id	sid	tid	token	lemma	pos
ejpam-6306	1	1	european	european	PROPN
ejpam-6306	1	2	journal	journal	PROPN
ejpam-6306	1	3	of	of	ADP
ejpam-6306	1	4	pure	pure	ADJ
ejpam-6306	1	5	and	and	CCONJ
ejpam-6306	1	6	applied	applied	ADJ
ejpam-6306	1	7	mathematics	mathematic	NOUN
ejpam-6306	1	8	2025	2025	NUM
ejpam-6306	1	9	,	,	PUNCT
ejpam-6306	1	10	vol	vol	NOUN
ejpam-6306	1	11	.	.	PROPN
ejpam-6306	1	12	18	18	NUM
ejpam-6306	1	13	,	,	PUNCT
ejpam-6306	1	14	issue	issue	NOUN
ejpam-6306	1	15	3	3	NUM
ejpam-6306	1	16	,	,	PUNCT
ejpam-6306	1	17	article	article	NOUN
ejpam-6306	1	18	number	number	NOUN
ejpam-6306	1	19	6306	6306	NUM
ejpam-6306	1	20	issn	issn	PROPN
ejpam-6306	1	21	1307	1307	NUM
ejpam-6306	1	22	-	-	SYM
ejpam-6306	1	23	5543	5543	NUM
ejpam-6306	1	24	–	–	PUNCT
ejpam-6306	1	25	ejpam.com	ejpam.com	X
ejpam-6306	1	26	published	publish	VERB
ejpam-6306	1	27	by	by	ADP
ejpam-6306	1	28	new	new	PROPN
ejpam-6306	1	29	york	york	PROPN
ejpam-6306	1	30	business	business	PROPN
ejpam-6306	1	31	global	global	PROPN
ejpam-6306	1	32	a	a	DET
ejpam-6306	1	33	new	new	ADJ
ejpam-6306	1	34	trend	trend	NOUN
ejpam-6306	1	35	of	of	ADP
ejpam-6306	1	36	fractional	fractional	ADJ
ejpam-6306	1	37	inequalities	inequality	NOUN
ejpam-6306	1	38	for	for	ADP
ejpam-6306	1	39	differentiable	differentiable	ADJ
ejpam-6306	1	40	monotone	monotone	NOUN
ejpam-6306	1	41	convexities	convexity	NOUN
ejpam-6306	1	42	through	through	ADP
ejpam-6306	1	43	generalized	generalized	ADJ
ejpam-6306	1	44	operators	operator	NOUN
ejpam-6306	1	45	with	with	ADP
ejpam-6306	1	46	applications	application	NOUN
ejpam-6306	1	47	r.s.ali1,∗	r.s.ali1,∗	PROPN
ejpam-6306	1	48	,	,	PUNCT
ejpam-6306	1	49	n.	n.	PROPN
ejpam-6306	1	50	talib1	talib1	PROPN
ejpam-6306	1	51	,	,	PUNCT
ejpam-6306	1	52	s.	s.	PROPN
ejpam-6306	1	53	etemad2,3,4	etemad2,3,4	PROPN
ejpam-6306	1	54	,	,	PUNCT
ejpam-6306	1	55	j.	j.	PROPN
ejpam-6306	1	56	tariboon5,∗	tariboon5,∗	PROPN
ejpam-6306	1	57	,	,	PUNCT
ejpam-6306	1	58	m.	m.	NOUN
ejpam-6306	1	59	i.	i.	PROPN
ejpam-6306	1	60	hafeez6	hafeez6	PROPN
ejpam-6306	2	1	1	1	NUM
ejpam-6306	2	2	department	department	NOUN
ejpam-6306	2	3	of	of	ADP
ejpam-6306	2	4	mathematics	mathematic	NOUN
ejpam-6306	2	5	and	and	CCONJ
ejpam-6306	2	6	statistics	statistic	NOUN
ejpam-6306	2	7	,	,	PUNCT
ejpam-6306	2	8	the	the	DET
ejpam-6306	2	9	university	university	NOUN
ejpam-6306	2	10	of	of	ADP
ejpam-6306	2	11	lahore	lahore	PROPN
ejpam-6306	2	12	,	,	PUNCT
ejpam-6306	2	13	punjab	punjab	ADJ
ejpam-6306	2	14	,	,	PUNCT
ejpam-6306	2	15	pakistan	pakistan	PROPN
ejpam-6306	2	16	2	2	NUM
ejpam-6306	2	17	department	department	NOUN
ejpam-6306	2	18	of	of	ADP
ejpam-6306	2	19	mathematics	mathematic	NOUN
ejpam-6306	2	20	,	,	PUNCT
ejpam-6306	2	21	saveetha	saveetha	PROPN
ejpam-6306	2	22	school	school	PROPN
ejpam-6306	2	23	of	of	ADP
ejpam-6306	2	24	engineering	engineering	PROPN
ejpam-6306	2	25	,	,	PUNCT
ejpam-6306	2	26	saveetha	saveetha	PROPN
ejpam-6306	2	27	institute	institute	PROPN
ejpam-6306	2	28	of	of	ADP
ejpam-6306	2	29	medical	medical	ADJ
ejpam-6306	2	30	and	and	CCONJ
ejpam-6306	2	31	technical	technical	ADJ
ejpam-6306	2	32	sciences	science	NOUN
ejpam-6306	2	33	,	,	PUNCT
ejpam-6306	2	34	saveetha	saveetha	PROPN
ejpam-6306	2	35	university	university	PROPN
ejpam-6306	2	36	,	,	PUNCT
ejpam-6306	2	37	chennai	chennai	VERB
ejpam-6306	2	38	602	602	NUM
ejpam-6306	2	39	105	105	NUM
ejpam-6306	2	40	,	,	PUNCT
ejpam-6306	2	41	tamil	tamil	PROPN
ejpam-6306	2	42	nadu	nadu	PROPN
ejpam-6306	2	43	,	,	PUNCT
ejpam-6306	2	44	india	india	PROPN
ejpam-6306	2	45	3	3	NUM
ejpam-6306	2	46	department	department	PROPN
ejpam-6306	2	47	of	of	ADP
ejpam-6306	2	48	mathematics	mathematics	PROPN
ejpam-6306	2	49	,	,	PUNCT
ejpam-6306	2	50	azarbaijan	azarbaijan	NOUN
ejpam-6306	2	51	shahid	shahid	PROPN
ejpam-6306	2	52	madani	madani	PROPN
ejpam-6306	2	53	university	university	PROPN
ejpam-6306	2	54	,	,	PUNCT
ejpam-6306	2	55	tabriz	tabriz	NOUN
ejpam-6306	2	56	,	,	PUNCT
ejpam-6306	2	57	iran	iran	PROPN
ejpam-6306	2	58	4	4	NUM
ejpam-6306	2	59	mathematics	mathematic	NOUN
ejpam-6306	2	60	in	in	ADP
ejpam-6306	2	61	applied	apply	VERB
ejpam-6306	2	62	sciences	science	NOUN
ejpam-6306	2	63	and	and	CCONJ
ejpam-6306	2	64	engineering	engineering	NOUN
ejpam-6306	2	65	research	research	NOUN
ejpam-6306	2	66	group	group	NOUN
ejpam-6306	2	67	,	,	PUNCT
ejpam-6306	2	68	scientific	scientific	ADJ
ejpam-6306	2	69	research	research	NOUN
ejpam-6306	2	70	center	center	NOUN
ejpam-6306	2	71	,	,	PUNCT
ejpam-6306	2	72	al	al	PROPN
ejpam-6306	2	73	-	-	PUNCT
ejpam-6306	2	74	ayen	ayen	PROPN
ejpam-6306	2	75	university	university	NOUN
ejpam-6306	2	76	,	,	PUNCT
ejpam-6306	2	77	nasiriyah	nasiriyah	NOUN
ejpam-6306	2	78	64001	64001	NUM
ejpam-6306	2	79	,	,	PUNCT
ejpam-6306	2	80	iraq	iraq	PROPN
ejpam-6306	2	81	.	.	PUNCT
ejpam-6306	3	1	5	5	NUM
ejpam-6306	3	2	intelligent	intelligent	ADJ
ejpam-6306	3	3	and	and	CCONJ
ejpam-6306	3	4	nonlinear	nonlinear	ADJ
ejpam-6306	3	5	dynamic	dynamic	ADJ
ejpam-6306	3	6	innovations	innovation	NOUN
ejpam-6306	3	7	research	research	NOUN
ejpam-6306	3	8	center	center	NOUN
ejpam-6306	3	9	,	,	PUNCT
ejpam-6306	3	10	department	department	NOUN
ejpam-6306	3	11	of	of	ADP
ejpam-6306	3	12	mathematics	mathematic	NOUN
ejpam-6306	3	13	,	,	PUNCT
ejpam-6306	3	14	faculty	faculty	NOUN
ejpam-6306	3	15	of	of	ADP
ejpam-6306	3	16	applied	apply	VERB
ejpam-6306	3	17	science	science	NOUN
ejpam-6306	3	18	,	,	PUNCT
ejpam-6306	3	19	king	king	PROPN
ejpam-6306	3	20	mongkut	mongkut	PROPN
ejpam-6306	3	21	’s	’s	PROPN
ejpam-6306	3	22	university	university	PROPN
ejpam-6306	3	23	of	of	ADP
ejpam-6306	3	24	technology	technology	PROPN
ejpam-6306	3	25	north	north	PROPN
ejpam-6306	3	26	bangkok	bangkok	PROPN
ejpam-6306	3	27	,	,	PUNCT
ejpam-6306	3	28	bangkok	bangkok	PROPN
ejpam-6306	3	29	10800	10800	NUM
ejpam-6306	3	30	,	,	PUNCT
ejpam-6306	3	31	thailand	thailand	PROPN
ejpam-6306	3	32	6department	6department	NUM
ejpam-6306	3	33	of	of	ADP
ejpam-6306	3	34	computer	computer	NOUN
ejpam-6306	3	35	science	science	NOUN
ejpam-6306	3	36	,	,	PUNCT
ejpam-6306	3	37	the	the	DET
ejpam-6306	3	38	university	university	NOUN
ejpam-6306	3	39	of	of	ADP
ejpam-6306	3	40	lahore	lahore	PROPN
ejpam-6306	3	41	,	,	PUNCT
ejpam-6306	3	42	sargodha	sargodha	PROPN
ejpam-6306	3	43	campus	campus	PROPN
ejpam-6306	3	44	,	,	PUNCT
ejpam-6306	3	45	sargodha	sargodha	PROPN
ejpam-6306	3	46	,	,	PUNCT
ejpam-6306	3	47	punjab	punjab	PROPN
ejpam-6306	3	48	,	,	PUNCT
ejpam-6306	3	49	pakistan	pakistan	PROPN
ejpam-6306	3	50	abstract	abstract	NOUN
ejpam-6306	3	51	.	.	PUNCT
ejpam-6306	4	1	this	this	DET
ejpam-6306	4	2	paper	paper	NOUN
ejpam-6306	4	3	’s	’s	PART
ejpam-6306	4	4	main	main	ADJ
ejpam-6306	4	5	goal	goal	NOUN
ejpam-6306	4	6	is	be	AUX
ejpam-6306	4	7	to	to	PART
ejpam-6306	4	8	describe	describe	VERB
ejpam-6306	4	9	the	the	DET
ejpam-6306	4	10	new	new	ADJ
ejpam-6306	4	11	fractional	fractional	ADJ
ejpam-6306	4	12	operators	operator	NOUN
ejpam-6306	4	13	for	for	ADP
ejpam-6306	4	14	monotone	monotone	ADJ
ejpam-6306	4	15	differentiable	differentiable	ADJ
ejpam-6306	4	16	function	function	NOUN
ejpam-6306	4	17	equipped	equip	VERB
ejpam-6306	4	18	with	with	ADP
ejpam-6306	4	19	generalized	generalized	ADJ
ejpam-6306	4	20	mittag	mittag	ADJ
ejpam-6306	4	21	-	-	PUNCT
ejpam-6306	4	22	leffler	leffler	NOUN
ejpam-6306	4	23	functions	function	NOUN
ejpam-6306	4	24	as	as	ADP
ejpam-6306	4	25	its	its	PRON
ejpam-6306	4	26	kernel	kernel	NOUN
ejpam-6306	4	27	,	,	PUNCT
ejpam-6306	4	28	and	and	CCONJ
ejpam-6306	4	29	develop	develop	VERB
ejpam-6306	4	30	the	the	DET
ejpam-6306	4	31	fractional	fractional	ADJ
ejpam-6306	4	32	inequalities	inequality	NOUN
ejpam-6306	4	33	for	for	ADP
ejpam-6306	4	34	a	a	DET
ejpam-6306	4	35	new	new	ADJ
ejpam-6306	4	36	family	family	NOUN
ejpam-6306	4	37	of	of	ADP
ejpam-6306	4	38	continuous	continuous	ADJ
ejpam-6306	4	39	differentiable	differentiable	ADJ
ejpam-6306	4	40	convex	convex	NOUN
ejpam-6306	4	41	functions	function	NOUN
ejpam-6306	4	42	by	by	ADP
ejpam-6306	4	43	implementation	implementation	NOUN
ejpam-6306	4	44	of	of	ADP
ejpam-6306	4	45	newly	newly	ADV
ejpam-6306	4	46	described	describe	VERB
ejpam-6306	4	47	fractional	fractional	ADJ
ejpam-6306	4	48	operators	operator	NOUN
ejpam-6306	4	49	.	.	PUNCT
ejpam-6306	5	1	due	due	ADP
ejpam-6306	5	2	to	to	ADP
ejpam-6306	5	3	the	the	DET
ejpam-6306	5	4	generalized	generalize	VERB
ejpam-6306	5	5	fractional	fractional	ADJ
ejpam-6306	5	6	operators	operator	NOUN
ejpam-6306	5	7	to	to	PART
ejpam-6306	5	8	obtain	obtain	VERB
ejpam-6306	5	9	the	the	DET
ejpam-6306	5	10	new	new	ADJ
ejpam-6306	5	11	version	version	NOUN
ejpam-6306	5	12	of	of	ADP
ejpam-6306	5	13	the	the	DET
ejpam-6306	5	14	hermite	hermite	ADJ
ejpam-6306	5	15	hadamard	hadamard	ADJ
ejpam-6306	5	16	type	type	NOUN
ejpam-6306	5	17	inequalities	inequality	NOUN
ejpam-6306	5	18	,	,	PUNCT
ejpam-6306	5	19	and	and	CCONJ
ejpam-6306	5	20	their	their	PRON
ejpam-6306	5	21	refinements	refinement	NOUN
ejpam-6306	5	22	for	for	ADP
ejpam-6306	5	23	continuous	continuous	ADJ
ejpam-6306	5	24	differentiable	differentiable	ADJ
ejpam-6306	5	25	monotone	monotone	ADJ
ejpam-6306	5	26	convexities	convexity	NOUN
ejpam-6306	5	27	,	,	PUNCT
ejpam-6306	5	28	all	all	DET
ejpam-6306	5	29	the	the	DET
ejpam-6306	5	30	results	result	NOUN
ejpam-6306	5	31	have	have	VERB
ejpam-6306	5	32	a	a	DET
ejpam-6306	5	33	significant	significant	ADJ
ejpam-6306	5	34	behavior	behavior	NOUN
ejpam-6306	5	35	in	in	ADP
ejpam-6306	5	36	the	the	DET
ejpam-6306	5	37	field	field	NOUN
ejpam-6306	5	38	of	of	ADP
ejpam-6306	5	39	analysis	analysis	NOUN
ejpam-6306	5	40	,	,	PUNCT
ejpam-6306	5	41	and	and	CCONJ
ejpam-6306	5	42	open	open	VERB
ejpam-6306	5	43	new	new	ADJ
ejpam-6306	5	44	horizon	horizon	NOUN
ejpam-6306	5	45	for	for	ADP
ejpam-6306	5	46	the	the	DET
ejpam-6306	5	47	modification	modification	NOUN
ejpam-6306	5	48	of	of	ADP
ejpam-6306	5	49	inequalities	inequality	NOUN
ejpam-6306	5	50	through	through	ADP
ejpam-6306	5	51	a	a	DET
ejpam-6306	5	52	new	new	ADJ
ejpam-6306	5	53	class	class	NOUN
ejpam-6306	5	54	of	of	ADP
ejpam-6306	5	55	convexities	convexity	NOUN
ejpam-6306	5	56	.	.	PUNCT
ejpam-6306	6	1	we	we	PRON
ejpam-6306	6	2	also	also	ADV
ejpam-6306	6	3	spoke	speak	VERB
ejpam-6306	6	4	about	about	ADP
ejpam-6306	6	5	a	a	DET
ejpam-6306	6	6	few	few	ADJ
ejpam-6306	6	7	unique	unique	ADJ
ejpam-6306	6	8	situations	situation	NOUN
ejpam-6306	6	9	involving	involve	VERB
ejpam-6306	6	10	the	the	DET
ejpam-6306	6	11	acquired	acquire	VERB
ejpam-6306	6	12	outcome	outcome	NOUN
ejpam-6306	6	13	in	in	ADP
ejpam-6306	6	14	the	the	DET
ejpam-6306	6	15	framework	framework	NOUN
ejpam-6306	6	16	of	of	ADP
ejpam-6306	6	17	the	the	DET
ejpam-6306	6	18	corollaries	corollary	NOUN
ejpam-6306	6	19	.	.	PUNCT
ejpam-6306	7	1	2020	2020	NUM
ejpam-6306	7	2	mathematics	mathematic	NOUN
ejpam-6306	7	3	subject	subject	NOUN
ejpam-6306	7	4	classifications	classification	NOUN
ejpam-6306	7	5	:	:	PUNCT
ejpam-6306	7	6	26a51	26a51	NUM
ejpam-6306	7	7	,	,	PUNCT
ejpam-6306	7	8	26a33	26a33	NUM
ejpam-6306	7	9	,	,	PUNCT
ejpam-6306	7	10	33e12	33e12	NUM
ejpam-6306	7	11	,	,	PUNCT
ejpam-6306	7	12	26d20	26d20	NUM
ejpam-6306	7	13	key	key	ADJ
ejpam-6306	7	14	words	word	NOUN
ejpam-6306	7	15	and	and	CCONJ
ejpam-6306	7	16	phrases	phrase	NOUN
ejpam-6306	7	17	:	:	PUNCT
ejpam-6306	7	18	monotone	monotone	ADJ
ejpam-6306	7	19	convex	convex	NOUN
ejpam-6306	7	20	functions	function	NOUN
ejpam-6306	7	21	,	,	PUNCT
ejpam-6306	7	22	fractional	fractional	ADJ
ejpam-6306	7	23	operators	operator	NOUN
ejpam-6306	7	24	,	,	PUNCT
ejpam-6306	7	25	generalized	generalized	ADJ
ejpam-6306	7	26	mittagleffler	mittagleffler	NOUN
ejpam-6306	7	27	function	function	NOUN
ejpam-6306	7	28	,	,	PUNCT
ejpam-6306	7	29	hermite	hermite	PROPN
ejpam-6306	7	30	-	-	PUNCT
ejpam-6306	7	31	hadamard	hadamard	ADJ
ejpam-6306	7	32	inequality	inequality	NOUN
ejpam-6306	7	33	∗corresponding	∗corresponde	VERB
ejpam-6306	7	34	author	author	NOUN
ejpam-6306	7	35	.	.	PUNCT
ejpam-6306	8	1	∗corresponding	∗corresponde	VERB
ejpam-6306	8	2	author	author	NOUN
ejpam-6306	8	3	.	.	PUNCT
ejpam-6306	9	1	doi	doi	NOUN
ejpam-6306	9	2	:	:	PUNCT
ejpam-6306	9	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6306	https://doi.org/10.29020/nybg.ejpam.v18i3.6306	ADJ
ejpam-6306	9	4	email	email	NOUN
ejpam-6306	9	5	addresses	address	NOUN
ejpam-6306	9	6	:	:	PUNCT
ejpam-6306	9	7	rsafdar0@gmail.com	rsafdar0@gmail.com	X
ejpam-6306	9	8	(	(	PUNCT
ejpam-6306	9	9	r.	r.	PROPN
ejpam-6306	9	10	s.	s.	PROPN
ejpam-6306	9	11	ali	ali	PROPN
ejpam-6306	9	12	)	)	PUNCT
ejpam-6306	9	13	,	,	PUNCT
ejpam-6306	9	14	20nailatalib@gmail.com	20nailatalib@gmail.com	PROPN
ejpam-6306	9	15	(	(	PUNCT
ejpam-6306	9	16	n.	n.	PROPN
ejpam-6306	9	17	talib	talib	PROPN
ejpam-6306	9	18	)	)	PUNCT
ejpam-6306	9	19	,	,	PUNCT
ejpam-6306	9	20	sina.etemad@gmail.com	sina.etemad@gmail.com	X
ejpam-6306	9	21	(	(	PUNCT
ejpam-6306	9	22	s.	s.	PROPN
ejpam-6306	9	23	etemad	etemad	PROPN
ejpam-6306	9	24	)	)	PUNCT
ejpam-6306	9	25	,	,	PUNCT
ejpam-6306	9	26	jessada.t@sci.kmutnb.ac.th	jessada.t@sci.kmutnb.ac.th	PROPN
ejpam-6306	9	27	(	(	PUNCT
ejpam-6306	9	28	t.	t.	PROPN
ejpam-6306	9	29	tariboon	tariboon	PROPN
ejpam-6306	9	30	)	)	PUNCT
ejpam-6306	9	31	,	,	PUNCT
ejpam-6306	9	32	muhammad.hafeez@cs.uol.edu.pk	muhammad.hafeez@cs.uol.edu.pk	PROPN
ejpam-6306	9	33	(	(	PUNCT
ejpam-6306	9	34	m.	m.	PROPN
ejpam-6306	9	35	i.	i.	PROPN
ejpam-6306	9	36	hafeez	hafeez	PROPN
ejpam-6306	9	37	)	)	PUNCT
ejpam-6306	9	38	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6306	10	1	1	1	NUM
ejpam-6306	10	2	copyright	copyright	NOUN
ejpam-6306	10	3	:	:	PUNCT
ejpam-6306	10	4	©	©	PROPN
ejpam-6306	10	5	2025	2025	NUM
ejpam-6306	10	6	the	the	DET
ejpam-6306	10	7	author(s	author(s	NOUN
ejpam-6306	10	8	)	)	PUNCT
ejpam-6306	10	9	.	.	PUNCT
ejpam-6306	11	1	(	(	PUNCT
ejpam-6306	11	2	cc	cc	NOUN
ejpam-6306	11	3	by	by	ADP
ejpam-6306	11	4	-	-	PUNCT
ejpam-6306	11	5	nc	nc	PROPN
ejpam-6306	11	6	4.0	4.0	NUM
ejpam-6306	11	7	)	)	PUNCT
ejpam-6306	11	8	r.	r.	PROPN
ejpam-6306	11	9	s.	s.	PROPN
ejpam-6306	11	10	ali	ali	PROPN
ejpam-6306	11	11	et	et	PROPN
ejpam-6306	11	12	al	al	PROPN
ejpam-6306	11	13	.	.	PUNCT
ejpam-6306	11	14	/	/	SYM
ejpam-6306	11	15	eur	eur	PROPN
ejpam-6306	11	16	.	.	PUNCT
ejpam-6306	12	1	j.	j.	PROPN
ejpam-6306	12	2	pure	pure	PROPN
ejpam-6306	12	3	appl	appl	PROPN
ejpam-6306	12	4	.	.	PROPN
ejpam-6306	12	5	math	math	PROPN
ejpam-6306	12	6	,	,	PUNCT
ejpam-6306	12	7	18	18	NUM
ejpam-6306	12	8	(	(	PUNCT
ejpam-6306	12	9	3	3	NUM
ejpam-6306	12	10	)	)	PUNCT
ejpam-6306	12	11	(	(	PUNCT
ejpam-6306	12	12	2025	2025	NUM
ejpam-6306	12	13	)	)	PUNCT
ejpam-6306	12	14	,	,	PUNCT
ejpam-6306	12	15	6306	6306	NUM
ejpam-6306	12	16	2	2	NUM
ejpam-6306	12	17	of	of	ADP
ejpam-6306	12	18	18	18	NUM
ejpam-6306	12	19	1	1	NUM
ejpam-6306	12	20	.	.	PUNCT
ejpam-6306	13	1	introduction	introduction	NOUN
ejpam-6306	13	2	fractional	fractional	ADJ
ejpam-6306	13	3	calculus	calculus	NOUN
ejpam-6306	13	4	(	(	PUNCT
ejpam-6306	13	5	fc	fc	INTJ
ejpam-6306	13	6	)	)	PUNCT
ejpam-6306	13	7	is	be	AUX
ejpam-6306	13	8	the	the	DET
ejpam-6306	13	9	generalization	generalization	NOUN
ejpam-6306	13	10	of	of	ADP
ejpam-6306	13	11	classical	classical	ADJ
ejpam-6306	13	12	calculus	calculus	NOUN
ejpam-6306	13	13	which	which	PRON
ejpam-6306	13	14	has	have	AUX
ejpam-6306	13	15	made	make	VERB
ejpam-6306	13	16	a	a	DET
ejpam-6306	13	17	great	great	ADJ
ejpam-6306	13	18	contribution	contribution	NOUN
ejpam-6306	13	19	in	in	ADP
ejpam-6306	13	20	many	many	ADJ
ejpam-6306	13	21	areas	area	NOUN
ejpam-6306	13	22	of	of	ADP
ejpam-6306	13	23	mathematics	mathematic	NOUN
ejpam-6306	13	24	,	,	PUNCT
ejpam-6306	13	25	due	due	ADP
ejpam-6306	13	26	to	to	ADP
ejpam-6306	13	27	its	its	PRON
ejpam-6306	13	28	numerous	numerous	ADJ
ejpam-6306	13	29	applications	application	NOUN
ejpam-6306	13	30	.	.	PUNCT
ejpam-6306	14	1	fractional	fractional	ADJ
ejpam-6306	14	2	operators	operator	NOUN
ejpam-6306	14	3	(	(	PUNCT
ejpam-6306	14	4	integral	integral	ADJ
ejpam-6306	14	5	and	and	CCONJ
ejpam-6306	14	6	differential	differential	NOUN
ejpam-6306	14	7	of	of	ADP
ejpam-6306	14	8	arbitrary	arbitrary	ADJ
ejpam-6306	14	9	order	order	NOUN
ejpam-6306	14	10	)	)	PUNCT
ejpam-6306	14	11	play	play	VERB
ejpam-6306	14	12	a	a	DET
ejpam-6306	14	13	vital	vital	ADJ
ejpam-6306	14	14	role	role	NOUN
ejpam-6306	14	15	in	in	ADP
ejpam-6306	14	16	the	the	DET
ejpam-6306	14	17	advancement	advancement	NOUN
ejpam-6306	14	18	of	of	ADP
ejpam-6306	14	19	modern	modern	ADJ
ejpam-6306	14	20	fc	fc	PROPN
ejpam-6306	14	21	.	.	PUNCT
ejpam-6306	15	1	in	in	ADP
ejpam-6306	15	2	recent	recent	ADJ
ejpam-6306	15	3	years	year	NOUN
ejpam-6306	15	4	,	,	PUNCT
ejpam-6306	15	5	the	the	DET
ejpam-6306	15	6	multi	multi	ADJ
ejpam-6306	15	7	-	-	ADJ
ejpam-6306	15	8	index	index	ADJ
ejpam-6306	15	9	special	special	ADJ
ejpam-6306	15	10	function	function	NOUN
ejpam-6306	15	11	has	have	AUX
ejpam-6306	15	12	been	be	AUX
ejpam-6306	15	13	used	use	VERB
ejpam-6306	15	14	in	in	ADP
ejpam-6306	15	15	extension	extension	NOUN
ejpam-6306	15	16	of	of	ADP
ejpam-6306	15	17	fractional	fractional	ADJ
ejpam-6306	15	18	operators	operator	NOUN
ejpam-6306	15	19	by	by	ADP
ejpam-6306	15	20	means	mean	NOUN
ejpam-6306	15	21	of	of	ADP
ejpam-6306	15	22	its	its	PRON
ejpam-6306	15	23	kernel	kernel	NOUN
ejpam-6306	15	24	.	.	PUNCT
ejpam-6306	16	1	many	many	ADJ
ejpam-6306	16	2	researchers	researcher	NOUN
ejpam-6306	16	3	,	,	PUNCT
ejpam-6306	16	4	including	include	VERB
ejpam-6306	16	5	riemann	riemann	PROPN
ejpam-6306	16	6	-	-	PUNCT
ejpam-6306	16	7	liouville	liouville	NOUN
ejpam-6306	16	8	(	(	PUNCT
ejpam-6306	16	9	rl	rl	NOUN
ejpam-6306	16	10	)	)	PUNCT
ejpam-6306	16	11	,	,	PUNCT
ejpam-6306	16	12	abel	abel	PROPN
ejpam-6306	16	13	,	,	PUNCT
ejpam-6306	16	14	laurent	laurent	NOUN
ejpam-6306	16	15	,	,	PUNCT
ejpam-6306	16	16	hardy	hardy	ADJ
ejpam-6306	16	17	,	,	PUNCT
ejpam-6306	16	18	and	and	CCONJ
ejpam-6306	16	19	littlewood	littlewood	PROPN
ejpam-6306	16	20	[	[	X
ejpam-6306	16	21	1–4	1–4	NOUN
ejpam-6306	16	22	]	]	X
ejpam-6306	16	23	,	,	PUNCT
ejpam-6306	16	24	and	and	CCONJ
ejpam-6306	16	25	others	other	NOUN
ejpam-6306	16	26	were	be	AUX
ejpam-6306	16	27	interested	interested	ADJ
ejpam-6306	16	28	in	in	ADP
ejpam-6306	16	29	this	this	DET
ejpam-6306	16	30	field	field	NOUN
ejpam-6306	16	31	.	.	PUNCT
ejpam-6306	17	1	the	the	DET
ejpam-6306	17	2	history	history	NOUN
ejpam-6306	17	3	of	of	ADP
ejpam-6306	17	4	fractional	fractional	ADJ
ejpam-6306	17	5	calculus	calculus	NOUN
ejpam-6306	17	6	was	be	AUX
ejpam-6306	17	7	covered	cover	VERB
ejpam-6306	17	8	in	in	ADP
ejpam-6306	17	9	detail	detail	NOUN
ejpam-6306	17	10	in	in	ADP
ejpam-6306	17	11	[	[	X
ejpam-6306	17	12	5	5	NUM
ejpam-6306	17	13	,	,	PUNCT
ejpam-6306	17	14	6	6	NUM
ejpam-6306	17	15	]	]	PUNCT
ejpam-6306	17	16	;	;	PUNCT
ejpam-6306	17	17	here	here	ADV
ejpam-6306	17	18	,	,	PUNCT
ejpam-6306	17	19	we	we	PRON
ejpam-6306	17	20	wanted	want	VERB
ejpam-6306	17	21	to	to	PART
ejpam-6306	17	22	concentrate	concentrate	VERB
ejpam-6306	17	23	on	on	ADP
ejpam-6306	17	24	a	a	DET
ejpam-6306	17	25	few	few	ADJ
ejpam-6306	17	26	significant	significant	ADJ
ejpam-6306	17	27	developments	development	NOUN
ejpam-6306	17	28	in	in	ADP
ejpam-6306	17	29	the	the	DET
ejpam-6306	17	30	many	many	ADJ
ejpam-6306	17	31	fields	field	NOUN
ejpam-6306	17	32	of	of	ADP
ejpam-6306	17	33	mathematics	mathematic	NOUN
ejpam-6306	17	34	.	.	PUNCT
ejpam-6306	18	1	although	although	SCONJ
ejpam-6306	18	2	leibniz	leibniz	PROPN
ejpam-6306	18	3	’s	’s	PART
ejpam-6306	18	4	“	"	PUNCT
ejpam-6306	18	5	paradoxes	paradox	NOUN
ejpam-6306	18	6	”	"	PUNCT
ejpam-6306	18	7	were	be	AUX
ejpam-6306	18	8	overcome	overcome	VERB
ejpam-6306	18	9	by	by	ADP
ejpam-6306	18	10	other	other	ADJ
ejpam-6306	18	11	writers	writer	NOUN
ejpam-6306	18	12	,	,	PUNCT
ejpam-6306	18	13	there	there	PRON
ejpam-6306	18	14	are	be	VERB
ejpam-6306	18	15	still	still	ADV
ejpam-6306	18	16	some	some	DET
ejpam-6306	18	17	unanswered	unanswered	ADJ
ejpam-6306	18	18	questions	question	NOUN
ejpam-6306	18	19	in	in	ADP
ejpam-6306	18	20	the	the	DET
ejpam-6306	18	21	domain	domain	NOUN
ejpam-6306	18	22	of	of	ADP
ejpam-6306	18	23	fractional	fractional	ADJ
ejpam-6306	18	24	calculus	calculus	NOUN
ejpam-6306	18	25	.	.	PUNCT
ejpam-6306	19	1	the	the	DET
ejpam-6306	19	2	availability	availability	NOUN
ejpam-6306	19	3	of	of	ADP
ejpam-6306	19	4	several	several	ADJ
ejpam-6306	19	5	contradictory	contradictory	ADJ
ejpam-6306	19	6	definitions	definition	NOUN
ejpam-6306	19	7	has	have	AUX
ejpam-6306	19	8	been	be	AUX
ejpam-6306	19	9	a	a	DET
ejpam-6306	19	10	persistent	persistent	ADJ
ejpam-6306	19	11	problem	problem	NOUN
ejpam-6306	19	12	throughout	throughout	ADP
ejpam-6306	19	13	the	the	DET
ejpam-6306	19	14	ages	age	NOUN
ejpam-6306	19	15	.	.	PUNCT
ejpam-6306	20	1	one	one	NUM
ejpam-6306	20	2	version	version	NOUN
ejpam-6306	20	3	was	be	AUX
ejpam-6306	20	4	created	create	VERB
ejpam-6306	20	5	by	by	ADP
ejpam-6306	20	6	liouville	liouville	NOUN
ejpam-6306	20	7	via	via	ADP
ejpam-6306	20	8	differentiating	differentiating	NOUN
ejpam-6306	20	9	of	of	ADP
ejpam-6306	20	10	the	the	DET
ejpam-6306	20	11	exponential	exponential	ADJ
ejpam-6306	20	12	functions	function	NOUN
ejpam-6306	20	13	,	,	PUNCT
ejpam-6306	20	14	and	and	CCONJ
ejpam-6306	20	15	another	another	DET
ejpam-6306	20	16	one	one	NOUN
ejpam-6306	20	17	was	be	AUX
ejpam-6306	20	18	introduced	introduce	VERB
ejpam-6306	20	19	by	by	ADP
ejpam-6306	20	20	lacroix	lacroix	NOUN
ejpam-6306	20	21	using	use	VERB
ejpam-6306	20	22	the	the	DET
ejpam-6306	20	23	integral	integral	ADJ
ejpam-6306	20	24	formula	formula	NOUN
ejpam-6306	20	25	for	for	ADP
ejpam-6306	20	26	inverse	inverse	ADJ
ejpam-6306	20	27	power	power	NOUN
ejpam-6306	20	28	functions	function	NOUN
ejpam-6306	20	29	.	.	PUNCT
ejpam-6306	21	1	some	some	DET
ejpam-6306	21	2	critics	critic	NOUN
ejpam-6306	21	3	have	have	AUX
ejpam-6306	21	4	concluded	conclude	VERB
ejpam-6306	21	5	that	that	SCONJ
ejpam-6306	21	6	one	one	NUM
ejpam-6306	21	7	definition	definition	NOUN
ejpam-6306	21	8	by	by	ADP
ejpam-6306	21	9	liouville	liouville	NOUN
ejpam-6306	21	10	and	and	CCONJ
ejpam-6306	21	11	one	one	NUM
ejpam-6306	21	12	by	by	ADP
ejpam-6306	21	13	lacroix	lacroix	NOUN
ejpam-6306	21	14	is	be	AUX
ejpam-6306	21	15	“	"	PUNCT
ejpam-6306	21	16	correct	correct	ADJ
ejpam-6306	21	17	”	"	PUNCT
ejpam-6306	21	18	while	while	SCONJ
ejpam-6306	21	19	the	the	DET
ejpam-6306	21	20	other	other	ADJ
ejpam-6306	21	21	is	be	AUX
ejpam-6306	21	22	“	"	PUNCT
ejpam-6306	21	23	wrong	wrong	ADJ
ejpam-6306	21	24	”	"	PUNCT
ejpam-6306	21	25	since	since	SCONJ
ejpam-6306	21	26	they	they	PRON
ejpam-6306	21	27	can	can	AUX
ejpam-6306	21	28	not	not	PART
ejpam-6306	21	29	be	be	AUX
ejpam-6306	21	30	used	use	VERB
ejpam-6306	21	31	interchangeably	interchangeably	ADV
ejpam-6306	21	32	.	.	PUNCT
ejpam-6306	22	1	but	but	CCONJ
ejpam-6306	22	2	according	accord	VERB
ejpam-6306	22	3	to	to	ADP
ejpam-6306	22	4	the	the	DET
ejpam-6306	22	5	de	de	PROPN
ejpam-6306	22	6	morgan	morgan	PROPN
ejpam-6306	22	7	’s	’s	PART
ejpam-6306	22	8	writings	writing	NOUN
ejpam-6306	22	9	[	[	X
ejpam-6306	22	10	7	7	NUM
ejpam-6306	22	11	]	]	PUNCT
ejpam-6306	22	12	,	,	PUNCT
ejpam-6306	22	13	“	"	PUNCT
ejpam-6306	22	14	both	both	CCONJ
ejpam-6306	22	15	these	these	DET
ejpam-6306	22	16	systems	system	NOUN
ejpam-6306	22	17	,	,	PUNCT
ejpam-6306	22	18	then	then	ADV
ejpam-6306	22	19	,	,	PUNCT
ejpam-6306	22	20	may	may	AUX
ejpam-6306	22	21	very	very	ADV
ejpam-6306	22	22	possibly	possibly	ADV
ejpam-6306	22	23	be	be	AUX
ejpam-6306	22	24	parts	part	NOUN
ejpam-6306	22	25	of	of	ADP
ejpam-6306	22	26	a	a	DET
ejpam-6306	22	27	more	more	ADV
ejpam-6306	22	28	general	general	ADJ
ejpam-6306	22	29	systems	system	NOUN
ejpam-6306	22	30	.	.	PUNCT
ejpam-6306	22	31	”	"	PUNCT
ejpam-6306	23	1	similarly	similarly	ADV
ejpam-6306	23	2	to	to	ADP
ejpam-6306	23	3	leibniz	leibniz	PROPN
ejpam-6306	23	4	’s	’s	PART
ejpam-6306	23	5	views	view	NOUN
ejpam-6306	23	6	from	from	ADP
ejpam-6306	23	7	hundreds	hundred	NOUN
ejpam-6306	23	8	of	of	ADP
ejpam-6306	23	9	years	year	NOUN
ejpam-6306	23	10	prior	prior	ADV
ejpam-6306	23	11	,	,	PUNCT
ejpam-6306	23	12	his	his	PRON
ejpam-6306	23	13	statements	statement	NOUN
ejpam-6306	23	14	were	be	AUX
ejpam-6306	23	15	predictive	predictive	ADJ
ejpam-6306	23	16	.	.	PUNCT
ejpam-6306	24	1	in	in	ADP
ejpam-6306	24	2	actuality	actuality	NOUN
ejpam-6306	24	3	,	,	PUNCT
ejpam-6306	24	4	the	the	DET
ejpam-6306	24	5	riemann	riemann	PROPN
ejpam-6306	24	6	-	-	PUNCT
ejpam-6306	24	7	liouville	liouville	VERB
ejpam-6306	24	8	formulation	formulation	NOUN
ejpam-6306	24	9	of	of	ADP
ejpam-6306	24	10	fractional	fractional	ADJ
ejpam-6306	24	11	calculus	calculus	NOUN
ejpam-6306	24	12	was	be	AUX
ejpam-6306	24	13	a	a	DET
ejpam-6306	24	14	particular	particular	ADJ
ejpam-6306	24	15	case	case	NOUN
ejpam-6306	24	16	of	of	ADP
ejpam-6306	24	17	both	both	DET
ejpam-6306	24	18	liouville	liouville	NOUN
ejpam-6306	24	19	’s	’s	PART
ejpam-6306	24	20	formula	formula	NOUN
ejpam-6306	24	21	and	and	CCONJ
ejpam-6306	24	22	lacroix	lacroix	NOUN
ejpam-6306	24	23	’s	’s	NOUN
ejpam-6306	24	24	.	.	PUNCT
ejpam-6306	25	1	for	for	ADP
ejpam-6306	25	2	this	this	PRON
ejpam-6306	25	3	,	,	PUNCT
ejpam-6306	25	4	an	an	DET
ejpam-6306	25	5	arbitrary	arbitrary	ADJ
ejpam-6306	25	6	integration	integration	NOUN
ejpam-6306	25	7	constant	constant	ADJ
ejpam-6306	25	8	c	c	PROPN
ejpam-6306	25	9	was	be	AUX
ejpam-6306	25	10	needed	need	VERB
ejpam-6306	25	11	.	.	PUNCT
ejpam-6306	26	1	setting	set	VERB
ejpam-6306	26	2	it	it	PRON
ejpam-6306	26	3	to	to	ADP
ejpam-6306	26	4	zero	zero	NUM
ejpam-6306	26	5	resulted	result	VERB
ejpam-6306	26	6	in	in	ADP
ejpam-6306	26	7	the	the	DET
ejpam-6306	26	8	liouville	liouville	NOUN
ejpam-6306	26	9	’s	’s	PART
ejpam-6306	26	10	formula	formula	NOUN
ejpam-6306	26	11	,	,	PUNCT
ejpam-6306	26	12	whereas	whereas	SCONJ
ejpam-6306	26	13	setting	set	VERB
ejpam-6306	26	14	it	it	PRON
ejpam-6306	26	15	to	to	ADP
ejpam-6306	26	16	−∞	−∞	NOUN
ejpam-6306	26	17	resulted	result	VERB
ejpam-6306	26	18	in	in	ADP
ejpam-6306	26	19	the	the	DET
ejpam-6306	26	20	lacroix	lacroix	NOUN
ejpam-6306	26	21	’s	’s	PART
ejpam-6306	26	22	formula	formula	NOUN
ejpam-6306	26	23	.	.	PUNCT
ejpam-6306	27	1	through	through	ADP
ejpam-6306	27	2	the	the	DET
ejpam-6306	27	3	use	use	NOUN
ejpam-6306	27	4	of	of	ADP
ejpam-6306	27	5	complex	complex	ADJ
ejpam-6306	27	6	analysis	analysis	NOUN
ejpam-6306	27	7	,	,	PUNCT
ejpam-6306	27	8	this	this	DET
ejpam-6306	27	9	generic	generic	ADJ
ejpam-6306	27	10	riemann	riemann	PROPN
ejpam-6306	27	11	-	-	PUNCT
ejpam-6306	27	12	liouville	liouville	NOUN
ejpam-6306	27	13	definition	definition	NOUN
ejpam-6306	27	14	for	for	ADP
ejpam-6306	27	15	the	the	DET
ejpam-6306	27	16	fractional	fractional	ADJ
ejpam-6306	27	17	derivative	derivative	ADJ
ejpam-6306	27	18	and	and	CCONJ
ejpam-6306	27	19	fractional	fractional	ADJ
ejpam-6306	27	20	integral	integral	ADJ
ejpam-6306	27	21	of	of	ADP
ejpam-6306	27	22	any	any	DET
ejpam-6306	27	23	function	function	NOUN
ejpam-6306	27	24	was	be	AUX
ejpam-6306	27	25	developed	develop	VERB
ejpam-6306	27	26	in	in	ADP
ejpam-6306	27	27	the	the	DET
ejpam-6306	27	28	late	late	ADJ
ejpam-6306	27	29	1800s	1800s	NUM
ejpam-6306	27	30	.	.	PUNCT
ejpam-6306	28	1	the	the	DET
ejpam-6306	28	2	riemann	riemann	PROPN
ejpam-6306	28	3	-	-	PUNCT
ejpam-6306	28	4	liouville	liouville	VERB
ejpam-6306	28	5	formula	formula	NOUN
ejpam-6306	28	6	is	be	AUX
ejpam-6306	28	7	primarily	primarily	ADV
ejpam-6306	28	8	utilized	utilize	VERB
ejpam-6306	28	9	in	in	ADP
ejpam-6306	28	10	real	real	ADJ
ejpam-6306	28	11	-	-	PUNCT
ejpam-6306	28	12	analysis	analysis	NOUN
ejpam-6306	28	13	contexts	context	NOUN
ejpam-6306	28	14	;	;	PUNCT
ejpam-6306	28	15	however	however	ADV
ejpam-6306	28	16	,	,	PUNCT
ejpam-6306	28	17	it	it	PRON
ejpam-6306	28	18	was	be	AUX
ejpam-6306	28	19	originally	originally	ADV
ejpam-6306	28	20	inspired	inspire	VERB
ejpam-6306	28	21	by	by	ADP
ejpam-6306	28	22	a	a	DET
ejpam-6306	28	23	generalization	generalization	NOUN
ejpam-6306	28	24	of	of	ADP
ejpam-6306	28	25	the	the	DET
ejpam-6306	28	26	cauchy	cauchy	ADJ
ejpam-6306	28	27	integral	integral	ADJ
ejpam-6306	28	28	formula	formula	NOUN
ejpam-6306	28	29	for	for	ADP
ejpam-6306	28	30	repeated	repeat	VERB
ejpam-6306	28	31	derivatives	derivative	NOUN
ejpam-6306	28	32	of	of	ADP
ejpam-6306	28	33	a	a	DET
ejpam-6306	28	34	complex	complex	ADJ
ejpam-6306	28	35	analytic	analytic	ADJ
ejpam-6306	28	36	function	function	NOUN
ejpam-6306	28	37	.	.	PUNCT
ejpam-6306	29	1	currently	currently	ADV
ejpam-6306	29	2	,	,	PUNCT
ejpam-6306	29	3	the	the	DET
ejpam-6306	29	4	most	most	ADV
ejpam-6306	29	5	commonly	commonly	ADV
ejpam-6306	29	6	used	use	VERB
ejpam-6306	29	7	definition	definition	NOUN
ejpam-6306	29	8	of	of	ADP
ejpam-6306	29	9	fractional	fractional	ADJ
ejpam-6306	29	10	calculus	calculus	NOUN
ejpam-6306	29	11	is	be	AUX
ejpam-6306	29	12	attributed	attribute	VERB
ejpam-6306	29	13	to	to	ADP
ejpam-6306	29	14	riemann	riemann	PROPN
ejpam-6306	29	15	-	-	PUNCT
ejpam-6306	29	16	liouville	liouville	NOUN
ejpam-6306	29	17	’s	’s	PART
ejpam-6306	29	18	definition	definition	NOUN
ejpam-6306	29	19	.	.	PUNCT
ejpam-6306	30	1	the	the	DET
ejpam-6306	30	2	left	left	ADJ
ejpam-6306	30	3	and	and	CCONJ
ejpam-6306	30	4	right	right	ADJ
ejpam-6306	30	5	side	side	NOUN
ejpam-6306	30	6	of	of	ADP
ejpam-6306	30	7	ξ	ξ	X
ejpam-6306	30	8	-	-	ADJ
ejpam-6306	30	9	rl	rl	ADJ
ejpam-6306	30	10	fractional	fractional	ADJ
ejpam-6306	30	11	integrals	integral	NOUN
ejpam-6306	30	12	of	of	ADP
ejpam-6306	30	13	a	a	DET
ejpam-6306	30	14	function	function	NOUN
ejpam-6306	30	15	f	f	NOUN
ejpam-6306	30	16	with	with	ADP
ejpam-6306	30	17	respect	respect	NOUN
ejpam-6306	30	18	to	to	ADP
ejpam-6306	30	19	the	the	DET
ejpam-6306	30	20	function	function	NOUN
ejpam-6306	30	21	ξ(x	ξ(x	NOUN
ejpam-6306	30	22	)	)	PUNCT
ejpam-6306	30	23	on	on	ADP
ejpam-6306	30	24	[	[	X
ejpam-6306	30	25	α	α	X
ejpam-6306	30	26	,	,	PUNCT
ejpam-6306	30	27	ρ	ρ	PROPN
ejpam-6306	30	28	]	]	X
ejpam-6306	30	29	are	be	AUX
ejpam-6306	30	30	respectively	respectively	ADV
ejpam-6306	30	31	defined	define	VERB
ejpam-6306	30	32	as	as	ADP
ejpam-6306	30	33	:	:	PUNCT
ejpam-6306	30	34	i℘,ξ	i℘,ξ	NOUN
ejpam-6306	30	35	α+	α+	PUNCT
ejpam-6306	30	36	f(x	f(x	PROPN
ejpam-6306	30	37	)	)	PUNCT
ejpam-6306	30	38	=	=	PUNCT
ejpam-6306	30	39	1	1	NUM
ejpam-6306	30	40	γ(℘	γ(℘	SYM
ejpam-6306	30	41	)	)	PUNCT
ejpam-6306	30	42	∫	∫	PROPN
ejpam-6306	31	1	x	x	X
ejpam-6306	31	2	α	α	X
ejpam-6306	31	3	ξ′(β)(ξ(x)−	ξ′(β)(ξ(x)−	PROPN
ejpam-6306	31	4	ξ(β))℘−1f(β)dβ	ξ(β))℘−1f(β)dβ	NOUN
ejpam-6306	31	5	,	,	PUNCT
ejpam-6306	31	6	i℘,ξ	i℘,ξ	PROPN
ejpam-6306	31	7	ρ−	ρ−	PROPN
ejpam-6306	31	8	f(x	f(x	PROPN
ejpam-6306	31	9	)	)	PUNCT
ejpam-6306	31	10	=	=	PUNCT
ejpam-6306	31	11	1	1	NUM
ejpam-6306	31	12	γ(℘	γ(℘	SYM
ejpam-6306	31	13	)	)	PUNCT
ejpam-6306	31	14	∫	∫	PROPN
ejpam-6306	32	1	ρ	ρ	PROPN
ejpam-6306	32	2	x	x	PROPN
ejpam-6306	32	3	ξ′(β)(ξ(β)−	ξ′(β)(ξ(β)−	X
ejpam-6306	32	4	ξ(x))℘−1f(β)dβ	ξ(x))℘−1f(β)dβ	NOUN
ejpam-6306	32	5	,	,	PUNCT
ejpam-6306	32	6	℘	℘	X
ejpam-6306	32	7	>	>	X
ejpam-6306	32	8	0	0	X
ejpam-6306	32	9	.	.	PUNCT
ejpam-6306	33	1	nevertheless	nevertheless	ADV
ejpam-6306	33	2	,	,	PUNCT
ejpam-6306	33	3	there	there	PRON
ejpam-6306	33	4	are	be	VERB
ejpam-6306	33	5	still	still	ADV
ejpam-6306	33	6	other	other	ADJ
ejpam-6306	33	7	proposed	propose	VERB
ejpam-6306	33	8	definitions	definition	NOUN
ejpam-6306	33	9	for	for	ADP
ejpam-6306	33	10	fractional	fractional	ADJ
ejpam-6306	33	11	calculus	calculus	NOUN
ejpam-6306	33	12	.	.	PUNCT
ejpam-6306	34	1	several	several	ADJ
ejpam-6306	34	2	contradictory	contradictory	ADJ
ejpam-6306	34	3	formulae	formulae	NOUN
ejpam-6306	34	4	are	be	AUX
ejpam-6306	34	5	still	still	ADV
ejpam-6306	34	6	in	in	ADP
ejpam-6306	34	7	use	use	NOUN
ejpam-6306	34	8	today	today	NOUN
ejpam-6306	34	9	,	,	PUNCT
ejpam-6306	34	10	which	which	PRON
ejpam-6306	34	11	confuses	confuse	VERB
ejpam-6306	34	12	many	many	ADJ
ejpam-6306	34	13	beginners	beginner	NOUN
ejpam-6306	34	14	in	in	ADP
ejpam-6306	34	15	the	the	DET
ejpam-6306	34	16	field	field	NOUN
ejpam-6306	34	17	who	who	PRON
ejpam-6306	34	18	assume	assume	VERB
ejpam-6306	34	19	that	that	SCONJ
ejpam-6306	34	20	there	there	PRON
ejpam-6306	34	21	is	be	VERB
ejpam-6306	34	22	only	only	ADV
ejpam-6306	34	23	one	one	NUM
ejpam-6306	34	24	definition	definition	NOUN
ejpam-6306	34	25	for	for	ADP
ejpam-6306	34	26	fractional	fractional	ADJ
ejpam-6306	34	27	derivatives	derivative	NOUN
ejpam-6306	34	28	,	,	PUNCT
ejpam-6306	34	29	just	just	ADV
ejpam-6306	34	30	as	as	SCONJ
ejpam-6306	34	31	there	there	PRON
ejpam-6306	34	32	is	be	VERB
ejpam-6306	34	33	only	only	ADV
ejpam-6306	34	34	one	one	NUM
ejpam-6306	34	35	definition	definition	NOUN
ejpam-6306	34	36	for	for	ADP
ejpam-6306	34	37	the	the	DET
ejpam-6306	34	38	first	first	ADJ
ejpam-6306	34	39	-	-	PUNCT
ejpam-6306	34	40	order	order	NOUN
ejpam-6306	34	41	derivative	derivative	NOUN
ejpam-6306	34	42	.	.	PUNCT
ejpam-6306	35	1	although	although	SCONJ
ejpam-6306	35	2	there	there	PRON
ejpam-6306	35	3	are	be	VERB
ejpam-6306	35	4	other	other	ADJ
ejpam-6306	35	5	methods	method	NOUN
ejpam-6306	35	6	to	to	PART
ejpam-6306	35	7	extend	extend	VERB
ejpam-6306	35	8	meaning	meaning	NOUN
ejpam-6306	35	9	,	,	PUNCT
ejpam-6306	35	10	fractional	fractional	ADJ
ejpam-6306	35	11	calculus	calculus	NOUN
ejpam-6306	35	12	is	be	AUX
ejpam-6306	35	13	sometimes	sometimes	ADV
ejpam-6306	35	14	referred	refer	VERB
ejpam-6306	35	15	to	to	ADP
ejpam-6306	35	16	as	as	ADP
ejpam-6306	35	17	a	a	DET
ejpam-6306	35	18	“	"	PUNCT
ejpam-6306	35	19	extension	extension	NOUN
ejpam-6306	35	20	of	of	ADP
ejpam-6306	35	21	meaning	meaning	NOUN
ejpam-6306	35	22	”	"	PUNCT
ejpam-6306	35	23	.	.	PUNCT
ejpam-6306	36	1	because	because	SCONJ
ejpam-6306	36	2	r.	r.	PROPN
ejpam-6306	36	3	s.	s.	PROPN
ejpam-6306	36	4	ali	ali	PROPN
ejpam-6306	36	5	et	et	PROPN
ejpam-6306	36	6	al	al	PROPN
ejpam-6306	36	7	.	.	PUNCT
ejpam-6306	36	8	/	/	SYM
ejpam-6306	36	9	eur	eur	PROPN
ejpam-6306	36	10	.	.	PUNCT
ejpam-6306	37	1	j.	j.	PROPN
ejpam-6306	37	2	pure	pure	PROPN
ejpam-6306	37	3	appl	appl	PROPN
ejpam-6306	37	4	.	.	PROPN
ejpam-6306	37	5	math	math	PROPN
ejpam-6306	37	6	,	,	PUNCT
ejpam-6306	37	7	18	18	NUM
ejpam-6306	37	8	(	(	PUNCT
ejpam-6306	37	9	3	3	NUM
ejpam-6306	37	10	)	)	PUNCT
ejpam-6306	37	11	(	(	PUNCT
ejpam-6306	37	12	2025	2025	NUM
ejpam-6306	37	13	)	)	PUNCT
ejpam-6306	37	14	,	,	PUNCT
ejpam-6306	37	15	6306	6306	NUM
ejpam-6306	37	16	3	3	NUM
ejpam-6306	37	17	of	of	ADP
ejpam-6306	37	18	18	18	NUM
ejpam-6306	37	19	of	of	ADP
ejpam-6306	37	20	the	the	DET
ejpam-6306	37	21	power	power	NOUN
ejpam-6306	37	22	-	-	PUNCT
ejpam-6306	37	23	function	function	NOUN
ejpam-6306	37	24	kernel	kernel	NOUN
ejpam-6306	37	25	in	in	ADP
ejpam-6306	37	26	the	the	DET
ejpam-6306	37	27	integral	integral	ADJ
ejpam-6306	37	28	transform	transform	NOUN
ejpam-6306	37	29	description	description	NOUN
ejpam-6306	37	30	,	,	PUNCT
