ϱ	ϱ	ADP
ejpam-6159	565	3	ϱ	ϱ	NOUN
ejpam-6159	565	4	)	)	PUNCT
ejpam-6159	565	5	2f1	2f1	PROPN
ejpam-6159	565	6	(	(	PUNCT
ejpam-6159	565	7	1	1	NUM
ejpam-6159	565	8	,	,	PUNCT
ejpam-6159	565	9	1	1	NUM
ejpam-6159	565	10	+	+	CCONJ
ejpam-6159	565	11	q	q	ADJ
ejpam-6159	565	12	,	,	PUNCT
ejpam-6159	565	13	2	2	NUM
ejpam-6159	565	14	+	+	CCONJ
ejpam-6159	565	15	q	q	NOUN
ejpam-6159	566	1	+	+	CCONJ
ejpam-6159	566	2	k	k	X
ejpam-6159	566	3	(	(	PUNCT
ejpam-6159	566	4	1	1	NUM
ejpam-6159	566	5	+	+	CCONJ
ejpam-6159	566	6	q	q	X
ejpam-6159	566	7	)	)	PUNCT
ejpam-6159	566	8	ϱ	ϱ	NOUN
ejpam-6159	566	9	,	,	PUNCT
ejpam-6159	566	10	1	1	NUM
ejpam-6159	566	11	)	)	PUNCT
ejpam-6159	566	12	+	+	CCONJ
ejpam-6159	566	13	β	β	X
ejpam-6159	566	14	(	(	PUNCT
ejpam-6159	566	15	1	1	NUM
ejpam-6159	566	16	+	+	NUM
ejpam-6159	566	17	q,−k	q,−k	NOUN
ejpam-6159	566	18	(	(	PUNCT
ejpam-6159	566	19	1	1	NUM
ejpam-6159	566	20	+	+	CCONJ
ejpam-6159	566	21	iq	iq	NOUN
ejpam-6159	566	22	)	)	PUNCT
ejpam-6159	567	1	+	+	CCONJ
ejpam-6159	567	2	ϱq	ϱq	ADP
ejpam-6159	567	3	qϱ	qϱ	NOUN
ejpam-6159	567	4	)	)	PUNCT
ejpam-6159	567	5	−	−	PROPN
ejpam-6159	568	1	β	β	X
ejpam-6159	568	2	(	(	PUNCT
ejpam-6159	568	3	λ	λ	PROPN
ejpam-6159	568	4	,	,	PUNCT
ejpam-6159	568	5	1	1	NUM
ejpam-6159	568	6	+	+	NUM
ejpam-6159	568	7	iq,−k	iq,−k	NOUN
ejpam-6159	568	8	(	(	PUNCT
ejpam-6159	568	9	1	1	NUM
ejpam-6159	568	10	+	+	CCONJ
ejpam-6159	568	11	iq	iq	NOUN
ejpam-6159	568	12	)	)	PUNCT
ejpam-6159	569	1	+	+	CCONJ
ejpam-6159	569	2	ϱq	ϱq	ADP
ejpam-6159	569	3	qϱ	qϱ	NOUN
ejpam-6159	569	4	)	)	PUNCT
ejpam-6159	569	5	]	]	PUNCT
ejpam-6159	569	6	.	.	PUNCT
ejpam-6159	570	1	(	(	PUNCT
ejpam-6159	570	2	39	39	NUM
ejpam-6159	570	3	)	)	PUNCT
ejpam-6159	570	4	proof	proof	NOUN
ejpam-6159	570	5	.	.	PUNCT
ejpam-6159	571	1	from	from	ADP
ejpam-6159	571	2	lemma	lemma	PROPN
ejpam-6159	571	3	2	2	NUM
ejpam-6159	571	4	and	and	CCONJ
ejpam-6159	571	5	a	a	DET
ejpam-6159	571	6	property	property	NOUN
ejpam-6159	571	7	of	of	ADP
ejpam-6159	571	8	the	the	DET
ejpam-6159	571	9	gfpp−s	gfpp−s	PROPN
ejpam-6159	571	10	function	function	NOUN
ejpam-6159	571	11	|f′′|q	|f′′|q	PROPN
ejpam-6159	571	12	,	,	PUNCT
ejpam-6159	571	13	and	and	CCONJ
ejpam-6159	571	14	the	the	DET
ejpam-6159	571	15	power	power	NOUN
ejpam-6159	571	16	meaniinequality	meaniinequality	NOUN
ejpam-6159	571	17	,	,	PUNCT
ejpam-6159	571	18	one	one	PRON
ejpam-6159	571	19	has	have	VERB
ejpam-6159	571	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	571	21	(	(	PUNCT
ejpam-6159	571	22	1−	1−	NUM
ejpam-6159	571	23	λ	λ	NOUN
ejpam-6159	571	24	)	)	PUNCT
ejpam-6159	571	25	[	[	PUNCT
ejpam-6159	571	26	ς	ς	X
ejpam-6159	571	27	ϱ	ϱ	PROPN
ejpam-6159	571	28	k	k	PROPN
ejpam-6159	571	29	∗	∗	X
ejpam-6159	571	30	(	(	PUNCT
ejpam-6159	571	31	b1	b1	NOUN
ejpam-6159	571	32	,	,	PUNCT
ejpam-6159	571	33	x)−	x)−	PROPN
ejpam-6159	571	34	ς	ς	PROPN
ejpam-6159	571	35	ϱ	ϱ	PROPN
ejpam-6159	571	36	k	k	PROPN
ejpam-6159	571	37	∗	∗	X
ejpam-6159	571	38	(	(	PUNCT
ejpam-6159	571	39	x	x	NOUN
ejpam-6159	571	40	,	,	PUNCT
ejpam-6159	571	41	a1	a1	NOUN
ejpam-6159	571	42	)	)	PUNCT
ejpam-6159	571	43	ς∗	ς∗	NOUN
ejpam-6159	571	44	(	(	PUNCT
ejpam-6159	571	45	b1	b1	NOUN
ejpam-6159	571	46	,	,	PUNCT
ejpam-6159	571	47	a1	a1	PROPN
ejpam-6159	571	48	)	)	PUNCT
ejpam-6159	571	49	]	]	PUNCT
ejpam-6159	571	50	f′	f′	PROPN
ejpam-6159	571	51	(	(	PUNCT
ejpam-6159	571	52	x	x	X
ejpam-6159	571	53	)	)	PUNCT
ejpam-6159	572	1	+	+	CCONJ
ejpam-6159	572	2	(	(	PUNCT
ejpam-6159	572	3	1	1	NUM
ejpam-6159	572	4	+	+	CCONJ
ejpam-6159	572	5	ϱ	ϱ	ADP
ejpam-6159	572	6	k	k	X
ejpam-6159	572	7	−	−	PROPN
ejpam-6159	572	8	λ	λ	PROPN
ejpam-6159	572	9	)	)	PUNCT
ejpam-6159	572	10	[	[	PUNCT
ejpam-6159	572	11	ς	ς	PROPN
ejpam-6159	572	12	ϱ	ϱ	PROPN
ejpam-6159	572	13	k	k	PROPN
ejpam-6159	572	14	∗	∗	X
ejpam-6159	572	15	(	(	PUNCT
ejpam-6159	572	16	b1	b1	NOUN
ejpam-6159	572	17	,	,	PUNCT
ejpam-6159	572	18	x	x	X
ejpam-6159	572	19	)	)	PUNCT
ejpam-6159	572	20	+	+	CCONJ
ejpam-6159	572	21	ς	ς	PROPN
ejpam-6159	572	22	ϱ	ϱ	PROPN
ejpam-6159	572	23	k	k	PROPN
ejpam-6159	572	24	∗	∗	X
ejpam-6159	572	25	(	(	PUNCT
ejpam-6159	572	26	x	x	NOUN
ejpam-6159	572	27	,	,	PUNCT
ejpam-6159	572	28	a1	a1	NOUN
ejpam-6159	572	29	)	)	PUNCT
ejpam-6159	572	30	ς∗	ς∗	NOUN
ejpam-6159	572	31	(	(	PUNCT
ejpam-6159	572	32	b1	b1	NOUN
ejpam-6159	572	33	,	,	PUNCT
ejpam-6159	572	34	a1	a1	PROPN
ejpam-6159	572	35	)	)	PUNCT
ejpam-6159	572	36	]	]	PUNCT
ejpam-6159	573	1	f	f	PROPN
ejpam-6159	573	2	(	(	PUNCT
ejpam-6159	573	3	x	x	X
ejpam-6159	573	4	)	)	PUNCT
ejpam-6159	574	1	+	+	NUM
ejpam-6159	574	2	λ	λ	X
ejpam-6159	574	3	[	[	PUNCT
ejpam-6159	574	4	ς	ς	PROPN
ejpam-6159	574	5	ϱ	ϱ	PROPN
ejpam-6159	574	6	k	k	PROPN
ejpam-6159	574	7	∗	∗	X
ejpam-6159	574	8	(	(	PUNCT
ejpam-6159	574	9	b1	b1	NOUN
ejpam-6159	574	10	,	,	PUNCT
ejpam-6159	574	11	x)f	x)f	X
ejpam-6159	574	12	(	(	PUNCT
ejpam-6159	574	13	b1	b1	NOUN
ejpam-6159	574	14	)	)	PUNCT
ejpam-6159	574	15	+	+	CCONJ
ejpam-6159	574	16	ς	ς	PROPN
ejpam-6159	574	17	ϱ	ϱ	PROPN
ejpam-6159	574	18	k	k	PROPN
ejpam-6159	574	19	∗	∗	X
ejpam-6159	574	20	(	(	PUNCT
ejpam-6159	574	21	x	x	X
ejpam-6159	574	22	,	,	PUNCT
ejpam-6159	574	23	a1)f	a1)f	PROPN
ejpam-6159	574	24	(	(	PUNCT
ejpam-6159	574	25	a1	a1	PROPN
ejpam-6159	574	26	)	)	PUNCT
ejpam-6159	574	27	ς∗	ς∗	NOUN
ejpam-6159	574	28	(	(	PUNCT
ejpam-6159	574	29	b1	b1	NOUN
ejpam-6159	574	30	,	,	PUNCT
ejpam-6159	574	31	a1	a1	PROPN
ejpam-6159	574	32	)	)	PUNCT
ejpam-6159	574	33	]	]	PUNCT
ejpam-6159	575	1	−	−	PROPN
ejpam-6159	575	2	γk	γk	X
ejpam-6159	575	3	(	(	PUNCT
ejpam-6159	575	4	ϱ+	ϱ+	NOUN
ejpam-6159	575	5	2k	2k	NUM
ejpam-6159	575	6	)	)	PUNCT
ejpam-6159	575	7	ς∗	ς∗	PROPN
ejpam-6159	575	8	(	(	PUNCT
ejpam-6159	575	9	b1	b1	NOUN
ejpam-6159	575	10	,	,	PUNCT
ejpam-6159	575	11	a1	a1	NOUN
ejpam-6159	575	12	)	)	PUNCT
ejpam-6159	575	13	{	{	PUNCT
ejpam-6159	575	14	jϱ,k	jϱ,k	X
ejpam-6159	575	15	(	(	PUNCT
ejpam-6159	575	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	575	17	,	,	PUNCT
ejpam-6159	575	18	a1	a1	NOUN
ejpam-6159	575	19	)	)	PUNCT
ejpam-6159	575	20	)	)	PUNCT
ejpam-6159	576	1	−	−	PROPN
ejpam-6159	576	2	f	f	X
ejpam-6159	576	3	(	(	PUNCT
ejpam-6159	576	4	a1	a1	PROPN
ejpam-6159	576	5	)	)	PUNCT
ejpam-6159	576	6	+	+	NUM
ejpam-6159	576	7	jϱ,k	jϱ,k	X
ejpam-6159	576	8	(	(	PUNCT
ejpam-6159	576	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	576	10	,	,	PUNCT
ejpam-6159	576	11	b1	b1	NOUN
ejpam-6159	576	12	)	)	PUNCT
ejpam-6159	576	13	)	)	PUNCT
ejpam-6159	577	1	+	+	CCONJ
ejpam-6159	577	2	f	f	X
ejpam-6159	577	3	(	(	PUNCT
ejpam-6159	577	4	b1	b1	PROPN
ejpam-6159	577	5	)	)	PUNCT
ejpam-6159	577	6	}	}	PUNCT
ejpam-6159	577	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	577	8	≤	≤	NUM
ejpam-6159	577	9	ς	ς	PROPN
ejpam-6159	577	10	ϱ	ϱ	PROPN
ejpam-6159	577	11	k	k	PROPN
ejpam-6159	577	12	+2	+2	PROPN
ejpam-6159	577	13	∗	∗	NOUN
ejpam-6159	577	14	(	(	PUNCT
ejpam-6159	577	15	x	x	NOUN
ejpam-6159	577	16	,	,	PUNCT
ejpam-6159	577	17	a1	a1	NOUN
ejpam-6159	577	18	)	)	PUNCT
ejpam-6159	577	19	ς∗	ς∗	NOUN
ejpam-6159	577	20	(	(	PUNCT
ejpam-6159	577	21	b1	b1	NOUN
ejpam-6159	577	22	,	,	PUNCT
ejpam-6159	577	23	a1	a1	PROPN
ejpam-6159	577	24	)	)	PUNCT
ejpam-6159	577	25	∫	∫	NOUN
ejpam-6159	577	26	1	1	NUM
ejpam-6159	577	27	0	0	NUM
ejpam-6159	577	28	|t	|t	PROPN
ejpam-6159	578	1	(	(	PUNCT
ejpam-6159	578	2	λ−	λ−	PROPN
ejpam-6159	578	3	t	t	PROPN
ejpam-6159	578	4	ϱ	ϱ	PROPN
ejpam-6159	578	5	k	k	PROPN
ejpam-6159	578	6	)	)	PUNCT
ejpam-6159	578	7	||f′′	||f′′	PROPN
ejpam-6159	578	8	(	(	PUNCT
ejpam-6159	578	9	a1	a1	NOUN
ejpam-6159	578	10	+	+	CCONJ
ejpam-6159	578	11	tς∗	tς∗	X
ejpam-6159	578	12	(	(	PUNCT
ejpam-6159	578	13	x	x	NOUN
ejpam-6159	578	14	,	,	PUNCT
ejpam-6159	578	15	a1	a1	NOUN
ejpam-6159	578	16	)	)	PUNCT
ejpam-6159	578	17	)	)	PUNCT
ejpam-6159	579	1	|dt	|dt	PROPN
ejpam-6159	580	1	+	+	X
ejpam-6159	580	2	ς	ς	PROPN
ejpam-6159	580	3	ϱ	ϱ	ADP
ejpam-6159	580	4	k	k	PROPN
ejpam-6159	580	5	+2	+2	PROPN
ejpam-6159	580	6	∗	∗	NOUN
ejpam-6159	580	7	(	(	PUNCT
ejpam-6159	580	8	b1	b1	NOUN
ejpam-6159	580	9	,	,	PUNCT
ejpam-6159	580	10	x	x	NOUN
ejpam-6159	580	11	)	)	PUNCT
ejpam-6159	580	12	ς∗	ς∗	PROPN
ejpam-6159	580	13	(	(	PUNCT
ejpam-6159	580	14	b1	b1	NOUN
ejpam-6159	580	15	,	,	PUNCT
ejpam-6159	580	16	a1	a1	PROPN
ejpam-6159	580	17	)	)	PUNCT
ejpam-6159	580	18	∫	∫	NOUN
ejpam-6159	580	19	1	1	NUM
ejpam-6159	580	20	0	0	NUM
ejpam-6159	580	21	|t	|t	PROPN
ejpam-6159	580	22	(	(	PUNCT
ejpam-6159	580	23	λ−	λ−	PROPN
ejpam-6159	580	24	t	t	PROPN
ejpam-6159	580	25	ϱ	ϱ	PROPN
ejpam-6159	580	26	k	k	PROPN
ejpam-6159	580	27	)	)	PUNCT
ejpam-6159	580	28	||f′′	||f′′	PROPN
ejpam-6159	580	29	(	(	PUNCT
ejpam-6159	580	30	b1	b1	NOUN
ejpam-6159	580	31	+	+	CCONJ
ejpam-6159	580	32	tς∗	tς∗	X
ejpam-6159	580	33	(	(	PUNCT
ejpam-6159	580	34	x	x	NOUN
ejpam-6159	580	35	,	,	PUNCT
ejpam-6159	580	36	b1	b1	NOUN
ejpam-6159	580	37	)	)	PUNCT
ejpam-6159	580	38	)	)	PUNCT
ejpam-6159	580	39	|dt	|dt	PRON
ejpam-6159	580	40	≤	≤	NOUN
ejpam-6159	580	41	(	(	PUNCT
ejpam-6159	580	42	∫	∫	PROPN
ejpam-6159	580	43	1	1	NUM
ejpam-6159	580	44	0	0	NUM
ejpam-6159	580	45	|tq	|tq	PROPN
ejpam-6159	580	46	(	(	PUNCT
ejpam-6159	580	47	λ−	λ−	PROPN
ejpam-6159	580	48	t	t	X
ejpam-6159	580	49	ϱ	ϱ	PROPN
ejpam-6159	580	50	k	k	PROPN
ejpam-6159	580	51	)	)	PUNCT
ejpam-6159	580	52	q	q	PROPN
ejpam-6159	580	53	dt	dt	NOUN
ejpam-6159	580	54	)	)	PUNCT
ejpam-6159	580	55	1	1	NUM
ejpam-6159	580	56	q	q	NOUN
ejpam-6159	580	57	×	×	NOUN
ejpam-6159	580	58	[	[	PUNCT
ejpam-6159	580	59	ς	ς	PROPN
ejpam-6159	580	60	ϱ	ϱ	ADP
ejpam-6159	580	61	k	k	PROPN
ejpam-6159	580	62	+2	+2	PROPN
ejpam-6159	580	63	∗	∗	NOUN
ejpam-6159	580	64	(	(	PUNCT
ejpam-6159	580	65	x	x	NOUN
ejpam-6159	580	66	,	,	PUNCT
ejpam-6159	580	67	a1	a1	NOUN
ejpam-6159	580	68	)	)	PUNCT
ejpam-6159	580	69	ς∗	ς∗	NOUN
ejpam-6159	580	70	(	(	PUNCT
ejpam-6159	580	71	b1	b1	NOUN
ejpam-6159	580	72	,	,	PUNCT
ejpam-6159	580	73	a1	a1	PROPN
ejpam-6159	580	74	)	)	PUNCT
ejpam-6159	580	75	∫	∫	NOUN
ejpam-6159	581	1	1	1	NUM
ejpam-6159	581	2	0	0	NUM
ejpam-6159	581	3	t	t	PROPN
ejpam-6159	581	4	(	(	PUNCT
ejpam-6159	581	5	λ−	λ−	PROPN
ejpam-6159	581	6	t	t	PROPN
ejpam-6159	581	7	ϱ	ϱ	PROPN
ejpam-6159	581	8	k	k	PROPN
ejpam-6159	581	9	)	)	PUNCT
ejpam-6159	581	10	×	×	NOUN
ejpam-6159	582	1	[	[	X
ejpam-6159	582	2	∑n	∑n	PROPN
ejpam-6159	582	3	i=1	i=1	PROPN
ejpam-6159	582	4	ai	ai	VERB
ejpam-6159	582	5	(	(	PUNCT
ejpam-6159	582	6	1−	1−	NUM
ejpam-6159	582	7	st	st	NOUN
ejpam-6159	582	8	)	)	PUNCT
ejpam-6159	582	9	1	1	NUM
ejpam-6159	582	10	i∑n	i∑n	PROPN
ejpam-6159	582	11	i=1	i=1	PROPN
ejpam-6159	582	12	ai	ai	VERB
ejpam-6159	582	13	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	582	14	(	(	PUNCT
ejpam-6159	582	15	a1	a1	PROPN
ejpam-6159	582	16	)	)	PUNCT
ejpam-6159	582	17	∣∣q	∣∣q	NUM
ejpam-6159	583	1	+	+	NUM
ejpam-6159	583	2	∑n	∑n	PROPN
ejpam-6159	583	3	i=1	i=1	PROPN
ejpam-6159	583	4	ai	ai	VERB
ejpam-6159	583	5	(	(	PUNCT
ejpam-6159	583	6	1−	1−	NUM
ejpam-6159	583	7	s	s	X
ejpam-6159	583	8	(	(	PUNCT
ejpam-6159	583	9	1−	1−	NUM
ejpam-6159	583	10	t	t	NOUN
ejpam-6159	583	11	)	)	PUNCT
ejpam-6159	583	12	)	)	PUNCT
ejpam-6159	583	13	1	1	NUM
ejpam-6159	583	14	i∑n	i∑n	PROPN
ejpam-6159	583	15	i=1	i=1	PROPN
ejpam-6159	583	16	ai	ai	VERB
ejpam-6159	583	17	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	583	18	(	(	PUNCT
ejpam-6159	583	19	x	x	NOUN
ejpam-6159	583	20	)	)	PUNCT
ejpam-6159	583	21	∣∣q	∣∣q	NUM
ejpam-6159	583	22	dt	dt	X
ejpam-6159	583	23	]	]	X
ejpam-6159	583	24	1	1	NUM
ejpam-6159	583	25	q	q	NOUN
ejpam-6159	584	1	+	+	NUM
ejpam-6159	584	2	ς	ς	PROPN
ejpam-6159	584	3	ϱ	ϱ	ADP
ejpam-6159	584	4	k	k	PROPN
ejpam-6159	584	5	+2	+2	PROPN
ejpam-6159	584	6	∗	∗	NOUN
ejpam-6159	584	7	(	(	PUNCT
ejpam-6159	584	8	b1	b1	NOUN
ejpam-6159	584	9	,	,	PUNCT
ejpam-6159	584	10	x	x	NOUN
ejpam-6159	584	11	)	)	PUNCT
ejpam-6159	584	12	ς∗	ς∗	PROPN
ejpam-6159	584	13	(	(	PUNCT
ejpam-6159	584	14	b1	b1	NOUN
ejpam-6159	584	15	,	,	PUNCT
ejpam-6159	584	16	a1	a1	PROPN
ejpam-6159	584	17	)	)	PUNCT
ejpam-6159	584	18	∫	∫	NOUN
ejpam-6159	584	19	1	1	NUM
ejpam-6159	584	20	0	0	NUM
ejpam-6159	584	21	t	t	PROPN
ejpam-6159	584	22	(	(	PUNCT
ejpam-6159	584	23	λ−	λ−	PROPN
ejpam-6159	584	24	t	t	PROPN
ejpam-6159	584	25	ϱ	ϱ	PROPN
ejpam-6159	584	26	k	k	PROPN
ejpam-6159	584	27	)	)	PUNCT
ejpam-6159	584	28	×	×	NOUN
ejpam-6159	585	1	[	[	X
ejpam-6159	585	2	∑n	∑n	PROPN
ejpam-6159	585	3	i=1	i=1	PROPN
ejpam-6159	585	4	ai	ai	VERB
ejpam-6159	585	5	(	(	PUNCT
ejpam-6159	585	6	1−	1−	NUM
ejpam-6159	585	7	st	st	NOUN
ejpam-6159	585	8	)	)	PUNCT
ejpam-6159	585	9	1	1	NUM
ejpam-6159	585	10	i∑n	i∑n	PROPN
ejpam-6159	585	11	i=1	i=1	PROPN
ejpam-6159	585	12	ai	ai	VERB
ejpam-6159	585	13	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	585	14	(	(	PUNCT
ejpam-6159	585	15	b1	b1	PROPN
ejpam-6159	585	16	)	)	PUNCT
ejpam-6159	585	17	∣∣q	∣∣q	NUM
ejpam-6159	586	1	+	+	NUM
ejpam-6159	586	2	∑n	∑n	PROPN
ejpam-6159	586	3	i=1	i=1	PROPN
ejpam-6159	586	4	ai	ai	VERB
ejpam-6159	586	5	(	(	PUNCT
ejpam-6159	586	6	1−	1−	NUM
ejpam-6159	586	7	s	s	X
ejpam-6159	586	8	(	(	PUNCT
ejpam-6159	586	9	1−	1−	NUM
ejpam-6159	586	10	t	t	NOUN
ejpam-6159	586	11	)	)	PUNCT
ejpam-6159	586	12	)	)	PUNCT
ejpam-6159	586	13	1	1	NUM
ejpam-6159	586	14	i∑n	i∑n	PROPN
ejpam-6159	586	15	i=1	i=1	PROPN
ejpam-6159	586	16	ai	ai	VERB
ejpam-6159	586	17	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	586	18	(	(	PUNCT
ejpam-6159	586	19	x	x	NOUN
ejpam-6159	586	20	)	)	PUNCT
ejpam-6159	586	21	∣∣q	∣∣q	NUM
ejpam-6159	586	22	dt	dt	X
ejpam-6159	586	23	]	]	X
ejpam-6159	586	24	1	1	NUM
ejpam-6159	586	25	q	q	NOUN
ejpam-6159	586	26	]	]	PUNCT
ejpam-6159	586	27	≤	≤	NUM
ejpam-6159	586	28	m	m	PROPN
ejpam-6159	586	29	1−	1−	NUM
ejpam-6159	586	30	1	1	NUM
ejpam-6159	586	31	q	q	NOUN
ejpam-6159	586	32	(	(	PUNCT
ejpam-6159	586	33	ϱ,k	ϱ,k	PROPN
ejpam-6159	586	34	,	,	PUNCT
ejpam-6159	586	35	λ	λ	NOUN
ejpam-6159	586	36	)	)	PUNCT
ejpam-6159	586	37	×	×	NOUN
ejpam-6159	586	38	[	[	PUNCT
ejpam-6159	586	39	ς	ς	PROPN
ejpam-6159	586	40	ϱ	ϱ	ADP
ejpam-6159	586	41	k	k	PROPN
ejpam-6159	586	42	+2	+2	PROPN
ejpam-6159	586	43	∗	∗	NOUN
ejpam-6159	586	44	(	(	PUNCT
ejpam-6159	586	45	x	x	NOUN
ejpam-6159	586	46	,	,	PUNCT
ejpam-6159	586	47	a1	a1	NOUN
ejpam-6159	586	48	)	)	PUNCT
ejpam-6159	586	49	ς∗	ς∗	NOUN
ejpam-6159	586	50	(	(	PUNCT
ejpam-6159	586	51	b1	b1	NOUN
ejpam-6159	586	52	,	,	PUNCT
ejpam-6159	586	53	a1	a1	PROPN
ejpam-6159	586	54	)	)	PUNCT
ejpam-6159	586	55	{	{	PUNCT
ejpam-6159	586	56	∫	∫	PROPN
ejpam-6159	586	57	1	1	NUM
ejpam-6159	586	58	0	0	NUM
ejpam-6159	586	59	t	t	PROPN
ejpam-6159	586	60	(	(	PUNCT
ejpam-6159	586	61	λ−	λ−	PROPN
ejpam-6159	586	62	t	t	PROPN
ejpam-6159	586	63	ϱ	ϱ	PROPN
ejpam-6159	586	64	k	k	PROPN
ejpam-6159	586	65	)	)	PUNCT
ejpam-6159	586	66	{	{	PUNCT
ejpam-6159	587	1	∑n	∑n	PROPN
ejpam-6159	587	2	i=1	i=1	PROPN
ejpam-6159	587	3	ai	ai	VERB
ejpam-6159	587	4	(	(	PUNCT
ejpam-6159	587	5	1−	1−	NUM
ejpam-6159	587	6	st	st	NOUN
ejpam-6159	587	7	)	)	PUNCT
ejpam-6159	587	8	1	1	NUM
ejpam-6159	587	9	i∑n	i∑n	PROPN
ejpam-6159	587	10	i=1	i=1	PROPN
ejpam-6159	587	11	ai	ai	VERB
ejpam-6159	587	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	587	13	(	(	PUNCT
ejpam-6159	587	14	a1	a1	PROPN
ejpam-6159	587	15	)	)	PUNCT
ejpam-6159	587	16	∣∣q	∣∣q	NUM
ejpam-6159	588	1	+	+	NUM
ejpam-6159	588	2	∑n	∑n	PROPN
ejpam-6159	588	3	i=1	i=1	PROPN
ejpam-6159	588	4	ai	ai	VERB
ejpam-6159	588	5	(	(	PUNCT
ejpam-6159	588	6	1−	1−	NUM
ejpam-6159	588	7	s	s	X
ejpam-6159	588	8	(	(	PUNCT
ejpam-6159	588	9	1−	1−	NUM
ejpam-6159	588	10	t	t	NOUN
ejpam-6159	588	11	)	)	PUNCT
ejpam-6159	588	12	)	)	PUNCT
ejpam-6159	588	13	1	1	NUM
ejpam-6159	588	14	i∑n	i∑n	PROPN
ejpam-6159	588	15	i=1	i=1	PROPN
ejpam-6159	588	16	ai	ai	VERB
ejpam-6159	588	17	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	588	18	(	(	PUNCT
ejpam-6159	588	19	x	x	NOUN
ejpam-6159	588	20	)	)	PUNCT
ejpam-6159	588	21	∣∣q	∣∣q	NUM
ejpam-6159	588	22	}	}	PUNCT
ejpam-6159	588	23	dt	dt	PROPN
ejpam-6159	588	24	}	}	PUNCT
ejpam-6159	588	25	1	1	NUM
ejpam-6159	588	26	q	q	NOUN
ejpam-6159	589	1	+	+	NUM
ejpam-6159	589	2	ς	ς	PROPN
ejpam-6159	589	3	ϱ	ϱ	ADP
ejpam-6159	589	4	k	k	PROPN
ejpam-6159	589	5	+2	+2	PROPN
ejpam-6159	589	6	∗	∗	NOUN
ejpam-6159	589	7	(	(	PUNCT
ejpam-6159	589	8	b1	b1	NOUN
ejpam-6159	589	9	,	,	PUNCT
ejpam-6159	589	10	x	x	NOUN
ejpam-6159	589	11	)	)	PUNCT
ejpam-6159	589	12	ς∗	ς∗	PROPN
ejpam-6159	589	13	(	(	PUNCT
ejpam-6159	589	14	b1	b1	NOUN
ejpam-6159	589	15	,	,	PUNCT
ejpam-6159	589	16	a1	a1	PROPN
ejpam-6159	589	17	)	)	PUNCT
ejpam-6159	589	18	{	{	PUNCT
ejpam-6159	589	19	∫	∫	PROPN
ejpam-6159	589	20	1	1	NUM
ejpam-6159	589	21	0	0	NUM
ejpam-6159	589	22	t	t	PROPN
ejpam-6159	589	23	(	(	PUNCT
ejpam-6159	589	24	λ−	λ−	PROPN
ejpam-6159	589	25	t	t	PROPN
ejpam-6159	589	26	ϱ	ϱ	PROPN
ejpam-6159	589	27	k	k	PROPN
ejpam-6159	589	28	)	)	PUNCT
ejpam-6159	589	29	{	{	PUNCT
ejpam-6159	590	1	∑n	∑n	PROPN
ejpam-6159	590	2	i=1	i=1	PROPN
ejpam-6159	590	3	ai	ai	VERB
ejpam-6159	590	4	(	(	PUNCT
ejpam-6159	590	5	1−	1−	NUM
ejpam-6159	590	6	st	st	NOUN
ejpam-6159	590	7	)	)	PUNCT
ejpam-6159	590	8	1	1	NUM
ejpam-6159	590	9	i∑n	i∑n	PROPN
ejpam-6159	590	10	i=1	i=1	PROPN
ejpam-6159	590	11	ai	ai	VERB
ejpam-6159	590	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	590	13	(	(	PUNCT
ejpam-6159	590	14	b1	b1	PROPN
ejpam-6159	590	15	)	)	PUNCT
ejpam-6159	590	16	∣∣q	∣∣q	PROPN
ejpam-6159	590	17	j.	j.	PROPN
ejpam-6159	590	18	nasir	nasir	PROPN
ejpam-6159	590	19	et	et	PROPN
ejpam-6159	590	20	al	al	PROPN
ejpam-6159	590	21	.	.	PUNCT
ejpam-6159	590	22	/	/	SYM
ejpam-6159	590	23	eur	eur	PROPN
ejpam-6159	590	24	.	.	PUNCT
ejpam-6159	591	1	j.	j.	PROPN
ejpam-6159	591	2	pure	pure	PROPN
ejpam-6159	591	3	appl	appl	PROPN
ejpam-6159	591	4	.	.	PROPN
ejpam-6159	591	5	math	math	PROPN
ejpam-6159	591	6	,	,	PUNCT
ejpam-6159	591	7	18	18	NUM
ejpam-6159	591	8	(	(	PUNCT
ejpam-6159	591	9	3	3	NUM
ejpam-6159	591	10	)	)	PUNCT
ejpam-6159	591	11	(	(	PUNCT
ejpam-6159	591	12	2025	2025	NUM
ejpam-6159	591	13	)	)	PUNCT
ejpam-6159	591	14	,	,	PUNCT
ejpam-6159	591	15	6159	6159	NUM
ejpam-6159	591	16	19	19	NUM
ejpam-6159	591	17	of	of	ADP
ejpam-6159	591	18	26	26	NUM
ejpam-6159	591	19	+	+	CCONJ
ejpam-6159	591	20	∑n	∑n	PROPN
ejpam-6159	592	1	i=1	i=1	PROPN
ejpam-6159	592	2	ai	ai	VERB
ejpam-6159	592	3	(	(	PUNCT
ejpam-6159	592	4	1−	1−	NUM
ejpam-6159	592	5	s	s	X
ejpam-6159	592	6	(	(	PUNCT
ejpam-6159	592	7	1−	1−	NUM
ejpam-6159	592	8	t	t	NOUN
ejpam-6159	592	9	)	)	PUNCT
ejpam-6159	592	10	)	)	PUNCT
ejpam-6159	592	11	1	1	NUM
ejpam-6159	592	12	i∑n	i∑n	PROPN
ejpam-6159	592	13	i=1	i=1	PROPN
ejpam-6159	592	14	ai	ai	VERB
ejpam-6159	592	15	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	592	16	(	(	PUNCT
ejpam-6159	592	17	x	x	NOUN