ejpam-6306	37	31	the	the	DET
ejpam-6306	37	32	riemann	riemann	PROPN
ejpam-6306	37	33	-	-	PUNCT
ejpam-6306	37	34	liouville	liouville	NOUN
ejpam-6306	37	35	model	model	NOUN
ejpam-6306	37	36	can	can	AUX
ejpam-6306	37	37	be	be	AUX
ejpam-6306	37	38	used	use	VERB
ejpam-6306	37	39	to	to	PART
ejpam-6306	37	40	explain	explain	VERB
ejpam-6306	37	41	processes	process	NOUN
ejpam-6306	37	42	with	with	ADP
ejpam-6306	37	43	power	power	NOUN
ejpam-6306	37	44	-	-	PUNCT
ejpam-6306	37	45	law	law	NOUN
ejpam-6306	37	46	behavior	behavior	NOUN
ejpam-6306	37	47	.	.	PUNCT
ejpam-6306	38	1	however	however	ADV
ejpam-6306	38	2	,	,	PUNCT
ejpam-6306	38	3	there	there	PRON
ejpam-6306	38	4	are	be	VERB
ejpam-6306	38	5	many	many	ADJ
ejpam-6306	38	6	other	other	ADJ
ejpam-6306	38	7	kinds	kind	NOUN
ejpam-6306	38	8	of	of	ADP
ejpam-6306	38	9	behavior	behavior	NOUN
ejpam-6306	38	10	found	find	VERB
ejpam-6306	38	11	in	in	ADP
ejpam-6306	38	12	nature	nature	NOUN
ejpam-6306	38	13	that	that	PRON
ejpam-6306	38	14	are	be	AUX
ejpam-6306	38	15	not	not	PART
ejpam-6306	38	16	amenable	amenable	ADJ
ejpam-6306	38	17	to	to	ADP
ejpam-6306	38	18	simple	simple	ADJ
ejpam-6306	38	19	power	power	NOUN
ejpam-6306	38	20	functions	function	NOUN
ejpam-6306	38	21	.	.	PUNCT
ejpam-6306	39	1	the	the	DET
ejpam-6306	39	2	hermite	hermite	ADJ
ejpam-6306	39	3	hadamard	hadamard	NOUN
ejpam-6306	39	4	(	(	PUNCT
ejpam-6306	39	5	h	h	NOUN
ejpam-6306	39	6	-	-	PUNCT
ejpam-6306	39	7	h	h	NOUN
ejpam-6306	39	8	)	)	PUNCT
ejpam-6306	39	9	dual	dual	ADJ
ejpam-6306	39	10	inequality	inequality	NOUN
ejpam-6306	39	11	is	be	AUX
ejpam-6306	39	12	the	the	DET
ejpam-6306	39	13	foundational	foundational	ADJ
ejpam-6306	39	14	discovery	discovery	NOUN
ejpam-6306	39	15	for	for	ADP
ejpam-6306	39	16	convex	convex	NOUN
ejpam-6306	39	17	functions	function	NOUN
ejpam-6306	39	18	on	on	ADP
ejpam-6306	39	19	a	a	DET
ejpam-6306	39	20	real	real	ADV
ejpam-6306	39	21	-	-	PUNCT
ejpam-6306	39	22	valued	value	VERB
ejpam-6306	39	23	interval	interval	NOUN
ejpam-6306	39	24	,	,	PUNCT
ejpam-6306	39	25	with	with	ADP
ejpam-6306	39	26	clear	clear	ADJ
ejpam-6306	39	27	mathematical	mathematical	ADJ
ejpam-6306	39	28	significance	significance	NOUN
ejpam-6306	39	29	and	and	CCONJ
ejpam-6306	39	30	limited	limited	ADJ
ejpam-6306	39	31	potential	potential	NOUN
ejpam-6306	39	32	for	for	ADP
ejpam-6306	39	33	specific	specific	ADJ
ejpam-6306	39	34	inequalities	inequality	NOUN
ejpam-6306	39	35	.	.	PUNCT
ejpam-6306	40	1	this	this	DET
ejpam-6306	40	2	research	research	NOUN
ejpam-6306	40	3	delves	delve	VERB
ejpam-6306	40	4	into	into	ADP
ejpam-6306	40	5	the	the	DET
ejpam-6306	40	6	basics	basic	NOUN
ejpam-6306	40	7	of	of	ADP
ejpam-6306	40	8	the	the	DET
ejpam-6306	40	9	hermite	hermite	ADJ
ejpam-6306	40	10	hadamard	hadamard	ADJ
ejpam-6306	40	11	inequality	inequality	NOUN
ejpam-6306	40	12	for	for	ADP
ejpam-6306	40	13	convex	convex	NOUN
ejpam-6306	40	14	functions	function	NOUN
ejpam-6306	40	15	and	and	CCONJ
ejpam-6306	40	16	presents	present	VERB
ejpam-6306	40	17	specific	specific	ADJ
ejpam-6306	40	18	results	result	NOUN
ejpam-6306	40	19	for	for	ADP
ejpam-6306	40	20	particular	particular	ADJ
ejpam-6306	40	21	means	mean	NOUN
ejpam-6306	40	22	.	.	PUNCT
ejpam-6306	41	1	it	it	PRON
ejpam-6306	41	2	also	also	ADV
ejpam-6306	41	3	introduces	introduce	VERB
ejpam-6306	41	4	the	the	DET
ejpam-6306	41	5	hermite	hermite	ADJ
ejpam-6306	41	6	hadamard	hadamard	ADJ
ejpam-6306	41	7	type	type	NOUN
ejpam-6306	41	8	inequalities	inequality	NOUN
ejpam-6306	41	9	for	for	ADP
ejpam-6306	41	10	various	various	ADJ
ejpam-6306	41	11	forms	form	NOUN
ejpam-6306	41	12	of	of	ADP
ejpam-6306	41	13	convexity	convexity	NOUN
ejpam-6306	41	14	and	and	CCONJ
ejpam-6306	41	15	emphasizes	emphasize	VERB
ejpam-6306	41	16	the	the	DET
ejpam-6306	41	17	characteristics	characteristic	NOUN
ejpam-6306	41	18	of	of	ADP
ejpam-6306	41	19	functions	function	NOUN
ejpam-6306	41	20	,	,	PUNCT
ejpam-6306	41	21	functionals	functional	NOUN
ejpam-6306	41	22	,	,	PUNCT
ejpam-6306	41	23	and	and	CCONJ
ejpam-6306	41	24	sequences	sequence	NOUN
ejpam-6306	41	25	that	that	PRON
ejpam-6306	41	26	can	can	AUX
ejpam-6306	41	27	be	be	AUX
ejpam-6306	41	28	used	use	VERB
ejpam-6306	41	29	to	to	PART
ejpam-6306	41	30	modify	modify	VERB
ejpam-6306	41	31	the	the	DET
ejpam-6306	41	32	hermite	hermite	ADJ
ejpam-6306	41	33	hadamard	hadamard	NOUN
ejpam-6306	41	34	result	result	NOUN
ejpam-6306	41	35	.	.	PUNCT
ejpam-6306	42	1	many	many	ADJ
ejpam-6306	42	2	researchers	researcher	NOUN
ejpam-6306	42	3	have	have	AUX
ejpam-6306	42	4	worked	work	VERB
ejpam-6306	42	5	to	to	PART
ejpam-6306	42	6	modify	modify	VERB
ejpam-6306	42	7	the	the	DET
ejpam-6306	42	8	hermite	hermite	PROPN
ejpam-6306	42	9	-	-	PUNCT
ejpam-6306	42	10	hadamard	hadamard	ADJ
ejpam-6306	42	11	fractional	fractional	ADJ
ejpam-6306	42	12	inequalities	inequality	NOUN
ejpam-6306	42	13	and	and	CCONJ
ejpam-6306	42	14	their	their	PRON
ejpam-6306	42	15	refinements	refinement	NOUN
ejpam-6306	42	16	,	,	PUNCT
ejpam-6306	42	17	which	which	PRON
ejpam-6306	42	18	have	have	AUX
ejpam-6306	42	19	made	make	VERB
ejpam-6306	42	20	a	a	DET
ejpam-6306	42	21	contribution	contribution	NOUN
ejpam-6306	42	22	in	in	ADP
ejpam-6306	42	23	the	the	DET
ejpam-6306	42	24	literature	literature	NOUN
ejpam-6306	43	1	[	[	X
ejpam-6306	43	2	8–10	8–10	NOUN
ejpam-6306	43	3	]	]	PUNCT
ejpam-6306	43	4	.	.	PUNCT
ejpam-6306	44	1	fractional	fractional	ADJ
ejpam-6306	44	2	calculus	calculus	NOUN
ejpam-6306	44	3	saw	see	VERB
ejpam-6306	44	4	a	a	DET
ejpam-6306	44	5	substantial	substantial	ADJ
ejpam-6306	44	6	rise	rise	NOUN
ejpam-6306	44	7	in	in	ADP
ejpam-6306	44	8	research	research	NOUN
ejpam-6306	44	9	output	output	NOUN
ejpam-6306	44	10	and	and	CCONJ
ejpam-6306	44	11	popularity	popularity	NOUN
ejpam-6306	44	12	in	in	ADP
ejpam-6306	44	13	the	the	DET
ejpam-6306	44	14	late	late	ADJ
ejpam-6306	44	15	twentieth	twentieth	ADJ
ejpam-6306	44	16	century	century	NOUN
ejpam-6306	44	17	.	.	PUNCT
ejpam-6306	45	1	since	since	SCONJ
ejpam-6306	45	2	then	then	ADV
ejpam-6306	45	3	,	,	PUNCT
ejpam-6306	45	4	there	there	PRON
ejpam-6306	45	5	have	have	AUX
ejpam-6306	45	6	been	be	AUX
ejpam-6306	45	7	several	several	ADJ
ejpam-6306	45	8	specialized	specialized	ADJ
ejpam-6306	45	9	journals	journal	NOUN
ejpam-6306	45	10	dedicated	dedicate	VERB
ejpam-6306	45	11	to	to	ADP
ejpam-6306	45	12	fractional	fractional	ADJ
ejpam-6306	45	13	calculus	calculus	NOUN
ejpam-6306	45	14	,	,	PUNCT
ejpam-6306	45	15	making	make	VERB
ejpam-6306	45	16	it	it	PRON
ejpam-6306	45	17	a	a	DET
ejpam-6306	45	18	very	very	ADV
ejpam-6306	45	19	active	active	ADJ
ejpam-6306	45	20	area	area	NOUN
ejpam-6306	45	21	of	of	ADP
ejpam-6306	45	22	study	study	NOUN
ejpam-6306	45	23	.	.	PUNCT
ejpam-6306	46	1	numerous	numerous	ADJ
ejpam-6306	46	2	scientific	scientific	ADJ
ejpam-6306	46	3	domains	domain	NOUN
ejpam-6306	46	4	have	have	AUX
ejpam-6306	46	5	found	find	VERB
ejpam-6306	46	6	applications	application	NOUN
ejpam-6306	46	7	,	,	PUNCT
ejpam-6306	46	8	as	as	SCONJ
ejpam-6306	46	9	enumerated	enumerate	VERB
ejpam-6306	46	10	in	in	ADP
ejpam-6306	46	11	[	[	X
ejpam-6306	46	12	11–13	11–13	NUM
ejpam-6306	46	13	]	]	PUNCT
ejpam-6306	46	14	and	and	CCONJ
ejpam-6306	46	15	the	the	DET
ejpam-6306	46	16	associated	associated	ADJ
ejpam-6306	46	17	references	reference	NOUN
ejpam-6306	46	18	.	.	PUNCT
ejpam-6306	47	1	specifically	specifically	ADV
ejpam-6306	47	2	,	,	PUNCT
ejpam-6306	47	3	the	the	DET
ejpam-6306	47	4	modeling	modeling	NOUN
ejpam-6306	47	5	of	of	ADP
ejpam-6306	47	6	some	some	DET
ejpam-6306	47	7	intermediate	intermediate	ADJ
ejpam-6306	47	8	physical	physical	ADJ
ejpam-6306	47	9	processes	process	NOUN
ejpam-6306	47	10	,	,	PUNCT
ejpam-6306	47	11	such	such	ADJ
ejpam-6306	47	12	as	as	ADP
ejpam-6306	47	13	viscoelasticity	viscoelasticity	NOUN
ejpam-6306	47	14	,	,	PUNCT
ejpam-6306	47	15	depends	depend	VERB
ejpam-6306	47	16	on	on	ADP
ejpam-6306	47	17	the	the	DET
ejpam-6306	47	18	intermediate	intermediate	ADJ
ejpam-6306	47	19	feature	feature	NOUN
ejpam-6306	47	20	of	of	ADP
ejpam-6306	47	21	fractional	fractional	ADJ
ejpam-6306	47	22	-	-	PUNCT
ejpam-6306	47	23	calculus	calculus	NOUN
ejpam-6306	47	24	operators	operator	NOUN
ejpam-6306	47	25	[	[	X
ejpam-6306	47	26	14	14	NUM
ejpam-6306	47	27	]	]	PUNCT
ejpam-6306	47	28	.	.	PUNCT
ejpam-6306	48	1	in	in	ADP
ejpam-6306	48	2	several	several	ADJ
ejpam-6306	48	3	universities	university	NOUN
ejpam-6306	48	4	,	,	PUNCT
ejpam-6306	48	5	fractional	fractional	ADJ
ejpam-6306	48	6	calculus	calculus	NOUN
ejpam-6306	48	7	is	be	AUX
ejpam-6306	48	8	now	now	ADV
ejpam-6306	48	9	taught	teach	VERB
ejpam-6306	48	10	as	as	ADP
ejpam-6306	48	11	a	a	DET
ejpam-6306	48	12	required	required	ADJ
ejpam-6306	48	13	subject	subject	NOUN
ejpam-6306	48	14	in	in	ADP
ejpam-6306	48	15	the	the	DET
ejpam-6306	48	16	graduate	graduate	NOUN
ejpam-6306	48	17	mathematics	mathematic	NOUN
ejpam-6306	48	18	program	program	NOUN
ejpam-6306	48	19	.	.	PUNCT
ejpam-6306	49	1	several	several	ADJ
ejpam-6306	49	2	textbooks	textbook	NOUN
ejpam-6306	49	3	[	[	X
ejpam-6306	49	4	15–17	15–17	NUM
ejpam-6306	49	5	]	]	PUNCT
ejpam-6306	49	6	serve	serve	VERB
ejpam-6306	49	7	as	as	ADP
ejpam-6306	49	8	introductory	introductory	ADJ
ejpam-6306	49	9	resources	resource	NOUN
ejpam-6306	49	10	for	for	ADP
ejpam-6306	49	11	students	student	NOUN
ejpam-6306	49	12	and	and	CCONJ
ejpam-6306	49	13	aspiring	aspire	VERB
ejpam-6306	49	14	researchers	researcher	NOUN
ejpam-6306	49	15	in	in	ADP
ejpam-6306	49	16	the	the	DET
ejpam-6306	49	17	topic	topic	NOUN
ejpam-6306	49	18	.	.	PUNCT
ejpam-6306	50	1	the	the	DET
ejpam-6306	50	2	study	study	NOUN
ejpam-6306	50	3	underscored	underscore	VERB
ejpam-6306	50	4	the	the	DET
ejpam-6306	50	5	characteristics	characteristic	NOUN
ejpam-6306	50	6	of	of	ADP
ejpam-6306	50	7	several	several	ADJ
ejpam-6306	50	8	functions	function	NOUN
ejpam-6306	50	9	and	and	CCONJ
ejpam-6306	50	10	sequences	sequence	NOUN
ejpam-6306	50	11	that	that	PRON
ejpam-6306	50	12	can	can	AUX
ejpam-6306	50	13	be	be	AUX
ejpam-6306	50	14	utilized	utilize	VERB
ejpam-6306	50	15	to	to	PART
ejpam-6306	50	16	adapt	adapt	VERB
ejpam-6306	50	17	the	the	DET
ejpam-6306	50	18	h	h	NOUN
ejpam-6306	50	19	-	-	PUNCT
ejpam-6306	50	20	h	h	NOUN
ejpam-6306	50	21	theorem	theorem	NOUN
ejpam-6306	50	22	.	.	PUNCT
ejpam-6306	51	1	research	research	NOUN
ejpam-6306	51	2	-	-	PUNCT
ejpam-6306	51	3	wise	wise	ADJ
ejpam-6306	51	4	,	,	PUNCT
ejpam-6306	51	5	there	there	PRON
ejpam-6306	51	6	are	be	VERB
ejpam-6306	51	7	currently	currently	ADV
ejpam-6306	51	8	a	a	DET
ejpam-6306	51	9	number	number	NOUN
ejpam-6306	51	10	of	of	ADP
ejpam-6306	51	11	alternative	alternative	ADJ
ejpam-6306	51	12	viewpoints	viewpoint	NOUN
ejpam-6306	51	13	and	and	CCONJ
ejpam-6306	51	14	lines	line	NOUN
ejpam-6306	51	15	of	of	ADP
ejpam-6306	51	16	inquiry	inquiry	NOUN
ejpam-6306	51	17	that	that	PRON
ejpam-6306	51	18	may	may	AUX
ejpam-6306	51	19	be	be	AUX
ejpam-6306	51	20	at	at	ADP
ejpam-6306	51	21	odds	odd	NOUN
ejpam-6306	51	22	with	with	ADP
ejpam-6306	51	23	one	one	NUM
ejpam-6306	51	24	another	another	DET
ejpam-6306	51	25	in	in	ADP
ejpam-6306	51	26	some	some	DET
ejpam-6306	51	27	situations	situation	NOUN
ejpam-6306	51	28	.	.	PUNCT
ejpam-6306	52	1	the	the	DET
ejpam-6306	52	2	gradual	gradual	ADJ
ejpam-6306	52	3	development	development	NOUN
ejpam-6306	52	4	of	of	ADP
ejpam-6306	52	5	new	new	ADJ
ejpam-6306	52	6	technologies	technology	NOUN
ejpam-6306	52	7	has	have	AUX
ejpam-6306	52	8	increased	increase	VERB
ejpam-6306	52	9	the	the	DET
ejpam-6306	52	10	demand	demand	NOUN
ejpam-6306	52	11	for	for	ADP
ejpam-6306	52	12	fractional	fractional	ADJ
ejpam-6306	52	13	operators	operator	NOUN
ejpam-6306	52	14	and	and	CCONJ
ejpam-6306	52	15	special	special	ADJ
ejpam-6306	52	16	functions	function	NOUN
ejpam-6306	52	17	.	.	PUNCT
ejpam-6306	53	1	in	in	ADP
ejpam-6306	53	2	the	the	DET
ejpam-6306	53	3	last	last	ADJ
ejpam-6306	53	4	few	few	ADJ
ejpam-6306	53	5	decades	decade	NOUN
ejpam-6306	53	6	,	,	PUNCT
ejpam-6306	53	7	many	many	ADJ
ejpam-6306	53	8	researchers	researcher	NOUN
ejpam-6306	53	9	have	have	AUX
ejpam-6306	53	10	worked	work	VERB
ejpam-6306	53	11	to	to	PART
ejpam-6306	53	12	develop	develop	VERB
ejpam-6306	53	13	fractional	fractional	ADJ
ejpam-6306	53	14	operators	operator	NOUN
ejpam-6306	53	15	having	have	VERB
ejpam-6306	53	16	generalized	generalize	VERB
ejpam-6306	53	17	special	special	ADJ
ejpam-6306	53	18	functions	function	NOUN
ejpam-6306	53	19	as	as	ADP
ejpam-6306	53	20	its	its	PRON
ejpam-6306	53	21	kernel	kernel	NOUN
ejpam-6306	53	22	,	,	PUNCT
ejpam-6306	53	23	which	which	PRON
ejpam-6306	53	24	have	have	VERB
ejpam-6306	53	25	many	many	ADJ
ejpam-6306	53	26	applications	application	NOUN
ejpam-6306	53	27	in	in	ADP
ejpam-6306	53	28	the	the	DET
ejpam-6306	53	29	field	field	NOUN
ejpam-6306	53	30	of	of	ADP
ejpam-6306	53	31	operator	operator	NOUN
ejpam-6306	53	32	theory	theory	NOUN
ejpam-6306	53	33	,	,	PUNCT
ejpam-6306	53	34	fractional	fractional	ADJ
ejpam-6306	53	35	inequalities	inequality	NOUN
ejpam-6306	53	36	.	.	PUNCT
ejpam-6306	54	1	such	such	ADJ
ejpam-6306	54	2	type	type	NOUN
ejpam-6306	54	3	of	of	ADP
ejpam-6306	54	4	fractional	fractional	ADJ
ejpam-6306	54	5	operators	operator	NOUN
ejpam-6306	54	6	have	have	AUX
ejpam-6306	54	7	resolved	resolve	VERB
ejpam-6306	54	8	many	many	ADJ
ejpam-6306	54	9	issues	issue	NOUN
ejpam-6306	54	10	which	which	PRON
ejpam-6306	54	11	are	be	AUX
ejpam-6306	54	12	facing	face	VERB
ejpam-6306	54	13	the	the	DET
ejpam-6306	54	14	research	research	NOUN
ejpam-6306	54	15	communities	community	NOUN
ejpam-6306	54	16	.	.	PUNCT
ejpam-6306	55	1	the	the	DET
ejpam-6306	55	2	formation	formation	NOUN
ejpam-6306	55	3	of	of	ADP
ejpam-6306	55	4	fractional	fractional	ADJ
ejpam-6306	55	5	and	and	CCONJ
ejpam-6306	55	6	differential	differential	NOUN
ejpam-6306	55	7	operators	operator	NOUN
ejpam-6306	55	8	can	can	AUX
ejpam-6306	55	9	be	be	AUX
ejpam-6306	55	10	possible	possible	ADJ
ejpam-6306	55	11	by	by	ADP
ejpam-6306	55	12	series	series	NOUN
ejpam-6306	55	13	functions	function	NOUN
ejpam-6306	55	14	in	in	ADP
ejpam-6306	55	15	riemann	riemann	PROPN
ejpam-6306	55	16	-	-	PUNCT
ejpam-6306	55	17	liouville	liouville	NOUN
ejpam-6306	55	18	system	system	NOUN
ejpam-6306	55	19	.	.	PUNCT
ejpam-6306	56	1	convexity	convexity	NOUN
ejpam-6306	56	2	has	have	AUX
ejpam-6306	56	3	greatly	greatly	ADV
ejpam-6306	56	4	benefited	benefit	VERB
ejpam-6306	56	5	mathematics	mathematic	NOUN
ejpam-6306	56	6	ever	ever	ADV
ejpam-6306	56	7	since	since	SCONJ
ejpam-6306	56	8	jensen	jensen	PROPN
ejpam-6306	56	9	’s	’s	PART
ejpam-6306	56	10	first	first	ADJ
ejpam-6306	56	11	convex	convex	NOUN
ejpam-6306	56	12	inequality	inequality	NOUN
ejpam-6306	56	13	was	be	AUX
ejpam-6306	56	14	introduced	introduce	VERB
ejpam-6306	56	15	.	.	PUNCT
ejpam-6306	57	1	convexity	convexity	NOUN
ejpam-6306	57	2	was	be	AUX
ejpam-6306	57	3	used	use	VERB
ejpam-6306	57	4	to	to	PART
ejpam-6306	57	5	derive	derive	VERB
ejpam-6306	57	6	many	many	ADJ
ejpam-6306	57	7	inequalities	inequality	NOUN
ejpam-6306	57	8	;	;	PUNCT
ejpam-6306	57	9	see	see	VERB
ejpam-6306	57	10	books	book	NOUN
ejpam-6306	57	11	[	[	X
ejpam-6306	57	12	18	18	NUM
ejpam-6306	57	13	,	,	PUNCT
ejpam-6306	57	14	19	19	NUM
ejpam-6306	57	15	]	]	PUNCT
ejpam-6306	57	16	.	.	PUNCT
ejpam-6306	58	1	applications	application	NOUN
ejpam-6306	58	2	of	of	ADP
ejpam-6306	58	3	inequality	inequality	NOUN
ejpam-6306	58	4	include	include	VERB
ejpam-6306	58	5	probability	probability	NOUN
ejpam-6306	58	6	theory	theory	NOUN
ejpam-6306	58	7	,	,	PUNCT
ejpam-6306	58	8	optimization	optimization	NOUN
ejpam-6306	58	9	,	,	PUNCT
ejpam-6306	58	10	and	and	CCONJ
ejpam-6306	58	11	analysis	analysis	NOUN
ejpam-6306	58	12	difficulties	difficulty	NOUN
ejpam-6306	58	13	.	.	PUNCT
ejpam-6306	59	1	we	we	PRON
ejpam-6306	59	2	direct	direct	VERB
ejpam-6306	59	3	readers	reader	NOUN
ejpam-6306	59	4	to	to	ADP
ejpam-6306	59	5	the	the	DET
ejpam-6306	59	6	papers	paper	NOUN
ejpam-6306	59	7	[	[	X
ejpam-6306	59	8	20–26	20–26	NUM
ejpam-6306	59	9	]	]	PUNCT
ejpam-6306	59	10	for	for	ADP
ejpam-6306	59	11	applications	application	NOUN
ejpam-6306	59	12	.	.	PUNCT
ejpam-6306	60	1	the	the	DET
ejpam-6306	60	2	hermite	hermite	ADJ
ejpam-6306	60	3	hadamard	hadamard	ADJ
ejpam-6306	60	4	inequality	inequality	NOUN
ejpam-6306	60	5	is	be	AUX
ejpam-6306	60	6	among	among	ADP
ejpam-6306	60	7	the	the	DET
ejpam-6306	60	8	highly	highly	ADV
ejpam-6306	60	9	elegant	elegant	ADJ
ejpam-6306	60	10	conclusions	conclusion	NOUN
ejpam-6306	60	11	in	in	ADP
ejpam-6306	60	12	the	the	DET
ejpam-6306	60	13	study	study	NOUN
ejpam-6306	60	14	of	of	ADP
ejpam-6306	60	15	convex	convex	PROPN
ejpam-6306	60	16	inequalities	inequality	NOUN
ejpam-6306	60	17	.	.	PUNCT
ejpam-6306	61	1	many	many	ADJ
ejpam-6306	61	2	mathematicians	mathematician	NOUN
ejpam-6306	61	3	have	have	AUX
ejpam-6306	61	4	been	be	AUX
ejpam-6306	61	5	interested	interested	ADJ
ejpam-6306	61	6	in	in	ADP
ejpam-6306	61	7	the	the	DET
ejpam-6306	61	8	well	well	ADV
ejpam-6306	61	9	-	-	PUNCT
ejpam-6306	61	10	known	know	VERB
ejpam-6306	61	11	hermite	hermite	ADJ
ejpam-6306	61	12	hadamard	hadamard	ADJ
ejpam-6306	61	13	inequality	inequality	NOUN
ejpam-6306	61	14	,	,	PUNCT
ejpam-6306	61	15	which	which	PRON
ejpam-6306	61	16	was	be	AUX
ejpam-6306	61	17	independently	independently	ADV
ejpam-6306	61	18	established	establish	VERB
ejpam-6306	61	19	by	by	ADP
ejpam-6306	61	20	jacques	jacques	PROPN
ejpam-6306	61	21	hadamard	hadamard	PROPN
ejpam-6306	61	22	and	and	CCONJ
ejpam-6306	61	23	charles	charle	NOUN
ejpam-6306	61	24	hermite	hermite	PROPN
ejpam-6306	61	25	.	.	PUNCT
ejpam-6306	62	1	they	they	PRON
ejpam-6306	62	2	have	have	AUX
ejpam-6306	62	3	employed	employ	VERB
ejpam-6306	62	4	different	different	ADJ
ejpam-6306	62	5	kinds	kind	NOUN
ejpam-6306	62	6	of	of	ADP
ejpam-6306	62	7	convex	convex	NOUN
ejpam-6306	62	8	functions	function	NOUN
ejpam-6306	62	9	to	to	PART
ejpam-6306	62	10	produce	produce	VERB
ejpam-6306	62	11	numerous	numerous	ADJ
ejpam-6306	62	12	generalizations	generalization	NOUN
ejpam-6306	62	13	of	of	ADP
ejpam-6306	62	14	this	this	DET
ejpam-6306	62	15	inequality	inequality	NOUN
ejpam-6306	62	16	in	in	ADP
ejpam-6306	62	17	the	the	DET
ejpam-6306	62	18	literature	literature	NOUN
ejpam-6306	62	19	.	.	PUNCT
ejpam-6306	63	1	the	the	DET
ejpam-6306	63	2	extensive	extensive	ADJ
ejpam-6306	63	3	range	range	NOUN
ejpam-6306	63	4	of	of	ADP
ejpam-6306	63	5	applications	application	NOUN
ejpam-6306	63	6	of	of	ADP
ejpam-6306	63	7	convexity	convexity	NOUN
ejpam-6306	63	8	has	have	AUX
ejpam-6306	63	9	captured	capture	VERB
ejpam-6306	63	10	the	the	DET
ejpam-6306	63	11	interest	interest	NOUN
ejpam-6306	63	12	of	of	ADP
ejpam-6306	63	13	many	many	ADJ
ejpam-6306	63	14	researchers	researcher	NOUN
ejpam-6306	63	15	,	,	PUNCT
ejpam-6306	63	16	leading	lead	VERB
ejpam-6306	63	17	to	to	ADP
ejpam-6306	63	18	the	the	DET
ejpam-6306	63	19	development	development	NOUN
ejpam-6306	63	20	of	of	ADP
ejpam-6306	63	21	several	several	ADJ
ejpam-6306	63	22	new	new	ADJ
ejpam-6306	63	23	interpretations	interpretation	NOUN
ejpam-6306	63	24	of	of	ADP
ejpam-6306	63	25	traditional	traditional	ADJ
ejpam-6306	63	26	conr	conr	NOUN
ejpam-6306	63	27	.	.	PUNCT
ejpam-6306	64	1	s.	s.	PROPN
ejpam-6306	64	2	ali	ali	PROPN
ejpam-6306	64	3	et	et	PROPN
ejpam-6306	64	4	al	al	PROPN
ejpam-6306	64	5	.	.	PUNCT
ejpam-6306	64	6	/	/	SYM
ejpam-6306	64	7	eur	eur	PROPN
ejpam-6306	64	8	.	.	PUNCT
ejpam-6306	65	1	j.	j.	PROPN
ejpam-6306	65	2	pure	pure	PROPN
ejpam-6306	65	3	appl	appl	PROPN
ejpam-6306	65	4	.	.	PROPN
ejpam-6306	65	5	math	math	PROPN
ejpam-6306	65	6	,	,	PUNCT
ejpam-6306	65	7	18	18	NUM
ejpam-6306	65	8	(	(	PUNCT
ejpam-6306	65	9	3	3	NUM
ejpam-6306	65	10	)	)	PUNCT
ejpam-6306	65	11	(	(	PUNCT
ejpam-6306	65	12	2025	2025	NUM
ejpam-6306	65	13	)	)	PUNCT
ejpam-6306	65	14	,	,	PUNCT
ejpam-6306	65	15	6306	6306	NUM
ejpam-6306	65	16	4	4	NUM
ejpam-6306	65	17	of	of	ADP
ejpam-6306	65	18	18	18	NUM
ejpam-6306	65	19	vexity	vexity	NOUN
ejpam-6306	65	20	in	in	ADP
ejpam-6306	65	21	various	various	ADJ
ejpam-6306	65	22	studies.convexity	studies.convexity	NOUN
ejpam-6306	65	23	has	have	AUX
ejpam-6306	65	24	piqued	pique	VERB
ejpam-6306	65	25	the	the	DET
ejpam-6306	65	26	interest	interest	NOUN
ejpam-6306	65	27	of	of	ADP
ejpam-6306	65	28	many	many	ADJ
ejpam-6306	65	29	researchers	researcher	NOUN
ejpam-6306	65	30	due	due	ADP
ejpam-6306	65	31	to	to	ADP
ejpam-6306	65	32	its	its	PRON
ejpam-6306	65	33	wide	wide	ADJ
ejpam-6306	65	34	range	range	NOUN
ejpam-6306	65	35	of	of	ADP
ejpam-6306	65	36	applications	application	NOUN
ejpam-6306	65	37	.	.	PUNCT
ejpam-6306	66	1	as	as	ADP
ejpam-6306	66	2	a	a	DET
ejpam-6306	66	3	result	result	NOUN
ejpam-6306	66	4	,	,	PUNCT
ejpam-6306	66	5	the	the	DET
ejpam-6306	66	6	literature	literature	NOUN
ejpam-6306	66	7	has	have	AUX
ejpam-6306	66	8	seen	see	VERB
ejpam-6306	66	9	the	the	DET
ejpam-6306	66	10	emergence	emergence	NOUN
ejpam-6306	66	11	of	of	ADP
ejpam-6306	66	12	several	several	ADJ
ejpam-6306	66	13	new	new	ADJ
ejpam-6306	66	14	adaptations	adaptation	NOUN
ejpam-6306	66	15	of	of	ADP
ejpam-6306	66	16	classical	classical	ADJ
ejpam-6306	66	17	convexity	convexity	NOUN
ejpam-6306	66	18	.	.	PUNCT
ejpam-6306	67	1	numerous	numerous	ADJ
ejpam-6306	67	2	prominent	prominent	ADJ
ejpam-6306	67	3	integral	integral	ADJ
ejpam-6306	67	4	inequality	inequality	NOUN
ejpam-6306	67	5	for	for	ADP
ejpam-6306	67	6	the	the	DET
ejpam-6306	67	7	convex	convex	NOUN
ejpam-6306	67	8	functions	function	NOUN
ejpam-6306	67	9	exist	exist	VERB
ejpam-6306	67	10	in	in	ADP
ejpam-6306	67	11	the	the	DET
ejpam-6306	67	12	literature	literature	NOUN
ejpam-6306	67	13	;	;	PUNCT
ejpam-6306	67	14	these	these	PRON
ejpam-6306	67	15	include	include	VERB
ejpam-6306	67	16	the	the	DET
ejpam-6306	67	17	following	follow	VERB
ejpam-6306	67	18	:	:	PUNCT
ejpam-6306	67	19	ostrowski	ostrowski	ADJ
ejpam-6306	67	20	integral	integral	ADJ
ejpam-6306	67	21	inequality	inequality	NOUN
ejpam-6306	67	22	[	[	X
ejpam-6306	67	23	27	27	NUM
ejpam-6306	67	24	]	]	PUNCT
ejpam-6306	67	25	,	,	PUNCT
ejpam-6306	67	26	simpson	simpson	PROPN
ejpam-6306	67	27	’s	’s	PART
ejpam-6306	67	28	integral	integral	ADJ
ejpam-6306	67	29	inequality	inequality	NOUN
ejpam-6306	67	30	[	[	X
ejpam-6306	67	31	28	28	NUM
ejpam-6306	67	32	]	]	X
ejpam-6306	67	33	,	,	PUNCT
ejpam-6306	67	34	hardy	hardy	ADJ
ejpam-6306	67	35	integral	integral	ADJ
ejpam-6306	67	36	inequality	inequality	NOUN
ejpam-6306	67	37	[	[	X
ejpam-6306	67	38	29	29	NUM
ejpam-6306	67	39	]	]	PUNCT
ejpam-6306	67	40	,	,	PUNCT
ejpam-6306	67	41	olsen	olsen	NOUN
ejpam-6306	67	42	integral	integral	ADJ
ejpam-6306	67	43	inequality	inequality	NOUN
ejpam-6306	67	44	[	[	X
ejpam-6306	67	45	30	30	NUM
ejpam-6306	67	46	]	]	PUNCT
ejpam-6306	67	47	,	,	PUNCT
ejpam-6306	67	48	gagliardo	gagliardo	PROPN
ejpam-6306	67	49	nirenberg	nirenberg	PROPN
ejpam-6306	67	50	integral	integral	ADJ
ejpam-6306	67	51	inequality	inequality	NOUN
ejpam-6306	67	52	[	[	X
ejpam-6306	67	53	31	31	NUM
ejpam-6306	67	54	]	]	PUNCT
ejpam-6306	67	55	,	,	PUNCT
ejpam-6306	67	56	fejr	fejr	ADJ
ejpam-6306	67	57	-	-	PUNCT
ejpam-6306	67	58	hermite	hermite	ADJ
ejpam-6306	67	59	hadamard	hadamard	ADJ
ejpam-6306	67	60	inequality	inequality	NOUN
ejpam-6306	67	61	[	[	X
ejpam-6306	67	62	32	32	NUM
ejpam-6306	67	63	]	]	PUNCT
ejpam-6306	67	64	,	,	PUNCT
ejpam-6306	67	65	and	and	CCONJ
ejpam-6306	67	66	q	q	ADJ
ejpam-6306	67	67	-	-	PUNCT
ejpam-6306	67	68	hermite	hermite	ADJ
ejpam-6306	67	69	hadamard	hadamard	ADJ
ejpam-6306	67	70	integral	integral	ADJ
ejpam-6306	67	71	inequality	inequality	NOUN
ejpam-6306	67	72	[	[	X
ejpam-6306	67	73	33	33	NUM
ejpam-6306	67	74	]	]	PUNCT
ejpam-6306	67	75	.	.	PUNCT
ejpam-6306	68	1	researchers	researcher	NOUN
ejpam-6306	68	2	have	have	AUX
ejpam-6306	68	3	been	be	AUX
ejpam-6306	68	4	described	describe	VERB
ejpam-6306	68	5	many	many	ADJ
ejpam-6306	68	6	classical	classical	ADJ
ejpam-6306	68	7	and	and	CCONJ
ejpam-6306	68	8	fractional	fractional	ADJ
ejpam-6306	68	9	integral	integral	ADJ
ejpam-6306	68	10	inequalities	inequality	NOUN
ejpam-6306	68	11	after	after	ADP
ejpam-6306	68	12	introducing	introduce	VERB
ejpam-6306	68	13	the	the	DET
ejpam-6306	68	14	hermite	hermite	ADJ
ejpam-6306	68	15	hadamard	hadamard	ADJ
ejpam-6306	68	16	type	type	NOUN
ejpam-6306	68	17	inequalities	inequality	NOUN
ejpam-6306	68	18	.	.	PUNCT
ejpam-6306	69	1	wu	wu	PROPN
ejpam-6306	69	2	et	et	PROPN
ejpam-6306	69	3	al	al	PROPN
ejpam-6306	69	4	.	.	PROPN
ejpam-6306	69	5	,	,	PUNCT
ejpam-6306	69	6	recently	recently	ADV
ejpam-6306	69	7	presented	present	VERB
ejpam-6306	69	8	a	a	DET
ejpam-6306	69	9	new	new	ADJ
ejpam-6306	69	10	family	family	NOUN
ejpam-6306	69	11	of	of	ADP
ejpam-6306	69	12	convex	convex	NOUN
ejpam-6306	69	13	sets	set	NOUN
ejpam-6306	69	14	and	and	CCONJ
ejpam-6306	69	15	convex	convex	NOUN
ejpam-6306	69	16	functions	function	NOUN
ejpam-6306	69	17	called	call	VERB
ejpam-6306	69	18	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	69	19	sets	set	NOUN
ejpam-6306	69	20	and	and	CCONJ
ejpam-6306	69	21	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	69	22	functions	function	NOUN
ejpam-6306	69	23	in	in	ADP
ejpam-6306	69	24	[	[	X
ejpam-6306	69	25	34	34	NUM
ejpam-6306	69	26	]	]	PUNCT
ejpam-6306	69	27	.	.	PUNCT
ejpam-6306	70	1	we	we	PRON
ejpam-6306	70	2	have	have	VERB
ejpam-6306	70	3	many	many	ADJ
ejpam-6306	70	4	more	more	ADJ
ejpam-6306	70	5	fractional	fractional	ADJ
ejpam-6306	70	6	inequalities	inequality	NOUN
ejpam-6306	70	7	as	as	ADV
ejpam-6306	70	8	well	well	ADV
ejpam-6306	70	9	,	,	PUNCT
ejpam-6306	70	10	but	but	CCONJ
ejpam-6306	70	11	hermite	hermite	ADJ
ejpam-6306	70	12	hadamard	hadamard	ADJ
ejpam-6306	70	13	type	type	NOUN
ejpam-6306	70	14	inequality	inequality	NOUN
ejpam-6306	70	15	is	be	AUX
ejpam-6306	70	16	the	the	DET
ejpam-6306	70	17	most	most	ADV
ejpam-6306	70	18	renowned	renowned	ADJ
ejpam-6306	70	19	.	.	PUNCT
ejpam-6306	71	1	hermite	hermite	ADJ
ejpam-6306	71	2	hadamard	hadamard	ADJ
ejpam-6306	71	3	inequalities	inequality	NOUN
ejpam-6306	71	4	of	of	ADP
ejpam-6306	71	5	many	many	ADJ
ejpam-6306	71	6	kinds	kind	NOUN
ejpam-6306	71	7	have	have	AUX
ejpam-6306	71	8	recently	recently	ADV
ejpam-6306	71	9	been	be	AUX
ejpam-6306	71	10	investigated	investigate	VERB
ejpam-6306	71	11	and	and	CCONJ
ejpam-6306	71	12	generalized	generalize	VERB
ejpam-6306	71	13	for	for	ADP
ejpam-6306	71	14	numerous	numerous	ADJ
ejpam-6306	71	15	kinds	kind	NOUN
ejpam-6306	71	16	of	of	ADP
ejpam-6306	71	17	convex	convex	NOUN
ejpam-6306	71	18	functions	function	NOUN
ejpam-6306	71	19	under	under	ADP
ejpam-6306	71	20	various	various	ADJ
ejpam-6306	71	21	circumstances	circumstance	NOUN
ejpam-6306	71	22	and	and	CCONJ
ejpam-6306	71	23	parameters	parameter	NOUN
ejpam-6306	71	24	.	.	PUNCT
ejpam-6306	72	1	the	the	DET
ejpam-6306	72	2	classical	classical	ADJ
ejpam-6306	72	3	and	and	CCONJ
ejpam-6306	72	4	fractional	fractional	ADJ
ejpam-6306	72	5	inequalities	inequality	NOUN
ejpam-6306	72	6	[	[	X
ejpam-6306	72	7	35	35	NUM
ejpam-6306	72	8	,	,	PUNCT
ejpam-6306	72	9	36	36	NUM
ejpam-6306	72	10	]	]	PUNCT
ejpam-6306	72	11	are	be	AUX
ejpam-6306	72	12	respectively	respectively	ADV
ejpam-6306	72	13	defined	define	VERB
ejpam-6306	72	14	as	as	SCONJ
ejpam-6306	72	15	follows	follow	VERB
ejpam-6306	72	16	f	f	PROPN
ejpam-6306	72	17	(	(	PUNCT
ejpam-6306	72	18	α+	α+	PROPN
ejpam-6306	72	19	ρ	ρ	PROPN
ejpam-6306	72	20	2	2	NUM
ejpam-6306	72	21	)	)	PUNCT
ejpam-6306	72	22	≤	≤	NOUN
ejpam-6306	72	23	1	1	NUM
ejpam-6306	72	24	ρ−	ρ−	NOUN
ejpam-6306	72	25	α	α	DET
ejpam-6306	72	26	∫	∫	PROPN
ejpam-6306	72	27	ρ	ρ	PROPN
ejpam-6306	72	28	α	α	PROPN
ejpam-6306	72	29	f(x)dx	f(x)dx	VERB
ejpam-6306	72	30	≤	≤	ADJ
ejpam-6306	72	31	f(α	f(α	NOUN
ejpam-6306	72	32	)	)	PUNCT
ejpam-6306	73	1	+	+	NUM
ejpam-6306	73	2	f(ρ	f(ρ	NOUN
ejpam-6306	73	3	)	)	PUNCT
ejpam-6306	73	4	2	2	NUM
ejpam-6306	73	5	,	,	PUNCT
ejpam-6306	73	6	(	(	PUNCT
ejpam-6306	73	7	1	1	NUM
ejpam-6306	73	8	)	)	PUNCT
ejpam-6306	73	9	and	and	CCONJ
ejpam-6306	73	10	f	f	PROPN
ejpam-6306	73	11	(	(	PUNCT
ejpam-6306	73	12	α+	α+	PROPN
ejpam-6306	73	13	ρ	ρ	PROPN
ejpam-6306	73	14	2	2	NUM
ejpam-6306	73	15	)	)	PUNCT
ejpam-6306	73	16	≤	≤	NOUN
ejpam-6306	73	17	γ(τ	γ(τ	PROPN
ejpam-6306	74	1	+	+	CCONJ
ejpam-6306	74	2	1	1	X
ejpam-6306	74	3	)	)	PUNCT
ejpam-6306	75	1	2(ρ−	2(ρ−	NUM
ejpam-6306	75	2	α)τ	α)τ	NUM
ejpam-6306	75	3	[	[	PUNCT
ejpam-6306	75	4	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	75	5	,	,	PUNCT
ejpam-6306	75	6	κ	κ	NOUN
ejpam-6306	75	7	ν	ν	PROPN
ejpam-6306	75	8	,	,	PUNCT
ejpam-6306	75	9	τ	τ	PROPN
ejpam-6306	75	10	,	,	PUNCT
ejpam-6306	75	11	j	j	PROPN
ejpam-6306	75	12	,	,	PUNCT
ejpam-6306	75	13	ω	ω	PROPN
ejpam-6306	75	14	,	,	PUNCT
ejpam-6306	75	15	α+f(α	α+f(α	NOUN
ejpam-6306	75	16	)	)	PUNCT
ejpam-6306	75	17	+	+	CCONJ
ejpam-6306	75	18	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	75	19	,	,	PUNCT
ejpam-6306	75	20	κ	κ	NOUN
ejpam-6306	75	21	ν	ν	PROPN
ejpam-6306	75	22	,	,	PUNCT
ejpam-6306	75	23	τ	τ	PROPN
ejpam-6306	75	24	,	,	PUNCT
ejpam-6306	75	25	j	j	PROPN
ejpam-6306	75	26	,	,	PUNCT
ejpam-6306	75	27	ω	ω	PROPN
ejpam-6306	75	28	,	,	PUNCT
ejpam-6306	75	29	ρ−f(ρ	ρ−f(ρ	NOUN
ejpam-6306	75	30	)	)	PUNCT
ejpam-6306	75	31	]	]	PUNCT
ejpam-6306	75	32	≤	≤	NUM
ejpam-6306	75	33	f(α	f(α	NOUN
ejpam-6306	75	34	)	)	PUNCT
ejpam-6306	75	35	+	+	NUM
ejpam-6306	75	36	f(ρ	f(ρ	NOUN
ejpam-6306	75	37	)	)	PUNCT
ejpam-6306	75	38	2	2	NUM
ejpam-6306	75	39	,	,	PUNCT
ejpam-6306	75	40	(	(	PUNCT
ejpam-6306	75	41	2	2	X
ejpam-6306	75	42	)	)	PUNCT
ejpam-6306	75	43	where	where	SCONJ
ejpam-6306	75	44	f	f	NOUN
ejpam-6306	75	45	:	:	PUNCT
ejpam-6306	75	46	⊆	⊆	NUM
ejpam-6306	75	47	r	r	NOUN
ejpam-6306	75	48	is	be	AUX
ejpam-6306	75	49	considered	consider	VERB
ejpam-6306	75	50	to	to	PART
ejpam-6306	75	51	be	be	AUX
ejpam-6306	75	52	a	a	DET
ejpam-6306	75	53	convex	convex	NOUN
ejpam-6306	75	54	function	function	NOUN
ejpam-6306	75	55	on	on	ADP
ejpam-6306	75	56	,	,	PUNCT
ejpam-6306	75	57	f	f	PROPN
ejpam-6306	75	58	∈	∈	PROPN
ejpam-6306	75	59	l1(α	l1(α	PROPN
ejpam-6306	75	60	,	,	PUNCT
ejpam-6306	75	61	ρ	ρ	PROPN
ejpam-6306	75	62	)	)	PUNCT
ejpam-6306	75	63	with	with	ADP
ejpam-6306	75	64	α	α	PROPN
ejpam-6306	75	65	<	<	X
ejpam-6306	75	66	ρ	ρ	PROPN
ejpam-6306	75	67	.	.	PUNCT
ejpam-6306	76	1	the	the	DET
ejpam-6306	76	2	mittag	mittag	ADJ
ejpam-6306	76	3	-	-	PUNCT
ejpam-6306	76	4	leffler	leffler	NOUN
ejpam-6306	76	5	function	function	NOUN
ejpam-6306	76	6	is	be	AUX
ejpam-6306	76	7	near	near	ADJ
ejpam-6306	76	8	to	to	ADP
ejpam-6306	76	9	the	the	DET
ejpam-6306	76	10	exponential	exponential	ADJ
ejpam-6306	76	11	function	function	NOUN
ejpam-6306	76	12	in	in	ADP
ejpam-6306	76	13	solving	solve	VERB
ejpam-6306	76	14	fractional	fractional	ADJ
ejpam-6306	76	15	integro	integro	ADJ
ejpam-6306	76	16	-	-	PUNCT
ejpam-6306	76	17	differential	differential	NOUN
ejpam-6306	76	18	equations	equation	NOUN
ejpam-6306	76	19	of	of	ADP
ejpam-6306	76	20	arbitrary	arbitrary	ADJ
ejpam-6306	76	21	order	order	NOUN
ejpam-6306	76	22	.	.	PUNCT
ejpam-6306	77	1	these	these	DET
ejpam-6306	77	2	functions	function	NOUN
ejpam-6306	77	3	need	need	VERB
ejpam-6306	77	4	more	more	ADJ
ejpam-6306	77	5	recognition	recognition	NOUN
ejpam-6306	77	6	because	because	SCONJ
ejpam-6306	77	7	of	of	ADP
ejpam-6306	77	8	their	their	PRON
ejpam-6306	77	9	extensive	extensive	ADJ
ejpam-6306	77	10	applications	application	NOUN
ejpam-6306	77	11	across	across	ADP
ejpam-6306	77	12	various	various	ADJ
ejpam-6306	77	13	fields	field	NOUN
ejpam-6306	77	14	.	.	PUNCT
ejpam-6306	78	1	they	they	PRON
ejpam-6306	78	2	are	be	AUX
ejpam-6306	78	3	instrumental	instrumental	ADJ
ejpam-6306	78	4	in	in	ADP
ejpam-6306	78	5	defining	define	VERB
ejpam-6306	78	6	new	new	ADJ
ejpam-6306	78	7	fractional	fractional	ADJ
ejpam-6306	78	8	integral	integral	ADJ
ejpam-6306	78	9	operators	operator	NOUN
ejpam-6306	78	10	,	,	PUNCT
ejpam-6306	78	11	which	which	PRON
ejpam-6306	78	12	in	in	ADP
ejpam-6306	78	13	turn	turn	NOUN
ejpam-6306	78	14	are	be	AUX
ejpam-6306	78	15	used	use	VERB
ejpam-6306	78	16	to	to	PART
ejpam-6306	78	17	extend	extend	VERB
ejpam-6306	78	18	mathematical	mathematical	ADJ
ejpam-6306	78	19	inequalities	inequality	NOUN
ejpam-6306	78	20	.	.	PUNCT
ejpam-6306	79	1	in	in	ADP
ejpam-6306	79	2	this	this	DET
ejpam-6306	79	3	paper	paper	NOUN
ejpam-6306	79	4	,	,	PUNCT
ejpam-6306	79	5	we	we	PRON
ejpam-6306	79	6	will	will	AUX
ejpam-6306	79	7	explore	explore	VERB
ejpam-6306	79	8	and	and	CCONJ
ejpam-6306	79	9	examine	examine	VERB
ejpam-6306	79	10	an	an	DET
ejpam-6306	79	11	integral	integral	ADJ
ejpam-6306	79	12	operator	operator	NOUN
ejpam-6306	79	13	with	with	ADP
ejpam-6306	79	14	a	a	DET
ejpam-6306	79	15	kernel	kernel	NOUN
ejpam-6306	79	16	that	that	PRON
ejpam-6306	79	17	is	be	AUX
ejpam-6306	79	18	a	a	DET
ejpam-6306	79	19	generalized	generalized	ADJ
ejpam-6306	79	20	mittag	mittag	ADJ
ejpam-6306	79	21	-	-	PUNCT
ejpam-6306	79	22	leffler	leffler	NOUN
ejpam-6306	79	23	function	function	NOUN
ejpam-6306	79	24	,	,	PUNCT
ejpam-6306	79	25	and	and	CCONJ
ejpam-6306	79	26	we	we	PRON
ejpam-6306	79	27	will	will	AUX
ejpam-6306	79	28	also	also	ADV
ejpam-6306	79	29	identify	identify	VERB
ejpam-6306	79	30	its	its	PRON
ejpam-6306	79	31	familiar	familiar	ADJ
ejpam-6306	79	32	special	special	ADJ
ejpam-6306	79	33	cases	case	NOUN
ejpam-6306	79	34	.	.	PUNCT
ejpam-6306	80	1	2	2	X
ejpam-6306	80	2	.	.	X
ejpam-6306	80	3	preliminaries	preliminary	NOUN
ejpam-6306	80	4	in	in	ADP
ejpam-6306	80	5	this	this	DET
ejpam-6306	80	6	section	section	NOUN
ejpam-6306	80	7	,	,	PUNCT
ejpam-6306	80	8	we	we	PRON
ejpam-6306	80	9	discuss	discuss	VERB
ejpam-6306	80	10	some	some	DET
ejpam-6306	80	11	definitions	definition	NOUN
ejpam-6306	80	12	that	that	PRON
ejpam-6306	80	13	help	help	VERB
ejpam-6306	80	14	us	we	PRON
ejpam-6306	80	15	to	to	PART
ejpam-6306	80	16	understand	understand	VERB
ejpam-6306	80	17	our	our	PRON
ejpam-6306	80	18	main	main	ADJ
ejpam-6306	80	19	results	result	NOUN
ejpam-6306	80	20	.	.	PUNCT
ejpam-6306	81	1	throughout	throughout	ADP
ejpam-6306	81	2	this	this	DET
ejpam-6306	81	3	section	section	NOUN
ejpam-6306	81	4	,	,	PUNCT
ejpam-6306	81	5	q	q	PROPN
ejpam-6306	81	6	denotes	denote	VERB
ejpam-6306	81	7	a	a	DET
ejpam-6306	81	8	subset	subset	NOUN
ejpam-6306	81	9	of	of	ADP
ejpam-6306	81	10	r.	r.	PROPN
ejpam-6306	81	11	definition	definition	NOUN
ejpam-6306	81	12	1	1	NUM
ejpam-6306	81	13	.	.	PUNCT
ejpam-6306	82	1	(	(	PUNCT
ejpam-6306	82	2	[	[	X
ejpam-6306	82	3	34	34	NUM
ejpam-6306	82	4	]	]	PUNCT
ejpam-6306	82	5	)	)	PUNCT
ejpam-6306	82	6	let	let	VERB
ejpam-6306	82	7	υ̌	υ̌	PART
ejpam-6306	82	8	be	be	AUX
ejpam-6306	82	9	continuous	continuous	ADJ
ejpam-6306	82	10	,	,	PUNCT
ejpam-6306	82	11	differentiable	differentiable	ADJ
ejpam-6306	82	12	and	and	CCONJ
ejpam-6306	82	13	strictly	strictly	ADV
ejpam-6306	82	14	monotone	monotone	ADJ
ejpam-6306	82	15	function	function	NOUN
ejpam-6306	82	16	;	;	PUNCT
ejpam-6306	82	17	then	then	ADV
ejpam-6306	82	18	the	the	DET
ejpam-6306	82	19	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	82	20	set	set	NOUN
ejpam-6306	82	21	is	be	AUX
ejpam-6306	82	22	denoted	denote	VERB
ejpam-6306	82	23	as	as	ADP
ejpam-6306	82	24	n	n	PROPN
ejpam-6306	82	25	[	[	X
ejpam-6306	82	26	υ̌	υ̌	PROPN
ejpam-6306	82	27	,	,	PUNCT
ejpam-6306	82	28	η](α	η](α	PROPN
ejpam-6306	82	29	,	,	PUNCT
ejpam-6306	82	30	ρ	ρ	PROPN
ejpam-6306	82	31	)	)	PUNCT
ejpam-6306	82	32	:	:	PUNCT
ejpam-6306	83	1	=	=	PUNCT
ejpam-6306	83	2	υ̌−1(ηυ̌(α	υ̌−1(ηυ̌(α	X
ejpam-6306	83	3	)	)	PUNCT
ejpam-6306	83	4	+	+	CCONJ
ejpam-6306	83	5	(	(	PUNCT
ejpam-6306	83	6	1	1	NUM
ejpam-6306	83	7	−	−	PROPN
ejpam-6306	83	8	η)υ̌(ρ	η)υ̌(ρ	NOUN
ejpam-6306	83	9	)	)	PUNCT
ejpam-6306	83	10	)	)	PUNCT
ejpam-6306	83	11	,	,	PUNCT
ejpam-6306	83	12	and	and	CCONJ
ejpam-6306	83	13	is	be	AUX
ejpam-6306	83	14	defined	define	VERB
ejpam-6306	83	15	,	,	PUNCT
ejpam-6306	83	16	for	for	ADP
ejpam-6306	83	17	each	each	DET
ejpam-6306	83	18	α	α	NOUN
ejpam-6306	83	19	,	,	PUNCT
ejpam-6306	83	20	ρ	ρ	PROPN
ejpam-6306	83	21	∈	∈	PROPN
ejpam-6306	83	22	q	q	NOUN
ejpam-6306	83	23	,	,	PUNCT
ejpam-6306	83	24	η	η	PROPN
ejpam-6306	83	25	∈	∈	PROPN
ejpam-6306	84	1	[	[	X
ejpam-6306	84	2	0	0	NUM
ejpam-6306	84	3	,	,	PUNCT
ejpam-6306	84	4	1	1	NUM
ejpam-6306	84	5	]	]	PUNCT
ejpam-6306	84	6	,	,	PUNCT
ejpam-6306	84	7	as	as	SCONJ
ejpam-6306	84	8	follows	follow	VERB
ejpam-6306	84	9	n	n	PRON
ejpam-6306	84	10	[	[	X
ejpam-6306	84	11	υ̌	υ̌	PROPN
ejpam-6306	84	12	,	,	PUNCT
ejpam-6306	84	13	η](α	η](α	PROPN
ejpam-6306	84	14	,	,	PUNCT
ejpam-6306	84	15	ρ	ρ	PROPN
ejpam-6306	84	16	)	)	PUNCT
ejpam-6306	84	17	∈	∈	PROPN
ejpam-6306	84	18	q.	q.	NOUN
ejpam-6306	84	19	(	(	PUNCT
ejpam-6306	84	20	3	3	X
ejpam-6306	84	21	)	)	PUNCT
ejpam-6306	84	22	r.	r.	PROPN
ejpam-6306	84	23	s.	s.	PROPN
ejpam-6306	84	24	ali	ali	PROPN
ejpam-6306	84	25	et	et	PROPN
ejpam-6306	84	26	al	al	PROPN
ejpam-6306	84	27	.	.	PUNCT
ejpam-6306	84	28	/	/	SYM
ejpam-6306	84	29	eur	eur	PROPN
ejpam-6306	84	30	.	.	PUNCT
ejpam-6306	85	1	j.	j.	PROPN
ejpam-6306	85	2	pure	pure	PROPN
ejpam-6306	85	3	appl	appl	PROPN
ejpam-6306	85	4	.	.	PROPN
ejpam-6306	85	5	math	math	PROPN
ejpam-6306	85	6	,	,	PUNCT
ejpam-6306	85	7	18	18	NUM
ejpam-6306	85	8	(	(	PUNCT
ejpam-6306	85	9	3	3	NUM
ejpam-6306	85	10	)	)	PUNCT
ejpam-6306	85	11	(	(	PUNCT
ejpam-6306	85	12	2025	2025	NUM
ejpam-6306	85	13	)	)	PUNCT
ejpam-6306	85	14	,	,	PUNCT
ejpam-6306	85	15	6306	6306	NUM
ejpam-6306	85	16	5	5	NUM
ejpam-6306	85	17	of	of	ADP
ejpam-6306	85	18	18	18	NUM
ejpam-6306	85	19	definition	definition	NOUN
ejpam-6306	85	20	2	2	NUM
ejpam-6306	85	21	.	.	PUNCT
ejpam-6306	86	1	(	(	PUNCT
ejpam-6306	86	2	[	[	X
ejpam-6306	86	3	34	34	NUM
ejpam-6306	86	4	]	]	SYM
ejpam-6306	86	5	)	)	PUNCT
ejpam-6306	86	6	f	f	NOUN
ejpam-6306	86	7	:	:	PUNCT
ejpam-6306	87	1	q→	q→	NOUN
ejpam-6306	87	2	r	r	NOUN
ejpam-6306	87	3	is	be	AUX
ejpam-6306	87	4	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	87	5	function	function	NOUN
ejpam-6306	87	6	w.r.t	w.r.t	NOUN
ejpam-6306	87	7	.	.	PUNCT
ejpam-6306	88	1	υ̌	υ̌	PROPN
ejpam-6306	88	2	if	if	SCONJ
ejpam-6306	88	3	f(n	f(n	PROPN
ejpam-6306	88	4	[	[	X
ejpam-6306	88	5	υ̌	υ̌	PROPN
ejpam-6306	88	6	,	,	PUNCT
ejpam-6306	88	7	η](α	η](α	PROPN
ejpam-6306	88	8	,	,	PUNCT
ejpam-6306	88	9	ρ	ρ	PROPN
ejpam-6306	88	10	)	)	PUNCT
ejpam-6306	88	11	)	)	PUNCT
ejpam-6306	88	12	≤	≤	NOUN
ejpam-6306	88	13	ηf(α	ηf(α	NOUN
ejpam-6306	88	14	)	)	PUNCT
ejpam-6306	89	1	+	+	CCONJ
ejpam-6306	89	2	(	(	PUNCT
ejpam-6306	89	3	1−	1−	NUM
ejpam-6306	89	4	η)f(ρ	η)f(ρ	NOUN
ejpam-6306	89	5	)	)	PUNCT
ejpam-6306	89	6	,	,	PUNCT
ejpam-6306	89	7	(	(	PUNCT
ejpam-6306	89	8	4	4	X
ejpam-6306	89	9	)	)	PUNCT
ejpam-6306	89	10	for	for	ADP
ejpam-6306	89	11	each	each	DET
ejpam-6306	89	12	α	α	NOUN
ejpam-6306	89	13	,	,	PUNCT
ejpam-6306	89	14	ρ	ρ	PROPN
ejpam-6306	89	15	∈	∈	PROPN
ejpam-6306	89	16	q	q	NOUN
ejpam-6306	89	17	,	,	PUNCT
ejpam-6306	89	18	η	η	PROPN
ejpam-6306	89	19	∈	∈	PROPN
ejpam-6306	90	1	[	[	X
ejpam-6306	90	2	0	0	NUM
ejpam-6306	90	3	,	,	PUNCT
ejpam-6306	90	4	1	1	NUM
ejpam-6306	90	5	]	]	PUNCT
ejpam-6306	90	6	.	.	PUNCT
ejpam-6306	91	1	remark	remark	PROPN
ejpam-6306	91	2	1	1	NUM
ejpam-6306	91	3	.	.	NOUN
ejpam-6306	91	4	•	•	NOUN
ejpam-6306	91	5	if	if	SCONJ
ejpam-6306	91	6	the	the	DET
ejpam-6306	91	7	inequality(4	inequality(4	NOUN
ejpam-6306	91	8	)	)	PUNCT
ejpam-6306	91	9	is	be	AUX
ejpam-6306	91	10	to	to	PART
ejpam-6306	91	11	be	be	AUX
ejpam-6306	91	12	held	hold	VERB
ejpam-6306	91	13	as	as	ADP
ejpam-6306	91	14	a	a	DET
ejpam-6306	91	15	strict	strict	ADJ
ejpam-6306	91	16	inequality	inequality	NOUN
ejpam-6306	91	17	for	for	ADP
ejpam-6306	91	18	all	all	DET
ejpam-6306	91	19	η	η	PROPN
ejpam-6306	91	20	∈	∈	PROPN
ejpam-6306	91	21	(	(	PUNCT
ejpam-6306	91	22	0	0	NUM
ejpam-6306	91	23	,	,	PUNCT
ejpam-6306	91	24	1	1	NUM
ejpam-6306	91	25	)	)	PUNCT
ejpam-6306	91	26	and	and	CCONJ
ejpam-6306	91	27	α	α	NOUN
ejpam-6306	91	28	,	,	PUNCT
ejpam-6306	91	29	ρ	ρ	PROPN
ejpam-6306	91	30	∈	∈	PROPN
ejpam-6306	92	1	q	q	NOUN
ejpam-6306	92	2	,	,	PUNCT
ejpam-6306	92	3	α	α	PROPN
ejpam-6306	92	4	̸=	̸=	PROPN
ejpam-6306	92	5	ρ	ρ	NUM
ejpam-6306	92	6	,	,	PUNCT
ejpam-6306	92	7	then	then	ADV
ejpam-6306	92	8	f	f	PROPN
ejpam-6306	92	9	is	be	AUX
ejpam-6306	92	10	a	a	DET
ejpam-6306	92	11	strictly	strictly	ADV
ejpam-6306	92	12	monotone	monotone	ADJ
ejpam-6306	92	13	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	92	14	function	function	NOUN
ejpam-6306	92	15	on	on	ADP
ejpam-6306	92	16	q.	q.	PROPN
ejpam-6306	92	17	•	•	ADP
ejpam-6306	92	18	if	if	SCONJ
ejpam-6306	92	19	−f	−f	PROPN
ejpam-6306	92	20	is	be	AUX
ejpam-6306	92	21	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	92	22	on	on	ADP
ejpam-6306	92	23	q	q	NOUN
ejpam-6306	92	24	in	in	ADP
ejpam-6306	92	25	(	(	PUNCT
ejpam-6306	92	26	4	4	NUM
ejpam-6306	92	27	)	)	PUNCT
ejpam-6306	92	28	,	,	PUNCT
ejpam-6306	92	29	then	then	ADV
ejpam-6306	92	30	f	f	PROPN
ejpam-6306	92	31	is	be	AUX
ejpam-6306	92	32	υ̌-concave	υ̌-concave	NOUN
ejpam-6306	92	33	function	function	NOUN
ejpam-6306	92	34	on	on	ADP
ejpam-6306	92	35	q.	q.	PROPN
ejpam-6306	92	36	•	•	ADP
ejpam-6306	93	1	if	if	SCONJ
ejpam-6306	93	2	−f	−f	PROPN
ejpam-6306	93	3	is	be	AUX
ejpam-6306	93	4	strictly	strictly	ADV
ejpam-6306	93	5	monotone	monotone	ADJ
ejpam-6306	93	6	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	93	7	on	on	ADP
ejpam-6306	93	8	q	q	NOUN
ejpam-6306	93	9	,	,	PUNCT
ejpam-6306	93	10	then	then	ADV
ejpam-6306	93	11	f	f	PROPN
ejpam-6306	93	12	is	be	AUX
ejpam-6306	93	13	a	a	DET
ejpam-6306	93	14	strictly	strictly	ADV
ejpam-6306	93	15	monotone	monotone	ADJ
ejpam-6306	93	16	υ̌-concave	υ̌-concave	NOUN
ejpam-6306	93	17	function	function	NOUN
ejpam-6306	93	18	on	on	ADP
ejpam-6306	93	19	q.	q.	PROPN
ejpam-6306	93	20	definition	definition	NOUN
ejpam-6306	93	21	3	3	NUM
ejpam-6306	93	22	.	.	PUNCT
ejpam-6306	94	1	(	(	PUNCT
ejpam-6306	94	2	[	[	X
ejpam-6306	94	3	37	37	NUM
ejpam-6306	94	4	]	]	PUNCT
ejpam-6306	94	5	)	)	PUNCT
ejpam-6306	94	6	let	let	VERB
ejpam-6306	94	7	µ	µ	PRON
ejpam-6306	94	8	∈	∈	NOUN
ejpam-6306	94	9	r	r	NOUN
ejpam-6306	94	10	,	,	PUNCT
ejpam-6306	94	11	then	then	ADV
ejpam-6306	94	12	for	for	ADP
ejpam-6306	94	13	positive	positive	ADJ
ejpam-6306	94	14	real	real	ADJ
ejpam-6306	94	15	numbers	number	NOUN
ejpam-6306	94	16	ν	ν	PROPN
ejpam-6306	94	17	,	,	PUNCT
ejpam-6306	94	18	τ	τ	PROPN
ejpam-6306	94	19	,	,	PUNCT
ejpam-6306	94	20	j	j	PROPN
ejpam-6306	94	21	,	,	PUNCT
ejpam-6306	94	22	ϑ	ϑ	X
ejpam-6306	94	23	,	,	PUNCT
ejpam-6306	94	24	z	z	NOUN
ejpam-6306	94	25	,	,	PUNCT
ejpam-6306	94	26	κ	κ	PROPN
ejpam-6306	94	27	,	,	PUNCT
ejpam-6306	94	28	the	the	DET
ejpam-6306	94	29	generalized	generalize	VERB
ejpam-6306	94	30	mittag	mittag	ADJ
ejpam-6306	94	31	-	-	PUNCT
ejpam-6306	94	32	leffler	leffler	NOUN
ejpam-6306	94	33	function	function	NOUN
ejpam-6306	94	34	is	be	AUX
ejpam-6306	94	35	defined	define	VERB
ejpam-6306	94	36	as	as	ADP
ejpam-6306	94	37	follows	follow	VERB
ejpam-6306	94	38	eϑ,z	eϑ,z	NOUN
ejpam-6306	94	39	,	,	PUNCT
ejpam-6306	94	40	κ	κ	X
ejpam-6306	94	41	ν	ν	PROPN
ejpam-6306	94	42	,	,	PUNCT
ejpam-6306	94	43	τ	τ	PROPN
ejpam-6306	94	44	,	,	PUNCT
ejpam-6306	94	45	j	j	PROPN
ejpam-6306	94	46	(	(	PUNCT
ejpam-6306	94	47	ξ(µ)v	ξ(µ)v	PROPN
ejpam-6306	94	48	)	)	PUNCT
ejpam-6306	94	49	=	=	PUNCT
ejpam-6306	95	1	∞∑	∞∑	NUM
ejpam-6306	95	2	n=0	n=0	NUM
ejpam-6306	95	3	(	(	PUNCT
ejpam-6306	95	4	ϑ)κn	ϑ)κn	PROPN
ejpam-6306	95	5	(	(	PUNCT
ejpam-6306	95	6	ξ(µ)v	ξ(µ)v	PROPN
ejpam-6306	95	7	)	)	PUNCT
ejpam-6306	95	8	γ(vn+	γ(vn+	PROPN
ejpam-6306	95	9	τ)(z)δn	τ)(z)δn	PROPN
ejpam-6306	95	10	.	.	PUNCT
ejpam-6306	96	1	(	(	PUNCT
ejpam-6306	96	2	5	5	NUM
ejpam-6306	96	3	)	)	PUNCT
ejpam-6306	96	4	3	3	NUM
ejpam-6306	96	5	.	.	X
ejpam-6306	96	6	modification	modification	NOUN
ejpam-6306	96	7	of	of	ADP
ejpam-6306	96	8	hermite	hermite	ADJ
ejpam-6306	96	9	hadamard	hadamard	ADJ
ejpam-6306	96	10	type	type	NOUN
ejpam-6306	96	11	inequalities	inequality	NOUN
ejpam-6306	96	12	for	for	ADP
ejpam-6306	96	13	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	96	14	function	function	NOUN
ejpam-6306	96	15	in	in	ADP
ejpam-6306	96	16	this	this	DET
ejpam-6306	96	17	section	section	NOUN
ejpam-6306	96	18	,	,	PUNCT
ejpam-6306	96	19	we	we	PRON
ejpam-6306	96	20	modify	modify	VERB
ejpam-6306	96	21	the	the	DET
ejpam-6306	96	22	hermite	hermite	ADJ
ejpam-6306	96	23	hadamard	hadamard	ADJ
ejpam-6306	96	24	type	type	NOUN
ejpam-6306	96	25	inequalities	inequality	NOUN
ejpam-6306	96	26	and	and	CCONJ
ejpam-6306	96	27	the	the	DET
ejpam-6306	96	28	related	related	ADJ
ejpam-6306	96	29	refinements	refinement	NOUN
ejpam-6306	96	30	for	for	ADP
ejpam-6306	96	31	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	96	32	function	function	NOUN
ejpam-6306	96	33	by	by	ADP
ejpam-6306	96	34	implementation	implementation	NOUN
ejpam-6306	96	35	of	of	ADP
ejpam-6306	96	36	generalized	generalized	ADJ
ejpam-6306	96	37	fractional	fractional	ADJ
ejpam-6306	96	38	operators	operator	NOUN
ejpam-6306	96	39	for	for	ADP
ejpam-6306	96	40	monotone	monotone	ADJ
ejpam-6306	96	41	differentiable	differentiable	ADJ
ejpam-6306	96	42	function	function	NOUN
ejpam-6306	96	43	having	having	AUX
ejpam-6306	96	44	extended	extend	VERB
ejpam-6306	96	45	mittag	mittag	ADJ
ejpam-6306	96	46	-	-	PUNCT
ejpam-6306	96	47	leffler	leffler	NOUN
ejpam-6306	96	48	function	function	NOUN
ejpam-6306	96	49	as	as	ADP
ejpam-6306	96	50	a	a	DET
ejpam-6306	96	51	kernel	kernel	NOUN
ejpam-6306	96	52	.	.	PUNCT
ejpam-6306	97	1	definition	definition	NOUN
ejpam-6306	97	2	4	4	NUM
ejpam-6306	97	3	.	.	PUNCT
ejpam-6306	98	1	let	let	AUX
ejpam-6306	98	2	(	(	PUNCT
ejpam-6306	98	3	α	α	NOUN
ejpam-6306	98	4	,	,	PUNCT
ejpam-6306	98	5	ρ	ρ	PROPN
ejpam-6306	98	6	)	)	PUNCT
ejpam-6306	98	7	⊆	⊆	NUM
ejpam-6306	98	8	r	r	NOUN
ejpam-6306	98	9	,	,	PUNCT
ejpam-6306	98	10	φ(x	φ(x	PROPN
ejpam-6306	98	11	)	)	PUNCT
ejpam-6306	98	12	be	be	AUX
ejpam-6306	98	13	differentiable	differentiable	ADJ
ejpam-6306	98	14	monotone	monotone	ADJ
ejpam-6306	98	15	-	-	PUNCT
ejpam-6306	98	16	positive	positive	ADJ
ejpam-6306	98	17	function	function	NOUN
ejpam-6306	98	18	on	on	ADP
ejpam-6306	98	19	(	(	PUNCT
ejpam-6306	98	20	α	α	X
ejpam-6306	98	21	,	,	PUNCT
ejpam-6306	98	22	ρ	ρ	NOUN
ejpam-6306	98	23	]	]	X
ejpam-6306	98	24	,	,	PUNCT
ejpam-6306	98	25	and	and	CCONJ
ejpam-6306	98	26	φ′(x	φ′(x	X
ejpam-6306	98	27	)	)	PUNCT
ejpam-6306	98	28	be	be	AUX
ejpam-6306	98	29	continuous	continuous	ADJ
ejpam-6306	98	30	on	on	ADP
ejpam-6306	98	31	(	(	PUNCT
ejpam-6306	98	32	α	α	X
ejpam-6306	98	33	,	,	PUNCT
ejpam-6306	98	34	ρ	ρ	NOUN
ejpam-6306	98	35	)	)	PUNCT
ejpam-6306	98	36	.	.	PUNCT
ejpam-6306	99	1	then	then	ADV
ejpam-6306	99	2	,	,	PUNCT
ejpam-6306	99	3	the	the	DET
ejpam-6306	99	4	left	left	ADJ
ejpam-6306	99	5	and	and	CCONJ
ejpam-6306	99	6	right	right	ADJ
ejpam-6306	99	7	-	-	PUNCT
ejpam-6306	99	8	side	side	NOUN
ejpam-6306	99	9	of	of	ADP
ejpam-6306	99	10	generalized	generalized	ADJ
ejpam-6306	99	11	fractional	fractional	ADJ
ejpam-6306	99	12	integral	integral	ADJ
ejpam-6306	99	13	operators	operator	NOUN
ejpam-6306	99	14	of	of	ADP
ejpam-6306	99	15	a	a	DET
ejpam-6306	99	16	function	function	NOUN
ejpam-6306	99	17	f	f	NOUN
ejpam-6306	99	18	with	with	ADP
ejpam-6306	99	19	respect	respect	NOUN
ejpam-6306	99	20	to	to	ADP
ejpam-6306	99	21	a	a	DET
ejpam-6306	99	22	function	function	NOUN
ejpam-6306	99	23	φ(x	φ(x	NOUN
ejpam-6306	99	24	)	)	PUNCT
ejpam-6306	99	25	on	on	ADP
ejpam-6306	99	26	[	[	X
ejpam-6306	99	27	α	α	X
ejpam-6306	99	28	,	,	PUNCT
ejpam-6306	99	29	ρ	ρ	PROPN
ejpam-6306	99	30	]	]	X
ejpam-6306	99	31	,	,	PUNCT
ejpam-6306	99	32	for	for	ADP
ejpam-6306	99	33	positive	positive	ADJ
ejpam-6306	99	34	real	real	ADJ
ejpam-6306	99	35	numbers	number	NOUN
ejpam-6306	99	36	ν	ν	PROPN
ejpam-6306	99	37	,	,	PUNCT
ejpam-6306	99	38	τ	τ	PROPN
ejpam-6306	99	39	,	,	PUNCT
ejpam-6306	99	40	j	j	PROPN
ejpam-6306	99	41	,	,	PUNCT
ejpam-6306	99	42	ϑ	ϑ	X
ejpam-6306	99	43	,	,	PUNCT
ejpam-6306	99	44	z	z	NOUN
ejpam-6306	99	45	,	,	PUNCT
ejpam-6306	99	46	κ	κ	NOUN
ejpam-6306	99	47	,	,	PUNCT
ejpam-6306	99	48	and	and	CCONJ
ejpam-6306	99	49	ω	ω	NUM
ejpam-6306	99	50	∈	∈	PROPN
ejpam-6306	99	51	r	r	NOUN
ejpam-6306	99	52	,	,	PUNCT
ejpam-6306	99	53	are	be	AUX
ejpam-6306	99	54	respectively	respectively	ADV
ejpam-6306	99	55	defined	define	VERB
ejpam-6306	99	56	as	as	SCONJ
ejpam-6306	99	57	follows	follow	VERB
ejpam-6306	99	58	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	99	59	,	,	PUNCT
ejpam-6306	99	60	κ	κ	NOUN
ejpam-6306	99	61	ν	ν	PROPN
ejpam-6306	99	62	,	,	PUNCT
ejpam-6306	99	63	τ	τ	PROPN
ejpam-6306	99	64	,	,	PUNCT
ejpam-6306	99	65	j	j	PROPN
ejpam-6306	99	66	,	,	PUNCT
ejpam-6306	99	67	ω	ω	PROPN
ejpam-6306	99	68	,	,	PUNCT
ejpam-6306	99	69	α+f(x	α+f(x	NOUN
ejpam-6306	99	70	)	)	PUNCT
ejpam-6306	99	71	=	=	SYM
ejpam-6306	100	1	∫	∫	PROPN
ejpam-6306	100	2	x	x	SYM
ejpam-6306	100	3	α	α	PROPN
ejpam-6306	100	4	(	(	PUNCT
ejpam-6306	100	5	φ(x)−	φ(x)−	PROPN
ejpam-6306	100	6	φ(µ	φ(µ	PROPN
ejpam-6306	100	7	)	)	PUNCT
ejpam-6306	100	8	)	)	PUNCT
ejpam-6306	100	9	τ−1eϑ,z	τ−1eϑ,z	PROPN
ejpam-6306	100	10	,	,	PUNCT
ejpam-6306	100	11	κ	κ	NOUN
ejpam-6306	100	12	ν	ν	PROPN
ejpam-6306	100	13	,	,	PUNCT
ejpam-6306	100	14	τ	τ	PROPN
ejpam-6306	100	15	,	,	PUNCT
ejpam-6306	100	16	j	j	PROPN
ejpam-6306	100	17	(	(	PUNCT
ejpam-6306	100	18	ξ(µ)n	ξ(µ)n	PROPN
ejpam-6306	100	19	)	)	PUNCT
ejpam-6306	100	20	φ′(µ)f(µ)dµ	φ′(µ)f(µ)dµ	PROPN
ejpam-6306	100	21	,	,	PUNCT
ejpam-6306	100	22	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	100	23	,	,	PUNCT
ejpam-6306	100	24	κ	κ	NOUN
ejpam-6306	100	25	ν	ν	PROPN
ejpam-6306	100	26	,	,	PUNCT
ejpam-6306	100	27	τ	τ	PROPN
ejpam-6306	100	28	,	,	PUNCT
ejpam-6306	100	29	j	j	PROPN
ejpam-6306	100	30	,	,	PUNCT
ejpam-6306	100	31	ω	ω	PROPN
ejpam-6306	100	32	,	,	PUNCT
ejpam-6306	100	33	ρ−f(x	ρ−f(x	NOUN
ejpam-6306	100	34	)	)	PUNCT
ejpam-6306	100	35	=	=	SYM
ejpam-6306	101	1	∫	∫	PROPN
ejpam-6306	101	2	ρ	ρ	PROPN
ejpam-6306	101	3	x	x	INTJ
ejpam-6306	101	4	(	(	PUNCT
ejpam-6306	101	5	φ(µ)−	φ(µ)−	PROPN
ejpam-6306	101	6	φ(x	φ(x	PROPN
ejpam-6306	101	7	)	)	PUNCT
ejpam-6306	101	8	)	)	PUNCT
ejpam-6306	102	1	τ−1eϑ,z	τ−1eϑ,z	PROPN
ejpam-6306	102	2	,	,	PUNCT
ejpam-6306	102	3	κ	κ	NOUN
ejpam-6306	102	4	ν	ν	PROPN
ejpam-6306	102	5	,	,	PUNCT
ejpam-6306	102	6	τ	τ	PROPN
ejpam-6306	102	7	,	,	PUNCT
ejpam-6306	102	8	j	j	PROPN
ejpam-6306	102	9	(	(	PUNCT
ejpam-6306	102	10	ξ(µ)n	ξ(µ)n	PROPN
ejpam-6306	102	11	)	)	PUNCT
ejpam-6306	102	12	φ′(µ)f(µ)dµ	φ′(µ)f(µ)dµ	PROPN
ejpam-6306	102	13	,	,	PUNCT
ejpam-6306	102	14	τ	τ	PROPN
ejpam-6306	102	15	>	>	X
ejpam-6306	102	16	0	0	NUM
ejpam-6306	102	17	.	.	PUNCT
ejpam-6306	103	1	(	(	PUNCT
ejpam-6306	103	2	6	6	NUM
ejpam-6306	103	3	)	)	PUNCT
ejpam-6306	103	4	theorem	theorem	NOUN
ejpam-6306	103	5	1	1	NUM
ejpam-6306	103	6	.	.	PUNCT
ejpam-6306	104	1	let	let	VERB
ejpam-6306	104	2	f	f	NOUN
ejpam-6306	104	3	:	:	PUNCT
ejpam-6306	105	1	[	[	X
ejpam-6306	105	2	α	α	X
ejpam-6306	105	3	,	,	PUNCT
ejpam-6306	105	4	ρ	ρ	PROPN
ejpam-6306	105	5	]	]	X
ejpam-6306	105	6	⊆	⊆	NUM
ejpam-6306	105	7	r	r	NOUN
ejpam-6306	105	8	→	→	SYM
ejpam-6306	105	9	r	r	NOUN
ejpam-6306	105	10	be	be	AUX
ejpam-6306	105	11	integrable	integrable	ADJ
ejpam-6306	105	12	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	105	13	and	and	CCONJ
ejpam-6306	105	14	f	f	PROPN
ejpam-6306	105	15	∈	∈	PROPN
ejpam-6306	105	16	l1(α	l1(α	PROPN
ejpam-6306	105	17	,	,	PUNCT
ejpam-6306	105	18	ρ	ρ	PROPN
ejpam-6306	105	19	)	)	PUNCT
ejpam-6306	105	20	with	with	ADP
ejpam-6306	105	21	0	0	NUM
ejpam-6306	105	22	≤	≤	NUM
ejpam-6306	105	23	α	α	PROPN
ejpam-6306	105	24	<	<	X
ejpam-6306	105	25	ρ	ρ	PROPN
ejpam-6306	105	26	,	,	PUNCT
ejpam-6306	105	27	and	and	CCONJ
ejpam-6306	105	28	the	the	DET
ejpam-6306	105	29	function	function	NOUN
ejpam-6306	105	30	υ̌	υ̌	AUX
ejpam-6306	105	31	be	be	AUX
ejpam-6306	105	32	positive	positive	ADJ
ejpam-6306	105	33	and	and	CCONJ
ejpam-6306	105	34	monotonically	monotonically	ADV
ejpam-6306	105	35	increasing	increase	VERB
ejpam-6306	105	36	on	on	ADP
ejpam-6306	105	37	(	(	PUNCT
ejpam-6306	105	38	α	α	X
ejpam-6306	105	39	,	,	PUNCT
ejpam-6306	105	40	ρ	ρ	NOUN
ejpam-6306	105	41	]	]	PUNCT
ejpam-6306	105	42	and	and	CCONJ
ejpam-6306	105	43	υ̌′(x	υ̌′(x	NOUN
ejpam-6306	105	44	)	)	PUNCT
ejpam-6306	105	45	is	be	AUX
ejpam-6306	105	46	continuous	continuous	ADJ
ejpam-6306	105	47	on	on	ADP
ejpam-6306	105	48	(	(	PUNCT
ejpam-6306	105	49	α	α	X
ejpam-6306	105	50	,	,	PUNCT
ejpam-6306	105	51	ρ	ρ	NOUN
ejpam-6306	105	52	)	)	PUNCT
ejpam-6306	105	53	.	.	PUNCT
ejpam-6306	106	1	then	then	ADV
ejpam-6306	106	2	,	,	PUNCT
ejpam-6306	106	3	we	we	PRON
ejpam-6306	106	4	have	have	VERB
ejpam-6306	106	5	,	,	PUNCT
ejpam-6306	106	6	for	for	ADP
ejpam-6306	106	7	τ	τ	PROPN
ejpam-6306	106	8	>	>	X
ejpam-6306	106	9	0	0	PUNCT
ejpam-6306	106	10	and	and	CCONJ
ejpam-6306	106	11	β	β	X
ejpam-6306	106	12	∈	∈	PROPN
ejpam-6306	106	13	r	r	PROPN
ejpam-6306	106	14	,	,	PUNCT
ejpam-6306	106	15	f	f	PROPN
ejpam-6306	106	16	(	(	PUNCT
ejpam-6306	106	17	υ̌−1	υ̌−1	X
ejpam-6306	106	18	(	(	PUNCT
ejpam-6306	106	19	υ̌(α	υ̌(α	PROPN
ejpam-6306	106	20	)	)	PUNCT
ejpam-6306	106	21	+	+	CCONJ
ejpam-6306	106	22	υ̌(ρ	υ̌(ρ	X
ejpam-6306	106	23	)	)	PUNCT
ejpam-6306	106	24	2	2	NUM
ejpam-6306	106	25	)	)	PUNCT
ejpam-6306	106	26	)	)	PUNCT
ejpam-6306	106	27	eϑ,z	eϑ,z	NOUN
ejpam-6306	106	28	,	,	PUNCT
ejpam-6306	106	29	κ	κ	X
ejpam-6306	106	30	ν	ν	PROPN
ejpam-6306	106	31	,	,	PUNCT
ejpam-6306	106	32	τ	τ	PROPN
ejpam-6306	106	33	,	,	PUNCT
ejpam-6306	106	34	j	j	PROPN
ejpam-6306	106	35	(	(	PUNCT
ejpam-6306	106	36	(	(	PUNCT
ejpam-6306	106	37	1−	1−	NUM
ejpam-6306	106	38	β)v	β)v	NOUN
ejpam-6306	106	39	)	)	PUNCT
ejpam-6306	106	40	≤	≤	NUM
ejpam-6306	106	41	1	1	NUM
ejpam-6306	106	42	2	2	NUM
ejpam-6306	106	43	(	(	PUNCT
ejpam-6306	106	44	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	106	45	υ̌(α	υ̌(α	NUM
ejpam-6306	106	46	)	)	PUNCT
ejpam-6306	106	47	)	)	PUNCT
ejpam-6306	106	48	τ	τ	PROPN
ejpam-6306	107	1	[	[	X
ejpam-6306	107	2	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	107	3	,	,	PUNCT
ejpam-6306	107	4	κ	κ	NOUN
ejpam-6306	107	5	ν	ν	PROPN
ejpam-6306	107	6	,	,	PUNCT
ejpam-6306	107	7	τ	τ	PROPN
ejpam-6306	107	8	,	,	PUNCT
ejpam-6306	107	9	j	j	PROPN
ejpam-6306	107	10	,	,	PUNCT
ejpam-6306	107	11	ω	ω	PROPN
ejpam-6306	107	12	,	,	PUNCT
ejpam-6306	107	13	α+f(α	α+f(α	NOUN
ejpam-6306	107	14	)	)	PUNCT
ejpam-6306	107	15	+	+	CCONJ
ejpam-6306	107	16	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	107	17	,	,	PUNCT
ejpam-6306	107	18	κ	κ	NOUN
ejpam-6306	107	19	ν	ν	PROPN
ejpam-6306	107	20	,	,	PUNCT
ejpam-6306	107	21	τ	τ	PROPN
ejpam-6306	107	22	,	,	PUNCT
ejpam-6306	107	23	j	j	PROPN
ejpam-6306	107	24	,	,	PUNCT
ejpam-6306	107	25	ω	ω	PROPN
ejpam-6306	107	26	,	,	PUNCT
ejpam-6306	107	27	ρ−f(ρ	ρ−f(ρ	NOUN
ejpam-6306	107	28	)	)	PUNCT
ejpam-6306	107	29	]	]	PUNCT
ejpam-6306	107	30	≤	≤	NUM
ejpam-6306	107	31	f(α	f(α	NOUN
ejpam-6306	107	32	)	)	PUNCT
ejpam-6306	107	33	+	+	NUM
ejpam-6306	107	34	f(ρ	f(ρ	NOUN
ejpam-6306	107	35	)	)	PUNCT
ejpam-6306	107	36	2	2	NUM
ejpam-6306	107	37	eϑ,z	eϑ,z	NOUN
ejpam-6306	107	38	,	,	PUNCT
ejpam-6306	107	39	κ	κ	X
ejpam-6306	107	40	ν	ν	PROPN
ejpam-6306	107	41	,	,	PUNCT
ejpam-6306	107	42	τ	τ	PROPN
ejpam-6306	107	43	,	,	PUNCT
ejpam-6306	107	44	j	j	PROPN
ejpam-6306	107	45	(	(	PUNCT
ejpam-6306	107	46	(	(	PUNCT
ejpam-6306	107	47	1−	1−	NUM
ejpam-6306	107	48	β)v	β)v	NOUN
ejpam-6306	107	49	)	)	PUNCT
ejpam-6306	107	50	,	,	PUNCT
ejpam-6306	107	51	(	(	PUNCT
ejpam-6306	107	52	7	7	X
ejpam-6306	107	53	)	)	PUNCT
ejpam-6306	107	54	where	where	SCONJ
ejpam-6306	107	55	(	(	PUNCT
ejpam-6306	107	56	ξ(µ)v)n	ξ(µ)v)n	NOUN
ejpam-6306	107	57	=	=	SYM
ejpam-6306	107	58	(	(	PUNCT
ejpam-6306	107	59	(	(	PUNCT
ejpam-6306	107	60	υ̌(µ)−υ̌(α	υ̌(µ)−υ̌(α	PROPN
ejpam-6306	107	61	)	)	PUNCT
ejpam-6306	107	62	υ̌(ρ)−υ̌(α	υ̌(ρ)−υ̌(α	PROPN
ejpam-6306	107	63	)	)	PUNCT
ejpam-6306	107	64	)	)	PUNCT
ejpam-6306	107	65	v)n	v)n	NOUN
ejpam-6306	107	66	and	and	CCONJ
ejpam-6306	107	67	(	(	PUNCT
ejpam-6306	107	68	ξ(ω)v)n	ξ(ω)v)n	PROPN
ejpam-6306	107	69	=	=	PUNCT
ejpam-6306	107	70	(	(	PUNCT
ejpam-6306	107	71	(	(	PUNCT
ejpam-6306	107	72	υ̌(ρ)−υ̌(ω	υ̌(ρ)−υ̌(ω	PROPN
ejpam-6306	107	73	)	)	PUNCT
ejpam-6306	107	74	υ̌(ρ)−υ̌(α	υ̌(ρ)−υ̌(α	PROPN
ejpam-6306	107	75	)	)	PUNCT
ejpam-6306	107	76	)	)	PUNCT
ejpam-6306	107	77	v)n	v)n	NOUN
ejpam-6306	107	78	.	.	PUNCT
ejpam-6306	108	1	r.	r.	PROPN
ejpam-6306	108	2	s.	s.	PROPN
ejpam-6306	108	3	ali	ali	PROPN
ejpam-6306	108	4	et	et	PROPN
ejpam-6306	108	5	al	al	PROPN
ejpam-6306	108	6	.	.	PUNCT
ejpam-6306	108	7	/	/	SYM
ejpam-6306	108	8	eur	eur	PROPN
ejpam-6306	108	9	.	.	PUNCT
ejpam-6306	109	1	j.	j.	PROPN
ejpam-6306	109	2	pure	pure	PROPN
ejpam-6306	109	3	appl	appl	PROPN
ejpam-6306	109	4	.	.	PROPN
ejpam-6306	109	5	math	math	PROPN
ejpam-6306	109	6	,	,	PUNCT
ejpam-6306	109	7	18	18	NUM
ejpam-6306	109	8	(	(	PUNCT
ejpam-6306	109	9	3	3	NUM
ejpam-6306	109	10	)	)	PUNCT
ejpam-6306	109	11	(	(	PUNCT
ejpam-6306	109	12	2025	2025	NUM
ejpam-6306	109	13	)	)	PUNCT
ejpam-6306	109	14	,	,	PUNCT
ejpam-6306	109	15	6306	6306	NUM
ejpam-6306	109	16	6	6	NUM
ejpam-6306	109	17	of	of	ADP
ejpam-6306	109	18	18	18	NUM
ejpam-6306	109	19	proof	proof	NOUN
ejpam-6306	109	20	.	.	PUNCT
ejpam-6306	110	1	consider	consider	VERB
ejpam-6306	110	2	the	the	DET
ejpam-6306	110	3	f	f	PROPN
ejpam-6306	110	4	as	as	ADP
ejpam-6306	110	5	a	a	DET
ejpam-6306	110	6	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	110	7	function	function	NOUN
ejpam-6306	110	8	,	,	PUNCT
ejpam-6306	110	9	i.e.	i.e.	X
ejpam-6306	110	10	,	,	PUNCT
ejpam-6306	110	11	f	f	X
ejpam-6306	110	12	(	(	PUNCT
ejpam-6306	110	13	υ̌−1	υ̌−1	X
ejpam-6306	110	14	(	(	PUNCT
ejpam-6306	110	15	υ̌(x	υ̌(x	PROPN
ejpam-6306	110	16	)	)	PUNCT
ejpam-6306	110	17	+	+	NUM
ejpam-6306	110	18	υ̌(y	υ̌(y	NUM
ejpam-6306	110	19	)	)	PUNCT
ejpam-6306	110	20	2	2	NUM
ejpam-6306	110	21	)	)	PUNCT
ejpam-6306	110	22	)	)	PUNCT
ejpam-6306	110	23	≤	≤	NUM
ejpam-6306	110	24	f(x	f(x	PROPN
ejpam-6306	110	25	)	)	PUNCT
ejpam-6306	111	1	+	+	SYM
ejpam-6306	111	2	f(y	f(y	NOUN
ejpam-6306	111	3	)	)	PUNCT
ejpam-6306	111	4	2	2	NUM
ejpam-6306	111	5	.	.	PUNCT
ejpam-6306	112	1	(	(	PUNCT
ejpam-6306	112	2	8)	8)	NUM
ejpam-6306	112	3	putting	put	VERB
ejpam-6306	112	4	the	the	DET
ejpam-6306	112	5	values	value	NOUN
ejpam-6306	112	6	x	x	PUNCT
ejpam-6306	112	7	=	=	SYM
ejpam-6306	112	8	υ̌−1	υ̌−1	X
ejpam-6306	112	9	(	(	PUNCT
ejpam-6306	112	10	βυ̌(α	βυ̌(α	NOUN
ejpam-6306	112	11	)	)	PUNCT
ejpam-6306	112	12	+	+	CCONJ
ejpam-6306	112	13	(	(	PUNCT
ejpam-6306	112	14	1	1	NUM
ejpam-6306	112	15	−	−	NOUN
ejpam-6306	112	16	β)υ̌(ρ	β)υ̌(ρ	PROPN
ejpam-6306	112	17	)	)	PUNCT
ejpam-6306	112	18	)	)	PUNCT
ejpam-6306	112	19	and	and	CCONJ
ejpam-6306	112	20	y	y	PROPN
ejpam-6306	112	21	=	=	PUNCT
ejpam-6306	113	1	υ̌−1	υ̌−1	INTJ
ejpam-6306	113	2	(	(	PUNCT
ejpam-6306	113	3	(	(	PUNCT
ejpam-6306	113	4	1	1	NUM
ejpam-6306	113	5	−	−	NUM
ejpam-6306	113	6	β)υ̌(α	β)υ̌(α	NUM
ejpam-6306	113	7	)	)	PUNCT
ejpam-6306	114	1	+	+	CCONJ
ejpam-6306	114	2	βυ̌(ρ	βυ̌(ρ	ADJ
ejpam-6306	114	3	)	)	PUNCT
ejpam-6306	114	4	)	)	PUNCT
ejpam-6306	114	5	,	,	PUNCT
ejpam-6306	114	6	in	in	ADP
ejpam-6306	114	7	equation	equation	NOUN
ejpam-6306	114	8	(	(	PUNCT
ejpam-6306	114	9	8)	8)	NUM
ejpam-6306	114	10	,	,	PUNCT
ejpam-6306	114	11	we	we	PRON
ejpam-6306	114	12	get	get	VERB
ejpam-6306	114	13	2f	2f	NUM
ejpam-6306	114	14	(	(	PUNCT
ejpam-6306	114	15	υ̌−1	υ̌−1	X
ejpam-6306	114	16	(	(	PUNCT
ejpam-6306	114	17	υ̌(α	υ̌(α	PROPN
ejpam-6306	114	18	)	)	PUNCT
ejpam-6306	114	19	+	+	CCONJ
ejpam-6306	114	20	υ̌(ρ	υ̌(ρ	X
ejpam-6306	114	21	)	)	PUNCT
ejpam-6306	114	22	2	2	NUM
ejpam-6306	114	23	)	)	PUNCT
ejpam-6306	114	24	)	)	PUNCT
ejpam-6306	115	1	≤	≤	NUM
ejpam-6306	115	2	f	f	X
ejpam-6306	115	3	(	(	PUNCT
ejpam-6306	115	4	υ̌−1	υ̌−1	X
ejpam-6306	115	5	(	(	PUNCT
ejpam-6306	115	6	βυ̌(α	βυ̌(α	NOUN
ejpam-6306	115	7	)	)	PUNCT
ejpam-6306	115	8	+	+	CCONJ
ejpam-6306	115	9	(	(	PUNCT
ejpam-6306	115	10	1−	1−	NUM
ejpam-6306	115	11	β)υ̌(ρ	β)υ̌(ρ	X
ejpam-6306	115	12	)	)	PUNCT
ejpam-6306	115	13	)	)	PUNCT
ejpam-6306	115	14	)	)	PUNCT
ejpam-6306	116	1	+	+	NOUN
ejpam-6306	116	2	f	f	X
ejpam-6306	116	3	(	(	PUNCT
ejpam-6306	116	4	υ̌−1	υ̌−1	X
ejpam-6306	116	5	(	(	PUNCT
ejpam-6306	116	6	(	(	PUNCT
ejpam-6306	116	7	1−	1−	NUM
ejpam-6306	116	8	β)υ̌(α	β)υ̌(α	NUM
ejpam-6306	116	9	)	)	PUNCT
ejpam-6306	116	10	+	+	CCONJ
ejpam-6306	116	11	βυ̌(ρ	βυ̌(ρ	ADJ
ejpam-6306	116	12	)	)	PUNCT
ejpam-6306	116	13	)	)	PUNCT
ejpam-6306	116	14	)	)	PUNCT
ejpam-6306	116	15	.	.	PUNCT
ejpam-6306	117	1	(	(	PUNCT
ejpam-6306	117	2	9	9	X
ejpam-6306	117	3	)	)	PUNCT
ejpam-6306	117	4	multiplying	multiply	VERB
ejpam-6306	117	5	both	both	DET
ejpam-6306	117	6	sides	side	NOUN
ejpam-6306	117	7	by	by	ADP
ejpam-6306	117	8	(	(	PUNCT
ejpam-6306	117	9	1−	1−	NUM
ejpam-6306	117	10	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	117	11	,	,	PUNCT
ejpam-6306	117	12	κ	κ	NOUN
ejpam-6306	117	13	ν	ν	PROPN
ejpam-6306	117	14	,	,	PUNCT
ejpam-6306	117	15	τ	τ	PROPN
ejpam-6306	117	16	,	,	PUNCT
ejpam-6306	117	17	j	j	PROPN
ejpam-6306	117	18	(	(	PUNCT
ejpam-6306	117	19	(	(	PUNCT
ejpam-6306	117	20	1−	1−	NUM
ejpam-6306	117	21	β)v	β)v	NOUN
ejpam-6306	117	22	)	)	PUNCT
ejpam-6306	117	23	of	of	ADP
ejpam-6306	117	24	equation	equation	NOUN
ejpam-6306	117	25	(	(	PUNCT
ejpam-6306	117	26	9	9	NUM
ejpam-6306	117	27	)	)	PUNCT
ejpam-6306	117	28	and	and	CCONJ
ejpam-6306	117	29	then	then	ADV
ejpam-6306	117	30	integrating	integrate	VERB
ejpam-6306	117	31	the	the	DET
ejpam-6306	117	32	resulting	result	VERB
ejpam-6306	117	33	inequality	inequality	NOUN
ejpam-6306	117	34	with	with	ADP
ejpam-6306	117	35	respect	respect	NOUN
ejpam-6306	117	36	to	to	ADP
ejpam-6306	117	37	β	β	NOUN
ejpam-6306	117	38	over	over	ADP
ejpam-6306	117	39	[	[	X
ejpam-6306	117	40	0	0	NUM
ejpam-6306	117	41	,	,	PUNCT
ejpam-6306	117	42	1	1	NUM
ejpam-6306	117	43	]	]	PUNCT
ejpam-6306	117	44	,	,	PUNCT
ejpam-6306	117	45	we	we	PRON
ejpam-6306	117	46	get∫	get∫	VERB
ejpam-6306	117	47	1	1	NUM
ejpam-6306	117	48	0	0	NUM
ejpam-6306	117	49	(	(	PUNCT
ejpam-6306	117	50	1−	1−	NUM
ejpam-6306	117	51	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	117	52	,	,	PUNCT
ejpam-6306	117	53	κ	κ	NOUN
ejpam-6306	117	54	ν	ν	PROPN
ejpam-6306	117	55	,	,	PUNCT
ejpam-6306	117	56	τ	τ	PROPN
ejpam-6306	117	57	,	,	PUNCT
ejpam-6306	117	58	j	j	PROPN
ejpam-6306	117	59	(	(	PUNCT
ejpam-6306	117	60	(	(	PUNCT
ejpam-6306	117	61	1−	1−	NUM
ejpam-6306	117	62	β)v	β)v	NOUN
ejpam-6306	117	63	)	)	PUNCT
ejpam-6306	117	64	f	f	NOUN
ejpam-6306	117	65	(	(	PUNCT
ejpam-6306	117	66	υ̌−1	υ̌−1	X
ejpam-6306	117	67	(	(	PUNCT
ejpam-6306	117	68	υ̌(α	υ̌(α	PROPN
ejpam-6306	117	69	)	)	PUNCT
ejpam-6306	117	70	+	+	CCONJ
ejpam-6306	117	71	υ̌(ρ	υ̌(ρ	X
ejpam-6306	117	72	)	)	PUNCT
ejpam-6306	117	73	2	2	NUM
ejpam-6306	117	74	)	)	PUNCT
ejpam-6306	117	75	)	)	PUNCT
ejpam-6306	118	1	dβ	dβ	ADP
ejpam-6306	118	2	≤	≤	NUM
ejpam-6306	118	3	∫	∫	PROPN
ejpam-6306	118	4	1	1	NUM
ejpam-6306	118	5	0	0	NUM
ejpam-6306	118	6	(	(	PUNCT
ejpam-6306	118	7	1−	1−	NUM
ejpam-6306	118	8	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	118	9	,	,	PUNCT
ejpam-6306	118	10	κ	κ	NOUN
ejpam-6306	118	11	ν	ν	PROPN
ejpam-6306	118	12	,	,	PUNCT
ejpam-6306	118	13	τ	τ	PROPN
ejpam-6306	118	14	,	,	PUNCT
ejpam-6306	118	15	j	j	PROPN
ejpam-6306	118	16	(	(	PUNCT
ejpam-6306	118	17	(	(	PUNCT
ejpam-6306	118	18	1−	1−	NUM
ejpam-6306	118	19	β)v	β)v	NOUN
ejpam-6306	118	20	)	)	PUNCT
ejpam-6306	118	21	f	f	NOUN
ejpam-6306	118	22	(	(	PUNCT
ejpam-6306	118	23	υ̌−1	υ̌−1	X
ejpam-6306	118	24	(	(	PUNCT
ejpam-6306	118	25	βυ̌(α	βυ̌(α	NOUN
ejpam-6306	118	26	)	)	PUNCT
ejpam-6306	118	27	+	+	CCONJ
ejpam-6306	118	28	(	(	PUNCT
ejpam-6306	118	29	1−	1−	NUM
ejpam-6306	118	30	β)υ̌(ρ	β)υ̌(ρ	X
ejpam-6306	118	31	)	)	PUNCT
ejpam-6306	118	32	)	)	PUNCT
ejpam-6306	118	33	)	)	PUNCT
ejpam-6306	119	1	dβ	dβ	ADP
ejpam-6306	119	2	+	+	NUM
ejpam-6306	119	3	∫	∫	PROPN
ejpam-6306	119	4	1	1	NUM
ejpam-6306	119	5	0	0	NUM
ejpam-6306	119	6	(	(	PUNCT
ejpam-6306	119	7	1−	1−	NUM
ejpam-6306	119	8	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	119	9	,	,	PUNCT
ejpam-6306	119	10	κ	κ	NOUN
ejpam-6306	119	11	ν	ν	PROPN
ejpam-6306	119	12	,	,	PUNCT
ejpam-6306	119	13	τ	τ	PROPN
ejpam-6306	119	14	,	,	PUNCT
ejpam-6306	119	15	j	j	PROPN
ejpam-6306	119	16	(	(	PUNCT
ejpam-6306	119	17	(	(	PUNCT
ejpam-6306	119	18	1−	1−	NUM
ejpam-6306	119	19	β)v	β)v	NOUN
ejpam-6306	119	20	)	)	PUNCT
ejpam-6306	119	21	f	f	NOUN
ejpam-6306	119	22	(	(	PUNCT
ejpam-6306	119	23	υ̌−1	υ̌−1	X
ejpam-6306	119	24	(	(	PUNCT
ejpam-6306	119	25	(	(	PUNCT
ejpam-6306	119	26	1−	1−	NUM
ejpam-6306	119	27	β)υ̌(α	β)υ̌(α	NUM
ejpam-6306	119	28	)	)	PUNCT
ejpam-6306	119	29	+	+	CCONJ
ejpam-6306	119	30	βυ̌(ρ	βυ̌(ρ	ADJ
ejpam-6306	119	31	)	)	PUNCT
ejpam-6306	119	32	)	)	PUNCT
ejpam-6306	119	33	)	)	PUNCT
ejpam-6306	120	1	dβ	dβ	ADJ
ejpam-6306	120	2	.	.	PUNCT
ejpam-6306	121	1	therefore	therefore	ADV
ejpam-6306	121	2	,	,	PUNCT
ejpam-6306	121	3	2f	2f	NUM
ejpam-6306	121	4	(	(	PUNCT
ejpam-6306	121	5	υ̌−1	υ̌−1	X
ejpam-6306	121	6	(	(	PUNCT
ejpam-6306	121	7	υ̌(α	υ̌(α	PROPN
ejpam-6306	121	8	)	)	PUNCT
ejpam-6306	121	9	+	+	CCONJ
ejpam-6306	121	10	υ̌(ρ	υ̌(ρ	X
ejpam-6306	121	11	)	)	PUNCT
ejpam-6306	121	12	2	2	NUM
ejpam-6306	121	13	)	)	PUNCT
ejpam-6306	121	14	)	)	PUNCT
ejpam-6306	121	15	∫	∫	PROPN
ejpam-6306	121	16	1	1	NUM
ejpam-6306	121	17	0	0	NUM
ejpam-6306	121	18	(	(	PUNCT
ejpam-6306	121	19	1−	1−	NUM
ejpam-6306	121	20	β)τ−1	β)τ−1	NOUN
ejpam-6306	122	1	∞∑	∞∑	NUM
ejpam-6306	122	2	n=0	n=0	NUM
ejpam-6306	122	3	(	(	PUNCT
ejpam-6306	122	4	ϑ)κn((1−	ϑ)κn((1−	NOUN
ejpam-6306	122	5	β)v)n	β)v)n	ADJ
ejpam-6306	122	6	γ(vn+	γ(vn+	NOUN
ejpam-6306	122	7	τ)(z)δn	τ)(z)δn	PROPN
ejpam-6306	122	8	dβ	dβ	ADP
ejpam-6306	122	9	≤	≤	NUM
ejpam-6306	122	10	∫	∫	PROPN
ejpam-6306	122	11	1	1	NUM
ejpam-6306	122	12	0	0	NUM
ejpam-6306	122	13	(	(	PUNCT
ejpam-6306	122	14	1−	1−	NUM
ejpam-6306	122	15	β)τ−1	β)τ−1	NOUN
ejpam-6306	123	1	∞∑	∞∑	NUM
ejpam-6306	123	2	n=0	n=0	NUM
ejpam-6306	123	3	(	(	PUNCT
ejpam-6306	123	4	ϑ)κn((1−	ϑ)κn((1−	NOUN
ejpam-6306	123	5	β)v)n	β)v)n	ADJ
ejpam-6306	123	6	γ(vn+	γ(vn+	PROPN
ejpam-6306	123	7	τ)(z)δn	τ)(z)δn	PROPN
ejpam-6306	123	8	f	f	PROPN
ejpam-6306	123	9	(	(	PUNCT
ejpam-6306	123	10	υ̌−1	υ̌−1	X
ejpam-6306	123	11	(	(	PUNCT
ejpam-6306	123	12	βυ̌(α	βυ̌(α	NOUN
ejpam-6306	123	13	)	)	PUNCT
ejpam-6306	123	14	+	+	CCONJ
ejpam-6306	123	15	(	(	PUNCT
ejpam-6306	123	16	1−	1−	NUM
ejpam-6306	123	17	β)υ̌(ρ	β)υ̌(ρ	X
ejpam-6306	123	18	)	)	PUNCT
ejpam-6306	123	19	)	)	PUNCT
ejpam-6306	123	20	)	)	PUNCT
ejpam-6306	124	1	dβ	dβ	ADP
ejpam-6306	124	2	≤	≤	NUM
ejpam-6306	124	3	∫	∫	PROPN
ejpam-6306	124	4	1	1	NUM
ejpam-6306	124	5	0	0	NUM
ejpam-6306	124	6	(	(	PUNCT
ejpam-6306	124	7	1−	1−	NUM
ejpam-6306	124	8	β)τ−1	β)τ−1	NOUN
ejpam-6306	124	9	∞∑	∞∑	NUM
ejpam-6306	124	10	n=0	n=0	NUM
ejpam-6306	124	11	(	(	PUNCT
ejpam-6306	124	12	ϑ)κn((1−	ϑ)κn((1−	NOUN
ejpam-6306	124	13	β)v)n	β)v)n	ADJ
ejpam-6306	124	14	γ(vn+	γ(vn+	PROPN
ejpam-6306	124	15	τ)(z)δn	τ)(z)δn	PROPN
ejpam-6306	124	16	f	f	PROPN
ejpam-6306	124	17	(	(	PUNCT
ejpam-6306	124	18	υ̌−1	υ̌−1	X
ejpam-6306	124	19	(	(	PUNCT
ejpam-6306	124	20	(	(	PUNCT
ejpam-6306	124	21	1−	1−	NUM
ejpam-6306	124	22	β)υ̌(α	β)υ̌(α	NUM
ejpam-6306	124	23	)	)	PUNCT
ejpam-6306	124	24	+	+	CCONJ
ejpam-6306	124	25	βυ̌(ρ	βυ̌(ρ	ADJ
ejpam-6306	124	26	)	)	PUNCT
ejpam-6306	124	27	)	)	PUNCT
ejpam-6306	124	28	)	)	PUNCT
ejpam-6306	125	1	dβ	dβ	ADJ
ejpam-6306	125	2	.	.	PUNCT
ejpam-6306	126	1	(	(	PUNCT
ejpam-6306	126	2	10	10	NUM
ejpam-6306	126	3	)	)	PUNCT
ejpam-6306	126	4	putting	put	VERB
ejpam-6306	126	5	the	the	DET
ejpam-6306	126	6	values	value	NOUN
ejpam-6306	126	7	µ	µ	X
ejpam-6306	126	8	=	=	SYM
ejpam-6306	126	9	υ̌−1	υ̌−1	INTJ
ejpam-6306	126	10	(	(	PUNCT
ejpam-6306	126	11	βυ̌(α	βυ̌(α	NOUN
ejpam-6306	126	12	)	)	PUNCT
ejpam-6306	127	1	+	+	CCONJ
ejpam-6306	127	2	(	(	PUNCT
ejpam-6306	127	3	1	1	NUM
ejpam-6306	127	4	−	−	NOUN
ejpam-6306	127	5	β)υ̌(ρ	β)υ̌(ρ	PROPN
ejpam-6306	127	6	)	)	PUNCT
ejpam-6306	127	7	)	)	PUNCT
ejpam-6306	127	8	and	and	CCONJ
ejpam-6306	127	9	ω	ω	X
ejpam-6306	127	10	=	=	X
ejpam-6306	128	1	υ̌−1	υ̌−1	INTJ
ejpam-6306	128	2	(	(	PUNCT
ejpam-6306	128	3	(	(	PUNCT
ejpam-6306	128	4	1	1	NUM
ejpam-6306	128	5	−	−	NUM
ejpam-6306	128	6	β)υ̌(α	β)υ̌(α	NUM
ejpam-6306	128	7	)	)	PUNCT
ejpam-6306	129	1	+	+	CCONJ
ejpam-6306	129	2	βυ̌(ρ	βυ̌(ρ	ADJ
ejpam-6306	129	3	)	)	PUNCT
ejpam-6306	129	4	)	)	PUNCT
ejpam-6306	130	1	in	in	ADP
ejpam-6306	130	2	equation	equation	NOUN
ejpam-6306	130	3	(	(	PUNCT
ejpam-6306	130	4	10	10	NUM
ejpam-6306	130	5	)	)	PUNCT
ejpam-6306	130	6	,	,	PUNCT
ejpam-6306	130	7	then	then	ADV
ejpam-6306	130	8	we	we	PRON
ejpam-6306	130	9	obtain	obtain	VERB
ejpam-6306	130	10	2f	2f	NUM
ejpam-6306	130	11	(	(	PUNCT
ejpam-6306	130	12	υ̌−1	υ̌−1	X
ejpam-6306	130	13	(	(	PUNCT
ejpam-6306	130	14	υ̌(α	υ̌(α	PROPN
ejpam-6306	130	15	)	)	PUNCT
ejpam-6306	130	16	+	+	CCONJ
ejpam-6306	131	1	υ̌(ρ	υ̌(ρ	X
ejpam-6306	131	2	)	)	PUNCT
ejpam-6306	131	3	2	2	NUM
ejpam-6306	131	4	)	)	PUNCT
ejpam-6306	131	5	)	)	PUNCT
ejpam-6306	132	1	∞∑	∞∑	PRON
ejpam-6306	132	2	n=0	n=0	NUM
ejpam-6306	132	3	(	(	PUNCT
ejpam-6306	132	4	ϑ)κn	ϑ)κn	PROPN
ejpam-6306	132	5	γ(vn+	γ(vn+	NOUN
ejpam-6306	132	6	τ)(z)δn	τ)(z)δn	NOUN
ejpam-6306	132	7	∫	∫	PROPN
ejpam-6306	132	8	1	1	NUM
ejpam-6306	132	9	0	0	NUM
ejpam-6306	132	10	(	(	PUNCT
ejpam-6306	132	11	1−	1−	NUM
ejpam-6306	132	12	β)τ−1((1−	β)τ−1((1−	PROPN
ejpam-6306	132	13	β)v)ndβ	β)v)ndβ	NOUN
ejpam-6306	132	14	≤	≤	NOUN
ejpam-6306	132	15	∞∑	∞∑	NUM
ejpam-6306	132	16	n=0	n=0	NUM
ejpam-6306	132	17	(	(	PUNCT
ejpam-6306	132	18	ϑ)κn	ϑ)κn	PROPN
ejpam-6306	132	19	γ(vn+	γ(vn+	NOUN
ejpam-6306	132	20	τ)(z)δn	τ)(z)δn	NOUN
ejpam-6306	132	21	∫	∫	PROPN
ejpam-6306	132	22	α	α	PROPN
ejpam-6306	132	23	ρ	ρ	PROPN
ejpam-6306	132	24	(	(	PUNCT
ejpam-6306	132	25	1−	1−	NUM
ejpam-6306	132	26	(	(	PUNCT
ejpam-6306	132	27	υ̌(µ)−	υ̌(µ)−	X
ejpam-6306	132	28	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	132	29	)	)	PUNCT
ejpam-6306	132	30	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	132	31	υ̌(α	υ̌(α	NUM