ejpam-6159	592	18	)	)	PUNCT
ejpam-6159	592	19	∣∣q	∣∣q	NUM
ejpam-6159	592	20	}	}	PUNCT
ejpam-6159	592	21	dt	dt	PROPN
ejpam-6159	592	22	}	}	PUNCT
ejpam-6159	592	23	1	1	NUM
ejpam-6159	592	24	q	q	NOUN
ejpam-6159	592	25	]	]	PUNCT
ejpam-6159	592	26	.	.	PUNCT
ejpam-6159	593	1	corollary	corollary	ADJ
ejpam-6159	593	2	11	11	NUM
ejpam-6159	593	3	.	.	PUNCT
ejpam-6159	594	1	if	if	SCONJ
ejpam-6159	594	2	one	one	PRON
ejpam-6159	594	3	can	can	AUX
ejpam-6159	594	4	take	take	VERB
ejpam-6159	594	5	s	s	PART
ejpam-6159	594	6	=	=	SYM
ejpam-6159	594	7	1	1	NUM
ejpam-6159	594	8	in	in	ADP
ejpam-6159	594	9	theorem	theorem	NOUN
ejpam-6159	594	10	7	7	NUM
ejpam-6159	594	11	,	,	PUNCT
ejpam-6159	594	12	then	then	ADV
ejpam-6159	594	13	we	we	PRON
ejpam-6159	594	14	have	have	VERB
ejpam-6159	594	15	the	the	DET
ejpam-6159	594	16	following	follow	VERB
ejpam-6159	594	17	inequalities	inequality	NOUN
ejpam-6159	594	18	for	for	ADP
ejpam-6159	594	19	a	a	DET
ejpam-6159	594	20	gfpp	gfpp	NOUN
ejpam-6159	594	21	function	function	NOUN
ejpam-6159	594	22	with	with	ADP
ejpam-6159	594	23	k−fractional	k−fractional	ADJ
ejpam-6159	594	24	integral	integral	ADJ
ejpam-6159	594	25	operators:∣∣∣∣	operators:∣∣∣∣	ADJ
ejpam-6159	594	26	(	(	PUNCT
ejpam-6159	594	27	1−	1−	NUM
ejpam-6159	594	28	λ	λ	NOUN
ejpam-6159	594	29	)	)	PUNCT
ejpam-6159	594	30	[	[	PUNCT
ejpam-6159	594	31	ς	ς	X
ejpam-6159	594	32	ϱ	ϱ	PROPN
ejpam-6159	594	33	k	k	PROPN
ejpam-6159	594	34	∗	∗	X
ejpam-6159	594	35	(	(	PUNCT
ejpam-6159	594	36	b1	b1	NOUN
ejpam-6159	594	37	,	,	PUNCT
ejpam-6159	594	38	x)−	x)−	PROPN
ejpam-6159	594	39	ς	ς	PROPN
ejpam-6159	594	40	ϱ	ϱ	PROPN
ejpam-6159	594	41	k	k	PROPN
ejpam-6159	594	42	∗	∗	X
ejpam-6159	594	43	(	(	PUNCT
ejpam-6159	594	44	x	x	NOUN
ejpam-6159	594	45	,	,	PUNCT
ejpam-6159	594	46	a1	a1	NOUN
ejpam-6159	594	47	)	)	PUNCT
ejpam-6159	594	48	ς∗	ς∗	NOUN
ejpam-6159	594	49	(	(	PUNCT
ejpam-6159	594	50	b1	b1	NOUN
ejpam-6159	594	51	,	,	PUNCT
ejpam-6159	594	52	a1	a1	PROPN
ejpam-6159	594	53	)	)	PUNCT
ejpam-6159	594	54	]	]	PUNCT
ejpam-6159	594	55	f′	f′	PROPN
ejpam-6159	594	56	(	(	PUNCT
ejpam-6159	594	57	x	x	X
ejpam-6159	594	58	)	)	PUNCT
ejpam-6159	595	1	+	+	CCONJ
ejpam-6159	595	2	(	(	PUNCT
ejpam-6159	595	3	1	1	NUM
ejpam-6159	595	4	+	+	CCONJ
ejpam-6159	595	5	ϱ	ϱ	ADP
ejpam-6159	595	6	k	k	X
ejpam-6159	595	7	−	−	PROPN
ejpam-6159	595	8	λ	λ	PROPN
ejpam-6159	595	9	)	)	PUNCT
ejpam-6159	595	10	[	[	PUNCT
ejpam-6159	595	11	ς	ς	PROPN
ejpam-6159	595	12	ϱ	ϱ	PROPN
ejpam-6159	595	13	k	k	PROPN
ejpam-6159	595	14	∗	∗	X
ejpam-6159	595	15	(	(	PUNCT
ejpam-6159	595	16	b1	b1	NOUN
ejpam-6159	595	17	,	,	PUNCT
ejpam-6159	595	18	x	x	X
ejpam-6159	595	19	)	)	PUNCT
ejpam-6159	595	20	+	+	CCONJ
ejpam-6159	595	21	ς	ς	PROPN
ejpam-6159	595	22	ϱ	ϱ	PROPN
ejpam-6159	595	23	k	k	PROPN
ejpam-6159	595	24	∗	∗	X
ejpam-6159	595	25	(	(	PUNCT
ejpam-6159	595	26	x	x	NOUN
ejpam-6159	595	27	,	,	PUNCT
ejpam-6159	595	28	a1	a1	NOUN
ejpam-6159	595	29	)	)	PUNCT
ejpam-6159	595	30	ς∗	ς∗	NOUN
ejpam-6159	595	31	(	(	PUNCT
ejpam-6159	595	32	b1	b1	NOUN
ejpam-6159	595	33	,	,	PUNCT
ejpam-6159	595	34	a1	a1	PROPN
ejpam-6159	595	35	)	)	PUNCT
ejpam-6159	595	36	]	]	PUNCT
ejpam-6159	596	1	f	f	PROPN
ejpam-6159	596	2	(	(	PUNCT
ejpam-6159	596	3	x	x	X
ejpam-6159	596	4	)	)	PUNCT
ejpam-6159	597	1	+	+	NUM
ejpam-6159	597	2	λ	λ	X
ejpam-6159	597	3	[	[	PUNCT
ejpam-6159	597	4	ς	ς	PROPN
ejpam-6159	597	5	ϱ	ϱ	PROPN
ejpam-6159	597	6	k	k	PROPN
ejpam-6159	597	7	∗	∗	X
ejpam-6159	597	8	(	(	PUNCT
ejpam-6159	597	9	b1	b1	NOUN
ejpam-6159	597	10	,	,	PUNCT
ejpam-6159	597	11	x)f	x)f	X
ejpam-6159	597	12	(	(	PUNCT
ejpam-6159	597	13	b1	b1	NOUN
ejpam-6159	597	14	)	)	PUNCT
ejpam-6159	597	15	+	+	CCONJ
ejpam-6159	597	16	ς	ς	PROPN
ejpam-6159	597	17	ϱ	ϱ	PROPN
ejpam-6159	597	18	k	k	PROPN
ejpam-6159	597	19	∗	∗	X
ejpam-6159	597	20	(	(	PUNCT
ejpam-6159	597	21	x	x	X
ejpam-6159	597	22	,	,	PUNCT
ejpam-6159	597	23	a1)f	a1)f	PROPN
ejpam-6159	597	24	(	(	PUNCT
ejpam-6159	597	25	a1	a1	PROPN
ejpam-6159	597	26	)	)	PUNCT
ejpam-6159	597	27	ς∗	ς∗	NOUN
ejpam-6159	597	28	(	(	PUNCT
ejpam-6159	597	29	b1	b1	NOUN
ejpam-6159	597	30	,	,	PUNCT
ejpam-6159	597	31	a1	a1	PROPN
ejpam-6159	597	32	)	)	PUNCT
ejpam-6159	597	33	]	]	PUNCT
ejpam-6159	598	1	−	−	PROPN
ejpam-6159	598	2	γk	γk	X
ejpam-6159	598	3	(	(	PUNCT
ejpam-6159	598	4	ϱ+	ϱ+	NOUN
ejpam-6159	598	5	2k	2k	NUM
ejpam-6159	598	6	)	)	PUNCT
ejpam-6159	598	7	ς∗	ς∗	PROPN
ejpam-6159	598	8	(	(	PUNCT
ejpam-6159	598	9	b1	b1	NOUN
ejpam-6159	598	10	,	,	PUNCT
ejpam-6159	598	11	a1	a1	NOUN
ejpam-6159	598	12	)	)	PUNCT
ejpam-6159	598	13	{	{	PUNCT
ejpam-6159	598	14	jϱ,k	jϱ,k	X
ejpam-6159	598	15	(	(	PUNCT
ejpam-6159	598	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	598	17	,	,	PUNCT
ejpam-6159	598	18	a1	a1	NOUN
ejpam-6159	598	19	)	)	PUNCT
ejpam-6159	598	20	)	)	PUNCT
ejpam-6159	599	1	−	−	PROPN
ejpam-6159	599	2	f	f	X
ejpam-6159	599	3	(	(	PUNCT
ejpam-6159	599	4	a1	a1	PROPN
ejpam-6159	599	5	)	)	PUNCT
ejpam-6159	599	6	+	+	NUM
ejpam-6159	599	7	jϱ,k	jϱ,k	X
ejpam-6159	599	8	(	(	PUNCT
ejpam-6159	599	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	599	10	,	,	PUNCT
ejpam-6159	599	11	b1	b1	NOUN
ejpam-6159	599	12	)	)	PUNCT
ejpam-6159	599	13	)	)	PUNCT
ejpam-6159	600	1	+	+	CCONJ
ejpam-6159	600	2	f	f	X
ejpam-6159	600	3	(	(	PUNCT
ejpam-6159	600	4	b1	b1	PROPN
ejpam-6159	600	5	)	)	PUNCT
ejpam-6159	600	6	}	}	PUNCT
ejpam-6159	600	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	600	8	≤	≤	NUM
ejpam-6159	600	9	m	m	VERB
ejpam-6159	600	10	1−	1−	NUM
ejpam-6159	600	11	1	1	NUM
ejpam-6159	600	12	q	q	NOUN
ejpam-6159	600	13	(	(	PUNCT
ejpam-6159	600	14	ϱ,k	ϱ,k	PROPN
ejpam-6159	600	15	,	,	PUNCT
ejpam-6159	600	16	λ	λ	NOUN
ejpam-6159	600	17	)	)	PUNCT
ejpam-6159	600	18	×	×	NOUN
ejpam-6159	600	19	[	[	PUNCT
ejpam-6159	600	20	ς	ς	PROPN
ejpam-6159	600	21	ϱ	ϱ	ADP
ejpam-6159	600	22	k	k	PROPN
ejpam-6159	600	23	+2	+2	PROPN
ejpam-6159	600	24	∗	∗	NOUN
ejpam-6159	600	25	(	(	PUNCT
ejpam-6159	600	26	x	x	NOUN
ejpam-6159	600	27	,	,	PUNCT
ejpam-6159	600	28	a1	a1	NOUN
ejpam-6159	600	29	)	)	PUNCT
ejpam-6159	600	30	ς∗	ς∗	NOUN
ejpam-6159	600	31	(	(	PUNCT
ejpam-6159	600	32	b1	b1	NOUN
ejpam-6159	600	33	,	,	PUNCT
ejpam-6159	600	34	a1	a1	PROPN
ejpam-6159	600	35	)	)	PUNCT
ejpam-6159	600	36	{	{	PUNCT
ejpam-6159	600	37	∫	∫	PROPN
ejpam-6159	600	38	1	1	NUM
ejpam-6159	600	39	0	0	NUM
ejpam-6159	600	40	t	t	PROPN
ejpam-6159	600	41	(	(	PUNCT
ejpam-6159	600	42	λ−	λ−	PROPN
ejpam-6159	600	43	t	t	PROPN
ejpam-6159	600	44	ϱ	ϱ	PROPN
ejpam-6159	600	45	k	k	PROPN
ejpam-6159	600	46	)	)	PUNCT
ejpam-6159	600	47	{	{	PUNCT
ejpam-6159	601	1	∑n	∑n	PROPN
ejpam-6159	601	2	i=1	i=1	PROPN
ejpam-6159	601	3	ai	ai	VERB
ejpam-6159	601	4	(	(	PUNCT
ejpam-6159	601	5	1−	1−	NUM
ejpam-6159	601	6	t	t	NOUN
ejpam-6159	601	7	)	)	PUNCT
ejpam-6159	601	8	1	1	NUM
ejpam-6159	601	9	i∑n	i∑n	PROPN
ejpam-6159	601	10	i=1	i=1	PROPN
ejpam-6159	601	11	ai	ai	VERB
ejpam-6159	601	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	601	13	(	(	PUNCT
ejpam-6159	601	14	a1	a1	PROPN
ejpam-6159	601	15	)	)	PUNCT
ejpam-6159	601	16	∣∣q	∣∣q	NUM
ejpam-6159	602	1	+	+	NUM
ejpam-6159	602	2	∑n	∑n	PROPN
ejpam-6159	602	3	i=1	i=1	PROPN
ejpam-6159	602	4	ai	ai	PROPN
ejpam-6159	602	5	(	(	PUNCT
ejpam-6159	602	6	t	t	NOUN
ejpam-6159	602	7	)	)	PUNCT
ejpam-6159	602	8	1	1	NUM
ejpam-6159	602	9	i∑n	i∑n	PROPN
ejpam-6159	602	10	i=1	i=1	PROPN
ejpam-6159	602	11	ai	ai	VERB
ejpam-6159	602	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	602	13	(	(	PUNCT
ejpam-6159	602	14	x	x	NOUN
ejpam-6159	602	15	)	)	PUNCT
ejpam-6159	602	16	∣∣q	∣∣q	NUM
ejpam-6159	602	17	}	}	PUNCT
ejpam-6159	602	18	dt	dt	PROPN
ejpam-6159	602	19	}	}	PUNCT
ejpam-6159	602	20	1	1	NUM
ejpam-6159	602	21	q	q	NOUN
ejpam-6159	603	1	+	+	NUM
ejpam-6159	603	2	ς	ς	PROPN
ejpam-6159	603	3	ϱ	ϱ	ADP
ejpam-6159	603	4	k	k	PROPN
ejpam-6159	603	5	+2	+2	PROPN
ejpam-6159	603	6	∗	∗	NOUN
ejpam-6159	603	7	(	(	PUNCT
ejpam-6159	603	8	b1	b1	NOUN
ejpam-6159	603	9	,	,	PUNCT
ejpam-6159	603	10	x	x	NOUN
ejpam-6159	603	11	)	)	PUNCT
ejpam-6159	603	12	ς∗	ς∗	PROPN
ejpam-6159	603	13	(	(	PUNCT
ejpam-6159	603	14	b1	b1	NOUN
ejpam-6159	603	15	,	,	PUNCT
ejpam-6159	603	16	a1	a1	PROPN
ejpam-6159	603	17	)	)	PUNCT
ejpam-6159	603	18	{	{	PUNCT
ejpam-6159	603	19	∫	∫	PROPN
ejpam-6159	603	20	1	1	NUM
ejpam-6159	603	21	0	0	NUM
ejpam-6159	603	22	t	t	PROPN
ejpam-6159	603	23	(	(	PUNCT
ejpam-6159	603	24	λ−	λ−	PROPN
ejpam-6159	603	25	t	t	PROPN
ejpam-6159	603	26	ϱ	ϱ	PROPN
ejpam-6159	603	27	k	k	PROPN
ejpam-6159	603	28	)	)	PUNCT
ejpam-6159	603	29	{	{	PUNCT
ejpam-6159	604	1	∑n	∑n	PROPN
ejpam-6159	604	2	i=1	i=1	PROPN
ejpam-6159	604	3	ai	ai	VERB
ejpam-6159	604	4	(	(	PUNCT
ejpam-6159	604	5	1−	1−	NUM
ejpam-6159	604	6	t	t	NOUN
ejpam-6159	604	7	)	)	PUNCT
ejpam-6159	604	8	1	1	NUM
ejpam-6159	604	9	i∑n	i∑n	PROPN
ejpam-6159	604	10	i=1	i=1	PROPN
ejpam-6159	604	11	ai	ai	VERB
ejpam-6159	604	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	604	13	(	(	PUNCT
ejpam-6159	604	14	b1	b1	PROPN
ejpam-6159	604	15	)	)	PUNCT
ejpam-6159	604	16	∣∣q	∣∣q	NUM
ejpam-6159	605	1	+	+	NUM
ejpam-6159	605	2	∑n	∑n	PROPN
ejpam-6159	605	3	i=1	i=1	PROPN
ejpam-6159	605	4	ait	ait	VERB
ejpam-6159	605	5	1	1	NUM
ejpam-6159	605	6	i∑n	i∑n	PROPN
ejpam-6159	605	7	i=1	i=1	PROPN
ejpam-6159	605	8	ai	ai	VERB
ejpam-6159	605	9	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	605	10	(	(	PUNCT
ejpam-6159	605	11	x	x	NOUN
ejpam-6159	605	12	)	)	PUNCT
ejpam-6159	605	13	∣∣q	∣∣q	NUM
ejpam-6159	605	14	}	}	PUNCT
ejpam-6159	605	15	dt	dt	PROPN
ejpam-6159	605	16	}	}	PUNCT
ejpam-6159	605	17	1	1	NUM
ejpam-6159	605	18	q	q	NOUN
ejpam-6159	605	19	]	]	PUNCT
ejpam-6159	605	20	.	.	PUNCT
ejpam-6159	606	1	corollary	corollary	ADJ
ejpam-6159	606	2	12	12	NUM
ejpam-6159	606	3	.	.	PUNCT
ejpam-6159	607	1	if	if	SCONJ
ejpam-6159	607	2	one	one	PRON
ejpam-6159	607	3	can	can	AUX
ejpam-6159	607	4	take	take	VERB
ejpam-6159	607	5	k	k	NOUN
ejpam-6159	607	6	=	=	PUNCT
ejpam-6159	607	7	1	1	NUM
ejpam-6159	607	8	in	in	ADP
ejpam-6159	607	9	corollary	corollary	ADJ
ejpam-6159	607	10	11	11	NUM
ejpam-6159	607	11	,	,	PUNCT
ejpam-6159	607	12	then	then	ADV
ejpam-6159	607	13	we	we	PRON
ejpam-6159	607	14	have	have	VERB
ejpam-6159	607	15	the	the	DET
ejpam-6159	607	16	following	follow	VERB
ejpam-6159	607	17	inequalities	inequality	NOUN
ejpam-6159	607	18	for	for	ADP
ejpam-6159	607	19	gfpp	gfpp	NOUN
ejpam-6159	607	20	function	function	NOUN
ejpam-6159	607	21	with	with	ADP
ejpam-6159	607	22	rl−fractional	rl−fractional	ADJ
ejpam-6159	607	23	integral	integral	ADJ
ejpam-6159	607	24	operators:∣∣∣∣	operators:∣∣∣∣	ADJ
ejpam-6159	607	25	(	(	PUNCT
ejpam-6159	607	26	1−	1−	NUM
ejpam-6159	607	27	λ	λ	NOUN
ejpam-6159	607	28	)	)	PUNCT
ejpam-6159	607	29	[	[	PUNCT
ejpam-6159	607	30	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	607	31	(	(	PUNCT
ejpam-6159	607	32	b1	b1	NOUN
ejpam-6159	607	33	,	,	PUNCT
ejpam-6159	607	34	x)−	x)−	PROPN
ejpam-6159	607	35	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	607	36	(	(	PUNCT
ejpam-6159	607	37	x	x	NOUN
ejpam-6159	607	38	,	,	PUNCT
ejpam-6159	607	39	a1	a1	NOUN
ejpam-6159	607	40	)	)	PUNCT
ejpam-6159	607	41	ς∗	ς∗	NOUN
ejpam-6159	607	42	(	(	PUNCT
ejpam-6159	607	43	b1	b1	NOUN
ejpam-6159	607	44	,	,	PUNCT
ejpam-6159	607	45	a1	a1	PROPN
ejpam-6159	607	46	)	)	PUNCT
ejpam-6159	607	47	]	]	PUNCT
ejpam-6159	607	48	f′	f′	PROPN
ejpam-6159	607	49	(	(	PUNCT
ejpam-6159	607	50	x	x	X
ejpam-6159	607	51	)	)	PUNCT
ejpam-6159	608	1	+	+	CCONJ
ejpam-6159	608	2	(	(	PUNCT
ejpam-6159	608	3	1	1	NUM
ejpam-6159	608	4	+	+	NUM
ejpam-6159	608	5	ϱ−	ϱ−	NOUN
ejpam-6159	608	6	λ	λ	NOUN
ejpam-6159	608	7	)	)	PUNCT
ejpam-6159	608	8	[	[	PUNCT
ejpam-6159	608	9	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	608	10	(	(	PUNCT
ejpam-6159	608	11	b1	b1	NOUN
ejpam-6159	608	12	,	,	PUNCT
ejpam-6159	608	13	x	x	X
ejpam-6159	608	14	)	)	PUNCT
ejpam-6159	609	1	+	+	NUM
ejpam-6159	609	2	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	609	3	(	(	PUNCT
ejpam-6159	609	4	x	x	NOUN
ejpam-6159	609	5	,	,	PUNCT
ejpam-6159	609	6	a1	a1	NOUN
ejpam-6159	609	7	)	)	PUNCT
ejpam-6159	609	8	ς∗	ς∗	NOUN
ejpam-6159	609	9	(	(	PUNCT
ejpam-6159	609	10	b1	b1	NOUN
ejpam-6159	609	11	,	,	PUNCT
ejpam-6159	609	12	a1	a1	PROPN
ejpam-6159	609	13	)	)	PUNCT
ejpam-6159	609	14	]	]	PUNCT
ejpam-6159	610	1	f	f	PROPN
ejpam-6159	610	2	(	(	PUNCT
ejpam-6159	610	3	x	x	X
ejpam-6159	610	4	)	)	PUNCT
ejpam-6159	611	1	+	+	NUM
ejpam-6159	611	2	λ	λ	X
ejpam-6159	611	3	[	[	PUNCT
ejpam-6159	611	4	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	611	5	(	(	PUNCT
ejpam-6159	611	6	b1	b1	NOUN
ejpam-6159	611	7	,	,	PUNCT
ejpam-6159	611	8	x)f	x)f	X
ejpam-6159	611	9	(	(	PUNCT
ejpam-6159	611	10	b1	b1	NOUN
ejpam-6159	611	11	)	)	PUNCT
ejpam-6159	612	1	+	+	NUM
ejpam-6159	612	2	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	612	3	(	(	PUNCT
ejpam-6159	612	4	x	x	X
ejpam-6159	612	5	,	,	PUNCT
ejpam-6159	612	6	a1)f	a1)f	PROPN
ejpam-6159	612	7	(	(	PUNCT
ejpam-6159	612	8	a1	a1	PROPN
ejpam-6159	612	9	)	)	PUNCT
ejpam-6159	612	10	ς∗	ς∗	NOUN
ejpam-6159	612	11	(	(	PUNCT
ejpam-6159	612	12	b1	b1	NOUN
ejpam-6159	612	13	,	,	PUNCT
ejpam-6159	612	14	a1	a1	PROPN
ejpam-6159	612	15	)	)	PUNCT
ejpam-6159	612	16	]	]	PUNCT
ejpam-6159	613	1	−	−	PROPN
ejpam-6159	613	2	γ	γ	X
ejpam-6159	613	3	(	(	PUNCT
ejpam-6159	613	4	ϱ+	ϱ+	X
ejpam-6159	613	5	2	2	X
ejpam-6159	613	6	)	)	PUNCT
ejpam-6159	613	7	ς∗	ς∗	NOUN
ejpam-6159	613	8	(	(	PUNCT
ejpam-6159	613	9	b1	b1	NOUN
ejpam-6159	613	10	,	,	PUNCT
ejpam-6159	613	11	a1	a1	NOUN
ejpam-6159	613	12	)	)	PUNCT
ejpam-6159	613	13	{	{	PUNCT
ejpam-6159	613	14	jϱ	jϱ	NOUN
ejpam-6159	613	15	(	(	PUNCT
ejpam-6159	613	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	613	17	,	,	PUNCT
ejpam-6159	613	18	a1	a1	NOUN
ejpam-6159	613	19	)	)	PUNCT
ejpam-6159	613	20	)	)	PUNCT
ejpam-6159	614	1	−	−	PROPN
ejpam-6159	615	1	f	f	X
ejpam-6159	615	2	(	(	PUNCT
ejpam-6159	615	3	a1	a1	PROPN
ejpam-6159	615	4	)	)	PUNCT
ejpam-6159	615	5	+	+	NUM
ejpam-6159	615	6	jϱ	jϱ	ADJ
ejpam-6159	615	7	(	(	PUNCT
ejpam-6159	615	8	b1+ς∗(x	b1+ς∗(x	PROPN
ejpam-6159	615	9	,	,	PUNCT
ejpam-6159	615	10	b1	b1	NOUN
ejpam-6159	615	11	)	)	PUNCT
ejpam-6159	615	12	)	)	PUNCT
ejpam-6159	616	1	+	+	CCONJ
ejpam-6159	616	2	f	f	X
ejpam-6159	616	3	(	(	PUNCT
ejpam-6159	616	4	b1	b1	PROPN
ejpam-6159	616	5	)	)	PUNCT
ejpam-6159	616	6	}	}	PUNCT
ejpam-6159	616	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	616	8	≤	≤	NUM
ejpam-6159	616	9	m	m	VERB
ejpam-6159	616	10	1−	1−	NUM
ejpam-6159	616	11	1	1	NUM
ejpam-6159	616	12	q	q	NOUN
ejpam-6159	616	13	(	(	PUNCT
ejpam-6159	616	14	ϱ	ϱ	PROPN
ejpam-6159	616	15	,	,	PUNCT
ejpam-6159	616	16	λ	λ	NOUN
ejpam-6159	616	17	)	)	PUNCT
ejpam-6159	616	18	×	×	NOUN
ejpam-6159	616	19	[	[	PUNCT
ejpam-6159	616	20	ςϱ+2	ςϱ+2	NUM
ejpam-6159	616	21	∗	∗	NOUN
ejpam-6159	616	22	(	(	PUNCT
ejpam-6159	616	23	x	x	NOUN
ejpam-6159	616	24	,	,	PUNCT
ejpam-6159	616	25	a1	a1	NOUN
ejpam-6159	616	26	)	)	PUNCT
ejpam-6159	616	27	ς∗	ς∗	NOUN
ejpam-6159	616	28	(	(	PUNCT
ejpam-6159	616	29	b1	b1	NOUN
ejpam-6159	616	30	,	,	PUNCT
ejpam-6159	616	31	a1	a1	PROPN
ejpam-6159	616	32	)	)	PUNCT
ejpam-6159	616	33	{	{	PUNCT
ejpam-6159	616	34	∫	∫	PROPN
ejpam-6159	616	35	1	1	NUM
ejpam-6159	616	36	0	0	NUM
ejpam-6159	616	37	t	t	PROPN
ejpam-6159	616	38	(	(	PUNCT
ejpam-6159	616	39	λ−	λ−	PROPN
ejpam-6159	616	40	tϱ	tϱ	X
ejpam-6159	616	41	)	)	PUNCT
ejpam-6159	616	42	{	{	PUNCT
ejpam-6159	617	1	∑n	∑n	PROPN
ejpam-6159	617	2	i=1	i=1	PROPN
ejpam-6159	617	3	ai	ai	VERB
ejpam-6159	617	4	(	(	PUNCT
ejpam-6159	617	5	1−	1−	NUM
ejpam-6159	617	6	t	t	NOUN
ejpam-6159	617	7	)	)	PUNCT
ejpam-6159	617	8	1	1	NUM
ejpam-6159	617	9	i∑n	i∑n	PROPN
ejpam-6159	617	10	i=1	i=1	PROPN
ejpam-6159	617	11	ai	ai	VERB
ejpam-6159	617	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	617	13	(	(	PUNCT
ejpam-6159	617	14	a1	a1	PROPN
ejpam-6159	617	15	)	)	PUNCT
ejpam-6159	617	16	∣∣q	∣∣q	NUM
ejpam-6159	618	1	+	+	NUM
ejpam-6159	618	2	∑n	∑n	PROPN
ejpam-6159	618	3	i=1	i=1	PROPN
ejpam-6159	618	4	ait	ait	VERB
ejpam-6159	618	5	1	1	NUM
ejpam-6159	618	6	i∑n	i∑n	PROPN
ejpam-6159	618	7	i=1	i=1	PROPN
ejpam-6159	618	8	ai	ai	VERB
ejpam-6159	618	9	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	618	10	(	(	PUNCT
ejpam-6159	618	11	x	x	NOUN
ejpam-6159	618	12	)	)	PUNCT
ejpam-6159	618	13	∣∣q	∣∣q	NUM
ejpam-6159	618	14	}	}	PUNCT
ejpam-6159	618	15	dt	dt	PROPN
ejpam-6159	618	16	}	}	PUNCT
ejpam-6159	618	17	1	1	NUM
ejpam-6159	618	18	q	q	NOUN
ejpam-6159	618	19	+	+	NUM
ejpam-6159	618	20	ςϱ+2	ςϱ+2	NUM
ejpam-6159	618	21	∗	∗	NOUN
ejpam-6159	618	22	(	(	PUNCT
ejpam-6159	618	23	b1	b1	NOUN
ejpam-6159	618	24	,	,	PUNCT
ejpam-6159	618	25	x	x	NOUN
ejpam-6159	618	26	)	)	PUNCT
ejpam-6159	618	27	ς∗	ς∗	PROPN
ejpam-6159	618	28	(	(	PUNCT
ejpam-6159	618	29	b1	b1	NOUN
ejpam-6159	618	30	,	,	PUNCT
ejpam-6159	618	31	a1	a1	PROPN
ejpam-6159	618	32	)	)	PUNCT
ejpam-6159	618	33	{	{	PUNCT
ejpam-6159	618	34	∫	∫	PROPN
ejpam-6159	618	35	1	1	NUM
ejpam-6159	618	36	0	0	NUM
ejpam-6159	618	37	t	t	PROPN
ejpam-6159	618	38	(	(	PUNCT
ejpam-6159	618	39	λ−	λ−	PROPN
ejpam-6159	618	40	tϱ	tϱ	X
ejpam-6159	618	41	)	)	PUNCT
ejpam-6159	618	42	{	{	PUNCT
ejpam-6159	618	43	∑n	∑n	PROPN
ejpam-6159	618	44	i=1	i=1	PROPN
ejpam-6159	618	45	ai	ai	VERB
ejpam-6159	618	46	(	(	PUNCT
ejpam-6159	618	47	1−	1−	NUM
ejpam-6159	618	48	t	t	NOUN
ejpam-6159	618	49	)	)	PUNCT
ejpam-6159	618	50	1	1	NUM
ejpam-6159	618	51	i∑n	i∑n	PROPN
ejpam-6159	618	52	i=1	i=1	PROPN
ejpam-6159	618	53	ai	ai	VERB
ejpam-6159	618	54	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	618	55	(	(	PUNCT
ejpam-6159	618	56	b1	b1	PROPN
ejpam-6159	618	57	)	)	PUNCT
ejpam-6159	618	58	∣∣q	∣∣q	PROPN
ejpam-6159	618	59	j.	j.	PROPN
ejpam-6159	618	60	nasir	nasir	PROPN
ejpam-6159	618	61	et	et	PROPN
ejpam-6159	618	62	al	al	PROPN
ejpam-6159	618	63	.	.	PUNCT
ejpam-6159	618	64	/	/	SYM
ejpam-6159	618	65	eur	eur	PROPN
ejpam-6159	618	66	.	.	PUNCT
ejpam-6159	619	1	j.	j.	PROPN
ejpam-6159	619	2	pure	pure	PROPN
ejpam-6159	619	3	appl	appl	PROPN
ejpam-6159	619	4	.	.	PROPN
ejpam-6159	619	5	math	math	PROPN
ejpam-6159	619	6	,	,	PUNCT
ejpam-6159	619	7	18	18	NUM
ejpam-6159	619	8	(	(	PUNCT
ejpam-6159	619	9	3	3	NUM
ejpam-6159	619	10	)	)	PUNCT
ejpam-6159	619	11	(	(	PUNCT
ejpam-6159	619	12	2025	2025	NUM
ejpam-6159	619	13	)	)	PUNCT
ejpam-6159	619	14	,	,	PUNCT
ejpam-6159	619	15	6159	6159	NUM
ejpam-6159	619	16	20	20	NUM
ejpam-6159	619	17	of	of	ADP
ejpam-6159	619	18	26	26	NUM
ejpam-6159	619	19	+	+	CCONJ
ejpam-6159	619	20	∑n	∑n	PROPN
ejpam-6159	619	21	i=1	i=1	PROPN
ejpam-6159	619	22	ait	ait	VERB
ejpam-6159	619	23	1	1	NUM
ejpam-6159	619	24	i∑n	i∑n	PROPN
ejpam-6159	619	25	i=1	i=1	PROPN
ejpam-6159	619	26	ai	ai	VERB
ejpam-6159	619	27	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	619	28	(	(	PUNCT
ejpam-6159	619	29	x	x	NOUN
ejpam-6159	619	30	)	)	PUNCT
ejpam-6159	619	31	∣∣q	∣∣q	NUM
ejpam-6159	619	32	}	}	PUNCT
ejpam-6159	619	33	dt	dt	PROPN
ejpam-6159	619	34	}	}	PUNCT
ejpam-6159	619	35	1	1	NUM
ejpam-6159	619	36	q	q	NOUN
ejpam-6159	619	37	]	]	PUNCT
ejpam-6159	620	1	where	where	SCONJ
ejpam-6159	620	2	m	m	VERB
ejpam-6159	620	3	(	(	PUNCT
ejpam-6159	620	4	ϱ	ϱ	PROPN
ejpam-6159	620	5	,	,	PUNCT
ejpam-6159	620	6	λ	λ	NOUN
ejpam-6159	620	7	)	)	PUNCT
ejpam-6159	620	8	=	=	SYM
ejpam-6159	620	9	∫	∫	PROPN
ejpam-6159	620	10	1	1	NUM
ejpam-6159	620	11	0	0	NUM
ejpam-6159	620	12	[	[	X
ejpam-6159	620	13	t	t	X
ejpam-6159	620	14	(	(	PUNCT
ejpam-6159	620	15	λ−	λ−	PROPN
ejpam-6159	620	16	tϱ)]qdt	tϱ)]qdt	NOUN
ejpam-6159	620	17	=	=	SYM
ejpam-6159	620	18	λ	λ	X
ejpam-6159	620	19	(	(	PUNCT
ejpam-6159	620	20	1+iq)+ϱq	1+iq)+ϱq	PROPN
ejpam-6159	620	21	q	q	X
ejpam-6159	620	22	ϱ	ϱ	PROPN
ejpam-6159	620	23	[	[	PUNCT
ejpam-6159	620	24	γ	γ	X
ejpam-6159	620	25	(	(	PUNCT
ejpam-6159	620	26	1	1	NUM
ejpam-6159	620	27	+	+	CCONJ
ejpam-6159	620	28	iq	iq	NOUN
ejpam-6159	620	29	)	)	PUNCT
ejpam-6159	620	30	γ	γ	PROPN
ejpam-6159	620	31	(	(	PUNCT
ejpam-6159	620	32	(	(	PUNCT
ejpam-6159	620	33	1	1	NUM
ejpam-6159	620	34	+	+	NUM
ejpam-6159	620	35	iq	iq	NOUN
ejpam-6159	620	36	)	)	PUNCT
ejpam-6159	620	37	+	+	CCONJ
ejpam-6159	620	38	ϱ	ϱ	ADP
ejpam-6159	620	39	ϱ	ϱ	NOUN
ejpam-6159	620	40	)	)	PUNCT
ejpam-6159	620	41	2f1	2f1	PROPN
ejpam-6159	620	42	(	(	PUNCT
ejpam-6159	620	43	1	1	NUM
ejpam-6159	620	44	,	,	PUNCT
ejpam-6159	620	45	1	1	NUM
ejpam-6159	620	46	+	+	CCONJ
ejpam-6159	620	47	iq	iq	NOUN
ejpam-6159	620	48	,	,	PUNCT
ejpam-6159	620	49	2	2	NUM
ejpam-6159	620	50	+	+	CCONJ
ejpam-6159	620	51	q	q	NOUN
ejpam-6159	621	1	+	+	CCONJ
ejpam-6159	621	2	(	(	PUNCT
ejpam-6159	621	3	1	1	NUM
ejpam-6159	621	4	+	+	CCONJ
ejpam-6159	621	5	q	q	X
ejpam-6159	621	6	)	)	PUNCT
ejpam-6159	621	7	ϱ	ϱ	NOUN
ejpam-6159	621	8	,	,	PUNCT
ejpam-6159	621	9	1	1	NUM
ejpam-6159	621	10	)	)	PUNCT
ejpam-6159	622	1	+	+	CCONJ
ejpam-6159	622	2	β	β	X
ejpam-6159	622	3	(	(	PUNCT
ejpam-6159	622	4	1	1	NUM
ejpam-6159	622	5	+	+	CCONJ
ejpam-6159	622	6	iq,−(1	iq,−(1	NOUN
ejpam-6159	622	7	+	+	CCONJ
ejpam-6159	622	8	iq	iq	NOUN
ejpam-6159	622	9	)	)	PUNCT
ejpam-6159	623	1	+	+	CCONJ
ejpam-6159	623	2	ϱq	ϱq	ADP
ejpam-6159	623	3	qϱ	qϱ	NOUN
ejpam-6159	623	4	)	)	PUNCT
ejpam-6159	623	5	−	−	PROPN
ejpam-6159	623	6	β	β	X
ejpam-6159	623	7	(	(	PUNCT
ejpam-6159	623	8	λ	λ	PROPN
ejpam-6159	623	9	,	,	PUNCT
ejpam-6159	623	10	1	1	NUM
ejpam-6159	623	11	+	+	CCONJ
ejpam-6159	623	12	iq,−(1	iq,−(1	NOUN
ejpam-6159	623	13	+	+	CCONJ
ejpam-6159	623	14	iq	iq	NOUN
ejpam-6159	623	15	)	)	PUNCT
ejpam-6159	624	1	+	+	CCONJ
ejpam-6159	624	2	ϱq	ϱq	ADP
ejpam-6159	624	3	qϱ	qϱ	NOUN
ejpam-6159	624	4	)	)	PUNCT
ejpam-6159	624	5	]	]	PUNCT
ejpam-6159	624	6	.	.	PUNCT
ejpam-6159	625	1	(	(	PUNCT
ejpam-6159	625	2	40	40	NUM
ejpam-6159	625	3	)	)	PUNCT
ejpam-6159	625	4	theorem	theorem	NOUN
ejpam-6159	625	5	8	8	NUM
ejpam-6159	625	6	.	.	PUNCT
ejpam-6159	626	1	suppose	suppose	VERB
ejpam-6159	626	2	f	f	X
ejpam-6159	627	1	:	:	PUNCT
ejpam-6159	627	2	x	x	PUNCT
ejpam-6159	627	3	=	=	PUNCT
ejpam-6159	628	1	[	[	X
ejpam-6159	628	2	a1	a1	NOUN
ejpam-6159	628	3	,	,	PUNCT
ejpam-6159	628	4	a1	a1	NOUN
ejpam-6159	628	5	+	+	CCONJ
ejpam-6159	628	6	ς∗	ς∗	PROPN
ejpam-6159	628	7	(	(	PUNCT
ejpam-6159	628	8	b1	b1	NOUN
ejpam-6159	628	9	,	,	PUNCT
ejpam-6159	628	10	a1	a1	NOUN
ejpam-6159	628	11	)	)	PUNCT
ejpam-6159	628	12	]	]	PUNCT
ejpam-6159	629	1	→	→	PUNCT
ejpam-6159	629	2	ℜ	ℜ	PROPN
ejpam-6159	629	3	is	be	AUX
ejpam-6159	629	4	a	a	DET
ejpam-6159	629	5	twice	twice	ADV
ejpam-6159	629	6	differentiable	differentiable	ADJ
ejpam-6159	629	7	function	function	NOUN
ejpam-6159	629	8	function	function	NOUN
ejpam-6159	629	9	on	on	ADP
ejpam-6159	629	10	xo	xo	PROPN
ejpam-6159	629	11	such	such	ADJ
ejpam-6159	629	12	that	that	SCONJ
ejpam-6159	629	13	f′′	f′′	NOUN
ejpam-6159	629	14	∈	∈	NOUN
ejpam-6159	629	15	l[a1	l[a1	NOUN
ejpam-6159	629	16	,	,	PUNCT
ejpam-6159	629	17	a1+ς∗	a1+ς∗	PROPN
ejpam-6159	629	18	(	(	PUNCT
ejpam-6159	629	19	b1	b1	NOUN
ejpam-6159	629	20	,	,	PUNCT
ejpam-6159	629	21	a1	a1	NOUN
ejpam-6159	629	22	)	)	PUNCT
ejpam-6159	629	23	]	]	PUNCT
ejpam-6159	629	24	and	and	CCONJ
ejpam-6159	629	25	consideration	consideration	NOUN
ejpam-6159	629	26	with	with	ADP
ejpam-6159	629	27	u∗.	u∗.	PROPN
ejpam-6159	629	28	let	let	VERB
ejpam-6159	629	29	for	for	ADP
ejpam-6159	629	30	some	some	PRON
ejpam-6159	629	31	q	q	NOUN
ejpam-6159	629	32	>	>	X
ejpam-6159	629	33	1	1	NUM
ejpam-6159	629	34	,	,	PUNCT
ejpam-6159	629	35	with	with	ADP
ejpam-6159	629	36	1	1	NUM
ejpam-6159	629	37	p	p	NOUN
ejpam-6159	629	38	+	+	NOUN
ejpam-6159	629	39	1	1	NUM
ejpam-6159	629	40	q	q	NOUN
ejpam-6159	629	41	=	=	SYM
ejpam-6159	629	42	1	1	NUM
ejpam-6159	629	43	,	,	PUNCT
ejpam-6159	629	44	|f′′|q	|f′′|q	PRON
ejpam-6159	629	45	be	be	AUX
ejpam-6159	629	46	a	a	DET
ejpam-6159	629	47	gfpp−s	gfpp−s	NOUN
ejpam-6159	629	48	function	function	NOUN
ejpam-6159	629	49	on	on	ADP
ejpam-6159	629	50	x	x	PRON
ejpam-6159	629	51	,	,	PUNCT
ejpam-6159	629	52	for	for	ADP
ejpam-6159	629	53	all	all	DET
ejpam-6159	629	54	x	x	SYM
ejpam-6159	629	55	∈	∈	PROPN
ejpam-6159	629	56	[	[	X
ejpam-6159	629	57	a1	a1	NOUN
ejpam-6159	629	58	,	,	PUNCT
ejpam-6159	629	59	a1	a1	NOUN
ejpam-6159	629	60	+	+	CCONJ
ejpam-6159	629	61	ς∗	ς∗	PROPN
ejpam-6159	629	62	(	(	PUNCT
ejpam-6159	629	63	b1	b1	NOUN
ejpam-6159	629	64	,	,	PUNCT
ejpam-6159	629	65	a1	a1	NOUN
ejpam-6159	629	66	)	)	PUNCT
ejpam-6159	629	67	]	]	PUNCT
ejpam-6159	629	68	.	.	PUNCT
ejpam-6159	630	1	then	then	ADV
ejpam-6159	630	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	630	3	(	(	PUNCT
ejpam-6159	630	4	1−	1−	NUM
ejpam-6159	630	5	λ	λ	NOUN
ejpam-6159	630	6	)	)	PUNCT
ejpam-6159	630	7	[	[	PUNCT
ejpam-6159	630	8	ς	ς	X
ejpam-6159	630	9	ϱ	ϱ	PROPN
ejpam-6159	630	10	k	k	PROPN
ejpam-6159	630	11	∗	∗	X
ejpam-6159	630	12	(	(	PUNCT
ejpam-6159	630	13	b1	b1	NOUN
ejpam-6159	630	14	,	,	PUNCT
ejpam-6159	630	15	x)−	x)−	PROPN
ejpam-6159	630	16	ς	ς	PROPN
ejpam-6159	630	17	ϱ	ϱ	PROPN
ejpam-6159	630	18	k	k	PROPN
ejpam-6159	630	19	∗	∗	X
ejpam-6159	630	20	(	(	PUNCT
ejpam-6159	630	21	x	x	NOUN
ejpam-6159	630	22	,	,	PUNCT
ejpam-6159	630	23	a1	a1	NOUN
ejpam-6159	630	24	)	)	PUNCT
ejpam-6159	630	25	ς∗	ς∗	NOUN
ejpam-6159	630	26	(	(	PUNCT
ejpam-6159	630	27	b1	b1	NOUN
ejpam-6159	630	28	,	,	PUNCT
ejpam-6159	630	29	a1	a1	PROPN
ejpam-6159	630	30	)	)	PUNCT
ejpam-6159	630	31	]	]	PUNCT
ejpam-6159	630	32	f′	f′	PROPN
ejpam-6159	630	33	(	(	PUNCT
ejpam-6159	630	34	x	x	X
ejpam-6159	630	35	)	)	PUNCT
ejpam-6159	630	36	+	+	CCONJ
ejpam-6159	630	37	(	(	PUNCT
ejpam-6159	630	38	1	1	NUM
ejpam-6159	630	39	+	+	CCONJ
ejpam-6159	630	40	ϱ	ϱ	ADP
ejpam-6159	630	41	k	k	X
ejpam-6159	630	42	−	−	PROPN
ejpam-6159	630	43	λ	λ	PROPN
ejpam-6159	630	44	)	)	PUNCT
ejpam-6159	630	45	[	[	PUNCT
ejpam-6159	630	46	ς	ς	PROPN
ejpam-6159	630	47	ϱ	ϱ	PROPN
ejpam-6159	630	48	k	k	PROPN
ejpam-6159	630	49	∗	∗	X
ejpam-6159	630	50	(	(	PUNCT
ejpam-6159	630	51	b1	b1	NOUN
ejpam-6159	630	52	,	,	PUNCT
ejpam-6159	630	53	x	x	X
ejpam-6159	630	54	)	)	PUNCT
ejpam-6159	630	55	+	+	CCONJ
ejpam-6159	630	56	ς	ς	PROPN
ejpam-6159	630	57	ϱ	ϱ	PROPN
ejpam-6159	630	58	k	k	PROPN
ejpam-6159	630	59	∗	∗	X
ejpam-6159	630	60	(	(	PUNCT
ejpam-6159	630	61	x	x	NOUN
ejpam-6159	630	62	,	,	PUNCT
ejpam-6159	630	63	a1	a1	NOUN
ejpam-6159	630	64	)	)	PUNCT
ejpam-6159	630	65	ς∗	ς∗	NOUN
ejpam-6159	630	66	(	(	PUNCT
ejpam-6159	630	67	b1	b1	NOUN
ejpam-6159	630	68	,	,	PUNCT
ejpam-6159	630	69	a1	a1	PROPN
ejpam-6159	630	70	)	)	PUNCT
ejpam-6159	630	71	]	]	PUNCT
ejpam-6159	631	1	f	f	PROPN
ejpam-6159	631	2	(	(	PUNCT
ejpam-6159	631	3	x	x	X
ejpam-6159	631	4	)	)	PUNCT
ejpam-6159	632	1	+	+	NUM
ejpam-6159	632	2	λ	λ	X
ejpam-6159	632	3	[	[	PUNCT
ejpam-6159	632	4	ς	ς	PROPN
ejpam-6159	632	5	ϱ	ϱ	PROPN
ejpam-6159	632	6	k	k	PROPN
ejpam-6159	632	7	∗	∗	X
ejpam-6159	632	8	(	(	PUNCT
ejpam-6159	632	9	b1	b1	NOUN
ejpam-6159	632	10	,	,	PUNCT
ejpam-6159	632	11	x)f	x)f	X
ejpam-6159	632	12	(	(	PUNCT
ejpam-6159	632	13	b1	b1	NOUN
ejpam-6159	632	14	)	)	PUNCT
ejpam-6159	632	15	+	+	CCONJ
ejpam-6159	632	16	ς	ς	PROPN
ejpam-6159	632	17	ϱ	ϱ	PROPN
ejpam-6159	632	18	k	k	PROPN
ejpam-6159	632	19	∗	∗	X
ejpam-6159	632	20	(	(	PUNCT
ejpam-6159	632	21	x	x	X
ejpam-6159	632	22	,	,	PUNCT
ejpam-6159	632	23	a1)f	a1)f	PROPN
ejpam-6159	632	24	(	(	PUNCT
ejpam-6159	632	25	a1	a1	PROPN
ejpam-6159	632	26	)	)	PUNCT
ejpam-6159	632	27	ς∗	ς∗	NOUN
ejpam-6159	632	28	(	(	PUNCT
ejpam-6159	632	29	b1	b1	NOUN
ejpam-6159	632	30	,	,	PUNCT
ejpam-6159	632	31	a1	a1	PROPN
ejpam-6159	632	32	)	)	PUNCT
ejpam-6159	632	33	]	]	PUNCT
ejpam-6159	633	1	−	−	PROPN
ejpam-6159	633	2	γk	γk	X
ejpam-6159	633	3	(	(	PUNCT
ejpam-6159	633	4	ϱ+	ϱ+	NOUN
ejpam-6159	633	5	2k	2k	NUM
ejpam-6159	633	6	)	)	PUNCT
ejpam-6159	633	7	ς∗	ς∗	PROPN
ejpam-6159	633	8	(	(	PUNCT
ejpam-6159	633	9	b1	b1	NOUN
ejpam-6159	633	10	,	,	PUNCT
ejpam-6159	633	11	a1	a1	NOUN
ejpam-6159	633	12	)	)	PUNCT
ejpam-6159	633	13	{	{	PUNCT
ejpam-6159	633	14	jϱ,k	jϱ,k	X
ejpam-6159	633	15	(	(	PUNCT
ejpam-6159	633	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	633	17	,	,	PUNCT
ejpam-6159	633	18	a1	a1	NOUN
ejpam-6159	633	19	)	)	PUNCT
ejpam-6159	633	20	)	)	PUNCT
ejpam-6159	634	1	−	−	PROPN
ejpam-6159	634	2	f	f	X
ejpam-6159	634	3	(	(	PUNCT
ejpam-6159	634	4	a1	a1	PROPN
ejpam-6159	634	5	)	)	PUNCT
ejpam-6159	634	6	+	+	NUM
ejpam-6159	634	7	jϱ,k	jϱ,k	X
ejpam-6159	634	8	(	(	PUNCT
ejpam-6159	634	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	634	10	,	,	PUNCT
ejpam-6159	634	11	b1	b1	NOUN
ejpam-6159	634	12	)	)	PUNCT
ejpam-6159	634	13	)	)	PUNCT
ejpam-6159	635	1	+	+	CCONJ
ejpam-6159	635	2	f	f	X
ejpam-6159	635	3	(	(	PUNCT
ejpam-6159	635	4	b1	b1	PROPN
ejpam-6159	635	5	)	)	PUNCT
ejpam-6159	635	6	}	}	PUNCT
ejpam-6159	635	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	635	8	≤	≤	NUM
ejpam-6159	635	9	m	m	VERB
ejpam-6159	635	10	1	1	NUM
ejpam-6159	635	11	p	p	NOUN
ejpam-6159	635	12	(	(	PUNCT
ejpam-6159	635	13	ϱ,k	ϱ,k	PROPN
ejpam-6159	635	14	,	,	PUNCT
ejpam-6159	635	15	λ	λ	NOUN
ejpam-6159	635	16	)	)	PUNCT
ejpam-6159	635	17	×	×	NOUN
ejpam-6159	635	18	[	[	PUNCT
ejpam-6159	635	19	ς	ς	PROPN
ejpam-6159	635	20	ϱ	ϱ	ADP
ejpam-6159	635	21	k	k	PROPN
ejpam-6159	635	22	+2	+2	PROPN
ejpam-6159	635	23	∗	∗	NOUN
ejpam-6159	635	24	(	(	PUNCT
ejpam-6159	635	25	x	x	NOUN
ejpam-6159	635	26	,	,	PUNCT
ejpam-6159	635	27	a1	a1	NOUN
ejpam-6159	635	28	)	)	PUNCT
ejpam-6159	635	29	ς∗	ς∗	NOUN
ejpam-6159	635	30	(	(	PUNCT
ejpam-6159	635	31	b1	b1	NOUN
ejpam-6159	635	32	,	,	PUNCT
ejpam-6159	635	33	a1	a1	NOUN
ejpam-6159	635	34	)	)	PUNCT
ejpam-6159	635	35	{	{	PUNCT
ejpam-6159	636	1	1∑n	1∑n	NUM
ejpam-6159	636	2	i=1	i=1	PROPN
ejpam-6159	636	3	ai	ai	VERB
ejpam-6159	637	1	n∑	n∑	PROPN
ejpam-6159	637	2	i=1	i=1	PROPN
ejpam-6159	638	1	ai	ai	INTJ
ejpam-6159	638	2	∫	∫	PROPN
ejpam-6159	638	3	1	1	NUM
ejpam-6159	638	4	0	0	NUM
ejpam-6159	638	5	{	{	PUNCT
ejpam-6159	638	6	(	(	PUNCT
ejpam-6159	638	7	1−	1−	NUM
ejpam-6159	638	8	st	st	NOUN
ejpam-6159	638	9	)	)	PUNCT
ejpam-6159	638	10	1	1	NUM
ejpam-6159	639	1	i	i	PRON
ejpam-6159	639	2	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	639	3	(	(	PUNCT
ejpam-6159	639	4	a1	a1	PROPN
ejpam-6159	639	5	)	)	PUNCT
ejpam-6159	639	6	∣∣q	∣∣q	NUM
ejpam-6159	639	7	+	+	CCONJ
ejpam-6159	639	8	(	(	PUNCT
ejpam-6159	639	9	1−	1−	NUM
ejpam-6159	639	10	s	s	X
ejpam-6159	639	11	(	(	PUNCT
ejpam-6159	639	12	1−	1−	NUM
ejpam-6159	639	13	t	t	NOUN
ejpam-6159	639	14	)	)	PUNCT
ejpam-6159	639	15	)	)	PUNCT
ejpam-6159	639	16	1	1	NUM
ejpam-6159	639	17	i	i	PRON
ejpam-6159	639	18	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	639	19	(	(	PUNCT
ejpam-6159	639	20	x	x	NOUN
ejpam-6159	639	21	)	)	PUNCT
ejpam-6159	639	22	∣∣q	∣∣q	NUM
ejpam-6159	639	23	}	}	PUNCT
ejpam-6159	639	24	dt	dt	PROPN
ejpam-6159	639	25	}	}	PUNCT
ejpam-6159	639	26	1	1	NUM
ejpam-6159	639	27	q	q	NOUN
ejpam-6159	639	28	+	+	NUM
ejpam-6159	639	29	ς	ς	PROPN
ejpam-6159	639	30	ϱ	ϱ	ADP
ejpam-6159	639	31	k	k	PROPN
ejpam-6159	639	32	+2	+2	PROPN
ejpam-6159	639	33	∗	∗	NOUN
ejpam-6159	639	34	(	(	PUNCT
ejpam-6159	639	35	x	x	NOUN
ejpam-6159	639	36	,	,	PUNCT
ejpam-6159	639	37	b1	b1	NOUN
ejpam-6159	639	38	)	)	PUNCT
ejpam-6159	639	39	ς∗	ς∗	PROPN
ejpam-6159	639	40	(	(	PUNCT
ejpam-6159	639	41	b1	b1	NOUN
ejpam-6159	639	42	,	,	PUNCT
ejpam-6159	639	43	a1	a1	PROPN
ejpam-6159	639	44	)	)	PUNCT
ejpam-6159	639	45	×	×	NOUN
ejpam-6159	639	46	{	{	PUNCT
ejpam-6159	639	47	1∑n	1∑n	NUM
ejpam-6159	639	48	i=1	i=1	PROPN
ejpam-6159	639	49	ai	ai	VERB
ejpam-6159	639	50	n∑	n∑	PROPN
ejpam-6159	639	51	i=1	i=1	PROPN
ejpam-6159	640	1	ai	ai	INTJ
ejpam-6159	640	2	∫	∫	PROPN
ejpam-6159	640	3	1	1	NUM
ejpam-6159	640	4	0	0	NUM
ejpam-6159	640	5	{	{	PUNCT
ejpam-6159	640	6	(	(	PUNCT
ejpam-6159	640	7	1−	1−	NUM
ejpam-6159	640	8	st	st	NOUN
ejpam-6159	640	9	)	)	PUNCT
ejpam-6159	640	10	1	1	NUM
ejpam-6159	641	1	i	i	PRON
ejpam-6159	641	2	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	641	3	(	(	PUNCT
ejpam-6159	641	4	b1	b1	PROPN
ejpam-6159	641	5	)	)	PUNCT
ejpam-6159	641	6	∣∣q	∣∣q	NUM
ejpam-6159	641	7	+	+	CCONJ
ejpam-6159	641	8	(	(	PUNCT
ejpam-6159	641	9	1−	1−	NUM
ejpam-6159	641	10	s	s	X
ejpam-6159	641	11	(	(	PUNCT
ejpam-6159	641	12	1−	1−	NUM
ejpam-6159	641	13	t	t	NOUN
ejpam-6159	641	14	)	)	PUNCT
ejpam-6159	641	15	)	)	PUNCT
ejpam-6159	641	16	1	1	NUM
ejpam-6159	641	17	i	i	PRON
ejpam-6159	641	18	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	641	19	(	(	PUNCT
ejpam-6159	641	20	x	x	NOUN
ejpam-6159	641	21	)	)	PUNCT
ejpam-6159	641	22	∣∣q	∣∣q	NUM
ejpam-6159	641	23	}	}	PUNCT
ejpam-6159	641	24	dt	dt	PROPN
ejpam-6159	641	25	}	}	PUNCT
ejpam-6159	641	26	1	1	NUM
ejpam-6159	641	27	q	q	NOUN
ejpam-6159	641	28	]	]	PUNCT
ejpam-6159	641	29	.	.	PUNCT
ejpam-6159	642	1	(	(	PUNCT
ejpam-6159	642	2	41	41	NUM
ejpam-6159	642	3	)	)	PUNCT
ejpam-6159	642	4	proof	proof	NOUN
ejpam-6159	642	5	.	.	PUNCT
ejpam-6159	643	1	from	from	ADP
ejpam-6159	643	2	lemma	lemma	PROPN
ejpam-6159	643	3	2	2	NUM
ejpam-6159	643	4	and	and	CCONJ
ejpam-6159	643	5	a	a	DET
ejpam-6159	643	6	propertyiof	propertyiof	NOUN
ejpam-6159	643	7	the	the	DET
ejpam-6159	643	8	gfpp−s	gfpp−s	PROPN
ejpam-6159	643	9	function	function	NOUN
ejpam-6159	643	10	|f′′|q	|f′′|q	PROPN
ejpam-6159	643	11	,	,	PUNCT
ejpam-6159	643	12	and	and	CCONJ
ejpam-6159	643	13	the	the	DET
ejpam-6159	643	14	hölderiinequality	hölderiinequality	NOUN
ejpam-6159	643	15	,	,	PUNCT
ejpam-6159	643	16	one	one	PRON
ejpam-6159	643	17	has	have	VERB
ejpam-6159	643	18	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6159	643	19	(	(	PUNCT
ejpam-6159	643	20	1−	1−	NUM
ejpam-6159	643	21	λ	λ	NOUN
ejpam-6159	643	22	)	)	PUNCT
ejpam-6159	643	23	[	[	PUNCT
ejpam-6159	643	24	ς	ς	X
ejpam-6159	643	25	ϱ	ϱ	PROPN
ejpam-6159	643	26	k	k	PROPN
ejpam-6159	643	27	∗	∗	X
ejpam-6159	643	28	(	(	PUNCT
ejpam-6159	643	29	b1	b1	NOUN
ejpam-6159	643	30	,	,	PUNCT
ejpam-6159	643	31	x)−	x)−	PROPN
ejpam-6159	643	32	ς	ς	PROPN
ejpam-6159	643	33	ϱ	ϱ	PROPN
ejpam-6159	643	34	k	k	PROPN
ejpam-6159	643	35	∗	∗	X
ejpam-6159	643	36	(	(	PUNCT
ejpam-6159	643	37	x	x	NOUN
ejpam-6159	643	38	,	,	PUNCT
ejpam-6159	643	39	a1	a1	NOUN
ejpam-6159	643	40	)	)	PUNCT
ejpam-6159	643	41	ς∗	ς∗	NOUN
ejpam-6159	643	42	(	(	PUNCT
ejpam-6159	643	43	b1	b1	NOUN
ejpam-6159	643	44	,	,	PUNCT
ejpam-6159	643	45	a1	a1	PROPN
ejpam-6159	643	46	)	)	PUNCT
ejpam-6159	643	47	]	]	PUNCT
ejpam-6159	643	48	f′	f′	PROPN
ejpam-6159	643	49	(	(	PUNCT
ejpam-6159	643	50	x	x	X
ejpam-6159	643	51	)	)	PUNCT
ejpam-6159	644	1	+	+	CCONJ
ejpam-6159	644	2	(	(	PUNCT
ejpam-6159	644	3	1	1	NUM
ejpam-6159	644	4	+	+	CCONJ
ejpam-6159	644	5	ϱ	ϱ	ADP
ejpam-6159	644	6	k	k	X
ejpam-6159	644	7	−	−	PROPN
ejpam-6159	644	8	λ	λ	PROPN
ejpam-6159	644	9	)	)	PUNCT
ejpam-6159	644	10	[	[	PUNCT
ejpam-6159	644	11	ς	ς	PROPN
ejpam-6159	644	12	ϱ	ϱ	PROPN
ejpam-6159	644	13	k	k	PROPN
ejpam-6159	644	14	∗	∗	X
ejpam-6159	644	15	(	(	PUNCT
ejpam-6159	644	16	b1	b1	NOUN
ejpam-6159	644	17	,	,	PUNCT
ejpam-6159	644	18	x	x	X
ejpam-6159	644	19	)	)	PUNCT
ejpam-6159	644	20	+	+	CCONJ
ejpam-6159	644	21	ς	ς	PROPN
ejpam-6159	644	22	ϱ	ϱ	PROPN
ejpam-6159	644	23	k	k	PROPN
ejpam-6159	644	24	∗	∗	X
ejpam-6159	644	25	(	(	PUNCT
ejpam-6159	644	26	x	x	NOUN
ejpam-6159	644	27	,	,	PUNCT
ejpam-6159	644	28	a1	a1	NOUN
ejpam-6159	644	29	)	)	PUNCT
ejpam-6159	644	30	ς∗	ς∗	NOUN
ejpam-6159	644	31	(	(	PUNCT
ejpam-6159	644	32	b1	b1	NOUN
ejpam-6159	644	33	,	,	PUNCT
ejpam-6159	644	34	a1	a1	PROPN
ejpam-6159	644	35	)	)	PUNCT
ejpam-6159	644	36	]	]	PUNCT
ejpam-6159	645	1	f	f	PROPN
ejpam-6159	645	2	(	(	PUNCT
ejpam-6159	645	3	x	x	X
ejpam-6159	645	4	)	)	PUNCT
ejpam-6159	646	1	+	+	NUM
ejpam-6159	646	2	λ	λ	X
ejpam-6159	646	3	[	[	PUNCT
ejpam-6159	646	4	ς	ς	PROPN
ejpam-6159	646	5	ϱ	ϱ	PROPN
ejpam-6159	646	6	k	k	PROPN
ejpam-6159	646	7	∗	∗	X
ejpam-6159	646	8	(	(	PUNCT
ejpam-6159	646	9	b1	b1	NOUN
ejpam-6159	646	10	,	,	PUNCT
ejpam-6159	646	11	x)f	x)f	X
ejpam-6159	646	12	(	(	PUNCT
ejpam-6159	646	13	b1	b1	NOUN
ejpam-6159	646	14	)	)	PUNCT
ejpam-6159	646	15	+	+	CCONJ
ejpam-6159	646	16	ς	ς	PROPN
ejpam-6159	646	17	ϱ	ϱ	PROPN
ejpam-6159	646	18	k	k	PROPN
ejpam-6159	646	19	∗	∗	X
ejpam-6159	646	20	(	(	PUNCT
ejpam-6159	646	21	x	x	X
ejpam-6159	646	22	,	,	PUNCT
ejpam-6159	646	23	a1)f	a1)f	PROPN
ejpam-6159	646	24	(	(	PUNCT
ejpam-6159	646	25	a1	a1	PROPN
ejpam-6159	646	26	)	)	PUNCT
ejpam-6159	646	27	ς∗	ς∗	NOUN
ejpam-6159	646	28	(	(	PUNCT
ejpam-6159	646	29	b1	b1	NOUN
ejpam-6159	646	30	,	,	PUNCT
ejpam-6159	646	31	a1	a1	PROPN
ejpam-6159	646	32	)	)	PUNCT
ejpam-6159	646	33	]	]	PUNCT
ejpam-6159	647	1	j.	j.	PROPN
ejpam-6159	647	2	nasir	nasir	PROPN
ejpam-6159	647	3	et	et	PROPN
ejpam-6159	647	4	al	al	PROPN
ejpam-6159	647	5	.	.	PUNCT
ejpam-6159	647	6	/	/	SYM
ejpam-6159	647	7	eur	eur	PROPN
ejpam-6159	647	8	.	.	PUNCT
ejpam-6159	648	1	j.	j.	PROPN
ejpam-6159	648	2	pure	pure	PROPN
ejpam-6159	648	3	appl	appl	PROPN
ejpam-6159	648	4	.	.	PROPN
ejpam-6159	648	5	math	math	PROPN
ejpam-6159	648	6	,	,	PUNCT
ejpam-6159	648	7	18	18	NUM
ejpam-6159	648	8	(	(	PUNCT
ejpam-6159	648	9	3	3	NUM
ejpam-6159	648	10	)	)	PUNCT
ejpam-6159	648	11	(	(	PUNCT
ejpam-6159	648	12	2025	2025	NUM
ejpam-6159	648	13	)	)	PUNCT
ejpam-6159	648	14	,	,	PUNCT
ejpam-6159	648	15	6159	6159	NUM
ejpam-6159	648	16	21	21	NUM
ejpam-6159	648	17	of	of	ADP
ejpam-6159	648	18	26	26	NUM
ejpam-6159	648	19	−	−	NOUN
ejpam-6159	648	20	γk	γk	NOUN
ejpam-6159	648	21	(	(	PUNCT
ejpam-6159	648	22	ϱ+	ϱ+	NOUN
ejpam-6159	648	23	2k	2k	NUM
ejpam-6159	648	24	)	)	PUNCT
ejpam-6159	648	25	ς∗	ς∗	PROPN
ejpam-6159	648	26	(	(	PUNCT