ejpam-6306	132	32	)	)	PUNCT
ejpam-6306	132	33	)	)	PUNCT
ejpam-6306	132	34	)	)	PUNCT
ejpam-6306	132	35	τ−1	τ−1	PROPN
ejpam-6306	132	36	(	(	PUNCT
ejpam-6306	132	37	(	(	PUNCT
ejpam-6306	132	38	1−	1−	NUM
ejpam-6306	132	39	(	(	PUNCT
ejpam-6306	132	40	υ̌(µ)−	υ̌(µ)−	X
ejpam-6306	132	41	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	132	42	)	)	PUNCT
ejpam-6306	132	43	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	132	44	υ̌(α	υ̌(α	NUM
ejpam-6306	132	45	)	)	PUNCT
ejpam-6306	132	46	)	)	PUNCT
ejpam-6306	132	47	)	)	PUNCT
ejpam-6306	132	48	v)n	v)n	NOUN
ejpam-6306	132	49	f(µ	f(µ	NUM
ejpam-6306	132	50	)	)	PUNCT
ejpam-6306	132	51	.	.	PUNCT
ejpam-6306	133	1	υ̌′(µ)dµ	υ̌′(µ)dµ	PROPN
ejpam-6306	133	2	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	133	3	υ̌(α	υ̌(α	PROPN
ejpam-6306	133	4	)	)	PUNCT
ejpam-6306	133	5	r.	r.	PROPN
ejpam-6306	133	6	s.	s.	PROPN
ejpam-6306	133	7	ali	ali	PROPN
ejpam-6306	133	8	et	et	PROPN
ejpam-6306	133	9	al	al	PROPN
ejpam-6306	133	10	.	.	PUNCT
ejpam-6306	133	11	/	/	SYM
ejpam-6306	133	12	eur	eur	PROPN
ejpam-6306	133	13	.	.	PUNCT
ejpam-6306	134	1	j.	j.	PROPN
ejpam-6306	134	2	pure	pure	PROPN
ejpam-6306	134	3	appl	appl	PROPN
ejpam-6306	134	4	.	.	PROPN
ejpam-6306	134	5	math	math	PROPN
ejpam-6306	134	6	,	,	PUNCT
ejpam-6306	134	7	18	18	NUM
ejpam-6306	134	8	(	(	PUNCT
ejpam-6306	134	9	3	3	NUM
ejpam-6306	134	10	)	)	PUNCT
ejpam-6306	134	11	(	(	PUNCT
ejpam-6306	134	12	2025	2025	NUM
ejpam-6306	134	13	)	)	PUNCT
ejpam-6306	134	14	,	,	PUNCT
ejpam-6306	134	15	6306	6306	NUM
ejpam-6306	134	16	7	7	NUM
ejpam-6306	134	17	of	of	ADP
ejpam-6306	134	18	18	18	NUM
ejpam-6306	134	19	+	+	NOUN
ejpam-6306	134	20	∞∑	∞∑	NUM
ejpam-6306	134	21	n=0	n=0	NUM
ejpam-6306	134	22	(	(	PUNCT
ejpam-6306	134	23	ϑ)κn	ϑ)κn	PROPN
ejpam-6306	134	24	γ(vn+	γ(vn+	NOUN
ejpam-6306	134	25	τ)(z)δn	τ)(z)δn	PROPN
ejpam-6306	134	26	∫	∫	PROPN
ejpam-6306	134	27	ρ	ρ	PROPN
ejpam-6306	134	28	α	α	PROPN
ejpam-6306	134	29	(	(	PUNCT
ejpam-6306	134	30	1−	1−	NUM
ejpam-6306	134	31	(	(	PUNCT
ejpam-6306	134	32	υ̌(ω)−	υ̌(ω)−	NOUN
ejpam-6306	134	33	υ̌(α	υ̌(α	NUM
ejpam-6306	134	34	)	)	PUNCT
ejpam-6306	134	35	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	134	36	υ̌(α	υ̌(α	NUM
ejpam-6306	134	37	)	)	PUNCT
ejpam-6306	134	38	)	)	PUNCT
ejpam-6306	134	39	)	)	PUNCT
ejpam-6306	135	1	τ−1	τ−1	PROPN
ejpam-6306	135	2	(	(	PUNCT
ejpam-6306	135	3	(	(	PUNCT
ejpam-6306	135	4	1−	1−	NUM
ejpam-6306	135	5	(	(	PUNCT
ejpam-6306	135	6	υ̌(ω)−	υ̌(ω)−	NOUN
ejpam-6306	135	7	υ̌(α	υ̌(α	NUM
ejpam-6306	135	8	)	)	PUNCT
ejpam-6306	135	9	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	135	10	υ̌(α	υ̌(α	NUM
ejpam-6306	135	11	)	)	PUNCT
ejpam-6306	135	12	)	)	PUNCT
ejpam-6306	135	13	)	)	PUNCT
ejpam-6306	135	14	v)n	v)n	NOUN
ejpam-6306	135	15	f(ω	f(ω	PROPN
ejpam-6306	135	16	)	)	PUNCT
ejpam-6306	135	17	.	.	PUNCT
ejpam-6306	136	1	υ̌′(ω)dω	υ̌′(ω)dω	PROPN
ejpam-6306	136	2	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	136	3	υ̌(α	υ̌(α	PROPN
ejpam-6306	136	4	)	)	PUNCT
ejpam-6306	136	5	.	.	PUNCT
ejpam-6306	137	1	hence	hence	ADV
ejpam-6306	137	2	,	,	PUNCT
ejpam-6306	137	3	2f	2f	NUM
ejpam-6306	137	4	(	(	PUNCT
ejpam-6306	137	5	υ̌−1	υ̌−1	X
ejpam-6306	137	6	(	(	PUNCT
ejpam-6306	137	7	υ̌(α	υ̌(α	PROPN
ejpam-6306	137	8	)	)	PUNCT
ejpam-6306	137	9	+	+	CCONJ
ejpam-6306	137	10	υ̌(ρ	υ̌(ρ	X
ejpam-6306	137	11	)	)	PUNCT
ejpam-6306	137	12	2	2	NUM
ejpam-6306	137	13	)	)	PUNCT
ejpam-6306	137	14	)	)	PUNCT
ejpam-6306	138	1	∞∑	∞∑	PRON
ejpam-6306	138	2	n=0	n=0	NUM
ejpam-6306	138	3	(	(	PUNCT
ejpam-6306	138	4	ϑ)κn	ϑ)κn	PROPN
ejpam-6306	138	5	γ(vn+	γ(vn+	NOUN
ejpam-6306	138	6	τ)(z)δn	τ)(z)δn	NOUN
ejpam-6306	138	7	(	(	PUNCT
ejpam-6306	138	8	1	1	NUM
ejpam-6306	138	9	τ	τ	X
ejpam-6306	138	10	+	+	NUM
ejpam-6306	138	11	vn	vn	PROPN
ejpam-6306	138	12	)	)	PUNCT
ejpam-6306	138	13	≤	≤	NOUN
ejpam-6306	139	1	∞∑	∞∑	NUM
ejpam-6306	139	2	n=0	n=0	NUM
ejpam-6306	139	3	(	(	PUNCT
ejpam-6306	139	4	ϑ)κn	ϑ)κn	PROPN
ejpam-6306	139	5	γ(vn+	γ(vn+	NOUN
ejpam-6306	139	6	τ)(z)δn	τ)(z)δn	NOUN
ejpam-6306	139	7	∫	∫	PROPN
ejpam-6306	139	8	α	α	PROPN
ejpam-6306	139	9	ρ	ρ	PROPN
ejpam-6306	139	10	(	(	PUNCT
ejpam-6306	139	11	υ̌(µ)−	υ̌(µ)−	NOUN
ejpam-6306	139	12	υ̌(α	υ̌(α	PROPN
ejpam-6306	139	13	)	)	PUNCT
ejpam-6306	139	14	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	139	15	υ̌(α	υ̌(α	NUM
ejpam-6306	139	16	)	)	PUNCT
ejpam-6306	139	17	)	)	PUNCT
ejpam-6306	139	18	τ−1((υ̌(µ)−	τ−1((υ̌(µ)−	PROPN
ejpam-6306	139	19	υ̌(α	υ̌(α	NUM
ejpam-6306	139	20	)	)	PUNCT
ejpam-6306	139	21	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	139	22	υ̌(α	υ̌(α	NUM
ejpam-6306	139	23	)	)	PUNCT
ejpam-6306	139	24	)	)	PUNCT
ejpam-6306	139	25	v)n	v)n	NOUN
ejpam-6306	139	26	υ̌′(µ	υ̌′(µ	ADJ
ejpam-6306	139	27	)	)	PUNCT
ejpam-6306	139	28	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	139	29	υ̌(α	υ̌(α	NUM
ejpam-6306	139	30	)	)	PUNCT
ejpam-6306	139	31	f(µ)dµ	f(µ)dµ	PART
ejpam-6306	140	1	+	+	PUNCT
ejpam-6306	141	1	∞∑	∞∑	NUM
ejpam-6306	141	2	n=0	n=0	NUM
ejpam-6306	141	3	(	(	PUNCT
ejpam-6306	141	4	ϑ)κn	ϑ)κn	PROPN
ejpam-6306	141	5	γ(vn+	γ(vn+	NOUN
ejpam-6306	141	6	τ)(z)δn	τ)(z)δn	PROPN
ejpam-6306	141	7	∫	∫	PROPN
ejpam-6306	141	8	ρ	ρ	PROPN
ejpam-6306	141	9	α	α	PROPN
ejpam-6306	141	10	(	(	PUNCT
ejpam-6306	141	11	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	141	12	υ̌(ω	υ̌(ω	ADJ
ejpam-6306	141	13	)	)	PUNCT
ejpam-6306	141	14	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	141	15	υ̌(α	υ̌(α	NUM
ejpam-6306	141	16	)	)	PUNCT
ejpam-6306	141	17	)	)	PUNCT
ejpam-6306	142	1	τ−1((υ̌(ρ)−	τ−1((υ̌(ρ)−	PROPN
ejpam-6306	142	2	υ̌(ω	υ̌(ω	PROPN
ejpam-6306	142	3	)	)	PUNCT
ejpam-6306	142	4	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	142	5	υ̌(α	υ̌(α	NUM
ejpam-6306	142	6	)	)	PUNCT
ejpam-6306	142	7	)	)	PUNCT
ejpam-6306	142	8	v)n	v)n	NOUN
ejpam-6306	142	9	υ̌′(ω	υ̌′(ω	NOUN
ejpam-6306	142	10	)	)	PUNCT
ejpam-6306	142	11	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	142	12	υ̌(α	υ̌(α	NUM
ejpam-6306	142	13	)	)	PUNCT
ejpam-6306	142	14	f(ω)dω	f(ω)dω	PROPN
ejpam-6306	142	15	.	.	PUNCT
ejpam-6306	143	1	(	(	PUNCT
ejpam-6306	143	2	11	11	NUM
ejpam-6306	143	3	)	)	PUNCT
ejpam-6306	143	4	so	so	ADV
ejpam-6306	143	5	,	,	PUNCT
ejpam-6306	143	6	2f	2f	NUM
ejpam-6306	143	7	(	(	PUNCT
ejpam-6306	143	8	υ̌−1	υ̌−1	X
ejpam-6306	143	9	(	(	PUNCT
ejpam-6306	143	10	υ̌(α	υ̌(α	PROPN
ejpam-6306	143	11	)	)	PUNCT
ejpam-6306	143	12	+	+	CCONJ
ejpam-6306	143	13	υ̌(ρ	υ̌(ρ	X
ejpam-6306	143	14	)	)	PUNCT
ejpam-6306	143	15	2	2	NUM
ejpam-6306	143	16	)	)	PUNCT
ejpam-6306	143	17	)	)	PUNCT
ejpam-6306	144	1	∞∑	∞∑	PRON
ejpam-6306	144	2	n=0	n=0	NUM
ejpam-6306	144	3	(	(	PUNCT
ejpam-6306	144	4	ϑ)κn((1−	ϑ)κn((1−	PROPN
ejpam-6306	144	5	β)v)n	β)v)n	NOUN
ejpam-6306	144	6	γ(vn+	γ(vn+	NOUN
ejpam-6306	144	7	τ	τ	PROPN
ejpam-6306	144	8	+	+	PROPN
ejpam-6306	144	9	1)(z)δn	1)(z)δn	NUM
ejpam-6306	144	10	≤	≤	NUM
ejpam-6306	144	11	1	1	NUM
ejpam-6306	144	12	(	(	PUNCT
ejpam-6306	144	13	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	144	14	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	144	15	∞∑	∞∑	NUM
ejpam-6306	144	16	n=0	n=0	NUM
ejpam-6306	144	17	(	(	PUNCT
ejpam-6306	144	18	ϑ)κn	ϑ)κn	PROPN
ejpam-6306	144	19	γ(vn+	γ(vn+	NOUN
ejpam-6306	144	20	τ)(z)δn	τ)(z)δn	NOUN
ejpam-6306	144	21	(	(	PUNCT
ejpam-6306	144	22	(	(	PUNCT
ejpam-6306	144	23	υ̌(µ)−	υ̌(µ)−	NOUN
ejpam-6306	144	24	υ̌(α	υ̌(α	PROPN
ejpam-6306	144	25	)	)	PUNCT
ejpam-6306	144	26	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	144	27	υ̌(α	υ̌(α	NUM
ejpam-6306	144	28	)	)	PUNCT
ejpam-6306	144	29	)	)	PUNCT
ejpam-6306	144	30	v)n	v)n	NOUN
ejpam-6306	144	31	∫	∫	PROPN
ejpam-6306	144	32	α	α	PROPN
ejpam-6306	144	33	ρ	ρ	PROPN
ejpam-6306	144	34	(	(	PUNCT
ejpam-6306	144	35	υ̌(µ)−	υ̌(µ)−	X
ejpam-6306	144	36	υ̌(α))τ−1υ̌′(µ)f(µ)dµ	υ̌(α))τ−1υ̌′(µ)f(µ)dµ	PROPN
ejpam-6306	145	1	+	+	CCONJ
ejpam-6306	145	2	1	1	NUM
ejpam-6306	145	3	(	(	PUNCT
ejpam-6306	145	4	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	145	5	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	145	6	∞∑	∞∑	NUM
ejpam-6306	145	7	n=0	n=0	NUM
ejpam-6306	145	8	(	(	PUNCT
ejpam-6306	145	9	ϑ)κn	ϑ)κn	PROPN
ejpam-6306	145	10	γ(vn+	γ(vn+	NOUN
ejpam-6306	145	11	τ)(z)δn	τ)(z)δn	NOUN
ejpam-6306	145	12	(	(	PUNCT
ejpam-6306	145	13	(	(	PUNCT
ejpam-6306	145	14	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	145	15	υ̌(ω	υ̌(ω	ADJ
ejpam-6306	145	16	)	)	PUNCT
ejpam-6306	145	17	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	145	18	υ̌(α	υ̌(α	NUM
ejpam-6306	145	19	)	)	PUNCT
ejpam-6306	145	20	)	)	PUNCT
ejpam-6306	145	21	v)n	v)n	NOUN
ejpam-6306	145	22	∫	∫	PROPN
ejpam-6306	145	23	ρ	ρ	PROPN
ejpam-6306	145	24	α	α	PROPN
ejpam-6306	145	25	(	(	PUNCT
ejpam-6306	145	26	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	145	27	υ̌(ω))τ−1υ̌′(ω)f(ω)dω	υ̌(ω))τ−1υ̌′(ω)f(ω)dω	PROPN
ejpam-6306	145	28	.	.	PUNCT
ejpam-6306	146	1	it	it	PRON
ejpam-6306	146	2	becomes	become	VERB
ejpam-6306	146	3	2f	2f	NUM
ejpam-6306	146	4	(	(	PUNCT
ejpam-6306	146	5	υ̌−1	υ̌−1	X
ejpam-6306	146	6	(	(	PUNCT
ejpam-6306	146	7	υ̌(α	υ̌(α	PROPN
ejpam-6306	146	8	)	)	PUNCT
ejpam-6306	146	9	+	+	CCONJ
ejpam-6306	146	10	υ̌(ρ	υ̌(ρ	X
ejpam-6306	146	11	)	)	PUNCT
ejpam-6306	146	12	2	2	NUM
ejpam-6306	146	13	)	)	PUNCT
ejpam-6306	146	14	)	)	PUNCT
ejpam-6306	146	15	eϑ,z	eϑ,z	NOUN
ejpam-6306	146	16	,	,	PUNCT
ejpam-6306	146	17	κ	κ	X
ejpam-6306	146	18	ν	ν	PROPN
ejpam-6306	146	19	,	,	PUNCT
ejpam-6306	146	20	τ	τ	PROPN
ejpam-6306	146	21	,	,	PUNCT
ejpam-6306	146	22	j	j	PROPN
ejpam-6306	146	23	(	(	PUNCT
ejpam-6306	146	24	(	(	PUNCT
ejpam-6306	146	25	1−	1−	NUM
ejpam-6306	146	26	β)v	β)v	NOUN
ejpam-6306	146	27	)	)	PUNCT
ejpam-6306	146	28	≤	≤	NUM
ejpam-6306	146	29	1	1	NUM
ejpam-6306	146	30	(	(	PUNCT
ejpam-6306	146	31	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	146	32	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	146	33	∞∑	∞∑	NUM
ejpam-6306	146	34	n=0	n=0	NUM
ejpam-6306	146	35	(	(	PUNCT
ejpam-6306	146	36	ϑ)κn)(ξ(µ	ϑ)κn)(ξ(µ	NOUN
ejpam-6306	146	37	)	)	PUNCT
ejpam-6306	146	38	v	v	NOUN
ejpam-6306	146	39	)	)	PUNCT
ejpam-6306	146	40	γ(vn+	γ(vn+	PROPN
ejpam-6306	146	41	τ)(z)δn	τ)(z)δn	PROPN
ejpam-6306	146	42	∫	∫	PROPN
ejpam-6306	146	43	α	α	PROPN
ejpam-6306	146	44	ρ	ρ	PROPN
ejpam-6306	146	45	(	(	PUNCT
ejpam-6306	146	46	υ̌(µ)−	υ̌(µ)−	X
ejpam-6306	146	47	υ̌(α))τ−1υ̌′(µ)f(µ)dµ	υ̌(α))τ−1υ̌′(µ)f(µ)dµ	PROPN
ejpam-6306	147	1	+	+	CCONJ
ejpam-6306	147	2	1	1	NUM
ejpam-6306	147	3	(	(	PUNCT
ejpam-6306	147	4	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	147	5	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	147	6	∞∑	∞∑	NUM
ejpam-6306	147	7	n=0	n=0	NUM
ejpam-6306	147	8	(	(	PUNCT
ejpam-6306	147	9	ϑ)κn)(ξ(ω	ϑ)κn)(ξ(ω	NOUN
ejpam-6306	147	10	)	)	PUNCT
ejpam-6306	147	11	v	v	NOUN
ejpam-6306	147	12	)	)	PUNCT
ejpam-6306	147	13	γ(vn+	γ(vn+	PROPN
ejpam-6306	147	14	τ)(z)δn	τ)(z)δn	PROPN
ejpam-6306	147	15	∫	∫	PROPN
ejpam-6306	147	16	ρ	ρ	PROPN
ejpam-6306	147	17	α	α	PROPN
ejpam-6306	147	18	(	(	PUNCT
ejpam-6306	147	19	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	147	20	υ̌(ω))τ−1υ̌′(ω)f(ω)dω	υ̌(ω))τ−1υ̌′(ω)f(ω)dω	PROPN
ejpam-6306	147	21	,	,	PUNCT
ejpam-6306	147	22	and	and	CCONJ
ejpam-6306	147	23	finally	finally	ADV
ejpam-6306	147	24	,	,	PUNCT
ejpam-6306	147	25	2f	2f	NUM
ejpam-6306	147	26	(	(	PUNCT
ejpam-6306	147	27	υ̌−1	υ̌−1	X
ejpam-6306	147	28	(	(	PUNCT
ejpam-6306	147	29	υ̌(α	υ̌(α	PROPN
ejpam-6306	147	30	)	)	PUNCT
ejpam-6306	147	31	+	+	CCONJ
ejpam-6306	147	32	υ̌(ρ	υ̌(ρ	X
ejpam-6306	147	33	)	)	PUNCT
ejpam-6306	147	34	2	2	NUM
ejpam-6306	147	35	)	)	PUNCT
ejpam-6306	147	36	)	)	PUNCT
ejpam-6306	147	37	eϑ,z	eϑ,z	NOUN
ejpam-6306	147	38	,	,	PUNCT
ejpam-6306	147	39	κ	κ	X
ejpam-6306	147	40	ν	ν	PROPN
ejpam-6306	147	41	,	,	PUNCT
ejpam-6306	147	42	τ	τ	PROPN
ejpam-6306	147	43	,	,	PUNCT
ejpam-6306	147	44	j	j	PROPN
ejpam-6306	147	45	(	(	PUNCT
ejpam-6306	147	46	(	(	PUNCT
ejpam-6306	147	47	1−	1−	NUM
ejpam-6306	147	48	β)v	β)v	NOUN
ejpam-6306	147	49	)	)	PUNCT
ejpam-6306	147	50	≤	≤	NUM
ejpam-6306	147	51	1	1	NUM
ejpam-6306	147	52	(	(	PUNCT
ejpam-6306	147	53	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	147	54	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	147	55	[	[	PUNCT
ejpam-6306	147	56	eϑ,z	eϑ,z	NOUN
ejpam-6306	147	57	,	,	PUNCT
ejpam-6306	147	58	κ	κ	X
ejpam-6306	147	59	ν	ν	PROPN
ejpam-6306	147	60	,	,	PUNCT
ejpam-6306	147	61	τ	τ	PROPN
ejpam-6306	147	62	,	,	PUNCT
ejpam-6306	147	63	j	j	PROPN
ejpam-6306	147	64	(	(	PUNCT
ejpam-6306	147	65	ξ(µ	ξ(µ	PROPN
ejpam-6306	147	66	)	)	PUNCT
ejpam-6306	147	67	v	v	NOUN
ejpam-6306	147	68	)	)	PUNCT
ejpam-6306	147	69	∫	∫	PROPN
ejpam-6306	148	1	α	α	PROPN
ejpam-6306	148	2	ρ	ρ	PROPN
ejpam-6306	148	3	(	(	PUNCT
ejpam-6306	148	4	υ̌(µ)−	υ̌(µ)−	PROPN
ejpam-6306	148	5	υ̌(α))τ−1υ̌′(µ)f(µ)dµ	υ̌(α))τ−1υ̌′(µ)f(µ)dµ	PROPN
ejpam-6306	148	6	r.	r.	PROPN
ejpam-6306	148	7	s.	s.	PROPN
ejpam-6306	148	8	ali	ali	PROPN
ejpam-6306	148	9	et	et	PROPN
ejpam-6306	148	10	al	al	PROPN
ejpam-6306	148	11	.	.	PUNCT
ejpam-6306	148	12	/	/	SYM
ejpam-6306	148	13	eur	eur	PROPN
ejpam-6306	148	14	.	.	PUNCT
ejpam-6306	149	1	j.	j.	PROPN
ejpam-6306	149	2	pure	pure	PROPN
ejpam-6306	149	3	appl	appl	PROPN
ejpam-6306	149	4	.	.	PROPN
ejpam-6306	149	5	math	math	PROPN
ejpam-6306	149	6	,	,	PUNCT
ejpam-6306	149	7	18	18	NUM
ejpam-6306	149	8	(	(	PUNCT
ejpam-6306	149	9	3	3	NUM
ejpam-6306	149	10	)	)	PUNCT
ejpam-6306	149	11	(	(	PUNCT
ejpam-6306	149	12	2025	2025	NUM
ejpam-6306	149	13	)	)	PUNCT
ejpam-6306	149	14	,	,	PUNCT
ejpam-6306	149	15	6306	6306	NUM
ejpam-6306	149	16	8	8	NUM
ejpam-6306	149	17	of	of	ADP
ejpam-6306	149	18	18	18	NUM
ejpam-6306	149	19	+	+	NUM
ejpam-6306	149	20	eϑ,z	eϑ,z	NOUN
ejpam-6306	149	21	,	,	PUNCT
ejpam-6306	149	22	κ	κ	X
ejpam-6306	149	23	ν	ν	PROPN
ejpam-6306	149	24	,	,	PUNCT
ejpam-6306	149	25	τ	τ	PROPN
ejpam-6306	149	26	,	,	PUNCT
ejpam-6306	149	27	j	j	PROPN
ejpam-6306	149	28	(	(	PUNCT
ejpam-6306	149	29	ξ(ω	ξ(ω	NOUN
ejpam-6306	149	30	)	)	PUNCT
ejpam-6306	149	31	v	v	NOUN
ejpam-6306	149	32	)	)	PUNCT
ejpam-6306	149	33	∫	∫	PROPN
ejpam-6306	150	1	ρ	ρ	PROPN
ejpam-6306	150	2	α	α	PROPN
ejpam-6306	150	3	(	(	PUNCT
ejpam-6306	150	4	υ̌(ρ)−	υ̌(ρ)−	PROPN
ejpam-6306	150	5	υ̌(ω))τ−1υ̌′(ω)f(ω)dω	υ̌(ω))τ−1υ̌′(ω)f(ω)dω	PROPN
ejpam-6306	150	6	]	]	PUNCT
ejpam-6306	150	7	,	,	PUNCT
ejpam-6306	150	8	and	and	CCONJ
ejpam-6306	150	9	thus	thus	ADV
ejpam-6306	150	10	,	,	PUNCT
ejpam-6306	150	11	f	f	PROPN
ejpam-6306	150	12	(	(	PUNCT
ejpam-6306	150	13	υ̌−1	υ̌−1	X
ejpam-6306	150	14	(	(	PUNCT
ejpam-6306	150	15	υ̌(α	υ̌(α	PROPN
ejpam-6306	150	16	)	)	PUNCT
ejpam-6306	150	17	+	+	CCONJ
ejpam-6306	150	18	υ̌(ρ	υ̌(ρ	X
ejpam-6306	150	19	)	)	PUNCT
ejpam-6306	150	20	2	2	NUM
ejpam-6306	150	21	)	)	PUNCT
ejpam-6306	150	22	)	)	PUNCT
ejpam-6306	150	23	eϑ,z	eϑ,z	NOUN
ejpam-6306	150	24	,	,	PUNCT
ejpam-6306	150	25	κ	κ	X
ejpam-6306	150	26	ν	ν	PROPN
ejpam-6306	150	27	,	,	PUNCT
ejpam-6306	150	28	τ	τ	PROPN
ejpam-6306	150	29	,	,	PUNCT
ejpam-6306	150	30	j	j	PROPN
ejpam-6306	150	31	(	(	PUNCT
ejpam-6306	150	32	(	(	PUNCT
ejpam-6306	150	33	1−	1−	NUM
ejpam-6306	150	34	β)v	β)v	NOUN
ejpam-6306	150	35	)	)	PUNCT
ejpam-6306	150	36	≤	≤	NUM
ejpam-6306	150	37	1	1	NUM
ejpam-6306	150	38	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	150	39	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	151	1	[	[	PUNCT
ejpam-6306	151	2	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	151	3	,	,	PUNCT
ejpam-6306	151	4	κ	κ	NOUN
ejpam-6306	151	5	ν	ν	PROPN
ejpam-6306	151	6	,	,	PUNCT
ejpam-6306	151	7	τ	τ	PROPN
ejpam-6306	151	8	,	,	PUNCT
ejpam-6306	151	9	j	j	PROPN
ejpam-6306	151	10	,	,	PUNCT
ejpam-6306	151	11	ω	ω	PROPN
ejpam-6306	151	12	,	,	PUNCT
ejpam-6306	151	13	α+f(α	α+f(α	NOUN
ejpam-6306	151	14	)	)	PUNCT
ejpam-6306	151	15	+	+	CCONJ
ejpam-6306	151	16	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	151	17	,	,	PUNCT
ejpam-6306	151	18	κ	κ	NOUN
ejpam-6306	151	19	ν	ν	PROPN
ejpam-6306	151	20	,	,	PUNCT
ejpam-6306	151	21	τ	τ	PROPN
ejpam-6306	151	22	,	,	PUNCT
ejpam-6306	151	23	j	j	PROPN
ejpam-6306	151	24	,	,	PUNCT
ejpam-6306	151	25	ω	ω	PROPN
ejpam-6306	151	26	,	,	PUNCT
ejpam-6306	151	27	ρ−f(ρ	ρ−f(ρ	NOUN
ejpam-6306	151	28	)	)	PUNCT
ejpam-6306	151	29	]	]	PUNCT
ejpam-6306	151	30	.	.	PUNCT
ejpam-6306	152	1	now	now	ADV
ejpam-6306	152	2	,	,	PUNCT
ejpam-6306	152	3	for	for	ADP
ejpam-6306	152	4	the	the	DET
ejpam-6306	152	5	second	second	ADJ
ejpam-6306	152	6	inequality	inequality	NOUN
ejpam-6306	152	7	,	,	PUNCT
ejpam-6306	152	8	we	we	PRON
ejpam-6306	152	9	consider	consider	VERB
ejpam-6306	152	10	the	the	DET
ejpam-6306	152	11	υ̌-convexity	υ̌-convexity	NOUN
ejpam-6306	152	12	f(υ̌−1(βυ̌(α	f(υ̌−1(βυ̌(α	PRON
ejpam-6306	152	13	)	)	PUNCT
ejpam-6306	153	1	+	+	CCONJ
ejpam-6306	153	2	(	(	PUNCT
ejpam-6306	153	3	1−	1−	NUM
ejpam-6306	153	4	β)υ̌(ρ	β)υ̌(ρ	ADJ
ejpam-6306	153	5	)	)	PUNCT
ejpam-6306	153	6	)	)	PUNCT
ejpam-6306	153	7	)	)	PUNCT
ejpam-6306	153	8	≤	≤	NOUN
ejpam-6306	153	9	βf(α	βf(α	PUNCT
ejpam-6306	153	10	)	)	PUNCT
ejpam-6306	154	1	+	+	CCONJ
ejpam-6306	154	2	(	(	PUNCT
ejpam-6306	154	3	1−	1−	NUM
ejpam-6306	154	4	β)f(ρ	β)f(ρ	NUM
ejpam-6306	154	5	)	)	PUNCT
ejpam-6306	154	6	,	,	PUNCT
ejpam-6306	154	7	(	(	PUNCT
ejpam-6306	154	8	12	12	NUM
ejpam-6306	154	9	)	)	PUNCT
ejpam-6306	154	10	and	and	CCONJ
ejpam-6306	154	11	f(υ̌−1((1−	f(υ̌−1((1−	PROPN
ejpam-6306	154	12	β)υ̌(α	β)υ̌(α	NUM
ejpam-6306	154	13	)	)	PUNCT
ejpam-6306	154	14	+	+	CCONJ
ejpam-6306	154	15	βυ̌(ρ	βυ̌(ρ	ADJ
ejpam-6306	154	16	)	)	PUNCT
ejpam-6306	154	17	)	)	PUNCT
ejpam-6306	154	18	)	)	PUNCT
ejpam-6306	155	1	≤	≤	NOUN
ejpam-6306	155	2	(	(	PUNCT
ejpam-6306	155	3	1−	1−	NUM
ejpam-6306	155	4	β)f(α	β)f(α	NOUN
ejpam-6306	155	5	)	)	PUNCT
ejpam-6306	155	6	+	+	NUM
ejpam-6306	155	7	βf(ρ	βf(ρ	NOUN
ejpam-6306	155	8	)	)	PUNCT
ejpam-6306	155	9	.	.	PUNCT
ejpam-6306	156	1	(	(	PUNCT
ejpam-6306	156	2	13	13	NUM
ejpam-6306	156	3	)	)	PUNCT
ejpam-6306	156	4	by	by	ADP
ejpam-6306	156	5	adding	add	VERB
ejpam-6306	156	6	the	the	DET
ejpam-6306	156	7	two	two	NUM
ejpam-6306	156	8	inequalities	inequality	NOUN
ejpam-6306	156	9	given	give	VERB
ejpam-6306	156	10	in	in	ADP
ejpam-6306	156	11	equations	equation	NOUN
ejpam-6306	156	12	(	(	PUNCT
ejpam-6306	156	13	12	12	NUM
ejpam-6306	156	14	)	)	PUNCT
ejpam-6306	156	15	and	and	CCONJ
ejpam-6306	156	16	(	(	PUNCT
ejpam-6306	156	17	13	13	NUM
ejpam-6306	156	18	)	)	PUNCT
ejpam-6306	156	19	,	,	PUNCT
ejpam-6306	156	20	we	we	PRON
ejpam-6306	156	21	get	get	VERB
ejpam-6306	156	22	f(υ̌−1(βυ̌(α	f(υ̌−1(βυ̌(α	VERB
ejpam-6306	156	23	)	)	PUNCT
ejpam-6306	157	1	+	+	CCONJ
ejpam-6306	157	2	(	(	PUNCT
ejpam-6306	157	3	1−	1−	NUM
ejpam-6306	157	4	β)υ̌(ρ	β)υ̌(ρ	ADJ
ejpam-6306	157	5	)	)	PUNCT
ejpam-6306	157	6	)	)	PUNCT
ejpam-6306	157	7	)	)	PUNCT
ejpam-6306	158	1	+	+	CCONJ
ejpam-6306	158	2	f(υ̌−1((1−	f(υ̌−1((1−	PROPN
ejpam-6306	158	3	β)υ̌(α	β)υ̌(α	NUM
ejpam-6306	158	4	)	)	PUNCT
ejpam-6306	158	5	+	+	CCONJ
ejpam-6306	158	6	βυ̌(ρ	βυ̌(ρ	ADJ
ejpam-6306	158	7	)	)	PUNCT
ejpam-6306	158	8	)	)	PUNCT
ejpam-6306	158	9	)	)	PUNCT
ejpam-6306	159	1	≤	≤	NUM
ejpam-6306	159	2	f(α	f(α	NOUN
ejpam-6306	159	3	)	)	PUNCT
ejpam-6306	159	4	+	+	NUM
ejpam-6306	159	5	f(ρ	f(ρ	NOUN
ejpam-6306	159	6	)	)	PUNCT
ejpam-6306	159	7	.	.	PUNCT
ejpam-6306	160	1	(	(	PUNCT
ejpam-6306	160	2	14	14	X
ejpam-6306	160	3	)	)	PUNCT
ejpam-6306	160	4	multiplying	multiply	VERB
ejpam-6306	160	5	both	both	DET
ejpam-6306	160	6	sides	side	NOUN
ejpam-6306	160	7	by	by	ADP
ejpam-6306	160	8	(	(	PUNCT
ejpam-6306	160	9	1−	1−	NUM
ejpam-6306	160	10	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	160	11	,	,	PUNCT
ejpam-6306	160	12	κ	κ	NOUN
ejpam-6306	160	13	ν	ν	PROPN
ejpam-6306	160	14	,	,	PUNCT
ejpam-6306	160	15	τ	τ	PROPN
ejpam-6306	160	16	,	,	PUNCT
ejpam-6306	160	17	j	j	PROPN
ejpam-6306	160	18	(	(	PUNCT
ejpam-6306	160	19	1−	1−	NUM
ejpam-6306	160	20	β)v	β)v	X
ejpam-6306	160	21	of	of	ADP
ejpam-6306	160	22	equation	equation	NOUN
ejpam-6306	160	23	(	(	PUNCT
ejpam-6306	160	24	14	14	NUM
ejpam-6306	160	25	)	)	PUNCT
ejpam-6306	160	26	and	and	CCONJ
ejpam-6306	160	27	then	then	ADV
ejpam-6306	160	28	integrating	integrate	VERB
ejpam-6306	160	29	with	with	ADP
ejpam-6306	160	30	respect	respect	NOUN
ejpam-6306	160	31	to	to	ADP
ejpam-6306	160	32	β	β	NOUN
ejpam-6306	160	33	over	over	ADP
ejpam-6306	160	34	[	[	X
ejpam-6306	160	35	0	0	NUM
ejpam-6306	160	36	,	,	PUNCT
ejpam-6306	160	37	1	1	NUM
ejpam-6306	160	38	]	]	PUNCT
ejpam-6306	160	39	,	,	PUNCT
ejpam-6306	160	40	we	we	PRON
ejpam-6306	160	41	can	can	AUX
ejpam-6306	160	42	obtain∫	obtain∫	VERB
ejpam-6306	160	43	1	1	NUM
ejpam-6306	160	44	0	0	NUM
ejpam-6306	160	45	(	(	PUNCT
ejpam-6306	160	46	1−	1−	NUM
ejpam-6306	160	47	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	160	48	,	,	PUNCT
ejpam-6306	160	49	κ	κ	NOUN
ejpam-6306	160	50	ν	ν	PROPN
ejpam-6306	160	51	,	,	PUNCT
ejpam-6306	160	52	τ	τ	PROPN
ejpam-6306	160	53	,	,	PUNCT
ejpam-6306	160	54	j	j	PROPN
ejpam-6306	160	55	(	(	PUNCT
ejpam-6306	160	56	1−	1−	NUM
ejpam-6306	160	57	β)vf(υ̌−1(βυ̌(α	β)vf(υ̌−1(βυ̌(α	NUM
ejpam-6306	160	58	)	)	PUNCT
ejpam-6306	161	1	+	+	CCONJ
ejpam-6306	161	2	(	(	PUNCT
ejpam-6306	161	3	1−	1−	NUM
ejpam-6306	161	4	β)υ̌(ρ)))dβ	β)υ̌(ρ)))dβ	NOUN
ejpam-6306	161	5	+	+	CCONJ
ejpam-6306	161	6	∫	∫	PROPN
ejpam-6306	161	7	1	1	NUM
ejpam-6306	161	8	0	0	NUM
ejpam-6306	161	9	(	(	PUNCT
ejpam-6306	161	10	1−	1−	NUM
ejpam-6306	161	11	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	161	12	,	,	PUNCT
ejpam-6306	161	13	κ	κ	NOUN
ejpam-6306	161	14	ν	ν	PROPN
ejpam-6306	161	15	,	,	PUNCT
ejpam-6306	161	16	τ	τ	PROPN
ejpam-6306	161	17	,	,	PUNCT
ejpam-6306	161	18	j	j	PROPN
ejpam-6306	161	19	(	(	PUNCT
ejpam-6306	161	20	1−	1−	NUM
ejpam-6306	161	21	β)vf(υ̌−1((1−	β)vf(υ̌−1((1−	NUM
ejpam-6306	161	22	β)υ̌(α	β)υ̌(α	PUNCT
ejpam-6306	161	23	)	)	PUNCT
ejpam-6306	162	1	+	+	CCONJ
ejpam-6306	162	2	βυ̌(ρ)))dβ	βυ̌(ρ)))dβ	AUX
ejpam-6306	162	3	≤	≤	NOUN
ejpam-6306	162	4	(	(	PUNCT
ejpam-6306	162	5	f(α	f(α	NOUN
ejpam-6306	162	6	)	)	PUNCT
ejpam-6306	162	7	+	+	CCONJ
ejpam-6306	162	8	f(ρ	f(ρ	NOUN
ejpam-6306	162	9	)	)	PUNCT
ejpam-6306	162	10	)	)	PUNCT
ejpam-6306	162	11	∫	∫	PROPN
ejpam-6306	163	1	1	1	NUM
ejpam-6306	163	2	0	0	NUM
ejpam-6306	163	3	(	(	PUNCT
ejpam-6306	163	4	1−	1−	NUM
ejpam-6306	163	5	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	163	6	,	,	PUNCT
ejpam-6306	163	7	κ	κ	NOUN
ejpam-6306	163	8	ν	ν	PROPN
ejpam-6306	163	9	,	,	PUNCT
ejpam-6306	163	10	τ	τ	PROPN
ejpam-6306	163	11	,	,	PUNCT
ejpam-6306	163	12	j	j	PROPN
ejpam-6306	163	13	(	(	PUNCT
ejpam-6306	163	14	1−	1−	NUM
ejpam-6306	163	15	β)vdβ	β)vdβ	PROPN
ejpam-6306	163	16	.	.	PUNCT
ejpam-6306	164	1	hence	hence	ADV
ejpam-6306	164	2	,	,	PUNCT
ejpam-6306	164	3	the	the	DET
ejpam-6306	164	4	required	require	VERB
ejpam-6306	164	5	result	result	NOUN
ejpam-6306	164	6	is	be	AUX
ejpam-6306	164	7	1	1	NUM
ejpam-6306	164	8	2(υ̌(α)−	2(υ̌(α)−	NUM
ejpam-6306	164	9	υ̌(ρ))τ	υ̌(ρ))τ	NOUN
ejpam-6306	164	10	[	[	PUNCT
ejpam-6306	164	11	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	164	12	,	,	PUNCT
ejpam-6306	164	13	κ	κ	NOUN
ejpam-6306	164	14	ν	ν	PROPN
ejpam-6306	164	15	,	,	PUNCT
ejpam-6306	164	16	τ	τ	PROPN
ejpam-6306	164	17	,	,	PUNCT
ejpam-6306	164	18	j	j	PROPN
ejpam-6306	164	19	,	,	PUNCT
ejpam-6306	164	20	ω	ω	PROPN
ejpam-6306	164	21	,	,	PUNCT
ejpam-6306	164	22	α+f(α	α+f(α	NOUN
ejpam-6306	164	23	)	)	PUNCT
ejpam-6306	164	24	+	+	CCONJ
ejpam-6306	164	25	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	164	26	,	,	PUNCT
ejpam-6306	164	27	κ	κ	NOUN
ejpam-6306	164	28	ν	ν	PROPN
ejpam-6306	164	29	,	,	PUNCT
ejpam-6306	164	30	τ	τ	PROPN
ejpam-6306	164	31	,	,	PUNCT
ejpam-6306	164	32	j	j	PROPN
ejpam-6306	164	33	,	,	PUNCT
ejpam-6306	164	34	ω	ω	PROPN
ejpam-6306	164	35	,	,	PUNCT
ejpam-6306	164	36	ρ−f(ρ	ρ−f(ρ	NOUN
ejpam-6306	164	37	)	)	PUNCT
ejpam-6306	164	38	]	]	PUNCT
ejpam-6306	164	39	≤	≤	NUM
ejpam-6306	164	40	f(α	f(α	NOUN
ejpam-6306	164	41	)	)	PUNCT
ejpam-6306	164	42	+	+	NUM
ejpam-6306	164	43	f(ρ	f(ρ	NOUN
ejpam-6306	164	44	)	)	PUNCT
ejpam-6306	164	45	2	2	NUM
ejpam-6306	164	46	eϑ,z	eϑ,z	NOUN
ejpam-6306	164	47	,	,	PUNCT
ejpam-6306	164	48	κ	κ	X
ejpam-6306	164	49	ν	ν	PROPN
ejpam-6306	164	50	,	,	PUNCT
ejpam-6306	164	51	τ	τ	PROPN
ejpam-6306	164	52	,	,	PUNCT
ejpam-6306	164	53	j	j	PROPN
ejpam-6306	164	54	(	(	PUNCT
ejpam-6306	164	55	(	(	PUNCT
ejpam-6306	164	56	1−	1−	NUM
ejpam-6306	164	57	β)v	β)v	NOUN
ejpam-6306	164	58	)	)	PUNCT
ejpam-6306	164	59	,	,	PUNCT
ejpam-6306	164	60	and	and	CCONJ
ejpam-6306	164	61	this	this	PRON
ejpam-6306	164	62	completes	complete	VERB
ejpam-6306	164	63	the	the	DET
ejpam-6306	164	64	proof	proof	NOUN
ejpam-6306	164	65	.	.	PUNCT
ejpam-6306	165	1	corollary	corollary	ADJ
ejpam-6306	165	2	1	1	NUM
ejpam-6306	165	3	.	.	PUNCT
ejpam-6306	166	1	by	by	ADP
ejpam-6306	166	2	the	the	DET
ejpam-6306	166	3	assumption	assumption	NOUN
ejpam-6306	166	4	of	of	ADP
ejpam-6306	166	5	theorem	theorem	NOUN
ejpam-6306	166	6	1	1	NUM
ejpam-6306	166	7	,	,	PUNCT
ejpam-6306	166	8	replace	replace	VERB
ejpam-6306	166	9	υ̌(x	υ̌(x	NUM
ejpam-6306	166	10	)	)	PUNCT
ejpam-6306	166	11	=	=	SYM
ejpam-6306	167	1	x	x	NOUN
ejpam-6306	167	2	;	;	PUNCT
ejpam-6306	167	3	then	then	ADV
ejpam-6306	167	4	the	the	DET
ejpam-6306	167	5	inequality	inequality	NOUN
ejpam-6306	167	6	(	(	PUNCT
ejpam-6306	167	7	7	7	NUM
ejpam-6306	167	8	)	)	PUNCT
ejpam-6306	167	9	reduces	reduce	VERB
ejpam-6306	167	10	to	to	ADP
ejpam-6306	167	11	inequality	inequality	NOUN
ejpam-6306	167	12	(	(	PUNCT
ejpam-6306	167	13	2	2	NUM
ejpam-6306	167	14	)	)	PUNCT
ejpam-6306	167	15	.	.	PUNCT
ejpam-6306	168	1	corollary	corollary	ADJ
ejpam-6306	168	2	2	2	NUM
ejpam-6306	168	3	.	.	PUNCT
ejpam-6306	169	1	by	by	ADP
ejpam-6306	169	2	the	the	DET
ejpam-6306	169	3	assumption	assumption	NOUN
ejpam-6306	169	4	of	of	ADP
ejpam-6306	169	5	theorem	theorem	NOUN
ejpam-6306	169	6	1	1	NUM
ejpam-6306	169	7	,	,	PUNCT
ejpam-6306	169	8	replace	replace	VERB
ejpam-6306	169	9	τ	τ	PROPN
ejpam-6306	169	10	=	=	SYM
ejpam-6306	169	11	1	1	NUM
ejpam-6306	169	12	;	;	PUNCT
ejpam-6306	169	13	then	then	ADV
ejpam-6306	169	14	we	we	PRON
ejpam-6306	169	15	have	have	VERB
ejpam-6306	169	16	f	f	X
ejpam-6306	169	17	(	(	PUNCT
ejpam-6306	169	18	υ̌−1	υ̌−1	X
ejpam-6306	169	19	(	(	PUNCT
ejpam-6306	169	20	υ̌(α	υ̌(α	PROPN
ejpam-6306	169	21	)	)	PUNCT
ejpam-6306	170	1	+	+	CCONJ
ejpam-6306	170	2	υ̌(ρ	υ̌(ρ	X
ejpam-6306	170	3	)	)	PUNCT
ejpam-6306	170	4	2	2	NUM
ejpam-6306	170	5	)	)	PUNCT
ejpam-6306	170	6	)	)	PUNCT
ejpam-6306	170	7	≤	≤	NUM
ejpam-6306	170	8	1	1	NUM
ejpam-6306	170	9	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	170	10	υ̌(α	υ̌(α	NUM
ejpam-6306	170	11	)	)	PUNCT
ejpam-6306	170	12	∫	∫	PROPN
ejpam-6306	171	1	ρ	ρ	PROPN
ejpam-6306	171	2	α	α	PROPN
ejpam-6306	171	3	f(x)υ̌′(x)dx	f(x)υ̌′(x)dx	PROPN
ejpam-6306	171	4	≤	≤	NOUN
ejpam-6306	171	5	f(α	f(α	NOUN
ejpam-6306	171	6	)	)	PUNCT
ejpam-6306	172	1	+	+	NUM
ejpam-6306	172	2	f(ρ	f(ρ	NOUN
ejpam-6306	172	3	)	)	PUNCT
ejpam-6306	172	4	2	2	NUM
ejpam-6306	172	5	,	,	PUNCT
ejpam-6306	172	6	(	(	PUNCT
ejpam-6306	172	7	15	15	NUM
ejpam-6306	172	8	)	)	PUNCT
ejpam-6306	172	9	which	which	PRON
ejpam-6306	172	10	was	be	AUX
ejpam-6306	172	11	already	already	ADV
ejpam-6306	172	12	established	establish	VERB
ejpam-6306	172	13	in	in	ADP
ejpam-6306	172	14	[	[	X
ejpam-6306	172	15	25	25	NUM
ejpam-6306	172	16	]	]	PUNCT
ejpam-6306	172	17	.	.	PUNCT
ejpam-6306	173	1	r.	r.	PROPN
ejpam-6306	173	2	s.	s.	PROPN
ejpam-6306	173	3	ali	ali	PROPN
ejpam-6306	173	4	et	et	PROPN
ejpam-6306	173	5	al	al	PROPN
ejpam-6306	173	6	.	.	PUNCT
ejpam-6306	173	7	/	/	SYM
ejpam-6306	173	8	eur	eur	PROPN
ejpam-6306	173	9	.	.	PUNCT
ejpam-6306	174	1	j.	j.	PROPN
ejpam-6306	174	2	pure	pure	PROPN
ejpam-6306	174	3	appl	appl	PROPN
ejpam-6306	174	4	.	.	PROPN
ejpam-6306	174	5	math	math	PROPN
ejpam-6306	174	6	,	,	PUNCT
ejpam-6306	174	7	18	18	NUM
ejpam-6306	174	8	(	(	PUNCT
ejpam-6306	174	9	3	3	NUM
ejpam-6306	174	10	)	)	PUNCT
ejpam-6306	174	11	(	(	PUNCT
ejpam-6306	174	12	2025	2025	NUM
ejpam-6306	174	13	)	)	PUNCT
ejpam-6306	174	14	,	,	PUNCT
ejpam-6306	174	15	6306	6306	NUM
ejpam-6306	174	16	9	9	NUM
ejpam-6306	174	17	of	of	ADP
ejpam-6306	174	18	18	18	NUM
ejpam-6306	174	19	corollary	corollary	ADJ
ejpam-6306	174	20	3	3	NUM
ejpam-6306	174	21	.	.	PUNCT
ejpam-6306	175	1	by	by	ADP
ejpam-6306	175	2	the	the	DET
ejpam-6306	175	3	assumption	assumption	NOUN
ejpam-6306	175	4	of	of	ADP
ejpam-6306	175	5	theorem	theorem	NOUN
ejpam-6306	175	6	1	1	NUM
ejpam-6306	175	7	,	,	PUNCT
ejpam-6306	175	8	replace	replace	VERB
ejpam-6306	175	9	υ̌(x	υ̌(x	NUM
ejpam-6306	175	10	)	)	PUNCT
ejpam-6306	175	11	=	=	SYM
ejpam-6306	175	12	x	x	NOUN
ejpam-6306	175	13	,	,	PUNCT
ejpam-6306	175	14	τ	τ	PROPN
ejpam-6306	175	15	=	=	SYM
ejpam-6306	175	16	1	1	NUM
ejpam-6306	175	17	;	;	PUNCT
ejpam-6306	175	18	then	then	ADV
ejpam-6306	175	19	we	we	PRON
ejpam-6306	175	20	have	have	VERB
ejpam-6306	175	21	the	the	DET
ejpam-6306	175	22	inequality	inequality	NOUN
ejpam-6306	175	23	(	(	PUNCT
ejpam-6306	175	24	1	1	NUM
ejpam-6306	175	25	)	)	PUNCT
ejpam-6306	175	26	.	.	PUNCT
ejpam-6306	176	1	theorem	theorem	NOUN
ejpam-6306	176	2	2	2	NUM
ejpam-6306	176	3	.	.	PUNCT
ejpam-6306	177	1	let	let	VERB
ejpam-6306	177	2	f	f	NOUN
ejpam-6306	177	3	:	:	PUNCT
ejpam-6306	178	1	[	[	X
ejpam-6306	178	2	α	α	X
ejpam-6306	178	3	,	,	PUNCT
ejpam-6306	178	4	ρ	ρ	PROPN
ejpam-6306	178	5	]	]	X
ejpam-6306	178	6	⊆	⊆	NUM
ejpam-6306	178	7	r	r	NOUN
ejpam-6306	178	8	→	→	SYM
ejpam-6306	178	9	r	r	NOUN
ejpam-6306	178	10	be	be	AUX
ejpam-6306	178	11	integrable	integrable	ADJ
ejpam-6306	178	12	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	178	13	,	,	PUNCT
ejpam-6306	178	14	and	and	CCONJ
ejpam-6306	178	15	f	f	PROPN
ejpam-6306	178	16	∈	∈	PROPN
ejpam-6306	178	17	l1(α	l1(α	PROPN
ejpam-6306	178	18	,	,	PUNCT
ejpam-6306	178	19	ρ	ρ	PROPN
ejpam-6306	178	20	)	)	PUNCT
ejpam-6306	178	21	with	with	ADP
ejpam-6306	178	22	0	0	NUM
ejpam-6306	178	23	≤	≤	NUM
ejpam-6306	178	24	α	α	PROPN
ejpam-6306	178	25	<	<	X
ejpam-6306	178	26	ρ	ρ	PROPN
ejpam-6306	178	27	.	.	PUNCT
ejpam-6306	179	1	moreover	moreover	ADV
ejpam-6306	179	2	,	,	PUNCT
ejpam-6306	179	3	the	the	DET
ejpam-6306	179	4	function	function	NOUN
ejpam-6306	179	5	υ̌	υ̌	PROPN
ejpam-6306	179	6	is	be	AUX
ejpam-6306	179	7	also	also	ADV
ejpam-6306	179	8	monotone	monotone	ADJ
ejpam-6306	179	9	and	and	CCONJ
ejpam-6306	179	10	positive	positive	ADJ
ejpam-6306	179	11	on	on	ADP
ejpam-6306	179	12	(	(	PUNCT
ejpam-6306	179	13	α	α	X
ejpam-6306	179	14	,	,	PUNCT
ejpam-6306	179	15	ρ	ρ	NOUN
ejpam-6306	179	16	]	]	X
ejpam-6306	179	17	,	,	PUNCT
ejpam-6306	179	18	and	and	CCONJ
ejpam-6306	179	19	υ̌′(x	υ̌′(x	NOUN
ejpam-6306	179	20	)	)	PUNCT
ejpam-6306	179	21	be	be	AUX
ejpam-6306	179	22	continuous	continuous	ADJ
ejpam-6306	179	23	on	on	ADP
ejpam-6306	179	24	(	(	PUNCT
ejpam-6306	179	25	α	α	X
ejpam-6306	179	26	,	,	PUNCT
ejpam-6306	179	27	ρ	ρ	PROPN
ejpam-6306	179	28	)	)	PUNCT
ejpam-6306	179	29	.	.	PUNCT
ejpam-6306	180	1	then	then	ADV
ejpam-6306	180	2	for	for	ADP
ejpam-6306	180	3	τ	τ	PROPN
ejpam-6306	180	4	>	>	X
ejpam-6306	180	5	0	0	PROPN
ejpam-6306	180	6	,	,	PUNCT
ejpam-6306	180	7	we	we	PRON
ejpam-6306	180	8	have	have	VERB
ejpam-6306	180	9	the	the	DET
ejpam-6306	180	10	following	follow	VERB
ejpam-6306	180	11	inequality	inequality	NOUN
ejpam-6306	180	12	f	f	PROPN
ejpam-6306	180	13	(	(	PUNCT
ejpam-6306	180	14	υ̌−1	υ̌−1	X
ejpam-6306	180	15	(	(	PUNCT
ejpam-6306	180	16	υ̌(α	υ̌(α	PROPN
ejpam-6306	180	17	)	)	PUNCT
ejpam-6306	180	18	+	+	CCONJ
ejpam-6306	180	19	υ̌(ρ	υ̌(ρ	X
ejpam-6306	180	20	)	)	PUNCT
ejpam-6306	180	21	2	2	NUM
ejpam-6306	180	22	)	)	PUNCT
ejpam-6306	180	23	)	)	PUNCT
ejpam-6306	180	24	eϑ,z	eϑ,z	NOUN
ejpam-6306	180	25	,	,	PUNCT
ejpam-6306	180	26	κ	κ	X
ejpam-6306	180	27	ν	ν	PROPN
ejpam-6306	180	28	,	,	PUNCT
ejpam-6306	180	29	τ	τ	PROPN
ejpam-6306	180	30	,	,	PUNCT
ejpam-6306	180	31	j	j	PROPN
ejpam-6306	180	32	(	(	PUNCT
ejpam-6306	180	33	(	(	PUNCT
ejpam-6306	180	34	1−	1−	NUM
ejpam-6306	180	35	β)v	β)v	NOUN
ejpam-6306	180	36	)	)	PUNCT
ejpam-6306	180	37	≤	≤	NUM
ejpam-6306	180	38	1	1	NUM
ejpam-6306	180	39	(	(	PUNCT
ejpam-6306	180	40	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	180	41	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	180	42	[	[	PUNCT
ejpam-6306	180	43	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	180	44	,	,	PUNCT
ejpam-6306	180	45	κ	κ	NOUN
ejpam-6306	180	46	ν	ν	PROPN
ejpam-6306	180	47	,	,	PUNCT
ejpam-6306	180	48	τ	τ	PROPN
ejpam-6306	180	49	,	,	PUNCT
ejpam-6306	180	50	j	j	PROPN
ejpam-6306	180	51	,	,	PUNCT
ejpam-6306	180	52	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	180	53	(	(	PUNCT
ejpam-6306	180	54	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	180	55	)	)	PUNCT
ejpam-6306	180	56	2	2	NUM
ejpam-6306	180	57	)	)	PUNCT
ejpam-6306	180	58	)	)	PUNCT
ejpam-6306	181	1	+	+	PUNCT
ejpam-6306	181	2	f(α	f(α	NOUN
ejpam-6306	181	3	)	)	PUNCT
ejpam-6306	181	4	+	+	CCONJ
ejpam-6306	182	1	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	182	2	,	,	PUNCT
ejpam-6306	182	3	κ	κ	NOUN
ejpam-6306	182	4	ν	ν	PROPN
ejpam-6306	182	5	,	,	PUNCT
ejpam-6306	182	6	τ	τ	PROPN
ejpam-6306	182	7	,	,	PUNCT
ejpam-6306	182	8	j	j	PROPN
ejpam-6306	182	9	,	,	PUNCT
ejpam-6306	182	10	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	182	11	(	(	PUNCT
ejpam-6306	182	12	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	182	13	)	)	PUNCT
ejpam-6306	182	14	2	2	NUM
ejpam-6306	182	15	)	)	PUNCT
ejpam-6306	182	16	)	)	PUNCT
ejpam-6306	182	17	−	−	ADP
ejpam-6306	182	18	f(ρ	f(ρ	NOUN
ejpam-6306	182	19	)	)	PUNCT
ejpam-6306	182	20	]	]	PUNCT
ejpam-6306	182	21	≤	≤	NUM
ejpam-6306	182	22	f(α	f(α	NOUN
ejpam-6306	182	23	)	)	PUNCT
ejpam-6306	182	24	+	+	NUM
ejpam-6306	182	25	f(ρ	f(ρ	NOUN
ejpam-6306	182	26	)	)	PUNCT
ejpam-6306	182	27	2	2	NUM
ejpam-6306	182	28	eϑ,z	eϑ,z	NOUN
ejpam-6306	182	29	,	,	PUNCT
ejpam-6306	182	30	κ	κ	X
ejpam-6306	182	31	ν	ν	PROPN
ejpam-6306	182	32	,	,	PUNCT
ejpam-6306	182	33	τ	τ	PROPN
ejpam-6306	182	34	,	,	PUNCT
ejpam-6306	182	35	j	j	PROPN
ejpam-6306	182	36	(	(	PUNCT
ejpam-6306	182	37	(	(	PUNCT
ejpam-6306	182	38	1−	1−	NUM
ejpam-6306	182	39	β)v	β)v	NOUN
ejpam-6306	182	40	)	)	PUNCT
ejpam-6306	182	41	,	,	PUNCT
ejpam-6306	182	42	(	(	PUNCT
ejpam-6306	182	43	16	16	NUM
ejpam-6306	182	44	)	)	PUNCT
ejpam-6306	182	45	where	where	SCONJ
ejpam-6306	182	46	(	(	PUNCT
ejpam-6306	182	47	ξ(µ)v)n	ξ(µ)v)n	NOUN
ejpam-6306	182	48	=	=	SYM
ejpam-6306	182	49	(	(	PUNCT
ejpam-6306	182	50	(	(	PUNCT
ejpam-6306	182	51	υ̌(µ)−υ̌(α	υ̌(µ)−υ̌(α	PROPN
ejpam-6306	182	52	)	)	PUNCT
ejpam-6306	182	53	υ̌(ρ)−υ̌(α	υ̌(ρ)−υ̌(α	PROPN
ejpam-6306	182	54	)	)	PUNCT
ejpam-6306	182	55	)	)	PUNCT
ejpam-6306	182	56	v)n	v)n	NOUN
ejpam-6306	182	57	and	and	CCONJ
ejpam-6306	182	58	(	(	PUNCT
ejpam-6306	182	59	ξ(ω)v)n	ξ(ω)v)n	PROPN
ejpam-6306	182	60	=	=	PUNCT
ejpam-6306	182	61	(	(	PUNCT
ejpam-6306	182	62	(	(	PUNCT
ejpam-6306	182	63	υ̌(ρ)−υ̌(ω	υ̌(ρ)−υ̌(ω	PROPN
ejpam-6306	182	64	)	)	PUNCT
ejpam-6306	182	65	υ̌(ρ)−υ̌(α	υ̌(ρ)−υ̌(α	PROPN
ejpam-6306	182	66	)	)	PUNCT
ejpam-6306	182	67	)	)	PUNCT
ejpam-6306	182	68	v)n	v)n	NOUN
ejpam-6306	182	69	.	.	PUNCT
ejpam-6306	183	1	proof	proof	NOUN