ejpam-6159	648	27	b1	b1	NOUN
ejpam-6159	648	28	,	,	PUNCT
ejpam-6159	648	29	a1	a1	NOUN
ejpam-6159	648	30	)	)	PUNCT
ejpam-6159	648	31	{	{	PUNCT
ejpam-6159	648	32	jϱ,k	jϱ,k	X
ejpam-6159	648	33	(	(	PUNCT
ejpam-6159	648	34	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	648	35	,	,	PUNCT
ejpam-6159	648	36	a1	a1	NOUN
ejpam-6159	648	37	)	)	PUNCT
ejpam-6159	648	38	)	)	PUNCT
ejpam-6159	649	1	−	−	PROPN
ejpam-6159	649	2	f	f	X
ejpam-6159	649	3	(	(	PUNCT
ejpam-6159	649	4	a1	a1	PROPN
ejpam-6159	649	5	)	)	PUNCT
ejpam-6159	649	6	+	+	NUM
ejpam-6159	649	7	jϱ,k	jϱ,k	X
ejpam-6159	649	8	(	(	PUNCT
ejpam-6159	649	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	649	10	,	,	PUNCT
ejpam-6159	649	11	b1	b1	NOUN
ejpam-6159	649	12	)	)	PUNCT
ejpam-6159	649	13	)	)	PUNCT
ejpam-6159	650	1	+	+	CCONJ
ejpam-6159	650	2	f	f	X
ejpam-6159	650	3	(	(	PUNCT
ejpam-6159	650	4	b1	b1	PROPN
ejpam-6159	650	5	)	)	PUNCT
ejpam-6159	650	6	}	}	PUNCT
ejpam-6159	650	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	650	8	≤	≤	NUM
ejpam-6159	650	9	ς	ς	PROPN
ejpam-6159	650	10	ϱ	ϱ	PROPN
ejpam-6159	650	11	k	k	PROPN
ejpam-6159	650	12	+2	+2	PROPN
ejpam-6159	650	13	∗	∗	NOUN
ejpam-6159	650	14	(	(	PUNCT
ejpam-6159	650	15	x	x	NOUN
ejpam-6159	650	16	,	,	PUNCT
ejpam-6159	650	17	a1	a1	NOUN
ejpam-6159	650	18	)	)	PUNCT
ejpam-6159	650	19	ς∗	ς∗	NOUN
ejpam-6159	650	20	(	(	PUNCT
ejpam-6159	650	21	b1	b1	NOUN
ejpam-6159	650	22	,	,	PUNCT
ejpam-6159	650	23	a1	a1	PROPN
ejpam-6159	650	24	)	)	PUNCT
ejpam-6159	650	25	∫	∫	NOUN
ejpam-6159	650	26	1	1	NUM
ejpam-6159	650	27	0	0	NUM
ejpam-6159	650	28	|t	|t	PROPN
ejpam-6159	651	1	(	(	PUNCT
ejpam-6159	651	2	λ−	λ−	PROPN
ejpam-6159	651	3	t	t	PROPN
ejpam-6159	651	4	ϱ	ϱ	PROPN
ejpam-6159	651	5	k	k	PROPN
ejpam-6159	651	6	)	)	PUNCT
ejpam-6159	651	7	||f′′	||f′′	PROPN
ejpam-6159	651	8	(	(	PUNCT
ejpam-6159	651	9	a1	a1	NOUN
ejpam-6159	651	10	+	+	CCONJ
ejpam-6159	651	11	tς∗	tς∗	X
ejpam-6159	651	12	(	(	PUNCT
ejpam-6159	651	13	x	x	NOUN
ejpam-6159	651	14	,	,	PUNCT
ejpam-6159	651	15	a1	a1	NOUN
ejpam-6159	651	16	)	)	PUNCT
ejpam-6159	651	17	)	)	PUNCT
ejpam-6159	652	1	|dt	|dt	PROPN
ejpam-6159	653	1	+	+	X
ejpam-6159	653	2	ς	ς	PROPN
ejpam-6159	653	3	ϱ	ϱ	ADP
ejpam-6159	653	4	k	k	PROPN
ejpam-6159	653	5	+2	+2	PROPN
ejpam-6159	653	6	∗	∗	NOUN
ejpam-6159	653	7	(	(	PUNCT
ejpam-6159	653	8	b1	b1	NOUN
ejpam-6159	653	9	,	,	PUNCT
ejpam-6159	653	10	x	x	NOUN
ejpam-6159	653	11	)	)	PUNCT
ejpam-6159	653	12	ς∗	ς∗	PROPN
ejpam-6159	653	13	(	(	PUNCT
ejpam-6159	653	14	b1	b1	NOUN
ejpam-6159	653	15	,	,	PUNCT
ejpam-6159	653	16	a1	a1	PROPN
ejpam-6159	653	17	)	)	PUNCT
ejpam-6159	653	18	∫	∫	NOUN
ejpam-6159	653	19	1	1	NUM
ejpam-6159	653	20	0	0	NUM
ejpam-6159	653	21	|t	|t	PROPN
ejpam-6159	653	22	(	(	PUNCT
ejpam-6159	653	23	λ−	λ−	PROPN
ejpam-6159	653	24	t	t	PROPN
ejpam-6159	653	25	ϱ	ϱ	PROPN
ejpam-6159	653	26	k	k	PROPN
ejpam-6159	653	27	)	)	PUNCT
ejpam-6159	653	28	||f′′	||f′′	PROPN
ejpam-6159	653	29	(	(	PUNCT
ejpam-6159	653	30	b1	b1	NOUN
ejpam-6159	653	31	+	+	CCONJ
ejpam-6159	653	32	tς∗	tς∗	X
ejpam-6159	653	33	(	(	PUNCT
ejpam-6159	653	34	x	x	NOUN
ejpam-6159	653	35	,	,	PUNCT
ejpam-6159	653	36	b1	b1	NOUN
ejpam-6159	653	37	)	)	PUNCT
ejpam-6159	653	38	)	)	PUNCT
ejpam-6159	653	39	|dt	|dt	PROPN
ejpam-6159	653	40	(	(	PUNCT
ejpam-6159	653	41	42	42	NUM
ejpam-6159	653	42	)	)	PUNCT
ejpam-6159	653	43	≤	≤	NOUN
ejpam-6159	653	44	(	(	PUNCT
ejpam-6159	653	45	∫	∫	PROPN
ejpam-6159	653	46	1	1	NUM
ejpam-6159	653	47	0	0	PROPN
ejpam-6159	653	48	∣∣∣t(λ−	∣∣∣t(λ−	PROPN
ejpam-6159	653	49	t	t	PROPN
ejpam-6159	653	50	ϱ	ϱ	PROPN
ejpam-6159	653	51	k	k	X
ejpam-6159	653	52	)	)	PUNCT
ejpam-6159	653	53	∣∣∣p	∣∣∣p	NOUN
ejpam-6159	653	54	dt	dt	PROPN
ejpam-6159	653	55	)	)	PUNCT
ejpam-6159	653	56	1	1	NUM
ejpam-6159	653	57	p	p	NOUN
ejpam-6159	653	58	×	×	NOUN
ejpam-6159	653	59	[	[	PUNCT
ejpam-6159	653	60	ς	ς	PROPN
ejpam-6159	653	61	ϱ	ϱ	ADP
ejpam-6159	653	62	k	k	PROPN
ejpam-6159	653	63	+2	+2	PROPN
ejpam-6159	653	64	∗	∗	NOUN
ejpam-6159	653	65	(	(	PUNCT
ejpam-6159	653	66	x	x	NOUN
ejpam-6159	653	67	,	,	PUNCT
ejpam-6159	653	68	a1	a1	NOUN
ejpam-6159	653	69	)	)	PUNCT
ejpam-6159	653	70	ς∗	ς∗	NOUN
ejpam-6159	653	71	(	(	PUNCT
ejpam-6159	653	72	b1	b1	NOUN
ejpam-6159	653	73	,	,	PUNCT
ejpam-6159	653	74	a1	a1	PROPN
ejpam-6159	653	75	)	)	PUNCT
ejpam-6159	653	76	{	{	PUNCT
ejpam-6159	653	77	∫	∫	PROPN
ejpam-6159	653	78	1	1	NUM
ejpam-6159	653	79	0	0	NUM
ejpam-6159	654	1	{	{	PUNCT
ejpam-6159	654	2	∑n	∑n	PROPN
ejpam-6159	654	3	i=1	i=1	PROPN
ejpam-6159	654	4	ai	ai	PROPN
ejpam-6159	654	5	(	(	PUNCT
ejpam-6159	654	6	1−	1−	NUM
ejpam-6159	654	7	st	st	NOUN
ejpam-6159	654	8	)	)	PUNCT
ejpam-6159	654	9	1	1	NUM
ejpam-6159	654	10	i∑n	i∑n	PROPN
ejpam-6159	654	11	i=1	i=1	PROPN
ejpam-6159	654	12	ai	ai	VERB
ejpam-6159	654	13	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	654	14	(	(	PUNCT
ejpam-6159	654	15	a1	a1	PROPN
ejpam-6159	654	16	)	)	PUNCT
ejpam-6159	654	17	∣∣q	∣∣q	NUM
ejpam-6159	655	1	+	+	NUM
ejpam-6159	655	2	∑n	∑n	PROPN
ejpam-6159	655	3	i=1	i=1	PROPN
ejpam-6159	655	4	ai	ai	VERB
ejpam-6159	655	5	(	(	PUNCT
ejpam-6159	655	6	1−	1−	NUM
ejpam-6159	655	7	s	s	X
ejpam-6159	655	8	(	(	PUNCT
ejpam-6159	655	9	1−	1−	NUM
ejpam-6159	655	10	t	t	NOUN
ejpam-6159	655	11	)	)	PUNCT
ejpam-6159	655	12	)	)	PUNCT
ejpam-6159	655	13	1	1	NUM
ejpam-6159	655	14	i∑n	i∑n	PROPN
ejpam-6159	655	15	i=1	i=1	PROPN
ejpam-6159	655	16	ai	ai	VERB
ejpam-6159	655	17	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	655	18	(	(	PUNCT
ejpam-6159	655	19	x	x	NOUN
ejpam-6159	655	20	)	)	PUNCT
ejpam-6159	655	21	∣∣q	∣∣q	NUM
ejpam-6159	655	22	}	}	PUNCT
ejpam-6159	655	23	dt	dt	PROPN
ejpam-6159	655	24	}	}	PUNCT
ejpam-6159	655	25	1	1	NUM
ejpam-6159	655	26	q	q	NOUN
ejpam-6159	656	1	+	+	NUM
ejpam-6159	656	2	ς	ς	PROPN
ejpam-6159	656	3	ϱ	ϱ	PROPN
ejpam-6159	656	4	k	k	PROPN
ejpam-6159	656	5	+1	+1	PROPN
ejpam-6159	656	6	∗	∗	NOUN
ejpam-6159	656	7	(	(	PUNCT
ejpam-6159	656	8	x	x	NOUN
ejpam-6159	656	9	,	,	PUNCT
ejpam-6159	656	10	b1	b1	NOUN
ejpam-6159	656	11	)	)	PUNCT
ejpam-6159	656	12	ς∗	ς∗	PROPN
ejpam-6159	656	13	(	(	PUNCT
ejpam-6159	656	14	b1	b1	NOUN
ejpam-6159	656	15	,	,	PUNCT
ejpam-6159	656	16	a1	a1	PROPN
ejpam-6159	656	17	)	)	PUNCT
ejpam-6159	656	18	{	{	PUNCT
ejpam-6159	656	19	∫	∫	PROPN
ejpam-6159	656	20	1	1	NUM
ejpam-6159	656	21	0	0	NUM
ejpam-6159	656	22	{	{	PUNCT
ejpam-6159	656	23	∑n	∑n	PROPN
ejpam-6159	656	24	i=1	i=1	PROPN
ejpam-6159	656	25	ai	ai	VERB
ejpam-6159	656	26	(	(	PUNCT
ejpam-6159	656	27	1−	1−	NUM
ejpam-6159	656	28	st	st	NOUN
ejpam-6159	656	29	)	)	PUNCT
ejpam-6159	656	30	1	1	NUM
ejpam-6159	656	31	i∑n	i∑n	PROPN
ejpam-6159	656	32	i=1	i=1	PROPN
ejpam-6159	656	33	ai	ai	VERB
ejpam-6159	656	34	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	656	35	(	(	PUNCT
ejpam-6159	656	36	b1	b1	PROPN
ejpam-6159	656	37	)	)	PUNCT
ejpam-6159	656	38	∣∣q	∣∣q	NUM
ejpam-6159	657	1	+	+	NUM
ejpam-6159	657	2	∑n	∑n	PROPN
ejpam-6159	657	3	i=1	i=1	PROPN
ejpam-6159	657	4	ai	ai	VERB
ejpam-6159	657	5	(	(	PUNCT
ejpam-6159	657	6	1−	1−	NUM
ejpam-6159	657	7	s	s	X
ejpam-6159	657	8	(	(	PUNCT
ejpam-6159	657	9	1−	1−	NUM
ejpam-6159	657	10	t	t	NOUN
ejpam-6159	657	11	)	)	PUNCT
ejpam-6159	657	12	)	)	PUNCT
ejpam-6159	657	13	1	1	NUM
ejpam-6159	657	14	i∑n	i∑n	PROPN
ejpam-6159	657	15	i=1	i=1	PROPN
ejpam-6159	657	16	ai	ai	VERB
ejpam-6159	657	17	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	657	18	(	(	PUNCT
ejpam-6159	657	19	x	x	NOUN
ejpam-6159	657	20	)	)	PUNCT
ejpam-6159	657	21	∣∣q}dt	∣∣q}dt	NOUN
ejpam-6159	657	22	}	}	PUNCT
ejpam-6159	657	23	1	1	NUM
ejpam-6159	657	24	q	q	NOUN
ejpam-6159	657	25	]	]	PUNCT
ejpam-6159	657	26	(	(	PUNCT
ejpam-6159	657	27	43	43	NUM
ejpam-6159	657	28	)	)	PUNCT
ejpam-6159	657	29	≤	≤	NUM
ejpam-6159	657	30	m	m	VERB
ejpam-6159	657	31	1	1	NUM
ejpam-6159	657	32	p	p	NOUN
ejpam-6159	657	33	(	(	PUNCT
ejpam-6159	657	34	ϱ,k	ϱ,k	PROPN
ejpam-6159	657	35	,	,	PUNCT
ejpam-6159	657	36	λ	λ	NOUN
ejpam-6159	657	37	)	)	PUNCT
ejpam-6159	657	38	×	×	NOUN
ejpam-6159	657	39	[	[	PUNCT
ejpam-6159	657	40	ς	ς	PROPN
ejpam-6159	657	41	ϱ	ϱ	ADP
ejpam-6159	657	42	k	k	PROPN
ejpam-6159	657	43	+2	+2	PROPN
ejpam-6159	657	44	∗	∗	NOUN
ejpam-6159	657	45	(	(	PUNCT
ejpam-6159	657	46	x	x	NOUN
ejpam-6159	657	47	,	,	PUNCT
ejpam-6159	657	48	a1	a1	NOUN
ejpam-6159	657	49	)	)	PUNCT
ejpam-6159	657	50	ς∗	ς∗	NOUN
ejpam-6159	657	51	(	(	PUNCT
ejpam-6159	657	52	b1	b1	NOUN
ejpam-6159	657	53	,	,	PUNCT
ejpam-6159	657	54	a1	a1	NOUN
ejpam-6159	657	55	)	)	PUNCT
ejpam-6159	657	56	{	{	PUNCT
ejpam-6159	658	1	1∑n	1∑n	NUM
ejpam-6159	658	2	i=1	i=1	PROPN
ejpam-6159	658	3	ai	ai	VERB
ejpam-6159	659	1	n∑	n∑	PROPN
ejpam-6159	659	2	i=1	i=1	PROPN
ejpam-6159	660	1	ai	ai	INTJ
ejpam-6159	660	2	∫	∫	PROPN
ejpam-6159	660	3	1	1	NUM
ejpam-6159	660	4	0	0	NUM
ejpam-6159	660	5	{	{	PUNCT
ejpam-6159	660	6	(	(	PUNCT
ejpam-6159	660	7	1−	1−	NUM
ejpam-6159	660	8	st	st	NOUN
ejpam-6159	660	9	)	)	PUNCT
ejpam-6159	660	10	1	1	NUM
ejpam-6159	661	1	i	i	PRON
ejpam-6159	661	2	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	661	3	(	(	PUNCT
ejpam-6159	661	4	a1	a1	PROPN
ejpam-6159	661	5	)	)	PUNCT
ejpam-6159	661	6	∣∣q	∣∣q	NUM
ejpam-6159	661	7	+	+	CCONJ
ejpam-6159	661	8	(	(	PUNCT
ejpam-6159	661	9	1−	1−	NUM
ejpam-6159	661	10	s	s	X
ejpam-6159	661	11	(	(	PUNCT
ejpam-6159	661	12	1−	1−	NUM
ejpam-6159	661	13	t	t	NOUN
ejpam-6159	661	14	)	)	PUNCT
ejpam-6159	661	15	)	)	PUNCT
ejpam-6159	661	16	1	1	NUM
ejpam-6159	661	17	i	i	PRON
ejpam-6159	661	18	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	661	19	(	(	PUNCT
ejpam-6159	661	20	x	x	NOUN
ejpam-6159	661	21	)	)	PUNCT
ejpam-6159	661	22	∣∣q	∣∣q	NUM
ejpam-6159	661	23	}	}	PUNCT
ejpam-6159	661	24	dt	dt	PROPN
ejpam-6159	661	25	}	}	PUNCT
ejpam-6159	661	26	1	1	NUM
ejpam-6159	661	27	q	q	NOUN
ejpam-6159	661	28	+	+	NUM
ejpam-6159	661	29	ς	ς	PROPN
ejpam-6159	661	30	ϱ	ϱ	ADP
ejpam-6159	661	31	k	k	PROPN
ejpam-6159	661	32	+2	+2	PROPN
ejpam-6159	661	33	∗	∗	NOUN
ejpam-6159	661	34	(	(	PUNCT
ejpam-6159	661	35	x	x	NOUN
ejpam-6159	661	36	,	,	PUNCT
ejpam-6159	661	37	b1	b1	NOUN
ejpam-6159	661	38	)	)	PUNCT
ejpam-6159	661	39	ς∗	ς∗	PROPN
ejpam-6159	661	40	(	(	PUNCT
ejpam-6159	661	41	b1	b1	NOUN
ejpam-6159	661	42	,	,	PUNCT
ejpam-6159	661	43	a1	a1	PROPN
ejpam-6159	661	44	)	)	PUNCT
ejpam-6159	661	45	×	×	NOUN
ejpam-6159	661	46	{	{	PUNCT
ejpam-6159	661	47	1∑n	1∑n	NUM
ejpam-6159	661	48	i=1	i=1	PROPN
ejpam-6159	661	49	ai	ai	VERB
ejpam-6159	661	50	n∑	n∑	PROPN
ejpam-6159	661	51	i=1	i=1	PROPN
ejpam-6159	662	1	ai	ai	INTJ
ejpam-6159	662	2	∫	∫	PROPN
ejpam-6159	662	3	1	1	NUM
ejpam-6159	662	4	0	0	NUM
ejpam-6159	662	5	{	{	PUNCT
ejpam-6159	662	6	(	(	PUNCT
ejpam-6159	662	7	1−	1−	NUM
ejpam-6159	662	8	st	st	NOUN
ejpam-6159	662	9	)	)	PUNCT
ejpam-6159	662	10	1	1	NUM
ejpam-6159	663	1	i	i	PRON
ejpam-6159	663	2	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	663	3	(	(	PUNCT
ejpam-6159	663	4	b1	b1	PROPN
ejpam-6159	663	5	)	)	PUNCT
ejpam-6159	663	6	∣∣q	∣∣q	NUM
ejpam-6159	663	7	+	+	CCONJ
ejpam-6159	663	8	(	(	PUNCT
ejpam-6159	663	9	1−	1−	NUM
ejpam-6159	663	10	s	s	X
ejpam-6159	663	11	(	(	PUNCT
ejpam-6159	663	12	1−	1−	NUM
ejpam-6159	663	13	t	t	NOUN
ejpam-6159	663	14	)	)	PUNCT
ejpam-6159	663	15	)	)	PUNCT
ejpam-6159	663	16	1	1	NUM
ejpam-6159	663	17	i	i	PRON
ejpam-6159	663	18	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	663	19	(	(	PUNCT
ejpam-6159	663	20	x	x	NOUN
ejpam-6159	663	21	)	)	PUNCT
ejpam-6159	663	22	∣∣q	∣∣q	NUM
ejpam-6159	663	23	}	}	PUNCT
ejpam-6159	663	24	dt	dt	PROPN
ejpam-6159	663	25	}	}	PUNCT
ejpam-6159	663	26	1	1	NUM
ejpam-6159	663	27	q	q	NOUN
ejpam-6159	663	28	]	]	PUNCT
ejpam-6159	663	29	.	.	PUNCT
ejpam-6159	664	1	corollary	corollary	ADJ
ejpam-6159	664	2	13	13	NUM
ejpam-6159	664	3	.	.	PUNCT
ejpam-6159	665	1	if	if	SCONJ
ejpam-6159	665	2	one	one	PRON
ejpam-6159	665	3	can	can	AUX
ejpam-6159	665	4	take	take	VERB
ejpam-6159	665	5	s	s	PART
ejpam-6159	665	6	=	=	SYM
ejpam-6159	665	7	1	1	NUM
ejpam-6159	665	8	initheorem	initheorem	VERB
ejpam-6159	665	9	8	8	NUM
ejpam-6159	665	10	,	,	PUNCT
ejpam-6159	665	11	then	then	ADV
ejpam-6159	665	12	we	we	PRON
ejpam-6159	665	13	have	have	VERB
ejpam-6159	665	14	the	the	DET
ejpam-6159	665	15	following	follow	VERB
ejpam-6159	665	16	inequalities	inequality	NOUN
ejpam-6159	665	17	for	for	ADP
ejpam-6159	665	18	gfpp	gfpp	NOUN
ejpam-6159	665	19	function	function	NOUN
ejpam-6159	665	20	with	with	ADP
ejpam-6159	665	21	k−fractional	k−fractional	ADJ
ejpam-6159	665	22	integral	integral	ADJ
ejpam-6159	665	23	operators:∣∣∣∣	operators:∣∣∣∣	ADJ
ejpam-6159	665	24	(	(	PUNCT
ejpam-6159	665	25	1−	1−	NUM
ejpam-6159	665	26	λ	λ	NOUN
ejpam-6159	665	27	)	)	PUNCT
ejpam-6159	665	28	[	[	PUNCT
ejpam-6159	665	29	ς	ς	X
ejpam-6159	665	30	ϱ	ϱ	PROPN
ejpam-6159	665	31	k	k	PROPN
ejpam-6159	665	32	∗	∗	X
ejpam-6159	665	33	(	(	PUNCT
ejpam-6159	665	34	b1	b1	NOUN
ejpam-6159	665	35	,	,	PUNCT
ejpam-6159	665	36	x)−	x)−	PROPN
ejpam-6159	665	37	ς	ς	PROPN
ejpam-6159	665	38	ϱ	ϱ	PROPN
ejpam-6159	665	39	k	k	PROPN
ejpam-6159	665	40	∗	∗	X
ejpam-6159	665	41	(	(	PUNCT
ejpam-6159	665	42	x	x	NOUN
ejpam-6159	665	43	,	,	PUNCT
ejpam-6159	665	44	a1	a1	NOUN
ejpam-6159	665	45	)	)	PUNCT
ejpam-6159	665	46	ς∗	ς∗	NOUN
ejpam-6159	665	47	(	(	PUNCT
ejpam-6159	665	48	b1	b1	NOUN
ejpam-6159	665	49	,	,	PUNCT
ejpam-6159	665	50	a1	a1	PROPN
ejpam-6159	665	51	)	)	PUNCT
ejpam-6159	665	52	]	]	PUNCT
ejpam-6159	665	53	f′	f′	PROPN
ejpam-6159	665	54	(	(	PUNCT
ejpam-6159	665	55	x	x	X
ejpam-6159	665	56	)	)	PUNCT
ejpam-6159	666	1	+	+	CCONJ
ejpam-6159	666	2	(	(	PUNCT
ejpam-6159	666	3	1	1	NUM
ejpam-6159	666	4	+	+	CCONJ
ejpam-6159	666	5	ϱ	ϱ	ADP
ejpam-6159	666	6	k	k	X
ejpam-6159	666	7	−	−	PROPN
ejpam-6159	666	8	λ	λ	PROPN
ejpam-6159	666	9	)	)	PUNCT
ejpam-6159	666	10	[	[	PUNCT
ejpam-6159	666	11	ς	ς	PROPN
ejpam-6159	666	12	ϱ	ϱ	PROPN
ejpam-6159	666	13	k	k	PROPN
ejpam-6159	666	14	∗	∗	X
ejpam-6159	666	15	(	(	PUNCT
ejpam-6159	666	16	b1	b1	NOUN
ejpam-6159	666	17	,	,	PUNCT
ejpam-6159	666	18	x	x	X
ejpam-6159	666	19	)	)	PUNCT
ejpam-6159	666	20	+	+	CCONJ
ejpam-6159	666	21	ς	ς	PROPN
ejpam-6159	666	22	ϱ	ϱ	PROPN
ejpam-6159	666	23	k	k	PROPN
ejpam-6159	666	24	∗	∗	X
ejpam-6159	666	25	(	(	PUNCT
ejpam-6159	666	26	x	x	NOUN
ejpam-6159	666	27	,	,	PUNCT
ejpam-6159	666	28	a1	a1	NOUN
ejpam-6159	666	29	)	)	PUNCT
ejpam-6159	666	30	ς∗	ς∗	NOUN
ejpam-6159	666	31	(	(	PUNCT
ejpam-6159	666	32	b1	b1	NOUN
ejpam-6159	666	33	,	,	PUNCT
ejpam-6159	666	34	a1	a1	PROPN
ejpam-6159	666	35	)	)	PUNCT
ejpam-6159	666	36	]	]	PUNCT
ejpam-6159	667	1	f	f	PROPN
ejpam-6159	667	2	(	(	PUNCT
ejpam-6159	667	3	x	x	X
ejpam-6159	667	4	)	)	PUNCT
ejpam-6159	668	1	+	+	NUM
ejpam-6159	668	2	λ	λ	X
ejpam-6159	668	3	[	[	PUNCT
ejpam-6159	668	4	ς	ς	PROPN
ejpam-6159	668	5	ϱ	ϱ	PROPN
ejpam-6159	668	6	k	k	PROPN
ejpam-6159	668	7	∗	∗	X
ejpam-6159	668	8	(	(	PUNCT
ejpam-6159	668	9	b1	b1	NOUN
ejpam-6159	668	10	,	,	PUNCT
ejpam-6159	668	11	x)f	x)f	X
ejpam-6159	668	12	(	(	PUNCT
ejpam-6159	668	13	b1	b1	NOUN
ejpam-6159	668	14	)	)	PUNCT
ejpam-6159	668	15	+	+	CCONJ
ejpam-6159	668	16	ς	ς	PROPN
ejpam-6159	668	17	ϱ	ϱ	PROPN
ejpam-6159	668	18	k	k	PROPN
ejpam-6159	668	19	∗	∗	X
ejpam-6159	668	20	(	(	PUNCT
ejpam-6159	668	21	x	x	X
ejpam-6159	668	22	,	,	PUNCT
ejpam-6159	668	23	a1)f	a1)f	PROPN
ejpam-6159	668	24	(	(	PUNCT
ejpam-6159	668	25	a1	a1	PROPN
ejpam-6159	668	26	)	)	PUNCT
ejpam-6159	668	27	ς∗	ς∗	NOUN
ejpam-6159	668	28	(	(	PUNCT
ejpam-6159	668	29	b1	b1	NOUN
ejpam-6159	668	30	,	,	PUNCT
ejpam-6159	668	31	a1	a1	PROPN
ejpam-6159	668	32	)	)	PUNCT
ejpam-6159	668	33	]	]	PUNCT
ejpam-6159	669	1	−	−	PROPN
ejpam-6159	669	2	γk	γk	X
ejpam-6159	669	3	(	(	PUNCT
ejpam-6159	669	4	ϱ+	ϱ+	NOUN
ejpam-6159	669	5	2k	2k	NUM
ejpam-6159	669	6	)	)	PUNCT
ejpam-6159	669	7	ς∗	ς∗	PROPN
ejpam-6159	669	8	(	(	PUNCT
ejpam-6159	669	9	b1	b1	NOUN
ejpam-6159	669	10	,	,	PUNCT
ejpam-6159	669	11	a1	a1	NOUN
ejpam-6159	669	12	)	)	PUNCT
ejpam-6159	669	13	{	{	PUNCT
ejpam-6159	669	14	jϱ,k	jϱ,k	X
ejpam-6159	669	15	(	(	PUNCT
ejpam-6159	669	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	669	17	,	,	PUNCT
ejpam-6159	669	18	a1	a1	NOUN
ejpam-6159	669	19	)	)	PUNCT
ejpam-6159	669	20	)	)	PUNCT
ejpam-6159	670	1	−	−	PROPN
ejpam-6159	670	2	f	f	X
ejpam-6159	670	3	(	(	PUNCT
ejpam-6159	670	4	a1	a1	PROPN
ejpam-6159	670	5	)	)	PUNCT
ejpam-6159	670	6	+	+	NUM
ejpam-6159	670	7	jϱ,k	jϱ,k	X
ejpam-6159	670	8	(	(	PUNCT
ejpam-6159	670	9	b1+ς∗(x	b1+ς∗(x	NOUN
ejpam-6159	670	10	,	,	PUNCT
ejpam-6159	670	11	b1	b1	NOUN
ejpam-6159	670	12	)	)	PUNCT
ejpam-6159	670	13	)	)	PUNCT
ejpam-6159	671	1	+	+	CCONJ
ejpam-6159	671	2	f	f	X
ejpam-6159	671	3	(	(	PUNCT
ejpam-6159	671	4	b1	b1	PROPN
ejpam-6159	671	5	)	)	PUNCT
ejpam-6159	671	6	}	}	PUNCT
ejpam-6159	671	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	671	8	j.	j.	PROPN
ejpam-6159	671	9	nasir	nasir	PROPN
ejpam-6159	671	10	et	et	PROPN
ejpam-6159	671	11	al	al	PROPN
ejpam-6159	671	12	.	.	PUNCT
ejpam-6159	671	13	/	/	SYM
ejpam-6159	671	14	eur	eur	PROPN
ejpam-6159	671	15	.	.	PUNCT
ejpam-6159	672	1	j.	j.	PROPN
ejpam-6159	672	2	pure	pure	PROPN
ejpam-6159	672	3	appl	appl	PROPN
ejpam-6159	672	4	.	.	PROPN
ejpam-6159	672	5	math	math	PROPN
ejpam-6159	672	6	,	,	PUNCT
ejpam-6159	672	7	18	18	NUM
ejpam-6159	672	8	(	(	PUNCT
ejpam-6159	672	9	3	3	NUM
ejpam-6159	672	10	)	)	PUNCT
ejpam-6159	672	11	(	(	PUNCT
ejpam-6159	672	12	2025	2025	NUM
ejpam-6159	672	13	)	)	PUNCT
ejpam-6159	672	14	,	,	PUNCT
ejpam-6159	672	15	6159	6159	NUM
ejpam-6159	672	16	22	22	NUM
ejpam-6159	672	17	of	of	ADP
ejpam-6159	672	18	26	26	NUM
ejpam-6159	672	19	≤	≤	NUM
ejpam-6159	672	20	m	m	VERB
ejpam-6159	672	21	1	1	NUM
ejpam-6159	672	22	p	p	NOUN
ejpam-6159	672	23	(	(	PUNCT
ejpam-6159	672	24	ϱ,k	ϱ,k	PROPN
ejpam-6159	672	25	,	,	PUNCT
ejpam-6159	672	26	λ	λ	NOUN
ejpam-6159	672	27	)	)	PUNCT
ejpam-6159	672	28	×	×	NOUN
ejpam-6159	672	29	[	[	PUNCT
ejpam-6159	672	30	ς	ς	PROPN
ejpam-6159	672	31	ϱ	ϱ	ADP
ejpam-6159	672	32	k	k	PROPN
ejpam-6159	672	33	+2	+2	PROPN
ejpam-6159	672	34	∗	∗	NOUN
ejpam-6159	672	35	(	(	PUNCT
ejpam-6159	672	36	x	x	NOUN
ejpam-6159	672	37	,	,	PUNCT
ejpam-6159	672	38	a1	a1	NOUN
ejpam-6159	672	39	)	)	PUNCT
ejpam-6159	672	40	ς∗	ς∗	NOUN
ejpam-6159	672	41	(	(	PUNCT
ejpam-6159	672	42	b1	b1	NOUN
ejpam-6159	672	43	,	,	PUNCT
ejpam-6159	672	44	a1	a1	NOUN
ejpam-6159	672	45	)	)	PUNCT
ejpam-6159	672	46	{	{	PUNCT
ejpam-6159	673	1	1∑n	1∑n	NUM
ejpam-6159	673	2	i=1	i=1	PROPN
ejpam-6159	673	3	ai	ai	VERB
ejpam-6159	674	1	n∑	n∑	PROPN
ejpam-6159	674	2	i=1	i=1	PROPN
ejpam-6159	675	1	ai	ai	INTJ
ejpam-6159	675	2	∫	∫	PROPN
ejpam-6159	675	3	1	1	NUM
ejpam-6159	675	4	0	0	NUM
ejpam-6159	675	5	{	{	PUNCT
ejpam-6159	675	6	(	(	PUNCT
ejpam-6159	675	7	1−	1−	NUM
ejpam-6159	675	8	t	t	NOUN
ejpam-6159	675	9	)	)	PUNCT
ejpam-6159	675	10	1	1	NUM
ejpam-6159	676	1	i	i	PRON
ejpam-6159	676	2	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	676	3	(	(	PUNCT
ejpam-6159	676	4	a1	a1	PROPN
ejpam-6159	676	5	)	)	PUNCT
ejpam-6159	676	6	∣∣q	∣∣q	NUM
ejpam-6159	677	1	+	+	NUM
ejpam-6159	677	2	t	t	PROPN
ejpam-6159	677	3	1	1	NUM
ejpam-6159	677	4	i	i	NOUN
ejpam-6159	677	5	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	677	6	(	(	PUNCT
ejpam-6159	677	7	x	x	NOUN
ejpam-6159	677	8	)	)	PUNCT
ejpam-6159	677	9	∣∣q	∣∣q	NUM
ejpam-6159	677	10	}	}	PUNCT
ejpam-6159	677	11	dt	dt	PROPN
ejpam-6159	677	12	}	}	PUNCT
ejpam-6159	677	13	1	1	NUM
ejpam-6159	677	14	q	q	NOUN
ejpam-6159	678	1	+	+	NUM
ejpam-6159	678	2	ς	ς	PROPN
ejpam-6159	678	3	ϱ	ϱ	ADP
ejpam-6159	678	4	k	k	PROPN
ejpam-6159	678	5	+2	+2	PROPN
ejpam-6159	678	6	∗	∗	NOUN
ejpam-6159	678	7	(	(	PUNCT
ejpam-6159	678	8	x	x	NOUN
ejpam-6159	678	9	,	,	PUNCT
ejpam-6159	678	10	b1	b1	NOUN
ejpam-6159	678	11	)	)	PUNCT
ejpam-6159	678	12	ς∗	ς∗	PROPN
ejpam-6159	678	13	(	(	PUNCT
ejpam-6159	678	14	b1	b1	NOUN
ejpam-6159	678	15	,	,	PUNCT
ejpam-6159	678	16	a1	a1	NOUN
ejpam-6159	678	17	)	)	PUNCT
ejpam-6159	678	18	{	{	PUNCT
ejpam-6159	679	1	1∑n	1∑n	NUM
ejpam-6159	679	2	i=1	i=1	PROPN
ejpam-6159	679	3	ai	ai	VERB
ejpam-6159	680	1	n∑	n∑	PROPN
ejpam-6159	680	2	i=1	i=1	PROPN
ejpam-6159	681	1	ai	ai	INTJ
ejpam-6159	681	2	∫	∫	PROPN
ejpam-6159	681	3	1	1	NUM
ejpam-6159	681	4	0	0	NUM
ejpam-6159	681	5	{	{	PUNCT
ejpam-6159	681	6	(	(	PUNCT
ejpam-6159	681	7	1−	1−	NUM
ejpam-6159	681	8	t	t	NOUN
ejpam-6159	681	9	)	)	PUNCT
ejpam-6159	681	10	1	1	NUM
ejpam-6159	681	11	i	i	PRON
ejpam-6159	681	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	681	13	(	(	PUNCT
ejpam-6159	681	14	b1	b1	PROPN
ejpam-6159	681	15	)	)	PUNCT
ejpam-6159	681	16	∣∣q	∣∣q	PROPN
ejpam-6159	682	1	+	+	NUM
ejpam-6159	682	2	t	t	PROPN
ejpam-6159	682	3	1	1	NUM
ejpam-6159	682	4	i	i	NOUN
ejpam-6159	682	5	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	682	6	(	(	PUNCT
ejpam-6159	682	7	x	x	NOUN
ejpam-6159	682	8	)	)	PUNCT
ejpam-6159	682	9	∣∣q	∣∣q	NUM
ejpam-6159	682	10	}	}	PUNCT
ejpam-6159	682	11	dt	dt	PROPN
ejpam-6159	682	12	}	}	PUNCT
ejpam-6159	682	13	1	1	NUM
ejpam-6159	682	14	q	q	NOUN
ejpam-6159	682	15	]	]	PUNCT
ejpam-6159	682	16	.	.	PUNCT
ejpam-6159	683	1	corollary	corollary	ADJ
ejpam-6159	683	2	14	14	NUM
ejpam-6159	683	3	.	.	PUNCT
ejpam-6159	684	1	if	if	SCONJ
ejpam-6159	684	2	one	one	PRON
ejpam-6159	684	3	can	can	AUX
ejpam-6159	684	4	take	take	VERB
ejpam-6159	684	5	k	k	NOUN
ejpam-6159	684	6	=	=	PUNCT
ejpam-6159	684	7	1	1	NUM
ejpam-6159	684	8	in	in	ADP
ejpam-6159	684	9	corollary	corollary	ADJ
ejpam-6159	684	10	13	13	NUM
ejpam-6159	684	11	,	,	PUNCT
ejpam-6159	684	12	then	then	ADV
ejpam-6159	684	13	we	we	PRON
ejpam-6159	684	14	have	have	VERB
ejpam-6159	684	15	the	the	DET
ejpam-6159	684	16	following	follow	VERB
ejpam-6159	684	17	inequalities	inequality	NOUN
ejpam-6159	684	18	for	for	ADP
ejpam-6159	684	19	gfpp	gfpp	NOUN
ejpam-6159	684	20	function	function	NOUN
ejpam-6159	684	21	with	with	ADP
ejpam-6159	684	22	rl−fractional	rl−fractional	ADJ
ejpam-6159	684	23	integral	integral	ADJ
ejpam-6159	684	24	operators:∣∣∣∣	operators:∣∣∣∣	ADJ
ejpam-6159	684	25	(	(	PUNCT
ejpam-6159	684	26	1−	1−	NUM
ejpam-6159	684	27	λ	λ	NOUN
ejpam-6159	684	28	)	)	PUNCT
ejpam-6159	684	29	[	[	PUNCT
ejpam-6159	684	30	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	684	31	(	(	PUNCT
ejpam-6159	684	32	b1	b1	NOUN
ejpam-6159	684	33	,	,	PUNCT
ejpam-6159	684	34	x)−	x)−	PROPN
ejpam-6159	684	35	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	684	36	(	(	PUNCT
ejpam-6159	684	37	x	x	NOUN
ejpam-6159	684	38	,	,	PUNCT
ejpam-6159	684	39	a1	a1	NOUN
ejpam-6159	684	40	)	)	PUNCT
ejpam-6159	684	41	ς∗	ς∗	NOUN
ejpam-6159	684	42	(	(	PUNCT
ejpam-6159	684	43	b1	b1	NOUN
ejpam-6159	684	44	,	,	PUNCT
ejpam-6159	684	45	a1	a1	PROPN
ejpam-6159	684	46	)	)	PUNCT
ejpam-6159	684	47	]	]	PUNCT
ejpam-6159	684	48	f′	f′	PROPN
ejpam-6159	684	49	(	(	PUNCT
ejpam-6159	684	50	x	x	X
ejpam-6159	684	51	)	)	PUNCT
ejpam-6159	685	1	+	+	CCONJ
ejpam-6159	685	2	(	(	PUNCT
ejpam-6159	685	3	1	1	NUM
ejpam-6159	685	4	+	+	NUM
ejpam-6159	685	5	ϱ−	ϱ−	NOUN
ejpam-6159	685	6	λ	λ	NOUN
ejpam-6159	685	7	)	)	PUNCT
ejpam-6159	685	8	[	[	PUNCT
ejpam-6159	685	9	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	685	10	(	(	PUNCT
ejpam-6159	685	11	b1	b1	NOUN
ejpam-6159	685	12	,	,	PUNCT
ejpam-6159	685	13	x	x	X
ejpam-6159	685	14	)	)	PUNCT
ejpam-6159	686	1	+	+	NUM
ejpam-6159	686	2	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	686	3	(	(	PUNCT
ejpam-6159	686	4	x	x	NOUN
ejpam-6159	686	5	,	,	PUNCT
ejpam-6159	686	6	a1	a1	NOUN
ejpam-6159	686	7	)	)	PUNCT
ejpam-6159	686	8	ς∗	ς∗	NOUN
ejpam-6159	686	9	(	(	PUNCT
ejpam-6159	686	10	b1	b1	NOUN
ejpam-6159	686	11	,	,	PUNCT
ejpam-6159	686	12	a1	a1	PROPN
ejpam-6159	686	13	)	)	PUNCT
ejpam-6159	686	14	]	]	PUNCT
ejpam-6159	687	1	f	f	PROPN
ejpam-6159	687	2	(	(	PUNCT
ejpam-6159	687	3	x	x	X
ejpam-6159	687	4	)	)	PUNCT
ejpam-6159	688	1	+	+	NUM
ejpam-6159	688	2	λ	λ	X
ejpam-6159	688	3	[	[	PUNCT
ejpam-6159	688	4	ςϱ∗	ςϱ∗	PROPN
ejpam-6159	688	5	(	(	PUNCT
ejpam-6159	688	6	b1	b1	NOUN
ejpam-6159	688	7	,	,	PUNCT
ejpam-6159	688	8	x)f	x)f	X
ejpam-6159	688	9	(	(	PUNCT
ejpam-6159	688	10	b1	b1	NOUN
ejpam-6159	688	11	)	)	PUNCT
ejpam-6159	689	1	+	+	NUM
ejpam-6159	689	2	ςϱ∗	ςϱ∗	NOUN
ejpam-6159	689	3	(	(	PUNCT
ejpam-6159	689	4	x	x	X
ejpam-6159	689	5	,	,	PUNCT
ejpam-6159	689	6	a1)f	a1)f	PROPN
ejpam-6159	689	7	(	(	PUNCT
ejpam-6159	689	8	a1	a1	PROPN
ejpam-6159	689	9	)	)	PUNCT
ejpam-6159	689	10	ς∗	ς∗	NOUN
ejpam-6159	689	11	(	(	PUNCT
ejpam-6159	689	12	b1	b1	NOUN
ejpam-6159	689	13	,	,	PUNCT
ejpam-6159	689	14	a1	a1	PROPN
ejpam-6159	689	15	)	)	PUNCT
ejpam-6159	689	16	]	]	PUNCT
ejpam-6159	690	1	−	−	PROPN
ejpam-6159	690	2	γ	γ	X
ejpam-6159	690	3	(	(	PUNCT
ejpam-6159	690	4	ϱ+	ϱ+	X
ejpam-6159	690	5	2	2	X
ejpam-6159	690	6	)	)	PUNCT
ejpam-6159	690	7	ς∗	ς∗	NOUN
ejpam-6159	690	8	(	(	PUNCT
ejpam-6159	690	9	b1	b1	NOUN
ejpam-6159	690	10	,	,	PUNCT
ejpam-6159	690	11	a1	a1	NOUN
ejpam-6159	690	12	)	)	PUNCT
ejpam-6159	690	13	{	{	PUNCT
ejpam-6159	690	14	jϱ	jϱ	NOUN
ejpam-6159	690	15	(	(	PUNCT
ejpam-6159	690	16	a1+ς∗(x	a1+ς∗(x	ADJ
ejpam-6159	690	17	,	,	PUNCT
ejpam-6159	690	18	a1	a1	NOUN
ejpam-6159	690	19	)	)	PUNCT
ejpam-6159	690	20	)	)	PUNCT
ejpam-6159	691	1	−	−	PROPN
ejpam-6159	692	1	f	f	X
ejpam-6159	692	2	(	(	PUNCT
ejpam-6159	692	3	a1	a1	PROPN
ejpam-6159	692	4	)	)	PUNCT
ejpam-6159	692	5	+	+	NUM
ejpam-6159	692	6	jϱ	jϱ	ADJ
ejpam-6159	692	7	(	(	PUNCT
ejpam-6159	692	8	b1+ς∗(x	b1+ς∗(x	PROPN
ejpam-6159	692	9	,	,	PUNCT
ejpam-6159	692	10	b1	b1	NOUN
ejpam-6159	692	11	)	)	PUNCT
ejpam-6159	692	12	)	)	PUNCT
ejpam-6159	693	1	+	+	CCONJ
ejpam-6159	693	2	f	f	X
ejpam-6159	693	3	(	(	PUNCT
ejpam-6159	693	4	b1	b1	PROPN
ejpam-6159	693	5	)	)	PUNCT
ejpam-6159	693	6	}	}	PUNCT
ejpam-6159	693	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6159	693	8	≤	≤	NUM
ejpam-6159	693	9	m	m	VERB
ejpam-6159	693	10	1	1	NUM
ejpam-6159	693	11	p	p	NOUN
ejpam-6159	693	12	(	(	PUNCT
ejpam-6159	693	13	ϱ	ϱ	PROPN
ejpam-6159	693	14	,	,	PUNCT
ejpam-6159	693	15	λ	λ	NOUN
ejpam-6159	693	16	)	)	PUNCT
ejpam-6159	693	17	×	×	NOUN
ejpam-6159	693	18	[	[	PUNCT
ejpam-6159	693	19	ςϱ+2	ςϱ+2	NUM
ejpam-6159	693	20	∗	∗	NOUN
ejpam-6159	693	21	(	(	PUNCT
ejpam-6159	693	22	x	x	NOUN
ejpam-6159	693	23	,	,	PUNCT
ejpam-6159	693	24	a1	a1	NOUN
ejpam-6159	693	25	)	)	PUNCT
ejpam-6159	693	26	ς∗	ς∗	NOUN
ejpam-6159	693	27	(	(	PUNCT
ejpam-6159	693	28	b1	b1	NOUN
ejpam-6159	693	29	,	,	PUNCT
ejpam-6159	693	30	a1	a1	NOUN
ejpam-6159	693	31	)	)	PUNCT
ejpam-6159	693	32	{	{	PUNCT
ejpam-6159	694	1	1∑n	1∑n	NUM
ejpam-6159	694	2	i=1	i=1	PROPN
ejpam-6159	694	3	ai	ai	VERB
ejpam-6159	695	1	n∑	n∑	PROPN
ejpam-6159	695	2	i=1	i=1	PROPN
ejpam-6159	696	1	ai	ai	INTJ
ejpam-6159	696	2	∫	∫	PROPN
ejpam-6159	696	3	1	1	NUM
ejpam-6159	696	4	0	0	NUM
ejpam-6159	696	5	{	{	PUNCT
ejpam-6159	696	6	(	(	PUNCT
ejpam-6159	696	7	1−	1−	NUM
ejpam-6159	696	8	t	t	NOUN
ejpam-6159	696	9	)	)	PUNCT
ejpam-6159	696	10	1	1	NUM
ejpam-6159	697	1	i	i	PRON
ejpam-6159	697	2	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	697	3	(	(	PUNCT
ejpam-6159	697	4	a1	a1	PROPN
ejpam-6159	697	5	)	)	PUNCT
ejpam-6159	697	6	∣∣q	∣∣q	NUM
ejpam-6159	698	1	+	+	NUM
ejpam-6159	698	2	t	t	PROPN
ejpam-6159	698	3	1	1	NUM
ejpam-6159	698	4	i	i	NOUN
ejpam-6159	698	5	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	698	6	(	(	PUNCT
ejpam-6159	698	7	x	x	NOUN
ejpam-6159	698	8	)	)	PUNCT
ejpam-6159	698	9	∣∣q	∣∣q	NUM
ejpam-6159	698	10	}	}	PUNCT
ejpam-6159	698	11	dt	dt	PROPN
ejpam-6159	698	12	}	}	PUNCT
ejpam-6159	698	13	1	1	NUM
ejpam-6159	698	14	q	q	NOUN
ejpam-6159	698	15	+	+	NUM
ejpam-6159	698	16	ςϱ+2	ςϱ+2	NUM
ejpam-6159	698	17	∗	∗	NOUN
ejpam-6159	698	18	(	(	PUNCT
ejpam-6159	698	19	x	x	NOUN
ejpam-6159	698	20	,	,	PUNCT
ejpam-6159	698	21	b1	b1	NOUN
ejpam-6159	698	22	)	)	PUNCT
ejpam-6159	698	23	ς∗	ς∗	PROPN
ejpam-6159	698	24	(	(	PUNCT
ejpam-6159	698	25	b1	b1	NOUN
ejpam-6159	698	26	,	,	PUNCT
ejpam-6159	698	27	a1	a1	NOUN
ejpam-6159	698	28	)	)	PUNCT
ejpam-6159	698	29	{	{	PUNCT
ejpam-6159	699	1	1∑n	1∑n	NUM
ejpam-6159	699	2	i=1	i=1	PROPN
ejpam-6159	699	3	ai	ai	VERB
ejpam-6159	700	1	n∑	n∑	PROPN
ejpam-6159	700	2	i=1	i=1	PROPN
ejpam-6159	701	1	ai	ai	INTJ
ejpam-6159	701	2	∫	∫	PROPN
ejpam-6159	701	3	1	1	NUM
ejpam-6159	701	4	0	0	NUM
ejpam-6159	701	5	{	{	PUNCT
ejpam-6159	701	6	(	(	PUNCT
ejpam-6159	701	7	1−	1−	NUM
ejpam-6159	701	8	t	t	NOUN
ejpam-6159	701	9	)	)	PUNCT
ejpam-6159	701	10	1	1	NUM
ejpam-6159	701	11	i	i	PRON
ejpam-6159	701	12	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	701	13	(	(	PUNCT
ejpam-6159	701	14	b1	b1	PROPN
ejpam-6159	701	15	)	)	PUNCT
ejpam-6159	701	16	∣∣q	∣∣q	PROPN
ejpam-6159	702	1	+	+	NUM
ejpam-6159	702	2	t	t	PROPN
ejpam-6159	702	3	1	1	NUM
ejpam-6159	702	4	i	i	NOUN
ejpam-6159	702	5	∣∣f′′	∣∣f′′	PROPN
ejpam-6159	702	6	(	(	PUNCT
ejpam-6159	702	7	x	x	NOUN
ejpam-6159	702	8	)	)	PUNCT
ejpam-6159	702	9	∣∣q	∣∣q	NUM
ejpam-6159	702	10	}	}	PUNCT
ejpam-6159	702	11	dt	dt	PROPN
ejpam-6159	702	12	}	}	PUNCT
ejpam-6159	702	13	1	1	NUM
ejpam-6159	702	14	q	q	NOUN
ejpam-6159	702	15	]	]	PUNCT
ejpam-6159	702	16	.	.	PUNCT
ejpam-6159	703	1	3	3	X
ejpam-6159	703	2	.	.	X
ejpam-6159	703	3	application	application	NOUN
ejpam-6159	703	4	to	to	ADP
ejpam-6159	703	5	matrices	matrix	NOUN
ejpam-6159	703	6	example	example	NOUN
ejpam-6159	703	7	:	:	PUNCT
ejpam-6159	703	8	denote	denote	VERB
ejpam-6159	703	9	by	by	ADP
ejpam-6159	703	10	pn	pn	PROPN
ejpam-6159	703	11	the	the	DET
ejpam-6159	703	12	set	set	NOUN
ejpam-6159	703	13	of	of	ADP
ejpam-6159	703	14	n×	n×	PROPN
ejpam-6159	703	15	n	n	NOUN
ejpam-6159	703	16	compleximatrices	compleximatrice	NOUN
ejpam-6159	703	17	,	,	PUNCT
ejpam-6159	703	18	by	by	ADP
ejpam-6159	703	19	nn	nn	INTJ
ejpam-6159	703	20	the	the	DET
ejpam-6159	703	21	algebra	algebra	NOUN
ejpam-6159	703	22	of	of	ADP
ejpam-6159	703	23	n×	n×	PROPN
ejpam-6159	703	24	n	n	PRON
ejpam-6159	703	25	complex	complex	ADJ
ejpam-6159	703	26	matrices	matrix	NOUN
ejpam-6159	703	27	,	,	PUNCT
ejpam-6159	703	28	and	and	CCONJ
ejpam-6159	703	29	by	by	ADP
ejpam-6159	703	30	n+	n+	NUM
ejpam-6159	703	31	n	n	CCONJ
ejpam-6159	703	32	the	the	DET
ejpam-6159	703	33	strictly	strictly	ADV
ejpam-6159	703	34	positiveimatrices	positiveimatrice	NOUN
ejpam-6159	703	35	in	in	ADP
ejpam-6159	703	36	nn	nn	PROPN
ejpam-6159	703	37	.	.	PROPN
ejpam-6159	703	38	that	that	PRON
ejpam-6159	703	39	is	be	AUX
ejpam-6159	703	40	,	,	PUNCT
ejpam-6159	703	41	d	d	PROPN
ejpam-6159	703	42	∈	∈	PROPN
ejpam-6159	703	43	n+	n+	PUNCT
ejpam-6159	703	44	n	n	CCONJ
ejpam-6159	703	45	if	if	SCONJ
ejpam-6159	703	46	⟨dx	⟨dx	NOUN
ejpam-6159	703	47	,	,	PUNCT
ejpam-6159	703	48	x⟩	x⟩	PUNCT
ejpam-6159	703	49	>	>	X
ejpam-6159	703	50	0	0	PUNCT
ejpam-6159	704	1	for	for	ADP
ejpam-6159	704	2	all	all	DET
ejpam-6159	704	3	nonzero	nonzero	NOUN
ejpam-6159	704	4	x	x	SYM
ejpam-6159	704	5	∈	∈	PROPN
ejpam-6159	704	6	ipn	ipn	PROPN
ejpam-6159	704	7	.	.	PUNCT
ejpam-6159	705	1	in	in	ADP
ejpam-6159	705	2	[	[	X
ejpam-6159	705	3	27	27	NUM
ejpam-6159	705	4	]	]	PUNCT
ejpam-6159	705	5	,	,	PUNCT
ejpam-6159	705	6	sababheh	sababheh	PROPN
ejpam-6159	705	7	proved	prove	VERB
ejpam-6159	705	8	that	that	SCONJ
ejpam-6159	705	9	the	the	DET
ejpam-6159	705	10	following	follow	VERB
ejpam-6159	705	11	mapping	mapping	NOUN
ejpam-6159	705	12	f(u	f(u	PROPN
ejpam-6159	705	13	)	)	PUNCT
ejpam-6159	705	14	=	=	PUNCT
ejpam-6159	705	15	∥∥duxb1−u	∥∥duxb1−u	VERB
ejpam-6159	706	1	+	+	ADV
ejpam-6159	706	2	d1−uxbu	d1−uxbu	ADJ
ejpam-6159	706	3	∥∥	∥∥	X
ejpam-6159	706	4	,	,	PUNCT
ejpam-6159	706	5	d	d	PROPN
ejpam-6159	706	6	,	,	PUNCT
ejpam-6159	706	7	ib	ib	PROPN
ejpam-6159	706	8	∈	∈	PROPN
ejpam-6159	706	9	m+	m+	NUM
ejpam-6159	706	10	n	n	NOUN
ejpam-6159	706	11	,	,	PUNCT
ejpam-6159	706	12	ix	ix	PROPN
ejpam-6159	706	13	∈	∈	PROPN
ejpam-6159	706	14	nn	nn	PROPN
ejpam-6159	706	15	isiconvex	isiconvex	NOUN
ejpam-6159	706	16	for	for	ADP
ejpam-6159	706	17	all	all	DET
ejpam-6159	706	18	u	u	NOUN
ejpam-6159	706	19	∈	∈	PROPN
ejpam-6159	707	1	[	[	X
ejpam-6159	707	2	0	0	NUM
ejpam-6159	707	3	,	,	PUNCT
ejpam-6159	707	4	1	1	NUM
ejpam-6159	707	5	]	]	PUNCT
ejpam-6159	707	6	.	.	PUNCT
ejpam-6159	708	1	then	then	ADV
ejpam-6159	708	2	by	by	ADP
ejpam-6159	708	3	using	use	VERB
ejpam-6159	708	4	theorem	theorem	NOUN
ejpam-6159	708	5	2	2	NUM
ejpam-6159	708	6	,	,	PUNCT
ejpam-6159	708	7	we	we	PRON
ejpam-6159	708	8	have	have	VERB
ejpam-6159	708	9	∑n	∑n	PROPN
ejpam-6159	708	10	i=1	i=1	PROPN
ejpam-6159	708	11	ai∑n	ai∑n	PROPN
ejpam-6159	709	1	i=1	i=1	PRON
ejpam-6159	709	2	ai	ai	VERB
ejpam-6159	709	3	(	(	PUNCT
ejpam-6159	709	4	1−	1−	NUM
ejpam-6159	709	5	s	s	NOUN
ejpam-6159	709	6	2	2	NUM
ejpam-6159	709	7	)	)	PUNCT
ejpam-6159	709	8	1	1	NUM
ejpam-6159	710	1	i	i	PRON
ejpam-6159	710	2	×	×	VERB
ejpam-6159	710	3	∥∥∥∥d	∥∥∥∥d	ADP
ejpam-6159	710	4	(	(	PUNCT
ejpam-6159	710	5	2a1+ς∗(b1,a1	2a1+ς∗(b1,a1	NUM
ejpam-6159	710	6	)	)	SYM
ejpam-6159	710	7	2	2	NUM
ejpam-6159	710	8	)	)	PUNCT
ejpam-6159	710	9	xb	xb	PROPN
ejpam-6159	710	10	1−	1−	NUM
ejpam-6159	710	11	(	(	PUNCT
ejpam-6159	710	12	2a1+ς∗(b1,a1	2a1+ς∗(b1,a1	NUM
ejpam-6159	710	13	)	)	PUNCT
ejpam-6159	710	14	2	2	NUM
ejpam-6159	710	15	)	)	PUNCT
ejpam-6159	711	1	+	+	ADP
ejpam-6159	711	2	d	d	PROPN
ejpam-6159	711	3	1−	1−	NUM
ejpam-6159	711	4	(	(	PUNCT
ejpam-6159	711	5	2a1+ς∗(b1,a1	2a1+ς∗(b1,a1	NUM
ejpam-6159	711	6	)	)	PUNCT
ejpam-6159	711	7	2	2	NUM
ejpam-6159	711	8	)	)	PUNCT
ejpam-6159	711	9	xb	xb	PROPN
ejpam-6159	711	10	(	(	PUNCT
ejpam-6159	711	11	2a1+ς∗(b1,a1	2a1+ς∗(b1,a1	NUM
ejpam-6159	711	12	)	)	PUNCT
ejpam-6159	711	13	2	2	NUM
ejpam-6159	711	14	)	)	PUNCT
ejpam-6159	711	15	∥∥∥∥	∥∥∥∥	PUNCT
ejpam-6159	711	16	≤	≤	NUM
ejpam-6159	711	17	γk	γk	X
ejpam-6159	711	18	(	(	PUNCT
ejpam-6159	711	19	ϱ+	ϱ+	X
ejpam-6159	711	20	k	k	NOUN
ejpam-6159	711	21	)	)	PUNCT
ejpam-6159	711	22	ς	ς	PROPN
ejpam-6159	711	23	ϱ	ϱ	PROPN
ejpam-6159	711	24	k	k	PROPN
ejpam-6159	711	25	∗	∗	X
ejpam-6159	711	26	(	(	PUNCT
ejpam-6159	711	27	b1	b1	NOUN
ejpam-6159	711	28	,	,	PUNCT
ejpam-6159	711	29	a1	a1	PROPN
ejpam-6159	711	30	)	)	PUNCT
ejpam-6159	711	31	j.	j.	PROPN
ejpam-6159	711	32	nasir	nasir	PROPN
ejpam-6159	711	33	et	et	PROPN
ejpam-6159	711	34	al	al	PROPN
ejpam-6159	711	35	.	.	PUNCT
ejpam-6159	711	36	/	/	SYM
ejpam-6159	711	37	eur	eur	PROPN
ejpam-6159	711	38	.	.	PUNCT
ejpam-6159	712	1	j.	j.	PROPN
ejpam-6159	712	2	pure	pure	PROPN
ejpam-6159	712	3	appl	appl	PROPN
ejpam-6159	712	4	.	.	PROPN
ejpam-6159	712	5	math	math	PROPN
ejpam-6159	712	6	,	,	PUNCT
ejpam-6159	712	7	18	18	NUM
ejpam-6159	712	8	(	(	PUNCT
ejpam-6159	712	9	3	3	NUM
ejpam-6159	712	10	)	)	PUNCT
ejpam-6159	712	11	(	(	PUNCT
ejpam-6159	712	12	2025	2025	NUM
ejpam-6159	712	13	)	)	PUNCT
ejpam-6159	712	14	,	,	PUNCT
ejpam-6159	712	15	6159	6159	NUM
ejpam-6159	712	16	23	23	NUM
ejpam-6159	712	17	of	of	ADP
ejpam-6159	712	18	26	26	NUM
ejpam-6159	712	19	×	×	NOUN
ejpam-6159	712	20	{	{	PUNCT
ejpam-6159	712	21	jϱ,k	jϱ,k	X
ejpam-6159	712	22	a1	a1	PROPN
ejpam-6159	712	23	+	+	CCONJ
ejpam-6159	712	24	∥∥∥d(a1+ς∗(b1,a1))xb1−(a1+ς∗(b1,a1	∥∥∥d(a1+ς∗(b1,a1))xb1−(a1+ς∗(b1,a1	NUM
ejpam-6159	712	25	)	)	PUNCT
ejpam-6159	712	26	)	)	PUNCT
ejpam-6159	713	1	+	+	ADV
ejpam-6159	713	2	d1−(a1+ς∗(b1,a1))xb(a1+ς∗(b1,a1	d1−(a1+ς∗(b1,a1))xb(a1+ς∗(b1,a1	NUM
ejpam-6159	713	3	)	)	PUNCT
ejpam-6159	713	4	)	)	PUNCT
ejpam-6159	713	5	∥∥∥	∥∥∥	PROPN
ejpam-6159	713	6	+	+	CCONJ
ejpam-6159	713	7	jϱ,k	jϱ,k	X
ejpam-6159	713	8	(	(	PUNCT
ejpam-6159	713	9	a1+ς∗(b1,a1	a1+ς∗(b1,a1	PROPN
ejpam-6159	713	10	)	)	PUNCT
ejpam-6159	713	11	)	)	PUNCT
ejpam-6159	713	12	−	−	ADP
ejpam-6159	714	1	∥∥∥d(a1)xb1−(a1	∥∥∥d(a1)xb1−(a1	NOUN
ejpam-6159	714	2	)	)	PUNCT
ejpam-6159	714	3	+	+	NOUN
ejpam-6159	714	4	d1−(a1)xb(a1	d1−(a1)xb(a1	NOUN
ejpam-6159	714	5	)	)	PUNCT
ejpam-6159	714	6	∥∥∥	∥∥∥	PROPN
ejpam-6159	714	7	}	}	PUNCT
ejpam-6159	714	8	≤	≤	NOUN
ejpam-6159	714	9	[	[	PUNCT
ejpam-6159	714	10	∥∥∥d(a1)xb1−(a1	∥∥∥d(a1)xb1−(a1	NUM
ejpam-6159	714	11	)	)	PUNCT
ejpam-6159	714	12	+	+	NOUN
ejpam-6159	714	13	d1−(a1)xb(a1	d1−(a1)xb(a1	NOUN
ejpam-6159	714	14	)	)	PUNCT
ejpam-6159	714	15	∥∥∥	∥∥∥	PROPN
ejpam-6159	715	1	+	+	CCONJ
ejpam-6159	715	2	∥∥∥d(a1+ς∗(b1,a1))xb1−(a1+ς∗(b1,a1	∥∥∥d(a1+ς∗(b1,a1))xb1−(a1+ς∗(b1,a1	NUM
ejpam-6159	715	3	)	)	PUNCT
ejpam-6159	715	4	)	)	PUNCT
ejpam-6159	716	1	+	+	ADV
ejpam-6159	716	2	d1−(a1+ς∗(b1,a1))xb(a1+ς∗(b1,a1	d1−(a1+ς∗(b1,a1))xb(a1+ς∗(b1,a1	NUM
ejpam-6159	716	3	)	)	PUNCT
ejpam-6159	716	4	)	)	PUNCT
ejpam-6159	716	5	∥∥∥	∥∥∥	PROPN
ejpam-6159	716	6	]	]	PUNCT
ejpam-6159	716	7	×	×	NOUN
ejpam-6159	716	8	∫	∫	PROPN
ejpam-6159	716	9	1	1	NUM
ejpam-6159	716	10	0	0	NUM
ejpam-6159	716	11	t	t	PROPN
ejpam-6159	716	12	ϱ	ϱ	PROPN
ejpam-6159	716	13	k	k	X
ejpam-6159	716	14	−1	−1	NOUN
ejpam-6159	716	15	{	{	PUNCT
ejpam-6159	716	16	∑n	∑n	PROPN
ejpam-6159	716	17	i=1	i=1	PROPN
ejpam-6159	716	18	ai	ai	VERB
ejpam-6159	716	19	(	(	PUNCT
ejpam-6159	716	20	1−	1−	NUM
ejpam-6159	716	21	st	st	NOUN
ejpam-6159	716	22	)	)	PUNCT
ejpam-6159	716	23	1	1	NUM
ejpam-6159	716	24	i∑n	i∑n	PROPN
ejpam-6159	716	25	i=1	i=1	PROPN
ejpam-6159	716	26	ai	ai	VERB
ejpam-6159	717	1	+	+	ADJ
ejpam-6159	717	2	∑n	∑n	PROPN
ejpam-6159	717	3	i=1	i=1	PROPN
ejpam-6159	717	4	ai	ai	VERB
ejpam-6159	717	5	(	(	PUNCT
ejpam-6159	717	6	1−	1−	NUM
ejpam-6159	717	7	s	s	X
ejpam-6159	717	8	(	(	PUNCT
ejpam-6159	717	9	1−	1−	NUM
ejpam-6159	717	10	t	t	NOUN
ejpam-6159	717	11	)	)	PUNCT
ejpam-6159	717	12	)	)	PUNCT
ejpam-6159	717	13	1	1	NUM
ejpam-6159	717	14	i∑n	i∑n	NOUN
ejpam-6159	717	15	i=1	i=1	PROPN
ejpam-6159	717	16	ai	ai	VERB
ejpam-6159	717	17	}	}	PUNCT
ejpam-6159	717	18	dt	dt	PROPN
ejpam-6159	717	19	..	..	PROPN