ejpam-6306	183	2	.	.	PUNCT
ejpam-6306	184	1	consider	consider	VERB
ejpam-6306	184	2	the	the	DET
ejpam-6306	184	3	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	184	4	function	function	NOUN
ejpam-6306	184	5	f	f	PROPN
ejpam-6306	184	6	.	.	PUNCT
ejpam-6306	185	1	we	we	PRON
ejpam-6306	185	2	have	have	VERB
ejpam-6306	185	3	f	f	X
ejpam-6306	185	4	(	(	PUNCT
ejpam-6306	185	5	υ̌−1	υ̌−1	X
ejpam-6306	185	6	(	(	PUNCT
ejpam-6306	185	7	υ̌(x	υ̌(x	PROPN
ejpam-6306	185	8	)	)	PUNCT
ejpam-6306	186	1	+	+	NUM
ejpam-6306	186	2	υ̌(y	υ̌(y	NUM
ejpam-6306	186	3	)	)	PUNCT
ejpam-6306	186	4	2	2	NUM
ejpam-6306	186	5	)	)	PUNCT
ejpam-6306	186	6	)	)	PUNCT
ejpam-6306	186	7	≤	≤	NUM
ejpam-6306	186	8	υ̌(x	υ̌(x	NUM
ejpam-6306	186	9	)	)	PUNCT
ejpam-6306	186	10	+	+	NUM
ejpam-6306	186	11	υ̌(y	υ̌(y	NUM
ejpam-6306	186	12	)	)	PUNCT
ejpam-6306	186	13	2	2	NUM
ejpam-6306	186	14	.	.	PUNCT
ejpam-6306	187	1	(	(	PUNCT
ejpam-6306	187	2	17	17	NUM
ejpam-6306	187	3	)	)	PUNCT
ejpam-6306	187	4	put	put	VERB
ejpam-6306	187	5	the	the	DET
ejpam-6306	187	6	values	value	NOUN
ejpam-6306	187	7	x	x	PUNCT
ejpam-6306	187	8	=	=	PUNCT
ejpam-6306	187	9	υ̌−1(β2	υ̌−1(β2	PROPN
ejpam-6306	187	10	υ̌(α	υ̌(α	PROPN
ejpam-6306	187	11	)	)	PUNCT
ejpam-6306	188	1	+	+	CCONJ
ejpam-6306	188	2	2−β	2−β	NUM
ejpam-6306	188	3	2	2	NUM
ejpam-6306	188	4	υ̌(ρ	υ̌(ρ	NOUN
ejpam-6306	188	5	)	)	PUNCT
ejpam-6306	188	6	)	)	PUNCT
ejpam-6306	188	7	and	and	CCONJ
ejpam-6306	188	8	y	y	PROPN
ejpam-6306	188	9	=	=	PUNCT
ejpam-6306	189	1	υ̌−1(2−β	υ̌−1(2−β	ADP
ejpam-6306	189	2	2	2	NUM
ejpam-6306	189	3	υ̌(α	υ̌(α	NUM
ejpam-6306	189	4	)	)	PUNCT
ejpam-6306	189	5	+	+	CCONJ
ejpam-6306	189	6	β	β	X
ejpam-6306	189	7	2	2	NUM
ejpam-6306	189	8	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	189	9	)	)	PUNCT
ejpam-6306	189	10	)	)	PUNCT
ejpam-6306	189	11	in	in	ADP
ejpam-6306	189	12	equation	equation	NOUN
ejpam-6306	189	13	(	(	PUNCT
ejpam-6306	189	14	17	17	NUM
ejpam-6306	189	15	)	)	PUNCT
ejpam-6306	189	16	to	to	PART
ejpam-6306	189	17	get	get	VERB
ejpam-6306	189	18	2f	2f	NUM
ejpam-6306	189	19	(	(	PUNCT
ejpam-6306	189	20	υ̌−1	υ̌−1	X
ejpam-6306	189	21	(	(	PUNCT
ejpam-6306	189	22	υ̌(α	υ̌(α	PROPN
ejpam-6306	189	23	)	)	PUNCT
ejpam-6306	189	24	+	+	CCONJ
ejpam-6306	189	25	υ̌(ρ	υ̌(ρ	X
ejpam-6306	189	26	)	)	PUNCT
ejpam-6306	189	27	2	2	NUM
ejpam-6306	189	28	)	)	PUNCT
ejpam-6306	189	29	)	)	PUNCT
ejpam-6306	190	1	≤	≤	NUM
ejpam-6306	190	2	f	f	X
ejpam-6306	190	3	(	(	PUNCT
ejpam-6306	190	4	υ̌−1	υ̌−1	PROPN
ejpam-6306	190	5	(	(	PUNCT
ejpam-6306	190	6	β	β	NOUN
ejpam-6306	190	7	2	2	NUM
ejpam-6306	190	8	υ̌(α	υ̌(α	NUM
ejpam-6306	190	9	)	)	PUNCT
ejpam-6306	190	10	+	+	CCONJ
ejpam-6306	190	11	(	(	PUNCT
ejpam-6306	190	12	2−	2−	NUM
ejpam-6306	190	13	β	β	SYM
ejpam-6306	190	14	2	2	NUM
ejpam-6306	190	15	)	)	PUNCT
ejpam-6306	190	16	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	190	17	)	)	PUNCT
ejpam-6306	190	18	)	)	PUNCT
ejpam-6306	190	19	)	)	PUNCT
ejpam-6306	191	1	+	+	CCONJ
ejpam-6306	191	2	f	f	X
ejpam-6306	191	3	(	(	PUNCT
ejpam-6306	191	4	υ̌−1	υ̌−1	PROPN
ejpam-6306	191	5	(	(	PUNCT
ejpam-6306	191	6	2−	2−	NUM
ejpam-6306	191	7	β	β	SYM
ejpam-6306	191	8	2	2	NUM
ejpam-6306	191	9	)	)	PUNCT
ejpam-6306	191	10	υ̌(α	υ̌(α	NUM
ejpam-6306	191	11	)	)	PUNCT
ejpam-6306	191	12	+	+	CCONJ
ejpam-6306	191	13	β	β	X
ejpam-6306	191	14	2	2	NUM
ejpam-6306	191	15	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	191	16	)	)	PUNCT
ejpam-6306	191	17	)	)	PUNCT
ejpam-6306	191	18	)	)	PUNCT
ejpam-6306	191	19	.	.	PUNCT
ejpam-6306	192	1	(	(	PUNCT
ejpam-6306	192	2	18	18	NUM
ejpam-6306	192	3	)	)	PUNCT
ejpam-6306	192	4	multiplying	multiply	VERB
ejpam-6306	192	5	both	both	DET
ejpam-6306	192	6	sides	side	NOUN
ejpam-6306	192	7	by	by	ADP
ejpam-6306	192	8	(	(	PUNCT
ejpam-6306	192	9	1−	1−	NUM
ejpam-6306	192	10	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	192	11	,	,	PUNCT
ejpam-6306	192	12	κ	κ	NOUN
ejpam-6306	192	13	ν	ν	PROPN
ejpam-6306	192	14	,	,	PUNCT
ejpam-6306	192	15	τ	τ	PROPN
ejpam-6306	192	16	,	,	PUNCT
ejpam-6306	192	17	j	j	PROPN
ejpam-6306	192	18	(	(	PUNCT
ejpam-6306	192	19	1−	1−	NUM
ejpam-6306	192	20	β)v	β)v	X
ejpam-6306	192	21	of	of	ADP
ejpam-6306	192	22	equation	equation	NOUN
ejpam-6306	192	23	(	(	PUNCT
ejpam-6306	192	24	18	18	NUM
ejpam-6306	192	25	)	)	PUNCT
ejpam-6306	192	26	,	,	PUNCT
ejpam-6306	192	27	and	and	CCONJ
ejpam-6306	192	28	then	then	ADV
ejpam-6306	192	29	integrating	integrate	VERB
ejpam-6306	192	30	the	the	DET
ejpam-6306	192	31	resulting	result	VERB
ejpam-6306	192	32	inequality	inequality	NOUN
ejpam-6306	192	33	with	with	ADP
ejpam-6306	192	34	respect	respect	NOUN
ejpam-6306	192	35	to	to	ADP
ejpam-6306	192	36	β	β	NOUN
ejpam-6306	192	37	over	over	ADP
ejpam-6306	192	38	[	[	X
ejpam-6306	192	39	0	0	NUM
ejpam-6306	192	40	,	,	PUNCT
ejpam-6306	192	41	1	1	NUM
ejpam-6306	192	42	]	]	PUNCT
ejpam-6306	192	43	,	,	PUNCT
ejpam-6306	192	44	give	give	VERB
ejpam-6306	192	45	2f	2f	NUM
ejpam-6306	192	46	(	(	PUNCT
ejpam-6306	192	47	υ̌−1	υ̌−1	X
ejpam-6306	192	48	(	(	PUNCT
ejpam-6306	192	49	υ̌(α	υ̌(α	PROPN
ejpam-6306	192	50	)	)	PUNCT
ejpam-6306	192	51	+	+	CCONJ
ejpam-6306	192	52	υ̌(ρ	υ̌(ρ	X
ejpam-6306	192	53	)	)	PUNCT
ejpam-6306	192	54	2	2	NUM
ejpam-6306	192	55	)	)	PUNCT
ejpam-6306	192	56	)	)	PUNCT
ejpam-6306	193	1	∫	∫	PROPN
ejpam-6306	193	2	1	1	NUM
ejpam-6306	193	3	0	0	NUM
ejpam-6306	193	4	(	(	PUNCT
ejpam-6306	193	5	1−	1−	NUM
ejpam-6306	193	6	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	193	7	,	,	PUNCT
ejpam-6306	193	8	κ	κ	NOUN
ejpam-6306	193	9	ν	ν	PROPN
ejpam-6306	193	10	,	,	PUNCT
ejpam-6306	193	11	τ	τ	PROPN
ejpam-6306	193	12	,	,	PUNCT
ejpam-6306	193	13	j	j	PROPN
ejpam-6306	193	14	(	(	PUNCT
ejpam-6306	193	15	(	(	PUNCT
ejpam-6306	193	16	1−	1−	NUM
ejpam-6306	193	17	β)v)dβ	β)v)dβ	PRON
ejpam-6306	193	18	≤	≤	NUM
ejpam-6306	193	19	∫	∫	PROPN
ejpam-6306	193	20	1	1	NUM
ejpam-6306	193	21	0	0	NUM
ejpam-6306	193	22	(	(	PUNCT
ejpam-6306	193	23	1−	1−	NUM
ejpam-6306	193	24	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	193	25	,	,	PUNCT
ejpam-6306	193	26	κ	κ	NOUN
ejpam-6306	193	27	ν	ν	PROPN
ejpam-6306	193	28	,	,	PUNCT
ejpam-6306	193	29	τ	τ	PROPN
ejpam-6306	193	30	,	,	PUNCT
ejpam-6306	193	31	j	j	PROPN
ejpam-6306	193	32	(	(	PUNCT
ejpam-6306	193	33	(	(	PUNCT
ejpam-6306	193	34	1−	1−	NUM
ejpam-6306	193	35	β)v)f(υ̌−1	β)v)f(υ̌−1	NOUN
ejpam-6306	193	36	(	(	PUNCT
ejpam-6306	193	37	β	β	X
ejpam-6306	193	38	2	2	NUM
ejpam-6306	193	39	υ̌(α	υ̌(α	NUM
ejpam-6306	193	40	)	)	PUNCT
ejpam-6306	193	41	+	+	CCONJ
ejpam-6306	194	1	(	(	PUNCT
ejpam-6306	194	2	2−	2−	NUM
ejpam-6306	194	3	β	β	SYM
ejpam-6306	194	4	2	2	NUM
ejpam-6306	194	5	)	)	PUNCT
ejpam-6306	194	6	υ̌(ρ)))dβ	υ̌(ρ)))dβ	NOUN
ejpam-6306	194	7	+	+	CCONJ
ejpam-6306	194	8	∫	∫	PROPN
ejpam-6306	194	9	1	1	NUM
ejpam-6306	194	10	0	0	NUM
ejpam-6306	194	11	(	(	PUNCT
ejpam-6306	194	12	1−	1−	NUM
ejpam-6306	194	13	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	194	14	,	,	PUNCT
ejpam-6306	194	15	κ	κ	NOUN
ejpam-6306	194	16	ν	ν	PROPN
ejpam-6306	194	17	,	,	PUNCT
ejpam-6306	194	18	τ	τ	PROPN
ejpam-6306	194	19	,	,	PUNCT
ejpam-6306	194	20	j	j	PROPN
ejpam-6306	194	21	(	(	PUNCT
ejpam-6306	194	22	(	(	PUNCT
ejpam-6306	194	23	1−	1−	NUM
ejpam-6306	194	24	β)v)f(υ̌−1	β)v)f(υ̌−1	NOUN
ejpam-6306	194	25	(	(	PUNCT
ejpam-6306	194	26	2−	2−	NUM
ejpam-6306	194	27	β	β	SYM
ejpam-6306	194	28	2	2	NUM
ejpam-6306	194	29	)	)	PUNCT
ejpam-6306	194	30	υ̌(α	υ̌(α	NUM
ejpam-6306	194	31	)	)	PUNCT
ejpam-6306	195	1	+	+	NUM
ejpam-6306	195	2	β	β	X
ejpam-6306	195	3	2	2	NUM
ejpam-6306	195	4	υ̌(ρ))dβ	υ̌(ρ))dβ	X
ejpam-6306	195	5	.	.	PUNCT
ejpam-6306	196	1	(	(	PUNCT
ejpam-6306	196	2	19	19	NUM
ejpam-6306	196	3	)	)	PUNCT
ejpam-6306	196	4	r.	r.	PROPN
ejpam-6306	196	5	s.	s.	PROPN
ejpam-6306	196	6	ali	ali	PROPN
ejpam-6306	196	7	et	et	PROPN
ejpam-6306	196	8	al	al	PROPN
ejpam-6306	196	9	.	.	PUNCT
ejpam-6306	196	10	/	/	SYM
ejpam-6306	196	11	eur	eur	PROPN
ejpam-6306	196	12	.	.	PUNCT
ejpam-6306	197	1	j.	j.	PROPN
ejpam-6306	197	2	pure	pure	PROPN
ejpam-6306	197	3	appl	appl	PROPN
ejpam-6306	197	4	.	.	PROPN
ejpam-6306	197	5	math	math	PROPN
ejpam-6306	197	6	,	,	PUNCT
ejpam-6306	197	7	18	18	NUM
ejpam-6306	197	8	(	(	PUNCT
ejpam-6306	197	9	3	3	NUM
ejpam-6306	197	10	)	)	PUNCT
ejpam-6306	197	11	(	(	PUNCT
ejpam-6306	197	12	2025	2025	NUM
ejpam-6306	197	13	)	)	PUNCT
ejpam-6306	197	14	,	,	PUNCT
ejpam-6306	197	15	6306	6306	NUM
ejpam-6306	197	16	10	10	NUM
ejpam-6306	197	17	of	of	ADP
ejpam-6306	197	18	18	18	NUM
ejpam-6306	197	19	by	by	ADP
ejpam-6306	197	20	changing	change	VERB
ejpam-6306	197	21	variables	variable	NOUN
ejpam-6306	197	22	µ	µ	X
ejpam-6306	197	23	=	=	SYM
ejpam-6306	197	24	υ̌−1(β2	υ̌−1(β2	NOUN
ejpam-6306	197	25	υ̌(α)+	υ̌(α)+	NOUN
ejpam-6306	197	26	(	(	PUNCT
ejpam-6306	197	27	2−β	2−β	NUM
ejpam-6306	197	28	2	2	NUM
ejpam-6306	197	29	)	)	PUNCT
ejpam-6306	197	30	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	197	31	)	)	PUNCT
ejpam-6306	197	32	)	)	PUNCT
ejpam-6306	197	33	and	and	CCONJ
ejpam-6306	197	34	ω	ω	X
ejpam-6306	197	35	=	=	PUNCT
ejpam-6306	198	1	υ̌−1(2−β	υ̌−1(2−β	ADP
ejpam-6306	198	2	2	2	X
ejpam-6306	198	3	)	)	PUNCT
ejpam-6306	198	4	υ̌(α)+	υ̌(α)+	NOUN
ejpam-6306	198	5	β	β	X
ejpam-6306	198	6	2	2	NUM
ejpam-6306	198	7	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	198	8	)	)	PUNCT
ejpam-6306	198	9	)	)	PUNCT
ejpam-6306	198	10	in	in	ADP
ejpam-6306	198	11	(	(	PUNCT
ejpam-6306	198	12	19	19	NUM
ejpam-6306	198	13	)	)	PUNCT
ejpam-6306	198	14	,	,	PUNCT
ejpam-6306	198	15	we	we	PRON
ejpam-6306	198	16	obtain	obtain	VERB
ejpam-6306	198	17	2f	2f	NUM
ejpam-6306	198	18	(	(	PUNCT
ejpam-6306	198	19	υ̌−1	υ̌−1	X
ejpam-6306	198	20	(	(	PUNCT
ejpam-6306	198	21	υ̌(α	υ̌(α	PROPN
ejpam-6306	198	22	)	)	PUNCT
ejpam-6306	198	23	+	+	CCONJ
ejpam-6306	198	24	υ̌(ρ	υ̌(ρ	X
ejpam-6306	198	25	)	)	PUNCT
ejpam-6306	198	26	2	2	NUM
ejpam-6306	198	27	)	)	PUNCT
ejpam-6306	198	28	)	)	PUNCT
ejpam-6306	199	1	∫	∫	PROPN
ejpam-6306	199	2	1	1	NUM
ejpam-6306	199	3	0	0	NUM
ejpam-6306	199	4	(	(	PUNCT
ejpam-6306	199	5	1−	1−	NUM
ejpam-6306	199	6	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	199	7	,	,	PUNCT
ejpam-6306	199	8	κ	κ	NOUN
ejpam-6306	199	9	ν	ν	PROPN
ejpam-6306	199	10	,	,	PUNCT
ejpam-6306	199	11	τ	τ	PROPN
ejpam-6306	199	12	,	,	PUNCT
ejpam-6306	199	13	j	j	PROPN
ejpam-6306	199	14	(	(	PUNCT
ejpam-6306	199	15	(	(	PUNCT
ejpam-6306	199	16	1−	1−	NUM
ejpam-6306	199	17	β)v)dβ	β)v)dβ	PRON
ejpam-6306	199	18	≤	≤	NOUN
ejpam-6306	199	19	∞∑	∞∑	NUM
ejpam-6306	199	20	n=0	n=0	ADJ
ejpam-6306	199	21	ϑκn	ϑκn	ADJ
ejpam-6306	199	22	γ(τ	γ(τ	PROPN
ejpam-6306	199	23	+	+	NUM
ejpam-6306	199	24	vn)(µ)δn	vn)(µ)δn	NUM
ejpam-6306	199	25	∫	∫	PROPN
ejpam-6306	199	26	ρ	ρ	PROPN
ejpam-6306	199	27	υ̌−1	υ̌−1	PROPN
ejpam-6306	199	28	(	(	PUNCT
ejpam-6306	199	29	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	199	30	)	)	PUNCT
ejpam-6306	199	31	2	2	NUM
ejpam-6306	199	32	)	)	PUNCT
ejpam-6306	199	33	(	(	PUNCT
ejpam-6306	199	34	1−	1−	NUM
ejpam-6306	199	35	2	2	NUM
ejpam-6306	199	36	(	(	PUNCT
ejpam-6306	199	37	υ̌(µ)−	υ̌(µ)−	NOUN
ejpam-6306	199	38	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	199	39	)	)	PUNCT
ejpam-6306	199	40	υ̌(α)−	υ̌(α)−	PUNCT
ejpam-6306	199	41	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	199	42	)	)	PUNCT
ejpam-6306	199	43	)	)	PUNCT
ejpam-6306	199	44	)	)	PUNCT
ejpam-6306	200	1	τ−1	τ−1	PROPN
ejpam-6306	200	2	×	×	NOUN
ejpam-6306	200	3	(	(	PUNCT
ejpam-6306	200	4	(	(	PUNCT
ejpam-6306	200	5	1−	1−	NUM
ejpam-6306	200	6	2	2	NUM
ejpam-6306	200	7	(	(	PUNCT
ejpam-6306	200	8	υ̌(µ)−	υ̌(µ)−	NOUN
ejpam-6306	200	9	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	200	10	)	)	PUNCT
ejpam-6306	200	11	υ̌(α)−	υ̌(α)−	PUNCT
ejpam-6306	200	12	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	200	13	)	)	PUNCT
ejpam-6306	200	14	)	)	PUNCT
ejpam-6306	200	15	)	)	PUNCT
ejpam-6306	200	16	v)n	v)n	NOUN
ejpam-6306	200	17	f(µ	f(µ	NUM
ejpam-6306	200	18	)	)	PUNCT
ejpam-6306	200	19	2υ̌′(µ	2υ̌′(µ	NUM
ejpam-6306	200	20	)	)	PUNCT
ejpam-6306	200	21	υ̌(α)−	υ̌(α)−	PUNCT
ejpam-6306	200	22	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	200	23	)	)	PUNCT
ejpam-6306	200	24	+	+	CCONJ
ejpam-6306	200	25	∞∑	∞∑	ADJ
ejpam-6306	200	26	n=0	n=0	ADJ
ejpam-6306	200	27	ϑκn	ϑκn	ADJ
ejpam-6306	200	28	γ(τ	γ(τ	PROPN
ejpam-6306	200	29	+	+	SYM
ejpam-6306	200	30	vn)(z)δn	vn)(z)δn	NUM
ejpam-6306	200	31	∫	∫	PROPN
ejpam-6306	200	32	α	α	PROPN
ejpam-6306	200	33	υ̌−1	υ̌−1	PROPN
ejpam-6306	200	34	(	(	PUNCT
ejpam-6306	200	35	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	200	36	)	)	PUNCT
ejpam-6306	200	37	2	2	NUM
ejpam-6306	200	38	)	)	PUNCT
ejpam-6306	200	39	(	(	PUNCT
ejpam-6306	200	40	1−	1−	NUM
ejpam-6306	200	41	2	2	NUM
ejpam-6306	200	42	(	(	PUNCT
ejpam-6306	200	43	υ̌(ω)−	υ̌(ω)−	NOUN
ejpam-6306	200	44	υ̌(α	υ̌(α	NUM
ejpam-6306	200	45	)	)	PUNCT
ejpam-6306	200	46	υ̌(α)−	υ̌(α)−	PUNCT
ejpam-6306	200	47	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	200	48	)	)	PUNCT
ejpam-6306	200	49	)	)	PUNCT
ejpam-6306	200	50	)	)	PUNCT
ejpam-6306	201	1	τ−1	τ−1	PROPN
ejpam-6306	201	2	×	×	NOUN
ejpam-6306	201	3	(	(	PUNCT
ejpam-6306	201	4	(	(	PUNCT
ejpam-6306	201	5	1−	1−	NUM
ejpam-6306	201	6	2	2	NUM
ejpam-6306	201	7	(	(	PUNCT
ejpam-6306	201	8	υ̌(ω)−	υ̌(ω)−	NOUN
ejpam-6306	201	9	υ̌(α	υ̌(α	NUM
ejpam-6306	201	10	)	)	PUNCT
ejpam-6306	201	11	υ̌(α)−	υ̌(α)−	PUNCT
ejpam-6306	201	12	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	201	13	)	)	PUNCT
ejpam-6306	201	14	)	)	PUNCT
ejpam-6306	201	15	)	)	PUNCT
ejpam-6306	201	16	v)n	v)n	NOUN
ejpam-6306	201	17	f(ω	f(ω	PROPN
ejpam-6306	201	18	)	)	PUNCT
ejpam-6306	201	19	2υ̌′(ω	2υ̌′(ω	NUM
ejpam-6306	201	20	)	)	PUNCT
ejpam-6306	201	21	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	201	22	υ̌(α	υ̌(α	NUM
ejpam-6306	201	23	)	)	PUNCT
ejpam-6306	201	24	dω	dω	ADV
ejpam-6306	201	25	.	.	PUNCT
ejpam-6306	202	1	it	it	PRON
ejpam-6306	202	2	gives	give	VERB
ejpam-6306	202	3	that	that	DET
ejpam-6306	202	4	2f	2f	NUM
ejpam-6306	202	5	(	(	PUNCT
ejpam-6306	202	6	υ̌−1	υ̌−1	X
ejpam-6306	202	7	(	(	PUNCT
ejpam-6306	202	8	υ̌(α	υ̌(α	PROPN
ejpam-6306	202	9	)	)	PUNCT
ejpam-6306	202	10	+	+	CCONJ
ejpam-6306	202	11	υ̌(ρ	υ̌(ρ	X
ejpam-6306	202	12	)	)	PUNCT
ejpam-6306	202	13	2	2	NUM
ejpam-6306	202	14	)	)	PUNCT
ejpam-6306	202	15	)	)	PUNCT
ejpam-6306	203	1	∞∑	∞∑	PRON
ejpam-6306	203	2	n=0	n=0	NUM
ejpam-6306	203	3	ϑκn	ϑκn	ADJ
ejpam-6306	203	4	γ(τ	γ(τ	PROPN
ejpam-6306	203	5	+	+	SYM
ejpam-6306	203	6	vn)(z)δn	vn)(z)δn	NUM
ejpam-6306	203	7	∫	∫	PROPN
ejpam-6306	203	8	1	1	NUM
ejpam-6306	203	9	0	0	NUM
ejpam-6306	203	10	(	(	PUNCT
ejpam-6306	203	11	1−	1−	NUM
ejpam-6306	203	12	β)τ+vn−1dβ	β)τ+vn−1dβ	NUM
ejpam-6306	203	13	≤	≤	NOUN
ejpam-6306	203	14	2	2	NUM
ejpam-6306	203	15	∞∑	∞∑	NUM
ejpam-6306	203	16	n=0	n=0	NUM
ejpam-6306	203	17	ϑκn	ϑκn	ADJ
ejpam-6306	203	18	γ(τ	γ(τ	PROPN
ejpam-6306	203	19	+	+	SYM
ejpam-6306	203	20	vn)(z)δn	vn)(z)δn	NUM
ejpam-6306	203	21	∫	∫	PROPN
ejpam-6306	203	22	ρ	ρ	PROPN
ejpam-6306	203	23	υ̌−1	υ̌−1	PROPN
ejpam-6306	203	24	(	(	PUNCT
ejpam-6306	203	25	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	203	26	)	)	PUNCT
ejpam-6306	203	27	2	2	NUM
ejpam-6306	203	28	)	)	PUNCT
ejpam-6306	203	29	(	(	PUNCT
ejpam-6306	203	30	υ̌(α	υ̌(α	PROPN
ejpam-6306	203	31	)	)	PUNCT
ejpam-6306	203	32	+	+	CCONJ
ejpam-6306	203	33	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	203	34	2υ̌(µ	2υ̌(µ	NUM
ejpam-6306	203	35	)	)	PUNCT
ejpam-6306	203	36	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	203	37	υ̌(α	υ̌(α	NUM
ejpam-6306	203	38	)	)	PUNCT
ejpam-6306	203	39	)	)	PUNCT
ejpam-6306	204	1	τ−1	τ−1	PROPN
ejpam-6306	204	2	×	×	NOUN
ejpam-6306	204	3	(	(	PUNCT
ejpam-6306	204	4	(	(	PUNCT
ejpam-6306	204	5	υ̌(α	υ̌(α	PROPN
ejpam-6306	204	6	)	)	PUNCT
ejpam-6306	204	7	+	+	CCONJ
ejpam-6306	204	8	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	204	9	2υ̌(µ	2υ̌(µ	NUM
ejpam-6306	204	10	)	)	PUNCT
ejpam-6306	204	11	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	204	12	υ̌(α	υ̌(α	NUM
ejpam-6306	204	13	)	)	PUNCT
ejpam-6306	204	14	)	)	PUNCT
ejpam-6306	204	15	v)n	v)n	NOUN
ejpam-6306	204	16	υ̌′(µ	υ̌′(µ	ADJ
ejpam-6306	204	17	)	)	PUNCT
ejpam-6306	204	18	(	(	PUNCT
ejpam-6306	204	19	υ̌(v)−	υ̌(v)−	NUM
ejpam-6306	204	20	υ̌(u	υ̌(u	PROPN
ejpam-6306	204	21	)	)	PUNCT
ejpam-6306	204	22	)	)	PUNCT
ejpam-6306	204	23	f(µ)dµ	f(µ)dµ	PROPN
ejpam-6306	205	1	+	+	CCONJ
ejpam-6306	205	2	∫	∫	PROPN
ejpam-6306	205	3	α	α	X
ejpam-6306	205	4	υ̌−1	υ̌−1	PROPN
ejpam-6306	205	5	(	(	PUNCT
ejpam-6306	205	6	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	205	7	)	)	PUNCT
ejpam-6306	205	8	2	2	NUM
ejpam-6306	205	9	)	)	PUNCT
ejpam-6306	205	10	(	(	PUNCT
ejpam-6306	205	11	υ̌(α	υ̌(α	PROPN
ejpam-6306	205	12	)	)	PUNCT
ejpam-6306	205	13	+	+	CCONJ
ejpam-6306	205	14	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	205	15	2υ̌(ω	2υ̌(ω	NUM
ejpam-6306	205	16	)	)	PUNCT
ejpam-6306	205	17	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	205	18	υ̌(α	υ̌(α	NUM
ejpam-6306	205	19	)	)	PUNCT
ejpam-6306	205	20	)	)	PUNCT
ejpam-6306	206	1	τ−1	τ−1	PROPN
ejpam-6306	206	2	×	×	NOUN
ejpam-6306	206	3	(	(	PUNCT
ejpam-6306	206	4	(	(	PUNCT
ejpam-6306	206	5	υ̌(α	υ̌(α	PROPN
ejpam-6306	206	6	)	)	PUNCT
ejpam-6306	206	7	+	+	CCONJ
ejpam-6306	206	8	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	206	9	2υ̌(ω	2υ̌(ω	NUM
ejpam-6306	206	10	)	)	PUNCT
ejpam-6306	206	11	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	206	12	υ̌(α	υ̌(α	NUM
ejpam-6306	206	13	)	)	PUNCT
ejpam-6306	206	14	)	)	PUNCT
ejpam-6306	206	15	v)n	v)n	NOUN
ejpam-6306	206	16	υ̌′(ω	υ̌′(ω	NOUN
ejpam-6306	206	17	)	)	PUNCT
ejpam-6306	206	18	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	206	19	υ̌(α	υ̌(α	NUM
ejpam-6306	206	20	)	)	PUNCT
ejpam-6306	206	21	f(ω)dω	f(ω)dω	NOUN
ejpam-6306	206	22	.	.	PUNCT
ejpam-6306	207	1	hence	hence	ADV
ejpam-6306	207	2	,	,	PUNCT
ejpam-6306	207	3	2f	2f	NUM
ejpam-6306	207	4	(	(	PUNCT
ejpam-6306	207	5	υ̌−1	υ̌−1	X
ejpam-6306	207	6	(	(	PUNCT
ejpam-6306	207	7	υ̌(α	υ̌(α	PROPN
ejpam-6306	207	8	)	)	PUNCT
ejpam-6306	207	9	+	+	CCONJ
ejpam-6306	207	10	υ̌(ρ	υ̌(ρ	X
ejpam-6306	207	11	)	)	PUNCT
ejpam-6306	207	12	2	2	NUM
ejpam-6306	207	13	)	)	PUNCT
ejpam-6306	207	14	)	)	PUNCT
ejpam-6306	207	15	eϑ,z	eϑ,z	NOUN
ejpam-6306	207	16	,	,	PUNCT
ejpam-6306	207	17	κ	κ	X
ejpam-6306	207	18	ν	ν	PROPN
ejpam-6306	207	19	,	,	PUNCT
ejpam-6306	207	20	τ	τ	PROPN
ejpam-6306	207	21	,	,	PUNCT
ejpam-6306	207	22	j	j	PROPN
ejpam-6306	207	23	(	(	PUNCT
ejpam-6306	207	24	(	(	PUNCT
ejpam-6306	207	25	1−	1−	NUM
ejpam-6306	207	26	β)v	β)v	NOUN
ejpam-6306	207	27	)	)	PUNCT
ejpam-6306	207	28	≤	≤	NUM
ejpam-6306	207	29	2	2	NUM
ejpam-6306	207	30	(	(	PUNCT
ejpam-6306	207	31	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	207	32	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	207	33	[	[	PUNCT
ejpam-6306	207	34	∞∑	∞∑	ADJ
ejpam-6306	207	35	n=0	n=0	NUM
ejpam-6306	207	36	ϑκn(ξ(µ	ϑκn(ξ(µ	NOUN
ejpam-6306	207	37	)	)	PUNCT
ejpam-6306	207	38	v)n	v)n	NOUN
ejpam-6306	208	1	γ(τ	γ(τ	PROPN
ejpam-6306	208	2	+	+	NUM
ejpam-6306	208	3	vn)(z)δn	vn)(z)δn	NUM
ejpam-6306	208	4	×	×	NOUN
ejpam-6306	208	5	∫	∫	PROPN
ejpam-6306	208	6	ρ	ρ	PROPN
ejpam-6306	208	7	υ̌−1	υ̌−1	PROPN
ejpam-6306	208	8	(	(	PUNCT
ejpam-6306	208	9	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	208	10	)	)	PUNCT
ejpam-6306	208	11	2	2	NUM
ejpam-6306	208	12	)	)	PUNCT
ejpam-6306	208	13	(	(	PUNCT
ejpam-6306	208	14	υ̌(α	υ̌(α	PROPN
ejpam-6306	208	15	)	)	PUNCT
ejpam-6306	208	16	+	+	CCONJ
ejpam-6306	208	17	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	208	18	2υ̌(µ	2υ̌(µ	NUM
ejpam-6306	208	19	)	)	PUNCT
ejpam-6306	208	20	)	)	PUNCT
ejpam-6306	209	1	τ−1	τ−1	PROPN
ejpam-6306	209	2	υ̌′(µ)f(µ)dµ	υ̌′(µ)f(µ)dµ	PROPN
ejpam-6306	210	1	+	+	PUNCT
ejpam-6306	210	2	∞∑	∞∑	ADJ
ejpam-6306	210	3	n=0	n=0	NUM
ejpam-6306	210	4	ϑκn(ξ(ω	ϑκn(ξ(ω	NOUN
ejpam-6306	210	5	)	)	PUNCT
ejpam-6306	210	6	v)n	v)n	NOUN
ejpam-6306	210	7	γ(τ	γ(τ	PROPN
ejpam-6306	210	8	+	+	SYM
ejpam-6306	210	9	vn)(z)δn	vn)(z)δn	NUM
ejpam-6306	211	1	∫	∫	PROPN
ejpam-6306	211	2	α	α	PROPN
ejpam-6306	211	3	υ̌−1	υ̌−1	PROPN
ejpam-6306	211	4	(	(	PUNCT
ejpam-6306	211	5	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	211	6	)	)	PUNCT
ejpam-6306	211	7	2	2	NUM
ejpam-6306	211	8	)	)	PUNCT
ejpam-6306	211	9	(	(	PUNCT
ejpam-6306	211	10	υ̌(α	υ̌(α	PROPN
ejpam-6306	211	11	)	)	PUNCT
ejpam-6306	211	12	+	+	CCONJ
ejpam-6306	211	13	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	211	14	2υ̌(ω	2υ̌(ω	NUM
ejpam-6306	211	15	)	)	PUNCT
ejpam-6306	211	16	)	)	PUNCT
ejpam-6306	212	1	τ−1	τ−1	PROPN
ejpam-6306	213	1	υ̌′(ω)f(ω)dω	υ̌′(ω)f(ω)dω	PROPN
ejpam-6306	213	2	]	]	PUNCT
ejpam-6306	213	3	,	,	PUNCT
ejpam-6306	213	4	r.	r.	PROPN
ejpam-6306	213	5	s.	s.	PROPN
ejpam-6306	213	6	ali	ali	PROPN
ejpam-6306	213	7	et	et	PROPN
ejpam-6306	213	8	al	al	PROPN
ejpam-6306	213	9	.	.	PUNCT
ejpam-6306	213	10	/	/	SYM
ejpam-6306	213	11	eur	eur	PROPN
ejpam-6306	213	12	.	.	PUNCT
ejpam-6306	214	1	j.	j.	PROPN
ejpam-6306	214	2	pure	pure	PROPN
ejpam-6306	214	3	appl	appl	PROPN
ejpam-6306	214	4	.	.	PROPN
ejpam-6306	214	5	math	math	PROPN
ejpam-6306	214	6	,	,	PUNCT
ejpam-6306	214	7	18	18	NUM
ejpam-6306	214	8	(	(	PUNCT
ejpam-6306	214	9	3	3	NUM
ejpam-6306	214	10	)	)	PUNCT
ejpam-6306	214	11	(	(	PUNCT
ejpam-6306	214	12	2025	2025	NUM
ejpam-6306	214	13	)	)	PUNCT
ejpam-6306	214	14	,	,	PUNCT
ejpam-6306	214	15	6306	6306	NUM
ejpam-6306	214	16	11	11	NUM
ejpam-6306	214	17	of	of	ADP
ejpam-6306	214	18	18	18	NUM
ejpam-6306	214	19	and	and	CCONJ
ejpam-6306	214	20	finally	finally	ADV
ejpam-6306	214	21	,	,	PUNCT
ejpam-6306	214	22	f	f	PROPN
ejpam-6306	214	23	(	(	PUNCT
ejpam-6306	214	24	υ̌−1	υ̌−1	X
ejpam-6306	214	25	(	(	PUNCT
ejpam-6306	214	26	υ̌(α	υ̌(α	PROPN
ejpam-6306	214	27	)	)	PUNCT
ejpam-6306	214	28	+	+	CCONJ
ejpam-6306	214	29	υ̌(ρ	υ̌(ρ	X
ejpam-6306	214	30	)	)	PUNCT
ejpam-6306	214	31	2	2	NUM
ejpam-6306	214	32	)	)	PUNCT
ejpam-6306	214	33	)	)	PUNCT
ejpam-6306	214	34	eϑ,z	eϑ,z	NOUN
ejpam-6306	214	35	,	,	PUNCT
ejpam-6306	214	36	κ	κ	X
ejpam-6306	214	37	ν	ν	PROPN
ejpam-6306	214	38	,	,	PUNCT
ejpam-6306	214	39	τ	τ	PROPN
ejpam-6306	214	40	,	,	PUNCT
ejpam-6306	214	41	j	j	PROPN
ejpam-6306	214	42	(	(	PUNCT
ejpam-6306	214	43	(	(	PUNCT
ejpam-6306	214	44	1−	1−	NUM
ejpam-6306	214	45	β)v	β)v	NOUN
ejpam-6306	214	46	)	)	PUNCT
ejpam-6306	214	47	(	(	PUNCT
ejpam-6306	214	48	20	20	NUM
ejpam-6306	214	49	)	)	PUNCT
ejpam-6306	214	50	≤	≤	NOUN
ejpam-6306	214	51	1	1	NUM
ejpam-6306	214	52	(	(	PUNCT
ejpam-6306	214	53	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	214	54	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	214	55	[	[	PUNCT
ejpam-6306	214	56	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	214	57	,	,	PUNCT
ejpam-6306	214	58	κ	κ	NOUN
ejpam-6306	214	59	ν	ν	PROPN
ejpam-6306	214	60	,	,	PUNCT
ejpam-6306	214	61	τ	τ	PROPN
ejpam-6306	214	62	,	,	PUNCT
ejpam-6306	214	63	j	j	PROPN
ejpam-6306	214	64	,	,	PUNCT
ejpam-6306	214	65	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	214	66	(	(	PUNCT
ejpam-6306	214	67	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	214	68	)	)	PUNCT
ejpam-6306	214	69	2	2	NUM
ejpam-6306	214	70	)	)	PUNCT
ejpam-6306	214	71	)	)	PUNCT
ejpam-6306	215	1	+	+	PUNCT
ejpam-6306	215	2	f(α	f(α	NOUN
ejpam-6306	215	3	)	)	PUNCT
ejpam-6306	215	4	+	+	CCONJ
ejpam-6306	216	1	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	216	2	,	,	PUNCT
ejpam-6306	216	3	κ	κ	NOUN
ejpam-6306	216	4	ν	ν	PROPN
ejpam-6306	216	5	,	,	PUNCT
ejpam-6306	216	6	τ	τ	PROPN
ejpam-6306	216	7	,	,	PUNCT
ejpam-6306	216	8	j	j	PROPN
ejpam-6306	216	9	,	,	PUNCT
ejpam-6306	216	10	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	216	11	(	(	PUNCT
ejpam-6306	216	12	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	216	13	)	)	PUNCT
ejpam-6306	216	14	2	2	NUM
ejpam-6306	216	15	)	)	PUNCT
ejpam-6306	216	16	)	)	PUNCT
ejpam-6306	216	17	−	−	ADP
ejpam-6306	216	18	f(ρ	f(ρ	NOUN
ejpam-6306	216	19	)	)	PUNCT
ejpam-6306	216	20	]	]	PUNCT
ejpam-6306	216	21	.	.	PUNCT
ejpam-6306	217	1	now	now	ADV
ejpam-6306	217	2	,	,	PUNCT
ejpam-6306	217	3	for	for	ADP
ejpam-6306	217	4	the	the	DET
ejpam-6306	217	5	second	second	ADJ
ejpam-6306	217	6	inequality	inequality	NOUN
ejpam-6306	217	7	,	,	PUNCT
ejpam-6306	217	8	we	we	PRON
ejpam-6306	217	9	consider	consider	VERB
ejpam-6306	217	10	the	the	DET
ejpam-6306	217	11	υ̌-convexity	υ̌-convexity	NOUN
ejpam-6306	217	12	f	f	X
ejpam-6306	217	13	(	(	PUNCT
ejpam-6306	217	14	υ̌−1	υ̌−1	X
ejpam-6306	217	15	(	(	PUNCT
ejpam-6306	217	16	β	β	X
ejpam-6306	217	17	2	2	NUM
ejpam-6306	217	18	υ̌(α	υ̌(α	NUM
ejpam-6306	217	19	)	)	PUNCT
ejpam-6306	217	20	+	+	CCONJ
ejpam-6306	218	1	(	(	PUNCT
ejpam-6306	218	2	2−	2−	NUM
ejpam-6306	218	3	β	β	SYM
ejpam-6306	218	4	2	2	NUM
ejpam-6306	218	5	)	)	PUNCT
ejpam-6306	218	6	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	218	7	)	)	PUNCT
ejpam-6306	218	8	)	)	PUNCT
ejpam-6306	218	9	)	)	PUNCT
ejpam-6306	219	1	≤	≤	NUM
ejpam-6306	219	2	β	β	X
ejpam-6306	219	3	2	2	NUM
ejpam-6306	219	4	f(α	f(α	NOUN
ejpam-6306	219	5	)	)	PUNCT
ejpam-6306	220	1	+	+	CCONJ
ejpam-6306	220	2	(	(	PUNCT
ejpam-6306	220	3	2−	2−	NUM
ejpam-6306	220	4	β	β	SYM
ejpam-6306	220	5	2	2	NUM
ejpam-6306	220	6	)	)	PUNCT
ejpam-6306	220	7	f(ρ	f(ρ	NOUN
ejpam-6306	220	8	)	)	PUNCT
ejpam-6306	220	9	,	,	PUNCT
ejpam-6306	220	10	(	(	PUNCT
ejpam-6306	220	11	21	21	NUM
ejpam-6306	220	12	)	)	PUNCT
ejpam-6306	220	13	and	and	CCONJ
ejpam-6306	220	14	f	f	PROPN
ejpam-6306	220	15	(	(	PUNCT
ejpam-6306	220	16	υ̌−1	υ̌−1	X
ejpam-6306	220	17	(	(	PUNCT
ejpam-6306	220	18	(	(	PUNCT
ejpam-6306	220	19	2−	2−	NUM
ejpam-6306	220	20	β	β	SYM
ejpam-6306	220	21	2	2	NUM
ejpam-6306	220	22	)	)	PUNCT
ejpam-6306	220	23	υ̌(α	υ̌(α	NUM
ejpam-6306	220	24	)	)	PUNCT
ejpam-6306	221	1	+	+	CCONJ
ejpam-6306	221	2	β	β	X
ejpam-6306	221	3	2	2	NUM
ejpam-6306	221	4	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	221	5	)	)	PUNCT
ejpam-6306	221	6	)	)	PUNCT
ejpam-6306	221	7	)	)	PUNCT
ejpam-6306	222	1	≤	≤	NUM
ejpam-6306	222	2	(	(	PUNCT
ejpam-6306	222	3	2−	2−	NUM
ejpam-6306	222	4	β	β	SYM
ejpam-6306	222	5	2	2	NUM
ejpam-6306	222	6	)	)	PUNCT
ejpam-6306	222	7	f(α	f(α	NOUN
ejpam-6306	222	8	)	)	PUNCT
ejpam-6306	222	9	+	+	CCONJ
ejpam-6306	222	10	β	β	NOUN
ejpam-6306	222	11	2	2	NUM
ejpam-6306	222	12	f(ρ	f(ρ	NOUN
ejpam-6306	222	13	)	)	PUNCT
ejpam-6306	222	14	.	.	PUNCT
ejpam-6306	223	1	(	(	PUNCT
ejpam-6306	223	2	22	22	NUM
ejpam-6306	223	3	)	)	PUNCT
ejpam-6306	223	4	by	by	ADP
ejpam-6306	223	5	adding	add	VERB
ejpam-6306	223	6	the	the	DET
ejpam-6306	223	7	two	two	NUM
ejpam-6306	223	8	inequalities	inequality	NOUN
ejpam-6306	223	9	given	give	VERB
ejpam-6306	223	10	in	in	ADP
ejpam-6306	223	11	(	(	PUNCT
ejpam-6306	223	12	21	21	NUM
ejpam-6306	223	13	)	)	PUNCT
ejpam-6306	223	14	and	and	CCONJ
ejpam-6306	223	15	(	(	PUNCT
ejpam-6306	223	16	22	22	NUM
ejpam-6306	223	17	)	)	PUNCT
ejpam-6306	223	18	,	,	PUNCT
ejpam-6306	223	19	we	we	PRON
ejpam-6306	223	20	get	get	VERB
ejpam-6306	223	21	f	f	X
ejpam-6306	223	22	(	(	PUNCT
ejpam-6306	223	23	υ̌−1	υ̌−1	X
ejpam-6306	223	24	(	(	PUNCT
ejpam-6306	223	25	β	β	X
ejpam-6306	223	26	2	2	NUM
ejpam-6306	223	27	υ̌(α	υ̌(α	NUM
ejpam-6306	223	28	)	)	PUNCT
ejpam-6306	223	29	+	+	CCONJ
ejpam-6306	223	30	(	(	PUNCT
ejpam-6306	223	31	2−	2−	NUM
ejpam-6306	223	32	β	β	SYM
ejpam-6306	223	33	2	2	NUM
ejpam-6306	223	34	)	)	PUNCT
ejpam-6306	223	35	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	223	36	)	)	PUNCT
ejpam-6306	223	37	)	)	PUNCT
ejpam-6306	223	38	)	)	PUNCT
ejpam-6306	224	1	+	+	CCONJ
ejpam-6306	225	1	f	f	X
ejpam-6306	225	2	(	(	PUNCT
ejpam-6306	225	3	υ̌−1	υ̌−1	X
ejpam-6306	225	4	(	(	PUNCT
ejpam-6306	225	5	(	(	PUNCT
ejpam-6306	225	6	2−	2−	NUM
ejpam-6306	225	7	β	β	SYM
ejpam-6306	225	8	2	2	NUM
ejpam-6306	225	9	)	)	PUNCT
ejpam-6306	225	10	υ̌(α	υ̌(α	NUM
ejpam-6306	225	11	)	)	PUNCT
ejpam-6306	225	12	+	+	CCONJ
ejpam-6306	225	13	β	β	X
ejpam-6306	225	14	2	2	NUM
ejpam-6306	225	15	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	225	16	)	)	PUNCT
ejpam-6306	225	17	)	)	PUNCT
ejpam-6306	225	18	)	)	PUNCT
ejpam-6306	225	19	≤	≤	NUM
ejpam-6306	225	20	f(α	f(α	NOUN
ejpam-6306	225	21	)	)	PUNCT
ejpam-6306	225	22	+	+	NUM
ejpam-6306	225	23	f(ρ	f(ρ	NOUN
ejpam-6306	225	24	)	)	PUNCT
ejpam-6306	225	25	.	.	PUNCT
ejpam-6306	226	1	(	(	PUNCT
ejpam-6306	226	2	23	23	X
ejpam-6306	226	3	)	)	PUNCT
ejpam-6306	226	4	multiplying	multiply	VERB
ejpam-6306	226	5	both	both	DET
ejpam-6306	226	6	sides	side	NOUN
ejpam-6306	226	7	by	by	ADP
ejpam-6306	226	8	(	(	PUNCT
ejpam-6306	226	9	1−	1−	NUM
ejpam-6306	226	10	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	226	11	,	,	PUNCT
ejpam-6306	226	12	κ	κ	NOUN
ejpam-6306	226	13	ν	ν	PROPN
ejpam-6306	226	14	,	,	PUNCT
ejpam-6306	226	15	τ	τ	PROPN
ejpam-6306	226	16	,	,	PUNCT
ejpam-6306	226	17	j	j	PROPN
ejpam-6306	226	18	(	(	PUNCT
ejpam-6306	226	19	1−	1−	NUM
ejpam-6306	226	20	β)v	β)v	X
ejpam-6306	226	21	of	of	ADP
ejpam-6306	226	22	equation	equation	NOUN
ejpam-6306	226	23	(	(	PUNCT
ejpam-6306	226	24	23	23	NUM
ejpam-6306	226	25	)	)	PUNCT
ejpam-6306	226	26	,	,	PUNCT
ejpam-6306	226	27	then	then	ADV
ejpam-6306	226	28	integrating	integrate	VERB
ejpam-6306	226	29	the	the	DET
ejpam-6306	226	30	resulting	result	VERB
ejpam-6306	226	31	inequality	inequality	NOUN
ejpam-6306	226	32	with	with	ADP
ejpam-6306	226	33	respect	respect	NOUN
ejpam-6306	226	34	to	to	ADP
ejpam-6306	226	35	β	β	NOUN
ejpam-6306	226	36	over	over	ADP
ejpam-6306	226	37	[	[	X
ejpam-6306	226	38	0	0	NUM
ejpam-6306	226	39	,	,	PUNCT
ejpam-6306	226	40	1	1	NUM
ejpam-6306	226	41	]	]	PUNCT
ejpam-6306	226	42	,	,	PUNCT
ejpam-6306	226	43	we	we	PRON
ejpam-6306	226	44	get∫	get∫	VERB
ejpam-6306	226	45	0	0	NUM
ejpam-6306	226	46	1	1	NUM
ejpam-6306	226	47	(	(	PUNCT
ejpam-6306	226	48	1−	1−	NUM
ejpam-6306	226	49	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	226	50	,	,	PUNCT
ejpam-6306	226	51	κ	κ	NOUN
ejpam-6306	226	52	ν	ν	PROPN
ejpam-6306	226	53	,	,	PUNCT
ejpam-6306	226	54	τ	τ	PROPN
ejpam-6306	226	55	,	,	PUNCT
ejpam-6306	226	56	j	j	PROPN
ejpam-6306	226	57	(	(	PUNCT
ejpam-6306	226	58	1−	1−	NUM
ejpam-6306	226	59	β)vf	β)vf	NOUN
ejpam-6306	226	60	(	(	PUNCT
ejpam-6306	226	61	υ̌−1	υ̌−1	X
ejpam-6306	226	62	(	(	PUNCT
ejpam-6306	226	63	β	β	X
ejpam-6306	226	64	2	2	NUM
ejpam-6306	226	65	υ̌(α	υ̌(α	NUM
ejpam-6306	226	66	)	)	PUNCT
ejpam-6306	227	1	+	+	CCONJ
ejpam-6306	227	2	(	(	PUNCT
ejpam-6306	227	3	2−	2−	NUM
ejpam-6306	227	4	β	β	SYM
ejpam-6306	227	5	2	2	NUM
ejpam-6306	227	6	)	)	PUNCT
ejpam-6306	227	7	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	227	8	)	)	PUNCT
ejpam-6306	227	9	)	)	PUNCT
ejpam-6306	227	10	)	)	PUNCT
ejpam-6306	228	1	dβ	dβ	ADP
ejpam-6306	228	2	+	+	NUM
ejpam-6306	228	3	∫	∫	PROPN
ejpam-6306	228	4	0	0	NUM
ejpam-6306	228	5	1	1	NUM
ejpam-6306	228	6	(	(	PUNCT
ejpam-6306	228	7	1−	1−	NUM
ejpam-6306	228	8	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	228	9	,	,	PUNCT
ejpam-6306	228	10	κ	κ	NOUN
ejpam-6306	228	11	ν	ν	PROPN
ejpam-6306	228	12	,	,	PUNCT
ejpam-6306	228	13	τ	τ	PROPN
ejpam-6306	228	14	,	,	PUNCT
ejpam-6306	228	15	j	j	PROPN
ejpam-6306	228	16	(	(	PUNCT
ejpam-6306	228	17	1−	1−	NUM
ejpam-6306	228	18	β)vf	β)vf	NOUN
ejpam-6306	228	19	(	(	PUNCT
ejpam-6306	228	20	υ̌−1	υ̌−1	X
ejpam-6306	228	21	(	(	PUNCT
ejpam-6306	228	22	(	(	PUNCT
ejpam-6306	228	23	2−	2−	NUM
ejpam-6306	228	24	β	β	SYM
ejpam-6306	228	25	2	2	NUM
ejpam-6306	228	26	)	)	PUNCT
ejpam-6306	228	27	υ̌(α	υ̌(α	NUM
ejpam-6306	228	28	)	)	PUNCT
ejpam-6306	228	29	+	+	CCONJ
ejpam-6306	228	30	β	β	X
ejpam-6306	228	31	2	2	NUM
ejpam-6306	228	32	υ̌(ρ	υ̌(ρ	PROPN
ejpam-6306	228	33	)	)	PUNCT
ejpam-6306	228	34	)	)	PUNCT
ejpam-6306	228	35	)	)	PUNCT
ejpam-6306	229	1	dβ	dβ	ADP
ejpam-6306	229	2	≤	≤	NUM
ejpam-6306	229	3	f(α	f(α	NOUN
ejpam-6306	229	4	)	)	PUNCT
ejpam-6306	229	5	+	+	NUM
ejpam-6306	229	6	f(ρ)(1−	f(ρ)(1−	NUM
ejpam-6306	229	7	β)τ−1eϑ,z	β)τ−1eϑ,z	NOUN
ejpam-6306	229	8	,	,	PUNCT
ejpam-6306	229	9	κ	κ	NOUN
ejpam-6306	229	10	ν	ν	PROPN
ejpam-6306	229	11	,	,	PUNCT
ejpam-6306	229	12	τ	τ	PROPN
ejpam-6306	229	13	,	,	PUNCT
ejpam-6306	229	14	j	j	PROPN
ejpam-6306	229	15	(	(	PUNCT
ejpam-6306	229	16	1−	1−	NUM
ejpam-6306	229	17	β)vdβ	β)vdβ	PROPN
ejpam-6306	229	18	1	1	NUM
ejpam-6306	229	19	(	(	PUNCT
ejpam-6306	229	20	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	229	21	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	229	22	×	×	NOUN
ejpam-6306	229	23	[	[	PUNCT
ejpam-6306	229	24	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	229	25	,	,	PUNCT
ejpam-6306	229	26	κ	κ	NOUN
ejpam-6306	229	27	ν	ν	PROPN
ejpam-6306	229	28	,	,	PUNCT
ejpam-6306	229	29	τ	τ	PROPN
ejpam-6306	229	30	,	,	PUNCT
ejpam-6306	229	31	j	j	PROPN
ejpam-6306	229	32	,	,	PUNCT
ejpam-6306	229	33	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	229	34	(	(	PUNCT
ejpam-6306	229	35	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	229	36	)	)	PUNCT
ejpam-6306	229	37	2	2	NUM
ejpam-6306	229	38	)	)	PUNCT
ejpam-6306	229	39	)	)	PUNCT
ejpam-6306	230	1	+	+	PUNCT
ejpam-6306	230	2	f(α	f(α	NOUN
ejpam-6306	230	3	)	)	PUNCT
ejpam-6306	230	4	+	+	CCONJ
ejpam-6306	231	1	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	231	2	,	,	PUNCT
ejpam-6306	231	3	κ	κ	NOUN
ejpam-6306	231	4	ν	ν	PROPN
ejpam-6306	231	5	,	,	PUNCT
ejpam-6306	231	6	τ	τ	PROPN
ejpam-6306	231	7	,	,	PUNCT
ejpam-6306	231	8	j	j	PROPN
ejpam-6306	231	9	,	,	PUNCT
ejpam-6306	231	10	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	231	11	(	(	PUNCT
ejpam-6306	231	12	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	231	13	)	)	PUNCT
ejpam-6306	231	14	2	2	NUM
ejpam-6306	231	15	)	)	PUNCT
ejpam-6306	231	16	)	)	PUNCT
ejpam-6306	231	17	−	−	ADP
ejpam-6306	231	18	f(ρ	f(ρ	NOUN
ejpam-6306	231	19	)	)	PUNCT
ejpam-6306	231	20	]	]	PUNCT
ejpam-6306	231	21	≤	≤	NUM
ejpam-6306	231	22	f(α	f(α	NOUN
ejpam-6306	231	23	)	)	PUNCT
ejpam-6306	231	24	+	+	NUM
ejpam-6306	231	25	f(ρ	f(ρ	NOUN
ejpam-6306	231	26	)	)	PUNCT
ejpam-6306	231	27	2	2	NUM
ejpam-6306	231	28	eϑ,z	eϑ,z	NOUN
ejpam-6306	231	29	,	,	PUNCT
ejpam-6306	231	30	κ	κ	X
ejpam-6306	231	31	ν	ν	PROPN
ejpam-6306	231	32	,	,	PUNCT
ejpam-6306	231	33	τ	τ	PROPN
ejpam-6306	231	34	,	,	PUNCT
ejpam-6306	231	35	j	j	PROPN
ejpam-6306	231	36	(	(	PUNCT
ejpam-6306	231	37	(	(	PUNCT
ejpam-6306	231	38	1−	1−	NUM
ejpam-6306	231	39	β)v	β)v	NOUN
ejpam-6306	231	40	)	)	PUNCT
ejpam-6306	231	41	.	.	PUNCT
ejpam-6306	232	1	(	(	PUNCT
ejpam-6306	232	2	24	24	NUM
ejpam-6306	232	3	)	)	PUNCT
ejpam-6306	232	4	from	from	ADP
ejpam-6306	232	5	the	the	DET
ejpam-6306	232	6	inequalities	inequality	NOUN
ejpam-6306	232	7	(	(	PUNCT
ejpam-6306	232	8	20	20	NUM
ejpam-6306	232	9	)	)	PUNCT
ejpam-6306	232	10	and	and	CCONJ
ejpam-6306	232	11	(	(	PUNCT
ejpam-6306	232	12	24	24	NUM
ejpam-6306	232	13	)	)	PUNCT
ejpam-6306	232	14	,	,	PUNCT
ejpam-6306	232	15	we	we	PRON
ejpam-6306	232	16	have	have	VERB
ejpam-6306	232	17	the	the	DET
ejpam-6306	232	18	required	require	VERB
ejpam-6306	232	19	result	result	NOUN
ejpam-6306	232	20	.	.	PUNCT
ejpam-6306	233	1	corollary	corollary	ADJ
ejpam-6306	233	2	4	4	NUM
ejpam-6306	233	3	.	.	PUNCT
ejpam-6306	233	4	specifically	specifically	ADV
ejpam-6306	233	5	,	,	PUNCT
ejpam-6306	233	6	in	in	ADP