ejpam-6159	717	20	4	4	X
ejpam-6159	717	21	.	.	PUNCT
ejpam-6159	717	22	applications	application	NOUN
ejpam-6159	717	23	with	with	ADP
ejpam-6159	717	24	bivariates	bivariate	NOUN
ejpam-6159	717	25	in	in	ADP
ejpam-6159	717	26	this	this	DET
ejpam-6159	717	27	section	section	NOUN
ejpam-6159	717	28	,	,	PUNCT
ejpam-6159	717	29	we	we	PRON
ejpam-6159	717	30	recall	recall	VERB
ejpam-6159	717	31	the	the	DET
ejpam-6159	717	32	following	follow	VERB
ejpam-6159	717	33	special	special	ADJ
ejpam-6159	717	34	means	mean	NOUN
ejpam-6159	717	35	of	of	ADP
ejpam-6159	717	36	two	two	NUM
ejpam-6159	717	37	positive	positive	ADJ
ejpam-6159	717	38	numbers	number	NOUN
ejpam-6159	717	39	a1	a1	NOUN
ejpam-6159	717	40	,	,	PUNCT
ejpam-6159	717	41	b1	b1	NOUN
ejpam-6159	717	42	with	with	ADP
ejpam-6159	717	43	a1	a1	NOUN
ejpam-6159	717	44	<	<	X
ejpam-6159	717	45	b1	b1	NOUN
ejpam-6159	717	46	(	(	PUNCT
ejpam-6159	717	47	see	see	VERB
ejpam-6159	717	48	[	[	X
ejpam-6159	717	49	28	28	NUM
ejpam-6159	717	50	]	]	PUNCT
ejpam-6159	717	51	):	):	PUNCT
ejpam-6159	717	52	(	(	PUNCT
ejpam-6159	717	53	i	i	NOUN
ejpam-6159	717	54	)	)	PUNCT
ejpam-6159	717	55	the	the	DET
ejpam-6159	717	56	arithmetic	arithmetic	ADJ
ejpam-6159	717	57	mean	mean	VERB
ejpam-6159	717	58	a	a	DET
ejpam-6159	717	59	=	=	PUNCT
ejpam-6159	717	60	a(a1	a(a1	ADJ
ejpam-6159	717	61	,	,	PUNCT
ejpam-6159	717	62	b1	b1	NOUN
ejpam-6159	717	63	)	)	PUNCT
ejpam-6159	717	64	=	=	SYM
ejpam-6159	717	65	a1	a1	NOUN
ejpam-6159	717	66	+	+	CCONJ
ejpam-6159	717	67	b1	b1	NOUN
ejpam-6159	717	68	2	2	NUM
ejpam-6159	717	69	.	.	PUNCT
ejpam-6159	718	1	(	(	PUNCT
ejpam-6159	718	2	ii	ii	NOUN
ejpam-6159	718	3	)	)	PUNCT
ejpam-6159	718	4	the	the	DET
ejpam-6159	718	5	harmonic	harmonic	ADJ
ejpam-6159	718	6	mean	mean	NOUN
ejpam-6159	718	7	h	h	NOUN
ejpam-6159	719	1	=	=	SYM
ejpam-6159	719	2	h(a1	h(a1	PROPN
ejpam-6159	719	3	,	,	PUNCT
ejpam-6159	719	4	b1	b1	NOUN
ejpam-6159	719	5	)	)	PUNCT
ejpam-6159	719	6	=	=	SYM
ejpam-6159	720	1	2a1b1	2a1b1	NUM
ejpam-6159	720	2	a1	a1	NOUN
ejpam-6159	720	3	+	+	CCONJ
ejpam-6159	720	4	b1	b1	NOUN
ejpam-6159	720	5	.	.	PUNCT
ejpam-6159	721	1	the	the	DET
ejpam-6159	721	2	next	next	ADJ
ejpam-6159	721	3	relationship	relationship	NOUN
ejpam-6159	721	4	is	be	AUX
ejpam-6159	721	5	well	well	ADV
ejpam-6159	721	6	-	-	PUNCT
ejpam-6159	721	7	knowniin	knowniin	VERB
ejpam-6159	721	8	the	the	DET
ejpam-6159	721	9	literature	literature	NOUN
ejpam-6159	721	10	:	:	PUNCT
ejpam-6159	721	11	h(a1	h(a1	PROPN
ejpam-6159	721	12	,	,	PUNCT
ejpam-6159	721	13	b1	b1	PROPN
ejpam-6159	721	14	)	)	PUNCT
ejpam-6159	721	15	≤	≤	NOUN
ejpam-6159	721	16	g(a1	g(a1	PROPN
ejpam-6159	721	17	,	,	PUNCT
ejpam-6159	721	18	b1	b1	NOUN
ejpam-6159	721	19	)	)	PUNCT
ejpam-6159	721	20	≤	≤	NOUN
ejpam-6159	721	21	a(a1	a(a1	NOUN
ejpam-6159	721	22	,	,	PUNCT
ejpam-6159	721	23	b1	b1	NOUN
ejpam-6159	721	24	)	)	PUNCT
ejpam-6159	721	25	.	.	PUNCT
ejpam-6159	722	1	proposition	proposition	NOUN
ejpam-6159	722	2	1	1	NUM
ejpam-6159	722	3	.	.	PUNCT
ejpam-6159	722	4	suppose	suppose	VERB
ejpam-6159	722	5	that	that	SCONJ
ejpam-6159	722	6	0	0	PUNCT
ejpam-6159	722	7	<	<	X
ejpam-6159	722	8	a1	a1	NOUN
ejpam-6159	722	9	<	<	X
ejpam-6159	722	10	b1	b1	NOUN
ejpam-6159	722	11	and	and	CCONJ
ejpam-6159	722	12	s	s	NOUN
ejpam-6159	722	13	∈	∈	PROPN
ejpam-6159	723	1	[	[	X
ejpam-6159	723	2	0	0	NUM
ejpam-6159	723	3	,	,	PUNCT
ejpam-6159	723	4	1	1	NUM
ejpam-6159	723	5	]	]	PUNCT
ejpam-6159	723	6	,	,	PUNCT
ejpam-6159	723	7	then∑n	then∑n	ADP
ejpam-6159	723	8	i=1	i=1	PRON
ejpam-6159	723	9	ai∑n	ai∑n	X
ejpam-6159	724	1	i=1	i=1	PRON
ejpam-6159	724	2	ai	ai	VERB
ejpam-6159	724	3	(	(	PUNCT
ejpam-6159	724	4	1−	1−	NUM
ejpam-6159	724	5	s	s	NOUN
ejpam-6159	724	6	2	2	NUM
ejpam-6159	724	7	)	)	PUNCT
ejpam-6159	724	8	1	1	NUM
ejpam-6159	724	9	i	i	PRON
ejpam-6159	724	10	a(2a1	a(2a1	VERB
ejpam-6159	724	11	,	,	PUNCT
ejpam-6159	724	12	ς∗	ς∗	PROPN
ejpam-6159	724	13	(	(	PUNCT
ejpam-6159	724	14	b1	b1	NOUN
ejpam-6159	724	15	,	,	PUNCT
ejpam-6159	724	16	a1	a1	NOUN
ejpam-6159	724	17	)	)	PUNCT
ejpam-6159	724	18	)	)	PUNCT
ejpam-6159	724	19	≤	≤	NUM
ejpam-6159	724	20	γk	γk	X
ejpam-6159	724	21	(	(	PUNCT
ejpam-6159	724	22	ϱ+	ϱ+	X
ejpam-6159	724	23	k	k	NOUN
ejpam-6159	724	24	)	)	PUNCT
ejpam-6159	724	25	ς	ς	PROPN
ejpam-6159	724	26	ϱ	ϱ	PROPN
ejpam-6159	724	27	k	k	PROPN
ejpam-6159	724	28	∗	∗	X
ejpam-6159	724	29	(	(	PUNCT
ejpam-6159	724	30	b1	b1	NOUN
ejpam-6159	724	31	,	,	PUNCT
ejpam-6159	724	32	a1	a1	NOUN
ejpam-6159	724	33	)	)	PUNCT
ejpam-6159	724	34	{	{	PUNCT
ejpam-6159	724	35	jϱ,k	jϱ,k	X
ejpam-6159	724	36	a1	a1	PROPN
ejpam-6159	724	37	+	+	X
ejpam-6159	724	38	2a	2a	NUM
ejpam-6159	724	39	(	(	PUNCT
ejpam-6159	724	40	a1	a1	NOUN
ejpam-6159	724	41	,	,	PUNCT
ejpam-6159	724	42	ς∗	ς∗	NOUN
ejpam-6159	724	43	(	(	PUNCT
ejpam-6159	724	44	b1	b1	NOUN
ejpam-6159	724	45	,	,	PUNCT
ejpam-6159	724	46	a1	a1	NOUN
ejpam-6159	724	47	)	)	PUNCT
ejpam-6159	724	48	)	)	PUNCT
ejpam-6159	725	1	+	+	CCONJ
ejpam-6159	725	2	jϱ,k	jϱ,k	X
ejpam-6159	725	3	(	(	PUNCT
ejpam-6159	725	4	a1+ς∗(b1,a1	a1+ς∗(b1,a1	PROPN
ejpam-6159	725	5	)	)	PUNCT
ejpam-6159	725	6	)	)	PUNCT
ejpam-6159	726	1	−	−	PROPN
ejpam-6159	726	2	(	(	PUNCT
ejpam-6159	726	3	a1	a1	NOUN
ejpam-6159	726	4	)	)	PUNCT
ejpam-6159	726	5	}	}	PUNCT
ejpam-6159	726	6	≤	≤	NUM
ejpam-6159	726	7	2a	2a	NUM
ejpam-6159	726	8	(	(	PUNCT
ejpam-6159	726	9	a1	a1	NOUN
ejpam-6159	726	10	,	,	PUNCT
ejpam-6159	726	11	a1	a1	NOUN
ejpam-6159	726	12	+	+	CCONJ
ejpam-6159	726	13	ς∗	ς∗	PROPN
ejpam-6159	726	14	(	(	PUNCT
ejpam-6159	726	15	b1	b1	NOUN
ejpam-6159	726	16	,	,	PUNCT
ejpam-6159	726	17	a1	a1	NOUN
ejpam-6159	726	18	)	)	PUNCT
ejpam-6159	726	19	)	)	PUNCT
ejpam-6159	727	1	×	×	NOUN
ejpam-6159	727	2	∫	∫	NOUN
ejpam-6159	727	3	1	1	NUM
ejpam-6159	727	4	0	0	NUM
ejpam-6159	727	5	t	t	PROPN
ejpam-6159	727	6	ϱ	ϱ	PROPN
ejpam-6159	727	7	k	k	X
ejpam-6159	727	8	−1	−1	NOUN
ejpam-6159	727	9	{	{	PUNCT
ejpam-6159	727	10	∑n	∑n	PROPN
ejpam-6159	727	11	i=1	i=1	PROPN
ejpam-6159	727	12	ai	ai	VERB
ejpam-6159	727	13	(	(	PUNCT
ejpam-6159	727	14	1−	1−	NUM
ejpam-6159	727	15	st	st	NOUN
ejpam-6159	727	16	)	)	PUNCT
ejpam-6159	727	17	1	1	NUM
ejpam-6159	727	18	i∑n	i∑n	PROPN
ejpam-6159	727	19	i=1	i=1	PROPN
ejpam-6159	727	20	ai	ai	VERB
ejpam-6159	727	21	+	+	ADJ
ejpam-6159	728	1	∑n	∑n	PROPN
ejpam-6159	728	2	i=1	i=1	PROPN
ejpam-6159	728	3	ai	ai	VERB
ejpam-6159	728	4	(	(	PUNCT
ejpam-6159	728	5	1−	1−	NUM
ejpam-6159	728	6	s	s	X
ejpam-6159	728	7	(	(	PUNCT
ejpam-6159	728	8	1−	1−	NUM
ejpam-6159	728	9	t	t	NOUN
ejpam-6159	728	10	)	)	PUNCT
ejpam-6159	728	11	)	)	PUNCT
ejpam-6159	728	12	1	1	NUM
ejpam-6159	728	13	i∑n	i∑n	NOUN
ejpam-6159	728	14	i=1	i=1	PROPN
ejpam-6159	728	15	ai	ai	VERB
ejpam-6159	728	16	}	}	PUNCT
ejpam-6159	728	17	dt	dt	PROPN
ejpam-6159	728	18	.	.	PUNCT
ejpam-6159	729	1	(	(	PUNCT
ejpam-6159	729	2	44	44	NUM
ejpam-6159	729	3	)	)	PUNCT
ejpam-6159	729	4	proof	proof	NOUN
ejpam-6159	729	5	.	.	PUNCT
ejpam-6159	730	1	we	we	PRON
ejpam-6159	730	2	attain	attain	VERB
ejpam-6159	730	3	the	the	DET
ejpam-6159	730	4	above	above	ADJ
ejpam-6159	730	5	inequality	inequality	NOUN
ejpam-6159	730	6	from	from	ADP
ejpam-6159	730	7	proposition	proposition	NOUN
ejpam-6159	730	8	1	1	NUM
ejpam-6159	730	9	if	if	SCONJ
ejpam-6159	730	10	we	we	PRON
ejpam-6159	730	11	put	put	VERB
ejpam-6159	730	12	f(u	f(u	PROPN
ejpam-6159	730	13	)	)	PUNCT
ejpam-6159	731	1	=	=	SYM
ejpam-6159	731	2	u	u	PROPN
ejpam-6159	731	3	for	for	ADP
ejpam-6159	731	4	u	u	PROPN
ejpam-6159	731	5	>	>	X
ejpam-6159	731	6	0	0	PUNCT
ejpam-6159	731	7	in	in	ADP
ejpam-6159	731	8	theorem	theorem	NOUN
ejpam-6159	731	9	2	2	NUM
ejpam-6159	731	10	.	.	PUNCT
ejpam-6159	732	1	j.	j.	PROPN
ejpam-6159	732	2	nasir	nasir	PROPN
ejpam-6159	732	3	et	et	PROPN
ejpam-6159	732	4	al	al	PROPN
ejpam-6159	732	5	.	.	PUNCT
ejpam-6159	732	6	/	/	SYM
ejpam-6159	732	7	eur	eur	PROPN
ejpam-6159	732	8	.	.	PUNCT
ejpam-6159	733	1	j.	j.	PROPN
ejpam-6159	733	2	pure	pure	PROPN
ejpam-6159	733	3	appl	appl	PROPN
ejpam-6159	733	4	.	.	PROPN
ejpam-6159	733	5	math	math	PROPN
ejpam-6159	733	6	,	,	PUNCT
ejpam-6159	733	7	18	18	NUM
ejpam-6159	733	8	(	(	PUNCT
ejpam-6159	733	9	3	3	NUM
ejpam-6159	733	10	)	)	PUNCT
ejpam-6159	733	11	(	(	PUNCT
ejpam-6159	733	12	2025	2025	NUM
ejpam-6159	733	13	)	)	PUNCT
ejpam-6159	733	14	,	,	PUNCT
ejpam-6159	733	15	6159	6159	NUM
ejpam-6159	733	16	24	24	NUM
ejpam-6159	733	17	of	of	ADP
ejpam-6159	733	18	26	26	NUM
ejpam-6159	733	19	proposition	proposition	NOUN
ejpam-6159	733	20	2	2	NUM
ejpam-6159	733	21	.	.	PUNCT
ejpam-6159	733	22	suppose	suppose	VERB
ejpam-6159	733	23	that	that	SCONJ
ejpam-6159	733	24	0	0	PUNCT
ejpam-6159	733	25	<	<	X
ejpam-6159	733	26	a1	a1	NOUN
ejpam-6159	733	27	<	<	X
ejpam-6159	733	28	b1	b1	NOUN
ejpam-6159	733	29	and	and	CCONJ
ejpam-6159	733	30	s	s	NOUN
ejpam-6159	733	31	∈	∈	PROPN
ejpam-6159	734	1	[	[	X
ejpam-6159	734	2	0	0	NUM
ejpam-6159	734	3	,	,	PUNCT
ejpam-6159	734	4	1	1	NUM
ejpam-6159	734	5	]	]	PUNCT
ejpam-6159	734	6	,	,	PUNCT
ejpam-6159	734	7	then∑n	then∑n	ADP
ejpam-6159	734	8	i=1	i=1	PRON
ejpam-6159	734	9	ai∑n	ai∑n	X
ejpam-6159	735	1	i=1	i=1	PRON
ejpam-6159	735	2	ai	ai	VERB
ejpam-6159	735	3	(	(	PUNCT
ejpam-6159	735	4	1−	1−	NUM
ejpam-6159	735	5	s	s	NOUN
ejpam-6159	735	6	2	2	NUM
ejpam-6159	735	7	)	)	PUNCT
ejpam-6159	735	8	1	1	NUM
ejpam-6159	735	9	i	i	PRON
ejpam-6159	735	10	a−1(2a1	a−1(2a1	VERB
ejpam-6159	735	11	,	,	PUNCT
ejpam-6159	735	12	ς∗	ς∗	PROPN
ejpam-6159	735	13	(	(	PUNCT
ejpam-6159	735	14	b1	b1	NOUN
ejpam-6159	735	15	,	,	PUNCT
ejpam-6159	735	16	a1	a1	NOUN
ejpam-6159	735	17	)	)	PUNCT
ejpam-6159	735	18	)	)	PUNCT
ejpam-6159	735	19	≤	≤	NUM
ejpam-6159	735	20	γk	γk	X
ejpam-6159	735	21	(	(	PUNCT
ejpam-6159	735	22	ϱ+	ϱ+	X
ejpam-6159	735	23	k	k	NOUN
ejpam-6159	735	24	)	)	PUNCT
ejpam-6159	735	25	ς	ς	PROPN
ejpam-6159	735	26	ϱ	ϱ	PROPN
ejpam-6159	735	27	k	k	PROPN
ejpam-6159	735	28	∗	∗	X
ejpam-6159	735	29	(	(	PUNCT
ejpam-6159	735	30	b1	b1	NOUN
ejpam-6159	735	31	,	,	PUNCT
ejpam-6159	735	32	a1	a1	NOUN
ejpam-6159	735	33	)	)	PUNCT
ejpam-6159	735	34	{	{	PUNCT
ejpam-6159	735	35	jϱ,k	jϱ,k	X
ejpam-6159	735	36	a1	a1	PROPN
ejpam-6159	735	37	+	+	X
ejpam-6159	735	38	2a−1	2a−1	NUM
ejpam-6159	735	39	(	(	PUNCT
ejpam-6159	735	40	a1	a1	PROPN
ejpam-6159	735	41	,	,	PUNCT
ejpam-6159	735	42	ς∗	ς∗	NOUN
ejpam-6159	735	43	(	(	PUNCT
ejpam-6159	735	44	b1	b1	NOUN
ejpam-6159	735	45	,	,	PUNCT
ejpam-6159	735	46	a1	a1	NOUN
ejpam-6159	735	47	)	)	PUNCT
ejpam-6159	735	48	)	)	PUNCT
ejpam-6159	736	1	+	+	CCONJ
ejpam-6159	736	2	jϱ,k	jϱ,k	X
ejpam-6159	736	3	(	(	PUNCT
ejpam-6159	736	4	a1+ς∗(b1,a1	a1+ς∗(b1,a1	PROPN
ejpam-6159	736	5	)	)	PUNCT
ejpam-6159	736	6	)	)	PUNCT
ejpam-6159	737	1	−	−	PROPN
ejpam-6159	738	1	(	(	PUNCT
ejpam-6159	738	2	a1	a1	NOUN
ejpam-6159	738	3	−1	−1	NOUN
ejpam-6159	738	4	)	)	PUNCT
ejpam-6159	738	5	}	}	PUNCT
ejpam-6159	738	6	≤	≤	NUM
ejpam-6159	739	1	2h−1	2h−1	NUM
ejpam-6159	739	2	(	(	PUNCT
ejpam-6159	739	3	a1	a1	NOUN
ejpam-6159	739	4	,	,	PUNCT
ejpam-6159	739	5	a1	a1	NOUN
ejpam-6159	739	6	+	+	CCONJ
ejpam-6159	739	7	ς∗	ς∗	PROPN
ejpam-6159	739	8	(	(	PUNCT
ejpam-6159	739	9	b1	b1	NOUN
ejpam-6159	739	10	,	,	PUNCT
ejpam-6159	739	11	a1	a1	NOUN
ejpam-6159	739	12	)	)	PUNCT
ejpam-6159	739	13	)	)	PUNCT
ejpam-6159	740	1	×	×	NOUN
ejpam-6159	740	2	∫	∫	NOUN
ejpam-6159	740	3	1	1	NUM
ejpam-6159	740	4	0	0	NUM
ejpam-6159	740	5	t	t	PROPN
ejpam-6159	740	6	ϱ	ϱ	PROPN
ejpam-6159	740	7	k	k	X
ejpam-6159	740	8	−1	−1	NOUN
ejpam-6159	740	9	{	{	PUNCT
ejpam-6159	740	10	∑n	∑n	PROPN
ejpam-6159	740	11	i=1	i=1	PROPN
ejpam-6159	740	12	ai	ai	VERB
ejpam-6159	740	13	(	(	PUNCT
ejpam-6159	740	14	1−	1−	NUM
ejpam-6159	740	15	st	st	NOUN
ejpam-6159	740	16	)	)	PUNCT
ejpam-6159	740	17	1	1	NUM
ejpam-6159	740	18	i∑n	i∑n	PROPN
ejpam-6159	740	19	i=1	i=1	PROPN
ejpam-6159	740	20	ai	ai	VERB
ejpam-6159	740	21	+	+	ADJ
ejpam-6159	741	1	∑n	∑n	PROPN
ejpam-6159	741	2	i=1	i=1	PROPN
ejpam-6159	741	3	ai	ai	VERB
ejpam-6159	741	4	(	(	PUNCT
ejpam-6159	741	5	1−	1−	NUM
ejpam-6159	741	6	s	s	X
ejpam-6159	741	7	(	(	PUNCT
ejpam-6159	741	8	1−	1−	NUM
ejpam-6159	741	9	t	t	NOUN
ejpam-6159	741	10	)	)	PUNCT
ejpam-6159	741	11	)	)	PUNCT
ejpam-6159	741	12	1	1	NUM
ejpam-6159	741	13	i∑n	i∑n	NOUN
ejpam-6159	741	14	i=1	i=1	PROPN
ejpam-6159	741	15	ai	ai	VERB
ejpam-6159	741	16	}	}	PUNCT
ejpam-6159	741	17	dt	dt	PROPN
ejpam-6159	741	18	.	.	PUNCT
ejpam-6159	742	1	(	(	PUNCT
ejpam-6159	742	2	45	45	NUM
ejpam-6159	742	3	)	)	PUNCT
ejpam-6159	742	4	proof	proof	NOUN
ejpam-6159	742	5	.	.	PUNCT
ejpam-6159	743	1	we	we	PRON
ejpam-6159	743	2	attain	attain	VERB
ejpam-6159	743	3	the	the	DET
ejpam-6159	743	4	above	above	ADJ
ejpam-6159	743	5	inequality	inequality	NOUN
ejpam-6159	743	6	from	from	ADP
ejpam-6159	743	7	proposition	proposition	NOUN
ejpam-6159	743	8	2	2	NUM
ejpam-6159	743	9	if	if	SCONJ
ejpam-6159	743	10	we	we	PRON
ejpam-6159	743	11	put	put	VERB
ejpam-6159	743	12	f(u	f(u	PROPN
ejpam-6159	743	13	)	)	PUNCT
ejpam-6159	743	14	=	=	SYM
ejpam-6159	743	15	1	1	NUM
ejpam-6159	743	16	u	u	NOUN
ejpam-6159	743	17	for	for	ADP
ejpam-6159	743	18	u	u	PROPN
ejpam-6159	743	19	>	>	X
ejpam-6159	743	20	0	0	PUNCT
ejpam-6159	743	21	in	in	ADP
ejpam-6159	743	22	theorem	theorem	NOUN
ejpam-6159	743	23	2	2	NUM
ejpam-6159	743	24	.	.	NOUN
ejpam-6159	743	25	5	5	NUM
ejpam-6159	743	26	.	.	X
ejpam-6159	743	27	conclusion	conclusion	NOUN
ejpam-6159	743	28	in	in	ADP
ejpam-6159	743	29	this	this	DET
ejpam-6159	743	30	article	article	NOUN
ejpam-6159	743	31	,	,	PUNCT
ejpam-6159	743	32	we	we	PRON
ejpam-6159	743	33	introduced	introduce	VERB
ejpam-6159	743	34	a	a	DET
ejpam-6159	743	35	novel	novel	ADJ
ejpam-6159	743	36	fractional	fractional	ADJ
ejpam-6159	743	37	integral	integral	ADJ
ejpam-6159	743	38	operator	operator	NOUN
ejpam-6159	743	39	for	for	ADP
ejpam-6159	743	40	functions	function	NOUN
ejpam-6159	743	41	,	,	PUNCT
ejpam-6159	743	42	leveraging	leverage	VERB
ejpam-6159	743	43	the	the	DET
ejpam-6159	743	44	concept	concept	NOUN
ejpam-6159	743	45	of	of	ADP
ejpam-6159	743	46	polynomial	polynomial	ADJ
ejpam-6159	743	47	n	n	CCONJ
ejpam-6159	743	48	-	-	PUNCT
ejpam-6159	743	49	fractional	fractional	ADJ
ejpam-6159	743	50	s	s	NOUN
ejpam-6159	743	51	-	-	PUNCT
ejpam-6159	743	52	like	like	ADJ
ejpam-6159	743	53	preinvexity	preinvexity	NOUN
ejpam-6159	743	54	.	.	PUNCT
ejpam-6159	744	1	the	the	DET
ejpam-6159	744	2	proposed	propose	VERB
ejpam-6159	744	3	operator	operator	NOUN
ejpam-6159	744	4	extends	extend	VERB
ejpam-6159	744	5	the	the	DET
ejpam-6159	744	6	classical	classical	ADJ
ejpam-6159	744	7	fractional	fractional	ADJ
ejpam-6159	744	8	calculus	calculus	NOUN
ejpam-6159	744	9	framework	framework	NOUN
ejpam-6159	744	10	by	by	ADP
ejpam-6159	744	11	incorporating	incorporate	VERB
ejpam-6159	744	12	polynomial	polynomial	ADJ
ejpam-6159	744	13	and	and	CCONJ
ejpam-6159	744	14	preinvexity	preinvexity	NOUN
ejpam-6159	744	15	properties	property	NOUN
ejpam-6159	744	16	,	,	PUNCT
ejpam-6159	744	17	offering	offer	VERB
ejpam-6159	744	18	a	a	DET
ejpam-6159	744	19	more	more	ADV
ejpam-6159	744	20	versatile	versatile	ADJ
ejpam-6159	744	21	tool	tool	NOUN
ejpam-6159	744	22	for	for	ADP
ejpam-6159	744	23	analyzing	analyze	VERB
ejpam-6159	744	24	functions	function	NOUN
ejpam-6159	744	25	with	with	ADP
ejpam-6159	744	26	specific	specific	ADJ
ejpam-6159	744	27	convexity	convexity	NOUN
ejpam-6159	744	28	and	and	CCONJ
ejpam-6159	744	29	fractional	fractional	ADJ
ejpam-6159	744	30	characteristics	characteristic	NOUN
ejpam-6159	744	31	.	.	PUNCT
ejpam-6159	745	1	we	we	PRON
ejpam-6159	745	2	established	establish	VERB
ejpam-6159	745	3	key	key	ADJ
ejpam-6159	745	4	properties	property	NOUN
ejpam-6159	745	5	of	of	ADP
ejpam-6159	745	6	the	the	DET
ejpam-6159	745	7	new	new	ADJ
ejpam-6159	745	8	operator	operator	NOUN
ejpam-6159	745	9	,	,	PUNCT
ejpam-6159	745	10	including	include	VERB
ejpam-6159	745	11	its	its	PRON
ejpam-6159	745	12	convergence	convergence	NOUN
ejpam-6159	745	13	,	,	PUNCT
ejpam-6159	745	14	boundedness	boundedness	NOUN
ejpam-6159	745	15	,	,	PUNCT
ejpam-6159	745	16	and	and	CCONJ
ejpam-6159	745	17	applicability	applicability	NOUN
ejpam-6159	745	18	to	to	ADP
ejpam-6159	745	19	various	various	ADJ
ejpam-6159	745	20	classes	class	NOUN
ejpam-6159	745	21	of	of	ADP
ejpam-6159	745	22	functions	function	NOUN
ejpam-6159	745	23	.	.	PUNCT
ejpam-6159	746	1	furthermore	furthermore	ADV
ejpam-6159	746	2	,	,	PUNCT
ejpam-6159	746	3	we	we	PRON
ejpam-6159	746	4	demonstrated	demonstrate	VERB
ejpam-6159	746	5	its	its	PRON
ejpam-6159	746	6	utility	utility	NOUN
ejpam-6159	746	7	in	in	ADP
ejpam-6159	746	8	solving	solve	VERB
ejpam-6159	746	9	fractional	fractional	ADJ
ejpam-6159	746	10	differential	differential	ADJ
ejpam-6159	746	11	equations	equation	NOUN
ejpam-6159	746	12	and	and	CCONJ
ejpam-6159	746	13	optimizing	optimize	VERB
ejpam-6159	746	14	problems	problem	NOUN
ejpam-6159	746	15	involving	involve	VERB
ejpam-6159	746	16	preinvex	preinvex	ADJ
ejpam-6159	746	17	functions	function	NOUN
ejpam-6159	746	18	.	.	PUNCT
ejpam-6159	747	1	the	the	DET
ejpam-6159	747	2	results	result	NOUN
ejpam-6159	747	3	presented	present	VERB
ejpam-6159	747	4	herein	herein	NOUN
ejpam-6159	747	5	not	not	PART
ejpam-6159	747	6	only	only	ADV
ejpam-6159	747	7	generalize	generalize	VERB
ejpam-6159	747	8	existing	exist	VERB
ejpam-6159	747	9	fractional	fractional	ADJ
ejpam-6159	747	10	integral	integral	ADJ
ejpam-6159	747	11	operators	operator	NOUN
ejpam-6159	747	12	but	but	CCONJ
ejpam-6159	747	13	also	also	ADV
ejpam-6159	747	14	open	open	VERB
ejpam-6159	747	15	new	new	ADJ
ejpam-6159	747	16	avenues	avenue	NOUN
ejpam-6159	747	17	for	for	ADP
ejpam-6159	747	18	research	research	NOUN
ejpam-6159	747	19	in	in	ADP
ejpam-6159	747	20	fractional	fractional	ADJ
ejpam-6159	747	21	calculus	calculus	NOUN
ejpam-6159	747	22	and	and	CCONJ
ejpam-6159	747	23	its	its	PRON
ejpam-6159	747	24	applications	application	NOUN
ejpam-6159	747	25	in	in	ADP
ejpam-6159	747	26	optimization	optimization	NOUN
ejpam-6159	747	27	,	,	PUNCT
ejpam-6159	747	28	mathematical	mathematical	ADJ
ejpam-6159	747	29	modeling	modeling	NOUN
ejpam-6159	747	30	,	,	PUNCT
ejpam-6159	747	31	and	and	CCONJ
ejpam-6159	747	32	applied	applied	ADJ
ejpam-6159	747	33	sciences	science	NOUN
ejpam-6159	747	34	.	.	PUNCT
ejpam-6159	748	1	future	future	ADJ
ejpam-6159	748	2	work	work	NOUN
ejpam-6159	748	3	could	could	AUX
ejpam-6159	748	4	explore	explore	VERB
ejpam-6159	748	5	the	the	DET
ejpam-6159	748	6	extension	extension	NOUN
ejpam-6159	748	7	of	of	ADP
ejpam-6159	748	8	this	this	DET
ejpam-6159	748	9	operator	operator	NOUN
ejpam-6159	748	10	to	to	ADP
ejpam-6159	748	11	higher	high	ADJ
ejpam-6159	748	12	dimensions	dimension	NOUN
ejpam-6159	748	13	,	,	PUNCT
ejpam-6159	748	14	its	its	PRON
ejpam-6159	748	15	application	application	NOUN
ejpam-6159	748	16	in	in	ADP
ejpam-6159	748	17	real	real	ADJ
ejpam-6159	748	18	-	-	PUNCT
ejpam-6159	748	19	world	world	NOUN
ejpam-6159	748	20	problems	problem	NOUN
ejpam-6159	748	21	,	,	PUNCT
ejpam-6159	748	22	and	and	CCONJ
ejpam-6159	748	23	its	its	PRON
ejpam-6159	748	24	relationship	relationship	NOUN
ejpam-6159	748	25	with	with	ADP
ejpam-6159	748	26	other	other	ADJ
ejpam-6159	748	27	fractional	fractional	ADJ
ejpam-6159	748	28	operators	operator	NOUN
ejpam-6159	748	29	.	.	PUNCT
ejpam-6159	749	1	authors	author	NOUN
ejpam-6159	749	2	’	'	PUNCT
ejpam-6159	749	3	contributions	contribution	NOUN
ejpam-6159	749	4	all	all	DET
ejpam-6159	749	5	authors	author	NOUN
ejpam-6159	749	6	contribute	contribute	VERB
ejpam-6159	749	7	equally	equally	ADV
ejpam-6159	749	8	in	in	ADP
ejpam-6159	749	9	this	this	DET
ejpam-6159	749	10	paper	paper	NOUN
ejpam-6159	749	11	.	.	PUNCT
ejpam-6159	750	1	conflict	conflict	NOUN
ejpam-6159	750	2	of	of	ADP
ejpam-6159	750	3	interest	interest	NOUN
ejpam-6159	750	4	the	the	DET
ejpam-6159	750	5	authors	author	NOUN
ejpam-6159	750	6	declare	declare	VERB
ejpam-6159	750	7	that	that	SCONJ
ejpam-6159	750	8	they	they	PRON
ejpam-6159	750	9	have	have	VERB
ejpam-6159	750	10	no	no	DET
ejpam-6159	750	11	conflict	conflict	NOUN
ejpam-6159	750	12	of	of	ADP
ejpam-6159	750	13	interest	interest	NOUN
ejpam-6159	750	14	.	.	PUNCT
ejpam-6159	751	1	acknowledgments	acknowledgment	NOUN
ejpam-6159	751	2	the	the	DET
ejpam-6159	751	3	authors	author	NOUN
ejpam-6159	751	4	extend	extend	VERB
ejpam-6159	751	5	their	their	PRON
ejpam-6159	751	6	appreciation	appreciation	NOUN
ejpam-6159	751	7	to	to	ADP
ejpam-6159	751	8	umm	umm	INTJ
ejpam-6159	751	9	al	al	PROPN
ejpam-6159	751	10	-	-	PUNCT
ejpam-6159	751	11	qura	qura	PROPN
ejpam-6159	751	12	university	university	PROPN
ejpam-6159	751	13	,	,	PUNCT
ejpam-6159	751	14	saudi	saudi	PROPN
ejpam-6159	751	15	arabia	arabia	PROPN
ejpam-6159	751	16	for	for	ADP
ejpam-6159	751	17	funding	fund	VERB
ejpam-6159	751	18	this	this	DET
ejpam-6159	751	19	research	research	NOUN
ejpam-6159	751	20	work	work	NOUN
ejpam-6159	751	21	through	through	ADP
ejpam-6159	751	22	grant	grant	NOUN
ejpam-6159	751	23	number	number	NOUN
ejpam-6159	751	24	:	:	PUNCT
ejpam-6159	751	25	25uqu4331214gssr06	25uqu4331214gssr06	PROPN
ejpam-6159	751	26	j.	j.	PROPN
ejpam-6159	751	27	nasir	nasir	PROPN
ejpam-6159	751	28	et	et	PROPN
ejpam-6159	751	29	al	al	PROPN
ejpam-6159	751	30	.	.	PUNCT
ejpam-6159	751	31	/	/	SYM
ejpam-6159	751	32	eur	eur	PROPN
ejpam-6159	751	33	.	.	PUNCT
ejpam-6159	752	1	j.	j.	PROPN
ejpam-6159	752	2	pure	pure	PROPN
ejpam-6159	752	3	appl	appl	PROPN
ejpam-6159	752	4	.	.	PROPN
ejpam-6159	752	5	math	math	PROPN
ejpam-6159	752	6	,	,	PUNCT
ejpam-6159	752	7	18	18	NUM
ejpam-6159	752	8	(	(	PUNCT
ejpam-6159	752	9	3	3	NUM
ejpam-6159	752	10	)	)	PUNCT
ejpam-6159	752	11	(	(	PUNCT
ejpam-6159	752	12	2025	2025	NUM
ejpam-6159	752	13	)	)	PUNCT
ejpam-6159	752	14	,	,	PUNCT
ejpam-6159	752	15	6159	6159	NUM
ejpam-6159	752	16	25	25	NUM
ejpam-6159	752	17	of	of	ADP
ejpam-6159	752	18	26	26	NUM
ejpam-6159	752	19	funding	funding	NOUN
ejpam-6159	752	20	this	this	DET
ejpam-6159	752	21	research	research	NOUN
ejpam-6159	752	22	work	work	NOUN
ejpam-6159	752	23	was	be	AUX
ejpam-6159	752	24	funded	fund	VERB
ejpam-6159	752	25	by	by	ADP
ejpam-6159	752	26	umm	umm	INTJ
ejpam-6159	752	27	al	al	PROPN
ejpam-6159	752	28	-	-	PUNCT
ejpam-6159	752	29	qura	qura	PROPN
ejpam-6159	752	30	university	university	NOUN
ejpam-6159	752	31	,	,	PUNCT
ejpam-6159	752	32	saudi	saudi	PROPN
ejpam-6159	752	33	arabia	arabia	PROPN
ejpam-6159	752	34	under	under	ADP
ejpam-6159	752	35	grant	grant	NOUN
ejpam-6159	752	36	number	number	NOUN
ejpam-6159	752	37	:	:	PUNCT
ejpam-6159	752	38	25uqu4331214gssr06	25uqu4331214gssr06	NUM
ejpam-6159	752	39	.	.	PUNCT
ejpam-6159	753	1	references	reference	NOUN
ejpam-6159	753	2	[	[	X
ejpam-6159	753	3	1	1	NUM
ejpam-6159	753	4	]	]	X
ejpam-6159	753	5	p.	p.	PROPN
ejpam-6159	753	6	agarwal	agarwal	PROPN
ejpam-6159	753	7	,	,	PUNCT
ejpam-6159	753	8	s.	s.	PROPN
ejpam-6159	753	9	s.	s.	PROPN
ejpam-6159	753	10	dragomir	dragomir	PROPN
ejpam-6159	753	11	,	,	PUNCT
ejpam-6159	753	12	m.	m.	NOUN
ejpam-6159	753	13	jleli	jleli	PROPN
ejpam-6159	753	14	,	,	PUNCT
ejpam-6159	753	15	and	and	CCONJ
ejpam-6159	753	16	b.	b.	PROPN
ejpam-6159	753	17	samet	samet	PROPN
ejpam-6159	753	18	.	.	PUNCT
ejpam-6159	754	1	advances	advance	NOUN
ejpam-6159	754	2	in	in	ADP
ejpam-6159	754	3	mathematical	mathematical	ADJ
ejpam-6159	754	4	inequalities	inequality	NOUN
ejpam-6159	754	5	and	and	CCONJ
ejpam-6159	754	6	applications	application	NOUN
ejpam-6159	754	7	.	.	PUNCT
ejpam-6159	755	1	springer	springer	NOUN
ejpam-6159	755	2	,	,	PUNCT
ejpam-6159	755	3	2018	2018	NUM
ejpam-6159	755	4	.	.	PUNCT
ejpam-6159	756	1	[	[	X
ejpam-6159	756	2	2	2	X
ejpam-6159	756	3	]	]	X
ejpam-6159	756	4	y.	y.	PROPN
ejpam-6159	756	5	qin	qin	PROPN
ejpam-6159	756	6	.	.	PUNCT
ejpam-6159	756	7	integral	integral	ADJ
ejpam-6159	756	8	and	and	CCONJ
ejpam-6159	756	9	discrete	discrete	ADJ
ejpam-6159	756	10	inequalities	inequality	NOUN
ejpam-6159	756	11	and	and	CCONJ
ejpam-6159	756	12	their	their	PRON
ejpam-6159	756	13	applications	application	NOUN
ejpam-6159	756	14	.	.	PUNCT
ejpam-6159	757	1	springer	springer	NOUN
ejpam-6159	757	2	,	,	PUNCT
ejpam-6159	757	3	2016	2016	NUM
ejpam-6159	757	4	.	.	PUNCT
ejpam-6159	758	1	[	[	X
ejpam-6159	758	2	3	3	X
ejpam-6159	758	3	]	]	PUNCT
ejpam-6159	758	4	t.	t.	X
ejpam-6159	758	5	du	du	PROPN
ejpam-6159	758	6	,	,	PUNCT
ejpam-6159	758	7	t.	t.	PROPN
ejpam-6159	758	8	s.	s.	PROPN
ejpam-6159	758	9	wu	wu	PROPN
ejpam-6159	758	10	,	,	PUNCT
ejpam-6159	758	11	and	and	CCONJ
ejpam-6159	758	12	s.	s.	PROPN
ejpam-6159	758	13	zhao	zhao	PROPN
ejpam-6159	758	14	.	.	PUNCT
ejpam-6159	759	1	riemann	riemann	PROPN
ejpam-6159	759	2	-	-	PUNCT
ejpam-6159	759	3	liouville	liouville	VERB
ejpam-6159	759	4	fractional	fractional	ADJ
ejpam-6159	759	5	hermite	hermite	PROPN
ejpam-6159	759	6	-	-	PUNCT
ejpam-6159	759	7	hadamard	hadamard	ADJ
ejpam-6159	759	8	inequalities	inequality	NOUN
ejpam-6159	759	9	for	for	ADP
ejpam-6159	759	10	h	h	NOUN
ejpam-6159	759	11	-	-	PUNCT
ejpam-6159	759	12	preinvex	preinvex	NOUN
ejpam-6159	759	13	functions	function	NOUN
ejpam-6159	759	14	.	.	PUNCT
ejpam-6159	760	1	journal	journal	NOUN
ejpam-6159	760	2	of	of	ADP
ejpam-6159	760	3	computational	computational	ADJ
ejpam-6159	760	4	analysis	analysis	NOUN
ejpam-6159	760	5	&	&	CCONJ
ejpam-6159	760	6	applications	application	NOUN
ejpam-6159	760	7	,	,	PUNCT
ejpam-6159	760	8	25(2	25(2	NUM
ejpam-6159	760	9	)	)	PUNCT
ejpam-6159	760	10	,	,	PUNCT
ejpam-6159	760	11	2018	2018	NUM
ejpam-6159	760	12	.	.	PUNCT
ejpam-6159	761	1	[	[	X
ejpam-6159	761	2	4	4	X
ejpam-6159	761	3	]	]	PUNCT
ejpam-6159	761	4	t.	t.	PROPN
ejpam-6159	761	5	du	du	PROPN
ejpam-6159	761	6	,	,	PUNCT
ejpam-6159	761	7	h.	h.	PROPN
ejpam-6159	761	8	w.	w.	PROPN
ejpam-6159	761	9	tingsong	tingsong	PROPN
ejpam-6159	761	10	,	,	PUNCT
ejpam-6159	761	11	m.	m.	NOUN
ejpam-6159	761	12	a.	a.	PROPN
ejpam-6159	761	13	khan	khan	PROPN
ejpam-6159	761	14	,	,	PUNCT
ejpam-6159	761	15	and	and	CCONJ
ejpam-6159	761	16	y.	y.	PROPN
ejpam-6159	761	17	zhag	zhag	PROPN
ejpam-6159	761	18	.	.	PUNCT
ejpam-6159	762	1	certain	certain	ADJ
ejpam-6159	762	2	integral	integral	ADJ
ejpam-6159	762	3	inequalities	inequality	NOUN
ejpam-6159	762	4	considering	consider	VERB
ejpam-6159	762	5	generalized	generalized	ADJ
ejpam-6159	762	6	m	m	NOUN
ejpam-6159	762	7	-	-	NOUN
ejpam-6159	762	8	convexity	convexity	NOUN
ejpam-6159	762	9	on	on	ADP
ejpam-6159	762	10	fractal	fractal	ADJ
ejpam-6159	762	11	sets	set	NOUN
ejpam-6159	762	12	and	and	CCONJ
ejpam-6159	762	13	their	their	PRON
ejpam-6159	762	14	applications	application	NOUN
ejpam-6159	762	15	.	.	PUNCT
ejpam-6159	763	1	fractals	fractal	NOUN
ejpam-6159	763	2	,	,	PUNCT
ejpam-6159	763	3	27(07):1950117	27(07):1950117	NUM
ejpam-6159	763	4	,	,	PUNCT
ejpam-6159	763	5	2019	2019	NUM
ejpam-6159	763	6	.	.	PUNCT
ejpam-6159	764	1	[	[	X
ejpam-6159	764	2	5	5	X
ejpam-6159	764	3	]	]	PUNCT
ejpam-6159	764	4	s.	s.	PROPN
ejpam-6159	764	5	qaisar	qaisar	PROPN
ejpam-6159	764	6	,	,	PUNCT
ejpam-6159	764	7	j.	j.	PROPN
ejpam-6159	764	8	nasir	nasir	PROPN
ejpam-6159	764	9	,	,	PUNCT
ejpam-6159	764	10	s.	s.	PROPN
ejpam-6159	764	11	i.	i.	PROPN
ejpam-6159	764	12	butt	butt	PROPN
ejpam-6159	764	13	,	,	PUNCT
ejpam-6159	764	14	and	and	CCONJ
ejpam-6159	764	15	s.	s.	PROPN
ejpam-6159	764	16	hussain	hussain	PROPN
ejpam-6159	764	17	.	.	PUNCT
ejpam-6159	765	1	on	on	ADP
ejpam-6159	765	2	some	some	DET
ejpam-6159	765	3	fractional	fractional	ADJ
ejpam-6159	765	4	integral	integral	ADJ
ejpam-6159	765	5	inequalities	inequality	NOUN
ejpam-6159	765	6	of	of	ADP
ejpam-6159	765	7	hermite	hermite	PROPN
ejpam-6159	765	8	-	-	PUNCT
ejpam-6159	765	9	hadamard	hadamard	PROPN
ejpam-6159	765	10	’s	’s	PART
ejpam-6159	765	11	type	type	NOUN
ejpam-6159	765	12	through	through	ADP
ejpam-6159	765	13	convexity	convexity	NOUN
ejpam-6159	765	14	.	.	PUNCT
ejpam-6159	765	15	symmetry	symmetry	NOUN
ejpam-6159	765	16	,	,	PUNCT
ejpam-6159	765	17	11(2):137	11(2):137	NUM
ejpam-6159	765	18	,	,	PUNCT
ejpam-6159	765	19	2019	2019	NUM
ejpam-6159	765	20	.	.	PUNCT
ejpam-6159	766	1	[	[	X
ejpam-6159	766	2	6	6	NUM
ejpam-6159	766	3	]	]	PUNCT
ejpam-6159	766	4	s.	s.	PROPN
ejpam-6159	766	5	s.	s.	PROPN
ejpam-6159	766	6	mitrinovic	mitrinovic	PROPN
ejpam-6159	766	7	,	,	PUNCT
ejpam-6159	766	8	j.	j.	PROPN
ejpam-6159	766	9	pecaric	pecaric	PROPN
ejpam-6159	766	10	,	,	PUNCT
ejpam-6159	766	11	and	and	CCONJ
ejpam-6159	766	12	a.	a.	NOUN
ejpam-6159	766	13	m.	m.	PROPN
ejpam-6159	766	14	arlington	arlington	PROPN
ejpam-6159	766	15	.	.	PUNCT
ejpam-6159	767	1	inequalities	inequality	NOUN
ejpam-6159	767	2	involving	involve	VERB
ejpam-6159	767	3	functions	function	NOUN
ejpam-6159	767	4	and	and	CCONJ
ejpam-6159	767	5	their	their	PRON
ejpam-6159	767	6	integrals	integral	NOUN
ejpam-6159	767	7	and	and	CCONJ
ejpam-6159	767	8	derivatives	derivative	NOUN
ejpam-6159	767	9	,	,	PUNCT
ejpam-6159	767	10	volume	volume	NOUN
ejpam-6159	767	11	53	53	NUM
ejpam-6159	767	12	.	.	PUNCT
ejpam-6159	768	1	springer	springer	PROPN
ejpam-6159	768	2	science	science	PROPN
ejpam-6159	768	3	&	&	CCONJ
ejpam-6159	768	4	business	business	NOUN
ejpam-6159	768	5	media	medium	NOUN
ejpam-6159	768	6	,	,	PUNCT
ejpam-6159	768	7	1991	1991	NUM
ejpam-6159	768	8	.	.	PUNCT
ejpam-6159	769	1	[	[	X
ejpam-6159	769	2	7	7	X
ejpam-6159	769	3	]	]	X
ejpam-6159	769	4	m.	m.	NOUN
ejpam-6159	769	5	ud	ud	PROPN
ejpam-6159	769	6	-	-	PUNCT
ejpam-6159	769	7	din	din	NOUN
ejpam-6159	769	8	junjua	junjua	NOUN
ejpam-6159	769	9	,	,	PUNCT
ejpam-6159	769	10	a.	a.	PROPN
ejpam-6159	769	11	qayyum	qayyum	PROPN
ejpam-6159	769	12	,	,	PUNCT
ejpam-6159	769	13	a.	a.	PROPN
ejpam-6159	769	14	m.	m.	PROPN
ejpam-6159	769	15	arslan	arslan	PROPN
ejpam-6159	769	16	,	,	PUNCT
ejpam-6159	769	17	h.	h.	PROPN
ejpam-6159	769	18	budak	budak	PROPN
ejpam-6159	769	19	,	,	PUNCT
ejpam-6159	769	20	m.	m.	PROPN
ejpam-6159	769	21	h.	h.	PROPN
ejpam-6159	769	22	saleem	saleem	PROPN
ejpam-6159	769	23	,	,	PUNCT
ejpam-6159	769	24	and	and	CCONJ
ejpam-6159	769	25	s.	s.	PROPN
ejpam-6159	769	26	s.	s.	PROPN
ejpam-6159	769	27	supadi	supadi	PROPN
ejpam-6159	769	28	.	.	PUNCT
ejpam-6159	770	1	a	a	DET
ejpam-6159	770	2	study	study	NOUN
ejpam-6159	770	3	of	of	ADP
ejpam-6159	770	4	some	some	DET
ejpam-6159	770	5	new	new	ADJ
ejpam-6159	770	6	hermite	hermite	ADJ
ejpam-6159	770	7	–	–	PUNCT
ejpam-6159	770	8	hadamard	hadamard	ADJ
ejpam-6159	770	9	inequalities	inequality	NOUN
ejpam-6159	770	10	via	via	ADP
ejpam-6159	770	11	specific	specific	ADJ
ejpam-6159	770	12	convex	convex	NOUN
ejpam-6159	770	13	functions	function	NOUN
ejpam-6159	770	14	with	with	ADP
ejpam-6159	770	15	applications	application	NOUN
ejpam-6159	770	16	.	.	PUNCT
ejpam-6159	771	1	mathematics	mathematic	NOUN
ejpam-6159	771	2	,	,	PUNCT
ejpam-6159	771	3	12(3):478	12(3):478	NUM
ejpam-6159	771	4	,	,	PUNCT
ejpam-6159	771	5	2024	2024	NUM
ejpam-6159	771	6	.	.	PUNCT
ejpam-6159	772	1	[	[	X
ejpam-6159	772	2	8	8	NUM
ejpam-6159	772	3	]	]	X
ejpam-6159	772	4	h.	h.	PROPN
ejpam-6159	772	5	budaka	budaka	PROPN
ejpam-6159	772	6	,	,	PUNCT
ejpam-6159	772	7	m.	m.	NOUN
ejpam-6159	772	8	z.	z.	PROPN
ejpam-6159	772	9	sarikaya	sarikaya	PROPN
ejpam-6159	772	10	,	,	PUNCT
ejpam-6159	772	11	and	and	CCONJ
ejpam-6159	772	12	a.	a.	PROPN
ejpam-6159	772	13	qayyum	qayyum	PROPN
ejpam-6159	772	14	.	.	PUNCT
ejpam-6159	773	1	improvement	improvement	NOUN
ejpam-6159	773	2	in	in	ADP
ejpam-6159	773	3	companion	companion	NOUN
ejpam-6159	773	4	of	of	ADP
ejpam-6159	773	5	ostrowski	ostrowski	ADJ
ejpam-6159	773	6	type	type	NOUN
ejpam-6159	773	7	inequalities	inequality	NOUN
ejpam-6159	773	8	for	for	ADP
ejpam-6159	773	9	mappings	mapping	NOUN
ejpam-6159	773	10	whose	whose	DET
ejpam-6159	773	11	first	first	ADJ
ejpam-6159	773	12	derivatives	derivative	NOUN
ejpam-6159	773	13	are	be	AUX
ejpam-6159	773	14	of	of	ADP
ejpam-6159	773	15	bounded	bounded	ADJ
ejpam-6159	773	16	variation	variation	NOUN
ejpam-6159	773	17	and	and	CCONJ
ejpam-6159	773	18	applications	application	NOUN
ejpam-6159	773	19	.	.	PUNCT
ejpam-6159	774	1	filomat	filomat	NOUN
ejpam-6159	774	2	,	,	PUNCT
ejpam-6159	774	3	31(16):5305–5314	31(16):5305–5314	NUM
ejpam-6159	774	4	,	,	PUNCT
ejpam-6159	774	5	2017	2017	NUM
ejpam-6159	774	6	.	.	PUNCT
ejpam-6159	775	1	[	[	X
ejpam-6159	775	2	9	9	NUM
ejpam-6159	775	3	]	]	SYM
ejpam-6159	775	4	a.	a.	NOUN
ejpam-6159	775	5	munir	munir	PROPN
ejpam-6159	775	6	,	,	PUNCT
ejpam-6159	775	7	a.	a.	PROPN
ejpam-6159	775	8	qayyum	qayyum	PROPN
ejpam-6159	775	9	,	,	PUNCT
ejpam-6159	775	10	l.	l.	PROPN
ejpam-6159	775	11	rathour	rathour	PROPN
ejpam-6159	775	12	,	,	PUNCT
ejpam-6159	775	13	g.	g.	PROPN
ejpam-6159	775	14	atta	atta	PROPN
ejpam-6159	775	15	,	,	PUNCT
ejpam-6159	775	16	s.	s.	PROPN
ejpam-6159	775	17	s.	s.	PROPN
ejpam-6159	775	18	supadi	supadi	PROPN
ejpam-6159	775	19	,	,	PUNCT
ejpam-6159	775	20	and	and	CCONJ
ejpam-6159	775	21	u.	u.	PROPN
ejpam-6159	775	22	ali	ali	PROPN
ejpam-6159	775	23	.	.	PUNCT
ejpam-6159	776	1	a	a	DET
ejpam-6159	776	2	study	study	NOUN
ejpam-6159	776	3	on	on	ADP
ejpam-6159	776	4	milne	milne	PROPN
ejpam-6159	776	5	-	-	PUNCT
ejpam-6159	776	6	type	type	NOUN
ejpam-6159	776	7	inequalities	inequality	NOUN
ejpam-6159	776	8	for	for	ADP
ejpam-6159	776	9	a	a	DET
ejpam-6159	776	10	specific	specific	ADJ
ejpam-6159	776	11	fractional	fractional	ADJ
ejpam-6159	776	12	integral	integral	ADJ
ejpam-6159	776	13	operator	operator	NOUN
ejpam-6159	776	14	with	with	ADP
ejpam-6159	776	15	applications	application	NOUN
ejpam-6159	776	16	.	.	PUNCT
ejpam-6159	777	1	korean	korean	ADJ
ejpam-6159	777	2	journal	journal	PROPN
ejpam-6159	777	3	of	of	ADP
ejpam-6159	777	4	mathematics	mathematic	NOUN
ejpam-6159	777	5	,	,	PUNCT
ejpam-6159	777	6	32(2):297–314	32(2):297–314	NOUN
ejpam-6159	777	7	,	,	PUNCT
ejpam-6159	777	8	2024	2024	NUM
ejpam-6159	777	9	.	.	PUNCT
ejpam-6159	778	1	[	[	X
ejpam-6159	778	2	10	10	NUM
ejpam-6159	778	3	]	]	X
ejpam-6159	778	4	j.	j.	PROPN
ejpam-6159	778	5	nasir	nasir	PROPN
ejpam-6159	778	6	,	,	PUNCT
ejpam-6159	778	7	s.	s.	PROPN
ejpam-6159	778	8	qaisar	qaisar	PROPN
ejpam-6159	778	9	,	,	PUNCT
ejpam-6159	778	10	s.	s.	PROPN
ejpam-6159	778	11	i.	i.	PROPN
ejpam-6159	778	12	butt	butt	PROPN
ejpam-6159	778	13	,	,	PUNCT
ejpam-6159	778	14	and	and	CCONJ
ejpam-6159	778	15	a.	a.	PROPN
ejpam-6159	778	16	qayyum	qayyum	PROPN
ejpam-6159	778	17	.	.	PUNCT
ejpam-6159	779	1	some	some	DET
ejpam-6159	779	2	ostrowski	ostrowski	ADJ
ejpam-6159	779	3	type	type	NOUN
ejpam-6159	779	4	inequalities	inequality	NOUN
ejpam-6159	779	5	for	for	ADP
ejpam-6159	779	6	mappings	mapping	NOUN
ejpam-6159	779	7	whose	whose	DET
ejpam-6159	779	8	second	second	ADJ
ejpam-6159	779	9	derivatives	derivative	NOUN
ejpam-6159	779	10	are	be	AUX
ejpam-6159	779	11	preinvex	preinvex	ADJ
ejpam-6159	779	12	function	function	NOUN
ejpam-6159	779	13	via	via	ADP
ejpam-6159	779	14	fractional	fractional	ADJ
ejpam-6159	779	15	integral	integral	ADJ
ejpam-6159	779	16	operator	operator	NOUN
ejpam-6159	779	17	,	,	PUNCT
ejpam-6159	779	18	2022	2022	NUM
ejpam-6159	779	19	.	.	PUNCT
ejpam-6159	780	1	[	[	X
ejpam-6159	780	2	11	11	NUM
ejpam-6159	780	3	]	]	PUNCT
ejpam-6159	780	4	t.	t.	PROPN
ejpam-6159	780	5	antczak	antczak	PROPN
ejpam-6159	780	6	.	.	PUNCT
ejpam-6159	781	1	mean	mean	ADJ
ejpam-6159	781	2	value	value	NOUN
ejpam-6159	781	3	in	in	ADP
ejpam-6159	781	4	invexity	invexity	NOUN
ejpam-6159	781	5	analysis	analysis	NOUN
ejpam-6159	781	6	.	.	PUNCT
ejpam-6159	782	1	nonlinear	nonlinear	ADJ
ejpam-6159	782	2	analysis	analysis	NOUN
ejpam-6159	782	3	:	:	PUNCT
ejpam-6159	782	4	theory	theory	NOUN
ejpam-6159	782	5	,	,	PUNCT
ejpam-6159	782	6	methods	method	NOUN
ejpam-6159	782	7	&	&	CCONJ
ejpam-6159	782	8	applications	application	NOUN
ejpam-6159	782	9	,	,	PUNCT
ejpam-6159	782	10	60(8):1473–1484	60(8):1473–1484	NUM
ejpam-6159	782	11	,	,	PUNCT
ejpam-6159	782	12	2005	2005	NUM
ejpam-6159	782	13	.	.	PUNCT
ejpam-6159	783	1	[	[	X
ejpam-6159	783	2	12	12	NUM
ejpam-6159	783	3	]	]	X
ejpam-6159	783	4	t.	t.	PROPN
ejpam-6159	783	5	weir	weir	PROPN
ejpam-6159	783	6	and	and	CCONJ
ejpam-6159	783	7	b.	b.	PROPN
ejpam-6159	783	8	mond	mond	PROPN
ejpam-6159	783	9	.	.	PUNCT
ejpam-6159	784	1	pre	pre	ADJ
ejpam-6159	784	2	-	-	ADJ
ejpam-6159	784	3	invex	invex	ADJ
ejpam-6159	784	4	functions	function	NOUN
ejpam-6159	784	5	in	in	ADP
ejpam-6159	784	6	multiple	multiple	ADJ
ejpam-6159	784	7	objective	objective	ADJ
ejpam-6159	784	8	optimization	optimization	NOUN
ejpam-6159	784	9	.	.	PUNCT
ejpam-6159	785	1	journal	journal	PROPN
ejpam-6159	785	2	of	of	ADP
ejpam-6159	785	3	mathematical	mathematical	ADJ
ejpam-6159	785	4	analysis	analysis	NOUN
ejpam-6159	785	5	and	and	CCONJ
ejpam-6159	785	6	applications	application	NOUN
ejpam-6159	785	7	,	,	PUNCT
ejpam-6159	785	8	136(1):29–38	136(1):29–38	NUM
ejpam-6159	785	9	,	,	PUNCT
ejpam-6159	785	10	1988	1988	NUM
ejpam-6159	785	11	.	.	PUNCT
ejpam-6159	786	1	[	[	X
ejpam-6159	786	2	13	13	NUM
ejpam-6159	786	3	]	]	PUNCT
ejpam-6159	786	4	s.	s.	PROPN
ejpam-6159	786	5	k.	k.	PROPN
ejpam-6159	786	6	mishra	mishra	PROPN
ejpam-6159	786	7	and	and	CCONJ
ejpam-6159	786	8	g.	g.	PROPN
ejpam-6159	786	9	giorgi	giorgi	PROPN
ejpam-6159	786	10	.	.	PUNCT
ejpam-6159	787	1	invexity	invexity	NOUN
ejpam-6159	787	2	and	and	CCONJ
ejpam-6159	787	3	optimization	optimization	NOUN
ejpam-6159	787	4	,	,	PUNCT
ejpam-6159	787	5	volume	volume	NOUN
ejpam-6159	787	6	88	88	NUM