ejpam-6306	233	7	theorem	theorem	NOUN
ejpam-6306	233	8	2	2	NUM
ejpam-6306	233	9	,	,	PUNCT
ejpam-6306	233	10	if	if	SCONJ
ejpam-6306	233	11	we	we	PRON
ejpam-6306	233	12	take	take	VERB
ejpam-6306	233	13	υ̌(x	υ̌(x	NUM
ejpam-6306	233	14	)	)	PUNCT
ejpam-6306	233	15	=	=	SYM
ejpam-6306	234	1	x	x	NOUN
ejpam-6306	234	2	,	,	PUNCT
ejpam-6306	234	3	then	then	ADV
ejpam-6306	234	4	the	the	DET
ejpam-6306	234	5	inequality	inequality	NOUN
ejpam-6306	234	6	(	(	PUNCT
ejpam-6306	234	7	16	16	NUM
ejpam-6306	234	8	)	)	PUNCT
ejpam-6306	234	9	is	be	AUX
ejpam-6306	234	10	simplified	simplify	VERB
ejpam-6306	234	11	to	to	ADP
ejpam-6306	234	12	the	the	DET
ejpam-6306	234	13	following	follow	VERB
ejpam-6306	234	14	inequality	inequality	NOUN
ejpam-6306	234	15	:	:	PUNCT
ejpam-6306	234	16	f	f	X
ejpam-6306	234	17	(	(	PUNCT
ejpam-6306	234	18	α+	α+	PROPN
ejpam-6306	234	19	ρ	ρ	PROPN
ejpam-6306	234	20	2	2	NUM
ejpam-6306	234	21	)	)	PUNCT
ejpam-6306	234	22	≤	≤	NOUN
ejpam-6306	234	23	1	1	NUM
ejpam-6306	234	24	(	(	PUNCT
ejpam-6306	234	25	ρ−	ρ−	NOUN
ejpam-6306	234	26	α)τ	α)τ	NUM
ejpam-6306	234	27	[	[	PUNCT
ejpam-6306	234	28	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	234	29	,	,	PUNCT
ejpam-6306	234	30	κ	κ	NOUN
ejpam-6306	234	31	ν	ν	PROPN
ejpam-6306	234	32	,	,	PUNCT
ejpam-6306	234	33	τ	τ	PROPN
ejpam-6306	234	34	,	,	PUNCT
ejpam-6306	234	35	j	j	PROPN
ejpam-6306	234	36	,	,	PUNCT
ejpam-6306	234	37	ω,(α+ρ	ω,(α+ρ	ADV
ejpam-6306	234	38	2	2	NUM
ejpam-6306	234	39	)	)	PUNCT
ejpam-6306	234	40	+	+	CCONJ
ejpam-6306	234	41	f(α	f(α	NOUN
ejpam-6306	234	42	)	)	PUNCT
ejpam-6306	234	43	+	+	CCONJ
ejpam-6306	234	44	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	234	45	,	,	PUNCT
ejpam-6306	234	46	κ	κ	NOUN
ejpam-6306	234	47	ν	ν	PROPN
ejpam-6306	234	48	,	,	PUNCT
ejpam-6306	234	49	τ	τ	PROPN
ejpam-6306	234	50	,	,	PUNCT
ejpam-6306	234	51	j	j	PROPN
ejpam-6306	234	52	,	,	PUNCT
ejpam-6306	234	53	ω,(α+ρ	ω,(α+ρ	ADV
ejpam-6306	234	54	2	2	NUM
ejpam-6306	234	55	)	)	PUNCT
ejpam-6306	234	56	−	−	PRON
ejpam-6306	234	57	f(ρ	f(ρ	NOUN
ejpam-6306	234	58	)	)	PUNCT
ejpam-6306	234	59	]	]	PUNCT
ejpam-6306	234	60	≤	≤	NUM
ejpam-6306	234	61	f(α	f(α	NOUN
ejpam-6306	234	62	)	)	PUNCT
ejpam-6306	234	63	+	+	NUM
ejpam-6306	234	64	f(ρ	f(ρ	NOUN
ejpam-6306	234	65	)	)	PUNCT
ejpam-6306	234	66	2	2	NUM
ejpam-6306	234	67	,	,	PUNCT
ejpam-6306	234	68	(	(	PUNCT
ejpam-6306	234	69	25	25	NUM
ejpam-6306	234	70	)	)	PUNCT
ejpam-6306	234	71	which	which	PRON
ejpam-6306	234	72	was	be	AUX
ejpam-6306	234	73	already	already	ADV
ejpam-6306	234	74	established	establish	VERB
ejpam-6306	234	75	in	in	ADP
ejpam-6306	234	76	[	[	X
ejpam-6306	234	77	29	29	NUM
ejpam-6306	234	78	]	]	PUNCT
ejpam-6306	234	79	.	.	PUNCT
ejpam-6306	235	1	r.	r.	PROPN
ejpam-6306	235	2	s.	s.	PROPN
ejpam-6306	235	3	ali	ali	PROPN
ejpam-6306	235	4	et	et	PROPN
ejpam-6306	235	5	al	al	PROPN
ejpam-6306	235	6	.	.	PUNCT
ejpam-6306	235	7	/	/	SYM
ejpam-6306	235	8	eur	eur	PROPN
ejpam-6306	235	9	.	.	PUNCT
ejpam-6306	236	1	j.	j.	PROPN
ejpam-6306	236	2	pure	pure	PROPN
ejpam-6306	236	3	appl	appl	PROPN
ejpam-6306	236	4	.	.	PROPN
ejpam-6306	236	5	math	math	PROPN
ejpam-6306	236	6	,	,	PUNCT
ejpam-6306	236	7	18	18	NUM
ejpam-6306	236	8	(	(	PUNCT
ejpam-6306	236	9	3	3	NUM
ejpam-6306	236	10	)	)	PUNCT
ejpam-6306	236	11	(	(	PUNCT
ejpam-6306	236	12	2025	2025	NUM
ejpam-6306	236	13	)	)	PUNCT
ejpam-6306	236	14	,	,	PUNCT
ejpam-6306	236	15	6306	6306	NUM
ejpam-6306	236	16	12	12	NUM
ejpam-6306	236	17	of	of	ADP
ejpam-6306	236	18	18	18	NUM
ejpam-6306	236	19	corollary	corollary	ADJ
ejpam-6306	236	20	5	5	NUM
ejpam-6306	236	21	.	.	PUNCT
ejpam-6306	237	1	if	if	SCONJ
ejpam-6306	237	2	we	we	PRON
ejpam-6306	237	3	take	take	VERB
ejpam-6306	237	4	τ	τ	PROPN
ejpam-6306	237	5	=	=	SYM
ejpam-6306	237	6	1	1	NUM
ejpam-6306	237	7	in	in	ADP
ejpam-6306	237	8	theorem	theorem	NOUN
ejpam-6306	237	9	2	2	NUM
ejpam-6306	237	10	,	,	PUNCT
ejpam-6306	237	11	then	then	ADV
ejpam-6306	237	12	f	f	PROPN
ejpam-6306	237	13	(	(	PUNCT
ejpam-6306	237	14	υ̌−1	υ̌−1	X
ejpam-6306	237	15	(	(	PUNCT
ejpam-6306	237	16	υ̌(α	υ̌(α	PROPN
ejpam-6306	237	17	)	)	PUNCT
ejpam-6306	237	18	+	+	CCONJ
ejpam-6306	237	19	υ̌(ρ	υ̌(ρ	X
ejpam-6306	237	20	)	)	PUNCT
ejpam-6306	237	21	2	2	NUM
ejpam-6306	237	22	)	)	PUNCT
ejpam-6306	237	23	)	)	PUNCT
ejpam-6306	237	24	≤	≤	NUM
ejpam-6306	237	25	1	1	NUM
ejpam-6306	237	26	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	237	27	υ̌(α	υ̌(α	NUM
ejpam-6306	237	28	)	)	PUNCT
ejpam-6306	237	29	∫	∫	PROPN
ejpam-6306	238	1	ρ	ρ	PROPN
ejpam-6306	238	2	α	α	PROPN
ejpam-6306	238	3	f(x)υ̌′(x)dx	f(x)υ̌′(x)dx	PROPN
ejpam-6306	238	4	≤	≤	NOUN
ejpam-6306	238	5	f(α	f(α	NOUN
ejpam-6306	238	6	)	)	PUNCT
ejpam-6306	239	1	+	+	NUM
ejpam-6306	239	2	f(ρ	f(ρ	NOUN
ejpam-6306	239	3	)	)	PUNCT
ejpam-6306	239	4	2	2	NUM
ejpam-6306	239	5	,	,	PUNCT
ejpam-6306	239	6	(	(	PUNCT
ejpam-6306	239	7	26	26	NUM
ejpam-6306	239	8	)	)	PUNCT
ejpam-6306	239	9	holds	hold	VERB
ejpam-6306	239	10	which	which	PRON
ejpam-6306	239	11	was	be	AUX
ejpam-6306	239	12	already	already	ADV
ejpam-6306	239	13	established	establish	VERB
ejpam-6306	239	14	in	in	ADP
ejpam-6306	239	15	[	[	X
ejpam-6306	239	16	25	25	NUM
ejpam-6306	239	17	]	]	PUNCT
ejpam-6306	239	18	.	.	PUNCT
ejpam-6306	240	1	corollary	corollary	ADJ
ejpam-6306	240	2	6	6	NUM
ejpam-6306	240	3	.	.	PUNCT
ejpam-6306	241	1	if	if	SCONJ
ejpam-6306	241	2	we	we	PRON
ejpam-6306	241	3	take	take	VERB
ejpam-6306	241	4	υ̌(x	υ̌(x	NUM
ejpam-6306	241	5	)	)	PUNCT
ejpam-6306	241	6	=	=	SYM
ejpam-6306	242	1	x	x	PROPN
ejpam-6306	242	2	and	and	CCONJ
ejpam-6306	242	3	τ	τ	X
ejpam-6306	242	4	=	=	NOUN
ejpam-6306	242	5	1	1	NUM
ejpam-6306	242	6	in	in	ADP
ejpam-6306	242	7	theorem	theorem	NOUN
ejpam-6306	242	8	2	2	NUM
ejpam-6306	242	9	,	,	PUNCT
ejpam-6306	242	10	then	then	ADV
ejpam-6306	242	11	inequality	inequality	NOUN
ejpam-6306	242	12	(	(	PUNCT
ejpam-6306	242	13	16	16	NUM
ejpam-6306	242	14	)	)	PUNCT
ejpam-6306	242	15	reduces	reduce	VERB
ejpam-6306	242	16	to	to	ADP
ejpam-6306	242	17	the	the	DET
ejpam-6306	242	18	inequality	inequality	NOUN
ejpam-6306	242	19	(	(	PUNCT
ejpam-6306	242	20	1	1	NUM
ejpam-6306	242	21	)	)	PUNCT
ejpam-6306	242	22	.	.	PUNCT
ejpam-6306	243	1	4	4	X
ejpam-6306	243	2	.	.	X
ejpam-6306	243	3	further	further	ADJ
ejpam-6306	243	4	consequences	consequence	NOUN
ejpam-6306	243	5	in	in	ADP
ejpam-6306	243	6	this	this	DET
ejpam-6306	243	7	section	section	NOUN
ejpam-6306	243	8	,	,	PUNCT
ejpam-6306	243	9	we	we	PRON
ejpam-6306	243	10	are	be	AUX
ejpam-6306	243	11	going	go	VERB
ejpam-6306	243	12	to	to	PART
ejpam-6306	243	13	discuss	discuss	VERB
ejpam-6306	243	14	some	some	DET
ejpam-6306	243	15	properties	property	NOUN
ejpam-6306	243	16	of	of	ADP
ejpam-6306	243	17	hermite	hermite	ADJ
ejpam-6306	243	18	hadamard	hadamard	PROPN
ejpam-6306	243	19	’s	’s	PART
ejpam-6306	243	20	type	type	NOUN
ejpam-6306	243	21	inequalities	inequality	NOUN
ejpam-6306	243	22	via	via	ADP
ejpam-6306	243	23	different	different	ADJ
ejpam-6306	243	24	convexities	convexity	NOUN
ejpam-6306	243	25	and	and	CCONJ
ejpam-6306	243	26	check	check	VERB
ejpam-6306	243	27	their	their	PRON
ejpam-6306	243	28	behavior	behavior	NOUN
ejpam-6306	243	29	for	for	ADP
ejpam-6306	243	30	generalized	generalized	ADJ
ejpam-6306	243	31	mittag	mittag	ADJ
ejpam-6306	243	32	-	-	PUNCT
ejpam-6306	243	33	leffler	leffler	NOUN
ejpam-6306	243	34	function	function	NOUN
ejpam-6306	243	35	as	as	ADP
ejpam-6306	243	36	a	a	DET
ejpam-6306	243	37	kernel	kernel	NOUN
ejpam-6306	243	38	.	.	PUNCT
ejpam-6306	244	1	as	as	ADP
ejpam-6306	244	2	the	the	DET
ejpam-6306	244	3	consequences	consequence	NOUN
ejpam-6306	244	4	for	for	ADP
ejpam-6306	244	5	the	the	DET
ejpam-6306	244	6	theorem	theorem	ADJ
ejpam-6306	244	7	1	1	NUM
ejpam-6306	244	8	and	and	CCONJ
ejpam-6306	244	9	theorem	theorem	VERB
ejpam-6306	244	10	2	2	NUM
ejpam-6306	244	11	,	,	PUNCT
ejpam-6306	244	12	we	we	PRON
ejpam-6306	244	13	get	get	VERB
ejpam-6306	244	14	the	the	DET
ejpam-6306	244	15	following	follow	VERB
ejpam-6306	244	16	results	result	NOUN
ejpam-6306	244	17	.	.	PUNCT
ejpam-6306	245	1	theorem	theorem	NOUN
ejpam-6306	245	2	3	3	X
ejpam-6306	245	3	.	.	PUNCT
ejpam-6306	246	1	let	let	VERB
ejpam-6306	246	2	f	f	NOUN
ejpam-6306	246	3	:	:	PUNCT
ejpam-6306	247	1	[	[	X
ejpam-6306	247	2	α	α	X
ejpam-6306	247	3	,	,	PUNCT
ejpam-6306	247	4	ρ	ρ	PROPN
ejpam-6306	247	5	]	]	X
ejpam-6306	247	6	⊆	⊆	NUM
ejpam-6306	247	7	r	r	NOUN
ejpam-6306	247	8	→	→	SYM
ejpam-6306	247	9	r	r	NOUN
ejpam-6306	247	10	be	be	AUX
ejpam-6306	247	11	an	an	DET
ejpam-6306	247	12	l1	l1	PROPN
ejpam-6306	247	13	integrable	integrable	ADJ
ejpam-6306	247	14	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	247	15	function	function	NOUN
ejpam-6306	247	16	and	and	CCONJ
ejpam-6306	248	1	f	f	NOUN
ejpam-6306	248	2	′	′	NOUN
ejpam-6306	248	3	∈	∈	PROPN
ejpam-6306	248	4	l1(α	l1(α	PROPN
ejpam-6306	248	5	,	,	PUNCT
ejpam-6306	248	6	ρ	ρ	PROPN
ejpam-6306	248	7	)	)	PUNCT
ejpam-6306	248	8	for	for	ADP
ejpam-6306	248	9	0	0	NUM
ejpam-6306	248	10	≤	≤	NUM
ejpam-6306	248	11	α	α	PRON
ejpam-6306	248	12	<	<	X
ejpam-6306	248	13	ρ	ρ	PROPN
ejpam-6306	248	14	.	.	PUNCT
ejpam-6306	249	1	moreover	moreover	ADV
ejpam-6306	249	2	,	,	PUNCT
ejpam-6306	249	3	the	the	DET
ejpam-6306	249	4	function	function	NOUN
ejpam-6306	249	5	υ̌	υ̌	PROPN
ejpam-6306	249	6	is	be	AUX
ejpam-6306	249	7	also	also	ADV
ejpam-6306	249	8	monotone	monotone	ADJ
ejpam-6306	249	9	and	and	CCONJ
ejpam-6306	249	10	positive	positive	ADJ
ejpam-6306	249	11	on	on	ADP
ejpam-6306	249	12	(	(	PUNCT
ejpam-6306	249	13	α	α	X
ejpam-6306	249	14	,	,	PUNCT
ejpam-6306	249	15	ρ	ρ	NOUN
ejpam-6306	249	16	]	]	PUNCT
ejpam-6306	249	17	and	and	CCONJ
ejpam-6306	249	18	υ̌′(x	υ̌′(x	NOUN
ejpam-6306	249	19	)	)	PUNCT
ejpam-6306	249	20	be	be	AUX
ejpam-6306	249	21	continuous	continuous	ADJ
ejpam-6306	249	22	on	on	ADP
ejpam-6306	249	23	(	(	PUNCT
ejpam-6306	249	24	α	α	X
ejpam-6306	249	25	,	,	PUNCT
ejpam-6306	249	26	ρ	ρ	NOUN
ejpam-6306	249	27	)	)	PUNCT
ejpam-6306	249	28	.	.	PUNCT
ejpam-6306	250	1	then	then	ADV
ejpam-6306	250	2	,	,	PUNCT
ejpam-6306	250	3	for	for	ADP
ejpam-6306	250	4	τ	τ	PROPN
ejpam-6306	250	5	>	>	X
ejpam-6306	250	6	0	0	PROPN
ejpam-6306	250	7	,	,	PUNCT
ejpam-6306	250	8	f(α	f(α	NOUN
ejpam-6306	250	9	)	)	PUNCT
ejpam-6306	250	10	+	+	CCONJ
ejpam-6306	250	11	f(ρ	f(ρ	NOUN
ejpam-6306	250	12	)	)	PUNCT
ejpam-6306	250	13	2	2	NUM
ejpam-6306	250	14	−	−	NOUN
ejpam-6306	250	15	1	1	NUM
ejpam-6306	250	16	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	250	17	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	250	18	[	[	PUNCT
ejpam-6306	250	19	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	250	20	,	,	PUNCT
ejpam-6306	250	21	κ	κ	NOUN
ejpam-6306	250	22	ν	ν	PROPN
ejpam-6306	250	23	,	,	PUNCT
ejpam-6306	250	24	τ	τ	PROPN
ejpam-6306	250	25	,	,	PUNCT
ejpam-6306	250	26	j	j	PROPN
ejpam-6306	250	27	,	,	PUNCT
ejpam-6306	250	28	ω	ω	PROPN
ejpam-6306	250	29	,	,	PUNCT
ejpam-6306	250	30	α+f(α	α+f(α	NOUN
ejpam-6306	250	31	)	)	PUNCT
ejpam-6306	250	32	+	+	CCONJ
ejpam-6306	250	33	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	250	34	,	,	PUNCT
ejpam-6306	250	35	κ	κ	NOUN
ejpam-6306	250	36	ν	ν	PROPN
ejpam-6306	250	37	,	,	PUNCT
ejpam-6306	250	38	τ	τ	PROPN
ejpam-6306	250	39	,	,	PUNCT
ejpam-6306	250	40	j	j	PROPN
ejpam-6306	250	41	,	,	PUNCT
ejpam-6306	250	42	ω	ω	PROPN
ejpam-6306	250	43	,	,	PUNCT
ejpam-6306	250	44	ρ−f(ρ	ρ−f(ρ	NOUN
ejpam-6306	250	45	)	)	PUNCT
ejpam-6306	250	46	]	]	PUNCT
ejpam-6306	250	47	=	=	SYM
ejpam-6306	250	48	1	1	NUM
ejpam-6306	250	49	2[υ̌(ρ)−	2[υ̌(ρ)−	NUM
ejpam-6306	250	50	υ̌(α)]τ	υ̌(α)]τ	NOUN
ejpam-6306	250	51	eϑ,z	eϑ,z	NOUN
ejpam-6306	250	52	,	,	PUNCT
ejpam-6306	250	53	κ	κ	X
ejpam-6306	250	54	ν	ν	PROPN
ejpam-6306	250	55	,	,	PUNCT
ejpam-6306	250	56	τ	τ	PROPN
ejpam-6306	250	57	,	,	PUNCT
ejpam-6306	250	58	j	j	PROPN
ejpam-6306	250	59	(	(	PUNCT
ejpam-6306	250	60	ξ(µ	ξ(µ	PROPN
ejpam-6306	250	61	)	)	PUNCT
ejpam-6306	250	62	v	v	NOUN
ejpam-6306	250	63	)	)	PUNCT
ejpam-6306	250	64	∫	∫	PROPN
ejpam-6306	250	65	ρ	ρ	PROPN
ejpam-6306	250	66	α	α	PROPN
ejpam-6306	250	67	(	(	PUNCT
ejpam-6306	250	68	(	(	PUNCT
ejpam-6306	250	69	υ̌(α)−	υ̌(α)−	NUM
ejpam-6306	250	70	υ̌(µ))τ	υ̌(µ))τ	NOUN
ejpam-6306	250	71	−	−	X
ejpam-6306	250	72	(	(	PUNCT
ejpam-6306	250	73	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	250	74	υ̌(µ))τ	υ̌(µ))τ	NOUN
ejpam-6306	250	75	)	)	PUNCT
ejpam-6306	250	76	f	f	NOUN
ejpam-6306	250	77	′(µ)dµ.	′(µ)dµ.	PROPN
ejpam-6306	250	78	proof	proof	NOUN
ejpam-6306	250	79	.	.	PUNCT
ejpam-6306	251	1	consider	consider	VERB
ejpam-6306	251	2	the	the	DET
ejpam-6306	251	3	integrals	integral	NOUN
ejpam-6306	251	4	i1	i1	NOUN
ejpam-6306	252	1	:	:	PUNCT
ejpam-6306	252	2	=	=	SYM
ejpam-6306	252	3	1	1	NUM
ejpam-6306	252	4	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	252	5	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	252	6	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	252	7	,	,	PUNCT
ejpam-6306	252	8	κ	κ	NOUN
ejpam-6306	252	9	ν	ν	PROPN
ejpam-6306	252	10	,	,	PUNCT
ejpam-6306	252	11	τ	τ	PROPN
ejpam-6306	252	12	,	,	PUNCT
ejpam-6306	252	13	j	j	PROPN
ejpam-6306	252	14	,	,	PUNCT
ejpam-6306	252	15	ω	ω	PROPN
ejpam-6306	252	16	,	,	PUNCT
ejpam-6306	252	17	α+f(α	α+f(α	NOUN
ejpam-6306	252	18	)	)	PUNCT
ejpam-6306	252	19	,	,	PUNCT
ejpam-6306	252	20	and	and	CCONJ
ejpam-6306	252	21	i2	i2	PROPN
ejpam-6306	252	22	:	:	PUNCT
ejpam-6306	252	23	=	=	SYM
ejpam-6306	252	24	1	1	NUM
ejpam-6306	252	25	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	252	26	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	252	27	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	252	28	,	,	PUNCT
ejpam-6306	252	29	κ	κ	NOUN
ejpam-6306	252	30	ν	ν	PROPN
ejpam-6306	252	31	,	,	PUNCT
ejpam-6306	252	32	τ	τ	PROPN
ejpam-6306	252	33	,	,	PUNCT
ejpam-6306	252	34	j	j	PROPN
ejpam-6306	252	35	,	,	PUNCT
ejpam-6306	252	36	ω	ω	PROPN
ejpam-6306	252	37	,	,	PUNCT
ejpam-6306	252	38	v−f(ρ	v−f(ρ	NOUN
ejpam-6306	252	39	)	)	PUNCT
ejpam-6306	252	40	.	.	PUNCT
ejpam-6306	253	1	in	in	ADP
ejpam-6306	253	2	this	this	DET
ejpam-6306	253	3	case	case	NOUN
ejpam-6306	253	4	,	,	PUNCT
ejpam-6306	253	5	by	by	ADP
ejpam-6306	253	6	definition	definition	NOUN
ejpam-6306	253	7	4	4	NUM
ejpam-6306	253	8	,	,	PUNCT
ejpam-6306	253	9	and	and	CCONJ
ejpam-6306	253	10	integrating	integrate	VERB
ejpam-6306	253	11	by	by	ADP
ejpam-6306	253	12	parts	part	NOUN
ejpam-6306	253	13	,	,	PUNCT
ejpam-6306	253	14	we	we	PRON
ejpam-6306	253	15	may	may	AUX
ejpam-6306	253	16	write	write	VERB
ejpam-6306	253	17	i1	i1	PROPN
ejpam-6306	253	18	:	:	PUNCT
ejpam-6306	253	19	=	=	SYM
ejpam-6306	253	20	1	1	NUM
ejpam-6306	253	21	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	253	22	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	253	23	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	253	24	,	,	PUNCT
ejpam-6306	253	25	κ	κ	NOUN
ejpam-6306	253	26	ν	ν	PROPN
ejpam-6306	253	27	,	,	PUNCT
ejpam-6306	253	28	τ	τ	PROPN
ejpam-6306	253	29	,	,	PUNCT
ejpam-6306	253	30	j	j	PROPN
ejpam-6306	253	31	,	,	PUNCT
ejpam-6306	253	32	ω	ω	PROPN
ejpam-6306	253	33	,	,	PUNCT
ejpam-6306	253	34	α+f(α	α+f(α	NOUN
ejpam-6306	253	35	)	)	PUNCT
ejpam-6306	253	36	=	=	SYM
ejpam-6306	253	37	1	1	NUM
ejpam-6306	253	38	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	253	39	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	253	40	[	[	PUNCT
ejpam-6306	253	41	∞∑	∞∑	NUM
ejpam-6306	253	42	n=0	n=0	NUM
ejpam-6306	253	43	(	(	PUNCT
ejpam-6306	253	44	ϑ)κn(ξ(µ	ϑ)κn(ξ(µ	NOUN
ejpam-6306	253	45	)	)	PUNCT
ejpam-6306	253	46	v)n	v)n	NOUN
ejpam-6306	254	1	γ(τ	γ(τ	PROPN
ejpam-6306	254	2	+	+	SYM
ejpam-6306	254	3	vn)(z)δn	vn)(z)δn	NUM
ejpam-6306	254	4	∫	∫	PROPN
ejpam-6306	254	5	ρ	ρ	PROPN
ejpam-6306	254	6	α	α	PROPN
ejpam-6306	254	7	(	(	PUNCT
ejpam-6306	254	8	υ̌(µ)−	υ̌(µ)−	NOUN
ejpam-6306	254	9	υ̌(ρ))τ−1υ̌′(µ)f(µ)dµ	υ̌(ρ))τ−1υ̌′(µ)f(µ)dµ	PROPN
ejpam-6306	254	10	]	]	PUNCT
ejpam-6306	254	11	=	=	PUNCT
ejpam-6306	254	12	−1	−1	NOUN
ejpam-6306	254	13	2(υ̌(ρ)−	2(υ̌(ρ)−	PROPN
ejpam-6306	254	14	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	254	15	∞∑	∞∑	PRON
ejpam-6306	254	16	n=0	n=0	NUM
ejpam-6306	254	17	(	(	PUNCT
ejpam-6306	254	18	ϑ)κn(ξ(µ	ϑ)κn(ξ(µ	NOUN
ejpam-6306	254	19	)	)	PUNCT
ejpam-6306	254	20	v)n	v)n	NOUN
ejpam-6306	255	1	γ(τ	γ(τ	PROPN
ejpam-6306	255	2	+	+	SYM
ejpam-6306	255	3	vn)(z)δn	vn)(z)δn	NUM
ejpam-6306	255	4	∫	∫	PROPN
ejpam-6306	255	5	ρ	ρ	PROPN
ejpam-6306	255	6	α	α	PROPN
ejpam-6306	255	7	f(µ)d(υ̌(µ)−	f(µ)d(υ̌(µ)−	NOUN
ejpam-6306	255	8	υ̌(ρ))τ	υ̌(ρ))τ	PROPN
ejpam-6306	255	9	r.	r.	PROPN
ejpam-6306	255	10	s.	s.	PROPN
ejpam-6306	255	11	ali	ali	PROPN
ejpam-6306	255	12	et	et	PROPN
ejpam-6306	255	13	al	al	PROPN
ejpam-6306	255	14	.	.	PUNCT
ejpam-6306	255	15	/	/	SYM
ejpam-6306	255	16	eur	eur	PROPN
ejpam-6306	255	17	.	.	PUNCT
ejpam-6306	256	1	j.	j.	PROPN
ejpam-6306	256	2	pure	pure	PROPN
ejpam-6306	256	3	appl	appl	PROPN
ejpam-6306	256	4	.	.	PROPN
ejpam-6306	256	5	math	math	PROPN
ejpam-6306	256	6	,	,	PUNCT
ejpam-6306	256	7	18	18	NUM
ejpam-6306	256	8	(	(	PUNCT
ejpam-6306	256	9	3	3	NUM
ejpam-6306	256	10	)	)	PUNCT
ejpam-6306	256	11	(	(	PUNCT
ejpam-6306	256	12	2025	2025	NUM
ejpam-6306	256	13	)	)	PUNCT
ejpam-6306	256	14	,	,	PUNCT
ejpam-6306	256	15	6306	6306	NUM
ejpam-6306	256	16	13	13	NUM
ejpam-6306	256	17	of	of	ADP
ejpam-6306	256	18	18	18	NUM
ejpam-6306	256	19	=	=	SYM
ejpam-6306	256	20	1	1	NUM
ejpam-6306	256	21	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	256	22	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	256	23	eϑ,z	eϑ,z	NOUN
ejpam-6306	256	24	,	,	PUNCT
ejpam-6306	256	25	κ	κ	X
ejpam-6306	256	26	ν	ν	PROPN
ejpam-6306	256	27	,	,	PUNCT
ejpam-6306	256	28	τ	τ	PROPN
ejpam-6306	256	29	,	,	PUNCT
ejpam-6306	256	30	j	j	PROPN
ejpam-6306	256	31	(	(	PUNCT
ejpam-6306	256	32	ξ(µ	ξ(µ	PROPN
ejpam-6306	256	33	)	)	PUNCT
ejpam-6306	256	34	v	v	NOUN
ejpam-6306	256	35	)	)	PUNCT
ejpam-6306	256	36	[	[	PUNCT
ejpam-6306	256	37	(	(	PUNCT
ejpam-6306	256	38	υ̌(α)−	υ̌(α)−	NUM
ejpam-6306	256	39	υ̌(ρ))τf(α	υ̌(ρ))τf(α	NOUN
ejpam-6306	256	40	)	)	PUNCT
ejpam-6306	257	1	+	+	NUM
ejpam-6306	257	2	∫	∫	PROPN
ejpam-6306	257	3	ρ	ρ	PROPN
ejpam-6306	257	4	α	α	PROPN
ejpam-6306	257	5	(	(	PUNCT
ejpam-6306	257	6	υ̌(α)−	υ̌(α)−	NUM
ejpam-6306	257	7	υ̌(µ))τf	υ̌(µ))τf	PROPN
ejpam-6306	257	8	′(µ)dµ	′(µ)dµ	PROPN
ejpam-6306	257	9	]	]	PUNCT
ejpam-6306	257	10	.	.	PUNCT
ejpam-6306	258	1	(	(	PUNCT
ejpam-6306	258	2	27	27	NUM
ejpam-6306	258	3	)	)	PUNCT
ejpam-6306	258	4	similarly	similarly	ADV
ejpam-6306	258	5	,	,	PUNCT
ejpam-6306	258	6	we	we	PRON
ejpam-6306	258	7	have	have	VERB
ejpam-6306	258	8	i2	i2	NOUN
ejpam-6306	258	9	:	:	PUNCT
ejpam-6306	259	1	=	=	SYM
ejpam-6306	259	2	1	1	NUM
ejpam-6306	259	3	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	259	4	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	259	5	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	259	6	,	,	PUNCT
ejpam-6306	259	7	κ	κ	NOUN
ejpam-6306	259	8	ν	ν	PROPN
ejpam-6306	259	9	,	,	PUNCT
ejpam-6306	259	10	τ	τ	PROPN
ejpam-6306	259	11	,	,	PUNCT
ejpam-6306	259	12	j	j	PROPN
ejpam-6306	259	13	,	,	PUNCT
ejpam-6306	259	14	ω	ω	PROPN
ejpam-6306	259	15	,	,	PUNCT
ejpam-6306	259	16	ρ−f(ρ	ρ−f(ρ	NOUN
ejpam-6306	259	17	)	)	PUNCT
ejpam-6306	259	18	=	=	SYM
ejpam-6306	259	19	1	1	NUM
ejpam-6306	259	20	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	259	21	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	259	22	[	[	PUNCT
ejpam-6306	259	23	∞∑	∞∑	NUM
ejpam-6306	259	24	n=0	n=0	NUM
ejpam-6306	259	25	(	(	PUNCT
ejpam-6306	259	26	ϑ)κn(ξ(µ	ϑ)κn(ξ(µ	NOUN
ejpam-6306	259	27	)	)	PUNCT
ejpam-6306	259	28	v)n	v)n	NOUN
ejpam-6306	259	29	γ(vn+	γ(vn+	PROPN
ejpam-6306	259	30	τ)(z)δn	τ)(z)δn	PROPN
ejpam-6306	259	31	∫	∫	PROPN
ejpam-6306	259	32	α	α	PROPN
ejpam-6306	259	33	ρ	ρ	PROPN
ejpam-6306	259	34	(	(	PUNCT
ejpam-6306	259	35	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	259	36	υ̌(µ))τ−1υ̌′(µ)f(µ)dµ	υ̌(µ))τ−1υ̌′(µ)f(µ)dµ	PROPN
ejpam-6306	259	37	]	]	PUNCT
ejpam-6306	259	38	=	=	PUNCT
ejpam-6306	259	39	−1	−1	NOUN
ejpam-6306	259	40	2(υ̌(ρ)−	2(υ̌(ρ)−	PROPN
ejpam-6306	259	41	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	260	1	∞∑	∞∑	PRON
ejpam-6306	260	2	n=0	n=0	NUM
ejpam-6306	260	3	(	(	PUNCT
ejpam-6306	260	4	ϑ)κn(ξ(µ	ϑ)κn(ξ(µ	NOUN
ejpam-6306	260	5	)	)	PUNCT
ejpam-6306	260	6	v)n	v)n	NOUN
ejpam-6306	261	1	γ(vn+	γ(vn+	PROPN
ejpam-6306	261	2	τ)(z)δn	τ)(z)δn	PROPN
ejpam-6306	261	3	∫	∫	PROPN
ejpam-6306	261	4	α	α	PROPN
ejpam-6306	261	5	ρ	ρ	PROPN
ejpam-6306	261	6	f(µ)d(υ̌(ρ)−	f(µ)d(υ̌(ρ)−	PROPN
ejpam-6306	261	7	υ̌(µ))τ	υ̌(µ))τ	PUNCT
ejpam-6306	261	8	=	=	SYM
ejpam-6306	261	9	1	1	NUM
ejpam-6306	261	10	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	261	11	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	261	12	eϑ,z	eϑ,z	NOUN
ejpam-6306	261	13	,	,	PUNCT
ejpam-6306	261	14	κ	κ	X
ejpam-6306	261	15	ν	ν	PROPN
ejpam-6306	261	16	,	,	PUNCT
ejpam-6306	261	17	τ	τ	PROPN
ejpam-6306	261	18	,	,	PUNCT
ejpam-6306	261	19	j	j	PROPN
ejpam-6306	261	20	(	(	PUNCT
ejpam-6306	261	21	ξ(µ	ξ(µ	PROPN
ejpam-6306	261	22	)	)	PUNCT
ejpam-6306	261	23	v	v	NOUN
ejpam-6306	261	24	)	)	PUNCT
ejpam-6306	261	25	[	[	PUNCT
ejpam-6306	261	26	(	(	PUNCT
ejpam-6306	261	27	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	261	28	υ̌(α))τf(ρ	υ̌(α))τf(ρ	NOUN
ejpam-6306	261	29	)	)	PUNCT
ejpam-6306	261	30	+	+	NUM
ejpam-6306	261	31	∫	∫	PROPN
ejpam-6306	261	32	α	α	PROPN
ejpam-6306	261	33	ρ	ρ	PROPN
ejpam-6306	261	34	(	(	PUNCT
ejpam-6306	261	35	υ̌(ρ)−	υ̌(ρ)−	INTJ
ejpam-6306	261	36	υ̌(µ))τf	υ̌(µ))τf	PROPN
ejpam-6306	261	37	′(µ)dµ	′(µ)dµ	PROPN
ejpam-6306	261	38	]	]	PUNCT
ejpam-6306	261	39	.	.	PUNCT
ejpam-6306	262	1	(	(	PUNCT
ejpam-6306	262	2	28	28	NUM
ejpam-6306	262	3	)	)	PUNCT
ejpam-6306	262	4	from	from	ADP
ejpam-6306	262	5	the	the	DET
ejpam-6306	262	6	identities	identity	NOUN
ejpam-6306	262	7	in	in	ADP
ejpam-6306	262	8	equations	equation	NOUN
ejpam-6306	262	9	(	(	PUNCT
ejpam-6306	262	10	27	27	NUM
ejpam-6306	262	11	)	)	PUNCT
ejpam-6306	262	12	and	and	CCONJ
ejpam-6306	262	13	(	(	PUNCT
ejpam-6306	262	14	28	28	NUM
ejpam-6306	262	15	)	)	PUNCT
ejpam-6306	262	16	,	,	PUNCT
ejpam-6306	262	17	we	we	PRON
ejpam-6306	262	18	have	have	VERB
ejpam-6306	262	19	f(α	f(α	NOUN
ejpam-6306	262	20	)	)	PUNCT
ejpam-6306	263	1	+	+	CCONJ
ejpam-6306	263	2	f(ρ	f(ρ	NOUN
ejpam-6306	263	3	)	)	PUNCT
ejpam-6306	263	4	2	2	NUM
ejpam-6306	263	5	−	−	PROPN
ejpam-6306	263	6	(	(	PUNCT
ejpam-6306	263	7	i1	i1	PROPN
ejpam-6306	263	8	+	+	CCONJ
ejpam-6306	263	9	i2	i2	PROPN
ejpam-6306	263	10	)	)	PUNCT
ejpam-6306	263	11	=	=	SYM
ejpam-6306	263	12	1	1	NUM
ejpam-6306	263	13	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	263	14	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	263	15	eϑ,z	eϑ,z	NOUN
ejpam-6306	263	16	,	,	PUNCT
ejpam-6306	263	17	κ	κ	X
ejpam-6306	263	18	ν	ν	PROPN
ejpam-6306	263	19	,	,	PUNCT
ejpam-6306	263	20	τ	τ	PROPN
ejpam-6306	263	21	,	,	PUNCT
ejpam-6306	263	22	j	j	PROPN
ejpam-6306	263	23	(	(	PUNCT
ejpam-6306	263	24	ξ(µ	ξ(µ	PROPN
ejpam-6306	263	25	)	)	PUNCT
ejpam-6306	263	26	v	v	NOUN
ejpam-6306	263	27	)	)	PUNCT
ejpam-6306	263	28	×	×	NOUN
ejpam-6306	263	29	∫	∫	NOUN
ejpam-6306	263	30	ρ	ρ	PROPN
ejpam-6306	263	31	α	α	PROPN
ejpam-6306	264	1	[	[	X
ejpam-6306	264	2	(	(	PUNCT
ejpam-6306	264	3	υ̌(α)−	υ̌(α)−	NUM
ejpam-6306	264	4	υ̌(µ))τ	υ̌(µ))τ	NOUN
ejpam-6306	264	5	−	−	PROPN
ejpam-6306	264	6	(	(	PUNCT
ejpam-6306	264	7	υ̌(ρ)−	υ̌(ρ)−	X
ejpam-6306	264	8	υ̌(µ))τ	υ̌(µ))τ	NOUN
ejpam-6306	264	9	]	]	X
ejpam-6306	264	10	f	f	PROPN
ejpam-6306	264	11	′(µ)dµ	′(µ)dµ	PROPN
ejpam-6306	264	12	,	,	PUNCT
ejpam-6306	264	13	which	which	PRON
ejpam-6306	264	14	is	be	AUX
ejpam-6306	264	15	the	the	DET
ejpam-6306	264	16	required	require	VERB
ejpam-6306	264	17	result	result	NOUN
ejpam-6306	264	18	.	.	PUNCT
ejpam-6306	265	1	corollary	corollary	ADJ
ejpam-6306	265	2	7	7	NUM
ejpam-6306	265	3	.	.	PUNCT
ejpam-6306	266	1	if	if	SCONJ
ejpam-6306	266	2	we	we	PRON
ejpam-6306	266	3	take	take	VERB
ejpam-6306	266	4	υ̌(x	υ̌(x	NUM
ejpam-6306	266	5	)	)	PUNCT
ejpam-6306	266	6	=	=	SYM
ejpam-6306	267	1	x	x	PROPN
ejpam-6306	267	2	and	and	CCONJ
ejpam-6306	267	3	τ	τ	X
ejpam-6306	267	4	=	=	NOUN
ejpam-6306	267	5	1	1	NUM
ejpam-6306	267	6	in	in	ADP
ejpam-6306	267	7	theorem	theorem	NOUN
ejpam-6306	267	8	3	3	NUM
ejpam-6306	267	9	,	,	PUNCT
ejpam-6306	267	10	then	then	ADV
ejpam-6306	267	11	we	we	PRON
ejpam-6306	267	12	have	have	VERB
ejpam-6306	267	13	the	the	DET
ejpam-6306	267	14	following	follow	VERB
ejpam-6306	267	15	identity	identity	NOUN
ejpam-6306	267	16	:	:	PUNCT
ejpam-6306	267	17	f(α	f(α	NOUN
ejpam-6306	267	18	)	)	PUNCT
ejpam-6306	268	1	+	+	NUM
ejpam-6306	268	2	f(ρ	f(ρ	NOUN
ejpam-6306	268	3	)	)	PUNCT
ejpam-6306	268	4	2	2	NUM
ejpam-6306	268	5	−	−	NOUN
ejpam-6306	268	6	1	1	NUM
ejpam-6306	268	7	2(ρ−	2(ρ−	NUM
ejpam-6306	268	8	α	α	NOUN
ejpam-6306	268	9	)	)	PUNCT
ejpam-6306	268	10	[	[	PUNCT
ejpam-6306	268	11	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	268	12	,	,	PUNCT
ejpam-6306	268	13	κ	κ	NOUN
ejpam-6306	268	14	ν	ν	PROPN
ejpam-6306	268	15	,	,	PUNCT
ejpam-6306	268	16	τ	τ	PROPN
ejpam-6306	268	17	,	,	PUNCT
ejpam-6306	268	18	j	j	PROPN
ejpam-6306	268	19	,	,	PUNCT
ejpam-6306	268	20	ω	ω	PROPN
ejpam-6306	268	21	,	,	PUNCT
ejpam-6306	268	22	α+f(α	α+f(α	NOUN
ejpam-6306	268	23	)	)	PUNCT
ejpam-6306	268	24	+	+	CCONJ
ejpam-6306	268	25	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	268	26	,	,	PUNCT
ejpam-6306	268	27	κ	κ	NOUN
ejpam-6306	268	28	ν	ν	PROPN
ejpam-6306	268	29	,	,	PUNCT
ejpam-6306	268	30	τ	τ	PROPN
ejpam-6306	268	31	,	,	PUNCT
ejpam-6306	268	32	j	j	PROPN
ejpam-6306	268	33	,	,	PUNCT
ejpam-6306	268	34	ω	ω	PROPN
ejpam-6306	268	35	,	,	PUNCT
ejpam-6306	268	36	ρ−f(ρ	ρ−f(ρ	NOUN
ejpam-6306	268	37	)	)	PUNCT
ejpam-6306	268	38	]	]	PUNCT
ejpam-6306	269	1	=	=	PUNCT
ejpam-6306	269	2	1	1	NUM
ejpam-6306	269	3	2(ρ−	2(ρ−	NUM
ejpam-6306	269	4	α	α	NUM
ejpam-6306	269	5	)	)	PUNCT
ejpam-6306	269	6	eϑ,z	eϑ,z	NOUN
ejpam-6306	269	7	,	,	PUNCT
ejpam-6306	269	8	κ	κ	X
ejpam-6306	269	9	ν	ν	PROPN
ejpam-6306	269	10	,	,	PUNCT
ejpam-6306	269	11	τ	τ	PROPN
ejpam-6306	269	12	,	,	PUNCT
ejpam-6306	269	13	j	j	PROPN
ejpam-6306	269	14	(	(	PUNCT
ejpam-6306	269	15	ξ(µ	ξ(µ	PROPN
ejpam-6306	269	16	)	)	PUNCT
ejpam-6306	269	17	v	v	NOUN
ejpam-6306	269	18	)	)	PUNCT
ejpam-6306	269	19	∫	∫	PROPN
ejpam-6306	270	1	ρ	ρ	PROPN
ejpam-6306	270	2	α	α	PROPN
ejpam-6306	270	3	(	(	PUNCT
ejpam-6306	270	4	α−	α−	ADP
ejpam-6306	270	5	ρ)f	ρ)f	X
ejpam-6306	270	6	′(µ)dµ.	′(µ)dµ.	NOUN
ejpam-6306	270	7	theorem	theorem	VERB
ejpam-6306	270	8	4	4	NUM
ejpam-6306	270	9	.	.	PUNCT
ejpam-6306	271	1	let	let	VERB
ejpam-6306	271	2	f	f	NOUN
ejpam-6306	271	3	:	:	PUNCT
ejpam-6306	272	1	[	[	X
ejpam-6306	272	2	α	α	X
ejpam-6306	272	3	,	,	PUNCT
ejpam-6306	272	4	ρ	ρ	PROPN
ejpam-6306	272	5	]	]	X
ejpam-6306	272	6	⊆	⊆	NUM
ejpam-6306	272	7	r	r	NOUN
ejpam-6306	272	8	→	→	SYM
ejpam-6306	272	9	r	r	NOUN
ejpam-6306	272	10	be	be	AUX
ejpam-6306	272	11	an	an	DET
ejpam-6306	272	12	l1	l1	PROPN
ejpam-6306	272	13	integrable	integrable	ADJ
ejpam-6306	272	14	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	272	15	function	function	NOUN
ejpam-6306	272	16	and	and	CCONJ
ejpam-6306	273	1	f	f	NOUN
ejpam-6306	273	2	′	′	NOUN
ejpam-6306	273	3	∈	∈	PROPN
ejpam-6306	273	4	l1(α	l1(α	PROPN
ejpam-6306	273	5	,	,	PUNCT
ejpam-6306	273	6	ρ	ρ	PROPN
ejpam-6306	273	7	)	)	PUNCT
ejpam-6306	273	8	for	for	ADP
ejpam-6306	273	9	0	0	NUM
ejpam-6306	273	10	≤	≤	NUM
ejpam-6306	273	11	α	α	PRON
ejpam-6306	273	12	<	<	X
ejpam-6306	273	13	ρ	ρ	PROPN
ejpam-6306	273	14	.	.	PUNCT
ejpam-6306	274	1	moreover	moreover	ADV
ejpam-6306	274	2	,	,	PUNCT
ejpam-6306	274	3	the	the	DET
ejpam-6306	274	4	function	function	NOUN
ejpam-6306	274	5	υ̌	υ̌	AUX
ejpam-6306	274	6	be	be	AUX
ejpam-6306	274	7	monotone	monotone	ADJ
ejpam-6306	274	8	and	and	CCONJ
ejpam-6306	274	9	positive	positive	ADJ
ejpam-6306	274	10	on	on	ADP
ejpam-6306	274	11	(	(	PUNCT
ejpam-6306	274	12	α	α	X
ejpam-6306	274	13	,	,	PUNCT
ejpam-6306	274	14	ρ	ρ	NOUN
ejpam-6306	274	15	]	]	PUNCT
ejpam-6306	274	16	and	and	CCONJ
ejpam-6306	274	17	υ̌′(x	υ̌′(x	NOUN
ejpam-6306	274	18	)	)	PUNCT
ejpam-6306	274	19	is	be	AUX
ejpam-6306	274	20	continuous	continuous	ADJ
ejpam-6306	274	21	on	on	ADP
ejpam-6306	274	22	(	(	PUNCT
ejpam-6306	274	23	α	α	X
ejpam-6306	274	24	,	,	PUNCT
ejpam-6306	274	25	ρ	ρ	NOUN
ejpam-6306	274	26	)	)	PUNCT
ejpam-6306	274	27	.	.	PUNCT
ejpam-6306	275	1	then	then	ADV
ejpam-6306	275	2	,	,	PUNCT
ejpam-6306	275	3	for	for	ADP
ejpam-6306	275	4	τ	τ	PROPN
ejpam-6306	275	5	>	>	X
ejpam-6306	275	6	0	0	PROPN
ejpam-6306	275	7	,	,	PUNCT
ejpam-6306	275	8	1	1	NUM
ejpam-6306	275	9	(	(	PUNCT
ejpam-6306	275	10	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	275	11	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	275	12	[	[	PUNCT
ejpam-6306	275	13	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	275	14	,	,	PUNCT
ejpam-6306	275	15	κ	κ	NOUN
ejpam-6306	275	16	ν	ν	PROPN
ejpam-6306	275	17	,	,	PUNCT
ejpam-6306	275	18	τ	τ	PROPN
ejpam-6306	275	19	,	,	PUNCT
ejpam-6306	275	20	j	j	PROPN
ejpam-6306	275	21	,	,	PUNCT
ejpam-6306	275	22	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	275	23	(	(	PUNCT
ejpam-6306	275	24	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	275	25	)	)	PUNCT
ejpam-6306	275	26	2	2	NUM
ejpam-6306	275	27	)	)	PUNCT
ejpam-6306	275	28	)	)	PUNCT
ejpam-6306	276	1	+	+	PUNCT
ejpam-6306	276	2	f(α	f(α	NOUN
ejpam-6306	276	3	)	)	PUNCT
ejpam-6306	276	4	+	+	CCONJ
ejpam-6306	277	1	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	277	2	,	,	PUNCT
ejpam-6306	277	3	κ	κ	NOUN
ejpam-6306	277	4	ν	ν	PROPN
ejpam-6306	277	5	,	,	PUNCT
ejpam-6306	277	6	τ	τ	PROPN
ejpam-6306	277	7	,	,	PUNCT
ejpam-6306	277	8	j	j	PROPN
ejpam-6306	277	9	,	,	PUNCT
ejpam-6306	277	10	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	277	11	(	(	PUNCT
ejpam-6306	277	12	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	277	13	)	)	PUNCT
ejpam-6306	277	14	2	2	NUM
ejpam-6306	277	15	)	)	PUNCT
ejpam-6306	277	16	)	)	PUNCT
ejpam-6306	277	17	−	−	ADP
ejpam-6306	277	18	f(ρ	f(ρ	NOUN
ejpam-6306	277	19	)	)	PUNCT
ejpam-6306	277	20	]	]	PUNCT
ejpam-6306	278	1	−	−	PROPN
ejpam-6306	278	2	f	f	X
ejpam-6306	278	3	(	(	PUNCT
ejpam-6306	278	4	υ̌−1	υ̌−1	X
ejpam-6306	278	5	(	(	PUNCT
ejpam-6306	278	6	υ̌(α	υ̌(α	PROPN
ejpam-6306	278	7	)	)	PUNCT
ejpam-6306	278	8	+	+	CCONJ
ejpam-6306	278	9	υ̌(ρ	υ̌(ρ	X
ejpam-6306	278	10	)	)	PUNCT
ejpam-6306	278	11	2	2	NUM
ejpam-6306	278	12	)	)	PUNCT
ejpam-6306	278	13	)	)	PUNCT
ejpam-6306	279	1	=	=	SYM
ejpam-6306	279	2	1	1	NUM
ejpam-6306	279	3	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	279	4	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	279	5	eϑ,z	eϑ,z	NOUN
ejpam-6306	279	6	,	,	PUNCT
ejpam-6306	279	7	κ	κ	X
ejpam-6306	279	8	ν	ν	PROPN
ejpam-6306	279	9	,	,	PUNCT
ejpam-6306	279	10	τ	τ	PROPN
ejpam-6306	279	11	,	,	PUNCT
ejpam-6306	279	12	j	j	PROPN
ejpam-6306	279	13	(	(	PUNCT
ejpam-6306	279	14	ξ(µ	ξ(µ	PROPN
ejpam-6306	279	15	)	)	PUNCT
ejpam-6306	279	16	v	v	NOUN
ejpam-6306	279	17	)	)	PUNCT
ejpam-6306	279	18	(	(	PUNCT
ejpam-6306	279	19	∫	∫	PROPN
ejpam-6306	279	20	ρ	ρ	PROPN
ejpam-6306	279	21	(	(	PUNCT
ejpam-6306	279	22	υ̌−1	υ̌−1	PROPN
ejpam-6306	279	23	(	(	PUNCT
ejpam-6306	279	24	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	279	25	)	)	PUNCT
ejpam-6306	279	26	2	2	NUM
ejpam-6306	279	27	)	)	PUNCT
ejpam-6306	279	28	)	)	PUNCT
ejpam-6306	280	1	+	+	CCONJ
ejpam-6306	280	2	(	(	PUNCT
ejpam-6306	280	3	υ̌(α	υ̌(α	PROPN
ejpam-6306	280	4	)	)	PUNCT
ejpam-6306	280	5	+	+	CCONJ
ejpam-6306	280	6	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	280	7	2υ̌(µ))τf	2υ̌(µ))τf	NUM
ejpam-6306	280	8	′(µ)dµ	′(µ)dµ	PROPN
ejpam-6306	280	9	r.	r.	PROPN
ejpam-6306	280	10	s.	s.	PROPN
ejpam-6306	280	11	ali	ali	PROPN
ejpam-6306	280	12	et	et	PROPN
ejpam-6306	280	13	al	al	PROPN
ejpam-6306	280	14	.	.	PUNCT
ejpam-6306	280	15	/	/	SYM
ejpam-6306	280	16	eur	eur	PROPN
ejpam-6306	280	17	.	.	PUNCT
ejpam-6306	281	1	j.	j.	PROPN
ejpam-6306	281	2	pure	pure	PROPN
ejpam-6306	281	3	appl	appl	PROPN
ejpam-6306	281	4	.	.	PROPN
ejpam-6306	281	5	math	math	PROPN
ejpam-6306	281	6	,	,	PUNCT
ejpam-6306	281	7	18	18	NUM
ejpam-6306	281	8	(	(	PUNCT
ejpam-6306	281	9	3	3	NUM
ejpam-6306	281	10	)	)	PUNCT
ejpam-6306	281	11	(	(	PUNCT
ejpam-6306	281	12	2025	2025	NUM
ejpam-6306	281	13	)	)	PUNCT
ejpam-6306	281	14	,	,	PUNCT
ejpam-6306	281	15	6306	6306	NUM
ejpam-6306	281	16	14	14	NUM
ejpam-6306	281	17	of	of	ADP
ejpam-6306	281	18	18	18	NUM
ejpam-6306	281	19	−	−	NOUN
ejpam-6306	281	20	∫	∫	PROPN
ejpam-6306	281	21	α	α	PROPN
ejpam-6306	281	22	(	(	PUNCT
ejpam-6306	281	23	υ̌−1	υ̌−1	PROPN
ejpam-6306	281	24	(	(	PUNCT
ejpam-6306	281	25	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	281	26	)	)	PUNCT
ejpam-6306	281	27	2	2	NUM
ejpam-6306	281	28	)	)	PUNCT
ejpam-6306	281	29	)	)	PUNCT
ejpam-6306	282	1	+	+	CCONJ
ejpam-6306	282	2	(	(	PUNCT
ejpam-6306	282	3	υ̌(α	υ̌(α	PROPN
ejpam-6306	282	4	)	)	PUNCT
ejpam-6306	282	5	+	+	CCONJ
ejpam-6306	282	6	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	282	7	2υ̌(µ))τf	2υ̌(µ))τf	NUM
ejpam-6306	282	8	′(µ)dµ	′(µ)dµ	PROPN
ejpam-6306	282	9	)	)	PUNCT
ejpam-6306	282	10	,	,	PUNCT
ejpam-6306	282	11	(	(	PUNCT
ejpam-6306	282	12	29	29	NUM
ejpam-6306	282	13	)	)	PUNCT
ejpam-6306	282	14	for	for	ADP
ejpam-6306	282	15	τ	τ	PROPN
ejpam-6306	282	16	>	>	X
ejpam-6306	282	17	0	0	PROPN
ejpam-6306	282	18	.	.	PUNCT
ejpam-6306	282	19	proof	proof	NOUN
ejpam-6306	282	20	.	.	PUNCT
ejpam-6306	283	1	consider	consider	VERB
ejpam-6306	283	2	the	the	DET
ejpam-6306	283	3	integrals	integral	NOUN
ejpam-6306	283	4	j1	j1	NOUN
ejpam-6306	283	5	:	:	PUNCT
ejpam-6306	283	6	=	=	SYM
ejpam-6306	283	7	1	1	NUM
ejpam-6306	283	8	(	(	PUNCT
ejpam-6306	283	9	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	283	10	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	283	11	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	283	12	,	,	PUNCT
ejpam-6306	283	13	κ	κ	NOUN
ejpam-6306	283	14	ν	ν	PROPN
ejpam-6306	283	15	,	,	PUNCT
ejpam-6306	283	16	τ	τ	PROPN
ejpam-6306	283	17	,	,	PUNCT
ejpam-6306	283	18	j	j	PROPN
ejpam-6306	283	19	,	,	PUNCT
ejpam-6306	283	20	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	283	21	(	(	PUNCT
ejpam-6306	283	22	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	283	23	)	)	PUNCT
ejpam-6306	283	24	2	2	NUM
ejpam-6306	283	25	)	)	PUNCT
ejpam-6306	283	26	)	)	PUNCT
ejpam-6306	284	1	+	+	PUNCT
ejpam-6306	284	2	f(α	f(α	NOUN
ejpam-6306	284	3	)	)	PUNCT
ejpam-6306	284	4	,	,	PUNCT
ejpam-6306	284	5	and	and	CCONJ
ejpam-6306	284	6	j2	j2	PROPN
ejpam-6306	284	7	:	:	PUNCT
ejpam-6306	284	8	=	=	SYM
ejpam-6306	284	9	1	1	NUM
ejpam-6306	284	10	(	(	PUNCT
ejpam-6306	284	11	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	284	12	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	284	13	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	284	14	,	,	PUNCT
ejpam-6306	284	15	κ	κ	NOUN
ejpam-6306	284	16	ν	ν	PROPN
ejpam-6306	284	17	,	,	PUNCT
ejpam-6306	284	18	τ	τ	PROPN
ejpam-6306	284	19	,	,	PUNCT
ejpam-6306	284	20	j	j	PROPN
ejpam-6306	284	21	,	,	PUNCT
ejpam-6306	284	22	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	284	23	(	(	PUNCT
ejpam-6306	284	24	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	284	25	)	)	PUNCT
ejpam-6306	284	26	2	2	NUM
ejpam-6306	284	27	)	)	PUNCT
ejpam-6306	284	28	)	)	PUNCT
ejpam-6306	284	29	−	−	ADP
ejpam-6306	284	30	f(ρ	f(ρ	NOUN
ejpam-6306	284	31	)	)	PUNCT
ejpam-6306	284	32	.	.	PUNCT
ejpam-6306	285	1	definition	definition	NOUN
ejpam-6306	285	2	4	4	NUM
ejpam-6306	285	3	and	and	CCONJ
ejpam-6306	285	4	integration	integration	NOUN
ejpam-6306	285	5	by	by	ADP
ejpam-6306	285	6	parts	part	NOUN
ejpam-6306	285	7	give	give	VERB
ejpam-6306	285	8	j1	j1	NOUN
ejpam-6306	285	9	:	:	PUNCT
ejpam-6306	285	10	=	=	SYM
ejpam-6306	285	11	1	1	NUM
ejpam-6306	285	12	(	(	PUNCT
ejpam-6306	285	13	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	285	14	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	285	15	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	285	16	,	,	PUNCT
ejpam-6306	285	17	κ	κ	NOUN
ejpam-6306	285	18	ν	ν	PROPN
ejpam-6306	285	19	,	,	PUNCT
ejpam-6306	285	20	τ	τ	PROPN
ejpam-6306	285	21	,	,	PUNCT
ejpam-6306	285	22	j	j	PROPN
ejpam-6306	285	23	,	,	PUNCT
ejpam-6306	285	24	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	285	25	(	(	PUNCT
ejpam-6306	285	26	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	285	27	)	)	PUNCT
ejpam-6306	285	28	2	2	NUM
ejpam-6306	285	29	)	)	PUNCT
ejpam-6306	285	30	)	)	PUNCT
ejpam-6306	286	1	+	+	PUNCT
ejpam-6306	286	2	f(α	f(α	NOUN
ejpam-6306	286	3	)	)	PUNCT
ejpam-6306	286	4	=	=	SYM
ejpam-6306	286	5	1	1	NUM
ejpam-6306	286	6	(	(	PUNCT
ejpam-6306	286	7	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	286	8	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	286	9	∞∑	∞∑	NUM
ejpam-6306	286	10	n=0	n=0	NUM
ejpam-6306	286	11	(	(	PUNCT
ejpam-6306	286	12	ϑ)κn(ξ(µ	ϑ)κn(ξ(µ	NOUN
ejpam-6306	286	13	)	)	PUNCT
ejpam-6306	286	14	v)n	v)n	NOUN
ejpam-6306	287	1	γ(τ	γ(τ	PROPN
ejpam-6306	287	2	+	+	SYM
ejpam-6306	287	3	vn)(z)δn	vn)(z)δn	NUM
ejpam-6306	287	4	∫	∫	PROPN
ejpam-6306	287	5	ρ	ρ	PROPN
ejpam-6306	287	6	(	(	PUNCT
ejpam-6306	287	7	υ̌−1	υ̌−1	PROPN
ejpam-6306	287	8	(	(	PUNCT
ejpam-6306	287	9	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	287	10	)	)	PUNCT
ejpam-6306	287	11	2	2	NUM
ejpam-6306	287	12	)	)	PUNCT
ejpam-6306	287	13	)	)	PUNCT
ejpam-6306	287	14	(	(	PUNCT
ejpam-6306	287	15	υ̌(α	υ̌(α	PROPN
ejpam-6306	287	16	)	)	PUNCT
ejpam-6306	287	17	+	+	CCONJ
ejpam-6306	287	18	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	287	19	2υ̌(µ))τ	2υ̌(µ))τ	NOUN
ejpam-6306	287	20	υ̌′(µ)f(µ)dµ	υ̌′(µ)f(µ)dµ	PROPN
ejpam-6306	287	21	=	=	PUNCT
ejpam-6306	287	22	−1	−1	NOUN
ejpam-6306	287	23	2(υ̌(ρ)−	2(υ̌(ρ)−	PROPN
ejpam-6306	287	24	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	287	25	∞∑	∞∑	PRON
ejpam-6306	287	26	n=0	n=0	NUM
ejpam-6306	287	27	(	(	PUNCT
ejpam-6306	287	28	ϑ)κn(ξ(µ	ϑ)κn(ξ(µ	NOUN
ejpam-6306	287	29	)	)	PUNCT
ejpam-6306	287	30	v)n	v)n	NOUN
ejpam-6306	288	1	γ(τ	γ(τ	PROPN
ejpam-6306	288	2	+	+	SYM
ejpam-6306	288	3	vn)(z)δn	vn)(z)δn	NUM
ejpam-6306	288	4	∫	∫	PROPN
ejpam-6306	288	5	ρ	ρ	PROPN
ejpam-6306	288	6	(	(	PUNCT
ejpam-6306	288	7	υ̌−1	υ̌−1	PROPN
ejpam-6306	288	8	(	(	PUNCT
ejpam-6306	288	9	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	288	10	)	)	PUNCT
ejpam-6306	288	11	2	2	NUM
ejpam-6306	288	12	)	)	PUNCT
ejpam-6306	288	13	)	)	PUNCT
ejpam-6306	288	14	f(µ)d(υ̌(α	f(µ)d(υ̌(α	PROPN
ejpam-6306	288	15	)	)	PUNCT
ejpam-6306	288	16	+	+	CCONJ
ejpam-6306	288	17	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	288	18	2υ̌(µ))τ	2υ̌(µ))τ	NOUN
ejpam-6306	288	19	=	=	SYM
ejpam-6306	288	20	1	1	NUM
ejpam-6306	288	21	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	288	22	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	288	23	∞∑	∞∑	NUM
ejpam-6306	288	24	n=0	n=0	NUM
ejpam-6306	288	25	(	(	PUNCT
ejpam-6306	288	26	ϑ)κn(ξ(µ	ϑ)κn(ξ(µ	NOUN
ejpam-6306	288	27	)	)	PUNCT
ejpam-6306	288	28	v)n	v)n	NOUN
ejpam-6306	289	1	γ(τ	γ(τ	PROPN
ejpam-6306	289	2	+	+	NUM
ejpam-6306	289	3	vn)(z)δn	vn)(z)δn	X
ejpam-6306	289	4	[	[	PUNCT
ejpam-6306	289	5	(	(	PUNCT
ejpam-6306	289	6	υ̌(α)−	υ̌(α)−	NOUN
ejpam-6306	289	7	υ̌(ρ))τf	υ̌(ρ))τf	NOUN
ejpam-6306	289	8	(	(	PUNCT
ejpam-6306	289	9	υ̌−1	υ̌−1	X
ejpam-6306	289	10	(	(	PUNCT
ejpam-6306	289	11	υ̌(α	υ̌(α	PROPN
ejpam-6306	289	12	)	)	PUNCT
ejpam-6306	289	13	+	+	CCONJ
ejpam-6306	289	14	υ̌(ρ	υ̌(ρ	X
ejpam-6306	289	15	)	)	PUNCT
ejpam-6306	289	16	2	2	NUM
ejpam-6306	289	17	)	)	PUNCT
ejpam-6306	289	18	)	)	PUNCT
ejpam-6306	290	1	+	+	CCONJ
ejpam-6306	290	2	∫	∫	PROPN
ejpam-6306	290	3	ρ	ρ	PROPN
ejpam-6306	290	4	(	(	PUNCT
ejpam-6306	290	5	υ̌−1	υ̌−1	PROPN
ejpam-6306	290	6	(	(	PUNCT
ejpam-6306	290	7	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	290	8	)	)	PUNCT
ejpam-6306	290	9	2	2	NUM
ejpam-6306	290	10	)	)	PUNCT
ejpam-6306	290	11	)	)	PUNCT
ejpam-6306	290	12	(	(	PUNCT
ejpam-6306	290	13	υ̌(α	υ̌(α	PROPN
ejpam-6306	290	14	)	)	PUNCT
ejpam-6306	290	15	+	+	CCONJ
ejpam-6306	290	16	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	290	17	2υ̌)τf	2υ̌)τf	NUM
ejpam-6306	290	18	′(µ)dµ	′(µ)dµ	NOUN
ejpam-6306	290	19	]	]	PUNCT
ejpam-6306	290	20	=	=	SYM
ejpam-6306	290	21	1	1	NUM
ejpam-6306	290	22	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	290	23	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	290	24	eϑ,z	eϑ,z	NOUN
ejpam-6306	290	25	,	,	PUNCT
ejpam-6306	290	26	κ	κ	X
ejpam-6306	290	27	ν	ν	PROPN
ejpam-6306	290	28	,	,	PUNCT
ejpam-6306	290	29	τ	τ	PROPN
ejpam-6306	290	30	,	,	PUNCT
ejpam-6306	290	31	j	j	PROPN
ejpam-6306	290	32	(	(	PUNCT
ejpam-6306	290	33	ξ(µ	ξ(µ	PROPN
ejpam-6306	290	34	)	)	PUNCT
ejpam-6306	290	35	v	v	NOUN
ejpam-6306	290	36	)	)	PUNCT
ejpam-6306	290	37	[	[	PUNCT
ejpam-6306	290	38	(	(	PUNCT
ejpam-6306	290	39	υ̌(α)−	υ̌(α)−	NOUN
ejpam-6306	290	40	υ̌(ρ))τf	υ̌(ρ))τf	NOUN
ejpam-6306	290	41	(	(	PUNCT
ejpam-6306	290	42	υ̌−1	υ̌−1	X
ejpam-6306	290	43	(	(	PUNCT
ejpam-6306	290	44	υ̌(α	υ̌(α	PROPN
ejpam-6306	290	45	)	)	PUNCT
ejpam-6306	290	46	+	+	CCONJ
ejpam-6306	290	47	υ̌(ρ	υ̌(ρ	X
ejpam-6306	290	48	)	)	PUNCT
ejpam-6306	290	49	2	2	NUM
ejpam-6306	290	50	)	)	PUNCT
ejpam-6306	290	51	)	)	PUNCT
ejpam-6306	291	1	+	+	CCONJ
ejpam-6306	291	2	∫	∫	PROPN
ejpam-6306	291	3	ρ	ρ	PROPN
ejpam-6306	291	4	(	(	PUNCT
ejpam-6306	291	5	υ̌−1	υ̌−1	PROPN
ejpam-6306	291	6	(	(	PUNCT
ejpam-6306	291	7	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	291	8	)	)	PUNCT
ejpam-6306	291	9	2	2	NUM
ejpam-6306	291	10	)	)	PUNCT
ejpam-6306	291	11	)	)	PUNCT
ejpam-6306	291	12	(	(	PUNCT
ejpam-6306	291	13	υ̌(α	υ̌(α	PROPN
ejpam-6306	291	14	)	)	PUNCT
ejpam-6306	291	15	+	+	CCONJ
ejpam-6306	291	16	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	291	17	2υ̌)τf	2υ̌)τf	NUM
ejpam-6306	291	18	′(µ)dµ	′(µ)dµ	PROPN
ejpam-6306	291	19	]	]	PUNCT
ejpam-6306	291	20	.	.	PUNCT
ejpam-6306	292	1	(	(	PUNCT
ejpam-6306	292	2	30	30	NUM
ejpam-6306	292	3	)	)	PUNCT
ejpam-6306	292	4	similarly	similarly	ADV
ejpam-6306	292	5	,	,	PUNCT
ejpam-6306	292	6	we	we	PRON
ejpam-6306	292	7	have	have	VERB
ejpam-6306	292	8	j2	j2	NOUN
ejpam-6306	292	9	:	:	PUNCT
ejpam-6306	292	10	=	=	SYM
ejpam-6306	292	11	1	1	NUM
ejpam-6306	292	12	(	(	PUNCT
ejpam-6306	292	13	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	292	14	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	292	15	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	292	16	,	,	PUNCT
ejpam-6306	292	17	κ	κ	NOUN
ejpam-6306	292	18	ν	ν	PROPN
ejpam-6306	292	19	,	,	PUNCT
ejpam-6306	292	20	τ	τ	PROPN
ejpam-6306	292	21	,	,	PUNCT
ejpam-6306	292	22	j	j	PROPN
ejpam-6306	292	23	,	,	PUNCT
ejpam-6306	292	24	ω,(υ̌−1	ω,(υ̌−1	PROPN
ejpam-6306	292	25	(	(	PUNCT
ejpam-6306	292	26	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	NOUN
ejpam-6306	292	27	)	)	PUNCT
ejpam-6306	292	28	2	2	NUM
ejpam-6306	292	29	)	)	PUNCT
ejpam-6306	292	30	)	)	PUNCT
ejpam-6306	292	31	−	−	ADP
ejpam-6306	292	32	f(ρ	f(ρ	NOUN
ejpam-6306	292	33	)	)	PUNCT
ejpam-6306	292	34	=	=	SYM
ejpam-6306	292	35	1	1	NUM
ejpam-6306	292	36	(	(	PUNCT
ejpam-6306	292	37	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	292	38	υ̌(α))τ	υ̌(α))τ	PROPN
ejpam-6306	292	39	∞∑	∞∑	NUM
ejpam-6306	292	40	n=0	n=0	NUM
ejpam-6306	292	41	(	(	PUNCT
ejpam-6306	292	42	ϑ)κn(ξ(µ	ϑ)κn(ξ(µ	NOUN
ejpam-6306	292	43	)	)	PUNCT
ejpam-6306	292	44	v)n	v)n	NOUN
ejpam-6306	293	1	γ(τ	γ(τ	PROPN
ejpam-6306	293	2	+	+	SYM
ejpam-6306	293	3	vn)(z)δn	vn)(z)δn	NUM
ejpam-6306	293	4	∫	∫	PROPN
ejpam-6306	293	5	α	α	PROPN
ejpam-6306	293	6	(	(	PUNCT
ejpam-6306	293	7	υ̌−1	υ̌−1	PROPN
ejpam-6306	293	8	(	(	PUNCT
ejpam-6306	293	9	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	293	10	)	)	PUNCT
ejpam-6306	293	11	2	2	NUM
ejpam-6306	293	12	)	)	PUNCT
ejpam-6306	293	13	)	)	PUNCT
ejpam-6306	293	14	(	(	PUNCT
ejpam-6306	293	15	υ̌(α	υ̌(α	PROPN
ejpam-6306	293	16	)	)	PUNCT
ejpam-6306	293	17	+	+	CCONJ
ejpam-6306	293	18	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	293	19	2υ̌(µ))τ	2υ̌(µ))τ	NOUN
ejpam-6306	293	20	υ̌′(µ)f(µ)dµ	υ̌′(µ)f(µ)dµ	PROPN
ejpam-6306	293	21	=	=	PUNCT
ejpam-6306	293	22	−1	−1	NOUN
ejpam-6306	293	23	2(υ̌(ρ)−	2(υ̌(ρ)−	PROPN
ejpam-6306	293	24	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	293	25	∞∑	∞∑	PRON
ejpam-6306	293	26	n=0	n=0	NUM
ejpam-6306	293	27	(	(	PUNCT
ejpam-6306	293	28	ϑ)κn(ξ(µ	ϑ)κn(ξ(µ	NOUN
ejpam-6306	293	29	)	)	PUNCT
ejpam-6306	293	30	v)n	v)n	NOUN
ejpam-6306	294	1	γ(τ	γ(τ	PROPN
ejpam-6306	294	2	+	+	SYM
ejpam-6306	294	3	vn)(z)δn	vn)(z)δn	NUM
ejpam-6306	294	4	∫	∫	PROPN
ejpam-6306	294	5	α	α	PROPN
ejpam-6306	294	6	(	(	PUNCT
ejpam-6306	294	7	υ̌−1	υ̌−1	PROPN
ejpam-6306	294	8	(	(	PUNCT
ejpam-6306	294	9	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	294	10	)	)	PUNCT
ejpam-6306	294	11	2	2	NUM
ejpam-6306	294	12	)	)	PUNCT
ejpam-6306	294	13	)	)	PUNCT
ejpam-6306	294	14	f(µ)d(υ̌(α	f(µ)d(υ̌(α	PROPN
ejpam-6306	294	15	)	)	PUNCT
ejpam-6306	294	16	+	+	CCONJ
ejpam-6306	294	17	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	294	18	2υ̌(µ))τ	2υ̌(µ))τ	NOUN
ejpam-6306	294	19	r.	r.	PROPN
ejpam-6306	294	20	s.	s.	PROPN
ejpam-6306	294	21	ali	ali	PROPN
ejpam-6306	294	22	et	et	PROPN
ejpam-6306	294	23	al	al	PROPN
ejpam-6306	294	24	.	.	PUNCT
ejpam-6306	294	25	/	/	SYM
ejpam-6306	294	26	eur	eur	PROPN
ejpam-6306	294	27	.	.	PUNCT
ejpam-6306	295	1	j.	j.	PROPN
ejpam-6306	295	2	pure	pure	PROPN
ejpam-6306	295	3	appl	appl	PROPN
ejpam-6306	295	4	.	.	PROPN
ejpam-6306	295	5	math	math	PROPN
ejpam-6306	295	6	,	,	PUNCT
ejpam-6306	295	7	18	18	NUM
ejpam-6306	295	8	(	(	PUNCT
ejpam-6306	295	9	3	3	NUM
ejpam-6306	295	10	)	)	PUNCT
ejpam-6306	295	11	(	(	PUNCT
ejpam-6306	295	12	2025	2025	NUM
ejpam-6306	295	13	)	)	PUNCT
ejpam-6306	295	14	,	,	PUNCT
ejpam-6306	295	15	6306	6306	NUM
ejpam-6306	295	16	15	15	NUM
ejpam-6306	295	17	of	of	ADP
ejpam-6306	295	18	18	18	NUM
ejpam-6306	295	19	=	=	SYM
ejpam-6306	295	20	1	1	NUM
ejpam-6306	295	21	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	295	22	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	296	1	∞∑	∞∑	NUM
ejpam-6306	296	2	n=0	n=0	NUM
ejpam-6306	296	3	(	(	PUNCT
ejpam-6306	296	4	ϑ)κn(ξ(µ	ϑ)κn(ξ(µ	NOUN
ejpam-6306	296	5	)	)	PUNCT
ejpam-6306	296	6	v)n	v)n	NOUN
ejpam-6306	297	1	γ(τ	γ(τ	PROPN
ejpam-6306	297	2	+	+	NUM
ejpam-6306	297	3	vn)(z)δn	vn)(z)δn	X
ejpam-6306	297	4	[	[	PUNCT
ejpam-6306	297	5	(	(	PUNCT
ejpam-6306	297	6	υ̌(α)−	υ̌(α)−	NOUN
ejpam-6306	297	7	υ̌(ρ))τf	υ̌(ρ))τf	NOUN
ejpam-6306	297	8	(	(	PUNCT
ejpam-6306	297	9	υ̌−1	υ̌−1	X
ejpam-6306	297	10	(	(	PUNCT
ejpam-6306	297	11	υ̌(α	υ̌(α	PROPN
ejpam-6306	297	12	)	)	PUNCT
ejpam-6306	297	13	+	+	CCONJ
ejpam-6306	297	14	υ̌(ρ	υ̌(ρ	X
ejpam-6306	297	15	)	)	PUNCT
ejpam-6306	297	16	2	2	NUM
ejpam-6306	297	17	)	)	PUNCT
ejpam-6306	297	18	)	)	PUNCT
ejpam-6306	298	1	+	+	CCONJ
ejpam-6306	298	2	∫	∫	PROPN
ejpam-6306	298	3	α	α	X
ejpam-6306	298	4	(	(	PUNCT
ejpam-6306	298	5	υ̌−1	υ̌−1	PROPN
ejpam-6306	298	6	(	(	PUNCT
ejpam-6306	298	7	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	298	8	)	)	PUNCT
ejpam-6306	298	9	2	2	NUM
ejpam-6306	298	10	)	)	PUNCT
ejpam-6306	298	11	)	)	PUNCT
ejpam-6306	298	12	(	(	PUNCT
ejpam-6306	298	13	υ̌(α	υ̌(α	PROPN
ejpam-6306	298	14	)	)	PUNCT
ejpam-6306	298	15	+	+	CCONJ
ejpam-6306	298	16	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	298	17	2υ̌)τf	2υ̌)τf	NUM
ejpam-6306	298	18	′(µ)dµ	′(µ)dµ	NOUN
ejpam-6306	298	19	]	]	PUNCT
ejpam-6306	298	20	=	=	SYM
ejpam-6306	298	21	1	1	NUM
ejpam-6306	298	22	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	298	23	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	298	24	eϑ,z	eϑ,z	NOUN
ejpam-6306	298	25	,	,	PUNCT
ejpam-6306	298	26	κ	κ	X
ejpam-6306	298	27	ν	ν	PROPN
ejpam-6306	298	28	,	,	PUNCT
ejpam-6306	298	29	τ	τ	PROPN
ejpam-6306	298	30	,	,	PUNCT
ejpam-6306	298	31	j	j	PROPN
ejpam-6306	298	32	(	(	PUNCT
ejpam-6306	298	33	ξ(µ	ξ(µ	PROPN
ejpam-6306	298	34	)	)	PUNCT
ejpam-6306	298	35	v	v	NOUN
ejpam-6306	298	36	)	)	PUNCT
ejpam-6306	298	37	[	[	PUNCT
ejpam-6306	298	38	(	(	PUNCT
ejpam-6306	298	39	υ̌(α)−	υ̌(α)−	NOUN
ejpam-6306	298	40	υ̌(ρ))τf	υ̌(ρ))τf	NOUN
ejpam-6306	298	41	(	(	PUNCT
ejpam-6306	298	42	υ̌−1	υ̌−1	X
ejpam-6306	298	43	(	(	PUNCT
ejpam-6306	298	44	υ̌(α	υ̌(α	PROPN
ejpam-6306	298	45	)	)	PUNCT
ejpam-6306	298	46	+	+	CCONJ
ejpam-6306	298	47	υ̌(ρ	υ̌(ρ	X
ejpam-6306	298	48	)	)	PUNCT
ejpam-6306	298	49	2	2	NUM
ejpam-6306	298	50	)	)	PUNCT
ejpam-6306	298	51	)	)	PUNCT
ejpam-6306	299	1	+	+	CCONJ
ejpam-6306	299	2	∫	∫	PROPN
ejpam-6306	299	3	ρ	ρ	PROPN
ejpam-6306	299	4	(	(	PUNCT
ejpam-6306	299	5	υ̌−1	υ̌−1	PROPN
ejpam-6306	299	6	(	(	PUNCT
ejpam-6306	299	7	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	299	8	)	)	PUNCT
ejpam-6306	299	9	2	2	NUM
ejpam-6306	299	10	)	)	PUNCT
ejpam-6306	299	11	)	)	PUNCT
ejpam-6306	299	12	(	(	PUNCT
ejpam-6306	299	13	υ̌(α	υ̌(α	PROPN
ejpam-6306	299	14	)	)	PUNCT
ejpam-6306	299	15	+	+	CCONJ
ejpam-6306	299	16	υ̌(ρ)−	υ̌(ρ)−	NUM
ejpam-6306	299	17	2υ̌)τf	2υ̌)τf	NUM
ejpam-6306	299	18	′(µ)dµ	′(µ)dµ	PROPN
ejpam-6306	299	19	]	]	PUNCT
ejpam-6306	299	20	.	.	PUNCT
ejpam-6306	300	1	(	(	PUNCT
ejpam-6306	300	2	31	31	NUM
ejpam-6306	300	3	)	)	PUNCT
ejpam-6306	300	4	from	from	ADP
ejpam-6306	300	5	the	the	DET
ejpam-6306	300	6	identities	identity	NOUN
ejpam-6306	300	7	in	in	ADP
ejpam-6306	300	8	(	(	PUNCT
ejpam-6306	300	9	30	30	NUM
ejpam-6306	300	10	)	)	PUNCT
ejpam-6306	300	11	and	and	CCONJ
ejpam-6306	300	12	(	(	PUNCT
ejpam-6306	300	13	31	31	NUM
ejpam-6306	300	14	)	)	PUNCT
ejpam-6306	300	15	,	,	PUNCT
ejpam-6306	300	16	we	we	PRON
ejpam-6306	300	17	have	have	VERB
ejpam-6306	300	18	j1	j1	NOUN
ejpam-6306	301	1	+	+	CCONJ
ejpam-6306	301	2	j2−f	j2−f	PROPN
ejpam-6306	301	3	(	(	PUNCT
ejpam-6306	301	4	υ̌−1	υ̌−1	X
ejpam-6306	301	5	(	(	PUNCT
ejpam-6306	301	6	υ̌(α	υ̌(α	PROPN
ejpam-6306	301	7	)	)	PUNCT
ejpam-6306	301	8	+	+	CCONJ
ejpam-6306	301	9	υ̌(ρ	υ̌(ρ	X
ejpam-6306	301	10	)	)	PUNCT
ejpam-6306	301	11	2	2	NUM
ejpam-6306	301	12	)	)	PUNCT
ejpam-6306	301	13	)	)	PUNCT
ejpam-6306	302	1	=	=	SYM
ejpam-6306	302	2	1	1	NUM
ejpam-6306	302	3	2(υ̌(ρ)−	2(υ̌(ρ)−	NUM
ejpam-6306	302	4	υ̌(α))τ	υ̌(α))τ	NUM
ejpam-6306	302	5	eϑ,z	eϑ,z	NOUN
ejpam-6306	302	6	,	,	PUNCT
ejpam-6306	302	7	κ	κ	X
ejpam-6306	302	8	ν	ν	PROPN
ejpam-6306	302	9	,	,	PUNCT
ejpam-6306	302	10	τ	τ	PROPN
ejpam-6306	302	11	,	,	PUNCT
ejpam-6306	302	12	j	j	PROPN
ejpam-6306	302	13	(	(	PUNCT
ejpam-6306	302	14	ξ(µ	ξ(µ	PROPN
ejpam-6306	302	15	)	)	PUNCT
ejpam-6306	302	16	v	v	NOUN
ejpam-6306	302	17	)	)	PUNCT
ejpam-6306	302	18	(	(	PUNCT
ejpam-6306	302	19	∫	∫	PROPN
ejpam-6306	302	20	ρ	ρ	PROPN
ejpam-6306	302	21	(	(	PUNCT
ejpam-6306	302	22	υ̌−1	υ̌−1	PROPN
ejpam-6306	302	23	(	(	PUNCT
ejpam-6306	302	24	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	302	25	)	)	PUNCT
ejpam-6306	302	26	2	2	NUM
ejpam-6306	302	27	)	)	PUNCT
ejpam-6306	302	28	)	)	PUNCT
ejpam-6306	302	29	(	(	PUNCT
ejpam-6306	302	30	υ̌(α	υ̌(α	PROPN
ejpam-6306	302	31	)	)	PUNCT
ejpam-6306	303	1	+	+	CCONJ
ejpam-6306	303	2	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	303	3	2υ̌(µ))τf	2υ̌(µ))τf	NUM
ejpam-6306	303	4	′(µ)dµ	′(µ)dµ	NOUN
ejpam-6306	303	5	−	−	NOUN
ejpam-6306	303	6	∫	∫	PROPN
ejpam-6306	304	1	α	α	PROPN
ejpam-6306	304	2	(	(	PUNCT
ejpam-6306	304	3	υ̌−1	υ̌−1	PROPN
ejpam-6306	304	4	(	(	PUNCT
ejpam-6306	304	5	υ̌(α)+υ̌(ρ	υ̌(α)+υ̌(ρ	ADJ
ejpam-6306	304	6	)	)	PUNCT
ejpam-6306	304	7	2	2	NUM
ejpam-6306	304	8	)	)	PUNCT
ejpam-6306	304	9	)	)	PUNCT
ejpam-6306	304	10	(	(	PUNCT
ejpam-6306	304	11	υ̌(α	υ̌(α	PROPN
ejpam-6306	304	12	)	)	PUNCT
ejpam-6306	304	13	+	+	CCONJ
ejpam-6306	304	14	υ̌(ρ)−	υ̌(ρ)−	NOUN
ejpam-6306	304	15	2υ̌(µ))τf	2υ̌(µ))τf	NUM
ejpam-6306	304	16	′(µ)dµ	′(µ)dµ	PROPN
ejpam-6306	304	17	)	)	PUNCT
ejpam-6306	304	18	,	,	PUNCT
ejpam-6306	304	19	which	which	PRON
ejpam-6306	304	20	is	be	AUX
ejpam-6306	304	21	the	the	DET
ejpam-6306	304	22	required	require	VERB
ejpam-6306	304	23	result	result	NOUN
ejpam-6306	304	24	.	.	PUNCT
ejpam-6306	305	1	corollary	corollary	ADJ
ejpam-6306	305	2	8	8	NUM
ejpam-6306	305	3	.	.	PUNCT
ejpam-6306	306	1	if	if	SCONJ
ejpam-6306	306	2	we	we	PRON
ejpam-6306	306	3	take	take	VERB
ejpam-6306	306	4	υ̌(x	υ̌(x	NUM
ejpam-6306	306	5	)	)	PUNCT
ejpam-6306	306	6	=	=	SYM
ejpam-6306	307	1	x	x	PROPN
ejpam-6306	307	2	and	and	CCONJ
ejpam-6306	307	3	τ	τ	X
ejpam-6306	307	4	=	=	NOUN
ejpam-6306	307	5	1	1	NUM
ejpam-6306	307	6	in	in	ADP
ejpam-6306	307	7	theorem	theorem	NOUN
ejpam-6306	307	8	4	4	NUM
ejpam-6306	307	9	,	,	PUNCT
ejpam-6306	307	10	then	then	ADV
ejpam-6306	307	11	we	we	PRON
ejpam-6306	307	12	have	have	VERB
ejpam-6306	307	13	the	the	DET
ejpam-6306	307	14	following	follow	VERB
ejpam-6306	307	15	identity	identity	NOUN
ejpam-6306	307	16	:	:	PUNCT
ejpam-6306	307	17	1	1	NUM
ejpam-6306	307	18	ρ−	ρ−	NOUN
ejpam-6306	307	19	α	α	X
ejpam-6306	307	20	[	[	PUNCT
ejpam-6306	307	21	ℑϑ,z	ℑϑ,z	PROPN
ejpam-6306	307	22	,	,	PUNCT
ejpam-6306	307	23	κ	κ	NOUN
ejpam-6306	307	24	ν	ν	PROPN
ejpam-6306	307	25	,	,	PUNCT
ejpam-6306	307	26	τ	τ	PROPN
ejpam-6306	307	27	,	,	PUNCT
ejpam-6306	307	28	j	j	PROPN
ejpam-6306	307	29	,	,	PUNCT
ejpam-6306	307	30	ω,(α+ρ	ω,(α+ρ	ADV
ejpam-6306	307	31	2	2	NUM
ejpam-6306	307	32	)	)	PUNCT
ejpam-6306	307	33	+	+	CCONJ
ejpam-6306	308	1	f(α	f(α	NOUN
ejpam-6306	308	2	)	)	PUNCT
ejpam-6306	309	1	+	+	CCONJ
ejpam-6306	309	2	ℑϑ,z	ℑϑ,z	NOUN
ejpam-6306	309	3	,	,	PUNCT
ejpam-6306	309	4	κ	κ	NOUN
ejpam-6306	309	5	ν	ν	PROPN
ejpam-6306	309	6	,	,	PUNCT
ejpam-6306	309	7	τ	τ	PROPN
ejpam-6306	309	8	,	,	PUNCT
ejpam-6306	309	9	j	j	PROPN
ejpam-6306	309	10	,	,	PUNCT
ejpam-6306	309	11	ω,(α+ρ	ω,(α+ρ	ADV
ejpam-6306	309	12	2	2	NUM
ejpam-6306	309	13	)	)	PUNCT
ejpam-6306	309	14	−	−	PRON
ejpam-6306	309	15	f(ρ	f(ρ	NOUN
ejpam-6306	309	16	)	)	PUNCT
ejpam-6306	309	17	]	]	PUNCT
ejpam-6306	310	1	−	−	PROPN
ejpam-6306	310	2	f	f	X
ejpam-6306	310	3	(	(	PUNCT
ejpam-6306	310	4	α+	α+	PROPN
ejpam-6306	310	5	ρ	ρ	PROPN
ejpam-6306	310	6	2	2	NUM
ejpam-6306	310	7	)	)	PUNCT
ejpam-6306	310	8	=	=	SYM
ejpam-6306	310	9	1	1	NUM
ejpam-6306	310	10	2(ρ−	2(ρ−	NUM
ejpam-6306	310	11	α	α	NUM
ejpam-6306	310	12	)	)	PUNCT
ejpam-6306	310	13	eϑ,z	eϑ,z	NOUN
ejpam-6306	310	14	,	,	PUNCT
ejpam-6306	310	15	κ	κ	X
ejpam-6306	310	16	ν	ν	PROPN
ejpam-6306	310	17	,	,	PUNCT
ejpam-6306	310	18	τ	τ	PROPN
ejpam-6306	310	19	,	,	PUNCT
ejpam-6306	310	20	j	j	PROPN
ejpam-6306	310	21	(	(	PUNCT
ejpam-6306	310	22	ξ(µ	ξ(µ	PROPN
ejpam-6306	310	23	)	)	PUNCT
ejpam-6306	310	24	v	v	NOUN
ejpam-6306	310	25	)	)	PUNCT
ejpam-6306	310	26	(	(	PUNCT
ejpam-6306	310	27	∫	∫	PROPN
ejpam-6306	310	28	ρ	ρ	X
ejpam-6306	310	29	α+ρ	α+ρ	NUM
ejpam-6306	310	30	2	2	NUM
ejpam-6306	310	31	+	+	CCONJ
ejpam-6306	310	32	(	(	PUNCT
ejpam-6306	310	33	α+	α+	PUNCT
ejpam-6306	310	34	ρ−	ρ−	NOUN
ejpam-6306	310	35	2µ)f	2µ)f	NUM
ejpam-6306	310	36	′(µ)dµ	′(µ)dµ	PROPN
ejpam-6306	310	37	−	−	NOUN
ejpam-6306	310	38	∫	∫	PROPN
ejpam-6306	310	39	α	α	NOUN
ejpam-6306	310	40	α+ρ	α+ρ	NUM
ejpam-6306	310	41	2	2	NUM
ejpam-6306	310	42	+	+	CCONJ
ejpam-6306	310	43	(	(	PUNCT
ejpam-6306	310	44	α+	α+	PUNCT
ejpam-6306	310	45	ρ−	ρ−	NOUN
ejpam-6306	310	46	2µ)f	2µ)f	NUM
ejpam-6306	310	47	′(µ)dµ	′(µ)dµ	PROPN
ejpam-6306	310	48	)	)	PUNCT
ejpam-6306	310	49	.	.	PUNCT
ejpam-6306	311	1	5	5	X
ejpam-6306	311	2	.	.	X
ejpam-6306	311	3	conclusion	conclusion	NOUN
ejpam-6306	311	4	in	in	ADP
ejpam-6306	311	5	this	this	DET
ejpam-6306	311	6	research	research	NOUN
ejpam-6306	311	7	work	work	NOUN
ejpam-6306	311	8	,	,	PUNCT
ejpam-6306	311	9	we	we	PRON
ejpam-6306	311	10	discussed	discuss	VERB
ejpam-6306	311	11	the	the	DET
ejpam-6306	311	12	generalized	generalize	VERB
ejpam-6306	311	13	fractional	fractional	ADJ
ejpam-6306	311	14	operators	operator	NOUN
ejpam-6306	311	15	for	for	ADP
ejpam-6306	311	16	the	the	DET
ejpam-6306	311	17	differentiable	differentiable	ADJ
ejpam-6306	311	18	monotone	monotone	ADJ
ejpam-6306	311	19	function	function	NOUN
ejpam-6306	311	20	with	with	ADP
ejpam-6306	311	21	generalized	generalized	ADJ
ejpam-6306	311	22	mittag	mittag	ADJ
ejpam-6306	311	23	-	-	PUNCT
ejpam-6306	311	24	leffler	leffler	NOUN
ejpam-6306	311	25	functions	function	NOUN
ejpam-6306	311	26	as	as	ADP
ejpam-6306	311	27	its	its	PRON
ejpam-6306	311	28	kernel	kernel	NOUN
ejpam-6306	311	29	and	and	CCONJ
ejpam-6306	311	30	established	establish	VERB
ejpam-6306	311	31	some	some	DET
ejpam-6306	311	32	relations	relation	NOUN
ejpam-6306	311	33	,	,	PUNCT
ejpam-6306	311	34	by	by	ADP
ejpam-6306	311	35	implementation	implementation	NOUN
ejpam-6306	311	36	of	of	ADP
ejpam-6306	311	37	newly	newly	ADV
ejpam-6306	311	38	defined	define	VERB
ejpam-6306	311	39	fractional	fractional	ADJ
ejpam-6306	311	40	operators	operator	NOUN
ejpam-6306	311	41	to	to	ADP
ejpam-6306	311	42	r.	r.	PROPN
ejpam-6306	311	43	s.	s.	PROPN
ejpam-6306	311	44	ali	ali	PROPN
ejpam-6306	311	45	et	et	PROPN
ejpam-6306	311	46	al	al	PROPN
ejpam-6306	311	47	.	.	PUNCT
ejpam-6306	311	48	/	/	SYM
ejpam-6306	311	49	eur	eur	PROPN
ejpam-6306	311	50	.	.	PUNCT
ejpam-6306	312	1	j.	j.	PROPN
ejpam-6306	312	2	pure	pure	PROPN
ejpam-6306	312	3	appl	appl	PROPN
ejpam-6306	312	4	.	.	PROPN
ejpam-6306	312	5	math	math	PROPN
ejpam-6306	312	6	,	,	PUNCT
ejpam-6306	312	7	18	18	NUM
ejpam-6306	312	8	(	(	PUNCT
ejpam-6306	312	9	3	3	NUM
ejpam-6306	312	10	)	)	PUNCT
ejpam-6306	312	11	(	(	PUNCT
ejpam-6306	312	12	2025	2025	NUM
ejpam-6306	312	13	)	)	PUNCT
ejpam-6306	312	14	,	,	PUNCT
ejpam-6306	312	15	6306	6306	NUM
ejpam-6306	312	16	16	16	NUM
ejpam-6306	312	17	of	of	ADP
ejpam-6306	312	18	18	18	NUM
ejpam-6306	312	19	modify	modify	VERB
ejpam-6306	312	20	some	some	DET
ejpam-6306	312	21	well	well	ADV
ejpam-6306	312	22	-	-	PUNCT
ejpam-6306	312	23	known	know	VERB
ejpam-6306	312	24	inequalities	inequality	NOUN
ejpam-6306	312	25	for	for	ADP
ejpam-6306	312	26	the	the	DET
ejpam-6306	312	27	υ̌-convex	υ̌-convex	NOUN
ejpam-6306	312	28	function	function	NOUN
ejpam-6306	312	29	.	.	PUNCT
ejpam-6306	313	1	we	we	PRON
ejpam-6306	313	2	discussed	discuss	VERB
ejpam-6306	313	3	the	the	DET
ejpam-6306	313	4	behavior	behavior	NOUN
ejpam-6306	313	5	of	of	ADP
ejpam-6306	313	6	hermite	hermite	ADJ
ejpam-6306	313	7	hadamard	hadamard	ADJ
ejpam-6306	313	8	inequalities	inequality	NOUN
ejpam-6306	313	9	and	and	CCONJ
ejpam-6306	313	10	their	their	PRON
ejpam-6306	313	11	consequences	consequence	NOUN
ejpam-6306	313	12	by	by	ADP
ejpam-6306	313	13	utilizing	utilize	VERB
ejpam-6306	313	14	newly	newly	ADV
ejpam-6306	313	15	defined	define	VERB
ejpam-6306	313	16	operators	operator	NOUN
ejpam-6306	313	17	for	for	ADP
ejpam-6306	313	18	continuous	continuous	ADJ
ejpam-6306	313	19	differentiable	differentiable	NOUN
ejpam-6306	313	20	strictly	strictly	ADV
ejpam-6306	313	21	monotone	monotone	ADJ
ejpam-6306	313	22	function	function	NOUN
ejpam-6306	313	23	.	.	PUNCT
ejpam-6306	314	1	in	in	ADP
ejpam-6306	314	2	future	future	NOUN
ejpam-6306	314	3	,	,	PUNCT
ejpam-6306	314	4	many	many	ADJ
ejpam-6306	314	5	researchers	researcher	NOUN
ejpam-6306	314	6	can	can	AUX
ejpam-6306	314	7	work	work	VERB
ejpam-6306	314	8	to	to	PART
ejpam-6306	314	9	develop	develop	VERB
ejpam-6306	314	10	such	such	DET
ejpam-6306	314	11	a	a	DET
ejpam-6306	314	12	type	type	NOUN
ejpam-6306	314	13	of	of	ADP
ejpam-6306	314	14	fractional	fractional	ADJ
ejpam-6306	314	15	operators	operator	NOUN
ejpam-6306	314	16	and	and	CCONJ
ejpam-6306	314	17	make	make	VERB
ejpam-6306	314	18	alterations	alteration	NOUN
ejpam-6306	314	19	to	to	ADP
ejpam-6306	314	20	some	some	DET
ejpam-6306	314	21	inequalities	inequality	NOUN
ejpam-6306	314	22	for	for	ADP
ejpam-6306	314	23	differentiable	differentiable	ADJ
ejpam-6306	314	24	monotone	monotone	NOUN
ejpam-6306	314	25	(	(	PUNCT
ejpam-6306	314	26	p	p	NOUN
ejpam-6306	314	27	,	,	PUNCT
ejpam-6306	314	28	q)-convexities	q)-convexitie	NOUN
ejpam-6306	314	29	.	.	PUNCT
ejpam-6306	315	1	acknowledgements	acknowledgement	NOUN
ejpam-6306	315	2	this	this	DET
ejpam-6306	315	3	research	research	NOUN
ejpam-6306	315	4	was	be	AUX
ejpam-6306	315	5	funded	fund	VERB
ejpam-6306	315	6	by	by	ADP
ejpam-6306	315	7	the	the	DET
ejpam-6306	315	8	national	national	ADJ
ejpam-6306	315	9	science	science	NOUN
ejpam-6306	315	10	,	,	PUNCT
ejpam-6306	315	11	research	research	NOUN
ejpam-6306	315	12	and	and	CCONJ
ejpam-6306	315	13	innovation	innovation	NOUN
ejpam-6306	315	14	fund	fund	NOUN
ejpam-6306	315	15	(	(	PUNCT
ejpam-6306	315	16	nsrf	nsrf	NOUN
ejpam-6306	315	17	)	)	PUNCT
ejpam-6306	315	18	and	and	CCONJ
ejpam-6306	315	19	king	king	PROPN
ejpam-6306	315	20	mongkut	mongkut	PROPN
ejpam-6306	315	21	’s	’s	PROPN
ejpam-6306	315	22	university	university	PROPN
ejpam-6306	315	23	of	of	ADP
ejpam-6306	315	24	technology	technology	PROPN
ejpam-6306	315	25	north	north	PROPN
ejpam-6306	315	26	bangkok	bangkok	PROPN
ejpam-6306	315	27	under	under	ADP
ejpam-6306	315	28	contract	contract	NOUN
ejpam-6306	315	29	no	no	PROPN
ejpam-6306	315	30	.	.	PUNCT
ejpam-6306	316	1	kmutnb	kmutnb	NOUN
ejpam-6306	316	2	-	-	PUNCT
ejpam-6306	316	3	ff-68	ff-68	NOUN
ejpam-6306	316	4	-	-	PUNCT
ejpam-6306	316	5	b-04	b-04	PROPN
ejpam-6306	316	6	.	.	PUNCT
ejpam-6306	317	1	conflict	conflict	NOUN
ejpam-6306	317	2	of	of	ADP
ejpam-6306	317	3	interest	interest	NOUN
ejpam-6306	317	4	the	the	DET
ejpam-6306	317	5	authors	author	NOUN
ejpam-6306	317	6	declare	declare	VERB
ejpam-6306	317	7	that	that	SCONJ
ejpam-6306	317	8	there	there	PRON
ejpam-6306	317	9	are	be	VERB
ejpam-6306	317	10	no	no	DET
ejpam-6306	317	11	conflicts	conflict	NOUN
ejpam-6306	317	12	of	of	ADP
ejpam-6306	317	13	interest	interest	NOUN
ejpam-6306	317	14	.	.	PUNCT
ejpam-6306	318	1	references	reference	NOUN
ejpam-6306	318	2	[	[	X
ejpam-6306	318	3	1	1	NUM
ejpam-6306	318	4	]	]	PUNCT
ejpam-6306	318	5	bernhard	bernhard	PROPN
ejpam-6306	318	6	riemann	riemann	PROPN
ejpam-6306	318	7	.	.	PUNCT
ejpam-6306	318	8	versuch	versuch	PROPN
ejpam-6306	318	9	einer	einer	PROPN
ejpam-6306	318	10	allgemeinen	allgemeinen	PROPN
ejpam-6306	318	11	auffassung	auffassung	PROPN
ejpam-6306	318	12	der	der	ADJ
ejpam-6306	318	13	integration	integration	NOUN
ejpam-6306	318	14	und	und	VERB
ejpam-6306	318	15	differentiation	differentiation	NOUN
ejpam-6306	318	16	.	.	PUNCT
ejpam-6306	319	1	gesammelte	gesammelte	PROPN
ejpam-6306	319	2	werke	werke	PROPN
ejpam-6306	319	3	,	,	PUNCT
ejpam-6306	319	4	62(1876	62(1876	NUM
ejpam-6306	319	5	)	)	PUNCT
ejpam-6306	319	6	,	,	PUNCT
ejpam-6306	319	7	1876	1876	NUM
ejpam-6306	319	8	.	.	PUNCT
ejpam-6306	320	1	[	[	X
ejpam-6306	320	2	2	2	NUM
ejpam-6306	320	3	]	]	X
ejpam-6306	320	4	joseph	joseph	PROPN
ejpam-6306	320	5	liouville	liouville	PROPN
ejpam-6306	320	6	.	.	PUNCT
ejpam-6306	321	1	mémoire	mémoire	NOUN
ejpam-6306	321	2	sur	sur	PROPN
ejpam-6306	321	3	quelques	quelques	PROPN
ejpam-6306	321	4	questions	question	NOUN
ejpam-6306	321	5	de	de	X
ejpam-6306	321	6	géométrie	géométrie	X
ejpam-6306	321	7	et	et	X
ejpam-6306	321	8	de	de	X
ejpam-6306	321	9	mécanique	mécanique	PROPN
ejpam-6306	321	10	,	,	PUNCT
ejpam-6306	321	11	et	et	PROPN
ejpam-6306	321	12	sur	sur	PROPN
ejpam-6306	321	13	un	un	PROPN
ejpam-6306	321	14	nouveau	nouveau	PROPN
ejpam-6306	321	15	genre	genre	PROPN
ejpam-6306	321	16	de	de	PROPN
ejpam-6306	321	17	calcul	calcul	PROPN
ejpam-6306	321	18	pour	pour	PROPN
ejpam-6306	321	19	résoudre	résoudre	NOUN
ejpam-6306	321	20	ces	ce	NOUN
ejpam-6306	321	21	questions	question	NOUN
ejpam-6306	321	22	.	.	PUNCT
ejpam-6306	322	1	1832	1832	NUM
ejpam-6306	322	2	.	.	PUNCT
ejpam-6306	323	1	[	[	X
ejpam-6306	323	2	3	3	X
ejpam-6306	323	3	]	]	PUNCT
ejpam-6306	323	4	niels	niels	PROPN
ejpam-6306	323	5	henrik	henrik	PROPN
ejpam-6306	323	6	abel	abel	PROPN
ejpam-6306	323	7	.	.	PUNCT
ejpam-6306	324	1	oeuvres	oeuvre	VERB
ejpam-6306	324	2	complètes	complètes	PROPN
ejpam-6306	324	3	de	de	PROPN
ejpam-6306	324	4	niels	niels	PROPN
ejpam-6306	324	5	henrik	henrik	PROPN
ejpam-6306	324	6	abel	abel	PROPN
ejpam-6306	324	7	:	:	PUNCT
ejpam-6306	324	8	nouvelle	nouvelle	PROPN
ejpam-6306	324	9	édition	édition	PROPN
ejpam-6306	324	10	,	,	PUNCT
ejpam-6306	324	11	volume	volume	NOUN
ejpam-6306	324	12	1	1	NUM
ejpam-6306	324	13	.	.	PUNCT
ejpam-6306	324	14	cambridge	cambridge	PROPN
ejpam-6306	324	15	university	university	PROPN
ejpam-6306	324	16	press	press	NOUN
ejpam-6306	324	17	,	,	PUNCT
ejpam-6306	324	18	2012	2012	NUM
ejpam-6306	324	19	.	.	PUNCT
ejpam-6306	325	1	[	[	X
ejpam-6306	325	2	4	4	NUM
ejpam-6306	325	3	]	]	X
ejpam-6306	325	4	h	h	NOUN
ejpam-6306	325	5	laurent	laurent	PROPN
ejpam-6306	325	6	.	.	PUNCT
ejpam-6306	326	1	sur	sur	PROPN
ejpam-6306	326	2	le	le	PROPN
ejpam-6306	326	3	calcul	calcul	PROPN
ejpam-6306	326	4	des	des	PROPN
ejpam-6306	326	5	dérivées	dérivées	PROPN
ejpam-6306	326	6	à	à	PROPN
ejpam-6306	326	7	indices	indice	VERB
ejpam-6306	326	8	quelconques	quelconque	NOUN
ejpam-6306	326	9	.	.	PUNCT
ejpam-6306	327	1	nouvelles	nouvelles	PROPN
ejpam-6306	327	2	annales	annales	PROPN
ejpam-6306	327	3	de	de	PROPN
ejpam-6306	327	4	mathématiques	mathématiques	PROPN
ejpam-6306	327	5	:	:	PUNCT
ejpam-6306	327	6	journal	journal	PROPN
ejpam-6306	327	7	des	des	PROPN
ejpam-6306	327	8	candidats	candidats	PROPN
ejpam-6306	327	9	aux	aux	PROPN
ejpam-6306	327	10	écoles	écoles	PROPN
ejpam-6306	327	11	polytechnique	polytechnique	X
ejpam-6306	327	12	et	et	X
ejpam-6306	327	13	normale	normale	PROPN
ejpam-6306	327	14	,	,	PUNCT
ejpam-6306	327	15	3:240–252	3:240–252	NUM
ejpam-6306	327	16	,	,	PUNCT
ejpam-6306	327	17	1884	1884	NUM
ejpam-6306	327	18	.	.	PUNCT
ejpam-6306	328	1	[	[	X
ejpam-6306	328	2	5	5	NUM
ejpam-6306	328	3	]	]	PUNCT
ejpam-6306	328	4	rudolf	rudolf	NOUN
ejpam-6306	328	5	hilfer	hilfer	NOUN
ejpam-6306	328	6	et	et	PROPN
ejpam-6306	328	7	al	al	PROPN
ejpam-6306	328	8	.	.	PUNCT
ejpam-6306	329	1	threefold	threefold	PROPN
ejpam-6306	329	2	introduction	introduction	NOUN
ejpam-6306	329	3	to	to	ADP
ejpam-6306	329	4	fractional	fractional	ADJ
ejpam-6306	329	5	derivatives	derivative	NOUN
ejpam-6306	329	6	.	.	PUNCT
ejpam-6306	330	1	anomalous	anomalous	ADJ
ejpam-6306	330	2	transport	transport	NOUN
ejpam-6306	330	3	:	:	PUNCT
ejpam-6306	330	4	foundations	foundation	NOUN
ejpam-6306	330	5	and	and	CCONJ
ejpam-6306	330	6	applications	application	NOUN
ejpam-6306	330	7	,	,	PUNCT
ejpam-6306	330	8	pages	page	NOUN
ejpam-6306	330	9	17–73	17–73	NUM
ejpam-6306	330	10	,	,	PUNCT
ejpam-6306	330	11	2008	2008	NUM
ejpam-6306	330	12	.	.	PUNCT
ejpam-6306	331	1	[	[	X
ejpam-6306	331	2	6	6	NUM
ejpam-6306	331	3	]	]	X
ejpam-6306	331	4	kai	kai	PROPN
ejpam-6306	331	5	diethelm	diethelm	PROPN
ejpam-6306	331	6	,	,	PUNCT
ejpam-6306	331	7	dumitru	dumitru	PROPN
ejpam-6306	331	8	baleanu	baleanu	NOUN
ejpam-6306	331	9	,	,	PUNCT
ejpam-6306	331	10	and	and	CCONJ
ejpam-6306	331	11	enrico	enrico	PROPN
ejpam-6306	331	12	scalas	scalas	PROPN
ejpam-6306	331	13	.	.	PUNCT
ejpam-6306	331	14	fractional	fractional	PROPN
ejpam-6306	331	15	calculus	calculus	NOUN
ejpam-6306	331	16	:	:	PUNCT
ejpam-6306	331	17	models	model	NOUN
ejpam-6306	331	18	and	and	CCONJ
ejpam-6306	331	19	numerical	numerical	ADJ
ejpam-6306	331	20	methods	method	NOUN
ejpam-6306	331	21	.	.	PUNCT
ejpam-6306	332	1	world	world	PROPN
ejpam-6306	332	2	scientific	scientific	ADJ
ejpam-6306	332	3	,	,	PUNCT
ejpam-6306	332	4	2012	2012	NUM
ejpam-6306	332	5	.	.	PUNCT
ejpam-6306	333	1	[	[	X
ejpam-6306	333	2	7	7	X
ejpam-6306	333	3	]	]	SYM
ejpam-6306	333	4	augustus	augustus	PROPN
ejpam-6306	333	5	de	de	PROPN
ejpam-6306	333	6	morgan	morgan	PROPN
ejpam-6306	333	7	.	.	PUNCT
ejpam-6306	334	1	the	the	DET
ejpam-6306	334	2	differential	differential	ADJ
ejpam-6306	334	3	and	and	CCONJ
ejpam-6306	334	4	integral	integral	ADJ
ejpam-6306	334	5	calculus	calculus	NOUN
ejpam-6306	334	6	.	.	PUNCT
ejpam-6306	335	1	baldwin	baldwin	PROPN
ejpam-6306	335	2	and	and	CCONJ
ejpam-6306	335	3	cradock	cradock	NOUN
ejpam-6306	335	4	,	,	PUNCT
ejpam-6306	335	5	1836	1836	NUM
ejpam-6306	335	6	.	.	PUNCT
ejpam-6306	336	1	[	[	X
ejpam-6306	336	2	8	8	NUM
ejpam-6306	336	3	]	]	PUNCT
ejpam-6306	336	4	jamshed	jamshed	PROPN
ejpam-6306	336	5	nasir	nasir	PROPN
ejpam-6306	336	6	,	,	PUNCT
ejpam-6306	336	7	shahid	shahid	PROPN
ejpam-6306	336	8	qaisar	qaisar	PROPN
ejpam-6306	336	9	,	,	PUNCT
ejpam-6306	336	10	saad	saad	PROPN
ejpam-6306	336	11	ihsan	ihsan	PROPN
ejpam-6306	336	12	butt	butt	PROPN
ejpam-6306	336	13	,	,	PUNCT
ejpam-6306	336	14	hassen	hassen	PROPN
ejpam-6306	336	15	aydi	aydi	ADV
ejpam-6306	336	16	,	,	PUNCT
ejpam-6306	336	17	and	and	CCONJ
ejpam-6306	336	18	manuel	manuel	PROPN
ejpam-6306	336	19	de	de	PROPN
ejpam-6306	336	20	la	la	PROPN
ejpam-6306	336	21	sen	sen	PROPN
ejpam-6306	336	22	.	.	PROPN
ejpam-6306	336	23	hermite	hermite	PROPN
ejpam-6306	336	24	-	-	PUNCT
ejpam-6306	336	25	hadamard	hadamard	PROPN
ejpam-6306	336	26	like	like	ADP
ejpam-6306	336	27	inequalities	inequality	NOUN
ejpam-6306	336	28	for	for	ADP
ejpam-6306	336	29	fractional	fractional	ADJ
ejpam-6306	336	30	integral	integral	ADJ
ejpam-6306	336	31	operator	operator	NOUN
ejpam-6306	336	32	via	via	ADP
ejpam-6306	336	33	convexity	convexity	NOUN
ejpam-6306	336	34	and	and	CCONJ
ejpam-6306	336	35	quasi	quasi	NOUN
ejpam-6306	336	36	-	-	NOUN
ejpam-6306	336	37	convexity	convexity	NOUN
ejpam-6306	336	38	with	with	ADP
ejpam-6306	336	39	their	their	PRON
ejpam-6306	336	40	applications	application	NOUN
ejpam-6306	336	41	.	.	PUNCT
ejpam-6306	337	1	aims	aim	VERB
ejpam-6306	337	2	math	math	NOUN
ejpam-6306	337	3	,	,	PUNCT
ejpam-6306	337	4	7(3):3418–3439	7(3):3418–3439	NOUN
ejpam-6306	337	5	,	,	PUNCT
ejpam-6306	337	6	2022	2022	NUM
ejpam-6306	337	7	.	.	PUNCT
ejpam-6306	338	1	[	[	X
ejpam-6306	338	2	9	9	NUM
ejpam-6306	338	3	]	]	PUNCT
ejpam-6306	338	4	jamshed	jamshed	PROPN
ejpam-6306	338	5	nasir	nasir	PROPN
ejpam-6306	338	6	,	,	PUNCT
ejpam-6306	338	7	saber	saber	PROPN
ejpam-6306	338	8	mansour	mansour	PROPN
ejpam-6306	338	9	,	,	PUNCT
ejpam-6306	338	10	shahid	shahid	PROPN
ejpam-6306	338	11	qaisar	qaisar	PROPN
ejpam-6306	338	12	,	,	PUNCT
ejpam-6306	338	13	and	and	CCONJ
ejpam-6306	338	14	hassen	hassen	PROPN
ejpam-6306	338	15	aydi	aydi	VERB
ejpam-6306	338	16	.	.	PUNCT
ejpam-6306	339	1	some	some	DET
ejpam-6306	339	2	variants	variant	NOUN
ejpam-6306	339	3	on	on	ADP
ejpam-6306	339	4	mercer	mercer	PROPN
ejpam-6306	339	5	’s	’s	PART