ejpam-6159	787	7	.	.	PUNCT
ejpam-6159	788	1	springer	springer	NOUN
ejpam-6159	788	2	science	science	PROPN
ejpam-6159	788	3	&	&	CCONJ
ejpam-6159	788	4	business	business	NOUN
ejpam-6159	788	5	media	medium	NOUN
ejpam-6159	788	6	,	,	PUNCT
ejpam-6159	788	7	2008	2008	NUM
ejpam-6159	788	8	.	.	PUNCT
ejpam-6159	789	1	[	[	X
ejpam-6159	789	2	14	14	NUM
ejpam-6159	789	3	]	]	X
ejpam-6159	789	4	s.	s.	PROPN
ejpam-6159	789	5	r.	r.	PROPN
ejpam-6159	789	6	mohan	mohan	PROPN
ejpam-6159	789	7	and	and	CCONJ
ejpam-6159	789	8	s.	s.	PROPN
ejpam-6159	789	9	k.	k.	PROPN
ejpam-6159	789	10	neogy	neogy	PROPN
ejpam-6159	789	11	.	.	PUNCT
ejpam-6159	790	1	on	on	ADP
ejpam-6159	790	2	invex	invex	NOUN
ejpam-6159	790	3	sets	set	NOUN
ejpam-6159	790	4	and	and	CCONJ
ejpam-6159	790	5	preinvex	preinvex	NOUN
ejpam-6159	790	6	functions	function	NOUN
ejpam-6159	790	7	.	.	PUNCT
ejpam-6159	791	1	journal	journal	NOUN
ejpam-6159	791	2	of	of	ADP
ejpam-6159	791	3	mathematical	mathematical	ADJ
ejpam-6159	791	4	analysis	analysis	NOUN
ejpam-6159	791	5	and	and	CCONJ
ejpam-6159	791	6	applications	application	NOUN
ejpam-6159	791	7	,	,	PUNCT
ejpam-6159	791	8	189(3):901–908	189(3):901–908	NUM
ejpam-6159	791	9	,	,	PUNCT
ejpam-6159	791	10	1995	1995	NUM
ejpam-6159	791	11	.	.	PUNCT
ejpam-6159	792	1	[	[	X
ejpam-6159	792	2	15	15	NUM
ejpam-6159	792	3	]	]	X
ejpam-6159	792	4	m.	m.	NOUN
ejpam-6159	792	5	a.	a.	PROPN
ejpam-6159	792	6	noor	noor	PROPN
ejpam-6159	792	7	.	.	PUNCT
ejpam-6159	793	1	hadamard	hadamard	ADJ
ejpam-6159	793	2	integral	integral	ADJ
ejpam-6159	793	3	inequalities	inequality	NOUN
ejpam-6159	793	4	for	for	ADP
ejpam-6159	793	5	product	product	NOUN
ejpam-6159	793	6	of	of	ADP
ejpam-6159	793	7	two	two	NUM
ejpam-6159	793	8	preinvex	preinvex	ADJ
ejpam-6159	793	9	function	function	NOUN
ejpam-6159	793	10	.	.	PUNCT
ejpam-6159	794	1	in	in	ADP
ejpam-6159	794	2	nonlinear	nonlinear	ADJ
ejpam-6159	794	3	analysis	analysis	NOUN
ejpam-6159	794	4	forum	forum	NOUN
ejpam-6159	794	5	,	,	PUNCT
ejpam-6159	794	6	volume	volume	NOUN
ejpam-6159	794	7	14	14	NUM
ejpam-6159	794	8	,	,	PUNCT
ejpam-6159	794	9	pages	page	NOUN
ejpam-6159	794	10	167–173	167–173	NUM
ejpam-6159	794	11	,	,	PUNCT
ejpam-6159	794	12	2009	2009	NUM
ejpam-6159	794	13	.	.	PUNCT
ejpam-6159	795	1	j.	j.	PROPN
ejpam-6159	795	2	nasir	nasir	PROPN
ejpam-6159	795	3	et	et	PROPN
ejpam-6159	795	4	al	al	PROPN
ejpam-6159	795	5	.	.	PUNCT
ejpam-6159	795	6	/	/	SYM
ejpam-6159	795	7	eur	eur	PROPN
ejpam-6159	795	8	.	.	PUNCT
ejpam-6159	796	1	j.	j.	PROPN
ejpam-6159	796	2	pure	pure	PROPN
ejpam-6159	796	3	appl	appl	PROPN
ejpam-6159	796	4	.	.	PROPN
ejpam-6159	796	5	math	math	PROPN
ejpam-6159	796	6	,	,	PUNCT
ejpam-6159	796	7	18	18	NUM
ejpam-6159	796	8	(	(	PUNCT
ejpam-6159	796	9	3	3	NUM
ejpam-6159	796	10	)	)	PUNCT
ejpam-6159	796	11	(	(	PUNCT
ejpam-6159	796	12	2025	2025	NUM
ejpam-6159	796	13	)	)	PUNCT
ejpam-6159	796	14	,	,	PUNCT
ejpam-6159	796	15	6159	6159	NUM
ejpam-6159	796	16	26	26	NUM
ejpam-6159	796	17	of	of	ADP
ejpam-6159	796	18	26	26	NUM
ejpam-6159	796	19	[	[	X
ejpam-6159	796	20	16	16	NUM
ejpam-6159	796	21	]	]	PUNCT
ejpam-6159	796	22	a.	a.	NOUN
ejpam-6159	796	23	ostrowski	ostrowski	PROPN
ejpam-6159	796	24	.	.	PUNCT
ejpam-6159	797	1	über	über	PROPN
ejpam-6159	797	2	die	die	VERB
ejpam-6159	797	3	absolutabweichung	absolutabweichung	PROPN
ejpam-6159	797	4	einer	einer	PROPN
ejpam-6159	797	5	differentiierbaren	differentiierbaren	PROPN
ejpam-6159	797	6	funktion	funktion	PROPN
ejpam-6159	797	7	von	von	PROPN
ejpam-6159	797	8	ihrem	ihrem	PROPN
ejpam-6159	797	9	integralmittelwert	integralmittelwert	PROPN
ejpam-6159	797	10	.	.	PUNCT
ejpam-6159	798	1	commentarii	commentarii	PROPN
ejpam-6159	798	2	mathematici	mathematici	PROPN
ejpam-6159	798	3	helvetici	helvetici	PROPN
ejpam-6159	798	4	,	,	PUNCT
ejpam-6159	798	5	10(1):226–227	10(1):226–227	NUM
ejpam-6159	798	6	,	,	PUNCT
ejpam-6159	798	7	1937	1937	NUM
ejpam-6159	798	8	.	.	PUNCT
ejpam-6159	799	1	[	[	X
ejpam-6159	799	2	17	17	NUM
ejpam-6159	799	3	]	]	PUNCT
ejpam-6159	799	4	p.	p.	NOUN
ejpam-6159	799	5	cerone	cerone	NOUN
ejpam-6159	799	6	,	,	PUNCT
ejpam-6159	799	7	s.	s.	PROPN
ejpam-6159	799	8	s.	s.	PROPN
ejpam-6159	799	9	dragomir	dragomir	PROPN
ejpam-6159	799	10	,	,	PUNCT
ejpam-6159	799	11	and	and	CCONJ
ejpam-6159	799	12	j.	j.	PROPN
ejpam-6159	799	13	roumeliotis	roumeliotis	PROPN
ejpam-6159	799	14	.	.	PUNCT
ejpam-6159	800	1	an	an	DET
ejpam-6159	800	2	inequality	inequality	NOUN
ejpam-6159	800	3	of	of	ADP
ejpam-6159	800	4	ostrowski	ostrowski	ADJ
ejpam-6159	800	5	type	type	NOUN
ejpam-6159	800	6	for	for	ADP
ejpam-6159	800	7	mappings	mapping	NOUN
ejpam-6159	800	8	whose	whose	DET
ejpam-6159	800	9	second	second	ADJ
ejpam-6159	800	10	derivatives	derivative	NOUN
ejpam-6159	800	11	are	be	AUX
ejpam-6159	800	12	bounded	bound	VERB
ejpam-6159	800	13	and	and	CCONJ
ejpam-6159	800	14	applications	application	NOUN
ejpam-6159	800	15	.	.	PUNCT
ejpam-6159	801	1	rgmia	rgmia	PROPN
ejpam-6159	801	2	research	research	NOUN
ejpam-6159	801	3	report	report	NOUN
ejpam-6159	801	4	collection	collection	NOUN
ejpam-6159	801	5	,	,	PUNCT
ejpam-6159	801	6	1(1	1(1	NUM
ejpam-6159	801	7	)	)	PUNCT
ejpam-6159	801	8	,	,	PUNCT
ejpam-6159	801	9	1998	1998	NUM
ejpam-6159	801	10	.	.	PUNCT
ejpam-6159	802	1	[	[	X
ejpam-6159	802	2	18	18	NUM
ejpam-6159	802	3	]	]	X
ejpam-6159	802	4	h.	h.	PROPN
ejpam-6159	802	5	budak	budak	PROPN
ejpam-6159	802	6	,	,	PUNCT
ejpam-6159	802	7	m.	m.	PROPN
ejpam-6159	802	8	z.	z.	PROPN
ejpam-6159	802	9	sarıkaya	sarıkaya	PROPN
ejpam-6159	802	10	,	,	PUNCT
ejpam-6159	802	11	and	and	CCONJ
ejpam-6159	802	12	a.	a.	PROPN
ejpam-6159	802	13	qayyum	qayyum	PROPN
ejpam-6159	802	14	.	.	PUNCT
ejpam-6159	803	1	new	new	ADJ
ejpam-6159	803	2	refinements	refinement	NOUN
ejpam-6159	803	3	and	and	CCONJ
ejpam-6159	803	4	applications	application	NOUN
ejpam-6159	803	5	of	of	ADP
ejpam-6159	803	6	ostrowski	ostrowski	ADJ
ejpam-6159	803	7	type	type	NOUN
ejpam-6159	803	8	inequalities	inequality	NOUN
ejpam-6159	803	9	for	for	ADP
ejpam-6159	803	10	mappings	mapping	NOUN
ejpam-6159	803	11	whose	whose	DET
ejpam-6159	803	12	nth	nth	NOUN
ejpam-6159	803	13	derivatives	derivative	NOUN
ejpam-6159	803	14	are	be	AUX
ejpam-6159	803	15	of	of	ADP
ejpam-6159	803	16	bounded	bounded	ADJ
ejpam-6159	803	17	variation	variation	NOUN
ejpam-6159	803	18	.	.	PUNCT
ejpam-6159	804	1	twms	twms	PROPN
ejpam-6159	804	2	journal	journal	PROPN
ejpam-6159	804	3	of	of	ADP
ejpam-6159	804	4	applied	apply	VERB
ejpam-6159	804	5	and	and	CCONJ
ejpam-6159	804	6	engineering	engineering	NOUN
ejpam-6159	804	7	mathematics	mathematic	NOUN
ejpam-6159	804	8	,	,	PUNCT
ejpam-6159	804	9	2021	2021	NUM
ejpam-6159	804	10	.	.	PUNCT
ejpam-6159	805	1	[	[	X
ejpam-6159	805	2	19	19	NUM
ejpam-6159	805	3	]	]	X
ejpam-6159	805	4	h.	h.	PROPN
ejpam-6159	805	5	budak	budak	PROPN
ejpam-6159	805	6	and	and	CCONJ
ejpam-6159	805	7	e.	e.	PROPN
ejpam-6159	805	8	pehlivan	pehlivan	PROPN
ejpam-6159	805	9	.	.	PUNCT
ejpam-6159	806	1	weighted	weight	VERB
ejpam-6159	806	2	ostrowski	ostrowski	NOUN
ejpam-6159	806	3	,	,	PUNCT
ejpam-6159	806	4	trapezoid	trapezoid	ADJ
ejpam-6159	806	5	and	and	CCONJ
ejpam-6159	806	6	midpoint	midpoint	NOUN
ejpam-6159	806	7	type	type	NOUN
ejpam-6159	806	8	inequalities	inequality	NOUN
ejpam-6159	806	9	for	for	ADP
ejpam-6159	806	10	riemann	riemann	PROPN
ejpam-6159	806	11	-	-	PUNCT
ejpam-6159	806	12	liouville	liouville	VERB
ejpam-6159	806	13	fractional	fractional	ADJ
ejpam-6159	806	14	integrals	integral	NOUN
ejpam-6159	806	15	.	.	PUNCT
ejpam-6159	807	1	aims	aim	VERB
ejpam-6159	807	2	mathematics	mathematic	NOUN
ejpam-6159	807	3	,	,	PUNCT
ejpam-6159	807	4	5(3):1960–1984	5(3):1960–1984	PROPN
ejpam-6159	807	5	,	,	PUNCT
ejpam-6159	807	6	2020	2020	NUM
ejpam-6159	807	7	.	.	PUNCT
ejpam-6159	808	1	[	[	X
ejpam-6159	808	2	20	20	NUM
ejpam-6159	808	3	]	]	PUNCT
ejpam-6159	808	4	s.	s.	PROPN
ejpam-6159	808	5	erden	erden	PROPN
ejpam-6159	808	6	,	,	PUNCT
ejpam-6159	808	7	h.	h.	PROPN
ejpam-6159	808	8	budak	budak	PROPN
ejpam-6159	808	9	,	,	PUNCT
ejpam-6159	808	10	and	and	CCONJ
ejpam-6159	808	11	m.	m.	PROPN
ejpam-6159	808	12	z.	z.	PROPN
ejpam-6159	808	13	sarikaya	sarikaya	PROPN
ejpam-6159	808	14	.	.	PUNCT
ejpam-6159	809	1	fractional	fractional	ADJ
ejpam-6159	809	2	ostrowski	ostrowski	ADJ
ejpam-6159	809	3	type	type	NOUN
ejpam-6159	809	4	inequalities	inequality	NOUN
ejpam-6159	809	5	for	for	ADP
ejpam-6159	809	6	functions	function	NOUN
ejpam-6159	809	7	of	of	ADP
ejpam-6159	809	8	bounded	bounded	ADJ
ejpam-6159	809	9	variation	variation	NOUN
ejpam-6159	809	10	with	with	ADP
ejpam-6159	809	11	two	two	NUM
ejpam-6159	809	12	variables	variable	NOUN
ejpam-6159	809	13	.	.	PUNCT
ejpam-6159	810	1	aims	aim	VERB
ejpam-6159	810	2	mathematics	mathematic	NOUN
ejpam-6159	810	3	,	,	PUNCT
ejpam-6159	810	4	5(2):1053	5(2):1053	NUM
ejpam-6159	810	5	–	–	PUNCT
ejpam-6159	810	6	1067	1067	NUM
ejpam-6159	810	7	,	,	PUNCT
ejpam-6159	810	8	2020	2020	NUM
ejpam-6159	810	9	.	.	PUNCT
ejpam-6159	811	1	[	[	X
ejpam-6159	811	2	21	21	NUM
ejpam-6159	811	3	]	]	X
ejpam-6159	811	4	s.	s.	PROPN
ejpam-6159	811	5	rashid	rashid	PROPN
ejpam-6159	811	6	,	,	PUNCT
ejpam-6159	811	7	i̇.	i̇.	NOUN
ejpam-6159	811	8	i̇şcan	i̇şcan	ADJ
ejpam-6159	811	9	,	,	PUNCT
ejpam-6159	811	10	s.	s.	PROPN
ejpam-6159	811	11	baleanu	baleanu	PROPN
ejpam-6159	811	12	,	,	PUNCT
ejpam-6159	811	13	and	and	CCONJ
ejpam-6159	811	14	y.	y.	PROPN
ejpam-6159	811	15	m.	m.	PROPN
ejpam-6159	811	16	chu	chu	PROPN
ejpam-6159	811	17	.	.	PUNCT
ejpam-6159	812	1	generation	generation	NOUN
ejpam-6159	812	2	of	of	ADP
ejpam-6159	812	3	new	new	ADJ
ejpam-6159	812	4	fractional	fractional	ADJ
ejpam-6159	812	5	inequalities	inequality	NOUN
ejpam-6159	812	6	via	via	ADP
ejpam-6159	812	7	n	n	ADP
ejpam-6159	812	8	polynomials	polynomial	NOUN
ejpam-6159	812	9	s	s	NOUN
ejpam-6159	812	10	-	-	PUNCT
ejpam-6159	812	11	type	type	NOUN
ejpam-6159	812	12	convexity	convexity	NOUN
ejpam-6159	812	13	with	with	ADP
ejpam-6159	812	14	applications	application	NOUN
ejpam-6159	812	15	.	.	PUNCT
ejpam-6159	813	1	advances	advance	NOUN
ejpam-6159	813	2	in	in	ADP
ejpam-6159	813	3	difference	difference	NOUN
ejpam-6159	813	4	equations	equation	NOUN
ejpam-6159	813	5	,	,	PUNCT
ejpam-6159	813	6	2020:1–20	2020:1–20	NUM
ejpam-6159	813	7	,	,	PUNCT
ejpam-6159	813	8	2020	2020	NUM
ejpam-6159	813	9	.	.	PUNCT
ejpam-6159	814	1	[	[	X
ejpam-6159	814	2	22	22	NUM
ejpam-6159	814	3	]	]	PUNCT
ejpam-6159	814	4	m.	m.	NOUN
ejpam-6159	814	5	a.	a.	PROPN
ejpam-6159	814	6	noor	noor	PROPN
ejpam-6159	814	7	.	.	PUNCT
ejpam-6159	815	1	hermite	hermite	PROPN
ejpam-6159	815	2	-	-	PUNCT
ejpam-6159	815	3	hadamard	hadamard	ADJ
ejpam-6159	815	4	integral	integral	ADJ
ejpam-6159	815	5	inequalities	inequality	NOUN
ejpam-6159	815	6	for	for	ADP
ejpam-6159	815	7	log	log	NOUN
ejpam-6159	815	8	-	-	PUNCT
ejpam-6159	815	9	preinvex	preinvex	NOUN
ejpam-6159	815	10	functions	function	NOUN
ejpam-6159	815	11	.	.	PUNCT
ejpam-6159	816	1	journal	journal	NOUN
ejpam-6159	816	2	of	of	ADP
ejpam-6159	816	3	mathematical	mathematical	ADJ
ejpam-6159	816	4	analysis	analysis	NOUN
ejpam-6159	816	5	and	and	CCONJ
ejpam-6159	816	6	approximation	approximation	NOUN
ejpam-6159	816	7	theory	theory	NOUN
ejpam-6159	816	8	,	,	PUNCT
ejpam-6159	816	9	2(2):126–131	2(2):126–131	NUM
ejpam-6159	816	10	,	,	PUNCT
ejpam-6159	816	11	2007	2007	NUM
ejpam-6159	816	12	.	.	PUNCT
ejpam-6159	817	1	[	[	X
ejpam-6159	817	2	23	23	NUM
ejpam-6159	817	3	]	]	PUNCT
ejpam-6159	817	4	m.	m.	NOUN
ejpam-6159	817	5	tariq	tariq	PROPN
ejpam-6159	817	6	,	,	PUNCT
ejpam-6159	817	7	s.	s.	PROPN
ejpam-6159	817	8	k.	k.	PROPN
ejpam-6159	817	9	sahoo	sahoo	PROPN
ejpam-6159	817	10	,	,	PUNCT
ejpam-6159	817	11	f.	f.	PROPN
ejpam-6159	817	12	jarad	jarad	PROPN
ejpam-6159	817	13	,	,	PUNCT
ejpam-6159	817	14	and	and	CCONJ
ejpam-6159	817	15	e.	e.	PROPN
ejpam-6159	817	16	kodamasingh	kodamasingh	PROPN
ejpam-6159	817	17	.	.	PUNCT
ejpam-6159	818	1	some	some	DET
ejpam-6159	818	2	integral	integral	ADJ
ejpam-6159	818	3	inequalities	inequality	NOUN
ejpam-6159	818	4	for	for	ADP
ejpam-6159	818	5	generalized	generalized	ADJ
ejpam-6159	818	6	preinvex	preinvex	NOUN
ejpam-6159	818	7	functions	function	NOUN
ejpam-6159	818	8	with	with	ADP
ejpam-6159	818	9	applications	application	NOUN
ejpam-6159	818	10	.	.	PUNCT
ejpam-6159	819	1	journal	journal	PROPN
ejpam-6159	819	2	of	of	ADP
ejpam-6159	819	3	inequalities	inequality	NOUN
ejpam-6159	819	4	and	and	CCONJ
ejpam-6159	819	5	applications	application	NOUN
ejpam-6159	819	6	,	,	PUNCT
ejpam-6159	819	7	2021:147	2021:147	NOUN
ejpam-6159	819	8	,	,	PUNCT
ejpam-6159	819	9	2021	2021	NUM
ejpam-6159	819	10	.	.	PUNCT
ejpam-6159	820	1	[	[	X
ejpam-6159	820	2	24	24	NUM
ejpam-6159	820	3	]	]	PUNCT
ejpam-6159	820	4	i̇.	i̇.	NOUN
ejpam-6159	820	5	i̇şcan	i̇şcan	PROPN
ejpam-6159	820	6	.	.	PUNCT
ejpam-6159	821	1	construction	construction	NOUN
ejpam-6159	821	2	of	of	ADP
ejpam-6159	821	3	a	a	DET
ejpam-6159	821	4	new	new	ADJ
ejpam-6159	821	5	class	class	NOUN
ejpam-6159	821	6	of	of	ADP
ejpam-6159	821	7	functions	function	NOUN
ejpam-6159	821	8	with	with	ADP
ejpam-6159	821	9	their	their	PRON
ejpam-6159	821	10	some	some	DET
ejpam-6159	821	11	properties	property	NOUN
ejpam-6159	821	12	and	and	CCONJ
ejpam-6159	821	13	certain	certain	ADJ
ejpam-6159	821	14	inequalities	inequality	NOUN
ejpam-6159	821	15	:	:	PUNCT
ejpam-6159	821	16	n	n	NUM
ejpam-6159	821	17	-	-	PUNCT
ejpam-6159	821	18	fractional	fractional	ADJ
ejpam-6159	821	19	polynomial	polynomial	ADJ
ejpam-6159	821	20	convex	convex	NOUN
ejpam-6159	821	21	functions	function	NOUN
ejpam-6159	821	22	.	.	PUNCT
ejpam-6159	822	1	miskolc	miskolc	ADJ
ejpam-6159	822	2	mathematical	mathematical	ADJ
ejpam-6159	822	3	notes	note	NOUN
ejpam-6159	822	4	,	,	PUNCT
ejpam-6159	822	5	24(3	24(3	NUM
ejpam-6159	822	6	)	)	PUNCT
ejpam-6159	822	7	,	,	PUNCT
ejpam-6159	822	8	2023	2023	NUM
ejpam-6159	822	9	.	.	PUNCT
ejpam-6159	823	1	[	[	X
ejpam-6159	823	2	25	25	NUM
ejpam-6159	823	3	]	]	PUNCT
ejpam-6159	823	4	j.	j.	PROPN
ejpam-6159	823	5	nasir	nasir	PROPN
ejpam-6159	823	6	,	,	PUNCT
ejpam-6159	823	7	s.	s.	PROPN
ejpam-6159	823	8	qaisar	qaisar	PROPN
ejpam-6159	823	9	,	,	PUNCT
ejpam-6159	823	10	s.	s.	PROPN
ejpam-6159	823	11	i.	i.	PROPN
ejpam-6159	823	12	butt	butt	PROPN
ejpam-6159	823	13	,	,	PUNCT
ejpam-6159	823	14	h.	h.	PROPN
ejpam-6159	823	15	aydi	aydi	PROPN
ejpam-6159	823	16	,	,	PUNCT
ejpam-6159	823	17	and	and	CCONJ
ejpam-6159	823	18	m.	m.	PROPN
ejpam-6159	823	19	de	de	PROPN
ejpam-6159	823	20	la	la	PROPN
ejpam-6159	823	21	sen	sen	PROPN
ejpam-6159	823	22	.	.	PROPN
ejpam-6159	823	23	hermite	hermite	PROPN
ejpam-6159	823	24	-	-	PUNCT
ejpam-6159	823	25	hadamard	hadamard	PROPN
ejpam-6159	823	26	like	like	ADP
ejpam-6159	823	27	inequalities	inequality	NOUN
ejpam-6159	823	28	for	for	ADP
ejpam-6159	823	29	fractional	fractional	ADJ
ejpam-6159	823	30	integral	integral	ADJ
ejpam-6159	823	31	operator	operator	NOUN
ejpam-6159	823	32	via	via	ADP
ejpam-6159	823	33	convexity	convexity	NOUN
ejpam-6159	823	34	and	and	CCONJ
ejpam-6159	823	35	quasi	quasi	NOUN
ejpam-6159	823	36	-	-	NOUN
ejpam-6159	823	37	convexity	convexity	NOUN
ejpam-6159	823	38	with	with	ADP
ejpam-6159	823	39	their	their	PRON
ejpam-6159	823	40	applications	application	NOUN
ejpam-6159	823	41	.	.	PUNCT
ejpam-6159	824	1	aims	aim	VERB
ejpam-6159	824	2	mathematics	mathematic	NOUN
ejpam-6159	824	3	,	,	PUNCT
ejpam-6159	824	4	7(3):3418–3439	7(3):3418–3439	NOUN
ejpam-6159	824	5	,	,	PUNCT
ejpam-6159	824	6	2022	2022	NUM
ejpam-6159	824	7	.	.	PUNCT
ejpam-6159	825	1	[	[	X
ejpam-6159	825	2	26	26	NUM
ejpam-6159	825	3	]	]	X
ejpam-6159	825	4	s.	s.	PROPN
ejpam-6159	825	5	mubeen	mubeen	PROPN
ejpam-6159	825	6	and	and	CCONJ
ejpam-6159	825	7	g.	g.	PROPN
ejpam-6159	825	8	m.	m.	PROPN
ejpam-6159	825	9	habibullah	habibullah	PROPN
ejpam-6159	825	10	.	.	PUNCT
ejpam-6159	826	1	k	k	ADJ
ejpam-6159	826	2	-	-	PUNCT
ejpam-6159	826	3	fractional	fractional	ADJ
ejpam-6159	826	4	integrals	integral	NOUN
ejpam-6159	826	5	and	and	CCONJ
ejpam-6159	826	6	application	application	NOUN
ejpam-6159	826	7	.	.	PUNCT
ejpam-6159	827	1	international	international	ADJ
ejpam-6159	827	2	journal	journal	PROPN
ejpam-6159	827	3	of	of	ADP
ejpam-6159	827	4	contemporary	contemporary	PROPN
ejpam-6159	827	5	mathematical	mathematical	PROPN
ejpam-6159	827	6	sciences	sciences	PROPN
ejpam-6159	827	7	,	,	PUNCT
ejpam-6159	827	8	7(2):89–94	7(2):89–94	NUM
ejpam-6159	827	9	,	,	PUNCT
ejpam-6159	827	10	2012	2012	NUM
ejpam-6159	827	11	.	.	PUNCT
ejpam-6159	828	1	[	[	X
ejpam-6159	828	2	27	27	NUM
ejpam-6159	828	3	]	]	PUNCT
ejpam-6159	828	4	m.	m.	NOUN
ejpam-6159	828	5	sababheh	sababheh	NOUN
ejpam-6159	828	6	.	.	PUNCT
ejpam-6159	829	1	convex	convex	NOUN
ejpam-6159	829	2	functions	function	NOUN
ejpam-6159	829	3	and	and	CCONJ
ejpam-6159	829	4	means	mean	NOUN
ejpam-6159	829	5	of	of	ADP
ejpam-6159	829	6	matrices	matrix	NOUN
ejpam-6159	829	7	,	,	PUNCT
ejpam-6159	829	8	2016	2016	NUM
ejpam-6159	829	9	.	.	PUNCT
ejpam-6159	830	1	arxiv:1606.08099	arxiv:1606.08099	PROPN
ejpam-6159	830	2	.	.	PUNCT
ejpam-6159	831	1	[	[	X
ejpam-6159	831	2	28	28	NUM
ejpam-6159	831	3	]	]	X
ejpam-6159	831	4	s.	s.	PROPN
ejpam-6159	831	5	i.	i.	PROPN
ejpam-6159	831	6	butt	butt	PROPN
ejpam-6159	831	7	,	,	PUNCT
ejpam-6159	831	8	b.	b.	PROPN
ejpam-6159	831	9	bayraktar	bayraktar	PROPN
ejpam-6159	831	10	,	,	PUNCT
ejpam-6159	831	11	and	and	CCONJ
ejpam-6159	831	12	j.	j.	PROPN
ejpam-6159	831	13	nasir	nasir	PROPN
ejpam-6159	831	14	.	.	PUNCT
ejpam-6159	832	1	novel	novel	ADJ
ejpam-6159	832	2	ostrowski	ostrowski	ADJ
ejpam-6159	832	3	type	type	NOUN
ejpam-6159	832	4	inequalities	inequality	NOUN
ejpam-6159	832	5	via	via	ADP
ejpam-6159	832	6	exponentially	exponentially	ADV
ejpam-6159	832	7	(	(	PUNCT
ejpam-6159	832	8	m1	m1	NOUN
ejpam-6159	832	9	,	,	PUNCT
ejpam-6159	832	10	m2)-convex	m2)-convex	PROPN
ejpam-6159	832	11	functions	function	NOUN
ejpam-6159	832	12	and	and	CCONJ
ejpam-6159	832	13	their	their	PRON
ejpam-6159	832	14	applications	application	NOUN
ejpam-6159	832	15	.	.	PUNCT
ejpam-6159	833	1	annals	annal	NOUN
ejpam-6159	833	2	of	of	ADP
ejpam-6159	833	3	the	the	DET
ejpam-6159	833	4	university	university	NOUN
ejpam-6159	833	5	of	of	ADP
ejpam-6159	833	6	craiova	craiova	PROPN
ejpam-6159	833	7	-	-	PUNCT
ejpam-6159	833	8	mathematics	mathematic	NOUN
ejpam-6159	833	9	and	and	CCONJ
ejpam-6159	833	10	computer	computer	NOUN
ejpam-6159	833	11	science	science	NOUN
ejpam-6159	833	12	series	series	NOUN
ejpam-6159	833	13	,	,	PUNCT
ejpam-6159	833	14	51(2):488–504	51(2):488–504	ADV
ejpam-6159	833	15	,	,	PUNCT
ejpam-6159	833	16	2024	2024	NUM
ejpam-6159	833	17	.	.	PUNCT