ejpam-6306	339	6	hermite	hermite	PROPN
ejpam-6306	339	7	-	-	PUNCT
ejpam-6306	339	8	hadamard	hadamard	ADJ
ejpam-6306	339	9	like	like	ADP
ejpam-6306	339	10	inclusions	inclusion	NOUN
ejpam-6306	339	11	of	of	ADP
ejpam-6306	339	12	interval	interval	NOUN
ejpam-6306	339	13	-	-	PUNCT
ejpam-6306	339	14	valued	value	VERB
ejpam-6306	339	15	functions	function	NOUN
ejpam-6306	339	16	for	for	ADP
ejpam-6306	339	17	strong	strong	ADJ
ejpam-6306	339	18	kernel	kernel	NOUN
ejpam-6306	339	19	.	.	PUNCT
ejpam-6306	340	1	aims	aim	VERB
ejpam-6306	340	2	math	math	NOUN
ejpam-6306	340	3	,	,	PUNCT
ejpam-6306	340	4	8(5):10001–10020	8(5):10001–10020	PROPN
ejpam-6306	340	5	,	,	PUNCT
ejpam-6306	340	6	2023	2023	NUM
ejpam-6306	340	7	.	.	PUNCT
ejpam-6306	341	1	[	[	X
ejpam-6306	341	2	10	10	NUM
ejpam-6306	341	3	]	]	X
ejpam-6306	341	4	pshtiwan	pshtiwan	PROPN
ejpam-6306	341	5	othman	othman	PROPN
ejpam-6306	341	6	mohammed	mohammed	PROPN
ejpam-6306	341	7	and	and	CCONJ
ejpam-6306	341	8	mehmet	mehmet	PROPN
ejpam-6306	341	9	zeki	zeki	PROPN
ejpam-6306	341	10	sarikaya	sarikaya	PROPN
ejpam-6306	341	11	.	.	PUNCT
ejpam-6306	342	1	on	on	ADP
ejpam-6306	342	2	generalized	generalized	ADJ
ejpam-6306	342	3	fractional	fractional	ADJ
ejpam-6306	342	4	integral	integral	ADJ
ejpam-6306	342	5	inequalities	inequality	NOUN
ejpam-6306	342	6	for	for	ADP
ejpam-6306	342	7	twice	twice	ADV
ejpam-6306	342	8	differentiable	differentiable	ADJ
ejpam-6306	342	9	convex	convex	NOUN
ejpam-6306	342	10	functions	function	NOUN
ejpam-6306	342	11	.	.	PUNCT
ejpam-6306	343	1	journal	journal	NOUN
ejpam-6306	343	2	of	of	ADP
ejpam-6306	343	3	computational	computational	ADJ
ejpam-6306	343	4	and	and	CCONJ
ejpam-6306	343	5	applied	applied	ADJ
ejpam-6306	343	6	mathematics	mathematic	NOUN
ejpam-6306	343	7	,	,	PUNCT
ejpam-6306	343	8	372:112740	372:112740	NUM
ejpam-6306	343	9	,	,	PUNCT
ejpam-6306	343	10	2020	2020	NUM
ejpam-6306	343	11	.	.	PUNCT
ejpam-6306	344	1	r.	r.	PROPN
ejpam-6306	344	2	s.	s.	PROPN
ejpam-6306	344	3	ali	ali	PROPN
ejpam-6306	344	4	et	et	PROPN
ejpam-6306	344	5	al	al	PROPN
ejpam-6306	344	6	.	.	PUNCT
ejpam-6306	344	7	/	/	SYM
ejpam-6306	344	8	eur	eur	PROPN
ejpam-6306	344	9	.	.	PUNCT
ejpam-6306	345	1	j.	j.	PROPN
ejpam-6306	345	2	pure	pure	PROPN
ejpam-6306	345	3	appl	appl	PROPN
ejpam-6306	345	4	.	.	PROPN
ejpam-6306	345	5	math	math	PROPN
ejpam-6306	345	6	,	,	PUNCT
ejpam-6306	345	7	18	18	NUM
ejpam-6306	345	8	(	(	PUNCT
ejpam-6306	345	9	3	3	NUM
ejpam-6306	345	10	)	)	PUNCT
ejpam-6306	345	11	(	(	PUNCT
ejpam-6306	345	12	2025	2025	NUM
ejpam-6306	345	13	)	)	PUNCT
ejpam-6306	345	14	,	,	PUNCT
ejpam-6306	345	15	6306	6306	NUM
ejpam-6306	345	16	17	17	NUM
ejpam-6306	345	17	of	of	ADP
ejpam-6306	345	18	18	18	NUM
ejpam-6306	345	19	[	[	SYM
ejpam-6306	345	20	11	11	NUM
ejpam-6306	345	21	]	]	X
ejpam-6306	345	22	dumitru	dumitru	PROPN
ejpam-6306	345	23	baleanu	baleanu	NOUN
ejpam-6306	345	24	and	and	CCONJ
ejpam-6306	345	25	antónio	antónio	VERB
ejpam-6306	345	26	mendes	mendes	PROPN
ejpam-6306	345	27	lopes	lopes	PROPN
ejpam-6306	345	28	.	.	PUNCT
ejpam-6306	346	1	applications	application	NOUN
ejpam-6306	346	2	in	in	ADP
ejpam-6306	346	3	engineering	engineering	NOUN
ejpam-6306	346	4	,	,	PUNCT
ejpam-6306	346	5	life	life	NOUN
ejpam-6306	346	6	and	and	CCONJ
ejpam-6306	346	7	social	social	ADJ
ejpam-6306	346	8	sciences	science	NOUN
ejpam-6306	346	9	,	,	PUNCT
ejpam-6306	346	10	part	part	NOUN
ejpam-6306	346	11	b.	b.	PROPN
ejpam-6306	346	12	2019	2019	NUM
ejpam-6306	346	13	.	.	PUNCT
ejpam-6306	347	1	[	[	X
ejpam-6306	347	2	12	12	NUM
ejpam-6306	347	3	]	]	PUNCT
ejpam-6306	347	4	rudolf	rudolf	NOUN
ejpam-6306	347	5	hilfer	hilfer	NOUN
ejpam-6306	347	6	.	.	PUNCT
ejpam-6306	348	1	applications	application	NOUN
ejpam-6306	348	2	of	of	ADP
ejpam-6306	348	3	fractional	fractional	ADJ
ejpam-6306	348	4	calculus	calculus	NOUN
ejpam-6306	348	5	in	in	ADP
ejpam-6306	348	6	physics	physics	PROPN
ejpam-6306	348	7	.	.	PUNCT
ejpam-6306	349	1	world	world	PROPN
ejpam-6306	349	2	scientific	scientific	PROPN
ejpam-6306	349	3	,	,	PUNCT
ejpam-6306	349	4	2000	2000	NUM
ejpam-6306	349	5	.	.	PUNCT
ejpam-6306	350	1	[	[	X
ejpam-6306	350	2	13	13	NUM
ejpam-6306	350	3	]	]	X
ejpam-6306	350	4	hongguang	hongguang	PROPN
ejpam-6306	350	5	sun	sun	PROPN
ejpam-6306	350	6	,	,	PUNCT
ejpam-6306	350	7	yong	yong	PROPN
ejpam-6306	350	8	zhang	zhang	PROPN
ejpam-6306	350	9	,	,	PUNCT
ejpam-6306	350	10	dumitru	dumitru	PROPN
ejpam-6306	350	11	baleanu	baleanu	PROPN
ejpam-6306	350	12	,	,	PUNCT
ejpam-6306	350	13	wen	wen	PROPN
ejpam-6306	350	14	chen	chen	PROPN
ejpam-6306	350	15	,	,	PUNCT
ejpam-6306	350	16	and	and	CCONJ
ejpam-6306	350	17	yangquan	yangquan	PROPN
ejpam-6306	350	18	chen	chen	PROPN
ejpam-6306	350	19	.	.	PUNCT
ejpam-6306	351	1	a	a	DET
ejpam-6306	351	2	new	new	ADJ
ejpam-6306	351	3	collection	collection	NOUN
ejpam-6306	351	4	of	of	ADP
ejpam-6306	351	5	real	real	ADJ
ejpam-6306	351	6	world	world	NOUN
ejpam-6306	351	7	applications	application	NOUN
ejpam-6306	351	8	of	of	ADP
ejpam-6306	351	9	fractional	fractional	ADJ
ejpam-6306	351	10	calculus	calculus	NOUN
ejpam-6306	351	11	in	in	ADP
ejpam-6306	351	12	science	science	NOUN
ejpam-6306	351	13	and	and	CCONJ
ejpam-6306	351	14	engineering	engineering	NOUN
ejpam-6306	351	15	.	.	PUNCT
ejpam-6306	352	1	communications	communication	NOUN
ejpam-6306	352	2	in	in	ADP
ejpam-6306	352	3	nonlinear	nonlinear	ADJ
ejpam-6306	352	4	science	science	NOUN
ejpam-6306	352	5	and	and	CCONJ
ejpam-6306	352	6	numerical	numerical	PROPN
ejpam-6306	352	7	simulation	simulation	PROPN
ejpam-6306	352	8	,	,	PUNCT
ejpam-6306	352	9	64:213–231	64:213–231	NUM
ejpam-6306	352	10	,	,	PUNCT
ejpam-6306	352	11	2018	2018	NUM
ejpam-6306	352	12	.	.	PUNCT
ejpam-6306	353	1	[	[	X
ejpam-6306	353	2	14	14	NUM
ejpam-6306	353	3	]	]	PUNCT
ejpam-6306	353	4	ahmed	ahmed	PROPN
ejpam-6306	353	5	ma	ma	PROPN
ejpam-6306	353	6	el	el	PROPN
ejpam-6306	353	7	-	-	PUNCT
ejpam-6306	353	8	sayed	say	VERB
ejpam-6306	353	9	and	and	CCONJ
ejpam-6306	353	10	fatma	fatma	PROPN
ejpam-6306	353	11	m	m	PROPN
ejpam-6306	353	12	gaafar	gaafar	NOUN
ejpam-6306	353	13	.	.	PUNCT
ejpam-6306	354	1	fractional	fractional	ADJ
ejpam-6306	354	2	calculus	calculus	NOUN
ejpam-6306	354	3	and	and	CCONJ
ejpam-6306	354	4	some	some	DET
ejpam-6306	354	5	intermediate	intermediate	ADJ
ejpam-6306	354	6	physical	physical	ADJ
ejpam-6306	354	7	processes	process	NOUN
ejpam-6306	354	8	.	.	PUNCT
ejpam-6306	355	1	applied	apply	VERB
ejpam-6306	355	2	mathematics	mathematic	NOUN
ejpam-6306	355	3	and	and	CCONJ
ejpam-6306	355	4	computation	computation	NOUN
ejpam-6306	355	5	,	,	PUNCT
ejpam-6306	355	6	144(1):117–126	144(1):117–126	NUM
ejpam-6306	355	7	,	,	PUNCT
ejpam-6306	355	8	2003	2003	NUM
ejpam-6306	355	9	.	.	PUNCT
ejpam-6306	356	1	[	[	X
ejpam-6306	356	2	15	15	X
ejpam-6306	356	3	]	]	X
ejpam-6306	356	4	stefan	stefan	PROPN
ejpam-6306	356	5	g	g	PROPN
ejpam-6306	356	6	samko	samko	PROPN
ejpam-6306	356	7	.	.	PUNCT
ejpam-6306	357	1	fractional	fractional	ADJ
ejpam-6306	357	2	integrals	integral	NOUN
ejpam-6306	357	3	and	and	CCONJ
ejpam-6306	357	4	derivatives	derivative	NOUN
ejpam-6306	357	5	.	.	PUNCT
ejpam-6306	358	1	theory	theory	NOUN
ejpam-6306	358	2	and	and	CCONJ
ejpam-6306	358	3	applications	application	NOUN
ejpam-6306	358	4	,	,	PUNCT
ejpam-6306	358	5	1993	1993	NUM
ejpam-6306	358	6	.	.	PUNCT
ejpam-6306	359	1	[	[	X
ejpam-6306	359	2	16	16	NUM
ejpam-6306	359	3	]	]	X
ejpam-6306	359	4	aa	aa	PROPN
ejpam-6306	359	5	kilbas	kilbas	PROPN
ejpam-6306	359	6	.	.	PUNCT
ejpam-6306	359	7	theory	theory	NOUN
ejpam-6306	359	8	and	and	CCONJ
ejpam-6306	359	9	applications	application	NOUN
ejpam-6306	359	10	of	of	ADP
ejpam-6306	359	11	fractional	fractional	ADJ
ejpam-6306	359	12	differential	differential	ADJ
ejpam-6306	359	13	equations	equation	NOUN
ejpam-6306	359	14	.	.	PUNCT
ejpam-6306	360	1	northholland	northholland	PROPN
ejpam-6306	360	2	mathematics	mathematics	PROPN
ejpam-6306	360	3	studies	study	NOUN
ejpam-6306	360	4	,	,	PUNCT
ejpam-6306	360	5	204	204	NUM
ejpam-6306	360	6	,	,	PUNCT
ejpam-6306	360	7	2006	2006	NUM
ejpam-6306	360	8	.	.	PUNCT
ejpam-6306	361	1	[	[	X
ejpam-6306	361	2	17	17	NUM
ejpam-6306	361	3	]	]	X
ejpam-6306	361	4	igor	igor	NOUN
ejpam-6306	361	5	podlubny	podlubny	PROPN
ejpam-6306	361	6	.	.	PUNCT
ejpam-6306	362	1	fractional	fractional	ADJ
ejpam-6306	362	2	differential	differential	ADJ
ejpam-6306	362	3	equations	equation	NOUN
ejpam-6306	362	4	:	:	PUNCT
ejpam-6306	362	5	an	an	DET
ejpam-6306	362	6	introduction	introduction	NOUN
ejpam-6306	362	7	to	to	ADP
ejpam-6306	362	8	fractional	fractional	ADJ
ejpam-6306	362	9	derivatives	derivative	NOUN
ejpam-6306	362	10	,	,	PUNCT
ejpam-6306	362	11	fractional	fractional	ADJ
ejpam-6306	362	12	differential	differential	ADJ
ejpam-6306	362	13	equations	equation	NOUN
ejpam-6306	362	14	,	,	PUNCT
ejpam-6306	362	15	to	to	ADP
ejpam-6306	362	16	methods	method	NOUN
ejpam-6306	362	17	of	of	ADP
ejpam-6306	362	18	their	their	PRON
ejpam-6306	362	19	solution	solution	NOUN
ejpam-6306	362	20	and	and	CCONJ
ejpam-6306	362	21	some	some	PRON
ejpam-6306	362	22	of	of	ADP
ejpam-6306	362	23	their	their	PRON
ejpam-6306	362	24	applications	application	NOUN
ejpam-6306	362	25	,	,	PUNCT
ejpam-6306	362	26	volume	volume	NOUN
ejpam-6306	362	27	198	198	NUM
ejpam-6306	362	28	.	.	PUNCT
ejpam-6306	363	1	elsevier	elsevier	NOUN
ejpam-6306	363	2	,	,	PUNCT
ejpam-6306	363	3	1998	1998	NUM
ejpam-6306	363	4	.	.	PUNCT
ejpam-6306	364	1	[	[	X
ejpam-6306	364	2	18	18	NUM
ejpam-6306	364	3	]	]	SYM
ejpam-6306	364	4	dragoslav	dragoslav	NOUN
ejpam-6306	364	5	s	s	PART
ejpam-6306	364	6	mitrinović.	mitrinović.	PROPN
ejpam-6306	364	7	general	general	ADJ
ejpam-6306	364	8	inequalities	inequality	NOUN
ejpam-6306	364	9	.	.	PUNCT
ejpam-6306	365	1	in	in	ADP
ejpam-6306	365	2	analytic	analytic	ADJ
ejpam-6306	365	3	inequalities	inequality	NOUN
ejpam-6306	365	4	,	,	PUNCT
ejpam-6306	365	5	pages	page	NOUN
ejpam-6306	365	6	27–185	27–185	PROPN
ejpam-6306	365	7	.	.	PUNCT
ejpam-6306	365	8	springer	springer	NOUN
ejpam-6306	365	9	,	,	PUNCT
ejpam-6306	365	10	1970	1970	NUM
ejpam-6306	365	11	.	.	PUNCT
ejpam-6306	366	1	[	[	X
ejpam-6306	366	2	19	19	NUM
ejpam-6306	366	3	]	]	X
ejpam-6306	366	4	josip	josip	PROPN
ejpam-6306	366	5	e	e	PROPN
ejpam-6306	366	6	peajcariaac	peajcariaac	PROPN
ejpam-6306	366	7	and	and	CCONJ
ejpam-6306	366	8	yung	yung	PROPN
ejpam-6306	366	9	liang	liang	PROPN
ejpam-6306	366	10	tong	tong	PROPN
ejpam-6306	366	11	.	.	PUNCT
ejpam-6306	367	1	convex	convex	PROPN
ejpam-6306	367	2	functions	function	NOUN
ejpam-6306	367	3	,	,	PUNCT
ejpam-6306	367	4	partial	partial	ADJ
ejpam-6306	367	5	orderings	ordering	NOUN
ejpam-6306	367	6	,	,	PUNCT
ejpam-6306	367	7	and	and	CCONJ
ejpam-6306	367	8	statistical	statistical	ADJ
ejpam-6306	367	9	applications	application	NOUN
ejpam-6306	367	10	.	.	PUNCT
ejpam-6306	368	1	academic	academic	ADJ
ejpam-6306	368	2	press	press	NOUN
ejpam-6306	368	3	,	,	PUNCT
ejpam-6306	368	4	1992	1992	NUM
ejpam-6306	368	5	.	.	PUNCT
ejpam-6306	369	1	[	[	X
ejpam-6306	369	2	20	20	NUM
ejpam-6306	369	3	]	]	PUNCT
ejpam-6306	369	4	mehmet	mehmet	PROPN
ejpam-6306	369	5	zeki	zeki	PROPN
ejpam-6306	369	6	sarikaya	sarikaya	PROPN
ejpam-6306	369	7	and	and	CCONJ
ejpam-6306	369	8	h	h	PROPN
ejpam-6306	369	9	seyin	seyin	PROPN
ejpam-6306	369	10	yildirim	yildirim	PROPN
ejpam-6306	369	11	.	.	PUNCT
ejpam-6306	370	1	on	on	ADP
ejpam-6306	370	2	hermite	hermite	PROPN
ejpam-6306	370	3	-	-	PUNCT
ejpam-6306	370	4	hadamard	hadamard	ADJ
ejpam-6306	370	5	type	type	NOUN
ejpam-6306	370	6	inequalities	inequality	NOUN
ejpam-6306	370	7	for	for	ADP
ejpam-6306	370	8	riemann	riemann	PROPN
ejpam-6306	370	9	-	-	PUNCT
ejpam-6306	370	10	liouville	liouville	VERB
ejpam-6306	370	11	fractional	fractional	ADJ
ejpam-6306	370	12	integrals	integral	NOUN
ejpam-6306	370	13	.	.	PUNCT
ejpam-6306	371	1	miskolc	miskolc	ADJ
ejpam-6306	371	2	mathematical	mathematical	ADJ
ejpam-6306	371	3	notes	note	NOUN
ejpam-6306	371	4	,	,	PUNCT
ejpam-6306	371	5	17(2):1049	17(2):1049	NUM
ejpam-6306	371	6	–	–	PUNCT
ejpam-6306	371	7	1059	1059	NUM
ejpam-6306	371	8	,	,	PUNCT
ejpam-6306	371	9	2016	2016	NUM
ejpam-6306	371	10	.	.	PUNCT
ejpam-6306	372	1	[	[	X
ejpam-6306	372	2	21	21	NUM
ejpam-6306	372	3	]	]	X
ejpam-6306	372	4	hua	hua	PROPN
ejpam-6306	372	5	chen	chen	PROPN
ejpam-6306	372	6	and	and	CCONJ
ejpam-6306	372	7	udita	udita	PROPN
ejpam-6306	372	8	n	n	PROPN
ejpam-6306	372	9	katugampola	katugampola	PROPN
ejpam-6306	372	10	.	.	PUNCT
ejpam-6306	373	1	hermite	hermite	PROPN
ejpam-6306	373	2	–	–	PUNCT
ejpam-6306	373	3	hadamard	hadamard	ADJ
ejpam-6306	373	4	and	and	CCONJ
ejpam-6306	373	5	hermite	hermite	ADJ
ejpam-6306	373	6	–	–	PUNCT
ejpam-6306	373	7	hadamard	hadamard	ADJ
ejpam-6306	373	8	–	–	PUNCT
ejpam-6306	373	9	fejér	fejér	NOUN
ejpam-6306	373	10	type	type	NOUN
ejpam-6306	373	11	inequalities	inequality	NOUN
ejpam-6306	373	12	for	for	ADP
ejpam-6306	373	13	generalized	generalized	ADJ
ejpam-6306	373	14	fractional	fractional	ADJ
ejpam-6306	373	15	integrals	integral	NOUN
ejpam-6306	373	16	.	.	PUNCT
ejpam-6306	374	1	journal	journal	NOUN
ejpam-6306	374	2	of	of	ADP
ejpam-6306	374	3	mathematical	mathematical	ADJ
ejpam-6306	374	4	analysis	analysis	NOUN
ejpam-6306	374	5	and	and	CCONJ
ejpam-6306	374	6	applications	application	NOUN
ejpam-6306	374	7	,	,	PUNCT
ejpam-6306	374	8	446(2):1274–1291	446(2):1274–1291	NOUN
ejpam-6306	374	9	,	,	PUNCT
ejpam-6306	374	10	2017	2017	NUM
ejpam-6306	374	11	.	.	PUNCT
ejpam-6306	375	1	[	[	X
ejpam-6306	375	2	22	22	NUM
ejpam-6306	375	3	]	]	X
ejpam-6306	375	4	jiangfeng	jiangfeng	PROPN
ejpam-6306	375	5	han	han	PROPN
ejpam-6306	375	6	,	,	PUNCT
ejpam-6306	375	7	pshtiwan	pshtiwan	PROPN
ejpam-6306	375	8	othman	othman	PROPN
ejpam-6306	375	9	mohammed	mohammed	PROPN
ejpam-6306	375	10	,	,	PUNCT
ejpam-6306	375	11	and	and	CCONJ
ejpam-6306	375	12	huidan	huidan	PROPN
ejpam-6306	375	13	zeng	zeng	PROPN
ejpam-6306	375	14	.	.	PUNCT
ejpam-6306	376	1	generalized	generalize	VERB
ejpam-6306	376	2	fractional	fractional	ADJ
ejpam-6306	376	3	integral	integral	ADJ
ejpam-6306	376	4	inequalities	inequality	NOUN
ejpam-6306	376	5	of	of	ADP
ejpam-6306	376	6	hermite	hermite	PROPN
ejpam-6306	376	7	-	-	PUNCT
ejpam-6306	376	8	hadamard	hadamard	NOUN
ejpam-6306	376	9	-	-	PUNCT
ejpam-6306	376	10	type	type	NOUN
ejpam-6306	376	11	for	for	ADP
ejpam-6306	376	12	a	a	DET
ejpam-6306	376	13	convex	convex	NOUN
ejpam-6306	376	14	function	function	NOUN
ejpam-6306	376	15	.	.	PUNCT
ejpam-6306	377	1	open	open	ADJ
ejpam-6306	377	2	mathematics	mathematic	NOUN
ejpam-6306	377	3	,	,	PUNCT
ejpam-6306	377	4	18(1):794–806	18(1):794–806	PROPN
ejpam-6306	377	5	,	,	PUNCT
ejpam-6306	377	6	2020	2020	NUM
ejpam-6306	377	7	.	.	PUNCT
ejpam-6306	378	1	[	[	X
ejpam-6306	378	2	23	23	NUM
ejpam-6306	378	3	]	]	PUNCT
ejpam-6306	378	4	muhammad	muhammad	PROPN
ejpam-6306	378	5	uzair	uzair	PROPN
ejpam-6306	378	6	awan	awan	PROPN
ejpam-6306	378	7	,	,	PUNCT
ejpam-6306	378	8	sadia	sadia	PROPN
ejpam-6306	378	9	talib	talib	PROPN
ejpam-6306	378	10	,	,	PUNCT
ejpam-6306	378	11	yu	yu	PROPN
ejpam-6306	378	12	-	-	PROPN
ejpam-6306	378	13	ming	ming	PROPN
ejpam-6306	378	14	chu	chu	PROPN
ejpam-6306	378	15	,	,	PUNCT
ejpam-6306	378	16	muhammad	muhammad	PROPN
ejpam-6306	378	17	aslam	aslam	PROPN
ejpam-6306	378	18	noor	noor	PROPN
ejpam-6306	378	19	,	,	PUNCT
ejpam-6306	378	20	and	and	CCONJ
ejpam-6306	378	21	khalida	khalida	PROPN
ejpam-6306	378	22	inayat	inayat	PROPN
ejpam-6306	378	23	noor	noor	PROPN
ejpam-6306	378	24	.	.	PUNCT
ejpam-6306	379	1	some	some	DET
ejpam-6306	379	2	new	new	ADJ
ejpam-6306	379	3	refinements	refinement	NOUN
ejpam-6306	379	4	of	of	ADP
ejpam-6306	379	5	hermite	hermite	ADJ
ejpam-6306	379	6	–	–	PUNCT
ejpam-6306	379	7	hadamard	hadamard	ADJ
ejpam-6306	379	8	-	-	PUNCT
ejpam-6306	379	9	type	type	NOUN
ejpam-6306	379	10	inequalities	inequality	NOUN
ejpam-6306	379	11	involving	involve	VERB
ejpam-6306	379	12	ψk	ψk	NOUN
ejpam-6306	379	13	-	-	PUNCT
ejpam-6306	379	14	riemann	riemann	NOUN
ejpam-6306	379	15	–	–	PUNCT
ejpam-6306	379	16	liouville	liouville	VERB
ejpam-6306	379	17	fractional	fractional	ADJ
ejpam-6306	379	18	integrals	integral	NOUN
ejpam-6306	379	19	and	and	CCONJ
ejpam-6306	379	20	applications	application	NOUN
ejpam-6306	379	21	.	.	PUNCT
ejpam-6306	380	1	mathematical	mathematical	ADJ
ejpam-6306	380	2	problems	problem	NOUN
ejpam-6306	380	3	in	in	ADP
ejpam-6306	380	4	engineering	engineering	NOUN
ejpam-6306	380	5	,	,	PUNCT
ejpam-6306	380	6	2020(1):3051920	2020(1):3051920	NUM
ejpam-6306	380	7	,	,	PUNCT
ejpam-6306	380	8	2020	2020	NUM
ejpam-6306	380	9	.	.	PUNCT
ejpam-6306	381	1	[	[	X
ejpam-6306	381	2	24	24	NUM
ejpam-6306	381	3	]	]	X
ejpam-6306	381	4	tariq	tariq	NOUN
ejpam-6306	381	5	a	a	DET
ejpam-6306	381	6	aljaaidi	aljaaidi	VERB
ejpam-6306	381	7	and	and	CCONJ
ejpam-6306	381	8	deepak	deepak	PROPN
ejpam-6306	381	9	b	b	PROPN
ejpam-6306	381	10	pachpatte	pachpatte	PROPN
ejpam-6306	381	11	.	.	PUNCT
ejpam-6306	382	1	the	the	DET
ejpam-6306	382	2	minkowski	minkowski	PROPN
ejpam-6306	382	3	’s	’s	PART
ejpam-6306	382	4	inequalities	inequality	NOUN
ejpam-6306	382	5	via	via	ADP
ejpam-6306	382	6	ψriemann	ψriemann	ADJ
ejpam-6306	382	7	–	–	PUNCT
ejpam-6306	382	8	liouville	liouville	VERB
ejpam-6306	382	9	fractional	fractional	ADJ
ejpam-6306	382	10	integral	integral	ADJ
ejpam-6306	382	11	operators	operator	NOUN
ejpam-6306	382	12	.	.	PUNCT
ejpam-6306	383	1	rendiconti	rendiconti	ADJ
ejpam-6306	383	2	del	del	PROPN
ejpam-6306	383	3	circolo	circolo	PROPN
ejpam-6306	383	4	matematico	matematico	NOUN
ejpam-6306	383	5	di	di	PROPN
ejpam-6306	383	6	palermo	palermo	PROPN
ejpam-6306	383	7	series	series	PROPN
ejpam-6306	383	8	2	2	NUM
ejpam-6306	383	9	,	,	PUNCT
ejpam-6306	383	10	70(2):893–906	70(2):893–906	NUM
ejpam-6306	383	11	,	,	PUNCT
ejpam-6306	383	12	2021	2021	NUM
ejpam-6306	383	13	.	.	PUNCT
ejpam-6306	384	1	[	[	X
ejpam-6306	384	2	25	25	NUM
ejpam-6306	384	3	]	]	X
ejpam-6306	384	4	pshtiwan	pshtiwan	PROPN
ejpam-6306	384	5	othman	othman	PROPN
ejpam-6306	384	6	mohammed	mohammed	PROPN
ejpam-6306	384	7	,	,	PUNCT
ejpam-6306	384	8	hassen	hassen	PROPN
ejpam-6306	384	9	aydi	aydi	VERB
ejpam-6306	384	10	,	,	PUNCT
ejpam-6306	384	11	artion	artion	NOUN
ejpam-6306	384	12	kashuri	kashuri	PROPN
ejpam-6306	384	13	,	,	PUNCT
ejpam-6306	384	14	yasser	yasser	PROPN
ejpam-6306	384	15	salah	salah	PROPN
ejpam-6306	384	16	hamed	hamed	PROPN
ejpam-6306	384	17	,	,	PUNCT
ejpam-6306	384	18	and	and	CCONJ
ejpam-6306	384	19	khadijah	khadijah	PROPN
ejpam-6306	384	20	m	m	PROPN
ejpam-6306	384	21	abualnaja	abualnaja	PROPN
ejpam-6306	384	22	.	.	PUNCT
ejpam-6306	385	1	midpoint	midpoint	NOUN
ejpam-6306	385	2	inequalities	inequality	NOUN
ejpam-6306	385	3	in	in	ADP
ejpam-6306	385	4	fractional	fractional	ADJ
ejpam-6306	385	5	calculus	calculus	NOUN
ejpam-6306	385	6	defined	define	VERB
ejpam-6306	385	7	using	use	VERB
ejpam-6306	385	8	positive	positive	ADJ
ejpam-6306	385	9	weighted	weight	VERB
ejpam-6306	385	10	symmetry	symmetry	NOUN
ejpam-6306	385	11	function	function	NOUN
ejpam-6306	385	12	kernels	kernel	NOUN
ejpam-6306	385	13	.	.	PUNCT
ejpam-6306	386	1	symmetry	symmetry	PROPN
ejpam-6306	386	2	,	,	PUNCT
ejpam-6306	386	3	13(4):550	13(4):550	PROPN
ejpam-6306	386	4	,	,	PUNCT
ejpam-6306	386	5	2021	2021	NUM
ejpam-6306	386	6	.	.	PUNCT
ejpam-6306	387	1	[	[	X
ejpam-6306	387	2	26	26	NUM
ejpam-6306	387	3	]	]	X
ejpam-6306	387	4	pshtiwan	pshtiwan	PROPN
ejpam-6306	387	5	othman	othman	PROPN
ejpam-6306	387	6	mohammed	mohammed	PROPN
ejpam-6306	387	7	,	,	PUNCT
ejpam-6306	387	8	thabet	thabet	ADJ
ejpam-6306	387	9	abdeljawad	abdeljawad	NOUN
ejpam-6306	387	10	,	,	PUNCT
ejpam-6306	387	11	fahd	fahd	PROPN
ejpam-6306	387	12	jarad	jarad	PROPN
ejpam-6306	387	13	,	,	PUNCT
ejpam-6306	387	14	and	and	CCONJ
ejpam-6306	387	15	yu	yu	PROPN
ejpam-6306	387	16	-	-	PROPN
ejpam-6306	387	17	ming	ming	PROPN
ejpam-6306	387	18	chu	chu	PROPN
ejpam-6306	387	19	.	.	PROPN
ejpam-6306	387	20	existence	existence	NOUN
ejpam-6306	387	21	and	and	CCONJ
ejpam-6306	387	22	uniqueness	uniqueness	NOUN
ejpam-6306	387	23	of	of	ADP
ejpam-6306	387	24	uncertain	uncertain	ADJ
ejpam-6306	387	25	fractional	fractional	ADJ
ejpam-6306	387	26	backward	backward	ADJ
ejpam-6306	387	27	difference	difference	NOUN
ejpam-6306	387	28	equations	equation	NOUN
ejpam-6306	387	29	of	of	ADP
ejpam-6306	387	30	riemann	riemann	PROPN
ejpam-6306	387	31	–	–	PUNCT
ejpam-6306	387	32	liouville	liouville	NOUN
ejpam-6306	387	33	type	type	NOUN
ejpam-6306	387	34	.	.	PUNCT
ejpam-6306	388	1	mathematical	mathematical	ADJ
ejpam-6306	388	2	problems	problem	NOUN
ejpam-6306	388	3	in	in	ADP
ejpam-6306	388	4	engineering	engineering	NOUN
ejpam-6306	388	5	,	,	PUNCT
ejpam-6306	388	6	2020(1):6598682	2020(1):6598682	NOUN
ejpam-6306	388	7	,	,	PUNCT
ejpam-6306	388	8	2020	2020	NUM
ejpam-6306	388	9	.	.	PUNCT
ejpam-6306	389	1	[	[	X
ejpam-6306	389	2	27	27	NUM
ejpam-6306	389	3	]	]	PUNCT
ejpam-6306	389	4	bogdan	bogdan	PROPN
ejpam-6306	389	5	gavrea	gavrea	PROPN
ejpam-6306	389	6	and	and	CCONJ
ejpam-6306	389	7	ioan	ioan	PROPN
ejpam-6306	389	8	gavrea	gavrea	PROPN
ejpam-6306	389	9	.	.	PUNCT
ejpam-6306	390	1	on	on	ADP
ejpam-6306	390	2	some	some	DET
ejpam-6306	390	3	ostrowski	ostrowski	ADJ
ejpam-6306	390	4	type	type	NOUN
ejpam-6306	390	5	inequalities	inequality	NOUN
ejpam-6306	390	6	.	.	PUNCT
ejpam-6306	391	1	gen	gen	PROPN
ejpam-6306	391	2	.	.	PROPN
ejpam-6306	391	3	math	math	PROPN
ejpam-6306	391	4	,	,	PUNCT
ejpam-6306	391	5	r.	r.	PROPN
ejpam-6306	391	6	s.	s.	PROPN
ejpam-6306	391	7	ali	ali	PROPN
ejpam-6306	391	8	et	et	PROPN
ejpam-6306	391	9	al	al	PROPN
ejpam-6306	391	10	.	.	PUNCT
ejpam-6306	391	11	/	/	SYM
ejpam-6306	391	12	eur	eur	PROPN
ejpam-6306	391	13	.	.	PUNCT
ejpam-6306	392	1	j.	j.	PROPN
ejpam-6306	392	2	pure	pure	PROPN
ejpam-6306	392	3	appl	appl	PROPN
ejpam-6306	392	4	.	.	PROPN
ejpam-6306	392	5	math	math	PROPN
ejpam-6306	392	6	,	,	PUNCT
ejpam-6306	392	7	18	18	NUM
ejpam-6306	392	8	(	(	PUNCT
ejpam-6306	392	9	3	3	NUM
ejpam-6306	392	10	)	)	PUNCT
ejpam-6306	392	11	(	(	PUNCT
ejpam-6306	392	12	2025	2025	NUM
ejpam-6306	392	13	)	)	PUNCT
ejpam-6306	392	14	,	,	PUNCT
ejpam-6306	392	15	6306	6306	NUM
ejpam-6306	392	16	18	18	NUM
ejpam-6306	392	17	of	of	ADP
ejpam-6306	392	18	18	18	NUM
ejpam-6306	392	19	18(1):33–44	18(1):33–44	NUM
ejpam-6306	392	20	,	,	PUNCT
ejpam-6306	392	21	2010	2010	NUM
ejpam-6306	392	22	.	.	PUNCT
ejpam-6306	393	1	[	[	X
ejpam-6306	393	2	28	28	NUM
ejpam-6306	393	3	]	]	X
ejpam-6306	393	4	miguel	miguel	PROPN
ejpam-6306	393	5	vivas	vivas	PROPN
ejpam-6306	393	6	-	-	PROPN
ejpam-6306	393	7	cortez	cortez	PROPN
ejpam-6306	393	8	,	,	PUNCT
ejpam-6306	393	9	thabet	thabet	ADJ
ejpam-6306	393	10	abdeljawad	abdeljawad	NOUN
ejpam-6306	393	11	,	,	PUNCT
ejpam-6306	393	12	pshtiwan	pshtiwan	PROPN
ejpam-6306	393	13	othman	othman	PROPN
ejpam-6306	393	14	mohammed	mohammed	PROPN
ejpam-6306	393	15	,	,	PUNCT
ejpam-6306	393	16	and	and	CCONJ
ejpam-6306	393	17	yenny	yenny	PROPN
ejpam-6306	393	18	rangel	rangel	PROPN
ejpam-6306	393	19	-	-	PUNCT
ejpam-6306	393	20	oliveros	oliveros	PROPN
ejpam-6306	393	21	.	.	PUNCT
ejpam-6306	394	1	simpson	simpson	PROPN
ejpam-6306	394	2	’s	’s	PART
ejpam-6306	394	3	integral	integral	ADJ
ejpam-6306	394	4	inequalities	inequality	NOUN
ejpam-6306	394	5	for	for	ADP
ejpam-6306	394	6	twice	twice	ADV
ejpam-6306	394	7	differentiable	differentiable	ADJ
ejpam-6306	394	8	convex	convex	NOUN
ejpam-6306	394	9	functions	function	NOUN
ejpam-6306	394	10	.	.	PUNCT
ejpam-6306	395	1	mathematical	mathematical	ADJ
ejpam-6306	395	2	problems	problem	NOUN
ejpam-6306	395	3	in	in	ADP
ejpam-6306	395	4	engineering	engineering	NOUN
ejpam-6306	395	5	,	,	PUNCT
ejpam-6306	395	6	2020(1):1936461	2020(1):1936461	NOUN
ejpam-6306	395	7	,	,	PUNCT
ejpam-6306	395	8	2020	2020	NUM
ejpam-6306	395	9	.	.	PUNCT
ejpam-6306	396	1	[	[	X
ejpam-6306	396	2	29	29	NUM
ejpam-6306	396	3	]	]	PUNCT
ejpam-6306	396	4	sten	sten	PROPN
ejpam-6306	396	5	kaijser	kaijser	PROPN
ejpam-6306	396	6	,	,	PUNCT
ejpam-6306	396	7	ludmila	ludmila	PROPN
ejpam-6306	396	8	nikolova	nikolova	PROPN
ejpam-6306	396	9	,	,	PUNCT
ejpam-6306	396	10	lars	lars	PROPN
ejpam-6306	396	11	-	-	PUNCT
ejpam-6306	396	12	erik	erik	PROPN
ejpam-6306	396	13	persson	persson	PROPN
ejpam-6306	396	14	,	,	PUNCT
ejpam-6306	396	15	and	and	CCONJ
ejpam-6306	396	16	anna	anna	PROPN
ejpam-6306	396	17	wedestig	wedestig	PROPN
ejpam-6306	396	18	.	.	PUNCT
ejpam-6306	397	1	hardy	hardy	ADJ
ejpam-6306	397	2	-	-	PUNCT
ejpam-6306	397	3	type	type	NOUN
ejpam-6306	397	4	inequalities	inequality	NOUN
ejpam-6306	397	5	via	via	ADP
ejpam-6306	397	6	convexity	convexity	NOUN
ejpam-6306	397	7	.	.	PUNCT
ejpam-6306	398	1	mathematical	mathematical	ADJ
ejpam-6306	398	2	inequalities	inequality	NOUN
ejpam-6306	398	3	&	&	CCONJ
ejpam-6306	398	4	applications	application	NOUN
ejpam-6306	398	5	,	,	PUNCT
ejpam-6306	398	6	8(3):403–417	8(3):403–417	NUM
ejpam-6306	398	7	,	,	PUNCT
ejpam-6306	398	8	2005	2005	NUM
ejpam-6306	398	9	.	.	PUNCT
ejpam-6306	399	1	[	[	X
ejpam-6306	399	2	30	30	NUM
ejpam-6306	399	3	]	]	X
ejpam-6306	399	4	hendra	hendra	PROPN
ejpam-6306	399	5	gunawan	gunawan	PROPN
ejpam-6306	399	6	et	et	PROPN
ejpam-6306	399	7	al	al	PROPN
ejpam-6306	399	8	.	.	PROPN
ejpam-6306	399	9	fractional	fractional	ADJ
ejpam-6306	399	10	integrals	integral	NOUN
ejpam-6306	399	11	and	and	CCONJ
ejpam-6306	399	12	generalized	generalized	ADJ
ejpam-6306	399	13	olsen	olsen	NOUN
ejpam-6306	399	14	inequalities	inequality	NOUN
ejpam-6306	399	15	.	.	PUNCT
ejpam-6306	400	1	kyungpook	kyungpook	PROPN
ejpam-6306	400	2	mathematical	mathematical	PROPN
ejpam-6306	400	3	journal	journal	PROPN
ejpam-6306	400	4	,	,	PUNCT
ejpam-6306	400	5	49(1):31–39	49(1):31–39	NUM
ejpam-6306	400	6	,	,	PUNCT
ejpam-6306	400	7	2009	2009	NUM
ejpam-6306	400	8	.	.	PUNCT
ejpam-6306	401	1	[	[	X
ejpam-6306	401	2	31	31	NUM
ejpam-6306	401	3	]	]	X
ejpam-6306	401	4	yoshihiro	yoshihiro	PROPN
ejpam-6306	401	5	sawano	sawano	PROPN
ejpam-6306	401	6	and	and	CCONJ
ejpam-6306	401	7	hidemitsu	hidemitsu	PROPN
ejpam-6306	401	8	wadade	wadade	ADJ
ejpam-6306	401	9	.	.	PUNCT
ejpam-6306	402	1	on	on	ADP
ejpam-6306	402	2	the	the	DET
ejpam-6306	402	3	gagliardo	gagliardo	NOUN
ejpam-6306	402	4	-	-	PUNCT
ejpam-6306	402	5	nirenberg	nirenberg	PROPN
ejpam-6306	402	6	type	type	NOUN
ejpam-6306	402	7	inequality	inequality	NOUN
ejpam-6306	402	8	in	in	ADP
ejpam-6306	402	9	the	the	DET
ejpam-6306	402	10	critical	critical	ADJ
ejpam-6306	402	11	sobolev	sobolev	NOUN
ejpam-6306	402	12	-	-	PUNCT
ejpam-6306	402	13	morrey	morrey	NOUN
ejpam-6306	402	14	space	space	NOUN
ejpam-6306	402	15	.	.	PUNCT
ejpam-6306	403	1	journal	journal	NOUN
ejpam-6306	403	2	of	of	ADP
ejpam-6306	403	3	fourier	fourier	ADJ
ejpam-6306	403	4	analysis	analysis	NOUN
ejpam-6306	403	5	and	and	CCONJ
ejpam-6306	403	6	applications	application	NOUN
ejpam-6306	403	7	,	,	PUNCT
ejpam-6306	403	8	19(1):20–47	19(1):20–47	NUM
ejpam-6306	403	9	,	,	PUNCT
ejpam-6306	403	10	2013	2013	NUM
ejpam-6306	403	11	.	.	PUNCT
ejpam-6306	404	1	[	[	X
ejpam-6306	404	2	32	32	NUM
ejpam-6306	404	3	]	]	X
ejpam-6306	404	4	mehmet	mehmet	PROPN
ejpam-6306	404	5	kunt	kunt	PROPN
ejpam-6306	404	6	and	and	CCONJ
ejpam-6306	404	7	i̇mdat	i̇mdat	ADJ
ejpam-6306	404	8	i̇şcan	i̇şcan	PROPN
ejpam-6306	404	9	.	.	PUNCT
ejpam-6306	405	1	hermite	hermite	ADJ
ejpam-6306	405	2	–	–	PUNCT
ejpam-6306	405	3	hadamard	hadamard	ADJ
ejpam-6306	405	4	–	–	PUNCT
ejpam-6306	405	5	fejér	fejér	ADJ
ejpam-6306	405	6	type	type	NOUN
ejpam-6306	405	7	inequalities	inequality	NOUN
ejpam-6306	405	8	for	for	ADP
ejpam-6306	405	9	pconvex	pconvex	NOUN
ejpam-6306	405	10	functions	function	NOUN
ejpam-6306	405	11	.	.	PUNCT
ejpam-6306	406	1	arab	arab	PROPN
ejpam-6306	406	2	journal	journal	PROPN
ejpam-6306	406	3	of	of	ADP
ejpam-6306	406	4	mathematical	mathematical	ADJ
ejpam-6306	406	5	sciences	sciences	PROPN
ejpam-6306	406	6	,	,	PUNCT
ejpam-6306	406	7	23(2):215–230	23(2):215–230	NUM
ejpam-6306	406	8	,	,	PUNCT
ejpam-6306	406	9	2017	2017	NUM
ejpam-6306	406	10	.	.	PUNCT
ejpam-6306	407	1	[	[	X
ejpam-6306	407	2	33	33	NUM
ejpam-6306	407	3	]	]	X
ejpam-6306	407	4	necmettin	necmettin	PROPN
ejpam-6306	407	5	alp	alp	PROPN
ejpam-6306	407	6	,	,	PUNCT
ejpam-6306	407	7	mehmet	mehmet	PROPN
ejpam-6306	407	8	zeki	zeki	PROPN
ejpam-6306	407	9	sarıkaya	sarıkaya	PROPN
ejpam-6306	407	10	,	,	PUNCT
ejpam-6306	407	11	mehmet	mehmet	PROPN
ejpam-6306	407	12	kunt	kunt	PROPN
ejpam-6306	407	13	,	,	PUNCT
ejpam-6306	407	14	and	and	CCONJ
ejpam-6306	407	15	i̇mdat	i̇mdat	PRON
ejpam-6306	407	16	i̇şcan	i̇şcan	PROPN
ejpam-6306	407	17	.	.	PUNCT
ejpam-6306	408	1	q	q	ADJ
ejpam-6306	408	2	-	-	PUNCT
ejpam-6306	408	3	hermite	hermite	ADJ
ejpam-6306	408	4	hadamard	hadamard	ADJ
ejpam-6306	408	5	inequalities	inequality	NOUN
ejpam-6306	408	6	and	and	CCONJ
ejpam-6306	408	7	quantum	quantum	NOUN
ejpam-6306	408	8	estimates	estimate	NOUN
ejpam-6306	408	9	for	for	ADP
ejpam-6306	408	10	midpoint	midpoint	NOUN
ejpam-6306	408	11	type	type	NOUN
ejpam-6306	408	12	inequalities	inequality	NOUN
ejpam-6306	408	13	via	via	ADP
ejpam-6306	408	14	convex	convex	NOUN
ejpam-6306	408	15	and	and	CCONJ
ejpam-6306	408	16	quasi	quasi	ADJ
ejpam-6306	408	17	-	-	ADJ
ejpam-6306	408	18	convex	convex	ADJ
ejpam-6306	408	19	functions	function	NOUN
ejpam-6306	408	20	.	.	PUNCT
ejpam-6306	409	1	journal	journal	NOUN
ejpam-6306	409	2	of	of	ADP
ejpam-6306	409	3	king	king	PROPN
ejpam-6306	409	4	saud	saud	PROPN
ejpam-6306	409	5	university	university	PROPN
ejpam-6306	409	6	-	-	PUNCT
ejpam-6306	409	7	science	science	NOUN
ejpam-6306	409	8	,	,	PUNCT
ejpam-6306	409	9	30(2):193	30(2):193	NUM
ejpam-6306	409	10	–	–	PUNCT
ejpam-6306	409	11	203	203	NUM
ejpam-6306	409	12	,	,	PUNCT
ejpam-6306	409	13	2018	2018	NUM
ejpam-6306	409	14	.	.	PUNCT
ejpam-6306	410	1	[	[	X
ejpam-6306	410	2	34	34	NUM
ejpam-6306	410	3	]	]	PUNCT
ejpam-6306	410	4	shanhe	shanhe	NOUN
ejpam-6306	410	5	wu	wu	PROPN
ejpam-6306	410	6	,	,	PUNCT
ejpam-6306	410	7	muhammad	muhammad	PROPN
ejpam-6306	410	8	uzair	uzair	PROPN
ejpam-6306	410	9	awan	awan	PROPN
ejpam-6306	410	10	,	,	PUNCT
ejpam-6306	410	11	muhammad	muhammad	PROPN
ejpam-6306	410	12	aslam	aslam	PROPN
ejpam-6306	410	13	noor	noor	PROPN
ejpam-6306	410	14	,	,	PUNCT
ejpam-6306	410	15	khalida	khalida	PROPN
ejpam-6306	410	16	inayat	inayat	PROPN
ejpam-6306	410	17	noor	noor	PROPN
ejpam-6306	410	18	,	,	PUNCT
ejpam-6306	410	19	and	and	CCONJ
ejpam-6306	410	20	sabah	sabah	PROPN
ejpam-6306	410	21	iftikhar	iftikhar	PROPN
ejpam-6306	410	22	.	.	PUNCT
ejpam-6306	411	1	on	on	ADP
ejpam-6306	411	2	a	a	DET
ejpam-6306	411	3	new	new	ADJ
ejpam-6306	411	4	class	class	NOUN
ejpam-6306	411	5	of	of	ADP
ejpam-6306	411	6	convex	convex	NOUN
ejpam-6306	411	7	functions	function	NOUN
ejpam-6306	411	8	and	and	CCONJ
ejpam-6306	411	9	integral	integral	ADJ
ejpam-6306	411	10	inequalities	inequality	NOUN
ejpam-6306	411	11	.	.	PUNCT
ejpam-6306	412	1	journal	journal	PROPN
ejpam-6306	412	2	of	of	ADP
ejpam-6306	412	3	inequalities	inequality	NOUN
ejpam-6306	412	4	and	and	CCONJ
ejpam-6306	412	5	applications	application	NOUN
ejpam-6306	412	6	,	,	PUNCT
ejpam-6306	412	7	2019:1–14	2019:1–14	ADP
ejpam-6306	412	8	,	,	PUNCT
ejpam-6306	412	9	2019	2019	NUM
ejpam-6306	412	10	.	.	PUNCT
ejpam-6306	413	1	[	[	X
ejpam-6306	413	2	35	35	NUM
ejpam-6306	413	3	]	]	X
ejpam-6306	413	4	jacques	jacques	PROPN
ejpam-6306	413	5	hadamard	hadamard	PROPN
ejpam-6306	413	6	.	.	PUNCT
ejpam-6306	414	1	étude	étude	VERB
ejpam-6306	414	2	sur	sur	PROPN
ejpam-6306	414	3	les	les	PROPN
ejpam-6306	414	4	propriétés	propriétés	PROPN
ejpam-6306	414	5	des	des	PROPN
ejpam-6306	414	6	fonctions	fonctions	PROPN
ejpam-6306	414	7	entières	entière	NOUN
ejpam-6306	414	8	et	et	PROPN
ejpam-6306	414	9	en	en	X
ejpam-6306	414	10	particulier	particulier	NOUN
ejpam-6306	414	11	d’une	d’une	CCONJ
ejpam-6306	414	12	fonction	fonction	PROPN
ejpam-6306	414	13	considérée	considérée	PROPN
ejpam-6306	414	14	par	par	PROPN
ejpam-6306	414	15	riemann	riemann	PROPN
ejpam-6306	414	16	.	.	PROPN
ejpam-6306	415	1	journal	journal	PROPN
ejpam-6306	415	2	de	de	PROPN
ejpam-6306	415	3	mathématiques	mathématiques	PROPN
ejpam-6306	415	4	pures	pure	NOUN
ejpam-6306	415	5	et	et	NOUN
ejpam-6306	415	6	appliquées	appliquée	NOUN
ejpam-6306	415	7	,	,	PUNCT
ejpam-6306	415	8	9:171–215	9:171–215	NUM
ejpam-6306	415	9	,	,	PUNCT
ejpam-6306	415	10	1893	1893	NUM
ejpam-6306	415	11	.	.	PUNCT
ejpam-6306	416	1	[	[	X
ejpam-6306	416	2	36	36	NUM
ejpam-6306	416	3	]	]	X
ejpam-6306	416	4	mehmet	mehmet	PROPN
ejpam-6306	416	5	zeki	zeki	PROPN
ejpam-6306	416	6	sarikaya	sarikaya	PROPN
ejpam-6306	416	7	,	,	PUNCT
ejpam-6306	416	8	erhan	erhan	SCONJ
ejpam-6306	416	9	set	set	VERB
ejpam-6306	416	10	,	,	PUNCT
ejpam-6306	416	11	hatice	hatice	NOUN
ejpam-6306	416	12	yaldiz	yaldiz	NOUN
ejpam-6306	416	13	,	,	PUNCT
ejpam-6306	416	14	and	and	CCONJ
ejpam-6306	416	15	nagihan	nagihan	ADP
ejpam-6306	416	16	başak	başak	PROPN
ejpam-6306	416	17	.	.	PUNCT
ejpam-6306	417	1	hermite	hermite	PROPN
ejpam-6306	417	2	–	–	PUNCT
ejpam-6306	417	3	hadamard	hadamard	NOUN
ejpam-6306	417	4	’s	’s	PART
ejpam-6306	417	5	inequalities	inequality	NOUN
ejpam-6306	417	6	for	for	ADP
ejpam-6306	417	7	fractional	fractional	ADJ
ejpam-6306	417	8	integrals	integral	NOUN
ejpam-6306	417	9	and	and	CCONJ
ejpam-6306	417	10	related	relate	VERB
ejpam-6306	417	11	fractional	fractional	ADJ
ejpam-6306	417	12	inequalities	inequality	NOUN
ejpam-6306	417	13	.	.	PUNCT
ejpam-6306	418	1	mathematical	mathematical	ADJ
ejpam-6306	418	2	and	and	CCONJ
ejpam-6306	418	3	computer	computer	NOUN
ejpam-6306	418	4	modelling	modelling	NOUN
ejpam-6306	418	5	,	,	PUNCT
ejpam-6306	418	6	57(9	57(9	NOUN
ejpam-6306	418	7	-	-	SYM
ejpam-6306	418	8	10):2403–2407	10):2403–2407	NOUN
ejpam-6306	418	9	,	,	PUNCT
ejpam-6306	418	10	2013	2013	NUM
ejpam-6306	418	11	.	.	PUNCT
ejpam-6306	419	1	[	[	X
ejpam-6306	419	2	37	37	NUM
ejpam-6306	419	3	]	]	X
ejpam-6306	419	4	tariq	tariq	NOUN
ejpam-6306	419	5	o	o	PROPN
ejpam-6306	419	6	salim	salim	PROPN
ejpam-6306	419	7	and	and	CCONJ
ejpam-6306	419	8	ahmad	ahmad	PROPN
ejpam-6306	419	9	w	w	PROPN
ejpam-6306	419	10	faraj	faraj	PROPN
ejpam-6306	419	11	.	.	PUNCT
ejpam-6306	420	1	a	a	DET
ejpam-6306	420	2	generalization	generalization	NOUN
ejpam-6306	420	3	of	of	ADP
ejpam-6306	420	4	mittag	mittag	ADJ
ejpam-6306	420	5	-	-	PUNCT
ejpam-6306	420	6	leffler	leffler	NOUN
ejpam-6306	420	7	function	function	NOUN
ejpam-6306	420	8	and	and	CCONJ
ejpam-6306	420	9	integral	integral	ADJ
ejpam-6306	420	10	operator	operator	NOUN
ejpam-6306	420	11	associated	associate	VERB
ejpam-6306	420	12	with	with	ADP
ejpam-6306	420	13	fractional	fractional	ADJ
ejpam-6306	420	14	calculus	calculus	NOUN
ejpam-6306	420	15	.	.	PUNCT
ejpam-6306	421	1	j.	j.	PROPN
ejpam-6306	421	2	fract	fract	PROPN
ejpam-6306	421	3	.	.	PUNCT
ejpam-6306	422	1	calc	calc	PROPN
ejpam-6306	422	2	.	.	PUNCT
ejpam-6306	423	1	appl	appl	PROPN
ejpam-6306	423	2	,	,	PUNCT
ejpam-6306	423	3	3(5):1–13	3(5):1–13	NUM
ejpam-6306	423	4	,	,	PUNCT
ejpam-6306	423	5	2012	2012	NUM
ejpam-6306	423	6	.	.	PUNCT